LMFDB - Embedded newform 231.2.e.a.188.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(188,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("231.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.e (of order $2$, degree $1$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.4
Character	$\chi$	$=$	231.188
Dual form			231.2.e.a.188.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33290i q^{2} +(1.41254 - 1.00236i) q^{3} -3.44244 q^{4} -4.22171 q^{5} +(-2.33841 - 3.29532i) q^{6} +(2.13159 - 1.56727i) q^{7} +3.36508i q^{8} +(0.990548 - 2.83175i) q^{9} +O(q^{10})$	\(q-2.33290i q^{2} +(1.41254 - 1.00236i) q^{3} -3.44244 q^{4} -4.22171 q^{5} +(-2.33841 - 3.29532i) q^{6} +(2.13159 - 1.56727i) q^{7} +3.36508i q^{8} +(0.990548 - 2.83175i) q^{9} +9.84884i q^{10} +1.00000i q^{11} +(-4.86259 + 3.45057i) q^{12} +1.39663i q^{13} +(-3.65629 - 4.97279i) q^{14} +(-5.96334 + 4.23167i) q^{15} +0.965521 q^{16} +1.76084 q^{17} +(-6.60620 - 2.31085i) q^{18} -0.456144i q^{19} +14.5330 q^{20} +(1.43999 - 4.35045i) q^{21} +2.33290 q^{22} -3.57846i q^{23} +(3.37302 + 4.75331i) q^{24} +12.8228 q^{25} +3.25820 q^{26} +(-1.43925 - 4.99285i) q^{27} +(-7.33787 + 5.39523i) q^{28} -6.15933i q^{29} +(9.87209 + 13.9119i) q^{30} -2.68916i q^{31} +4.47769i q^{32} +(1.00236 + 1.41254i) q^{33} -4.10788i q^{34} +(-8.99895 + 6.61655i) q^{35} +(-3.40990 + 9.74814i) q^{36} +3.07199 q^{37} -1.06414 q^{38} +(1.39992 + 1.97279i) q^{39} -14.2064i q^{40} +8.68626 q^{41} +(-10.1492 - 3.35936i) q^{42} -4.97879 q^{43} -3.44244i q^{44} +(-4.18180 + 11.9548i) q^{45} -8.34822 q^{46} +0.712189 q^{47} +(1.36384 - 0.967800i) q^{48} +(2.08734 - 6.68154i) q^{49} -29.9144i q^{50} +(2.48727 - 1.76500i) q^{51} -4.80780i q^{52} +10.2336i q^{53} +(-11.6478 + 3.35762i) q^{54} -4.22171i q^{55} +(5.27398 + 7.17296i) q^{56} +(-0.457221 - 0.644323i) q^{57} -14.3691 q^{58} +9.93745 q^{59} +(20.5285 - 14.5673i) q^{60} +0.721923i q^{61} -6.27355 q^{62} +(-2.32667 - 7.58858i) q^{63} +12.3771 q^{64} -5.89615i q^{65} +(3.29532 - 2.33841i) q^{66} +2.01128 q^{67} -6.06160 q^{68} +(-3.58691 - 5.05473i) q^{69} +(15.4358 + 20.9937i) q^{70} +15.3900i q^{71} +(9.52906 + 3.33327i) q^{72} +7.85395i q^{73} -7.16665i q^{74} +(18.1128 - 12.8531i) q^{75} +1.57025i q^{76} +(1.56727 + 2.13159i) q^{77} +(4.60234 - 3.26589i) q^{78} -7.33162 q^{79} -4.07615 q^{80} +(-7.03763 - 5.60997i) q^{81} -20.2642i q^{82} -9.00326 q^{83} +(-4.95709 + 14.9762i) q^{84} -7.43377 q^{85} +11.6150i q^{86} +(-6.17387 - 8.70031i) q^{87} -3.36508 q^{88} +10.9751 q^{89} +(27.8895 + 9.75575i) q^{90} +(2.18889 + 2.97703i) q^{91} +12.3187i q^{92} +(-2.69550 - 3.79855i) q^{93} -1.66147i q^{94} +1.92571i q^{95} +(4.48826 + 6.32492i) q^{96} +6.09294i q^{97} +(-15.5874 - 4.86957i) q^{98} +(2.83175 + 0.990548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	2.33290i		−	1.64961i	−0.565416	−	0.824806i	$-0.691284\pi$
$2$		−	2.33290i		−	1.64961i	0.565416	−	0.824806i	$-0.308716\pi$
$3$	1.41254	−	1.00236i	0.815531	−	0.578713i
$3$	1.41254	−	1.00236i	0.815531	−	0.578713i
$4$	−3.44244			−1.72122
$5$	−4.22171			−1.88801			−0.944003	−	0.329937i	$-0.892972\pi$
$5$	−4.22171			−1.88801			−0.944003	+	0.329937i	$0.892972\pi$
$6$	−2.33841	−	3.29532i	−0.954652	−	1.34531i
$7$	2.13159	−	1.56727i	0.805665	−	0.592372i
$7$	2.13159	−	1.56727i	0.805665	−	0.592372i
$8$			3.36508i			1.18973i
$9$	0.990548	−	2.83175i	0.330183	−	0.943917i
$10$			9.84884i			3.11448i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−4.86259	+	3.45057i	−1.40371	+	0.996093i
$13$			1.39663i			0.387354i	0.981065	+	0.193677i	$0.0620414\pi$
$13$			1.39663i			0.387354i	−0.981065	+	0.193677i	$0.937959\pi$
$14$	−3.65629	−	4.97279i	−0.977183	−	1.32903i
$15$	−5.96334	+	4.23167i	−1.53973	+	1.09261i
$16$	0.965521			0.241380
$17$	1.76084			0.427067			0.213534	−	0.976936i	$-0.431503\pi$
$17$	1.76084			0.427067			0.213534	+	0.976936i	$0.431503\pi$
$18$	−6.60620	−	2.31085i	−1.55710	−	0.544673i
$19$		−	0.456144i		−	0.104647i	−0.998630	−	0.0523234i	$-0.983337\pi$
$19$		−	0.456144i		−	0.104647i	0.998630	−	0.0523234i	$-0.0166627\pi$
$20$	14.5330			3.24967
$21$	1.43999	−	4.35045i	0.314232	−	0.949346i
$22$	2.33290			0.497377
$23$		−	3.57846i		−	0.746162i	−0.927799	−	0.373081i	$-0.878301\pi$
$23$		−	3.57846i		−	0.746162i	0.927799	−	0.373081i	$-0.121699\pi$
$24$	3.37302	+	4.75331i	0.688515	+	0.970266i
$25$	12.8228			2.56457
$26$	3.25820			0.638985
$27$	−1.43925	−	4.99285i	−0.276983	−	0.960875i
$28$	−7.33787	+	5.39523i	−1.38673	+	1.01960i
$29$		−	6.15933i		−	1.14376i	−0.820338	−	0.571879i	$-0.806215\pi$
$29$		−	6.15933i		−	1.14376i	0.820338	−	0.571879i	$-0.193785\pi$
$30$	9.87209	+	13.9119i	1.80239	+	2.53995i
$31$		−	2.68916i		−	0.482987i	−0.970402	−	0.241493i	$-0.922363\pi$
$31$		−	2.68916i		−	0.482987i	0.970402	−	0.241493i	$-0.0776372\pi$
$32$			4.47769i			0.791551i
$33$	1.00236	+	1.41254i	0.174489	+	0.245892i
$34$		−	4.10788i		−	0.704496i
$35$	−8.99895	+	6.61655i	−1.52110	+	1.11840i
$36$	−3.40990	+	9.74814i	−0.568317	+	1.62469i
$37$	3.07199			0.505031			0.252516	−	0.967593i	$-0.418742\pi$
$37$	3.07199			0.505031			0.252516	+	0.967593i	$0.418742\pi$
$38$	−1.06414			−0.172627
$39$	1.39992	+	1.97279i	0.224167	+	0.315900i
$40$		−	14.2064i		−	2.24623i
$41$	8.68626			1.35657			0.678283	−	0.734801i	$-0.262724\pi$
$41$	8.68626			1.35657			0.678283	+	0.734801i	$0.262724\pi$
$42$	−10.1492	−	3.35936i	−1.56605	−	0.518361i
$43$	−4.97879			−0.759258			−0.379629	−	0.925139i	$-0.623948\pi$
$43$	−4.97879			−0.759258			−0.379629	+	0.925139i	$0.623948\pi$
$44$		−	3.44244i		−	0.518968i
$45$	−4.18180	+	11.9548i	−0.623387	+	1.78212i
$46$	−8.34822			−1.23088
$47$	0.712189			0.103883			0.0519417	−	0.998650i	$-0.483459\pi$
$47$	0.712189			0.103883			0.0519417	+	0.998650i	$0.483459\pi$
$48$	1.36384	−	0.967800i	0.196853	−	0.139690i
$49$	2.08734	−	6.68154i	0.298192	−	0.954506i
$50$		−	29.9144i		−	4.23054i
$51$	2.48727	−	1.76500i	0.348287	−	0.247150i
$52$		−	4.80780i		−	0.666722i
$53$			10.2336i			1.40570i	0.711340	+	0.702848i	$0.248089\pi$
$53$			10.2336i			1.40570i	−0.711340	+	0.702848i	$0.751911\pi$
$54$	−11.6478	+	3.35762i	−1.58507	+	0.456914i
$55$		−	4.22171i		−	0.569255i
$56$	5.27398	+	7.17296i	0.704765	+	0.958527i
$57$	−0.457221	−	0.644323i	−0.0605604	−	0.0853427i
$58$	−14.3691			−1.88676
$59$	9.93745			1.29375			0.646873	−	0.762598i	$-0.276076\pi$
$59$	9.93745			1.29375			0.646873	+	0.762598i	$0.276076\pi$
$60$	20.5285	−	14.5673i	2.65021	−	1.88063i
$61$			0.721923i			0.0924327i	0.998931	+	0.0462164i	$0.0147164\pi$
$61$			0.721923i			0.0924327i	−0.998931	+	0.0462164i	$0.985284\pi$
$62$	−6.27355			−0.796741
$63$	−2.32667	−	7.58858i	−0.293133	−	0.956072i
$64$	12.3771			1.54713
$65$		−	5.89615i		−	0.731327i
$66$	3.29532	−	2.33841i	0.405626	−	0.287838i
$67$	2.01128			0.245717			0.122859	−	0.992424i	$-0.460794\pi$
$67$	2.01128			0.245717			0.122859	+	0.992424i	$0.460794\pi$
$68$	−6.06160			−0.735077
$69$	−3.58691	−	5.05473i	−0.431813	−	0.608518i
$70$	15.4358	+	20.9937i	1.84493	+	2.50923i
$71$			15.3900i			1.82646i	0.407446	+	0.913229i	$0.366419\pi$
$71$			15.3900i			1.82646i	−0.407446	+	0.913229i	$0.633581\pi$
$72$	9.52906	+	3.33327i	1.12301	+	0.392830i
$73$			7.85395i			0.919236i	0.888117	+	0.459618i	$0.152014\pi$
$73$			7.85395i			0.919236i	−0.888117	+	0.459618i	$0.847986\pi$
$74$		−	7.16665i		−	0.833106i
$75$	18.1128	−	12.8531i	2.09148	−	1.48415i
$76$			1.57025i			0.180120i
$77$	1.56727	+	2.13159i	0.178607	+	0.242917i
$78$	4.60234	−	3.26589i	0.521112	−	0.369789i
$79$	−7.33162			−0.824871			−0.412436	−	0.910987i	$-0.635322\pi$
$79$	−7.33162			−0.824871			−0.412436	+	0.910987i	$0.635322\pi$
$80$	−4.07615			−0.455727
$81$	−7.03763	−	5.60997i	−0.781959	−	0.623330i
$82$		−	20.2642i		−	2.23781i
$83$	−9.00326			−0.988236			−0.494118	−	0.869395i	$-0.664509\pi$
$83$	−9.00326			−0.988236			−0.494118	+	0.869395i	$0.664509\pi$
$84$	−4.95709	+	14.9762i	−0.540862	+	1.63403i
$85$	−7.43377			−0.806306
$86$			11.6150i			1.25248i
$87$	−6.17387	−	8.70031i	−0.661908	−	0.932771i
$88$	−3.36508			−0.358718
$89$	10.9751			1.16336			0.581678	−	0.813419i	$-0.302396\pi$
$89$	10.9751			1.16336			0.581678	+	0.813419i	$0.302396\pi$
$90$	27.8895	+	9.75575i	2.93981	+	1.02835i
$91$	2.18889	+	2.97703i	0.229458	+	0.312078i
$92$			12.3187i			1.28431i
$93$	−2.69550	−	3.79855i	−0.279511	−	0.393891i
$94$		−	1.66147i		−	0.171367i
$95$			1.92571i			0.197574i
$96$	4.48826	+	6.32492i	0.458081	+	0.645535i
$97$			6.09294i			0.618644i	0.950957	+	0.309322i	$0.100102\pi$
$97$			6.09294i			0.618644i	−0.950957	+	0.309322i	$0.899898\pi$
$98$	−15.5874	−	4.86957i	−1.57456	−	0.491901i
$99$	2.83175	+	0.990548i	0.284602	+	0.0995538i
$100$	−44.1418			−4.41418
$101$	−2.78878			−0.277494			−0.138747	−	0.990328i	$-0.544307\pi$
$101$	−2.78878			−0.277494			−0.138747	+	0.990328i	$0.544307\pi$
$102$	−4.11758	−	5.80255i	−0.407701	−	0.574538i
$103$		−	5.36994i		−	0.529116i	−0.964370	−	0.264558i	$-0.914774\pi$
$103$		−	5.36994i		−	0.529116i	0.964370	−	0.264558i	$-0.0852260\pi$
$104$	−4.69976			−0.460849
$105$	−6.07922	+	18.3663i	−0.593272	+	1.79237i
$106$	23.8741			2.31885
$107$		−	1.01127i		−	0.0977629i	−0.998805	−	0.0488814i	$-0.984434\pi$
$107$		−	1.01127i		−	0.0977629i	0.998805	−	0.0488814i	$-0.0155656\pi$
$108$	4.95452	+	17.1876i	0.476749	+	1.65388i
$109$	−12.9197			−1.23748			−0.618740	−	0.785596i	$-0.712357\pi$
$109$	−12.9197			−1.23748			−0.618740	+	0.785596i	$0.712357\pi$
$110$	−9.84884			−0.939050
$111$	4.33931	−	3.07924i	0.411869	−	0.292268i
$112$	2.05809	−	1.51323i	0.194472	−	0.142987i
$113$			5.64281i			0.530831i	0.964134	+	0.265416i	$0.0855092\pi$
$113$			5.64281i			0.530831i	−0.964134	+	0.265416i	$0.914491\pi$
$114$	−1.50314	+	1.06665i	−0.140782	+	0.0999012i
$115$			15.1072i			1.40876i
$116$			21.2031i			1.96866i
$117$	3.95490	+	1.38342i	0.365630	+	0.127898i
$118$		−	23.1831i		−	2.13418i
$119$	3.75340	−	2.75971i	0.344073	−	0.252983i
$120$	−14.2399	−	20.0671i	−1.29992	−	1.83187i
$121$	−1.00000			−0.0909091
$122$	1.68418			0.152478
$123$	12.2697	−	8.70676i	1.10632	−	0.785063i
$124$			9.25727i			0.831327i
$125$	−33.0257			−2.95391
$126$	−17.7034	+	5.42790i	−1.57715	+	0.483556i
$127$	3.17060			0.281345			0.140672	−	0.990056i	$-0.455074\pi$
$127$	3.17060			0.281345			0.140672	+	0.990056i	$0.455074\pi$
$128$		−	19.9191i		−	1.76062i
$129$	−7.03275	+	4.99054i	−0.619199	+	0.439393i
$130$	−13.7552			−1.20641
$131$	17.1907			1.50196			0.750981	−	0.660324i	$-0.229581\pi$
$131$	17.1907			1.50196			0.750981	+	0.660324i	$0.229581\pi$
$132$	−3.45057	−	4.86259i	−0.300333	−	0.423234i
$133$	−0.714901	−	0.972313i	−0.0619897	−	0.0843102i
$134$		−	4.69213i		−	0.405338i
$135$	6.07608	+	21.0784i	0.522945	+	1.81414i
$136$			5.92538i			0.508097i
$137$		−	2.97587i		−	0.254246i	−0.991887	−	0.127123i	$-0.959426\pi$
$137$		−	2.97587i		−	0.254246i	0.991887	−	0.127123i	$-0.0405743\pi$
$138$	−11.7922	+	8.36792i	−1.00382	+	0.712325i
$139$			19.0060i			1.61207i	0.591868	+	0.806035i	$0.298391\pi$
$139$			19.0060i			1.61207i	−0.591868	+	0.806035i	$0.701609\pi$
$140$	30.9784	−	22.7771i	2.61815	−	1.92501i
$141$	1.00600	−	0.713870i	0.0847202	−	0.0601187i
$142$	35.9034			3.01295
$143$	−1.39663			−0.116792
$144$	0.956394	−	2.73411i	0.0796995	−	0.227843i
$145$			26.0029i			2.15942i
$146$	18.3225			1.51638
$147$	−3.74885	−	11.5302i	−0.309200	−	0.950997i
$148$	−10.5751			−0.869270
$149$			13.6074i			1.11476i	0.830257	+	0.557382i	$0.188194\pi$
$149$			13.6074i			1.11476i	−0.830257	+	0.557382i	$0.811806\pi$
$150$	−29.9850	−	42.2554i	−2.44827	−	3.45014i
$151$	−1.51546			−0.123326			−0.0616631	−	0.998097i	$-0.519640\pi$
$151$	−1.51546			−0.123326			−0.0616631	+	0.998097i	$0.519640\pi$
$152$	1.53496			0.124502
$153$	1.74420	−	4.98627i	0.141010	−	0.403116i
$154$	4.97279	−	3.65629i	0.400719	−	0.294632i
$155$			11.3528i			0.911882i
$156$	−4.81915	−	6.79122i	−0.385841	−	0.543733i
$157$		−	13.8255i		−	1.10340i	−0.834044	−	0.551698i	$-0.813980\pi$
$157$		−	13.8255i		−	1.10340i	0.834044	−	0.551698i	$-0.186020\pi$
$158$			17.1040i			1.36072i
$159$	10.2578	+	14.4554i	0.813494	+	1.14639i
$160$		−	18.9035i		−	1.49445i
$161$	−5.60841	−	7.62782i	−0.442005	−	0.601156i
$162$	−13.0875	+	16.4181i	−1.02825	+	1.28993i
$163$	11.1174			0.870784			0.435392	−	0.900241i	$-0.356610\pi$
$163$	11.1174			0.870784			0.435392	+	0.900241i	$0.356610\pi$
$164$	−29.9020			−2.33495
$165$	−4.23167	−	5.96334i	−0.329435	−	0.464245i
$166$			21.0037i			1.63021i
$167$	9.91348			0.767128			0.383564	−	0.923514i	$-0.374696\pi$
$167$	9.91348			0.767128			0.383564	+	0.923514i	$0.374696\pi$
$168$	14.6396	+	4.84568i	1.12947	+	0.373852i
$169$	11.0494			0.849957
$170$			17.3423i			1.33009i
$171$	−1.29169	−	0.451833i	−0.0987778	−	0.0345525i
$172$	17.1392			1.30685
$173$	−19.5711			−1.48796			−0.743982	−	0.668200i	$-0.767065\pi$
$173$	−19.5711			−1.48796			−0.743982	+	0.668200i	$0.767065\pi$
$174$	−20.2970	+	14.4030i	−1.53871	+	1.09189i
$175$	27.3330	−	20.0968i	2.06618	−	1.51918i
$176$			0.965521i			0.0727789i
$177$	14.0371	−	9.96091i	1.05509	−	0.748708i
$178$		−	25.6038i		−	1.91909i
$179$		−	22.7774i		−	1.70246i	−0.524791	−	0.851231i	$-0.675856\pi$
$179$		−	22.7774i		−	1.70246i	0.524791	−	0.851231i	$-0.324144\pi$
$180$	14.3956	−	41.1538i	1.07299	−	3.06742i
$181$		−	5.55932i		−	0.413221i	−0.978423	−	0.206610i	$-0.933757\pi$
$181$		−	5.55932i		−	0.413221i	0.978423	−	0.206610i	$-0.0662433\pi$
$182$	6.94513	−	5.10646i	0.514807	−	0.378516i
$183$	0.723627	+	1.01975i	0.0534920	+	0.0753818i
$184$	12.0418			0.887734
$185$	−12.9690			−0.953502
$186$	−8.86165	+	6.28835i	−0.649767	+	0.461085i
$187$			1.76084i			0.128766i
$188$	−2.45167			−0.178806
$189$	−10.8930	−	8.38703i	−0.792350	−	0.610066i
$190$	4.49250			0.325920
$191$		−	19.3330i		−	1.39888i	−0.714690	−	0.699442i	$-0.753432\pi$
$191$		−	19.3330i		−	1.39888i	0.714690	−	0.699442i	$-0.246568\pi$
$192$	17.4831	−	12.4063i	1.26173	−	0.895346i
$193$	−1.84175			−0.132572			−0.0662859	−	0.997801i	$-0.521115\pi$
$193$	−1.84175			−0.132572			−0.0662859	+	0.997801i	$0.521115\pi$
$194$	14.2142			1.02052
$195$	−5.91007	−	8.32856i	−0.423229	−	0.596420i
$196$	−7.18556	+	23.0008i	−0.513254	+	1.64292i
$197$		−	10.1222i		−	0.721180i	−0.932724	−	0.360590i	$-0.882575\pi$
$197$		−	10.1222i		−	0.721180i	0.932724	−	0.360590i	$-0.117425\pi$
$198$	2.31085	−	6.60620i	0.164225	−	0.469482i
$199$			3.46931i			0.245933i	0.992411	+	0.122967i	$0.0392408\pi$
$199$			3.46931i			0.245933i	−0.992411	+	0.122967i	$0.960759\pi$
$200$			43.1498i			3.05115i
$201$	2.84102	−	2.01603i	0.200390	−	0.142200i
$202$			6.50595i			0.457757i
$203$	−9.65332	−	13.1292i	−0.677530	−	0.921486i
$204$	−8.56227	+	6.07591i	−0.599479	+	0.425399i
$205$	−36.6709			−2.56121
$206$	−12.5276			−0.872836
$207$	−10.1333	−	3.54464i	−0.704315	−	0.246370i
$208$			1.34847i			0.0934997i
$209$	0.456144			0.0315522
$210$	42.8469	+	14.1822i	2.95672	+	0.978668i
$211$	−12.2254			−0.841629			−0.420815	−	0.907147i	$-0.638256\pi$
$211$	−12.2254			−0.841629			−0.420815	+	0.907147i	$0.638256\pi$
$212$		−	35.2286i		−	2.41951i
$213$	15.4263	+	21.7390i	1.05700	+	1.48953i
$214$	−2.35919			−0.161271
$215$	21.0190			1.43348
$216$	16.8013	−	4.84317i	1.14319	−	0.329536i
$217$	−4.21463	−	5.73218i	−0.286108	−	0.389126i
$218$			30.1404i			2.04136i
$219$	7.87249	+	11.0940i	0.531974	+	0.749666i
$220$			14.5330i			0.979814i
$221$			2.45924i			0.165426i
$222$	−7.18356	−	10.1232i	−0.482129	−	0.679424i
$223$		−	0.0580297i		−	0.00388596i	−0.999998	−	0.00194298i	$-0.999382\pi$
$223$		−	0.0580297i		−	0.00388596i	0.999998	−	0.00194298i	$-0.000618470\pi$
$224$	7.01774	+	9.54459i	0.468892	+	0.637725i
$225$	12.7016	−	36.3111i	0.846775	−	2.42074i
$226$	13.1641			0.875666
$227$	−13.0324			−0.864988			−0.432494	−	0.901637i	$-0.642366\pi$
$227$	−13.0324			−0.864988			−0.432494	+	0.901637i	$0.642366\pi$
$228$	1.57396	+	2.21804i	0.104238	+	0.146894i
$229$			20.7664i			1.37229i	0.727467	+	0.686143i	$0.240697\pi$
$229$			20.7664i			1.37229i	−0.727467	+	0.686143i	$0.759303\pi$
$230$	35.2437			2.32390
$231$	4.35045	+	1.43999i	0.286239	+	0.0947445i
$232$	20.7266			1.36077
$233$			12.5818i			0.824263i	0.911124	+	0.412132i	$0.135216\pi$
$233$			12.5818i			0.824263i	−0.911124	+	0.412132i	$0.864784\pi$
$234$	3.22740	−	9.22640i	0.210982	−	0.603149i
$235$	−3.00666			−0.196133
$236$	−34.2091			−2.22682
$237$	−10.3562	+	7.34892i	−0.672708	+	0.477364i
$238$	−6.43815	−	8.75631i	−0.417323	−	0.567588i
$239$			0.726359i			0.0469842i	0.999724	+	0.0234921i	$0.00747846\pi$
$239$			0.726359i			0.0469842i	−0.999724	+	0.0234921i	$0.992522\pi$
$240$	−5.75773	+	4.08577i	−0.371660	+	0.263735i
$241$		−	12.0144i		−	0.773915i	−0.922098	−	0.386958i	$-0.873526\pi$
$241$		−	12.0144i		−	0.773915i	0.922098	−	0.386958i	$-0.126474\pi$
$242$			2.33290i			0.149965i
$243$	−15.5642	−	0.870073i	−0.998441	−	0.0558152i
$244$		−	2.48518i		−	0.159097i
$245$	−8.81216	+	28.2075i	−0.562988	+	1.80211i
$246$	−20.3120	−	28.6240i	−1.29505	−	1.82500i
$247$	0.637063			0.0405354
$248$	9.04922			0.574626
$249$	−12.7175	+	9.02451i	−0.805938	+	0.571905i
$250$			77.0458i			4.87281i
$251$	5.01779			0.316720			0.158360	−	0.987381i	$-0.449379\pi$
$251$	5.01779			0.316720			0.158360	+	0.987381i	$0.449379\pi$
$252$	8.00943	+	26.1233i	0.504547	+	1.64561i
$253$	3.57846			0.224976
$254$		−	7.39670i		−	0.464110i
$255$	−10.5005	+	7.45132i	−0.657568	+	0.466620i
$256$	−21.7153			−1.35720
$257$	−3.04989			−0.190247			−0.0951234	−	0.995465i	$-0.530325\pi$
$257$	−3.04989			−0.190247			−0.0951234	+	0.995465i	$0.530325\pi$
$258$	11.6425	+	16.4067i	0.724828	+	1.02144i
$259$	6.54821	−	4.81462i	0.406886	−	0.299166i
$260$			20.2972i			1.25878i
$261$	−17.4417	−	6.10111i	−1.07961	−	0.377649i
$262$		−	40.1043i		−	2.47765i
$263$			15.1174i			0.932181i	0.884737	+	0.466090i	$0.154338\pi$
$263$			15.1174i			0.932181i	−0.884737	+	0.466090i	$0.845662\pi$
$264$	−4.75331	+	3.37302i	−0.292546	+	0.207595i
$265$		−	43.2034i		−	2.65396i
$266$	−2.26831	+	1.66779i	−0.139079	+	0.102259i
$267$	15.5027	−	11.0010i	0.948753	−	0.673249i
$268$	−6.92372			−0.422934
$269$	−3.94371			−0.240452			−0.120226	−	0.992747i	$-0.538362\pi$
$269$	−3.94371			−0.240452			−0.120226	+	0.992747i	$0.538362\pi$
$270$	49.1738	−	14.1749i	2.99262	−	0.862657i
$271$		−	20.5319i		−	1.24722i	−0.781734	−	0.623612i	$-0.785665\pi$
$271$		−	20.5319i		−	1.24722i	0.781734	−	0.623612i	$-0.214335\pi$
$272$	1.70013			0.103086
$273$	6.07595	+	2.01113i	0.367733	+	0.121719i
$274$	−6.94242			−0.419407
$275$			12.8228i			0.773246i
$276$	12.3477	+	17.4006i	0.743246	+	1.04739i
$277$	25.7064			1.54455			0.772273	−	0.635291i	$-0.219120\pi$
$277$	25.7064			1.54455			0.772273	+	0.635291i	$0.219120\pi$
$278$	44.3392			2.65929
$279$	−7.61503	−	2.66374i	−0.455900	−	0.159474i
$280$	−22.2652	−	30.2822i	−1.33060	−	1.80971i
$281$			7.79683i			0.465120i	0.972582	+	0.232560i	$0.0747102\pi$
$281$			7.79683i			0.465120i	−0.972582	+	0.232560i	$0.925290\pi$
$282$	−1.66539	−	2.34689i	−0.0991726	−	0.139756i
$283$			4.91821i			0.292357i	0.989258	+	0.146179i	$0.0466974\pi$
$283$			4.91821i			0.292357i	−0.989258	+	0.146179i	$0.953303\pi$
$284$		−	52.9792i		−	3.14374i
$285$	1.93025	+	2.72014i	0.114338	+	0.161127i
$286$			3.25820i			0.192661i
$287$	18.5155	−	13.6137i	1.09294	−	0.803591i
$288$	12.6797	+	4.43536i	0.747158	+	0.261356i
$289$	−13.8994			−0.817613
$290$	60.6623			3.56221
$291$	6.10732	+	8.60653i	0.358017	+	0.504524i
$292$		−	27.0368i		−	1.58221i
$293$	−8.27555			−0.483463			−0.241731	−	0.970343i	$-0.577715\pi$
$293$	−8.27555			−0.483463			−0.241731	+	0.970343i	$0.577715\pi$
$294$	−26.8989	+	8.74571i	−1.56878	+	0.510060i
$295$	−41.9530			−2.44260
$296$			10.3375i			0.600853i
$297$	4.99285	−	1.43925i	0.289715	−	0.0835135i
$298$	31.7448			1.83893
$299$	4.99778			0.289029
$300$	−62.3522	+	44.2460i	−3.59991	+	2.55455i
$301$	−10.6127	+	7.80310i	−0.611708	+	0.449763i
$302$			3.53542i			0.203440i
$303$	−3.93926	+	2.79536i	−0.226305	+	0.160589i
$304$		−	0.440417i		−	0.0252596i
$305$		−	3.04775i		−	0.174514i
$306$	−11.6325	−	4.06905i	−0.664986	−	0.232612i
$307$			26.5030i			1.51261i	0.654220	+	0.756304i	$0.272997\pi$
$307$			26.5030i			1.51261i	−0.654220	+	0.756304i	$0.727003\pi$
$308$	−5.39523	−	7.33787i	−0.307422	−	0.418114i
$309$	−5.38261	−	7.58526i	−0.306206	−	0.431511i
$310$	26.4851			1.50425
$311$	−22.2310			−1.26060			−0.630302	−	0.776350i	$-0.717069\pi$
$311$	−22.2310			−1.26060			−0.630302	+	0.776350i	$0.717069\pi$
$312$	−6.63860	+	4.71085i	−0.375837	+	0.266699i
$313$		−	22.5268i		−	1.27329i	−0.771158	−	0.636644i	$-0.780322\pi$
$313$		−	22.5268i		−	1.27329i	0.771158	−	0.636644i	$-0.219678\pi$
$314$	−32.2536			−1.82018
$315$	9.82253	+	32.0368i	0.553437	+	1.80507i
$316$	25.2387			1.41979
$317$			5.45436i			0.306347i	0.988199	+	0.153174i	$0.0489494\pi$
$317$			5.45436i			0.306347i	−0.988199	+	0.153174i	$0.951051\pi$
$318$	33.7231	−	23.9304i	1.89110	−	1.34195i
$319$	6.15933			0.344856
$320$	−52.2523			−2.92100
$321$	−1.01365	−	1.42846i	−0.0565767	−	0.0797287i
$322$	−17.7950	+	13.0839i	−0.991675	+	0.729137i
$323$		−	0.803199i		−	0.0446912i
$324$	24.2266	+	19.3120i	1.34592	+	1.07289i
$325$			17.9087i			0.993396i
$326$		−	25.9359i		−	1.43646i
$327$	−18.2496	+	12.9502i	−1.00920	+	0.716146i
$328$			29.2299i			1.61395i
$329$	1.51809	−	1.11619i	0.0836953	−	0.0615376i
$330$	−13.9119	+	9.87209i	−0.765825	+	0.543441i
$331$	1.10614			0.0607992			0.0303996	−	0.999538i	$-0.490322\pi$
$331$	1.10614			0.0607992			0.0303996	+	0.999538i	$0.490322\pi$
$332$	30.9932			1.70097
$333$	3.04295	−	8.69910i	0.166752	−	0.476708i
$334$		−	23.1272i		−	1.26546i
$335$	−8.49105			−0.463916
$336$	1.39034	−	4.20045i	0.0758493	−	0.229153i
$337$	−16.1939			−0.882140			−0.441070	−	0.897473i	$-0.645401\pi$
$337$	−16.1939			−0.882140			−0.441070	+	0.897473i	$0.645401\pi$
$338$		−	25.7773i		−	1.40210i
$339$	5.65613	+	7.97071i	0.307199	+	0.432909i
$340$	25.5903			1.38783
$341$	2.68916			0.145626
$342$	−1.05408	+	3.01338i	−0.0569983	+	0.162945i
$343$	−6.02241	−	17.5137i	−0.325179	−	0.945652i
$344$		−	16.7540i		−	0.903316i
$345$	15.1429	+	21.3396i	0.815266	+	1.14889i
$346$			45.6575i			2.45456i
$347$		−	27.5304i		−	1.47791i	−0.673757	−	0.738953i	$-0.735320\pi$
$347$		−	27.5304i		−	1.47791i	0.673757	−	0.738953i	$-0.264680\pi$
$348$	21.2532	+	29.9503i	1.13929	+	1.60550i
$349$			28.2953i			1.51461i	0.653059	+	0.757307i	$0.273485\pi$
$349$			28.2953i			1.51461i	−0.653059	+	0.757307i	$0.726515\pi$
$350$	−46.8839	−	63.7653i	−2.50605	−	3.40840i
$351$	6.97315	−	2.01009i	0.372199	−	0.107291i
$352$	−4.47769			−0.238662
$353$	−2.65575			−0.141351			−0.0706757	−	0.997499i	$-0.522516\pi$
$353$	−2.65575			−0.141351			−0.0706757	+	0.997499i	$0.522516\pi$
$354$	−23.2378	−	32.7471i	−1.23508	−	1.74049i
$355$		−	64.9722i		−	3.44836i
$356$	−37.7811			−2.00239
$357$	2.53560	−	7.66047i	0.134198	−	0.405435i
$358$	−53.1375			−2.80840
$359$		−	3.71514i		−	0.196077i	−0.995183	−	0.0980387i	$-0.968743\pi$
$359$		−	3.71514i		−	0.196077i	0.995183	−	0.0980387i	$-0.0312569\pi$
$360$	−40.2289	−	14.0721i	−2.12025	−	0.741665i
$361$	18.7919			0.989049
$362$	−12.9694			−0.681654
$363$	−1.41254	+	1.00236i	−0.0741392	+	0.0526103i
$364$	−7.53512	−	10.2483i	−0.394947	−	0.537155i
$365$		−	33.1571i		−	1.73552i
$366$	2.37897	−	1.68815i	0.124351	−	0.0882411i
$367$		−	9.34148i		−	0.487621i	−0.969823	−	0.243811i	$-0.921602\pi$
$367$		−	9.34148i		−	0.487621i	0.969823	−	0.243811i	$-0.0783976\pi$
$368$		−	3.45508i		−	0.180109i
$369$	8.60416	−	24.5973i	0.447914	−	1.28049i
$370$			30.2555i			1.57291i
$371$	16.0388	+	21.8139i	0.832694	+	1.13252i
$372$	9.27912	+	13.0763i	0.481100	+	0.677973i
$373$	5.36579			0.277830			0.138915	−	0.990304i	$-0.455639\pi$
$373$	5.36579			0.277830			0.138915	+	0.990304i	$0.455639\pi$
$374$	4.10788			0.212413
$375$	−46.6502	+	33.1037i	−2.40901	+	1.70947i
$376$			2.39657i			0.123594i
$377$	8.60228			0.443040
$378$	−19.5661	+	25.4124i	−1.00637	+	1.30707i
$379$	1.03755			0.0532956			0.0266478	−	0.999645i	$-0.491517\pi$
$379$	1.03755			0.0532956			0.0266478	+	0.999645i	$0.491517\pi$
$380$		−	6.62914i		−	0.340068i
$381$	4.47860	−	3.17808i	0.229446	−	0.162818i
$382$	−45.1019			−2.30762
$383$	7.76843			0.396948			0.198474	−	0.980106i	$-0.436401\pi$
$383$	7.76843			0.396948			0.198474	+	0.980106i	$0.436401\pi$
$384$	−19.9661	−	28.1366i	−1.01889	−	1.43584i
$385$	−6.61655	−	8.99895i	−0.337211	−	0.458629i
$386$			4.29662i			0.218692i
$387$	−4.93173	+	14.0987i	−0.250694	+	0.716677i
$388$		−	20.9746i		−	1.06482i
$389$			2.42551i			0.122978i	0.998108	+	0.0614891i	$0.0195849\pi$
$389$			2.42551i			0.122978i	−0.998108	+	0.0614891i	$0.980415\pi$
$390$	−19.4297	+	13.7876i	−0.983862	+	0.698163i
$391$		−	6.30112i		−	0.318661i
$392$	22.4839	+	7.02407i	1.13561	+	0.354769i
$393$	24.2826	−	17.2313i	1.22490	−	0.869205i
$394$	−23.6142			−1.18967
$395$	30.9520			1.55736
$396$	−9.74814	−	3.40990i	−0.489862	−	0.171354i
$397$			21.0381i			1.05587i	0.849285	+	0.527935i	$0.177033\pi$
$397$			21.0381i			1.05587i	−0.849285	+	0.527935i	$0.822967\pi$
$398$	8.09358			0.405694
$399$	−1.98443	−	0.656844i	−0.0993460	−	0.0328833i
$400$	12.3807			0.619035
$401$		−	11.7702i		−	0.587774i	−0.955840	−	0.293887i	$-0.905051\pi$
$401$		−	11.7702i		−	0.587774i	0.955840	−	0.293887i	$-0.0949490\pi$
$402$	−4.70320	−	6.62783i	−0.234575	−	0.330566i
$403$	3.75575			0.187087
$404$	9.60020			0.477628
$405$	29.7108	+	23.6837i	1.47634	+	1.17685i
$406$	−30.6291	+	22.5203i	−1.52009	+	1.11766i
$407$			3.07199i			0.152273i
$408$	5.93936	+	8.36984i	0.294042	+	0.414369i
$409$			17.8387i			0.882067i	0.897491	+	0.441033i	$0.145388\pi$
$409$			17.8387i			0.882067i	−0.897491	+	0.441033i	$0.854612\pi$
$410$			85.5496i			4.22500i
$411$	−2.98290	−	4.20354i	−0.147135	−	0.207345i
$412$			18.4857i			0.910725i
$413$	21.1826	−	15.5746i	1.04233	−	0.766378i
$414$	−8.26930	+	23.6401i	−0.406414	+	1.16185i
$415$	38.0092			1.86580
$416$	−6.25366			−0.306611
$417$	19.0509	+	26.8468i	0.932926	+	1.31469i
$418$		−	1.06414i		−	0.0520489i
$419$	15.5168			0.758048			0.379024	−	0.925387i	$-0.376260\pi$
$419$	15.5168			0.758048			0.379024	+	0.925387i	$0.376260\pi$
$420$	20.9274	−	63.2251i	1.02115	−	3.08507i
$421$	10.6424			0.518678			0.259339	−	0.965786i	$-0.416495\pi$
$421$	10.6424			0.518678			0.259339	+	0.965786i	$0.416495\pi$
$422$			28.5206i			1.38836i
$423$	0.705457	−	2.01674i	0.0343005	−	0.0980574i
$424$	−34.4369			−1.67240
$425$	22.5790			1.09524
$426$	50.7151	−	35.9882i	2.45715	−	1.74363i
$427$	1.13145	+	1.53884i	0.0547545	+	0.0744698i
$428$			3.48123i			0.168272i
$429$	−1.97279	+	1.39992i	−0.0952473	+	0.0675889i
$430$		−	49.0353i		−	2.36469i
$431$			4.29755i			0.207006i	0.994629	+	0.103503i	$0.0330051\pi$
$431$			4.29755i			0.207006i	−0.994629	+	0.103503i	$0.966995\pi$
$432$	−1.38962	−	4.82070i	−0.0668582	−	0.231936i
$433$			28.1918i			1.35481i	0.735609	+	0.677407i	$0.236896\pi$
$433$			28.1918i			1.35481i	−0.735609	+	0.677407i	$0.763104\pi$
$434$	−13.3726	+	9.83233i	−0.641906	+	0.471967i
$435$	26.0643	+	36.7302i	1.24969	+	1.76108i
$436$	44.4752			2.12998
$437$	−1.63230			−0.0780834
$438$	25.8813	−	18.3658i	1.23666	−	0.877550i
$439$			3.25991i			0.155587i	0.996969	+	0.0777936i	$0.0247875\pi$
$439$			3.25991i			0.155587i	−0.996969	+	0.0777936i	$0.975212\pi$
$440$	14.2064			0.677263
$441$	−16.8529	−	12.5292i	−0.802517	−	0.596630i
$442$	5.73717			0.272890
$443$		−	11.1033i		−	0.527535i	−0.964586	−	0.263768i	$-0.915035\pi$
$443$		−	11.1033i		−	0.527535i	0.964586	−	0.263768i	$-0.0849652\pi$
$444$	−14.9378	+	10.6001i	−0.708917	+	0.503058i
$445$	−46.3336			−2.19642
$446$	−0.135378			−0.00641032
$447$	13.6395	+	19.2210i	0.645128	+	0.909124i
$448$	26.3828	−	19.3982i	1.24647	−	0.916477i
$449$			27.4107i			1.29359i	0.762663	+	0.646796i	$0.223891\pi$
$449$			27.4107i			1.29359i	−0.762663	+	0.646796i	$0.776109\pi$
$450$	−84.7102	−	29.6317i	−3.99328	−	1.39685i
$451$			8.68626i			0.409020i
$452$		−	19.4251i		−	0.913678i
$453$	−2.14065	+	1.51903i	−0.100576	+	0.0713704i
$454$			30.4033i			1.42690i
$455$	−9.24085	−	12.5682i	−0.433218	−	0.589205i
$456$	2.16820	−	1.53858i	0.101535	−	0.0720508i
$457$	−11.6143			−0.543294			−0.271647	−	0.962397i	$-0.587568\pi$
$457$	−11.6143			−0.543294			−0.271647	+	0.962397i	$0.587568\pi$
$458$	48.4461			2.26374
$459$	−2.53429	−	8.79164i	−0.118290	−	0.410358i
$460$		−	52.0058i		−	2.42478i
$461$	−4.11680			−0.191738			−0.0958691	−	0.995394i	$-0.530563\pi$
$461$	−4.11680			−0.191738			−0.0958691	+	0.995394i	$0.530563\pi$
$462$	3.35936	−	10.1492i	0.156292	−	0.472183i
$463$	−4.35586			−0.202434			−0.101217	−	0.994864i	$-0.532274\pi$
$463$	−4.35586			−0.202434			−0.101217	+	0.994864i	$0.532274\pi$
$464$		−	5.94696i		−	0.276081i
$465$	11.3796	+	16.0364i	0.527718	+	0.743668i
$466$	29.3522			1.35972
$467$	−10.3404			−0.478495			−0.239248	−	0.970959i	$-0.576901\pi$
$467$	−10.3404			−0.478495			−0.239248	+	0.970959i	$0.576901\pi$
$468$	−13.6145	−	4.76236i	−0.629331	−	0.220140i
$469$	4.28723	−	3.15222i	0.197966	−	0.145556i
$470$			7.01424i			0.323543i
$471$	−13.8582	−	19.5291i	−0.638550	−	0.899854i
$472$			33.4403i			1.53921i
$473$		−	4.97879i		−	0.228925i
$474$	17.1443	+	24.1601i	0.787465	+	1.10971i
$475$		−	5.84906i		−	0.268373i
$476$	−12.9208	+	9.50016i	−0.592226	+	0.435439i
$477$	28.9791	+	10.1369i	1.32686	+	0.464136i
$478$	1.69453			0.0775058
$479$	13.8894			0.634624			0.317312	−	0.948321i	$-0.397220\pi$
$479$	13.8894			0.634624			0.317312	+	0.948321i	$0.397220\pi$
$480$	−18.9481	−	26.7020i	−0.864859	−	1.21877i
$481$			4.29041i			0.195626i
$482$	−28.0284			−1.27666
$483$	−15.5679	−	5.15296i	−0.708366	−	0.234468i
$484$	3.44244			0.156475
$485$		−	25.7226i		−	1.16800i
$486$	−2.02980	+	36.3097i	−0.0920734	+	1.64704i
$487$	14.9643			0.678098			0.339049	−	0.940769i	$-0.389895\pi$
$487$	14.9643			0.678098			0.339049	+	0.940769i	$0.389895\pi$
$488$	−2.42933			−0.109970
$489$	15.7038	−	11.1437i	0.710152	−	0.503934i
$490$	65.8055	+	20.5579i	2.97279	+	0.928712i
$491$			2.78126i			0.125517i	0.998029	+	0.0627583i	$0.0199897\pi$
$491$			2.78126i			0.125517i	−0.998029	+	0.0627583i	$0.980010\pi$
$492$	−42.2377	+	29.9725i	−1.90422	+	1.35127i
$493$		−	10.8456i		−	0.488462i
$494$		−	1.48621i		−	0.0668676i
$495$	−11.9548	−	4.18180i	−0.537330	−	0.187958i
$496$		−	2.59644i		−	0.116583i
$497$	24.1203	+	32.8052i	1.08194	+	1.47151i
$498$	21.0533	+	29.6687i	0.943422	+	1.32948i
$499$	1.56108			0.0698836			0.0349418	−	0.999389i	$-0.488875\pi$
$499$	1.56108			0.0698836			0.0349418	+	0.999389i	$0.488875\pi$
$500$	113.689			5.08433
$501$	14.0032	−	9.93688i	0.625617	−	0.443947i
$502$		−	11.7060i		−	0.522465i
$503$	−33.5372			−1.49535			−0.747675	−	0.664065i	$-0.768830\pi$
$503$	−33.5372			−1.49535			−0.747675	+	0.664065i	$0.768830\pi$
$504$	25.5362	−	7.82943i	1.13747	−	0.348751i
$505$	11.7734			0.523910
$506$		−	8.34822i		−	0.371123i
$507$	15.6078	−	11.0755i	0.693166	−	0.491881i
$508$	−10.9146			−0.484257
$509$	13.1763			0.584027			0.292014	−	0.956414i	$-0.405675\pi$
$509$	13.1763			0.584027			0.292014	+	0.956414i	$0.405675\pi$
$510$	17.3832	+	24.4967i	0.769742	+	1.08473i
$511$	12.3092	+	16.7414i	0.544529	+	0.740596i
$512$			10.8214i			0.478243i
$513$	−2.27746	+	0.656504i	−0.100552	+	0.0289854i
$514$			7.11510i			0.313834i
$515$			22.6703i			0.998974i
$516$	24.2098	−	17.1796i	1.06578	−	0.756292i
$517$			0.712189i			0.0313220i
$518$	−11.2321	−	15.2763i	−0.493508	−	0.671204i
$519$	−27.6450	+	19.6173i	−1.21348	+	0.861104i
$520$	19.8410			0.870086
$521$	−41.1855			−1.80437			−0.902185	−	0.431348i	$-0.858038\pi$
$521$	−41.1855			−1.80437			−0.902185	+	0.431348i	$0.858038\pi$
$522$	−14.2333	+	40.6898i	−0.622975	+	1.78094i
$523$			40.0637i			1.75186i	0.482437	+	0.875931i	$0.339752\pi$
$523$			40.0637i			1.75186i	−0.482437	+	0.875931i	$0.660248\pi$
$524$	−59.1781			−2.58521
$525$	18.4648	−	55.7851i	0.805868	−	2.43466i
$526$	35.2675			1.53774
$527$		−	4.73519i		−	0.206268i
$528$	0.967800	+	1.36384i	0.0421181	+	0.0593534i
$529$	10.1946			0.443243
$530$	−100.789			−4.37801
$531$	9.84352	−	28.1404i	0.427172	−	1.22119i
$532$	2.46100	+	3.34713i	0.106698	+	0.145116i
$533$			12.1315i			0.525472i
$534$	−25.6642	−	36.1664i	−1.11060	−	1.56507i
$535$			4.26928i			0.184577i
$536$			6.76812i			0.292338i
$537$	−22.8312	−	32.1740i	−0.985237	−	1.38841i
$538$			9.20031i			0.396653i
$539$	6.68154	+	2.08734i	0.287794	+	0.0899082i
$540$	−20.9165	−	72.5611i	−0.900104	−	3.12253i
$541$	1.57817			0.0678506			0.0339253	−	0.999424i	$-0.489199\pi$
$541$	1.57817			0.0678506			0.0339253	+	0.999424i	$0.489199\pi$
$542$	−47.8989			−2.05743
$543$	−5.57244	−	7.85277i	−0.239136	−	0.336994i
$544$			7.88451i			0.338046i
$545$	54.5431			2.33637
$546$	4.69177	−	14.1746i	0.200789	−	0.606618i
$547$	−2.44818			−0.104676			−0.0523382	−	0.998629i	$-0.516667\pi$
$547$	−2.44818			−0.104676			−0.0523382	+	0.998629i	$0.516667\pi$
$548$			10.2443i			0.437613i
$549$	2.04431	+	0.715099i	0.0872488	+	0.0305197i
$550$	29.9144			1.27556
$551$	−2.80954			−0.119691
$552$	17.0096	−	12.0702i	0.723975	−	0.513743i
$553$	−15.6280	+	11.4906i	−0.664570	+	0.488630i
$554$		−	59.9705i		−	2.54790i
$555$	−18.3193	+	12.9996i	−0.777611	+	0.551804i
$556$		−	65.4271i		−	2.77473i
$557$			31.2684i			1.32488i	0.749114	+	0.662441i	$0.230480\pi$
$557$			31.2684i			1.32488i	−0.749114	+	0.662441i	$0.769520\pi$
$558$	−6.21425	+	17.7651i	−0.263070	+	0.752058i
$559$		−	6.95351i		−	0.294102i
$560$	−8.68867	+	6.38842i	−0.367163	+	0.269960i
$561$	1.76500	+	2.48727i	0.0745184	+	0.105012i
$562$	18.1893			0.767267
$563$	−11.6013			−0.488937			−0.244469	−	0.969657i	$-0.578614\pi$
$563$	−11.6013			−0.488937			−0.244469	+	0.969657i	$0.578614\pi$
$564$	−3.46309	+	2.45746i	−0.145822	+	0.103478i
$565$		−	23.8223i		−	1.00221i
$566$	11.4737			0.482276
$567$	−23.7937	−	0.928296i	−0.999240	−	0.0389848i
$568$	−51.7886			−2.17300
$569$		−	3.72158i		−	0.156017i	−0.996953	−	0.0780083i	$-0.975144\pi$
$569$		−	3.72158i		−	0.156017i	0.996953	−	0.0780083i	$-0.0248561\pi$
$570$	6.34584	−	4.50310i	0.265798	−	0.188614i
$571$	8.16109			0.341531			0.170765	−	0.985312i	$-0.445376\pi$
$571$	8.16109			0.341531			0.170765	+	0.985312i	$0.445376\pi$
$572$	4.80780			0.201024
$573$	−19.3786	−	27.3086i	−0.809552	−	1.14083i
$574$	−31.7595	−	43.1950i	−1.32561	−	1.80292i
$575$		−	45.8861i		−	1.91358i
$576$	12.2601	−	35.0488i	0.510836	−	1.46036i
$577$		−	19.1499i		−	0.797219i	−0.917121	−	0.398609i	$-0.869493\pi$
$577$		−	19.1499i		−	0.797219i	0.917121	−	0.398609i	$-0.130507\pi$
$578$			32.4260i			1.34875i
$579$	−2.60154	+	1.84609i	−0.108116	+	0.0767210i
$580$		−	89.5134i		−	3.71684i
$581$	−19.1913	+	14.1105i	−0.796187	+	0.585403i
$582$	20.0782	−	14.2478i	0.832269	−	0.590590i
$583$	−10.2336			−0.423833
$584$	−26.4292			−1.09365
$585$	−16.6964	−	5.84042i	−0.690312	−	0.241472i
$586$			19.3061i			0.797526i
$587$	5.98496			0.247026			0.123513	−	0.992343i	$-0.460584\pi$
$587$	5.98496			0.247026			0.123513	+	0.992343i	$0.460584\pi$
$588$	12.9052	+	39.6921i	0.532202	+	1.63688i
$589$	−1.22664			−0.0505430
$590$			97.8724i			4.02934i
$591$	−10.1461	−	14.2981i	−0.417356	−	0.588145i
$592$	2.96607			0.121905
$593$	−42.6279			−1.75052			−0.875259	−	0.483654i	$-0.839309\pi$
$593$	−42.6279			−1.75052			−0.875259	+	0.483654i	$0.839309\pi$
$594$	−3.35762	−	11.6478i	−0.137765	−	0.477917i
$595$	−15.8457	+	11.6507i	−0.649612	+	0.477633i
$596$		−	46.8427i		−	1.91875i
$597$	3.47750	+	4.90055i	0.142325	+	0.200566i
$598$		−	11.6593i		−	0.476786i
$599$			22.7263i			0.928571i	0.885686	+	0.464285i	$0.153689\pi$
$599$			22.7263i			0.928571i	−0.885686	+	0.464285i	$0.846311\pi$
$600$	43.2517	+	60.9509i	1.76574	+	2.48831i
$601$		−	39.7328i		−	1.62074i	−0.585921	−	0.810368i	$-0.699267\pi$
$601$		−	39.7328i		−	1.62074i	0.585921	−	0.810368i	$-0.300733\pi$
$602$	18.2039	+	24.7585i	0.741935	+	1.00908i
$603$	1.99227	−	5.69545i	0.0811316	−	0.231937i
$604$	5.21687			0.212272
$605$	4.22171			0.171637
$606$	6.52130	+	9.18992i	0.264910	+	0.373315i
$607$		−	29.4597i		−	1.19573i	−0.801596	−	0.597867i	$-0.796015\pi$
$607$		−	29.4597i		−	1.19573i	0.801596	−	0.597867i	$-0.203985\pi$
$608$	2.04247			0.0828332
$609$	−26.7959	−	8.86938i	−1.08582	−	0.359405i
$610$	−7.11010			−0.287880
$611$			0.994662i			0.0402397i
$612$	−6.00431	+	17.1650i	−0.242710	+	0.693852i
$613$	31.7134			1.28089			0.640446	−	0.768003i	$-0.278750\pi$
$613$	31.7134			1.28089			0.640446	+	0.768003i	$0.278750\pi$
$614$	61.8290			2.49522
$615$	−51.7991	+	36.7574i	−2.08874	+	1.48220i
$616$	−7.17296	+	5.27398i	−0.289007	+	0.212495i
$617$			30.1079i			1.21210i	0.795428	+	0.606048i	$0.207246\pi$
$617$			30.1079i			1.21210i	−0.795428	+	0.606048i	$0.792754\pi$
$618$	−17.6957	+	12.5571i	−0.711825	+	0.505122i
$619$			25.6706i			1.03179i	0.856653	+	0.515893i	$0.172540\pi$
$619$			25.6706i			1.03179i	−0.856653	+	0.515893i	$0.827460\pi$
$620$		−	39.0815i		−	1.56955i
$621$	−17.8667	+	5.15029i	−0.716968	+	0.206674i
$622$			51.8628i			2.07951i
$623$	23.3943	−	17.2009i	0.937275	−	0.689139i
$624$	1.35165	+	1.90477i	0.0541095	+	0.0762519i
$625$	75.3108			3.01243
$626$	−52.5528			−2.10043
$627$	0.644323	−	0.457221i	0.0257318	−	0.0182597i
$628$			47.5935i			1.89919i
$629$	5.40929			0.215682
$630$	74.7388	−	22.9150i	2.97766	−	0.912957i
$631$	25.5038			1.01529			0.507645	−	0.861566i	$-0.330516\pi$
$631$	25.5038			1.01529			0.507645	+	0.861566i	$0.330516\pi$
$632$		−	24.6715i		−	0.981378i
$633$	−17.2688	+	12.2542i	−0.686375	+	0.487062i
$634$	12.7245			0.505354
$635$	−13.3853			−0.531181
$636$	−35.3118	−	49.7619i	−1.40020	−	1.97319i
$637$	9.33162	+	2.91524i	0.369732	+	0.115506i
$638$		−	14.3691i		−	0.568879i
$639$	43.5807	+	15.2445i	1.72403	+	0.603065i
$640$			84.0927i			3.32406i
$641$		−	6.90270i		−	0.272640i	−0.990665	−	0.136320i	$-0.956472\pi$
$641$		−	6.90270i		−	0.272640i	0.990665	−	0.136320i	$-0.0435276\pi$
$642$	−3.33245	+	2.36476i	−0.131521	+	0.0933295i
$643$		−	10.4172i		−	0.410813i	−0.978677	−	0.205406i	$-0.934148\pi$
$643$		−	10.4172i		−	0.410813i	0.978677	−	0.205406i	$-0.0658516\pi$
$644$	19.3066	+	26.2583i	0.760788	+	1.03472i
$645$	29.6902	−	21.0686i	1.16905	−	0.829576i
$646$	−1.87379			−0.0737232
$647$	34.7709			1.36699			0.683493	−	0.729957i	$-0.260460\pi$
$647$	34.7709			1.36699			0.683493	+	0.729957i	$0.260460\pi$
$648$	18.8780	−	23.6822i	0.741597	−	0.930324i
$649$			9.93745i			0.390079i
$650$	41.7793			1.63872
$651$	−11.6990	−	3.87236i	−0.458522	−	0.151770i
$652$	−38.2711			−1.49881
$653$		−	23.3723i		−	0.914628i	−0.889305	−	0.457314i	$-0.848812\pi$
$653$		−	23.3723i		−	0.914628i	0.889305	−	0.457314i	$-0.151188\pi$
$654$	30.2115	+	42.5745i	1.18136	+	1.66479i
$655$	−72.5743			−2.83571
$656$	8.38677			0.327448
$657$	22.2404	+	7.77972i	0.867682	+	0.303516i
$658$	−2.60397	−	3.54157i	−0.101513	−	0.138065i
$659$			9.07120i			0.353364i	0.984268	+	0.176682i	$0.0565364\pi$
$659$			9.07120i			0.353364i	−0.984268	+	0.176682i	$0.943464\pi$
$660$	14.5673	+	20.5285i	0.567031	+	0.799069i
$661$			40.3605i			1.56984i	0.619597	+	0.784920i	$0.287296\pi$
$661$			40.3605i			1.56984i	−0.619597	+	0.784920i	$0.712704\pi$
$662$		−	2.58053i		−	0.100295i
$663$	2.46505	+	3.47378i	0.0957345	+	0.134910i
$664$		−	30.2967i		−	1.17574i
$665$	3.01810	+	4.10482i	0.117037	+	0.159178i
$666$	−20.2942	−	7.09890i	−0.786383	−	0.275077i
$667$	−22.0409			−0.853429
$668$	−34.1266			−1.32040
$669$	−0.0581667	−	0.0819694i	−0.00224885	−	0.00316912i
$670$			19.8088i			0.765281i
$671$	−0.721923			−0.0278695
$672$	19.4800	+	6.44783i	0.751456	+	0.248730i
$673$	−32.4425			−1.25057			−0.625283	−	0.780398i	$-0.715016\pi$
$673$	−32.4425			−1.25057			−0.625283	+	0.780398i	$0.715016\pi$
$674$			37.7789i			1.45519i
$675$	−18.4552	−	64.0225i	−0.710341	−	2.46423i
$676$	−38.0370			−1.46296
$677$	−26.6595			−1.02461			−0.512304	−	0.858804i	$-0.671208\pi$
$677$	−26.6595			−1.02461			−0.512304	+	0.858804i	$0.671208\pi$
$678$	18.5949	−	13.1952i	0.714133	−	0.506759i
$679$	9.54927	+	12.9876i	0.366467	+	0.498420i
$680$		−	25.0152i		−	0.959290i
$681$	−18.4088	+	13.0631i	−0.705425	+	0.500580i
$682$		−	6.27355i		−	0.240227i
$683$		−	26.9280i		−	1.03037i	−0.857079	−	0.515185i	$-0.827723\pi$
$683$		−	26.9280i		−	1.03037i	0.857079	−	0.515185i	$-0.172277\pi$
$684$	4.44656	+	1.55541i	0.170018	+	0.0594725i
$685$			12.5633i			0.480018i
$686$	−40.8578	+	14.0497i	−1.55996	+	0.536420i
$687$	20.8155	+	29.3335i	0.794159	+	1.11914i
$688$	−4.80712			−0.183270
$689$	−14.2925			−0.544502
$690$	49.7833	−	35.3269i	1.89522	−	1.34487i
$691$		−	27.5077i		−	1.04644i	−0.852197	−	0.523222i	$-0.824730\pi$
$691$		−	27.5077i		−	1.04644i	0.852197	−	0.523222i	$-0.175270\pi$
$692$	67.3724			2.56111
$693$	7.58858	−	2.32667i	0.288266	−	0.0883830i
$694$	−64.2257			−2.43797
$695$		−	80.2379i		−	3.04360i
$696$	29.2772	−	20.7755i	1.10975	−	0.787495i
$697$	15.2952			0.579345
$698$	66.0103			2.49853
$699$	12.6115	+	17.7724i	0.477012	+	0.672213i
$700$	−94.0923	+	69.1821i	−3.55635	+	2.61484i
$701$			28.3585i			1.07108i	0.844508	+	0.535542i	$0.179893\pi$
$701$			28.3585i			1.07108i	−0.844508	+	0.535542i	$0.820107\pi$
$702$	−4.68934	−	16.2677i	−0.176988	−	0.613984i
$703$		−	1.40127i		−	0.0528499i
$704$			12.3771i			0.466478i
$705$	−4.24703	+	3.01375i	−0.159952	+	0.113504i
$706$			6.19561i			0.233175i
$707$	−5.94453	+	4.37076i	−0.223567	+	0.164379i
$708$	−48.3218	+	34.2898i	−1.81604	+	1.28869i
$709$	5.93771			0.222995			0.111498	−	0.993765i	$-0.464435\pi$
$709$	5.93771			0.222995			0.111498	+	0.993765i	$0.464435\pi$
$710$	−151.574			−5.68846
$711$	−7.26232	+	20.7613i	−0.272358	+	0.778610i
$712$			36.9320i			1.38408i
$713$	−9.62306			−0.360386
$714$	−17.8711	−	5.91531i	−0.668810	−	0.221375i
$715$	5.89615			0.220504
$716$			78.4098i			2.93031i
$717$	0.728073	+	1.02601i	0.0271904	+	0.0383171i
$718$	−8.66705			−0.323452
$719$	37.6469			1.40399			0.701997	−	0.712180i	$-0.252292\pi$
$719$	37.6469			1.40399			0.701997	+	0.712180i	$0.252292\pi$
$720$	−4.03762	+	11.5426i	−0.150473	+	0.430169i
$721$	−8.41613	−	11.4465i	−0.313433	−	0.426290i
$722$		−	43.8398i		−	1.63155i
$723$	−12.0428	−	16.9708i	−0.447875	−	0.631152i
$724$			19.1376i			0.711244i
$725$		−	78.9800i		−	2.93324i
$726$	2.33841	+	3.29532i	0.0867866	+	0.122301i
$727$			33.7264i			1.25084i	0.780287	+	0.625421i	$0.215073\pi$
$727$			33.7264i			1.25084i	−0.780287	+	0.625421i	$0.784927\pi$
$728$	−10.0179	+	7.36578i	−0.371290	+	0.272994i
$729$	−22.8571	+	14.3719i	−0.846561	+	0.532292i
$730$	−77.3524			−2.86294
$731$	−8.76687			−0.324255
$732$	−2.49104	−	3.51042i	−0.0920716	−	0.129749i
$733$			35.8521i			1.32423i	0.749403	+	0.662114i	$0.230341\pi$
$733$			35.8521i			1.32423i	−0.749403	+	0.662114i	$0.769659\pi$
$734$	−21.7928			−0.804386
$735$	15.8266	+	48.6773i	0.583772	+	1.79549i
$736$	16.0233			0.590625
$737$			2.01128i			0.0740866i
$738$	−57.3832	−	20.0727i	−2.11231	−	0.738885i
$739$	50.5304			1.85879			0.929396	−	0.369084i	$-0.120329\pi$
$739$	50.5304			1.85879			0.929396	+	0.369084i	$0.120329\pi$
$740$	44.6451			1.64119
$741$	0.899878	−	0.638567i	0.0330579	−	0.0234583i
$742$	50.8897	−	37.4170i	1.86822	−	1.37362i
$743$		−	34.0237i		−	1.24821i	−0.781341	−	0.624104i	$-0.785464\pi$
$743$		−	34.0237i		−	1.24821i	0.781341	−	0.624104i	$-0.214536\pi$
$744$	12.7824	−	9.07058i	0.468626	−	0.332544i
$745$		−	57.4466i		−	2.10468i
$746$		−	12.5179i		−	0.458312i
$747$	−8.91816	+	25.4950i	−0.326298	+	0.932813i
$748$		−	6.06160i		−	0.221634i
$749$	−1.58493	−	2.15561i	−0.0579120	−	0.0787641i
$750$	77.2277	+	108.830i	2.81996	+	3.97393i
$751$	37.5408			1.36988			0.684942	−	0.728597i	$-0.259827\pi$
$751$	37.5408			1.36988			0.684942	+	0.728597i	$0.259827\pi$
$752$	0.687633			0.0250754
$753$	7.08783	−	5.02963i	0.258295	−	0.183290i
$754$		−	20.0683i		−	0.730844i
$755$	6.39782			0.232840
$756$	37.4986	+	28.8718i	1.36381	+	1.05006i
$757$	−10.0932			−0.366844			−0.183422	−	0.983034i	$-0.558718\pi$
$757$	−10.0932			−0.366844			−0.183422	+	0.983034i	$0.558718\pi$
$758$		−	2.42052i		−	0.0879171i
$759$	5.05473	−	3.58691i	0.183475	−	0.130197i
$760$	−6.48016			−0.235060
$761$	15.1522			0.549267			0.274633	−	0.961549i	$-0.411443\pi$
$761$	15.1522			0.549267			0.274633	+	0.961549i	$0.411443\pi$
$762$	−7.41415	−	10.4481i	−0.268586	−	0.378496i
$763$	−27.5394	+	20.2486i	−0.996994	+	0.733048i
$764$			66.5526i			2.40779i
$765$	−7.36351	+	21.0506i	−0.266228	+	0.761086i
$766$		−	18.1230i		−	0.654811i
$767$			13.8789i			0.501138i
$768$	−30.6737	+	21.7665i	−1.10684	+	0.785432i
$769$		−	25.0082i		−	0.901820i	−0.892569	−	0.450910i	$-0.851100\pi$
$769$		−	25.0082i		−	0.901820i	0.892569	−	0.450910i	$-0.148900\pi$
$770$	−20.9937	+	15.4358i	−0.756560	+	0.556267i
$771$	−4.30810	+	3.05709i	−0.155152	+	0.110098i
$772$	6.34010			0.228185
$773$	−22.0311			−0.792403			−0.396202	−	0.918164i	$-0.629672\pi$
$773$	−22.0311			−0.792403			−0.396202	+	0.918164i	$0.629672\pi$
$774$	32.8909	+	11.5052i	1.18224	+	0.413548i
$775$		−	34.4826i		−	1.23865i
$776$	−20.5032			−0.736023
$777$	4.42363	−	13.3645i	0.158697	−	0.479450i
$778$	5.65848			0.202866
$779$		−	3.96219i		−	0.141960i
$780$	20.3451	+	28.6706i	0.728470	+	1.02657i
$781$	−15.3900			−0.550698
$782$	−14.6999			−0.525668
$783$	−30.7526	+	8.86479i	−1.09901	+	0.316802i
$784$	2.01537	−	6.45117i	0.0719776	−	0.230399i
$785$			58.3673i			2.08322i
$786$	−40.1990	−	56.6491i	−1.43385	−	2.02060i
$787$			7.29340i			0.259982i	0.991515	+	0.129991i	$0.0414948\pi$
$787$			7.29340i			0.259982i	−0.991515	+	0.129991i	$0.958505\pi$
$788$			34.8452i			1.24131i
$789$	15.1531	+	21.3540i	0.539465	+	0.760222i
$790$		−	72.2079i		−	2.56904i
$791$	8.84380	+	12.0282i	0.314449	+	0.427672i
$792$	−3.33327	+	9.52906i	−0.118443	+	0.338601i
$793$	−1.00826			−0.0358042
$794$	49.0798			1.74178
$795$	−43.3053	−	61.0266i	−1.53588	−	2.16439i
$796$		−	11.9429i		−	0.423305i
$797$	49.9500			1.76932			0.884660	−	0.466236i	$-0.154390\pi$
$797$	49.9500			1.76932			0.884660	+	0.466236i	$0.154390\pi$
$798$	−1.53235	+	4.62949i	−0.0542447	+	0.163882i
$799$	1.25405			0.0443653
$800$			57.4166i			2.02998i
$801$	10.8713	−	31.0787i	0.384120	−	1.09811i
$802$	−27.4587			−0.969599
$803$	−7.85395			−0.277160
$804$	−9.78005	+	6.94007i	−0.344916	+	0.244757i
$805$	23.6771	+	32.2024i	0.834508	+	1.13499i
$806$		−	8.76180i		−	0.308621i
$807$	−5.57066	+	3.95302i	−0.196097	+	0.139153i
$808$		−	9.38445i		−	0.330144i
$809$			45.4705i			1.59866i	0.600893	+	0.799329i	$0.294812\pi$
$809$			45.4705i			1.59866i	−0.600893	+	0.799329i	$0.705188\pi$
$810$	55.2517	−	69.3125i	1.94135	−	2.43539i
$811$		−	21.8557i		−	0.767457i	−0.923446	−	0.383728i	$-0.874640\pi$
$811$		−	21.8557i		−	0.767457i	0.923446	−	0.383728i	$-0.125360\pi$
$812$	33.2310	+	45.1964i	1.16618	+	1.58608i
$813$	−20.5803	−	29.0021i	−0.721784	−	1.01715i
$814$	7.16665			0.251191
$815$	−46.9345			−1.64405
$816$	2.40151	−	1.70414i	0.0840696	−	0.0596570i
$817$			2.27105i			0.0794539i
$818$	41.6160			1.45507
$819$	10.5984	−	3.24949i	0.370339	−	0.113546i
$820$	126.237			4.40840
$821$		−	22.9451i		−	0.800788i	−0.916343	−	0.400394i	$-0.868873\pi$
$821$		−	22.9451i		−	0.800788i	0.916343	−	0.400394i	$-0.131127\pi$
$822$	−9.80646	+	6.95881i	−0.342040	+	0.242716i
$823$	−14.6323			−0.510050			−0.255025	−	0.966934i	$-0.582084\pi$
$823$	−14.6323			−0.510050			−0.255025	+	0.966934i	$0.582084\pi$
$824$	18.0703			0.629508
$825$	12.8531	+	18.1128i	0.447487	+	0.630606i
$826$	−36.3342	−	49.4169i	−1.26423	−	1.71943i
$827$		−	54.2583i		−	1.88675i	−0.331733	−	0.943373i	$-0.607633\pi$
$827$		−	54.2583i		−	1.88675i	0.331733	−	0.943373i	$-0.392367\pi$
$828$	34.8834	+	12.2022i	1.21228	+	0.424056i
$829$		−	14.4417i		−	0.501582i	−0.968041	−	0.250791i	$-0.919309\pi$
$829$		−	14.4417i		−	0.501582i	0.968041	−	0.250791i	$-0.0806907\pi$
$830$		−	88.6717i		−	3.07784i
$831$	36.3113	−	25.7670i	1.25963	−	0.893849i
$832$			17.2861i			0.599289i
$833$	3.67549	−	11.7652i	0.127348	−	0.407638i
$834$	62.6310	−	44.4439i	2.16873	−	1.53897i
$835$	−41.8518			−1.44834
$836$	−1.57025			−0.0543083
$837$	−13.4266	+	3.87036i	−0.464090	+	0.133779i
$838$		−	36.1993i		−	1.25048i
$839$	−26.2227			−0.905309			−0.452655	−	0.891686i	$-0.649523\pi$
$839$	−26.2227			−0.905309			−0.452655	+	0.891686i	$0.649523\pi$
$840$	−61.8042	−	20.4571i	−2.13245	−	0.705836i
$841$	−8.93732			−0.308184
$842$		−	24.8277i		−	0.855618i
$843$	7.81523	+	11.0133i	0.269171	+	0.379320i
$844$	42.0851			1.44863
$845$	−46.6475			−1.60472
$846$	−4.70487	−	1.64576i	−0.161757	−	0.0565825i
$847$	−2.13159	+	1.56727i	−0.0732423	+	0.0538520i
$848$			9.88077i			0.339307i
$849$	4.92982	+	6.94718i	0.169191	+	0.238427i
$850$		−	52.6747i		−	1.80673i
$851$		−	10.9930i		−	0.376835i
$852$	−53.1043	−	74.8354i	−1.81932	−	2.56382i
$853$		−	45.5754i		−	1.56047i	−0.625486	−	0.780236i	$-0.715099\pi$
$853$		−	45.5754i		−	1.56047i	0.625486	−	0.780236i	$-0.284901\pi$
$854$	3.58997	−	2.63956i	0.122846	−	0.0903237i
$855$	5.45313	+	1.90751i	0.186493	+	0.0652354i
$856$	3.40299			0.116312
$857$	18.5675			0.634254			0.317127	−	0.948383i	$-0.397282\pi$
$857$	18.5675			0.634254			0.317127	+	0.948383i	$0.397282\pi$
$858$	3.26589	+	4.60234i	0.111495	+	0.157121i
$859$		−	0.709731i		−	0.0242157i	−0.999927	−	0.0121079i	$-0.996146\pi$
$859$		−	0.709731i		−	0.0242157i	0.999927	−	0.0121079i	$-0.00385414\pi$
$860$	−72.3567			−2.46734
$861$	12.5081	−	37.7892i	0.426276	−	1.28785i
$862$	10.0258			0.341480
$863$		−	35.5210i		−	1.20915i	−0.796549	−	0.604574i	$-0.793343\pi$
$863$		−	35.5210i		−	1.20915i	0.796549	−	0.604574i	$-0.206657\pi$
$864$	22.3564	−	6.44449i	0.760581	−	0.219246i
$865$	82.6235			2.80928
$866$	65.7689			2.23492
$867$	−19.6335	+	13.9322i	−0.666789	+	0.473163i
$868$	14.5086	+	19.7327i	0.492455	+	0.669771i
$869$		−	7.33162i		−	0.248708i
$870$	85.6880	−	60.8054i	2.90509	−	2.06150i
$871$			2.80901i			0.0951797i
$872$		−	43.4757i		−	1.47227i
$873$	17.2537	+	6.03535i	0.583949	+	0.204266i
$874$			3.80799i			0.128807i
$875$	−70.3973	+	51.7601i	−2.37986	+	1.74981i
$876$	−27.1006	−	38.1906i	−0.915644	−	1.29034i
$877$	−41.8338			−1.41263			−0.706314	−	0.707899i	$-0.749643\pi$
$877$	−41.8338			−1.41263			−0.706314	+	0.707899i	$0.749643\pi$
$878$	7.60506			0.256658
$879$	−11.6896	+	8.29508i	−0.394279	+	0.279786i
$880$		−	4.07615i		−	0.137407i
$881$	24.7157			0.832694			0.416347	−	0.909206i	$-0.363310\pi$
$881$	24.7157			0.832694			0.416347	+	0.909206i	$0.363310\pi$
$882$	−29.2295	+	39.3161i	−0.984208	+	1.32384i
$883$	−48.8801			−1.64495			−0.822473	−	0.568804i	$-0.807406\pi$
$883$	−48.8801			−1.64495			−0.822473	+	0.568804i	$0.807406\pi$
$884$		−	8.46580i		−	0.284736i
$885$	−59.2604	+	42.0521i	−1.99202	+	1.41356i
$886$	−25.9030			−0.870228
$887$	−0.101179			−0.00339727			−0.00169863	−	0.999999i	$-0.500541\pi$
$887$	−0.101179			−0.00339727			−0.00169863	+	0.999999i	$0.500541\pi$
$888$	10.3619	+	14.6021i	0.347722	+	0.490015i
$889$	6.75841	−	4.96917i	0.226670	−	0.166661i
$890$			108.092i			3.62324i
$891$	5.60997	−	7.03763i	0.187941	−	0.235770i
$892$			0.199764i			0.00668859i
$893$		−	0.324861i		−	0.0108711i
$894$	44.8408	−	31.8197i	1.49970	−	1.06421i
$895$			96.1595i			3.21426i
$896$	−31.2186	−	42.4594i	−1.04294	−	1.41847i
$897$	7.05957	−	5.00957i	0.235712	−	0.167265i
$898$	63.9465			2.13392
$899$	−16.5634			−0.552420
$900$	−43.7246	+	124.999i	−1.45749	+	4.16662i
$901$			18.0198i			0.600327i
$902$	20.2642			0.674725
$903$	−7.16941	+	21.6600i	−0.238583	+	0.720799i
$904$	−18.9885			−0.631548
$905$			23.4698i			0.780163i
$906$	3.54376	+	4.99392i	0.117734	+	0.165912i
$907$	17.2441			0.572581			0.286290	−	0.958143i	$-0.407578\pi$
$907$	17.2441			0.572581			0.286290	+	0.958143i	$0.407578\pi$
$908$	44.8632			1.48884
$909$	−2.76242	+	7.89712i	−0.0916236	+	0.261931i
$910$	−29.3203	+	21.5580i	−0.971960	+	0.714641i
$911$		−	1.75215i		−	0.0580512i	−0.999579	−	0.0290256i	$-0.990760\pi$
$911$		−	1.75215i		−	0.0580512i	0.999579	−	0.0290256i	$-0.00924043\pi$
$912$	−0.441456	−	0.622107i	−0.0146181	−	0.0206000i
$913$		−	9.00326i		−	0.297964i
$914$			27.0950i			0.896224i
$915$	−3.05494	−	4.30507i	−0.100993	−	0.142321i
$916$		−	71.4873i		−	2.36201i
$917$	36.6436	−	26.9425i	1.21008	−	0.889719i
$918$	−20.5100	+	5.91225i	−0.676932	+	0.195133i
$919$	11.9003			0.392553			0.196277	−	0.980549i	$-0.437115\pi$
$919$	11.9003			0.392553			0.196277	+	0.980549i	$0.437115\pi$
$920$	−50.8370			−1.67605
$921$	26.5656	+	37.4366i	0.875366	+	1.23358i
$922$			9.60409i			0.316294i
$923$	−21.4941			−0.707487
$924$	−14.9762	−	4.95709i	−0.492680	−	0.163076i
$925$	39.3915			1.29519
$926$			10.1618i			0.333938i
$927$	−15.2063	−	5.31918i	−0.499442	−	0.174705i
$928$	27.5796			0.905343
$929$	−33.9719			−1.11458			−0.557290	−	0.830318i	$-0.688159\pi$
$929$	−33.9719			−1.11458			−0.557290	+	0.830318i	$0.688159\pi$
$930$	37.4113	−	26.5476i	1.22676	−	0.870530i
$931$	−3.04775	−	0.952130i	−0.0998859	−	0.0312048i
$932$		−	43.3122i		−	1.41874i
$933$	−31.4022	+	22.2835i	−1.02806	+	0.729528i
$934$			24.1231i			0.789331i
$935$		−	7.43377i		−	0.243110i
$936$	−4.65533	+	13.3085i	−0.152164	+	0.435003i
$937$		−	49.8460i		−	1.62840i	−0.580587	−	0.814198i	$-0.697177\pi$
$937$		−	49.8460i		−	1.62840i	0.580587	−	0.814198i	$-0.302823\pi$
$938$	−7.35382	−	10.0017i	−0.240111	−	0.326567i
$939$	−22.5799	−	31.8200i	−0.736869	−	1.03841i
$940$	10.3502			0.337588
$941$	27.0230			0.880924			0.440462	−	0.897771i	$-0.354815\pi$
$941$	27.0230			0.880924			0.440462	+	0.897771i	$0.354815\pi$
$942$	−45.5596	+	32.3297i	−1.48441	+	1.05336i
$943$		−	31.0835i		−	1.01222i
$944$	9.59482			0.312285
$945$	45.9871	+	35.4076i	1.49596	+	1.15181i
$946$	−11.6150			−0.377637
$947$			59.8276i			1.94414i	0.234698	+	0.972068i	$0.424590\pi$
$947$			59.8276i			1.94414i	−0.234698	+	0.972068i	$0.575410\pi$
$948$	35.6507	−	25.2982i	1.15788	−	0.821648i
$949$	−10.9690			−0.356070
$950$	−13.6453			−0.442712
$951$	5.46723	+	7.70451i	0.177287	+	0.249836i
$952$	9.28665	+	12.6305i	0.300982	+	0.409356i
$953$			34.8664i			1.12943i	0.825285	+	0.564717i	$0.191015\pi$
$953$			34.8664i			1.12943i	−0.825285	+	0.564717i	$0.808985\pi$
$954$	23.6484	−	67.6054i	0.765645	−	2.18880i
$955$			81.6181i			2.64110i
$956$		−	2.50045i		−	0.0808702i
$957$	8.70031	−	6.17387i	0.281241	−	0.199573i
$958$		−	32.4027i		−	1.04688i
$959$	−4.66399	−	6.34333i	−0.150608	−	0.204837i
$960$	−73.8086	+	52.3757i	−2.38216	+	1.69042i
$961$	23.7684			0.766724
$962$	10.0091			0.322707
$963$	−2.86366	−	1.00171i	−0.0922801	−	0.0322796i
$964$			41.3588i			1.33208i
$965$	7.77532			0.250296
$966$	−12.0214	+	36.3185i	−0.386781	+	1.16853i
$967$	−54.0650			−1.73861			−0.869306	−	0.494274i	$-0.835434\pi$
$967$	−54.0650			−1.73861			−0.869306	+	0.494274i	$0.835434\pi$
$968$		−	3.36508i		−	0.108158i
$969$	−0.805095	−	1.13455i	−0.0258634	−	0.0364471i
$970$	−60.0084			−1.92675
$971$	−29.3809			−0.942877			−0.471439	−	0.881899i	$-0.656265\pi$
$971$	−29.3809			−0.942877			−0.471439	+	0.881899i	$0.656265\pi$
$972$	53.5787	+	2.99517i	1.71854	+	0.0960703i
$973$	29.7875	+	40.5130i	0.954944	+	1.29879i
$974$		−	34.9103i		−	1.11860i
$975$	17.9510	+	25.2968i	0.574891	+	0.810146i
$976$			0.697031i			0.0223114i
$977$		−	13.5831i		−	0.434561i	−0.976109	−	0.217281i	$-0.930281\pi$
$977$		−	13.5831i		−	0.434561i	0.976109	−	0.217281i	$-0.0697186\pi$
$978$	−25.9971	−	36.6355i	−0.831296	−	1.17147i
$979$			10.9751i			0.350765i
$980$	30.3353	−	97.1028i	0.969027	−	3.10183i
$981$	−12.7975	+	36.5853i	−0.408594	+	1.16808i
$982$	6.48842			0.207054
$983$	53.7873			1.71555			0.857775	−	0.514026i	$-0.171847\pi$
$983$	53.7873			1.71555			0.857775	+	0.514026i	$0.171847\pi$
$984$	29.2989	+	41.2885i	0.934016	+	1.31623i
$985$			42.7332i			1.36159i
$986$	−25.3018			−0.805773
$987$	1.02555	−	3.09834i	0.0326435	−	0.0986214i
$988$	−2.19305			−0.0697703
$989$			17.8164i			0.566529i
$990$	−9.75575	+	27.8895i	−0.310058	+	0.886386i
$991$	32.4114			1.02958			0.514791	−	0.857316i	$-0.327869\pi$
$991$	32.4114			1.02958			0.514791	+	0.857316i	$0.327869\pi$
$992$	12.0412			0.382309
$993$	1.56248	−	1.10876i	0.0495837	−	0.0351853i
$994$	76.5313	−	56.2703i	2.42743	−	1.78478i
$995$		−	14.6464i		−	0.464323i
$996$	43.7792	−	31.0664i	1.38720	−	0.984375i
$997$		−	37.2409i		−	1.17943i	−0.807611	−	0.589716i	$-0.799240\pi$
$997$		−	37.2409i		−	1.17943i	0.807611	−	0.589716i	$-0.200760\pi$
$998$		−	3.64185i		−	0.115281i
$999$	−4.42134	−	15.3380i	−0.139885	−	0.485272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.e.a.188.4	yes	28
3.2	odd	2	inner	231.2.e.a.188.25	yes	28
7.6	odd	2	inner	231.2.e.a.188.3	✓	28
21.20	even	2	inner	231.2.e.a.188.26	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.e.a.188.3	✓	28	7.6	odd	2	inner
231.2.e.a.188.4	yes	28	1.1	even	1	trivial
231.2.e.a.188.25	yes	28	3.2	odd	2	inner
231.2.e.a.188.26	yes	28	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.33290i q^{2} +(1.41254 - 1.00236i) q^{3} -3.44244 q^{4} -4.22171 q^{5} +(-2.33841 - 3.29532i) q^{6} +(2.13159 - 1.56727i) q^{7} +3.36508i q^{8} +(0.990548 - 2.83175i) q^{9} +O(q^{10})\)	\(q-2.33290i q^{2} +(1.41254 - 1.00236i) q^{3} -3.44244 q^{4} -4.22171 q^{5} +(-2.33841 - 3.29532i) q^{6} +(2.13159 - 1.56727i) q^{7} +3.36508i q^{8} +(0.990548 - 2.83175i) q^{9} +9.84884i q^{10} +1.00000i q^{11} +(-4.86259 + 3.45057i) q^{12} +1.39663i q^{13} +(-3.65629 - 4.97279i) q^{14} +(-5.96334 + 4.23167i) q^{15} +0.965521 q^{16} +1.76084 q^{17} +(-6.60620 - 2.31085i) q^{18} -0.456144i q^{19} +14.5330 q^{20} +(1.43999 - 4.35045i) q^{21} +2.33290 q^{22} -3.57846i q^{23} +(3.37302 + 4.75331i) q^{24} +12.8228 q^{25} +3.25820 q^{26} +(-1.43925 - 4.99285i) q^{27} +(-7.33787 + 5.39523i) q^{28} -6.15933i q^{29} +(9.87209 + 13.9119i) q^{30} -2.68916i q^{31} +4.47769i q^{32} +(1.00236 + 1.41254i) q^{33} -4.10788i q^{34} +(-8.99895 + 6.61655i) q^{35} +(-3.40990 + 9.74814i) q^{36} +3.07199 q^{37} -1.06414 q^{38} +(1.39992 + 1.97279i) q^{39} -14.2064i q^{40} +8.68626 q^{41} +(-10.1492 - 3.35936i) q^{42} -4.97879 q^{43} -3.44244i q^{44} +(-4.18180 + 11.9548i) q^{45} -8.34822 q^{46} +0.712189 q^{47} +(1.36384 - 0.967800i) q^{48} +(2.08734 - 6.68154i) q^{49} -29.9144i q^{50} +(2.48727 - 1.76500i) q^{51} -4.80780i q^{52} +10.2336i q^{53} +(-11.6478 + 3.35762i) q^{54} -4.22171i q^{55} +(5.27398 + 7.17296i) q^{56} +(-0.457221 - 0.644323i) q^{57} -14.3691 q^{58} +9.93745 q^{59} +(20.5285 - 14.5673i) q^{60} +0.721923i q^{61} -6.27355 q^{62} +(-2.32667 - 7.58858i) q^{63} +12.3771 q^{64} -5.89615i q^{65} +(3.29532 - 2.33841i) q^{66} +2.01128 q^{67} -6.06160 q^{68} +(-3.58691 - 5.05473i) q^{69} +(15.4358 + 20.9937i) q^{70} +15.3900i q^{71} +(9.52906 + 3.33327i) q^{72} +7.85395i q^{73} -7.16665i q^{74} +(18.1128 - 12.8531i) q^{75} +1.57025i q^{76} +(1.56727 + 2.13159i) q^{77} +(4.60234 - 3.26589i) q^{78} -7.33162 q^{79} -4.07615 q^{80} +(-7.03763 - 5.60997i) q^{81} -20.2642i q^{82} -9.00326 q^{83} +(-4.95709 + 14.9762i) q^{84} -7.43377 q^{85} +11.6150i q^{86} +(-6.17387 - 8.70031i) q^{87} -3.36508 q^{88} +10.9751 q^{89} +(27.8895 + 9.75575i) q^{90} +(2.18889 + 2.97703i) q^{91} +12.3187i q^{92} +(-2.69550 - 3.79855i) q^{93} -1.66147i q^{94} +1.92571i q^{95} +(4.48826 + 6.32492i) q^{96} +6.09294i q^{97} +(-15.5874 - 4.86957i) q^{98} +(2.83175 + 0.990548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

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