LMFDB - Embedded newform 121.2.g.a.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,2,Mod(4,121)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("121.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	121.g (of order $55$, degree $40$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.966189864457$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$10$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	121.4
Dual form			121.2.g.a.91.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.790346 - 0.0451936i) q^{2} +(-0.0254779 + 0.0784129i) q^{3} +(-1.36436 - 0.156546i) q^{4} +(0.532875 + 1.00991i) q^{5} +(0.0236801 - 0.0608219i) q^{6} +(4.07073 + 1.72030i) q^{7} +(2.63133 + 0.455369i) q^{8} +(2.42155 + 1.75936i) q^{9} +O(q^{10})$	\(q+(-0.790346 - 0.0451936i) q^{2} +(-0.0254779 + 0.0784129i) q^{3} +(-1.36436 - 0.156546i) q^{4} +(0.532875 + 1.00991i) q^{5} +(0.0236801 - 0.0608219i) q^{6} +(4.07073 + 1.72030i) q^{7} +(2.63133 + 0.455369i) q^{8} +(2.42155 + 1.75936i) q^{9} +(-0.375515 - 0.822262i) q^{10} +(-0.0917343 - 3.31536i) q^{11} +(0.0470362 - 0.102995i) q^{12} +(-3.97773 + 2.24633i) q^{13} +(-3.13954 - 1.54361i) q^{14} +(-0.0927666 + 0.0160539i) q^{15} +(0.616161 + 0.143282i) q^{16} +(-0.931282 + 0.332281i) q^{17} +(-1.83435 - 1.49994i) q^{18} +(0.00159925 - 0.0559810i) q^{19} +(-0.568936 - 1.46130i) q^{20} +(-0.238608 + 0.275368i) q^{21} +(-0.0773311 + 2.62443i) q^{22} +(0.516024 + 0.595524i) q^{23} +(-0.102747 + 0.194728i) q^{24} +(2.08625 - 3.05105i) q^{25} +(3.24530 - 1.59561i) q^{26} +(-0.399758 + 0.290441i) q^{27} +(-5.28463 - 2.98437i) q^{28} +(-4.91294 - 7.18495i) q^{29} +(0.0740432 - 0.00849567i) q^{30} +(-2.08477 + 10.2887i) q^{31} +(-5.60504 - 1.64579i) q^{32} +(0.262304 + 0.0772751i) q^{33} +(0.751053 - 0.220529i) q^{34} +(0.431837 + 5.02778i) q^{35} +(-3.02844 - 2.77948i) q^{36} +(4.53177 - 4.15922i) q^{37} +(-0.00379394 + 0.0441721i) q^{38} +(-0.0747967 - 0.369136i) q^{39} +(0.942287 + 2.90006i) q^{40} +(-2.36843 - 9.01044i) q^{41} +(0.201027 - 0.206852i) q^{42} +(-0.220129 - 1.53103i) q^{43} +(-0.393846 + 4.53770i) q^{44} +(-0.486412 + 3.38307i) q^{45} +(-0.380924 - 0.493991i) q^{46} +(5.22268 - 4.27056i) q^{47} +(-0.0269337 + 0.0446644i) q^{48} +(8.73283 + 8.98587i) q^{49} +(-1.78675 + 2.31710i) q^{50} +(-0.00232799 - 0.0814903i) q^{51} +(5.77870 - 2.44210i) q^{52} +(-7.80452 + 1.81486i) q^{53} +(0.329074 - 0.211483i) q^{54} +(3.29933 - 1.85931i) q^{55} +(9.92805 + 6.38037i) q^{56} +(0.00434888 + 0.00155168i) q^{57} +(3.55821 + 5.90063i) q^{58} +(-0.0907786 + 0.345358i) q^{59} +(0.129080 - 0.00738106i) q^{60} +(-11.4899 + 0.657016i) q^{61} +(2.11267 - 8.03745i) q^{62} +(6.83085 + 11.3277i) q^{63} +(3.16392 + 1.12888i) q^{64} +(-4.38822 - 2.82014i) q^{65} +(-0.203818 - 0.0729286i) q^{66} +(9.50358 - 6.10758i) q^{67} +(1.32262 - 0.307562i) q^{68} +(-0.0598439 + 0.0252903i) q^{69} +(-0.114077 - 3.99321i) q^{70} +(1.75222 - 2.27232i) q^{71} +(5.57074 + 5.73215i) q^{72} +(-0.907253 + 1.50451i) q^{73} +(-3.76964 + 3.08242i) q^{74} +(0.186088 + 0.241323i) q^{75} +(-0.0109455 + 0.0761278i) q^{76} +(5.33000 - 13.6537i) q^{77} +(0.0424327 + 0.295126i) q^{78} +(-5.94541 + 6.11768i) q^{79} +(0.183635 + 0.698620i) q^{80} +(2.76226 + 8.50137i) q^{81} +(1.46466 + 7.22841i) q^{82} +(0.0664344 - 0.773482i) q^{83} +(0.368654 - 0.338348i) q^{84} +(-0.831832 - 0.763448i) q^{85} +(0.104785 + 1.21999i) q^{86} +(0.688564 - 0.202181i) q^{87} +(1.26833 - 8.76556i) q^{88} +(-13.1845 - 3.87133i) q^{89} +(0.537327 - 2.65182i) q^{90} +(-20.0566 + 2.30128i) q^{91} +(-0.610816 - 0.893290i) q^{92} +(-0.753654 - 0.425608i) q^{93} +(-4.32073 + 3.13919i) q^{94} +(0.0573880 - 0.0282158i) q^{95} +(0.271855 - 0.397576i) q^{96} +(3.56105 - 6.74893i) q^{97} +(-6.49585 - 7.49661i) q^{98} +(5.61077 - 8.18970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9}+O(q^{10}) $ 400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9	\( 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9} - 22 q^{10} - 33 q^{11} + 6 q^{12} - 11 q^{13} - 18 q^{14} + 16 q^{15} - 30 q^{16} - 44 q^{17} + 11 q^{18} - 44 q^{19} - 36 q^{20} - 11 q^{21} - 34 q^{23} + 77 q^{24} - 31 q^{25} - 38 q^{26} + 40 q^{27} - 44 q^{28} - 44 q^{29} - 11 q^{30} - 17 q^{31} - 44 q^{32} - 11 q^{33} - 76 q^{34} - 44 q^{35} + 57 q^{36} - 4 q^{37} + 34 q^{38} - 11 q^{39} + 33 q^{40} - 44 q^{41} + 3 q^{42} - 44 q^{43} - 33 q^{44} - 12 q^{45} - 44 q^{46} - 36 q^{47} + 9 q^{48} + 16 q^{49} + 88 q^{50} + 154 q^{51} + 110 q^{52} + 78 q^{53} + 231 q^{54} + 44 q^{55} - 55 q^{56} + 66 q^{57} + 73 q^{58} - 33 q^{59} + 15 q^{60} - 44 q^{61} + 11 q^{62} + 121 q^{63} + 96 q^{64} - 11 q^{65} - 41 q^{67} - 44 q^{68} + 8 q^{69} + 24 q^{70} + 15 q^{71} + 77 q^{72} - 22 q^{73} - 44 q^{74} + 7 q^{75} + 176 q^{76} + 88 q^{77} - 21 q^{78} + 44 q^{79} + 171 q^{80} + 37 q^{81} + 22 q^{82} - 44 q^{83} - 11 q^{84} + 66 q^{85} - 20 q^{86} - 11 q^{87} + 77 q^{88} + 3 q^{89} + 264 q^{90} + 79 q^{91} + 228 q^{92} + 49 q^{93} + 143 q^{94} + 44 q^{95} + 121 q^{96} + 10 q^{97} + 132 q^{98} + 143 q^{99}+O(q^{100}) \) 400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9 - 22 * q^10 - 33 * q^11 + 6 * q^12 - 11 * q^13 - 18 * q^14 + 16 * q^15 - 30 * q^16 - 44 * q^17 + 11 * q^18 - 44 * q^19 - 36 * q^20 - 11 * q^21 - 34 * q^23 + 77 * q^24 - 31 * q^25 - 38 * q^26 + 40 * q^27 - 44 * q^28 - 44 * q^29 - 11 * q^30 - 17 * q^31 - 44 * q^32 - 11 * q^33 - 76 * q^34 - 44 * q^35 + 57 * q^36 - 4 * q^37 + 34 * q^38 - 11 * q^39 + 33 * q^40 - 44 * q^41 + 3 * q^42 - 44 * q^43 - 33 * q^44 - 12 * q^45 - 44 * q^46 - 36 * q^47 + 9 * q^48 + 16 * q^49 + 88 * q^50 + 154 * q^51 + 110 * q^52 + 78 * q^53 + 231 * q^54 + 44 * q^55 - 55 * q^56 + 66 * q^57 + 73 * q^58 - 33 * q^59 + 15 * q^60 - 44 * q^61 + 11 * q^62 + 121 * q^63 + 96 * q^64 - 11 * q^65 - 41 * q^67 - 44 * q^68 + 8 * q^69 + 24 * q^70 + 15 * q^71 + 77 * q^72 - 22 * q^73 - 44 * q^74 + 7 * q^75 + 176 * q^76 + 88 * q^77 - 21 * q^78 + 44 * q^79 + 171 * q^80 + 37 * q^81 + 22 * q^82 - 44 * q^83 - 11 * q^84 + 66 * q^85 - 20 * q^86 - 11 * q^87 + 77 * q^88 + 3 * q^89 + 264 * q^90 + 79 * q^91 + 228 * q^92 + 49 * q^93 + 143 * q^94 + 44 * q^95 + 121 * q^96 + 10 * q^97 + 132 * q^98 + 143 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{55}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.790346	−	0.0451936i	−0.558859	−	0.0319567i	−0.224622	−	0.974446i	$-0.572115\pi$
$2$	−0.790346	−	0.0451936i	−0.558859	−	0.0319567i	−0.334237	+	0.942489i	$0.608479\pi$
$3$	−0.0254779	+	0.0784129i	−0.0147097	+	0.0452717i	−0.958142	−	0.286294i	$-0.907577\pi$
$3$	−0.0254779	+	0.0784129i	−0.0147097	+	0.0452717i	0.943432	+	0.331565i	$0.107577\pi$
$4$	−1.36436	−	0.156546i	−0.682179	−	0.0782728i
$5$	0.532875	+	1.00991i	0.238309	+	0.451646i	0.974272	−	0.225376i	$-0.0723611\pi$
$5$	0.532875	+	1.00991i	0.238309	+	0.451646i	−0.735963	+	0.677022i	$0.763270\pi$
$6$	0.0236801	−	0.0608219i	0.00966737	−	0.0248304i
$7$	4.07073	+	1.72030i	1.53859	+	0.650214i	0.983390	−	0.181502i	$-0.0580960\pi$
$7$	4.07073	+	1.72030i	1.53859	+	0.650214i	0.555201	+	0.831716i	$0.312641\pi$
$8$	2.63133	+	0.455369i	0.930315	+	0.160997i
$9$	2.42155	+	1.75936i	0.807184	+	0.586453i
$10$	−0.375515	−	0.822262i	−0.118748	−	0.260022i
$11$	−0.0917343	−	3.31536i	−0.0276589	−	0.999617i
$11$	−0.0917343	−	3.31536i	−0.0276589	−	0.999617i
$12$	0.0470362	−	0.102995i	0.0135782	−	0.0297320i
$13$	−3.97773	+	2.24633i	−1.10322	+	0.623019i	−0.932089	−	0.362229i	$-0.882016\pi$
$13$	−3.97773	+	2.24633i	−1.10322	+	0.623019i	−0.171134	+	0.985248i	$0.554743\pi$
$14$	−3.13954	−	1.54361i	−0.839077	−	0.412546i
$15$	−0.0927666	+	0.0160539i	−0.0239522	+	0.00414510i
$16$	0.616161	+	0.143282i	0.154040	+	0.0358205i
$17$	−0.931282	+	0.332281i	−0.225869	+	0.0805900i	−0.446559	−	0.894754i	$-0.647351\pi$
$17$	−0.931282	+	0.332281i	−0.225869	+	0.0805900i	0.220690	+	0.975344i	$0.429169\pi$
$18$	−1.83435	−	1.49994i	−0.432361	−	0.353540i
$19$	0.00159925	−	0.0559810i	0.000366893	−	0.0128429i	−0.999388	−	0.0349769i	$-0.988864\pi$
$19$	0.00159925	−	0.0559810i	0.000366893	−	0.0128429i	0.999755	+	0.0221340i	$0.00704605\pi$
$20$	−0.568936	−	1.46130i	−0.127218	−	0.326757i
$21$	−0.238608	+	0.275368i	−0.0520684	+	0.0600902i
$22$	−0.0773311	+	2.62443i	−0.0164870	+	0.559529i
$23$	0.516024	+	0.595524i	0.107599	+	0.124175i	0.806994	−	0.590559i	$-0.201093\pi$
$23$	0.516024	+	0.595524i	0.107599	+	0.124175i	−0.699396	+	0.714735i	$0.746547\pi$
$24$	−0.102747	+	0.194728i	−0.0209732	+	0.0397487i
$25$	2.08625	−	3.05105i	0.417250	−	0.610209i
$26$	3.24530	−	1.59561i	0.636456	−	0.312924i
$27$	−0.399758	+	0.290441i	−0.0769335	+	0.0558955i
$28$	−5.28463	−	2.98437i	−0.998701	−	0.563992i
$29$	−4.91294	−	7.18495i	−0.912310	−	1.33421i	−0.942338	−	0.334662i	$-0.891378\pi$
$29$	−4.91294	−	7.18495i	−0.912310	−	1.33421i	0.0300280	−	0.999549i	$-0.490440\pi$
$30$	0.0740432	−	0.00849567i	0.0135184	−	0.00155109i
$31$	−2.08477	+	10.2887i	−0.374436	+	1.84791i	0.139688	+	0.990196i	$0.455390\pi$
$31$	−2.08477	+	10.2887i	−0.374436	+	1.84791i	−0.514123	+	0.857716i	$0.671883\pi$
$32$	−5.60504	−	1.64579i	−0.990840	−	0.290937i
$33$	0.262304	+	0.0772751i	0.0456612	+	0.0134519i
$34$	0.751053	−	0.220529i	0.128804	−	0.0378204i
$35$	0.431837	+	5.02778i	0.0729937	+	0.849850i
$36$	−3.02844	−	2.77948i	−0.504741	−	0.463247i
$37$	4.53177	−	4.15922i	0.745019	−	0.683772i	−0.210865	−	0.977515i	$-0.567628\pi$
$37$	4.53177	−	4.15922i	0.745019	−	0.683772i	0.955885	+	0.293743i	$0.0949009\pi$
$38$	−0.00379394	+	0.0441721i	−0.000615459	+	0.00716566i
$39$	−0.0747967	−	0.369136i	−0.0119771	−	0.0591091i
$40$	0.942287	+	2.90006i	0.148989	+	0.458540i
$41$	−2.36843	−	9.01044i	−0.369887	−	1.40719i	−0.848512	−	0.529175i	$-0.822501\pi$
$41$	−2.36843	−	9.01044i	−0.369887	−	1.40719i	0.478626	−	0.878019i	$-0.341135\pi$
$42$	0.201027	−	0.206852i	0.0310192	−	0.0319180i
$43$	−0.220129	−	1.53103i	−0.0335693	−	0.233480i	0.966128	−	0.258061i	$-0.0830837\pi$
$43$	−0.220129	−	1.53103i	−0.0335693	−	0.233480i	−0.999698	+	0.0245817i	$0.992175\pi$
$44$	−0.393846	+	4.53770i	−0.0593745	+	0.684083i
$45$	−0.486412	+	3.38307i	−0.0725101	+	0.504319i
$46$	−0.380924	−	0.493991i	−0.0561642	−	0.0728350i
$47$	5.22268	−	4.27056i	0.761806	−	0.622926i	−0.170183	−	0.985413i	$-0.554436\pi$
$47$	5.22268	−	4.27056i	0.761806	−	0.622926i	0.931989	+	0.362487i	$0.118072\pi$
$48$	−0.0269337	+	0.0446644i	−0.00388754	+	0.00644676i
$49$	8.73283	+	8.98587i	1.24755	+	1.28370i
$50$	−1.78675	+	2.31710i	−0.252685	+	0.327687i
$51$	−0.00232799	−	0.0814903i	−0.000325984	−	0.0114109i
$52$	5.77870	−	2.44210i	0.801361	−	0.338658i
$53$	−7.80452	+	1.81486i	−1.07203	+	0.249291i	−0.725131	−	0.688610i	$-0.758221\pi$
$53$	−7.80452	+	1.81486i	−1.07203	+	0.249291i	−0.346902	+	0.937901i	$0.612766\pi$
$54$	0.329074	−	0.211483i	0.0447813	−	0.0287792i
$55$	3.29933	−	1.85931i	0.444882	−	0.250710i
$56$	9.92805	+	6.38037i	1.32669	+	0.852613i
$57$	0.00434888	+	0.00155168i	0.000576024	+	0.000205525i
$58$	3.55821	+	5.90063i	0.467216	+	0.774791i
$59$	−0.0907786	+	0.345358i	−0.0118184	+	0.0449617i	−0.972795	−	0.231669i	$-0.925581\pi$
$59$	−0.0907786	+	0.345358i	−0.0118184	+	0.0449617i	0.960976	+	0.276631i	$0.0892178\pi$
$60$	0.129080	−	0.00738106i	0.0166642	−	0.000952891i
$61$	−11.4899	+	0.657016i	−1.47113	+	0.0841222i	−0.774165	−	0.632983i	$-0.781830\pi$
$61$	−11.4899	+	0.657016i	−1.47113	+	0.0841222i	−0.696964	+	0.717106i	$0.745466\pi$
$62$	2.11267	−	8.03745i	0.268310	−	1.02076i
$63$	6.83085	+	11.3277i	0.860606	+	1.42715i
$64$	3.16392	+	1.12888i	0.395490	+	0.141111i
$65$	−4.38822	−	2.82014i	−0.544292	−	0.349795i
$66$	−0.203818	−	0.0729286i	−0.0250883	−	0.00897688i
$67$	9.50358	−	6.10758i	1.16105	−	0.746159i	0.189238	−	0.981931i	$-0.439398\pi$
$67$	9.50358	−	6.10758i	1.16105	−	0.746159i	0.971808	+	0.235772i	$0.0757618\pi$
$68$	1.32262	−	0.307562i	0.160391	−	0.0372974i
$69$	−0.0598439	+	0.0252903i	−0.00720436	+	0.00304459i
$70$	−0.114077	−	3.99321i	−0.0136348	−	0.477279i
$71$	1.75222	−	2.27232i	0.207951	−	0.269675i	−0.676363	−	0.736568i	$-0.736445\pi$
$71$	1.75222	−	2.27232i	0.207951	−	0.269675i	0.884314	+	0.466893i	$0.154627\pi$
$72$	5.57074	+	5.73215i	0.656517	+	0.675541i
$73$	−0.907253	+	1.50451i	−0.106186	+	0.176090i	−0.904904	−	0.425616i	$-0.860057\pi$
$73$	−0.907253	+	1.50451i	−0.106186	+	0.176090i	0.798718	+	0.601706i	$0.205512\pi$
$74$	−3.76964	+	3.08242i	−0.438212	+	0.358324i
$75$	0.186088	+	0.241323i	0.0214876	+	0.0278656i
$76$	−0.0109455	+	0.0761278i	−0.00125554	+	0.00873246i
$77$	5.33000	−	13.6537i	0.607409	−	1.55599i
$78$	0.0424327	+	0.295126i	0.00480456	+	0.0334164i
$79$	−5.94541	+	6.11768i	−0.668911	+	0.688293i	−0.963615	−	0.267296i	$-0.913870\pi$
$79$	−5.94541	+	6.11768i	−0.668911	+	0.688293i	0.294704	+	0.955589i	$0.404779\pi$
$80$	0.183635	+	0.698620i	0.0205310	+	0.0781081i
$81$	2.76226	+	8.50137i	0.306918	+	0.944596i
$82$	1.46466	+	7.22841i	0.161745	+	0.798244i
$83$	0.0664344	−	0.773482i	0.00729212	−	0.0849006i	−0.991781	−	0.127948i	$-0.959161\pi$
$83$	0.0664344	−	0.773482i	0.00729212	−	0.0849006i	0.999073	+	0.0430470i	$0.0137065\pi$
$84$	0.368654	−	0.338348i	0.0402234	−	0.0369167i
$85$	−0.831832	−	0.763448i	−0.0902248	−	0.0828076i
$86$	0.104785	+	1.21999i	0.0112993	+	0.131555i
$87$	0.688564	−	0.202181i	0.0738218	−	0.0216760i
$88$	1.26833	−	8.76556i	0.135204	−	0.934412i
$89$	−13.1845	−	3.87133i	−1.39756	−	0.410360i	−0.505712	−	0.862702i	$-0.668770\pi$
$89$	−13.1845	−	3.87133i	−1.39756	−	0.410360i	−0.891844	+	0.452343i	$0.850588\pi$
$90$	0.537327	−	2.65182i	0.0566393	−	0.279526i
$91$	−20.0566	+	2.30128i	−2.10250	+	0.241240i
$92$	−0.610816	−	0.893290i	−0.0636819	−	0.0931319i
$93$	−0.753654	−	0.425608i	−0.0781503	−	0.0441335i
$94$	−4.32073	+	3.13919i	−0.445649	+	0.323783i
$95$	0.0573880	−	0.0282158i	0.00588789	−	0.00289488i
$96$	0.271855	−	0.397576i	0.0277461	−	0.0405774i
$97$	3.56105	−	6.74893i	0.361570	−	0.685250i	−0.634586	−	0.772852i	$-0.718829\pi$
$97$	3.56105	−	6.74893i	0.361570	−	0.685250i	0.996156	+	0.0876018i	$0.0279203\pi$
$98$	−6.49585	−	7.49661i	−0.656180	−	0.757272i
$99$	5.61077	−	8.18970i	0.563903	−	0.823096i
$100$	−3.32402	+	3.83613i	−0.332402	+	0.383613i
$101$	−1.38479	−	3.55682i	−0.137792	−	0.353916i	0.846012	−	0.533164i	$-0.178997\pi$
$101$	−1.38479	−	3.55682i	−0.137792	−	0.353916i	−0.983804	+	0.179248i	$0.942634\pi$
$102$	−0.00184293	+	0.0645108i	−0.000182477	+	0.00638752i
$103$	−2.38655	−	1.95147i	−0.235153	−	0.192284i	0.508092	−	0.861303i	$-0.330351\pi$
$103$	−2.38655	−	1.95147i	−0.235153	−	0.192284i	−0.743245	+	0.669019i	$0.766715\pi$
$104$	−11.4896	+	4.09948i	−1.12665	+	0.401987i
$105$	−0.405245	−	0.0942357i	−0.0395479	−	0.00919646i
$106$	6.25030	−	1.08166i	0.607082	−	0.105060i
$107$	9.86519	+	4.85039i	0.953704	+	0.468905i	0.850628	−	0.525769i	$-0.176222\pi$
$107$	9.86519	+	4.85039i	0.953704	+	0.468905i	0.103076	+	0.994673i	$0.467131\pi$
$108$	0.590881	−	0.333686i	0.0568576	−	0.0321089i
$109$	−0.157096	+	0.343993i	−0.0150471	+	0.0329485i	−0.917006	−	0.398873i	$-0.869402\pi$
$109$	−0.157096	+	0.343993i	−0.0150471	+	0.0329485i	0.901959	+	0.431821i	$0.142129\pi$
$110$	−2.69164	+	1.32039i	−0.256638	+	0.125895i
$111$	0.210677	+	0.461318i	0.0199965	+	0.0437863i
$112$	2.26174	+	1.64325i	0.213714	+	0.155272i
$113$	−4.91142	−	0.849955i	−0.462028	−	0.0799571i	−0.0652445	−	0.997869i	$-0.520783\pi$
$113$	−4.91142	−	0.849955i	−0.462028	−	0.0799571i	−0.396784	+	0.917912i	$0.629874\pi$
$114$	−0.00336700	−	0.00142291i	−0.000315348	−	0.000133267i
$115$	−0.326450	+	0.838479i	−0.0304416	+	0.0781886i
$116$	5.57824	+	10.5719i	0.517927	+	0.981580i
$117$	−13.5844	−	1.55866i	−1.25587	−	0.144098i
$118$	0.0873545	−	0.268849i	0.00804163	−	0.0247496i
$119$	−4.36262	−	0.249464i	−0.399921	−	0.0228683i
$120$	−0.251410			−0.0229504
$121$	−10.9832	+	0.608264i	−0.998470	+	0.0552967i
$122$	9.11069			0.824843
$123$	0.766877	+	0.0438516i	0.0691470	+	0.00395397i
$124$	4.45503	−	13.7112i	0.400073	−	1.23130i
$125$	9.86515	+	1.13192i	0.882366	+	0.101242i
$126$	−4.88679	−	9.26151i	−0.435350	−	0.825080i
$127$	5.28934	−	13.5856i	0.469353	−	1.20552i	−0.475991	−	0.879450i	$-0.657911\pi$
$127$	5.28934	−	13.5856i	0.469353	−	1.20552i	0.945344	−	0.326074i	$-0.105726\pi$
$128$	8.31222	+	3.51278i	0.734704	+	0.310488i
$129$	0.125661	+	0.0217465i	0.0110638	+	0.00191467i
$130$	3.34076	+	2.42721i	0.293004	+	0.212880i
$131$	5.64090	+	12.3519i	0.492848	+	1.07919i	0.978728	+	0.205161i	$0.0657719\pi$
$131$	5.64090	+	12.3519i	0.492848	+	1.07919i	−0.485880	+	0.874025i	$0.661501\pi$
$132$	−0.345779	−	0.146493i	−0.0300962	−	0.0127506i
$133$	0.102814	−	0.225132i	0.00891514	−	0.0195214i
$134$	−7.78714	+	4.39760i	−0.672706	+	0.379895i
$135$	−0.506341	−	0.248951i	−0.0435789	−	0.0214263i
$136$	−2.60182	+	0.450262i	−0.223104	+	0.0386097i
$137$	2.96885	+	0.690376i	0.253646	+	0.0589828i	0.351391	−	0.936229i	$-0.385709\pi$
$137$	2.96885	+	0.690376i	0.253646	+	0.0589828i	−0.0977457	+	0.995211i	$0.531163\pi$
$138$	0.0484404	−	0.0172835i	0.00412352	−	0.00147127i
$139$	−7.53043	−	6.15760i	−0.638723	−	0.522281i	0.257276	−	0.966338i	$-0.417175\pi$
$139$	−7.53043	−	6.15760i	−0.638723	−	0.522281i	−0.895999	+	0.444057i	$0.853539\pi$
$140$	0.197897	−	6.92730i	0.0167254	−	0.585464i
$141$	0.201804	+	0.518330i	0.0169950	+	0.0436513i
$142$	−1.48756	+	1.71673i	−0.124833	+	0.144065i
$143$	7.81226	+	12.9815i	0.653294	+	1.08557i
$144$	1.23998	+	1.43101i	0.103332	+	0.119251i
$145$	4.63817	−	8.79031i	0.385179	−	0.729996i
$146$	0.785038	−	1.14808i	0.0649702	−	0.0950159i
$147$	−0.927101	+	0.455825i	−0.0764660	+	0.0375958i
$148$	−6.83407	+	4.96525i	−0.561757	+	0.408141i
$149$	3.69561	+	2.08701i	0.302756	+	0.170974i	0.635623	−	0.771999i	$-0.280743\pi$
$149$	3.69561	+	2.08701i	0.302756	+	0.170974i	−0.332867	+	0.942974i	$0.608016\pi$
$150$	−0.136168	−	0.199139i	−0.0111180	−	0.0162596i
$151$	−11.5377	+	1.32383i	−0.938926	+	0.107732i	−0.569924	−	0.821697i	$-0.693028\pi$
$151$	−11.5377	+	1.32383i	−0.938926	+	0.107732i	−0.369001	+	0.929429i	$0.620300\pi$
$152$	0.0297002	−	0.146576i	0.00240900	−	0.0118889i
$153$	−2.83975	−	0.833826i	−0.229580	−	0.0674108i
$154$	−4.82960	+	10.5503i	−0.389181	+	0.850167i
$155$	−11.5016	+	3.37718i	−0.923833	+	0.271262i
$156$	0.0442629	+	0.515344i	0.00354387	+	0.0412605i
$157$	3.70474	+	3.40018i	0.295671	+	0.271364i	0.810257	−	0.586074i	$-0.199327\pi$
$157$	3.70474	+	3.40018i	0.295671	+	0.271364i	−0.514587	+	0.857438i	$0.672055\pi$
$158$	4.97541	−	4.56639i	0.395822	−	0.363283i
$159$	0.0565340	−	0.658214i	0.00448344	−	0.0521998i
$160$	−1.32469	−	6.53759i	−0.104726	−	0.516842i
$161$	1.07611	+	3.31194i	0.0848096	+	0.261017i
$162$	−1.79894	−	6.84386i	−0.141338	−	0.537705i
$163$	1.10031	−	1.13219i	0.0861828	−	0.0886800i	−0.672668	−	0.739944i	$-0.734852\pi$
$163$	1.10031	−	1.13219i	0.0861828	−	0.0886800i	0.758851	+	0.651264i	$0.225761\pi$
$164$	1.82084	+	12.6642i	0.142184	+	0.988911i
$165$	0.0617342	+	0.306081i	0.00480600	+	0.0238284i
$166$	−0.0874626	+	0.608316i	−0.00678842	+	0.0472145i
$167$	1.38453	+	1.79549i	0.107138	+	0.138939i	0.842418	−	0.538824i	$-0.181131\pi$
$167$	1.38453	+	1.79549i	0.107138	+	0.138939i	−0.735280	+	0.677763i	$0.762949\pi$
$168$	−0.753249	+	0.615928i	−0.0581144	+	0.0475199i
$169$	4.06316	−	6.73799i	0.312551	−	0.518307i
$170$	0.622932	+	0.640982i	0.0477767	+	0.0491611i
$171$	0.102363	−	0.132747i	0.00782792	−	0.0101514i
$172$	0.0606588	+	2.12333i	0.00462519	+	0.161903i
$173$	9.26149	−	3.91394i	0.704138	−	0.297571i	−0.00764493	−	0.999971i	$-0.502433\pi$
$173$	9.26149	−	3.91394i	0.704138	−	0.297571i	0.711783	+	0.702400i	$0.247888\pi$
$174$	−0.553341	+	0.128674i	−0.0419487	+	0.00975475i
$175$	13.7413	−	8.83099i	1.03874	−	0.667560i
$176$	0.418508	−	2.05594i	0.0315462	−	0.154972i
$177$	−0.0247676	−	0.0159172i	−0.00186165	−	0.00119641i
$178$	10.2454	+	3.65554i	0.767924	+	0.273995i
$179$	3.48314	+	5.77614i	0.260342	+	0.431729i	0.958866	−	0.283857i	$-0.0916143\pi$
$179$	3.48314	+	5.77614i	0.260342	+	0.431729i	−0.698525	+	0.715586i	$0.746160\pi$
$180$	1.19325	−	4.53958i	0.0889393	−	0.338360i
$181$	14.4042	−	0.823664i	1.07066	−	0.0612225i	0.487141	−	0.873323i	$-0.338040\pi$
$181$	14.4042	−	0.823664i	1.07066	−	0.0612225i	0.583517	+	0.812101i	$0.301676\pi$
$182$	15.9557	−	0.912378i	1.18271	−	0.0676300i
$183$	0.241220	−	0.917695i	0.0178315	−	0.0678379i
$184$	1.08665	+	1.80200i	0.0801086	+	0.132845i
$185$	6.61532	+	2.36034i	0.486368	+	0.173536i
$186$	0.576413	+	0.370438i	0.0422646	+	0.0271618i
$187$	1.18706	+	3.05705i	0.0868064	+	0.223554i
$188$	−7.79415	+	5.00899i	−0.568447	+	0.365318i
$189$	−2.12696	+	0.494602i	−0.154713	+	0.0359770i
$190$	−0.0466316	+	0.0197067i	−0.00338301	+	0.00142967i
$191$	0.456939	+	15.9950i	0.0330629	+	1.15735i	0.831588	+	0.555393i	$0.187432\pi$
$191$	0.456939	+	15.9950i	0.0330629	+	1.15735i	−0.798525	+	0.601961i	$0.794386\pi$
$192$	−0.169129	+	0.219330i	−0.0122058	+	0.0158288i
$193$	−9.05403	−	9.31637i	−0.651723	−	0.670607i	0.308054	−	0.951369i	$-0.400322\pi$
$193$	−9.05403	−	9.31637i	−0.651723	−	0.670607i	−0.959778	+	0.280761i	$0.909413\pi$
$194$	−3.11947	+	5.17306i	−0.223965	+	0.371404i
$195$	0.332938	−	0.272242i	0.0238422	−	0.0194956i
$196$	−10.5080	−	13.6270i	−0.750572	−	0.973359i
$197$	−3.56118	+	24.7686i	−0.253724	+	1.76469i	0.321709	+	0.946839i	$0.395743\pi$
$197$	−3.56118	+	24.7686i	−0.253724	+	1.76469i	−0.575433	+	0.817849i	$0.695166\pi$
$198$	−4.80457	+	6.21913i	−0.341446	+	0.441974i
$199$	1.73873	+	12.0932i	0.123255	+	0.857261i	0.953829	+	0.300351i	$0.0971039\pi$
$199$	1.73873	+	12.0932i	0.123255	+	0.857261i	−0.830573	+	0.556910i	$0.811987\pi$
$200$	6.87896	−	7.07828i	0.486416	−	0.500510i
$201$	0.236782	+	0.900811i	0.0167013	+	0.0635383i
$202$	0.933722	+	2.87370i	0.0656964	+	0.202193i
$203$	−7.63896	−	37.6997i	−0.536150	−	2.64600i
$204$	−0.00958074	+	0.111546i	−0.000670786	+	0.00780982i
$205$	7.83767	−	7.19334i	0.547406	−	0.502405i
$206$	1.79800	+	1.65019i	0.125273	+	0.114974i
$207$	0.201839	+	2.34996i	0.0140288	+	0.163334i
$208$	−2.77278	+	0.814161i	−0.192258	+	0.0564519i
$209$	−0.185744		0.000166699i	−0.0128482		1.15308e-5i
$210$	0.316025	+	0.0927934i	0.0218078	+	0.00640335i
$211$	1.23902	−	6.11483i	0.0852980	−	0.420962i	−0.914565	−	0.404438i	$-0.867467\pi$
$211$	1.23902	−	6.11483i	0.0852980	−	0.420962i	0.999863	−	0.0165242i	$-0.00526007\pi$
$212$	10.9323	−	1.25436i	0.750832	−	0.0861499i
$213$	0.133536	+	0.195291i	0.00914977	+	0.0133811i
$214$	−7.57771	−	4.27933i	−0.518002	−	0.292529i
$215$	1.42890	−	1.03816i	0.0974503	−	0.0708018i
$216$	−1.18415	+	0.582209i	−0.0805714	+	0.0396143i
$217$	−26.1863	+	38.2962i	−1.77764	+	2.59972i
$218$	0.139707	−	0.264774i	0.00946214	−	0.0179327i
$219$	−0.0948581	−	0.109472i	−0.00640991	−	0.00739744i
$220$	−4.79254	+	2.02028i	−0.323113	+	0.136207i
$221$	2.95798	−	3.41369i	0.198975	−	0.229629i
$222$	−0.145659	−	0.374122i	−0.00977599	−	0.0251094i
$223$	−0.452742	+	15.8480i	−0.0303179	+	1.06126i	0.831962	+	0.554832i	$0.187217\pi$
$223$	−0.452742	+	15.8480i	−0.0303179	+	1.06126i	−0.862280	+	0.506431i	$0.830964\pi$
$224$	−19.9853	−	16.3419i	−1.33533	−	1.09189i
$225$	10.4199	−	3.71780i	0.694657	−	0.247853i
$226$	3.84331	+	0.893724i	0.255653	+	0.0594497i
$227$	−6.46903	+	1.11951i	−0.429365	+	0.0743045i	−0.381108	−	0.924531i	$-0.624457\pi$
$227$	−6.46903	+	1.11951i	−0.429365	+	0.0743045i	−0.0482565	+	0.998835i	$0.515367\pi$
$228$	−0.00569053	−	0.00279784i	−0.000376864	−	0.000185292i
$229$	13.9699	−	7.88918i	0.923158	−	0.521331i	0.0446202	−	0.999004i	$-0.485792\pi$
$229$	13.9699	−	7.88918i	0.923158	−	0.521331i	0.878538	+	0.477673i	$0.158519\pi$
$230$	0.295902	−	0.647935i	0.0195112	−	0.0427236i
$231$	0.934831	+	0.765808i	0.0615074	+	0.0503865i
$232$	−9.65575	−	21.1431i	−0.633931	−	1.38812i
$233$	−6.23096	−	4.52706i	−0.408204	−	0.296578i	0.364670	−	0.931137i	$-0.381182\pi$
$233$	−6.23096	−	4.52706i	−0.408204	−	0.296578i	−0.772874	+	0.634559i	$0.781182\pi$
$234$	10.6659	+	1.84581i	0.697252	+	0.120664i
$235$	7.09593	+	2.99876i	0.462887	+	0.195618i
$236$	0.177919	−	0.456981i	0.0115815	−	0.0297469i
$237$	−0.328228	−	0.622062i	−0.0213207	−	0.0404073i
$238$	3.43671	+	0.394326i	0.222769	+	0.0255603i
$239$	2.00183	−	6.16100i	0.129488	−	0.398522i	−0.865204	−	0.501420i	$-0.832811\pi$
$239$	2.00183	−	6.16100i	0.129488	−	0.398522i	0.994692	+	0.102897i	$0.0328113\pi$
$240$	−0.0594594	−	0.00340001i	−0.00383809	−	0.000219470i
$241$	11.2976			0.727741			0.363871	−	0.931449i	$-0.381455\pi$
$241$	11.2976			0.727741			0.363871	+	0.931449i	$0.381455\pi$
$242$	8.70800	+	0.0156303i	0.559771	+	0.00100475i
$243$	−2.21938			−0.142373
$244$	15.7792	+	0.902286i	1.01016	+	0.0577630i
$245$	−4.42142	+	13.6077i	−0.282474	+	0.869366i
$246$	−0.604117	−	0.0693159i	−0.0385171	−	0.00441942i
$247$	0.119390	+	0.226269i	0.00759661	+	0.0143972i
$248$	−10.1709	+	26.1237i	−0.645852	+	1.65886i
$249$	0.0589583	+	0.0249160i	0.00373633	+	0.00157899i
$250$	−7.74573	−	1.34045i	−0.489883	−	0.0847776i
$251$	−9.74668	−	7.08138i	−0.615205	−	0.446973i	0.236038	−	0.971744i	$-0.424151\pi$
$251$	−9.74668	−	7.08138i	−0.615205	−	0.446973i	−0.851243	+	0.524771i	$0.824151\pi$
$252$	−7.54642	−	16.5244i	−0.475380	−	1.04094i
$253$	1.92704	−	1.76543i	0.121152	−	0.110992i
$254$	−4.79439	+	10.4983i	−0.300827	+	0.658719i
$255$	0.0810575	−	0.0457753i	0.00507602	−	0.00286656i
$256$	−12.4400	−	6.11634i	−0.777500	−	0.382271i
$257$	−19.0972	+	3.30489i	−1.19125	+	0.206154i	−0.731466	−	0.681878i	$-0.761163\pi$
$257$	−19.0972	+	3.30489i	−1.19125	+	0.206154i	−0.459782	+	0.888032i	$0.652073\pi$
$258$	−0.0983328	−	0.0228663i	−0.00612193	−	0.00142359i
$259$	25.6028	−	9.13505i	1.59088	−	0.567624i
$260$	5.54563	+	4.53464i	0.343925	+	0.281226i
$261$	0.743970	−	26.0424i	0.0460506	−	1.61198i
$262$	−3.90004	−	10.0172i	−0.240945	−	0.618863i
$263$	14.0564	−	16.2220i	0.866757	−	1.00029i	−0.133201	−	0.991089i	$-0.542525\pi$
$263$	14.0564	−	16.2220i	0.866757	−	1.00029i	0.999958	−	0.00920192i	$-0.00292910\pi$
$264$	0.655018	+	0.322781i	0.0403136	+	0.0198658i
$265$	−5.99169	−	6.91478i	−0.368067	−	0.424771i
$266$	−0.0914336	+	0.173286i	−0.00560615	+	0.0106248i
$267$	0.639475	−	0.935203i	0.0391353	−	0.0572335i
$268$	−13.9224	+	6.84518i	−0.850446	+	0.418136i
$269$	−21.2483	+	15.4378i	−1.29553	+	0.941261i	−0.999901	−	0.0140412i	$-0.995530\pi$
$269$	−21.2483	+	15.4378i	−1.29553	+	0.941261i	−0.295633	+	0.955302i	$0.595530\pi$
$270$	0.388934	+	0.219641i	0.0236698	+	0.0133669i
$271$	14.5332	+	21.2541i	0.882829	+	1.29110i	0.955877	+	0.293768i	$0.0949092\pi$
$271$	14.5332	+	21.2541i	0.882829	+	1.29110i	−0.0730479	+	0.997328i	$0.523273\pi$
$272$	−0.621430	+	0.0713025i	−0.0376797	+	0.00432335i
$273$	0.330550	−	1.63133i	0.0200058	−	0.0987325i
$274$	−2.31522	−	0.679809i	−0.139867	−	0.0410688i
$275$	−10.3067	−	6.63678i	−0.621516	−	0.400213i
$276$	0.0856077	−	0.0251367i	0.00515298	−	0.00151305i
$277$	−0.663943	−	7.73015i	−0.0398925	−	0.464459i	−0.988835	−	0.149012i	$-0.952391\pi$
$277$	−0.663943	−	7.73015i	−0.0398925	−	0.464459i	0.948943	−	0.315448i	$-0.102155\pi$
$278$	5.67337	+	5.20697i	0.340266	+	0.312293i
$279$	−23.1500	+	21.2469i	−1.38595	+	1.27202i
$280$	−1.15319	+	13.4264i	−0.0689165	+	0.802380i
$281$	−1.24152	−	6.12715i	−0.0740630	−	0.365515i	0.925861	−	0.377865i	$-0.123342\pi$
$281$	−1.24152	−	6.12715i	−0.0740630	−	0.365515i	−0.999924	+	0.0123497i	$0.996069\pi$
$282$	−0.136070	−	0.418781i	−0.00810286	−	0.0249380i
$283$	1.82599	+	6.94678i	0.108544	+	0.412943i	0.999122	−	0.0418859i	$-0.0133366\pi$
$283$	1.82599	+	6.94678i	0.108544	+	0.412943i	−0.890579	+	0.454829i	$0.849700\pi$
$284$	−2.74638	+	2.82596i	−0.162968	+	0.167690i
$285$	0.000750356		0.00521884i	4.44472e−5		0.000309137i
$286$	−5.58771	−	10.6130i	−0.330408	−	0.627557i
$287$	5.85947	−	40.7535i	0.345873	−	2.40560i
$288$	−10.6774	−	13.8466i	−0.629169	−	0.815921i
$289$	−12.4035	+	10.1423i	−0.729619	+	0.596607i
$290$	−4.06303	+	6.73778i	−0.238589	+	0.395656i
$291$	0.438475	+	0.451180i	0.0257039	+	0.0264487i
$292$	1.47334	−	1.91067i	0.0862209	−	0.111813i
$293$	0.541888	+	18.9685i	0.0316574	+	1.10815i	0.847804	+	0.530309i	$0.177924\pi$
$293$	0.541888	+	18.9685i	0.0316574	+	1.10815i	−0.816147	+	0.577845i	$0.803894\pi$
$294$	0.753332	−	0.318361i	0.0439352	−	0.0185672i
$295$	−0.397154	+	0.0923542i	−0.0231232	+	0.00537707i
$296$	13.8186	−	8.88065i	0.803188	−	0.516177i
$297$	0.999588	+	1.29870i	0.0580020	+	0.0753581i
$298$	−2.82650	−	1.81648i	−0.163734	−	0.105226i
$299$	−3.39034	−	1.20967i	−0.196069	−	0.0699572i
$300$	−0.216113	−	0.358383i	−0.0124773	−	0.0206912i
$301$	1.73775	−	6.61110i	0.100162	−	0.381057i
$302$	9.17862	−	0.524852i	0.528170	−	0.0302019i
$303$	0.314182	−	0.0179656i	0.0180493	−	0.00103209i
$304$	0.00900647	−	0.0342642i	0.000516557	−	0.00196519i
$305$	−6.78621	−	11.2537i	−0.388577	−	0.644383i
$306$	2.20670	+	0.787350i	0.126149	+	0.0450098i
$307$	−6.33551	−	4.07159i	−0.361587	−	0.232378i	0.347215	−	0.937786i	$-0.387127\pi$
$307$	−6.33551	−	4.07159i	−0.361587	−	0.232378i	−0.708802	+	0.705408i	$0.750764\pi$
$308$	−9.40946	+	17.7942i	−0.536154	+	1.01392i
$309$	0.213824	−	0.137417i	0.0121640	−	0.00781735i
$310$	9.24290	−	2.14934i	0.524962	−	0.122075i
$311$	19.7418	−	8.34294i	1.11945	−	0.473084i	0.250568	−	0.968099i	$-0.419383\pi$
$311$	19.7418	−	8.34294i	1.11945	−	0.473084i	0.868885	+	0.495015i	$0.164837\pi$
$312$	−0.0287214	−	1.00538i	−0.00162603	−	0.0569184i
$313$	4.29212	−	5.56611i	0.242605	−	0.314615i	−0.654818	−	0.755786i	$-0.727255\pi$
$313$	4.29212	−	5.56611i	0.242605	−	0.314615i	0.897423	+	0.441171i	$0.145437\pi$
$314$	−2.77436	−	2.85475i	−0.156566	−	0.161103i
$315$	−7.79997	+	12.9348i	−0.439478	+	0.728793i
$316$	9.06936	−	7.41598i	0.510192	−	0.417182i
$317$	11.2736	+	14.6199i	0.633189	+	0.821134i	0.993753	−	0.111600i	$-0.0355977\pi$
$317$	11.2736	+	14.6199i	0.633189	+	0.821134i	−0.360564	+	0.932734i	$0.617416\pi$
$318$	−0.0744286	+	0.517662i	−0.00417375	+	0.0290290i
$319$	−23.3700	+	16.9473i	−1.30847	+	0.948864i
$320$	0.545902	+	3.79683i	0.0305168	+	0.212249i
$321$	−0.631677	+	0.649980i	−0.0352568	+	0.0362784i
$322$	−0.700824	−	2.66621i	−0.0390554	−	0.148582i
$323$	0.0171121	+	0.0526655i	0.000952141	+	0.00293039i
$324$	−2.43786	−	12.0313i	−0.135437	−	0.668407i
$325$	−1.44490	+	16.8226i	−0.0801484	+	0.933151i
$326$	−0.920793	+	0.845096i	−0.0509980	+	0.0468055i
$327$	−0.0229710	−	0.0210826i	−0.00127030	−	0.00116587i
$328$	−2.12904	−	24.7879i	−0.117556	−	1.36868i
$329$	28.6068	−	8.39971i	1.57714	−	0.463091i
$330$	−0.0349585	−	0.244700i	−0.00192440	−	0.0134703i
$331$	−17.2056	−	5.05202i	−0.945705	−	0.277684i	−0.227707	−	0.973730i	$-0.573123\pi$
$331$	−17.2056	−	5.05202i	−0.945705	−	0.277684i	−0.717998	+	0.696046i	$0.754941\pi$
$332$	−0.211725	+	1.04491i	−0.0116199	+	0.0573467i
$333$	18.2915	−	2.09875i	1.00237	−	0.115011i
$334$	−1.01311	−	1.48163i	−0.0554350	−	0.0810712i
$335$	11.2323	+	6.34319i	0.613688	+	0.346565i
$336$	−0.186476	+	0.135483i	−0.0101731	+	0.00739119i
$337$	−9.03310	+	4.44128i	−0.492064	+	0.241932i	−0.670347	−	0.742048i	$-0.733855\pi$
$337$	−9.03310	+	4.44128i	−0.492064	+	0.241932i	0.178283	+	0.983979i	$0.442946\pi$
$338$	−3.51582	+	5.14172i	−0.191235	+	0.279673i
$339$	0.191780	−	0.363464i	0.0104161	−	0.0197406i
$340$	1.01540	+	1.17184i	0.0550679	+	0.0635518i
$341$	34.3021	+	5.96792i	1.85756	+	0.323181i
$342$	−0.0869018	+	0.100290i	−0.00469911	+	0.00542307i
$343$	8.86703	+	22.7748i	0.478775	+	1.22972i
$344$	0.117953	−	4.12888i	0.00635958	−	0.222614i
$345$	−0.0574303	−	0.0469605i	−0.00309194	−	0.00252827i
$346$	−7.49667	+	2.67481i	−0.403023	+	0.143798i
$347$	5.15703	+	1.19922i	0.276844	+	0.0643773i	0.362620	−	0.931937i	$-0.381882\pi$
$347$	5.15703	+	1.19922i	0.276844	+	0.0643773i	−0.0857758	+	0.996314i	$0.527337\pi$
$348$	−0.971098	+	0.168055i	−0.0520563	+	0.00900870i
$349$	−10.3495	−	5.08852i	−0.553998	−	0.272382i	0.142677	−	0.989769i	$-0.454429\pi$
$349$	−10.3495	−	5.08852i	−0.553998	−	0.272382i	−0.696675	+	0.717387i	$0.745338\pi$
$350$	−11.2595	+	6.35852i	−0.601845	+	0.339877i
$351$	0.937703	−	2.05328i	0.0500509	−	0.109596i
$352$	−4.94220	+	18.7337i	−0.263420	+	0.998508i
$353$	−1.22611	−	2.68481i	−0.0652595	−	0.142898i	0.874192	−	0.485581i	$-0.161392\pi$
$353$	−1.22611	−	2.68481i	−0.0652595	−	0.142898i	−0.939451	+	0.342682i	$0.888665\pi$
$354$	0.0188556	+	0.0136994i	0.00100217	+	0.000728117i
$355$	3.22856	+	0.558724i	0.171354	+	0.0296540i
$356$	17.3824	+	7.34585i	0.921264	+	0.389330i
$357$	0.130712	−	0.335730i	0.00691799	−	0.0177687i
$358$	−2.49184	−	4.72256i	−0.131698	−	0.249595i
$359$	0.0958791	+	0.0110011i	0.00506031	+	0.000580616i	0.116521	−	0.993188i	$-0.462826\pi$
$359$	0.0958791	+	0.0110011i	0.00506031	+	0.000580616i	−0.111461	+	0.993769i	$0.535553\pi$
$360$	−2.82046	+	8.68047i	−0.148651	+	0.457501i
$361$	18.9659	+	1.08451i	0.998204	+	0.0570794i
$362$	−11.4216			−0.600304
$363$	0.232132	−	0.876719i	0.0121838	−	0.0460158i
$364$	27.7247			1.45317
$365$	−2.00287	−	0.114529i	−0.104835	−	0.00599470i
$366$	−0.232121	+	0.714395i	−0.0121332	+	0.0373420i
$367$	31.0200	+	3.55921i	1.61923	+	0.185789i	0.875680	−	0.482892i	$-0.160414\pi$
$367$	31.0200	+	3.55921i	1.61923	+	0.185789i	0.743549	+	0.668681i	$0.233141\pi$
$368$	0.232626	+	0.440876i	0.0121265	+	0.0229822i
$369$	10.1173	−	25.9862i	0.526687	−	1.35279i
$370$	−5.12172	−	2.16446i	−0.266266	−	0.112525i
$371$	−34.8922	−	6.03834i	−1.81151	−	0.313495i
$372$	0.961627	+	0.698663i	0.0498580	+	0.0362240i
$373$	11.5408	+	25.2707i	0.597558	+	1.30847i	0.930766	+	0.365616i	$0.119142\pi$
$373$	11.5408	+	25.2707i	0.597558	+	1.30847i	−0.333208	+	0.942853i	$0.608131\pi$
$374$	−0.800029	−	2.46978i	−0.0413685	−	0.127709i
$375$	−0.340100	+	0.744716i	−0.0175627	+	0.0384570i
$376$	15.6873	−	8.85900i	0.809009	−	0.456868i
$377$	35.6821	+	17.5437i	1.83772	+	0.903546i
$378$	1.70338	−	0.294782i	0.0876127	−	0.0151620i
$379$	−11.2675	−	2.62015i	−0.578774	−	0.134588i	−0.0731181	−	0.997323i	$-0.523295\pi$
$379$	−11.2675	−	2.62015i	−0.578774	−	0.134588i	−0.505656	+	0.862735i	$0.668750\pi$
$380$	−0.0827149	+	0.0295126i	−0.00424318	+	0.00151397i
$381$	0.930522	+	0.760884i	0.0476721	+	0.0389813i
$382$	0.361730	−	12.6622i	0.0185077	−	0.647855i
$383$	6.79286	+	17.4473i	0.347099	+	0.891517i	0.991883	+	0.127152i	$0.0405837\pi$
$383$	6.79286	+	17.4473i	0.347099	+	0.891517i	−0.644784	+	0.764365i	$0.723053\pi$
$384$	−0.487225	+	0.562287i	−0.0248636	+	0.0286941i
$385$	16.6293	−	1.89291i	0.847506	−	0.0964718i
$386$	6.73478	+	7.77235i	0.342791	+	0.395602i
$387$	2.16058	−	4.09475i	0.109828	−	0.208148i
$388$	−5.91506	+	8.65050i	−0.300292	+	0.439163i
$389$	−16.4706	+	8.09807i	−0.835095	+	0.410588i	−0.808099	−	0.589047i	$-0.799503\pi$
$389$	−16.4706	+	8.09807i	−0.835095	+	0.410588i	−0.0269961	+	0.999636i	$0.508594\pi$
$390$	−0.275440	+	0.200119i	−0.0139474	+	0.0101334i
$391$	−0.678446	−	0.383136i	−0.0343105	−	0.0193760i
$392$	18.8870	+	27.6214i	0.953939	+	1.39509i
$393$	−1.11226	+	0.127620i	−0.0561062	+	0.00643759i
$394$	3.93395	−	19.4148i	0.198190	−	0.978104i
$395$	−9.34647	−	2.74437i	−0.470272	−	0.138084i
$396$	−8.93716	+	10.2953i	−0.449109	+	0.517361i
$397$	−14.6558	+	4.30334i	−0.735555	+	0.215978i	−0.627992	−	0.778220i	$-0.716123\pi$
$397$	−14.6558	+	4.30334i	−0.735555	+	0.215978i	−0.107563	+	0.994198i	$0.534305\pi$
$398$	−0.827668	−	9.63636i	−0.0414872	−	0.483027i
$399$	0.0150338	+	0.0137979i	0.000752630	+	0.000690757i
$400$	1.72263	−	1.58101i	0.0861314	−	0.0790507i
$401$	0.739318	−	8.60772i	0.0369198	−	0.429849i	−0.954414	−	0.298485i	$-0.903519\pi$
$401$	0.739318	−	8.60772i	0.0369198	−	0.429849i	0.991334	−	0.131364i	$-0.0419358\pi$
$402$	−0.146429	−	0.722653i	−0.00730319	−	0.0360427i
$403$	−14.8192	−	45.6089i	−0.738198	−	2.27194i
$404$	1.33255	+	5.06956i	0.0662970	+	0.252220i
$405$	−7.11368	+	7.31981i	−0.353482	+	0.363724i
$406$	4.33363	+	30.1411i	0.215075	+	1.49588i
$407$	−14.2050	−	14.6429i	−0.704117	−	0.725822i
$408$	0.0309825	−	0.215488i	0.00153386	−	0.0106682i
$409$	6.37976	+	8.27343i	0.315459	+	0.409095i	0.922759	−	0.385378i	$-0.125929\pi$
$409$	6.37976	+	8.27343i	0.315459	+	0.409095i	−0.607300	+	0.794473i	$0.707747\pi$
$410$	−6.51956	+	5.33102i	−0.321978	+	0.263280i
$411$	−0.129774	+	0.215206i	−0.00640129	+	0.0106154i
$412$	2.95061	+	3.03611i	0.145366	+	0.149578i
$413$	−0.963655	+	1.24969i	−0.0474184	+	0.0614932i
$414$	−0.0533190	−	1.86641i	−0.00262048	−	0.0917289i
$415$	0.816549	−	0.345076i	0.0400828	−	0.0169391i
$416$	25.9923	−	6.04425i	1.27438	−	0.296344i
$417$	0.674695	−	0.433600i	0.0330400	−	0.0212335i
$418$	0.146794	+	0.00852618i	0.00717994	+	0.000417029i
$419$	−10.1747	−	6.53887i	−0.497066	−	0.319445i	0.267976	−	0.963426i	$-0.413645\pi$
$419$	−10.1747	−	6.53887i	−0.497066	−	0.319445i	−0.765042	+	0.643981i	$0.777282\pi$
$420$	0.538147	+	0.192011i	0.0262589	+	0.00936916i
$421$	−12.5487	−	20.8097i	−0.611585	−	1.01420i	−0.995853	−	0.0909787i	$-0.971000\pi$
$421$	−12.5487	−	20.8097i	−0.611585	−	1.01420i	0.384267	−	0.923222i	$-0.374454\pi$
$422$	−1.25561	+	4.77684i	−0.0611221	+	0.232533i
$423$	20.1605	−	1.15282i	0.980235	−	0.0560518i
$424$	−21.3627	+	1.22156i	−1.03746	+	0.0593243i
$425$	−0.929085	+	3.53461i	−0.0450673	+	0.171454i
$426$	−0.0967141	−	0.160382i	−0.00468581	−	0.00777055i
$427$	−47.9025	−	17.0916i	−2.31816	−	0.827119i
$428$	−12.7003	−	8.16202i	−0.613895	−	0.394526i
$429$	−1.21696	+	0.281840i	−0.0587553	+	0.0136074i
$430$	−1.17625	+	0.755927i	−0.0567236	+	0.0364541i
$431$	−32.9733	+	7.66760i	−1.58827	+	0.369335i	−0.925277	−	0.379293i	$-0.876167\pi$
$431$	−32.9733	+	7.66760i	−1.58827	+	0.369335i	−0.662990	+	0.748629i	$0.730713\pi$
$432$	−0.287931	+	0.121681i	−0.0138531	+	0.00585436i
$433$	−0.325918	−	11.4086i	−0.0156626	−	0.548263i	−0.969099	−	0.246670i	$-0.920664\pi$
$433$	−0.325918	−	11.4086i	−0.0156626	−	0.548263i	0.953437	−	0.301593i	$-0.0975183\pi$
$434$	22.4270	−	29.0838i	1.07653	−	1.39607i
$435$	0.571103	+	0.587651i	0.0273823	+	0.0281757i
$436$	0.268186	−	0.444737i	0.0128438	−	0.0212990i
$437$	0.0341633	−	0.0279352i	0.00163425	−	0.00133632i
$438$	0.0700233	+	0.0908078i	0.00334584	+	0.00433896i
$439$	−2.16593	+	15.0643i	−0.103374	+	0.718982i	0.870545	+	0.492088i	$0.163766\pi$
$439$	−2.16593	+	15.0643i	−0.103374	+	0.718982i	−0.973919	+	0.226894i	$0.927143\pi$
$440$	9.52829	−	3.39005i	0.454244	−	0.161614i
$441$	5.33761	+	37.1239i	0.254172	+	1.76781i
$442$	−2.49210	+	2.56431i	−0.118537	+	0.121972i
$443$	−5.69272	−	21.6573i	−0.270469	−	1.02897i	−0.954184	−	0.299222i	$-0.903273\pi$
$443$	−5.69272	−	21.6573i	−0.270469	−	1.02897i	0.683714	−	0.729750i	$-0.260363\pi$
$444$	−0.215221	−	0.662383i	−0.0102140	−	0.0314353i
$445$	−3.11601	−	15.3781i	−0.147713	−	0.728993i
$446$	1.07405	−	12.5050i	0.0508579	−	0.592128i
$447$	−0.257805	+	0.236611i	−0.0121937	+	0.0111913i
$448$	10.9374	+	10.0383i	0.516745	+	0.474264i
$449$	0.578792	+	6.73876i	0.0273149	+	0.318022i	0.997219	+	0.0745327i	$0.0237465\pi$
$449$	0.578792	+	6.73876i	0.0273149	+	0.318022i	−0.969904	+	0.243489i	$0.921708\pi$
$450$	−8.40331	+	2.46744i	−0.396136	+	0.116316i
$451$	−29.6555	+	8.67875i	−1.39643	+	0.408667i
$452$	6.56789	+	1.92851i	0.308927	+	0.0907093i
$453$	0.190151	−	0.938433i	0.00893409	−	0.0440914i
$454$	5.16337	−	0.592441i	0.242329	−	0.0278046i
$455$	−13.0118	−	19.0291i	−0.610001	−	0.892098i
$456$	0.0107367	+	0.00606332i	0.000502794	+	0.000283941i
$457$	−6.12703	+	4.45155i	−0.286611	+	0.208235i	−0.721796	−	0.692106i	$-0.756683\pi$
$457$	−6.12703	+	4.45155i	−0.286611	+	0.208235i	0.435185	+	0.900341i	$0.356683\pi$
$458$	−11.3976	+	5.60383i	−0.532575	+	0.261850i
$459$	0.275780	−	0.403315i	0.0128723	−	0.0188251i
$460$	0.576654	−	1.09288i	0.0268866	−	0.0509559i
$461$	−12.0032	−	13.8524i	−0.559045	−	0.645172i	0.403921	−	0.914794i	$-0.367647\pi$
$461$	−12.0032	−	13.8524i	−0.559045	−	0.645172i	−0.962966	+	0.269621i	$0.913101\pi$
$462$	−0.704230	−	0.647502i	−0.0327638	−	0.0301245i
$463$	13.8951	−	16.0358i	0.645762	−	0.745249i	−0.334621	−	0.942353i	$-0.608608\pi$
$463$	13.8951	−	16.0358i	0.645762	−	0.745249i	0.980383	+	0.197104i	$0.0631537\pi$
$464$	−1.99769	−	5.13102i	−0.0927404	−	0.238202i
$465$	0.0282226	−	0.987920i	0.00130879	−	0.0458137i
$466$	4.72003	+	3.85955i	0.218651	+	0.178790i
$467$	−32.5467	+	11.6126i	−1.50608	+	0.537369i	−0.954877	−	0.297002i	$-0.904013\pi$
$467$	−32.5467	+	11.6126i	−1.50608	+	0.537369i	−0.551204	+	0.834370i	$0.685832\pi$
$468$	18.2899	+	4.25314i	0.845453	+	0.196602i
$469$	49.1934	−	8.51325i	2.27154	−	0.393105i
$470$	−5.47272	−	2.69075i	−0.252438	−	0.124115i
$471$	−0.361007	+	0.203870i	−0.0166343	+	0.00939383i
$472$	−0.396133	+	0.867411i	−0.0182335	+	0.0399258i
$473$	−5.05571	+	0.870253i	−0.232462	+	0.0400143i
$474$	0.231301	+	0.506478i	0.0106240	+	0.0232633i
$475$	−0.167464	−	0.121670i	−0.00768378	−	0.00558259i
$476$	5.91313	+	1.02331i	0.271028	+	0.0469032i
$477$	−22.0921	−	9.33618i	−1.01153	−	0.427474i
$478$	−1.86058	+	4.77886i	−0.0851009	+	0.218580i
$479$	−2.96251	−	5.61459i	−0.135361	−	0.256537i	0.807402	−	0.590002i	$-0.200873\pi$
$479$	−2.96251	−	5.61459i	−0.135361	−	0.256537i	−0.942763	+	0.333465i	$0.891782\pi$
$480$	0.546382	+	0.0626914i	0.0249388	+	0.00286146i
$481$	−8.68319	+	26.7241i	−0.395919	+	1.21851i
$482$	−8.92900	−	0.510579i	−0.406705	−	0.0232562i
$483$	−0.287115			−0.0130642
$484$	15.0802	+	0.889476i	0.685464	+	0.0404307i
$485$	8.71342			0.395656
$486$	1.75408	+	0.100302i	0.0795666	+	0.00454978i
$487$	0.626243	−	1.92738i	0.0283778	−	0.0873378i	−0.935865	−	0.352360i	$-0.885379\pi$
$487$	0.626243	−	1.92738i	0.0283778	−	0.0873378i	0.964242	+	0.265022i	$0.0853793\pi$
$488$	−30.5328	−	3.50332i	−1.38216	−	0.158588i
$489$	0.0607448	+	0.115124i	0.00274697	+	0.00520610i
$490$	4.10943	−	10.5550i	0.185645	−	0.476826i
$491$	−19.6020	−	8.28388i	−0.884626	−	0.373846i	−0.100859	−	0.994901i	$-0.532159\pi$
$491$	−19.6020	−	8.28388i	−0.884626	−	0.373846i	−0.783767	+	0.621055i	$0.786704\pi$
$492$	−1.03943	−	0.179881i	−0.0468611	−	0.00810964i
$493$	6.96276	+	5.05874i	0.313587	+	0.227834i
$494$	−0.0841336	−	0.184227i	−0.00378535	−	0.00828876i
$495$	11.2607	+	1.30229i	0.506131	+	0.0585334i
$496$	−2.75875	+	6.04081i	−0.123871	+	0.271240i
$497$	11.0419	−	6.23566i	0.495298	−	0.279707i
$498$	−0.0454714	−	0.0223568i	−0.00203762	−	0.00100183i
$499$	19.6401	−	3.39885i	0.879211	−	0.152153i	0.286994	−	0.957932i	$-0.407344\pi$
$499$	19.6401	−	3.39885i	0.879211	−	0.152153i	0.592217	+	0.805779i	$0.298253\pi$
$500$	−13.2824	−	3.08869i	−0.594007	−	0.138131i
$501$	−0.176064	+	0.0628196i	−0.00786597	+	0.00280657i
$502$	7.38322	+	6.03723i	0.329529	+	0.269455i
$503$	0.983402	−	34.4236i	0.0438477	−	1.53487i	−0.618566	−	0.785732i	$-0.712286\pi$
$503$	0.983402	−	34.4236i	0.0438477	−	1.53487i	0.662414	−	0.749138i	$-0.269532\pi$
$504$	12.8159	+	32.9174i	0.570866	+	1.46626i
$505$	2.85415	−	3.29386i	0.127008	−	0.146575i
$506$	−1.60281	+	1.30821i	−0.0712537	+	0.0581572i
$507$	0.424825	+	0.490274i	0.0188671	+	0.0217738i
$508$	−9.34332	+	17.7076i	−0.414543	+	0.785646i
$509$	−21.1493	+	30.9298i	−0.937425	+	1.37094i	−0.00878358	+	0.999961i	$0.502796\pi$
$509$	−21.1493	+	30.9298i	−0.937425	+	1.37094i	−0.928641	+	0.370979i	$0.879022\pi$
$510$	−0.0661322	+	0.0325150i	−0.00292838	+	0.00143979i
$511$	−6.28140	+	4.56370i	−0.277873	+	0.201886i
$512$	−6.15974	−	3.47856i	−0.272225	−	0.153732i
$513$	0.0156199	+	0.0228434i	0.000689635	+	0.00100856i
$514$	15.2427	−	1.74894i	0.672328	−	0.0771424i
$515$	0.699078	−	3.45009i	0.0308051	−	0.152029i
$516$	−0.168042	−	0.0493416i	−0.00739764	−	0.00217214i
$517$	−14.6375	−	16.9233i	−0.643758	−	0.744285i
$518$	−20.6479	+	6.06277i	−0.907216	+	0.266383i
$519$	0.0709399	+	0.825939i	0.00311392	+	0.0362547i
$520$	−10.2626	−	9.41897i	−0.450047	−	0.413049i
$521$	15.1635	−	13.9169i	0.664323	−	0.609710i	−0.271391	−	0.962469i	$-0.587484\pi$
$521$	15.1635	−	13.9169i	0.664323	−	0.609710i	0.935714	+	0.352759i	$0.114756\pi$
$522$	−1.76494	+	20.5489i	−0.0772494	+	0.899399i
$523$	−0.136609	−	0.674193i	−0.00597351	−	0.0294804i	0.976985	−	0.213308i	$-0.0684238\pi$
$523$	−0.136609	−	0.674193i	−0.00597351	−	0.0294804i	−0.982958	+	0.183828i	$0.941151\pi$
$524$	−5.76259	−	17.7354i	−0.251740	−	0.774775i
$525$	0.342364	+	1.30249i	0.0149420	+	0.0568453i
$526$	−11.8426	+	12.1857i	−0.516361	+	0.531323i
$527$	−1.47724	−	10.2745i	−0.0643497	−	0.447562i
$528$	0.150549	+	0.0851974i	0.00655182	+	0.00370774i
$529$	3.18487	−	22.1513i	0.138473	−	0.963099i
$530$	4.42301	+	5.73586i	0.192123	+	0.249150i
$531$	−0.827433	+	0.676589i	−0.0359076	+	0.0293615i
$532$	−0.175519	+	0.291066i	−0.00760972	+	0.0126193i
$533$	29.6613	+	30.5208i	1.28478	+	1.32200i
$534$	−0.547672	+	0.710234i	−0.0237001	+	0.0307348i
$535$	0.358457	+	12.5476i	0.0154974	+	0.542481i
$536$	27.7882	−	11.7434i	1.20027	−	0.507238i
$537$	−0.541666	+	0.125959i	−0.0233746	+	0.00543554i
$538$	17.4912	−	11.2409i	0.754101	−	0.484631i
$539$	28.9902	−	29.7767i	1.24870	−	1.28258i
$540$	0.651859	+	0.418924i	0.0280515	+	0.0180276i
$541$	−23.3722	−	8.33920i	−1.00485	−	0.358530i	−0.218184	−	0.975908i	$-0.570013\pi$
$541$	−23.3722	−	8.33920i	−1.00485	−	0.358530i	−0.786667	+	0.617377i	$0.788195\pi$
$542$	−10.5257	−	17.4549i	−0.452118	−	0.749753i
$543$	−0.302404	+	1.15046i	−0.0129774	+	0.0493711i
$544$	5.76674	−	0.329754i	0.247247	−	0.0141381i
$545$	−0.431115	+	0.0246520i	−0.0184669	+	0.00105598i
$546$	−0.334975	+	1.27438i	−0.0143356	+	0.0545382i
$547$	19.2218	+	31.8757i	0.821864	+	1.36291i	0.929540	+	0.368722i	$0.120205\pi$
$547$	19.2218	+	31.8757i	0.821864	+	1.36291i	−0.107676	+	0.994186i	$0.534341\pi$
$548$	−3.94250	−	1.40668i	−0.168415	−	0.0600904i
$549$	−28.9793	−	18.6239i	−1.23681	−	0.794847i
$550$	7.84591	+	5.71115i	0.334551	+	0.243524i
$551$	−0.410077	+	0.263541i	−0.0174699	+	0.0112272i
$552$	−0.168985	+	0.0392959i	−0.00719250	+	0.00167254i
$553$	−34.7264	+	14.6755i	−1.47672	+	0.624066i
$554$	0.175391	+	6.13950i	0.00745166	+	0.260842i
$555$	−0.353625	+	0.458590i	−0.0150106	+	0.0194660i
$556$	9.31027	+	9.58004i	0.394843	+	0.406284i
$557$	2.23153	−	3.70058i	0.0945530	−	0.156799i	−0.805476	−	0.592628i	$-0.798090\pi$
$557$	2.23153	−	3.70058i	0.0945530	−	0.156799i	0.900029	+	0.435830i	$0.143545\pi$
$558$	19.2567	−	15.7461i	0.815202	−	0.666587i
$559$	4.31480	+	5.59554i	0.182497	+	0.236666i
$560$	−0.454311	+	3.15980i	−0.0191981	+	0.133526i
$561$	−0.269956	+	0.0151936i	−0.0113975	+	0.000641474i
$562$	0.704324	+	4.89868i	0.0297101	+	0.206638i
$563$	10.8621	−	11.1769i	0.457785	−	0.471049i	−0.448460	−	0.893803i	$-0.648027\pi$
$563$	10.8621	−	11.1769i	0.457785	−	0.471049i	0.906245	+	0.422754i	$0.138936\pi$
$564$	−0.194191	−	0.738780i	−0.00817692	−	0.0311082i
$565$	−1.75880	−	5.41302i	−0.0739932	−	0.227728i
$566$	−1.12921	−	5.57289i	−0.0474644	−	0.234246i
$567$	−3.38052	+	39.3587i	−0.141969	+	1.65291i
$568$	5.64542	−	5.18132i	0.236876	−	0.217403i
$569$	30.3541	+	27.8587i	1.27251	+	1.16790i	0.977159	+	0.212510i	$0.0681637\pi$
$569$	30.3541	+	27.8587i	1.27251	+	1.16790i	0.295351	+	0.955389i	$0.404564\pi$
$570$	−0.000357182	−	0.00415860i	−1.49607e−5	−	0.000174185i
$571$	38.1528	−	11.2027i	1.59665	−	0.468818i	0.642036	−	0.766674i	$-0.278090\pi$
$571$	38.1528	−	11.2027i	1.59665	−	0.468818i	0.954611	+	0.297857i	$0.0962717\pi$
$572$	−8.62653	−	18.9344i	−0.360693	−	0.791688i
$573$	−1.26585	−	0.371688i	−0.0528817	−	0.0155275i
$574$	−6.47281	+	31.9446i	−0.270170	+	1.33334i
$575$	2.89353	−	0.332001i	0.120668	−	0.0138454i
$576$	5.67548	+	8.30012i	0.236478	+	0.345838i
$577$	−9.48580	−	5.35688i	−0.394899	−	0.223010i	0.281474	−	0.959569i	$-0.409177\pi$
$577$	−9.48580	−	5.35688i	−0.394899	−	0.223010i	−0.676373	+	0.736559i	$0.736449\pi$
$578$	10.2615	−	7.45538i	0.426820	−	0.310103i
$579$	0.961201	−	0.472591i	0.0399462	−	0.0196402i
$580$	−7.70422	+	11.2671i	−0.319900	+	0.467839i
$581$	1.60106	−	3.03435i	0.0664232	−	0.125886i
$582$	−0.326157	−	0.376405i	−0.0135196	−	0.0156025i
$583$	6.73286	+	25.7083i	0.278847	+	1.06473i
$584$	−3.07239	+	3.54572i	−0.127136	+	0.146723i
$585$	−5.66466	−	14.5496i	−0.234205	−	0.601551i
$586$	0.428978	−	15.0162i	0.0177209	−	0.620314i
$587$	35.2585	+	28.8307i	1.45527	+	1.18997i	0.943732	+	0.330712i	$0.107289\pi$
$587$	35.2585	+	28.8307i	1.45527	+	1.18997i	0.511541	+	0.859259i	$0.329075\pi$
$588$	1.33626	−	0.476775i	0.0551063	−	0.0196619i
$589$	0.572640	+	0.133162i	0.0235952	+	0.00548683i
$590$	0.318063	−	0.0550430i	0.0130945	−	0.00226608i
$591$	−1.85144	−	0.910293i	−0.0761582	−	0.0374445i
$592$	3.38825	−	1.91343i	0.139256	−	0.0786415i
$593$	−11.0443	+	24.1836i	−0.453535	+	0.993103i	0.535379	+	0.844612i	$0.320169\pi$
$593$	−11.0443	+	24.1836i	−0.453535	+	0.993103i	−0.988914	+	0.148491i	$0.952558\pi$
$594$	−0.731328	−	1.07160i	−0.0300068	−	0.0439681i
$595$	−2.07280	−	4.53879i	−0.0849764	−	0.186072i
$596$	−4.71543	−	3.42596i	−0.193152	−	0.140333i
$597$	−0.992558	−	0.171769i	−0.0406227	−	0.00703003i
$598$	2.62488	+	1.10928i	0.107339	+	0.0453619i
$599$	8.41615	−	21.6167i	0.343875	−	0.883235i	−0.648639	−	0.761097i	$-0.724661\pi$
$599$	8.41615	−	21.6167i	0.343875	−	0.883235i	0.992513	−	0.122138i	$-0.0389751\pi$
$600$	0.379767	+	0.719739i	0.0155039	+	0.0293832i
$601$	2.85649	+	0.327752i	0.116519	+	0.0133693i	0.172055	−	0.985087i	$-0.444959\pi$
$601$	2.85649	+	0.327752i	0.116519	+	0.0133693i	−0.0555359	+	0.998457i	$0.517687\pi$
$602$	−1.67221	+	5.14652i	−0.0681540	+	0.209756i
$603$	33.7588	+	1.93040i	1.37477	+	0.0786119i
$604$	15.9488			0.648948
$605$	−6.46695	−	10.7679i	−0.262919	−	0.437777i
$606$	−0.249124			−0.0101200
$607$	−0.633964	−	0.0362514i	−0.0257318	−	0.00147140i	0.0442182	−	0.999022i	$-0.485920\pi$
$607$	−0.633964	−	0.0362514i	−0.0257318	−	0.00147140i	−0.0699500	+	0.997551i	$0.522284\pi$
$608$	−0.101097	+	0.311144i	−0.00410001	+	0.0126185i
$609$	3.15077	+	0.361517i	0.127676	+	0.0146494i
$610$	4.85486	+	9.20098i	0.196568	+	0.372537i
$611$	−11.1813	+	28.7190i	−0.452348	+	1.16185i
$612$	3.74391	+	1.58219i	0.151338	+	0.0639562i
$613$	5.38010	+	0.931063i	0.217300	+	0.0376053i	0.278132	−	0.960543i	$-0.410285\pi$
$613$	5.38010	+	0.931063i	0.217300	+	0.0376053i	−0.0608323	+	0.998148i	$0.519375\pi$
$614$	4.82324	+	3.50429i	0.194650	+	0.141422i
$615$	0.364364	+	0.797845i	0.0146926	+	0.0321722i
$616$	20.2424	−	33.5003i	0.815591	−	1.34977i
$617$	−14.5660	+	31.8952i	−0.586407	+	1.28405i	0.351182	+	0.936307i	$0.385780\pi$
$617$	−14.5660	+	31.8952i	−0.586407	+	1.28405i	−0.937589	+	0.347745i	$0.886948\pi$
$618$	−0.175206	+	0.0989432i	−0.00704780	+	0.00398008i
$619$	−20.8055	−	10.2294i	−0.836242	−	0.411152i	−0.0277180	−	0.999616i	$-0.508824\pi$
$619$	−20.8055	−	10.2294i	−0.836242	−	0.411152i	−0.808524	+	0.588463i	$0.799733\pi$
$620$	16.2210	−	2.80716i	0.651452	−	0.112738i
$621$	−0.379250	−	0.0881908i	−0.0152188	−	0.00353897i
$622$	−15.9799	+	5.70161i	−0.640734	+	0.228614i
$623$	−47.0108	−	38.4405i	−1.88345	−	1.54009i
$624$	0.00680382	−	0.238165i	0.000272371	−	0.00953422i
$625$	−2.59115	−	6.65532i	−0.103646	−	0.266213i
$626$	−3.64381	+	4.20518i	−0.145636	+	0.168073i
$627$	0.00474542	−	0.0145604i	0.000189514	−	0.000581488i
$628$	−4.52231	−	5.21903i	−0.180460	−	0.208262i
$629$	−2.83833	+	5.37924i	−0.113172	+	0.214484i
$630$	6.74924	−	9.87046i	0.268896	−	0.393248i
$631$	15.7246	−	7.73125i	0.625985	−	0.307776i	−0.100522	−	0.994935i	$-0.532051\pi$
$631$	15.7246	−	7.73125i	0.625985	−	0.307776i	0.726507	+	0.687159i	$0.241142\pi$
$632$	−18.4301	+	13.3903i	−0.733111	+	0.532636i
$633$	0.447913	+	0.252948i	0.0178030	+	0.0100538i
$634$	−8.24933	−	12.0643i	−0.327623	−	0.479133i
$635$	16.5388	−	1.89765i	0.656321	−	0.0753058i
$636$	−0.180173	+	0.889190i	−0.00714433	+	0.0352587i
$637$	−54.9220	−	16.1265i	−2.17609	−	0.638957i
$638$	19.2363	−	12.3380i	0.761572	−	0.488467i
$639$	8.24093	−	2.41976i	0.326006	−	0.0957241i
$640$	0.881789	+	10.2665i	0.0348558	+	0.405818i
$641$	0.0135603	+	0.0124455i	0.000535598	+	0.000491568i	0.676443	−	0.736495i	$-0.263521\pi$
$641$	0.0135603	+	0.0124455i	0.000535598	+	0.000491568i	−0.675907	+	0.736987i	$0.736248\pi$
$642$	0.528618	−	0.485162i	0.0208629	−	0.0191478i
$643$	−3.43189	+	39.9568i	−0.135341	+	1.57574i	0.542194	+	0.840253i	$0.317594\pi$
$643$	−3.43189	+	39.9568i	−0.135341	+	1.57574i	−0.677535	+	0.735490i	$0.736952\pi$
$644$	−0.949735	−	4.68713i	−0.0374248	−	0.184699i
$645$	0.0449996	+	0.138494i	0.00177186	+	0.00545321i
$646$	−0.0111443	−	0.0423973i	−0.000438467	−	0.00166810i
$647$	−6.41268	+	6.59849i	−0.252108	+	0.259413i	−0.831359	−	0.555736i	$-0.812436\pi$
$647$	−6.41268	+	6.59849i	−0.252108	+	0.259413i	0.579250	+	0.815150i	$0.303345\pi$
$648$	3.39715	+	23.6277i	0.133453	+	0.928185i
$649$	1.15331	+	0.269282i	0.0452714	+	0.0105703i
$650$	1.90224	−	13.2304i	0.0746122	−	0.518939i
$651$	−2.33575	−	3.02905i	−0.0915451	−	0.118718i
$652$	−1.67845	+	1.37247i	−0.0657334	+	0.0537499i
$653$	17.0963	−	28.3510i	0.669030	−	1.10946i	−0.317871	−	0.948134i	$-0.602968\pi$
$653$	17.0963	−	28.3510i	0.669030	−	1.10946i	0.986901	−	0.161328i	$-0.0515777\pi$
$654$	0.0172022	+	0.0177007i	0.000672661	+	0.000692151i
$655$	−9.46838	+	12.2788i	−0.369960	+	0.479773i
$656$	−0.168299	−	5.89124i	−0.00657098	−	0.230014i
$657$	−4.84394	+	2.04706i	−0.188980	+	0.0798636i
$658$	−22.9889	+	5.34584i	−0.896200	+	0.208402i
$659$	0.180755	−	0.116164i	0.00704121	−	0.00452511i	−0.537115	−	0.843509i	$-0.680486\pi$
$659$	0.180755	−	0.116164i	0.00704121	−	0.00452511i	0.544157	+	0.838984i	$0.316850\pi$
$660$	−0.0363119	−	0.427269i	−0.00141344	−	0.0166314i
$661$	21.2130	+	13.6328i	0.825091	+	0.530254i	0.883715	−	0.468026i	$-0.155035\pi$
$661$	21.2130	+	13.6328i	0.825091	+	0.530254i	−0.0586235	+	0.998280i	$0.518671\pi$
$662$	13.3701	+	4.77043i	0.519642	+	0.185408i
$663$	0.192314	+	0.318917i	0.00746885	+	0.0123857i
$664$	0.527030	−	2.00503i	0.0204527	−	0.0778103i
$665$	0.282151	−	0.0161340i	0.0109413	−	0.000625648i
$666$	−14.5515	+	0.832083i	−0.563858	+	0.0322426i
$667$	1.74361	−	6.63338i	0.0675129	−	0.256846i
$668$	−1.60792	−	2.66643i	−0.0622122	−	0.103167i
$669$	−1.23116	−	0.439275i	−0.0475992	−	0.0169834i
$670$	−8.59076	−	5.52095i	−0.331890	−	0.213293i
$671$	3.23226	+	38.0328i	0.124780	+	1.46824i
$672$	1.79060	−	1.15075i	0.0690740	−	0.0443911i
$673$	34.4113	−	8.00201i	1.32646	−	0.308455i	0.497354	−	0.867548i	$-0.334305\pi$
$673$	34.4113	−	8.00201i	1.32646	−	0.308455i	0.829105	+	0.559093i	$0.188851\pi$
$674$	7.33999	−	3.10191i	0.282726	−	0.119481i
$675$	0.0521536	+	1.82562i	0.00200739	+	0.0702680i
$676$	−6.59841	+	8.55697i	−0.253785	+	0.329114i
$677$	−3.63512	−	3.74045i	−0.139709	−	0.143757i	0.643666	−	0.765307i	$-0.277413\pi$
$677$	−3.63512	−	3.74045i	−0.139709	−	0.143757i	−0.783375	+	0.621549i	$0.786504\pi$
$678$	−0.167999	+	0.278595i	−0.00645196	+	0.0106994i
$679$	26.1063	−	21.3470i	1.00187	−	0.819223i
$680$	−1.84117	−	2.38767i	−0.0706057	−	0.0915630i
$681$	0.0770332	−	0.535778i	0.00295192	−	0.0205311i
$682$	−26.8408	−	6.26696i	−1.02779	−	0.239974i
$683$	3.75754	+	26.1342i	0.143778	+	0.999999i	0.926141	+	0.377177i	$0.123105\pi$
$683$	3.75754	+	26.1342i	0.143778	+	0.999999i	−0.782363	+	0.622822i	$0.785986\pi$
$684$	−0.160441	+	0.165090i	−0.00613463	+	0.00631238i
$685$	0.884807	+	3.36616i	0.0338067	+	0.128614i
$686$	−5.97875	−	18.4007i	−0.228270	−	0.702542i
$687$	0.262689	+	1.29642i	0.0100222	+	0.0494615i
$688$	0.0837344	−	0.974902i	0.00319234	−	0.0371678i
$689$	26.9675	−	24.7505i	1.02738	−	0.942920i
$690$	0.0432675	+	0.0397105i	0.00164717	+	0.00151175i
$691$	−1.74529	−	20.3201i	−0.0663940	−	0.773011i	−0.951505	−	0.307632i	$-0.900463\pi$
$691$	−1.74529	−	20.3201i	−0.0663940	−	0.773011i	0.885111	−	0.465379i	$-0.154082\pi$
$692$	−13.2487	+	3.89017i	−0.503640	+	0.147882i
$693$	36.9287	−	23.6858i	1.40280	−	0.899750i
$694$	−4.02165	−	1.18086i	−0.152660	−	0.0448249i
$695$	2.20585	−	10.8863i	0.0836727	−	0.412941i
$696$	1.90390	−	0.218452i	0.0721672	−	0.00828042i
$697$	5.19967	+	7.60428i	0.196952	+	0.288033i
$698$	7.94974	+	4.48943i	0.300902	+	0.169927i
$699$	0.513732	−	0.373248i	0.0194311	−	0.0141175i
$700$	−20.1305	+	9.89750i	−0.760862	+	0.374090i
$701$	−7.98904	+	11.6836i	−0.301742	+	0.441284i	−0.946309	−	0.323265i	$-0.895220\pi$
$701$	−7.98904	+	11.6836i	−0.301742	+	0.441284i	0.644567	+	0.764548i	$0.277038\pi$
$702$	−0.833906	+	1.58043i	−0.0314737	+	0.0596494i
$703$	−0.225590	−	0.260345i	−0.00850829	−	0.00981909i
$704$	3.45241	−	10.5931i	0.130118	−	0.399242i
$705$	−0.415931	+	0.480010i	−0.0156649	+	0.0180782i
$706$	0.847718	+	2.17735i	0.0319043	+	0.0819455i
$707$	0.481683	−	16.8611i	0.0181156	−	0.634127i
$708$	0.0313002	+	0.0255940i	0.00117633	+	0.000961882i
$709$	−0.845642	+	0.301724i	−0.0317588	+	0.0113315i	−0.351881	−	0.936045i	$-0.614458\pi$
$709$	−0.845642	+	0.301724i	−0.0317588	+	0.0113315i	0.320122	+	0.947376i	$0.396276\pi$
$710$	−2.52643	−	0.587496i	−0.0948152	−	0.0220483i
$711$	−25.1603	+	4.35416i	−0.943585	+	0.163294i
$712$	−32.9299	−	16.1905i	−1.23410	−	0.606766i
$713$	−7.20298	+	4.06771i	−0.269754	+	0.152337i
$714$	−0.118480	+	0.259436i	−0.00443401	+	0.00970913i
$715$	−8.94721	+	14.8072i	−0.334607	+	0.553759i
$716$	−3.84802	−	8.42599i	−0.143807	−	0.314894i
$717$	0.432100	+	0.313939i	0.0161371	+	0.0117243i
$718$	−0.0752805	−	0.0130278i	−0.00280944	−	0.000486193i
$719$	18.9877	+	8.02428i	0.708123	+	0.299255i	0.713426	−	0.700731i	$-0.247143\pi$
$719$	18.9877	+	8.02428i	0.708123	+	0.299255i	−0.00530290	+	0.999986i	$0.501688\pi$
$720$	−0.784442	+	2.01482i	−0.0292344	+	0.0750880i
$721$	−6.35786	−	12.0495i	−0.236779	−	0.448746i
$722$	−14.9406	−	1.71427i	−0.556032	−	0.0637987i
$723$	−0.287839	+	0.885876i	−0.0107048	+	0.0329461i
$724$	−19.7815	−	1.13115i	−0.735173	−	0.0420387i
$725$	−32.1712			−1.19481
$726$	−0.223087	+	0.682421i	−0.00827953	+	0.0253270i
$727$	41.1216			1.52512			0.762558	−	0.646920i	$-0.223943\pi$
$727$	41.1216			1.52512			0.762558	+	0.646920i	$0.223943\pi$
$728$	−53.8234	−	3.07773i	−1.99483	−	0.114068i
$729$	−8.23024	+	25.3301i	−0.304824	+	0.938151i
$730$	1.57779	+	0.181034i	0.0583966	+	0.00670038i
$731$	0.713734	+	1.35268i	0.0263984	+	0.0500305i
$732$	−0.472771	+	1.21430i	−0.0174741	+	0.0448819i
$733$	30.1443	+	12.7391i	1.11341	+	0.470529i	0.866835	−	0.498595i	$-0.166151\pi$
$733$	30.1443	+	12.7391i	1.11341	+	0.470529i	0.246571	+	0.969125i	$0.420696\pi$
$734$	−24.3557	−	4.21491i	−0.898984	−	0.155575i
$735$	−0.954372	−	0.693392i	−0.0352026	−	0.0255762i
$736$	−1.91223	−	4.18720i	−0.0704858	−	0.154342i
$737$	−21.1206	−	30.9475i	−0.777987	−	1.13996i
$738$	−9.17061	+	20.0808i	−0.337575	+	0.739186i
$739$	−10.6439	+	6.01089i	−0.391542	+	0.221114i	−0.674915	−	0.737896i	$-0.735820\pi$
$739$	−10.6439	+	6.01089i	−0.391542	+	0.221114i	0.283372	+	0.959010i	$0.408547\pi$
$740$	−8.65617	−	4.25595i	−0.318207	−	0.156452i
$741$	−0.0207842	+	0.00359685i	−0.000763528	+	0.000132134i
$742$	27.3040	+	6.34928i	1.00236	+	0.233090i
$743$	−20.6588	+	7.37103i	−0.757897	+	0.270417i	−0.686597	−	0.727038i	$-0.740896\pi$
$743$	−20.6588	+	7.37103i	−0.757897	+	0.270417i	−0.0712995	+	0.997455i	$0.522715\pi$
$744$	−1.78930	−	1.46310i	−0.0655990	−	0.0536400i
$745$	−0.138392	+	4.84436i	−0.00507030	+	0.177484i
$746$	−7.97912	−	20.4942i	−0.292136	−	0.750346i
$747$	1.52171	−	1.75614i	0.0556763	−	0.0642539i
$748$	−1.14101	−	4.35674i	−0.0417194	−	0.159298i
$749$	31.8144	+	36.7157i	1.16247	+	1.34156i
$750$	0.302454	−	0.573213i	0.0110440	−	0.0209308i
$751$	27.0263	−	39.5247i	0.986204	−	1.44228i	0.0914021	−	0.995814i	$-0.470865\pi$
$751$	27.0263	−	39.5247i	0.986204	−	1.44228i	0.894802	−	0.446463i	$-0.147317\pi$
$752$	3.82991	−	1.88304i	0.139662	−	0.0686674i
$753$	0.803596	−	0.583847i	0.0292847	−	0.0212766i
$754$	−27.4083	−	15.4782i	−0.998152	−	0.563682i
$755$	−7.48511	−	10.9466i	−0.272411	−	0.398389i
$756$	2.97936	−	0.341850i	0.108358	−	0.0124329i
$757$	−8.12115	+	40.0795i	−0.295168	+	1.45671i	0.508204	+	0.861237i	$0.330309\pi$
$757$	−8.12115	+	40.0795i	−0.295168	+	1.45671i	−0.803373	+	0.595477i	$0.796963\pi$
$758$	8.78684	+	2.58005i	0.319152	+	0.0937116i
$759$	0.0893360	+	0.196084i	0.00324269	+	0.00711740i
$760$	0.163855	−	0.0481122i	0.00594365	−	0.00174521i
$761$	2.78229	+	32.3936i	0.100858	+	1.17427i	0.855383	+	0.517995i	$0.173322\pi$
$761$	2.78229	+	32.3936i	0.100858	+	1.17427i	−0.754526	+	0.656271i	$0.772133\pi$
$762$	−0.701047	−	0.643415i	−0.0253963	−	0.0233085i
$763$	−1.23127	+	1.13005i	−0.0445749	+	0.0409105i
$764$	1.88051	−	21.8944i	0.0680345	−	0.792111i
$765$	−0.671143	−	3.31222i	−0.0242652	−	0.119754i
$766$	−4.58021	−	14.0964i	−0.165490	−	0.509325i
$767$	−0.414693	−	1.57766i	−0.0149737	−	0.0569659i
$768$	0.796545	−	0.819625i	0.0287428	−	0.0295757i
$769$	3.30560	+	22.9909i	0.119203	+	0.829074i	0.958437	+	0.285304i	$0.0920946\pi$
$769$	3.30560	+	22.9909i	0.119203	+	0.829074i	−0.839234	+	0.543770i	$0.816996\pi$
$770$	−13.2284	+	0.744519i	−0.476720	+	0.0268306i
$771$	0.227409	−	1.58166i	0.00818994	−	0.0569623i
$772$	10.8945	+	14.1282i	0.392102	+	0.508487i
$773$	22.2322	−	18.1792i	0.799638	−	0.653861i	−0.142234	−	0.989833i	$-0.545429\pi$
$773$	22.2322	−	18.1792i	0.799638	−	0.653861i	0.941872	+	0.335972i	$0.109065\pi$
$774$	−1.89266	+	3.13863i	−0.0680304	+	0.112816i
$775$	27.0421	+	27.8256i	0.971380	+	0.999526i
$776$	12.4435	−	16.1371i	0.446697	−	0.579287i
$777$	0.0640010	+	2.24033i	0.00229602	+	0.0803713i
$778$	13.3835	−	5.65591i	0.479822	−	0.202774i
$779$	−0.508201	+	0.118177i	−0.0182082	+	0.00423413i
$780$	−0.496865	+	0.319316i	−0.0177906	+	0.0114333i
$781$	−7.69430	−	5.60079i	−0.275324	−	0.200412i
$782$	0.518892	+	0.333472i	0.0185555	+	0.0119249i
$783$	4.05080	+	1.44532i	0.144764	+	0.0516516i
$784$	4.09332	+	6.78800i	0.146190	+	0.242429i
$785$	−1.45972	+	5.55333i	−0.0520995	+	0.198207i
$786$	0.884840	−	0.0505970i	0.0315612	−	0.00180474i
$787$	−12.6911	+	0.725705i	−0.452390	+	0.0258686i	−0.281799	−	0.959473i	$-0.590931\pi$
$787$	−12.6911	+	0.725705i	−0.452390	+	0.0258686i	−0.170591	+	0.985342i	$0.554568\pi$
$788$	8.73614	−	33.2357i	0.311212	−	1.18397i
$789$	0.913885	+	1.51551i	0.0325352	+	0.0539535i
$790$	7.26292	+	2.59141i	0.258403	+	0.0921981i
$791$	−18.5309	−	11.9091i	−0.658883	−	0.423438i
$792$	18.4931	−	18.9948i	0.657123	−	0.674951i
$793$	44.2278	−	28.4235i	1.57057	−	1.00935i
$794$	11.7777	−	2.73878i	0.417974	−	0.0971956i
$795$	0.694863	−	0.293652i	0.0246443	−	0.0104147i
$796$	−0.479126	−	16.7716i	−0.0169822	−	0.594453i
$797$	16.2175	−	21.0312i	0.574452	−	0.744963i	−0.411606	−	0.911362i	$-0.635032\pi$
$797$	16.2175	−	21.0312i	0.574452	−	0.744963i	0.986059	+	0.166399i	$0.0532139\pi$
$798$	−0.0112583	−	0.0115845i	−0.000398540	−	0.000410088i
$799$	−3.44476	+	5.71250i	−0.121867	+	0.202094i
$800$	−16.7149	+	13.6677i	−0.590961	+	0.483226i
$801$	−25.1159	−	32.5709i	−0.887428	−	1.15084i
$802$	−0.973331	+	6.76967i	−0.0343695	+	0.239045i
$803$	5.07121	+	2.86985i	0.178959	+	0.101275i
$804$	−0.182037	−	1.26610i	−0.00641995	−	0.0446518i
$805$	−2.77133	+	2.85163i	−0.0976764	+	0.100507i
$806$	9.65108	+	36.7165i	0.339945	+	1.29328i
$807$	−0.669161	−	2.05947i	−0.0235556	−	0.0724966i
$808$	−2.02418	−	9.98974i	−0.0712105	−	0.351438i
$809$	2.08936	−	24.3260i	0.0734580	−	0.855256i	−0.863166	−	0.504920i	$-0.831522\pi$
$809$	2.08936	−	24.3260i	0.0734580	−	0.855256i	0.936624	−	0.350336i	$-0.113933\pi$
$810$	5.95308	−	5.46369i	0.209170	−	0.191975i
$811$	8.50714	+	7.80779i	0.298726	+	0.274168i	0.811496	−	0.584358i	$-0.198653\pi$
$811$	8.50714	+	7.80779i	0.298726	+	0.274168i	−0.512770	+	0.858526i	$0.671381\pi$
$812$	4.52055	+	52.6318i	0.158640	+	1.84701i
$813$	−2.03687	+	0.598080i	−0.0714362	+	0.0209756i
$814$	10.5651	+	12.2149i	0.370308	+	0.428133i
$815$	1.72974	+	0.507897i	0.0605901	+	0.0177909i
$816$	0.0102417	−	0.0505448i	0.000358531	−	0.00176942i
$817$	−0.0860606	+	0.00987453i	−0.00301088	+	0.000345466i
$818$	−4.66832	−	6.82720i	−0.163224	−	0.238707i
$819$	−52.6169	−	29.7141i	−1.83858	−	1.03830i
$820$	−11.8195	+	8.58735i	−0.412754	+	0.299883i
$821$	−22.3129	+	10.9705i	−0.778725	+	0.382873i	−0.786890	−	0.617093i	$-0.788310\pi$
$821$	−22.3129	+	10.9705i	−0.778725	+	0.382873i	0.00816496	+	0.999967i	$0.497401\pi$
$822$	0.112293	−	0.164223i	0.00391665	−	0.00572792i
$823$	−16.0983	+	30.5097i	−0.561153	+	1.06350i	0.426150	+	0.904653i	$0.359870\pi$
$823$	−16.0983	+	30.5097i	−0.561153	+	1.06350i	−0.987303	+	0.158850i	$0.949221\pi$
$824$	−5.39114	−	6.22171i	−0.187809	−	0.216744i
$825$	0.783002	−	0.639085i	0.0272606	−	0.0222501i
$826$	0.818099	−	0.944137i	0.0284653	−	0.0328507i
$827$	0.327767	+	0.841863i	0.0113976	+	0.0292745i	0.937448	−	0.348126i	$-0.113182\pi$
$827$	0.327767	+	0.841863i	0.0113976	+	0.0292745i	−0.926050	+	0.377400i	$0.876818\pi$
$828$	0.0924963	−	3.23779i	0.00321447	−	0.112521i
$829$	−22.2507	−	18.1943i	−0.772798	−	0.631914i	0.162123	−	0.986771i	$-0.448166\pi$
$829$	−22.2507	−	18.1943i	−0.772798	−	0.631914i	−0.934921	+	0.354857i	$0.884530\pi$
$830$	−0.660952	+	0.235827i	−0.0229420	+	0.00818568i
$831$	0.623059	+	0.144886i	0.0216137	+	0.00502604i
$832$	−15.1210	+	2.61680i	−0.524228	+	0.0907212i
$833$	−11.1186	−	5.46663i	−0.385235	−	0.189407i
$834$	−0.552839	+	0.312202i	−0.0191432	+	0.0108107i
$835$	−1.07550	+	2.35502i	−0.0372193	+	0.0814989i
$836$	0.253395	+	0.0293048i	0.00876384	+	0.00101353i
$837$	−2.15487	−	4.71851i	−0.0744833	−	0.163096i
$838$	7.74601	+	5.62780i	0.267581	+	0.194409i
$839$	−36.2033	−	6.26523i	−1.24988	−	0.216300i	−0.493100	−	0.869973i	$-0.664136\pi$
$839$	−36.2033	−	6.26523i	−1.24988	−	0.216300i	−0.756777	+	0.653673i	$0.773227\pi$
$840$	−1.02342	−	0.432501i	−0.0353114	−	0.0149227i
$841$	−16.9651	+	43.5744i	−0.585002	+	1.50256i
$842$	8.97734	+	17.0140i	0.309380	+	0.586340i
$843$	0.512079	+	0.0587556i	0.0176369	+	0.00202365i
$844$	−2.64772	+	8.14885i	−0.0911384	+	0.280495i
$845$	8.96993	+	0.512919i	0.308575	+	0.0176450i
$846$	−15.9858			−0.549604
$847$	−45.7559	−	16.4183i	−1.57219	−	0.564140i
$848$	−5.06888			−0.174066
$849$	−0.591240	−	0.0338083i	−0.0202913	−	0.00116030i
$850$	0.894041	−	2.75158i	0.0306654	−	0.0943782i
$851$	4.81542	+	0.552518i	0.165071	+	0.0189401i
$852$	−0.151620	−	0.287351i	−0.00519440	−	0.00984449i
$853$	11.0476	−	28.3755i	0.378262	−	0.971558i	−0.606098	−	0.795390i	$-0.707266\pi$
$853$	11.0476	−	28.3755i	0.378262	−	0.971558i	0.984360	−	0.176168i	$-0.0563702\pi$
$854$	37.0871	+	15.6732i	1.26910	+	0.536324i
$855$	0.188610	+	0.0326402i	0.00645032	+	0.00111627i
$856$	23.7498	+	17.2553i	0.811752	+	0.589773i
$857$	−9.56623	−	20.9471i	−0.326776	−	0.715540i	0.672932	−	0.739705i	$-0.265035\pi$
$857$	−9.56623	−	20.9471i	−0.326776	−	0.715540i	−0.999708	+	0.0241644i	$0.992307\pi$
$858$	0.974555	−	0.167753i	0.0332708	−	0.00572698i
$859$	−5.31040	+	11.6281i	−0.181188	+	0.396747i	−0.978332	−	0.207043i	$-0.933616\pi$
$859$	−5.31040	+	11.6281i	−0.181188	+	0.396747i	0.797144	+	0.603790i	$0.206343\pi$
$860$	−2.11205	+	1.19273i	−0.0720205	+	0.0406718i
$861$	3.04631	+	1.49777i	0.103818	+	0.0510439i
$862$	26.4068	−	4.56988i	0.899420	−	0.155651i
$863$	−33.2143	−	7.72365i	−1.13063	−	0.262916i	−0.380870	−	0.924629i	$-0.624375\pi$
$863$	−33.2143	−	7.72365i	−1.13063	−	0.262916i	−0.749758	+	0.661712i	$0.769830\pi$
$864$	2.71867	−	0.970018i	0.0924909	−	0.0330007i
$865$	8.88795	+	7.26764i	0.302199	+	0.247107i
$866$	−0.258009	+	9.03148i	−0.00876749	+	0.306902i
$867$	−0.479272	−	1.23100i	−0.0162769	−	0.0418070i
$868$	41.7226	−	48.1504i	1.41616	−	1.63433i
$869$	20.8277	+	19.1499i	0.706531	+	0.649617i
$870$	−0.424811	−	0.490258i	−0.0144024	−	0.0166213i
$871$	−24.0830	+	45.6424i	−0.816022	+	1.54653i
$872$	−0.570015	+	0.833621i	−0.0193032	+	0.0282300i
$873$	20.4971	−	10.0777i	0.693721	−	0.341079i
$874$	−0.0282633	+	0.0205345i	−0.000956021	+	0.000694590i
$875$	38.2111	+	21.5788i	1.29177	+	0.729497i
$876$	0.112283	+	0.164209i	0.00379369	+	0.00554810i
$877$	−18.7352	+	2.14966i	−0.632641	+	0.0725888i	−0.424380	−	0.905484i	$-0.639508\pi$
$877$	−18.7352	+	2.14966i	−0.632641	+	0.0725888i	−0.208262	+	0.978073i	$0.566781\pi$
$878$	2.39264	−	11.8082i	0.0807478	−	0.398506i
$879$	−1.50118	−	0.440787i	−0.0506337	−	0.0148674i
$880$	2.29933	−	0.672903i	0.0775103	−	0.0226835i
$881$	−43.1716	+	12.6763i	−1.45449	+	0.427076i	−0.911023	−	0.412356i	$-0.864706\pi$
$881$	−43.1716	+	12.6763i	−1.45449	+	0.427076i	−0.543465	+	0.839432i	$0.682888\pi$
$882$	−2.54080	−	29.5820i	−0.0855531	−	0.996077i
$883$	−22.8467	−	20.9685i	−0.768852	−	0.705646i	0.192400	−	0.981317i	$-0.438373\pi$
$883$	−22.8467	−	20.9685i	−0.768852	−	0.705646i	−0.961252	+	0.275671i	$0.911100\pi$
$884$	−4.57014	+	4.19443i	−0.153710	+	0.141074i
$885$	0.00287689	−	0.0334950i	9.67055e−5	−	0.00112592i
$886$	3.52044	+	17.3741i	0.118272	+	0.583693i
$887$	17.0251	+	52.3977i	0.571646	+	1.75934i	0.647327	+	0.762212i	$0.275887\pi$
$887$	17.0251	+	52.3977i	0.571646	+	1.75934i	−0.0756819	+	0.997132i	$0.524113\pi$
$888$	0.344290	+	1.30981i	0.0115536	+	0.0439545i
$889$	44.9028	−	46.2039i	1.50599	−	1.54963i
$890$	1.76774	+	12.2949i	0.0592546	+	0.412125i
$891$	27.9317	−	9.93775i	0.935746	−	0.332927i
$892$	3.09864	−	21.5515i	0.103750	−	0.721599i
$893$	−0.230718	−	0.299200i	−0.00772069	−	0.0100124i
$894$	0.214448	−	0.175354i	0.00717223	−	0.00586470i
$895$	−3.97731	+	6.59562i	−0.132947	+	0.220467i
$896$	27.7938	+	28.5991i	0.928525	+	0.955429i
$897$	0.181233	−	0.235027i	0.00605118	−	0.00784731i
$898$	−0.152897	−	5.35211i	−0.00510225	−	0.178602i
$899$	84.1664	−	35.5690i	2.80711	−	1.18629i
$900$	−14.7984	+	3.44123i	−0.493281	+	0.114708i
$901$	6.66517	−	4.28345i	0.222049	−	0.142702i
$902$	23.8304	−	5.51898i	0.793465	−	0.183762i
$903$	0.474121	+	0.304699i	0.0157777	+	0.0101397i
$904$	−12.5365	−	4.47302i	−0.416958	−	0.148770i
$905$	8.50749	+	14.1081i	0.282799	+	0.468969i
$906$	−0.192697	+	0.733094i	−0.00640191	+	0.0243554i
$907$	48.7237	−	2.78612i	1.61784	−	0.0925117i	0.775463	−	0.631393i	$-0.217516\pi$
$907$	48.7237	−	2.78612i	1.61784	−	0.0925117i	0.842382	+	0.538881i	$0.181153\pi$
$908$	9.00133	−	0.514715i	0.298720	−	0.0170814i
$909$	2.90437	−	11.0494i	0.0963318	−	0.366484i
$910$	9.42380	+	15.6276i	0.312396	+	0.518051i
$911$	46.5598	+	16.6125i	1.54259	+	0.550396i	0.964157	−	0.265331i	$-0.0854812\pi$
$911$	46.5598	+	16.6125i	1.54259	+	0.550396i	0.578437	+	0.815727i	$0.303663\pi$
$912$	0.00245729	+	0.00157920i	8.13689e−5	+	5.22926e-5i
$913$	−2.57046	−	0.149299i	−0.0850698	−	0.00494107i
$914$	5.04366	−	3.24136i	0.166829	−	0.107215i
$915$	1.05533	−	0.245406i	0.0348881	−	0.00811289i
$916$	−20.2950	+	8.57674i	−0.670565	+	0.283383i
$917$	1.71364	+	59.9851i	0.0565893	+	1.98088i
$918$	−0.236189	+	0.306295i	−0.00779539	+	0.0101092i
$919$	−0.735466	−	0.756777i	−0.0242608	−	0.0249638i	0.704893	−	0.709314i	$-0.250995\pi$
$919$	−0.735466	−	0.756777i	−0.0242608	−	0.0249638i	−0.729154	+	0.684350i	$0.760086\pi$
$920$	−1.24081	+	2.05766i	−0.0409084	+	0.0678389i
$921$	0.480680	−	0.393050i	0.0158390	−	0.0129514i
$922$	8.86065	+	11.4907i	0.291810	+	0.378426i
$923$	−1.86549	+	12.9747i	−0.0614032	+	0.427069i
$924$	−1.15556	−	1.19118i	−0.0380152	−	0.0391870i
$925$	−3.23556	−	22.5038i	−0.106385	−	0.739922i
$926$	−11.7067	+	12.0459i	−0.384706	+	0.395853i
$927$	−2.34581	−	8.92437i	−0.0770464	−	0.293115i
$928$	15.7123	+	48.3576i	0.515782	+	1.58741i
$929$	5.95261	+	29.3773i	0.195299	+	0.963837i	0.951064	+	0.308994i	$0.0999924\pi$
$929$	5.95261	+	29.3773i	0.195299	+	0.963837i	−0.755765	+	0.654843i	$0.772735\pi$
$930$	−0.0669533	+	0.779523i	−0.00219549	+	0.0255616i
$931$	0.517004	−	0.474502i	0.0169441	−	0.0155512i
$932$	7.79258	+	7.15196i	0.255254	+	0.234270i
$933$	0.151215	+	1.76057i	0.00495057	+	0.0576384i
$934$	26.2480	−	7.70710i	0.858860	−	0.252184i
$935$	−2.45479	+	2.82785i	−0.0802804	+	0.0924807i
$936$	−35.0351	−	10.2872i	−1.14516	−	0.336249i
$937$	3.47851	−	17.1671i	0.113638	−	0.560825i	−0.882293	−	0.470701i	$-0.844001\pi$
$937$	3.47851	−	17.1671i	0.113638	−	0.560825i	0.995931	−	0.0901239i	$-0.0287263\pi$
$938$	−39.2646	+	4.50519i	−1.28203	+	0.147100i
$939$	0.327101	+	0.478370i	0.0106745	+	0.0156110i
$940$	−9.21195	−	5.20223i	−0.300461	−	0.169678i
$941$	−3.24518	+	2.35776i	−0.105790	+	0.0768609i	−0.639423	−	0.768856i	$-0.720827\pi$
$941$	−3.24518	+	2.35776i	−0.105790	+	0.0768609i	0.533633	+	0.845716i	$0.320827\pi$
$942$	0.294534	−	0.144813i	0.00959644	−	0.00471825i
$943$	4.14377	−	6.06006i	0.134940	−	0.197343i
$944$	−0.105418	+	0.199789i	−0.00343106	+	0.00650258i
$945$	−1.63291	−	1.88447i	−0.0531185	−	0.0613020i
$946$	4.03510	−	0.459315i	0.131192	−	0.0149336i
$947$	19.8437	−	22.9009i	0.644834	−	0.744178i	−0.335388	−	0.942080i	$-0.608867\pi$
$947$	19.8437	−	22.9009i	0.644834	−	0.744178i	0.980222	+	0.197902i	$0.0634128\pi$
$948$	0.350440	+	0.900098i	0.0113818	+	0.0292338i
$949$	0.229185	−	8.02251i	0.00743965	−	0.260422i
$950$	0.126856	+	0.103730i	0.00411575	+	0.00336543i
$951$	−1.43361	+	0.511512i	−0.0464881	+	0.0165869i
$952$	−11.3659	−	2.64302i	−0.368371	−	0.0856609i
$953$	48.7017	−	8.42815i	1.57760	−	0.273015i	0.686607	−	0.727029i	$-0.259099\pi$
$953$	48.7017	−	8.42815i	1.57760	−	0.273015i	0.890994	+	0.454014i	$0.150008\pi$
$954$	17.0384	+	8.37724i	0.551640	+	0.271223i
$955$	−15.9100	+	8.98478i	−0.514835	+	0.290741i
$956$	−3.69569	+	8.09244i	−0.119527	+	0.261728i
$957$	−0.733465	−	2.26429i	−0.0237096	−	0.0731940i
$958$	2.08767	+	4.57136i	0.0674495	+	0.147694i
$959$	10.8977	+	7.91765i	0.351906	+	0.255674i
$960$	−0.311629	−	0.0539295i	−0.0100578	−	0.00174057i
$961$	−72.9571	−	30.8319i	−2.35345	−	0.994578i
$962$	8.07048	−	20.7289i	0.260203	−	0.668325i
$963$	15.3555	+	29.1019i	0.494824	+	0.937795i
$964$	−15.4140	−	1.76859i	−0.496450	−	0.0569623i
$965$	4.58404	−	14.1082i	0.147566	−	0.454160i
$966$	0.226921	+	0.0129758i	0.00730105	+	0.000417489i
$967$	16.9760			0.545913			0.272956	−	0.962026i	$-0.411999\pi$
$967$	16.9760			0.545913			0.272956	+	0.962026i	$0.411999\pi$
$968$	−29.1773	−	3.40085i	−0.937794	−	0.109308i
$969$	−0.00456563			−0.000146669
$970$	−6.88662	−	0.393791i	−0.221116	−	0.0126439i
$971$	3.42352	−	10.5365i	0.109866	−	0.338132i	−0.880976	−	0.473161i	$-0.843113\pi$
$971$	3.42352	−	10.5365i	0.109866	−	0.338132i	0.990842	+	0.135029i	$0.0431128\pi$
$972$	3.02803	+	0.347434i	0.0971241	+	0.0111439i
$973$	−20.0614	−	38.0206i	−0.643139	−	1.21888i
$974$	−0.582054	+	1.49499i	−0.0186502	+	0.0479027i
$975$	−1.28230	−	0.541903i	−0.0410664	−	0.0173548i
$976$	−7.17377	−	1.24147i	−0.229627	−	0.0397385i
$977$	−35.0690	−	25.4791i	−1.12196	−	0.815150i	−0.137453	−	0.990508i	$-0.543892\pi$
$977$	−35.0690	−	25.4791i	−1.12196	−	0.815150i	−0.984505	+	0.175358i	$0.943892\pi$
$978$	−0.0428065	−	0.0937332i	−0.00136880	−	0.00299726i
$979$	−11.6253	+	44.0665i	−0.371548	+	1.40837i
$980$	8.16263	−	17.8737i	0.260746	−	0.570953i
$981$	−0.985624	+	0.556607i	−0.0314686	+	0.0177711i
$982$	15.1180	+	7.43302i	0.482435	+	0.237197i
$983$	−53.7074	+	9.29444i	−1.71300	+	0.296447i	−0.940808	−	0.338941i	$-0.889931\pi$
$983$	−53.7074	+	9.29444i	−1.71300	+	0.296447i	−0.772194	+	0.635387i	$0.780840\pi$
$984$	1.99794	+	0.464600i	0.0636919	+	0.0148109i
$985$	−26.9117	+	9.60208i	−0.857479	+	0.305948i
$986$	−5.27437	−	4.31283i	−0.167970	−	0.137348i
$987$	−0.0701950	+	2.45715i	−0.00223433	+	0.0782119i
$988$	−0.127469	−	0.327403i	−0.00405534	−	0.0104161i
$989$	0.798173	−	0.921141i	0.0253804	−	0.0292906i
$990$	−8.84100	−	1.53817i	−0.280986	−	0.0488862i
$991$	−25.2931	−	29.1898i	−0.803463	−	0.927245i	0.195103	−	0.980783i	$-0.437496\pi$
$991$	−25.2931	−	29.1898i	−0.803463	−	0.927245i	−0.998566	+	0.0535373i	$0.982950\pi$
$992$	28.6183	−	54.2377i	0.908632	−	1.72205i
$993$	0.834505	−	1.22043i	0.0264822	−	0.0387290i
$994$	−9.00875	+	4.42930i	−0.285740	+	0.140489i
$995$	−11.2865	+	8.20011i	−0.357806	+	0.259961i
$996$	−0.0765398	−	0.0432240i	−0.00242526	−	0.00136960i
$997$	2.87523	+	4.20488i	0.0910593	+	0.133170i	0.868312	−	0.496019i	$-0.165205\pi$
$997$	2.87523	+	4.20488i	0.0910593	+	0.133170i	−0.777252	+	0.629189i	$0.783387\pi$
$998$	−15.6761	+	1.79866i	−0.496217	+	0.0569357i
$999$	−0.603603	+	2.97890i	−0.0190972	+	0.0942482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.g.a.4.5	✓	400
121.91	even	55	inner	121.2.g.a.91.5	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.g.a.4.5	✓	400	1.1	even	1	trivial
121.2.g.a.91.5	yes	400	121.91	even	55	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.g (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.790346 - 0.0451936i) q^{2} +(-0.0254779 + 0.0784129i) q^{3} +(-1.36436 - 0.156546i) q^{4} +(0.532875 + 1.00991i) q^{5} +(0.0236801 - 0.0608219i) q^{6} +(4.07073 + 1.72030i) q^{7} +(2.63133 + 0.455369i) q^{8} +(2.42155 + 1.75936i) q^{9} +O(q^{10})\)	\(q+(-0.790346 - 0.0451936i) q^{2} +(-0.0254779 + 0.0784129i) q^{3} +(-1.36436 - 0.156546i) q^{4} +(0.532875 + 1.00991i) q^{5} +(0.0236801 - 0.0608219i) q^{6} +(4.07073 + 1.72030i) q^{7} +(2.63133 + 0.455369i) q^{8} +(2.42155 + 1.75936i) q^{9} +(-0.375515 - 0.822262i) q^{10} +(-0.0917343 - 3.31536i) q^{11} +(0.0470362 - 0.102995i) q^{12} +(-3.97773 + 2.24633i) q^{13} +(-3.13954 - 1.54361i) q^{14} +(-0.0927666 + 0.0160539i) q^{15} +(0.616161 + 0.143282i) q^{16} +(-0.931282 + 0.332281i) q^{17} +(-1.83435 - 1.49994i) q^{18} +(0.00159925 - 0.0559810i) q^{19} +(-0.568936 - 1.46130i) q^{20} +(-0.238608 + 0.275368i) q^{21} +(-0.0773311 + 2.62443i) q^{22} +(0.516024 + 0.595524i) q^{23} +(-0.102747 + 0.194728i) q^{24} +(2.08625 - 3.05105i) q^{25} +(3.24530 - 1.59561i) q^{26} +(-0.399758 + 0.290441i) q^{27} +(-5.28463 - 2.98437i) q^{28} +(-4.91294 - 7.18495i) q^{29} +(0.0740432 - 0.00849567i) q^{30} +(-2.08477 + 10.2887i) q^{31} +(-5.60504 - 1.64579i) q^{32} +(0.262304 + 0.0772751i) q^{33} +(0.751053 - 0.220529i) q^{34} +(0.431837 + 5.02778i) q^{35} +(-3.02844 - 2.77948i) q^{36} +(4.53177 - 4.15922i) q^{37} +(-0.00379394 + 0.0441721i) q^{38} +(-0.0747967 - 0.369136i) q^{39} +(0.942287 + 2.90006i) q^{40} +(-2.36843 - 9.01044i) q^{41} +(0.201027 - 0.206852i) q^{42} +(-0.220129 - 1.53103i) q^{43} +(-0.393846 + 4.53770i) q^{44} +(-0.486412 + 3.38307i) q^{45} +(-0.380924 - 0.493991i) q^{46} +(5.22268 - 4.27056i) q^{47} +(-0.0269337 + 0.0446644i) q^{48} +(8.73283 + 8.98587i) q^{49} +(-1.78675 + 2.31710i) q^{50} +(-0.00232799 - 0.0814903i) q^{51} +(5.77870 - 2.44210i) q^{52} +(-7.80452 + 1.81486i) q^{53} +(0.329074 - 0.211483i) q^{54} +(3.29933 - 1.85931i) q^{55} +(9.92805 + 6.38037i) q^{56} +(0.00434888 + 0.00155168i) q^{57} +(3.55821 + 5.90063i) q^{58} +(-0.0907786 + 0.345358i) q^{59} +(0.129080 - 0.00738106i) q^{60} +(-11.4899 + 0.657016i) q^{61} +(2.11267 - 8.03745i) q^{62} +(6.83085 + 11.3277i) q^{63} +(3.16392 + 1.12888i) q^{64} +(-4.38822 - 2.82014i) q^{65} +(-0.203818 - 0.0729286i) q^{66} +(9.50358 - 6.10758i) q^{67} +(1.32262 - 0.307562i) q^{68} +(-0.0598439 + 0.0252903i) q^{69} +(-0.114077 - 3.99321i) q^{70} +(1.75222 - 2.27232i) q^{71} +(5.57074 + 5.73215i) q^{72} +(-0.907253 + 1.50451i) q^{73} +(-3.76964 + 3.08242i) q^{74} +(0.186088 + 0.241323i) q^{75} +(-0.0109455 + 0.0761278i) q^{76} +(5.33000 - 13.6537i) q^{77} +(0.0424327 + 0.295126i) q^{78} +(-5.94541 + 6.11768i) q^{79} +(0.183635 + 0.698620i) q^{80} +(2.76226 + 8.50137i) q^{81} +(1.46466 + 7.22841i) q^{82} +(0.0664344 - 0.773482i) q^{83} +(0.368654 - 0.338348i) q^{84} +(-0.831832 - 0.763448i) q^{85} +(0.104785 + 1.21999i) q^{86} +(0.688564 - 0.202181i) q^{87} +(1.26833 - 8.76556i) q^{88} +(-13.1845 - 3.87133i) q^{89} +(0.537327 - 2.65182i) q^{90} +(-20.0566 + 2.30128i) q^{91} +(-0.610816 - 0.893290i) q^{92} +(-0.753654 - 0.425608i) q^{93} +(-4.32073 + 3.13919i) q^{94} +(0.0573880 - 0.0282158i) q^{95} +(0.271855 - 0.397576i) q^{96} +(3.56105 - 6.74893i) q^{97} +(-6.49585 - 7.49661i) q^{98} +(5.61077 - 8.18970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9}+O(q^{10}) \) 400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9	\( 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9} - 22 q^{10} - 33 q^{11} + 6 q^{12} - 11 q^{13} - 18 q^{14} + 16 q^{15} - 30 q^{16} - 44 q^{17} + 11 q^{18} - 44 q^{19} - 36 q^{20} - 11 q^{21} - 34 q^{23} + 77 q^{24} - 31 q^{25} - 38 q^{26} + 40 q^{27} - 44 q^{28} - 44 q^{29} - 11 q^{30} - 17 q^{31} - 44 q^{32} - 11 q^{33} - 76 q^{34} - 44 q^{35} + 57 q^{36} - 4 q^{37} + 34 q^{38} - 11 q^{39} + 33 q^{40} - 44 q^{41} + 3 q^{42} - 44 q^{43} - 33 q^{44} - 12 q^{45} - 44 q^{46} - 36 q^{47} + 9 q^{48} + 16 q^{49} + 88 q^{50} + 154 q^{51} + 110 q^{52} + 78 q^{53} + 231 q^{54} + 44 q^{55} - 55 q^{56} + 66 q^{57} + 73 q^{58} - 33 q^{59} + 15 q^{60} - 44 q^{61} + 11 q^{62} + 121 q^{63} + 96 q^{64} - 11 q^{65} - 41 q^{67} - 44 q^{68} + 8 q^{69} + 24 q^{70} + 15 q^{71} + 77 q^{72} - 22 q^{73} - 44 q^{74} + 7 q^{75} + 176 q^{76} + 88 q^{77} - 21 q^{78} + 44 q^{79} + 171 q^{80} + 37 q^{81} + 22 q^{82} - 44 q^{83} - 11 q^{84} + 66 q^{85} - 20 q^{86} - 11 q^{87} + 77 q^{88} + 3 q^{89} + 264 q^{90} + 79 q^{91} + 228 q^{92} + 49 q^{93} + 143 q^{94} + 44 q^{95} + 121 q^{96} + 10 q^{97} + 132 q^{98} + 143 q^{99}+O(q^{100}) \) 400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9 - 22 * q^10 - 33 * q^11 + 6 * q^12 - 11 * q^13 - 18 * q^14 + 16 * q^15 - 30 * q^16 - 44 * q^17 + 11 * q^18 - 44 * q^19 - 36 * q^20 - 11 * q^21 - 34 * q^23 + 77 * q^24 - 31 * q^25 - 38 * q^26 + 40 * q^27 - 44 * q^28 - 44 * q^29 - 11 * q^30 - 17 * q^31 - 44 * q^32 - 11 * q^33 - 76 * q^34 - 44 * q^35 + 57 * q^36 - 4 * q^37 + 34 * q^38 - 11 * q^39 + 33 * q^40 - 44 * q^41 + 3 * q^42 - 44 * q^43 - 33 * q^44 - 12 * q^45 - 44 * q^46 - 36 * q^47 + 9 * q^48 + 16 * q^49 + 88 * q^50 + 154 * q^51 + 110 * q^52 + 78 * q^53 + 231 * q^54 + 44 * q^55 - 55 * q^56 + 66 * q^57 + 73 * q^58 - 33 * q^59 + 15 * q^60 - 44 * q^61 + 11 * q^62 + 121 * q^63 + 96 * q^64 - 11 * q^65 - 41 * q^67 - 44 * q^68 + 8 * q^69 + 24 * q^70 + 15 * q^71 + 77 * q^72 - 22 * q^73 - 44 * q^74 + 7 * q^75 + 176 * q^76 + 88 * q^77 - 21 * q^78 + 44 * q^79 + 171 * q^80 + 37 * q^81 + 22 * q^82 - 44 * q^83 - 11 * q^84 + 66 * q^85 - 20 * q^86 - 11 * q^87 + 77 * q^88 + 3 * q^89 + 264 * q^90 + 79 * q^91 + 228 * q^92 + 49 * q^93 + 143 * q^94 + 44 * q^95 + 121 * q^96 + 10 * q^97 + 132 * q^98 + 143 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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