LMFDB - Embedded newform 93.2.m.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7 x^{15} + 24 x^{14} - 36 x^{13} + 17 x^{12} + 18 x^{11} - 52 x^{10} + 59 x^{9} + 51 x^{8} + \cdots + 1 $ x^16 - 7x^15 + 24x^14 - 36x^13 + 17x^12 + 18x^11 - 52x^10 + 59x^9 + 51x^8 - 59x^7 - 52x^6 - 18x^5 + 17x^4 + 36x^3 + 24x^2 + 7*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			19.1
Root			$-0.826604 - 0.175700i$ of defining polynomial
Character	$\chi$	$=$	93.19
Dual form			93.2.m.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.125340 + 0.0910649i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.610617 - 1.87928i) q^{4} +(1.58103 - 2.73842i) q^{5} +(-0.0774644 - 0.134172i) q^{6} +(-1.81041 + 2.01066i) q^{7} +(0.190353 - 0.585848i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(0.125340 + 0.0910649i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.610617 - 1.87928i) q^{4} +(1.58103 - 2.73842i) q^{5} +(-0.0774644 - 0.134172i) q^{6} +(-1.81041 + 2.01066i) q^{7} +(0.190353 - 0.585848i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.447540 - 0.199258i) q^{10} +(5.26298 + 1.11868i) q^{11} +(-0.206548 + 1.96517i) q^{12} +(-0.209270 - 1.99107i) q^{13} +(-0.410018 + 0.0871520i) q^{14} +(-2.55816 + 1.85861i) q^{15} +(-3.12002 + 2.26683i) q^{16} +(-1.94323 + 0.413047i) q^{17} +(0.0161945 + 0.154080i) q^{18} +(-0.840072 + 7.99276i) q^{19} +(-6.11167 - 1.29908i) q^{20} +(2.47170 - 1.10047i) q^{21} +(0.557790 + 0.619489i) q^{22} +(1.18719 - 3.65380i) q^{23} +(-0.412182 + 0.457775i) q^{24} +(-2.49930 - 4.32891i) q^{25} +(0.155087 - 0.268618i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(4.88408 + 2.17453i) q^{28} +(4.87566 + 3.54238i) q^{29} -0.489894 q^{30} +(5.43100 - 1.22649i) q^{31} -1.82949 q^{32} +(-4.35297 - 3.16262i) q^{33} +(-0.281179 - 0.125189i) q^{34} +(2.64373 + 8.13658i) q^{35} +(0.987999 - 1.71126i) q^{36} +(-3.16145 - 5.47578i) q^{37} +(-0.833154 + 0.925312i) q^{38} +(-0.618664 + 1.90405i) q^{39} +(-1.30334 - 1.44751i) q^{40} +(-1.61956 + 0.721074i) q^{41} +(0.410018 + 0.0871520i) q^{42} +(0.00951391 - 0.0905188i) q^{43} +(-1.11134 - 10.5737i) q^{44} +(3.09296 - 0.657428i) q^{45} +(0.481536 - 0.349856i) q^{46} +(-3.08032 + 2.23798i) q^{47} +(3.77228 - 0.801824i) q^{48} +(-0.0334860 - 0.318598i) q^{49} +(0.0809497 - 0.770185i) q^{50} +(1.94323 + 0.413047i) q^{51} +(-3.61400 + 1.60906i) q^{52} +(4.56969 + 5.07516i) q^{53} +(0.0478757 - 0.147346i) q^{54} +(11.3843 - 12.6436i) q^{55} +(0.833325 + 1.44336i) q^{56} +(4.01839 - 6.96006i) q^{57} +(0.288530 + 0.888004i) q^{58} +(-8.32515 - 3.70660i) q^{59} +(5.05491 + 3.67261i) q^{60} -7.13537 q^{61} +(0.792412 + 0.340844i) q^{62} -2.70562 q^{63} +(6.01073 + 4.36705i) q^{64} +(-5.78325 - 2.57487i) q^{65} +(-0.257598 - 0.792805i) q^{66} +(-1.81027 + 3.13548i) q^{67} +(1.96280 + 3.39968i) q^{68} +(-2.57069 + 2.85504i) q^{69} +(-0.409591 + 1.26059i) q^{70} +(-4.92802 - 5.47312i) q^{71} +(0.562741 - 0.250548i) q^{72} +(-3.00758 - 0.639281i) q^{73} +(0.102396 - 0.974232i) q^{74} +(0.522496 + 4.97121i) q^{75} +(15.5336 - 3.30177i) q^{76} +(-11.7775 + 8.55682i) q^{77} +(-0.250936 + 0.182315i) q^{78} +(-5.51633 + 1.17253i) q^{79} +(1.27469 + 12.1278i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.268660 - 0.0571055i) q^{82} +(4.04402 - 1.80051i) q^{83} +(-3.57736 - 3.97307i) q^{84} +(-1.94121 + 5.97443i) q^{85} +(0.00943556 - 0.0104793i) q^{86} +(-3.01333 - 5.21923i) q^{87} +(1.65720 - 2.87036i) q^{88} +(-1.85086 - 5.69637i) q^{89} +(0.447540 + 0.199258i) q^{90} +(4.38224 + 3.18388i) q^{91} -7.59145 q^{92} +(-5.46032 - 1.08853i) q^{93} -0.589889 q^{94} +(20.5593 + 14.9372i) q^{95} +(1.67132 + 0.744119i) q^{96} +(0.732984 + 2.25589i) q^{97} +(0.0248159 - 0.0429825i) q^{98} +(2.69028 + 4.65970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9} - 16 q^{10} + 10 q^{11} - 10 q^{12} + 3 q^{13} - 12 q^{14} - 8 q^{15} + 6 q^{16} + 3 q^{17} - 32 q^{19} - 10 q^{20} - 6 q^{21} - 9 q^{22} - 22 q^{23} + 20 q^{24} + 12 q^{25} + 18 q^{26} + 4 q^{27} + 30 q^{28} + 38 q^{29} - 2 q^{30} - 8 q^{31} + 10 q^{33} - 52 q^{34} + 3 q^{35} - 5 q^{36} - 8 q^{37} + 7 q^{38} + 6 q^{39} + 37 q^{40} - 40 q^{41} + 12 q^{42} + q^{43} + q^{45} - 7 q^{46} - 23 q^{47} + 18 q^{48} + 25 q^{49} - 21 q^{50} - 3 q^{51} - 45 q^{52} + 30 q^{53} - 5 q^{54} + 46 q^{55} - 6 q^{56} - 8 q^{57} + 48 q^{58} - 40 q^{59} + 15 q^{60} + 26 q^{61} + 40 q^{62} - 12 q^{63} + 38 q^{64} + 12 q^{65} + 12 q^{66} - 32 q^{67} + 15 q^{68} - 11 q^{69} + 33 q^{70} + 17 q^{71} + 5 q^{72} + 27 q^{73} - 70 q^{74} + 3 q^{75} - 15 q^{76} - 9 q^{77} - 9 q^{78} + 21 q^{80} + 2 q^{81} - 32 q^{82} - 17 q^{83} - 15 q^{84} - 64 q^{85} + 26 q^{86} - 6 q^{87} - 22 q^{88} - 43 q^{89} - 16 q^{90} - 140 q^{92} - q^{93} + 88 q^{94} - 2 q^{95} - 35 q^{96} + 12 q^{97} - 32 q^{98}+O(q^{100}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9 - 16 * q^10 + 10 * q^11 - 10 * q^12 + 3 * q^13 - 12 * q^14 - 8 * q^15 + 6 * q^16 + 3 * q^17 - 32 * q^19 - 10 * q^20 - 6 * q^21 - 9 * q^22 - 22 * q^23 + 20 * q^24 + 12 * q^25 + 18 * q^26 + 4 * q^27 + 30 * q^28 + 38 * q^29 - 2 * q^30 - 8 * q^31 + 10 * q^33 - 52 * q^34 + 3 * q^35 - 5 * q^36 - 8 * q^37 + 7 * q^38 + 6 * q^39 + 37 * q^40 - 40 * q^41 + 12 * q^42 + q^43 + q^45 - 7 * q^46 - 23 * q^47 + 18 * q^48 + 25 * q^49 - 21 * q^50 - 3 * q^51 - 45 * q^52 + 30 * q^53 - 5 * q^54 + 46 * q^55 - 6 * q^56 - 8 * q^57 + 48 * q^58 - 40 * q^59 + 15 * q^60 + 26 * q^61 + 40 * q^62 - 12 * q^63 + 38 * q^64 + 12 * q^65 + 12 * q^66 - 32 * q^67 + 15 * q^68 - 11 * q^69 + 33 * q^70 + 17 * q^71 + 5 * q^72 + 27 * q^73 - 70 * q^74 + 3 * q^75 - 15 * q^76 - 9 * q^77 - 9 * q^78 + 21 * q^80 + 2 * q^81 - 32 * q^82 - 17 * q^83 - 15 * q^84 - 64 * q^85 + 26 * q^86 - 6 * q^87 - 22 * q^88 - 43 * q^89 - 16 * q^90 - 140 * q^92 - q^93 + 88 * q^94 - 2 * q^95 - 35 * q^96 + 12 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.125340	+	0.0910649i	0.0886288	+	0.0643926i	0.631217	−	0.775606i	$-0.282556\pi$
$2$	0.125340	+	0.0910649i	0.0886288	+	0.0643926i	−0.542588	+	0.839999i	$0.682556\pi$
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	−0.610617	−	1.87928i	−0.305308	−	0.939642i
$5$	1.58103	−	2.73842i	0.707057	−	1.22466i	−0.258887	−	0.965908i	$-0.583356\pi$
$5$	1.58103	−	2.73842i	0.707057	−	1.22466i	0.965944	−	0.258751i	$-0.0833110\pi$
$6$	−0.0774644	−	0.134172i	−0.0316247	−	0.0547756i
$7$	−1.81041	+	2.01066i	−0.684271	+	0.759959i	−0.980790	−	0.195067i	$-0.937507\pi$
$7$	−1.81041	+	2.01066i	−0.684271	+	0.759959i	0.296519	+	0.955027i	$0.404174\pi$
$8$	0.190353	−	0.585848i	0.0673001	−	0.207128i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	0.447540	−	0.199258i	0.141525	−	0.0630108i
$11$	5.26298	+	1.11868i	1.58685	+	0.337295i	0.915019	−	0.403410i	$-0.132175\pi$
$11$	5.26298	+	1.11868i	1.58685	+	0.337295i	0.671830	+	0.740705i	$0.265508\pi$
$12$	−0.206548	+	1.96517i	−0.0596253	+	0.567296i
$13$	−0.209270	−	1.99107i	−0.0580410	−	0.552223i	−0.984445	−	0.175693i	$-0.943784\pi$
$13$	−0.209270	−	1.99107i	−0.0580410	−	0.552223i	0.926404	−	0.376531i	$-0.122883\pi$
$14$	−0.410018	+	0.0871520i	−0.109582	+	0.0232923i
$15$	−2.55816	+	1.85861i	−0.660513	+	0.479891i
$16$	−3.12002	+	2.26683i	−0.780005	+	0.566707i
$17$	−1.94323	+	0.413047i	−0.471303	+	0.100179i	−0.437440	−	0.899248i	$-0.644115\pi$
$17$	−1.94323	+	0.413047i	−0.471303	+	0.100179i	−0.0338639	+	0.999426i	$0.510781\pi$
$18$	0.0161945	+	0.154080i	0.00381707	+	0.0363170i
$19$	−0.840072	+	7.99276i	−0.192726	+	1.83366i	0.288985	+	0.957334i	$0.406682\pi$
$19$	−0.840072	+	7.99276i	−0.192726	+	1.83366i	−0.481711	+	0.876330i	$0.659984\pi$
$20$	−6.11167	−	1.29908i	−1.36661	−	0.290482i
$21$	2.47170	−	1.10047i	0.539370	−	0.240143i
$22$	0.557790	+	0.619489i	0.118921	+	0.132075i
$23$	1.18719	−	3.65380i	0.247547	−	0.761870i	−0.747661	−	0.664081i	$-0.768823\pi$
$23$	1.18719	−	3.65380i	0.247547	−	0.761870i	0.995207	−	0.0977891i	$-0.0311771\pi$
$24$	−0.412182	+	0.457775i	−0.0841364	+	0.0934429i
$25$	−2.49930	−	4.32891i	−0.499860	−	0.865782i
$26$	0.155087	−	0.268618i	0.0304150	−	0.0526803i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	4.88408	+	2.17453i	0.923004	+	0.410948i
$29$	4.87566	+	3.54238i	0.905388	+	0.657803i	0.939844	−	0.341603i	$-0.110970\pi$
$29$	4.87566	+	3.54238i	0.905388	+	0.657803i	−0.0344563	+	0.999406i	$0.510970\pi$
$30$	−0.489894			−0.0894419
$31$	5.43100	−	1.22649i	0.975436	−	0.220285i
$31$	5.43100	−	1.22649i	0.975436	−	0.220285i
$32$	−1.82949			−0.323410
$33$	−4.35297	−	3.16262i	−0.757754	−	0.550541i
$34$	−0.281179	−	0.125189i	−0.0482218	−	0.0214697i
$35$	2.64373	+	8.13658i	0.446873	+	1.37533i
$36$	0.987999	−	1.71126i	0.164666	−	0.285211i
$37$	−3.16145	−	5.47578i	−0.519738	−	0.900213i	−0.999737	−	0.0229440i	$-0.992696\pi$
$37$	−3.16145	−	5.47578i	−0.519738	−	0.900213i	0.479998	−	0.877269i	$-0.340637\pi$
$38$	−0.833154	+	0.925312i	−0.135155	+	0.150105i
$39$	−0.618664	+	1.90405i	−0.0990654	+	0.304892i
$40$	−1.30334	−	1.44751i	−0.206077	−	0.228871i
$41$	−1.61956	+	0.721074i	−0.252933	+	0.112613i	−0.529287	−	0.848443i	$-0.677540\pi$
$41$	−1.61956	+	0.721074i	−0.252933	+	0.112613i	0.276354	+	0.961056i	$0.410874\pi$
$42$	0.410018	+	0.0871520i	0.0632671	+	0.0134478i
$43$	0.00951391	−	0.0905188i	0.00145086	−	0.0138040i	−0.993773	−	0.111428i	$-0.964458\pi$
$43$	0.00951391	−	0.0905188i	0.00145086	−	0.0138040i	0.995223	+	0.0976240i	$0.0311242\pi$
$44$	−1.11134	−	10.5737i	−0.167541	−	1.59405i
$45$	3.09296	−	0.657428i	0.461071	−	0.0980036i
$46$	0.481536	−	0.349856i	0.0709986	−	0.0515835i
$47$	−3.08032	+	2.23798i	−0.449311	+	0.326443i	−0.789324	−	0.613977i	$-0.789569\pi$
$47$	−3.08032	+	2.23798i	−0.449311	+	0.326443i	0.340013	+	0.940421i	$0.389569\pi$
$48$	3.77228	−	0.801824i	0.544482	−	0.115733i
$49$	−0.0334860	−	0.318598i	−0.00478371	−	0.0455140i
$50$	0.0809497	−	0.770185i	0.0114480	−	0.108921i
$51$	1.94323	+	0.413047i	0.272107	+	0.0578382i
$52$	−3.61400	+	1.60906i	−0.501172	+	0.223136i
$53$	4.56969	+	5.07516i	0.627695	+	0.697126i	0.970177	−	0.242398i	$-0.0779340\pi$
$53$	4.56969	+	5.07516i	0.627695	+	0.697126i	−0.342481	+	0.939525i	$0.611267\pi$
$54$	0.0478757	−	0.147346i	0.00651505	−	0.0200513i
$55$	11.3843	−	12.6436i	1.53507	−	1.70486i
$56$	0.833325	+	1.44336i	0.111358	+	0.192877i
$57$	4.01839	−	6.96006i	0.532249	−	0.921882i
$58$	0.288530	+	0.888004i	0.0378858	+	0.116601i
$59$	−8.32515	−	3.70660i	−1.08384	−	0.482558i	−0.214478	−	0.976729i	$-0.568805\pi$
$59$	−8.32515	−	3.70660i	−1.08384	−	0.482558i	−0.869365	+	0.494171i	$0.835472\pi$
$60$	5.05491	+	3.67261i	0.652586	+	0.474132i
$61$	−7.13537			−0.913591			−0.456795	−	0.889572i	$-0.651003\pi$
$61$	−7.13537			−0.913591			−0.456795	+	0.889572i	$0.651003\pi$
$62$	0.792412	+	0.340844i	0.100636	+	0.0432873i
$63$	−2.70562			−0.340875
$64$	6.01073	+	4.36705i	0.751342	+	0.545882i
$65$	−5.78325	−	2.57487i	−0.717324	−	0.319373i
$66$	−0.257598	−	0.792805i	−0.0317081	−	0.0975875i
$67$	−1.81027	+	3.13548i	−0.221159	+	0.383059i	−0.955160	−	0.296089i	$-0.904317\pi$
$67$	−1.81027	+	3.13548i	−0.221159	+	0.383059i	0.734001	+	0.679149i	$0.237651\pi$
$68$	1.96280	+	3.39968i	0.238025	+	0.412271i
$69$	−2.57069	+	2.85504i	−0.309475	+	0.343706i
$70$	−0.409591	+	1.26059i	−0.0489555	+	0.150669i
$71$	−4.92802	−	5.47312i	−0.584848	−	0.649539i	0.375999	−	0.926620i	$-0.377300\pi$
$71$	−4.92802	−	5.47312i	−0.584848	−	0.649539i	−0.960847	+	0.277081i	$0.910633\pi$
$72$	0.562741	−	0.250548i	0.0663197	−	0.0295274i
$73$	−3.00758	−	0.639281i	−0.352011	−	0.0748222i	0.0285128	−	0.999593i	$-0.490923\pi$
$73$	−3.00758	−	0.639281i	−0.352011	−	0.0748222i	−0.380524	+	0.924771i	$0.624256\pi$
$74$	0.102396	−	0.974232i	0.0119033	−	0.113252i
$75$	0.522496	+	4.97121i	0.0603326	+	0.574026i
$76$	15.5336	−	3.30177i	1.78183	−	0.378739i
$77$	−11.7775	+	8.55682i	−1.34217	+	0.975140i
$78$	−0.250936	+	0.182315i	−0.0284129	+	0.0206431i
$79$	−5.51633	+	1.17253i	−0.620636	+	0.131920i	−0.507489	−	0.861658i	$-0.669426\pi$
$79$	−5.51633	+	1.17253i	−0.620636	+	0.131920i	−0.113147	+	0.993578i	$0.536093\pi$
$80$	1.27469	+	12.1278i	0.142514	+	1.35593i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−0.268660	−	0.0571055i	−0.0296686	−	0.00630625i
$83$	4.04402	−	1.80051i	0.443889	−	0.197632i	−0.172606	−	0.984991i	$-0.555219\pi$
$83$	4.04402	−	1.80051i	0.443889	−	0.197632i	0.616495	+	0.787359i	$0.288552\pi$
$84$	−3.57736	−	3.97307i	−0.390322	−	0.433497i
$85$	−1.94121	+	5.97443i	−0.210554	+	0.648018i
$86$	0.00943556	−	0.0104793i	0.00101746	−	0.00113001i
$87$	−3.01333	−	5.21923i	−0.323062	−	0.559561i
$88$	1.65720	−	2.87036i	0.176659	−	0.305982i
$89$	−1.85086	−	5.69637i	−0.196191	−	0.603814i	−0.999961	−	0.00887319i	$-0.997176\pi$
$89$	−1.85086	−	5.69637i	−0.196191	−	0.603814i	0.803770	−	0.594941i	$-0.202824\pi$
$90$	0.447540	+	0.199258i	0.0471749	+	0.0210036i
$91$	4.38224	+	3.18388i	0.459383	+	0.333761i
$92$	−7.59145			−0.791464
$93$	−5.46032	−	1.08853i	−0.566209	−	0.112875i
$94$	−0.589889			−0.0608424
$95$	20.5593	+	14.9372i	2.10934	+	1.53253i
$96$	1.67132	+	0.744119i	0.170578	+	0.0759463i
$97$	0.732984	+	2.25589i	0.0744232	+	0.229051i	0.981347	−	0.192243i	$-0.0615761\pi$
$97$	0.732984	+	2.25589i	0.0744232	+	0.229051i	−0.906924	+	0.421294i	$0.861576\pi$
$98$	0.0248159	−	0.0429825i	0.00250679	−	0.00434188i
$99$	2.69028	+	4.65970i	0.270383	+	0.468318i
$100$	−6.60915	+	7.34020i	−0.660915	+	0.734020i
$101$	1.61154	−	4.95981i	0.160354	−	0.493519i	−0.838310	−	0.545194i	$-0.816456\pi$
$101$	1.61154	−	4.95981i	0.160354	−	0.493519i	0.998664	+	0.0516748i	$0.0164559\pi$
$102$	0.205951	+	0.228732i	0.0203922	+	0.0226478i
$103$	−17.6055	+	7.83846i	−1.73472	+	0.772346i	−0.739667	+	0.672973i	$0.765017\pi$
$103$	−17.6055	+	7.83846i	−1.73472	+	0.772346i	−0.995050	+	0.0993733i	$0.968316\pi$
$104$	−1.20630	−	0.256407i	−0.118287	−	0.0251428i
$105$	0.894273	−	8.50844i	0.0872721	−	0.830339i
$106$	0.110597	+	1.05226i	0.0107421	+	0.102204i
$107$	−17.9305	+	3.81124i	−1.73341	+	0.368447i	−0.963082	−	0.269206i	$-0.913239\pi$
$107$	−17.9305	+	3.81124i	−1.73341	+	0.368447i	−0.770324	+	0.637653i	$0.779905\pi$
$108$	−1.59862	+	1.16146i	−0.153827	+	0.111762i
$109$	4.32335	−	3.14110i	0.414102	−	0.300863i	−0.361158	−	0.932504i	$-0.617619\pi$
$109$	4.32335	−	3.14110i	0.414102	−	0.300863i	0.775260	+	0.631642i	$0.217619\pi$
$110$	2.57830	−	0.548035i	0.245832	−	0.0522531i
$111$	0.660922	+	6.28825i	0.0627319	+	0.596855i
$112$	1.09069	−	10.3772i	0.103060	−	0.980553i
$113$	16.6635	+	3.54194i	1.56757	+	0.333198i	0.908173	−	0.418596i	$-0.137478\pi$
$113$	16.6635	+	3.54194i	1.56757	+	0.333198i	0.659399	+	0.751793i	$0.270811\pi$
$114$	1.13748	−	0.506440i	0.106535	−	0.0474324i
$115$	−8.12866	−	9.02779i	−0.758002	−	0.841846i
$116$	3.67997	−	11.3258i	0.341677	−	1.05157i
$117$	1.33962	−	1.48780i	0.123848	−	0.137547i
$118$	−0.705934	−	1.22271i	−0.0649865	−	0.112560i
$119$	2.68755	−	4.65497i	0.246367	−	0.426721i
$120$	0.601908	+	1.85248i	0.0549465	+	0.169108i
$121$	16.3986	+	7.30111i	1.49078	+	0.663737i
$122$	−0.894348	−	0.649782i	−0.0809705	−	0.0588285i
$123$	1.77283			0.159851
$124$	−5.62119	−	9.45747i	−0.504797	−	0.849306i
$125$	0.00443727			0.000396882
$126$	−0.339122	−	0.246387i	−0.0302114	−	0.0219499i
$127$	11.9713	+	5.32995i	1.06228	+	0.472956i	0.862066	−	0.506796i	$-0.169170\pi$
$127$	11.9713	+	5.32995i	1.06228	+	0.472956i	0.200212	+	0.979753i	$0.435837\pi$
$128$	1.48638	+	4.57462i	0.131379	+	0.404343i
$129$	−0.0455087	+	0.0788234i	−0.00400682	+	0.00694001i
$130$	−0.490393	−	0.849385i	−0.0430103	−	0.0744960i
$131$	5.21748	−	5.79460i	0.455853	−	0.506276i	−0.470776	−	0.882253i	$-0.656026\pi$
$131$	5.21748	−	5.79460i	0.455853	−	0.506276i	0.926629	+	0.375977i	$0.122693\pi$
$132$	−3.28546	+	10.1116i	−0.285963	+	0.880103i
$133$	−14.5499	−	16.1593i	−1.26163	−	1.40119i
$134$	−0.512431	+	0.228149i	−0.0442673	+	0.0197091i
$135$	−3.09296	−	0.657428i	−0.266199	−	0.0565824i
$136$	−0.127919	+	1.21706i	−0.0109689	+	0.104362i
$137$	−1.59658	−	15.1904i	−0.136405	−	1.29780i	−0.821860	−	0.569689i	$-0.807064\pi$
$137$	−1.59658	−	15.1904i	−0.136405	−	1.29780i	0.685456	−	0.728114i	$-0.259603\pi$
$138$	−0.582204	+	0.123751i	−0.0495605	+	0.0105344i
$139$	−12.0824	+	8.77840i	−1.02482	+	0.744574i	−0.967265	−	0.253768i	$-0.918330\pi$
$139$	−12.0824	+	8.77840i	−1.02482	+	0.744574i	−0.0575533	+	0.998342i	$0.518330\pi$
$140$	13.6766	−	9.93666i	1.15589	−	0.839801i
$141$	3.72428	−	0.791620i	0.313641	−	0.0666665i
$142$	−0.119269	−	1.13477i	−0.0100088	−	0.0952278i
$143$	1.12599	−	10.7131i	0.0941600	−	0.895872i
$144$	−3.77228	−	0.801824i	−0.314357	−	0.0668186i
$145$	17.4091	−	7.75102i	1.44575	−	0.643687i
$146$	−0.318754	−	0.354013i	−0.0263803	−	0.0292983i
$147$	−0.0989944	+	0.304673i	−0.00816492	+	0.0251290i
$148$	−8.36013	+	9.28486i	−0.687198	+	0.763211i
$149$	−1.35751	−	2.35128i	−0.111212	−	0.192624i	0.805047	−	0.593211i	$-0.202140\pi$
$149$	−1.35751	−	2.35128i	−0.111212	−	0.192624i	−0.916259	+	0.400586i	$0.868806\pi$
$150$	−0.387213	+	0.670673i	−0.0316158	+	0.0547603i
$151$	3.58182	+	11.0237i	0.291484	+	0.897096i	0.984380	+	0.176058i	$0.0563347\pi$
$151$	3.58182	+	11.0237i	0.291484	+	0.897096i	−0.692895	+	0.721038i	$0.743665\pi$
$152$	4.52263	+	2.01360i	0.366833	+	0.163325i
$153$	−1.60723	−	1.16772i	−0.129937	−	0.0944047i
$154$	−2.25541			−0.181746
$155$	5.22790	−	16.8115i	0.419915	−	1.35033i
$156$	3.95602			0.316735
$157$	−0.766716	−	0.557051i	−0.0611906	−	0.0444575i	0.556769	−	0.830667i	$-0.312041\pi$
$157$	−0.766716	−	0.557051i	−0.0611906	−	0.0444575i	−0.617960	+	0.786209i	$0.712041\pi$
$158$	−0.798194	−	0.355379i	−0.0635009	−	0.0282724i
$159$	−2.11037	−	6.49505i	−0.167363	−	0.515091i
$160$	−2.89247	+	5.00990i	−0.228670	+	0.396067i
$161$	5.19726	+	9.00192i	0.409602	+	0.709451i
$162$	−0.103668	+	0.115135i	−0.00814490	+	0.00904583i
$163$	−3.63924	+	11.2004i	−0.285047	+	0.877285i	0.701337	+	0.712830i	$0.252587\pi$
$163$	−3.63924	+	11.2004i	−0.285047	+	0.877285i	−0.986385	+	0.164455i	$0.947413\pi$
$164$	2.34403	+	2.60331i	0.183038	+	0.203285i
$165$	−15.5427	+	6.92007i	−1.21000	+	0.538727i
$166$	0.670841	+	0.142592i	0.0520674	+	0.0110673i
$167$	0.222270	−	2.11476i	0.0171998	−	0.163645i	−0.982550	−	0.185997i	$-0.940449\pi$
$167$	0.222270	−	2.11476i	0.0171998	−	0.163645i	0.999750	+	0.0223515i	$0.00711531\pi$
$168$	−0.174212	−	1.65752i	−0.0134408	−	0.127880i
$169$	8.79535	−	1.86951i	0.676566	−	0.143808i
$170$	−0.787372	+	0.572060i	−0.0603887	+	0.0438750i
$171$	−6.50189	+	4.72390i	−0.497212	+	0.361246i
$172$	−0.175920	+	0.0373930i	−0.0134138	+	0.00285119i
$173$	0.864773	+	8.22777i	0.0657475	+	0.625546i	0.976933	+	0.213548i	$0.0685020\pi$
$173$	0.864773	+	8.22777i	0.0657475	+	0.625546i	−0.911185	+	0.411997i	$0.864831\pi$
$174$	0.0975985	−	0.928587i	0.00739892	−	0.0703960i
$175$	13.2287	+	2.81186i	0.999999	+	0.212556i
$176$	−18.9565	+	8.43997i	−1.42890	+	0.636187i
$177$	6.09780	+	6.77229i	0.458338	+	0.509036i
$178$	0.286752	−	0.882532i	0.0214930	−	0.0661486i
$179$	3.52992	−	3.92038i	0.263839	−	0.293023i	−0.596640	−	0.802509i	$-0.703498\pi$
$179$	3.52992	−	3.92038i	0.263839	−	0.293023i	0.860479	+	0.509486i	$0.170165\pi$
$180$	−3.12411	−	5.41111i	−0.232857	−	0.403320i
$181$	2.88407	−	4.99536i	0.214371	−	0.371302i	−0.738707	−	0.674027i	$-0.764563\pi$
$181$	2.88407	−	4.99536i	0.214371	−	0.371302i	0.953078	+	0.302725i	$0.0978964\pi$
$182$	0.259330	+	0.798136i	0.0192228	+	0.0591618i
$183$	6.51849	+	2.90222i	0.481860	+	0.214538i
$184$	−1.91458	−	1.39103i	−0.141145	−	0.102548i
$185$	−19.9933			−1.46994
$186$	−0.585270	−	0.633680i	−0.0429141	−	0.0464637i
$187$	−10.6893			−0.781677
$188$	6.08670	+	4.42225i	0.443918	+	0.322526i
$189$	2.47170	+	1.10047i	0.179790	+	0.0800476i
$190$	1.21665	+	3.74447i	0.0882652	+	0.271652i
$191$	3.15695	−	5.46800i	0.228429	−	0.395650i	−0.728914	−	0.684606i	$-0.759974\pi$
$191$	3.15695	−	5.46800i	0.228429	−	0.395650i	0.957343	+	0.288955i	$0.0933078\pi$
$192$	−3.71484	−	6.43429i	−0.268095	−	0.464355i
$193$	0.180300	−	0.200243i	0.0129783	−	0.0144138i	−0.736621	−	0.676306i	$-0.763580\pi$
$193$	0.180300	−	0.200243i	0.0129783	−	0.0144138i	0.749599	+	0.661892i	$0.230246\pi$
$194$	−0.113560	+	0.349503i	−0.00815316	+	0.0250928i
$195$	4.23597	+	4.70452i	0.303344	+	0.336898i
$196$	−0.578289	+	0.257471i	−0.0413063	+	0.0183908i
$197$	21.8701	+	4.64863i	1.55818	+	0.331201i	0.904803	−	0.425831i	$-0.140018\pi$
$197$	21.8701	+	4.64863i	1.55818	+	0.331201i	0.653377	+	0.757032i	$0.273351\pi$
$198$	−0.0871354	+	0.829038i	−0.00619244	+	0.0589172i
$199$	−1.43787	−	13.6804i	−0.101928	−	0.969780i	−0.919270	−	0.393627i	$-0.871220\pi$
$199$	−1.43787	−	13.6804i	−0.101928	−	0.969780i	0.817342	−	0.576153i	$-0.195447\pi$
$200$	−3.01183	+	0.640185i	−0.212969	+	0.0452679i
$201$	2.92907	−	2.12810i	0.206601	−	0.150104i
$202$	0.653655	−	0.474908i	0.0459910	−	0.0334144i
$203$	−15.9495	+	3.39017i	−1.11943	+	0.237943i
$204$	−0.410338	−	3.90410i	−0.0287294	−	0.273342i
$205$	−0.585964	+	5.57507i	−0.0409255	+	0.389380i
$206$	−2.92048	−	0.620767i	−0.203479	−	0.0432509i
$207$	3.50969	−	1.56261i	0.243940	−	0.108609i
$208$	5.16634	+	5.73780i	0.358221	+	0.397845i
$209$	−13.3626	+	41.1260i	−0.924313	+	2.84474i
$210$	0.886908	−	0.985012i	0.0612025	−	0.0679723i
$211$	−1.48372	−	2.56988i	−0.102143	−	0.176918i	0.810424	−	0.585844i	$-0.199237\pi$
$211$	−1.48372	−	2.56988i	−0.102143	−	0.176918i	−0.912568	+	0.408926i	$0.865903\pi$
$212$	6.74734	−	11.6867i	0.463409	−	0.802648i
$213$	2.27585	+	7.00434i	0.155939	+	0.479930i
$214$	−2.59448	−	1.15514i	−0.177355	−	0.0789635i
$215$	−0.232837	−	0.169166i	−0.0158793	−	0.0115370i
$216$	−0.615997			−0.0419133
$217$	−7.36626	+	13.1404i	−0.500054	+	0.892026i
$218$	0.827933			0.0560747
$219$	2.48754	+	1.80731i	0.168093	+	0.122126i
$220$	−30.7124	−	13.6740i	−2.07063	−	0.921904i
$221$	1.22907	+	3.78268i	0.0826759	+	0.254450i
$222$	−0.489799	+	0.848357i	−0.0328732	+	0.0569380i
$223$	−5.14531	−	8.91194i	−0.344556	−	0.596788i	0.640717	−	0.767777i	$-0.278637\pi$
$223$	−5.14531	−	8.91194i	−0.344556	−	0.596788i	−0.985273	+	0.170989i	$0.945304\pi$
$224$	3.31212	−	3.67848i	0.221300	−	0.245779i
$225$	1.54465	−	4.75395i	0.102977	−	0.316930i
$226$	1.76606	+	1.96141i	0.117477	+	0.130471i
$227$	−2.97472	+	1.32443i	−0.197439	+	0.0879056i	−0.503074	−	0.864243i	$-0.667798\pi$
$227$	−2.97472	+	1.32443i	−0.197439	+	0.0879056i	0.305635	+	0.952149i	$0.401131\pi$
$228$	−15.5336	−	3.30177i	−1.02874	−	0.218665i
$229$	0.736702	−	7.00925i	0.0486826	−	0.463184i	−0.942840	−	0.333247i	$-0.891856\pi$
$229$	0.736702	−	7.00925i	0.0486826	−	0.463184i	0.991522	−	0.129937i	$-0.0414776\pi$
$230$	−0.196732	−	1.87178i	−0.0129721	−	0.123422i
$231$	14.2396	−	3.02672i	0.936898	−	0.199144i
$232$	3.00339	−	2.18209i	0.197182	−	0.143261i
$233$	−0.408414	+	0.296730i	−0.0267561	+	0.0194394i	−0.601083	−	0.799187i	$-0.705264\pi$
$233$	−0.408414	+	0.296730i	−0.0267561	+	0.0194394i	0.574327	+	0.818626i	$0.305264\pi$
$234$	0.303395	−	0.0644887i	0.0198336	−	0.00421576i
$235$	1.25847	+	11.9735i	0.0820934	+	0.781066i
$236$	−1.88227	+	17.9086i	−0.122526	+	1.16575i
$237$	5.51633	+	1.17253i	0.358324	+	0.0761642i
$238$	0.760763	−	0.338713i	0.0493129	−	0.0219555i
$239$	9.84196	+	10.9306i	0.636623	+	0.707042i	0.971984	−	0.235048i	$-0.0755247\pi$
$239$	9.84196	+	10.9306i	0.636623	+	0.707042i	−0.335360	+	0.942090i	$0.608858\pi$
$240$	3.76835	−	11.5978i	0.243246	−	0.748635i
$241$	−5.22317	+	5.80092i	−0.336454	+	0.373670i	−0.887502	−	0.460803i	$-0.847561\pi$
$241$	−5.22317	+	5.80092i	−0.336454	+	0.373670i	0.551048	+	0.834473i	$0.314228\pi$
$242$	1.39052	+	2.40845i	0.0893861	+	0.154821i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.35698	+	13.4094i	0.278927	+	0.858448i
$245$	−0.925397	−	0.412013i	−0.0591214	−	0.0263226i
$246$	0.222207	+	0.161442i	0.0141674	+	0.0102932i
$247$	16.0899			1.02378
$248$	0.315271	−	3.41520i	0.0200197	−	0.216866i
$249$	−4.42673			−0.280532
$250$	0.000556168	0	0.000404080i	3.51752e−5	0	2.55563e-5i
$251$	−20.4350	−	9.09825i	−1.28985	−	0.574276i	−0.356850	−	0.934162i	$-0.616149\pi$
$251$	−20.4350	−	9.09825i	−1.28985	−	0.574276i	−0.932997	+	0.359885i	$0.882816\pi$
$252$	1.65209	+	5.08462i	0.104072	+	0.320301i
$253$	10.3356	−	17.9018i	0.649795	−	1.12548i
$254$	1.01511	+	1.75822i	0.0636935	+	0.110320i
$255$	4.20340	−	4.66835i	0.263227	−	0.292344i
$256$	4.36151	−	13.4233i	0.272594	−	0.838959i
$257$	−13.9529	−	15.4963i	−0.870358	−	0.966630i	0.129330	−	0.991602i	$-0.458717\pi$
$257$	−13.9529	−	15.4963i	−0.870358	−	0.966630i	−0.999688	+	0.0249713i	$0.992051\pi$
$258$	−0.0128821	+	0.00573549i	−0.000802005	+	0.000357076i
$259$	16.7335	+	3.55681i	1.03977	+	0.221009i
$260$	−1.30756	+	12.4406i	−0.0810916	+	0.771535i
$261$	0.629957	+	5.99364i	0.0389933	+	0.370997i
$262$	1.18164	−	0.251166i	0.0730022	−	0.0155171i
$263$	23.9573	−	17.4060i	1.47727	−	1.07330i	0.498844	−	0.866692i	$-0.333758\pi$
$263$	23.9573	−	17.4060i	1.47727	−	1.07330i	0.978424	−	0.206607i	$-0.0662420\pi$
$264$	−2.68141	+	1.94816i	−0.165030	+	0.119901i
$265$	21.1227	−	4.48977i	1.29756	−	0.275805i
$266$	−0.352140	−	3.35039i	−0.0215911	−	0.205425i
$267$	−0.626075	+	5.95671i	−0.0383152	+	0.364544i
$268$	6.99783	+	1.48744i	0.427461	+	0.0908596i
$269$	−12.4294	+	5.53394i	−0.757835	+	0.337410i	−0.749017	−	0.662551i	$-0.769474\pi$
$269$	−12.4294	+	5.53394i	−0.757835	+	0.337410i	−0.00881859	+	0.999961i	$0.502807\pi$
$270$	−0.327803	−	0.364062i	−0.0199494	−	0.0221561i
$271$	7.89881	−	24.3100i	0.479818	−	1.47673i	−0.359529	−	0.933134i	$-0.617063\pi$
$271$	7.89881	−	24.3100i	0.479818	−	1.47673i	0.839348	−	0.543595i	$-0.182937\pi$
$272$	5.12662	−	5.69369i	0.310847	−	0.345231i
$273$	−2.70837	−	4.69104i	−0.163918	−	0.283914i
$274$	1.18320	−	2.04936i	0.0714796	−	0.123806i
$275$	−8.31109	−	25.5789i	−0.501178	−	1.54247i
$276$	6.93514	+	3.08772i	0.417446	+	0.185859i
$277$	6.59018	+	4.78804i	0.395965	+	0.287686i	0.767896	−	0.640575i	$-0.221304\pi$
$277$	6.59018	+	4.78804i	0.395965	+	0.287686i	−0.371930	+	0.928261i	$0.621304\pi$
$278$	−2.31382			−0.138774
$279$	4.54551	+	3.21533i	0.272132	+	0.192497i
$280$	5.27004			0.314945
$281$	−22.3519	−	16.2396i	−1.33341	−	0.968776i	−0.999659	−	0.0261125i	$-0.991687\pi$
$281$	−22.3519	−	16.2396i	−1.33341	−	0.968776i	−0.333746	−	0.942663i	$-0.608313\pi$
$282$	0.538891	+	0.239930i	0.0320905	+	0.0142876i
$283$	−0.900612	−	2.77180i	−0.0535358	−	0.164766i	0.920714	−	0.390239i	$-0.127607\pi$
$283$	−0.900612	−	2.77180i	−0.0535358	−	0.164766i	−0.974250	+	0.225472i	$0.927607\pi$
$284$	−7.27642	+	12.6031i	−0.431776	+	0.747858i
$285$	−12.7064	−	22.0081i	−0.752661	−	1.30365i
$286$	1.11672	−	1.24024i	0.0660329	−	0.0733369i
$287$	1.48223	−	4.56183i	0.0874932	−	0.269276i
$288$	−1.22416	−	1.35957i	−0.0721346	−	0.0801136i
$289$	−11.9247	+	5.30923i	−0.701454	+	0.312308i
$290$	2.88790	+	0.613842i	0.169583	+	0.0360461i
$291$	0.247940	−	2.35899i	0.0145345	−	0.138287i
$292$	0.635088	+	6.04246i	0.0371657	+	0.353608i
$293$	−2.64692	+	0.562619i	−0.154634	+	0.0328686i	−0.284578	−	0.958653i	$-0.591854\pi$
$293$	−2.64692	+	0.562619i	−0.154634	+	0.0328686i	0.129944	+	0.991521i	$0.458520\pi$
$294$	−0.0401530	+	0.0291729i	−0.00234177	+	0.00170140i
$295$	−23.3125	+	16.9375i	−1.35731	+	0.986141i
$296$	−3.80977	+	0.809791i	−0.221438	+	0.0470682i
$297$	−0.562422	−	5.35109i	−0.0326350	−	0.310502i
$298$	0.0439684	−	0.418331i	0.00254702	−	0.0242333i
$299$	−7.52342	−	1.59915i	−0.435090	−	0.0924813i
$300$	9.02328	−	4.01742i	0.520959	−	0.231946i
$301$	0.164779	+	0.183005i	0.00949770	+	0.0105483i
$302$	−0.554927	+	1.70789i	−0.0319325	+	0.0982780i
$303$	−3.48955	+	3.87554i	−0.200469	+	0.222644i
$304$	−15.4972	−	26.8419i	−0.888823	−	1.53949i
$305$	−11.2812	+	19.5396i	−0.645961	+	1.11884i
$306$	−0.0951120	−	0.292725i	−0.00543719	−	0.0167340i
$307$	−19.9138	−	8.86619i	−1.13654	−	0.506020i	−0.249804	−	0.968296i	$-0.580366\pi$
$307$	−19.9138	−	8.86619i	−1.13654	−	0.506020i	−0.886736	+	0.462276i	$0.847033\pi$
$308$	23.2722	+	16.9083i	1.32606	+	0.963437i
$309$	19.2716			1.09632
$310$	2.18620	−	1.63107i	0.124168	−	0.0926387i
$311$	12.5498			0.711635			0.355817	−	0.934556i	$-0.384203\pi$
$311$	12.5498			0.711635			0.355817	+	0.934556i	$0.384203\pi$
$312$	0.997719	+	0.724885i	0.0564847	+	0.0410385i
$313$	23.5351	+	10.4785i	1.33028	+	0.592281i	0.943953	−	0.330079i	$-0.107075\pi$
$313$	23.5351	+	10.4785i	1.33028	+	0.592281i	0.386331	+	0.922360i	$0.373742\pi$
$314$	−0.0453724	−	0.139642i	−0.00256051	−	0.00788044i
$315$	−4.27765	+	7.40911i	−0.241018	+	0.417456i
$316$	5.57189	+	9.65079i	0.313443	+	0.542900i
$317$	−19.8788	+	22.0777i	−1.11651	+	1.24001i	−0.148546	+	0.988906i	$0.547459\pi$
$317$	−19.8788	+	22.0777i	−1.11651	+	1.24001i	−0.967961	+	0.251101i	$0.919207\pi$
$318$	0.326957	−	1.00627i	0.0183348	−	0.0564288i
$319$	21.6977	+	24.0978i	1.21484	+	1.34922i
$320$	21.4620	−	9.55549i	1.19976	−	0.534168i
$321$	17.9305	+	3.81124i	1.00078	+	0.212723i
$322$	−0.168334	+	1.60159i	−0.00938088	+	0.0892531i
$323$	−1.66893	−	15.8788i	−0.0928616	−	0.883519i
$324$	1.93282	−	0.410833i	0.107379	−	0.0228240i
$325$	−8.09614	+	5.88219i	−0.449093	+	0.326285i
$326$	−1.47611	+	1.07246i	−0.0817541	+	0.0593978i
$327$	−5.22718	+	1.11107i	−0.289064	+	0.0614423i
$328$	0.114151	+	1.08607i	0.00630294	+	0.0599684i
$329$	1.07681	−	10.2452i	0.0593664	−	0.564833i
$330$	−2.57830	−	0.548035i	−0.141931	−	0.0301683i
$331$	1.82751	−	0.813660i	0.100449	−	0.0447228i	−0.355897	−	0.934525i	$-0.615825\pi$
$331$	1.82751	−	0.813660i	0.100449	−	0.0447228i	0.456346	+	0.889802i	$0.349158\pi$
$332$	−5.85302	−	6.50044i	−0.321226	−	0.356758i
$333$	1.95388	−	6.01343i	0.107072	−	0.329534i
$334$	0.220440	−	0.244823i	0.0120619	−	0.0133961i
$335$	5.72417	+	9.91455i	0.312745	+	0.541690i
$336$	−5.21718	+	9.03642i	−0.284621	+	0.492977i
$337$	−6.02713	−	18.5496i	−0.328319	−	1.01046i	−0.969920	−	0.243423i	$-0.921730\pi$
$337$	−6.02713	−	18.5496i	−0.328319	−	1.01046i	0.641601	−	0.767038i	$-0.278270\pi$
$338$	1.27266	+	0.566623i	0.0692234	+	0.0308203i
$339$	−13.7822	−	10.0134i	−0.748549	−	0.543852i
$340$	12.4130			0.673189
$341$	29.9553	−	0.379458i	1.62217	−	0.0205488i
$342$	−1.24513			−0.0673289
$343$	−14.6210	−	10.6228i	−0.789460	−	0.573576i
$344$	−0.0512192	−	0.0228043i	−0.00276156	−	0.00122952i
$345$	3.75397	+	11.5535i	0.202107	+	0.622021i
$346$	−0.640870	+	1.11002i	−0.0344534	+	0.0596750i
$347$	13.3956	+	23.2018i	0.719112	+	1.24554i	0.961352	+	0.275323i	$0.0887847\pi$
$347$	13.3956	+	23.2018i	0.719112	+	1.24554i	−0.242240	+	0.970216i	$0.577882\pi$
$348$	−7.96844	+	8.84985i	−0.427153	+	0.474402i
$349$	−3.86202	+	11.8861i	−0.206729	+	0.636247i	0.792909	+	0.609340i	$0.208566\pi$
$349$	−3.86202	+	11.8861i	−0.206729	+	0.636247i	−0.999638	+	0.0269067i	$0.991434\pi$
$350$	1.40203	+	1.55711i	0.0749417	+	0.0832311i
$351$	−1.82895	+	0.814302i	−0.0976222	+	0.0434642i
$352$	−9.62855	−	2.04661i	−0.513204	−	0.109085i
$353$	−3.23032	+	30.7345i	−0.171933	+	1.63583i	0.479796	+	0.877380i	$0.340711\pi$
$353$	−3.23032	+	30.7345i	−0.171933	+	1.63583i	−0.651729	+	0.758452i	$0.725956\pi$
$354$	0.147580	+	1.40413i	0.00784381	+	0.0746289i
$355$	−22.7790	+	4.84183i	−1.20899	+	0.256978i
$356$	−9.57493	+	6.95660i	−0.507470	+	0.368699i
$357$	−4.34855	+	3.15941i	−0.230150	+	0.167213i
$358$	0.799450	−	0.169928i	0.0422522	−	0.00898099i
$359$	−1.24702	−	11.8646i	−0.0658152	−	0.626190i	−0.976860	−	0.213881i	$-0.931389\pi$
$359$	−1.24702	−	11.8646i	−0.0658152	−	0.626190i	0.911044	−	0.412308i	$-0.135277\pi$
$360$	0.203602	−	1.93715i	0.0107308	−	0.102097i
$361$	−44.5936	−	9.47867i	−2.34703	−	0.498877i
$362$	0.816391	−	0.363481i	0.0429086	−	0.0191041i
$363$	−12.0112	−	13.3398i	−0.630424	−	0.700157i
$364$	3.30755	−	10.1796i	0.173363	−	0.533556i
$365$	−6.50569	+	7.22530i	−0.340523	+	0.378190i
$366$	0.552737	+	0.957369i	0.0288920	+	0.0500425i
$367$	4.61495	−	7.99332i	0.240898	−	0.417248i	−0.720072	−	0.693899i	$-0.755891\pi$
$367$	4.61495	−	7.99332i	0.240898	−	0.417248i	0.960970	+	0.276651i	$0.0892247\pi$
$368$	4.57848	+	14.0911i	0.238670	+	0.734549i
$369$	−1.61956	−	0.721074i	−0.0843109	−	0.0375376i
$370$	−2.50597	−	1.82069i	−0.130279	−	0.0946532i
$371$	−18.4774			−0.959301
$372$	1.28851	+	10.9262i	0.0668061	+	0.566496i
$373$	−5.40979			−0.280108			−0.140054	−	0.990144i	$-0.544728\pi$
$373$	−5.40979			−0.280108			−0.140054	+	0.990144i	$0.544728\pi$
$374$	−1.33980	−	0.973418i	−0.0692792	−	0.0503343i
$375$	−0.00405365	−	0.00180480i	−0.000209330	−	9.31996e-5i
$376$	0.724768	+	2.23061i	0.0373770	+	0.115035i
$377$	6.03279	−	10.4491i	0.310704	−	0.538156i
$378$	0.209589	+	0.363019i	0.0107801	+	0.0186717i
$379$	0.636227	−	0.706602i	0.0326808	−	0.0362957i	−0.726583	−	0.687079i	$-0.758893\pi$
$379$	0.636227	−	0.706602i	0.0326808	−	0.0362957i	0.759264	+	0.650783i	$0.225559\pi$
$380$	15.5175	−	47.7578i	0.796028	−	2.44992i
$381$	−8.76841	−	9.73830i	−0.449219	−	0.498908i
$382$	0.893635	−	0.397872i	0.0457223	−	0.0203569i
$383$	−6.07176	−	1.29059i	−0.310253	−	0.0659462i	0.0501541	−	0.998741i	$-0.484029\pi$
$383$	−6.07176	−	1.29059i	−0.310253	−	0.0659462i	−0.360407	+	0.932795i	$0.617362\pi$
$384$	0.502786	−	4.78369i	0.0256577	−	0.244117i
$385$	4.81169	+	45.7802i	0.245227	+	2.33317i
$386$	0.0408339	−	0.00867951i	0.00207839	−	0.000441776i
$387$	0.0736346	−	0.0534987i	0.00374306	−	0.00271949i
$388$	3.79189	−	2.75497i	0.192504	−	0.139862i
$389$	24.9780	−	5.30923i	1.26643	−	0.269189i	0.474750	−	0.880120i	$-0.342538\pi$
$389$	24.9780	−	5.30923i	1.26643	−	0.269189i	0.791683	+	0.610932i	$0.209205\pi$
$390$	0.102520	+	0.975413i	0.00519130	+	0.0493919i
$391$	−0.797800	+	7.59056i	−0.0403465	+	0.383871i
$392$	−0.193024	−	0.0410285i	−0.00974918	−	0.00207225i
$393$	−7.12328	+	3.17149i	−0.359322	+	0.159980i
$394$	2.31787	+	2.57426i	0.116773	+	0.129689i
$395$	−5.51059	+	16.9598i	−0.277268	+	0.853343i
$396$	7.11418	−	7.90110i	0.357501	−	0.397045i
$397$	4.57234	+	7.91952i	0.229479	+	0.397469i	0.957654	−	0.287922i	$-0.0929644\pi$
$397$	4.57234	+	7.91952i	0.229479	+	0.397469i	−0.728175	+	0.685392i	$0.759631\pi$
$398$	1.06558	−	1.84565i	0.0534129	−	0.0925139i
$399$	6.71940	+	20.6802i	0.336391	+	1.03530i
$400$	17.6108	+	7.84082i	0.880538	+	0.392041i
$401$	−17.6288	−	12.8081i	−0.880341	−	0.639605i	0.0530004	−	0.998594i	$-0.483122\pi$
$401$	−17.6288	−	12.8081i	−0.880341	−	0.639605i	−0.933342	+	0.358989i	$0.883122\pi$
$402$	0.560925			0.0279764
$403$	−3.57858	−	10.5568i	−0.178262	−	0.525873i
$404$	−10.3049			−0.512689
$405$	2.55816	+	1.85861i	0.127116	+	0.0923551i
$406$	−2.30783	−	1.02751i	−0.114536	−	0.0509947i
$407$	−10.5130	−	32.3556i	−0.521109	−	1.60381i
$408$	0.611884	−	1.05981i	0.0302928	−	0.0524686i
$409$	6.07750	+	10.5265i	0.300513	+	0.520504i	0.976252	−	0.216637i	$-0.0695088\pi$
$409$	6.07750	+	10.5265i	0.300513	+	0.520504i	−0.675739	+	0.737141i	$0.736175\pi$
$410$	−0.581138	+	0.645420i	−0.0287004	+	0.0318750i
$411$	−4.71995	+	14.5265i	−0.232818	+	0.716540i
$412$	25.4809	+	28.2994i	1.25535	+	1.39421i
$413$	22.5247	−	10.0286i	1.10837	−	0.493476i
$414$	0.582204	+	0.123751i	0.0286138	+	0.00608205i
$415$	1.46314	−	13.9209i	0.0718229	−	0.683349i
$416$	0.382856	+	3.64263i	0.0187711	+	0.178595i
$417$	14.6083	−	3.10510i	0.715374	−	0.152057i
$418$	−5.42001	+	3.93787i	−0.265101	+	0.192607i
$419$	19.0466	−	13.8382i	0.930487	−	0.676038i	−0.0156251	−	0.999878i	$-0.504974\pi$
$419$	19.0466	−	13.8382i	0.930487	−	0.676038i	0.946112	+	0.323840i	$0.104974\pi$
$420$	−16.5358	+	3.51480i	−0.806866	+	0.171505i
$421$	1.19427	+	11.3627i	0.0582052	+	0.553785i	0.984301	+	0.176497i	$0.0564767\pi$
$421$	1.19427	+	11.3627i	0.0582052	+	0.553785i	−0.926096	+	0.377288i	$0.876857\pi$
$422$	0.0480561	−	0.457223i	0.00233933	−	0.0222573i
$423$	−3.72428	−	0.791620i	−0.181081	−	0.0384899i
$424$	3.84313	−	1.71107i	0.186639	−	0.0830969i
$425$	6.64477	+	7.37976i	0.322318	+	0.357971i
$426$	−0.352595	+	1.08518i	−0.0170833	+	0.0525769i
$427$	12.9179	−	14.3468i	0.625143	−	0.694292i
$428$	18.1111	+	31.3693i	0.875432	+	1.51629i
$429$	−5.38604	+	9.32890i	−0.260041	+	0.450404i
$430$	−0.0137787	−	0.0424065i	−0.000664469	−	0.00204502i
$431$	−33.4869	−	14.9093i	−1.61301	−	0.718157i	−0.615461	−	0.788167i	$-0.711030\pi$
$431$	−33.4869	−	14.9093i	−1.61301	−	0.718157i	−0.997546	+	0.0700099i	$0.977697\pi$
$432$	3.12002	+	2.26683i	0.150112	+	0.109063i
$433$	18.4277			0.885577			0.442788	−	0.896626i	$-0.353989\pi$
$433$	18.4277			0.885577			0.442788	+	0.896626i	$0.353989\pi$
$434$	−2.11991	+	0.976206i	−0.101759	+	0.0468594i
$435$	−19.0566			−0.913694
$436$	−8.54293	−	6.20680i	−0.409132	−	0.297252i
$437$	28.2066	+	12.5584i	1.34931	+	0.600749i
$438$	0.147207	+	0.453056i	0.00703381	+	0.0216478i
$439$	9.55628	−	16.5520i	0.456096	−	0.789982i	−0.542654	−	0.839956i	$-0.682581\pi$
$439$	9.55628	−	16.5520i	0.456096	−	0.789982i	0.998751	+	0.0499741i	$0.0159139\pi$
$440$	−5.24017	−	9.07625i	−0.249815	−	0.432693i
$441$	0.214358	−	0.238068i	0.0102075	−	0.0113366i
$442$	−0.190418	+	0.586046i	−0.00905725	+	0.0278754i
$443$	−6.25865	−	6.95094i	−0.297358	−	0.330249i	0.575889	−	0.817528i	$-0.304656\pi$
$443$	−6.25865	−	6.95094i	−0.297358	−	0.330249i	−0.873246	+	0.487279i	$0.837989\pi$
$444$	11.4138	−	5.08177i	0.541677	−	0.241170i
$445$	−18.5253	−	3.93768i	−0.878184	−	0.186664i
$446$	0.166651	−	1.58558i	0.00789117	−	0.0750794i
$447$	0.283797	+	2.70015i	0.0134231	+	0.127713i
$448$	−19.6626	+	4.17941i	−0.928969	+	0.197458i
$449$	6.33442	−	4.60222i	0.298940	−	0.217192i	−0.428196	−	0.903686i	$-0.640851\pi$
$449$	6.33442	−	4.60222i	0.298940	−	0.217192i	0.727136	+	0.686493i	$0.240851\pi$
$450$	0.626525	−	0.455197i	0.0295347	−	0.0214582i
$451$	−9.33037	+	1.98323i	−0.439350	+	0.0933867i
$452$	−3.51871	−	33.4783i	−0.165506	−	1.57468i
$453$	1.21159	−	11.5275i	0.0569255	−	0.541610i
$454$	−0.493461	−	0.104888i	−0.0231593	−	0.00492266i
$455$	15.6472	−	6.96660i	0.733554	−	0.326599i
$456$	−3.31262	−	3.67904i	−0.155128	−	0.172287i
$457$	7.07001	−	21.7593i	0.330721	−	1.01786i	−0.638070	−	0.769978i	$-0.720267\pi$
$457$	7.07001	−	21.7593i	0.330721	−	1.01786i	0.968791	−	0.247877i	$-0.0797329\pi$
$458$	0.730635	−	0.811453i	0.0341403	−	0.0379167i
$459$	0.993323	+	1.72049i	0.0463644	+	0.0803054i
$460$	−12.0023	+	20.7886i	−0.559610	+	0.969273i
$461$	−10.7439	−	33.0664i	−0.500395	−	1.54006i	−0.808378	−	0.588664i	$-0.799654\pi$
$461$	−10.7439	−	33.0664i	−0.500395	−	1.54006i	0.307983	−	0.951392i	$-0.400346\pi$
$462$	2.06042	+	0.917359i	0.0958595	+	0.0426794i
$463$	−23.9223	−	17.3805i	−1.11176	−	0.807742i	−0.128821	−	0.991668i	$-0.541119\pi$
$463$	−23.9223	−	17.3805i	−1.11176	−	0.807742i	−0.982940	+	0.183926i	$0.941119\pi$
$464$	−23.2421			−1.07899
$465$	−11.6138	+	13.2317i	−0.538576	+	0.613604i
$466$	−0.0782124			−0.00362312
$467$	25.6178	+	18.6124i	1.18545	+	0.861280i	0.992776	−	0.119983i	$-0.0382839\pi$
$467$	25.6178	+	18.6124i	1.18545	+	0.861280i	0.192674	+	0.981263i	$0.438284\pi$
$468$	−3.61400	−	1.60906i	−0.167057	−	0.0743787i
$469$	−3.02706	−	9.31634i	−0.139777	−	0.430188i
$470$	−0.932631	+	1.61536i	−0.0430191	+	0.0745112i
$471$	0.473856	+	0.820743i	0.0218341	+	0.0378178i
$472$	−3.75622	+	4.17171i	−0.172894	+	0.192018i
$473$	0.151333	−	0.465756i	0.00695831	−	0.0214155i
$474$	0.584641	+	0.649310i	0.0268535	+	0.0298238i
$475$	36.6995	−	16.3397i	1.68389	−	0.749716i
$476$	−10.3891	−	2.20827i	−0.476183	−	0.101216i
$477$	−0.713856	+	6.79189i	−0.0326852	+	0.310979i
$478$	0.238198	+	2.26630i	0.0108949	+	0.103658i
$479$	22.1613	−	4.71053i	1.01258	−	0.215230i	0.328394	−	0.944541i	$-0.393493\pi$
$479$	22.1613	−	4.71053i	1.01258	−	0.215230i	0.684182	+	0.729311i	$0.260159\pi$
$480$	4.68011	−	3.40030i	0.213617	−	0.155202i
$481$	−10.2411	+	7.44058i	−0.466953	+	0.339261i
$482$	−1.18293	+	0.251440i	−0.0538811	+	0.0114528i
$483$	−1.08652	−	10.3376i	−0.0494385	−	0.470376i
$484$	3.70763	−	35.2757i	0.168529	−	1.60344i
$485$	7.33645	+	1.55941i	0.333131	+	0.0708092i
$486$	0.141535	−	0.0630152i	0.00642014	−	0.00285843i
$487$	9.59018	+	10.6510i	0.434572	+	0.482641i	0.920158	−	0.391548i	$-0.128060\pi$
$487$	9.59018	+	10.6510i	0.434572	+	0.482641i	−0.485585	+	0.874189i	$0.661394\pi$
$488$	−1.35824	+	4.18024i	−0.0614847	+	0.189231i
$489$	7.88023	−	8.75189i	0.356356	−	0.395774i
$490$	−0.0784694	−	0.135913i	−0.00354489	−	0.00613992i
$491$	−7.87212	+	13.6349i	−0.355264	+	0.615335i	−0.987163	−	0.159715i	$-0.948942\pi$
$491$	−7.87212	+	13.6349i	−0.355264	+	0.615335i	0.631899	+	0.775051i	$0.282276\pi$
$492$	−1.08252	−	3.33165i	−0.0488037	−	0.150202i
$493$	−10.9377	−	4.86979i	−0.492610	−	0.219324i
$494$	2.01671	+	1.46523i	0.0907363	+	0.0659237i
$495$	17.0136			0.764706
$496$	−14.1646	+	16.1378i	−0.636008	+	0.724609i
$497$	19.9263			0.893818
$498$	−0.554846	−	0.403120i	−0.0248633	−	0.0180642i
$499$	14.2464	+	6.34290i	0.637756	+	0.283947i	0.700032	−	0.714112i	$-0.253169\pi$
$499$	14.2464	+	6.34290i	0.637756	+	0.283947i	−0.0622756	+	0.998059i	$0.519836\pi$
$500$	−0.00270947	−	0.00833890i	−0.000121171	−	0.000372927i
$501$	−1.06320	+	1.84152i	−0.0475005	+	0.0822733i
$502$	−1.73279	−	3.00129i	−0.0773384	−	0.133954i
$503$	23.5418	−	26.1458i	1.04968	−	1.16578i	0.0638590	−	0.997959i	$-0.479659\pi$
$503$	23.5418	−	26.1458i	1.04968	−	1.16578i	0.985817	−	0.167824i	$-0.0536741\pi$
$504$	−0.515023	+	1.58508i	−0.0229410	+	0.0706050i
$505$	−11.0342	−	12.2547i	−0.491013	−	0.545326i
$506$	2.92569	−	1.30260i	0.130063	−	0.0579078i
$507$	−8.79535	−	1.86951i	−0.390615	−	0.0830279i
$508$	2.70664	−	25.7520i	0.120088	−	1.14256i
$509$	1.45667	+	13.8593i	0.0645658	+	0.614303i	0.978186	+	0.207733i	$0.0666085\pi$
$509$	1.45667	+	13.8593i	0.0645658	+	0.614303i	−0.913620	+	0.406570i	$0.866725\pi$
$510$	0.951978	−	0.202349i	0.0421543	−	0.00896017i
$511$	6.73033	−	4.88987i	0.297732	−	0.216315i
$512$	9.55188	−	6.93985i	0.422137	−	0.306701i
$513$	7.86116	−	1.67094i	0.347079	−	0.0737738i
$514$	−0.337692	−	3.21292i	−0.0148949	−	0.141716i
$515$	−6.36973	+	60.6040i	−0.280684	+	2.67053i
$516$	0.175920	+	0.0373930i	0.00774445	+	0.00164613i
$517$	−18.7153	+	8.33257i	−0.823096	+	0.366466i
$518$	1.77347	+	1.96964i	0.0779220	+	0.0865411i
$519$	2.55652	−	7.86817i	0.112219	−	0.345375i
$520$	−2.60934	+	2.89797i	−0.114427	+	0.127084i
$521$	10.2713	+	17.7904i	0.449993	+	0.779411i	0.998385	−	0.0568107i	$-0.0180931\pi$
$521$	10.2713	+	17.7904i	0.449993	+	0.779411i	−0.548392	+	0.836221i	$0.684760\pi$
$522$	−0.466851	+	0.808610i	−0.0204335	+	0.0353919i
$523$	−2.63918	−	8.12256i	−0.115403	−	0.355175i	0.876628	−	0.481169i	$-0.159788\pi$
$523$	−2.63918	−	8.12256i	−0.115403	−	0.355175i	−0.992031	+	0.125995i	$0.959788\pi$
$524$	−14.0756	−	6.26685i	−0.614894	−	0.273769i
$525$	−10.9414	−	7.94937i	−0.477521	−	0.346939i
$526$	4.58788			0.200041
$527$	−10.0471	+	4.62662i	−0.437658	+	0.201539i
$528$	20.7505			0.903048
$529$	6.66655	+	4.84353i	0.289850	+	0.210588i
$530$	3.05638	+	1.36079i	0.132761	+	0.0591090i
$531$	−2.81608	−	8.66699i	−0.122207	−	0.376115i
$532$	−21.4835	+	37.2105i	−0.931427	+	1.61328i
$533$	1.77463	+	3.07376i	0.0768680	+	0.133139i
$534$	−0.620919	+	0.689601i	−0.0268698	+	0.0298419i
$535$	−17.9118	+	55.1269i	−0.774395	+	2.38334i
$536$	1.49232	+	1.65739i	0.0644584	+	0.0715883i
$537$	−4.81931	+	2.14569i	−0.207968	+	0.0925935i
$538$	−2.06185	−	0.438260i	−0.0888928	−	0.0188947i
$539$	0.180173	−	1.71424i	0.00776062	−	0.0738373i
$540$	0.653116	+	6.21398i	0.0281056	+	0.267407i
$541$	5.40363	−	1.14858i	0.232320	−	0.0493812i	−0.0902803	−	0.995916i	$-0.528776\pi$
$541$	5.40363	−	1.14858i	0.232320	−	0.0493812i	0.322600	+	0.946535i	$0.395443\pi$
$542$	3.20383	−	2.32772i	0.137616	−	0.0999840i
$543$	−4.66652	+	3.39043i	−0.200260	+	0.145497i
$544$	3.55512	−	0.755664i	0.152424	−	0.0323988i
$545$	−1.76631	−	16.8053i	−0.0756604	−	0.719861i
$546$	0.0877213	−	0.834612i	0.00375413	−	0.0357181i
$547$	17.5047	+	3.72075i	0.748449	+	0.159088i	0.566318	−	0.824187i	$-0.308367\pi$
$547$	17.5047	+	3.72075i	0.748449	+	0.159088i	0.182130	+	0.983274i	$0.441701\pi$
$548$	−27.5722	+	12.2759i	−1.17783	+	0.524402i
$549$	−4.77449	−	5.30261i	−0.203770	−	0.226310i
$550$	1.28763	−	3.96291i	0.0549047	−	0.168979i
$551$	−32.4093	+	35.9941i	−1.38068	+	1.53340i
$552$	1.18328	+	2.04950i	0.0503637	+	0.0872325i
$553$	7.62926	−	13.2143i	0.324429	−	0.561927i
$554$	0.389991	+	1.20027i	0.0165691	+	0.0509945i
$555$	18.2648	+	8.13202i	0.775298	+	0.345185i
$556$	23.8748	+	17.3461i	1.01252	+	0.735638i
$557$	−6.20674			−0.262988			−0.131494	−	0.991317i	$-0.541977\pi$
$557$	−6.20674			−0.262988			−0.131494	+	0.991317i	$0.541977\pi$
$558$	0.276930	+	0.816946i	0.0117234	+	0.0345841i
$559$	−0.182220			−0.00770710
$560$	−26.6927	−	19.3934i	−1.12797	−	0.819521i
$561$	9.76514	+	4.34772i	0.412285	+	0.183561i
$562$	−1.32273	−	4.07096i	−0.0557961	−	0.171723i
$563$	−14.6137	+	25.3117i	−0.615894	+	1.06676i	0.374333	+	0.927294i	$0.377872\pi$
$563$	−14.6137	+	25.3117i	−0.615894	+	1.06676i	−0.990227	+	0.139465i	$0.955462\pi$
$564$	−3.76179	−	6.51561i	−0.158400	−	0.274357i
$565$	36.0448	−	40.0318i	1.51642	−	1.68415i
$566$	0.139531	−	0.429432i	0.00586492	−	0.0180504i
$567$	−1.81041	−	2.01066i	−0.0760301	−	0.0844399i
$568$	−4.14448	+	1.84524i	−0.173898	+	0.0774246i
$569$	−37.3994	−	7.94948i	−1.56786	−	0.333260i	−0.659586	−	0.751629i	$-0.729268\pi$
$569$	−37.3994	−	7.94948i	−1.56786	−	0.333260i	−0.908277	+	0.418369i	$0.862602\pi$
$570$	0.411546	−	3.91560i	0.0172378	−	0.164006i
$571$	−0.962260	−	9.15529i	−0.0402693	−	0.383137i	−0.996032	−	0.0889976i	$-0.971634\pi$
$571$	−0.962260	−	9.15529i	−0.0402693	−	0.383137i	0.955763	−	0.294139i	$-0.0950330\pi$
$572$	−20.8205	+	4.42553i	−0.870548	+	0.185041i
$573$	−5.10805	+	3.71122i	−0.213392	+	0.155038i
$574$	0.601205	−	0.436801i	0.0250938	−	0.0182317i
$575$	−18.7841	+	3.99269i	−0.783352	+	0.166507i
$576$	0.776613	+	7.38898i	0.0323589	+	0.307874i
$577$	0.924473	−	8.79577i	0.0384863	−	0.366173i	−0.958281	−	0.285828i	$-0.907731\pi$
$577$	0.924473	−	8.79577i	0.0384863	−	0.366173i	0.996767	−	0.0803445i	$-0.0256020\pi$
$578$	−1.97813	−	0.420465i	−0.0822794	−	0.0174890i
$579$	−0.246158	+	0.109597i	−0.0102300	+	0.00455468i
$580$	−25.1966	−	27.9837i	−1.04623	−	1.16196i
$581$	−3.70110	+	11.3908i	−0.153548	+	0.472571i
$582$	0.245898	−	0.273098i	0.0101928	−	0.0113203i
$583$	18.3727	+	31.8225i	0.760921	+	1.31795i
$584$	−0.947025	+	1.64030i	−0.0391882	+	0.0678759i
$585$	−1.95625	−	6.02071i	−0.0808809	−	0.248926i
$586$	−0.382999	−	0.170522i	−0.0158216	−	0.00704421i
$587$	2.84133	+	2.06435i	0.117274	+	0.0852047i	0.644876	−	0.764287i	$-0.276909\pi$
$587$	2.84133	+	2.06435i	0.117274	+	0.0852047i	−0.527602	+	0.849492i	$0.676909\pi$
$588$	0.633016			0.0261051
$589$	5.24063	+	44.4390i	0.215936	+	1.83108i
$590$	−4.46441			−0.183797
$591$	−18.0886	−	13.1421i	−0.744064	−	0.540594i
$592$	22.2764	+	9.91811i	0.915556	+	0.407632i
$593$	8.01108	+	24.6556i	0.328976	+	1.01248i	0.969614	+	0.244640i	$0.0786699\pi$
$593$	8.01108	+	24.6556i	0.328976	+	1.01248i	−0.640638	+	0.767843i	$0.721330\pi$
$594$	0.416802	−	0.721923i	0.0171016	−	0.0296208i
$595$	−8.49819	−	14.7193i	−0.348392	−	0.603432i
$596$	−3.58980	+	3.98688i	−0.147044	+	0.163309i
$597$	−4.25077	+	13.0825i	−0.173973	+	0.535432i
$598$	−0.797359	−	0.885557i	−0.0326064	−	0.0362131i
$599$	−5.39048	+	2.39999i	−0.220249	+	0.0980611i	−0.513895	−	0.857853i	$-0.671798\pi$
$599$	−5.39048	+	2.39999i	−0.220249	+	0.0980611i	0.293646	+	0.955914i	$0.405131\pi$
$600$	3.01183	+	0.640185i	0.122958	+	0.0261354i
$601$	−1.77119	+	16.8517i	−0.0722482	+	0.687395i	0.897121	+	0.441786i	$0.145655\pi$
$601$	−1.77119	+	16.8517i	−0.0722482	+	0.687395i	−0.969369	+	0.245610i	$0.921012\pi$
$602$	0.00398802	+	0.0379435i	0.000162540	+	0.00154646i
$603$	−3.54142	+	0.752752i	−0.144218	+	0.0306544i
$604$	18.5296	−	13.4625i	0.753957	−	0.547782i
$605$	45.9201	−	33.3629i	1.86692	−	1.35639i
$606$	−0.790306	+	0.167985i	−0.0321040	+	0.00682391i
$607$	−2.23801	−	21.2933i	−0.0908381	−	0.864267i	−0.941150	−	0.337988i	$-0.890254\pi$
$607$	−2.23801	−	21.2933i	−0.0908381	−	0.864267i	0.850312	−	0.526278i	$-0.176413\pi$
$608$	1.53690	−	14.6226i	0.0623295	−	0.593026i
$609$	15.9495	+	3.39017i	0.646305	+	0.137376i
$610$	−3.19336	+	1.42178i	−0.129296	+	0.0575661i
$611$	5.10060	+	5.66479i	0.206348	+	0.229173i
$612$	−1.21308	+	3.73348i	−0.0490358	+	0.150917i
$613$	−23.2657	+	25.8392i	−0.939692	+	1.04363i	0.0592770	+	0.998242i	$0.481120\pi$
$613$	−23.2657	+	25.8392i	−0.939692	+	1.04363i	−0.998969	+	0.0453923i	$0.985546\pi$
$614$	−1.68860	−	2.92474i	−0.0681463	−	0.118033i
$615$	2.80289	−	4.85475i	0.113023	−	0.195762i
$616$	2.77111	+	8.52861i	0.111651	+	0.343628i
$617$	3.57802	+	1.59304i	0.144046	+	0.0641333i	0.477494	−	0.878635i	$-0.341545\pi$
$617$	3.57802	+	1.59304i	0.144046	+	0.0641333i	−0.333448	+	0.942769i	$0.608212\pi$
$618$	2.41550	+	1.75496i	0.0971657	+	0.0705950i
$619$	−1.13132			−0.0454718			−0.0227359	−	0.999742i	$-0.507238\pi$
$619$	−1.13132			−0.0454718			−0.0227359	+	0.999742i	$0.507238\pi$
$620$	−34.7858	+	0.440648i	−1.39703	+	0.0176969i
$621$	−3.84183			−0.154167
$622$	1.57299	+	1.14285i	0.0630713	+	0.0458240i
$623$	14.8043	+	6.59130i	0.593122	+	0.264075i
$624$	−2.38591	−	7.34308i	−0.0955129	−	0.293959i
$625$	12.5035	−	21.6567i	0.500140	−	0.866268i
$626$	1.99567	+	3.45660i	0.0797631	+	0.138154i
$627$	28.9348	−	32.1354i	1.15555	−	1.28336i
$628$	−0.578689	+	1.78102i	−0.0230922	+	0.0710705i
$629$	8.40519	+	9.33490i	0.335137	+	0.372207i
$630$	−1.21087	+	0.539115i	−0.0482423	+	0.0214788i
$631$	−2.07115	−	0.440237i	−0.0824512	−	0.0175255i	0.166501	−	0.986041i	$-0.446753\pi$
$631$	−2.07115	−	0.440237i	−0.0824512	−	0.0175255i	−0.248953	+	0.968516i	$0.580086\pi$
$632$	−0.363127	+	3.45493i	−0.0144444	+	0.137430i
$633$	0.310182	+	2.95118i	0.0123286	+	0.117299i
$634$	−4.50212	+	0.956955i	−0.178802	+	0.0380055i
$635$	33.5225	−	24.3556i	1.33030	−	0.966521i
$636$	−10.9174	+	7.93197i	−0.432904	+	0.314523i
$637$	−0.627343	+	0.133346i	−0.0248562	+	0.00528335i
$638$	0.525135	+	4.99632i	0.0207903	+	0.197806i
$639$	0.769832	−	7.32446i	0.0304541	−	0.289751i
$640$	14.8773	+	3.16226i	0.588075	+	0.124999i
$641$	7.86882	−	3.50342i	0.310800	−	0.138377i	−0.245409	−	0.969420i	$-0.578922\pi$
$641$	7.86882	−	3.50342i	0.310800	−	0.138377i	0.556209	+	0.831043i	$0.312256\pi$
$642$	1.90034	+	2.11054i	0.0750004	+	0.0832964i
$643$	−14.2096	+	43.7326i	−0.560371	+	1.72464i	0.120949	+	0.992659i	$0.461406\pi$
$643$	−14.2096	+	43.7326i	−0.560371	+	1.72464i	−0.681320	+	0.731986i	$0.738594\pi$
$644$	13.7436	−	15.2639i	0.541575	−	0.601480i
$645$	0.143901	+	0.249244i	0.00566610	+	0.00981397i
$646$	1.23682	−	2.14223i	0.0486619	−	0.0842849i
$647$	−6.55674	−	20.1796i	−0.257772	−	0.793341i	−0.993271	−	0.115815i	$-0.963052\pi$
$647$	−6.55674	−	20.1796i	−0.257772	−	0.793341i	0.735499	−	0.677526i	$-0.236948\pi$
$648$	0.562741	+	0.250548i	0.0221066	+	0.00984247i
$649$	−39.6686	−	28.8210i	−1.55713	−	1.13132i
$650$	−1.55043			−0.0608129
$651$	12.0741	−	9.00819i	0.473221	−	0.353059i
$652$	23.2710			0.911361
$653$	4.93494	+	3.58544i	0.193119	+	0.140309i	0.680143	−	0.733079i	$-0.261918\pi$
$653$	4.93494	+	3.58544i	0.193119	+	0.140309i	−0.487024	+	0.873389i	$0.661918\pi$
$654$	−0.756354	−	0.336751i	−0.0295758	−	0.0131680i
$655$	−7.61906	−	23.4491i	−0.297701	−	0.916231i
$656$	3.41851	−	5.92103i	0.133470	−	0.231177i
$657$	−1.53739	−	2.66283i	−0.0599791	−	0.103887i
$658$	1.06794	−	1.18607i	0.0416327	−	0.0462378i
$659$	−2.17718	+	6.70068i	−0.0848110	+	0.261021i	−0.984465	−	0.175583i	$-0.943819\pi$
$659$	−2.17718	+	6.70068i	−0.0848110	+	0.261021i	0.899654	+	0.436604i	$0.143819\pi$
$660$	22.4954	+	24.9837i	0.875634	+	0.972490i
$661$	25.9098	−	11.5358i	1.00777	−	0.448690i	0.164617	−	0.986358i	$-0.447361\pi$
$661$	25.9098	−	11.5358i	1.00777	−	0.448690i	0.843157	+	0.537668i	$0.180695\pi$
$662$	0.303156	+	0.0644378i	0.0117825	+	0.00250445i
$663$	0.415745	−	3.95555i	0.0161462	−	0.153621i
$664$	−0.285033	−	2.71191i	−0.0110614	−	0.105243i
$665$	−67.2546	+	14.2954i	−2.60802	+	0.554352i
$666$	0.792512	−	0.575793i	0.0307092	−	0.0223115i
$667$	18.7315	−	13.6092i	0.725286	−	0.526951i
$668$	−4.10996	+	0.873599i	−0.159019	+	0.0338006i
$669$	1.07566	+	10.2343i	0.0415875	+	0.395679i
$670$	−0.185400	+	1.76396i	−0.00716262	+	0.0681478i
$671$	−37.5533	−	7.98221i	−1.44973	−	0.308150i
$672$	−4.52194	+	2.01330i	−0.174438	+	0.0776647i
$673$	−18.8787	−	20.9669i	−0.727719	−	0.808214i	0.259809	−	0.965660i	$-0.416341\pi$
$673$	−18.8787	−	20.9669i	−0.727719	−	0.808214i	−0.987528	+	0.157446i	$0.949674\pi$
$674$	0.933777	−	2.87387i	0.0359677	−	0.110697i
$675$	−3.34471	+	3.71468i	−0.128738	+	0.142978i
$676$	−8.88393	−	15.3874i	−0.341690	−	0.591824i
$677$	−9.19983	+	15.9346i	−0.353578	+	0.612415i	−0.986874	−	0.161495i	$-0.948368\pi$
$677$	−9.19983	+	15.9346i	−0.353578	+	0.612415i	0.633295	+	0.773910i	$0.281702\pi$
$678$	−0.815599	−	2.51016i	−0.0313229	−	0.0964020i
$679$	−5.86284	−	2.61031i	−0.224995	−	0.100174i
$680$	3.13059	+	2.27451i	0.120053	+	0.0872234i
$681$	3.25624			0.124779
$682$	3.78916	+	2.68032i	0.145094	+	0.102635i
$683$	29.2656			1.11982			0.559909	−	0.828554i	$-0.310836\pi$
$683$	29.2656			1.11982			0.559909	+	0.828554i	$0.310836\pi$
$684$	12.8477	+	9.33442i	0.491245	+	0.356910i
$685$	−44.1219	−	19.6444i	−1.68581	−	0.750572i
$686$	−0.865235	−	2.66292i	−0.0330348	−	0.101671i
$687$	−3.52393	+	6.10363i	−0.134446	+	0.232868i
$688$	0.175507	+	0.303987i	0.00669114	+	0.0115894i
$689$	9.14869	−	10.1607i	0.348537	−	0.387090i
$690$	−0.581598	+	1.78997i	−0.0221411	+	0.0681432i
$691$	8.75489	+	9.72329i	0.333052	+	0.369891i	0.886289	−	0.463132i	$-0.153274\pi$
$691$	8.75489	+	9.72329i	0.333052	+	0.369891i	−0.553238	+	0.833024i	$0.686608\pi$
$692$	14.9343	−	6.64917i	0.567716	−	0.252763i
$693$	−14.2396	−	3.02672i	−0.540918	−	0.114976i
$694$	−0.433869	+	4.12799i	−0.0164694	+	0.156696i
$695$	4.93629	+	46.9657i	0.187244	+	1.78151i
$696$	−3.63127	+	0.771851i	−0.137643	+	0.0292569i
$697$	2.84935	−	2.07017i	0.107927	−	0.0784133i
$698$	−1.56647	+	1.13811i	−0.0592918	+	0.0430780i
$699$	0.493796	−	0.104960i	0.0186771	−	0.00396994i
$700$	−2.79341	−	26.5775i	−0.105581	−	1.00454i
$701$	2.99463	−	28.4920i	0.113105	−	1.07613i	−0.779845	−	0.625972i	$-0.784702\pi$
$701$	2.99463	−	28.4920i	0.113105	−	1.07613i	0.892951	−	0.450154i	$-0.148631\pi$
$702$	−0.303395	−	0.0644887i	−0.0114509	−	0.00243397i
$703$	46.4224	−	20.6686i	1.75086	−	0.779531i
$704$	26.7491	+	29.7078i	1.00814	+	1.11966i
$705$	3.72040	−	11.4502i	0.140118	−	0.431240i
$706$	−3.20372	+	3.55809i	−0.120574	+	0.133911i
$707$	7.05496	+	12.2195i	0.265329	+	0.459563i
$708$	9.00364	−	15.5948i	0.338378	−	0.586087i
$709$	13.5244	+	41.6238i	0.507919	+	1.56321i	0.795807	+	0.605551i	$0.207047\pi$
$709$	13.5244	+	41.6238i	0.507919	+	1.56321i	−0.287887	+	0.957664i	$0.592953\pi$
$710$	−3.29605	−	1.46749i	−0.123698	−	0.0550741i
$711$	−4.56251	−	3.31486i	−0.171107	−	0.124317i
$712$	−3.68952			−0.138271
$713$	1.96627	−	21.2999i	0.0736375	−	0.797686i
$714$	−0.832758			−0.0311652
$715$	−27.5567	−	20.0211i	−1.03056	−	0.748747i
$716$	−9.52293	−	4.23988i	−0.355889	−	0.158452i
$717$	−4.54520	−	13.9887i	−0.169744	−	0.522417i
$718$	0.924147	−	1.60067i	0.0344889	−	0.0597365i
$719$	1.30460	+	2.25963i	0.0486533	+	0.0842700i	0.889326	−	0.457273i	$-0.151174\pi$
$719$	1.30460	+	2.25963i	0.0486533	+	0.0842700i	−0.840673	+	0.541543i	$0.817840\pi$
$720$	−8.15982	+	9.06239i	−0.304098	+	0.337735i
$721$	16.1126	−	49.5895i	0.600065	−	1.84681i
$722$	−4.72619	−	5.24897i	−0.175891	−	0.195346i
$723$	7.13105	−	3.17495i	0.265207	−	0.118078i
$724$	−11.1488	−	2.36974i	−0.414340	−	0.0880708i
$725$	3.14890	−	29.9598i	0.116947	−	1.11268i
$726$	−0.290698	−	2.76581i	−0.0107888	−	0.102649i
$727$	43.0047	−	9.14093i	1.59496	−	0.339018i	0.677088	−	0.735902i	$-0.263242\pi$
$727$	43.0047	−	9.14093i	1.59496	−	0.339018i	0.917869	+	0.396884i	$0.129908\pi$
$728$	2.69944	−	1.96126i	0.100048	−	0.0726891i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.47340	+	0.313180i	−0.0545328	+	0.0115913i
$731$	0.0189008	+	0.179829i	0.000699071	+	0.00665121i
$732$	1.47380	−	14.0222i	0.0544731	−	0.518277i
$733$	12.8604	+	2.73357i	0.475011	+	0.100967i	0.439195	−	0.898392i	$-0.355264\pi$
$733$	12.8604	+	2.73357i	0.475011	+	0.100967i	0.0358157	+	0.999358i	$0.488597\pi$
$734$	1.30635	−	0.581624i	0.0482182	−	0.0214681i
$735$	0.677811	+	0.752786i	0.0250014	+	0.0277669i
$736$	−2.17195	+	6.68458i	−0.0800592	+	0.246397i
$737$	−13.0350	+	14.4768i	−0.480151	+	0.533261i
$738$	−0.137331	−	0.237865i	−0.00505523	−	0.00875592i
$739$	−25.1989	+	43.6458i	−0.926958	+	1.60554i	−0.138576	+	0.990352i	$0.544252\pi$
$739$	−25.1989	+	43.6458i	−0.926958	+	1.60554i	−0.788382	+	0.615186i	$0.789081\pi$
$740$	12.2083	+	37.5732i	0.448785	+	1.38122i
$741$	−14.6989	−	6.54437i	−0.539977	−	0.240413i
$742$	−2.31597	−	1.68265i	−0.0850218	−	0.0617719i
$743$	16.9568			0.622084			0.311042	−	0.950396i	$-0.399322\pi$
$743$	16.9568			0.622084			0.311042	+	0.950396i	$0.399322\pi$
$744$	−1.67710	+	2.99171i	−0.0614856	+	0.109681i
$745$	−8.58505			−0.314532
$746$	−0.678063	−	0.492642i	−0.0248257	−	0.0180369i
$747$	4.04402	+	1.80051i	0.147963	+	0.0658773i
$748$	6.52705	+	20.0882i	0.238653	+	0.734497i
$749$	24.7984	−	42.9521i	0.906114	−	1.56944i
$750$	−0.000343731	0	0.000595359i	−1.25513e−5	0	2.17395e-5i
$751$	−24.1437	+	26.8143i	−0.881016	+	0.978467i	−0.999896	−	0.0144417i	$-0.995403\pi$
$751$	−24.1437	+	26.8143i	−0.881016	+	0.978467i	0.118880	+	0.992909i	$0.462070\pi$
$752$	4.53754	−	13.9651i	0.165467	−	0.509255i
$753$	14.9677	+	16.6233i	0.545454	+	0.605788i
$754$	1.70770	−	0.760316i	0.0621906	−	0.0276891i
$755$	35.8505	+	7.62026i	1.30473	+	0.277330i
$756$	0.558839	−	5.31700i	0.0203248	−	0.193377i
$757$	2.65259	+	25.2377i	0.0964101	+	0.917280i	0.930658	+	0.365891i	$0.119236\pi$
$757$	2.65259	+	25.2377i	0.0964101	+	0.917280i	−0.834248	+	0.551390i	$0.814098\pi$
$758$	0.144091	−	0.0306276i	0.00523363	−	0.00111244i
$759$	−16.7234	+	12.1502i	−0.607020	+	0.441026i
$760$	12.6645	−	9.20129i	0.459389	−	0.333766i
$761$	17.0565	−	3.62547i	0.618297	−	0.131423i	0.111894	−	0.993720i	$-0.464308\pi$
$761$	17.0565	−	3.62547i	0.618297	−	0.131423i	0.506403	+	0.862297i	$0.330975\pi$
$762$	−0.212215	−	2.01909i	−0.00768775	−	0.0731440i
$763$	−1.51134	+	14.3795i	−0.0547143	+	0.520572i
$764$	−12.2036	−	2.59396i	−0.441511	−	0.0938461i
$765$	−5.73879	+	2.55507i	−0.207486	+	0.0923789i
$766$	−0.643508	−	0.714688i	−0.0232509	−	0.0258227i
$767$	−5.63789	+	17.3516i	−0.203572	+	0.626531i
$768$	−9.44420	+	10.4888i	−0.340788	+	0.378484i
$769$	21.6229	+	37.4520i	0.779742	+	1.35055i	0.932090	+	0.362226i	$0.117983\pi$
$769$	21.6229	+	37.4520i	0.779742	+	1.35055i	−0.152348	+	0.988327i	$0.548684\pi$
$770$	−3.56587	+	6.17627i	−0.128505	+	0.222577i
$771$	6.44371	+	19.8317i	0.232064	+	0.714221i
$772$	−0.486408	−	0.216563i	−0.0175062	−	0.00779426i
$773$	−25.0464	−	18.1973i	−0.900858	−	0.654512i	0.0378283	−	0.999284i	$-0.487956\pi$
$773$	−25.0464	−	18.1973i	−0.900858	−	0.654512i	−0.938686	+	0.344773i	$0.887956\pi$
$774$	0.0141012			0.000506858
$775$	−18.8831	−	20.4449i	−0.678300	−	0.734404i
$776$	1.46114			0.0524517
$777$	−13.8401	−	10.0554i	−0.496511	−	0.360736i
$778$	3.61423	+	1.60916i	0.129576	+	0.0576911i
$779$	−4.40282	−	13.5505i	−0.157748	−	0.485497i
$780$	6.25458	−	10.8332i	0.223950	−	0.387892i
$781$	−19.8134	−	34.3178i	−0.708979	−	1.22799i
$782$	−0.791230	+	0.878750i	−0.0282943	+	0.0314240i
$783$	1.86234	−	5.73169i	0.0665545	−	0.204834i
$784$	0.826683	+	0.918125i	0.0295244	+	0.0327902i
$785$	−2.73764	+	1.21888i	−0.0977106	+	0.0435035i
$786$	−1.18164	−	0.251166i	−0.0421478	−	0.00895880i
$787$	−1.91586	+	18.2282i	−0.0682929	+	0.649764i	0.905814	+	0.423676i	$0.139260\pi$
$787$	−1.91586	+	18.2282i	−0.0682929	+	0.649764i	−0.974107	+	0.226088i	$0.927406\pi$
$788$	−4.61814	−	43.9387i	−0.164514	−	1.56525i
$789$	−28.9657	+	6.15685i	−1.03121	+	0.219190i
$790$	−2.23514	+	1.62393i	−0.0795229	+	0.0577768i
$791$	−37.2894	+	27.0924i	−1.32586	+	0.963293i
$792$	3.24198	−	0.689104i	0.115199	−	0.0244863i
$793$	1.49322	+	14.2070i	0.0530257	+	0.504506i
$794$	−0.148093	+	1.40901i	−0.00525563	+	0.0500040i
$795$	−21.1227	−	4.48977i	−0.749146	−	0.159236i
$796$	−24.8314	+	11.0557i	−0.880127	+	0.391858i
$797$	−20.7534	−	23.0490i	−0.735125	−	0.816439i	0.253422	−	0.967356i	$-0.418444\pi$
$797$	−20.7534	−	23.0490i	−0.735125	−	0.816439i	−0.988546	+	0.150917i	$0.951777\pi$
$798$	−1.04103	+	3.20396i	−0.0368520	+	0.113419i
$799$	5.06139	−	5.62124i	0.179059	−	0.198865i
$800$	4.57243	+	7.91968i	0.161660	+	0.280003i
$801$	2.99476	−	5.18707i	0.105815	−	0.183276i
$802$	−1.04323	−	3.21073i	−0.0368378	−	0.113375i
$803$	−15.1137	−	6.72905i	−0.533351	−	0.237463i
$804$	−5.78784	−	4.20511i	−0.204121	−	0.148303i
$805$	32.8681			1.15845
$806$	0.512817	−	1.64908i	0.0180632	−	0.0580862i
$807$	13.6057			0.478943
$808$	−2.59893	−	1.88823i	−0.0914300	−	0.0664278i
$809$	−0.488728	−	0.217596i	−0.0171828	−	0.00765026i	0.398127	−	0.917330i	$-0.369660\pi$
$809$	−0.488728	−	0.217596i	−0.0171828	−	0.00765026i	−0.415310	+	0.909680i	$0.636327\pi$
$810$	0.151385	+	0.465917i	0.00531914	+	0.0163706i
$811$	−21.8607	+	37.8638i	−0.767632	+	1.32958i	0.171212	+	0.985234i	$0.445232\pi$
$811$	−21.8607	+	37.8638i	−0.767632	+	1.32958i	−0.938844	+	0.344344i	$0.888102\pi$
$812$	16.1101	+	27.9035i	0.565354	+	0.979222i
$813$	−17.1037	+	18.9956i	−0.599853	+	0.666204i
$814$	1.62876	−	5.01282i	0.0570881	−	0.175699i
$815$	24.9177	+	27.6739i	0.872830	+	0.969376i
$816$	−6.99924	+	3.11626i	−0.245022	+	0.109091i
$817$	0.715502	+	0.152085i	0.0250323	+	0.00532077i
$818$	−0.196844	+	1.87284i	−0.00688248	+	0.0654824i
$819$	0.566204	+	5.38707i	0.0197848	+	0.188239i
$820$	10.8350	−	2.30304i	0.378373	−	0.0804257i
$821$	22.7140	−	16.5027i	0.792724	−	0.575948i	−0.116047	−	0.993244i	$-0.537022\pi$
$821$	22.7140	−	16.5027i	0.792724	−	0.575948i	0.908771	+	0.417296i	$0.137022\pi$
$822$	−1.91445	+	1.39093i	−0.0667742	+	0.0485143i
$823$	−22.7817	+	4.84239i	−0.794119	+	0.168795i	−0.587071	−	0.809536i	$-0.699719\pi$
$823$	−22.7817	+	4.84239i	−0.794119	+	0.168795i	−0.207048	+	0.978331i	$0.566386\pi$
$824$	1.24088	+	11.8062i	0.0432281	+	0.411288i
$825$	−2.81132	+	26.7479i	−0.0978776	+	0.931243i
$826$	3.73650	+	0.794217i	0.130009	+	0.0276343i
$827$	7.80476	−	3.47490i	0.271398	−	0.120834i	−0.266525	−	0.963828i	$-0.585876\pi$
$827$	7.80476	−	3.47490i	0.271398	−	0.120834i	0.537923	+	0.842994i	$0.319209\pi$
$828$	−5.07967	−	5.64155i	−0.176531	−	0.196057i
$829$	1.97400	−	6.07534i	0.0685598	−	0.211005i	−0.910907	−	0.412612i	$-0.864616\pi$
$829$	1.97400	−	6.07534i	0.0685598	−	0.211005i	0.979466	+	0.201607i	$0.0646164\pi$
$830$	1.45109	−	1.61160i	0.0503682	−	0.0559396i
$831$	−4.07295	−	7.05456i	−0.141289	−	0.244720i
$832$	7.43724	−	12.8817i	0.257840	−	0.446592i
$833$	0.196667	+	0.605279i	0.00681411	+	0.0209717i
$834$	2.11378	+	0.941114i	0.0731941	+	0.0325881i
$835$	−5.43969	−	3.95217i	−0.188248	−	0.136770i
$836$	85.4469			2.95524
$837$	−2.84473	−	4.78618i	−0.0983284	−	0.165434i
$838$	3.64747			0.126000
$839$	−8.17149	−	5.93694i	−0.282111	−	0.204966i	0.437727	−	0.899108i	$-0.355784\pi$
$839$	−8.17149	−	5.93694i	−0.282111	−	0.204966i	−0.719838	+	0.694142i	$0.755784\pi$
$840$	−4.81442	−	2.14352i	−0.166113	−	0.0739584i
$841$	2.26217	+	6.96223i	0.0780057	+	0.240077i
$842$	−0.885056	+	1.53296i	−0.0305010	+	0.0528293i
$843$	13.8143	+	23.9270i	0.475788	+	0.824090i
$844$	−3.92355	+	4.35754i	−0.135054	+	0.149993i
$845$	8.78619	−	27.0411i	0.302254	−	0.930243i
$846$	−0.394713	−	0.438373i	−0.0135705	−	0.0150716i
$847$	−44.3682	+	19.7540i	−1.52451	+	0.678755i
$848$	−25.7620	−	5.47589i	−0.884672	−	0.188043i
$849$	−0.304642	+	2.89848i	−0.0104553	+	0.0994755i
$850$	0.160818	+	1.53008i	0.00551603	+	0.0524815i
$851$	−23.7607	+	5.05049i	−0.814505	+	0.173128i
$852$	11.7735	−	8.55394i	0.403353	−	0.293053i
$853$	−26.0889	+	18.9547i	−0.893267	+	0.648997i	−0.936728	−	0.350059i	$-0.886162\pi$
$853$	−26.0889	+	18.9547i	−0.893267	+	0.648997i	0.0434606	+	0.999055i	$0.486162\pi$
$854$	2.92563	−	0.621862i	0.100113	−	0.0212797i
$855$	2.65636	+	25.2735i	0.0908455	+	0.864337i
$856$	−1.18032	+	11.2300i	−0.0403426	+	0.383834i
$857$	18.9472	+	4.02735i	0.647223	+	0.137571i	0.519815	−	0.854279i	$-0.326001\pi$
$857$	18.9472	+	4.02735i	0.647223	+	0.137571i	0.127408	+	0.991850i	$0.459334\pi$
$858$	−1.52462	+	0.678806i	−0.0520498	+	0.0231740i
$859$	−17.3515	−	19.2708i	−0.592026	−	0.657511i	0.370458	−	0.928849i	$-0.379201\pi$
$859$	−17.3515	−	19.2708i	−0.592026	−	0.657511i	−0.962484	+	0.271338i	$0.912534\pi$
$860$	−0.175737	+	0.540862i	−0.00599258	+	0.0184433i
$861$	−3.20955	+	3.56456i	−0.109381	+	0.121480i
$862$	−2.83954	−	4.91822i	−0.0967149	−	0.167515i
$863$	0.142187	−	0.246276i	0.00484011	−	0.00838332i	−0.863595	−	0.504186i	$-0.831793\pi$
$863$	0.142187	−	0.246276i	0.00484011	−	0.00838332i	0.868435	+	0.495802i	$0.165126\pi$
$864$	0.565342	+	1.73994i	0.0192333	+	0.0591941i
$865$	23.8983	+	10.6402i	0.812567	+	0.361778i
$866$	2.30972	+	1.67811i	0.0784876	+	0.0570246i
$867$	13.0532			0.443311
$868$	29.1924	+	5.81958i	0.990856	+	0.197529i
$869$	−30.3441			−1.02935
$870$	−2.38856	−	1.73539i	−0.0809797	−	0.0588352i
$871$	6.62179	+	2.94821i	0.224371	+	0.0998963i
$872$	−1.01724	−	3.13074i	−0.0344481	−	0.106020i
$873$	−1.18599	+	2.05420i	−0.0401398	+	0.0695241i
$874$	2.39179	+	4.14270i	0.0809035	+	0.140129i
$875$	−0.00803328	+	0.00892187i	−0.000271575	+	0.000301614i
$876$	1.87751	−	5.77837i	0.0634351	−	0.195233i
$877$	−34.0542	−	37.8210i	−1.14993	−	1.27712i	−0.955099	−	0.296287i	$-0.904252\pi$
$877$	−34.0542	−	37.8210i	−1.14993	−	1.27712i	−0.194828	−	0.980837i	$-0.562415\pi$
$878$	2.70509	−	1.20438i	0.0912923	−	0.0406460i
$879$	2.64692	+	0.562619i	0.0892782	+	0.0189767i
$880$	−6.85854	+	65.2547i	−0.231201	+	2.19973i
$881$	−1.37311	−	13.0642i	−0.0462611	−	0.440145i	−0.992998	−	0.118135i	$-0.962308\pi$
$881$	−1.37311	−	13.0642i	−0.0462611	−	0.440145i	0.946736	−	0.322010i	$-0.104358\pi$
$882$	0.0485473	−	0.0103190i	0.00163467	−	0.000347460i
$883$	34.2497	−	24.8839i	1.15259	−	0.837409i	0.163771	−	0.986498i	$-0.447634\pi$
$883$	34.2497	−	24.8839i	1.15259	−	0.837409i	0.988824	+	0.149090i	$0.0476343\pi$
$884$	6.35824	−	4.61953i	0.213851	−	0.155372i
$885$	28.1862	−	5.99115i	0.947467	−	0.201390i
$886$	−0.151474	−	1.44117i	−0.00508885	−	0.0484172i
$887$	1.40721	−	13.3887i	0.0472494	−	0.449548i	−0.945163	−	0.326598i	$-0.894098\pi$
$887$	1.40721	−	13.3887i	0.0472494	−	0.449548i	0.992413	−	0.122950i	$-0.0392356\pi$
$888$	3.80977	+	0.809791i	0.127847	+	0.0271748i
$889$	−32.3896	+	14.4208i	−1.08631	+	0.483658i
$890$	−1.96338	−	2.18056i	−0.0658127	−	0.0730924i
$891$	−1.66269	+	5.11722i	−0.0557021	+	0.171433i
$892$	−13.6063	+	15.1113i	−0.455571	+	0.505963i
$893$	−15.3000	−	26.5003i	−0.511994	−	0.886799i
$894$	−0.210318	+	0.364281i	−0.00703408	+	0.0121834i
$895$	−5.15473	−	15.8646i	−0.172304	−	0.530296i
$896$	−11.8890	−	5.29332i	−0.397183	−	0.176837i
$897$	6.22255	+	4.52095i	0.207765	+	0.150950i
$898$	1.21306			0.0404803
$899$	30.8244	+	13.2587i	1.02805	+	0.442201i
$900$	−9.87721			−0.329240
$901$	−10.9763	−	7.97472i	−0.365672	−	0.265676i
$902$	−1.35007	−	0.601091i	−0.0449525	−	0.0200141i
$903$	−0.0760979	−	0.234205i	−0.00253238	−	0.00779387i
$904$	5.24699	−	9.08806i	0.174512	−	0.302264i
$905$	−9.11959	−	15.7956i	−0.303145	−	0.525063i
$906$	1.20161	−	1.33453i	0.0399209	−	0.0443367i
$907$	7.72596	−	23.7781i	0.256536	−	0.789537i	−0.736987	−	0.675907i	$-0.763752\pi$
$907$	7.72596	−	23.7781i	0.256536	−	0.789537i	0.993523	−	0.113630i	$-0.0362479\pi$
$908$	4.30540	+	4.78163i	0.142880	+	0.158684i
$909$	4.76419	−	2.12115i	0.158018	−	0.0703542i
$910$	2.59564	+	0.551720i	0.0860446	+	0.0182893i
$911$	−0.381727	+	3.63189i	−0.0126472	+	0.120330i	−0.999024	−	0.0441720i	$-0.985935\pi$
$911$	−0.381727	+	3.63189i	−0.0126472	+	0.120330i	0.986377	+	0.164502i	$0.0526017\pi$
$912$	3.23979	+	30.8245i	0.107280	+	1.02070i
$913$	23.2978	−	4.95210i	0.771045	−	0.163891i
$914$	2.86766	−	2.08348i	0.0948538	−	0.0689153i
$915$	18.2534	−	13.2619i	0.603439	−	0.438424i
$916$	−13.6222	+	2.89549i	−0.450091	+	0.0956698i
$917$	2.20521	+	20.9812i	0.0728225	+	0.692860i
$918$	−0.0321727	+	0.306103i	−0.00106186	+	0.0101029i
$919$	−18.6060	−	3.95483i	−0.613756	−	0.130458i	−0.109463	−	0.993991i	$-0.534913\pi$
$919$	−18.6060	−	3.95483i	−0.613756	−	0.130458i	−0.504292	+	0.863533i	$0.668247\pi$
$920$	−6.83623	+	3.04369i	−0.225384	+	0.100347i
$921$	14.5859	+	16.1993i	0.480623	+	0.533786i
$922$	1.66454	−	5.12294i	0.0548189	−	0.168715i
$923$	−9.86607	+	10.9574i	−0.324746	+	0.360667i
$924$	−14.3830	−	24.9121i	−0.473167	−	0.819548i
$925$	−15.8028	+	27.3712i	−0.519593	+	0.899961i
$926$	−1.41566	−	4.35696i	−0.0465215	−	0.143178i
$927$	−17.6055	−	7.83846i	−0.578239	−	0.257449i
$928$	−8.91996	−	6.48073i	−0.292812	−	0.212740i
$929$	−38.2180			−1.25389			−0.626946	−	0.779062i	$-0.715696\pi$
$929$	−38.2180			−1.25389			−0.626946	+	0.779062i	$0.715696\pi$
$930$	−2.66061	+	0.600851i	−0.0872449	+	0.0197027i
$931$	2.57460			0.0843793
$932$	0.807025	+	0.586338i	0.0264350	+	0.0192061i
$933$	−11.4648	−	5.10447i	−0.375341	−	0.167113i
$934$	1.51600	+	4.66576i	0.0496050	+	0.152668i
$935$	−16.9000	+	29.2717i	−0.552691	+	0.957288i
$936$	−0.616624	−	1.06802i	−0.0201550	−	0.0349095i
$937$	17.5514	−	19.4929i	0.573381	−	0.636804i	−0.384789	−	0.923005i	$-0.625726\pi$
$937$	17.5514	−	19.4929i	0.573381	−	0.636804i	0.958170	+	0.286201i	$0.0923924\pi$
$938$	0.468979	−	1.44337i	0.0153127	−	0.0471277i
$939$	−17.2384	−	19.1452i	−0.562555	−	0.624780i
$940$	21.7332	−	9.67625i	0.708859	−	0.315605i
$941$	48.0712	+	10.2178i	1.56707	+	0.333092i	0.907995	−	0.418981i	$-0.137613\pi$
$941$	48.0712	+	10.2178i	1.56707	+	0.333092i	0.659080	+	0.752073i	$0.270946\pi$
$942$	−0.0153477	+	0.146024i	−0.000500055	+	0.00475771i
$943$	0.711934	+	6.77360i	0.0231838	+	0.220579i
$944$	34.3769	−	7.30703i	1.11887	−	0.237823i
$945$	6.92139	−	5.02868i	0.225153	−	0.163583i
$946$	0.0613822	−	0.0445968i	0.00199571	−	0.00144997i
$947$	30.5124	−	6.48562i	0.991521	−	0.210754i	0.316532	−	0.948582i	$-0.397482\pi$
$947$	30.5124	−	6.48562i	0.991521	−	0.210754i	0.674989	+	0.737828i	$0.264148\pi$
$948$	−1.16484	−	11.0827i	−0.0378323	−	0.359950i
$949$	−0.643457	+	6.12209i	−0.0208875	+	0.198731i
$950$	6.08789	+	1.29402i	0.197517	+	0.0419836i
$951$	27.1400	−	12.0835i	0.880076	−	0.391835i
$952$	−2.21552	−	2.46059i	−0.0718055	−	0.0797481i
$953$	14.6125	−	44.9728i	0.473347	−	1.45681i	−0.374828	−	0.927095i	$-0.622298\pi$
$953$	14.6125	−	44.9728i	0.473347	−	1.45681i	0.848174	−	0.529717i	$-0.177702\pi$
$954$	−0.707977	+	0.786288i	−0.0229216	+	0.0254570i
$955$	−9.98245	−	17.2901i	−0.323025	−	0.559495i
$956$	14.5321	−	25.1703i	0.470000	−	0.814064i
$957$	−10.0204	−	30.8397i	−0.323914	−	0.996906i
$958$	3.20666	+	1.42770i	0.103603	+	0.0461268i
$959$	33.4332	+	24.2907i	1.07962	+	0.784387i
$960$	−23.4931			−0.758235
$961$	27.9914	−	13.3222i	0.902949	−	0.429747i
$962$	−1.96119			−0.0632314
$963$	−14.8301	−	10.7747i	−0.477895	−	0.347211i
$964$	14.0909	+	6.27369i	0.453839	+	0.202062i
$965$	−0.263291	−	0.810326i	−0.00847564	−	0.0260853i
$966$	0.805206	−	1.39466i	0.0259071	−	0.0448724i
$967$	1.78096	+	3.08472i	0.0572719	+	0.0991979i	0.893240	−	0.449580i	$-0.148426\pi$
$967$	1.78096	+	3.08472i	0.0572719	+	0.0991979i	−0.835968	+	0.548778i	$0.815093\pi$
$968$	7.39886	−	8.21727i	0.237808	−	0.264113i
$969$	−4.93384	+	15.1848i	−0.158498	+	0.487806i
$970$	0.777544	+	0.863550i	0.0249654	+	0.0277269i
$971$	14.8327	−	6.60394i	0.476004	−	0.211931i	−0.154689	−	0.987963i	$-0.549437\pi$
$971$	14.8327	−	6.60394i	0.476004	−	0.211931i	0.630693	+	0.776033i	$0.282771\pi$
$972$	−1.93282	−	0.410833i	−0.0619951	−	0.0131775i
$973$	4.22374	−	40.1862i	0.135407	−	1.28831i
$974$	0.232104	+	2.20832i	0.00743709	+	0.0707592i
$975$	9.78869	−	2.08065i	0.313489	−	0.0666341i
$976$	22.2625	−	16.1747i	0.712605	−	0.517738i
$977$	−44.5853	+	32.3931i	−1.42641	+	1.03635i	−0.435739	+	0.900073i	$0.643513\pi$
$977$	−44.5853	+	32.3931i	−1.42641	+	1.03635i	−0.990671	+	0.136274i	$0.956487\pi$
$978$	1.78470	−	0.379349i	0.0570684	−	0.0121303i
$979$	−3.36864	−	32.0504i	−0.107662	−	1.02434i
$980$	−0.209227	+	1.99067i	−0.00668353	+	0.0635895i
$981$	5.22718	+	1.11107i	0.166891	+	0.0354738i
$982$	−2.22836	+	0.992128i	−0.0711097	+	0.0316601i
$983$	−26.2037	−	29.1021i	−0.835767	−	0.928214i	0.162521	−	0.986705i	$-0.448038\pi$
$983$	−26.2037	−	29.1021i	−0.835767	−	0.928214i	−0.998288	+	0.0584916i	$0.981371\pi$
$984$	0.337464	−	1.03861i	0.0107580	−	0.0331096i
$985$	47.3072	−	52.5399i	1.50733	−	1.67406i
$986$	−0.927468	−	1.60642i	−0.0295366	−	0.0511589i
$987$	−5.15079	+	8.92143i	−0.163952	+	0.283972i
$988$	−9.82478	−	30.2376i	−0.312568	−	0.961985i
$989$	−0.319443	−	0.142225i	−0.0101577	−	0.00452250i
$990$	2.13249	+	1.54935i	0.0677750	+	0.0492414i
$991$	40.4652			1.28542			0.642709	−	0.766110i	$-0.277810\pi$
$991$	40.4652			1.28542			0.642709	+	0.766110i	$0.277810\pi$
$992$	−9.93593	+	2.24385i	−0.315466	+	0.0712424i
$993$	−2.00046			−0.0634826
$994$	2.49757	+	1.81459i	0.0792180	+	0.0575553i
$995$	−39.7361	−	17.6916i	−1.25972	−	0.560863i
$996$	2.70303	+	8.31908i	0.0856489	+	0.263600i
$997$	−17.3735	+	30.0918i	−0.550224	+	0.953015i	0.448034	+	0.894016i	$0.352124\pi$
$997$	−17.3735	+	30.0918i	−0.550224	+	0.953015i	−0.998258	+	0.0589991i	$0.981209\pi$
$998$	1.20803	+	2.09237i	0.0382395	+	0.0662327i
$999$	−4.23084	+	4.69882i	−0.133858	+	0.148664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.a.19.1	✓	16
3.2	odd	2		279.2.y.b.19.2		16
31.7	even	15		2883.2.a.m.1.6		8
31.18	even	15	inner	93.2.m.a.49.1	yes	16
31.24	odd	30		2883.2.a.n.1.6		8
93.38	odd	30		8649.2.a.bj.1.3		8
93.80	odd	30		279.2.y.b.235.2		16
93.86	even	30		8649.2.a.bi.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.a.19.1	✓	16	1.1	even	1	trivial
93.2.m.a.49.1	yes	16	31.18	even	15	inner
279.2.y.b.19.2		16	3.2	odd	2
279.2.y.b.235.2		16	93.80	odd	30
2883.2.a.m.1.6		8	31.7	even	15
2883.2.a.n.1.6		8	31.24	odd	30
8649.2.a.bi.1.3		8	93.86	even	30
8649.2.a.bj.1.3		8	93.38	odd	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.125340 + 0.0910649i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.610617 - 1.87928i) q^{4} +(1.58103 - 2.73842i) q^{5} +(-0.0774644 - 0.134172i) q^{6} +(-1.81041 + 2.01066i) q^{7} +(0.190353 - 0.585848i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.125340 + 0.0910649i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.610617 - 1.87928i) q^{4} +(1.58103 - 2.73842i) q^{5} +(-0.0774644 - 0.134172i) q^{6} +(-1.81041 + 2.01066i) q^{7} +(0.190353 - 0.585848i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.447540 - 0.199258i) q^{10} +(5.26298 + 1.11868i) q^{11} +(-0.206548 + 1.96517i) q^{12} +(-0.209270 - 1.99107i) q^{13} +(-0.410018 + 0.0871520i) q^{14} +(-2.55816 + 1.85861i) q^{15} +(-3.12002 + 2.26683i) q^{16} +(-1.94323 + 0.413047i) q^{17} +(0.0161945 + 0.154080i) q^{18} +(-0.840072 + 7.99276i) q^{19} +(-6.11167 - 1.29908i) q^{20} +(2.47170 - 1.10047i) q^{21} +(0.557790 + 0.619489i) q^{22} +(1.18719 - 3.65380i) q^{23} +(-0.412182 + 0.457775i) q^{24} +(-2.49930 - 4.32891i) q^{25} +(0.155087 - 0.268618i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(4.88408 + 2.17453i) q^{28} +(4.87566 + 3.54238i) q^{29} -0.489894 q^{30} +(5.43100 - 1.22649i) q^{31} -1.82949 q^{32} +(-4.35297 - 3.16262i) q^{33} +(-0.281179 - 0.125189i) q^{34} +(2.64373 + 8.13658i) q^{35} +(0.987999 - 1.71126i) q^{36} +(-3.16145 - 5.47578i) q^{37} +(-0.833154 + 0.925312i) q^{38} +(-0.618664 + 1.90405i) q^{39} +(-1.30334 - 1.44751i) q^{40} +(-1.61956 + 0.721074i) q^{41} +(0.410018 + 0.0871520i) q^{42} +(0.00951391 - 0.0905188i) q^{43} +(-1.11134 - 10.5737i) q^{44} +(3.09296 - 0.657428i) q^{45} +(0.481536 - 0.349856i) q^{46} +(-3.08032 + 2.23798i) q^{47} +(3.77228 - 0.801824i) q^{48} +(-0.0334860 - 0.318598i) q^{49} +(0.0809497 - 0.770185i) q^{50} +(1.94323 + 0.413047i) q^{51} +(-3.61400 + 1.60906i) q^{52} +(4.56969 + 5.07516i) q^{53} +(0.0478757 - 0.147346i) q^{54} +(11.3843 - 12.6436i) q^{55} +(0.833325 + 1.44336i) q^{56} +(4.01839 - 6.96006i) q^{57} +(0.288530 + 0.888004i) q^{58} +(-8.32515 - 3.70660i) q^{59} +(5.05491 + 3.67261i) q^{60} -7.13537 q^{61} +(0.792412 + 0.340844i) q^{62} -2.70562 q^{63} +(6.01073 + 4.36705i) q^{64} +(-5.78325 - 2.57487i) q^{65} +(-0.257598 - 0.792805i) q^{66} +(-1.81027 + 3.13548i) q^{67} +(1.96280 + 3.39968i) q^{68} +(-2.57069 + 2.85504i) q^{69} +(-0.409591 + 1.26059i) q^{70} +(-4.92802 - 5.47312i) q^{71} +(0.562741 - 0.250548i) q^{72} +(-3.00758 - 0.639281i) q^{73} +(0.102396 - 0.974232i) q^{74} +(0.522496 + 4.97121i) q^{75} +(15.5336 - 3.30177i) q^{76} +(-11.7775 + 8.55682i) q^{77} +(-0.250936 + 0.182315i) q^{78} +(-5.51633 + 1.17253i) q^{79} +(1.27469 + 12.1278i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.268660 - 0.0571055i) q^{82} +(4.04402 - 1.80051i) q^{83} +(-3.57736 - 3.97307i) q^{84} +(-1.94121 + 5.97443i) q^{85} +(0.00943556 - 0.0104793i) q^{86} +(-3.01333 - 5.21923i) q^{87} +(1.65720 - 2.87036i) q^{88} +(-1.85086 - 5.69637i) q^{89} +(0.447540 + 0.199258i) q^{90} +(4.38224 + 3.18388i) q^{91} -7.59145 q^{92} +(-5.46032 - 1.08853i) q^{93} -0.589889 q^{94} +(20.5593 + 14.9372i) q^{95} +(1.67132 + 0.744119i) q^{96} +(0.732984 + 2.25589i) q^{97} +(0.0248159 - 0.0429825i) q^{98} +(2.69028 + 4.65970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9} - 16 q^{10} + 10 q^{11} - 10 q^{12} + 3 q^{13} - 12 q^{14} - 8 q^{15} + 6 q^{16} + 3 q^{17} - 32 q^{19} - 10 q^{20} - 6 q^{21} - 9 q^{22} - 22 q^{23} + 20 q^{24} + 12 q^{25} + 18 q^{26} + 4 q^{27} + 30 q^{28} + 38 q^{29} - 2 q^{30} - 8 q^{31} + 10 q^{33} - 52 q^{34} + 3 q^{35} - 5 q^{36} - 8 q^{37} + 7 q^{38} + 6 q^{39} + 37 q^{40} - 40 q^{41} + 12 q^{42} + q^{43} + q^{45} - 7 q^{46} - 23 q^{47} + 18 q^{48} + 25 q^{49} - 21 q^{50} - 3 q^{51} - 45 q^{52} + 30 q^{53} - 5 q^{54} + 46 q^{55} - 6 q^{56} - 8 q^{57} + 48 q^{58} - 40 q^{59} + 15 q^{60} + 26 q^{61} + 40 q^{62} - 12 q^{63} + 38 q^{64} + 12 q^{65} + 12 q^{66} - 32 q^{67} + 15 q^{68} - 11 q^{69} + 33 q^{70} + 17 q^{71} + 5 q^{72} + 27 q^{73} - 70 q^{74} + 3 q^{75} - 15 q^{76} - 9 q^{77} - 9 q^{78} + 21 q^{80} + 2 q^{81} - 32 q^{82} - 17 q^{83} - 15 q^{84} - 64 q^{85} + 26 q^{86} - 6 q^{87} - 22 q^{88} - 43 q^{89} - 16 q^{90} - 140 q^{92} - q^{93} + 88 q^{94} - 2 q^{95} - 35 q^{96} + 12 q^{97} - 32 q^{98}+O(q^{100}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9 - 16 * q^10 + 10 * q^11 - 10 * q^12 + 3 * q^13 - 12 * q^14 - 8 * q^15 + 6 * q^16 + 3 * q^17 - 32 * q^19 - 10 * q^20 - 6 * q^21 - 9 * q^22 - 22 * q^23 + 20 * q^24 + 12 * q^25 + 18 * q^26 + 4 * q^27 + 30 * q^28 + 38 * q^29 - 2 * q^30 - 8 * q^31 + 10 * q^33 - 52 * q^34 + 3 * q^35 - 5 * q^36 - 8 * q^37 + 7 * q^38 + 6 * q^39 + 37 * q^40 - 40 * q^41 + 12 * q^42 + q^43 + q^45 - 7 * q^46 - 23 * q^47 + 18 * q^48 + 25 * q^49 - 21 * q^50 - 3 * q^51 - 45 * q^52 + 30 * q^53 - 5 * q^54 + 46 * q^55 - 6 * q^56 - 8 * q^57 + 48 * q^58 - 40 * q^59 + 15 * q^60 + 26 * q^61 + 40 * q^62 - 12 * q^63 + 38 * q^64 + 12 * q^65 + 12 * q^66 - 32 * q^67 + 15 * q^68 - 11 * q^69 + 33 * q^70 + 17 * q^71 + 5 * q^72 + 27 * q^73 - 70 * q^74 + 3 * q^75 - 15 * q^76 - 9 * q^77 - 9 * q^78 + 21 * q^80 + 2 * q^81 - 32 * q^82 - 17 * q^83 - 15 * q^84 - 64 * q^85 + 26 * q^86 - 6 * q^87 - 22 * q^88 - 43 * q^89 - 16 * q^90 - 140 * q^92 - q^93 + 88 * q^94 - 2 * q^95 - 35 * q^96 + 12 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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