LMFDB - Embedded newform 432.2.bg.a.13.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(13,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 16]))

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

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

chi := DirichletCharacter("432.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.bg (of order $36$, degree $12$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$70$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.16
Character	$\chi$	$=$	432.13
Dual form			432.2.bg.a.133.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09259 + 0.897911i) q^{2} +(1.51775 + 0.834518i) q^{3} +(0.387511 - 1.96210i) q^{4} +(-2.33873 + 0.204612i) q^{5} +(-2.40761 + 0.451022i) q^{6} +(-0.349949 + 0.961477i) q^{7} +(1.33840 + 2.49172i) q^{8} +(1.60716 + 2.53319i) q^{9} +O(q^{10})$	\(q+(-1.09259 + 0.897911i) q^{2} +(1.51775 + 0.834518i) q^{3} +(0.387511 - 1.96210i) q^{4} +(-2.33873 + 0.204612i) q^{5} +(-2.40761 + 0.451022i) q^{6} +(-0.349949 + 0.961477i) q^{7} +(1.33840 + 2.49172i) q^{8} +(1.60716 + 2.53319i) q^{9} +(2.37155 - 2.32353i) q^{10} +(-0.118528 + 1.35478i) q^{11} +(2.22555 - 2.65460i) q^{12} +(0.761766 - 0.533394i) q^{13} +(-0.480969 - 1.36472i) q^{14} +(-3.72037 - 1.64116i) q^{15} +(-3.69967 - 1.52067i) q^{16} +(-3.00905 + 5.21183i) q^{17} +(-4.03055 - 1.32465i) q^{18} +(-0.689817 + 2.57443i) q^{19} +(-0.504814 + 4.66811i) q^{20} +(-1.33351 + 1.16725i) q^{21} +(-1.08697 - 1.58665i) q^{22} +(-0.636948 - 1.75000i) q^{23} +(-0.0480244 + 4.89874i) q^{24} +(0.503752 - 0.0888251i) q^{25} +(-0.353358 + 1.26678i) q^{26} +(0.325285 + 5.18596i) q^{27} +(1.75090 + 1.05922i) q^{28} +(-5.06872 + 7.23889i) q^{29} +(5.53846 - 1.54745i) q^{30} +(3.59535 - 1.30860i) q^{31} +(5.40765 - 1.66050i) q^{32} +(-1.31048 + 1.95731i) q^{33} +(-1.39210 - 8.39626i) q^{34} +(0.621706 - 2.32024i) q^{35} +(5.59316 - 2.17177i) q^{36} +(-1.13311 - 4.22883i) q^{37} +(-1.55792 - 3.43219i) q^{38} +(1.60130 - 0.173854i) q^{39} +(-3.63999 - 5.55361i) q^{40} +(7.03504 + 1.24047i) q^{41} +(0.408893 - 2.47269i) q^{42} +(-0.351791 + 4.02099i) q^{43} +(2.61228 + 0.757554i) q^{44} +(-4.27703 - 5.59560i) q^{45} +(2.26727 + 1.34011i) q^{46} +(-6.72720 - 2.44850i) q^{47} +(-4.34617 - 5.39545i) q^{48} +(4.56034 + 3.82658i) q^{49} +(-0.470638 + 0.549374i) q^{50} +(-8.91636 + 5.39917i) q^{51} +(-0.751380 - 1.70136i) q^{52} +(7.66271 - 7.66271i) q^{53} +(-5.01194 - 5.37406i) q^{54} -3.19271i q^{55} +(-2.86411 + 0.414864i) q^{56} +(-3.19538 + 3.33169i) q^{57} +(-0.961835 - 12.4604i) q^{58} +(-11.4355 + 1.00048i) q^{59} +(-4.66181 + 6.66377i) q^{60} +(-0.143518 - 0.307774i) q^{61} +(-2.75324 + 4.65807i) q^{62} +(-2.99802 + 0.658761i) q^{63} +(-4.41737 + 6.66985i) q^{64} +(-1.67243 + 1.40333i) q^{65} +(-0.325667 - 3.31523i) q^{66} +(-2.92446 + 2.04773i) q^{67} +(9.06008 + 7.92370i) q^{68} +(0.493676 - 3.18762i) q^{69} +(1.40410 + 3.09331i) q^{70} +(8.18337 + 4.72467i) q^{71} +(-4.16098 + 7.39502i) q^{72} +(10.2135 - 5.89678i) q^{73} +(5.03514 + 3.60295i) q^{74} +(0.838699 + 0.285576i) q^{75} +(4.78398 + 2.35111i) q^{76} +(-1.26111 - 0.588064i) q^{77} +(-1.59346 + 1.62778i) q^{78} +(0.275726 + 1.56372i) q^{79} +(8.96368 + 2.79944i) q^{80} +(-3.83407 + 8.14247i) q^{81} +(-8.80025 + 4.96152i) q^{82} +(6.88999 - 9.83993i) q^{83} +(1.77351 + 3.06879i) q^{84} +(5.97095 - 12.8047i) q^{85} +(-3.22613 - 4.70917i) q^{86} +(-13.7341 + 6.75692i) q^{87} +(-3.53437 + 1.51790i) q^{88} +(13.9368 - 8.04639i) q^{89} +(9.69740 + 2.27330i) q^{90} +(0.246267 + 0.919081i) q^{91} +(-3.68050 + 0.571611i) q^{92} +(6.54891 + 1.01425i) q^{93} +(9.54862 - 3.36522i) q^{94} +(1.08653 - 6.16204i) q^{95} +(9.59321 + 1.99255i) q^{96} +(6.06620 - 5.09014i) q^{97} +(-8.41851 - 0.0861070i) q^{98} +(-3.62240 + 1.87709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8}+O(q^{10}) $ 840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8	\( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 30 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 12 q^{18} - 6 q^{19} - 54 q^{20} - 12 q^{21} - 12 q^{22} + 18 q^{24} - 24 q^{26} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 24 q^{33} - 6 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 12 q^{40} - 72 q^{42} - 12 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 24 q^{47} - 12 q^{48} - 24 q^{49} - 168 q^{50} + 6 q^{51} - 12 q^{52} - 24 q^{53} + 156 q^{54} - 54 q^{56} + 42 q^{58} - 48 q^{59} - 72 q^{60} - 12 q^{61} + 60 q^{62} - 24 q^{63} - 6 q^{64} - 24 q^{65} - 198 q^{66} - 12 q^{67} - 66 q^{68} - 12 q^{69} - 54 q^{70} - 144 q^{72} - 96 q^{74} - 96 q^{75} - 12 q^{76} - 12 q^{77} - 90 q^{78} - 24 q^{79} - 204 q^{80} - 24 q^{81} - 24 q^{82} + 48 q^{83} + 36 q^{84} + 18 q^{85} - 72 q^{86} - 12 q^{88} - 66 q^{90} - 6 q^{91} + 102 q^{92} - 12 q^{93} - 12 q^{94} - 24 q^{95} - 120 q^{96} - 24 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) \) 840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 30 * q^12 - 12 * q^13 - 12 * q^14 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 12 * q^18 - 6 * q^19 - 54 * q^20 - 12 * q^21 - 12 * q^22 + 18 * q^24 - 24 * q^26 - 12 * q^27 - 24 * q^28 - 12 * q^29 - 12 * q^30 - 24 * q^31 - 12 * q^32 - 24 * q^33 - 6 * q^35 - 12 * q^36 - 6 * q^37 - 12 * q^38 - 12 * q^40 - 72 * q^42 - 12 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 - 24 * q^47 - 12 * q^48 - 24 * q^49 - 168 * q^50 + 6 * q^51 - 12 * q^52 - 24 * q^53 + 156 * q^54 - 54 * q^56 + 42 * q^58 - 48 * q^59 - 72 * q^60 - 12 * q^61 + 60 * q^62 - 24 * q^63 - 6 * q^64 - 24 * q^65 - 198 * q^66 - 12 * q^67 - 66 * q^68 - 12 * q^69 - 54 * q^70 - 144 * q^72 - 96 * q^74 - 96 * q^75 - 12 * q^76 - 12 * q^77 - 90 * q^78 - 24 * q^79 - 204 * q^80 - 24 * q^81 - 24 * q^82 + 48 * q^83 + 36 * q^84 + 18 * q^85 - 72 * q^86 - 12 * q^88 - 66 * q^90 - 6 * q^91 + 102 * q^92 - 12 * q^93 - 12 * q^94 - 24 * q^95 - 120 * q^96 - 24 * q^97 - 6 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−1.09259	+	0.897911i	−0.772579	+	0.634919i
$2$	−1.09259	+	0.897911i	−0.772579	+	0.634919i
$3$	1.51775	+	0.834518i	0.876276	+	0.481809i
$3$	1.51775	+	0.834518i	0.876276	+	0.481809i
$4$	0.387511	−	1.96210i	0.193756	−	0.981050i
$5$	−2.33873	+	0.204612i	−1.04591	+	0.0915054i	−0.597137	−	0.802139i	$-0.703695\pi$
$5$	−2.33873	+	0.204612i	−1.04591	+	0.0915054i	−0.448775	+	0.893645i	$0.648140\pi$
$6$	−2.40761	+	0.451022i	−0.982902	+	0.184129i
$7$	−0.349949	+	0.961477i	−0.132268	+	0.363404i	−0.988092	−	0.153863i	$-0.950828\pi$
$7$	−0.349949	+	0.961477i	−0.132268	+	0.363404i	0.855824	+	0.517267i	$0.173051\pi$
$8$	1.33840	+	2.49172i	0.473196	+	0.880957i
$9$	1.60716	+	2.53319i	0.535720	+	0.844396i
$10$	2.37155	−	2.32353i	0.749951	−	0.734764i
$11$	−0.118528	+	1.35478i	−0.0357374	+	0.408481i	0.957164	+	0.289545i	$0.0935039\pi$
$11$	−0.118528	+	1.35478i	−0.0357374	+	0.408481i	−0.992902	+	0.118936i	$0.962052\pi$
$12$	2.22555	−	2.65460i	0.642462	−	0.766317i
$13$	0.761766	−	0.533394i	0.211276	−	0.147937i	−0.463149	−	0.886280i	$-0.653281\pi$
$13$	0.761766	−	0.533394i	0.211276	−	0.147937i	0.674425	+	0.738343i	$0.264392\pi$
$14$	−0.480969	−	1.36472i	−0.128545	−	0.364738i
$15$	−3.72037	−	1.64116i	−0.960596	−	0.423746i
$16$	−3.69967	−	1.52067i	−0.924918	−	0.380168i
$17$	−3.00905	+	5.21183i	−0.729802	+	1.26405i	0.227165	+	0.973856i	$0.427054\pi$
$17$	−3.00905	+	5.21183i	−0.729802	+	1.26405i	−0.956967	+	0.290197i	$0.906279\pi$
$18$	−4.03055	−	1.32465i	−0.950009	−	0.312223i
$19$	−0.689817	+	2.57443i	−0.158255	+	0.590615i	0.840550	+	0.541734i	$0.182232\pi$
$19$	−0.689817	+	2.57443i	−0.158255	+	0.590615i	−0.998805	+	0.0488807i	$0.984435\pi$
$20$	−0.504814	+	4.66811i	−0.112880	+	1.04382i
$21$	−1.33351	+	1.16725i	−0.290995	+	0.254714i
$22$	−1.08697	−	1.58665i	−0.231742	−	0.338274i
$23$	−0.636948	−	1.75000i	−0.132813	−	0.364901i	0.855404	−	0.517962i	$-0.173309\pi$
$23$	−0.636948	−	1.75000i	−0.132813	−	0.364901i	−0.988217	+	0.153061i	$0.951087\pi$
$24$	−0.0480244	+	4.89874i	−0.00980294	+	0.999952i
$25$	0.503752	−	0.0888251i	0.100750	−	0.0177650i
$26$	−0.353358	+	1.26678i	−0.0692992	+	0.248436i
$27$	0.325285	+	5.18596i	0.0626012	+	0.998039i
$28$	1.75090	+	1.05922i	0.330890	+	0.200173i
$29$	−5.06872	+	7.23889i	−0.941238	+	1.34423i	−0.00235289	+	0.999997i	$0.500749\pi$
$29$	−5.06872	+	7.23889i	−0.941238	+	1.34423i	−0.938885	+	0.344230i	$0.888140\pi$
$30$	5.53846	−	1.54745i	1.01118	−	0.282524i
$31$	3.59535	−	1.30860i	0.645744	−	0.235031i	0.00167430	−	0.999999i	$-0.499467\pi$
$31$	3.59535	−	1.30860i	0.645744	−	0.235031i	0.644069	+	0.764967i	$0.277245\pi$
$32$	5.40765	−	1.66050i	0.955947	−	0.293538i
$33$	−1.31048	+	1.95731i	−0.228126	+	0.340723i
$34$	−1.39210	−	8.39626i	−0.238743	−	1.43995i
$35$	0.621706	−	2.32024i	0.105087	−	0.392192i
$36$	5.59316	−	2.17177i	0.932193	−	0.361962i
$37$	−1.13311	−	4.22883i	−0.186282	−	0.695215i	−0.994352	−	0.106129i	$-0.966155\pi$
$37$	−1.13311	−	4.22883i	−0.186282	−	0.695215i	0.808070	−	0.589086i	$-0.200512\pi$
$38$	−1.55792	−	3.43219i	−0.252728	−	0.556776i
$39$	1.60130	−	0.173854i	0.256413	−	0.0278390i
$40$	−3.63999	−	5.55361i	−0.575533	−	0.878104i
$41$	7.03504	+	1.24047i	1.09869	+	0.193728i	0.693466	−	0.720490i	$-0.256083\pi$
$41$	7.03504	+	1.24047i	1.09869	+	0.193728i	0.405223	+	0.914218i	$0.367194\pi$
$42$	0.408893	−	2.47269i	0.0630935	−	0.381545i
$43$	−0.351791	+	4.02099i	−0.0536476	+	0.613195i	0.921017	+	0.389523i	$0.127360\pi$
$43$	−0.351791	+	4.02099i	−0.0536476	+	0.613195i	−0.974664	+	0.223672i	$0.928196\pi$
$44$	2.61228	+	0.757554i	0.393816	+	0.114206i
$45$	−4.27703	−	5.59560i	−0.637583	−	0.834142i
$46$	2.26727	+	1.34011i	0.334291	+	0.197589i
$47$	−6.72720	−	2.44850i	−0.981263	−	0.357151i	−0.198932	−	0.980013i	$-0.563747\pi$
$47$	−6.72720	−	2.44850i	−0.981263	−	0.357151i	−0.782331	+	0.622863i	$0.785970\pi$
$48$	−4.34617	−	5.39545i	−0.627315	−	0.778766i
$49$	4.56034	+	3.82658i	0.651477	+	0.546654i
$50$	−0.470638	+	0.549374i	−0.0665583	+	0.0776933i
$51$	−8.91636	+	5.39917i	−1.24854	+	0.756035i
$52$	−0.751380	−	1.70136i	−0.104198	−	0.235936i
$53$	7.66271	−	7.66271i	1.05255	−	1.05255i	0.0540145	−	0.998540i	$-0.482798\pi$
$53$	7.66271	−	7.66271i	1.05255	−	1.05255i	0.998540	−	0.0540145i	$-0.0172017\pi$
$54$	−5.01194	−	5.37406i	−0.682038	−	0.731317i
$55$		−	3.19271i		−	0.430505i
$56$	−2.86411	+	0.414864i	−0.382732	+	0.0554386i
$57$	−3.19538	+	3.33169i	−0.423239	+	0.441293i
$58$	−0.961835	−	12.4604i	−0.126295	−	1.63613i
$59$	−11.4355	+	1.00048i	−1.48878	+	0.130251i	−0.802309	−	0.596909i	$-0.796395\pi$
$59$	−11.4355	+	1.00048i	−1.48878	+	0.130251i	−0.686468	+	0.727160i	$0.740840\pi$
$60$	−4.66181	+	6.66377i	−0.601836	+	0.860289i
$61$	−0.143518	−	0.307774i	−0.0183755	−	0.0394065i	0.896906	−	0.442222i	$-0.145810\pi$
$61$	−0.143518	−	0.307774i	−0.0183755	−	0.0394065i	−0.915281	+	0.402815i	$0.868032\pi$
$62$	−2.75324	+	4.65807i	−0.349662	+	0.591575i
$63$	−2.99802	+	0.658761i	−0.377715	+	0.0829961i
$64$	−4.41737	+	6.66985i	−0.552171	+	0.833731i
$65$	−1.67243	+	1.40333i	−0.207439	+	0.174062i
$66$	−0.325667	−	3.31523i	−0.0400868	−	0.408077i
$67$	−2.92446	+	2.04773i	−0.357280	+	0.250170i	−0.738411	−	0.674351i	$-0.764424\pi$
$67$	−2.92446	+	2.04773i	−0.357280	+	0.250170i	0.381131	+	0.924521i	$0.375535\pi$
$68$	9.06008	+	7.92370i	1.09870	+	0.960889i
$69$	0.493676	−	3.18762i	0.0594316	−	0.383744i
$70$	1.40410	+	3.09331i	0.167822	+	0.369721i
$71$	8.18337	+	4.72467i	0.971188	+	0.560715i	0.899598	−	0.436719i	$-0.143860\pi$
$71$	8.18337	+	4.72467i	0.971188	+	0.560715i	0.0715895	+	0.997434i	$0.477193\pi$
$72$	−4.16098	+	7.39502i	−0.490376	+	0.871511i
$73$	10.2135	−	5.89678i	1.19540	−	0.690166i	0.235875	−	0.971783i	$-0.424204\pi$
$73$	10.2135	−	5.89678i	1.19540	−	0.690166i	0.959527	+	0.281618i	$0.0908709\pi$
$74$	5.03514	+	3.60295i	0.585323	+	0.418834i
$75$	0.838699	+	0.285576i	0.0968446	+	0.0329754i
$76$	4.78398	+	2.35111i	0.548760	+	0.269691i
$77$	−1.26111	−	0.588064i	−0.143717	−	0.0670161i
$78$	−1.59346	+	1.62778i	−0.180424	+	0.184310i
$79$	0.275726	+	1.56372i	0.0310216	+	0.175932i	0.996382	−	0.0849881i	$-0.0270852\pi$
$79$	0.275726	+	1.56372i	0.0310216	+	0.175932i	−0.965360	+	0.260920i	$0.915974\pi$
$80$	8.96368	+	2.79944i	1.00217	+	0.312987i
$81$	−3.83407	+	8.14247i	−0.426008	+	0.904719i
$82$	−8.80025	+	4.96152i	−0.971825	+	0.547908i
$83$	6.88999	−	9.83993i	0.756275	−	1.08007i	−0.237793	−	0.971316i	$-0.576424\pi$
$83$	6.88999	−	9.83993i	0.756275	−	1.08007i	0.994068	−	0.108757i	$-0.0346871\pi$
$84$	1.77351	+	3.06879i	0.193505	+	0.334833i
$85$	5.97095	−	12.8047i	0.647640	−	1.38887i
$86$	−3.22613	−	4.70917i	−0.347882	−	0.507803i
$87$	−13.7341	+	6.75692i	−1.47245	+	0.724417i
$88$	−3.53437	+	1.51790i	−0.376765	+	0.161808i
$89$	13.9368	−	8.04639i	1.47729	−	0.852916i	0.477623	−	0.878565i	$-0.341499\pi$
$89$	13.9368	−	8.04639i	1.47729	−	0.852916i	0.999671	+	0.0256493i	$0.00816532\pi$
$90$	9.69740	+	2.27330i	1.02220	+	0.239627i
$91$	0.246267	+	0.919081i	0.0258158	+	0.0963458i
$92$	−3.68050	+	0.571611i	−0.383719	+	0.0595946i
$93$	6.54891	+	1.01425i	0.679090	+	0.105173i
$94$	9.54862	−	3.36522i	0.984865	−	0.347096i
$95$	1.08653	−	6.16204i	0.111476	−	0.632212i
$96$	9.59321	+	1.99255i	0.979103	+	0.203363i
$97$	6.06620	−	5.09014i	0.615929	−	0.516826i	−0.280592	−	0.959827i	$-0.590531\pi$
$97$	6.06620	−	5.09014i	0.615929	−	0.516826i	0.896521	+	0.443001i	$0.146086\pi$
$98$	−8.41851	−	0.0861070i	−0.850398	−	0.00869812i
$99$	−3.62240	+	1.87709i	−0.364065	+	0.188655i
$100$	0.0209259	−	1.02283i	0.00209259	−	0.102283i
$101$	0.120446	−	0.0561649i	0.0119848	−	0.00558862i	−0.416617	−	0.909082i	$-0.636784\pi$
$101$	0.120446	−	0.0561649i	0.0119848	−	0.00558862i	0.428601	+	0.903494i	$0.359006\pi$
$102$	4.89396	−	13.9052i	0.484575	−	1.37682i
$103$	−7.13215	+	8.49977i	−0.702752	+	0.837507i	−0.992835	−	0.119494i	$-0.961873\pi$
$103$	−7.13215	+	8.49977i	−0.702752	+	0.837507i	0.290083	+	0.957002i	$0.406317\pi$
$104$	2.34862	+	1.18422i	0.230301	+	0.116122i
$105$	2.87988	−	3.00273i	0.281047	−	0.293036i
$106$	−1.49178	+	15.2526i	−0.144894	+	1.48147i
$107$	2.87162	−	2.87162i	0.277610	−	0.277610i	−0.554544	−	0.832154i	$-0.687107\pi$
$107$	2.87162	−	2.87162i	0.277610	−	0.277610i	0.832154	+	0.554544i	$0.187107\pi$
$108$	10.3014	+	1.37138i	0.991255	+	0.131961i
$109$	0.559907	+	0.559907i	0.0536294	+	0.0536294i	0.733413	−	0.679783i	$-0.237926\pi$
$109$	0.559907	+	0.559907i	0.0536294	+	0.0536294i	−0.679783	+	0.733413i	$0.737926\pi$
$110$	2.86677	+	3.48833i	0.273336	+	0.332599i
$111$	1.80925	−	7.36392i	0.171726	−	0.698953i
$112$	2.75678	−	3.02499i	0.260492	−	0.285835i
$113$	−0.770934	−	0.646890i	−0.0725234	−	0.0608543i	0.605805	−	0.795613i	$-0.292851\pi$
$113$	−0.770934	−	0.646890i	−0.0725234	−	0.0608543i	−0.678329	+	0.734759i	$0.737295\pi$
$114$	0.499683	−	6.50934i	0.0467996	−	0.609656i
$115$	1.84772	+	3.96245i	0.172301	+	0.369501i
$116$	12.2392	+	12.7505i	1.13638	+	1.18385i
$117$	2.57547	+	1.07245i	0.238102	+	0.0991476i
$118$	11.5960	−	11.3612i	1.06750	−	1.04588i
$119$	−3.95804	−	4.71700i	−0.362833	−	0.432407i
$120$	−0.890027	−	11.4667i	−0.0812480	−	1.04676i
$121$	9.01151	+	1.58897i	0.819228	+	0.144452i
$122$	0.433160	+	0.207406i	0.0392165	+	0.0187776i
$123$	9.64227	+	7.75359i	0.869414	+	0.699118i
$124$	−1.17437	−	7.56153i	−0.105461	−	0.679045i
$125$	10.1784	−	2.72729i	0.910382	−	0.243936i
$126$	2.68411	−	3.41172i	0.239119	−	0.303940i
$127$	−0.570732	−	0.988537i	−0.0506443	−	0.0877185i	0.839592	−	0.543218i	$-0.182794\pi$
$127$	−0.570732	−	0.988537i	−0.0506443	−	0.0877185i	−0.890236	+	0.455499i	$0.849461\pi$
$128$	−1.16255	−	11.2538i	−0.102756	−	0.994707i
$129$	−3.88952	+	5.80930i	−0.342453	+	0.511480i
$130$	0.567210	−	3.03496i	0.0497476	−	0.266183i
$131$	3.79508	+	1.76968i	0.331578	+	0.154617i	0.581276	−	0.813706i	$-0.302554\pi$
$131$	3.79508	+	1.76968i	0.331578	+	0.154617i	−0.249698	+	0.968324i	$0.580331\pi$
$132$	3.33260	+	3.32977i	0.290066	+	0.289820i
$133$	−2.23385	−	1.56416i	−0.193700	−	0.135630i
$134$	1.35656	−	4.86324i	0.117189	−	0.420120i
$135$	−1.82187	−	12.0620i	−0.156801	−	1.03813i
$136$	−17.0137	−	0.522210i	−1.45892	−	0.0447792i
$137$	10.0439	−	1.77102i	0.858112	−	0.151308i	0.272755	−	0.962084i	$-0.412065\pi$
$137$	10.0439	−	1.77102i	0.858112	−	0.151308i	0.585358	+	0.810775i	$0.300954\pi$
$138$	2.32281	+	3.92604i	0.197731	+	0.334207i
$139$	0.251813	−	0.540015i	0.0213585	−	0.0458035i	−0.895339	−	0.445385i	$-0.853067\pi$
$139$	0.251813	−	0.540015i	0.0213585	−	0.0458035i	0.916698	+	0.399582i	$0.130845\pi$
$140$	−4.31162	−	2.11897i	−0.364398	−	0.179085i
$141$	−8.16693	−	9.33020i	−0.687779	−	0.785744i
$142$	−13.1834	+	2.18581i	−1.10633	+	0.183429i
$143$	0.632340	+	1.09525i	0.0528789	+	0.0915890i
$144$	−2.09382	−	11.8159i	−0.174485	−	0.984660i
$145$	10.3732	−	17.9669i	0.861448	−	1.49207i
$146$	−5.86442	+	15.6136i	−0.485343	+	1.29219i
$147$	3.72813	+	9.61349i	0.307491	+	0.792907i
$148$	−8.73647	+	0.584559i	−0.718133	+	0.0480504i
$149$	4.15944	+	5.94030i	0.340755	+	0.486648i	0.952556	−	0.304363i	$-0.0984437\pi$
$149$	4.15944	+	5.94030i	0.340755	+	0.486648i	−0.611801	+	0.791011i	$0.709555\pi$
$150$	−1.17278	+	0.441060i	−0.0957568	+	0.0360124i
$151$	14.8731	+	17.7251i	1.21036	+	1.44245i	0.863367	+	0.504576i	$0.168351\pi$
$151$	14.8731	+	17.7251i	1.21036	+	1.44245i	0.346988	+	0.937870i	$0.387204\pi$
$152$	−7.33802	+	1.72679i	−0.595192	+	0.140061i
$153$	−18.0386	+	0.753754i	−1.45833	+	0.0609374i
$154$	1.90591	−	0.489849i	0.153582	−	0.0394732i
$155$	−8.14079	+	3.79611i	−0.653884	+	0.304911i
$156$	0.279402	−	3.20928i	0.0223701	−	0.256948i
$157$	1.27489	+	14.5721i	0.101748	+	1.16298i	0.859746	+	0.510723i	$0.170622\pi$
$157$	1.27489	+	14.5721i	0.101748	+	1.16298i	−0.757998	+	0.652257i	$0.773822\pi$
$158$	−1.70534	−	1.46093i	−0.135669	−	0.116225i
$159$	18.0248	−	5.23545i	1.42946	−	0.415198i
$160$	−12.3073	+	4.98994i	−0.972976	+	0.394490i
$161$	1.90548			0.150173
$162$	−3.12214	−	12.3391i	−0.245299	−	0.969448i
$163$	−12.8858	−	12.8858i	−1.00929	−	1.00929i	−0.999956	−	0.00933642i	$-0.997028\pi$
$163$	−12.8858	−	12.8858i	−1.00929	−	1.00929i	−0.00933642	−	0.999956i	$-0.502972\pi$
$164$	5.16008	−	13.3228i	0.402934	−	1.04033i
$165$	2.66437	−	4.84575i	0.207421	−	0.377241i
$166$	1.30744	+	16.9376i	0.101477	+	1.31461i
$167$	−7.28650	+	8.68371i	−0.563846	+	0.671966i	−0.970356	−	0.241681i	$-0.922301\pi$
$167$	−7.28650	+	8.68371i	−0.563846	+	0.671966i	0.406509	+	0.913647i	$0.366746\pi$
$168$	−4.69322	−	1.76048i	−0.362090	−	0.135824i
$169$	−4.15048	+	11.4034i	−0.319268	+	0.877182i
$170$	4.97371	+	19.3517i	0.381466	+	1.48421i
$171$	−7.63016	+	2.39009i	−0.583493	+	0.182775i
$172$	7.75326	+	2.24843i	0.591180	+	0.171441i
$173$	−24.0945	−	2.10800i	−1.83187	−	0.160268i	−0.881664	−	0.471878i	$-0.843576\pi$
$173$	−24.0945	−	2.10800i	−1.83187	−	0.160268i	−0.950210	+	0.311610i	$0.899132\pi$
$174$	8.93860	−	19.7145i	0.677634	−	1.49455i
$175$	−0.0908843	+	0.515430i	−0.00687021	+	0.0389629i
$176$	2.49868	−	4.83199i	0.188345	−	0.364225i
$177$	−18.1912	−	8.02466i	−1.36734	−	0.603170i
$178$	−8.00224	+	21.3054i	−0.599793	+	1.59691i
$179$	0.00983748	−	0.00263594i	0.000735288	−	0.000197020i	−0.258451	−	0.966024i	$-0.583212\pi$
$179$	0.00983748	−	0.00263594i	0.000735288	−	0.000197020i	0.259187	+	0.965827i	$0.416546\pi$
$180$	−12.6365	+	6.22361i	−0.941870	+	0.463881i
$181$	−0.242568	−	0.0649960i	−0.0180300	−	0.00483111i	0.249793	−	0.968299i	$-0.419637\pi$
$181$	−0.242568	−	0.0649960i	−0.0180300	−	0.00483111i	−0.267823	+	0.963468i	$0.586304\pi$
$182$	−1.09432	−	0.783054i	−0.0811165	−	0.0580438i
$183$	0.0390187	−	0.586894i	0.00288435	−	0.0433845i
$184$	3.50803	−	3.92930i	0.258615	−	0.289672i
$185$	3.51531	+	9.65823i	0.258451	+	0.710087i
$186$	−8.06598	+	4.77218i	−0.591427	+	0.349913i
$187$	−6.70421	−	4.69434i	−0.490260	−	0.343284i
$188$	−7.41107	+	12.2506i	−0.540508	+	0.893468i
$189$	−5.10001	−	1.50207i	−0.370971	−	0.109259i
$190$	4.34583	+	7.70821i	0.315280	+	0.559212i
$191$	−2.97478	−	16.8708i	−0.215247	−	1.22073i	−0.880477	−	0.474090i	$-0.842777\pi$
$191$	−2.97478	−	16.8708i	−0.215247	−	1.22073i	0.665229	−	0.746639i	$-0.268334\pi$
$192$	−12.2706	+	6.43682i	−0.885554	+	0.464537i
$193$	20.3881	−	7.42066i	1.46757	−	0.534151i	0.520128	−	0.854088i	$-0.325884\pi$
$193$	20.3881	−	7.42066i	1.46757	−	0.534151i	0.947439	+	0.319937i	$0.103662\pi$
$194$	−2.05738	+	11.0084i	−0.147711	+	0.790354i
$195$	−3.70944	+	0.734245i	−0.265638	+	0.0525804i
$196$	9.27531	−	7.46500i	0.662522	−	0.533214i
$197$	−4.52419	−	1.21225i	−0.322335	−	0.0863694i	0.0940234	−	0.995570i	$-0.470027\pi$
$197$	−4.52419	−	1.21225i	−0.322335	−	0.0863694i	−0.416358	+	0.909201i	$0.636694\pi$
$198$	2.27234	−	5.30348i	0.161488	−	0.376902i
$199$	−7.17036	−	4.13981i	−0.508294	−	0.293463i	0.223838	−	0.974626i	$-0.428141\pi$
$199$	−7.17036	−	4.13981i	−0.508294	−	0.293463i	−0.732132	+	0.681163i	$0.761475\pi$
$200$	0.895550	+	1.13633i	0.0633249	+	0.0803505i
$201$	−6.14749	+	0.667437i	−0.433610	+	0.0470774i
$202$	−0.0811672	+	0.169515i	−0.00571091	+	0.0119270i
$203$	−5.18623	−	7.40670i	−0.364002	−	0.519848i
$204$	7.13852	+	19.5870i	0.499796	+	1.37137i
$205$	−16.7069	−	1.46166i	−1.16686	−	0.102087i
$206$	0.160490	−	15.6908i	0.0111819	−	1.09323i
$207$	3.40940	−	4.42604i	0.236970	−	0.307631i
$208$	−3.62940	+	0.814988i	−0.251654	+	0.0565092i
$209$	−3.40602	−	1.23969i	−0.235599	−	0.0857511i
$210$	−0.450345	+	5.86663i	−0.0310768	+	0.404836i
$211$	0.907848	+	10.3767i	0.0624988	+	0.714365i	0.961209	+	0.275821i	$0.0889499\pi$
$211$	0.907848	+	10.3767i	0.0624988	+	0.714365i	−0.898710	+	0.438543i	$0.855495\pi$
$212$	−12.0656	−	18.0044i	−0.828670	−	1.23655i
$213$	8.47753	+	14.0001i	0.580871	+	0.959269i
$214$	−0.559047	+	5.71597i	−0.0382157	+	0.390736i
$215$		−	9.47598i		−	0.646257i
$216$	−12.4866	+	7.75141i	−0.849607	+	0.527417i
$217$			3.91479i			0.265753i
$218$	−1.11450	−	0.109003i	−0.0754832	−	0.00738260i
$219$	20.4226	−	0.426500i	1.38003	−	0.0288202i
$220$	−6.26442	−	1.23721i	−0.422347	−	0.0834127i
$221$	0.487767	+	5.57520i	0.0328108	+	0.375029i
$222$	4.63538	+	9.67030i	0.311106	+	0.649028i
$223$	6.67704	+	2.43024i	0.447128	+	0.162741i	0.555764	−	0.831340i	$-0.312426\pi$
$223$	6.67704	+	2.43024i	0.447128	+	0.162741i	−0.108636	+	0.994082i	$0.534648\pi$
$224$	−0.295867	+	5.78042i	−0.0197684	+	0.386221i
$225$	1.03462	+	1.13334i	0.0689748	+	0.0755562i
$226$	1.42317	+	0.0145566i	0.0946676	+	0.000968288i
$227$	−22.6900	−	1.98512i	−1.50599	−	0.131757i	−0.695931	−	0.718108i	$-0.745008\pi$
$227$	−22.6900	−	1.98512i	−1.50599	−	0.131757i	−0.810057	+	0.586351i	$0.800564\pi$
$228$	5.29886	+	7.56072i	0.350926	+	0.500721i
$229$	−3.58552	−	5.12065i	−0.236938	−	0.338382i	0.683020	−	0.730400i	$-0.260666\pi$
$229$	−3.58552	−	5.12065i	−0.236938	−	0.338382i	−0.919958	+	0.392018i	$0.871777\pi$
$230$	−5.57674	−	2.67025i	−0.367719	−	0.176071i
$231$	−1.42330	−	1.94495i	−0.0936464	−	0.127969i
$232$	−24.8213	−	2.94133i	−1.62960	−	0.193108i
$233$	−4.06013	−	2.34412i	−0.265988	−	0.153568i	0.361075	−	0.932537i	$-0.382410\pi$
$233$	−4.06013	−	2.34412i	−0.265988	−	0.153568i	−0.627063	+	0.778969i	$0.715743\pi$
$234$	−3.77689	+	1.14080i	−0.246903	+	0.0745762i
$235$	16.2341	+	4.34991i	1.05900	+	0.283757i
$236$	−2.46835	+	22.8253i	−0.160676	+	1.48580i
$237$	−0.886466	+	2.60344i	−0.0575822	+	0.169111i
$238$	8.55996	+	1.59979i	0.554860	+	0.103699i
$239$	28.0872	−	10.2229i	1.81681	−	0.661264i	0.820881	−	0.571099i	$-0.193483\pi$
$239$	28.0872	−	10.2229i	1.81681	−	0.661264i	0.995927	−	0.0901651i	$-0.0287395\pi$
$240$	11.2685	+	11.7292i	0.727377	+	0.757117i
$241$	3.17904	+	18.0292i	0.204780	+	1.16136i	0.897786	+	0.440432i	$0.145175\pi$
$241$	3.17904	+	18.0292i	0.204780	+	1.16136i	−0.693006	+	0.720932i	$0.743714\pi$
$242$	−11.2727	+	6.35544i	−0.724634	+	0.408543i
$243$	−12.6142	+	9.15868i	−0.809203	+	0.587529i
$244$	−0.659499	+	0.162330i	−0.0422201	+	0.0103921i
$245$	−11.4484	−	8.01623i	−0.731409	−	0.512138i
$246$	−17.4971	+	0.186400i	−1.11557	+	0.0118844i
$247$	0.847708	+	2.32906i	0.0539384	+	0.148194i
$248$	8.07268	+	7.20718i	0.512616	+	0.457657i
$249$	18.6689	−	9.18478i	1.18309	−	0.582062i
$250$	−8.67194	+	12.1191i	−0.548462	+	0.766479i
$251$	−27.5561	−	7.38365i	−1.73933	−	0.466052i	−0.757031	−	0.653379i	$-0.773351\pi$
$251$	−27.5561	−	7.38365i	−1.73933	−	0.466052i	−0.982297	+	0.187328i	$0.940017\pi$
$252$	0.130787	+	6.13770i	0.00823880	+	0.386639i
$253$	2.44636	−	0.655500i	0.153801	−	0.0412109i
$254$	1.51120	+	0.567600i	0.0948209	+	0.0356144i
$255$	19.7482	−	14.4516i	1.23668	−	0.904994i
$256$	11.3751	+	11.2520i	0.710945	+	0.703248i
$257$	4.76262	−	27.0102i	0.297084	−	1.68485i	−0.361525	−	0.932362i	$-0.617744\pi$
$257$	4.76262	−	27.0102i	0.297084	−	1.68485i	0.658609	−	0.752485i	$-0.271145\pi$
$258$	−0.966580	−	9.83963i	−0.0601767	−	0.612589i
$259$	4.46245	+	0.390414i	0.277283	+	0.0242591i
$260$	2.10539	+	3.82527i	0.130571	+	0.237233i
$261$	−26.4837	−	1.20597i	−1.63930	−	0.0746479i
$262$	−5.73549	+	1.47411i	−0.354340	+	0.0910711i
$263$	7.43268	−	20.4211i	0.458319	−	1.25922i	−0.468417	−	0.883507i	$-0.655176\pi$
$263$	7.43268	−	20.4211i	0.458319	−	1.25922i	0.926736	−	0.375713i	$-0.122602\pi$
$264$	−6.63102	−	0.645699i	−0.408111	−	0.0397400i
$265$	−16.3531	+	19.4889i	−1.00456	+	1.19719i
$266$	3.84517	−	0.296814i	0.235762	−	0.0181988i
$267$	27.8674	−	0.581977i	1.70546	−	0.0356164i
$268$	2.88459	+	6.53161i	0.176204	+	0.398981i
$269$	18.8474	+	18.8474i	1.14915	+	1.14915i	0.986721	+	0.162426i	$0.0519319\pi$
$269$	18.8474	+	18.8474i	1.14915	+	1.14915i	0.162426	+	0.986721i	$0.448068\pi$
$270$	12.8212	+	11.5430i	0.780271	+	0.702483i
$271$	−32.7479			−1.98929			−0.994645	−	0.103347i	$-0.967045\pi$
$271$	−32.7479			−1.98929			−0.994645	+	0.103347i	$0.967045\pi$
$272$	19.0580	−	14.7063i	1.15556	−	0.891698i
$273$	−0.393216	+	1.60045i	−0.0237985	+	0.0968639i
$274$	−9.38371	+	10.9536i	−0.566891	+	0.661730i
$275$	0.0606297	+	0.693001i	0.00365611	+	0.0417895i
$276$	−6.06312	−	2.20388i	−0.364957	−	0.132658i
$277$	−4.08543	+	1.90507i	−0.245470	+	0.114464i	−0.541460	−	0.840727i	$-0.682128\pi$
$277$	−4.08543	+	1.90507i	−0.245470	+	0.114464i	0.295990	+	0.955191i	$0.404350\pi$
$278$	0.209757	+	0.816122i	0.0125804	+	0.0489478i
$279$	9.09323	+	7.00456i	0.544397	+	0.419352i
$280$	6.61348	−	1.55629i	0.395231	−	0.0930060i
$281$	−15.9282	−	18.9825i	−0.950195	−	1.13240i	−0.991084	−	0.133235i	$-0.957464\pi$
$281$	−15.9282	−	18.9825i	−0.950195	−	1.13240i	0.0408893	−	0.999164i	$-0.486981\pi$
$282$	17.3008	+	2.86091i	1.03025	+	0.170365i
$283$	2.89281	+	4.13136i	0.171959	+	0.245584i	0.895876	−	0.444304i	$-0.146549\pi$
$283$	2.89281	+	4.13136i	0.171959	+	0.245584i	−0.723917	+	0.689887i	$0.757660\pi$
$284$	12.4414	−	14.2257i	0.738263	−	0.844142i
$285$	6.79143	−	8.44574i	0.402290	−	0.500282i
$286$	−1.67432	−	0.628870i	−0.0990047	−	0.0371859i
$287$	−3.65458	+	6.32992i	−0.215723	+	0.373644i
$288$	12.8973	+	11.0299i	0.759983	+	0.649943i
$289$	−9.60876	−	16.6429i	−0.565221	−	0.978992i
$290$	4.79902	+	28.9447i	0.281808	+	1.69969i
$291$	13.4548	−	2.66324i	0.788735	−	0.156122i
$292$	−7.61222	−	22.3250i	−0.445471	−	1.30647i
$293$	2.46373	−	5.28348i	0.143933	−	0.308664i	−0.821104	−	0.570778i	$-0.806642\pi$
$293$	2.46373	−	5.28348i	0.143933	−	0.308664i	0.965037	+	0.262113i	$0.0844195\pi$
$294$	−12.7054	−	7.15609i	−0.740993	−	0.417352i
$295$	26.5399	−	4.67970i	1.54521	−	0.272462i
$296$	9.02051	−	8.48326i	0.524306	−	0.493079i
$297$	−7.06438	−	0.173991i	−0.409917	−	0.0100960i
$298$	−9.87842	−	2.75551i	−0.572242	−	0.159622i
$299$	−1.41865	−	0.993347i	−0.0820424	−	0.0574467i
$300$	0.885333	−	1.53495i	0.0511147	−	0.0886202i
$301$	−3.74298	−	1.74538i	−0.215742	−	0.100602i
$302$	−32.1657	−	6.01153i	−1.85093	−	0.345925i
$303$	0.229678	+	0.0152698i	0.0131947	+	0.000877227i
$304$	6.46696	−	8.47556i	0.370905	−	0.486107i
$305$	0.398623	+	0.690436i	0.0228251	+	0.0395342i
$306$	19.0320	−	17.0206i	1.08798	−	0.973001i
$307$	−5.30660	+	1.42190i	−0.302864	+	0.0811521i	−0.407050	−	0.913406i	$-0.633443\pi$
$307$	−5.30660	+	1.42190i	−0.302864	+	0.0811521i	0.104187	+	0.994558i	$0.466776\pi$
$308$	−1.64253	+	2.24654i	−0.0935921	+	0.128008i
$309$	−17.9181	+	6.94866i	−1.01932	+	0.395295i
$310$	5.48599	−	11.4573i	0.311583	−	0.650731i
$311$	2.92379	+	0.515543i	0.165793	+	0.0292338i	0.255928	−	0.966696i	$-0.417619\pi$
$311$	2.92379	+	0.515543i	0.165793	+	0.0292338i	−0.0901355	+	0.995930i	$0.528730\pi$
$312$	2.57638	+	3.75731i	0.145859	+	0.212716i
$313$	−2.70584	−	3.22469i	−0.152943	−	0.182270i	0.684133	−	0.729358i	$-0.260181\pi$
$313$	−2.70584	−	3.22469i	−0.152943	−	0.182270i	−0.837075	+	0.547087i	$0.815737\pi$
$314$	−14.4774	−	14.7766i	−0.817006	−	0.833892i
$315$	6.87678	−	2.15410i	0.387462	−	0.121370i
$316$	3.17502	+	0.0649568i	0.178609	+	0.00365411i
$317$	10.6061	+	22.7448i	0.595697	+	1.27748i	0.940816	+	0.338917i	$0.110061\pi$
$317$	10.6061	+	22.7448i	0.595697	+	1.27748i	−0.345120	+	0.938559i	$0.612162\pi$
$318$	−14.9928	+	21.9049i	−0.840752	+	1.22836i
$319$	−9.20630	−	7.72500i	−0.515454	−	0.432517i
$320$	8.96630	−	16.5028i	0.501232	−	0.922535i
$321$	6.75484	−	1.96200i	0.377018	−	0.109508i
$322$	−2.08192	+	1.71096i	−0.116021	+	0.0953479i
$323$	−11.3418	−	11.3418i	−0.631074	−	0.631074i
$324$	14.4906	+	10.6781i	0.805033	+	0.593230i
$325$	0.336363	−	0.336363i	0.0186580	−	0.0186580i
$326$	25.6492	+	2.50861i	1.42058	+	0.138939i
$327$	0.382549	+	1.31705i	0.0211550	+	0.0728333i
$328$	6.32480	+	19.1896i	0.349228	+	1.05957i
$329$	4.70835	−	5.61120i	0.259580	−	0.309355i
$330$	1.43998	+	7.68680i	0.0792685	+	0.423144i
$331$	8.11173	−	3.78256i	0.445861	−	0.207908i	−0.186703	−	0.982416i	$-0.559780\pi$
$331$	8.11173	−	3.78256i	0.445861	−	0.207908i	0.632564	+	0.774508i	$0.282002\pi$
$332$	−16.6370	−	17.3319i	−0.913073	−	0.951214i
$333$	8.89132	−	9.66678i	0.487241	−	0.529736i
$334$	0.163963	−	16.0304i	0.00897168	−	0.877143i
$335$	6.42054	−	5.38747i	0.350791	−	0.294349i
$336$	6.70853	−	2.29061i	0.365980	−	0.124963i
$337$	−1.38686	+	7.86529i	−0.0755472	+	0.428450i	0.923452	+	0.383715i	$0.125355\pi$
$337$	−1.38686	+	7.86529i	−0.0755472	+	0.428450i	−0.998999	+	0.0447349i	$0.985756\pi$
$338$	−5.70442	−	16.1860i	−0.310280	−	0.880401i
$339$	−0.630247	−	1.62518i	−0.0342303	−	0.0882676i
$340$	−22.8104	−	16.6776i	−1.23707	−	0.904469i
$341$	1.34671	+	5.02600i	0.0729286	+	0.272173i
$342$	6.19056	−	9.46260i	0.334747	−	0.511679i
$343$	−11.4778	+	6.62669i	−0.619741	+	0.357808i
$344$	−10.4900	+	4.50512i	−0.565584	+	0.242900i
$345$	−0.502348	+	7.55599i	−0.0270455	+	0.406801i
$346$	28.2183	−	19.3316i	1.51702	−	1.03927i
$347$	−8.85018	+	18.9793i	−0.475103	+	1.01886i	0.512031	+	0.858967i	$0.328893\pi$
$347$	−8.85018	+	18.9793i	−0.475103	+	1.01886i	−0.987134	+	0.159894i	$0.948885\pi$
$348$	7.93564	+	29.5660i	0.425395	+	1.58490i
$349$	17.0671	−	24.3744i	0.913583	−	1.30473i	−0.0386167	−	0.999254i	$-0.512295\pi$
$349$	17.0671	−	24.3744i	0.913583	−	1.30473i	0.952199	−	0.305477i	$-0.0988160\pi$
$350$	−0.363511	−	0.644761i	−0.0194305	−	0.0344639i
$351$	3.01395	+	3.77698i	0.160873	+	0.201600i
$352$	1.60866	+	7.52298i	0.0857417	+	0.400976i
$353$	4.10901	+	23.3034i	0.218701	+	1.24031i	0.874368	+	0.485263i	$0.161276\pi$
$353$	4.10901	+	23.3034i	0.218701	+	1.24031i	−0.655668	+	0.755050i	$0.727613\pi$
$354$	27.0810	−	7.56643i	1.43934	−	0.402151i
$355$	−20.1054	−	9.37531i	−1.06709	−	0.497590i
$356$	−10.3872	−	30.4634i	−0.550519	−	1.61456i
$357$	−2.07090	−	10.4623i	−0.109604	−	0.553724i
$358$	−0.00838150	+	0.0117132i	−0.000442976	+	0.000619062i
$359$	12.1565	−	7.01858i	0.641597	−	0.370426i	−0.143632	−	0.989631i	$-0.545878\pi$
$359$	12.1565	−	7.01858i	0.641597	−	0.370426i	0.785230	+	0.619205i	$0.212545\pi$
$360$	8.21829	−	18.1463i	0.433142	−	0.956396i
$361$	10.3026	+	5.94823i	0.542244	+	0.313065i
$362$	0.323389	−	0.146791i	0.0169969	−	0.00771515i
$363$	12.3512	+	9.93194i	0.648272	+	0.521292i
$364$	1.89876	−	0.127046i	0.0995220	−	0.00665904i
$365$	−22.6801	+	15.8808i	−1.18713	+	0.831238i
$366$	0.484347	+	0.676271i	0.0253172	+	0.0353492i
$367$	−12.8955	+	10.8206i	−0.673140	+	0.564832i	−0.913993	−	0.405730i	$-0.867017\pi$
$367$	−12.8955	+	10.8206i	−0.673140	+	0.564832i	0.240853	+	0.970562i	$0.422573\pi$
$368$	−0.304677	+	7.44302i	−0.0158824	+	0.387994i
$369$	8.16410	+	19.8147i	0.425006	+	1.03151i
$370$	−12.5130	−	7.39606i	−0.650522	−	0.384503i
$371$	4.68596	+	10.0491i	0.243283	+	0.521722i
$372$	4.52783	−	12.4566i	0.234757	−	0.645843i
$373$	−6.73279	+	0.589043i	−0.348611	+	0.0304995i	−0.260117	−	0.965577i	$-0.583761\pi$
$373$	−6.73279	+	0.589043i	−0.348611	+	0.0304995i	−0.0884941	+	0.996077i	$0.528205\pi$
$374$	11.5401	−	0.890792i	0.596722	−	0.0460618i
$375$	17.7243	+	4.35468i	0.915277	+	0.224875i
$376$	−2.90270	−	20.0394i	−0.149695	−	1.03345i
$377$			8.21796i			0.423247i
$378$	6.92095	−	2.93821i	0.355975	−	0.151125i
$379$	13.3387	−	13.3387i	0.685163	−	0.685163i	−0.275995	−	0.961159i	$-0.589007\pi$
$379$	13.3387	−	13.3387i	0.685163	−	0.685163i	0.961159	+	0.275995i	$0.0890075\pi$
$380$	−11.6695	−	4.51975i	−0.598633	−	0.231858i
$381$	−0.0412797	−	1.97664i	−0.00211482	−	0.101267i
$382$	18.3987	+	15.7618i	0.941360	+	0.806444i
$383$	11.1411	+	9.34846i	0.569282	+	0.477684i	0.881407	−	0.472357i	$-0.156597\pi$
$383$	11.1411	+	9.34846i	0.569282	+	0.477684i	−0.312126	+	0.950041i	$0.601041\pi$
$384$	7.62705	−	18.0507i	0.389216	−	0.921146i
$385$	3.06972	+	1.11729i	0.156447	+	0.0569421i
$386$	−15.6128	+	26.4144i	−0.794669	+	1.34446i
$387$	−10.7513	+	5.57122i	−0.546519	+	0.283201i
$388$	−7.63665	−	13.8750i	−0.387692	−	0.704395i
$389$	−2.11155	+	24.1351i	−0.107060	+	1.22370i	0.732628	+	0.680629i	$0.238293\pi$
$389$	−2.11155	+	24.1351i	−0.107060	+	1.22370i	−0.839688	+	0.543069i	$0.817262\pi$
$390$	3.39361	−	4.13297i	0.171842	−	0.209281i
$391$	11.0373	+	1.94618i	0.558181	+	0.0984224i
$392$	−3.43122	+	16.4846i	−0.173303	+	0.832598i
$393$	4.28318	+	5.85300i	0.216058	+	0.295245i
$394$	6.03158	−	2.73782i	0.303867	−	0.137929i
$395$	−0.964804	−	3.60070i	−0.0485445	−	0.181171i
$396$	2.27932	+	7.83490i	0.114540	+	0.393718i
$397$	0.160982	−	0.600793i	0.00807945	−	0.0301529i	−0.961768	−	0.273864i	$-0.911698\pi$
$397$	0.160982	−	0.600793i	0.00807945	−	0.0301529i	0.969848	+	0.243711i	$0.0783649\pi$
$398$	11.5515	−	1.91523i	0.579022	−	0.0960017i
$399$	−2.08512	−	4.23821i	−0.104387	−	0.212176i
$400$	−1.99879	−	0.437418i	−0.0999396	−	0.0218709i
$401$	−25.4846	+	9.27564i	−1.27264	+	0.463204i	−0.887992	−	0.459859i	$-0.847900\pi$
$401$	−25.4846	+	9.27564i	−1.27264	+	0.463204i	−0.384649	+	0.923063i	$0.625678\pi$
$402$	6.11739	−	6.24913i	0.305108	−	0.311678i
$403$	2.04081	−	2.91458i	0.101660	−	0.145186i
$404$	−0.0635270	−	0.258092i	−0.00316059	−	0.0128405i
$405$	7.30081	−	19.8275i	0.362780	−	0.985239i
$406$	12.3170	+	3.43572i	0.611282	+	0.170512i
$407$	5.86342	−	1.03388i	0.290639	−	0.0512475i
$408$	−25.3869	−	14.9909i	−1.25684	−	0.742158i
$409$	6.57629	+	18.0682i	0.325177	+	0.893415i	0.989313	+	0.145804i	$0.0465770\pi$
$409$	6.57629	+	18.0682i	0.325177	+	0.893415i	−0.664137	+	0.747611i	$0.731201\pi$
$410$	19.5662	−	13.4043i	0.966307	−	0.661991i
$411$	16.7222	+	5.69388i	0.824845	+	0.280858i
$412$	13.9136	+	17.2878i	0.685474	+	0.851706i
$413$	3.03991	−	11.3451i	0.149584	−	0.558256i
$414$	0.249109	+	7.89720i	0.0122430	+	0.388126i
$415$	−14.1005	+	24.4227i	−0.692165	+	1.19886i
$416$	3.23366	−	4.14933i	0.158543	−	0.203437i
$417$	0.832843	−	0.609468i	0.0407845	−	0.0298458i
$418$	4.83452	−	1.70383i	0.236464	−	0.0833370i
$419$	−3.06337	+	2.14500i	−0.149656	+	0.104790i	−0.646006	−	0.763332i	$-0.723562\pi$
$419$	−3.06337	+	2.14500i	−0.149656	+	0.104790i	0.496351	+	0.868122i	$0.334673\pi$
$420$	−4.77567	−	6.81420i	−0.233029	−	0.332499i
$421$	0.0518659	−	0.592829i	0.00252779	−	0.0288927i	−0.994826	−	0.101593i	$-0.967606\pi$
$421$	0.0518659	−	0.592829i	0.00252779	−	0.0288927i	0.997354	+	0.0727002i	$0.0231616\pi$
$422$	−10.3093	−	10.5224i	−0.501849	−	0.512221i
$423$	−4.60918	−	20.9764i	−0.224106	−	1.01991i
$424$	29.3491	+	8.83759i	1.42532	+	0.429191i
$425$	−1.05287	+	2.89275i	−0.0510719	+	0.140319i
$426$	−21.8333	−	7.68428i	−1.05783	−	0.372304i
$427$	0.346142	−	0.0302835i	0.0167510	−	0.00146552i
$428$	−4.52162	−	6.74719i	−0.218561	−	0.326138i
$429$	0.0457357	+	2.19001i	0.00220814	+	0.105735i
$430$	8.50859	+	10.3534i	0.410321	+	0.499284i
$431$	5.28277			0.254462			0.127231	−	0.991873i	$-0.459391\pi$
$431$	5.28277			0.254462			0.127231	+	0.991873i	$0.459391\pi$
$432$	6.68269	−	19.6810i	0.321521	−	0.946902i
$433$	−24.1081			−1.15856			−0.579281	−	0.815128i	$-0.696667\pi$
$433$	−24.1081			−1.15856			−0.579281	+	0.815128i	$0.696667\pi$
$434$	−3.51513	−	4.27726i	−0.168732	−	0.205315i
$435$	30.7377	−	18.6128i	1.47376	−	0.892413i
$436$	1.31556	−	0.881624i	0.0630041	−	0.0422221i
$437$	4.94464	−	0.432600i	0.236534	−	0.0206940i
$438$	−21.9306	+	18.8037i	−1.04788	+	0.898474i
$439$	9.42571	−	25.8969i	0.449865	−	1.23599i	−0.482953	−	0.875646i	$-0.660436\pi$
$439$	9.42571	−	25.8969i	0.449865	−	1.23599i	0.932818	−	0.360347i	$-0.117342\pi$
$440$	7.95535	−	4.27312i	0.379256	−	0.203713i
$441$	−2.36424	+	17.7021i	−0.112583	+	0.842958i
$442$	−5.53897	−	5.65344i	−0.263462	−	0.268907i
$443$	−0.381681	+	4.36263i	−0.0181342	+	0.207275i	0.981722	+	0.190320i	$0.0609526\pi$
$443$	−0.381681	+	4.36263i	−0.0181342	+	0.207275i	−0.999856	+	0.0169546i	$0.994603\pi$
$444$	−13.7476	−	6.40352i	−0.652434	−	0.303898i
$445$	−30.9479	+	21.6700i	−1.46707	+	1.02726i
$446$	−9.47742	+	3.34013i	−0.448769	+	0.158160i
$447$	1.35573	+	12.4870i	0.0641237	+	0.590617i
$448$	−4.86705	−	6.58130i	−0.229946	−	0.310937i
$449$	−2.94224	+	5.09612i	−0.138853	+	0.240501i	−0.927063	−	0.374906i	$-0.877675\pi$
$449$	−2.94224	+	5.09612i	−0.138853	+	0.240501i	0.788210	+	0.615407i	$0.211008\pi$
$450$	−2.14806	−	0.309282i	−0.101260	−	0.0145797i
$451$	−2.51440	+	9.38388i	−0.118399	+	0.441870i
$452$	−1.56801	+	1.26197i	−0.0737529	+	0.0593582i
$453$	7.78183	+	39.3142i	0.365622	+	1.84714i
$454$	26.5734	−	18.2047i	1.24715	−	0.854388i
$455$	−0.764007	−	2.09909i	−0.0358172	−	0.0984070i
$456$	−12.5784	−	3.50287i	−0.589035	−	0.164037i
$457$	22.6085	−	3.98649i	1.05758	−	0.186480i	0.382298	−	0.924039i	$-0.375133\pi$
$457$	22.6085	−	3.98649i	1.05758	−	0.186480i	0.675283	+	0.737559i	$0.264022\pi$
$458$	8.51539	+	2.37530i	0.397898	+	0.110991i
$459$	−28.0071	−	13.9095i	−1.30726	−	0.649239i
$460$	8.49074	−	2.08992i	0.395883	−	0.0974431i
$461$	−10.2594	+	14.6520i	−0.477829	+	0.682410i	−0.983622	−	0.180245i	$-0.942311\pi$
$461$	−10.2594	+	14.6520i	−0.477829	+	0.682410i	0.505793	+	0.862655i	$0.331200\pi$
$462$	3.30148	+	0.847041i	0.153599	+	0.0394079i
$463$	−23.6350	+	8.60242i	−1.09841	+	0.399788i	−0.826730	−	0.562599i	$-0.809801\pi$
$463$	−23.6350	+	8.60242i	−1.09841	+	0.399788i	−0.271680	+	0.962388i	$0.587579\pi$
$464$	29.7606	−	19.0736i	1.38160	−	0.885471i
$465$	−15.5237	−	1.03207i	−0.719892	−	0.0478609i
$466$	6.54087	−	1.08447i	0.303000	−	0.0502373i
$467$	−3.10813	+	11.5997i	−0.143827	+	0.536770i	0.855978	+	0.517013i	$0.172956\pi$
$467$	−3.10813	+	11.5997i	−0.143827	+	0.536770i	−0.999805	+	0.0197574i	$0.993711\pi$
$468$	3.10227	−	4.63774i	0.143402	−	0.214380i
$469$	−0.945433	−	3.52840i	−0.0436560	−	0.162927i
$470$	−21.6431	+	9.82410i	−0.998321	+	0.453152i
$471$	−10.2257	+	23.1808i	−0.471175	+	1.06811i
$472$	−17.7982	−	27.1551i	−0.819229	−	1.24991i
$473$	−5.40585	−	0.953196i	−0.248561	−	0.0438280i
$474$	−1.36911	−	3.64046i	−0.0628853	−	0.167212i
$475$	−0.118823	+	1.35815i	−0.00545196	+	0.0623161i
$476$	−10.7890	+	5.93817i	−0.494514	+	0.272176i
$477$	31.7263	+	7.09588i	1.45265	+	0.324898i
$478$	−21.5085	+	36.3892i	−0.983778	+	1.66440i
$479$	11.7637	+	4.28164i	0.537498	+	0.195633i	0.596483	−	0.802626i	$-0.296564\pi$
$479$	11.7637	+	4.28164i	0.537498	+	0.195633i	−0.0589853	+	0.998259i	$0.518787\pi$
$480$	−22.8436	−	2.69714i	−1.04266	−	0.123107i
$481$	−3.11880	−	2.61698i	−0.142205	−	0.119324i
$482$	−19.6620	−	16.8441i	−0.895581	−	0.767226i
$483$	2.89206	+	1.59016i	0.131593	+	0.0723548i
$484$	6.60978	−	17.0657i	0.300445	−	0.775716i
$485$	−13.1457	+	13.1457i	−0.596915	+	0.596915i
$486$	5.55851	−	21.3331i	0.252139	−	0.967691i
$487$			19.7774i			0.896198i	0.893984	+	0.448099i	$0.147899\pi$
$487$			19.7774i			0.896198i	−0.893984	+	0.448099i	$0.852101\pi$
$488$	0.574805	−	0.769531i	0.0260202	−	0.0348350i
$489$	−8.80405	−	30.3109i	−0.398133	−	1.37071i
$490$	19.7062	−	1.52115i	0.890237	−	0.0687186i
$491$	27.6865	−	2.42225i	1.24947	−	0.109315i	0.556849	−	0.830614i	$-0.312010\pi$
$491$	27.6865	−	2.42225i	1.24947	−	0.109315i	0.692624	+	0.721299i	$0.256455\pi$
$492$	18.9498	−	15.9145i	0.854323	−	0.717481i
$493$	−22.4758	−	48.1995i	−1.01226	−	2.17079i
$494$	−3.01749	−	1.78354i	−0.135763	−	0.0802454i
$495$	8.08773	−	5.13120i	0.363517	−	0.230630i
$496$	−15.2916	−	0.625953i	−0.686611	−	0.0281061i
$497$	−7.40642	+	6.21473i	−0.332223	+	0.278769i
$498$	−12.1504	+	26.7982i	−0.544472	+	1.20086i
$499$	11.8048	−	8.26579i	0.528454	−	0.370028i	−0.278691	−	0.960381i	$-0.589900\pi$
$499$	11.8048	−	8.26579i	0.528454	−	0.370028i	0.807145	+	0.590353i	$0.201012\pi$
$500$	−1.40698	−	21.0278i	−0.0629219	−	0.940394i
$501$	−18.3058	+	7.09903i	−0.817845	+	0.317161i
$502$	36.7375	−	16.6757i	1.63967	−	0.744271i
$503$	19.7646	+	11.4111i	0.881261	+	0.508796i	0.871074	−	0.491152i	$-0.163424\pi$
$503$	19.7646	+	11.4111i	0.881261	+	0.508796i	0.0101869	+	0.999948i	$0.496757\pi$
$504$	−5.65400	−	6.58856i	−0.251849	−	0.293478i
$505$	−0.270199	+	0.155999i	−0.0120237	+	0.00694188i
$506$	−2.08429	+	2.91281i	−0.0926580	+	0.129490i
$507$	−15.8157	+	13.8439i	−0.702401	+	0.614827i
$508$	−2.16077	+	0.736765i	−0.0958689	+	0.0326886i
$509$	16.8768	+	7.86978i	0.748051	+	0.348822i	0.758976	−	0.651119i	$-0.225700\pi$
$509$	16.8768	+	7.86978i	0.748051	+	0.348822i	−0.0109254	+	0.999940i	$0.503478\pi$
$510$	−8.60049	+	33.5218i	−0.380836	+	1.48437i
$511$	2.09540	+	11.8836i	0.0926953	+	0.525701i
$512$	−22.5316	−	2.07995i	−0.995766	−	0.0919215i
$513$	−13.5753	−	2.73994i	−0.599363	−	0.120971i
$514$	19.0491	+	33.7875i	0.840221	+	1.49030i
$515$	14.9410	−	21.3380i	0.658380	−	0.940264i
$516$	9.89119	+	9.88279i	0.435435	+	0.435066i
$517$	4.11453	−	8.82365i	0.180957	−	0.388064i
$518$	−5.22619	+	3.58032i	−0.229626	+	0.157310i
$519$	−34.8104	−	23.3068i	−1.52801	−	1.02305i
$520$	−5.73509	−	2.28900i	−0.251500	−	0.100379i
$521$	2.71572	−	1.56792i	0.118978	−	0.0686918i	−0.439330	−	0.898326i	$-0.644784\pi$
$521$	2.71572	−	1.56792i	0.118978	−	0.0686918i	0.558308	+	0.829634i	$0.311451\pi$
$522$	30.0187	−	22.4624i	1.31388	−	0.983151i
$523$	−3.29025	−	12.2794i	−0.143873	−	0.536940i	−0.999803	−	0.0198491i	$-0.993681\pi$
$523$	−3.29025	−	12.2794i	−0.143873	−	0.536940i	0.855930	−	0.517091i	$-0.172985\pi$
$524$	4.94292	−	6.76056i	0.215932	−	0.295337i
$525$	−0.568076	+	0.706452i	−0.0247929	+	0.0308321i
$526$	10.2155	+	28.9858i	0.445416	+	1.26384i
$527$	−3.99839	+	22.6760i	−0.174172	+	0.987781i
$528$	7.82477	−	5.24858i	0.340529	−	0.228415i
$529$	14.9622	−	12.5548i	0.650531	−	0.545861i
$530$	0.367984	−	35.9771i	0.0159842	−	1.56274i
$531$	−20.9131	−	27.3604i	−0.907551	−	1.18734i
$532$	−3.93468	+	3.77692i	−0.170590	+	0.163750i
$533$	6.02071	−	2.80750i	0.260786	−	0.121606i
$534$	−29.9252	+	25.6584i	−1.29499	+	1.11035i
$535$	−6.12838	+	7.30352i	−0.264953	+	0.315759i
$536$	−9.01648	−	4.54627i	−0.389453	−	0.196369i
$537$	0.0171306	+	0.00420883i	0.000739241	+	0.000181625i
$538$	−37.5158	−	3.66921i	−1.61742	−	0.158191i
$539$	−5.72469	+	5.72469i	−0.246580	+	0.246580i
$540$	−24.3728	−	1.09948i	−1.04884	−	0.0473140i
$541$	−23.3854	−	23.3854i	−1.00542	−	1.00542i	−0.999985	−	0.00543094i	$-0.998271\pi$
$541$	−23.3854	−	23.3854i	−1.00542	−	1.00542i	−0.00543094	−	0.999985i	$-0.501729\pi$
$542$	35.7800	−	29.4047i	1.53688	−	1.26304i
$543$	−0.313919	−	0.301075i	−0.0134715	−	0.0129204i
$544$	−7.61764	+	33.1803i	−0.326604	+	1.42259i
$545$	−1.42404	−	1.19491i	−0.0609990	−	0.0511842i
$546$	−1.00744	−	2.10171i	−0.0431145	−	0.0899451i
$547$	16.7946	+	36.0162i	0.718087	+	1.53994i	0.837100	+	0.547050i	$0.184249\pi$
$547$	16.7946	+	36.0162i	0.718087	+	1.53994i	−0.119012	+	0.992893i	$0.537973\pi$
$548$	0.417225	−	20.3935i	0.0178230	−	0.871168i
$549$	0.548994	−	0.858200i	0.0234305	−	0.0366271i
$550$	−0.688496	−	0.702726i	−0.0293576	−	0.0299643i
$551$	−15.1395	−	18.0426i	−0.644965	−	0.768640i
$552$	8.60340	−	3.03620i	0.366185	−	0.129229i
$553$	−1.59997	−	0.282118i	−0.0680376	−	0.0119969i
$554$	2.75312	−	5.74981i	0.116969	−	0.244286i
$555$	−2.72459	+	17.5924i	−0.115652	+	0.746757i
$556$	−0.961984	−	0.703345i	−0.0407972	−	0.0298285i
$557$	28.3556	−	7.59786i	1.20146	−	0.321932i	0.398057	−	0.917361i	$-0.369685\pi$
$557$	28.3556	−	7.59786i	1.20146	−	0.321932i	0.803408	+	0.595429i	$0.203018\pi$
$558$	−16.2247	+	0.511790i	−0.686844	+	0.0216658i
$559$	1.87679	+	3.25069i	0.0793797	+	0.137490i
$560$	−5.82842	+	7.63870i	−0.246296	+	0.322794i
$561$	−6.25784	−	12.7196i	−0.264206	−	0.537023i
$562$	34.4475	+	6.43798i	1.45308	+	0.271570i
$563$	35.3096	+	16.4651i	1.48812	+	0.693923i	0.985358	−	0.170500i	$-0.0545384\pi$
$563$	35.3096	+	16.4651i	1.48812	+	0.693923i	0.502765	+	0.864423i	$0.332316\pi$
$564$	−21.4715	+	12.4088i	−0.904115	+	0.522503i
$565$	1.93537	+	1.35516i	0.0814215	+	0.0570120i
$566$	−6.87024	−	1.91640i	−0.288778	−	0.0805523i
$567$	−6.48707	−	6.53582i	−0.272431	−	0.274479i
$568$	−0.819951	+	26.7142i	−0.0344044	+	1.12090i
$569$	−2.54999	+	0.449632i	−0.106901	+	0.0188496i	−0.226843	−	0.973931i	$-0.572840\pi$
$569$	−2.54999	+	0.449632i	−0.106901	+	0.0188496i	0.119942	+	0.992781i	$0.461729\pi$
$570$	0.163269	+	15.3258i	0.00683858	+	0.641929i
$571$	15.5641	−	33.3773i	0.651336	−	1.39679i	−0.251943	−	0.967742i	$-0.581070\pi$
$571$	15.5641	−	33.3773i	0.651336	−	1.39679i	0.903279	−	0.429053i	$-0.141153\pi$
$572$	2.39402	−	0.816295i	0.100099	−	0.0341310i
$573$	9.56401	−	28.0883i	0.399542	−	1.17340i
$574$	−1.69074	−	10.1975i	−0.0705703	−	0.425636i
$575$	−0.476308	−	0.824990i	−0.0198634	−	0.0344045i
$576$	−23.9954	−	0.470518i	−0.999808	−	0.0196049i
$577$	16.3671	−	28.3486i	0.681371	−	1.18017i	−0.293192	−	0.956054i	$-0.594718\pi$
$577$	16.3671	−	28.3486i	0.681371	−	1.18017i	0.974563	−	0.224115i	$-0.0719491\pi$
$578$	25.4423	+	9.55603i	1.05826	+	0.397478i
$579$	37.1368	+	5.75149i	1.54335	+	0.239024i
$580$	−31.2332	−	27.3156i	−1.29689	−	1.13422i
$581$	7.04972	+	10.0680i	0.292472	+	0.417693i
$582$	−12.3093	+	14.9911i	−0.510235	+	0.621400i
$583$	9.47303	+	11.2895i	0.392333	+	0.467564i
$584$	28.3629	+	17.5570i	1.17367	+	0.726515i
$585$	−6.24276	−	1.98119i	−0.258106	−	0.0819121i
$586$	2.05225	+	7.98490i	0.0847777	+	0.329853i
$587$	−12.1595	+	5.67008i	−0.501877	+	0.234029i	−0.657034	−	0.753861i	$-0.728189\pi$
$587$	−12.1595	+	5.67008i	−0.501877	+	0.234029i	0.155157	+	0.987890i	$0.450412\pi$
$588$	20.3073	−	3.58962i	0.837460	−	0.148034i
$589$	0.888768	+	10.1587i	0.0366211	+	0.418581i
$590$	−24.7953	+	28.9434i	−1.02081	+	1.19158i
$591$	−5.85496	−	5.61542i	−0.240841	−	0.230987i
$592$	−2.23852	+	17.3683i	−0.0920025	+	0.713835i
$593$	−11.3372			−0.465563			−0.232782	−	0.972529i	$-0.574783\pi$
$593$	−11.3372			−0.465563			−0.232782	+	0.972529i	$0.574783\pi$
$594$	7.87470	−	6.15308i	0.323103	−	0.252464i
$595$	10.2219	+	10.2219i	0.419058	+	0.419058i
$596$	13.2673	−	5.85930i	0.543449	−	0.240006i
$597$	−7.42811	−	12.2670i	−0.304012	−	0.502056i
$598$	2.44194	−	0.188496i	0.0998583	−	0.00770819i
$599$	−26.2107	+	31.2367i	−1.07094	+	1.27630i	−0.111690	+	0.993743i	$0.535626\pi$
$599$	−26.2107	+	31.2367i	−1.07094	+	1.27630i	−0.959251	+	0.282555i	$0.908818\pi$
$600$	0.410939	+	2.47202i	0.0167765	+	0.100920i
$601$	−4.60687	+	12.6573i	−0.187918	+	0.516301i	−0.997497	−	0.0707105i	$-0.977473\pi$
$601$	−4.60687	+	12.6573i	−0.187918	+	0.516301i	0.809579	+	0.587011i	$0.199696\pi$
$602$	5.65674	−	1.45387i	0.230551	−	0.0592555i
$603$	−9.88737	−	4.11718i	−0.402645	−	0.167665i
$604$	40.5418	−	22.3138i	1.64962	−	0.907937i
$605$	−21.4006	−	1.87231i	−0.870059	−	0.0761203i
$606$	−0.264655	+	0.189547i	−0.0107509	+	0.00769982i
$607$	−4.68106	+	26.5476i	−0.189999	+	1.07754i	0.729365	+	0.684125i	$0.239816\pi$
$607$	−4.68106	+	26.5476i	−0.189999	+	1.07754i	−0.919363	+	0.393410i	$0.871295\pi$
$608$	0.544562	+	15.0671i	0.0220849	+	0.611051i
$609$	−1.69040	−	15.5695i	−0.0684984	−	0.630910i
$610$	−1.05548	−	0.396436i	−0.0427352	−	0.0160512i
$611$	−6.43057	+	1.72307i	−0.260153	+	0.0697078i
$612$	−5.51120	+	35.6855i	−0.222777	+	1.44250i
$613$	10.4441	+	2.79849i	0.421834	+	0.113030i	0.463491	−	0.886102i	$-0.346597\pi$
$613$	10.4441	+	2.79849i	0.421834	+	0.113030i	−0.0416564	+	0.999132i	$0.513263\pi$
$614$	4.52121	−	6.31841i	0.182461	−	0.254990i
$615$	−24.1372	−	16.1606i	−0.973304	−	0.651659i
$616$	−0.222573	−	3.92940i	−0.00896774	−	0.158320i
$617$	−13.2545	−	36.4165i	−0.533607	−	1.46607i	−0.854749	−	0.519042i	$-0.826289\pi$
$617$	−13.2545	−	36.4165i	−0.533607	−	1.46607i	0.321142	−	0.947031i	$-0.395933\pi$
$618$	13.3378	−	23.6809i	0.536527	−	0.952585i
$619$	−39.3321	−	27.5406i	−1.58089	−	1.10695i	−0.940960	−	0.338517i	$-0.890075\pi$
$619$	−39.3321	−	27.5406i	−1.58089	−	1.10695i	−0.639930	−	0.768434i	$-0.721036\pi$
$620$	4.29371	+	17.4441i	0.172439	+	0.700571i
$621$	8.86825	−	3.87244i	0.355871	−	0.155396i
$622$	−3.65742	+	2.06203i	−0.146649	+	0.0826797i
$623$	2.85926	+	16.2157i	0.114554	+	0.649668i
$624$	−6.18866	−	1.79185i	−0.247745	−	0.0717313i
$625$	−25.6498	+	9.33577i	−1.02599	+	0.373431i
$626$	5.85186	+	1.09367i	0.233887	+	0.0437118i
$627$	−4.13496	−	4.72393i	−0.165134	−	0.188655i
$628$	29.0859	+	3.14538i	1.16066	+	0.125514i
$629$	25.4495	+	6.81917i	1.01474	+	0.271898i
$630$	−5.57932	+	8.52828i	−0.222285	+	0.339775i
$631$	−35.5765	−	20.5401i	−1.41628	−	0.817689i	−0.420310	−	0.907381i	$-0.638079\pi$
$631$	−35.5765	−	20.5401i	−1.41628	−	0.817689i	−0.995970	+	0.0896915i	$0.971412\pi$
$632$	−3.52732	+	2.77991i	−0.140309	+	0.110579i
$633$	−7.28169	+	16.5070i	−0.289421	+	0.656093i
$634$	−32.0109	−	15.3275i	−1.27132	−	0.608731i
$635$	1.53706	+	2.19514i	0.0609962	+	0.0871116i
$636$	−3.28767	−	37.3952i	−0.130365	−	1.48282i
$637$	5.51498	+	0.482499i	0.218512	+	0.0191173i
$638$	16.9951	+	0.173831i	0.672842	+	0.00688202i
$639$	1.18351	+	28.3233i	0.0468189	+	1.12045i
$640$	5.02156	+	26.0818i	0.198494	+	1.03097i
$641$	37.3021	+	13.5768i	1.47334	+	0.536253i	0.949006	−	0.315258i	$-0.102091\pi$
$641$	37.3021	+	13.5768i	1.47334	+	0.536253i	0.524337	+	0.851511i	$0.324313\pi$
$642$	−5.61858	+	8.20891i	−0.221747	+	0.323980i
$643$	−3.92223	−	44.8313i	−0.154678	−	1.76797i	−0.536656	−	0.843801i	$-0.680313\pi$
$643$	−3.92223	−	44.8313i	−0.154678	−	1.76797i	0.381978	−	0.924171i	$-0.375243\pi$
$644$	0.738396	−	3.73875i	0.0290969	−	0.147327i
$645$	7.90788	−	14.3822i	0.311372	−	0.566299i
$646$	22.5759	+	2.20802i	0.888236	+	0.0868734i
$647$		−	20.0216i		−	0.787131i	−0.919297	−	0.393566i	$-0.871241\pi$
$647$		−	20.0216i		−	0.787131i	0.919297	−	0.393566i	$-0.128759\pi$
$648$	−25.4203	+	1.34444i	−0.998604	+	0.0528145i
$649$		−	15.6112i		−	0.612792i
$650$	−0.0654831	+	0.669531i	−0.00256846	+	0.0262611i
$651$	−3.26696	+	5.94169i	−0.128042	+	0.232873i
$652$	−30.2766	+	20.2898i	−1.18572	+	0.794610i
$653$	−0.0727503	−	0.831540i	−0.00284694	−	0.0325407i	0.994638	−	0.103414i	$-0.0329768\pi$
$653$	−0.0727503	−	0.831540i	−0.00284694	−	0.0325407i	−0.997485	+	0.0708738i	$0.977421\pi$
$654$	−1.60057	−	1.09551i	−0.0625872	−	0.0428377i
$655$	−9.23777	−	3.36227i	−0.360950	−	0.131375i
$656$	−24.1410	−	15.2873i	−0.942547	−	0.596869i
$657$	31.3524	+	16.3957i	1.22317	+	0.639657i
$658$	−0.105949	+	10.3584i	−0.00413032	+	0.403814i
$659$	22.3300	+	1.95362i	0.869853	+	0.0761023i	0.513337	−	0.858187i	$-0.328409\pi$
$659$	22.3300	+	1.95362i	0.869853	+	0.0761023i	0.356516	+	0.934289i	$0.383965\pi$
$660$	−8.47537	−	7.10555i	−0.329903	−	0.276583i
$661$	6.36483	+	9.08992i	0.247563	+	0.353557i	0.923631	−	0.383282i	$-0.125206\pi$
$661$	6.36483	+	9.08992i	0.247563	+	0.353557i	−0.676068	+	0.736839i	$0.736317\pi$
$662$	−5.46640	+	11.4164i	−0.212458	+	0.443711i
$663$	−3.91229	+	8.86884i	−0.151941	+	0.344437i
$664$	33.7400	+	3.99820i	1.30936	+	0.155160i
$665$	5.54443	+	3.20108i	0.215004	+	0.124132i
$666$	−1.03466	+	18.5455i	−0.0400924	+	0.718622i
$667$	15.8966	+	4.25947i	0.615518	+	0.164928i
$668$	14.2147	+	17.6619i	0.549984	+	0.683359i
$669$	8.10603	+	9.26063i	0.313397	+	0.358037i
$670$	−2.17755	+	11.6514i	−0.0841262	+	0.450132i
$671$	0.433977	−	0.157955i	0.0167535	−	0.00609777i
$672$	−5.27292	+	8.52636i	−0.203407	+	0.328912i
$673$	4.67860	+	26.5337i	0.180347	+	1.02280i	0.931790	+	0.362999i	$0.118247\pi$
$673$	4.67860	+	26.5337i	0.180347	+	1.02280i	−0.751443	+	0.659798i	$0.770642\pi$
$674$	−5.54706	−	9.83883i	−0.213665	−	0.378977i
$675$	0.624507	+	2.58355i	0.0240373	+	0.0994408i
$676$	20.7662	+	12.5626i	0.798699	+	0.483177i
$677$	27.9694	+	19.5844i	1.07495	+	0.752690i	0.970321	−	0.241821i	$-0.0777448\pi$
$677$	27.9694	+	19.5844i	1.07495	+	0.752690i	0.104631	+	0.994511i	$0.466634\pi$
$678$	2.14787	+	1.20975i	0.0824884	+	0.0464602i
$679$	2.77120	+	7.61380i	0.106349	+	0.292191i
$680$	39.8974	−	2.25991i	1.53000	−	0.0866637i
$681$	−32.7812	−	21.9481i	−1.25618	−	0.841054i
$682$	−5.98431	−	4.28214i	−0.229151	−	0.163971i
$683$	7.41301	+	1.98631i	0.283651	+	0.0760040i	0.397839	−	0.917455i	$-0.369760\pi$
$683$	7.41301	+	1.98631i	0.283651	+	0.0760040i	−0.114189	+	0.993459i	$0.536427\pi$
$684$	1.73282	+	15.8973i	0.0662560	+	0.607849i
$685$	−23.1277	+	6.19705i	−0.883664	+	0.236777i
$686$	6.59032	−	17.5463i	0.251620	−	0.669920i
$687$	−1.16866	−	10.7641i	−0.0445873	−	0.410675i
$688$	7.41611	−	14.3414i	0.282736	−	0.546760i
$689$	1.74995	−	9.92444i	0.0666677	−	0.378091i
$690$	−6.23575	−	8.70667i	−0.237391	−	0.331457i
$691$	43.0688	+	3.76804i	1.63842	+	0.143343i	0.868800	−	0.495164i	$-0.164892\pi$
$691$	43.0688	+	3.76804i	1.63842	+	0.143343i	0.769616	+	0.638507i	$0.220448\pi$
$692$	−13.4730	+	46.4590i	−0.512167	+	1.76611i
$693$	−0.537125	−	4.13974i	−0.0204037	−	0.157256i
$694$	−7.37207	−	28.6833i	−0.279840	−	1.08880i
$695$	−0.478430	+	1.31447i	−0.0181479	+	0.0498609i
$696$	−35.2180	−	25.1780i	−1.33494	−	0.954370i
$697$	−27.6339	+	32.9328i	−1.04671	+	1.24742i
$698$	3.23864	+	41.9560i	0.122584	+	1.58806i
$699$	−4.20607	−	6.94604i	−0.159088	−	0.262724i
$700$	0.976107	+	0.378059i	0.0368934	+	0.0142893i
$701$	34.8141	+	34.8141i	1.31491	+	1.31491i	0.917749	+	0.397161i	$0.130005\pi$
$701$	34.8141	+	34.8141i	1.31491	+	1.31491i	0.397161	+	0.917749i	$0.369995\pi$
$702$	−6.68441	−	1.42044i	−0.252287	−	0.0536109i
$703$	11.6685			0.440084
$704$	−8.51257	−	6.77512i	−0.320830	−	0.255347i
$705$	21.0093	+	20.1498i	0.791256	+	0.758884i
$706$	−25.4138	−	21.7715i	−0.956461	−	0.819382i
$707$	0.0118513	+	0.135461i	0.000445714	+	0.00509453i
$708$	−22.7945	+	32.5834i	−0.856669	+	1.22456i
$709$	−14.2658	+	6.65227i	−0.535765	+	0.249831i	−0.671618	−	0.740898i	$-0.734400\pi$
$709$	−14.2658	+	6.65227i	−0.535765	+	0.249831i	0.135853	+	0.990729i	$0.456623\pi$
$710$	30.3852	−	7.80950i	1.14034	−	0.293085i
$711$	−3.51805	+	3.21161i	−0.131937	+	0.120445i
$712$	38.7023	+	23.9573i	1.45043	+	0.897836i
$713$	−4.58010	−	5.45835i	−0.171526	−	0.204417i
$714$	11.6569	+	9.57154i	0.436248	+	0.358206i
$715$	−1.70297	−	2.43210i	−0.0636876	−	0.0909553i
$716$	−0.00135985	−	0.0203236i	−5.08201e−5	−	0.000759528i
$717$	51.1606	+	7.92340i	1.91063	+	0.295905i
$718$	−6.98006	+	18.5839i	−0.260494	+	0.693546i
$719$	−20.0215	+	34.6782i	−0.746676	+	1.29328i	0.202732	+	0.979234i	$0.435018\pi$
$719$	−20.0215	+	34.6782i	−0.746676	+	1.29328i	−0.949408	+	0.314046i	$0.898315\pi$
$720$	7.31456	+	27.2058i	0.272598	+	1.01390i
$721$	−5.67644	−	9.83188i	−0.211402	−	0.366158i
$722$	−16.5975	+	2.75187i	−0.617697	+	0.102414i
$723$	−10.2207	+	30.0169i	−0.380112	+	1.11634i
$724$	−0.221526	+	0.450756i	−0.00823297	+	0.0167522i
$725$	−1.91039	+	4.09684i	−0.0709500	+	0.152153i
$726$	−22.4129	+	0.238768i	−0.831819	+	0.00886152i
$727$	−43.0309	+	7.58751i	−1.59593	+	0.281405i	−0.899731	−	0.436446i	$-0.856237\pi$
$727$	−43.0309	+	7.58751i	−1.59593	+	0.281405i	−0.696197	+	0.717851i	$0.745126\pi$
$728$	−1.96049	+	1.84373i	−0.0726606	+	0.0683331i
$729$	−26.7884	+	3.37383i	−0.992162	+	0.124957i
$730$	10.5206	−	37.7159i	0.389383	−	1.39593i
$731$	−19.8981	−	13.9328i	−0.735959	−	0.515324i
$732$	−1.13642	−	0.303987i	−0.0420035	−	0.0112357i
$733$	14.5408	+	6.78049i	0.537077	+	0.250443i	0.672179	−	0.740389i	$-0.265358\pi$
$733$	14.5408	+	6.78049i	0.537077	+	0.250443i	−0.135102	+	0.990832i	$0.543136\pi$
$734$	4.37357	−	23.4015i	0.161431	−	0.863766i
$735$	−10.6861	−	21.7205i	−0.394164	−	0.801174i
$736$	−6.35028	−	8.40575i	−0.234074	−	0.309840i
$737$	−2.42759	−	4.20471i	−0.0894214	−	0.154882i
$738$	−26.7119	−	14.3187i	−0.983277	−	0.527080i
$739$	1.12042	−	0.300215i	0.0412152	−	0.0110436i	−0.238153	−	0.971228i	$-0.576542\pi$
$739$	1.12042	−	0.300215i	0.0412152	−	0.0110436i	0.279368	+	0.960184i	$0.409875\pi$
$740$	20.3126	−	3.15471i	0.746707	−	0.115970i
$741$	−0.657028	+	4.24237i	−0.0241365	+	0.155847i
$742$	−14.1430	−	6.77196i	−0.519207	−	0.248606i
$743$	0.310254	+	0.0547062i	0.0113821	+	0.00200697i	0.179336	−	0.983788i	$-0.442605\pi$
$743$	0.310254	+	0.0547062i	0.0113821	+	0.00200697i	−0.167954	+	0.985795i	$0.553716\pi$
$744$	6.23783	+	17.6755i	0.228690	+	0.648017i
$745$	−10.9433	−	13.0417i	−0.400930	−	0.477810i
$746$	6.82728	−	6.68903i	0.249964	−	0.244903i
$747$	35.9997	+	1.63930i	1.31716	+	0.0599789i
$748$	−11.8087	+	11.3352i	−0.431769	+	0.414457i
$749$	1.75608	+	3.76592i	0.0641656	+	0.137604i
$750$	−23.2755	+	11.1569i	−0.849900	+	0.407393i
$751$	−24.9688	−	20.9513i	−0.911123	−	0.764523i	0.0612094	−	0.998125i	$-0.480504\pi$
$751$	−24.9688	−	20.9513i	−0.911123	−	0.764523i	−0.972332	+	0.233602i	$0.924949\pi$
$752$	21.1651	+	19.2885i	0.771811	+	0.703380i
$753$	−35.6617	−	34.2027i	−1.29958	−	1.24641i
$754$	−7.37900	−	8.97888i	−0.268727	−	0.326991i
$755$	−38.4109	−	38.4109i	−1.39792	−	1.39792i
$756$	−4.92352	+	9.42467i	−0.179067	+	0.342772i
$757$	24.8229	−	24.8229i	0.902202	−	0.902202i	−0.0934240	−	0.995626i	$-0.529781\pi$
$757$	24.8229	−	24.8229i	0.902202	−	0.902202i	0.995626	+	0.0934240i	$0.0297812\pi$
$758$	−2.59678	+	26.5507i	−0.0943193	+	0.964366i
$759$	4.26000	+	1.04664i	0.154628	+	0.0379907i
$760$	16.8083	−	5.53994i	0.609702	−	0.200955i
$761$	−2.16675	+	2.58223i	−0.0785446	+	0.0936058i	−0.803886	−	0.594784i	$-0.797238\pi$
$761$	−2.16675	+	2.58223i	−0.0785446	+	0.0936058i	0.725341	+	0.688390i	$0.241682\pi$
$762$	1.81995	+	2.12260i	0.0659299	+	0.0768936i
$763$	−0.734277	+	0.342399i	−0.0265826	+	0.0123957i
$764$	−34.2550	−	0.700813i	−1.23930	−	0.0253545i
$765$	42.0331	−	5.45374i	1.51971	−	0.197180i
$766$	−20.5667	−	0.210362i	−0.743106	−	0.00760070i
$767$	−8.17754	+	6.86177i	−0.295274	+	0.247764i
$768$	7.87468	+	26.5705i	0.284153	+	0.958779i
$769$	−2.26370	+	12.8381i	−0.0816312	+	0.462954i	0.916402	+	0.400260i	$0.131080\pi$
$769$	−2.26370	+	12.8381i	−0.0816312	+	0.462954i	−0.998033	+	0.0626937i	$0.980031\pi$
$770$	−4.35717	+	1.53560i	−0.157021	+	0.0553391i
$771$	29.7689	−	37.0203i	1.07210	−	1.33325i
$772$	−6.65946	−	42.8791i	−0.239679	−	1.54325i
$773$	−11.7532	−	43.8636i	−0.422734	−	1.57766i	−0.768823	−	0.639462i	$-0.779157\pi$
$773$	−11.7532	−	43.8636i	−0.422734	−	1.57766i	0.346090	−	0.938201i	$-0.387509\pi$
$774$	6.74431	−	15.7408i	0.242419	−	0.565790i
$775$	1.69493	−	0.978568i	0.0608836	−	0.0351512i
$776$	20.8022	+	8.30264i	0.746756	+	0.298047i
$777$	6.44709	+	4.31654i	0.231288	+	0.154855i
$778$	−19.3641	−	28.2658i	−0.694237	−	1.01338i
$779$	−8.04638	+	17.2555i	−0.288292	+	0.618243i
$780$	0.00321299	+	7.56281i	0.000115044	+	0.270792i
$781$	−7.37083	+	10.5266i	−0.263749	+	0.376673i
$782$	−13.8068	+	7.78415i	−0.493729	+	0.278361i
$783$	−39.1894	−	23.9315i	−1.40051	−	0.855242i
$784$	−11.0528	−	21.0919i	−0.394742	−	0.753280i
$785$	−5.96326	−	33.8193i	−0.212838	−	1.20706i
$786$	−9.93524	−	2.54902i	−0.354378	−	0.0909206i
$787$	−20.5966	−	9.60436i	−0.734190	−	0.342358i	0.0193038	−	0.999814i	$-0.493855\pi$
$787$	−20.5966	−	9.60436i	−0.734190	−	0.342358i	−0.753493	+	0.657455i	$0.771633\pi$
$788$	−4.13173	+	8.40714i	−0.147187	+	0.299492i
$789$	28.3228	−	24.7916i	1.00832	−	0.882603i
$790$	4.28724	+	3.06778i	0.152533	+	0.109147i
$791$	0.891757	−	0.514856i	0.0317072	−	0.0183062i
$792$	−9.52541	−	6.51371i	−0.338471	−	0.231455i
$793$	−0.273492	−	0.157901i	−0.00971198	−	0.00560722i
$794$	0.363571	+	0.800969i	0.0129027	+	0.0284253i
$795$	−41.0839	+	15.9324i	−1.45710	+	0.565064i
$796$	−10.9013	+	12.4647i	−0.386387	+	0.441801i
$797$	−28.4861	+	19.9462i	−1.00903	+	0.706530i	−0.956393	−	0.292084i	$-0.905651\pi$
$797$	−28.4861	+	19.9462i	−1.00903	+	0.706530i	−0.0526362	+	0.998614i	$0.516762\pi$
$798$	6.08372	+	2.75837i	0.215361	+	0.0976453i
$799$	33.0036	−	27.6933i	1.16759	−	0.979720i
$800$	2.57662	−	1.31682i	0.0910974	−	0.0465566i
$801$	42.7816	+	22.3726i	1.51161	+	0.790496i
$802$	19.5156	−	33.0174i	0.689119	−	1.16589i
$803$	6.77824	+	14.5360i	0.239199	+	0.512964i
$804$	−1.07264	+	12.3206i	−0.0378291	+	0.434515i
$805$	−4.45641	+	0.389886i	−0.157068	+	0.0137417i
$806$	0.387263	+	5.01692i	0.0136407	+	0.176713i
$807$	12.8772	+	44.3342i	0.453301	+	1.56064i
$808$	0.301153	+	0.224947i	0.0105945	+	0.00791362i
$809$			0.224251i			0.00788424i	0.999992	+	0.00394212i	$0.00125482\pi$
$809$			0.224251i			0.00788424i	−0.999992	+	0.00394212i	$0.998745\pi$
$810$	9.82657	+	28.2189i	0.345271	+	0.991510i
$811$	−9.02577	+	9.02577i	−0.316938	+	0.316938i	−0.847590	−	0.530652i	$-0.821947\pi$
$811$	−9.02577	+	9.02577i	−0.316938	+	0.316938i	0.530652	+	0.847590i	$0.321947\pi$
$812$	−16.5424	+	7.30571i	−0.580524	+	0.256380i
$813$	−49.7032	−	27.3287i	−1.74317	−	0.958458i
$814$	−5.47799	+	6.39444i	−0.192004	+	0.224125i
$815$	32.7730	+	27.4998i	1.14799	+	0.963276i
$816$	41.1980	−	6.41630i	1.44222	−	0.224615i
$817$	−10.1091	−	3.67941i	−0.353672	−	0.128726i
$818$	−23.4088	−	13.8362i	−0.818471	−	0.483773i
$819$	−1.93241	+	2.10095i	−0.0675240	+	0.0734131i
$820$	−9.34202	+	32.2141i	−0.326238	+	1.12497i
$821$	1.89650	−	21.6771i	0.0661885	−	0.756538i	−0.888489	−	0.458897i	$-0.848245\pi$
$821$	1.89650	−	21.6771i	0.0661885	−	0.756538i	0.954678	−	0.297641i	$-0.0961997\pi$
$822$	−23.3831	+	8.79397i	−0.815580	+	0.306725i
$823$	40.5848	+	7.15620i	1.41470	+	0.249449i	0.828169	−	0.560479i	$-0.189383\pi$
$823$	40.5848	+	7.15620i	1.41470	+	0.249449i	0.586529	+	0.809928i	$0.300494\pi$
$824$	−30.7247	−	6.39526i	−1.07035	−	0.222790i
$825$	−0.486300	+	1.10240i	−0.0169308	+	0.0383807i
$826$	6.86551	+	15.1251i	0.238882	+	0.526270i
$827$	−9.16588	−	34.2075i	−0.318729	−	1.18951i	−0.920467	−	0.390819i	$-0.872192\pi$
$827$	−9.16588	−	34.2075i	−0.318729	−	1.18951i	0.601738	−	0.798693i	$-0.294475\pi$
$828$	−7.36315	−	8.40473i	−0.255887	−	0.292085i
$829$	0.0871047	−	0.325079i	0.00302527	−	0.0112905i	−0.964397	−	0.264460i	$-0.914806\pi$
$829$	0.0871047	−	0.325079i	0.00302527	−	0.0112905i	0.967422	+	0.253169i	$0.0814730\pi$
$830$	−6.52339	−	39.3450i	−0.226430	−	1.36569i
$831$	−7.79049	−	0.517939i	−0.270249	−	0.0179671i
$832$	0.192654	+	7.43706i	0.00667909	+	0.257834i
$833$	−33.6657	+	12.2533i	−1.16645	+	0.424553i
$834$	−0.362709	+	1.41372i	−0.0125596	+	0.0489531i
$835$	15.2644	−	21.7998i	0.528245	−	0.754412i
$836$	−3.75226	+	6.20255i	−0.129775	+	0.214520i
$837$	7.95586	+	18.2197i	0.274995	+	0.629764i
$838$	1.42100	−	5.09424i	0.0490876	−	0.175978i
$839$	36.0774	−	6.36142i	1.24553	−	0.219621i	0.488246	−	0.872706i	$-0.337637\pi$
$839$	36.0774	−	6.36142i	1.24553	−	0.219621i	0.757285	+	0.653085i	$0.226526\pi$
$840$	11.3364	+	3.15701i	0.391143	+	0.108927i
$841$	−16.7909	−	46.1327i	−0.578998	−	1.59078i
$842$	0.475640	+	0.694291i	0.0163916	+	0.0239269i
$843$	−8.33386	−	42.1031i	−0.287034	−	1.45011i
$844$	20.7120	+	2.23982i	0.712937	+	0.0770977i
$845$	7.37359	−	27.5186i	0.253659	−	0.946669i
$846$	23.8709	+	18.7800i	0.820698	+	0.645669i
$847$	−4.68133	+	8.10830i	−0.160852	+	0.278604i
$848$	−40.0020	+	16.6970i	−1.37367	+	0.573379i
$849$	0.942881	+	8.68448i	0.0323596	+	0.298051i
$850$	−1.44707	−	4.10598i	−0.0496341	−	0.140834i
$851$	−6.67872	+	4.67649i	−0.228944	+	0.160308i
$852$	30.7547	−	11.2086i	1.05364	−	0.384000i
$853$	−1.33884	+	15.3030i	−0.0458411	+	0.523966i	0.938208	+	0.346071i	$0.112484\pi$
$853$	−1.33884	+	15.3030i	−0.0458411	+	0.523966i	−0.984049	+	0.177895i	$0.943071\pi$
$854$	−0.350999	+	0.343892i	−0.0120110	+	0.0117677i
$855$	17.3558	−	7.15099i	0.593557	−	0.244559i
$856$	10.9987	+	3.31191i	0.375927	+	0.113199i
$857$	3.96537	−	10.8948i	0.135455	−	0.372158i	−0.853357	−	0.521327i	$-0.825437\pi$
$857$	3.96537	−	10.8948i	0.135455	−	0.372158i	0.988812	+	0.149168i	$0.0476596\pi$
$858$	−2.01641	−	2.35172i	−0.0688390	−	0.0802865i
$859$	−21.7360	+	1.90166i	−0.741624	+	0.0648837i	−0.451705	−	0.892167i	$-0.649184\pi$
$859$	−21.7360	+	1.90166i	−0.741624	+	0.0648837i	−0.289919	+	0.957051i	$0.593628\pi$
$860$	−18.5928	−	3.67205i	−0.634010	−	0.125216i
$861$	−10.8292	+	6.55746i	−0.369058	+	0.223478i
$862$	−5.77191	+	4.74346i	−0.196592	+	0.161563i
$863$	−25.4308			−0.865676			−0.432838	−	0.901472i	$-0.642488\pi$
$863$	−25.4308			−0.865676			−0.432838	+	0.901472i	$0.642488\pi$
$864$	10.3703	+	27.5037i	0.352806	+	0.935696i
$865$	56.7820			1.93064
$866$	26.3403	−	21.6469i	0.895080	−	0.735593i
$867$	−0.694979	−	33.2785i	−0.0236027	−	1.13020i
$868$	7.68120	+	1.51702i	0.260717	+	0.0514911i
$869$	−2.15117	+	0.188203i	−0.0729735	+	0.00638435i
$870$	−16.8711	+	47.9359i	−0.571985	+	1.62518i
$871$	−1.13551	+	3.11978i	−0.0384752	+	0.105710i
$872$	−0.645754	+	2.14451i	−0.0218680	+	0.0726224i
$873$	22.6436	+	7.18614i	0.766371	+	0.243214i
$874$	−5.01403	+	4.91250i	−0.169602	+	0.166168i
$875$	−0.939688	+	10.7407i	−0.0317673	+	0.363101i
$876$	7.07714	−	40.2364i	0.239115	−	1.35946i
$877$	45.1465	−	31.6120i	1.52449	−	1.06746i	0.552192	−	0.833717i	$-0.313791\pi$
$877$	45.1465	−	31.6120i	1.52449	−	1.06746i	0.972298	−	0.233743i	$-0.0750974\pi$
$878$	12.9547	+	36.7582i	0.437200	+	1.24053i
$879$	8.14850	−	5.96301i	0.274842	−	0.201127i
$880$	−4.85506	+	11.8120i	−0.163664	+	0.398182i
$881$	5.42845	−	9.40235i	0.182889	−	0.316773i	−0.759974	−	0.649953i	$-0.774788\pi$
$881$	5.42845	−	9.40235i	0.182889	−	0.316773i	0.942863	+	0.333180i	$0.108122\pi$
$882$	−13.3118	−	21.4641i	−0.448231	−	0.722732i
$883$	6.24607	−	23.3106i	0.210197	−	0.784466i	−0.777605	−	0.628753i	$-0.783566\pi$
$883$	6.24607	−	23.3106i	0.210197	−	0.784466i	0.987802	−	0.155713i	$-0.0497675\pi$
$884$	11.1281	+	1.20341i	0.374279	+	0.0404749i
$885$	44.1863	+	15.0454i	1.48531	+	0.505744i
$886$	−3.50023	−	5.10929i	−0.117593	−	0.171650i
$887$	−3.94566	−	10.8406i	−0.132482	−	0.363992i	0.855659	−	0.517540i	$-0.173152\pi$
$887$	−3.94566	−	10.8406i	−0.132482	−	0.363992i	−0.988141	+	0.153548i	$0.950930\pi$
$888$	20.7704	−	5.34773i	0.697007	−	0.179458i
$889$	1.15018	−	0.202808i	0.0385759	−	0.00680197i
$890$	14.3557	−	51.4649i	0.481205	−	1.72511i
$891$	−10.5768	−	6.15942i	−0.354336	−	0.206348i
$892$	7.35581	−	12.1593i	0.246291	−	0.407123i
$893$	10.9440	−	15.6297i	0.366228	−	0.523028i
$894$	−12.6935	−	12.4259i	−0.424534	−	0.415584i
$895$	−0.0224679	+	0.00817763i	−0.000751018	+	0.000273348i
$896$	11.2271	+	2.82050i	0.375072	+	0.0942263i
$897$	−1.32419	−	2.69154i	−0.0442135	−	0.0898680i
$898$	−1.36119	−	8.20984i	−0.0454235	−	0.273966i
$899$	−8.75102	+	32.6592i	−0.291863	+	1.08925i
$900$	2.62466	−	1.59085i	0.0874886	−	0.0530282i
$901$	16.8792	+	62.9942i	0.562329	+	2.09864i
$902$	−5.67868	−	12.5105i	−0.189079	−	0.416553i
$903$	−4.22437	−	5.77264i	−0.140578	−	0.192101i
$904$	0.580054	−	2.78675i	0.0192923	−	0.0926860i
$905$	0.580601	+	0.102376i	0.0192998	+	0.00340308i
$906$	−43.8030	−	35.9669i	−1.45526	−	1.19492i
$907$	3.01092	−	34.4150i	0.0999759	−	1.14273i	−0.766067	−	0.642760i	$-0.777789\pi$
$907$	3.01092	−	34.4150i	0.0999759	−	1.14273i	0.866043	−	0.499969i	$-0.166655\pi$
$908$	−12.6876	+	43.7508i	−0.421054	+	1.45192i
$909$	0.335852	+	0.214846i	0.0111395	+	0.00712601i
$910$	2.71955	+	1.60744i	0.0901521	+	0.0532861i
$911$	28.2676	+	10.2886i	0.936546	+	0.340875i	0.764801	−	0.644266i	$-0.222837\pi$
$911$	28.2676	+	10.2886i	0.936546	+	0.340875i	0.171745	+	0.985141i	$0.445059\pi$
$912$	16.8883	−	7.46704i	0.559226	−	0.247258i
$913$	12.5143	+	10.5007i	0.414162	+	0.347523i
$914$	−21.1223	+	24.6560i	−0.698665	+	0.815549i
$915$	0.0288315	+	1.38057i	0.000953139	+	0.0456403i
$916$	−11.4367	+	5.05083i	−0.377878	+	0.166884i
$917$	−3.02959	+	3.02959i	−0.100046	+	0.100046i
$918$	43.0898	−	9.95053i	1.42218	−	0.328417i
$919$		−	26.6508i		−	0.879128i	−0.898211	−	0.439564i	$-0.855133\pi$
$919$		−	26.6508i		−	0.879128i	0.898211	−	0.439564i	$-0.144867\pi$
$920$	−7.40035	+	9.90736i	−0.243982	+	0.326636i
$921$	−9.24072	−	2.27036i	−0.304492	−	0.0748108i
$922$	−1.94681	−	25.2206i	−0.0641149	−	0.830598i
$923$	8.75393	−	0.765869i	0.288139	−	0.0252089i
$924$	−4.36774	+	2.03897i	−0.143688	+	0.0670772i
$925$	−0.946433	−	2.02963i	−0.0311185	−	0.0667339i
$926$	18.0991	−	30.6210i	0.594775	−	1.00627i
$927$	−32.9940	−	4.40659i	−1.08367	−	0.144731i
$928$	−15.3897	+	47.5620i	−0.505192	+	1.56130i
$929$	24.0333	−	20.1663i	0.788506	−	0.661635i	−0.156869	−	0.987619i	$-0.550140\pi$
$929$	24.0333	−	20.1663i	0.788506	−	0.661635i	0.945375	+	0.325984i	$0.105696\pi$
$930$	17.8877	−	12.8112i	0.586561	−	0.420097i
$931$	−12.9971	+	9.10064i	−0.425961	+	0.298261i
$932$	−6.17273	+	7.05801i	−0.202195	+	0.231193i
$933$	4.00737	+	3.22242i	0.131195	+	0.105497i
$934$	−7.01959	−	15.4646i	−0.229688	−	0.506016i
$935$	16.6399	+	9.60702i	0.544181	+	0.314183i
$936$	0.774767	+	7.85271i	0.0253241	+	0.256674i
$937$	5.76230	−	3.32687i	0.188246	−	0.108684i	−0.402915	−	0.915237i	$-0.632003\pi$
$937$	5.76230	−	3.32687i	0.188246	−	0.108684i	0.591161	+	0.806553i	$0.298670\pi$
$938$	4.20117	+	3.00619i	0.137173	+	0.0981555i
$939$	−1.41574	−	7.15236i	−0.0462008	−	0.233408i
$940$	14.8259	−	30.1673i	0.483566	−	0.983948i
$941$	2.05299	+	0.957323i	0.0669254	+	0.0312078i	0.455793	−	0.890086i	$-0.349356\pi$
$941$	2.05299	+	0.957323i	0.0669254	+	0.0312078i	−0.388867	+	0.921294i	$0.627134\pi$
$942$	−9.64178	−	34.5089i	−0.314146	−	1.12436i
$943$	−2.31014	−	13.1014i	−0.0752284	−	0.426642i
$944$	43.8290	+	13.6882i	1.42651	+	0.445513i
$945$	12.2349	+	2.46940i	0.398001	+	0.0803297i
$946$	6.76227	−	3.81252i	0.219860	−	0.123956i
$947$	−10.6981	+	15.2784i	−0.347640	+	0.496482i	−0.954452	−	0.298364i	$-0.903559\pi$
$947$	−10.6981	+	15.2784i	−0.347640	+	0.496482i	0.606812	+	0.794845i	$0.292448\pi$
$948$	4.76469	+	2.74820i	0.154750	+	0.0892573i
$949$	4.63500	−	9.93980i	0.150459	−	0.322660i
$950$	−1.08967	−	1.59059i	−0.0353536	−	0.0516057i
$951$	−2.88352	+	43.3720i	−0.0935045	+	1.40643i
$952$	6.45603	−	16.1756i	0.209241	−	0.524253i
$953$	32.7287	−	18.8959i	1.06019	−	0.612099i	0.134703	−	0.990886i	$-0.456992\pi$
$953$	32.7287	−	18.8959i	1.06019	−	0.612099i	0.925484	+	0.378787i	$0.123659\pi$
$954$	−41.0353	+	20.7345i	−1.32857	+	0.671304i
$955$	10.4092	+	38.8476i	0.336833	+	1.25708i
$956$	−9.17425	−	59.0713i	−0.296716	−	1.91050i
$957$	−7.52625	−	19.4075i	−0.243289	−	0.627354i
$958$	−16.6975	+	5.88469i	−0.539471	+	0.190126i
$959$	−1.81207	+	10.2768i	−0.0585150	+	0.331855i
$960$	27.3805	−	17.5647i	0.883703	−	0.566898i
$961$	−12.5333	+	10.5167i	−0.404299	+	0.339247i
$962$	5.75739	+	0.0588882i	0.185626	+	0.00189863i
$963$	11.8895	+	2.65920i	0.383134	+	0.0856915i
$964$	36.6070	+	0.748933i	1.17903	+	0.0241215i
$965$	−46.1639	+	21.5266i	−1.48607	+	0.692965i
$966$	−4.58766	+	0.859416i	−0.147606	+	0.0276513i
$967$	−1.03148	+	1.22927i	−0.0331703	+	0.0395308i	−0.782375	−	0.622808i	$-0.785992\pi$
$967$	−1.03148	+	1.22927i	−0.0331703	+	0.0395308i	0.749204	+	0.662339i	$0.230436\pi$
$968$	8.10173	+	24.5809i	0.260399	+	0.790059i
$969$	−7.74914	−	26.6790i	−0.248938	−	0.857053i
$970$	2.55920	−	26.1665i	0.0821711	−	0.840157i
$971$	20.2705	−	20.2705i	0.650511	−	0.650511i	−0.302605	−	0.953116i	$-0.597856\pi$
$971$	20.2705	−	20.2705i	0.650511	−	0.650511i	0.953116	+	0.302605i	$0.0978562\pi$
$972$	13.0821	+	28.2995i	0.419608	+	0.907705i
$973$	0.431090	+	0.431090i	0.0138201	+	0.0138201i
$974$	−17.7583	−	21.6086i	−0.569013	−	0.692384i
$975$	0.791217	−	0.229815i	0.0253392	−	0.00735998i
$976$	0.0629441	+	1.35691i	0.00201479	+	0.0434335i
$977$	−27.8468	−	23.3662i	−0.890897	−	0.747551i	0.0774930	−	0.996993i	$-0.475308\pi$
$977$	−27.8468	−	23.3662i	−0.890897	−	0.747551i	−0.968390	+	0.249442i	$0.919753\pi$
$978$	36.8357	+	25.2122i	1.17788	+	0.806196i
$979$	9.24918	+	19.8349i	0.295605	+	0.633927i
$980$	−20.1650	+	19.3565i	−0.644148	+	0.618319i
$981$	−0.518489	+	2.31821i	−0.0165541	+	0.0740148i
$982$	−28.0750	+	27.5065i	−0.895910	+	0.877769i
$983$	−16.2218	−	19.3324i	−0.517395	−	0.616608i	0.442567	−	0.896735i	$-0.354068\pi$
$983$	−16.2218	−	19.3324i	−0.517395	−	0.616608i	−0.959963	+	0.280127i	$0.909623\pi$
$984$	−6.41458	+	34.4033i	−0.204489	+	1.09674i
$985$	10.8289	+	1.90943i	0.345037	+	0.0608394i
$986$	67.8357	+	32.4811i	2.16033	+	1.03441i
$987$	11.8288	−	4.58722i	0.376514	−	0.146013i
$988$	4.89834	−	0.760751i	0.155837	−	0.0242027i
$989$	7.26081	−	1.94553i	0.230880	−	0.0618642i
$990$	−4.22923	+	12.8684i	−0.134414	+	0.408984i
$991$	10.0355	+	17.3819i	0.318787	+	0.552155i	0.980235	−	0.197836i	$-0.0633913\pi$
$991$	10.0355	+	17.3819i	0.318787	+	0.552155i	−0.661449	+	0.749991i	$0.730058\pi$
$992$	17.2695	−	13.0465i	0.548306	−	0.414228i
$993$	15.4682	+	1.02838i	0.490869	+	0.0326347i
$994$	2.51192	−	13.4405i	0.0796733	−	0.426306i
$995$	17.6166	+	8.21476i	0.558484	+	0.260425i
$996$	−10.7870	−	40.1895i	−0.341801	−	1.27345i
$997$	−23.4462	−	16.4172i	−0.742549	−	0.519938i	0.140004	−	0.990151i	$-0.455288\pi$
$997$	−23.4462	−	16.4172i	−0.742549	−	0.519938i	−0.882553	+	0.470212i	$0.844177\pi$
$998$	−5.47584	+	19.6308i	−0.173335	+	0.621401i
$999$	21.5619	−	7.25184i	0.682190	−	0.229438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.bg.a.13.16	✓	840
16.5	even	4	inner	432.2.bg.a.229.64	yes	840
27.25	even	9	inner	432.2.bg.a.349.64	yes	840
432.133	even	36	inner	432.2.bg.a.133.16	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.bg.a.13.16	✓	840	1.1	even	1	trivial
432.2.bg.a.133.16	yes	840	432.133	even	36	inner
432.2.bg.a.229.64	yes	840	16.5	even	4	inner
432.2.bg.a.349.64	yes	840	27.25	even	9	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.bg (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09259 + 0.897911i) q^{2} +(1.51775 + 0.834518i) q^{3} +(0.387511 - 1.96210i) q^{4} +(-2.33873 + 0.204612i) q^{5} +(-2.40761 + 0.451022i) q^{6} +(-0.349949 + 0.961477i) q^{7} +(1.33840 + 2.49172i) q^{8} +(1.60716 + 2.53319i) q^{9} +O(q^{10})\)	\(q+(-1.09259 + 0.897911i) q^{2} +(1.51775 + 0.834518i) q^{3} +(0.387511 - 1.96210i) q^{4} +(-2.33873 + 0.204612i) q^{5} +(-2.40761 + 0.451022i) q^{6} +(-0.349949 + 0.961477i) q^{7} +(1.33840 + 2.49172i) q^{8} +(1.60716 + 2.53319i) q^{9} +(2.37155 - 2.32353i) q^{10} +(-0.118528 + 1.35478i) q^{11} +(2.22555 - 2.65460i) q^{12} +(0.761766 - 0.533394i) q^{13} +(-0.480969 - 1.36472i) q^{14} +(-3.72037 - 1.64116i) q^{15} +(-3.69967 - 1.52067i) q^{16} +(-3.00905 + 5.21183i) q^{17} +(-4.03055 - 1.32465i) q^{18} +(-0.689817 + 2.57443i) q^{19} +(-0.504814 + 4.66811i) q^{20} +(-1.33351 + 1.16725i) q^{21} +(-1.08697 - 1.58665i) q^{22} +(-0.636948 - 1.75000i) q^{23} +(-0.0480244 + 4.89874i) q^{24} +(0.503752 - 0.0888251i) q^{25} +(-0.353358 + 1.26678i) q^{26} +(0.325285 + 5.18596i) q^{27} +(1.75090 + 1.05922i) q^{28} +(-5.06872 + 7.23889i) q^{29} +(5.53846 - 1.54745i) q^{30} +(3.59535 - 1.30860i) q^{31} +(5.40765 - 1.66050i) q^{32} +(-1.31048 + 1.95731i) q^{33} +(-1.39210 - 8.39626i) q^{34} +(0.621706 - 2.32024i) q^{35} +(5.59316 - 2.17177i) q^{36} +(-1.13311 - 4.22883i) q^{37} +(-1.55792 - 3.43219i) q^{38} +(1.60130 - 0.173854i) q^{39} +(-3.63999 - 5.55361i) q^{40} +(7.03504 + 1.24047i) q^{41} +(0.408893 - 2.47269i) q^{42} +(-0.351791 + 4.02099i) q^{43} +(2.61228 + 0.757554i) q^{44} +(-4.27703 - 5.59560i) q^{45} +(2.26727 + 1.34011i) q^{46} +(-6.72720 - 2.44850i) q^{47} +(-4.34617 - 5.39545i) q^{48} +(4.56034 + 3.82658i) q^{49} +(-0.470638 + 0.549374i) q^{50} +(-8.91636 + 5.39917i) q^{51} +(-0.751380 - 1.70136i) q^{52} +(7.66271 - 7.66271i) q^{53} +(-5.01194 - 5.37406i) q^{54} -3.19271i q^{55} +(-2.86411 + 0.414864i) q^{56} +(-3.19538 + 3.33169i) q^{57} +(-0.961835 - 12.4604i) q^{58} +(-11.4355 + 1.00048i) q^{59} +(-4.66181 + 6.66377i) q^{60} +(-0.143518 - 0.307774i) q^{61} +(-2.75324 + 4.65807i) q^{62} +(-2.99802 + 0.658761i) q^{63} +(-4.41737 + 6.66985i) q^{64} +(-1.67243 + 1.40333i) q^{65} +(-0.325667 - 3.31523i) q^{66} +(-2.92446 + 2.04773i) q^{67} +(9.06008 + 7.92370i) q^{68} +(0.493676 - 3.18762i) q^{69} +(1.40410 + 3.09331i) q^{70} +(8.18337 + 4.72467i) q^{71} +(-4.16098 + 7.39502i) q^{72} +(10.2135 - 5.89678i) q^{73} +(5.03514 + 3.60295i) q^{74} +(0.838699 + 0.285576i) q^{75} +(4.78398 + 2.35111i) q^{76} +(-1.26111 - 0.588064i) q^{77} +(-1.59346 + 1.62778i) q^{78} +(0.275726 + 1.56372i) q^{79} +(8.96368 + 2.79944i) q^{80} +(-3.83407 + 8.14247i) q^{81} +(-8.80025 + 4.96152i) q^{82} +(6.88999 - 9.83993i) q^{83} +(1.77351 + 3.06879i) q^{84} +(5.97095 - 12.8047i) q^{85} +(-3.22613 - 4.70917i) q^{86} +(-13.7341 + 6.75692i) q^{87} +(-3.53437 + 1.51790i) q^{88} +(13.9368 - 8.04639i) q^{89} +(9.69740 + 2.27330i) q^{90} +(0.246267 + 0.919081i) q^{91} +(-3.68050 + 0.571611i) q^{92} +(6.54891 + 1.01425i) q^{93} +(9.54862 - 3.36522i) q^{94} +(1.08653 - 6.16204i) q^{95} +(9.59321 + 1.99255i) q^{96} +(6.06620 - 5.09014i) q^{97} +(-8.41851 - 0.0861070i) q^{98} +(-3.62240 + 1.87709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8}+O(q^{10}) \) 840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8	\( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 30 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 12 q^{18} - 6 q^{19} - 54 q^{20} - 12 q^{21} - 12 q^{22} + 18 q^{24} - 24 q^{26} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 24 q^{33} - 6 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 12 q^{40} - 72 q^{42} - 12 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 24 q^{47} - 12 q^{48} - 24 q^{49} - 168 q^{50} + 6 q^{51} - 12 q^{52} - 24 q^{53} + 156 q^{54} - 54 q^{56} + 42 q^{58} - 48 q^{59} - 72 q^{60} - 12 q^{61} + 60 q^{62} - 24 q^{63} - 6 q^{64} - 24 q^{65} - 198 q^{66} - 12 q^{67} - 66 q^{68} - 12 q^{69} - 54 q^{70} - 144 q^{72} - 96 q^{74} - 96 q^{75} - 12 q^{76} - 12 q^{77} - 90 q^{78} - 24 q^{79} - 204 q^{80} - 24 q^{81} - 24 q^{82} + 48 q^{83} + 36 q^{84} + 18 q^{85} - 72 q^{86} - 12 q^{88} - 66 q^{90} - 6 q^{91} + 102 q^{92} - 12 q^{93} - 12 q^{94} - 24 q^{95} - 120 q^{96} - 24 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) \) 840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 30 * q^12 - 12 * q^13 - 12 * q^14 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 12 * q^18 - 6 * q^19 - 54 * q^20 - 12 * q^21 - 12 * q^22 + 18 * q^24 - 24 * q^26 - 12 * q^27 - 24 * q^28 - 12 * q^29 - 12 * q^30 - 24 * q^31 - 12 * q^32 - 24 * q^33 - 6 * q^35 - 12 * q^36 - 6 * q^37 - 12 * q^38 - 12 * q^40 - 72 * q^42 - 12 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 - 24 * q^47 - 12 * q^48 - 24 * q^49 - 168 * q^50 + 6 * q^51 - 12 * q^52 - 24 * q^53 + 156 * q^54 - 54 * q^56 + 42 * q^58 - 48 * q^59 - 72 * q^60 - 12 * q^61 + 60 * q^62 - 24 * q^63 - 6 * q^64 - 24 * q^65 - 198 * q^66 - 12 * q^67 - 66 * q^68 - 12 * q^69 - 54 * q^70 - 144 * q^72 - 96 * q^74 - 96 * q^75 - 12 * q^76 - 12 * q^77 - 90 * q^78 - 24 * q^79 - 204 * q^80 - 24 * q^81 - 24 * q^82 + 48 * q^83 + 36 * q^84 + 18 * q^85 - 72 * q^86 - 12 * q^88 - 66 * q^90 - 6 * q^91 + 102 * q^92 - 12 * q^93 - 12 * q^94 - 24 * q^95 - 120 * q^96 - 24 * q^97 - 6 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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