LMFDB - Embedded newform 380.2.bj.a.263.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			263.7
Character	$\chi$	$=$	380.263
Dual form			380.2.bj.a.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27309 - 0.615834i) q^{2} +(-0.279354 + 0.599076i) q^{3} +(1.24150 + 1.56802i) q^{4} +(1.95101 - 1.09250i) q^{5} +(0.724572 - 0.590640i) q^{6} +(-0.490187 + 1.82940i) q^{7} +(-0.614896 - 2.76078i) q^{8} +(1.64751 + 1.96343i) q^{9} +O(q^{10})$	\(q+(-1.27309 - 0.615834i) q^{2} +(-0.279354 + 0.599076i) q^{3} +(1.24150 + 1.56802i) q^{4} +(1.95101 - 1.09250i) q^{5} +(0.724572 - 0.590640i) q^{6} +(-0.490187 + 1.82940i) q^{7} +(-0.614896 - 2.76078i) q^{8} +(1.64751 + 1.96343i) q^{9} +(-3.15660 + 0.189349i) q^{10} +(1.54063 + 0.889483i) q^{11} +(-1.28618 + 0.305720i) q^{12} +(-1.03920 - 2.22857i) q^{13} +(1.75066 - 2.02712i) q^{14} +(0.109468 + 1.47400i) q^{15} +(-0.917365 + 3.89338i) q^{16} +(-0.526200 + 0.0460365i) q^{17} +(-0.888279 - 3.51420i) q^{18} +(-3.49372 + 2.60652i) q^{19} +(4.13524 + 1.70289i) q^{20} +(-0.959016 - 0.804710i) q^{21} +(-1.41358 - 2.08116i) q^{22} +(4.62156 + 3.23605i) q^{23} +(1.82569 + 0.402864i) q^{24} +(2.61289 - 4.26296i) q^{25} +(-0.0494376 + 3.47714i) q^{26} +(-3.55193 + 0.951737i) q^{27} +(-3.47711 + 1.50258i) q^{28} +(5.17298 + 6.16492i) q^{29} +(0.768374 - 1.94394i) q^{30} +(3.36737 - 1.94415i) q^{31} +(3.56556 - 4.39167i) q^{32} +(-0.963248 + 0.674474i) q^{33} +(0.698248 + 0.265443i) q^{34} +(1.04226 + 4.10472i) q^{35} +(-1.03331 + 5.02091i) q^{36} +(0.166786 - 0.166786i) q^{37} +(6.05299 - 1.16677i) q^{38} +1.62539 q^{39} +(-4.21582 - 4.71454i) q^{40} +(6.13856 - 2.23425i) q^{41} +(0.725343 + 1.61506i) q^{42} +(1.61250 + 2.30289i) q^{43} +(0.517963 + 3.52003i) q^{44} +(5.35935 + 2.03076i) q^{45} +(-3.89078 - 6.96589i) q^{46} +(1.04455 + 0.0913863i) q^{47} +(-2.07616 - 1.63720i) q^{48} +(2.95574 + 1.70650i) q^{49} +(-5.95171 + 3.81801i) q^{50} +(0.119416 - 0.328094i) q^{51} +(2.20428 - 4.39625i) q^{52} +(-1.56986 + 2.24199i) q^{53} +(5.10802 + 0.975754i) q^{54} +(3.97755 + 0.0522536i) q^{55} +(5.35199 + 0.228406i) q^{56} +(-0.585517 - 2.82114i) q^{57} +(-2.78909 - 11.0342i) q^{58} +(-7.66708 - 6.43344i) q^{59} +(-2.17535 + 2.00161i) q^{60} +(-1.16019 - 6.57974i) q^{61} +(-5.48423 + 0.401334i) q^{62} +(-4.39949 + 2.05151i) q^{63} +(-7.24381 + 3.39518i) q^{64} +(-4.46220 - 3.21264i) q^{65} +(1.64166 - 0.265463i) q^{66} +(2.76818 + 0.242184i) q^{67} +(-0.725462 - 0.767936i) q^{68} +(-3.22969 + 1.86466i) q^{69} +(1.20093 - 5.86752i) q^{70} +(1.50058 + 0.264593i) q^{71} +(4.40754 - 5.75571i) q^{72} +(-8.80771 - 4.10710i) q^{73} +(-0.315045 + 0.109621i) q^{74} +(1.82392 + 2.75619i) q^{75} +(-8.42451 - 2.24223i) q^{76} +(-2.38242 + 2.38242i) q^{77} +(-2.06926 - 1.00097i) q^{78} +(0.721664 - 0.262664i) q^{79} +(2.46373 + 8.59826i) q^{80} +(-0.913135 + 5.17865i) q^{81} +(-9.19084 - 0.935933i) q^{82} +(-8.75861 - 2.34686i) q^{83} +(0.0711836 - 2.50280i) q^{84} +(-0.976326 + 0.664691i) q^{85} +(-0.634658 - 3.92482i) q^{86} +(-5.13835 + 1.37682i) q^{87} +(1.50834 - 4.80028i) q^{88} +(-3.72309 + 10.2291i) q^{89} +(-5.57231 - 5.88580i) q^{90} +(4.58636 - 0.808699i) q^{91} +(0.663470 + 11.2643i) q^{92} +(0.224007 + 2.56042i) q^{93} +(-1.27352 - 0.759611i) q^{94} +(-3.96867 + 8.90223i) q^{95} +(1.63489 + 3.36287i) q^{96} +(-13.2098 + 1.15571i) q^{97} +(-2.71200 - 3.99277i) q^{98} +(0.791769 + 4.49034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.27309	−	0.615834i	−0.900208	−	0.435460i
$2$	−1.27309	−	0.615834i	−0.900208	−	0.435460i
$3$	−0.279354	+	0.599076i	−0.161285	+	0.345877i	−0.970298	−	0.241915i	$-0.922225\pi$
$3$	−0.279354	+	0.599076i	−0.161285	+	0.345877i	0.809013	+	0.587791i	$0.200002\pi$
$4$	1.24150	+	1.56802i	0.620749	+	0.784009i
$5$	1.95101	−	1.09250i	0.872519	−	0.488581i
$5$	1.95101	−	1.09250i	0.872519	−	0.488581i
$6$	0.724572	−	0.590640i	0.295805	−	0.241128i
$7$	−0.490187	+	1.82940i	−0.185273	+	0.691450i	0.809299	+	0.587398i	$0.199847\pi$
$7$	−0.490187	+	1.82940i	−0.185273	+	0.691450i	−0.994572	+	0.104052i	$0.966819\pi$
$8$	−0.614896	−	2.76078i	−0.217399	−	0.976083i
$9$	1.64751	+	1.96343i	0.549170	+	0.654475i
$10$	−3.15660	+	0.189349i	−0.998206	+	0.0598773i
$11$	1.54063	+	0.889483i	0.464517	+	0.268189i	0.713942	−	0.700205i	$-0.246908\pi$
$11$	1.54063	+	0.889483i	0.464517	+	0.268189i	−0.249424	+	0.968394i	$0.580241\pi$
$12$	−1.28618	+	0.305720i	−0.371288	+	0.0882537i
$13$	−1.03920	−	2.22857i	−0.288222	−	0.618095i	0.707877	−	0.706336i	$-0.249653\pi$
$13$	−1.03920	−	2.22857i	−0.288222	−	0.618095i	−0.996099	+	0.0882413i	$0.971875\pi$
$14$	1.75066	−	2.02712i	0.467883	−	0.541769i
$15$	0.109468	+	1.47400i	0.0282645	+	0.380584i
$16$	−0.917365	+	3.89338i	−0.229341	+	0.973346i
$17$	−0.526200	+	0.0460365i	−0.127622	+	0.0111655i	−0.150788	−	0.988566i	$-0.548181\pi$
$17$	−0.526200	+	0.0460365i	−0.127622	+	0.0111655i	0.0231657	+	0.999732i	$0.492625\pi$
$18$	−0.888279	−	3.51420i	−0.209369	−	0.828305i
$19$	−3.49372	+	2.60652i	−0.801514	+	0.597976i
$19$	−3.49372	+	2.60652i	−0.801514	+	0.597976i
$20$	4.13524	+	1.70289i	0.924667	+	0.380777i
$21$	−0.959016	−	0.804710i	−0.209274	−	0.175602i
$22$	−1.41358	−	2.08116i	−0.301377	−	0.443705i
$23$	4.62156	+	3.23605i	0.963663	+	0.674764i	0.945688	−	0.325075i	$-0.105389\pi$
$23$	4.62156	+	3.23605i	0.963663	+	0.674764i	0.0179742	+	0.999838i	$0.494278\pi$
$24$	1.82569	+	0.402864i	0.372667	+	0.0822343i
$25$	2.61289	−	4.26296i	0.522578	−	0.852592i
$26$	−0.0494376	+	3.47714i	−0.00969552	+	0.681923i
$27$	−3.55193	+	0.951737i	−0.683569	+	0.183162i
$28$	−3.47711	+	1.50258i	−0.657111	+	0.283961i
$29$	5.17298	+	6.16492i	0.960599	+	1.14480i	0.989401	+	0.145212i	$0.0463865\pi$
$29$	5.17298	+	6.16492i	0.960599	+	1.14480i	−0.0288015	+	0.999585i	$0.509169\pi$
$30$	0.768374	−	1.94394i	0.140285	−	0.354913i
$31$	3.36737	−	1.94415i	0.604797	−	0.349180i	−0.166129	−	0.986104i	$-0.553127\pi$
$31$	3.36737	−	1.94415i	0.604797	−	0.349180i	0.770927	+	0.636924i	$0.219794\pi$
$32$	3.56556	−	4.39167i	0.630308	−	0.776345i
$33$	−0.963248	+	0.674474i	−0.167680	+	0.117411i
$34$	0.698248	+	0.265443i	0.119749	+	0.0455231i
$35$	1.04226	+	4.10472i	0.176174	+	0.693824i
$36$	−1.03331	+	5.02091i	−0.172218	+	0.836819i
$37$	0.166786	−	0.166786i	0.0274194	−	0.0274194i	−0.693264	−	0.720684i	$-0.743828\pi$
$37$	0.166786	−	0.166786i	0.0274194	−	0.0274194i	0.720684	+	0.693264i	$0.243828\pi$
$38$	6.05299	−	1.16677i	0.981924	−	0.189275i
$39$	1.62539			0.260270
$40$	−4.21582	−	4.71454i	−0.666580	−	0.745434i
$41$	6.13856	−	2.23425i	0.958682	−	0.348932i	0.185165	−	0.982707i	$-0.440718\pi$
$41$	6.13856	−	2.23425i	0.958682	−	0.348932i	0.773517	+	0.633776i	$0.218496\pi$
$42$	0.725343	+	1.61506i	0.111923	+	0.249209i
$43$	1.61250	+	2.30289i	0.245905	+	0.351188i	0.923063	−	0.384649i	$-0.125678\pi$
$43$	1.61250	+	2.30289i	0.245905	+	0.351188i	−0.677158	+	0.735837i	$0.736789\pi$
$44$	0.517963	+	3.52003i	0.0780859	+	0.530664i
$45$	5.35935	+	2.03076i	0.798925	+	0.302728i
$46$	−3.89078	−	6.96589i	−0.573664	−	1.02706i
$47$	1.04455	+	0.0913863i	0.152363	+	0.0133301i	0.163082	−	0.986612i	$-0.447856\pi$
$47$	1.04455	+	0.0913863i	0.152363	+	0.0133301i	−0.0107189	+	0.999943i	$0.503412\pi$
$48$	−2.07616	−	1.63720i	−0.299668	−	0.236310i
$49$	2.95574	+	1.70650i	0.422249	+	0.243786i
$50$	−5.95171	+	3.81801i	−0.841698	+	0.539948i
$51$	0.119416	−	0.328094i	0.0167216	−	0.0459423i
$52$	2.20428	−	4.39625i	0.305678	−	0.609650i
$53$	−1.56986	+	2.24199i	−0.215637	+	0.307961i	−0.912368	−	0.409371i	$-0.865748\pi$
$53$	−1.56986	+	2.24199i	−0.215637	+	0.307961i	0.696731	+	0.717332i	$0.254637\pi$
$54$	5.10802	+	0.975754i	0.695114	+	0.132783i
$55$	3.97755	+	0.0522536i	0.536332	+	0.00704587i
$56$	5.35199	+	0.228406i	0.715190	+	0.0305220i
$57$	−0.585517	−	2.82114i	−0.0775536	−	0.373669i
$58$	−2.78909	−	11.0342i	−0.366225	−	1.44886i
$59$	−7.66708	−	6.43344i	−0.998168	−	0.837563i	−0.0114387	−	0.999935i	$-0.503641\pi$
$59$	−7.66708	−	6.43344i	−0.998168	−	0.837563i	−0.986730	+	0.162372i	$0.948086\pi$
$60$	−2.17535	+	2.00161i	−0.280837	+	0.258407i
$61$	−1.16019	−	6.57974i	−0.148547	−	0.842450i	−0.964451	−	0.264263i	$-0.914871\pi$
$61$	−1.16019	−	6.57974i	−0.148547	−	0.842450i	0.815904	−	0.578187i	$-0.196240\pi$
$62$	−5.48423	+	0.401334i	−0.696497	+	0.0509695i
$63$	−4.39949	+	2.05151i	−0.554283	+	0.258466i
$64$	−7.24381	+	3.39518i	−0.905476	+	0.424398i
$65$	−4.46220	−	3.21264i	−0.553468	−	0.398479i
$66$	1.64166	−	0.265463i	0.202075	−	0.0326762i
$67$	2.76818	+	0.242184i	0.338186	+	0.0295875i	0.254984	−	0.966945i	$-0.417930\pi$
$67$	2.76818	+	0.242184i	0.338186	+	0.0295875i	0.0832022	+	0.996533i	$0.473485\pi$
$68$	−0.725462	−	0.767936i	−0.0879752	−	0.0931260i
$69$	−3.22969	+	1.86466i	−0.388809	+	0.224479i
$70$	1.20093	−	5.86752i	0.143539	−	0.701303i
$71$	1.50058	+	0.264593i	0.178086	+	0.0314014i	0.261980	−	0.965073i	$-0.415625\pi$
$71$	1.50058	+	0.264593i	0.178086	+	0.0314014i	−0.0838940	+	0.996475i	$0.526736\pi$
$72$	4.40754	−	5.75571i	0.519433	−	0.678317i
$73$	−8.80771	−	4.10710i	−1.03086	−	0.480700i	−0.167815	−	0.985819i	$-0.553671\pi$
$73$	−8.80771	−	4.10710i	−1.03086	−	0.480700i	−0.863050	+	0.505118i	$0.831449\pi$
$74$	−0.315045	+	0.109621i	−0.0366233	+	0.0127431i
$75$	1.82392	+	2.75619i	0.210608	+	0.318258i
$76$	−8.42451	−	2.24223i	−0.966358	−	0.257202i
$77$	−2.38242	+	2.38242i	−0.271502	+	0.271502i
$78$	−2.06926	−	1.00097i	−0.234297	−	0.113337i
$79$	0.721664	−	0.262664i	0.0811935	−	0.0295520i	−0.301104	−	0.953591i	$-0.597355\pi$
$79$	0.721664	−	0.262664i	0.0811935	−	0.0295520i	0.382298	+	0.924039i	$0.375133\pi$
$80$	2.46373	+	8.59826i	0.275454	+	0.961314i
$81$	−0.913135	+	5.17865i	−0.101459	+	0.575405i
$82$	−9.19084	−	0.935933i	−1.01496	−	0.103357i
$83$	−8.75861	−	2.34686i	−0.961382	−	0.257602i	−0.256197	−	0.966625i	$-0.582470\pi$
$83$	−8.75861	−	2.34686i	−0.961382	−	0.257602i	−0.705185	+	0.709023i	$0.749136\pi$
$84$	0.0711836	−	2.50280i	0.00776676	−	0.273078i
$85$	−0.976326	+	0.664691i	−0.105897	+	0.0720958i
$86$	−0.634658	−	3.92482i	−0.0684369	−	0.423224i
$87$	−5.13835	+	1.37682i	−0.550889	+	0.147610i
$88$	1.50834	−	4.80028i	0.160789	−	0.511711i
$89$	−3.72309	+	10.2291i	−0.394647	+	1.08428i	0.570208	+	0.821501i	$0.306863\pi$
$89$	−3.72309	+	10.2291i	−0.394647	+	1.08428i	−0.964855	+	0.262783i	$0.915360\pi$
$90$	−5.57231	−	5.88580i	−0.587373	−	0.620418i
$91$	4.58636	−	0.808699i	0.480781	−	0.0847747i
$92$	0.663470	+	11.2643i	0.0691716	+	1.17438i
$93$	0.224007	+	2.56042i	0.0232285	+	0.265503i
$94$	−1.27352	−	0.759611i	−0.131354	−	0.0783479i
$95$	−3.96867	+	8.90223i	−0.407177	+	0.913349i
$96$	1.63489	+	3.36287i	0.166860	+	0.343221i
$97$	−13.2098	+	1.15571i	−1.34125	+	0.117344i	−0.735075	−	0.677985i	$-0.762853\pi$
$97$	−13.2098	+	1.15571i	−1.34125	+	0.117344i	−0.606177	+	0.795330i	$0.707298\pi$
$98$	−2.71200	−	3.99277i	−0.273953	−	0.403330i
$99$	0.791769	+	4.49034i	0.0795757	+	0.451296i
$100$	9.92829	−	1.19540i	0.992829	−	0.119540i
$101$	−1.62198	−	0.590351i	−0.161393	−	0.0587421i	0.260060	−	0.965592i	$-0.416258\pi$
$101$	−1.62198	−	0.590351i	−0.161393	−	0.0587421i	−0.421453	+	0.906850i	$0.638480\pi$
$102$	−0.354079	+	0.344151i	−0.0350590	+	0.0340760i
$103$	−4.46746	−	16.6728i	−0.440192	−	1.64282i	−0.728327	−	0.685230i	$-0.759702\pi$
$103$	−4.46746	−	16.6728i	−0.440192	−	1.64282i	0.288134	−	0.957590i	$-0.406965\pi$
$104$	−5.51359	+	4.23934i	−0.540652	+	0.415702i
$105$	−2.75020	−	0.522273i	−0.268392	−	0.0509686i
$106$	3.37926	−	1.88748i	0.328222	−	0.183328i
$107$	3.98722	−	14.8805i	0.385459	−	1.43855i	−0.451983	−	0.892027i	$-0.649283\pi$
$107$	3.98722	−	14.8805i	0.385459	−	1.43855i	0.837442	−	0.546526i	$-0.184050\pi$
$108$	−5.90205	−	4.38791i	−0.567925	−	0.422227i
$109$	−10.6908	−	1.88508i	−1.02400	−	0.180558i	−0.363662	−	0.931531i	$-0.618474\pi$
$109$	−10.6908	−	1.88508i	−1.02400	−	0.180558i	−0.660333	+	0.750973i	$0.729585\pi$
$110$	−5.03158	−	2.51603i	−0.479742	−	0.239894i
$111$	0.0533251	+	0.146510i	0.00506140	+	0.0139061i
$112$	−6.67289	−	3.58672i	−0.630529	−	0.338913i
$113$	8.74306	+	8.74306i	0.822478	+	0.822478i	0.986463	−	0.163985i	$-0.0524348\pi$
$113$	8.74306	+	8.74306i	0.822478	+	0.822478i	−0.163985	+	0.986463i	$0.552435\pi$
$114$	−0.991940	+	3.95214i	−0.0929037	+	0.370152i
$115$	12.5521	+	1.26452i	1.17049	+	0.117917i
$116$	−3.24446	+	15.7651i	−0.301241	+	1.46375i
$117$	2.66354	−	5.71198i	0.246245	−	0.528073i
$118$	5.79892	+	12.9120i	0.533834	+	1.18864i
$119$	0.173717	−	0.985198i	0.0159246	−	0.0903129i
$120$	4.00207	−	1.20857i	0.365337	−	0.110327i
$121$	−3.91764	−	6.78555i	−0.356149	−	0.616868i
$122$	−2.57501	+	9.09106i	−0.233130	+	0.823066i
$123$	−0.376342	+	4.30161i	−0.0339336	+	0.387863i
$124$	7.22905	+	2.86644i	0.649188	+	0.257414i
$125$	0.440494	−	11.1717i	0.0393989	−	0.999224i
$126$	6.86432	+	0.0975962i	0.611522	+	0.00869456i
$127$	6.43505	+	13.8000i	0.571018	+	1.22455i	0.953724	+	0.300683i	$0.0972145\pi$
$127$	6.43505	+	13.8000i	0.571018	+	1.22455i	−0.382706	+	0.923870i	$0.625008\pi$
$128$	11.3129	+	0.138614i	0.999925	+	0.0122519i
$129$	−1.83007	+	0.322690i	−0.161128	+	0.0284113i
$130$	3.70232	+	6.83795i	0.324715	+	0.599728i
$131$	11.8446	−	14.1158i	1.03487	−	1.23330i	0.0629394	−	0.998017i	$-0.479953\pi$
$131$	11.8446	−	14.1158i	1.03487	−	1.23330i	0.971926	−	0.235287i	$-0.0756030\pi$
$132$	−2.25346	−	0.673033i	−0.196138	−	0.0585800i
$133$	−3.05579	−	7.66910i	−0.264971	−	0.664996i
$134$	−3.37498	−	2.01306i	−0.291554	−	0.173902i
$135$	−5.89008	+	5.73733i	−0.506937	+	0.493791i
$136$	0.450655	+	1.42441i	0.0386433	+	0.122142i
$137$	4.61782	+	3.23343i	0.394527	+	0.276251i	0.753960	−	0.656920i	$-0.228141\pi$
$137$	4.61782	+	3.23343i	0.394527	+	0.276251i	−0.359433	+	0.933171i	$0.617030\pi$
$138$	5.26000	−	0.384925i	0.447761	−	0.0327670i
$139$	−20.2404	−	7.36690i	−1.71677	−	0.624852i	−0.719215	−	0.694787i	$-0.755499\pi$
$139$	−20.2404	−	7.36690i	−1.71677	−	0.624852i	−0.997552	+	0.0699350i	$0.977721\pi$
$140$	−5.14230	+	6.73028i	−0.434604	+	0.568813i
$141$	−0.346546	+	0.600235i	−0.0291844	+	0.0505489i
$142$	−1.74742	−	1.26096i	−0.146640	−	0.105817i
$143$	0.381254	−	4.35775i	0.0318821	−	0.364414i
$144$	−9.15574	+	4.61321i	−0.762978	+	0.384434i
$145$	16.8277	+	6.37635i	1.39747	+	0.529527i
$146$	8.68369	+	10.6528i	0.718667	+	0.881631i
$147$	−1.84802	+	1.29400i	−0.152422	+	0.106727i
$148$	0.468588	+	0.0544590i	0.0385177	+	0.00447650i
$149$	−4.08005	−	11.2098i	−0.334251	−	0.918346i	−0.986993	−	0.160766i	$-0.948604\pi$
$149$	−4.08005	−	11.2098i	−0.334251	−	0.918346i	0.652742	−	0.757580i	$-0.273619\pi$
$150$	−0.624647	−	4.63210i	−0.0510022	−	0.378209i
$151$		−	20.0837i		−	1.63439i	−0.576362	−	0.817194i	$-0.695528\pi$
$151$		−	20.0837i		−	1.63439i	0.576362	−	0.817194i	$-0.304472\pi$
$152$	9.34429	+	8.04265i	0.757922	+	0.652345i
$153$	−0.957308	−	0.957308i	−0.0773938	−	0.0773938i
$154$	4.50020	−	1.56585i	0.362636	−	0.126180i
$155$	4.44579	−	7.47191i	0.357094	−	0.600158i
$156$	2.01792	+	2.54864i	0.161563	+	0.204054i
$157$	11.4150	+	16.3024i	0.911019	+	1.30107i	0.953319	+	0.301965i	$0.0976427\pi$
$157$	11.4150	+	16.3024i	0.911019	+	1.30107i	−0.0422997	+	0.999105i	$0.513468\pi$
$158$	−1.08050	−	0.110031i	−0.0859598	−	0.00875356i
$159$	−0.904576	−	1.56677i	−0.0717375	−	0.124253i
$160$	2.15855	−	12.4636i	0.170648	−	0.985332i
$161$	−8.18548	+	6.86843i	−0.645106	+	0.541308i
$162$	4.35168	−	6.03053i	0.341901	−	0.473803i
$163$	−5.12935	−	19.1430i	−0.401762	−	1.49940i	−0.809950	−	0.586498i	$-0.800506\pi$
$163$	−5.12935	−	19.1430i	−0.401762	−	1.49940i	0.408188	−	0.912898i	$-0.366161\pi$
$164$	11.1244	+	6.85155i	0.868666	+	0.535016i
$165$	−1.14245	+	2.36825i	−0.0889393	+	0.184368i
$166$	9.70519	+	8.38160i	0.753269	+	0.650539i
$167$	−3.96883	+	5.66807i	−0.307117	+	0.438609i	−0.942809	−	0.333335i	$-0.891826\pi$
$167$	−3.96883	+	5.66807i	−0.307117	+	0.438609i	0.635692	+	0.771943i	$0.280715\pi$
$168$	−1.63193	+	3.14244i	−0.125906	+	0.242445i
$169$	4.46964	−	5.32672i	0.343819	−	0.409747i
$170$	1.65229	−	0.244954i	0.126725	−	0.0187871i
$171$	−10.8736	−	2.56540i	−0.831528	−	0.196181i
$172$	−1.60906	+	5.38748i	−0.122690	+	0.410791i
$173$	0.196646	+	2.24767i	0.0149507	+	0.170887i	0.999999	−	0.00139086i	$-0.000442726\pi$
$173$	0.196646	+	2.24767i	0.0149507	+	0.170887i	−0.985048	+	0.172278i	$0.944887\pi$
$174$	7.38945	+	1.41156i	0.560193	+	0.107010i
$175$	6.51787	+	6.86967i	0.492704	+	0.519299i
$176$	−4.87642	+	5.18228i	−0.367574	+	0.390629i
$177$	5.99594	−	2.79595i	0.450683	−	0.210157i
$178$	11.0393	−	10.7297i	0.827427	−	0.804228i
$179$	9.03664	−	15.6519i	0.675430	−	1.16988i	−0.300913	−	0.953652i	$-0.597291\pi$
$179$	9.03664	−	15.6519i	0.675430	−	1.16988i	0.976343	−	0.216228i	$-0.0693753\pi$
$180$	3.46935	+	10.9247i	0.258590	+	0.814283i
$181$	1.54891	−	1.29969i	0.115129	−	0.0966051i	−0.583405	−	0.812181i	$-0.698280\pi$
$181$	1.54891	−	1.29969i	0.115129	−	0.0966051i	0.698535	+	0.715576i	$0.253836\pi$
$182$	−6.33686	−	1.79489i	−0.469719	−	0.133046i
$183$	4.26587	+	1.14304i	0.315342	+	0.0844956i
$184$	6.09225	−	14.7490i	0.449127	−	1.08731i
$185$	0.143188	−	0.507615i	0.0105274	−	0.0373206i
$186$	1.29161	−	3.39758i	0.0947054	−	0.249123i
$187$	−0.851627	−	0.397120i	−0.0622772	−	0.0290403i
$188$	1.15351	+	1.75133i	0.0841285	+	0.127729i
$189$		−	6.96444i		−	0.506589i
$190$	10.5347	−	8.88927i	0.764271	−	0.644895i
$191$			2.08127i			0.150595i	0.997161	+	0.0752976i	$0.0239907\pi$
$191$			2.08127i			0.150595i	−0.997161	+	0.0752976i	$0.976009\pi$
$192$	−0.0103897	−	5.28805i	−0.000749810	−	0.381632i
$193$	−3.69269	−	1.72193i	−0.265806	−	0.123947i	0.285147	−	0.958484i	$-0.407958\pi$
$193$	−3.69269	−	1.72193i	−0.265806	−	0.123947i	−0.550952	+	0.834537i	$0.685735\pi$
$194$	17.5289	+	6.66372i	1.25850	+	0.478427i
$195$	3.17115	−	1.77574i	0.227091	−	0.127163i
$196$	0.993728	+	6.75328i	0.0709806	+	0.482377i
$197$	8.81168	+	2.36108i	0.627806	+	0.168220i	0.558674	−	0.829387i	$-0.311310\pi$
$197$	8.81168	+	2.36108i	0.627806	+	0.168220i	0.0691321	+	0.997608i	$0.477977\pi$
$198$	1.75731	−	6.20419i	0.124887	−	0.440913i
$199$	−3.71202	+	3.11476i	−0.263138	+	0.220799i	−0.764805	−	0.644262i	$-0.777165\pi$
$199$	−3.71202	+	3.11476i	−0.263138	+	0.220799i	0.501667	+	0.865061i	$0.332720\pi$
$200$	−13.3757	−	4.59233i	−0.945808	−	0.324727i
$201$	−0.918386	+	1.59069i	−0.0647780	+	0.112199i
$202$	1.70136	+	1.75043i	0.119707	+	0.123160i
$203$	−13.8139	+	6.44151i	−0.969543	+	0.452105i
$204$	0.662712	−	0.220081i	0.0463992	−	0.0154087i
$205$	9.53547	−	11.0654i	0.665986	−	0.772843i
$206$	−4.58020	+	23.9771i	−0.319118	+	1.67057i
$207$	1.26032	+	14.4055i	0.0875983	+	1.00125i
$208$	9.63001	−	2.00159i	0.667721	−	0.138785i
$209$	−7.70098	+	0.908071i	−0.532688	+	0.0628126i
$210$	3.17960	+	2.35856i	0.219413	+	0.162756i
$211$	−16.4741	+	19.6330i	−1.13412	+	1.35159i	−0.206333	+	0.978482i	$0.566153\pi$
$211$	−16.4741	+	19.6330i	−1.13412	+	1.35159i	−0.927787	+	0.373110i	$0.878291\pi$
$212$	−5.46446	+	0.321859i	−0.375300	+	0.0221054i
$213$	−0.577703	+	0.825045i	−0.0395836	+	0.0565312i
$214$	−14.2400	+	16.4887i	−0.973426	+	1.12714i
$215$	5.66193	+	2.73131i	0.386140	+	0.186274i
$216$	4.81160	+	9.22087i	0.327388	+	0.627401i
$217$	1.90600	+	7.11328i	0.129387	+	0.482881i
$218$	12.4495	+	8.98364i	0.843183	+	0.608449i
$219$	4.92093	−	4.12915i	0.332526	−	0.279022i
$220$	4.85618	+	6.30174i	0.327404	+	0.424863i
$221$	0.649422	+	1.12483i	0.0436849	+	0.0756644i
$222$	0.0223380	−	0.219359i	0.00149923	−	0.0147224i
$223$	16.6515	+	23.7809i	1.11507	+	1.59248i	0.749910	+	0.661540i	$0.230097\pi$
$223$	16.6515	+	23.7809i	1.11507	+	1.59248i	0.365160	+	0.930945i	$0.381014\pi$
$224$	6.28635	+	8.67559i	0.420024	+	0.579662i
$225$	12.6748	−	1.89305i	0.844984	−	0.126204i
$226$	−5.74640	−	16.5149i	−0.382245	−	1.09856i
$227$	−5.82549	−	5.82549i	−0.386651	−	0.386651i	0.486840	−	0.873491i	$-0.338150\pi$
$227$	−5.82549	−	5.82549i	−0.386651	−	0.386651i	−0.873491	+	0.486840i	$0.838150\pi$
$228$	3.69668	−	4.42054i	0.244819	−	0.292758i
$229$			22.1462i			1.46346i	0.681595	+	0.731730i	$0.261287\pi$
$229$			22.1462i			1.46346i	−0.681595	+	0.731730i	$0.738713\pi$
$230$	−15.2012	−	9.33985i	−1.00234	−	0.615852i
$231$	−0.761712	−	2.09279i	−0.0501170	−	0.137695i
$232$	13.8391	−	18.0723i	0.908584	−	1.18650i
$233$	−6.64589	+	4.65350i	−0.435387	+	0.304861i	−0.770644	−	0.637265i	$-0.780066\pi$
$233$	−6.64589	+	4.65350i	−0.435387	+	0.304861i	0.335258	+	0.942127i	$0.391177\pi$
$234$	−6.90855	+	5.63155i	−0.451626	+	0.368146i
$235$	2.13777	−	0.962875i	0.139453	−	0.0628110i
$236$	0.569094	−	20.0092i	0.0370448	−	1.30249i
$237$	−0.0442437	+	0.505707i	−0.00287393	+	0.0328492i
$238$	−0.827875	+	1.14726i	−0.0536631	+	0.0743659i
$239$	−0.492467	+	0.852978i	−0.0318550	+	0.0551746i	−0.881513	−	0.472159i	$-0.843475\pi$
$239$	−0.492467	+	0.852978i	−0.0318550	+	0.0551746i	0.849658	+	0.527334i	$0.176808\pi$
$240$	−5.83926	−	0.925991i	−0.376923	−	0.0597725i
$241$	−20.6693	−	7.52300i	−1.33143	−	0.484599i	−0.424324	−	0.905511i	$-0.639488\pi$
$241$	−20.6693	−	7.52300i	−1.33143	−	0.484599i	−0.907102	+	0.420911i	$0.861710\pi$
$242$	0.808724	+	11.0512i	0.0519868	+	0.710399i
$243$	−11.8839	−	8.32122i	−0.762355	−	0.533807i
$244$	8.87679	−	9.98793i	0.568278	−	0.639412i
$245$	7.63104	+	0.100250i	0.487529	+	0.00640474i
$246$	3.12819	−	5.24455i	0.199446	−	0.334381i
$247$	9.43948	+	5.07731i	0.600620	+	0.323062i
$248$	−7.43796	−	8.10111i	−0.472311	−	0.514421i
$249$	3.85270	−	4.59147i	0.244155	−	0.290972i
$250$	−7.44067	+	13.9512i	−0.470589	+	0.882352i
$251$	20.9021	−	3.68560i	1.31933	−	0.232633i	0.530730	−	0.847541i	$-0.321918\pi$
$251$	20.9021	−	3.68560i	1.31933	−	0.232633i	0.788599	+	0.614908i	$0.210807\pi$
$252$	−8.67876	−	4.35152i	−0.546711	−	0.274120i
$253$	4.24170	+	9.09636i	0.266674	+	0.571883i
$254$	0.306133	−	21.5315i	0.0192085	−	1.35101i
$255$	−0.125460	−	0.770577i	−0.00785659	−	0.0482554i
$256$	−14.3169	−	7.14331i	−0.894805	−	0.446457i
$257$	0.578452	−	6.61173i	0.0360828	−	0.412429i	−0.956576	−	0.291482i	$-0.905852\pi$
$257$	0.578452	−	6.61173i	0.0360828	−	0.412429i	0.992659	−	0.120946i	$-0.0385929\pi$
$258$	2.52856	+	0.716204i	0.157421	+	0.0445889i
$259$	0.223362	+	0.386875i	0.0138791	+	0.0240392i
$260$	−0.502336	−	10.9853i	−0.0311536	−	0.681280i
$261$	−3.58182	+	20.3135i	−0.221709	+	1.25738i
$262$	−23.7722	+	10.6764i	−1.46865	+	0.659588i
$263$	−4.32520	+	9.27542i	−0.266703	+	0.571947i	−0.993359	−	0.115055i	$-0.963296\pi$
$263$	−4.32520	+	9.27542i	−0.266703	+	0.571947i	0.726656	+	0.687002i	$0.241073\pi$
$264$	2.45437	+	2.24458i	0.151056	+	0.138145i
$265$	−0.613437	+	6.08922i	−0.0376831	+	0.374058i
$266$	−0.832603	+	11.6453i	−0.0510502	+	0.714019i
$267$	−5.08795	−	5.08795i	−0.311378	−	0.311378i
$268$	3.05694	+	4.64122i	0.186732	+	0.283508i
$269$	−4.41791	−	12.1381i	−0.269364	−	0.740073i	−0.998450	−	0.0556505i	$-0.982277\pi$
$269$	−4.41791	−	12.1381i	−0.269364	−	0.740073i	0.729086	−	0.684422i	$-0.239945\pi$
$270$	11.0318	−	3.67681i	0.671375	−	0.223763i
$271$	−1.21285	−	0.213858i	−0.0736754	−	0.0129910i	0.136689	−	0.990614i	$-0.456354\pi$
$271$	−1.21285	−	0.213858i	−0.0736754	−	0.0129910i	−0.210364	+	0.977623i	$0.567465\pi$
$272$	0.303479	−	2.09093i	0.0184011	−	0.126781i
$273$	−0.796744	+	2.97349i	−0.0482211	+	0.179964i
$274$	−3.88762	−	6.96024i	−0.234860	−	0.420484i
$275$	7.81732	−	4.24352i	0.471402	−	0.255894i
$276$	−6.93348	−	2.74924i	−0.417347	−	0.165485i
$277$	−4.52481	−	16.8868i	−0.271870	−	1.01463i	−0.957910	−	0.287068i	$-0.907319\pi$
$277$	−4.52481	−	16.8868i	−0.271870	−	1.01463i	0.686040	−	0.727563i	$-0.259347\pi$
$278$	21.2310	+	21.8434i	1.27335	+	1.31008i
$279$	9.36497	+	3.40857i	0.560666	+	0.204066i
$280$	10.6913	−	5.40143i	0.638929	−	0.322797i
$281$	−3.06150	−	17.3626i	−0.182634	−	1.03577i	−0.928958	−	0.370186i	$-0.879294\pi$
$281$	−3.06150	−	17.3626i	−0.182634	−	1.03577i	0.746324	−	0.665583i	$-0.231817\pi$
$282$	0.810828	−	0.550737i	0.0482841	−	0.0327959i
$283$	−7.93509	+	0.694230i	−0.471692	+	0.0412677i	−0.320524	−	0.947240i	$-0.603859\pi$
$283$	−7.93509	+	0.694230i	−0.471692	+	0.0412677i	−0.151168	+	0.988508i	$0.548303\pi$
$284$	1.44808	+	2.68143i	0.0859277	+	0.159113i
$285$	−4.22445	−	4.86440i	−0.250235	−	0.288142i
$286$	−3.16902	+	5.31301i	−0.187388	+	0.314165i
$287$	1.07831	+	12.3251i	0.0636504	+	0.727528i
$288$	14.4970	−	0.234607i	0.854245	−	0.0138243i
$289$	−16.4670	+	2.90357i	−0.968645	+	0.170798i
$290$	−17.4964	−	18.4807i	−1.02742	−	1.08523i
$291$	2.99785	−	8.23652i	0.175737	−	0.482834i
$292$	−4.49474	−	18.9096i	−0.263035	−	1.10660i
$293$	5.44710	−	1.45955i	0.318223	−	0.0852676i	−0.0961721	−	0.995365i	$-0.530660\pi$
$293$	5.44710	−	1.45955i	0.318223	−	0.0852676i	0.414395	+	0.910097i	$0.363993\pi$
$294$	3.14958	−	0.509298i	0.183687	−	0.0297029i
$295$	−21.9871	−	4.17544i	−1.28014	−	0.243103i
$296$	−0.563015	−	0.357903i	−0.0327246	−	0.0208027i
$297$	−6.31876	−	1.69311i	−0.366652	−	0.0982440i
$298$	−1.70914	+	16.7837i	−0.0990079	+	0.972255i
$299$	2.40905	−	13.6624i	0.139319	−	0.790116i
$300$	−2.05737	+	6.28174i	−0.118782	+	0.362676i
$301$	−5.00335	+	1.82107i	−0.288388	+	0.104965i
$302$	−12.3682	+	25.5683i	−0.711711	+	1.47129i
$303$	0.806769	−	0.806769i	0.0463477	−	0.0463477i
$304$	−6.94315	−	15.9935i	−0.398217	−	0.917291i
$305$	−9.45190	−	11.5696i	−0.541214	−	0.662476i
$306$	0.629194	+	1.80828i	0.0359686	+	0.103372i
$307$	−18.4528	−	8.60468i	−1.05316	−	0.491095i	−0.182613	−	0.983185i	$-0.558455\pi$
$307$	−18.4528	−	8.60468i	−1.05316	−	0.491095i	−0.870544	+	0.492090i	$0.836233\pi$
$308$	−6.69345	−	0.777909i	−0.381395	−	0.0443255i
$309$	11.2363	+	1.98126i	0.639209	+	0.112710i
$310$	−10.2613	+	6.77452i	−0.582804	+	0.384767i
$311$	18.4685	−	10.6628i	1.04725	−	0.604631i	0.125373	−	0.992110i	$-0.459987\pi$
$311$	18.4685	−	10.6628i	1.04725	−	0.604631i	0.921879	+	0.387478i	$0.126654\pi$
$312$	−0.999444	−	4.48734i	−0.0565824	−	0.254045i
$313$	13.6186	+	1.19147i	0.769766	+	0.0673458i	0.465271	−	0.885168i	$-0.345957\pi$
$313$	13.6186	+	1.19147i	0.769766	+	0.0673458i	0.304495	+	0.952514i	$0.401512\pi$
$314$	−4.49279	−	27.7841i	−0.253543	−	1.56795i
$315$	−6.34217	+	8.80896i	−0.357341	+	0.496329i
$316$	1.30781	+	0.805485i	0.0735698	+	0.0453121i
$317$	−21.7844	+	10.1582i	−1.22354	+	0.570544i	−0.923579	−	0.383409i	$-0.874750\pi$
$317$	−21.7844	+	10.1582i	−1.22354	+	0.570544i	−0.299957	+	0.953953i	$0.596972\pi$
$318$	0.186733	+	2.55170i	0.0104715	+	0.143092i
$319$	2.48606	+	14.0991i	0.139193	+	0.789400i
$320$	−10.4235	+	14.5379i	−0.582692	+	0.812693i
$321$	7.80071	+	6.54557i	0.435393	+	0.365338i
$322$	14.6506	−	3.70322i	0.816448	−	0.206372i
$323$	1.71840	−	1.53239i	0.0956143	−	0.0852642i
$324$	−9.25387	+	4.99747i	−0.514104	+	0.277637i
$325$	−12.2156	−	1.39294i	−0.677601	−	0.0772666i
$326$	−5.25880	+	27.5295i	−0.291258	+	1.52472i
$327$	4.11583	−	5.87801i	0.227606	−	0.325055i
$328$	−9.94285	−	15.5734i	−0.549002	−	0.859895i
$329$	−0.679207	+	1.86611i	−0.0374459	+	0.102882i
$330$	2.91288	−	2.31144i	0.160349	−	0.127240i
$331$	−2.28360	−	1.31844i	−0.125518	−	0.0724679i	0.435926	−	0.899982i	$-0.356421\pi$
$331$	−2.28360	−	1.31844i	−0.125518	−	0.0724679i	−0.561444	+	0.827514i	$0.689754\pi$
$332$	−7.19387	−	16.6473i	−0.394815	−	0.913639i
$333$	0.602253	+	0.0526903i	0.0330033	+	0.00288741i
$334$	8.54325	−	4.77181i	0.467466	−	0.261102i
$335$	5.66533	−	2.55173i	0.309530	−	0.139416i
$336$	4.01281	−	2.99560i	0.218917	−	0.163424i
$337$	7.37993	+	10.5396i	0.402010	+	0.574130i	0.968210	−	0.250138i	$-0.0804759\pi$
$337$	7.37993	+	10.5396i	0.402010	+	0.574130i	−0.566200	+	0.824268i	$0.691587\pi$
$338$	−8.97061	+	4.02881i	−0.487937	+	0.219138i
$339$	−7.68016	+	2.79535i	−0.417129	+	0.151823i
$340$	−2.25435	−	0.705686i	−0.122260	−	0.0382712i
$341$	6.91716			0.374585
$342$	12.2632	+	9.96232i	0.663119	+	0.538701i
$343$	−13.9453	+	13.9453i	−0.752973	+	0.752973i
$344$	5.36626	−	5.86781i	0.289329	−	0.316371i
$345$	−4.26402	+	7.16642i	−0.229567	+	0.385827i
$346$	1.13385	−	2.98258i	0.0609559	−	0.160345i
$347$	26.7851	−	18.7551i	1.43790	−	1.00683i	0.444061	−	0.895997i	$-0.353537\pi$
$347$	26.7851	−	18.7551i	1.43790	−	1.00683i	0.993839	−	0.110832i	$-0.0353516\pi$
$348$	−8.53812	−	6.34771i	−0.457691	−	0.340273i
$349$	1.15790	−	0.668512i	0.0619808	−	0.0357846i	−0.468689	−	0.883363i	$-0.655274\pi$
$349$	1.15790	−	0.668512i	0.0619808	−	0.0357846i	0.530670	+	0.847578i	$0.321940\pi$
$350$	−4.06723	−	12.7596i	−0.217403	−	0.682030i
$351$	5.81218	+	6.92668i	0.310231	+	0.369719i
$352$	9.39952	−	3.59443i	0.500996	−	0.191584i
$353$	16.8369	−	4.51143i	0.896137	−	0.240119i	0.218780	−	0.975774i	$-0.429792\pi$
$353$	16.8369	−	4.51143i	0.896137	−	0.240119i	0.677356	+	0.735655i	$0.263126\pi$
$354$	−9.35520	−	0.133011i	−0.497223	−	0.00706947i
$355$	3.21671	−	1.12316i	0.170725	−	0.0596111i
$356$	−20.6617	+	6.86155i	−1.09507	+	0.363661i
$357$	0.541680	+	0.379288i	0.0286687	+	0.0200741i
$358$	−21.1434	+	14.3612i	−1.11746	+	0.759012i
$359$	5.30073	+	4.44784i	0.279762	+	0.234748i	0.771861	−	0.635791i	$-0.219326\pi$
$359$	5.30073	+	4.44784i	0.279762	+	0.234748i	−0.492099	+	0.870539i	$0.663770\pi$
$360$	2.31104	−	16.0447i	0.121802	−	0.845630i
$361$	5.41215	−	18.2129i	0.284850	−	0.958572i
$362$	−2.77229	+	0.700746i	−0.145708	+	0.0368304i
$363$	5.15947	−	0.451395i	0.270802	−	0.0236921i
$364$	6.96201	+	6.18750i	0.364909	+	0.324313i
$365$	−21.6710	+	1.60942i	−1.13431	+	0.0842408i
$366$	−4.72690	−	4.08225i	−0.247079	−	0.213382i
$367$	3.93632	+	8.44146i	0.205474	+	0.440640i	0.981857	−	0.189620i	$-0.0607257\pi$
$367$	3.93632	+	8.44146i	0.205474	+	0.440640i	−0.776383	+	0.630261i	$0.782948\pi$
$368$	−16.8389	+	15.0249i	−0.877786	+	0.783226i
$369$	14.5001	+	8.37165i	0.754846	+	0.435811i
$370$	−0.494896	+	0.558058i	−0.0257284	+	0.0290120i
$371$	−3.33198	−	3.97090i	−0.172988	−	0.206159i
$372$	−3.73667	+	3.53000i	−0.193738	+	0.183022i
$373$	−2.30679	+	8.60907i	−0.119441	+	0.445761i	−0.999581	−	0.0289543i	$-0.990782\pi$
$373$	−2.30679	+	8.60907i	−0.119441	+	0.445761i	0.880139	+	0.474715i	$0.157449\pi$
$374$	0.839635	+	1.03003i	0.0434165	+	0.0532615i
$375$	6.56962	+	3.38473i	0.339254	+	0.174787i
$376$	−0.389992	−	2.93996i	−0.0201123	−	0.151617i
$377$	8.36321	−	17.9350i	0.430727	−	0.923697i
$378$	−4.28894	+	8.86633i	−0.220599	+	0.456035i
$379$	−12.9714			−0.666296			−0.333148	−	0.942874i	$-0.608111\pi$
$379$	−12.9714			−0.666296			−0.333148	+	0.942874i	$0.608111\pi$
$380$	−18.8860	+	4.82916i	−0.968829	+	0.247730i
$381$	−10.0649			−0.515641
$382$	1.28171	−	2.64963i	0.0655782	−	0.135567i
$383$	−10.5244	+	22.5696i	−0.537772	+	1.15325i	0.430324	+	0.902674i	$0.358399\pi$
$383$	−10.5244	+	22.5696i	−0.537772	+	1.15325i	−0.968096	+	0.250580i	$0.919379\pi$
$384$	−3.24333	+	6.73854i	−0.165510	+	0.343875i
$385$	−2.04533	+	7.25092i	−0.104240	+	0.369541i
$386$	3.64069	+	4.46625i	0.185306	+	0.227326i
$387$	−1.86495	+	6.96007i	−0.0948005	+	0.353800i
$388$	−18.2121	−	19.2784i	−0.924580	−	0.978713i
$389$	−13.4393	−	16.0163i	−0.681398	−	0.812058i	0.308889	−	0.951098i	$-0.400043\pi$
$389$	−13.4393	−	16.0163i	−0.681398	−	0.812058i	−0.990287	+	0.139040i	$0.955598\pi$
$390$	−5.13070	+	0.307765i	−0.259803	+	0.0155843i
$391$	−2.58084	−	1.49005i	−0.130519	−	0.0753550i
$392$	2.89379	−	9.20948i	0.146159	−	0.465149i
$393$	5.14762	+	11.0391i	0.259663	+	0.556849i
$394$	−9.76399	−	8.43239i	−0.491903	−	0.424818i
$395$	1.12101	−	1.30088i	0.0564043	−	0.0654543i
$396$	−6.05796	+	6.81626i	−0.304424	+	0.342530i
$397$	30.9632	−	2.70893i	1.55400	−	0.135957i	0.722454	−	0.691419i	$-0.243014\pi$
$397$	30.9632	−	2.70893i	1.55400	−	0.135957i	0.831542	+	0.555462i	$0.187458\pi$
$398$	6.64390	−	1.67937i	0.333028	−	0.0841791i
$399$	5.44802	+	0.311741i	0.272742	+	0.0156065i
$400$	14.2004	+	14.0837i	0.710018	+	0.704183i
$401$	−18.2611	−	15.3229i	−0.911917	−	0.765189i	0.0605661	−	0.998164i	$-0.480709\pi$
$401$	−18.2611	−	15.3229i	−0.911917	−	0.765189i	−0.972483	+	0.232975i	$0.925154\pi$
$402$	2.14879	−	1.45951i	0.107172	−	0.0727940i
$403$	−7.83205	−	5.48406i	−0.390142	−	0.273181i
$404$	−1.08800	−	3.27621i	−0.0541299	−	0.162997i
$405$	3.87613	+	11.1012i	0.192607	+	0.551623i
$406$	21.5531	+	0.306441i	1.06966	+	0.0152084i
$407$	0.405308	−	0.108602i	0.0200904	−	0.00538321i
$408$	−0.979223	−	0.127939i	−0.0484788	−	0.00633391i
$409$	1.22600	+	1.46109i	0.0606219	+	0.0722464i	0.795503	−	0.605949i	$-0.207207\pi$
$409$	1.22600	+	1.46109i	0.0606219	+	0.0722464i	−0.734881	+	0.678196i	$0.762762\pi$
$410$	−18.9539	+	8.21498i	−0.936068	+	0.405709i
$411$	−3.22707	+	1.86315i	−0.159180	+	0.0919025i
$412$	20.5969	−	27.7043i	1.01474	−	1.36489i
$413$	15.5277	−	10.8726i	0.764066	−	0.535005i
$414$	7.26691	−	19.1156i	0.357149	−	0.939482i
$415$	−19.6521	+	4.99002i	−0.964683	+	0.244951i
$416$	−13.4925	−	3.38228i	−0.661523	−	0.165830i
$417$	10.0676	−	10.0676i	0.493010	−	0.493010i
$418$	10.3632	+	3.58647i	0.506882	+	0.175420i
$419$	−22.4224			−1.09541			−0.547704	−	0.836672i	$-0.684498\pi$
$419$	−22.4224			−1.09541			−0.547704	+	0.836672i	$0.684498\pi$
$420$	−2.59543	−	4.96076i	−0.126644	−	0.242060i
$421$	29.8007	−	10.8466i	1.45240	−	0.528630i	0.509138	−	0.860685i	$-0.329964\pi$
$421$	29.8007	−	10.8466i	1.45240	−	0.528630i	0.943260	+	0.332055i	$0.107742\pi$
$422$	33.0636	−	14.8492i	1.60951	−	0.722850i
$423$	1.54148	+	2.20146i	0.0749491	+	0.107038i
$424$	7.15494	+	2.95544i	0.347474	+	0.143529i
$425$	−1.17865	+	2.36346i	−0.0571729	+	0.114644i
$426$	1.24356	−	0.694585i	0.0602505	−	0.0336528i
$427$	12.6057	+	1.10286i	0.610033	+	0.0533710i
$428$	28.2830	−	12.2221i	1.36711	−	0.590777i
$429$	2.50412	+	1.44575i	0.120900	+	0.0698017i
$430$	−5.52609	−	6.96400i	−0.266492	−	0.335834i
$431$	−3.68840	+	10.1338i	−0.177664	+	0.488128i	−0.996276	−	0.0862185i	$-0.972522\pi$
$431$	−3.68840	+	10.1338i	−0.177664	+	0.488128i	0.818612	+	0.574347i	$0.194744\pi$
$432$	−0.447062	−	14.7021i	−0.0215093	−	0.707356i
$433$	−11.4721	+	16.3839i	−0.551315	+	0.787360i	−0.994007	−	0.109314i	$-0.965135\pi$
$433$	−11.4721	+	16.3839i	−0.551315	+	0.787360i	0.442692	+	0.896674i	$0.354023\pi$
$434$	1.95410	−	10.2296i	0.0937996	−	0.491036i
$435$	−8.52080	+	8.29983i	−0.408541	+	0.397946i
$436$	−10.3168	−	19.1037i	−0.494085	−	0.914903i
$437$	−24.5813	+	0.740314i	−1.17588	+	0.0354140i
$438$	−8.80764	+	2.22629i	−0.420846	+	0.106376i
$439$	21.1824	+	17.7742i	1.01098	+	0.848314i	0.988468	−	0.151432i	$-0.0483885\pi$
$439$	21.1824	+	17.7742i	1.01098	+	0.848314i	0.0225141	+	0.999747i	$0.492833\pi$
$440$	−2.30152	−	11.0133i	−0.109720	−	0.525036i
$441$	1.51903	+	8.61486i	0.0723349	+	0.410231i
$442$	−0.134061	−	1.83194i	−0.00637664	−	0.0871367i
$443$	27.3218	−	12.7404i	1.29810	−	0.605314i	0.354084	−	0.935214i	$-0.384793\pi$
$443$	27.3218	−	12.7404i	1.29810	−	0.605314i	0.944016	+	0.329900i	$0.107015\pi$
$444$	−0.163527	+	0.265506i	−0.00776064	+	0.0126004i
$445$	3.91151	+	24.0246i	0.185423	+	1.13887i
$446$	−6.55380	−	40.5297i	−0.310331	−	1.91914i
$447$	7.85532	+	0.687251i	0.371544	+	0.0325059i
$448$	−2.66034	−	14.9161i	−0.125689	−	0.704720i
$449$	16.9373	−	9.77873i	0.799318	−	0.461487i	−0.0439144	−	0.999035i	$-0.513983\pi$
$449$	16.9373	−	9.77873i	0.799318	−	0.461487i	0.843233	+	0.537549i	$0.180650\pi$
$450$	−17.3019	−	5.39552i	−0.815618	−	0.254347i
$451$	11.4446	+	2.01799i	0.538904	+	0.0950233i
$452$	−2.85479	+	24.5638i	−0.134278	+	1.15538i
$453$	12.0317	+	5.61045i	0.565297	+	0.263602i
$454$	3.82882	+	11.0039i	0.179695	+	0.516438i
$455$	8.06453	−	6.58838i	0.378071	−	0.308868i
$456$	−7.42852	+	3.35119i	−0.347872	+	0.156934i
$457$	27.4045	−	27.4045i	1.28193	−	1.28193i	0.342356	−	0.939570i	$-0.388775\pi$
$457$	27.4045	−	27.4045i	1.28193	−	1.28193i	0.939570	−	0.342356i	$-0.111225\pi$
$458$	13.6383	−	28.1940i	0.637278	−	1.31742i
$459$	1.82521	−	0.664322i	0.0851935	−	0.0310079i
$460$	13.6006	+	21.2518i	0.634133	+	0.990872i
$461$	1.31806	−	7.47512i	0.0613884	−	0.348151i	−0.938607	−	0.344989i	$-0.887883\pi$
$461$	1.31806	−	7.47512i	0.0613884	−	0.348151i	0.999995	−	0.00316154i	$-0.00100635\pi$
$462$	−0.319083	+	3.13339i	−0.0148451	+	0.145778i
$463$	8.85321	+	2.37221i	0.411443	+	0.110246i	0.458603	−	0.888641i	$-0.348350\pi$
$463$	8.85321	+	2.37221i	0.411443	+	0.110246i	−0.0471592	+	0.998887i	$0.515017\pi$
$464$	−28.7479	+	14.4849i	−1.33459	+	0.672446i
$465$	3.23429	+	4.75067i	0.149987	+	0.220307i
$466$	11.3266	−	1.83155i	0.524694	−	0.0848449i
$467$	−23.8372	+	6.38716i	−1.10305	+	0.295562i	−0.764008	−	0.645207i	$-0.776771\pi$
$467$	−23.8372	+	6.38716i	−1.10305	+	0.295562i	−0.339047	+	0.940770i	$0.610104\pi$
$468$	12.2633	−	2.91493i	0.566870	−	0.134743i
$469$	−1.79998	+	4.94539i	−0.0831152	+	0.228357i
$470$	−3.31453	−	0.0906862i	−0.152888	−	0.00418304i
$471$	−12.9552	+	2.28435i	−0.596943	+	0.105257i
$472$	−13.0469	+	25.1230i	−0.600530	+	1.15638i
$473$	0.435886	+	4.98220i	0.0200421	+	0.229082i
$474$	0.367757	−	0.616562i	0.0168917	−	0.0283196i
$475$	1.98277	+	21.7041i	0.0909756	+	0.995853i
$476$	1.76048	−	0.950730i	0.0806914	−	0.0435766i
$477$	−6.98833	+	0.611400i	−0.319974	+	0.0279941i
$478$	1.15225	−	0.782637i	0.0527025	−	0.0357970i
$479$	1.30825	+	7.41943i	0.0597752	+	0.339002i	0.999999	−	0.00155565i	$-0.000495178\pi$
$479$	1.30825	+	7.41943i	0.0597752	+	0.339002i	−0.940224	+	0.340558i	$0.889384\pi$
$480$	6.86363	+	4.77488i	0.313280	+	0.217942i
$481$	−0.545018	−	0.198370i	−0.0248507	−	0.00904491i
$482$	21.6809	+	22.3063i	0.987536	+	1.01602i
$483$	−1.82807	−	6.82244i	−0.0831800	−	0.310432i
$484$	5.77613	−	14.5672i	0.262551	−	0.662145i
$485$	−24.5099	+	16.6865i	−1.11294	+	0.757695i
$486$	10.0048	+	17.9122i	0.453827	+	0.812512i
$487$	3.74749	−	13.9858i	0.169815	−	0.633758i	−0.827562	−	0.561375i	$-0.810273\pi$
$487$	3.74749	−	13.9858i	0.169815	−	0.633758i	0.997377	−	0.0723837i	$-0.0230606\pi$
$488$	−17.4518	+	7.24888i	−0.790007	+	0.328141i
$489$	12.9010	+	2.27480i	0.583404	+	0.102870i
$490$	−9.65324	−	4.82708i	−0.436089	−	0.218065i
$491$	12.8870	+	35.4066i	0.581580	+	1.59788i	0.785480	+	0.618887i	$0.212416\pi$
$491$	12.8870	+	35.4066i	0.581580	+	1.59788i	−0.203900	+	0.978992i	$0.565362\pi$
$492$	−7.21223	+	4.75033i	−0.325152	+	0.214161i
$493$	−3.00583	−	3.00583i	−0.135376	−	0.135376i
$494$	−8.89049	−	12.2770i	−0.400002	−	0.552369i
$495$	6.45045	+	7.89570i	0.289926	+	0.354885i
$496$	4.48022	+	14.8940i	0.201168	+	0.668759i
$497$	−1.21961	+	2.61546i	−0.0547070	+	0.117320i
$498$	−7.73240	+	3.47271i	−0.346497	+	0.155616i
$499$	−4.23125	+	23.9966i	−0.189417	+	1.07424i	0.730731	+	0.682666i	$0.239179\pi$
$499$	−4.23125	+	23.9966i	−0.189417	+	1.07424i	−0.920148	+	0.391571i	$0.871932\pi$
$500$	18.0642	−	13.1789i	0.807857	−	0.589378i
$501$	−2.28690	−	3.96102i	−0.102171	−	0.176966i
$502$	−28.8799	−	8.18012i	−1.28897	−	0.365097i
$503$	−0.882453	+	10.0865i	−0.0393466	+	0.449734i	0.950810	+	0.309773i	$0.100253\pi$
$503$	−0.882453	+	10.0865i	−0.0393466	+	0.449734i	−0.990157	+	0.139961i	$0.955302\pi$
$504$	8.36900	+	10.8845i	0.372785	+	0.484836i
$505$	−3.80945	+	0.620227i	−0.169518	+	0.0275997i
$506$	0.201790	−	14.1926i	0.00897064	−	0.630940i
$507$	1.94249	+	4.16569i	0.0862692	+	0.185005i
$508$	−13.6496	+	27.2230i	−0.605602	+	1.20782i
$509$	6.07797	−	1.07171i	0.269401	−	0.0475027i	−0.0373156	−	0.999304i	$-0.511881\pi$
$509$	6.07797	−	1.07171i	0.269401	−	0.0475027i	0.306717	+	0.951801i	$0.400770\pi$
$510$	−0.314826	+	1.05827i	−0.0139407	+	0.0468611i
$511$	11.8310	−	14.0996i	0.523372	−	0.623730i
$512$	13.8275	+	17.9109i	0.611097	+	0.791556i
$513$	9.92873	−	12.5833i	0.438364	−	0.555564i
$514$	−4.80815	+	8.06108i	−0.212078	+	0.355559i
$515$	−26.9311	−	27.6481i	−1.18673	−	1.21832i
$516$	−2.77801	−	2.46896i	−0.122295	−	0.108690i
$517$	1.52798	+	1.06990i	0.0672004	+	0.0470542i
$518$	−0.0461090	−	0.630079i	−0.00202591	−	0.0276841i
$519$	−1.40146	−	0.510090i	−0.0615173	−	0.0223905i
$520$	−6.12560	+	14.2946i	−0.268625	+	0.626860i
$521$	−3.44462	+	5.96625i	−0.150911	+	0.261386i	−0.931563	−	0.363581i	$-0.881554\pi$
$521$	−3.44462	+	5.96625i	−0.150911	+	0.261386i	0.780651	+	0.624967i	$0.214887\pi$
$522$	17.0697	−	23.6551i	0.747122	−	1.03535i
$523$	−0.313946	+	3.58842i	−0.0137279	+	0.156911i	−0.999964	−	0.00842967i	$-0.997317\pi$
$523$	−0.313946	+	3.58842i	−0.0137279	+	0.156911i	0.986237	+	0.165340i	$0.0528723\pi$
$524$	36.8389	+	1.04776i	1.60931	+	0.0457714i
$525$	−5.93624	+	1.98563i	−0.259079	+	0.0866599i
$526$	11.2185	−	9.14481i	0.489148	−	0.398733i
$527$	−1.68241	+	1.17803i	−0.0732868	+	0.0513160i
$528$	−1.74234	−	4.36903i	−0.0758254	−	0.190138i
$529$	3.02034	+	8.29832i	0.131319	+	0.360797i
$530$	4.53090	−	7.37432i	0.196810	−	0.320320i
$531$		−	25.6529i		−	1.11324i
$532$	8.23154	−	14.3127i	0.356882	−	0.620535i
$533$	−11.3584	−	11.3584i	−0.491986	−	0.491986i
$534$	3.34407	+	9.61074i	0.144712	+	0.415897i
$535$	−8.47784	−	33.3881i	−0.366529	−	1.44349i
$536$	−1.03352	−	7.79124i	−0.0446414	−	0.336530i
$537$	6.85227	+	9.78605i	0.295697	+	0.422299i
$538$	−1.85067	+	18.1735i	−0.0797881	+	0.783517i
$539$	3.03580	+	5.25817i	0.130761	+	0.226485i
$540$	−16.3088	−	2.11287i	−0.701818	−	0.0909235i
$541$	−6.72312	+	5.64137i	−0.289050	+	0.242541i	−0.775769	−	0.631017i	$-0.782638\pi$
$541$	−6.72312	+	5.64137i	−0.289050	+	0.242541i	0.486719	+	0.873558i	$0.338193\pi$
$542$	1.41236	+	1.01917i	0.0606661	+	0.0437773i
$543$	0.345919	+	1.29099i	0.0148448	+	0.0554015i
$544$	−1.67402	+	2.47504i	−0.0717730	+	0.106117i
$545$	−22.9174	+	8.00191i	−0.981673	+	0.342764i
$546$	2.84550	−	3.29485i	0.121776	−	0.141006i
$547$	−9.19105	+	13.1262i	−0.392981	+	0.561235i	−0.966077	−	0.258253i	$-0.916853\pi$
$547$	−9.19105	+	13.1262i	−0.392981	+	0.561235i	0.573096	+	0.819488i	$0.305742\pi$
$548$	0.662932	+	11.2551i	0.0283191	+	0.480795i
$549$	11.0074	−	13.1181i	0.469785	−	0.559868i
$550$	−12.5654	+	0.588199i	−0.535792	+	0.0250809i
$551$	−34.1419	−	8.05505i	−1.45449	−	0.343156i
$552$	7.13385	+	7.76989i	0.303637	+	0.330709i
$553$	0.126768	+	1.44897i	0.00539074	+	0.0616164i
$554$	−4.63900	+	24.2849i	−0.197092	+	1.03177i
$555$	0.264100	+	0.227584i	0.0112104	+	0.00966041i
$556$	−13.5770	−	40.8833i	−0.575792	−	1.73384i
$557$	4.79197	−	2.23453i	0.203042	−	0.0946802i	−0.318437	−	0.947944i	$-0.603158\pi$
$557$	4.79197	−	2.23453i	0.203042	−	0.0946802i	0.521480	+	0.853264i	$0.325380\pi$
$558$	−9.82331	−	10.1067i	−0.415854	−	0.427849i
$559$	3.45645	−	5.98675i	0.146192	−	0.253213i
$560$	−16.9374	+	0.292406i	−0.715735	+	0.0123564i
$561$	0.475810	−	0.399252i	0.0200887	−	0.0168564i
$562$	−6.79494	+	23.9895i	−0.286627	+	1.01194i
$563$	24.2156	+	6.48854i	1.02056	+	0.273459i	0.730037	−	0.683408i	$-0.239503\pi$
$563$	24.2156	+	6.48854i	1.02056	+	0.273459i	0.290527	+	0.956867i	$0.406169\pi$
$564$	−1.37142	+	0.201800i	−0.0577471	+	0.00849733i
$565$	26.6096	+	7.50602i	1.11947	+	0.315781i
$566$	10.5296	+	4.00288i	0.442591	+	0.168253i
$567$	−9.02623	−	4.20900i	−0.379066	−	0.176761i
$568$	−0.192218	−	4.30546i	−0.00806531	−	0.180653i
$569$		−	11.5280i		−	0.483280i	−0.970366	−	0.241640i	$-0.922315\pi$
$569$		−	11.5280i		−	0.483280i	0.970366	−	0.241640i	$-0.0776853\pi$
$570$	2.38242	+	8.79436i	0.0997888	+	0.368355i
$571$			25.4897i			1.06671i	0.845891	+	0.533355i	$0.179069\pi$
$571$			25.4897i			1.06671i	−0.845891	+	0.533355i	$0.820931\pi$
$572$	7.30636	−	4.81233i	0.305494	−	0.201214i
$573$	−1.24684	−	0.581409i	−0.0520873	−	0.0242887i
$574$	6.21743	−	16.3550i	0.259511	−	0.682643i
$575$	25.8708	−	11.2461i	1.07889	−	0.468994i
$576$	−18.6004	−	8.62907i	−0.775018	−	0.359545i
$577$	−28.3453	−	7.59510i	−1.18003	−	0.316188i	−0.385092	−	0.922878i	$-0.625830\pi$
$577$	−28.3453	−	7.59510i	−1.18003	−	0.316188i	−0.794939	+	0.606690i	$0.792497\pi$
$578$	22.7520	+	6.44441i	0.946358	+	0.268052i
$579$	2.06313	−	1.73117i	0.0857409	−	0.0719451i
$580$	10.8934	+	34.3024i	0.452322	+	1.42433i
$581$	8.58672	−	14.8726i	0.356237	−	0.617021i
$582$	−8.88885	+	8.63963i	−0.368455	+	0.358124i
$583$	−4.41278	+	2.05771i	−0.182759	+	0.0852218i
$584$	−5.92298	+	26.8416i	−0.245095	+	1.11071i
$585$	−1.04374	−	14.0541i	−0.0431534	−	0.581064i
$586$	−7.83346	−	1.49638i	−0.323597	−	0.0618148i
$587$	−1.82585	−	20.8696i	−0.0753609	−	0.861379i	−0.935962	−	0.352100i	$-0.885468\pi$
$587$	−1.82585	−	20.8696i	−0.0753609	−	0.861379i	0.860601	−	0.509279i	$-0.170088\pi$
$588$	−4.32333	−	1.29123i	−0.178291	−	0.0532496i
$589$	−6.69718	+	15.5694i	−0.275953	+	0.641527i
$590$	25.4201	+	18.8561i	1.04653	+	0.776292i
$591$	−3.87604	+	4.61929i	−0.159439	+	0.190012i
$592$	0.496358	+	0.802365i	0.0204002	+	0.0329770i
$593$	11.0775	−	15.8204i	0.454900	−	0.649665i	−0.524543	−	0.851384i	$-0.675764\pi$
$593$	11.0775	−	15.8204i	0.454900	−	0.649665i	0.979443	+	0.201719i	$0.0646528\pi$
$594$	7.00166	+	6.04678i	0.287281	+	0.248102i
$595$	−0.737405	−	2.11192i	−0.0302306	−	0.0865802i
$596$	12.5119	−	20.3146i	0.512506	−	0.832118i
$597$	−0.829008	−	3.09390i	−0.0339291	−	0.126625i
$598$	−11.4807	+	15.9098i	−0.469480	+	0.650601i
$599$	19.6987	−	16.5292i	0.804867	−	0.675363i	−0.144510	−	0.989503i	$-0.546161\pi$
$599$	19.6987	−	16.5292i	0.804867	−	0.675363i	0.949377	+	0.314140i	$0.101716\pi$
$600$	6.48772	−	6.73020i	0.264860	−	0.274759i
$601$	20.6175	+	35.7106i	0.841006	+	1.45666i	0.889045	+	0.457819i	$0.151369\pi$
$601$	20.6175	+	35.7106i	0.841006	+	1.45666i	−0.0480397	+	0.998845i	$0.515297\pi$
$602$	7.49118	+	0.762851i	0.305318	+	0.0310915i
$603$	4.08508	+	5.83411i	0.166358	+	0.237583i
$604$	31.4916	−	24.9339i	1.28138	−	1.01455i
$605$	−15.0566	−	8.95867i	−0.612137	−	0.364222i
$606$	−1.52392	+	0.530251i	−0.0619051	+	0.0215400i
$607$	16.6654	+	16.6654i	0.676428	+	0.676428i	0.959190	−	0.282762i	$-0.0912507\pi$
$607$	16.6654	+	16.6654i	0.676428	+	0.676428i	−0.282762	+	0.959190i	$0.591251\pi$
$608$	−1.01011	+	24.6370i	−0.0409654	+	0.999161i
$609$		−	10.0750i		−	0.408260i
$610$	4.90811	+	20.5500i	0.198724	+	0.832044i
$611$	−0.881835	−	2.42282i	−0.0356752	−	0.0980169i
$612$	0.312581	−	2.68957i	0.0126353	−	0.108720i
$613$	−5.76032	+	4.03342i	−0.232657	+	0.162908i	−0.684092	−	0.729396i	$-0.739801\pi$
$613$	−5.76032	+	4.03342i	−0.232657	+	0.162908i	0.451435	+	0.892304i	$0.350912\pi$
$614$	18.1930	+	22.3184i	0.734208	+	0.900696i
$615$	3.96526	+	8.80364i	0.159895	+	0.354997i
$616$	8.04228	+	5.11239i	0.324033	+	0.205984i
$617$	−4.12156	+	47.1096i	−0.165928	+	1.89656i	0.222270	+	0.974985i	$0.428654\pi$
$617$	−4.12156	+	47.1096i	−0.165928	+	1.89656i	−0.388197	+	0.921576i	$0.626902\pi$
$618$	−13.0846	−	9.44199i	−0.526341	−	0.379812i
$619$	7.86266	−	13.6185i	0.316027	−	0.547375i	−0.663628	−	0.748063i	$-0.730984\pi$
$619$	7.86266	−	13.6185i	0.316027	−	0.547375i	0.979655	+	0.200688i	$0.0643176\pi$
$620$	17.2355	−	2.30528i	0.692196	−	0.0925824i
$621$	−19.4953	−	7.09572i	−0.782321	−	0.284742i
$622$	−30.0785	+	2.20114i	−1.20604	+	0.0882575i
$623$	−16.8882	−	11.8252i	−0.676610	−	0.473767i
$624$	−1.49107	+	6.32826i	−0.0596907	+	0.253333i
$625$	−11.3456	−	22.2773i	−0.453825	−	0.891091i
$626$	−16.6039	−	9.90361i	−0.663624	−	0.395828i
$627$	1.60729	−	4.86714i	0.0641891	−	0.194375i
$628$	−11.3907	+	38.1383i	−0.454537	+	1.52189i
$629$	−0.0800844	+	0.0954409i	−0.00319318	+	0.00380548i
$630$	13.4990	−	7.30885i	0.537812	−	0.291192i
$631$	−46.4467	+	8.18981i	−1.84901	+	0.326031i	−0.984337	−	0.176298i	$-0.943588\pi$
$631$	−46.4467	+	8.18981i	−1.84901	+	0.326031i	−0.864677	+	0.502329i	$0.832477\pi$
$632$	−1.16891	−	1.83084i	−0.0464966	−	0.0728270i
$633$	−7.15957	−	15.3538i	−0.284568	−	0.610257i
$634$	33.9893	+	0.483256i	1.34989	+	0.0191926i
$635$	27.6314	+	19.8937i	1.09652	+	0.789457i
$636$	1.33370	−	3.36354i	0.0528845	−	0.133373i
$637$	0.731447	−	8.36048i	0.0289810	−	0.331254i
$638$	5.51776	−	19.4804i	0.218450	−	0.771237i
$639$	1.95271	+	3.38219i	0.0772480	+	0.133797i
$640$	22.2230	−	12.0889i	0.878439	−	0.477854i
$641$	−3.52306	+	19.9803i	−0.139153	+	0.789173i	0.832725	+	0.553687i	$0.186779\pi$
$641$	−3.52306	+	19.9803i	−0.139153	+	0.789173i	−0.971878	+	0.235487i	$0.924332\pi$
$642$	−5.89999	−	13.1370i	−0.232854	−	0.518477i
$643$	10.2106	−	21.8968i	0.402668	−	0.863525i	−0.595519	−	0.803341i	$-0.703054\pi$
$643$	10.2106	−	21.8968i	0.402668	−	0.863525i	0.998187	−	0.0601836i	$-0.0191686\pi$
$644$	−20.9321	−	4.30784i	−0.824840	−	0.169753i
$645$	−3.21794	+	2.62892i	−0.126706	+	0.103514i
$646$	−3.13136	+	0.892612i	−0.123202	+	0.0351194i
$647$	−24.0584	−	24.0584i	−0.945832	−	0.945832i	0.0527749	−	0.998606i	$-0.483193\pi$
$647$	−24.0584	−	24.0584i	−0.945832	−	0.945832i	−0.998606	+	0.0527749i	$0.983193\pi$
$648$	14.8586	−	0.663365i	0.583700	−	0.0260594i
$649$	−6.08969	−	16.7313i	−0.239041	−	0.656760i
$650$	14.6937	+	9.29613i	0.576335	+	0.364624i
$651$	−4.79384	−	0.845283i	−0.187885	−	0.0331293i
$652$	23.6485	−	31.8089i	0.926147	−	1.24573i
$653$	−6.48877	+	24.2164i	−0.253925	+	0.947662i	0.714760	+	0.699370i	$0.246536\pi$
$653$	−6.48877	+	24.2164i	−0.253925	+	0.947662i	−0.968685	+	0.248292i	$0.920131\pi$
$654$	−8.85968	+	4.94855i	−0.346441	+	0.193504i
$655$	7.68737	−	40.4803i	0.300371	−	1.58170i
$656$	3.06751	+	25.9494i	0.119766	+	1.01315i
$657$	−6.44680	−	24.0598i	−0.251514	−	0.938662i
$658$	2.01390	−	1.95744i	0.0785100	−	0.0763088i
$659$	11.4194	+	4.15631i	0.444835	+	0.161907i	0.554719	−	0.832038i	$-0.312826\pi$
$659$	11.4194	+	4.15631i	0.444835	+	0.161907i	−0.109884	+	0.993944i	$0.535048\pi$
$660$	−5.13181	+	1.14881i	−0.199755	+	0.0447172i
$661$	3.03668	+	17.2218i	0.118113	+	0.669852i	0.985162	+	0.171629i	$0.0549029\pi$
$661$	3.03668	+	17.2218i	0.118113	+	0.669852i	−0.867049	+	0.498223i	$0.833986\pi$
$662$	2.09528	+	3.08480i	0.0814355	+	0.119894i
$663$	−0.855278	+	0.0748271i	−0.0332162	+	0.00290605i
$664$	−1.09353	+	25.6237i	−0.0424374	+	0.994391i
$665$	−14.3404	−	11.6241i	−0.556096	−	0.450761i
$666$	−0.734272	−	0.437967i	−0.0284525	−	0.0169709i
$667$	3.95726	+	45.2316i	0.153226	+	1.75138i
$668$	−13.8149	+	0.813707i	−0.534516	+	0.0314833i
$669$	−18.8982	+	3.33226i	−0.730647	+	0.128833i
$670$	−8.78389	−	0.240329i	−0.339351	−	0.00928470i
$671$	4.06515	−	11.1689i	0.156933	−	0.431171i
$672$	−6.95345	+	1.34244i	−0.268235	+	0.0517857i
$673$	−15.2482	+	4.08575i	−0.587775	+	0.157494i	−0.540436	−	0.841385i	$-0.681741\pi$
$673$	−15.2482	+	4.08575i	−0.587775	+	0.157494i	−0.0473390	+	0.998879i	$0.515074\pi$
$674$	−2.90463	−	17.9627i	−0.111882	−	0.691896i
$675$	−5.22358	+	17.6285i	−0.201056	+	0.678522i
$676$	13.9014	+	0.395379i	0.534671	+	0.0152069i
$677$	−19.9464	−	5.34462i	−0.766602	−	0.205410i	−0.145732	−	0.989324i	$-0.546554\pi$
$677$	−19.9464	−	5.34462i	−0.766602	−	0.205410i	−0.620870	+	0.783914i	$0.713220\pi$
$678$	11.4990	+	1.17098i	0.441616	+	0.0449712i
$679$	4.36102	−	24.7326i	0.167361	−	0.949149i
$680$	2.43540	+	2.28671i	0.0933935	+	0.0876912i
$681$	5.11728	−	1.86254i	0.196095	−	0.0713726i
$682$	−8.80614	−	4.25982i	−0.337205	−	0.163117i
$683$	−0.568931	+	0.568931i	−0.0217695	+	0.0217695i	−0.717908	−	0.696138i	$-0.754900\pi$
$683$	−0.568931	+	0.568931i	−0.0217695	+	0.0217695i	0.696138	+	0.717908i	$0.254900\pi$
$684$	−9.47701	−	20.2350i	−0.362362	−	0.773705i
$685$	12.5419	+	1.26349i	0.479203	+	0.0482756i
$686$	26.3415	−	9.16556i	1.00572	−	0.349943i
$687$	−13.2672	−	6.18661i	−0.506176	−	0.236034i
$688$	−10.4453	+	4.16550i	−0.398224	+	0.158808i
$689$	6.62783	+	1.16867i	0.252500	+	0.0445226i
$690$	9.84178	−	6.49754i	0.374670	−	0.247357i
$691$	1.57781	−	0.910952i	0.0600229	−	0.0346542i	−0.469688	−	0.882832i	$-0.655634\pi$
$691$	1.57781	−	0.910952i	0.0600229	−	0.0346542i	0.529711	+	0.848178i	$0.322300\pi$
$692$	−3.28026	+	3.09883i	−0.124697	+	0.117800i
$693$	−8.60276	−	0.752644i	−0.326792	−	0.0285906i
$694$	−45.6498	+	7.38174i	−1.73284	+	0.280207i
$695$	−47.5375	+	7.73972i	−1.80320	+	0.293584i
$696$	6.96063	+	13.3392i	0.263842	+	0.505623i
$697$	−3.12725	+	1.45826i	−0.118453	+	0.0552355i
$698$	−1.88579	+	0.138002i	−0.0713783	+	0.00522345i
$699$	−0.931247	−	5.28137i	−0.0352230	−	0.199760i
$700$	−2.67986	+	18.7488i	−0.101289	+	0.708639i
$701$	39.4256	+	33.0820i	1.48909	+	1.24949i	0.895767	+	0.444524i	$0.146627\pi$
$701$	39.4256	+	33.0820i	1.48909	+	1.24949i	0.593319	+	0.804967i	$0.297817\pi$
$702$	−3.13372	−	12.3976i	−0.118275	−	0.467917i
$703$	−0.147973	+	1.01743i	−0.00558091	+	0.0383732i
$704$	−14.1800	−	1.21252i	−0.534428	−	0.0456985i
$705$	−0.0203582	+	1.54967i	−0.000766734	+	0.0583638i
$706$	−24.2131	−	4.62528i	−0.911272	−	0.174075i
$707$	1.87506	−	2.67786i	0.0705189	−	0.100711i
$708$	11.8281	+	5.93058i	0.444526	+	0.222885i
$709$	11.5846	−	31.8285i	0.435070	−	1.19534i	−0.507593	−	0.861597i	$-0.669465\pi$
$709$	11.5846	−	31.8285i	0.435070	−	1.19534i	0.942663	−	0.333747i	$-0.108313\pi$
$710$	−4.78683	−	0.551081i	−0.179647	−	0.0206817i
$711$	1.70467	+	0.984191i	0.0639301	+	0.0369100i
$712$	30.5296	+	3.98880i	1.14415	+	0.149486i
$713$	21.8539	+	1.91197i	0.818435	+	0.0716038i
$714$	−0.456027	−	0.816451i	−0.0170664	−	0.0305549i
$715$	−4.01701	−	8.91855i	−0.150228	−	0.333535i
$716$	35.7615	−	5.26221i	1.33647	−	0.196658i
$717$	−0.373426	−	0.533308i	−0.0139458	−	0.0199167i
$718$	−4.00916	−	8.92686i	−0.149621	−	0.333147i
$719$	33.3698	−	12.1456i	1.24448	−	0.452955i	0.365950	−	0.930634i	$-0.380744\pi$
$719$	33.3698	−	12.1456i	1.24448	−	0.452955i	0.878534	+	0.477679i	$0.158522\pi$
$720$	−12.8230	+	19.0031i	−0.477885	+	0.708202i
$721$	32.6912			1.21748
$722$	−18.1062	+	19.8536i	−0.673844	+	0.738873i
$723$	10.2809	−	10.2809i	0.382350	−	0.382350i
$724$	3.96090	+	0.815157i	0.147206	+	0.0302951i
$725$	39.7972	−	5.94396i	1.47803	−	0.220753i
$726$	−6.84643	−	2.60271i	−0.254095	−	0.0965955i
$727$	27.7709	−	19.4454i	1.02996	−	0.721189i	0.0689315	−	0.997621i	$-0.478041\pi$
$727$	27.7709	−	19.4454i	1.02996	−	0.721189i	0.961033	+	0.276432i	$0.0891521\pi$
$728$	−5.05277	−	12.1647i	−0.187268	−	0.450852i
$729$	−5.35721	+	3.09299i	−0.198415	+	0.114555i
$730$	28.5801	+	11.2968i	1.05780	+	0.418112i
$731$	−0.954516	−	1.13755i	−0.0353041	−	0.0420737i
$732$	3.50376	+	8.10803i	0.129503	+	0.299682i
$733$	−25.2913	+	6.77678i	−0.934155	+	0.250306i	−0.693625	−	0.720336i	$-0.743988\pi$
$733$	−25.2913	+	6.77678i	−0.934155	+	0.250306i	−0.240529	+	0.970642i	$0.577321\pi$
$734$	0.187262	−	13.1708i	0.00691195	−	0.486144i
$735$	−2.19182	+	4.54357i	−0.0808464	+	0.167592i
$736$	30.6901	−	8.75804i	1.13125	−	0.322826i
$737$	4.04931	+	2.83536i	0.149158	+	0.104442i
$738$	−13.3044	−	19.5875i	−0.489740	−	0.721025i
$739$	−37.8264	−	31.7401i	−1.39147	−	1.16758i	−0.964743	−	0.263195i	$-0.915224\pi$
$739$	−37.8264	−	31.7401i	−1.39147	−	1.16758i	−0.426722	−	0.904383i	$-0.640332\pi$
$740$	0.973716	−	0.405682i	0.0357945	−	0.0149132i
$741$	−5.67865	+	4.23660i	−0.208610	+	0.155635i
$742$	1.79649	+	7.10724i	0.0659510	+	0.260915i
$743$	28.7518	−	2.51546i	1.05480	−	0.0922833i	0.453462	−	0.891276i	$-0.350189\pi$
$743$	28.7518	−	2.51546i	1.05480	−	0.0922833i	0.601341	+	0.798993i	$0.294633\pi$
$744$	6.93100	−	2.19282i	0.254103	−	0.0803928i
$745$	−20.2070	−	17.4131i	−0.740326	−	0.637966i
$746$	8.23851	−	9.53949i	0.301633	−	0.349266i
$747$	−9.82200	−	21.0634i	−0.359368	−	0.770668i
$748$	−0.434602	−	1.82839i	−0.0158906	−	0.0668526i
$749$	25.2680	+	14.5885i	0.923271	+	0.533051i
$750$	−6.27926	−	8.35485i	−0.229286	−	0.305076i
$751$	15.3708	+	18.3182i	0.560889	+	0.668442i	0.969734	−	0.244162i	$-0.0785128\pi$
$751$	15.3708	+	18.3182i	0.560889	+	0.668442i	−0.408845	+	0.912604i	$0.634068\pi$
$752$	−1.31403	+	3.98300i	−0.0479179	+	0.145245i
$753$	−3.63112	+	13.5515i	−0.132325	+	0.493845i
$754$	−21.6920	+	17.6824i	−0.789977	+	0.643955i
$755$	−21.9414	−	39.1835i	−0.798531	−	1.42603i
$756$	10.9204	−	8.64634i	0.397170	−	0.314464i
$757$	9.37573	−	20.1063i	0.340767	−	0.730777i	−0.659005	−	0.752139i	$-0.729022\pi$
$757$	9.37573	−	20.1063i	0.340767	−	0.730777i	0.999772	+	0.0213617i	$0.00680017\pi$
$758$	16.5137	+	7.98823i	0.599805	+	0.290145i
$759$	−6.63434			−0.240811
$760$	27.0174	+	5.48267i	0.980024	+	0.198877i
$761$	9.17667			0.332654			0.166327	−	0.986071i	$-0.446809\pi$
$761$	9.17667			0.332654			0.166327	+	0.986071i	$0.446809\pi$
$762$	12.8135	+	6.19831i	0.464184	+	0.224541i
$763$	8.68908	−	18.6338i	0.314566	−	0.674589i
$764$	−3.26346	+	2.58389i	−0.118068	+	0.0934818i
$765$	−2.91358	−	0.821860i	−0.105341	−	0.0297144i
$766$	27.2976	−	22.2518i	0.986303	−	0.803991i
$767$	−6.36976	+	23.7723i	−0.229999	+	0.858367i
$768$	8.27885	−	6.58139i	0.298737	−	0.237485i
$769$	20.9888	+	25.0135i	0.756876	+	0.902009i	0.997646	−	0.0685728i	$-0.0218445\pi$
$769$	20.9888	+	25.0135i	0.756876	+	0.902009i	−0.240770	+	0.970582i	$0.577400\pi$
$770$	7.06925	−	7.97146i	0.254758	−	0.287272i
$771$	3.79934	+	2.19355i	0.136830	+	0.0789987i
$772$	−1.88445	−	7.92798i	−0.0678229	−	0.285334i
$773$	−19.2299	−	41.2386i	−0.691650	−	1.48325i	−0.866773	−	0.498703i	$-0.833810\pi$
$773$	−19.2299	−	41.2386i	−0.691650	−	1.48325i	0.175123	−	0.984547i	$-0.443968\pi$
$774$	6.66048	−	7.71228i	0.239406	−	0.277212i
$775$	0.510724	−	19.4348i	0.0183457	−	0.698119i
$776$	11.3133	+	35.7587i	0.406124	+	1.28366i
$777$	−0.294165	+	0.0257361i	−0.0105531	+	0.000923276i
$778$	7.24598	+	28.6665i	0.259781	+	1.02774i
$779$	−15.6228	+	23.8061i	−0.559744	+	0.852942i
$780$	6.72136	+	2.76785i	0.240663	+	0.0991049i
$781$	2.07649	+	1.74238i	0.0743025	+	0.0623472i
$782$	2.36801	+	3.48633i	0.0846799	+	0.124671i
$783$	−24.2415	−	16.9741i	−0.866319	−	0.606603i
$784$	−9.35555	+	9.94237i	−0.334127	+	0.355085i
$785$	40.0812	+	19.3352i	1.43056	+	0.690102i
$786$	0.244887	−	17.2238i	0.00873481	−	0.614353i
$787$	−4.35346	+	1.16651i	−0.155184	+	0.0415814i	−0.335575	−	0.942014i	$-0.608930\pi$
$787$	−4.35346	+	1.16651i	−0.155184	+	0.0415814i	0.180391	+	0.983595i	$0.442264\pi$
$788$	7.23746	+	16.7482i	0.257824	+	0.596628i
$789$	−4.34842	−	5.18224i	−0.154808	−	0.184493i
$790$	−2.22827	+	0.965772i	−0.0792783	+	0.0343606i
$791$	−20.2803	+	11.7089i	−0.721085	+	0.416319i
$792$	11.9100	−	4.94699i	0.423203	−	0.175784i
$793$	−13.4578	+	9.42323i	−0.477899	+	0.334629i
$794$	−41.0870	−	15.6195i	−1.45812	−	0.554314i
$795$	−3.47654	−	2.06854i	−0.123300	−	0.0733635i
$796$	−9.49247	−	1.95356i	−0.336452	−	0.0692419i
$797$	−28.1927	+	28.1927i	−0.998636	+	0.998636i	−0.999999	−	0.00136272i	$-0.999566\pi$
$797$	−28.1927	+	28.1927i	−0.998636	+	0.998636i	0.00136272	+	0.999999i	$0.499566\pi$
$798$	−6.74382	−	3.75195i	−0.238729	−	0.132817i
$799$	−0.553849			−0.0195938
$800$	−9.40510	−	26.6748i	−0.332520	−	0.943096i
$801$	−26.2179	+	9.54255i	−0.926365	+	0.337169i
$802$	13.8116	+	30.7532i	0.487705	+	1.08593i
$803$	−9.91622	−	14.1618i	−0.349936	−	0.499760i
$804$	−3.63441	+	0.534794i	−0.128176	+	0.0188607i
$805$	−8.46620	+	22.3430i	−0.298394	+	0.787488i
$806$	6.59361	+	11.8049i	0.232250	+	0.415811i
$807$	8.50580	+	0.744161i	0.299418	+	0.0261957i
$808$	−0.632482	+	4.84092i	−0.0222506	+	0.170303i
$809$	−45.7529	−	26.4154i	−1.60859	−	0.928717i	−0.989687	−	0.143246i	$-0.954246\pi$
$809$	−45.7529	−	26.4154i	−1.60859	−	0.928717i	−0.618898	−	0.785471i	$-0.712421\pi$
$810$	1.90184	−	16.5198i	0.0668237	−	0.580448i
$811$	−10.7532	+	29.5442i	−0.377596	+	1.03744i	0.594754	+	0.803908i	$0.297249\pi$
$811$	−10.7532	+	29.5442i	−0.377596	+	1.03744i	−0.972350	+	0.233528i	$0.924973\pi$
$812$	−27.2503	−	13.6633i	−0.956298	−	0.479487i
$813$	0.466931	−	0.666847i	0.0163760	−	0.0233873i
$814$	−0.582874	−	0.111343i	−0.0204297	−	0.00390256i
$815$	−30.9212	−	31.7444i	−1.08312	−	1.11196i
$816$	1.16785	+	0.765916i	0.0408828	+	0.0268124i
$817$	−11.6362	−	3.84265i	−0.407098	−	0.134437i
$818$	−0.661017	−	2.61511i	−0.0231119	−	0.0914352i
$819$	9.14389	+	7.67263i	0.319513	+	0.268104i
$820$	29.1891	+	1.21410i	1.01933	+	0.0423981i
$821$	−0.902101	−	5.11607i	−0.0314835	−	0.178552i	0.965011	−	0.262209i	$-0.0844511\pi$
$821$	−0.902101	−	5.11607i	−0.0314835	−	0.178552i	−0.996495	+	0.0836571i	$0.973340\pi$
$822$	5.25573	−	0.384613i	0.183315	−	0.0134149i
$823$	1.85792	−	0.866364i	0.0647631	−	0.0301996i	−0.389967	−	0.920829i	$-0.627514\pi$
$823$	1.85792	−	0.866364i	0.0647631	−	0.0301996i	0.454730	+	0.890629i	$0.349736\pi$
$824$	−43.2829	+	22.5857i	−1.50783	+	0.786811i
$825$	0.358393	+	5.86861i	0.0124776	+	0.204319i
$826$	−26.4638	+	4.27929i	−0.920792	+	0.148895i
$827$	−4.46365	−	0.390519i	−0.155216	−	0.0135797i	0.00928273	−	0.999957i	$-0.497045\pi$
$827$	−4.46365	−	0.390519i	−0.155216	−	0.0135797i	−0.164499	+	0.986377i	$0.552601\pi$
$828$	−21.0234	+	19.8606i	−0.730615	+	0.690205i
$829$	−7.03701	+	4.06282i	−0.244405	+	0.141107i	−0.617200	−	0.786806i	$-0.711733\pi$
$829$	−7.03701	+	4.06282i	−0.244405	+	0.141107i	0.372794	+	0.927914i	$0.378400\pi$
$830$	28.0918	+	5.74968i	0.975082	+	0.199574i
$831$	11.3805	+	2.00669i	0.394786	+	0.0696114i
$832$	15.0942	+	12.6151i	0.523296	+	0.437349i
$833$	−1.63387	−	0.761887i	−0.0566103	−	0.0263978i
$834$	−19.0168	+	6.61693i	−0.658498	+	0.229126i
$835$	−1.55086	+	15.3944i	−0.0536696	+	0.532746i
$836$	−10.9846	−	10.9479i	−0.379911	−	0.378641i
$837$	−10.1103	+	10.1103i	−0.349464	+	0.349464i
$838$	28.5457	+	13.8085i	0.986095	+	0.477007i
$839$	24.5363	−	8.93050i	0.847088	−	0.308315i	0.118236	−	0.992986i	$-0.462276\pi$
$839$	24.5363	−	8.93050i	0.847088	−	0.308315i	0.728853	+	0.684671i	$0.240054\pi$
$840$	0.249203	+	7.91383i	0.00859833	+	0.273053i
$841$	−6.21071	+	35.2227i	−0.214162	+	1.21457i
$842$	−44.6186	−	4.54365i	−1.53766	−	0.156585i
$843$	11.2568	+	3.01625i	0.387704	+	0.103885i
$844$	−51.2374	−	1.45727i	−1.76366	−	0.0501614i
$845$	2.90089	−	15.2756i	0.0997937	−	0.525495i
$846$	−0.606702	−	3.75194i	−0.0208588	−	0.128994i
$847$	14.3339	−	3.84075i	0.492518	−	0.131970i
$848$	−7.28879	−	8.16878i	−0.250298	−	0.280517i
$849$	1.80080	−	4.94765i	0.0618033	−	0.169803i
$850$	2.95602	−	2.28303i	0.101391	−	0.0783073i
$851$	1.31054	−	0.231084i	0.0449247	−	0.00792144i
$852$	−2.01090	+	0.118443i	−0.0688924	+	0.00405780i
$853$	−2.48758	−	28.4332i	−0.0851731	−	0.973533i	−0.911760	−	0.410724i	$-0.865276\pi$
$853$	−2.48758	−	28.4332i	−0.0851731	−	0.973533i	0.826587	−	0.562810i	$-0.190280\pi$
$854$	−15.3690	−	9.16705i	−0.525916	−	0.313690i
$855$	−24.0173	+	6.87432i	−0.821374	+	0.235097i
$856$	−43.5335	−	1.85787i	−1.48795	−	0.0635007i
$857$	−39.5737	+	3.46225i	−1.35181	+	0.118268i	−0.739932	−	0.672682i	$-0.765142\pi$
$857$	−39.5737	+	3.46225i	−1.35181	+	0.118268i	−0.611881	+	0.790950i	$0.709587\pi$
$858$	−2.29762	−	3.38269i	−0.0784393	−	0.115483i
$859$	7.86569	+	44.6085i	0.268374	+	1.52202i	0.759253	+	0.650796i	$0.225565\pi$
$859$	7.86569	+	44.6085i	0.268374	+	1.52202i	−0.490879	+	0.871228i	$0.663324\pi$
$860$	2.74652	+	12.2689i	0.0936556	+	0.418367i
$861$	−7.68490	−	2.79707i	−0.261901	−	0.0953240i
$862$	10.9364	−	10.6298i	0.372495	−	0.362051i
$863$	10.1579	+	37.9097i	0.345778	+	1.29046i	0.891701	+	0.452625i	$0.149512\pi$
$863$	10.1579	+	37.9097i	0.345778	+	1.29046i	−0.545923	+	0.837835i	$0.683821\pi$
$864$	−8.48491	+	18.9924i	−0.288662	+	0.646134i
$865$	2.83924	+	4.17040i	0.0965371	+	0.141798i
$866$	24.6948	−	13.7932i	0.839162	−	0.468712i
$867$	2.86065	−	10.6761i	0.0971527	−	0.362579i
$868$	−8.78746	+	11.8198i	−0.298266	+	0.401189i
$869$	1.34545	+	0.237239i	0.0456413	+	0.00804780i
$870$	15.9590	−	5.31900i	0.541062	−	0.180331i
$871$	−2.33696	−	6.42075i	−0.0791850	−	0.217559i
$872$	1.36945	+	30.6742i	0.0463756	+	1.03876i
$873$	−24.0324	−	24.0324i	−0.813374	−	0.813374i
$874$	31.7500	+	14.1955i	1.07396	+	0.480169i
$875$	20.2215	+	6.28204i	0.683613	+	0.212372i
$876$	12.5839	+	2.58978i	0.425171	+	0.0875005i
$877$	15.9248	−	34.1509i	0.537743	−	1.15319i	−0.430364	−	0.902655i	$-0.641615\pi$
$877$	15.9248	−	34.1509i	0.537743	−	1.15319i	0.968107	−	0.250538i	$-0.0806075\pi$
$878$	−16.0211	−	35.6729i	−0.540687	−	1.20390i
$879$	−0.647288	+	3.67095i	−0.0218325	+	0.123818i
$880$	−3.85230	+	15.4382i	−0.129861	+	0.520421i
$881$	−18.5150	−	32.0689i	−0.623787	−	1.08043i	−0.988774	−	0.149418i	$-0.952260\pi$
$881$	−18.5150	−	32.0689i	−0.623787	−	1.08043i	0.364988	−	0.931012i	$-0.381073\pi$
$882$	3.37146	−	11.9029i	0.113523	−	0.400793i
$883$	3.22364	−	36.8464i	0.108484	−	1.23998i	−0.725512	−	0.688210i	$-0.758397\pi$
$883$	3.22364	−	36.8464i	0.108484	−	1.23998i	0.833996	−	0.551770i	$-0.186048\pi$
$884$	−0.957501	+	2.41478i	−0.0322043	+	0.0812179i
$885$	8.64357	−	12.0055i	0.290551	−	0.403561i
$886$	−42.6290	−	0.606096i	−1.43215	−	0.0203622i
$887$	−6.48161	−	13.8999i	−0.217631	−	0.466712i	0.766935	−	0.641725i	$-0.221781\pi$
$887$	−6.48161	−	13.8999i	−0.217631	−	0.466712i	−0.984566	+	0.175013i	$0.944003\pi$
$888$	0.371691	−	0.237307i	0.0124731	−	0.00796351i
$889$	−28.4002	+	5.00772i	−0.952511	+	0.167953i
$890$	9.81546	−	32.9942i	0.329015	−	1.10597i
$891$	−6.01312	+	7.16616i	−0.201447	+	0.240075i
$892$	−16.6160	+	55.6338i	−0.556344	+	1.86276i
$893$	−3.88756	+	2.40336i	−0.130092	+	0.0804253i
$894$	−9.57727	−	5.71250i	−0.320312	−	0.191055i
$895$	0.530866	−	40.4096i	0.0177449	−	1.35074i
$896$	−5.79900	+	20.6278i	−0.193731	+	0.689128i
$897$	7.51183	+	5.25984i	0.250813	+	0.175621i
$898$	−27.5847	+	2.01864i	−0.920512	+	0.0673628i
$899$	29.4049	+	10.7025i	0.980708	+	0.356949i
$900$	18.7040	+	17.5240i	0.623468	+	0.584135i
$901$	0.722845	−	1.25200i	0.0240815	−	0.0417103i
$902$	−13.3272	−	9.61702i	−0.443747	−	0.320212i
$903$	0.306745	−	3.50611i	0.0102078	−	0.116676i
$904$	18.7616	−	29.5137i	0.624001	−	0.981613i
$905$	1.60203	−	4.22789i	0.0532532	−	0.140540i
$906$	−11.8622	−	14.5521i	−0.394096	−	0.483461i
$907$	1.81125	−	1.26825i	0.0601416	−	0.0421116i	−0.543119	−	0.839656i	$-0.682757\pi$
$907$	1.81125	−	1.26825i	0.0601416	−	0.0421116i	0.603261	+	0.797544i	$0.293868\pi$
$908$	1.90214	−	16.3668i	0.0631248	−	0.543152i
$909$	−1.51311	−	4.15724i	−0.0501867	−	0.137887i
$910$	−14.3242	+	3.42116i	−0.474842	+	0.113410i
$911$			9.21582i			0.305334i	0.988278	+	0.152667i	$0.0487862\pi$
$911$			9.21582i			0.305334i	−0.988278	+	0.152667i	$0.951214\pi$
$912$	11.5209	+	0.308373i	0.381496	+	0.0102112i
$913$	−11.4063	−	11.4063i	−0.377493	−	0.377493i
$914$	−51.7648	+	18.0117i	−1.71223	+	0.595773i
$915$	9.57152	−	2.43038i	0.316425	−	0.0803460i
$916$	−34.7256	+	27.4944i	−1.14737	+	0.908441i
$917$	20.0175	+	28.5879i	0.661035	+	0.944056i
$918$	−2.73276	−	0.278286i	−0.0901945	−	0.00918480i
$919$	−8.80046	−	15.2428i	−0.290301	−	0.502815i	0.683580	−	0.729875i	$-0.260422\pi$
$919$	−8.80046	−	15.2428i	−0.290301	−	0.502815i	−0.973881	+	0.227060i	$0.927089\pi$
$920$	−4.22718	−	35.4312i	−0.139366	−	1.16813i
$921$	10.3097	−	8.65088i	0.339717	−	0.285056i
$922$	−6.28144	+	8.70476i	−0.206868	+	0.286676i
$923$	−0.969738	−	3.61911i	−0.0319193	−	0.119124i
$924$	2.33587	−	3.79257i	0.0768443	−	0.124766i
$925$	−0.275208	−	1.14679i	−0.00904880	−	0.0377064i
$926$	−9.81001	−	8.47213i	−0.322377	−	0.278411i
$927$	25.3756	−	36.2401i	0.833445	−	1.19028i
$928$	45.5189	−	0.736637i	1.49423	−	0.0241813i
$929$	−22.3912	+	26.6848i	−0.734631	+	0.875499i	−0.995964	−	0.0897499i	$-0.971393\pi$
$929$	−22.3912	+	26.6848i	−0.734631	+	0.875499i	0.261334	+	0.965248i	$0.415838\pi$
$930$	−1.19191	−	8.03980i	−0.0390844	−	0.263635i
$931$	−14.7746	+	1.74216i	−0.484217	+	0.0570971i
$932$	−15.5476	−	4.64357i	−0.509280	−	0.152105i
$933$	1.22858	+	14.0427i	0.0402218	+	0.459738i
$934$	34.2802	+	6.54834i	1.12168	+	0.214268i
$935$	−2.09539	+	0.155616i	−0.0685265	+	0.00508920i
$936$	−17.4073	−	3.84118i	−0.568976	−	0.125553i
$937$	−32.8957	+	15.3395i	−1.07465	+	0.501120i	−0.877659	−	0.479285i	$-0.840896\pi$
$937$	−32.8957	+	15.3395i	−1.07465	+	0.501120i	−0.196995	+	0.980405i	$0.563118\pi$
$938$	5.33706	−	5.18743i	0.174261	−	0.169376i
$939$	−4.51817	+	7.82571i	−0.147445	+	0.255382i
$940$	4.16384	+	2.15665i	0.135809	+	0.0703422i
$941$	15.5400	−	13.0396i	0.506591	−	0.425080i	−0.353337	−	0.935496i	$-0.614953\pi$
$941$	15.5400	−	13.0396i	0.506591	−	0.425080i	0.859928	+	0.510416i	$0.170509\pi$
$942$	17.8998	+	5.07006i	0.583208	+	0.165192i
$943$	35.5999	+	9.53896i	1.15929	+	0.310631i
$944$	32.0814	−	23.9491i	1.04416	−	0.779476i
$945$	−7.60865	−	13.5877i	−0.247509	−	0.442008i
$946$	2.51329	−	6.61121i	0.0817140	−	0.214949i
$947$	−27.3401	−	12.7489i	−0.888435	−	0.414284i	−0.0758446	−	0.997120i	$-0.524165\pi$
$947$	−27.3401	−	12.7489i	−0.888435	−	0.414284i	−0.812590	+	0.582836i	$0.801943\pi$
$948$	−0.847887	+	0.558460i	−0.0275381	+	0.0181379i
$949$			23.8967i			0.775720i
$950$	10.8419	−	28.8523i	0.351757	−	0.936091i
$951$		−	15.8883i		−	0.515212i
$952$	−2.82673	+	0.126200i	−0.0916149	+	0.00409017i
$953$	16.3825	+	7.63928i	0.530681	+	0.247461i	0.669441	−	0.742865i	$-0.266534\pi$
$953$	16.3825	+	7.63928i	0.530681	+	0.247461i	−0.138760	+	0.990326i	$0.544312\pi$
$954$	9.27327	+	3.52529i	0.300233	+	0.114135i
$955$	2.27378	+	4.06057i	0.0735779	+	0.131397i
$956$	−1.94888	+	0.286773i	−0.0630314	+	0.00927490i
$957$	−9.14094	−	2.44931i	−0.295485	−	0.0791749i
$958$	2.90362	−	10.2512i	0.0938118	−	0.331202i
$959$	−8.17884	+	6.86286i	−0.264109	+	0.221613i
$960$	−5.79746	−	10.3057i	−0.187112	−	0.332615i
$961$	−7.94055	+	13.7534i	−0.256147	+	0.443659i
$962$	0.571692	+	0.588183i	0.0184321	+	0.0189638i
$963$	35.7858	−	16.6872i	1.15318	−	0.537737i
$964$	−13.8647	−	41.7496i	−0.446551	−	1.34466i
$965$	−9.08569	+	0.674759i	−0.292479	+	0.0217213i
$966$	−1.87420	+	9.81135i	−0.0603014	+	0.315675i
$967$	−0.000159151	−	0.00181910i	−5.11795e−6	−	5.84984e-5i	0.996192	−	0.0871850i	$-0.0277871\pi$
$967$	−0.000159151	−	0.00181910i	−5.11795e−6	−	5.84984e-5i	−0.996197	+	0.0871265i	$0.972232\pi$
$968$	−16.3245	+	14.9882i	−0.524688	+	0.481737i
$969$	0.437974	+	1.45753i	0.0140698	+	0.0468226i
$970$	41.4793	−	6.14937i	1.33182	−	0.197444i
$971$	−3.73374	+	4.44970i	−0.119821	+	0.142798i	−0.822621	−	0.568591i	$-0.807489\pi$
$971$	−3.73374	+	4.44970i	−0.119821	+	0.142798i	0.702799	+	0.711388i	$0.251933\pi$
$972$	−1.70606	−	28.9650i	−0.0547217	−	0.929054i
$973$	23.3986	−	33.4167i	0.750125	−	1.07129i
$974$	−13.3838	+	15.4973i	−0.428845	+	0.496567i
$975$	4.24696	−	6.92896i	0.136011	−	0.221904i
$976$	26.6818	+	1.51897i	0.854063	+	0.0486211i
$977$	10.4576	+	39.0285i	0.334570	+	1.24863i	0.904335	+	0.426824i	$0.140368\pi$
$977$	10.4576	+	39.0285i	0.334570	+	1.24863i	−0.569765	+	0.821808i	$0.692966\pi$
$978$	−15.0232	−	10.8409i	−0.480389	−	0.346653i
$979$	−14.8345	+	12.4476i	−0.474114	+	0.397829i
$980$	9.31673	+	12.0901i	0.297612	+	0.386203i
$981$	−13.9120	−	24.0963i	−0.444177	−	0.769337i
$982$	5.39838	−	53.0119i	0.172269	−	1.69168i
$983$	−5.30789	−	7.58045i	−0.169295	−	0.241779i	0.725535	−	0.688185i	$-0.241592\pi$
$983$	−5.30789	−	7.58045i	−0.169295	−	0.241779i	−0.894830	+	0.446407i	$0.852704\pi$
$984$	12.1072	−	1.60604i	0.385963	−	0.0511988i
$985$	19.7712	−	5.02026i	0.629962	−	0.159959i
$986$	1.97559	+	5.67778i	0.0629157	+	0.180817i
$987$	−0.928200	−	0.928200i	−0.0295449	−	0.0295449i
$988$	3.75778	+	21.1048i	0.119551	+	0.671432i
$989$			15.8611i			0.504354i
$990$	−3.34954	−	14.0243i	−0.106455	−	0.445722i
$991$	10.4795	+	28.7922i	0.332893	+	0.914615i	0.987356	+	0.158521i	$0.0506725\pi$
$991$	10.4795	+	28.7922i	0.332893	+	0.914615i	−0.654463	+	0.756094i	$0.727105\pi$
$992$	3.46849	−	21.7204i	0.110125	−	0.689622i
$993$	1.42778	−	0.999739i	0.0453091	−	0.0317258i
$994$	3.16336	−	2.57863i	0.100336	−	0.0817893i
$995$	−3.83933	+	10.1323i	−0.121715	+	0.321216i
$996$	11.9826	+	0.340805i	0.379684	+	0.0107988i
$997$	−2.21319	+	25.2969i	−0.0700925	+	0.801161i	0.877061	+	0.480379i	$0.159501\pi$
$997$	−2.21319	+	25.2969i	−0.0700925	+	0.801161i	−0.947153	+	0.320781i	$0.896055\pi$
$998$	20.1647	−	27.9440i	0.638302	−	0.884553i
$999$	−0.433675	+	0.751148i	−0.0137209	+	0.0237653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.263.7	yes	672
4.3	odd	2	inner	380.2.bj.a.263.12	yes	672
5.2	odd	4	inner	380.2.bj.a.187.36	yes	672
19.6	even	9	inner	380.2.bj.a.63.19	✓	672
20.7	even	4	inner	380.2.bj.a.187.19	yes	672
76.63	odd	18	inner	380.2.bj.a.63.36	yes	672
95.82	odd	36	inner	380.2.bj.a.367.12	yes	672
380.367	even	36	inner	380.2.bj.a.367.7	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.63.19	✓	672	19.6	even	9	inner
380.2.bj.a.63.36	yes	672	76.63	odd	18	inner
380.2.bj.a.187.19	yes	672	20.7	even	4	inner
380.2.bj.a.187.36	yes	672	5.2	odd	4	inner
380.2.bj.a.263.7	yes	672	1.1	even	1	trivial
380.2.bj.a.263.12	yes	672	4.3	odd	2	inner
380.2.bj.a.367.7	yes	672	380.367	even	36	inner
380.2.bj.a.367.12	yes	672	95.82	odd	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27309 - 0.615834i) q^{2} +(-0.279354 + 0.599076i) q^{3} +(1.24150 + 1.56802i) q^{4} +(1.95101 - 1.09250i) q^{5} +(0.724572 - 0.590640i) q^{6} +(-0.490187 + 1.82940i) q^{7} +(-0.614896 - 2.76078i) q^{8} +(1.64751 + 1.96343i) q^{9} +O(q^{10})\)	\(q+(-1.27309 - 0.615834i) q^{2} +(-0.279354 + 0.599076i) q^{3} +(1.24150 + 1.56802i) q^{4} +(1.95101 - 1.09250i) q^{5} +(0.724572 - 0.590640i) q^{6} +(-0.490187 + 1.82940i) q^{7} +(-0.614896 - 2.76078i) q^{8} +(1.64751 + 1.96343i) q^{9} +(-3.15660 + 0.189349i) q^{10} +(1.54063 + 0.889483i) q^{11} +(-1.28618 + 0.305720i) q^{12} +(-1.03920 - 2.22857i) q^{13} +(1.75066 - 2.02712i) q^{14} +(0.109468 + 1.47400i) q^{15} +(-0.917365 + 3.89338i) q^{16} +(-0.526200 + 0.0460365i) q^{17} +(-0.888279 - 3.51420i) q^{18} +(-3.49372 + 2.60652i) q^{19} +(4.13524 + 1.70289i) q^{20} +(-0.959016 - 0.804710i) q^{21} +(-1.41358 - 2.08116i) q^{22} +(4.62156 + 3.23605i) q^{23} +(1.82569 + 0.402864i) q^{24} +(2.61289 - 4.26296i) q^{25} +(-0.0494376 + 3.47714i) q^{26} +(-3.55193 + 0.951737i) q^{27} +(-3.47711 + 1.50258i) q^{28} +(5.17298 + 6.16492i) q^{29} +(0.768374 - 1.94394i) q^{30} +(3.36737 - 1.94415i) q^{31} +(3.56556 - 4.39167i) q^{32} +(-0.963248 + 0.674474i) q^{33} +(0.698248 + 0.265443i) q^{34} +(1.04226 + 4.10472i) q^{35} +(-1.03331 + 5.02091i) q^{36} +(0.166786 - 0.166786i) q^{37} +(6.05299 - 1.16677i) q^{38} +1.62539 q^{39} +(-4.21582 - 4.71454i) q^{40} +(6.13856 - 2.23425i) q^{41} +(0.725343 + 1.61506i) q^{42} +(1.61250 + 2.30289i) q^{43} +(0.517963 + 3.52003i) q^{44} +(5.35935 + 2.03076i) q^{45} +(-3.89078 - 6.96589i) q^{46} +(1.04455 + 0.0913863i) q^{47} +(-2.07616 - 1.63720i) q^{48} +(2.95574 + 1.70650i) q^{49} +(-5.95171 + 3.81801i) q^{50} +(0.119416 - 0.328094i) q^{51} +(2.20428 - 4.39625i) q^{52} +(-1.56986 + 2.24199i) q^{53} +(5.10802 + 0.975754i) q^{54} +(3.97755 + 0.0522536i) q^{55} +(5.35199 + 0.228406i) q^{56} +(-0.585517 - 2.82114i) q^{57} +(-2.78909 - 11.0342i) q^{58} +(-7.66708 - 6.43344i) q^{59} +(-2.17535 + 2.00161i) q^{60} +(-1.16019 - 6.57974i) q^{61} +(-5.48423 + 0.401334i) q^{62} +(-4.39949 + 2.05151i) q^{63} +(-7.24381 + 3.39518i) q^{64} +(-4.46220 - 3.21264i) q^{65} +(1.64166 - 0.265463i) q^{66} +(2.76818 + 0.242184i) q^{67} +(-0.725462 - 0.767936i) q^{68} +(-3.22969 + 1.86466i) q^{69} +(1.20093 - 5.86752i) q^{70} +(1.50058 + 0.264593i) q^{71} +(4.40754 - 5.75571i) q^{72} +(-8.80771 - 4.10710i) q^{73} +(-0.315045 + 0.109621i) q^{74} +(1.82392 + 2.75619i) q^{75} +(-8.42451 - 2.24223i) q^{76} +(-2.38242 + 2.38242i) q^{77} +(-2.06926 - 1.00097i) q^{78} +(0.721664 - 0.262664i) q^{79} +(2.46373 + 8.59826i) q^{80} +(-0.913135 + 5.17865i) q^{81} +(-9.19084 - 0.935933i) q^{82} +(-8.75861 - 2.34686i) q^{83} +(0.0711836 - 2.50280i) q^{84} +(-0.976326 + 0.664691i) q^{85} +(-0.634658 - 3.92482i) q^{86} +(-5.13835 + 1.37682i) q^{87} +(1.50834 - 4.80028i) q^{88} +(-3.72309 + 10.2291i) q^{89} +(-5.57231 - 5.88580i) q^{90} +(4.58636 - 0.808699i) q^{91} +(0.663470 + 11.2643i) q^{92} +(0.224007 + 2.56042i) q^{93} +(-1.27352 - 0.759611i) q^{94} +(-3.96867 + 8.90223i) q^{95} +(1.63489 + 3.36287i) q^{96} +(-13.2098 + 1.15571i) q^{97} +(-2.71200 - 3.99277i) q^{98} +(0.791769 + 4.49034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more