LMFDB - Embedded newform 352.2.n.a.45.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(45,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("352.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.n (of order $8$, degree $4$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.10
Character	$\chi$	$=$	352.45
Dual form			352.2.n.a.133.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17562 - 0.786075i) q^{2} +(-0.821814 + 1.98403i) q^{3} +(0.764172 + 1.84825i) q^{4} +(0.279093 - 0.115604i) q^{5} +(2.52574 - 1.68647i) q^{6} +(2.72415 - 2.72415i) q^{7} +(0.554489 - 2.77354i) q^{8} +(-1.13970 - 1.13970i) q^{9} +(-0.418981 - 0.0834812i) q^{10} +(0.382683 + 0.923880i) q^{11} +(-4.29501 - 0.00277694i) q^{12} +(0.251096 + 0.104007i) q^{13} +(-5.34396 + 1.06118i) q^{14} +0.648734i q^{15} +(-2.83208 + 2.82477i) q^{16} -5.55843i q^{17} +(0.443964 + 2.23574i) q^{18} +(5.77761 + 2.39317i) q^{19} +(0.426940 + 0.427492i) q^{20} +(3.16607 + 7.64356i) q^{21} +(0.276348 - 1.38695i) q^{22} +(5.15795 + 5.15795i) q^{23} +(5.04712 + 3.37946i) q^{24} +(-3.47101 + 3.47101i) q^{25} +(-0.213436 - 0.319653i) q^{26} +(-2.75429 + 1.14086i) q^{27} +(7.11665 + 2.95320i) q^{28} +(-1.39035 + 3.35661i) q^{29} +(0.509954 - 0.762666i) q^{30} +6.50679 q^{31} +(5.54994 - 1.09463i) q^{32} -2.14750 q^{33} +(-4.36934 + 6.53461i) q^{34} +(0.445368 - 1.07521i) q^{35} +(1.23552 - 2.97737i) q^{36} +(5.40065 - 2.23702i) q^{37} +(-4.91108 - 7.35509i) q^{38} +(-0.412708 + 0.412708i) q^{39} +(-0.165879 - 0.838176i) q^{40} +(-7.01666 - 7.01666i) q^{41} +(2.28632 - 11.4747i) q^{42} +(2.85804 + 6.89992i) q^{43} +(-1.41513 + 1.41330i) q^{44} +(-0.449834 - 0.186327i) q^{45} +(-2.00926 - 10.1183i) q^{46} +0.365097i q^{47} +(-3.27699 - 7.94038i) q^{48} -7.84202i q^{49} +(6.80906 - 1.35212i) q^{50} +(11.0281 + 4.56800i) q^{51} +(-0.000351444 + 0.543568i) q^{52} +(-1.06100 - 2.56149i) q^{53} +(4.13481 + 0.823854i) q^{54} +(0.213608 + 0.213608i) q^{55} +(-6.04504 - 9.06607i) q^{56} +(-9.49625 + 9.49625i) q^{57} +(4.27307 - 2.85318i) q^{58} +(-3.70202 + 1.53343i) q^{59} +(-1.19903 + 0.495745i) q^{60} +(-3.00271 + 7.24917i) q^{61} +(-7.64952 - 5.11482i) q^{62} -6.20941 q^{63} +(-7.38508 - 3.07580i) q^{64} +0.0821026 q^{65} +(2.52465 + 1.68810i) q^{66} +(3.55646 - 8.58605i) q^{67} +(10.2734 - 4.24760i) q^{68} +(-14.4724 + 5.99467i) q^{69} +(-1.36878 + 0.913951i) q^{70} +(-8.35963 + 8.35963i) q^{71} +(-3.79294 + 2.52905i) q^{72} +(5.80236 + 5.80236i) q^{73} +(-8.10758 - 1.61542i) q^{74} +(-4.03407 - 9.73912i) q^{75} +(-0.00808658 + 12.5073i) q^{76} +(3.55928 + 1.47430i) q^{77} +(0.809608 - 0.160769i) q^{78} -9.98829i q^{79} +(-0.463859 + 1.11577i) q^{80} -11.2375i q^{81} +(2.73331 + 13.7646i) q^{82} +(2.72696 + 1.12954i) q^{83} +(-11.7078 + 11.6927i) q^{84} +(-0.642576 - 1.55132i) q^{85} +(2.06388 - 10.3583i) q^{86} +(-5.51701 - 5.51701i) q^{87} +(2.77461 - 0.549108i) q^{88} +(4.52615 - 4.52615i) q^{89} +(0.382367 + 0.572653i) q^{90} +(0.967355 - 0.400692i) q^{91} +(-5.59164 + 13.4748i) q^{92} +(-5.34737 + 12.9097i) q^{93} +(0.286994 - 0.429216i) q^{94} +1.88915 q^{95} +(-2.38924 + 11.9108i) q^{96} +8.32160 q^{97} +(-6.16441 + 9.21924i) q^{98} +(0.616799 - 1.48908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 16 q^{10} - 16 q^{14} - 16 q^{20} + 24 q^{24} - 48 q^{27} + 40 q^{28} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 56 q^{36} - 16 q^{38} - 48 q^{39} - 64 q^{40} - 104 q^{48} - 80 q^{50} + 32 q^{51} + 64 q^{54}+ \cdots + 56 q^{98}+O(q^{100}) $ 160 * q - 16 * q^10 - 16 * q^14 - 16 * q^20 + 24 * q^24 - 48 * q^27 + 40 * q^28 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 56 * q^36 - 16 * q^38 - 48 * q^39 - 64 * q^40 - 104 * q^48 - 80 * q^50 + 32 * q^51 + 64 * q^54 - 40 * q^56 + 8 * q^58 + 32 * q^59 - 8 * q^60 - 64 * q^61 + 24 * q^62 - 24 * q^64 + 48 * q^68 - 64 * q^69 - 24 * q^70 + 32 * q^71 + 72 * q^72 - 128 * q^78 - 16 * q^80 + 40 * q^82 - 80 * q^83 - 152 * q^84 - 64 * q^86 - 112 * q^87 + 144 * q^90 - 72 * q^92 + 96 * q^94 + 56 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.17562	−	0.786075i	−0.831290	−	0.555839i
$2$	−1.17562	−	0.786075i	−0.831290	−	0.555839i
$3$	−0.821814	+	1.98403i	−0.474475	+	1.14548i	0.487691	+	0.873017i	$0.337839\pi$
$3$	−0.821814	+	1.98403i	−0.474475	+	1.14548i	−0.962165	+	0.272467i	$0.912161\pi$
$4$	0.764172	+	1.84825i	0.382086	+	0.924127i
$5$	0.279093	−	0.115604i	0.124814	−	0.0516996i	−0.319402	−	0.947619i	$-0.603482\pi$
$5$	0.279093	−	0.115604i	0.124814	−	0.0516996i	0.444216	+	0.895920i	$0.353482\pi$
$6$	2.52574	−	1.68647i	1.03113	−	0.688497i
$7$	2.72415	−	2.72415i	1.02963	−	1.02963i	0.0300857	−	0.999547i	$-0.490422\pi$
$7$	2.72415	−	2.72415i	1.02963	−	1.02963i	0.999547	−	0.0300857i	$-0.00957801\pi$
$8$	0.554489	−	2.77354i	0.196041	−	0.980596i
$9$	−1.13970	−	1.13970i	−0.379899	−	0.379899i
$10$	−0.418981	−	0.0834812i	−0.132493	−	0.0263991i
$11$	0.382683	+	0.923880i	0.115383	+	0.278560i
$11$	0.382683	+	0.923880i	0.115383	+	0.278560i
$12$	−4.29501	−	0.00277694i	−1.23986	−	0.000801633i
$13$	0.251096	+	0.104007i	0.0696414	+	0.0288464i	0.417232	−	0.908800i	$-0.363000\pi$
$13$	0.251096	+	0.104007i	0.0696414	+	0.0288464i	−0.347591	+	0.937646i	$0.613000\pi$
$14$	−5.34396	+	1.06118i	−1.42823	+	0.283613i
$15$			0.648734i			0.167502i
$16$	−2.83208	+	2.82477i	−0.708021	+	0.706192i
$17$		−	5.55843i		−	1.34812i	−0.738678	−	0.674059i	$-0.764549\pi$
$17$		−	5.55843i		−	1.34812i	0.738678	−	0.674059i	$-0.235451\pi$
$18$	0.443964	+	2.23574i	0.104643	+	0.526968i
$19$	5.77761	+	2.39317i	1.32548	+	0.549030i	0.929361	−	0.369172i	$-0.120359\pi$
$19$	5.77761	+	2.39317i	1.32548	+	0.549030i	0.396114	+	0.918201i	$0.370359\pi$
$20$	0.426940	+	0.427492i	0.0954667	+	0.0955902i
$21$	3.16607	+	7.64356i	0.690892	+	1.66796i
$22$	0.276348	−	1.38695i	0.0589175	−	0.295699i
$23$	5.15795	+	5.15795i	1.07551	+	1.07551i	0.996906	+	0.0786003i	$0.0250451\pi$
$23$	5.15795	+	5.15795i	1.07551	+	1.07551i	0.0786003	+	0.996906i	$0.474955\pi$
$24$	5.04712	+	3.37946i	1.03024	+	0.689830i
$25$	−3.47101	+	3.47101i	−0.694201	+	0.694201i
$26$	−0.213436	−	0.319653i	−0.0418583	−	0.0626892i
$27$	−2.75429	+	1.14086i	−0.530064	+	0.219560i
$28$	7.11665	+	2.95320i	1.34492	+	0.558103i
$29$	−1.39035	+	3.35661i	−0.258182	+	0.623306i	−0.998818	−	0.0485998i	$-0.984524\pi$
$29$	−1.39035	+	3.35661i	−0.258182	+	0.623306i	0.740636	+	0.671906i	$0.234524\pi$
$30$	0.509954	−	0.762666i	0.0931044	−	0.139243i
$31$	6.50679			1.16865			0.584327	−	0.811518i	$-0.301359\pi$
$31$	6.50679			1.16865			0.584327	+	0.811518i	$0.301359\pi$
$32$	5.54994	−	1.09463i	0.981099	−	0.193505i
$33$	−2.14750			−0.373832
$34$	−4.36934	+	6.53461i	−0.749336	+	1.12068i
$35$	0.445368	−	1.07521i	0.0752809	−	0.181744i
$36$	1.23552	−	2.97737i	0.205920	−	0.496228i
$37$	5.40065	−	2.23702i	0.887861	−	0.367764i	0.108321	−	0.994116i	$-0.465453\pi$
$37$	5.40065	−	2.23702i	0.887861	−	0.367764i	0.779540	+	0.626352i	$0.215453\pi$
$38$	−4.91108	−	7.35509i	−0.796682	−	1.19315i
$39$	−0.412708	+	0.412708i	−0.0660862	+	0.0660862i
$40$	−0.165879	−	0.838176i	−0.0262277	−	0.132527i
$41$	−7.01666	−	7.01666i	−1.09582	−	1.09582i	−0.994894	−	0.100924i	$-0.967820\pi$
$41$	−7.01666	−	7.01666i	−1.09582	−	1.09582i	−0.100924	−	0.994894i	$-0.532180\pi$
$42$	2.28632	−	11.4747i	0.352786	−	1.77058i
$43$	2.85804	+	6.89992i	0.435847	+	1.05223i	0.977369	+	0.211541i	$0.0678483\pi$
$43$	2.85804	+	6.89992i	0.435847	+	1.05223i	−0.541522	+	0.840687i	$0.682152\pi$
$44$	−1.41513	+	1.41330i	−0.213339	+	0.213063i
$45$	−0.449834	−	0.186327i	−0.0670573	−	0.0277760i
$46$	−2.00926	−	10.1183i	−0.296249	−	1.49187i
$47$			0.365097i			0.0532549i	0.999645	+	0.0266274i	$0.00847678\pi$
$47$			0.365097i			0.0532549i	−0.999645	+	0.0266274i	$0.991523\pi$
$48$	−3.27699	−	7.94038i	−0.472993	−	1.14610i
$49$		−	7.84202i		−	1.12029i
$50$	6.80906	−	1.35212i	0.962946	−	0.191218i
$51$	11.0281	+	4.56800i	1.54425	+	0.639648i
$52$	−0.000351444		0.543568i	−4.87365e−5		0.0753793i
$53$	−1.06100	−	2.56149i	−0.145740	−	0.351848i	0.834105	−	0.551605i	$-0.185985\pi$
$53$	−1.06100	−	2.56149i	−0.145740	−	0.351848i	−0.979845	+	0.199758i	$0.935985\pi$
$54$	4.13481	+	0.823854i	0.562676	+	0.112112i
$55$	0.213608	+	0.213608i	0.0288029	+	0.0288029i
$56$	−6.04504	−	9.06607i	−0.807803	−	1.21150i
$57$	−9.49625	+	9.49625i	−1.25781	+	1.25781i
$58$	4.27307	−	2.85318i	0.561082	−	0.374641i
$59$	−3.70202	+	1.53343i	−0.481962	+	0.199635i	−0.610417	−	0.792080i	$-0.708998\pi$
$59$	−3.70202	+	1.53343i	−0.481962	+	0.199635i	0.128455	+	0.991715i	$0.458998\pi$
$60$	−1.19903	+	0.495745i	−0.154794	+	0.0640003i
$61$	−3.00271	+	7.24917i	−0.384457	+	0.928162i	0.606635	+	0.794981i	$0.292519\pi$
$61$	−3.00271	+	7.24917i	−0.384457	+	0.928162i	−0.991092	+	0.133181i	$0.957481\pi$
$62$	−7.64952	−	5.11482i	−0.971490	−	0.649583i
$63$	−6.20941			−0.782312
$64$	−7.38508	−	3.07580i	−0.923136	−	0.384475i
$65$	0.0821026			0.0101836
$66$	2.52465	+	1.68810i	0.310763	+	0.207791i
$67$	3.55646	−	8.58605i	0.434490	−	1.04895i	−0.543332	−	0.839518i	$-0.682838\pi$
$67$	3.55646	−	8.58605i	0.434490	−	1.04895i	0.977823	−	0.209435i	$-0.0671624\pi$
$68$	10.2734	−	4.24760i	1.24583	−	0.515097i
$69$	−14.4724	+	5.99467i	−1.74228	+	0.721674i
$70$	−1.36878	+	0.913951i	−0.163601	+	0.109238i
$71$	−8.35963	+	8.35963i	−0.992106	+	0.992106i	−0.999969	−	0.00786328i	$-0.997497\pi$
$71$	−8.35963	+	8.35963i	−0.992106	+	0.992106i	0.00786328	+	0.999969i	$0.497497\pi$
$72$	−3.79294	+	2.52905i	−0.447003	+	0.298051i
$73$	5.80236	+	5.80236i	0.679115	+	0.679115i	0.959800	−	0.280685i	$-0.0905616\pi$
$73$	5.80236	+	5.80236i	0.679115	+	0.679115i	−0.280685	+	0.959800i	$0.590562\pi$
$74$	−8.10758	−	1.61542i	−0.942488	−	0.187789i
$75$	−4.03407	−	9.73912i	−0.465815	−	1.12458i
$76$	−0.00808658	+	12.5073i	−0.000927595	+	1.43468i
$77$	3.55928	+	1.47430i	0.405617	+	0.168012i
$78$	0.809608	−	0.160769i	0.0916701	−	0.0182035i
$79$		−	9.98829i		−	1.12377i	−0.827215	−	0.561885i	$-0.810076\pi$
$79$		−	9.98829i		−	1.12377i	0.827215	−	0.561885i	$-0.189924\pi$
$80$	−0.463859	+	1.11577i	−0.0518610	+	0.124747i
$81$		−	11.2375i		−	1.24861i
$82$	2.73331	+	13.7646i	0.301844	+	1.52004i
$83$	2.72696	+	1.12954i	0.299323	+	0.123983i	0.527290	−	0.849685i	$-0.323208\pi$
$83$	2.72696	+	1.12954i	0.299323	+	0.123983i	−0.227968	+	0.973669i	$0.573208\pi$
$84$	−11.7078	+	11.6927i	−1.27743	+	1.27578i
$85$	−0.642576	−	1.55132i	−0.0696972	−	0.168264i
$86$	2.06388	−	10.3583i	0.222554	−	1.11697i
$87$	−5.51701	−	5.51701i	−0.591486	−	0.591486i
$88$	2.77461	−	0.549108i	0.295775	−	0.0585351i
$89$	4.52615	−	4.52615i	0.479771	−	0.479771i	−0.425288	−	0.905058i	$-0.639827\pi$
$89$	4.52615	−	4.52615i	0.479771	−	0.479771i	0.905058	+	0.425288i	$0.139827\pi$
$90$	0.382367	+	0.572653i	0.0403050	+	0.0603630i
$91$	0.967355	−	0.400692i	0.101406	−	0.0420039i
$92$	−5.59164	+	13.4748i	−0.582968	+	1.40484i
$93$	−5.34737	+	12.9097i	−0.554497	+	1.33867i
$94$	0.286994	−	0.429216i	0.0296011	−	0.0442702i
$95$	1.88915			0.193822
$96$	−2.38924	+	11.9108i	−0.243850	+	1.21565i
$97$	8.32160			0.844931			0.422465	−	0.906379i	$-0.361165\pi$
$97$	8.32160			0.844931			0.422465	+	0.906379i	$0.361165\pi$
$98$	−6.16441	+	9.21924i	−0.622700	+	0.931284i
$99$	0.616799	−	1.48908i	0.0619906	−	0.149659i
$100$	−9.06774	−	3.76285i	−0.906774	−	0.376285i
$101$	0.718167	−	0.297474i	0.0714603	−	0.0295998i	−0.346667	−	0.937988i	$-0.612687\pi$
$101$	0.718167	−	0.297474i	0.0714603	−	0.0295998i	0.418127	+	0.908388i	$0.362687\pi$
$102$	−9.37411	−	14.0392i	−0.928175	−	1.39008i
$103$	2.13637	−	2.13637i	0.210503	−	0.210503i	−0.593978	−	0.804481i	$-0.702444\pi$
$103$	2.13637	−	2.13637i	0.210503	−	0.210503i	0.804481	+	0.593978i	$0.202444\pi$
$104$	0.427698	−	0.638754i	0.0419393	−	0.0626350i
$105$	1.76725	+	1.76725i	0.172466	+	0.172466i
$106$	−0.766185	+	3.84537i	−0.0744184	+	0.373496i
$107$	−7.79568	−	18.8204i	−0.753637	−	1.81944i	−0.537945	−	0.842980i	$-0.680799\pi$
$107$	−7.79568	−	18.8204i	−0.753637	−	1.81944i	−0.215692	−	0.976461i	$-0.569201\pi$
$108$	−4.21336	−	4.21881i	−0.405431	−	0.405955i
$109$	−7.93026	−	3.28482i	−0.759581	−	0.314629i	−0.0309371	−	0.999521i	$-0.509849\pi$
$109$	−7.93026	−	3.28482i	−0.759581	−	0.314629i	−0.728644	+	0.684892i	$0.759849\pi$
$110$	−0.0832103	−	0.419034i	−0.00793379	−	0.0399534i
$111$			12.5535i			1.19152i
$112$	−0.0199268	+	15.4101i	−0.00188291	+	1.45612i
$113$		−	2.05944i		−	0.193736i	−0.995297	−	0.0968678i	$-0.969118\pi$
$113$		−	2.05944i		−	0.193736i	0.995297	−	0.0968678i	$-0.0308824\pi$
$114$	18.6288	−	3.69923i	1.74474	−	0.346465i
$115$	2.03582	+	0.843266i	0.189842	+	0.0786349i
$116$	−7.26633	−	0.00469804i	−0.674662	−	0.000436202i
$117$	−0.167636	−	0.404709i	−0.0154980	−	0.0374154i
$118$	5.55756	+	1.10734i	0.511615	+	0.101938i
$119$	−15.1420	−	15.1420i	−1.38807	−	1.38807i
$120$	1.79929	+	0.359716i	0.164252	+	0.0328374i
$121$	−0.707107	+	0.707107i	−0.0642824	+	0.0642824i
$122$	9.22844	−	6.16193i	0.835504	−	0.557875i
$123$	19.6877	−	8.15490i	1.77518	−	0.735303i
$124$	4.97231	+	12.0262i	0.446526	+	1.07998i
$125$	−1.14549	+	2.76546i	−0.102456	+	0.247350i
$126$	7.29992	+	4.88106i	0.650328	+	0.434840i
$127$	−14.0744			−1.24890			−0.624449	−	0.781065i	$-0.714676\pi$
$127$	−14.0744			−1.24890			−0.624449	+	0.781065i	$0.714676\pi$
$128$	6.26426	+	9.42120i	0.553687	+	0.832725i
$129$	−16.0385			−1.41211
$130$	−0.0965216	−	0.0645388i	−0.00846550	−	0.00566043i
$131$	−1.90215	+	4.59221i	−0.166192	+	0.401223i	−0.984932	−	0.172941i	$-0.944673\pi$
$131$	−1.90215	+	4.59221i	−0.166192	+	0.401223i	0.818740	+	0.574164i	$0.194673\pi$
$132$	−1.64106	−	3.96913i	−0.142836	−	0.345469i
$133$	22.2584	−	9.21975i	1.93005	−	0.799454i
$134$	−10.9303	+	7.29830i	−0.944236	+	0.630477i
$135$	−0.636814	+	0.636814i	−0.0548082	+	0.0548082i
$136$	−15.4165	−	3.08209i	−1.32196	−	0.264287i
$137$	−8.10813	−	8.10813i	−0.692724	−	0.692724i	0.270106	−	0.962830i	$-0.412941\pi$
$137$	−8.10813	−	8.10813i	−0.692724	−	0.692724i	−0.962830	+	0.270106i	$0.912941\pi$
$138$	21.7264	+	4.32894i	1.84947	+	0.368504i
$139$	−3.46056	−	8.35454i	−0.293521	−	0.708623i	−1.00000		0.000888214i	$-0.999717\pi$
$139$	−3.46056	−	8.35454i	−0.293521	−	0.708623i	0.706478	−	0.707735i	$-0.250283\pi$
$140$	2.32760	+	0.00150491i	0.196719	+	0.000127188i
$141$	−0.724365	−	0.300042i	−0.0610025	−	0.0252681i
$142$	16.3991	−	3.25647i	1.37618	−	0.273277i
$143$			0.271784i			0.0227277i
$144$	6.44709	+	0.00833673i	0.537257	+	0.000694727i
$145$			1.09753i			0.0911452i
$146$	−2.26029	−	11.3825i	−0.187063	−	0.942020i
$147$	15.5588	+	6.44468i	1.28327	+	0.531548i
$148$	8.26161	+	8.27230i	0.679100	+	0.679979i
$149$	2.77508	+	6.69963i	0.227343	+	0.548855i	0.995852	−	0.0909838i	$-0.0290012\pi$
$149$	2.77508	+	6.69963i	0.227343	+	0.548855i	−0.768509	+	0.639839i	$0.779001\pi$
$150$	−2.91313	+	14.6206i	−0.237856	+	1.19377i
$151$	6.90311	+	6.90311i	0.561768	+	0.561768i	0.929809	−	0.368042i	$-0.119972\pi$
$151$	6.90311	+	6.90311i	0.561768	+	0.561768i	−0.368042	+	0.929809i	$0.619972\pi$
$152$	9.84117	−	14.6975i	0.798224	−	1.19212i
$153$	−6.33492	+	6.33492i	−0.512148	+	0.512148i
$154$	−3.02545	−	4.53108i	−0.243798	−	0.365125i
$155$	1.81600	−	0.752210i	0.145864	−	0.0604190i
$156$	−1.07817	−	0.447409i	−0.0863226	−	0.0358214i
$157$	1.99930	−	4.82675i	0.159562	−	0.385216i	−0.823798	−	0.566883i	$-0.808149\pi$
$157$	1.99930	−	4.82675i	0.159562	−	0.385216i	0.983360	+	0.181667i	$0.0581492\pi$
$158$	−7.85155	+	11.7425i	−0.624636	+	0.934179i
$159$	5.95404			0.472186
$160$	1.42240	−	0.947097i	0.112451	−	0.0748746i
$161$	28.1021			2.21475
$162$	−8.83352	+	13.2111i	−0.694027	+	1.03796i
$163$	−3.17889	+	7.67452i	−0.248990	+	0.601115i	−0.998119	−	0.0613095i	$-0.980472\pi$
$163$	−3.17889	+	7.67452i	−0.248990	+	0.601115i	0.749129	+	0.662424i	$0.230472\pi$
$164$	7.60663	−	18.3305i	0.593978	−	1.43137i
$165$	−0.599352	+	0.248260i	−0.0466595	+	0.0193270i
$166$	−2.31797	−	3.47151i	−0.179909	−	0.269441i
$167$	17.7689	−	17.7689i	1.37500	−	1.37500i	0.522132	−	0.852865i	$-0.325137\pi$
$167$	17.7689	−	17.7689i	1.37500	−	1.37500i	0.852865	−	0.522132i	$-0.174863\pi$
$168$	22.9553	−	4.54295i	1.77104	−	0.350496i
$169$	−9.14016	−	9.14016i	−0.703089	−	0.703089i
$170$	−0.464025	+	2.32887i	−0.0355891	+	0.178617i
$171$	−3.85724	−	9.31220i	−0.294970	−	0.712122i
$172$	−10.5688	+	10.5551i	−0.805861	+	0.804820i
$173$	7.00356	+	2.90097i	0.532471	+	0.220557i	0.632685	−	0.774409i	$-0.281953\pi$
$173$	7.00356	+	2.90097i	0.532471	+	0.220557i	−0.100214	+	0.994966i	$0.531953\pi$
$174$	2.14913	+	10.8227i	0.162925	+	0.820467i
$175$			18.9111i			1.42954i
$176$	−3.69354	−	1.53551i	−0.278411	−	0.115744i
$177$		−	8.60512i		−	0.646801i
$178$	−8.87893	+	1.76314i	−0.665504	+	0.132153i
$179$	17.2459	+	7.14347i	1.28902	+	0.533928i	0.918692	−	0.394975i	$-0.129247\pi$
$179$	17.2459	+	7.14347i	1.28902	+	0.533928i	0.370324	+	0.928903i	$0.379247\pi$
$180$	0.000629606	−	0.973793i	4.69280e−5	−	0.0725822i
$181$	−5.80099	−	14.0048i	−0.431184	−	1.04097i	−0.978906	−	0.204311i	$-0.934505\pi$
$181$	−5.80099	−	14.0048i	−0.431184	−	1.04097i	0.547722	−	0.836661i	$-0.315495\pi$
$182$	−1.45222	−	0.289352i	−0.107645	−	0.0214482i
$183$	−11.9149	−	11.9149i	−0.880778	−	0.880778i
$184$	17.1658	−	11.4458i	1.26548	−	0.843793i
$185$	1.24867	−	1.24867i	0.0918042	−	0.0918042i
$186$	16.4345	−	10.9735i	1.20503	−	0.804615i
$187$	5.13532	−	2.12712i	0.375532	−	0.155550i
$188$	−0.674792	+	0.278997i	−0.0492142	+	0.0203479i
$189$	−4.39522	+	10.6110i	−0.319705	+	0.771837i
$190$	−2.22092	−	1.48501i	−0.161123	−	0.107734i
$191$	−9.36570			−0.677678			−0.338839	−	0.940844i	$-0.610034\pi$
$191$	−9.36570			−0.677678			−0.338839	+	0.940844i	$0.610034\pi$
$192$	12.1717	−	12.1245i	0.878414	−	0.875013i
$193$	−17.3226			−1.24691			−0.623455	−	0.781859i	$-0.714272\pi$
$193$	−17.3226			−1.24691			−0.623455	+	0.781859i	$0.714272\pi$
$194$	−9.78305	−	6.54140i	−0.702382	−	0.469645i
$195$	−0.0674731	+	0.162894i	−0.00483185	+	0.0116651i
$196$	14.4940	−	5.99265i	1.03529	−	0.428046i
$197$	−5.20892	+	2.15761i	−0.371120	+	0.153723i	−0.560445	−	0.828191i	$-0.689370\pi$
$197$	−5.20892	+	2.15761i	−0.371120	+	0.153723i	0.189325	+	0.981914i	$0.439370\pi$
$198$	−1.89565	+	1.26575i	−0.134718	+	0.0899529i
$199$	−18.6782	+	18.6782i	−1.32406	+	1.32406i	−0.413605	+	0.910456i	$0.635731\pi$
$199$	−18.6782	+	18.6782i	−1.32406	+	1.32406i	−0.910456	+	0.413605i	$0.864269\pi$
$200$	7.70235	+	11.5516i	0.544638	+	0.816823i
$201$	14.1123	+	14.1123i	0.995403	+	0.995403i
$202$	−1.07813	−	0.214816i	−0.0758569	−	0.0151144i
$203$	5.35638	+	12.9314i	0.375944	+	0.907609i
$204$	−0.0154354	+	23.8735i	−0.00108069	+	1.67148i
$205$	−2.76945	−	1.14714i	−0.193427	−	0.0801200i
$206$	−4.19091	+	0.832215i	−0.291994	+	0.0579831i
$207$		−	11.7570i		−	0.817167i
$208$	−1.00492	+	0.414730i	−0.0696787	+	0.0287563i
$209$			6.25364i			0.432574i
$210$	−0.688427	−	3.46681i	−0.0475059	−	0.239233i
$211$	−10.8905	−	4.51099i	−0.749733	−	0.310550i	−0.0251004	−	0.999685i	$-0.507991\pi$
$211$	−10.8905	−	4.51099i	−0.749733	−	0.310550i	−0.724633	+	0.689135i	$0.757991\pi$
$212$	3.92350	−	3.91843i	0.269467	−	0.269119i
$213$	−9.71574	−	23.4559i	−0.665711	−	1.60717i
$214$	−5.62951	+	28.2537i	−0.384825	+	1.93138i
$215$	1.59532	+	1.59532i	0.108800	+	0.108800i
$216$	1.63701	+	8.27174i	0.111385	+	0.562821i
$217$	17.7255	−	17.7255i	1.20328	−	1.20328i
$218$	6.74087	+	10.0955i	0.456549	+	0.683753i
$219$	−16.2806	+	6.74363i	−1.10014	+	0.455692i
$220$	−0.231569	+	0.558035i	−0.0156124	+	0.0376227i
$221$	0.578117	−	1.39570i	0.0388884	−	0.0938848i
$222$	9.86799	−	14.7582i	0.662296	−	0.990502i
$223$	1.52490			0.102115			0.0510575	−	0.998696i	$-0.483741\pi$
$223$	1.52490			0.102115			0.0510575	+	0.998696i	$0.483741\pi$
$224$	12.1369	−	18.1008i	0.810933	−	1.20941i
$225$	7.91178			0.527452
$226$	−1.61887	+	2.42112i	−0.107686	+	0.161050i
$227$	−2.97342	+	7.17847i	−0.197353	+	0.476452i	−0.991314	−	0.131517i	$-0.958015\pi$
$227$	−2.97342	+	7.17847i	−0.197353	+	0.476452i	0.793961	+	0.607969i	$0.208015\pi$
$228$	−24.8082	−	10.2947i	−1.64297	−	0.681784i
$229$	−11.0149	+	4.56253i	−0.727886	+	0.301500i	−0.715683	−	0.698425i	$-0.753884\pi$
$229$	−11.0149	+	4.56253i	−0.727886	+	0.301500i	−0.0122030	+	0.999926i	$0.503884\pi$
$230$	−1.73049	−	2.59167i	−0.114105	−	0.170890i
$231$	−5.85013	+	5.85013i	−0.384910	+	0.384910i
$232$	8.53876	+	5.71740i	0.560597	+	0.375366i
$233$	−11.9515	−	11.9515i	−0.782972	−	0.782972i	0.197359	−	0.980331i	$-0.436763\pi$
$233$	−11.9515	−	11.9515i	−0.782972	−	0.782972i	−0.980331	+	0.197359i	$0.936763\pi$
$234$	−0.121055	+	0.607560i	−0.00791363	+	0.0397174i
$235$	0.0422066	+	0.101896i	0.00275326	+	0.00664695i
$236$	−5.66314	−	5.67047i	−0.368639	−	0.369116i
$237$	19.8171	+	8.20852i	1.28726	+	0.533201i
$238$	5.89852	+	29.7040i	0.382344	+	1.92543i
$239$			13.7692i			0.890658i	0.895367	+	0.445329i	$0.146913\pi$
$239$			13.7692i			0.890658i	−0.895367	+	0.445329i	$0.853087\pi$
$240$	−1.83252	−	1.83727i	−0.118289	−	0.118595i
$241$		−	1.67949i		−	0.108185i	−0.998536	−	0.0540927i	$-0.982773\pi$
$241$		−	1.67949i		−	0.108185i	0.998536	−	0.0540927i	$-0.0172267\pi$
$242$	1.38713	−	0.275451i	0.0891680	−	0.0177067i
$243$	14.0327	+	5.81255i	0.900200	+	0.372875i
$244$	−15.6929	−	0.0101462i	−1.00463	−	0.000649547i
$245$	−0.906568	−	2.18865i	−0.0579185	−	0.139828i
$246$	−29.5556	−	5.88891i	−1.88440	−	0.375463i
$247$	1.20183	+	1.20183i	0.0764704	+	0.0764704i
$248$	3.60794	−	18.0469i	0.229105	−	1.14598i
$249$	−4.48211	+	4.48211i	−0.284042	+	0.284042i
$250$	3.52052	−	2.35069i	0.222657	−	0.148671i
$251$	−26.3170	+	10.9008i	−1.66111	+	0.688055i	−0.998162	−	0.0606076i	$-0.980696\pi$
$251$	−26.3170	+	10.9008i	−1.66111	+	0.688055i	−0.662951	+	0.748663i	$0.730696\pi$
$252$	−4.74506	−	11.4766i	−0.298911	−	0.722956i
$253$	−2.79146	+	6.73918i	−0.175498	+	0.423689i
$254$	16.5461	+	11.0635i	1.03820	+	0.694186i
$255$	3.60594			0.225813
$256$	0.0413791	−	15.9999i	0.00258620	−	0.999997i
$257$	20.5895			1.28433			0.642167	−	0.766565i	$-0.278035\pi$
$257$	20.5895			1.28433			0.642167	+	0.766565i	$0.278035\pi$
$258$	18.8552	+	12.6074i	1.17387	+	0.784905i
$259$	8.61820	−	20.8062i	0.535509	−	1.29283i
$260$	0.0627405	+	0.151746i	0.00389100	+	0.00941091i
$261$	5.41009	−	2.24093i	0.334876	−	0.138710i
$262$	5.84603	−	3.90346i	0.361169	−	0.241157i
$263$	−2.87995	+	2.87995i	−0.177585	+	0.177585i	−0.790302	−	0.612717i	$-0.790077\pi$
$263$	−2.87995	+	2.87995i	−0.177585	+	0.177585i	0.612717	+	0.790302i	$0.290077\pi$
$264$	−1.19077	+	5.95619i	−0.0732866	+	0.366578i
$265$	−0.592237	−	0.592237i	−0.0363808	−	0.0363808i
$266$	−33.4149	−	6.65787i	−2.04880	−	0.408220i
$267$	5.26038	+	12.6997i	0.321930	+	0.777208i
$268$	18.5869	+	0.0120174i	1.13538	+	0.000734079i
$269$	18.2849	+	7.57386i	1.11485	+	0.461787i	0.862606	−	0.505877i	$-0.168831\pi$
$269$	18.2849	+	7.57386i	1.11485	+	0.461787i	0.252246	+	0.967663i	$0.418831\pi$
$270$	1.24924	−	0.248069i	0.0760260	−	0.0150970i
$271$			17.8837i			1.08636i	0.839617	+	0.543179i	$0.182779\pi$
$271$			17.8837i			1.08636i	−0.839617	+	0.543179i	$0.817221\pi$
$272$	15.7013	+	15.7419i	0.952030	+	0.954495i
$273$			2.24856i			0.136089i
$274$	3.15849	+	15.9057i	0.190811	+	0.960898i
$275$	−4.53509	−	1.87849i	−0.273476	−	0.113277i
$276$	−22.1391	−	22.1677i	−1.33262	−	1.33434i
$277$	−6.73562	−	16.2612i	−0.404704	−	0.977042i	−0.986508	−	0.163713i	$-0.947653\pi$
$277$	−6.73562	−	16.2612i	−0.404704	−	0.977042i	0.581804	−	0.813329i	$-0.302347\pi$
$278$	−2.49898	+	12.5420i	−0.149879	+	0.752222i
$279$	−7.41576	−	7.41576i	−0.443970	−	0.443970i
$280$	−2.73520	−	1.83144i	−0.163459	−	0.109450i
$281$	−8.05805	+	8.05805i	−0.480703	+	0.480703i	−0.905356	−	0.424653i	$-0.860396\pi$
$281$	−8.05805	+	8.05805i	−0.480703	+	0.480703i	0.424653	+	0.905356i	$0.360396\pi$
$282$	0.615724	+	0.922141i	0.0366658	+	0.0549127i
$283$	17.9168	−	7.42137i	1.06504	−	0.441154i	0.219803	−	0.975544i	$-0.429459\pi$
$283$	17.9168	−	7.42137i	1.06504	−	0.441154i	0.845238	+	0.534390i	$0.179459\pi$
$284$	−21.8389	−	9.06252i	−1.29590	−	0.537762i
$285$	−1.55253	+	3.74814i	−0.0919638	+	0.222020i
$286$	0.213643	−	0.319515i	0.0126330	−	0.0188933i
$287$	−38.2289			−2.25658
$288$	−7.57278	−	5.07769i	−0.446230	−	0.299206i
$289$	−13.8962			−0.817421
$290$	0.862744	−	1.29028i	0.0506621	−	0.0757681i
$291$	−6.83881	+	16.5103i	−0.400898	+	0.967854i
$292$	−6.29023	+	15.1582i	−0.368108	+	0.887069i
$293$	−10.7660	+	4.45941i	−0.628954	+	0.260521i	−0.674309	−	0.738450i	$-0.735558\pi$
$293$	−10.7660	+	4.45941i	−0.628954	+	0.260521i	0.0453546	+	0.998971i	$0.485558\pi$
$294$	−13.2253	−	19.8069i	−0.771315	−	1.15516i
$295$	−0.855935	+	0.855935i	−0.0498345	+	0.0498345i
$296$	−3.20988	−	16.2193i	−0.186570	−	0.942730i
$297$	−2.10804	−	2.10804i	−0.122321	−	0.122321i
$298$	2.00397	−	10.0576i	0.116087	−	0.582624i
$299$	0.758675	+	1.83160i	0.0438753	+	0.105924i
$300$	14.9176	−	14.8984i	0.861270	−	0.860157i
$301$	26.5822	+	11.0107i	1.53217	+	0.634646i
$302$	−2.68908	−	13.5418i	−0.154739	−	0.779244i
$303$			1.66934i			0.0959009i
$304$	−23.1228	+	9.54277i	−1.32618	+	0.547315i
$305$			2.37031i			0.135724i
$306$	12.4272	−	2.46775i	0.710415	−	0.141072i
$307$	−17.1029	−	7.08424i	−0.976112	−	0.404319i	−0.163128	−	0.986605i	$-0.552158\pi$
$307$	−17.1029	−	7.08424i	−0.976112	−	0.404319i	−0.812984	+	0.582286i	$0.802158\pi$
$308$	−0.00498171	+	7.70507i	−0.000283859	+	0.439037i
$309$	2.48293	+	5.99433i	0.141249	+	0.341005i
$310$	−2.72622	−	0.543195i	−0.154839	−	0.0308514i
$311$	−0.0226995	−	0.0226995i	−0.00128717	−	0.00128717i	0.706463	−	0.707750i	$-0.250290\pi$
$311$	−0.0226995	−	0.0226995i	−0.00128717	−	0.00128717i	−0.707750	+	0.706463i	$0.750290\pi$
$312$	0.915822	+	1.37351i	0.0518482	+	0.0777595i
$313$	−10.9476	+	10.9476i	−0.618792	+	0.618792i	−0.945222	−	0.326429i	$-0.894154\pi$
$313$	−10.9476	+	10.9476i	−0.618792	+	0.618792i	0.326429	+	0.945222i	$0.394154\pi$
$314$	−6.14461	+	4.10283i	−0.346760	+	0.231536i
$315$	−1.73300	+	0.717832i	−0.0976435	+	0.0404453i
$316$	18.4609	−	7.63278i	1.03851	−	0.429377i
$317$	−4.08911	+	9.87200i	−0.229668	+	0.554467i	−0.996137	−	0.0878144i	$-0.972012\pi$
$317$	−4.08911	+	9.87200i	−0.229668	+	0.554467i	0.766469	+	0.642281i	$0.222012\pi$
$318$	−6.99969	−	4.68032i	−0.392523	−	0.262459i
$319$	−3.63317			−0.203418
$320$	−2.41670	−	0.00468755i	−0.135097	−	0.000262042i
$321$	43.7470			2.44172
$322$	−33.0374	−	22.0903i	−1.84110	−	1.23105i
$323$	13.3022	−	32.1145i	0.740157	−	1.78690i
$324$	20.7698	−	8.58739i	1.15388	−	0.477077i
$325$	−1.23256	+	0.510545i	−0.0683704	+	0.0283199i
$326$	9.76992	−	6.52348i	0.541106	−	0.361302i
$327$	13.0344	−	13.0344i	0.720804	−	0.720804i
$328$	−23.3517	+	15.5703i	−1.28938	+	0.859728i
$329$	0.994580	+	0.994580i	0.0548330	+	0.0548330i
$330$	0.899762	+	0.179276i	0.0495303	+	0.00986883i
$331$	−7.01025	−	16.9242i	−0.385318	−	0.930240i	−0.990918	−	0.134470i	$-0.957067\pi$
$331$	−7.01025	−	16.9242i	−0.385318	−	0.930240i	0.605600	−	0.795769i	$-0.292933\pi$
$332$	−0.00381676	+	5.90328i	−0.000209472	+	0.323984i
$333$	−8.70462	−	3.60557i	−0.477010	−	0.197584i
$334$	−34.8571	+	6.92180i	−1.90730	+	0.378744i
$335$		−	2.80744i		−	0.153387i
$336$	−30.5578	−	12.7038i	−1.66707	−	0.693049i
$337$			6.99294i			0.380930i	0.981694	+	0.190465i	$0.0609995\pi$
$337$			6.99294i			0.380930i	−0.981694	+	0.190465i	$0.939000\pi$
$338$	3.56052	+	17.9302i	0.193667	+	0.975275i
$339$	4.08600	+	1.69247i	0.221921	+	0.0919226i
$340$	2.37619	−	2.37312i	0.128867	−	0.128700i
$341$	2.49004	+	6.01149i	0.134843	+	0.325540i
$342$	−2.78543	+	13.9797i	−0.150619	+	0.755936i
$343$	−2.29378	−	2.29378i	−0.123853	−	0.123853i
$344$	20.7220	−	4.10097i	1.11725	−	0.221109i
$345$	−3.34614	+	3.34614i	−0.180150	+	0.180150i
$346$	−5.95316	−	8.91577i	−0.320044	−	0.479315i
$347$	−20.7533	+	8.59628i	−1.11409	+	0.461472i	−0.862345	−	0.506321i	$-0.831005\pi$
$347$	−20.7533	+	8.59628i	−1.11409	+	0.461472i	−0.251748	+	0.967793i	$0.581005\pi$
$348$	5.98089	−	14.4128i	0.320610	−	0.772607i
$349$	9.84623	−	23.7709i	0.527057	−	1.27243i	−0.406386	−	0.913701i	$-0.633211\pi$
$349$	9.84623	−	23.7709i	0.527057	−	1.27243i	0.933443	−	0.358726i	$-0.116789\pi$
$350$	14.8655	−	22.2323i	0.794597	−	1.18837i
$351$	−0.810249			−0.0432479
$352$	3.13517	+	4.70858i	0.167105	+	0.250968i
$353$	−10.3749			−0.552200			−0.276100	−	0.961129i	$-0.589042\pi$
$353$	−10.3749			−0.552200			−0.276100	+	0.961129i	$0.589042\pi$
$354$	−6.76427	+	10.1164i	−0.359517	+	0.537679i
$355$	−1.36670	+	3.29952i	−0.0725372	+	0.175120i
$356$	11.8242	+	4.90671i	0.626683	+	0.260055i
$357$	42.4862	−	17.5984i	2.24861	−	0.931404i
$358$	−14.6593	−	21.9545i	−0.774768	−	1.16033i
$359$	24.0714	−	24.0714i	1.27044	−	1.27044i	0.324581	−	0.945858i	$-0.394777\pi$
$359$	24.0714	−	24.0714i	1.27044	−	1.27044i	0.945858	−	0.324581i	$-0.105223\pi$
$360$	−0.766214	+	1.14432i	−0.0403830	+	0.0603108i
$361$	14.2185	+	14.2185i	0.748344	+	0.748344i
$362$	−4.18908	+	21.0244i	−0.220173	+	1.10502i
$363$	−0.821814	−	1.98403i	−0.0431341	−	0.104135i
$364$	1.47981	+	1.48172i	0.0775629	+	0.0776632i
$365$	2.29017	+	0.948620i	0.119873	+	0.0496530i
$366$	4.64143	+	23.3735i	0.242611	+	1.22175i
$367$			20.4487i			1.06741i	0.845670	+	0.533705i	$0.179201\pi$
$367$			20.4487i			1.06741i	−0.845670	+	0.533705i	$0.820799\pi$
$368$	−29.1777	−	0.0377297i	−1.52099	−	0.00196680i
$369$			15.9937i			0.832599i
$370$	−2.44952	+	0.486416i	−0.127344	+	0.0252876i
$371$	−9.86823	−	4.08756i	−0.512333	−	0.212215i
$372$	−27.9467	−	0.0180689i	−1.44897	−	0.000936831i
$373$	−4.53764	−	10.9548i	−0.234950	−	0.567220i	0.761797	−	0.647816i	$-0.224318\pi$
$373$	−4.53764	−	10.9548i	−0.234950	−	0.567220i	−0.996747	+	0.0805961i	$0.974318\pi$
$374$	−7.70927	−	1.53606i	−0.398637	−	0.0794278i
$375$	−4.54538	−	4.54538i	−0.234723	−	0.234723i
$376$	1.01261	+	0.202442i	0.0522215	+	0.0104402i
$377$	−0.698223	+	0.698223i	−0.0359603	+	0.0359603i
$378$	13.5082	−	9.01955i	0.694785	−	0.463915i
$379$	−16.2142	+	6.71614i	−0.832868	+	0.344985i	−0.758037	−	0.652211i	$-0.773842\pi$
$379$	−16.2142	+	6.71614i	−0.832868	+	0.344985i	−0.0748303	+	0.997196i	$0.523842\pi$
$380$	1.44363	+	3.49162i	0.0740569	+	0.179117i
$381$	11.5665	−	27.9240i	0.592571	−	1.43059i
$382$	11.0105	+	7.36214i	0.563347	+	0.376680i
$383$	−5.80591			−0.296668			−0.148334	−	0.988937i	$-0.547391\pi$
$383$	−5.80591			−0.296668			−0.148334	+	0.988937i	$0.547391\pi$
$384$	−23.8401	+	4.68602i	−1.21658	+	0.239133i
$385$	1.16380			0.0593129
$386$	20.3649	+	13.6169i	1.03654	+	0.693081i
$387$	4.60651	−	11.1211i	0.234162	−	0.565318i
$388$	6.35914	+	15.3804i	0.322836	+	0.780823i
$389$	−18.9478	+	7.84843i	−0.960691	+	0.397931i	−0.807239	−	0.590225i	$-0.799039\pi$
$389$	−18.9478	+	7.84843i	−0.960691	+	0.397931i	−0.153452	+	0.988156i	$0.549039\pi$
$390$	0.207370	−	0.138463i	0.0105006	−	0.00701136i
$391$	28.6701	−	28.6701i	1.44991	−	1.44991i
$392$	−21.7502	−	4.34831i	−1.09855	−	0.219623i
$393$	−7.54788	−	7.54788i	−0.380740	−	0.380740i
$394$	7.81976	+	1.55808i	0.393954	+	0.0784947i
$395$	−1.15469	−	2.78766i	−0.0580986	−	0.140262i
$396$	3.22355	+	0.00208418i	0.161989	+	0.000104734i
$397$	−11.4268	−	4.73313i	−0.573493	−	0.237549i	0.0770379	−	0.997028i	$-0.475454\pi$
$397$	−11.4268	−	4.73313i	−0.573493	−	0.237549i	−0.650531	+	0.759479i	$0.725454\pi$
$398$	36.6409	−	7.27602i	1.83664	−	0.364714i
$399$			51.7385i			2.59016i
$400$	0.0253900	−	19.6350i	0.00126950	−	0.981748i
$401$		−	6.07686i		−	0.303464i	−0.988422	−	0.151732i	$-0.951515\pi$
$401$		−	6.07686i		−	0.303464i	0.988422	−	0.151732i	$-0.0484850\pi$
$402$	−5.49739	−	27.6840i	−0.274185	−	1.38075i
$403$	1.63383	+	0.676753i	0.0813867	+	0.0337115i
$404$	1.09861	+	1.10003i	0.0546580	+	0.0547287i
$405$	−1.29910	−	3.13630i	−0.0645528	−	0.155844i
$406$	3.86801	−	19.4130i	0.191966	−	0.963451i
$407$	4.13348	+	4.13348i	0.204889	+	0.204889i
$408$	18.7845	−	28.0541i	0.929972	−	1.38888i
$409$	15.2277	−	15.2277i	0.752960	−	0.752960i	−0.222070	−	0.975031i	$-0.571282\pi$
$409$	15.2277	−	15.2277i	0.752960	−	0.752960i	0.975031	+	0.222070i	$0.0712815\pi$
$410$	2.35408	+	3.52560i	0.116260	+	0.174117i
$411$	22.7502	−	9.42343i	1.12218	−	0.464824i
$412$	5.58110	+	2.31600i	0.274961	+	0.114101i
$413$	−5.90758	+	14.2621i	−0.290693	+	0.701794i
$414$	−9.24187	+	13.8218i	−0.454213	+	0.679302i
$415$	0.891653			0.0437695
$416$	1.50741	+	0.302377i	0.0739071	+	0.0148253i
$417$	19.4196			0.950984
$418$	4.91583	−	7.35192i	0.240441	−	0.359594i
$419$	−1.15755	+	2.79457i	−0.0565499	+	0.136524i	−0.949629	−	0.313376i	$-0.898540\pi$
$419$	−1.15755	+	2.79457i	−0.0565499	+	0.136524i	0.893079	+	0.449899i	$0.148540\pi$
$420$	−1.91584	+	4.61681i	−0.0934836	+	0.225277i
$421$	−26.7434	+	11.0775i	−1.30339	+	0.539883i	−0.922949	−	0.384921i	$-0.874229\pi$
$421$	−26.7434	+	11.0775i	−1.30339	+	0.539883i	−0.380443	+	0.924804i	$0.624229\pi$
$422$	9.25713	+	13.8640i	0.450630	+	0.674888i
$423$	0.416099	−	0.416099i	0.0202314	−	0.0202314i
$424$	−7.69272	+	1.52242i	−0.373592	+	0.0739354i
$425$	19.2933	+	19.2933i	0.935865	+	0.935865i
$426$	−7.01604	+	35.2125i	−0.339928	+	1.70605i
$427$	11.5680	+	27.9277i	0.559816	+	1.35152i
$428$	28.8277	−	28.7905i	1.39344	−	1.39164i
$429$	−0.539229	−	0.223356i	−0.0260342	−	0.0107837i
$430$	−0.621450	−	3.12953i	−0.0299690	−	0.150919i
$431$		−	14.7602i		−	0.710975i	−0.934681	−	0.355488i	$-0.884315\pi$
$431$		−	14.7602i		−	0.710975i	0.934681	−	0.355488i	$-0.115685\pi$
$432$	4.57770	−	11.0113i	0.220245	−	0.529779i
$433$		−	24.7701i		−	1.19037i	−0.803587	−	0.595187i	$-0.797078\pi$
$433$		−	24.7701i		−	1.19037i	0.803587	−	0.595187i	$-0.202922\pi$
$434$	−34.7720	+	6.90490i	−1.66911	+	0.331446i
$435$	−2.17755	−	0.901969i	−0.104405	−	0.0432461i
$436$	0.0110995	−	17.1673i	0.000531571	−	0.822165i
$437$	17.4568	+	42.1444i	0.835072	+	2.01604i
$438$	24.4408	+	4.86978i	1.16782	+	0.232687i
$439$	14.3662	+	14.3662i	0.685659	+	0.685659i	0.961269	−	0.275610i	$-0.0888799\pi$
$439$	14.3662	+	14.3662i	0.685659	+	0.685659i	−0.275610	+	0.961269i	$0.588880\pi$
$440$	0.710895	−	0.474008i	0.0338906	−	0.0225975i
$441$	−8.93751	+	8.93751i	−0.425596	+	0.425596i
$442$	−1.77677	+	1.18637i	−0.0845124	+	0.0564299i
$443$	−32.0878	+	13.2912i	−1.52454	+	0.631484i	−0.978495	−	0.206272i	$-0.933867\pi$
$443$	−32.0878	+	13.2912i	−1.52454	+	0.631484i	−0.546044	+	0.837757i	$0.683867\pi$
$444$	−23.2020	+	9.59303i	−1.10112	+	0.455265i
$445$	0.739974	−	1.78645i	0.0350781	−	0.0846860i
$446$	−1.79271	−	1.19869i	−0.0848872	−	0.0567595i
$447$	−15.5729			−0.736572
$448$	−28.4970	+	11.7392i	−1.34636	+	0.554623i
$449$	30.9450			1.46039			0.730193	−	0.683241i	$-0.239430\pi$
$449$	30.9450			1.46039			0.730193	+	0.683241i	$0.239430\pi$
$450$	−9.30126	−	6.21925i	−0.438466	−	0.293178i
$451$	3.79739	−	9.16770i	0.178812	−	0.431690i
$452$	3.80636	−	1.57376i	0.179036	−	0.0740237i
$453$	−19.3691	+	8.02294i	−0.910040	+	0.376951i
$454$	9.13843	−	6.10183i	0.428888	−	0.286373i
$455$	0.223660	−	0.223660i	0.0104853	−	0.0104853i
$456$	21.0727	+	31.6038i	0.986819	+	1.47998i
$457$	−5.70032	−	5.70032i	−0.266650	−	0.266650i	0.561099	−	0.827749i	$-0.310379\pi$
$457$	−5.70032	−	5.70032i	−0.266650	−	0.266650i	−0.827749	+	0.561099i	$0.810379\pi$
$458$	16.5359	+	3.29474i	0.772670	+	0.153953i
$459$	6.34142	+	15.3095i	0.295992	+	0.714588i
$460$	−0.00284942	+	4.40712i	−0.000132855	+	0.205483i
$461$	20.8017	+	8.61636i	0.968833	+	0.401304i	0.810278	−	0.586046i	$-0.199316\pi$
$461$	20.8017	+	8.61636i	0.968833	+	0.401304i	0.158555	+	0.987350i	$0.449316\pi$
$462$	11.4762	−	2.27890i	0.533920	−	0.106024i
$463$		−	29.6511i		−	1.37800i	−0.724761	−	0.689001i	$-0.758050\pi$
$463$		−	29.6511i		−	1.37800i	0.724761	−	0.689001i	$-0.241950\pi$
$464$	−5.54404	−	13.4336i	−0.257376	−	0.623640i
$465$			4.22118i			0.195752i
$466$	4.65568	+	23.4453i	0.215670	+	1.08608i
$467$	−7.40433	−	3.06697i	−0.342632	−	0.141923i	0.204731	−	0.978818i	$-0.434368\pi$
$467$	−7.40433	−	3.06697i	−0.342632	−	0.141923i	−0.547362	+	0.836896i	$0.684368\pi$
$468$	0.619903	−	0.619102i	0.0286550	−	0.0286180i
$469$	−13.7014	−	33.0780i	−0.632671	−	1.52740i
$470$	0.0304787	−	0.152969i	0.00140588	−	0.00705591i
$471$	7.93338	+	7.93338i	0.365551	+	0.365551i
$472$	2.20030	+	11.1180i	0.101277	+	0.511746i
$473$	−5.28097	+	5.28097i	−0.242819	+	0.242819i
$474$	−16.8449	−	25.2279i	−0.773713	−	1.15875i
$475$	−28.3608	+	11.7474i	−1.30128	+	0.539009i
$476$	16.4152	−	39.5574i	0.752389	−	1.81311i
$477$	−1.71010	+	4.12854i	−0.0783000	+	0.189033i
$478$	10.8237	−	16.1874i	0.495062	−	0.740395i
$479$	4.44419			0.203060			0.101530	−	0.994832i	$-0.467626\pi$
$479$	4.44419			0.203060			0.101530	+	0.994832i	$0.467626\pi$
$480$	0.710123	+	3.60043i	0.0324125	+	0.164337i
$481$	1.58875			0.0724406
$482$	−1.32020	+	1.97444i	−0.0601337	+	0.0899335i
$483$	−23.0947	+	55.7555i	−1.05084	+	2.53696i
$484$	−1.84726	−	0.766561i	−0.0839665	−	0.0348437i
$485$	2.32250	−	0.962010i	0.105459	−	0.0436826i
$486$	−11.9281	−	17.8641i	−0.541069	−	0.810334i
$487$	28.6477	−	28.6477i	1.29815	−	1.29815i	0.368536	−	0.929614i	$-0.379859\pi$
$487$	28.6477	−	28.6477i	1.29815	−	1.29815i	0.929614	−	0.368536i	$-0.120141\pi$
$488$	18.4409	+	12.3477i	0.834782	+	0.558955i
$489$	−12.6141	−	12.6141i	−0.570427	−	0.570427i
$490$	−0.654661	+	3.28565i	−0.0295746	+	0.148431i
$491$	−1.68814	−	4.07554i	−0.0761848	−	0.183926i	0.881199	−	0.472746i	$-0.156737\pi$
$491$	−1.68814	−	4.07554i	−0.0761848	−	0.183926i	−0.957384	+	0.288820i	$0.906737\pi$
$492$	30.1171	+	30.1561i	1.35778	+	1.35954i
$493$	18.6575	+	7.72818i	0.840290	+	0.348060i
$494$	−0.468168	−	2.35762i	−0.0210639	−	0.106074i
$495$		−	0.486897i		−	0.0218844i
$496$	−18.4278	+	18.3802i	−0.827431	+	0.825294i
$497$			45.5458i			2.04301i
$498$	8.79253	−	1.74599i	0.394003	−	0.0782396i
$499$	−16.8230	−	6.96830i	−0.753099	−	0.311944i	−0.0270938	−	0.999633i	$-0.508625\pi$
$499$	−16.8230	−	6.96830i	−0.753099	−	0.311944i	−0.726005	+	0.687689i	$0.758625\pi$
$500$	−5.98662	−	0.00387065i	−0.267730	−	0.000173101i
$501$	20.6514	+	49.8568i	0.922634	+	2.22744i
$502$	39.5077	+	7.87184i	1.76331	+	0.351338i
$503$	22.0450	+	22.0450i	0.982939	+	0.982939i	0.999857	−	0.0169182i	$-0.00538549\pi$
$503$	22.0450	+	22.0450i	0.982939	+	0.982939i	−0.0169182	+	0.999857i	$0.505385\pi$
$504$	−3.44305	+	17.2221i	−0.153366	+	0.767132i
$505$	0.166046	−	0.166046i	0.00738894	−	0.00738894i
$506$	8.57921	−	5.72843i	0.381392	−	0.254660i
$507$	25.6459	−	10.6229i	1.13897	−	0.471779i
$508$	−10.7552	−	26.0130i	−0.477187	−	1.15414i
$509$	−9.17238	+	22.1441i	−0.406559	+	0.981519i	0.579478	+	0.814988i	$0.303257\pi$
$509$	−9.17238	+	22.1441i	−0.406559	+	0.981519i	−0.986036	+	0.166531i	$0.946743\pi$
$510$	−4.23923	−	2.83454i	−0.187716	−	0.125516i
$511$	31.6130			1.39848
$512$	−12.6258	+	18.7774i	−0.557987	+	0.829850i
$513$	−18.6435			−0.823131
$514$	−24.2054	−	16.1849i	−1.06765	−	0.713883i
$515$	0.349272	−	0.843217i	0.0153908	−	0.0371566i
$516$	−12.2561	−	29.6431i	−0.539547	−	1.30497i
$517$	−0.337306	+	0.139717i	−0.0148347	+	0.00614473i
$518$	−26.4870	+	17.6856i	−1.16377	+	0.777062i
$519$	−11.5113	+	11.5113i	−0.505288	+	0.505288i
$520$	0.0455250	−	0.227715i	0.00199640	−	0.00998597i
$521$	−11.9094	−	11.9094i	−0.521759	−	0.521759i	0.396343	−	0.918102i	$-0.370279\pi$
$521$	−11.9094	−	11.9094i	−0.521759	−	0.521759i	−0.918102	+	0.396343i	$0.870279\pi$
$522$	−8.12176	−	1.61825i	−0.355480	−	0.0708288i
$523$	−15.3738	−	37.1156i	−0.672249	−	1.62295i	−0.777781	−	0.628536i	$-0.783655\pi$
$523$	−15.3738	−	37.1156i	−0.672249	−	1.62295i	0.105532	−	0.994416i	$-0.466345\pi$
$524$	−9.94114	−	0.00642744i	−0.434281	−	0.000280784i
$525$	−37.5203	−	15.5414i	−1.63752	−	0.678283i
$526$	5.64959	−	1.12187i	0.246334	−	0.0489161i
$527$		−	36.1675i		−	1.57548i
$528$	6.08191	−	6.06620i	0.264681	−	0.263997i
$529$			30.2089i			1.31343i
$530$	0.230704	+	1.16179i	0.0100211	+	0.0504649i
$531$	5.96681	+	2.47153i	0.258938	+	0.107255i
$532$	34.0497	+	34.0938i	1.47624	+	1.47815i
$533$	−1.03207	−	2.49164i	−0.0447039	−	0.107925i
$534$	3.79869	−	19.0651i	0.164385	−	0.825027i
$535$	−4.35143	−	4.35143i	−0.188129	−	0.188129i
$536$	−21.8418	−	14.6249i	−0.943420	−	0.631698i
$537$	−28.3458	+	28.3458i	−1.22321	+	1.22321i
$538$	−15.5425	−	23.2773i	−0.670086	−	1.00356i
$539$	7.24508	−	3.00101i	0.312068	−	0.129263i
$540$	−1.66363	−	0.690358i	−0.0715912	−	0.0297083i
$541$	6.99925	−	16.8977i	0.300921	−	0.726488i	−0.699014	−	0.715108i	$-0.746378\pi$
$541$	6.99925	−	16.8977i	0.300921	−	0.726488i	0.999935	−	0.0113801i	$-0.00362247\pi$
$542$	14.0579	−	21.0245i	0.603840	−	0.903078i
$543$	32.5534			1.39700
$544$	−6.08442	−	30.8489i	−0.260867	−	1.32264i
$545$	−2.59301			−0.111073
$546$	1.76754	−	2.64346i	0.0756436	−	0.113129i
$547$	−17.2623	+	41.6749i	−0.738082	+	1.78189i	−0.124558	+	0.992212i	$0.539751\pi$
$547$	−17.2623	+	41.6749i	−0.738082	+	1.78189i	−0.613525	+	0.789676i	$0.710249\pi$
$548$	8.78987	−	21.1819i	0.375485	−	0.904845i
$549$	11.6840	−	4.83968i	0.498662	−	0.206553i
$550$	3.85491	+	5.77332i	0.164374	+	0.246175i
$551$	−16.0658	+	16.0658i	−0.684427	+	0.684427i
$552$	8.60169	+	43.4639i	0.366112	+	1.84995i
$553$	−27.2096	−	27.2096i	−1.15707	−	1.15707i
$554$	−4.86400	+	24.4117i	−0.206652	+	1.03716i
$555$	1.45123	+	3.50359i	0.0616014	+	0.148719i
$556$	12.7968	−	12.7803i	0.542707	−	0.542006i
$557$	−6.08758	−	2.52156i	−0.257939	−	0.106842i	0.249967	−	0.968254i	$-0.419580\pi$
$557$	−6.08758	−	2.52156i	−0.257939	−	0.106842i	−0.507906	+	0.861413i	$0.669580\pi$
$558$	2.88878	+	14.5475i	0.122292	+	0.615843i
$559$			2.02980i			0.0858513i
$560$	1.77591	+	4.30315i	0.0750459	+	0.181841i
$561$			11.9368i			0.503970i
$562$	15.8075	−	3.13899i	0.666797	−	0.132410i
$563$	−30.0995	−	12.4676i	−1.26854	−	0.525447i	−0.356021	−	0.934478i	$-0.615867\pi$
$563$	−30.0995	−	12.4676i	−1.26854	−	0.525447i	−0.912521	+	0.409031i	$0.865867\pi$
$564$	0.00101385	−	1.56809i	4.26908e−5	−	0.0660287i
$565$	−0.238079	−	0.574774i	−0.0100161	−	0.0241809i
$566$	−26.8971	−	5.35920i	−1.13057	−	0.225264i
$567$	−30.6127	−	30.6127i	−1.28561	−	1.28561i
$568$	18.5505	+	27.8211i	0.778361	+	1.16735i
$569$	4.35398	−	4.35398i	0.182528	−	0.182528i	−0.609928	−	0.792457i	$-0.708802\pi$
$569$	4.35398	−	4.35398i	0.182528	−	0.182528i	0.792457	+	0.609928i	$0.208802\pi$
$570$	4.77150	−	3.18598i	0.199856	−	0.133446i
$571$	−0.774022	+	0.320611i	−0.0323918	+	0.0134171i	−0.398821	−	0.917029i	$-0.630580\pi$
$571$	−0.774022	+	0.320611i	−0.0323918	+	0.0134171i	0.366429	+	0.930446i	$0.380580\pi$
$572$	−0.502326	+	0.207690i	−0.0210033	+	0.00868395i
$573$	7.69686	−	18.5819i	0.321541	−	0.776269i
$574$	44.9427	+	30.0508i	1.87587	+	1.25430i
$575$	−35.8065			−1.49324
$576$	4.91127	+	11.9222i	0.204636	+	0.496759i
$577$	−3.26228			−0.135810			−0.0679052	−	0.997692i	$-0.521632\pi$
$577$	−3.26228			−0.135810			−0.0679052	+	0.997692i	$0.521632\pi$
$578$	16.3366	+	10.9234i	0.679514	+	0.454355i
$579$	14.2360	−	34.3687i	0.591627	−	1.42831i
$580$	−2.02852	+	0.838705i	−0.0842298	+	0.0348253i
$581$	10.5057	−	4.35160i	0.435850	−	0.180535i
$582$	21.0182	−	14.0341i	0.871233	−	0.581732i
$583$	1.96048	−	1.96048i	0.0811948	−	0.0811948i
$584$	19.3104	−	12.8758i	0.799072	−	0.532803i
$585$	−0.0935720	−	0.0935720i	−0.00386872	−	0.00386872i
$586$	16.1621	+	3.22028i	0.667651	+	0.133028i
$587$	6.07085	+	14.6563i	0.250571	+	0.604932i	0.998250	−	0.0591281i	$-0.0188320\pi$
$587$	6.07085	+	14.6563i	0.250571	+	0.604932i	−0.747679	+	0.664060i	$0.768832\pi$
$588$	−0.0217768	+	33.6815i	−0.000898059	+	1.38900i
$589$	37.5937	+	15.5718i	1.54902	+	0.641626i
$590$	1.67909	−	0.333427i	0.0691269	−	0.0137270i
$591$		−	12.1078i		−	0.498050i
$592$	−8.97601	+	21.5910i	−0.368912	+	0.887385i
$593$		−	2.22582i		−	0.0914035i	−0.998955	−	0.0457018i	$-0.985448\pi$
$593$		−	2.22582i		−	0.0914035i	0.998955	−	0.0457018i	$-0.0145524\pi$
$594$	0.821181	+	4.13534i	0.0336935	+	0.169675i
$595$	−5.97650	−	2.47555i	−0.245013	−	0.101488i
$596$	−10.2620	+	10.2487i	−0.420347	+	0.419804i
$597$	−21.7082	−	52.4082i	−0.888457	−	2.14492i
$598$	0.547863	−	2.74965i	0.0224038	−	0.112441i
$599$	25.3522	+	25.3522i	1.03586	+	1.03586i	0.999333	+	0.0365303i	$0.0116305\pi$
$599$	25.3522	+	25.3522i	1.03586	+	1.03586i	0.0365303	+	0.999333i	$0.488369\pi$
$600$	−29.2487	+	5.78845i	−1.19407	+	0.236312i
$601$	16.0246	−	16.0246i	0.653658	−	0.653658i	−0.300214	−	0.953872i	$-0.597058\pi$
$601$	16.0246	−	16.0246i	0.653658	−	0.653658i	0.953872	+	0.300214i	$0.0970581\pi$
$602$	−22.5953	−	33.8400i	−0.920918	−	1.37922i
$603$	−13.8388	+	5.73220i	−0.563558	+	0.233433i
$604$	−7.48354	+	18.0339i	−0.304501	+	0.733788i
$605$	−0.115604	+	0.279093i	−0.00469997	+	0.0113467i
$606$	1.31222	−	1.96251i	0.0533055	−	0.0797215i
$607$	30.8222			1.25103			0.625517	−	0.780211i	$-0.284888\pi$
$607$	30.8222			1.25103			0.625517	+	0.780211i	$0.284888\pi$
$608$	34.6850	+	6.95758i	1.40666	+	0.282167i
$609$	−30.0584			−1.21803
$610$	1.86325	−	2.78659i	0.0754406	−	0.112826i
$611$	−0.0379727	+	0.0916743i	−0.00153621	+	0.00370875i
$612$	−16.5495	−	6.86757i	−0.668974	−	0.277605i
$613$	28.8221	−	11.9385i	1.16411	−	0.482191i	0.284871	−	0.958566i	$-0.408049\pi$
$613$	28.8221	−	11.9385i	1.16411	−	0.482191i	0.879242	+	0.476375i	$0.158049\pi$
$614$	14.5378	+	21.7725i	0.586696	+	0.878668i
$615$	4.55195	−	4.55195i	0.183552	−	0.183552i
$616$	6.06262	−	9.05433i	0.244270	−	0.364809i
$617$	11.5935	+	11.5935i	0.466739	+	0.466739i	0.900856	−	0.434118i	$-0.142940\pi$
$617$	11.5935	+	11.5935i	0.466739	+	0.466739i	−0.434118	+	0.900856i	$0.642940\pi$
$618$	1.79300	−	8.99883i	0.0721252	−	0.361986i
$619$	1.95940	+	4.73042i	0.0787551	+	0.190132i	0.958353	−	0.285586i	$-0.0921883\pi$
$619$	1.95940	+	4.73042i	0.0787551	+	0.190132i	−0.879598	+	0.475718i	$0.842188\pi$
$620$	2.77801	+	2.78160i	0.111568	+	0.111712i
$621$	−20.0910	−	8.32197i	−0.806224	−	0.333949i
$622$	0.00884252	+	0.0445296i	0.000354553	+	0.00178547i
$623$		−	24.6598i		−	0.987975i
$624$	0.00301891	−	2.33463i	0.000120853	−	0.0934599i
$625$		−	23.6395i		−	0.945579i
$626$	21.4758	−	4.26458i	0.858345	−	0.170447i
$627$	−12.4074	−	5.13933i	−0.495506	−	0.205245i
$628$	10.4489	+	0.00675571i	0.416955	+	0.000269582i
$629$	−12.4343	−	30.0191i	−0.495789	−	1.19694i
$630$	2.60162	+	0.518369i	0.103651	+	0.0206523i
$631$	−2.06817	−	2.06817i	−0.0823326	−	0.0823326i	0.664741	−	0.747074i	$-0.268542\pi$
$631$	−2.06817	−	2.06817i	−0.0823326	−	0.0823326i	−0.747074	+	0.664741i	$0.768542\pi$
$632$	−27.7030	−	5.53840i	−1.10196	−	0.220306i
$633$	17.8999	−	17.8999i	0.711459	−	0.711459i
$634$	12.5674	−	8.39138i	0.499114	−	0.333264i
$635$	−3.92805	+	1.62705i	−0.155880	+	0.0645676i
$636$	4.54991	+	11.0046i	0.180416	+	0.436360i
$637$	0.815627	−	1.96910i	0.0323163	−	0.0780185i
$638$	4.27123	+	2.85594i	0.169100	+	0.113068i
$639$	19.0549			0.753799
$640$	2.83744	+	1.90522i	0.112159	+	0.0753102i
$641$	−4.65107			−0.183706			−0.0918532	−	0.995773i	$-0.529279\pi$
$641$	−4.65107			−0.183706			−0.0918532	+	0.995773i	$0.529279\pi$
$642$	−51.4299	−	34.3884i	−2.02978	−	1.35720i
$643$	7.20076	−	17.3842i	0.283970	−	0.685565i	−0.715950	−	0.698151i	$-0.754006\pi$
$643$	7.20076	−	17.3842i	0.283970	−	0.685565i	0.999921	+	0.0125861i	$0.00400637\pi$
$644$	21.4748	+	51.9398i	0.846227	+	2.04671i
$645$	−4.47621	+	1.85411i	−0.176251	+	0.0730055i
$646$	−40.8828	+	27.2979i	−1.60851	+	1.07402i
$647$	26.9444	−	26.9444i	1.05930	−	1.05930i	0.0611678	−	0.998127i	$-0.480518\pi$
$647$	26.9444	−	26.9444i	1.05930	−	1.05930i	0.998127	−	0.0611678i	$-0.0194825\pi$
$648$	−31.1677	−	6.23107i	−1.22438	−	0.244780i
$649$	−2.83340	−	2.83340i	−0.111221	−	0.111221i
$650$	1.85036	+	0.368681i	0.0725769	+	0.0144608i
$651$	20.6009	+	49.7350i	0.807414	+	1.94927i
$652$	−16.6137	−	0.0107416i	−0.650642	−	0.000420672i
$653$	23.1213	+	9.57714i	0.904805	+	0.374783i	0.786066	−	0.618143i	$-0.212115\pi$
$653$	23.1213	+	9.57714i	0.904805	+	0.374783i	0.118739	+	0.992925i	$0.462115\pi$
$654$	−25.5695	+	5.07751i	−0.999848	+	0.198546i
$655$			1.50155i			0.0586703i
$656$	39.6922	+	0.0513260i	1.54972	+	0.00200394i
$657$		−	13.2259i		−	0.515990i
$658$	−0.387435	−	1.95106i	−0.0151038	−	0.0760604i
$659$	37.2662	+	15.4362i	1.45169	+	0.601308i	0.962600	−	0.270927i	$-0.0873303\pi$
$659$	37.2662	+	15.4362i	1.45169	+	0.601308i	0.489086	+	0.872235i	$0.337330\pi$
$660$	−0.916855	−	0.918042i	−0.0356885	−	0.0357347i
$661$	−6.90985	−	16.6818i	−0.268762	−	0.648849i	0.730664	−	0.682738i	$-0.239211\pi$
$661$	−6.90985	−	16.6818i	−0.268762	−	0.648849i	−0.999426	+	0.0338889i	$0.989211\pi$
$662$	−5.06232	+	25.4071i	−0.196753	+	0.987474i
$663$	2.29401	+	2.29401i	0.0890920	+	0.0890920i
$664$	4.64491	−	6.93702i	0.180257	−	0.269209i
$665$	5.14633	−	5.14633i	0.199566	−	0.199566i
$666$	7.39909	+	11.0813i	0.286709	+	0.429390i
$667$	−24.4846	+	10.1418i	−0.948046	+	0.392694i
$668$	46.4199	+	19.2629i	1.79604	+	0.745304i
$669$	−1.25319	+	3.02546i	−0.0484510	+	0.116971i
$670$	−2.20686	+	3.30049i	−0.0852584	+	0.127509i
$671$	−7.84645			−0.302909
$672$	25.9383	+	38.9556i	1.00059	+	1.50275i
$673$	−44.4228			−1.71237			−0.856187	−	0.516665i	$-0.827173\pi$
$673$	−44.4228			−1.71237			−0.856187	+	0.516665i	$0.827173\pi$
$674$	5.49697	−	8.22105i	0.211736	−	0.316663i
$675$	5.60021	−	13.5201i	0.215552	−	0.520389i
$676$	9.90867	−	23.8780i	0.381103	−	0.918384i
$677$	−0.146587	+	0.0607181i	−0.00563378	+	0.00233359i	−0.385499	−	0.922708i	$-0.625971\pi$
$677$	−0.146587	+	0.0607181i	−0.00563378	+	0.00233359i	0.379865	+	0.925042i	$0.375971\pi$
$678$	−3.47317	−	5.20161i	−0.133386	−	0.199767i
$679$	22.6693	−	22.6693i	0.869968	−	0.869968i
$680$	−4.65895	+	0.922026i	−0.178662	+	0.0353581i
$681$	−11.7987	−	11.7987i	−0.452129	−	0.452129i
$682$	1.79814	−	9.02459i	0.0688542	−	0.345570i
$683$	−15.1096	−	36.4777i	−0.578151	−	1.39578i	−0.894470	−	0.447128i	$-0.852447\pi$
$683$	−15.1096	−	36.4777i	−0.578151	−	1.39578i	0.316319	−	0.948653i	$-0.397553\pi$
$684$	14.2637	−	14.2453i	0.545387	−	0.544682i
$685$	−3.20025	−	1.32559i	−0.122275	−	0.0506481i
$686$	0.893535	+	4.49971i	0.0341153	+	0.171800i
$687$		−	25.6035i		−	0.976835i
$688$	−27.5849	−	11.4678i	−1.05166	−	0.437207i
$689$		−	0.753532i		−	0.0287073i
$690$	6.56411	−	1.30348i	0.249891	−	0.0496225i
$691$	−12.4011	−	5.13670i	−0.471760	−	0.195409i	0.134121	−	0.990965i	$-0.457179\pi$
$691$	−12.4011	−	5.13670i	−0.471760	−	0.195409i	−0.605880	+	0.795556i	$0.707179\pi$
$692$	−0.00980247	+	15.1612i	−0.000372634	+	0.576342i
$693$	−2.37624	−	5.73675i	−0.0902658	−	0.217921i
$694$	31.1553	+	6.20764i	1.18264	+	0.235639i
$695$	−1.93163	−	1.93163i	−0.0732711	−	0.0732711i
$696$	−18.3608	+	12.2426i	−0.695964	+	0.464053i
$697$	−39.0016	+	39.0016i	−1.47729	+	1.47729i
$698$	−30.2611	+	20.2057i	−1.14540	+	0.764797i
$699$	33.5342	−	13.8903i	1.26838	−	0.525381i
$700$	−34.9525	+	14.4513i	−1.32108	+	0.546209i
$701$	0.193851	−	0.467998i	0.00732166	−	0.0176761i	−0.920176	−	0.391504i	$-0.871955\pi$
$701$	0.193851	−	0.467998i	0.00732166	−	0.0176761i	0.927498	+	0.373828i	$0.121955\pi$
$702$	0.952546	+	0.636917i	0.0359515	+	0.0240389i
$703$	36.5564			1.37875
$704$	0.0155172	−	7.99998i	0.000584826	−	0.301511i
$705$	−0.236851			−0.00892032
$706$	12.1970	+	8.15545i	0.459038	+	0.306934i
$707$	1.14603	−	2.76676i	0.0431009	−	0.104055i
$708$	15.9044	−	6.57579i	0.597726	−	0.247133i
$709$	−46.6527	+	19.3242i	−1.75208	+	0.725734i	−0.754491	+	0.656311i	$0.772116\pi$
$709$	−46.6527	+	19.3242i	−1.75208	+	0.725734i	−0.997587	+	0.0694237i	$0.977884\pi$
$710$	4.20040	−	2.80465i	0.157638	−	0.105257i
$711$	−11.3836	+	11.3836i	−0.426919	+	0.426919i
$712$	−10.0438	−	15.0632i	−0.376406	−	0.564516i
$713$	33.5617	+	33.5617i	1.25689	+	1.25689i
$714$	−63.7813	−	12.7083i	−2.38696	−	0.475597i
$715$	0.0314193	+	0.0758529i	0.00117502	+	0.00283674i
$716$	−0.0241380	+	37.3335i	−0.000902080	+	1.39522i
$717$	−27.3186	−	11.3158i	−1.02023	−	0.422594i
$718$	−47.2207	+	9.37692i	−1.76226	+	0.349944i
$719$			43.3523i			1.61677i	0.588654	+	0.808385i	$0.299658\pi$
$719$			43.3523i			1.61677i	−0.588654	+	0.808385i	$0.700342\pi$
$720$	1.80030	−	0.742982i	0.0670931	−	0.0276893i
$721$		−	11.6396i		−	0.433481i
$722$	−5.53878	−	27.8925i	−0.206132	−	1.03805i
$723$	3.33217	+	1.38023i	0.123925	+	0.0513312i
$724$	21.4515	−	21.4238i	0.797240	−	0.796209i
$725$	−6.82488	−	16.4767i	−0.253470	−	0.611930i
$726$	−0.593458	+	2.97848i	−0.0220253	+	0.110542i
$727$	23.7898	+	23.7898i	0.882316	+	0.882316i	0.993770	−	0.111454i	$-0.0355506\pi$
$727$	23.7898	+	23.7898i	0.882316	+	0.882316i	−0.111454	+	0.993770i	$0.535551\pi$
$728$	−0.574948	−	2.90518i	−0.0213090	−	0.107673i
$729$	0.773756	−	0.773756i	0.0286576	−	0.0286576i
$730$	−1.94669	−	2.91547i	−0.0720502	−	0.107906i
$731$	38.3527	−	15.8862i	1.41853	−	0.587573i
$732$	12.9168	−	31.1269i	0.477418	−	1.15048i
$733$	−1.34772	+	3.25368i	−0.0497791	+	0.120177i	−0.946813	−	0.321784i	$-0.895717\pi$
$733$	−1.34772	+	3.25368i	−0.0497791	+	0.120177i	0.897034	+	0.441962i	$0.145717\pi$
$734$	16.0742	−	24.0399i	0.593309	−	0.887328i
$735$	5.08738			0.187651
$736$	34.2723	+	22.9802i	1.26329	+	0.847063i
$737$	9.29347			0.342329
$738$	12.5723	−	18.8025i	0.462791	−	0.692131i
$739$	−5.76254	+	13.9120i	−0.211979	+	0.511761i	−0.993727	−	0.111832i	$-0.964328\pi$
$739$	−5.76254	+	13.9120i	−0.211979	+	0.511761i	0.781749	+	0.623594i	$0.214328\pi$
$740$	3.26206	+	1.35366i	0.119916	+	0.0497616i
$741$	−3.37215	+	1.39679i	−0.123879	+	0.0513123i
$742$	8.38818	+	12.5626i	0.307940	+	0.461187i
$743$	5.33317	−	5.33317i	0.195655	−	0.195655i	−0.602479	−	0.798134i	$-0.705820\pi$
$743$	5.33317	−	5.33317i	0.195655	−	0.195655i	0.798134	+	0.602479i	$0.205820\pi$
$744$	32.8405	+	21.9894i	1.20399	+	0.806172i
$745$	1.54901	+	1.54901i	0.0567512	+	0.0567512i
$746$	−3.27678	+	16.4457i	−0.119971	+	0.602119i
$747$	−1.82057	−	4.39524i	−0.0666111	−	0.160813i
$748$	7.85572	+	7.86589i	0.287234	+	0.287605i
$749$	−72.5064	−	30.0331i	−2.64933	−	1.09739i
$750$	1.77064	+	8.91666i	0.0646545	+	0.325590i
$751$			48.6218i			1.77423i	0.461544	+	0.887117i	$0.347296\pi$
$751$			48.6218i			1.77423i	−0.461544	+	0.887117i	$0.652704\pi$
$752$	−1.03131	−	1.03398i	−0.0376081	−	0.0377055i
$753$		−	61.1723i		−	2.22924i
$754$	1.36970	−	0.271990i	0.0498816	−	0.00990530i
$755$	2.72463	+	1.12858i	0.0991596	+	0.0410733i
$756$	−22.9705	−	0.0148516i	−0.835430	−	0.000540147i
$757$	8.09704	+	19.5480i	0.294292	+	0.710484i	0.999998	+	0.00197905i	$0.000629952\pi$
$757$	8.09704	+	19.5480i	0.294292	+	0.710484i	−0.705706	+	0.708505i	$0.749370\pi$
$758$	24.3412	+	4.84994i	0.884111	+	0.176158i
$759$	−11.0767	−	11.0767i	−0.402059	−	0.402059i
$760$	1.04751	−	5.23963i	0.0379972	−	0.190061i
$761$	31.5664	−	31.5664i	1.14428	−	1.14428i	0.156622	−	0.987659i	$-0.449940\pi$
$761$	31.5664	−	31.5664i	1.14428	−	1.14428i	0.987659	−	0.156622i	$-0.0500604\pi$
$762$	−35.5482	+	23.7360i	−1.28778	+	0.859863i
$763$	−30.5516	+	12.6549i	−1.10604	+	0.458138i
$764$	−7.15701	−	17.3102i	−0.258931	−	0.626261i
$765$	−1.03569	+	2.50037i	−0.0374453	+	0.0904011i
$766$	6.82556	+	4.56388i	0.246617	+	0.164900i
$767$	−1.08905			−0.0393233
$768$	31.7104	+	13.2311i	1.14425	+	0.477435i
$769$	−32.7171			−1.17981			−0.589904	−	0.807473i	$-0.700835\pi$
$769$	−32.7171			−1.17981			−0.589904	+	0.807473i	$0.700835\pi$
$770$	−1.36819	−	0.914836i	−0.0493062	−	0.0329684i
$771$	−16.9207	+	40.8502i	−0.609384	+	1.47118i
$772$	−13.2375	−	32.0166i	−0.476427	−	1.15230i
$773$	12.3642	−	5.12141i	0.444709	−	0.184204i	−0.149080	−	0.988825i	$-0.547631\pi$
$773$	12.3642	−	5.12141i	0.444709	−	0.184204i	0.593789	+	0.804621i	$0.297631\pi$
$774$	−14.1575	+	9.45315i	−0.508882	+	0.339786i
$775$	−22.5851	+	22.5851i	−0.811281	+	0.811281i
$776$	4.61424	−	23.0803i	0.165641	−	0.828535i
$777$	34.1976	+	34.1976i	1.22683	+	1.22683i
$778$	28.4449	+	5.66760i	1.01980	+	0.203193i
$779$	−23.7475	−	57.3315i	−0.850843	−	2.05412i
$780$	−0.352631		0.000227994i	−0.0126262		8.16348e-6i
$781$	−10.9224	−	4.52420i	−0.390834	−	0.161889i
$782$	−56.2420	+	11.1683i	−2.01121	+	0.399379i
$783$		−	10.8313i		−	0.387078i
$784$	22.1519	+	22.2092i	0.791138	+	0.793187i
$785$		−	1.57824i		−	0.0563297i
$786$	2.94025	+	14.8067i	0.104875	+	0.528136i
$787$	−17.2813	−	7.15816i	−0.616013	−	0.255161i	0.0527842	−	0.998606i	$-0.483190\pi$
$787$	−17.2813	−	7.15816i	−0.616013	−	0.255161i	−0.668797	+	0.743445i	$0.733190\pi$
$788$	−7.96832	−	7.97863i	−0.283860	−	0.284227i
$789$	−3.34714	−	8.08071i	−0.119161	−	0.287681i
$790$	−0.833835	+	4.18490i	−0.0296665	+	0.148892i
$791$	−5.61022	−	5.61022i	−0.199477	−	0.199477i
$792$	−3.78803	−	2.53640i	−0.134602	−	0.0901270i
$793$	−1.50793	+	1.50793i	−0.0535483	+	0.0535483i
$794$	9.71297	+	14.5467i	0.344700	+	0.516242i
$795$	1.66173	−	0.688310i	0.0589354	−	0.0244118i
$796$	−48.7954	−	20.2487i	−1.72951	−	0.717695i
$797$	−11.1858	+	27.0049i	−0.396221	+	0.956563i	0.592332	+	0.805694i	$0.298207\pi$
$797$	−11.1858	+	27.0049i	−0.396221	+	0.956563i	−0.988554	+	0.150869i	$0.951793\pi$
$798$	40.6703	−	60.8248i	1.43971	−	2.15318i
$799$	2.02937			0.0717938
$800$	−15.4644	+	23.0633i	−0.546749	+	0.815411i
$801$	−10.3169			−0.364528
$802$	−4.77687	+	7.14408i	−0.168677	+	0.252266i
$803$	−3.14022	+	7.58115i	−0.110816	+	0.267533i
$804$	−15.2989	+	36.8673i	−0.539549	+	1.30021i
$805$	7.84308	−	3.24871i	0.276432	−	0.114502i
$806$	−1.38878	−	2.07992i	−0.0489178	−	0.0732619i
$807$	−30.0536	+	30.0536i	−1.05794	+	1.05794i
$808$	−0.426843	−	2.15681i	−0.0150163	−	0.0758764i
$809$	−9.38726	−	9.38726i	−0.330039	−	0.330039i	0.522562	−	0.852601i	$-0.324976\pi$
$809$	−9.38726	−	9.38726i	−0.330039	−	0.330039i	−0.852601	+	0.522562i	$0.824976\pi$
$810$	−0.938121	+	4.70830i	−0.0329622	+	0.165433i
$811$	10.8757	+	26.2563i	0.381898	+	0.921983i	0.991599	+	0.129351i	$0.0412895\pi$
$811$	10.8757	+	26.2563i	0.381898	+	0.921983i	−0.609701	+	0.792632i	$0.708710\pi$
$812$	−19.8074	+	19.7818i	−0.695103	+	0.694205i
$813$	−35.4819	−	14.6971i	−1.24440	−	0.515449i
$814$	−1.61018	−	8.10863i	−0.0564368	−	0.284207i
$815$			2.50939i			0.0879002i
$816$	−44.1361	+	18.2149i	−1.54507	+	0.637650i
$817$			46.7048i			1.63400i
$818$	−29.8721	+	5.93189i	−1.04445	+	0.207404i
$819$	−1.55916	−	0.645824i	−0.0544813	−	0.0225669i
$820$	0.00387623	−	5.99526i	0.000135364	−	0.209364i
$821$	−15.5118	−	37.4489i	−0.541366	−	1.30697i	−0.923759	−	0.382974i	$-0.874900\pi$
$821$	−15.5118	−	37.4489i	−0.541366	−	1.30697i	0.382393	−	0.924000i	$-0.375100\pi$
$822$	−34.1531	−	6.80496i	−1.19123	−	0.237350i
$823$	−6.76353	−	6.76353i	−0.235762	−	0.235762i	0.579331	−	0.815093i	$-0.303314\pi$
$823$	−6.76353	−	6.76353i	−0.235762	−	0.235762i	−0.815093	+	0.579331i	$0.803314\pi$
$824$	−4.74072	−	7.10990i	−0.165151	−	0.247685i
$825$	7.45400	−	7.45400i	0.259515	−	0.259515i
$826$	18.1562	−	12.1231i	0.631735	−	0.421816i
$827$	20.0221	−	8.29344i	0.696238	−	0.288391i	−0.00635861	−	0.999980i	$-0.502024\pi$
$827$	20.0221	−	8.29344i	0.696238	−	0.288391i	0.702596	+	0.711589i	$0.252024\pi$
$828$	21.7299	−	8.98436i	0.755166	−	0.312228i
$829$	19.8375	−	47.8919i	0.688984	−	1.66335i	−0.0578342	−	0.998326i	$-0.518419\pi$
$829$	19.8375	−	47.8919i	0.688984	−	1.66335i	0.746818	−	0.665028i	$-0.231581\pi$
$830$	−1.04825	−	0.700906i	−0.0363852	−	0.0243288i
$831$	37.7982			1.31121
$832$	−1.53446	−	1.54042i	−0.0531978	−	0.0534045i
$833$	−43.5893			−1.51028
$834$	−22.8301	−	15.2653i	−0.790543	−	0.528594i
$835$	2.90501	−	7.01331i	0.100532	−	0.242706i
$836$	−11.5583	+	4.77886i	−0.399753	+	0.165280i
$837$	−17.9216	+	7.42337i	−0.619461	+	0.256589i
$838$	3.55758	−	2.37543i	0.122895	−	0.0820580i
$839$	−30.5305	+	30.5305i	−1.05403	+	1.05403i	−0.0555750	+	0.998455i	$0.517699\pi$
$839$	−30.5305	+	30.5305i	−1.05403	+	1.05403i	−0.998455	+	0.0555750i	$0.982301\pi$
$840$	5.88147	−	3.92163i	0.202930	−	0.135309i
$841$	11.1724	+	11.1724i	0.385254	+	0.385254i
$842$	40.1478	+	7.99939i	1.38359	+	0.275677i
$843$	−9.36524	−	22.6097i	−0.322556	−	0.778719i
$844$	0.0152428	−	23.5756i	0.000524679	−	0.811505i
$845$	−3.60759	−	1.49431i	−0.124105	−	0.0514059i
$846$	−0.816261	+	0.162090i	−0.0280636	+	0.00557277i
$847$			3.85253i			0.132375i
$848$	10.2405	+	4.25726i	0.351659	+	0.146195i
$849$			41.6465i			1.42930i
$850$	−7.51566	−	37.8477i	−0.257785	−	1.29817i
$851$	39.3947	+	16.3178i	1.35043	+	0.559368i
$852$	35.9279	−	35.8815i	1.23087	−	1.22928i
$853$	10.6799	+	25.7837i	0.365674	+	0.882816i	0.994448	+	0.105228i	$0.0335572\pi$
$853$	10.6799	+	25.7837i	0.365674	+	0.882816i	−0.628774	+	0.777588i	$0.716443\pi$
$854$	8.35364	−	41.9257i	0.285856	−	1.43467i
$855$	−2.15305	−	2.15305i	−0.0736329	−	0.0736329i
$856$	−56.5219	+	11.1859i	−1.93188	+	0.382328i
$857$	10.9017	−	10.9017i	0.372396	−	0.372396i	−0.495953	−	0.868349i	$-0.665181\pi$
$857$	10.9017	−	10.9017i	0.372396	−	0.372396i	0.868349	+	0.495953i	$0.165181\pi$
$858$	0.458355	+	0.686457i	0.0156480	+	0.0234352i
$859$	39.9944	−	16.5662i	1.36459	−	0.565233i	0.424275	−	0.905533i	$-0.360529\pi$
$859$	39.9944	−	16.5662i	1.36459	−	0.565233i	0.940317	+	0.340301i	$0.110529\pi$
$860$	−1.72945	+	4.16764i	−0.0589738	+	0.142115i
$861$	31.4170	−	75.8475i	1.07069	−	2.58487i
$862$	−11.6026	+	17.3524i	−0.395188	+	0.591027i
$863$	14.1255			0.480836			0.240418	−	0.970669i	$-0.422715\pi$
$863$	14.1255			0.480836			0.240418	+	0.970669i	$0.422715\pi$
$864$	−14.0373	+	9.34665i	−0.477559	+	0.317980i
$865$	2.29001			0.0778625
$866$	−19.4711	+	29.1202i	−0.661656	+	0.989546i
$867$	11.4201	−	27.5705i	0.387846	−	0.936342i
$868$	46.3065	+	19.2159i	1.57175	+	0.652229i
$869$	9.22798	−	3.82235i	0.313038	−	0.129665i
$870$	1.85095	+	2.77209i	0.0627532	+	0.0939826i
$871$	1.78602	−	1.78602i	0.0605171	−	0.0605171i
$872$	−13.5078	+	20.1735i	−0.457433	+	0.683162i
$873$	−9.48409	−	9.48409i	−0.320988	−	0.320988i
$874$	12.6061	−	63.2683i	0.426408	−	2.14008i
$875$	4.41304	+	10.6540i	0.149188	+	0.360171i
$876$	−24.9051	−	24.9373i	−0.841464	−	0.842553i
$877$	−31.4662	−	13.0337i	−1.06254	−	0.440118i	−0.218187	−	0.975907i	$-0.570014\pi$
$877$	−31.4662	−	13.0337i	−1.06254	−	0.440118i	−0.844352	+	0.535789i	$0.820014\pi$
$878$	−5.59629	−	28.1820i	−0.188865	−	0.951098i
$879$		−	25.0248i		−	0.844067i
$880$	−1.20835	−	0.00156252i	−0.0407334	−	5.26724e-5i
$881$			22.1244i			0.745390i	0.927954	+	0.372695i	$0.121566\pi$
$881$			22.1244i			0.745390i	−0.927954	+	0.372695i	$0.878434\pi$
$882$	17.5327	−	3.48158i	0.590356	−	0.117231i
$883$	3.53105	+	1.46261i	0.118829	+	0.0492207i	0.441306	−	0.897357i	$-0.354515\pi$
$883$	3.53105	+	1.46261i	0.118829	+	0.0492207i	−0.322477	+	0.946577i	$0.604515\pi$
$884$	3.02139	+	0.00195348i	0.101620	+	6.57025e-5i
$885$	−0.994786	−	2.40163i	−0.0334394	−	0.0807298i
$886$	48.1710	+	9.59800i	1.61834	+	0.322451i
$887$	−20.4384	−	20.4384i	−0.686253	−	0.686253i	0.275149	−	0.961402i	$-0.411273\pi$
$887$	−20.4384	−	20.4384i	−0.686253	−	0.686253i	−0.961402	+	0.275149i	$0.911273\pi$
$888$	34.8176	+	6.96077i	1.16840	+	0.233588i
$889$	−38.3407	+	38.3407i	−1.28591	+	1.28591i
$890$	−2.27422	+	1.51852i	−0.0762319	+	0.0509009i
$891$	10.3821	−	4.30041i	0.347814	−	0.144069i
$892$	1.16529	+	2.81841i	0.0390167	+	0.0943672i
$893$	−0.873737	+	2.10939i	−0.0292385	+	0.0705880i
$894$	18.3078	+	12.2415i	0.612305	+	0.409416i
$895$	5.63900			0.188491
$896$	42.7296	+	8.60001i	1.42750	+	0.287306i
$897$	−4.25745			−0.142152
$898$	−36.3796	−	24.3251i	−1.21400	−	0.811739i
$899$	−9.04673	+	21.8407i	−0.301725	+	0.728429i
$900$	6.04596	+	14.6230i	0.201532	+	0.487432i
$901$	−14.2379	+	5.89752i	−0.474332	+	0.196475i
$902$	−11.6708	+	7.79272i	−0.388595	+	0.259469i
$903$	−43.6912	+	43.6912i	−1.45395	+	1.45395i
$904$	−5.71194	−	1.14194i	−0.189976	−	0.0379802i
$905$	−3.23803	−	3.23803i	−0.107636	−	0.107636i
$906$	29.0774	+	5.79362i	0.966031	+	0.192480i
$907$	0.0920114	+	0.222135i	0.00305519	+	0.00737588i	0.925400	−	0.378992i	$-0.123729\pi$
$907$	0.0920114	+	0.222135i	0.00305519	+	0.00737588i	−0.922345	+	0.386368i	$0.873729\pi$
$908$	−15.5398	−	0.0100473i	−0.515708	−	0.000333431i
$909$	−1.15752	−	0.479461i	−0.0383926	−	0.0159027i
$910$	−0.438753	+	0.0871260i	−0.0145445	+	0.00288820i
$911$			1.96264i			0.0650253i	0.999471	+	0.0325126i	$0.0103509\pi$
$911$			1.96264i			0.0650253i	−0.999471	+	0.0325126i	$0.989649\pi$
$912$	0.0694639	−	53.7188i	0.00230018	−	1.77881i
$913$			2.95164i			0.0976850i
$914$	2.22054	+	11.1823i	0.0734489	+	0.369877i
$915$	−4.70279	−	1.94796i	−0.155469	−	0.0643975i
$916$	−16.8500	−	16.8718i	−0.556740	−	0.557460i
$917$	7.32812	+	17.6916i	0.241996	+	0.584229i
$918$	4.57934	−	22.9831i	0.151141	−	0.758554i
$919$	29.3334	+	29.3334i	0.967619	+	0.967619i	0.999492	−	0.0318729i	$-0.0101472\pi$
$919$	29.3334	+	29.3334i	0.967619	+	0.967619i	−0.0318729	+	0.999492i	$0.510147\pi$
$920$	3.46768	−	5.17886i	0.114326	−	0.170742i
$921$	28.1108	−	28.1108i	0.926281	−	0.926281i
$922$	−17.6819	−	26.4813i	−0.582321	−	0.872115i
$923$	−2.96853	+	1.22961i	−0.0977104	+	0.0404730i
$924$	−15.2830	−	6.34202i	−0.502775	−	0.208637i
$925$	−10.9810	+	26.5104i	−0.361052	+	0.871656i
$926$	−23.3080	+	34.8584i	−0.765947	+	1.14552i
$927$	−4.86962			−0.159939
$928$	−4.04213	+	20.1509i	−0.132689	+	0.661485i
$929$	20.9234			0.686474			0.343237	−	0.939249i	$-0.388477\pi$
$929$	20.9234			0.686474			0.343237	+	0.939249i	$0.388477\pi$
$930$	3.31816	−	4.96251i	0.108807	−	0.162727i
$931$	18.7672	−	45.3081i	0.615072	−	1.48491i
$932$	12.9565	−	31.2225i	0.424403	−	1.02273i
$933$	0.0636914	−	0.0263818i	0.00208516	−	0.000863703i
$934$	6.29382	+	9.42596i	0.205940	+	0.308427i
$935$	1.18733	−	1.18733i	0.0388297	−	0.0388297i
$936$	−1.21543	+	0.240539i	−0.0397276	+	0.00786227i
$937$	27.8878	+	27.8878i	0.911054	+	0.911054i	0.996355	−	0.0853010i	$-0.0271852\pi$
$937$	27.8878	+	27.8878i	0.911054	+	0.911054i	−0.0853010	+	0.996355i	$0.527185\pi$
$938$	−9.89419	+	49.6576i	−0.323057	+	1.62138i
$939$	−12.7235	−	30.7172i	−0.415215	−	1.00242i
$940$	−0.156076	+	0.155875i	−0.00509064	+	0.00508407i
$941$	26.6462	+	11.0372i	0.868642	+	0.359803i	0.772081	−	0.635524i	$-0.219216\pi$
$941$	26.6462	+	11.0372i	0.868642	+	0.359803i	0.0965608	+	0.995327i	$0.469216\pi$
$942$	−3.09042	−	15.5629i	−0.100691	−	0.507066i
$943$		−	72.3831i		−	2.35712i
$944$	6.15285	−	14.8001i	0.200258	−	0.481703i
$945$			3.46956i			0.112865i
$946$	10.3597	−	2.05718i	0.336822	−	0.0668848i
$947$	15.4448	+	6.39745i	0.501889	+	0.207889i	0.619241	−	0.785201i	$-0.287441\pi$
$947$	15.4448	+	6.39745i	0.501889	+	0.207889i	−0.117352	+	0.993090i	$0.537441\pi$
$948$	−0.0277369	+	42.8998i	−0.000900851	+	1.39332i
$949$	0.853461	+	2.06044i	0.0277045	+	0.0668846i
$950$	42.5760	+	8.48319i	1.38135	+	0.275231i
$951$	−16.2259	−	16.2259i	−0.526161	−	0.526161i
$952$	−50.3931	+	33.6010i	−1.63325	+	1.08901i
$953$	−38.4854	+	38.4854i	−1.24666	+	1.24666i	−0.289480	+	0.957184i	$0.593482\pi$
$953$	−38.4854	+	38.4854i	−1.24666	+	1.24666i	−0.957184	+	0.289480i	$0.906518\pi$
$954$	5.25577	−	3.50934i	0.170162	−	0.113619i
$955$	−2.61390	+	1.08271i	−0.0845837	+	0.0350357i
$956$	−25.4490	+	10.5221i	−0.823081	+	0.340308i
$957$	2.98579	−	7.20833i	0.0965168	−	0.233012i
$958$	−5.22468	−	3.49346i	−0.168802	−	0.112869i
$959$	−44.1756			−1.42650
$960$	1.99538	−	4.79096i	0.0644005	−	0.154627i
$961$	11.3383			0.365752
$962$	−1.86776	−	1.24887i	−0.0602191	−	0.0402653i
$963$	−12.5649	+	30.3343i	−0.404897	+	0.977509i
$964$	3.10412	−	1.28342i	0.0999771	−	0.0413361i
$965$	−4.83462	+	2.00256i	−0.155632	+	0.0644648i
$966$	70.9786	−	47.3932i	2.28370	−	1.52485i
$967$	18.6035	−	18.6035i	0.598248	−	0.598248i	−0.341598	−	0.939846i	$-0.610968\pi$
$967$	18.6035	−	18.6035i	0.598248	−	0.598248i	0.939846	+	0.341598i	$0.110968\pi$
$968$	1.56911	+	2.35327i	0.0504331	+	0.0756371i
$969$	52.7842	+	52.7842i	1.69567	+	1.69567i
$970$	−3.48659	−	0.694697i	−0.111948	−	0.0223054i
$971$	11.2997	+	27.2799i	0.362624	+	0.875453i	0.994915	+	0.100721i	$0.0321150\pi$
$971$	11.2997	+	27.2799i	0.362624	+	0.875453i	−0.632290	+	0.774732i	$0.717885\pi$
$972$	−0.0196408	+	30.3778i	−0.000629979	+	0.974369i
$973$	−32.1861	−	13.3319i	−1.03184	−	0.427402i
$974$	−56.1980	+	11.1596i	−1.80070	+	0.357577i
$975$		−	2.86502i		−	0.0917542i
$976$	−11.9733	−	29.0122i	−0.383257	−	0.928658i
$977$			38.7297i			1.23907i	0.784967	+	0.619537i	$0.212680\pi$
$977$			38.7297i			1.23907i	−0.784967	+	0.619537i	$0.787320\pi$
$978$	4.91376	+	24.7450i	0.157125	+	0.791256i
$979$	5.91370	+	2.44953i	0.189003	+	0.0782874i
$980$	3.35240	−	3.34807i	0.107089	−	0.106950i
$981$	5.29439	+	12.7818i	0.169037	+	0.408091i
$982$	−1.21906	+	6.11829i	−0.0389018	+	0.195243i
$983$	−7.56002	−	7.56002i	−0.241127	−	0.241127i	0.576189	−	0.817316i	$-0.304539\pi$
$983$	−7.56002	−	7.56002i	−0.241127	−	0.241127i	−0.817316	+	0.576189i	$0.804539\pi$
$984$	−11.7014	−	59.1264i	−0.373026	−	1.88488i
$985$	−1.20434	+	1.20434i	−0.0383736	+	0.0383736i
$986$	−15.8592	−	23.7516i	−0.505060	−	0.756404i
$987$	−2.79064	+	1.15592i	−0.0888271	+	0.0367934i
$988$	−1.30288	+	3.13968i	−0.0414501	+	0.0998867i
$989$	−20.8478	+	50.3311i	−0.662922	+	1.60043i
$990$	−0.382737	+	0.572406i	−0.0121642	+	0.0181923i
$991$	29.8486			0.948173			0.474086	−	0.880478i	$-0.342778\pi$
$991$	29.8486			0.948173			0.474086	+	0.880478i	$0.342778\pi$
$992$	36.1123	−	7.12251i	1.14657	−	0.226140i
$993$	39.3394			1.24840
$994$	35.8024	−	53.5447i	1.13558	−	1.69833i
$995$	−3.05367	+	7.37221i	−0.0968079	+	0.233715i
$996$	−11.7092	−	4.85897i	−0.371019	−	0.153962i
$997$	18.4105	−	7.62586i	0.583065	−	0.241514i	−0.0715988	−	0.997434i	$-0.522810\pi$
$997$	18.4105	−	7.62586i	0.583065	−	0.241514i	0.654664	+	0.755920i	$0.272810\pi$
$998$	14.2998	+	21.4162i	0.452653	+	0.677918i
$999$	−12.3228	+	12.3228i	−0.389877	+	0.389877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.n.a.45.10	✓	160
32.5	even	8	inner	352.2.n.a.133.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.n.a.45.10	✓	160	1.1	even	1	trivial
352.2.n.a.133.10	yes	160	32.5	even	8	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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17562 - 0.786075i) q^{2} +(-0.821814 + 1.98403i) q^{3} +(0.764172 + 1.84825i) q^{4} +(0.279093 - 0.115604i) q^{5} +(2.52574 - 1.68647i) q^{6} +(2.72415 - 2.72415i) q^{7} +(0.554489 - 2.77354i) q^{8} +(-1.13970 - 1.13970i) q^{9} +(-0.418981 - 0.0834812i) q^{10} +(0.382683 + 0.923880i) q^{11} +(-4.29501 - 0.00277694i) q^{12} +(0.251096 + 0.104007i) q^{13} +(-5.34396 + 1.06118i) q^{14} +0.648734i q^{15} +(-2.83208 + 2.82477i) q^{16} -5.55843i q^{17} +(0.443964 + 2.23574i) q^{18} +(5.77761 + 2.39317i) q^{19} +(0.426940 + 0.427492i) q^{20} +(3.16607 + 7.64356i) q^{21} +(0.276348 - 1.38695i) q^{22} +(5.15795 + 5.15795i) q^{23} +(5.04712 + 3.37946i) q^{24} +(-3.47101 + 3.47101i) q^{25} +(-0.213436 - 0.319653i) q^{26} +(-2.75429 + 1.14086i) q^{27} +(7.11665 + 2.95320i) q^{28} +(-1.39035 + 3.35661i) q^{29} +(0.509954 - 0.762666i) q^{30} +6.50679 q^{31} +(5.54994 - 1.09463i) q^{32} -2.14750 q^{33} +(-4.36934 + 6.53461i) q^{34} +(0.445368 - 1.07521i) q^{35} +(1.23552 - 2.97737i) q^{36} +(5.40065 - 2.23702i) q^{37} +(-4.91108 - 7.35509i) q^{38} +(-0.412708 + 0.412708i) q^{39} +(-0.165879 - 0.838176i) q^{40} +(-7.01666 - 7.01666i) q^{41} +(2.28632 - 11.4747i) q^{42} +(2.85804 + 6.89992i) q^{43} +(-1.41513 + 1.41330i) q^{44} +(-0.449834 - 0.186327i) q^{45} +(-2.00926 - 10.1183i) q^{46} +0.365097i q^{47} +(-3.27699 - 7.94038i) q^{48} -7.84202i q^{49} +(6.80906 - 1.35212i) q^{50} +(11.0281 + 4.56800i) q^{51} +(-0.000351444 + 0.543568i) q^{52} +(-1.06100 - 2.56149i) q^{53} +(4.13481 + 0.823854i) q^{54} +(0.213608 + 0.213608i) q^{55} +(-6.04504 - 9.06607i) q^{56} +(-9.49625 + 9.49625i) q^{57} +(4.27307 - 2.85318i) q^{58} +(-3.70202 + 1.53343i) q^{59} +(-1.19903 + 0.495745i) q^{60} +(-3.00271 + 7.24917i) q^{61} +(-7.64952 - 5.11482i) q^{62} -6.20941 q^{63} +(-7.38508 - 3.07580i) q^{64} +0.0821026 q^{65} +(2.52465 + 1.68810i) q^{66} +(3.55646 - 8.58605i) q^{67} +(10.2734 - 4.24760i) q^{68} +(-14.4724 + 5.99467i) q^{69} +(-1.36878 + 0.913951i) q^{70} +(-8.35963 + 8.35963i) q^{71} +(-3.79294 + 2.52905i) q^{72} +(5.80236 + 5.80236i) q^{73} +(-8.10758 - 1.61542i) q^{74} +(-4.03407 - 9.73912i) q^{75} +(-0.00808658 + 12.5073i) q^{76} +(3.55928 + 1.47430i) q^{77} +(0.809608 - 0.160769i) q^{78} -9.98829i q^{79} +(-0.463859 + 1.11577i) q^{80} -11.2375i q^{81} +(2.73331 + 13.7646i) q^{82} +(2.72696 + 1.12954i) q^{83} +(-11.7078 + 11.6927i) q^{84} +(-0.642576 - 1.55132i) q^{85} +(2.06388 - 10.3583i) q^{86} +(-5.51701 - 5.51701i) q^{87} +(2.77461 - 0.549108i) q^{88} +(4.52615 - 4.52615i) q^{89} +(0.382367 + 0.572653i) q^{90} +(0.967355 - 0.400692i) q^{91} +(-5.59164 + 13.4748i) q^{92} +(-5.34737 + 12.9097i) q^{93} +(0.286994 - 0.429216i) q^{94} +1.88915 q^{95} +(-2.38924 + 11.9108i) q^{96} +8.32160 q^{97} +(-6.16441 + 9.21924i) q^{98} +(0.616799 - 1.48908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 16 q^{10} - 16 q^{14} - 16 q^{20} + 24 q^{24} - 48 q^{27} + 40 q^{28} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 56 q^{36} - 16 q^{38} - 48 q^{39} - 64 q^{40} - 104 q^{48} - 80 q^{50} + 32 q^{51} + 64 q^{54}+ \cdots + 56 q^{98}+O(q^{100}) \) 160 * q - 16 * q^10 - 16 * q^14 - 16 * q^20 + 24 * q^24 - 48 * q^27 + 40 * q^28 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 56 * q^36 - 16 * q^38 - 48 * q^39 - 64 * q^40 - 104 * q^48 - 80 * q^50 + 32 * q^51 + 64 * q^54 - 40 * q^56 + 8 * q^58 + 32 * q^59 - 8 * q^60 - 64 * q^61 + 24 * q^62 - 24 * q^64 + 48 * q^68 - 64 * q^69 - 24 * q^70 + 32 * q^71 + 72 * q^72 - 128 * q^78 - 16 * q^80 + 40 * q^82 - 80 * q^83 - 152 * q^84 - 64 * q^86 - 112 * q^87 + 144 * q^90 - 72 * q^92 + 96 * q^94 + 56 * q^96 + 56 * q^98

Introduction

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