LMFDB - Embedded newform 240.2.bb.a.173.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(173,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("240.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bb (of order $4$, degree $2$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			173.20
Character	$\chi$	$=$	240.173
Dual form			240.2.bb.a.197.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.269844 + 1.38823i) q^{2} +(0.147625 - 1.72575i) q^{3} +(-1.85437 - 0.749211i) q^{4} +(2.12868 - 0.684619i) q^{5} +(2.35590 + 0.670621i) q^{6} +(-1.09901 - 1.09901i) q^{7} +(1.54047 - 2.37212i) q^{8} +(-2.95641 - 0.509529i) q^{9} +O(q^{10})$	\(q+(-0.269844 + 1.38823i) q^{2} +(0.147625 - 1.72575i) q^{3} +(-1.85437 - 0.749211i) q^{4} +(2.12868 - 0.684619i) q^{5} +(2.35590 + 0.670621i) q^{6} +(-1.09901 - 1.09901i) q^{7} +(1.54047 - 2.37212i) q^{8} +(-2.95641 - 0.509529i) q^{9} +(0.375997 + 3.13984i) q^{10} +(-2.54294 - 2.54294i) q^{11} +(-1.56670 + 3.08957i) q^{12} -4.11643i q^{13} +(1.82224 - 1.22912i) q^{14} +(-0.867232 - 3.77464i) q^{15} +(2.87736 + 2.77863i) q^{16} +(4.70528 + 4.70528i) q^{17} +(1.50511 - 3.96669i) q^{18} +(3.02587 - 3.02587i) q^{19} +(-4.46029 - 0.325298i) q^{20} +(-2.05886 + 1.73437i) q^{21} +(4.21638 - 2.84399i) q^{22} +(2.21250 + 2.21250i) q^{23} +(-3.86627 - 3.00865i) q^{24} +(4.06259 - 2.91468i) q^{25} +(5.71456 + 1.11079i) q^{26} +(-1.31576 + 5.02681i) q^{27} +(1.21458 + 2.86136i) q^{28} +(1.33233 + 1.33233i) q^{29} +(5.47409 - 0.185354i) q^{30} -7.52589 q^{31} +(-4.63382 + 3.24465i) q^{32} +(-4.76387 + 4.01307i) q^{33} +(-7.80171 + 5.26232i) q^{34} +(-3.09185 - 1.58704i) q^{35} +(5.10054 + 3.15983i) q^{36} +4.02304i q^{37} +(3.38409 + 5.01712i) q^{38} +(-7.10392 - 0.607690i) q^{39} +(1.65517 - 6.10413i) q^{40} -0.746050 q^{41} +(-1.85214 - 3.32618i) q^{42} +7.11316 q^{43} +(2.81035 + 6.62074i) q^{44} +(-6.64210 + 0.939392i) q^{45} +(-3.66849 + 2.47443i) q^{46} +(-0.644960 - 0.644960i) q^{47} +(5.21998 - 4.55541i) q^{48} -4.58435i q^{49} +(2.94998 + 6.42632i) q^{50} +(8.81475 - 7.42551i) q^{51} +(-3.08408 + 7.63338i) q^{52} +10.4662i q^{53} +(-6.62332 - 3.18303i) q^{54} +(-7.15406 - 3.67217i) q^{55} +(-4.29998 + 0.913994i) q^{56} +(-4.77520 - 5.66859i) q^{57} +(-2.20910 + 1.49006i) q^{58} +(-1.06245 + 1.06245i) q^{59} +(-1.21984 + 7.64931i) q^{60} +(0.875750 + 0.875750i) q^{61} +(2.03082 - 10.4477i) q^{62} +(2.68915 + 3.80911i) q^{63} +(-3.25391 - 7.30835i) q^{64} +(-2.81819 - 8.76258i) q^{65} +(-4.28556 - 7.69626i) q^{66} +14.9587 q^{67} +(-5.20007 - 12.2506i) q^{68} +(4.14484 - 3.49160i) q^{69} +(3.03750 - 3.86395i) q^{70} -8.10028 q^{71} +(-5.76293 + 6.22806i) q^{72} +(-6.75108 + 6.75108i) q^{73} +(-5.58491 - 1.08559i) q^{74} +(-4.43025 - 7.44129i) q^{75} +(-7.87810 + 3.34406i) q^{76} +5.58943i q^{77} +(2.76057 - 9.69790i) q^{78} +7.62633i q^{79} +(8.02730 + 3.94492i) q^{80} +(8.48076 + 3.01276i) q^{81} +(0.201317 - 1.03569i) q^{82} -7.28706 q^{83} +(5.11729 - 1.67365i) q^{84} +(13.2374 + 6.79473i) q^{85} +(-1.91944 + 9.87471i) q^{86} +(2.49595 - 2.10258i) q^{87} +(-9.94948 + 2.11484i) q^{88} +7.85095i q^{89} +(0.488240 - 9.47426i) q^{90} +(-4.52400 + 4.52400i) q^{91} +(-2.44516 - 5.76042i) q^{92} +(-1.11101 + 12.9878i) q^{93} +(1.06939 - 0.721315i) q^{94} +(4.36955 - 8.51269i) q^{95} +(4.91538 + 8.47579i) q^{96} +(5.44033 - 5.44033i) q^{97} +(6.36414 + 1.23706i) q^{98} +(6.22228 + 8.81368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^4 - 4 * q^6	$ 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.269844	+	1.38823i	−0.190809	+	0.981627i
$2$	−0.269844	+	1.38823i	−0.190809	+	0.981627i
$3$	0.147625	−	1.72575i	0.0852316	−	0.996361i
$3$	0.147625	−	1.72575i	0.0852316	−	0.996361i
$4$	−1.85437	−	0.749211i	−0.927184	−	0.374606i
$5$	2.12868	−	0.684619i	0.951977	−	0.306171i
$5$	2.12868	−	0.684619i	0.951977	−	0.306171i
$6$	2.35590	+	0.670621i	0.961792	+	0.273780i
$7$	−1.09901	−	1.09901i	−0.415387	−	0.415387i	0.468223	−	0.883610i	$-0.344894\pi$
$7$	−1.09901	−	1.09901i	−0.415387	−	0.415387i	−0.883610	+	0.468223i	$0.844894\pi$
$8$	1.54047	−	2.37212i	0.544638	−	0.838671i
$9$	−2.95641	−	0.509529i	−0.985471	−	0.169843i
$10$	0.375997	+	3.13984i	0.118901	+	0.992906i
$11$	−2.54294	−	2.54294i	−0.766725	−	0.766725i	0.210803	−	0.977528i	$-0.432392\pi$
$11$	−2.54294	−	2.54294i	−0.766725	−	0.766725i	−0.977528	+	0.210803i	$0.932392\pi$
$12$	−1.56670	+	3.08957i	−0.452268	+	0.891882i
$13$		−	4.11643i		−	1.14169i	−0.821057	−	0.570846i	$-0.806615\pi$
$13$		−	4.11643i		−	1.14169i	0.821057	−	0.570846i	$-0.193385\pi$
$14$	1.82224	−	1.22912i	0.487014	−	0.328496i
$15$	−0.867232	−	3.77464i	−0.223918	−	0.974608i
$16$	2.87736	+	2.77863i	0.719341	+	0.694657i
$17$	4.70528	+	4.70528i	1.14120	+	1.14120i	0.988231	+	0.152967i	$0.0488828\pi$
$17$	4.70528	+	4.70528i	1.14120	+	1.14120i	0.152967	+	0.988231i	$0.451117\pi$
$18$	1.50511	−	3.96669i	0.354759	−	0.934958i
$19$	3.02587	−	3.02587i	0.694182	−	0.694182i	−0.268967	−	0.963149i	$-0.586682\pi$
$19$	3.02587	−	3.02587i	0.694182	−	0.694182i	0.963149	+	0.268967i	$0.0866822\pi$
$20$	−4.46029	−	0.325298i	−0.997351	−	0.0727389i
$21$	−2.05886	+	1.73437i	−0.449279	+	0.378471i
$22$	4.21638	−	2.84399i	0.898936	−	0.606340i
$23$	2.21250	+	2.21250i	0.461338	+	0.461338i	0.899094	−	0.437756i	$-0.144226\pi$
$23$	2.21250	+	2.21250i	0.461338	+	0.461338i	−0.437756	+	0.899094i	$0.644226\pi$
$24$	−3.86627	−	3.00865i	−0.789199	−	0.614137i
$25$	4.06259	−	2.91468i	0.812519	−	0.582935i
$26$	5.71456	+	1.11079i	1.12072	+	0.217845i
$27$	−1.31576	+	5.02681i	−0.253218	+	0.967409i
$28$	1.21458	+	2.86136i	0.229534	+	0.540746i
$29$	1.33233	+	1.33233i	0.247407	+	0.247407i	0.819906	−	0.572498i	$-0.194026\pi$
$29$	1.33233	+	1.33233i	0.247407	+	0.247407i	−0.572498	+	0.819906i	$0.694026\pi$
$30$	5.47409	−	0.185354i	0.999427	−	0.0338409i
$31$	−7.52589			−1.35169			−0.675845	−	0.737044i	$-0.736221\pi$
$31$	−7.52589			−1.35169			−0.675845	+	0.737044i	$0.736221\pi$
$32$	−4.63382	+	3.24465i	−0.819151	+	0.573578i
$33$	−4.76387	+	4.01307i	−0.829284	+	0.698586i
$34$	−7.80171	+	5.26232i	−1.33798	+	0.902481i
$35$	−3.09185	−	1.58704i	−0.522618	−	0.268259i
$36$	5.10054	+	3.15983i	0.850089	+	0.526639i
$37$			4.02304i			0.661384i	0.943739	+	0.330692i	$0.107282\pi$
$37$			4.02304i			0.661384i	−0.943739	+	0.330692i	$0.892718\pi$
$38$	3.38409	+	5.01712i	0.548972	+	0.813884i
$39$	−7.10392	−	0.607690i	−1.13754	−	0.0973083i
$40$	1.65517	−	6.10413i	0.261706	−	0.965148i
$41$	−0.746050			−0.116513			−0.0582567	−	0.998302i	$-0.518554\pi$
$41$	−0.746050			−0.116513			−0.0582567	+	0.998302i	$0.518554\pi$
$42$	−1.85214	−	3.32618i	−0.285791	−	0.513240i
$43$	7.11316			1.08475			0.542373	−	0.840138i	$-0.317526\pi$
$43$	7.11316			1.08475			0.542373	+	0.840138i	$0.317526\pi$
$44$	2.81035	+	6.62074i	0.423676	+	0.998115i
$45$	−6.64210	+	0.939392i	−0.990146	+	0.140036i
$46$	−3.66849	+	2.47443i	−0.540890	+	0.364835i
$47$	−0.644960	−	0.644960i	−0.0940771	−	0.0940771i	0.658502	−	0.752579i	$-0.271190\pi$
$47$	−0.644960	−	0.644960i	−0.0940771	−	0.0940771i	−0.752579	+	0.658502i	$0.771190\pi$
$48$	5.21998	−	4.55541i	0.753440	−	0.657517i
$49$		−	4.58435i		−	0.654908i
$50$	2.94998	+	6.42632i	0.417190	+	0.908819i
$51$	8.81475	−	7.42551i	1.23431	−	1.03978i
$52$	−3.08408	+	7.63338i	−0.427685	+	1.05856i
$53$			10.4662i			1.43764i	0.695194	+	0.718822i	$0.255318\pi$
$53$			10.4662i			1.43764i	−0.695194	+	0.718822i	$0.744682\pi$
$54$	−6.62332	−	3.18303i	−0.901319	−	0.433156i
$55$	−7.15406	−	3.67217i	−0.964653	−	0.495155i
$56$	−4.29998	+	0.913994i	−0.574608	+	0.122138i
$57$	−4.77520	−	5.66859i	−0.632490	−	0.750823i
$58$	−2.20910	+	1.49006i	−0.290069	+	0.195654i
$59$	−1.06245	+	1.06245i	−0.138319	+	0.138319i	−0.772876	−	0.634557i	$-0.781183\pi$
$59$	−1.06245	+	1.06245i	−0.138319	+	0.138319i	0.634557	+	0.772876i	$0.281183\pi$
$60$	−1.21984	+	7.64931i	−0.157480	+	0.987522i
$61$	0.875750	+	0.875750i	0.112128	+	0.112128i	0.760945	−	0.648817i	$-0.224736\pi$
$61$	0.875750	+	0.875750i	0.112128	+	0.112128i	−0.648817	+	0.760945i	$0.724736\pi$
$62$	2.03082	−	10.4477i	0.257914	−	1.32685i
$63$	2.68915	+	3.80911i	0.338801	+	0.479902i
$64$	−3.25391	−	7.30835i	−0.406739	−	0.913544i
$65$	−2.81819	−	8.76258i	−0.349553	−	1.08686i
$66$	−4.28556	−	7.69626i	−0.527516	−	0.947344i
$67$	14.9587			1.82750			0.913751	−	0.406275i	$-0.133172\pi$
$67$	14.9587			1.82750			0.913751	+	0.406275i	$0.133172\pi$
$68$	−5.20007	−	12.2506i	−0.630602	−	1.48560i
$69$	4.14484	−	3.49160i	0.498980	−	0.420339i
$70$	3.03750	−	3.86395i	0.363050	−	0.461830i
$71$	−8.10028			−0.961326			−0.480663	−	0.876905i	$-0.659604\pi$
$71$	−8.10028			−0.961326			−0.480663	+	0.876905i	$0.659604\pi$
$72$	−5.76293	+	6.22806i	−0.679167	+	0.733984i
$73$	−6.75108	+	6.75108i	−0.790154	+	0.790154i	−0.981519	−	0.191365i	$-0.938709\pi$
$73$	−6.75108	+	6.75108i	−0.790154	+	0.790154i	0.191365	+	0.981519i	$0.438709\pi$
$74$	−5.58491	−	1.08559i	−0.649232	−	0.126198i
$75$	−4.43025	−	7.44129i	−0.511562	−	0.859247i
$76$	−7.87810	+	3.34406i	−0.903680	+	0.383590i
$77$			5.58943i			0.636975i
$78$	2.76057	−	9.69790i	0.312572	−	1.09807i
$79$			7.62633i			0.858029i	0.903298	+	0.429015i	$0.141139\pi$
$79$			7.62633i			0.858029i	−0.903298	+	0.429015i	$0.858861\pi$
$80$	8.02730	+	3.94492i	0.897480	+	0.441056i
$81$	8.48076	+	3.01276i	0.942307	+	0.334751i
$82$	0.201317	−	1.03569i	0.0222318	−	0.114373i
$83$	−7.28706			−0.799859			−0.399929	−	0.916546i	$-0.630965\pi$
$83$	−7.28706			−0.799859			−0.399929	+	0.916546i	$0.630965\pi$
$84$	5.11729	−	1.67365i	0.558342	−	0.182610i
$85$	13.2374	+	6.79473i	1.43580	+	0.736992i
$86$	−1.91944	+	9.87471i	−0.206979	+	1.06482i
$87$	2.49595	−	2.10258i	0.267594	−	0.225420i
$88$	−9.94948	+	2.11484i	−1.06062	+	0.225443i
$89$			7.85095i			0.832199i	0.909319	+	0.416100i	$0.136603\pi$
$89$			7.85095i			0.832199i	−0.909319	+	0.416100i	$0.863397\pi$
$90$	0.488240	−	9.47426i	0.0514650	−	0.998675i
$91$	−4.52400	+	4.52400i	−0.474244	+	0.474244i
$92$	−2.44516	−	5.76042i	−0.254926	−	0.600566i
$93$	−1.11101	+	12.9878i	−0.115207	+	1.34677i
$94$	1.06939	−	0.721315i	0.110299	−	0.0743979i
$95$	4.36955	−	8.51269i	0.448307	−	0.873384i
$96$	4.91538	+	8.47579i	0.501674	+	0.865057i
$97$	5.44033	−	5.44033i	0.552382	−	0.552382i	−0.374745	−	0.927128i	$-0.622270\pi$
$97$	5.44033	−	5.44033i	0.552382	−	0.552382i	0.927128	+	0.374745i	$0.122270\pi$
$98$	6.36414	+	1.23706i	0.642875	+	0.124962i
$99$	6.22228	+	8.81368i	0.625363	+	0.885808i
$100$	−9.71725	+	2.36114i	−0.971725	+	0.236114i
$101$	−2.07858	−	2.07858i	−0.206827	−	0.206827i	0.596090	−	0.802917i	$-0.296720\pi$
$101$	−2.07858	−	2.07858i	−0.206827	−	0.206827i	−0.802917	+	0.596090i	$0.796720\pi$
$102$	7.92971	+	14.2406i	0.785159	+	1.41003i
$103$	6.52055	−	6.52055i	0.642489	−	0.642489i	−0.308678	−	0.951167i	$-0.599886\pi$
$103$	6.52055	−	6.52055i	0.642489	−	0.642489i	0.951167	+	0.308678i	$0.0998864\pi$
$104$	−9.76467	−	6.34123i	−0.957505	−	0.621809i
$105$	−3.19527	+	5.10147i	−0.311827	+	0.497852i
$106$	−14.5295	−	2.82424i	−1.41123	−	0.274315i
$107$	14.2338			1.37603			0.688016	−	0.725695i	$-0.258482\pi$
$107$	14.2338			1.37603			0.688016	+	0.725695i	$0.258482\pi$
$108$	6.20604	−	8.33577i	0.597177	−	0.802110i
$109$	−3.35191	+	3.35191i	−0.321055	+	0.321055i	−0.849172	−	0.528117i	$-0.822898\pi$
$109$	−3.35191	+	3.35191i	−0.321055	+	0.321055i	0.528117	+	0.849172i	$0.322898\pi$
$110$	7.02830	−	8.94057i	0.670122	−	0.852450i
$111$	6.94275	+	0.593903i	0.658977	+	0.0563708i
$112$	−0.108512	−	6.21599i	−0.0102535	−	0.587356i
$113$	4.26326	−	4.26326i	0.401054	−	0.401054i	−0.477551	−	0.878604i	$-0.658475\pi$
$113$	4.26326	−	4.26326i	0.401054	−	0.401054i	0.878604	+	0.477551i	$0.158475\pi$
$114$	9.15786	−	5.09944i	0.857713	−	0.477606i
$115$	6.22444	+	3.19500i	0.580432	+	0.297935i
$116$	−1.47243	−	3.46883i	−0.136712	−	0.322073i
$117$	−2.09744	+	12.1699i	−0.193908	+	1.12511i
$118$	−1.18823	−	1.76162i	−0.109385	−	0.162170i
$119$		−	10.3423i		−	0.948077i
$120$	−10.2898	−	3.75753i	−0.939330	−	0.343014i
$121$			1.93308i			0.175734i
$122$	−1.45206	+	0.979427i	−0.131463	+	0.0886731i
$123$	−0.110136	+	1.28749i	−0.00993063	+	0.116089i
$124$	13.9558	+	5.63848i	1.25326	+	0.506350i
$125$	6.65253	−	8.98575i	0.595021	−	0.803710i
$126$	−6.01357	+	2.70530i	−0.535731	+	0.241007i
$127$	−3.46693	+	3.46693i	−0.307641	+	0.307641i	−0.843994	−	0.536353i	$-0.819802\pi$
$127$	−3.46693	+	3.46693i	−0.307641	+	0.307641i	0.536353	+	0.843994i	$0.319802\pi$
$128$	11.0237	−	2.54507i	0.974369	−	0.224954i
$129$	1.05008	−	12.2755i	0.0924547	−	1.08080i
$130$	12.9250	−	1.54776i	1.13359	−	0.135748i
$131$	−0.0333276	+	0.0333276i	−0.00291184	+	0.00291184i	−0.708561	−	0.705649i	$-0.750655\pi$
$131$	−0.0333276	+	0.0333276i	−0.00291184	+	0.00291184i	0.705649	+	0.708561i	$0.250655\pi$
$132$	11.8406	−	3.87256i	1.03059	−	0.337063i
$133$	−6.65093			−0.576708
$134$	−4.03653	+	20.7662i	−0.348703	+	1.79393i
$135$	0.640610	+	11.6013i	0.0551349	+	0.998479i
$136$	18.4098	−	3.91316i	1.57863	−	0.335551i
$137$	13.1570	−	13.1570i	1.12408	−	1.12408i	0.132955	−	0.991122i	$-0.457553\pi$
$137$	13.1570	−	13.1570i	1.12408	−	1.12408i	0.991122	−	0.132955i	$-0.0424466\pi$
$138$	3.72868	+	6.69618i	0.317407	+	0.570017i
$139$	1.83788	+	1.83788i	0.155887	+	0.155887i	0.780741	−	0.624855i	$-0.214842\pi$
$139$	1.83788	+	1.83788i	0.155887	+	0.155887i	−0.624855	+	0.780741i	$0.714842\pi$
$140$	4.54440	+	5.25941i	0.384072	+	0.444501i
$141$	−1.20825	+	1.01783i	−0.101753	+	0.0857164i
$142$	2.18581	−	11.2451i	0.183429	−	0.943664i
$143$	−10.4678	+	10.4678i	−0.875364	+	0.875364i
$144$	−7.09089	−	9.68087i	−0.590907	−	0.806739i
$145$	3.74825	+	1.92397i	0.311275	+	0.159777i
$146$	−7.55031	−	11.1938i	−0.624868	−	0.926405i
$147$	−7.91144	−	0.676767i	−0.652525	−	0.0558188i
$148$	3.01411	−	7.46020i	0.247758	−	0.613225i
$149$	13.8816	−	13.8816i	1.13722	−	1.13722i	0.148277	−	0.988946i	$-0.452627\pi$
$149$	13.8816	−	13.8816i	1.13722	−	1.13722i	0.988946	−	0.148277i	$-0.0473727\pi$
$150$	11.5257	−	4.14223i	0.941070	−	0.338211i
$151$			5.06298i			0.412020i	0.978550	+	0.206010i	$0.0660479\pi$
$151$			5.06298i			0.412020i	−0.978550	+	0.206010i	$0.933952\pi$
$152$	−2.51647	−	11.8390i	−0.204113	−	0.960269i
$153$	−11.5133	−	16.3082i	−0.930793	−	1.31844i
$154$	−7.75942	−	1.50827i	−0.625272	−	0.121540i
$155$	−16.0202	+	5.15237i	−1.28678	+	0.413848i
$156$	12.7180	+	6.44922i	1.01826	+	0.516351i
$157$	−13.1231			−1.04734			−0.523669	−	0.851922i	$-0.675437\pi$
$157$	−13.1231			−1.04734			−0.523669	+	0.851922i	$0.675437\pi$
$158$	−10.5871	−	2.05792i	−0.842265	−	0.163719i
$159$	18.0620	+	1.54508i	1.43241	+	0.122533i
$160$	−7.64258	+	10.0792i	−0.604199	+	0.796833i
$161$		−	4.86312i		−	0.383268i
$162$	−6.47088	+	10.9603i	−0.508400	+	0.861121i
$163$			5.41315i			0.423991i	0.977271	+	0.211995i	$0.0679962\pi$
$163$			5.41315i			0.423991i	−0.977271	+	0.211995i	$0.932004\pi$
$164$	1.38345	+	0.558949i	0.108029	+	0.0436466i
$165$	−7.39336	+	11.8040i	−0.575572	+	0.918940i
$166$	1.96637	−	10.1161i	0.152620	−	0.785163i
$167$	−8.14595	+	8.14595i	−0.630352	+	0.630352i	−0.948156	−	0.317804i	$-0.897055\pi$
$167$	−8.14595	+	8.14595i	−0.630352	+	0.630352i	0.317804	+	0.948156i	$0.397055\pi$
$168$	0.942538	+	7.55560i	0.0727184	+	0.582927i
$169$	−3.94501			−0.303462
$170$	−13.0047	+	16.5430i	−0.997414	+	1.26879i
$171$	−10.4875	+	7.40396i	−0.801999	+	0.566195i
$172$	−13.1904	−	5.32926i	−1.00576	−	0.406352i
$173$	2.66094			0.202307			0.101154	−	0.994871i	$-0.467747\pi$
$173$	2.66094			0.202307			0.101154	+	0.994871i	$0.467747\pi$
$174$	2.24535	+	4.03233i	0.170219	+	0.305690i
$175$	−7.66809	−	1.26157i	−0.579653	−	0.0953659i
$176$	−0.251081	−	14.3828i	−0.0189259	−	1.08415i
$177$	1.67668	+	1.99036i	0.126027	+	0.149605i
$178$	−10.8989	−	2.11853i	−0.816909	−	0.158791i
$179$	−2.85874	−	2.85874i	−0.213672	−	0.213672i	0.592153	−	0.805825i	$-0.298278\pi$
$179$	−2.85874	−	2.85874i	−0.213672	−	0.213672i	−0.805825	+	0.592153i	$0.798278\pi$
$180$	13.0207	+	3.23436i	0.970506	+	0.241075i
$181$	13.3897	−	13.3897i	0.995252	−	0.995252i	−0.00473703	−	0.999989i	$-0.501508\pi$
$181$	13.3897	−	13.3897i	0.995252	−	0.995252i	0.999989	+	0.00473703i	$0.00150785\pi$
$182$	−5.05958	−	7.50113i	−0.375041	−	0.556021i
$183$	1.64061	−	1.38204i	0.121277	−	0.102163i
$184$	8.65661	−	1.84003i	0.638174	−	0.135649i
$185$	2.75425	+	8.56378i	0.202497	+	0.629622i
$186$	−17.7302	−	5.04702i	−1.30004	−	0.370065i
$187$		−	23.9305i		−	1.74997i
$188$	0.712782	+	1.67921i	0.0519850	+	0.122469i
$189$	6.97054	−	4.07848i	0.507033	−	0.296666i
$190$	10.6385	+	8.36305i	0.771797	+	0.606719i
$191$			25.4774i			1.84348i	0.387804	+	0.921742i	$0.373234\pi$
$191$			25.4774i			1.84348i	−0.387804	+	0.921742i	$0.626766\pi$
$192$	−13.0927	+	4.53654i	−0.944887	+	0.327396i
$193$	−15.8534	−	15.8534i	−1.14115	−	1.14115i	−0.988240	−	0.152910i	$-0.951135\pi$
$193$	−15.8534	−	15.8534i	−1.14115	−	1.14115i	−0.152910	−	0.988240i	$-0.548865\pi$
$194$	6.08440	+	9.02048i	0.436834	+	0.647633i
$195$	−15.5380	+	3.56990i	−1.11270	+	0.255646i
$196$	−3.43465	+	8.50108i	−0.245332	+	0.607220i
$197$	−25.6861			−1.83006			−0.915031	−	0.403384i	$-0.867834\pi$
$197$	−25.6861			−1.83006			−0.915031	+	0.403384i	$0.867834\pi$
$198$	−13.9145	+	6.25964i	−0.988858	+	0.444853i
$199$	5.53158			0.392123			0.196062	−	0.980592i	$-0.437185\pi$
$199$	5.53158			0.392123			0.196062	+	0.980592i	$0.437185\pi$
$200$	−0.655667	−	14.1269i	−0.0463627	−	0.998925i
$201$	2.20829	−	25.8150i	0.155761	−	1.82085i
$202$	3.44645	−	2.32466i	0.242491	−	0.163563i
$203$		−	2.92849i		−	0.205540i
$204$	−21.9091	+	7.16552i	−1.53394	+	0.501687i
$205$	−1.58810	+	0.510760i	−0.110918	+	0.0356730i
$206$	7.29250	+	10.8116i	0.508092	+	0.753277i
$207$	−5.41374	−	7.66840i	−0.376281	−	0.532991i
$208$	11.4380	−	11.8445i	0.793085	−	0.821266i
$209$	−15.3892			−1.06449
$210$	−6.21979	−	5.81237i	−0.429206	−	0.401092i
$211$	2.93232	+	2.93232i	0.201870	+	0.201870i	0.800801	−	0.598931i	$-0.204408\pi$
$211$	2.93232	+	2.93232i	0.201870	+	0.201870i	−0.598931	+	0.800801i	$0.704408\pi$
$212$	7.84140	−	19.4082i	0.538550	−	1.33296i
$213$	−1.19581	+	13.9790i	−0.0819354	+	0.957828i
$214$	−3.84090	+	19.7598i	−0.262559	+	1.35075i
$215$	15.1417	−	4.86981i	1.03265	−	0.332118i
$216$	9.89730	+	10.8648i	0.673426	+	0.739254i
$217$	8.27103	+	8.27103i	0.561474	+	0.561474i
$218$	−3.74873	−	5.55772i	−0.253896	−	0.376416i
$219$	10.6540	+	12.6473i	0.719932	+	0.854625i
$220$	10.5150	+	12.1695i	0.708923	+	0.820465i
$221$	19.3690	−	19.3690i	1.30290	−	1.30290i
$222$	−2.69794	+	9.47788i	−0.181074	+	0.636114i
$223$	5.92300	+	5.92300i	0.396633	+	0.396633i	0.877044	−	0.480410i	$-0.159512\pi$
$223$	5.92300	+	5.92300i	0.396633	+	0.396633i	−0.480410	+	0.877044i	$0.659512\pi$
$224$	8.65851	+	1.52671i	0.578521	+	0.102007i
$225$	−13.4958	+	6.54698i	−0.899721	+	0.436465i
$226$	4.76797	+	7.06880i	0.317161	+	0.470210i
$227$			21.4524i			1.42385i	0.702257	+	0.711923i	$0.252176\pi$
$227$			21.4524i			1.42385i	−0.702257	+	0.711923i	$0.747824\pi$
$228$	4.60800	+	14.0893i	0.305172	+	0.933085i
$229$	−2.76748	−	2.76748i	−0.182880	−	0.182880i	0.609729	−	0.792610i	$-0.291278\pi$
$229$	−2.76748	−	2.76748i	−0.182880	−	0.182880i	−0.792610	+	0.609729i	$0.791278\pi$
$230$	−6.11502	+	7.77881i	−0.403212	+	0.512919i
$231$	9.64595	+	0.825142i	0.634657	+	0.0542904i
$232$	5.21286	−	1.10804i	0.342241	−	0.0727461i
$233$	7.21622	+	7.21622i	0.472751	+	0.472751i	0.902804	−	0.430053i	$-0.141505\pi$
$233$	7.21622	+	7.21622i	0.472751	+	0.472751i	−0.430053	+	0.902804i	$0.641505\pi$
$234$	−16.3286	−	6.19570i	−1.06743	−	0.405025i
$235$	−1.81447	−	0.931364i	−0.118363	−	0.0607555i
$236$	2.76617	−	1.17417i	0.180062	−	0.0764322i
$237$	13.1611	+	1.12584i	0.854907	+	0.0731312i
$238$	14.3575	+	2.79081i	0.930659	+	0.180901i
$239$	−11.4514			−0.740726			−0.370363	−	0.928887i	$-0.620767\pi$
$239$	−11.4514			−0.740726			−0.370363	+	0.928887i	$0.620767\pi$
$240$	7.99298	−	13.2707i	0.515944	−	0.856622i
$241$	3.81085			0.245479			0.122739	−	0.992439i	$-0.460832\pi$
$241$	3.81085			0.245479			0.122739	+	0.992439i	$0.460832\pi$
$242$	−2.68356	−	0.521629i	−0.172506	−	0.0335316i
$243$	6.45123	−	14.1909i	0.413847	−	0.910347i
$244$	−0.967841	−	2.28008i	−0.0619597	−	0.145967i
$245$	−3.13854	−	9.75864i	−0.200514	−	0.623457i
$246$	−1.75762	−	0.500317i	−0.112062	−	0.0318990i
$247$	−12.4558	−	12.4558i	−0.792543	−	0.792543i
$248$	−11.5934	+	17.8523i	−0.736181	+	1.13362i
$249$	−1.07576	+	12.5756i	−0.0681732	+	0.796948i
$250$	10.6792	+	11.6600i	0.675409	+	0.737443i
$251$	8.57032	+	8.57032i	0.540954	+	0.540954i	0.923808	−	0.382855i	$-0.125059\pi$
$251$	8.57032	+	8.57032i	0.540954	+	0.540954i	−0.382855	+	0.923808i	$0.625059\pi$
$252$	−2.13285	−	9.07823i	−0.134357	−	0.571875i
$253$		−	11.2525i		−	0.707439i
$254$	−3.87737	−	5.74843i	−0.243288	−	0.360689i
$255$	13.6802	−	21.8413i	0.856685	−	1.36776i
$256$	0.558453	+	15.9903i	0.0349033	+	0.999391i
$257$	−0.533755	−	0.533755i	−0.0332947	−	0.0332947i	0.690263	−	0.723558i	$-0.257495\pi$
$257$	−0.533755	−	0.533755i	−0.0332947	−	0.0332947i	−0.723558	+	0.690263i	$0.757495\pi$
$258$	16.7579	+	4.77023i	1.04330	+	0.296982i
$259$	4.42136	−	4.42136i	0.274730	−	0.274730i
$260$	−1.33907	+	18.3605i	−0.0830455	+	1.13867i
$261$	−3.26006	−	4.61778i	−0.201793	−	0.285833i
$262$	−0.0372731	−	0.0552596i	−0.00230274	−	0.00341395i
$263$	−8.62392	−	8.62392i	−0.531774	−	0.531774i	0.389326	−	0.921100i	$-0.372708\pi$
$263$	−8.62392	−	8.62392i	−0.531774	−	0.531774i	−0.921100	+	0.389326i	$0.872708\pi$
$264$	2.18089	+	17.4825i	0.134224	+	1.07597i
$265$	7.16537	+	22.2793i	0.440165	+	1.36860i
$266$	1.79471	−	9.23302i	0.110041	−	0.566113i
$267$	13.5488	+	1.15900i	0.829171	+	0.0709297i
$268$	−27.7390	−	11.2073i	−1.69443	−	0.684593i
$269$	−9.50264	−	9.50264i	−0.579386	−	0.579386i	0.355348	−	0.934734i	$-0.384362\pi$
$269$	−9.50264	−	9.50264i	−0.579386	−	0.579386i	−0.934734	+	0.355348i	$0.884362\pi$
$270$	−16.2781	−	2.24122i	−0.990654	−	0.136396i
$271$	−30.6408			−1.86129			−0.930647	−	0.365918i	$-0.880755\pi$
$271$	−30.6408			−1.86129			−0.930647	+	0.365918i	$0.880755\pi$
$272$	0.464583	+	26.6130i	0.0281695	+	1.61365i
$273$	7.13943	+	8.47514i	0.432098	+	0.512939i
$274$	14.7146	+	21.8153i	0.888941	+	1.31791i
$275$	−17.7428	−	2.91908i	−1.06993	−	0.176027i
$276$	−10.3020	+	3.36935i	−0.620108	+	0.202811i
$277$		−	12.3925i		−	0.744595i	−0.928113	−	0.372298i	$-0.878570\pi$
$277$		−	12.3925i		−	0.744595i	0.928113	−	0.372298i	$-0.121430\pi$
$278$	−3.04734	+	2.05546i	−0.182767	+	0.123278i
$279$	22.2496	+	3.83466i	1.33205	+	0.229575i
$280$	−8.52755	+	4.88945i	−0.509619	+	0.292201i
$281$	−29.8116			−1.77841			−0.889205	−	0.457509i	$-0.848742\pi$
$281$	−29.8116			−1.77841			−0.889205	+	0.457509i	$0.848742\pi$
$282$	−1.08694	−	1.95199i	−0.0647262	−	0.116239i
$283$	1.46138			0.0868701			0.0434351	−	0.999056i	$-0.486170\pi$
$283$	1.46138			0.0868701			0.0434351	+	0.999056i	$0.486170\pi$
$284$	15.0209	+	6.06882i	0.891327	+	0.360118i
$285$	−14.0457	−	8.79744i	−0.831996	−	0.521115i
$286$	−11.7071	−	17.3564i	−0.692254	−	1.02631i
$287$	0.819916	+	0.819916i	0.0483981	+	0.0483981i
$288$	15.3527	−	7.23146i	0.904668	−	0.426118i
$289$			27.2793i			1.60467i
$290$	−3.68236	+	4.68426i	−0.216236	+	0.275069i
$291$	−8.58551	−	10.1918i	−0.503292	−	0.597453i
$292$	17.5770	−	7.46100i	1.02861	−	0.436622i
$293$		−	4.69939i		−	0.274541i	−0.990534	−	0.137271i	$-0.956167\pi$
$293$		−	4.69939i		−	0.274541i	0.990534	−	0.137271i	$-0.0438330\pi$
$294$	3.07436	−	10.8003i	0.179301	−	0.629885i
$295$	−1.53425	+	2.98899i	−0.0893272	+	0.174026i
$296$	9.54314	+	6.19737i	0.554684	+	0.360215i
$297$	16.1288	−	9.43696i	0.935885	−	0.547588i
$298$	15.5250	+	23.0167i	0.899337	+	1.33332i
$299$	9.10761	−	9.10761i	0.526707	−	0.526707i
$300$	2.64022	+	17.1181i	0.152433	+	0.988314i
$301$	−7.81744	−	7.81744i	−0.450590	−	0.450590i
$302$	−7.02858	−	1.36621i	−0.404450	−	0.0786168i
$303$	−3.89397	+	3.28026i	−0.223703	+	0.188446i
$304$	17.1143	−	0.298764i	0.981573	−	0.0171353i
$305$	2.46375	+	1.26464i	0.141074	+	0.0724131i
$306$	25.7464	−	11.5824i	1.47182	−	0.662122i
$307$	−12.6587			−0.722468			−0.361234	−	0.932475i	$-0.617644\pi$
$307$	−12.6587			−0.722468			−0.361234	+	0.932475i	$0.617644\pi$
$308$	4.18767	−	10.3649i	0.238614	−	0.590593i
$309$	−10.2902	−	12.2154i	−0.585391	−	0.694912i
$310$	−2.82971	−	23.6301i	−0.160717	−	1.34210i
$311$	−8.99471			−0.510043			−0.255022	−	0.966935i	$-0.582083\pi$
$311$	−8.99471			−0.510043			−0.255022	+	0.966935i	$0.582083\pi$
$312$	−12.3849	+	15.9152i	−0.701156	+	0.901023i
$313$	−5.17058	+	5.17058i	−0.292259	+	0.292259i	−0.837972	−	0.545713i	$-0.816259\pi$
$313$	−5.17058	+	5.17058i	−0.292259	+	0.292259i	0.545713	+	0.837972i	$0.316259\pi$
$314$	3.54119	−	18.2179i	0.199841	−	1.02810i
$315$	8.33214	+	6.26734i	0.469463	+	0.353125i
$316$	5.71373	−	14.1420i	0.321423	−	0.795551i
$317$			20.8535i			1.17125i	0.810582	+	0.585626i	$0.199151\pi$
$317$			20.8535i			1.17125i	−0.810582	+	0.585626i	$0.800849\pi$
$318$	−7.01886	+	24.6573i	−0.393598	+	1.38272i
$319$		−	6.77607i		−	0.379387i
$320$	−11.9300	−	13.3295i	−0.666907	−	0.745141i
$321$	2.10127	−	24.5639i	0.117281	−	1.37103i
$322$	6.75114	+	1.31228i	0.376226	+	0.0731308i
$323$	28.4751			1.58440
$324$	−13.4693	−	11.9406i	−0.748292	−	0.663369i
$325$	−11.9981	−	16.7234i	−0.665533	−	0.927646i
$326$	−7.51470	−	1.46071i	−0.416201	−	0.0809011i
$327$	5.28973	+	6.27938i	0.292523	+	0.347251i
$328$	−1.14927	+	1.76972i	−0.0634576	+	0.0977165i
$329$			1.41764i			0.0781568i
$330$	−14.3916	−	13.4489i	−0.792232	−	0.740339i
$331$	−0.329638	+	0.329638i	−0.0181185	+	0.0181185i	−0.716108	−	0.697989i	$-0.754078\pi$
$331$	−0.329638	+	0.329638i	−0.0181185	+	0.0181185i	0.697989	+	0.716108i	$0.254078\pi$
$332$	13.5129	+	5.45955i	0.741616	+	0.299632i
$333$	2.04985	−	11.8938i	0.112331	−	0.651775i
$334$	−9.11032	−	13.5066i	−0.498494	−	0.739048i
$335$	31.8425	−	10.2410i	1.73974	−	0.559528i
$336$	−10.7433	−	0.730374i	−0.586093	−	0.0398451i
$337$	−22.7476	+	22.7476i	−1.23914	+	1.23914i	−0.278787	+	0.960353i	$0.589932\pi$
$337$	−22.7476	+	22.7476i	−1.23914	+	1.23914i	−0.960353	+	0.278787i	$0.910068\pi$
$338$	1.06454	−	5.47658i	0.0579031	−	0.297887i
$339$	−6.72795	−	7.98668i	−0.365412	−	0.433777i
$340$	−19.4563	−	22.5175i	−1.05517	−	1.22118i
$341$	19.1379	+	19.1379i	1.03637	+	1.03637i
$342$	−7.44841	−	16.5570i	−0.402764	−	0.895299i
$343$	−12.7313	+	12.7313i	−0.687427	+	0.687427i
$344$	10.9576	−	16.8733i	0.590794	−	0.909746i
$345$	6.43264	−	10.2702i	0.346322	−	0.552926i
$346$	−0.718038	+	3.69399i	−0.0386020	+	0.198590i
$347$	−7.83663			−0.420692			−0.210346	−	0.977627i	$-0.567459\pi$
$347$	−7.83663			−0.420692			−0.210346	+	0.977627i	$0.567459\pi$
$348$	−6.20369	+	2.02896i	−0.332553	+	0.108764i
$349$	2.27745	−	2.27745i	0.121909	−	0.121909i	−0.643520	−	0.765429i	$-0.722527\pi$
$349$	2.27745	−	2.27745i	0.121909	−	0.121909i	0.765429	+	0.643520i	$0.222527\pi$
$350$	3.82054	−	10.3046i	0.204217	−	0.550807i
$351$	20.6925	+	5.41624i	1.10448	+	0.289097i
$352$	20.0345	+	3.53257i	1.06784	+	0.188286i
$353$	16.6489	−	16.6489i	0.886134	−	0.886134i	−0.108016	−	0.994149i	$-0.534450\pi$
$353$	16.6489	−	16.6489i	0.886134	−	0.886134i	0.994149	+	0.108016i	$0.0344497\pi$
$354$	−3.21553	+	1.79052i	−0.170903	+	0.0951653i
$355$	−17.2429	+	5.54561i	−0.915160	+	0.294330i
$356$	5.88202	−	14.5586i	0.311747	−	0.771602i
$357$	−17.8482	−	1.52679i	−0.944627	−	0.0808061i
$358$	4.74000	−	3.19718i	0.250517	−	0.168976i
$359$			8.00706i			0.422596i	0.977422	+	0.211298i	$0.0677691\pi$
$359$			8.00706i			0.422596i	−0.977422	+	0.211298i	$0.932231\pi$
$360$	−8.00360	+	17.2030i	−0.421827	+	0.906676i
$361$			0.688208i			0.0362215i
$362$	14.9749	+	22.2012i	0.787064	+	1.16687i
$363$	3.33601	+	0.285371i	0.175095	+	0.0149781i
$364$	11.7786	−	4.99973i	0.617366	−	0.262057i
$365$	−9.74899	+	18.9928i	−0.510286	+	0.994130i
$366$	1.47588	+	2.65048i	0.0771457	+	0.138543i
$367$	20.8700	−	20.8700i	1.08940	−	1.08940i	0.0938134	−	0.995590i	$-0.470094\pi$
$367$	20.8700	−	20.8700i	1.08940	−	1.08940i	0.995590	−	0.0938134i	$-0.0299057\pi$
$368$	0.218455	+	12.5139i	0.0113877	+	0.652332i
$369$	2.20563	+	0.380134i	0.114821	+	0.0197890i
$370$	−12.6317	+	1.51265i	−0.656692	+	0.0786389i
$371$	11.5025	−	11.5025i	0.597178	−	0.597178i
$372$	11.7908	−	23.2518i	0.611326	−	1.20555i
$373$	−17.2160			−0.891413			−0.445707	−	0.895179i	$-0.647048\pi$
$373$	−17.2160			−0.891413			−0.445707	+	0.895179i	$0.647048\pi$
$374$	33.2210	+	6.45750i	1.71782	+	0.333909i
$375$	−14.5251	−	12.8071i	−0.750071	−	0.661357i
$376$	−2.52346	+	0.536383i	−0.130138	+	0.0276618i
$377$	5.48444	−	5.48444i	0.282463	−	0.282463i
$378$	3.78091	+	10.7773i	0.194469	+	0.554323i
$379$	5.52639	+	5.52639i	0.283872	+	0.283872i	0.834651	−	0.550779i	$-0.185669\pi$
$379$	5.52639	+	5.52639i	0.283872	+	0.283872i	−0.550779	+	0.834651i	$0.685669\pi$
$380$	−14.4806	+	12.5120i	−0.742838	+	0.641849i
$381$	5.47125	+	6.49486i	0.280300	+	0.332742i
$382$	−35.3686	−	6.87494i	−1.80961	−	0.351752i
$383$	−0.512201	+	0.512201i	−0.0261722	+	0.0261722i	−0.720072	−	0.693900i	$-0.755891\pi$
$383$	−0.512201	+	0.512201i	−0.0261722	+	0.0261722i	0.693900	+	0.720072i	$0.255891\pi$
$384$	−2.76476	−	19.3999i	−0.141089	−	0.989997i
$385$	3.82663	+	11.8981i	0.195023	+	0.606385i
$386$	26.2861	−	17.7302i	1.33793	−	0.902443i
$387$	−21.0294	−	3.62436i	−1.06899	−	0.184237i
$388$	−14.1643	+	6.01242i	−0.719086	+	0.305235i
$389$	−9.94589	+	9.94589i	−0.504276	+	0.504276i	−0.912764	−	0.408487i	$-0.866056\pi$
$389$	−9.94589	+	9.94589i	−0.504276	+	0.504276i	0.408487	+	0.912764i	$0.366056\pi$
$390$	−0.762999	−	22.5337i	−0.0386359	−	1.14104i
$391$			20.8209i			1.05296i
$392$	−10.8746	−	7.06205i	−0.549252	−	0.356687i
$393$	0.0525950	+	0.0624350i	0.00265307	+	0.00314943i
$394$	6.93125	−	35.6583i	0.349191	−	1.79644i
$395$	5.22113	+	16.2341i	0.262704	+	0.816824i
$396$	−4.93509	−	21.0056i	−0.247997	−	1.05557i
$397$	17.4618			0.876383			0.438191	−	0.898882i	$-0.355619\pi$
$397$	17.4618			0.876383			0.438191	+	0.898882i	$0.355619\pi$
$398$	−1.49266	+	7.67911i	−0.0748205	+	0.384919i
$399$	−0.981846	+	11.4778i	−0.0491538	+	0.574610i
$400$	19.7884	+	2.90185i	0.989418	+	0.145092i
$401$			37.1467i			1.85502i	0.373800	+	0.927509i	$0.378055\pi$
$401$			37.1467i			1.85502i	−0.373800	+	0.927509i	$0.621945\pi$
$402$	35.2413	+	10.0317i	1.75768	+	0.500333i
$403$			30.9798i			1.54321i
$404$	2.29716	+	5.41176i	0.114288	+	0.269245i
$405$	20.1155	+	0.607113i	0.999545	+	0.0301677i
$406$	4.06542	+	0.790235i	0.201763	+	0.0392187i
$407$	10.2303	−	10.2303i	0.507099	−	0.507099i
$408$	−4.03537	−	32.3484i	−0.199780	−	1.60149i
$409$	5.35076			0.264578			0.132289	−	0.991211i	$-0.457767\pi$
$409$	5.35076			0.264578			0.132289	+	0.991211i	$0.457767\pi$
$410$	−0.280512	−	2.34248i	−0.0138535	−	0.115687i
$411$	−20.7633	−	24.6479i	−1.02418	−	1.21579i
$412$	−16.9768	+	7.20623i	−0.836386	+	0.355026i
$413$	2.33529			0.114912
$414$	12.1064	−	5.44624i	0.594996	−	0.267668i
$415$	−15.5119	+	4.98886i	−0.761447	+	0.244894i
$416$	13.3564	+	19.0748i	0.654850	+	0.935218i
$417$	3.44303	−	2.90039i	0.168606	−	0.142033i
$418$	4.15269	−	21.3638i	0.203115	−	1.04494i
$419$	−5.60933	−	5.60933i	−0.274034	−	0.274034i	0.556688	−	0.830722i	$-0.312072\pi$
$419$	−5.60933	−	5.60933i	−0.274034	−	0.274034i	−0.830722	+	0.556688i	$0.812072\pi$
$420$	9.74729	−	7.06606i	0.475619	−	0.344789i
$421$	23.8344	−	23.8344i	1.16162	−	1.16162i	0.177497	−	0.984121i	$-0.443200\pi$
$421$	23.8344	−	23.8344i	1.16162	−	1.16162i	0.984121	−	0.177497i	$-0.0568000\pi$
$422$	−4.86201	+	3.27947i	−0.236679	+	0.159642i
$423$	1.57814	+	2.23539i	0.0767320	+	0.108689i
$424$	24.8271	+	16.1229i	1.20571	+	0.782995i
$425$	32.8300	+	5.40127i	1.59249	+	0.262000i
$426$	−19.0835	−	5.43222i	−0.924596	−	0.263192i
$427$		−	1.92492i		−	0.0931532i
$428$	−26.3947	−	10.6641i	−1.27584	−	0.515470i
$429$	16.5195	+	19.6102i	0.797570	+	0.946788i
$430$	2.67452	+	22.3342i	0.128977	+	1.07705i
$431$		−	20.9319i		−	1.00826i	−0.863629	−	0.504128i	$-0.831814\pi$
$431$		−	20.9319i		−	1.00826i	0.863629	−	0.504128i	$-0.168186\pi$
$432$	−17.7535	+	10.8079i	−0.854168	+	0.519997i
$433$	1.23955	+	1.23955i	0.0595688	+	0.0595688i	0.736264	−	0.676695i	$-0.236588\pi$
$433$	1.23955	+	1.23955i	0.0595688	+	0.0595688i	−0.676695	+	0.736264i	$0.736588\pi$
$434$	−13.7140	+	9.25020i	−0.658292	+	0.444024i
$435$	3.87363	−	6.18451i	0.185726	−	0.296524i
$436$	8.72697	−	3.70439i	0.417946	−	0.177408i
$437$	13.3895			0.640506
$438$	−20.4323	+	11.3775i	−0.976292	+	0.543636i
$439$	8.05593			0.384489			0.192244	−	0.981347i	$-0.438423\pi$
$439$	8.05593			0.384489			0.192244	+	0.981347i	$0.438423\pi$
$440$	−19.7314	+	11.3134i	−0.940659	+	0.539347i
$441$	−2.33586	+	13.5532i	−0.111231	+	0.645393i
$442$	21.6620	+	32.1152i	1.03036	+	1.52756i
$443$		−	24.7040i		−	1.17372i	−0.809688	−	0.586861i	$-0.800363\pi$
$443$		−	24.7040i		−	1.17372i	0.809688	−	0.586861i	$-0.199637\pi$
$444$	−12.4295	−	6.30291i	−0.589876	−	0.299123i
$445$	5.37491	+	16.7122i	0.254795	+	0.792234i
$446$	−9.82078	+	6.62420i	−0.465027	+	0.313665i
$447$	−21.9068	−	26.0054i	−1.03616	−	1.23001i
$448$	−4.45587	+	11.6080i	−0.210520	+	0.548428i
$449$	−1.50342			−0.0709508			−0.0354754	−	0.999371i	$-0.511295\pi$
$449$	−1.50342			−0.0709508			−0.0354754	+	0.999371i	$0.511295\pi$
$450$	−5.44695	−	20.5020i	−0.256772	−	0.966472i
$451$	1.89716	+	1.89716i	0.0893338	+	0.0893338i
$452$	−11.0997	+	4.71157i	−0.522088	+	0.221614i
$453$	8.73743	+	0.747425i	0.410520	+	0.0351171i
$454$	−29.7809	−	5.78880i	−1.39769	−	0.271682i
$455$	−6.53295	+	12.7274i	−0.306269	+	0.596669i
$456$	−20.8026	+	2.59506i	−0.974172	+	0.121525i
$457$	6.91711	+	6.91711i	0.323569	+	0.323569i	0.850134	−	0.526566i	$-0.176521\pi$
$457$	6.91711	+	6.91711i	0.323569	+	0.323569i	−0.526566	+	0.850134i	$0.676521\pi$
$458$	4.58869	−	3.09511i	0.214415	−	0.144625i
$459$	−29.8436	+	17.4615i	−1.39298	+	0.815033i
$460$	−9.14867	−	10.5881i	−0.426559	−	0.493674i
$461$	−14.5119	+	14.5119i	−0.675886	+	0.675886i	−0.959067	−	0.283181i	$-0.908610\pi$
$461$	−14.5119	+	14.5119i	−0.675886	+	0.675886i	0.283181	+	0.959067i	$0.408610\pi$
$462$	−3.74839	+	13.1681i	−0.174391	+	0.612638i
$463$	7.51032	+	7.51032i	0.349034	+	0.349034i	0.859750	−	0.510715i	$-0.170619\pi$
$463$	7.51032	+	7.51032i	0.349034	+	0.349034i	−0.510715	+	0.859750i	$0.670619\pi$
$464$	0.131550	+	7.53565i	0.00610704	+	0.349834i
$465$	6.52669	+	28.4075i	0.302668	+	1.31737i
$466$	−11.9650	+	8.07053i	−0.554270	+	0.373860i
$467$			15.2697i			0.706598i	0.935511	+	0.353299i	$0.114940\pi$
$467$			15.2697i			0.706598i	−0.935511	+	0.353299i	$0.885060\pi$
$468$	13.0072	−	20.9960i	0.601260	−	0.970540i
$469$	−16.4398	−	16.4398i	−0.759120	−	0.759120i
$470$	1.78257	−	2.26758i	0.0822239	−	0.104596i
$471$	−1.93731	+	22.6472i	−0.0892663	+	1.04353i
$472$	0.883588	+	4.15693i	0.0406705	+	0.191338i
$473$	−18.0883	−	18.0883i	−0.831702	−	0.831702i
$474$	−5.11438	+	17.9669i	−0.234911	+	0.825246i
$475$	3.47345	−	21.1123i	0.159373	−	0.968700i
$476$	−7.74857	+	19.1784i	−0.355155	+	0.879042i
$477$	5.33283	−	30.9424i	0.244174	−	1.41676i
$478$	3.09008	−	15.8971i	0.141337	−	0.727117i
$479$	−10.6782			−0.487898			−0.243949	−	0.969788i	$-0.578443\pi$
$479$	−10.6782			−0.487898			−0.243949	+	0.969788i	$0.578443\pi$
$480$	16.2660	+	14.6771i	0.742437	+	0.669916i
$481$	16.5606			0.755097
$482$	−1.02834	+	5.29035i	−0.0468394	+	0.240969i
$483$	−8.39253	−	0.717921i	−0.381873	−	0.0326665i
$484$	1.44828	−	3.58464i	0.0658311	−	0.162938i
$485$	7.85620	−	15.3053i	0.356732	−	0.694978i
$486$	17.9594	+	12.7851i	0.814656	+	0.579945i
$487$	13.6554	+	13.6554i	0.618787	+	0.618787i	0.945220	−	0.326433i	$-0.105847\pi$
$487$	13.6554	+	13.6554i	0.618787	+	0.618787i	−0.326433	+	0.945220i	$0.605847\pi$
$488$	3.42645	−	0.728319i	0.155108	−	0.0329695i
$489$	9.34174	+	0.799119i	0.422448	+	0.0361374i
$490$	14.3942	−	1.72370i	0.650262	−	0.0778689i
$491$	−6.72816	−	6.72816i	−0.303638	−	0.303638i	0.538798	−	0.842435i	$-0.318879\pi$
$491$	−6.72816	−	6.72816i	−0.303638	−	0.303638i	−0.842435	+	0.538798i	$0.818879\pi$
$492$	1.16884	−	2.30497i	0.0526953	−	0.103916i
$493$			12.5380i			0.564682i
$494$	20.6526	−	13.9304i	0.929206	−	0.626758i
$495$	19.2793	+	14.5016i	0.866539	+	0.651801i
$496$	−21.6547	−	20.9116i	−0.972326	−	0.938960i
$497$	8.90229	+	8.90229i	0.399322	+	0.399322i
$498$	−17.1676	−	4.88686i	−0.769298	−	0.218985i
$499$	−19.6497	+	19.6497i	−0.879640	+	0.879640i	−0.993497	−	0.113857i	$-0.963679\pi$
$499$	−19.6497	+	19.6497i	−0.879640	+	0.879640i	0.113857	+	0.993497i	$0.463679\pi$
$500$	−19.0685	+	11.6787i	−0.852768	+	0.522289i
$501$	12.8553	+	15.2604i	0.574333	+	0.681784i
$502$	−14.2102	+	9.58493i	−0.634233	+	0.427796i
$503$	14.7028	+	14.7028i	0.655566	+	0.655566i	0.954328	−	0.298762i	$-0.0965736\pi$
$503$	14.7028	+	14.7028i	0.655566	+	0.655566i	−0.298762	+	0.954328i	$0.596574\pi$
$504$	13.1782	−	0.511184i	0.587004	−	0.0227700i
$505$	−5.84769	−	3.00161i	−0.260219	−	0.133570i
$506$	15.6211	+	3.03642i	0.694442	+	0.134985i
$507$	−0.582383	+	6.80809i	−0.0258645	+	0.302358i
$508$	9.02644	−	3.83151i	0.400483	−	0.169996i
$509$	−28.8837	−	28.8837i	−1.28025	−	1.28025i	−0.940527	−	0.339719i	$-0.889668\pi$
$509$	−28.8837	−	28.8837i	−1.28025	−	1.28025i	−0.339719	−	0.940527i	$-0.610332\pi$
$510$	26.6293	+	24.8850i	1.17916	+	1.10193i
$511$	14.8390			0.656439
$512$	−22.3489	−	3.53961i	−0.987689	−	0.156430i
$513$	11.2291	+	19.1918i	0.495779	+	0.847338i
$514$	0.885006	−	0.596944i	0.0390359	−	0.0263301i
$515$	9.41610	−	18.3443i	0.414923	−	0.808346i
$516$	−11.1442	+	21.9766i	−0.490596	+	0.967466i
$517$			3.28019i			0.144263i
$518$	4.94479	+	7.33095i	0.217262	+	0.322103i
$519$	0.392822	−	4.59211i	0.0172430	−	0.201571i
$520$	−25.1272	−	6.81340i	−1.10190	−	0.298787i
$521$	−24.7913			−1.08613			−0.543063	−	0.839692i	$-0.682736\pi$
$521$	−24.7913			−1.08613			−0.543063	+	0.839692i	$0.682736\pi$
$522$	7.29025	−	3.27963i	0.319086	−	0.143546i
$523$	23.1268			1.01127			0.505633	−	0.862749i	$-0.331259\pi$
$523$	23.1268			1.01127			0.505633	+	0.862749i	$0.331259\pi$
$524$	0.0867710	−	0.0368322i	0.00379061	−	0.00160902i
$525$	−3.30916	+	13.0470i	−0.144424	+	0.569416i
$526$	14.2991	−	9.64488i	0.623470	−	0.420537i
$527$	−35.4114	−	35.4114i	−1.54255	−	1.54255i
$528$	−24.8582	−	1.68997i	−1.08182	−	0.0735466i
$529$		−	13.2097i		−	0.574334i
$530$	−32.8623	+	3.93526i	−1.42745	+	0.170937i
$531$	3.68239	−	2.59969i	0.159802	−	0.112817i
$532$	12.3333	+	4.98295i	0.534715	+	0.216038i
$533$			3.07106i			0.133023i
$534$	−5.26501	+	18.4961i	−0.227839	+	0.800403i
$535$	30.2992	−	9.74473i	1.30995	−	0.421301i
$536$	23.0435	−	35.4840i	0.995327	−	1.53267i
$537$	−5.35549	+	4.51144i	−0.231106	+	0.194683i
$538$	15.7561	−	10.6276i	0.679293	−	0.458189i
$539$	−11.6577	+	11.6577i	−0.502134	+	0.502134i
$540$	7.50388	−	21.9930i	0.322916	−	0.946428i
$541$	−4.24717	−	4.24717i	−0.182600	−	0.182600i	0.609888	−	0.792488i	$-0.291214\pi$
$541$	−4.24717	−	4.24717i	−0.182600	−	0.182600i	−0.792488	+	0.609888i	$0.791214\pi$
$542$	8.26823	−	42.5364i	0.355151	−	1.82710i
$543$	−21.1307	−	25.0840i	−0.906803	−	1.07646i
$544$	−37.0704	−	6.53642i	−1.58938	−	0.280247i
$545$	−4.84038	+	9.42995i	−0.207339	+	0.403935i
$546$	−13.6920	+	7.62420i	−0.585963	+	0.326286i
$547$	14.4418			0.617488			0.308744	−	0.951145i	$-0.400091\pi$
$547$	14.4418			0.617488			0.308744	+	0.951145i	$0.400091\pi$
$548$	−34.2553	+	14.5405i	−1.46331	+	0.621141i
$549$	−2.14286	−	3.03530i	−0.0914550	−	0.129543i
$550$	8.84014	−	23.8434i	0.376945	−	1.01668i
$551$	8.06292			0.343492
$552$	−1.89750	−	15.2108i	−0.0807628	−	0.647413i
$553$	8.38142	−	8.38142i	0.356414	−	0.356414i
$554$	17.2037	+	3.34405i	0.730915	+	0.142075i
$555$	15.1855	−	3.48891i	0.644590	−	0.148096i
$556$	−2.03114	−	4.78506i	−0.0861396	−	0.202932i
$557$			31.4799i			1.33385i	0.745126	+	0.666924i	$0.232389\pi$
$557$			31.4799i			1.33385i	−0.745126	+	0.666924i	$0.767611\pi$
$558$	−11.3273	+	29.8529i	−0.479524	+	1.26377i
$559$		−	29.2808i		−	1.23845i
$560$	−4.48658	−	13.1576i	−0.189592	−	0.556010i
$561$	−41.2980	−	3.53275i	−1.74360	−	0.149153i
$562$	8.04448	−	41.3854i	0.339336	−	1.74574i
$563$	21.5332			0.907518			0.453759	−	0.891124i	$-0.350083\pi$
$563$	21.5332			0.907518			0.453759	+	0.891124i	$0.350083\pi$
$564$	3.00311	−	0.982189i	0.126454	−	0.0413576i
$565$	6.15642	−	11.9938i	0.259003	−	0.504585i
$566$	−0.394345	+	2.02874i	−0.0165756	+	0.0852741i
$567$	−6.00939	−	12.6315i	−0.252371	−	0.530473i
$568$	−12.4782	+	19.2148i	−0.523575	+	0.806237i
$569$			2.98961i			0.125331i	0.998035	+	0.0626655i	$0.0199601\pi$
$569$			2.98961i			0.125331i	−0.998035	+	0.0626655i	$0.980040\pi$
$570$	16.0030	−	17.1247i	0.670293	−	0.717277i
$571$	−17.4066	+	17.4066i	−0.728445	+	0.728445i	−0.970310	−	0.241865i	$-0.922241\pi$
$571$	−17.4066	+	17.4066i	−0.728445	+	0.728445i	0.241865	+	0.970310i	$0.422241\pi$
$572$	27.2538	−	11.5686i	1.13954	−	0.483707i
$573$	43.9677	+	3.76112i	1.83678	+	0.157123i
$574$	−1.35948	+	0.916984i	−0.0567437	+	0.0382742i
$575$	15.4372	+	2.53977i	0.643777	+	0.105916i
$576$	5.89610	+	23.2645i	0.245671	+	0.969353i
$577$	−15.7970	+	15.7970i	−0.657636	+	0.657636i	−0.954820	−	0.297184i	$-0.903952\pi$
$577$	−15.7970	+	15.7970i	−0.657636	+	0.657636i	0.297184	+	0.954820i	$0.403952\pi$
$578$	−37.8700	−	7.36116i	−1.57518	−	0.306184i
$579$	−29.6993	+	25.0186i	−1.23426	+	1.03974i
$580$	−5.50917	−	6.37598i	−0.228756	−	0.264748i
$581$	8.00855	+	8.00855i	0.332251	+	0.332251i
$582$	16.4653	−	9.16848i	0.682508	−	0.380046i
$583$	26.6149	−	26.6149i	1.10228	−	1.10228i
$584$	5.61455	+	26.4142i	0.232332	+	1.09303i
$585$	3.86694	+	27.3418i	0.159878	+	1.13044i
$586$	6.52384	+	1.26810i	0.269497	+	0.0523848i
$587$	−22.2447			−0.918137			−0.459068	−	0.888401i	$-0.651817\pi$
$587$	−22.2447			−0.918137			−0.459068	+	0.888401i	$0.651817\pi$
$588$	14.1637	+	7.18232i	0.584100	+	0.296194i
$589$	−22.7724	+	22.7724i	−0.938319	+	0.938319i
$590$	−3.73540	−	2.93645i	−0.153784	−	0.120892i
$591$	−3.79193	+	44.3278i	−0.155979	+	1.82340i
$592$	−11.1785	+	11.5758i	−0.459435	+	0.475761i
$593$	−23.4419	+	23.4419i	−0.962645	+	0.962645i	−0.999327	−	0.0366816i	$-0.988321\pi$
$593$	−23.4419	+	23.4419i	−0.962645	+	0.962645i	0.0366816	+	0.999327i	$0.488321\pi$
$594$	8.74843	+	24.9369i	0.358952	+	1.02318i
$595$	−7.08054	−	22.0155i	−0.290274	−	0.902547i
$596$	−36.1418	+	15.3413i	−1.48043	+	0.628405i
$597$	0.816602	−	9.54611i	0.0334213	−	0.390696i
$598$	10.1858	+	15.1011i	0.416530	+	0.617530i
$599$			20.1061i			0.821515i	0.911745	+	0.410757i	$0.134736\pi$
$599$			20.1061i			0.821515i	−0.911745	+	0.410757i	$0.865264\pi$
$600$	−24.4763	−	0.953977i	−0.999241	−	0.0389460i
$601$			25.6681i			1.04703i	0.852018	+	0.523513i	$0.175379\pi$
$601$			25.6681i			1.04703i	−0.852018	+	0.523513i	$0.824621\pi$
$602$	12.9619	−	8.74292i	0.528287	−	0.356335i
$603$	−44.2242	−	7.62191i	−1.80095	−	0.310388i
$604$	3.79324	−	9.38863i	0.154345	−	0.382018i
$605$	1.32342	+	4.11491i	0.0538048	+	0.167295i
$606$	−3.50300	−	6.29088i	−0.142300	−	0.255550i
$607$	−25.2536	+	25.2536i	−1.02501	+	1.02501i	−0.0253316	+	0.999679i	$0.508064\pi$
$607$	−25.2536	+	25.2536i	−1.02501	+	1.02501i	−0.999679	+	0.0253316i	$0.991936\pi$
$608$	−4.20344	+	23.8392i	−0.170472	+	0.966808i
$609$	−5.05383	−	0.432319i	−0.204792	−	0.0175185i
$610$	−2.42044	+	3.07900i	−0.0980007	+	0.124665i
$611$	−2.65493	+	2.65493i	−0.107407	+	0.107407i
$612$	9.13155	+	38.8673i	0.369121	+	1.57112i
$613$	13.4200			0.542028			0.271014	−	0.962575i	$-0.412641\pi$
$613$	13.4200			0.542028			0.271014	+	0.962575i	$0.412641\pi$
$614$	3.41586	−	17.5731i	0.137853	−	0.709194i
$615$	0.646999	+	2.81607i	0.0260895	+	0.113555i
$616$	13.2588	+	8.61034i	0.534213	+	0.346921i
$617$	17.3496	−	17.3496i	0.698467	−	0.698467i	−0.265613	−	0.964080i	$-0.585574\pi$
$617$	17.3496	−	17.3496i	0.698467	−	0.698467i	0.964080	+	0.265613i	$0.0855742\pi$
$618$	19.7346	−	10.9890i	0.793842	−	0.442041i
$619$	−22.9881	−	22.9881i	−0.923970	−	0.923970i	0.0733370	−	0.997307i	$-0.476635\pi$
$619$	−22.9881	−	22.9881i	−0.923970	−	0.923970i	−0.997307	+	0.0733370i	$0.976635\pi$
$620$	33.5676	+	2.44816i	1.34811	+	0.0983204i
$621$	−14.0329	+	8.21069i	−0.563122	+	0.329484i
$622$	2.42717	−	12.4867i	0.0973206	−	0.500672i
$623$	8.62828	−	8.62828i	0.345685	−	0.345685i
$624$	−18.7520	−	21.4877i	−0.750682	−	0.860197i
$625$	8.00933	−	23.6823i	0.320373	−	0.947291i
$626$	−5.78271	−	8.57321i	−0.231124	−	0.342655i
$627$	−2.27184	+	26.5579i	−0.0907285	+	1.06062i
$628$	24.3351	+	9.83199i	0.971076	+	0.392339i
$629$	−18.9295	+	18.9295i	−0.754770	+	0.754770i
$630$	−10.9489	+	9.87573i	−0.436214	+	0.393458i
$631$		−	21.2721i		−	0.846830i	−0.905936	−	0.423415i	$-0.860831\pi$
$631$		−	21.2721i		−	0.846830i	0.905936	−	0.423415i	$-0.139169\pi$
$632$	18.0906	+	11.7481i	0.719605	+	0.467315i
$633$	5.49334	−	4.62757i	0.218341	−	0.183929i
$634$	−28.9495	−	5.62720i	−1.14973	−	0.223485i
$635$	−5.00648	+	9.75354i	−0.198676	+	0.387057i
$636$	−32.3361	−	16.3974i	−1.28221	−	0.650200i
$637$	−18.8712			−0.747703
$638$	9.40675	+	1.82848i	0.372417	+	0.0723903i
$639$	23.9478	+	4.12732i	0.947359	+	0.163274i
$640$	21.7236	−	12.9647i	0.858702	−	0.512475i
$641$		−	7.22731i		−	0.285462i	−0.989762	−	0.142731i	$-0.954412\pi$
$641$		−	7.22731i		−	0.285462i	0.989762	−	0.142731i	$-0.0455883\pi$
$642$	33.5334	+	9.54548i	1.32346	+	0.376730i
$643$		−	27.2953i		−	1.07642i	−0.842811	−	0.538210i	$-0.819101\pi$
$643$		−	27.2953i		−	1.07642i	0.842811	−	0.538210i	$-0.180899\pi$
$644$	−3.64351	+	9.01802i	−0.143574	+	0.355360i
$645$	−6.16876	−	26.8496i	−0.242895	−	1.05720i
$646$	−7.68385	+	39.5301i	−0.302317	+	1.55529i
$647$	28.8520	−	28.8520i	1.13429	−	1.13429i	0.144835	−	0.989456i	$-0.453735\pi$
$647$	28.8520	−	28.8520i	1.13429	−	1.13429i	0.989456	−	0.144835i	$-0.0462652\pi$
$648$	20.2110	−	15.4763i	0.793962	−	0.607968i
$649$	5.40349			0.212105
$650$	26.4535	−	12.1434i	1.03759	−	0.476302i
$651$	15.4947	−	13.0527i	0.607286	−	0.511575i
$652$	4.05560	−	10.0380i	0.158829	−	0.393118i
$653$	−7.13115			−0.279063			−0.139532	−	0.990218i	$-0.544560\pi$
$653$	−7.13115			−0.279063			−0.139532	+	0.990218i	$0.544560\pi$
$654$	−10.1446	+	5.64891i	−0.396687	+	0.220890i
$655$	−0.0481272	+	0.0937606i	−0.00188048	+	0.00366353i
$656$	−2.14666	−	2.07300i	−0.0838129	−	0.0809369i
$657$	23.3988	−	16.5191i	0.912876	−	0.644472i
$658$	−1.96801	−	0.382540i	−0.0767208	−	0.0149130i
$659$	−30.9043	−	30.9043i	−1.20386	−	1.20386i	−0.972982	−	0.230879i	$-0.925840\pi$
$659$	−30.9043	−	30.9043i	−1.20386	−	1.20386i	−0.230879	−	0.972982i	$-0.574160\pi$
$660$	22.5537	−	16.3498i	0.877902	−	0.636414i
$661$	−14.2118	+	14.2118i	−0.552775	+	0.552775i	−0.927241	−	0.374465i	$-0.877826\pi$
$661$	−14.2118	+	14.2118i	−0.552775	+	0.552775i	0.374465	+	0.927241i	$0.377826\pi$
$662$	−0.368662	−	0.546564i	−0.0143285	−	0.0212428i
$663$	−30.5666	−	36.2853i	−1.18711	−	1.40920i
$664$	−11.2255	+	17.2858i	−0.435633	+	0.670819i
$665$	−14.1577	+	4.55335i	−0.549013	+	0.176571i
$666$	15.9582	+	6.05513i	0.618366	+	0.234632i
$667$			5.89556i			0.228277i
$668$	21.2086	−	9.00255i	0.820586	−	0.348319i
$669$	11.0960	−	9.34722i	0.428996	−	0.361384i
$670$	5.62444	+	46.9682i	0.217291	+	1.81454i
$671$		−	4.45396i		−	0.171943i
$672$	3.91293	−	14.7170i	0.150945	−	0.567722i
$673$	−18.5386	−	18.5386i	−0.714611	−	0.714611i	0.252886	−	0.967496i	$-0.418620\pi$
$673$	−18.5386	−	18.5386i	−0.714611	−	0.714611i	−0.967496	+	0.252886i	$0.918620\pi$
$674$	−25.4406	−	37.7172i	−0.979935	−	1.45281i
$675$	9.30611	+	24.2569i	0.358192	+	0.933648i
$676$	7.31549	+	2.95564i	0.281365	+	0.113679i
$677$	−30.0900			−1.15645			−0.578226	−	0.815877i	$-0.696255\pi$
$677$	−30.0900			−1.15645			−0.578226	+	0.815877i	$0.696255\pi$
$678$	12.9028	−	7.18478i	0.495531	−	0.275930i
$679$	−11.9580			−0.458905
$680$	36.5097	−	20.9336i	1.40008	−	0.802767i
$681$	37.0215	+	3.16692i	1.41867	+	0.121357i
$682$	−31.7320	+	21.4035i	−1.21508	+	0.819584i
$683$		−	43.9005i		−	1.67980i	−0.542738	−	0.839902i	$-0.682612\pi$
$683$		−	43.9005i		−	1.67980i	0.542738	−	0.839902i	$-0.317388\pi$
$684$	24.9948	−	5.87232i	0.955700	−	0.224534i
$685$	18.9995	−	37.0146i	0.725935	−	1.41425i
$686$	−14.2385	−	21.1095i	−0.543630	−	0.805964i
$687$	−5.18453	+	4.36743i	−0.197802	+	0.166628i
$688$	20.4672	+	19.7648i	0.780303	+	0.753527i
$689$	43.0834			1.64135
$690$	12.5215	+	11.7013i	0.476686	+	0.445462i
$691$	−3.68201	−	3.68201i	−0.140070	−	0.140070i	0.633595	−	0.773665i	$-0.281579\pi$
$691$	−3.68201	−	3.68201i	−0.140070	−	0.140070i	−0.773665	+	0.633595i	$0.781579\pi$
$692$	−4.93436	−	1.99360i	−0.187576	−	0.0757855i
$693$	2.84798	−	16.5247i	0.108186	−	0.627720i
$694$	2.11467	−	10.8791i	0.0802717	−	0.412963i
$695$	5.17050	+	2.65401i	0.196128	+	0.100672i
$696$	−1.14264	−	9.15966i	−0.0433116	−	0.347196i
$697$	−3.51037	−	3.51037i	−0.132965	−	0.132965i
$698$	2.54706	+	3.77618i	0.0964078	+	0.142930i
$699$	13.5187	−	11.3881i	0.511324	−	0.430737i
$700$	13.2743	+	8.08444i	0.501721	+	0.305563i
$701$	18.5706	−	18.5706i	0.701403	−	0.701403i	−0.263309	−	0.964712i	$-0.584814\pi$
$701$	18.5706	−	18.5706i	0.701403	−	0.701403i	0.964712	+	0.263309i	$0.0848139\pi$
$702$	−13.1027	+	27.2644i	−0.494531	+	1.02903i
$703$	12.1732	+	12.1732i	0.459121	+	0.459121i
$704$	−10.3102	+	26.8592i	−0.388580	+	1.01229i
$705$	−1.87516	+	2.99382i	−0.0706227	+	0.112754i
$706$	18.6199	+	27.6052i	0.700771	+	1.03893i
$707$			4.56877i			0.171826i
$708$	−1.61797	−	4.94705i	−0.0608070	−	0.185922i
$709$	34.3841	+	34.3841i	1.29132	+	1.29132i	0.933969	+	0.357355i	$0.116321\pi$
$709$	34.3841	+	34.3841i	1.29132	+	1.29132i	0.357355	+	0.933969i	$0.383679\pi$
$710$	−3.04568	−	25.4336i	−0.114302	−	0.954507i
$711$	3.88584	−	22.5466i	0.145730	−	0.845563i
$712$	18.6234	+	12.0941i	0.697942	+	0.453247i
$713$	−16.6510	−	16.6510i	−0.623586	−	0.623586i
$714$	6.93576	−	24.3654i	0.259564	−	0.911854i
$715$	−15.1162	+	29.4492i	−0.565315	+	1.10134i
$716$	3.15936	+	7.44296i	0.118071	+	0.278156i
$717$	−1.69051	+	19.7621i	−0.0631333	+	0.738031i
$718$	−11.1156	−	2.16066i	−0.414832	−	0.0806350i
$719$	45.0408			1.67974			0.839869	−	0.542789i	$-0.182632\pi$
$719$	45.0408			1.67974			0.839869	+	0.542789i	$0.182632\pi$
$720$	−21.7220	−	15.7530i	−0.809530	−	0.587078i
$721$	−14.3323			−0.533763
$722$	−0.955391	−	0.185709i	−0.0355560	−	0.00691136i
$723$	0.562579	−	6.57658i	0.0209225	−	0.244585i
$724$	−34.8613	+	14.7978i	−1.29561	+	0.549955i
$725$	9.29603	+	1.52940i	0.345246	+	0.0568007i
$726$	−1.29636	+	4.55414i	−0.0481125	+	0.169020i
$727$	24.4064	+	24.4064i	0.905182	+	0.905182i	0.995879	−	0.0906967i	$-0.0289094\pi$
$727$	24.4064	+	24.4064i	0.905182	+	0.905182i	−0.0906967	+	0.995879i	$0.528909\pi$
$728$	3.76240	+	17.7006i	0.139444	+	0.656026i
$729$	−23.5376	−	13.2281i	−0.871761	−	0.489931i
$730$	−23.7357	−	18.6590i	−0.878498	−	0.690599i
$731$	33.4694	+	33.4694i	1.23791	+	1.23791i
$732$	−4.07773	+	1.33365i	−0.150717	+	0.0492932i
$733$		−	35.9689i		−	1.32854i	−0.747492	−	0.664271i	$-0.768742\pi$
$733$		−	35.9689i		−	1.32854i	0.747492	−	0.664271i	$-0.231258\pi$
$734$	23.3407	+	34.6040i	0.861520	+	1.27726i
$735$	−17.3043	+	3.97570i	−0.638278	+	0.146646i
$736$	−17.4311	−	3.07353i	−0.642520	−	0.113292i
$737$	−38.0392	−	38.0392i	−1.40119	−	1.40119i
$738$	−1.12289	+	2.95935i	−0.0413342	+	0.108935i
$739$	29.8916	−	29.8916i	1.09958	−	1.09958i	0.105122	−	0.994459i	$-0.466477\pi$
$739$	29.8916	−	29.8916i	1.09958	−	1.09958i	0.994459	−	0.105122i	$-0.0335232\pi$
$740$	1.30869	−	17.9439i	0.0481083	−	0.659632i
$741$	−23.3343	+	19.6568i	−0.857209	+	0.722109i
$742$	12.8642	+	19.0720i	0.472260	+	0.700153i
$743$	1.18443	+	1.18443i	0.0434525	+	0.0434525i	0.728499	−	0.685047i	$-0.240218\pi$
$743$	1.18443	+	1.18443i	0.0434525	+	0.0434525i	−0.685047	+	0.728499i	$0.740218\pi$
$744$	29.0971	+	22.6427i	1.06675	+	0.830123i
$745$	20.0459	−	39.0531i	0.734425	−	1.43079i
$746$	4.64565	−	23.8998i	0.170089	−	0.875035i
$747$	21.5436	+	3.71297i	0.788238	+	0.135850i
$748$	−17.9290	+	44.3759i	−0.655549	+	1.62254i
$749$	−15.6431	−	15.6431i	−0.571586	−	0.571586i
$750$	21.6987	−	16.7082i	0.792326	−	0.610098i
$751$	7.01380			0.255937			0.127969	−	0.991778i	$-0.459154\pi$
$751$	7.01380			0.255937			0.127969	+	0.991778i	$0.459154\pi$
$752$	−0.0636812	−	3.64789i	−0.00232221	−	0.133025i
$753$	16.0554	−	13.5250i	0.585091	−	0.492879i
$754$	6.13373	+	9.09362i	0.223377	+	0.331170i
$755$	3.46621	+	10.7775i	0.126148	+	0.392233i
$756$	−15.9816	+	2.34059i	−0.581245	+	0.0851263i
$757$			26.3468i			0.957590i	0.877927	+	0.478795i	$0.158926\pi$
$757$			26.3468i			0.957590i	−0.877927	+	0.478795i	$0.841074\pi$
$758$	−9.16317	+	6.18064i	−0.332821	+	0.224491i
$759$	−19.4190	−	1.66116i	−0.704865	−	0.0602962i
$760$	−13.4620	−	23.4786i	−0.488317	−	0.851660i
$761$	−24.7103			−0.895746			−0.447873	−	0.894097i	$-0.647818\pi$
$761$	−24.7103			−0.895746			−0.447873	+	0.894097i	$0.647818\pi$
$762$	−10.4927	+	5.84275i	−0.380112	+	0.211661i
$763$	7.36757			0.266724
$764$	19.0880	−	47.2446i	0.690579	−	1.70925i
$765$	−35.6731	−	26.8329i	−1.28976	−	0.970144i
$766$	−0.572838	−	0.849267i	−0.0206975	−	0.0306853i
$767$	4.37350	+	4.37350i	0.157918	+	0.157918i
$768$	27.6776	+	1.39682i	0.998729	+	0.0504033i
$769$		−	11.7595i		−	0.424059i	−0.977263	−	0.212030i	$-0.931993\pi$
$769$		−	11.7595i		−	0.424059i	0.977263	−	0.212030i	$-0.0680073\pi$
$770$	−17.5499	+	2.10161i	−0.632456	+	0.0757367i
$771$	−0.999922	+	0.842331i	−0.0360113	+	0.0303358i
$772$	17.5205	+	41.2755i	0.630575	+	1.48554i
$773$		−	16.4566i		−	0.591903i	−0.955203	−	0.295952i	$-0.904363\pi$
$773$		−	16.4566i		−	0.591903i	0.955203	−	0.295952i	$-0.0956367\pi$
$774$	10.7061	−	28.2157i	0.384823	−	1.01419i
$775$	−30.5746	+	21.9355i	−1.09827	+	0.787947i
$776$	−4.52447	−	21.2858i	−0.162419	−	0.764115i
$777$	−6.97745	−	8.28286i	−0.250315	−	0.297146i
$778$	−11.1233	−	16.4910i	−0.398791	−	0.591232i
$779$	−2.25745	+	2.25745i	−0.0808816	+	0.0808816i
$780$	31.4879	+	5.02137i	1.12745	+	0.179794i
$781$	20.5985	+	20.5985i	0.737073	+	0.737073i
$782$	−28.9042	−	5.61839i	−1.03361	−	0.200913i
$783$	−8.45039	+	4.94434i	−0.301992	+	0.176696i
$784$	12.7382	−	13.1909i	0.454936	−	0.471102i
$785$	−27.9350	+	8.98433i	−0.997042	+	0.320665i
$786$	−0.100867	+	0.0561663i	−0.00359779	+	0.00200338i
$787$	3.72616			0.132823			0.0664116	−	0.997792i	$-0.478845\pi$
$787$	3.72616			0.132823			0.0664116	+	0.997792i	$0.478845\pi$
$788$	47.6316	+	19.2443i	1.69680	+	0.685551i
$789$	−16.1558	+	13.6096i	−0.575163	+	0.484515i
$790$	−23.9455	+	2.86747i	−0.851943	+	0.102020i
$791$	−9.37073			−0.333185
$792$	30.4923	−	1.18280i	1.08350	−	0.0420290i
$793$	3.60496	−	3.60496i	0.128016	−	0.128016i
$794$	−4.71196	+	24.2410i	−0.167221	+	0.860281i
$795$	39.5062	−	9.07663i	1.40114	−	0.321915i
$796$	−10.2576	−	4.14432i	−0.363571	−	0.146892i
$797$		−	14.4291i		−	0.511106i	−0.966795	−	0.255553i	$-0.917742\pi$
$797$		−	14.4291i		−	0.511106i	0.966795	−	0.255553i	$-0.0822576\pi$
$798$	−15.6689	−	4.46025i	−0.554674	−	0.157891i
$799$		−	6.06944i		−	0.214721i
$800$	−9.36821	+	26.6878i	−0.331216	+	0.943555i
$801$	4.00029	−	23.2107i	0.141343	−	0.820108i
$802$	−51.5682	−	10.0238i	−1.82094	−	0.353953i
$803$	34.3352			1.21166
$804$	−23.4359	+	46.2161i	−0.826521	+	1.62992i
$805$	−3.32939	−	10.3521i	−0.117346	−	0.364862i
$806$	−43.0071	−	8.35971i	−1.51486	−	0.294458i
$807$	−17.8020	+	14.9963i	−0.626660	+	0.527896i
$808$	−8.13265	+	1.72866i	−0.286106	+	0.0608140i
$809$			17.3333i			0.609406i	0.952447	+	0.304703i	$0.0985571\pi$
$809$			17.3333i			0.609406i	−0.952447	+	0.304703i	$0.901443\pi$
$810$	−6.27085	+	27.7611i	−0.220335	+	0.975424i
$811$	27.2381	−	27.2381i	0.956458	−	0.956458i	−0.0426328	−	0.999091i	$-0.513575\pi$
$811$	27.2381	−	27.2381i	0.956458	−	0.956458i	0.999091	+	0.0426328i	$0.0135746\pi$
$812$	−2.19406	+	5.43050i	−0.0769963	+	0.190573i
$813$	−4.52336	+	52.8782i	−0.158641	+	1.85452i
$814$	11.4415	+	16.9627i	0.401024	+	0.594542i
$815$	3.70595	+	11.5229i	0.129814	+	0.403629i
$816$	45.9960	+	3.12701i	1.61018	+	0.109467i
$817$	21.5235	−	21.5235i	0.753012	−	0.753012i
$818$	−1.44387	+	7.42809i	−0.0504838	+	0.259717i
$819$	15.6799	−	11.0697i	0.547901	−	0.386807i
$820$	3.32760	+	0.242689i	0.116205	+	0.00847506i
$821$	22.2784	+	22.2784i	0.777521	+	0.777521i	0.979409	−	0.201888i	$-0.0647077\pi$
$821$	22.2784	+	22.2784i	0.777521	+	0.777521i	−0.201888	+	0.979409i	$0.564708\pi$
$822$	39.8199	−	22.1732i	1.38888	−	0.773379i
$823$	−21.6370	+	21.6370i	−0.754220	+	0.754220i	−0.975264	−	0.221044i	$-0.929054\pi$
$823$	−21.6370	+	21.6370i	−0.754220	+	0.754220i	0.221044	+	0.975264i	$0.429054\pi$
$824$	−5.42283	−	25.5122i	−0.188913	−	0.888761i
$825$	−7.65689	+	30.1886i	−0.266579	+	1.05103i
$826$	−0.630163	+	3.24191i	−0.0219262	+	0.112801i
$827$	38.9448			1.35424			0.677122	−	0.735871i	$-0.263227\pi$
$827$	38.9448			1.35424			0.677122	+	0.735871i	$0.263227\pi$
$828$	4.29381	+	18.2761i	0.149220	+	0.635138i
$829$	20.7041	−	20.7041i	0.719085	−	0.719085i	−0.249333	−	0.968418i	$-0.580211\pi$
$829$	20.7041	−	20.7041i	0.719085	−	0.719085i	0.968418	+	0.249333i	$0.0802114\pi$
$830$	−2.73991	−	22.8802i	−0.0951037	−	0.794185i
$831$	−21.3864	−	1.82945i	−0.741886	−	0.0634631i
$832$	−30.0843	+	13.3945i	−1.04299	+	0.464371i
$833$	21.5707	−	21.5707i	0.747379	−	0.747379i
$834$	3.09733	+	5.56237i	0.107252	+	0.192609i
$835$	−11.7633	+	22.9170i	−0.407085	+	0.793076i
$836$	28.5373	+	11.5298i	0.986982	+	0.398766i
$837$	9.90226	−	37.8312i	0.342272	−	1.30764i
$838$	9.30069	−	6.27340i	0.321287	−	0.216711i
$839$			16.1422i			0.557289i	0.960394	+	0.278645i	$0.0898852\pi$
$839$			16.1422i			0.557289i	−0.960394	+	0.278645i	$0.910115\pi$
$840$	7.17908	+	15.4382i	0.247702	+	0.532669i
$841$		−	25.4498i		−	0.877579i
$842$	26.6561	+	39.5192i	0.918630	+	1.36192i
$843$	−4.40095	+	51.4473i	−0.151577	+	1.77194i
$844$	−3.24068	−	7.63454i	−0.111549	−	0.262792i
$845$	−8.39767	+	2.70083i	−0.288889	+	0.0929112i
$846$	−3.52910	+	1.58762i	−0.121333	+	0.0545835i
$847$	2.12447	−	2.12447i	0.0729977	−	0.0729977i
$848$	−29.0817	+	30.1151i	−0.998670	+	1.03416i
$849$	0.215737	−	2.52198i	0.00740408	−	0.0865540i
$850$	−16.3572	+	44.1181i	−0.561047	+	1.51324i
$851$	−8.90098	+	8.90098i	−0.305122	+	0.305122i
$852$	12.6907	−	25.0264i	0.434777	−	0.857390i
$853$	5.06375			0.173380			0.0866898	−	0.996235i	$-0.472371\pi$
$853$	5.06375			0.173380			0.0866898	+	0.996235i	$0.472371\pi$
$854$	2.67223	+	0.519427i	0.0914417	+	0.0177744i
$855$	−17.2557	+	22.9406i	−0.590132	+	0.784553i
$856$	21.9267	−	33.7643i	0.749439	−	1.15404i
$857$	−13.4059	+	13.4059i	−0.457938	+	0.457938i	−0.897978	−	0.440040i	$-0.854964\pi$
$857$	−13.4059	+	13.4059i	−0.457938	+	0.457938i	0.440040	+	0.897978i	$0.354964\pi$
$858$	−31.6811	+	17.6412i	−1.08158	+	0.602262i
$859$	−9.86520	−	9.86520i	−0.336596	−	0.336596i	0.518488	−	0.855085i	$-0.326495\pi$
$859$	−9.86520	−	9.86520i	−0.336596	−	0.336596i	−0.855085	+	0.518488i	$0.826495\pi$
$860$	−31.7268	−	2.31390i	−1.08187	−	0.0789033i
$861$	1.53601	−	1.29393i	0.0523471	−	0.0440970i
$862$	29.0583	+	5.64835i	0.989731	+	0.192384i
$863$	−34.1863	+	34.1863i	−1.16372	+	1.16372i	−0.180061	+	0.983655i	$0.557630\pi$
$863$	−34.1863	+	34.1863i	−1.16372	+	1.16372i	−0.983655	+	0.180061i	$0.942370\pi$
$864$	−10.2132	−	27.5625i	−0.347461	−	0.937694i
$865$	5.66429	−	1.82173i	0.192592	−	0.0619406i
$866$	−2.05526	+	1.38629i	−0.0698406	+	0.0471082i
$867$	47.0773	+	4.02712i	1.59883	+	0.136768i
$868$	−9.14078	−	21.5343i	−0.310258	−	0.730921i
$869$	19.3933	−	19.3933i	0.657873	−	0.657873i
$870$	7.54025	+	7.04634i	0.255638	+	0.238893i
$871$		−	61.5767i		−	2.08645i
$872$	2.78763	+	13.1147i	0.0944009	+	0.444118i
$873$	−18.8559	+	13.3119i	−0.638175	+	0.450539i
$874$	−3.61307	+	18.5877i	−0.122214	+	0.628738i
$875$	−17.1866	+	2.56423i	−0.581014	+	0.0866869i
$876$	−10.2810	−	31.4349i	−0.347363	−	1.06209i
$877$	−18.4807			−0.624050			−0.312025	−	0.950074i	$-0.601007\pi$
$877$	−18.4807			−0.624050			−0.312025	+	0.950074i	$0.601007\pi$
$878$	−2.17385	+	11.1835i	−0.0733637	+	0.377425i
$879$	−8.10996	−	0.693750i	−0.273542	−	0.0233996i
$880$	−10.3812	−	30.4446i	−0.349952	−	1.02629i
$881$		−	19.2670i		−	0.649123i	−0.945865	−	0.324562i	$-0.894783\pi$
$881$		−	19.2670i		−	0.649123i	0.945865	−	0.324562i	$-0.105217\pi$
$882$	−18.1847	−	6.89997i	−0.612311	−	0.232334i
$883$		−	11.6258i		−	0.391240i	−0.980680	−	0.195620i	$-0.937328\pi$
$883$		−	11.6258i		−	0.391240i	0.980680	−	0.195620i	$-0.0626719\pi$
$884$	−50.4286	+	21.4057i	−1.69610	+	0.719953i
$885$	4.93175	+	3.08897i	0.165779	+	0.103835i
$886$	34.2948	+	6.66622i	1.15216	+	0.223956i
$887$	−16.8437	+	16.8437i	−0.565557	+	0.565557i	−0.930881	−	0.365323i	$-0.880958\pi$
$887$	−16.8437	+	16.8437i	−0.565557	+	0.565557i	0.365323	+	0.930881i	$0.380958\pi$
$888$	12.1039	−	15.5542i	0.406180	−	0.521964i
$889$	7.62039			0.255580
$890$	−24.6508	+	2.95193i	−0.826296	+	0.0989490i
$891$	−13.9048	−	29.2273i	−0.465828	−	0.979152i
$892$	−6.54584	−	15.4210i	−0.219171	−	0.516333i
$893$	−3.90313			−0.130613
$894$	42.0129	−	23.3943i	1.40512	−	0.782424i
$895$	−8.04250	−	4.12821i	−0.268831	−	0.137991i
$896$	−14.9122	−	9.31814i	−0.498183	−	0.311297i
$897$	−14.3729	−	17.0620i	−0.479898	−	0.569682i
$898$	0.405689	−	2.08709i	0.0135380	−	0.0696472i
$899$	−10.0270	−	10.0270i	−0.334418	−	0.334418i
$900$	29.9313	−	2.02929i	0.997710	−	0.0676431i
$901$	−49.2464	+	49.2464i	−1.64064	+	1.64064i
$902$	−3.14563	+	2.12176i	−0.104738	+	0.0706468i
$903$	−14.6450	+	12.3369i	−0.487354	+	0.410545i
$904$	−3.54555	−	16.6804i	−0.117923	−	0.554781i
$905$	19.3357	−	37.6694i	0.642739	−	1.25217i
$906$	−3.39534	+	11.9279i	−0.112803	+	0.396277i
$907$			42.5835i			1.41396i	0.707232	+	0.706981i	$0.249944\pi$
$907$			42.5835i			1.41396i	−0.707232	+	0.706981i	$0.750056\pi$
$908$	16.0724	−	39.7807i	0.533381	−	1.32017i
$909$	5.08606	+	7.20425i	0.168694	+	0.238950i
$910$	−15.9057	−	12.5036i	−0.527268	−	0.414492i
$911$			1.81987i			0.0602949i	0.999545	+	0.0301474i	$0.00959768\pi$
$911$			1.81987i			0.0602949i	−0.999545	+	0.0301474i	$0.990402\pi$
$912$	2.01092	−	29.5791i	0.0665881	−	0.979461i
$913$	18.5305	+	18.5305i	0.613272	+	0.613272i
$914$	−11.4691	+	7.73600i	−0.379363	+	0.255884i
$915$	2.54616	−	4.06512i	0.0841735	−	0.134389i
$916$	3.05850	+	7.20536i	0.101056	+	0.238072i
$917$	0.0732547			0.00241908
$918$	−16.1875	−	46.1416i	−0.534267	−	1.52290i
$919$	−33.0813			−1.09125			−0.545625	−	0.838029i	$-0.683708\pi$
$919$	−33.0813			−1.09125			−0.545625	+	0.838029i	$0.683708\pi$
$920$	17.1675	−	9.84333i	0.565995	−	0.324525i
$921$	−1.86874	+	21.8457i	−0.0615771	+	0.719839i
$922$	−16.2299	−	24.0618i	−0.534503	−	0.792433i
$923$			33.3442i			1.09754i
$924$	−17.2689	−	8.75698i	−0.568106	−	0.288083i
$925$	11.7259	+	16.3440i	0.385544	+	0.537387i
$926$	−12.4527	+	8.39944i	−0.409220	+	0.276023i
$927$	−22.5999	+	15.9550i	−0.742277	+	0.524032i
$928$	−10.4967	−	1.85083i	−0.344572	−	0.0607564i
$929$	−23.5437			−0.772444			−0.386222	−	0.922406i	$-0.626220\pi$
$929$	−23.5437			−0.772444			−0.386222	+	0.922406i	$0.626220\pi$
$930$	−41.1974	+	1.39496i	−1.35091	+	0.0457424i
$931$	−13.8717	−	13.8717i	−0.454625	−	0.454625i
$932$	−7.97506	−	18.7880i	−0.261232	−	0.615422i
$933$	−1.32785	+	15.5226i	−0.0434718	+	0.508187i
$934$	−21.1979	−	4.12044i	−0.693616	−	0.134825i
$935$	−16.3833	−	50.9404i	−0.535790	−	1.66593i
$936$	25.6374	+	23.7227i	0.837984	+	0.775400i
$937$	−23.0528	−	23.0528i	−0.753101	−	0.753101i	0.221956	−	0.975057i	$-0.428756\pi$
$937$	−23.0528	−	23.0528i	−0.753101	−	0.753101i	−0.975057	+	0.221956i	$0.928756\pi$
$938$	27.2584	−	18.3861i	0.890020	−	0.600326i
$939$	8.15982	+	9.68644i	0.266286	+	0.316105i
$940$	2.66690	+	3.08651i	0.0869848	+	0.100671i
$941$	8.47249	−	8.47249i	0.276195	−	0.276195i	−0.555393	−	0.831588i	$-0.687432\pi$
$941$	8.47249	−	8.47249i	0.276195	−	0.276195i	0.831588	+	0.555393i	$0.187432\pi$
$942$	−30.9167	−	8.80063i	−1.00732	−	0.286740i
$943$	−1.65064	−	1.65064i	−0.0537521	−	0.0537521i
$944$	−6.00920	+	0.104903i	−0.195583	+	0.00341429i
$945$	12.0459	−	13.4540i	0.391853	−	0.437657i
$946$	29.9918	−	20.2297i	0.975118	−	0.657726i
$947$			30.1055i			0.978296i	0.872201	+	0.489148i	$0.162692\pi$
$947$			30.1055i			0.978296i	−0.872201	+	0.489148i	$0.837308\pi$
$948$	−23.5621	−	11.9482i	−0.765261	−	0.388059i
$949$	27.7903	+	27.7903i	0.902113	+	0.902113i
$950$	28.3715	+	10.5190i	0.920492	+	0.341281i
$951$	35.9880	+	3.07851i	1.16699	+	0.0998276i
$952$	−24.5332	−	15.9320i	−0.795125	−	0.516359i
$953$	34.9281	+	34.9281i	1.13143	+	1.13143i	0.989939	+	0.141493i	$0.0451902\pi$
$953$	34.9281	+	34.9281i	1.13143	+	1.13143i	0.141493	+	0.989939i	$0.454810\pi$
$954$	41.5162	+	15.7528i	1.34414	+	0.510017i
$955$	17.4424	+	54.2334i	0.564421	+	1.75495i
$956$	21.2350	+	8.57948i	0.686790	+	0.277480i
$957$	−11.6938	−	1.00032i	−0.378006	−	0.0323358i
$958$	2.88144	−	14.8238i	0.0930951	−	0.478934i
$959$	−28.9193			−0.933854
$960$	−24.7645	+	18.6204i	−0.799271	+	0.600971i
$961$	25.6390			0.827064
$962$	−4.46877	+	22.9899i	−0.144079	+	0.741224i
$963$	−42.0810	−	7.25253i	−1.35604	−	0.233709i
$964$	−7.06673	−	2.85514i	−0.227604	−	0.0919577i
$965$	−44.6003	−	22.8933i	−1.43574	−	0.736961i
$966$	3.26131	−	11.4570i	0.104931	−	0.368624i
$967$	−14.8708	−	14.8708i	−0.478212	−	0.478212i	0.426347	−	0.904560i	$-0.359800\pi$
$967$	−14.8708	−	14.8708i	−0.478212	−	0.478212i	−0.904560	+	0.426347i	$0.859800\pi$
$968$	4.58549	+	2.97784i	0.147383	+	0.0957116i
$969$	4.20366	−	49.1409i	0.135041	−	1.57863i
$970$	19.1274	+	15.0363i	0.614142	+	0.482785i
$971$	−11.8722	−	11.8722i	−0.380998	−	0.380998i	0.490464	−	0.871462i	$-0.336827\pi$
$971$	−11.8722	−	11.8722i	−0.380998	−	0.380998i	−0.871462	+	0.490464i	$0.836827\pi$
$972$	−22.5949	+	21.4818i	−0.724733	+	0.689030i
$973$		−	4.03969i		−	0.129506i
$974$	−22.6417	+	15.2721i	−0.725488	+	0.489349i
$975$	−30.6316	+	18.2368i	−0.980995	+	0.584046i
$976$	0.0864685	+	4.95323i	0.00276779	+	0.158549i
$977$	23.0742	+	23.0742i	0.738208	+	0.738208i	0.972231	−	0.234023i	$-0.0751892\pi$
$977$	23.0742	+	23.0742i	0.738208	+	0.738208i	−0.234023	+	0.972231i	$0.575189\pi$
$978$	−3.63017	+	12.7529i	−0.116080	+	0.407791i
$979$	19.9645	−	19.9645i	0.638068	−	0.638068i
$980$	−1.49128	+	20.4475i	−0.0476373	+	0.653173i
$981$	11.6175	−	8.20174i	0.370919	−	0.261861i
$982$	11.1558	−	7.52469i	0.355996	−	0.240122i
$983$	16.7550	+	16.7550i	0.534400	+	0.534400i	0.921879	−	0.387478i	$-0.126654\pi$
$983$	16.7550	+	16.7550i	0.534400	+	0.534400i	−0.387478	+	0.921879i	$0.626654\pi$
$984$	2.88443	+	2.24460i	0.0919523	+	0.0715552i
$985$	−54.6777	+	17.5852i	−1.74218	+	0.560312i
$986$	−17.4056	−	3.38330i	−0.554307	−	0.107746i
$987$	2.44648	+	0.209279i	0.0778724	+	0.00666143i
$988$	13.7656	+	32.4296i	0.437942	+	1.03172i
$989$	15.7379	+	15.7379i	0.500435	+	0.500435i
$990$	−25.3340	+	22.8509i	−0.805168	+	0.726249i
$991$	54.4865			1.73082			0.865411	−	0.501062i	$-0.167057\pi$
$991$	54.4865			1.73082			0.865411	+	0.501062i	$0.167057\pi$
$992$	34.8736	−	24.4189i	1.10724	−	0.775300i
$993$	0.520209	+	0.617535i	0.0165083	+	0.0195969i
$994$	−14.7607	+	9.95620i	−0.468180	+	0.315792i
$995$	11.7750	−	3.78703i	0.373292	−	0.120057i
$996$	11.4167	−	22.5139i	0.361751	−	0.713380i
$997$			6.68269i			0.211643i	0.994385	+	0.105821i	$0.0337472\pi$
$997$			6.68269i			0.211643i	−0.994385	+	0.105821i	$0.966253\pi$
$998$	−21.9759	−	32.5806i	−0.695636	−	1.03132i
$999$	−20.2230	−	5.29336i	−0.639829	−	0.167474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bb.a.173.20	✓	88
3.2	odd	2	inner	240.2.bb.a.173.25	yes	88
4.3	odd	2		960.2.bb.a.593.20		88
5.2	odd	4		240.2.bf.a.77.3	yes	88
12.11	even	2		960.2.bb.a.593.25		88
15.2	even	4		240.2.bf.a.77.42	yes	88
16.5	even	4		240.2.bf.a.53.42	yes	88
16.11	odd	4		960.2.bf.a.113.44		88
20.7	even	4		960.2.bf.a.17.44		88
48.5	odd	4		240.2.bf.a.53.3	yes	88
48.11	even	4		960.2.bf.a.113.43		88
60.47	odd	4		960.2.bf.a.17.43		88
80.27	even	4		960.2.bb.a.497.25		88
80.37	odd	4	inner	240.2.bb.a.197.25	yes	88
240.107	odd	4		960.2.bb.a.497.20		88
240.197	even	4	inner	240.2.bb.a.197.20	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.20	✓	88	1.1	even	1	trivial
240.2.bb.a.173.25	yes	88	3.2	odd	2	inner
240.2.bb.a.197.20	yes	88	240.197	even	4	inner
240.2.bb.a.197.25	yes	88	80.37	odd	4	inner
240.2.bf.a.53.3	yes	88	48.5	odd	4
240.2.bf.a.53.42	yes	88	16.5	even	4
240.2.bf.a.77.3	yes	88	5.2	odd	4
240.2.bf.a.77.42	yes	88	15.2	even	4
960.2.bb.a.497.20		88	240.107	odd	4
960.2.bb.a.497.25		88	80.27	even	4
960.2.bb.a.593.20		88	4.3	odd	2
960.2.bb.a.593.25		88	12.11	even	2
960.2.bf.a.17.43		88	60.47	odd	4
960.2.bf.a.17.44		88	20.7	even	4
960.2.bf.a.113.43		88	48.11	even	4
960.2.bf.a.113.44		88	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.269844 + 1.38823i) q^{2} +(0.147625 - 1.72575i) q^{3} +(-1.85437 - 0.749211i) q^{4} +(2.12868 - 0.684619i) q^{5} +(2.35590 + 0.670621i) q^{6} +(-1.09901 - 1.09901i) q^{7} +(1.54047 - 2.37212i) q^{8} +(-2.95641 - 0.509529i) q^{9} +O(q^{10})\)	\(q+(-0.269844 + 1.38823i) q^{2} +(0.147625 - 1.72575i) q^{3} +(-1.85437 - 0.749211i) q^{4} +(2.12868 - 0.684619i) q^{5} +(2.35590 + 0.670621i) q^{6} +(-1.09901 - 1.09901i) q^{7} +(1.54047 - 2.37212i) q^{8} +(-2.95641 - 0.509529i) q^{9} +(0.375997 + 3.13984i) q^{10} +(-2.54294 - 2.54294i) q^{11} +(-1.56670 + 3.08957i) q^{12} -4.11643i q^{13} +(1.82224 - 1.22912i) q^{14} +(-0.867232 - 3.77464i) q^{15} +(2.87736 + 2.77863i) q^{16} +(4.70528 + 4.70528i) q^{17} +(1.50511 - 3.96669i) q^{18} +(3.02587 - 3.02587i) q^{19} +(-4.46029 - 0.325298i) q^{20} +(-2.05886 + 1.73437i) q^{21} +(4.21638 - 2.84399i) q^{22} +(2.21250 + 2.21250i) q^{23} +(-3.86627 - 3.00865i) q^{24} +(4.06259 - 2.91468i) q^{25} +(5.71456 + 1.11079i) q^{26} +(-1.31576 + 5.02681i) q^{27} +(1.21458 + 2.86136i) q^{28} +(1.33233 + 1.33233i) q^{29} +(5.47409 - 0.185354i) q^{30} -7.52589 q^{31} +(-4.63382 + 3.24465i) q^{32} +(-4.76387 + 4.01307i) q^{33} +(-7.80171 + 5.26232i) q^{34} +(-3.09185 - 1.58704i) q^{35} +(5.10054 + 3.15983i) q^{36} +4.02304i q^{37} +(3.38409 + 5.01712i) q^{38} +(-7.10392 - 0.607690i) q^{39} +(1.65517 - 6.10413i) q^{40} -0.746050 q^{41} +(-1.85214 - 3.32618i) q^{42} +7.11316 q^{43} +(2.81035 + 6.62074i) q^{44} +(-6.64210 + 0.939392i) q^{45} +(-3.66849 + 2.47443i) q^{46} +(-0.644960 - 0.644960i) q^{47} +(5.21998 - 4.55541i) q^{48} -4.58435i q^{49} +(2.94998 + 6.42632i) q^{50} +(8.81475 - 7.42551i) q^{51} +(-3.08408 + 7.63338i) q^{52} +10.4662i q^{53} +(-6.62332 - 3.18303i) q^{54} +(-7.15406 - 3.67217i) q^{55} +(-4.29998 + 0.913994i) q^{56} +(-4.77520 - 5.66859i) q^{57} +(-2.20910 + 1.49006i) q^{58} +(-1.06245 + 1.06245i) q^{59} +(-1.21984 + 7.64931i) q^{60} +(0.875750 + 0.875750i) q^{61} +(2.03082 - 10.4477i) q^{62} +(2.68915 + 3.80911i) q^{63} +(-3.25391 - 7.30835i) q^{64} +(-2.81819 - 8.76258i) q^{65} +(-4.28556 - 7.69626i) q^{66} +14.9587 q^{67} +(-5.20007 - 12.2506i) q^{68} +(4.14484 - 3.49160i) q^{69} +(3.03750 - 3.86395i) q^{70} -8.10028 q^{71} +(-5.76293 + 6.22806i) q^{72} +(-6.75108 + 6.75108i) q^{73} +(-5.58491 - 1.08559i) q^{74} +(-4.43025 - 7.44129i) q^{75} +(-7.87810 + 3.34406i) q^{76} +5.58943i q^{77} +(2.76057 - 9.69790i) q^{78} +7.62633i q^{79} +(8.02730 + 3.94492i) q^{80} +(8.48076 + 3.01276i) q^{81} +(0.201317 - 1.03569i) q^{82} -7.28706 q^{83} +(5.11729 - 1.67365i) q^{84} +(13.2374 + 6.79473i) q^{85} +(-1.91944 + 9.87471i) q^{86} +(2.49595 - 2.10258i) q^{87} +(-9.94948 + 2.11484i) q^{88} +7.85095i q^{89} +(0.488240 - 9.47426i) q^{90} +(-4.52400 + 4.52400i) q^{91} +(-2.44516 - 5.76042i) q^{92} +(-1.11101 + 12.9878i) q^{93} +(1.06939 - 0.721315i) q^{94} +(4.36955 - 8.51269i) q^{95} +(4.91538 + 8.47579i) q^{96} +(5.44033 - 5.44033i) q^{97} +(6.36414 + 1.23706i) q^{98} +(6.22228 + 8.81368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^4 - 4 * q^6	\( 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Introduction

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