LMFDB - Embedded newform 633.2.d.a.632.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(632,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("633.632");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.d (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:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			632.4
Character	$\chi$	$=$	633.632
Dual form			633.2.d.a.632.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60443 q^{2} +(1.06993 + 1.36207i) q^{3} +4.78303 q^{4} +2.83866i q^{5} +(-2.78656 - 3.54742i) q^{6} -2.67377i q^{7} -7.24820 q^{8} +(-0.710484 + 2.91465i) q^{9} +O(q^{10})$	\(q-2.60443 q^{2} +(1.06993 + 1.36207i) q^{3} +4.78303 q^{4} +2.83866i q^{5} +(-2.78656 - 3.54742i) q^{6} -2.67377i q^{7} -7.24820 q^{8} +(-0.710484 + 2.91465i) q^{9} -7.39308i q^{10} -4.00561i q^{11} +(5.11753 + 6.51484i) q^{12} +4.27277 q^{13} +6.96364i q^{14} +(-3.86646 + 3.03718i) q^{15} +9.31134 q^{16} +3.03278 q^{17} +(1.85040 - 7.59100i) q^{18} +5.31878 q^{19} +13.5774i q^{20} +(3.64187 - 2.86076i) q^{21} +10.4323i q^{22} +8.38938 q^{23} +(-7.75510 - 9.87258i) q^{24} -3.05799 q^{25} -11.1281 q^{26} +(-4.73014 + 2.15076i) q^{27} -12.7887i q^{28} +1.19566 q^{29} +(10.0699 - 7.91010i) q^{30} +7.62034i q^{31} -9.75429 q^{32} +(5.45593 - 4.28574i) q^{33} -7.89864 q^{34} +7.58993 q^{35} +(-3.39827 + 13.9409i) q^{36} -11.4488 q^{37} -13.8524 q^{38} +(4.57158 + 5.81983i) q^{39} -20.5752i q^{40} -6.58440 q^{41} +(-9.48499 + 7.45064i) q^{42} +1.33032 q^{43} -19.1590i q^{44} +(-8.27371 - 2.01682i) q^{45} -21.8495 q^{46} -12.0520i q^{47} +(9.96252 + 12.6827i) q^{48} -0.149062 q^{49} +7.96430 q^{50} +(3.24487 + 4.13086i) q^{51} +20.4368 q^{52} +0.189379i q^{53} +(12.3193 - 5.60149i) q^{54} +11.3706 q^{55} +19.3801i q^{56} +(5.69074 + 7.24457i) q^{57} -3.11402 q^{58} +12.0485i q^{59} +(-18.4934 + 14.5269i) q^{60} +1.59509i q^{61} -19.8466i q^{62} +(7.79313 + 1.89967i) q^{63} +6.78165 q^{64} +12.1289i q^{65} +(-14.2096 + 11.1619i) q^{66} +3.48685i q^{67} +14.5059 q^{68} +(8.97608 + 11.4269i) q^{69} -19.7674 q^{70} +7.44086i q^{71} +(5.14973 - 21.1260i) q^{72} -11.4311 q^{73} +29.8176 q^{74} +(-3.27184 - 4.16520i) q^{75} +25.4399 q^{76} -10.7101 q^{77} +(-11.9063 - 15.1573i) q^{78} -1.49990 q^{79} +26.4317i q^{80} +(-7.99043 - 4.14163i) q^{81} +17.1486 q^{82} +2.51241i q^{83} +(17.4192 - 13.6831i) q^{84} +8.60902i q^{85} -3.46471 q^{86} +(1.27928 + 1.62858i) q^{87} +29.0335i q^{88} +3.02207 q^{89} +(21.5483 + 5.25266i) q^{90} -11.4244i q^{91} +40.1267 q^{92} +(-10.3795 + 8.15326i) q^{93} +31.3885i q^{94} +15.0982i q^{95} +(-10.4364 - 13.2861i) q^{96} -10.5085i q^{97} +0.388221 q^{98} +(11.6750 + 2.84592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9}+O(q^{10}) $ 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9	$ 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9} - 16 q^{13} + 56 q^{16} + 4 q^{19} + 8 q^{21} - 38 q^{24} - 60 q^{25} - 14 q^{30} - 32 q^{34} - 18 q^{36} - 28 q^{37} + 40 q^{43} - 2 q^{45} - 8 q^{46} - 80 q^{49} + 16 q^{51} - 16 q^{52} + 52 q^{54} + 16 q^{55} - 40 q^{58} + 28 q^{64} + 18 q^{66} - 10 q^{69} + 80 q^{70} - 8 q^{76} + 32 q^{78} - 40 q^{79} - 28 q^{81} - 44 q^{82} + 84 q^{84} - 44 q^{87} - 10 q^{93} - 56 q^{96} + 68 q^{99}+O(q^{100}) $ 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9 - 16 * q^13 + 56 * q^16 + 4 * q^19 + 8 * q^21 - 38 * q^24 - 60 * q^25 - 14 * q^30 - 32 * q^34 - 18 * q^36 - 28 * q^37 + 40 * q^43 - 2 * q^45 - 8 * q^46 - 80 * q^49 + 16 * q^51 - 16 * q^52 + 52 * q^54 + 16 * q^55 - 40 * q^58 + 28 * q^64 + 18 * q^66 - 10 * q^69 + 80 * q^70 - 8 * q^76 + 32 * q^78 - 40 * q^79 - 28 * q^81 - 44 * q^82 + 84 * q^84 - 44 * q^87 - 10 * q^93 - 56 * q^96 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$.

$n$	$212$	$424$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.60443			−1.84161			−0.920804	−	0.390027i	$-0.872466\pi$
$2$	−2.60443			−1.84161			−0.920804	+	0.390027i	$0.872466\pi$
$3$	1.06993	+	1.36207i	0.617726	+	0.786393i
$3$	1.06993	+	1.36207i	0.617726	+	0.786393i
$4$	4.78303			2.39152
$5$			2.83866i			1.26949i	0.772723	+	0.634744i	$0.218894\pi$
$5$			2.83866i			1.26949i	−0.772723	+	0.634744i	$0.781106\pi$
$6$	−2.78656	−	3.54742i	−1.13761	−	1.44823i
$7$		−	2.67377i		−	1.01059i	−0.862946	−	0.505296i	$-0.831383\pi$
$7$		−	2.67377i		−	1.01059i	0.862946	−	0.505296i	$-0.168617\pi$
$8$	−7.24820			−2.56263
$9$	−0.710484	+	2.91465i	−0.236828	+	0.971552i
$10$		−	7.39308i		−	2.33790i
$11$		−	4.00561i		−	1.20774i	−0.797084	−	0.603869i	$-0.793625\pi$
$11$		−	4.00561i		−	1.20774i	0.797084	−	0.603869i	$-0.206375\pi$
$12$	5.11753	+	6.51484i	1.47730	+	1.88067i
$13$	4.27277			1.18505			0.592527	−	0.805551i	$-0.298130\pi$
$13$	4.27277			1.18505			0.592527	+	0.805551i	$0.298130\pi$
$14$			6.96364i			1.86111i
$15$	−3.86646	+	3.03718i	−0.998316	+	0.784196i
$16$	9.31134			2.32784
$17$	3.03278			0.735557			0.367778	−	0.929914i	$-0.380119\pi$
$17$	3.03278			0.735557			0.367778	+	0.929914i	$0.380119\pi$
$18$	1.85040	−	7.59100i	0.436144	−	1.78922i
$19$	5.31878			1.22021			0.610106	−	0.792320i	$-0.291127\pi$
$19$	5.31878			1.22021			0.610106	+	0.792320i	$0.291127\pi$
$20$			13.5774i			3.03600i
$21$	3.64187	−	2.86076i	0.794722	−	0.624269i
$22$			10.4323i			2.22418i
$23$	8.38938			1.74931			0.874653	−	0.484749i	$-0.161089\pi$
$23$	8.38938			1.74931			0.874653	+	0.484749i	$0.161089\pi$
$24$	−7.75510	−	9.87258i	−1.58300	−	2.01523i
$25$	−3.05799			−0.611597
$26$	−11.1281			−2.18240
$27$	−4.73014	+	2.15076i	−0.910316	+	0.413913i
$28$		−	12.7887i		−	2.41685i
$29$	1.19566			0.222029			0.111015	−	0.993819i	$-0.464590\pi$
$29$	1.19566			0.222029			0.111015	+	0.993819i	$0.464590\pi$
$30$	10.0699	−	7.91010i	1.83851	−	1.44418i
$31$			7.62034i			1.36865i	0.729176	+	0.684327i	$0.239904\pi$
$31$			7.62034i			1.36865i	−0.729176	+	0.684327i	$0.760096\pi$
$32$	−9.75429			−1.72433
$33$	5.45593	−	4.28574i	0.949756	−	0.746051i
$34$	−7.89864			−1.35461
$35$	7.58993			1.28293
$36$	−3.39827	+	13.9409i	−0.566378	+	2.32348i
$37$	−11.4488			−1.88217			−0.941087	−	0.338164i	$-0.890194\pi$
$37$	−11.4488			−1.88217			−0.941087	+	0.338164i	$0.890194\pi$
$38$	−13.8524			−2.24715
$39$	4.57158	+	5.81983i	0.732039	+	0.931918i
$40$		−	20.5752i		−	3.25322i
$41$	−6.58440			−1.02831			−0.514155	−	0.857697i	$-0.671894\pi$
$41$	−6.58440			−1.02831			−0.514155	+	0.857697i	$0.671894\pi$
$42$	−9.48499	+	7.45064i	−1.46357	+	1.14966i
$43$	1.33032			0.202871			0.101436	−	0.994842i	$-0.467656\pi$
$43$	1.33032			0.202871			0.101436	+	0.994842i	$0.467656\pi$
$44$		−	19.1590i		−	2.88832i
$45$	−8.27371	−	2.01682i	−1.23337	−	0.300650i
$46$	−21.8495			−3.22154
$47$		−	12.0520i		−	1.75796i	−0.476854	−	0.878982i	$-0.658223\pi$
$47$		−	12.0520i		−	1.75796i	0.476854	−	0.878982i	$-0.341777\pi$
$48$	9.96252	+	12.6827i	1.43797	+	1.83059i
$49$	−0.149062			−0.0212946
$50$	7.96430			1.12632
$51$	3.24487	+	4.13086i	0.454373	+	0.578437i
$52$	20.4368			2.83408
$53$			0.189379i			0.0260132i	0.999915	+	0.0130066i	$0.00414025\pi$
$53$			0.189379i			0.0260132i	−0.999915	+	0.0130066i	$0.995860\pi$
$54$	12.3193	−	5.60149i	1.67644	−	0.762266i
$55$	11.3706			1.53321
$56$			19.3801i			2.58977i
$57$	5.69074	+	7.24457i	0.753757	+	0.959566i
$58$	−3.11402			−0.408891
$59$			12.0485i			1.56858i	0.620394	+	0.784290i	$0.286973\pi$
$59$			12.0485i			1.56858i	−0.620394	+	0.784290i	$0.713027\pi$
$60$	−18.4934	+	14.5269i	−2.38749	+	1.87542i
$61$			1.59509i			0.204231i	0.994773	+	0.102115i	$0.0325611\pi$
$61$			1.59509i			0.204231i	−0.994773	+	0.102115i	$0.967439\pi$
$62$		−	19.8466i		−	2.52052i
$63$	7.79313	+	1.89967i	0.981841	+	0.239336i
$64$	6.78165			0.847706
$65$			12.1289i			1.50441i
$66$	−14.2096	+	11.1619i	−1.74908	+	1.37393i
$67$			3.48685i			0.425987i	0.977054	+	0.212993i	$0.0683213\pi$
$67$			3.48685i			0.425987i	−0.977054	+	0.212993i	$0.931679\pi$
$68$	14.5059			1.75910
$69$	8.97608	+	11.4269i	1.08059	+	1.37564i
$70$	−19.7674			−2.36266
$71$			7.44086i			0.883068i	0.897245	+	0.441534i	$0.145565\pi$
$71$			7.44086i			0.883068i	−0.897245	+	0.441534i	$0.854435\pi$
$72$	5.14973	−	21.1260i	0.606902	−	2.48972i
$73$	−11.4311			−1.33791			−0.668954	−	0.743304i	$-0.733258\pi$
$73$	−11.4311			−1.33791			−0.668954	+	0.743304i	$0.733258\pi$
$74$	29.8176			3.46623
$75$	−3.27184	−	4.16520i	−0.377800	−	0.480956i
$76$	25.4399			2.91816
$77$	−10.7101			−1.22053
$78$	−11.9063	−	15.1573i	−1.34813	−	1.71623i
$79$	−1.49990			−0.168752			−0.0843762	−	0.996434i	$-0.526890\pi$
$79$	−1.49990			−0.168752			−0.0843762	+	0.996434i	$0.526890\pi$
$80$			26.4317i			2.95516i
$81$	−7.99043	−	4.14163i	−0.887825	−	0.460181i
$82$	17.1486			1.89374
$83$			2.51241i			0.275773i	0.990448	+	0.137886i	$0.0440309\pi$
$83$			2.51241i			0.275773i	−0.990448	+	0.137886i	$0.955969\pi$
$84$	17.4192	−	13.6831i	1.90059	−	1.49295i
$85$			8.60902i			0.933780i
$86$	−3.46471			−0.373609
$87$	1.27928	+	1.62858i	0.137153	+	0.174602i
$88$			29.0335i			3.09498i
$89$	3.02207			0.320339			0.160169	−	0.987090i	$-0.448796\pi$
$89$	3.02207			0.320339			0.160169	+	0.987090i	$0.448796\pi$
$90$	21.5483	+	5.25266i	2.27139	+	0.553679i
$91$		−	11.4244i		−	1.19761i
$92$	40.1267			4.18350
$93$	−10.3795	+	8.15326i	−1.07630	+	0.845453i
$94$			31.3885i			3.23748i
$95$			15.0982i			1.54904i
$96$	−10.4364	−	13.2861i	−1.06517	−	1.35600i
$97$		−	10.5085i		−	1.06697i	−0.845808	−	0.533487i	$-0.820881\pi$
$97$		−	10.5085i		−	1.06697i	0.845808	−	0.533487i	$-0.179119\pi$
$98$	0.388221			0.0392162
$99$	11.6750	+	2.84592i	1.17338	+	0.286026i
$100$	−14.6265			−1.46265
$101$		−	2.65687i		−	0.264368i	−0.991225	−	0.132184i	$-0.957801\pi$
$101$		−	2.65687i		−	0.264368i	0.991225	−	0.132184i	$-0.0421990\pi$
$102$	−8.45102	−	10.7585i	−0.836776	−	1.06525i
$103$	3.94264			0.388479			0.194240	−	0.980954i	$-0.437776\pi$
$103$	3.94264			0.388479			0.194240	+	0.980954i	$0.437776\pi$
$104$	−30.9699			−3.03685
$105$	8.12072	+	10.3380i	0.792501	+	1.00889i
$106$		−	0.493224i		−	0.0479062i
$107$		−	15.8158i		−	1.52897i	−0.644643	−	0.764484i	$-0.722994\pi$
$107$		−	15.8158i		−	1.52897i	0.644643	−	0.764484i	$-0.277006\pi$
$108$	−22.6244	+	10.2871i	−2.17704	+	0.989881i
$109$	8.03247			0.769371			0.384685	−	0.923048i	$-0.374310\pi$
$109$	8.03247			0.769371			0.384685	+	0.923048i	$0.374310\pi$
$110$	−29.6138			−2.82356
$111$	−12.2495	−	15.5941i	−1.16267	−	1.48013i
$112$		−	24.8964i		−	2.35249i
$113$		−	1.60593i		−	0.151073i	−0.997143	−	0.0755364i	$-0.975933\pi$
$113$		−	1.60593i		−	0.151073i	0.997143	−	0.0755364i	$-0.0240669\pi$
$114$	−14.8211	−	18.8679i	−1.38813	−	1.76714i
$115$			23.8146i			2.22072i
$116$	5.71890			0.530987
$117$	−3.03574	+	12.4537i	−0.280654	+	1.15134i
$118$		−	31.3794i		−	2.88871i
$119$		−	8.10896i		−	0.743347i
$120$	28.0249	−	22.0141i	2.55831	−	2.00960i
$121$	−5.04492			−0.458629
$122$		−	4.15430i		−	0.376113i
$123$	−7.04487	−	8.96843i	−0.635214	−	0.808656i
$124$			36.4483i			3.27316i
$125$			5.51271i			0.493072i
$126$	−20.2966	−	4.94756i	−1.80817	−	0.440763i
$127$			6.67600i			0.592399i	0.955126	+	0.296199i	$0.0957193\pi$
$127$			6.67600i			0.592399i	−0.955126	+	0.296199i	$0.904281\pi$
$128$	1.84629			0.163191
$129$	1.42335	+	1.81199i	0.125319	+	0.159537i
$130$		−	31.5889i		−	2.77053i
$131$	5.19935			0.454269			0.227135	−	0.973863i	$-0.427064\pi$
$131$	5.19935			0.454269			0.227135	+	0.973863i	$0.427064\pi$
$132$	26.0959	−	20.4988i	2.27136	−	1.78419i
$133$		−	14.2212i		−	1.23314i
$134$		−	9.08124i		−	0.784500i
$135$	−6.10527	−	13.4273i	−0.525458	−	1.15563i
$136$	−21.9822			−1.88496
$137$		−	3.35142i		−	0.286331i	−0.989699	−	0.143165i	$-0.954272\pi$
$137$		−	3.35142i		−	0.286331i	0.989699	−	0.143165i	$-0.0457281\pi$
$138$	−23.3775	−	29.7606i	−1.99003	−	2.53339i
$139$	5.79040			0.491135			0.245567	−	0.969380i	$-0.421026\pi$
$139$	5.79040			0.491135			0.245567	+	0.969380i	$0.421026\pi$
$140$	36.3029			3.06815
$141$	16.4157	−	12.8948i	1.38245	−	1.08594i
$142$		−	19.3792i		−	1.62626i
$143$		−	17.1151i		−	1.43123i
$144$	−6.61556	+	27.1394i	−0.551297	+	2.26161i
$145$			3.39408i			0.281863i
$146$	29.7714			2.46390
$147$	−0.159486	−	0.203033i	−0.0131542	−	0.0167459i
$148$	−54.7601			−4.50125
$149$	−0.190749			−0.0156267			−0.00781337	−	0.999969i	$-0.502487\pi$
$149$	−0.190749			−0.0156267			−0.00781337	+	0.999969i	$0.502487\pi$
$150$	8.52127	+	10.8480i	0.695759	+	0.885732i
$151$	−15.6862			−1.27653			−0.638264	−	0.769818i	$-0.720347\pi$
$151$	−15.6862			−1.27653			−0.638264	+	0.769818i	$0.720347\pi$
$152$	−38.5516			−3.12695
$153$	−2.15474	+	8.83950i	−0.174200	+	0.714631i
$154$	27.8936			2.24773
$155$	−21.6315			−1.73749
$156$	21.8660	+	27.8364i	1.75068	+	2.22870i
$157$		−	7.57682i		−	0.604696i	−0.953198	−	0.302348i	$-0.902230\pi$
$157$		−	7.57682i		−	0.604696i	0.953198	−	0.302348i	$-0.0977704\pi$
$158$	3.90639			0.310776
$159$	−0.257948	+	0.202623i	−0.0204566	+	0.0160691i
$160$		−	27.6891i		−	2.18902i
$161$		−	22.4313i		−	1.76783i
$162$	20.8105	+	10.7866i	1.63502	+	0.847473i
$163$	9.92829			0.777643			0.388822	−	0.921313i	$-0.372882\pi$
$163$	9.92829			0.777643			0.388822	+	0.921313i	$0.372882\pi$
$164$	−31.4934			−2.45922
$165$	12.1657	+	15.4875i	0.947102	+	1.20570i
$166$		−	6.54339i		−	0.507865i
$167$	−14.1703			−1.09653			−0.548265	−	0.836305i	$-0.684711\pi$
$167$	−14.1703			−1.09653			−0.548265	+	0.836305i	$0.684711\pi$
$168$	−26.3970	+	20.7354i	−2.03658	+	1.59977i
$169$	5.25659			0.404353
$170$		−	22.4216i		−	1.71966i
$171$	−3.77891	+	15.5024i	−0.288980	+	1.18550i
$172$	6.36294			0.485170
$173$			13.3353i			1.01386i	0.861987	+	0.506931i	$0.169220\pi$
$173$			13.3353i			1.01386i	−0.861987	+	0.506931i	$0.830780\pi$
$174$	−3.33179	−	4.24152i	−0.252583	−	0.321549i
$175$			8.17636i			0.618075i
$176$		−	37.2976i		−	2.81141i
$177$	−16.4109	+	12.8911i	−1.23352	+	0.968954i
$178$	−7.87075			−0.589938
$179$			12.1440i			0.907685i	0.891082	+	0.453843i	$0.149947\pi$
$179$			12.1440i			0.907685i	−0.891082	+	0.453843i	$0.850053\pi$
$180$	−39.5734	−	9.64653i	−2.94963	−	0.719010i
$181$			18.1588i			1.34973i	0.737939	+	0.674867i	$0.235799\pi$
$181$			18.1588i			1.34973i	−0.737939	+	0.674867i	$0.764201\pi$
$182$			29.7541i			2.20552i
$183$	−2.17263	+	1.70665i	−0.160606	+	0.126159i
$184$	−60.8079			−4.48282
$185$		−	32.4993i		−	2.38940i
$186$	27.0325	−	21.2345i	1.98212	−	1.55699i
$187$		−	12.1481i		−	0.888359i
$188$		−	57.6451i		−	4.20420i
$189$	5.75064	+	12.6473i	0.418297	+	0.919958i
$190$		−	39.3222i		−	2.85273i
$191$	−2.52885			−0.182981			−0.0914907	−	0.995806i	$-0.529163\pi$
$191$	−2.52885			−0.182981			−0.0914907	+	0.995806i	$0.529163\pi$
$192$	7.25591	+	9.23710i	0.523650	+	0.666630i
$193$	17.6522			1.27063			0.635317	−	0.772252i	$-0.280870\pi$
$193$	17.6522			1.27063			0.635317	+	0.772252i	$0.280870\pi$
$194$			27.3685i			1.96495i
$195$	−16.5205	+	12.9772i	−1.18306	+	0.929314i
$196$	−0.712968			−0.0509263
$197$	14.7739			1.05259			0.526297	−	0.850301i	$-0.323580\pi$
$197$	14.7739			1.05259			0.526297	+	0.850301i	$0.323580\pi$
$198$	−30.4066	−	7.41199i	−2.16090	−	0.526747i
$199$	10.5651			0.748938			0.374469	−	0.927239i	$-0.377825\pi$
$199$	10.5651			0.748938			0.374469	+	0.927239i	$0.377825\pi$
$200$	22.1649			1.56730
$201$	−4.74934	+	3.73070i	−0.334993	+	0.263143i
$202$			6.91961i			0.486862i
$203$		−	3.19693i		−	0.224381i
$204$	15.5203	+	19.7581i	1.08664	+	1.38334i
$205$		−	18.6909i		−	1.30543i
$206$	−10.2683			−0.715426
$207$	−5.96052	+	24.4521i	−0.414285	+	1.69954i
$208$	39.7853			2.75861
$209$		−	21.3050i		−	1.47370i
$210$	−21.1498	−	26.9247i	−1.45948	−	1.85798i
$211$	6.46845	+	13.0061i	0.445307	+	0.895378i
$211$	6.46845	+	13.0061i	0.445307	+	0.895378i
$212$			0.905807i			0.0622111i
$213$	−10.1350	+	7.96123i	−0.694438	+	0.545494i
$214$			41.1910i			2.81576i
$215$			3.77631i			0.257542i
$216$	34.2850	−	15.5891i	2.33280	−	1.06071i
$217$	20.3751			1.38315
$218$	−20.9200			−1.41688
$219$	−12.2305	−	15.5700i	−0.826461	−	1.05212i
$220$	54.3858			3.66669
$221$	12.9584			0.871674
$222$	31.9029	+	40.6137i	2.14118	+	2.72582i
$223$		−	7.76417i		−	0.519927i	−0.965618	−	0.259964i	$-0.916289\pi$
$223$		−	7.76417i		−	0.519927i	0.965618	−	0.259964i	$-0.0837106\pi$
$224$			26.0808i			1.74259i
$225$	2.17265	−	8.91298i	0.144843	−	0.594198i
$226$			4.18251i			0.278217i
$227$		−	11.1889i		−	0.742631i	−0.928507	−	0.371316i	$-0.878907\pi$
$227$		−	11.1889i		−	0.742631i	0.928507	−	0.371316i	$-0.121093\pi$
$228$	27.2190	+	34.6510i	1.80262	+	2.29482i
$229$		−	21.6475i		−	1.43050i	−0.698866	−	0.715252i	$-0.746312\pi$
$229$		−	21.6475i		−	1.43050i	0.698866	−	0.715252i	$-0.253688\pi$
$230$		−	62.0233i		−	4.08970i
$231$	−11.4591	−	14.5879i	−0.753953	−	0.959815i
$232$	−8.66642			−0.568978
$233$	−2.22752			−0.145929			−0.0729647	−	0.997335i	$-0.523246\pi$
$233$	−2.22752			−0.145929			−0.0729647	+	0.997335i	$0.523246\pi$
$234$	7.90635	−	32.4346i	0.516854	−	2.12032i
$235$	34.2115			2.23171
$236$			57.6283i			3.75129i
$237$	−1.60480	−	2.04298i	−0.104243	−	0.132706i
$238$			21.1192i			1.36895i
$239$	10.2579			0.663529			0.331764	−	0.943362i	$-0.392356\pi$
$239$	10.2579			0.663529			0.331764	+	0.943362i	$0.392356\pi$
$240$	−36.0019	+	28.2802i	−2.32392	+	1.82548i
$241$	−9.64200			−0.621096			−0.310548	−	0.950558i	$-0.600512\pi$
$241$	−9.64200			−0.621096			−0.310548	+	0.950558i	$0.600512\pi$
$242$	13.1391			0.844614
$243$	−2.90802	−	15.3148i	−0.186550	−	0.982446i
$244$			7.62939i			0.488422i
$245$		−	0.423136i		−	0.0270332i
$246$	18.3478	+	23.3576i	1.16982	+	1.48923i
$247$	22.7259			1.44602
$248$		−	55.2338i		−	3.50735i
$249$	−3.42209	+	2.68811i	−0.216866	+	0.170352i
$250$		−	14.3575i		−	0.908045i
$251$	−30.2946			−1.91218			−0.956088	−	0.293079i	$-0.905320\pi$
$251$	−30.2946			−1.91218			−0.956088	+	0.293079i	$0.905320\pi$
$252$	37.2748	+	9.08620i	2.34809	+	0.572377i
$253$		−	33.6046i		−	2.11270i
$254$		−	17.3871i		−	1.09097i
$255$	−11.7261	+	9.21108i	−0.734318	+	0.576820i
$256$	−18.3718			−1.14824
$257$		−	18.1552i		−	1.13249i	−0.824237	−	0.566245i	$-0.808395\pi$
$257$		−	18.1552i		−	1.13249i	0.824237	−	0.566245i	$-0.191605\pi$
$258$	−3.70701	−	4.71918i	−0.230788	−	0.293804i
$259$			30.6115i			1.90211i
$260$			58.0132i			3.59782i
$261$	−0.849500	+	3.48495i	−0.0525827	+	0.215713i
$262$	−13.5413			−0.836585
$263$			19.9341i			1.22919i	0.788843	+	0.614594i	$0.210680\pi$
$263$			19.9341i			1.22919i	−0.788843	+	0.614594i	$0.789320\pi$
$264$	−39.5457	+	31.0639i	−2.43387	+	1.91185i
$265$	−0.537583			−0.0330235
$266$			37.0381i			2.27095i
$267$	3.23341	+	4.11628i	0.197882	+	0.251912i
$268$			16.6777i			1.01875i
$269$		−	6.95515i		−	0.424063i	−0.977263	−	0.212031i	$-0.931992\pi$
$269$		−	6.95515i		−	0.424063i	0.977263	−	0.212031i	$-0.0680079\pi$
$270$	15.9007	+	34.9703i	0.967686	+	2.12823i
$271$		−	4.12708i		−	0.250702i	−0.992112	−	0.125351i	$-0.959994\pi$
$271$		−	4.12708i		−	0.250702i	0.992112	−	0.125351i	$-0.0400057\pi$
$272$	28.2392			1.71225
$273$	15.5609	−	12.2234i	0.941788	−	0.739792i
$274$			8.72851i			0.527309i
$275$			12.2491i			0.738649i
$276$	42.9329	+	54.6555i	2.58426	+	3.28987i
$277$	−3.94942			−0.237298			−0.118649	−	0.992936i	$-0.537856\pi$
$277$	−3.94942			−0.237298			−0.118649	+	0.992936i	$0.537856\pi$
$278$	−15.0807			−0.904478
$279$	−22.2107	−	5.41413i	−1.32972	−	0.324135i
$280$	−55.0134			−3.28768
$281$			12.9398i			0.771924i	0.922515	+	0.385962i	$0.126130\pi$
$281$			12.9398i			0.771924i	−0.922515	+	0.385962i	$0.873870\pi$
$282$	−42.7535	+	33.5836i	−2.54593	+	1.99988i
$283$		−	18.7408i		−	1.11403i	−0.830504	−	0.557013i	$-0.811947\pi$
$283$		−	18.7408i		−	1.11403i	0.830504	−	0.557013i	$-0.188053\pi$
$284$			35.5899i			2.11187i
$285$	−20.5649	+	16.1541i	−1.21816	+	0.956885i
$286$			44.5749i			2.63577i
$287$			17.6052i			1.03920i
$288$	6.93027	−	28.4304i	0.408370	−	1.67528i
$289$	−7.80226			−0.458957
$290$		−	8.83964i		−	0.519081i
$291$	14.3133	−	11.2434i	0.839061	−	0.659098i
$292$	−54.6753			−3.19963
$293$		−	12.1343i		−	0.708894i	−0.935076	−	0.354447i	$-0.884669\pi$
$293$		−	12.1343i		−	0.708894i	0.935076	−	0.354447i	$-0.115331\pi$
$294$	0.415371	+	0.528785i	0.0242249	+	0.0308394i
$295$	−34.2016			−1.99129
$296$	82.9834			4.82331
$297$	8.61509	+	18.9471i	0.499898	+	1.09942i
$298$	0.496791			0.0287783
$299$	35.8459			2.07302
$300$	−15.6493	−	19.9223i	−0.903515	−	1.15021i
$301$		−	3.55696i		−	0.205020i
$302$	40.8536			2.35086
$303$	3.61884	−	2.84267i	0.207897	−	0.163307i
$304$	49.5250			2.84045
$305$	−4.52793			−0.259268
$306$	5.61186	−	23.0218i	0.320809	−	1.31607i
$307$	−33.2422			−1.89723			−0.948616	−	0.316429i	$-0.897516\pi$
$307$	−33.2422			−1.89723			−0.948616	+	0.316429i	$0.897516\pi$
$308$	−51.2267			−2.91891
$309$	4.21836	+	5.37016i	0.239974	+	0.305498i
$310$	56.3377			3.19977
$311$			6.24375i			0.354051i	0.984206	+	0.177025i	$0.0566475\pi$
$311$			6.24375i			0.354051i	−0.984206	+	0.177025i	$0.943353\pi$
$312$	−33.1358	−	42.1833i	−1.87594	−	2.38816i
$313$		−	5.48331i		−	0.309935i	−0.987920	−	0.154968i	$-0.950473\pi$
$313$		−	5.48331i		−	0.309935i	0.987920	−	0.154968i	$-0.0495273\pi$
$314$			19.7333i			1.11361i
$315$	−5.39252	+	22.1220i	−0.303834	+	1.24644i
$316$	−7.17409			−0.403574
$317$	24.4738			1.37459			0.687294	−	0.726380i	$-0.258799\pi$
$317$	24.4738			1.37459			0.687294	+	0.726380i	$0.258799\pi$
$318$	0.671807	−	0.527717i	0.0376731	−	0.0295929i
$319$		−	4.78936i		−	0.268153i
$320$			19.2508i			1.07615i
$321$	21.5422	−	16.9218i	1.20237	−	0.944484i
$322$			58.4206i			3.25566i
$323$	16.1307			0.897535
$324$	−38.2185	−	19.8096i	−2.12325	−	1.10053i
$325$	−13.0661			−0.724776
$326$	−25.8575			−1.43211
$327$	8.59421	+	10.9408i	0.475261	+	0.605028i
$328$	47.7251			2.63518
$329$	−32.2243			−1.77658
$330$	−31.6848	−	40.3361i	−1.74419	−	2.22043i
$331$	0.990165			0.0544244			0.0272122	−	0.999630i	$-0.491337\pi$
$331$	0.990165			0.0544244			0.0272122	+	0.999630i	$0.491337\pi$
$332$			12.0169i			0.659516i
$333$	8.13420	−	33.3694i	0.445751	−	1.82863i
$334$	36.9055			2.01938
$335$	−9.89798			−0.540784
$336$	33.9107	−	26.6375i	1.84998	−	1.45320i
$337$	−4.14326			−0.225698			−0.112849	−	0.993612i	$-0.535998\pi$
$337$	−4.14326			−0.225698			−0.112849	+	0.993612i	$0.535998\pi$
$338$	−13.6904			−0.744659
$339$	2.18739	−	1.71823i	0.118803	−	0.0933216i
$340$			41.1772i			2.23315i
$341$	30.5241			1.65297
$342$	9.84189	−	40.3749i	0.532188	−	2.18322i
$343$		−	18.3179i		−	0.989071i
$344$	−9.64240			−0.519883
$345$	−32.4372	+	25.4800i	−1.74636	+	1.37180i
$346$		−	34.7307i		−	1.86713i
$347$			0.0980850i			0.00526548i	0.999997	+	0.00263274i	$0.000838028\pi$
$347$			0.0980850i			0.00526548i	−0.999997	+	0.00263274i	$0.999162\pi$
$348$	6.11885	+	7.78956i	0.328005	+	0.417564i
$349$			7.36417i			0.394195i	0.980384	+	0.197097i	$0.0631515\pi$
$349$			7.36417i			0.394195i	−0.980384	+	0.197097i	$0.936848\pi$
$350$		−	21.2947i		−	1.13825i
$351$	−20.2108	+	9.18969i	−1.07877	+	0.490510i
$352$			39.0719i			2.08254i
$353$	−32.4960			−1.72959			−0.864795	−	0.502126i	$-0.832551\pi$
$353$	−32.4960			−1.72959			−0.864795	+	0.502126i	$0.832551\pi$
$354$	42.7410	−	33.5739i	2.27166	−	1.78443i
$355$	−21.1221			−1.12104
$356$	14.4547			0.766095
$357$	11.0450	−	8.67605i	0.584563	−	0.459185i
$358$		−	31.6281i		−	1.67160i
$359$		−	5.89919i		−	0.311347i	−0.987809	−	0.155674i	$-0.950245\pi$
$359$		−	5.89919i		−	0.311347i	0.987809	−	0.155674i	$-0.0497548\pi$
$360$	59.9696	+	14.6183i	3.16067	+	0.770454i
$361$	9.28944			0.488918
$362$		−	47.2933i		−	2.48568i
$363$	−5.39773	−	6.87154i	−0.283307	−	0.360663i
$364$		−	54.6434i		−	2.86409i
$365$		−	32.4490i		−	1.69846i
$366$	5.65847	−	4.44483i	0.295773	−	0.232335i
$367$		−	9.83580i		−	0.513425i	−0.966488	−	0.256712i	$-0.917361\pi$
$367$		−	9.83580i		−	0.513425i	0.966488	−	0.256712i	$-0.0826393\pi$
$368$	78.1164			4.07210
$369$	4.67811	−	19.1912i	0.243533	−	0.999056i
$370$			84.6420i			4.40033i
$371$	0.506357			0.0262887
$372$	−49.6453	+	38.9973i	−2.57399	+	2.02192i
$373$		−	23.4375i		−	1.21355i	−0.794875	−	0.606774i	$-0.792463\pi$
$373$		−	23.4375i		−	1.21355i	0.794875	−	0.606774i	$-0.207537\pi$
$374$			31.6389i			1.63601i
$375$	−7.50872	+	5.89824i	−0.387748	+	0.304584i
$376$			87.3553i			4.50501i
$377$	5.10880			0.263117
$378$	−14.9771	−	32.9390i	−0.770339	−	1.69420i
$379$		−	27.3361i		−	1.40416i	−0.712097	−	0.702081i	$-0.752255\pi$
$379$		−	27.3361i		−	1.40416i	0.712097	−	0.702081i	$-0.247745\pi$
$380$			72.2152i			3.70456i
$381$	−9.09319	+	7.14287i	−0.465858	+	0.365940i
$382$	6.58621			0.336980
$383$			12.0477i			0.615607i	0.951450	+	0.307803i	$0.0995939\pi$
$383$			12.0477i			0.615607i	−0.951450	+	0.307803i	$0.900406\pi$
$384$	1.97541	+	2.51478i	0.100807	+	0.128332i
$385$		−	30.4023i		−	1.54945i
$386$	−45.9739			−2.34001
$387$	−0.945168	+	3.87741i	−0.0480456	+	0.197100i
$388$		−	50.2624i		−	2.55169i
$389$			34.3652i			1.74239i	0.490940	+	0.871193i	$0.336653\pi$
$389$			34.3652i			1.74239i	−0.490940	+	0.871193i	$0.663347\pi$
$390$	43.0264	−	33.7981i	2.17873	−	1.71143i
$391$	25.4431			1.28671
$392$	1.08043			0.0545700
$393$	5.56296	+	7.08189i	0.280614	+	0.357234i
$394$	−38.4774			−1.93846
$395$		−	4.25772i		−	0.214229i
$396$	55.8418	+	13.6121i	2.80616	+	0.684036i
$397$			12.0810i			0.606328i	0.952938	+	0.303164i	$0.0980429\pi$
$397$			12.0810i			0.606328i	−0.952938	+	0.303164i	$0.901957\pi$
$398$	−27.5159			−1.37925
$399$	19.3703	−	15.2158i	0.969729	−	0.761741i
$400$	−28.4740			−1.42370
$401$	−2.03950			−0.101848			−0.0509239	−	0.998703i	$-0.516217\pi$
$401$	−2.03950			−0.101848			−0.0509239	+	0.998703i	$0.516217\pi$
$402$	12.3693	−	9.71633i	0.616925	−	0.484606i
$403$			32.5600i			1.62193i
$404$		−	12.7079i		−	0.632240i
$405$	11.7567	−	22.6821i	0.584194	−	1.12708i
$406$			8.32618i			0.413221i
$407$			45.8595i			2.27317i
$408$	−23.5195	−	29.9413i	−1.16439	−	1.48232i
$409$		−	1.99479i		−	0.0986360i	−0.998783	−	0.0493180i	$-0.984295\pi$
$409$		−	1.99479i		−	0.0986360i	0.998783	−	0.0493180i	$-0.0157048\pi$
$410$			48.6790i			2.40408i
$411$	4.56487	−	3.58579i	0.225168	−	0.176874i
$412$	18.8578			0.929055
$413$	32.2149			1.58519
$414$	15.5237	−	63.6838i	0.762950	−	3.12989i
$415$	−7.13188			−0.350090
$416$	−41.6779			−2.04343
$417$	6.19534	+	7.88694i	0.303387	+	0.386225i
$418$			55.4872i			2.71397i
$419$		−	32.2820i		−	1.57708i	−0.614985	−	0.788539i	$-0.710838\pi$
$419$		−	32.2820i		−	1.57708i	0.614985	−	0.788539i	$-0.289162\pi$
$420$	38.8417	+	49.4472i	1.89528	+	2.41278i
$421$		−	37.5332i		−	1.82925i	−0.404298	−	0.914627i	$-0.632484\pi$
$421$		−	37.5332i		−	1.82925i	0.404298	−	0.914627i	$-0.367516\pi$
$422$	−16.8466	−	33.8735i	−0.820080	−	1.64893i
$423$	35.1274	+	8.56275i	1.70795	+	0.416335i
$424$		−	1.37266i		−	0.0666622i
$425$	−9.27419			−0.449864
$426$	26.3958	−	20.7344i	1.27888	−	1.00459i
$427$	4.26492			0.206394
$428$		−	75.6473i		−	3.65655i
$429$	23.3120	−	18.3120i	1.12551	−	0.884111i
$430$		−	9.83513i		−	0.474292i
$431$			0.861842i			0.0415135i	0.999785	+	0.0207567i	$0.00660755\pi$
$431$			0.861842i			0.0415135i	−0.999785	+	0.0207567i	$0.993392\pi$
$432$	−44.0440	+	20.0264i	−2.11907	+	0.963522i
$433$	−29.0169			−1.39446			−0.697232	−	0.716846i	$-0.745585\pi$
$433$	−29.0169			−1.39446			−0.697232	+	0.716846i	$0.745585\pi$
$434$	−53.0653			−2.54722
$435$	−4.62299	+	3.63144i	−0.221655	+	0.174114i
$436$	38.4196			1.83996
$437$	44.6213			2.13453
$438$	31.8534	+	40.5508i	1.52202	+	1.93759i
$439$		−	29.8125i		−	1.42287i	−0.702751	−	0.711436i	$-0.748045\pi$
$439$		−	29.8125i		−	1.42287i	0.702751	−	0.711436i	$-0.251955\pi$
$440$	−82.4162			−3.92904
$441$	0.105906	−	0.434464i	0.00504315	−	0.0206888i
$442$	−33.7491			−1.60528
$443$		−	30.2694i		−	1.43814i	−0.694936	−	0.719072i	$-0.744567\pi$
$443$		−	30.2694i		−	1.43814i	0.694936	−	0.719072i	$-0.255433\pi$
$444$	−58.5897	−	74.5872i	−2.78054	−	3.53975i
$445$			8.57862i			0.406666i
$446$			20.2212i			0.957502i
$447$	−0.204089	−	0.259814i	−0.00965306	−	0.0122888i
$448$		−	18.1326i		−	0.856684i
$449$	−40.4788			−1.91031			−0.955156	−	0.296104i	$-0.904313\pi$
$449$	−40.4788			−1.91031			−0.955156	+	0.296104i	$0.904313\pi$
$450$	−5.65851	+	23.2132i	−0.266745	+	1.09428i
$451$			26.3745i			1.24193i
$452$		−	7.68120i		−	0.361293i
$453$	−16.7832	−	21.3658i	−0.788545	−	1.00385i
$454$			29.1406i			1.36763i
$455$	32.4300			1.52034
$456$	−41.2477	−	52.5101i	−1.93160	−	2.45901i
$457$		−	16.1239i		−	0.754243i	−0.926164	−	0.377122i	$-0.876914\pi$
$457$		−	16.1239i		−	0.754243i	0.926164	−	0.377122i	$-0.123086\pi$
$458$			56.3792i			2.63443i
$459$	−14.3455	+	6.52277i	−0.669589	+	0.304457i
$460$			113.906i			5.31089i
$461$	−25.1233			−1.17011			−0.585055	−	0.810993i	$-0.698927\pi$
$461$	−25.1233			−1.17011			−0.585055	+	0.810993i	$0.698927\pi$
$462$	29.8443	+	37.9932i	1.38848	+	1.76760i
$463$			25.7026i			1.19450i	0.802054	+	0.597251i	$0.203740\pi$
$463$			25.7026i			1.19450i	−0.802054	+	0.597251i	$0.796260\pi$
$464$	11.1332			0.516848
$465$	−23.1443	−	29.4637i	−1.07329	−	1.36635i
$466$	5.80140			0.268745
$467$			0.943557i			0.0436626i	0.999762	+	0.0218313i	$0.00694968\pi$
$467$			0.943557i			0.0436626i	−0.999762	+	0.0218313i	$0.993050\pi$
$468$	−14.5200	+	59.5663i	−0.671189	+	2.75345i
$469$	9.32305			0.430498
$470$	−89.1014			−4.10994
$471$	10.3202	−	8.10669i	0.475528	−	0.373537i
$472$		−	87.3299i		−	4.01969i
$473$		−	5.32873i		−	0.245015i
$474$	4.17958	+	5.32078i	0.191974	+	0.244392i
$475$	−16.2648			−0.746279
$476$		−	38.7854i		−	1.77773i
$477$	−0.551975	−	0.134551i	−0.0252732	−	0.00616066i
$478$	−26.7159			−1.22196
$479$	−22.0717			−1.00848			−0.504241	−	0.863563i	$-0.668228\pi$
$479$	−22.0717			−1.00848			−0.504241	+	0.863563i	$0.668228\pi$
$480$	37.7146	−	29.6255i	1.72143	−	1.35221i
$481$	−48.9182			−2.23048
$482$	25.1119			1.14381
$483$	30.5531	−	24.0000i	1.39021	−	1.09204i
$484$	−24.1300			−1.09682
$485$	29.8300			1.35451
$486$	7.57373	+	39.8863i	0.343551	+	1.80928i
$487$	22.6821			1.02783			0.513913	−	0.857843i	$-0.328196\pi$
$487$	22.6821			1.02783			0.513913	+	0.857843i	$0.328196\pi$
$488$		−	11.5616i		−	0.523368i
$489$	10.6226	+	13.5230i	0.480371	+	0.611533i
$490$			1.10203i			0.0497845i
$491$		−	8.08338i		−	0.364798i	−0.983225	−	0.182399i	$-0.941614\pi$
$491$		−	8.08338i		−	0.364798i	0.983225	−	0.182399i	$-0.0583862\pi$
$492$	−33.6958	−	42.8963i	−1.51913	−	1.93391i
$493$	3.62618			0.163315
$494$	−59.1880			−2.66300
$495$	−8.07860	+	33.1413i	−0.363106	+	1.48959i
$496$			70.9556i			3.18600i
$497$	19.8952			0.892420
$498$	8.91257	−	7.00099i	0.399382	−	0.313722i
$499$			29.2947i			1.31141i	0.755017	+	0.655706i	$0.227629\pi$
$499$			29.2947i			1.31141i	−0.755017	+	0.655706i	$0.772371\pi$
$500$			26.3675i			1.17919i
$501$	−15.1613	−	19.3010i	−0.677356	−	0.862304i
$502$	78.9000			3.52148
$503$			24.9232i			1.11127i	0.831426	+	0.555635i	$0.187525\pi$
$503$			24.9232i			1.11127i	−0.831426	+	0.555635i	$0.812475\pi$
$504$	−56.4862	−	13.7692i	−2.51609	−	0.613330i
$505$	7.54193			0.335612
$506$			87.5207i			3.89077i
$507$	5.62420	+	7.15985i	0.249779	+	0.317980i
$508$			31.9315i			1.41673i
$509$			0.0876411i			0.00388462i	0.999998	+	0.00194231i	$0.000618258\pi$
$509$			0.0876411i			0.00388462i	−0.999998	+	0.00194231i	$0.999382\pi$
$510$	30.5398	−	23.9896i	1.35232	−	1.06228i
$511$			30.5641i			1.35208i
$512$	44.1555			1.95141
$513$	−25.1586	+	11.4394i	−1.11078	+	0.505062i
$514$			47.2839i			2.08560i
$515$			11.1918i			0.493170i
$516$	6.80793	+	8.66679i	0.299702	+	0.381534i
$517$	−48.2756			−2.12316
$518$		−	79.7255i		−	3.50294i
$519$	−18.1636	+	14.2678i	−0.797293	+	0.626289i
$520$		−	87.9131i		−	3.85524i
$521$			4.70299i			0.206042i	0.994679	+	0.103021i	$0.0328508\pi$
$521$			4.70299i			0.206042i	−0.994679	+	0.103021i	$0.967149\pi$
$522$	2.21246	−	9.07629i	0.0968367	−	0.397258i
$523$	−21.9983			−0.961920			−0.480960	−	0.876743i	$-0.659712\pi$
$523$	−21.9983			−0.961920			−0.480960	+	0.876743i	$0.659712\pi$
$524$	24.8687			1.08639
$525$	−11.1368	+	8.74817i	−0.486050	+	0.381801i
$526$		−	51.9168i		−	2.26368i
$527$			23.1108i			1.00672i
$528$	50.8021	−	39.9060i	2.21088	−	1.73668i
$529$	47.3817			2.06007
$530$	1.40009			0.0608162
$531$	−35.1172	−	8.56026i	−1.52396	−	0.371484i
$532$		−	68.0205i		−	2.94906i
$533$	−28.1336			−1.21860
$534$	−8.42118	−	10.7205i	−0.364420	−	0.463923i
$535$	44.8956			1.94100
$536$		−	25.2734i		−	1.09164i
$537$	−16.5410	+	12.9933i	−0.713797	+	0.560701i
$538$			18.1142i			0.780957i
$539$			0.597084i			0.0257182i
$540$	−29.2017	−	64.2230i	−1.25664	−	2.76372i
$541$	15.3018			0.657876			0.328938	−	0.944351i	$-0.393309\pi$
$541$	15.3018			0.657876			0.328938	+	0.944351i	$0.393309\pi$
$542$			10.7487i			0.461695i
$543$	−24.7336	+	19.4287i	−1.06142	+	0.833767i
$544$	−29.5826			−1.26834
$545$			22.8014i			0.976706i
$546$	−40.5272	+	31.8349i	−1.73440	+	1.36241i
$547$	−20.8233			−0.890339			−0.445170	−	0.895446i	$-0.646857\pi$
$547$	−20.8233			−0.890339			−0.445170	+	0.895446i	$0.646857\pi$
$548$		−	16.0299i		−	0.684765i
$549$	−4.64915	−	1.13329i	−0.198421	−	0.0483676i
$550$		−	31.9019i		−	1.36030i
$551$	6.35948			0.270923
$552$	−65.0605	−	82.8248i	−2.76916	−	3.52526i
$553$			4.01040i			0.170540i
$554$	10.2860			0.437009
$555$	44.2664	−	34.7721i	1.87900	−	1.47599i
$556$	27.6957			1.17456
$557$	8.47490			0.359093			0.179547	−	0.983749i	$-0.442537\pi$
$557$	8.47490			0.359093			0.179547	+	0.983749i	$0.442537\pi$
$558$	57.8460	+	14.1007i	2.44882	+	0.596930i
$559$	5.68414			0.240413
$560$	70.6725			2.98646
$561$	16.5466	−	12.9977i	0.698599	−	0.548763i
$562$		−	33.7008i		−	1.42158i
$563$	1.25801			0.0530187			0.0265093	−	0.999649i	$-0.491561\pi$
$563$	1.25801			0.0530187			0.0265093	+	0.999649i	$0.491561\pi$
$564$	78.5168	−	61.6764i	3.30616	−	2.59705i
$565$	4.55868			0.191785
$566$			48.8091i			2.05160i
$567$	−11.0738	+	21.3646i	−0.465055	+	0.897228i
$568$		−	53.9329i		−	2.26297i
$569$	−17.1642			−0.719561			−0.359780	−	0.933037i	$-0.617148\pi$
$569$	−17.1642			−0.719561			−0.359780	+	0.933037i	$0.617148\pi$
$570$	53.5596	−	42.0721i	2.24337	−	1.76221i
$571$		−	20.8467i		−	0.872409i	−0.899848	−	0.436204i	$-0.856322\pi$
$571$		−	20.8467i		−	0.872409i	0.899848	−	0.436204i	$-0.143678\pi$
$572$		−	81.8619i		−	3.42282i
$573$	−2.70570	−	3.44448i	−0.113032	−	0.143895i
$574$		−	45.8514i		−	1.91380i
$575$	−25.6546			−1.06987
$576$	−4.81825	+	19.7662i	−0.200760	+	0.823590i
$577$			29.1825i			1.21488i	0.794364	+	0.607442i	$0.207804\pi$
$577$			29.1825i			1.21488i	−0.794364	+	0.607442i	$0.792196\pi$
$578$	20.3204			0.845218
$579$	18.8867	+	24.0436i	0.784904	+	0.999217i
$580$			16.2340i			0.674081i
$581$	6.71762			0.278694
$582$	−37.2779	+	29.2825i	−1.54522	+	1.21380i
$583$	0.758579			0.0314171
$584$	82.8548			3.42856
$585$	−35.3517	−	8.61742i	−1.46161	−	0.356286i
$586$			31.6029i			1.30550i
$587$	−6.20647			−0.256169			−0.128084	−	0.991763i	$-0.540883\pi$
$587$	−6.20647			−0.256169			−0.128084	+	0.991763i	$0.540883\pi$
$588$	−0.762829	−	0.971115i	−0.0314585	−	0.0400481i
$589$			40.5309i			1.67005i
$590$	89.0754			3.66718
$591$	15.8070	+	20.1231i	0.650215	+	0.827752i
$592$	−106.604			−4.38139
$593$		−	23.7656i		−	0.975937i	−0.872861	−	0.487969i	$-0.837738\pi$
$593$		−	23.7656i		−	0.975937i	0.872861	−	0.487969i	$-0.162262\pi$
$594$	−22.4374	−	49.3463i	−0.920617	−	2.02470i
$595$	23.0186			0.943669
$596$	−0.912358			−0.0373716
$597$	11.3039	+	14.3904i	0.462639	+	0.588960i
$598$	−93.3580			−3.81769
$599$	−21.2707			−0.869096			−0.434548	−	0.900649i	$-0.643092\pi$
$599$	−21.2707			−0.869096			−0.434548	+	0.900649i	$0.643092\pi$
$600$	23.7150	+	30.1902i	0.968160	+	1.23251i
$601$	−10.5998			−0.432373			−0.216187	−	0.976352i	$-0.569362\pi$
$601$	−10.5998			−0.432373			−0.216187	+	0.976352i	$0.569362\pi$
$602$			9.26384i			0.377566i
$603$	−10.1630	−	2.47735i	−0.413868	−	0.100886i
$604$	−75.0278			−3.05284
$605$		−	14.3208i		−	0.582223i
$606$	−9.42501	+	7.40352i	−0.382865	+	0.300747i
$607$	−10.5545			−0.428394			−0.214197	−	0.976791i	$-0.568713\pi$
$607$	−10.5545			−0.428394			−0.214197	+	0.976791i	$0.568713\pi$
$608$	−51.8810			−2.10405
$609$	4.35446	−	3.42051i	0.176451	−	0.138606i
$610$	11.7927			0.477471
$611$		−	51.4954i		−	2.08328i
$612$	−10.3062	+	42.2796i	−0.416603	+	1.70905i
$613$			40.8047i			1.64809i	0.566527	+	0.824043i	$0.308287\pi$
$613$			40.8047i			1.64809i	−0.566527	+	0.824043i	$0.691713\pi$
$614$	86.5768			3.49396
$615$	25.4583	−	19.9980i	1.02658	−	0.806396i
$616$	77.6289			3.12776
$617$	−44.8052			−1.80379			−0.901894	−	0.431958i	$-0.857823\pi$
$617$	−44.8052			−1.80379			−0.901894	+	0.431958i	$0.857823\pi$
$618$	−10.9864	−	13.9862i	−0.441938	−	0.562606i
$619$		−	44.0116i		−	1.76898i	−0.466563	−	0.884488i	$-0.654508\pi$
$619$		−	44.0116i		−	1.76898i	0.466563	−	0.884488i	$-0.345492\pi$
$620$	−103.464			−4.15523
$621$	−39.6830	+	18.0435i	−1.59242	+	0.724061i
$622$		−	16.2614i		−	0.652023i
$623$		−	8.08033i		−	0.323731i
$624$	42.5676	+	54.1904i	1.70407	+	2.16935i
$625$	−30.9387			−1.23755
$626$			14.2809i			0.570779i
$627$	29.0189	−	22.7949i	1.15890	−	0.910341i
$628$		−	36.2402i		−	1.44614i
$629$	−34.7217			−1.38445
$630$	14.0444	−	57.6152i	0.559543	−	2.29544i
$631$	29.4340			1.17175			0.585875	−	0.810401i	$-0.300751\pi$
$631$	29.4340			1.17175			0.585875	+	0.810401i	$0.300751\pi$
$632$	10.8716			0.432449
$633$	−10.7945	+	22.7262i	−0.429041	+	0.903285i
$634$	−63.7403			−2.53145
$635$	−18.9509			−0.752043
$636$	−1.23377	+	0.969153i	−0.0489224	+	0.0384294i
$637$	−0.636908			−0.0252352
$638$			12.4735i			0.493832i
$639$	−21.6875	−	5.28661i	−0.857946	−	0.209135i
$640$			5.24099i			0.207168i
$641$	6.73170			0.265886			0.132943	−	0.991124i	$-0.457557\pi$
$641$	6.73170			0.265886			0.132943	+	0.991124i	$0.457557\pi$
$642$	−56.1051	+	44.0716i	−2.21429	+	1.73937i
$643$		−	20.6308i		−	0.813600i	−0.913517	−	0.406800i	$-0.866645\pi$
$643$		−	20.6308i		−	0.813600i	0.913517	−	0.406800i	$-0.133355\pi$
$644$		−	107.290i		−	4.22780i
$645$	−5.14361	+	4.04040i	−0.202530	+	0.159091i
$646$	−42.0112			−1.65291
$647$			33.2764i			1.30823i	0.756396	+	0.654114i	$0.226958\pi$
$647$			33.2764i			1.30823i	−0.756396	+	0.654114i	$0.773042\pi$
$648$	57.9162	+	30.0194i	2.27516	+	1.17927i
$649$	48.2616			1.89443
$650$	34.0296			1.33475
$651$	21.8000	+	27.7523i	0.854408	+	1.08770i
$652$	47.4873			1.85975
$653$		−	9.26024i		−	0.362381i	−0.983448	−	0.181191i	$-0.942005\pi$
$653$		−	9.26024i		−	0.362381i	0.983448	−	0.181191i	$-0.0579951\pi$
$654$	−22.3830	−	28.4945i	−0.875243	−	1.11422i
$655$			14.7592i			0.576689i
$656$	−61.3096			−2.39374
$657$	8.12160	−	33.3177i	0.316854	−	1.29985i
$658$	83.9258			3.27177
$659$	44.5742			1.73637			0.868183	−	0.496245i	$-0.165288\pi$
$659$	44.5742			1.73637			0.868183	+	0.496245i	$0.165288\pi$
$660$	58.1892	+	74.0774i	2.26501	+	2.88346i
$661$		−	6.04276i		−	0.235036i	−0.993071	−	0.117518i	$-0.962506\pi$
$661$		−	6.04276i		−	0.235036i	0.993071	−	0.117518i	$-0.0374938\pi$
$662$	−2.57881			−0.100228
$663$	13.8646	+	17.6502i	0.538456	+	0.685479i
$664$		−	18.2105i		−	0.706703i
$665$	40.3692			1.56545
$666$	−21.1849	+	86.9080i	−0.820899	+	3.36762i
$667$	10.0309			0.388397
$668$	−67.7770			−2.62237
$669$	10.5754	−	8.30715i	0.408867	−	0.321173i
$670$	25.7786			0.995913
$671$	6.38933			0.246657
$672$	−35.5239	+	27.9047i	−1.37036	+	1.07645i
$673$			0.739616i			0.0285101i	0.999898	+	0.0142550i	$0.00453768\pi$
$673$			0.739616i			0.0285101i	−0.999898	+	0.0142550i	$0.995462\pi$
$674$	10.7908			0.415646
$675$	14.4647	−	6.57699i	0.556747	−	0.253148i
$676$	25.1424			0.967017
$677$			29.7963i			1.14517i	0.819847	+	0.572583i	$0.194058\pi$
$677$			29.7963i			1.14517i	−0.819847	+	0.572583i	$0.805942\pi$
$678$	−5.69689	+	4.47501i	−0.218788	+	0.171862i
$679$	−28.0973			−1.07827
$680$		−	62.4000i		−	2.39293i
$681$	15.2400	−	11.9713i	0.584000	−	0.458743i
$682$	−79.4978			−3.04413
$683$	35.6382			1.36366			0.681828	−	0.731512i	$-0.261185\pi$
$683$	35.6382			1.36366			0.681828	+	0.731512i	$0.261185\pi$
$684$	−18.0746	+	74.1486i	−0.691101	+	2.83514i
$685$	9.51353			0.363493
$686$			47.7075i			1.82148i
$687$	29.4854	−	23.1613i	1.12494	−	0.883661i
$688$	12.3870			0.472251
$689$			0.809174i			0.0308271i
$690$	84.4803	−	66.3609i	3.21611	−	2.52631i
$691$	32.9647			1.25404			0.627018	−	0.779005i	$-0.284275\pi$
$691$	32.9647			1.25404			0.627018	+	0.779005i	$0.284275\pi$
$692$			63.7830i			2.42467i
$693$	7.60935	−	31.2162i	0.289055	−	1.18581i
$694$		−	0.255455i		−	0.00969694i
$695$			16.4370i			0.623489i
$696$	−9.27249	−	11.8043i	−0.351473	−	0.447440i
$697$	−19.9690			−0.756380
$698$		−	19.1794i		−	0.725952i
$699$	−2.38329	−	3.03404i	−0.0901444	−	0.114758i
$700$			39.1078i			1.47814i
$701$	41.7741			1.57779			0.788893	−	0.614530i	$-0.210654\pi$
$701$	41.7741			1.57779			0.788893	+	0.614530i	$0.210654\pi$
$702$	52.6376	−	23.9339i	1.98668	−	0.903326i
$703$	−60.8938			−2.29665
$704$		−	27.1646i		−	1.02381i
$705$	36.6041	+	46.5986i	1.37859	+	1.75500i
$706$	84.6335			3.18522
$707$	−7.10385			−0.267168
$708$	−78.4940	+	61.6585i	−2.94999	+	2.31727i
$709$	−24.6524			−0.925841			−0.462920	−	0.886400i	$-0.653198\pi$
$709$	−24.6524			−0.925841			−0.462920	+	0.886400i	$0.653198\pi$
$710$	55.0109			2.06452
$711$	1.06566	−	4.37170i	0.0399653	−	0.163952i
$712$	−21.9046			−0.820909
$713$			63.9299i			2.39419i
$714$	−28.7659	+	22.5961i	−1.07654	+	0.845639i
$715$	48.5838			1.81693
$716$			58.0852i			2.17074i
$717$	10.9753	+	13.9720i	0.409879	+	0.521794i
$718$			15.3640i			0.573379i
$719$	−6.66650			−0.248619			−0.124309	−	0.992244i	$-0.539672\pi$
$719$	−6.66650			−0.248619			−0.124309	+	0.992244i	$0.539672\pi$
$720$	−77.0394	−	18.7793i	−2.87109	−	0.699864i
$721$		−	10.5417i		−	0.392594i
$722$	−24.1937			−0.900394
$723$	−10.3163	−	13.1331i	−0.383667	−	0.488425i
$724$			86.8542i			3.22791i
$725$	−3.65633			−0.135793
$726$	14.0580	+	17.8964i	0.521741	+	0.664199i
$727$			6.22603i			0.230911i	0.993313	+	0.115455i	$0.0368327\pi$
$727$			6.22603i			0.230911i	−0.993313	+	0.115455i	$0.963167\pi$
$728$			82.8066i			3.06902i
$729$	17.7485	−	20.3468i	0.657352	−	0.753584i
$730$			84.5109i			3.12789i
$731$	4.03455			0.149223
$732$	−10.3918	+	8.16294i	−0.384091	+	0.301711i
$733$	−25.9175			−0.957285			−0.478643	−	0.878010i	$-0.658871\pi$
$733$	−25.9175			−0.957285			−0.478643	+	0.878010i	$0.658871\pi$
$734$			25.6166i			0.945526i
$735$	0.576342	−	0.452728i	0.0212587	−	0.0166991i
$736$	−81.8325			−3.01638
$737$	13.9670			0.514480
$738$	−12.1838	+	49.9822i	−0.448491	+	1.83987i
$739$			10.8843i			0.400386i	0.979757	+	0.200193i	$0.0641569\pi$
$739$			10.8843i			0.400386i	−0.979757	+	0.200193i	$0.935843\pi$
$740$		−	155.445i		−	5.71428i
$741$	24.3153	+	30.9544i	0.893243	+	1.13714i
$742$	−1.31877			−0.0484135
$743$	37.2599			1.36693			0.683467	−	0.729981i	$-0.260471\pi$
$743$	37.2599			1.36693			0.683467	+	0.729981i	$0.260471\pi$
$744$	75.2324	−	59.0965i	2.75815	−	2.16658i
$745$		−	0.541471i		−	0.0198380i
$746$			61.0412i			2.23488i
$747$	−7.32281	−	1.78503i	−0.267928	−	0.0653107i
$748$		−	58.1049i		−	2.12453i
$749$	−42.2878			−1.54516
$750$	19.5559	−	15.3615i	0.714080	−	0.560923i
$751$		−	5.03354i		−	0.183677i	−0.995774	−	0.0918383i	$-0.970726\pi$
$751$		−	5.03354i		−	0.183677i	0.995774	−	0.0918383i	$-0.0292743\pi$
$752$		−	112.220i		−	4.09225i
$753$	−32.4132	−	41.2634i	−1.18120	−	1.50372i
$754$	−13.3055			−0.484557
$755$		−	44.5279i		−	1.62054i
$756$	27.5055	+	60.4926i	1.00036	+	2.20009i
$757$			18.2358i			0.662792i	0.943492	+	0.331396i	$0.107520\pi$
$757$			18.2358i			0.662792i	−0.943492	+	0.331396i	$0.892480\pi$
$758$			71.1949i			2.58591i
$759$	45.7719	−	35.9547i	1.66141	−	1.30507i
$760$		−	109.435i		−	3.96962i
$761$	10.3122			0.373819			0.186909	−	0.982377i	$-0.440153\pi$
$761$	10.3122			0.373819			0.186909	+	0.982377i	$0.440153\pi$
$762$	23.6825	−	18.6031i	0.857928	−	0.673919i
$763$		−	21.4770i		−	0.777519i
$764$	−12.0956			−0.437603
$765$	−25.0923	−	6.11657i	−0.907215	−	0.221145i
$766$		−	31.3772i		−	1.13371i
$767$			51.4805i			1.85885i
$768$	−19.6566	−	25.0238i	−0.709298	−	0.902967i
$769$	26.4219			0.952799			0.476399	−	0.879229i	$-0.341942\pi$
$769$	26.4219			0.952799			0.476399	+	0.879229i	$0.341942\pi$
$770$			79.1806i			2.85347i
$771$	24.7287	−	19.4249i	0.890583	−	0.699570i
$772$	84.4311			3.03874
$773$	−7.39190			−0.265868			−0.132934	−	0.991125i	$-0.542440\pi$
$773$	−7.39190			−0.265868			−0.132934	+	0.991125i	$0.542440\pi$
$774$	2.46162	−	10.0984i	0.0884811	−	0.362981i
$775$		−	23.3029i		−	0.837065i
$776$			76.1676i			2.73426i
$777$	−41.6951	+	32.7523i	−1.49581	+	1.17498i
$778$		−	89.5017i		−	3.20879i
$779$	−35.0210			−1.25476
$780$	−79.0181	+	62.0702i	−2.82930	+	2.22247i
$781$	29.8052			1.06651
$782$	−66.2647			−2.36962
$783$	−5.65566	+	2.57158i	−0.202117	+	0.0919009i
$784$	−1.38797			−0.0495703
$785$	21.5080			0.767653
$786$	−14.4883	−	18.4443i	−0.516781	−	0.657885i
$787$	−16.9518			−0.604267			−0.302133	−	0.953266i	$-0.597699\pi$
$787$	−16.9518			−0.604267			−0.302133	+	0.953266i	$0.597699\pi$
$788$	70.6638			2.51730
$789$	−27.1517	+	21.3282i	−0.966625	+	0.759302i
$790$			11.0889i			0.394526i
$791$	−4.29388			−0.152673
$792$	−84.6226	−	20.6278i	−3.00693	−	0.732978i
$793$			6.81548i			0.242025i
$794$		−	31.4640i		−	1.11662i
$795$	−0.575178	−	0.732227i	−0.0203995	−	0.0259694i
$796$	50.5331			1.79110
$797$	13.4962			0.478061			0.239031	−	0.971012i	$-0.423170\pi$
$797$	13.4962			0.478061			0.239031	+	0.971012i	$0.423170\pi$
$798$	−50.4486	+	39.6283i	−1.78586	+	1.40283i
$799$		−	36.5510i		−	1.29308i
$800$	29.8285			1.05460
$801$	−2.14713	+	8.80829i	−0.0758651	+	0.311226i
$802$	5.31173			0.187564
$803$			45.7885i			1.61584i
$804$	−22.7163	+	17.8441i	−0.801141	+	0.629311i
$805$	63.6748			2.24424
$806$		−	84.8000i		−	2.98695i
$807$	9.47342	−	7.44155i	0.333480	−	0.261955i
$808$			19.2575i			0.677477i
$809$			3.38626i			0.119055i	0.998227	+	0.0595273i	$0.0189593\pi$
$809$			3.38626i			0.119055i	−0.998227	+	0.0595273i	$0.981041\pi$
$810$	−30.6194	+	59.0738i	−1.07586	+	2.07564i
$811$	−21.4756			−0.754109			−0.377055	−	0.926191i	$-0.623063\pi$
$811$	−21.4756			−0.754109			−0.377055	+	0.926191i	$0.623063\pi$
$812$		−	15.2910i		−	0.536610i
$813$	5.62138	−	4.41570i	0.197151	−	0.154865i
$814$		−	119.438i		−	4.18629i
$815$			28.1830i			0.987208i
$816$	30.2141	+	38.4639i	1.05771	+	1.34651i
$817$	7.07566			0.247546
$818$			5.19528i			0.181649i
$819$	33.2983	+	8.11687i	1.16354	+	0.283626i
$820$		−	89.3990i		−	3.12195i
$821$		−	42.8408i		−	1.49515i	−0.664175	−	0.747577i	$-0.731217\pi$
$821$		−	42.8408i		−	1.49515i	0.664175	−	0.747577i	$-0.268783\pi$
$822$	−11.8889	+	9.33893i	−0.414672	+	0.325733i
$823$			3.91460i			0.136454i	0.997670	+	0.0682272i	$0.0217343\pi$
$823$			3.91460i			0.136454i	−0.997670	+	0.0682272i	$0.978266\pi$
$824$	−28.5770			−0.995528
$825$	−16.6842	+	13.1057i	−0.580868	+	0.456283i
$826$	−83.9014			−2.91930
$827$		−	36.0565i		−	1.25381i	−0.779097	−	0.626904i	$-0.784322\pi$
$827$		−	36.0565i		−	1.25381i	0.779097	−	0.626904i	$-0.215678\pi$
$828$	−28.5094	+	116.955i	−0.990769	+	4.06448i
$829$	−22.5998			−0.784922			−0.392461	−	0.919769i	$-0.628376\pi$
$829$	−22.5998			−0.784922			−0.392461	+	0.919769i	$0.628376\pi$
$830$	18.5745			0.644729
$831$	−4.22562	−	5.37940i	−0.146585	−	0.186609i
$832$	28.9764			1.00458
$833$	−0.452072			−0.0156634
$834$	−16.1353	−	20.5409i	−0.558720	−	0.711275i
$835$		−	40.2246i		−	1.39203i
$836$		−	101.902i		−	3.52437i
$837$	−16.3895	−	36.0453i	−0.566504	−	1.24591i
$838$			84.0760i			2.90436i
$839$	32.0631			1.10694			0.553471	−	0.832869i	$-0.313303\pi$
$839$	32.0631			1.10694			0.553471	+	0.832869i	$0.313303\pi$
$840$	−58.8607	−	74.9322i	−2.03089	−	2.58541i
$841$	−27.5704			−0.950703
$842$			97.7523i			3.36877i
$843$	−17.6250	+	13.8447i	−0.607036	+	0.476838i
$844$	30.9388	+	62.2087i	1.06496	+	2.14131i
$845$			14.9217i			0.513321i
$846$	−91.4867	−	22.3010i	−3.14538	−	0.766726i
$847$			13.4890i			0.463486i
$848$			1.76337i			0.0605545i
$849$	25.5264	−	20.0514i	0.876062	−	0.688163i
$850$	24.1539			0.828474
$851$	−96.0485			−3.29250
$852$	−48.4760	+	38.0788i	−1.66076	+	1.30456i
$853$	35.5252			1.21636			0.608179	−	0.793800i	$-0.291900\pi$
$853$	35.5252			1.21636			0.608179	+	0.793800i	$0.291900\pi$
$854$	−11.1077			−0.380097
$855$	−44.0061	−	10.7270i	−1.50498	−	0.366857i
$856$			114.636i			3.91817i
$857$		−	0.699379i		−	0.0238903i	−0.999929	−	0.0119452i	$-0.996198\pi$
$857$		−	0.699379i		−	0.0238903i	0.999929	−	0.0119452i	$-0.00380236\pi$
$858$	−60.7143	+	47.6922i	−2.07275	+	1.62818i
$859$			41.4321i			1.41365i	0.707391	+	0.706823i	$0.249872\pi$
$859$			41.4321i			1.41365i	−0.707391	+	0.706823i	$0.750128\pi$
$860$			18.0622i			0.615917i
$861$	−23.9795	+	18.8364i	−0.817221	+	0.641942i
$862$		−	2.24460i		−	0.0764515i
$863$		−	11.7049i		−	0.398438i	−0.979955	−	0.199219i	$-0.936159\pi$
$863$		−	11.7049i		−	0.398438i	0.979955	−	0.199219i	$-0.0638405\pi$
$864$	46.1392	−	20.9791i	1.56969	−	0.713724i
$865$	−37.8543			−1.28708
$866$	75.5724			2.56805
$867$	−8.34790	−	10.6272i	−0.283510	−	0.360920i
$868$	97.4546			3.30782
$869$			6.00803i			0.203808i
$870$	12.0402	−	9.45783i	0.408202	−	0.320650i
$871$			14.8985i			0.504817i
$872$	−58.2210			−1.97161
$873$	30.6286	+	7.46610i	1.03662	+	0.252689i
$874$	−116.213			−3.93096
$875$	14.7397			0.498294
$876$	−58.4989	−	74.4717i	−1.97649	−	2.51617i
$877$		−	55.7596i		−	1.88287i	−0.337199	−	0.941434i	$-0.609479\pi$
$877$		−	55.7596i		−	1.88287i	0.337199	−	0.941434i	$-0.390521\pi$
$878$			77.6444i			2.62037i
$879$	16.5278	−	12.9829i	0.557469	−	0.437903i
$880$	105.875			3.56905
$881$		−	50.4728i		−	1.70047i	−0.526401	−	0.850237i	$-0.676459\pi$
$881$		−	50.4728i		−	1.70047i	0.526401	−	0.850237i	$-0.323541\pi$
$882$	−0.275825	+	1.13153i	−0.00928750	+	0.0381006i
$883$			37.9307i			1.27647i	0.769842	+	0.638234i	$0.220335\pi$
$883$			37.9307i			1.27647i	−0.769842	+	0.638234i	$0.779665\pi$
$884$	61.9803			2.08462
$885$	−36.5934	−	46.5850i	−1.23007	−	1.56594i
$886$			78.8344i			2.64849i
$887$		−	47.6303i		−	1.59927i	−0.600487	−	0.799634i	$-0.705027\pi$
$887$		−	47.6303i		−	1.59927i	0.600487	−	0.799634i	$-0.294973\pi$
$888$	88.7867	+	113.029i	2.97949	+	3.79302i
$889$	17.8501			0.598673
$890$		−	22.3424i		−	0.748919i
$891$	−16.5898	+	32.0065i	−0.555778	+	1.07226i
$892$		−	37.1363i		−	1.24341i
$893$		−	64.1019i		−	2.14509i
$894$	0.531533	+	0.676665i	0.0177771	+	0.0226311i
$895$	−34.4727			−1.15229
$896$		−	4.93656i		−	0.164919i
$897$	38.3527	+	48.8247i	1.28056	+	1.63021i
$898$	105.424			3.51804
$899$			9.11136i			0.303881i
$900$	10.3919	−	42.6311i	0.346395	−	1.42104i
$901$			0.574345i			0.0191342i
$902$		−	68.6905i		−	2.28714i
$903$	4.84484	−	3.80571i	0.161226	−	0.126646i
$904$			11.6401i			0.387143i
$905$	−51.5467			−1.71347
$906$	43.7107	+	55.6456i	1.45219	+	1.84870i
$907$			42.0363i			1.39579i	0.716199	+	0.697897i	$0.245880\pi$
$907$			42.0363i			1.39579i	−0.716199	+	0.697897i	$0.754120\pi$
$908$		−	53.5167i		−	1.77601i
$909$	7.74384	+	1.88766i	0.256847	+	0.0626097i
$910$	−84.4617			−2.79988
$911$	−2.41183			−0.0799076			−0.0399538	−	0.999202i	$-0.512721\pi$
$911$	−2.41183			−0.0799076			−0.0399538	+	0.999202i	$0.512721\pi$
$912$	52.9885	+	67.4567i	1.75462	+	2.23371i
$913$	10.0637			0.333061
$914$			41.9935i			1.38902i
$915$	−4.84458	−	6.16737i	−0.160157	−	0.203887i
$916$		−	103.541i		−	3.42108i
$917$		−	13.9019i		−	0.459080i
$918$	37.3617	−	16.9881i	1.23312	−	0.560690i
$919$		−	27.1252i		−	0.894779i	−0.894339	−	0.447389i	$-0.852354\pi$
$919$		−	27.1252i		−	0.894779i	0.894339	−	0.447389i	$-0.147646\pi$
$920$		−	172.613i		−	5.69088i
$921$	−35.5669	−	45.2783i	−1.17197	−	1.49197i
$922$	65.4319			2.15488
$923$			31.7931i			1.04648i
$924$	−54.8092	−	69.7745i	−1.80309	−	2.29541i
$925$	35.0103			1.15113
$926$		−	66.9406i		−	2.19980i
$927$	−2.80118	+	11.4914i	−0.0920028	+	0.377428i
$928$	−11.6629			−0.382852
$929$	−18.8266			−0.617680			−0.308840	−	0.951114i	$-0.599941\pi$
$929$	−18.8266			−0.617680			−0.308840	+	0.951114i	$0.599941\pi$
$930$	60.2777	+	76.7361i	1.97658	+	2.51628i
$931$	−0.792828			−0.0259839
$932$	−10.6543			−0.348993
$933$	−8.50445	+	6.68040i	−0.278423	+	0.218707i
$934$		−	2.45743i		−	0.0804094i
$935$	34.4844			1.12776
$936$	22.0036	−	90.2667i	0.719211	−	2.95046i
$937$	−32.8495			−1.07315			−0.536573	−	0.843854i	$-0.680281\pi$
$937$	−32.8495			−1.07315			−0.536573	+	0.843854i	$0.680281\pi$
$938$	−24.2812			−0.792809
$939$	7.46867	−	5.86678i	0.243731	−	0.191455i
$940$	163.635			5.33718
$941$	−8.68997			−0.283285			−0.141642	−	0.989918i	$-0.545238\pi$
$941$	−8.68997			−0.283285			−0.141642	+	0.989918i	$0.545238\pi$
$942$	−26.8781	+	21.1133i	−0.875737	+	0.687908i
$943$	−55.2390			−1.79883
$944$			112.188i			3.65140i
$945$	−35.9015	+	16.3241i	−1.16787	+	0.531023i
$946$			13.8783i			0.451222i
$947$			23.3729i			0.759517i	0.925086	+	0.379759i	$0.123993\pi$
$947$			23.3729i			0.759517i	−0.925086	+	0.379759i	$0.876007\pi$
$948$	−7.67580	−	9.77163i	−0.249298	−	0.317368i
$949$	−48.8424			−1.58549
$950$	42.3604			1.37435
$951$	26.1854	+	33.3351i	0.849119	+	1.08097i
$952$			58.7754i			1.90492i
$953$		−	38.8296i		−	1.25781i	−0.777480	−	0.628907i	$-0.783502\pi$
$953$		−	38.8296i		−	1.25781i	0.777480	−	0.628907i	$-0.216498\pi$
$954$	1.43758	+	0.350428i	0.0465433	+	0.0113455i
$955$		−	7.17855i		−	0.232292i
$956$	49.0639			1.58684
$957$	6.52346	−	5.12430i	0.210874	−	0.165645i
$958$	57.4842			1.85723
$959$	−8.96092			−0.289363
$960$	−26.2210	+	20.5971i	−0.846278	+	0.664767i
$961$	−27.0695			−0.873211
$962$	127.404			4.10766
$963$	46.0975	+	11.2368i	1.48547	+	0.362102i
$964$	−46.1180			−1.48536
$965$			50.1086i			1.61305i
$966$	−79.5732	+	62.5062i	−2.56022	+	2.01110i
$967$	23.6665			0.761062			0.380531	−	0.924768i	$-0.375741\pi$
$967$	23.6665			0.761062			0.380531	+	0.924768i	$0.375741\pi$
$968$	36.5666			1.17529
$969$	17.2588	+	21.9712i	0.554431	+	0.705815i
$970$	−77.6900			−2.49447
$971$	53.9704			1.73199			0.865997	−	0.500050i	$-0.166685\pi$
$971$	53.9704			1.73199			0.865997	+	0.500050i	$0.166685\pi$
$972$	−13.9092	−	73.2513i	−0.446137	−	2.34953i
$973$		−	15.4822i		−	0.496337i
$974$	−59.0739			−1.89285
$975$	−13.9798	−	17.7970i	−0.447713	−	0.569959i
$976$			14.8525i			0.475416i
$977$	−17.0649			−0.545953			−0.272977	−	0.962021i	$-0.588008\pi$
$977$	−17.0649			−0.545953			−0.272977	+	0.962021i	$0.588008\pi$
$978$	−27.6658	−	35.2198i	−0.884655	−	1.12620i
$979$		−	12.1052i		−	0.386885i
$980$		−	2.02387i		−	0.0646503i
$981$	−5.70694	+	23.4119i	−0.182208	+	0.747483i
$982$			21.0526i			0.671814i
$983$		−	17.5635i		−	0.560188i	−0.959973	−	0.280094i	$-0.909634\pi$
$983$		−	17.5635i		−	0.560188i	0.959973	−	0.280094i	$-0.0903656\pi$
$984$	51.0626	+	65.0050i	1.62782	+	2.07228i
$985$			41.9379i			1.33625i
$986$	−9.44412			−0.300762
$987$	−34.4779	−	43.8918i	−1.09744	−	1.39709i
$988$	108.699			3.45817
$989$	11.1605			0.354884
$990$	21.0401	−	86.3140i	0.668699	−	2.74324i
$991$			51.3495i			1.63117i	0.578636	+	0.815586i	$0.303585\pi$
$991$			51.3495i			1.63117i	−0.578636	+	0.815586i	$0.696415\pi$
$992$		−	74.3310i		−	2.36001i
$993$	1.05941	+	1.34868i	0.0336194	+	0.0427990i
$994$	−51.8155			−1.64349
$995$			29.9906i			0.950767i
$996$	−16.3680	+	12.8573i	−0.518639	+	0.407400i
$997$		−	59.5476i		−	1.88589i	−0.332948	−	0.942945i	$-0.608044\pi$
$997$		−	59.5476i		−	1.88589i	0.332948	−	0.942945i	$-0.391956\pi$
$998$		−	76.2959i		−	2.41510i
$999$	54.1545	−	24.6236i	1.71337	−	0.779057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.d.a.632.4	yes	68
3.2	odd	2	inner	633.2.d.a.632.66	yes	68
211.210	odd	2	inner	633.2.d.a.632.65	yes	68
633.632	even	2	inner	633.2.d.a.632.3	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.d.a.632.3	✓	68	633.632	even	2	inner
633.2.d.a.632.4	yes	68	1.1	even	1	trivial
633.2.d.a.632.65	yes	68	211.210	odd	2	inner
633.2.d.a.632.66	yes	68	3.2	odd	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:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.60443 q^{2} +(1.06993 + 1.36207i) q^{3} +4.78303 q^{4} +2.83866i q^{5} +(-2.78656 - 3.54742i) q^{6} -2.67377i q^{7} -7.24820 q^{8} +(-0.710484 + 2.91465i) q^{9} +O(q^{10})\)	\(q-2.60443 q^{2} +(1.06993 + 1.36207i) q^{3} +4.78303 q^{4} +2.83866i q^{5} +(-2.78656 - 3.54742i) q^{6} -2.67377i q^{7} -7.24820 q^{8} +(-0.710484 + 2.91465i) q^{9} -7.39308i q^{10} -4.00561i q^{11} +(5.11753 + 6.51484i) q^{12} +4.27277 q^{13} +6.96364i q^{14} +(-3.86646 + 3.03718i) q^{15} +9.31134 q^{16} +3.03278 q^{17} +(1.85040 - 7.59100i) q^{18} +5.31878 q^{19} +13.5774i q^{20} +(3.64187 - 2.86076i) q^{21} +10.4323i q^{22} +8.38938 q^{23} +(-7.75510 - 9.87258i) q^{24} -3.05799 q^{25} -11.1281 q^{26} +(-4.73014 + 2.15076i) q^{27} -12.7887i q^{28} +1.19566 q^{29} +(10.0699 - 7.91010i) q^{30} +7.62034i q^{31} -9.75429 q^{32} +(5.45593 - 4.28574i) q^{33} -7.89864 q^{34} +7.58993 q^{35} +(-3.39827 + 13.9409i) q^{36} -11.4488 q^{37} -13.8524 q^{38} +(4.57158 + 5.81983i) q^{39} -20.5752i q^{40} -6.58440 q^{41} +(-9.48499 + 7.45064i) q^{42} +1.33032 q^{43} -19.1590i q^{44} +(-8.27371 - 2.01682i) q^{45} -21.8495 q^{46} -12.0520i q^{47} +(9.96252 + 12.6827i) q^{48} -0.149062 q^{49} +7.96430 q^{50} +(3.24487 + 4.13086i) q^{51} +20.4368 q^{52} +0.189379i q^{53} +(12.3193 - 5.60149i) q^{54} +11.3706 q^{55} +19.3801i q^{56} +(5.69074 + 7.24457i) q^{57} -3.11402 q^{58} +12.0485i q^{59} +(-18.4934 + 14.5269i) q^{60} +1.59509i q^{61} -19.8466i q^{62} +(7.79313 + 1.89967i) q^{63} +6.78165 q^{64} +12.1289i q^{65} +(-14.2096 + 11.1619i) q^{66} +3.48685i q^{67} +14.5059 q^{68} +(8.97608 + 11.4269i) q^{69} -19.7674 q^{70} +7.44086i q^{71} +(5.14973 - 21.1260i) q^{72} -11.4311 q^{73} +29.8176 q^{74} +(-3.27184 - 4.16520i) q^{75} +25.4399 q^{76} -10.7101 q^{77} +(-11.9063 - 15.1573i) q^{78} -1.49990 q^{79} +26.4317i q^{80} +(-7.99043 - 4.14163i) q^{81} +17.1486 q^{82} +2.51241i q^{83} +(17.4192 - 13.6831i) q^{84} +8.60902i q^{85} -3.46471 q^{86} +(1.27928 + 1.62858i) q^{87} +29.0335i q^{88} +3.02207 q^{89} +(21.5483 + 5.25266i) q^{90} -11.4244i q^{91} +40.1267 q^{92} +(-10.3795 + 8.15326i) q^{93} +31.3885i q^{94} +15.0982i q^{95} +(-10.4364 - 13.2861i) q^{96} -10.5085i q^{97} +0.388221 q^{98} +(11.6750 + 2.84592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9}+O(q^{10}) \) 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9	\( 68 q + 64 q^{4} - 14 q^{6} - 4 q^{9} - 16 q^{13} + 56 q^{16} + 4 q^{19} + 8 q^{21} - 38 q^{24} - 60 q^{25} - 14 q^{30} - 32 q^{34} - 18 q^{36} - 28 q^{37} + 40 q^{43} - 2 q^{45} - 8 q^{46} - 80 q^{49} + 16 q^{51} - 16 q^{52} + 52 q^{54} + 16 q^{55} - 40 q^{58} + 28 q^{64} + 18 q^{66} - 10 q^{69} + 80 q^{70} - 8 q^{76} + 32 q^{78} - 40 q^{79} - 28 q^{81} - 44 q^{82} + 84 q^{84} - 44 q^{87} - 10 q^{93} - 56 q^{96} + 68 q^{99}+O(q^{100}) \) 68 * q + 64 * q^4 - 14 * q^6 - 4 * q^9 - 16 * q^13 + 56 * q^16 + 4 * q^19 + 8 * q^21 - 38 * q^24 - 60 * q^25 - 14 * q^30 - 32 * q^34 - 18 * q^36 - 28 * q^37 + 40 * q^43 - 2 * q^45 - 8 * q^46 - 80 * q^49 + 16 * q^51 - 16 * q^52 + 52 * q^54 + 16 * q^55 - 40 * q^58 + 28 * q^64 + 18 * q^66 - 10 * q^69 + 80 * q^70 - 8 * q^76 + 32 * q^78 - 40 * q^79 - 28 * q^81 - 44 * q^82 + 84 * q^84 - 44 * q^87 - 10 * q^93 - 56 * q^96 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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