LMFDB - Embedded newform 570.2.bh.b.67.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			67.9
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.b.553.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.11555 + 1.93792i) q^{5} +(0.766044 + 0.642788i) q^{6} +(3.25218 - 0.871419i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(0.819152 + 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.11555 + 1.93792i) q^{5} +(0.766044 + 0.642788i) q^{6} +(3.25218 - 0.871419i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(-0.197741 + 2.22731i) q^{10} +(-2.88718 - 5.00075i) q^{11} +(0.258819 + 0.965926i) q^{12} +(0.401923 + 4.59400i) q^{13} +(3.16385 + 1.15155i) q^{14} +(0.942405 + 2.02778i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(0.200317 - 0.286083i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.33080 - 0.494170i) q^{19} +(-1.43951 + 1.71108i) q^{20} +(3.31575 - 0.584657i) q^{21} +(0.503269 - 5.75239i) q^{22} +(3.27331 - 7.01964i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(-2.51109 + 4.32370i) q^{25} +(-2.30577 + 3.99372i) q^{26} +(0.965926 + 0.258819i) q^{27} +(1.93118 + 2.75801i) q^{28} +(-0.112711 + 0.639219i) q^{29} +(-0.391111 + 2.20160i) q^{30} +(-2.15476 - 1.24405i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-2.44035 - 5.23335i) q^{33} +(0.328181 - 0.119448i) q^{34} +(5.31671 + 5.33036i) q^{35} +(0.173648 + 0.984808i) q^{36} +(-5.40752 + 5.40752i) q^{37} +(-3.26414 - 2.88884i) q^{38} +4.61155i q^{39} +(-2.16062 + 0.575968i) q^{40} +(-1.70268 - 2.02918i) q^{41} +(3.05145 + 1.42291i) q^{42} +(-7.53775 + 3.51491i) q^{43} +(3.71169 - 4.42342i) q^{44} +(0.762086 + 2.10220i) q^{45} +(6.70764 - 3.87266i) q^{46} +(0.588273 - 0.411913i) q^{47} +(-0.819152 + 0.573576i) q^{48} +(3.75512 - 2.16802i) q^{49} +(-4.53694 + 2.10147i) q^{50} +(0.224489 - 0.267536i) q^{51} +(-4.17948 + 1.94892i) q^{52} +(11.2948 + 5.26685i) q^{53} +(0.642788 + 0.766044i) q^{54} +(6.47027 - 11.1737i) q^{55} +3.36690i q^{56} +(-4.27125 - 0.869743i) q^{57} +(-0.458969 + 0.458969i) q^{58} +(-1.10144 - 6.24659i) q^{59} +(-1.58316 + 1.57911i) q^{60} +(11.3283 - 4.12318i) q^{61} +(-1.05152 - 2.25498i) q^{62} +(3.35409 - 0.293445i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-8.45445 + 5.90373i) q^{65} +(1.00271 - 5.68664i) q^{66} +(3.80251 + 5.43055i) q^{67} +(0.337343 + 0.0903907i) q^{68} +(3.87266 - 6.70764i) q^{69} +(1.29783 + 7.41592i) q^{70} +(0.392833 - 1.07930i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(1.19150 - 13.6189i) q^{73} +(-7.53120 + 1.32795i) q^{74} +(-2.87837 + 4.08839i) q^{75} +(-1.01685 - 4.23863i) q^{76} +(-13.7474 - 13.7474i) q^{77} +(-2.64507 + 3.77756i) q^{78} +(-10.6616 + 8.94611i) q^{79} +(-2.10023 - 0.767473i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.230867 - 2.63883i) q^{82} +(-1.18938 - 4.43884i) q^{83} +(1.68345 + 2.91582i) q^{84} +(0.777871 + 0.0690597i) q^{85} +(-8.19063 - 1.44423i) q^{86} +(-0.167994 + 0.626963i) q^{87} +(5.57761 - 1.49452i) q^{88} +(-3.74877 - 3.14559i) q^{89} +(-0.581505 + 2.15913i) q^{90} +(5.31042 + 14.5903i) q^{91} +(7.71584 + 0.675049i) q^{92} +(-2.03813 - 1.42712i) q^{93} +0.718148 q^{94} +(-3.87356 - 8.94402i) q^{95} -1.00000 q^{96} +(-13.5638 - 9.49748i) q^{97} +(4.31953 + 0.377910i) q^{98} +(-1.97495 - 5.42613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^5 + 12 * q^7	$ 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	0.996195	+	0.0871557i	0.575153	+	0.0503194i
$3$	0.996195	+	0.0871557i	0.575153	+	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	1.11555	+	1.93792i	0.498890	+	0.866666i
$5$	1.11555	+	1.93792i	0.498890	+	0.866666i
$6$	0.766044	+	0.642788i	0.312736	+	0.262417i
$7$	3.25218	−	0.871419i	1.22921	−	0.329365i	0.414937	−	0.909850i	$-0.363804\pi$
$7$	3.25218	−	0.871419i	1.22921	−	0.329365i	0.814271	+	0.580485i	$0.197137\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	−0.197741	+	2.22731i	−0.0625313	+	0.704336i
$11$	−2.88718	−	5.00075i	−0.870519	−	1.50778i	−0.861461	−	0.507823i	$-0.830450\pi$
$11$	−2.88718	−	5.00075i	−0.870519	−	1.50778i	−0.00905737	−	0.999959i	$-0.502883\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	0.401923	+	4.59400i	0.111473	+	1.27415i	0.821597	+	0.570069i	$0.193083\pi$
$13$	0.401923	+	4.59400i	0.111473	+	1.27415i	−0.710124	+	0.704077i	$0.751361\pi$
$14$	3.16385	+	1.15155i	0.845575	+	0.307764i
$15$	0.942405	+	2.02778i	0.243328	+	0.523569i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	0.200317	−	0.286083i	0.0485841	−	0.0693853i	−0.794125	−	0.607754i	$-0.792070\pi$
$17$	0.200317	−	0.286083i	0.0485841	−	0.0693853i	0.842709	+	0.538369i	$0.180959\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−4.33080	−	0.494170i	−0.993553	−	0.113370i
$19$	−4.33080	−	0.494170i	−0.993553	−	0.113370i
$20$	−1.43951	+	1.71108i	−0.321884	+	0.382610i
$21$	3.31575	−	0.584657i	0.723556	−	0.127583i
$22$	0.503269	−	5.75239i	0.107297	−	1.22641i
$23$	3.27331	−	7.01964i	0.682533	−	1.46370i	−0.193329	−	0.981134i	$-0.561928\pi$
$23$	3.27331	−	7.01964i	0.682533	−	1.46370i	0.875862	−	0.482562i	$-0.160294\pi$
$24$	−0.342020	+	0.939693i	−0.0698146	+	0.191814i
$25$	−2.51109	+	4.32370i	−0.502218	+	0.864741i
$26$	−2.30577	+	3.99372i	−0.452199	+	0.783232i
$27$	0.965926	+	0.258819i	0.185893	+	0.0498097i
$28$	1.93118	+	2.75801i	0.364958	+	0.521214i
$29$	−0.112711	+	0.639219i	−0.0209300	+	0.118700i	−0.993483	−	0.113983i	$-0.963639\pi$
$29$	−0.112711	+	0.639219i	−0.0209300	+	0.118700i	0.972553	+	0.232683i	$0.0747503\pi$
$30$	−0.391111	+	2.20160i	−0.0714068	+	0.401955i
$31$	−2.15476	−	1.24405i	−0.387006	−	0.223438i	0.293856	−	0.955850i	$-0.405061\pi$
$31$	−2.15476	−	1.24405i	−0.387006	−	0.223438i	−0.680862	+	0.732412i	$0.738395\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	−2.44035	−	5.23335i	−0.424811	−	0.911010i
$34$	0.328181	−	0.119448i	0.0562826	−	0.0204852i
$35$	5.31671	+	5.33036i	0.898689	+	0.900995i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	−5.40752	+	5.40752i	−0.888991	+	0.888991i	−0.994426	−	0.105436i	$-0.966376\pi$
$37$	−5.40752	+	5.40752i	−0.888991	+	0.888991i	0.105436	+	0.994426i	$0.466376\pi$
$38$	−3.26414	−	2.88884i	−0.529513	−	0.468632i
$39$			4.61155i			0.738438i
$40$	−2.16062	+	0.575968i	−0.341623	+	0.0910685i
$41$	−1.70268	−	2.02918i	−0.265915	−	0.316905i	0.616520	−	0.787339i	$-0.288542\pi$
$41$	−1.70268	−	2.02918i	−0.265915	−	0.316905i	−0.882435	+	0.470434i	$0.844097\pi$
$42$	3.05145	+	1.42291i	0.470849	+	0.219560i
$43$	−7.53775	+	3.51491i	−1.14950	+	0.536019i	−0.901516	−	0.432746i	$-0.857545\pi$
$43$	−7.53775	+	3.51491i	−1.14950	+	0.536019i	−0.247980	+	0.968765i	$0.579767\pi$
$44$	3.71169	−	4.42342i	0.559559	−	0.666856i
$45$	0.762086	+	2.10220i	0.113605	+	0.313377i
$46$	6.70764	−	3.87266i	0.988988	−	0.570992i
$47$	0.588273	−	0.411913i	0.0858084	−	0.0600837i	−0.529885	−	0.848070i	$-0.677765\pi$
$47$	0.588273	−	0.411913i	0.0858084	−	0.0600837i	0.615693	+	0.787986i	$0.288876\pi$
$48$	−0.819152	+	0.573576i	−0.118234	+	0.0827886i
$49$	3.75512	−	2.16802i	0.536445	−	0.309717i
$50$	−4.53694	+	2.10147i	−0.641620	+	0.297192i
$51$	0.224489	−	0.267536i	0.0314347	−	0.0374625i
$52$	−4.17948	+	1.94892i	−0.579590	+	0.270267i
$53$	11.2948	+	5.26685i	1.55146	+	0.723457i	0.994267	−	0.106927i	$-0.0341010\pi$
$53$	11.2948	+	5.26685i	1.55146	+	0.723457i	0.557192	+	0.830384i	$0.311879\pi$
$54$	0.642788	+	0.766044i	0.0874723	+	0.104245i
$55$	6.47027	−	11.1737i	0.872450	−	1.50667i
$56$			3.36690i			0.449921i
$57$	−4.27125	−	0.869743i	−0.565740	−	0.115200i
$58$	−0.458969	+	0.458969i	−0.0602655	+	0.0602655i
$59$	−1.10144	−	6.24659i	−0.143396	−	0.813237i	−0.968641	−	0.248463i	$-0.920074\pi$
$59$	−1.10144	−	6.24659i	−0.143396	−	0.813237i	0.825246	−	0.564774i	$-0.191037\pi$
$60$	−1.58316	+	1.57911i	−0.204386	+	0.203862i
$61$	11.3283	−	4.12318i	1.45045	−	0.527919i	0.507730	−	0.861516i	$-0.330485\pi$
$61$	11.3283	−	4.12318i	1.45045	−	0.527919i	0.942716	+	0.333597i	$0.108262\pi$
$62$	−1.05152	−	2.25498i	−0.133543	−	0.286383i
$63$	3.35409	−	0.293445i	0.422576	−	0.0369706i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−8.45445	+	5.90373i	−1.04865	+	0.732268i
$66$	1.00271	−	5.68664i	0.123425	−	0.699977i
$67$	3.80251	+	5.43055i	0.464551	+	0.663447i	0.981254	−	0.192717i	$-0.0617299\pi$
$67$	3.80251	+	5.43055i	0.464551	+	0.663447i	−0.516704	+	0.856164i	$0.672841\pi$
$68$	0.337343	+	0.0903907i	0.0409088	+	0.0109615i
$69$	3.87266	−	6.70764i	0.466213	−	0.807505i
$70$	1.29783	+	7.41592i	0.155120	+	0.886372i
$71$	0.392833	−	1.07930i	0.0466207	−	0.128089i	−0.914197	−	0.405270i	$-0.867178\pi$
$71$	0.392833	−	1.07930i	0.0466207	−	0.128089i	0.960818	+	0.277180i	$0.0893999\pi$
$72$	−0.422618	+	0.906308i	−0.0498060	+	0.106809i
$73$	1.19150	−	13.6189i	0.139455	−	1.59397i	−0.527947	−	0.849277i	$-0.677038\pi$
$73$	1.19150	−	13.6189i	0.139455	−	1.59397i	0.667402	−	0.744698i	$-0.267406\pi$
$74$	−7.53120	+	1.32795i	−0.875485	+	0.154372i
$75$	−2.87837	+	4.08839i	−0.332366	+	0.472087i
$76$	−1.01685	−	4.23863i	−0.116641	−	0.486205i
$77$	−13.7474	−	13.7474i	−1.56666	−	1.56666i
$78$	−2.64507	+	3.77756i	−0.299496	+	0.427724i
$79$	−10.6616	+	8.94611i	−1.19952	+	1.00652i	−0.199875	+	0.979821i	$0.564054\pi$
$79$	−10.6616	+	8.94611i	−1.19952	+	1.00652i	−0.999644	+	0.0266940i	$0.991502\pi$
$80$	−2.10023	−	0.767473i	−0.234813	−	0.0858061i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	−0.230867	−	2.63883i	−0.0254950	−	0.291410i
$83$	−1.18938	−	4.43884i	−0.130552	−	0.487226i	0.869425	−	0.494066i	$-0.164490\pi$
$83$	−1.18938	−	4.43884i	−0.130552	−	0.487226i	−0.999977	+	0.00683904i	$0.997823\pi$
$84$	1.68345	+	2.91582i	0.183680	+	0.318142i
$85$	0.777871	+	0.0690597i	0.0843720	+	0.00749057i
$86$	−8.19063	−	1.44423i	−0.883219	−	0.155735i
$87$	−0.167994	+	0.626963i	−0.0180109	+	0.0672175i
$88$	5.57761	−	1.49452i	0.594575	−	0.159316i
$89$	−3.74877	−	3.14559i	−0.397369	−	0.333432i	0.422107	−	0.906546i	$-0.361291\pi$
$89$	−3.74877	−	3.14559i	−0.397369	−	0.333432i	−0.819475	+	0.573114i	$0.805735\pi$
$90$	−0.581505	+	2.15913i	−0.0612960	+	0.227593i
$91$	5.31042	+	14.5903i	0.556683	+	1.52947i
$92$	7.71584	+	0.675049i	0.804432	+	0.0703787i
$93$	−2.03813	−	1.42712i	−0.211345	−	0.147985i
$94$	0.718148			0.0740713
$95$	−3.87356	−	8.94402i	−0.397419	−	0.917637i
$96$	−1.00000			−0.102062
$97$	−13.5638	−	9.49748i	−1.37720	−	0.964323i	−0.999259	−	0.0384914i	$-0.987745\pi$
$97$	−13.5638	−	9.49748i	−1.37720	−	0.964323i	−0.377937	−	0.925831i	$-0.623366\pi$
$98$	4.31953	+	0.377910i	0.436339	+	0.0381747i
$99$	−1.97495	−	5.42613i	−0.198490	−	0.545347i
$100$	−4.92180	−	0.880861i	−0.492180	−	0.0880861i
$101$	−4.02802	−	3.37991i	−0.400803	−	0.336314i	0.420001	−	0.907524i	$-0.362030\pi$
$101$	−4.02802	−	3.37991i	−0.400803	−	0.336314i	−0.820804	+	0.571210i	$0.806474\pi$
$102$	0.337343	−	0.0903907i	0.0334019	−	0.00895001i
$103$	1.99554	−	7.44745i	0.196626	−	0.733819i	−0.795214	−	0.606329i	$-0.792641\pi$
$103$	1.99554	−	7.44745i	0.196626	−	0.733819i	0.991840	−	0.127489i	$-0.0406919\pi$
$104$	−4.54149	−	0.800787i	−0.445329	−	0.0785236i
$105$	4.83191	+	5.77346i	0.471546	+	0.563432i
$106$	6.23121	+	10.7928i	0.605229	+	1.04829i
$107$	−3.94986	−	14.7411i	−0.381847	−	1.42507i	−0.843077	−	0.537793i	$-0.819258\pi$
$107$	−3.94986	−	14.7411i	−0.381847	−	1.42507i	0.461230	−	0.887281i	$-0.347408\pi$
$108$	0.0871557	+	0.996195i	0.00838657	+	0.0958589i
$109$	13.1800	+	4.79714i	1.26242	+	0.459483i	0.884580	−	0.466389i	$-0.154445\pi$
$109$	13.1800	+	4.79714i	1.26242	+	0.459483i	0.377839	+	0.925871i	$0.376667\pi$
$110$	11.7091	−	5.44179i	1.11642	−	0.518854i
$111$	−5.85824	+	4.91564i	−0.556039	+	0.466572i
$112$	−1.93118	+	2.75801i	−0.182479	+	0.260607i
$113$	6.87761	+	6.87761i	0.646991	+	0.646991i	0.952265	−	0.305274i	$-0.0987479\pi$
$113$	6.87761	+	6.87761i	0.646991	+	0.646991i	−0.305274	+	0.952265i	$0.598748\pi$
$114$	−2.99994	−	3.16234i	−0.280970	−	0.296180i
$115$	17.2551	−	1.48734i	1.60904	−	0.138695i
$116$	−0.639219	+	0.112711i	−0.0593500	+	0.0104650i
$117$	−0.401923	+	4.59400i	−0.0371578	+	0.424715i
$118$	2.68065	−	5.74867i	0.246774	−	0.529208i
$119$	0.402170	−	1.10495i	0.0368669	−	0.101291i
$120$	−2.20259	+	0.385466i	−0.201068	+	0.0351881i
$121$	−11.1717	+	19.3499i	−1.01561	+	1.75908i
$122$	11.6446	+	3.12016i	1.05425	+	0.282486i
$123$	−1.51935	−	2.16986i	−0.136995	−	0.195649i
$124$	0.432054	−	2.45030i	0.0387996	−	0.220044i
$125$	−11.1803	−	0.0429911i	−0.999993	−	0.00384524i
$126$	2.91582	+	1.68345i	0.259762	+	0.149974i
$127$	2.95458	−	0.258492i	0.262177	−	0.0229375i	0.0446905	−	0.999001i	$-0.485770\pi$
$127$	2.95458	−	0.258492i	0.262177	−	0.0229375i	0.217486	+	0.976063i	$0.430214\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	−7.81541	+	2.84458i	−0.688109	+	0.250451i
$130$	−10.3117	−	0.0132171i	−0.904398	−	0.00115921i
$131$	0.943513	+	5.35093i	0.0824352	+	0.467513i	0.997881	+	0.0650710i	$0.0207274\pi$
$131$	0.943513	+	5.35093i	0.0824352	+	0.467513i	−0.915445	+	0.402442i	$0.868162\pi$
$132$	4.08309	−	4.08309i	0.355388	−	0.355388i
$133$	−14.5152	+	2.16681i	−1.25862	+	0.187886i
$134$			6.62948i			0.572700i
$135$	0.575968	+	2.16062i	0.0495714	+	0.185956i
$136$	0.224489	+	0.267536i	0.0192498	+	0.0229410i
$137$	−11.4440	−	5.33644i	−0.977730	−	0.455923i	−0.133000	−	0.991116i	$-0.542461\pi$
$137$	−11.4440	−	5.33644i	−0.977730	−	0.455923i	−0.844730	+	0.535193i	$0.820239\pi$
$138$	7.01964	−	3.27331i	0.597551	−	0.278643i
$139$	−7.97251	+	9.50127i	−0.676220	+	0.805887i	−0.989616	−	0.143735i	$-0.954089\pi$
$139$	−7.97251	+	9.50127i	−0.676220	+	0.805887i	0.313397	+	0.949622i	$0.398533\pi$
$140$	−3.19048	+	6.81917i	−0.269645	+	0.576325i
$141$	0.621935	−	0.359074i	0.0523764	−	0.0302395i
$142$	0.940851	−	0.658791i	0.0789545	−	0.0552845i
$143$	21.8130	−	15.2736i	1.82409	−	1.27724i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	−1.36449	+	0.494655i	−0.113315	+	0.0410788i
$146$	8.78752	−	10.4726i	0.727260	−	0.866715i
$147$	3.92978	−	1.83249i	0.324123	−	0.151141i
$148$	−6.93089	−	3.23192i	−0.569715	−	0.265663i
$149$	−1.08183	−	1.28927i	−0.0886268	−	0.105621i	0.719909	−	0.694069i	$-0.244184\pi$
$149$	−1.08183	−	1.28927i	−0.0886268	−	0.105621i	−0.808535	+	0.588448i	$0.799739\pi$
$150$	−4.70283	+	1.69805i	−0.383985	+	0.138645i
$151$		−	6.53648i		−	0.531931i	−0.963983	−	0.265965i	$-0.914309\pi$
$151$		−	6.53648i		−	0.531931i	0.963983	−	0.265965i	$-0.0856907\pi$
$152$	1.59822	−	4.05533i	0.129633	−	0.328930i
$153$	0.246952	−	0.246952i	0.0199649	−	0.0199649i
$154$	−3.37602	−	19.1464i	−0.272048	−	1.54286i
$155$	0.00713110	−	5.56356i	0.000572784	−	0.446876i
$156$	−4.33344	+	1.57724i	−0.346953	+	0.126280i
$157$	2.22957	+	4.78133i	0.177939	+	0.381592i	0.974967	−	0.222351i	$-0.0713732\pi$
$157$	2.22957	+	4.78133i	0.177939	+	0.381592i	−0.797027	+	0.603943i	$0.793595\pi$
$158$	−13.8647	+	1.21300i	−1.10302	+	0.0965015i
$159$	10.7928	+	6.23121i	0.855923	+	0.494167i
$160$	−1.28021	−	1.83332i	−0.101209	−	0.144937i
$161$	4.52835	−	25.6815i	0.356884	−	2.02399i
$162$	0.573576	+	0.819152i	0.0450644	+	0.0643587i
$163$	2.20951	+	0.592038i	0.173063	+	0.0463720i	0.344310	−	0.938856i	$-0.388113\pi$
$163$	2.20951	+	0.592038i	0.173063	+	0.0463720i	−0.171247	+	0.985228i	$0.554780\pi$
$164$	1.32445	−	2.29402i	0.103422	−	0.179133i
$165$	7.41950	−	10.5673i	0.577607	−	0.822662i
$166$	1.57173	−	4.31829i	0.121990	−	0.335164i
$167$	−1.54104	+	3.30477i	−0.119249	+	0.255731i	−0.956867	−	0.290526i	$-0.906170\pi$
$167$	−1.54104	+	3.30477i	−0.119249	+	0.255731i	0.837618	+	0.546257i	$0.183948\pi$
$168$	−0.293445	+	3.35409i	−0.0226398	+	0.258774i
$169$	−8.14077	+	1.43544i	−0.626213	+	0.110418i
$170$	0.597584	+	0.502739i	0.0458326	+	0.0385583i
$171$	−4.17919	−	1.23870i	−0.319591	−	0.0947255i
$172$	−5.88100	−	5.88100i	−0.448422	−	0.448422i
$173$	−2.31771	+	3.31003i	−0.176212	+	0.251657i	−0.897536	−	0.440941i	$-0.854645\pi$
$173$	−2.31771	+	3.31003i	−0.176212	+	0.251657i	0.721324	+	0.692597i	$0.243534\pi$
$174$	−0.497224	+	0.417220i	−0.0376944	+	0.0316294i
$175$	−4.39876	+	16.2497i	−0.332515	+	1.22836i
$176$	5.42613	+	1.97495i	0.409010	+	0.148867i
$177$	−0.552825	−	6.31882i	−0.0415529	−	0.474952i
$178$	−1.26657	−	4.72692i	−0.0949338	−	0.354298i
$179$	11.3811	+	19.7127i	0.850666	+	1.47340i	0.880609	+	0.473845i	$0.157134\pi$
$179$	11.3811	+	19.7127i	0.850666	+	1.47340i	−0.0299429	+	0.999552i	$0.509533\pi$
$180$	−1.71477	+	1.43512i	−0.127811	+	0.106968i
$181$	2.38949	+	0.421331i	0.177609	+	0.0313173i	0.261745	−	0.965137i	$-0.415702\pi$
$181$	2.38949	+	0.421331i	0.177609	+	0.0313173i	−0.0841361	+	0.996454i	$0.526813\pi$
$182$	−4.01859	+	14.9976i	−0.297877	+	1.11169i
$183$	11.6446	−	3.12016i	0.860793	−	0.230649i
$184$	5.93326	+	4.97859i	0.437405	+	0.367027i
$185$	−16.5117	−	4.44699i	−1.21397	−	0.326949i
$186$	−0.850981	−	2.33805i	−0.0623969	−	0.171434i
$187$	−2.00898	−	0.175763i	−0.146911	−	0.0128531i
$188$	0.588273	+	0.411913i	0.0429042	+	0.0300418i
$189$	3.36690			0.244906
$190$	1.95704	−	9.54830i	0.141979	−	0.692706i
$191$	−0.00779395			−0.000563950			−0.000281975	−	1.00000i	$-0.500090\pi$
$191$	−0.00779395			−0.000563950			−0.000281975		1.00000i	$0.500090\pi$
$192$	−0.819152	−	0.573576i	−0.0591172	−	0.0413943i
$193$	20.2737	+	1.77372i	1.45933	+	0.127675i	0.789003	−	0.614390i	$-0.210598\pi$
$193$	20.2737	+	1.77372i	1.45933	+	0.127675i	0.670328	+	0.742065i	$0.266153\pi$
$194$	−5.66329	−	15.5598i	−0.406600	−	1.11713i
$195$	−8.93682	+	5.14441i	−0.639979	+	0.368399i
$196$	3.32160	+	2.78715i	0.237257	+	0.199082i
$197$	−15.4040	+	4.12750i	−1.09749	+	0.294072i	−0.761743	−	0.647879i	$-0.775656\pi$
$197$	−15.4040	+	4.12750i	−1.09749	+	0.294072i	−0.335750	+	0.941951i	$0.608990\pi$
$198$	1.49452	−	5.57761i	0.106211	−	0.396383i
$199$	18.9285	+	3.33761i	1.34181	+	0.236597i	0.798022	−	0.602628i	$-0.205880\pi$
$199$	18.9285	+	3.33761i	1.34181	+	0.236597i	0.543785	+	0.839225i	$0.316991\pi$
$200$	−3.52646	−	3.54459i	−0.249358	−	0.250640i
$201$	3.31474	+	5.74130i	0.233804	+	0.404960i
$202$	−1.36093	−	5.07904i	−0.0957544	−	0.357360i
$203$	0.190469	+	2.17707i	0.0133683	+	0.152800i
$204$	0.328181	+	0.119448i	0.0229773	+	0.00836304i
$205$	2.03296	−	5.56333i	0.141988	−	0.388560i
$206$	5.90633	−	4.95600i	0.411513	−	0.345301i
$207$	4.44253	−	6.34459i	0.308777	−	0.440980i
$208$	−3.26086	−	3.26086i	−0.226100	−	0.226100i
$209$	10.0326	+	23.0840i	0.693968	+	1.59675i
$210$	0.646549	+	7.50081i	0.0446161	+	0.517605i
$211$	24.8746	−	4.38606i	1.71244	−	0.301949i	0.770424	−	0.637531i	$-0.220044\pi$
$211$	24.8746	−	4.38606i	1.71244	−	0.301949i	0.942011	+	0.335583i	$0.108933\pi$
$212$	−1.08617	+	12.4150i	−0.0745986	+	0.852666i
$213$	0.485405	−	1.04096i	0.0332594	−	0.0713251i
$214$	5.21960	−	14.3407i	0.356804	−	0.980312i
$215$	−15.2204	−	10.6865i	−1.03802	−	0.728815i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−8.09175	−	2.16818i	−0.549304	−	0.147185i
$218$	8.04493	+	11.4893i	0.544871	+	0.778157i
$219$	2.37394	−	13.4633i	0.160416	−	0.909762i
$220$	12.7128	+	2.25842i	0.857099	+	0.152263i
$221$	1.39478	+	0.805275i	0.0938228	+	0.0541686i
$222$	−7.61828	+	0.666514i	−0.511306	+	0.0447335i
$223$	−4.89862	−	10.5051i	−0.328036	−	0.703475i	0.671251	−	0.741230i	$-0.265757\pi$
$223$	−4.89862	−	10.5051i	−0.328036	−	0.703475i	−0.999287	+	0.0377550i	$0.987979\pi$
$224$	−3.16385	+	1.15155i	−0.211394	+	0.0769411i
$225$	−3.22375	+	3.82197i	−0.214916	+	0.254798i
$226$	1.68897	+	9.57864i	0.112349	+	0.637162i
$227$	−7.59900	+	7.59900i	−0.504364	+	0.504364i	−0.912791	−	0.408427i	$-0.866077\pi$
$227$	−7.59900	+	7.59900i	−0.504364	+	0.504364i	0.408427	+	0.912791i	$0.366077\pi$
$228$	−0.643561	−	4.31113i	−0.0426209	−	0.285511i
$229$			10.9597i			0.724235i	0.932132	+	0.362118i	$0.117946\pi$
$229$			10.9597i			0.724235i	−0.932132	+	0.362118i	$0.882054\pi$
$230$	14.9876	+	8.67874i	0.988255	+	0.572259i
$231$	−12.4969	−	14.8932i	−0.822236	−	0.979903i
$232$	−0.588266	−	0.274313i	−0.0386215	−	0.0180095i
$233$	16.2552	−	7.57991i	1.06491	−	0.496576i	0.190463	−	0.981694i	$-0.439001\pi$
$233$	16.2552	−	7.57991i	1.06491	−	0.496576i	0.874449	+	0.485118i	$0.161223\pi$
$234$	−2.96424	+	3.53265i	−0.193779	+	0.230936i
$235$	1.45450	+	0.680517i	0.0948814	+	0.0443921i
$236$	5.49316	−	3.17148i	0.357574	−	0.206446i
$237$	−11.4007	+	7.98285i	−0.740554	+	0.518542i
$238$	0.963214	−	0.674449i	0.0624359	−	0.0437181i
$239$	−9.47907	+	5.47274i	−0.613150	+	0.354002i	−0.774197	−	0.632944i	$-0.781846\pi$
$239$	−9.47907	+	5.47274i	−0.613150	+	0.354002i	0.161047	+	0.986947i	$0.448513\pi$
$240$	−2.02535	−	0.947600i	−0.130736	−	0.0611673i
$241$	−2.34554	+	2.79530i	−0.151089	+	0.180061i	−0.836280	−	0.548302i	$-0.815274\pi$
$241$	−2.34554	+	2.79530i	−0.151089	+	0.180061i	0.685191	+	0.728364i	$0.259719\pi$
$242$	−20.2499	+	9.44269i	−1.30171	+	0.606999i
$243$	0.906308	+	0.422618i	0.0581397	+	0.0271110i
$244$	7.74905	+	9.23495i	0.496082	+	0.591207i
$245$	8.39047	+	4.85859i	0.536048	+	0.310404i
$246$		−	2.64891i		−	0.168888i
$247$	0.529568	−	20.0943i	0.0336956	−	1.27857i
$248$	1.75935	−	1.75935i	0.111719	−	0.111719i
$249$	−0.797988	−	4.52562i	−0.0505704	−	0.286799i
$250$	−9.13367	−	6.44795i	−0.577664	−	0.407804i
$251$	−18.6273	+	6.77980i	−1.17575	+	0.427937i	−0.854698	−	0.519126i	$-0.826258\pi$
$251$	−18.6273	+	6.77980i	−1.17575	+	0.427937i	−0.321049	+	0.947063i	$0.604035\pi$
$252$	1.42291	+	3.05145i	0.0896352	+	0.192223i
$253$	−44.5541	+	3.89798i	−2.80109	+	0.245064i
$254$	2.56852	+	1.48293i	0.161163	+	0.0930476i
$255$	0.768892	+	0.136593i	0.0481499	+	0.00855377i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	11.1365	+	15.9045i	0.694675	+	0.992098i	0.999216	+	0.0395992i	$0.0126081\pi$
$257$	11.1365	+	15.9045i	0.694675	+	0.992098i	−0.304541	+	0.952499i	$0.598503\pi$
$258$	−8.03359	−	2.15260i	−0.500150	−	0.134015i
$259$	−12.8740	+	22.2984i	−0.799952	+	1.38556i
$260$	−8.43929	−	5.92539i	−0.523382	−	0.367477i
$261$	−0.221998	+	0.609935i	−0.0137413	+	0.0377540i
$262$	−2.29629	+	4.92440i	−0.141865	+	0.304231i
$263$	−1.66309	+	19.0092i	−0.102551	+	1.17216i	0.754277	+	0.656556i	$0.227987\pi$
$263$	−1.66309	+	19.0092i	−0.102551	+	1.17216i	−0.856828	+	0.515603i	$0.827568\pi$
$264$	5.68664	−	1.00271i	0.349989	−	0.0617124i
$265$	2.39317	+	27.7639i	0.147011	+	1.70552i
$266$	−13.1329	−	6.55060i	−0.805233	−	0.401643i
$267$	−3.46035	−	3.46035i	−0.211770	−	0.211770i
$268$	−3.80251	+	5.43055i	−0.232275	+	0.331724i
$269$	−6.19697	+	5.19987i	−0.377836	+	0.317042i	−0.811852	−	0.583863i	$-0.801540\pi$
$269$	−6.19697	+	5.19987i	−0.377836	+	0.317042i	0.434016	+	0.900905i	$0.357096\pi$
$270$	−0.767473	+	2.10023i	−0.0467069	+	0.127816i
$271$	21.1848	+	7.71064i	1.28689	+	0.468388i	0.892704	−	0.450644i	$-0.148806\pi$
$271$	21.1848	+	7.71064i	1.28689	+	0.468388i	0.394182	+	0.919032i	$0.371028\pi$
$272$	0.0304385	+	0.347914i	0.00184561	+	0.0210954i
$273$	4.01859	+	14.9976i	0.243216	+	0.907694i
$274$	−6.31355	−	10.9354i	−0.381416	−	0.660631i
$275$	28.8717	+	0.0740129i	1.74103	+	0.00446315i
$276$	7.62765	+	1.34496i	0.459130	+	0.0809571i
$277$	4.18180	−	15.6067i	0.251260	−	0.937714i	−0.718873	−	0.695141i	$-0.755342\pi$
$277$	4.18180	−	15.6067i	0.251260	−	0.937714i	0.970133	−	0.242573i	$-0.0779914\pi$
$278$	−11.9804	+	3.21014i	−0.718537	+	0.192531i
$279$	−1.90600	−	1.59932i	−0.114109	−	0.0957488i
$280$	−6.52480	+	3.75595i	−0.389931	+	0.224461i
$281$	2.56049	+	7.03488i	0.152746	+	0.419666i	0.992338	−	0.123551i	$-0.0394284\pi$
$281$	2.56049	+	7.03488i	0.152746	+	0.419666i	−0.839592	+	0.543217i	$0.817206\pi$
$282$	0.715416	+	0.0625908i	0.0426024	+	0.00372723i
$283$	16.6906	+	11.6869i	0.992152	+	0.694712i	0.952512	−	0.304502i	$-0.0984900\pi$
$283$	16.6906	+	11.6869i	0.992152	+	0.694712i	0.0396400	+	0.999214i	$0.487379\pi$
$284$	1.14857			0.0681549
$285$	−3.07930	−	9.24759i	−0.182402	−	0.547780i
$286$	26.6288			1.57459
$287$	−7.30570	−	5.11551i	−0.431242	−	0.301959i
$288$	−0.996195	−	0.0871557i	−0.0587013	−	0.00513570i
$289$	5.77263	+	15.8602i	0.339566	+	0.932951i
$290$	−1.40145	−	0.377443i	−0.0822959	−	0.0221642i
$291$	−12.6844	−	10.6435i	−0.743574	−	0.623933i
$292$	13.2051	−	3.53830i	0.772771	−	0.207063i
$293$	−1.47742	+	5.51380i	−0.0863117	+	0.322120i	−0.995559	−	0.0941359i	$-0.969991\pi$
$293$	−1.47742	+	5.51380i	−0.0863117	+	0.322120i	0.909248	+	0.416256i	$0.136658\pi$
$294$	4.27016	+	0.752945i	0.249041	+	0.0439126i
$295$	10.8767	−	9.10291i	0.633266	−	0.529992i
$296$	−3.82369	−	6.62283i	−0.222248	−	0.384944i
$297$	−1.49452	−	5.57761i	−0.0867206	−	0.323646i
$298$	−0.146685	−	1.67662i	−0.00849725	−	0.0971240i
$299$	33.5638	+	12.2162i	1.94105	+	0.706483i
$300$	−4.82630	−	1.30647i	−0.278646	−	0.0754292i
$301$	−21.4512	+	17.9997i	−1.23642	+	1.03748i
$302$	3.74917	−	5.35437i	0.215740	−	0.308109i
$303$	−3.71812	−	3.71812i	−0.213600	−	0.213600i
$304$	3.63523	−	2.40523i	0.208495	−	0.137949i
$305$	20.6278	+	17.3538i	1.18114	+	0.993678i
$306$	0.343937	−	0.0606454i	0.0196616	−	0.00346687i
$307$	0.399207	−	4.56296i	0.0227839	−	0.260422i	−0.976256	−	0.216619i	$-0.930497\pi$
$307$	0.399207	−	4.56296i	0.0227839	−	0.260422i	0.999040	−	0.0438028i	$-0.0139473\pi$
$308$	8.21643	−	17.6202i	0.468175	−	1.00400i
$309$	2.63703	−	7.24518i	0.150015	−	0.412164i
$310$	3.19697	−	4.55331i	0.181576	−	0.258611i
$311$	−1.46737	+	2.54157i	−0.0832072	+	0.144119i	−0.904626	−	0.426207i	$-0.859850\pi$
$311$	−1.46737	+	2.54157i	−0.0832072	+	0.144119i	0.821419	+	0.570326i	$0.193183\pi$
$312$	−4.45441	−	1.19356i	−0.252181	−	0.0675718i
$313$	−9.09425	−	12.9879i	−0.514038	−	0.734122i	0.475290	−	0.879829i	$-0.342343\pi$
$313$	−9.09425	−	12.9879i	−0.514038	−	0.734122i	−0.989328	+	0.145707i	$0.953454\pi$
$314$	−0.916101	+	5.19547i	−0.0516986	+	0.293197i
$315$	4.31033	+	6.17262i	0.242860	+	0.347788i
$316$	−12.0531	−	6.95883i	−0.678037	−	0.391465i
$317$	21.5185	−	1.88263i	1.20860	−	0.105739i	0.535012	−	0.844844i	$-0.320307\pi$
$317$	21.5185	−	1.88263i	1.20860	−	0.105739i	0.673590	+	0.739106i	$0.264752\pi$
$318$	5.26685	+	11.2948i	0.295350	+	0.633380i
$319$	3.52199	−	1.28190i	0.197194	−	0.0717726i
$320$	0.00286608	−	2.23607i	0.000160219	−	0.125000i
$321$	−2.65006	−	15.0292i	−0.147912	−	0.838850i
$322$	18.4397	−	18.4397i	1.02761	−	1.02761i
$323$	−1.00891	+	1.13998i	−0.0561371	+	0.0634300i
$324$			1.00000i			0.0555556i
$325$	−20.8724	−	9.79816i	−1.15779	−	0.543504i
$326$	1.47035	+	1.75229i	0.0814351	+	0.0970506i
$327$	12.7118	+	5.92760i	0.702963	+	0.327797i
$328$	2.40073	−	1.11948i	0.132558	−	0.0618128i
$329$	1.55422	−	1.85225i	0.0856869	−	0.102118i
$330$	12.1388	−	4.40057i	0.668221	−	0.242243i
$331$	−4.21945	+	2.43610i	−0.231922	+	0.133900i	−0.611458	−	0.791277i	$-0.709417\pi$
$331$	−4.21945	+	2.43610i	−0.231922	+	0.133900i	0.379537	+	0.925177i	$0.376083\pi$
$332$	3.76436	−	2.63583i	0.206596	−	0.144660i
$333$	−6.26437	+	4.38636i	−0.343285	+	0.240371i
$334$	−3.15789	+	1.82321i	−0.172792	+	0.0997615i
$335$	−6.28209	+	13.4270i	−0.343227	+	0.733597i
$336$	−2.16420	+	2.57920i	−0.118067	+	0.140707i
$337$	−1.93705	+	0.903261i	−0.105518	+	0.0492037i	−0.474660	−	0.880169i	$-0.657429\pi$
$337$	−1.93705	+	0.903261i	−0.105518	+	0.0492037i	0.369143	+	0.929373i	$0.379651\pi$
$338$	−7.49186	−	3.49351i	−0.407504	−	0.190022i
$339$	6.25202	+	7.45086i	0.339563	+	0.404675i
$340$	0.201153	+	0.754580i	0.0109090	+	0.0409228i
$341$			14.3672i			0.778028i
$342$	−2.71290	−	3.41177i	−0.146697	−	0.184487i
$343$	−6.34226	+	6.34226i	−0.342450	+	0.342450i
$344$	−1.44423	−	8.19063i	−0.0778677	−	0.441609i
$345$	17.3190	+	0.0221987i	0.932426	+	0.00119514i
$346$	−3.79711	+	1.38203i	−0.204134	+	0.0742986i
$347$	1.53317	+	3.28788i	0.0823046	+	0.176503i	0.943153	−	0.332358i	$-0.107844\pi$
$347$	1.53317	+	3.28788i	0.0823046	+	0.176503i	−0.860849	+	0.508861i	$0.830067\pi$
$348$	−0.646610	+	0.0565710i	−0.0346619	+	0.00303252i
$349$	−4.33530	−	2.50299i	−0.232063	−	0.133982i	0.379460	−	0.925208i	$-0.376110\pi$
$349$	−4.33530	−	2.50299i	−0.232063	−	0.133982i	−0.611523	+	0.791226i	$0.709443\pi$
$350$	−12.9237	+	10.7879i	−0.690800	+	0.576639i
$351$	−0.800787	+	4.54149i	−0.0427428	+	0.242407i
$352$	3.31204	+	4.73008i	0.176532	+	0.252114i
$353$	3.84214	+	1.02950i	0.204496	+	0.0547946i	0.359613	−	0.933102i	$-0.382909\pi$
$353$	3.84214	+	1.02950i	0.204496	+	0.0547946i	−0.155117	+	0.987896i	$0.549575\pi$
$354$	3.17148	−	5.49316i	0.168562	−	0.291958i
$355$	2.52983	−	0.442734i	0.134269	−	0.0234979i
$356$	1.67373	−	4.59854i	0.0887077	−	0.243722i
$357$	0.496943	−	1.06570i	0.0263010	−	0.0564027i
$358$	−1.98386	+	22.6756i	−0.104850	+	1.19845i
$359$	−16.0930	+	2.83762i	−0.849354	+	0.149764i	−0.581350	−	0.813654i	$-0.697475\pi$
$359$	−16.0930	+	2.83762i	−0.849354	+	0.149764i	−0.268004	+	0.963418i	$0.586364\pi$
$360$	−2.22781	+	0.192031i	−0.117416	+	0.0101209i
$361$	18.5116	+	4.28030i	0.974294	+	0.225279i
$362$	1.71569	+	1.71569i	0.0901746	+	0.0901746i
$363$	−12.8156	+	18.3026i	−0.672644	+	0.960636i
$364$	−11.8941	+	9.98032i	−0.623420	+	0.523111i
$365$	27.7216	−	12.8836i	1.45102	−	0.674357i
$366$	11.3283	+	4.12318i	0.592142	+	0.215522i
$367$	0.198344	+	2.26708i	0.0103535	+	0.118341i	0.999613	−	0.0278316i	$-0.00886022\pi$
$367$	0.198344	+	2.26708i	0.0103535	+	0.118341i	−0.989259	+	0.146172i	$0.953305\pi$
$368$	2.00464	+	7.48140i	0.104499	+	0.389995i
$369$	−1.32445	−	2.29402i	−0.0689483	−	0.119422i
$370$	−10.9749	−	13.1135i	−0.570559	−	0.681738i
$371$	41.3223	+	7.28624i	2.14535	+	0.378283i
$372$	0.643968	−	2.40332i	0.0333882	−	0.124606i
$373$	−37.1410	+	9.95190i	−1.92309	+	0.515290i	−0.936919	+	0.349546i	$0.886336\pi$
$373$	−37.1410	+	9.95190i	−1.92309	+	0.515290i	−0.986169	+	0.165744i	$0.946998\pi$
$374$	−1.54485	−	1.29628i	−0.0798822	−	0.0670291i
$375$	−11.1340	−	1.01725i	−0.574956	−	0.0525306i
$376$	0.245621	+	0.674839i	0.0126669	+	0.0348021i
$377$	−2.98187	−	0.260880i	−0.153574	−	0.0134360i
$378$	2.75801	+	1.93118i	0.141856	+	0.0993290i
$379$	4.33757			0.222806			0.111403	−	0.993775i	$-0.464466\pi$
$379$	4.33757			0.222806			0.111403	+	0.993775i	$0.464466\pi$
$380$	7.07980	−	6.69899i	0.363186	−	0.343651i
$381$	2.96587			0.151946
$382$	−0.00638443	−	0.00447042i	−0.000326656	−	0.000228727i
$383$	−25.8252	−	2.25942i	−1.31961	−	0.115451i	−0.594505	−	0.804092i	$-0.702652\pi$
$383$	−25.8252	−	2.25942i	−1.31961	−	0.115451i	−0.725102	+	0.688641i	$0.758208\pi$
$384$	−0.342020	−	0.939693i	−0.0174536	−	0.0479535i
$385$	11.3055	−	41.9773i	0.576180	−	2.13936i
$386$	15.5899	+	13.0814i	0.793503	+	0.665828i
$387$	−8.03359	+	2.15260i	−0.408371	+	0.109423i
$388$	4.28562	−	15.9941i	0.217569	−	0.811979i
$389$	−32.8534	−	5.79293i	−1.66573	−	0.293713i	−0.740201	−	0.672386i	$-0.765270\pi$
$389$	−32.8534	−	5.79293i	−1.66573	−	0.293713i	−0.925531	+	0.378672i	$0.876381\pi$
$390$	−10.2713	−	0.911893i	−0.520109	−	0.0461755i
$391$	−1.35250	−	2.34260i	−0.0683988	−	0.118470i
$392$	1.12225	+	4.18829i	0.0566821	+	0.211540i
$393$	0.473559	+	5.41280i	0.0238879	+	0.273040i
$394$	−14.9857	−	5.45435i	−0.754968	−	0.274786i
$395$	−29.2304	−	10.6814i	−1.47074	−	0.537441i
$396$	4.42342	−	3.71169i	0.222285	−	0.186520i
$397$	−2.48557	+	3.54976i	−0.124747	+	0.178157i	−0.876668	−	0.481096i	$-0.840239\pi$
$397$	−2.48557	+	3.54976i	−0.124747	+	0.178157i	0.751921	+	0.659254i	$0.229128\pi$
$398$	13.5910	+	13.5910i	0.681253	+	0.681253i
$399$	−14.6488	+	0.893485i	−0.733356	+	0.0447302i
$400$	−0.855615	−	4.92625i	−0.0427808	−	0.246312i
$401$	12.6016	−	2.22200i	0.629292	−	0.110961i	0.150099	−	0.988671i	$-0.452041\pi$
$401$	12.6016	−	2.22200i	0.629292	−	0.110961i	0.479193	+	0.877710i	$0.340930\pi$
$402$	−0.577797	+	6.60425i	−0.0288179	+	0.329390i
$403$	4.84912	−	10.3990i	0.241552	−	0.518009i
$404$	1.79841	−	4.94110i	0.0894744	−	0.245829i
$405$	0.385466	+	2.20259i	0.0191540	+	0.109448i
$406$	−1.09269	+	1.89260i	−0.0542295	+	0.0939282i
$407$	42.6541	+	11.4291i	2.11429	+	0.566521i
$408$	0.200317	+	0.286083i	0.00991719	+	0.0141632i
$409$	−3.69630	+	20.9627i	−0.182770	+	1.03654i	0.746017	+	0.665927i	$0.231964\pi$
$409$	−3.69630	+	20.9627i	−0.182770	+	1.03654i	−0.928787	+	0.370614i	$0.879147\pi$
$410$	4.85630	−	3.39115i	0.239836	−	0.167477i
$411$	−10.9354	−	6.31355i	−0.539403	−	0.311425i
$412$	7.68082	−	0.671985i	0.378407	−	0.0331063i
$413$	−9.02549	−	19.3552i	−0.444115	−	0.952408i
$414$	7.27822	−	2.64905i	0.357705	−	0.130194i
$415$	7.27532	−	7.25669i	0.357131	−	0.356217i
$416$	−0.800787	−	4.54149i	−0.0392618	−	0.222665i
$417$	−8.77026	+	8.77026i	−0.429482	+	0.429482i
$418$	−5.02221	+	24.6637i	−0.245645	+	1.20634i
$419$		−	23.3730i		−	1.14184i	−0.821004	−	0.570922i	$-0.806586\pi$
$419$		−	23.3730i		−	1.14184i	0.821004	−	0.570922i	$-0.193414\pi$
$420$	−3.77267	+	6.51515i	−0.184087	+	0.317907i
$421$	4.77389	+	5.68930i	0.232665	+	0.277279i	0.869727	−	0.493533i	$-0.164295\pi$
$421$	4.77389	+	5.68930i	0.232665	+	0.277279i	−0.637062	+	0.770813i	$0.719850\pi$
$422$	22.8918	+	10.6746i	1.11435	+	0.519632i
$423$	0.650863	−	0.303503i	0.0316461	−	0.0147568i
$424$	−8.01069	+	9.54677i	−0.389034	+	0.463632i
$425$	0.733923	+	1.58449i	0.0356005	+	0.0768592i
$426$	0.994688	−	0.574283i	0.0481928	−	0.0278241i
$427$	33.2488	−	23.2811i	1.60902	−	1.12665i
$428$	12.5011	−	8.75340i	0.604266	−	0.423111i
$429$	23.0612	−	13.3144i	1.11340	−	0.642824i
$430$	−6.33826	−	17.4839i	−0.305658	−	0.843150i
$431$	−16.8267	+	20.0532i	−0.810511	+	0.965930i	−0.999872	−	0.0159777i	$-0.994914\pi$
$431$	−16.8267	+	20.0532i	−0.810511	+	0.965930i	0.189361	+	0.981908i	$0.439358\pi$
$432$	−0.906308	+	0.422618i	−0.0436048	+	0.0203332i
$433$	−15.3712	−	7.16769i	−0.738690	−	0.344457i	0.0165868	−	0.999862i	$-0.494720\pi$
$433$	−15.3712	−	7.16769i	−0.738690	−	0.344457i	−0.755277	+	0.655405i	$0.772498\pi$
$434$	−5.38476	−	6.41730i	−0.258477	−	0.308040i
$435$	−1.40241	+	0.373849i	−0.0672405	+	0.0179247i
$436$			14.0259i			0.671719i
$437$	−17.6449	+	28.7831i	−0.844072	+	1.37688i
$438$	9.66682	−	9.66682i	0.461898	−	0.461898i
$439$	−3.20679	−	18.1866i	−0.153052	−	0.867999i	−0.960545	−	0.278123i	$-0.910288\pi$
$439$	−3.20679	−	18.1866i	−0.153052	−	0.867999i	0.807494	−	0.589876i	$-0.200823\pi$
$440$	9.11837	+	9.14177i	0.434701	+	0.435817i
$441$	4.07454	−	1.48301i	0.194026	−	0.0706196i
$442$	0.680648	+	1.45965i	0.0323751	+	0.0694286i
$443$	32.4024	−	2.83484i	1.53948	−	0.134687i	0.714415	−	0.699722i	$-0.246693\pi$
$443$	32.4024	−	2.83484i	1.53948	−	0.134687i	0.825067	+	0.565035i	$0.191137\pi$
$444$	−6.62283	−	3.82369i	−0.314306	−	0.181464i
$445$	1.91397	−	10.7739i	0.0907308	−	0.510731i
$446$	2.01278	−	11.4150i	0.0953077	−	0.540517i
$447$	−0.965344	−	1.37865i	−0.0456592	−	0.0652081i
$448$	−3.25218	−	0.871419i	−0.153651	−	0.0411707i
$449$	1.00086	−	1.73354i	0.0472336	−	0.0818110i	−0.841442	−	0.540347i	$-0.818293\pi$
$449$	1.00086	−	1.73354i	0.0472336	−	0.0818110i	0.888676	+	0.458536i	$0.151626\pi$
$450$	−4.83293	+	1.28171i	−0.227827	+	0.0604204i
$451$	−5.23146	+	14.3733i	−0.246340	+	0.676813i
$452$	−4.11056	+	8.81512i	−0.193344	+	0.414628i
$453$	0.569692	−	6.51160i	0.0267664	−	0.305942i
$454$	−10.5833	+	1.86613i	−0.496701	+	0.0875818i
$455$	−22.3508	+	26.5674i	−1.04782	+	1.24550i
$456$	1.94559	−	3.90060i	0.0911105	−	0.182662i
$457$	−16.8807	−	16.8807i	−0.789644	−	0.789644i	0.191792	−	0.981436i	$-0.438570\pi$
$457$	−16.8807	−	16.8807i	−0.789644	−	0.789644i	−0.981436	+	0.191792i	$0.938570\pi$
$458$	−6.28621	+	8.97763i	−0.293735	+	0.419497i
$459$	0.267536	−	0.224489i	0.0124875	−	0.0104782i
$460$	7.29922	+	15.7058i	0.340328	+	0.732285i
$461$	−16.1521	−	5.87890i	−0.752281	−	0.273808i	−0.0627155	−	0.998031i	$-0.519976\pi$
$461$	−16.1521	−	5.87890i	−0.752281	−	0.273808i	−0.689565	+	0.724224i	$0.742198\pi$
$462$	−1.69446	−	19.3678i	−0.0788333	−	0.901069i
$463$	5.49343	+	20.5018i	0.255301	+	0.952797i	0.967923	+	0.251248i	$0.0808411\pi$
$463$	5.49343	+	20.5018i	0.255301	+	0.952797i	−0.712621	+	0.701549i	$0.752492\pi$
$464$	−0.324540	−	0.562119i	−0.0150664	−	0.0260957i
$465$	0.492000	−	5.54177i	0.0228160	−	0.256993i
$466$	17.6631	+	3.11448i	0.818228	+	0.144276i
$467$	1.33080	−	4.96661i	0.0615820	−	0.229827i	−0.928275	−	0.371895i	$-0.878708\pi$
$467$	1.33080	−	4.96661i	0.0615820	−	0.229827i	0.989857	+	0.142067i	$0.0453750\pi$
$468$	−4.45441	+	1.19356i	−0.205905	+	0.0551721i
$469$	17.0987	+	14.3475i	0.789546	+	0.662508i
$470$	0.801131	+	1.39172i	0.0369534	+	0.0641951i
$471$	1.80437	+	4.95746i	0.0831408	+	0.228427i
$472$	6.31882	+	0.552825i	0.290847	+	0.0254458i
$473$	39.3401	+	27.5462i	1.80886	+	1.26658i
$474$	−13.9177			−0.639260
$475$	13.0117	−	17.4842i	0.597016	−	0.802229i
$476$	1.17587			0.0538958
$477$	10.2086	+	7.14815i	0.467421	+	0.327291i
$478$	−10.9038	−	0.953962i	−0.498730	−	0.0436332i
$479$	5.07767	+	13.9508i	0.232005	+	0.637427i	0.999995	−	0.00303343i	$-0.000965571\pi$
$479$	5.07767	+	13.9508i	0.232005	+	0.637427i	−0.767991	+	0.640461i	$0.778743\pi$
$480$	−1.11555	−	1.93792i	−0.0509177	−	0.0884537i
$481$	−27.0155	−	22.6687i	−1.23180	−	1.03360i
$482$	−3.52467	+	0.944433i	−0.160544	+	0.0430177i
$483$	6.74941	−	25.1891i	0.307109	−	1.14615i
$484$	−22.0039	−	3.87988i	−1.00018	−	0.176358i
$485$	3.27427	−	36.8805i	0.148677	−	1.67466i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−0.618109	−	2.30681i	−0.0280092	−	0.104532i	0.950506	−	0.310706i	$-0.100565\pi$
$487$	−0.618109	−	2.30681i	−0.0280092	−	0.104532i	−0.978515	+	0.206174i	$0.933899\pi$
$488$	1.05070	+	12.0095i	0.0475627	+	0.543645i
$489$	2.14951	+	0.782357i	0.0972041	+	0.0353794i
$490$	4.08630	+	8.79250i	0.184600	+	0.397205i
$491$	−28.8243	+	24.1865i	−1.30082	+	1.09152i	−0.310820	+	0.950469i	$0.600604\pi$
$491$	−28.8243	+	24.1865i	−1.30082	+	1.09152i	−0.990002	+	0.141051i	$0.954952\pi$
$492$	1.51935	−	2.16986i	0.0684976	−	0.0978247i
$493$	0.160291	+	0.160291i	0.00721916	+	0.00721916i
$494$	11.9594	−	16.1565i	0.538079	−	0.726917i
$495$	8.31227	−	9.88043i	0.373609	−	0.444092i
$496$	2.45030	−	0.432054i	0.110022	−	0.0193998i
$497$	0.337041	−	3.85240i	0.0151184	−	0.172804i
$498$	1.94211	−	4.16487i	0.0870281	−	0.186632i
$499$	12.2425	−	33.6359i	0.548049	−	1.50575i	−0.288293	−	0.957542i	$-0.593088\pi$
$499$	12.2425	−	33.6359i	0.548049	−	1.50575i	0.836341	−	0.548209i	$-0.184690\pi$
$500$	−3.78347	−	10.5207i	−0.169202	−	0.470500i
$501$	−1.82321	+	3.15789i	−0.0814549	+	0.141084i
$502$	−19.1474	−	5.13052i	−0.854588	−	0.228986i
$503$	−19.4269	−	27.7444i	−0.866201	−	1.23706i	−0.970156	−	0.242481i	$-0.922039\pi$
$503$	−19.4269	−	27.7444i	−0.866201	−	1.23706i	0.103955	−	0.994582i	$-0.466850\pi$
$504$	−0.584657	+	3.31575i	−0.0260427	+	0.147695i
$505$	2.05655	−	11.5765i	0.0915151	−	0.515146i
$506$	−38.7324	−	22.3621i	−1.72186	−	0.994119i
$507$	−8.23490	+	0.720460i	−0.365725	+	0.0319968i
$508$	1.25343	+	2.68799i	0.0556120	+	0.119260i
$509$	21.8699	−	7.95999i	0.969366	−	0.352820i	0.191669	−	0.981460i	$-0.438610\pi$
$509$	21.8699	−	7.95999i	0.969366	−	0.352820i	0.777697	+	0.628639i	$0.216388\pi$
$510$	0.551493	+	0.552909i	0.0244205	+	0.0244832i
$511$	−7.99281	−	45.3295i	−0.353581	−	2.00526i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.05533	−	1.59822i	−0.179047	−	0.0705633i
$514$			19.4159i			0.856397i
$515$	16.6587	−	4.44081i	0.734070	−	0.195685i
$516$	−5.34606	−	6.37118i	−0.235347	−	0.280476i
$517$	−3.75832	−	1.75254i	−0.165291	−	0.0770764i
$518$	−23.3356	+	10.8816i	−1.02531	+	0.478109i
$519$	−2.59737	+	3.09543i	−0.114012	+	0.135874i
$520$	−3.51440	−	9.69437i	−0.154116	−	0.425126i
$521$	28.0798	−	16.2119i	1.23020	−	0.710255i	0.263127	−	0.964761i	$-0.415246\pi$
$521$	28.0798	−	16.2119i	1.23020	−	0.710255i	0.967071	+	0.254506i	$0.0819129\pi$
$522$	−0.531695	+	0.372297i	−0.0232717	+	0.0162950i
$523$	3.32820	−	2.33043i	0.145532	−	0.101903i	−0.498543	−	0.866865i	$-0.666131\pi$
$523$	3.32820	−	2.33043i	0.145532	−	0.101903i	0.644075	+	0.764962i	$0.277242\pi$
$524$	−4.70553	+	2.71674i	−0.205562	+	0.118681i
$525$	−5.79828	+	15.8045i	−0.253058	+	0.689763i
$526$	−12.2656	+	14.6175i	−0.534804	+	0.637355i
$527$	−0.787537	+	0.367235i	−0.0343057	+	0.0159970i
$528$	5.23335	+	2.44035i	0.227752	+	0.106203i
$529$	−23.7767	−	28.3359i	−1.03377	−	1.23200i
$530$	−13.9643	+	24.1155i	−0.606572	+	1.04751i
$531$		−	6.34296i		−	0.275261i
$532$	−7.00061	−	12.8987i	−0.303515	−	0.559229i
$533$	8.63770	−	8.63770i	0.374140	−	0.374140i
$534$	−0.849777	−	4.81932i	−0.0367734	−	0.208552i
$535$	24.1608	−	24.0989i	1.04456	−	1.04189i
$536$	−6.22967	+	2.26742i	−0.269081	+	0.0979374i
$537$	9.61975	+	20.6296i	0.415123	+	0.890234i
$538$	−8.05878	+	0.705052i	−0.347439	+	0.0303970i
$539$	−21.6834	−	12.5189i	−0.933971	−	0.539228i
$540$	−1.83332	+	1.28021i	−0.0788936	+	0.0550913i
$541$	0.961679	−	5.45395i	0.0413458	−	0.234484i	−0.957131	−	0.289655i	$-0.906459\pi$
$541$	0.961679	−	5.45395i	0.0413458	−	0.234484i	0.998477	+	0.0551714i	$0.0175705\pi$
$542$	12.9309	+	18.4673i	0.555432	+	0.793238i
$543$	2.34367	+	0.627986i	0.100577	+	0.0269494i
$544$	−0.174621	+	0.302453i	−0.00748683	+	0.0129676i
$545$	5.40651	+	30.8934i	0.231590	+	1.32333i
$546$	−5.31042	+	14.5903i	−0.227265	+	0.624405i
$547$	−11.0428	+	23.6814i	−0.472156	+	1.01254i	0.515643	+	0.856804i	$0.327553\pi$
$547$	−11.0428	+	23.6814i	−0.472156	+	1.01254i	−0.987798	+	0.155738i	$0.950225\pi$
$548$	1.10052	−	12.5791i	0.0470121	−	0.537350i
$549$	11.8722	−	2.09339i	0.506694	−	0.0893439i
$550$	23.6079	+	16.6208i	1.00664	+	0.708712i
$551$	0.804013	−	2.71263i	0.0342521	−	0.115562i
$552$	5.47677	+	5.47677i	0.233107	+	0.233107i
$553$	−26.8775	+	38.3850i	−1.14295	+	1.63230i
$554$	12.3771	−	10.3857i	0.525855	−	0.441244i
$555$	−16.0613	−	5.86916i	−0.681764	−	0.249132i
$556$	−11.6550	−	4.24208i	−0.494283	−	0.179904i
$557$	1.60245	+	18.3161i	0.0678979	+	0.776077i	0.951462	+	0.307766i	$0.0995815\pi$
$557$	1.60245	+	18.3161i	0.0678979	+	0.776077i	−0.883564	+	0.468310i	$0.844863\pi$
$558$	−0.643968	−	2.40332i	−0.0272613	−	0.101741i
$559$	−19.1771	−	33.2157i	−0.811104	−	1.40487i
$560$	−7.49913	−	0.665775i	−0.316896	−	0.0281341i
$561$	−1.98602	−	0.350189i	−0.0838498	−	0.0147850i
$562$	−1.93761	+	7.23127i	−0.0817332	+	0.305033i
$563$	−27.6940	+	7.42057i	−1.16716	+	0.312740i	−0.789822	−	0.613336i	$-0.789827\pi$
$563$	−27.6940	+	7.42057i	−1.16716	+	0.312740i	−0.377339	+	0.926075i	$0.623161\pi$
$564$	0.550134	+	0.461617i	0.0231648	+	0.0194376i
$565$	−5.65596	+	21.0006i	−0.237948	+	0.883502i
$566$	6.96881	+	19.1466i	0.292921	+	0.804793i
$567$	3.35409	+	0.293445i	0.140859	+	0.0123235i
$568$	0.940851	+	0.658791i	0.0394772	+	0.0276423i
$569$	−9.61328			−0.403010			−0.201505	−	0.979488i	$-0.564583\pi$
$569$	−9.61328			−0.403010			−0.201505	+	0.979488i	$0.564583\pi$
$570$	2.78179	−	9.34140i	0.116516	−	0.391268i
$571$	−36.3673			−1.52192			−0.760962	−	0.648796i	$-0.775273\pi$
$571$	−36.3673			−1.52192			−0.760962	+	0.648796i	$0.775273\pi$
$572$	21.8130	+	15.2736i	0.912047	+	0.638622i
$573$	−0.00776429		0.000679287i	−0.000324358		2.83776e-5i
$574$	−3.05035	−	8.38076i	−0.127319	−	0.349806i
$575$	22.1313	+	31.7798i	0.922937	+	1.32531i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−24.2182	+	6.48926i	−1.00822	+	0.270151i	−0.724885	−	0.688870i	$-0.758107\pi$
$577$	−24.2182	+	6.48926i	−1.00822	+	0.270151i	−0.283334	+	0.959021i	$0.591440\pi$
$578$	−4.36836	+	16.3029i	−0.181700	+	0.678112i
$579$	20.0419	+	3.53393i	0.832914	+	0.146865i
$580$	−0.931507	−	1.11302i	−0.0386787	−	0.0462157i
$581$	−7.73618	−	13.3995i	−0.320951	−	0.555903i
$582$	−4.28562	−	15.9941i	−0.177644	−	0.662978i
$583$	−6.27195	−	71.6888i	−0.259758	−	2.96904i
$584$	12.8465	+	4.67574i	0.531591	+	0.193483i
$585$	−9.35118	+	4.34594i	−0.386624	+	0.179683i
$586$	−4.37282	+	3.66923i	−0.180639	+	0.151574i
$587$	12.5648	−	17.9444i	0.518605	−	0.740644i	−0.471363	−	0.881939i	$-0.656238\pi$
$587$	12.5648	−	17.9444i	0.518605	−	0.740644i	0.989968	+	0.141295i	$0.0451266\pi$
$588$	3.06604	+	3.06604i	0.126441	+	0.126441i
$589$	8.71705	+	6.45254i	0.359180	+	0.265872i
$590$	14.1309	−	1.21804i	0.581759	−	0.0501461i
$591$	−15.7052	+	2.76924i	−0.646024	+	0.113911i
$592$	0.666514	−	7.61828i	0.0273935	−	0.313110i
$593$	15.6174	−	33.4917i	0.641331	−	1.37534i	−0.269678	−	0.962951i	$-0.586917\pi$
$593$	15.6174	−	33.4917i	0.641331	−	1.37534i	0.911008	−	0.412388i	$-0.135305\pi$
$594$	1.97495	−	5.42613i	0.0810332	−	0.222637i
$595$	2.58996	−	0.453257i	0.106178	−	0.0185817i
$596$	0.841513	−	1.45754i	0.0344697	−	0.0597033i
$597$	18.5656	+	4.97464i	0.759839	+	0.203598i
$598$	20.4869	+	29.2584i	0.837773	+	1.19646i
$599$	7.35781	−	41.7282i	0.300632	−	1.70497i	−0.342753	−	0.939426i	$-0.611359\pi$
$599$	7.35781	−	41.7282i	0.300632	−	1.70497i	0.643385	−	0.765543i	$-0.277530\pi$
$600$	−3.20411	−	3.83845i	−0.130807	−	0.156704i
$601$	14.1951	+	8.19554i	0.579030	+	0.334303i	0.760748	−	0.649048i	$-0.224832\pi$
$601$	14.1951	+	8.19554i	0.579030	+	0.334303i	−0.181718	+	0.983351i	$0.558166\pi$
$602$	−27.8959	+	2.44058i	−1.13695	+	0.0994705i
$603$	2.80174	+	6.00835i	0.114096	+	0.244679i
$604$	6.14228	−	2.23561i	0.249926	−	0.0909656i
$605$	−49.9611	−	0.0640377i	−2.03121	−	0.00260350i
$606$	−0.913079	−	5.17833i	−0.0370913	−	0.210355i
$607$	−12.7226	+	12.7226i	−0.516393	+	0.516393i	−0.916478	−	0.400085i	$-0.868980\pi$
$607$	−12.7226	+	12.7226i	−0.516393	+	0.516393i	0.400085	+	0.916478i	$0.368980\pi$
$608$	4.35739	+	0.114835i	0.176715	+	0.00465719i
$609$			2.18539i			0.0885564i
$610$	6.94351	+	26.0470i	0.281135	+	1.05461i
$611$	2.12877	+	2.53697i	0.0861207	+	0.102635i
$612$	0.316521	+	0.147596i	0.0127946	+	0.00596623i
$613$	27.2767	−	12.7193i	1.10170	−	0.513729i	0.215249	−	0.976559i	$-0.430944\pi$
$613$	27.2767	−	12.7193i	1.10170	−	0.513729i	0.886447	+	0.462830i	$0.153166\pi$
$614$	2.94422	−	3.50878i	0.118819	−	0.141603i
$615$	2.51010	−	5.36497i	0.101217	−	0.216337i
$616$	16.8370	−	9.72087i	0.678383	−	0.391665i
$617$	8.70783	−	6.09729i	0.350564	−	0.245468i	−0.385009	−	0.922913i	$-0.625802\pi$
$617$	8.70783	−	6.09729i	0.350564	−	0.245468i	0.735573	+	0.677445i	$0.236913\pi$
$618$	6.31580	−	4.42237i	0.254059	−	0.177894i
$619$	8.65742	−	4.99836i	0.347971	−	0.200901i	−0.315820	−	0.948819i	$-0.602280\pi$
$619$	8.65742	−	4.99836i	0.347971	−	0.200901i	0.663791	+	0.747918i	$0.268946\pi$
$620$	5.23047	−	1.89615i	0.210061	−	0.0761511i
$621$	4.97859	−	5.93326i	0.199784	−	0.238093i
$622$	−2.65979	+	1.24028i	−0.106648	+	0.0497306i
$623$	−14.9328	−	6.96327i	−0.598269	−	0.278978i
$624$	−2.96424	−	3.53265i	−0.118665	−	0.141419i
$625$	−12.3888	−	21.7144i	−0.495553	−	0.868578i
$626$		−	15.8553i		−	0.633707i
$627$	7.98251	+	23.8705i	0.318791	+	0.953297i
$628$	−3.73042	+	3.73042i	−0.148860	+	0.148860i
$629$	0.463779	+	2.63022i	0.0184921	+	0.104874i
$630$	−0.00964982	+	7.52862i	−0.000384458	+	0.299947i
$631$	17.7618	−	6.46475i	0.707084	−	0.257358i	0.0366517	−	0.999328i	$-0.488331\pi$
$631$	17.7618	−	6.46475i	0.707084	−	0.257358i	0.670433	+	0.741970i	$0.266109\pi$
$632$	−5.88186	−	12.6137i	−0.233968	−	0.501746i
$633$	25.1622	−	2.20140i	1.00011	−	0.0874980i
$634$	18.7068	+	10.8004i	0.742941	+	0.428937i
$635$	3.79693	+	5.43739i	0.150676	+	0.215776i
$636$	−2.16408	+	12.2731i	−0.0858112	+	0.486660i
$637$	11.4691	+	16.3796i	0.454424	+	0.648984i
$638$	3.62031	+	0.970060i	0.143330	+	0.0384050i
$639$	0.574283	−	0.994688i	0.0227183	−	0.0393493i
$640$	1.28490	−	1.83003i	0.0507902	−	0.0723385i
$641$	−4.44456	+	12.2113i	−0.175549	+	0.482318i	−0.995995	−	0.0894062i	$-0.971503\pi$
$641$	−4.44456	+	12.2113i	−0.175549	+	0.482318i	0.820446	+	0.571724i	$0.193725\pi$
$642$	6.44961	−	13.8312i	0.254546	−	0.545875i
$643$	−3.45633	+	39.5060i	−0.136304	+	1.55797i	0.552806	+	0.833310i	$0.313557\pi$
$643$	−3.45633	+	39.5060i	−0.136304	+	1.55797i	−0.689110	+	0.724656i	$0.741999\pi$
$644$	25.6815	−	4.52835i	1.01199	−	0.178442i
$645$	−14.2311	−	11.9724i	−0.560348	−	0.471413i
$646$	−1.48031	+	0.355128i	−0.0582421	+	0.0139723i
$647$	−7.51063	−	7.51063i	−0.295273	−	0.295273i	0.543886	−	0.839159i	$-0.316952\pi$
$647$	−7.51063	−	7.51063i	−0.295273	−	0.295273i	−0.839159	+	0.543886i	$0.816952\pi$
$648$	−0.573576	+	0.819152i	−0.0225322	+	0.0321793i
$649$	−28.0576	+	23.5431i	−1.10136	+	0.924148i
$650$	−11.4776	−	19.9981i	−0.450190	−	0.784389i
$651$	−7.87199	−	2.86517i	−0.308527	−	0.112295i
$652$	0.199365	+	2.27875i	0.00780774	+	0.0892429i
$653$	−0.791135	−	2.95255i	−0.0309595	−	0.115542i	0.948717	−	0.316127i	$-0.102383\pi$
$653$	−0.791135	−	2.95255i	−0.0309595	−	0.115542i	−0.979676	+	0.200585i	$0.935716\pi$
$654$	7.01295	+	12.1468i	0.274228	+	0.474977i
$655$	−9.31716	+	7.79769i	−0.364051	+	0.304681i
$656$	2.60866	+	0.459978i	0.101851	+	0.0179591i
$657$	3.53830	−	13.2051i	0.138042	−	0.515181i
$658$	2.33555	−	0.625808i	0.0910491	−	0.0243965i
$659$	6.16622	+	5.17407i	0.240202	+	0.201553i	0.754939	−	0.655795i	$-0.227666\pi$
$659$	6.16622	+	5.17407i	0.240202	+	0.201553i	−0.514738	+	0.857348i	$0.672111\pi$
$660$	12.4676	+	3.35782i	0.485302	+	0.130703i
$661$	−0.509874	−	1.40087i	−0.0198318	−	0.0544875i	0.929382	−	0.369120i	$-0.120341\pi$
$661$	−0.509874	−	1.40087i	−0.0198318	−	0.0544875i	−0.949214	+	0.314633i	$0.898119\pi$
$662$	−4.85366	−	0.424640i	−0.188643	−	0.0165041i
$663$	1.31928	+	0.923773i	0.0512368	+	0.0358764i
$664$	4.59543			0.178337
$665$	−20.3915	−	25.7121i	−0.790748	−	0.997071i
$666$	−7.64739			−0.296330
$667$	4.11814	+	2.88356i	0.159455	+	0.111652i
$668$	−3.63254	−	0.317806i	−0.140547	−	0.0122963i
$669$	−3.96440	−	10.8921i	−0.153272	−	0.421112i
$670$	−12.8474	+	7.39552i	−0.496339	+	0.285714i
$671$	−53.3260	−	44.7458i	−2.05863	−	1.72739i
$672$	−3.25218	+	0.871419i	−0.125456	+	0.0336157i
$673$	−0.657282	+	2.45301i	−0.0253364	+	0.0945566i	−0.977436	−	0.211231i	$-0.932253\pi$
$673$	−0.657282	+	2.45301i	−0.0253364	+	0.0945566i	0.952100	+	0.305787i	$0.0989196\pi$
$674$	−2.10483	−	0.371138i	−0.0810749	−	0.0142957i
$675$	−3.54459	+	3.52646i	−0.136431	+	0.135733i
$676$	−4.13318	−	7.15887i	−0.158968	−	0.275341i
$677$	−5.77139	−	21.5391i	−0.221813	−	0.827816i	−0.983656	−	0.180055i	$-0.942372\pi$
$677$	−5.77139	−	21.5391i	−0.221813	−	0.827816i	0.761844	−	0.647761i	$-0.224294\pi$
$678$	0.847712	+	9.68940i	0.0325562	+	0.372119i
$679$	−52.3882	−	19.0677i	−2.01047	−	0.731753i
$680$	−0.268034	+	0.733492i	−0.0102786	+	0.0281281i
$681$	−8.23238	+	6.90779i	−0.315466	+	0.264707i
$682$	−8.24069	+	11.7689i	−0.315552	+	0.450655i
$683$	27.6566	+	27.6566i	1.05825	+	1.05825i	0.998195	+	0.0600543i	$0.0191274\pi$
$683$	27.6566	+	27.6566i	1.05825	+	1.05825i	0.0600543	+	0.998195i	$0.480873\pi$
$684$	−0.265373	−	4.35081i	−0.0101468	−	0.166358i
$685$	−2.42479	−	28.1307i	−0.0926466	−	1.07482i
$686$	−8.83305	+	1.55750i	−0.337247	+	0.0594658i
$687$	−0.955198	+	10.9180i	−0.0364431	+	0.416546i
$688$	3.51491	−	7.53775i	0.134005	−	0.287374i
$689$	−19.6562	+	54.0051i	−0.748843	+	2.05743i
$690$	14.1742	+	9.95198i	0.539602	+	0.378865i
$691$	−16.4318	+	28.4608i	−0.625097	+	1.08270i	0.363425	+	0.931623i	$0.381607\pi$
$691$	−16.4318	+	28.4608i	−0.625097	+	1.08270i	−0.988522	+	0.151076i	$0.951726\pi$
$692$	−3.90311	−	1.04584i	−0.148374	−	0.0397567i
$693$	−11.1513	−	15.9257i	−0.423604	−	0.604969i
$694$	−0.629957	+	3.57266i	−0.0239128	+	0.135616i
$695$	−27.3065	−	4.85096i	−1.03579	−	0.184008i
$696$	−0.562119	−	0.324540i	−0.0213071	−	0.0123016i
$697$	−0.921592	+	0.0806288i	−0.0349078	+	0.00305403i
$698$	−2.11561	−	4.53695i	−0.0800772	−	0.171726i
$699$	16.8539	−	6.13433i	0.637475	−	0.232022i
$700$	−16.7742	+	1.42423i	−0.634004	+	0.0538308i
$701$	1.12604	+	6.38606i	0.0425298	+	0.241198i	0.998660	−	0.0517421i	$-0.0164774\pi$
$701$	1.12604	+	6.38606i	0.0425298	+	0.241198i	−0.956131	+	0.292940i	$0.905366\pi$
$702$	−3.26086	+	3.26086i	−0.123073	+	0.123073i
$703$	26.0911	−	20.7466i	0.984044	−	0.782474i
$704$			5.77437i			0.217630i
$705$	1.38966	+	0.804696i	0.0523375	+	0.0303066i
$706$	2.55680	+	3.04707i	0.0962264	+	0.114678i
$707$	−16.0452	−	7.48199i	−0.603441	−	0.281389i
$708$	5.74867	−	2.68065i	0.216048	−	0.100745i
$709$	12.4651	−	14.8554i	0.468138	−	0.557905i	−0.479380	−	0.877607i	$-0.659138\pi$
$709$	12.4651	−	14.8554i	0.468138	−	0.557905i	0.947518	+	0.319702i	$0.103583\pi$
$710$	2.32625	+	1.08838i	0.0873027	+	0.0408462i
$711$	−12.0531	+	6.95883i	−0.452025	+	0.260977i
$712$	4.00866	−	2.80689i	0.150231	−	0.105193i
$713$	−15.7860	+	11.0535i	−0.591190	+	0.413955i
$714$	1.01833	−	0.587933i	0.0381101	−	0.0220029i
$715$	53.9326	+	25.2334i	2.01697	+	0.943676i
$716$	−14.6313	+	17.4369i	−0.546797	+	0.651648i
$717$	−9.91998	+	4.62576i	−0.370469	+	0.172752i
$718$	−14.8102	−	6.90610i	−0.552711	−	0.257733i
$719$	−11.0645	−	13.1861i	−0.412635	−	0.491760i	0.519194	−	0.854656i	$-0.326232\pi$
$719$	−11.0645	−	13.1861i	−0.412635	−	0.491760i	−0.931829	+	0.362897i	$0.881788\pi$
$720$	−1.93506	−	1.12052i	−0.0721153	−	0.0417591i
$721$		−	25.9594i		−	0.966777i
$722$	12.7087	+	14.1240i	0.472970	+	0.525642i
$723$	−2.58024	+	2.58024i	−0.0959601	+	0.0959601i
$724$	0.421331	+	2.38949i	0.0156587	+	0.0888047i
$725$	−2.48076	−	2.09247i	−0.0921332	−	0.0777123i
$726$	−20.9958	+	7.64186i	−0.779229	+	0.283616i
$727$	16.4918	+	35.3667i	0.611646	+	1.31168i	0.931337	+	0.364157i	$0.118643\pi$
$727$	16.4918	+	35.3667i	0.611646	+	1.31168i	−0.319691	+	0.947522i	$0.603579\pi$
$728$	−15.4675	+	1.35323i	−0.573265	+	0.0501542i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	30.0979	+	5.34686i	1.11397	+	0.197896i
$731$	−0.504387	+	2.86052i	−0.0186554	+	0.105800i
$732$	6.91468	+	9.87519i	0.255574	+	0.364997i
$733$	48.7560	+	13.0641i	1.80084	+	0.482535i	0.994110	−	0.108379i	$-0.0345660\pi$
$733$	48.7560	+	13.0641i	1.80084	+	0.482535i	0.806735	+	0.590914i	$0.201233\pi$
$734$	−1.13787	+	1.97085i	−0.0419995	+	0.0727453i
$735$	7.93509	+	5.57138i	0.292690	+	0.205504i
$736$	−2.64905	+	7.27822i	−0.0976454	+	0.268279i
$737$	16.1783	−	34.6944i	0.595934	−	1.27798i
$738$	0.230867	−	2.63883i	0.00849835	−	0.0971366i
$739$	−0.634070	+	0.111804i	−0.0233246	+	0.00411276i	−0.185298	−	0.982682i	$-0.559325\pi$
$739$	−0.634070	+	0.111804i	−0.0233246	+	0.00411276i	0.161974	+	0.986795i	$0.448214\pi$
$740$	−1.46853	−	17.0369i	−0.0539844	−	0.626289i
$741$	2.27889	−	19.9717i	0.0837170	−	0.733677i
$742$	29.6700	+	29.6700i	1.08922	+	1.08922i
$743$	9.23027	−	13.1822i	0.338626	−	0.483608i	−0.613337	−	0.789821i	$-0.710173\pi$
$743$	9.23027	−	13.1822i	0.338626	−	0.483608i	0.951963	+	0.306214i	$0.0990622\pi$
$744$	1.90600	−	1.59932i	0.0698772	−	0.0586339i
$745$	1.29168	−	3.53475i	0.0473234	−	0.129503i
$746$	−36.1323	−	13.1511i	−1.32290	−	0.481495i
$747$	−0.400518	−	4.57794i	−0.0146542	−	0.167498i
$748$	−0.521949	−	1.94794i	−0.0190843	−	0.0712237i
$749$	−25.6913	−	44.4986i	−0.938739	−	1.62594i
$750$	−8.53694	−	7.21946i	−0.311725	−	0.263618i
$751$	24.9555	+	4.40033i	0.910641	+	0.160570i	0.609294	−	0.792944i	$-0.291453\pi$
$751$	24.9555	+	4.40033i	0.910641	+	0.160570i	0.301346	+	0.953515i	$0.402564\pi$
$752$	−0.185870	+	0.693678i	−0.00677800	+	0.0252958i
$753$	−19.1474	+	5.13052i	−0.697768	+	0.186966i
$754$	−2.29297	−	1.92403i	−0.0835051	−	0.0700691i
$755$	12.6672	−	7.29177i	0.461006	−	0.265375i
$756$	1.15155	+	3.16385i	0.0418814	+	0.115068i
$757$	26.3974	+	2.30948i	0.959431	+	0.0839394i	0.556101	−	0.831115i	$-0.312297\pi$
$757$	26.3974	+	2.30948i	0.959431	+	0.0839394i	0.403331	+	0.915054i	$0.367852\pi$
$758$	3.55313	+	2.48793i	0.129055	+	0.0903656i
$759$	−44.7243			−1.62339
$760$	9.64181	−	1.42669i	0.349745	−	0.0517515i
$761$	−6.15041			−0.222952			−0.111476	−	0.993767i	$-0.535558\pi$
$761$	−6.15041			−0.222952			−0.111476	+	0.993767i	$0.535558\pi$
$762$	2.42950	+	1.70115i	0.0880114	+	0.0616262i
$763$	47.0442	+	4.11583i	1.70311	+	0.149003i
$764$	−0.00266569	−	0.00732392i	−9.64412e−5	−	0.000264970i
$765$	0.754061	+	0.203086i	0.0272631	+	0.00734260i
$766$	−19.8588	−	16.6635i	−0.717529	−	0.602079i
$767$	28.2541	−	7.57068i	1.02020	−	0.273361i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	3.88384	+	0.684826i	0.140055	+	0.0246955i	0.243236	−	0.969967i	$-0.421791\pi$
$769$	3.88384	+	0.684826i	0.140055	+	0.0246955i	−0.103181	+	0.994663i	$0.532902\pi$
$770$	33.3381	−	27.9012i	1.20142	−	1.00549i
$771$	9.70793	+	16.8146i	0.349623	+	0.605564i
$772$	5.26726	+	19.6577i	0.189573	+	0.707495i
$773$	−0.972107	−	11.1112i	−0.0349642	−	0.399643i	−0.993430	−	0.114437i	$-0.963494\pi$
$773$	−0.972107	−	11.1112i	−0.0349642	−	0.399643i	0.958466	−	0.285206i	$-0.0920620\pi$
$774$	−7.81541	−	2.84458i	−0.280919	−	0.102246i
$775$	10.7897	−	6.19261i	0.387578	−	0.222445i
$776$	12.6844	−	10.6435i	0.455345	−	0.382079i
$777$	−14.7684	+	21.0915i	−0.529815	+	0.756654i
$778$	−23.5892	−	23.5892i	−0.845714	−	0.845714i
$779$	6.37122	+	9.62938i	0.228273	+	0.345008i
$780$	−7.89074	−	6.63837i	−0.282534	−	0.237692i
$781$	−6.53149	+	1.15168i	−0.233715	+	0.0412103i
$782$	0.235756	−	2.69470i	0.00843061	−	0.0963624i
$783$	−0.274313	+	0.588266i	−0.00980314	+	0.0210229i
$784$	−1.48301	+	4.07454i	−0.0529647	+	0.145519i
$785$	−6.77865	+	9.65455i	−0.241940	+	0.344586i
$786$	−2.71674	+	4.70553i	−0.0969029	+	0.167841i
$787$	34.2375	+	9.17392i	1.22044	+	0.327015i	0.810849	−	0.585256i	$-0.199006\pi$
$787$	34.2375	+	9.17392i	1.22044	+	0.327015i	0.409588	+	0.912271i	$0.365673\pi$
$788$	−9.14708	−	13.0634i	−0.325851	−	0.465364i
$789$	−3.31353	+	18.7919i	−0.117965	+	0.669011i
$790$	−17.8175	−	25.5156i	−0.633918	−	0.907803i
$791$	28.3605	+	16.3739i	1.00838	+	0.582190i
$792$	5.75239	−	0.503269i	0.204402	−	0.0178829i
$793$	23.4950	+	50.3852i	0.834332	+	1.78923i
$794$	−4.07212	+	1.48213i	−0.144514	+	0.0525988i
$795$	−0.0357183	+	27.8668i	−0.00126680	+	0.988334i
$796$	3.33761	+	18.9285i	0.118298	+	0.670904i
$797$	32.3817	−	32.3817i	1.14702	−	1.14702i	0.159884	−	0.987136i	$-0.448888\pi$
$797$	32.3817	−	32.3817i	1.14702	−	1.14702i	0.987136	−	0.159884i	$-0.0511119\pi$
$798$	−12.5120	−	7.67029i	−0.442922	−	0.271525i
$799$		−	0.250808i		−	0.00887295i
$800$	2.12470	−	4.52611i	0.0751195	−	0.160022i
$801$	−3.14559	−	3.74877i	−0.111144	−	0.132456i
$802$	11.5971	+	5.40781i	0.409507	+	0.190956i
$803$	−71.5449	+	33.3619i	−2.52476	+	1.17732i
$804$	−4.26135	+	5.07847i	−0.150286	+	0.179104i
$805$	54.8205	−	19.8735i	1.93217	−	0.700448i
$806$	9.93677	−	5.73700i	0.350008	−	0.202077i
$807$	−6.62658	+	4.63998i	−0.233267	+	0.163335i
$808$	4.30727	−	3.01599i	0.151529	−	0.106102i
$809$	−8.51655	+	4.91703i	−0.299426	+	0.172874i	−0.642185	−	0.766550i	$-0.721972\pi$
$809$	−8.51655	+	4.91703i	−0.299426	+	0.172874i	0.342759	+	0.939423i	$0.388639\pi$
$810$	−0.947600	+	2.02535i	−0.0332953	+	0.0711636i
$811$	−17.1102	+	20.3912i	−0.600821	+	0.716030i	−0.977647	−	0.210254i	$-0.932571\pi$
$811$	−17.1102	+	20.3912i	−0.600821	+	0.716030i	0.376826	+	0.926284i	$0.377015\pi$
$812$	−1.98063	+	0.923585i	−0.0695066	+	0.0324115i
$813$	20.4322	+	9.52768i	0.716588	+	0.334150i
$814$	28.3847	+	33.8276i	0.994884	+	1.18566i
$815$	1.31750	+	4.94232i	0.0461501	+	0.173122i
$816$			0.349243i			0.0122259i
$817$	34.3814	−	11.4974i	1.20285	−	0.402244i
$818$	−15.0516	+	15.0516i	−0.526266	+	0.526266i
$819$	2.69617	+	15.2907i	0.0942118	+	0.534302i
$820$	5.92313	+	0.00759198i	0.206845	+	0.000265124i
$821$	9.24198	−	3.36381i	0.322547	−	0.117398i	−0.175672	−	0.984449i	$-0.556210\pi$
$821$	9.24198	−	3.36381i	0.322547	−	0.117398i	0.498219	+	0.867051i	$0.333988\pi$
$822$	−5.33644	−	11.4440i	−0.186130	−	0.399157i
$823$	−13.8802	+	1.21436i	−0.483833	+	0.0423299i	−0.326463	−	0.945210i	$-0.605857\pi$
$823$	−13.8802	+	1.21436i	−0.483833	+	0.0423299i	−0.157369	+	0.987540i	$0.550301\pi$
$824$	6.67720	+	3.85508i	0.232611	+	0.134298i
$825$	28.7554	+	2.59007i	1.00114	+	0.0901746i
$826$	3.70845	−	21.0317i	0.129034	−	0.731786i
$827$	−26.0202	−	37.1607i	−0.904810	−	1.29220i	−0.955956	−	0.293511i	$-0.905176\pi$
$827$	−26.0202	−	37.1607i	−0.904810	−	1.29220i	0.0511456	−	0.998691i	$-0.483713\pi$
$828$	7.48140	+	2.00464i	0.259997	+	0.0696659i
$829$	10.8372	−	18.7707i	0.376393	−	0.651932i	−0.614141	−	0.789196i	$-0.710498\pi$
$829$	10.8372	−	18.7707i	0.376393	−	0.651932i	0.990535	+	0.137264i	$0.0438309\pi$
$830$	10.1219	−	1.77138i	0.351335	−	0.0614856i
$831$	5.52609	−	15.1828i	0.191698	−	0.526686i
$832$	1.94892	−	4.17948i	0.0675668	−	0.144897i
$833$	0.131982	−	1.50857i	0.00457292	−	0.0522687i
$834$	−12.2146	+	2.15376i	−0.422957	+	0.0745787i
$835$	−8.12351	+	0.700224i	−0.281126	+	0.0242323i
$836$	−18.2605	+	17.3227i	−0.631553	+	0.599119i
$837$	−1.75935	−	1.75935i	−0.0608121	−	0.0608121i
$838$	13.4062	−	19.1460i	0.463109	−	0.661388i
$839$	17.0705	−	14.3238i	0.589339	−	0.494514i	−0.298660	−	0.954360i	$-0.596540\pi$
$839$	17.0705	−	14.3238i	0.589339	−	0.494514i	0.887999	+	0.459845i	$0.152095\pi$
$840$	−6.82732	+	3.17299i	−0.235565	+	0.109478i
$841$	26.8552	+	9.77449i	0.926041	+	0.337051i
$842$	0.647292	+	7.39859i	0.0223072	+	0.254972i
$843$	1.93761	+	7.23127i	0.0667349	+	0.249058i
$844$	12.6291	+	21.8743i	0.434713	+	0.752945i
$845$	−11.8632	−	14.1749i	−0.408107	−	0.487631i
$846$	0.707238	+	0.124705i	0.0243153	+	0.00428745i
$847$	−19.4704	+	72.6644i	−0.669010	+	2.49678i
$848$	−12.0378	+	3.22551i	−0.413379	+	0.110765i
$849$	15.6085	+	13.0971i	0.535682	+	0.449490i
$850$	−0.307634	+	1.71890i	−0.0105518	+	0.0589579i
$851$	20.2583	+	55.6593i	0.694447	+	1.90798i
$852$	1.14420	+	0.100104i	0.0391995	+	0.00342951i
$853$	−23.3981	−	16.3835i	−0.801136	−	0.560962i	0.0997522	−	0.995012i	$-0.468195\pi$
$853$	−23.3981	−	16.3835i	−0.801136	−	0.560962i	−0.900888	+	0.434051i	$0.857084\pi$
$854$	40.5893			1.38894
$855$	−2.26160	−	9.48078i	−0.0773451	−	0.324236i
$856$	15.2611			0.521613
$857$	37.0617	+	25.9509i	1.26600	+	0.886464i	0.997055	−	0.0766908i	$-0.0244354\pi$
$857$	37.0617	+	25.9509i	1.26600	+	0.886464i	0.268947	+	0.963155i	$0.413324\pi$
$858$	26.5274	+	2.32085i	0.905631	+	0.0792325i
$859$	8.37731	+	23.0165i	0.285830	+	0.785312i	0.996638	+	0.0819260i	$0.0261071\pi$
$859$	8.37731	+	23.0165i	0.285830	+	0.785312i	−0.710808	+	0.703386i	$0.751671\pi$
$860$	4.83637	−	17.9575i	0.164919	−	0.612345i
$861$	−6.83205	−	5.73277i	−0.232836	−	0.195372i
$862$	−25.2856	+	6.77527i	−0.861232	+	0.230767i
$863$	−11.0499	+	41.2389i	−0.376144	+	1.40379i	0.475522	+	0.879704i	$0.342259\pi$
$863$	−11.0499	+	41.2389i	−0.376144	+	1.40379i	−0.851666	+	0.524085i	$0.824407\pi$
$864$	−0.984808	−	0.173648i	−0.0335038	−	0.00590763i
$865$	−9.00010	−	0.799032i	−0.306012	−	0.0271679i
$866$	−8.48009	−	14.6880i	−0.288165	−	0.499117i
$867$	4.36836	+	16.3029i	0.148357	+	0.553676i
$868$	−0.730120	−	8.34532i	−0.0247819	−	0.283258i
$869$	75.5191	+	27.4867i	2.56181	+	0.932422i
$870$	−1.36322	−	0.498151i	−0.0462175	−	0.0168889i
$871$	−23.4196	+	19.6514i	−0.793544	+	0.665862i
$872$	−8.04493	+	11.4893i	−0.272436	+	0.389078i
$873$	−11.7085	−	11.7085i	−0.396273	−	0.396273i
$874$	−30.9632	+	13.4570i	−1.04734	+	0.455189i
$875$	−36.3977	+	9.60287i	−1.23047	+	0.324636i
$876$	13.4633	−	2.37394i	0.454881	−	0.0802078i
$877$	−4.11394	+	47.0225i	−0.138918	+	1.58784i	0.532285	+	0.846565i	$0.321333\pi$
$877$	−4.11394	+	47.0225i	−0.138918	+	1.58784i	−0.671203	+	0.741273i	$0.734222\pi$
$878$	7.80456	−	16.7369i	0.263391	−	0.564844i
$879$	−1.95236	+	5.36405i	−0.0658513	+	0.180925i
$880$	2.22582	+	12.7186i	0.0750325	+	0.428743i
$881$	13.8632	−	24.0118i	0.467064	−	0.808978i	−0.532228	−	0.846601i	$-0.678645\pi$
$881$	13.8632	−	24.0118i	0.467064	−	0.808978i	0.999292	+	0.0376226i	$0.0119785\pi$
$882$	4.18829	+	1.12225i	0.141027	+	0.0377881i
$883$	−18.9559	−	27.0719i	−0.637918	−	0.911041i	0.361857	−	0.932233i	$-0.382143\pi$
$883$	−18.9559	−	27.0719i	−0.637918	−	0.911041i	−0.999775	+	0.0211920i	$0.993254\pi$
$884$	−0.279669	+	1.58608i	−0.00940628	+	0.0533457i
$885$	11.6287	−	8.12030i	0.390894	−	0.272961i
$886$	28.1684	+	16.2631i	0.946338	+	0.546368i
$887$	13.6580	−	1.19492i	0.458590	−	0.0401214i	0.144479	−	0.989508i	$-0.453849\pi$
$887$	13.6580	−	1.19492i	0.458590	−	0.0401214i	0.314110	+	0.949386i	$0.398294\pi$
$888$	−3.23192	−	6.93089i	−0.108456	−	0.232585i
$889$	9.38357	−	3.41534i	0.314715	−	0.114547i
$890$	7.74748	−	7.72765i	0.259696	−	0.259031i
$891$	−1.00271	−	5.68664i	−0.0335920	−	0.190510i
$892$	8.19616	−	8.19616i	0.274428	−	0.274428i
$893$	−2.75124	+	1.49320i	−0.0920669	+	0.0499682i
$894$		−	1.68303i		−	0.0562888i
$895$	−25.5055	+	44.0463i	−0.852553	+	1.47230i
$896$	−2.16420	−	2.57920i	−0.0723010	−	0.0861649i
$897$	32.3714	+	15.0950i	1.08085	+	0.504008i
$898$	1.81418	−	0.845965i	0.0605399	−	0.0282302i
$899$	1.03809	−	1.23714i	0.0346221	−	0.0412610i
$900$	−4.69406	−	1.72214i	−0.156469	−	0.0574047i
$901$	3.76930	−	2.17621i	0.125574	−	0.0724999i
$902$	−12.5296	+	8.77329i	−0.417189	+	0.292119i
$903$	−22.9383	+	16.0616i	−0.763339	+	0.534496i
$904$	−8.42332	+	4.86321i	−0.280155	+	0.161748i
$905$	1.84909	+	5.10066i	0.0614658	+	0.169552i
$906$	4.20157	−	5.00723i	0.139588	−	0.166354i
$907$	27.7682	−	12.9485i	0.922028	−	0.429949i	0.0971569	−	0.995269i	$-0.469025\pi$
$907$	27.7682	−	12.9485i	0.922028	−	0.429949i	0.824872	+	0.565320i	$0.191247\pi$
$908$	−9.73974	−	4.54171i	−0.323225	−	0.150722i
$909$	−3.37991	−	4.02802i	−0.112105	−	0.133601i
$910$	−33.5471	+	8.94284i	−1.11207	+	0.296452i
$911$			38.7845i			1.28499i	0.766290	+	0.642494i	$0.222100\pi$
$911$			38.7845i			1.28499i	−0.766290	+	0.642494i	$0.777900\pi$
$912$	3.83102	−	2.07924i	0.126858	−	0.0688506i
$913$	−18.7636	+	18.7636i	−0.620984	+	0.620984i
$914$	−4.14548	−	23.5102i	−0.137120	−	0.777647i
$915$	19.0368	+	19.0856i	0.629336	+	0.630952i
$916$	−10.2987	+	3.74843i	−0.340279	+	0.123852i
$917$	7.73137	+	16.5800i	0.255312	+	0.547519i
$918$	0.347914	−	0.0304385i	0.0114829	−	0.00100462i
$919$	−30.3213	−	17.5060i	−1.00021	−	0.577470i	−0.0918972	−	0.995769i	$-0.529293\pi$
$919$	−30.3213	−	17.5060i	−1.00021	−	0.577470i	−0.908309	+	0.418299i	$0.862626\pi$
$920$	−3.02928	+	17.0521i	−0.0998724	+	0.562190i
$921$	0.795376	−	4.51080i	0.0262085	−	0.148636i
$922$	−9.85907	−	14.0802i	−0.324691	−	0.463707i
$923$	5.11619	+	1.37088i	0.168401	+	0.0451230i
$924$	9.72087	−	16.8370i	0.319793	−	0.553898i
$925$	−9.80173	−	36.9593i	−0.322279	−	1.21521i
$926$	−7.25937	+	19.9450i	−0.238558	+	0.655432i
$927$	3.25846	−	6.98778i	0.107022	−	0.229509i
$928$	0.0565710	−	0.646610i	0.00185703	−	0.0212260i
$929$	44.9063	−	7.91820i	1.47333	−	0.259788i	0.621420	−	0.783478i	$-0.286556\pi$
$929$	44.9063	−	7.91820i	1.47333	−	0.259788i	0.851909	+	0.523690i	$0.175445\pi$
$930$	3.58165	−	4.25735i	0.117447	−	0.139604i
$931$	−17.3340	+	7.53358i	−0.568099	+	0.246903i
$932$	12.6824	+	12.6824i	0.415425	+	0.415425i
$933$	−1.68330	+	2.40401i	−0.0551089	+	0.0787036i
$934$	3.93886	−	3.30509i	0.128883	−	0.108146i
$935$	−1.90051	−	4.08933i	−0.0621532	−	0.133735i
$936$	−4.33344	−	1.57724i	−0.141643	−	0.0515538i
$937$	−3.80349	−	43.4741i	−0.124255	−	1.42024i	−0.760795	−	0.648992i	$-0.775191\pi$
$937$	−3.80349	−	43.4741i	−0.124255	−	1.42024i	0.636540	−	0.771243i	$-0.280365\pi$
$938$	5.77705	+	21.5602i	0.188627	+	0.703967i
$939$	−7.92767	−	13.7311i	−0.258710	−	0.448099i
$940$	−0.142008	+	1.59954i	−0.00463177	+	0.0521712i
$941$	−12.9053	−	2.27556i	−0.420702	−	0.0741811i	−0.0407102	−	0.999171i	$-0.512962\pi$
$941$	−12.9053	−	2.27556i	−0.420702	−	0.0741811i	−0.379992	+	0.924990i	$0.624073\pi$
$942$	−1.36543	+	5.09585i	−0.0444881	+	0.166032i
$943$	−19.8175	+	5.31009i	−0.645348	+	0.172920i
$944$	4.85899	+	4.07717i	0.158147	+	0.132701i
$945$	3.75595	+	6.52480i	0.122181	+	0.212252i
$946$	16.4256	+	45.1291i	0.534043	+	1.46727i
$947$	−54.5447	−	4.77204i	−1.77246	−	0.155070i	−0.846427	−	0.532504i	$-0.821251\pi$
$947$	−54.5447	−	4.77204i	−1.77246	−	0.155070i	−0.926036	+	0.377434i	$0.876806\pi$
$948$	−11.4007	−	7.98285i	−0.370277	−	0.259271i
$949$	63.0442			2.04650
$950$	20.6870	−	6.85901i	0.671176	−	0.222536i
$951$	21.6007			0.700452
$952$	0.963214	+	0.674449i	0.0312179	+	0.0218590i
$953$	8.01485	+	0.701208i	0.259626	+	0.0227144i	0.216226	−	0.976343i	$-0.430625\pi$
$953$	8.01485	+	0.701208i	0.259626	+	0.0227144i	0.0434006	+	0.999058i	$0.486181\pi$
$954$	4.26240	+	11.7108i	0.138000	+	0.379153i
$955$	−0.00869455	−	0.0151041i	−0.000281349	−	0.000488756i
$956$	−8.38473	−	7.03562i	−0.271182	−	0.227548i
$957$	3.62031	−	0.970060i	0.117028	−	0.0313576i
$958$	−3.84246	+	14.3402i	−0.124144	+	0.463312i
$959$	−41.8683	−	7.38252i	−1.35200	−	0.238394i
$960$	0.197741	−	2.22731i	0.00638207	−	0.0718860i
$961$	−12.4047	−	21.4855i	−0.400151	−	0.693082i
$962$	−9.12758	−	34.0646i	−0.294285	−	1.09829i
$963$	−1.33009	−	15.2030i	−0.0428616	−	0.489910i
$964$	−3.42895	−	1.24803i	−0.110439	−	0.0401965i
$965$	19.1790	+	41.2675i	0.617393	+	1.32845i
$966$	19.9767	−	16.7624i	0.642740	−	0.539323i
$967$	6.47933	−	9.25345i	0.208361	−	0.297571i	−0.701346	−	0.712821i	$-0.747417\pi$
$967$	6.47933	−	9.25345i	0.208361	−	0.297571i	0.909707	+	0.415250i	$0.136306\pi$
$968$	−15.7991	−	15.7991i	−0.507803	−	0.507803i
$969$	−1.10442	+	1.04771i	−0.0354792	+	0.0336572i
$970$	23.8359	−	28.3327i	0.765325	−	0.909709i
$971$	−24.1573	+	4.25958i	−0.775244	+	0.136696i	−0.547253	−	0.836967i	$-0.684327\pi$
$971$	−24.1573	+	4.25958i	−0.775244	+	0.136696i	−0.227990	+	0.973663i	$0.573216\pi$
$972$	−0.0871557	+	0.996195i	−0.00279552	+	0.0319530i
$973$	−17.6484	+	37.8472i	−0.565783	+	1.21333i
$974$	0.816808	−	2.24416i	0.0261722	−	0.0719076i
$975$	−19.9390	−	11.5800i	−0.638558	−	0.370857i
$976$	−6.02769	+	10.4403i	−0.192942	+	0.334185i
$977$	−33.0876	−	8.86580i	−1.05857	−	0.283642i	−0.312779	−	0.949826i	$-0.601260\pi$
$977$	−33.0876	−	8.86580i	−1.05857	−	0.283642i	−0.745787	+	0.666184i	$0.767927\pi$
$978$	1.31203	+	1.87378i	0.0419542	+	0.0599167i
$979$	−4.90692	+	27.8285i	−0.156826	+	0.889404i
$980$	−1.69587	+	9.54620i	−0.0541727	+	0.304942i
$981$	12.1468	+	7.01295i	0.387817	+	0.223906i
$982$	−37.4843	+	3.27945i	−1.19617	+	0.104651i
$983$	−7.74848	−	16.6167i	−0.247138	−	0.529990i	0.743132	−	0.669144i	$-0.233339\pi$
$983$	−7.74848	−	16.6167i	−0.247138	−	0.529990i	−0.990271	+	0.139155i	$0.955561\pi$
$984$	2.48916	−	0.905980i	0.0793515	−	0.0288816i
$985$	−25.1828	−	25.2474i	−0.802390	−	0.804450i
$986$	0.0393637	+	0.223243i	0.00125359	+	0.00710949i
$987$	1.70974	−	1.70974i	0.0544216	−	0.0544216i
$988$	19.0636	−	6.37502i	0.606493	−	0.202816i
$989$			64.4177i			2.04836i
$990$	12.4762	−	3.32585i	0.396519	−	0.105702i
$991$	8.96775	+	10.6873i	0.284870	+	0.339495i	0.889436	−	0.457061i	$-0.151098\pi$
$991$	8.96775	+	10.6873i	0.284870	+	0.339495i	−0.604566	+	0.796555i	$0.706653\pi$
$992$	2.25498	+	1.05152i	0.0715958	+	0.0333857i
$993$	−4.41571	+	2.05908i	−0.140128	+	0.0653429i
$994$	2.48573	−	2.96238i	0.0788426	−	0.0939610i
$995$	14.6477	+	40.4053i	0.464363	+	1.28093i
$996$	3.97976	−	2.29772i	0.126103	−	0.0728059i
$997$	28.7035	−	20.0984i	0.909050	−	0.636524i	−0.0226535	−	0.999743i	$-0.507211\pi$
$997$	28.7035	−	20.0984i	0.909050	−	0.636524i	0.931704	+	0.363220i	$0.118323\pi$
$998$	29.3212	−	20.5309i	0.928147	−	0.649896i
$999$	−6.62283	+	3.82369i	−0.209537	+	0.120976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.67.9	✓	120
5.3	odd	4	inner	570.2.bh.b.523.10	yes	120
19.2	odd	18	inner	570.2.bh.b.97.10	yes	120
95.78	even	36	inner	570.2.bh.b.553.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.67.9	✓	120	1.1	even	1	trivial
570.2.bh.b.97.10	yes	120	19.2	odd	18	inner
570.2.bh.b.523.10	yes	120	5.3	odd	4	inner
570.2.bh.b.553.9	yes	120	95.78	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.11555 + 1.93792i) q^{5} +(0.766044 + 0.642788i) q^{6} +(3.25218 - 0.871419i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(0.819152 + 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.11555 + 1.93792i) q^{5} +(0.766044 + 0.642788i) q^{6} +(3.25218 - 0.871419i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(-0.197741 + 2.22731i) q^{10} +(-2.88718 - 5.00075i) q^{11} +(0.258819 + 0.965926i) q^{12} +(0.401923 + 4.59400i) q^{13} +(3.16385 + 1.15155i) q^{14} +(0.942405 + 2.02778i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(0.200317 - 0.286083i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-4.33080 - 0.494170i) q^{19} +(-1.43951 + 1.71108i) q^{20} +(3.31575 - 0.584657i) q^{21} +(0.503269 - 5.75239i) q^{22} +(3.27331 - 7.01964i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(-2.51109 + 4.32370i) q^{25} +(-2.30577 + 3.99372i) q^{26} +(0.965926 + 0.258819i) q^{27} +(1.93118 + 2.75801i) q^{28} +(-0.112711 + 0.639219i) q^{29} +(-0.391111 + 2.20160i) q^{30} +(-2.15476 - 1.24405i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-2.44035 - 5.23335i) q^{33} +(0.328181 - 0.119448i) q^{34} +(5.31671 + 5.33036i) q^{35} +(0.173648 + 0.984808i) q^{36} +(-5.40752 + 5.40752i) q^{37} +(-3.26414 - 2.88884i) q^{38} +4.61155i q^{39} +(-2.16062 + 0.575968i) q^{40} +(-1.70268 - 2.02918i) q^{41} +(3.05145 + 1.42291i) q^{42} +(-7.53775 + 3.51491i) q^{43} +(3.71169 - 4.42342i) q^{44} +(0.762086 + 2.10220i) q^{45} +(6.70764 - 3.87266i) q^{46} +(0.588273 - 0.411913i) q^{47} +(-0.819152 + 0.573576i) q^{48} +(3.75512 - 2.16802i) q^{49} +(-4.53694 + 2.10147i) q^{50} +(0.224489 - 0.267536i) q^{51} +(-4.17948 + 1.94892i) q^{52} +(11.2948 + 5.26685i) q^{53} +(0.642788 + 0.766044i) q^{54} +(6.47027 - 11.1737i) q^{55} +3.36690i q^{56} +(-4.27125 - 0.869743i) q^{57} +(-0.458969 + 0.458969i) q^{58} +(-1.10144 - 6.24659i) q^{59} +(-1.58316 + 1.57911i) q^{60} +(11.3283 - 4.12318i) q^{61} +(-1.05152 - 2.25498i) q^{62} +(3.35409 - 0.293445i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-8.45445 + 5.90373i) q^{65} +(1.00271 - 5.68664i) q^{66} +(3.80251 + 5.43055i) q^{67} +(0.337343 + 0.0903907i) q^{68} +(3.87266 - 6.70764i) q^{69} +(1.29783 + 7.41592i) q^{70} +(0.392833 - 1.07930i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(1.19150 - 13.6189i) q^{73} +(-7.53120 + 1.32795i) q^{74} +(-2.87837 + 4.08839i) q^{75} +(-1.01685 - 4.23863i) q^{76} +(-13.7474 - 13.7474i) q^{77} +(-2.64507 + 3.77756i) q^{78} +(-10.6616 + 8.94611i) q^{79} +(-2.10023 - 0.767473i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.230867 - 2.63883i) q^{82} +(-1.18938 - 4.43884i) q^{83} +(1.68345 + 2.91582i) q^{84} +(0.777871 + 0.0690597i) q^{85} +(-8.19063 - 1.44423i) q^{86} +(-0.167994 + 0.626963i) q^{87} +(5.57761 - 1.49452i) q^{88} +(-3.74877 - 3.14559i) q^{89} +(-0.581505 + 2.15913i) q^{90} +(5.31042 + 14.5903i) q^{91} +(7.71584 + 0.675049i) q^{92} +(-2.03813 - 1.42712i) q^{93} +0.718148 q^{94} +(-3.87356 - 8.94402i) q^{95} -1.00000 q^{96} +(-13.5638 - 9.49748i) q^{97} +(4.31953 + 0.377910i) q^{98} +(-1.97495 - 5.42613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^5 + 12 * q^7	\( 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more