LMFDB - Embedded newform 512.2.i.a.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, not 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	512.97
Dual form			512.2.i.a.417.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.152968 + 0.769021i) q^{3} +(2.78737 - 1.86246i) q^{5} +(3.13672 + 1.29927i) q^{7} +(2.20364 - 0.912779i) q^{9} +O(q^{10})$	\(q+(0.152968 + 0.769021i) q^{3} +(2.78737 - 1.86246i) q^{5} +(3.13672 + 1.29927i) q^{7} +(2.20364 - 0.912779i) q^{9} +(-1.79402 - 0.356853i) q^{11} +(-4.34710 - 2.90464i) q^{13} +(1.85865 + 1.85865i) q^{15} +(-1.16196 + 1.16196i) q^{17} +(-0.00265155 + 0.00396832i) q^{19} +(-0.519350 + 2.61095i) q^{21} +(-1.78945 - 4.32013i) q^{23} +(2.38726 - 5.76336i) q^{25} +(2.34588 + 3.51086i) q^{27} +(1.70191 - 0.338531i) q^{29} +9.42685i q^{31} -1.43423i q^{33} +(11.1630 - 2.22047i) q^{35} +(1.47130 + 2.20195i) q^{37} +(1.56876 - 3.78733i) q^{39} +(0.497436 + 1.20092i) q^{41} +(0.104068 - 0.523183i) q^{43} +(4.44236 - 6.64846i) q^{45} +(0.378819 - 0.378819i) q^{47} +(3.20113 + 3.20113i) q^{49} +(-1.07132 - 0.715832i) q^{51} +(3.63594 + 0.723233i) q^{53} +(-5.66523 + 2.34662i) q^{55} +(-0.00345732 - 0.00143207i) q^{57} +(-11.1857 + 7.47403i) q^{59} +(1.29788 + 6.52488i) q^{61} +8.09815 q^{63} -17.5268 q^{65} +(1.46964 + 7.38837i) q^{67} +(3.04854 - 2.03697i) q^{69} +(-5.03495 - 2.08554i) q^{71} +(-4.53632 + 1.87901i) q^{73} +(4.79732 + 0.954247i) q^{75} +(-5.16369 - 3.45027i) q^{77} +(-11.3984 - 11.3984i) q^{79} +(2.71871 - 2.71871i) q^{81} +(3.35370 - 5.01916i) q^{83} +(-1.07471 + 5.40294i) q^{85} +(0.520675 + 1.25702i) q^{87} +(4.25907 - 10.2823i) q^{89} +(-9.86171 - 14.7591i) q^{91} +(-7.24944 + 1.44200i) q^{93} +0.0159996i q^{95} +12.2846i q^{97} +(-4.27911 + 0.851169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$1$

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
$3$	0.152968	+	0.769021i	0.0883160	+	0.443995i	0.999489	+	0.0319702i	$0.0101782\pi$
$3$	0.152968	+	0.769021i	0.0883160	+	0.443995i	−0.911173	+	0.412024i	$0.864822\pi$
$4$		0			0
$5$	2.78737	−	1.86246i	1.24655	−	0.832919i	0.255553	−	0.966795i	$-0.417742\pi$
$5$	2.78737	−	1.86246i	1.24655	−	0.832919i	0.990998	+	0.133876i	$0.0427425\pi$
$6$		0			0
$7$	3.13672	+	1.29927i	1.18557	+	0.491078i	0.886309	−	0.463094i	$-0.153261\pi$
$7$	3.13672	+	1.29927i	1.18557	+	0.491078i	0.299258	+	0.954172i	$0.403261\pi$
$8$		0			0
$9$	2.20364	−	0.912779i	0.734548	−	0.304260i
$10$		0			0
$11$	−1.79402	−	0.356853i	−0.540918	−	0.107595i	−0.0829328	−	0.996555i	$-0.526429\pi$
$11$	−1.79402	−	0.356853i	−0.540918	−	0.107595i	−0.457985	+	0.888960i	$0.651429\pi$
$12$		0			0
$13$	−4.34710	−	2.90464i	−1.20567	−	0.805603i	−0.220200	−	0.975455i	$-0.570671\pi$
$13$	−4.34710	−	2.90464i	−1.20567	−	0.805603i	−0.985470	+	0.169852i	$0.945671\pi$
$14$		0			0
$15$	1.85865	+	1.85865i	0.479902	+	0.479902i
$16$		0			0
$17$	−1.16196	+	1.16196i	−0.281818	+	0.281818i	−0.833834	−	0.552016i	$-0.813859\pi$
$17$	−1.16196	+	1.16196i	−0.281818	+	0.281818i	0.552016	+	0.833834i	$0.313859\pi$
$18$		0			0
$19$	−0.00265155	+	0.00396832i	−0.000608307	+	0.000910395i	−0.831774	−	0.555115i	$-0.812674\pi$
$19$	−0.00265155	+	0.00396832i	−0.000608307	+	0.000910395i	0.831165	+	0.556025i	$0.187674\pi$
$20$		0			0
$21$	−0.519350	+	2.61095i	−0.113331	+	0.569755i
$22$		0			0
$23$	−1.78945	−	4.32013i	−0.373127	−	0.900809i	−0.993217	−	0.116278i	$-0.962904\pi$
$23$	−1.78945	−	4.32013i	−0.373127	−	0.900809i	0.620090	−	0.784531i	$-0.287096\pi$
$24$		0			0
$25$	2.38726	−	5.76336i	0.477452	−	1.15267i
$26$		0			0
$27$	2.34588	+	3.51086i	0.451465	+	0.675665i
$28$		0			0
$29$	1.70191	−	0.338531i	0.316037	−	0.0628637i	−0.0345231	−	0.999404i	$-0.510991\pi$
$29$	1.70191	−	0.338531i	0.316037	−	0.0628637i	0.350560	+	0.936540i	$0.385991\pi$
$30$		0			0
$31$			9.42685i			1.69311i	0.532300	+	0.846556i	$0.321328\pi$
$31$			9.42685i			1.69311i	−0.532300	+	0.846556i	$0.678672\pi$
$32$		0			0
$33$		−	1.43423i		−	0.249667i
$34$		0			0
$35$	11.1630	−	2.22047i	1.88690	−	0.375327i
$36$		0			0
$37$	1.47130	+	2.20195i	0.241880	+	0.361999i	0.932470	−	0.361248i	$-0.117649\pi$
$37$	1.47130	+	2.20195i	0.241880	+	0.361999i	−0.690590	+	0.723246i	$0.742649\pi$
$38$		0			0
$39$	1.56876	−	3.78733i	0.251203	−	0.606458i
$40$		0			0
$41$	0.497436	+	1.20092i	0.0776864	+	0.187552i	0.957951	−	0.286931i	$-0.0926351\pi$
$41$	0.497436	+	1.20092i	0.0776864	+	0.187552i	−0.880265	+	0.474483i	$0.842635\pi$
$42$		0			0
$43$	0.104068	−	0.523183i	0.0158702	−	0.0797847i	−0.972039	−	0.234821i	$-0.924550\pi$
$43$	0.104068	−	0.523183i	0.0158702	−	0.0797847i	0.987909	+	0.155037i	$0.0495495\pi$
$44$		0			0
$45$	4.44236	−	6.64846i	0.662228	−	0.991094i
$46$		0			0
$47$	0.378819	−	0.378819i	0.0552564	−	0.0552564i	−0.678939	−	0.734195i	$-0.737560\pi$
$47$	0.378819	−	0.378819i	0.0552564	−	0.0552564i	0.734195	+	0.678939i	$0.237560\pi$
$48$		0			0
$49$	3.20113	+	3.20113i	0.457305	+	0.457305i
$50$		0			0
$51$	−1.07132	−	0.715832i	−0.150015	−	0.100237i
$52$		0			0
$53$	3.63594	+	0.723233i	0.499435	+	0.0993438i	0.438378	−	0.898791i	$-0.355553\pi$
$53$	3.63594	+	0.723233i	0.499435	+	0.0993438i	0.0610565	+	0.998134i	$0.480553\pi$
$54$		0			0
$55$	−5.66523	+	2.34662i	−0.763900	+	0.316418i
$56$		0			0
$57$	−0.00345732	−	0.00143207i	−0.000457934	−	0.000189682i
$58$		0			0
$59$	−11.1857	+	7.47403i	−1.45625	+	0.973036i	−0.459874	+	0.887984i	$0.652105\pi$
$59$	−11.1857	+	7.47403i	−1.45625	+	0.973036i	−0.996377	+	0.0850514i	$0.972895\pi$
$60$		0			0
$61$	1.29788	+	6.52488i	0.166176	+	0.835425i	0.970475	+	0.241200i	$0.0775410\pi$
$61$	1.29788	+	6.52488i	0.166176	+	0.835425i	−0.804299	+	0.594225i	$0.797459\pi$
$62$		0			0
$63$	8.09815			1.02027
$64$		0			0
$65$	−17.5268			−2.17393
$66$		0			0
$67$	1.46964	+	7.38837i	0.179545	+	0.902633i	0.960550	+	0.278108i	$0.0897074\pi$
$67$	1.46964	+	7.38837i	0.179545	+	0.902633i	−0.781005	+	0.624525i	$0.785293\pi$
$68$		0			0
$69$	3.04854	−	2.03697i	0.367001	−	0.245222i
$70$		0			0
$71$	−5.03495	−	2.08554i	−0.597538	−	0.247508i	0.0633517	−	0.997991i	$-0.479821\pi$
$71$	−5.03495	−	2.08554i	−0.597538	−	0.247508i	−0.660890	+	0.750483i	$0.729821\pi$
$72$		0			0
$73$	−4.53632	+	1.87901i	−0.530936	+	0.219921i	−0.632013	−	0.774958i	$-0.717771\pi$
$73$	−4.53632	+	1.87901i	−0.530936	+	0.219921i	0.101077	+	0.994879i	$0.467771\pi$
$74$		0			0
$75$	4.79732	+	0.954247i	0.553947	+	0.110187i
$76$		0			0
$77$	−5.16369	−	3.45027i	−0.588457	−	0.393194i
$78$		0			0
$79$	−11.3984	−	11.3984i	−1.28242	−	1.28242i	−0.939287	−	0.343133i	$-0.888512\pi$
$79$	−11.3984	−	11.3984i	−1.28242	−	1.28242i	−0.343133	−	0.939287i	$-0.611488\pi$
$80$		0			0
$81$	2.71871	−	2.71871i	0.302079	−	0.302079i
$82$		0			0
$83$	3.35370	−	5.01916i	0.368116	−	0.550925i	−0.600456	−	0.799658i	$-0.705014\pi$
$83$	3.35370	−	5.01916i	0.368116	−	0.550925i	0.968572	+	0.248733i	$0.0800142\pi$
$84$		0			0
$85$	−1.07471	+	5.40294i	−0.116569	+	0.586032i
$86$		0			0
$87$	0.520675	+	1.25702i	0.0558223	+	0.134767i
$88$		0			0
$89$	4.25907	−	10.2823i	0.451460	−	1.08992i	−0.520307	−	0.853980i	$-0.674182\pi$
$89$	4.25907	−	10.2823i	0.451460	−	1.08992i	0.971767	−	0.235942i	$-0.0758177\pi$
$90$		0			0
$91$	−9.86171	−	14.7591i	−1.03379	−	1.54717i
$92$		0			0
$93$	−7.24944	+	1.44200i	−0.751732	+	0.149529i
$94$		0			0
$95$			0.0159996i			0.00164152i
$96$		0			0
$97$			12.2846i			1.24731i	0.781698	+	0.623657i	$0.214354\pi$
$97$			12.2846i			1.24731i	−0.781698	+	0.623657i	$0.785646\pi$
$98$		0			0
$99$	−4.27911	+	0.851169i	−0.430067	+	0.0855457i
$100$		0			0
$101$	1.04551	+	1.56472i	0.104032	+	0.155695i	0.879833	−	0.475282i	$-0.157654\pi$
$101$	1.04551	+	1.56472i	0.104032	+	0.155695i	−0.775801	+	0.630978i	$0.782654\pi$
$102$		0			0
$103$	4.50995	−	10.8880i	0.444379	−	1.07283i	−0.530017	−	0.847987i	$-0.677814\pi$
$103$	4.50995	−	10.8880i	0.444379	−	1.07283i	0.974396	−	0.224839i	$-0.0721856\pi$
$104$		0			0
$105$	3.41517	+	8.24495i	0.333287	+	0.804625i
$106$		0			0
$107$	2.90641	−	14.6115i	0.280973	−	1.41255i	−0.540042	−	0.841638i	$-0.681592\pi$
$107$	2.90641	−	14.6115i	0.280973	−	1.41255i	0.821014	−	0.570907i	$-0.193408\pi$
$108$		0			0
$109$	−8.04402	+	12.0387i	−0.770478	+	1.15310i	0.213870	+	0.976862i	$0.431393\pi$
$109$	−8.04402	+	12.0387i	−0.770478	+	1.15310i	−0.984347	+	0.176239i	$0.943607\pi$
$110$		0			0
$111$	−1.46829	+	1.46829i	−0.139364	+	0.139364i
$112$		0			0
$113$	9.94034	+	9.94034i	0.935109	+	0.935109i	0.998019	−	0.0629105i	$-0.0200383\pi$
$113$	9.94034	+	9.94034i	0.935109	+	0.935109i	−0.0629105	+	0.998019i	$0.520038\pi$
$114$		0			0
$115$	−13.0340	−	8.70901i	−1.21542	−	0.812119i
$116$		0			0
$117$	−12.2308	−	2.43285i	−1.13073	−	0.224917i
$118$		0			0
$119$	−5.15446	+	2.13505i	−0.472508	+	0.195719i
$120$		0			0
$121$	−7.07151	−	2.92911i	−0.642864	−	0.266283i
$122$		0			0
$123$	−0.847439	+	0.566240i	−0.0764110	+	0.0510562i
$124$		0			0
$125$	−0.809807	−	4.07117i	−0.0724313	−	0.364137i
$126$		0			0
$127$	−13.3100			−1.18107			−0.590534	−	0.807013i	$-0.701083\pi$
$127$	−13.3100			−1.18107			−0.590534	+	0.807013i	$0.701083\pi$
$128$		0			0
$129$	0.418258			0.0368255
$130$		0			0
$131$	0.318596	+	1.60169i	0.0278359	+	0.139940i	0.992204	−	0.124623i	$-0.0397721\pi$
$131$	0.318596	+	1.60169i	0.0278359	+	0.139940i	−0.964368	+	0.264563i	$0.914772\pi$
$132$		0			0
$133$	−0.0134731	+	0.00900242i	−0.00116826	+	0.000780609i
$134$		0			0
$135$	13.0777	+	5.41695i	1.12555	+	0.466217i
$136$		0			0
$137$	−6.96260	+	2.88400i	−0.594855	+	0.246397i	−0.659738	−	0.751496i	$-0.729333\pi$
$137$	−6.96260	+	2.88400i	−0.594855	+	0.246397i	0.0648827	+	0.997893i	$0.479333\pi$
$138$		0			0
$139$	−4.03376	−	0.802365i	−0.342139	−	0.0680557i	0.0210303	−	0.999779i	$-0.493305\pi$
$139$	−4.03376	−	0.802365i	−0.342139	−	0.0680557i	−0.363169	+	0.931723i	$0.618305\pi$
$140$		0			0
$141$	0.349267	+	0.233372i	0.0294136	+	0.0196535i
$142$		0			0
$143$	6.76227	+	6.76227i	0.565489	+	0.565489i
$144$		0			0
$145$	4.11336	−	4.11336i	0.341596	−	0.341596i
$146$		0			0
$147$	−1.97207	+	2.95141i	−0.162654	+	0.243428i
$148$		0			0
$149$	−0.992028	+	4.98726i	−0.0812701	+	0.408573i	0.918639	+	0.395098i	$0.129289\pi$
$149$	−0.992028	+	4.98726i	−0.0812701	+	0.408573i	−0.999909	+	0.0134748i	$0.995711\pi$
$150$		0			0
$151$	0.957754	+	2.31222i	0.0779409	+	0.188166i	0.958047	−	0.286611i	$-0.0925287\pi$
$151$	0.957754	+	2.31222i	0.0779409	+	0.188166i	−0.880106	+	0.474777i	$0.842529\pi$
$152$		0			0
$153$	−1.49994	+	3.62117i	−0.121263	+	0.292754i
$154$		0			0
$155$	17.5572	+	26.2761i	1.41022	+	2.11055i
$156$		0			0
$157$	12.6061	−	2.50752i	1.00608	−	0.200122i	0.335564	−	0.942017i	$-0.391073\pi$
$157$	12.6061	−	2.50752i	1.00608	−	0.200122i	0.670515	+	0.741896i	$0.266073\pi$
$158$		0			0
$159$			2.90675i			0.230520i
$160$		0			0
$161$		−	15.8760i		−	1.25120i
$162$		0			0
$163$	−12.1793	+	2.42260i	−0.953953	+	0.189753i	−0.647443	−	0.762114i	$-0.724161\pi$
$163$	−12.1793	+	2.42260i	−0.953953	+	0.189753i	−0.306510	+	0.951867i	$0.599161\pi$
$164$		0			0
$165$	−2.67120	−	3.99773i	−0.207952	−	0.311223i
$166$		0			0
$167$	−4.69682	+	11.3391i	−0.363451	+	0.877448i	0.631339	+	0.775507i	$0.282505\pi$
$167$	−4.69682	+	11.3391i	−0.363451	+	0.877448i	−0.994790	+	0.101942i	$0.967495\pi$
$168$		0			0
$169$	5.48548	+	13.2431i	0.421960	+	1.01870i
$170$		0			0
$171$	−0.00222087	+	0.0111650i	−0.000169834	+	0.000853812i
$172$		0			0
$173$	3.09606	−	4.63358i	0.235389	−	0.352285i	−0.694903	−	0.719103i	$-0.744553\pi$
$173$	3.09606	−	4.63358i	0.235389	−	0.352285i	0.930293	+	0.366818i	$0.119553\pi$
$174$		0			0
$175$	14.9763	−	14.9763i	1.13210	−	1.13210i
$176$		0			0
$177$	−7.45873	−	7.45873i	−0.560633	−	0.560633i
$178$		0			0
$179$	−0.829076	−	0.553971i	−0.0619681	−	0.0414057i	0.524200	−	0.851595i	$-0.324364\pi$
$179$	−0.829076	−	0.553971i	−0.0619681	−	0.0414057i	−0.586168	+	0.810189i	$0.699364\pi$
$180$		0			0
$181$	−17.2786	−	3.43692i	−1.28430	−	0.255464i	−0.494691	−	0.869069i	$-0.664719\pi$
$181$	−17.2786	−	3.43692i	−1.28430	−	0.255464i	−0.789613	+	0.613605i	$0.789719\pi$
$182$		0			0
$183$	−4.81923	+	1.99619i	−0.356248	+	0.147563i
$184$		0			0
$185$	8.20211	+	3.39743i	0.603031	+	0.249784i
$186$		0			0
$187$	2.49924	−	1.66994i	0.182763	−	0.122118i
$188$		0			0
$189$	2.79681	+	14.0605i	0.203438	+	1.02275i
$190$		0			0
$191$	6.00046			0.434178			0.217089	−	0.976152i	$-0.430344\pi$
$191$	6.00046			0.434178			0.217089	+	0.976152i	$0.430344\pi$
$192$		0			0
$193$	8.98517			0.646767			0.323383	−	0.946268i	$-0.395180\pi$
$193$	8.98517			0.646767			0.323383	+	0.946268i	$0.395180\pi$
$194$		0			0
$195$	−2.68103	−	13.4785i	−0.191993	−	0.965213i
$196$		0			0
$197$	9.91120	−	6.62245i	0.706144	−	0.471830i	−0.149921	−	0.988698i	$-0.547902\pi$
$197$	9.91120	−	6.62245i	0.706144	−	0.471830i	0.856065	+	0.516868i	$0.172902\pi$
$198$		0			0
$199$	−0.782393	−	0.324078i	−0.0554624	−	0.0229733i	0.354780	−	0.934950i	$-0.384556\pi$
$199$	−0.782393	−	0.324078i	−0.0554624	−	0.0229733i	−0.410242	+	0.911977i	$0.634556\pi$
$200$		0			0
$201$	−5.45701	+	2.26037i	−0.384908	+	0.159434i
$202$		0			0
$203$	5.77826	+	1.14937i	0.405554	+	0.0806697i
$204$		0			0
$205$	3.62320	+	2.42095i	0.253055	+	0.169086i
$206$		0			0
$207$	−7.88664	−	7.88664i	−0.548160	−	0.548160i
$208$		0			0
$209$	0.00617304	−	0.00617304i	0.000426998	−	0.000426998i
$210$		0			0
$211$	−4.82250	+	7.21737i	−0.331994	+	0.496865i	−0.959485	−	0.281759i	$-0.909082\pi$
$211$	−4.82250	+	7.21737i	−0.331994	+	0.496865i	0.627491	+	0.778624i	$0.284082\pi$
$212$		0			0
$213$	0.833642	−	4.19100i	0.0571202	−	0.287163i
$214$		0			0
$215$	−0.684334	−	1.65213i	−0.0466712	−	0.112674i
$216$		0			0
$217$	−12.2480	+	29.5693i	−0.831450	+	2.00730i
$218$		0			0
$219$	−2.13891	−	3.20110i	−0.144534	−	0.216310i
$220$		0			0
$221$	8.42627	−	1.67609i	0.566812	−	0.112746i
$222$		0			0
$223$		−	10.1030i		−	0.676547i	−0.941048	−	0.338273i	$-0.890157\pi$
$223$		−	10.1030i		−	0.676547i	0.941048	−	0.338273i	$-0.109843\pi$
$224$		0			0
$225$		−	14.8794i		−	0.991963i
$226$		0			0
$227$	17.3254	−	3.44624i	1.14993	−	0.228735i	0.416912	−	0.908947i	$-0.363112\pi$
$227$	17.3254	−	3.44624i	1.14993	−	0.228735i	0.733016	+	0.680212i	$0.238112\pi$
$228$		0			0
$229$	−3.76160	−	5.62963i	−0.248574	−	0.372017i	0.686110	−	0.727498i	$-0.259317\pi$
$229$	−3.76160	−	5.62963i	−0.248574	−	0.372017i	−0.934683	+	0.355481i	$0.884317\pi$
$230$		0			0
$231$	1.86345	−	4.49876i	0.122606	−	0.295997i
$232$		0			0
$233$	−11.2794	−	27.2309i	−0.738939	−	1.78396i	−0.610152	−	0.792285i	$-0.708892\pi$
$233$	−11.2794	−	27.2309i	−0.738939	−	1.78396i	−0.128787	−	0.991672i	$-0.541108\pi$
$234$		0			0
$235$	0.350373	−	1.76144i	0.0228558	−	0.114904i
$236$		0			0
$237$	7.02202	−	10.5092i	0.456129	−	0.682646i
$238$		0			0
$239$	−4.91117	+	4.91117i	−0.317677	+	0.317677i	−0.847874	−	0.530197i	$-0.822118\pi$
$239$	−4.91117	+	4.91117i	−0.317677	+	0.317677i	0.530197	+	0.847874i	$0.322118\pi$
$240$		0			0
$241$	−15.9105	−	15.9105i	−1.02488	−	1.02488i	−0.999682	−	0.0252016i	$-0.991977\pi$
$241$	−15.9105	−	15.9105i	−1.02488	−	1.02488i	−0.0252016	−	0.999682i	$-0.508023\pi$
$242$		0			0
$243$	13.0392	+	8.71251i	0.836465	+	0.558908i
$244$		0			0
$245$	14.8848	+	2.96076i	0.950952	+	0.189156i
$246$		0			0
$247$	0.0230531	−	0.00954890i	0.00146683	−	0.000607582i
$248$		0			0
$249$	4.37285	+	1.81129i	0.277118	+	0.114786i
$250$		0			0
$251$	13.4114	−	8.96124i	0.846523	−	0.565628i	−0.0549377	−	0.998490i	$-0.517496\pi$
$251$	13.4114	−	8.96124i	0.846523	−	0.565628i	0.901461	+	0.432861i	$0.142496\pi$
$252$		0			0
$253$	1.66867	+	8.38897i	0.104908	+	0.527410i
$254$		0			0
$255$	−4.31938			−0.270490
$256$		0			0
$257$	13.4126			0.836653			0.418327	−	0.908297i	$-0.362617\pi$
$257$	13.4126			0.836653			0.418327	+	0.908297i	$0.362617\pi$
$258$		0			0
$259$	1.75411	+	8.81851i	0.108995	+	0.547956i
$260$		0			0
$261$	3.44140	−	2.29947i	0.213017	−	0.142334i
$262$		0			0
$263$	5.51629	+	2.28492i	0.340149	+	0.140894i	0.546218	−	0.837643i	$-0.316067\pi$
$263$	5.51629	+	2.28492i	0.340149	+	0.140894i	−0.206069	+	0.978538i	$0.566067\pi$
$264$		0			0
$265$	11.4817	−	4.75588i	0.705316	−	0.292152i
$266$		0			0
$267$	8.55881	+	1.70245i	0.523791	+	0.104188i
$268$		0			0
$269$	7.39748	+	4.94284i	0.451032	+	0.301370i	0.760261	−	0.649617i	$-0.225071\pi$
$269$	7.39748	+	4.94284i	0.451032	+	0.301370i	−0.309229	+	0.950988i	$0.600071\pi$
$270$		0			0
$271$	−3.27670	−	3.27670i	−0.199046	−	0.199046i	0.600545	−	0.799591i	$-0.294950\pi$
$271$	−3.27670	−	3.27670i	−0.199046	−	0.199046i	−0.799591	+	0.600545i	$0.794950\pi$
$272$		0			0
$273$	9.84153	−	9.84153i	0.595637	−	0.595637i
$274$		0			0
$275$	−6.33947	+	9.48769i	−0.382285	+	0.572129i
$276$		0			0
$277$	1.81203	−	9.10969i	0.108874	−	0.547348i	−0.887392	−	0.461016i	$-0.847485\pi$
$277$	1.81203	−	9.10969i	0.108874	−	0.547348i	0.996266	−	0.0863327i	$-0.0275148\pi$
$278$		0			0
$279$	8.60463	+	20.7734i	0.515146	+	1.24367i
$280$		0			0
$281$	7.02651	−	16.9635i	0.419166	−	1.01196i	−0.563424	−	0.826168i	$-0.690516\pi$
$281$	7.02651	−	16.9635i	0.419166	−	1.01196i	0.982590	−	0.185789i	$-0.0594840\pi$
$282$		0			0
$283$	2.58111	+	3.86291i	0.153431	+	0.229626i	0.900220	−	0.435435i	$-0.143405\pi$
$283$	2.58111	+	3.86291i	0.153431	+	0.229626i	−0.746789	+	0.665061i	$0.768405\pi$
$284$		0			0
$285$	−0.0123040	+	0.00244742i	−0.000728828	+	0.000144973i
$286$		0			0
$287$			4.41324i			0.260505i
$288$		0			0
$289$			14.2997i			0.841158i
$290$		0			0
$291$	−9.44714	+	1.87915i	−0.553801	+	0.110158i
$292$		0			0
$293$	−4.12834	−	6.17849i	−0.241180	−	0.360951i	0.691057	−	0.722801i	$-0.257146\pi$
$293$	−4.12834	−	6.17849i	−0.241180	−	0.360951i	−0.932237	+	0.361849i	$0.882146\pi$
$294$		0			0
$295$	−17.2585	+	41.6658i	−1.00483	+	2.42588i
$296$		0			0
$297$	−2.95570	−	7.13569i	−0.171507	−	0.414055i
$298$		0			0
$299$	−4.76947	+	23.9778i	−0.275826	+	1.38667i
$300$		0			0
$301$	1.00619	−	1.50586i	0.0579956	−	0.0867966i
$302$		0			0
$303$	−1.04337	+	1.04337i	−0.0599402	+	0.0599402i
$304$		0			0
$305$	15.7700	+	15.7700i	0.902988	+	0.902988i
$306$		0			0
$307$	−4.22026	−	2.81989i	−0.240863	−	0.160939i	0.429280	−	0.903171i	$-0.358767\pi$
$307$	−4.22026	−	2.81989i	−0.240863	−	0.160939i	−0.670143	+	0.742232i	$0.733767\pi$
$308$		0			0
$309$	9.06298	+	1.80274i	0.515575	+	0.102554i
$310$		0			0
$311$	28.5642	−	11.8317i	1.61972	−	0.670912i	0.625699	−	0.780064i	$-0.284814\pi$
$311$	28.5642	−	11.8317i	1.61972	−	0.670912i	0.994025	+	0.109152i	$0.0348136\pi$
$312$		0			0
$313$	−8.76475	−	3.63048i	−0.495413	−	0.205207i	0.120966	−	0.992657i	$-0.461401\pi$
$313$	−8.76475	−	3.63048i	−0.495413	−	0.205207i	−0.616379	+	0.787450i	$0.711401\pi$
$314$		0			0
$315$	22.5726	−	15.0825i	1.27182	−	0.849803i
$316$		0			0
$317$	−3.95679	−	19.8921i	−0.222235	−	1.11725i	−0.917267	−	0.398274i	$-0.869609\pi$
$317$	−3.95679	−	19.8921i	−0.222235	−	1.11725i	0.695031	−	0.718980i	$-0.255391\pi$
$318$		0			0
$319$	−3.17407			−0.177714
$320$		0			0
$321$	11.6811			0.651977
$322$		0			0
$323$	−0.00153004	−	0.00769205i	−8.51339e−5	−	0.000427997i
$324$		0			0
$325$	−27.1182	+	18.1198i	−1.50425	+	1.00510i
$326$		0			0
$327$	−10.4885	−	4.34449i	−0.580016	−	0.240251i
$328$		0			0
$329$	1.68043	−	0.696058i	0.0926453	−	0.0383749i
$330$		0			0
$331$	25.0847	+	4.98965i	1.37878	+	0.274256i	0.828155	−	0.560498i	$-0.189390\pi$
$331$	25.0847	+	4.98965i	1.37878	+	0.274256i	0.550622	+	0.834754i	$0.314390\pi$
$332$		0			0
$333$	5.25211	+	3.50935i	0.287814	+	0.192311i
$334$		0			0
$335$	17.8570	+	17.8570i	0.975632	+	0.975632i
$336$		0			0
$337$	1.30903	−	1.30903i	0.0713075	−	0.0713075i	−0.670554	−	0.741861i	$-0.733943\pi$
$337$	1.30903	−	1.30903i	0.0713075	−	0.0713075i	0.741861	+	0.670554i	$0.233943\pi$
$338$		0			0
$339$	−6.12378	+	9.16489i	−0.332598	+	0.497768i
$340$		0			0
$341$	3.36400	−	16.9120i	0.182171	−	0.915834i
$342$		0			0
$343$	−3.21298	−	7.75682i	−0.173485	−	0.418829i
$344$		0			0
$345$	4.70364	−	11.3556i	0.253235	−	0.611364i
$346$		0			0
$347$	−17.1922	−	25.7299i	−0.922925	−	1.38125i	−0.924470	−	0.381256i	$-0.875492\pi$
$347$	−17.1922	−	25.7299i	−0.922925	−	1.38125i	0.00154489	−	0.999999i	$-0.499508\pi$
$348$		0			0
$349$	0.252228	−	0.0501713i	0.0135015	−	0.00268561i	−0.188335	−	0.982105i	$-0.560309\pi$
$349$	0.252228	−	0.0501713i	0.0135015	−	0.00268561i	0.201836	+	0.979419i	$0.435309\pi$
$350$		0			0
$351$		−	22.0760i		−	1.17833i
$352$		0			0
$353$			6.17608i			0.328719i	0.986400	+	0.164360i	$0.0525558\pi$
$353$			6.17608i			0.328719i	−0.986400	+	0.164360i	$0.947444\pi$
$354$		0			0
$355$	−17.9185	+	3.56422i	−0.951016	+	0.189169i
$356$		0			0
$357$	−2.43036	−	3.63729i	−0.128628	−	0.192506i
$358$		0			0
$359$	10.7708	−	26.0029i	0.568459	−	1.37238i	−0.334395	−	0.942433i	$-0.608532\pi$
$359$	10.7708	−	26.0029i	0.568459	−	1.37238i	0.902854	−	0.429948i	$-0.141468\pi$
$360$		0			0
$361$	7.27098	+	17.5537i	0.382683	+	0.923878i
$362$		0			0
$363$	1.17084	−	5.88620i	0.0614530	−	0.308945i
$364$		0			0
$365$	−9.14484	+	13.6862i	−0.478663	+	0.716370i
$366$		0			0
$367$	−6.85490	+	6.85490i	−0.357823	+	0.357823i	−0.863010	−	0.505187i	$-0.831424\pi$
$367$	−6.85490	+	6.85490i	−0.357823	+	0.357823i	0.505187	+	0.863010i	$0.331424\pi$
$368$		0			0
$369$	2.19234	+	2.19234i	0.114129	+	0.114129i
$370$		0			0
$371$	10.4652	+	6.99265i	0.543328	+	0.363040i
$372$		0			0
$373$	15.4393	+	3.07108i	0.799419	+	0.159014i	0.577863	−	0.816133i	$-0.303887\pi$
$373$	15.4393	+	3.07108i	0.799419	+	0.159014i	0.221555	+	0.975148i	$0.428887\pi$
$374$		0			0
$375$	3.00694	−	1.24552i	0.155278	−	0.0643182i
$376$		0			0
$377$	−8.38169	−	3.47181i	−0.431679	−	0.178807i
$378$		0			0
$379$	−25.8812	+	17.2933i	−1.32943	+	0.888295i	−0.998467	−	0.0553495i	$-0.982373\pi$
$379$	−25.8812	+	17.2933i	−1.32943	+	0.888295i	−0.330961	+	0.943645i	$0.607373\pi$
$380$		0			0
$381$	−2.03600	−	10.2356i	−0.104307	−	0.524388i
$382$		0			0
$383$	26.3304			1.34542			0.672711	−	0.739905i	$-0.265130\pi$
$383$	26.3304			1.34542			0.672711	+	0.739905i	$0.265130\pi$
$384$		0			0
$385$	−20.8191			−1.06104
$386$		0			0
$387$	−0.248223	−	1.24790i	−0.0126179	−	0.0634343i
$388$		0			0
$389$	−20.4392	+	13.6570i	−1.03631	+	0.692439i	−0.952654	−	0.304056i	$-0.901659\pi$
$389$	−20.4392	+	13.6570i	−1.03631	+	0.692439i	−0.0836539	+	0.996495i	$0.526659\pi$
$390$		0			0
$391$	7.09912	+	2.94055i	0.359018	+	0.148710i
$392$		0			0
$393$	−1.18300	+	0.490015i	−0.0596745	+	0.0247180i
$394$		0			0
$395$	−53.0007	−	10.5425i	−2.66675	−	0.530450i
$396$		0			0
$397$	22.8836	+	15.2903i	1.14850	+	0.767400i	0.976034	−	0.217616i	$-0.0698281\pi$
$397$	22.8836	+	15.2903i	1.14850	+	0.767400i	0.172461	+	0.985016i	$0.444828\pi$
$398$		0			0
$399$	−0.00898400	−	0.00898400i	−0.000449762	−	0.000449762i
$400$		0			0
$401$	−24.4437	+	24.4437i	−1.22066	+	1.22066i	−0.253263	+	0.967398i	$0.581504\pi$
$401$	−24.4437	+	24.4437i	−1.22066	+	1.22066i	−0.967398	+	0.253263i	$0.918496\pi$
$402$		0			0
$403$	27.3816	−	40.9795i	1.36397	−	2.04133i
$404$		0			0
$405$	2.51456	−	12.6415i	0.124950	−	0.628164i
$406$		0			0
$407$	−1.85377	−	4.47539i	−0.0918878	−	0.221837i
$408$		0			0
$409$	−12.0633	+	29.1234i	−0.596492	+	1.44006i	0.280641	+	0.959813i	$0.409453\pi$
$409$	−12.0633	+	29.1234i	−0.596492	+	1.44006i	−0.877134	+	0.480247i	$0.840547\pi$
$410$		0			0
$411$	−3.28291	−	4.91323i	−0.161934	−	0.242352i
$412$		0			0
$413$	−44.7971	+	8.91069i	−2.20432	+	0.438466i
$414$		0			0
$415$		−	20.2364i		−	0.993367i
$416$		0			0
$417$		−	3.22478i		−	0.157918i
$418$		0			0
$419$	−11.3813	+	2.26388i	−0.556012	+	0.110598i	−0.465095	−	0.885261i	$-0.653980\pi$
$419$	−11.3813	+	2.26388i	−0.556012	+	0.110598i	−0.0909169	+	0.995858i	$0.528980\pi$
$420$		0			0
$421$	3.35311	+	5.01829i	0.163421	+	0.244576i	0.904138	−	0.427240i	$-0.140514\pi$
$421$	3.35311	+	5.01829i	0.163421	+	0.244576i	−0.740717	+	0.671817i	$0.765514\pi$
$422$		0			0
$423$	0.489004	−	1.18056i	0.0237762	−	0.0574007i
$424$		0			0
$425$	3.92291	+	9.47073i	0.190289	+	0.459398i
$426$		0			0
$427$	−4.40650	+	22.1530i	−0.213246	+	1.07206i
$428$		0			0
$429$	−4.16592	+	6.23474i	−0.201132	+	0.301016i
$430$		0			0
$431$	−19.6711	+	19.6711i	−0.947521	+	0.947521i	−0.998690	−	0.0511686i	$-0.983705\pi$
$431$	−19.6711	+	19.6711i	−0.947521	+	0.947521i	0.0511686	+	0.998690i	$0.483705\pi$
$432$		0			0
$433$	−18.2910	−	18.2910i	−0.879011	−	0.879011i	0.114421	−	0.993432i	$-0.463499\pi$
$433$	−18.2910	−	18.2910i	−0.879011	−	0.879011i	−0.993432	+	0.114421i	$0.963499\pi$
$434$		0			0
$435$	3.79247	+	2.53405i	0.181835	+	0.121498i
$436$		0			0
$437$	0.0218885	+	0.00435389i	0.00104707	+	0.000208275i
$438$		0			0
$439$	−10.7707	+	4.46137i	−0.514057	+	0.212929i	−0.624604	−	0.780941i	$-0.714740\pi$
$439$	−10.7707	+	4.46137i	−0.514057	+	0.212929i	0.110547	+	0.993871i	$0.464740\pi$
$440$		0			0
$441$	9.97609	+	4.13223i	0.475052	+	0.196773i
$442$		0			0
$443$	9.77026	−	6.52828i	0.464199	−	0.310168i	−0.301386	−	0.953502i	$-0.597449\pi$
$443$	9.77026	−	6.52828i	0.464199	−	0.310168i	0.765586	+	0.643334i	$0.222449\pi$
$444$		0			0
$445$	−7.27880	−	36.5930i	−0.345048	−	1.73467i
$446$		0			0
$447$	−3.98706			−0.188581
$448$		0			0
$449$	26.5341			1.25222			0.626111	−	0.779734i	$-0.284646\pi$
$449$	26.5341			1.25222			0.626111	+	0.779734i	$0.284646\pi$
$450$		0			0
$451$	−0.463860	−	2.33198i	−0.0218423	−	0.109809i
$452$		0			0
$453$	−1.63164	+	1.09023i	−0.0766613	+	0.0512234i
$454$		0			0
$455$	−54.9765	−	22.7720i	−2.57734	−	1.06757i
$456$		0			0
$457$	23.9069	−	9.90258i	1.11832	−	0.463223i	0.254525	−	0.967066i	$-0.418081\pi$
$457$	23.9069	−	9.90258i	1.11832	−	0.463223i	0.863795	+	0.503843i	$0.168081\pi$
$458$		0			0
$459$	−6.80532	−	1.35366i	−0.317645	−	0.0631835i
$460$		0			0
$461$	−23.9755	−	16.0199i	−1.11665	−	0.746121i	−0.146640	−	0.989190i	$-0.546846\pi$
$461$	−23.9755	−	16.0199i	−1.11665	−	0.746121i	−0.970009	+	0.243069i	$0.921846\pi$
$462$		0			0
$463$	19.4799	+	19.4799i	0.905307	+	0.905307i	0.995889	−	0.0905817i	$-0.0288726\pi$
$463$	19.4799	+	19.4799i	0.905307	+	0.905307i	−0.0905817	+	0.995889i	$0.528873\pi$
$464$		0			0
$465$	−17.5212	+	17.5212i	−0.812527	+	0.812527i
$466$		0			0
$467$	11.7398	−	17.5698i	0.543252	−	0.813035i	−0.453691	−	0.891159i	$-0.649893\pi$
$467$	11.7398	−	17.5698i	0.543252	−	0.813035i	0.996944	+	0.0781243i	$0.0248931\pi$
$468$		0			0
$469$	−4.98965	+	25.0847i	−0.230401	+	1.15830i
$470$		0			0
$471$	3.85667	+	9.31081i	0.177706	+	0.429020i
$472$		0			0
$473$	−0.373399	+	0.901465i	−0.0171689	+	0.0414494i
$474$		0			0
$475$	0.0165409	+	0.0247552i	0.000758950	+	0.00113585i
$476$		0			0
$477$	8.67247	−	1.72506i	0.397085	−	0.0789851i
$478$		0			0
$479$			12.7073i			0.580611i	0.956934	+	0.290305i	$0.0937569\pi$
$479$			12.7073i			0.580611i	−0.956934	+	0.290305i	$0.906243\pi$
$480$		0			0
$481$		−	13.8457i		−	0.631310i
$482$		0			0
$483$	12.2090	−	2.42852i	0.555528	−	0.110501i
$484$		0			0
$485$	22.8797	+	34.2418i	1.03891	+	1.55484i
$486$		0			0
$487$	5.38031	−	12.9892i	0.243805	−	0.588597i	−0.753850	−	0.657047i	$-0.771805\pi$
$487$	5.38031	−	12.9892i	0.243805	−	0.588597i	0.997655	+	0.0684497i	$0.0218053\pi$
$488$		0			0
$489$	−3.72607	−	8.99553i	−0.168499	−	0.406792i
$490$		0			0
$491$	−2.14334	+	10.7753i	−0.0967275	+	0.486282i	0.901806	+	0.432141i	$0.142242\pi$
$491$	−2.14334	+	10.7753i	−0.0967275	+	0.486282i	−0.998533	+	0.0541404i	$0.982758\pi$
$492$		0			0
$493$	−1.58420	+	2.37092i	−0.0713487	+	0.106781i
$494$		0			0
$495$	−10.3422	+	10.3422i	−0.464848	+	0.464848i
$496$		0			0
$497$	−13.0835	−	13.0835i	−0.586876	−	0.586876i
$498$		0			0
$499$	7.97175	+	5.32655i	0.356864	+	0.238449i	0.721059	−	0.692874i	$-0.243656\pi$
$499$	7.97175	+	5.32655i	0.356864	+	0.238449i	−0.364195	+	0.931323i	$0.618656\pi$
$500$		0			0
$501$	−9.43849	−	1.87743i	−0.421681	−	0.0838775i
$502$		0			0
$503$	7.63705	−	3.16337i	0.340519	−	0.141048i	−0.205869	−	0.978579i	$-0.566002\pi$
$503$	7.63705	−	3.16337i	0.340519	−	0.141048i	0.546389	+	0.837532i	$0.316002\pi$
$504$		0			0
$505$	5.82846	+	2.41423i	0.259363	+	0.107432i
$506$		0			0
$507$	−9.34513	+	6.24422i	−0.415032	+	0.277316i
$508$		0			0
$509$	2.95926	+	14.8772i	0.131167	+	0.659420i	0.989288	+	0.145974i	$0.0466314\pi$
$509$	2.95926	+	14.8772i	0.131167	+	0.659420i	−0.858122	+	0.513446i	$0.828369\pi$
$510$		0			0
$511$	−16.6705			−0.737459
$512$		0			0
$513$	−0.0201524			−0.000889751
$514$		0			0
$515$	−7.70756	−	38.7485i	−0.339636	−	1.70746i
$516$		0			0
$517$	−0.814791	+	0.544426i	−0.0358345	+	0.0239438i
$518$		0			0
$519$	4.03692	+	1.67215i	0.177201	+	0.0733992i
$520$		0			0
$521$	10.0424	−	4.15970i	0.439966	−	0.182240i	−0.151694	−	0.988427i	$-0.548473\pi$
$521$	10.0424	−	4.15970i	0.439966	−	0.182240i	0.591660	+	0.806188i	$0.298473\pi$
$522$		0			0
$523$	−3.45679	−	0.687599i	−0.151155	−	0.0300666i	0.118933	−	0.992902i	$-0.462053\pi$
$523$	−3.45679	−	0.687599i	−0.151155	−	0.0300666i	−0.270088	+	0.962836i	$0.587053\pi$
$524$		0			0
$525$	13.8080	+	9.22622i	0.602631	+	0.402665i
$526$		0			0
$527$	−10.9537	−	10.9537i	−0.477149	−	0.477149i
$528$		0			0
$529$	0.802117	−	0.802117i	0.0348746	−	0.0348746i
$530$		0			0
$531$	−17.8271	+	26.6801i	−0.773630	+	1.15782i
$532$		0			0
$533$	1.32583	−	6.66538i	0.0574279	−	0.288710i
$534$		0			0
$535$	−19.1121	−	46.1407i	−0.826289	−	1.99484i
$536$		0			0
$537$	0.299194	−	0.722317i	0.0129112	−	0.0311703i
$538$		0			0
$539$	−4.60057	−	6.88524i	−0.198161	−	0.296568i
$540$		0			0
$541$	4.58170	−	0.911357i	0.196983	−	0.0391823i	−0.0956128	−	0.995419i	$-0.530481\pi$
$541$	4.58170	−	0.911357i	0.196983	−	0.0391823i	0.292595	+	0.956236i	$0.405481\pi$
$542$		0			0
$543$		−	13.8133i		−	0.592786i
$544$		0			0
$545$			48.5381i			2.07915i
$546$		0			0
$547$	7.46021	−	1.48393i	0.318975	−	0.0634482i	−0.0330060	−	0.999455i	$-0.510508\pi$
$547$	7.46021	−	1.48393i	0.318975	−	0.0634482i	0.351981	+	0.936007i	$0.385508\pi$
$548$		0			0
$549$	8.81583	+	13.1938i	0.376251	+	0.563099i
$550$		0			0
$551$	−0.00316930	+	0.00765136i	−0.000135017	+	0.000325959i
$552$		0			0
$553$	−20.9439	−	50.5631i	−0.890626	−	2.15016i
$554$		0			0
$555$	−1.35803	+	6.82729i	−0.0576453	+	0.289803i
$556$		0			0
$557$	−8.06578	+	12.0713i	−0.341758	+	0.511477i	−0.962042	−	0.272900i	$-0.912017\pi$
$557$	−8.06578	+	12.0713i	−0.341758	+	0.511477i	0.620284	+	0.784377i	$0.287017\pi$
$558$		0			0
$559$	−1.97205	+	1.97205i	−0.0834089	+	0.0834089i
$560$		0			0
$561$	1.66652	+	1.66652i	0.0703606	+	0.0703606i
$562$		0			0
$563$	13.7599	+	9.19410i	0.579912	+	0.387485i	0.810650	−	0.585531i	$-0.199114\pi$
$563$	13.7599	+	9.19410i	0.579912	+	0.387485i	−0.230738	+	0.973016i	$0.574114\pi$
$564$		0			0
$565$	46.2210	+	9.19392i	1.94453	+	0.386791i
$566$		0			0
$567$	12.0602	−	4.99548i	0.506479	−	0.209790i
$568$		0			0
$569$	10.7745	+	4.46295i	0.451691	+	0.187097i	0.596919	−	0.802302i	$-0.296391\pi$
$569$	10.7745	+	4.46295i	0.451691	+	0.187097i	−0.145228	+	0.989398i	$0.546391\pi$
$570$		0			0
$571$	38.3434	−	25.6202i	1.60462	−	1.07217i	0.656471	−	0.754351i	$-0.272049\pi$
$571$	38.3434	−	25.6202i	1.60462	−	1.07217i	0.948150	−	0.317822i	$-0.102951\pi$
$572$		0			0
$573$	0.917878	+	4.61448i	0.0383449	+	0.192773i
$574$		0			0
$575$	−29.1703			−1.21649
$576$		0			0
$577$	5.30739			0.220949			0.110475	−	0.993879i	$-0.464763\pi$
$577$	5.30739			0.220949			0.110475	+	0.993879i	$0.464763\pi$
$578$		0			0
$579$	1.37444	+	6.90979i	0.0571199	+	0.287161i
$580$		0			0
$581$	17.0408	−	11.3863i	0.706973	−	0.472384i
$582$		0			0
$583$	−6.26487	−	2.59499i	−0.259464	−	0.107474i
$584$		0			0
$585$	−38.6228	+	15.9981i	−1.59686	+	0.661439i
$586$		0			0
$587$	−1.07653	−	0.214135i	−0.0444331	−	0.00883830i	0.172824	−	0.984953i	$-0.444711\pi$
$587$	−1.07653	−	0.214135i	−0.0444331	−	0.00883830i	−0.217257	+	0.976114i	$0.569711\pi$
$588$		0			0
$589$	−0.0374087	−	0.0249957i	−0.00154140	−	0.00102993i
$590$		0			0
$591$	6.60890	+	6.60890i	0.271854	+	0.271854i
$592$		0			0
$593$	−9.71203	+	9.71203i	−0.398825	+	0.398825i	−0.877819	−	0.478993i	$-0.841002\pi$
$593$	−9.71203	+	9.71203i	−0.398825	+	0.398825i	0.478993	+	0.877819i	$0.341002\pi$
$594$		0			0
$595$	−10.3910	+	15.5512i	−0.425987	+	0.637535i
$596$		0			0
$597$	0.129542	−	0.651251i	0.00530179	−	0.0266539i
$598$		0			0
$599$	−1.51141	−	3.64886i	−0.0617545	−	0.149088i	0.889990	−	0.455980i	$-0.150711\pi$
$599$	−1.51141	−	3.64886i	−0.0617545	−	0.149088i	−0.951745	+	0.306891i	$0.900711\pi$
$600$		0			0
$601$	−4.10853	+	9.91887i	−0.167591	+	0.404599i	−0.985254	−	0.171097i	$-0.945269\pi$
$601$	−4.10853	+	9.91887i	−0.167591	+	0.404599i	0.817664	+	0.575696i	$0.195269\pi$
$602$		0			0
$603$	9.98251	+	14.9399i	0.406519	+	0.608399i
$604$		0			0
$605$	−25.1663	+	5.00589i	−1.02316	+	0.203518i
$606$		0			0
$607$			43.0657i			1.74798i	0.485943	+	0.873991i	$0.338476\pi$
$607$			43.0657i			1.74798i	−0.485943	+	0.873991i	$0.661524\pi$
$608$		0			0
$609$			4.61942i			0.187188i
$610$		0			0
$611$	−2.74710	+	0.546431i	−0.111136	+	0.0221062i
$612$		0			0
$613$	−25.9537	−	38.8424i	−1.04826	−	1.56883i	−0.799872	−	0.600170i	$-0.795099\pi$
$613$	−25.9537	−	38.8424i	−1.04826	−	1.56883i	−0.248387	−	0.968661i	$-0.579901\pi$
$614$		0			0
$615$	−1.30753	+	3.15665i	−0.0527245	+	0.127288i
$616$		0			0
$617$	−10.4503	−	25.2293i	−0.420715	−	1.01570i	−0.982137	−	0.188166i	$-0.939746\pi$
$617$	−10.4503	−	25.2293i	−0.420715	−	1.01570i	0.561422	−	0.827529i	$-0.310254\pi$
$618$		0			0
$619$	7.81639	−	39.2957i	0.314167	−	1.57943i	−0.424546	−	0.905406i	$-0.639566\pi$
$619$	7.81639	−	39.2957i	0.314167	−	1.57943i	0.738713	−	0.674020i	$-0.235434\pi$
$620$		0			0
$621$	10.9695	−	16.4170i	0.440191	−	0.658792i
$622$		0			0
$623$	26.7190	−	26.7190i	1.07047	−	1.07047i
$624$		0			0
$625$	12.2158	+	12.2158i	0.488631	+	0.488631i
$626$		0			0
$627$	0.00569148	+	0.00380292i	0.000227296	+	0.000151874i
$628$		0			0
$629$	−4.26819	−	0.848995i	−0.170184	−	0.0338516i
$630$		0			0
$631$	30.5309	−	12.6463i	1.21542	−	0.503442i	0.319467	−	0.947597i	$-0.396496\pi$
$631$	30.5309	−	12.6463i	1.21542	−	0.503442i	0.895950	+	0.444155i	$0.146496\pi$
$632$		0			0
$633$	−6.28800	−	2.60458i	−0.249926	−	0.103523i
$634$		0			0
$635$	−37.0998	+	24.7893i	−1.47226	+	0.983733i
$636$		0			0
$637$	−4.61751	−	23.2138i	−0.182953	−	0.919765i
$638$		0			0
$639$	−12.9989			−0.514227
$640$		0			0
$641$	−30.0254			−1.18593			−0.592966	−	0.805227i	$-0.702043\pi$
$641$	−30.0254			−1.18593			−0.592966	+	0.805227i	$0.702043\pi$
$642$		0			0
$643$	−1.92684	−	9.68687i	−0.0759871	−	0.382013i	0.924013	−	0.382361i	$-0.124889\pi$
$643$	−1.92684	−	9.68687i	−0.0759871	−	0.382013i	−1.00000		0.000348458i	$0.999889\pi$
$644$		0			0
$645$	1.16584	−	0.778990i	0.0459049	−	0.0306727i
$646$		0			0
$647$	32.0095	+	13.2588i	1.25842	+	0.521257i	0.909426	−	0.415867i	$-0.136522\pi$
$647$	32.0095	+	13.2588i	1.25842	+	0.521257i	0.348999	+	0.937123i	$0.386522\pi$
$648$		0			0
$649$	22.7345	−	9.41693i	0.892406	−	0.369647i
$650$		0			0
$651$	−24.6130	−	4.89583i	−0.964660	−	0.191883i
$652$		0			0
$653$	−30.9545	−	20.6832i	−1.21134	−	0.809394i	−0.225043	−	0.974349i	$-0.572252\pi$
$653$	−30.9545	−	20.6832i	−1.21134	−	0.809394i	−0.986301	+	0.164954i	$0.947252\pi$
$654$		0			0
$655$	3.87114	+	3.87114i	0.151258	+	0.151258i
$656$		0			0
$657$	−8.28132	+	8.28132i	−0.323085	+	0.323085i
$658$		0			0
$659$	−6.96386	+	10.4222i	−0.271273	+	0.405989i	−0.941946	−	0.335764i	$-0.891006\pi$
$659$	−6.96386	+	10.4222i	−0.271273	+	0.405989i	0.670673	+	0.741753i	$0.266006\pi$
$660$		0			0
$661$	−4.07042	+	20.4634i	−0.158321	+	0.795934i	0.817256	+	0.576275i	$0.195494\pi$
$661$	−4.07042	+	20.4634i	−0.158321	+	0.795934i	−0.975577	+	0.219659i	$0.929506\pi$
$662$		0			0
$663$	2.57790	+	6.22359i	0.100117	+	0.241704i
$664$		0			0
$665$	−0.0207878	+	0.0501862i	−0.000806116	+	0.00194614i
$666$		0			0
$667$	−4.50799	−	6.74668i	−0.174550	−	0.261233i
$668$		0			0
$669$	7.76942	−	1.54543i	0.300383	−	0.0597499i
$670$		0			0
$671$		−	12.1689i		−	0.469776i
$672$		0			0
$673$			3.76884i			0.145278i	0.997358	+	0.0726390i	$0.0231421\pi$
$673$			3.76884i			0.145278i	−0.997358	+	0.0726390i	$0.976858\pi$
$674$		0			0
$675$	25.8346	−	5.13882i	0.994373	−	0.197793i
$676$		0			0
$677$	12.4716	+	18.6650i	0.479321	+	0.717354i	0.989789	−	0.142543i	$-0.0455278\pi$
$677$	12.4716	+	18.6650i	0.479321	+	0.717354i	−0.510468	+	0.859897i	$0.670528\pi$
$678$		0			0
$679$	−15.9610	+	38.5334i	−0.612529	+	1.47878i
$680$		0			0
$681$	5.30046	+	12.7964i	0.203114	+	0.490361i
$682$		0			0
$683$	−7.81275	+	39.2773i	−0.298946	+	1.50291i	0.480811	+	0.876824i	$0.340342\pi$
$683$	−7.81275	+	39.2773i	−0.298946	+	1.50291i	−0.779758	+	0.626081i	$0.784658\pi$
$684$		0			0
$685$	−14.0360	+	21.0064i	−0.536289	+	0.802613i
$686$		0			0
$687$	3.75390	−	3.75390i	0.143220	−	0.143220i
$688$		0			0
$689$	−13.7051	−	13.7051i	−0.522122	−	0.522122i
$690$		0			0
$691$	28.3968	+	18.9741i	1.08027	+	0.721811i	0.962514	−	0.271232i	$-0.0874312\pi$
$691$	28.3968	+	18.9741i	1.08027	+	0.721811i	0.117752	+	0.993043i	$0.462431\pi$
$692$		0			0
$693$	−14.5283	−	2.88985i	−0.551883	−	0.109776i
$694$		0			0
$695$	−12.7380	+	5.27624i	−0.483179	+	0.200139i
$696$		0			0
$697$	−1.97343	−	0.817420i	−0.0747488	−	0.0309620i
$698$		0			0
$699$	19.2158	−	12.8396i	0.726807	−	0.485637i
$700$		0			0
$701$	3.21632	+	16.1695i	0.121479	+	0.610715i	0.992778	+	0.119963i	$0.0382777\pi$
$701$	3.21632	+	16.1695i	0.121479	+	0.610715i	−0.871300	+	0.490752i	$0.836722\pi$
$702$		0			0
$703$	−0.0126393			−0.000476699
$704$		0			0
$705$	1.40818			0.0530353
$706$		0			0
$707$	1.24648	+	6.26648i	0.0468787	+	0.235675i
$708$		0			0
$709$	2.10981	−	1.40973i	0.0792355	−	0.0529435i	−0.515321	−	0.856997i	$-0.672327\pi$
$709$	2.10981	−	1.40973i	0.0792355	−	0.0529435i	0.594557	+	0.804053i	$0.297327\pi$
$710$		0			0
$711$	−35.5222	−	14.7138i	−1.33219	−	0.551810i
$712$		0			0
$713$	40.7252	−	16.8689i	1.52517	−	0.631746i
$714$		0			0
$715$	31.4434	+	6.25449i	1.17592	+	0.233905i
$716$		0			0
$717$	−4.52805	−	3.02554i	−0.169103	−	0.112991i
$718$		0			0
$719$	13.6165	+	13.6165i	0.507809	+	0.507809i	0.913854	−	0.406044i	$-0.133092\pi$
$719$	13.6165	+	13.6165i	0.507809	+	0.507809i	−0.406044	+	0.913854i	$0.633092\pi$
$720$		0			0
$721$	28.2929	−	28.2929i	1.05368	−	1.05368i
$722$		0			0
$723$	9.80170	−	14.6693i	0.364529	−	0.545557i
$724$		0			0
$725$	2.11183	−	10.6169i	0.0784314	−	0.394301i
$726$		0			0
$727$	7.57477	+	18.2871i	0.280933	+	0.678231i	0.999858	−	0.0168560i	$-0.00536569\pi$
$727$	7.57477	+	18.2871i	0.280933	+	0.678231i	−0.718925	+	0.695087i	$0.755366\pi$
$728$		0			0
$729$	−0.291465	+	0.703658i	−0.0107950	+	0.0260614i
$730$		0			0
$731$	0.486997	+	0.728843i	0.0180122	+	0.0269572i
$732$		0			0
$733$	34.5625	−	6.87491i	1.27660	−	0.253931i	0.490176	−	0.871623i	$-0.336932\pi$
$733$	34.5625	−	6.87491i	1.27660	−	0.253931i	0.786420	+	0.617693i	$0.211932\pi$
$734$		0			0
$735$			11.8996i			0.438923i
$736$		0			0
$737$		−	13.7793i		−	0.507569i
$738$		0			0
$739$	−25.3933	+	5.05105i	−0.934109	+	0.185806i	−0.638604	−	0.769535i	$-0.720488\pi$
$739$	−25.3933	+	5.05105i	−0.934109	+	0.185806i	−0.295505	+	0.955341i	$0.595488\pi$
$740$		0			0
$741$	0.0108697	+	0.0162676i	0.000399308	+	0.000597607i
$742$		0			0
$743$	10.2227	−	24.6798i	0.375034	−	0.905413i	−0.617846	−	0.786299i	$-0.711995\pi$
$743$	10.2227	−	24.6798i	0.375034	−	0.905413i	0.992881	−	0.119114i	$-0.0380054\pi$
$744$		0			0
$745$	6.52344	+	15.7490i	0.239000	+	0.576998i
$746$		0			0
$747$	2.80897	−	14.1216i	0.102775	−	0.516684i
$748$		0			0
$749$	28.1008	−	42.0559i	1.02678	−	1.53669i
$750$		0			0
$751$	18.2054	−	18.2054i	0.664326	−	0.664326i	−0.292071	−	0.956397i	$-0.594344\pi$
$751$	18.2054	−	18.2054i	0.664326	−	0.664326i	0.956397	+	0.292071i	$0.0943442\pi$
$752$		0			0
$753$	8.94290	+	8.94290i	0.325898	+	0.325898i
$754$		0			0
$755$	6.97605	+	4.66124i	0.253884	+	0.169640i
$756$		0			0
$757$	8.14973	+	1.62108i	0.296207	+	0.0589192i	0.340957	−	0.940079i	$-0.389249\pi$
$757$	8.14973	+	1.62108i	0.296207	+	0.0589192i	−0.0447498	+	0.998998i	$0.514249\pi$
$758$		0			0
$759$	−6.19604	+	2.56649i	−0.224902	+	0.0931575i
$760$		0			0
$761$	37.0579	+	15.3499i	1.34335	+	0.556433i	0.934433	−	0.356139i	$-0.115907\pi$
$761$	37.0579	+	15.3499i	1.34335	+	0.556433i	0.408916	+	0.912572i	$0.365907\pi$
$762$		0			0
$763$	−40.8734	+	27.3107i	−1.47972	+	0.988714i
$764$		0			0
$765$	2.56341	+	12.8871i	0.0926803	+	0.465936i
$766$		0			0
$767$	70.3346			2.53964
$768$		0			0
$769$	44.7180			1.61257			0.806287	−	0.591525i	$-0.201474\pi$
$769$	44.7180			1.61257			0.806287	+	0.591525i	$0.201474\pi$
$770$		0			0
$771$	2.05169	+	10.3146i	0.0738899	+	0.371470i
$772$		0			0
$773$	29.7197	−	19.8581i	1.06894	−	0.714245i	0.108887	−	0.994054i	$-0.465271\pi$
$773$	29.7197	−	19.8581i	1.06894	−	0.714245i	0.960056	+	0.279809i	$0.0902712\pi$
$774$		0			0
$775$	54.3303	+	22.5044i	1.95160	+	0.808380i
$776$		0			0
$777$	−6.51330	+	2.69790i	−0.233663	+	0.0967865i
$778$		0			0
$779$	−0.00608460	−	0.00121030i	−0.000218003	−	4.33636e-5i
$780$		0			0
$781$	8.28857	+	5.53825i	0.296588	+	0.198174i
$782$		0			0
$783$	5.18101	+	5.18101i	0.185154	+	0.185154i
$784$		0			0
$785$	30.4678	−	30.4678i	1.08744	−	1.08744i
$786$		0			0
$787$	12.8406	−	19.2173i	0.457717	−	0.685022i	−0.528788	−	0.848754i	$-0.677353\pi$
$787$	12.8406	−	19.2173i	0.457717	−	0.685022i	0.986505	+	0.163732i	$0.0523533\pi$
$788$		0			0
$789$	−0.913339	+	4.59167i	−0.0325157	+	0.163468i
$790$		0			0
$791$	18.2648	+	44.0952i	0.649423	+	1.56785i
$792$		0			0
$793$	13.3104	−	32.1342i	0.472667	−	1.14112i
$794$		0			0
$795$	5.41371	+	8.10219i	0.192004	+	0.287355i
$796$		0			0
$797$	9.16130	−	1.82230i	0.324510	−	0.0645491i	−0.0301471	−	0.999545i	$-0.509598\pi$
$797$	9.16130	−	1.82230i	0.324510	−	0.0645491i	0.354657	+	0.934996i	$0.384598\pi$
$798$		0			0
$799$			0.880347i			0.0311445i
$800$		0			0
$801$		−	26.5461i		−	0.937961i
$802$		0			0
$803$	8.80879	−	1.75218i	0.310856	−	0.0618330i
$804$		0			0
$805$	−29.5684	−	44.2523i	−1.04215	−	1.55969i
$806$		0			0
$807$	−2.66957	+	6.44491i	−0.0939733	+	0.226872i
$808$		0			0
$809$	10.1941	+	24.6108i	0.358406	+	0.865268i	0.995525	+	0.0945027i	$0.0301261\pi$
$809$	10.1941	+	24.6108i	0.358406	+	0.865268i	−0.637119	+	0.770766i	$0.719874\pi$
$810$		0			0
$811$	2.07144	−	10.4138i	0.0727380	−	0.365679i	−0.927223	−	0.374510i	$-0.877811\pi$
$811$	2.07144	−	10.4138i	0.0727380	−	0.365679i	0.999961	+	0.00883095i	$0.00281102\pi$
$812$		0			0
$813$	2.01863	−	3.02109i	0.0707963	−	0.105954i
$814$		0			0
$815$	−29.4361	+	29.4361i	−1.03110	+	1.03110i
$816$		0			0
$817$	0.00180022	+	0.00180022i	6.29816e−5	+	6.29816e-5i
$818$		0			0
$819$	−35.2035	−	23.5222i	−1.23011	−	0.821933i
$820$		0			0
$821$	−53.6020	−	10.6621i	−1.87072	−	0.372110i	−0.876677	−	0.481079i	$-0.840245\pi$
$821$	−53.6020	−	10.6621i	−1.87072	−	0.372110i	−0.994045	+	0.108969i	$0.965245\pi$
$822$		0			0
$823$	−25.4170	+	10.5281i	−0.885982	+	0.366986i	−0.778814	−	0.627255i	$-0.784178\pi$
$823$	−25.4170	+	10.5281i	−0.885982	+	0.366986i	−0.107168	+	0.994241i	$0.534178\pi$
$824$		0			0
$825$	−8.26597	−	3.42388i	−0.287784	−	0.119204i
$826$		0			0
$827$	22.6824	−	15.1559i	0.788743	−	0.527021i	−0.0947301	−	0.995503i	$-0.530199\pi$
$827$	22.6824	−	15.1559i	0.788743	−	0.527021i	0.883473	+	0.468482i	$0.155199\pi$
$828$		0			0
$829$	−2.14763	−	10.7969i	−0.0745902	−	0.374990i	0.925402	−	0.378988i	$-0.123728\pi$
$829$	−2.14763	−	10.7969i	−0.0745902	−	0.374990i	−0.999992	+	0.00399713i	$0.998728\pi$
$830$		0			0
$831$	7.28273			0.252635
$832$		0			0
$833$	−7.43921			−0.257753
$834$		0			0
$835$	8.02692	+	40.3540i	0.277783	+	1.39651i
$836$		0			0
$837$	−33.0963	+	22.1142i	−1.14398	+	0.764380i
$838$		0			0
$839$	−17.6575	−	7.31397i	−0.609604	−	0.252506i	0.0564551	−	0.998405i	$-0.482020\pi$
$839$	−17.6575	−	7.31397i	−0.609604	−	0.252506i	−0.666059	+	0.745899i	$0.732020\pi$
$840$		0			0
$841$	−24.0106	+	9.94552i	−0.827952	+	0.342949i
$842$		0			0
$843$	14.1201	+	2.80866i	0.486322	+	0.0967356i
$844$		0			0
$845$	39.9549	+	26.6970i	1.37449	+	0.918405i
$846$		0			0
$847$	−18.3756	−	18.3756i	−0.631393	−	0.631393i
$848$		0			0
$849$	−2.57583	+	2.57583i	−0.0884023	+	0.0884023i
$850$		0			0
$851$	6.87989	−	10.2965i	0.235840	−	0.352959i
$852$		0			0
$853$	8.92566	−	44.8723i	0.305609	−	1.53640i	−0.456957	−	0.889489i	$-0.651061\pi$
$853$	8.92566	−	44.8723i	0.305609	−	1.53640i	0.762566	−	0.646911i	$-0.223939\pi$
$854$		0			0
$855$	0.0146041	+	0.0352574i	0.000499450	+	0.00120578i
$856$		0			0
$857$	4.18475	−	10.1029i	0.142948	−	0.345108i	−0.836148	−	0.548503i	$-0.815198\pi$
$857$	4.18475	−	10.1029i	0.142948	−	0.345108i	0.979097	+	0.203396i	$0.0651978\pi$
$858$		0			0
$859$	3.25686	+	4.87424i	0.111123	+	0.166307i	0.882862	−	0.469632i	$-0.155613\pi$
$859$	3.25686	+	4.87424i	0.111123	+	0.166307i	−0.771740	+	0.635938i	$0.780613\pi$
$860$		0			0
$861$	−3.39387	+	0.675083i	−0.115663	+	0.0230068i
$862$		0			0
$863$			1.43064i			0.0486996i	0.999704	+	0.0243498i	$0.00775154\pi$
$863$			1.43064i			0.0486996i	−0.999704	+	0.0243498i	$0.992248\pi$
$864$		0			0
$865$		−	18.6818i		−	0.635201i
$866$		0			0
$867$	−10.9968	+	2.18739i	−0.373469	+	0.0742877i
$868$		0			0
$869$	16.3814	+	24.5165i	0.555701	+	0.831666i
$870$		0			0
$871$	15.0719	−	36.3868i	0.510692	−	1.23292i
$872$		0			0
$873$	11.2132	+	27.0709i	0.379508	+	0.916213i
$874$		0			0
$875$	2.74942	−	13.8223i	0.0929474	−	0.467278i
$876$		0			0
$877$	−20.5649	+	30.7776i	−0.694428	+	1.03929i	0.301872	+	0.953348i	$0.402388\pi$
$877$	−20.5649	+	30.7776i	−0.694428	+	1.03929i	−0.996301	+	0.0859368i	$0.972612\pi$
$878$		0			0
$879$	4.11989	−	4.11989i	0.138960	−	0.138960i
$880$		0			0
$881$	10.5814	+	10.5814i	0.356496	+	0.356496i	0.862520	−	0.506023i	$-0.168885\pi$
$881$	10.5814	+	10.5814i	0.356496	+	0.356496i	−0.506023	+	0.862520i	$0.668885\pi$
$882$		0			0
$883$	−46.6957	−	31.2011i	−1.57144	−	1.05000i	−0.967469	−	0.252991i	$-0.918586\pi$
$883$	−46.6957	−	31.2011i	−1.57144	−	1.05000i	−0.603968	−	0.797009i	$-0.706414\pi$
$884$		0			0
$885$	−34.6819	−	6.89866i	−1.16582	−	0.231896i
$886$		0			0
$887$	−47.8447	+	19.8179i	−1.60647	+	0.665421i	−0.992312	−	0.123764i	$-0.960503\pi$
$887$	−47.8447	+	19.8179i	−1.60647	+	0.665421i	−0.614156	+	0.789185i	$0.710503\pi$
$888$		0			0
$889$	−41.7495	−	17.2932i	−1.40023	−	0.579996i
$890$		0			0
$891$	−5.84760	+	3.90724i	−0.195902	+	0.130898i
$892$		0			0
$893$	0.000498818		0.00250773i	1.66923e−5		8.39179e-5i
$894$		0			0
$895$	−3.34270			−0.111734
$896$		0			0
$897$	−19.1690			−0.640034
$898$		0			0
$899$	3.19128	+	16.0437i	0.106435	+	0.535086i
$900$		0			0
$901$	−5.06520	+	3.38446i	−0.168746	+	0.112753i
$902$		0			0
$903$	1.31196	+	0.543430i	0.0436592	+	0.0180842i
$904$		0			0
$905$	−54.5629	+	22.6007i	−1.81373	+	0.751272i
$906$		0			0
$907$	39.2228	+	7.80190i	1.30237	+	0.259058i	0.797071	−	0.603886i	$-0.206382\pi$
$907$	39.2228	+	7.80190i	1.30237	+	0.259058i	0.505300	+	0.862943i	$0.331382\pi$
$908$		0			0
$909$	3.73218	+	2.49376i	0.123789	+	0.0827129i
$910$		0			0
$911$	−28.9692	−	28.9692i	−0.959794	−	0.959794i	0.0394285	−	0.999222i	$-0.487446\pi$
$911$	−28.9692	−	28.9692i	−0.959794	−	0.959794i	−0.999222	+	0.0394285i	$0.987446\pi$
$912$		0			0
$913$	−7.80771	+	7.80771i	−0.258397	+	0.258397i
$914$		0			0
$915$	−9.71517	+	14.5398i	−0.321174	+	0.480670i
$916$		0			0
$917$	−1.08168	+	5.43799i	−0.0357204	+	0.179578i
$918$		0			0
$919$	−4.60437	−	11.1159i	−0.151884	−	0.366681i	0.829563	−	0.558413i	$-0.188589\pi$
$919$	−4.60437	−	11.1159i	−0.151884	−	0.366681i	−0.981447	+	0.191732i	$0.938589\pi$
$920$		0			0
$921$	1.52299	−	3.67682i	0.0501842	−	0.121155i
$922$		0			0
$923$	15.8297	+	23.6908i	0.521040	+	0.779792i
$924$		0			0
$925$	16.2030	−	3.22298i	0.532752	−	0.105971i
$926$		0			0
$927$		−	28.1099i		−	0.923249i
$928$		0			0
$929$		−	27.6140i		−	0.905987i	−0.891514	−	0.452994i	$-0.850356\pi$
$929$		−	27.6140i		−	0.905987i	0.891514	−	0.452994i	$-0.149644\pi$
$930$		0			0
$931$	−0.0211911	+	0.00421517i	−0.000694510	+	0.000138147i
$932$		0			0
$933$	13.4682	+	20.1566i	0.440929	+	0.659897i
$934$		0			0
$935$	3.85611	−	9.30948i	0.126108	−	0.304453i
$936$		0			0
$937$	8.53902	+	20.6150i	0.278958	+	0.673464i	0.999807	−	0.0196280i	$-0.00624818\pi$
$937$	8.53902	+	20.6150i	0.278958	+	0.673464i	−0.720850	+	0.693091i	$0.756248\pi$
$938$		0			0
$939$	1.45119	−	7.29563i	0.0473578	−	0.238084i
$940$		0			0
$941$	21.1132	−	31.5981i	0.688270	−	1.03007i	−0.308614	−	0.951187i	$-0.599865\pi$
$941$	21.1132	−	31.5981i	0.688270	−	1.03007i	0.996884	−	0.0788810i	$-0.0251347\pi$
$942$		0			0
$943$	4.29797	−	4.29797i	0.139961	−	0.139961i
$944$		0			0
$945$	33.9829	+	33.9829i	1.10546	+	1.10546i
$946$		0			0
$947$	−23.9627	−	16.0114i	−0.778683	−	0.520299i	0.101556	−	0.994830i	$-0.467618\pi$
$947$	−23.9627	−	16.0114i	−0.778683	−	0.520299i	−0.880239	+	0.474531i	$0.842618\pi$
$948$		0			0
$949$	25.1777	+	5.00816i	0.817303	+	0.162572i
$950$		0			0
$951$	14.6922	−	6.08571i	0.476427	−	0.197343i
$952$		0			0
$953$	−46.7611	−	19.3691i	−1.51474	−	0.627426i	−0.538211	−	0.842810i	$-0.680899\pi$
$953$	−46.7611	−	19.3691i	−1.51474	−	0.627426i	−0.976529	+	0.215385i	$0.930899\pi$
$954$		0			0
$955$	16.7255	−	11.1756i	0.541226	−	0.361635i
$956$		0			0
$957$	−0.485531	−	2.44093i	−0.0156950	−	0.0789040i
$958$		0			0
$959$	−25.5868			−0.826241
$960$		0			0
$961$	−57.8654			−1.86663
$962$		0			0
$963$	−6.93238	−	34.8514i	−0.223393	−	1.12307i
$964$		0			0
$965$	25.0450	−	16.7346i	0.806228	−	0.538704i
$966$		0			0
$967$	49.7556	+	20.6095i	1.60003	+	0.662755i	0.991420	−	0.130712i	$-0.0417265\pi$
$967$	49.7556	+	20.6095i	1.60003	+	0.662755i	0.608612	+	0.793468i	$0.291726\pi$
$968$		0			0
$969$	0.00568130	−	0.00235327i	0.000182510	−	7.55980e-5i
$970$		0			0
$971$	20.0337	+	3.98496i	0.642913	+	0.127883i	0.505771	−	0.862668i	$-0.331208\pi$
$971$	20.0337	+	3.98496i	0.642913	+	0.127883i	0.137142	+	0.990551i	$0.456208\pi$
$972$		0			0
$973$	−11.6103	−	7.75773i	−0.372208	−	0.248701i
$974$		0			0
$975$	−18.0827	−	18.0827i	−0.579110	−	0.579110i
$976$		0			0
$977$	8.15858	−	8.15858i	0.261016	−	0.261016i	−0.564451	−	0.825467i	$-0.690912\pi$
$977$	8.15858	−	8.15858i	0.261016	−	0.261016i	0.825467	+	0.564451i	$0.190912\pi$
$978$		0			0
$979$	−11.3101	+	16.9268i	−0.361473	+	0.540983i
$980$		0			0
$981$	−6.73746	+	33.8715i	−0.215111	+	1.08143i
$982$		0			0
$983$	−3.28561	−	7.93217i	−0.104795	−	0.252997i	0.862781	−	0.505578i	$-0.168721\pi$
$983$	−3.28561	−	7.93217i	−0.104795	−	0.252997i	−0.967576	+	0.252581i	$0.918721\pi$
$984$		0			0
$985$	15.2921	−	36.9185i	0.487248	−	1.17632i
$986$		0			0
$987$	0.792336	+	1.18581i	0.0252203	+	0.0377449i
$988$		0			0
$989$	−2.44644	+	0.486627i	−0.0777923	+	0.0154738i
$990$		0			0
$991$		−	21.7977i		−	0.692427i	−0.938156	−	0.346213i	$-0.887467\pi$
$991$		−	21.7977i		−	0.692427i	0.938156	−	0.346213i	$-0.112533\pi$
$992$		0			0
$993$			20.0539i			0.636391i
$994$		0			0
$995$	−2.78441	+	0.553853i	−0.0882716	+	0.0175583i
$996$		0			0
$997$	−8.81651	−	13.1948i	−0.279222	−	0.417885i	0.665178	−	0.746685i	$-0.268356\pi$
$997$	−8.81651	−	13.1948i	−0.279222	−	0.417885i	−0.944400	+	0.328800i	$0.893356\pi$
$998$		0			0
$999$	−4.27925	+	10.3310i	−0.135390	+	0.326859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.a.97.5		56
4.3	odd	2		512.2.i.b.97.3		56
8.3	odd	2		64.2.i.a.21.7	✓	56
8.5	even	2		256.2.i.a.177.3		56
24.11	even	2		576.2.bd.a.469.1		56
64.3	odd	16		512.2.i.b.417.3		56
64.29	even	16		256.2.i.a.81.3		56
64.35	odd	16		64.2.i.a.61.7	yes	56
64.61	even	16	inner	512.2.i.a.417.5		56
192.35	even	16		576.2.bd.a.253.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.7	✓	56	8.3	odd	2
64.2.i.a.61.7	yes	56	64.35	odd	16
256.2.i.a.81.3		56	64.29	even	16
256.2.i.a.177.3		56	8.5	even	2
512.2.i.a.97.5		56	1.1	even	1	trivial
512.2.i.a.417.5		56	64.61	even	16	inner
512.2.i.b.97.3		56	4.3	odd	2
512.2.i.b.417.3		56	64.3	odd	16
576.2.bd.a.253.1		56	192.35	even	16
576.2.bd.a.469.1		56	24.11	even	2

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.152968 + 0.769021i) q^{3} +(2.78737 - 1.86246i) q^{5} +(3.13672 + 1.29927i) q^{7} +(2.20364 - 0.912779i) q^{9} +O(q^{10})\)	\(q+(0.152968 + 0.769021i) q^{3} +(2.78737 - 1.86246i) q^{5} +(3.13672 + 1.29927i) q^{7} +(2.20364 - 0.912779i) q^{9} +(-1.79402 - 0.356853i) q^{11} +(-4.34710 - 2.90464i) q^{13} +(1.85865 + 1.85865i) q^{15} +(-1.16196 + 1.16196i) q^{17} +(-0.00265155 + 0.00396832i) q^{19} +(-0.519350 + 2.61095i) q^{21} +(-1.78945 - 4.32013i) q^{23} +(2.38726 - 5.76336i) q^{25} +(2.34588 + 3.51086i) q^{27} +(1.70191 - 0.338531i) q^{29} +9.42685i q^{31} -1.43423i q^{33} +(11.1630 - 2.22047i) q^{35} +(1.47130 + 2.20195i) q^{37} +(1.56876 - 3.78733i) q^{39} +(0.497436 + 1.20092i) q^{41} +(0.104068 - 0.523183i) q^{43} +(4.44236 - 6.64846i) q^{45} +(0.378819 - 0.378819i) q^{47} +(3.20113 + 3.20113i) q^{49} +(-1.07132 - 0.715832i) q^{51} +(3.63594 + 0.723233i) q^{53} +(-5.66523 + 2.34662i) q^{55} +(-0.00345732 - 0.00143207i) q^{57} +(-11.1857 + 7.47403i) q^{59} +(1.29788 + 6.52488i) q^{61} +8.09815 q^{63} -17.5268 q^{65} +(1.46964 + 7.38837i) q^{67} +(3.04854 - 2.03697i) q^{69} +(-5.03495 - 2.08554i) q^{71} +(-4.53632 + 1.87901i) q^{73} +(4.79732 + 0.954247i) q^{75} +(-5.16369 - 3.45027i) q^{77} +(-11.3984 - 11.3984i) q^{79} +(2.71871 - 2.71871i) q^{81} +(3.35370 - 5.01916i) q^{83} +(-1.07471 + 5.40294i) q^{85} +(0.520675 + 1.25702i) q^{87} +(4.25907 - 10.2823i) q^{89} +(-9.86171 - 14.7591i) q^{91} +(-7.24944 + 1.44200i) q^{93} +0.0159996i q^{95} +12.2846i q^{97} +(-4.27911 + 0.851169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q - 8 q^{3} + 8 q^{5} + 8 q^{7} - 8 q^{9} - 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} - 8 q^{19} + 8 q^{21} + 8 q^{23} - 8 q^{25} - 8 q^{27} + 8 q^{29} - 8 q^{35} + 8 q^{37} + 8 q^{39} - 8 q^{41} - 8 q^{43} + 8 q^{45} + 8 q^{47} - 8 q^{49} + 24 q^{51} + 8 q^{53} - 56 q^{55} - 8 q^{57} + 56 q^{59} + 8 q^{61} - 64 q^{63} - 16 q^{65} + 72 q^{67} + 8 q^{69} - 56 q^{71} - 8 q^{73} + 56 q^{75} + 8 q^{77} - 24 q^{79} - 8 q^{81} - 8 q^{83} + 8 q^{85} + 8 q^{87} - 8 q^{89} - 8 q^{91} - 16 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 + 8 * q^5 + 8 * q^7 - 8 * q^9 - 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 - 8 * q^19 + 8 * q^21 + 8 * q^23 - 8 * q^25 - 8 * q^27 + 8 * q^29 - 8 * q^35 + 8 * q^37 + 8 * q^39 - 8 * q^41 - 8 * q^43 + 8 * q^45 + 8 * q^47 - 8 * q^49 + 24 * q^51 + 8 * q^53 - 56 * q^55 - 8 * q^57 + 56 * q^59 + 8 * q^61 - 64 * q^63 - 16 * q^65 + 72 * q^67 + 8 * q^69 - 56 * q^71 - 8 * q^73 + 56 * q^75 + 8 * q^77 - 24 * q^79 - 8 * q^81 - 8 * q^83 + 8 * q^85 + 8 * q^87 - 8 * q^89 - 8 * q^91 - 16 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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