LMFDB - Embedded newform 459.2.y.a.260.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(44,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([40, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.44"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$459 = 3^{3} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	459.y (of order $48$ , degree $16$ , not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			260.4
Character	$\chi$	$=$	459.260
Dual form			459.2.y.a.143.4

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40306 - 1.07661i) q^{2} +(0.291859 + 1.08923i) q^{4} +(-0.349197 + 0.398183i) q^{5} +(0.487217 - 0.427278i) q^{7} +(-0.590386 + 1.42532i) q^{8} +(0.918630 - 0.182727i) q^{10} +(0.244047 + 0.0159957i) q^{11} +(-5.52628 + 1.48076i) q^{13} +(-1.14360 + 0.0749557i) q^{14} +(4.31601 - 2.49185i) q^{16} +(-1.99496 + 3.60834i) q^{17} +(-0.687279 - 1.65924i) q^{19} +(-0.535630 - 0.264144i) q^{20} +(-0.325191 - 0.285185i) q^{22} +(-4.02242 + 1.98364i) q^{23} +(0.616020 + 4.67914i) q^{25} +(9.34790 + 3.87203i) q^{26} +(0.607604 + 0.405988i) q^{28} +(-0.725663 + 0.246329i) q^{29} +(0.156475 + 2.38734i) q^{31} +(-5.67926 - 0.747688i) q^{32} +(6.68381 - 2.91493i) q^{34} +0.343205i q^{35} +(3.47283 + 5.19746i) q^{37} +(-0.822052 + 3.06794i) q^{38} +(-0.361376 - 0.732799i) q^{40} +(-0.0906083 + 0.266923i) q^{41} +(-7.58989 + 0.999228i) q^{43} +(0.0538043 + 0.270493i) q^{44} +(7.77930 + 1.54740i) q^{46} +(7.65665 + 2.05159i) q^{47} +(-0.858869 + 6.52376i) q^{49} +(4.17327 - 7.22832i) q^{50} +(-3.22579 - 5.58724i) q^{52} +(6.47242 - 2.68096i) q^{53} +(-0.0915896 + 0.0915896i) q^{55} +(0.321361 + 0.946698i) q^{56} +(1.28335 + 0.435638i) q^{58} +(4.10474 + 5.34940i) q^{59} +(-5.55704 - 6.33659i) q^{61} +(2.35068 - 3.51804i) q^{62} +(0.115352 + 0.115352i) q^{64} +(1.34015 - 2.71755i) q^{65} +(2.60816 + 1.50582i) q^{67} +(-4.51257 - 1.11985i) q^{68} +(0.369497 - 0.481538i) q^{70} +(-7.48130 + 4.99884i) q^{71} +(-1.88124 + 9.45764i) q^{73} +(0.723024 - 11.0312i) q^{74} +(1.60671 - 1.23287i) q^{76} +(0.125738 - 0.0964824i) q^{77} +(0.344325 - 5.25338i) q^{79} +(-0.514926 + 2.58871i) q^{80} +(0.414500 - 0.276960i) q^{82} +(0.612737 - 0.798534i) q^{83} +(-0.740144 - 2.05438i) q^{85} +(11.7248 + 6.76934i) q^{86} +(-0.166881 + 0.338401i) q^{88} +(-10.5558 - 10.5558i) q^{89} +(-2.05980 + 3.08271i) q^{91} +(-3.33463 - 3.80241i) q^{92} +(-8.53398 - 11.1217i) q^{94} +(0.900676 + 0.305738i) q^{95} +(1.32665 + 3.90819i) q^{97} +(8.22856 - 8.22856i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100})$ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$ .

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{16}\right)$

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

)

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

$2$	−1.40306	−	1.07661i	−0.992113	−	0.761275i	−0.0209719	−	0.999780i	$-0.506676\pi$
$2$	−1.40306	−	1.07661i	−0.992113	−	0.761275i	−0.971141	+	0.238505i	$0.923343\pi$
$3$		0			0
$3$		0			0
$4$	0.291859	+	1.08923i	0.145930	+	0.544617i
$5$	−0.349197	+	0.398183i	−0.156166	+	0.178073i	−0.824632	−	0.565670i	$-0.808618\pi$
$5$	−0.349197	+	0.398183i	−0.156166	+	0.178073i	0.668466	+	0.743742i	$0.266951\pi$
$6$		0			0
$7$	0.487217	−	0.427278i	0.184151	−	0.161496i	−0.562307	−	0.826928i	$-0.690086\pi$
$7$	0.487217	−	0.427278i	0.184151	−	0.161496i	0.746458	+	0.665433i	$0.231753\pi$
$8$	−0.590386	+	1.42532i	−0.208733	+	0.503926i
$9$		0			0
$10$	0.918630	−	0.182727i	0.290496	−	0.0577833i
$11$	0.244047	+	0.0159957i	0.0735829	+	0.00482288i	0.102150	−	0.994769i	$-0.467428\pi$
$11$	0.244047	+	0.0159957i	0.0735829	+	0.00482288i	−0.0285672	+	0.999592i	$0.509094\pi$
$12$		0			0
$13$	−5.52628	+	1.48076i	−1.53271	+	0.410690i	−0.923903	−	0.382626i	$-0.875020\pi$
$13$	−5.52628	+	1.48076i	−1.53271	+	0.410690i	−0.608811	+	0.793315i	$0.708353\pi$
$14$	−1.14360	+	0.0749557i	−0.305641	+	0.0200328i
$15$		0			0
$16$	4.31601	−	2.49185i	1.07900	−	0.622963i
$17$	−1.99496	+	3.60834i	−0.483849	+	0.875151i
$17$	−1.99496	+	3.60834i	−0.483849	+	0.875151i
$18$		0			0
$19$	−0.687279	−	1.65924i	−0.157673	−	0.380656i	0.825226	−	0.564803i	$-0.191048\pi$
$19$	−0.687279	−	1.65924i	−0.157673	−	0.380656i	−0.982899	+	0.184147i	$0.941048\pi$
$20$	−0.535630	−	0.264144i	−0.119771	−	0.0590643i
$21$		0			0
$22$	−0.325191	−	0.285185i	−0.0693310	−	0.0608017i
$23$	−4.02242	+	1.98364i	−0.838733	+	0.413617i	−0.810326	−	0.585979i	$-0.800710\pi$
$23$	−4.02242	+	1.98364i	−0.838733	+	0.413617i	−0.0284068	+	0.999596i	$0.509043\pi$
$24$		0			0
$25$	0.616020	+	4.67914i	0.123204	+	0.935827i
$26$	9.34790	+	3.87203i	1.83327	+	0.759367i
$27$		0			0
$28$	0.607604	+	0.405988i	0.114826	+	0.0767245i
$29$	−0.725663	+	0.246329i	−0.134752	+	0.0457422i	−0.388001	−	0.921659i	$-0.626834\pi$
$29$	−0.725663	+	0.246329i	−0.134752	+	0.0457422i	0.253249	+	0.967401i	$0.418501\pi$
$30$		0			0
$31$	0.156475	+	2.38734i	0.0281037	+	0.428779i	0.988608	+	0.150514i	$0.0480928\pi$
$31$	0.156475	+	2.38734i	0.0281037	+	0.428779i	−0.960504	+	0.278265i	$0.910241\pi$
$32$	−5.67926	−	0.747688i	−1.00396	−	0.132174i
$33$		0			0
$34$	6.68381	−	2.91493i	1.14626	−	0.499906i
$35$			0.343205i			0.0580123i
$36$		0			0
$37$	3.47283	+	5.19746i	0.570930	+	0.854457i	0.998779	−	0.0493930i	$-0.0157287\pi$
$37$	3.47283	+	5.19746i	0.570930	+	0.854457i	−0.427849	+	0.903850i	$0.640729\pi$
$38$	−0.822052	+	3.06794i	−0.133354	+	0.497686i
$39$		0			0
$40$	−0.361376	−	0.732799i	−0.0571386	−	0.115866i
$41$	−0.0906083	+	0.266923i	−0.0141506	+	0.0416864i	−0.953776	−	0.300518i	$-0.902840\pi$
$41$	−0.0906083	+	0.266923i	−0.0141506	+	0.0416864i	0.939625	+	0.342205i	$0.111174\pi$
$42$		0			0
$43$	−7.58989	+	0.999228i	−1.15745	+	0.152381i	−0.684705	−	0.728820i	$-0.740069\pi$
$43$	−7.58989	+	0.999228i	−1.15745	+	0.152381i	−0.472742	+	0.881201i	$0.656736\pi$
$44$	0.0538043	+	0.270493i	0.00811130	+	0.0407783i
$45$		0			0
$46$	7.77930	+	1.54740i	1.14699	+	0.228151i
$47$	7.65665	+	2.05159i	1.11684	+	0.299256i	0.769603	−	0.638523i	$-0.220454\pi$
$47$	7.65665	+	2.05159i	1.11684	+	0.299256i	0.347234	+	0.937778i	$0.387121\pi$
$48$		0			0
$49$	−0.858869	+	6.52376i	−0.122696	+	0.931966i
$50$	4.17327	−	7.22832i	0.590190	−	1.02224i
$51$		0			0
$52$	−3.22579	−	5.58724i	−0.447337	−	0.774810i
$53$	6.47242	−	2.68096i	0.889055	−	0.368259i	0.109053	−	0.994036i	$-0.465218\pi$
$53$	6.47242	−	2.68096i	0.889055	−	0.368259i	0.780002	+	0.625777i	$0.215218\pi$
$54$		0			0
$55$	−0.0915896	+	0.0915896i	−0.0123499	+	0.0123499i
$56$	0.321361	+	0.946698i	0.0429436	+	0.126508i
$57$		0			0
$58$	1.28335	+	0.435638i	0.168512	+	0.0572021i
$59$	4.10474	+	5.34940i	0.534392	+	0.696433i	0.980046	−	0.198772i	$-0.0636954\pi$
$59$	4.10474	+	5.34940i	0.534392	+	0.696433i	−0.445654	+	0.895205i	$0.647029\pi$
$60$		0			0
$61$	−5.55704	−	6.33659i	−0.711506	−	0.811317i	0.277259	−	0.960795i	$-0.410574\pi$
$61$	−5.55704	−	6.33659i	−0.711506	−	0.811317i	−0.988765	+	0.149478i	$0.952241\pi$
$62$	2.35068	−	3.51804i	0.298537	−	0.446792i
$63$		0			0
$64$	0.115352	+	0.115352i	0.0144191	+	0.0144191i
$65$	1.34015	−	2.71755i	0.166225	−	0.337070i
$66$		0			0
$67$	2.60816	+	1.50582i	0.318637	+	0.183965i	0.650785	−	0.759262i	$-0.274440\pi$
$67$	2.60816	+	1.50582i	0.318637	+	0.183965i	−0.332148	+	0.943227i	$0.607773\pi$
$68$	−4.51257	−	1.11985i	−0.547230	−	0.135802i
$69$		0			0
$70$	0.369497	−	0.481538i	0.0441633	−	0.0575547i
$71$	−7.48130	+	4.99884i	−0.887867	+	0.593254i	−0.913690	−	0.406413i	$-0.866779\pi$
$71$	−7.48130	+	4.99884i	−0.887867	+	0.593254i	0.0258226	+	0.999667i	$0.491779\pi$
$72$		0			0
$73$	−1.88124	+	9.45764i	−0.220183	+	1.10693i	0.699609	+	0.714526i	$0.253358\pi$
$73$	−1.88124	+	9.45764i	−0.220183	+	1.10693i	−0.919792	+	0.392407i	$0.871642\pi$
$74$	0.723024	−	11.0312i	0.0840499	−	1.28235i
$75$		0			0
$76$	1.60671	−	1.23287i	0.184302	−	0.141420i
$77$	0.125738	−	0.0964824i	0.0143292	−	0.0109952i
$78$		0			0
$79$	0.344325	−	5.25338i	0.0387396	−	0.591052i	−0.933723	−	0.357995i	$-0.883460\pi$
$79$	0.344325	−	5.25338i	0.0387396	−	0.591052i	0.972463	−	0.233057i	$-0.0748729\pi$
$80$	−0.514926	+	2.58871i	−0.0575705	+	0.289427i
$81$		0			0
$82$	0.414500	−	0.276960i	0.0457739	−	0.0305851i
$83$	0.612737	−	0.798534i	0.0672566	−	0.0876505i	−0.758514	−	0.651657i	$-0.774074\pi$
$83$	0.612737	−	0.798534i	0.0672566	−	0.0876505i	0.825770	+	0.564007i	$0.190741\pi$
$84$		0			0
$85$	−0.740144	−	2.05438i	−0.0802799	−	0.222829i
$86$	11.7248	+	6.76934i	1.26432	+	0.729957i
$87$		0			0
$88$	−0.166881	+	0.338401i	−0.0177896	+	0.0360737i
$89$	−10.5558	−	10.5558i	−1.11891	−	1.11891i	−0.991901	−	0.127011i	$-0.959462\pi$
$89$	−10.5558	−	10.5558i	−1.11891	−	1.11891i	−0.127011	−	0.991901i	$-0.540538\pi$
$90$		0			0
$91$	−2.05980	+	3.08271i	−0.215926	+	0.323156i
$92$	−3.33463	−	3.80241i	−0.347659	−	0.396429i
$93$		0			0
$94$	−8.53398	−	11.1217i	−0.880213	−	1.14712i
$95$	0.900676	+	0.305738i	0.0924074	+	0.0313681i
$96$		0			0
$97$	1.32665	+	3.90819i	0.134701	+	0.396817i	0.993261	−	0.115896i	$-0.0369739\pi$
$97$	1.32665	+	3.90819i	0.134701	+	0.396817i	−0.858560	+	0.512713i	$0.828641\pi$
$98$	8.22856	−	8.22856i	0.831210	−	0.831210i
$99$		0			0
$100$	−4.91688	+	2.03664i	−0.491688	+	0.203664i
$101$	−2.89538	−	5.01494i	−0.288101	−	0.499006i	0.685255	−	0.728303i	$-0.259691\pi$
$101$	−2.89538	−	5.01494i	−0.288101	−	0.499006i	−0.973356	+	0.229297i	$0.926357\pi$
$102$		0			0
$103$	−1.57613	+	2.72994i	−0.155301	+	0.268989i	−0.933169	−	0.359439i	$-0.882968\pi$
$103$	−1.57613	+	2.72994i	−0.155301	+	0.268989i	0.777868	+	0.628428i	$0.216301\pi$
$104$	1.15208	−	8.75093i	0.112971	−	0.858100i
$105$		0			0
$106$	−11.9675	−	3.20669i	−1.16239	−	0.311461i
$107$	−18.5391	−	3.68766i	−1.79225	−	0.356500i	−0.816831	−	0.576877i	$-0.804271\pi$
$107$	−18.5391	−	3.68766i	−1.79225	−	0.356500i	−0.975415	+	0.220378i	$0.929271\pi$
$108$		0			0
$109$	−3.09723	−	15.5708i	−0.296661	−	1.49141i	−0.785402	−	0.618986i	$-0.787544\pi$
$109$	−3.09723	−	15.5708i	−0.296661	−	1.49141i	0.488741	−	0.872429i	$-0.337456\pi$
$110$	0.227112	−	0.0298998i	0.0216542	−	0.00285084i
$111$		0			0
$112$	1.03812	−	3.05821i	0.0980933	−	0.288973i
$113$	−7.96981	−	16.1612i	−0.749736	−	1.52031i	−0.850832	−	0.525438i	$-0.823901\pi$
$113$	−7.96981	−	16.1612i	−0.749736	−	1.52031i	0.101095	−	0.994877i	$-0.467765\pi$
$114$		0			0
$115$	0.614767	−	2.29434i	0.0573273	−	0.213948i
$116$	−0.480102	−	0.718523i	−0.0445763	−	0.0667132i
$117$		0			0
$118$		−	11.9247i		−	1.09776i
$119$	0.569784	+	2.61045i	0.0522320	+	0.239299i
$120$		0			0
$121$	−10.8466	−	1.42798i	−0.986054	−	0.129816i
$122$	0.974851	+	14.8734i	0.0882589	+	1.34657i
$123$		0			0
$124$	−2.55470	+	0.867205i	−0.229419	+	0.0778773i
$125$	−4.28004	−	2.85983i	−0.382819	−	0.255791i
$126$		0			0
$127$	16.7213	+	6.92619i	1.48377	+	0.614600i	0.969952	−	0.243297i	$-0.0782289\pi$
$127$	16.7213	+	6.92619i	1.48377	+	0.614600i	0.513823	+	0.857896i	$0.328229\pi$
$128$	1.45772	+	11.0725i	0.128845	+	0.978678i
$129$		0			0
$130$	−4.80603	+	2.37007i	−0.421517	+	0.207869i
$131$	10.0771	+	8.83742i	0.880444	+	0.772129i	0.974723	−	0.223417i	$-0.0717211\pi$
$131$	10.0771	+	8.83742i	0.880444	+	0.772129i	−0.0942786	+	0.995546i	$0.530054\pi$
$132$		0			0
$133$	−1.04381	−	0.514750i	−0.0905098	−	0.0446345i
$134$	−2.03823	−	4.92071i	−0.176076	−	0.425085i
$135$		0			0
$136$	−3.96524	−	4.97377i	−0.340016	−	0.426497i
$137$	−17.9198	+	10.3460i	−1.53099	+	0.883918i	−0.531675	+	0.846948i	$0.678437\pi$
$137$	−17.9198	+	10.3460i	−1.53099	+	0.883918i	−0.999316	+	0.0369701i	$0.988229\pi$
$138$		0			0
$139$	13.2779	−	0.870277i	1.12621	−	0.0738159i	0.509113	−	0.860700i	$-0.329974\pi$
$139$	13.2779	−	0.870277i	1.12621	−	0.0738159i	0.617101	+	0.786884i	$0.288307\pi$
$140$	−0.373831	+	0.100168i	−0.0315945	+	0.00846571i
$141$		0			0
$142$	15.8785	+	1.04073i	1.33249	+	0.0873363i
$143$	−1.37236	+	0.272979i	−0.114762	+	0.0228276i
$144$		0			0
$145$	0.155315	−	0.374964i	0.0128982	−	0.0311391i
$146$	12.8216	−	11.2443i	1.06113	−	0.930583i
$147$		0			0
$148$	−4.64767	+	5.29965i	−0.382036	+	0.435629i
$149$	−0.525508	−	1.96122i	−0.0430513	−	0.160670i	0.941054	−	0.338257i	$-0.109837\pi$
$149$	−0.525508	−	1.96122i	−0.0430513	−	0.160670i	−0.984105	+	0.177588i	$0.943171\pi$
$150$		0			0
$151$	−19.0924	−	14.6501i	−1.55371	−	1.19221i	−0.900353	−	0.435160i	$-0.856692\pi$
$151$	−19.0924	−	14.6501i	−1.55371	−	1.19221i	−0.653361	−	0.757047i	$-0.726641\pi$
$152$	2.77071			0.224734
$153$		0			0
$154$	−0.280292			−0.0225866
$155$	−1.00524	−	0.771346i	−0.0807427	−	0.0619560i
$156$		0			0
$157$	−3.21662	−	12.0046i	−0.256714	−	0.958070i	−0.967129	−	0.254287i	$-0.918159\pi$
$157$	−3.21662	−	12.0046i	−0.256714	−	0.958070i	0.710415	−	0.703783i	$-0.248507\pi$
$158$	−6.13893	+	7.00011i	−0.488387	+	0.556899i
$159$		0			0
$160$	2.28090	−	2.00029i	0.180321	−	0.158137i
$161$	−1.11223	+	2.68515i	−0.0876557	+	0.211620i
$162$		0			0
$163$	−9.85980	+	1.96124i	−0.772279	+	0.153616i	−0.565474	−	0.824766i	$-0.691307\pi$
$163$	−9.85980	+	1.96124i	−0.772279	+	0.153616i	−0.206805	+	0.978382i	$0.566307\pi$
$164$	−0.317187	−	0.0207895i	−0.0247681	−	0.00162339i
$165$		0			0
$166$	−1.71941	+	0.460715i	−0.133452	+	0.0357584i
$167$	13.0470	−	0.855149i	1.00961	−	0.0661734i	0.448389	−	0.893839i	$-0.351998\pi$
$167$	13.0470	−	0.855149i	1.00961	−	0.0661734i	0.561222	+	0.827665i	$0.310331\pi$
$168$		0			0
$169$	17.0888	−	9.86622i	1.31452	−	0.758940i
$170$	−1.17329	+	3.67926i	−0.0899874	+	0.282187i
$171$		0			0
$172$	−3.30357	−	7.97553i	−0.251895	−	0.608128i
$173$	12.8042	+	6.31436i	0.973489	+	0.480072i	0.858231	−	0.513264i	$-0.171564\pi$
$173$	12.8042	+	6.31436i	0.973489	+	0.480072i	0.115258	+	0.993336i	$0.463230\pi$
$174$		0			0
$175$	2.29942	+	2.01654i	0.173820	+	0.152436i
$176$	1.09317	−	0.539091i	0.0824007	−	0.0406355i
$177$		0			0
$178$	3.44599	+	26.1749i	0.258288	+	1.96189i
$179$	13.5833	+	5.62640i	1.01527	+	0.420537i	0.827373	−	0.561653i	$-0.189834\pi$
$179$	13.5833	+	5.62640i	1.01527	+	0.420537i	0.187893	+	0.982190i	$0.439834\pi$
$180$		0			0
$181$	10.2817	+	6.86999i	0.764231	+	0.510643i	0.875541	−	0.483143i	$-0.160505\pi$
$181$	10.2817	+	6.86999i	0.764231	+	0.510643i	−0.111311	+	0.993786i	$0.535505\pi$
$182$	6.20888	−	2.10763i	0.460233	−	0.156228i
$183$		0			0
$184$	−0.452535	−	6.90435i	−0.0333613	−	0.508995i
$185$	−3.28224	−	0.432115i	−0.241315	−	0.0317697i
$186$		0			0
$187$	−0.544582	+	0.848694i	−0.0398238	+	0.0620626i
$188$			8.93865i			0.651918i
$189$		0			0
$190$	−0.934543	−	1.39864i	−0.0677989	−	0.101468i
$191$	−4.57355	+	17.0687i	−0.330930	+	1.23505i	0.577284	+	0.816543i	$0.304112\pi$
$191$	−4.57355	+	17.0687i	−0.330930	+	1.23505i	−0.908215	+	0.418505i	$0.862554\pi$
$192$		0			0
$193$	3.05315	+	6.19118i	0.219771	+	0.445651i	0.978637	−	0.205595i	$-0.0659131\pi$
$193$	3.05315	+	6.19118i	0.219771	+	0.445651i	−0.758866	+	0.651247i	$0.774246\pi$
$194$	2.34621	−	6.91171i	0.168448	−	0.496232i
$195$		0			0
$196$	−7.35657	+	0.968510i	−0.525469	+	0.0691793i
$197$	−2.57804	−	12.9607i	−0.183678	−	0.923410i	−0.957153	−	0.289583i	$-0.906483\pi$
$197$	−2.57804	−	12.9607i	−0.183678	−	0.923410i	0.773475	−	0.633827i	$-0.218517\pi$
$198$		0			0
$199$	13.8219	+	2.74935i	0.979809	+	0.194896i	0.658914	−	0.752219i	$-0.271016\pi$
$199$	13.8219	+	2.74935i	0.979809	+	0.194896i	0.320895	+	0.947115i	$0.396016\pi$
$200$	−7.03295	−	1.88447i	−0.497305	−	0.133252i
$201$		0			0
$202$	−1.33673	+	10.1535i	−0.0940518	+	0.714394i
$203$	−0.248304	+	0.430075i	−0.0174275	+	0.0301854i
$204$		0			0
$205$	−0.0746442	−	0.129287i	−0.00521337	−	0.00902983i
$206$	5.15047	−	2.13340i	0.358850	−	0.148641i
$207$		0			0
$208$	−20.1617	+	20.1617i	−1.39796	+	1.39796i
$209$	−0.141188	−	0.415926i	−0.00976616	−	0.0287702i
$210$		0			0
$211$	26.9539	+	9.14962i	1.85558	+	0.629886i	0.992091	+	0.125524i	$0.0400611\pi$
$211$	26.9539	+	9.14962i	1.85558	+	0.629886i	0.863492	+	0.504362i	$0.168272\pi$
$212$	4.80923	+	6.26751i	0.330299	+	0.430454i
$213$		0			0
$214$	22.0414	+	25.1333i	1.50672	+	1.71808i
$215$	2.25249	−	3.37109i	0.153619	−	0.229906i
$216$		0			0
$217$	1.09629	+	1.09629i	0.0744213	+	0.0744213i
$218$	−12.4180	+	25.1813i	−0.841056	+	1.70549i
$219$		0			0
$220$	−0.126494	−	0.0730312i	−0.00852821	−	0.00492376i
$221$	5.68163	−	22.8948i	0.382188	−	1.54007i
$222$		0			0
$223$	5.34259	−	6.96260i	0.357766	−	0.466250i	−0.579445	−	0.815011i	$-0.696731\pi$
$223$	5.34259	−	6.96260i	0.357766	−	0.466250i	0.937212	+	0.348761i	$0.113397\pi$
$224$	−3.08650	+	2.06233i	−0.206225	+	0.137795i
$225$		0			0
$226$	−6.21709	+	31.2554i	−0.413555	+	2.07908i
$227$	−0.397273	+	6.06121i	−0.0263679	+	0.402297i	0.964191	+	0.265209i	$0.0854409\pi$
$227$	−0.397273	+	6.06121i	−0.0263679	+	0.402297i	−0.990559	+	0.137088i	$0.956226\pi$
$228$		0			0
$229$	−4.61365	+	3.54018i	−0.304879	+	0.233942i	−0.749857	−	0.661599i	$-0.769878\pi$
$229$	−4.61365	+	3.54018i	−0.304879	+	0.233942i	0.444979	+	0.895541i	$0.353211\pi$
$230$	−3.33265	+	2.55724i	−0.219749	+	0.168619i
$231$		0			0
$232$	0.0773236	−	1.17973i	0.00507654	−	0.0774531i
$233$	−1.43162	+	7.19722i	−0.0937883	+	0.471506i	0.905135	+	0.425123i	$0.139769\pi$
$233$	−1.43162	+	7.19722i	−0.0937883	+	0.471506i	−0.998924	+	0.0463824i	$0.985231\pi$
$234$		0			0
$235$	−3.49059	+	2.33234i	−0.227701	+	0.152145i
$236$	−4.62874	+	6.03229i	−0.301305	+	0.392669i
$237$		0			0
$238$	2.01098	−	4.27605i	0.130352	−	0.277175i
$239$	−8.24749	−	4.76169i	−0.533486	−	0.308008i	0.208949	−	0.977927i	$-0.432996\pi$
$239$	−8.24749	−	4.76169i	−0.533486	−	0.308008i	−0.742435	+	0.669918i	$0.766329\pi$
$240$		0			0
$241$	−11.8861	+	24.1026i	−0.765651	+	1.55259i	0.0663392	+	0.997797i	$0.478868\pi$
$241$	−11.8861	+	24.1026i	−0.765651	+	1.55259i	−0.831990	+	0.554790i	$0.812799\pi$
$242$	13.6810	+	13.6810i	0.879451	+	0.879451i
$243$		0			0
$244$	5.28015	−	7.90231i	0.338027	−	0.505893i
$245$	−2.29773	−	2.62006i	−0.146797	−	0.167390i
$246$		0			0
$247$	6.25504	+	8.15172i	0.397999	+	0.518682i
$248$	−3.49510	−	1.18643i	−0.221939	−	0.0753382i
$249$		0			0
$250$	2.92624	+	8.62043i	0.185072	+	0.545204i
$251$	11.7486	−	11.7486i	0.741566	−	0.741566i	−0.231313	−	0.972879i	$-0.574302\pi$
$251$	11.7486	−	11.7486i	0.741566	−	0.741566i	0.972879	+	0.231313i	$0.0743023\pi$
$252$		0			0
$253$	−1.01339	+	0.419760i	−0.0637112	+	0.0263901i
$254$	−16.0042	−	27.7201i	−1.00419	−	1.73931i
$255$		0			0
$256$	10.0386	−	17.3873i	0.627410	−	1.08671i
$257$	0.957479	−	7.27278i	0.0597259	−	0.453663i	−0.935285	−	0.353896i	$-0.884857\pi$
$257$	0.957479	−	7.27278i	0.0597259	−	0.453663i	0.995011	−	0.0997676i	$-0.0318099\pi$
$258$		0			0
$259$	3.91278	+	1.04843i	0.243128	+	0.0651460i
$260$	3.35118	+	0.666591i	0.207831	+	0.0413402i
$261$		0			0
$262$	−4.62442	−	23.2485i	−0.285698	−	1.43630i
$263$	1.34211	−	0.176692i	0.0827582	−	0.0108953i	−0.0890334	−	0.996029i	$-0.528378\pi$
$263$	1.34211	−	0.176692i	0.0827582	−	0.0108953i	0.171792	+	0.985133i	$0.445044\pi$
$264$		0			0
$265$	−1.19264	+	3.51339i	−0.0732630	+	0.215826i
$266$	0.910345	+	1.84600i	0.0558168	+	0.113185i
$267$		0			0
$268$	−0.878975	+	3.28038i	−0.0536919	+	0.200381i
$269$	13.6075	+	20.3650i	0.829663	+	1.24168i	0.967914	+	0.251281i	$0.0808519\pi$
$269$	13.6075	+	20.3650i	0.829663	+	1.24168i	−0.138251	+	0.990397i	$0.544148\pi$
$270$		0			0
$271$		−	25.1760i		−	1.52933i	−0.644428	−	0.764665i	$-0.722904\pi$
$271$		−	25.1760i		−	1.52933i	0.644428	−	0.764665i	$-0.277096\pi$
$272$	0.381165	+	20.5448i	0.0231115	+	1.24571i
$273$		0			0
$274$	36.2811	+	4.77650i	2.19182	+	0.288559i
$275$	0.0754918	+	1.15178i	0.00455233	+	0.0694551i
$276$		0			0
$277$	7.77465	−	2.63914i	0.467134	−	0.158571i	−0.0779410	−	0.996958i	$-0.524835\pi$
$277$	7.77465	−	2.63914i	0.467134	−	0.158571i	0.545075	+	0.838387i	$0.316501\pi$
$278$	−19.5666	−	13.0740i	−1.17353	−	0.784125i
$279$		0			0
$280$	−0.489177	−	0.202624i	−0.0292339	−	0.0121091i
$281$	−1.08881	−	8.27035i	−0.0649531	−	0.493368i	−0.992742	−	0.120262i	$-0.961626\pi$
$281$	−1.08881	−	8.27035i	−0.0649531	−	0.493368i	0.927789	−	0.373105i	$-0.121707\pi$
$282$		0			0
$283$	−20.0534	+	9.88927i	−1.19205	+	0.587856i	−0.926520	−	0.376246i	$-0.877215\pi$
$283$	−20.0534	+	9.88927i	−1.19205	+	0.587856i	−0.265534	+	0.964102i	$0.585548\pi$
$284$	−7.62839	−	6.68992i	−0.452662	−	0.396974i
$285$		0			0
$286$	2.21939	+	1.09448i	0.131235	+	0.0647181i
$287$	0.0699045	+	0.168764i	0.00412633	+	0.00996185i
$288$		0			0
$289$	−9.04025	−	14.3970i	−0.531779	−	0.846883i
$290$	−0.621605	+	0.358884i	−0.0365019	+	0.0210744i
$291$		0			0
$292$	−10.8506	+	0.711188i	−0.634985	+	0.0416191i
$293$	−3.37684	+	0.904821i	−0.197277	+	0.0528602i	−0.356105	−	0.934446i	$-0.615895\pi$
$293$	−3.37684	+	0.904821i	−0.197277	+	0.0528602i	0.158827	+	0.987306i	$0.449229\pi$
$294$		0			0
$295$	−3.56340	−	0.233558i	−0.207469	−	0.0135983i
$296$	−9.45835	+	1.88138i	−0.549755	+	0.109353i
$297$		0			0
$298$	−1.37414	+	3.31748i	−0.0796020	+	0.192176i
$299$	19.2917	−	16.9184i	1.11567	−	0.978416i
$300$		0			0
$301$	−3.27097	+	3.72983i	−0.188536	+	0.214984i
$302$	11.0154	+	41.1099i	0.633863	+	2.36561i
$303$		0			0
$304$	−7.10089	−	5.44870i	−0.407264	−	0.312504i
$305$	4.46362			0.255586
$306$		0			0
$307$	1.87250			0.106869			0.0534347	−	0.998571i	$-0.482983\pi$
$307$	1.87250			0.106869			0.0534347	+	0.998571i	$0.482983\pi$
$308$	0.141790	+	0.108799i	0.00807922	+	0.00619940i
$309$		0			0
$310$	0.579973	+	2.16449i	0.0329403	+	0.122935i
$311$	−17.1493	+	19.5550i	−0.972448	+	1.10886i	0.0215832	+	0.999767i	$0.493129\pi$
$311$	−17.1493	+	19.5550i	−0.972448	+	1.10886i	−0.994031	+	0.109097i	$0.965204\pi$
$312$		0			0
$313$	−8.46470	+	7.42334i	−0.478453	+	0.419592i	−0.864305	−	0.502969i	$-0.832241\pi$
$313$	−8.46470	+	7.42334i	−0.478453	+	0.419592i	0.385851	+	0.922561i	$0.373908\pi$
$314$	−8.41110	+	20.3062i	−0.474666	+	1.14594i
$315$		0			0
$316$	5.82266	−	1.15820i	0.327550	−	0.0651538i
$317$	8.00334	+	0.524567i	0.449512	+	0.0294626i	0.288479	−	0.957486i	$-0.406851\pi$
$317$	8.00334	+	0.524567i	0.449512	+	0.0294626i	0.161034	+	0.986949i	$0.448517\pi$
$318$		0			0
$319$	−0.181036	+	0.0485084i	−0.0101361	+	0.00271595i
$320$	−0.0862120	+	0.00565064i	−0.00481940	+	0.000315880i
$321$		0			0
$322$	4.45137	−	2.57000i	0.248065	−	0.143221i
$323$	7.35820	+	0.830182i	0.409421	+	0.0461925i
$324$		0			0
$325$	−10.3330	−	24.9460i	−0.573171	−	1.38376i
$326$	15.9454	+	7.86339i	0.883132	+	0.435513i
$327$		0			0
$328$	−0.326957	−	0.286734i	−0.0180532	−	0.0158322i
$329$	4.60705	−	2.27194i	0.253995	−	0.125256i
$330$		0			0
$331$	1.00765	+	7.65388i	0.0553856	+	0.420695i	0.996567	+	0.0827930i	$0.0263840\pi$
$331$	1.00765	+	7.65388i	0.0553856	+	0.420695i	−0.941181	+	0.337902i	$0.890283\pi$
$332$	1.04862	+	0.434354i	0.0575507	+	0.0238383i
$333$		0			0
$334$	−19.2265	−	12.8467i	−1.05202	−	0.702940i
$335$	−1.51035	+	0.512695i	−0.0825193	+	0.0280115i
$336$		0			0
$337$	−1.78687	−	27.2624i	−0.0973370	−	1.48508i	−0.715272	−	0.698846i	$-0.753697\pi$
$337$	−1.78687	−	27.2624i	−0.0973370	−	1.48508i	0.617935	−	0.786229i	$-0.287970\pi$
$338$	−34.5986	−	4.55500i	−1.88192	−	0.247759i
$339$		0			0
$340$	2.02168	−	1.40578i	0.109641	−	0.0762391i
$341$			0.585126i			0.0316863i
$342$		0			0
$343$	4.88919	+	7.31720i	0.263992	+	0.395091i
$344$	3.05675	−	11.4079i	0.164809	−	0.615075i
$345$		0			0
$346$	−11.1671	−	22.6446i	−0.600345	−	1.21738i
$347$	2.97495	−	8.76392i	0.159704	−	0.470472i	−0.837394	−	0.546599i	$-0.815922\pi$
$347$	2.97495	−	8.76392i	0.159704	−	0.470472i	0.997098	+	0.0761272i	$0.0242555\pi$
$348$		0			0
$349$	3.03163	−	0.399122i	0.162280	−	0.0213645i	−0.0489486	−	0.998801i	$-0.515587\pi$
$349$	3.03163	−	0.399122i	0.162280	−	0.0213645i	0.211228	+	0.977437i	$0.432254\pi$
$350$	−1.05521	−	5.30490i	−0.0564034	−	0.283559i
$351$		0			0
$352$	−1.37405	−	0.273315i	−0.0732369	−	0.0145677i
$353$	−9.66444	−	2.58958i	−0.514386	−	0.137829i	−0.00771755	−	0.999970i	$-0.502457\pi$
$353$	−9.66444	−	2.58958i	−0.514386	−	0.137829i	−0.506669	+	0.862141i	$0.669123\pi$
$354$		0			0
$355$	0.621993	−	4.72451i	0.0330120	−	0.250751i
$356$	8.41692	−	14.5785i	0.446096	−	0.772661i
$357$		0			0
$358$	−13.0008	−	22.5181i	−0.687115	−	1.19012i
$359$	−14.8144	+	6.13631i	−0.781873	+	0.323862i	−0.737671	−	0.675160i	$-0.764074\pi$
$359$	−14.8144	+	6.13631i	−0.781873	+	0.323862i	−0.0442016	+	0.999023i	$0.514074\pi$
$360$		0			0
$361$	11.1543	−	11.1543i	0.587069	−	0.587069i
$362$	−7.02953	−	20.7083i	−0.369464	−	1.08841i
$363$		0			0
$364$	−3.95896	−	1.34389i	−0.207506	−	0.0704388i
$365$	−3.10895	−	4.05166i	−0.162730	−	0.212073i
$366$		0			0
$367$	12.8186	+	14.6169i	0.669128	+	0.762994i	0.982424	−	0.186661i	$-0.0597667\pi$
$367$	12.8186	+	14.6169i	0.669128	+	0.762994i	−0.313297	+	0.949655i	$0.601433\pi$
$368$	−12.4179	+	18.5847i	−0.647328	+	0.968794i
$369$		0			0
$370$	4.13996	+	4.13996i	0.215226	+	0.215226i
$371$	2.00795	−	4.07173i	0.104248	−	0.211394i
$372$		0			0
$373$	−4.29974	−	2.48246i	−0.222632	−	0.128537i	0.384536	−	0.923110i	$-0.374361\pi$
$373$	−4.29974	−	2.48246i	−0.222632	−	0.128537i	−0.607169	+	0.794573i	$0.707695\pi$
$374$	1.67779	−	0.604468i	0.0867565	−	0.0312563i
$375$		0			0
$376$	−7.44455	+	9.70193i	−0.383924	+	0.500339i
$377$	3.64546	−	2.43582i	0.187751	−	0.125451i
$378$		0			0
$379$	1.68309	−	8.46144i	0.0864543	−	0.434635i	−0.913179	−	0.407559i	$-0.866380\pi$
$379$	1.68309	−	8.46144i	0.0864543	−	0.434635i	0.999633	−	0.0270765i	$-0.00861977\pi$
$380$	−0.0701498	+	1.07028i	−0.00359861	+	0.0549042i
$381$		0			0
$382$	24.7932	−	19.0245i	1.26853	−	0.973379i
$383$	−21.2761	+	16.3257i	−1.08716	+	0.834204i	−0.986992	−	0.160767i	$-0.948603\pi$
$383$	−21.2761	+	16.3257i	−1.08716	+	0.834204i	−0.100164	+	0.994971i	$0.531937\pi$
$384$		0			0
$385$	−0.00548980	+	0.0837582i	−0.000279786	+	0.00426871i
$386$	2.38171	−	11.9736i	0.121226	−	0.609443i
$387$		0			0
$388$	−3.86974	+	2.58568i	−0.196456	+	0.131268i
$389$	13.9649	−	18.1995i	0.708051	−	0.922749i	−0.291376	−	0.956609i	$-0.594113\pi$
$389$	13.9649	−	18.1995i	0.708051	−	0.922749i	0.999427	+	0.0338592i	$0.0107798\pi$
$390$		0			0
$391$	0.866935	−	18.4716i	0.0438428	−	0.934147i
$392$	−8.79137	−	5.07570i	−0.444031	−	0.256362i
$393$		0			0
$394$	−10.3364	+	20.9601i	−0.520740	+	1.05596i
$395$	1.97157	+	1.97157i	0.0992005	+	0.0992005i
$396$		0			0
$397$	−9.09048	+	13.6049i	−0.456238	+	0.682809i	−0.986265	−	0.165172i	$-0.947182\pi$
$397$	−9.09048	+	13.6049i	−0.456238	+	0.682809i	0.530026	+	0.847981i	$0.322182\pi$
$398$	−16.4330	−	18.7382i	−0.823712	−	0.939263i
$399$		0			0
$400$	14.3185	+	18.6602i	0.715923	+	0.933009i
$401$	23.4876	+	7.97296i	1.17291	+	0.398150i	0.838830	−	0.544393i	$-0.183240\pi$
$401$	23.4876	+	7.97296i	1.17291	+	0.398150i	0.334083	+	0.942544i	$0.391573\pi$
$402$		0			0
$403$	−4.39981	−	12.9614i	−0.219170	−	0.645654i
$404$	4.61740	−	4.61740i	0.229724	−	0.229724i
$405$		0			0
$406$	0.811407	−	0.336096i	0.0402694	−	0.0166802i
$407$	0.764397	+	1.32397i	0.0378897	+	0.0656270i
$408$		0			0
$409$	−11.5900	+	20.0744i	−0.573088	+	0.992618i	0.423158	+	0.906056i	$0.360921\pi$
$409$	−11.5900	+	20.0744i	−0.573088	+	0.992618i	−0.996246	+	0.0865619i	$0.972412\pi$
$410$	−0.0344614	+	0.261760i	−0.00170193	+	0.0129274i
$411$		0			0
$412$	−3.43355	−	0.920016i	−0.169159	−	0.0453260i
$413$	4.28558	+	0.852454i	0.210880	+	0.0419465i
$414$		0			0
$415$	0.103997	+	0.522827i	0.00510500	+	0.0256646i
$416$	32.4923	−	4.27770i	1.59307	−	0.209731i
$417$		0			0
$418$	−0.249693	+	0.735572i	−0.0122129	+	0.0359780i
$419$	1.10663	+	2.24403i	0.0540626	+	0.109628i	0.922227	−	0.386648i	$-0.126367\pi$
$419$	1.10663	+	2.24403i	0.0540626	+	0.109628i	−0.868165	+	0.496276i	$0.834700\pi$
$420$		0			0
$421$	1.78389	−	6.65758i	0.0869417	−	0.324471i	−0.908733	−	0.417378i	$-0.862949\pi$
$421$	1.78389	−	6.65758i	0.0869417	−	0.324471i	0.995675	+	0.0929069i	$0.0296159\pi$
$422$	−27.9674	−	41.8562i	−1.36143	−	2.03753i
$423$		0			0
$424$			10.8081i			0.524886i
$425$	−18.1129	−	7.11189i	−0.878602	−	0.344977i
$426$		0			0
$427$	−5.41497	−	0.712894i	−0.262049	−	0.0344993i
$428$	−1.39409	−	21.2697i	−0.0673859	−	1.02811i
$429$		0			0
$430$	−6.78972	+	2.30480i	−0.327429	+	0.111147i
$431$	27.2261	+	18.1919i	1.31144	+	0.876273i	0.997324	−	0.0731128i	$-0.0232933\pi$
$431$	27.2261	+	18.1919i	1.31144	+	0.876273i	0.314112	+	0.949386i	$0.398293\pi$
$432$		0			0
$433$	−15.1633	−	6.28082i	−0.728699	−	0.301837i	−0.0126820	−	0.999920i	$-0.504037\pi$
$433$	−15.1633	−	6.28082i	−0.728699	−	0.301837i	−0.716017	+	0.698082i	$0.754037\pi$
$434$	−0.357890	−	2.71844i	−0.0171793	−	0.130489i
$435$		0			0
$436$	16.0563	−	7.91810i	0.768958	−	0.379208i
$437$	6.05586	+	5.31085i	0.289691	+	0.254052i
$438$		0			0
$439$	−2.52344	−	1.24442i	−0.120437	−	0.0593931i	0.381072	−	0.924545i	$-0.375555\pi$
$439$	−2.52344	−	1.24442i	−0.120437	−	0.0593931i	−0.501509	+	0.865152i	$0.667222\pi$
$440$	−0.0764711	−	0.184618i	−0.00364562	−	0.00880130i
$441$		0			0
$442$	−32.6203	+	26.0059i	−1.55159	+	1.23697i
$443$	−8.64073	+	4.98873i	−0.410533	+	0.237021i	−0.691019	−	0.722837i	$-0.742838\pi$
$443$	−8.64073	+	4.98873i	−0.410533	+	0.237021i	0.280486	+	0.959858i	$0.409505\pi$
$444$		0			0
$445$	7.88919	−	0.517085i	0.373984	−	0.0245122i
$446$	−14.9920	+	4.01708i	−0.709890	+	0.190214i
$447$		0			0
$448$	0.105489	+	0.00691412i	0.00498389	+	0.000326661i
$449$	15.7406	−	3.13100i	0.742846	−	0.147761i	0.190863	−	0.981617i	$-0.438871\pi$
$449$	15.7406	−	3.13100i	0.742846	−	0.147761i	0.551983	+	0.833855i	$0.313871\pi$
$450$		0			0
$451$	−0.0263823	+	0.0636925i	−0.00124229	+	0.00299916i
$452$	15.2772	−	13.3978i	0.718580	−	0.630178i
$453$		0			0
$454$	7.08293	−	8.07654i	0.332419	−	0.379051i
$455$	−0.508206	−	1.89665i	−0.0238250	−	0.0889163i
$456$		0			0
$457$	−21.8169	−	16.7407i	−1.02055	−	0.783096i	−0.0441412	−	0.999025i	$-0.514055\pi$
$457$	−21.8169	−	16.7407i	−1.02055	−	0.783096i	−0.976409	+	0.215930i	$0.930722\pi$
$458$	10.2846			0.480569
$459$		0			0
$460$	2.67850			0.124886
$461$	−7.81145	−	5.99393i	−0.363815	−	0.279165i	0.410635	−	0.911800i	$-0.365307\pi$
$461$	−7.81145	−	5.99393i	−0.363815	−	0.279165i	−0.774451	+	0.632634i	$0.781974\pi$
$462$		0			0
$463$	2.92124	+	10.9022i	0.135762	+	0.506669i	0.999994	+	0.00357567i	$0.00113817\pi$
$463$	2.92124	+	10.9022i	0.135762	+	0.506669i	−0.864232	+	0.503093i	$0.832195\pi$
$464$	−2.51815	+	2.87141i	−0.116902	+	0.133302i
$465$		0			0
$466$	9.75722	−	8.55685i	0.451994	−	0.396388i
$467$	2.85969	−	6.90389i	0.132330	−	0.319474i	−0.843800	−	0.536657i	$-0.819687\pi$
$467$	2.85969	−	6.90389i	0.132330	−	0.319474i	0.976131	+	0.217183i	$0.0696869\pi$
$468$		0			0
$469$	1.91414	−	0.380746i	0.0883868	−	0.0175812i
$470$	7.40851	+	0.485579i	0.341729	+	0.0223981i
$471$		0			0
$472$	−10.0480	+	2.69235i	−0.462496	+	0.123925i
$473$	−1.86827	+	0.122453i	−0.0859032	+	0.00563040i
$474$		0			0
$475$	7.34043	−	4.23800i	0.336802	−	0.194453i
$476$	−2.67709	+	1.38251i	−0.122704	+	0.0633673i
$477$		0			0
$478$	6.44526	+	15.5602i	0.294799	+	0.711709i
$479$	19.1553	+	9.44633i	0.875226	+	0.431614i	0.823679	−	0.567057i	$-0.191918\pi$
$479$	19.1553	+	9.44633i	0.875226	+	0.431614i	0.0515474	+	0.998671i	$0.483585\pi$
$480$		0			0
$481$	−26.8880	−	23.5802i	−1.22599	−	1.07516i
$482$	42.6260	−	21.0208i	1.94156	−	0.957471i
$483$		0			0
$484$	−1.61027	−	12.2312i	−0.0731942	−	0.555965i
$485$	−2.01944	−	0.836479i	−0.0916980	−	0.0379826i
$486$		0			0
$487$	12.8519	+	8.58738i	0.582376	+	0.389131i	0.811575	−	0.584248i	$-0.198611\pi$
$487$	12.8519	+	8.58738i	0.582376	+	0.389131i	−0.229199	+	0.973380i	$0.573611\pi$
$488$	12.3125	−	4.17952i	0.557359	−	0.189198i
$489$		0			0
$490$	0.403083	+	6.14986i	0.0182094	+	0.277822i
$491$	16.4877	+	2.17064i	0.744077	+	0.0979597i	0.493027	−	0.870014i	$-0.335891\pi$
$491$	16.4877	+	2.17064i	0.744077	+	0.0979597i	0.251051	+	0.967974i	$0.419224\pi$
$492$		0			0
$493$	0.558830	−	3.10986i	0.0251684	−	0.140061i
$494$		−	18.1716i		−	0.817578i
$495$		0			0
$496$	6.62424	+	9.91388i	0.297437	+	0.445146i
$497$	−1.50912	+	5.63211i	−0.0676933	+	0.252635i
$498$		0			0
$499$	11.2063	+	22.7241i	0.501663	+	1.01727i	0.989526	+	0.144352i	$0.0461097\pi$
$499$	11.2063	+	22.7241i	0.501663	+	1.01727i	−0.487863	+	0.872920i	$0.662224\pi$
$500$	1.86586	−	5.49663i	0.0834436	−	0.245817i
$501$		0			0
$502$	−29.1326	+	3.83538i	−1.30025	+	0.171182i
$503$	2.13202	+	10.7184i	0.0950619	+	0.477908i	0.998762	+	0.0497426i	$0.0158401\pi$
$503$	2.13202	+	10.7184i	0.0950619	+	0.477908i	−0.903700	+	0.428166i	$0.859160\pi$
$504$		0			0
$505$	3.00792	+	0.598313i	0.133851	+	0.0266246i
$506$	1.87376	+	0.502073i	0.0832989	+	0.0223199i
$507$		0			0
$508$	−2.66397	+	20.2349i	−0.118195	+	0.897777i
$509$	−4.23473	+	7.33477i	−0.187701	+	0.325108i	−0.944483	−	0.328559i	$-0.893437\pi$
$509$	−4.23473	+	7.33477i	−0.187701	+	0.325108i	0.756782	+	0.653667i	$0.226770\pi$
$510$		0			0
$511$	3.12446	+	5.41173i	0.138218	+	0.239401i
$512$	−12.1682	+	5.04021i	−0.537761	+	0.222748i
$513$		0			0
$514$	−9.17332	+	9.17332i	−0.404618	+	0.404618i
$515$	−0.536634	−	1.58087i	−0.0236469	−	0.0696616i
$516$		0			0
$517$	1.83576	+	0.623158i	0.0807368	+	0.0274065i
$518$	−4.36112	−	5.68352i	−0.191617	−	0.249720i
$519$		0			0
$520$	3.08217	+	3.51454i	0.135162	+	0.154123i
$521$	−11.6214	+	17.3927i	−0.509143	+	0.761987i	−0.993615	−	0.112820i	$-0.964012\pi$
$521$	−11.6214	+	17.3927i	−0.509143	+	0.761987i	0.484472	+	0.874807i	$0.339012\pi$
$522$		0			0
$523$	30.2405	+	30.2405i	1.32232	+	1.32232i	0.911890	+	0.410434i	$0.134623\pi$
$523$	30.2405	+	30.2405i	1.32232	+	1.32232i	0.410434	+	0.911890i	$0.365377\pi$
$524$	−6.68491	+	13.5556i	−0.292031	+	0.592181i
$525$		0			0
$526$	−2.07329	−	1.19702i	−0.0903998	−	0.0521924i
$527$	−8.92650	−	4.19804i	−0.388844	−	0.182870i
$528$		0			0
$529$	−1.75646	+	2.28906i	−0.0763677	+	0.0995243i
$530$	5.45588	−	3.64550i	0.236988	−	0.158350i
$531$		0			0
$532$	0.256037	−	1.28719i	0.0111006	−	0.0558066i
$533$	0.105477	−	1.60926i	0.00456870	−	0.0697049i
$534$		0			0
$535$	7.94217	−	6.09424i	0.343370	−	0.263477i
$536$	−3.68609	+	2.82844i	−0.159215	+	0.122170i
$537$		0			0
$538$	2.83300	−	43.2233i	0.122139	−	1.86349i
$539$	−0.313956	+	1.57837i	−0.0135231	+	0.0679850i
$540$		0			0
$541$	−12.9382	+	8.64503i	−0.556256	+	0.371679i	−0.801695	−	0.597734i	$-0.796068\pi$
$541$	−12.9382	+	8.64503i	−0.556256	+	0.371679i	0.245438	+	0.969412i	$0.421068\pi$
$542$	−27.1046	+	35.3234i	−1.16424	+	1.51727i
$543$		0			0
$544$	14.0278	−	19.0011i	0.601438	−	0.814665i
$545$	7.28158	+	4.20402i	0.311909	+	0.180081i
$546$		0			0
$547$	−2.79457	+	5.66682i	−0.119487	+	0.242296i	−0.948396	−	0.317087i	$-0.897295\pi$
$547$	−2.79457	+	5.66682i	−0.119487	+	0.242296i	0.828909	+	0.559383i	$0.188962\pi$
$548$	−16.4993	−	16.4993i	−0.704814	−	0.704814i
$549$		0			0
$550$	1.13410	−	1.69729i	0.0483580	−	0.0723729i
$551$	0.907452	+	1.03475i	0.0386588	+	0.0440819i
$552$		0			0
$553$	−2.07689	−	2.70666i	−0.0883184	−	0.115099i
$554$	−13.7496	−	4.66737i	−0.584165	−	0.198297i
$555$		0			0
$556$	4.82320	+	14.2087i	0.204549	+	0.602583i
$557$	26.0867	−	26.0867i	1.10533	−	1.10533i	0.111574	−	0.993756i	$-0.464411\pi$
$557$	26.0867	−	26.0867i	1.10533	−	1.10533i	0.993756	−	0.111574i	$-0.0355892\pi$
$558$		0			0
$559$	40.4642	−	16.7608i	1.71146	−	0.708908i
$560$	0.855217	+	1.48128i	0.0361395	+	0.0625955i
$561$		0			0
$562$	−7.37624	+	12.7760i	−0.311148	+	0.538924i
$563$	−3.31115	+	25.1507i	−0.139548	+	1.05998i	0.768126	+	0.640299i	$0.221190\pi$
$563$	−3.31115	+	25.1507i	−0.139548	+	1.05998i	−0.907674	+	0.419676i	$0.862144\pi$
$564$		0			0
$565$	9.21813	+	2.46999i	0.387810	+	0.103913i
$566$	38.7830	+	7.71442i	1.63017	+	0.324261i
$567$		0			0
$568$	−2.70809	−	13.6145i	−0.113629	−	0.571251i
$569$	−0.251252	+	0.0330779i	−0.0105330	+	0.00138670i	−0.135791	−	0.990738i	$-0.543358\pi$
$569$	−0.251252	+	0.0330779i	−0.0105330	+	0.00138670i	0.125258	+	0.992124i	$0.460024\pi$
$570$		0			0
$571$	0.822225	−	2.42220i	0.0344090	−	0.101366i	−0.928368	−	0.371662i	$-0.878788\pi$
$571$	0.822225	−	2.42220i	0.0344090	−	0.101366i	0.962777	+	0.270296i	$0.0871215\pi$
$572$	−0.697873	−	1.41515i	−0.0291795	−	0.0591702i
$573$		0			0
$574$	0.0836125	−	0.312046i	0.00348992	−	0.0130246i
$575$	−11.7596	−	17.5995i	−0.490410	−	0.733950i
$576$		0			0
$577$			5.40760i			0.225121i	0.993645	+	0.112561i	$0.0359053\pi$
$577$			5.40760i			0.225121i	−0.993645	+	0.112561i	$0.964095\pi$
$578$	−2.81589	+	29.9327i	−0.117126	+	1.24503i
$579$		0			0
$580$	0.453753	+	0.0597378i	0.0188411	+	0.00248048i
$581$	−0.0426601	−	0.650868i	−0.00176984	−	0.0270025i
$582$		0			0
$583$	1.62246	−	0.550750i	0.0671953	−	0.0228097i
$584$	−12.3695	−	8.26503i	−0.511853	−	0.342009i
$585$		0			0
$586$	5.71204	+	2.36601i	0.235962	+	0.0977388i
$587$	1.32165	+	10.0389i	0.0545503	+	0.414351i	0.996832	+	0.0795309i	$0.0253422\pi$
$587$	1.32165	+	10.0389i	0.0545503	+	0.414351i	−0.942282	+	0.334820i	$0.891324\pi$
$588$		0			0
$589$	3.85363	−	1.90040i	0.158786	−	0.0783045i
$590$	4.74822	+	4.16408i	0.195481	+	0.171432i
$591$		0			0
$592$	27.9401	+	13.7785i	1.14833	+	0.566294i
$593$	14.8623	+	35.8809i	0.610323	+	1.47345i	0.862646	+	0.505807i	$0.168805\pi$
$593$	14.8623	+	35.8809i	0.610323	+	1.47345i	−0.252323	+	0.967643i	$0.581195\pi$
$594$		0			0
$595$	−1.23840	−	0.684682i	−0.0507695	−	0.0280692i
$596$	1.98285	−	1.14480i	0.0812209	−	0.0468929i
$597$		0			0
$598$	−45.2819	+	2.96793i	−1.85172	+	0.121368i
$599$	27.9063	−	7.47748i	1.14022	−	0.305521i	0.361181	−	0.932496i	$-0.382374\pi$
$599$	27.9063	−	7.47748i	1.14022	−	0.305521i	0.779040	+	0.626974i	$0.215707\pi$
$600$		0			0
$601$	32.3833	+	2.12252i	1.32094	+	0.0865792i	0.709498	−	0.704707i	$-0.248922\pi$
$601$	32.3833	+	2.12252i	1.32094	+	0.0865792i	0.611446	+	0.791286i	$0.290588\pi$
$602$	8.60493	−	1.71163i	0.350711	−	0.0697607i
$603$		0			0
$604$	10.3851	−	25.0718i	0.422563	−	1.02016i
$605$	4.35619	−	3.82028i	0.177104	−	0.155316i
$606$		0			0
$607$	−7.29010	+	8.31276i	−0.295896	+	0.337405i	−0.880616	−	0.473830i	$-0.842871\pi$
$607$	−7.29010	+	8.31276i	−0.295896	+	0.337405i	0.584720	+	0.811235i	$0.301204\pi$
$608$	2.66264	+	9.93712i	0.107984	+	0.403003i
$609$		0			0
$610$	−6.26273	−	4.80556i	−0.253571	−	0.194572i
$611$	−45.3507			−1.83469
$612$		0			0
$613$	−26.2555			−1.06045			−0.530224	−	0.847857i	$-0.677892\pi$
$613$	−26.2555			−1.06045			−0.530224	+	0.847857i	$0.677892\pi$
$614$	−2.62724	−	2.01595i	−0.106027	−	0.0813571i
$615$		0			0
$616$	0.0632840	+	0.236179i	0.00254978	+	0.00951592i
$617$	12.0867	−	13.7822i	0.486592	−	0.554852i	−0.455487	−	0.890242i	$-0.650535\pi$
$617$	12.0867	−	13.7822i	0.486592	−	0.554852i	0.942079	+	0.335391i	$0.108868\pi$
$618$		0			0
$619$	−18.8012	+	16.4882i	−0.755683	+	0.662716i	−0.947875	−	0.318641i	$-0.896774\pi$
$619$	−18.8012	+	16.4882i	−0.755683	+	0.662716i	0.192193	+	0.981357i	$0.438440\pi$
$620$	0.546788	−	1.32006i	0.0219595	−	0.0530150i
$621$		0			0
$622$	45.1146	−	8.97385i	1.80893	−	0.359818i
$623$	−9.65322	−	0.632705i	−0.386748	−	0.0253488i
$624$		0			0
$625$	−20.1602	+	5.40190i	−0.806407	+	0.216076i
$626$	19.8685	−	1.30225i	0.794105	−	0.0520484i
$627$		0			0
$628$	12.1370	−	7.00730i	0.484319	−	0.279622i
$629$	−25.6824	+	2.16242i	−1.02402	+	0.0862214i
$630$		0			0
$631$	−13.6701	−	33.0026i	−0.544198	−	1.31381i	−0.921736	−	0.387817i	$-0.873229\pi$
$631$	−13.6701	−	33.0026i	−0.544198	−	1.31381i	0.377538	−	0.925994i	$-0.376771\pi$
$632$	7.28446	+	3.59230i	0.289760	+	0.142894i
$633$		0			0
$634$	−10.6644	−	9.35244i	−0.423538	−	0.371433i
$635$	−8.59691	+	4.23953i	−0.341158	+	0.168241i
$636$		0			0
$637$	−4.91379	−	37.3239i	−0.194691	−	1.47883i
$638$	0.306229	+	0.126844i	0.0121237	+	0.00502181i
$639$		0			0
$640$	−4.91790	−	3.28604i	−0.194397	−	0.129892i
$641$	−16.3246	+	5.54145i	−0.644782	+	0.218874i	−0.624628	−	0.780923i	$-0.714749\pi$
$641$	−16.3246	+	5.54145i	−0.644782	+	0.218874i	−0.0201547	+	0.999797i	$0.506416\pi$
$642$		0			0
$643$	1.78121	+	27.1760i	0.0702440	+	1.07172i	0.876893	+	0.480686i	$0.159612\pi$
$643$	1.78121	+	27.1760i	0.0702440	+	1.07172i	−0.806649	+	0.591031i	$0.798721\pi$
$644$	−3.24937	−	0.427788i	−0.128043	−	0.0168572i
$645$		0			0
$646$	−9.43021	−	9.08667i	−0.371027	−	0.357510i
$647$		−	25.4973i		−	1.00240i	−0.865330	−	0.501202i	$-0.832891\pi$
$647$		−	25.4973i		−	1.00240i	0.865330	−	0.501202i	$-0.167109\pi$
$648$		0			0
$649$	0.916182	+	1.37116i	0.0359633	+	0.0538229i
$650$	−12.3592	+	46.1253i	−0.484770	+	1.80918i
$651$		0			0
$652$	−5.01392	−	10.1672i	−0.196360	−	0.398179i
$653$	−1.88115	+	5.54168i	−0.0736150	+	0.216863i	−0.977509	−	0.210894i	$-0.932363\pi$
$653$	−1.88115	+	5.54168i	−0.0736150	+	0.216863i	0.903894	+	0.427757i	$0.140696\pi$
$654$		0			0
$655$	−7.03782	+	0.926546i	−0.274990	+	0.0362032i
$656$	0.274067	+	1.37783i	0.0107005	+	0.0537951i
$657$		0			0
$658$	−8.90995	−	1.77230i	−0.347346	−	0.0690914i
$659$	−7.51008	−	2.01232i	−0.292551	−	0.0783889i	0.109558	−	0.993980i	$-0.465056\pi$
$659$	−7.51008	−	2.01232i	−0.292551	−	0.0783889i	−0.402110	+	0.915591i	$0.631723\pi$
$660$		0			0
$661$	−1.69114	+	12.8455i	−0.0657776	+	0.499631i	0.926567	+	0.376130i	$0.122745\pi$
$661$	−1.69114	+	12.8455i	−0.0657776	+	0.499631i	−0.992344	+	0.123501i	$0.960588\pi$
$662$	6.82642	−	11.8237i	0.265316	−	0.459541i
$663$		0			0
$664$	0.776414	+	1.34479i	0.0301307	+	0.0521879i
$665$	0.569460	−	0.235878i	0.0220827	−	0.00914695i
$666$		0			0
$667$	2.43029	−	2.43029i	0.0941014	−	0.0941014i
$668$	4.73936	+	13.9617i	0.183371	+	0.540194i
$669$		0			0
$670$	2.67108	+	0.906711i	0.103193	+	0.0350293i
$671$	−1.25482	−	1.63531i	−0.0484418	−	0.0631306i
$672$		0			0
$673$	31.7325	+	36.1839i	1.22320	+	1.39479i	0.892498	+	0.451052i	$0.148951\pi$
$673$	31.7325	+	36.1839i	1.22320	+	1.39479i	0.330699	+	0.943736i	$0.392716\pi$
$674$	−26.8437	+	40.1745i	−1.03398	+	1.54746i
$675$		0			0
$676$	15.7341	+	15.7341i	0.605159	+	0.605159i
$677$	−3.86886	+	7.84527i	−0.148692	+	0.301518i	−0.958457	−	0.285236i	$-0.907928\pi$
$677$	−3.86886	+	7.84527i	−0.148692	+	0.301518i	0.809765	+	0.586754i	$0.199595\pi$
$678$		0			0
$679$	2.31625	+	1.33729i	0.0888896	+	0.0513204i
$680$	3.36512	+	0.157937i	0.129046	+	0.00605660i
$681$		0			0
$682$	0.629950	−	0.820967i	0.0241220	−	0.0314364i
$683$	−14.5914	+	9.74966i	−0.558324	+	0.373060i	−0.802483	−	0.596675i	$-0.796488\pi$
$683$	−14.5914	+	9.74966i	−0.558324	+	0.373060i	0.244159	+	0.969735i	$0.421488\pi$
$684$		0			0
$685$	2.13794	−	10.7481i	0.0816865	−	0.410666i
$686$	1.01790	−	15.5302i	0.0388637	−	0.592946i
$687$		0			0
$688$	−30.2681	+	23.2256i	−1.15396	+	0.885466i
$689$	−31.7985	+	24.3999i	−1.21143	+	0.929561i
$690$		0			0
$691$	1.93866	−	29.5782i	0.0737500	−	1.12521i	−0.787260	−	0.616621i	$-0.788501\pi$
$691$	1.93866	−	29.5782i	0.0737500	−	1.12521i	0.861010	−	0.508587i	$-0.169832\pi$
$692$	−3.14077	+	15.7897i	−0.119394	+	0.600235i
$693$		0			0
$694$	−13.6093	+	9.09346i	−0.516603	+	0.345183i
$695$	−4.29006	+	5.59091i	−0.162731	+	0.212075i
$696$		0			0
$697$	−0.782390	−	0.859448i	−0.0296352	−	0.0325539i
$698$	−4.68326	−	2.70388i	−0.177264	−	0.102343i
$699$		0			0
$700$	−1.52538	+	3.09316i	−0.0576538	+	0.116910i
$701$	−20.0615	−	20.0615i	−0.757711	−	0.757711i	0.218195	−	0.975905i	$-0.429983\pi$
$701$	−20.0615	−	20.0615i	−0.757711	−	0.757711i	−0.975905	+	0.218195i	$0.929983\pi$
$702$		0			0
$703$	6.23702	−	9.33436i	0.235234	−	0.352052i
$704$	0.0263063	+	0.0299965i	0.000991454	+	0.00113054i
$705$		0			0
$706$	10.7718	+	14.0381i	0.405403	+	0.528332i
$707$	−3.55345	−	1.20623i	−0.133641	−	0.0453651i
$708$		0			0
$709$	−7.23970	−	21.3275i	−0.271892	−	0.800969i	−0.994019	−	0.109208i	$-0.965168\pi$
$709$	−7.23970	−	21.3275i	−0.271892	−	0.800969i	0.722126	−	0.691761i	$-0.243165\pi$
$710$	−5.95912	+	5.95912i	−0.223642	+	0.223642i
$711$		0			0
$712$	21.2774	−	8.81338i	0.797404	−	0.330295i
$713$	−5.36503	−	9.29250i	−0.200922	−	0.348007i
$714$		0			0
$715$	0.370528	−	0.641773i	0.0138569	−	0.0240009i
$716$	−2.16404	+	16.4375i	−0.0808741	+	0.614300i
$717$		0			0
$718$	27.3918	+	7.33962i	1.02225	+	0.273912i
$719$	45.9582	+	9.14165i	1.71395	+	0.340926i	0.951857	−	0.306541i	$-0.0991716\pi$
$719$	45.9582	+	9.14165i	1.71395	+	0.340926i	0.762094	+	0.647467i	$0.224172\pi$
$720$		0			0
$721$	0.398524	+	2.00352i	0.0148418	+	0.0746148i
$722$	−27.6590	+	3.64137i	−1.02936	+	0.135518i
$723$		0			0
$724$	−4.48223	+	13.2042i	−0.166581	+	0.490731i
$725$	−1.59963	−	3.24373i	−0.0594088	−	0.120469i
$726$		0			0
$727$	−3.93738	+	14.6945i	−0.146029	+	0.544989i	0.853678	+	0.520801i	$0.174367\pi$
$727$	−3.93738	+	14.6945i	−0.146029	+	0.544989i	−0.999707	+	0.0241878i	$0.992300\pi$
$728$	−3.17776	−	4.75586i	−0.117776	−	0.176264i
$729$		0			0
$730$			9.03183i			0.334283i
$731$	11.5360	−	29.3803i	0.426674	−	1.08667i
$732$		0			0
$733$	0.187203	+	0.0246457i	0.00691449	+	0.000910310i	0.133983	−	0.990984i	$-0.457223\pi$
$733$	0.187203	+	0.0246457i	0.00691449	+	0.000910310i	−0.127068	+	0.991894i	$0.540557\pi$
$734$	−2.24873	−	34.3090i	−0.0830021	−	1.26637i
$735$		0			0
$736$	24.3275	−	8.25808i	0.896724	−	0.304397i
$737$	0.612426	+	0.409210i	0.0225590	+	0.0150734i
$738$		0			0
$739$	−29.8113	−	12.3483i	−1.09663	−	0.454238i	−0.240315	−	0.970695i	$-0.577251\pi$
$739$	−29.8113	−	12.3483i	−1.09663	−	0.454238i	−0.856313	+	0.516457i	$0.827251\pi$
$740$	−0.487278	−	3.70124i	−0.0179127	−	0.136060i
$741$		0			0
$742$	−7.20093	+	3.55111i	−0.264354	+	0.130365i
$743$	−27.4652	−	24.0864i	−1.00760	−	0.883643i	−0.0143821	−	0.999897i	$-0.504578\pi$
$743$	−27.4652	−	24.0864i	−1.00760	−	0.883643i	−0.993220	+	0.116254i	$0.962911\pi$
$744$		0			0
$745$	0.964431	+	0.475605i	0.0353340	+	0.0174248i
$746$	3.36017	+	8.11217i	0.123025	+	0.297007i
$747$		0			0
$748$	−1.08337	−	0.345478i	−0.0396118	−	0.0126319i
$749$	−10.6082	+	6.12466i	−0.387616	+	0.223790i
$750$		0			0
$751$	37.3677	−	2.44921i	1.36357	−	0.0893730i	0.634028	−	0.773310i	$-0.281401\pi$
$751$	37.3677	−	2.44921i	1.36357	−	0.0893730i	0.729541	+	0.683937i	$0.239734\pi$
$752$	38.1585	−	10.2245i	1.39150	−	0.372850i
$753$		0			0
$754$	−7.73722	−	0.507124i	−0.281773	−	0.0184684i
$755$	12.5004	−	2.48648i	0.454936	−	0.0904924i
$756$		0			0
$757$	−14.6941	+	35.4746i	−0.534065	+	1.28935i	0.394746	+	0.918790i	$0.370833\pi$
$757$	−14.6941	+	35.4746i	−0.534065	+	1.28935i	−0.928810	+	0.370556i	$0.879167\pi$
$758$	−11.4711	+	10.0599i	−0.416649	+	0.365392i
$759$		0			0
$760$	−0.967522	+	1.10325i	−0.0350957	+	0.0400190i
$761$	4.74914	+	17.7240i	0.172156	+	0.642496i	0.997019	+	0.0771621i	$0.0245859\pi$
$761$	4.74914	+	17.7240i	0.172156	+	0.642496i	−0.824862	+	0.565334i	$0.808747\pi$
$762$		0			0
$763$	−8.16209	−	6.26299i	−0.295487	−	0.226735i
$764$	−19.9266			−0.720920
$765$		0			0
$766$	47.4279			1.71364
$767$	−30.6052	−	23.4842i	−1.10509	−	0.847964i
$768$		0			0
$769$	−5.31142	−	19.8225i	−0.191535	−	0.714817i	−0.993137	−	0.116959i	$-0.962685\pi$
$769$	−5.31142	−	19.8225i	−0.191535	−	0.714817i	0.801602	−	0.597858i	$-0.203981\pi$
$770$	0.0978771	−	0.111607i	0.00352724	−	0.00402205i
$771$		0			0
$772$	−5.85255	+	5.13255i	−0.210638	+	0.184725i
$773$	12.5389	−	30.2715i	0.450992	−	1.08879i	−0.520954	−	0.853585i	$-0.674424\pi$
$773$	12.5389	−	30.2715i	0.450992	−	1.08879i	0.971946	−	0.235206i	$-0.0755764\pi$
$774$		0			0
$775$	−11.0743	+	2.20281i	−0.397800	+	0.0791274i
$776$	−6.35366	−	0.416441i	−0.228083	−	0.0149494i
$777$		0			0
$778$	−39.1873	+	10.5002i	−1.40493	+	0.376451i
$779$	0.505163	−	0.0331101i	0.0180993	−	0.00118629i
$780$		0			0
$781$	−1.90575	+	1.10028i	−0.0681930	+	0.0393713i
$782$	−21.1029	+	24.9834i	−0.754640	+	0.893403i
$783$		0			0
$784$	12.5494	+	30.2968i	0.448191	+	1.08203i
$785$	5.90325	+	2.91116i	0.210696	+	0.103904i
$786$		0			0
$787$	−7.67569	−	6.73140i	−0.273609	−	0.239948i	0.511534	−	0.859263i	$-0.329077\pi$
$787$	−7.67569	−	6.73140i	−0.273609	−	0.239948i	−0.785143	+	0.619314i	$0.787411\pi$
$788$	13.3648	−	6.59078i	0.476101	−	0.234787i
$789$		0			0
$790$	−0.643627	−	4.88884i	−0.0228992	−	0.173937i
$791$	−10.7883	−	4.46867i	−0.383589	−	0.158888i
$792$		0			0
$793$	40.0928	+	26.7891i	1.42374	+	0.951310i
$794$	27.4016	−	9.30158i	0.972445	−	0.330101i
$795$		0			0
$796$	1.03937	+	15.8577i	0.0368394	+	0.562061i
$797$	47.2869	+	6.22544i	1.67499	+	0.220516i	0.907352	−	0.420371i	$-0.138100\pi$
$797$	47.2869	+	6.22544i	1.67499	+	0.220516i	0.767635	+	0.640887i	$0.221433\pi$
$798$		0			0
$799$	−22.6776	+	23.5349i	−0.802275	+	0.832607i
$800$		−	27.0346i		−	0.955818i
$801$		0			0
$802$	−24.3707	−	36.4734i	−0.860561	−	1.28792i
$803$	−0.610392	+	2.27802i	−0.0215403	+	0.0803894i
$804$		0			0
$805$	−0.680795	−	1.38052i	−0.0239949	−	0.0486568i
$806$	−7.78114	+	22.9225i	−0.274079	+	0.807410i
$807$		0			0
$808$	8.85729	−	1.16608i	0.311598	−	0.0410227i
$809$	6.61554	+	33.2586i	0.232590	+	1.16931i	0.903771	+	0.428016i	$0.140787\pi$
$809$	6.61554	+	33.2586i	0.232590	+	1.16931i	−0.671181	+	0.741294i	$0.734213\pi$
$810$		0			0
$811$	9.51440	+	1.89253i	0.334096	+	0.0664558i	0.359288	−	0.933227i	$-0.383020\pi$
$811$	9.51440	+	1.89253i	0.334096	+	0.0664558i	−0.0251920	+	0.999683i	$0.508020\pi$
$812$	−0.540922	−	0.144940i	−0.0189826	−	0.00508638i
$813$		0			0
$814$	0.352904	−	2.68057i	0.0123693	−	0.0939539i
$815$	2.66208	−	4.61086i	0.0932487	−	0.161511i
$816$		0			0
$817$	6.87433	+	11.9067i	0.240502	+	0.416562i
$818$	37.8737	−	15.6878i	1.32422	−	0.548511i
$819$		0			0
$820$	0.119039	−	0.119039i	0.00415701	−	0.00415701i
$821$	3.15917	+	9.30661i	0.110256	+	0.324803i	0.988028	−	0.154276i	$-0.0493043\pi$
$821$	3.15917	+	9.30661i	0.110256	+	0.324803i	−0.877772	+	0.479078i	$0.840971\pi$
$822$		0			0
$823$	34.4564	+	11.6964i	1.20108	+	0.407710i	0.849066	−	0.528286i	$-0.177165\pi$
$823$	34.4564	+	11.6964i	1.20108	+	0.407710i	0.352009	+	0.935997i	$0.385499\pi$
$824$	−2.96051	−	3.85821i	−0.103134	−	0.134407i
$825$		0			0
$826$	−5.09517	−	5.80992i	−0.177283	−	0.202153i
$827$	19.7223	−	29.5165i	0.685810	−	1.02639i	−0.311292	−	0.950314i	$-0.600762\pi$
$827$	19.7223	−	29.5165i	0.685810	−	1.02639i	0.997102	−	0.0760735i	$-0.0242384\pi$
$828$		0			0
$829$	20.4905	+	20.4905i	0.711666	+	0.711666i	0.966884	−	0.255218i	$-0.0821471\pi$
$829$	20.4905	+	20.4905i	0.711666	+	0.711666i	−0.255218	+	0.966884i	$0.582147\pi$
$830$	0.416965	−	0.845521i	0.0144731	−	0.0293485i
$831$		0			0
$832$	−0.808279	−	0.466660i	−0.0280220	−	0.0161785i
$833$	−21.8265	−	16.1138i	−0.756245	−	0.558308i
$834$		0			0
$835$	−4.21548	+	5.49373i	−0.145883	+	0.190118i
$836$	0.411833	−	0.275178i	0.0142435	−	0.00951723i
$837$		0			0
$838$	0.863263	−	4.33992i	0.0298209	−	0.149920i
$839$	−2.82718	+	43.1344i	−0.0976049	+	1.48916i	0.615517	+	0.788123i	$0.288947\pi$
$839$	−2.82718	+	43.1344i	−0.0976049	+	1.48916i	−0.713122	+	0.701040i	$0.752719\pi$
$840$		0			0
$841$	−22.5413	+	17.2966i	−0.777288	+	0.596434i
$842$	−9.67050	+	7.42044i	−0.333268	+	0.255725i
$843$		0			0
$844$	−2.09932	+	32.0295i	−0.0722617	+	1.10250i
$845$	−2.03880	+	10.2497i	−0.0701367	+	0.352601i
$846$		0			0
$847$	−5.89478	+	3.93877i	−0.202547	+	0.135338i
$848$	21.2545	−	27.6994i	0.729882	−	0.951201i
$849$		0			0
$850$	17.7567	+	29.4788i	0.609050	+	1.01111i
$851$	−24.2791	−	14.0175i	−0.832276	−	0.480515i
$852$		0			0
$853$	20.0459	−	40.6490i	0.686358	−	1.39180i	−0.222600	−	0.974910i	$-0.571455\pi$
$853$	20.0459	−	40.6490i	0.686358	−	1.39180i	0.908958	−	0.416887i	$-0.136879\pi$
$854$	6.83002	+	6.83002i	0.233718	+	0.233718i
$855$		0			0
$856$	16.2013	−	24.2470i	0.553751	−	0.828746i
$857$	0.680782	+	0.776283i	0.0232551	+	0.0265173i	0.763350	−	0.645985i	$-0.223553\pi$
$857$	0.680782	+	0.776283i	0.0232551	+	0.0265173i	−0.740095	+	0.672502i	$0.765220\pi$
$858$		0			0
$859$	−2.96156	−	3.85958i	−0.101047	−	0.131687i	0.740093	−	0.672505i	$-0.234782\pi$
$859$	−2.96156	−	3.85958i	−0.101047	−	0.131687i	−0.841140	+	0.540818i	$0.818115\pi$
$860$	4.32931	+	1.46960i	0.147628	+	0.0501131i
$861$		0			0
$862$	−18.6144	−	54.8361i	−0.634007	−	1.86773i
$863$	−4.14890	+	4.14890i	−0.141230	+	0.141230i	−0.774187	−	0.632957i	$-0.781841\pi$
$863$	−4.14890	+	4.14890i	−0.141230	+	0.141230i	0.632957	+	0.774187i	$0.281841\pi$
$864$		0			0
$865$	−6.98547	+	2.89348i	−0.237513	+	0.0983812i
$866$	14.5130	+	25.1372i	0.493171	+	0.854198i
$867$		0			0
$868$	−0.874156	+	1.51408i	−0.0296708	+	0.0513913i
$869$	0.168063	−	1.27656i	0.00570114	−	0.0433045i
$870$		0			0
$871$	−16.6432	−	4.45952i	−0.563932	−	0.151105i
$872$	24.0220	+	4.77826i	0.813486	+	0.161812i
$873$		0			0
$874$	−2.77905	−	13.9712i	−0.0940026	−	0.472583i
$875$	−3.30725	+	0.435408i	−0.111805	+	0.0147195i
$876$		0			0
$877$	18.1442	−	53.4512i	0.612687	−	1.80492i	0.0195610	−	0.999809i	$-0.493773\pi$
$877$	18.1442	−	53.4512i	0.612687	−	1.80492i	0.593126	−	0.805110i	$-0.297894\pi$
$878$	2.20079	+	4.46275i	0.0742729	+	0.150611i
$879$		0			0
$880$	−0.167074	+	0.623530i	−0.00563207	+	0.0210192i
$881$	−3.00833	−	4.50228i	−0.101353	−	0.151686i	0.777327	−	0.629097i	$-0.216575\pi$
$881$	−3.00833	−	4.50228i	−0.101353	−	0.151686i	−0.878680	+	0.477411i	$0.841575\pi$
$882$		0			0
$883$			23.2342i			0.781895i	0.920413	+	0.390947i	$0.127853\pi$
$883$			23.2342i			0.781895i	−0.920413	+	0.390947i	$0.872147\pi$
$884$	26.5960	−	0.493432i	0.894520	−	0.0165959i
$885$		0			0
$886$	17.4943	+	2.30317i	0.587734	+	0.0773767i
$887$	1.71620	+	26.1841i	0.0576243	+	0.879177i	0.924627	+	0.380873i	$0.124377\pi$
$887$	1.71620	+	26.1841i	0.0576243	+	0.879177i	−0.867003	+	0.498303i	$0.833957\pi$
$888$		0			0
$889$	11.1063	−	3.77008i	0.372493	−	0.126444i
$890$	−11.6257	−	7.76805i	−0.389695	−	0.260386i
$891$		0			0
$892$	9.14318	+	3.78723i	0.306136	+	0.126806i
$893$	−1.85817	−	14.1142i	−0.0621814	−	0.472315i
$894$		0			0
$895$	−6.98360	+	3.44393i	−0.233436	+	0.115118i
$896$	5.44125	+	4.77185i	0.181779	+	0.159416i
$897$		0			0
$898$	−25.4559	−	12.5535i	−0.849474	−	0.418914i
$899$	−0.701620	−	1.69386i	−0.0234003	−	0.0564934i
$900$		0			0
$901$	−3.23840	+	28.7031i	−0.107887	+	0.956240i
$902$	0.105588	−	0.0609610i	0.00351568	−	0.00202978i
$903$		0			0
$904$	27.7401	−	1.81818i	0.922621	−	0.0604718i
$905$	−6.32584	+	1.69500i	−0.210278	+	0.0563438i
$906$		0			0
$907$	−9.64874	−	0.632412i	−0.320381	−	0.0209989i	−0.0956357	−	0.995416i	$-0.530488\pi$
$907$	−9.64874	−	0.632412i	−0.320381	−	0.0209989i	−0.224745	+	0.974418i	$0.572155\pi$
$908$	−6.71802	+	1.33630i	−0.222945	+	0.0443466i
$909$		0			0
$910$	−1.32890	+	3.20825i	−0.0440526	+	0.106352i
$911$	18.6461	−	16.3522i	0.617774	−	0.541773i	−0.292243	−	0.956344i	$-0.594402\pi$
$911$	18.6461	−	16.3522i	0.617774	−	0.541773i	0.910017	+	0.414571i	$0.136068\pi$
$912$		0			0
$913$	0.162310	−	0.185079i	0.00537166	−	0.00612521i
$914$	12.5873	+	46.9763i	0.416350	+	1.55384i
$915$		0			0
$916$	−5.20262	−	3.99211i	−0.171899	−	0.131903i
$917$	8.68578			0.286830
$918$		0			0
$919$	−54.6299			−1.80207			−0.901037	−	0.433743i	$-0.857193\pi$
$919$	−54.6299			−1.80207			−0.901037	+	0.433743i	$0.857193\pi$
$920$	2.90722	+	2.23079i	0.0958481	+	0.0735468i
$921$		0			0
$922$	4.50682	+	16.8197i	0.148424	+	0.553927i
$923$	33.9417	−	38.7030i	1.11720	−	1.27393i
$924$		0			0
$925$	−22.1803	+	19.4516i	−0.729283	+	0.639564i
$926$	7.63872	−	18.4415i	0.251024	−	0.606025i
$927$		0			0
$928$	4.30540	−	0.856398i	0.141332	−	0.0281126i
$929$	12.6499	+	0.829120i	0.415030	+	0.0272025i	0.271488	−	0.962442i	$-0.412484\pi$
$929$	12.6499	+	0.829120i	0.415030	+	0.0272025i	0.143542	+	0.989644i	$0.454151\pi$
$930$		0			0
$931$	11.4148	−	3.05858i	0.374104	−	0.100241i
$932$	−8.25729	+	0.541211i	−0.270476	+	0.0177280i
$933$		0			0
$934$	−11.4451	+	6.60782i	−0.374494	+	0.216214i
$935$	−0.147769	−	0.513204i	−0.00483255	−	0.0167836i
$936$		0			0
$937$	7.40961	+	17.8884i	0.242061	+	0.584388i	0.997487	−	0.0708461i	$-0.0225699\pi$
$937$	7.40961	+	17.8884i	0.242061	+	0.584388i	−0.755426	+	0.655234i	$0.772570\pi$
$938$	−3.09557	−	1.52656i	−0.101074	−	0.0498441i
$939$		0			0
$940$	−3.55922	−	3.12135i	−0.116089	−	0.101807i
$941$	−41.8877	+	20.6567i	−1.36550	+	0.673390i	−0.969553	−	0.244883i	$-0.921251\pi$
$941$	−41.8877	+	20.6567i	−1.36550	+	0.673390i	−0.395948	+	0.918273i	$0.629584\pi$
$942$		0			0
$943$	−0.165015	−	1.25341i	−0.00537362	−	0.0408167i
$944$	31.0460	+	12.8597i	1.01046	+	0.418547i
$945$		0			0
$946$	2.75313	+	1.83958i	0.0895120	+	0.0598100i
$947$	29.4772	−	10.0062i	0.957881	−	0.325157i	0.201647	−	0.979458i	$-0.435371\pi$
$947$	29.4772	−	10.0062i	0.957881	−	0.325157i	0.756234	+	0.654301i	$0.227037\pi$
$948$		0			0
$949$	−3.60825	−	55.0512i	−0.117129	−	1.78704i
$950$	−14.8617	−	1.95658i	−0.482178	−	0.0634799i
$951$		0			0
$952$	−4.05711	−	0.729048i	−0.131492	−	0.0236286i
$953$		−	3.63734i		−	0.117825i	−0.998263	−	0.0589124i	$-0.981237\pi$
$953$		−	3.63734i		−	0.117825i	0.998263	−	0.0589124i	$-0.0187633\pi$
$954$		0			0
$955$	−5.19940	−	7.78145i	−0.168248	−	0.251802i
$956$	2.77949	−	10.3732i	0.0898950	−	0.335493i
$957$		0			0
$958$	−16.7060	−	33.8764i	−0.539746	−	1.09450i
$959$	−4.31021	+	12.6975i	−0.139184	+	0.410023i
$960$		0			0
$961$	25.0599	−	3.29920i	0.808383	−	0.106426i
$962$	12.3390	+	62.0322i	0.397825	+	2.00000i
$963$		0			0
$964$	−29.7225	−	5.91217i	−0.957296	−	0.190418i
$965$	−3.53138	−	0.946229i	−0.113679	−	0.0304602i
$966$		0			0
$967$	−0.590458	+	4.48498i	−0.0189879	+	0.144227i	−0.998313	−	0.0580669i	$-0.981506\pi$
$967$	−0.590458	+	4.48498i	−0.0189879	+	0.144227i	0.979325	+	0.202294i	$0.0648397\pi$
$968$	8.43901	−	14.6168i	0.271240	−	0.469801i
$969$		0			0
$970$	1.93284	+	3.34777i	0.0620596	+	0.107490i
$971$	−8.08819	+	3.35024i	−0.259562	+	0.107514i	−0.508670	−	0.860962i	$-0.669863\pi$
$971$	−8.08819	+	3.35024i	−0.259562	+	0.107514i	0.249108	+	0.968476i	$0.419863\pi$
$972$		0			0
$973$	6.09734	−	6.09734i	0.195472	−	0.195472i
$974$	−8.78679	−	25.8851i	−0.281547	−	0.829411i
$975$		0			0
$976$	−39.7741	−	13.5015i	−1.27314	−	0.432172i
$977$	−12.2359	−	15.9462i	−0.391462	−	0.510164i	0.555496	−	0.831519i	$-0.312528\pi$
$977$	−12.2359	−	15.9462i	−0.391462	−	0.510164i	−0.946959	+	0.321355i	$0.895862\pi$
$978$		0			0
$979$	−2.40726	−	2.74496i	−0.0769365	−	0.0877292i
$980$	2.18325	−	3.26746i	0.0697413	−	0.104375i
$981$		0			0
$982$	−20.7962	−	20.7962i	−0.663635	−	0.663635i
$983$	8.53183	−	17.3008i	0.272123	−	0.551811i	−0.717318	−	0.696746i	$-0.754631\pi$
$983$	8.53183	−	17.3008i	0.272123	−	0.551811i	0.989441	+	0.144935i	$0.0462973\pi$
$984$		0			0
$985$	6.06096	+	3.49930i	0.193118	+	0.111497i
$986$	−4.13216	+	3.76168i	−0.131595	+	0.119796i
$987$		0			0
$988$	−7.05354	+	9.19235i	−0.224403	+	0.292448i
$989$	28.5476	−	19.0749i	0.907762	−	0.606547i
$990$		0			0
$991$	7.79334	−	39.1798i	0.247564	−	1.24459i	−0.634302	−	0.773085i	$-0.718712\pi$
$991$	7.79334	−	39.1798i	0.247564	−	1.24459i	0.881866	−	0.471501i	$-0.156288\pi$
$992$	0.896327	−	13.6753i	0.0284584	−	0.434192i
$993$		0			0
$994$	8.18095	−	6.27746i	0.259484	−	0.199109i
$995$	−5.92131	+	4.54358i	−0.187718	+	0.144041i
$996$		0			0
$997$	1.81560	−	27.7008i	0.0575008	−	0.877292i	−0.867526	−	0.497391i	$-0.834291\pi$
$997$	1.81560	−	27.7008i	0.0575008	−	0.877292i	0.925027	−	0.379901i	$-0.124042\pi$
$998$	8.74182	−	43.9481i	0.276717	−	1.39115i
$999$		0			0

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.260.4		256
3.2	odd	2		153.2.s.a.5.13	✓	256
9.2	odd	6	inner	459.2.y.a.413.13		256
9.7	even	3		153.2.s.a.56.4	yes	256
17.7	odd	16	inner	459.2.y.a.449.13		256
51.41	even	16		153.2.s.a.41.4	yes	256
153.7	odd	48		153.2.s.a.92.13	yes	256
153.92	even	48	inner	459.2.y.a.143.4		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.5.13	✓	256	3.2	odd	2
153.2.s.a.41.4	yes	256	51.41	even	16
153.2.s.a.56.4	yes	256	9.7	even	3
153.2.s.a.92.13	yes	256	153.7	odd	48
459.2.y.a.143.4		256	153.92	even	48	inner
459.2.y.a.260.4		256	1.1	even	1	trivial
459.2.y.a.413.13		256	9.2	odd	6	inner
459.2.y.a.449.13		256	17.7	odd	16	inner

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

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	459.2.y.a.260.4

Level	$459$
Weight	$2$
Character	459.260
Analytic conductor	$3.665$
Analytic rank	$0$
Dimension	$256$
Inner twists	$4$