LMFDB - Embedded newform 845.2.t.i.418.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(188,845)]

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, 5]))

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

//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);

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: 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			418.32
Character	$\chi$	$=$	845.418
Dual form			845.2.t.i.657.32

$q$-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} +(0.604804 - 2.25716i) q^{3} +(1.81419 - 3.14226i) q^{4} +(0.598181 - 2.15457i) q^{5} +(-1.43485 - 5.35492i) q^{6} +(-1.86917 + 3.23750i) q^{7} -3.86318i q^{8} +(-2.13090 - 1.23027i) q^{9} +(-1.32677 - 5.13630i) q^{10} +(0.467511 - 1.74477i) q^{11} +(-5.99536 - 5.99536i) q^{12} +8.86890i q^{14} +(-4.50143 - 2.65328i) q^{15} +(-0.954169 - 1.65267i) q^{16} +(0.372153 - 0.0997182i) q^{17} -5.83745 q^{18} +(-5.29032 + 1.41754i) q^{19} +(-5.68502 - 5.78843i) q^{20} +(6.17706 + 6.17706i) q^{21} +(-1.10913 - 4.13933i) q^{22} +(8.92587 + 2.39168i) q^{23} +(-8.71981 - 2.33647i) 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} +(-12.3959 - 0.111731i) 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} +(5.85732 + 5.96387i) 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} +(2.94635 + 0.789472i) q^{41} +(20.0185 + 5.36394i) q^{42} +(-0.489998 - 1.82870i) q^{43} +(-4.63438 - 4.63438i) q^{44} +(-3.92538 + 3.85525i) q^{45} +(21.1759 - 5.67406i) q^{46} -1.94248 q^{47} +(-4.30742 + 1.15417i) q^{48} +(-3.48758 - 6.04067i) q^{49} +(-11.8602 - 0.213823i) q^{50} -0.900318i q^{51} +(-1.18715 - 1.18715i) q^{53} +(0.774031 - 2.88872i) q^{54} +(-3.47958 - 2.05098i) q^{55} +(12.5070 + 7.22094i) q^{56} +12.7984i q^{57} +(-0.906945 + 1.57087i) q^{58} +(1.64935 + 6.15548i) q^{59} +(-16.5037 + 9.33112i) q^{60} +(1.85832 - 3.21870i) q^{61} +(2.84189 - 10.6061i) q^{62} +(7.96601 - 4.59918i) q^{63} +11.4060 q^{64} -10.0139 q^{66} +(-9.57490 + 5.52807i) q^{67} +(0.361815 - 1.35031i) q^{68} +(10.7968 - 18.7006i) q^{69} +(19.1087 + 5.30521i) q^{70} +(2.87143 + 10.7163i) q^{71} +(-4.75277 + 8.23204i) q^{72} +4.49691i q^{73} +(2.37553 + 1.37151i) q^{74} +(-8.40935 + 8.11150i) q^{75} +(-5.14335 + 19.1952i) q^{76} +(4.77484 + 4.77484i) q^{77} +7.15052i q^{79} +(-4.13156 + 1.06723i) q^{80} +(-5.16367 - 8.94374i) q^{81} +(6.98997 - 1.87296i) q^{82} -11.4388 q^{83} +(30.6163 - 8.20360i) q^{84} +(0.00776503 - 0.861480i) q^{85} +(-3.17596 - 3.17596i) q^{86} +(0.462417 + 1.72576i) q^{87} +(-6.74037 - 1.80608i) q^{88} +(-2.23792 - 0.599649i) 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} +(-0.110383 + 12.2463i) 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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	0.454164	−	0.890918i	$-0.349938\pi$
$2$	2.05458	−	1.18621i	1.45280	−	0.838777i	0.998640	+	0.0521412i	$0.0166046\pi$
$3$	0.604804	−	2.25716i	0.349184	−	1.30317i	−0.538465	−	0.842648i	$-0.680995\pi$
$3$	0.604804	−	2.25716i	0.349184	−	1.30317i	0.887648	−	0.460522i	$-0.152338\pi$
$4$	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
$6$	−1.43485	−	5.35492i	−0.585774	−	2.18614i
$7$	−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
$10$	−1.32677	−	5.13630i	−0.419560	−	1.62424i
$11$	0.467511	−	1.74477i	0.140960	−	0.526069i	−0.858942	−	0.512072i	$-0.828878\pi$
$11$	0.467511	−	1.74477i	0.140960	−	0.526069i	0.999902	−	0.0139966i	$-0.00445540\pi$
$12$	−5.99536	−	5.99536i	−1.73071	−	1.73071i
$13$		0			0
$13$		0			0
$14$			8.86890i			2.37031i
$15$	−4.50143	−	2.65328i	−1.16226	−	0.685074i
$16$	−0.954169	−	1.65267i	−0.238542	−	0.413167i
$17$	0.372153	−	0.0997182i	0.0902604	−	0.0241852i	−0.213406	−	0.976964i	$-0.568456\pi$
$17$	0.372153	−	0.0997182i	0.0902604	−	0.0241852i	0.303667	+	0.952778i	$0.401789\pi$
$18$	−5.83745			−1.37590
$19$	−5.29032	+	1.41754i	−1.21368	+	0.325205i	−0.808205	−	0.588901i	$-0.799561\pi$
$19$	−5.29032	+	1.41754i	−1.21368	+	0.325205i	−0.405476	+	0.914106i	$0.632894\pi$
$20$	−5.68502	−	5.78843i	−1.27121	−	1.29433i
$21$	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	$-0.00303588\pi$
$23$	8.92587	+	2.39168i	1.86117	+	0.498699i	0.861217	+	0.508237i	$0.169703\pi$
$24$	−8.71981	−	2.33647i	−1.77992	−	0.476929i
$25$	−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	−0.560217	−	0.828346i	$-0.689282\pi$
$29$	−0.662140	+	0.382287i	−0.122956	+	0.0709889i	0.437260	+	0.899335i	$0.355949\pi$
$30$	−12.3959	−	0.111731i	−2.26317	−	0.0203992i
$31$	3.27268	−	3.27268i	0.587792	−	0.587792i	−0.349241	−	0.937033i	$-0.613561\pi$
$31$	3.27268	−	3.27268i	0.587792	−	0.587792i	0.937033	+	0.349241i	$0.113561\pi$
$32$	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
$35$	5.85732	+	5.96387i	0.990067	+	1.00808i
$36$	−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
$41$	2.94635	+	0.789472i	0.460142	+	0.123295i	0.481441	−	0.876478i	$-0.340113\pi$
$41$	2.94635	+	0.789472i	0.460142	+	0.123295i	−0.0212988	+	0.999773i	$0.506780\pi$
$42$	20.0185	+	5.36394i	3.08892	+	0.827675i
$43$	−0.489998	−	1.82870i	−0.0747240	−	0.278874i	0.918447	−	0.395545i	$-0.129444\pi$
$43$	−0.489998	−	1.82870i	−0.0747240	−	0.278874i	−0.993171	+	0.116671i	$0.962778\pi$
$44$	−4.63438	−	4.63438i	−0.698660	−	0.698660i
$45$	−3.92538	+	3.85525i	−0.585161	+	0.574706i
$46$	21.1759	−	5.67406i	3.12222	−	0.836595i
$47$	−1.94248			−0.283340			−0.141670	−	0.989914i	$-0.545247\pi$
$47$	−1.94248			−0.283340			−0.141670	+	0.989914i	$0.545247\pi$
$48$	−4.30742	+	1.15417i	−0.621723	+	0.166590i
$49$	−3.48758	−	6.04067i	−0.498226	−	0.862953i
$50$	−11.8602	−	0.213823i	−1.67728	−	0.0302391i
$51$		−	0.900318i		−	0.126070i
$52$		0			0
$53$	−1.18715	−	1.18715i	−0.163068	−	0.163068i	0.620856	−	0.783924i	$-0.286785\pi$
$53$	−1.18715	−	1.18715i	−0.163068	−	0.163068i	−0.783924	+	0.620856i	$0.786785\pi$
$54$	0.774031	−	2.88872i	0.105332	−	0.393105i
$55$	−3.47958	−	2.05098i	−0.469187	−	0.276553i
$56$	12.5070	+	7.22094i	1.67132	+	0.964938i
$57$			12.7984i			1.69519i
$58$	−0.906945	+	1.57087i	−0.119088	+	0.206266i
$59$	1.64935	+	6.15548i	0.214728	+	0.801375i	0.986262	+	0.165187i	$0.0528228\pi$
$59$	1.64935	+	6.15548i	0.214728	+	0.801375i	−0.771535	+	0.636187i	$0.780510\pi$
$60$	−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	$0.0901966\pi$
$62$	2.84189	−	10.6061i	0.360920	−	1.34697i
$63$	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	−0.953623	−	0.301002i	$-0.902679\pi$
$67$	−9.57490	+	5.52807i	−1.16976	+	0.675361i	−0.216136	+	0.976363i	$0.569346\pi$
$68$	0.361815	−	1.35031i	0.0438765	−	0.163749i
$69$	10.7968	−	18.7006i	1.29978	−	2.25129i
$70$	19.1087	+	5.30521i	2.28393	+	0.634094i
$71$	2.87143	+	10.7163i	0.340776	+	1.27179i	0.897470	+	0.441075i	$0.145403\pi$
$71$	2.87143	+	10.7163i	0.340776	+	1.27179i	−0.556695	+	0.830717i	$0.687931\pi$
$72$	−4.75277	+	8.23204i	−0.560119	+	0.970155i
$73$			4.49691i			0.526323i	0.964752	+	0.263161i	$0.0847652\pi$
$73$			4.49691i			0.526323i	−0.964752	+	0.263161i	$0.915235\pi$
$74$	2.37553	+	1.37151i	0.276150	+	0.159435i
$75$	−8.40935	+	8.11150i	−0.971028	+	0.936636i
$76$	−5.14335	+	19.1952i	−0.589982	+	2.20184i
$77$	4.77484	+	4.77484i	0.544144	+	0.544144i
$78$		0			0
$79$			7.15052i			0.804496i	0.915531	+	0.402248i	$0.131771\pi$
$79$			7.15052i			0.804496i	−0.915531	+	0.402248i	$0.868229\pi$
$80$	−4.13156	+	1.06723i	−0.461923	+	0.119320i
$81$	−5.16367	−	8.94374i	−0.573741	−	0.993749i
$82$	6.98997	−	1.87296i	0.771914	−	0.206834i
$83$	−11.4388			−1.25557			−0.627783	−	0.778388i	$-0.716038\pi$
$83$	−11.4388			−1.25557			−0.627783	+	0.778388i	$0.716038\pi$
$84$	30.6163	−	8.20360i	3.34051	−	0.895087i
$85$	0.00776503	−	0.861480i	0.000842235	−	0.0934407i
$86$	−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
$89$	−2.23792	−	0.599649i	−0.237219	−	0.0635626i	0.138251	−	0.990397i	$-0.455852\pi$
$89$	−2.23792	−	0.599649i	−0.237219	−	0.0635626i	−0.375470	+	0.926835i	$0.622519\pi$
$90$	−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
$95$	−0.110383	+	12.2463i	−0.0113251	+	1.25644i
$96$	5.28585	−	5.28585i	0.539485	−	0.539485i
$97$	−0.764675	−	0.441485i	−0.0776409	−	0.0448260i	0.460677	−	0.887568i	$-0.347607\pi$
$97$	−0.764675	−	0.441485i	−0.0776409	−	0.0448260i	−0.538318	+	0.842742i	$0.680940\pi$
$98$	−14.3310	−	8.27401i	−1.44765	−	0.835801i
$99$	−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	$-0.795965\pi$
$101$	−6.87788	+	3.97094i	−0.684374	+	0.395124i	0.117127	+	0.993117i	$0.462632\pi$
$102$	−1.06797	−	1.84977i	−0.105744	−	0.183155i
$103$	10.7428	−	10.7428i	1.05852	−	1.05852i	0.0603388	−	0.998178i	$-0.480782\pi$
$103$	10.7428	−	10.7428i	1.05852	−	1.05852i	0.998178	−	0.0603388i	$-0.0192181\pi$
$104$		0			0
$105$	17.0039	−	9.61392i	1.65941	−	0.938222i
$106$	−3.84731	−	1.03088i	−0.373684	−	0.100128i
$107$	−10.0926	−	2.70430i	−0.975686	−	0.261434i	−0.264459	−	0.964397i	$-0.585193\pi$
$107$	−10.0926	−	2.70430i	−0.975686	−	0.261434i	−0.711227	+	0.702963i	$0.751860\pi$
$108$	−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	$0.840348\pi$
$110$	−9.58195	−	0.0863677i	−0.913603	−	0.00823484i
$111$	2.60976	−	0.699283i	0.247707	−	0.0663730i
$112$	7.13401			0.674101
$113$	14.1646	−	3.79539i	1.33249	−	0.357040i	0.478849	−	0.877897i	$-0.341054\pi$
$113$	14.1646	−	3.79539i	1.33249	−	0.357040i	0.853644	+	0.520857i	$0.174388\pi$
$114$	15.1816	+	26.2953i	1.42189	+	2.46278i
$115$	10.4923	−	17.8008i	0.978414	−	1.65993i
$116$			2.77416i			0.257574i
$117$		0			0
$118$	10.6904	+	10.6904i	0.984132	+	0.984132i
$119$	−0.372780	+	1.39123i	−0.0341727	+	0.127534i
$120$	−10.2501	+	17.3898i	−0.935702	+	1.58747i
$121$	6.70061	+	3.86860i	0.609146	+	0.351691i
$122$		−	8.81743i		−	0.798292i
$123$	3.56393	−	6.17290i	0.321348	−	0.556592i
$124$	−4.34637	−	16.2209i	−0.390316	−	1.45668i
$125$	−8.11655	+	7.68906i	−0.725966	+	0.687730i
$126$	10.9112	−	18.8987i	0.972046	−	1.68363i
$127$	1.82032	−	6.79351i	0.161527	−	0.602827i	−0.836931	−	0.547309i	$-0.815652\pi$
$127$	1.82032	−	6.79351i	0.161527	−	0.602827i	0.998458	−	0.0555178i	$-0.0176810\pi$
$128$	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
$133$	5.29923	−	19.7770i	0.459501	−	1.71488i
$134$	−13.1149	+	22.7157i	−1.13295	+	1.96233i
$135$	−1.38731	−	2.45371i	−0.119401	−	0.211181i
$136$	−0.385229	−	1.43770i	−0.0330331	−	0.123281i
$137$	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	0.132234	−	0.991219i	$-0.457785\pi$
$139$	−7.78210	−	4.49300i	−0.660069	−	0.381091i	−0.792303	+	0.610127i	$0.791118\pi$
$140$	29.3663	−	7.58566i	2.48190	−	0.641105i
$141$	−1.17482	+	4.38449i	−0.0989377	+	0.369241i
$142$	18.6113	+	18.6113i	1.56183	+	1.56183i
$143$		0			0
$144$			4.69556i			0.391297i
$145$	0.427585	+	1.65531i	0.0355090	+	0.137466i
$146$	5.33427	+	9.23923i	0.441467	+	0.764644i
$147$	−15.7441	+	4.21861i	−1.29855	+	0.347945i
$148$	4.19518			0.344842
$149$	−12.2774	+	3.28972i	−1.00581	+	0.269505i	−0.723876	−	0.689930i	$-0.757641\pi$
$149$	−12.2774	+	3.28972i	−1.00581	+	0.269505i	−0.281930	+	0.959435i	$0.590974\pi$
$150$	−7.65570	+	26.6409i	−0.625086	+	2.17522i
$151$	2.96123	+	2.96123i	0.240981	+	0.240981i	0.817256	−	0.576275i	$-0.195494\pi$
$151$	2.96123	+	2.96123i	0.240981	+	0.240981i	−0.576275	+	0.817256i	$0.695494\pi$
$152$	5.47620	+	20.4374i	0.444178	+	1.65770i
$153$	−0.915701	−	0.245361i	−0.0740300	−	0.0198363i
$154$	15.4742	+	4.14631i	1.24695	+	0.334119i
$155$	−5.09358	−	9.00889i	−0.409126	−	0.723612i
$156$		0			0
$157$	−13.0366	+	13.0366i	−1.04044	+	1.04044i	−0.0412907	+	0.999147i	$0.513147\pi$
$157$	−13.0366	+	13.0366i	−1.04044	+	1.04044i	−0.999147	+	0.0412907i	$0.986853\pi$
$158$	8.48201	+	14.6913i	0.674793	+	1.16878i
$159$	−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
$162$	−21.2183	−	12.2504i	−1.66707	−	0.962482i
$163$	13.7211	+	7.92191i	1.07472	+	0.620492i	0.929468	−	0.368903i	$-0.120266\pi$
$163$	13.7211	+	7.92191i	1.07472	+	0.620492i	0.145255	+	0.989394i	$0.453600\pi$
$164$	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
$167$	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
$171$	13.0171	+	3.48792i	0.995441	+	0.266728i
$172$	−6.63520	−	1.77790i	−0.505929	−	0.135563i
$173$	−4.18301	−	15.6112i	−0.318029	−	1.18690i	−0.921137	−	0.389239i	$-0.872738\pi$
$173$	−4.18301	−	15.6112i	−0.318029	−	1.18690i	0.603108	−	0.797660i	$-0.293929\pi$
$174$	2.99719	+	2.99719i	0.227216	+	0.227216i
$175$	16.3533	−	9.05254i	1.23619	−	0.684307i
$176$	−3.32962	+	0.892168i	−0.250979	+	0.0672497i
$177$	14.8914			1.11931
$178$	−5.30928	+	1.42262i	−0.397947	+	0.106630i
$179$	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	$0.591191\pi$
$180$	4.99283	+	19.3287i	0.372143	+	1.44068i
$181$		−	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
$184$	9.23949	−	34.4822i	0.681144	−	2.54206i
$185$	2.50321	−	0.646609i	0.184040	−	0.0475396i
$186$	−22.2208	−	12.8292i	−1.62931	−	0.940681i
$187$		−	0.695942i		−	0.0508923i
$188$	−3.52402	+	6.10379i	−0.257016	+	0.445164i
$189$	1.21968	+	4.55190i	0.0887185	+	0.331102i
$190$	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	$0.261894\pi$
$192$	6.89839	−	25.7451i	0.497849	−	1.85800i
$193$	−20.1326	+	11.6235i	−1.44917	+	0.836681i	−0.998432	−	0.0559740i	$-0.982174\pi$
$193$	−20.1326	+	11.6235i	−1.44917	+	0.836681i	−0.450741	+	0.892655i	$0.648840\pi$
$194$	−2.09477			−0.150396
$195$		0			0
$196$	−25.3085			−1.80775
$197$	19.1122	−	11.0344i	1.36169	−	0.786172i	0.371840	−	0.928297i	$-0.378727\pi$
$197$	19.1122	−	11.0344i	1.36169	−	0.786172i	0.989849	+	0.142125i	$0.0453935\pi$
$198$	−2.72907	+	10.1850i	−0.193947	+	0.723819i
$199$	−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
$201$	6.68679	+	24.9554i	0.471650	+	1.76022i
$202$	−9.42075	+	16.3172i	−0.662841	+	1.14807i
$203$		−	2.85823i		−	0.200609i
$204$	−2.82904	−	1.63335i	−0.198072	−	0.114357i
$205$	3.46342	−	5.87587i	0.241896	−	0.410389i
$206$	9.32865	−	34.8150i	0.649958	−	2.42568i
$207$	−16.0777	−	16.0777i	−1.11748	−	1.11748i
$208$		0			0
$209$			9.89312i			0.684321i
$210$	23.5317	−	39.9227i	1.62384	−	2.75493i
$211$	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	$0.508274\pi$
$212$	−5.88407	+	1.57663i	−0.404120	+	0.108284i
$213$	25.9250			1.77635
$214$	−23.9438	+	6.41572i	−1.63676	+	0.438570i
$215$	−4.23317	−	0.0381560i	−0.288700	−	0.00260222i
$216$	−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
$219$	10.1502	+	2.71974i	0.685889	+	0.183783i
$220$	−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
$225$	5.95832	+	10.7636i	0.397221	+	0.717576i
$226$	24.6001	−	24.6001i	1.63637	−	1.63637i
$227$	6.81284	+	3.93339i	0.452184	+	0.261068i	0.708752	−	0.705458i	$-0.249259\pi$
$227$	6.81284	+	3.93339i	0.452184	+	0.261068i	−0.256568	+	0.966526i	$0.582592\pi$
$228$	40.2160	+	23.2187i	2.66337	+	1.53770i
$229$	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
$232$	1.47684	+	2.55797i	0.0969595	+	0.167939i
$233$	−1.52992	+	1.52992i	−0.100228	+	0.100228i	−0.755443	−	0.655214i	$-0.772578\pi$
$233$	−1.52992	+	1.52992i	−0.100228	+	0.100228i	0.655214	+	0.755443i	$0.272578\pi$
$234$		0			0
$235$	−1.16196	+	4.18522i	−0.0757976	+	0.273013i
$236$	22.3344	+	5.98447i	1.45384	+	0.389556i
$237$	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	$0.645346\pi$
$240$	−0.0898749	+	9.97105i	−0.00580140	+	0.643628i
$241$	−13.9984	+	3.75087i	−0.901719	+	0.241615i	−0.679755	−	0.733440i	$-0.737914\pi$
$241$	−13.9984	+	3.75087i	−0.901719	+	0.241615i	−0.221965	+	0.975055i	$0.571247\pi$
$242$	18.3559			1.17996
$243$	−19.6576	+	5.26723i	−1.26103	+	0.337893i
$244$	−6.74268	−	11.6787i	−0.431656	−	0.747649i
$245$	−15.1013	+	3.90084i	−0.964785	+	0.249215i
$246$		−	16.9102i		−	1.07816i
$247$		0			0
$248$	−12.6430	−	12.6430i	−0.802829	−	0.802829i
$249$	−6.91820	+	25.8191i	−0.438423	+	1.63622i
$250$	−7.55522	+	25.4257i	−0.477834	+	1.60806i
$251$	15.3843	+	8.88214i	0.971050	+	0.560636i	0.899556	−	0.436805i	$-0.143890\pi$
$251$	15.3843	+	8.88214i	0.971050	+	0.560636i	0.0714936	+	0.997441i	$0.477223\pi$
$252$		−	33.3751i		−	2.10243i
$253$	8.34588	−	14.4555i	0.524701	−	0.908808i
$254$	−4.31855	−	16.1171i	−0.270970	−	1.01127i
$255$	−1.93980	−	0.538553i	−0.121475	−	0.0337255i
$256$	13.1033	−	22.6956i	0.818955	−	1.41847i
$257$	2.33322	−	8.70771i	0.145543	−	0.543172i	−0.854188	−	0.519964i	$-0.825945\pi$
$257$	2.33322	−	8.70771i	0.145543	−	0.543172i	0.999731	−	0.0232081i	$-0.00738802\pi$
$258$	−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
$263$	−1.10325	+	4.11740i	−0.0680295	+	0.253890i	−0.991563	−	0.129629i	$-0.958621\pi$
$263$	−1.10325	+	4.11740i	−0.0680295	+	0.253890i	0.923533	+	0.383519i	$0.125288\pi$
$264$	−8.15321	+	14.1218i	−0.501795	+	0.869135i
$265$	−3.26794	+	1.84768i	−0.200748	+	0.113502i
$266$	−12.5720	−	46.9193i	−0.770838	−	2.87681i
$267$	−2.70700	+	4.68867i	−0.165666	+	0.286942i
$268$			40.1158i			2.45046i
$269$	−1.55678	−	0.898805i	−0.0949183	−	0.0548011i	0.451790	−	0.892125i	$-0.350786\pi$
$269$	−1.55678	−	0.898805i	−0.0949183	−	0.0548011i	−0.546708	+	0.837323i	$0.684119\pi$
$270$	−5.76095	−	3.39568i	−0.350600	−	0.206655i
$271$	−0.763276	+	2.84859i	−0.0463657	+	0.173039i	−0.985226	−	0.171259i	$-0.945216\pi$
$271$	−0.763276	+	2.84859i	−0.0463657	+	0.173039i	0.938860	+	0.344298i	$0.111883\pi$
$272$	−0.519898	−	0.519898i	−0.0315235	−	0.0315235i
$273$		0			0
$274$		−	32.4979i		−	1.96327i
$275$	−6.50039	+	6.27016i	−0.391989	+	0.378105i
$276$	−39.1748	−	67.8527i	−2.35804	−	4.08425i
$277$	−27.5242	+	7.37510i	−1.65377	+	0.443127i	−0.960665	−	0.277709i	$-0.910425\pi$
$277$	−27.5242	+	7.37510i	−1.65377	+	0.443127i	−0.693106	+	0.720836i	$0.743758\pi$
$278$	−21.3186			−1.27860
$279$	−11.0001	+	2.94746i	−0.658556	+	0.176460i
$280$	23.0395	−	22.6279i	1.37687	−	1.35227i
$281$	−2.57874	−	2.57874i	−0.153835	−	0.153835i	0.625993	−	0.779828i	$-0.284694\pi$
$281$	−2.57874	−	2.57874i	−0.153835	−	0.153835i	−0.779828	+	0.625993i	$0.784694\pi$
$282$	2.78717	+	10.4018i	0.165973	+	0.619421i
$283$	−7.54151	−	2.02074i	−0.448296	−	0.120121i	0.0276057	−	0.999619i	$-0.491212\pi$
$283$	−7.54151	−	2.02074i	−0.448296	−	0.120121i	−0.475902	+	0.879498i	$0.657878\pi$
$284$	38.8827	+	10.4186i	2.30727	+	0.618230i
$285$	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
$290$	2.84204	+	2.89374i	0.166891	+	0.169927i
$291$	−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	−0.194612	−	0.980880i	$-0.562345\pi$
$293$	−19.5374	−	11.2799i	−1.14139	−	0.658979i	−0.946773	+	0.321901i	$0.895678\pi$
$294$	−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
$297$	−1.13851	−	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
$301$	6.83629	+	1.83178i	0.394037	+	0.105582i
$302$	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
$305$	−5.82332	−	5.92925i	−0.333442	−	0.339508i
$306$	−2.17243	+	0.582100i	−0.124189	+	0.0332764i
$307$	20.4085			1.16477			0.582387	−	0.812912i	$-0.302119\pi$
$307$	20.4085			1.16477			0.582387	+	0.812912i	$0.302119\pi$
$308$	23.6662	−	6.34135i	1.34851	−	0.361332i
$309$	−17.7509	−	30.7454i	−1.00981	−	1.74904i
$310$	−21.1516	−	12.4674i	−1.20133	−	0.708100i
$311$			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	0.543772	−	0.839233i	$-0.316996\pi$
$313$	−5.22723	−	5.22723i	−0.295461	−	0.295461i	−0.839233	+	0.543772i	$0.816996\pi$
$314$	−11.3206	+	42.2490i	−0.638857	+	2.38425i
$315$	−5.14415	−	19.9145i	−0.289840	−	1.12205i
$316$	22.4688	+	12.9724i	1.26397	+	0.729753i
$317$		−	25.8830i		−	1.45373i	−0.686779	−	0.726867i	$-0.740976\pi$
$317$		−	25.8830i		−	1.45373i	0.686779	−	0.726867i	$-0.259024\pi$
$318$	−4.65374	+	8.06051i	−0.260969	+	0.452011i
$319$	0.357446	+	1.33401i	0.0200132	+	0.0746901i
$320$	6.82285	−	24.5751i	0.381409	−	1.37379i
$321$	−12.2080	+	21.1450i	−0.681387	+	1.18020i
$322$	−21.2116	+	79.1627i	−1.18207	+	4.41156i
$323$	−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
$328$	3.04987	−	11.3823i	0.168401	−	0.628481i
$329$	3.63083	−	6.28878i	0.200174	−	0.346711i
$330$	−5.99015	+	21.5757i	−0.329747	+	1.18771i
$331$	2.72380	+	10.1654i	0.149714	+	0.558738i	0.999500	+	0.0316117i	$0.0100640\pi$
$331$	2.72380	+	10.1654i	0.149714	+	0.558738i	−0.849787	+	0.527127i	$0.823269\pi$
$332$	−20.7520	+	35.9436i	−1.13892	+	1.97266i
$333$		−	2.84492i		−	0.155901i
$334$	25.6480	+	14.8079i	1.40340	+	0.810251i
$335$	6.18310	+	23.9366i	0.337819	+	1.30780i
$336$	4.31468	−	16.1026i	0.235385	−	0.878468i
$337$	−6.67935	−	6.67935i	−0.363847	−	0.363847i	0.501380	−	0.865227i	$-0.332826\pi$
$337$	−6.67935	−	6.67935i	−0.363847	−	0.363847i	−0.865227	+	0.501380i	$0.832826\pi$
$338$		0			0
$339$		−	34.2672i		−	1.86114i
$340$	−2.69291	−	1.58729i	−0.146044	−	0.0860826i
$341$	−4.18008	−	7.24011i	−0.226364	−	0.392074i
$342$	30.8820	−	8.27480i	1.66991	−	0.447450i
$343$	−0.0928245			−0.00501205
$344$	−7.06459	+	1.89295i	−0.380897	+	0.102061i
$345$	−33.8333	−	34.4488i	−1.82153	−	1.85466i
$346$	−27.1125	−	27.1125i	−1.45758	−	1.45758i
$347$	−1.84430	−	6.88301i	−0.0990071	−	0.369500i	0.898589	−	0.438791i	$-0.144593\pi$
$347$	−1.84430	−	6.88301i	−0.0990071	−	0.369500i	−0.997596	+	0.0692910i	$0.977926\pi$
$348$	6.26171	+	1.67782i	0.335663	+	0.0899406i
$349$	−31.5009	−	8.44064i	−1.68620	−	0.451817i	−0.716798	−	0.697281i	$-0.754393\pi$
$349$	−31.5009	−	8.44064i	−1.68620	−	0.451817i	−0.969406	+	0.245464i	$0.921060\pi$
$350$	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
$355$	24.8067	+	0.223597i	1.31660	+	0.0118673i
$356$	−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	−0.955693	−	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
$362$	−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
$366$	−19.9023	−	5.33281i	−1.04031	−	0.278751i
$367$	33.6660	+	9.02077i	1.75735	+	0.470880i	0.986170	−	0.165738i	$-0.0530006\pi$
$367$	33.6660	+	9.02077i	1.75735	+	0.470880i	0.771179	+	0.636618i	$0.219667\pi$
$368$	−4.56413	−	17.0336i	−0.237922	−	0.887936i
$369$	−5.30710	−	5.30710i	−0.276277	−	0.276277i
$370$	4.37602	−	4.29784i	0.227499	−	0.223434i
$371$	6.06240	−	1.62442i	0.314744	−	0.0843354i
$372$	−39.2418			−2.03459
$373$	−14.4253	+	3.86524i	−0.746912	+	0.200135i	−0.612148	−	0.790743i	$-0.709694\pi$
$373$	−14.4253	+	3.86524i	−0.746912	+	0.200135i	−0.134764	+	0.990878i	$0.543028\pi$
$374$	−0.825533	−	1.42987i	−0.0426873	−	0.0739366i
$375$	12.4465	+	22.9707i	0.642735	+	1.18620i
$376$			7.50416i			0.386997i
$377$		0			0
$378$	7.90543	+	7.90543i	0.406611	+	0.406611i
$379$	8.38303	−	31.2859i	0.430607	−	1.60705i	−0.320758	−	0.947161i	$-0.603938\pi$
$379$	8.38303	−	31.2859i	0.430607	−	1.60705i	0.751365	−	0.659887i	$-0.229396\pi$
$380$	38.2809	+	22.5639i	1.96377	+	1.15751i
$381$	−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	$-0.141269\pi$
$384$	−12.4964	−	46.6371i	−0.637702	−	2.37994i
$385$	13.1440	−	7.43152i	0.669878	−	0.378745i
$386$	−27.5759	+	47.7629i	−1.40358	+	2.43107i
$387$	−1.20566	+	4.49960i	−0.0612874	+	0.228728i
$388$	−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
$393$	−5.65339	+	21.0987i	−0.285176	+	1.06429i
$394$	26.1783	−	45.3422i	1.31884	−	2.28431i
$395$	15.4063	+	4.27730i	0.775175	+	0.215214i
$396$	4.17383	+	15.5770i	0.209743	+	0.782772i
$397$	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
$400$	−0.171996	+	9.54014i	−0.00859978	+	0.477007i
$401$	4.27393	−	15.9505i	0.213430	−	0.796531i	−0.773284	−	0.634060i	$-0.781387\pi$
$401$	4.27393	−	15.9505i	0.213430	−	0.796531i	0.986713	−	0.162471i	$-0.0519463\pi$
$402$	43.3409	+	43.3409i	2.16165	+	2.16165i
$403$		0			0
$404$			28.8161i			1.43366i
$405$	−22.3588	+	5.77553i	−1.11102	+	0.286988i
$406$	−3.39047	−	5.87246i	−0.168266	−	0.291445i
$407$	2.01733	−	0.540543i	0.0999955	−	0.0267937i
$408$	−3.47809			−0.172191
$409$	4.07993	−	1.09321i	0.201740	−	0.0540560i	−0.156534	−	0.987673i	$-0.550032\pi$
$409$	4.07993	−	1.09321i	0.201740	−	0.0540560i	0.358274	+	0.933617i	$0.383365\pi$
$410$	0.145847	−	16.1808i	0.00720286	−	0.799111i
$411$	−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
$414$	−52.1043	−	13.9613i	−2.56079	−	0.686161i
$415$	−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	−0.815704	−	0.578470i	$-0.803650\pi$
$419$	−14.7910	+	8.53958i	−0.722587	+	0.417186i	0.0931173	+	0.995655i	$0.470317\pi$
$420$	0.638812	−	70.8722i	0.0311709	−	3.45821i
$421$	−9.26544	+	9.26544i	−0.451570	+	0.451570i	−0.895875	−	0.444305i	$-0.853451\pi$
$421$	−9.26544	+	9.26544i	−0.451570	+	0.451570i	0.444305	+	0.895875i	$0.353451\pi$
$422$	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
$425$	−1.85148	−	0.532051i	−0.0898098	−	0.0258083i
$426$	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
$431$	−10.3496	−	2.77316i	−0.498521	−	0.133578i	0.000792423	−	1.00000i	$-0.499748\pi$
$431$	−10.3496	−	2.77316i	−0.498521	−	0.133578i	−0.499314	+	0.866421i	$0.666414\pi$
$432$	−2.32364	−	0.622619i	−0.111796	−	0.0299558i
$433$	−1.32163	−	4.93240i	−0.0635136	−	0.237036i	0.926870	−	0.375381i	$-0.122488\pi$
$433$	−1.32163	−	4.93240i	−0.0635136	−	0.237036i	−0.990384	+	0.138345i	$0.955822\pi$
$434$	29.0251	+	29.0251i	1.39325	+	1.39325i
$435$	3.99489	+	0.0360083i	0.191540	+	0.00172646i
$436$	−20.4937	+	5.49126i	−0.981468	+	0.262984i
$437$	−50.6109			−2.42105
$438$	24.0806	−	6.45237i	1.15061	−	0.308306i
$439$	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	$0.672886\pi$
$440$	−7.92329	+	13.4423i	−0.377728	+	0.640835i
$441$			17.1627i			0.817273i
$442$		0			0
$443$	2.66083	+	2.66083i	0.126420	+	0.126420i	0.767486	−	0.641066i	$-0.221508\pi$
$443$	2.66083	+	2.66083i	0.126420	+	0.126420i	−0.641066	+	0.767486i	$0.721508\pi$
$444$	2.53726	−	9.46918i	0.120413	−	0.449387i
$445$	−2.63067	+	4.46306i	−0.124706	+	0.211569i
$446$	−60.6551	−	35.0192i	−2.87210	−	1.65821i
$447$			29.7017i			1.40484i
$448$	−21.3197	+	36.9269i	−1.00726	+	1.74463i
$449$	7.97615	+	29.7674i	0.376418	+	1.40481i	0.851262	+	0.524741i	$0.175838\pi$
$449$	7.97615	+	29.7674i	0.376418	+	1.40481i	−0.474844	+	0.880070i	$0.657495\pi$
$450$	25.0097	+	15.0469i	1.17897	+	0.709317i
$451$	2.75490	−	4.77163i	0.129723	−	0.224687i
$452$	13.7711	−	51.3944i	0.647737	−	2.41739i
$453$	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	−0.279424	−	0.960168i	$-0.590143\pi$
$457$	8.81597	−	5.08990i	0.412394	−	0.238096i	0.691818	+	0.722072i	$0.256810\pi$
$458$	10.8033	−	40.3186i	0.504807	−	1.88396i
$459$	0.242839	−	0.420610i	0.0113348	−	0.0196324i
$460$	−36.8996	−	65.2635i	−1.72045	−	3.04293i
$461$	−4.98920	−	18.6200i	−0.232370	−	0.867218i	−0.979317	−	0.202334i	$-0.935147\pi$
$461$	−4.98920	−	18.6200i	−0.232370	−	0.867218i	0.746946	−	0.664884i	$-0.231519\pi$
$462$	18.7177	−	32.4201i	0.870828	−	1.50832i
$463$			16.7929i			0.780432i	0.920723	+	0.390216i	$0.127600\pi$
$463$			16.7929i			0.780432i	−0.920723	+	0.390216i	$0.872400\pi$
$464$	1.26359	+	0.729533i	0.0586606	+	0.0338677i
$465$	−23.4151	+	6.04840i	−1.08585	+	0.280488i
$466$	−1.32853	+	4.95814i	−0.0615430	+	0.229681i
$467$	−9.75781	−	9.75781i	−0.451538	−	0.451538i	0.444327	−	0.895865i	$-0.353443\pi$
$467$	−9.75781	−	9.75781i	−0.451538	−	0.451538i	−0.895865	+	0.444327i	$0.853443\pi$
$468$		0			0
$469$		−	41.3316i		−	1.90851i
$470$	2.57722	+	9.97717i	0.118878	+	0.460212i
$471$	21.5412	+	37.3104i	0.992564	+	1.71917i
$472$	23.7797	−	6.37175i	1.09455	−	0.293284i
$473$	−3.41974			−0.157240
$474$	38.2905	−	10.2599i	1.75874	−	0.471253i
$475$	26.3195	+	7.56334i	1.20762	+	0.347030i
$476$	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
$479$	−13.3490	−	3.57686i	−0.609933	−	0.163431i	−0.0593859	−	0.998235i	$-0.518914\pi$
$479$	−13.3490	−	3.57686i	−0.609933	−	0.163431i	−0.550547	+	0.834804i	$0.685581\pi$
$480$	−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
$485$	−1.40862	+	1.38346i	−0.0639624	+	0.0628196i
$486$	−34.1399	+	34.1399i	−1.54862	+	1.54862i
$487$	17.7182	+	10.2296i	0.802887	+	0.463547i	0.844480	−	0.535587i	$-0.179910\pi$
$487$	17.7182	+	10.2296i	0.802887	+	0.463547i	−0.0415923	+	0.999135i	$0.513243\pi$
$488$	−12.4344	−	7.17902i	−0.562880	−	0.324979i
$489$	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	$-0.740509\pi$
$491$	−8.82381	+	5.09443i	−0.398213	+	0.229908i	0.287500	+	0.957781i	$0.407176\pi$
$492$	−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
$496$	−8.53136	−	2.28597i	−0.383069	−	0.102643i
$497$	−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	$0.830469\pi$
$500$	9.43612	+	39.4537i	0.421996	+	1.76442i
$501$	28.1769	−	7.54998i	1.25885	−	0.337308i
$502$	42.1443			1.88099
$503$	−13.6747	+	3.66412i	−0.609723	+	0.163375i	−0.550452	−	0.834867i	$-0.685545\pi$
$503$	−13.6747	+	3.66412i	−0.609723	+	0.163375i	−0.0592717	+	0.998242i	$0.518878\pi$
$504$	−17.7675	−	30.7741i	−0.791426	−	1.37079i
$505$	4.44147	+	17.1942i	0.197643	+	0.765133i
$506$		−	39.5998i		−	1.76043i
$507$		0			0
$508$	−18.0446	−	18.0446i	−0.800600	−	0.800600i
$509$	6.00073	−	22.3950i	0.265978	−	0.992643i	−0.695671	−	0.718360i	$-0.744893\pi$
$509$	6.00073	−	22.3950i	0.265978	−	0.992643i	0.961649	−	0.274283i	$-0.0884404\pi$
$510$	−4.62430	+	1.19451i	−0.204768	+	0.0528939i
$511$	−14.5587	−	8.40548i	−0.644039	−	0.371836i
$512$		−	20.8492i		−	0.921415i
$513$	−3.45206	+	5.97914i	−0.152412	+	0.263986i
$514$	−5.53539	−	20.6583i	−0.244155	−	0.911200i
$515$	−16.7200	−	29.5722i	−0.736769	−	1.30311i
$516$	−8.02598	+	13.9014i	−0.353324	+	0.611975i
$517$	−0.908131	+	3.38919i	−0.0399396	+	0.149056i
$518$	−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
$523$	10.4519	−	39.0069i	0.457029	−	1.70565i	−0.225026	−	0.974353i	$-0.572247\pi$
$523$	10.4519	−	39.0069i	0.457029	−	1.70565i	0.682055	−	0.731301i	$-0.261087\pi$
$524$	−16.9581	+	29.3722i	−0.740817	+	1.28313i
$525$	−10.5425	−	42.3870i	−0.460111	−	1.84992i
$526$	2.61738	+	9.76819i	0.114123	+	0.425913i
$527$	0.891594	−	1.54429i	0.0388384	−	0.0672702i
$528$			8.05506i			0.350551i
$529$	54.0324	+	31.1956i	2.34923	+	1.35633i
$530$	−4.52250	+	7.67266i	−0.196445	+	0.333279i
$531$	4.05832	−	15.1458i	0.176116	−	0.657274i
$532$	−52.5307	−	52.5307i	−2.27749	−	2.27749i
$533$		0			0
$534$			12.8443i			0.555827i
$535$	−11.8638	+	20.1275i	−0.512916	+	0.870188i
$536$	21.3559	+	36.9895i	0.922435	+	1.59771i
$537$	41.6403	−	11.1575i	1.79691	−	0.481481i
$538$	−4.26468			−0.183864
$539$	−12.1701	+	3.26097i	−0.524203	+	0.140460i
$540$	−10.2270	−	0.0921822i	−0.440101	−	0.00396689i
$541$	−16.7846	−	16.7846i	−0.721626	−	0.721626i	0.247310	−	0.968936i	$-0.420453\pi$
$541$	−16.7846	−	16.7846i	−0.721626	−	0.721626i	−0.968936	+	0.247310i	$0.920453\pi$
$542$	1.81081	+	6.75804i	0.0777810	+	0.290283i
$543$	−4.94279	−	1.32442i	−0.212116	−	0.0568362i
$544$	1.19051	+	0.318997i	0.0510428	+	0.0136769i
$545$	−11.3819	+	6.43528i	−0.487549	+	0.275657i
$546$		0			0
$547$	10.0151	−	10.0151i	0.428216	−	0.428216i	−0.459804	−	0.888020i	$-0.652080\pi$
$547$	10.0151	−	10.0151i	0.428216	−	0.428216i	0.888020	+	0.459804i	$0.152080\pi$
$548$	−24.8511	−	43.0434i	−1.06159	−	1.83872i
$549$	−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
$552$	−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
$555$	0.0544530	−	6.04121i	0.00231140	−	0.256435i
$556$	−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
$561$	−1.57085	−	0.420908i	−0.0663214	−	0.0177708i
$562$	−8.35714	−	2.23929i	−0.352525	−	0.0944587i
$563$	3.89312	+	14.5293i	0.164075	+	0.612338i	0.998156	+	0.0606957i	$0.0193319\pi$
$563$	3.89312	+	14.5293i	0.164075	+	0.612338i	−0.834081	+	0.551642i	$0.814001\pi$
$564$	11.6459	+	11.6459i	0.490380	+	0.490380i
$565$	0.295546	−	32.7890i	0.0124337	−	1.37944i
$566$	−17.8916	+	4.79405i	−0.752041	+	0.201509i
$567$	38.6071			1.62135
$568$	41.3990	−	11.0928i	1.73706	−	0.465445i
$569$	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	$0.681133\pi$
$570$	65.7364	−	16.9805i	2.75340	−	0.711234i
$571$		−	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
$574$	−7.00175	+	26.1309i	−0.292247	+	1.09068i
$575$	−32.0767	−	33.2545i	−1.33769	−	1.38681i
$576$	−24.3050	−	14.0325i	−1.01271	−	0.584688i
$577$		−	21.1801i		−	0.881741i	−0.897571	−	0.440870i	$-0.854670\pi$
$577$		−	21.1801i		−	0.881741i	0.897571	−	0.440870i	$-0.145330\pi$
$578$	−19.9895	+	34.6228i	−0.831453	+	1.44012i
$579$	14.0599	+	52.4723i	0.584310	+	2.18068i
$580$	5.97712	+	1.65945i	0.248186	+	0.0689048i
$581$	21.3810	−	37.0329i	0.887032	−	1.53638i
$582$	−1.26693	+	4.72824i	−0.0525158	+	0.195992i
$583$	−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	0.265539	−	0.964100i	$-0.414450\pi$
$587$	29.8791	−	17.2507i	1.23324	−	0.712013i	0.967705	+	0.252087i	$0.0811168\pi$
$588$	−15.3067	+	57.1253i	−0.631237	+	2.35581i
$589$	−12.6744	+	21.9527i	−0.522239	+	0.904544i
$590$	29.4280	−	16.6385i	1.21153	−	0.684994i
$591$	−13.3473	−	49.8130i	−0.549036	−	2.04903i
$592$	1.10322	−	1.91084i	0.0453423	−	0.0785351i
$593$			28.3656i			1.16483i	0.812890	+	0.582417i	$0.197893\pi$
$593$			28.3656i			1.16483i	−0.812890	+	0.582417i	$0.802107\pi$
$594$	−4.67830	−	2.70102i	−0.191953	−	0.110824i
$595$	2.77452	+	1.63539i	0.113744	+	0.0670445i
$596$	−11.9363	+	44.5470i	−0.488932	+	1.82472i
$597$	13.4452	+	13.4452i	0.550276	+	0.550276i
$598$		0			0
$599$			3.01612i			0.123235i	0.998100	+	0.0616176i	$0.0196259\pi$
$599$			3.01612i			0.123235i	−0.998100	+	0.0616176i	$0.980374\pi$
$600$	31.3362	+	32.4868i	1.27930	+	1.32627i
$601$	−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	$0.922669\pi$
$602$	16.2185	−	4.34575i	0.661019	−	0.177119i
$603$	27.2042			1.10784
$604$	14.6772	−	3.93274i	0.597206	−	0.160021i
$605$	12.3434	−	12.1228i	0.501829	−	0.492863i
$606$	31.1328	+	31.1328i	1.26468	+	1.26468i
$607$	−9.28061	−	34.6357i	−0.376689	−	1.40582i	−0.850862	−	0.525389i	$-0.823920\pi$
$607$	−9.28061	−	34.6357i	−0.376689	−	1.40582i	0.474173	−	0.880431i	$-0.342747\pi$
$608$	−16.9236	−	4.53467i	−0.686344	−	0.183905i
$609$	−6.45149	−	1.72867i	−0.261427	−	0.0700493i
$610$	−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
$615$	−11.1681	−	11.3712i	−0.450341	−	0.458533i
$616$	18.4461	−	18.4461i	0.743213	−	0.743213i
$617$	−33.3160	−	19.2350i	−1.34125	−	0.774372i	−0.354260	−	0.935147i	$-0.615267\pi$
$617$	−33.3160	−	19.2350i	−1.34125	−	0.774372i	−0.986991	+	0.160776i	$0.948600\pi$
$618$	−72.9410	−	42.1125i	−2.93412	−	1.69401i
$619$	−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
$622$	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
$626$	−16.9403	−	4.53915i	−0.677072	−	0.181421i
$627$	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
$630$	−34.1918	−	34.8138i	−1.36223	−	1.38701i
$631$	−36.0825	+	9.66827i	−1.43642	+	0.384888i	−0.891279	−	0.453456i	$-0.850191\pi$
$631$	−36.0825	+	9.66827i	−1.43642	+	0.384888i	−0.545142	+	0.838344i	$0.683524\pi$
$632$	27.6237			1.09881
$633$	55.9176	−	14.9831i	2.22252	−	0.595524i
$634$	−30.7026	−	53.1785i	−1.21936	−	2.11199i
$635$	−13.5482	−	7.98575i	−0.537645	−	0.316905i
$636$			14.2348i			0.564448i
$637$		0			0
$638$	2.31681	+	2.31681i	0.0917235	+	0.0917235i
$639$	7.06528	−	26.3680i	0.279498	−	1.04310i
$640$	−11.5551	−	44.7330i	−0.456754	−	1.76823i
$641$	2.97232	+	1.71607i	0.117399	+	0.0677806i	0.557550	−	0.830143i	$-0.311742\pi$
$641$	2.97232	+	1.71607i	0.117399	+	0.0677806i	−0.440150	+	0.897924i	$0.645075\pi$
$642$			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	$0.0614324\pi$
$644$	32.4409	+	121.071i	1.27835	+	4.77087i
$645$	−2.64636	+	9.53185i	−0.104200	+	0.375316i
$646$	−2.50309	+	4.33549i	−0.0984829	+	0.170577i
$647$	4.93784	−	18.4283i	0.194127	−	0.724490i	−0.798365	−	0.602174i	$-0.794301\pi$
$647$	4.93784	−	18.4283i	0.194127	−	0.724490i	0.992491	−	0.122316i	$-0.0390321\pi$
$648$	−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
$653$	−9.90911	+	36.9813i	−0.387773	+	1.44719i	0.445975	+	0.895046i	$0.352857\pi$
$653$	−9.90911	+	36.9813i	−0.387773	+	1.44719i	−0.833748	+	0.552145i	$0.813810\pi$
$654$	−16.2085	+	28.0740i	−0.633803	+	1.09778i
$655$	−5.59149	+	20.1398i	−0.218477	+	0.786928i
$656$	−1.50658	−	5.62263i	−0.0588220	−	0.219527i
$657$	5.53243	−	9.58244i	0.215841	−	0.373847i
$658$		−	17.2277i		−	0.671605i
$659$	−34.0246	−	19.6441i	−1.32541	−	0.765225i	−0.340823	−	0.940128i	$-0.610706\pi$
$659$	−34.0246	−	19.6441i	−1.32541	−	0.765225i	−0.984586	+	0.174903i	$0.944039\pi$
$660$	8.56501	+	33.1577i	0.333393	+	1.29066i
$661$	−7.01565	+	26.1828i	−0.272877	+	1.01839i	0.684373	+	0.729132i	$0.260076\pi$
$661$	−7.01565	+	26.1828i	−0.272877	+	1.01839i	−0.957251	+	0.289260i	$0.906591\pi$
$662$	17.6545	+	17.6545i	0.686161	+	0.686161i
$663$		0			0
$664$			44.1900i			1.71490i
$665$	−39.4410	−	23.2478i	−1.52946	−	0.901510i
$666$	−3.37468	−	5.84511i	−0.130766	−	0.226493i
$667$	−6.82448	+	1.82861i	−0.264245	+	0.0708042i
$668$	45.2943			1.75249
$669$	−66.6357	+	17.8550i	−2.57629	+	0.690314i
$670$	41.0974	+	41.8451i	1.58773	+	1.61662i
$671$	−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	$-0.372954\pi$
$673$	6.86071	+	1.83832i	0.264461	+	0.0708621i	−0.124152	+	0.992263i	$0.539621\pi$
$674$	−21.6463	−	5.80011i	−0.833785	−	0.223412i
$675$	−6.11655	+	1.52130i	−0.235426	+	0.0585550i
$676$		0			0
$677$	19.2265	−	19.2265i	0.738933	−	0.738933i	−0.233439	−	0.972372i	$-0.574998\pi$
$677$	19.2265	−	19.2265i	0.738933	−	0.738933i	0.972372	+	0.233439i	$0.0749978\pi$
$678$	−40.6481	−	70.4045i	−1.56108	−	2.70387i
$679$	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
$682$	−17.1766	−	9.91690i	−0.657725	−	0.379738i
$683$	−3.99823	−	2.30838i	−0.152988	−	0.0883277i	0.421552	−	0.906804i	$-0.361486\pi$
$683$	−3.99823	−	2.30838i	−0.152988	−	0.0883277i	−0.574540	+	0.818477i	$0.694819\pi$
$684$	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
$687$	−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
$691$	10.2265	+	2.74019i	0.389036	+	0.104242i	0.448035	−	0.894016i	$-0.352124\pi$
$691$	10.2265	+	2.74019i	0.389036	+	0.104242i	−0.0589986	+	0.998258i	$0.518791\pi$
$692$	−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
$695$	−14.3356	+	14.0795i	−0.543780	+	0.534065i
$696$	6.66694	−	1.78640i	0.252710	−	0.0677133i
$697$	1.17522			0.0445146
$698$	−74.7333	+	20.0247i	−2.82870	+	0.757947i
$699$	2.52797	+	4.37857i	0.0956166	+	0.165613i
$700$	1.22251	−	67.8094i	0.0462065	−	2.56295i
$701$		−	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
$704$	5.33243	−	19.9009i	0.200973	−	0.750043i
$705$	8.74394	+	5.15395i	0.329316	+	0.194109i
$706$	26.5461	+	15.3264i	0.999076	+	0.576817i
$707$		−	29.6895i		−	1.11659i
$708$	27.0158	−	46.7927i	1.01532	−	1.75858i
$709$	−6.37565	−	23.7942i	−0.239442	−	0.893611i	−0.976096	−	0.217341i	$-0.930262\pi$
$709$	−6.37565	−	23.7942i	−0.239442	−	0.893611i	0.736653	−	0.676271i	$-0.236405\pi$
$710$	51.2324	−	28.9665i	1.92272	−	1.08709i
$711$	8.79710	−	15.2370i	0.329917	−	0.571433i
$712$	−2.31655	+	8.64548i	−0.0868164	+	0.324003i
$713$	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
$718$	−10.8810	+	40.6084i	−0.406074	+	1.51549i
$719$	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
$721$	14.6996	+	54.8597i	0.547442	+	2.04308i
$722$	13.0446	−	22.5938i	0.485468	−	0.840856i
$723$			33.8652i			1.25946i
$724$	−6.88102	−	3.97276i	−0.255731	−	0.147646i
$725$	3.82225	+	0.0689099i	0.141955	+	0.00255925i
$726$	11.1017	−	41.4321i	0.412023	−	1.53769i
$727$	16.4412	+	16.4412i	0.609770	+	0.609770i	0.942886	−	0.333116i	$-0.108100\pi$
$727$	16.4412	+	16.4412i	0.609770	+	0.609770i	−0.333116	+	0.942886i	$0.608100\pi$
$728$		0			0
$729$			16.5738i			0.613846i
$730$	23.0974	−	5.96634i	0.854875	−	0.220824i
$731$	−0.364709	−	0.631694i	−0.0134892	−	0.0233641i
$732$	−30.4386	+	8.15599i	−1.12504	+	0.301454i
$733$	30.6968			1.13381			0.566907	−	0.823782i	$-0.308140\pi$
$733$	30.6968			1.13381			0.566907	+	0.823782i	$0.308140\pi$
$734$	79.8698	−	21.4010i	2.94805	−	0.789927i
$735$	−0.328502	+	36.4452i	−0.0121170	+	1.34430i
$736$	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
$739$	33.3434	+	8.93434i	1.22656	+	0.328655i	0.813238	−	0.581931i	$-0.197703\pi$
$739$	33.3434	+	8.93434i	1.22656	+	0.328655i	0.413319	+	0.910586i	$0.364369\pi$
$740$	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
$745$	−0.256170	+	28.4204i	−0.00938534	+	1.04124i
$746$	−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
$750$	52.8203	+	32.4309i	1.92873	+	1.18421i
$751$	18.1008	−	10.4505i	0.660509	−	0.381345i	−0.131962	−	0.991255i	$-0.542128\pi$
$751$	18.1008	−	10.4505i	0.660509	−	0.381345i	0.792471	+	0.609910i	$0.208794\pi$
$752$	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
$756$	16.5160	+	4.42545i	0.600681	+	0.160952i
$757$	32.4416	+	8.69270i	1.17911	+	0.315942i	0.794573	−	0.607168i	$-0.207695\pi$
$757$	32.4416	+	8.69270i	1.17911	+	0.315942i	0.384537	+	0.923110i	$0.374361\pi$
$758$	−19.8881	−	74.2232i	−0.722367	−	2.69591i
$759$	−27.5807	−	27.5807i	−1.00112	−	1.00112i
$760$	47.3097	+	0.426430i	1.71610	+	0.0154682i
$761$	46.3730	−	12.4256i	1.68102	−	0.450428i	0.712973	−	0.701192i	$-0.247348\pi$
$761$	46.3730	−	12.4256i	1.68102	−	0.450428i	0.968048	+	0.250764i	$0.0806817\pi$
$762$	−38.9906			−1.41248
$763$	21.1148	−	5.65768i	0.764406	−	0.204822i
$764$	14.7789	+	25.5979i	0.534684	+	0.926099i
$765$	−1.07640	+	1.82617i	−0.0389175	+	0.0660254i
$766$		−	76.4612i		−	2.76266i
$767$		0			0
$768$	−43.3025	−	43.3025i	−1.56255	−	1.56255i
$769$	−6.05983	+	22.6156i	−0.218523	+	0.815539i	0.766374	+	0.642395i	$0.222059\pi$
$769$	−6.05983	+	22.6156i	−0.218523	+	0.815539i	−0.984897	+	0.173144i	$0.944608\pi$
$770$	18.1899	−	30.8601i	0.655519	−	1.11212i
$771$	−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	$0.327357\pi$
$774$	2.86034	+	10.6749i	0.102813	+	0.383703i
$775$	−22.4572	+	5.58553i	−0.806686	+	0.200638i
$776$	−1.70554	+	2.95408i	−0.0612252	+	0.106045i
$777$	−2.61416	+	9.75617i	−0.0937823	+	0.350000i
$778$	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
$783$	−0.249452	+	0.930966i	−0.00891467	+	0.0332700i
$784$	−6.65549	+	11.5276i	−0.237696	+	0.411702i
$785$	20.2901	+	35.8867i	0.724186	+	1.28085i
$786$	13.4122	+	50.0551i	0.478398	+	1.78540i
$787$	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
$790$	36.7272	−	9.48706i	1.30669	−	0.337535i
$791$	−14.1885	+	52.9520i	−0.504483	+	1.88276i
$792$	12.1411	+	12.1411i	0.431414	+	0.431414i
$793$		0			0
$794$		−	19.3299i		−	0.685994i
$795$	2.19403	+	8.49375i	0.0778144	+	0.301242i
$796$	14.7620	+	25.5686i	0.523227	+	0.906256i
$797$	−12.0194	+	3.22058i	−0.425748	+	0.114079i	−0.465330	−	0.885138i	$-0.654064\pi$
$797$	−12.0194	+	3.22058i	−0.425748	+	0.114079i	0.0395816	+	0.999216i	$0.487397\pi$
$798$	−113.508			−4.01813
$799$	−0.722901	+	0.193701i	−0.0255744	+	0.00685264i
$800$	−7.74646	−	13.9939i	−0.273879	−	0.494759i
$801$	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
$804$	90.5476	+	24.2622i	3.19337	+	0.855661i
$805$	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	−0.386084	−	0.922463i	$-0.626173\pi$
$809$	6.25034	−	3.60863i	0.219750	−	0.126873i	0.605835	+	0.795591i	$0.292839\pi$
$810$	−39.0867	+	38.3884i	−1.37337	+	1.34883i
$811$	15.0515	−	15.0515i	0.528530	−	0.528530i	−0.391604	−	0.920134i	$-0.628080\pi$
$811$	15.0515	−	15.0515i	0.528530	−	0.528530i	0.920134	+	0.391604i	$0.128080\pi$
$812$	−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
$815$	25.2760	−	24.8245i	0.885381	−	0.869563i
$816$	−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
$821$	−16.9404	−	4.53915i	−0.591222	−	0.158418i	−0.0492105	−	0.998788i	$-0.515671\pi$
$821$	−16.9404	−	4.53915i	−0.591222	−	0.158418i	−0.542012	+	0.840371i	$0.682337\pi$
$822$	−73.3529	−	19.6548i	−2.55847	−	0.685541i
$823$	−2.83413	−	10.5771i	−0.0987916	−	0.368695i	0.898775	−	0.438409i	$-0.144458\pi$
$823$	−2.83413	−	10.5771i	−0.0987916	−	0.368695i	−0.997567	+	0.0697141i	$0.977791\pi$
$824$	−41.5013	−	41.5013i	−1.44576	−	1.44576i
$825$	10.2213	+	18.4646i	0.355859	+	0.642856i
$826$	−54.5923	+	14.6280i	−1.89951	+	0.508972i
$827$	−1.86613			−0.0648917			−0.0324458	−	0.999473i	$-0.510330\pi$
$827$	−1.86613			−0.0648917			−0.0324458	+	0.999473i	$0.510330\pi$
$828$	−79.6882	+	21.3524i	−2.76936	+	0.742047i
$829$	−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	$-0.373116\pi$
$830$	15.1766	+	58.7529i	0.526786	+	2.03934i
$831$			66.5870i			2.30988i
$832$		0			0
$833$	−1.90028	−	1.90028i	−0.0658408	−	0.0658408i
$834$	−12.8935	+	48.1193i	−0.446467	+	1.66624i
$835$	27.0265	−	6.98127i	0.935291	−	0.241597i
$836$	31.0868	+	17.9480i	1.07516	+	0.620743i
$837$		−	5.83431i		−	0.201663i
$838$	−20.2595	+	35.0904i	−0.699851	+	1.21218i
$839$	−5.02241	−	18.7439i	−0.173393	−	0.647111i	−0.996820	−	0.0796889i	$-0.974607\pi$
$839$	−5.02241	−	18.7439i	−0.173393	−	0.647111i	0.823427	−	0.567422i	$-0.192059\pi$
$840$	−37.1403	−	65.6892i	−1.28146	−	2.26649i
$841$	−14.2077	+	24.6085i	−0.489921	+	0.848568i
$842$	−8.04579	+	30.0273i	−0.277276	+	1.03481i
$843$	−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
$848$	−0.829228	+	3.09472i	−0.0284758	+	0.106273i
$849$	−9.12227	+	15.8002i	−0.313075	+	0.542263i
$850$	−4.43512	+	1.10310i	−0.152123	+	0.0378360i
$851$	2.76530	+	10.3202i	0.0947931	+	0.353773i
$852$	47.0328	−	81.4633i	1.61132	−	2.79089i
$853$		−	2.67051i		−	0.0914364i	−0.998954	−	0.0457182i	$-0.985442\pi$
$853$		−	2.67051i		−	0.0914364i	0.998954	−	0.0457182i	$-0.0145576\pi$
$854$	28.5464	+	16.4813i	0.976837	+	0.563977i
$855$	15.3015	−	25.9598i	0.523301	−	0.887807i
$856$	−10.4472	+	38.9894i	−0.357077	+	1.33263i
$857$	−17.5773	−	17.5773i	−0.600430	−	0.600430i	0.339996	−	0.940427i	$-0.389574\pi$
$857$	−17.5773	−	17.5773i	−0.600430	−	0.600430i	−0.940427	+	0.339996i	$0.889574\pi$
$858$		0			0
$859$			52.8699i			1.80390i	0.431844	+	0.901949i	$0.357863\pi$
$859$			52.8699i			1.80390i	−0.431844	+	0.901949i	$0.642137\pi$
$860$	−7.79965	+	13.2325i	−0.265966	+	0.451225i
$861$	13.3232	+	23.0764i	0.454052	+	0.786441i
$862$	−24.5535	+	6.57909i	−0.836296	+	0.224085i
$863$	3.40127			0.115780			0.0578902	−	0.998323i	$-0.481563\pi$
$863$	3.40127			0.115780			0.0578902	+	0.998323i	$0.481563\pi$
$864$	3.89517	−	1.04371i	0.132516	−	0.0355076i
$865$	−36.1377	−	0.325730i	−1.22872	−	0.0110752i
$866$	−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
$869$	12.4760	+	3.34294i	0.423220	+	0.113402i
$870$	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
$875$	−9.72210	−	40.6494i	−0.328667	−	1.37420i
$876$	26.9605	−	26.9605i	0.910912	−	0.910912i
$877$	−17.0391	−	9.83752i	−0.575369	−	0.332189i	0.183922	−	0.982941i	$-0.441121\pi$
$877$	−17.0391	−	9.83752i	−0.575369	−	0.332189i	−0.759291	+	0.650751i	$0.774454\pi$
$878$	41.5832	+	24.0080i	1.40336	+	0.810232i
$879$	−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	$-0.679446\pi$
$881$	−2.06350	+	1.19137i	−0.0695212	+	0.0401381i	0.464836	+	0.885397i	$0.346113\pi$
$882$	20.3586	+	35.2621i	0.685510	+	1.18734i
$883$	−30.4180	+	30.4180i	−1.02365	+	1.02365i	−0.0239343	+	0.999714i	$0.507619\pi$
$883$	−30.4180	+	30.4180i	−1.02365	+	1.02365i	−0.999714	+	0.0239343i	$0.992381\pi$
$884$		0			0
$885$	8.90776	−	32.0846i	0.299431	−	1.07851i
$886$	8.62317	+	2.31057i	0.289701	+	0.0776252i
$887$	21.9337	+	5.87711i	0.736461	+	0.197334i	0.607504	−	0.794316i	$-0.292171\pi$
$887$	21.9337	+	5.87711i	0.736461	+	0.197334i	0.128956	+	0.991650i	$0.458837\pi$
$888$	−2.70146	−	10.0820i	−0.0906550	−	0.338329i
$889$	18.5915	+	18.5915i	0.623538	+	0.623538i
$890$	−0.110779	+	12.2902i	−0.00371332	+	0.411969i
$891$	−18.0189	+	4.82814i	−0.603655	+	0.161749i
$892$	−107.117			−3.58653
$893$	10.2763	−	2.75354i	0.343885	−	0.0921436i
$894$	35.2325	+	61.0244i	1.17835	+	2.04096i
$895$	39.9402	−	10.3170i	1.33505	−	0.344860i
$896$			77.2410i			2.58044i
$897$		0			0
$898$	51.6980	+	51.6980i	1.72518	+	1.72518i
$899$	−0.915872	+	3.41808i	−0.0305460	+	0.113999i
$900$	44.6317	+	0.804648i	1.48772	+	0.0268216i
$901$	−0.560184	−	0.323423i	−0.0186624	−	0.0107748i
$902$		−	13.0716i		−	0.435235i
$903$	8.26923	−	14.3227i	0.275183	−	0.476630i
$904$	−14.6623	−	54.7204i	−0.487660	−	1.81997i
$905$	−4.71815	−	1.30992i	−0.156837	−	0.0435431i
$906$	11.6082	−	20.1061i	0.385658	−	0.667980i
$907$	−5.99131	+	22.3599i	−0.198938	+	0.742448i	0.792274	+	0.610166i	$0.208897\pi$
$907$	−5.99131	+	22.3599i	−0.198938	+	0.742448i	−0.991212	+	0.132282i	$0.957770\pi$
$908$	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
$913$	−5.34774	+	19.9580i	−0.176984	+	0.660515i
$914$	12.0754	−	20.9152i	0.399418	−	0.691813i
$915$	−16.9052	+	9.55812i	−0.558869	+	0.315982i
$916$	−16.5226	−	61.6632i	−0.545922	−	2.03741i
$917$	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	$0.0554565\pi$
$919$	49.3350	+	28.4836i	1.62741	+	0.939586i	0.642549	+	0.766245i	$0.277877\pi$
$920$	−68.7676	−	40.5337i	−2.26720	−	1.33636i
$921$	12.3431	−	46.0652i	0.406720	−	1.51790i
$922$	−32.3379	−	32.3379i	−1.06499	−	1.06499i
$923$		0			0
$924$		−	57.2537i		−	1.88351i
$925$	0.104208	−	5.78014i	0.00342634	−	0.190050i
$926$	19.9199	+	34.5023i	0.654608	+	1.13381i
$927$	−36.1083	+	9.67519i	−1.18595	+	0.317775i
$928$	−2.44586			−0.0802892
$929$	28.2256	−	7.56304i	0.926053	−	0.248135i	0.235882	−	0.971782i	$-0.424202\pi$
$929$	28.2256	−	7.56304i	0.926053	−	0.248135i	0.690171	+	0.723647i	$0.257535\pi$
$930$	−40.9334	+	40.2021i	−1.34226	+	1.31828i
$931$	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
$934$	−31.6230	−	8.47335i	−1.03473	−	0.277256i
$935$	−1.49946	−	0.416299i	−0.0490375	−	0.0136144i
$936$		0			0
$937$	−1.77191	+	1.77191i	−0.0578859	+	0.0578859i	−0.735457	−	0.677571i	$-0.763033\pi$
$937$	−1.77191	+	1.77191i	−0.0578859	+	0.0578859i	0.677571	+	0.735457i	$0.263033\pi$
$938$	−49.0279	−	84.9188i	−1.60082	−	2.77270i
$939$	−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	−0.406253	−	0.913761i	$-0.633165\pi$
$941$	15.5682	−	15.5682i	0.507507	−	0.507507i	0.913761	+	0.406253i	$0.133165\pi$
$942$	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
$945$	10.5370	+	0.0949760i	0.342768	+	0.00308957i
$946$	−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
$951$	−58.4220	−	15.6541i	−1.89446	−	0.507620i
$952$	5.37459	+	1.44012i	0.174191	+	0.0466745i
$953$	−10.4907	−	39.1517i	−0.339826	−	1.26825i	−0.898541	−	0.438889i	$-0.855372\pi$
$953$	−10.4907	−	39.1517i	−0.339826	−	1.26825i	0.558715	−	0.829360i	$-0.311295\pi$
$954$	6.92996	+	6.92996i	0.224366	+	0.224366i
$955$	12.7639	+	12.9960i	0.413029	+	0.420542i
$956$	34.9894	−	9.37537i	1.13164	−	0.303221i
$957$	3.22725			0.104322
$958$	−31.6695	+	8.48582i	−1.02320	+	0.274164i
$959$	25.6043	+	44.3479i	0.826805	+	1.43207i
$960$	−51.3433	−	30.2633i	−1.65710	−	0.976745i
$961$			9.57907i			0.309002i
$962$		0			0
$963$	18.1792	+	18.1792i	0.585817	+	0.585817i
$964$	−13.6096	+	50.7916i	−0.438334	+	1.63589i
$965$	13.0008	+	50.3300i	0.418512	+	1.62018i
$966$	165.854	+	95.7557i	5.33626	+	3.08089i
$967$		−	12.2654i		−	0.394430i	−0.980360	−	0.197215i	$-0.936810\pi$
$967$		−	12.2654i		−	0.394430i	0.980360	−	0.197215i	$-0.0631897\pi$
$968$	14.9451	−	25.8857i	0.480354	−	0.831997i
$969$	1.27623	+	4.76297i	0.0409985	+	0.153009i
$970$	−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	$0.284898\pi$
$972$	−19.1115	+	71.3250i	−0.613001	+	2.28775i
$973$	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	0.0738385	−	0.997270i	$-0.476475\pi$
$977$	30.4574	−	17.5846i	0.974419	−	0.562581i	0.900581	+	0.434689i	$0.143142\pi$
$978$	22.7335	−	84.8424i	0.726936	−	2.71296i
$979$	−2.09250	+	3.62432i	−0.0668767	+	0.115834i
$980$	−15.1391	+	54.5290i	−0.483600	+	1.74186i
$981$	3.72385	+	13.8976i	0.118893	+	0.443716i
$982$	−12.0861	+	20.9338i	−0.385684	+	0.668024i
$983$		−	12.2764i		−	0.391555i	−0.980648	−	0.195778i	$-0.937277\pi$
$983$		−	12.2764i		−	0.391555i	0.980648	−	0.195778i	$-0.0627231\pi$
$984$	−23.8470	−	13.7681i	−0.760215	−	0.438911i
$985$	−12.3419	−	47.7792i	−0.393247	−	1.52237i
$986$	−0.180878	+	0.675045i	−0.00576032	+	0.0214978i
$987$	−11.9988	−	11.9988i	−0.381927	−	0.381927i
$988$		0			0
$989$		−	17.4946i		−	0.556297i
$990$	20.3119	+	11.9725i	0.645555	+	0.380510i
$991$	−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	$-0.343463\pi$
$992$	14.3013	−	3.83202i	0.454066	−	0.121667i
$993$	24.5922			0.780409
$994$	−95.0419	+	25.4664i	−3.01455	+	0.807745i
$995$	12.7493	+	12.9812i	0.404179	+	0.411531i
$996$	68.5794	+	68.5794i	2.17302	+	2.17302i
$997$	−9.72750	−	36.3035i	−0.308073	−	1.14974i	−0.930268	−	0.366882i	$-0.880425\pi$
$997$	−9.72750	−	36.3035i	−0.308073	−	1.14974i	0.622194	−	0.782863i	$-0.286241\pi$
$998$	−25.6070	−	6.86138i	−0.810576	−	0.217193i
$999$	1.40784	+	0.377229i	0.0445421	+	0.0119350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.i.418.32		144
5.2	odd	4		845.2.o.i.587.32		144
13.2	odd	12		845.2.k.f.268.32	yes	72
13.3	even	3		845.2.f.f.408.32	yes	72
13.4	even	6	inner	845.2.t.i.188.32		144
13.5	odd	4		845.2.o.i.258.5		144
13.6	odd	12		845.2.o.i.488.5		144
13.7	odd	12		845.2.o.i.488.32		144
13.8	odd	4		845.2.o.i.258.32		144
13.9	even	3	inner	845.2.t.i.188.5		144
13.10	even	6		845.2.f.f.408.5	✓	72
13.11	odd	12		845.2.k.f.268.5	yes	72
13.12	even	2	inner	845.2.t.i.418.5		144
65.2	even	12		845.2.f.f.437.32	yes	72
65.7	even	12	inner	845.2.t.i.657.32		144
65.12	odd	4		845.2.o.i.587.5		144
65.17	odd	12		845.2.o.i.357.5		144
65.22	odd	12		845.2.o.i.357.32		144
65.32	even	12	inner	845.2.t.i.657.5		144
65.37	even	12		845.2.f.f.437.5	yes	72
65.42	odd	12		845.2.k.f.577.5	yes	72
65.47	even	4	inner	845.2.t.i.427.5		144
65.57	even	4	inner	845.2.t.i.427.32		144
65.62	odd	12		845.2.k.f.577.32	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.f.f.408.5	✓	72	13.10	even	6
845.2.f.f.408.32	yes	72	13.3	even	3
845.2.f.f.437.5	yes	72	65.37	even	12
845.2.f.f.437.32	yes	72	65.2	even	12
845.2.k.f.268.5	yes	72	13.11	odd	12
845.2.k.f.268.32	yes	72	13.2	odd	12
845.2.k.f.577.5	yes	72	65.42	odd	12
845.2.k.f.577.32	yes	72	65.62	odd	12
845.2.o.i.258.5		144	13.5	odd	4
845.2.o.i.258.32		144	13.8	odd	4
845.2.o.i.357.5		144	65.17	odd	12
845.2.o.i.357.32		144	65.22	odd	12
845.2.o.i.488.5		144	13.6	odd	12
845.2.o.i.488.32		144	13.7	odd	12
845.2.o.i.587.5		144	65.12	odd	4
845.2.o.i.587.32		144	5.2	odd	4
845.2.t.i.188.5		144	13.9	even	3	inner
845.2.t.i.188.32		144	13.4	even	6	inner
845.2.t.i.418.5		144	13.12	even	2	inner
845.2.t.i.418.32		144	1.1	even	1	trivial
845.2.t.i.427.5		144	65.47	even	4	inner
845.2.t.i.427.32		144	65.57	even	4	inner
845.2.t.i.657.5		144	65.32	even	12	inner
845.2.t.i.657.32		144	65.7	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.05458 - 1.18621i) q^{2} +(0.604804 - 2.25716i) q^{3} +(1.81419 - 3.14226i) q^{4} +(0.598181 - 2.15457i) q^{5} +(-1.43485 - 5.35492i) q^{6} +(-1.86917 + 3.23750i) q^{7} -3.86318i q^{8} +(-2.13090 - 1.23027i) q^{9} +(-1.32677 - 5.13630i) q^{10} +(0.467511 - 1.74477i) q^{11} +(-5.99536 - 5.99536i) q^{12} +8.86890i q^{14} +(-4.50143 - 2.65328i) q^{15} +(-0.954169 - 1.65267i) q^{16} +(0.372153 - 0.0997182i) q^{17} -5.83745 q^{18} +(-5.29032 + 1.41754i) q^{19} +(-5.68502 - 5.78843i) q^{20} +(6.17706 + 6.17706i) q^{21} +(-1.10913 - 4.13933i) q^{22} +(8.92587 + 2.39168i) q^{23} +(-8.71981 - 2.33647i) 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} +(-12.3959 - 0.111731i) 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} +(5.85732 + 5.96387i) 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} +(2.94635 + 0.789472i) q^{41} +(20.0185 + 5.36394i) q^{42} +(-0.489998 - 1.82870i) q^{43} +(-4.63438 - 4.63438i) q^{44} +(-3.92538 + 3.85525i) q^{45} +(21.1759 - 5.67406i) q^{46} -1.94248 q^{47} +(-4.30742 + 1.15417i) q^{48} +(-3.48758 - 6.04067i) q^{49} +(-11.8602 - 0.213823i) q^{50} -0.900318i q^{51} +(-1.18715 - 1.18715i) q^{53} +(0.774031 - 2.88872i) q^{54} +(-3.47958 - 2.05098i) q^{55} +(12.5070 + 7.22094i) q^{56} +12.7984i q^{57} +(-0.906945 + 1.57087i) q^{58} +(1.64935 + 6.15548i) q^{59} +(-16.5037 + 9.33112i) q^{60} +(1.85832 - 3.21870i) q^{61} +(2.84189 - 10.6061i) q^{62} +(7.96601 - 4.59918i) q^{63} +11.4060 q^{64} -10.0139 q^{66} +(-9.57490 + 5.52807i) q^{67} +(0.361815 - 1.35031i) q^{68} +(10.7968 - 18.7006i) q^{69} +(19.1087 + 5.30521i) q^{70} +(2.87143 + 10.7163i) q^{71} +(-4.75277 + 8.23204i) q^{72} +4.49691i q^{73} +(2.37553 + 1.37151i) q^{74} +(-8.40935 + 8.11150i) q^{75} +(-5.14335 + 19.1952i) q^{76} +(4.77484 + 4.77484i) q^{77} +7.15052i q^{79} +(-4.13156 + 1.06723i) q^{80} +(-5.16367 - 8.94374i) q^{81} +(6.98997 - 1.87296i) q^{82} -11.4388 q^{83} +(30.6163 - 8.20360i) q^{84} +(0.00776503 - 0.861480i) q^{85} +(-3.17596 - 3.17596i) q^{86} +(0.462417 + 1.72576i) q^{87} +(-6.74037 - 1.80608i) q^{88} +(-2.23792 - 0.599649i) 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} +(-0.110383 + 12.2463i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more