LMFDB - Embedded newform 336.2.bo.a.173.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			173.44
Character	$\chi$	$=$	336.173
Dual form			336.2.bo.a.101.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.859759 + 1.12286i) q^{2} +(1.71659 - 0.230895i) q^{3} +(-0.521627 + 1.93078i) q^{4} +(0.128294 + 0.478799i) q^{5} +(1.73512 + 1.72898i) q^{6} +(-1.18449 + 2.36579i) q^{7} +(-2.61647 + 1.07429i) q^{8} +(2.89338 - 0.792704i) q^{9} +O(q^{10})$	\(q+(0.859759 + 1.12286i) q^{2} +(1.71659 - 0.230895i) q^{3} +(-0.521627 + 1.93078i) q^{4} +(0.128294 + 0.478799i) q^{5} +(1.73512 + 1.72898i) q^{6} +(-1.18449 + 2.36579i) q^{7} +(-2.61647 + 1.07429i) q^{8} +(2.89338 - 0.792704i) q^{9} +(-0.427322 + 0.555708i) q^{10} +(0.388770 - 1.45091i) q^{11} +(-0.449614 + 3.43480i) q^{12} +(0.486926 - 0.486926i) q^{13} +(-3.67483 + 0.703993i) q^{14} +(0.330780 + 0.792280i) q^{15} +(-3.45581 - 2.01429i) q^{16} +(-1.59268 - 2.75860i) q^{17} +(3.37770 + 2.56732i) q^{18} +(0.722159 + 2.69513i) q^{19} +(-0.991377 - 0.00204771i) q^{20} +(-1.48704 + 4.33459i) q^{21} +(1.96342 - 0.810899i) q^{22} +(2.26818 - 3.92860i) q^{23} +(-4.24336 + 2.44825i) q^{24} +(4.11734 - 2.37715i) q^{25} +(0.965390 + 0.128110i) q^{26} +(4.78371 - 2.02882i) q^{27} +(-3.94996 - 3.52106i) q^{28} +(-1.56573 + 1.56573i) q^{29} +(-0.605228 + 1.05259i) q^{30} +(-0.851744 + 0.491755i) q^{31} +(-0.709397 - 5.61220i) q^{32} +(0.332352 - 2.58038i) q^{33} +(1.72820 - 4.16009i) q^{34} +(-1.28470 - 0.263618i) q^{35} +(0.0212733 + 5.99996i) q^{36} +(-0.395551 - 1.47622i) q^{37} +(-2.40537 + 3.12805i) q^{38} +(0.723425 - 0.948283i) q^{39} +(-0.850046 - 1.11494i) q^{40} -2.87800i q^{41} +(-6.14564 + 2.05697i) q^{42} +(5.20338 - 5.20338i) q^{43} +(2.59859 + 1.50746i) q^{44} +(0.750749 + 1.28365i) q^{45} +(6.36135 - 0.830805i) q^{46} +(-6.34245 + 10.9854i) q^{47} +(-6.39731 - 2.65979i) q^{48} +(-4.19395 - 5.60453i) q^{49} +(6.20912 + 2.57942i) q^{50} +(-3.37093 - 4.36765i) q^{51} +(0.686153 + 1.19414i) q^{52} +(-0.451615 + 1.68545i) q^{53} +(6.39092 + 3.62714i) q^{54} +0.744571 q^{55} +(0.557639 - 7.46251i) q^{56} +(1.86194 + 4.45970i) q^{57} +(-3.10424 - 0.411943i) q^{58} +(-12.7832 - 3.42524i) q^{59} +(-1.70226 + 0.225389i) q^{60} +(-3.12260 - 11.6537i) q^{61} +(-1.28447 - 0.533599i) q^{62} +(-1.55181 + 7.78408i) q^{63} +(5.69180 - 5.62169i) q^{64} +(0.295610 + 0.170670i) q^{65} +(3.18315 - 1.84532i) q^{66} +(-3.29710 + 12.3049i) q^{67} +(6.15703 - 1.63615i) q^{68} +(2.98644 - 7.26751i) q^{69} +(-0.808530 - 1.66919i) q^{70} +11.3218 q^{71} +(-6.71883 + 5.18241i) q^{72} +(-5.65102 - 9.78785i) q^{73} +(1.31750 - 1.71334i) q^{74} +(6.51892 - 5.03126i) q^{75} +(-5.58040 - 0.0115264i) q^{76} +(2.97205 + 2.63834i) q^{77} +(1.68676 - 0.00299026i) q^{78} +(-3.58163 + 6.20356i) q^{79} +(0.521083 - 1.91306i) q^{80} +(7.74324 - 4.58718i) q^{81} +(3.23159 - 2.47439i) q^{82} +(4.94774 + 4.94774i) q^{83} +(-7.59346 - 5.13219i) q^{84} +(1.11649 - 1.11649i) q^{85} +(10.3163 + 1.36901i) q^{86} +(-2.32620 + 3.04923i) q^{87} +(0.541495 + 4.21391i) q^{88} +(9.31634 + 5.37879i) q^{89} +(-0.795892 + 1.94661i) q^{90} +(0.575206 + 1.72873i) q^{91} +(6.40211 + 6.42861i) q^{92} +(-1.34855 + 1.04081i) q^{93} +(-17.7881 + 2.32316i) q^{94} +(-1.19778 + 0.691538i) q^{95} +(-2.51357 - 9.47006i) q^{96} -4.48178i q^{97} +(2.68731 - 9.52777i) q^{98} +(-0.0252849 - 4.50620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.859759	+	1.12286i	0.607942	+	0.793982i
$2$	0.859759	+	1.12286i	0.607942	+	0.793982i
$3$	1.71659	−	0.230895i	0.991075	−	0.133307i
$3$	1.71659	−	0.230895i	0.991075	−	0.133307i
$4$	−0.521627	+	1.93078i	−0.260814	+	0.965389i
$5$	0.128294	+	0.478799i	0.0573748	+	0.214126i	0.988661	−	0.150162i	$-0.0479794\pi$
$5$	0.128294	+	0.478799i	0.0573748	+	0.214126i	−0.931287	+	0.364287i	$0.881313\pi$
$6$	1.73512	+	1.72898i	0.708359	+	0.705852i
$7$	−1.18449	+	2.36579i	−0.447696	+	0.894186i
$7$	−1.18449	+	2.36579i	−0.447696	+	0.894186i
$8$	−2.61647	+	1.07429i	−0.925061	+	0.379819i
$9$	2.89338	−	0.792704i	0.964458	−	0.264235i
$10$	−0.427322	+	0.555708i	−0.135131	+	0.175730i
$11$	0.388770	−	1.45091i	0.117219	−	0.437465i	−0.882225	−	0.470828i	$-0.843955\pi$
$11$	0.388770	−	1.45091i	0.117219	−	0.437465i	0.999443	+	0.0333630i	$0.0106217\pi$
$12$	−0.449614	+	3.43480i	−0.129792	+	0.991541i
$13$	0.486926	−	0.486926i	0.135049	−	0.135049i	−0.636351	−	0.771400i	$-0.719557\pi$
$13$	0.486926	−	0.486926i	0.135049	−	0.135049i	0.771400	+	0.636351i	$0.219557\pi$
$14$	−3.67483	+	0.703993i	−0.982140	+	0.188150i
$15$	0.330780	+	0.792280i	0.0854072	+	0.204566i
$16$	−3.45581	−	2.01429i	−0.863953	−	0.503573i
$17$	−1.59268	−	2.75860i	−0.386282	−	0.669059i	0.605665	−	0.795720i	$-0.292907\pi$
$17$	−1.59268	−	2.75860i	−0.386282	−	0.669059i	−0.991946	+	0.126661i	$0.959574\pi$
$18$	3.37770	+	2.56732i	0.796132	+	0.605123i
$19$	0.722159	+	2.69513i	0.165675	+	0.618306i	0.997953	+	0.0639485i	$0.0203693\pi$
$19$	0.722159	+	2.69513i	0.165675	+	0.618306i	−0.832279	+	0.554358i	$0.812964\pi$
$20$	−0.991377	−	0.00204771i	−0.221679	−	0.000457881i
$21$	−1.48704	+	4.33459i	−0.324499	+	0.945886i
$22$	1.96342	−	0.810899i	0.418602	−	0.172884i
$23$	2.26818	−	3.92860i	0.472948	−	0.819169i	−0.526573	−	0.850130i	$-0.676523\pi$
$23$	2.26818	−	3.92860i	0.472948	−	0.819169i	0.999521	+	0.0309606i	$0.00985664\pi$
$24$	−4.24336	+	2.44825i	−0.866172	+	0.499746i
$25$	4.11734	−	2.37715i	0.823468	−	0.475429i
$26$	0.965390	+	0.128110i	0.189329	+	0.0251245i
$27$	4.78371	−	2.02882i	0.920626	−	0.390446i
$28$	−3.94996	−	3.52106i	−0.746472	−	0.665417i
$29$	−1.56573	+	1.56573i	−0.290748	+	0.290748i	−0.837376	−	0.546627i	$-0.815911\pi$
$29$	−1.56573	+	1.56573i	−0.290748	+	0.290748i	0.546627	+	0.837376i	$0.315911\pi$
$30$	−0.605228	+	1.05259i	−0.110499	+	0.192176i
$31$	−0.851744	+	0.491755i	−0.152978	+	0.0883218i	−0.574535	−	0.818480i	$-0.694817\pi$
$31$	−0.851744	+	0.491755i	−0.152978	+	0.0883218i	0.421557	+	0.906802i	$0.361484\pi$
$32$	−0.709397	−	5.61220i	−0.125405	−	0.992106i
$33$	0.332352	−	2.58038i	0.0578550	−	0.449187i
$34$	1.72820	−	4.16009i	0.296384	−	0.713450i
$35$	−1.28470	−	0.263618i	−0.217154	−	0.0445596i
$36$	0.0212733	+	5.99996i	0.00354556	+	0.999994i
$37$	−0.395551	−	1.47622i	−0.0650282	−	0.242688i	0.925760	−	0.378113i	$-0.123427\pi$
$37$	−0.395551	−	1.47622i	−0.0650282	−	0.242688i	−0.990788	+	0.135424i	$0.956760\pi$
$38$	−2.40537	+	3.12805i	−0.390203	+	0.507437i
$39$	0.723425	−	0.948283i	0.115841	−	0.151847i
$40$	−0.850046	−	1.11494i	−0.134404	−	0.176287i
$41$		−	2.87800i		−	0.449468i	−0.974420	−	0.224734i	$-0.927849\pi$
$41$		−	2.87800i		−	0.449468i	0.974420	−	0.224734i	$-0.0721514\pi$
$42$	−6.14564	+	2.05697i	−0.948293	+	0.317397i
$43$	5.20338	−	5.20338i	0.793507	−	0.793507i	−0.188555	−	0.982063i	$-0.560380\pi$
$43$	5.20338	−	5.20338i	0.793507	−	0.793507i	0.982063	+	0.188555i	$0.0603805\pi$
$44$	2.59859	+	1.50746i	0.391752	+	0.227258i
$45$	0.750749	+	1.28365i	0.111915	+	0.191355i
$46$	6.36135	−	0.830805i	0.937930	−	0.122496i
$47$	−6.34245	+	10.9854i	−0.925141	+	1.60239i	−0.133807	+	0.991007i	$0.542720\pi$
$47$	−6.34245	+	10.9854i	−0.925141	+	1.60239i	−0.791334	+	0.611384i	$0.790613\pi$
$48$	−6.39731	−	2.65979i	−0.923371	−	0.383908i
$49$	−4.19395	−	5.60453i	−0.599136	−	0.800647i
$50$	6.20912	+	2.57942i	0.878102	+	0.364785i
$51$	−3.37093	−	4.36765i	−0.472024	−	0.611594i
$52$	0.686153	+	1.19414i	0.0951523	+	0.165598i
$53$	−0.451615	+	1.68545i	−0.0620341	+	0.231514i	−0.989982	−	0.141197i	$-0.954905\pi$
$53$	−0.451615	+	1.68545i	−0.0620341	+	0.231514i	0.927947	+	0.372711i	$0.121572\pi$
$54$	6.39092	+	3.62714i	0.869694	+	0.493592i
$55$	0.744571			0.100398
$56$	0.557639	−	7.46251i	0.0745176	−	0.997220i
$57$	1.86194	+	4.45970i	0.246621	+	0.590702i
$58$	−3.10424	−	0.411943i	−0.407607	−	0.0540908i
$59$	−12.7832	−	3.42524i	−1.66423	−	0.445928i	−0.700682	−	0.713474i	$-0.747121\pi$
$59$	−12.7832	−	3.42524i	−1.66423	−	0.445928i	−0.963545	+	0.267545i	$0.913787\pi$
$60$	−1.70226	+	0.225389i	−0.219761	+	0.0290976i
$61$	−3.12260	−	11.6537i	−0.399808	−	1.49210i	−0.813434	−	0.581657i	$-0.802405\pi$
$61$	−3.12260	−	11.6537i	−0.399808	−	1.49210i	0.413626	−	0.910447i	$-0.364262\pi$
$62$	−1.28447	−	0.533599i	−0.163127	−	0.0677671i
$63$	−1.55181	+	7.78408i	−0.195510	+	0.980702i
$64$	5.69180	−	5.62169i	0.711475	−	0.702712i
$65$	0.295610	+	0.170670i	0.0366659	+	0.0211691i
$66$	3.18315	−	1.84532i	0.391819	−	0.227144i
$67$	−3.29710	+	12.3049i	−0.402804	+	1.50329i	0.405265	+	0.914199i	$0.367179\pi$
$67$	−3.29710	+	12.3049i	−0.402804	+	1.50329i	−0.808069	+	0.589087i	$0.799487\pi$
$68$	6.15703	−	1.63615i	0.746650	−	0.198412i
$69$	2.98644	−	7.26751i	0.359525	−	0.874905i
$70$	−0.808530	−	1.66919i	−0.0966378	−	0.199506i
$71$	11.3218			1.34365			0.671827	−	0.740708i	$-0.265510\pi$
$71$	11.3218			1.34365			0.671827	+	0.740708i	$0.265510\pi$
$72$	−6.71883	+	5.18241i	−0.791821	+	0.610753i
$73$	−5.65102	−	9.78785i	−0.661402	−	1.14558i	−0.980247	−	0.197775i	$-0.936629\pi$
$73$	−5.65102	−	9.78785i	−0.661402	−	1.14558i	0.318846	−	0.947807i	$-0.396705\pi$
$74$	1.31750	−	1.71334i	0.153157	−	0.199172i
$75$	6.51892	−	5.03126i	0.752740	−	0.580960i
$76$	−5.58040	−	0.0115264i	−0.640116	−	0.00132217i
$77$	2.97205	+	2.63834i	0.338697	+	0.300667i
$78$	1.68676	−	0.00299026i	0.190988	−	0.000338581i
$79$	−3.58163	+	6.20356i	−0.402965	+	0.697955i	−0.994082	−	0.108630i	$-0.965354\pi$
$79$	−3.58163	+	6.20356i	−0.402965	+	0.697955i	0.591118	+	0.806585i	$0.298687\pi$
$80$	0.521083	−	1.91306i	0.0582588	−	0.213887i
$81$	7.74324	−	4.58718i	0.860360	−	0.509687i
$82$	3.23159	−	2.47439i	0.356870	−	0.273251i
$83$	4.94774	+	4.94774i	0.543085	+	0.543085i	0.924432	−	0.381347i	$-0.124540\pi$
$83$	4.94774	+	4.94774i	0.543085	+	0.543085i	−0.381347	+	0.924432i	$0.624540\pi$
$84$	−7.59346	−	5.13219i	−0.828514	−	0.559968i
$85$	1.11649	−	1.11649i	0.121100	−	0.121100i
$86$	10.3163	+	1.36901i	1.11244	+	0.147624i
$87$	−2.32620	+	3.04923i	−0.249395	+	0.326912i
$88$	0.541495	+	4.21391i	0.0577235	+	0.449204i
$89$	9.31634	+	5.37879i	0.987530	+	0.570151i	0.904535	−	0.426399i	$-0.140218\pi$
$89$	9.31634	+	5.37879i	0.987530	+	0.570151i	0.0829951	+	0.996550i	$0.473551\pi$
$90$	−0.795892	+	1.94661i	−0.0838944	+	0.205191i
$91$	0.575206	+	1.72873i	0.0602980	+	0.181220i
$92$	6.40211	+	6.42861i	0.667466	+	0.670229i
$93$	−1.34855	+	1.04081i	−0.139839	+	0.107927i
$94$	−17.7881	+	2.32316i	−1.83470	+	0.239616i
$95$	−1.19778	+	0.691538i	−0.122890	+	0.0709503i
$96$	−2.51357	−	9.47006i	−0.256540	−	0.966533i
$97$		−	4.48178i		−	0.455056i	−0.973772	−	0.227528i	$-0.926936\pi$
$97$		−	4.48178i		−	0.455056i	0.973772	−	0.227528i	$-0.0730643\pi$
$98$	2.68731	−	9.52777i	0.271460	−	0.962450i
$99$	−0.0252849	−	4.50620i	−0.00254123	−	0.452890i
$100$	2.44203	+	9.18965i	0.244203	+	0.918965i
$101$	−0.355340	−	0.0952131i	−0.0353577	−	0.00947406i	0.241097	−	0.970501i	$-0.422493\pi$
$101$	−0.355340	−	0.0952131i	−0.0353577	−	0.00947406i	−0.276455	+	0.961027i	$0.589160\pi$
$102$	2.00607	−	7.54021i	0.198631	−	0.746592i
$103$	−3.07387	+	5.32410i	−0.302877	+	0.524599i	−0.976786	−	0.214215i	$-0.931281\pi$
$103$	−3.07387	+	5.32410i	−0.302877	+	0.524599i	0.673909	+	0.738814i	$0.264614\pi$
$104$	−0.750926	+	1.79713i	−0.0736344	+	0.176223i
$105$	−2.26618	−	0.155893i	−0.221156	−	0.0152136i
$106$	−2.28080	+	0.941981i	−0.221531	+	0.0914933i
$107$	−17.7921	+	4.76737i	−1.72002	+	0.460879i	−0.977846	−	0.209325i	$-0.932873\pi$
$107$	−17.7921	+	4.76737i	−1.72002	+	0.460879i	−0.742177	+	0.670204i	$0.766207\pi$
$108$	1.42188	+	10.2946i	0.136820	+	0.990596i
$109$	1.53813	−	5.74038i	0.147326	−	0.549828i	−0.852315	−	0.523029i	$-0.824802\pi$
$109$	1.53813	−	5.74038i	0.147326	−	0.549828i	0.999641	−	0.0267992i	$-0.00853147\pi$
$110$	0.640152	+	0.836048i	0.0610361	+	0.0797141i
$111$	−1.01985	−	2.44273i	−0.0967999	−	0.231854i
$112$	8.85878	−	5.78981i	0.837076	−	0.547086i
$113$		−	8.26517i		−	0.777521i	−0.921339	−	0.388761i	$-0.872903\pi$
$113$		−	8.26517i		−	0.777521i	0.921339	−	0.388761i	$-0.127097\pi$
$114$	−3.40679	+	5.92497i	−0.319076	+	0.554925i
$115$	2.17200	+	0.581986i	0.202540	+	0.0542705i
$116$	−2.20635	−	3.83980i	−0.204854	−	0.356517i
$117$	1.02287	−	1.79485i	0.0945646	−	0.165934i
$118$	−7.14439	−	17.2986i	−0.657694	−	1.59246i
$119$	8.41280	−	0.500404i	0.771200	−	0.0458719i
$120$	−1.71662	−	1.71762i	−0.156705	−	0.156797i
$121$	7.57228	+	4.37186i	0.688390	+	0.397442i
$122$	10.4008	−	13.5256i	0.941643	−	1.22455i
$123$	−0.664516	−	4.94036i	−0.0599174	−	0.445457i
$124$	−0.505177	−	1.90104i	−0.0453662	−	0.170719i
$125$	3.41893	+	3.41893i	0.305799	+	0.305799i
$126$	−10.0746	+	4.94997i	−0.897518	+	0.440979i
$127$	13.5133			1.19911			0.599557	−	0.800332i	$-0.295343\pi$
$127$	13.5133			1.19911			0.599557	+	0.800332i	$0.295343\pi$
$128$	11.2059	+	1.55779i	0.990475	+	0.137690i
$129$	7.73064	−	10.1335i	0.680645	−	0.892205i
$130$	0.0625144	+	0.478664i	0.00548288	+	0.0419816i
$131$	−11.8733	+	3.18143i	−1.03737	+	0.277963i	−0.737024	−	0.675867i	$-0.763769\pi$
$131$	−11.8733	+	3.18143i	−1.03737	+	0.277963i	−0.300348	+	0.953830i	$0.597103\pi$
$132$	4.80878	+	1.98770i	0.418551	+	0.173007i
$133$	−7.23152	−	1.48389i	−0.627052	−	0.128670i
$134$	−16.6514	+	6.87710i	−1.43846	+	0.594091i
$135$	1.58512	+	2.03015i	0.136425	+	0.174728i
$136$	7.13073	+	5.50679i	0.611455	+	0.472203i
$137$	5.89498	+	10.2104i	0.503642	+	0.872334i	0.999991	+	0.00421094i	$0.00134039\pi$
$137$	5.89498	+	10.2104i	0.503642	+	0.872334i	−0.496349	+	0.868123i	$0.665326\pi$
$138$	10.7280	−	2.89496i	0.913229	−	0.246435i
$139$	−2.58545	−	2.58545i	−0.219295	−	0.219295i	0.588906	−	0.808201i	$-0.299559\pi$
$139$	−2.58545	−	2.58545i	−0.219295	−	0.219295i	−0.808201	+	0.588906i	$0.799559\pi$
$140$	1.17912	−	2.34297i	0.0996541	−	0.198017i
$141$	−8.35091	+	20.3220i	−0.703274	+	1.71142i
$142$	9.73406	+	12.7128i	0.816864	+	1.06684i
$143$	−0.517184	−	0.895788i	−0.0432491	−	0.0749096i
$144$	−11.5957	−	3.08867i	−0.966308	−	0.257389i
$145$	−0.950543	−	0.548796i	−0.0789383	−	0.0455750i
$146$	6.13187	−	14.7605i	0.507477	−	1.22159i
$147$	−8.49336	−	8.65233i	−0.700520	−	0.713632i
$148$	3.05658	+	0.00631342i	0.251249	+	0.000518960i
$149$	−17.5190	+	4.69419i	−1.43521	+	0.384563i	−0.890853	−	0.454291i	$-0.849893\pi$
$149$	−17.5190	+	4.69419i	−1.43521	+	0.384563i	−0.544356	+	0.838854i	$0.683226\pi$
$150$	11.2541	+	2.99415i	0.918894	+	0.244472i
$151$	−11.0224	+	6.36377i	−0.896987	+	0.517876i	−0.876222	−	0.481908i	$-0.839944\pi$
$151$	−11.0224	+	6.36377i	−0.896987	+	0.517876i	−0.0207658	+	0.999784i	$0.506610\pi$
$152$	−4.78486	−	6.27592i	−0.388104	−	0.509044i
$153$	−6.79498	−	6.71915i	−0.549341	−	0.543211i
$154$	−0.407235	+	5.60554i	−0.0328159	+	0.451707i
$155$	−0.344725	−	0.344725i	−0.0276890	−	0.0276890i
$156$	1.45357	+	1.89142i	0.116378	+	0.151435i
$157$	−12.3396	−	3.30638i	−0.984805	−	0.263878i	−0.269738	−	0.962934i	$-0.586937\pi$
$157$	−12.3396	−	3.30638i	−0.984805	−	0.263878i	−0.715067	+	0.699056i	$0.753604\pi$
$158$	−10.0451	+	1.31191i	−0.799142	+	0.104370i
$159$	−0.386077	+	2.99751i	−0.0306179	+	0.237718i
$160$	2.59610	−	1.05967i	0.205240	−	0.0837742i
$161$	6.60761	+	10.0194i	0.520752	+	0.789642i
$162$	11.8081	+	4.75070i	0.927731	+	0.373250i
$163$	9.91268	−	2.65609i	0.776421	−	0.208041i	0.151215	−	0.988501i	$-0.451682\pi$
$163$	9.91268	−	2.65609i	0.776421	−	0.208041i	0.625206	+	0.780460i	$0.285015\pi$
$164$	5.55678	+	1.50124i	0.433912	+	0.117227i
$165$	1.27812	−	0.171918i	0.0995018	−	0.0133838i
$166$	−1.30175	+	9.80948i	−0.101035	+	0.761363i
$167$			11.7120i			0.906298i	0.891435	+	0.453149i	$0.149700\pi$
$167$			11.7120i			0.906298i	−0.891435	+	0.453149i	$0.850300\pi$
$168$	−0.765817	−	12.9388i	−0.0590841	−	0.998253i
$169$			12.5258i			0.963523i
$170$	2.21357	+	0.293747i	0.169773	+	0.0225294i
$171$	4.22592	+	7.22557i	0.323164	+	0.552553i
$172$	7.33234	+	12.7608i	0.559086	+	0.973001i
$173$	−25.0053	+	6.70016i	−1.90112	+	0.509404i	−0.904580	+	0.426304i	$0.859815\pi$
$173$	−25.0053	+	6.70016i	−1.90112	+	0.509404i	−0.996541	+	0.0830993i	$0.973518\pi$
$174$	−5.42383	+	0.00961529i	−0.411180	+	0.000728933i
$175$	0.746875	+	12.5565i	0.0564584	+	0.949181i
$176$	−4.26607	+	4.23097i	−0.321567	+	0.318921i
$177$	−22.7344	−	2.92817i	−1.70882	−	0.220095i
$178$	1.97018	+	15.0854i	0.147672	+	1.13070i
$179$	5.89102	+	1.57850i	0.440316	+	0.117982i	0.472165	−	0.881510i	$-0.343473\pi$
$179$	5.89102	+	1.57850i	0.440316	+	0.117982i	−0.0318487	+	0.999493i	$0.510139\pi$
$180$	−2.87005	+	0.779944i	−0.213921	+	0.0581336i
$181$	4.18491	+	4.18491i	0.311062	+	0.311062i	0.845321	−	0.534259i	$-0.179409\pi$
$181$	4.18491	+	4.18491i	0.311062	+	0.311062i	−0.534259	+	0.845321i	$0.679409\pi$
$182$	−1.44658	+	2.13217i	−0.107228	+	0.158047i
$183$	−8.05101	−	19.2837i	−0.595148	−	1.42549i
$184$	−1.71415	+	12.7157i	−0.126369	+	0.937416i
$185$	0.656064	−	0.378779i	0.0482348	−	0.0278484i
$186$	−2.32811	−	0.619394i	−0.170705	−	0.0454162i
$187$	−4.62167	+	1.23837i	−0.337970	+	0.0905587i
$188$	−17.9021	−	17.9762i	−1.30564	−	1.31105i
$189$	−0.866520	+	13.7204i	−0.0630300	+	0.998012i
$190$	−1.80630	−	0.750381i	−0.131043	−	0.0544384i
$191$	11.4487	+	6.60991i	0.828399	+	0.478276i	0.853304	−	0.521414i	$-0.174595\pi$
$191$	11.4487	+	6.60991i	0.828399	+	0.478276i	−0.0249054	+	0.999690i	$0.507928\pi$
$192$	8.47247	−	10.9644i	0.611448	−	0.791284i
$193$	9.96849	+	17.2659i	0.717548	+	1.24283i	0.961969	+	0.273160i	$0.0880689\pi$
$193$	9.96849	+	17.2659i	0.717548	+	1.24283i	−0.244421	+	0.969669i	$0.578598\pi$
$194$	5.03241	−	3.85326i	0.361306	−	0.276648i
$195$	0.546848	+	0.224717i	0.0391606	+	0.0160923i
$196$	13.0088	−	5.17411i	0.929199	−	0.369579i
$197$	−8.37075	−	8.37075i	−0.596391	−	0.596391i	0.342959	−	0.939350i	$-0.388571\pi$
$197$	−8.37075	−	8.37075i	−0.596391	−	0.596391i	−0.939350	+	0.342959i	$0.888571\pi$
$198$	5.03809	−	3.90264i	0.358042	−	0.277349i
$199$	8.18748	+	14.1811i	0.580395	+	1.00527i	0.995432	+	0.0954689i	$0.0304351\pi$
$199$	8.18748	+	14.1811i	0.580395	+	1.00527i	−0.415038	+	0.909804i	$0.636232\pi$
$200$	−8.21913	+	10.6429i	−0.581180	+	0.752570i
$201$	−2.81862	+	21.8838i	−0.198810	+	1.54357i
$202$	−0.198596	−	0.480858i	−0.0139732	−	0.0338330i
$203$	−1.84959	−	5.55878i	−0.129816	−	0.390150i
$204$	10.1913	−	4.23023i	0.713536	−	0.296175i
$205$	1.37799	−	0.369230i	0.0962427	−	0.0257881i
$206$	−8.62100	+	1.12592i	−0.600654	+	0.0784466i
$207$	3.44847	−	13.1649i	0.239685	−	0.915024i
$208$	−2.66354	+	0.701913i	−0.184683	+	0.0486689i
$209$	4.19115			0.289908
$210$	−1.77332	−	2.67863i	−0.122371	−	0.184843i
$211$	−8.45390	−	8.45390i	−0.581990	−	0.581990i	0.353460	−	0.935450i	$-0.385005\pi$
$211$	−8.45390	−	8.45390i	−0.581990	−	0.581990i	−0.935450	+	0.353460i	$0.885005\pi$
$212$	−3.01866	−	1.75114i	−0.207322	−	0.120269i
$213$	19.4350	−	2.61415i	1.33166	−	0.179119i
$214$	−20.6500	−	15.8792i	−1.41160	−	1.08548i
$215$	3.15893	+	1.82381i	0.215437	+	0.124383i
$216$	−10.3369	+	10.4474i	−0.703336	+	0.710857i
$217$	−0.154504	−	2.59753i	−0.0104884	−	0.176332i
$218$	7.76806	−	3.20824i	0.526119	−	0.217289i
$219$	−11.9605	−	15.4970i	−0.808213	−	1.04719i
$220$	−0.388388	+	1.43760i	−0.0261851	+	0.0969231i
$221$	−2.11875	−	0.567719i	−0.142523	−	0.0381889i
$222$	1.86602	−	3.24531i	0.125239	−	0.217811i
$223$		−	17.2064i		−	1.15222i	−0.817371	−	0.576112i	$-0.804569\pi$
$223$		−	17.2064i		−	1.15222i	0.817371	−	0.576112i	$-0.195431\pi$
$224$	14.1176	+	4.96932i	0.943270	+	0.332027i
$225$	10.0286	−	10.1418i	0.668575	−	0.676120i
$226$	9.28062	−	7.10605i	0.617338	−	0.472688i
$227$	−4.72407	+	17.6305i	−0.313547	+	1.17018i	0.611787	+	0.791023i	$0.290451\pi$
$227$	−4.72407	+	17.6305i	−0.313547	+	1.17018i	−0.925334	+	0.379152i	$0.876216\pi$
$228$	−9.58194	+	1.26870i	−0.634579	+	0.0840217i
$229$	6.38196	−	1.71004i	0.421732	−	0.113003i	−0.0417108	−	0.999130i	$-0.513281\pi$
$229$	6.38196	−	1.71004i	0.421732	−	0.113003i	0.463442	+	0.886127i	$0.346614\pi$
$230$	1.21391	+	2.93922i	0.0800429	+	0.193807i
$231$	5.71098	+	3.84272i	0.375755	+	0.252833i
$232$	2.41463	−	5.77872i	0.158528	−	0.379392i
$233$	1.23993	−	2.14762i	0.0812304	−	0.140695i	−0.822548	−	0.568695i	$-0.807448\pi$
$233$	1.23993	−	2.14762i	0.0812304	−	0.140695i	0.903779	+	0.428000i	$0.140782\pi$
$234$	2.89479	−	0.394597i	0.189238	−	0.0257956i
$235$	−6.07352	−	1.62739i	−0.396193	−	0.106159i
$236$	13.2814	−	22.8948i	0.864547	−	1.49032i
$237$	−4.71582	+	11.4760i	−0.306326	+	0.745444i
$238$	7.79487	+	9.01617i	0.505266	+	0.584431i
$239$		−	19.9191i		−	1.28846i	−0.764833	−	0.644229i	$-0.777179\pi$
$239$		−	19.9191i		−	1.28846i	0.764833	−	0.644229i	$-0.222821\pi$
$240$	0.452771	−	3.40426i	0.0292262	−	0.219744i
$241$	−7.32694	+	4.23021i	−0.471970	+	0.272492i	−0.717064	−	0.697007i	$-0.754514\pi$
$241$	−7.32694	+	4.23021i	−0.471970	+	0.272492i	0.245094	+	0.969499i	$0.421181\pi$
$242$	1.60136	+	12.2614i	0.102939	+	0.788190i
$243$	12.2328	−	9.66219i	0.784736	−	0.619830i
$244$	24.1296	+	0.0498400i	1.54474	+	0.00319068i
$245$	2.14539	−	2.72709i	0.137064	−	0.174227i
$246$	4.97600	−	4.99368i	0.317258	−	0.318385i
$247$	1.66397	+	0.960694i	0.105876	+	0.0611275i
$248$	1.70027	−	2.20168i	0.107967	−	0.139807i
$249$	9.63566	+	7.35084i	0.610635	+	0.465841i
$250$	−0.899521	+	6.77844i	−0.0568907	+	0.428706i
$251$	11.5508	−	11.5508i	0.729078	−	0.729078i	−0.241358	−	0.970436i	$-0.577593\pi$
$251$	11.5508	−	11.5508i	0.729078	−	0.729078i	0.970436	+	0.241358i	$0.0775929\pi$
$252$	−14.2199	−	7.05659i	−0.895767	−	0.444523i
$253$	−4.81824	−	4.81824i	−0.302920	−	0.302920i
$254$	11.6182	+	15.1736i	0.728992	+	0.952075i
$255$	1.65876	−	2.17434i	0.103876	−	0.136163i
$256$	7.88525	+	13.9220i	0.492828	+	0.870127i
$257$	−8.29276	+	14.3635i	−0.517288	+	0.895970i	0.482510	+	0.875890i	$0.339725\pi$
$257$	−8.29276	+	14.3635i	−0.517288	+	0.895970i	−0.999798	+	0.0200792i	$0.993608\pi$
$258$	18.0250	−	0.0319544i	1.12219	−	0.00198940i
$259$	3.96095	+	0.812777i	0.246121	+	0.0505035i
$260$	−0.483725	+	0.481731i	−0.0299993	+	0.0298757i
$261$	−3.28908	+	5.77140i	−0.203589	+	0.357241i
$262$	−13.7804	−	10.5967i	−0.851359	−	0.654668i
$263$	−8.90599	−	15.4256i	−0.549167	−	0.951185i	−0.998332	−	0.0577361i	$-0.981612\pi$
$263$	−8.90599	−	15.4256i	−0.549167	−	0.951185i	0.449165	−	0.893449i	$-0.351722\pi$
$264$	1.90249	+	7.10853i	0.117090	+	0.437500i
$265$	−0.864932			−0.0531323
$266$	−4.55117	−	9.39577i	−0.279050	−	0.576092i
$267$	17.2343	+	7.08210i	1.05472	+	0.433417i
$268$	−22.0382	−	12.7845i	−1.34620	−	0.780941i
$269$	5.16292	−	19.2683i	0.314789	−	1.17481i	−0.609397	−	0.792865i	$-0.708588\pi$
$269$	5.16292	−	19.2683i	0.314789	−	1.17481i	0.924186	−	0.381943i	$-0.124745\pi$
$270$	−0.916758	+	3.52531i	−0.0557921	+	0.214543i
$271$	−22.5220	−	13.0031i	−1.36811	−	0.789879i	−0.377425	−	0.926040i	$-0.623190\pi$
$271$	−22.5220	−	13.0031i	−1.36811	−	0.789879i	−0.990687	+	0.136161i	$0.956524\pi$
$272$	−0.0526351	+	12.7413i	−0.00319147	+	0.772557i
$273$	1.38655	+	2.83471i	0.0839177	+	0.171564i
$274$	−6.39659	+	15.3977i	−0.386432	+	0.930211i
$275$	−1.84833	−	6.89804i	−0.111458	−	0.415968i
$276$	12.4741	+	9.55709i	0.750855	+	0.575269i
$277$	29.8171	+	7.98946i	1.79153	+	0.480040i	0.992605	−	0.121386i	$-0.0387338\pi$
$277$	29.8171	+	7.98946i	1.79153	+	0.480040i	0.798929	+	0.601426i	$0.205400\pi$
$278$	0.680233	−	5.12597i	0.0407977	−	0.307435i
$279$	−2.07460	+	2.09801i	−0.124203	+	0.125605i
$280$	3.64459	−	0.690397i	0.217806	−	0.0412591i
$281$	9.67354			0.577075			0.288537	−	0.957469i	$-0.406831\pi$
$281$	9.67354			0.577075			0.288537	+	0.957469i	$0.406831\pi$
$282$	−29.9985	+	8.09509i	−1.78638	+	0.482056i
$283$	−6.85354	+	25.5777i	−0.407400	+	1.52044i	0.392185	+	0.919886i	$0.371719\pi$
$283$	−6.85354	+	25.5777i	−0.407400	+	1.52044i	−0.799585	+	0.600553i	$0.794947\pi$
$284$	−5.90578	+	21.8600i	−0.350443	+	1.29715i
$285$	−1.89643	+	1.46365i	−0.112335	+	0.0866991i
$286$	0.561191	−	1.35089i	0.0331839	−	0.0798796i
$287$	6.80876	+	3.40897i	0.401908	+	0.201225i
$288$	−6.50137	−	15.6758i	−0.383097	−	0.923708i
$289$	3.42674	−	5.93529i	0.201573	−	0.349135i
$290$	−0.201017	−	1.53916i	−0.0118041	−	0.0903825i
$291$	−1.03482	−	7.69339i	−0.0606623	−	0.450995i
$292$	21.8459	−	5.80525i	1.27843	−	0.339727i
$293$	−4.86775	+	4.86775i	−0.284377	+	0.284377i	−0.834852	−	0.550475i	$-0.814447\pi$
$293$	−4.86775	+	4.86775i	−0.284377	+	0.284377i	0.550475	+	0.834852i	$0.314447\pi$
$294$	2.41311	−	16.9758i	0.140735	−	0.990047i
$295$		−	6.56001i		−	0.381939i
$296$	2.62083	+	3.43753i	0.152333	+	0.199803i
$297$	−1.08386	−	7.72947i	−0.0628921	−	0.448510i
$298$	−20.3330	−	15.6355i	−1.17786	−	0.905738i
$299$	−0.808503	−	3.01737i	−0.0467569	−	0.174499i
$300$	6.31381	+	15.2110i	0.364528	+	0.878209i
$301$	6.14674	+	18.4735i	0.354292	+	1.06479i
$302$	−16.6222	−	6.90526i	−0.956500	−	0.397353i
$303$	−0.631958	−	0.0813958i	−0.0363051	−	0.00467607i
$304$	2.93315	−	10.7685i	0.168227	−	0.617616i
$305$	5.17917	−	2.99020i	0.296559	−	0.171218i
$306$	1.70261	−	13.4067i	0.0973319	−	0.766407i
$307$	6.83909	−	6.83909i	0.390327	−	0.390327i	−0.484477	−	0.874804i	$-0.660990\pi$
$307$	6.83909	−	6.83909i	0.390327	−	0.390327i	0.874804	+	0.484477i	$0.160990\pi$
$308$	−6.64436	+	4.36215i	−0.378597	+	0.248556i
$309$	−4.04727	+	9.84904i	−0.230241	+	0.560292i
$310$	0.0906973	−	0.683459i	0.00515126	−	0.0388179i
$311$	20.0828	−	11.5948i	1.13879	−	0.657481i	0.192660	−	0.981266i	$-0.438289\pi$
$311$	20.0828	−	11.5948i	1.13879	−	0.657481i	0.946131	+	0.323785i	$0.104955\pi$
$312$	−0.874087	+	3.25832i	−0.0494854	+	0.184466i
$313$	0.557103	−	0.964930i	0.0314893	−	0.0545411i	−0.849851	−	0.527023i	$-0.823308\pi$
$313$	0.557103	−	0.964930i	0.0314893	−	0.0545411i	0.881341	+	0.472482i	$0.156642\pi$
$314$	−6.89647	−	16.6983i	−0.389190	−	0.942340i
$315$	−3.92610	+	0.255644i	−0.221211	+	0.0144039i
$316$	−10.1094	−	10.1513i	−0.568700	−	0.571054i
$317$	−5.79442	−	21.6251i	−0.325447	−	1.21458i	−0.913862	−	0.406025i	$-0.866915\pi$
$317$	−5.79442	−	21.6251i	−0.325447	−	1.21458i	0.588415	−	0.808559i	$-0.299752\pi$
$318$	−3.69771	+	2.14362i	−0.207357	+	0.120208i
$319$	1.66302	+	2.88044i	0.0931113	+	0.161274i
$320$	3.42188	+	2.00400i	0.191289	+	0.112027i
$321$	−29.4409	+	12.2917i	−1.64323	+	0.686057i
$322$	−5.56947	+	16.0337i	−0.310374	+	0.893524i
$323$	6.28463	−	6.28463i	0.349686	−	0.349686i
$324$	4.81775	+	17.3433i	0.267653	+	0.963515i
$325$	0.847345	−	3.16234i	0.0470023	−	0.175415i
$326$	11.5049	+	8.84694i	0.637200	+	0.489987i
$327$	1.31492	−	10.2090i	0.0727151	−	0.564561i
$328$	3.09181	+	7.53020i	0.170717	+	0.415786i
$329$	−18.4767	−	28.0171i	−1.01865	−	1.54463i
$330$	1.29192	+	1.28735i	0.0711178	+	0.0708661i
$331$	−6.93122	−	25.8676i	−0.380974	−	1.42181i	−0.844416	−	0.535687i	$-0.820053\pi$
$331$	−6.93122	−	25.8676i	−0.380974	−	1.42181i	0.463442	−	0.886127i	$-0.346614\pi$
$332$	−12.1339	+	6.97211i	−0.665932	+	0.382644i
$333$	−2.31468	−	3.95769i	−0.126844	−	0.216880i
$334$	−13.1509	+	10.0695i	−0.719584	+	0.550977i
$335$	−6.31459			−0.345003
$336$	13.8701	−	11.9842i	0.756675	−	0.653791i
$337$	1.87049			0.101892			0.0509462	−	0.998701i	$-0.483776\pi$
$337$	1.87049			0.101892			0.0509462	+	0.998701i	$0.483776\pi$
$338$	−14.0647	+	10.7692i	−0.765020	+	0.585766i
$339$	−1.90838	−	14.1879i	−0.103649	−	0.770582i
$340$	1.57330	+	2.73808i	0.0853240	+	0.148493i
$341$	0.382359	+	1.42698i	0.0207059	+	0.0772755i
$342$	−4.48003	+	10.9574i	−0.242252	+	0.592507i
$343$	18.2269	−	3.28348i	0.984158	−	0.177292i
$344$	−8.02452	+	19.2044i	−0.432653	+	1.03543i
$345$	3.86282	+	0.497529i	0.207967	+	0.0267861i
$346$	−29.0219	−	22.3170i	−1.56023	−	1.19977i
$347$	1.11836	−	4.17378i	0.0600368	−	0.224060i	−0.929389	−	0.369103i	$-0.879665\pi$
$347$	1.11836	−	4.17378i	0.0600368	−	0.224060i	0.989425	+	0.145042i	$0.0463318\pi$
$348$	−4.67399	−	6.08194i	−0.250552	−	0.326026i
$349$	−0.764040	+	0.764040i	−0.0408981	+	0.0408981i	−0.727260	−	0.686362i	$-0.759207\pi$
$349$	−0.764040	+	0.764040i	−0.0408981	+	0.0408981i	0.686362	+	0.727260i	$0.259207\pi$
$350$	−13.4570	+	11.6342i	−0.719309	+	0.621874i
$351$	1.34143	−	3.31720i	0.0716004	−	0.177059i
$352$	−8.41858	−	1.15258i	−0.448712	−	0.0614329i
$353$	13.8774	+	24.0364i	0.738620	+	1.27933i	0.953117	+	0.302602i	$0.0978554\pi$
$353$	13.8774	+	24.0364i	0.738620	+	1.27933i	−0.214497	+	0.976725i	$0.568811\pi$
$354$	−16.2582	−	28.0450i	−0.864111	−	1.49058i
$355$	1.45252	+	5.42089i	0.0770919	+	0.287711i
$356$	−15.2449	+	15.1821i	−0.807979	+	0.804648i
$357$	14.3258	−	2.80146i	0.758202	−	0.148269i
$358$	3.29244	+	7.97192i	0.174011	+	0.421329i
$359$	11.5863	−	20.0681i	0.611504	−	1.05916i	−0.379484	−	0.925198i	$-0.623898\pi$
$359$	11.5863	−	20.0681i	0.611504	−	1.05916i	0.990987	−	0.133957i	$-0.0427684\pi$
$360$	−3.34332	−	2.55210i	−0.176208	−	0.134507i
$361$	9.71225	−	5.60737i	0.511171	−	0.295125i
$362$	−1.10105	+	8.29709i	−0.0578699	+	0.436085i
$363$	14.0080	+	5.75630i	0.735227	+	0.302127i
$364$	−3.63783	+	0.208843i	−0.190674	+	0.0109464i
$365$	3.96142	−	3.96142i	0.207350	−	0.207350i
$366$	14.7309	−	25.6195i	0.769997	−	1.33915i
$367$	3.58369	−	2.06904i	0.187067	−	0.108003i	−0.403542	−	0.914961i	$-0.632221\pi$
$367$	3.58369	−	2.06904i	0.187067	−	0.108003i	0.590609	+	0.806958i	$0.298888\pi$
$368$	−15.7517	+	9.00771i	−0.821116	+	0.469560i
$369$	−2.28141	−	8.32714i	−0.118765	−	0.433494i
$370$	0.989373	+	0.411009i	0.0514351	+	0.0213674i
$371$	−3.45249	−	3.06483i	−0.179244	−	0.159118i
$372$	−1.30612	−	3.14667i	−0.0677193	−	0.163147i
$373$	−4.55576	−	17.0023i	−0.235888	−	0.880348i	−0.977746	−	0.209791i	$-0.932722\pi$
$373$	−4.55576	−	17.0023i	−0.235888	−	0.880348i	0.741858	−	0.670557i	$-0.233945\pi$
$374$	−5.36404	−	4.12478i	−0.277368	−	0.213287i
$375$	6.65832	+	5.07950i	0.343834	+	0.262304i
$376$	4.79324	−	35.5567i	0.247193	−	1.83370i
$377$			1.52479i			0.0785306i
$378$	−16.1511	+	10.8233i	−0.830721	+	0.556688i
$379$	−7.35479	+	7.35479i	−0.377790	+	0.377790i	−0.870304	−	0.492514i	$-0.836078\pi$
$379$	−7.35479	+	7.35479i	−0.377790	+	0.377790i	0.492514	+	0.870304i	$0.336078\pi$
$380$	−0.710413	−	2.67337i	−0.0364434	−	0.137141i
$381$	23.1969	−	3.12016i	1.18841	−	0.159851i
$382$	2.42113	+	18.5382i	0.123876	+	0.948497i
$383$	−8.74610	+	15.1487i	−0.446905	+	0.774062i	−0.998183	−	0.0602596i	$-0.980807\pi$
$383$	−8.74610	+	15.1487i	−0.446905	+	0.774062i	0.551278	+	0.834322i	$0.314140\pi$
$384$	19.5957	+	0.0866875i	0.999990	+	0.00442375i
$385$	−0.881939	+	1.76150i	−0.0449478	+	0.0897744i
$386$	−10.8167	+	26.0378i	−0.550556	+	1.32529i
$387$	10.9306	−	19.1801i	0.555633	−	0.974977i
$388$	8.65333	+	2.33782i	0.439306	+	0.118685i
$389$	4.96778	−	18.5400i	0.251877	−	0.940016i	−0.717925	−	0.696120i	$-0.754908\pi$
$389$	4.96778	−	18.5400i	0.251877	−	0.940016i	0.969802	−	0.243896i	$-0.0784254\pi$
$390$	0.217833	+	0.807236i	0.0110304	+	0.0408760i
$391$	−14.4499			−0.730764
$392$	16.9942	+	10.1586i	0.858338	+	0.513084i
$393$	−19.6470	+	8.20269i	−0.991058	+	0.413771i
$394$	2.20234	−	16.5960i	0.110952	−	0.836094i
$395$	−3.42976	−	0.919002i	−0.172570	−	0.0462400i
$396$	8.71367	+	2.30174i	0.437878	+	0.115667i
$397$	2.12679	+	7.93727i	0.106740	+	0.398360i	0.998537	−	0.0540765i	$-0.0172215\pi$
$397$	2.12679	+	7.93727i	0.106740	+	0.398360i	−0.891797	+	0.452437i	$0.850555\pi$
$398$	−8.88415	+	21.3857i	−0.445322	+	1.07197i
$399$	−12.7562	−	0.877513i	−0.638608	−	0.0439306i
$400$	−19.0170	−	0.0785603i	−0.950850	−	0.00392802i
$401$	28.7394	+	16.5927i	1.43517	+	0.828599i	0.997509	−	0.0705391i	$-0.0224720\pi$
$401$	28.7394	+	16.5927i	1.43517	+	0.828599i	0.437666	+	0.899138i	$0.355805\pi$
$402$	−26.9958	+	15.6499i	−1.34643	+	0.780546i
$403$	−0.175288	+	0.654185i	−0.00873174	+	0.0325873i
$404$	0.369191	−	0.636417i	0.0183679	−	0.0316630i
$405$	3.18975	+	3.11895i	0.158500	+	0.154982i
$406$	4.65153	−	6.85605i	0.230851	−	0.340260i
$407$	−2.29563			−0.113790
$408$	13.5121	+	7.80646i	0.668946	+	0.386477i
$409$	−8.76642	−	15.1839i	−0.433471	−	0.750794i	0.563698	−	0.825981i	$-0.309378\pi$
$409$	−8.76642	−	15.1839i	−0.433471	−	0.750794i	−0.997169	+	0.0751865i	$0.976045\pi$
$410$	1.59933	+	1.22983i	0.0789852	+	0.0607372i
$411$	12.4768	+	16.1660i	0.615436	+	0.797409i
$412$	−8.67624	−	8.71215i	−0.427448	−	0.429217i
$413$	23.2450	−	26.1852i	1.14381	−	1.28849i
$414$	17.7472	−	7.44650i	0.872227	−	0.365976i
$415$	−1.73421	+	3.00374i	−0.0851290	+	0.147448i
$416$	−3.07815	−	2.38730i	−0.150919	−	0.117047i
$417$	−5.03514	−	3.84120i	−0.246572	−	0.188104i
$418$	3.60338	+	4.70607i	0.176247	+	0.230181i
$419$	11.8036	+	11.8036i	0.576645	+	0.576645i	0.933977	−	0.357332i	$-0.116314\pi$
$419$	11.8036	+	11.8036i	0.576645	+	0.576645i	−0.357332	+	0.933977i	$0.616314\pi$
$420$	1.48310	−	4.29417i	0.0723676	−	0.209534i
$421$	−27.0336	+	27.0336i	−1.31753	+	1.31753i	−0.401813	+	0.915722i	$0.631620\pi$
$421$	−27.0336	+	27.0336i	−1.31753	+	1.31753i	−0.915722	+	0.401813i	$0.868380\pi$
$422$	2.22422	−	16.7609i	0.108273	−	0.815906i
$423$	−9.64287	+	36.8127i	−0.468852	+	1.78989i
$424$	−0.629028	−	4.89509i	−0.0305483	−	0.237727i
$425$	−13.1152	−	7.57206i	−0.636181	−	0.367299i
$426$	19.6447	+	19.5752i	0.951790	+	0.948421i
$427$	31.2689	+	6.41631i	1.51321	+	0.310507i
$428$	0.0760923	−	36.8393i	0.00367806	−	1.78070i
$429$	−1.09463	−	1.41829i	−0.0528490	−	0.0684756i
$430$	0.668039	+	5.11508i	0.0322157	+	0.246671i
$431$	23.2323	−	13.4132i	1.11906	−	0.646090i	0.177900	−	0.984049i	$-0.443070\pi$
$431$	23.2323	−	13.4132i	1.11906	−	0.646090i	0.941161	+	0.337959i	$0.109736\pi$
$432$	−20.6182	−	2.62460i	−0.991995	−	0.126276i
$433$		−	6.51222i		−	0.312958i	−0.987681	−	0.156479i	$-0.949986\pi$
$433$		−	6.51222i		−	0.312958i	0.987681	−	0.156479i	$-0.0500143\pi$
$434$	2.78383	−	2.40674i	0.133628	−	0.115527i
$435$	−1.75841	−	0.722584i	−0.0843092	−	0.0346452i
$436$	10.2811	+	5.96412i	0.492374	+	0.285630i
$437$	12.2261	+	3.27597i	0.584853	+	0.156711i
$438$	7.11779	−	26.7536i	0.340101	−	1.27833i
$439$	10.8000	−	18.7062i	0.515457	−	0.892798i	−0.484382	−	0.874857i	$-0.660955\pi$
$439$	10.8000	−	18.7062i	0.515457	−	0.892798i	0.999839	−	0.0179414i	$-0.00571124\pi$
$440$	−1.94814	+	0.799886i	−0.0928742	+	0.0381331i
$441$	−16.5774	−	12.8915i	−0.789400	−	0.613879i
$442$	−1.18415	−	2.86717i	−0.0563243	−	0.136377i
$443$	−13.9256	+	3.73136i	−0.661627	+	0.177282i	−0.573980	−	0.818869i	$-0.694601\pi$
$443$	−13.9256	+	3.73136i	−0.661627	+	0.177282i	−0.0876466	+	0.996152i	$0.527935\pi$
$444$	5.24835	−	0.694910i	0.249076	−	0.0329790i
$445$	−1.38013	+	5.15072i	−0.0654245	+	0.244168i
$446$	19.3203	−	14.7933i	0.914845	−	0.700485i
$447$	−28.9891	+	12.1031i	−1.37114	+	0.572455i
$448$	6.55786	+	20.1245i	0.309830	+	0.950792i
$449$		−	17.3114i		−	0.816977i	−0.912764	−	0.408488i	$-0.866056\pi$
$449$		−	17.3114i		−	0.816977i	0.912764	−	0.408488i	$-0.133944\pi$
$450$	20.0100	+	2.54123i	0.943282	+	0.119795i
$451$	−4.17572	−	1.11888i	−0.196627	−	0.0526860i
$452$	15.9582	+	4.31134i	0.750611	+	0.202788i
$453$	−17.4515	+	13.4690i	−0.819945	+	0.632829i
$454$	−23.8581	+	9.85349i	−1.11972	+	0.462447i
$455$	−0.753918	+	0.497193i	−0.0353442	+	0.0233088i
$456$	−9.66273	−	9.66839i	−0.452499	−	0.452764i
$457$	−3.12831	−	1.80613i	−0.146336	−	0.0844873i	0.425044	−	0.905173i	$-0.360259\pi$
$457$	−3.12831	−	1.80613i	−0.146336	−	0.0844873i	−0.571380	+	0.820685i	$0.693592\pi$
$458$	7.40708	+	5.69582i	0.346110	+	0.266148i
$459$	−13.2156	−	9.96511i	−0.616852	−	0.465131i
$460$	−2.25666	+	3.89008i	−0.105217	+	0.181376i
$461$	10.9932	+	10.9932i	0.512005	+	0.512005i	0.915141	−	0.403135i	$-0.132080\pi$
$461$	10.9932	+	10.9932i	0.512005	+	0.512005i	−0.403135	+	0.915141i	$0.632080\pi$
$462$	0.595234	+	9.71645i	0.0276928	+	0.452050i
$463$	−8.28850			−0.385199			−0.192600	−	0.981277i	$-0.561692\pi$
$463$	−8.28850			−0.385199			−0.192600	+	0.981277i	$0.561692\pi$
$464$	8.56470	−	2.25702i	0.397606	−	0.104780i
$465$	−0.671348	−	0.512158i	−0.0311330	−	0.0237507i
$466$	3.47751	−	0.454170i	0.161093	−	0.0210390i
$467$	2.17619	−	0.583107i	0.100702	−	0.0269830i	−0.208116	−	0.978104i	$-0.566733\pi$
$467$	2.17619	−	0.583107i	0.100702	−	0.0269830i	0.308818	+	0.951121i	$0.400067\pi$
$468$	2.93190	+	2.91118i	0.135527	+	0.134569i
$469$	−25.2055	−	22.3754i	−1.16388	−	1.03320i
$470$	−3.39443	−	8.21887i	−0.156573	−	0.379108i
$471$	−21.9454	−	2.82656i	−1.01119	−	0.130241i
$472$	37.1264	−	4.77082i	1.70888	−	0.219595i
$473$	−5.52671	−	9.57254i	−0.254118	−	0.440146i
$474$	−16.9404	+	4.57136i	−0.778097	+	0.209970i
$475$	9.38010	+	9.38010i	0.430388	+	0.430388i
$476$	−3.42218	+	16.5043i	−0.156855	+	0.756472i
$477$	0.0293723	+	5.23464i	0.00134486	+	0.239678i
$478$	22.3663	−	17.1256i	1.02301	−	0.783307i
$479$	−3.53273	−	6.11886i	−0.161414	−	0.279578i	0.773962	−	0.633232i	$-0.218272\pi$
$479$	−3.53273	−	6.11886i	−0.161414	−	0.279578i	−0.935376	+	0.353654i	$0.884939\pi$
$480$	4.21178	−	2.41845i	0.192241	−	0.110386i
$481$	−0.911413	−	0.526205i	−0.0415569	−	0.0239929i
$482$	−11.0493	−	4.59016i	−0.503284	−	0.209076i
$483$	13.6560	+	15.6736i	0.621370	+	0.713174i
$484$	−12.3910	+	12.3399i	−0.563227	+	0.560906i
$485$	2.14587	−	0.574985i	0.0974391	−	0.0261087i
$486$	21.3666	+	5.42858i	0.969208	+	0.246245i
$487$	−19.5940	+	11.3126i	−0.887890	+	0.512623i	−0.873252	−	0.487270i	$-0.837993\pi$
$487$	−19.5940	+	11.3126i	−0.887890	+	0.512623i	−0.0146380	+	0.999893i	$0.504660\pi$
$488$	20.6896	+	27.1369i	0.936576	+	1.22843i
$489$	16.4027	−	6.84821i	0.741758	−	0.309687i
$490$	4.90665	+	0.0643299i	0.221660	+	0.00290613i
$491$	25.4191	+	25.4191i	1.14715	+	1.14715i	0.987111	+	0.160034i	$0.0511605\pi$
$491$	25.4191	+	25.4191i	1.14715	+	1.14715i	0.160034	+	0.987111i	$0.448839\pi$
$492$	9.88536	+	1.29399i	0.445666	+	0.0583376i
$493$	6.81293	+	1.82552i	0.306839	+	0.0822172i
$494$	0.351890	+	2.69437i	0.0158323	+	0.121225i
$495$	2.15432	−	0.590225i	0.0968296	−	0.0265286i
$496$	3.93401	+	0.0162516i	0.176642	+	0.000729718i
$497$	−13.4106	+	26.7851i	−0.601549	+	1.20148i
$498$	0.0303845	+	17.1394i	0.00136156	+	0.768037i
$499$	−13.1116	+	3.51324i	−0.586955	+	0.157274i	−0.540061	−	0.841626i	$-0.681599\pi$
$499$	−13.1116	+	3.51324i	−0.586955	+	0.157274i	−0.0468940	+	0.998900i	$0.514932\pi$
$500$	−8.38461	+	4.81779i	−0.374971	+	0.215458i
$501$	2.70423	+	20.1046i	0.120816	+	0.898209i
$502$	22.9008	+	3.03901i	1.02211	+	0.135638i
$503$			16.8100i			0.749519i	0.927122	+	0.374760i	$0.122275\pi$
$503$			16.8100i			0.749519i	−0.927122	+	0.374760i	$0.877725\pi$
$504$	−4.30211	−	22.0339i	−0.191631	−	0.981467i
$505$		−	0.182352i		−	0.00811455i
$506$	1.26768	−	9.55273i	0.0563552	−	0.424671i
$507$	2.89214	+	21.5017i	0.128445	+	0.954924i
$508$	−7.04893	+	26.0913i	−0.312746	+	1.15761i
$509$	13.9927	−	3.74932i	0.620214	−	0.166186i	0.0649891	−	0.997886i	$-0.479299\pi$
$509$	13.9927	−	3.74932i	0.620214	−	0.166186i	0.555225	+	0.831700i	$0.312632\pi$
$510$	3.86761	−	0.00685644i	0.171261	−	0.000303608i
$511$	29.8496	−	1.77549i	1.32047	−	0.0785432i
$512$	−8.85307	+	20.8236i	−0.391254	+	0.920283i
$513$	8.92253	+	11.4276i	0.393939	+	0.504542i
$514$	−23.2580	+	3.03754i	−1.02586	+	0.133980i
$515$	−2.94353	−	0.788717i	−0.129708	−	0.0347550i
$516$	15.5330	+	20.2121i	0.683804	+	0.889786i
$517$	13.4731	+	13.4731i	0.592547	+	0.592547i
$518$	2.49283	+	5.14638i	0.109529	+	0.226119i
$519$	−41.3769	+	17.2750i	−1.81625	+	0.758290i
$520$	−0.956803	−	0.128983i	−0.0419586	−	0.00565626i
$521$	−17.9780	+	10.3796i	−0.787632	+	0.454739i	−0.839128	−	0.543934i	$-0.816934\pi$
$521$	−17.9780	+	10.3796i	−0.787632	+	0.454739i	0.0514964	+	0.998673i	$0.483601\pi$
$522$	−9.30829	+	1.26884i	−0.407413	+	0.0555357i
$523$	−1.83822	+	0.492550i	−0.0803798	+	0.0215377i	−0.298785	−	0.954321i	$-0.596581\pi$
$523$	−1.83822	+	0.492550i	−0.0803798	+	0.0215377i	0.218405	+	0.975858i	$0.429915\pi$
$524$	0.0507790	−	24.5841i	0.00221829	−	1.07396i
$525$	4.18131	+	21.3819i	0.182487	+	0.933183i
$526$	9.66380	−	23.2625i	0.421362	−	1.01429i
$527$	2.71311	+	1.56642i	0.118185	+	0.0682342i
$528$	−6.34619	+	8.24786i	−0.276183	+	0.358942i
$529$	1.21074	+	2.09707i	0.0526411	+	0.0911770i
$530$	−0.743633	−	0.971197i	−0.0323014	−	0.0421861i
$531$	−39.7017	+	0.222772i	−1.72291	+	0.00966748i
$532$	6.63722	−	13.1884i	0.287760	−	0.571791i
$533$	−1.40138	−	1.40138i	−0.0607003	−	0.0607003i
$534$	6.86515	+	25.4406i	0.297084	+	1.10092i
$535$	−4.56522	−	7.90720i	−0.197372	−	0.341858i
$536$	−4.59233	−	35.7375i	−0.198358	−	1.54362i
$537$	10.4770	+	1.34942i	0.452114	+	0.0582320i
$538$	26.0744	−	10.7689i	1.12415	−	0.464278i
$539$	−9.76215	+	3.90617i	−0.420485	+	0.168251i
$540$	−4.74662	+	2.00152i	−0.204262	+	0.0861319i
$541$	16.5866	−	4.44435i	0.713112	−	0.191078i	0.116016	−	0.993247i	$-0.462988\pi$
$541$	16.5866	−	4.44435i	0.713112	−	0.191078i	0.597096	+	0.802170i	$0.296321\pi$
$542$	−4.76286	−	36.4685i	−0.204582	−	1.56646i
$543$	8.15006	+	6.21751i	0.349753	+	0.266819i
$544$	−14.3520	+	10.8954i	−0.615336	+	0.467135i
$545$	2.94582			0.126185
$546$	−1.99088	+	3.99407i	−0.0852019	+	0.170930i
$547$	14.2581	+	14.2581i	0.609631	+	0.609631i	0.942850	−	0.333218i	$-0.108135\pi$
$547$	14.2581	+	14.2581i	0.609631	+	0.609631i	−0.333218	+	0.942850i	$0.608135\pi$
$548$	−22.7890	+	6.05588i	−0.973499	+	0.258694i
$549$	−18.2728	−	31.2432i	−0.779864	−	1.33343i
$550$	6.15642	−	8.00607i	0.262511	−	0.341380i
$551$	−5.35055	−	3.08914i	−0.227941	−	0.131602i
$552$	−0.00650556	+	22.2235i	−0.000276895	+	0.945895i
$553$	−10.4339	−	15.8215i	−0.443696	−	0.672797i
$554$	16.6645	+	40.3494i	0.708005	+	1.71428i
$555$	1.03874	−	0.801691i	0.0440919	−	0.0340299i
$556$	6.34058	−	3.64330i	0.268901	−	0.154510i
$557$	11.8190	+	3.16690i	0.500789	+	0.134186i	0.500366	−	0.865814i	$-0.333199\pi$
$557$	11.8190	+	3.16690i	0.500789	+	0.134186i	0.000422644		1.00000i	$0.499865\pi$
$558$	−4.13943	−	0.525698i	−0.175236	−	0.0222546i
$559$		−	5.06732i		−	0.214325i
$560$	3.90869	+	3.49878i	0.165172	+	0.147851i
$561$	−7.64758	+	3.19290i	−0.322881	+	0.134804i
$562$	8.31692	+	10.8620i	0.350828	+	0.458187i
$563$	−6.84970	+	25.5634i	−0.288680	+	1.07737i	0.657427	+	0.753518i	$0.271645\pi$
$563$	−6.84970	+	25.5634i	−0.288680	+	1.07737i	−0.946108	+	0.323852i	$0.895022\pi$
$564$	−34.8811	−	26.7242i	−1.46876	−	1.12529i
$565$	3.95735	−	1.06037i	0.166487	−	0.0446101i
$566$	−34.6126	+	14.2952i	−1.45488	+	0.600870i
$567$	1.68051	+	23.7524i	0.0705747	+	0.997506i
$568$	−29.6232	+	12.1629i	−1.24296	+	0.510346i
$569$	−14.6506	+	25.3756i	−0.614187	+	1.06380i	0.376340	+	0.926482i	$0.377182\pi$
$569$	−14.6506	+	25.3756i	−0.614187	+	1.06380i	−0.990527	+	0.137321i	$0.956151\pi$
$570$	−3.27394	−	0.871033i	−0.137130	−	0.0364835i
$571$	−22.9658	−	6.15367i	−0.961090	−	0.257523i	−0.256028	−	0.966669i	$-0.582414\pi$
$571$	−22.9658	−	6.15367i	−0.961090	−	0.257523i	−0.705062	+	0.709146i	$0.749081\pi$
$572$	1.99935	−	0.531299i	0.0835968	−	0.0222147i
$573$	21.1789	+	8.70307i	0.884763	+	0.363576i
$574$	2.02609	+	10.5762i	0.0845675	+	0.441441i
$575$		−	21.5672i		−	0.899412i
$576$	12.0122	−	20.7776i	0.500507	−	0.865733i
$577$	−6.62027	+	3.82222i	−0.275606	+	0.159121i	−0.631432	−	0.775431i	$-0.717533\pi$
$577$	−6.62027	+	3.82222i	−0.275606	+	0.159121i	0.355827	+	0.934552i	$0.384199\pi$
$578$	9.61067	−	1.25517i	0.399751	−	0.0522083i
$579$	21.0985	+	27.3369i	0.876822	+	1.13608i
$580$	1.55543	−	1.54902i	0.0645858	−	0.0643196i
$581$	−17.5659	+	5.84476i	−0.728756	+	0.242481i
$582$	7.74890	−	7.77643i	0.321202	−	0.322343i
$583$	2.26986	+	1.31050i	0.0940080	+	0.0542755i
$584$	25.3007	+	19.5388i	1.04695	+	0.808519i
$585$	0.990601	+	0.259482i	0.0409563	+	0.0107283i
$586$	−9.65090	−	1.28071i	−0.398675	−	0.0529055i
$587$	29.4710	−	29.4710i	1.21640	−	1.21640i	0.247513	−	0.968885i	$-0.420387\pi$
$587$	29.4710	−	29.4710i	1.21640	−	1.21640i	0.968885	−	0.247513i	$-0.0796134\pi$
$588$	21.1361	−	11.8855i	0.871638	−	0.490150i
$589$	−1.94044	−	1.94044i	−0.0799544	−	0.0799544i
$590$	7.36597	−	5.64003i	0.303252	−	0.232196i
$591$	−16.3019	−	12.4364i	−0.670571	−	0.511565i
$592$	−1.60658	+	5.89828i	−0.0660302	+	0.242418i
$593$	1.89529	−	3.28274i	0.0778303	−	0.134806i	−0.824483	−	0.565886i	$-0.808534\pi$
$593$	1.89529	−	3.28274i	0.0778303	−	0.134806i	0.902314	+	0.431080i	$0.141867\pi$
$594$	7.74725	−	7.86251i	0.317874	−	0.322603i
$595$	1.31890	+	3.96384i	0.0540698	+	0.162502i
$596$	0.0749244	−	36.2739i	0.00306902	−	1.48584i
$597$	17.3289	+	22.4528i	0.709225	+	0.918930i
$598$	2.69297	−	3.50205i	0.110124	−	0.143210i
$599$	−20.1244	−	34.8564i	−0.822260	−	1.42420i	−0.903996	−	0.427542i	$-0.859380\pi$
$599$	−20.1244	−	34.8564i	−0.822260	−	1.42420i	0.0817360	−	0.996654i	$-0.473954\pi$
$600$	−11.6515	+	20.1673i	−0.475670	+	0.823328i
$601$	22.9360			0.935578			0.467789	−	0.883840i	$-0.345051\pi$
$601$	22.9360			0.935578			0.467789	+	0.883840i	$0.345051\pi$
$602$	−15.4584	+	22.7847i	−0.630037	+	0.928634i
$603$	0.214438	+	38.2164i	0.00873257	+	1.55629i
$604$	−6.53745	−	24.6013i	−0.266005	−	1.00101i
$605$	−1.12177	+	4.18649i	−0.0456063	+	0.170205i
$606$	−0.451936	−	0.779581i	−0.0183586	−	0.0316683i
$607$	12.7058	+	7.33571i	0.515714	+	0.297747i	0.735179	−	0.677873i	$-0.237098\pi$
$607$	12.7058	+	7.33571i	0.515714	+	0.297747i	−0.219466	+	0.975620i	$0.570431\pi$
$608$	14.6133	−	5.96482i	0.592649	−	0.241905i
$609$	−4.45849	−	9.11510i	−0.180667	−	0.369363i
$610$	7.81041	+	3.24463i	0.316234	+	0.131371i
$611$	2.26080	+	8.43741i	0.0914620	+	0.341341i
$612$	16.5176	−	9.61470i	0.667686	−	0.388651i
$613$	−5.36352	−	1.43715i	−0.216631	−	0.0580460i	0.148871	−	0.988857i	$-0.452436\pi$
$613$	−5.36352	−	1.43715i	−0.216631	−	0.0580460i	−0.365502	+	0.930811i	$0.619103\pi$
$614$	13.5593	+	1.79936i	0.547209	+	0.0726165i
$615$	2.28018	−	0.951987i	0.0919459	−	0.0383878i
$616$	−10.6106	−	3.71028i	−0.427514	−	0.149492i
$617$	13.1235			0.528332			0.264166	−	0.964477i	$-0.414903\pi$
$617$	13.1235			0.528332			0.264166	+	0.964477i	$0.414903\pi$
$618$	−14.5388	+	3.92329i	−0.584835	+	0.157818i
$619$	8.06306	−	30.0918i	0.324082	−	1.20949i	−0.591150	−	0.806562i	$-0.701326\pi$
$619$	8.06306	−	30.0918i	0.324082	−	1.20949i	0.915232	−	0.402928i	$-0.132007\pi$
$620$	0.845407	−	0.485770i	0.0339523	−	0.0195090i
$621$	2.87991	−	23.3950i	0.115567	−	0.938809i
$622$	30.2857	+	12.5814i	1.21435	+	0.504469i
$623$	−23.7603	+	15.6694i	−0.951934	+	0.627781i
$624$	−4.41014	+	1.81989i	−0.176547	+	0.0728541i
$625$	10.6874	−	18.5111i	0.427495	−	0.740443i
$626$	1.56245	−	0.204060i	0.0624483	−	0.00815587i
$627$	7.19449	−	0.967714i	0.287320	−	0.0386468i
$628$	12.8205	−	22.1003i	0.511595	−	0.881897i
$629$	−3.44231	+	3.44231i	−0.137254	+	0.137254i
$630$	−3.66255	−	4.18866i	−0.145920	−	0.166880i
$631$		−	44.2183i		−	1.76030i	−0.474695	−	0.880150i	$-0.657442\pi$
$631$		−	44.2183i		−	1.76030i	0.474695	−	0.880150i	$-0.342558\pi$
$632$	2.70678	−	20.0791i	0.107670	−	0.798705i
$633$	−16.4639	−	12.5599i	−0.654379	−	0.499212i
$634$	19.3001	−	25.0987i	0.766505	−	0.996795i
$635$	1.73368	+	6.47018i	0.0687989	+	0.256761i
$636$	−5.58613	−	2.30901i	−0.221504	−	0.0915582i
$637$	−4.77114	−	0.686850i	−0.189039	−	0.0272140i
$638$	−1.80453	+	4.34382i	−0.0714420	+	0.171974i
$639$	32.7583	−	8.97487i	1.29590	−	0.355040i
$640$	0.691788	+	5.56525i	0.0273453	+	0.219986i
$641$	−16.4206	+	9.48043i	−0.648574	+	0.374454i	−0.787910	−	0.615791i	$-0.788837\pi$
$641$	−16.4206	+	9.48043i	−0.648574	+	0.374454i	0.139336	+	0.990245i	$0.455503\pi$
$642$	−39.1140	−	22.4901i	−1.54371	−	0.887614i
$643$	−13.2656	+	13.2656i	−0.523144	+	0.523144i	−0.918520	−	0.395375i	$-0.870615\pi$
$643$	−13.2656	+	13.2656i	−0.523144	+	0.523144i	0.395375	+	0.918520i	$0.370615\pi$
$644$	−22.7920	+	7.53141i	−0.898131	+	0.296779i
$645$	5.84371	+	2.40136i	0.230096	+	0.0945534i
$646$	12.4600	+	1.65349i	0.490234	+	0.0650556i
$647$	−8.74834	+	5.05086i	−0.343933	+	0.198570i	−0.662010	−	0.749495i	$-0.730296\pi$
$647$	−8.74834	+	5.05086i	−0.343933	+	0.198570i	0.318077	+	0.948065i	$0.396963\pi$
$648$	−15.3320	+	20.3207i	−0.602296	+	0.798273i
$649$	−9.93942	+	17.2156i	−0.390157	+	0.675771i
$650$	4.27937	−	1.76740i	0.167851	−	0.0693231i
$651$	−0.864978	−	4.42323i	−0.0339011	−	0.173360i
$652$	−0.0423941	+	20.5247i	−0.00166028	+	0.803808i
$653$	−2.23161	−	8.32848i	−0.0873296	−	0.325919i	0.908416	−	0.418068i	$-0.137293\pi$
$653$	−2.23161	−	8.32848i	−0.0873296	−	0.325919i	−0.995745	+	0.0921499i	$0.970626\pi$
$654$	12.5938	−	7.30084i	0.492457	−	0.285486i
$655$	−3.04653	−	5.27675i	−0.119038	−	0.206180i
$656$	−5.79714	+	9.94583i	−0.226340	+	0.388319i
$657$	−24.1094	−	23.8403i	−0.940597	−	0.930100i
$658$	15.5738	−	44.8347i	0.607128	−	1.74784i
$659$	−3.66207	+	3.66207i	−0.142654	+	0.142654i	−0.774827	−	0.632173i	$-0.782163\pi$
$659$	−3.66207	+	3.66207i	−0.142654	+	0.142654i	0.632173	+	0.774827i	$0.282163\pi$
$660$	−0.334770	+	2.55745i	−0.0130309	+	0.0995487i
$661$	2.47133	−	9.22313i	0.0961236	−	0.358738i	−0.901064	−	0.433687i	$-0.857213\pi$
$661$	2.47133	−	9.22313i	0.0961236	−	0.358738i	0.997187	+	0.0749483i	$0.0238792\pi$
$662$	23.0866	−	30.0227i	0.897285	−	1.16687i
$663$	−3.76812	−	0.485331i	−0.146342	−	0.0188487i
$664$	−18.2609	−	7.63028i	−0.708661	−	0.296112i
$665$	−0.217274	−	3.65282i	−0.00842553	−	0.141650i
$666$	2.45386	−	6.00173i	0.0950853	−	0.232562i
$667$	2.59977	+	9.70247i	0.100663	+	0.375681i
$668$	−22.6132	−	6.10928i	−0.874931	−	0.236375i
$669$	−3.97286	−	29.5363i	−0.153600	−	1.14194i
$670$	−5.42903	−	7.09040i	−0.209742	−	0.273926i
$671$	−18.1224			−0.699609
$672$	25.3815	+	5.27063i	0.979113	+	0.203319i
$673$	−40.0505			−1.54383			−0.771916	−	0.635724i	$-0.780702\pi$
$673$	−40.0505			−1.54383			−0.771916	+	0.635724i	$0.780702\pi$
$674$	1.60818	+	2.10030i	0.0619446	+	0.0809006i
$675$	14.8734	−	19.7249i	0.572476	−	0.759212i
$676$	−24.1846	−	6.53380i	−0.930175	−	0.251300i
$677$	−6.56130	−	24.4871i	−0.252171	−	0.941115i	−0.969642	−	0.244527i	$-0.921367\pi$
$677$	−6.56130	−	24.4871i	−0.252171	−	0.941115i	0.717471	−	0.696588i	$-0.245299\pi$
$678$	14.2903	−	14.3410i	0.548815	−	0.550764i
$679$	10.6030	+	5.30864i	0.406905	+	0.203727i
$680$	−1.72182	+	4.12068i	−0.0660287	+	0.158021i
$681$	−4.03851	+	31.3551i	−0.154756	+	1.20153i
$682$	−1.27356	+	1.65620i	−0.0487673	+	0.0634191i
$683$	−11.3444	+	42.3377i	−0.434080	+	1.62001i	0.309178	+	0.951004i	$0.399946\pi$
$683$	−11.3444	+	42.3377i	−0.434080	+	1.62001i	−0.743258	+	0.669005i	$0.766721\pi$
$684$	−16.1553	+	4.39026i	−0.617715	+	0.167866i
$685$	−4.13245	+	4.13245i	−0.157893	+	0.157893i
$686$	19.3576	+	17.6432i	0.739077	+	0.673621i
$687$	10.5604	−	4.40900i	0.402903	−	0.168214i
$688$	−28.4630	+	7.50075i	−1.08514	+	0.285964i
$689$	0.600787	+	1.04059i	0.0228882	+	0.0396435i
$690$	2.76244	+	4.76516i	0.105164	+	0.181407i
$691$	−10.3957	−	38.7972i	−0.395470	−	1.47591i	−0.820978	−	0.570960i	$-0.806571\pi$
$691$	−10.3957	−	38.7972i	−0.395470	−	1.47591i	0.425508	−	0.904955i	$-0.360095\pi$
$692$	0.106942	−	51.7748i	0.00406532	−	1.96818i
$693$	10.6907	+	5.27775i	0.406106	+	0.200485i
$694$	5.64810	−	2.33269i	0.214399	−	0.0885476i
$695$	0.906215	−	1.56961i	0.0343747	−	0.0595387i
$696$	2.81065	−	10.4772i	0.106538	−	0.397139i
$697$	−7.93926	+	4.58374i	−0.300721	+	0.173621i
$698$	−1.51480	−	0.201019i	−0.0573360	−	0.00760868i
$699$	1.63258	−	3.97288i	0.0617497	−	0.150268i
$700$	−24.6334	−	5.10775i	−0.931054	−	0.193055i
$701$	0.587547	−	0.587547i	0.0221914	−	0.0221914i	−0.695924	−	0.718115i	$-0.745005\pi$
$701$	0.587547	−	0.587547i	0.0221914	−	0.0221914i	0.718115	+	0.695924i	$0.245005\pi$
$702$	4.87806	−	1.34575i	0.184110	−	0.0507922i
$703$	3.69295	−	2.13213i	0.139282	−	0.0804146i
$704$	−5.94376	−	10.4438i	−0.224014	−	0.393616i
$705$	−10.8015	−	1.39123i	−0.406808	−	0.0523967i
$706$	−15.0582	+	36.2479i	−0.566724	+	1.36421i
$707$	0.646153	−	0.727882i	0.0243011	−	0.0273748i
$708$	17.5125	−	42.3676i	0.658160	−	1.59227i
$709$	0.575708	+	2.14857i	0.0216212	+	0.0806913i	0.975893	−	0.218248i	$-0.0700340\pi$
$709$	0.575708	+	2.14857i	0.0216212	+	0.0806913i	−0.954272	+	0.298939i	$0.903367\pi$
$710$	−4.83807	+	6.29164i	−0.181570	+	0.236121i
$711$	−5.44540	+	20.7884i	−0.204218	+	0.779626i
$712$	−30.1543	−	4.06497i	−1.13008	−	0.152341i
$713$			4.46155i			0.167086i
$714$	15.4624	+	13.6773i	0.578665	+	0.511859i
$715$	0.362551	−	0.362551i	0.0135586	−	0.0135586i
$716$	−6.12064	+	10.5509i	−0.228739	+	0.394305i
$717$	−4.59921	−	34.1929i	−0.171761	−	1.27696i
$718$	32.4952	−	4.24393i	1.21271	−	0.158382i
$719$	25.3872	−	43.9719i	0.946783	−	1.63988i	0.194641	−	0.980875i	$-0.437646\pi$
$719$	25.3872	−	43.9719i	0.946783	−	1.63988i	0.752142	−	0.659001i	$-0.229021\pi$
$720$	−0.00880373	−	5.94827i	−0.000328096	−	0.221679i
$721$	−8.95473	−	13.5785i	−0.333492	−	0.505690i
$722$	14.6465	+	6.08450i	0.545086	+	0.226442i
$723$	−11.6006	+	8.95330i	−0.431432	+	0.332977i
$724$	−10.2631	+	5.89717i	−0.381425	+	0.219167i
$725$	−2.72467	+	10.1686i	−0.101192	+	0.377652i
$726$	5.57996	+	20.6780i	0.207092	+	0.767433i
$727$	−26.5391			−0.984281			−0.492141	−	0.870516i	$-0.663785\pi$
$727$	−26.5391			−0.984281			−0.492141	+	0.870516i	$0.663785\pi$
$728$	−3.36216	−	3.90522i	−0.124610	−	0.144737i
$729$	18.7678	−	19.4105i	0.695104	−	0.718909i
$730$	7.85400	+	1.04225i	0.290689	+	0.0385754i
$731$	−22.6414	−	6.06673i	−0.837421	−	0.224386i
$732$	41.4321	−	5.48583i	1.53137	−	0.202762i
$733$	5.31855	+	19.8491i	0.196445	+	0.733143i	0.991888	+	0.127115i	$0.0405716\pi$
$733$	5.31855	+	19.8491i	0.196445	+	0.733143i	−0.795443	+	0.606029i	$0.792762\pi$
$734$	5.40435	+	2.24510i	0.199478	+	0.0828681i
$735$	3.05308	−	5.17665i	0.112615	−	0.190944i
$736$	−23.6571	−	9.94252i	−0.872012	−	0.366486i
$737$	16.5715	+	9.56757i	0.610420	+	0.352426i
$738$	7.38875	−	9.72104i	0.271984	−	0.357836i
$739$	−0.907491	+	3.38680i	−0.0333826	+	0.124586i	−0.980606	−	0.195988i	$-0.937209\pi$
$739$	−0.907491	+	3.38680i	−0.0333826	+	0.124586i	0.947224	+	0.320573i	$0.103875\pi$
$740$	0.389117	+	1.46430i	0.0143042	+	0.0538286i
$741$	3.07818	+	1.26492i	0.113080	+	0.0464679i
$742$	0.473065	−	6.51168i	0.0173667	−	0.239051i
$743$	−21.4331			−0.786303			−0.393152	−	0.919474i	$-0.628615\pi$
$743$	−21.4331			−0.786303			−0.393152	+	0.919474i	$0.628615\pi$
$744$	2.41032	−	4.17197i	0.0883666	−	0.152952i
$745$	−4.49515	−	7.78583i	−0.164690	−	0.285251i
$746$	15.1744	−	19.7334i	0.555573	−	0.722491i
$747$	18.2378	+	10.3936i	0.667285	+	0.380281i
$748$	0.0197657	−	9.56938i	0.000722707	−	0.349891i
$749$	9.79597	−	47.7392i	0.357937	−	1.74435i
$750$	0.0209960	+	11.8435i	0.000766665	+	0.432464i
$751$	−22.4704	+	38.9198i	−0.819955	+	1.42020i	0.0857599	+	0.996316i	$0.472668\pi$
$751$	−22.4704	+	38.9198i	−0.819955	+	1.42020i	−0.905715	+	0.423888i	$0.860665\pi$
$752$	44.0462	−	25.1880i	1.60620	−	0.918514i
$753$	17.1609	−	22.4950i	0.625379	−	0.819762i
$754$	−1.71212	+	1.31095i	−0.0623519	+	0.0477421i
$755$	−4.46107	−	4.46107i	−0.162355	−	0.162355i
$756$	−26.0390	−	8.82999i	−0.947031	−	0.321144i
$757$	8.74678	−	8.74678i	0.317907	−	0.317907i	−0.530056	−	0.847963i	$-0.677829\pi$
$757$	8.74678	−	8.74678i	0.317907	−	0.317907i	0.847963	+	0.530056i	$0.177829\pi$
$758$	−14.5817	−	1.93505i	−0.529633	−	0.0702840i
$759$	−9.38346	−	7.15844i	−0.340598	−	0.259835i
$760$	2.39104	−	3.09615i	0.0867320	−	0.112309i
$761$	−19.1228	−	11.0405i	−0.693200	−	0.400219i	0.111609	−	0.993752i	$-0.464399\pi$
$761$	−19.1228	−	11.0405i	−0.693200	−	0.400219i	−0.804810	+	0.593533i	$0.797733\pi$
$762$	23.4472	+	23.3643i	0.849404	+	0.846398i
$763$	11.7586	+	10.4383i	0.425691	+	0.377893i
$764$	−18.7342	+	18.6570i	−0.677780	+	0.674986i
$765$	2.34537	−	4.11545i	0.0847970	−	0.148795i
$766$	−24.5294	+	3.20359i	−0.886283	+	0.115750i
$767$	−7.89231	+	4.55662i	−0.284975	+	0.164530i
$768$	16.7503	+	22.0778i	0.604423	+	0.796663i
$769$			17.2185i			0.620915i	0.950587	+	0.310457i	$0.100482\pi$
$769$			17.2185i			0.620915i	−0.950587	+	0.310457i	$0.899518\pi$
$770$	−2.73617	+	0.524173i	−0.0986048	+	0.0188899i
$771$	−10.9188	+	26.5710i	−0.393232	+	0.956931i
$772$	−38.5365	+	10.2406i	−1.38696	+	0.368566i
$773$	8.05682	+	2.15882i	0.289784	+	0.0776473i	0.400783	−	0.916173i	$-0.368738\pi$
$773$	8.05682	+	2.15882i	0.289784	+	0.0776473i	−0.110999	+	0.993821i	$0.535405\pi$
$774$	30.9342	−	4.21673i	1.11191	−	0.151567i
$775$	−2.33795	+	4.04944i	−0.0839815	+	0.145460i
$776$	4.81474	+	11.7264i	0.172839	+	0.420955i
$777$	6.98700	+	0.480644i	0.250657	+	0.0172430i
$778$	25.0889	−	10.3618i	0.899482	−	0.371490i
$779$	7.75660	−	2.07838i	0.277909	−	0.0744655i
$780$	−0.719129	+	0.938624i	−0.0257489	+	0.0336081i
$781$	4.40159	−	16.4270i	0.157501	−	0.587803i
$782$	−12.4235	−	16.2252i	−0.444262	−	0.580213i
$783$	−4.31342	+	10.6666i	−0.154149	+	0.381192i
$784$	3.20432	+	27.8160i	0.114440	+	0.993430i
$785$		−	6.33237i		−	0.226012i
$786$	−26.1021	−	15.0084i	−0.931032	−	0.535333i
$787$	−2.73196	−	0.732027i	−0.0973839	−	0.0260939i	0.209798	−	0.977745i	$-0.432719\pi$
$787$	−2.73196	−	0.732027i	−0.0973839	−	0.0260939i	−0.307182	+	0.951651i	$0.599386\pi$
$788$	20.5285	−	11.7956i	0.731296	−	0.420202i
$789$	−18.8496	−	24.4232i	−0.671065	−	0.869487i
$790$	−1.91686	−	4.64126i	−0.0681988	−	0.165129i
$791$	19.5537	+	9.79004i	0.695248	+	0.348094i
$792$	4.90713	+	11.7632i	0.174367	+	0.417986i
$793$	−7.19497	−	4.15402i	−0.255501	−	0.147514i
$794$	−7.08392	+	9.21222i	−0.251399	+	0.326930i
$795$	−1.48473	+	0.199708i	−0.0526581	+	0.00708292i
$796$	−31.6514	+	8.41094i	−1.12185	+	0.298118i
$797$	32.5582	+	32.5582i	1.15327	+	1.15327i	0.985893	+	0.167376i	$0.0535293\pi$
$797$	32.5582	+	32.5582i	1.15327	+	1.15327i	0.167376	+	0.985893i	$0.446471\pi$
$798$	−9.98193	−	15.0779i	−0.353357	−	0.533751i
$799$	40.4059			1.42946
$800$	−16.2618	−	21.4210i	−0.574943	−	0.757346i
$801$	31.2195	+	8.17776i	1.10309	+	0.288947i
$802$	6.07769	+	46.5360i	0.214611	+	1.64324i
$803$	−16.3982	+	4.39389i	−0.578681	+	0.155057i
$804$	−40.7825	−	16.8573i	−1.43829	−	0.594512i
$805$	−3.94958	+	4.44915i	−0.139204	+	0.156812i
$806$	−0.885264	+	0.365618i	−0.0311821	+	0.0128783i
$807$	4.41368	−	34.2679i	0.155369	−	1.20629i
$808$	1.03202	−	0.132617i	0.0363064	−	0.00466544i
$809$	14.9133	+	25.8307i	0.524325	+	0.908158i	0.999599	+	0.0283202i	$0.00901580\pi$
$809$	14.9133	+	25.8307i	0.524325	+	0.908158i	−0.475273	+	0.879838i	$0.657651\pi$
$810$	−0.759725	+	6.26319i	−0.0266940	+	0.220066i
$811$	4.30849	+	4.30849i	0.151291	+	0.151291i	0.778695	−	0.627403i	$-0.215882\pi$
$811$	4.30849	+	4.30849i	0.151291	+	0.151291i	−0.627403	+	0.778695i	$0.715882\pi$
$812$	11.6976	−	0.671542i	0.410504	−	0.0235665i
$813$	−41.6633	−	17.1207i	−1.46120	−	0.600450i
$814$	−1.97369	−	2.57767i	−0.0691779	−	0.0903474i
$815$	2.54347	+	4.40542i	0.0890939	+	0.154315i
$816$	2.85155	+	21.8838i	0.0998244	+	0.766087i
$817$	17.7815	+	10.2661i	0.622094	+	0.359166i
$818$	9.51235	−	22.8979i	0.332592	−	0.800608i
$819$	3.03466	+	4.54589i	0.106040	+	0.158846i
$820$	−0.00589331	+	2.85318i	−0.000205803	+	0.0996375i
$821$	−11.2508	+	3.01464i	−0.392655	+	0.105212i	−0.449744	−	0.893158i	$-0.648485\pi$
$821$	−11.2508	+	3.01464i	−0.392655	+	0.105212i	0.0570892	+	0.998369i	$0.481818\pi$
$822$	−7.42507	+	27.9086i	−0.258979	+	0.973423i
$823$	21.9180	−	12.6544i	0.764013	−	0.441103i	−0.0667219	−	0.997772i	$-0.521254\pi$
$823$	21.9180	−	12.6544i	0.764013	−	0.441103i	0.830735	+	0.556669i	$0.187921\pi$
$824$	2.32305	−	17.2326i	0.0809272	−	0.600324i
$825$	−4.76554	−	11.4144i	−0.165915	−	0.397397i
$826$	49.3874	+	3.58792i	1.71841	+	0.124840i
$827$	12.8188	+	12.8188i	0.445752	+	0.445752i	0.893940	−	0.448187i	$-0.147930\pi$
$827$	12.8188	+	12.8188i	0.445752	+	0.445752i	−0.448187	+	0.893940i	$0.647930\pi$
$828$	23.6197	+	13.5254i	0.820841	+	0.470040i
$829$	1.45280	+	0.389278i	0.0504580	+	0.0135202i	0.283960	−	0.958836i	$-0.408352\pi$
$829$	1.45280	+	0.389278i	0.0504580	+	0.0135202i	−0.233502	+	0.972356i	$0.575018\pi$
$830$	−4.86378	+	0.635219i	−0.168824	+	0.0220488i
$831$	53.0285	+	6.83003i	1.83954	+	0.236931i
$832$	0.0341362	−	5.50884i	0.00118346	−	0.190985i
$833$	−8.78106	+	20.4957i	−0.304246	+	0.710133i
$834$	−0.0158775	−	8.95626i	−0.000549794	−	0.310130i
$835$	−5.60768	+	1.50257i	−0.194062	+	0.0519987i
$836$	−2.18622	+	8.09218i	−0.0756119	+	0.279874i
$837$	−3.07682	+	4.08045i	−0.106350	+	0.141041i
$838$	−3.10554	+	23.4021i	−0.107279	+	0.808412i
$839$			21.2284i			0.732886i	0.930440	+	0.366443i	$0.119425\pi$
$839$			21.2284i			0.732886i	−0.930440	+	0.366443i	$0.880575\pi$
$840$	6.09686	−	2.02665i	0.210362	−	0.0699259i
$841$			24.0970i			0.830931i
$842$	−53.5972	−	7.11253i	−1.84708	−	0.245114i
$843$	16.6055	−	2.23357i	0.571924	−	0.0769282i
$844$	20.7324	−	11.9128i	0.713638	−	0.410056i
$845$	−5.99735	+	1.60698i	−0.206315	+	0.0552819i
$846$	−49.6260	+	20.8225i	−1.70618	+	0.715891i
$847$	−19.3122	+	12.7360i	−0.663576	+	0.437615i
$848$	4.95569	−	4.91491i	0.170179	−	0.168779i
$849$	−5.85895	+	45.4890i	−0.201079	+	1.56118i
$850$	−2.77355	−	21.2367i	−0.0951321	−	0.728412i
$851$	−6.69664	−	1.79436i	−0.229558	−	0.0615098i
$852$	−5.09046	+	38.8882i	−0.174396	+	1.33229i
$853$	−11.6339	−	11.6339i	−0.398337	−	0.398337i	0.479309	−	0.877646i	$-0.340887\pi$
$853$	−11.6339	−	11.6339i	−0.398337	−	0.398337i	−0.877646	+	0.479309i	$0.840887\pi$
$854$	19.6792	+	40.6271i	0.673407	+	1.39023i
$855$	−2.91744	+	2.95036i	−0.0997743	+	0.100900i
$856$	41.4308	−	31.5875i	1.41608	−	1.07964i
$857$	−10.1671	+	5.86996i	−0.347301	+	0.200514i	−0.663496	−	0.748180i	$-0.730928\pi$
$857$	−10.1671	+	5.86996i	−0.347301	+	0.200514i	0.316195	+	0.948694i	$0.397595\pi$
$858$	0.651423	−	2.44850i	0.0222392	−	0.0835903i
$859$	−24.7860	+	6.64138i	−0.845686	+	0.226601i	−0.655545	−	0.755156i	$-0.727561\pi$
$859$	−24.7860	+	6.64138i	−0.845686	+	0.226601i	−0.190141	+	0.981757i	$0.560895\pi$
$860$	−5.16916	+	5.14785i	−0.176267	+	0.175540i
$861$	12.4750	+	4.27971i	0.425146	+	0.145852i
$862$	35.0353	+	14.5545i	1.19331	+	0.495729i
$863$	25.9379	+	14.9752i	0.882936	+	0.509763i	0.871625	−	0.490173i	$-0.163066\pi$
$863$	25.9379	+	14.9752i	0.882936	+	0.509763i	0.0113106	+	0.999936i	$0.496400\pi$
$864$	−14.7797	−	25.4079i	−0.502814	−	0.864394i
$865$	−6.41606	−	11.1129i	−0.218153	−	0.377852i
$866$	7.31231	−	5.59895i	0.248483	−	0.190260i
$867$	4.51189	−	10.9797i	0.153232	−	0.372890i
$868$	5.09585	+	1.05663i	0.172964	+	0.0358643i
$869$	7.60837	+	7.60837i	0.258096	+	0.258096i
$870$	−0.700448	−	2.59569i	−0.0237474	−	0.0880023i
$871$	4.38615	+	7.59704i	0.148619	+	0.257416i
$872$	2.14237	+	16.6719i	0.0725498	+	0.564582i
$873$	−3.55273	−	12.9675i	−0.120242	−	0.438883i
$874$	6.83304	+	16.5447i	0.231131	+	0.559633i
$875$	−12.1382	+	4.03878i	−0.410346	+	0.136536i
$876$	36.1601	−	15.0094i	1.22174	−	0.507119i
$877$	32.6044	−	8.73633i	1.10097	−	0.295005i	0.337812	−	0.941214i	$-0.390313\pi$
$877$	32.6044	−	8.73633i	1.10097	−	0.295005i	0.763161	+	0.646209i	$0.223646\pi$
$878$	30.2899	−	3.95592i	1.02223	−	0.133506i
$879$	−7.23200	+	9.47988i	−0.243929	+	0.319748i
$880$	−2.57310	−	1.49978i	−0.0867390	−	0.0505577i
$881$	13.3633			0.450221			0.225110	−	0.974333i	$-0.427726\pi$
$881$	13.3633			0.450221			0.225110	+	0.974333i	$0.427726\pi$
$882$	0.222704	−	29.6976i	0.00749884	−	0.999972i
$883$	−14.4528	−	14.4528i	−0.486374	−	0.486374i	0.420786	−	0.907160i	$-0.361754\pi$
$883$	−14.4528	−	14.4528i	−0.486374	−	0.486374i	−0.907160	+	0.420786i	$0.861754\pi$
$884$	2.20134	−	3.79471i	0.0740390	−	0.127630i
$885$	−1.51467	−	11.2609i	−0.0509152	−	0.378530i
$886$	−16.1625	−	12.4285i	−0.542989	−	0.417542i
$887$	−0.640290	−	0.369671i	−0.0214988	−	0.0124124i	0.489212	−	0.872165i	$-0.337284\pi$
$887$	−0.640290	−	0.369671i	−0.0214988	−	0.0124124i	−0.510711	+	0.859753i	$0.670618\pi$
$888$	5.29261	+	5.29571i	0.177608	+	0.177712i
$889$	−16.0065	+	31.9698i	−0.536839	+	1.07223i
$890$	−6.97012	+	2.87869i	−0.233639	+	0.0964939i
$891$	−3.64525	−	13.0181i	−0.122120	−	0.436123i
$892$	33.2217	+	8.97531i	1.11234	+	0.300516i
$893$	−34.1875	−	9.16051i	−1.14404	−	0.306545i
$894$	−38.5136	−	22.1449i	−1.28809	−	0.740637i
$895$			3.02313i			0.101052i
$896$	−16.9588	+	24.6658i	−0.566553	+	0.824025i
$897$	−2.08457	−	4.99292i	−0.0696016	−	0.166709i
$898$	19.4383	−	14.8837i	0.648664	−	0.496674i
$899$	0.563646	−	2.10355i	0.0187986	−	0.0701575i
$900$	14.3504	+	24.6533i	0.478346	+	0.821777i
$901$	5.36876	−	1.43856i	0.178859	−	0.0479252i
$902$	−2.33377	−	5.65071i	−0.0777060	−	0.188148i
$903$	14.8169	+	30.2922i	0.493075	+	1.00806i
$904$	8.87919	+	21.6255i	0.295318	+	0.719255i
$905$	−1.46683	+	2.54063i	−0.0487592	+	0.0844534i
$906$	−30.1279	−	8.01553i	−1.00093	−	0.266298i
$907$	−9.96471	−	2.67004i	−0.330873	−	0.0886571i	0.0895583	−	0.995982i	$-0.471454\pi$
$907$	−9.96471	−	2.67004i	−0.330873	−	0.0886571i	−0.420431	+	0.907324i	$0.638121\pi$
$908$	−31.5763	−	18.3177i	−1.04790	−	0.607893i
$909$	−1.10361	+	0.00619250i	−0.0366044	+	0.000205392i
$910$	−1.20647	−	0.419078i	−0.0399940	−	0.0138923i
$911$		−	12.3633i		−	0.409613i	−0.978802	−	0.204807i	$-0.934343\pi$
$911$		−	12.3633i		−	0.409613i	0.978802	−	0.204807i	$-0.0656566\pi$
$912$	2.54862	−	19.1624i	0.0843932	−	0.634530i
$913$	9.10225	−	5.25519i	0.301240	−	0.173921i
$914$	−0.661564	−	5.06549i	−0.0218826	−	0.167552i
$915$	8.20011	−	6.32879i	0.271087	−	0.209223i
$916$	−0.0272941	+	13.2141i	−0.000901821	+	0.436608i
$917$	6.53719	−	31.8580i	0.215877	−	1.05205i
$918$	−0.172836	−	23.4069i	−0.00570445	−	0.772542i
$919$	21.4978	+	12.4118i	0.709147	+	0.409426i	0.810745	−	0.585399i	$-0.199062\pi$
$919$	21.4978	+	12.4118i	0.709147	+	0.409426i	−0.101598	+	0.994826i	$0.532396\pi$
$920$	−6.30820	+	0.810615i	−0.207975	+	0.0267252i
$921$	10.1608	−	13.3190i	0.334810	−	0.438877i
$922$	−2.89232	+	21.7954i	−0.0952534	+	0.717792i
$923$	5.51290	−	5.51290i	0.181459	−	0.181459i
$924$	−10.3985	+	9.02217i	−0.342084	+	0.296808i
$925$	−5.13780	−	5.13780i	−0.168930	−	0.168930i
$926$	−7.12612	−	9.30682i	−0.234179	−	0.305841i
$927$	−4.67342	+	17.8413i	−0.153495	+	0.585984i
$928$	9.89790	+	7.67645i	0.324914	+	0.251992i
$929$	20.1109	−	34.8331i	0.659818	−	1.14284i	−0.320845	−	0.947132i	$-0.603967\pi$
$929$	20.1109	−	34.8331i	0.659818	−	1.14284i	0.980663	−	0.195706i	$-0.0626999\pi$
$930$	−0.00211699	−	1.19416i	−6.94189e−5	−	0.0391581i
$931$	12.0763	−	15.3506i	0.395784	−	0.503096i
$932$	3.49980	+	3.51428i	0.114640	+	0.115114i
$933$	31.7968	−	24.5406i	1.04098	−	0.803422i
$934$	2.52574	+	1.94222i	0.0826448	+	0.0635513i
$935$	−1.18586	−	2.05397i	−0.0387819	−	0.0671722i
$936$	−0.748121	+	5.79503i	−0.0244531	+	0.189416i
$937$	34.7658			1.13575			0.567875	−	0.823115i	$-0.307766\pi$
$937$	34.7658			1.13575			0.567875	+	0.823115i	$0.307766\pi$
$938$	3.45369	−	47.5397i	0.112767	−	1.55223i
$939$	0.733520	−	1.78502i	0.0239375	−	0.0582520i
$940$	6.31025	−	10.8777i	0.205818	−	0.354792i
$941$	−6.62185	+	24.7131i	−0.215866	+	0.805623i	0.769994	+	0.638051i	$0.220259\pi$
$941$	−6.62185	+	24.7131i	−0.215866	+	0.805623i	−0.985860	+	0.167572i	$0.946407\pi$
$942$	−15.6940	−	27.0718i	−0.511337	−	0.882047i
$943$	−11.3065	−	6.52782i	−0.368191	−	0.212575i
$944$	37.2768	+	37.5860i	1.21326	+	1.22332i
$945$	−6.68048	+	1.34535i	−0.217316	+	0.0437643i
$946$	5.99698	−	14.4358i	0.194979	−	0.469348i
$947$	−0.116078	−	0.433210i	−0.00377203	−	0.0140774i	0.964014	−	0.265851i	$-0.0856529\pi$
$947$	−0.116078	−	0.433210i	−0.00377203	−	0.0140774i	−0.967786	+	0.251773i	$0.918986\pi$
$948$	−19.6976	−	15.0914i	−0.639749	−	0.490145i
$949$	−7.51759	−	2.01433i	−0.244031	−	0.0653880i
$950$	−2.46790	+	18.5972i	−0.0800694	+	0.603372i
$951$	−14.9398	−	35.7835i	−0.484455	−	1.16036i
$952$	−21.4742	+	10.3471i	−0.695984	+	0.335351i
$953$	43.7385			1.41683			0.708414	−	0.705797i	$-0.249411\pi$
$953$	43.7385			1.41683			0.708414	+	0.705797i	$0.249411\pi$
$954$	−5.85251	+	4.53351i	−0.189482	+	0.146778i
$955$	−1.69602	+	6.32964i	−0.0548820	+	0.204822i
$956$	38.4593	+	10.3903i	1.24386	+	0.336047i
$957$	3.51981	+	4.56055i	0.113779	+	0.147422i
$958$	3.83333	−	9.22751i	0.123849	−	0.298127i
$959$	−31.1383	+	1.85214i	−1.00551	+	0.0598088i
$960$	6.33669	+	2.64995i	0.204516	+	0.0855269i
$961$	−15.0164	+	26.0091i	−0.484399	+	0.839003i
$962$	−0.192742	−	1.47580i	−0.00621426	−	0.0475816i
$963$	−47.7000	+	27.8976i	−1.53711	+	0.898988i
$964$	−4.34567	−	16.3533i	−0.139965	−	0.526704i
$965$	−6.98802	+	6.98802i	−0.224952	+	0.224952i
$966$	−5.85840	+	28.8093i	−0.188491	+	0.926925i
$967$			14.8702i			0.478194i	0.970996	+	0.239097i	$0.0768515\pi$
$967$			14.8702i			0.478194i	−0.970996	+	0.239097i	$0.923149\pi$
$968$	−24.5093	−	3.30399i	−0.787758	−	0.106194i
$969$	9.33706	−	12.2392i	0.299950	−	0.393181i
$970$	2.49056	+	1.91517i	0.0799672	+	0.0614923i
$971$	−1.54033	−	5.74858i	−0.0494314	−	0.184481i	0.936796	−	0.349877i	$-0.113776\pi$
$971$	−1.54033	−	5.74858i	−0.0494314	−	0.184481i	−0.986227	+	0.165396i	$0.947110\pi$
$972$	12.2746	+	28.6589i	0.393707	+	0.919236i
$973$	9.17910	−	3.05419i	0.294268	−	0.0979130i
$974$	−29.5486	−	12.2752i	−0.946799	−	0.393323i
$975$	0.724379	−	5.62409i	0.0231987	−	0.180115i
$976$	−12.6829	+	46.5628i	−0.405968	+	1.49044i
$977$	−32.2106	+	18.5968i	−1.03051	+	0.594964i	−0.917130	−	0.398588i	$-0.869500\pi$
$977$	−32.2106	+	18.5968i	−1.03051	+	0.594964i	−0.113378	+	0.993552i	$0.536167\pi$
$978$	21.7920	+	12.5302i	0.696831	+	0.400670i
$979$	11.4261	−	11.4261i	0.365178	−	0.365178i
$980$	4.14631	+	5.56479i	0.132449	+	0.177761i
$981$	−0.100037	−	17.8283i	−0.00319395	−	0.569215i
$982$	−6.68776	+	50.3963i	−0.213415	+	1.60821i
$983$	21.4615	−	12.3908i	0.684515	−	0.395205i	−0.117039	−	0.993127i	$-0.537340\pi$
$983$	21.4615	−	12.3908i	0.684515	−	0.395205i	0.801554	+	0.597923i	$0.204007\pi$
$984$	7.04606	+	12.2124i	0.224620	+	0.389317i
$985$	2.93399	−	5.08182i	0.0934847	−	0.161920i
$986$	3.80768	+	9.21946i	0.121261	+	0.293608i
$987$	−38.1859	−	43.8277i	−1.21547	−	1.39505i
$988$	−2.72286	+	2.71163i	−0.0866257	+	0.0862686i
$989$	−8.63979	−	32.2441i	−0.274729	−	1.02530i
$990$	2.51494	+	1.91155i	0.0799300	+	0.0607531i
$991$	−2.66875	−	4.62241i	−0.0847757	−	0.146836i	0.820520	−	0.571618i	$-0.193684\pi$
$991$	−2.66875	−	4.62241i	−0.0847757	−	0.146836i	−0.905296	+	0.424782i	$0.860351\pi$
$992$	3.36405	+	4.43131i	0.106809	+	0.140694i
$993$	−17.8708	−	42.8038i	−0.567112	−	1.35834i
$994$	−41.6058	+	7.97049i	−1.31966	+	0.252809i
$995$	−5.73951	+	5.73951i	−0.181955	+	0.181955i
$996$	−19.2191	+	14.7699i	−0.608979	+	0.468003i
$997$	−12.2891	+	45.8634i	−0.389199	+	1.45251i	0.442242	+	0.896896i	$0.354183\pi$
$997$	−12.2891	+	45.8634i	−0.389199	+	1.45251i	−0.831441	+	0.555613i	$0.812484\pi$
$998$	−15.2177	−	11.7019i	−0.481707	−	0.370418i
$999$	−4.88717	−	6.25930i	−0.154623	−	0.198035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.173.44	yes	240
3.2	odd	2	inner	336.2.bo.a.173.17	yes	240
7.3	odd	6	inner	336.2.bo.a.269.4	yes	240
16.5	even	4	inner	336.2.bo.a.5.57	yes	240
21.17	even	6	inner	336.2.bo.a.269.57	yes	240
48.5	odd	4	inner	336.2.bo.a.5.4	✓	240
112.101	odd	12	inner	336.2.bo.a.101.17	yes	240
336.101	even	12	inner	336.2.bo.a.101.44	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.4	✓	240	48.5	odd	4	inner
336.2.bo.a.5.57	yes	240	16.5	even	4	inner
336.2.bo.a.101.17	yes	240	112.101	odd	12	inner
336.2.bo.a.101.44	yes	240	336.101	even	12	inner
336.2.bo.a.173.17	yes	240	3.2	odd	2	inner
336.2.bo.a.173.44	yes	240	1.1	even	1	trivial
336.2.bo.a.269.4	yes	240	7.3	odd	6	inner
336.2.bo.a.269.57	yes	240	21.17	even	6	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.859759 + 1.12286i) q^{2} +(1.71659 - 0.230895i) q^{3} +(-0.521627 + 1.93078i) q^{4} +(0.128294 + 0.478799i) q^{5} +(1.73512 + 1.72898i) q^{6} +(-1.18449 + 2.36579i) q^{7} +(-2.61647 + 1.07429i) q^{8} +(2.89338 - 0.792704i) q^{9} +O(q^{10})\)	\(q+(0.859759 + 1.12286i) q^{2} +(1.71659 - 0.230895i) q^{3} +(-0.521627 + 1.93078i) q^{4} +(0.128294 + 0.478799i) q^{5} +(1.73512 + 1.72898i) q^{6} +(-1.18449 + 2.36579i) q^{7} +(-2.61647 + 1.07429i) q^{8} +(2.89338 - 0.792704i) q^{9} +(-0.427322 + 0.555708i) q^{10} +(0.388770 - 1.45091i) q^{11} +(-0.449614 + 3.43480i) q^{12} +(0.486926 - 0.486926i) q^{13} +(-3.67483 + 0.703993i) q^{14} +(0.330780 + 0.792280i) q^{15} +(-3.45581 - 2.01429i) q^{16} +(-1.59268 - 2.75860i) q^{17} +(3.37770 + 2.56732i) q^{18} +(0.722159 + 2.69513i) q^{19} +(-0.991377 - 0.00204771i) q^{20} +(-1.48704 + 4.33459i) q^{21} +(1.96342 - 0.810899i) q^{22} +(2.26818 - 3.92860i) q^{23} +(-4.24336 + 2.44825i) q^{24} +(4.11734 - 2.37715i) q^{25} +(0.965390 + 0.128110i) q^{26} +(4.78371 - 2.02882i) q^{27} +(-3.94996 - 3.52106i) q^{28} +(-1.56573 + 1.56573i) q^{29} +(-0.605228 + 1.05259i) q^{30} +(-0.851744 + 0.491755i) q^{31} +(-0.709397 - 5.61220i) q^{32} +(0.332352 - 2.58038i) q^{33} +(1.72820 - 4.16009i) q^{34} +(-1.28470 - 0.263618i) q^{35} +(0.0212733 + 5.99996i) q^{36} +(-0.395551 - 1.47622i) q^{37} +(-2.40537 + 3.12805i) q^{38} +(0.723425 - 0.948283i) q^{39} +(-0.850046 - 1.11494i) q^{40} -2.87800i q^{41} +(-6.14564 + 2.05697i) q^{42} +(5.20338 - 5.20338i) q^{43} +(2.59859 + 1.50746i) q^{44} +(0.750749 + 1.28365i) q^{45} +(6.36135 - 0.830805i) q^{46} +(-6.34245 + 10.9854i) q^{47} +(-6.39731 - 2.65979i) q^{48} +(-4.19395 - 5.60453i) q^{49} +(6.20912 + 2.57942i) q^{50} +(-3.37093 - 4.36765i) q^{51} +(0.686153 + 1.19414i) q^{52} +(-0.451615 + 1.68545i) q^{53} +(6.39092 + 3.62714i) q^{54} +0.744571 q^{55} +(0.557639 - 7.46251i) q^{56} +(1.86194 + 4.45970i) q^{57} +(-3.10424 - 0.411943i) q^{58} +(-12.7832 - 3.42524i) q^{59} +(-1.70226 + 0.225389i) q^{60} +(-3.12260 - 11.6537i) q^{61} +(-1.28447 - 0.533599i) q^{62} +(-1.55181 + 7.78408i) q^{63} +(5.69180 - 5.62169i) q^{64} +(0.295610 + 0.170670i) q^{65} +(3.18315 - 1.84532i) q^{66} +(-3.29710 + 12.3049i) q^{67} +(6.15703 - 1.63615i) q^{68} +(2.98644 - 7.26751i) q^{69} +(-0.808530 - 1.66919i) q^{70} +11.3218 q^{71} +(-6.71883 + 5.18241i) q^{72} +(-5.65102 - 9.78785i) q^{73} +(1.31750 - 1.71334i) q^{74} +(6.51892 - 5.03126i) q^{75} +(-5.58040 - 0.0115264i) q^{76} +(2.97205 + 2.63834i) q^{77} +(1.68676 - 0.00299026i) q^{78} +(-3.58163 + 6.20356i) q^{79} +(0.521083 - 1.91306i) q^{80} +(7.74324 - 4.58718i) q^{81} +(3.23159 - 2.47439i) q^{82} +(4.94774 + 4.94774i) q^{83} +(-7.59346 - 5.13219i) q^{84} +(1.11649 - 1.11649i) q^{85} +(10.3163 + 1.36901i) q^{86} +(-2.32620 + 3.04923i) q^{87} +(0.541495 + 4.21391i) q^{88} +(9.31634 + 5.37879i) q^{89} +(-0.795892 + 1.94661i) q^{90} +(0.575206 + 1.72873i) q^{91} +(6.40211 + 6.42861i) q^{92} +(-1.34855 + 1.04081i) q^{93} +(-17.7881 + 2.32316i) q^{94} +(-1.19778 + 0.691538i) q^{95} +(-2.51357 - 9.47006i) q^{96} -4.48178i q^{97} +(2.68731 - 9.52777i) q^{98} +(-0.0252849 - 4.50620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

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