LMFDB - Embedded newform 308.2.y.b.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(9,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 18]))

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

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

chi := DirichletCharacter("308.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.y (of order $15$, degree $8$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			289.3
Character	$\chi$	$=$	308.289
Dual form			308.2.y.b.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.599375 - 0.665674i) q^{3} +(-4.03246 + 1.79536i) q^{5} +(0.860089 + 2.50205i) q^{7} +(0.229715 + 2.18559i) q^{9} +(-0.394957 - 3.29302i) q^{11} +(-3.36615 + 2.44565i) q^{13} +(-1.22183 + 3.76040i) q^{15} +(-0.518194 + 4.93028i) q^{17} +(-0.672120 - 0.142864i) q^{19} +(2.18106 + 0.927127i) q^{21} +(-2.70042 + 4.67727i) q^{23} +(9.69171 - 10.7637i) q^{25} +(3.76661 + 2.73660i) q^{27} +(1.02571 - 3.15682i) q^{29} +(6.03074 + 2.68506i) q^{31} +(-2.42881 - 1.71084i) q^{33} +(-7.96036 - 8.54522i) q^{35} +(-1.71306 - 1.90255i) q^{37} +(-0.389581 + 3.70662i) q^{39} +(-1.30788 - 4.02523i) q^{41} +4.76487 q^{43} +(-4.85024 - 8.40087i) q^{45} +(-3.55158 - 0.754911i) q^{47} +(-5.52049 + 4.30397i) q^{49} +(2.97137 + 3.30004i) q^{51} +(-1.29690 - 0.577416i) q^{53} +(7.50483 + 12.5699i) q^{55} +(-0.497953 + 0.361784i) q^{57} +(-5.60294 + 1.19094i) q^{59} +(5.37231 - 2.39191i) q^{61} +(-5.27087 + 2.45456i) q^{63} +(9.18301 - 15.9054i) q^{65} +(0.225280 + 0.390196i) q^{67} +(1.49497 + 4.60104i) q^{69} +(-7.43196 - 5.39964i) q^{71} +(2.52044 - 0.535737i) q^{73} +(-1.35616 - 12.9030i) q^{75} +(7.89961 - 3.82050i) q^{77} +(1.14016 + 10.8479i) q^{79} +(-2.36952 + 0.503656i) q^{81} +(5.68790 + 4.13250i) q^{83} +(-6.76206 - 20.8115i) q^{85} +(-1.48663 - 2.57491i) q^{87} +(1.82999 - 3.16963i) q^{89} +(-9.01432 - 6.31879i) q^{91} +(5.40205 - 2.40515i) q^{93} +(2.96679 - 0.630610i) q^{95} +(4.83319 - 3.51152i) q^{97} +(7.10647 - 1.61967i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{3} + 7 q^{5} - 7 q^{7} + 13 q^{9} - 5 q^{11} - 8 q^{13} - 48 q^{15} + 19 q^{17} + 13 q^{19} - 22 q^{21} - 30 q^{23} - 7 q^{25} + 26 q^{27} - 12 q^{29} + 3 q^{31} - 28 q^{33} + 37 q^{35} + 19 q^{37}+ \cdots + 140 q^{99}+O(q^{100}) $ 48 * q - q^3 + 7 * q^5 - 7 * q^7 + 13 * q^9 - 5 * q^11 - 8 * q^13 - 48 * q^15 + 19 * q^17 + 13 * q^19 - 22 * q^21 - 30 * q^23 - 7 * q^25 + 26 * q^27 - 12 * q^29 + 3 * q^31 - 28 * q^33 + 37 * q^35 + 19 * q^37 + 3 * q^39 - 10 * q^41 + 84 * q^43 - 24 * q^45 + 11 * q^47 + 51 * q^49 - 21 * q^51 + 33 * q^53 + 48 * q^55 - 108 * q^57 + 23 * q^59 + 46 * q^61 - 90 * q^63 - 54 * q^65 - 8 * q^67 - 82 * q^69 - 64 * q^71 + 4 * q^73 - 15 * q^75 + 6 * q^77 - 14 * q^79 + 7 * q^81 - 28 * q^83 + 50 * q^85 - 66 * q^87 - 58 * q^89 + 70 * q^91 - 42 * q^93 + 4 * q^95 - 100 * q^97 + 140 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.599375	−	0.665674i	0.346049	−	0.384327i	−0.544845	−	0.838537i	$-0.683412\pi$
$3$	0.599375	−	0.665674i	0.346049	−	0.384327i	0.890895	+	0.454210i	$0.150078\pi$
$4$		0			0
$5$	−4.03246	+	1.79536i	−1.80337	+	0.802912i	−0.836355	+	0.548189i	$0.815318\pi$
$5$	−4.03246	+	1.79536i	−1.80337	+	0.802912i	−0.967014	+	0.254723i	$0.918016\pi$
$6$		0			0
$7$	0.860089	+	2.50205i	0.325083	+	0.945685i
$7$	0.860089	+	2.50205i	0.325083	+	0.945685i
$8$		0			0
$9$	0.229715	+	2.18559i	0.0765716	+	0.728530i
$10$		0			0
$11$	−0.394957	−	3.29302i	−0.119084	−	0.992884i
$11$	−0.394957	−	3.29302i	−0.119084	−	0.992884i
$12$		0			0
$13$	−3.36615	+	2.44565i	−0.933602	+	0.678301i	−0.946872	−	0.321611i	$-0.895776\pi$
$13$	−3.36615	+	2.44565i	−0.933602	+	0.678301i	0.0132703	+	0.999912i	$0.495776\pi$
$14$		0			0
$15$	−1.22183	+	3.76040i	−0.315474	+	0.970930i
$16$		0			0
$17$	−0.518194	+	4.93028i	−0.125680	+	1.19577i	0.731897	+	0.681415i	$0.238635\pi$
$17$	−0.518194	+	4.93028i	−0.125680	+	1.19577i	−0.857578	+	0.514354i	$0.828032\pi$
$18$		0			0
$19$	−0.672120	−	0.142864i	−0.154195	−	0.0327751i	0.130167	−	0.991492i	$-0.458449\pi$
$19$	−0.672120	−	0.142864i	−0.154195	−	0.0327751i	−0.284362	+	0.958717i	$0.591782\pi$
$20$		0			0
$21$	2.18106	+	0.927127i	0.475947	+	0.202316i
$22$		0			0
$23$	−2.70042	+	4.67727i	−0.563077	+	0.975279i	0.434148	+	0.900841i	$0.357049\pi$
$23$	−2.70042	+	4.67727i	−0.563077	+	0.975279i	−0.997226	+	0.0744373i	$0.976284\pi$
$24$		0			0
$25$	9.69171	−	10.7637i	1.93834	−	2.15275i
$26$		0			0
$27$	3.76661	+	2.73660i	0.724885	+	0.526659i
$28$		0			0
$29$	1.02571	−	3.15682i	0.190470	−	0.586207i	−0.809529	−	0.587079i	$-0.800278\pi$
$29$	1.02571	−	3.15682i	0.190470	−	0.586207i	1.00000		0.000872197i	$0.000277629\pi$
$30$		0			0
$31$	6.03074	+	2.68506i	1.08315	+	0.482250i	0.869133	−	0.494579i	$-0.164678\pi$
$31$	6.03074	+	2.68506i	1.08315	+	0.482250i	0.214019	+	0.976829i	$0.431344\pi$
$32$		0			0
$33$	−2.42881	−	1.71084i	−0.422801	−	0.297820i
$34$		0			0
$35$	−7.96036	−	8.54522i	−1.34555	−	1.44441i
$36$		0			0
$37$	−1.71306	−	1.90255i	−0.281625	−	0.312777i	0.585691	−	0.810535i	$-0.300823\pi$
$37$	−1.71306	−	1.90255i	−0.281625	−	0.312777i	−0.867316	+	0.497758i	$0.834157\pi$
$38$		0			0
$39$	−0.389581	+	3.70662i	−0.0623829	+	0.593534i
$40$		0			0
$41$	−1.30788	−	4.02523i	−0.204256	−	0.628635i	−0.999743	−	0.0226649i	$-0.992785\pi$
$41$	−1.30788	−	4.02523i	−0.204256	−	0.628635i	0.795487	−	0.605971i	$-0.207215\pi$
$42$		0			0
$43$	4.76487			0.726636			0.363318	−	0.931665i	$-0.381644\pi$
$43$	4.76487			0.726636			0.363318	+	0.931665i	$0.381644\pi$
$44$		0			0
$45$	−4.85024	−	8.40087i	−0.723032	−	1.25233i
$46$		0			0
$47$	−3.55158	−	0.754911i	−0.518051	−	0.110115i	−0.0585361	−	0.998285i	$-0.518643\pi$
$47$	−3.55158	−	0.754911i	−0.518051	−	0.110115i	−0.459515	+	0.888170i	$0.651977\pi$
$48$		0			0
$49$	−5.52049	+	4.30397i	−0.788642	+	0.614853i
$50$		0			0
$51$	2.97137	+	3.30004i	0.416075	+	0.462098i
$52$		0			0
$53$	−1.29690	−	0.577416i	−0.178143	−	0.0793142i	0.315727	−	0.948850i	$-0.397751\pi$
$53$	−1.29690	−	0.577416i	−0.178143	−	0.0793142i	−0.493870	+	0.869536i	$0.664418\pi$
$54$		0			0
$55$	7.50483	+	12.5699i	1.01195	+	1.69492i
$56$		0			0
$57$	−0.497953	+	0.361784i	−0.0659554	+	0.0479194i
$58$		0			0
$59$	−5.60294	+	1.19094i	−0.729441	+	0.155047i	−0.557638	−	0.830084i	$-0.688292\pi$
$59$	−5.60294	+	1.19094i	−0.729441	+	0.155047i	−0.171803	+	0.985131i	$0.554959\pi$
$60$		0			0
$61$	5.37231	−	2.39191i	0.687854	−	0.306252i	−0.0328850	−	0.999459i	$-0.510469\pi$
$61$	5.37231	−	2.39191i	0.687854	−	0.306252i	0.720739	+	0.693207i	$0.243803\pi$
$62$		0			0
$63$	−5.27087	+	2.45456i	−0.664068	+	0.309245i
$64$		0			0
$65$	9.18301	−	15.9054i	1.13901	−	1.97283i
$66$		0			0
$67$	0.225280	+	0.390196i	0.0275223	+	0.0476700i	0.879458	−	0.475976i	$-0.157905\pi$
$67$	0.225280	+	0.390196i	0.0275223	+	0.0476700i	−0.851936	+	0.523646i	$0.824572\pi$
$68$		0			0
$69$	1.49497	+	4.60104i	0.179973	+	0.553900i
$70$		0			0
$71$	−7.43196	−	5.39964i	−0.882012	−	0.640819i	0.0517714	−	0.998659i	$-0.483513\pi$
$71$	−7.43196	−	5.39964i	−0.882012	−	0.640819i	−0.933783	+	0.357840i	$0.883513\pi$
$72$		0			0
$73$	2.52044	−	0.535737i	0.294996	−	0.0627033i	−0.0580364	−	0.998314i	$-0.518484\pi$
$73$	2.52044	−	0.535737i	0.294996	−	0.0627033i	0.353032	+	0.935611i	$0.385151\pi$
$74$		0			0
$75$	−1.35616	−	12.9030i	−0.156596	−	1.48991i
$76$		0			0
$77$	7.89961	−	3.82050i	0.900244	−	0.435386i
$78$		0			0
$79$	1.14016	+	10.8479i	0.128278	+	1.22049i	0.849427	+	0.527706i	$0.176948\pi$
$79$	1.14016	+	10.8479i	0.128278	+	1.22049i	−0.721149	+	0.692780i	$0.756386\pi$
$80$		0			0
$81$	−2.36952	+	0.503656i	−0.263280	+	0.0559618i
$82$		0			0
$83$	5.68790	+	4.13250i	0.624328	+	0.453601i	0.854431	−	0.519565i	$-0.173906\pi$
$83$	5.68790	+	4.13250i	0.624328	+	0.453601i	−0.230102	+	0.973166i	$0.573906\pi$
$84$		0			0
$85$	−6.76206	−	20.8115i	−0.733449	−	2.25732i
$86$		0			0
$87$	−1.48663	−	2.57491i	−0.159383	−	0.276060i
$88$		0			0
$89$	1.82999	−	3.16963i	0.193978	−	0.335980i	−0.752587	−	0.658493i	$-0.771194\pi$
$89$	1.82999	−	3.16963i	0.193978	−	0.335980i	0.946565	+	0.322513i	$0.104528\pi$
$90$		0			0
$91$	−9.01432	−	6.31879i	−0.944958	−	0.662389i
$92$		0			0
$93$	5.40205	−	2.40515i	0.560166	−	0.249402i
$94$		0			0
$95$	2.96679	−	0.630610i	0.304386	−	0.0646992i
$96$		0			0
$97$	4.83319	−	3.51152i	0.490736	−	0.356541i	−0.314731	−	0.949181i	$-0.601914\pi$
$97$	4.83319	−	3.51152i	0.490736	−	0.356541i	0.805467	+	0.592640i	$0.201914\pi$
$98$		0			0
$99$	7.10647	−	1.61967i	0.714227	−	0.162783i
$100$		0			0
$101$	9.04158	+	4.02557i	0.899671	+	0.400559i	0.803845	−	0.594839i	$-0.202784\pi$
$101$	9.04158	+	4.02557i	0.899671	+	0.400559i	0.0958259	+	0.995398i	$0.469451\pi$
$102$		0			0
$103$	1.58177	+	1.75673i	0.155856	+	0.173096i	0.816016	−	0.578029i	$-0.196178\pi$
$103$	1.58177	+	1.75673i	0.155856	+	0.173096i	−0.660160	+	0.751125i	$0.729511\pi$
$104$		0			0
$105$	−10.4596	+	0.177207i	−1.02075	+	0.0172937i
$106$		0			0
$107$	15.8767	+	3.37470i	1.53486	+	0.326244i	0.896342	−	0.443363i	$-0.146215\pi$
$107$	15.8767	+	3.37470i	1.53486	+	0.326244i	0.638517	+	0.769608i	$0.279548\pi$
$108$		0			0
$109$	9.01410	+	15.6129i	0.863394	+	1.49544i	0.868633	+	0.495457i	$0.164999\pi$
$109$	9.01410	+	15.6129i	0.863394	+	1.49544i	−0.00523819	+	0.999986i	$0.501667\pi$
$110$		0			0
$111$	−2.29324			−0.217665
$112$		0			0
$113$	2.21077	+	6.80406i	0.207972	+	0.640072i	0.999578	+	0.0290405i	$0.00924519\pi$
$113$	2.21077	+	6.80406i	0.207972	+	0.640072i	−0.791606	+	0.611032i	$0.790755\pi$
$114$		0			0
$115$	2.49193	−	23.7091i	0.232374	−	2.21089i
$116$		0			0
$117$	−6.11844	−	6.79522i	−0.565650	−	0.628218i
$118$		0			0
$119$	−12.7815	+	2.94394i	−1.17168	+	0.269870i
$120$		0			0
$121$	−10.6880	+	2.60121i	−0.971638	+	0.236473i
$122$		0			0
$123$	−3.46340	−	1.54200i	−0.312284	−	0.139038i
$124$		0			0
$125$	−12.9364	+	39.8143i	−1.15707	+	3.56110i
$126$		0			0
$127$	7.68158	+	5.58100i	0.681630	+	0.495233i	0.873898	−	0.486109i	$-0.161584\pi$
$127$	7.68158	+	5.58100i	0.681630	+	0.495233i	−0.192268	+	0.981342i	$0.561584\pi$
$128$		0			0
$129$	2.85594	−	3.17185i	0.251452	−	0.279266i
$130$		0			0
$131$	−6.94191	+	12.0237i	−0.606517	+	1.05052i	0.385292	+	0.922795i	$0.374101\pi$
$131$	−6.94191	+	12.0237i	−0.606517	+	1.05052i	−0.991810	+	0.127724i	$0.959233\pi$
$132$		0			0
$133$	−0.220632	−	1.80455i	−0.0191312	−	0.156475i
$134$		0			0
$135$	−20.1019	−	4.27279i	−1.73010	−	0.367743i
$136$		0			0
$137$	−0.578130	+	5.50054i	−0.0493930	+	0.469943i	0.941669	+	0.336541i	$0.109257\pi$
$137$	−0.578130	+	5.50054i	−0.0493930	+	0.469943i	−0.991062	+	0.133402i	$0.957410\pi$
$138$		0			0
$139$	−1.83605	+	5.65079i	−0.155732	+	0.479293i	−0.998234	−	0.0593991i	$-0.981082\pi$
$139$	−1.83605	+	5.65079i	−0.155732	+	0.479293i	0.842502	+	0.538693i	$0.181082\pi$
$140$		0			0
$141$	−2.63125	+	1.91172i	−0.221591	+	0.160996i
$142$		0			0
$143$	9.38307	+	10.1189i	0.784652	+	0.846184i
$144$		0			0
$145$	1.53150	+	14.5713i	0.127184	+	1.21008i
$146$		0			0
$147$	−0.443806	+	6.25454i	−0.0366045	+	0.515866i
$148$		0			0
$149$	19.6509	−	8.74916i	1.60987	−	0.716759i	0.612582	−	0.790407i	$-0.290131\pi$
$149$	19.6509	−	8.74916i	1.60987	−	0.716759i	0.997284	+	0.0736480i	$0.0234641\pi$
$150$		0			0
$151$	8.47633	−	9.41391i	0.689794	−	0.766094i	−0.291923	−	0.956442i	$-0.594295\pi$
$151$	8.47633	−	9.41391i	0.689794	−	0.766094i	0.981717	+	0.190348i	$0.0609617\pi$
$152$		0			0
$153$	−10.8946			−0.880777
$154$		0			0
$155$	−29.1393			−2.34053
$156$		0			0
$157$	−11.0356	+	12.2563i	−0.880739	+	0.978159i	−0.999892	−	0.0147167i	$-0.995315\pi$
$157$	−11.0356	+	12.2563i	−0.880739	+	0.978159i	0.119153	+	0.992876i	$0.461982\pi$
$158$		0			0
$159$	−1.16170	+	0.517222i	−0.0921288	+	0.0410184i
$160$		0			0
$161$	−14.0254	−	2.73372i	−1.10535	−	0.215447i
$162$		0			0
$163$	1.13415	+	10.7907i	0.0888337	+	0.845196i	0.944686	+	0.327976i	$0.106366\pi$
$163$	1.13415	+	10.7907i	0.0888337	+	0.845196i	−0.855852	+	0.517220i	$0.826967\pi$
$164$		0			0
$165$	12.8656	+	2.53831i	1.00159	+	0.197607i
$166$		0			0
$167$	16.6920	−	12.1274i	1.29166	−	0.938448i	0.291826	−	0.956471i	$-0.405737\pi$
$167$	16.6920	−	12.1274i	1.29166	−	0.938448i	0.999838	+	0.0180230i	$0.00573721\pi$
$168$		0			0
$169$	1.33253	−	4.10111i	0.102502	−	0.315470i
$170$		0			0
$171$	0.157845	−	1.50180i	0.0120707	−	0.114845i
$172$		0			0
$173$	−17.1888	−	3.65359i	−1.30684	−	0.277777i	−0.498703	−	0.866773i	$-0.666190\pi$
$173$	−17.1888	−	3.65359i	−1.30684	−	0.277777i	−0.808136	+	0.588996i	$0.799523\pi$
$174$		0			0
$175$	35.2671	+	14.9913i	2.66594	+	1.13324i
$176$		0			0
$177$	−2.56549	+	4.44355i	−0.192834	+	0.333998i
$178$		0			0
$179$	5.31740	−	5.90557i	0.397441	−	0.441403i	−0.510896	−	0.859643i	$-0.670686\pi$
$179$	5.31740	−	5.90557i	0.397441	−	0.441403i	0.908337	+	0.418240i	$0.137353\pi$
$180$		0			0
$181$	−20.3678	−	14.7981i	−1.51393	−	1.09993i	−0.964397	−	0.264461i	$-0.914806\pi$
$181$	−20.3678	−	14.7981i	−1.51393	−	1.09993i	−0.549532	−	0.835473i	$-0.685194\pi$
$182$		0			0
$183$	1.62780	−	5.00985i	0.120330	−	0.370339i
$184$		0			0
$185$	10.3236	+	4.59636i	0.759006	+	0.337931i
$186$		0			0
$187$	16.4402	−	0.240825i	1.20223	−	0.0176109i
$188$		0			0
$189$	−3.60749	+	11.7780i	−0.262406	+	0.856721i
$190$		0			0
$191$	−3.55122	−	3.94403i	−0.256957	−	0.285380i	0.600839	−	0.799370i	$-0.294833\pi$
$191$	−3.55122	−	3.94403i	−0.256957	−	0.285380i	−0.857796	+	0.513990i	$0.828167\pi$
$192$		0			0
$193$	1.69762	−	16.1518i	0.122197	−	1.16263i	−0.745838	−	0.666127i	$-0.767951\pi$
$193$	1.69762	−	16.1518i	0.122197	−	1.16263i	0.868035	−	0.496502i	$-0.165383\pi$
$194$		0			0
$195$	−5.08376	−	15.6462i	−0.364056	−	1.12045i
$196$		0			0
$197$	4.88001			0.347687			0.173843	−	0.984773i	$-0.444381\pi$
$197$	4.88001			0.347687			0.173843	+	0.984773i	$0.444381\pi$
$198$		0			0
$199$	2.03855	+	3.53087i	0.144509	+	0.250297i	0.929190	−	0.369603i	$-0.120506\pi$
$199$	2.03855	+	3.53087i	0.144509	+	0.250297i	−0.784681	+	0.619900i	$0.787173\pi$
$200$		0			0
$201$	0.394770	+	0.0839110i	0.0278449	+	0.00591862i
$202$		0			0
$203$	8.78073	−	0.148764i	0.616286	−	0.0104412i
$204$		0			0
$205$	12.5007	+	13.8834i	0.873088	+	0.969662i
$206$		0			0
$207$	−10.8429	−	4.82758i	−0.753635	−	0.335540i
$208$		0			0
$209$	−0.204995	+	2.26973i	−0.0141798	+	0.157001i
$210$		0			0
$211$	−8.48368	+	6.16376i	−0.584041	+	0.424331i	−0.840179	−	0.542310i	$-0.817550\pi$
$211$	−8.48368	+	6.16376i	−0.584041	+	0.424331i	0.256138	+	0.966640i	$0.417550\pi$
$212$		0			0
$213$	−8.04893	+	1.71085i	−0.551503	+	0.117226i
$214$		0			0
$215$	−19.2141	+	8.55468i	−1.31039	+	0.583424i
$216$		0			0
$217$	−1.53117	+	17.3986i	−0.103943	+	1.18109i
$218$		0			0
$219$	1.15407	−	1.99890i	0.0779845	−	0.135073i
$220$		0			0
$221$	−10.3134	−	17.8634i	−0.693756	−	1.20162i
$222$		0			0
$223$	−0.475969	−	1.46488i	−0.0318733	−	0.0980959i	0.933854	−	0.357654i	$-0.116423\pi$
$223$	−0.475969	−	1.46488i	−0.0318733	−	0.0980959i	−0.965728	+	0.259558i	$0.916423\pi$
$224$		0			0
$225$	25.7514	+	18.7095i	1.71676	+	1.24730i
$226$		0			0
$227$	−18.4766	+	3.92732i	−1.22633	+	0.260665i	−0.775157	−	0.631769i	$-0.782329\pi$
$227$	−18.4766	+	3.92732i	−1.22633	+	0.260665i	−0.451177	+	0.892434i	$0.648996\pi$
$228$		0			0
$229$	−0.846580	−	8.05467i	−0.0559436	−	0.532268i	−0.986224	−	0.165418i	$-0.947103\pi$
$229$	−0.846580	−	8.05467i	−0.0559436	−	0.532268i	0.930280	−	0.366850i	$-0.119564\pi$
$230$		0			0
$231$	2.19163	−	7.54847i	0.144198	−	0.496653i
$232$		0			0
$233$	−0.156016	−	1.48439i	−0.0102209	−	0.0972455i	0.988222	−	0.153026i	$-0.0489019\pi$
$233$	−0.156016	−	1.48439i	−0.0102209	−	0.0972455i	−0.998443	+	0.0557807i	$0.982235\pi$
$234$		0			0
$235$	15.6769	−	3.33223i	1.02265	−	0.217371i
$236$		0			0
$237$	7.90456	+	5.74300i	0.513456	+	0.373048i
$238$		0			0
$239$	0.0784979	+	0.241592i	0.00507761	+	0.0156273i	0.953563	−	0.301193i	$-0.0973848\pi$
$239$	0.0784979	+	0.241592i	0.00507761	+	0.0156273i	−0.948486	+	0.316820i	$0.897385\pi$
$240$		0			0
$241$	−5.03093	−	8.71383i	−0.324071	−	0.561307i	0.657253	−	0.753670i	$-0.271718\pi$
$241$	−5.03093	−	8.71383i	−0.324071	−	0.561307i	−0.981324	+	0.192363i	$0.938385\pi$
$242$		0			0
$243$	−8.06864	+	13.9753i	−0.517603	+	0.896515i
$244$		0			0
$245$	14.5339	−	27.2669i	0.928539	−	1.74202i
$246$		0			0
$247$	2.61185	−	1.16287i	0.166188	−	0.0739917i
$248$		0			0
$249$	6.16009	−	1.30937i	0.390380	−	0.0829777i
$250$		0			0
$251$	3.64939	−	2.65144i	0.230347	−	0.167357i	−0.466625	−	0.884455i	$-0.654530\pi$
$251$	3.64939	−	2.65144i	0.230347	−	0.167357i	0.696972	+	0.717098i	$0.254530\pi$
$252$		0			0
$253$	16.4689	+	7.04524i	1.03539	+	0.442931i
$254$		0			0
$255$	−17.9067	−	7.97256i	−1.12136	−	0.499261i
$256$		0			0
$257$	3.05864	+	3.39697i	0.190793	+	0.211897i	0.830950	−	0.556347i	$-0.187797\pi$
$257$	3.05864	+	3.39697i	0.190793	+	0.211897i	−0.640157	+	0.768244i	$0.721131\pi$
$258$		0			0
$259$	3.28688	−	5.92252i	0.204237	−	0.368007i
$260$		0			0
$261$	7.13514	+	1.51662i	0.441654	+	0.0938765i
$262$		0			0
$263$	10.1326	+	17.5501i	0.624801	+	1.08219i	0.988579	+	0.150701i	$0.0481532\pi$
$263$	10.1326	+	17.5501i	0.624801	+	1.08219i	−0.363778	+	0.931485i	$0.618513\pi$
$264$		0			0
$265$	6.26636			0.384939
$266$		0			0
$267$	−1.01309	−	3.11797i	−0.0620001	−	0.190817i
$268$		0			0
$269$	−1.82352	+	17.3496i	−0.111182	+	1.05783i	0.786623	+	0.617433i	$0.211827\pi$
$269$	−1.82352	+	17.3496i	−0.111182	+	1.05783i	−0.897805	+	0.440393i	$0.854839\pi$
$270$		0			0
$271$	−13.3458	−	14.8221i	−0.810703	−	0.900376i	0.185914	−	0.982566i	$-0.440475\pi$
$271$	−13.3458	−	14.8221i	−0.810703	−	0.900376i	−0.996617	+	0.0821896i	$0.973809\pi$
$272$		0			0
$273$	−9.60921	+	2.21327i	−0.581576	+	0.133953i
$274$		0			0
$275$	−39.2730	−	27.6638i	−2.36825	−	1.66819i
$276$		0			0
$277$	−24.4646	−	10.8924i	−1.46994	−	0.654458i	−0.493399	−	0.869803i	$-0.664246\pi$
$277$	−24.4646	−	10.8924i	−1.46994	−	0.654458i	−0.976538	+	0.215345i	$0.930912\pi$
$278$		0			0
$279$	−4.48308	+	13.7975i	−0.268395	+	0.826035i
$280$		0			0
$281$	−2.20627	−	1.60295i	−0.131615	−	0.0956241i	0.520030	−	0.854148i	$-0.325921\pi$
$281$	−2.20627	−	1.60295i	−0.131615	−	0.0956241i	−0.651645	+	0.758524i	$0.725921\pi$
$282$		0			0
$283$	12.8829	−	14.3079i	0.765807	−	0.850514i	−0.226540	−	0.974002i	$-0.572741\pi$
$283$	12.8829	−	14.3079i	0.765807	−	0.850514i	0.992346	+	0.123488i	$0.0394079\pi$
$284$		0			0
$285$	1.35844	−	2.35288i	0.0804669	−	0.139373i
$286$		0			0
$287$	8.94643	−	6.73443i	0.528091	−	0.397521i
$288$		0			0
$289$	−7.41065	−	1.57518i	−0.435921	−	0.0926578i
$290$		0			0
$291$	0.559369	−	5.32204i	0.0327908	−	0.311984i
$292$		0			0
$293$	9.45298	−	29.0933i	0.552249	−	1.69965i	−0.150851	−	0.988557i	$-0.548201\pi$
$293$	9.45298	−	29.0933i	0.552249	−	1.69965i	0.703100	−	0.711091i	$-0.251799\pi$
$294$		0			0
$295$	20.4554	−	14.8617i	1.19096	−	0.865284i
$296$		0			0
$297$	7.52405	−	13.4844i	0.436590	−	0.782443i
$298$		0			0
$299$	−2.34894	−	22.3487i	−0.135843	−	1.29246i
$300$		0			0
$301$	4.09821	+	11.9219i	0.236217	+	0.687169i
$302$		0			0
$303$	8.09902	−	3.60591i	0.465276	−	0.207154i
$304$		0			0
$305$	−17.3692	+	19.2905i	−0.994560	+	1.10457i
$306$		0			0
$307$	1.35405			0.0772796			0.0386398	−	0.999253i	$-0.487698\pi$
$307$	1.35405			0.0772796			0.0386398	+	0.999253i	$0.487698\pi$
$308$		0			0
$309$	2.11748			0.120459
$310$		0			0
$311$	16.0347	−	17.8084i	0.909245	−	1.00982i	−0.0906576	−	0.995882i	$-0.528897\pi$
$311$	16.0347	−	17.8084i	0.909245	−	1.00982i	0.999903	−	0.0139370i	$-0.00443643\pi$
$312$		0			0
$313$	9.44814	−	4.20659i	0.534041	−	0.237770i	−0.121954	−	0.992536i	$-0.538916\pi$
$313$	9.44814	−	4.20659i	0.534041	−	0.237770i	0.655995	+	0.754766i	$0.272249\pi$
$314$		0			0
$315$	16.8477	−	19.3610i	0.949262	−	1.09087i
$316$		0			0
$317$	1.48267	+	14.1067i	0.0832752	+	0.792311i	0.953852	+	0.300278i	$0.0970794\pi$
$317$	1.48267	+	14.1067i	0.0832752	+	0.792311i	−0.870577	+	0.492033i	$0.836254\pi$
$318$		0			0
$319$	−10.8006	−	2.13089i	−0.604718	−	0.119307i
$320$		0			0
$321$	11.7626	−	8.54599i	0.656522	−	0.476991i
$322$		0			0
$323$	1.05265	−	3.23971i	0.0585708	−	0.180262i
$324$		0			0
$325$	−6.29941	+	59.9349i	−0.349428	+	3.32459i
$326$		0			0
$327$	15.7959	+	3.35753i	0.873516	+	0.185672i
$328$		0			0
$329$	−1.16585	−	9.53551i	−0.0642754	−	0.525709i
$330$		0			0
$331$	0.241586	−	0.418440i	0.0132788	−	0.0229995i	−0.859310	−	0.511456i	$-0.829106\pi$
$331$	0.241586	−	0.418440i	0.0132788	−	0.0229995i	0.872588	+	0.488456i	$0.162440\pi$
$332$		0			0
$333$	3.76467	−	4.18109i	0.206303	−	0.229122i
$334$		0			0
$335$	−1.60897	−	1.16899i	−0.0879076	−	0.0638686i
$336$		0			0
$337$	−6.14808	+	18.9218i	−0.334907	+	1.03074i	0.631861	+	0.775082i	$0.282292\pi$
$337$	−6.14808	+	18.9218i	−0.334907	+	1.03074i	−0.966768	+	0.255656i	$0.917708\pi$
$338$		0			0
$339$	5.85437	+	2.60653i	0.317966	+	0.141567i
$340$		0			0
$341$	6.46008	−	20.9198i	0.349833	−	1.13287i
$342$		0			0
$343$	−15.5169	−	10.1107i	−0.837832	−	0.545929i
$344$		0			0
$345$	−14.2889	−	15.8695i	−0.769291	−	0.854384i
$346$		0			0
$347$	−2.31444	+	22.0204i	−0.124245	+	1.18212i	0.737705	+	0.675123i	$0.235910\pi$
$347$	−2.31444	+	22.0204i	−0.124245	+	1.18212i	−0.861950	+	0.506993i	$0.830757\pi$
$348$		0			0
$349$	−4.75386	−	14.6309i	−0.254468	−	0.783172i	−0.993934	−	0.109978i	$-0.964922\pi$
$349$	−4.75386	−	14.6309i	−0.254468	−	0.783172i	0.739466	−	0.673194i	$-0.235078\pi$
$350$		0			0
$351$	−19.3717			−1.03399
$352$		0			0
$353$	−2.28348	−	3.95511i	−0.121537	−	0.210509i	0.798837	−	0.601548i	$-0.205449\pi$
$353$	−2.28348	−	3.95511i	−0.121537	−	0.210509i	−0.920374	+	0.391039i	$0.872116\pi$
$354$		0			0
$355$	39.6634	+	8.43071i	2.10511	+	0.447456i
$356$		0			0
$357$	−5.70121	+	10.2728i	−0.301740	+	0.543696i
$358$		0			0
$359$	10.6868	+	11.8688i	0.564025	+	0.626413i	0.955931	−	0.293592i	$-0.0948507\pi$
$359$	10.6868	+	11.8688i	0.564025	+	0.626413i	−0.391906	+	0.920005i	$0.628184\pi$
$360$		0			0
$361$	−16.9260	−	7.53595i	−0.890844	−	0.396629i
$362$		0			0
$363$	−4.67458	+	8.67383i	−0.245352	+	0.455258i
$364$		0			0
$365$	−9.20174	+	6.68545i	−0.481641	+	0.349933i
$366$		0			0
$367$	8.50097	−	1.80694i	0.443747	−	0.0943213i	0.0193812	−	0.999812i	$-0.493830\pi$
$367$	8.50097	−	1.80694i	0.443747	−	0.0943213i	0.424366	+	0.905491i	$0.360497\pi$
$368$		0			0
$369$	8.49706	−	3.78314i	0.442339	−	0.196942i
$370$		0			0
$371$	0.329275	−	3.74153i	0.0170951	−	0.194251i
$372$		0			0
$373$	7.29217	−	12.6304i	0.377574	−	0.653978i	−0.613135	−	0.789979i	$-0.710092\pi$
$373$	7.29217	−	12.6304i	0.377574	−	0.653978i	0.990709	+	0.136001i	$0.0434250\pi$
$374$		0			0
$375$	18.7495	+	32.4751i	0.968221	+	1.67701i
$376$		0			0
$377$	4.26778	+	13.1349i	0.219802	+	0.676480i
$378$		0			0
$379$	−20.3656	−	14.7964i	−1.04611	−	0.760042i	−0.0746398	−	0.997211i	$-0.523781\pi$
$379$	−20.3656	−	14.7964i	−1.04611	−	0.760042i	−0.971469	+	0.237168i	$0.923781\pi$
$380$		0			0
$381$	8.31927	−	1.76832i	0.426209	−	0.0905935i
$382$		0			0
$383$	2.69604	+	25.6511i	0.137761	+	1.31071i	0.816934	+	0.576731i	$0.195672\pi$
$383$	2.69604	+	25.6511i	0.137761	+	1.31071i	−0.679173	+	0.733978i	$0.737662\pi$
$384$		0			0
$385$	−24.9956	+	29.5887i	−1.27390	+	1.50798i
$386$		0			0
$387$	1.09456	+	10.4140i	0.0556396	+	0.529376i
$388$		0			0
$389$	−32.2744	+	6.86014i	−1.63638	+	0.347823i	−0.932128	−	0.362129i	$-0.882050\pi$
$389$	−32.2744	+	6.86014i	−1.63638	+	0.347823i	−0.704250	+	0.709952i	$0.748717\pi$
$390$		0			0
$391$	−21.6609	−	15.7376i	−1.09544	−	0.795884i
$392$		0			0
$393$	3.84308	+	11.8278i	0.193858	+	0.596632i
$394$		0			0
$395$	−24.0736	−	41.6968i	−1.21128	−	2.09799i
$396$		0			0
$397$	−0.190703	+	0.330307i	−0.00957110	+	0.0165776i	−0.870771	−	0.491688i	$-0.836380\pi$
$397$	−0.190703	+	0.330307i	−0.00957110	+	0.0165776i	0.861200	+	0.508266i	$0.169713\pi$
$398$		0			0
$399$	−1.33348	−	0.934735i	−0.0667577	−	0.0467953i
$400$		0			0
$401$	−11.9276	+	5.31049i	−0.595634	+	0.265193i	−0.682333	−	0.731041i	$-0.739035\pi$
$401$	−11.9276	+	5.31049i	−0.595634	+	0.265193i	0.0866996	+	0.996234i	$0.472368\pi$
$402$		0			0
$403$	−26.8671	+	5.71077i	−1.33834	+	0.284474i
$404$		0			0
$405$	8.65072	−	6.28512i	0.429858	−	0.312310i
$406$		0			0
$407$	−5.58854	+	6.39257i	−0.277014	+	0.316868i
$408$		0			0
$409$	20.7364	+	9.23242i	1.02535	+	0.456514i	0.849324	−	0.527872i	$-0.177010\pi$
$409$	20.7364	+	9.23242i	1.02535	+	0.456514i	0.176023	+	0.984386i	$0.443677\pi$
$410$		0			0
$411$	3.31505	+	3.68174i	0.163519	+	0.181607i
$412$		0			0
$413$	−7.79883	−	12.9945i	−0.383755	−	0.639418i
$414$		0			0
$415$	−30.3556	−	6.45227i	−1.49010	−	0.316730i
$416$		0			0
$417$	2.66110	+	4.60915i	0.130314	+	0.225711i
$418$		0			0
$419$	17.5285			0.856321			0.428161	−	0.903703i	$-0.359162\pi$
$419$	17.5285			0.856321			0.428161	+	0.903703i	$0.359162\pi$
$420$		0			0
$421$	−7.89590	−	24.3011i	−0.384823	−	1.18436i	−0.936609	−	0.350377i	$-0.886054\pi$
$421$	−7.89590	−	24.3011i	−0.384823	−	1.18436i	0.551786	−	0.833986i	$-0.313946\pi$
$422$		0			0
$423$	0.834076	−	7.93570i	0.0405542	−	0.385847i
$424$		0			0
$425$	48.0461	+	53.3606i	2.33058	+	2.58837i
$426$		0			0
$427$	10.6053	+	11.3845i	0.513228	+	0.550936i
$428$		0			0
$429$	12.3599	−	0.181054i	0.596739	−	0.00874137i
$430$		0			0
$431$	28.7396	+	12.7957i	1.38434	+	0.616347i	0.957619	−	0.288037i	$-0.0930026\pi$
$431$	28.7396	+	12.7957i	1.38434	+	0.616347i	0.426719	+	0.904384i	$0.359669\pi$
$432$		0			0
$433$	7.30350	−	22.4778i	0.350984	−	1.08022i	−0.607318	−	0.794459i	$-0.707755\pi$
$433$	7.30350	−	22.4778i	0.350984	−	1.08022i	0.958302	−	0.285758i	$-0.0922453\pi$
$434$		0			0
$435$	10.6177	+	7.71418i	0.509078	+	0.369867i
$436$		0			0
$437$	2.48322	−	2.75790i	0.118789	−	0.131928i
$438$		0			0
$439$	4.70830	−	8.15501i	0.224715	−	0.389217i	−0.731519	−	0.681821i	$-0.761188\pi$
$439$	4.70830	−	8.15501i	0.224715	−	0.389217i	0.956234	+	0.292604i	$0.0945217\pi$
$440$		0			0
$441$	−10.6748	−	11.0768i	−0.508326	−	0.527469i
$442$		0			0
$443$	6.00844	+	1.27713i	0.285470	+	0.0606784i	0.348421	−	0.937338i	$-0.386718\pi$
$443$	6.00844	+	1.27713i	0.285470	+	0.0606784i	−0.0629514	+	0.998017i	$0.520051\pi$
$444$		0			0
$445$	−1.68870	+	16.0669i	−0.0800519	+	0.761643i
$446$		0			0
$447$	5.95420	−	18.3251i	0.281624	−	0.866749i
$448$		0			0
$449$	9.95124	−	7.23000i	0.469628	−	0.341205i	−0.327668	−	0.944793i	$-0.606263\pi$
$449$	9.95124	−	7.23000i	0.469628	−	0.341205i	0.797296	+	0.603588i	$0.206263\pi$
$450$		0			0
$451$	−12.7386	+	5.89666i	−0.599839	+	0.277663i
$452$		0			0
$453$	−1.18609	−	11.2849i	−0.0557276	−	0.530212i
$454$		0			0
$455$	47.6944	+	9.29624i	2.23595	+	0.435814i
$456$		0			0
$457$	−4.57921	+	2.03879i	−0.214206	+	0.0953708i	−0.511035	−	0.859560i	$-0.670738\pi$
$457$	−4.57921	+	2.03879i	−0.214206	+	0.0953708i	0.296829	+	0.954931i	$0.404071\pi$
$458$		0			0
$459$	−15.4441	+	17.1524i	−0.720867	+	0.800604i
$460$		0			0
$461$	1.26864			0.0590865			0.0295433	−	0.999564i	$-0.490595\pi$
$461$	1.26864			0.0590865			0.0295433	+	0.999564i	$0.490595\pi$
$462$		0			0
$463$	−1.07973			−0.0501795			−0.0250898	−	0.999685i	$-0.507987\pi$
$463$	−1.07973			−0.0501795			−0.0250898	+	0.999685i	$0.507987\pi$
$464$		0			0
$465$	−17.4654	+	19.3973i	−0.809938	+	0.899527i
$466$		0			0
$467$	−3.64221	+	1.62162i	−0.168541	+	0.0750395i	−0.489273	−	0.872131i	$-0.662738\pi$
$467$	−3.64221	+	1.62162i	−0.168541	+	0.0750395i	0.320732	+	0.947170i	$0.396071\pi$
$468$		0			0
$469$	−0.782528	+	0.899264i	−0.0361338	+	0.0415241i
$470$		0			0
$471$	1.54422	+	14.6922i	0.0711538	+	0.676983i
$472$		0			0
$473$	−1.88192	−	15.6908i	−0.0865307	−	0.721465i
$474$		0			0
$475$	−8.05173	+	5.84993i	−0.369439	+	0.268413i
$476$		0			0
$477$	0.964078	−	2.96713i	0.0441421	−	0.135855i
$478$		0			0
$479$	−1.29549	+	12.3257i	−0.0591923	+	0.563177i	0.924229	+	0.381840i	$0.124709\pi$
$479$	−1.29549	+	12.3257i	−0.0591923	+	0.563177i	−0.983421	+	0.181338i	$0.941957\pi$
$480$		0			0
$481$	10.4194	+	2.21471i	0.475083	+	0.100982i
$482$		0			0
$483$	−10.2262	+	7.69779i	−0.465309	+	0.350262i
$484$		0			0
$485$	−13.1852	+	22.8374i	−0.598708	+	1.03699i
$486$		0			0
$487$	−15.5663	+	17.2881i	−0.705376	+	0.783399i	−0.984222	−	0.176936i	$-0.943381\pi$
$487$	−15.5663	+	17.2881i	−0.705376	+	0.783399i	0.278846	+	0.960336i	$0.410048\pi$
$488$		0			0
$489$	7.86289	+	5.71273i	0.355572	+	0.258338i
$490$		0			0
$491$	3.37656	−	10.3920i	0.152382	−	0.468984i	−0.845504	−	0.533969i	$-0.820700\pi$
$491$	3.37656	−	10.3920i	0.152382	−	0.468984i	0.997886	+	0.0649849i	$0.0206999\pi$
$492$		0			0
$493$	15.0325	+	6.69290i	0.677030	+	0.301433i
$494$		0			0
$495$	−25.7486	+	19.2900i	−1.15731	+	0.867019i
$496$		0			0
$497$	7.11800	−	23.2393i	0.319286	−	1.04242i
$498$		0			0
$499$	−12.6724	−	14.0741i	−0.567293	−	0.630042i	0.389426	−	0.921058i	$-0.372673\pi$
$499$	−12.6724	−	14.0741i	−0.567293	−	0.630042i	−0.956718	+	0.291016i	$0.906007\pi$
$500$		0			0
$501$	1.93185	−	18.3803i	0.0863085	−	0.821171i
$502$		0			0
$503$	4.60103	+	14.1605i	0.205150	+	0.631386i	0.999707	+	0.0241968i	$0.00770285\pi$
$503$	4.60103	+	14.1605i	0.205150	+	0.631386i	−0.794558	+	0.607189i	$0.792297\pi$
$504$		0			0
$505$	−43.6871			−1.94405
$506$		0			0
$507$	−1.93132	−	3.34514i	−0.0857727	−	0.148563i
$508$		0			0
$509$	−2.28273	−	0.485209i	−0.101180	−	0.0215065i	0.157043	−	0.987592i	$-0.449804\pi$
$509$	−2.28273	−	0.485209i	−0.101180	−	0.0215065i	−0.258223	+	0.966085i	$0.583137\pi$
$510$		0			0
$511$	3.50825	+	5.84549i	0.155196	+	0.258589i
$512$		0			0
$513$	−2.14065	−	2.37744i	−0.0945122	−	0.104966i
$514$		0			0
$515$	−9.53239	−	4.24409i	−0.420047	−	0.187017i
$516$		0			0
$517$	−1.08322	+	11.9936i	−0.0476400	+	0.527477i
$518$		0			0
$519$	−12.7346	+	9.25225i	−0.558988	+	0.406129i
$520$		0			0
$521$	15.6945	−	3.33598i	0.687590	−	0.146152i	0.149149	−	0.988815i	$-0.452347\pi$
$521$	15.6945	−	3.33598i	0.687590	−	0.146152i	0.538441	+	0.842663i	$0.319013\pi$
$522$		0			0
$523$	37.4534	−	16.6753i	1.63772	−	0.729161i	0.638540	−	0.769589i	$-0.279539\pi$
$523$	37.4534	−	16.6753i	1.63772	−	0.729161i	0.999182	+	0.0404282i	$0.0128722\pi$
$524$		0			0
$525$	31.1176	−	14.4909i	1.35808	−	0.632437i
$526$		0			0
$527$	−16.3632	+	28.3419i	−0.712791	+	1.23459i
$528$		0			0
$529$	−3.08459	−	5.34266i	−0.134112	−	0.232289i
$530$		0			0
$531$	−3.88999	−	11.9722i	−0.168811	−	0.519547i
$532$		0			0
$533$	14.2468	+	10.3509i	0.617098	+	0.448348i
$534$		0			0
$535$	−70.0809	+	14.8962i	−3.02986	+	0.644017i
$536$		0			0
$537$	−0.744065	−	7.07930i	−0.0321088	−	0.305494i
$538$		0			0
$539$	16.3534	+	16.4792i	0.704392	+	0.709811i
$540$		0			0
$541$	0.965287	+	9.18409i	0.0415009	+	0.394855i	0.995479	+	0.0949793i	$0.0302785\pi$
$541$	0.965287	+	9.18409i	0.0415009	+	0.394855i	−0.953978	+	0.299876i	$0.903055\pi$
$542$		0			0
$543$	−22.0587	+	4.68871i	−0.946628	+	0.201212i
$544$		0			0
$545$	−64.3798	−	46.7747i	−2.75773	−	2.00361i
$546$		0			0
$547$	5.56329	+	17.1220i	0.237869	+	0.732086i	0.996728	+	0.0808305i	$0.0257572\pi$
$547$	5.56329	+	17.1220i	0.237869	+	0.732086i	−0.758859	+	0.651255i	$0.774243\pi$
$548$		0			0
$549$	6.46182	+	11.1922i	0.275784	+	0.477672i
$550$		0			0
$551$	−1.14040	+	1.97523i	−0.0485826	+	0.0841475i
$552$		0			0
$553$	−26.1614	+	12.1829i	−1.11250	+	0.518071i
$554$		0			0
$555$	9.24739	−	4.11720i	0.392530	−	0.174765i
$556$		0			0
$557$	13.6836	−	2.90854i	0.579793	−	0.123239i	0.0913256	−	0.995821i	$-0.470890\pi$
$557$	13.6836	−	2.90854i	0.579793	−	0.123239i	0.488467	+	0.872582i	$0.337556\pi$
$558$		0			0
$559$	−16.0393	+	11.6532i	−0.678388	+	0.492878i
$560$		0			0
$561$	9.69354	−	11.0882i	0.409262	−	0.468142i
$562$		0			0
$563$	1.89574	+	0.844040i	0.0798961	+	0.0355720i	0.446296	−	0.894886i	$-0.352743\pi$
$563$	1.89574	+	0.844040i	0.0798961	+	0.0355720i	−0.366400	+	0.930458i	$0.619410\pi$
$564$		0			0
$565$	−21.1306	−	23.4679i	−0.888972	−	0.987303i
$566$		0			0
$567$	−3.29817	−	5.49546i	−0.138510	−	0.230787i
$568$		0			0
$569$	26.8985	+	5.71745i	1.12764	+	0.239688i	0.733717	−	0.679455i	$-0.237784\pi$
$569$	26.8985	+	5.71745i	1.12764	+	0.239688i	0.393925	+	0.919143i	$0.371117\pi$
$570$		0			0
$571$	1.80258	+	3.12216i	0.0754357	+	0.130658i	0.901276	−	0.433246i	$-0.142632\pi$
$571$	1.80258	+	3.12216i	0.0754357	+	0.130658i	−0.825840	+	0.563905i	$0.809299\pi$
$572$		0			0
$573$	−4.75395			−0.198599
$574$		0			0
$575$	24.1732	+	74.3974i	1.00809	+	3.10259i
$576$		0			0
$577$	1.09176	−	10.3874i	0.0454506	−	0.432434i	−0.948008	−	0.318245i	$-0.896907\pi$
$577$	1.09176	−	10.3874i	0.0454506	−	0.432434i	0.993459	−	0.114189i	$-0.0364268\pi$
$578$		0			0
$579$	−9.73429	−	10.8110i	−0.404543	−	0.449291i
$580$		0			0
$581$	−5.44762	+	17.7857i	−0.226005	+	0.737876i
$582$		0			0
$583$	−1.38923	+	4.49877i	−0.0575359	+	0.186320i
$584$		0			0
$585$	36.8722	+	16.4166i	1.52448	+	0.678742i
$586$		0			0
$587$	11.2820	−	34.7223i	0.465657	−	1.43314i	−0.392498	−	0.919753i	$-0.628389\pi$
$587$	11.2820	−	34.7223i	0.465657	−	1.43314i	0.858155	−	0.513391i	$-0.171611\pi$
$588$		0			0
$589$	−3.66978	−	2.66625i	−0.151211	−	0.109861i
$590$		0			0
$591$	2.92496	−	3.24850i	0.120317	−	0.133625i
$592$		0			0
$593$	−4.07690	+	7.06140i	−0.167418	+	0.289977i	−0.937511	−	0.347954i	$-0.886876\pi$
$593$	−4.07690	+	7.06140i	−0.167418	+	0.289977i	0.770093	+	0.637931i	$0.220210\pi$
$594$		0			0
$595$	46.2554	−	34.8188i	1.89629	−	1.42743i
$596$		0			0
$597$	3.57226	+	0.759307i	0.146203	+	0.0310764i
$598$		0			0
$599$	3.08912	−	29.3910i	0.126218	−	1.20088i	−0.729699	−	0.683769i	$-0.760340\pi$
$599$	3.08912	−	29.3910i	0.126218	−	1.20088i	0.855917	−	0.517114i	$-0.172994\pi$
$600$		0			0
$601$	8.38018	−	25.7915i	0.341834	−	1.05206i	−0.621422	−	0.783476i	$-0.713445\pi$
$601$	8.38018	−	25.7915i	0.341834	−	1.05206i	0.963257	−	0.268582i	$-0.0865552\pi$
$602$		0			0
$603$	−0.801058	+	0.582002i	−0.0326216	+	0.0237010i
$604$		0			0
$605$	38.4288	−	29.6781i	1.56235	−	1.20659i
$606$		0			0
$607$	4.09234	+	38.9360i	0.166103	+	1.58037i	0.686943	+	0.726711i	$0.258952\pi$
$607$	4.09234	+	38.9360i	0.166103	+	1.58037i	−0.520840	+	0.853654i	$0.674381\pi$
$608$		0			0
$609$	5.16392	−	5.93426i	0.209253	−	0.240469i
$610$		0			0
$611$	13.8014	−	6.14477i	0.558344	−	0.248591i
$612$		0			0
$613$	−7.24841	+	8.05018i	−0.292761	+	0.325144i	−0.871525	−	0.490351i	$-0.836868\pi$
$613$	−7.24841	+	8.05018i	−0.292761	+	0.325144i	0.578764	+	0.815495i	$0.303535\pi$
$614$		0			0
$615$	16.7345			0.674799
$616$		0			0
$617$	35.7293			1.43841			0.719204	−	0.694799i	$-0.244506\pi$
$617$	35.7293			1.43841			0.719204	+	0.694799i	$0.244506\pi$
$618$		0			0
$619$	−15.9304	+	17.6925i	−0.640297	+	0.711122i	−0.972713	−	0.232011i	$-0.925469\pi$
$619$	−15.9304	+	17.6925i	−0.640297	+	0.711122i	0.332416	+	0.943133i	$0.392136\pi$
$620$		0			0
$621$	−22.9713	+	10.2275i	−0.921806	+	0.410414i
$622$		0			0
$623$	9.50452	+	1.85255i	0.380790	+	0.0742208i
$624$		0			0
$625$	−11.7455	−	111.751i	−0.469822	−	4.47006i
$626$		0			0
$627$	1.38803	+	1.49688i	0.0554327	+	0.0597797i
$628$		0			0
$629$	10.2678	−	7.45998i	0.409403	−	0.297449i
$630$		0			0
$631$	7.29837	−	22.4621i	0.290543	−	0.894200i	−0.694139	−	0.719841i	$-0.744215\pi$
$631$	7.29837	−	22.4621i	0.290543	−	0.894200i	0.984682	−	0.174359i	$-0.0557854\pi$
$632$		0			0
$633$	−0.981859	+	9.34177i	−0.0390254	+	0.371302i
$634$		0			0
$635$	−40.9956	−	8.71387i	−1.62686	−	0.345800i
$636$		0			0
$637$	8.05679	−	27.9890i	0.319222	−	1.10896i
$638$		0			0
$639$	10.0942	−	17.4836i	0.399319	−	0.691640i
$640$		0			0
$641$	−13.2339	+	14.6977i	−0.522706	+	0.580524i	−0.945467	−	0.325717i	$-0.894394\pi$
$641$	−13.2339	+	14.6977i	−0.522706	+	0.580524i	0.422761	+	0.906241i	$0.361061\pi$
$642$		0			0
$643$	−0.816222	−	0.593020i	−0.0321886	−	0.0233864i	0.571575	−	0.820550i	$-0.306333\pi$
$643$	−0.816222	−	0.593020i	−0.0321886	−	0.0233864i	−0.603763	+	0.797164i	$0.706333\pi$
$644$		0			0
$645$	−5.82184	+	17.9178i	−0.229235	+	0.705512i
$646$		0			0
$647$	−15.8927	−	7.07590i	−0.624807	−	0.278182i	0.0698114	−	0.997560i	$-0.477760\pi$
$647$	−15.8927	−	7.07590i	−0.624807	−	0.278182i	−0.694619	+	0.719378i	$0.744427\pi$
$648$		0			0
$649$	6.13472	+	17.9803i	0.240809	+	0.705787i
$650$		0			0
$651$	10.6640	+	11.4475i	0.417956	+	0.448664i
$652$		0			0
$653$	−15.5262	−	17.2436i	−0.607587	−	0.674794i	0.358345	−	0.933589i	$-0.383341\pi$
$653$	−15.5262	−	17.2436i	−0.607587	−	0.674794i	−0.965932	+	0.258795i	$0.916674\pi$
$654$		0			0
$655$	6.40594	−	60.9484i	0.250301	−	2.38145i
$656$		0			0
$657$	1.74988	+	5.38559i	0.0682695	+	0.210112i
$658$		0			0
$659$	48.7099			1.89747			0.948733	−	0.316078i	$-0.102366\pi$
$659$	48.7099			1.89747			0.948733	+	0.316078i	$0.102366\pi$
$660$		0			0
$661$	−20.0951	−	34.8057i	−0.781609	−	1.35379i	−0.931004	−	0.365009i	$-0.881066\pi$
$661$	−20.0951	−	34.8057i	−0.781609	−	1.35379i	0.149395	−	0.988778i	$-0.452267\pi$
$662$		0			0
$663$	−18.0728	−	3.84149i	−0.701889	−	0.149191i
$664$		0			0
$665$	4.12952	+	6.88066i	0.160136	+	0.266821i
$666$		0			0
$667$	11.9955	+	13.3223i	0.464466	+	0.515842i
$668$		0			0
$669$	−1.26042	−	0.561174i	−0.0487306	−	0.0216963i
$670$		0			0
$671$	−9.99843	−	16.7464i	−0.385985	−	0.646489i
$672$		0			0
$673$	10.0399	−	7.29443i	0.387010	−	0.281179i	−0.377219	−	0.926124i	$-0.623120\pi$
$673$	10.0399	−	7.29443i	0.387010	−	0.281179i	0.764229	+	0.644945i	$0.223120\pi$
$674$		0			0
$675$	65.9609	−	14.0204i	2.53884	−	0.539647i
$676$		0			0
$677$	5.31910	−	2.36822i	0.204430	−	0.0910180i	−0.301968	−	0.953318i	$-0.597644\pi$
$677$	5.31910	−	2.36822i	0.204430	−	0.0910180i	0.506398	+	0.862300i	$0.330977\pi$
$678$		0			0
$679$	12.9430	+	9.07266i	0.496705	+	0.348177i
$680$		0			0
$681$	−8.46009	+	14.6533i	−0.324191	+	0.561516i
$682$		0			0
$683$	11.1841	+	19.3714i	0.427948	+	0.741227i	0.996691	−	0.0812884i	$-0.0259035\pi$
$683$	11.1841	+	19.3714i	0.427948	+	0.741227i	−0.568743	+	0.822515i	$0.692570\pi$
$684$		0			0
$685$	−7.54420	−	23.2186i	−0.288249	−	0.887139i
$686$		0			0
$687$	−5.86920	−	4.26422i	−0.223924	−	0.162690i
$688$		0			0
$689$	5.77771	−	1.22809i	0.220113	−	0.0467865i
$690$		0			0
$691$	−0.0267020	−	0.254053i	−0.00101579	−	0.00966462i	0.994002	−	0.109360i	$-0.0348800\pi$
$691$	−0.0267020	−	0.254053i	−0.00101579	−	0.00966462i	−0.995018	+	0.0996949i	$0.968213\pi$
$692$		0			0
$693$	10.1647	+	16.3877i	0.386125	+	0.622516i
$694$		0			0
$695$	−2.74143	−	26.0829i	−0.103988	−	0.989382i
$696$		0			0
$697$	20.5233	−	4.36235i	0.777374	−	0.165236i
$698$		0			0
$699$	−1.08163	−	0.785850i	−0.0409110	−	0.0297236i
$700$		0			0
$701$	3.40926	+	10.4926i	0.128766	+	0.396301i	0.994568	−	0.104085i	$-0.0331914\pi$
$701$	3.40926	+	10.4926i	0.128766	+	0.396301i	−0.865802	+	0.500386i	$0.833191\pi$
$702$		0			0
$703$	0.879577	+	1.52347i	0.0331739	+	0.0574589i
$704$		0			0
$705$	7.17817	−	12.4330i	0.270346	−	0.468252i
$706$		0			0
$707$	−2.29561	+	26.0848i	−0.0863351	+	0.981021i
$708$		0			0
$709$	−35.7743	+	15.9277i	−1.34353	+	0.598179i	−0.947411	−	0.320020i	$-0.896310\pi$
$709$	−35.7743	+	15.9277i	−1.34353	+	0.598179i	−0.396121	+	0.918199i	$0.629644\pi$
$710$		0			0
$711$	−23.4472	+	4.98385i	−0.879338	+	0.186909i
$712$		0			0
$713$	−28.8443	+	20.9566i	−1.08023	+	0.784831i
$714$		0			0
$715$	−56.0039	−	23.9579i	−2.09443	−	0.895975i
$716$		0			0
$717$	0.207871	+	0.0925501i	0.00776308	+	0.00345635i
$718$		0			0
$719$	−12.9050	−	14.3325i	−0.481277	−	0.534512i	0.452787	−	0.891619i	$-0.350430\pi$
$719$	−12.9050	−	14.3325i	−0.481277	−	0.534512i	−0.934064	+	0.357107i	$0.883763\pi$
$720$		0			0
$721$	−3.03497	+	5.46861i	−0.113028	+	0.203662i
$722$		0			0
$723$	−8.81598	−	1.87390i	−0.327870	−	0.0696909i
$724$		0			0
$725$	−24.0383	−	41.6355i	−0.892759	−	1.54630i
$726$		0			0
$727$	48.2582			1.78980			0.894899	−	0.446268i	$-0.147247\pi$
$727$	48.2582			1.78980			0.894899	+	0.446268i	$0.147247\pi$
$728$		0			0
$729$	2.22110	+	6.83586i	0.0822631	+	0.253180i
$730$		0			0
$731$	−2.46912	+	23.4921i	−0.0913238	+	0.868888i
$732$		0			0
$733$	−8.14609	−	9.04715i	−0.300883	−	0.334164i	0.573677	−	0.819081i	$-0.305516\pi$
$733$	−8.14609	−	9.04715i	−0.300883	−	0.334164i	−0.874560	+	0.484917i	$0.838850\pi$
$734$		0			0
$735$	−9.43955	−	26.0179i	−0.348183	−	0.959686i
$736$		0			0
$737$	1.19595	−	0.895962i	0.0440533	−	0.0330032i
$738$		0			0
$739$	−26.0984	−	11.6197i	−0.960044	−	0.427439i	−0.133961	−	0.990987i	$-0.542770\pi$
$739$	−26.0984	−	11.6197i	−0.960044	−	0.427439i	−0.826084	+	0.563547i	$0.809436\pi$
$740$		0			0
$741$	0.791386	−	2.43564i	0.0290723	−	0.0894753i
$742$		0			0
$743$	−0.0158205	−	0.0114942i	−0.000580396	−	0.000421683i	0.587495	−	0.809228i	$-0.300114\pi$
$743$	−0.0158205	−	0.0114942i	−0.000580396	−	0.000421683i	−0.588075	+	0.808806i	$0.700114\pi$
$744$		0			0
$745$	−63.5336	+	70.5612i	−2.32769	+	2.58516i
$746$		0			0
$747$	−7.72536	+	13.3807i	−0.282656	+	0.489575i
$748$		0			0
$749$	5.21173	+	42.6268i	0.190432	+	1.55755i
$750$		0			0
$751$	16.1653	+	3.43603i	0.589879	+	0.125383i	0.493174	−	0.869930i	$-0.335836\pi$
$751$	16.1653	+	3.43603i	0.589879	+	0.125383i	0.0967046	+	0.995313i	$0.469170\pi$
$752$		0			0
$753$	0.422362	−	4.01851i	0.0153917	−	0.146443i
$754$		0			0
$755$	−17.2790	+	53.1793i	−0.628847	+	1.93539i
$756$		0			0
$757$	−42.3873	+	30.7962i	−1.54059	+	1.11931i	−0.590629	+	0.806943i	$0.701120\pi$
$757$	−42.3873	+	30.7962i	−1.54059	+	1.11931i	−0.949963	+	0.312363i	$0.898880\pi$
$758$		0			0
$759$	14.5609	−	6.74018i	0.528527	−	0.244653i
$760$		0			0
$761$	−1.22927	−	11.6958i	−0.0445611	−	0.423971i	−0.993947	−	0.109859i	$-0.964960\pi$
$761$	−1.22927	−	11.6958i	−0.0445611	−	0.423971i	0.949386	−	0.314112i	$-0.101707\pi$
$762$		0			0
$763$	−31.3113	+	35.9822i	−1.13354	+	1.30264i
$764$		0			0
$765$	43.9320	−	19.5598i	1.58837	−	0.707186i
$766$		0			0
$767$	15.9477	−	17.7117i	0.575838	−	0.639533i
$768$		0			0
$769$	−5.88557			−0.212239			−0.106119	−	0.994353i	$-0.533843\pi$
$769$	−5.88557			−0.212239			−0.106119	+	0.994353i	$0.533843\pi$
$770$		0			0
$771$	4.09454			0.147461
$772$		0			0
$773$	−1.49809	+	1.66379i	−0.0538824	+	0.0598425i	−0.769483	−	0.638667i	$-0.779486\pi$
$773$	−1.49809	+	1.66379i	−0.0538824	+	0.0598425i	0.715601	+	0.698509i	$0.246153\pi$
$774$		0			0
$775$	87.3494	−	38.8904i	3.13768	−	1.39699i
$776$		0			0
$777$	−1.97239	−	5.73780i	−0.0707591	−	0.205842i
$778$		0			0
$779$	0.303991	+	2.89229i	0.0108916	+	0.103627i
$780$		0			0
$781$	−14.8458	+	26.6063i	−0.531225	+	0.952047i
$782$		0			0
$783$	12.5024	−	9.08355i	0.446801	−	0.324620i
$784$		0			0
$785$	22.4961	−	69.2359i	0.802921	−	2.47114i
$786$		0			0
$787$	−1.87055	+	17.7971i	−0.0666779	+	0.634398i	0.909242	+	0.416268i	$0.136662\pi$
$787$	−1.87055	+	17.7971i	−0.0666779	+	0.634398i	−0.975920	+	0.218130i	$0.930004\pi$
$788$		0			0
$789$	17.7559	+	3.77413i	0.632125	+	0.134362i
$790$		0			0
$791$	−15.1226	+	11.3836i	−0.537699	+	0.404753i
$792$		0			0
$793$	−12.2342	+	21.1903i	−0.434450	+	0.752490i
$794$		0			0
$795$	3.75590	−	4.17135i	0.133208	−	0.147942i
$796$		0			0
$797$	1.01634	+	0.738413i	0.0360006	+	0.0261559i	0.605640	−	0.795739i	$-0.292917\pi$
$797$	1.01634	+	0.738413i	0.0360006	+	0.0261559i	−0.569639	+	0.821895i	$0.692917\pi$
$798$		0			0
$799$	5.56233	−	17.1191i	0.196781	−	0.605630i
$800$		0			0
$801$	7.34788	+	3.27149i	0.259625	+	0.115592i
$802$		0			0
$803$	−2.75966	−	8.08829i	−0.0973864	−	0.285430i
$804$		0			0
$805$	61.4647	−	14.1570i	2.16635	−	0.498970i
$806$		0			0
$807$	10.4562	+	11.6128i	0.368076	+	0.408790i
$808$		0			0
$809$	−2.21899	+	21.1123i	−0.0780155	+	0.742268i	0.883670	+	0.468111i	$0.155065\pi$
$809$	−2.21899	+	21.1123i	−0.0780155	+	0.742268i	−0.961685	+	0.274156i	$0.911601\pi$
$810$		0			0
$811$	16.5677	+	50.9900i	0.581769	+	1.79050i	0.611875	+	0.790954i	$0.290415\pi$
$811$	16.5677	+	50.9900i	0.581769	+	1.79050i	−0.0301064	+	0.999547i	$0.509585\pi$
$812$		0			0
$813$	−17.8658			−0.626582
$814$		0			0
$815$	−23.9467	−	41.4769i	−0.838817	−	1.45287i
$816$		0			0
$817$	−3.20256	−	0.680726i	−0.112043	−	0.0238156i
$818$		0			0
$819$	11.7396	−	21.1531i	0.410213	−	0.739150i
$820$		0			0
$821$	−13.5191	−	15.0144i	−0.471818	−	0.524007i	0.459518	−	0.888169i	$-0.348022\pi$
$821$	−13.5191	−	15.0144i	−0.471818	−	0.524007i	−0.931336	+	0.364161i	$0.881356\pi$
$822$		0			0
$823$	35.3064	+	15.7194i	1.23070	+	0.547945i	0.915975	−	0.401236i	$-0.131419\pi$
$823$	35.3064	+	15.7194i	1.23070	+	0.547945i	0.314730	+	0.949181i	$0.398086\pi$
$824$		0			0
$825$	−41.9544	+	9.56202i	−1.46066	+	0.332907i
$826$		0			0
$827$	−9.17686	+	6.66738i	−0.319111	+	0.231847i	−0.735796	−	0.677203i	$-0.763192\pi$
$827$	−9.17686	+	6.66738i	−0.319111	+	0.231847i	0.416685	+	0.909051i	$0.363192\pi$
$828$		0			0
$829$	26.3238	−	5.59530i	0.914264	−	0.194333i	0.273323	−	0.961922i	$-0.411877\pi$
$829$	26.3238	−	5.59530i	0.914264	−	0.194333i	0.640942	+	0.767590i	$0.278544\pi$
$830$		0			0
$831$	−21.9142	+	9.75685i	−0.760197	+	0.338461i
$832$		0			0
$833$	−18.3591	−	29.4479i	−0.636105	−	1.02031i
$834$		0			0
$835$	−45.5365	+	78.8715i	−1.57585	+	2.72946i
$836$		0			0
$837$	15.3675	+	26.6173i	0.531179	+	0.920028i
$838$		0			0
$839$	−13.0171	−	40.0626i	−0.449401	−	1.38311i	−0.877585	−	0.479422i	$-0.840846\pi$
$839$	−13.0171	−	40.0626i	−0.449401	−	1.38311i	0.428184	−	0.903692i	$-0.359154\pi$
$840$		0			0
$841$	14.5481	+	10.5698i	0.501657	+	0.364475i
$842$		0			0
$843$	−2.38943	+	0.507889i	−0.0822963	+	0.0174926i
$844$		0			0
$845$	1.98962	+	18.9299i	0.0684449	+	0.651210i
$846$		0			0
$847$	−15.7010	−	24.5047i	−0.539493	−	0.841990i
$848$		0			0
$849$	−1.80270	−	17.1516i	−0.0618686	−	0.588640i
$850$		0			0
$851$	13.5247	−	2.87477i	0.463621	−	0.0985457i
$852$		0			0
$853$	11.6805	+	8.48639i	0.399933	+	0.290568i	0.769514	−	0.638630i	$-0.220499\pi$
$853$	11.6805	+	8.48639i	0.399933	+	0.290568i	−0.369581	+	0.929199i	$0.620499\pi$
$854$		0			0
$855$	2.05977	+	6.33931i	0.0704426	+	0.216800i
$856$		0			0
$857$	−12.0477	−	20.8672i	−0.411542	−	0.712811i	0.583517	−	0.812101i	$-0.301676\pi$
$857$	−12.0477	−	20.8672i	−0.411542	−	0.712811i	−0.995059	+	0.0992900i	$0.968343\pi$
$858$		0			0
$859$	−17.8814	+	30.9715i	−0.610105	+	1.05673i	0.381117	+	0.924527i	$0.375539\pi$
$859$	−17.8814	+	30.9715i	−0.610105	+	1.05673i	−0.991222	+	0.132206i	$0.957794\pi$
$860$		0			0
$861$	0.879337	−	9.99185i	0.0299677	−	0.340521i
$862$		0			0
$863$	−8.36832	+	3.72582i	−0.284861	+	0.126828i	−0.544193	−	0.838960i	$-0.683164\pi$
$863$	−8.36832	+	3.72582i	−0.284861	+	0.126828i	0.259332	+	0.965788i	$0.416498\pi$
$864$		0			0
$865$	75.8725	−	16.1272i	2.57974	−	0.548341i
$866$		0			0
$867$	−5.49032	+	3.98895i	−0.186461	+	0.135472i
$868$		0			0
$869$	35.2722	−	8.03905i	1.19653	−	0.272706i
$870$		0			0
$871$	−1.71261	−	0.762502i	−0.0580295	−	0.0258364i
$872$		0			0
$873$	8.78499	+	9.75672i	0.297327	+	0.330215i
$874$		0			0
$875$	−110.744	+	1.87623i	−3.74382	+	0.0634282i
$876$		0			0
$877$	12.5623	+	2.67020i	0.424198	+	0.0901661i	0.415064	−	0.909792i	$-0.363759\pi$
$877$	12.5623	+	2.67020i	0.424198	+	0.0901661i	0.00913404	+	0.999958i	$0.497093\pi$
$878$		0			0
$879$	−13.7007	−	23.7304i	−0.462115	−	0.800406i
$880$		0			0
$881$	15.9926			0.538804			0.269402	−	0.963028i	$-0.413174\pi$
$881$	15.9926			0.538804			0.269402	+	0.963028i	$0.413174\pi$
$882$		0			0
$883$	−7.12592	−	21.9313i	−0.239806	−	0.738048i	−0.996447	−	0.0842175i	$-0.973161\pi$
$883$	−7.12592	−	21.9313i	−0.239806	−	0.738048i	0.756641	−	0.653830i	$-0.226839\pi$
$884$		0			0
$885$	2.36741	−	22.5244i	0.0795796	−	0.757150i
$886$		0			0
$887$	−26.5988	−	29.5409i	−0.893099	−	0.991887i	0.106898	−	0.994270i	$-0.465908\pi$
$887$	−26.5988	−	29.5409i	−0.893099	−	0.991887i	−0.999997	+	0.00238316i	$0.999241\pi$
$888$		0			0
$889$	−7.35707	+	24.0198i	−0.246748	+	0.805600i
$890$		0			0
$891$	2.59441	+	7.60395i	0.0869160	+	0.254742i
$892$		0			0
$893$	2.27924	+	1.01478i	0.0762717	+	0.0339584i
$894$		0			0
$895$	−10.8395	+	33.3606i	−0.362325	+	1.11512i
$896$		0			0
$897$	−16.2848	−	11.8316i	−0.543735	−	0.395046i
$898$		0			0
$899$	14.6621	−	16.2839i	0.489007	−	0.543097i
$900$		0			0
$901$	3.51887	−	6.09486i	0.117231	−	0.203049i
$902$		0			0
$903$	10.3925	+	4.41764i	0.345840	+	0.147010i
$904$		0			0
$905$	108.700	+	23.1050i	3.61332	+	0.768035i
$906$		0			0
$907$	−5.87566	+	55.9032i	−0.195098	+	1.85624i	0.259762	+	0.965673i	$0.416356\pi$
$907$	−5.87566	+	55.9032i	−0.195098	+	1.85624i	−0.454860	+	0.890563i	$0.650311\pi$
$908$		0			0
$909$	−6.72126	+	20.6859i	−0.222930	+	0.686108i
$910$		0			0
$911$	24.0010	−	17.4377i	0.795187	−	0.577737i	−0.114311	−	0.993445i	$-0.536466\pi$
$911$	24.0010	−	17.4377i	0.795187	−	0.577737i	0.909498	+	0.415708i	$0.136466\pi$
$912$		0			0
$913$	11.3620	−	20.3626i	0.376026	−	0.673902i
$914$		0			0
$915$	2.43048	+	23.1245i	0.0803493	+	0.764472i
$916$		0			0
$917$	−36.0546	−	7.02750i	−1.19063	−	0.232069i
$918$		0			0
$919$	38.2693	−	17.0386i	1.26239	−	0.562051i	0.337153	−	0.941450i	$-0.390536\pi$
$919$	38.2693	−	17.0386i	1.26239	−	0.562051i	0.925233	+	0.379399i	$0.123869\pi$
$920$		0			0
$921$	0.811583	−	0.901354i	0.0267426	−	0.0297006i
$922$		0			0
$923$	38.2227			1.25812
$924$		0			0
$925$	−37.0810			−1.21921
$926$		0			0
$927$	−3.47614	+	3.86064i	−0.114171	+	0.126800i
$928$		0			0
$929$	−38.0046	+	16.9208i	−1.24689	+	0.555152i	−0.920744	−	0.390167i	$-0.872417\pi$
$929$	−38.0046	+	16.9208i	−1.24689	+	0.555152i	−0.326148	+	0.945319i	$0.605751\pi$
$930$		0			0
$931$	4.32531	−	2.10411i	0.141756	−	0.0689593i
$932$		0			0
$933$	−2.24374	−	21.3478i	−0.0734568	−	0.698895i
$934$		0			0
$935$	−65.8620	+	30.4873i	−2.15392	+	0.997041i
$936$		0			0
$937$	−12.0025	+	8.72031i	−0.392104	+	0.284880i	−0.766317	−	0.642462i	$-0.777913\pi$
$937$	−12.0025	+	8.72031i	−0.392104	+	0.284880i	0.374213	+	0.927343i	$0.377913\pi$
$938$		0			0
$939$	2.86277	−	8.81070i	0.0934230	−	0.287526i
$940$		0			0
$941$	−1.02215	+	9.72514i	−0.0333212	+	0.317030i	0.965147	+	0.261707i	$0.0842855\pi$
$941$	−1.02215	+	9.72514i	−0.0333212	+	0.317030i	−0.998469	+	0.0553230i	$0.982381\pi$
$942$		0			0
$943$	22.3589	+	4.75254i	0.728107	+	0.154764i
$944$		0			0
$945$	−6.59870	−	53.9709i	−0.214656	−	1.75567i
$946$		0			0
$947$	−23.3535	+	40.4494i	−0.758886	+	1.31443i	0.184533	+	0.982826i	$0.440923\pi$
$947$	−23.3535	+	40.4494i	−0.758886	+	1.31443i	−0.943419	+	0.331603i	$0.892410\pi$
$948$		0			0
$949$	−7.17397	+	7.96750i	−0.232877	+	0.258636i
$950$		0			0
$951$	10.2791	+	7.46823i	0.333324	+	0.242174i
$952$		0			0
$953$	−11.0408	+	33.9801i	−0.357646	+	1.10072i	0.596813	+	0.802380i	$0.296433\pi$
$953$	−11.0408	+	33.9801i	−0.357646	+	1.10072i	−0.954459	+	0.298342i	$0.903567\pi$
$954$		0			0
$955$	21.4011	+	9.52840i	0.692524	+	0.308332i
$956$		0			0
$957$	−7.89209	+	5.91247i	−0.255115	+	0.191123i
$958$		0			0
$959$	−14.2599	+	3.28445i	−0.460475	+	0.106060i
$960$		0			0
$961$	8.41720	+	9.34825i	0.271523	+	0.301556i
$962$		0			0
$963$	−3.72859	+	35.4752i	−0.120152	+	1.14317i
$964$		0			0
$965$	22.1527	+	68.1791i	0.713122	+	2.19476i
$966$		0			0
$967$	−54.6267			−1.75668			−0.878338	−	0.478041i	$-0.841347\pi$
$967$	−54.6267			−1.75668			−0.878338	+	0.478041i	$0.841347\pi$
$968$		0			0
$969$	−1.52566	−	2.64252i	−0.0490113	−	0.0848900i
$970$		0			0
$971$	41.3334	+	8.78569i	1.32645	+	0.281946i	0.816046	−	0.577987i	$-0.196162\pi$
$971$	41.3334	+	8.78569i	1.32645	+	0.281946i	0.510407	+	0.859933i	$0.329495\pi$
$972$		0			0
$973$	−15.7177	+	0.266291i	−0.503887	+	0.00853691i
$974$		0			0
$975$	36.1213	+	40.1168i	1.15681	+	1.28477i
$976$		0			0
$977$	45.9896	+	20.4759i	1.47134	+	0.655081i	0.976815	−	0.214084i	$-0.0686767\pi$
$977$	45.9896	+	20.4759i	1.47134	+	0.655081i	0.494521	+	0.869166i	$0.335343\pi$
$978$		0			0
$979$	−11.1604	−	4.77432i	−0.356689	−	0.152588i
$980$		0			0
$981$	−32.0527	+	23.2876i	−1.02336	+	0.743517i
$982$		0			0
$983$	57.3962	−	12.1999i	1.83065	−	0.389117i	0.842018	−	0.539449i	$-0.181368\pi$
$983$	57.3962	−	12.1999i	1.83065	−	0.389117i	0.988636	+	0.150332i	$0.0480343\pi$
$984$		0			0
$985$	−19.6784	+	8.76140i	−0.627007	+	0.279162i
$986$		0			0
$987$	−7.04632	−	4.93927i	−0.224287	−	0.157219i
$988$		0			0
$989$	−12.8672	+	22.2866i	−0.409152	+	0.708672i
$990$		0			0
$991$	−11.4388	−	19.8126i	−0.363366	−	0.629368i	0.625147	−	0.780507i	$-0.285039\pi$
$991$	−11.4388	−	19.8126i	−0.363366	−	0.629368i	−0.988512	+	0.151139i	$0.951706\pi$
$992$		0			0
$993$	−0.133744	−	0.411620i	−0.00424422	−	0.0130624i
$994$		0			0
$995$	−14.5595	−	10.5781i	−0.461569	−	0.335349i
$996$		0			0
$997$	11.6048	−	2.46667i	0.367527	−	0.0781203i	−0.0204461	−	0.999791i	$-0.506509\pi$
$997$	11.6048	−	2.46667i	0.367527	−	0.0781203i	0.387973	+	0.921671i	$0.373175\pi$
$998$		0			0
$999$	−1.24592	−	11.8541i	−0.0394191	−	0.375048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.y.b.289.3	yes	48
7.4	even	3	inner	308.2.y.b.25.4	✓	48
11.4	even	5	inner	308.2.y.b.37.4	yes	48
77.4	even	15	inner	308.2.y.b.81.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.y.b.25.4	✓	48	7.4	even	3	inner
308.2.y.b.37.4	yes	48	11.4	even	5	inner
308.2.y.b.81.3	yes	48	77.4	even	15	inner
308.2.y.b.289.3	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599375 - 0.665674i) q^{3} +(-4.03246 + 1.79536i) q^{5} +(0.860089 + 2.50205i) q^{7} +(0.229715 + 2.18559i) q^{9} +(-0.394957 - 3.29302i) q^{11} +(-3.36615 + 2.44565i) q^{13} +(-1.22183 + 3.76040i) q^{15} +(-0.518194 + 4.93028i) q^{17} +(-0.672120 - 0.142864i) q^{19} +(2.18106 + 0.927127i) q^{21} +(-2.70042 + 4.67727i) q^{23} +(9.69171 - 10.7637i) q^{25} +(3.76661 + 2.73660i) q^{27} +(1.02571 - 3.15682i) q^{29} +(6.03074 + 2.68506i) q^{31} +(-2.42881 - 1.71084i) q^{33} +(-7.96036 - 8.54522i) q^{35} +(-1.71306 - 1.90255i) q^{37} +(-0.389581 + 3.70662i) q^{39} +(-1.30788 - 4.02523i) q^{41} +4.76487 q^{43} +(-4.85024 - 8.40087i) q^{45} +(-3.55158 - 0.754911i) q^{47} +(-5.52049 + 4.30397i) q^{49} +(2.97137 + 3.30004i) q^{51} +(-1.29690 - 0.577416i) q^{53} +(7.50483 + 12.5699i) q^{55} +(-0.497953 + 0.361784i) q^{57} +(-5.60294 + 1.19094i) q^{59} +(5.37231 - 2.39191i) q^{61} +(-5.27087 + 2.45456i) q^{63} +(9.18301 - 15.9054i) q^{65} +(0.225280 + 0.390196i) q^{67} +(1.49497 + 4.60104i) q^{69} +(-7.43196 - 5.39964i) q^{71} +(2.52044 - 0.535737i) q^{73} +(-1.35616 - 12.9030i) q^{75} +(7.89961 - 3.82050i) q^{77} +(1.14016 + 10.8479i) q^{79} +(-2.36952 + 0.503656i) q^{81} +(5.68790 + 4.13250i) q^{83} +(-6.76206 - 20.8115i) q^{85} +(-1.48663 - 2.57491i) q^{87} +(1.82999 - 3.16963i) q^{89} +(-9.01432 - 6.31879i) q^{91} +(5.40205 - 2.40515i) q^{93} +(2.96679 - 0.630610i) q^{95} +(4.83319 - 3.51152i) q^{97} +(7.10647 - 1.61967i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{3} + 7 q^{5} - 7 q^{7} + 13 q^{9} - 5 q^{11} - 8 q^{13} - 48 q^{15} + 19 q^{17} + 13 q^{19} - 22 q^{21} - 30 q^{23} - 7 q^{25} + 26 q^{27} - 12 q^{29} + 3 q^{31} - 28 q^{33} + 37 q^{35} + 19 q^{37}+ \cdots + 140 q^{99}+O(q^{100}) \) 48 * q - q^3 + 7 * q^5 - 7 * q^7 + 13 * q^9 - 5 * q^11 - 8 * q^13 - 48 * q^15 + 19 * q^17 + 13 * q^19 - 22 * q^21 - 30 * q^23 - 7 * q^25 + 26 * q^27 - 12 * q^29 + 3 * q^31 - 28 * q^33 + 37 * q^35 + 19 * q^37 + 3 * q^39 - 10 * q^41 + 84 * q^43 - 24 * q^45 + 11 * q^47 + 51 * q^49 - 21 * q^51 + 33 * q^53 + 48 * q^55 - 108 * q^57 + 23 * q^59 + 46 * q^61 - 90 * q^63 - 54 * q^65 - 8 * q^67 - 82 * q^69 - 64 * q^71 + 4 * q^73 - 15 * q^75 + 6 * q^77 - 14 * q^79 + 7 * q^81 - 28 * q^83 + 50 * q^85 - 66 * q^87 - 58 * q^89 + 70 * q^91 - 42 * q^93 + 4 * q^95 - 100 * q^97 + 140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more