LMFDB - Embedded newform 525.2.bv.a.52.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(52,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(60))

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

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

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

chi := DirichletCharacter("525.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bv (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$40$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			52.19
Character	$\chi$	$=$	525.52
Dual form			525.2.bv.a.313.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0754782 - 0.196628i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(1.45332 - 1.30858i) q^{4} +(-2.18626 + 0.469349i) q^{5} +(0.200308 - 0.0650841i) q^{6} +(-2.39330 + 1.12789i) q^{7} +(-0.742319 - 0.378230i) q^{8} +(-0.994522 - 0.104528i) q^{9} +O(q^{10})$	\(q+(-0.0754782 - 0.196628i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(1.45332 - 1.30858i) q^{4} +(-2.18626 + 0.469349i) q^{5} +(0.200308 - 0.0650841i) q^{6} +(-2.39330 + 1.12789i) q^{7} +(-0.742319 - 0.378230i) q^{8} +(-0.994522 - 0.104528i) q^{9} +(0.257302 + 0.394452i) q^{10} +(-0.565768 - 5.38292i) q^{11} +(1.23072 + 1.51982i) q^{12} +(-0.378499 - 2.38975i) q^{13} +(0.402416 + 0.385457i) q^{14} +(-0.354286 - 2.20782i) q^{15} +(0.390499 - 3.71535i) q^{16} +(1.31345 - 0.852963i) q^{17} +(0.0545116 + 0.203440i) q^{18} +(5.69560 - 6.32561i) q^{19} +(-2.56316 + 3.54300i) q^{20} +(-1.00109 - 2.44905i) q^{21} +(-1.01573 + 0.517539i) q^{22} +(-0.862997 + 0.331273i) q^{23} +(0.416562 - 0.721506i) q^{24} +(4.55942 - 2.05223i) q^{25} +(-0.441322 + 0.254797i) q^{26} +(0.156434 - 0.987688i) q^{27} +(-2.00231 + 4.77100i) q^{28} +(-8.61030 - 2.79766i) q^{29} +(-0.407378 + 0.236305i) q^{30} +(-1.91043 + 8.98786i) q^{31} +(-2.36949 + 0.634902i) q^{32} +(5.40515 - 0.283272i) q^{33} +(-0.266853 - 0.193880i) q^{34} +(4.70299 - 3.58914i) q^{35} +(-1.58215 + 1.14950i) q^{36} +(4.99509 - 4.04495i) q^{37} +(-1.67368 - 0.642467i) q^{38} +(2.40628 - 0.252911i) q^{39} +(1.80042 + 0.478501i) q^{40} +(-2.50266 + 3.44461i) q^{41} +(-0.405990 + 0.381691i) q^{42} +(-4.70882 + 4.70882i) q^{43} +(-7.86622 - 7.08277i) q^{44} +(2.22334 - 0.238252i) q^{45} +(0.130275 + 0.144685i) q^{46} +(-0.296606 + 0.456733i) q^{47} +(3.68982 + 0.584410i) q^{48} +(4.45574 - 5.39874i) q^{49} +(-0.747663 - 0.741609i) q^{50} +(0.783054 + 1.35629i) q^{51} +(-3.67726 - 2.97778i) q^{52} +(-5.62771 - 0.294936i) q^{53} +(-0.206014 + 0.0437897i) q^{54} +(3.76338 + 11.5029i) q^{55} +(2.20319 + 0.0679659i) q^{56} +(6.01886 + 6.01886i) q^{57} +(0.0997941 + 1.90418i) q^{58} +(3.74493 - 1.66735i) q^{59} +(-3.40400 - 2.74507i) q^{60} +(0.0510287 - 0.114612i) q^{61} +(1.91146 - 0.302745i) q^{62} +(2.49808 - 0.871541i) q^{63} +(-4.08803 - 5.62669i) q^{64} +(1.94912 + 5.04695i) q^{65} +(-0.463670 - 1.04142i) q^{66} +(-5.55948 - 8.56085i) q^{67} +(0.792696 - 2.95838i) q^{68} +(-0.285654 - 0.879152i) q^{69} +(-1.06070 - 0.653835i) q^{70} +(0.211147 - 0.649843i) q^{71} +(0.698716 + 0.453752i) q^{72} +(1.85222 - 2.28730i) q^{73} +(-1.17237 - 0.676867i) q^{74} +(1.81080 + 4.66058i) q^{75} -16.6463i q^{76} +(7.42537 + 12.2448i) q^{77} +(-0.231351 - 0.454052i) q^{78} +(-0.616872 - 2.90215i) q^{79} +(0.890064 + 8.30598i) q^{80} +(0.978148 + 0.207912i) q^{81} +(0.866201 + 0.232098i) q^{82} +(-4.20039 + 8.24373i) q^{83} +(-4.65967 - 2.24926i) q^{84} +(-2.47120 + 2.48126i) q^{85} +(1.28130 + 0.570470i) q^{86} +(3.24445 - 8.45208i) q^{87} +(-1.61600 + 4.20983i) q^{88} +(5.43126 + 2.41815i) q^{89} +(-0.214661 - 0.419187i) q^{90} +(3.60123 + 5.29248i) q^{91} +(-0.820717 + 1.61075i) q^{92} +(-8.87556 - 2.37820i) q^{93} +(0.112194 + 0.0238475i) q^{94} +(-9.48313 + 16.5026i) q^{95} +(-0.510022 - 2.39947i) q^{96} +(5.93595 + 11.6500i) q^{97} +(-1.39785 - 0.468635i) q^{98} +5.41257i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8	$ 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + 12 q^{10} + 8 q^{15} - 80 q^{16} - 72 q^{22} + 48 q^{23} - 12 q^{25} - 36 q^{28} - 80 q^{29} + 32 q^{30} - 24 q^{32} + 36 q^{33} - 64 q^{35} + 160 q^{36} - 4 q^{37} - 192 q^{38} - 12 q^{40} - 16 q^{42} + 120 q^{43} + 60 q^{47} + 288 q^{50} - 432 q^{52} - 136 q^{53} - 16 q^{57} - 4 q^{58} - 240 q^{59} - 20 q^{60} - 4 q^{63} + 120 q^{64} + 4 q^{65} - 8 q^{67} - 132 q^{68} + 76 q^{70} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 60 q^{77} - 80 q^{78} + 12 q^{80} - 80 q^{81} - 252 q^{82} - 160 q^{84} + 72 q^{85} + 24 q^{87} + 152 q^{88} + 56 q^{92} - 96 q^{93} + 172 q^{95} - 488 q^{98}+O(q^{100}) $ 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8 + 12 * q^10 + 8 * q^15 - 80 * q^16 - 72 * q^22 + 48 * q^23 - 12 * q^25 - 36 * q^28 - 80 * q^29 + 32 * q^30 - 24 * q^32 + 36 * q^33 - 64 * q^35 + 160 * q^36 - 4 * q^37 - 192 * q^38 - 12 * q^40 - 16 * q^42 + 120 * q^43 + 60 * q^47 + 288 * q^50 - 432 * q^52 - 136 * q^53 - 16 * q^57 - 4 * q^58 - 240 * q^59 - 20 * q^60 - 4 * q^63 + 120 * q^64 + 4 * q^65 - 8 * q^67 - 132 * q^68 + 76 * q^70 - 12 * q^72 - 36 * q^73 - 48 * q^75 - 60 * q^77 - 80 * q^78 + 12 * q^80 - 80 * q^81 - 252 * q^82 - 160 * q^84 + 72 * q^85 + 24 * q^87 + 152 * q^88 + 56 * q^92 - 96 * q^93 + 172 * q^95 - 488 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.0754782	−	0.196628i	−0.0533712	−	0.139037i	0.904303	−	0.426891i	$-0.140391\pi$
$2$	−0.0754782	−	0.196628i	−0.0533712	−	0.139037i	−0.957674	+	0.287855i	$0.907058\pi$
$3$	−0.0523360	+	0.998630i	−0.0302162	+	0.576559i
$3$	−0.0523360	+	0.998630i	−0.0302162	+	0.576559i
$4$	1.45332	−	1.30858i	0.726662	−	0.654290i
$5$	−2.18626	+	0.469349i	−0.977723	+	0.209899i
$5$	−2.18626	+	0.469349i	−0.977723	+	0.209899i
$6$	0.200308	−	0.0650841i	0.0817755	−	0.0265705i
$7$	−2.39330	+	1.12789i	−0.904581	+	0.426301i
$7$	−2.39330	+	1.12789i	−0.904581	+	0.426301i
$8$	−0.742319	−	0.378230i	−0.262449	−	0.133725i
$9$	−0.994522	−	0.104528i	−0.331507	−	0.0348428i
$10$	0.257302	+	0.394452i	0.0813659	+	0.124737i
$11$	−0.565768	−	5.38292i	−0.170585	−	1.62301i	−0.660212	−	0.751079i	$-0.729534\pi$
$11$	−0.565768	−	5.38292i	−0.170585	−	1.62301i	0.489627	−	0.871932i	$-0.337133\pi$
$12$	1.23072	+	1.51982i	0.355280	+	0.438734i
$13$	−0.378499	−	2.38975i	−0.104977	−	0.662797i	−0.982920	−	0.184033i	$-0.941085\pi$
$13$	−0.378499	−	2.38975i	−0.104977	−	0.662797i	0.877943	−	0.478765i	$-0.158915\pi$
$14$	0.402416	+	0.385457i	0.107550	+	0.103018i
$15$	−0.354286	−	2.20782i	−0.0914762	−	0.570057i
$16$	0.390499	−	3.71535i	0.0976247	−	0.928837i
$17$	1.31345	−	0.852963i	0.318558	−	0.206874i	−0.375448	−	0.926844i	$-0.622511\pi$
$17$	1.31345	−	0.852963i	0.318558	−	0.206874i	0.694006	+	0.719970i	$0.255844\pi$
$18$	0.0545116	+	0.203440i	0.0128485	+	0.0479513i
$19$	5.69560	−	6.32561i	1.30666	−	1.45119i	0.492791	−	0.870148i	$-0.335977\pi$
$19$	5.69560	−	6.32561i	1.30666	−	1.45119i	0.813870	−	0.581047i	$-0.197357\pi$
$20$	−2.56316	+	3.54300i	−0.573139	+	0.792240i
$21$	−1.00109	−	2.44905i	−0.218455	−	0.534426i
$22$	−1.01573	+	0.517539i	−0.216554	+	0.110340i
$23$	−0.862997	+	0.331273i	−0.179947	+	0.0690753i	−0.446673	−	0.894697i	$-0.647391\pi$
$23$	−0.862997	+	0.331273i	−0.179947	+	0.0690753i	0.266726	+	0.963772i	$0.414058\pi$
$24$	0.416562	−	0.721506i	0.0850303	−	0.147277i
$25$	4.55942	−	2.05223i	0.911885	−	0.410446i
$26$	−0.441322	+	0.254797i	−0.0865504	+	0.0499699i
$27$	0.156434	−	0.987688i	0.0301058	−	0.190081i
$28$	−2.00231	+	4.77100i	−0.378401	+	0.901635i
$29$	−8.61030	−	2.79766i	−1.59889	−	0.519512i	−0.632060	−	0.774920i	$-0.717790\pi$
$29$	−8.61030	−	2.79766i	−1.59889	−	0.519512i	−0.966833	+	0.255408i	$0.917790\pi$
$30$	−0.407378	+	0.236305i	−0.0743767	+	0.0431432i
$31$	−1.91043	+	8.98786i	−0.343123	+	1.61427i	0.380986	+	0.924581i	$0.375585\pi$
$31$	−1.91043	+	8.98786i	−0.343123	+	1.61427i	−0.724109	+	0.689686i	$0.757749\pi$
$32$	−2.36949	+	0.634902i	−0.418870	+	0.112236i
$33$	5.40515	−	0.283272i	0.940916	−	0.0493113i
$34$	−0.266853	−	0.193880i	−0.0457649	−	0.0332501i
$35$	4.70299	−	3.58914i	0.794950	−	0.606675i
$36$	−1.58215	+	1.14950i	−0.263691	+	0.191583i
$37$	4.99509	−	4.04495i	0.821188	−	0.664985i	−0.123721	−	0.992317i	$-0.539483\pi$
$37$	4.99509	−	4.04495i	0.821188	−	0.664985i	0.944909	+	0.327332i	$0.106150\pi$
$38$	−1.67368	−	0.642467i	−0.271507	−	0.104222i
$39$	2.40628	−	0.252911i	0.385314	−	0.0404981i
$40$	1.80042	+	0.478501i	0.284671	+	0.0756577i
$41$	−2.50266	+	3.44461i	−0.390849	+	0.537958i	−0.958418	−	0.285368i	$-0.907884\pi$
$41$	−2.50266	+	3.44461i	−0.390849	+	0.537958i	0.567569	+	0.823326i	$0.307884\pi$
$42$	−0.405990	+	0.381691i	−0.0626456	+	0.0588962i
$43$	−4.70882	+	4.70882i	−0.718088	+	0.718088i	−0.968214	−	0.250125i	$-0.919528\pi$
$43$	−4.70882	+	4.70882i	−0.718088	+	0.718088i	0.250125	+	0.968214i	$0.419528\pi$
$44$	−7.86622	−	7.08277i	−1.18588	−	1.06777i
$45$	2.22334	−	0.238252i	0.331436	−	0.0355165i
$46$	0.130275	+	0.144685i	0.0192080	+	0.0213326i
$47$	−0.296606	+	0.456733i	−0.0432644	+	0.0666214i	−0.859641	−	0.510899i	$-0.829313\pi$
$47$	−0.296606	+	0.456733i	−0.0432644	+	0.0666214i	0.816377	+	0.577520i	$0.195979\pi$
$48$	3.68982	+	0.584410i	0.532579	+	0.0843523i
$49$	4.45574	−	5.39874i	0.636535	−	0.771248i
$50$	−0.747663	−	0.741609i	−0.105735	−	0.104879i
$51$	0.783054	+	1.35629i	0.109649	+	0.189918i
$52$	−3.67726	−	2.97778i	−0.509944	−	0.412944i
$53$	−5.62771	−	0.294936i	−0.773025	−	0.0405125i	−0.338256	−	0.941054i	$-0.609837\pi$
$53$	−5.62771	−	0.294936i	−0.773025	−	0.0405125i	−0.434769	+	0.900542i	$0.643170\pi$
$54$	−0.206014	+	0.0437897i	−0.0280350	+	0.00595902i
$55$	3.76338	+	11.5029i	0.507454	+	1.55105i
$56$	2.20319	+	0.0679659i	0.294414	+	0.00908232i
$57$	6.01886	+	6.01886i	0.797217	+	0.797217i
$58$	0.0997941	+	1.90418i	0.0131036	+	0.250032i
$59$	3.74493	−	1.66735i	0.487549	−	0.217071i	−0.148214	−	0.988955i	$-0.547352\pi$
$59$	3.74493	−	1.66735i	0.487549	−	0.217071i	0.635763	+	0.771885i	$0.280686\pi$
$60$	−3.40400	−	2.74507i	−0.439455	−	0.354387i
$61$	0.0510287	−	0.114612i	0.00653355	−	0.0146746i	−0.910249	−	0.414061i	$-0.864110\pi$
$61$	0.0510287	−	0.114612i	0.00653355	−	0.0146746i	0.916783	+	0.399386i	$0.130777\pi$
$62$	1.91146	−	0.302745i	0.242755	−	0.0384486i
$63$	2.49808	−	0.871541i	0.314729	−	0.109804i
$64$	−4.08803	−	5.62669i	−0.511003	−	0.703336i
$65$	1.94912	+	5.04695i	0.241759	+	0.625998i
$66$	−0.463670	−	1.04142i	−0.0570739	−	0.128190i
$67$	−5.55948	−	8.56085i	−0.679199	−	1.04587i	−0.995271	−	0.0971391i	$-0.969031\pi$
$67$	−5.55948	−	8.56085i	−0.679199	−	1.04587i	0.316072	−	0.948735i	$-0.397636\pi$
$68$	0.792696	−	2.95838i	0.0961285	−	0.358757i
$69$	−0.285654	−	0.879152i	−0.0343887	−	0.105837i
$70$	−1.06070	−	0.653835i	−0.126778	−	0.0781482i
$71$	0.211147	−	0.649843i	0.0250585	−	0.0771222i	−0.937745	−	0.347324i	$-0.887090\pi$
$71$	0.211147	−	0.649843i	0.0250585	−	0.0771222i	0.962804	+	0.270202i	$0.0870904\pi$
$72$	0.698716	+	0.453752i	0.0823445	+	0.0534751i
$73$	1.85222	−	2.28730i	0.216786	−	0.267709i	−0.657139	−	0.753770i	$-0.728233\pi$
$73$	1.85222	−	2.28730i	0.216786	−	0.267709i	0.873925	+	0.486061i	$0.161567\pi$
$74$	−1.17237	−	0.676867i	−0.136285	−	0.0786842i
$75$	1.81080	+	4.66058i	0.209093	+	0.538157i
$76$		−	16.6463i		−	1.90946i
$77$	7.42537	+	12.2448i	0.846200	+	1.39542i
$78$	−0.231351	−	0.454052i	−0.0261954	−	0.0514113i
$79$	−0.616872	−	2.90215i	−0.0694035	−	0.326518i	0.929725	−	0.368254i	$-0.120044\pi$
$79$	−0.616872	−	2.90215i	−0.0694035	−	0.326518i	−0.999129	+	0.0417364i	$0.986711\pi$
$80$	0.890064	+	8.30598i	0.0995121	+	0.928636i
$81$	0.978148	+	0.207912i	0.108683	+	0.0231013i
$82$	0.866201	+	0.232098i	0.0956559	+	0.0256309i
$83$	−4.20039	+	8.24373i	−0.461053	+	0.904867i	0.537065	+	0.843541i	$0.319533\pi$
$83$	−4.20039	+	8.24373i	−0.461053	+	0.904867i	−0.998118	+	0.0613259i	$0.980467\pi$
$84$	−4.65967	−	2.24926i	−0.508412	−	0.245414i
$85$	−2.47120	+	2.48126i	−0.268039	+	0.269130i
$86$	1.28130	+	0.570470i	0.138166	+	0.0615154i
$87$	3.24445	−	8.45208i	0.347842	−	0.906159i
$88$	−1.61600	+	4.20983i	−0.172266	+	0.448770i
$89$	5.43126	+	2.41815i	0.575712	+	0.256324i	0.673873	−	0.738847i	$-0.264629\pi$
$89$	5.43126	+	2.41815i	0.575712	+	0.256324i	−0.0981610	+	0.995171i	$0.531296\pi$
$90$	−0.214661	−	0.419187i	−0.0226272	−	0.0441862i
$91$	3.60123	+	5.29248i	0.377511	+	0.554802i
$92$	−0.820717	+	1.61075i	−0.0855656	+	0.167932i
$93$	−8.87556	−	2.37820i	−0.920352	−	0.246608i
$94$	0.112194	+	0.0238475i	0.0115719	+	0.00245968i
$95$	−9.48313	+	16.5026i	−0.972948	+	1.69313i
$96$	−0.510022	−	2.39947i	−0.0520539	−	0.244894i
$97$	5.93595	+	11.6500i	0.602704	+	1.18287i	0.967757	+	0.251887i	$0.0810511\pi$
$97$	5.93595	+	11.6500i	0.602704	+	1.18287i	−0.365052	+	0.930987i	$0.618949\pi$
$98$	−1.39785	−	0.468635i	−0.141204	−	0.0473392i
$99$			5.41257i			0.543984i
$100$	3.94081	−	8.94892i	0.394081	−	0.894892i
$101$	−5.57526	−	3.21888i	−0.554759	−	0.320290i	0.196280	−	0.980548i	$-0.437114\pi$
$101$	−5.57526	−	3.21888i	−0.554759	−	0.320290i	−0.751039	+	0.660258i	$0.770447\pi$
$102$	0.207580	−	0.256340i	0.0205535	−	0.0253815i
$103$	−11.8983	−	7.72687i	−1.17238	−	0.761352i	−0.196680	−	0.980468i	$-0.563016\pi$
$103$	−11.8983	−	7.72687i	−1.17238	−	0.761352i	−0.975699	+	0.219116i	$0.929683\pi$
$104$	−0.622909	+	1.91712i	−0.0610812	+	0.187989i
$105$	3.33809	+	4.88438i	0.325764	+	0.476667i
$106$	0.366777	+	1.12882i	0.0356245	+	0.109641i
$107$	4.73891	−	17.6858i	0.458127	−	1.70975i	−0.220600	−	0.975364i	$-0.570801\pi$
$107$	4.73891	−	17.6858i	0.458127	−	1.70975i	0.678727	−	0.734390i	$-0.262532\pi$
$108$	−1.06512	−	1.64014i	−0.102491	−	0.157822i
$109$	6.52338	+	14.6518i	0.624827	+	1.40338i	0.897387	+	0.441245i	$0.145463\pi$
$109$	6.52338	+	14.6518i	0.624827	+	1.40338i	−0.272560	+	0.962139i	$0.587870\pi$
$110$	1.97773	−	1.60820i	0.188569	−	0.153336i
$111$	3.77798	+	5.19994i	0.358590	+	0.493557i
$112$	3.25591	+	9.33237i	0.307655	+	0.881826i
$113$	12.4935	−	1.97878i	1.17529	−	0.186148i	0.461911	−	0.886926i	$-0.347164\pi$
$113$	12.4935	−	1.97878i	1.17529	−	0.186148i	0.713378	+	0.700779i	$0.247164\pi$
$114$	0.729180	−	1.63777i	0.0682940	−	0.153391i
$115$	1.73125	−	1.12929i	0.161440	−	0.105307i
$116$	−16.1745	+	7.20136i	−1.50177	+	0.668629i
$117$	0.126629	+	2.41622i	0.0117068	+	0.223380i
$118$	−0.610509	−	0.610509i	−0.0562019	−	0.0562019i
$119$	−2.18143	+	3.52281i	−0.199971	+	0.322936i
$120$	−0.572072	+	1.77291i	−0.0522228	+	0.161844i
$121$	−17.8961	+	3.80393i	−1.62692	+	0.345812i
$122$	−0.0263875	−	0.00138291i	−0.00238901	−	0.000125203i
$123$	−3.30891	−	2.67950i	−0.298354	−	0.241603i
$124$	8.98485	+	15.5622i	0.806863	+	1.39753i
$125$	−9.00485	+	6.62666i	−0.805418	+	0.592707i
$126$	−0.359920	−	0.425410i	−0.0320642	−	0.0378985i
$127$	4.15327	+	0.657813i	0.368543	+	0.0583715i	0.337959	−	0.941161i	$-0.390263\pi$
$127$	4.15327	+	0.657813i	0.368543	+	0.0583715i	0.0305837	+	0.999532i	$0.490263\pi$
$128$	−3.46988	+	5.34315i	−0.306697	+	0.472272i
$129$	−4.45593	−	4.94881i	−0.392322	−	0.435718i
$130$	0.845254	−	0.764186i	0.0741337	−	0.0670236i
$131$	0.653561	+	0.588469i	0.0571019	+	0.0514148i	0.697188	−	0.716889i	$-0.254434\pi$
$131$	0.653561	+	0.588469i	0.0571019	+	0.0514148i	−0.640086	+	0.768304i	$0.721101\pi$
$132$	7.48475	−	7.48475i	0.651464	−	0.651464i
$133$	−6.49670	+	21.5631i	−0.563336	+	1.86975i
$134$	−1.26368	+	1.73931i	−0.109165	+	0.150253i
$135$	0.121565	+	2.23276i	0.0104626	+	0.192165i
$136$	−1.29761	+	0.136385i	−0.111269	+	0.0116949i
$137$	19.6992	+	7.56181i	1.68302	+	0.646049i	0.996694	−	0.0812488i	$-0.0258908\pi$
$137$	19.6992	+	7.56181i	1.68302	+	0.646049i	0.686322	+	0.727298i	$0.259224\pi$
$138$	−0.151305	+	0.122524i	−0.0128799	+	0.0104300i
$139$	0.410343	−	0.298132i	0.0348049	−	0.0252872i	−0.570247	−	0.821473i	$-0.693152\pi$
$139$	0.410343	−	0.298132i	0.0348049	−	0.0252872i	0.605052	+	0.796186i	$0.293152\pi$
$140$	2.13829	−	11.3704i	0.180719	−	0.960975i
$141$	−0.440584	−	0.320103i	−0.0371039	−	0.0269576i
$142$	−0.143714	+	0.00753174i	−0.0120602	+	0.000632049i
$143$	−12.6497	+	3.38947i	−1.05782	+	0.283442i
$144$	−0.776719	+	3.65418i	−0.0647266	+	0.304515i
$145$	20.1374	+	2.07516i	1.67232	+	0.172332i
$146$	−0.589549	−	0.191556i	−0.0487915	−	0.0158533i
$147$	5.15814	+	4.73218i	0.425436	+	0.390304i
$148$	1.96636	−	12.4151i	0.161634	−	1.02051i
$149$	16.8616	−	9.73502i	1.38135	−	0.797524i	0.389032	−	0.921224i	$-0.372809\pi$
$149$	16.8616	−	9.73502i	1.38135	−	0.797524i	0.992320	+	0.123700i	$0.0394761\pi$
$150$	0.779723	−	0.707825i	0.0636641	−	0.0577937i
$151$	0.848691	−	1.46998i	0.0690655	−	0.119625i	−0.829425	−	0.558619i	$-0.811332\pi$
$151$	0.848691	−	1.46998i	0.0690655	−	0.119625i	0.898490	+	0.438994i	$0.144665\pi$
$152$	−6.62049	+	2.54137i	−0.536993	+	0.206132i
$153$	−1.39541	+	0.710998i	−0.112812	+	0.0574808i
$154$	1.84721	−	2.38425i	0.148853	−	0.192128i
$155$	−0.0417564	−	20.5464i	−0.00335395	−	1.65033i
$156$	3.16616	−	3.51637i	0.253495	−	0.281535i
$157$	−3.26886	−	12.1995i	−0.260883	−	0.973630i	−0.964722	−	0.263270i	$-0.915199\pi$
$157$	−3.26886	−	12.1995i	−0.260883	−	0.973630i	0.703839	−	0.710360i	$-0.251468\pi$
$158$	−0.524083	+	0.340343i	−0.0416938	+	0.0270763i
$159$	0.589063	−	5.60456i	0.0467157	−	0.444470i
$160$	4.88231	−	2.50017i	0.385980	−	0.197656i
$161$	1.69177	−	1.76620i	0.133330	−	0.139196i
$162$	−0.0329477	−	0.208024i	−0.00258862	−	0.0163439i
$163$	7.06448	+	8.72390i	0.553333	+	0.683309i	0.974684	−	0.223589i	$-0.0717773\pi$
$163$	7.06448	+	8.72390i	0.553333	+	0.683309i	−0.421351	+	0.906898i	$0.638444\pi$
$164$	0.870374	+	8.28106i	0.0679648	+	0.646642i
$165$	−11.6841	+	3.15621i	−0.909605	+	0.245710i
$166$	1.93798	+	0.203690i	0.150417	+	0.0158094i
$167$	6.34634	+	3.23362i	0.491095	+	0.250225i	0.681958	−	0.731391i	$-0.261129\pi$
$167$	6.34634	+	3.23362i	0.491095	+	0.250225i	−0.190863	+	0.981617i	$0.561129\pi$
$168$	−0.183179	+	2.19661i	−0.0141326	+	0.169472i
$169$	6.79609	−	2.20818i	0.522776	−	0.169860i
$170$	0.674406	+	0.298624i	0.0517246	+	0.0229034i
$171$	−6.32561	+	5.69560i	−0.483731	+	0.435554i
$172$	−0.681579	+	13.0053i	−0.0519699	+	0.991645i
$173$	3.83112	+	9.98040i	0.291274	+	0.758796i	0.998649	+	0.0519572i	$0.0165459\pi$
$173$	3.83112	+	9.98040i	0.291274	+	0.758796i	−0.707375	+	0.706839i	$0.750121\pi$
$174$	−1.90680			−0.144554
$175$	−8.59737	+	10.0541i	−0.649900	+	0.760020i
$176$	−20.2203			−1.52417
$177$	1.46907	+	3.82706i	0.110422	+	0.287660i
$178$	0.0655335	−	1.25045i	0.00491194	−	0.0937254i
$179$	4.11898	−	3.70875i	0.307867	−	0.277205i	−0.500685	−	0.865630i	$-0.666918\pi$
$179$	4.11898	−	3.70875i	0.307867	−	0.277205i	0.808552	+	0.588425i	$0.200252\pi$
$180$	2.91946	−	3.25567i	0.217604	−	0.242663i
$181$	7.12255	−	2.31426i	0.529415	−	0.172017i	−0.0320987	−	0.999485i	$-0.510219\pi$
$181$	7.12255	−	2.31426i	0.529415	−	0.172017i	0.561514	+	0.827467i	$0.310219\pi$
$182$	0.768832	−	1.10757i	0.0569896	−	0.0820984i
$183$	0.111785	+	0.0569571i	0.00826336	+	0.00421039i
$184$	0.765916	+	0.0805010i	0.0564641	+	0.00593462i
$185$	−9.02205	+	11.1877i	−0.663315	+	0.822538i
$186$	0.202292	+	1.92468i	0.0148328	+	0.141124i
$187$	−5.33454	−	6.58760i	−0.390100	−	0.481733i
$188$	0.166607	+	1.05191i	0.0121511	+	0.0767187i
$189$	0.739607	+	2.54027i	0.0537985	+	0.184778i
$190$	3.96064	+	0.619055i	0.287335	+	0.0449110i
$191$	1.47072	−	13.9929i	0.106417	−	1.01249i	−0.802821	−	0.596219i	$-0.796669\pi$
$191$	1.47072	−	13.9929i	0.106417	−	1.01249i	0.909239	−	0.416275i	$-0.136665\pi$
$192$	5.83292	−	3.78795i	0.420955	−	0.273371i
$193$	−0.0831508	−	0.310323i	−0.00598533	−	0.0223375i	0.962869	−	0.269971i	$-0.0870140\pi$
$193$	−0.0831508	−	0.310323i	−0.00598533	−	0.0223375i	−0.968854	+	0.247633i	$0.920347\pi$
$194$	1.84267	−	2.04649i	0.132296	−	0.146929i
$195$	−5.14205	+	1.68231i	−0.368230	+	0.120473i
$196$	−0.589035	−	13.6768i	−0.0420740	−	0.976915i
$197$	6.20099	−	3.15956i	0.441802	−	0.225109i	−0.218916	−	0.975744i	$-0.570252\pi$
$197$	6.20099	−	3.15956i	0.441802	−	0.225109i	0.660718	+	0.750634i	$0.270252\pi$
$198$	1.06426	−	0.408531i	0.0756337	−	0.0290331i
$199$	1.98770	−	3.44280i	0.140905	−	0.244054i	−0.786933	−	0.617038i	$-0.788332\pi$
$199$	1.98770	−	3.44280i	0.140905	−	0.244054i	0.927837	+	0.372985i	$0.121666\pi$
$200$	−4.16076	−	0.201102i	−0.294210	−	0.0142200i
$201$	8.84008	−	5.10382i	0.623531	−	0.359996i
$202$	−0.212109	+	1.33920i	−0.0149239	+	0.0942261i
$203$	23.7625	−	3.01582i	1.66780	−	0.211669i
$204$	2.91284	+	0.946440i	0.203940	+	0.0662640i
$205$	3.85472	−	8.70541i	0.269225	−	0.608013i
$206$	−0.621250	+	2.92275i	−0.0432846	+	0.203638i
$207$	0.892897	−	0.239251i	0.0620606	−	0.0166291i
$208$	−9.02655	+	0.473061i	−0.625879	+	0.0328009i
$209$	−37.2726	−	27.0802i	−2.57820	−	1.87317i
$210$	0.708451	−	1.02502i	0.0488878	−	0.0707334i
$211$	−8.15974	+	5.92840i	−0.561740	+	0.408128i	−0.832095	−	0.554633i	$-0.812859\pi$
$211$	−8.15974	+	5.92840i	−0.561740	+	0.408128i	0.270356	+	0.962761i	$0.412859\pi$
$212$	−8.56483	+	6.93566i	−0.588235	+	0.476343i
$213$	0.637902	+	0.244868i	0.0437083	+	0.0167781i
$214$	−3.83521	+	0.403097i	−0.262169	+	0.0275551i
$215$	8.08460	−	12.5048i	0.551365	−	0.852818i
$216$	−0.489698	+	0.674011i	−0.0333197	+	0.0458607i
$217$	−5.56506	−	23.6654i	−0.377781	−	1.60651i
$218$	2.38857	−	2.38857i	0.161774	−	0.161774i
$219$	2.18723	+	1.96939i	0.147799	+	0.133079i
$220$	20.5219	+	11.7928i	1.38358	+	0.795067i
$221$	−2.53551	−	2.81597i	−0.170557	−	0.189422i
$222$	0.737297	−	1.13534i	0.0494841	−	0.0761988i
$223$	−9.76577	−	1.54675i	−0.653964	−	0.103578i	−0.179369	−	0.983782i	$-0.557406\pi$
$223$	−9.76577	−	1.54675i	−0.653964	−	0.103578i	−0.474595	+	0.880204i	$0.657406\pi$
$224$	4.95478	−	4.19202i	0.331055	−	0.280091i
$225$	−4.74896	+	1.56440i	−0.316598	+	0.104293i
$226$	−1.33207	−	2.30721i	−0.0886079	−	0.153473i
$227$	−12.2665	−	9.93323i	−0.814157	−	0.659292i	0.128998	−	0.991645i	$-0.458824\pi$
$227$	−12.2665	−	9.93323i	−0.814157	−	0.659292i	−0.943155	+	0.332353i	$0.892157\pi$
$228$	16.6235	+	0.871201i	1.10092	+	0.0576967i
$229$	10.6525	−	2.26425i	0.703936	−	0.149626i	0.157983	−	0.987442i	$-0.449501\pi$
$229$	10.6525	−	2.26425i	0.703936	−	0.149626i	0.545953	+	0.837816i	$0.316168\pi$
$230$	−0.352722	−	0.255174i	−0.0232578	−	0.0168257i
$231$	−12.6166	+	6.77435i	−0.830114	+	0.445720i
$232$	5.33343	+	5.33343i	0.350157	+	0.350157i
$233$	−0.103597	−	1.97674i	−0.00678683	−	0.129501i	−0.999922	−	0.0125244i	$-0.996013\pi$
$233$	−0.103597	−	1.97674i	−0.00678683	−	0.129501i	0.993135	−	0.116976i	$-0.0373201\pi$
$234$	0.465538	−	0.207271i	0.0304332	−	0.0135497i
$235$	0.434089	−	1.13775i	0.0283169	−	0.0742185i
$236$	3.26074	−	7.32375i	0.212256	−	0.476735i
$237$	2.93046	−	0.464139i	0.190354	−	0.0301491i
$238$	0.857333	+	0.163032i	0.0555726	+	0.0105678i
$239$	−0.827426	−	1.13885i	−0.0535218	−	0.0736664i	0.781417	−	0.624009i	$-0.214497\pi$
$239$	−0.827426	−	1.13885i	−0.0535218	−	0.0736664i	−0.834939	+	0.550343i	$0.814497\pi$
$240$	−8.34117	+	0.454143i	−0.538421	+	0.0293148i
$241$	−6.58326	−	14.7862i	−0.424065	−	0.952466i	−0.991627	−	0.129135i	$-0.958780\pi$
$241$	−6.58326	−	14.7862i	−0.424065	−	0.952466i	0.567562	−	0.823331i	$-0.307887\pi$
$242$	2.09872	+	3.23175i	0.134911	+	0.207745i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−0.0758180	−	0.233344i	−0.00485375	−	0.0149383i
$245$	−7.20750	+	13.8943i	−0.460470	+	0.887675i
$246$	−0.277113	+	0.852867i	−0.0176681	+	0.0543768i
$247$	−17.2724	−	11.2168i	−1.09902	−	0.713710i
$248$	4.81763	−	5.94927i	0.305920	−	0.377779i
$249$	−8.01260	−	4.62608i	−0.507778	−	0.293166i
$250$	1.98265	+	1.27043i	0.125394	+	0.0803492i
$251$			8.63817i			0.545236i	0.962122	+	0.272618i	$0.0878896\pi$
$251$			8.63817i			0.545236i	−0.962122	+	0.272618i	$0.912110\pi$
$252$	2.49004	−	4.53557i	0.156858	−	0.285714i
$253$	2.27147	+	4.45802i	0.142806	+	0.280273i
$254$	−0.184137	−	0.866298i	−0.0115538	−	0.0543564i
$255$	−2.34853	−	2.59767i	−0.147070	−	0.162672i
$256$	−12.2935	−	2.61305i	−0.768341	−	0.163316i
$257$	9.62301	+	2.57848i	0.600267	+	0.160841i	0.546141	−	0.837693i	$-0.316096\pi$
$257$	9.62301	+	2.57848i	0.600267	+	0.160841i	0.0541256	+	0.998534i	$0.482763\pi$
$258$	−0.636746	+	1.24969i	−0.0396421	+	0.0778020i
$259$	−7.39250	+	15.3147i	−0.459347	+	0.951606i
$260$	9.43704	+	4.78428i	0.585261	+	0.296709i
$261$	8.27070	+	3.68235i	0.511943	+	0.227932i
$262$	0.0663796	−	0.172925i	0.00410094	−	0.0106833i
$263$	−3.84382	+	10.0135i	−0.237020	+	0.617459i	−0.999565	−	0.0294761i	$-0.990616\pi$
$263$	−3.84382	+	10.0135i	−0.237020	+	0.617459i	0.762545	+	0.646935i	$0.223949\pi$
$264$	−4.11949	−	1.83411i	−0.253537	−	0.112882i
$265$	12.4420	−	1.99655i	0.764308	−	0.122647i
$266$	4.73025	−	0.350111i	0.290030	−	0.0214667i
$267$	−2.69909	+	5.29726i	−0.165182	+	0.324187i
$268$	−19.2823	−	5.16667i	−1.17785	−	0.315605i
$269$	18.7502	+	3.98549i	1.14322	+	0.243000i	0.740327	−	0.672246i	$-0.234670\pi$
$269$	18.7502	+	3.98549i	1.14322	+	0.243000i	0.402895	+	0.915246i	$0.368004\pi$
$270$	0.429847	−	0.192428i	0.0261596	−	0.0117108i
$271$	−2.71634	−	12.7794i	−0.165006	−	0.776291i	−0.980342	−	0.197304i	$-0.936782\pi$
$271$	−2.71634	−	12.7794i	−0.165006	−	0.776291i	0.815337	−	0.578987i	$-0.196552\pi$
$272$	−2.65615	−	5.21300i	−0.161053	−	0.316084i
$273$	−5.47370	+	3.31931i	−0.331283	+	0.200894i
$274$		−	4.44416i		−	0.268481i
$275$	−13.6266	−	23.3819i	−0.821713	−	1.40998i
$276$	−1.56559	−	0.903892i	−0.0942373	−	0.0544079i
$277$	−0.957982	+	1.18301i	−0.0575596	+	0.0710802i	−0.805113	−	0.593122i	$-0.797895\pi$
$277$	−0.957982	+	1.18301i	−0.0575596	+	0.0710802i	0.747553	+	0.664202i	$0.231229\pi$
$278$	−0.0895930	−	0.0581824i	−0.00537343	−	0.00348955i
$279$	2.83945	−	8.73893i	0.169993	−	0.523186i
$280$	−4.84864	+	0.885474i	−0.289761	+	0.0529172i
$281$	6.80522	+	20.9443i	0.405965	+	1.24943i	0.920086	+	0.391715i	$0.128118\pi$
$281$	6.80522	+	20.9443i	0.405965	+	1.24943i	−0.514121	+	0.857718i	$0.671882\pi$
$282$	−0.0296866	+	0.110792i	−0.00176781	+	0.00659756i
$283$	3.36791	+	5.18612i	0.200201	+	0.308283i	0.924484	−	0.381220i	$-0.124496\pi$
$283$	3.36791	+	5.18612i	0.200201	+	0.308283i	−0.724283	+	0.689503i	$0.757829\pi$
$284$	−0.543506	−	1.22074i	−0.0322512	−	0.0724373i
$285$	−15.9837	−	10.3338i	−0.946793	−	0.612122i
$286$	1.62124	+	2.23145i	0.0958659	+	0.131948i
$287$	2.10447	−	11.0667i	0.124223	−	0.653246i
$288$	2.42287	−	0.383745i	0.142769	−	0.0226124i
$289$	−5.91692	+	13.2896i	−0.348054	+	0.781743i
$290$	−1.11190	−	4.11620i	−0.0652931	−	0.241711i
$291$	−11.9447	+	5.31810i	−0.700208	+	0.311753i
$292$	−0.301238	−	5.74797i	−0.0176286	−	0.336375i
$293$	−19.8314	−	19.8314i	−1.15856	−	1.15856i	−0.984785	−	0.173779i	$-0.944402\pi$
$293$	−19.8314	−	19.8314i	−1.15856	−	1.15856i	−0.173779	−	0.984785i	$-0.555598\pi$
$294$	0.541150	−	1.37141i	0.0315605	−	0.0799823i
$295$	−7.40481	+	5.40294i	−0.431125	+	0.314571i
$296$	−5.23787	+	1.11334i	−0.304445	+	0.0647118i
$297$	−5.40515	−	0.283272i	−0.313639	−	0.0164371i
$298$	−3.18685	−	2.58066i	−0.184609	−	0.149494i
$299$	1.11830	+	1.93696i	0.0646732	+	0.112017i
$300$	8.73041	+	4.40376i	0.504051	+	0.254251i
$301$	5.95859	−	16.5806i	0.343447	−	0.955691i
$302$	−0.353095	−	0.0559248i	−0.0203184	−	0.00321811i
$303$	3.50625	−	5.39915i	0.201429	−	0.310173i
$304$	−21.2777	−	23.6313i	−1.22036	−	1.35535i
$305$	−0.0577686	+	0.274522i	−0.00330782	+	0.0157191i
$306$	0.245125	+	0.220712i	0.0140129	+	0.0126172i
$307$	−12.7093	+	12.7093i	−0.725361	+	0.725361i	−0.969692	−	0.244331i	$-0.921432\pi$
$307$	−12.7093	+	12.7093i	−0.725361	+	0.725361i	0.244331	+	0.969692i	$0.421432\pi$
$308$	26.8148	+	8.07898i	1.52791	+	0.460343i
$309$	8.33900	−	11.4776i	0.474389	−	0.652940i
$310$	−4.03684	+	1.55902i	−0.229277	+	0.0885462i
$311$	11.9343	−	1.25435i	0.676733	−	0.0711275i	0.240074	−	0.970755i	$-0.422828\pi$
$311$	11.9343	−	1.25435i	0.676733	−	0.0711275i	0.436659	+	0.899627i	$0.356162\pi$
$312$	−1.88189	−	0.722389i	−0.106541	−	0.0408972i
$313$	−9.74137	+	7.88841i	−0.550615	+	0.445879i	−0.863816	−	0.503808i	$-0.831932\pi$
$313$	−9.74137	+	7.88841i	−0.550615	+	0.445879i	0.313201	+	0.949687i	$0.398599\pi$
$314$	−2.15204	+	1.56355i	−0.121447	+	0.0882361i
$315$	−5.05239	+	3.07788i	−0.284670	+	0.173419i
$316$	−4.69421	−	3.41054i	−0.264070	−	0.191858i
$317$	11.7213	−	0.614286i	0.658333	−	0.0345018i	0.279755	−	0.960071i	$-0.409747\pi$
$317$	11.7213	−	0.614286i	0.658333	−	0.0345018i	0.378577	+	0.925570i	$0.376413\pi$
$318$	−1.14647	+	0.307196i	−0.0642910	+	0.0172267i
$319$	−10.1881	+	47.9314i	−0.570426	+	2.68364i
$320$	11.5783	+	10.3827i	0.647249	+	0.580408i
$321$	17.4136	+	5.65802i	0.971932	+	0.315800i
$322$	−0.474975	−	0.199339i	−0.0264693	−	0.0111087i
$323$	2.08537	−	13.1665i	0.116033	−	0.732604i
$324$	1.69363	−	0.977820i	0.0940908	−	0.0543234i
$325$	−6.63006	−	10.1191i	−0.367770	−	0.561307i
$326$	1.18215	−	2.04754i	0.0654730	−	0.113403i
$327$	−14.9731	+	5.74763i	−0.828013	+	0.317845i
$328$	3.16062	−	1.61042i	0.174516	−	0.0889205i
$329$	0.194723	−	1.42764i	0.0107354	−	0.0787082i
$330$	1.50249	+	2.05919i	0.0827094	+	0.113355i
$331$	7.42565	−	8.24702i	0.408150	−	0.453297i	−0.503664	−	0.863900i	$-0.668015\pi$
$331$	7.42565	−	8.24702i	0.408150	−	0.453297i	0.911814	+	0.410603i	$0.134682\pi$
$332$	4.68304	+	17.4774i	0.257015	+	0.959194i
$333$	−5.39054	+	3.50066i	−0.295400	+	0.191835i
$334$	0.156809	−	1.49193i	0.00858018	−	0.0816350i
$335$	16.1725	+	16.1069i	0.883596	+	0.880012i
$336$	−9.48998	+	2.76303i	−0.517721	+	0.150736i
$337$	0.473449	+	2.98924i	0.0257904	+	0.162834i	0.997222	−	0.0744849i	$-0.0237313\pi$
$337$	0.473449	+	2.98924i	0.0257904	+	0.162834i	−0.971432	+	0.237319i	$0.923731\pi$
$338$	−0.947147	−	1.16963i	−0.0515180	−	0.0636194i
$339$	1.32220	+	12.5799i	0.0718123	+	0.683248i
$340$	−0.344523	+	6.83983i	−0.0186844	+	0.370942i
$341$	49.4618	+	5.19864i	2.67850	+	0.281522i
$342$	1.59736	+	0.813895i	0.0863753	+	0.0440104i
$343$	−4.57475	+	17.9464i	−0.247013	+	0.969012i
$344$	5.27646	−	1.71443i	0.284488	−	0.0924357i
$345$	1.03714	+	1.78798i	0.0558378	+	0.0962615i
$346$	1.67326	−	1.50661i	0.0899548	−	0.0809956i
$347$	1.77573	−	33.8829i	0.0953260	−	1.81893i	−0.364811	−	0.931081i	$-0.618866\pi$
$347$	1.77573	−	33.8829i	0.0953260	−	1.81893i	0.460137	−	0.887848i	$-0.347800\pi$
$348$	−6.34498	−	16.5292i	−0.340127	−	0.886060i
$349$	−3.70138			−0.198130			−0.0990652	−	0.995081i	$-0.531585\pi$
$349$	−3.70138			−0.198130			−0.0990652	+	0.995081i	$0.531585\pi$
$350$	2.62583	+	0.931613i	0.140357	+	0.0497968i
$351$	−2.41954			−0.129145
$352$	4.75820	+	12.3955i	0.253613	+	0.660684i
$353$	1.20625	−	23.0166i	0.0642022	−	1.22505i	−0.756615	−	0.653860i	$-0.773148\pi$
$353$	1.20625	−	23.0166i	0.0642022	−	1.22505i	0.820817	−	0.571191i	$-0.193518\pi$
$354$	0.641623	−	0.577720i	0.0341019	−	0.0307055i
$355$	−0.156618	+	1.51982i	−0.00831241	+	0.0806639i
$356$	11.0577	−	3.59287i	0.586058	−	0.190422i
$357$	−3.40382	−	2.36281i	−0.180149	−	0.125053i
$358$	−1.04014	−	0.529975i	−0.0549729	−	0.0280101i
$359$	−12.4105	−	1.30439i	−0.655000	−	0.0688432i	−0.228802	−	0.973473i	$-0.573481\pi$
$359$	−12.4105	−	1.30439i	−0.655000	−	0.0688432i	−0.426198	+	0.904630i	$0.640147\pi$
$360$	−1.74054	−	0.664075i	−0.0917345	−	0.0349998i
$361$	−5.58739	−	53.1604i	−0.294073	−	2.79792i
$362$	−0.992645	−	1.22581i	−0.0521722	−	0.0644274i
$363$	−2.86211	−	18.0707i	−0.150222	−	0.948463i
$364$	12.1594	+	2.97919i	0.637324	+	0.156152i
$365$	−2.97589	+	5.86997i	−0.155765	+	0.307248i
$366$	0.00276203	−	0.0262790i	0.000144374	−	0.00137362i
$367$	−14.1672	+	9.20030i	−0.739523	+	0.480252i	−0.858608	−	0.512632i	$-0.828670\pi$
$367$	−14.1672	+	9.20030i	−0.739523	+	0.480252i	0.119085	+	0.992884i	$0.462004\pi$
$368$	0.893797	+	3.33569i	0.0465924	+	0.173885i
$369$	2.84901	−	3.16414i	0.148313	−	0.164719i
$370$	2.88078	+	0.929555i	0.149765	+	0.0483253i
$371$	13.8014	−	5.64155i	0.716534	−	0.292895i
$372$	−16.0111	+	8.15807i	−0.830138	+	0.422976i
$373$	16.8773	−	6.47860i	0.873876	−	0.335449i	0.120242	−	0.992745i	$-0.461633\pi$
$373$	16.8773	−	6.47860i	0.873876	−	0.335449i	0.753633	+	0.657295i	$0.228300\pi$
$374$	−0.892663	+	1.54614i	−0.0461585	+	0.0799489i
$375$	−6.14630	−	9.33932i	−0.317394	−	0.482281i
$376$	0.392927	−	0.226856i	0.0202636	−	0.0116992i
$377$	−3.42671	+	21.6354i	−0.176484	+	1.11428i
$378$	0.443663	−	0.337162i	0.0228196	−	0.0173418i
$379$	2.56476	+	0.833340i	0.131743	+	0.0428058i	0.374146	−	0.927370i	$-0.377936\pi$
$379$	2.56476	+	0.833340i	0.131743	+	0.0428058i	−0.242404	+	0.970176i	$0.577936\pi$
$380$	7.81293	+	36.3931i	0.400795	+	1.86693i
$381$	−0.874277	+	4.11315i	−0.0447906	+	0.210723i
$382$	−2.86241	+	0.766979i	−0.146453	+	0.0392421i
$383$	25.0781	−	1.31429i	1.28143	−	0.0671569i	0.600571	−	0.799572i	$-0.294940\pi$
$383$	25.0781	−	1.31429i	1.28143	−	0.0671569i	0.680859	+	0.732415i	$0.261607\pi$
$384$	−5.15423	−	3.74476i	−0.263026	−	0.191099i
$385$	−21.9808	−	23.2852i	−1.12025	−	1.18672i
$386$	−0.0547420	+	0.0397724i	−0.00278629	+	0.00202436i
$387$	5.17523	−	4.19082i	0.263072	−	0.213031i
$388$	23.8718	+	9.16351i	1.21190	+	0.465207i
$389$	26.6005	−	2.79582i	1.34870	−	0.141754i	0.597520	−	0.801854i	$-0.296153\pi$
$389$	26.6005	−	2.79582i	1.34870	−	0.141754i	0.751178	+	0.660100i	$0.229486\pi$
$390$	0.718902	+	0.884090i	0.0364030	+	0.0447676i
$391$	−0.850937	+	1.17121i	−0.0430338	+	0.0592309i
$392$	−5.34955	+	2.32229i	−0.270193	+	0.117293i
$393$	−0.621867	+	0.621867i	−0.0313691	+	0.0313691i
$394$	−1.08930	−	0.980807i	−0.0548780	−	0.0494123i
$395$	2.71076	+	6.05532i	0.136393	+	0.304676i
$396$	7.08277	+	7.86622i	0.355923	+	0.395292i
$397$	13.7861	−	21.2287i	0.691905	−	1.06544i	−0.301796	−	0.953373i	$-0.597586\pi$
$397$	13.7861	−	21.2287i	0.691905	−	1.06544i	0.993701	−	0.112068i	$-0.0357473\pi$
$398$	−0.826978	−	0.130980i	−0.0414527	−	0.00656546i
$399$	−21.1935	−	7.61632i	−1.06100	−	0.381293i
$400$	−5.84431	−	17.7412i	−0.292215	−	0.887062i
$401$	17.0332	+	29.5024i	0.850598	+	1.47328i	0.880669	+	0.473732i	$0.157093\pi$
$401$	17.0332	+	29.5024i	0.850598	+	1.47328i	−0.0300708	+	0.999548i	$0.509573\pi$
$402$	−1.67079	−	1.35298i	−0.0833312	−	0.0674803i
$403$	22.2018	+	1.16355i	1.10595	+	0.0579605i
$404$	−12.3148	+	2.61759i	−0.612685	+	0.130230i
$405$	−2.23606	+	0.00454434i	−0.111111	+	0.000225810i
$406$	−2.38654	−	4.44472i	−0.118442	−	0.220588i
$407$	−24.5997	−	24.5997i	−1.21936	−	1.21936i
$408$	−0.0682859	−	1.30297i	−0.00338066	−	0.0645068i
$409$	28.6294	−	12.7466i	1.41563	−	0.630281i	0.450677	−	0.892687i	$-0.351183\pi$
$409$	28.6294	−	12.7466i	1.41563	−	0.630281i	0.964958	+	0.262406i	$0.0845160\pi$
$410$	−2.00267	−	0.100875i	−0.0989049	−	0.00498185i
$411$	−8.58242	+	19.2764i	−0.423340	+	0.950837i
$412$	−27.4034	+	4.34027i	−1.35007	+	0.213830i
$413$	−7.08216	+	8.21433i	−0.348490	+	0.404201i
$414$	−0.114438	−	0.157510i	−0.00562430	−	0.00774119i
$415$	5.31394	−	19.9943i	0.260851	−	0.981484i
$416$	2.41410	+	5.42217i	0.118361	+	0.265844i
$417$	0.276248	+	0.425384i	0.0135279	+	0.0208311i
$418$	−2.51143	+	9.37279i	−0.122838	+	0.458438i
$419$	−1.53459	−	4.72297i	−0.0749694	−	0.230732i	0.906549	−	0.422101i	$-0.138707\pi$
$419$	−1.53459	−	4.72297i	−0.0749694	−	0.230732i	−0.981518	+	0.191369i	$0.938707\pi$
$420$	11.2429	+	2.73044i	0.548598	+	0.133232i
$421$	−7.84908	+	24.1570i	−0.382541	+	1.17734i	0.555708	+	0.831378i	$0.312447\pi$
$421$	−7.84908	+	24.1570i	−0.382541	+	1.17734i	−0.938249	+	0.345962i	$0.887553\pi$
$422$	1.78157	+	1.15696i	0.0867254	+	0.0563201i
$423$	0.342723	−	0.423228i	0.0166638	−	0.0205780i
$424$	4.06600	+	2.34751i	0.197462	+	0.114005i
$425$	4.23809	−	6.58452i	0.205577	−	0.319396i
$426$		−	0.143911i		−	0.00697253i
$427$	0.00714291	+	0.331856i	0.000345670	+	0.0160596i
$428$	−16.2562	−	31.9045i	−0.785771	−	1.54216i
$429$	−2.72279	−	12.8097i	−0.131458	−	0.618460i
$430$	−3.06899	−	0.645818i	−0.148000	−	0.0311441i
$431$	5.79652	+	1.23209i	0.279208	+	0.0593476i	0.345387	−	0.938460i	$-0.387748\pi$
$431$	5.79652	+	1.23209i	0.279208	+	0.0593476i	−0.0661791	+	0.997808i	$0.521081\pi$
$432$	−3.60852	−	0.966899i	−0.173615	−	0.0465200i
$433$	−10.4871	+	20.5820i	−0.503977	+	0.989110i	0.489165	+	0.872191i	$0.337302\pi$
$433$	−10.4871	+	20.5820i	−0.503977	+	0.989110i	−0.993142	+	0.116918i	$0.962698\pi$
$434$	−4.23322	+	2.88046i	−0.203201	+	0.138267i
$435$	−3.12622	+	20.0012i	−0.149891	+	0.958984i
$436$	28.6536	+	12.7574i	1.37226	+	0.610968i
$437$	−2.81978	+	7.34578i	−0.134888	+	0.351396i
$438$	0.222148	−	0.578716i	0.0106147	−	0.0276521i
$439$	−19.4053	−	8.63981i	−0.926166	−	0.412356i	−0.112476	−	0.993654i	$-0.535878\pi$
$439$	−19.4053	−	8.63981i	−0.926166	−	0.412356i	−0.813690	+	0.581299i	$0.802545\pi$
$440$	1.55712	−	9.96223i	0.0742326	−	0.474931i
$441$	−4.99566	+	4.90341i	−0.237888	+	0.233496i
$442$	−0.362321	+	0.711095i	−0.0172338	+	0.0338233i
$443$	−37.6914	−	10.0994i	−1.79077	−	0.479836i	−0.798296	−	0.602266i	$-0.794265\pi$
$443$	−37.6914	−	10.0994i	−1.79077	−	0.479836i	−0.992477	+	0.122430i	$0.960931\pi$
$444$	12.2952	+	2.61342i	0.583503	+	0.124027i
$445$	−13.0091	−	2.73754i	−0.616689	−	0.129772i
$446$	0.432970	+	2.03697i	0.0205017	+	0.0964531i
$447$	8.83921	+	17.3479i	0.418080	+	0.820529i
$448$	16.1301	+	8.85550i	0.762077	+	0.418383i
$449$		−	27.7953i		−	1.31174i	−0.754872	−	0.655872i	$-0.772301\pi$
$449$		−	27.7953i		−	1.31174i	0.754872	−	0.655872i	$-0.227699\pi$
$450$	0.666048	+	0.815699i	0.0313978	+	0.0384524i
$451$	19.9580	+	11.5227i	0.939784	+	0.542585i
$452$	15.5677	−	19.2245i	0.732244	−	0.904246i
$453$	1.42354	+	0.924460i	0.0668839	+	0.0434349i
$454$	−1.02729	+	3.16168i	−0.0482132	+	0.148385i
$455$	−10.3572	−	9.88047i	−0.485554	−	0.463204i
$456$	−2.19140	−	6.74442i	−0.102622	−	0.315837i
$457$	−0.896313	+	3.34509i	−0.0419278	+	0.156477i	−0.983716	−	0.179730i	$-0.942477\pi$
$457$	−0.896313	+	3.34509i	−0.0419278	+	0.156477i	0.941788	+	0.336207i	$0.109144\pi$
$458$	−1.24925	−	1.92367i	−0.0583734	−	0.0898871i
$459$	−0.636993	−	1.43071i	−0.0297323	−	0.0667798i
$460$	1.03829	−	3.90671i	0.0484107	−	0.182151i
$461$	12.4515	+	17.1381i	0.579926	+	0.798200i	0.993687	−	0.112186i	$-0.0357852\pi$
$461$	12.4515	+	17.1381i	0.579926	+	0.798200i	−0.413761	+	0.910385i	$0.635785\pi$
$462$	2.28431	+	1.96946i	0.106276	+	0.0916277i
$463$	−24.6813	+	3.90913i	−1.14704	+	0.181673i	−0.700878	−	0.713281i	$-0.747208\pi$
$463$	−24.6813	+	3.90913i	−1.14704	+	0.181673i	−0.446159	+	0.894954i	$0.647208\pi$
$464$	−13.7566	+	30.8978i	−0.638633	+	1.43439i
$465$	20.5204	+	1.03362i	0.951612	+	0.0479328i
$466$	−0.380862	+	0.169571i	−0.0176431	+	0.00785521i
$467$	1.70340	+	32.5029i	0.0788241	+	1.50405i	0.696464	+	0.717592i	$0.254756\pi$
$467$	1.70340	+	32.5029i	0.0788241	+	1.50405i	−0.617640	+	0.786461i	$0.711911\pi$
$468$	3.34585	+	3.34585i	0.154662	+	0.154662i
$469$	22.9612	+	14.2182i	1.06025	+	0.656535i
$470$	−0.256477		0.000521237i	−0.0118304		2.40429e-5i
$471$	12.3539	−	2.62590i	0.569238	−	0.120995i
$472$	−3.41058	−	0.178741i	−0.156985	−	0.00822721i
$473$	28.0113	+	22.6831i	1.28796	+	1.04297i
$474$	−0.312449	−	0.541177i	−0.0143512	−	0.0248571i
$475$	12.9871	−	40.5298i	0.595887	−	1.85964i
$476$	1.43956	+	7.97436i	0.0659823	+	0.365504i
$477$	5.56605	+	0.881575i	0.254852	+	0.0403646i
$478$	−0.161478	+	0.248654i	−0.00738581	+	0.0113732i
$479$	14.2930	+	15.8740i	0.653066	+	0.725303i	0.975184	−	0.221396i	$-0.0710614\pi$
$479$	14.2930	+	15.8740i	0.653066	+	0.725303i	−0.322118	+	0.946700i	$0.604395\pi$
$480$	2.24123	+	5.00647i	0.102297	+	0.228513i
$481$	−11.5570	−	10.4060i	−0.526956	−	0.474473i
$482$	−2.41049	+	2.41049i	−0.109795	+	0.109795i
$483$	1.67524	+	1.78189i	0.0762260	+	0.0810786i
$484$	−21.0311	+	28.9468i	−0.955958	+	1.31576i
$485$	−18.4454	−	22.6838i	−0.837562	−	1.03002i
$486$	0.209463	−	0.0220154i	0.00950143	−	0.000998640i
$487$	−19.7812	−	7.59329i	−0.896372	−	0.344085i	−0.133815	−	0.991006i	$-0.542723\pi$
$487$	−19.7812	−	7.59329i	−0.896372	−	0.344085i	−0.762557	+	0.646921i	$0.776056\pi$
$488$	−0.0812294	+	0.0657783i	−0.00367708	+	0.00297764i
$489$	−9.08167	+	6.59822i	−0.410688	+	0.298382i
$490$	3.27601	+	0.368475i	0.147995	+	0.0166460i
$491$	−24.3471	−	17.6892i	−1.09877	−	0.798301i	−0.117909	−	0.993024i	$-0.537619\pi$
$491$	−24.3471	−	17.6892i	−1.09877	−	0.798301i	−0.980858	+	0.194723i	$0.937619\pi$
$492$	−8.31526	+	0.435784i	−0.374881	+	0.0196467i
$493$	−13.6955	+	3.66969i	−0.616813	+	0.165275i
$494$	−0.901847	+	4.24286i	−0.0405760	+	0.190895i
$495$	−2.54038	−	11.8333i	−0.114182	−	0.531865i
$496$	32.6470	+	10.6076i	1.46589	+	0.476297i
$497$	0.227612	+	1.79342i	0.0102098	+	0.0804458i
$498$	−0.304837	+	1.92467i	−0.0136601	+	0.0862463i
$499$	2.36560	−	1.36578i	0.105899	−	0.0611407i	−0.446115	−	0.894976i	$-0.647193\pi$
$499$	2.36560	−	1.36578i	0.105899	−	0.0611407i	0.552014	+	0.833835i	$0.313860\pi$
$500$	−4.41546	+	21.4142i	−0.197465	+	0.957674i
$501$	−3.56133	+	6.16841i	−0.159109	+	0.275584i
$502$	1.69850	−	0.651994i	0.0758079	−	0.0290999i
$503$	7.18004	−	3.65841i	0.320142	−	0.163121i	−0.286533	−	0.958070i	$-0.592503\pi$
$503$	7.18004	−	3.65841i	0.320142	−	0.163121i	0.606675	+	0.794950i	$0.292503\pi$
$504$	−2.18402	−	0.297890i	−0.0972838	−	0.0132691i
$505$	13.6997	+	4.42054i	0.609629	+	0.196712i
$506$	0.705122	−	0.783118i	0.0313465	−	0.0348138i
$507$	1.84948	+	6.90235i	0.0821382	+	0.306544i
$508$	6.89685	−	4.47887i	0.305998	−	0.198718i
$509$	−2.50330	+	23.8173i	−0.110957	+	1.05568i	0.787408	+	0.616432i	$0.211423\pi$
$509$	−2.50330	+	23.8173i	−0.110957	+	1.05568i	−0.898365	+	0.439251i	$0.855244\pi$
$510$	−0.333510	+	0.657853i	−0.0147681	+	0.0291302i
$511$	−1.85310	+	7.56329i	−0.0819762	+	0.334580i
$512$	2.40737	+	15.1995i	0.106392	+	0.671731i
$513$	−5.35674	−	6.61503i	−0.236506	−	0.292061i
$514$	−0.219328	−	2.08677i	−0.00967415	−	0.0920434i
$515$	29.6394	+	11.3084i	1.30607	+	0.498310i
$516$	−12.9518	−	1.36129i	−0.570172	−	0.0599275i
$517$	2.62637	+	1.33820i	0.115508	+	0.0588540i
$518$	3.56926	+	0.297645i	0.156824	+	0.0130778i
$519$	−10.1672	+	3.30353i	−0.446292	+	0.145009i
$520$	0.462041	−	4.48367i	0.0202619	−	0.196622i
$521$	−22.4021	+	20.1709i	−0.981452	+	0.883703i	−0.993223	−	0.116227i	$-0.962920\pi$
$521$	−22.4021	+	20.1709i	−0.981452	+	0.883703i	0.0117706	+	0.999931i	$0.496253\pi$
$522$	0.0997941	−	1.90418i	0.00436787	−	0.0833439i
$523$	3.75843	+	9.79105i	0.164345	+	0.428133i	0.990879	−	0.134753i	$-0.0430242\pi$
$523$	3.75843	+	9.79105i	0.164345	+	0.428133i	−0.826534	+	0.562886i	$0.809691\pi$
$524$	1.71989			0.0751339
$525$	−9.59039	−	9.11178i	−0.418559	−	0.397671i
$526$	2.25905			0.0984995
$527$	5.15706	+	13.4346i	0.224645	+	0.585221i
$528$	1.05825	−	20.1926i	0.0460545	−	0.878771i
$529$	−16.4573	+	14.8182i	−0.715535	+	0.644271i
$530$	−1.33168	−	2.29575i	−0.0578445	−	0.0997210i
$531$	−3.89871	+	1.26677i	−0.169189	+	0.0549730i
$532$	18.7752	+	39.8396i	0.814006	+	1.72726i
$533$	9.17901	+	4.67694i	0.397587	+	0.202581i
$534$	1.24531	+	0.130887i	0.0538898	+	0.00566405i
$535$	−2.05963	+	40.8900i	−0.0890457	+	1.76783i
$536$	0.888934	+	8.45764i	0.0383961	+	0.365315i
$537$	3.48809	+	4.30744i	0.150522	+	0.185880i
$538$	−0.631579	−	3.98763i	−0.0272293	−	0.171919i
$539$	−31.5819	−	20.9305i	−1.36033	−	0.901539i
$540$	3.09842	+	3.08585i	0.133335	+	0.132794i
$541$	−2.77550	+	26.4071i	−0.119328	+	1.13533i	0.756933	+	0.653493i	$0.226697\pi$
$541$	−2.77550	+	26.4071i	−0.119328	+	1.13533i	−0.876261	+	0.481837i	$0.839970\pi$
$542$	−2.30775	+	1.49867i	−0.0991263	+	0.0643734i
$543$	1.93832	+	7.23391i	0.0831813	+	0.310437i
$544$	−2.57065	+	2.85499i	−0.110216	+	0.122407i
$545$	−21.1386	−	28.9707i	−0.905476	−	1.24097i
$546$	1.06581	+	0.825744i	0.0456125	+	0.0353386i
$547$	6.74425	−	3.43637i	0.288363	−	0.146928i	−0.303825	−	0.952728i	$-0.598264\pi$
$547$	6.74425	−	3.43637i	0.288363	−	0.146928i	0.592189	+	0.805799i	$0.298264\pi$
$548$	38.5245	−	14.7882i	1.64569	−	0.631720i
$549$	−0.0627294	+	0.108651i	−0.00267723	+	0.00463709i
$550$	−3.56902	+	4.44419i	−0.152184	+	0.189501i
$551$	−66.7378	+	38.5311i	−2.84312	+	1.64148i
$552$	−0.120476	+	0.760654i	−0.00512779	+	0.0323756i
$553$	4.74966	+	6.24995i	0.201976	+	0.265775i
$554$	0.304919	+	0.0990742i	0.0129548	+	0.00420926i
$555$	−10.7002	−	9.59521i	−0.454199	−	0.407294i
$556$	0.206233	−	0.970249i	0.00874622	−	0.0411477i
$557$	9.74722	−	2.61176i	0.413003	−	0.110664i	−0.0463338	−	0.998926i	$-0.514754\pi$
$557$	9.74722	−	2.61176i	0.413003	−	0.110664i	0.459337	+	0.888262i	$0.348087\pi$
$558$	−1.93263	+	0.101285i	−0.0818148	+	0.00428773i
$559$	13.0352	+	9.47062i	0.551330	+	0.400564i
$560$	−11.4984	−	18.8748i	−0.485896	−	0.797605i
$561$	6.85776	−	4.98246i	0.289535	−	0.210360i
$562$	3.60458	−	2.91893i	0.152050	−	0.123128i
$563$	−29.3202	−	11.2550i	−1.23570	−	0.474341i	−0.349191	−	0.937051i	$-0.613544\pi$
$563$	−29.3202	−	11.2550i	−1.23570	−	0.474341i	−0.886510	+	0.462710i	$0.846877\pi$
$564$	−1.05919	+	0.111326i	−0.0446000	+	0.00468765i
$565$	−26.3852	+	10.1899i	−1.11004	+	0.428693i
$566$	0.765531	−	1.05366i	0.0321776	−	0.0442887i
$567$	−2.57550	+	0.605645i	−0.108161	+	0.0254347i
$568$	−0.402529	+	0.402529i	−0.0168897	+	0.0168897i
$569$	3.45375	+	3.10977i	0.144789	+	0.130368i	0.738342	−	0.674426i	$-0.235609\pi$
$569$	3.45375	+	3.10977i	0.144789	+	0.130368i	−0.593554	+	0.804794i	$0.702276\pi$
$570$	−0.825491	+	3.92281i	−0.0345760	+	0.164309i
$571$	−2.67442	−	2.97025i	−0.111921	−	0.124301i	0.684581	−	0.728937i	$-0.259985\pi$
$571$	−2.67442	−	2.97025i	−0.111921	−	0.124301i	−0.796502	+	0.604636i	$0.793319\pi$
$572$	−13.9487	+	21.4791i	−0.583224	+	0.898087i
$573$	13.8968	+	2.20104i	0.580547	+	0.0919496i
$574$	−2.33486	+	0.421498i	−0.0974551	+	0.0175930i
$575$	−3.25492	+	3.28149i	−0.135739	+	0.136847i
$576$	3.47748	+	6.02318i	0.144895	+	0.250966i
$577$	−33.2716	−	26.9428i	−1.38512	−	1.12164i	−0.978079	−	0.208233i	$-0.933229\pi$
$577$	−33.2716	−	26.9428i	−1.38512	−	1.12164i	−0.407037	−	0.913412i	$-0.633438\pi$
$578$	3.05971	+	0.160352i	0.127267	+	0.00666978i
$579$	0.314249	−	0.0667958i	0.0130598	−	0.00277594i
$580$	31.9817	−	23.3355i	1.32797	−	0.968954i
$581$	0.754787	−	24.4673i	0.0313138	−	1.01507i
$582$	1.94725	+	1.94725i	0.0807160	+	0.0807160i
$583$	1.59636	+	30.4604i	0.0661145	+	1.26154i
$584$	−2.24007	+	0.997342i	−0.0926946	+	0.0412703i
$585$	−1.41089	−	5.22305i	−0.0583333	−	0.215946i
$586$	−2.40256	+	5.39624i	−0.0992489	+	0.222917i
$587$	−25.3368	+	4.01296i	−1.04576	+	0.165633i	−0.655596	−	0.755111i	$-0.727583\pi$
$587$	−25.3368	+	4.01296i	−1.04576	+	0.165633i	−0.390167	+	0.920744i	$0.627583\pi$
$588$	13.6889	+	0.127561i	0.564520	+	0.00526051i
$589$	45.9726	+	63.2759i	1.89427	+	2.60724i
$590$	1.62127	+	1.04819i	0.0667466	+	0.0431531i
$591$	2.83070	+	6.35785i	0.116439	+	0.261527i
$592$	−13.0778	−	20.1380i	−0.537494	−	0.827668i
$593$	5.07026	−	18.9225i	0.208211	−	0.777053i	−0.780236	−	0.625485i	$-0.784901\pi$
$593$	5.07026	−	18.9225i	0.208211	−	0.777053i	0.988447	−	0.151568i	$-0.0484323\pi$
$594$	0.352272	+	1.08418i	0.0144539	+	0.0444846i
$595$	3.11572	−	8.72562i	0.127732	−	0.357716i
$596$	11.7663	−	36.2128i	0.481965	−	1.48333i
$597$	3.33406	+	2.16516i	0.136454	+	0.0886141i
$598$	0.296452	−	0.366088i	0.0121228	−	0.0149704i
$599$	9.87356	+	5.70050i	0.403423	+	0.232916i	0.687960	−	0.725749i	$-0.258507\pi$
$599$	9.87356	+	5.70050i	0.403423	+	0.232916i	−0.284537	+	0.958665i	$0.591840\pi$
$600$	0.418583	−	4.14453i	0.0170886	−	0.169200i
$601$		−	6.11336i		−	0.249369i	−0.992196	−	0.124684i	$-0.960208\pi$
$601$		−	6.11336i		−	0.249369i	0.992196	−	0.124684i	$-0.0397919\pi$
$602$	−3.70995	+	0.0798535i	−0.151206	+	0.00325458i
$603$	4.63417	+	9.09508i	0.188718	+	0.370380i
$604$	−0.690156	−	3.24693i	−0.0280821	−	0.132116i
$605$	37.3401	−	16.7159i	1.51809	−	0.679597i
$606$	−1.32627	−	0.281907i	−0.0538760	−	0.0114517i
$607$	−24.3640	−	6.52833i	−0.988906	−	0.264977i	−0.272115	−	0.962265i	$-0.587723\pi$
$607$	−24.3640	−	6.52833i	−0.988906	−	0.264977i	−0.716791	+	0.697288i	$0.754390\pi$
$608$	−9.47951	+	18.6046i	−0.384445	+	0.754516i
$609$	1.76806	+	23.8877i	0.0716454	+	0.967979i
$610$	0.0583389	−	0.00936154i	0.00236207	−	0.000379038i
$611$	1.20374	+	0.535941i	0.0486982	+	0.0216819i
$612$	−1.09759	+	2.85932i	−0.0443674	+	0.115581i
$613$	15.5818	−	40.5920i	0.629344	−	1.63950i	−0.132078	−	0.991239i	$-0.542165\pi$
$613$	15.5818	−	40.5920i	0.629344	−	1.63950i	0.761422	−	0.648257i	$-0.224502\pi$
$614$	3.45829	+	1.53973i	0.139565	+	0.0621384i
$615$	8.49174	+	4.30504i	0.342420	+	0.173596i
$616$	−0.880639	−	11.8980i	−0.0354819	−	0.479386i
$617$	2.62423	−	5.15033i	0.105647	−	0.207345i	−0.832131	−	0.554579i	$-0.812879\pi$
$617$	2.62423	−	5.15033i	0.105647	−	0.207345i	0.937778	+	0.347235i	$0.112879\pi$
$618$	−2.88623	−	0.773364i	−0.116101	−	0.0311093i
$619$	12.7148	+	2.70262i	0.511052	+	0.108627i	0.456218	−	0.889868i	$-0.349204\pi$
$619$	12.7148	+	2.70262i	0.511052	+	0.108627i	0.0548338	+	0.998495i	$0.482537\pi$
$620$	−26.9473	−	29.8059i	−1.08223	−	1.19704i
$621$	0.192192	+	0.904194i	0.00771242	+	0.0362841i
$622$	−1.14742	−	2.25194i	−0.0460074	−	0.0902946i
$623$	−15.7260	+	0.338489i	−0.630050	+	0.0135613i
$624$		−	9.03894i		−	0.361847i
$625$	16.5767	−	18.7140i	0.663067	−	0.748560i
$626$	2.28634	+	1.32002i	0.0913805	+	0.0527586i
$627$	28.9937	−	35.8043i	1.15790	−	1.42989i
$628$	−20.7148	−	13.4523i	−0.826610	−	0.536807i
$629$	3.11060	−	9.57345i	0.124028	−	0.381719i
$630$	0.986542	+	0.761126i	0.0393048	+	0.0303240i
$631$	4.56040	+	14.0355i	0.181547	+	0.558743i	0.999872	−	0.0160126i	$-0.00509718\pi$
$631$	4.56040	+	14.0355i	0.181547	+	0.558743i	−0.818325	+	0.574755i	$0.805097\pi$
$632$	−0.639767	+	2.38764i	−0.0254486	+	0.0949753i
$633$	−5.49322	−	8.45882i	−0.218336	−	0.336208i
$634$	−1.00549	−	2.25836i	−0.0399330	−	0.0896910i
$635$	−9.38885	+	0.511184i	−0.372585	+	0.0202857i
$636$	−6.47791	−	8.91608i	−0.256866	−	0.353545i
$637$	−14.5881	−	8.60469i	−0.578003	−	0.340930i
$638$	10.1936	−	1.61451i	0.403569	−	0.0639190i
$639$	−0.277917	+	0.624213i	−0.0109942	+	0.0246935i
$640$	5.07825	−	13.3101i	0.200735	−	0.526127i
$641$	−1.28427	+	0.571794i	−0.0507256	+	0.0225845i	−0.431943	−	0.901901i	$-0.642172\pi$
$641$	−1.28427	+	0.571794i	−0.0507256	+	0.0225845i	0.381217	+	0.924486i	$0.375505\pi$
$642$	−0.201825	−	3.85105i	−0.00796539	−	0.151989i
$643$	11.8727	+	11.8727i	0.468215	+	0.468215i	0.901336	−	0.433121i	$-0.142588\pi$
$643$	11.8727	+	11.8727i	0.468215	+	0.468215i	−0.433121	+	0.901336i	$0.642588\pi$
$644$	0.147478	−	4.78067i	0.00581146	−	0.188385i
$645$	12.0645	+	8.72797i	0.475040	+	0.343664i
$646$	−2.74630	+	0.583743i	−0.108052	+	0.0229671i
$647$	−11.7462	−	0.615590i	−0.461789	−	0.0242013i	−0.179977	−	0.983671i	$-0.557602\pi$
$647$	−11.7462	−	0.615590i	−0.461789	−	0.0242013i	−0.281812	+	0.959470i	$0.590936\pi$
$648$	−0.647459	−	0.524302i	−0.0254346	−	0.0205965i
$649$	−11.0940	−	19.2153i	−0.435477	−	0.754268i
$650$	−1.48927	+	2.06743i	−0.0584140	+	0.0810911i
$651$	23.9242	−	4.31889i	0.937663	−	0.169271i
$652$	21.6829	+	3.43423i	0.849168	+	0.134495i
$653$	−9.68664	+	14.9161i	−0.379068	+	0.583713i	−0.975783	−	0.218740i	$-0.929805\pi$
$653$	−9.68664	+	14.9161i	−0.379068	+	0.583713i	0.596716	+	0.802453i	$0.296472\pi$
$654$	2.26028	+	2.51030i	0.0883841	+	0.0981605i
$655$	−1.70505	−	0.979796i	−0.0666218	−	0.0382838i
$656$	11.8206	+	10.6433i	0.461518	+	0.415553i
$657$	−2.08116	+	2.08116i	−0.0811939	+	0.0811939i
$658$	−0.295410	+	0.0694676i	−0.0115163	+	0.00270813i
$659$	13.5674	−	18.6739i	0.528511	−	0.727433i	−0.458392	−	0.888750i	$-0.651574\pi$
$659$	13.5674	−	18.6739i	0.528511	−	0.727433i	0.986903	+	0.161318i	$0.0515744\pi$
$660$	−12.8506	+	19.8765i	−0.500210	+	0.773693i
$661$	−4.22785	+	0.444365i	−0.164444	+	0.0172838i	−0.186393	−	0.982475i	$-0.559680\pi$
$661$	−4.22785	+	0.444365i	−0.164444	+	0.0172838i	0.0219484	+	0.999759i	$0.493013\pi$
$662$	−2.18207	−	0.837616i	−0.0848084	−	0.0325549i
$663$	2.94481	−	2.38466i	0.114367	−	0.0926124i
$664$	6.23605	−	4.53076i	0.242006	−	0.175828i
$665$	4.08285	−	50.1916i	0.158326	−	1.94635i
$666$	1.09519	+	0.795705i	0.0424379	+	0.0308329i
$667$	8.35745	−	0.437996i	0.323602	−	0.0169593i
$668$	13.4547	−	3.60519i	0.520580	−	0.139489i
$669$	2.05573	−	9.67144i	0.0794790	−	0.373919i
$670$	1.94638	−	4.39567i	0.0751954	−	0.169820i
$671$	−0.645819	−	0.209839i	−0.0249316	−	0.00810076i
$672$	3.92696	+	5.16739i	0.151486	+	0.199336i
$673$	3.33219	−	21.0386i	0.128447	−	0.810980i	−0.836391	−	0.548133i	$-0.815339\pi$
$673$	3.33219	−	21.0386i	0.128447	−	0.810980i	0.964838	−	0.262847i	$-0.0846613\pi$
$674$	0.552032	−	0.318716i	0.0212635	−	0.0122765i
$675$	−1.31371	−	4.82433i	−0.0505649	−	0.185689i
$676$	6.98734	−	12.1024i	0.268744	−	0.465478i
$677$	13.1388	−	5.04351i	0.504965	−	0.193838i	−0.0925312	−	0.995710i	$-0.529496\pi$
$677$	13.1388	−	5.04351i	0.504965	−	0.193838i	0.597496	+	0.801872i	$0.296162\pi$
$678$	2.37376	−	1.20949i	0.0911639	−	0.0464503i
$679$	−27.3463	−	21.1867i	−1.04946	−	0.813072i
$680$	2.77290	−	0.907205i	0.106336	−	0.0347897i
$681$	10.5616	−	11.7298i	0.404721	−	0.449488i
$682$	−2.71109	−	10.1179i	−0.103813	−	0.387436i
$683$	22.5730	−	14.6591i	0.863731	−	0.560913i	−0.0350133	−	0.999387i	$-0.511147\pi$
$683$	22.5730	−	14.6591i	0.863731	−	0.560913i	0.898744	+	0.438473i	$0.144481\pi$
$684$	−1.74001	+	16.5551i	−0.0665311	+	0.633001i
$685$	−46.6166	−	7.28626i	−1.78113	−	0.278394i
$686$	3.87404	−	0.455037i	0.147912	−	0.0173734i
$687$	1.70364	+	10.7564i	0.0649981	+	0.410382i
$688$	15.6561	+	19.3337i	0.596884	+	0.737090i
$689$	1.42526	+	13.5604i	0.0542981	+	0.516612i
$690$	0.273284	−	0.338884i	0.0104038	−	0.0129011i
$691$	8.14874	+	0.856467i	0.309993	+	0.0325815i	0.258247	−	0.966079i	$-0.416855\pi$
$691$	8.14874	+	0.856467i	0.309993	+	0.0325815i	0.0517451	+	0.998660i	$0.483522\pi$
$692$	18.6280	+	9.49144i	0.708130	+	0.360810i
$693$	−6.10477	−	12.9539i	−0.231901	−	0.492077i
$694$	−6.79634	+	2.20826i	−0.257986	+	0.0838246i
$695$	−0.757188	+	0.844387i	−0.0287218	+	0.0320294i
$696$	−5.60525	+	5.04699i	−0.212466	+	0.191306i
$697$	−0.348983	+	6.65899i	−0.0132187	+	0.252227i
$698$	0.279374	+	0.727794i	0.0105745	+	0.0275474i
$699$	1.97945			0.0748698
$700$	0.661840	+	25.8622i	0.0250152	+	0.977500i
$701$	22.4862			0.849293			0.424647	−	0.905359i	$-0.360398\pi$
$701$	22.4862			0.849293			0.424647	+	0.905359i	$0.360398\pi$
$702$	0.182622	+	0.475748i	0.00689264	+	0.0179559i
$703$	2.86332	−	54.6354i	0.107992	−	2.06061i
$704$	−27.9751	+	25.1889i	−1.05435	+	0.949343i
$705$	1.11347	+	0.493040i	0.0419357	+	0.0185689i
$706$	−4.61675	+	1.50007i	−0.173754	+	0.0564560i
$707$	16.9738	+	1.41547i	0.638364	+	0.0532341i
$708$	7.14306	+	3.63957i	0.268452	+	0.136783i
$709$	−9.56850	−	1.00569i	−0.359352	−	0.0377695i	−0.0768678	−	0.997041i	$-0.524492\pi$
$709$	−9.56850	−	1.00569i	−0.359352	−	0.0377695i	−0.282485	+	0.959272i	$0.591159\pi$
$710$	0.310661	−	0.0839183i	0.0116589	−	0.00314940i
$711$	0.310135	+	2.95074i	0.0116310	+	0.110661i
$712$	−3.11711	−	3.84931i	−0.116819	−	0.144259i
$713$	−1.32875	−	8.38937i	−0.0497619	−	0.314184i
$714$	−0.207678	+	0.847625i	−0.00777217	+	0.0317216i
$715$	26.0646	−	13.3474i	0.974761	−	0.499163i
$716$	1.13303	−	10.7800i	0.0423432	−	0.402868i
$717$	1.18060	−	0.766689i	0.0440903	−	0.0286325i
$718$	0.680241	+	2.53869i	0.0253864	+	0.0947432i
$719$	24.2081	−	26.8858i	0.902809	−	1.00267i	−0.0971637	−	0.995268i	$-0.530977\pi$
$719$	24.2081	−	26.8858i	0.902809	−	1.00267i	0.999973	−	0.00740240i	$-0.00235628\pi$
$720$	−0.0169768	−	8.35351i	−0.000632688	−	0.311317i
$721$	37.1913	+	5.07272i	1.38508	+	0.188918i
$722$	−10.0311	+	5.11109i	−0.373318	+	0.190215i
$723$	15.1105	−	5.80039i	0.561966	−	0.215719i
$724$	7.32299	−	12.6838i	0.272157	−	0.471389i
$725$	−44.9995	+	4.91464i	−1.67124	+	0.182525i
$726$	−3.33716	+	1.92671i	−0.123854	+	0.0715070i
$727$	4.20060	−	26.5215i	0.155791	−	0.983629i	−0.778636	−	0.627476i	$-0.784088\pi$
$727$	4.20060	−	26.5215i	0.155791	−	0.983629i	0.934428	−	0.356153i	$-0.115912\pi$
$728$	−0.671484	−	5.29080i	−0.0248869	−	0.196090i
$729$	−0.951057	−	0.309017i	−0.0352243	−	0.0114451i
$730$	1.37881	+	0.142086i	0.0510321	+	0.00525886i
$731$	−2.16834	+	10.2012i	−0.0801990	+	0.377307i
$732$	0.236992	−	0.0635019i	0.00875948	−	0.00234710i
$733$	−28.1479	+	1.47517i	−1.03966	+	0.0544865i	−0.564519	−	0.825420i	$-0.690938\pi$
$733$	−28.1479	+	1.47517i	−1.03966	+	0.0544865i	−0.475146	+	0.879907i	$0.657605\pi$
$734$	2.87835	+	2.09124i	0.106242	+	0.0771892i
$735$	−13.4981	−	7.92479i	−0.497883	−	0.292310i
$736$	1.83453	−	1.33287i	0.0676217	−	0.0491301i
$737$	−42.9370	+	34.7697i	−1.58160	+	1.28076i
$738$	−0.837195	−	0.321369i	−0.0308176	−	0.0118298i
$739$	17.5102	−	1.84040i	0.644125	−	0.0677002i	0.223167	−	0.974780i	$-0.428361\pi$
$739$	17.5102	−	1.84040i	0.644125	−	0.0677002i	0.420958	+	0.907080i	$0.361694\pi$
$740$	1.52805	+	28.0655i	0.0561722	+	1.03171i
$741$	12.1054	−	16.6617i	0.444704	−	0.612082i
$742$	−2.15099	−	2.28793i	−0.0789654	−	0.0839924i
$743$	−20.3759	+	20.3759i	−0.747521	+	0.747521i	−0.974013	−	0.226492i	$-0.927274\pi$
$743$	−20.3759	+	20.3759i	−0.747521	+	0.747521i	0.226492	+	0.974013i	$0.427274\pi$
$744$	5.68898	+	5.12238i	0.208568	+	0.187796i
$745$	−32.2945	+	29.1972i	−1.18318	+	1.06970i
$746$	−2.54774	−	2.82956i	−0.0932795	−	0.103597i
$747$	5.03908	−	7.75951i	0.184370	−	0.283906i
$748$	−16.3732	−	2.59326i	−0.598664	−	0.0948191i
$749$	8.60602	+	47.6724i	0.314457	+	1.74191i
$750$	−1.37246	+	1.91345i	−0.0501150	+	0.0698693i
$751$	−4.17895	−	7.23816i	−0.152492	−	0.264124i	0.779651	−	0.626214i	$-0.215397\pi$
$751$	−4.17895	−	7.23816i	−0.152492	−	0.264124i	−0.932143	+	0.362090i	$0.882063\pi$
$752$	1.58110	+	1.28035i	0.0576567	+	0.0466895i
$753$	−8.62633	−	0.452087i	−0.314361	−	0.0164750i
$754$	4.51275	−	0.959215i	0.164345	−	0.0349326i
$755$	−1.16552	+	3.61207i	−0.0424177	+	0.131457i
$756$	4.39903	+	2.72401i	0.159991	+	0.0990711i
$757$	−9.87015	−	9.87015i	−0.358737	−	0.358737i	0.504611	−	0.863347i	$-0.331636\pi$
$757$	−9.87015	−	9.87015i	−0.358737	−	0.358737i	−0.863347	+	0.504611i	$0.831636\pi$
$758$	−0.0297258	−	0.567201i	−0.00107969	−	0.0206017i
$759$	−4.57079	+	2.03505i	−0.165909	+	0.0738675i
$760$	13.2813	−	8.66340i	0.481763	−	0.314254i
$761$	3.75942	−	8.44379i	0.136279	−	0.306087i	−0.832495	−	0.554032i	$-0.813089\pi$
$761$	3.75942	−	8.44379i	0.136279	−	0.306087i	0.968774	+	0.247945i	$0.0797552\pi$
$762$	0.874748	−	0.138546i	0.0316888	−	0.00501901i
$763$	−32.1379	−	27.7084i	−1.16347	−	1.00311i
$764$	−16.1734	−	22.2608i	−0.585135	−	0.805369i
$765$	2.71702	−	2.20936i	0.0982341	−	0.0798795i
$766$	−2.15127	−	4.83184i	−0.0777287	−	0.174581i
$767$	−5.40201	−	8.31836i	−0.195055	−	0.300359i
$768$	3.25286	−	12.1399i	0.117378	−	0.438059i
$769$	4.57740	+	14.0878i	0.165065	+	0.508019i	0.999041	−	0.0437823i	$-0.0139408\pi$
$769$	4.57740	+	14.0878i	0.165065	+	0.508019i	−0.833976	+	0.551801i	$0.813941\pi$
$770$	−2.91943	+	6.07956i	−0.105209	+	0.219092i
$771$	−3.07857	+	9.47487i	−0.110872	+	0.341229i
$772$	−0.526927	−	0.342191i	−0.0189645	−	0.0123157i
$773$	19.3160	−	23.8533i	0.694750	−	0.857945i	−0.300652	−	0.953734i	$-0.597204\pi$
$773$	19.3160	−	23.8533i	0.694750	−	0.857945i	0.995402	+	0.0957893i	$0.0305375\pi$
$774$	−1.21465	−	0.701277i	−0.0436596	−	0.0252069i
$775$	9.73472	+	44.9001i	0.349681	+	1.61286i
$776$		−	10.8931i		−	0.391041i
$777$	−14.9068	−	8.18387i	−0.534777	−	0.293595i
$778$	−2.55749	−	5.01937i	−0.0916906	−	0.179953i
$779$	7.53512	+	35.4500i	0.269974	+	1.27013i
$780$	−5.27162	+	9.17372i	−0.188754	+	0.328472i
$781$	−3.61751	−	0.768926i	−0.129445	−	0.0275143i
$782$	0.294520	+	0.0789165i	0.0105320	+	0.00282205i
$783$	−4.11016	+	8.06665i	−0.146885	+	0.288278i
$784$	−18.3182	−	18.6628i	−0.654222	−	0.666529i
$785$	12.8724	+	25.1371i	0.459436	+	0.897181i
$786$	0.169214	+	0.0753388i	0.00603565	+	0.00268725i
$787$	−5.26532	+	13.7166i	−0.187688	+	0.488945i	−0.994847	−	0.101390i	$-0.967671\pi$
$787$	−5.26532	+	13.7166i	−0.187688	+	0.488945i	0.807158	+	0.590335i	$0.201004\pi$
$788$	4.87751	−	12.7063i	0.173754	−	0.452645i
$789$	−9.79860	−	4.36262i	−0.348840	−	0.155313i
$790$	0.986039	−	0.990055i	0.0350817	−	0.0352246i
$791$	−27.6688	+	18.8270i	−0.983790	+	0.669413i
$792$	2.04720	−	4.01785i	0.0727440	−	0.142768i
$793$	−0.293209	−	0.0785651i	−0.0104122	−	0.00278993i
$794$	−5.21471	−	1.10842i	−0.185063	−	0.0393364i
$795$	1.34265	+	12.5295i	0.0476189	+	0.444375i
$796$	−1.61640	−	7.60457i	−0.0572919	−	0.269537i
$797$	−3.25598	−	6.39023i	−0.115333	−	0.226354i	0.826123	−	0.563490i	$-0.190542\pi$
$797$	−3.25598	−	6.39023i	−0.115333	−	0.226354i	−0.941456	+	0.337136i	$0.890542\pi$
$798$	0.102069	+	4.74209i	0.00361322	+	0.167868i
$799$			0.852890i			0.0301731i
$800$	−9.50052	+	7.75752i	−0.335894	+	0.274270i
$801$	−5.14874	−	2.97263i	−0.181922	−	0.105033i
$802$	4.51535	−	5.57599i	0.159442	−	0.196895i
$803$	−13.3603	−	8.67628i	−0.471475	−	0.306179i
$804$	6.16875	−	18.9854i	0.217555	−	0.669565i
$805$	−2.86968	+	4.65539i	−0.101143	+	0.164081i
$806$	−1.44697	−	4.45331i	−0.0509673	−	0.156861i
$807$	−4.96134	+	18.5160i	−0.174647	+	0.651793i
$808$	2.92114	+	4.49816i	0.102765	+	0.158245i
$809$	−7.32306	−	16.4479i	−0.257465	−	0.578276i	0.737849	−	0.674965i	$-0.235841\pi$
$809$	−7.32306	−	16.4479i	−0.257465	−	0.578276i	−0.995315	+	0.0966891i	$0.969175\pi$
$810$	0.169668	+	0.439329i	0.00596151	+	0.0154364i
$811$	0.287077	+	0.395127i	0.0100806	+	0.0138748i	0.814028	−	0.580826i	$-0.197270\pi$
$811$	0.287077	+	0.395127i	0.0100806	+	0.0138748i	−0.803947	+	0.594701i	$0.797270\pi$
$812$	30.5881	−	35.4780i	1.07343	−	1.24503i
$813$	12.9040	−	2.04379i	0.452563	−	0.0716790i
$814$	−2.98023	+	6.69371i	−0.104457	+	0.234615i
$815$	−19.5393	−	15.7570i	−0.684432	−	0.551943i
$816$	5.34486	−	2.37969i	0.187108	−	0.0833057i
$817$	2.96658	+	56.6057i	0.103788	+	1.98038i
$818$	−4.66724	−	4.66724i	−0.163186	−	0.163186i
$819$	−3.02829	−	5.63991i	−0.105817	−	0.197075i
$820$	−5.78956	−	17.6960i	−0.202180	−	0.617971i
$821$	20.6981	−	4.39952i	0.722370	−	0.153544i	0.167967	−	0.985793i	$-0.446280\pi$
$821$	20.6981	−	4.39952i	0.722370	−	0.153544i	0.554403	+	0.832248i	$0.312947\pi$
$822$	4.43807	+	0.232589i	0.154795	+	0.00811248i
$823$	21.2105	+	17.1759i	0.739350	+	0.598714i	0.923236	−	0.384234i	$-0.125534\pi$
$823$	21.2105	+	17.1759i	0.739350	+	0.598714i	−0.183886	+	0.982948i	$0.558868\pi$
$824$	5.90982	+	10.2361i	0.205878	+	0.356592i
$825$	24.0630	−	12.3842i	0.837767	−	0.431162i
$826$	2.14971	+	0.772544i	0.0747981	+	0.0268802i
$827$	12.2460	+	1.93957i	0.425834	+	0.0674455i	0.365673	−	0.930743i	$-0.380839\pi$
$827$	12.2460	+	1.93957i	0.425834	+	0.0674455i	0.0601606	+	0.998189i	$0.480839\pi$
$828$	0.984590	−	1.51614i	0.0342169	−	0.0526893i
$829$	22.5777	+	25.0751i	0.784155	+	0.870893i	0.994283	−	0.106782i	$-0.0340545\pi$
$829$	22.5777	+	25.0751i	0.784155	+	0.870893i	−0.210127	+	0.977674i	$0.567388\pi$
$830$	−4.33253	+	0.464271i	−0.150384	+	0.0161151i
$831$	−1.13125	−	1.01858i	−0.0392427	−	0.0353343i
$832$	−11.8991	+	11.8991i	−0.412525	+	0.412525i
$833$	1.24746	−	10.8915i	0.0432220	−	0.377370i
$834$	0.0627915	−	0.0864252i	0.00217429	−	0.00299266i
$835$	−15.3924	−	4.09088i	−0.532677	−	0.141571i
$836$	−89.6057	+	9.41794i	−3.09908	+	0.325726i
$837$	8.57834	+	3.29292i	0.296511	+	0.113820i
$838$	−0.812838	+	0.658223i	−0.0280790	+	0.0227380i
$839$	−42.4405	+	30.8348i	−1.46521	+	1.06454i	−0.483239	+	0.875488i	$0.660540\pi$
$839$	−42.4405	+	30.8348i	−1.46521	+	1.06454i	−0.981968	+	0.189047i	$0.939460\pi$
$840$	−0.630502	−	4.88833i	−0.0217544	−	0.168663i
$841$	42.8489	+	31.1316i	1.47755	+	1.07350i
$842$	5.34236	−	0.279981i	0.184110	−	0.00964880i
$843$	−21.2718	+	5.69975i	−0.732639	+	0.196310i
$844$	−4.10097	+	19.2935i	−0.141161	+	0.664111i
$845$	−13.8216	+	8.01739i	−0.475477	+	0.275807i
$846$	−0.109086	−	0.0354443i	−0.00375046	−	0.00121860i
$847$	38.5403	−	29.2887i	1.32426	−	1.00637i
$848$	−3.29340	+	20.7937i	−0.113096	+	0.714059i
$849$	−5.35528	+	3.09187i	−0.183793	+	0.106113i
$850$	−1.61458	−	0.336337i	−0.0553797	−	0.0115363i
$851$	−2.97077	+	5.14552i	−0.101837	+	0.176386i
$852$	1.24751	−	0.478873i	0.0427389	−	0.0164059i
$853$	18.6598	−	9.50766i	0.638901	−	0.325536i	−0.104358	−	0.994540i	$-0.533279\pi$
$853$	18.6598	−	9.50766i	0.638901	−	0.325536i	0.743259	+	0.669004i	$0.233279\pi$
$854$	0.0647129	−	0.0264524i	0.00221443	−	0.000905182i
$855$	11.1562	−	15.4210i	0.381533	−	0.527386i
$856$	−10.2071	+	11.3361i	−0.348871	+	0.387461i
$857$	−8.21176	−	30.6467i	−0.280508	−	1.04687i	−0.952059	−	0.305913i	$-0.901038\pi$
$857$	−8.21176	−	30.6467i	−0.280508	−	1.04687i	0.671551	−	0.740958i	$-0.265628\pi$
$858$	−2.31324	+	1.50223i	−0.0789726	+	0.0512854i
$859$	3.86749	−	36.7967i	0.131957	−	1.25549i	−0.705391	−	0.708818i	$-0.749229\pi$
$859$	3.86749	−	36.7967i	0.131957	−	1.25549i	0.837348	−	0.546670i	$-0.184105\pi$
$860$	−4.61392	−	28.7528i	−0.157333	−	0.980463i
$861$	10.9414	+	2.68077i	0.372881	+	0.0913604i
$862$	−0.195248	−	1.23275i	−0.00665019	−	0.0419876i
$863$	27.1035	+	33.4700i	0.922614	+	1.13933i	0.989924	+	0.141601i	$0.0452251\pi$
$863$	27.1035	+	33.4700i	0.922614	+	1.13933i	−0.0673097	+	0.997732i	$0.521442\pi$
$864$	0.256416	+	2.43963i	0.00872344	+	0.0829980i
$865$	−13.0601	−	20.0216i	−0.444056	−	0.680754i
$866$	4.83854	+	0.508551i	0.164420	+	0.0172813i
$867$	−12.9617	−	6.60434i	−0.440204	−	0.224295i
$868$	−39.0558	−	27.1111i	−1.32564	−	0.920211i
$869$	−15.2730	+	4.96251i	−0.518103	+	0.168342i
$870$	4.16875	−	0.894953i	0.141334	−	0.0303418i
$871$	−18.3540	+	16.5260i	−0.621903	+	0.559964i
$872$	0.699309	−	13.3436i	0.0236816	−	0.451872i
$873$	−4.68568	−	12.2066i	−0.158586	−	0.413131i
$874$	1.65722			0.0560562
$875$	14.0772	−	26.0160i	0.475895	−	0.879502i
$876$	5.75586			0.194473
$877$	1.54856	+	4.03415i	0.0522913	+	0.136223i	0.957238	−	0.289301i	$-0.0934229\pi$
$877$	1.54856	+	4.03415i	0.0522913	+	0.136223i	−0.904947	+	0.425525i	$0.860090\pi$
$878$	−0.234144	+	4.46774i	−0.00790199	+	0.150779i
$879$	20.8421	−	18.7663i	0.702987	−	0.632973i
$880$	44.2068	−	9.49039i	1.49021	−	0.319921i
$881$	−23.5117	+	7.63942i	−0.792130	+	0.257379i	−0.677011	−	0.735973i	$-0.736725\pi$
$881$	−23.5117	+	7.63942i	−0.792130	+	0.257379i	−0.115119	+	0.993352i	$0.536725\pi$
$882$	1.34121	+	0.612183i	0.0451609	+	0.0206133i
$883$	46.1179	+	23.4982i	1.55199	+	0.790778i	0.999098	−	0.0424747i	$-0.0135242\pi$
$883$	46.1179	+	23.4982i	1.55199	+	0.790778i	0.552892	+	0.833253i	$0.313524\pi$
$884$	−7.36983	−	0.774600i	−0.247874	−	0.0260526i
$885$	−5.00800	−	7.67743i	−0.168342	−	0.258074i
$886$	0.859065	+	8.17345i	0.0288608	+	0.274593i
$887$	−33.4740	−	41.3369i	−1.12395	−	1.38796i	−0.911757	−	0.410730i	$-0.865274\pi$
$887$	−33.4740	−	41.3369i	−1.12395	−	1.38796i	−0.212189	−	0.977229i	$-0.568059\pi$
$888$	−0.837689	−	5.28896i	−0.0281110	−	0.177486i
$889$	−10.6819	+	3.11008i	−0.358261	+	0.104309i
$890$	0.443626	+	2.76457i	0.0148704	+	0.0926685i
$891$	0.565768	−	5.38292i	0.0189539	−	0.180335i
$892$	−16.2169	+	10.5314i	−0.542981	+	0.352616i
$893$	1.19977	+	4.47759i	0.0401486	+	0.149837i
$894$	2.74391	−	3.04742i	0.0917702	−	0.101921i
$895$	−7.26445	+	10.0415i	−0.242824	+	0.335651i
$896$	2.27799	−	16.7014i	0.0761023	−	0.557954i
$897$	−1.99283	+	1.01540i	−0.0665387	+	0.0339032i
$898$	−5.46533	+	2.09794i	−0.182380	+	0.0700093i
$899$	41.5943	−	72.0434i	1.38725	−	2.40278i
$900$	−4.85464	+	8.48797i	−0.161821	+	0.282932i
$901$	−7.64327	+	4.41284i	−0.254634	+	0.147013i
$902$	0.759296	−	4.79400i	0.0252818	−	0.159623i
$903$	16.2461	+	6.81819i	0.540635	+	0.226895i
$904$	−10.0226	−	3.25654i	−0.333346	−	0.108311i
$905$	−14.4855	+	8.40252i	−0.481515	+	0.279309i
$906$	0.0743278	−	0.349685i	0.00246937	−	0.0116175i
$907$	5.22388	−	1.39973i	0.173456	−	0.0464774i	−0.171046	−	0.985263i	$-0.554715\pi$
$907$	5.22388	−	1.39973i	0.173456	−	0.0464774i	0.344502	+	0.938786i	$0.388048\pi$
$908$	−30.8256	+	1.61550i	−1.02298	+	0.0536124i
$909$	5.20825	+	3.78402i	0.172747	+	0.125508i
$910$	−1.16103	+	2.78228i	−0.0384877	+	0.0922315i
$911$	34.2570	−	24.8892i	1.13499	−	0.824615i	0.148573	−	0.988901i	$-0.452532\pi$
$911$	34.2570	−	24.8892i	1.13499	−	0.824615i	0.986413	+	0.164286i	$0.0525321\pi$
$912$	24.7125	−	20.0118i	0.818312	−	0.662656i
$913$	46.7518	+	17.9463i	1.54726	+	0.593936i
$914$	0.725388	−	0.0762414i	0.0239937	−	0.00252184i
$915$	−0.271122	−	0.0720568i	−0.00896303	−	0.00238212i
$916$	12.5185	−	17.2303i	0.413625	−	0.569305i
$917$	−2.22789	−	0.671238i	−0.0735715	−	0.0221662i
$918$	−0.233238	+	0.233238i	−0.00769800	+	0.00769800i
$919$	3.56792	+	3.21257i	0.117695	+	0.105973i	0.725877	−	0.687825i	$-0.241434\pi$
$919$	3.56792	+	3.21257i	0.117695	+	0.105973i	−0.608182	+	0.793798i	$0.708101\pi$
$920$	−1.71227	+	0.183486i	−0.0564519	+	0.00604935i
$921$	−12.0268	−	13.3571i	−0.396296	−	0.440131i
$922$	2.43000	−	3.74187i	0.0800277	−	0.123232i
$923$	−1.63288	−	0.258623i	−0.0537470	−	0.00851268i
$924$	−9.47128	+	26.3552i	−0.311582	+	0.867022i
$925$	14.4736	−	28.6937i	0.475888	−	0.943443i
$926$	2.63154	+	4.55797i	0.0864779	+	0.149784i
$927$	11.0255	+	8.92826i	0.362124	+	0.293243i
$928$	22.1782	+	1.16231i	0.728036	+	0.0381547i
$929$	−16.2664	+	3.45753i	−0.533684	+	0.113438i	−0.466867	−	0.884327i	$-0.654617\pi$
$929$	−16.2664	+	3.45753i	−0.533684	+	0.113438i	−0.0668164	+	0.997765i	$0.521284\pi$
$930$	−1.34561	−	4.11290i	−0.0441243	−	0.134867i
$931$	−8.77216	−	58.9344i	−0.287496	−	1.93150i
$932$	−2.73728	−	2.73728i	−0.0896626	−	0.0896626i
$933$	0.628035	+	11.9836i	0.0205609	+	0.392326i
$934$	6.26239	−	2.78820i	0.204912	−	0.0912325i
$935$	14.7545	+	11.8984i	0.482525	+	0.389120i
$936$	0.819889	−	1.84150i	0.0267989	−	0.0601914i
$937$	45.5522	−	7.21477i	1.48813	−	0.235696i	0.641187	−	0.767385i	$-0.278442\pi$
$937$	45.5522	−	7.21477i	1.48813	−	0.235696i	0.846940	+	0.531689i	$0.178442\pi$
$938$	1.06262	−	5.58796i	0.0346958	−	0.182453i
$939$	−7.36777	−	10.1409i	−0.240438	−	0.330935i
$940$	−0.857960	−	2.22156i	−0.0279836	−	0.0724592i
$941$	6.38829	+	14.3483i	0.208252	+	0.467742i	0.987228	−	0.159311i	$-0.0509274\pi$
$941$	6.38829	+	14.3483i	0.208252	+	0.467742i	−0.778976	+	0.627053i	$0.784261\pi$
$942$	−1.44878	−	2.23092i	−0.0472037	−	0.0726873i
$943$	1.01868	−	3.80175i	0.0331727	−	0.123802i
$944$	−4.73240	−	14.5648i	−0.154026	−	0.474045i
$945$	−2.80924	−	5.20655i	−0.0913847	−	0.169369i
$946$	2.34588	−	7.21987i	0.0762711	−	0.234738i
$947$	1.52086	+	0.987660i	0.0494214	+	0.0320946i	0.569113	−	0.822259i	$-0.307287\pi$
$947$	1.52086	+	0.987660i	0.0494214	+	0.0320946i	−0.519692	+	0.854354i	$0.673953\pi$
$948$	3.65155	−	4.50928i	0.118597	−	0.146455i
$949$	−6.16715	−	3.56060i	−0.200194	−	0.115582i
$950$	−8.94952	+	0.505509i	−0.290361	+	0.0164009i
$951$			11.7374i			0.380610i
$952$	2.95175	−	1.78997i	0.0956667	−	0.0580133i
$953$	−7.59496	−	14.9060i	−0.246025	−	0.482851i	0.734662	−	0.678433i	$-0.237341\pi$
$953$	−7.59496	−	14.9060i	−0.246025	−	0.482851i	−0.980687	+	0.195582i	$0.937341\pi$
$954$	−0.246774	−	1.16098i	−0.00798959	−	0.0375881i
$955$	3.35221	+	31.2824i	0.108475	+	1.01228i
$956$	−2.69280	−	0.572372i	−0.0870914	−	0.0185118i
$957$	−47.3325	−	12.6827i	−1.53004	−	0.409974i
$958$	2.04246	−	4.00855i	0.0659889	−	0.129510i
$959$	−55.6749	+	4.12080i	−1.79784	+	0.133068i
$960$	−10.9744	+	11.0191i	−0.354197	+	0.355640i
$961$	−48.8119	−	21.7325i	−1.57458	−	0.701047i
$962$	−1.17380	+	3.05786i	−0.0378449	+	0.0985894i
$963$	−6.56162	+	17.0936i	−0.211445	+	0.550834i
$964$	−28.9166	−	12.8745i	−0.931340	−	0.414659i
$965$	0.327439	+	0.639419i	0.0105406	+	0.0205836i
$966$	0.223924	−	0.463892i	0.00720463	−	0.0149255i
$967$	13.1916	−	25.8899i	0.424212	−	0.832563i	−0.575677	−	0.817677i	$-0.695261\pi$
$967$	13.1916	−	25.8899i	0.424212	−	0.832563i	0.999889	−	0.0148862i	$-0.00473858\pi$
$968$	14.7234	+	3.94511i	0.473227	+	0.126801i
$969$	13.0393	+	2.77159i	0.418883	+	0.0890364i
$970$	−3.06802	+	5.33900i	−0.0985083	+	0.171425i
$971$	11.8697	+	55.8427i	0.380918	+	1.79208i	0.582745	+	0.812655i	$0.301979\pi$
$971$	11.8697	+	55.8427i	0.380918	+	1.79208i	−0.201827	+	0.979421i	$0.564688\pi$
$972$	0.887842	+	1.74249i	0.0284776	+	0.0558903i
$973$	−0.645815	+	1.17634i	−0.0207039	+	0.0377117i
$974$			4.46266i			0.142993i
$975$	10.4522	−	6.09138i	0.334739	−	0.195080i
$976$	−0.405898	−	0.234345i	−0.0129925	−	0.00750121i
$977$	−6.63405	+	8.19237i	−0.212242	+	0.262097i	−0.872138	−	0.489260i	$-0.837267\pi$
$977$	−6.63405	+	8.19237i	−0.212242	+	0.262097i	0.659896	+	0.751357i	$0.270600\pi$
$978$	1.98286	+	1.28769i	0.0634049	+	0.0411756i
$979$	9.94389	−	30.6041i	0.317808	−	0.978112i
$980$	7.70697	+	29.6245i	0.246190	+	0.946321i
$981$	−4.95612	−	15.2534i	−0.158237	−	0.487003i
$982$	−1.64051	+	6.12245i	−0.0523506	+	0.195375i
$983$	19.8174	+	30.5162i	0.632078	+	0.973314i	0.999071	+	0.0430908i	$0.0137205\pi$
$983$	19.8174	+	30.5162i	0.632078	+	0.973314i	−0.366993	+	0.930224i	$0.619613\pi$
$984$	1.44280	+	3.24057i	0.0459947	+	0.103306i
$985$	−12.0740	+	9.81803i	−0.384710	+	0.312829i
$986$	1.75527	+	2.41593i	0.0558993	+	0.0769388i
$987$	1.41549	+	0.269173i	0.0450555	+	0.00856787i
$988$	−39.7805	+	6.30061i	−1.26559	+	0.200449i
$989$	2.50379	−	5.62360i	0.0796159	−	0.178820i
$990$	−2.13500	+	1.39266i	−0.0678548	+	0.0442617i
$991$	35.5042	−	15.8075i	1.12783	−	0.502141i	0.243917	−	0.969796i	$-0.421568\pi$
$991$	35.5042	−	15.8075i	1.12783	−	0.502141i	0.883911	+	0.467655i	$0.154901\pi$
$992$	−1.17967	−	22.5095i	−0.0374547	−	0.714678i
$993$	7.84708	+	7.84708i	0.249020	+	0.249020i
$994$	0.335456	−	0.180119i	0.0106400	−	0.00571303i
$995$	−2.72975	+	8.45977i	−0.0865389	+	0.268193i
$996$	−17.6985	+	3.76193i	−0.560798	+	0.119201i
$997$	−31.2085	−	1.63557i	−0.988382	−	0.0517989i	−0.448713	−	0.893676i	$-0.648117\pi$
$997$	−31.2085	−	1.63557i	−0.988382	−	0.0517989i	−0.539669	+	0.841877i	$0.681451\pi$
$998$	−0.447101	−	0.362055i	−0.0141527	−	0.0114607i
$999$	−3.21374	−	5.56636i	−0.101678	−	0.176112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bv.a.52.19	✓	640
7.5	odd	6	inner	525.2.bv.a.502.19	yes	640
25.13	odd	20	inner	525.2.bv.a.388.19	yes	640
175.138	even	60	inner	525.2.bv.a.313.19	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bv.a.52.19	✓	640	1.1	even	1	trivial
525.2.bv.a.313.19	yes	640	175.138	even	60	inner
525.2.bv.a.388.19	yes	640	25.13	odd	20	inner
525.2.bv.a.502.19	yes	640	7.5	odd	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0754782 - 0.196628i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(1.45332 - 1.30858i) q^{4} +(-2.18626 + 0.469349i) q^{5} +(0.200308 - 0.0650841i) q^{6} +(-2.39330 + 1.12789i) q^{7} +(-0.742319 - 0.378230i) q^{8} +(-0.994522 - 0.104528i) q^{9} +O(q^{10})\)	\(q+(-0.0754782 - 0.196628i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(1.45332 - 1.30858i) q^{4} +(-2.18626 + 0.469349i) q^{5} +(0.200308 - 0.0650841i) q^{6} +(-2.39330 + 1.12789i) q^{7} +(-0.742319 - 0.378230i) q^{8} +(-0.994522 - 0.104528i) q^{9} +(0.257302 + 0.394452i) q^{10} +(-0.565768 - 5.38292i) q^{11} +(1.23072 + 1.51982i) q^{12} +(-0.378499 - 2.38975i) q^{13} +(0.402416 + 0.385457i) q^{14} +(-0.354286 - 2.20782i) q^{15} +(0.390499 - 3.71535i) q^{16} +(1.31345 - 0.852963i) q^{17} +(0.0545116 + 0.203440i) q^{18} +(5.69560 - 6.32561i) q^{19} +(-2.56316 + 3.54300i) q^{20} +(-1.00109 - 2.44905i) q^{21} +(-1.01573 + 0.517539i) q^{22} +(-0.862997 + 0.331273i) q^{23} +(0.416562 - 0.721506i) q^{24} +(4.55942 - 2.05223i) q^{25} +(-0.441322 + 0.254797i) q^{26} +(0.156434 - 0.987688i) q^{27} +(-2.00231 + 4.77100i) q^{28} +(-8.61030 - 2.79766i) q^{29} +(-0.407378 + 0.236305i) q^{30} +(-1.91043 + 8.98786i) q^{31} +(-2.36949 + 0.634902i) q^{32} +(5.40515 - 0.283272i) q^{33} +(-0.266853 - 0.193880i) q^{34} +(4.70299 - 3.58914i) q^{35} +(-1.58215 + 1.14950i) q^{36} +(4.99509 - 4.04495i) q^{37} +(-1.67368 - 0.642467i) q^{38} +(2.40628 - 0.252911i) q^{39} +(1.80042 + 0.478501i) q^{40} +(-2.50266 + 3.44461i) q^{41} +(-0.405990 + 0.381691i) q^{42} +(-4.70882 + 4.70882i) q^{43} +(-7.86622 - 7.08277i) q^{44} +(2.22334 - 0.238252i) q^{45} +(0.130275 + 0.144685i) q^{46} +(-0.296606 + 0.456733i) q^{47} +(3.68982 + 0.584410i) q^{48} +(4.45574 - 5.39874i) q^{49} +(-0.747663 - 0.741609i) q^{50} +(0.783054 + 1.35629i) q^{51} +(-3.67726 - 2.97778i) q^{52} +(-5.62771 - 0.294936i) q^{53} +(-0.206014 + 0.0437897i) q^{54} +(3.76338 + 11.5029i) q^{55} +(2.20319 + 0.0679659i) q^{56} +(6.01886 + 6.01886i) q^{57} +(0.0997941 + 1.90418i) q^{58} +(3.74493 - 1.66735i) q^{59} +(-3.40400 - 2.74507i) q^{60} +(0.0510287 - 0.114612i) q^{61} +(1.91146 - 0.302745i) q^{62} +(2.49808 - 0.871541i) q^{63} +(-4.08803 - 5.62669i) q^{64} +(1.94912 + 5.04695i) q^{65} +(-0.463670 - 1.04142i) q^{66} +(-5.55948 - 8.56085i) q^{67} +(0.792696 - 2.95838i) q^{68} +(-0.285654 - 0.879152i) q^{69} +(-1.06070 - 0.653835i) q^{70} +(0.211147 - 0.649843i) q^{71} +(0.698716 + 0.453752i) q^{72} +(1.85222 - 2.28730i) q^{73} +(-1.17237 - 0.676867i) q^{74} +(1.81080 + 4.66058i) q^{75} -16.6463i q^{76} +(7.42537 + 12.2448i) q^{77} +(-0.231351 - 0.454052i) q^{78} +(-0.616872 - 2.90215i) q^{79} +(0.890064 + 8.30598i) q^{80} +(0.978148 + 0.207912i) q^{81} +(0.866201 + 0.232098i) q^{82} +(-4.20039 + 8.24373i) q^{83} +(-4.65967 - 2.24926i) q^{84} +(-2.47120 + 2.48126i) q^{85} +(1.28130 + 0.570470i) q^{86} +(3.24445 - 8.45208i) q^{87} +(-1.61600 + 4.20983i) q^{88} +(5.43126 + 2.41815i) q^{89} +(-0.214661 - 0.419187i) q^{90} +(3.60123 + 5.29248i) q^{91} +(-0.820717 + 1.61075i) q^{92} +(-8.87556 - 2.37820i) q^{93} +(0.112194 + 0.0238475i) q^{94} +(-9.48313 + 16.5026i) q^{95} +(-0.510022 - 2.39947i) q^{96} +(5.93595 + 11.6500i) q^{97} +(-1.39785 - 0.468635i) q^{98} +5.41257i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8	\( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + 12 q^{10} + 8 q^{15} - 80 q^{16} - 72 q^{22} + 48 q^{23} - 12 q^{25} - 36 q^{28} - 80 q^{29} + 32 q^{30} - 24 q^{32} + 36 q^{33} - 64 q^{35} + 160 q^{36} - 4 q^{37} - 192 q^{38} - 12 q^{40} - 16 q^{42} + 120 q^{43} + 60 q^{47} + 288 q^{50} - 432 q^{52} - 136 q^{53} - 16 q^{57} - 4 q^{58} - 240 q^{59} - 20 q^{60} - 4 q^{63} + 120 q^{64} + 4 q^{65} - 8 q^{67} - 132 q^{68} + 76 q^{70} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 60 q^{77} - 80 q^{78} + 12 q^{80} - 80 q^{81} - 252 q^{82} - 160 q^{84} + 72 q^{85} + 24 q^{87} + 152 q^{88} + 56 q^{92} - 96 q^{93} + 172 q^{95} - 488 q^{98}+O(q^{100}) \) 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8 + 12 * q^10 + 8 * q^15 - 80 * q^16 - 72 * q^22 + 48 * q^23 - 12 * q^25 - 36 * q^28 - 80 * q^29 + 32 * q^30 - 24 * q^32 + 36 * q^33 - 64 * q^35 + 160 * q^36 - 4 * q^37 - 192 * q^38 - 12 * q^40 - 16 * q^42 + 120 * q^43 + 60 * q^47 + 288 * q^50 - 432 * q^52 - 136 * q^53 - 16 * q^57 - 4 * q^58 - 240 * q^59 - 20 * q^60 - 4 * q^63 + 120 * q^64 + 4 * q^65 - 8 * q^67 - 132 * q^68 + 76 * q^70 - 12 * q^72 - 36 * q^73 - 48 * q^75 - 60 * q^77 - 80 * q^78 + 12 * q^80 - 80 * q^81 - 252 * q^82 - 160 * q^84 + 72 * q^85 + 24 * q^87 + 152 * q^88 + 56 * q^92 - 96 * q^93 + 172 * q^95 - 488 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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