LMFDB - Embedded newform 980.2.c.d.979.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(979,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.979"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.5
Character	$\chi$	$=$	980.979
Dual form			980.2.c.d.979.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.940044 - 1.05656i) q^{2} -2.59619i q^{3} +(-0.232633 + 1.98642i) q^{4} +(1.75874 - 1.38089i) q^{5} +(-2.74302 + 2.44053i) q^{6} +(2.31746 - 1.62154i) q^{8} -3.74018 q^{9} +(-3.11228 - 0.560116i) q^{10} -3.60275i q^{11} +(5.15713 + 0.603960i) q^{12} +0.818282 q^{13} +(-3.58504 - 4.56601i) q^{15} +(-3.89176 - 0.924218i) q^{16} +7.39628 q^{17} +(3.51594 + 3.95172i) q^{18} -3.30658 q^{19} +(2.33388 + 3.81484i) q^{20} +(-3.80652 + 3.38675i) q^{22} -2.53515 q^{23} +(-4.20981 - 6.01656i) q^{24} +(1.18631 - 4.85723i) q^{25} +(-0.769222 - 0.864563i) q^{26} +1.92166i q^{27} -2.04334 q^{29} +(-1.45417 + 8.08005i) q^{30} -1.91145 q^{31} +(2.68194 + 4.98068i) q^{32} -9.35342 q^{33} +(-6.95283 - 7.81461i) q^{34} +(0.870092 - 7.42959i) q^{36} -7.16720i q^{37} +(3.10833 + 3.49360i) q^{38} -2.12441i q^{39} +(1.83665 - 6.05200i) q^{40} +2.65824i q^{41} -2.39696 q^{43} +(7.15660 + 0.838121i) q^{44} +(-6.57800 + 5.16476i) q^{45} +(2.38315 + 2.67854i) q^{46} -1.33475i q^{47} +(-2.39944 + 10.1037i) q^{48} +(-6.24713 + 3.31260i) q^{50} -19.2021i q^{51} +(-0.190360 + 1.62546i) q^{52} -1.81101i q^{53} +(2.03034 - 1.80644i) q^{54} +(-4.97499 - 6.33630i) q^{55} +8.58450i q^{57} +(1.92083 + 2.15891i) q^{58} +1.91145 q^{59} +(9.90403 - 6.05920i) q^{60} +9.77598i q^{61} +(1.79685 + 2.01956i) q^{62} +(2.74124 - 7.51569i) q^{64} +(1.43914 - 1.12995i) q^{65} +(8.79263 + 9.88244i) q^{66} +9.26225 q^{67} +(-1.72062 + 14.6922i) q^{68} +6.58172i q^{69} +1.38422i q^{71} +(-8.66773 + 6.06484i) q^{72} -7.39628 q^{73} +(-7.57256 + 6.73748i) q^{74} +(-12.6103 - 3.07989i) q^{75} +(0.769222 - 6.56827i) q^{76} +(-2.24457 + 1.99704i) q^{78} +7.74780i q^{79} +(-8.12083 + 3.74862i) q^{80} -6.23157 q^{81} +(2.80858 - 2.49886i) q^{82} +10.4973i q^{83} +(13.0081 - 10.2134i) q^{85} +(2.25325 + 2.53253i) q^{86} +5.30490i q^{87} +(-5.84199 - 8.34924i) q^{88} +10.6132i q^{89} +(11.6405 + 2.09494i) q^{90} +(0.589761 - 5.03589i) q^{92} +4.96249i q^{93} +(-1.41024 + 1.25473i) q^{94} +(-5.81541 + 4.56601i) q^{95} +(12.9308 - 6.96281i) q^{96} +7.32005 q^{97} +13.4750i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{4} - 8 q^{9} - 36 q^{16} + 52 q^{25} + 52 q^{30} - 28 q^{36} + 52 q^{44} + 44 q^{46} + 36 q^{50} - 8 q^{60} + 36 q^{64} + 8 q^{65} - 28 q^{74} - 144 q^{81} + 20 q^{85} - 16 q^{86}+O(q^{100}) $ 32 * q - 12 * q^4 - 8 * q^9 - 36 * q^16 + 52 * q^25 + 52 * q^30 - 28 * q^36 + 52 * q^44 + 44 * q^46 + 36 * q^50 - 8 * q^60 + 36 * q^64 + 8 * q^65 - 28 * q^74 - 144 * q^81 + 20 * q^85 - 16 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.940044	−	1.05656i	−0.664712	−	0.747100i
$2$	−0.940044	−	1.05656i	−0.664712	−	0.747100i
$3$		−	2.59619i		−	1.49891i	−0.662056	−	0.749454i	$-0.730316\pi$
$3$		−	2.59619i		−	1.49891i	0.662056	−	0.749454i	$-0.269684\pi$
$4$	−0.232633	+	1.98642i	−0.116317	+	0.993212i
$5$	1.75874	−	1.38089i	0.786531	−	0.617551i
$5$	1.75874	−	1.38089i	0.786531	−	0.617551i
$6$	−2.74302	+	2.44053i	−1.11983	+	0.996342i
$7$		0			0
$7$		0			0
$8$	2.31746	−	1.62154i	0.819346	−	0.573300i
$9$	−3.74018			−1.24673
$10$	−3.11228	−	0.560116i	−0.984188	−	0.177124i
$11$		−	3.60275i		−	1.08627i	−0.839645	−	0.543136i	$-0.817237\pi$
$11$		−	3.60275i		−	1.08627i	0.839645	−	0.543136i	$-0.182763\pi$
$12$	5.15713	+	0.603960i	1.48873	+	0.174348i
$13$	0.818282			0.226951			0.113475	−	0.993541i	$-0.463802\pi$
$13$	0.818282			0.226951			0.113475	+	0.993541i	$0.463802\pi$
$14$		0			0
$15$	−3.58504	−	4.56601i	−0.925652	−	1.17894i
$16$	−3.89176	−	0.924218i	−0.972941	−	0.231054i
$17$	7.39628			1.79386			0.896931	−	0.442170i	$-0.145791\pi$
$17$	7.39628			1.79386			0.896931	+	0.442170i	$0.145791\pi$
$18$	3.51594	+	3.95172i	0.828715	+	0.931431i
$19$	−3.30658			−0.758582			−0.379291	−	0.925277i	$-0.623832\pi$
$19$	−3.30658			−0.758582			−0.379291	+	0.925277i	$0.623832\pi$
$20$	2.33388	+	3.81484i	0.521872	+	0.853024i
$21$		0			0
$22$	−3.80652	+	3.38675i	−0.811553	+	0.722057i
$23$	−2.53515			−0.528615			−0.264308	−	0.964438i	$-0.585143\pi$
$23$	−2.53515			−0.528615			−0.264308	+	0.964438i	$0.585143\pi$
$24$	−4.20981	−	6.01656i	−0.859324	−	1.22812i
$25$	1.18631	−	4.85723i	0.237262	−	0.971446i
$26$	−0.769222	−	0.864563i	−0.150857	−	0.169555i
$27$			1.92166i			0.369823i
$28$		0			0
$29$	−2.04334			−0.379439			−0.189720	−	0.981838i	$-0.560758\pi$
$29$	−2.04334			−0.379439			−0.189720	+	0.981838i	$0.560758\pi$
$30$	−1.45417	+	8.08005i	−0.265493	+	1.47521i
$31$	−1.91145			−0.343307			−0.171654	−	0.985157i	$-0.554911\pi$
$31$	−1.91145			−0.343307			−0.171654	+	0.985157i	$0.554911\pi$
$32$	2.68194	+	4.98068i	0.474104	+	0.880469i
$33$	−9.35342			−1.62822
$34$	−6.95283	−	7.81461i	−1.19240	−	1.34019i
$35$		0			0
$36$	0.870092	−	7.42959i	0.145015	−	1.23827i
$37$		−	7.16720i		−	1.17828i	−0.808031	−	0.589140i	$-0.799467\pi$
$37$		−	7.16720i		−	1.17828i	0.808031	−	0.589140i	$-0.200533\pi$
$38$	3.10833	+	3.49360i	0.504238	+	0.566736i
$39$		−	2.12441i		−	0.340178i
$40$	1.83665	−	6.05200i	0.290400	−	0.956905i
$41$			2.65824i			0.415147i	0.978219	+	0.207573i	$0.0665566\pi$
$41$			2.65824i			0.415147i	−0.978219	+	0.207573i	$0.933443\pi$
$42$		0			0
$43$	−2.39696			−0.365533			−0.182766	−	0.983156i	$-0.558505\pi$
$43$	−2.39696			−0.365533			−0.182766	+	0.983156i	$0.558505\pi$
$44$	7.15660	+	0.838121i	1.07890	+	0.126352i
$45$	−6.57800	+	5.16476i	−0.980590	+	0.769918i
$46$	2.38315	+	2.67854i	0.351377	+	0.394929i
$47$		−	1.33475i		−	0.194694i	−0.995251	−	0.0973468i	$-0.968964\pi$
$47$		−	1.33475i		−	0.194694i	0.995251	−	0.0973468i	$-0.0310356\pi$
$48$	−2.39944	+	10.1037i	−0.346330	+	1.45835i
$49$		0			0
$50$	−6.24713	+	3.31260i	−0.883478	+	0.468472i
$51$		−	19.2021i		−	2.68884i
$52$	−0.190360	+	1.62546i	−0.0263982	+	0.225410i
$53$		−	1.81101i		−	0.248761i	−0.992235	−	0.124380i	$-0.960306\pi$
$53$		−	1.81101i		−	0.248761i	0.992235	−	0.124380i	$-0.0396943\pi$
$54$	2.03034	−	1.80644i	0.276295	−	0.245826i
$55$	−4.97499	−	6.33630i	−0.670827	−	0.854386i
$56$		0			0
$57$			8.58450i			1.13705i
$58$	1.92083	+	2.15891i	0.252218	+	0.283479i
$59$	1.91145			0.248850			0.124425	−	0.992229i	$-0.460291\pi$
$59$	1.91145			0.248850			0.124425	+	0.992229i	$0.460291\pi$
$60$	9.90403	−	6.05920i	1.27860	−	0.782239i
$61$			9.77598i			1.25169i	0.779949	+	0.625843i	$0.215245\pi$
$61$			9.77598i			1.25169i	−0.779949	+	0.625843i	$0.784755\pi$
$62$	1.79685	+	2.01956i	0.228200	+	0.256485i
$63$		0			0
$64$	2.74124	−	7.51569i	0.342655	−	0.939461i
$65$	1.43914	−	1.12995i	0.178504	−	0.140154i
$66$	8.79263	+	9.88244i	1.08230	+	1.21644i
$67$	9.26225			1.13156			0.565782	−	0.824555i	$-0.308574\pi$
$67$	9.26225			1.13156			0.565782	+	0.824555i	$0.308574\pi$
$68$	−1.72062	+	14.6922i	−0.208656	+	1.78169i
$69$			6.58172i			0.792346i
$70$		0			0
$71$			1.38422i			0.164277i	0.996621	+	0.0821385i	$0.0261750\pi$
$71$			1.38422i			0.164277i	−0.996621	+	0.0821385i	$0.973825\pi$
$72$	−8.66773	+	6.06484i	−1.02150	+	0.714749i
$73$	−7.39628			−0.865669			−0.432835	−	0.901473i	$-0.642487\pi$
$73$	−7.39628			−0.865669			−0.432835	+	0.901473i	$0.642487\pi$
$74$	−7.57256	+	6.73748i	−0.880293	+	0.783216i
$75$	−12.6103	−	3.07989i	−1.45611	−	0.355635i
$76$	0.769222	−	6.56827i	0.0882358	−	0.753433i
$77$		0			0
$78$	−2.24457	+	1.99704i	−0.254147	+	0.226121i
$79$			7.74780i			0.871695i	0.900021	+	0.435848i	$0.143551\pi$
$79$			7.74780i			0.871695i	−0.900021	+	0.435848i	$0.856449\pi$
$80$	−8.12083	+	3.74862i	−0.907936	+	0.419109i
$81$	−6.23157			−0.692397
$82$	2.80858	−	2.49886i	0.310156	−	0.275953i
$83$			10.4973i			1.15223i	0.817370	+	0.576113i	$0.195431\pi$
$83$			10.4973i			1.15223i	−0.817370	+	0.576113i	$0.804569\pi$
$84$		0			0
$85$	13.0081	−	10.2134i	1.41093	−	1.10780i
$86$	2.25325	+	2.53253i	0.242974	+	0.273089i
$87$			5.30490i			0.568745i
$88$	−5.84199	−	8.34924i	−0.622759	−	0.890032i
$89$			10.6132i			1.12500i	0.826797	+	0.562500i	$0.190160\pi$
$89$			10.6132i			1.12500i	−0.826797	+	0.562500i	$0.809840\pi$
$90$	11.6405	+	2.09494i	1.22702	+	0.220826i
$91$		0			0
$92$	0.589761	−	5.03589i	0.0614868	−	0.525027i
$93$			4.96249i			0.514586i
$94$	−1.41024	+	1.25473i	−0.145456	+	0.129415i
$95$	−5.81541	+	4.56601i	−0.596648	+	0.468463i
$96$	12.9308	−	6.96281i	1.31974	−	0.710639i
$97$	7.32005			0.743239			0.371619	−	0.928385i	$-0.378803\pi$
$97$	7.32005			0.743239			0.371619	+	0.928385i	$0.378803\pi$
$98$		0			0
$99$			13.4750i			1.35428i
$100$	9.37254	+	3.48647i	0.937254	+	0.348647i
$101$		−	6.35787i		−	0.632632i	−0.948654	−	0.316316i	$-0.897554\pi$
$101$		−	6.35787i		−	0.632632i	0.948654	−	0.316316i	$-0.102446\pi$
$102$	−20.2882	+	18.0509i	−2.00883	+	1.78730i
$103$		−	1.02208i		−	0.100708i	−0.998731	−	0.0503541i	$-0.983965\pi$
$103$		−	1.02208i		−	0.100708i	0.998731	−	0.0503541i	$-0.0160350\pi$
$104$	1.89634	−	1.32687i	0.185951	−	0.130111i
$105$		0			0
$106$	−1.91343	+	1.70243i	−0.185849	+	0.165354i
$107$	7.25156			0.701035			0.350517	−	0.936556i	$-0.386006\pi$
$107$	7.25156			0.701035			0.350517	+	0.936556i	$0.386006\pi$
$108$	−3.81722	−	0.447042i	−0.367313	−	0.0430166i
$109$	−7.97176			−0.763556			−0.381778	−	0.924254i	$-0.624688\pi$
$109$	−7.97176			−0.763556			−0.381778	+	0.924254i	$0.624688\pi$
$110$	−2.01796	+	11.2128i	−0.192405	+	1.06910i
$111$	−18.6074			−1.76613
$112$		0			0
$113$			7.61610i			0.716462i	0.933633	+	0.358231i	$0.116620\pi$
$113$			7.61610i			0.716462i	−0.933633	+	0.358231i	$0.883380\pi$
$114$	9.07003	−	8.06981i	0.849486	−	0.755807i
$115$	−4.45866	+	3.50075i	−0.415773	+	0.326447i
$116$	0.475350	−	4.05895i	0.0441351	−	0.376864i
$117$	−3.06053			−0.282946
$118$	−1.79685	−	2.01956i	−0.165414	−	0.185916i
$119$		0			0
$120$	−15.7121	−	4.76828i	−1.43431	−	0.435283i
$121$	−1.97983			−0.179985
$122$	10.3289	−	9.18986i	0.935135	−	0.832010i
$123$	6.90128			0.622267
$124$	0.444668	−	3.79696i	0.0399324	−	0.340977i
$125$	−4.62086	−	10.1807i	−0.413303	−	0.910594i
$126$		0			0
$127$	−8.78136			−0.779220			−0.389610	−	0.920980i	$-0.627390\pi$
$127$	−8.78136			−0.779220			−0.389610	+	0.920980i	$0.627390\pi$
$128$	−10.5177	+	4.16880i	−0.929638	+	0.368473i
$129$			6.22295i			0.547900i
$130$	−2.54672	−	0.458333i	−0.223362	−	0.0401985i
$131$	13.3893			1.16983			0.584916	−	0.811094i	$-0.301127\pi$
$131$	13.3893			1.16983			0.584916	+	0.811094i	$0.301127\pi$
$132$	2.17592	−	18.5799i	0.189389	−	1.61717i
$133$		0			0
$134$	−8.70692	−	9.78611i	−0.752164	−	0.845391i
$135$	2.65359	+	3.37969i	0.228384	+	0.290877i
$136$	17.1406	−	11.9933i	1.46979	−	1.02842i
$137$		−	5.22416i		−	0.446330i	−0.974781	−	0.223165i	$-0.928361\pi$
$137$		−	5.22416i		−	0.446330i	0.974781	−	0.223165i	$-0.0716389\pi$
$138$	6.95398	−	6.18711i	0.591962	−	0.526682i
$139$	21.9442			1.86128			0.930641	−	0.365933i	$-0.119250\pi$
$139$	21.9442			1.86128			0.930641	+	0.365933i	$0.119250\pi$
$140$		0			0
$141$	−3.46527			−0.291828
$142$	1.46251	−	1.30123i	0.122731	−	0.109197i
$143$		−	2.94807i		−	0.246530i
$144$	14.5559	+	3.45674i	1.21299	+	0.288062i
$145$	−3.59370	+	2.82162i	−0.298441	+	0.234323i
$146$	6.95283	+	7.81461i	0.575421	+	0.646742i
$147$		0			0
$148$	14.2371	+	1.66733i	1.17028	+	0.137054i
$149$	−23.9497			−1.96204			−0.981019	−	0.193914i	$-0.937882\pi$
$149$	−23.9497			−1.96204			−0.981019	+	0.193914i	$0.937882\pi$
$150$	8.60013	+	16.2187i	0.702198	+	1.32425i
$151$			7.00761i			0.570271i	0.958487	+	0.285135i	$0.0920386\pi$
$151$			7.00761i			0.570271i	−0.958487	+	0.285135i	$0.907961\pi$
$152$	−7.66287	+	5.36174i	−0.621541	+	0.434895i
$153$	−27.6635			−2.23646
$154$		0			0
$155$	−3.36174	+	2.63950i	−0.270022	+	0.212010i
$156$	4.21999	+	0.494210i	0.337869	+	0.0395684i
$157$	6.42554			0.512814			0.256407	−	0.966569i	$-0.417461\pi$
$157$	6.42554			0.512814			0.256407	+	0.966569i	$0.417461\pi$
$158$	8.18600	−	7.28327i	0.651243	−	0.579426i
$159$	−4.70171			−0.372870
$160$	11.5946	+	5.05626i	0.916632	+	0.399733i
$161$		0			0
$162$	5.85796	+	6.58403i	0.460245	+	0.517290i
$163$	18.4790			1.44739			0.723693	−	0.690122i	$-0.242443\pi$
$163$	18.4790			1.44739			0.723693	+	0.690122i	$0.242443\pi$
$164$	−5.28038	−	0.618395i	−0.412329	−	0.0482885i
$165$	−16.4502	+	12.9160i	−1.28065	+	1.00551i
$166$	11.0910	−	9.86790i	0.860827	−	0.765898i
$167$			1.82894i			0.141527i	0.997493	+	0.0707637i	$0.0225436\pi$
$167$			1.82894i			0.141527i	−0.997493	+	0.0707637i	$0.977456\pi$
$168$		0			0
$169$	−12.3304			−0.948493
$170$	−23.0193	−	4.14278i	−1.76550	−	0.317736i
$171$	12.3672			0.945745
$172$	0.557613	−	4.76137i	0.0425176	−	0.363051i
$173$	15.2495			1.15940			0.579700	−	0.814830i	$-0.303170\pi$
$173$	15.2495			1.15940			0.579700	+	0.814830i	$0.303170\pi$
$174$	5.60494	−	4.98684i	0.424909	−	0.378051i
$175$		0			0
$176$	−3.32973	+	14.0211i	−0.250988	+	1.05688i
$177$		−	4.96249i		−	0.373004i
$178$	11.2135	−	9.97691i	0.840488	−	0.747801i
$179$		−	12.5369i		−	0.937050i	−0.883450	−	0.468525i	$-0.844786\pi$
$179$		−	12.5369i		−	0.937050i	0.883450	−	0.468525i	$-0.155214\pi$
$180$	−8.72915	−	14.2682i	−0.650633	−	1.06349i
$181$		−	8.01839i		−	0.596002i	−0.954566	−	0.298001i	$-0.903680\pi$
$181$		−	8.01839i		−	0.596002i	0.954566	−	0.298001i	$-0.0963199\pi$
$182$		0			0
$183$	25.3803			1.87616
$184$	−5.87511	+	4.11084i	−0.433119	+	0.303055i
$185$	−9.89707	−	12.6052i	−0.727647	−	0.926754i
$186$	5.24316	−	4.66496i	0.384447	−	0.342051i
$187$		−	26.6470i		−	1.94862i
$188$	2.65139	+	0.310508i	0.193372	+	0.0226461i
$189$		0			0
$190$	10.2910	+	1.85207i	0.746587	+	0.134363i
$191$		−	6.75938i		−	0.489091i	−0.969638	−	0.244546i	$-0.921361\pi$
$191$		−	6.75938i		−	0.489091i	0.969638	−	0.244546i	$-0.0786388\pi$
$192$	−19.5121	−	7.11678i	−1.40817	−	0.513609i
$193$			2.36003i			0.169878i	0.996386	+	0.0849392i	$0.0270696\pi$
$193$			2.36003i			0.169878i	−0.996386	+	0.0849392i	$0.972930\pi$
$194$	−6.88118	−	7.73407i	−0.494040	−	0.555274i
$195$	−2.93357	−	3.73628i	−0.210077	−	0.267561i
$196$		0			0
$197$		−	20.3205i		−	1.44777i	−0.689918	−	0.723887i	$-0.742353\pi$
$197$		−	20.3205i		−	1.44777i	0.689918	−	0.723887i	$-0.257647\pi$
$198$	14.2371	−	12.6671i	1.01179	−	0.900209i
$199$	−11.4582			−0.812249			−0.406125	−	0.913818i	$-0.633120\pi$
$199$	−11.4582			−0.812249			−0.406125	+	0.913818i	$0.633120\pi$
$200$	−5.12694	−	13.1801i	−0.362529	−	0.931972i
$201$		−	24.0465i		−	1.69611i
$202$	−6.71746	+	5.97668i	−0.472639	+	0.420518i
$203$		0			0
$204$	38.1436	+	4.46706i	2.67058	+	0.312757i
$205$	3.67072	+	4.67514i	0.256374	+	0.326526i
$206$	−1.07988	+	0.960796i	−0.0752390	+	0.0669419i
$207$	9.48193			0.659040
$208$	−3.18456	−	0.756271i	−0.220810	−	0.0524380i
$209$			11.9128i			0.824026i
$210$		0			0
$211$		−	22.0647i		−	1.51900i	−0.650510	−	0.759498i	$-0.725445\pi$
$211$		−	22.0647i		−	1.51900i	0.650510	−	0.759498i	$-0.274555\pi$
$212$	3.59743	+	0.421301i	0.247072	+	0.0289350i
$213$	3.59370			0.246236
$214$	−6.81679	−	7.66170i	−0.465986	−	0.523743i
$215$	−4.21562	+	3.30992i	−0.287503	+	0.225735i
$216$	3.11603	+	4.45336i	0.212019	+	0.303013i
$217$		0			0
$218$	7.49381	+	8.42263i	0.507545	+	0.570453i
$219$			19.2021i			1.29756i
$220$	13.7439	−	8.40840i	0.926615	−	0.566895i
$221$	6.05225			0.407118
$222$	17.4918	+	19.6598i	1.17397	+	1.31948i
$223$		−	23.5776i		−	1.57887i	−0.613833	−	0.789436i	$-0.710373\pi$
$223$		−	23.5776i		−	1.57887i	0.613833	−	0.789436i	$-0.289627\pi$
$224$		0			0
$225$	−4.43703	+	18.1669i	−0.295802	+	1.21113i
$226$	8.04686	−	7.15947i	0.535269	−	0.476241i
$227$			20.9267i			1.38896i	0.719514	+	0.694478i	$0.244364\pi$
$227$			20.9267i			1.38896i	−0.719514	+	0.694478i	$0.755636\pi$
$228$	−17.0525	−	1.99704i	−1.12933	−	0.132257i
$229$		−	5.18155i		−	0.342406i	−0.985236	−	0.171203i	$-0.945235\pi$
$229$		−	5.18155i		−	0.342406i	0.985236	−	0.171203i	$-0.0547655\pi$
$230$	7.89009	+	1.41998i	0.520257	+	0.0936306i
$231$		0			0
$232$	−4.73536	+	3.31335i	−0.310892	+	0.217532i
$233$		−	20.7694i		−	1.36065i	−0.732912	−	0.680324i	$-0.761839\pi$
$233$		−	20.7694i		−	1.36065i	0.732912	−	0.680324i	$-0.238161\pi$
$234$	2.87703	+	3.23363i	0.188077	+	0.211389i
$235$	−1.84314	−	2.34748i	−0.120233	−	0.153133i
$236$	−0.444668	+	3.79696i	−0.0289454	+	0.247161i
$237$	20.1147			1.30659
$238$		0			0
$239$			21.1286i			1.36670i	0.730092	+	0.683349i	$0.239477\pi$
$239$			21.1286i			1.36670i	−0.730092	+	0.683349i	$0.760523\pi$
$240$	9.73212	+	21.0832i	0.628206	+	1.36091i
$241$			1.81806i			0.117111i	0.998284	+	0.0585557i	$0.0186495\pi$
$241$			1.81806i			0.117111i	−0.998284	+	0.0585557i	$0.981350\pi$
$242$	1.86113	+	2.09181i	0.119638	+	0.134467i
$243$			21.9433i			1.40766i
$244$	−19.4192	−	2.27422i	−1.24319	−	0.145592i
$245$		0			0
$246$	−6.48750	−	7.29160i	−0.413628	−	0.464896i
$247$	−2.70572			−0.172161
$248$	−4.42972	+	3.09949i	−0.281287	+	0.196818i
$249$	27.2529			1.72708
$250$	−6.41274	+	14.4526i	−0.405578	+	0.914061i
$251$	14.0187			0.884856			0.442428	−	0.896804i	$-0.354117\pi$
$251$	14.0187			0.884856			0.442428	+	0.896804i	$0.354117\pi$
$252$		0			0
$253$			9.13352i			0.574220i
$254$	8.25487	+	9.27803i	0.517957	+	0.582155i
$255$	−26.5159	−	33.7715i	−1.66049	−	2.11485i
$256$	14.2916	+	7.19367i	0.893228	+	0.449605i
$257$	−17.8725			−1.11485			−0.557427	−	0.830226i	$-0.688211\pi$
$257$	−17.8725			−1.11485			−0.557427	+	0.830226i	$0.688211\pi$
$258$	6.57491	−	5.84985i	0.409336	−	0.364196i
$259$		0			0
$260$	1.90977	+	3.12161i	0.118439	+	0.193594i
$261$	7.64248			0.473057
$262$	−12.5866	−	14.1466i	−0.777601	−	0.873982i
$263$	−21.8965			−1.35019			−0.675097	−	0.737729i	$-0.735898\pi$
$263$	−21.8965			−1.35019			−0.675097	+	0.737729i	$0.735898\pi$
$264$	−21.6762	+	15.1669i	−1.33408	+	0.933459i
$265$	−2.50079	−	3.18508i	−0.153622	−	0.195658i
$266$		0			0
$267$	27.5539			1.68627
$268$	−2.15471	+	18.3988i	−0.131620	+	1.12388i
$269$			2.88283i			0.175769i	0.996131	+	0.0878847i	$0.0280107\pi$
$269$			2.88283i			0.175769i	−0.996131	+	0.0878847i	$0.971989\pi$
$270$	1.07635	−	5.98073i	0.0655046	−	0.363975i
$271$	16.9559			1.02999			0.514997	−	0.857192i	$-0.327793\pi$
$271$	16.9559			1.02999			0.514997	+	0.857192i	$0.327793\pi$
$272$	−28.7846	−	6.83578i	−1.74532	−	0.414480i
$273$		0			0
$274$	−5.51963	+	4.91094i	−0.333453	+	0.296681i
$275$	−17.4994	−	4.27399i	−1.05525	−	0.257731i
$276$	−13.0741	−	1.53113i	−0.786968	−	0.0921632i
$277$		−	26.8515i		−	1.61335i	−0.590993	−	0.806677i	$-0.701264\pi$
$277$		−	26.8515i		−	1.61335i	0.590993	−	0.806677i	$-0.298736\pi$
$278$	−20.6285	−	23.1853i	−1.23722	−	1.39056i
$279$	7.14919			0.428011
$280$		0			0
$281$	24.9497			1.48838			0.744188	−	0.667971i	$-0.232837\pi$
$281$	24.9497			1.48838			0.744188	+	0.667971i	$0.232837\pi$
$282$	3.25750	+	3.66126i	0.193982	+	0.218025i
$283$		−	9.83821i		−	0.584821i	−0.956293	−	0.292410i	$-0.905543\pi$
$283$		−	9.83821i		−	0.584821i	0.956293	−	0.292410i	$-0.0944573\pi$
$284$	−2.74966	−	0.322017i	−0.163162	−	0.0191082i
$285$	11.8542	+	15.0979i	0.702183	+	0.894321i
$286$	−3.11481	+	2.77132i	−0.184183	+	0.163871i
$287$		0			0
$288$	−10.0309	−	18.6287i	−0.591079	−	1.09770i
$289$	37.7050			2.21794
$290$	6.35945	+	1.14451i	0.373440	+	0.0672079i
$291$		−	19.0042i		−	1.11405i
$292$	1.72062	−	14.6922i	0.100692	−	0.859793i
$293$	23.4039			1.36727			0.683636	−	0.729823i	$-0.260398\pi$
$293$	23.4039			1.36727			0.683636	+	0.729823i	$0.260398\pi$
$294$		0			0
$295$	3.36174	−	2.63950i	0.195728	−	0.153678i
$296$	−11.6219	−	16.6097i	−0.675507	−	0.965419i
$297$	6.92325			0.401728
$298$	22.5138	+	25.3043i	1.30419	+	1.46584i
$299$	−2.07447			−0.119970
$300$	9.05153	−	24.3329i	0.522591	−	1.40486i
$301$		0			0
$302$	7.40395	−	6.58746i	0.426049	−	0.379066i
$303$	−16.5062			−0.948257
$304$	12.8684	+	3.05600i	0.738055	+	0.175274i
$305$	13.4995	+	17.1934i	0.772980	+	0.984490i
$306$	26.0049	+	29.2281i	1.48660	+	1.67086i
$307$		−	2.18529i		−	0.124721i	−0.998054	−	0.0623606i	$-0.980137\pi$
$307$		−	2.18529i		−	0.124721i	0.998054	−	0.0623606i	$-0.0198629\pi$
$308$		0			0
$309$	−2.65350			−0.150952
$310$	5.94897	+	1.07064i	0.337879	+	0.0608080i
$311$	28.9001			1.63878			0.819388	−	0.573239i	$-0.194313\pi$
$311$	28.9001			1.63878			0.819388	+	0.573239i	$0.194313\pi$
$312$	−3.44481	−	4.92324i	−0.195024	−	0.278724i
$313$	−6.35304			−0.359095			−0.179548	−	0.983749i	$-0.557463\pi$
$313$	−6.35304			−0.359095			−0.179548	+	0.983749i	$0.557463\pi$
$314$	−6.04030	−	6.78897i	−0.340874	−	0.383124i
$315$		0			0
$316$	−15.3904	−	1.80240i	−0.865778	−	0.101393i
$317$			18.8031i			1.05609i	0.849218	+	0.528043i	$0.177074\pi$
$317$			18.8031i			1.05609i	−0.849218	+	0.528043i	$0.822926\pi$
$318$	4.41981	+	4.96763i	0.247851	+	0.278571i
$319$			7.36166i			0.412174i
$320$	−5.55718	−	17.0035i	−0.310656	−	0.950522i
$321$		−	18.8264i		−	1.05079i
$322$		0			0
$323$	−24.4564			−1.36079
$324$	1.44967	−	12.3786i	0.0805374	−	0.687697i
$325$	0.970738	−	3.97458i	0.0538469	−	0.220470i
$326$	−17.3711	−	19.5241i	−0.962095	−	1.08134i
$327$			20.6962i			1.14450i
$328$	4.31042	+	6.16035i	0.238003	+	0.340149i
$329$		0			0
$330$	29.1104	+	5.23900i	1.60248	+	0.288398i
$331$			13.0888i			0.719427i	0.933063	+	0.359713i	$0.117126\pi$
$331$			13.0888i			0.719427i	−0.933063	+	0.359713i	$0.882874\pi$
$332$	−20.8520	−	2.44202i	−1.14440	−	0.134023i
$333$			26.8066i			1.46899i
$334$	1.93238	−	1.71928i	0.105735	−	0.0940749i
$335$	16.2899	−	12.7901i	0.890010	−	0.698798i
$336$		0			0
$337$		−	11.7319i		−	0.639079i	−0.947573	−	0.319539i	$-0.896472\pi$
$337$		−	11.7319i		−	0.639079i	0.947573	−	0.319539i	$-0.103528\pi$
$338$	11.5911	+	13.0278i	0.630475	+	0.708619i
$339$	19.7728			1.07391
$340$	17.2621	+	28.2156i	0.936167	+	1.53021i
$341$			6.88650i			0.372925i
$342$	−11.6257	−	13.0667i	−0.628648	−	0.706566i
$343$		0			0
$344$	−5.55485	+	3.88675i	−0.299498	+	0.209560i
$345$	9.08861	+	11.5755i	0.489314	+	0.623205i
$346$	−14.3352	−	16.1120i	−0.770666	−	0.866187i
$347$	−4.41171			−0.236833			−0.118416	−	0.992964i	$-0.537782\pi$
$347$	−4.41171			−0.236833			−0.118416	+	0.992964i	$0.537782\pi$
$348$	−10.5378	−	1.23410i	−0.564884	−	0.0661545i
$349$			18.3479i			0.982142i	0.871120	+	0.491071i	$0.163394\pi$
$349$			18.3479i			0.982142i	−0.871120	+	0.491071i	$0.836606\pi$
$350$		0			0
$351$			1.57246i			0.0839316i
$352$	17.9442	−	9.66237i	0.956428	−	0.515006i
$353$	11.7481			0.625289			0.312645	−	0.949870i	$-0.398785\pi$
$353$	11.7481			0.625289			0.312645	+	0.949870i	$0.398785\pi$
$354$	−5.24316	+	4.66496i	−0.278671	+	0.247940i
$355$	1.91145	+	2.43449i	0.101449	+	0.129209i
$356$	−21.0824	−	2.46899i	−1.11736	−	0.130856i
$357$		0			0
$358$	−13.2459	+	11.7852i	−0.700070	+	0.622868i
$359$			0.197902i			0.0104449i	0.999986	+	0.00522243i	$0.00166236\pi$
$359$			0.197902i			0.0104449i	−0.999986	+	0.00522243i	$0.998338\pi$
$360$	−6.86940	+	22.6356i	−0.362049	+	1.19300i
$361$	−8.06652			−0.424554
$362$	−8.47190	+	7.53764i	−0.445273	+	0.396170i
$363$			5.14002i			0.269781i
$364$		0			0
$365$	−13.0081	+	10.2134i	−0.680876	+	0.534595i
$366$	−23.8586	−	26.8158i	−1.24711	−	1.40168i
$367$		−	7.52824i		−	0.392971i	−0.980507	−	0.196485i	$-0.937047\pi$
$367$		−	7.52824i		−	0.392971i	0.980507	−	0.196485i	$-0.0629528\pi$
$368$	9.86621	+	2.34303i	0.514312	+	0.122139i
$369$		−	9.94229i		−	0.517575i
$370$	−4.01446	+	22.3063i	−0.208702	+	1.15965i
$371$		0			0
$372$	−9.85761	−	1.15444i	−0.511093	−	0.0598550i
$373$			31.1392i			1.61233i	0.591693	+	0.806164i	$0.298460\pi$
$373$			31.1392i			1.61233i	−0.591693	+	0.806164i	$0.701540\pi$
$374$	−28.1541	+	25.0493i	−1.45581	+	1.29527i
$375$	−26.4311	+	11.9966i	−1.36490	+	0.619503i
$376$	−2.16435	−	3.09324i	−0.111618	−	0.159521i
$377$	−1.67203			−0.0861140
$378$		0			0
$379$		−	16.3396i		−	0.839307i	−0.907684	−	0.419654i	$-0.862152\pi$
$379$		−	16.3396i		−	0.839307i	0.907684	−	0.419654i	$-0.137848\pi$
$380$	−7.71717	−	12.6141i	−0.395883	−	0.647088i
$381$			22.7981i			1.16798i
$382$	−7.14168	+	6.35411i	−0.365400	+	0.325105i
$383$		−	8.84868i		−	0.452147i	−0.974110	−	0.226073i	$-0.927411\pi$
$383$		−	8.84868i		−	0.452147i	0.974110	−	0.226073i	$-0.0725889\pi$
$384$	10.8230	+	27.3058i	0.552307	+	1.39344i
$385$		0			0
$386$	2.49351	−	2.21853i	0.126916	−	0.112920i
$387$	8.96506			0.455720
$388$	−1.70289	+	14.5407i	−0.0864511	+	0.738194i
$389$	9.34528			0.473824			0.236912	−	0.971531i	$-0.423865\pi$
$389$	9.34528			0.473824			0.236912	+	0.971531i	$0.423865\pi$
$390$	−1.18992	+	6.61176i	−0.0602538	+	0.334800i
$391$	−18.7507			−0.948263
$392$		0			0
$393$		−	34.7612i		−	1.75347i
$394$	−21.4698	+	19.1022i	−1.08163	+	0.962353i
$395$	10.6988	+	13.6263i	0.538316	+	0.685615i
$396$	−26.7670	−	3.13473i	−1.34509	−	0.157526i
$397$	20.3026			1.01896			0.509480	−	0.860482i	$-0.329838\pi$
$397$	20.3026			1.01896			0.509480	+	0.860482i	$0.329838\pi$
$398$	10.7712	+	12.1063i	0.539912	+	0.606831i
$399$		0			0
$400$	−9.10598	+	17.8068i	−0.455299	+	0.890339i
$401$	−11.0867			−0.553643			−0.276821	−	0.960921i	$-0.589281\pi$
$401$	−11.0867			−0.553643			−0.276821	+	0.960921i	$0.589281\pi$
$402$	−25.4066	+	22.6048i	−1.26716	+	1.12742i
$403$	−1.56411			−0.0779138
$404$	12.6294	+	1.47905i	0.628338	+	0.0735857i
$405$	−10.9597	+	8.60509i	−0.544592	+	0.427590i
$406$		0			0
$407$	−25.8216			−1.27993
$408$	−31.1369	−	44.5002i	−1.54151	−	2.20309i
$409$			5.88680i			0.291084i	0.989352	+	0.145542i	$0.0464925\pi$
$409$			5.88680i			0.291084i	−0.989352	+	0.145542i	$0.953507\pi$
$410$	1.48892	−	8.27317i	0.0735325	−	0.408583i
$411$	−13.5629			−0.669008
$412$	2.03028	+	0.237769i	0.100025	+	0.0117140i
$413$		0			0
$414$	−8.91343	−	10.0182i	−0.438071	−	0.492369i
$415$	14.4955	+	18.4619i	0.711557	+	0.906261i
$416$	2.19458	+	4.07560i	0.107598	+	0.199823i
$417$		−	56.9712i		−	2.78989i
$418$	12.5866	−	11.1986i	0.615629	−	0.547739i
$419$	−16.7262			−0.817126			−0.408563	−	0.912730i	$-0.633970\pi$
$419$	−16.7262			−0.817126			−0.408563	+	0.912730i	$0.633970\pi$
$420$		0			0
$421$	−1.18823			−0.0579109			−0.0289555	−	0.999581i	$-0.509218\pi$
$421$	−1.18823			−0.0579109			−0.0289555	+	0.999581i	$0.509218\pi$
$422$	−23.3126	+	20.7418i	−1.13484	+	1.00969i
$423$			4.99222i			0.242730i
$424$	−2.93661	−	4.19693i	−0.142614	−	0.203821i
$425$	8.77430	−	35.9254i	0.425616	−	1.74264i
$426$	−3.37824	−	3.79696i	−0.163676	−	0.183963i
$427$		0			0
$428$	−1.68696	+	14.4047i	−0.0815421	+	0.696276i
$429$	−7.65374			−0.369526
$430$	7.46000	+	1.34257i	0.359753	+	0.0647447i
$431$			24.0950i			1.16061i	0.814398	+	0.580307i	$0.197068\pi$
$431$			24.0950i			1.16061i	−0.814398	+	0.580307i	$0.802932\pi$
$432$	1.77603	−	7.47863i	0.0854492	−	0.359816i
$433$	14.9805			0.719916			0.359958	−	0.932968i	$-0.382791\pi$
$433$	14.9805			0.719916			0.359958	+	0.932968i	$0.382791\pi$
$434$		0			0
$435$	7.32546	+	9.32992i	0.351229	+	0.447335i
$436$	1.85450	−	15.8353i	0.0888144	−	0.758373i
$437$	8.38268			0.400998
$438$	20.2882	−	18.0509i	0.969407	−	0.862503i
$439$	17.3253			0.826893			0.413446	−	0.910528i	$-0.364325\pi$
$439$	17.3253			0.826893			0.413446	+	0.910528i	$0.364325\pi$
$440$	−21.8039	−	6.61699i	−1.03946	−	0.315453i
$441$		0			0
$442$	−5.68938	−	6.39456i	−0.270616	−	0.304158i
$443$	−25.2325			−1.19883			−0.599416	−	0.800438i	$-0.704600\pi$
$443$	−25.2325			−1.19883			−0.599416	+	0.800438i	$0.704600\pi$
$444$	4.32870	−	36.9621i	0.205431	−	1.75415i
$445$	14.6557	+	18.6659i	0.694745	+	0.884848i
$446$	−24.9111	+	22.1640i	−1.17957	+	1.04949i
$447$			62.1779i			2.94091i
$448$		0			0
$449$	7.06145			0.333251			0.166625	−	0.986020i	$-0.446713\pi$
$449$	7.06145			0.333251			0.166625	+	0.986020i	$0.446713\pi$
$450$	23.3654	−	12.3897i	1.10146	−	0.584058i
$451$	9.57697			0.450962
$452$	−15.1288	−	1.77176i	−0.711599	−	0.0833365i
$453$	18.1931			0.854784
$454$	22.1103	−	19.6720i	1.03769	−	0.923255i
$455$		0			0
$456$	13.9201	+	19.8942i	0.651867	+	0.931633i
$457$		−	18.8816i		−	0.883242i	−0.897202	−	0.441621i	$-0.854404\pi$
$457$		−	18.8816i		−	0.883242i	0.897202	−	0.441621i	$-0.145596\pi$
$458$	−5.47461	+	4.87089i	−0.255812	+	0.227602i
$459$			14.2131i			0.663411i
$460$	−5.91674	−	9.67119i	−0.275870	−	0.450922i
$461$			34.6087i			1.61189i	0.591992	+	0.805944i	$0.298342\pi$
$461$			34.6087i			1.61189i	−0.591992	+	0.805944i	$0.701658\pi$
$462$		0			0
$463$	−15.0235			−0.698202			−0.349101	−	0.937085i	$-0.613513\pi$
$463$	−15.0235			−0.698202			−0.349101	+	0.937085i	$0.613513\pi$
$464$	7.95221	+	1.88849i	0.369172	+	0.0876711i
$465$	6.85263	+	8.72772i	0.317783	+	0.404738i
$466$	−21.9441	+	19.5241i	−1.01654	+	0.904439i
$467$			25.4391i			1.17718i	0.808432	+	0.588590i	$0.200317\pi$
$467$			25.4391i			1.17718i	−0.808432	+	0.588590i	$0.799683\pi$
$468$	0.711981	−	6.07950i	0.0329113	−	0.281025i
$469$		0			0
$470$	−0.747616	+	4.15412i	−0.0344850	+	0.191615i
$471$		−	16.6819i		−	0.768662i
$472$	4.42972	−	3.09949i	0.203894	−	0.142666i
$473$			8.63565i			0.397067i
$474$	−18.9087	−	21.2524i	−0.868507	−	0.976155i
$475$	−3.92264	+	16.0608i	−0.179983	+	0.736921i
$476$		0			0
$477$			6.77350i			0.310137i
$478$	22.3237	−	19.8619i	1.02106	−	0.908460i
$479$	−20.5688			−0.939811			−0.469905	−	0.882717i	$-0.655712\pi$
$479$	−20.5688			−0.939811			−0.469905	+	0.882717i	$0.655712\pi$
$480$	13.1270	−	30.1017i	0.599163	−	1.37395i
$481$		−	5.86479i		−	0.267411i
$482$	1.92089	−	1.70906i	0.0874939	−	0.0778453i
$483$		0			0
$484$	0.460576	−	3.93279i	0.0209353	−	0.178763i
$485$	12.8741	−	10.1082i	0.584581	−	0.458988i
$486$	23.1844	−	20.6277i	1.05167	−	0.935690i
$487$	29.0590			1.31679			0.658394	−	0.752674i	$-0.271236\pi$
$487$	29.0590			1.31679			0.658394	+	0.752674i	$0.271236\pi$
$488$	15.8521	+	22.6554i	0.717591	+	1.02556i
$489$		−	47.9749i		−	2.16950i
$490$		0			0
$491$		−	9.51815i		−	0.429548i	−0.976664	−	0.214774i	$-0.931098\pi$
$491$		−	9.51815i		−	0.429548i	0.976664	−	0.214774i	$-0.0689015\pi$
$492$	−1.60547	+	13.7089i	−0.0723801	+	0.618043i
$493$	−15.1131			−0.680662
$494$	2.54349	+	2.85875i	0.114437	+	0.128621i
$495$	18.6074	+	23.6989i	0.836339	+	1.06519i
$496$	7.43893	+	1.76660i	0.334018	+	0.0793226i
$497$		0			0
$498$	−25.6189	−	28.7943i	−1.14801	−	1.29030i
$499$		−	20.1905i		−	0.903853i	−0.892055	−	0.451927i	$-0.850737\pi$
$499$		−	20.1905i		−	0.903853i	0.892055	−	0.451927i	$-0.149263\pi$
$500$	21.2983	−	6.81061i	0.952487	−	0.304580i
$501$	4.74826			0.212137
$502$	−13.1782	−	14.8116i	−0.588174	−	0.661076i
$503$		−	13.3134i		−	0.593616i	−0.954937	−	0.296808i	$-0.904078\pi$
$503$		−	13.3134i		−	0.593616i	0.954937	−	0.296808i	$-0.0959221\pi$
$504$		0			0
$505$	−8.77949	−	11.1818i	−0.390682	−	0.497585i
$506$	9.65011	−	8.58592i	0.429000	−	0.381691i
$507$			32.0121i			1.42171i
$508$	2.04284	−	17.4435i	0.0906363	−	0.773931i
$509$		−	14.3523i		−	0.636153i	−0.948065	−	0.318077i	$-0.896963\pi$
$509$		−	14.3523i		−	0.636153i	0.948065	−	0.318077i	$-0.103037\pi$
$510$	−10.7554	+	59.7624i	−0.476258	+	2.64632i
$511$		0			0
$512$	−5.83424	−	21.8623i	−0.257839	−	0.966188i
$513$		−	6.35411i		−	0.280541i
$514$	16.8009	+	18.8833i	0.741057	+	0.832908i
$515$	−1.41137	−	1.79756i	−0.0621924	−	0.0792101i
$516$	−12.3614	−	1.44767i	−0.544181	−	0.0637299i
$517$	−4.80879			−0.211490
$518$		0			0
$519$		−	39.5906i		−	1.73783i
$520$	1.50290	−	4.95225i	0.0659064	−	0.217170i
$521$		−	36.9009i		−	1.61666i	−0.588730	−	0.808330i	$-0.700372\pi$
$521$		−	36.9009i		−	1.61666i	0.588730	−	0.808330i	$-0.299628\pi$
$522$	−7.18427	−	8.07473i	−0.314447	−	0.353421i
$523$		−	18.1502i		−	0.793652i	−0.917894	−	0.396826i	$-0.870112\pi$
$523$		−	18.1502i		−	0.793652i	0.917894	−	0.396826i	$-0.129888\pi$
$524$	−3.11481	+	26.5969i	−0.136071	+	1.16189i
$525$		0			0
$526$	20.5837	+	23.1349i	0.897490	+	1.00873i
$527$	−14.1377			−0.615846
$528$	36.4013	+	8.64460i	1.58416	+	0.376208i
$529$	−16.5730			−0.720566
$530$	−1.01437	+	5.63635i	−0.0440616	+	0.244828i
$531$	−7.14919			−0.310248
$532$		0			0
$533$			2.17519i			0.0942178i
$534$	−25.9019	−	29.1124i	−1.12089	−	1.25981i
$535$	12.7536	−	10.0136i	0.551386	−	0.432924i
$536$	21.4649	−	15.0191i	0.927142	−	0.648725i
$537$	−32.5481			−1.40455
$538$	3.04588	−	2.70999i	0.131317	−	0.116836i
$539$		0			0
$540$	−7.33081	+	4.48492i	−0.315468	+	0.193000i
$541$	−18.7526			−0.806236			−0.403118	−	0.915148i	$-0.632074\pi$
$541$	−18.7526			−0.806236			−0.403118	+	0.915148i	$0.632074\pi$
$542$	−15.9393	−	17.9149i	−0.684649	−	0.769509i
$543$	−20.8172			−0.893353
$544$	19.8364	+	36.8385i	0.850478	+	1.57944i
$545$	−14.0202	+	11.0081i	−0.600561	+	0.471535i
$546$		0			0
$547$	34.1580			1.46049			0.730246	−	0.683185i	$-0.239406\pi$
$547$	34.1580			1.46049			0.730246	+	0.683185i	$0.239406\pi$
$548$	10.3774	+	1.21531i	0.443300	+	0.0519157i
$549$		−	36.5640i		−	1.56051i
$550$	11.9345	+	22.5069i	0.508888	+	0.959697i
$551$	6.75648			0.287836
$552$	10.6725	+	15.2529i	0.454252	+	0.649206i
$553$		0			0
$554$	−28.3702	+	25.2416i	−1.20534	+	1.07241i
$555$	−32.7255	+	25.6947i	−1.38912	+	1.09068i
$556$	−5.10495	+	43.5905i	−0.216498	+	1.84865i
$557$			40.4367i			1.71336i	0.515851	+	0.856679i	$0.327476\pi$
$557$			40.4367i			1.71336i	−0.515851	+	0.856679i	$0.672524\pi$
$558$	−6.72055	−	7.55354i	−0.284504	−	0.319767i
$559$	−1.96139			−0.0829579
$560$		0			0
$561$	−69.1805			−2.92080
$562$	−23.4538	−	26.3608i	−0.989340	−	1.11197i
$563$		−	0.318930i		−	0.0134413i	−0.999977	−	0.00672065i	$-0.997861\pi$
$563$		−	0.318930i		−	0.0134413i	0.999977	−	0.00672065i	$-0.00213926\pi$
$564$	0.806137	−	6.88349i	0.0339445	−	0.289847i
$565$	10.5170	+	13.3947i	0.442452	+	0.563520i
$566$	−10.3946	+	9.24835i	−0.436920	+	0.388737i
$567$		0			0
$568$	2.24457	+	3.20788i	0.0941800	+	0.134600i
$569$	30.6115			1.28330			0.641651	−	0.766997i	$-0.278250\pi$
$569$	30.6115			1.28330			0.641651	+	0.766997i	$0.278250\pi$
$570$	4.80832	−	26.7174i	0.201398	−	1.11907i
$571$			8.48799i			0.355211i	0.984102	+	0.177606i	$0.0568351\pi$
$571$			8.48799i			0.355211i	−0.984102	+	0.177606i	$0.943165\pi$
$572$	5.85612	+	0.685820i	0.244857	+	0.0286756i
$573$	−17.5486			−0.733103
$574$		0			0
$575$	−3.00748	+	12.3138i	−0.125421	+	0.513521i
$576$	−10.2528	+	28.1101i	−0.427198	+	1.17125i
$577$	3.36502			0.140088			0.0700438	−	0.997544i	$-0.477686\pi$
$577$	3.36502			0.140088			0.0700438	+	0.997544i	$0.477686\pi$
$578$	−35.4444	−	39.8376i	−1.47429	−	1.65702i
$579$	6.12707			0.254632
$580$	−4.76892	−	7.79502i	−0.198019	−	0.323671i
$581$		0			0
$582$	−20.0791	+	17.8648i	−0.832305	+	0.740520i
$583$	−6.52461			−0.270222
$584$	−17.1406	+	11.9933i	−0.709283	+	0.496288i
$585$	−5.38266	+	4.22624i	−0.222546	+	0.174733i
$586$	−22.0007	−	24.7276i	−0.908842	−	1.02149i
$587$		−	2.02359i		−	0.0835225i	−0.999128	−	0.0417613i	$-0.986703\pi$
$587$		−	2.02359i		−	0.0835225i	0.999128	−	0.0417613i	$-0.0132969\pi$
$588$		0			0
$589$	6.32038			0.260427
$590$	−5.94897	−	1.07064i	−0.244915	−	0.0440774i
$591$	−52.7558			−2.17008
$592$	−6.62405	+	27.8930i	−0.272247	+	1.14640i
$593$	26.8258			1.10160			0.550802	−	0.834636i	$-0.314322\pi$
$593$	26.8258			1.10160			0.550802	+	0.834636i	$0.314322\pi$
$594$	−6.50817	−	7.31483i	−0.267033	−	0.300131i
$595$		0			0
$596$	5.57151	−	47.5743i	0.228218	−	1.94872i
$597$			29.7476i			1.21749i
$598$	1.95009	+	2.19180i	0.0797452	+	0.0896293i
$599$			37.0618i			1.51430i	0.653239	+	0.757152i	$0.273410\pi$
$599$			37.0618i			1.51430i	−0.653239	+	0.757152i	$0.726590\pi$
$600$	−34.2179	+	13.3105i	−1.39694	+	0.543398i
$601$			1.27911i			0.0521761i	0.999660	+	0.0260880i	$0.00830503\pi$
$601$			1.27911i			0.0521761i	−0.999660	+	0.0260880i	$0.991695\pi$
$602$		0			0
$603$	−34.6425			−1.41075
$604$	−13.9201	−	1.63020i	−0.566400	−	0.0663320i
$605$	−3.48201	+	2.73392i	−0.141564	+	0.111150i
$606$	15.5166	+	17.4398i	0.630318	+	0.708443i
$607$		−	22.6090i		−	0.917672i	−0.888521	−	0.458836i	$-0.848267\pi$
$607$		−	22.6090i		−	0.917672i	0.888521	−	0.458836i	$-0.151733\pi$
$608$	−8.86805	−	16.4690i	−0.359647	−	0.667907i
$609$		0			0
$610$	5.47568	−	30.4256i	0.221704	−	1.23190i
$611$		−	1.09220i		−	0.0441859i
$612$	6.43545	−	54.9514i	0.260138	−	2.22128i
$613$			3.01945i			0.121955i	0.998139	+	0.0609773i	$0.0194217\pi$
$613$			3.01945i			0.121955i	−0.998139	+	0.0609773i	$0.980578\pi$
$614$	−2.30889	+	2.05427i	−0.0931792	+	0.0829037i
$615$	12.1375	−	9.52987i	0.489432	−	0.384281i
$616$		0			0
$617$			14.3344i			0.577081i	0.957468	+	0.288540i	$0.0931700\pi$
$617$			14.3344i			0.577081i	−0.957468	+	0.288540i	$0.906830\pi$
$618$	2.49441	+	2.80358i	0.100340	+	0.112776i
$619$	−21.7973			−0.876109			−0.438055	−	0.898948i	$-0.644332\pi$
$619$	−21.7973			−0.876109			−0.438055	+	0.898948i	$0.644332\pi$
$620$	−4.46111	−	7.29189i	−0.179162	−	0.292849i
$621$		−	4.87169i		−	0.195494i
$622$	−27.1674	−	30.5347i	−1.08931	−	1.22433i
$623$		0			0
$624$	−1.96342	+	8.26771i	−0.0785997	+	0.330973i
$625$	−22.1853	−	11.5244i	−0.887413	−	0.460975i
$626$	5.97214	+	6.71236i	0.238695	+	0.268280i
$627$	30.9278			1.23514
$628$	−1.49480	+	12.7639i	−0.0596489	+	0.509333i
$629$		−	53.0106i		−	2.11367i
$630$		0			0
$631$			15.1512i			0.603160i	0.953441	+	0.301580i	$0.0975140\pi$
$631$			15.1512i			0.603160i	−0.953441	+	0.301580i	$0.902486\pi$
$632$	12.5633	+	17.9552i	0.499742	+	0.714220i
$633$	−57.2841			−2.27684
$634$	19.8665	−	17.6757i	0.789001	−	0.701992i
$635$	−15.4441	+	12.1261i	−0.612881	+	0.481208i
$636$	1.09378	−	9.33959i	0.0433710	−	0.370339i
$637$		0			0
$638$	7.77803	−	6.92029i	0.307935	−	0.273977i
$639$		−	5.17725i		−	0.204809i
$640$	−12.7412	+	21.8555i	−0.503639	+	0.863914i
$641$	29.9921			1.18462			0.592308	−	0.805712i	$-0.298217\pi$
$641$	29.9921			1.18462			0.592308	+	0.805712i	$0.298217\pi$
$642$	−19.8912	+	17.6976i	−0.785043	+	0.698470i
$643$		−	1.63196i		−	0.0643583i	−0.999482	−	0.0321792i	$-0.989755\pi$
$643$		−	1.63196i		−	0.0643583i	0.999482	−	0.0321792i	$-0.0102447\pi$
$644$		0			0
$645$	8.59318	+	10.9445i	0.338356	+	0.430940i
$646$	22.9901	+	25.8396i	0.904534	+	1.01665i
$647$			32.7664i			1.28818i	0.764950	+	0.644090i	$0.222764\pi$
$647$			32.7664i			1.28818i	−0.764950	+	0.644090i	$0.777236\pi$
$648$	−14.4414	+	10.1047i	−0.567313	+	0.396951i
$649$		−	6.88650i		−	0.270319i
$650$	−5.11192	+	2.71064i	−0.200506	+	0.106320i
$651$		0			0
$652$	−4.29883	+	36.7071i	−0.168355	+	1.43756i
$653$			22.5293i			0.881638i	0.897596	+	0.440819i	$0.145312\pi$
$653$			22.5293i			0.881638i	−0.897596	+	0.440819i	$0.854688\pi$
$654$	21.8667	−	19.4553i	0.855057	−	0.760763i
$655$	23.5483	−	18.4891i	0.920109	−	0.722431i
$656$	2.45679	−	10.3452i	0.0959215	−	0.403913i
$657$	27.6635			1.07925
$658$		0			0
$659$		−	19.2525i		−	0.749969i	−0.927031	−	0.374985i	$-0.877648\pi$
$659$		−	19.2525i		−	0.749969i	0.927031	−	0.374985i	$-0.122352\pi$
$660$	−21.8298	−	35.6818i	−0.849723	−	1.38891i
$661$			34.7656i			1.35223i	0.736798	+	0.676113i	$0.236337\pi$
$661$			34.7656i			1.35223i	−0.736798	+	0.676113i	$0.763663\pi$
$662$	13.8291	−	12.3041i	0.537484	−	0.478212i
$663$		−	15.7128i		−	0.610233i
$664$	17.0217	+	24.3270i	0.660570	+	0.944071i
$665$		0			0
$666$	28.3228	−	25.1994i	1.09749	−	0.976458i
$667$	5.18018			0.200577
$668$	−3.63304	−	0.425472i	−0.140567	−	0.0164620i
$669$	−61.2118			−2.36658
$670$	−28.8267	−	5.18793i	−1.11367	−	0.200427i
$671$	35.2205			1.35967
$672$		0			0
$673$			42.6368i			1.64353i	0.569827	+	0.821764i	$0.307010\pi$
$673$			42.6368i			1.64353i	−0.569827	+	0.821764i	$0.692990\pi$
$674$	−12.3955	+	11.0285i	−0.477456	+	0.424803i
$675$	9.33392	+	2.27968i	0.359263	+	0.0877451i
$676$	2.86847	−	24.4934i	0.110326	−	0.942055i
$677$	−1.78530			−0.0686145			−0.0343073	−	0.999411i	$-0.510922\pi$
$677$	−1.78530			−0.0686145			−0.0343073	+	0.999411i	$0.510922\pi$
$678$	−18.5873	−	20.8911i	−0.713842	−	0.802319i
$679$		0			0
$680$	13.5844	−	44.7623i	0.520937	−	1.71656i
$681$	54.3297			2.08192
$682$	7.27599	−	6.47361i	0.278612	−	0.247887i
$683$	8.60526			0.329271			0.164636	−	0.986354i	$-0.447355\pi$
$683$	8.60526			0.329271			0.164636	+	0.986354i	$0.447355\pi$
$684$	−2.87703	+	24.5666i	−0.110006	+	0.939326i
$685$	−7.21396	−	9.18792i	−0.275631	−	0.351052i
$686$		0			0
$687$	−13.4523			−0.513236
$688$	9.32839	+	2.21531i	0.355642	+	0.0844579i
$689$		−	1.48191i		−	0.0564564i
$690$	3.68653	−	20.4841i	0.140344	−	0.779818i
$691$	40.3022			1.53317			0.766583	−	0.642145i	$-0.221955\pi$
$691$	40.3022			1.53317			0.766583	+	0.642145i	$0.221955\pi$
$692$	−3.54755	+	30.2920i	−0.134858	+	1.15153i
$693$		0			0
$694$	4.14720	+	4.66123i	0.157426	+	0.176938i
$695$	38.5941	−	30.3024i	1.46396	−	1.14944i
$696$	8.60208	+	12.2939i	0.326061	+	0.465999i
$697$			19.6611i			0.744716i
$698$	19.3857	−	17.2479i	0.733758	−	0.652841i
$699$	−53.9212			−2.03949
$700$		0			0
$701$	37.3051			1.40899			0.704497	−	0.709707i	$-0.251172\pi$
$701$	37.3051			1.40899			0.704497	+	0.709707i	$0.251172\pi$
$702$	1.66139	−	1.47818i	0.0627053	−	0.0557903i
$703$			23.6989i			0.893822i
$704$	−27.0772	−	9.87602i	−1.02051	−	0.372217i
$705$	−6.09449	+	4.78514i	−0.229532	+	0.180219i
$706$	−11.0438	−	12.4126i	−0.415637	−	0.467154i
$707$		0			0
$708$	9.85761	+	1.15444i	0.370472	+	0.0433866i
$709$	−8.05731			−0.302599			−0.151299	−	0.988488i	$-0.548346\pi$
$709$	−8.05731			−0.302599			−0.151299	+	0.988488i	$0.548346\pi$
$710$	0.775326	−	4.30809i	0.0290975	−	0.161680i
$711$		−	28.9782i		−	1.08677i
$712$	17.2097	+	24.5957i	0.644962	+	0.921765i
$713$	4.84582			0.181477
$714$		0			0
$715$	−4.07095	−	5.18488i	−0.152245	−	0.193903i
$716$	24.9035	+	2.91650i	0.930689	+	0.108995i
$717$	54.8539			2.04856
$718$	0.209095	−	0.186037i	0.00780336	−	0.00694283i
$719$	−11.7448			−0.438008			−0.219004	−	0.975724i	$-0.570281\pi$
$719$	−11.7448			−0.438008			−0.219004	+	0.975724i	$0.570281\pi$
$720$	30.3734	−	14.0205i	1.13195	−	0.522515i
$721$		0			0
$722$	7.58289	+	8.52275i	0.282206	+	0.317184i
$723$	4.72002			0.175539
$724$	15.9279	+	1.86535i	0.591957	+	0.0693250i
$725$	−2.42404	+	9.92498i	−0.0900267	+	0.368605i
$726$	5.43073	−	4.83185i	0.201553	−	0.179327i
$727$			33.3549i			1.23706i	0.785760	+	0.618532i	$0.212272\pi$
$727$			33.3549i			1.23706i	−0.785760	+	0.618532i	$0.787728\pi$
$728$		0			0
$729$	38.2742			1.41756
$730$	23.0193	+	4.14278i	0.851982	+	0.153331i
$731$	−17.7286			−0.655715
$732$	−5.90430	+	50.4160i	−0.218229	+	1.86343i
$733$	−11.5001			−0.424764			−0.212382	−	0.977187i	$-0.568122\pi$
$733$	−11.5001			−0.424764			−0.212382	+	0.977187i	$0.568122\pi$
$734$	−7.95403	+	7.07688i	−0.293588	+	0.261212i
$735$		0			0
$736$	−6.79912	−	12.6268i	−0.250619	−	0.465429i
$737$		−	33.3696i		−	1.22919i
$738$	−10.5046	+	9.34619i	−0.386680	+	0.344038i
$739$		−	11.2041i		−	0.412148i	−0.978536	−	0.206074i	$-0.933931\pi$
$739$		−	11.2041i		−	0.412148i	0.978536	−	0.206074i	$-0.0660688\pi$
$740$	27.3417	−	16.7274i	1.00510	−	0.614911i
$741$			7.02455i			0.258053i
$742$		0			0
$743$	43.7950			1.60668			0.803341	−	0.595520i	$-0.203054\pi$
$743$	43.7950			1.60668			0.803341	+	0.595520i	$0.203054\pi$
$744$	8.04686	+	11.5004i	0.295012	+	0.421624i
$745$	−42.1213	+	33.0718i	−1.54320	+	1.21166i
$746$	32.9004	−	29.2722i	1.20457	−	1.07173i
$747$		−	39.2617i		−	1.43651i
$748$	52.9322	+	6.19898i	1.93539	+	0.226657i
$749$		0			0
$750$	37.5216	+	16.6487i	1.37009	+	0.607924i
$751$			51.4214i			1.87639i	0.346103	+	0.938196i	$0.387505\pi$
$751$			51.4214i			1.87639i	−0.346103	+	0.938196i	$0.612495\pi$
$752$	−1.23360	+	5.19454i	−0.0449848	+	0.189425i
$753$		−	36.3953i		−	1.32632i
$754$	1.57178	+	1.76660i	0.0572410	+	0.0643357i
$755$	9.67670	+	12.3245i	0.352171	+	0.448536i
$756$		0			0
$757$		−	18.1453i		−	0.659502i	−0.944068	−	0.329751i	$-0.893035\pi$
$757$		−	18.1453i		−	0.659502i	0.944068	−	0.329751i	$-0.106965\pi$
$758$	−17.2637	+	15.3599i	−0.627046	+	0.557897i
$759$	23.7123			0.860703
$760$	−6.07303	+	20.0114i	−0.220292	+	0.725891i
$761$			32.8928i			1.19236i	0.802850	+	0.596181i	$0.203316\pi$
$761$			32.8928i			1.19236i	−0.802850	+	0.596181i	$0.796684\pi$
$762$	24.0875	−	21.4312i	0.872598	−	0.776370i
$763$		0			0
$764$	13.4270	+	1.57246i	0.485771	+	0.0568895i
$765$	−48.6528	+	38.2001i	−1.75904	+	1.38113i
$766$	−9.34915	+	8.31815i	−0.337799	+	0.300547i
$767$	1.56411			0.0564767
$768$	18.6761	−	37.1038i	0.673916	−	1.33887i
$769$			20.8502i			0.751876i	0.926645	+	0.375938i	$0.122679\pi$
$769$			20.8502i			0.751876i	−0.926645	+	0.375938i	$0.877321\pi$
$770$		0			0
$771$			46.4003i			1.67107i
$772$	−4.68802	−	0.549021i	−0.168725	−	0.0197597i
$773$	8.68759			0.312471			0.156236	−	0.987720i	$-0.450064\pi$
$773$	8.68759			0.312471			0.156236	+	0.987720i	$0.450064\pi$
$774$	−8.42756	−	9.47212i	−0.302922	−	0.340468i
$775$	−2.26758	+	9.28437i	−0.0814539	+	0.333504i
$776$	16.9639	−	11.8697i	0.608970	−	0.426099i
$777$		0			0
$778$	−8.78497	−	9.87384i	−0.314957	−	0.353994i
$779$		−	8.78967i		−	0.314923i
$780$	8.10429	−	4.95813i	0.290180	−	0.177530i
$781$	4.98702			0.178449
$782$	17.6265	+	19.8112i	0.630322	+	0.708447i
$783$		−	3.92660i		−	0.140325i
$784$		0			0
$785$	11.3008	−	8.87294i	0.403344	−	0.316689i
$786$	−36.7273	+	32.6771i	−1.31002	+	1.16555i
$787$		−	37.2125i		−	1.32648i	−0.748406	−	0.663241i	$-0.769180\pi$
$787$		−	37.2125i		−	1.32648i	0.748406	−	0.663241i	$-0.230820\pi$
$788$	40.3651	+	4.72723i	1.43795	+	0.168400i
$789$			56.8473i			2.02382i
$790$	4.33966	−	24.1133i	0.154398	−	0.857912i
$791$		0			0
$792$	21.8501	+	31.2277i	0.776411	+	1.10963i
$793$			7.99951i			0.284071i
$794$	−19.0854	−	21.4509i	−0.677315	−	0.761265i
$795$	−8.26907	+	6.49252i	−0.293274	+	0.230266i
$796$	2.66556	−	22.7608i	0.0944782	−	0.806736i
$797$	21.3900			0.757671			0.378835	−	0.925464i	$-0.376325\pi$
$797$	21.3900			0.757671			0.378835	+	0.925464i	$0.376325\pi$
$798$		0			0
$799$		−	9.87221i		−	0.349254i
$800$	27.3739	−	7.11815i	0.967815	−	0.251664i
$801$		−	39.6955i		−	1.40257i
$802$	10.4220	+	11.7137i	0.368013	+	0.413626i
$803$			26.6470i			0.940352i
$804$	47.7666	+	5.59403i	1.68460	+	0.197286i
$805$		0			0
$806$	1.47033	+	1.65257i	0.0517902	+	0.0582094i
$807$	7.48437			0.263462
$808$	−10.3095	−	14.7341i	−0.362687	−	0.518344i
$809$	24.3414			0.855799			0.427900	−	0.903826i	$-0.359254\pi$
$809$	24.3414			0.855799			0.427900	+	0.903826i	$0.359254\pi$
$810$	19.3944	+	3.49041i	0.681449	+	0.122640i
$811$	31.3778			1.10183			0.550913	−	0.834563i	$-0.314280\pi$
$811$	31.3778			1.10183			0.550913	+	0.834563i	$0.314280\pi$
$812$		0			0
$813$		−	44.0206i		−	1.54387i
$814$	24.2735	+	27.2821i	0.850785	+	0.956237i
$815$	32.4997	−	25.5174i	1.13841	−	0.893834i
$816$	−17.7469	+	74.7301i	−0.621267	+	2.61608i
$817$	7.92573			0.277286
$818$	6.21976	−	5.53386i	0.217469	−	0.193487i
$819$		0			0
$820$	−10.1407	+	6.20401i	−0.354130	+	0.216653i
$821$	0.157136			0.00548409			0.00274204	−	0.999996i	$-0.499127\pi$
$821$	0.157136			0.00548409			0.00274204	+	0.999996i	$0.499127\pi$
$822$	12.7497	+	14.3300i	0.444697	+	0.499816i
$823$	18.6951			0.651669			0.325835	−	0.945427i	$-0.394355\pi$
$823$	18.6951			0.651669			0.325835	+	0.945427i	$0.394355\pi$
$824$	−1.65733	−	2.36862i	−0.0577359	−	0.0825148i
$825$	−11.0961	+	45.4317i	−0.386316	+	1.58173i
$826$		0			0
$827$	35.2960			1.22736			0.613681	−	0.789554i	$-0.289688\pi$
$827$	35.2960			1.22736			0.613681	+	0.789554i	$0.289688\pi$
$828$	−2.20581	+	18.8351i	−0.0766574	+	0.654566i
$829$		−	16.4649i		−	0.571850i	−0.958252	−	0.285925i	$-0.907699\pi$
$829$		−	16.4649i		−	0.571850i	0.958252	−	0.285925i	$-0.0923008\pi$
$830$	5.87969	−	32.6704i	0.204087	−	1.13401i
$831$	−69.7116			−2.41827
$832$	2.24311	−	6.14996i	0.0777659	−	0.213211i
$833$		0			0
$834$	−60.1934	+	53.5555i	−2.08433	+	1.85447i
$835$	2.52555	+	3.21662i	0.0874003	+	0.111316i
$836$	−23.6639	−	2.77132i	−0.818432	−	0.0958480i
$837$		−	3.67316i		−	0.126963i
$838$	15.7233	+	17.6722i	0.543153	+	0.610475i
$839$	−54.8000			−1.89191			−0.945953	−	0.324303i	$-0.894870\pi$
$839$	−54.8000			−1.89191			−0.945953	+	0.324303i	$0.894870\pi$
$840$		0			0
$841$	−24.8248			−0.856026
$842$	1.11699	+	1.25544i	0.0384941	+	0.0432652i
$843$		−	64.7741i		−	2.23094i
$844$	43.8298	+	5.13299i	1.50869	+	0.176685i
$845$	−21.6860	+	17.0269i	−0.746020	+	0.585743i
$846$	5.27458	−	4.69291i	0.181344	−	0.161346i
$847$		0			0
$848$	−1.67376	+	7.04801i	−0.0574773	+	0.242030i
$849$	−25.5418			−0.876593
$850$	−46.2056	+	24.5009i	−1.58484	+	0.840375i
$851$			18.1699i			0.622857i
$852$	−0.836015	+	7.13862i	−0.0286414	+	0.244565i
$853$	−38.9225			−1.33268			−0.666340	−	0.745648i	$-0.732140\pi$
$853$	−38.9225			−1.33268			−0.666340	+	0.745648i	$0.732140\pi$
$854$		0			0
$855$	21.7507	−	17.0777i	0.743858	−	0.584046i
$856$	16.8052	−	11.7587i	0.574390	−	0.401903i
$857$	29.3531			1.00268			0.501342	−	0.865249i	$-0.332840\pi$
$857$	29.3531			1.00268			0.501342	+	0.865249i	$0.332840\pi$
$858$	7.19485	+	8.08663i	0.245628	+	0.276073i
$859$	−47.3747			−1.61640			−0.808202	−	0.588905i	$-0.799559\pi$
$859$	−47.3747			−1.61640			−0.808202	+	0.588905i	$0.799559\pi$
$860$	−5.59422	−	9.14400i	−0.190761	−	0.311808i
$861$		0			0
$862$	25.4578	−	22.6504i	0.867095	−	0.771474i
$863$	23.7011			0.806794			0.403397	−	0.915025i	$-0.367829\pi$
$863$	23.7011			0.806794			0.403397	+	0.915025i	$0.367829\pi$
$864$	−9.57116	+	5.15377i	−0.325617	+	0.175335i
$865$	26.8199	−	21.0578i	0.911903	−	0.715988i
$866$	−14.0823	−	15.8278i	−0.478537	−	0.537849i
$867$		−	97.8892i		−	3.32449i
$868$		0			0
$869$	27.9134			0.946897
$870$	2.97136	−	16.5103i	0.100738	−	0.559752i
$871$	7.57913			0.256809
$872$	−18.4742	+	12.9265i	−0.625616	+	0.437746i
$873$	−27.3784			−0.926617
$874$	−7.88009	−	8.85680i	−0.266548	−	0.299586i
$875$		0			0
$876$	−38.1436	−	4.46706i	−1.28875	−	0.150928i
$877$		−	33.2040i		−	1.12122i	−0.828080	−	0.560610i	$-0.810567\pi$
$877$		−	33.2040i		−	1.12122i	0.828080	−	0.560610i	$-0.189433\pi$
$878$	−16.2866	−	18.3052i	−0.549645	−	0.617772i
$879$		−	60.7610i		−	2.04942i
$880$	13.5054	+	29.2573i	0.455266	+	0.986265i
$881$		−	19.2043i		−	0.647008i	−0.946227	−	0.323504i	$-0.895139\pi$
$881$		−	19.2043i		−	0.647008i	0.946227	−	0.323504i	$-0.104861\pi$
$882$		0			0
$883$	−8.57526			−0.288581			−0.144290	−	0.989535i	$-0.546090\pi$
$883$	−8.57526			−0.288581			−0.144290	+	0.989535i	$0.546090\pi$
$884$	−1.40796	+	12.0223i	−0.0473547	+	0.404355i
$885$	−6.85263	−	8.72772i	−0.230349	−	0.293379i
$886$	23.7196	+	26.6596i	0.796877	+	0.895647i
$887$			14.7509i			0.495285i	0.968851	+	0.247643i	$0.0796559\pi$
$887$			14.7509i			0.495285i	−0.968851	+	0.247643i	$0.920344\pi$
$888$	−43.1219	+	30.1725i	−1.44707	+	1.01252i
$889$		0			0
$890$	5.94464	−	33.0313i	0.199265	−	1.10721i
$891$			22.4508i			0.752131i
$892$	46.8351	+	5.48493i	1.56815	+	0.183649i
$893$			4.41347i			0.147691i
$894$	65.6946	−	58.4500i	2.19716	−	1.95486i
$895$	−17.3120	−	22.0491i	−0.578676	−	0.737019i
$896$		0			0
$897$			5.38571i			0.179824i
$898$	−6.63808	−	7.46084i	−0.221516	−	0.248972i
$899$	3.90575			0.130264
$900$	−35.0550	−	13.0401i	−1.16850	−	0.434668i
$901$		−	13.3947i		−	0.446243i
$902$	−9.00277	−	10.1186i	−0.299760	−	0.336914i
$903$		0			0
$904$	12.3498	+	17.6500i	0.410747	+	0.587030i
$905$	−11.0725	−	14.1022i	−0.368062	−	0.468774i
$906$	−17.1023	−	19.2220i	−0.568185	−	0.638609i
$907$	−47.5891			−1.58017			−0.790085	−	0.612997i	$-0.789964\pi$
$907$	−47.5891			−1.58017			−0.790085	+	0.612997i	$0.789964\pi$
$908$	−41.5693	−	4.86826i	−1.37953	−	0.161559i
$909$			23.7796i			0.788720i
$910$		0			0
$911$			34.7074i			1.14991i	0.818186	+	0.574954i	$0.194980\pi$
$911$			34.7074i			1.14991i	−0.818186	+	0.574954i	$0.805020\pi$
$912$	7.93395	−	33.4089i	0.262719	−	1.10628i
$913$	37.8191			1.25163
$914$	−19.9495	+	17.7495i	−0.659870	+	0.587101i
$915$	44.6372	−	35.0472i	1.47566	−	1.15863i
$916$	10.2928	+	1.20540i	0.340082	+	0.0398276i
$917$		0			0
$918$	15.0170	−	13.3610i	0.495635	−	0.440977i
$919$		−	51.8772i		−	1.71127i	−0.517579	−	0.855635i	$-0.673167\pi$
$919$		−	51.8772i		−	1.71127i	0.517579	−	0.855635i	$-0.326833\pi$
$920$	−4.65618	+	15.3427i	−0.153510	+	0.505835i
$921$	−5.67343			−0.186946
$922$	36.5661	−	32.5337i	1.20424	−	1.07144i
$923$			1.13269i			0.0372828i
$924$		0			0
$925$	−34.8127	−	8.50253i	−1.14463	−	0.279562i
$926$	14.1228	+	15.8732i	0.464103	+	0.521627i
$927$			3.82275i			0.125556i
$928$	−5.48012	−	10.1772i	−0.179894	−	0.334084i
$929$		−	43.7860i		−	1.43657i	−0.695748	−	0.718286i	$-0.744927\pi$
$929$		−	43.7860i		−	1.43657i	0.695748	−	0.718286i	$-0.255073\pi$
$930$	2.77957	−	15.4446i	0.0911457	−	0.506450i
$931$		0			0
$932$	41.2568	+	4.83166i	1.35141	+	0.158266i
$933$		−	75.0301i		−	2.45638i
$934$	26.8779	−	23.9138i	0.879471	−	0.782485i
$935$	−36.7964	−	46.8650i	−1.20337	−	1.53265i
$936$	−7.09265	+	4.96275i	−0.231830	+	0.162213i
$937$	−14.2224			−0.464624			−0.232312	−	0.972641i	$-0.574629\pi$
$937$	−14.2224			−0.464624			−0.232312	+	0.972641i	$0.574629\pi$
$938$		0			0
$939$			16.4937i			0.538251i
$940$	5.09187	−	3.11516i	0.166078	−	0.101605i
$941$			5.54338i			0.180709i	0.995910	+	0.0903544i	$0.0288000\pi$
$941$			5.54338i			0.180709i	−0.995910	+	0.0903544i	$0.971200\pi$
$942$	−17.6254	+	15.6817i	−0.574267	+	0.510939i
$943$		−	6.73903i		−	0.219453i
$944$	−7.43893	−	1.76660i	−0.242116	−	0.0574979i
$945$		0			0
$946$	9.12407	−	8.11789i	0.296649	−	0.263935i
$947$	59.5762			1.93597			0.967983	−	0.251015i	$-0.0807642\pi$
$947$	59.5762			1.93597			0.967983	+	0.251015i	$0.0807642\pi$
$948$	−4.67936	+	39.9564i	−0.151978	+	1.29772i
$949$	−6.05225			−0.196464
$950$	20.6567	−	10.9534i	0.670190	−	0.355375i
$951$	48.8163			1.58298
$952$		0			0
$953$			12.2577i			0.397065i	0.980094	+	0.198532i	$0.0636175\pi$
$953$			12.2577i			0.397065i	−0.980094	+	0.198532i	$0.936383\pi$
$954$	7.15660	−	6.36739i	0.231703	−	0.206152i
$955$	−9.33392	−	11.8880i	−0.302039	−	0.384686i
$956$	−41.9704	−	4.91523i	−1.35742	−	0.158970i
$957$	19.1122			0.617811
$958$	19.3355	+	21.7321i	0.624703	+	0.702133i
$959$		0			0
$960$	−44.1442	+	14.4275i	−1.42475	+	0.465645i
$961$	−27.3463			−0.882140
$962$	−6.19650	+	5.51316i	−0.199783	+	0.177751i
$963$	−27.1222			−0.874000
$964$	−3.61143	−	0.422941i	−0.116316	−	0.0136220i
$965$	3.25893	+	4.15067i	0.104909	+	0.133615i
$966$		0			0
$967$	−53.4551			−1.71900			−0.859499	−	0.511137i	$-0.829225\pi$
$967$	−53.4551			−1.71900			−0.859499	+	0.511137i	$0.829225\pi$
$968$	−4.58819	+	3.21037i	−0.147470	+	0.103185i
$969$			63.4934i			2.03970i
$970$	−22.7820	−	4.10008i	−0.731487	−	0.131646i
$971$	−22.2567			−0.714253			−0.357126	−	0.934056i	$-0.616243\pi$
$971$	−22.2567			−0.714253			−0.357126	+	0.934056i	$0.616243\pi$
$972$	−43.5887	−	5.10475i	−1.39811	−	0.163735i
$973$		0			0
$974$	−27.3167	−	30.7025i	−0.875284	−	0.983772i
$975$	−10.3188	−	2.52022i	−0.330465	−	0.0807116i
$976$	9.03513	−	38.0458i	0.289208	−	1.21782i
$977$		−	31.7948i		−	1.01721i	−0.861001	−	0.508603i	$-0.830162\pi$
$977$		−	31.7948i		−	1.01721i	0.861001	−	0.508603i	$-0.169838\pi$
$978$	−50.6883	+	45.0985i	−1.62083	+	1.44209i
$979$	38.2369			1.22206
$980$		0			0
$981$	29.8158			0.951947
$982$	−10.0565	+	8.94749i	−0.320916	+	0.285526i
$983$			20.5854i			0.656573i	0.944578	+	0.328287i	$0.106471\pi$
$983$			20.5854i			0.656573i	−0.944578	+	0.328287i	$0.893529\pi$
$984$	15.9934	−	11.1907i	0.509852	−	0.356745i
$985$	−28.0603	−	35.7384i	−0.894074	−	1.13872i
$986$	14.2070	+	15.9679i	0.452444	+	0.508522i
$987$		0			0
$988$	0.629440	−	5.37470i	0.0200252	−	0.170992i
$989$	6.07665			0.193226
$990$	7.54754	−	41.9378i	0.239877	−	1.33287i
$991$		−	37.2779i		−	1.18417i	−0.805875	−	0.592086i	$-0.798304\pi$
$991$		−	37.2779i		−	1.18417i	0.805875	−	0.592086i	$-0.201696\pi$
$992$	−5.12640	−	9.52034i	−0.162763	−	0.302271i
$993$	33.9810			1.07836
$994$		0			0
$995$	−20.1519	+	15.8224i	−0.638859	+	0.501605i
$996$	−6.33993	+	54.1358i	−0.200888	+	1.71536i
$997$	−12.6422			−0.400383			−0.200191	−	0.979757i	$-0.564156\pi$
$997$	−12.6422			−0.400383			−0.200191	+	0.979757i	$0.564156\pi$
$998$	−21.3325	+	18.9800i	−0.675269	+	0.600802i
$999$	13.7729			0.435755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.c.d.979.5		32
4.3	odd	2	inner	980.2.c.d.979.26		32
5.4	even	2	inner	980.2.c.d.979.28		32
7.2	even	3		980.2.s.e.619.7		32
7.3	odd	6		980.2.s.e.19.15		32
7.4	even	3		140.2.s.b.19.15	yes	32
7.5	odd	6		140.2.s.b.59.7	yes	32
7.6	odd	2	inner	980.2.c.d.979.6		32
20.19	odd	2	inner	980.2.c.d.979.7		32
28.3	even	6		980.2.s.e.19.10		32
28.11	odd	6		140.2.s.b.19.10	yes	32
28.19	even	6		140.2.s.b.59.2	yes	32
28.23	odd	6		980.2.s.e.619.2		32
28.27	even	2	inner	980.2.c.d.979.25		32
35.4	even	6		140.2.s.b.19.2	✓	32
35.9	even	6		980.2.s.e.619.10		32
35.12	even	12		700.2.p.e.451.2		32
35.18	odd	12		700.2.p.e.551.7		32
35.19	odd	6		140.2.s.b.59.10	yes	32
35.24	odd	6		980.2.s.e.19.2		32
35.32	odd	12		700.2.p.e.551.10		32
35.33	even	12		700.2.p.e.451.15		32
35.34	odd	2	inner	980.2.c.d.979.27		32
140.19	even	6		140.2.s.b.59.15	yes	32
140.39	odd	6		140.2.s.b.19.7	yes	32
140.47	odd	12		700.2.p.e.451.10		32
140.59	even	6		980.2.s.e.19.7		32
140.67	even	12		700.2.p.e.551.2		32
140.79	odd	6		980.2.s.e.619.15		32
140.103	odd	12		700.2.p.e.451.7		32
140.123	even	12		700.2.p.e.551.15		32
140.139	even	2	inner	980.2.c.d.979.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.2	✓	32	35.4	even	6
140.2.s.b.19.7	yes	32	140.39	odd	6
140.2.s.b.19.10	yes	32	28.11	odd	6
140.2.s.b.19.15	yes	32	7.4	even	3
140.2.s.b.59.2	yes	32	28.19	even	6
140.2.s.b.59.7	yes	32	7.5	odd	6
140.2.s.b.59.10	yes	32	35.19	odd	6
140.2.s.b.59.15	yes	32	140.19	even	6
700.2.p.e.451.2		32	35.12	even	12
700.2.p.e.451.7		32	140.103	odd	12
700.2.p.e.451.10		32	140.47	odd	12
700.2.p.e.451.15		32	35.33	even	12
700.2.p.e.551.2		32	140.67	even	12
700.2.p.e.551.7		32	35.18	odd	12
700.2.p.e.551.10		32	35.32	odd	12
700.2.p.e.551.15		32	140.123	even	12
980.2.c.d.979.5		32	1.1	even	1	trivial
980.2.c.d.979.6		32	7.6	odd	2	inner
980.2.c.d.979.7		32	20.19	odd	2	inner
980.2.c.d.979.8		32	140.139	even	2	inner
980.2.c.d.979.25		32	28.27	even	2	inner
980.2.c.d.979.26		32	4.3	odd	2	inner
980.2.c.d.979.27		32	35.34	odd	2	inner
980.2.c.d.979.28		32	5.4	even	2	inner
980.2.s.e.19.2		32	35.24	odd	6
980.2.s.e.19.7		32	140.59	even	6
980.2.s.e.19.10		32	28.3	even	6
980.2.s.e.19.15		32	7.3	odd	6
980.2.s.e.619.2		32	28.23	odd	6
980.2.s.e.619.7		32	7.2	even	3
980.2.s.e.619.10		32	35.9	even	6
980.2.s.e.619.15		32	140.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.940044 - 1.05656i) q^{2} -2.59619i q^{3} +(-0.232633 + 1.98642i) q^{4} +(1.75874 - 1.38089i) q^{5} +(-2.74302 + 2.44053i) q^{6} +(2.31746 - 1.62154i) q^{8} -3.74018 q^{9} +(-3.11228 - 0.560116i) q^{10} -3.60275i q^{11} +(5.15713 + 0.603960i) q^{12} +0.818282 q^{13} +(-3.58504 - 4.56601i) q^{15} +(-3.89176 - 0.924218i) q^{16} +7.39628 q^{17} +(3.51594 + 3.95172i) q^{18} -3.30658 q^{19} +(2.33388 + 3.81484i) q^{20} +(-3.80652 + 3.38675i) q^{22} -2.53515 q^{23} +(-4.20981 - 6.01656i) q^{24} +(1.18631 - 4.85723i) q^{25} +(-0.769222 - 0.864563i) q^{26} +1.92166i q^{27} -2.04334 q^{29} +(-1.45417 + 8.08005i) q^{30} -1.91145 q^{31} +(2.68194 + 4.98068i) q^{32} -9.35342 q^{33} +(-6.95283 - 7.81461i) q^{34} +(0.870092 - 7.42959i) q^{36} -7.16720i q^{37} +(3.10833 + 3.49360i) q^{38} -2.12441i q^{39} +(1.83665 - 6.05200i) q^{40} +2.65824i q^{41} -2.39696 q^{43} +(7.15660 + 0.838121i) q^{44} +(-6.57800 + 5.16476i) q^{45} +(2.38315 + 2.67854i) q^{46} -1.33475i q^{47} +(-2.39944 + 10.1037i) q^{48} +(-6.24713 + 3.31260i) q^{50} -19.2021i q^{51} +(-0.190360 + 1.62546i) q^{52} -1.81101i q^{53} +(2.03034 - 1.80644i) q^{54} +(-4.97499 - 6.33630i) q^{55} +8.58450i q^{57} +(1.92083 + 2.15891i) q^{58} +1.91145 q^{59} +(9.90403 - 6.05920i) q^{60} +9.77598i q^{61} +(1.79685 + 2.01956i) q^{62} +(2.74124 - 7.51569i) q^{64} +(1.43914 - 1.12995i) q^{65} +(8.79263 + 9.88244i) q^{66} +9.26225 q^{67} +(-1.72062 + 14.6922i) q^{68} +6.58172i q^{69} +1.38422i q^{71} +(-8.66773 + 6.06484i) q^{72} -7.39628 q^{73} +(-7.57256 + 6.73748i) q^{74} +(-12.6103 - 3.07989i) q^{75} +(0.769222 - 6.56827i) q^{76} +(-2.24457 + 1.99704i) q^{78} +7.74780i q^{79} +(-8.12083 + 3.74862i) q^{80} -6.23157 q^{81} +(2.80858 - 2.49886i) q^{82} +10.4973i q^{83} +(13.0081 - 10.2134i) q^{85} +(2.25325 + 2.53253i) q^{86} +5.30490i q^{87} +(-5.84199 - 8.34924i) q^{88} +10.6132i q^{89} +(11.6405 + 2.09494i) q^{90} +(0.589761 - 5.03589i) q^{92} +4.96249i q^{93} +(-1.41024 + 1.25473i) q^{94} +(-5.81541 + 4.56601i) q^{95} +(12.9308 - 6.96281i) q^{96} +7.32005 q^{97} +13.4750i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{4} - 8 q^{9} - 36 q^{16} + 52 q^{25} + 52 q^{30} - 28 q^{36} + 52 q^{44} + 44 q^{46} + 36 q^{50} - 8 q^{60} + 36 q^{64} + 8 q^{65} - 28 q^{74} - 144 q^{81} + 20 q^{85} - 16 q^{86}+O(q^{100}) \) 32 * q - 12 * q^4 - 8 * q^9 - 36 * q^16 + 52 * q^25 + 52 * q^30 - 28 * q^36 + 52 * q^44 + 44 * q^46 + 36 * q^50 - 8 * q^60 + 36 * q^64 + 8 * q^65 - 28 * q^74 - 144 * q^81 + 20 * q^85 - 16 * q^86

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