LMFDB - Embedded newform 153.2.s.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	153.5
Dual form			153.2.s.a.92.13

$q$-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} +(0.184815 + 1.72216i) q^{3} +(0.291859 + 1.08923i) q^{4} +(0.349197 - 0.398183i) q^{5} +(-1.59478 + 2.61527i) q^{6} +(0.487217 - 0.427278i) q^{7} +(0.590386 - 1.42532i) q^{8} +(-2.93169 + 0.636563i) q^{9} +(0.918630 - 0.182727i) q^{10} +(-0.244047 - 0.0159957i) q^{11} +(-1.82190 + 0.703936i) q^{12} +(-5.52628 + 1.48076i) q^{13} +(1.14360 - 0.0749557i) q^{14} +(0.750272 + 0.527784i) q^{15} +(4.31601 - 2.49185i) q^{16} +(1.99496 - 3.60834i) q^{17} +(-4.79866 - 2.26313i) q^{18} +(-0.687279 - 1.65924i) q^{19} +(0.535630 + 0.264144i) q^{20} +(0.825886 + 0.760099i) q^{21} +(-0.325191 - 0.285185i) q^{22} +(4.02242 - 1.98364i) q^{23} +(2.56374 + 0.753321i) q^{24} +(0.616020 + 4.67914i) q^{25} +(-9.34790 - 3.87203i) q^{26} +(-1.63809 - 4.93119i) q^{27} +(0.607604 + 0.405988i) q^{28} +(0.725663 - 0.246329i) q^{29} +(0.484462 + 1.54826i) q^{30} +(0.156475 + 2.38734i) q^{31} +(5.67926 + 0.747688i) q^{32} +(-0.0175564 - 0.423245i) q^{33} +(6.68381 - 2.91493i) q^{34} -0.343205i q^{35} +(-1.54901 - 3.00750i) q^{36} +(3.47283 + 5.19746i) q^{37} +(0.822052 - 3.06794i) q^{38} +(-3.57145 - 9.24349i) q^{39} +(-0.361376 - 0.732799i) q^{40} +(0.0906083 - 0.266923i) q^{41} +(0.340441 + 1.95562i) q^{42} +(-7.58989 + 0.999228i) q^{43} +(-0.0538043 - 0.270493i) q^{44} +(-0.770268 + 1.38963i) q^{45} +(7.77930 + 1.54740i) q^{46} +(-7.65665 - 2.05159i) q^{47} +(5.08904 + 6.97235i) q^{48} +(-0.858869 + 6.52376i) q^{49} +(-4.17327 + 7.22832i) q^{50} +(6.58285 + 2.76877i) q^{51} +(-3.22579 - 5.58724i) q^{52} +(-6.47242 + 2.68096i) q^{53} +(3.01062 - 8.68233i) q^{54} +(-0.0915896 + 0.0915896i) q^{55} +(-0.321361 - 0.946698i) q^{56} +(2.73046 - 1.49026i) q^{57} +(1.28335 + 0.435638i) q^{58} +(-4.10474 - 5.34940i) q^{59} +(-0.355906 + 0.971260i) q^{60} +(-5.55704 - 6.33659i) q^{61} +(-2.35068 + 3.51804i) q^{62} +(-1.15638 + 1.56279i) q^{63} +(0.115352 + 0.115352i) q^{64} +(-1.34015 + 2.71755i) q^{65} +(0.431035 - 0.612739i) q^{66} +(2.60816 + 1.50582i) q^{67} +(4.51257 + 1.11985i) q^{68} +(4.15955 + 6.56066i) q^{69} +(0.369497 - 0.481538i) q^{70} +(7.48130 - 4.99884i) q^{71} +(-0.823522 + 4.55441i) q^{72} +(-1.88124 + 9.45764i) q^{73} +(-0.723024 + 11.0312i) q^{74} +(-7.94438 + 1.92566i) q^{75} +(1.60671 - 1.23287i) q^{76} +(-0.125738 + 0.0964824i) q^{77} +(4.94063 - 16.8142i) q^{78} +(0.344325 - 5.25338i) q^{79} +(0.514926 - 2.58871i) q^{80} +(8.18957 - 3.73241i) q^{81} +(0.414500 - 0.276960i) q^{82} +(-0.612737 + 0.798534i) q^{83} +(-0.586883 + 1.12142i) q^{84} +(-0.740144 - 2.05438i) q^{85} +(-11.7248 - 6.76934i) q^{86} +(0.558333 + 1.20418i) q^{87} +(-0.166881 + 0.338401i) q^{88} +(10.5558 + 10.5558i) q^{89} +(-2.57682 + 1.12046i) q^{90} +(-2.05980 + 3.08271i) q^{91} +(3.33463 + 3.80241i) q^{92} +(-4.08247 + 0.710691i) q^{93} +(-8.53398 - 11.1217i) q^{94} +(-0.900676 - 0.305738i) q^{95} +(-0.238028 + 9.91879i) q^{96} +(1.32665 + 3.90819i) q^{97} +(-8.22856 + 8.22856i) q^{98} +(0.725651 - 0.108457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22}+ \cdots + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{6}\right)$

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	0.971141	−	0.238505i	$-0.0766573\pi$
$2$	1.40306	+	1.07661i	0.992113	+	0.761275i	0.0209719	+	0.999780i	$0.493324\pi$
$3$	0.184815	+	1.72216i	0.106703	+	0.994291i
$3$	0.184815	+	1.72216i	0.106703	+	0.994291i
$4$	0.291859	+	1.08923i	0.145930	+	0.544617i
$5$	0.349197	−	0.398183i	0.156166	−	0.178073i	−0.668466	−	0.743742i	$-0.733049\pi$
$5$	0.349197	−	0.398183i	0.156166	−	0.178073i	0.824632	+	0.565670i	$0.191382\pi$
$6$	−1.59478	+	2.61527i	−0.651068	+	1.06768i
$7$	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
$9$	−2.93169	+	0.636563i	−0.977229	+	0.212188i
$10$	0.918630	−	0.182727i	0.290496	−	0.0577833i
$11$	−0.244047	−	0.0159957i	−0.0735829	−	0.00482288i	0.0285672	−	0.999592i	$-0.490906\pi$
$11$	−0.244047	−	0.0159957i	−0.0735829	−	0.00482288i	−0.102150	+	0.994769i	$0.532572\pi$
$12$	−1.82190	+	0.703936i	−0.525936	+	0.203209i
$13$	−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
$15$	0.750272	+	0.527784i	0.193719	+	0.136273i
$16$	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
$18$	−4.79866	−	2.26313i	−1.13106	−	0.533426i
$19$	−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
$21$	0.825886	+	0.760099i	0.180223	+	0.165867i
$22$	−0.325191	−	0.285185i	−0.0693310	−	0.0608017i
$23$	4.02242	−	1.98364i	0.838733	−	0.413617i	0.0284068	−	0.999596i	$-0.490957\pi$
$23$	4.02242	−	1.98364i	0.838733	−	0.413617i	0.810326	+	0.585979i	$0.199290\pi$
$24$	2.56374	+	0.753321i	0.523322	+	0.153771i
$25$	0.616020	+	4.67914i	0.123204	+	0.935827i
$26$	−9.34790	−	3.87203i	−1.83327	−	0.759367i
$27$	−1.63809	−	4.93119i	−0.315250	−	0.949009i
$28$	0.607604	+	0.405988i	0.114826	+	0.0767245i
$29$	0.725663	−	0.246329i	0.134752	−	0.0457422i	−0.253249	−	0.967401i	$-0.581499\pi$
$29$	0.725663	−	0.246329i	0.134752	−	0.0457422i	0.388001	+	0.921659i	$0.373166\pi$
$30$	0.484462	+	1.54826i	0.0884503	+	0.282672i
$31$	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
$33$	−0.0175564	−	0.423245i	−0.00305618	−	0.0736774i
$34$	6.68381	−	2.91493i	1.14626	−	0.499906i
$35$		−	0.343205i		−	0.0580123i
$36$	−1.54901	−	3.00750i	−0.258168	−	0.501251i
$37$	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
$39$	−3.57145	−	9.24349i	−0.571890	−	1.48014i
$40$	−0.361376	−	0.732799i	−0.0571386	−	0.115866i
$41$	0.0906083	−	0.266923i	0.0141506	−	0.0416864i	−0.939625	−	0.342205i	$-0.888826\pi$
$41$	0.0906083	−	0.266923i	0.0141506	−	0.0416864i	0.953776	+	0.300518i	$0.0971597\pi$
$42$	0.340441	+	1.95562i	0.0525312	+	0.301758i
$43$	−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
$45$	−0.770268	+	1.38963i	−0.114825	+	0.207154i
$46$	7.77930	+	1.54740i	1.14699	+	0.228151i
$47$	−7.65665	−	2.05159i	−1.11684	−	0.299256i	−0.347234	−	0.937778i	$-0.612879\pi$
$47$	−7.65665	−	2.05159i	−1.11684	−	0.299256i	−0.769603	+	0.638523i	$0.779546\pi$
$48$	5.08904	+	6.97235i	0.734539	+	1.00637i
$49$	−0.858869	+	6.52376i	−0.122696	+	0.931966i
$50$	−4.17327	+	7.22832i	−0.590190	+	1.02224i
$51$	6.58285	+	2.76877i	0.921783	+	0.387706i
$52$	−3.22579	−	5.58724i	−0.447337	−	0.774810i
$53$	−6.47242	+	2.68096i	−0.889055	+	0.368259i	−0.780002	−	0.625777i	$-0.784782\pi$
$53$	−6.47242	+	2.68096i	−0.889055	+	0.368259i	−0.109053	+	0.994036i	$0.534782\pi$
$54$	3.01062	−	8.68233i	0.409694	−	1.18152i
$55$	−0.0915896	+	0.0915896i	−0.0123499	+	0.0123499i
$56$	−0.321361	−	0.946698i	−0.0429436	−	0.126508i
$57$	2.73046	−	1.49026i	0.361658	−	0.197390i
$58$	1.28335	+	0.435638i	0.168512	+	0.0572021i
$59$	−4.10474	−	5.34940i	−0.534392	−	0.696433i	0.445654	−	0.895205i	$-0.352971\pi$
$59$	−4.10474	−	5.34940i	−0.534392	−	0.696433i	−0.980046	+	0.198772i	$0.936305\pi$
$60$	−0.355906	+	0.971260i	−0.0459472	+	0.125389i
$61$	−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
$63$	−1.15638	+	1.56279i	−0.145690	+	0.196893i
$64$	0.115352	+	0.115352i	0.0144191	+	0.0144191i
$65$	−1.34015	+	2.71755i	−0.166225	+	0.337070i
$66$	0.431035	−	0.612739i	0.0530567	−	0.0754229i
$67$	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
$69$	4.15955	+	6.56066i	0.500751	+	0.789810i
$70$	0.369497	−	0.481538i	0.0441633	−	0.0575547i
$71$	7.48130	−	4.99884i	0.887867	−	0.593254i	−0.0258226	−	0.999667i	$-0.508221\pi$
$71$	7.48130	−	4.99884i	0.887867	−	0.593254i	0.913690	+	0.406413i	$0.133221\pi$
$72$	−0.823522	+	4.55441i	−0.0970530	+	0.536742i
$73$	−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
$75$	−7.94438	+	1.92566i	−0.917338	+	0.222356i
$76$	1.60671	−	1.23287i	0.184302	−	0.141420i
$77$	−0.125738	+	0.0964824i	−0.0143292	+	0.0109952i
$78$	4.94063	−	16.8142i	0.559416	−	1.90383i
$79$	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
$81$	8.18957	−	3.73241i	0.909953	−	0.414712i
$82$	0.414500	−	0.276960i	0.0457739	−	0.0305851i
$83$	−0.612737	+	0.798534i	−0.0672566	+	0.0876505i	−0.825770	−	0.564007i	$-0.809259\pi$
$83$	−0.612737	+	0.798534i	−0.0672566	+	0.0876505i	0.758514	+	0.651657i	$0.225926\pi$
$84$	−0.586883	+	1.12142i	−0.0640341	+	0.122357i
$85$	−0.740144	−	2.05438i	−0.0802799	−	0.222829i
$86$	−11.7248	−	6.76934i	−1.26432	−	0.729957i
$87$	0.558333	+	1.20418i	0.0598595	+	0.129102i
$88$	−0.166881	+	0.338401i	−0.0177896	+	0.0360737i
$89$	10.5558	+	10.5558i	1.11891	+	1.11891i	0.991901	+	0.127011i	$0.0405385\pi$
$89$	10.5558	+	10.5558i	1.11891	+	1.11891i	0.127011	+	0.991901i	$0.459462\pi$
$90$	−2.57682	+	1.12046i	−0.271621	+	0.118107i
$91$	−2.05980	+	3.08271i	−0.215926	+	0.323156i
$92$	3.33463	+	3.80241i	0.347659	+	0.396429i
$93$	−4.08247	+	0.710691i	−0.423332	+	0.0736952i
$94$	−8.53398	−	11.1217i	−0.880213	−	1.14712i
$95$	−0.900676	−	0.305738i	−0.0924074	−	0.0313681i
$96$	−0.238028	+	9.91879i	−0.0242937	+	1.01233i
$97$	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
$99$	0.725651	−	0.108457i	0.0729307	−	0.0109003i
$100$	−4.91688	+	2.03664i	−0.491688	+	0.203664i
$101$	2.89538	+	5.01494i	0.288101	+	0.499006i	0.973356	−	0.229297i	$-0.0736428\pi$
$101$	2.89538	+	5.01494i	0.288101	+	0.499006i	−0.685255	+	0.728303i	$0.740309\pi$
$102$	6.25525	+	10.9719i	0.619362	+	1.08638i
$103$	−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
$105$	0.591055	−	0.0634295i	0.0576811	−	0.00619009i
$106$	−11.9675	−	3.20669i	−1.16239	−	0.311461i
$107$	18.5391	+	3.68766i	1.79225	+	0.356500i	0.975415	−	0.220378i	$-0.0707289\pi$
$107$	18.5391	+	3.68766i	1.79225	+	0.356500i	0.816831	+	0.576877i	$0.195729\pi$
$108$	4.89313	−	3.22347i	0.470842	−	0.310179i
$109$	−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
$111$	−8.30904	+	6.94135i	−0.788659	+	0.658844i
$112$	1.03812	−	3.05821i	0.0980933	−	0.288973i
$113$	7.96981	+	16.1612i	0.749736	+	1.52031i	0.850832	+	0.525438i	$0.176099\pi$
$113$	7.96981	+	16.1612i	0.749736	+	1.52031i	−0.101095	+	0.994877i	$0.532235\pi$
$114$	5.43542	+	0.848706i	0.509074	+	0.0794886i
$115$	0.614767	−	2.29434i	0.0573273	−	0.213948i
$116$	0.480102	+	0.718523i	0.0445763	+	0.0667132i
$117$	15.2587	−	7.85896i	1.41067	−	0.726561i
$118$		−	11.9247i		−	1.09776i
$119$	−0.569784	−	2.61045i	−0.0522320	−	0.239299i
$120$	1.19521	−	0.757781i	0.109107	−	0.0691756i
$121$	−10.8466	−	1.42798i	−0.986054	−	0.129816i
$122$	−0.974851	−	14.8734i	−0.0882589	−	1.34657i
$123$	0.476431	+	0.106711i	0.0429584	+	0.00962178i
$124$	−2.55470	+	0.867205i	−0.229419	+	0.0778773i
$125$	4.28004	+	2.85983i	0.382819	+	0.255791i
$126$	−3.30497	+	0.947723i	−0.294430	+	0.0844299i
$127$	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
$129$	−3.12356	−	12.8863i	−0.275014	−	1.13458i
$130$	−4.80603	+	2.37007i	−0.421517	+	0.207869i
$131$	−10.0771	−	8.83742i	−0.880444	−	0.772129i	0.0942786	−	0.995546i	$-0.469946\pi$
$131$	−10.0771	−	8.83742i	−0.880444	−	0.772129i	−0.974723	+	0.223417i	$0.928279\pi$
$132$	0.455888	−	0.142651i	0.0396800	−	0.0124162i
$133$	−1.04381	−	0.514750i	−0.0905098	−	0.0446345i
$134$	2.03823	+	4.92071i	0.176076	+	0.425085i
$135$	−2.53553	−	1.06970i	−0.218224	−	0.0920652i
$136$	−3.96524	−	4.97377i	−0.340016	−	0.426497i
$137$	17.9198	−	10.3460i	1.53099	−	0.883918i	0.531675	−	0.846948i	$-0.321563\pi$
$137$	17.9198	−	10.3460i	1.53099	−	0.883918i	0.999316	−	0.0369701i	$-0.0117706\pi$
$138$	−1.22714	+	13.6832i	−0.104461	+	1.16479i
$139$	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
$141$	2.11811	−	13.5652i	0.178377	−	1.14239i
$142$	15.8785	+	1.04073i	1.33249	+	0.0873363i
$143$	1.37236	−	0.272979i	0.114762	−	0.0228276i
$144$	−11.0670	+	10.0527i	−0.922248	+	0.837729i
$145$	0.155315	−	0.374964i	0.0128982	−	0.0311391i
$146$	−12.8216	+	11.2443i	−1.06113	+	0.930583i
$147$	−11.3937	−	0.273423i	−0.939737	−	0.0225516i
$148$	−4.64767	+	5.29965i	−0.382036	+	0.435629i
$149$	0.525508	+	1.96122i	0.0430513	+	0.160670i	0.984105	−	0.177588i	$-0.0568293\pi$
$149$	0.525508	+	1.96122i	0.0430513	+	0.160670i	−0.941054	+	0.338257i	$0.890163\pi$
$150$	−13.2196	−	5.85115i	−1.07938	−	0.477744i
$151$	−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
$153$	−3.55167	+	11.8484i	−0.287135	+	0.957890i
$154$	−0.280292			−0.0225866
$155$	1.00524	+	0.771346i	0.0807427	+	0.0619560i
$156$	9.02595	−	6.58794i	0.722655	−	0.527458i
$157$	−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
$159$	−5.81326	−	10.6511i	−0.461021	−	0.844685i
$160$	2.28090	−	2.00029i	0.180321	−	0.158137i
$161$	1.11223	−	2.68515i	0.0876557	−	0.211620i
$162$	15.5088	+	3.58015i	1.21849	+	0.281283i
$163$	−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
$165$	−0.174659	−	0.140805i	−0.0135972	−	0.0109617i
$166$	−1.71941	+	0.460715i	−0.133452	+	0.0357584i
$167$	−13.0470	+	0.855149i	−1.00961	+	0.0661734i	−0.561222	−	0.827665i	$-0.689669\pi$
$167$	−13.0470	+	0.855149i	−1.00961	+	0.0661734i	−0.448389	+	0.893839i	$0.648002\pi$
$168$	1.57098	−	0.728399i	0.121203	−	0.0561972i
$169$	17.0888	−	9.86622i	1.31452	−	0.758940i
$170$	1.17329	−	3.67926i	0.0899874	−	0.282187i
$171$	3.07110	+	4.42687i	0.234853	+	0.338531i
$172$	−3.30357	−	7.97553i	−0.251895	−	0.608128i
$173$	−12.8042	−	6.31436i	−0.973489	−	0.480072i	−0.115258	−	0.993336i	$-0.536770\pi$
$173$	−12.8042	−	6.31436i	−0.973489	−	0.480072i	−0.858231	+	0.513264i	$0.828436\pi$
$174$	−0.513057	+	2.29065i	−0.0388948	+	0.173653i
$175$	2.29942	+	2.01654i	0.173820	+	0.152436i
$176$	−1.09317	+	0.539091i	−0.0824007	+	0.0406355i
$177$	8.45392	−	8.05768i	0.635436	−	0.605652i
$178$	3.44599	+	26.1749i	0.258288	+	1.96189i
$179$	−13.5833	−	5.62640i	−1.01527	−	0.420537i	−0.187893	−	0.982190i	$-0.560166\pi$
$179$	−13.5833	−	5.62640i	−1.01527	−	0.420537i	−0.827373	+	0.561653i	$0.810166\pi$
$180$	−1.73844	−	0.433424i	−0.129576	−	0.0323055i
$181$	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
$183$	9.88561	−	10.7412i	0.730766	−	0.794014i
$184$	−0.452535	−	6.90435i	−0.0333613	−	0.508995i
$185$	3.28224	+	0.432115i	0.241315	+	0.0317697i
$186$	−6.49308	−	3.39807i	−0.476096	−	0.249158i
$187$	−0.544582	+	0.848694i	−0.0398238	+	0.0620626i
$188$		−	8.93865i		−	0.651918i
$189$	−2.90509	−	1.70264i	−0.211314	−	0.123849i
$190$	−0.934543	−	1.39864i	−0.0677989	−	0.101468i
$191$	4.57355	−	17.0687i	0.330930	−	1.23505i	−0.577284	−	0.816543i	$-0.695888\pi$
$191$	4.57355	−	17.0687i	0.330930	−	1.23505i	0.908215	−	0.418505i	$-0.137446\pi$
$192$	−0.177337	+	0.219974i	−0.0127982	+	0.0158753i
$193$	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
$195$	−4.92774	−	1.80571i	−0.352883	−	0.129309i
$196$	−7.35657	+	0.968510i	−0.525469	+	0.0691793i
$197$	2.57804	+	12.9607i	0.183678	+	0.923410i	0.957153	+	0.289583i	$0.0935167\pi$
$197$	2.57804	+	12.9607i	0.183678	+	0.923410i	−0.773475	+	0.633827i	$0.781483\pi$
$198$	1.13490	+	0.629069i	0.0806537	+	0.0447060i
$199$	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
$201$	−2.11124	+	4.76997i	−0.148915	+	0.336447i
$202$	−1.33673	+	10.1535i	−0.0940518	+	0.714394i
$203$	0.248304	−	0.430075i	0.0174275	−	0.0301854i
$204$	−1.09458	+	7.97835i	−0.0766356	+	0.558596i
$205$	−0.0746442	−	0.129287i	−0.00521337	−	0.00902983i
$206$	−5.15047	+	2.13340i	−0.358850	+	0.148641i
$207$	−10.5298	+	8.37593i	−0.731870	+	0.582168i
$208$	−20.1617	+	20.1617i	−1.39796	+	1.39796i
$209$	0.141188	+	0.415926i	0.00976616	+	0.0287702i
$210$	0.897575	+	0.547338i	0.0619385	+	0.0377699i
$211$	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
$213$	9.99148	+	11.9602i	0.684605	+	0.819496i
$214$	22.0414	+	25.1333i	1.50672	+	1.71808i
$215$	−2.25249	+	3.37109i	−0.153619	+	0.229906i
$216$	−7.99563	−	0.576516i	−0.544033	−	0.0392270i
$217$	1.09629	+	1.09629i	0.0744213	+	0.0744213i
$218$	12.4180	−	25.1813i	0.841056	−	1.70549i
$219$	−16.6353	−	1.49189i	−1.12411	−	0.100813i
$220$	−0.126494	−	0.0730312i	−0.00852821	−	0.00492376i
$221$	−5.68163	+	22.8948i	−0.382188	+	1.54007i
$222$	−19.1312	+	0.793570i	−1.28400	+	0.0532610i
$223$	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
$225$	−4.78454	−	13.3256i	−0.318970	−	0.888375i
$226$	−6.21709	+	31.2554i	−0.413555	+	2.07908i
$227$	0.397273	−	6.06121i	0.0263679	−	0.402297i	−0.964191	−	0.265209i	$-0.914559\pi$
$227$	0.397273	−	6.06121i	0.0263679	−	0.402297i	0.990559	−	0.137088i	$-0.0437743\pi$
$228$	2.42015	+	2.53916i	0.160278	+	0.168160i
$229$	−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
$231$	−0.189397	−	0.198710i	−0.0124614	−	0.0130742i
$232$	0.0773236	−	1.17973i	0.00507654	−	0.0774531i
$233$	1.43162	−	7.19722i	0.0937883	−	0.471506i	−0.905135	−	0.425123i	$-0.860231\pi$
$233$	1.43162	−	7.19722i	0.0937883	−	0.471506i	0.998924	−	0.0463824i	$-0.0147693\pi$
$234$	29.8699	+	5.40104i	1.95266	+	0.353077i
$235$	−3.49059	+	2.33234i	−0.227701	+	0.152145i
$236$	4.62874	−	6.03229i	0.301305	−	0.392669i
$237$	9.11082	−	0.377921i	0.591811	−	0.0245486i
$238$	2.01098	−	4.27605i	0.130352	−	0.277175i
$239$	8.24749	+	4.76169i	0.533486	+	0.308008i	0.742435	−	0.669918i	$-0.233671\pi$
$239$	8.24749	+	4.76169i	0.533486	+	0.308008i	−0.208949	+	0.977927i	$0.567004\pi$
$240$	4.55334	+	0.408354i	0.293917	+	0.0263591i
$241$	−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
$243$	7.94137	+	13.4140i	0.509439	+	0.860507i
$244$	5.28015	−	7.90231i	0.338027	−	0.505893i
$245$	2.29773	+	2.62006i	0.146797	+	0.167390i
$246$	0.553576	+	0.662650i	0.0352947	+	0.0422490i
$247$	6.25504	+	8.15172i	0.397999	+	0.518682i
$248$	3.49510	+	1.18643i	0.221939	+	0.0753382i
$249$	−1.48845	−	0.907651i	−0.0943266	−	0.0575200i
$250$	2.92624	+	8.62043i	0.185072	+	0.545204i
$251$	−11.7486	+	11.7486i	−0.741566	+	0.741566i	−0.972879	−	0.231313i	$-0.925698\pi$
$251$	−11.7486	+	11.7486i	−0.741566	+	0.741566i	0.231313	+	0.972879i	$0.425698\pi$
$252$	−2.03974	−	0.803451i	−0.128492	−	0.0506126i
$253$	−1.01339	+	0.419760i	−0.0637112	+	0.0263901i
$254$	16.0042	+	27.7201i	1.00419	+	1.73931i
$255$	3.40119	−	1.65433i	0.212991	−	0.103598i
$256$	10.0386	−	17.3873i	0.627410	−	1.08671i
$257$	−0.957479	+	7.27278i	−0.0597259	+	0.453663i	0.935285	+	0.353896i	$0.115143\pi$
$257$	−0.957479	+	7.27278i	−0.0597259	+	0.453663i	−0.995011	+	0.0997676i	$0.968190\pi$
$258$	9.49098	−	21.4432i	0.590883	−	1.33499i
$259$	3.91278	+	1.04843i	0.243128	+	0.0651460i
$260$	−3.35118	−	0.666591i	−0.207831	−	0.0413402i
$261$	−1.97061	+	1.18409i	−0.121978	+	0.0732934i
$262$	−4.62442	−	23.2485i	−0.285698	−	1.43630i
$263$	−1.34211	+	0.176692i	−0.0827582	+	0.0108953i	−0.171792	−	0.985133i	$-0.554956\pi$
$263$	−1.34211	+	0.176692i	−0.0827582	+	0.0108953i	0.0890334	+	0.996029i	$0.471622\pi$
$264$	−0.613624	−	0.224854i	−0.0377659	−	0.0138388i
$265$	−1.19264	+	3.51339i	−0.0732630	+	0.215826i
$266$	−0.910345	−	1.84600i	−0.0558168	−	0.113185i
$267$	−16.2279	+	20.1297i	−0.993133	+	1.23192i
$268$	−0.878975	+	3.28038i	−0.0536919	+	0.200381i
$269$	−13.6075	−	20.3650i	−0.829663	−	1.24168i	−0.967914	−	0.251281i	$-0.919148\pi$
$269$	−13.6075	−	20.3650i	−0.829663	−	1.24168i	0.138251	−	0.990397i	$-0.455852\pi$
$270$	−2.40586	−	4.23062i	−0.146416	−	0.257467i
$271$		−	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
$273$	−5.68961	−	2.97758i	−0.344351	−	0.180211i
$274$	36.2811	+	4.77650i	2.19182	+	0.288559i
$275$	−0.0754918	−	1.15178i	−0.00455233	−	0.0694551i
$276$	−5.93208	+	6.44551i	−0.357069	+	0.387974i
$277$	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
$279$	−1.97843	−	6.89933i	−0.118445	−	0.413052i
$280$	−0.489177	−	0.202624i	−0.0292339	−	0.0121091i
$281$	1.08881	+	8.27035i	0.0649531	+	0.493368i	0.992742	+	0.120262i	$0.0383736\pi$
$281$	1.08881	+	8.27035i	0.0649531	+	0.493368i	−0.927789	+	0.373105i	$0.878293\pi$
$282$	17.5762	−	16.7524i	1.04665	−	0.997588i
$283$	−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
$285$	0.360073	−	1.60762i	0.0213289	−	0.0952270i
$286$	2.21939	+	1.09448i	0.131235	+	0.0647181i
$287$	−0.0699045	−	0.168764i	−0.00412633	−	0.00996185i
$288$	−17.1258	+	1.42322i	−1.00914	+	0.0838639i
$289$	−9.04025	−	14.3970i	−0.531779	−	0.846883i
$290$	0.621605	−	0.358884i	0.0365019	−	0.0210744i
$291$	−6.48536	+	3.00701i	−0.380179	+	0.176274i
$292$	−10.8506	+	0.711188i	−0.634985	+	0.0416191i
$293$	3.37684	−	0.904821i	0.197277	−	0.0528602i	−0.158827	−	0.987306i	$-0.550771\pi$
$293$	3.37684	−	0.904821i	0.197277	−	0.0528602i	0.356105	+	0.934446i	$0.384105\pi$
$294$	−15.6917	−	12.6502i	−0.915158	−	0.737772i
$295$	−3.56340	−	0.233558i	−0.207469	−	0.0135983i
$296$	9.45835	−	1.88138i	0.549755	−	0.109353i
$297$	0.320892	+	1.22964i	0.0186200	+	0.0713512i
$298$	−1.37414	+	3.31748i	−0.0796020	+	0.192176i
$299$	−19.2917	+	16.9184i	−1.11567	+	0.978416i
$300$	−4.41614	−	8.09126i	−0.254966	−	0.467149i
$301$	−3.27097	+	3.72983i	−0.188536	+	0.214984i
$302$	−11.0154	−	41.1099i	−0.633863	−	2.36561i
$303$	−8.10144	+	5.91315i	−0.465416	+	0.339702i
$304$	−7.10089	−	5.44870i	−0.407264	−	0.312504i
$305$	−4.46362			−0.255586
$306$	−17.7393	+	12.8003i	−1.01409	+	0.731746i
$307$	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
$309$	−4.99269	−	2.20982i	−0.284024	−	0.125712i
$310$	0.579973	+	2.16449i	0.0329403	+	0.122935i
$311$	17.1493	−	19.5550i	0.972448	−	1.10886i	−0.0215832	−	0.999767i	$-0.506871\pi$
$311$	17.1493	−	19.5550i	0.972448	−	1.10886i	0.994031	−	0.109097i	$-0.0347960\pi$
$312$	−15.2835	−	0.366768i	−0.865255	−	0.0207642i
$313$	−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
$315$	0.218472	+	1.00617i	0.0123095	+	0.0566913i
$316$	5.82266	−	1.15820i	0.327550	−	0.0651538i
$317$	−8.00334	−	0.524567i	−0.449512	−	0.0294626i	−0.161034	−	0.986949i	$-0.551483\pi$
$317$	−8.00334	−	0.524567i	−0.449512	−	0.0294626i	−0.288479	+	0.957486i	$0.593149\pi$
$318$	3.31066	−	21.2027i	0.185653	−	1.18899i
$319$	−0.181036	+	0.0485084i	−0.0101361	+	0.00271595i
$320$	0.0862120	−	0.00565064i	0.00481940	−	0.000315880i
$321$	−2.92444	+	32.6089i	−0.163226	+	1.82005i
$322$	4.45137	−	2.57000i	0.248065	−	0.143221i
$323$	−7.35820	−	0.830182i	−0.409421	−	0.0461925i
$324$	6.45567	+	7.83102i	0.358648	+	0.435057i
$325$	−10.3330	−	24.9460i	−0.573171	−	1.38376i
$326$	−15.9454	−	7.86339i	−0.883132	−	0.435513i
$327$	26.2431	−	8.21166i	1.45125	−	0.454106i
$328$	−0.326957	−	0.286734i	−0.0180532	−	0.0158322i
$329$	−4.60705	+	2.27194i	−0.253995	+	0.125256i
$330$	−0.0934660	−	0.385597i	−0.00514513	−	0.0212264i
$331$	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
$333$	−13.4898	−	13.0266i	−0.739235	−	0.713856i
$334$	−19.2265	−	12.8467i	−1.05202	−	0.702940i
$335$	1.51035	−	0.512695i	0.0825193	−	0.0280115i
$336$	5.45859	+	1.22261i	0.297791	+	0.0666989i
$337$	−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
$339$	−26.3592	+	16.7121i	−1.43164	+	0.907678i
$340$	2.02168	−	1.40578i	0.109641	−	0.0762391i
$341$		−	0.585126i		−	0.0316863i
$342$	−0.457061	+	9.51753i	−0.0247151	+	0.514649i
$343$	4.88919	+	7.31720i	0.263992	+	0.395091i
$344$	−3.05675	+	11.4079i	−0.164809	+	0.615075i
$345$	4.06484	+	0.634699i	0.218844	+	0.0341711i
$346$	−11.1671	−	22.6446i	−0.600345	−	1.21738i
$347$	−2.97495	+	8.76392i	−0.159704	+	0.470472i	−0.997098	−	0.0761272i	$-0.975744\pi$
$347$	−2.97495	+	8.76392i	−0.159704	+	0.470472i	0.837394	+	0.546599i	$0.184078\pi$
$348$	−1.14868	+	0.959607i	−0.0615759	+	0.0514403i
$349$	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
$351$	16.3544	+	24.8256i	0.872936	+	1.32509i
$352$	−1.37405	−	0.273315i	−0.0732369	−	0.0145677i
$353$	9.66444	+	2.58958i	0.514386	+	0.137829i	0.506669	−	0.862141i	$-0.330877\pi$
$353$	9.66444	+	2.58958i	0.514386	+	0.137829i	0.00771755	+	0.999970i	$0.497543\pi$
$354$	20.5363	−	2.20387i	1.09149	−	0.117134i
$355$	0.621993	−	4.72451i	0.0330120	−	0.250751i
$356$	−8.41692	+	14.5785i	−0.446096	+	0.772661i
$357$	4.39031	−	1.46371i	0.232360	−	0.0774678i
$358$	−13.0008	−	22.5181i	−0.687115	−	1.19012i
$359$	14.8144	−	6.13631i	0.781873	−	0.323862i	0.0442016	−	0.999023i	$-0.485926\pi$
$359$	14.8144	−	6.13631i	0.781873	−	0.323862i	0.737671	+	0.675160i	$0.235926\pi$
$360$	1.52591	+	1.91830i	0.0804228	+	0.101103i
$361$	11.1543	−	11.1543i	0.587069	−	0.587069i
$362$	7.02953	+	20.7083i	0.369464	+	1.08841i
$363$	0.454601	−	18.9435i	0.0238604	−	0.994276i
$364$	−3.95896	−	1.34389i	−0.207506	−	0.0704388i
$365$	3.10895	+	4.05166i	0.162730	+	0.212073i
$366$	25.4342	−	4.42767i	1.32947	−	0.231438i
$367$	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
$369$	−0.0957215	+	0.840214i	−0.00498306	+	0.0437398i
$370$	4.13996	+	4.13996i	0.215226	+	0.215226i
$371$	−2.00795	+	4.07173i	−0.104248	+	0.211394i
$372$	−1.96561	−	4.23934i	−0.101912	−	0.219800i
$373$	−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
$375$	−4.13408	+	7.89947i	−0.213483	+	0.407927i
$376$	−7.44455	+	9.70193i	−0.383924	+	0.500339i
$377$	−3.64546	+	2.43582i	−0.187751	+	0.125451i
$378$	−2.24294	−	5.51655i	−0.115364	−	0.283741i
$379$	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
$381$	−8.83767	+	30.0768i	−0.452768	+	1.54088i
$382$	24.7932	−	19.0245i	1.26853	−	0.973379i
$383$	21.2761	−	16.3257i	1.08716	−	0.834204i	0.100164	−	0.994971i	$-0.468063\pi$
$383$	21.2761	−	16.3257i	1.08716	−	0.834204i	0.986992	+	0.160767i	$0.0513966\pi$
$384$	18.7992	−	4.55679i	0.959343	−	0.232538i
$385$	−0.00548980	+	0.0837582i	−0.000279786	+	0.00426871i
$386$	−2.38171	+	11.9736i	−0.121226	+	0.609443i
$387$	21.6151	−	7.76087i	1.09876	−	0.394507i
$388$	−3.86974	+	2.58568i	−0.196456	+	0.131268i
$389$	−13.9649	+	18.1995i	−0.708051	+	0.922749i	−0.999427	−	0.0338592i	$-0.989220\pi$
$389$	−13.9649	+	18.1995i	−0.708051	+	0.922749i	0.291376	+	0.956609i	$0.405887\pi$
$390$	−4.96988	−	7.83874i	−0.251660	−	0.396930i
$391$	0.866935	−	18.4716i	0.0438428	−	0.934147i
$392$	8.79137	+	5.07570i	0.444031	+	0.256362i
$393$	13.3571	−	18.9878i	0.673775	−	0.957806i
$394$	−10.3364	+	20.9601i	−0.520740	+	1.05596i
$395$	−1.97157	−	1.97157i	−0.0992005	−	0.0992005i
$396$	0.329923	+	0.758749i	0.0165793	+	0.0381286i
$397$	−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
$399$	0.693571	−	1.89274i	0.0347220	−	0.0947557i
$400$	14.3185	+	18.6602i	0.715923	+	0.933009i
$401$	−23.4876	−	7.97296i	−1.17291	−	0.398150i	−0.334083	−	0.942544i	$-0.608427\pi$
$401$	−23.4876	−	7.97296i	−1.17291	−	0.398150i	−0.838830	+	0.544393i	$0.816760\pi$
$402$	−8.09757	+	4.41958i	−0.403870	+	0.220428i
$403$	−4.39981	−	12.9614i	−0.219170	−	0.645654i
$404$	−4.61740	+	4.61740i	−0.229724	+	0.229724i
$405$	1.37359	−	4.56429i	0.0682544	−	0.226802i
$406$	0.811407	−	0.336096i	0.0402694	−	0.0166802i
$407$	−0.764397	−	1.32397i	−0.0378897	−	0.0656270i
$408$	7.83281	−	7.74801i	0.387782	−	0.383584i
$409$	−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
$411$	21.1293	+	28.9487i	1.04223	+	1.42793i
$412$	−3.43355	−	0.920016i	−0.169159	−	0.0453260i
$413$	−4.28558	−	0.852454i	−0.210880	−	0.0419465i
$414$	−23.7915	+	0.415527i	−1.16929	+	0.0204220i
$415$	0.103997	+	0.522827i	0.00510500	+	0.0256646i
$416$	−32.4923	+	4.27770i	−1.59307	+	0.209731i
$417$	3.95271	+	22.7058i	0.193565	+	1.11191i
$418$	−0.249693	+	0.735572i	−0.0122129	+	0.0359780i
$419$	−1.10663	−	2.24403i	−0.0540626	−	0.109628i	0.868165	−	0.496276i	$-0.165300\pi$
$419$	−1.10663	−	2.24403i	−0.0540626	−	0.109628i	−0.922227	+	0.386648i	$0.873633\pi$
$420$	0.241594	+	0.625285i	0.0117886	+	0.0305108i
$421$	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
$423$	23.7529	+	1.14069i	1.15490	+	0.0554621i
$424$			10.8081i			0.524886i
$425$	18.1129	+	7.11189i	0.878602	+	0.344977i
$426$	1.14228	+	27.5377i	0.0553435	+	1.33421i
$427$	−5.41497	−	0.712894i	−0.262049	−	0.0344993i
$428$	1.39409	+	21.2697i	0.0673859	+	1.02811i
$429$	0.723746	+	2.31297i	0.0349428	+	0.111671i
$430$	−6.78972	+	2.30480i	−0.327429	+	0.111147i
$431$	−27.2261	−	18.1919i	−1.31144	−	0.876273i	−0.314112	−	0.949386i	$-0.601707\pi$
$431$	−27.2261	−	18.1919i	−1.31144	−	0.876273i	−0.997324	+	0.0731128i	$0.976707\pi$
$432$	−19.3578	−	17.2012i	−0.931353	−	0.827595i
$433$	−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
$435$	0.674453	+	0.198179i	0.0323376	+	0.00950195i
$436$	16.0563	−	7.91810i	0.768958	−	0.379208i
$437$	−6.05586	−	5.31085i	−0.289691	−	0.254052i
$438$	−21.7341	−	20.0028i	−1.03850	−	0.955773i
$439$	−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
$441$	−1.63485	−	19.6723i	−0.0778500	−	0.936778i
$442$	−32.6203	+	26.0059i	−1.55159	+	1.23697i
$443$	8.64073	−	4.98873i	0.410533	−	0.237021i	−0.280486	−	0.959858i	$-0.590495\pi$
$443$	8.64073	−	4.98873i	0.410533	−	0.237021i	0.691019	+	0.722837i	$0.257162\pi$
$444$	−9.98582	−	7.02458i	−0.473906	−	0.333372i
$445$	7.88919	−	0.517085i	0.373984	−	0.0245122i
$446$	14.9920	−	4.01708i	0.709890	−	0.190214i
$447$	−3.28042	+	1.26747i	−0.155159	+	0.0599494i
$448$	0.105489	+	0.00691412i	0.00498389	+	0.000326661i
$449$	−15.7406	+	3.13100i	−0.742846	+	0.147761i	−0.551983	−	0.833855i	$-0.686129\pi$
$449$	−15.7406	+	3.13100i	−0.742846	+	0.147761i	−0.190863	+	0.981617i	$0.561129\pi$
$450$	7.63344	−	23.8477i	0.359844	−	1.12419i
$451$	−0.0263823	+	0.0636925i	−0.00124229	+	0.00299916i
$452$	−15.2772	+	13.3978i	−0.718580	+	0.630178i
$453$	21.7013	−	35.5877i	1.01961	−	1.67206i
$454$	7.08293	−	8.07654i	0.332419	−	0.379051i
$455$	0.508206	+	1.89665i	0.0238250	+	0.0889163i
$456$	−0.512068	−	4.77160i	−0.0239798	−	0.223451i
$457$	−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
$459$	−21.0613	−	3.92678i	−0.983060	−	0.183286i
$460$	2.67850			0.124886
$461$	7.81145	+	5.99393i	0.363815	+	0.279165i	0.774451	−	0.632634i	$-0.218026\pi$
$461$	7.81145	+	5.99393i	0.363815	+	0.279165i	−0.410635	+	0.911800i	$0.634693\pi$
$462$	−0.0518022	−	0.482708i	−0.00241005	−	0.0224576i
$463$	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
$465$	−1.14260	+	1.87374i	−0.0529868	+	0.0868926i
$466$	9.75722	−	8.55685i	0.451994	−	0.396388i
$467$	−2.85969	+	6.90389i	−0.132330	+	0.319474i	−0.976131	−	0.217183i	$-0.930313\pi$
$467$	−2.85969	+	6.90389i	−0.132330	+	0.319474i	0.843800	+	0.536657i	$0.180313\pi$
$468$	13.0136	+	14.3266i	0.601556	+	0.662248i
$469$	1.91414	−	0.380746i	0.0883868	−	0.0175812i
$470$	−7.40851	−	0.485579i	−0.341729	−	0.0223981i
$471$	20.0794	−	7.75817i	0.925208	−	0.357478i
$472$	−10.0480	+	2.69235i	−0.462496	+	0.123925i
$473$	1.86827	−	0.122453i	0.0859032	−	0.00563040i
$474$	13.1899	+	9.27851i	0.605832	+	0.426176i
$475$	7.34043	−	4.23800i	0.336802	−	0.194453i
$476$	2.67709	−	1.38251i	0.122704	−	0.0633673i
$477$	17.2685	−	11.9799i	0.790670	−	0.548520i
$478$	6.44526	+	15.5602i	0.294799	+	0.711709i
$479$	−19.1553	−	9.44633i	−0.875226	−	0.431614i	−0.0515474	−	0.998671i	$-0.516415\pi$
$479$	−19.1553	−	9.44633i	−0.875226	−	0.431614i	−0.823679	+	0.567057i	$0.808082\pi$
$480$	3.86637	+	3.55839i	0.176475	+	0.162418i
$481$	−26.8880	−	23.5802i	−1.22599	−	1.07516i
$482$	−42.6260	+	21.0208i	−1.94156	+	0.957471i
$483$	4.82982	+	1.41918i	0.219765	+	0.0645748i
$484$	−1.61027	−	12.2312i	−0.0731942	−	0.555965i
$485$	2.01944	+	0.836479i	0.0916980	+	0.0379826i
$486$	−3.29934	+	27.3703i	−0.149661	+	1.24154i
$487$	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
$489$	−5.19981	−	16.6177i	−0.235143	−	0.751479i
$490$	0.403083	+	6.14986i	0.0182094	+	0.277822i
$491$	−16.4877	−	2.17064i	−0.744077	−	0.0979597i	−0.251051	−	0.967974i	$-0.580776\pi$
$491$	−16.4877	−	2.17064i	−0.744077	−	0.0979597i	−0.493027	+	0.870014i	$0.664109\pi$
$492$	0.0228180	+	0.550089i	0.00102871	+	0.0247999i
$493$	0.558830	−	3.10986i	0.0251684	−	0.140061i
$494$			18.1716i			0.817578i
$495$	0.210210	−	0.326815i	0.00944822	−	0.0146892i
$496$	6.62424	+	9.91388i	0.297437	+	0.445146i
$497$	1.50912	−	5.63211i	0.0676933	−	0.252635i
$498$	−1.11120	−	2.87596i	−0.0497941	−	0.128875i
$499$	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
$501$	−3.88400	−	22.3111i	−0.173524	−	0.996786i
$502$	−29.1326	+	3.83538i	−1.30025	+	0.171182i
$503$	−2.13202	−	10.7184i	−0.0950619	−	0.477908i	−0.998762	−	0.0497426i	$-0.984160\pi$
$503$	−2.13202	−	10.7184i	−0.0950619	−	0.477908i	0.903700	−	0.428166i	$-0.140840\pi$
$504$	1.54476	+	2.57086i	0.0688092	+	0.114515i
$505$	3.00792	+	0.598313i	0.133851	+	0.0266246i
$506$	−1.87376	−	0.502073i	−0.0832989	−	0.0223199i
$507$	20.1495	+	27.6063i	0.894871	+	1.22604i
$508$	−2.66397	+	20.2349i	−0.118195	+	0.897777i
$509$	4.23473	−	7.33477i	0.187701	−	0.325108i	−0.756782	−	0.653667i	$-0.773230\pi$
$509$	4.23473	−	7.33477i	0.187701	−	0.325108i	0.944483	+	0.328559i	$0.106563\pi$
$510$	6.55313	+	1.34062i	0.290178	+	0.0593634i
$511$	3.12446	+	5.41173i	0.138218	+	0.239401i
$512$	12.1682	−	5.04021i	0.537761	−	0.222748i
$513$	−7.05621	+	6.10708i	−0.311539	+	0.269634i
$514$	−9.17332	+	9.17332i	−0.404618	+	0.404618i
$515$	0.536634	+	1.58087i	0.0236469	+	0.0696616i
$516$	13.1246	−	7.16328i	0.577778	−	0.315346i
$517$	1.83576	+	0.623158i	0.0807368	+	0.0274065i
$518$	4.36112	+	5.68352i	0.191617	+	0.249720i
$519$	8.50793	−	23.2180i	0.373457	−	1.01916i
$520$	3.08217	+	3.51454i	0.135162	+	0.154123i
$521$	11.6214	−	17.3927i	0.509143	−	0.761987i	−0.484472	−	0.874807i	$-0.660988\pi$
$521$	11.6214	−	17.3927i	0.509143	−	0.761987i	0.993615	+	0.112820i	$0.0359883\pi$
$522$	−4.03969	−	0.460222i	−0.176812	−	0.0201434i
$523$	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
$525$	−3.04784	+	4.33267i	−0.133019	+	0.189093i
$526$	−2.07329	−	1.19702i	−0.0903998	−	0.0521924i
$527$	8.92650	+	4.19804i	0.388844	+	0.182870i
$528$	−1.13044	−	1.78298i	−0.0491959	−	0.0775943i
$529$	−1.75646	+	2.28906i	−0.0763677	+	0.0995243i
$530$	−5.45588	+	3.64550i	−0.236988	+	0.158350i
$531$	15.4390	+	13.0698i	0.669998	+	0.567183i
$532$	0.256037	−	1.28719i	0.0111006	−	0.0558066i
$533$	−0.105477	+	1.60926i	−0.00456870	+	0.0697049i
$534$	−44.4405	+	10.7721i	−1.92313	+	0.466152i
$535$	7.94217	−	6.09424i	0.343370	−	0.263477i
$536$	3.68609	−	2.82844i	0.159215	−	0.122170i
$537$	7.17917	−	24.4326i	0.309804	−	1.05434i
$538$	2.83300	−	43.2233i	0.122139	−	1.86349i
$539$	0.313956	−	1.57837i	0.0135231	−	0.0679850i
$540$	0.425136	−	3.07399i	0.0182949	−	0.132283i
$541$	−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
$543$	−9.93104	+	18.9764i	−0.426182	+	0.814355i
$544$	14.0278	−	19.0011i	0.601438	−	0.814665i
$545$	−7.28158	−	4.20402i	−0.311909	−	0.180081i
$546$	−4.77718	−	10.3032i	−0.204444	−	0.440936i
$547$	−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
$549$	20.3251	+	15.0395i	0.867456	+	0.641870i
$550$	1.13410	−	1.69729i	0.0483580	−	0.0723729i
$551$	−0.907452	−	1.03475i	−0.0386588	−	0.0440819i
$552$	11.8068	−	2.05537i	0.502530	−	0.0874822i
$553$	−2.07689	−	2.70666i	−0.0883184	−	0.115099i
$554$	13.7496	+	4.66737i	0.584165	+	0.198297i
$555$	−0.137565	+	5.73241i	−0.00583931	+	0.243327i
$556$	4.82320	+	14.2087i	0.204549	+	0.602583i
$557$	−26.0867	+	26.0867i	−1.10533	+	1.10533i	−0.111574	+	0.993756i	$0.535589\pi$
$557$	−26.0867	+	26.0867i	−1.10533	+	1.10533i	−0.993756	+	0.111574i	$0.964411\pi$
$558$	4.65200	−	11.8102i	0.196935	−	0.499964i
$559$	40.4642	−	16.7608i	1.71146	−	0.708908i
$560$	−0.855217	−	1.48128i	−0.0361395	−	0.0625955i
$561$	−1.56224	−	0.781008i	−0.0659576	−	0.0329742i
$562$	−7.37624	+	12.7760i	−0.311148	+	0.538924i
$563$	3.31115	−	25.1507i	0.139548	−	1.05998i	−0.768126	−	0.640299i	$-0.778810\pi$
$563$	3.31115	−	25.1507i	0.139548	−	1.05998i	0.907674	−	0.419676i	$-0.137856\pi$
$564$	15.3938	−	1.65200i	0.648196	−	0.0695617i
$565$	9.21813	+	2.46999i	0.387810	+	0.103913i
$566$	−38.7830	−	7.71442i	−1.63017	−	0.324261i
$567$	2.39532	−	5.31771i	0.100594	−	0.223323i
$568$	−2.70809	−	13.6145i	−0.113629	−	0.571251i
$569$	0.251252	−	0.0330779i	0.0105330	−	0.00138670i	−0.125258	−	0.992124i	$-0.539976\pi$
$569$	0.251252	−	0.0330779i	0.0105330	−	0.00138670i	0.135791	+	0.990738i	$0.456642\pi$
$570$	2.23597	−	1.86793i	0.0936546	−	0.0782388i
$571$	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
$573$	30.2403	+	4.72183i	1.26331	+	0.197257i
$574$	0.0836125	−	0.312046i	0.00348992	−	0.0130246i
$575$	11.7596	+	17.5995i	0.490410	+	0.733950i
$576$	−0.411606	−	0.264748i	−0.0171503	−	0.0110312i
$577$			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
$579$	−10.0980	+	6.40225i	−0.419657	+	0.266069i
$580$	0.453753	+	0.0597378i	0.0188411	+	0.00248048i
$581$	0.0426601	+	0.650868i	0.00176984	+	0.0270025i
$582$	−12.3367	−	2.76317i	−0.511373	−	0.114537i
$583$	1.62246	−	0.550750i	0.0671953	−	0.0228097i
$584$	12.3695	+	8.26503i	0.511853	+	0.342009i
$585$	2.19900	−	8.82009i	0.0909174	−	0.364666i
$586$	5.71204	+	2.36601i	0.235962	+	0.0977388i
$587$	−1.32165	−	10.0389i	−0.0545503	−	0.414351i	−0.996832	−	0.0795309i	$-0.974658\pi$
$587$	−1.32165	−	10.0389i	−0.0545503	−	0.414351i	0.942282	−	0.334820i	$-0.108676\pi$
$588$	−3.02754	−	12.4902i	−0.124854	−	0.515088i
$589$	3.85363	−	1.90040i	0.158786	−	0.0783045i
$590$	−4.74822	−	4.16408i	−0.195481	−	0.171432i
$591$	−21.8439	+	6.83513i	−0.898539	+	0.281160i
$592$	27.9401	+	13.7785i	1.14833	+	0.566294i
$593$	−14.8623	−	35.8809i	−0.610323	−	1.47345i	−0.862646	−	0.505807i	$-0.831195\pi$
$593$	−14.8623	−	35.8809i	−0.610323	−	1.47345i	0.252323	−	0.967643i	$-0.418805\pi$
$594$	−0.873612	+	2.07074i	−0.0358448	+	0.0849635i
$595$	−1.23840	−	0.684682i	−0.0507695	−	0.0280692i
$596$	−1.98285	+	1.14480i	−0.0812209	+	0.0468929i
$597$	−2.18033	+	24.3117i	−0.0892348	+	0.995011i
$598$	−45.2819	+	2.96793i	−1.85172	+	0.121368i
$599$	−27.9063	+	7.47748i	−1.14022	+	0.305521i	−0.779040	−	0.626974i	$-0.784293\pi$
$599$	−27.9063	+	7.47748i	−1.14022	+	0.305521i	−0.361181	+	0.932496i	$0.617626\pi$
$600$	−1.94557	+	12.4602i	−0.0794277	+	0.508684i
$601$	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
$603$	−8.60485	−	2.75434i	−0.350416	−	0.112165i
$604$	10.3851	−	25.0718i	0.422563	−	1.02016i
$605$	−4.35619	+	3.82028i	−0.177104	+	0.155316i
$606$	−17.7329	−	0.425550i	−0.720351	−	0.0172868i
$607$	−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
$609$	0.786550	+	0.348135i	0.0318726	+	0.0141072i
$610$	−6.26273	−	4.80556i	−0.253571	−	0.194572i
$611$	45.3507			1.83469
$612$	−13.9423	−	0.410518i	−0.563584	−	0.0165942i
$613$	−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
$615$	0.208859	−	0.152444i	0.00842199	−	0.00614712i
$616$	0.0632840	+	0.236179i	0.00254978	+	0.00951592i
$617$	−12.0867	+	13.7822i	−0.486592	+	0.554852i	−0.942079	−	0.335391i	$-0.891132\pi$
$617$	−12.0867	+	13.7822i	−0.486592	+	0.554852i	0.455487	+	0.890242i	$0.349465\pi$
$618$	−4.62594	−	8.47567i	−0.186083	−	0.340941i
$619$	−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
$621$	−16.3708	−	16.5860i	−0.656937	−	0.665572i
$622$	45.1146	−	8.97385i	1.80893	−	0.359818i
$623$	9.65322	+	0.632705i	0.386748	+	0.0253488i
$624$	−38.4478	−	30.9955i	−1.53915	−	1.24081i
$625$	−20.1602	+	5.40190i	−0.806407	+	0.216076i
$626$	−19.8685	+	1.30225i	−0.794105	+	0.0520484i
$627$	−0.690198	+	0.320018i	−0.0275638	+	0.0127803i
$628$	12.1370	−	7.00730i	0.484319	−	0.279622i
$629$	25.6824	−	2.16242i	1.02402	−	0.0862214i
$630$	−0.776720	+	1.64693i	−0.0309453	+	0.0656151i
$631$	−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
$633$	−10.7756	+	48.1100i	−0.428293	+	1.91220i
$634$	−10.6644	−	9.35244i	−0.423538	−	0.371433i
$635$	8.59691	−	4.23953i	0.341158	−	0.168241i
$636$	9.90485	−	9.44061i	0.392753	−	0.374344i
$637$	−4.91379	−	37.3239i	−0.194691	−	1.47883i
$638$	−0.306229	−	0.126844i	−0.0121237	−	0.00502181i
$639$	−18.7507	+	19.4174i	−0.741768	+	0.768139i
$640$	−4.91790	−	3.28604i	−0.194397	−	0.129892i
$641$	16.3246	−	5.54145i	0.644782	−	0.218874i	0.0201547	−	0.999797i	$-0.493584\pi$
$641$	16.3246	−	5.54145i	0.644782	−	0.218874i	0.624628	+	0.780923i	$0.285251\pi$
$642$	−39.2101	+	42.6038i	−1.54750	+	1.68144i
$643$	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
$645$	−6.22186	−	3.25613i	−0.244985	−	0.128210i
$646$	−9.43021	−	9.08667i	−0.371027	−	0.357510i
$647$			25.4973i			1.00240i	0.865330	+	0.501202i	$0.167109\pi$
$647$			25.4973i			1.00240i	−0.865330	+	0.501202i	$0.832891\pi$
$648$	−0.484858	−	13.8763i	−0.0190470	−	0.545113i
$649$	0.916182	+	1.37116i	0.0359633	+	0.0538229i
$650$	12.3592	−	46.1253i	0.484770	−	1.80918i
$651$	−1.68538	+	2.09061i	−0.0660554	+	0.0819374i
$652$	−5.01392	−	10.1672i	−0.196360	−	0.398179i
$653$	1.88115	−	5.54168i	0.0736150	−	0.216863i	−0.903894	−	0.427757i	$-0.859304\pi$
$653$	1.88115	−	5.54168i	0.0736150	−	0.216863i	0.977509	+	0.210894i	$0.0676374\pi$
$654$	45.6613	+	16.7320i	1.78550	+	0.654273i
$655$	−7.03782	+	0.926546i	−0.274990	+	0.0362032i
$656$	−0.274067	−	1.37783i	−0.0107005	−	0.0537951i
$657$	−0.505175	−	28.9244i	−0.0197087	−	1.12845i
$658$	−8.90995	−	1.77230i	−0.347346	−	0.0690914i
$659$	7.51008	+	2.01232i	0.292551	+	0.0783889i	0.402110	−	0.915591i	$-0.368277\pi$
$659$	7.51008	+	2.01232i	0.292551	+	0.0783889i	−0.109558	+	0.993980i	$0.534944\pi$
$660$	0.102394	−	0.231340i	0.00398567	−	0.00900490i
$661$	−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
$663$	−40.4786	−	5.55339i	−1.57206	−	0.215676i
$664$	0.776414	+	1.34479i	0.0301307	+	0.0521879i
$665$	−0.569460	+	0.235878i	−0.0220827	+	0.00914695i
$666$	−4.90239	−	32.8003i	−0.189964	−	1.27099i
$667$	2.43029	−	2.43029i	0.0941014	−	0.0941014i
$668$	−4.73936	−	13.9617i	−0.183371	−	0.540194i
$669$	12.9781	+	7.91402i	0.501763	+	0.305974i
$670$	2.67108	+	0.906711i	0.103193	+	0.0350293i
$671$	1.25482	+	1.63531i	0.0484418	+	0.0631306i
$672$	4.12210	+	4.93430i	0.159014	+	0.190345i
$673$	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
$675$	22.0646	−	10.7025i	0.849268	−	0.411941i
$676$	15.7341	+	15.7341i	0.605159	+	0.605159i
$677$	3.86886	−	7.84527i	0.148692	−	0.301518i	−0.809765	−	0.586754i	$-0.800405\pi$
$677$	3.86886	−	7.84527i	0.148692	−	0.301518i	0.958457	+	0.285236i	$0.0920721\pi$
$678$	−54.9759	−	4.93037i	−2.11134	−	0.189350i
$679$	2.31625	+	1.33729i	0.0888896	+	0.0513204i
$680$	−3.36512	−	0.157937i	−0.129046	−	0.00605660i
$681$	10.5118	−	0.436035i	0.402814	−	0.0167089i
$682$	0.629950	−	0.820967i	0.0241220	−	0.0314364i
$683$	14.5914	−	9.74966i	0.558324	−	0.373060i	−0.244159	−	0.969735i	$-0.578512\pi$
$683$	14.5914	−	9.74966i	0.558324	−	0.373060i	0.802483	+	0.596675i	$0.203512\pi$
$684$	−3.92557	+	4.63717i	−0.150098	+	0.177306i
$685$	2.13794	−	10.7481i	0.0816865	−	0.410666i
$686$	−1.01790	+	15.5302i	−0.0388637	+	0.592946i
$687$	−6.94944	−	7.29118i	−0.265138	−	0.278176i
$688$	−30.2681	+	23.2256i	−1.15396	+	0.885466i
$689$	31.7985	−	24.3999i	1.21143	−	0.929561i
$690$	5.01990	+	5.26676i	0.191104	+	0.200502i
$691$	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
$693$	0.307208	−	0.362897i	0.0116699	−	0.0137853i
$694$	−13.6093	+	9.09346i	−0.516603	+	0.345183i
$695$	4.29006	−	5.59091i	0.162731	−	0.212075i
$696$	2.04598	−	0.0848682i	0.0775526	−	0.00321692i
$697$	−0.782390	−	0.859448i	−0.0296352	−	0.0325539i
$698$	4.68326	+	2.70388i	0.177264	+	0.102343i
$699$	12.6594	+	1.13532i	0.478821	+	0.0429418i
$700$	−1.52538	+	3.09316i	−0.0576538	+	0.116910i
$701$	20.0615	+	20.0615i	0.757711	+	0.757711i	0.975905	−	0.218195i	$-0.0700168\pi$
$701$	20.0615	+	20.0615i	0.757711	+	0.757711i	−0.218195	+	0.975905i	$0.570017\pi$
$702$	−3.78106	+	52.4390i	−0.142707	+	1.97918i
$703$	6.23702	−	9.33436i	0.235234	−	0.352052i
$704$	−0.0263063	−	0.0299965i	−0.000991454	−	0.00113054i
$705$	−4.66177	−	5.58031i	−0.175573	−	0.210167i
$706$	10.7718	+	14.0381i	0.405403	+	0.528332i
$707$	3.55345	+	1.20623i	0.133641	+	0.0453651i
$708$	11.2441	+	6.85659i	0.422577	+	0.257686i
$709$	−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
$711$	2.33466	+	15.6205i	0.0875565	+	0.585813i
$712$	21.2774	−	8.81338i	0.797404	−	0.330295i
$713$	5.36503	+	9.29250i	0.200922	+	0.348007i
$714$	7.73570	+	2.67296i	0.289501	+	0.100033i
$715$	0.370528	−	0.641773i	0.0138569	−	0.0240009i
$716$	2.16404	−	16.4375i	0.0808741	−	0.614300i
$717$	−6.67615	+	15.0836i	−0.249325	+	0.563306i
$718$	27.3918	+	7.33962i	1.02225	+	0.273912i
$719$	−45.9582	−	9.14165i	−1.71395	−	0.340926i	−0.762094	−	0.647467i	$-0.775828\pi$
$719$	−45.9582	−	9.14165i	−1.71395	−	0.340926i	−0.951857	+	0.306541i	$0.900828\pi$
$720$	0.138275	+	7.91707i	0.00515319	+	0.295052i
$721$	0.398524	+	2.00352i	0.0148418	+	0.0746148i
$722$	27.6590	−	3.64137i	1.02936	−	0.135518i
$723$	−43.7054	−	16.0153i	−1.62542	−	0.595614i
$724$	−4.48223	+	13.2042i	−0.166581	+	0.490731i
$725$	1.59963	+	3.24373i	0.0594088	+	0.120469i
$726$	21.0325	−	26.0894i	0.780590	−	0.968270i
$727$	−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
$729$	−21.6334	+	16.1554i	−0.801235	+	0.598349i
$730$			9.03183i			0.334283i
$731$	−11.5360	+	29.3803i	−0.426674	+	1.08667i
$732$	14.5849	+	7.63282i	0.539074	+	0.282117i
$733$	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
$735$	−4.08752	+	4.44130i	−0.150770	+	0.163820i
$736$	24.3275	−	8.25808i	0.896724	−	0.304397i
$737$	−0.612426	−	0.409210i	−0.0225590	−	0.0150734i
$738$	−1.03888	+	1.07582i	−0.0382418	+	0.0396013i
$739$	−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
$741$	−12.8826	+	12.2788i	−0.473253	+	0.451071i
$742$	−7.20093	+	3.55111i	−0.264354	+	0.130365i
$743$	27.4652	+	24.0864i	1.00760	+	0.883643i	0.993220	−	0.116254i	$-0.0370885\pi$
$743$	27.4652	+	24.0864i	1.00760	+	0.883643i	0.0143821	+	0.999897i	$0.495422\pi$
$744$	−1.39727	+	6.23840i	−0.0512265	+	0.228711i
$745$	0.964431	+	0.475605i	0.0353340	+	0.0174248i
$746$	−3.36017	−	8.11217i	−0.123025	−	0.297007i
$747$	1.28803	−	2.73110i	0.0471267	−	0.0999256i
$748$	−1.08337	−	0.345478i	−0.0396118	−	0.0126319i
$749$	10.6082	−	6.12466i	0.387616	−	0.223790i
$750$	−14.3050	+	6.63265i	−0.522344	+	0.242190i
$751$	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
$753$	−22.4043	−	18.0617i	−0.816459	−	0.658205i
$754$	−7.73722	−	0.507124i	−0.281773	−	0.0184684i
$755$	−12.5004	+	2.48648i	−0.454936	+	0.0904924i
$756$	1.00670	−	3.66125i	0.0366133	−	0.133159i
$757$	−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
$759$	−0.910184	−	1.66764i	−0.0330376	−	0.0605316i
$760$	−0.967522	+	1.10325i	−0.0350957	+	0.0400190i
$761$	−4.74914	−	17.7240i	−0.172156	−	0.642496i	−0.997019	−	0.0771621i	$-0.975414\pi$
$761$	−4.74914	−	17.7240i	−0.172156	−	0.642496i	0.824862	−	0.565334i	$-0.191253\pi$
$762$	−44.7807	+	32.6849i	−1.62223	+	1.18405i
$763$	−8.16209	−	6.26299i	−0.295487	−	0.226735i
$764$	19.9266			0.720920
$765$	3.47762	+	5.55165i	0.125733	+	0.200720i
$766$	47.4279			1.71364
$767$	30.6052	+	23.4842i	1.10509	+	0.847964i
$768$	31.7990	+	14.0746i	1.14745	+	0.507873i
$769$	−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
$771$	−12.7019	−	0.304816i	−0.457446	−	0.0109777i
$772$	−5.85255	+	5.13255i	−0.210638	+	0.184725i
$773$	−12.5389	+	30.2715i	−0.450992	+	1.08879i	0.520954	+	0.853585i	$0.325576\pi$
$773$	−12.5389	+	30.2715i	−0.450992	+	1.08879i	−0.971946	+	0.235206i	$0.924424\pi$
$774$	38.6827	+	12.3820i	1.39042	+	0.445061i
$775$	−11.0743	+	2.20281i	−0.397800	+	0.0791274i
$776$	6.35366	+	0.416441i	0.228083	+	0.0149494i
$777$	−1.08242	+	6.93221i	−0.0388316	+	0.248691i
$778$	−39.1873	+	10.5002i	−1.40493	+	0.376451i
$779$	−0.505163	+	0.0331101i	−0.0180993	+	0.00118629i
$780$	0.528629	−	5.89447i	0.0189280	−	0.211056i
$781$	−1.90575	+	1.10028i	−0.0681930	+	0.0393713i
$782$	21.1029	−	24.9834i	0.754640	−	0.893403i
$783$	−2.40340	−	3.17488i	−0.0858903	−	0.113461i
$784$	12.5494	+	30.2968i	0.448191	+	1.08203i
$785$	−5.90325	−	2.91116i	−0.210696	−	0.103904i
$786$	39.1831	−	12.2607i	1.39762	−	0.437324i
$787$	−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
$789$	−0.552336	−	2.27868i	−0.0196637	−	0.0811231i
$790$	−0.643627	−	4.88884i	−0.0228992	−	0.173937i
$791$	10.7883	+	4.46867i	0.383589	+	0.158888i
$792$	0.273829	−	1.09832i	0.00973009	−	0.0390270i
$793$	40.0928	+	26.7891i	1.42374	+	0.951310i
$794$	−27.4016	+	9.30158i	−0.972445	+	0.330101i
$795$	−6.27105	−	1.40458i	−0.222411	−	0.0498155i
$796$	1.03937	+	15.8577i	0.0368394	+	0.562061i
$797$	−47.2869	−	6.22544i	−1.67499	−	0.220516i	−0.767635	−	0.640887i	$-0.778567\pi$
$797$	−47.2869	−	6.22544i	−1.67499	−	0.220516i	−0.907352	+	0.420371i	$0.861900\pi$
$798$	3.01086	−	1.90893i	0.106583	−	0.0675754i
$799$	−22.6776	+	23.5349i	−0.802275	+	0.832607i
$800$			27.0346i			0.955818i
$801$	−37.6657	−	24.2269i	−1.33085	−	0.856014i
$802$	−24.3707	−	36.4734i	−0.860561	−	1.28792i
$803$	0.610392	−	2.27802i	0.0215403	−	0.0803894i
$804$	−5.81179	−	0.907474i	−0.204966	−	0.0320041i
$805$	−0.680795	−	1.38052i	−0.0239949	−	0.0486568i
$806$	7.78114	−	22.9225i	0.274079	−	0.807410i
$807$	32.5570	−	27.1981i	1.14606	−	0.957417i
$808$	8.85729	−	1.16608i	0.311598	−	0.0410227i
$809$	−6.61554	−	33.2586i	−0.232590	−	1.16931i	−0.903771	−	0.428016i	$-0.859213\pi$
$809$	−6.61554	−	33.2586i	−0.232590	−	1.16931i	0.671181	−	0.741294i	$-0.265787\pi$
$810$	6.84118	−	4.92516i	0.240375	−	0.173052i
$811$	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
$813$	43.3571	−	4.65290i	1.52060	−	0.163184i
$814$	0.352904	−	2.68057i	0.0123693	−	0.0939539i
$815$	−2.66208	+	4.61086i	−0.0932487	+	0.161511i
$816$	35.3110	−	4.45342i	1.23613	−	0.155901i
$817$	6.87433	+	11.9067i	0.240502	+	0.416562i
$818$	−37.8737	+	15.6878i	−1.32422	+	0.548511i
$819$	4.07635	−	10.3487i	0.142439	−	0.361614i
$820$	0.119039	−	0.119039i	0.00415701	−	0.00415701i
$821$	−3.15917	−	9.30661i	−0.110256	−	0.324803i	0.877772	−	0.479078i	$-0.159029\pi$
$821$	−3.15917	−	9.30661i	−0.110256	−	0.324803i	−0.988028	+	0.154276i	$0.950696\pi$
$822$	−1.52061	+	63.3647i	−0.0530374	+	2.21010i
$823$	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
$825$	1.96960	−	0.342876i	0.0685728	−	0.0119374i
$826$	−5.09517	−	5.80992i	−0.177283	−	0.202153i
$827$	−19.7223	+	29.5165i	−0.685810	+	1.02639i	0.311292	+	0.950314i	$0.399238\pi$
$827$	−19.7223	+	29.5165i	−0.685810	+	1.02639i	−0.997102	+	0.0760735i	$0.975762\pi$
$828$	−12.1966	−	9.02478i	−0.423860	−	0.313633i
$829$	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
$831$	5.98190	+	12.9015i	0.207510	+	0.447547i
$832$	−0.808279	−	0.466660i	−0.0280220	−	0.0161785i
$833$	21.8265	+	16.1138i	0.756245	+	0.558308i
$834$	−18.8993	+	36.1131i	−0.654429	+	1.25049i
$835$	−4.21548	+	5.49373i	−0.145883	+	0.190118i
$836$	−0.411833	+	0.275178i	−0.0142435	+	0.00951723i
$837$	11.5161	−	4.68227i	0.398055	−	0.161843i
$838$	0.863263	−	4.33992i	0.0298209	−	0.149920i
$839$	2.82718	−	43.1344i	0.0976049	−	1.48916i	−0.615517	−	0.788123i	$-0.711053\pi$
$839$	2.82718	−	43.1344i	0.0976049	−	1.48916i	0.713122	−	0.701040i	$-0.247281\pi$
$840$	0.258544	−	0.879890i	0.00892060	−	0.0303591i
$841$	−22.5413	+	17.2966i	−0.777288	+	0.596434i
$842$	9.67050	−	7.42044i	0.333268	−	0.255725i
$843$	−14.0417	+	3.40360i	−0.483620	+	0.117226i
$844$	−2.09932	+	32.0295i	−0.0722617	+	1.10250i
$845$	2.03880	−	10.2497i	0.0701367	−	0.352601i
$846$	32.0986	+	27.1729i	1.10357	+	0.934224i
$847$	−5.89478	+	3.93877i	−0.202547	+	0.135338i
$848$	−21.2545	+	27.6994i	−0.729882	+	0.951201i
$849$	−20.7371	−	32.7076i	−0.711695	−	1.12252i
$850$	17.7567	+	29.4788i	0.609050	+	1.01111i
$851$	24.2791	+	14.0175i	0.832276	+	0.480515i
$852$	−10.1113	+	14.3737i	−0.346407	+	0.492436i
$853$	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
$855$	2.83512	+	0.322992i	0.0969591	+	0.0110461i
$856$	16.2013	−	24.2470i	0.553751	−	0.828746i
$857$	−0.680782	−	0.776283i	−0.0232551	−	0.0265173i	0.740095	−	0.672502i	$-0.234780\pi$
$857$	−0.680782	−	0.776283i	−0.0232551	−	0.0265173i	−0.763350	+	0.645985i	$0.776447\pi$
$858$	−1.47470	+	4.02443i	−0.0503454	+	0.137392i
$859$	−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
$861$	0.277720	−	0.151577i	0.00946468	−	0.00516573i
$862$	−18.6144	−	54.8361i	−0.634007	−	1.86773i
$863$	4.14890	−	4.14890i	0.141230	−	0.141230i	−0.632957	−	0.774187i	$-0.718159\pi$
$863$	4.14890	−	4.14890i	0.141230	−	0.141230i	0.774187	+	0.632957i	$0.218159\pi$
$864$	−5.61611	−	29.2303i	−0.191064	−	0.994435i
$865$	−6.98547	+	2.89348i	−0.237513	+	0.0983812i
$866$	−14.5130	−	25.1372i	−0.493171	−	0.854198i
$867$	23.1232	−	18.2296i	0.785306	−	0.619108i
$868$	−0.874156	+	1.51408i	−0.0296708	+	0.0513913i
$869$	−0.168063	+	1.27656i	−0.00570114	+	0.0433045i
$870$	0.732938	+	1.00418i	0.0248489	+	0.0340448i
$871$	−16.6432	−	4.45952i	−0.563932	−	0.151105i
$872$	−24.0220	−	4.77826i	−0.813486	−	0.161812i
$873$	−6.37715	−	10.6131i	−0.215834	−	0.359199i
$874$	−2.77905	−	13.9712i	−0.0940026	−	0.472583i
$875$	3.30725	−	0.435408i	0.111805	−	0.0147195i
$876$	−3.23014	−	18.5551i	−0.109136	−	0.626919i
$877$	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
$879$	2.18234	+	5.64824i	0.0736085	+	0.190510i
$880$	−0.167074	+	0.623530i	−0.00563207	+	0.0210192i
$881$	3.00833	+	4.50228i	0.101353	+	0.151686i	0.878680	−	0.477411i	$-0.158425\pi$
$881$	3.00833	+	4.50228i	0.101353	+	0.151686i	−0.777327	+	0.629097i	$0.783425\pi$
$882$	18.8856	−	29.3616i	0.635910	−	0.988656i
$883$			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
$885$	−0.256346	−	6.17992i	−0.00861699	−	0.207736i
$886$	17.4943	+	2.30317i	0.587734	+	0.0773767i
$887$	−1.71620	−	26.1841i	−0.0576243	−	0.879177i	−0.924627	−	0.380873i	$-0.875623\pi$
$887$	−1.71620	−	26.1841i	−0.0576243	−	0.879177i	0.867003	−	0.498303i	$-0.166043\pi$
$888$	4.98809	+	15.9411i	0.167389	+	0.534948i
$889$	11.1063	−	3.77008i	0.372493	−	0.126444i
$890$	11.6257	+	7.76805i	0.389695	+	0.260386i
$891$	−2.05834	+	0.779885i	−0.0689571	+	0.0261271i
$892$	9.14318	+	3.78723i	0.306136	+	0.126806i
$893$	1.85817	+	14.1142i	0.0621814	+	0.472315i
$894$	−5.96720	−	1.75338i	−0.199573	−	0.0586418i
$895$	−6.98360	+	3.44393i	−0.233436	+	0.115118i
$896$	−5.44125	−	4.77185i	−0.181779	−	0.159416i
$897$	−32.7016	−	30.0967i	−1.09188	−	1.00490i
$898$	−25.4559	−	12.5535i	−0.849474	−	0.418914i
$899$	0.701620	+	1.69386i	0.0234003	+	0.0564934i
$900$	13.1183	−	9.10069i	0.437277	−	0.303356i
$901$	−3.23840	+	28.7031i	−0.107887	+	0.956240i
$902$	−0.105588	+	0.0609610i	−0.00351568	+	0.00202978i
$903$	−7.02790	−	4.94382i	−0.233874	−	0.164520i
$904$	27.7401	−	1.81818i	0.922621	−	0.0604718i
$905$	6.32584	−	1.69500i	0.210278	−	0.0563438i
$906$	68.7621	−	26.5680i	2.28447	−	0.882662i
$907$	−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
$909$	−11.6807	−	12.8592i	−0.387424	−	0.426511i
$910$	−1.32890	+	3.20825i	−0.0440526	+	0.106352i
$911$	−18.6461	+	16.3522i	−0.617774	+	0.541773i	−0.910017	−	0.414571i	$-0.863932\pi$
$911$	−18.6461	+	16.3522i	−0.617774	+	0.541773i	0.292243	+	0.956344i	$0.405598\pi$
$912$	8.07120	−	13.2359i	0.267264	−	0.438284i
$913$	0.162310	−	0.185079i	0.00537166	−	0.00612521i
$914$	−12.5873	−	46.9763i	−0.416350	−	1.55384i
$915$	−0.824945	−	7.68708i	−0.0272718	−	0.254127i
$916$	−5.20262	−	3.99211i	−0.171899	−	0.131903i
$917$	−8.68578			−0.286830
$918$	−25.3227	−	28.1843i	−0.835775	−	0.930220i
$919$	−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
$921$	0.346067	+	3.22476i	0.0114033	+	0.106259i
$922$	4.50682	+	16.8197i	0.148424	+	0.553927i
$923$	−33.9417	+	38.7030i	−1.11720	+	1.27393i
$924$	0.161165	−	0.264293i	0.00530193	−	0.00869459i
$925$	−22.1803	+	19.4516i	−0.729283	+	0.639564i
$926$	−7.63872	+	18.4415i	−0.251024	+	0.606025i
$927$	2.88294	−	9.00663i	0.0946883	−	0.295817i
$928$	4.30540	−	0.856398i	0.141332	−	0.0281126i
$929$	−12.6499	−	0.829120i	−0.415030	−	0.0272025i	−0.143542	−	0.989644i	$-0.545849\pi$
$929$	−12.6499	−	0.829120i	−0.415030	−	0.0272025i	−0.271488	+	0.962442i	$0.587516\pi$
$930$	−3.62042	+	1.39884i	−0.118718	+	0.0458697i
$931$	11.4148	−	3.05858i	0.374104	−	0.100241i
$932$	8.25729	−	0.541211i	0.270476	−	0.0177280i
$933$	36.8464	+	25.9198i	1.20630	+	0.848577i
$934$	−11.4451	+	6.60782i	−0.374494	+	0.216214i
$935$	0.147769	+	0.513204i	0.00483255	+	0.0167836i
$936$	−2.19298	−	26.3884i	−0.0716797	−	0.862531i
$937$	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
$939$	−14.3486	−	13.2056i	−0.468249	−	0.430950i
$940$	−3.55922	−	3.12135i	−0.116089	−	0.101807i
$941$	41.8877	−	20.6567i	1.36550	−	0.673390i	0.395948	−	0.918273i	$-0.370416\pi$
$941$	41.8877	−	20.6567i	1.36550	−	0.673390i	0.969553	+	0.244883i	$0.0787495\pi$
$942$	36.5250	+	10.7324i	1.19005	+	0.349680i
$943$	−0.165015	−	1.25341i	−0.00537362	−	0.0408167i
$944$	−31.0460	−	12.8597i	−1.01046	−	0.418547i
$945$	−1.69241	+	0.562199i	−0.0550542	+	0.0182884i
$946$	2.75313	+	1.83958i	0.0895120	+	0.0598100i
$947$	−29.4772	+	10.0062i	−0.957881	+	0.325157i	−0.756234	−	0.654301i	$-0.772963\pi$
$947$	−29.4772	+	10.0062i	−0.957881	+	0.325157i	−0.201647	+	0.979458i	$0.564629\pi$
$948$	3.07072	+	9.81351i	0.0997324	+	0.318728i
$949$	−3.60825	−	55.0512i	−0.117129	−	1.78704i
$950$	14.8617	+	1.95658i	0.482178	+	0.0634799i
$951$	−0.575749	−	13.8800i	−0.0186699	−	0.450090i
$952$	−4.05711	−	0.729048i	−0.131492	−	0.0236286i
$953$			3.63734i			0.117825i	0.998263	+	0.0589124i	$0.0187633\pi$
$953$			3.63734i			0.117825i	−0.998263	+	0.0589124i	$0.981237\pi$
$954$	37.1263	+	1.78292i	1.20201	+	0.0577242i
$955$	−5.19940	−	7.78145i	−0.168248	−	0.251802i
$956$	−2.77949	+	10.3732i	−0.0898950	+	0.335493i
$957$	−0.116998	−	0.302808i	−0.00378200	−	0.00978840i
$958$	−16.7060	−	33.8764i	−0.539746	−	1.09450i
$959$	4.31021	−	12.6975i	0.139184	−	0.410023i
$960$	0.0256646	+	0.147427i	0.000828321	+	0.00475818i
$961$	25.0599	−	3.29920i	0.808383	−	0.106426i
$962$	−12.3390	−	62.0322i	−0.397825	−	2.00000i
$963$	−56.6984	+	0.990258i	−1.82708	+	0.0319106i
$964$	−29.7225	−	5.91217i	−0.957296	−	0.190418i
$965$	3.53138	+	0.946229i	0.113679	+	0.0304602i
$966$	5.24864	+	7.19101i	0.168872	+	0.231367i
$967$	−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
$969$	0.0698017	−	12.8254i	0.00224235	−	0.412013i
$970$	1.93284	+	3.34777i	0.0620596	+	0.107490i
$971$	8.08819	−	3.35024i	0.259562	−	0.107514i	−0.249108	−	0.968476i	$-0.580137\pi$
$971$	8.08819	−	3.35024i	0.259562	−	0.107514i	0.508670	+	0.860962i	$0.330137\pi$
$972$	−12.2932	+	12.5650i	−0.394304	+	0.403022i
$973$	6.09734	−	6.09734i	0.195472	−	0.195472i
$974$	8.78679	+	25.8851i	0.281547	+	0.829411i
$975$	41.0514	−	22.4055i	1.31470	−	0.717550i
$976$	−39.7741	−	13.5015i	−1.27314	−	0.432172i
$977$	12.2359	+	15.9462i	0.391462	+	0.510164i	0.946959	−	0.321355i	$-0.104138\pi$
$977$	12.2359	+	15.9462i	0.391462	+	0.510164i	−0.555496	+	0.831519i	$0.687472\pi$
$978$	10.5951	−	28.9138i	0.338793	−	0.924561i
$979$	−2.40726	−	2.74496i	−0.0769365	−	0.0877292i
$980$	−2.18325	+	3.26746i	−0.0697413	+	0.104375i
$981$	18.9919	+	43.6772i	0.606366	+	1.39451i
$982$	−20.7962	−	20.7962i	−0.663635	−	0.663635i
$983$	−8.53183	+	17.3008i	−0.272123	+	0.551811i	−0.989441	−	0.144935i	$-0.953703\pi$
$983$	−8.53183	+	17.3008i	−0.272123	+	0.551811i	0.717318	+	0.696746i	$0.245369\pi$
$984$	0.433375	−	0.616066i	0.0138155	−	0.0196395i
$985$	6.06096	+	3.49930i	0.193118	+	0.111497i
$986$	4.13216	−	3.76168i	0.131595	−	0.119796i
$987$	−4.76411	−	7.51419i	−0.151643	−	0.239179i
$988$	−7.05354	+	9.19235i	−0.224403	+	0.292448i
$989$	−28.5476	+	19.0749i	−0.907762	+	0.606547i
$990$	0.646787	−	0.232228i	0.0205562	−	0.00738069i
$991$	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
$993$	−12.9950	+	3.14989i	−0.412384	+	0.0999589i
$994$	8.18095	−	6.27746i	0.259484	−	0.199109i
$995$	5.92131	−	4.54358i	0.187718	−	0.144041i
$996$	0.554227	−	1.88617i	0.0175613	−	0.0597657i
$997$	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
$999$	19.9409	−	25.6391i	0.630902	−	0.811185i

Twists

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

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

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40306 + 1.07661i) q^{2} +(0.184815 + 1.72216i) q^{3} +(0.291859 + 1.08923i) q^{4} +(0.349197 - 0.398183i) q^{5} +(-1.59478 + 2.61527i) q^{6} +(0.487217 - 0.427278i) q^{7} +(0.590386 - 1.42532i) q^{8} +(-2.93169 + 0.636563i) q^{9} +(0.918630 - 0.182727i) q^{10} +(-0.244047 - 0.0159957i) q^{11} +(-1.82190 + 0.703936i) q^{12} +(-5.52628 + 1.48076i) q^{13} +(1.14360 - 0.0749557i) q^{14} +(0.750272 + 0.527784i) q^{15} +(4.31601 - 2.49185i) q^{16} +(1.99496 - 3.60834i) q^{17} +(-4.79866 - 2.26313i) q^{18} +(-0.687279 - 1.65924i) q^{19} +(0.535630 + 0.264144i) q^{20} +(0.825886 + 0.760099i) q^{21} +(-0.325191 - 0.285185i) q^{22} +(4.02242 - 1.98364i) q^{23} +(2.56374 + 0.753321i) q^{24} +(0.616020 + 4.67914i) q^{25} +(-9.34790 - 3.87203i) q^{26} +(-1.63809 - 4.93119i) q^{27} +(0.607604 + 0.405988i) q^{28} +(0.725663 - 0.246329i) q^{29} +(0.484462 + 1.54826i) q^{30} +(0.156475 + 2.38734i) q^{31} +(5.67926 + 0.747688i) q^{32} +(-0.0175564 - 0.423245i) q^{33} +(6.68381 - 2.91493i) q^{34} -0.343205i q^{35} +(-1.54901 - 3.00750i) q^{36} +(3.47283 + 5.19746i) q^{37} +(0.822052 - 3.06794i) q^{38} +(-3.57145 - 9.24349i) q^{39} +(-0.361376 - 0.732799i) q^{40} +(0.0906083 - 0.266923i) q^{41} +(0.340441 + 1.95562i) q^{42} +(-7.58989 + 0.999228i) q^{43} +(-0.0538043 - 0.270493i) q^{44} +(-0.770268 + 1.38963i) q^{45} +(7.77930 + 1.54740i) q^{46} +(-7.65665 - 2.05159i) q^{47} +(5.08904 + 6.97235i) q^{48} +(-0.858869 + 6.52376i) q^{49} +(-4.17327 + 7.22832i) q^{50} +(6.58285 + 2.76877i) q^{51} +(-3.22579 - 5.58724i) q^{52} +(-6.47242 + 2.68096i) q^{53} +(3.01062 - 8.68233i) q^{54} +(-0.0915896 + 0.0915896i) q^{55} +(-0.321361 - 0.946698i) q^{56} +(2.73046 - 1.49026i) q^{57} +(1.28335 + 0.435638i) q^{58} +(-4.10474 - 5.34940i) q^{59} +(-0.355906 + 0.971260i) q^{60} +(-5.55704 - 6.33659i) q^{61} +(-2.35068 + 3.51804i) q^{62} +(-1.15638 + 1.56279i) q^{63} +(0.115352 + 0.115352i) q^{64} +(-1.34015 + 2.71755i) q^{65} +(0.431035 - 0.612739i) q^{66} +(2.60816 + 1.50582i) q^{67} +(4.51257 + 1.11985i) q^{68} +(4.15955 + 6.56066i) q^{69} +(0.369497 - 0.481538i) q^{70} +(7.48130 - 4.99884i) q^{71} +(-0.823522 + 4.55441i) q^{72} +(-1.88124 + 9.45764i) q^{73} +(-0.723024 + 11.0312i) q^{74} +(-7.94438 + 1.92566i) q^{75} +(1.60671 - 1.23287i) q^{76} +(-0.125738 + 0.0964824i) q^{77} +(4.94063 - 16.8142i) q^{78} +(0.344325 - 5.25338i) q^{79} +(0.514926 - 2.58871i) q^{80} +(8.18957 - 3.73241i) q^{81} +(0.414500 - 0.276960i) q^{82} +(-0.612737 + 0.798534i) q^{83} +(-0.586883 + 1.12142i) q^{84} +(-0.740144 - 2.05438i) q^{85} +(-11.7248 - 6.76934i) q^{86} +(0.558333 + 1.20418i) q^{87} +(-0.166881 + 0.338401i) q^{88} +(10.5558 + 10.5558i) q^{89} +(-2.57682 + 1.12046i) q^{90} +(-2.05980 + 3.08271i) q^{91} +(3.33463 + 3.80241i) q^{92} +(-4.08247 + 0.710691i) q^{93} +(-8.53398 - 11.1217i) q^{94} +(-0.900676 - 0.305738i) q^{95} +(-0.238028 + 9.91879i) q^{96} +(1.32665 + 3.90819i) q^{97} +(-8.22856 + 8.22856i) q^{98} +(0.725651 - 0.108457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22}+ \cdots + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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