LMFDB - Embedded newform 845.2.o.i.357.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(258,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("845.258");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, degree $4$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.5
Character	$\chi$	$=$	845.357
Dual form			845.2.o.i.258.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18621 + 2.05458i) q^{2} +(0.604804 + 2.25716i) q^{3} +(-1.81419 - 3.14226i) q^{4} +(-2.15457 + 0.598181i) q^{5} +(-5.35492 - 1.43485i) q^{6} +(-3.23750 + 1.86917i) q^{7} +3.86318 q^{8} +(-2.13090 + 1.23027i) q^{9} +(1.32677 - 5.13630i) q^{10} +(1.74477 - 0.467511i) q^{11} +(5.99536 - 5.99536i) q^{12} -8.86890i q^{14} +(-2.65328 - 4.50143i) q^{15} +(-0.954169 + 1.65267i) q^{16} +(-0.372153 - 0.0997182i) q^{17} -5.83745i q^{18} +(1.41754 - 5.29032i) q^{19} +(5.78843 + 5.68502i) q^{20} +(-6.17706 - 6.17706i) q^{21} +(-1.10913 + 4.13933i) q^{22} +(-8.92587 + 2.39168i) q^{23} +(2.33647 + 8.71981i) q^{24} +(4.28436 - 2.57765i) q^{25} +(0.891365 + 0.891365i) q^{27} +(11.7468 + 6.78204i) q^{28} +(-0.662140 - 0.382287i) q^{29} +(12.3959 - 0.111731i) q^{30} +(-3.27268 + 3.27268i) q^{31} +(1.59949 + 2.77040i) q^{32} +(2.11049 + 3.65548i) q^{33} +(0.646330 - 0.646330i) q^{34} +(5.85732 - 5.96387i) q^{35} +(7.73169 + 4.46389i) q^{36} +(-1.00131 - 0.578108i) q^{37} +(9.18786 + 9.18786i) q^{38} +(-8.32350 + 2.31088i) q^{40} +(0.789472 + 2.94635i) q^{41} +(20.0185 - 5.36394i) q^{42} +(0.489998 - 1.82870i) q^{43} +(-4.63438 - 4.63438i) q^{44} +(3.85525 - 3.92538i) q^{45} +(5.67406 - 21.1759i) q^{46} +1.94248i q^{47} +(-4.30742 - 1.15417i) q^{48} +(3.48758 - 6.04067i) q^{49} +(0.213823 + 11.8602i) q^{50} -0.900318i q^{51} +(-1.18715 + 1.18715i) q^{53} +(-2.88872 + 0.774031i) q^{54} +(-3.47958 + 2.05098i) q^{55} +(-12.5070 + 7.22094i) q^{56} +12.7984 q^{57} +(1.57087 - 0.906945i) q^{58} +(-6.15548 - 1.64935i) q^{59} +(-9.33112 + 16.5037i) q^{60} +(1.85832 + 3.21870i) q^{61} +(-2.84189 - 10.6061i) q^{62} +(4.59918 - 7.96601i) q^{63} -11.4060 q^{64} -10.0139 q^{66} +(5.52807 - 9.57490i) q^{67} +(0.361815 + 1.35031i) q^{68} +(-10.7968 - 18.7006i) q^{69} +(5.30521 + 19.1087i) q^{70} +(10.7163 + 2.87143i) q^{71} +(-8.23204 + 4.75277i) q^{72} -4.49691 q^{73} +(2.37553 - 1.37151i) q^{74} +(8.40935 + 8.11150i) q^{75} +(-19.1952 + 5.14335i) q^{76} +(-4.77484 + 4.77484i) q^{77} -7.15052i q^{79} +(1.06723 - 4.13156i) q^{80} +(-5.16367 + 8.94374i) q^{81} +(-6.98997 - 1.87296i) q^{82} -11.4388i q^{83} +(-8.20360 + 30.6163i) q^{84} +(0.861480 - 0.00776503i) q^{85} +(3.17596 + 3.17596i) q^{86} +(0.462417 - 1.72576i) q^{87} +(6.74037 - 1.80608i) q^{88} +(0.599649 + 2.23792i) q^{89} +(3.49185 + 12.5772i) q^{90} +(23.7085 + 23.7085i) q^{92} +(-9.36630 - 5.40763i) q^{93} +(-3.99098 - 2.30419i) q^{94} +(0.110383 + 12.2463i) q^{95} +(-5.28585 + 5.28585i) q^{96} +(-0.441485 - 0.764675i) q^{97} +(8.27401 + 14.3310i) q^{98} +(-3.14277 + 3.14277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 4 q^{3} - 80 q^{4} - 12 q^{10} - 128 q^{12} - 80 q^{16} + 8 q^{17} - 24 q^{22} + 36 q^{23} + 96 q^{25} - 128 q^{27} - 4 q^{30} - 80 q^{35} - 56 q^{38} - 48 q^{40} + 56 q^{42} + 76 q^{43} + 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) $ 144 * q + 4 * q^3 - 80 * q^4 - 12 * q^10 - 128 * q^12 - 80 * q^16 + 8 * q^17 - 24 * q^22 + 36 * q^23 + 96 * q^25 - 128 * q^27 - 4 * q^30 - 80 * q^35 - 56 * q^38 - 48 * q^40 + 56 * q^42 + 76 * q^43 + 76 * q^48 + 8 * q^49 - 32 * q^53 - 12 * q^55 - 8 * q^61 + 148 * q^62 + 240 * q^64 + 80 * q^66 + 48 * q^68 - 40 * q^69 - 164 * q^75 - 344 * q^77 - 16 * q^81 + 44 * q^82 - 20 * q^87 + 124 * q^88 + 600 * q^90 - 8 * q^92 - 92 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.18621	+	2.05458i	−0.838777	+	1.45280i	0.0521412	+	0.998640i	$0.483395\pi$
$2$	−1.18621	+	2.05458i	−0.838777	+	1.45280i	−0.890918	+	0.454164i	$0.849938\pi$
$3$	0.604804	+	2.25716i	0.349184	+	1.30317i	0.887648	+	0.460522i	$0.152338\pi$
$3$	0.604804	+	2.25716i	0.349184	+	1.30317i	−0.538465	+	0.842648i	$0.680995\pi$
$4$	−1.81419	−	3.14226i	−0.907093	−	1.57113i
$5$	−2.15457	+	0.598181i	−0.963554	+	0.267515i
$5$	−2.15457	+	0.598181i	−0.963554	+	0.267515i
$6$	−5.35492	−	1.43485i	−2.18614	−	0.585774i
$7$	−3.23750	+	1.86917i	−1.22366	+	0.706479i	−0.965696	−	0.259676i	$-0.916384\pi$
$7$	−3.23750	+	1.86917i	−1.22366	+	0.706479i	−0.257962	+	0.966155i	$0.583051\pi$
$8$	3.86318			1.36584
$9$	−2.13090	+	1.23027i	−0.710299	+	0.410091i
$10$	1.32677	−	5.13630i	0.419560	−	1.62424i
$11$	1.74477	−	0.467511i	0.526069	−	0.140960i	0.0139966	−	0.999902i	$-0.495545\pi$
$11$	1.74477	−	0.467511i	0.526069	−	0.140960i	0.512072	+	0.858942i	$0.328878\pi$
$12$	5.99536	−	5.99536i	1.73071	−	1.73071i
$13$		0			0
$13$		0			0
$14$		−	8.86890i		−	2.37031i
$15$	−2.65328	−	4.50143i	−0.685074	−	1.16226i
$16$	−0.954169	+	1.65267i	−0.238542	+	0.413167i
$17$	−0.372153	−	0.0997182i	−0.0902604	−	0.0241852i	0.213406	−	0.976964i	$-0.431544\pi$
$17$	−0.372153	−	0.0997182i	−0.0902604	−	0.0241852i	−0.303667	+	0.952778i	$0.598211\pi$
$18$		−	5.83745i		−	1.37590i
$19$	1.41754	−	5.29032i	0.325205	−	1.21368i	−0.588901	−	0.808205i	$-0.700439\pi$
$19$	1.41754	−	5.29032i	0.325205	−	1.21368i	0.914106	−	0.405476i	$-0.132894\pi$
$20$	5.78843	+	5.68502i	1.29433	+	1.27121i
$21$	−6.17706	−	6.17706i	−1.34794	−	1.34794i
$22$	−1.10913	+	4.13933i	−0.236468	+	0.882509i
$23$	−8.92587	+	2.39168i	−1.86117	+	0.498699i	−0.999955	−	0.00953735i	$-0.996964\pi$
$23$	−8.92587	+	2.39168i	−1.86117	+	0.498699i	−0.861217	+	0.508237i	$0.830297\pi$
$24$	2.33647	+	8.71981i	0.476929	+	1.77992i
$25$	4.28436	−	2.57765i	0.856872	−	0.515529i
$26$		0			0
$27$	0.891365	+	0.891365i	0.171543	+	0.171543i
$28$	11.7468	+	6.78204i	2.21994	+	1.28169i
$29$	−0.662140	−	0.382287i	−0.122956	−	0.0709889i	0.437260	−	0.899335i	$-0.355949\pi$
$29$	−0.662140	−	0.382287i	−0.122956	−	0.0709889i	−0.560217	+	0.828346i	$0.689282\pi$
$30$	12.3959	−	0.111731i	2.26317	−	0.0203992i
$31$	−3.27268	+	3.27268i	−0.587792	+	0.587792i	−0.937033	−	0.349241i	$-0.886439\pi$
$31$	−3.27268	+	3.27268i	−0.587792	+	0.587792i	0.349241	+	0.937033i	$0.386439\pi$
$32$	1.59949	+	2.77040i	0.282753	+	0.489742i
$33$	2.11049	+	3.65548i	0.367389	+	0.636337i
$34$	0.646330	−	0.646330i	0.110845	−	0.110845i
$35$	5.85732	−	5.96387i	0.990067	−	1.00808i
$36$	7.73169	+	4.46389i	1.28861	+	0.743982i
$37$	−1.00131	−	0.578108i	−0.164615	−	0.0950403i	0.415429	−	0.909625i	$-0.363631\pi$
$37$	−1.00131	−	0.578108i	−0.164615	−	0.0950403i	−0.580044	+	0.814585i	$0.696965\pi$
$38$	9.18786	+	9.18786i	1.49047	+	1.49047i
$39$		0			0
$40$	−8.32350	+	2.31088i	−1.31606	+	0.365382i
$41$	0.789472	+	2.94635i	0.123295	+	0.460142i	0.999773	−	0.0212988i	$-0.00678014\pi$
$41$	0.789472	+	2.94635i	0.123295	+	0.460142i	−0.876478	+	0.481441i	$0.840113\pi$
$42$	20.0185	−	5.36394i	3.08892	−	0.827675i
$43$	0.489998	−	1.82870i	0.0747240	−	0.278874i	−0.918447	−	0.395545i	$-0.870556\pi$
$43$	0.489998	−	1.82870i	0.0747240	−	0.278874i	0.993171	+	0.116671i	$0.0372224\pi$
$44$	−4.63438	−	4.63438i	−0.698660	−	0.698660i
$45$	3.85525	−	3.92538i	0.574706	−	0.585161i
$46$	5.67406	−	21.1759i	0.836595	−	3.12222i
$47$			1.94248i			0.283340i	0.989914	+	0.141670i	$0.0452472\pi$
$47$			1.94248i			0.283340i	−0.989914	+	0.141670i	$0.954753\pi$
$48$	−4.30742	−	1.15417i	−0.621723	−	0.166590i
$49$	3.48758	−	6.04067i	0.498226	−	0.862953i
$50$	0.213823	+	11.8602i	0.0302391	+	1.67728i
$51$		−	0.900318i		−	0.126070i
$52$		0			0
$53$	−1.18715	+	1.18715i	−0.163068	+	0.163068i	−0.783924	−	0.620856i	$-0.786785\pi$
$53$	−1.18715	+	1.18715i	−0.163068	+	0.163068i	0.620856	+	0.783924i	$0.286785\pi$
$54$	−2.88872	+	0.774031i	−0.393105	+	0.105332i
$55$	−3.47958	+	2.05098i	−0.469187	+	0.276553i
$56$	−12.5070	+	7.22094i	−1.67132	+	0.964938i
$57$	12.7984			1.69519
$58$	1.57087	−	0.906945i	0.206266	−	0.119088i
$59$	−6.15548	−	1.64935i	−0.801375	−	0.214728i	−0.165187	−	0.986262i	$-0.552823\pi$
$59$	−6.15548	−	1.64935i	−0.801375	−	0.214728i	−0.636187	+	0.771535i	$0.719490\pi$
$60$	−9.33112	+	16.5037i	−1.20464	+	2.13062i
$61$	1.85832	+	3.21870i	0.237933	+	0.412113i	0.960121	−	0.279584i	$-0.0901966\pi$
$61$	1.85832	+	3.21870i	0.237933	+	0.412113i	−0.722188	+	0.691697i	$0.756863\pi$
$62$	−2.84189	−	10.6061i	−0.360920	−	1.34697i
$63$	4.59918	−	7.96601i	0.579442	−	1.00362i
$64$	−11.4060			−1.42575
$65$		0			0
$66$	−10.0139			−1.23263
$67$	5.52807	−	9.57490i	0.675361	−	1.16976i	−0.301002	−	0.953623i	$-0.597321\pi$
$67$	5.52807	−	9.57490i	0.675361	−	1.16976i	0.976363	−	0.216136i	$-0.0693455\pi$
$68$	0.361815	+	1.35031i	0.0438765	+	0.163749i
$69$	−10.7968	−	18.7006i	−1.29978	−	2.25129i
$70$	5.30521	+	19.1087i	0.634094	+	2.28393i
$71$	10.7163	+	2.87143i	1.27179	+	0.340776i	0.830717	−	0.556695i	$-0.187931\pi$
$71$	10.7163	+	2.87143i	1.27179	+	0.340776i	0.441075	+	0.897470i	$0.354597\pi$
$72$	−8.23204	+	4.75277i	−0.970155	+	0.560119i
$73$	−4.49691			−0.526323			−0.263161	−	0.964752i	$-0.584765\pi$
$73$	−4.49691			−0.526323			−0.263161	+	0.964752i	$0.584765\pi$
$74$	2.37553	−	1.37151i	0.276150	−	0.159435i
$75$	8.40935	+	8.11150i	0.971028	+	0.936636i
$76$	−19.1952	+	5.14335i	−2.20184	+	0.589982i
$77$	−4.77484	+	4.77484i	−0.544144	+	0.544144i
$78$		0			0
$79$		−	7.15052i		−	0.804496i	−0.915531	−	0.402248i	$-0.868229\pi$
$79$		−	7.15052i		−	0.804496i	0.915531	−	0.402248i	$-0.131771\pi$
$80$	1.06723	−	4.13156i	0.119320	−	0.461923i
$81$	−5.16367	+	8.94374i	−0.573741	+	0.993749i
$82$	−6.98997	−	1.87296i	−0.771914	−	0.206834i
$83$		−	11.4388i		−	1.25557i	−0.778388	−	0.627783i	$-0.783962\pi$
$83$		−	11.4388i		−	1.25557i	0.778388	−	0.627783i	$-0.216038\pi$
$84$	−8.20360	+	30.6163i	−0.895087	+	3.34051i
$85$	0.861480	−	0.00776503i	0.0934407	−	0.000842235i
$86$	3.17596	+	3.17596i	0.342472	+	0.342472i
$87$	0.462417	−	1.72576i	0.0495763	−	0.185021i
$88$	6.74037	−	1.80608i	0.718526	−	0.192529i
$89$	0.599649	+	2.23792i	0.0635626	+	0.237219i	0.990397	−	0.138251i	$-0.0441480\pi$
$89$	0.599649	+	2.23792i	0.0635626	+	0.237219i	−0.926835	+	0.375470i	$0.877481\pi$
$90$	3.49185	+	12.5772i	0.368074	+	1.32575i
$91$		0			0
$92$	23.7085	+	23.7085i	2.47178	+	2.47178i
$93$	−9.36630	−	5.40763i	−0.971240	−	0.560746i
$94$	−3.99098	−	2.30419i	−0.411638	−	0.237659i
$95$	0.110383	+	12.2463i	0.0113251	+	1.25644i
$96$	−5.28585	+	5.28585i	−0.539485	+	0.539485i
$97$	−0.441485	−	0.764675i	−0.0448260	−	0.0776409i	0.842742	−	0.538318i	$-0.180940\pi$
$97$	−0.441485	−	0.764675i	−0.0448260	−	0.0776409i	−0.887568	+	0.460677i	$0.847607\pi$
$98$	8.27401	+	14.3310i	0.835801	+	1.44765i
$99$	−3.14277	+	3.14277i	−0.315860	+	0.315860i
$100$	−15.8723	−	8.78625i	−1.58723	−	0.878625i
$101$	6.87788	+	3.97094i	0.684374	+	0.395124i	0.801501	−	0.597993i	$-0.204035\pi$
$101$	6.87788	+	3.97094i	0.684374	+	0.395124i	−0.117127	+	0.993117i	$0.537368\pi$
$102$	1.84977	+	1.06797i	0.183155	+	0.105744i
$103$	−10.7428	−	10.7428i	−1.05852	−	1.05852i	−0.998178	−	0.0603388i	$-0.980782\pi$
$103$	−10.7428	−	10.7428i	−1.05852	−	1.05852i	−0.0603388	−	0.998178i	$-0.519218\pi$
$104$		0			0
$105$	17.0039	+	9.61392i	1.65941	+	0.938222i
$106$	−1.03088	−	3.84731i	−0.100128	−	0.373684i
$107$	−10.0926	+	2.70430i	−0.975686	+	0.261434i	−0.711227	−	0.702963i	$-0.751860\pi$
$107$	−10.0926	+	2.70430i	−0.975686	+	0.261434i	−0.264459	+	0.964397i	$0.585193\pi$
$108$	1.18380	−	4.41800i	0.113911	−	0.425123i
$109$	−4.13475	−	4.13475i	−0.396037	−	0.396037i	0.480796	−	0.876833i	$-0.340348\pi$
$109$	−4.13475	−	4.13475i	−0.396037	−	0.396037i	−0.876833	+	0.480796i	$0.840348\pi$
$110$	−0.0863677	−	9.58195i	−0.00823484	−	0.913603i
$111$	0.699283	−	2.60976i	0.0663730	−	0.247707i
$112$		−	7.13401i		−	0.674101i
$113$	14.1646	+	3.79539i	1.33249	+	0.357040i	0.853644	−	0.520857i	$-0.174388\pi$
$113$	14.1646	+	3.79539i	1.33249	+	0.357040i	0.478849	+	0.877897i	$0.341054\pi$
$114$	−15.1816	+	26.2953i	−1.42189	+	2.46278i
$115$	17.8008	−	10.4923i	1.65993	−	0.978414i
$116$			2.77416i			0.257574i
$117$		0			0
$118$	10.6904	−	10.6904i	0.984132	−	0.984132i
$119$	1.39123	−	0.372780i	0.127534	−	0.0341727i
$120$	−10.2501	−	17.3898i	−0.935702	−	1.58747i
$121$	−6.70061	+	3.86860i	−0.609146	+	0.351691i
$122$	−8.81743			−0.798292
$123$	−6.17290	+	3.56393i	−0.556592	+	0.321348i
$124$	16.2209	+	4.34637i	1.45668	+	0.390316i
$125$	−7.68906	+	8.11655i	−0.687730	+	0.725966i
$126$	10.9112	+	18.8987i	0.972046	+	1.68363i
$127$	−1.82032	−	6.79351i	−0.161527	−	0.602827i	−0.998458	−	0.0555178i	$-0.982319\pi$
$127$	−1.82032	−	6.79351i	−0.161527	−	0.602827i	0.836931	−	0.547309i	$-0.184348\pi$
$128$	10.3309	−	17.8937i	0.913134	−	1.58159i
$129$	4.42401			0.389513
$130$		0			0
$131$	−9.34748			−0.816693			−0.408347	−	0.912827i	$-0.633895\pi$
$131$	−9.34748			−0.816693			−0.408347	+	0.912827i	$0.633895\pi$
$132$	7.65764	−	13.2634i	0.666512	−	1.15443i
$133$	5.29923	+	19.7770i	0.459501	+	1.71488i
$134$	13.1149	+	22.7157i	1.13295	+	1.96233i
$135$	−2.45371	−	1.38731i	−0.211181	−	0.119401i
$136$	−1.43770	−	0.385229i	−0.123281	−	0.0330331i
$137$	11.8630	−	6.84910i	1.01352	−	0.585158i	0.101303	−	0.994856i	$-0.467699\pi$
$137$	11.8630	−	6.84910i	1.01352	−	0.585158i	0.912222	+	0.409697i	$0.134366\pi$
$138$	51.2290			4.36090
$139$	−7.78210	+	4.49300i	−0.660069	+	0.381091i	−0.792303	−	0.610127i	$-0.791118\pi$
$139$	−7.78210	+	4.49300i	−0.660069	+	0.381091i	0.132234	+	0.991219i	$0.457785\pi$
$140$	−29.3663	−	7.58566i	−2.48190	−	0.641105i
$141$	−4.38449	+	1.17482i	−0.369241	+	0.0989377i
$142$	−18.6113	+	18.6113i	−1.56183	+	1.56183i
$143$		0			0
$144$		−	4.69556i		−	0.391297i
$145$	1.65531	+	0.427585i	0.137466	+	0.0355090i
$146$	5.33427	−	9.23923i	0.441467	−	0.764644i
$147$	15.7441	+	4.21861i	1.29855	+	0.347945i
$148$			4.19518i			0.344842i
$149$	3.28972	−	12.2774i	0.269505	−	1.00581i	−0.689930	−	0.723876i	$-0.742359\pi$
$149$	3.28972	−	12.2774i	0.269505	−	1.00581i	0.959435	−	0.281930i	$-0.0909745\pi$
$150$	−26.6409	+	7.65570i	−2.17522	+	0.625086i
$151$	−2.96123	−	2.96123i	−0.240981	−	0.240981i	0.576275	−	0.817256i	$-0.304506\pi$
$151$	−2.96123	−	2.96123i	−0.240981	−	0.240981i	−0.817256	+	0.576275i	$0.804506\pi$
$152$	5.47620	−	20.4374i	0.444178	−	1.65770i
$153$	0.915701	−	0.245361i	0.0740300	−	0.0198363i
$154$	−4.14631	−	15.4742i	−0.334119	−	1.24695i
$155$	5.09358	−	9.00889i	0.409126	−	0.723612i
$156$		0			0
$157$	−13.0366	−	13.0366i	−1.04044	−	1.04044i	−0.999147	−	0.0412907i	$-0.986853\pi$
$157$	−13.0366	−	13.0366i	−1.04044	−	1.04044i	−0.0412907	−	0.999147i	$-0.513147\pi$
$158$	14.6913	+	8.48201i	1.16878	+	0.674793i
$159$	−3.39759	−	1.96160i	−0.269446	−	0.155565i
$160$	−5.10342	−	5.01224i	−0.403461	−	0.396252i
$161$	24.4270	−	24.4270i	1.92512	−	1.92512i
$162$	−12.2504	−	21.2183i	−0.962482	−	1.66707i
$163$	−7.92191	−	13.7211i	−0.620492	−	1.07472i	−0.989394	−	0.145255i	$-0.953600\pi$
$163$	−7.92191	−	13.7211i	−0.620492	−	1.07472i	0.368903	−	0.929468i	$-0.379734\pi$
$164$	7.82595	−	7.82595i	0.611104	−	0.611104i
$165$	−6.73384	−	6.61353i	−0.524229	−	0.514863i
$166$	23.5018	+	13.5688i	1.82409	+	1.05314i
$167$	−10.8109	−	6.24168i	−0.836573	−	0.482996i	0.0195249	−	0.999809i	$-0.493785\pi$
$167$	−10.8109	−	6.24168i	−0.836573	−	0.482996i	−0.856098	+	0.516814i	$0.827118\pi$
$168$	−23.8631	−	23.8631i	−1.84108	−	1.84108i
$169$		0			0
$170$	−1.00594	+	1.77919i	−0.0771523	+	0.136457i
$171$	3.48792	+	13.0171i	0.266728	+	0.995441i
$172$	−6.63520	+	1.77790i	−0.505929	+	0.135563i
$173$	4.18301	−	15.6112i	0.318029	−	1.18690i	−0.603108	−	0.797660i	$-0.706071\pi$
$173$	4.18301	−	15.6112i	0.318029	−	1.18690i	0.921137	−	0.389239i	$-0.127262\pi$
$174$	2.99719	+	2.99719i	0.227216	+	0.227216i
$175$	−9.05254	+	16.3533i	−0.684307	+	1.23619i
$176$	−0.892168	+	3.32962i	−0.0672497	+	0.250979i
$177$		−	14.8914i		−	1.11931i
$178$	−5.30928	−	1.42262i	−0.397947	−	0.106630i
$179$	−9.22405	+	15.9765i	−0.689438	+	1.19414i	0.282582	+	0.959243i	$0.408809\pi$
$179$	−9.22405	+	15.9765i	−0.689438	+	1.19414i	−0.972020	+	0.234898i	$0.924524\pi$
$180$	−19.3287	−	4.99283i	−1.44068	−	0.372143i
$181$		−	2.18983i		−	0.162769i	−0.996683	−	0.0813844i	$-0.974066\pi$
$181$		−	2.18983i		−	0.162769i	0.996683	−	0.0813844i	$-0.0259342\pi$
$182$		0			0
$183$	−6.14120	+	6.14120i	−0.453971	+	0.453971i
$184$	−34.4822	+	9.23949i	−2.54206	+	0.681144i
$185$	2.50321	+	0.646609i	0.184040	+	0.0475396i
$186$	22.2208	−	12.8292i	1.62931	−	0.940681i
$187$	−0.695942			−0.0508923
$188$	6.10379	−	3.52402i	0.445164	−	0.257016i
$189$	−4.55190	−	1.21968i	−0.331102	−	0.0887185i
$190$	−25.2919	−	14.2999i	−1.83487	−	1.03742i
$191$	−4.07316	−	7.05492i	−0.294724	−	0.510476i	0.680197	−	0.733029i	$-0.261894\pi$
$191$	−4.07316	−	7.05492i	−0.294724	−	0.510476i	−0.974921	+	0.222553i	$0.928561\pi$
$192$	−6.89839	−	25.7451i	−0.497849	−	1.85800i
$193$	−11.6235	+	20.1326i	−0.836681	+	1.44917i	0.0559740	+	0.998432i	$0.482174\pi$
$193$	−11.6235	+	20.1326i	−0.836681	+	1.44917i	−0.892655	+	0.450741i	$0.851160\pi$
$194$	2.09477			0.150396
$195$		0			0
$196$	−25.3085			−1.80775
$197$	−11.0344	+	19.1122i	−0.786172	+	1.36169i	0.142125	+	0.989849i	$0.454606\pi$
$197$	−11.0344	+	19.1122i	−0.786172	+	1.36169i	−0.928297	+	0.371840i	$0.878727\pi$
$198$	−2.72907	−	10.1850i	−0.193947	−	0.723819i
$199$	4.06851	+	7.04686i	0.288409	+	0.499538i	0.973430	−	0.228984i	$-0.0735405\pi$
$199$	4.06851	+	7.04686i	0.288409	+	0.499538i	−0.685021	+	0.728523i	$0.740207\pi$
$200$	16.5513	−	9.95792i	1.17035	−	0.704131i
$201$	24.9554	+	6.68679i	1.76022	+	0.471650i
$202$	−16.3172	+	9.42075i	−1.14807	+	0.662841i
$203$	2.85823			0.200609
$204$	−2.82904	+	1.63335i	−0.198072	+	0.114357i
$205$	−3.46342	−	5.87587i	−0.241896	−	0.410389i
$206$	34.8150	−	9.32865i	2.42568	−	0.649958i
$207$	16.0777	−	16.0777i	1.11748	−	1.11748i
$208$		0			0
$209$		−	9.89312i		−	0.684321i
$210$	−39.9227	+	23.5317i	−2.75493	+	1.62384i
$211$	12.3867	−	21.4544i	0.852737	−	1.47698i	−0.0259913	−	0.999662i	$-0.508274\pi$
$211$	12.3867	−	21.4544i	0.852737	−	1.47698i	0.878729	−	0.477322i	$-0.158392\pi$
$212$	5.88407	+	1.57663i	0.404120	+	0.108284i
$213$			25.9250i			1.77635i
$214$	6.41572	−	23.9438i	0.438570	−	1.63676i
$215$	0.0381560	+	4.23317i	0.00260222	+	0.288700i
$216$	3.44350	+	3.44350i	0.234301	+	0.234301i
$217$	4.47810	−	16.7125i	0.303993	−	1.13452i
$218$	13.3998	−	3.59047i	0.907551	−	0.243177i
$219$	−2.71974	−	10.1502i	−0.183783	−	0.685889i
$220$	12.7573	+	7.21291i	0.860098	+	0.486295i
$221$		0			0
$222$	4.53245	+	4.53245i	0.304198	+	0.304198i
$223$	−25.5668	−	14.7610i	−1.71208	−	0.988469i	−0.931752	−	0.363096i	$-0.881720\pi$
$223$	−25.5668	−	14.7610i	−1.71208	−	0.988469i	−0.780326	−	0.625373i	$-0.784947\pi$
$224$	−10.3567	−	5.97944i	−0.691986	−	0.399518i
$225$	−5.95832	+	10.7636i	−0.397221	+	0.717576i
$226$	−24.6001	+	24.6001i	−1.63637	+	1.63637i
$227$	3.93339	+	6.81284i	0.261068	+	0.452184i	0.966526	−	0.256568i	$-0.0825918\pi$
$227$	3.93339	+	6.81284i	0.261068	+	0.452184i	−0.705458	+	0.708752i	$0.749259\pi$
$228$	−23.2187	−	40.2160i	−1.53770	−	2.66337i
$229$	12.4410	−	12.4410i	0.822125	−	0.822125i	−0.164288	−	0.986412i	$-0.552533\pi$
$229$	12.4410	−	12.4410i	0.822125	−	0.822125i	0.986412	+	0.164288i	$0.0525326\pi$
$230$	0.441838	+	49.0191i	0.0291339	+	3.23222i
$231$	−13.6654	−	7.88973i	−0.899118	−	0.519106i
$232$	−2.55797	−	1.47684i	−0.167939	−	0.0969595i
$233$	1.52992	+	1.52992i	0.100228	+	0.100228i	0.755443	−	0.655214i	$-0.227422\pi$
$233$	1.52992	+	1.52992i	0.100228	+	0.100228i	−0.655214	+	0.755443i	$0.727422\pi$
$234$		0			0
$235$	−1.16196	−	4.18522i	−0.0757976	−	0.273013i
$236$	5.98447	+	22.3344i	0.389556	+	1.45384i
$237$	16.1398	−	4.32466i	1.04840	−	0.280917i
$238$	−0.884391	+	3.30059i	−0.0573265	+	0.213946i
$239$	7.05936	+	7.05936i	0.456632	+	0.456632i	0.897548	−	0.440916i	$-0.145346\pi$
$239$	7.05936	+	7.05936i	0.456632	+	0.456632i	−0.440916	+	0.897548i	$0.645346\pi$
$240$	9.97105	−	0.0898749i	0.643628	−	0.00580140i
$241$	−3.75087	+	13.9984i	−0.241615	+	0.901719i	0.733440	+	0.679755i	$0.237914\pi$
$241$	−3.75087	+	13.9984i	−0.241615	+	0.901719i	−0.975055	+	0.221965i	$0.928753\pi$
$242$		−	18.3559i		−	1.17996i
$243$	−19.6576	−	5.26723i	−1.26103	−	0.337893i
$244$	6.74268	−	11.6787i	0.431656	−	0.747649i
$245$	−3.90084	+	15.1013i	−0.249215	+	0.964785i
$246$		−	16.9102i		−	1.07816i
$247$		0			0
$248$	−12.6430	+	12.6430i	−0.802829	+	0.802829i
$249$	25.8191	−	6.91820i	1.63622	−	0.438423i
$250$	−7.55522	−	25.4257i	−0.477834	−	1.60806i
$251$	−15.3843	+	8.88214i	−0.971050	+	0.560636i	−0.899556	−	0.436805i	$-0.856110\pi$
$251$	−15.3843	+	8.88214i	−0.971050	+	0.560636i	−0.0714936	+	0.997441i	$0.522777\pi$
$252$	−33.3751			−2.10243
$253$	−14.4555	+	8.34588i	−0.908808	+	0.524701i
$254$	16.1171	+	4.31855i	1.01127	+	0.270970i
$255$	0.538553	+	1.93980i	0.0337255	+	0.121475i
$256$	13.1033	+	22.6956i	0.818955	+	1.41847i
$257$	−2.33322	−	8.70771i	−0.145543	−	0.543172i	−0.999731	−	0.0232081i	$-0.992612\pi$
$257$	−2.33322	−	8.70771i	−0.145543	−	0.543172i	0.854188	−	0.519964i	$-0.174055\pi$
$258$	−5.24781	+	9.08947i	−0.326714	+	0.565885i
$259$	4.32232			0.268576
$260$		0			0
$261$	1.88127			0.116448
$262$	11.0881	−	19.2051i	0.685023	−	1.18650i
$263$	−1.10325	−	4.11740i	−0.0680295	−	0.253890i	0.923533	−	0.383519i	$-0.125288\pi$
$263$	−1.10325	−	4.11740i	−0.0680295	−	0.253890i	−0.991563	+	0.129629i	$0.958621\pi$
$264$	8.15321	+	14.1218i	0.501795	+	0.869135i
$265$	1.84768	−	3.26794i	0.113502	−	0.200748i
$266$	−46.9193	−	12.5720i	−2.87681	−	0.770838i
$267$	−4.68867	+	2.70700i	−0.286942	+	0.165666i
$268$	−40.1158			−2.45046
$269$	−1.55678	+	0.898805i	−0.0949183	+	0.0548011i	−0.546708	−	0.837323i	$-0.684119\pi$
$269$	−1.55678	+	0.898805i	−0.0949183	+	0.0548011i	0.451790	+	0.892125i	$0.350786\pi$
$270$	5.76095	−	3.39568i	0.350600	−	0.206655i
$271$	−2.84859	+	0.763276i	−0.173039	+	0.0463657i	−0.344298	−	0.938860i	$-0.611883\pi$
$271$	−2.84859	+	0.763276i	−0.173039	+	0.0463657i	0.171259	+	0.985226i	$0.445216\pi$
$272$	0.519898	−	0.519898i	0.0315235	−	0.0315235i
$273$		0			0
$274$			32.4979i			1.96327i
$275$	6.27016	−	6.50039i	0.378105	−	0.391989i
$276$	−39.1748	+	67.8527i	−2.35804	+	4.08425i
$277$	27.5242	+	7.37510i	1.65377	+	0.443127i	0.960665	−	0.277709i	$-0.0895752\pi$
$277$	27.5242	+	7.37510i	1.65377	+	0.443127i	0.693106	+	0.720836i	$0.256242\pi$
$278$		−	21.3186i		−	1.27860i
$279$	2.94746	−	11.0001i	0.176460	−	0.658556i
$280$	22.6279	−	23.0395i	1.35227	−	1.37687i
$281$	2.57874	+	2.57874i	0.153835	+	0.153835i	0.779828	−	0.625993i	$-0.215306\pi$
$281$	2.57874	+	2.57874i	0.153835	+	0.153835i	−0.625993	+	0.779828i	$0.715306\pi$
$282$	2.78717	−	10.4018i	0.165973	−	0.619421i
$283$	7.54151	−	2.02074i	0.448296	−	0.120121i	−0.0276057	−	0.999619i	$-0.508788\pi$
$283$	7.54151	−	2.02074i	0.448296	−	0.120121i	0.475902	+	0.879498i	$0.342122\pi$
$284$	−10.4186	−	38.8827i	−0.618230	−	2.30727i
$285$	−27.5751	+	7.65576i	−1.63341	+	0.453488i
$286$		0			0
$287$	−8.06314	−	8.06314i	−0.475952	−	0.475952i
$288$	−6.81670	−	3.93563i	−0.401678	−	0.231909i
$289$	−14.5939	−	8.42578i	−0.858463	−	0.495634i
$290$	−2.84204	+	2.89374i	−0.166891	+	0.169927i
$291$	1.45898	−	1.45898i	0.0855269	−	0.0855269i
$292$	8.15822	+	14.1305i	0.477424	+	0.826922i
$293$	11.2799	+	19.5374i	0.658979	+	1.14139i	0.980880	+	0.194612i	$0.0623449\pi$
$293$	11.2799	+	19.5374i	0.658979	+	1.14139i	−0.321901	+	0.946773i	$0.604322\pi$
$294$	−27.3432	+	27.3432i	−1.59469	+	1.59469i
$295$	14.2490	−	0.128435i	0.829610	−	0.00747776i
$296$	−3.86825	−	2.23333i	−0.224837	−	0.129810i
$297$	1.97195	+	1.13851i	0.114424	+	0.0660629i
$298$	21.3226	+	21.3226i	1.23518	+	1.23518i
$299$		0			0
$300$	10.2323	−	41.1402i	0.590765	−	2.37523i
$301$	1.83178	+	6.83629i	0.105582	+	0.394037i
$302$	9.59671	−	2.57143i	0.552229	−	0.147969i
$303$	−4.80328	+	17.9261i	−0.275941	+	1.02983i
$304$	7.39057	+	7.39057i	0.423878	+	0.423878i
$305$	−5.92925	−	5.82332i	−0.339508	−	0.333442i
$306$	−0.582100	+	2.17243i	−0.0332764	+	0.124189i
$307$		−	20.4085i		−	1.16477i	−0.812912	−	0.582387i	$-0.802119\pi$
$307$		−	20.4085i		−	1.16477i	0.812912	−	0.582387i	$-0.197881\pi$
$308$	23.6662	+	6.34135i	1.34851	+	0.361332i
$309$	17.7509	−	30.7454i	1.00981	−	1.74904i
$310$	12.4674	+	21.1516i	0.708100	+	1.20133i
$311$			21.3762i			1.21213i	0.795413	+	0.606067i	$0.207254\pi$
$311$			21.3762i			1.21213i	−0.795413	+	0.606067i	$0.792746\pi$
$312$		0			0
$313$	−5.22723	+	5.22723i	−0.295461	+	0.295461i	−0.839233	−	0.543772i	$-0.816996\pi$
$313$	−5.22723	+	5.22723i	−0.295461	+	0.295461i	0.543772	+	0.839233i	$0.316996\pi$
$314$	42.2490	−	11.3206i	2.38425	−	0.638857i
$315$	−5.14415	+	19.9145i	−0.289840	+	1.12205i
$316$	−22.4688	+	12.9724i	−1.26397	+	0.729753i
$317$	−25.8830			−1.45373			−0.726867	−	0.686779i	$-0.759024\pi$
$317$	−25.8830			−1.45373			−0.726867	+	0.686779i	$0.759024\pi$
$318$	8.06051	−	4.65374i	0.452011	−	0.260969i
$319$	−1.33401	−	0.357446i	−0.0746901	−	0.0200132i
$320$	24.5751	−	6.82285i	1.37379	−	0.381409i
$321$	−12.2080	−	21.1450i	−0.681387	−	1.18020i
$322$	21.2116	+	79.1627i	1.18207	+	4.41156i
$323$	−1.05508	+	1.82745i	−0.0587063	+	0.101682i
$324$	37.4715			2.08175
$325$		0			0
$326$	37.5882			2.08182
$327$	6.83207	−	11.8335i	0.377814	−	0.654393i
$328$	3.04987	+	11.3823i	0.168401	+	0.628481i
$329$	−3.63083	−	6.28878i	−0.200174	−	0.346711i
$330$	21.5757	−	5.99015i	1.18771	−	0.329747i
$331$	10.1654	+	2.72380i	0.558738	+	0.149714i	0.527127	−	0.849787i	$-0.323269\pi$
$331$	10.1654	+	2.72380i	0.558738	+	0.149714i	0.0316117	+	0.999500i	$0.489936\pi$
$332$	−35.9436	+	20.7520i	−1.97266	+	1.13892i
$333$	2.84492			0.155901
$334$	25.6480	−	14.8079i	1.40340	−	0.810251i
$335$	−6.18310	+	23.9366i	−0.337819	+	1.30780i
$336$	16.1026	−	4.31468i	0.878468	−	0.235385i
$337$	6.67935	−	6.67935i	0.363847	−	0.363847i	−0.501380	−	0.865227i	$-0.667174\pi$
$337$	6.67935	−	6.67935i	0.363847	−	0.363847i	0.865227	+	0.501380i	$0.167174\pi$
$338$		0			0
$339$			34.2672i			1.86114i
$340$	−1.58729	−	2.69291i	−0.0860826	−	0.146044i
$341$	−4.18008	+	7.24011i	−0.226364	+	0.392074i
$342$	−30.8820	−	8.27480i	−1.66991	−	0.447450i
$343$		−	0.0928245i		−	0.00501205i
$344$	1.89295	−	7.06459i	0.102061	−	0.380897i
$345$	34.4488	+	33.8333i	1.85466	+	1.82153i
$346$	27.1125	+	27.1125i	1.45758	+	1.45758i
$347$	−1.84430	+	6.88301i	−0.0990071	+	0.369500i	−0.997596	−	0.0692910i	$-0.977926\pi$
$347$	−1.84430	+	6.88301i	−0.0990071	+	0.369500i	0.898589	+	0.438791i	$0.144593\pi$
$348$	−6.26171	+	1.67782i	−0.335663	+	0.0899406i
$349$	8.44064	+	31.5009i	0.451817	+	1.68620i	0.697281	+	0.716798i	$0.254393\pi$
$349$	8.44064	+	31.5009i	0.451817	+	1.68620i	−0.245464	+	0.969406i	$0.578940\pi$
$350$	−22.8609	−	37.9976i	−1.22197	−	2.03106i
$351$		0			0
$352$	4.08594	+	4.08594i	0.217781	+	0.217781i
$353$	11.1895	+	6.46025i	0.595556	+	0.343844i	0.767291	−	0.641299i	$-0.221604\pi$
$353$	11.1895	+	6.46025i	0.595556	+	0.343844i	−0.171736	+	0.985143i	$0.554937\pi$
$354$	30.5955	+	17.6643i	1.62613	+	0.938849i
$355$	−24.8067	+	0.223597i	−1.31660	+	0.0118673i
$356$	5.94425	−	5.94425i	0.315045	−	0.315045i
$357$	1.68285	+	2.91478i	0.0890657	+	0.154266i
$358$	−21.8833	−	37.9030i	−1.15657	−	2.00324i
$359$	−12.5304	+	12.5304i	−0.661330	+	0.661330i	−0.955693	−	0.294364i	$-0.904892\pi$
$359$	−12.5304	+	12.5304i	−0.661330	+	0.661330i	0.294364	+	0.955693i	$0.404892\pi$
$360$	14.8935	−	15.1644i	0.784957	−	0.799236i
$361$	−9.52355	−	5.49842i	−0.501239	−	0.289391i
$362$	4.49917	+	2.59760i	0.236471	+	0.136527i
$363$	−12.7846	−	12.7846i	−0.671017	−	0.671017i
$364$		0			0
$365$	9.68891	−	2.68996i	0.507140	−	0.140799i
$366$	−5.33281	−	19.9023i	−0.278751	−	1.04031i
$367$	33.6660	−	9.02077i	1.75735	−	0.470880i	0.771179	−	0.636618i	$-0.219667\pi$
$367$	33.6660	−	9.02077i	1.75735	−	0.470880i	0.986170	+	0.165738i	$0.0530006\pi$
$368$	4.56413	−	17.0336i	0.237922	−	0.887936i
$369$	−5.30710	−	5.30710i	−0.276277	−	0.276277i
$370$	−4.29784	+	4.37602i	−0.223434	+	0.227499i
$371$	1.62442	−	6.06240i	0.0843354	−	0.314744i
$372$			39.2418i			2.03459i
$373$	−14.4253	−	3.86524i	−0.746912	−	0.200135i	−0.134764	−	0.990878i	$-0.543028\pi$
$373$	−14.4253	−	3.86524i	−0.746912	−	0.200135i	−0.612148	+	0.790743i	$0.709694\pi$
$374$	0.825533	−	1.42987i	0.0426873	−	0.0739366i
$375$	−22.9707	−	12.4465i	−1.18620	−	0.642735i
$376$			7.50416i			0.386997i
$377$		0			0
$378$	7.90543	−	7.90543i	0.406611	−	0.406611i
$379$	−31.2859	+	8.38303i	−1.60705	+	0.430607i	−0.947161	−	0.320758i	$-0.896062\pi$
$379$	−31.2859	+	8.38303i	−1.60705	+	0.430607i	−0.659887	+	0.751365i	$0.729396\pi$
$380$	38.2809	−	22.5639i	1.96377	−	1.15751i
$381$	14.2331	−	8.21748i	0.729183	−	0.420994i
$382$	19.3265			0.988829
$383$	−27.9113	+	16.1146i	−1.42620	+	0.823418i	−0.996819	−	0.0797046i	$-0.974602\pi$
$383$	−27.9113	+	16.1146i	−1.42620	+	0.823418i	−0.429383	+	0.903122i	$0.641269\pi$
$384$	46.6371	+	12.4964i	2.37994	+	0.637702i
$385$	7.43152	−	13.1440i	0.378745	−	0.669878i
$386$	−27.5759	−	47.7629i	−1.40358	−	2.43107i
$387$	1.20566	+	4.49960i	0.0612874	+	0.228728i
$388$	−1.60187	+	2.77452i	−0.0813227	+	0.140855i
$389$	−11.7818			−0.597359			−0.298679	−	0.954354i	$-0.596546\pi$
$389$	−11.7818			−0.597359			−0.298679	+	0.954354i	$0.596546\pi$
$390$		0			0
$391$	3.56028			0.180051
$392$	13.4732	−	23.3362i	0.680498	−	1.17866i
$393$	−5.65339	−	21.0987i	−0.285176	−	1.06429i
$394$	−26.1783	−	45.3422i	−1.31884	−	2.28431i
$395$	4.27730	+	15.4063i	0.215214	+	0.775175i
$396$	15.5770	+	4.17383i	0.782772	+	0.209743i
$397$	7.05618	−	4.07389i	0.354139	−	0.204462i	−0.312367	−	0.949961i	$-0.601122\pi$
$397$	7.05618	−	4.07389i	0.354139	−	0.204462i	0.666507	+	0.745499i	$0.267789\pi$
$398$	−19.3044			−0.967642
$399$	−41.4348	+	23.9224i	−2.07433	+	1.19762i
$400$	0.171996	+	9.54014i	0.00859978	+	0.477007i
$401$	15.9505	−	4.27393i	0.796531	−	0.213430i	0.162471	−	0.986713i	$-0.448054\pi$
$401$	15.9505	−	4.27393i	0.796531	−	0.213430i	0.634060	+	0.773284i	$0.281387\pi$
$402$	−43.3409	+	43.3409i	−2.16165	+	2.16165i
$403$		0			0
$404$		−	28.8161i		−	1.43366i
$405$	5.77553	−	22.3588i	0.286988	−	1.11102i
$406$	−3.39047	+	5.87246i	−0.168266	+	0.291445i
$407$	−2.01733	−	0.540543i	−0.0999955	−	0.0267937i
$408$		−	3.47809i		−	0.172191i
$409$	−1.09321	+	4.07993i	−0.0540560	+	0.201740i	−0.987673	−	0.156534i	$-0.949968\pi$
$409$	−1.09321	+	4.07993i	−0.0540560	+	0.201740i	0.933617	+	0.358274i	$0.116635\pi$
$410$	16.1808	−	0.145847i	0.799111	−	0.00720286i
$411$	22.6343	+	22.6343i	1.11647	+	1.11647i
$412$	−14.2672	+	53.2460i	−0.702895	+	2.62324i
$413$	23.0112	−	6.16584i	1.13231	−	0.303401i
$414$	13.9613	+	52.1043i	0.686161	+	2.56079i
$415$	6.84245	+	24.6456i	0.335882	+	1.20981i
$416$		0			0
$417$	−14.8481	−	14.8481i	−0.727112	−	0.727112i
$418$	20.3261	+	11.7353i	0.994184	+	0.573993i
$419$	−14.7910	−	8.53958i	−0.722587	−	0.417186i	0.0931173	−	0.995655i	$-0.470317\pi$
$419$	−14.7910	−	8.53958i	−0.722587	−	0.417186i	−0.815704	+	0.578470i	$0.803650\pi$
$420$	−0.638812	−	70.8722i	−0.0311709	−	3.45821i
$421$	9.26544	−	9.26544i	0.451570	−	0.451570i	−0.444305	−	0.895875i	$-0.646549\pi$
$421$	9.26544	−	9.26544i	0.451570	−	0.451570i	0.895875	+	0.444305i	$0.146549\pi$
$422$	29.3865	+	50.8989i	1.43051	+	2.47772i
$423$	−2.38979	−	4.13923i	−0.116195	−	0.201256i
$424$	−4.58619	+	4.58619i	−0.222725	+	0.222725i
$425$	−1.85148	+	0.532051i	−0.0898098	+	0.0258083i
$426$	−53.2649	−	30.7525i	−2.58070	−	1.48997i
$427$	−12.0326	−	6.94703i	−0.582299	−	0.336190i
$428$	26.8074	+	26.8074i	1.29578	+	1.29578i
$429$		0			0
$430$	−8.74262	−	4.94303i	−0.421607	−	0.238374i
$431$	−2.77316	−	10.3496i	−0.133578	−	0.498521i	0.866421	−	0.499314i	$-0.166414\pi$
$431$	−2.77316	−	10.3496i	−0.133578	−	0.498521i	−1.00000		0.000792423i	$0.999748\pi$
$432$	−2.32364	+	0.622619i	−0.111796	+	0.0299558i
$433$	1.32163	−	4.93240i	0.0635136	−	0.237036i	−0.926870	−	0.375381i	$-0.877512\pi$
$433$	1.32163	−	4.93240i	0.0635136	−	0.237036i	0.990384	+	0.138345i	$0.0441784\pi$
$434$	29.0251	+	29.0251i	1.39325	+	1.39325i
$435$	0.0360083	+	3.99489i	0.00172646	+	0.191540i
$436$	−5.49126	+	20.4937i	−0.262984	+	0.981468i
$437$			50.6109i			2.42105i
$438$	24.0806	+	6.45237i	1.15061	+	0.308306i
$439$	−10.1196	+	17.5277i	−0.482985	+	0.836554i	−0.999809	−	0.0195376i	$-0.993781\pi$
$439$	−10.1196	+	17.5277i	−0.482985	+	0.836554i	0.516825	+	0.856091i	$0.327114\pi$
$440$	−13.4423	+	7.92329i	−0.640835	+	0.377728i
$441$			17.1627i			0.817273i
$442$		0			0
$443$	2.66083	−	2.66083i	0.126420	−	0.126420i	−0.641066	−	0.767486i	$-0.721508\pi$
$443$	2.66083	−	2.66083i	0.126420	−	0.126420i	0.767486	+	0.641066i	$0.221508\pi$
$444$	−9.46918	+	2.53726i	−0.449387	+	0.120413i
$445$	−2.63067	−	4.46306i	−0.124706	−	0.211569i
$446$	60.6551	−	35.0192i	2.87210	−	1.65821i
$447$	29.7017			1.40484
$448$	36.9269	−	21.3197i	1.74463	−	1.00726i
$449$	−29.7674	−	7.97615i	−1.40481	−	0.376418i	−0.524741	−	0.851262i	$-0.675838\pi$
$449$	−29.7674	−	7.97615i	−1.40481	−	0.376418i	−0.880070	+	0.474844i	$0.842505\pi$
$450$	−15.0469	−	25.0097i	−0.709317	−	1.17897i
$451$	2.75490	+	4.77163i	0.129723	+	0.224687i
$452$	−13.7711	−	51.3944i	−0.647737	−	2.41739i
$453$	4.89300	−	8.47493i	0.229893	−	0.398187i
$454$	−18.6633			−0.875913
$455$		0			0
$456$	49.4426			2.31536
$457$	−5.08990	+	8.81597i	−0.238096	+	0.412394i	−0.960168	−	0.279424i	$-0.909857\pi$
$457$	−5.08990	+	8.81597i	−0.238096	+	0.412394i	0.722072	+	0.691818i	$0.243190\pi$
$458$	10.8033	+	40.3186i	0.504807	+	1.88396i
$459$	−0.242839	−	0.420610i	−0.0113348	−	0.0196324i
$460$	−65.2635	−	36.8996i	−3.04293	−	1.72045i
$461$	−18.6200	−	4.98920i	−0.867218	−	0.232370i	−0.202334	−	0.979317i	$-0.564853\pi$
$461$	−18.6200	−	4.98920i	−0.867218	−	0.232370i	−0.664884	+	0.746946i	$0.731519\pi$
$462$	32.4201	−	18.7177i	1.50832	−	0.870828i
$463$	−16.7929			−0.780432			−0.390216	−	0.920723i	$-0.627600\pi$
$463$	−16.7929			−0.780432			−0.390216	+	0.920723i	$0.627600\pi$
$464$	1.26359	−	0.729533i	0.0586606	−	0.0338677i
$465$	23.4151	+	6.04840i	1.08585	+	0.280488i
$466$	−4.95814	+	1.32853i	−0.229681	+	0.0615430i
$467$	9.75781	−	9.75781i	0.451538	−	0.451538i	−0.444327	−	0.895865i	$-0.646557\pi$
$467$	9.75781	−	9.75781i	0.451538	−	0.451538i	0.895865	+	0.444327i	$0.146557\pi$
$468$		0			0
$469$			41.3316i			1.90851i
$470$	9.97717	+	2.57722i	0.460212	+	0.118878i
$471$	21.5412	−	37.3104i	0.992564	−	1.71917i
$472$	−23.7797	−	6.37175i	−1.09455	−	0.293284i
$473$		−	3.41974i		−	0.157240i
$474$	−10.2599	+	38.2905i	−0.471253	+	1.75874i
$475$	−7.56334	−	26.3195i	−0.347030	−	1.20762i
$476$	−3.69533	−	3.69533i	−0.169375	−	0.169375i
$477$	1.06918	−	3.99023i	0.0489543	−	0.182700i
$478$	−22.8779	+	6.13011i	−1.04641	+	0.280384i
$479$	3.57686	+	13.3490i	0.163431	+	0.609933i	0.998235	+	0.0593859i	$0.0189142\pi$
$479$	3.57686	+	13.3490i	0.163431	+	0.609933i	−0.834804	+	0.550547i	$0.814419\pi$
$480$	8.22685	−	14.5506i	0.375503	−	0.664143i
$481$		0			0
$482$	−24.3115	−	24.3115i	−1.10736	−	1.10736i
$483$	69.9091	+	40.3621i	3.18098	+	1.83654i
$484$	24.3123	+	14.0367i	1.10510	+	0.638033i
$485$	1.40862	+	1.38346i	0.0639624	+	0.0628196i
$486$	34.1399	−	34.1399i	1.54862	−	1.54862i
$487$	10.2296	+	17.7182i	0.463547	+	0.802887i	0.999135	−	0.0415923i	$-0.0132431\pi$
$487$	10.2296	+	17.7182i	0.463547	+	0.802887i	−0.535587	+	0.844480i	$0.679910\pi$
$488$	7.17902	+	12.4344i	0.324979	+	0.562880i
$489$	26.1796	−	26.1796i	1.18388	−	1.18388i
$490$	−26.3995	−	25.9278i	−1.19261	−	1.17130i
$491$	8.82381	+	5.09443i	0.398213	+	0.229908i	0.685713	−	0.727872i	$-0.259491\pi$
$491$	8.82381	+	5.09443i	0.398213	+	0.229908i	−0.287500	+	0.957781i	$0.592824\pi$
$492$	22.3976	+	12.9312i	1.00976	+	0.582986i
$493$	0.208297	+	0.208297i	0.00938121	+	0.00938121i
$494$		0			0
$495$	4.89137	−	8.65126i	0.219851	−	0.388845i
$496$	−2.28597	−	8.53136i	−0.102643	−	0.383069i
$497$	−40.0612	+	10.7344i	−1.79699	+	0.481502i
$498$	−16.4129	+	61.2537i	−0.735478	+	2.74484i
$499$	−7.90149	−	7.90149i	−0.353719	−	0.353719i	0.507772	−	0.861491i	$-0.330469\pi$
$499$	−7.90149	−	7.90149i	−0.353719	−	0.353719i	−0.861491	+	0.507772i	$0.830469\pi$
$500$	39.4537	+	9.43612i	1.76442	+	0.421996i
$501$	7.54998	−	28.1769i	0.337308	−	1.25885i
$502$		−	42.1443i		−	1.88099i
$503$	−13.6747	−	3.66412i	−0.609723	−	0.163375i	−0.0592717	−	0.998242i	$-0.518878\pi$
$503$	−13.6747	−	3.66412i	−0.609723	−	0.163375i	−0.550452	+	0.834867i	$0.685545\pi$
$504$	17.7675	−	30.7741i	0.791426	−	1.37079i
$505$	−17.1942	−	4.44147i	−0.765133	−	0.197643i
$506$		−	39.5998i		−	1.76043i
$507$		0			0
$508$	−18.0446	+	18.0446i	−0.800600	+	0.800600i
$509$	−22.3950	+	6.00073i	−0.992643	+	0.265978i	−0.718360	−	0.695671i	$-0.755107\pi$
$509$	−22.3950	+	6.00073i	−0.992643	+	0.265978i	−0.274283	+	0.961649i	$0.588440\pi$
$510$	−4.62430	−	1.19451i	−0.204768	−	0.0528939i
$511$	14.5587	−	8.40548i	0.644039	−	0.371836i
$512$	−20.8492			−0.921415
$513$	5.97914	−	3.45206i	0.263986	−	0.152412i
$514$	20.6583	+	5.53539i	0.911200	+	0.244155i
$515$	29.5722	+	16.7200i	1.30311	+	0.736769i
$516$	−8.02598	−	13.9014i	−0.353324	−	0.611975i
$517$	0.908131	+	3.38919i	0.0399396	+	0.149056i
$518$	−5.12718	+	8.88054i	−0.225275	+	0.390188i
$519$	37.7669			1.65778
$520$		0			0
$521$	−35.0306			−1.53472			−0.767359	−	0.641218i	$-0.778429\pi$
$521$	−35.0306			−1.53472			−0.767359	+	0.641218i	$0.778429\pi$
$522$	−2.23158	+	3.86521i	−0.0976737	+	0.169176i
$523$	10.4519	+	39.0069i	0.457029	+	1.70565i	0.682055	+	0.731301i	$0.261087\pi$
$523$	10.4519	+	39.0069i	0.457029	+	1.70565i	−0.225026	+	0.974353i	$0.572247\pi$
$524$	16.9581	+	29.3722i	0.740817	+	1.28313i
$525$	−42.3870	−	10.5425i	−1.84992	−	0.460111i
$526$	9.76819	+	2.61738i	0.425913	+	0.114123i
$527$	1.54429	−	0.891594i	0.0672702	−	0.0388384i
$528$	−8.05506			−0.350551
$529$	54.0324	−	31.1956i	2.34923	−	1.35633i
$530$	4.52250	+	7.67266i	0.196445	+	0.333279i
$531$	15.1458	−	4.05832i	0.657274	−	0.176116i
$532$	52.5307	−	52.5307i	2.27749	−	2.27749i
$533$		0			0
$534$		−	12.8443i		−	0.555827i
$535$	20.1275	−	11.8638i	0.870188	−	0.512916i
$536$	21.3559	−	36.9895i	0.922435	−	1.59771i
$537$	−41.6403	−	11.1575i	−1.79691	−	0.481481i
$538$		−	4.26468i		−	0.183864i
$539$	3.26097	−	12.1701i	0.140460	−	0.524203i
$540$	0.0921822	+	10.2270i	0.00396689	+	0.440101i
$541$	16.7846	+	16.7846i	0.721626	+	0.721626i	0.968936	−	0.247310i	$-0.0795467\pi$
$541$	16.7846	+	16.7846i	0.721626	+	0.721626i	−0.247310	+	0.968936i	$0.579547\pi$
$542$	1.81081	−	6.75804i	0.0777810	−	0.290283i
$543$	4.94279	−	1.32442i	0.212116	−	0.0568362i
$544$	−0.318997	−	1.19051i	−0.0136769	−	0.0510428i
$545$	11.3819	+	6.43528i	0.487549	+	0.275657i
$546$		0			0
$547$	10.0151	+	10.0151i	0.428216	+	0.428216i	0.888020	−	0.459804i	$-0.152080\pi$
$547$	10.0151	+	10.0151i	0.428216	+	0.428216i	−0.459804	+	0.888020i	$0.652080\pi$
$548$	−43.0434	−	24.8511i	−1.83872	−	1.06159i
$549$	−7.91978	−	4.57249i	−0.338008	−	0.195149i
$550$	5.91783	+	20.5933i	0.252337	+	0.878103i
$551$	−2.96103	+	2.96103i	−0.126144	+	0.126144i
$552$	−41.7100	−	72.2438i	−1.77529	−	3.07490i
$553$	13.3655	+	23.1498i	0.568360	+	0.984428i
$554$	−47.8022	+	47.8022i	−2.03092	+	2.03092i
$555$	0.0544530	+	6.04121i	0.00231140	+	0.256435i
$556$	28.2364	+	16.3023i	1.19749	+	0.691370i
$557$	15.5555	+	8.98097i	0.659108	+	0.380536i	0.791937	−	0.610603i	$-0.209073\pi$
$557$	15.5555	+	8.98097i	0.659108	+	0.380536i	−0.132829	+	0.991139i	$0.542406\pi$
$558$	19.1041	+	19.1041i	0.808743	+	0.808743i
$559$		0			0
$560$	4.26743	+	15.3707i	0.180332	+	0.649532i
$561$	−0.420908	−	1.57085i	−0.0177708	−	0.0663214i
$562$	−8.35714	+	2.23929i	−0.352525	+	0.0944587i
$563$	−3.89312	+	14.5293i	−0.164075	+	0.612338i	0.834081	+	0.551642i	$0.185999\pi$
$563$	−3.89312	+	14.5293i	−0.164075	+	0.612338i	−0.998156	+	0.0606957i	$0.980668\pi$
$564$	11.6459	+	11.6459i	0.490380	+	0.490380i
$565$	−32.7890	+	0.295546i	−1.37944	+	0.0124337i
$566$	−4.79405	+	17.8916i	−0.201509	+	0.752041i
$567$		−	38.6071i		−	1.62135i
$568$	41.3990	+	11.0928i	1.73706	+	0.465445i
$569$	−10.9760	+	19.0110i	−0.460138	+	0.796983i	−0.998967	−	0.0454320i	$-0.985534\pi$
$569$	−10.9760	+	19.0110i	−0.460138	+	0.796983i	0.538829	+	0.842415i	$0.318867\pi$
$570$	16.9805	−	65.7364i	0.711234	−	2.75340i
$571$		−	12.0101i		−	0.502606i	−0.967908	−	0.251303i	$-0.919141\pi$
$571$		−	12.0101i		−	0.502606i	0.967908	−	0.251303i	$-0.0808590\pi$
$572$		0			0
$573$	13.4606	−	13.4606i	0.562325	−	0.562325i
$574$	26.1309	−	7.00175i	1.09068	−	0.292247i
$575$	−32.0767	+	33.2545i	−1.33769	+	1.38681i
$576$	24.3050	−	14.0325i	1.01271	−	0.584688i
$577$	−21.1801			−0.881741			−0.440870	−	0.897571i	$-0.645330\pi$
$577$	−21.1801			−0.881741			−0.440870	+	0.897571i	$0.645330\pi$
$578$	34.6228	−	19.9895i	1.44012	−	0.831453i
$579$	−52.4723	−	14.0599i	−2.18068	−	0.584310i
$580$	−1.65945	−	5.97712i	−0.0689048	−	0.248186i
$581$	21.3810	+	37.0329i	0.887032	+	1.53638i
$582$	1.26693	+	4.72824i	0.0525158	+	0.195992i
$583$	−1.51631	+	2.62632i	−0.0627991	+	0.108771i
$584$	−17.3724			−0.718873
$585$		0			0
$586$	−53.5214			−2.21095
$587$	−17.2507	+	29.8791i	−0.712013	+	1.23324i	0.252087	+	0.967705i	$0.418883\pi$
$587$	−17.2507	+	29.8791i	−0.712013	+	1.23324i	−0.964100	+	0.265539i	$0.914450\pi$
$588$	−15.3067	−	57.1253i	−0.631237	−	2.35581i
$589$	12.6744	+	21.9527i	0.522239	+	0.904544i
$590$	−16.6385	+	29.4280i	−0.684994	+	1.21153i
$591$	−49.8130	−	13.3473i	−2.04903	−	0.549036i
$592$	1.91084	−	1.10322i	0.0785351	−	0.0453423i
$593$	−28.3656			−1.16483			−0.582417	−	0.812890i	$-0.697893\pi$
$593$	−28.3656			−1.16483			−0.582417	+	0.812890i	$0.697893\pi$
$594$	−4.67830	+	2.70102i	−0.191953	+	0.110824i
$595$	−2.77452	+	1.63539i	−0.113744	+	0.0670445i
$596$	−44.5470	+	11.9363i	−1.82472	+	0.488932i
$597$	−13.4452	+	13.4452i	−0.550276	+	0.550276i
$598$		0			0
$599$		−	3.01612i		−	0.123235i	−0.998100	−	0.0616176i	$-0.980374\pi$
$599$		−	3.01612i		−	0.123235i	0.998100	−	0.0616176i	$-0.0196259\pi$
$600$	32.4868	+	31.3362i	1.32627	+	1.27930i
$601$	−6.79040	+	11.7613i	−0.276986	+	0.479754i	−0.970634	−	0.240560i	$-0.922669\pi$
$601$	−6.79040	+	11.7613i	−0.276986	+	0.479754i	0.693648	+	0.720314i	$0.256002\pi$
$602$	−16.2185	−	4.34575i	−0.661019	−	0.177119i
$603$			27.2042i			1.10784i
$604$	−3.93274	+	14.6772i	−0.160021	+	0.597206i
$605$	12.1228	−	12.3434i	0.492863	−	0.501829i
$606$	−31.1328	−	31.1328i	−1.26468	−	1.26468i
$607$	−9.28061	+	34.6357i	−0.376689	+	1.40582i	0.474173	+	0.880431i	$0.342747\pi$
$607$	−9.28061	+	34.6357i	−0.376689	+	1.40582i	−0.850862	+	0.525389i	$0.823920\pi$
$608$	16.9236	−	4.53467i	0.686344	−	0.183905i
$609$	1.72867	+	6.45149i	0.0700493	+	0.261427i
$610$	18.9978	−	5.27442i	0.769198	−	0.213555i
$611$		0			0
$612$	−2.43224	−	2.43224i	−0.0983175	−	0.0983175i
$613$	3.89843	+	2.25076i	0.157456	+	0.0909074i	0.576658	−	0.816986i	$-0.304357\pi$
$613$	3.89843	+	2.25076i	0.157456	+	0.0909074i	−0.419202	+	0.907893i	$0.637690\pi$
$614$	41.9308	+	24.2087i	1.69219	+	0.976986i
$615$	11.1681	−	11.3712i	0.450341	−	0.458533i
$616$	−18.4461	+	18.4461i	−0.743213	+	0.743213i
$617$	−19.2350	−	33.3160i	−0.774372	−	1.34125i	−0.935147	−	0.354260i	$-0.884733\pi$
$617$	−19.2350	−	33.3160i	−0.774372	−	1.34125i	0.160776	−	0.986991i	$-0.448600\pi$
$618$	42.1125	+	72.9410i	1.69401	+	2.93412i
$619$	−5.85514	+	5.85514i	−0.235338	+	0.235338i	−0.814916	−	0.579578i	$-0.803217\pi$
$619$	−5.85514	+	5.85514i	−0.235338	+	0.235338i	0.579578	+	0.814916i	$0.303217\pi$
$620$	−37.5490	+	0.338451i	−1.50800	+	0.0135925i
$621$	−10.0881	−	5.82435i	−0.404820	−	0.233723i
$622$	−43.9191	−	25.3567i	−1.76099	−	1.01671i
$623$	−6.12441	−	6.12441i	−0.245369	−	0.245369i
$624$		0			0
$625$	11.7115	−	22.0871i	0.468459	−	0.883485i
$626$	−4.53915	−	16.9403i	−0.181421	−	0.677072i
$627$	22.3303	−	5.98339i	0.891787	−	0.238954i
$628$	−17.3137	+	64.6155i	−0.690890	+	2.57844i
$629$	0.314994	+	0.314994i	0.0125596	+	0.0125596i
$630$	−34.8138	−	34.1918i	−1.38701	−	1.36223i
$631$	−9.66827	+	36.0825i	−0.384888	+	1.43642i	0.453456	+	0.891279i	$0.350191\pi$
$631$	−9.66827	+	36.0825i	−0.384888	+	1.43642i	−0.838344	+	0.545142i	$0.816476\pi$
$632$		−	27.6237i		−	1.09881i
$633$	55.9176	+	14.9831i	2.22252	+	0.595524i
$634$	30.7026	−	53.1785i	1.21936	−	2.11199i
$635$	7.98575	+	13.5482i	0.316905	+	0.537645i
$636$			14.2348i			0.564448i
$637$		0			0
$638$	2.31681	−	2.31681i	0.0917235	−	0.0917235i
$639$	−26.3680	+	7.06528i	−1.04310	+	0.279498i
$640$	−11.5551	+	44.7330i	−0.456754	+	1.76823i
$641$	−2.97232	+	1.71607i	−0.117399	+	0.0677806i	−0.557550	−	0.830143i	$-0.688258\pi$
$641$	−2.97232	+	1.71607i	−0.117399	+	0.0677806i	0.440150	+	0.897924i	$0.354925\pi$
$642$	57.9252			2.28613
$643$	−14.2572	+	8.23137i	−0.562247	+	0.324614i	−0.754047	−	0.656820i	$-0.771901\pi$
$643$	−14.2572	+	8.23137i	−0.562247	+	0.324614i	0.191800	+	0.981434i	$0.438568\pi$
$644$	−121.071	−	32.4409i	−4.77087	−	1.27835i
$645$	−9.53185	+	2.64636i	−0.375316	+	0.104200i
$646$	−2.50309	−	4.33549i	−0.0984829	−	0.170577i
$647$	−4.93784	−	18.4283i	−0.194127	−	0.724490i	−0.992491	−	0.122316i	$-0.960968\pi$
$647$	−4.93784	−	18.4283i	−0.194127	−	0.724490i	0.798365	−	0.602174i	$-0.205699\pi$
$648$	−19.9482	+	34.5513i	−0.783639	+	1.35730i
$649$	−11.5110			−0.451846
$650$		0			0
$651$	40.4311			1.58462
$652$	−28.7436	+	49.7854i	−1.12569	+	1.94975i
$653$	−9.90911	−	36.9813i	−0.387773	−	1.44719i	−0.833748	−	0.552145i	$-0.813810\pi$
$653$	−9.90911	−	36.9813i	−0.387773	−	1.44719i	0.445975	−	0.895046i	$-0.352857\pi$
$654$	16.2085	+	28.0740i	0.633803	+	1.09778i
$655$	20.1398	−	5.59149i	0.786928	−	0.218477i
$656$	−5.62263	−	1.50658i	−0.219527	−	0.0588220i
$657$	9.58244	−	5.53243i	0.373847	−	0.215841i
$658$	17.2277			0.671605
$659$	−34.0246	+	19.6441i	−1.32541	+	0.765225i	−0.984586	−	0.174903i	$-0.944039\pi$
$659$	−34.0246	+	19.6441i	−1.32541	+	0.765225i	−0.340823	+	0.940128i	$0.610706\pi$
$660$	−8.56501	+	33.1577i	−0.333393	+	1.29066i
$661$	−26.1828	+	7.01565i	−1.01839	+	0.272877i	−0.729132	−	0.684373i	$-0.760076\pi$
$661$	−26.1828	+	7.01565i	−1.01839	+	0.272877i	−0.289260	+	0.957251i	$0.593409\pi$
$662$	−17.6545	+	17.6545i	−0.686161	+	0.686161i
$663$		0			0
$664$		−	44.1900i		−	1.71490i
$665$	−23.2478	−	39.4410i	−0.901510	−	1.52946i
$666$	−3.37468	+	5.84511i	−0.130766	+	0.226493i
$667$	6.82448	+	1.82861i	0.264245	+	0.0708042i
$668$			45.2943i			1.75249i
$669$	17.8550	−	66.6357i	0.690314	−	2.57629i
$670$	−41.8451	−	41.0974i	−1.61662	−	1.58773i
$671$	4.74713	+	4.74713i	0.183261	+	0.183261i
$672$	7.23277	−	26.9931i	0.279010	−	1.04128i
$673$	−6.86071	+	1.83832i	−0.264461	+	0.0708621i	−0.388613	−	0.921401i	$-0.627046\pi$
$673$	−6.86071	+	1.83832i	−0.264461	+	0.0708621i	0.124152	+	0.992263i	$0.460379\pi$
$674$	5.80011	+	21.6463i	0.223412	+	0.833785i
$675$	6.11655	+	1.52130i	0.235426	+	0.0585550i
$676$		0			0
$677$	19.2265	+	19.2265i	0.738933	+	0.738933i	0.972372	−	0.233439i	$-0.0749978\pi$
$677$	19.2265	+	19.2265i	0.738933	+	0.738933i	−0.233439	+	0.972372i	$0.574998\pi$
$678$	−70.4045	−	40.6481i	−2.70387	−	1.56108i
$679$	2.85861	+	1.65042i	0.109703	+	0.0633373i
$680$	3.32805	−	0.0299977i	0.127625	−	0.00115036i
$681$	−12.9987	+	12.9987i	−0.498112	+	0.498112i
$682$	−9.91690	−	17.1766i	−0.379738	−	0.657725i
$683$	2.30838	+	3.99823i	0.0883277	+	0.152988i	0.906804	−	0.421552i	$-0.138514\pi$
$683$	2.30838	+	3.99823i	0.0883277	+	0.152988i	−0.818477	+	0.574540i	$0.805181\pi$
$684$	34.5753	−	34.5753i	1.32202	−	1.32202i
$685$	−21.4627	+	21.8531i	−0.820047	+	0.834964i
$686$	0.190715	+	0.110109i	0.00728153	+	0.00420399i
$687$	35.6057	+	20.5569i	1.35844	+	0.784296i
$688$	2.55469	+	2.55469i	0.0973967	+	0.0973967i
$689$		0			0
$690$	−110.377	+	30.6442i	−4.20197	+	1.16661i
$691$	2.74019	+	10.2265i	0.104242	+	0.389036i	0.998258	−	0.0589986i	$-0.0187907\pi$
$691$	2.74019	+	10.2265i	0.104242	+	0.389036i	−0.894016	+	0.448035i	$0.852124\pi$
$692$	−56.6433	+	15.1775i	−2.15326	+	0.576963i
$693$	4.30033	−	16.0491i	0.163356	−	0.609653i
$694$	−11.9539	−	11.9539i	−0.453766	−	0.453766i
$695$	14.0795	−	14.3356i	0.534065	−	0.543780i
$696$	1.78640	−	6.66694i	0.0677133	−	0.252710i
$697$		−	1.17522i		−	0.0445146i
$698$	−74.7333	−	20.0247i	−2.82870	−	0.757947i
$699$	−2.52797	+	4.37857i	−0.0956166	+	0.165613i
$700$	67.8094	−	1.22251i	2.56295	−	0.0462065i
$701$		−	48.9646i		−	1.84937i	−0.380735	−	0.924684i	$-0.624329\pi$
$701$		−	48.9646i		−	1.84937i	0.380735	−	0.924684i	$-0.375671\pi$
$702$		0			0
$703$	−4.47777	+	4.47777i	−0.168882	+	0.168882i
$704$	−19.9009	+	5.33243i	−0.750043	+	0.200973i
$705$	8.74394	−	5.15395i	0.329316	−	0.194109i
$706$	−26.5461	+	15.3264i	−0.999076	+	0.576817i
$707$	−29.6895			−1.11659
$708$	−46.7927	+	27.0158i	−1.75858	+	1.01532i
$709$	23.7942	+	6.37565i	0.893611	+	0.239442i	0.676271	−	0.736653i	$-0.263595\pi$
$709$	23.7942	+	6.37565i	0.893611	+	0.239442i	0.217341	+	0.976096i	$0.430262\pi$
$710$	28.9665	−	51.2324i	1.08709	−	1.92272i
$711$	8.79710	+	15.2370i	0.329917	+	0.571433i
$712$	2.31655	+	8.64548i	0.0868164	+	0.324003i
$713$	21.3843	−	37.0388i	0.800850	−	1.38711i
$714$	−7.98484			−0.298825
$715$		0			0
$716$	66.9366			2.50154
$717$	−11.6646	+	20.2036i	−0.435621	+	0.754518i
$718$	−10.8810	−	40.6084i	−0.406074	−	1.51549i
$719$	−23.3017	−	40.3597i	−0.869007	−	1.50516i	−0.863012	−	0.505183i	$-0.831425\pi$
$719$	−23.3017	−	40.3597i	−0.869007	−	1.50516i	−0.00599476	−	0.999982i	$-0.501908\pi$
$720$	2.80879	+	10.1169i	0.104678	+	0.377035i
$721$	54.8597	+	14.6996i	2.04308	+	0.547442i
$722$	22.5938	−	13.0446i	0.840856	−	0.485468i
$723$	−33.8652			−1.25946
$724$	−6.88102	+	3.97276i	−0.255731	+	0.147646i
$725$	−3.82225	+	0.0689099i	−0.141955	+	0.00255925i
$726$	41.4321	−	11.1017i	1.53769	−	0.412023i
$727$	−16.4412	+	16.4412i	−0.609770	+	0.609770i	−0.942886	−	0.333116i	$-0.891900\pi$
$727$	−16.4412	+	16.4412i	−0.609770	+	0.609770i	0.333116	+	0.942886i	$0.391900\pi$
$728$		0			0
$729$		−	16.5738i		−	0.613846i
$730$	−5.96634	+	23.0974i	−0.220824	+	0.854875i
$731$	−0.364709	+	0.631694i	−0.0134892	+	0.0233641i
$732$	30.4386	+	8.15599i	1.12504	+	0.301454i
$733$			30.6968i			1.13381i	0.823782	+	0.566907i	$0.191860\pi$
$733$			30.6968i			1.13381i	−0.823782	+	0.566907i	$0.808140\pi$
$734$	−21.4010	+	79.8698i	−0.789927	+	2.94805i
$735$	−36.4452	+	0.328502i	−1.34430	+	0.0121170i
$736$	−20.9028	−	20.9028i	−0.770486	−	0.770486i
$737$	5.16886	−	19.2905i	0.190397	−	0.710573i
$738$	17.1992	−	4.60850i	0.633110	−	0.169641i
$739$	−8.93434	−	33.3434i	−0.328655	−	1.22656i	−0.910586	−	0.413319i	$-0.864369\pi$
$739$	−8.93434	−	33.3434i	−0.328655	−	1.22656i	0.581931	−	0.813238i	$-0.302297\pi$
$740$	−2.50948	−	9.03881i	−0.0922502	−	0.332273i
$741$		0			0
$742$	10.5288	+	10.5288i	0.386523	+	0.386523i
$743$	−0.266725	−	0.153994i	−0.00978520	−	0.00564949i	0.495099	−	0.868836i	$-0.335132\pi$
$743$	−0.266725	−	0.153994i	−0.00978520	−	0.00564949i	−0.504885	+	0.863187i	$0.668465\pi$
$744$	−36.1837	−	20.8907i	−1.32656	−	0.765889i
$745$	0.256170	+	28.4204i	0.00938534	+	1.04124i
$746$	25.0528	−	25.0528i	0.917249	−	0.917249i
$747$	14.0728	+	24.3748i	0.514897	+	0.891828i
$748$	1.26257	+	2.18683i	0.0461641	+	0.0799586i
$749$	27.6199	−	27.6199i	1.00921	−	1.00921i
$750$	52.8203	−	32.4309i	1.92873	−	1.18421i
$751$	−18.1008	−	10.4505i	−0.660509	−	0.381345i	0.131962	−	0.991255i	$-0.457872\pi$
$751$	−18.1008	−	10.4505i	−0.660509	−	0.381345i	−0.792471	+	0.609910i	$0.791206\pi$
$752$	−3.21028	−	1.85346i	−0.117067	−	0.0675886i
$753$	−29.3529	−	29.3529i	−1.06968	−	1.06968i
$754$		0			0
$755$	8.15153	+	4.60883i	0.296665	+	0.167733i
$756$	4.42545	+	16.5160i	0.160952	+	0.600681i
$757$	32.4416	−	8.69270i	1.17911	−	0.315942i	0.384537	−	0.923110i	$-0.374361\pi$
$757$	32.4416	−	8.69270i	1.17911	−	0.315942i	0.794573	+	0.607168i	$0.207695\pi$
$758$	19.8881	−	74.2232i	0.722367	−	2.69591i
$759$	−27.5807	−	27.5807i	−1.00112	−	1.00112i
$760$	0.426430	+	47.3097i	0.0154682	+	1.71610i
$761$	12.4256	−	46.3730i	0.450428	−	1.68102i	−0.250764	−	0.968048i	$-0.580682\pi$
$761$	12.4256	−	46.3730i	0.450428	−	1.68102i	0.701192	−	0.712973i	$-0.252652\pi$
$762$			38.9906i			1.41248i
$763$	21.1148	+	5.65768i	0.764406	+	0.204822i
$764$	−14.7789	+	25.5979i	−0.534684	+	0.926099i
$765$	−1.82617	+	1.07640i	−0.0660254	+	0.0389175i
$766$		−	76.4612i		−	2.76266i
$767$		0			0
$768$	−43.3025	+	43.3025i	−1.56255	+	1.56255i
$769$	22.6156	−	6.05983i	0.815539	−	0.218523i	0.173144	−	0.984897i	$-0.444608\pi$
$769$	22.6156	−	6.05983i	0.815539	−	0.218523i	0.642395	+	0.766374i	$0.277941\pi$
$770$	18.1899	+	30.8601i	0.655519	+	1.11212i
$771$	18.2435	−	10.5329i	0.657025	−	0.379334i
$772$	84.3490			3.03579
$773$	23.2908	−	13.4470i	0.837712	−	0.483653i	−0.0187736	−	0.999824i	$-0.505976\pi$
$773$	23.2908	−	13.4470i	0.837712	−	0.483653i	0.856486	+	0.516170i	$0.172643\pi$
$774$	−10.6749	−	2.86034i	−0.383703	−	0.102813i
$775$	−5.58553	+	22.4572i	−0.200638	+	0.806686i
$776$	−1.70554	−	2.95408i	−0.0612252	−	0.106045i
$777$	2.61416	+	9.75617i	0.0937823	+	0.350000i
$778$	13.9756	−	24.2065i	0.501051	−	0.867845i
$779$	16.7062			0.598563
$780$		0			0
$781$	20.0399			0.717086
$782$	−4.22324	+	7.31487i	−0.151023	+	0.261579i
$783$	−0.249452	−	0.930966i	−0.00891467	−	0.0332700i
$784$	6.65549	+	11.5276i	0.237696	+	0.411702i
$785$	35.8867	+	20.2901i	1.28085	+	0.724186i
$786$	50.0551	+	13.4122i	1.78540	+	0.478398i
$787$	1.25975	−	0.727317i	0.0449053	−	0.0259261i	−0.477379	−	0.878697i	$-0.658413\pi$
$787$	1.25975	−	0.727317i	0.0449053	−	0.0259261i	0.522285	+	0.852771i	$0.325080\pi$
$788$	80.0741			2.85252
$789$	8.62637	−	4.98043i	0.307107	−	0.177308i
$790$	−36.7272	−	9.48706i	−1.30669	−	0.337535i
$791$	−52.9520	+	14.1885i	−1.88276	+	0.504483i
$792$	−12.1411	+	12.1411i	−0.431414	+	0.431414i
$793$		0			0
$794$			19.3299i			0.685994i
$795$	8.49375	+	2.19403i	0.301242	+	0.0778144i
$796$	14.7620	−	25.5686i	0.523227	−	0.906256i
$797$	12.0194	+	3.22058i	0.425748	+	0.114079i	0.465330	−	0.885138i	$-0.345936\pi$
$797$	12.0194	+	3.22058i	0.425748	+	0.114079i	−0.0395816	+	0.999216i	$0.512603\pi$
$798$		−	113.508i		−	4.01813i
$799$	0.193701	−	0.722901i	0.00685264	−	0.0255744i
$800$	13.9939	+	7.74646i	0.494759	+	0.273879i
$801$	−4.03104	−	4.03104i	−0.142430	−	0.142430i
$802$	−10.1396	+	37.8413i	−0.358040	+	1.33622i
$803$	−7.84608	+	2.10235i	−0.276882	+	0.0741904i
$804$	−24.2622	−	90.5476i	−0.855661	−	3.19337i
$805$	−38.0180	+	67.2415i	−1.33996	+	2.36995i
$806$		0			0
$807$	−2.97029	−	2.97029i	−0.104559	−	0.104559i
$808$	26.5705	+	15.3405i	0.934746	+	0.539676i
$809$	6.25034	+	3.60863i	0.219750	+	0.126873i	0.605835	−	0.795591i	$-0.292839\pi$
$809$	6.25034	+	3.60863i	0.219750	+	0.126873i	−0.386084	+	0.922463i	$0.626173\pi$
$810$	39.0867	+	38.3884i	1.37337	+	1.34883i
$811$	−15.0515	+	15.0515i	−0.528530	+	0.528530i	−0.920134	−	0.391604i	$-0.871920\pi$
$811$	−15.0515	+	15.0515i	−0.528530	+	0.528530i	0.391604	+	0.920134i	$0.371920\pi$
$812$	−5.18537	−	8.98132i	−0.181971	−	0.315183i
$813$	−3.44567	−	5.96807i	−0.120845	−	0.209309i
$814$	3.50357	−	3.50357i	0.122800	−	0.122800i
$815$	25.2760	+	24.8245i	0.885381	+	0.869563i
$816$	1.48793	+	0.859056i	0.0520879	+	0.0300730i
$817$	−8.97980	−	5.18449i	−0.314163	−	0.181382i
$818$	−7.08575	−	7.08575i	−0.247747	−	0.247747i
$819$		0			0
$820$	−12.1802	+	21.5429i	−0.425352	+	0.752311i
$821$	−4.53915	−	16.9404i	−0.158418	−	0.591222i	−0.998788	−	0.0492105i	$-0.984329\pi$
$821$	−4.53915	−	16.9404i	−0.158418	−	0.591222i	0.840371	−	0.542012i	$-0.182337\pi$
$822$	−73.3529	+	19.6548i	−2.55847	+	0.685541i
$823$	2.83413	−	10.5771i	0.0987916	−	0.368695i	−0.898775	−	0.438409i	$-0.855542\pi$
$823$	2.83413	−	10.5771i	0.0987916	−	0.368695i	0.997567	+	0.0697141i	$0.0222087\pi$
$824$	−41.5013	−	41.5013i	−1.44576	−	1.44576i
$825$	18.4646	+	10.2213i	0.642856	+	0.355859i
$826$	−14.6280	+	54.5923i	−0.508972	+	1.89951i
$827$			1.86613i			0.0648917i	0.999473	+	0.0324458i	$0.0103296\pi$
$827$			1.86613i			0.0648917i	−0.999473	+	0.0324458i	$0.989670\pi$
$828$	−79.6882	−	21.3524i	−2.76936	−	0.742047i
$829$	17.3922	−	30.1241i	0.604055	−	1.04625i	−0.388145	−	0.921598i	$-0.626884\pi$
$829$	17.3922	−	30.1241i	0.604055	−	1.04625i	0.992200	−	0.124656i	$-0.0397826\pi$
$830$	−58.7529	−	15.1766i	−2.03934	−	0.526786i
$831$			66.5870i			2.30988i
$832$		0			0
$833$	−1.90028	+	1.90028i	−0.0658408	+	0.0658408i
$834$	48.1193	−	12.8935i	1.66624	−	0.446467i
$835$	27.0265	+	6.98127i	0.935291	+	0.241597i
$836$	−31.0868	+	17.9480i	−1.07516	+	0.620743i
$837$	−5.83431			−0.201663
$838$	35.0904	−	20.2595i	1.21218	−	0.699851i
$839$	18.7439	+	5.02241i	0.647111	+	0.173393i	0.567422	−	0.823427i	$-0.307941\pi$
$839$	18.7439	+	5.02241i	0.647111	+	0.173393i	0.0796889	+	0.996820i	$0.474607\pi$
$840$	65.6892	+	37.1403i	2.26649	+	1.28146i
$841$	−14.2077	−	24.6085i	−0.489921	−	0.848568i
$842$	8.04579	+	30.0273i	0.277276	+	1.03481i
$843$	−4.26099	+	7.38026i	−0.146756	+	0.254190i
$844$	−89.8873			−3.09405
$845$		0			0
$846$	11.3391			0.389848
$847$	14.4621	−	25.0491i	0.496925	−	0.860699i
$848$	−0.829228	−	3.09472i	−0.0284758	−	0.106273i
$849$	9.12227	+	15.8002i	0.313075	+	0.542263i
$850$	1.10310	−	4.43512i	0.0378360	−	0.152123i
$851$	10.3202	+	2.76530i	0.353773	+	0.0947931i
$852$	81.4633	−	47.0328i	2.79089	−	1.61132i
$853$	2.67051			0.0914364			0.0457182	−	0.998954i	$-0.485442\pi$
$853$	2.67051			0.0914364			0.0457182	+	0.998954i	$0.485442\pi$
$854$	28.5464	−	16.4813i	0.976837	−	0.563977i
$855$	−15.3015	−	25.9598i	−0.523301	−	0.887807i
$856$	−38.9894	+	10.4472i	−1.33263	+	0.357077i
$857$	17.5773	−	17.5773i	0.600430	−	0.600430i	−0.339996	−	0.940427i	$-0.610426\pi$
$857$	17.5773	−	17.5773i	0.600430	−	0.600430i	0.940427	+	0.339996i	$0.110426\pi$
$858$		0			0
$859$		−	52.8699i		−	1.80390i	−0.431844	−	0.901949i	$-0.642137\pi$
$859$		−	52.8699i		−	1.80390i	0.431844	−	0.901949i	$-0.357863\pi$
$860$	13.2325	−	7.79965i	0.451225	−	0.265966i
$861$	13.3232	−	23.0764i	0.454052	−	0.786441i
$862$	24.5535	+	6.57909i	0.836296	+	0.224085i
$863$			3.40127i			0.115780i	0.998323	+	0.0578902i	$0.0184373\pi$
$863$			3.40127i			0.115780i	−0.998323	+	0.0578902i	$0.981563\pi$
$864$	−1.04371	+	3.89517i	−0.0355076	+	0.132516i
$865$	0.325730	+	36.1377i	0.0110752	+	1.22872i
$866$	8.56625	+	8.56625i	0.291093	+	0.291093i
$867$	10.1919	−	38.0366i	0.346134	−	1.29179i
$868$	−60.6392	+	16.2482i	−2.05823	+	0.551500i
$869$	−3.34294	−	12.4760i	−0.113402	−	0.423220i
$870$	−8.25052	−	4.66479i	−0.279719	−	0.158151i
$871$		0			0
$872$	−15.9733	−	15.9733i	−0.540923	−	0.540923i
$873$	1.88152	+	1.08630i	0.0636798	+	0.0367655i
$874$	−103.984	−	60.0352i	−3.51731	−	2.03072i
$875$	9.72210	−	40.6494i	0.328667	−	1.37420i
$876$	−26.9605	+	26.9605i	−0.910912	+	0.910912i
$877$	−9.83752	−	17.0391i	−0.332189	−	0.575369i	0.650751	−	0.759291i	$-0.274454\pi$
$877$	−9.83752	−	17.0391i	−0.332189	−	0.575369i	−0.982941	+	0.183922i	$0.941121\pi$
$878$	−24.0080	−	41.5832i	−0.810232	−	1.40336i
$879$	−37.2768	+	37.2768i	−1.25732	+	1.25732i
$880$	−0.0694729	−	7.70758i	−0.00234193	−	0.259822i
$881$	2.06350	+	1.19137i	0.0695212	+	0.0401381i	0.534358	−	0.845258i	$-0.320554\pi$
$881$	2.06350	+	1.19137i	0.0695212	+	0.0401381i	−0.464836	+	0.885397i	$0.653887\pi$
$882$	−35.2621	−	20.3586i	−1.18734	−	0.685510i
$883$	30.4180	+	30.4180i	1.02365	+	1.02365i	0.999714	+	0.0239343i	$0.00761926\pi$
$883$	30.4180	+	30.4180i	1.02365	+	1.02365i	0.0239343	+	0.999714i	$0.492381\pi$
$884$		0			0
$885$	8.90776	+	32.0846i	0.299431	+	1.07851i
$886$	2.31057	+	8.62317i	0.0776252	+	0.289701i
$887$	21.9337	−	5.87711i	0.736461	−	0.197334i	0.128956	−	0.991650i	$-0.458837\pi$
$887$	21.9337	−	5.87711i	0.736461	−	0.197334i	0.607504	+	0.794316i	$0.292171\pi$
$888$	2.70146	−	10.0820i	0.0906550	−	0.338329i
$889$	18.5915	+	18.5915i	0.623538	+	0.623538i
$890$	12.2902	−	0.110779i	0.411969	−	0.00371332i
$891$	−4.82814	+	18.0189i	−0.161749	+	0.603655i
$892$			107.117i			3.58653i
$893$	10.2763	+	2.75354i	0.343885	+	0.0921436i
$894$	−35.2325	+	61.0244i	−1.17835	+	2.04096i
$895$	10.3170	−	39.9402i	0.344860	−	1.33505i
$896$			77.2410i			2.58044i
$897$		0			0
$898$	51.6980	−	51.6980i	1.72518	−	1.72518i
$899$	3.41808	−	0.915872i	0.113999	−	0.0305460i
$900$	44.6317	−	0.804648i	1.48772	−	0.0268216i
$901$	0.560184	−	0.323423i	0.0186624	−	0.0107748i
$902$	−13.0716			−0.435235
$903$	−14.3227	+	8.26923i	−0.476630	+	0.275183i
$904$	54.7204	+	14.6623i	1.81997	+	0.487660i
$905$	1.30992	+	4.71815i	0.0435431	+	0.156837i
$906$	11.6082	+	20.1061i	0.385658	+	0.667980i
$907$	5.99131	+	22.3599i	0.198938	+	0.742448i	0.991212	+	0.132282i	$0.0422305\pi$
$907$	5.99131	+	22.3599i	0.198938	+	0.742448i	−0.792274	+	0.610166i	$0.791103\pi$
$908$	14.2718	−	24.7195i	0.473627	−	0.820345i
$909$	−19.5414			−0.648147
$910$		0			0
$911$	−23.7450			−0.786707			−0.393354	−	0.919387i	$-0.628685\pi$
$911$	−23.7450			−0.786707			−0.393354	+	0.919387i	$0.628685\pi$
$912$	−12.2118	+	21.1515i	−0.404375	+	0.700397i
$913$	−5.34774	−	19.9580i	−0.176984	−	0.660515i
$914$	−12.0754	−	20.9152i	−0.399418	−	0.691813i
$915$	9.55812	−	16.9052i	0.315982	−	0.558869i
$916$	−61.6632	−	16.5226i	−2.03741	−	0.545922i
$917$	30.2624	−	17.4720i	0.999354	−	0.576977i
$918$	1.15223			0.0380293
$919$	49.3350	−	28.4836i	1.62741	−	0.939586i	0.642549	−	0.766245i	$-0.277877\pi$
$919$	49.3350	−	28.4836i	1.62741	−	0.939586i	0.984862	−	0.173342i	$-0.0554565\pi$
$920$	68.7676	−	40.5337i	2.26720	−	1.33636i
$921$	46.0652	−	12.3431i	1.51790	−	0.406720i
$922$	32.3379	−	32.3379i	1.06499	−	1.06499i
$923$		0			0
$924$			57.2537i			1.88351i
$925$	−5.78014	+	0.104208i	−0.190050	+	0.00342634i
$926$	19.9199	−	34.5023i	0.654608	−	1.13381i
$927$	36.1083	+	9.67519i	1.18595	+	0.317775i
$928$		−	2.44586i		−	0.0802892i
$929$	−7.56304	+	28.2256i	−0.248135	+	0.926053i	0.723647	+	0.690171i	$0.242465\pi$
$929$	−7.56304	+	28.2256i	−0.248135	+	0.926053i	−0.971782	+	0.235882i	$0.924202\pi$
$930$	−40.2021	+	40.9334i	−1.31828	+	1.34226i
$931$	−27.0133	−	27.0133i	−0.885325	−	0.885325i
$932$	2.03185	−	7.58297i	0.0665555	−	0.248388i
$933$	−48.2495	+	12.9284i	−1.57962	+	0.423257i
$934$	8.47335	+	31.6230i	0.277256	+	1.03473i
$935$	1.49946	−	0.416299i	0.0490375	−	0.0136144i
$936$		0			0
$937$	−1.77191	−	1.77191i	−0.0578859	−	0.0578859i	0.677571	−	0.735457i	$-0.263033\pi$
$937$	−1.77191	−	1.77191i	−0.0578859	−	0.0578859i	−0.735457	+	0.677571i	$0.763033\pi$
$938$	−84.9188	−	49.0279i	−2.77270	−	1.60082i
$939$	−14.9601	−	8.63724i	−0.488205	−	0.281866i
$940$	−11.0430	+	11.2439i	−0.360184	+	0.366737i
$941$	−15.5682	+	15.5682i	−0.507507	+	0.507507i	−0.913761	−	0.406253i	$-0.866835\pi$
$941$	−15.5682	+	15.5682i	−0.507507	+	0.507507i	0.406253	+	0.913761i	$0.366835\pi$
$942$	51.1047	+	88.5159i	1.66508	+	2.88400i
$943$	−14.0934	−	24.4106i	−0.458946	−	0.794917i
$944$	8.59920	−	8.59920i	0.279880	−	0.279880i
$945$	10.5370	−	0.0949760i	0.342768	−	0.00308957i
$946$	7.02612	+	4.05653i	0.228439	+	0.131889i
$947$	−0.313387	−	0.180934i	−0.0101837	−	0.00587957i	0.494899	−	0.868950i	$-0.335205\pi$
$947$	−0.313387	−	0.180934i	−0.0101837	−	0.00587957i	−0.505083	+	0.863071i	$0.668538\pi$
$948$	−42.8699	−	42.8699i	−1.39235	−	1.39235i
$949$		0			0
$950$	63.0471	+	15.6810i	2.04552	+	0.508760i
$951$	−15.6541	−	58.4220i	−0.507620	−	1.89446i
$952$	5.37459	−	1.44012i	0.174191	−	0.0466745i
$953$	10.4907	−	39.1517i	0.339826	−	1.26825i	−0.558715	−	0.829360i	$-0.688705\pi$
$953$	10.4907	−	39.1517i	0.339826	−	1.26825i	0.898541	−	0.438889i	$-0.144628\pi$
$954$	6.92996	+	6.92996i	0.224366	+	0.224366i
$955$	12.9960	+	12.7639i	0.420542	+	0.413029i
$956$	9.37537	−	34.9894i	0.303221	−	1.13164i
$957$		−	3.22725i		−	0.104322i
$958$	−31.6695	−	8.48582i	−1.02320	−	0.274164i
$959$	−25.6043	+	44.3479i	−0.826805	+	1.43207i
$960$	30.2633	+	51.3433i	0.976745	+	1.65710i
$961$			9.57907i			0.309002i
$962$		0			0
$963$	18.1792	−	18.1792i	0.585817	−	0.585817i
$964$	50.7916	−	13.6096i	1.63589	−	0.438334i
$965$	13.0008	−	50.3300i	0.418512	−	1.62018i
$966$	−165.854	+	95.7557i	−5.33626	+	3.08089i
$967$	−12.2654			−0.394430			−0.197215	−	0.980360i	$-0.563190\pi$
$967$	−12.2654			−0.394430			−0.197215	+	0.980360i	$0.563190\pi$
$968$	−25.8857	+	14.9451i	−0.831997	+	0.480354i
$969$	−4.76297	−	1.27623i	−0.153009	−	0.0409985i
$970$	−4.51334	+	1.25305i	−0.144915	+	0.0402332i
$971$	−11.3099	−	19.5894i	−0.362953	−	0.628654i	0.625492	−	0.780231i	$-0.284898\pi$
$971$	−11.3099	−	19.5894i	−0.362953	−	0.628654i	−0.988445	+	0.151577i	$0.951565\pi$
$972$	19.1115	+	71.3250i	0.613001	+	2.28775i
$973$	16.7963	−	29.0921i	0.538466	−	0.932651i
$974$	−48.5378			−1.55525
$975$		0			0
$976$	−7.09261			−0.227029
$977$	−17.5846	+	30.4574i	−0.562581	+	0.974419i	0.434689	+	0.900581i	$0.356858\pi$
$977$	−17.5846	+	30.4574i	−0.562581	+	0.974419i	−0.997270	+	0.0738385i	$0.976475\pi$
$978$	22.7335	+	84.8424i	0.726936	+	2.71296i
$979$	2.09250	+	3.62432i	0.0668767	+	0.115834i
$980$	54.5290	−	15.1391i	1.74186	−	0.483600i
$981$	13.8976	+	3.72385i	0.443716	+	0.118893i
$982$	−20.9338	+	12.0861i	−0.668024	+	0.385684i
$983$	12.2764			0.391555			0.195778	−	0.980648i	$-0.437277\pi$
$983$	12.2764			0.391555			0.195778	+	0.980648i	$0.437277\pi$
$984$	−23.8470	+	13.7681i	−0.760215	+	0.438911i
$985$	12.3419	−	47.7792i	0.393247	−	1.52237i
$986$	−0.675045	+	0.180878i	−0.0214978	+	0.00576032i
$987$	11.9988	−	11.9988i	0.381927	−	0.381927i
$988$		0			0
$989$			17.4946i			0.556297i
$990$	11.9725	+	20.3119i	0.380510	+	0.645555i
$991$	−16.5995	+	28.7512i	−0.527301	+	0.913312i	0.472193	+	0.881495i	$0.343463\pi$
$991$	−16.5995	+	28.7512i	−0.527301	+	0.913312i	−0.999494	+	0.0318165i	$0.989871\pi$
$992$	−14.3013	−	3.83202i	−0.454066	−	0.121667i
$993$			24.5922i			0.780409i
$994$	25.4664	−	95.0419i	0.807745	−	3.01455i
$995$	−12.9812	−	12.7493i	−0.411531	−	0.404179i
$996$	−68.5794	−	68.5794i	−2.17302	−	2.17302i
$997$	−9.72750	+	36.3035i	−0.308073	+	1.14974i	0.622194	+	0.782863i	$0.286241\pi$
$997$	−9.72750	+	36.3035i	−0.308073	+	1.14974i	−0.930268	+	0.366882i	$0.880425\pi$
$998$	25.6070	−	6.86138i	0.810576	−	0.217193i
$999$	−0.377229	−	1.40784i	−0.0119350	−	0.0445421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.i.357.5		144
5.3	odd	4		845.2.t.i.188.32		144
13.2	odd	12		845.2.t.i.427.5		144
13.3	even	3	inner	845.2.o.i.587.5		144
13.4	even	6		845.2.k.f.577.5	yes	72
13.5	odd	4		845.2.t.i.657.32		144
13.6	odd	12		845.2.f.f.437.5	yes	72
13.7	odd	12		845.2.f.f.437.32	yes	72
13.8	odd	4		845.2.t.i.657.5		144
13.9	even	3		845.2.k.f.577.32	yes	72
13.10	even	6	inner	845.2.o.i.587.32		144
13.11	odd	12		845.2.t.i.427.32		144
13.12	even	2	inner	845.2.o.i.357.32		144
65.3	odd	12		845.2.t.i.418.5		144
65.8	even	4	inner	845.2.o.i.488.5		144
65.18	even	4	inner	845.2.o.i.488.32		144
65.23	odd	12		845.2.t.i.418.32		144
65.28	even	12	inner	845.2.o.i.258.32		144
65.33	even	12		845.2.k.f.268.32	yes	72
65.38	odd	4		845.2.t.i.188.5		144
65.43	odd	12		845.2.f.f.408.32	yes	72
65.48	odd	12		845.2.f.f.408.5	✓	72
65.58	even	12		845.2.k.f.268.5	yes	72
65.63	even	12	inner	845.2.o.i.258.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.f.f.408.5	✓	72	65.48	odd	12
845.2.f.f.408.32	yes	72	65.43	odd	12
845.2.f.f.437.5	yes	72	13.6	odd	12
845.2.f.f.437.32	yes	72	13.7	odd	12
845.2.k.f.268.5	yes	72	65.58	even	12
845.2.k.f.268.32	yes	72	65.33	even	12
845.2.k.f.577.5	yes	72	13.4	even	6
845.2.k.f.577.32	yes	72	13.9	even	3
845.2.o.i.258.5		144	65.63	even	12	inner
845.2.o.i.258.32		144	65.28	even	12	inner
845.2.o.i.357.5		144	1.1	even	1	trivial
845.2.o.i.357.32		144	13.12	even	2	inner
845.2.o.i.488.5		144	65.8	even	4	inner
845.2.o.i.488.32		144	65.18	even	4	inner
845.2.o.i.587.5		144	13.3	even	3	inner
845.2.o.i.587.32		144	13.10	even	6	inner
845.2.t.i.188.5		144	65.38	odd	4
845.2.t.i.188.32		144	5.3	odd	4
845.2.t.i.418.5		144	65.3	odd	12
845.2.t.i.418.32		144	65.23	odd	12
845.2.t.i.427.5		144	13.2	odd	12
845.2.t.i.427.32		144	13.11	odd	12
845.2.t.i.657.5		144	13.8	odd	4
845.2.t.i.657.32		144	13.5	odd	4

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.18621 + 2.05458i) q^{2} +(0.604804 + 2.25716i) q^{3} +(-1.81419 - 3.14226i) q^{4} +(-2.15457 + 0.598181i) q^{5} +(-5.35492 - 1.43485i) q^{6} +(-3.23750 + 1.86917i) q^{7} +3.86318 q^{8} +(-2.13090 + 1.23027i) q^{9} +(1.32677 - 5.13630i) q^{10} +(1.74477 - 0.467511i) q^{11} +(5.99536 - 5.99536i) q^{12} -8.86890i q^{14} +(-2.65328 - 4.50143i) q^{15} +(-0.954169 + 1.65267i) q^{16} +(-0.372153 - 0.0997182i) q^{17} -5.83745i q^{18} +(1.41754 - 5.29032i) q^{19} +(5.78843 + 5.68502i) q^{20} +(-6.17706 - 6.17706i) q^{21} +(-1.10913 + 4.13933i) q^{22} +(-8.92587 + 2.39168i) q^{23} +(2.33647 + 8.71981i) q^{24} +(4.28436 - 2.57765i) q^{25} +(0.891365 + 0.891365i) q^{27} +(11.7468 + 6.78204i) q^{28} +(-0.662140 - 0.382287i) q^{29} +(12.3959 - 0.111731i) q^{30} +(-3.27268 + 3.27268i) q^{31} +(1.59949 + 2.77040i) q^{32} +(2.11049 + 3.65548i) q^{33} +(0.646330 - 0.646330i) q^{34} +(5.85732 - 5.96387i) q^{35} +(7.73169 + 4.46389i) q^{36} +(-1.00131 - 0.578108i) q^{37} +(9.18786 + 9.18786i) q^{38} +(-8.32350 + 2.31088i) q^{40} +(0.789472 + 2.94635i) q^{41} +(20.0185 - 5.36394i) q^{42} +(0.489998 - 1.82870i) q^{43} +(-4.63438 - 4.63438i) q^{44} +(3.85525 - 3.92538i) q^{45} +(5.67406 - 21.1759i) q^{46} +1.94248i q^{47} +(-4.30742 - 1.15417i) q^{48} +(3.48758 - 6.04067i) q^{49} +(0.213823 + 11.8602i) q^{50} -0.900318i q^{51} +(-1.18715 + 1.18715i) q^{53} +(-2.88872 + 0.774031i) q^{54} +(-3.47958 + 2.05098i) q^{55} +(-12.5070 + 7.22094i) q^{56} +12.7984 q^{57} +(1.57087 - 0.906945i) q^{58} +(-6.15548 - 1.64935i) q^{59} +(-9.33112 + 16.5037i) q^{60} +(1.85832 + 3.21870i) q^{61} +(-2.84189 - 10.6061i) q^{62} +(4.59918 - 7.96601i) q^{63} -11.4060 q^{64} -10.0139 q^{66} +(5.52807 - 9.57490i) q^{67} +(0.361815 + 1.35031i) q^{68} +(-10.7968 - 18.7006i) q^{69} +(5.30521 + 19.1087i) q^{70} +(10.7163 + 2.87143i) q^{71} +(-8.23204 + 4.75277i) q^{72} -4.49691 q^{73} +(2.37553 - 1.37151i) q^{74} +(8.40935 + 8.11150i) q^{75} +(-19.1952 + 5.14335i) q^{76} +(-4.77484 + 4.77484i) q^{77} -7.15052i q^{79} +(1.06723 - 4.13156i) q^{80} +(-5.16367 + 8.94374i) q^{81} +(-6.98997 - 1.87296i) q^{82} -11.4388i q^{83} +(-8.20360 + 30.6163i) q^{84} +(0.861480 - 0.00776503i) q^{85} +(3.17596 + 3.17596i) q^{86} +(0.462417 - 1.72576i) q^{87} +(6.74037 - 1.80608i) q^{88} +(0.599649 + 2.23792i) q^{89} +(3.49185 + 12.5772i) q^{90} +(23.7085 + 23.7085i) q^{92} +(-9.36630 - 5.40763i) q^{93} +(-3.99098 - 2.30419i) q^{94} +(0.110383 + 12.2463i) q^{95} +(-5.28585 + 5.28585i) q^{96} +(-0.441485 - 0.764675i) q^{97} +(8.27401 + 14.3310i) q^{98} +(-3.14277 + 3.14277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 4 q^{3} - 80 q^{4} - 12 q^{10} - 128 q^{12} - 80 q^{16} + 8 q^{17} - 24 q^{22} + 36 q^{23} + 96 q^{25} - 128 q^{27} - 4 q^{30} - 80 q^{35} - 56 q^{38} - 48 q^{40} + 56 q^{42} + 76 q^{43} + 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) \) 144 * q + 4 * q^3 - 80 * q^4 - 12 * q^10 - 128 * q^12 - 80 * q^16 + 8 * q^17 - 24 * q^22 + 36 * q^23 + 96 * q^25 - 128 * q^27 - 4 * q^30 - 80 * q^35 - 56 * q^38 - 48 * q^40 + 56 * q^42 + 76 * q^43 + 76 * q^48 + 8 * q^49 - 32 * q^53 - 12 * q^55 - 8 * q^61 + 148 * q^62 + 240 * q^64 + 80 * q^66 + 48 * q^68 - 40 * q^69 - 164 * q^75 - 344 * q^77 - 16 * q^81 + 44 * q^82 - 20 * q^87 + 124 * q^88 + 600 * q^90 - 8 * q^92 - 92 * q^95

Introduction

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