LMFDB - Embedded newform 845.2.t.i.427.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(188,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.188"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [144,0,4,80,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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			427.5
Character	$\chi$	$=$	845.427
Dual form			845.2.t.i.188.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05458 + 1.18621i) q^{2} +(-2.25716 - 0.604804i) q^{3} +(1.81419 - 3.14226i) q^{4} +(0.598181 + 2.15457i) q^{5} +(5.35492 - 1.43485i) q^{6} +(-1.86917 + 3.23750i) q^{7} +3.86318i q^{8} +(2.13090 + 1.23027i) q^{9} +(-3.78478 - 3.71716i) q^{10} +(-1.74477 - 0.467511i) q^{11} +(-5.99536 + 5.99536i) q^{12} -8.86890i q^{14} +(-0.0470959 - 5.22499i) q^{15} +(-0.954169 - 1.65267i) q^{16} +(-0.0997182 - 0.372153i) q^{17} -5.83745 q^{18} +(1.41754 + 5.29032i) q^{19} +(7.85544 + 2.02915i) q^{20} +(6.17706 - 6.17706i) q^{21} +(4.13933 - 1.10913i) q^{22} +(-2.39168 + 8.92587i) q^{23} +(2.33647 - 8.71981i) q^{24} +(-4.28436 + 2.57765i) q^{25} +(0.891365 + 0.891365i) q^{27} +(6.78204 + 11.7468i) q^{28} +(0.662140 - 0.382287i) q^{29} +(6.29470 + 10.6793i) q^{30} +(3.27268 + 3.27268i) q^{31} +(-2.77040 - 1.59949i) q^{32} +(3.65548 + 2.11049i) q^{33} +(0.646330 + 0.646330i) q^{34} +(-8.09352 - 2.09065i) q^{35} +(7.73169 - 4.46389i) q^{36} +(0.578108 + 1.00131i) q^{37} +(-9.18786 - 9.18786i) q^{38} +(-8.32350 + 2.31088i) q^{40} +(-0.789472 + 2.94635i) q^{41} +(-5.36394 + 20.0185i) q^{42} +(1.82870 - 0.489998i) q^{43} +(-4.63438 + 4.63438i) q^{44} +(-1.37605 + 5.32710i) q^{45} +(-5.67406 - 21.1759i) q^{46} -1.94248 q^{47} +(1.15417 + 4.30742i) q^{48} +(-3.48758 - 6.04067i) q^{49} +(5.74491 - 10.3781i) q^{50} +0.900318i q^{51} +(-1.18715 + 1.18715i) q^{53} +(-2.88872 - 0.774031i) q^{54} +(-0.0364049 - 4.03890i) q^{55} +(-12.5070 - 7.22094i) q^{56} -12.7984i q^{57} +(-0.906945 + 1.57087i) q^{58} +(-6.15548 + 1.64935i) q^{59} +(-16.5037 - 9.33112i) q^{60} +(1.85832 - 3.21870i) q^{61} +(-10.6061 - 2.84189i) q^{62} +(-7.96601 + 4.59918i) q^{63} +11.4060 q^{64} -10.0139 q^{66} +(9.57490 - 5.52807i) q^{67} +(-1.35031 - 0.361815i) q^{68} +(10.7968 - 18.7006i) q^{69} +(19.1087 - 5.30521i) q^{70} +(-10.7163 + 2.87143i) q^{71} +(-4.75277 + 8.23204i) q^{72} -4.49691i q^{73} +(-2.37553 - 1.37151i) q^{74} +(11.2294 - 3.22696i) q^{75} +(19.1952 + 5.14335i) q^{76} +(4.77484 - 4.77484i) q^{77} -7.15052i q^{79} +(2.99003 - 3.04442i) q^{80} +(-5.16367 - 8.94374i) q^{81} +(-1.87296 - 6.98997i) q^{82} -11.4388 q^{83} +(-8.20360 - 30.6163i) q^{84} +(0.742181 - 0.437465i) q^{85} +(-3.17596 + 3.17596i) q^{86} +(-1.72576 + 0.462417i) q^{87} +(1.80608 - 6.74037i) q^{88} +(0.599649 - 2.23792i) q^{89} +(-3.49185 - 12.5772i) q^{90} +(23.7085 + 23.7085i) q^{92} +(-5.40763 - 9.36630i) q^{93} +(3.99098 - 2.30419i) q^{94} +(-10.5504 + 6.21875i) q^{95} +(5.28585 + 5.28585i) q^{96} +(0.764675 + 0.441485i) q^{97} +(14.3310 + 8.27401i) 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.05458	+	1.18621i	−1.45280	+	0.838777i	−0.998640	−	0.0521412i	$-0.983395\pi$
$2$	−2.05458	+	1.18621i	−1.45280	+	0.838777i	−0.454164	+	0.890918i	$0.650062\pi$
$3$	−2.25716	−	0.604804i	−1.30317	−	0.349184i	−0.460522	−	0.887648i	$-0.652338\pi$
$3$	−2.25716	−	0.604804i	−1.30317	−	0.349184i	−0.842648	+	0.538465i	$0.819005\pi$
$4$	1.81419	−	3.14226i	0.907093	−	1.57113i
$5$	0.598181	+	2.15457i	0.267515	+	0.963554i
$5$	0.598181	+	2.15457i	0.267515	+	0.963554i
$6$	5.35492	−	1.43485i	2.18614	−	0.585774i
$7$	−1.86917	+	3.23750i	−0.706479	+	1.22366i	0.259676	+	0.965696i	$0.416384\pi$
$7$	−1.86917	+	3.23750i	−0.706479	+	1.22366i	−0.966155	+	0.257962i	$0.916949\pi$
$8$			3.86318i			1.36584i
$9$	2.13090	+	1.23027i	0.710299	+	0.410091i
$10$	−3.78478	−	3.71716i	−1.19685	−	1.17547i
$11$	−1.74477	−	0.467511i	−0.526069	−	0.140960i	−0.0139966	−	0.999902i	$-0.504455\pi$
$11$	−1.74477	−	0.467511i	−0.526069	−	0.140960i	−0.512072	+	0.858942i	$0.671122\pi$
$12$	−5.99536	+	5.99536i	−1.73071	+	1.73071i
$13$		0			0
$13$		0			0
$14$		−	8.86890i		−	2.37031i
$15$	−0.0470959	−	5.22499i	−0.0121601	−	1.34909i
$16$	−0.954169	−	1.65267i	−0.238542	−	0.413167i
$17$	−0.0997182	−	0.372153i	−0.0241852	−	0.0902604i	0.952778	−	0.303667i	$-0.0982109\pi$
$17$	−0.0997182	−	0.372153i	−0.0241852	−	0.0902604i	−0.976964	+	0.213406i	$0.931544\pi$
$18$	−5.83745			−1.37590
$19$	1.41754	+	5.29032i	0.325205	+	1.21368i	0.914106	+	0.405476i	$0.132894\pi$
$19$	1.41754	+	5.29032i	0.325205	+	1.21368i	−0.588901	+	0.808205i	$0.700439\pi$
$20$	7.85544	+	2.02915i	1.75653	+	0.453732i
$21$	6.17706	−	6.17706i	1.34794	−	1.34794i
$22$	4.13933	−	1.10913i	0.882509	−	0.236468i
$23$	−2.39168	+	8.92587i	−0.498699	+	1.86117i	0.00953735	+	0.999955i	$0.496964\pi$
$23$	−2.39168	+	8.92587i	−0.498699	+	1.86117i	−0.508237	+	0.861217i	$0.669703\pi$
$24$	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
$28$	6.78204	+	11.7468i	1.28169	+	2.21994i
$29$	0.662140	−	0.382287i	0.122956	−	0.0709889i	−0.437260	−	0.899335i	$-0.644051\pi$
$29$	0.662140	−	0.382287i	0.122956	−	0.0709889i	0.560217	+	0.828346i	$0.310718\pi$
$30$	6.29470	+	10.6793i	1.14925	+	1.94976i
$31$	3.27268	+	3.27268i	0.587792	+	0.587792i	0.937033	−	0.349241i	$-0.113561\pi$
$31$	3.27268	+	3.27268i	0.587792	+	0.587792i	−0.349241	+	0.937033i	$0.613561\pi$
$32$	−2.77040	−	1.59949i	−0.489742	−	0.282753i
$33$	3.65548	+	2.11049i	0.636337	+	0.367389i
$34$	0.646330	+	0.646330i	0.110845	+	0.110845i
$35$	−8.09352	−	2.09065i	−1.36805	−	0.353384i
$36$	7.73169	−	4.46389i	1.28861	−	0.743982i
$37$	0.578108	+	1.00131i	0.0950403	+	0.164615i	0.909625	−	0.415429i	$-0.136369\pi$
$37$	0.578108	+	1.00131i	0.0950403	+	0.164615i	−0.814585	+	0.580044i	$0.803035\pi$
$38$	−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	$-0.993220\pi$
$41$	−0.789472	+	2.94635i	−0.123295	+	0.460142i	0.876478	+	0.481441i	$0.159887\pi$
$42$	−5.36394	+	20.0185i	−0.827675	+	3.08892i
$43$	1.82870	−	0.489998i	0.278874	−	0.0747240i	−0.116671	−	0.993171i	$-0.537222\pi$
$43$	1.82870	−	0.489998i	0.278874	−	0.0747240i	0.395545	+	0.918447i	$0.370556\pi$
$44$	−4.63438	+	4.63438i	−0.698660	+	0.698660i
$45$	−1.37605	+	5.32710i	−0.205130	+	0.794117i
$46$	−5.67406	−	21.1759i	−0.836595	−	3.12222i
$47$	−1.94248			−0.283340			−0.141670	−	0.989914i	$-0.545247\pi$
$47$	−1.94248			−0.283340			−0.141670	+	0.989914i	$0.545247\pi$
$48$	1.15417	+	4.30742i	0.166590	+	0.621723i
$49$	−3.48758	−	6.04067i	−0.498226	−	0.862953i
$50$	5.74491	−	10.3781i	0.812453	−	1.46769i
$51$			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
$55$	−0.0364049	−	4.03890i	−0.00490884	−	0.544605i
$56$	−12.5070	−	7.22094i	−1.67132	−	0.964938i
$57$		−	12.7984i		−	1.69519i
$58$	−0.906945	+	1.57087i	−0.119088	+	0.206266i
$59$	−6.15548	+	1.64935i	−0.801375	+	0.214728i	−0.636187	−	0.771535i	$-0.719490\pi$
$59$	−6.15548	+	1.64935i	−0.801375	+	0.214728i	−0.165187	+	0.986262i	$0.552823\pi$
$60$	−16.5037	−	9.33112i	−2.13062	−	1.20464i
$61$	1.85832	−	3.21870i	0.237933	−	0.412113i	−0.722188	−	0.691697i	$-0.756863\pi$
$61$	1.85832	−	3.21870i	0.237933	−	0.412113i	0.960121	+	0.279584i	$0.0901966\pi$
$62$	−10.6061	−	2.84189i	−1.34697	−	0.360920i
$63$	−7.96601	+	4.59918i	−1.00362	+	0.579442i
$64$	11.4060			1.42575
$65$		0			0
$66$	−10.0139			−1.23263
$67$	9.57490	−	5.52807i	1.16976	−	0.675361i	0.216136	−	0.976363i	$-0.430654\pi$
$67$	9.57490	−	5.52807i	1.16976	−	0.675361i	0.953623	+	0.301002i	$0.0973211\pi$
$68$	−1.35031	−	0.361815i	−0.163749	−	0.0438765i
$69$	10.7968	−	18.7006i	1.29978	−	2.25129i
$70$	19.1087	−	5.30521i	2.28393	−	0.634094i
$71$	−10.7163	+	2.87143i	−1.27179	+	0.340776i	−0.830717	−	0.556695i	$-0.812069\pi$
$71$	−10.7163	+	2.87143i	−1.27179	+	0.340776i	−0.441075	+	0.897470i	$0.645403\pi$
$72$	−4.75277	+	8.23204i	−0.560119	+	0.970155i
$73$		−	4.49691i		−	0.526323i	−0.964752	−	0.263161i	$-0.915235\pi$
$73$		−	4.49691i		−	0.526323i	0.964752	−	0.263161i	$-0.0847652\pi$
$74$	−2.37553	−	1.37151i	−0.276150	−	0.159435i
$75$	11.2294	−	3.22696i	1.29666	−	0.372617i
$76$	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	$-0.131771\pi$
$80$	2.99003	−	3.04442i	0.334295	−	0.340377i
$81$	−5.16367	−	8.94374i	−0.573741	−	0.993749i
$82$	−1.87296	−	6.98997i	−0.206834	−	0.771914i
$83$	−11.4388			−1.25557			−0.627783	−	0.778388i	$-0.716038\pi$
$83$	−11.4388			−1.25557			−0.627783	+	0.778388i	$0.716038\pi$
$84$	−8.20360	−	30.6163i	−0.895087	−	3.34051i
$85$	0.742181	−	0.437465i	0.0805009	−	0.0474497i
$86$	−3.17596	+	3.17596i	−0.342472	+	0.342472i
$87$	−1.72576	+	0.462417i	−0.185021	+	0.0495763i
$88$	1.80608	−	6.74037i	0.192529	−	0.718526i
$89$	0.599649	−	2.23792i	0.0635626	−	0.237219i	−0.926835	−	0.375470i	$-0.877481\pi$
$89$	0.599649	−	2.23792i	0.0635626	−	0.237219i	0.990397	+	0.138251i	$0.0441480\pi$
$90$	−3.49185	−	12.5772i	−0.368074	−	1.32575i
$91$		0			0
$92$	23.7085	+	23.7085i	2.47178	+	2.47178i
$93$	−5.40763	−	9.36630i	−0.560746	−	0.971240i
$94$	3.99098	−	2.30419i	0.411638	−	0.237659i
$95$	−10.5504	+	6.21875i	−1.08245	+	0.638030i
$96$	5.28585	+	5.28585i	0.539485	+	0.539485i
$97$	0.764675	+	0.441485i	0.0776409	+	0.0448260i	0.538318	−	0.842742i	$-0.319060\pi$
$97$	0.764675	+	0.441485i	0.0776409	+	0.0448260i	−0.460677	+	0.887568i	$0.652393\pi$
$98$	14.3310	+	8.27401i	1.44765	+	0.835801i
$99$	−3.14277	−	3.14277i	−0.315860	−	0.315860i
$100$	0.327020	+	18.1389i	0.0327020	+	1.81389i
$101$	6.87788	−	3.97094i	0.684374	−	0.395124i	−0.117127	−	0.993117i	$-0.537368\pi$
$101$	6.87788	−	3.97094i	0.684374	−	0.395124i	0.801501	+	0.597993i	$0.204035\pi$
$102$	−1.06797	−	1.84977i	−0.105744	−	0.183155i
$103$	10.7428	+	10.7428i	1.05852	+	1.05852i	0.998178	+	0.0603388i	$0.0192181\pi$
$103$	10.7428	+	10.7428i	1.05852	+	1.05852i	0.0603388	+	0.998178i	$0.480782\pi$
$104$		0			0
$105$	17.0039	+	9.61392i	1.65941	+	0.938222i
$106$	1.03088	−	3.84731i	0.100128	−	0.373684i
$107$	2.70430	−	10.0926i	0.261434	−	0.975686i	−0.702963	−	0.711227i	$-0.748140\pi$
$107$	2.70430	−	10.0926i	0.261434	−	0.975686i	0.964397	−	0.264459i	$-0.0851934\pi$
$108$	4.41800	−	1.18380i	0.425123	−	0.113911i
$109$	−4.13475	+	4.13475i	−0.396037	+	0.396037i	−0.876833	−	0.480796i	$-0.840348\pi$
$109$	−4.13475	+	4.13475i	−0.396037	+	0.396037i	0.480796	+	0.876833i	$0.340348\pi$
$110$	4.86577	+	8.25503i	0.463933	+	0.787086i
$111$	−0.699283	−	2.60976i	−0.0663730	−	0.247707i
$112$	7.13401			0.674101
$113$	−3.79539	−	14.1646i	−0.357040	−	1.33249i	−0.877897	−	0.478849i	$-0.841054\pi$
$113$	−3.79539	−	14.1646i	−0.357040	−	1.33249i	0.520857	−	0.853644i	$-0.325612\pi$
$114$	15.1816	+	26.2953i	1.42189	+	2.46278i
$115$	−20.6621	+	0.186239i	−1.92675	+	0.0173669i
$116$		−	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
$120$	20.1851	−	0.181940i	1.84264	−	0.0166088i
$121$	−6.70061	−	3.86860i	−0.609146	−	0.351691i
$122$			8.81743i			0.798292i
$123$	3.56393	−	6.17290i	0.321348	−	0.556592i
$124$	16.2209	−	4.34637i	1.45668	−	0.390316i
$125$	−8.11655	−	7.68906i	−0.725966	−	0.687730i
$126$	10.9112	−	18.8987i	0.972046	−	1.68363i
$127$	−6.79351	−	1.82032i	−0.602827	−	0.161527i	−0.0555178	−	0.998458i	$-0.517681\pi$
$127$	−6.79351	−	1.82032i	−0.602827	−	0.161527i	−0.547309	+	0.836931i	$0.684348\pi$
$128$	−17.8937	+	10.3309i	−1.58159	+	0.913134i
$129$	−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	$0.633895\pi$
$132$	13.2634	−	7.65764i	1.15443	−	0.666512i
$133$	−19.7770	−	5.29923i	−1.71488	−	0.459501i
$134$	−13.1149	+	22.7157i	−1.13295	+	1.96233i
$135$	−1.38731	+	2.45371i	−0.119401	+	0.211181i
$136$	1.43770	−	0.385229i	0.123281	−	0.0330331i
$137$	6.84910	−	11.8630i	0.585158	−	1.01352i	−0.409697	−	0.912222i	$-0.634366\pi$
$137$	6.84910	−	11.8630i	0.585158	−	1.01352i	0.994856	−	0.101303i	$-0.0323010\pi$
$138$			51.2290i			4.36090i
$139$	7.78210	+	4.49300i	0.660069	+	0.381091i	0.792303	−	0.610127i	$-0.208882\pi$
$139$	7.78210	+	4.49300i	0.660069	+	0.381091i	−0.132234	+	0.991219i	$0.542215\pi$
$140$	−21.2525	+	21.6391i	−1.79617	+	1.82884i
$141$	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
$145$	1.21974	+	1.19795i	0.101294	+	0.0994845i
$146$	5.33427	+	9.23923i	0.441467	+	0.764644i
$147$	4.21861	+	15.7441i	0.347945	+	1.29855i
$148$	4.19518			0.344842
$149$	3.28972	+	12.2774i	0.269505	+	1.00581i	0.959435	+	0.281930i	$0.0909745\pi$
$149$	3.28972	+	12.2774i	0.269505	+	1.00581i	−0.689930	+	0.723876i	$0.742359\pi$
$150$	−19.2439	+	19.9505i	−1.57126	+	1.62895i
$151$	2.96123	−	2.96123i	0.240981	−	0.240981i	−0.576275	−	0.817256i	$-0.695494\pi$
$151$	2.96123	−	2.96123i	0.240981	−	0.240981i	0.817256	+	0.576275i	$0.195494\pi$
$152$	−20.4374	+	5.47620i	−1.65770	+	0.444178i
$153$	0.245361	−	0.915701i	0.0198363	−	0.0740300i
$154$	−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	$-0.513147\pi$
$158$	8.48201	+	14.6913i	0.674793	+	1.16878i
$159$	3.39759	−	1.96160i	0.269446	−	0.155565i
$160$	1.78902	−	6.92581i	0.141434	−	0.547533i
$161$	−24.4270	−	24.4270i	−1.92512	−	1.92512i
$162$	21.2183	+	12.2504i	1.66707	+	0.962482i
$163$	−13.7211	−	7.92191i	−1.07472	−	0.620492i	−0.145255	−	0.989394i	$-0.546400\pi$
$163$	−13.7211	−	7.92191i	−1.07472	−	0.620492i	−0.929468	+	0.368903i	$0.879734\pi$
$164$	7.82595	+	7.82595i	0.611104	+	0.611104i
$165$	−2.36057	+	9.13844i	−0.183770	+	0.711427i
$166$	23.5018	−	13.5688i	1.82409	−	1.05314i
$167$	6.24168	+	10.8109i	0.482996	+	0.836573i	0.999809	−	0.0195249i	$-0.00621537\pi$
$167$	6.24168	+	10.8109i	0.482996	+	0.836573i	−0.516814	+	0.856098i	$0.672882\pi$
$168$	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
$172$	1.77790	−	6.63520i	0.135563	−	0.505929i
$173$	15.6112	−	4.18301i	1.18690	−	0.318029i	0.389239	−	0.921137i	$-0.372738\pi$
$173$	15.6112	−	4.18301i	1.18690	−	0.318029i	0.797660	+	0.603108i	$0.206071\pi$
$174$	2.99719	−	2.99719i	0.227216	−	0.227216i
$175$	−0.336931	−	18.6887i	−0.0254696	−	1.41273i
$176$	0.892168	+	3.32962i	0.0672497	+	0.250979i
$177$	14.8914			1.11931
$178$	1.42262	+	5.30928i	0.106630	+	0.397947i
$179$	9.22405	+	15.9765i	0.689438	+	1.19414i	0.972020	+	0.234898i	$0.0754757\pi$
$179$	9.22405	+	15.9765i	0.689438	+	1.19414i	−0.282582	+	0.959243i	$0.591191\pi$
$180$	14.2427	+	13.9883i	1.06159	+	1.04262i
$181$			2.18983i			0.162769i	0.996683	+	0.0813844i	$0.0259342\pi$
$181$			2.18983i			0.162769i	−0.996683	+	0.0813844i	$0.974066\pi$
$182$		0			0
$183$	−6.14120	+	6.14120i	−0.453971	+	0.453971i
$184$	−34.4822	−	9.23949i	−2.54206	−	0.681144i
$185$	−1.81159	+	1.84454i	−0.133190	+	0.135613i
$186$	22.2208	+	12.8292i	1.62931	+	0.940681i
$187$			0.695942i			0.0508923i
$188$	−3.52402	+	6.10379i	−0.257016	+	0.445164i
$189$	−4.55190	+	1.21968i	−0.331102	+	0.0887185i
$190$	14.2999	−	25.2919i	1.03742	−	1.83487i
$191$	−4.07316	+	7.05492i	−0.294724	+	0.510476i	−0.974921	−	0.222553i	$-0.928561\pi$
$191$	−4.07316	+	7.05492i	−0.294724	+	0.510476i	0.680197	+	0.733029i	$0.261894\pi$
$192$	−25.7451	−	6.89839i	−1.85800	−	0.497849i
$193$	20.1326	−	11.6235i	1.44917	−	0.836681i	0.450741	−	0.892655i	$-0.351160\pi$
$193$	20.1326	−	11.6235i	1.44917	−	0.836681i	0.998432	+	0.0559740i	$0.0178264\pi$
$194$	−2.09477			−0.150396
$195$		0			0
$196$	−25.3085			−1.80775
$197$	−19.1122	+	11.0344i	−1.36169	+	0.786172i	−0.989849	−	0.142125i	$-0.954606\pi$
$197$	−19.1122	+	11.0344i	−1.36169	+	0.786172i	−0.371840	+	0.928297i	$0.621273\pi$
$198$	10.1850	+	2.72907i	0.723819	+	0.193947i
$199$	−4.06851	+	7.04686i	−0.288409	+	0.499538i	−0.973430	−	0.228984i	$-0.926460\pi$
$199$	−4.06851	+	7.04686i	−0.288409	+	0.499538i	0.685021	+	0.728523i	$0.259793\pi$
$200$	−9.95792	−	16.5513i	−0.704131	−	1.17035i
$201$	−24.9554	+	6.68679i	−1.76022	+	0.471650i
$202$	−9.42075	+	16.3172i	−0.662841	+	1.14807i
$203$			2.85823i			0.200609i
$204$	2.82904	+	1.63335i	0.198072	+	0.114357i
$205$	−6.82037	+	0.0614760i	−0.476355	+	0.00429367i
$206$	−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
$210$	−46.3399	+	0.417689i	−3.19776	+	0.0288233i
$211$	12.3867	+	21.4544i	0.852737	+	1.47698i	0.878729	+	0.477322i	$0.158392\pi$
$211$	12.3867	+	21.4544i	0.852737	+	1.47698i	−0.0259913	+	0.999662i	$0.508274\pi$
$212$	1.57663	+	5.88407i	0.108284	+	0.404120i
$213$	25.9250			1.77635
$214$	6.41572	+	23.9438i	0.438570	+	1.63676i
$215$	2.14963	+	3.64695i	0.146603	+	0.248720i
$216$	−3.44350	+	3.44350i	−0.234301	+	0.234301i
$217$	−16.7125	+	4.47810i	−1.13452	+	0.303993i
$218$	3.59047	−	13.3998i	0.243177	−	0.907551i
$219$	−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
$223$	−14.7610	−	25.5668i	−0.988469	−	1.71208i	−0.625373	−	0.780326i	$-0.715053\pi$
$223$	−14.7610	−	25.5668i	−0.988469	−	1.71208i	−0.363096	−	0.931752i	$-0.618280\pi$
$224$	10.3567	−	5.97944i	0.691986	−	0.399518i
$225$	−12.3007	+	0.221766i	−0.820050	+	0.0147844i
$226$	24.6001	+	24.6001i	1.63637	+	1.63637i
$227$	−6.81284	−	3.93339i	−0.452184	−	0.261068i	0.256568	−	0.966526i	$-0.417408\pi$
$227$	−6.81284	−	3.93339i	−0.452184	−	0.261068i	−0.708752	+	0.705458i	$0.750741\pi$
$228$	−40.2160	−	23.2187i	−2.66337	−	1.53770i
$229$	12.4410	+	12.4410i	0.822125	+	0.822125i	0.986412	−	0.164288i	$-0.0525326\pi$
$229$	12.4410	+	12.4410i	0.822125	+	0.822125i	−0.164288	+	0.986412i	$0.552533\pi$
$230$	42.2309	−	24.8922i	2.78462	−	1.64134i
$231$	−13.6654	+	7.88973i	−0.899118	+	0.519106i
$232$	1.47684	+	2.55797i	0.0969595	+	0.167939i
$233$	−1.52992	−	1.52992i	−0.100228	−	0.100228i	0.655214	−	0.755443i	$-0.272578\pi$
$233$	−1.52992	−	1.52992i	−0.100228	−	0.100228i	−0.755443	+	0.655214i	$0.772578\pi$
$234$		0			0
$235$	−1.16196	−	4.18522i	−0.0757976	−	0.273013i
$236$	−5.98447	+	22.3344i	−0.389556	+	1.45384i
$237$	−4.32466	+	16.1398i	−0.280917	+	1.04840i
$238$	−3.30059	+	0.884391i	−0.213946	+	0.0573265i
$239$	7.05936	−	7.05936i	0.456632	−	0.456632i	−0.440916	−	0.897548i	$-0.645346\pi$
$239$	7.05936	−	7.05936i	0.456632	−	0.456632i	0.897548	+	0.440916i	$0.145346\pi$
$240$	−8.59024	+	5.06336i	−0.554498	+	0.326838i
$241$	3.75087	+	13.9984i	0.241615	+	0.901719i	0.975055	+	0.221965i	$0.0712470\pi$
$241$	3.75087	+	13.9984i	0.241615	+	0.901719i	−0.733440	+	0.679755i	$0.762086\pi$
$242$	18.3559			1.17996
$243$	5.26723	+	19.6576i	0.337893	+	1.26103i
$244$	−6.74268	−	11.6787i	−0.431656	−	0.747649i
$245$	10.9289	−	11.1277i	0.698219	−	0.710921i
$246$			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
$250$	25.7969	+	6.16982i	1.63154	+	0.390214i
$251$	−15.3843	−	8.88214i	−0.971050	−	0.560636i	−0.0714936	−	0.997441i	$-0.522777\pi$
$251$	−15.3843	−	8.88214i	−0.971050	−	0.560636i	−0.899556	+	0.436805i	$0.856110\pi$
$252$			33.3751i			2.10243i
$253$	8.34588	−	14.4555i	0.524701	−	0.908808i
$254$	16.1171	−	4.31855i	1.01127	−	0.270970i
$255$	−1.93980	+	0.538553i	−0.121475	+	0.0337255i
$256$	13.1033	−	22.6956i	0.818955	−	1.41847i
$257$	−8.70771	−	2.33322i	−0.543172	−	0.145543i	−0.0232081	−	0.999731i	$-0.507388\pi$
$257$	−8.70771	−	2.33322i	−0.543172	−	0.145543i	−0.519964	+	0.854188i	$0.674055\pi$
$258$	9.08947	−	5.24781i	0.565885	−	0.326714i
$259$	−4.32232			−0.268576
$260$		0			0
$261$	1.88127			0.116448
$262$	19.2051	−	11.0881i	1.18650	−	0.685023i
$263$	4.11740	+	1.10325i	0.253890	+	0.0680295i	0.383519	−	0.923533i	$-0.374712\pi$
$263$	4.11740	+	1.10325i	0.253890	+	0.0680295i	−0.129629	+	0.991563i	$0.541379\pi$
$264$	−8.15321	+	14.1218i	−0.501795	+	0.869135i
$265$	−3.26794	−	1.84768i	−0.200748	−	0.113502i
$266$	46.9193	−	12.5720i	2.87681	−	0.770838i
$267$	−2.70700	+	4.68867i	−0.165666	+	0.286942i
$268$		−	40.1158i		−	2.45046i
$269$	1.55678	+	0.898805i	0.0949183	+	0.0548011i	0.546708	−	0.837323i	$-0.315881\pi$
$269$	1.55678	+	0.898805i	0.0949183	+	0.0548011i	−0.451790	+	0.892125i	$0.649214\pi$
$270$	−0.0602736	−	6.68697i	−0.00366813	−	0.406956i
$271$	2.84859	+	0.763276i	0.173039	+	0.0463657i	0.344298	−	0.938860i	$-0.388117\pi$
$271$	2.84859	+	0.763276i	0.173039	+	0.0463657i	−0.171259	+	0.985226i	$0.554784\pi$
$272$	−0.519898	+	0.519898i	−0.0315235	+	0.0315235i
$273$		0			0
$274$			32.4979i			1.96327i
$275$	8.68031	−	2.49443i	0.523443	−	0.150420i
$276$	−39.1748	−	67.8527i	−2.35804	−	4.08425i
$277$	7.37510	+	27.5242i	0.443127	+	1.65377i	0.720836	+	0.693106i	$0.243758\pi$
$277$	7.37510	+	27.5242i	0.443127	+	1.65377i	−0.277709	+	0.960665i	$0.589575\pi$
$278$	−21.3186			−1.27860
$279$	2.94746	+	11.0001i	0.176460	+	0.658556i
$280$	8.07656	−	31.2667i	0.482667	−	1.86854i
$281$	−2.57874	+	2.57874i	−0.153835	+	0.153835i	−0.779828	−	0.625993i	$-0.784694\pi$
$281$	−2.57874	+	2.57874i	−0.153835	+	0.153835i	0.625993	+	0.779828i	$0.284694\pi$
$282$	−10.4018	+	2.78717i	−0.619421	+	0.165973i
$283$	2.02074	−	7.54151i	0.120121	−	0.448296i	−0.879498	−	0.475902i	$-0.842122\pi$
$283$	2.02074	−	7.54151i	0.120121	−	0.448296i	0.999619	+	0.0276057i	$0.00878830\pi$
$284$	−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
$288$	−3.93563	−	6.81670i	−0.231909	−	0.401678i
$289$	14.5939	−	8.42578i	0.858463	−	0.495634i
$290$	−3.92708	−	1.01441i	−0.230606	−	0.0595682i
$291$	−1.45898	−	1.45898i	−0.0855269	−	0.0855269i
$292$	−14.1305	−	8.15822i	−0.826922	−	0.477424i
$293$	19.5374	+	11.2799i	1.14139	+	0.658979i	0.946773	−	0.321901i	$-0.104322\pi$
$293$	19.5374	+	11.2799i	1.14139	+	0.658979i	0.194612	+	0.980880i	$0.437655\pi$
$294$	−27.3432	−	27.3432i	−1.59469	−	1.59469i
$295$	−7.23574	−	12.2758i	−0.421281	−	0.714725i
$296$	−3.86825	+	2.23333i	−0.224837	+	0.129810i
$297$	−1.13851	−	1.97195i	−0.0660629	−	0.114424i
$298$	−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
$302$	−2.57143	+	9.59671i	−0.147969	+	0.552229i
$303$	−17.9261	+	4.80328i	−1.02983	+	0.275941i
$304$	7.39057	−	7.39057i	0.423878	−	0.423878i
$305$	8.04654	+	2.07852i	0.460744	+	0.119015i
$306$	0.582100	+	2.17243i	0.0332764	+	0.124189i
$307$	20.4085			1.16477			0.582387	−	0.812912i	$-0.302119\pi$
$307$	20.4085			1.16477			0.582387	+	0.812912i	$0.302119\pi$
$308$	−6.34135	−	23.6662i	−0.361332	−	1.34851i
$309$	−17.7509	−	30.7454i	−1.00981	−	1.74904i
$310$	−0.221297	−	24.5515i	−0.0125688	−	1.39443i
$311$		−	21.3762i		−	1.21213i	−0.795413	−	0.606067i	$-0.792746\pi$
$311$		−	21.3762i		−	1.21213i	0.795413	−	0.606067i	$-0.207254\pi$
$312$		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
$315$	−14.6744	−	14.4122i	−0.826808	−	0.812036i
$316$	−22.4688	−	12.9724i	−1.26397	−	0.729753i
$317$			25.8830i			1.45373i	0.686779	+	0.726867i	$0.259024\pi$
$317$			25.8830i			1.45373i	−0.686779	+	0.726867i	$0.740976\pi$
$318$	−4.65374	+	8.06051i	−0.260969	+	0.452011i
$319$	−1.33401	+	0.357446i	−0.0746901	+	0.0200132i
$320$	6.82285	+	24.5751i	0.381409	+	1.37379i
$321$	−12.2080	+	21.1450i	−0.681387	+	1.18020i
$322$	79.1627	+	21.2116i	4.41156	+	1.18207i
$323$	1.82745	−	1.05508i	0.101682	−	0.0587063i
$324$	−37.4715			−2.08175
$325$		0			0
$326$	37.5882			2.08182
$327$	11.8335	−	6.83207i	0.654393	−	0.377814i
$328$	−11.3823	−	3.04987i	−0.628481	−	0.168401i
$329$	3.63083	−	6.28878i	0.200174	−	0.346711i
$330$	−5.99015	−	21.5757i	−0.329747	−	1.18771i
$331$	−10.1654	+	2.72380i	−0.558738	+	0.149714i	−0.527127	−	0.849787i	$-0.676731\pi$
$331$	−10.1654	+	2.72380i	−0.558738	+	0.149714i	−0.0316117	+	0.999500i	$0.510064\pi$
$332$	−20.7520	+	35.9436i	−1.13892	+	1.97266i
$333$			2.84492i			0.155901i
$334$	−25.6480	−	14.8079i	−1.40340	−	0.810251i
$335$	17.6381	+	17.3230i	0.963675	+	0.946457i
$336$	−16.1026	−	4.31468i	−0.878468	−	0.235385i
$337$	−6.67935	+	6.67935i	−0.363847	+	0.363847i	−0.865227	−	0.501380i	$-0.832826\pi$
$337$	−6.67935	+	6.67935i	−0.363847	+	0.363847i	0.501380	+	0.865227i	$0.332826\pi$
$338$		0			0
$339$			34.2672i			1.86114i
$340$	−0.0281744	−	3.12577i	−0.00152797	−	0.169519i
$341$	−4.18008	−	7.24011i	−0.226364	−	0.392074i
$342$	−8.27480	−	30.8820i	−0.447450	−	1.66991i
$343$	−0.0928245			−0.00501205
$344$	1.89295	+	7.06459i	0.102061	+	0.380897i
$345$	46.7502	+	12.0761i	2.51695	+	0.650157i
$346$	−27.1125	+	27.1125i	−1.45758	+	1.45758i
$347$	6.88301	−	1.84430i	0.369500	−	0.0990071i	−0.0692910	−	0.997596i	$-0.522074\pi$
$347$	6.88301	−	1.84430i	0.369500	−	0.0990071i	0.438791	+	0.898589i	$0.355407\pi$
$348$	−1.67782	+	6.26171i	−0.0899406	+	0.335663i
$349$	8.44064	−	31.5009i	0.451817	−	1.68620i	−0.245464	−	0.969406i	$-0.578940\pi$
$349$	8.44064	−	31.5009i	0.451817	−	1.68620i	0.697281	−	0.716798i	$-0.254393\pi$
$350$	22.8609	+	37.9976i	1.22197	+	2.03106i
$351$		0			0
$352$	4.08594	+	4.08594i	0.217781	+	0.217781i
$353$	6.46025	+	11.1895i	0.343844	+	0.595556i	0.985143	−	0.171736i	$-0.0549375\pi$
$353$	6.46025	+	11.1895i	0.343844	+	0.595556i	−0.641299	+	0.767291i	$0.721604\pi$
$354$	−30.5955	+	17.6643i	−1.62613	+	0.938849i
$355$	−12.5970	−	21.3714i	−0.668578	−	1.13428i
$356$	−5.94425	−	5.94425i	−0.315045	−	0.315045i
$357$	−2.91478	−	1.68285i	−0.154266	−	0.0890657i
$358$	−37.9030	−	21.8833i	−2.00324	−	1.15657i
$359$	−12.5304	−	12.5304i	−0.661330	−	0.661330i	0.294364	−	0.955693i	$-0.404892\pi$
$359$	−12.5304	−	12.5304i	−0.661330	−	0.661330i	−0.955693	+	0.294364i	$0.904892\pi$
$360$	−20.5795	−	5.31594i	−1.08464	−	0.280174i
$361$	−9.52355	+	5.49842i	−0.501239	+	0.289391i
$362$	−2.59760	−	4.49917i	−0.136527	−	0.236471i
$363$	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
$367$	−9.02077	+	33.6660i	−0.470880	+	1.75735i	0.165738	+	0.986170i	$0.446999\pi$
$367$	−9.02077	+	33.6660i	−0.470880	+	1.75735i	−0.636618	+	0.771179i	$0.719667\pi$
$368$	17.0336	−	4.56413i	0.887936	−	0.237922i
$369$	−5.30710	+	5.30710i	−0.276277	+	0.276277i
$370$	1.53403	−	5.93867i	0.0797503	−	0.308737i
$371$	−1.62442	−	6.06240i	−0.0843354	−	0.314744i
$372$	−39.2418			−2.03459
$373$	3.86524	+	14.4253i	0.200135	+	0.746912i	0.990878	+	0.134764i	$0.0430277\pi$
$373$	3.86524	+	14.4253i	0.200135	+	0.746912i	−0.790743	+	0.612148i	$0.790306\pi$
$374$	−0.825533	−	1.42987i	−0.0426873	−	0.0739366i
$375$	13.6700	+	22.2643i	0.705914	+	1.14973i
$376$		−	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	−0.659887	−	0.751365i	$-0.729396\pi$
$379$	−31.2859	−	8.38303i	−1.60705	−	0.430607i	−0.947161	+	0.320758i	$0.896062\pi$
$380$	0.400511	+	44.4342i	0.0205458	+	2.27942i
$381$	14.2331	+	8.21748i	0.729183	+	0.420994i
$382$		−	19.3265i		−	0.988829i
$383$	16.1146	−	27.9113i	0.823418	−	1.42620i	−0.0797046	−	0.996819i	$-0.525398\pi$
$383$	16.1146	−	27.9113i	0.823418	−	1.42620i	0.903122	−	0.429383i	$-0.141269\pi$
$384$	46.6371	−	12.4964i	2.37994	−	0.637702i
$385$	13.1440	+	7.43152i	0.669878	+	0.378745i
$386$	−27.5759	+	47.7629i	−1.40358	+	2.43107i
$387$	4.49960	+	1.20566i	0.228728	+	0.0612874i
$388$	2.77452	−	1.60187i	0.140855	−	0.0813227i
$389$	11.7818			0.597359			0.298679	−	0.954354i	$-0.403454\pi$
$389$	11.7818			0.597359			0.298679	+	0.954354i	$0.403454\pi$
$390$		0			0
$391$	3.56028			0.180051
$392$	23.3362	−	13.4732i	1.17866	−	0.680498i
$393$	21.0987	+	5.65339i	1.06429	+	0.285176i
$394$	26.1783	−	45.3422i	1.31884	−	2.28431i
$395$	15.4063	−	4.27730i	0.775175	−	0.215214i
$396$	−15.5770	+	4.17383i	−0.782772	+	0.209743i
$397$	4.07389	−	7.05618i	0.204462	−	0.354139i	−0.745499	−	0.666507i	$-0.767789\pi$
$397$	4.07389	−	7.05618i	0.204462	−	0.354139i	0.949961	+	0.312367i	$0.101122\pi$
$398$		−	19.3044i		−	0.967642i
$399$	41.4348	+	23.9224i	2.07433	+	1.19762i
$400$	8.34800	+	4.62112i	0.417400	+	0.231056i
$401$	−15.9505	−	4.27393i	−0.796531	−	0.213430i	−0.162471	−	0.986713i	$-0.551946\pi$
$401$	−15.9505	−	4.27393i	−0.796531	−	0.213430i	−0.634060	+	0.773284i	$0.718613\pi$
$402$	43.3409	−	43.3409i	2.16165	−	2.16165i
$403$		0			0
$404$		−	28.8161i		−	1.43366i
$405$	16.1811	−	16.4755i	0.804047	−	0.818673i
$406$	−3.39047	−	5.87246i	−0.168266	−	0.291445i
$407$	−0.540543	−	2.01733i	−0.0267937	−	0.0999955i
$408$	−3.47809			−0.172191
$409$	−1.09321	−	4.07993i	−0.0540560	−	0.201740i	0.933617	−	0.358274i	$-0.116635\pi$
$409$	−1.09321	−	4.07993i	−0.0540560	−	0.201740i	−0.987673	+	0.156534i	$0.949968\pi$
$410$	13.9400	−	8.21669i	0.688449	−	0.405793i
$411$	−22.6343	+	22.6343i	−1.11647	+	1.11647i
$412$	53.2460	−	14.2672i	2.62324	−	0.702895i
$413$	6.16584	−	23.0112i	0.303401	−	1.13231i
$414$	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
$418$	11.7353	+	20.3261i	0.573993	+	0.994184i
$419$	14.7910	−	8.53958i	0.722587	−	0.417186i	−0.0931173	−	0.995655i	$-0.529683\pi$
$419$	14.7910	−	8.53958i	0.722587	−	0.417186i	0.815704	+	0.578470i	$0.196350\pi$
$420$	61.0577	−	35.9893i	2.97931	−	1.75610i
$421$	−9.26544	−	9.26544i	−0.451570	−	0.451570i	0.444305	−	0.895875i	$-0.353451\pi$
$421$	−9.26544	−	9.26544i	−0.451570	−	0.451570i	−0.895875	+	0.444305i	$0.853451\pi$
$422$	−50.8989	−	29.3865i	−2.47772	−	1.43051i
$423$	−4.13923	−	2.38979i	−0.201256	−	0.116195i
$424$	−4.58619	−	4.58619i	−0.222725	−	0.222725i
$425$	1.38651	+	1.33740i	0.0672555	+	0.0648734i
$426$	−53.2649	+	30.7525i	−2.58070	+	1.48997i
$427$	6.94703	+	12.0326i	0.336190	+	0.582299i
$428$	−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	$-0.833586\pi$
$431$	2.77316	−	10.3496i	0.133578	−	0.498521i	1.00000		0.000792423i	$0.000252236\pi$
$432$	0.622619	−	2.32364i	0.0299558	−	0.111796i
$433$	4.93240	−	1.32163i	0.237036	−	0.0635136i	−0.138345	−	0.990384i	$-0.544178\pi$
$433$	4.93240	−	1.32163i	0.237036	−	0.0635136i	0.375381	+	0.926870i	$0.377512\pi$
$434$	29.0251	−	29.0251i	1.39325	−	1.39325i
$435$	−2.02863	−	3.44167i	−0.0972653	−	0.165016i
$436$	5.49126	+	20.4937i	0.262984	+	0.981468i
$437$	−50.6109			−2.42105
$438$	−6.45237	−	24.0806i	−0.308306	−	1.15061i
$439$	10.1196	+	17.5277i	0.482985	+	0.836554i	0.999809	−	0.0195376i	$-0.00621940\pi$
$439$	10.1196	+	17.5277i	0.482985	+	0.836554i	−0.516825	+	0.856091i	$0.672886\pi$
$440$	15.6030	−	0.140639i	0.743843	−	0.00670469i
$441$		−	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
$445$	5.18046	−	0.0466945i	0.245577	−	0.00221353i
$446$	60.6551	+	35.0192i	2.87210	+	1.65821i
$447$		−	29.7017i		−	1.40484i
$448$	−21.3197	+	36.9269i	−1.00726	+	1.74463i
$449$	−29.7674	+	7.97615i	−1.40481	+	0.376418i	−0.880070	−	0.474844i	$-0.842505\pi$
$449$	−29.7674	+	7.97615i	−1.40481	+	0.376418i	−0.524741	+	0.851262i	$0.675838\pi$
$450$	25.0097	−	15.0469i	1.17897	−	0.709317i
$451$	2.75490	−	4.77163i	0.129723	−	0.224687i
$452$	−51.3944	−	13.7711i	−2.41739	−	0.647737i
$453$	−8.47493	+	4.89300i	−0.398187	+	0.229893i
$454$	18.6633			0.875913
$455$		0			0
$456$	49.4426			2.31536
$457$	−8.81597	+	5.08990i	−0.412394	+	0.238096i	−0.691818	−	0.722072i	$-0.743190\pi$
$457$	−8.81597	+	5.08990i	−0.412394	+	0.238096i	0.279424	+	0.960168i	$0.409857\pi$
$458$	−40.3186	−	10.8033i	−1.88396	−	0.504807i
$459$	0.242839	−	0.420610i	0.0113348	−	0.0196324i
$460$	−36.8996	+	65.2635i	−1.72045	+	3.04293i
$461$	18.6200	−	4.98920i	0.867218	−	0.232370i	0.202334	−	0.979317i	$-0.435147\pi$
$461$	18.6200	−	4.98920i	0.867218	−	0.232370i	0.664884	+	0.746946i	$0.268481\pi$
$462$	18.7177	−	32.4201i	0.870828	−	1.50832i
$463$		−	16.7929i		−	0.780432i	−0.920723	−	0.390216i	$-0.872400\pi$
$463$		−	16.7929i		−	0.780432i	0.920723	−	0.390216i	$-0.127600\pi$
$464$	−1.26359	−	0.729533i	−0.0586606	−	0.0338677i
$465$	16.9456	−	17.2539i	0.785834	−	0.800129i
$466$	4.95814	+	1.32853i	0.229681	+	0.0615430i
$467$	−9.75781	+	9.75781i	−0.451538	+	0.451538i	−0.895865	−	0.444327i	$-0.853443\pi$
$467$	−9.75781	+	9.75781i	−0.451538	+	0.451538i	0.444327	+	0.895865i	$0.353443\pi$
$468$		0			0
$469$			41.3316i			1.90851i
$470$	7.35187	+	7.22052i	0.339116	+	0.333058i
$471$	21.5412	+	37.3104i	0.992564	+	1.71917i
$472$	−6.37175	−	23.7797i	−0.293284	−	1.09455i
$473$	−3.41974			−0.157240
$474$	−10.2599	−	38.2905i	−0.471253	−	1.75874i
$475$	−19.7098	−	19.0117i	−0.904348	−	0.872317i
$476$	3.69533	−	3.69533i	0.169375	−	0.169375i
$477$	−3.99023	+	1.06918i	−0.182700	+	0.0489543i
$478$	−6.13011	+	22.8779i	−0.280384	+	1.04641i
$479$	3.57686	−	13.3490i	0.163431	−	0.609933i	−0.834804	−	0.550547i	$-0.814419\pi$
$479$	3.57686	−	13.3490i	0.163431	−	0.609933i	0.998235	−	0.0593859i	$-0.0189142\pi$
$480$	−8.22685	+	14.5506i	−0.375503	+	0.664143i
$481$		0			0
$482$	−24.3115	−	24.3115i	−1.10736	−	1.10736i
$483$	40.3621	+	69.9091i	1.83654	+	3.18098i
$484$	−24.3123	+	14.0367i	−1.10510	+	0.638033i
$485$	−0.493798	+	1.91163i	−0.0224222	+	0.0868028i
$486$	−34.1399	−	34.1399i	−1.54862	−	1.54862i
$487$	−17.7182	−	10.2296i	−0.802887	−	0.463547i	0.0415923	−	0.999135i	$-0.486757\pi$
$487$	−17.7182	−	10.2296i	−0.802887	−	0.463547i	−0.844480	+	0.535587i	$0.820090\pi$
$488$	12.4344	+	7.17902i	0.562880	+	0.324979i
$489$	26.1796	+	26.1796i	1.18388	+	1.18388i
$490$	−9.25442	+	35.8265i	−0.418072	+	1.61848i
$491$	8.82381	−	5.09443i	0.398213	−	0.229908i	−0.287500	−	0.957781i	$-0.592824\pi$
$491$	8.82381	−	5.09443i	0.398213	−	0.229908i	0.685713	+	0.727872i	$0.259491\pi$
$492$	−12.9312	−	22.3976i	−0.582986	−	1.00976i
$493$	−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
$497$	10.7344	−	40.0612i	0.481502	−	1.79699i
$498$	−61.2537	+	16.4129i	−2.74484	+	0.735478i
$499$	−7.90149	+	7.90149i	−0.353719	+	0.353719i	−0.861491	−	0.507772i	$-0.830469\pi$
$499$	−7.90149	+	7.90149i	−0.353719	+	0.353719i	0.507772	+	0.861491i	$0.330469\pi$
$500$	−38.8860	+	11.5549i	−1.73903	+	0.516753i
$501$	−7.54998	−	28.1769i	−0.337308	−	1.25885i
$502$	42.1443			1.88099
$503$	3.66412	+	13.6747i	0.163375	+	0.609723i	0.998242	+	0.0592717i	$0.0188778\pi$
$503$	3.66412	+	13.6747i	0.163375	+	0.609723i	−0.834867	+	0.550452i	$0.814455\pi$
$504$	−17.7675	−	30.7741i	−0.791426	−	1.37079i
$505$	12.6699	+	12.4435i	0.563803	+	0.553730i
$506$			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	−0.274283	−	0.961649i	$-0.588440\pi$
$509$	−22.3950	−	6.00073i	−0.992643	−	0.265978i	−0.718360	+	0.695671i	$0.755107\pi$
$510$	3.34663	−	3.40751i	0.148191	−	0.150887i
$511$	14.5587	+	8.40548i	0.644039	+	0.371836i
$512$			20.8492i			0.921415i
$513$	−3.45206	+	5.97914i	−0.152412	+	0.263986i
$514$	20.6583	−	5.53539i	0.911200	−	0.244155i
$515$	−16.7200	+	29.5722i	−0.736769	+	1.30311i
$516$	−8.02598	+	13.9014i	−0.353324	+	0.611975i
$517$	3.38919	+	0.908131i	0.149056	+	0.0399396i
$518$	8.88054	−	5.12718i	0.390188	−	0.225275i
$519$	−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	$0.778429\pi$
$522$	−3.86521	+	2.23158i	−0.169176	+	0.0976737i
$523$	−39.0069	−	10.4519i	−1.70565	−	0.457029i	−0.731301	−	0.682055i	$-0.761087\pi$
$523$	−39.0069	−	10.4519i	−1.70565	−	0.457029i	−0.974353	+	0.225026i	$0.927753\pi$
$524$	−16.9581	+	29.3722i	−0.740817	+	1.28313i
$525$	−10.5425	+	42.3870i	−0.460111	+	1.84992i
$526$	−9.76819	+	2.61738i	−0.425913	+	0.114123i
$527$	0.891594	−	1.54429i	0.0388384	−	0.0672702i
$528$		−	8.05506i		−	0.350551i
$529$	−54.0324	−	31.1956i	−2.34923	−	1.35633i
$530$	8.90597	−	0.0802747i	0.386850	−	0.00348691i
$531$	−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
$535$	23.3628	−	0.210583i	1.01006	−	0.00910429i
$536$	21.3559	+	36.9895i	0.922435	+	1.59771i
$537$	−11.1575	−	41.6403i	−0.481481	−	1.79691i
$538$	−4.26468			−0.183864
$539$	3.26097	+	12.1701i	0.140460	+	0.524203i
$540$	5.19335	+	8.81078i	0.223486	+	0.379156i
$541$	−16.7846	+	16.7846i	−0.721626	+	0.721626i	−0.968936	−	0.247310i	$-0.920453\pi$
$541$	−16.7846	+	16.7846i	−0.721626	+	0.721626i	0.247310	+	0.968936i	$0.420453\pi$
$542$	−6.75804	+	1.81081i	−0.290283	+	0.0777810i
$543$	1.32442	−	4.94279i	0.0568362	−	0.212116i
$544$	−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	$0.652080\pi$
$548$	−24.8511	−	43.0434i	−1.06159	−	1.83872i
$549$	7.91978	−	4.57249i	0.338008	−	0.195149i
$550$	−14.8754	+	15.4217i	−0.634291	+	0.657582i
$551$	2.96103	+	2.96103i	0.126144	+	0.126144i
$552$	72.2438	+	41.7100i	3.07490	+	1.77529i
$553$	23.1498	+	13.3655i	0.984428	+	0.568360i
$554$	−47.8022	−	47.8022i	−2.03092	−	2.03092i
$555$	5.20462	−	3.06776i	0.220924	−	0.130219i
$556$	28.2364	−	16.3023i	1.19749	−	0.691370i
$557$	−8.98097	−	15.5555i	−0.380536	−	0.659108i	0.610603	−	0.791937i	$-0.290927\pi$
$557$	−8.98097	−	15.5555i	−0.380536	−	0.659108i	−0.991139	+	0.132829i	$0.957594\pi$
$558$	−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
$562$	2.23929	−	8.35714i	0.0944587	−	0.352525i
$563$	−14.5293	+	3.89312i	−0.612338	+	0.164075i	−0.551642	−	0.834081i	$-0.685999\pi$
$563$	−14.5293	+	3.89312i	−0.612338	+	0.164075i	−0.0606957	+	0.998156i	$0.519332\pi$
$564$	11.6459	−	11.6459i	0.490380	−	0.490380i
$565$	28.2483	−	16.6504i	1.18841	−	0.700489i
$566$	4.79405	+	17.8916i	0.201509	+	0.752041i
$567$	38.6071			1.62135
$568$	−11.0928	−	41.3990i	−0.465445	−	1.73706i
$569$	10.9760	+	19.0110i	0.460138	+	0.796983i	0.998967	−	0.0454320i	$-0.0144664\pi$
$569$	10.9760	+	19.0110i	0.460138	+	0.796983i	−0.538829	+	0.842415i	$0.681133\pi$
$570$	−47.5737	+	48.4392i	−1.99265	+	2.02889i
$571$			12.0101i			0.502606i	0.967908	+	0.251303i	$0.0808590\pi$
$571$			12.0101i			0.502606i	−0.967908	+	0.251303i	$0.919141\pi$
$572$		0			0
$573$	13.4606	−	13.4606i	0.562325	−	0.562325i
$574$	26.1309	+	7.00175i	1.09068	+	0.292247i
$575$	−12.7609	−	44.4065i	−0.532167	−	1.85188i
$576$	24.3050	+	14.0325i	1.01271	+	0.584688i
$577$			21.1801i			0.881741i	0.897571	+	0.440870i	$0.145330\pi$
$577$			21.1801i			0.881741i	−0.897571	+	0.440870i	$0.854670\pi$
$578$	−19.9895	+	34.6228i	−0.831453	+	1.44012i
$579$	−52.4723	+	14.0599i	−2.18068	+	0.584310i
$580$	5.97712	−	1.65945i	0.248186	−	0.0689048i
$581$	21.3810	−	37.0329i	0.887032	−	1.53638i
$582$	4.72824	+	1.26693i	0.195992	+	0.0525158i
$583$	2.62632	−	1.51631i	0.108771	−	0.0627991i
$584$	17.3724			0.718873
$585$		0			0
$586$	−53.5214			−2.21095
$587$	−29.8791	+	17.2507i	−1.23324	+	0.712013i	−0.967705	−	0.252087i	$-0.918883\pi$
$587$	−29.8791	+	17.2507i	−1.23324	+	0.712013i	−0.265539	+	0.964100i	$0.585550\pi$
$588$	57.1253	+	15.3067i	2.35581	+	0.631237i
$589$	−12.6744	+	21.9527i	−0.522239	+	0.904544i
$590$	29.4280	+	16.6385i	1.21153	+	0.684994i
$591$	49.8130	−	13.3473i	2.04903	−	0.549036i
$592$	1.10322	−	1.91084i	0.0453423	−	0.0785351i
$593$		−	28.3656i		−	1.16483i	−0.812890	−	0.582417i	$-0.802107\pi$
$593$		−	28.3656i		−	1.16483i	0.812890	−	0.582417i	$-0.197893\pi$
$594$	4.67830	+	2.70102i	0.191953	+	0.110824i
$595$	0.0290283	+	3.22050i	0.00119004	+	0.132028i
$596$	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	$-0.0196259\pi$
$600$	12.4663	+	43.3814i	0.508936	+	1.77104i
$601$	−6.79040	−	11.7613i	−0.276986	−	0.479754i	0.693648	−	0.720314i	$-0.256002\pi$
$601$	−6.79040	−	11.7613i	−0.276986	−	0.479754i	−0.970634	+	0.240560i	$0.922669\pi$
$602$	−4.34575	−	16.2185i	−0.177119	−	0.661019i
$603$	27.2042			1.10784
$604$	−3.93274	−	14.6772i	−0.160021	−	0.597206i
$605$	4.32700	−	16.7511i	0.175917	−	0.681028i
$606$	31.1328	−	31.1328i	1.26468	−	1.26468i
$607$	34.6357	−	9.28061i	1.40582	−	0.376689i	0.525389	−	0.850862i	$-0.323920\pi$
$607$	34.6357	−	9.28061i	1.40582	−	0.376689i	0.880431	+	0.474173i	$0.157253\pi$
$608$	4.53467	−	16.9236i	0.183905	−	0.686344i
$609$	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
$613$	2.25076	+	3.89843i	0.0909074	+	0.157456i	0.907893	−	0.419202i	$-0.137690\pi$
$613$	2.25076	+	3.89843i	0.0909074	+	0.157456i	−0.816986	+	0.576658i	$0.804357\pi$
$614$	−41.9308	+	24.2087i	−1.69219	+	0.976986i
$615$	15.4318	+	3.98622i	0.622271	+	0.160740i
$616$	18.4461	+	18.4461i	0.743213	+	0.743213i
$617$	33.3160	+	19.2350i	1.34125	+	0.774372i	0.986991	−	0.160776i	$-0.0513995\pi$
$617$	33.3160	+	19.2350i	1.34125	+	0.774372i	0.354260	+	0.935147i	$0.384733\pi$
$618$	72.9410	+	42.1125i	2.93412	+	1.69401i
$619$	−5.85514	−	5.85514i	−0.235338	−	0.235338i	0.579578	−	0.814916i	$-0.303217\pi$
$619$	−5.85514	−	5.85514i	−0.235338	−	0.235338i	−0.814916	+	0.579578i	$0.803217\pi$
$620$	19.0676	+	32.3492i	0.765773	+	1.29917i
$621$	−10.0881	+	5.82435i	−0.404820	+	0.233723i
$622$	25.3567	+	43.9191i	1.01671	+	1.76099i
$623$	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
$627$	−5.98339	+	22.3303i	−0.238954	+	0.891787i
$628$	−64.6155	+	17.3137i	−2.57844	+	0.690890i
$629$	0.314994	−	0.314994i	0.0125596	−	0.0125596i
$630$	47.2455	+	12.2041i	1.88231	+	0.486222i
$631$	9.66827	+	36.0825i	0.384888	+	1.43642i	0.838344	+	0.545142i	$0.183524\pi$
$631$	9.66827	+	36.0825i	0.384888	+	1.43642i	−0.453456	+	0.891279i	$0.649809\pi$
$632$	27.6237			1.09881
$633$	−14.9831	−	55.9176i	−0.595524	−	2.22252i
$634$	−30.7026	−	53.1785i	−1.21936	−	2.11199i
$635$	−0.141747	−	15.7260i	−0.00562508	−	0.624067i
$636$		−	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
$640$	−32.9624	−	32.3735i	−1.30295	−	1.27967i
$641$	−2.97232	−	1.71607i	−0.117399	−	0.0677806i	0.440150	−	0.897924i	$-0.354925\pi$
$641$	−2.97232	−	1.71607i	−0.117399	−	0.0677806i	−0.557550	+	0.830143i	$0.688258\pi$
$642$		−	57.9252i		−	2.28613i
$643$	8.23137	−	14.2572i	0.324614	−	0.562247i	−0.656820	−	0.754047i	$-0.728099\pi$
$643$	8.23137	−	14.2572i	0.324614	−	0.562247i	0.981434	+	0.191800i	$0.0614324\pi$
$644$	−121.071	+	32.4409i	−4.77087	+	1.27835i
$645$	−2.64636	−	9.53185i	−0.104200	−	0.375316i
$646$	−2.50309	+	4.33549i	−0.0984829	+	0.170577i
$647$	−18.4283	−	4.93784i	−0.724490	−	0.194127i	−0.122316	−	0.992491i	$-0.539032\pi$
$647$	−18.4283	−	4.93784i	−0.724490	−	0.194127i	−0.602174	+	0.798365i	$0.705699\pi$
$648$	34.5513	−	19.9482i	1.35730	−	0.783639i
$649$	11.5110			0.451846
$650$		0			0
$651$	40.4311			1.58462
$652$	−49.7854	+	28.7436i	−1.94975	+	1.12569i
$653$	36.9813	+	9.90911i	1.44719	+	0.387773i	0.895046	−	0.445975i	$-0.147143\pi$
$653$	36.9813	+	9.90911i	1.44719	+	0.387773i	0.552145	+	0.833748i	$0.313810\pi$
$654$	−16.2085	+	28.0740i	−0.633803	+	1.09778i
$655$	−5.59149	−	20.1398i	−0.218477	−	0.786928i
$656$	5.62263	−	1.50658i	0.219527	−	0.0588220i
$657$	5.53243	−	9.58244i	0.215841	−	0.373847i
$658$			17.2277i			0.671605i
$659$	34.0246	+	19.6441i	1.32541	+	0.765225i	0.984586	−	0.174903i	$-0.0559611\pi$
$659$	34.0246	+	19.6441i	1.32541	+	0.765225i	0.340823	+	0.940128i	$0.389294\pi$
$660$	24.4329	+	23.9964i	0.951048	+	0.934057i
$661$	26.1828	+	7.01565i	1.01839	+	0.272877i	0.729132	−	0.684373i	$-0.239924\pi$
$661$	26.1828	+	7.01565i	1.01839	+	0.272877i	0.289260	+	0.957251i	$0.406591\pi$
$662$	17.6545	−	17.6545i	0.686161	−	0.686161i
$663$		0			0
$664$		−	44.1900i		−	1.71490i
$665$	−0.412649	−	45.7808i	−0.0160019	−	1.77530i
$666$	−3.37468	−	5.84511i	−0.130766	−	0.226493i
$667$	1.82861	+	6.82448i	0.0708042	+	0.264245i
$668$	45.2943			1.75249
$669$	17.8550	+	66.6357i	0.690314	+	2.57629i
$670$	−56.7876	−	14.6689i	−2.19390	−	0.566709i
$671$	−4.74713	+	4.74713i	−0.183261	+	0.183261i
$672$	−26.9931	+	7.23277i	−1.04128	+	0.279010i
$673$	−1.83832	+	6.86071i	−0.0708621	+	0.264461i	−0.992263	−	0.124152i	$-0.960379\pi$
$673$	−1.83832	+	6.86071i	−0.0708621	+	0.264461i	0.921401	+	0.388613i	$0.127046\pi$
$674$	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	$0.574998\pi$
$678$	−40.6481	−	70.4045i	−1.56108	−	2.70387i
$679$	−2.85861	+	1.65042i	−0.109703	+	0.0633373i
$680$	1.69001	+	2.86718i	0.0648088	+	0.109951i
$681$	12.9987	+	12.9987i	0.498112	+	0.498112i
$682$	17.1766	+	9.91690i	0.657725	+	0.379738i
$683$	3.99823	+	2.30838i	0.152988	+	0.0883277i	0.574540	−	0.818477i	$-0.305181\pi$
$683$	3.99823	+	2.30838i	0.152988	+	0.0883277i	−0.421552	+	0.906804i	$0.638514\pi$
$684$	34.5753	+	34.5753i	1.32202	+	1.32202i
$685$	29.6567	+	7.66067i	1.13312	+	0.292699i
$686$	0.190715	−	0.110109i	0.00728153	−	0.00420399i
$687$	−20.5569	−	35.6057i	−0.784296	−	1.35844i
$688$	−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	$-0.981209\pi$
$691$	−2.74019	+	10.2265i	−0.104242	+	0.389036i	0.894016	+	0.448035i	$0.147876\pi$
$692$	15.1775	−	56.6433i	0.576963	−	2.15326i
$693$	16.0491	−	4.30033i	0.609653	−	0.163356i
$694$	−11.9539	+	11.9539i	−0.453766	+	0.453766i
$695$	−5.02538	+	19.4547i	−0.190624	+	0.737960i
$696$	−1.78640	−	6.66694i	−0.0677133	−	0.252710i
$697$	1.17522			0.0445146
$698$	20.0247	+	74.7333i	0.757947	+	2.82870i
$699$	2.52797	+	4.37857i	0.0956166	+	0.165613i
$700$	−59.3359	−	32.8460i	−2.24269	−	1.24146i
$701$			48.9646i			1.84937i	0.380735	+	0.924684i	$0.375671\pi$
$701$			48.9646i			1.84937i	−0.380735	+	0.924684i	$0.624329\pi$
$702$		0			0
$703$	−4.47777	+	4.47777i	−0.168882	+	0.168882i
$704$	−19.9009	−	5.33243i	−0.750043	−	0.200973i
$705$	0.0914829	+	10.1494i	0.00344545	+	0.382250i
$706$	−26.5461	−	15.3264i	−0.999076	−	0.576817i
$707$			29.6895i			1.11659i
$708$	27.0158	−	46.7927i	1.01532	−	1.75858i
$709$	23.7942	−	6.37565i	0.893611	−	0.239442i	0.217341	−	0.976096i	$-0.430262\pi$
$709$	23.7942	−	6.37565i	0.893611	−	0.239442i	0.676271	+	0.736653i	$0.263595\pi$
$710$	51.2324	+	28.9665i	1.92272	+	1.08709i
$711$	8.79710	−	15.2370i	0.329917	−	0.571433i
$712$	8.64548	+	2.31655i	0.324003	+	0.0868164i
$713$	−37.0388	+	21.3843i	−1.38711	+	0.800850i
$714$	7.98484			0.298825
$715$		0			0
$716$	66.9366			2.50154
$717$	−20.2036	+	11.6646i	−0.754518	+	0.435621i
$718$	40.6084	+	10.8810i	1.51549	+	0.406074i
$719$	23.3017	−	40.3597i	0.869007	−	1.50516i	0.00599476	−	0.999982i	$-0.498092\pi$
$719$	23.3017	−	40.3597i	0.869007	−	1.50516i	0.863012	−	0.505183i	$-0.168575\pi$
$720$	10.1169	−	2.80879i	0.377035	−	0.104678i
$721$	−54.8597	+	14.6996i	−2.04308	+	0.547442i
$722$	13.0446	−	22.5938i	0.485468	−	0.840856i
$723$		−	33.8652i		−	1.25946i
$724$	6.88102	+	3.97276i	0.255731	+	0.147646i
$725$	−1.85145	+	3.34462i	−0.0687610	+	0.124216i
$726$	−41.4321	−	11.1017i	−1.53769	−	0.412023i
$727$	16.4412	−	16.4412i	0.609770	−	0.609770i	−0.333116	−	0.942886i	$-0.608100\pi$
$727$	16.4412	−	16.4412i	0.609770	−	0.609770i	0.942886	+	0.333116i	$0.108100\pi$
$728$		0			0
$729$		−	16.5738i		−	0.613846i
$730$	−16.7157	+	17.0198i	−0.618677	+	0.629931i
$731$	−0.364709	−	0.631694i	−0.0134892	−	0.0233641i
$732$	8.15599	+	30.4386i	0.301454	+	1.12504i
$733$	30.6968			1.13381			0.566907	−	0.823782i	$-0.308140\pi$
$733$	30.6968			1.13381			0.566907	+	0.823782i	$0.308140\pi$
$734$	−21.4010	−	79.8698i	−0.789927	−	2.94805i
$735$	−31.3982	+	18.5071i	−1.15814	+	0.682644i
$736$	20.9028	−	20.9028i	0.770486	−	0.770486i
$737$	−19.2905	+	5.16886i	−0.710573	+	0.190397i
$738$	4.60850	−	17.1992i	0.169641	−	0.633110i
$739$	−8.93434	+	33.3434i	−0.328655	+	1.22656i	0.581931	+	0.813238i	$0.302297\pi$
$739$	−8.93434	+	33.3434i	−0.328655	+	1.22656i	−0.910586	+	0.413319i	$0.864369\pi$
$740$	2.50948	+	9.03881i	0.0922502	+	0.332273i
$741$		0			0
$742$	10.5288	+	10.5288i	0.386523	+	0.386523i
$743$	−0.153994	−	0.266725i	−0.00564949	−	0.00978520i	0.863187	−	0.504885i	$-0.168465\pi$
$743$	−0.153994	−	0.266725i	−0.00564949	−	0.00978520i	−0.868836	+	0.495099i	$0.835132\pi$
$744$	36.1837	−	20.8907i	1.32656	−	0.765889i
$745$	−24.4847	+	14.4321i	−0.897051	+	0.528750i
$746$	−25.0528	−	25.0528i	−0.917249	−	0.917249i
$747$	−24.3748	−	14.0728i	−0.891828	−	0.514897i
$748$	2.18683	+	1.26257i	0.0799586	+	0.0461641i
$749$	27.6199	+	27.6199i	1.00921	+	1.00921i
$750$	−54.4961	−	29.5283i	−1.98992	−	1.07822i
$751$	−18.1008	+	10.4505i	−0.660509	+	0.381345i	−0.792471	−	0.609910i	$-0.791206\pi$
$751$	−18.1008	+	10.4505i	−0.660509	+	0.381345i	0.131962	+	0.991255i	$0.457872\pi$
$752$	1.85346	+	3.21028i	0.0675886	+	0.117067i
$753$	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
$757$	−8.69270	+	32.4416i	−0.315942	+	1.17911i	0.607168	+	0.794573i	$0.292305\pi$
$757$	−8.69270	+	32.4416i	−0.315942	+	1.17911i	−0.923110	+	0.384537i	$0.874361\pi$
$758$	74.2232	−	19.8881i	2.69591	−	0.722367i
$759$	−27.5807	+	27.5807i	−1.00112	+	1.00112i
$760$	−24.0241	−	40.7582i	−0.871447	−	1.47845i
$761$	−12.4256	−	46.3730i	−0.450428	−	1.68102i	−0.701192	−	0.712973i	$-0.747348\pi$
$761$	−12.4256	−	46.3730i	−0.450428	−	1.68102i	0.250764	−	0.968048i	$-0.419318\pi$
$762$	−38.9906			−1.41248
$763$	−5.65768	−	21.1148i	−0.204822	−	0.764406i
$764$	14.7789	+	25.5979i	0.534684	+	0.926099i
$765$	2.11971	−	0.0191062i	0.0766384	−	0.000690787i
$766$			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	0.642395	−	0.766374i	$-0.277941\pi$
$769$	22.6156	+	6.05983i	0.815539	+	0.218523i	0.173144	+	0.984897i	$0.444608\pi$
$770$	−35.8206	+	0.322872i	−1.29088	+	0.0116355i
$771$	18.2435	+	10.5329i	0.657025	+	0.379334i
$772$		−	84.3490i		−	3.03579i
$773$	−13.4470	+	23.2908i	−0.483653	+	0.837712i	−0.999824	−	0.0187736i	$-0.994024\pi$
$773$	−13.4470	+	23.2908i	−0.483653	+	0.837712i	0.516170	+	0.856486i	$0.327357\pi$
$774$	−10.6749	+	2.86034i	−0.383703	+	0.102813i
$775$	−22.4572	−	5.58553i	−0.806686	−	0.200638i
$776$	−1.70554	+	2.95408i	−0.0612252	+	0.106045i
$777$	9.75617	+	2.61416i	0.350000	+	0.0937823i
$778$	−24.2065	+	13.9756i	−0.867845	+	0.501051i
$779$	−16.7062			−0.598563
$780$		0			0
$781$	20.0399			0.717086
$782$	−7.31487	+	4.22324i	−0.261579	+	0.151023i
$783$	0.930966	+	0.249452i	0.0332700	+	0.00891467i
$784$	−6.65549	+	11.5276i	−0.237696	+	0.411702i
$785$	20.2901	−	35.8867i	0.724186	−	1.28085i
$786$	−50.0551	+	13.4122i	−1.78540	+	0.478398i
$787$	0.727317	−	1.25975i	0.0259261	−	0.0449053i	−0.852771	−	0.522285i	$-0.825080\pi$
$787$	0.727317	−	1.25975i	0.0259261	−	0.0449053i	0.878697	+	0.477379i	$0.158413\pi$
$788$			80.0741i			2.85252i
$789$	−8.62637	−	4.98043i	−0.307107	−	0.177308i
$790$	−26.5796	+	27.0631i	−0.945661	+	0.962863i
$791$	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
$795$	6.25878	+	6.14696i	0.221976	+	0.218010i
$796$	14.7620	+	25.5686i	0.523227	+	0.906256i
$797$	3.22058	+	12.0194i	0.114079	+	0.425748i	0.999216	−	0.0395816i	$-0.0126025\pi$
$797$	3.22058	+	12.0194i	0.114079	+	0.425748i	−0.885138	+	0.465330i	$0.845936\pi$
$798$	−113.508			−4.01813
$799$	0.193701	+	0.722901i	0.00685264	+	0.0255744i
$800$	15.9923	−	0.288320i	0.565414	−	0.0101936i
$801$	4.03104	−	4.03104i	0.142430	−	0.142430i
$802$	37.8413	−	10.1396i	1.33622	−	0.358040i
$803$	−2.10235	+	7.84608i	−0.0741904	+	0.276882i
$804$	−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
$808$	15.3405	+	26.5705i	0.539676	+	0.934746i
$809$	−6.25034	+	3.60863i	−0.219750	+	0.126873i	−0.605835	−	0.795591i	$-0.707161\pi$
$809$	−6.25034	+	3.60863i	−0.219750	+	0.126873i	0.386084	+	0.922463i	$0.373827\pi$
$810$	−13.7020	+	53.0443i	−0.481438	+	1.86379i
$811$	15.0515	+	15.0515i	0.528530	+	0.528530i	0.920134	−	0.391604i	$-0.128080\pi$
$811$	15.0515	+	15.0515i	0.528530	+	0.528530i	−0.391604	+	0.920134i	$0.628080\pi$
$812$	8.98132	+	5.18537i	0.315183	+	0.181971i
$813$	−5.96807	−	3.44567i	−0.209309	−	0.120845i
$814$	3.50357	+	3.50357i	0.122800	+	0.122800i
$815$	8.86059	−	34.3019i	0.310373	−	1.20154i
$816$	1.48793	−	0.859056i	0.0520879	−	0.0300730i
$817$	5.18449	+	8.97980i	0.181382	+	0.314163i
$818$	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	−0.840371	−	0.542012i	$-0.817663\pi$
$821$	4.53915	−	16.9404i	0.158418	−	0.591222i	0.998788	−	0.0492105i	$-0.0156705\pi$
$822$	19.6548	−	73.3529i	0.685541	−	2.55847i
$823$	10.5771	−	2.83413i	0.368695	−	0.0987916i	−0.0697141	−	0.997567i	$-0.522209\pi$
$823$	10.5771	−	2.83413i	0.368695	−	0.0987916i	0.438409	+	0.898775i	$0.355542\pi$
$824$	−41.5013	+	41.5013i	−1.44576	+	1.44576i
$825$	−21.1015	+	0.380431i	−0.734659	+	0.0132449i
$826$	14.6280	+	54.5923i	0.508972	+	1.89951i
$827$	−1.86613			−0.0648917			−0.0324458	−	0.999473i	$-0.510330\pi$
$827$	−1.86613			−0.0648917			−0.0324458	+	0.999473i	$0.510330\pi$
$828$	21.3524	+	79.6882i	0.742047	+	2.76936i
$829$	−17.3922	−	30.1241i	−0.604055	−	1.04625i	−0.992200	−	0.124656i	$-0.960217\pi$
$829$	−17.3922	−	30.1241i	−0.604055	−	1.04625i	0.388145	−	0.921598i	$-0.373116\pi$
$830$	43.2932	+	42.5197i	1.50273	+	1.47588i
$831$		−	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
$835$	−19.5592	+	19.9150i	−0.676875	+	0.689188i
$836$	−31.0868	−	17.9480i	−1.07516	−	0.620743i
$837$			5.83431i			0.201663i
$838$	−20.2595	+	35.0904i	−0.699851	+	1.21218i
$839$	18.7439	−	5.02241i	0.647111	−	0.173393i	0.0796889	−	0.996820i	$-0.474607\pi$
$839$	18.7439	−	5.02241i	0.647111	−	0.173393i	0.567422	+	0.823427i	$0.307941\pi$
$840$	−37.1403	+	65.6892i	−1.28146	+	2.26649i
$841$	−14.2077	+	24.6085i	−0.489921	+	0.848568i
$842$	30.0273	+	8.04579i	1.03481	+	0.277276i
$843$	7.38026	−	4.26099i	0.254190	−	0.146756i
$844$	89.8873			3.09405
$845$		0			0
$846$	11.3391			0.389848
$847$	25.0491	−	14.4621i	0.860699	−	0.496925i
$848$	3.09472	+	0.829228i	0.106273	+	0.0284758i
$849$	−9.12227	+	15.8002i	−0.313075	+	0.542263i
$850$	−4.43512	−	1.10310i	−0.152123	−	0.0378360i
$851$	−10.3202	+	2.76530i	−0.353773	+	0.0947931i
$852$	47.0328	−	81.4633i	1.61132	−	2.79089i
$853$			2.67051i			0.0914364i	0.998954	+	0.0457182i	$0.0145576\pi$
$853$			2.67051i			0.0914364i	−0.998954	+	0.0457182i	$0.985442\pi$
$854$	−28.5464	−	16.4813i	−0.976837	−	0.563977i
$855$	−30.1326	+	0.271603i	−1.03051	+	0.00928863i
$856$	38.9894	+	10.4472i	1.33263	+	0.357077i
$857$	−17.5773	+	17.5773i	−0.600430	+	0.600430i	−0.940427	−	0.339996i	$-0.889574\pi$
$857$	−17.5773	+	17.5773i	−0.600430	+	0.600430i	0.339996	+	0.940427i	$0.389574\pi$
$858$		0			0
$859$		−	52.8699i		−	1.80390i	−0.431844	−	0.901949i	$-0.642137\pi$
$859$		−	52.8699i		−	1.80390i	0.431844	−	0.901949i	$-0.357863\pi$
$860$	15.3595	−	0.138444i	0.523755	−	0.00472091i
$861$	13.3232	+	23.0764i	0.454052	+	0.786441i
$862$	6.57909	+	24.5535i	0.224085	+	0.836296i
$863$	3.40127			0.115780			0.0578902	−	0.998323i	$-0.481563\pi$
$863$	3.40127			0.115780			0.0578902	+	0.998323i	$0.481563\pi$
$864$	−1.04371	−	3.89517i	−0.0355076	−	0.132516i
$865$	18.3509	+	31.1333i	0.623951	+	1.05856i
$866$	−8.56625	+	8.56625i	−0.291093	+	0.291093i
$867$	−38.0366	+	10.1919i	−1.29179	+	0.346134i
$868$	−16.2482	+	60.6392i	−0.551500	+	2.05823i
$869$	−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
$873$	1.08630	+	1.88152i	0.0367655	+	0.0636798i
$874$	103.984	−	60.0352i	3.51731	−	2.03072i
$875$	40.0645	−	11.9051i	1.35443	−	0.402467i
$876$	26.9605	+	26.9605i	0.910912	+	0.910912i
$877$	17.0391	+	9.83752i	0.575369	+	0.332189i	0.759291	−	0.650751i	$-0.225546\pi$
$877$	17.0391	+	9.83752i	0.575369	+	0.332189i	−0.183922	+	0.982941i	$0.558879\pi$
$878$	−41.5832	−	24.0080i	−1.40336	−	0.810232i
$879$	−37.2768	−	37.2768i	−1.25732	−	1.25732i
$880$	−6.64022	+	3.91395i	−0.223842	+	0.131939i
$881$	2.06350	−	1.19137i	0.0695212	−	0.0401381i	−0.464836	−	0.885397i	$-0.653887\pi$
$881$	2.06350	−	1.19137i	0.0695212	−	0.0401381i	0.534358	+	0.845258i	$0.320554\pi$
$882$	20.3586	+	35.2621i	0.685510	+	1.18734i
$883$	−30.4180	−	30.4180i	−1.02365	−	1.02365i	−0.999714	−	0.0239343i	$-0.992381\pi$
$883$	−30.4180	−	30.4180i	−1.02365	−	1.02365i	−0.0239343	−	0.999714i	$-0.507619\pi$
$884$		0			0
$885$	8.90776	+	32.0846i	0.299431	+	1.07851i
$886$	−2.31057	+	8.62317i	−0.0776252	+	0.289701i
$887$	−5.87711	+	21.9337i	−0.197334	+	0.736461i	0.794316	+	0.607504i	$0.207829\pi$
$887$	−5.87711	+	21.9337i	−0.197334	+	0.736461i	−0.991650	+	0.128956i	$0.958837\pi$
$888$	10.0820	−	2.70146i	0.338329	−	0.0906550i
$889$	18.5915	−	18.5915i	0.623538	−	0.623538i
$890$	−10.5882	+	6.24104i	−0.354919	+	0.209200i
$891$	4.82814	+	18.0189i	0.161749	+	0.603655i
$892$	−107.117			−3.58653
$893$	−2.75354	−	10.2763i	−0.0921436	−	0.343885i
$894$	35.2325	+	61.0244i	1.17835	+	2.04096i
$895$	−28.9049	+	29.4307i	−0.966185	+	0.983761i
$896$		−	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
$900$	−21.6190	+	39.0545i	−0.720633	+	1.30182i
$901$	0.560184	+	0.323423i	0.0186624	+	0.0107748i
$902$			13.0716i			0.435235i
$903$	8.26923	−	14.3227i	0.275183	−	0.476630i
$904$	54.7204	−	14.6623i	1.81997	−	0.487660i
$905$	−4.71815	+	1.30992i	−0.156837	+	0.0435431i
$906$	11.6082	−	20.1061i	0.385658	−	0.667980i
$907$	22.3599	+	5.99131i	0.742448	+	0.198938i	0.610166	−	0.792274i	$-0.291103\pi$
$907$	22.3599	+	5.99131i	0.742448	+	0.198938i	0.132282	+	0.991212i	$0.457770\pi$
$908$	−24.7195	+	14.2718i	−0.820345	+	0.473627i
$909$	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	$0.628685\pi$
$912$	−21.1515	+	12.2118i	−0.700397	+	0.404375i
$913$	19.9580	+	5.34774i	0.660515	+	0.176984i
$914$	12.0754	−	20.9152i	0.399418	−	0.691813i
$915$	−16.9052	−	9.55812i	−0.558869	−	0.315982i
$916$	61.6632	−	16.5226i	2.03741	−	0.545922i
$917$	17.4720	−	30.2624i	0.576977	−	0.999354i
$918$			1.15223i			0.0380293i
$919$	−49.3350	−	28.4836i	−1.62741	−	0.939586i	−0.984862	−	0.173342i	$-0.944544\pi$
$919$	−49.3350	−	28.4836i	−1.62741	−	0.939586i	−0.642549	−	0.766245i	$-0.722123\pi$
$920$	−0.719476	−	79.8213i	−0.0237204	−	2.63163i
$921$	−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
$925$	−5.05785	−	2.79982i	−0.166301	−	0.0920576i
$926$	19.9199	+	34.5023i	0.654608	+	1.13381i
$927$	9.67519	+	36.1083i	0.317775	+	1.18595i
$928$	−2.44586			−0.0802892
$929$	−7.56304	−	28.2256i	−0.248135	−	0.926053i	−0.971782	−	0.235882i	$-0.924202\pi$
$929$	−7.56304	−	28.2256i	−0.248135	−	0.926053i	0.723647	−	0.690171i	$-0.242465\pi$
$930$	−14.3493	+	55.5504i	−0.470533	+	1.82157i
$931$	27.0133	−	27.0133i	0.885325	−	0.885325i
$932$	−7.58297	+	2.03185i	−0.248388	+	0.0665555i
$933$	−12.9284	+	48.2495i	−0.423257	+	1.57962i
$934$	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	$0.763033\pi$
$938$	−49.0279	−	84.9188i	−1.60082	−	2.77270i
$939$	14.9601	−	8.63724i	0.488205	−	0.281866i
$940$	−15.2591	−	3.94159i	−0.497695	−	0.128561i
$941$	15.5682	+	15.5682i	0.507507	+	0.507507i	0.913761	−	0.406253i	$-0.133165\pi$
$941$	15.5682	+	15.5682i	0.507507	+	0.507507i	−0.406253	+	0.913761i	$0.633165\pi$
$942$	−88.5159	−	51.1047i	−2.88400	−	1.66508i
$943$	−24.4106	−	14.0934i	−0.794917	−	0.458946i
$944$	8.59920	+	8.59920i	0.279880	+	0.279880i
$945$	−5.35075	−	9.07781i	−0.174060	−	0.295301i
$946$	7.02612	−	4.05653i	0.228439	−	0.131889i
$947$	0.180934	+	0.313387i	0.00587957	+	0.0101837i	0.868950	−	0.494899i	$-0.164795\pi$
$947$	0.180934	+	0.313387i	0.00587957	+	0.0101837i	−0.863071	+	0.505083i	$0.831462\pi$
$948$	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
$952$	−1.44012	+	5.37459i	−0.0466745	+	0.174191i
$953$	39.1517	−	10.4907i	1.26825	−	0.339826i	0.438889	−	0.898541i	$-0.355372\pi$
$953$	39.1517	−	10.4907i	1.26825	−	0.339826i	0.829360	+	0.558715i	$0.188705\pi$
$954$	6.92996	−	6.92996i	0.224366	−	0.224366i
$955$	−17.6368	−	4.55580i	−0.570714	−	0.147422i
$956$	−9.37537	−	34.9894i	−0.303221	−	1.13164i
$957$	3.22725			0.104322
$958$	8.48582	+	31.6695i	0.274164	+	1.02320i
$959$	25.6043	+	44.3479i	0.826805	+	1.43207i
$960$	−0.537176	−	59.5963i	−0.0173373	−	1.92346i
$961$		−	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
$965$	37.0867	+	36.4241i	1.19386	+	1.17253i
$966$	−165.854	−	95.7557i	−5.33626	−	3.08089i
$967$			12.2654i			0.394430i	0.980360	+	0.197215i	$0.0631897\pi$
$967$			12.2654i			0.394430i	−0.980360	+	0.197215i	$0.936810\pi$
$968$	14.9451	−	25.8857i	0.480354	−	0.831997i
$969$	−4.76297	+	1.27623i	−0.153009	+	0.0409985i
$970$	−1.25305	−	4.51334i	−0.0402332	−	0.144915i
$971$	−11.3099	+	19.5894i	−0.362953	+	0.628654i	−0.988445	−	0.151577i	$-0.951565\pi$
$971$	−11.3099	+	19.5894i	−0.362953	+	0.628654i	0.625492	+	0.780231i	$0.284898\pi$
$972$	71.3250	+	19.1115i	2.28775	+	0.613001i
$973$	−29.0921	+	16.7963i	−0.932651	+	0.538466i
$974$	48.5378			1.55525
$975$		0			0
$976$	−7.09261			−0.227029
$977$	−30.4574	+	17.5846i	−0.974419	+	0.562581i	−0.900581	−	0.434689i	$-0.856858\pi$
$977$	−30.4574	+	17.5846i	−0.974419	+	0.562581i	−0.0738385	+	0.997270i	$0.523525\pi$
$978$	−84.8424	−	22.7335i	−2.71296	−	0.726936i
$979$	−2.09250	+	3.62432i	−0.0668767	+	0.115834i
$980$	−15.1391	−	54.5290i	−0.483600	−	1.74186i
$981$	−13.8976	+	3.72385i	−0.443716	+	0.118893i
$982$	−12.0861	+	20.9338i	−0.385684	+	0.668024i
$983$			12.2764i			0.391555i	0.980648	+	0.195778i	$0.0627231\pi$
$983$			12.2764i			0.391555i	−0.980648	+	0.195778i	$0.937277\pi$
$984$	23.8470	+	13.7681i	0.760215	+	0.438911i
$985$	−35.2071	−	34.5781i	−1.12179	−	1.10175i
$986$	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
$990$	0.212512	+	23.5769i	0.00675407	+	0.749322i
$991$	−16.5995	−	28.7512i	−0.527301	−	0.913312i	−0.999494	−	0.0318165i	$-0.989871\pi$
$991$	−16.5995	−	28.7512i	−0.527301	−	0.913312i	0.472193	−	0.881495i	$-0.343463\pi$
$992$	−3.83202	−	14.3013i	−0.121667	−	0.454066i
$993$	24.5922			0.780409
$994$	25.4664	+	95.0419i	0.807745	+	3.01455i
$995$	−17.6167	−	4.55059i	−0.558486	−	0.144263i
$996$	68.5794	−	68.5794i	2.17302	−	2.17302i
$997$	36.3035	−	9.72750i	1.14974	−	0.308073i	0.366882	−	0.930268i	$-0.380425\pi$
$997$	36.3035	−	9.72750i	1.14974	−	0.308073i	0.782863	+	0.622194i	$0.213759\pi$
$998$	6.86138	−	25.6070i	0.217193	−	0.810576i
$999$	−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.t.i.427.5		144
5.3	odd	4		845.2.o.i.258.32		144
13.2	odd	12		845.2.k.f.577.5	yes	72
13.3	even	3		845.2.f.f.437.5	yes	72
13.4	even	6	inner	845.2.t.i.657.5		144
13.5	odd	4		845.2.o.i.587.32		144
13.6	odd	12		845.2.o.i.357.32		144
13.7	odd	12		845.2.o.i.357.5		144
13.8	odd	4		845.2.o.i.587.5		144
13.9	even	3	inner	845.2.t.i.657.32		144
13.10	even	6		845.2.f.f.437.32	yes	72
13.11	odd	12		845.2.k.f.577.32	yes	72
13.12	even	2	inner	845.2.t.i.427.32		144
65.3	odd	12		845.2.k.f.268.5	yes	72
65.8	even	4	inner	845.2.t.i.418.5		144
65.18	even	4	inner	845.2.t.i.418.32		144
65.23	odd	12		845.2.k.f.268.32	yes	72
65.28	even	12		845.2.f.f.408.32	yes	72
65.33	even	12	inner	845.2.t.i.188.32		144
65.38	odd	4		845.2.o.i.258.5		144
65.43	odd	12		845.2.o.i.488.5		144
65.48	odd	12		845.2.o.i.488.32		144
65.58	even	12	inner	845.2.t.i.188.5		144
65.63	even	12		845.2.f.f.408.5	✓	72

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

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

\(f(q)\)	\(=\)	\(q+(-2.05458 + 1.18621i) q^{2} +(-2.25716 - 0.604804i) q^{3} +(1.81419 - 3.14226i) q^{4} +(0.598181 + 2.15457i) q^{5} +(5.35492 - 1.43485i) q^{6} +(-1.86917 + 3.23750i) q^{7} +3.86318i q^{8} +(2.13090 + 1.23027i) q^{9} +(-3.78478 - 3.71716i) q^{10} +(-1.74477 - 0.467511i) q^{11} +(-5.99536 + 5.99536i) q^{12} -8.86890i q^{14} +(-0.0470959 - 5.22499i) q^{15} +(-0.954169 - 1.65267i) q^{16} +(-0.0997182 - 0.372153i) q^{17} -5.83745 q^{18} +(1.41754 + 5.29032i) q^{19} +(7.85544 + 2.02915i) q^{20} +(6.17706 - 6.17706i) q^{21} +(4.13933 - 1.10913i) q^{22} +(-2.39168 + 8.92587i) q^{23} +(2.33647 - 8.71981i) q^{24} +(-4.28436 + 2.57765i) q^{25} +(0.891365 + 0.891365i) q^{27} +(6.78204 + 11.7468i) q^{28} +(0.662140 - 0.382287i) q^{29} +(6.29470 + 10.6793i) q^{30} +(3.27268 + 3.27268i) q^{31} +(-2.77040 - 1.59949i) q^{32} +(3.65548 + 2.11049i) q^{33} +(0.646330 + 0.646330i) q^{34} +(-8.09352 - 2.09065i) q^{35} +(7.73169 - 4.46389i) q^{36} +(0.578108 + 1.00131i) q^{37} +(-9.18786 - 9.18786i) q^{38} +(-8.32350 + 2.31088i) q^{40} +(-0.789472 + 2.94635i) q^{41} +(-5.36394 + 20.0185i) q^{42} +(1.82870 - 0.489998i) q^{43} +(-4.63438 + 4.63438i) q^{44} +(-1.37605 + 5.32710i) q^{45} +(-5.67406 - 21.1759i) q^{46} -1.94248 q^{47} +(1.15417 + 4.30742i) q^{48} +(-3.48758 - 6.04067i) q^{49} +(5.74491 - 10.3781i) q^{50} +0.900318i q^{51} +(-1.18715 + 1.18715i) q^{53} +(-2.88872 - 0.774031i) q^{54} +(-0.0364049 - 4.03890i) q^{55} +(-12.5070 - 7.22094i) q^{56} -12.7984i q^{57} +(-0.906945 + 1.57087i) q^{58} +(-6.15548 + 1.64935i) q^{59} +(-16.5037 - 9.33112i) q^{60} +(1.85832 - 3.21870i) q^{61} +(-10.6061 - 2.84189i) q^{62} +(-7.96601 + 4.59918i) q^{63} +11.4060 q^{64} -10.0139 q^{66} +(9.57490 - 5.52807i) q^{67} +(-1.35031 - 0.361815i) q^{68} +(10.7968 - 18.7006i) q^{69} +(19.1087 - 5.30521i) q^{70} +(-10.7163 + 2.87143i) q^{71} +(-4.75277 + 8.23204i) q^{72} -4.49691i q^{73} +(-2.37553 - 1.37151i) q^{74} +(11.2294 - 3.22696i) q^{75} +(19.1952 + 5.14335i) q^{76} +(4.77484 - 4.77484i) q^{77} -7.15052i q^{79} +(2.99003 - 3.04442i) q^{80} +(-5.16367 - 8.94374i) q^{81} +(-1.87296 - 6.98997i) q^{82} -11.4388 q^{83} +(-8.20360 - 30.6163i) q^{84} +(0.742181 - 0.437465i) q^{85} +(-3.17596 + 3.17596i) q^{86} +(-1.72576 + 0.462417i) q^{87} +(1.80608 - 6.74037i) q^{88} +(0.599649 - 2.23792i) q^{89} +(-3.49185 - 12.5772i) q^{90} +(23.7085 + 23.7085i) q^{92} +(-5.40763 - 9.36630i) q^{93} +(3.99098 - 2.30419i) q^{94} +(-10.5504 + 6.21875i) q^{95} +(5.28585 + 5.28585i) q^{96} +(0.764675 + 0.441485i) q^{97} +(14.3310 + 8.27401i) 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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