LMFDB - Embedded newform 802.2.e.b.45.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [802,2,Mod(45,802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(802, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("802.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 802 = 2 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	802.e (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:	$6.40400224211$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.16
Character	$\chi$	$=$	802.45
Dual form			802.2.e.b.303.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(2.73669 + 1.13357i) q^{3} +1.00000i q^{4} +0.245522 q^{5} +(1.13357 + 2.73669i) q^{6} +(1.24807 - 1.24807i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(4.08315 + 4.08315i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(2.73669 + 1.13357i) q^{3} +1.00000i q^{4} +0.245522 q^{5} +(1.13357 + 2.73669i) q^{6} +(1.24807 - 1.24807i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(4.08315 + 4.08315i) q^{9} +(0.173610 + 0.173610i) q^{10} +(0.802805 + 0.802805i) q^{11} +(-1.13357 + 2.73669i) q^{12} +(4.09879 - 1.69777i) q^{13} +1.76504 q^{14} +(0.671917 + 0.278317i) q^{15} -1.00000 q^{16} +(-6.03141 + 2.49829i) q^{17} +5.77444i q^{18} +(-2.60020 - 6.27743i) q^{19} +0.245522i q^{20} +(4.83036 - 2.00080i) q^{21} +1.13534i q^{22} +(-3.19829 - 7.72135i) q^{23} +(-2.73669 + 1.13357i) q^{24} -4.93972 q^{25} +(4.09879 + 1.69777i) q^{26} +(3.14504 + 7.59279i) q^{27} +(1.24807 + 1.24807i) q^{28} -3.56159 q^{29} +(0.278317 + 0.671917i) q^{30} +(4.04471 + 9.76480i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.28699 + 3.10706i) q^{33} +(-6.03141 - 2.49829i) q^{34} +(0.306429 - 0.306429i) q^{35} +(-4.08315 + 4.08315i) q^{36} +(1.37965 + 0.571470i) q^{37} +(2.60020 - 6.27743i) q^{38} +13.1416 q^{39} +(-0.173610 + 0.173610i) q^{40} -3.79040 q^{41} +(4.83036 + 2.00080i) q^{42} +(5.24736 - 5.24736i) q^{43} +(-0.802805 + 0.802805i) q^{44} +(1.00250 + 1.00250i) q^{45} +(3.19829 - 7.72135i) q^{46} +(0.754114 + 0.754114i) q^{47} +(-2.73669 - 1.13357i) q^{48} +3.88464i q^{49} +(-3.49291 - 3.49291i) q^{50} -19.3381 q^{51} +(1.69777 + 4.09879i) q^{52} +(-4.27873 + 10.3298i) q^{53} +(-3.14504 + 7.59279i) q^{54} +(0.197106 + 0.197106i) q^{55} +1.76504i q^{56} -20.1269i q^{57} +(-2.51842 - 2.51842i) q^{58} +(-5.77060 + 2.39026i) q^{59} +(-0.278317 + 0.671917i) q^{60} +(0.870786 + 2.10226i) q^{61} +(-4.04471 + 9.76480i) q^{62} +10.1921 q^{63} -1.00000i q^{64} +(1.00634 - 0.416840i) q^{65} +(-1.28699 + 3.10706i) q^{66} +(-4.19378 + 10.1247i) q^{67} +(-2.49829 - 6.03141i) q^{68} -24.7564i q^{69} +0.433356 q^{70} +(3.30400 - 7.97656i) q^{71} -5.77444 q^{72} +(9.42686 - 9.42686i) q^{73} +(0.571470 + 1.37965i) q^{74} +(-13.5185 - 5.59953i) q^{75} +(6.27743 - 2.60020i) q^{76} +2.00392 q^{77} +(9.29254 + 9.29254i) q^{78} +(-3.89830 - 9.41132i) q^{79} -0.245522 q^{80} +7.02088i q^{81} +(-2.68022 - 2.68022i) q^{82} -8.87362 q^{83} +(2.00080 + 4.83036i) q^{84} +(-1.48084 + 0.613386i) q^{85} +7.42089 q^{86} +(-9.74695 - 4.03732i) q^{87} -1.13534 q^{88} +(6.42985 - 6.42985i) q^{89} +1.41775i q^{90} +(2.99663 - 7.23452i) q^{91} +(7.72135 - 3.19829i) q^{92} +31.3082i q^{93} +1.06648i q^{94} +(-0.638406 - 1.54125i) q^{95} +(-1.13357 - 2.73669i) q^{96} +(4.38494 + 10.5862i) q^{97} +(-2.74685 + 2.74685i) q^{98} +6.55595i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 68 * q + 4 * q^6 + 20 * q^9	$ 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) $ 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/802\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	2.73669	+	1.13357i	1.58003	+	0.654469i	0.988418	−	0.151756i	$-0.0484929\pi$
$3$	2.73669	+	1.13357i	1.58003	+	0.654469i	0.591609	+	0.806225i	$0.298493\pi$
$4$			1.00000i			0.500000i
$5$	0.245522			0.109801			0.0549004	−	0.998492i	$-0.482516\pi$
$5$	0.245522			0.109801			0.0549004	+	0.998492i	$0.482516\pi$
$6$	1.13357	+	2.73669i	0.462779	+	1.11725i
$7$	1.24807	−	1.24807i	0.471727	−	0.471727i	−0.430746	−	0.902473i	$-0.641750\pi$
$7$	1.24807	−	1.24807i	0.471727	−	0.471727i	0.902473	+	0.430746i	$0.141750\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	4.08315	+	4.08315i	1.36105	+	1.36105i
$10$	0.173610	+	0.173610i	0.0549004	+	0.0549004i
$11$	0.802805	+	0.802805i	0.242055	+	0.242055i	0.817700	−	0.575645i	$-0.195249\pi$
$11$	0.802805	+	0.802805i	0.242055	+	0.242055i	−0.575645	+	0.817700i	$0.695249\pi$
$12$	−1.13357	+	2.73669i	−0.327234	+	0.790014i
$13$	4.09879	−	1.69777i	1.13680	−	0.470877i	0.266712	−	0.963776i	$-0.414063\pi$
$13$	4.09879	−	1.69777i	1.13680	−	0.470877i	0.870087	+	0.492899i	$0.164063\pi$
$14$	1.76504			0.471727
$15$	0.671917	+	0.278317i	0.173488	+	0.0718611i
$16$	−1.00000			−0.250000
$17$	−6.03141	+	2.49829i	−1.46283	+	0.605925i	−0.965212	−	0.261470i	$-0.915793\pi$
$17$	−6.03141	+	2.49829i	−1.46283	+	0.605925i	−0.497621	+	0.867395i	$0.665793\pi$
$18$			5.77444i			1.36105i
$19$	−2.60020	−	6.27743i	−0.596526	−	1.44014i	−0.877099	−	0.480309i	$-0.840524\pi$
$19$	−2.60020	−	6.27743i	−0.596526	−	1.44014i	0.280573	−	0.959833i	$-0.409476\pi$
$20$			0.245522i			0.0549004i
$21$	4.83036	−	2.00080i	1.05407	−	0.436610i
$22$			1.13534i			0.242055i
$23$	−3.19829	−	7.72135i	−0.666889	−	1.61001i	−0.786785	−	0.617227i	$-0.788256\pi$
$23$	−3.19829	−	7.72135i	−0.666889	−	1.61001i	0.119896	−	0.992786i	$-0.461744\pi$
$24$	−2.73669	+	1.13357i	−0.558624	+	0.231390i
$25$	−4.93972			−0.987944
$26$	4.09879	+	1.69777i	0.803838	+	0.332961i
$27$	3.14504	+	7.59279i	0.605262	+	1.46123i
$28$	1.24807	+	1.24807i	0.235863	+	0.235863i
$29$	−3.56159			−0.661370			−0.330685	−	0.943741i	$-0.607280\pi$
$29$	−3.56159			−0.661370			−0.330685	+	0.943741i	$0.607280\pi$
$30$	0.278317	+	0.671917i	0.0508135	+	0.122675i
$31$	4.04471	+	9.76480i	0.726452	+	1.75381i	0.654071	+	0.756433i	$0.273060\pi$
$31$	4.04471	+	9.76480i	0.726452	+	1.75381i	0.0723814	+	0.997377i	$0.476940\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.28699	+	3.10706i	0.224036	+	0.540871i
$34$	−6.03141	−	2.49829i	−1.03438	−	0.428454i
$35$	0.306429	−	0.306429i	0.0517959	−	0.0517959i
$36$	−4.08315	+	4.08315i	−0.680525	+	0.680525i
$37$	1.37965	+	0.571470i	0.226813	+	0.0939491i	0.493196	−	0.869918i	$-0.335829\pi$
$37$	1.37965	+	0.571470i	0.226813	+	0.0939491i	−0.266383	+	0.963867i	$0.585829\pi$
$38$	2.60020	−	6.27743i	0.421808	−	1.01833i
$39$	13.1416			2.10435
$40$	−0.173610	+	0.173610i	−0.0274502	+	0.0274502i
$41$	−3.79040			−0.591961			−0.295980	−	0.955194i	$-0.595646\pi$
$41$	−3.79040			−0.591961			−0.295980	+	0.955194i	$0.595646\pi$
$42$	4.83036	+	2.00080i	0.745341	+	0.308730i
$43$	5.24736	−	5.24736i	0.800215	−	0.800215i	−0.182914	−	0.983129i	$-0.558553\pi$
$43$	5.24736	−	5.24736i	0.800215	−	0.800215i	0.983129	+	0.182914i	$0.0585530\pi$
$44$	−0.802805	+	0.802805i	−0.121027	+	0.121027i
$45$	1.00250	+	1.00250i	0.149444	+	0.149444i
$46$	3.19829	−	7.72135i	0.471562	−	1.13845i
$47$	0.754114	+	0.754114i	0.109999	+	0.109999i	0.759964	−	0.649965i	$-0.225217\pi$
$47$	0.754114	+	0.754114i	0.109999	+	0.109999i	−0.649965	+	0.759964i	$0.725217\pi$
$48$	−2.73669	−	1.13357i	−0.395007	−	0.163617i
$49$			3.88464i			0.554948i
$50$	−3.49291	−	3.49291i	−0.493972	−	0.493972i
$51$	−19.3381			−2.70787
$52$	1.69777	+	4.09879i	0.235439	+	0.568399i
$53$	−4.27873	+	10.3298i	−0.587729	+	1.41890i	0.297940	+	0.954585i	$0.403700\pi$
$53$	−4.27873	+	10.3298i	−0.587729	+	1.41890i	−0.885669	+	0.464318i	$0.846300\pi$
$54$	−3.14504	+	7.59279i	−0.427985	+	1.03325i
$55$	0.197106	+	0.197106i	0.0265778	+	0.0265778i
$56$			1.76504i			0.235863i
$57$		−	20.1269i		−	2.66587i
$58$	−2.51842	−	2.51842i	−0.330685	−	0.330685i
$59$	−5.77060	+	2.39026i	−0.751268	+	0.311185i	−0.725259	−	0.688476i	$-0.758280\pi$
$59$	−5.77060	+	2.39026i	−0.751268	+	0.311185i	−0.0260092	+	0.999662i	$0.508280\pi$
$60$	−0.278317	+	0.671917i	−0.0359306	+	0.0867441i
$61$	0.870786	+	2.10226i	0.111493	+	0.269167i	0.969771	−	0.244018i	$-0.0784655\pi$
$61$	0.870786	+	2.10226i	0.111493	+	0.269167i	−0.858278	+	0.513185i	$0.828465\pi$
$62$	−4.04471	+	9.76480i	−0.513679	+	1.24013i
$63$	10.1921			1.28409
$64$		−	1.00000i		−	0.125000i
$65$	1.00634	−	0.416840i	0.124821	−	0.0517027i
$66$	−1.28699	+	3.10706i	−0.158417	+	0.382453i
$67$	−4.19378	+	10.1247i	−0.512352	+	1.23693i	0.430159	+	0.902753i	$0.358457\pi$
$67$	−4.19378	+	10.1247i	−0.512352	+	1.23693i	−0.942511	+	0.334174i	$0.891543\pi$
$68$	−2.49829	−	6.03141i	−0.302963	−	0.731416i
$69$		−	24.7564i		−	2.98032i
$70$	0.433356			0.0517959
$71$	3.30400	−	7.97656i	0.392113	−	0.946644i	−0.597367	−	0.801968i	$-0.703786\pi$
$71$	3.30400	−	7.97656i	0.392113	−	0.946644i	0.989479	−	0.144675i	$-0.0462137\pi$
$72$	−5.77444			−0.680525
$73$	9.42686	−	9.42686i	1.10333	−	1.10333i	0.109324	−	0.994006i	$-0.465131\pi$
$73$	9.42686	−	9.42686i	1.10333	−	1.10333i	0.994006	−	0.109324i	$-0.0348685\pi$
$74$	0.571470	+	1.37965i	0.0664321	+	0.160381i
$75$	−13.5185	−	5.59953i	−1.56098	−	0.646578i
$76$	6.27743	−	2.60020i	0.720071	−	0.298263i
$77$	2.00392			0.228367
$78$	9.29254	+	9.29254i	1.05217	+	1.05217i
$79$	−3.89830	−	9.41132i	−0.438593	−	1.05886i	−0.976435	−	0.215811i	$-0.930761\pi$
$79$	−3.89830	−	9.41132i	−0.438593	−	1.05886i	0.537843	−	0.843045i	$-0.319239\pi$
$80$	−0.245522			−0.0274502
$81$			7.02088i			0.780098i
$82$	−2.68022	−	2.68022i	−0.295980	−	0.295980i
$83$	−8.87362			−0.974006			−0.487003	−	0.873400i	$-0.661910\pi$
$83$	−8.87362			−0.974006			−0.487003	+	0.873400i	$0.661910\pi$
$84$	2.00080	+	4.83036i	0.218305	+	0.527035i
$85$	−1.48084	+	0.613386i	−0.160620	+	0.0665310i
$86$	7.42089			0.800215
$87$	−9.74695	−	4.03732i	−1.04498	−	0.432846i
$88$	−1.13534			−0.121027
$89$	6.42985	−	6.42985i	0.681563	−	0.681563i	−0.278789	−	0.960352i	$-0.589933\pi$
$89$	6.42985	−	6.42985i	0.681563	−	0.681563i	0.960352	+	0.278789i	$0.0899331\pi$
$90$			1.41775i			0.149444i
$91$	2.99663	−	7.23452i	0.314133	−	0.758383i
$92$	7.72135	−	3.19829i	0.805007	−	0.333445i
$93$			31.3082i			3.24651i
$94$			1.06648i			0.109999i
$95$	−0.638406	−	1.54125i	−0.0654990	−	0.158129i
$96$	−1.13357	−	2.73669i	−0.115695	−	0.279312i
$97$	4.38494	+	10.5862i	0.445223	+	1.07486i	0.974090	+	0.226160i	$0.0726171\pi$
$97$	4.38494	+	10.5862i	0.445223	+	1.07486i	−0.528867	+	0.848705i	$0.677383\pi$
$98$	−2.74685	+	2.74685i	−0.277474	+	0.277474i
$99$			6.55595i			0.658897i
$100$		−	4.93972i		−	0.493972i
$101$	−3.17708	+	7.67015i	−0.316131	+	0.763208i	0.683321	+	0.730118i	$0.260535\pi$
$101$	−3.17708	+	7.67015i	−0.316131	+	0.763208i	−0.999452	+	0.0330903i	$0.989465\pi$
$102$	−13.6741	−	13.6741i	−1.35394	−	1.35394i
$103$	−5.20222	+	5.20222i	−0.512590	+	0.512590i	−0.915319	−	0.402729i	$-0.868062\pi$
$103$	−5.20222	+	5.20222i	−0.512590	+	0.512590i	0.402729	+	0.915319i	$0.368062\pi$
$104$	−1.69777	+	4.09879i	−0.166480	+	0.401919i
$105$	1.18596	−	0.491240i	0.115738	−	0.0479402i
$106$	−10.3298	+	4.27873i	−1.00332	+	0.415587i
$107$	15.4311	−	6.39176i	1.49178	−	0.617915i	0.520076	−	0.854120i	$-0.325904\pi$
$107$	15.4311	−	6.39176i	1.49178	−	0.617915i	0.971703	+	0.236205i	$0.0759036\pi$
$108$	−7.59279	+	3.14504i	−0.730616	+	0.302631i
$109$	−11.6725	−	11.6725i	−1.11802	−	1.11802i	−0.992032	−	0.125989i	$-0.959790\pi$
$109$	−11.6725	−	11.6725i	−1.11802	−	1.11802i	−0.125989	−	0.992032i	$-0.540210\pi$
$110$			0.278750i			0.0265778i
$111$	3.12787	+	3.12787i	0.296884	+	0.296884i
$112$	−1.24807	+	1.24807i	−0.117932	+	0.117932i
$113$		−	20.4260i		−	1.92152i	−0.277381	−	0.960760i	$-0.589466\pi$
$113$		−	20.4260i		−	1.92152i	0.277381	−	0.960760i	$-0.410534\pi$
$114$	14.2319	−	14.2319i	1.33294	−	1.33294i
$115$	−0.785250	−	1.89576i	−0.0732250	−	0.176781i
$116$		−	3.56159i		−	0.330685i
$117$	23.6682	+	9.80369i	2.18813	+	0.906352i
$118$	−5.77060	−	2.39026i	−0.531227	−	0.220041i
$119$	−4.40958	+	10.6457i	−0.404226	+	0.975888i
$120$	−0.671917	+	0.278317i	−0.0613373	+	0.0254068i
$121$		−	9.71101i		−	0.882819i
$122$	−0.870786	+	2.10226i	−0.0788373	+	0.190330i
$123$	−10.3731	−	4.29669i	−0.935314	−	0.387420i
$124$	−9.76480	+	4.04471i	−0.876905	+	0.363226i
$125$	−2.44042			−0.218278
$126$	7.20692	+	7.20692i	0.642043	+	0.642043i
$127$	5.97324	+	14.4207i	0.530039	+	1.27963i	0.931497	+	0.363750i	$0.118504\pi$
$127$	5.97324	+	14.4207i	0.530039	+	1.27963i	−0.401458	+	0.915877i	$0.631496\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	20.3086	−	8.41212i	1.78808	−	0.740645i
$130$	1.00634	+	0.416840i	0.0882620	+	0.0365593i
$131$	2.10983	−	5.09358i	0.184337	−	0.445028i	−0.804515	−	0.593933i	$-0.797575\pi$
$131$	2.10983	−	5.09358i	0.184337	−	0.445028i	0.988852	+	0.148904i	$0.0475746\pi$
$132$	−3.10706	+	1.28699i	−0.270435	+	0.112018i
$133$	−11.0799	−	4.58945i	−0.960750	−	0.397956i
$134$	−10.1247	+	4.19378i	−0.874639	+	0.362288i
$135$	0.772175	+	1.86420i	0.0664583	+	0.160444i
$136$	2.49829	−	6.03141i	0.214227	−	0.517189i
$137$	18.1185	+	7.50494i	1.54797	+	0.641191i	0.982948	−	0.183885i	$-0.0588673\pi$
$137$	18.1185	+	7.50494i	1.54797	+	0.641191i	0.565023	+	0.825075i	$0.308867\pi$
$138$	17.5054	−	17.5054i	1.49016	−	1.49016i
$139$	2.65299	−	1.09890i	0.225024	−	0.0932078i	−0.267323	−	0.963607i	$-0.586139\pi$
$139$	2.65299	−	1.09890i	0.225024	−	0.0932078i	0.492347	+	0.870399i	$0.336139\pi$
$140$	0.306429	+	0.306429i	0.0258980	+	0.0258980i
$141$	1.20893	+	2.91862i	0.101810	+	0.245792i
$142$	7.97656	−	3.30400i	0.669378	−	0.277265i
$143$	4.65351	+	1.92755i	0.389146	+	0.161189i
$144$	−4.08315	−	4.08315i	−0.340262	−	0.340262i
$145$	−0.874448			−0.0726190
$146$	13.3316			1.10333
$147$	−4.40352	+	10.6310i	−0.363196	+	0.876833i
$148$	−0.571470	+	1.37965i	−0.0469746	+	0.113407i
$149$			10.2934i			0.843267i	0.906766	+	0.421634i	$0.138543\pi$
$149$			10.2934i			0.843267i	−0.906766	+	0.421634i	$0.861457\pi$
$150$	−5.59953	−	13.5185i	−0.457200	−	1.10378i
$151$	11.0918	+	11.0918i	0.902638	+	0.902638i	0.995664	−	0.0930257i	$-0.0296539\pi$
$151$	11.0918	+	11.0918i	0.902638	+	0.902638i	−0.0930257	+	0.995664i	$0.529654\pi$
$152$	6.27743	+	2.60020i	0.509167	+	0.210904i
$153$	−34.8281	−	14.4263i	−2.81568	−	1.16629i
$154$	1.41698	+	1.41698i	0.114184	+	0.114184i
$155$	0.993066	+	2.39747i	0.0797650	+	0.192570i
$156$			13.1416i			1.05217i
$157$	18.5446	−	7.68144i	1.48002	−	0.613045i	0.510903	−	0.859638i	$-0.329311\pi$
$157$	18.5446	−	7.68144i	1.48002	−	0.613045i	0.969119	+	0.246593i	$0.0793111\pi$
$158$	3.89830	−	9.41132i	0.310132	−	0.748724i
$159$	−23.4191	+	23.4191i	−1.85725	+	1.85725i
$160$	−0.173610	−	0.173610i	−0.0137251	−	0.0137251i
$161$	−13.6285	−	5.64511i	−1.07408	−	0.444897i
$162$	−4.96451	+	4.96451i	−0.390049	+	0.390049i
$163$	0.147173	−	0.0609610i	0.0115275	−	0.00477484i	−0.376912	−	0.926249i	$-0.623014\pi$
$163$	0.147173	−	0.0609610i	0.0115275	−	0.00477484i	0.388440	+	0.921474i	$0.373014\pi$
$164$		−	3.79040i		−	0.295980i
$165$	0.315984	+	0.762853i	0.0245993	+	0.0593880i
$166$	−6.27459	−	6.27459i	−0.487003	−	0.487003i
$167$	−2.57240	−	6.21033i	−0.199058	−	0.480570i	0.792556	−	0.609799i	$-0.208750\pi$
$167$	−2.57240	−	6.21033i	−0.199058	−	0.480570i	−0.991615	+	0.129229i	$0.958750\pi$
$168$	−2.00080	+	4.83036i	−0.154365	+	0.372670i
$169$	4.72522	−	4.72522i	0.363479	−	0.363479i
$170$	−1.48084	−	0.613386i	−0.113576	−	0.0470445i
$171$	15.0147	−	36.2487i	1.14820	−	2.77201i
$172$	5.24736	+	5.24736i	0.400107	+	0.400107i
$173$	5.51864			0.419574			0.209787	−	0.977747i	$-0.432723\pi$
$173$	5.51864			0.419574			0.209787	+	0.977747i	$0.432723\pi$
$174$	−4.03732	−	9.74695i	−0.306068	−	0.738915i
$175$	−6.16512	+	6.16512i	−0.466039	+	0.466039i
$176$	−0.802805	−	0.802805i	−0.0605137	−	0.0605137i
$177$	−18.5019			−1.39069
$178$	9.09318			0.681563
$179$			13.6170i			1.01778i	0.860831	+	0.508891i	$0.169945\pi$
$179$			13.6170i			1.01778i	−0.860831	+	0.508891i	$0.830055\pi$
$180$	−1.00250	+	1.00250i	−0.0747221	+	0.0747221i
$181$	−6.83457	+	6.83457i	−0.508010	+	0.508010i	−0.913915	−	0.405905i	$-0.866956\pi$
$181$	−6.83457	+	6.83457i	−0.508010	+	0.508010i	0.405905	+	0.913915i	$0.366956\pi$
$182$	7.23452	−	2.99663i	0.536258	−	0.222125i
$183$			6.74034i			0.498260i
$184$	7.72135	+	3.19829i	0.569226	+	0.235781i
$185$	0.338735	+	0.140309i	0.0249043	+	0.0103157i
$186$	−22.1382	+	22.1382i	−1.62325	+	1.62325i
$187$	−6.84769	−	2.83641i	−0.500753	−	0.207419i
$188$	−0.754114	+	0.754114i	−0.0549994	+	0.0549994i
$189$	13.4016	+	5.55111i	0.974821	+	0.403784i
$190$	0.638406	−	1.54125i	0.0463148	−	0.111814i
$191$	3.40566	+	1.41067i	0.246425	+	0.102072i	0.502477	−	0.864590i	$-0.332422\pi$
$191$	3.40566	+	1.41067i	0.246425	+	0.102072i	−0.256053	+	0.966663i	$0.582422\pi$
$192$	1.13357	−	2.73669i	0.0818086	−	0.197503i
$193$	−0.545845	+	0.226097i	−0.0392908	+	0.0162748i	−0.402242	−	0.915533i	$-0.631769\pi$
$193$	−0.545845	+	0.226097i	−0.0392908	+	0.0162748i	0.362952	+	0.931808i	$0.381769\pi$
$194$	−4.38494	+	10.5862i	−0.314821	+	0.760044i
$195$	3.22656			0.231059
$196$	−3.88464			−0.277474
$197$			7.90881i			0.563480i	0.959491	+	0.281740i	$0.0909115\pi$
$197$			7.90881i			0.563480i	−0.959491	+	0.281740i	$0.909088\pi$
$198$	−4.63575	+	4.63575i	−0.329449	+	0.329449i
$199$	11.2742	−	4.66991i	0.799204	−	0.331041i	0.0545663	−	0.998510i	$-0.482622\pi$
$199$	11.2742	−	4.66991i	0.799204	−	0.331041i	0.744638	+	0.667469i	$0.232622\pi$
$200$	3.49291	−	3.49291i	0.246986	−	0.246986i
$201$	−22.9541	+	22.9541i	−1.61906	+	1.61906i
$202$	−7.67015	+	3.17708i	−0.539670	+	0.223539i
$203$	−4.44512	+	4.44512i	−0.311986	+	0.311986i
$204$		−	19.3381i		−	1.35394i
$205$	−0.930626			−0.0649977
$206$	−7.35705			−0.512590
$207$	18.4683	−	44.5865i	1.28364	−	3.09898i
$208$	−4.09879	+	1.69777i	−0.284200	+	0.117719i
$209$	2.95210	−	7.12701i	0.204201	−	0.492985i
$210$	1.18596	+	0.491240i	0.0818390	+	0.0338988i
$211$	−1.06686	+	2.57563i	−0.0734457	+	0.177314i	−0.956339	−	0.292261i	$-0.905593\pi$
$211$	−1.06686	+	2.57563i	−0.0734457	+	0.177314i	0.882893	+	0.469574i	$0.155593\pi$
$212$	−10.3298	−	4.27873i	−0.709451	−	0.293864i
$213$	18.0840	−	18.0840i	1.23910	−	1.23910i
$214$	15.4311	+	6.39176i	1.05485	+	0.436932i
$215$	1.28834	−	1.28834i	0.0878642	−	0.0878642i
$216$	−7.59279	−	3.14504i	−0.516624	−	0.213993i
$217$	17.2353	+	7.13908i	1.17001	+	0.484632i
$218$		−	16.5074i		−	1.11802i
$219$	36.4844	−	15.1123i	2.46539	−	1.02120i
$220$	−0.197106	+	0.197106i	−0.0132889	+	0.0132889i
$221$	−20.4799	+	20.4799i	−1.37763	+	1.37763i
$222$			4.42348i			0.296884i
$223$	11.9271			0.798700			0.399350	−	0.916798i	$-0.369236\pi$
$223$	11.9271			0.798700			0.399350	+	0.916798i	$0.369236\pi$
$224$	−1.76504			−0.117932
$225$	−20.1696	−	20.1696i	−1.34464	−	1.34464i
$226$	14.4434	−	14.4434i	0.960760	−	0.960760i
$227$	−8.61377	−	20.7955i	−0.571716	−	1.38024i	−0.900093	−	0.435697i	$-0.856502\pi$
$227$	−8.61377	−	20.7955i	−0.571716	−	1.38024i	0.328377	−	0.944547i	$-0.393498\pi$
$228$	20.1269			1.33294
$229$	−11.2384	−	11.2384i	−0.742657	−	0.742657i	0.230432	−	0.973088i	$-0.425986\pi$
$229$	−11.2384	−	11.2384i	−0.742657	−	0.742657i	−0.973088	+	0.230432i	$0.925986\pi$
$230$	0.785250	−	1.89576i	0.0517779	−	0.125003i
$231$	5.48409	+	2.27158i	0.360827	+	0.149459i
$232$	2.51842	−	2.51842i	0.165343	−	0.165343i
$233$	−0.537026	+	1.29650i	−0.0351817	+	0.0849362i	−0.940494	−	0.339811i	$-0.889637\pi$
$233$	−0.537026	+	1.29650i	−0.0351817	+	0.0849362i	0.905312	+	0.424747i	$0.139637\pi$
$234$	9.80369	+	23.6682i	0.640887	+	1.54724i
$235$	0.185151	+	0.185151i	0.0120779	+	0.0120779i
$236$	−2.39026	−	5.77060i	−0.155593	−	0.375634i
$237$		−	30.1748i		−	1.96007i
$238$	−10.6457	+	4.40958i	−0.690057	+	0.285831i
$239$	−19.4765	+	19.4765i	−1.25983	+	1.25983i	−0.308655	+	0.951174i	$0.599879\pi$
$239$	−19.4765	+	19.4765i	−1.25983	+	1.25983i	−0.951174	+	0.308655i	$0.900121\pi$
$240$	−0.671917	−	0.278317i	−0.0433720	−	0.0179653i
$241$	5.90266	+	5.90266i	0.380223	+	0.380223i	0.871183	−	0.490959i	$-0.163354\pi$
$241$	5.90266	+	5.90266i	0.380223	+	0.380223i	−0.490959	+	0.871183i	$0.663354\pi$
$242$	6.86672	−	6.86672i	0.441409	−	0.441409i
$243$	1.47643	−	3.56442i	0.0947130	−	0.228657i
$244$	−2.10226	+	0.870786i	−0.134584	+	0.0557464i
$245$			0.953764i			0.0609337i
$246$	−4.29669	−	10.3731i	−0.273947	−	0.661367i
$247$	−21.3153	−	21.3153i	−1.35626	−	1.35626i
$248$	−9.76480	−	4.04471i	−0.620066	−	0.256840i
$249$	−24.2843	−	10.0589i	−1.53896	−	0.637456i
$250$	−1.72564	−	1.72564i	−0.109139	−	0.109139i
$251$	1.94566	+	4.69723i	0.122809	+	0.296486i	0.973313	−	0.229482i	$-0.0737031\pi$
$251$	1.94566	+	4.69723i	0.122809	+	0.296486i	−0.850504	+	0.525968i	$0.823703\pi$
$252$			10.1921i			0.642043i
$253$	3.63114	−	8.76634i	0.228288	−	0.551135i
$254$	−5.97324	+	14.4207i	−0.374794	+	0.904833i
$255$	−4.74793			−0.297327
$256$	1.00000			0.0625000
$257$	−0.509011	−	0.509011i	−0.0317512	−	0.0317512i	0.691053	−	0.722804i	$-0.257147\pi$
$257$	−0.509011	−	0.509011i	−0.0317512	−	0.0317512i	−0.722804	+	0.691053i	$0.757147\pi$
$258$	20.3086	+	8.41212i	1.26436	+	0.523715i
$259$	2.43514	−	1.00867i	0.151312	−	0.0626755i
$260$	0.416840	+	1.00634i	0.0258513	+	0.0624107i
$261$	−14.5425	−	14.5425i	−0.900158	−	0.900158i
$262$	5.09358	−	2.10983i	0.314683	−	0.130346i
$263$	−14.2744	+	14.2744i	−0.880200	+	0.880200i	−0.993555	−	0.113355i	$-0.963840\pi$
$263$	−14.2744	+	14.2744i	−0.880200	+	0.880200i	0.113355	+	0.993555i	$0.463840\pi$
$264$	−3.10706	−	1.28699i	−0.191227	−	0.0792087i
$265$	−1.05052	+	2.53618i	−0.0645330	+	0.155797i
$266$	−4.58945	−	11.0799i	−0.281397	−	0.679353i
$267$	24.8852	−	10.3078i	1.52295	−	0.630826i
$268$	−10.1247	−	4.19378i	−0.618463	−	0.256176i
$269$	−4.85251	+	2.00997i	−0.295863	+	0.122550i	−0.525677	−	0.850684i	$-0.676188\pi$
$269$	−4.85251	+	2.00997i	−0.295863	+	0.122550i	0.229815	+	0.973234i	$0.426188\pi$
$270$	−0.772175	+	1.86420i	−0.0469931	+	0.113451i
$271$	9.97117	+	4.13019i	0.605705	+	0.250891i	0.664391	−	0.747385i	$-0.268691\pi$
$271$	9.97117	+	4.13019i	0.605705	+	0.250891i	−0.0586856	+	0.998277i	$0.518691\pi$
$272$	6.03141	−	2.49829i	0.365708	−	0.151481i
$273$	16.4017	−	16.4017i	0.992676	−	0.992676i
$274$	7.50494	+	18.1185i	0.453390	+	1.09458i
$275$	−3.96563	−	3.96563i	−0.239137	−	0.239137i
$276$	24.7564			1.49016
$277$	−5.20538	+	2.15614i	−0.312761	+	0.129550i	−0.533542	−	0.845774i	$-0.679139\pi$
$277$	−5.20538	+	2.15614i	−0.312761	+	0.129550i	0.220781	+	0.975323i	$0.429139\pi$
$278$	2.65299	+	1.09890i	0.159116	+	0.0659079i
$279$	−23.3560	+	56.3863i	−1.39829	+	3.37576i
$280$			0.433356i			0.0258980i
$281$	−1.88411	+	0.780424i	−0.112397	+	0.0465562i	−0.438173	−	0.898891i	$-0.644374\pi$
$281$	−1.88411	+	0.780424i	−0.112397	+	0.0465562i	0.325776	+	0.945447i	$0.394374\pi$
$282$	−1.20893	+	2.91862i	−0.0719907	+	0.173801i
$283$	−0.121876	−	0.0504827i	−0.00724477	−	0.00300088i	0.379058	−	0.925373i	$-0.376248\pi$
$283$	−0.121876	−	0.0504827i	−0.00724477	−	0.00300088i	−0.386303	+	0.922372i	$0.626248\pi$
$284$	7.97656	+	3.30400i	0.473322	+	0.196056i
$285$		−	4.94159i		−	0.292715i
$286$	1.92755	+	4.65351i	0.113978	+	0.275168i
$287$	−4.73069	+	4.73069i	−0.279244	+	0.279244i
$288$		−	5.77444i		−	0.340262i
$289$	18.1157	−	18.1157i	1.06563	−	1.06563i
$290$	−0.618328	−	0.618328i	−0.0363095	−	0.0363095i
$291$			33.9417i			1.98970i
$292$	9.42686	+	9.42686i	0.551665	+	0.551665i
$293$	7.73051	−	3.20208i	0.451621	−	0.187068i	−0.145266	−	0.989393i	$-0.546404\pi$
$293$	7.73051	−	3.20208i	0.451621	−	0.187068i	0.596887	+	0.802325i	$0.296404\pi$
$294$	−10.6310	+	4.40352i	−0.620015	+	0.256818i
$295$	−1.41681	+	0.586861i	−0.0824898	+	0.0341684i
$296$	−1.37965	+	0.571470i	−0.0801906	+	0.0332160i
$297$	−3.57068	+	8.62038i	−0.207192	+	0.500205i
$298$	−7.27852	+	7.27852i	−0.421634	+	0.421634i
$299$	−26.2182	−	26.2182i	−1.51624	−	1.51624i
$300$	5.59953	−	13.5185i	0.323289	−	0.780489i
$301$		−	13.0982i		−	0.754965i
$302$			15.6862i			0.902638i
$303$	−17.3893	+	17.3893i	−0.998992	+	0.998992i
$304$	2.60020	+	6.27743i	0.149132	+	0.360035i
$305$	0.213797	+	0.516152i	0.0122420	+	0.0295548i
$306$	−14.4263	−	34.8281i	−0.824694	−	1.99099i
$307$			18.0509i			1.03022i	0.857124	+	0.515110i	$0.172249\pi$
$307$			18.0509i			1.03022i	−0.857124	+	0.515110i	$0.827751\pi$
$308$			2.00392i			0.114184i
$309$	−20.1339	+	8.33975i	−1.14538	+	0.474432i
$310$	−0.993066	+	2.39747i	−0.0564024	+	0.136167i
$311$			0.889836i			0.0504580i	0.999682	+	0.0252290i	$0.00803149\pi$
$311$			0.889836i			0.0504580i	−0.999682	+	0.0252290i	$0.991969\pi$
$312$	−9.29254	+	9.29254i	−0.526087	+	0.526087i
$313$	−26.9537			−1.52351			−0.761756	−	0.647864i	$-0.775663\pi$
$313$	−26.9537			−1.52351			−0.761756	+	0.647864i	$0.775663\pi$
$314$	18.5446	+	7.68144i	1.04653	+	0.433488i
$315$	2.50239			0.140994
$316$	9.41132	−	3.89830i	0.529428	−	0.219296i
$317$	2.44619	+	5.90563i	0.137392	+	0.331693i	0.977568	−	0.210621i	$-0.0675485\pi$
$317$	2.44619	+	5.90563i	0.137392	+	0.331693i	−0.840176	+	0.542314i	$0.817548\pi$
$318$	−33.1196			−1.85725
$319$	−2.85926	−	2.85926i	−0.160088	−	0.160088i
$320$		−	0.245522i		−	0.0137251i
$321$	49.4756			2.76146
$322$	−5.64511	−	13.6285i	−0.314589	−	0.759486i
$323$	31.3657	+	31.3657i	1.74524	+	1.74524i
$324$	−7.02088			−0.390049
$325$	−20.2468	+	8.38652i	−1.12309	+	0.465200i
$326$	0.147173	+	0.0609610i	0.00815116	+	0.00337632i
$327$	−18.7123	−	45.1755i	−1.03479	−	2.49821i
$328$	2.68022	−	2.68022i	0.147990	−	0.147990i
$329$	1.88237			0.103779
$330$	−0.315984	+	0.762853i	−0.0173943	+	0.0419936i
$331$	12.3478			0.678695			0.339348	−	0.940661i	$-0.389794\pi$
$331$	12.3478			0.678695			0.339348	+	0.940661i	$0.389794\pi$
$332$		−	8.87362i		−	0.487003i
$333$	3.29992	+	7.96672i	0.180835	+	0.436574i
$334$	2.57240	−	6.21033i	0.140756	−	0.339814i
$335$	−1.02967	+	2.48583i	−0.0562566	+	0.135816i
$336$	−4.83036	+	2.00080i	−0.263518	+	0.109153i
$337$		−	10.2742i		−	0.559674i	−0.960048	−	0.279837i	$-0.909720\pi$
$337$		−	10.2742i		−	0.559674i	0.960048	−	0.279837i	$-0.0902804\pi$
$338$	6.68247			0.363479
$339$	23.1544	−	55.8997i	1.25757	−	3.03605i
$340$	−0.613386	−	1.48084i	−0.0332655	−	0.0803101i
$341$	−4.59212	+	11.0864i	−0.248677	+	0.600360i
$342$	36.2487	−	15.0147i	1.96010	−	0.811902i
$343$	13.5848	+	13.5848i	0.733510	+	0.733510i
$344$			7.42089i			0.400107i
$345$		−	6.07825i		−	0.327242i
$346$	3.90227	+	3.90227i	0.209787	+	0.209787i
$347$	−4.98576	+	12.0367i	−0.267650	+	0.646164i	−0.999372	−	0.0354393i	$-0.988717\pi$
$347$	−4.98576	+	12.0367i	−0.267650	+	0.646164i	0.731722	+	0.681603i	$0.238717\pi$
$348$	4.03732	−	9.74695i	0.216423	−	0.522492i
$349$	−10.8425	−	26.1761i	−0.580385	−	1.40117i	−0.892464	−	0.451118i	$-0.851025\pi$
$349$	−10.8425	−	26.1761i	−0.580385	−	1.40117i	0.312079	−	0.950056i	$-0.398975\pi$
$350$	−8.71880			−0.466039
$351$	25.7817	+	25.7817i	1.37612	+	1.37612i
$352$		−	1.13534i		−	0.0605137i
$353$	−28.3883	−	11.7588i	−1.51096	−	0.625859i	−0.535202	−	0.844724i	$-0.679764\pi$
$353$	−28.3883	−	11.7588i	−1.51096	−	0.625859i	−0.975755	+	0.218866i	$0.929764\pi$
$354$	−13.0828	−	13.0828i	−0.695343	−	0.695343i
$355$	0.811204	−	1.95842i	0.0430543	−	0.103942i
$356$	6.42985	+	6.42985i	0.340781	+	0.340781i
$357$	−24.1353	+	24.1353i	−1.27738	+	1.27738i
$358$	−9.62868	+	9.62868i	−0.508891	+	0.508891i
$359$	30.7532	+	12.7384i	1.62309	+	0.672307i	0.994433	−	0.105373i	$-0.0336036\pi$
$359$	30.7532	+	12.7384i	1.62309	+	0.672307i	0.628660	+	0.777680i	$0.283604\pi$
$360$	−1.41775			−0.0747221
$361$	−19.2101	+	19.2101i	−1.01106	+	1.01106i
$362$	−9.66554			−0.508010
$363$	11.0081	−	26.5760i	0.577777	−	1.39488i
$364$	7.23452	+	2.99663i	0.379192	+	0.157066i
$365$	2.31450	−	2.31450i	0.121146	−	0.121146i
$366$	−4.76614	+	4.76614i	−0.249130	+	0.249130i
$367$	9.44834	+	3.91363i	0.493199	+	0.204290i	0.615399	−	0.788216i	$-0.288995\pi$
$367$	9.44834	+	3.91363i	0.493199	+	0.204290i	−0.122200	+	0.992506i	$0.538995\pi$
$368$	3.19829	+	7.72135i	0.166722	+	0.402503i
$369$	−15.4768	−	15.4768i	−0.805688	−	0.805688i
$370$	0.140309	+	0.338735i	0.00729429	+	0.0176100i
$371$	7.55212	+	18.2324i	0.392087	+	0.946581i
$372$	−31.3082			−1.62325
$373$	−1.51728	−	1.51728i	−0.0785618	−	0.0785618i	0.666734	−	0.745296i	$-0.267692\pi$
$373$	−1.51728	−	1.51728i	−0.0785618	−	0.0785618i	−0.745296	+	0.666734i	$0.767692\pi$
$374$	−2.83641	−	6.84769i	−0.146667	−	0.354086i
$375$	−6.67866	−	2.76639i	−0.344885	−	0.142856i
$376$	−1.06648			−0.0549994
$377$	−14.5982	+	6.04677i	−0.751845	+	0.311424i
$378$	5.55111	+	13.4016i	0.285518	+	0.689302i
$379$		−	10.2295i		−	0.525454i	−0.964870	−	0.262727i	$-0.915378\pi$
$379$		−	10.2295i		−	0.525454i	0.964870	−	0.262727i	$-0.0846219\pi$
$380$	1.54125	−	0.638406i	0.0790643	−	0.0327495i
$381$			46.2359i			2.36874i
$382$	1.41067	+	3.40566i	0.0721761	+	0.174249i
$383$			23.7160i			1.21183i	0.795528	+	0.605916i	$0.207193\pi$
$383$			23.7160i			1.21183i	−0.795528	+	0.605916i	$0.792807\pi$
$384$	2.73669	−	1.13357i	0.139656	−	0.0578474i
$385$	0.492005			0.0250749
$386$	−0.545845	−	0.226097i	−0.0277828	−	0.0115080i
$387$	42.8515			2.17826
$388$	−10.5862	+	4.38494i	−0.537432	+	0.222612i
$389$	0.707261	−	1.70748i	0.0358595	−	0.0865726i	−0.904935	−	0.425549i	$-0.860081\pi$
$389$	0.707261	−	1.70748i	0.0358595	−	0.0865726i	0.940795	+	0.338977i	$0.110081\pi$
$390$	2.28152	+	2.28152i	0.115529	+	0.115529i
$391$	38.5804	+	38.5804i	1.95110	+	1.95110i
$392$	−2.74685	−	2.74685i	−0.138737	−	0.138737i
$393$	11.5479	−	11.5479i	0.582514	−	0.582514i
$394$	−5.59238	+	5.59238i	−0.281740	+	0.281740i
$395$	−0.957117	−	2.31069i	−0.0481578	−	0.116263i
$396$	−6.55595			−0.329449
$397$			25.5169i			1.28066i	0.768101	+	0.640328i	$0.221202\pi$
$397$			25.5169i			1.28066i	−0.768101	+	0.640328i	$0.778798\pi$
$398$	11.2742	+	4.66991i	0.565122	+	0.234081i
$399$	−25.1198	−	25.1198i	−1.25756	−	1.25756i
$400$	4.93972			0.246986
$401$	3.37227	+	19.7390i	0.168403	+	0.985718i
$401$	3.37227	+	19.7390i	0.168403	+	0.985718i
$402$	−32.4620			−1.61906
$403$	33.1568	+	33.1568i	1.65166	+	1.65166i
$404$	−7.67015	−	3.17708i	−0.381604	−	0.158066i
$405$			1.72378i			0.0856553i
$406$	−6.28634			−0.311986
$407$	0.648812	+	1.56637i	0.0321604	+	0.0776421i
$408$	13.6741	−	13.6741i	0.676969	−	0.676969i
$409$	−25.1463	+	25.1463i	−1.24340	+	1.24340i	−0.284824	+	0.958580i	$0.591935\pi$
$409$	−25.1463	+	25.1463i	−1.24340	+	1.24340i	−0.958580	+	0.284824i	$0.908065\pi$
$410$	−0.658052	−	0.658052i	−0.0324989	−	0.0324989i
$411$	41.0774	+	41.0774i	2.02620	+	2.02620i
$412$	−5.20222	−	5.20222i	−0.256295	−	0.256295i
$413$	−4.21890	+	10.1853i	−0.207599	+	0.501187i
$414$	44.5865	−	18.4683i	2.19131	−	0.907670i
$415$	−2.17867			−0.106947
$416$	−4.09879	−	1.69777i	−0.200959	−	0.0832401i
$417$	8.50609			0.416545
$418$	7.12701	−	2.95210i	0.348593	−	0.144392i
$419$			14.5169i			0.709199i	0.935018	+	0.354600i	$0.115383\pi$
$419$			14.5169i			0.709199i	−0.935018	+	0.354600i	$0.884617\pi$
$420$	0.491240	+	1.18596i	0.0239701	+	0.0578689i
$421$		−	10.6737i		−	0.520205i	−0.965581	−	0.260102i	$-0.916244\pi$
$421$		−	10.6737i		−	0.520205i	0.965581	−	0.260102i	$-0.0837563\pi$
$422$	−2.57563	+	1.06686i	−0.125380	+	0.0519339i
$423$			6.15832i			0.299428i
$424$	−4.27873	−	10.3298i	−0.207793	−	0.501658i
$425$	29.7935	−	12.3409i	1.44520	−	0.598620i
$426$	25.5747			1.23910
$427$	3.71058	+	1.53697i	0.179567	+	0.0743793i
$428$	6.39176	+	15.4311i	0.308958	+	0.745890i
$429$	10.5502	+	10.5502i	0.509367	+	0.509367i
$430$	1.82199			0.0878642
$431$	−7.75334	−	18.7182i	−0.373465	−	0.901625i	−0.993158	−	0.116780i	$-0.962743\pi$
$431$	−7.75334	−	18.7182i	−0.373465	−	0.901625i	0.619693	−	0.784845i	$-0.287257\pi$
$432$	−3.14504	−	7.59279i	−0.151316	−	0.365308i
$433$	−0.526729	−	0.526729i	−0.0253130	−	0.0253130i	0.694337	−	0.719650i	$-0.255698\pi$
$433$	−0.526729	−	0.526729i	−0.0253130	−	0.0253130i	−0.719650	+	0.694337i	$0.755698\pi$
$434$	7.13908	+	17.2353i	0.342687	+	0.827319i
$435$	−2.39309	−	0.991251i	−0.114740	−	0.0475268i
$436$	11.6725	−	11.6725i	0.559010	−	0.559010i
$437$	−40.1541	+	40.1541i	−1.92083	+	1.92083i
$438$	36.4844	+	15.1123i	1.74329	+	0.722095i
$439$	3.61271	−	8.72186i	0.172425	−	0.416271i	−0.813917	−	0.580982i	$-0.802669\pi$
$439$	3.61271	−	8.72186i	0.172425	−	0.416271i	0.986342	+	0.164710i	$0.0526689\pi$
$440$	−0.278750			−0.0132889
$441$	−15.8616	+	15.8616i	−0.755312	+	0.755312i
$442$	−28.9630			−1.37763
$443$	−25.5364	−	10.5775i	−1.21327	−	0.502554i	−0.318007	−	0.948088i	$-0.603014\pi$
$443$	−25.5364	−	10.5775i	−1.21327	−	0.502554i	−0.895265	+	0.445535i	$0.853014\pi$
$444$	−3.12787	+	3.12787i	−0.148442	+	0.148442i
$445$	1.57867	−	1.57867i	0.0748361	−	0.0748361i
$446$	8.43376	+	8.43376i	0.399350	+	0.399350i
$447$	−11.6683	+	28.1698i	−0.551892	+	1.33239i
$448$	−1.24807	−	1.24807i	−0.0589658	−	0.0589658i
$449$	−23.7589	−	9.84125i	−1.12125	−	0.464437i	−0.256453	−	0.966557i	$-0.582554\pi$
$449$	−23.7589	−	9.84125i	−1.12125	−	0.464437i	−0.864798	+	0.502119i	$0.832554\pi$
$450$		−	28.5241i		−	1.34464i
$451$	−3.04295	−	3.04295i	−0.143287	−	0.143287i
$452$	20.4260			0.960760
$453$	17.7814	+	42.9282i	0.835444	+	2.01694i
$454$	8.61377	−	20.7955i	0.404264	−	0.975980i
$455$	0.735740	−	1.77623i	0.0344920	−	0.0832711i
$456$	14.2319	+	14.2319i	0.666468	+	0.666468i
$457$		−	30.3246i		−	1.41853i	−0.704944	−	0.709263i	$-0.749028\pi$
$457$		−	30.3246i		−	1.41853i	0.704944	−	0.709263i	$-0.250972\pi$
$458$		−	15.8935i		−	0.742657i
$459$	−37.9380	−	37.9380i	−1.77079	−	1.77079i
$460$	1.89576	−	0.785250i	0.0883903	−	0.0366125i
$461$	−9.43420	+	22.7762i	−0.439395	+	1.06079i	0.536764	+	0.843733i	$0.319647\pi$
$461$	−9.43420	+	22.7762i	−0.439395	+	1.06079i	−0.976158	+	0.217060i	$0.930353\pi$
$462$	2.27158	+	5.48409i	0.105684	+	0.255143i
$463$	3.01699	−	7.28365i	0.140211	−	0.338500i	−0.838139	−	0.545457i	$-0.816356\pi$
$463$	3.01699	−	7.28365i	0.140211	−	0.338500i	0.978350	+	0.206957i	$0.0663561\pi$
$464$	3.56159			0.165343
$465$			7.68685i			0.356469i
$466$	−1.29650	+	0.537026i	−0.0600590	+	0.0248772i
$467$	−1.78308	+	4.30473i	−0.0825110	+	0.199199i	−0.959751	−	0.280854i	$-0.909382\pi$
$467$	−1.78308	+	4.30473i	−0.0825110	+	0.199199i	0.877240	+	0.480053i	$0.159382\pi$
$468$	−9.80369	+	23.6682i	−0.453176	+	1.09406i
$469$	7.40219	+	17.8705i	0.341801	+	0.825181i
$470$			0.261844i			0.0120779i
$471$	59.4583			2.73969
$472$	2.39026	−	5.77060i	0.110021	−	0.265613i
$473$	8.42521			0.387392
$474$	21.3368	−	21.3368i	0.980033	−	0.980033i
$475$	12.8442	+	31.0088i	0.589334	+	1.42278i
$476$	−10.6457	−	4.40958i	−0.487944	−	0.202113i
$477$	−59.6487	+	24.7073i	−2.73112	+	1.13127i
$478$	−27.5439			−1.25983
$479$	11.6991	+	11.6991i	0.534544	+	0.534544i	0.921921	−	0.387377i	$-0.126619\pi$
$479$	11.6991	+	11.6991i	0.534544	+	0.534544i	−0.387377	+	0.921921i	$0.626619\pi$
$480$	−0.278317	−	0.671917i	−0.0127034	−	0.0306687i
$481$	6.62512			0.302080
$482$			8.34762i			0.380223i
$483$	−30.8978	−	30.8978i	−1.40590	−	1.40590i
$484$	9.71101			0.441409
$485$	1.07660	+	2.59914i	0.0488859	+	0.118021i
$486$	3.56442	−	1.47643i	0.161685	−	0.0669722i
$487$	−11.8779			−0.538240			−0.269120	−	0.963107i	$-0.586733\pi$
$487$	−11.8779			−0.538240			−0.269120	+	0.963107i	$0.586733\pi$
$488$	−2.10226	−	0.870786i	−0.0951650	−	0.0394186i
$489$	0.471870			0.0213387
$490$	−0.674413	+	0.674413i	−0.0304669	+	0.0304669i
$491$			5.53464i			0.249775i	0.992171	+	0.124887i	$0.0398570\pi$
$491$			5.53464i			0.249775i	−0.992171	+	0.124887i	$0.960143\pi$
$492$	4.29669	−	10.3731i	0.193710	−	0.467657i
$493$	21.4814	−	8.89789i	0.967474	−	0.400741i
$494$		−	30.1444i		−	1.35626i
$495$			1.60963i			0.0723474i
$496$	−4.04471	−	9.76480i	−0.181613	−	0.438453i
$497$	−5.83169	−	14.0789i	−0.261587	−	0.631527i
$498$	−10.0589	−	24.2843i	−0.450750	−	1.08821i
$499$	10.9945	−	10.9945i	0.492181	−	0.492181i	−0.416812	−	0.908993i	$-0.636852\pi$
$499$	10.9945	−	10.9945i	0.492181	−	0.492181i	0.908993	+	0.416812i	$0.136852\pi$
$500$		−	2.44042i		−	0.109139i
$501$		−	19.9117i		−	0.889590i
$502$	−1.94566	+	4.69723i	−0.0868389	+	0.209648i
$503$	−0.0233629	−	0.0233629i	−0.00104170	−	0.00104170i	0.706586	−	0.707627i	$-0.250234\pi$
$503$	−0.0233629	−	0.0233629i	−0.00104170	−	0.00104170i	−0.707627	+	0.706586i	$0.750234\pi$
$504$	−7.20692	+	7.20692i	−0.321022	+	0.321022i
$505$	−0.780043	+	1.88319i	−0.0347114	+	0.0838008i
$506$	8.76634	−	3.63114i	0.389712	−	0.161424i
$507$	18.2878	−	7.57507i	0.812191	−	0.336421i
$508$	−14.4207	+	5.97324i	−0.639814	+	0.265019i
$509$	17.4393	−	7.22358i	0.772982	−	0.320180i	0.0389025	−	0.999243i	$-0.487614\pi$
$509$	17.4393	−	7.22358i	0.772982	−	0.320180i	0.734080	+	0.679063i	$0.237614\pi$
$510$	−3.35729	−	3.35729i	−0.148663	−	0.148663i
$511$		−	23.5308i		−	1.04094i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	39.4855	−	39.4855i	1.74333	−	1.74333i
$514$		−	0.719850i		−	0.0317512i
$515$	−1.27726	+	1.27726i	−0.0562828	+	0.0562828i
$516$	8.41212	+	20.3086i	0.370323	+	0.894038i
$517$			1.21081i			0.0532515i
$518$	2.43514	+	1.00867i	0.106994	+	0.0443183i
$519$	15.1028	+	6.25578i	0.662939	+	0.274598i
$520$	−0.416840	+	1.00634i	−0.0182797	+	0.0441310i
$521$	−28.9647	+	11.9976i	−1.26896	+	0.525622i	−0.912649	−	0.408743i	$-0.865967\pi$
$521$	−28.9647	+	11.9976i	−1.26896	+	0.525622i	−0.356315	+	0.934366i	$0.615967\pi$
$522$		−	20.5662i		−	0.900158i
$523$	−3.12512	+	7.54471i	−0.136652	+	0.329907i	−0.977360	−	0.211581i	$-0.932139\pi$
$523$	−3.12512	+	7.54471i	−0.136652	+	0.329907i	0.840709	+	0.541488i	$0.182139\pi$
$524$	5.09358	+	2.10983i	0.222514	+	0.0921684i
$525$	−23.8606	+	9.88339i	−1.04136	+	0.431347i
$526$	−20.1871			−0.880200
$527$	−48.7907	−	48.7907i	−2.12536	−	2.12536i
$528$	−1.28699	−	3.10706i	−0.0560090	−	0.135218i
$529$	−33.1268	+	33.1268i	−1.44030	+	1.44030i
$530$	−2.53618	+	1.05052i	−0.110165	+	0.0456317i
$531$	−33.3220	−	13.8024i	−1.44605	−	0.598974i
$532$	4.58945	−	11.0799i	0.198978	−	0.480375i
$533$	−15.5360	+	6.43523i	−0.672940	+	0.278741i
$534$	24.8852	+	10.3078i	1.07689	+	0.446062i
$535$	3.78867	−	1.56932i	0.163798	−	0.0678476i
$536$	−4.19378	−	10.1247i	−0.181144	−	0.437320i
$537$	−15.4359	+	37.2655i	−0.666107	+	1.60812i
$538$	−4.85251	−	2.00997i	−0.209206	−	0.0866562i
$539$	−3.11861	+	3.11861i	−0.134328	+	0.134328i
$540$	−1.86420	+	0.772175i	−0.0802222	+	0.0332291i
$541$	4.16256	+	4.16256i	0.178962	+	0.178962i	0.790903	−	0.611941i	$-0.209611\pi$
$541$	4.16256	+	4.16256i	0.178962	+	0.178962i	−0.611941	+	0.790903i	$0.709611\pi$
$542$	4.13019	+	9.97117i	0.177407	+	0.428298i
$543$	−26.4516	+	10.9566i	−1.13515	+	0.470193i
$544$	6.03141	+	2.49829i	0.258595	+	0.107113i
$545$	−2.86585	−	2.86585i	−0.122760	−	0.122760i
$546$	23.1955			0.992676
$547$	38.5582			1.64863			0.824314	−	0.566132i	$-0.191561\pi$
$547$	38.5582			1.64863			0.824314	+	0.566132i	$0.191561\pi$
$548$	−7.50494	+	18.1185i	−0.320595	+	0.773985i
$549$	−5.02831	+	12.1394i	−0.214603	+	0.518097i
$550$		−	5.60825i		−	0.239137i
$551$	9.26083	+	22.3576i	0.394525	+	0.952467i
$552$	17.5054	+	17.5054i	0.745081	+	0.745081i
$553$	−16.6113	−	6.88064i	−0.706386	−	0.292595i
$554$	−5.20538	−	2.15614i	−0.221155	−	0.0916056i
$555$	0.767961	+	0.767961i	0.0325981	+	0.0325981i
$556$	1.09890	+	2.65299i	0.0466039	+	0.112512i
$557$		−	32.9878i		−	1.39774i	−0.715249	−	0.698870i	$-0.753687\pi$
$557$		−	32.9878i		−	1.39774i	0.715249	−	0.698870i	$-0.246313\pi$
$558$	−56.3863	+	23.3560i	−2.38702	+	0.988737i
$559$	12.5990	−	30.4166i	0.532880	−	1.28649i
$560$	−0.306429	+	0.306429i	−0.0129490	+	0.0129490i
$561$	−15.5247	−	15.5247i	−0.655454	−	0.655454i
$562$	−1.88411	−	0.780424i	−0.0794764	−	0.0329202i
$563$	18.4030	−	18.4030i	0.775593	−	0.775593i	−0.203485	−	0.979078i	$-0.565227\pi$
$563$	18.4030	−	18.4030i	0.775593	−	0.775593i	0.979078	+	0.203485i	$0.0652267\pi$
$564$	−2.91862	+	1.20893i	−0.122896	+	0.0509051i
$565$		−	5.01504i		−	0.210984i
$566$	−0.0504827	−	0.121876i	−0.00212195	−	0.00512283i
$567$	8.76255	+	8.76255i	0.367993	+	0.367993i
$568$	3.30400	+	7.97656i	0.138633	+	0.334689i
$569$	12.0790	−	29.1613i	0.506378	−	1.22250i	−0.439577	−	0.898205i	$-0.644871\pi$
$569$	12.0790	−	29.1613i	0.506378	−	1.22250i	0.945955	−	0.324299i	$-0.105129\pi$
$570$	3.49423	−	3.49423i	0.146357	−	0.146357i
$571$	1.93069	+	0.799719i	0.0807970	+	0.0334672i	0.422716	−	0.906262i	$-0.361077\pi$
$571$	1.93069	+	0.799719i	0.0807970	+	0.0334672i	−0.341919	+	0.939729i	$0.611077\pi$
$572$	−1.92755	+	4.65351i	−0.0805947	+	0.194573i
$573$	7.72112	+	7.72112i	0.322554	+	0.322554i
$574$	−6.69020			−0.279244
$575$	15.7987	+	38.1413i	0.658849	+	1.59060i
$576$	4.08315	−	4.08315i	0.170131	−	0.170131i
$577$	−17.9807	−	17.9807i	−0.748547	−	0.748547i	0.225659	−	0.974206i	$-0.427546\pi$
$577$	−17.9807	−	17.9807i	−0.748547	−	0.748547i	−0.974206	+	0.225659i	$0.927546\pi$
$578$	25.6194			1.06563
$579$	−1.75010			−0.0727319
$580$		−	0.874448i		−	0.0363095i
$581$	−11.0749	+	11.0749i	−0.459464	+	0.459464i
$582$	−24.0004	+	24.0004i	−0.994850	+	0.994850i
$583$	−11.7278	+	4.85780i	−0.485715	+	0.201190i
$584$			13.3316i			0.551665i
$585$	5.81106	+	2.40702i	0.240258	+	0.0995181i
$586$	7.73051	+	3.20208i	0.319344	+	0.132277i
$587$	7.81406	−	7.81406i	0.322521	−	0.322521i	−0.527213	−	0.849733i	$-0.676763\pi$
$587$	7.81406	−	7.81406i	0.322521	−	0.322521i	0.849733	+	0.527213i	$0.176763\pi$
$588$	−10.6310	−	4.40352i	−0.438417	−	0.181598i
$589$	50.7808	−	50.7808i	2.09239	−	2.09239i
$590$	−1.41681	−	0.586861i	−0.0583291	−	0.0241607i
$591$	−8.96522	+	21.6440i	−0.368780	+	0.890313i
$592$	−1.37965	−	0.571470i	−0.0567033	−	0.0234873i
$593$	−0.242926	+	0.586475i	−0.00997577	+	0.0240836i	−0.928789	−	0.370609i	$-0.879149\pi$
$593$	−0.242926	+	0.586475i	−0.00997577	+	0.0240836i	0.918813	+	0.394693i	$0.129149\pi$
$594$	−8.62038	+	3.57068i	−0.353698	+	0.146507i
$595$	−1.08265	+	2.61375i	−0.0443843	+	0.107153i
$596$	−10.2934			−0.421634
$597$	36.1475			1.47942
$598$		−	37.0781i		−	1.51624i
$599$	1.31167	−	1.31167i	0.0535935	−	0.0535935i	−0.679802	−	0.733396i	$-0.737934\pi$
$599$	1.31167	−	1.31167i	0.0535935	−	0.0535935i	0.733396	+	0.679802i	$0.237934\pi$
$600$	13.5185	−	5.59953i	0.551889	−	0.228600i
$601$	9.78187	−	9.78187i	0.399011	−	0.399011i	−0.478873	−	0.877884i	$-0.658955\pi$
$601$	9.78187	−	9.78187i	0.399011	−	0.399011i	0.877884	+	0.478873i	$0.158955\pi$
$602$	9.26179	−	9.26179i	0.377483	−	0.377483i
$603$	−58.4644	+	24.2168i	−2.38086	+	0.986183i
$604$	−11.0918	+	11.0918i	−0.451319	+	0.451319i
$605$		−	2.38427i		−	0.0969342i
$606$	−24.5922			−0.998992
$607$	−19.2364			−0.780783			−0.390391	−	0.920649i	$-0.627660\pi$
$607$	−19.2364			−0.780783			−0.390391	+	0.920649i	$0.627660\pi$
$608$	−2.60020	+	6.27743i	−0.105452	+	0.254584i
$609$	−17.2038	+	7.12603i	−0.697131	+	0.288761i
$610$	−0.213797	+	0.516152i	−0.00865639	+	0.0208984i
$611$	4.37126	+	1.81064i	0.176842	+	0.0732505i
$612$	14.4263	−	34.8281i	0.583147	−	1.40784i
$613$	−22.9546	−	9.50809i	−0.927126	−	0.384028i	−0.132539	−	0.991178i	$-0.542313\pi$
$613$	−22.9546	−	9.50809i	−0.927126	−	0.384028i	−0.794587	+	0.607150i	$0.792313\pi$
$614$	−12.7639	+	12.7639i	−0.515110	+	0.515110i
$615$	−2.54683	−	1.05493i	−0.102698	−	0.0425390i
$616$	−1.41698	+	1.41698i	−0.0570918	+	0.0570918i
$617$	−31.4161	−	13.0130i	−1.26477	−	0.523883i	−0.353396	−	0.935474i	$-0.614973\pi$
$617$	−31.4161	−	13.0130i	−1.26477	−	0.523883i	−0.911369	+	0.411591i	$0.864973\pi$
$618$	−20.1339	−	8.33975i	−0.809906	−	0.335474i
$619$		−	31.0764i		−	1.24907i	−0.780998	−	0.624533i	$-0.785289\pi$
$619$		−	31.0764i		−	1.24907i	0.780998	−	0.624533i	$-0.214711\pi$
$620$	−2.39747	+	0.993066i	−0.0962849	+	0.0398825i
$621$	48.5679	−	48.5679i	1.94896	−	1.94896i
$622$	−0.629209	+	0.629209i	−0.0252290	+	0.0252290i
$623$		−	16.0498i		−	0.643023i
$624$	−13.1416			−0.526087
$625$	24.0994			0.963977
$626$	−19.0591	−	19.0591i	−0.761756	−	0.761756i
$627$	16.1580	−	16.1580i	0.645287	−	0.645287i
$628$	7.68144	+	18.5446i	0.306523	+	0.740011i
$629$	−9.74895			−0.388716
$630$	1.76946	+	1.76946i	0.0704968	+	0.0704968i
$631$	8.57361	−	20.6985i	0.341310	−	0.823996i	−0.656274	−	0.754523i	$-0.727868\pi$
$631$	8.57361	−	20.6985i	0.341310	−	0.823996i	0.997584	−	0.0694728i	$-0.0221317\pi$
$632$	9.41132	+	3.89830i	0.374362	+	0.155066i
$633$	−5.83933	+	5.83933i	−0.232092	+	0.232092i
$634$	−2.44619	+	5.90563i	−0.0971506	+	0.234542i
$635$	1.46656	+	3.54059i	0.0581987	+	0.140504i
$636$	−23.4191	−	23.4191i	−0.928627	−	0.928627i
$637$	6.59523	+	15.9223i	0.261313	+	0.630864i
$638$		−	4.04361i		−	0.160088i
$639$	46.0602	−	19.0788i	1.82211	−	0.754744i
$640$	0.173610	−	0.173610i	0.00686255	−	0.00686255i
$641$	−3.88205	−	1.60800i	−0.153332	−	0.0635120i	0.304698	−	0.952449i	$-0.401445\pi$
$641$	−3.88205	−	1.60800i	−0.153332	−	0.0635120i	−0.458029	+	0.888937i	$0.651445\pi$
$642$	34.9845	+	34.9845i	1.38073	+	1.38073i
$643$	1.06772	−	1.06772i	0.0421067	−	0.0421067i	−0.685740	−	0.727847i	$-0.740521\pi$
$643$	1.06772	−	1.06772i	0.0421067	−	0.0421067i	0.727847	+	0.685740i	$0.240521\pi$
$644$	5.64511	−	13.6285i	0.222448	−	0.537038i
$645$	4.98622	−	2.06536i	0.196332	−	0.0813234i
$646$			44.3578i			1.74524i
$647$	0.309293	+	0.746701i	0.0121596	+	0.0293558i	0.929843	−	0.367957i	$-0.119943\pi$
$647$	0.309293	+	0.746701i	0.0121596	+	0.0293558i	−0.917683	+	0.397313i	$0.869943\pi$
$648$	−4.96451	−	4.96451i	−0.195024	−	0.195024i
$649$	−6.55158	−	2.71375i	−0.257172	−	0.106524i
$650$	−20.2468	−	8.38652i	−0.794147	−	0.328946i
$651$	39.0748	+	39.0748i	1.53146	+	1.53146i
$652$	0.0609610	+	0.147173i	0.00238742	+	0.00576374i
$653$			25.5129i			0.998397i	0.866488	+	0.499198i	$0.166372\pi$
$653$			25.5129i			0.998397i	−0.866488	+	0.499198i	$0.833628\pi$
$654$	18.7123	−	45.1755i	0.731710	−	1.76650i
$655$	0.518010	−	1.25059i	0.0202403	−	0.0488645i
$656$	3.79040			0.147990
$657$	76.9825			3.00337
$658$	1.33104	+	1.33104i	0.0518893	+	0.0518893i
$659$	36.7097	+	15.2057i	1.43001	+	0.592328i	0.957353	−	0.288920i	$-0.0932962\pi$
$659$	36.7097	+	15.2057i	1.43001	+	0.592328i	0.472653	+	0.881248i	$0.343296\pi$
$660$	−0.762853	+	0.315984i	−0.0296940	+	0.0122997i
$661$	7.14286	+	17.2444i	0.277825	+	0.670729i	0.999775	−	0.0212163i	$-0.00675387\pi$
$661$	7.14286	+	17.2444i	0.277825	+	0.670729i	−0.721950	+	0.691945i	$0.756754\pi$
$662$	8.73120	+	8.73120i	0.339348	+	0.339348i
$663$	−79.2627	+	32.8317i	−3.07831	+	1.27508i
$664$	6.27459	−	6.27459i	0.243501	−	0.243501i
$665$	−2.72036	−	1.12681i	−0.105491	−	0.0436959i
$666$	−3.29992	+	7.96672i	−0.127869	+	0.308704i
$667$	11.3910	+	27.5003i	0.441061	+	1.06482i
$668$	6.21033	−	2.57240i	0.240285	−	0.0995292i
$669$	32.6408	+	13.5203i	1.26197	+	0.522724i
$670$	−2.48583	+	1.02967i	−0.0960361	+	0.0397794i
$671$	−0.988636	+	2.38678i	−0.0381659	+	0.0921406i
$672$	−4.83036	−	2.00080i	−0.186335	−	0.0771826i
$673$	9.06265	−	3.75387i	0.349339	−	0.144701i	−0.201112	−	0.979568i	$-0.564456\pi$
$673$	9.06265	−	3.75387i	0.349339	−	0.144701i	0.550452	+	0.834867i	$0.314456\pi$
$674$	7.26499	−	7.26499i	0.279837	−	0.279837i
$675$	−15.5356	−	37.5062i	−0.597965	−	1.44362i
$676$	4.72522	+	4.72522i	0.181739	+	0.181739i
$677$	−11.2952			−0.434109			−0.217054	−	0.976160i	$-0.569645\pi$
$677$	−11.2952			−0.434109			−0.217054	+	0.976160i	$0.569645\pi$
$678$	55.8997	−	23.1544i	2.14681	−	0.889240i
$679$	18.6850	+	7.73959i	0.717066	+	0.297018i
$680$	0.613386	−	1.48084i	0.0235223	−	0.0567878i
$681$		−	66.6750i		−	2.55499i
$682$	−11.0864	+	4.59212i	−0.424518	+	0.175841i
$683$	−8.37649	+	20.2226i	−0.320518	+	0.773798i	0.678706	+	0.734410i	$0.262541\pi$
$683$	−8.37649	+	20.2226i	−0.320518	+	0.773798i	−0.999224	+	0.0393882i	$0.987459\pi$
$684$	36.2487	+	15.0147i	1.38600	+	0.574101i
$685$	4.44850	+	1.84263i	0.169968	+	0.0704032i
$686$			19.2118i			0.733510i
$687$	−18.0165	−	43.4957i	−0.687372	−	1.65946i
$688$	−5.24736	+	5.24736i	−0.200054	+	0.200054i
$689$			49.6038i			1.88975i
$690$	4.29797	−	4.29797i	0.163621	−	0.163621i
$691$	−1.12345	−	1.12345i	−0.0427381	−	0.0427381i	0.685415	−	0.728153i	$-0.259621\pi$
$691$	−1.12345	−	1.12345i	−0.0427381	−	0.0427381i	−0.728153	+	0.685415i	$0.759621\pi$
$692$			5.51864i			0.209787i
$693$	8.18229	+	8.18229i	0.310819	+	0.310819i
$694$	−12.0367	+	4.98576i	−0.456907	+	0.189257i
$695$	0.651367	−	0.269805i	0.0247078	−	0.0102343i
$696$	9.74695	−	4.03732i	0.369457	−	0.153034i
$697$	22.8615	−	9.46952i	0.865939	−	0.358684i
$698$	10.8425	−	26.1761i	0.410394	−	0.990780i
$699$	−2.93934	+	2.93934i	−0.111176	+	0.111176i
$700$	−6.16512	−	6.16512i	−0.233020	−	0.233020i
$701$	−5.49476	+	13.2655i	−0.207534	+	0.501032i	−0.993034	−	0.117830i	$-0.962406\pi$
$701$	−5.49476	+	13.2655i	−0.207534	+	0.501032i	0.785499	+	0.618862i	$0.212406\pi$
$702$			36.4608i			1.37612i
$703$		−	10.1466i		−	0.382686i
$704$	0.802805	−	0.802805i	0.0302569	−	0.0302569i
$705$	0.296819	+	0.716584i	0.0111788	+	0.0269881i
$706$	−11.7588	−	28.3883i	−0.442549	−	1.06841i
$707$	5.60767	+	13.5381i	0.210898	+	0.509153i
$708$		−	18.5019i		−	0.695343i
$709$		−	26.4290i		−	0.992563i	−0.868162	−	0.496281i	$-0.834698\pi$
$709$		−	26.4290i		−	0.992563i	0.868162	−	0.496281i	$-0.165302\pi$
$710$	1.95842	−	0.811204i	0.0734982	−	0.0304440i
$711$	22.5105	−	54.3451i	0.844210	−	2.03810i
$712$			9.09318i			0.340781i
$713$	62.4613	−	62.4613i	2.33920	−	2.33920i
$714$	−34.1325			−1.27738
$715$	1.14254	+	0.473255i	0.0427285	+	0.0176987i
$716$	−13.6170			−0.508891
$717$	−75.3791	+	31.2230i	−2.81508	+	1.16605i
$718$	12.7384	+	30.7532i	0.475393	+	1.14770i
$719$	−28.7698			−1.07293			−0.536467	−	0.843921i	$-0.680241\pi$
$719$	−28.7698			−1.07293			−0.536467	+	0.843921i	$0.680241\pi$
$720$	−1.00250	−	1.00250i	−0.0373611	−	0.0373611i
$721$			12.9855i			0.483605i
$722$	−27.1672			−1.01106
$723$	9.46263	+	22.8448i	0.351919	+	0.849608i
$724$	−6.83457	−	6.83457i	−0.254005	−	0.254005i
$725$	17.5932			0.653397
$726$	26.5760	−	11.0081i	0.986328	−	0.408550i
$727$	16.6586	+	6.90021i	0.617832	+	0.255915i	0.669573	−	0.742746i	$-0.266477\pi$
$727$	16.6586	+	6.90021i	0.617832	+	0.255915i	−0.0517409	+	0.998661i	$0.516477\pi$
$728$	2.99663	+	7.23452i	0.111063	+	0.268129i
$729$	22.9746	−	22.9746i	0.850910	−	0.850910i
$730$	3.27320			0.121146
$731$	−18.5395	+	44.7584i	−0.685710	+	1.65545i
$732$	−6.74034			−0.249130
$733$		−	44.1869i		−	1.63208i	−0.577994	−	0.816041i	$-0.696164\pi$
$733$		−	44.1869i		−	1.63208i	0.577994	−	0.816041i	$-0.303836\pi$
$734$	3.91363	+	9.44834i	0.144455	+	0.348745i
$735$	−1.08116	+	2.61015i	−0.0398792	+	0.0962769i
$736$	−3.19829	+	7.72135i	−0.117891	+	0.284613i
$737$	−11.4949	+	4.76136i	−0.423421	+	0.175387i
$738$		−	21.8874i		−	0.805688i
$739$	−18.8486			−0.693356			−0.346678	−	0.937984i	$-0.612690\pi$
$739$	−18.8486			−0.693356			−0.346678	+	0.937984i	$0.612690\pi$
$740$	−0.140309	+	0.338735i	−0.00515784	+	0.0124521i
$741$	−34.1709	−	82.4958i	−1.25530	−	3.03056i
$742$	−7.55212	+	18.2324i	−0.277247	+	0.669334i
$743$	−21.5215	+	8.91449i	−0.789547	+	0.327041i	−0.740761	−	0.671768i	$-0.765535\pi$
$743$	−21.5215	+	8.91449i	−0.789547	+	0.327041i	−0.0487854	+	0.998809i	$0.515535\pi$
$744$	−22.1382	−	22.1382i	−0.811627	−	0.811627i
$745$			2.52725i			0.0925914i
$746$		−	2.14576i		−	0.0785618i
$747$	−36.2323	−	36.2323i	−1.32567	−	1.32567i
$748$	2.83641	−	6.84769i	0.103709	−	0.250376i
$749$	11.2817	−	27.2365i	0.412225	−	0.995199i
$750$	−2.76639	−	6.67866i	−0.101014	−	0.243870i
$751$	−21.1172			−0.770576			−0.385288	−	0.922796i	$-0.625898\pi$
$751$	−21.1172			−0.770576			−0.385288	+	0.922796i	$0.625898\pi$
$752$	−0.754114	−	0.754114i	−0.0274997	−	0.0274997i
$753$			15.0604i			0.548831i
$754$	−14.5982	−	6.04677i	−0.531635	−	0.220210i
$755$	2.72328	+	2.72328i	0.0991103	+	0.0991103i
$756$	−5.55111	+	13.4016i	−0.201892	+	0.487410i
$757$	−5.99681	−	5.99681i	−0.217958	−	0.217958i	0.589680	−	0.807637i	$-0.299254\pi$
$757$	−5.99681	−	5.99681i	−0.217958	−	0.217958i	−0.807637	+	0.589680i	$0.799254\pi$
$758$	7.23335	−	7.23335i	0.262727	−	0.262727i
$759$	19.8746	−	19.8746i	0.721402	−	0.721402i
$760$	1.54125	+	0.638406i	0.0559069	+	0.0231574i
$761$	22.0892			0.800734			0.400367	−	0.916355i	$-0.368883\pi$
$761$	22.0892			0.800734			0.400367	+	0.916355i	$0.368883\pi$
$762$	−32.6938	+	32.6938i	−1.18437	+	1.18437i
$763$	−29.1362			−1.05480
$764$	−1.41067	+	3.40566i	−0.0510362	+	0.123212i
$765$	−8.55105	−	3.54196i	−0.309164	−	0.128060i
$766$	−16.7698	+	16.7698i	−0.605916	+	0.605916i
$767$	−19.5943	+	19.5943i	−0.707510	+	0.707510i
$768$	2.73669	+	1.13357i	0.0987517	+	0.0409043i
$769$	6.91058	+	16.6836i	0.249202	+	0.601626i	0.998137	−	0.0610172i	$-0.0194345\pi$
$769$	6.91058	+	16.6836i	0.249202	+	0.601626i	−0.748935	+	0.662644i	$0.769434\pi$
$770$	0.347900	+	0.347900i	0.0125375	+	0.0125375i
$771$	−0.816003	−	1.97001i	−0.0293876	−	0.0709480i
$772$	−0.226097	−	0.545845i	−0.00813739	−	0.0196454i
$773$	−1.48645			−0.0534639			−0.0267320	−	0.999643i	$-0.508510\pi$
$773$	−1.48645			−0.0534639			−0.0267320	+	0.999643i	$0.508510\pi$
$774$	30.3006	+	30.3006i	1.08913	+	1.08913i
$775$	−19.9798	−	48.2354i	−0.717694	−	1.73267i
$776$	−10.5862	−	4.38494i	−0.380022	−	0.157410i
$777$	7.80761			0.280096
$778$	1.70748	−	0.707261i	0.0612161	−	0.0253565i
$779$	9.85578	+	23.7940i	0.353120	+	0.852507i
$780$			3.22656i			0.115529i
$781$	9.05609	−	3.75116i	0.324052	−	0.134227i
$782$			54.5609i			1.95110i
$783$	−11.2013	−	27.0424i	−0.400303	−	0.966416i
$784$		−	3.88464i		−	0.138737i
$785$	4.55311	−	1.88596i	0.162508	−	0.0673128i
$786$	16.3312			0.582514
$787$	7.76682	+	3.21712i	0.276857	+	0.114678i	0.516792	−	0.856111i	$-0.327126\pi$
$787$	7.76682	+	3.21712i	0.276857	+	0.114678i	−0.239935	+	0.970789i	$0.577126\pi$
$788$	−7.90881			−0.281740
$789$	−55.2458	+	22.8836i	−1.96680	+	0.814676i
$790$	0.957117	−	2.31069i	0.0340527	−	0.0822105i
$791$	−25.4931	−	25.4931i	−0.906432	−	0.906432i
$792$	−4.63575	−	4.63575i	−0.164724	−	0.164724i
$793$	7.13833	+	7.13833i	0.253490	+	0.253490i
$794$	−18.0432	+	18.0432i	−0.640328	+	0.640328i
$795$	−5.74990	+	5.74990i	−0.203928	+	0.203928i
$796$	4.66991	+	11.2742i	0.165521	+	0.399602i
$797$	56.0382			1.98498			0.992488	−	0.122345i	$-0.0390415\pi$
$797$	56.0382			1.98498			0.992488	+	0.122345i	$0.0390415\pi$
$798$		−	35.5247i		−	1.25756i
$799$	−6.43237	−	2.66437i	−0.227561	−	0.0942588i
$800$	3.49291	+	3.49291i	0.123493	+	0.123493i
$801$	52.5081			1.85528
$802$	−11.5730	+	16.3421i	−0.408657	+	0.577061i
$803$	15.1359			0.534133
$804$	−22.9541	−	22.9541i	−0.809530	−	0.809530i
$805$	−3.34609	−	1.38600i	−0.117934	−	0.0488500i
$806$			46.8908i			1.65166i
$807$	−15.5583			−0.547676
$808$	−3.17708	−	7.67015i	−0.111769	−	0.269835i
$809$	18.7678	−	18.7678i	0.659839	−	0.659839i	−0.295503	−	0.955342i	$-0.595487\pi$
$809$	18.7678	−	18.7678i	0.659839	−	0.659839i	0.955342	+	0.295503i	$0.0954872\pi$
$810$	−1.21890	+	1.21890i	−0.0428276	+	0.0428276i
$811$	−12.9745	−	12.9745i	−0.455597	−	0.455597i	0.441610	−	0.897207i	$-0.354407\pi$
$811$	−12.9745	−	12.9745i	−0.455597	−	0.455597i	−0.897207	+	0.441610i	$0.854407\pi$
$812$	−4.44512	−	4.44512i	−0.155993	−	0.155993i
$813$	22.6061	+	22.6061i	0.792830	+	0.792830i
$814$	−0.648812	+	1.56637i	−0.0227408	+	0.0549013i
$815$	0.0361342	−	0.0149673i	0.00126573	−	0.000524281i
$816$	19.3381			0.676969
$817$	−46.5841	−	19.2958i	−1.62977	−	0.675074i
$818$	−35.5622			−1.24340
$819$	41.7753	−	17.3039i	1.45975	−	0.604647i
$820$		−	0.930626i		−	0.0324989i
$821$	−0.912010	−	2.20179i	−0.0318294	−	0.0768429i	0.907166	−	0.420774i	$-0.138241\pi$
$821$	−0.912010	−	2.20179i	−0.0318294	−	0.0768429i	−0.938995	+	0.343931i	$0.888241\pi$
$822$			58.0922i			2.02620i
$823$	9.87294	−	4.08951i	0.344149	−	0.142551i	−0.203913	−	0.978989i	$-0.565366\pi$
$823$	9.87294	−	4.08951i	0.344149	−	0.142551i	0.548062	+	0.836438i	$0.315366\pi$
$824$		−	7.35705i		−	0.256295i
$825$	−6.35736	−	15.3480i	−0.221335	−	0.534350i
$826$	−10.1853	+	4.21890i	−0.354393	+	0.146794i
$827$	−32.4081			−1.12694			−0.563469	−	0.826137i	$-0.690534\pi$
$827$	−32.4081			−1.12694			−0.563469	+	0.826137i	$0.690534\pi$
$828$	44.5865	+	18.4683i	1.54949	+	0.641819i
$829$	−6.32741	−	15.2757i	−0.219760	−	0.530547i	0.775096	−	0.631843i	$-0.217701\pi$
$829$	−6.32741	−	15.2757i	−0.219760	−	0.530547i	−0.994856	+	0.101296i	$0.967701\pi$
$830$	−1.54055	−	1.54055i	−0.0534733	−	0.0534733i
$831$	−16.6896			−0.578957
$832$	−1.69777	−	4.09879i	−0.0588597	−	0.142100i
$833$	−9.70496	−	23.4299i	−0.336257	−	0.811796i
$834$	6.01471	+	6.01471i	0.208272	+	0.208272i
$835$	−0.631581	−	1.52477i	−0.0218568	−	0.0527669i
$836$	7.12701	+	2.95210i	0.246493	+	0.102101i
$837$	−61.4213	+	61.4213i	−2.12303	+	2.12303i
$838$	−10.2650	+	10.2650i	−0.354600	+	0.354600i
$839$	20.0855	+	8.31967i	0.693427	+	0.287227i	0.701427	−	0.712741i	$-0.252547\pi$
$839$	20.0855	+	8.31967i	0.693427	+	0.287227i	−0.00800029	+	0.999968i	$0.502547\pi$
$840$	−0.491240	+	1.18596i	−0.0169494	+	0.0409195i
$841$	−16.3151			−0.562589
$842$	7.54745	−	7.54745i	0.260102	−	0.260102i
$843$	−6.04089			−0.208059
$844$	−2.57563	−	1.06686i	−0.0886568	−	0.0367228i
$845$	1.16015	−	1.16015i	0.0399102	−	0.0399102i
$846$	−4.35459	+	4.35459i	−0.149714	+	0.149714i
$847$	−12.1200	−	12.1200i	−0.416449	−	0.416449i
$848$	4.27873	−	10.3298i	0.146932	−	0.354726i
$849$	−0.276311	−	0.276311i	−0.00948296	−	0.00948296i
$850$	29.7935	+	12.3409i	1.02191	+	0.423288i
$851$		−	12.4805i		−	0.427826i
$852$	18.0840	+	18.0840i	0.619549	+	0.619549i
$853$	−2.61498			−0.0895353			−0.0447676	−	0.998997i	$-0.514255\pi$
$853$	−2.61498			−0.0895353			−0.0447676	+	0.998997i	$0.514255\pi$
$854$	1.53697	+	3.71058i	0.0525941	+	0.126973i
$855$	3.68644	−	8.89985i	0.126074	−	0.304368i
$856$	−6.39176	+	15.4311i	−0.218466	+	0.527424i
$857$	−3.07590	−	3.07590i	−0.105071	−	0.105071i	0.652617	−	0.757688i	$-0.273671\pi$
$857$	−3.07590	−	3.07590i	−0.105071	−	0.105071i	−0.757688	+	0.652617i	$0.773671\pi$
$858$			14.9202i			0.509367i
$859$		−	8.19760i		−	0.279698i	−0.990173	−	0.139849i	$-0.955338\pi$
$859$		−	8.19760i		−	0.279698i	0.990173	−	0.139849i	$-0.0446618\pi$
$860$	1.28834	+	1.28834i	0.0439321	+	0.0439321i
$861$	−18.3090	+	7.58383i	−0.623969	+	0.258456i
$862$	7.75334	−	18.7182i	0.264080	−	0.637545i
$863$	9.61700	+	23.2175i	0.327367	+	0.790333i	0.998786	+	0.0492555i	$0.0156849\pi$
$863$	9.61700	+	23.2175i	0.327367	+	0.790333i	−0.671420	+	0.741077i	$0.734315\pi$
$864$	3.14504	−	7.59279i	0.106996	−	0.258312i
$865$	1.35495			0.0460696
$866$		−	0.744908i		−	0.0253130i
$867$	70.1123	−	29.0415i	2.38114	−	0.986300i
$868$	−7.13908	+	17.2353i	−0.242316	+	0.585003i
$869$	4.42588	−	10.6850i	0.150138	−	0.362465i
$870$	−0.991251	−	2.39309i	−0.0336065	−	0.0811334i
$871$			48.6190i			1.64739i
$872$	16.5074			0.559010
$873$	−25.3206	+	61.1294i	−0.856973	+	2.06892i
$874$	−56.7865			−1.92083
$875$	−3.04582	+	3.04582i	−0.102967	+	0.102967i
$876$	15.1123	+	36.4844i	0.510598	+	1.23269i
$877$	44.9233	+	18.6078i	1.51695	+	0.628342i	0.976978	−	0.213340i	$-0.0684342\pi$
$877$	44.9233	+	18.6078i	1.51695	+	0.628342i	0.539974	+	0.841682i	$0.318434\pi$
$878$	8.72186	−	3.61271i	0.294348	−	0.121923i
$879$	24.7858			0.836004
$880$	−0.197106	−	0.197106i	−0.00664445	−	0.00664445i
$881$	−16.3969	−	39.5857i	−0.552427	−	1.33368i	−0.915651	−	0.401974i	$-0.868324\pi$
$881$	−16.3969	−	39.5857i	−0.552427	−	1.33368i	0.363224	−	0.931702i	$-0.381676\pi$
$882$	−22.4316			−0.755312
$883$		−	3.43911i		−	0.115735i	−0.998324	−	0.0578676i	$-0.981570\pi$
$883$		−	3.43911i		−	0.115735i	0.998324	−	0.0578676i	$-0.0184301\pi$
$884$	−20.4799	−	20.4799i	−0.688815	−	0.688815i
$885$	−4.54261			−0.152698
$886$	−10.5775	−	25.5364i	−0.355359	−	0.857913i
$887$	42.4296	−	17.5749i	1.42465	−	0.590108i	0.468623	−	0.883398i	$-0.344750\pi$
$887$	42.4296	−	17.5749i	1.42465	−	0.590108i	0.956023	+	0.293291i	$0.0947503\pi$
$888$	−4.42348			−0.148442
$889$	25.4530	+	10.5430i	0.853667	+	0.353601i
$890$	2.23258			0.0748361
$891$	−5.63640	+	5.63640i	−0.188826	+	0.188826i
$892$			11.9271i			0.399350i
$893$	2.77305	−	6.69474i	0.0927967	−	0.224031i
$894$	−28.1698	+	11.6683i	−0.942139	+	0.390247i
$895$			3.34327i			0.111753i
$896$		−	1.76504i		−	0.0589658i
$897$	−42.0308	−	101.471i	−1.40337	−	3.38803i
$898$	−9.84125	−	23.7589i	−0.328407	−	0.792844i
$899$	−14.4056	−	34.7782i	−0.480454	−	1.15992i
$900$	20.1696	−	20.1696i	0.672320	−	0.672320i
$901$		−	72.9926i		−	2.43174i
$902$		−	4.30338i		−	0.143287i
$903$	14.8477	−	35.8455i	0.494101	−	1.19287i
$904$	14.4434	+	14.4434i	0.480380	+	0.480380i
$905$	−1.67804	+	1.67804i	−0.0557798	+	0.0557798i
$906$	−17.7814	+	42.9282i	−0.590748	+	1.42619i
$907$	−46.6556	+	19.3254i	−1.54917	+	0.641689i	−0.983167	−	0.182711i	$-0.941513\pi$
$907$	−46.6556	+	19.3254i	−1.54917	+	0.641689i	−0.566008	+	0.824400i	$0.691513\pi$
$908$	20.7955	−	8.61377i	0.690122	−	0.285858i
$909$	−44.2908	+	18.3459i	−1.46903	+	0.608494i
$910$	1.77623	−	0.735740i	0.0588815	−	0.0243895i
$911$	28.2065	+	28.2065i	0.934521	+	0.934521i	0.997984	−	0.0634628i	$-0.0202144\pi$
$911$	28.2065	+	28.2065i	0.934521	+	0.934521i	−0.0634628	+	0.997984i	$0.520214\pi$
$912$			20.1269i			0.666468i
$913$	−7.12378	−	7.12378i	−0.235763	−	0.235763i
$914$	21.4427	−	21.4427i	0.709263	−	0.709263i
$915$			1.65490i			0.0547093i
$916$	11.2384	−	11.2384i	0.371328	−	0.371328i
$917$	−3.72393	−	8.99037i	−0.122975	−	0.296888i
$918$		−	53.6525i		−	1.77079i
$919$	26.5961	+	11.0164i	0.877323	+	0.363399i	0.775458	−	0.631399i	$-0.217519\pi$
$919$	26.5961	+	11.0164i	0.877323	+	0.363399i	0.101865	+	0.994798i	$0.467519\pi$
$920$	1.89576	+	0.785250i	0.0625014	+	0.0258889i
$921$	−20.4620	+	49.3997i	−0.674246	+	1.62777i
$922$	−22.7762	+	9.43420i	−0.750093	+	0.310699i
$923$		−	38.3036i		−	1.26078i
$924$	−2.27158	+	5.48409i	−0.0747296	+	0.180413i
$925$	−6.81509	−	2.82290i	−0.224079	−	0.0928165i
$926$	7.28365	−	3.01699i	0.239356	−	0.0991444i
$927$	−42.4829			−1.39532
$928$	2.51842	+	2.51842i	0.0826713	+	0.0826713i
$929$	1.96349	+	4.74028i	0.0644200	+	0.155524i	0.952811	−	0.303564i	$-0.0981765\pi$
$929$	1.96349	+	4.74028i	0.0644200	+	0.155524i	−0.888391	+	0.459087i	$0.848177\pi$
$930$	−5.43542	+	5.43542i	−0.178235	+	0.178235i
$931$	24.3855	−	10.1008i	0.799204	−	0.331041i
$932$	−1.29650	−	0.537026i	−0.0424681	−	0.0175909i
$933$	−1.00869	+	2.43520i	−0.0330232	+	0.0797250i
$934$	−4.30473	+	1.78308i	−0.140855	+	0.0583441i
$935$	−1.68126	−	0.696400i	−0.0549830	−	0.0227747i
$936$	−23.6682	+	9.80369i	−0.773620	+	0.320444i
$937$	−0.857593	−	2.07041i	−0.0280163	−	0.0676374i	0.909252	−	0.416246i	$-0.136654\pi$
$937$	−0.857593	−	2.07041i	−0.0280163	−	0.0676374i	−0.937269	+	0.348608i	$0.886654\pi$
$938$	−7.40219	+	17.8705i	−0.241690	+	0.583491i
$939$	−73.7638	−	30.5540i	−2.40719	−	0.997091i
$940$	−0.185151	+	0.185151i	−0.00603897	+	0.00603897i
$941$	43.0960	−	17.8510i	1.40489	−	0.581925i	0.453875	−	0.891066i	$-0.350041\pi$
$941$	43.0960	−	17.8510i	1.40489	−	0.581925i	0.951016	+	0.309141i	$0.100041\pi$
$942$	42.0434	+	42.0434i	1.36985	+	1.36985i
$943$	12.1228	+	29.2670i	0.394772	+	0.953065i
$944$	5.77060	−	2.39026i	0.187817	−	0.0777964i
$945$	3.29038	+	1.36292i	0.107036	+	0.0443358i
$946$	5.95752	+	5.95752i	0.193696	+	0.193696i
$947$	−33.5852			−1.09137			−0.545687	−	0.837989i	$-0.683731\pi$
$947$	−33.5852			−1.09137			−0.545687	+	0.837989i	$0.683731\pi$
$948$	30.1748			0.980033
$949$	22.6340	−	54.6433i	0.734731	−	1.77380i
$950$	−12.8442	+	31.0088i	−0.416722	+	1.00606i
$951$			18.9348i			0.614002i
$952$	−4.40958	−	10.6457i	−0.142915	−	0.345028i
$953$	30.6761	+	30.6761i	0.993697	+	0.993697i	0.999980	−	0.00628333i	$-0.00200006\pi$
$953$	30.6761	+	30.6761i	0.993697	+	0.993697i	−0.00628333	+	0.999980i	$0.502000\pi$
$954$	−59.6487	−	24.7073i	−1.93120	−	0.799928i
$955$	0.836164	+	0.346350i	0.0270576	+	0.0112076i
$956$	−19.4765	−	19.4765i	−0.629915	−	0.629915i
$957$	−4.58372	−	11.0661i	−0.148171	−	0.357716i
$958$			16.5450i			0.534544i
$959$	31.9799	−	13.2465i	1.03269	−	0.427752i
$960$	0.278317	−	0.671917i	0.00898264	−	0.0216860i
$961$	−57.0714	+	57.0714i	−1.84101	+	1.84101i
$962$	4.68467	+	4.68467i	0.151040	+	0.151040i
$963$	89.1059	+	36.9089i	2.87140	+	1.18937i
$964$	−5.90266	+	5.90266i	−0.190112	+	0.190112i
$965$	−0.134017	+	0.0555117i	−0.00431416	+	0.00178698i
$966$		−	43.6961i		−	1.40590i
$967$	−4.06208	−	9.80673i	−0.130628	−	0.315363i	0.845010	−	0.534750i	$-0.179594\pi$
$967$	−4.06208	−	9.80673i	−0.130628	−	0.315363i	−0.975638	+	0.219387i	$0.929594\pi$
$968$	6.86672	+	6.86672i	0.220705	+	0.220705i
$969$	50.2829	+	121.394i	1.61532	+	3.89972i
$970$	−1.07660	+	2.59914i	−0.0345675	+	0.0834534i
$971$	19.7987	−	19.7987i	0.635371	−	0.635371i	−0.314039	−	0.949410i	$-0.601682\pi$
$971$	19.7987	−	19.7987i	0.635371	−	0.635371i	0.949410	+	0.314039i	$0.101682\pi$
$972$	3.56442	+	1.47643i	0.114329	+	0.0473565i
$973$	1.93961	−	4.68263i	0.0621810	−	0.150118i
$974$	−8.39896	−	8.39896i	−0.269120	−	0.269120i
$975$	−64.9160			−2.07898
$976$	−0.870786	−	2.10226i	−0.0278732	−	0.0672918i
$977$	0.958253	−	0.958253i	0.0306572	−	0.0306572i	−0.691612	−	0.722269i	$-0.743099\pi$
$977$	0.958253	−	0.958253i	0.0306572	−	0.0306572i	0.722269	+	0.691612i	$0.243099\pi$
$978$	0.333663	+	0.333663i	0.0106694	+	0.0106694i
$979$	10.3238			0.329951
$980$	−0.953764			−0.0304669
$981$		−	95.3209i		−	3.04336i
$982$	−3.91358	+	3.91358i	−0.124887	+	0.124887i
$983$	2.16593	−	2.16593i	0.0690823	−	0.0690823i	−0.671721	−	0.740804i	$-0.734445\pi$
$983$	2.16593	−	2.16593i	0.0690823	−	0.0690823i	0.740804	+	0.671721i	$0.234445\pi$
$984$	10.3731	−	4.29669i	0.330683	−	0.136974i
$985$			1.94179i			0.0618705i
$986$	21.4814	+	8.89789i	0.684107	+	0.283367i
$987$	5.15147	+	2.13381i	0.163973	+	0.0679199i
$988$	21.3153	−	21.3153i	0.678130	−	0.678130i
$989$	−57.2993	−	23.7341i	−1.82201	−	0.754702i
$990$	−1.13818	+	1.13818i	−0.0361737	+	0.0361737i
$991$	9.58253	+	3.96921i	0.304399	+	0.126086i	0.529654	−	0.848214i	$-0.322322\pi$
$991$	9.58253	+	3.96921i	0.304399	+	0.126086i	−0.225255	+	0.974300i	$0.572322\pi$
$992$	4.04471	−	9.76480i	0.128420	−	0.310033i
$993$	33.7920	+	13.9971i	1.07236	+	0.444185i
$994$	5.83169	−	14.0789i	0.184970	−	0.446557i
$995$	2.76805	−	1.14657i	0.0877532	−	0.0363486i
$996$	10.0589	−	24.2843i	0.318728	−	0.769478i
$997$	50.0464			1.58498			0.792492	−	0.609882i	$-0.208783\pi$
$997$	50.0464			1.58498			0.792492	+	0.609882i	$0.208783\pi$
$998$	15.5486			0.492181
$999$			12.2727i			0.388291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	802.2.e.b.45.16	✓	68
401.303	even	8	inner	802.2.e.b.303.16	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
802.2.e.b.45.16	✓	68	1.1	even	1	trivial
802.2.e.b.303.16	yes	68	401.303	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:	\( N \)	\(=\)	\( 802 = 2 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	802.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(2.73669 + 1.13357i) q^{3} +1.00000i q^{4} +0.245522 q^{5} +(1.13357 + 2.73669i) q^{6} +(1.24807 - 1.24807i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(4.08315 + 4.08315i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(2.73669 + 1.13357i) q^{3} +1.00000i q^{4} +0.245522 q^{5} +(1.13357 + 2.73669i) q^{6} +(1.24807 - 1.24807i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(4.08315 + 4.08315i) q^{9} +(0.173610 + 0.173610i) q^{10} +(0.802805 + 0.802805i) q^{11} +(-1.13357 + 2.73669i) q^{12} +(4.09879 - 1.69777i) q^{13} +1.76504 q^{14} +(0.671917 + 0.278317i) q^{15} -1.00000 q^{16} +(-6.03141 + 2.49829i) q^{17} +5.77444i q^{18} +(-2.60020 - 6.27743i) q^{19} +0.245522i q^{20} +(4.83036 - 2.00080i) q^{21} +1.13534i q^{22} +(-3.19829 - 7.72135i) q^{23} +(-2.73669 + 1.13357i) q^{24} -4.93972 q^{25} +(4.09879 + 1.69777i) q^{26} +(3.14504 + 7.59279i) q^{27} +(1.24807 + 1.24807i) q^{28} -3.56159 q^{29} +(0.278317 + 0.671917i) q^{30} +(4.04471 + 9.76480i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.28699 + 3.10706i) q^{33} +(-6.03141 - 2.49829i) q^{34} +(0.306429 - 0.306429i) q^{35} +(-4.08315 + 4.08315i) q^{36} +(1.37965 + 0.571470i) q^{37} +(2.60020 - 6.27743i) q^{38} +13.1416 q^{39} +(-0.173610 + 0.173610i) q^{40} -3.79040 q^{41} +(4.83036 + 2.00080i) q^{42} +(5.24736 - 5.24736i) q^{43} +(-0.802805 + 0.802805i) q^{44} +(1.00250 + 1.00250i) q^{45} +(3.19829 - 7.72135i) q^{46} +(0.754114 + 0.754114i) q^{47} +(-2.73669 - 1.13357i) q^{48} +3.88464i q^{49} +(-3.49291 - 3.49291i) q^{50} -19.3381 q^{51} +(1.69777 + 4.09879i) q^{52} +(-4.27873 + 10.3298i) q^{53} +(-3.14504 + 7.59279i) q^{54} +(0.197106 + 0.197106i) q^{55} +1.76504i q^{56} -20.1269i q^{57} +(-2.51842 - 2.51842i) q^{58} +(-5.77060 + 2.39026i) q^{59} +(-0.278317 + 0.671917i) q^{60} +(0.870786 + 2.10226i) q^{61} +(-4.04471 + 9.76480i) q^{62} +10.1921 q^{63} -1.00000i q^{64} +(1.00634 - 0.416840i) q^{65} +(-1.28699 + 3.10706i) q^{66} +(-4.19378 + 10.1247i) q^{67} +(-2.49829 - 6.03141i) q^{68} -24.7564i q^{69} +0.433356 q^{70} +(3.30400 - 7.97656i) q^{71} -5.77444 q^{72} +(9.42686 - 9.42686i) q^{73} +(0.571470 + 1.37965i) q^{74} +(-13.5185 - 5.59953i) q^{75} +(6.27743 - 2.60020i) q^{76} +2.00392 q^{77} +(9.29254 + 9.29254i) q^{78} +(-3.89830 - 9.41132i) q^{79} -0.245522 q^{80} +7.02088i q^{81} +(-2.68022 - 2.68022i) q^{82} -8.87362 q^{83} +(2.00080 + 4.83036i) q^{84} +(-1.48084 + 0.613386i) q^{85} +7.42089 q^{86} +(-9.74695 - 4.03732i) q^{87} -1.13534 q^{88} +(6.42985 - 6.42985i) q^{89} +1.41775i q^{90} +(2.99663 - 7.23452i) q^{91} +(7.72135 - 3.19829i) q^{92} +31.3082i q^{93} +1.06648i q^{94} +(-0.638406 - 1.54125i) q^{95} +(-1.13357 - 2.73669i) q^{96} +(4.38494 + 10.5862i) q^{97} +(-2.74685 + 2.74685i) q^{98} +6.55595i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 68 * q + 4 * q^6 + 20 * q^9	\( 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

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