LMFDB - Embedded newform 378.2.bf.a.227.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			227.19
Character	$\chi$	$=$	378.227
Dual form			378.2.bf.a.5.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(0.261649 - 1.71217i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.00558222 - 0.0316584i) q^{5} +(0.554990 - 1.64073i) q^{6} +(2.62068 + 0.363383i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.86308 - 0.895977i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(0.261649 - 1.71217i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.00558222 - 0.0316584i) q^{5} +(0.554990 - 1.64073i) q^{6} +(2.62068 + 0.363383i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.86308 - 0.895977i) q^{9} -0.0321467i q^{10} +(2.92477 + 0.515715i) q^{11} +(0.831468 - 1.51943i) q^{12} +(-0.559326 - 0.666578i) q^{13} +(2.51776 + 0.812939i) q^{14} +(-0.0556652 + 0.00127436i) q^{15} +(0.766044 + 0.642788i) q^{16} -4.59537 q^{17} +(-2.66400 - 1.37953i) q^{18} -4.51782i q^{19} +(0.00558222 - 0.0316584i) q^{20} +(1.30787 - 4.39198i) q^{21} +(2.79078 + 1.01576i) q^{22} +(-0.272249 - 0.324454i) q^{23} +(1.08268 - 1.35196i) q^{24} +(4.69749 - 1.70975i) q^{25} +(-0.435078 - 0.753577i) q^{26} +(-2.28319 + 4.66766i) q^{27} +(2.33835 + 1.23779i) q^{28} +(-4.29676 + 5.12068i) q^{29} +(-0.0550408 - 0.00841116i) q^{30} +(-1.02474 + 2.81544i) q^{31} +(0.642788 + 0.766044i) q^{32} +(1.64826 - 4.87277i) q^{33} +(-4.52555 - 0.797977i) q^{34} +(-0.00312508 - 0.0849948i) q^{35} +(-2.38397 - 1.82117i) q^{36} +(-2.07847 + 3.60002i) q^{37} +(0.784511 - 4.44918i) q^{38} +(-1.28764 + 0.783253i) q^{39} +(0.0109948 - 0.0302080i) q^{40} +(2.16243 - 1.81450i) q^{41} +(2.05066 - 4.09814i) q^{42} +(-2.94595 + 1.07224i) q^{43} +(2.57200 + 1.48494i) q^{44} +(-0.0123828 + 0.0956419i) q^{45} +(-0.211772 - 0.366800i) q^{46} +(-6.19437 + 2.25457i) q^{47} +(1.30100 - 1.14342i) q^{48} +(6.73590 + 1.90462i) q^{49} +(4.92302 - 0.868061i) q^{50} +(-1.20237 + 7.86807i) q^{51} +(-0.297611 - 0.817679i) q^{52} +(4.47143 + 2.58158i) q^{53} +(-3.05903 + 4.20027i) q^{54} -0.0954721i q^{55} +(2.08788 + 1.62504i) q^{56} +(-7.73529 - 1.18208i) q^{57} +(-5.12068 + 4.29676i) q^{58} +(-3.99921 + 3.35573i) q^{59} +(-0.0527440 - 0.0178411i) q^{60} +(0.208437 + 0.572675i) q^{61} +(-1.49806 + 2.59472i) q^{62} +(-7.17763 - 3.38846i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.0179805 + 0.0214283i) q^{65} +(2.46936 - 4.51253i) q^{66} +(2.60275 + 14.7609i) q^{67} +(-4.31823 - 1.57171i) q^{68} +(-0.626755 + 0.381245i) q^{69} +(0.0116816 - 0.0842462i) q^{70} +(-14.2036 + 8.20047i) q^{71} +(-2.03151 - 2.20748i) q^{72} +(10.4214 - 6.01679i) q^{73} +(-2.67203 + 3.18441i) q^{74} +(-1.69829 - 8.49028i) q^{75} +(1.54519 - 4.24536i) q^{76} +(7.47747 + 2.41434i) q^{77} +(-1.40409 + 0.547757i) q^{78} +(1.37293 - 7.78630i) q^{79} +(0.0160734 - 0.0278399i) q^{80} +(7.39445 + 5.13051i) q^{81} +(2.44466 - 1.41143i) q^{82} +(2.72631 + 2.28764i) q^{83} +(2.73114 - 3.67979i) q^{84} +(0.0256524 + 0.145482i) q^{85} +(-3.08738 + 0.544389i) q^{86} +(7.64325 + 8.69662i) q^{87} +(2.27507 + 1.90901i) q^{88} -4.71645 q^{89} +(-0.0288027 + 0.0920387i) q^{90} +(-1.22359 - 1.95014i) q^{91} +(-0.144861 - 0.398002i) q^{92} +(4.55240 + 2.49119i) q^{93} +(-6.49177 + 1.14467i) q^{94} +(-0.143027 + 0.0252195i) q^{95} +(1.47979 - 0.900129i) q^{96} +(-2.81241 - 7.72703i) q^{97} +(6.30284 + 3.04536i) q^{98} +(-7.91177 - 4.09706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) $ 144 * q + 18 * q^6 - 12 * q^9	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	0.261649	−	1.71217i	0.151063	−	0.988524i
$3$	0.261649	−	1.71217i	0.151063	−	0.988524i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−0.00558222	−	0.0316584i	−0.00249645	−	0.0141580i	0.983534	−	0.180723i	$-0.0578437\pi$
$5$	−0.00558222	−	0.0316584i	−0.00249645	−	0.0141580i	−0.986031	+	0.166565i	$0.946733\pi$
$6$	0.554990	−	1.64073i	0.226574	−	0.669824i
$7$	2.62068	+	0.363383i	0.990523	+	0.137346i
$7$	2.62068	+	0.363383i	0.990523	+	0.137346i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−2.86308	−	0.895977i	−0.954360	−	0.298659i
$10$		−	0.0321467i		−	0.0101657i
$11$	2.92477	+	0.515715i	0.881850	+	0.155494i	0.596196	−	0.802839i	$-0.296678\pi$
$11$	2.92477	+	0.515715i	0.881850	+	0.155494i	0.285654	+	0.958333i	$0.407789\pi$
$12$	0.831468	−	1.51943i	0.240024	−	0.438621i
$13$	−0.559326	−	0.666578i	−0.155129	−	0.184876i	0.682882	−	0.730528i	$-0.260726\pi$
$13$	−0.559326	−	0.666578i	−0.155129	−	0.184876i	−0.838011	+	0.545653i	$0.816282\pi$
$14$	2.51776	+	0.812939i	0.672900	+	0.217267i
$15$	−0.0556652	+	0.00127436i	−0.0143727	+	0.000329038i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−4.59537			−1.11454			−0.557270	−	0.830331i	$-0.688151\pi$
$17$	−4.59537			−1.11454			−0.557270	+	0.830331i	$0.688151\pi$
$18$	−2.66400	−	1.37953i	−0.627910	−	0.325159i
$19$		−	4.51782i		−	1.03646i	−0.855242	−	0.518230i	$-0.826591\pi$
$19$		−	4.51782i		−	1.03646i	0.855242	−	0.518230i	$-0.173409\pi$
$20$	0.00558222	−	0.0316584i	0.00124822	−	0.00707902i
$21$	1.30787	−	4.39198i	0.285401	−	0.958408i
$22$	2.79078	+	1.01576i	0.594996	+	0.216561i
$23$	−0.272249	−	0.324454i	−0.0567679	−	0.0676533i	0.736913	−	0.675987i	$-0.236283\pi$
$23$	−0.272249	−	0.324454i	−0.0567679	−	0.0676533i	−0.793681	+	0.608334i	$0.791838\pi$
$24$	1.08268	−	1.35196i	0.221001	−	0.275968i
$25$	4.69749	−	1.70975i	0.939498	−	0.341949i
$26$	−0.435078	−	0.753577i	−0.0853258	−	0.147789i
$27$	−2.28319	+	4.66766i	−0.439400	+	0.898291i
$28$	2.33835	+	1.23779i	0.441906	+	0.233921i
$29$	−4.29676	+	5.12068i	−0.797888	+	0.950886i	−0.999592	−	0.0285604i	$-0.990908\pi$
$29$	−4.29676	+	5.12068i	−0.797888	+	0.950886i	0.201704	+	0.979447i	$0.435352\pi$
$30$	−0.0550408	−	0.00841116i	−0.0100490	−	0.00153566i
$31$	−1.02474	+	2.81544i	−0.184048	+	0.505668i	−0.997064	−	0.0765735i	$-0.975602\pi$
$31$	−1.02474	+	2.81544i	−0.184048	+	0.505668i	0.813016	+	0.582242i	$0.197824\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	1.64826	−	4.87277i	0.286925	−	0.848241i
$34$	−4.52555	−	0.797977i	−0.776126	−	0.136852i
$35$	−0.00312508	−	0.0849948i	−0.000528236	−	0.0143667i
$36$	−2.38397	−	1.82117i	−0.397329	−	0.303529i
$37$	−2.07847	+	3.60002i	−0.341699	+	0.591840i	−0.984748	−	0.173985i	$-0.944336\pi$
$37$	−2.07847	+	3.60002i	−0.341699	+	0.591840i	0.643049	+	0.765825i	$0.277669\pi$
$38$	0.784511	−	4.44918i	0.127265	−	0.721753i
$39$	−1.28764	+	0.783253i	−0.206188	+	0.125421i
$40$	0.0109948	−	0.0302080i	0.00173844	−	0.00477631i
$41$	2.16243	−	1.81450i	0.337715	−	0.283377i	−0.458120	−	0.888891i	$-0.651477\pi$
$41$	2.16243	−	1.81450i	0.337715	−	0.283377i	0.795835	+	0.605514i	$0.207032\pi$
$42$	2.05066	−	4.09814i	0.316424	−	0.632357i
$43$	−2.94595	+	1.07224i	−0.449252	+	0.163515i	−0.556731	−	0.830693i	$-0.687945\pi$
$43$	−2.94595	+	1.07224i	−0.449252	+	0.163515i	0.107478	+	0.994207i	$0.465722\pi$
$44$	2.57200	+	1.48494i	0.387743	+	0.223864i
$45$	−0.0123828	+	0.0956419i	−0.00184592	+	0.0142575i
$46$	−0.211772	−	0.366800i	−0.0312241	−	0.0540818i
$47$	−6.19437	+	2.25457i	−0.903542	+	0.328863i	−0.751671	−	0.659538i	$-0.770752\pi$
$47$	−6.19437	+	2.25457i	−0.903542	+	0.328863i	−0.151871	+	0.988400i	$0.548530\pi$
$48$	1.30100	−	1.14342i	0.187783	−	0.165038i
$49$	6.73590	+	1.90462i	0.962272	+	0.272089i
$50$	4.92302	−	0.868061i	0.696220	−	0.122762i
$51$	−1.20237	+	7.86807i	−0.168366	+	1.10175i
$52$	−0.297611	−	0.817679i	−0.0412712	−	0.113392i
$53$	4.47143	+	2.58158i	0.614198	+	0.354607i	0.774607	−	0.632443i	$-0.217948\pi$
$53$	4.47143	+	2.58158i	0.614198	+	0.354607i	−0.160409	+	0.987051i	$0.551281\pi$
$54$	−3.05903	+	4.20027i	−0.416282	+	0.571585i
$55$		−	0.0954721i		−	0.0128735i
$56$	2.08788	+	1.62504i	0.279005	+	0.217155i
$57$	−7.73529	−	1.18208i	−1.02456	−	0.156571i
$58$	−5.12068	+	4.29676i	−0.672378	+	0.564192i
$59$	−3.99921	+	3.35573i	−0.520652	+	0.436879i	−0.864859	−	0.502015i	$-0.832592\pi$
$59$	−3.99921	+	3.35573i	−0.520652	+	0.436879i	0.344207	+	0.938894i	$0.388148\pi$
$60$	−0.0527440	−	0.0178411i	−0.00680922	−	0.00230328i
$61$	0.208437	+	0.572675i	0.0266876	+	0.0733236i	0.952321	−	0.305098i	$-0.0986892\pi$
$61$	0.208437	+	0.572675i	0.0266876	+	0.0733236i	−0.925633	+	0.378422i	$0.876467\pi$
$62$	−1.49806	+	2.59472i	−0.190254	+	0.329530i
$63$	−7.17763	−	3.38846i	−0.904296	−	0.426906i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.0179805	+	0.0214283i	−0.00223021	+	0.00265786i
$66$	2.46936	−	4.51253i	0.303958	−	0.555454i
$67$	2.60275	+	14.7609i	0.317977	+	1.80334i	0.555019	+	0.831838i	$0.312711\pi$
$67$	2.60275	+	14.7609i	0.317977	+	1.80334i	−0.237042	+	0.971499i	$0.576178\pi$
$68$	−4.31823	−	1.57171i	−0.523663	−	0.190598i
$69$	−0.626755	+	0.381245i	−0.0754525	+	0.0458965i
$70$	0.0116816	−	0.0842462i	0.00139622	−	0.0100694i
$71$	−14.2036	+	8.20047i	−1.68566	+	0.973216i	−0.727884	+	0.685700i	$0.759496\pi$
$71$	−14.2036	+	8.20047i	−1.68566	+	0.973216i	−0.957776	+	0.287516i	$0.907171\pi$
$72$	−2.03151	−	2.20748i	−0.239416	−	0.260154i
$73$	10.4214	−	6.01679i	1.21973	−	0.704212i	0.254871	−	0.966975i	$-0.417967\pi$
$73$	10.4214	−	6.01679i	1.21973	−	0.704212i	0.964860	+	0.262763i	$0.0846336\pi$
$74$	−2.67203	+	3.18441i	−0.310618	+	0.370180i
$75$	−1.69829	−	8.49028i	−0.196102	−	0.980373i
$76$	1.54519	−	4.24536i	0.177245	−	0.486976i
$77$	7.47747	+	2.41434i	0.852137	+	0.275139i
$78$	−1.40409	+	0.547757i	−0.158982	+	0.0620212i
$79$	1.37293	−	7.78630i	0.154467	−	0.876027i	−0.804804	−	0.593540i	$-0.797730\pi$
$79$	1.37293	−	7.78630i	0.154467	−	0.876027i	0.959271	−	0.282486i	$-0.0911592\pi$
$80$	0.0160734	−	0.0278399i	0.00179706	−	0.00311259i
$81$	7.39445	+	5.13051i	0.821606	+	0.570056i
$82$	2.44466	−	1.41143i	0.269968	−	0.155866i
$83$	2.72631	+	2.28764i	0.299251	+	0.251101i	0.780032	−	0.625739i	$-0.215203\pi$
$83$	2.72631	+	2.28764i	0.299251	+	0.251101i	−0.480781	+	0.876840i	$0.659647\pi$
$84$	2.73114	−	3.67979i	0.297992	−	0.401498i
$85$	0.0256524	+	0.145482i	0.00278239	+	0.0157797i
$86$	−3.08738	+	0.544389i	−0.332921	+	0.0587029i
$87$	7.64325	+	8.69662i	0.819442	+	0.932376i
$88$	2.27507	+	1.90901i	0.242523	+	0.203501i
$89$	−4.71645			−0.499943			−0.249972	−	0.968253i	$-0.580421\pi$
$89$	−4.71645			−0.499943			−0.249972	+	0.968253i	$0.580421\pi$
$90$	−0.0288027	+	0.0920387i	−0.00303608	+	0.00970173i
$91$	−1.22359	−	1.95014i	−0.128267	−	0.204430i
$92$	−0.144861	−	0.398002i	−0.0151028	−	0.0414945i
$93$	4.55240	+	2.49119i	0.472062	+	0.258324i
$94$	−6.49177	+	1.14467i	−0.669575	+	0.118064i
$95$	−0.143027	+	0.0252195i	−0.0146742	+	0.00258746i
$96$	1.47979	−	0.900129i	0.151030	−	0.0918691i
$97$	−2.81241	−	7.72703i	−0.285557	−	0.784561i	−0.996674	−	0.0814878i	$-0.974033\pi$
$97$	−2.81241	−	7.72703i	−0.285557	−	0.784561i	0.711117	−	0.703073i	$-0.248189\pi$
$98$	6.30284	+	3.04536i	0.636683	+	0.307628i
$99$	−7.91177	−	4.09706i	−0.795163	−	0.411770i
$100$	4.99897			0.499897
$101$	−7.67399	−	6.43924i	−0.763591	−	0.640729i	0.175468	−	0.984485i	$-0.443856\pi$
$101$	−7.67399	−	6.43924i	−0.763591	−	0.640729i	−0.939059	+	0.343756i	$0.888301\pi$
$102$	−2.55038	+	7.53974i	−0.252525	+	0.746546i
$103$	−3.13246	+	0.552337i	−0.308650	+	0.0544234i	−0.325828	−	0.945429i	$-0.605643\pi$
$103$	−3.13246	+	0.552337i	−0.308650	+	0.0544234i	0.0171777	+	0.999852i	$0.494532\pi$
$104$	−0.151101	−	0.856937i	−0.0148167	−	0.0840295i
$105$	−0.146344	−	0.0168881i	−0.0142817	−	0.00164811i
$106$	3.95521	+	3.31882i	0.384164	+	0.322352i
$107$	−11.6918	+	6.75029i	−1.13029	+	0.652575i	−0.944008	−	0.329921i	$-0.892978\pi$
$107$	−11.6918	+	6.75029i	−1.13029	+	0.652575i	−0.186284	+	0.982496i	$0.559645\pi$
$108$	−3.74193	+	3.60527i	−0.360067	+	0.346917i
$109$	3.52968	−	6.11358i	0.338082	−	0.585575i	−0.645990	−	0.763346i	$-0.723555\pi$
$109$	3.52968	−	6.11358i	0.338082	−	0.585575i	0.984072	+	0.177771i	$0.0568886\pi$
$110$	0.0165786	−	0.0940217i	0.00158070	−	0.00896462i
$111$	5.62003	+	4.50065i	0.533430	+	0.427183i
$112$	1.77398	+	1.96291i	0.167625	+	0.185477i
$113$	1.80898	−	4.97013i	0.170175	−	0.467551i	−0.825062	−	0.565043i	$-0.808860\pi$
$113$	1.80898	−	4.97013i	0.170175	−	0.467551i	0.995236	+	0.0974918i	$0.0310820\pi$
$114$	−7.41251	−	2.50734i	−0.694245	−	0.234834i
$115$	−0.00875192	+	0.0104301i	−0.000816121	+	0.000972615i
$116$	−5.78901	+	3.34229i	−0.537496	+	0.310323i
$117$	1.00415	+	2.40961i	0.0928341	+	0.222768i
$118$	−4.52117	+	2.61030i	−0.416207	+	0.240297i
$119$	−12.0430	−	1.66988i	−1.10398	−	0.153078i
$120$	−0.0488446	−	0.0267290i	−0.00445889	−	0.00244001i
$121$	−2.04832	−	0.745527i	−0.186211	−	0.0677752i
$122$	0.105826	+	0.600170i	0.00958105	+	0.0543368i
$123$	−2.54093	−	4.17722i	−0.229108	−	0.376647i
$124$	−1.92588	+	2.29517i	−0.172949	+	0.206112i
$125$	−0.160717	−	0.278370i	−0.0143750	−	0.0248982i
$126$	−6.48018	−	4.58337i	−0.577300	−	0.408319i
$127$	9.68010	−	16.7664i	0.858970	−	1.48778i	−0.0139428	−	0.999903i	$-0.504438\pi$
$127$	9.68010	−	16.7664i	0.858970	−	1.48778i	0.872913	−	0.487877i	$-0.162228\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	1.06505	+	5.32452i	0.0937726	+	0.468798i
$130$	−0.0214283	+	0.0179805i	−0.00187939	+	0.00157699i
$131$	15.0574	−	12.6347i	1.31557	−	1.10390i	0.328349	−	0.944557i	$-0.393508\pi$
$131$	15.0574	−	12.6347i	1.31557	−	1.10390i	0.987224	−	0.159340i	$-0.0509366\pi$
$132$	3.21544	−	4.01517i	0.279868	−	0.349476i
$133$	1.64170	−	11.8398i	0.142354	−	1.02664i
$134$			14.9887i			1.29482i
$135$	0.160516	+	0.0462261i	0.0138150	+	0.00397851i
$136$	−3.97970	−	2.29768i	−0.341257	−	0.197025i
$137$	−1.96970	−	5.41171i	−0.168283	−	0.462353i	0.826671	−	0.562685i	$-0.190232\pi$
$137$	−1.96970	−	5.41171i	−0.168283	−	0.462353i	−0.994954	+	0.100332i	$0.968010\pi$
$138$	−0.683436	+	0.266618i	−0.0581779	+	0.0226960i
$139$	−10.1396	+	1.78789i	−0.860031	+	0.151647i	−0.586235	−	0.810141i	$-0.699391\pi$
$139$	−10.1396	+	1.78789i	−0.860031	+	0.151647i	−0.273796	+	0.961788i	$0.588279\pi$
$140$	0.0261333	−	0.0809379i	0.00220867	−	0.00684050i
$141$	2.23946	+	11.1958i	0.188597	+	0.942852i
$142$	−15.4118	+	5.60945i	−1.29333	+	0.470734i
$143$	−1.29213	−	2.23804i	−0.108054	−	0.187154i
$144$	−1.61732	−	2.52671i	−0.134777	−	0.210559i
$145$	0.186098	+	0.107444i	0.0154546	+	0.00892270i
$146$	11.3079	−	4.11573i	0.935846	−	0.340620i
$147$	5.02349	−	11.0347i	0.414330	−	0.910127i
$148$	−3.18441	+	2.67203i	−0.261756	+	0.219640i
$149$	−0.576203	+	1.58310i	−0.0472044	+	0.129693i	−0.961055	−	0.276358i	$-0.910872\pi$
$149$	−0.576203	+	1.58310i	−0.0472044	+	0.129693i	0.913850	+	0.406051i	$0.133095\pi$
$150$	−0.198169	−	8.65620i	−0.0161804	−	0.706775i
$151$	−1.81800	+	10.3104i	−0.147947	+	0.839048i	0.817007	+	0.576628i	$0.195632\pi$
$151$	−1.81800	+	10.3104i	−0.147947	+	0.839048i	−0.964954	+	0.262420i	$0.915479\pi$
$152$	2.25891	−	3.91255i	0.183222	−	0.317349i
$153$	13.1569	+	4.11734i	1.06367	+	0.332867i
$154$	6.94463	+	3.67611i	0.559614	+	0.296229i
$155$	0.0948525	+	0.0167251i	0.00761874	+	0.00134339i
$156$	−1.47788	+	0.295617i	−0.118325	+	0.0236683i
$157$	12.0249	+	14.3308i	0.959695	+	1.14372i	0.989554	+	0.144166i	$0.0460499\pi$
$157$	12.0249	+	14.3308i	0.959695	+	1.14372i	−0.0298586	+	0.999554i	$0.509506\pi$
$158$	2.70415	−	7.42960i	0.215131	−	0.591067i
$159$	5.59006	−	6.98039i	0.443320	−	0.553581i
$160$	0.0206635	−	0.0246258i	0.00163359	−	0.00194684i
$161$	−0.595576	−	0.949220i	−0.0469380	−	0.0748090i
$162$	6.39121	+	6.33660i	0.502141	+	0.497850i
$163$	−10.8913	−	18.8643i	−0.853074	−	1.47757i	−0.878420	−	0.477889i	$-0.841402\pi$
$163$	−10.8913	−	18.8643i	−0.853074	−	1.47757i	0.0253459	−	0.999679i	$-0.491931\pi$
$164$	2.65262	−	0.965473i	0.207134	−	0.0753908i
$165$	−0.163465	−	0.0249802i	−0.0127257	−	0.00194471i
$166$	2.28764	+	2.72631i	0.177556	+	0.211602i
$167$	19.8882	+	7.23871i	1.53900	+	0.560149i	0.965804	−	0.259273i	$-0.0834829\pi$
$167$	19.8882	+	7.23871i	1.53900	+	0.560149i	0.573191	+	0.819422i	$0.305705\pi$
$168$	3.32864	−	3.14963i	0.256810	−	0.242999i
$169$	2.12594	−	12.0568i	0.163534	−	0.927449i
$170$			0.147726i			0.0113301i
$171$	−4.04786	+	12.9349i	−0.309548	+	0.989155i
$172$	−3.13501			−0.239042
$173$	−13.8190	−	11.5955i	−1.05064	−	0.881591i	−0.0574790	−	0.998347i	$-0.518306\pi$
$173$	−13.8190	−	11.5955i	−1.05064	−	0.881591i	−0.993161	+	0.116755i	$0.962751\pi$
$174$	6.01698	+	9.89174i	0.456146	+	0.749891i
$175$	12.9319	−	2.77371i	0.977560	−	0.209672i
$176$	1.90901	+	2.27507i	0.143897	+	0.171489i
$177$	4.69921	+	7.72536i	0.353214	+	0.580674i
$178$	−4.64480	−	0.819004i	−0.348143	−	0.0613869i
$179$		−	12.1928i		−	0.911330i	−0.890151	−	0.455665i	$-0.849402\pi$
$179$		−	12.1928i		−	0.911330i	0.890151	−	0.455665i	$-0.150598\pi$
$180$	−0.0443475	+	0.0856388i	−0.00330547	+	0.00638314i
$181$	−5.21108	−	3.00862i	−0.387336	−	0.223629i	0.293669	−	0.955907i	$-0.405124\pi$
$181$	−5.21108	−	3.00862i	−0.387336	−	0.223629i	−0.681005	+	0.732278i	$0.738457\pi$
$182$	−0.866362	−	2.13298i	−0.0642190	−	0.158107i
$183$	1.03506	−	0.207040i	0.0765136	−	0.0153048i
$184$	−0.0735477	−	0.417110i	−0.00542201	−	0.0307498i
$185$	0.125573	+	0.0457049i	0.00923233	+	0.00336029i
$186$	4.05065	+	3.24385i	0.297008	+	0.237851i
$187$	−13.4404	−	2.36990i	−0.982858	−	0.173304i
$188$	−6.59192			−0.480765
$189$	−7.67966	+	11.4028i	−0.558613	+	0.829429i
$190$	−0.145233			−0.0105363
$191$	3.45873	+	0.609868i	0.250265	+	0.0441285i	0.297373	−	0.954761i	$-0.403889\pi$
$191$	3.45873	+	0.609868i	0.250265	+	0.0441285i	−0.0471082	+	0.998890i	$0.515001\pi$
$192$	1.61361	−	0.629492i	0.116452	−	0.0454297i
$193$	25.0581	+	9.12040i	1.80372	+	0.656501i	0.997931	+	0.0642988i	$0.0204811\pi$
$193$	25.0581	+	9.12040i	1.80372	+	0.656501i	0.805790	+	0.592202i	$0.201741\pi$
$194$	−1.42790	−	8.09801i	−0.102517	−	0.581403i
$195$	0.0319844	+	0.0363924i	0.00229045	+	0.00260612i
$196$	5.67826	+	4.09357i	0.405590	+	0.292398i
$197$	16.6593	+	9.61825i	1.18693	+	0.685272i	0.957607	−	0.288079i	$-0.0930166\pi$
$197$	16.6593	+	9.61825i	1.18693	+	0.685272i	0.229320	+	0.973351i	$0.426350\pi$
$198$	−7.08013	−	5.40868i	−0.503163	−	0.384378i
$199$			16.8478i			1.19431i	0.802125	+	0.597156i	$0.203703\pi$
$199$			16.8478i			1.19431i	−0.802125	+	0.597156i	$0.796297\pi$
$200$	4.92302	+	0.868061i	0.348110	+	0.0613812i
$201$	25.9543	−	0.594180i	1.83068	−	0.0419102i
$202$	−6.43924	−	7.67399i	−0.453064	−	0.539940i
$203$	−13.1212	+	11.8583i	−0.920927	+	0.832288i
$204$	−3.82090	+	6.98233i	−0.267516	+	0.488861i
$205$	−0.0695151	−	0.0583301i	−0.00485515	−	0.00407395i
$206$	−3.18078			−0.221616
$207$	0.488768	+	1.17287i	0.0339717	+	0.0815199i
$208$		−	0.870156i		−	0.0603345i
$209$	2.32991	−	13.2136i	0.161163	−	0.914002i
$210$	−0.141188	−	0.0420439i	−0.00974288	−	0.00290130i
$211$	−6.83576	−	2.48801i	−0.470593	−	0.171282i	0.0958279	−	0.995398i	$-0.469450\pi$
$211$	−6.83576	−	2.48801i	−0.470593	−	0.171282i	−0.566421	+	0.824116i	$0.691672\pi$
$212$	3.31882	+	3.95521i	0.227937	+	0.271645i
$213$	10.3243	+	26.4647i	0.707407	+	1.81333i
$214$	−12.6864	+	4.61747i	−0.867224	+	0.315644i
$215$	0.0503902	+	0.0872783i	0.00343658	+	0.00595233i
$216$	−4.31113	+	2.90072i	−0.293335	+	0.197369i
$217$	−3.70859	+	7.00599i	−0.251755	+	0.475598i
$218$	4.53767	−	5.40778i	0.307330	−	0.366261i
$219$	−7.57505	−	19.4175i	−0.511874	−	1.31211i
$220$	0.0326534	−	0.0897145i	0.00220149	−	0.00604855i
$221$	2.57031	+	3.06317i	0.172897	+	0.206051i
$222$	4.75312	+	5.40818i	0.319009	+	0.362973i
$223$	7.37971	+	1.30124i	0.494182	+	0.0871376i	0.415184	−	0.909737i	$-0.363717\pi$
$223$	7.37971	+	1.30124i	0.494182	+	0.0871376i	0.0789973	+	0.996875i	$0.474828\pi$
$224$	1.40617	+	2.24113i	0.0939538	+	0.149742i
$225$	−14.9812	+	0.686297i	−0.998746	+	0.0457531i
$226$	2.64455	−	4.58050i	0.175913	−	0.304690i
$227$	−1.93210	+	10.9575i	−0.128238	+	0.727274i	0.851094	+	0.525014i	$0.175940\pi$
$227$	−1.93210	+	10.9575i	−0.128238	+	0.727274i	−0.979332	+	0.202260i	$0.935171\pi$
$228$	−6.86450	−	3.75642i	−0.454613	−	0.248775i
$229$	2.34428	−	6.44085i	0.154914	−	0.425624i	−0.837821	−	0.545946i	$-0.816171\pi$
$229$	2.34428	−	6.44085i	0.154914	−	0.425624i	0.992735	+	0.120322i	$0.0383927\pi$
$230$	−0.0104301	+	0.00875192i	−0.000687743	+	0.000577085i
$231$	6.09024	−	12.1710i	0.400708	−	0.800794i
$232$	−6.28144	+	2.28626i	−0.412397	+	0.150100i
$233$	−9.87392	−	5.70071i	−0.646862	−	0.373466i	0.140391	−	0.990096i	$-0.455164\pi$
$233$	−9.87392	−	5.70071i	−0.646862	−	0.373466i	−0.787253	+	0.616630i	$0.788497\pi$
$234$	0.570475	+	2.54737i	0.0372931	+	0.166527i
$235$	0.105954	+	0.183518i	0.00691169	+	0.0119714i
$236$	−4.90575	+	1.78555i	−0.319337	+	0.116229i
$237$	−12.9723	−	4.38798i	−0.842639	−	0.285030i
$238$	−11.5700	−	3.73575i	−0.749975	−	0.242153i
$239$	28.6275	−	5.04779i	1.85176	−	0.326515i	0.866711	−	0.498811i	$-0.166230\pi$
$239$	28.6275	−	5.04779i	1.85176	−	0.326515i	0.985045	+	0.172296i	$0.0551186\pi$
$240$	−0.0434612	−	0.0348047i	−0.00280541	−	0.00224663i
$241$	−5.90021	−	16.2107i	−0.380066	−	1.04422i	−0.971328	−	0.237743i	$-0.923592\pi$
$241$	−5.90021	−	16.2107i	−0.380066	−	1.04422i	0.591262	−	0.806479i	$-0.298630\pi$
$242$	−1.88774	−	1.08989i	−0.121349	−	0.0700606i
$243$	10.7191	−	11.3182i	0.687629	−	0.726062i
$244$			0.609428i			0.0390147i
$245$	0.0226959	−	0.223880i	0.00144999	−	0.0143031i
$246$	−1.77697	−	4.55499i	−0.113295	−	0.290415i
$247$	−3.01148	+	2.52693i	−0.191616	+	0.160785i
$248$	−2.29517	+	1.92588i	−0.145743	+	0.122293i
$249$	4.63018	−	4.06935i	0.293426	−	0.257885i
$250$	−0.109937	−	0.302049i	−0.00695302	−	0.0191033i
$251$	13.2659	−	22.9773i	0.837338	−	1.45031i	−0.0547750	−	0.998499i	$-0.517444\pi$
$251$	13.2659	−	22.9773i	0.837338	−	1.45031i	0.892113	−	0.451813i	$-0.149223\pi$
$252$	−5.58584	−	5.63901i	−0.351875	−	0.355224i
$253$	−0.628940	−	1.08936i	−0.0395411	−	0.0684872i
$254$	12.4445	−	14.8308i	0.780837	−	0.930565i
$255$	0.255802	−	0.00585615i	0.0160189	−	0.000366726i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.68677	−	0.977906i	−0.167596	−	0.0610001i	0.256859	−	0.966449i	$-0.417312\pi$
$257$	−2.68677	−	0.977906i	−0.167596	−	0.0610001i	−0.424456	+	0.905449i	$0.639535\pi$
$258$	0.124278	+	5.42857i	0.00773720	+	0.337968i
$259$	−6.75520	+	8.67921i	−0.419747	+	0.539300i
$260$	−0.0242250	+	0.0139863i	−0.00150237	+	0.000867396i
$261$	16.8900	−	10.8111i	1.04546	−	0.669191i
$262$	17.0226	−	9.82803i	1.05166	−	0.607178i
$263$	8.94405	−	10.6591i	0.551514	−	0.657268i	−0.416214	−	0.909267i	$-0.636643\pi$
$263$	8.94405	−	10.6591i	0.551514	−	0.657268i	0.967728	+	0.251998i	$0.0810877\pi$
$264$	3.86382	−	3.39582i	0.237802	−	0.208998i
$265$	0.0567681	−	0.155969i	0.00348723	−	0.00958110i
$266$	3.67271	−	11.3748i	0.225188	−	0.697434i
$267$	−1.23406	+	8.07539i	−0.0755230	+	0.494206i
$268$	−2.60275	+	14.7609i	−0.158988	+	0.901669i
$269$	9.80823	−	16.9884i	0.598019	−	1.03580i	−0.395095	−	0.918640i	$-0.629288\pi$
$269$	9.80823	−	16.9884i	0.598019	−	1.03580i	0.993113	−	0.117158i	$-0.0373784\pi$
$270$	0.150050	+	0.0733971i	0.00913175	+	0.00446681i
$271$	−15.0724	+	8.70205i	−0.915583	+	0.528612i	−0.882223	−	0.470831i	$-0.843954\pi$
$271$	−15.0724	+	8.70205i	−0.915583	+	0.528612i	−0.0333596	+	0.999443i	$0.510621\pi$
$272$	−3.52025	−	2.95384i	−0.213447	−	0.179103i
$273$	−3.65912	+	1.58475i	−0.221460	+	0.0959132i
$274$	−1.00004	−	5.67153i	−0.0604148	−	0.342629i
$275$	14.6208	−	2.57804i	0.881668	−	0.155462i
$276$	−0.719351	+	0.143890i	−0.0432998	+	0.00866117i
$277$	−2.31013	−	1.93843i	−0.138802	−	0.116469i	0.570743	−	0.821129i	$-0.306655\pi$
$277$	−2.31013	−	1.93843i	−0.138802	−	0.116469i	−0.709545	+	0.704660i	$0.751100\pi$
$278$	−10.2960			−0.617515
$279$	5.45647	−	7.14269i	0.326671	−	0.427622i
$280$	0.0397910	−	0.0751702i	0.00237797	−	0.00449228i
$281$	−5.11356	−	14.0494i	−0.305049	−	0.838116i	−0.993603	−	0.112931i	$-0.963976\pi$
$281$	−5.11356	−	14.0494i	−0.305049	−	0.838116i	0.688554	−	0.725185i	$-0.258246\pi$
$282$	0.261316	+	11.4145i	0.0155612	+	0.679726i
$283$	−19.8563	+	3.50121i	−1.18034	+	0.208125i	−0.729182	−	0.684320i	$-0.760099\pi$
$283$	−19.8563	+	3.50121i	−1.18034	+	0.208125i	−0.451156	+	0.892445i	$0.648988\pi$
$284$	−16.1518	+	2.84799i	−0.958431	+	0.168997i
$285$	0.00575733	+	0.251485i	0.000341035	+	0.0148967i
$286$	−0.883871	−	2.42841i	−0.0522644	−	0.143595i
$287$	6.32639	−	3.96942i	0.373435	−	0.234307i
$288$	−1.15399	−	2.76917i	−0.0679997	−	0.163175i
$289$	4.11739			0.242200
$290$	0.164613	+	0.138127i	0.00966641	+	0.00811108i
$291$	−13.9659	+	2.79356i	−0.818695	+	0.163762i
$292$	11.8508	−	2.08961i	0.693514	−	0.122285i
$293$	3.22855	+	18.3100i	0.188614	+	1.06968i	0.921223	+	0.389034i	$0.127191\pi$
$293$	3.22855	+	18.3100i	0.188614	+	1.06968i	−0.732609	+	0.680650i	$0.761698\pi$
$294$	6.86332	−	9.99474i	0.400277	−	0.582905i
$295$	0.128561	+	0.107876i	0.00748514	+	0.00628078i
$296$	−3.60002	+	2.07847i	−0.209247	+	0.120809i
$297$	−9.08498	+	12.4743i	−0.527164	+	0.723835i
$298$	−0.842352	+	1.45900i	−0.0487961	+	0.0845174i
$299$	−0.0639980	+	0.362951i	−0.00370110	+	0.0209900i
$300$	1.30797	−	8.55910i	0.0755159	−	0.494160i
$301$	−8.11001	+	1.73948i	−0.467453	+	0.100262i
$302$	−3.58076	+	9.83807i	−0.206050	+	0.566117i
$303$	−13.0330	+	11.4544i	−0.748726	+	0.658037i
$304$	2.90400	−	3.46085i	0.166556	−	0.198493i
$305$	0.0169664	−	0.00979557i	0.000971494	−	0.000560892i
$306$	12.2420	+	6.33946i	0.699831	+	0.362403i
$307$	−25.0909	+	14.4862i	−1.43201	+	0.826772i	−0.997274	−	0.0737854i	$-0.976492\pi$
$307$	−25.0909	+	14.4862i	−1.43201	+	0.826772i	−0.434737	+	0.900557i	$0.643159\pi$
$308$	6.20077	+	4.82618i	0.353322	+	0.274997i
$309$	0.126092	+	5.50783i	0.00717314	+	0.313330i
$310$	0.0905072	+	0.0329419i	0.00514047	+	0.00187098i
$311$	−3.79670	−	21.5322i	−0.215291	−	1.22098i	−0.880400	−	0.474231i	$-0.842726\pi$
$311$	−3.79670	−	21.5322i	−0.215291	−	1.22098i	0.665109	−	0.746746i	$-0.268385\pi$
$312$	−1.50676	+	0.0344947i	−0.0853035	+	0.00195288i
$313$	−13.8756	+	16.5363i	−0.784294	+	0.934686i	−0.999119	−	0.0419669i	$-0.986638\pi$
$313$	−13.8756	+	16.5363i	−0.784294	+	0.934686i	0.214825	+	0.976653i	$0.431082\pi$
$314$	9.35375	+	16.2012i	0.527862	+	0.914284i
$315$	−0.0672061	+	0.246147i	−0.00378663	+	0.0138688i
$316$	3.95321	−	6.84715i	0.222385	−	0.385182i
$317$	0.371978	+	1.02200i	0.0208924	+	0.0574013i	0.949700	−	0.313160i	$-0.101388\pi$
$317$	0.371978	+	1.02200i	0.0208924	+	0.0574013i	−0.928808	+	0.370561i	$0.879165\pi$
$318$	6.71727	−	5.90364i	0.376686	−	0.331060i
$319$	−15.2078	+	12.7609i	−0.851475	+	0.714473i
$320$	0.0246258	−	0.0206635i	0.00137663	−	0.00115513i
$321$	8.49851	+	21.7847i	0.474340	+	1.21590i
$322$	−0.421698	−	1.03822i	−0.0235003	−	0.0578577i
$323$			20.7610i			1.15518i
$324$	5.19377	+	7.35015i	0.288543	+	0.408342i
$325$	−3.76711	−	2.17494i	−0.208962	−	0.120644i
$326$	−7.45010	−	20.4690i	−0.412623	−	1.13367i
$327$	−9.54398	−	7.64304i	−0.527783	−	0.422661i
$328$	2.77997	−	0.490183i	0.153498	−	0.0270659i
$329$	−17.0527	+	3.65756i	−0.940148	+	0.201648i
$330$	−0.156644	−	0.0529861i	−0.00862296	−	0.00291679i
$331$	−12.9038	+	4.69661i	−0.709258	+	0.258149i	−0.671359	−	0.741133i	$-0.734289\pi$
$331$	−12.9038	+	4.69661i	−0.709258	+	0.258149i	−0.0378997	+	0.999282i	$0.512067\pi$
$332$	1.77947	+	3.08213i	0.0976611	+	0.169154i
$333$	9.17637	−	8.44488i	0.502862	−	0.462777i
$334$	18.3291	+	10.5823i	1.00292	+	0.579037i
$335$	0.452778	−	0.164798i	0.0247379	−	0.00900386i
$336$	3.82500	−	2.52377i	0.208671	−	0.137683i
$337$	14.1389	−	11.8639i	0.770193	−	0.646269i	−0.170565	−	0.985346i	$-0.554559\pi$
$337$	14.1389	−	11.8639i	0.770193	−	0.646269i	0.940758	+	0.339078i	$0.110115\pi$
$338$	4.18729	−	11.5045i	0.227759	−	0.625762i
$339$	−8.03641	−	4.39772i	−0.436478	−	0.238851i
$340$	−0.0256524	+	0.145482i	−0.00139119	+	0.00788985i
$341$	−4.44908	+	7.70604i	−0.240931	+	0.417305i
$342$	−6.23249	+	12.0355i	−0.337014	+	0.650803i
$343$	16.9605	+	7.43912i	0.915782	+	0.401675i
$344$	−3.08738	−	0.544389i	−0.166460	−	0.0293515i
$345$	0.0155683	+	0.0177138i	0.000838168	+	0.000953682i
$346$	−11.5955	−	13.8190i	−0.623379	−	0.742914i
$347$	−6.05953	+	16.6484i	−0.325293	+	0.893734i	0.663993	+	0.747739i	$0.268861\pi$
$347$	−6.05953	+	16.6484i	−0.325293	+	0.893734i	−0.989285	+	0.145995i	$0.953362\pi$
$348$	4.20789	+	10.7863i	0.225566	+	0.578206i
$349$	−11.1285	+	13.2624i	−0.595694	+	0.709920i	−0.976690	−	0.214656i	$-0.931137\pi$
$349$	−11.1285	+	13.2624i	−0.595694	+	0.709920i	0.380996	+	0.924577i	$0.375581\pi$
$350$	13.2171	−	0.485965i	0.706483	−	0.0259759i
$351$	4.38841	−	1.08882i	0.234236	−	0.0581167i
$352$	1.48494	+	2.57200i	0.0791477	+	0.137088i
$353$	12.4714	−	4.53922i	0.663785	−	0.241598i	0.0119155	−	0.999929i	$-0.496207\pi$
$353$	12.4714	−	4.53922i	0.663785	−	0.241598i	0.651870	+	0.758331i	$0.273985\pi$
$354$	3.28632	+	8.42401i	0.174666	+	0.447731i
$355$	0.338901	+	0.403886i	0.0179870	+	0.0214361i
$356$	−4.43202	−	1.61312i	−0.234896	−	0.0854953i
$357$	−6.01016	+	20.1827i	−0.318091	+	1.06818i
$358$	2.11725	−	12.0075i	0.111900	−	0.634618i
$359$		−	7.19962i		−	0.379981i	−0.981786	−	0.189991i	$-0.939154\pi$
$359$		−	7.19962i		−	0.379981i	0.981786	−	0.189991i	$-0.0608457\pi$
$360$	−0.0585448	+	0.0766369i	−0.00308558	+	0.00403912i
$361$	−1.41070			−0.0742474
$362$	−4.60947	−	3.86780i	−0.242268	−	0.203287i
$363$	−1.81241	+	3.31201i	−0.0951270	+	0.173835i
$364$	−0.482811	−	2.25102i	−0.0253062	−	0.117986i
$365$	−0.248656	−	0.296337i	−0.0130153	−	0.0155110i
$366$	1.05528	−	0.0241589i	0.0551606	−	0.00126281i
$367$	−16.7504	−	2.95355i	−0.874366	−	0.154174i	−0.281583	−	0.959537i	$-0.590860\pi$
$367$	−16.7504	−	2.95355i	−0.874366	−	0.154174i	−0.592783	+	0.805362i	$0.701971\pi$
$368$		−	0.423545i		−	0.0220788i
$369$	−7.81696	+	3.25756i	−0.406935	+	0.169582i
$370$	0.115729	+	0.0668161i	0.00601646	+	0.00347360i
$371$	10.7801	+	8.39033i	0.559673	+	0.435604i
$372$	3.42582	+	3.89796i	0.177621	+	0.202100i
$373$	0.770912	+	4.37206i	0.0399163	+	0.226377i	0.998240	−	0.0593091i	$-0.0188897\pi$
$373$	0.770912	+	4.37206i	0.0399163	+	0.226377i	−0.958323	+	0.285686i	$0.907779\pi$
$374$	−12.8247	−	4.66779i	−0.663147	−	0.241366i
$375$	−0.518669	+	0.202340i	−0.0267840	+	0.0104488i
$376$	−6.49177	−	1.14467i	−0.334787	−	0.0590321i
$377$	5.81662			0.299571
$378$	−9.54305	+	9.89597i	−0.490842	+	0.508994i
$379$	−12.4720			−0.640643			−0.320322	−	0.947309i	$-0.603791\pi$
$379$	−12.4720			−0.640643			−0.320322	+	0.947309i	$0.603791\pi$
$380$	−0.143027	−	0.0252195i	−0.00733712	−	0.00129373i
$381$	−26.1742	−	20.9609i	−1.34095	−	1.07386i
$382$	3.30028	+	1.20120i	0.168857	+	0.0614590i
$383$	1.50341	+	8.52625i	0.0768205	+	0.435671i	0.998824	+	0.0484886i	$0.0154405\pi$
$383$	1.50341	+	8.52625i	0.0768205	+	0.435671i	−0.922003	+	0.387182i	$0.873448\pi$
$384$	1.69841	−	0.339728i	0.0866714	−	0.0173367i
$385$	0.0346930	−	0.250202i	0.00176812	−	0.0127515i
$386$	23.0937	+	13.3331i	1.17544	+	0.678638i
$387$	9.39518	−	0.430399i	0.477584	−	0.0218784i
$388$		−	8.22293i		−	0.417456i
$389$	−2.01668	−	0.355594i	−0.102250	−	0.0180294i	0.122289	−	0.992495i	$-0.460976\pi$
$389$	−2.01668	−	0.355594i	−0.102250	−	0.0180294i	−0.224539	+	0.974465i	$0.572088\pi$
$390$	0.0251790	+	0.0413936i	0.00127499	+	0.00209605i
$391$	1.25108	+	1.49098i	0.0632701	+	0.0754023i
$392$	4.88115	+	5.01740i	0.246536	+	0.253417i
$393$	−17.6930	−	29.0868i	−0.892494	−	1.46723i
$394$	14.7360	+	12.3650i	0.742390	+	0.622939i
$395$	−0.254165			−0.0127884
$396$	−6.03336	−	6.55596i	−0.303188	−	0.329449i
$397$			23.7916i			1.19406i	0.802218	+	0.597032i	$0.203653\pi$
$397$			23.7916i			1.19406i	−0.802218	+	0.597032i	$0.796347\pi$
$398$	−2.92560	+	16.5919i	−0.146647	+	0.831676i
$399$	−19.8422	−	5.90874i	−0.993351	−	0.295807i
$400$	4.69749	+	1.70975i	0.234875	+	0.0854874i
$401$	−3.45415	−	4.11650i	−0.172492	−	0.205568i	0.672871	−	0.739759i	$-0.265061\pi$
$401$	−3.45415	−	4.11650i	−0.172492	−	0.205568i	−0.845364	+	0.534191i	$0.820616\pi$
$402$	25.6632	+	3.92177i	1.27996	+	0.195600i
$403$	2.44987	−	0.891681i	0.122037	−	0.0444178i
$404$	−5.00884	−	8.67557i	−0.249199	−	0.431626i
$405$	0.121146	−	0.262736i	0.00601979	−	0.0130554i
$406$	−14.9810	+	9.39965i	−0.743496	+	0.466497i
$407$	−7.93564	+	9.45732i	−0.393355	+	0.468782i
$408$	−4.97532	+	6.21276i	−0.246315	+	0.307577i
$409$	−5.87626	+	16.1449i	−0.290562	+	0.798314i	0.705422	+	0.708788i	$0.250758\pi$
$409$	−5.87626	+	16.1449i	−0.290562	+	0.798314i	−0.995984	+	0.0895263i	$0.971465\pi$
$410$	−0.0583301	−	0.0695151i	−0.00288072	−	0.00343311i
$411$	−9.78116	+	1.95650i	−0.482469	+	0.0965071i
$412$	−3.13246	−	0.552337i	−0.154325	−	0.0272117i
$413$	−11.7001	+	7.34105i	−0.575722	+	0.361229i
$414$	0.277676	+	1.23992i	0.0136470	+	0.0609388i
$415$	0.0572041	−	0.0990805i	0.00280804	−	0.00486367i
$416$	0.151101	−	0.856937i	0.00740834	−	0.0420148i
$417$	0.408155	+	17.8286i	0.0199874	+	0.873070i
$418$	4.58903	−	12.6082i	0.224457	−	0.616689i
$419$	−0.410446	+	0.344405i	−0.0200516	+	0.0168253i	−0.652758	−	0.757566i	$-0.726388\pi$
$419$	−0.410446	+	0.344405i	−0.0200516	+	0.0168253i	0.632707	+	0.774391i	$0.281944\pi$
$420$	−0.131742	−	0.0659221i	−0.00642835	−	0.00321667i
$421$	37.6710	−	13.7111i	1.83597	−	0.668239i	0.844898	−	0.534928i	$-0.179661\pi$
$421$	37.6710	−	13.7111i	1.83597	−	0.668239i	0.991074	−	0.133311i	$-0.0425611\pi$
$422$	−6.29987	−	3.63723i	−0.306673	−	0.177058i
$423$	19.7550	−	0.904989i	0.960522	−	0.0440021i
$424$	2.58158	+	4.47143i	0.125373	+	0.217152i
$425$	−21.5867	+	7.85692i	−1.04711	+	0.381116i
$426$	5.57186	+	27.8554i	0.269958	+	1.34960i
$427$	0.338145	+	1.57654i	0.0163640	+	0.0762941i
$428$	−13.2955	+	2.34435i	−0.642661	+	0.113318i
$429$	−4.17000	+	1.62678i	−0.201329	+	0.0785414i
$430$	0.0344689	+	0.0947025i	0.00166224	+	0.00456696i
$431$	4.28625	+	2.47467i	0.206462	+	0.119201i	0.599666	−	0.800250i	$-0.295300\pi$
$431$	4.28625	+	2.47467i	0.206462	+	0.119201i	−0.393204	+	0.919451i	$0.628633\pi$
$432$	−4.74934	+	2.10803i	−0.228503	+	0.101423i
$433$		−	37.4260i		−	1.79858i	−0.437355	−	0.899289i	$-0.644085\pi$
$433$		−	37.4260i		−	1.79858i	0.437355	−	0.899289i	$-0.355915\pi$
$434$	−4.86883	+	6.25557i	−0.233711	+	0.300277i
$435$	0.232654	−	0.290519i	0.0111549	−	0.0139293i
$436$	5.40778	−	4.53767i	0.258986	−	0.217315i
$437$	−1.46582	+	1.22997i	−0.0701199	+	0.0588376i
$438$	−4.08815	−	20.4379i	−0.195339	−	0.976562i
$439$	9.08552	+	24.9623i	0.433628	+	1.19138i	0.943569	+	0.331175i	$0.107445\pi$
$439$	9.08552	+	24.9623i	0.433628	+	1.19138i	−0.509941	+	0.860209i	$0.670333\pi$
$440$	0.0477361	−	0.0826813i	0.00227573	−	0.00394168i
$441$	−17.5789	−	11.4883i	−0.837092	−	0.547062i
$442$	1.99934	+	3.46296i	0.0950991	+	0.164716i
$443$	−19.1590	+	22.8328i	−0.910270	+	1.08482i	0.0858052	+	0.996312i	$0.472654\pi$
$443$	−19.1590	+	22.8328i	−0.910270	+	1.08482i	−0.996076	+	0.0885061i	$0.971791\pi$
$444$	3.74179	+	6.15139i	0.177577	+	0.291932i
$445$	0.0263283	+	0.149315i	0.00124808	+	0.00707822i
$446$	7.04164	+	2.56295i	0.333431	+	0.121359i
$447$	2.55979	+	1.40078i	0.121074	+	0.0662545i
$448$	0.995640	+	2.45127i	0.0470396	+	0.115811i
$449$	13.7440	−	7.93511i	0.648620	−	0.374481i	−0.139307	−	0.990249i	$-0.544488\pi$
$449$	13.7440	−	7.93511i	0.648620	−	0.374481i	0.787927	+	0.615768i	$0.211154\pi$
$450$	−14.8728	−	1.92559i	−0.701109	−	0.0907730i
$451$	7.26037	−	4.19178i	0.341878	−	0.197383i
$452$	3.39977	−	4.05169i	0.159912	−	0.190575i
$453$	17.1775	+	5.81044i	0.807070	+	0.272998i
$454$	−3.80550	+	10.4555i	−0.178601	+	0.490702i
$455$	−0.0549078	+	0.0496229i	−0.00257412	+	0.00232636i
$456$	−6.10792	−	4.89136i	−0.286030	−	0.229059i
$457$	−0.509969	+	2.89218i	−0.0238553	+	0.135290i	−0.994409	−	0.105593i	$-0.966326\pi$
$457$	−0.509969	+	2.89218i	−0.0238553	+	0.135290i	0.970554	+	0.240883i	$0.0774371\pi$
$458$	3.42711	−	5.93592i	0.160138	−	0.277367i
$459$	10.4921	−	21.4496i	0.489729	−	1.00118i
$460$	−0.0117914	+	0.00680779i	−0.000549778	+	0.000317415i
$461$	−11.6265	−	9.75582i	−0.541501	−	0.454374i	0.330550	−	0.943789i	$-0.392766\pi$
$461$	−11.6265	−	9.75582i	−0.541501	−	0.454374i	−0.872051	+	0.489415i	$0.837210\pi$
$462$	8.11119	−	10.9286i	0.377367	−	0.508443i
$463$	−3.20976	−	18.2034i	−0.149170	−	0.845986i	−0.963924	−	0.266178i	$-0.914239\pi$
$463$	−3.20976	−	18.2034i	−0.149170	−	0.845986i	0.814754	−	0.579807i	$-0.196872\pi$
$464$	−6.58302	+	1.16076i	−0.305609	+	0.0538871i
$465$	0.0534543	−	0.158028i	0.00247888	−	0.00732837i
$466$	−8.73399	−	7.32869i	−0.404594	−	0.339495i
$467$	0.799112			0.0369785			0.0184892	−	0.999829i	$-0.494114\pi$
$467$	0.799112			0.0369785			0.0184892	+	0.999829i	$0.494114\pi$
$468$	0.119462	+	2.60773i	0.00552212	+	0.120543i
$469$	1.45709	+	39.6295i	0.0672824	+	1.82992i
$470$	0.0724770	+	0.199129i	0.00334311	+	0.00918513i
$471$	27.6831	−	16.8392i	1.27557	−	0.775908i
$472$	−5.14128	+	0.906547i	−0.236647	+	0.0417272i
$473$	−9.16917	+	1.61677i	−0.421599	+	0.0743393i
$474$	−12.0132	−	6.57392i	−0.551786	−	0.301950i
$475$	−7.72433	−	21.2224i	−0.354417	−	0.973752i
$476$	−10.7456	−	5.68811i	−0.492522	−	0.260714i
$477$	−10.4890	−	11.3976i	−0.480259	−	0.521859i
$478$	29.0691			1.32959
$479$	32.2043	+	27.0226i	1.47145	+	1.23470i	0.914773	+	0.403968i	$0.132369\pi$
$479$	32.2043	+	27.0226i	1.47145	+	1.23470i	0.556679	+	0.830727i	$0.312075\pi$
$480$	−0.0367571	−	0.0418229i	−0.00167772	−	0.00190894i
$481$	3.56224	−	0.628119i	0.162424	−	0.0286398i
$482$	−2.99562	−	16.9890i	−0.136447	−	0.773827i
$483$	−1.78106	+	0.771368i	−0.0810411	+	0.0350984i
$484$	−1.66980	−	1.40113i	−0.0759002	−	0.0636878i
$485$	−0.228926	+	0.132170i	−0.0103950	+	0.00600154i
$486$	12.5216	−	9.28490i	0.567992	−	0.421171i
$487$	9.72384	−	16.8422i	0.440629	−	0.763192i	−0.557107	−	0.830441i	$-0.688089\pi$
$487$	9.72384	−	16.8422i	0.440629	−	0.763192i	0.997736	+	0.0672487i	$0.0214221\pi$
$488$	−0.105826	+	0.600170i	−0.00479052	+	0.0271684i
$489$	−35.1487	+	13.7120i	−1.58948	+	0.620078i
$490$	0.0612274	−	0.216537i	0.00276597	−	0.00978216i
$491$	1.76144	−	4.83951i	0.0794926	−	0.218404i	−0.893580	−	0.448905i	$-0.851814\pi$
$491$	1.76144	−	4.83951i	0.0794926	−	0.218404i	0.973072	+	0.230501i	$0.0740364\pi$
$492$	−0.959004	−	4.79435i	−0.0432352	−	0.216146i
$493$	19.7452	−	23.5314i	0.889278	−	1.05980i
$494$	−3.40453	+	1.96560i	−0.153177	+	0.0884367i
$495$	−0.0855409	+	0.273344i	−0.00384478	+	0.0122859i
$496$	−2.59472	+	1.49806i	−0.116507	+	0.0672651i
$497$	−40.2030	+	16.3294i	−1.80335	+	0.732474i
$498$	5.26647	−	3.20351i	0.235996	−	0.143553i
$499$	−7.00734	−	2.55046i	−0.313691	−	0.114174i	0.180377	−	0.983598i	$-0.442268\pi$
$499$	−7.00734	−	2.55046i	−0.313691	−	0.114174i	−0.494068	+	0.869423i	$0.664491\pi$
$500$	−0.0558164	−	0.316551i	−0.00249619	−	0.0141566i
$501$	17.5977	−	32.1581i	0.786206	−	1.43672i
$502$	17.0543	−	20.3246i	0.761173	−	0.907130i
$503$	13.3443	+	23.1130i	0.594994	+	1.03056i	0.993548	+	0.113414i	$0.0361787\pi$
$503$	13.3443	+	23.1130i	0.594994	+	1.03056i	−0.398554	+	0.917145i	$0.630488\pi$
$504$	−4.52178	−	6.52331i	−0.201416	−	0.290571i
$505$	−0.161018	+	0.278891i	−0.00716520	+	0.0124105i
$506$	−0.430220	−	1.18202i	−0.0191256	−	0.0525472i
$507$	−20.0871	−	6.79465i	−0.892101	−	0.301761i
$508$	14.8308	−	12.4445i	0.658009	−	0.552135i
$509$	−12.8265	+	10.7627i	−0.568525	+	0.477049i	−0.881156	−	0.472825i	$-0.843234\pi$
$509$	−12.8265	+	10.7627i	−0.568525	+	0.477049i	0.312631	+	0.949875i	$0.398790\pi$
$510$	0.252933	+	0.0386524i	0.0112000	+	0.00171156i
$511$	29.4975	−	11.9811i	1.30489	−	0.530013i
$512$			1.00000i			0.0441942i
$513$	21.0876	+	10.3150i	0.931042	+	0.455420i
$514$	−2.47614	−	1.42960i	−0.109218	−	0.0630571i
$515$	0.0349721	+	0.0960852i	0.00154106	+	0.00423402i
$516$	−0.820272	+	5.36768i	−0.0361105	+	0.236299i
$517$	−19.2798	+	3.39955i	−0.847925	+	0.149512i
$518$	−8.15970	+	7.37433i	−0.358517	+	0.324009i
$519$	−23.4693	+	20.6266i	−1.03019	+	0.905407i
$520$	−0.0262857	+	0.00956722i	−0.00115270	+	0.000419550i
$521$	−14.6626	−	25.3963i	−0.642378	−	1.11263i	−0.984900	−	0.173122i	$-0.944614\pi$
$521$	−14.6626	−	25.3963i	−0.642378	−	1.11263i	0.342522	−	0.939510i	$-0.388719\pi$
$522$	18.5107	−	7.71395i	0.810192	−	0.337631i
$523$	28.2572	+	16.3143i	1.23560	+	0.713374i	0.968192	−	0.250210i	$-0.0804995\pi$
$523$	28.2572	+	16.3143i	1.23560	+	0.713374i	0.267408	+	0.963583i	$0.413833\pi$
$524$	18.4707	−	6.72277i	0.806894	−	0.293686i
$525$	−1.36545	−	22.8674i	−0.0595930	−	0.998016i
$526$	10.6591	−	8.94405i	0.464759	−	0.389979i
$527$	4.70904	−	12.9380i	0.205129	−	0.563587i
$528$	4.39480	−	2.67328i	0.191259	−	0.116340i
$529$	3.96276	−	22.4739i	0.172294	−	0.977127i
$530$	0.0829894	−	0.143742i	0.00360483	−	0.00624374i
$531$	14.4567	−	6.02453i	0.627368	−	0.261442i
$532$	5.59213	−	10.5642i	0.242449	−	0.458018i
$533$	−2.41901	−	0.426536i	−0.104779	−	0.0184753i
$534$	−2.61758	+	7.73842i	−0.113274	+	0.334874i
$535$	0.278969	+	0.332463i	0.0120609	+	0.0143736i
$536$	−5.12642	+	14.0847i	−0.221428	+	0.608368i
$537$	−20.8761	−	3.19022i	−0.900872	−	0.137668i
$538$	12.6092	−	15.0271i	0.543622	−	0.647864i
$539$	18.7187	+	9.04439i	0.806272	+	0.389569i
$540$	0.135025	+	0.0983380i	0.00581056	+	0.00423179i
$541$	−11.9760	−	20.7431i	−0.514890	−	0.891815i	−0.999851	−	0.0172794i	$-0.994500\pi$
$541$	−11.9760	−	20.7431i	−0.514890	−	0.891815i	0.484961	−	0.874536i	$-0.338834\pi$
$542$	−16.3545	+	5.95255i	−0.702486	+	0.255684i
$543$	−6.51475	+	8.13507i	−0.279575	+	0.349109i
$544$	−2.95384	−	3.52025i	−0.126645	−	0.150930i
$545$	−0.213249	−	0.0776164i	−0.00913460	−	0.00332472i
$546$	−3.87872	+	0.925269i	−0.165994	+	0.0395979i
$547$	−2.72205	+	15.4375i	−0.116386	+	0.660059i	0.869668	+	0.493637i	$0.164333\pi$
$547$	−2.72205	+	15.4375i	−0.116386	+	0.660059i	−0.986055	+	0.166423i	$0.946778\pi$
$548$		−	5.75902i		−	0.246013i
$549$	−0.0836671	−	1.82637i	−0.00357082	−	0.0779476i
$550$	14.8464			0.633051
$551$	23.1343	+	19.4120i	0.985555	+	0.826978i
$552$	−0.733409	+	0.0167901i	−0.0312159	+	0.000714636i
$553$	6.42743	−	19.9065i	0.273322	−	0.846509i
$554$	−1.93843	−	2.31013i	−0.0823560	−	0.0981481i
$555$	0.111111	−	0.203045i	0.00471639	−	0.00861876i
$556$	−10.1396	−	1.78789i	−0.430016	−	0.0758234i
$557$		−	9.23861i		−	0.391453i	−0.980659	−	0.195726i	$-0.937294\pi$
$557$		−	9.23861i		−	0.391453i	0.980659	−	0.195726i	$-0.0627064\pi$
$558$	6.61389	−	6.08667i	0.279988	−	0.257669i
$559$	2.36247	+	1.36397i	0.0999219	+	0.0576900i
$560$	0.0522397	−	0.0671186i	0.00220753	−	0.00283628i
$561$	−7.57434	+	22.3922i	−0.319789	+	0.945399i
$562$	−2.59622	−	14.7239i	−0.109515	−	0.621090i
$563$	−18.4779	−	6.72540i	−0.778750	−	0.283442i	−0.0780984	−	0.996946i	$-0.524885\pi$
$563$	−18.4779	−	6.72540i	−0.778750	−	0.283442i	−0.700651	+	0.713504i	$0.747107\pi$
$564$	−1.72477	+	11.2865i	−0.0726258	+	0.475248i
$565$	−0.167444	−	0.0295250i	−0.00704444	−	0.00124212i
$566$	−20.1627			−0.847500
$567$	17.5141	+	16.1324i	0.735524	+	0.677498i
$568$	−16.4009			−0.688168
$569$	38.5747	+	6.80176i	1.61714	+	0.285145i	0.907698	−	0.419624i	$-0.137838\pi$
$569$	38.5747	+	6.80176i	1.61714	+	0.285145i	0.709438	+	0.704768i	$0.248949\pi$
$570$	−0.0380001	+	0.248664i	−0.00159165	+	0.0104154i
$571$	14.0829	+	5.12576i	0.589351	+	0.214506i	0.619444	−	0.785041i	$-0.287358\pi$
$571$	14.0829	+	5.12576i	0.589351	+	0.214506i	−0.0300929	+	0.999547i	$0.509580\pi$
$572$	−0.448753	−	2.54500i	−0.0187633	−	0.106412i
$573$	1.94917	−	5.76238i	0.0814279	−	0.240727i
$574$	6.91956	−	2.81055i	0.288817	−	0.117310i
$575$	−1.83362	−	1.05864i	−0.0764674	−	0.0441484i
$576$	−0.655601	−	2.92749i	−0.0273167	−	0.121979i
$577$			36.2649i			1.50973i	0.655881	+	0.754864i	$0.272297\pi$
$577$			36.2649i			1.50973i	−0.655881	+	0.754864i	$0.727703\pi$
$578$	4.05484	+	0.714978i	0.168659	+	0.0297391i
$579$	22.1721	−	40.5175i	0.921442	−	1.68385i
$580$	0.138127	+	0.164613i	0.00573540	+	0.00683519i
$581$	6.31348	+	6.98587i	0.261927	+	0.289823i
$582$	−14.2388	+	0.325973i	−0.590218	+	0.0135120i
$583$	11.7465	+	9.85650i	0.486491	+	0.408215i
$584$	12.0336			0.497953
$585$	0.0706789	−	0.0452409i	0.00292221	−	0.00187048i
$586$			18.5925i			0.768049i
$587$	7.08546	−	40.1836i	0.292448	−	1.65856i	−0.384949	−	0.922938i	$-0.625781\pi$
$587$	7.08546	−	40.1836i	0.292448	−	1.65856i	0.677397	−	0.735618i	$-0.263108\pi$
$588$	8.49462	−	8.65109i	0.350312	−	0.356765i
$589$	12.7197	+	4.62958i	0.524104	+	0.190758i
$590$	0.107876	+	0.128561i	0.00444118	+	0.00529279i
$591$	20.8270	−	26.0070i	0.856709	−	1.06979i
$592$	−3.90625	+	1.42176i	−0.160546	+	0.0584339i
$593$	−1.81408	−	3.14208i	−0.0744953	−	0.129030i	0.826371	−	0.563125i	$-0.190401\pi$
$593$	−1.81408	−	3.14208i	−0.0744953	−	0.129030i	−0.900867	+	0.434096i	$0.857068\pi$
$594$	−11.1131	+	10.7072i	−0.455976	+	0.439323i
$595$	0.0143609	+	0.390582i	0.000588740	+	0.0160123i
$596$	−1.08291	+	1.29056i	−0.0443576	+	0.0528633i
$597$	28.8464	+	4.40822i	1.18061	+	0.180416i
$598$	−0.126051	+	0.346324i	−0.00515463	+	0.0141622i
$599$	10.0228	+	11.9447i	0.409520	+	0.488046i	0.930898	−	0.365279i	$-0.119026\pi$
$599$	10.0228	+	11.9447i	0.409520	+	0.488046i	−0.521378	+	0.853326i	$0.674582\pi$
$600$	2.77438	−	8.20194i	0.113263	−	0.334843i
$601$	−1.88777	−	0.332864i	−0.0770036	−	0.0135778i	0.135014	−	0.990844i	$-0.456892\pi$
$601$	−1.88777	−	0.332864i	−0.0770036	−	0.0135778i	−0.212017	+	0.977266i	$0.568003\pi$
$602$	−8.28886	+	0.304764i	−0.337829	+	0.0124213i
$603$	5.77358	−	44.5938i	0.235118	−	1.81600i
$604$	−5.23473	+	9.06681i	−0.212998	+	0.368923i
$605$	−0.0121680	+	0.0690081i	−0.000494699	+	0.00280558i
$606$	−14.8240	+	9.01721i	−0.602185	+	0.366299i
$607$	−7.33248	+	20.1458i	−0.297616	+	0.817694i	0.697281	+	0.716798i	$0.254393\pi$
$607$	−7.33248	+	20.1458i	−0.297616	+	0.817694i	−0.994897	+	0.100896i	$0.967829\pi$
$608$	3.46085	−	2.90400i	0.140356	−	0.117773i
$609$	16.8703	+	25.5685i	0.683619	+	1.03609i
$610$	0.0184096	−	0.00670056i	0.000745385	−	0.000271298i
$611$	4.96752	+	2.86800i	0.200964	+	0.116027i
$612$	10.9552	+	8.36896i	0.442839	+	0.338295i
$613$	−17.5229	−	30.3505i	−0.707742	−	1.22585i	−0.965693	−	0.259688i	$-0.916380\pi$
$613$	−17.5229	−	30.3505i	−0.707742	−	1.22585i	0.257950	−	0.966158i	$-0.416953\pi$
$614$	−27.2252	+	9.90916i	−1.09872	+	0.399901i
$615$	−0.118060	+	0.103760i	−0.00476063	+	0.00418401i
$616$	5.26851	+	5.82961i	0.212274	+	0.234882i
$617$	−3.81802	+	0.673221i	−0.153708	+	0.0271028i	−0.249973	−	0.968253i	$-0.580422\pi$
$617$	−3.81802	+	0.673221i	−0.153708	+	0.0271028i	0.0962647	+	0.995356i	$0.469310\pi$
$618$	−0.832248	+	5.44605i	−0.0334779	+	0.219072i
$619$	13.2202	+	36.3221i	0.531363	+	1.45991i	0.857450	+	0.514568i	$0.172048\pi$
$619$	13.2202	+	36.3221i	0.531363	+	1.45991i	−0.326087	+	0.945340i	$0.605730\pi$
$620$	0.0834119	+	0.0481579i	0.00334990	+	0.00193407i
$621$	2.13604	−	0.529976i	0.0857162	−	0.0212672i
$622$		−	21.8643i		−	0.876680i
$623$	−12.3603	−	1.71388i	−0.495205	−	0.0686652i
$624$	−1.48986	−	0.227675i	−0.0596421	−	0.00911431i
$625$	19.1392	−	16.0597i	0.765569	−	0.642389i
$626$	−16.5363	+	13.8756i	−0.660923	+	0.554580i
$627$	−22.0143	−	7.44653i	−0.879167	−	0.297386i
$628$	6.39834	+	17.5793i	0.255322	+	0.701490i
$629$	9.55134	−	16.5434i	0.380837	−	0.659629i
$630$	−0.108928	+	0.230737i	−0.00433980	+	0.00919279i
$631$	−1.64761	−	2.85375i	−0.0655905	−	0.113606i	0.831365	−	0.555726i	$-0.187560\pi$
$631$	−1.64761	−	2.85375i	−0.0655905	−	0.113606i	−0.896956	+	0.442120i	$0.854226\pi$
$632$	5.08214	−	6.05666i	0.202157	−	0.240921i
$633$	−6.04848	+	11.0530i	−0.240406	+	0.439318i
$634$	0.188858	+	1.07107i	0.00750051	+	0.0425375i
$635$	−0.584834	−	0.212862i	−0.0232084	−	0.00844717i
$636$	7.64037	−	4.64751i	0.302960	−	0.184286i
$637$	−2.49798	−	5.55531i	−0.0989738	−	0.220109i
$638$	−17.1927	+	9.92621i	−0.680665	+	0.392982i
$639$	48.0135	−	10.7525i	1.89939	−	0.425361i
$640$	0.0278399	−	0.0160734i	0.00110047	−	0.000635356i
$641$	18.5432	−	22.0989i	0.732412	−	0.872855i	−0.263361	−	0.964697i	$-0.584831\pi$
$641$	18.5432	−	22.0989i	0.732412	−	0.872855i	0.995774	+	0.0918423i	$0.0292756\pi$
$642$	4.58653	+	22.9295i	0.181016	+	0.904954i
$643$	12.2023	−	33.5255i	0.481212	−	1.32212i	−0.427244	−	0.904137i	$-0.640515\pi$
$643$	12.2023	−	33.5255i	0.481212	−	1.32212i	0.908455	−	0.417982i	$-0.137262\pi$
$644$	−0.235006	−	1.09567i	−0.00926054	−	0.0431756i
$645$	0.162620	−	0.0634404i	0.00640316	−	0.00249796i
$646$	−3.60512	+	20.4456i	−0.141841	+	0.804423i
$647$	5.35623	−	9.27726i	0.210575	−	0.364727i	−0.741320	−	0.671152i	$-0.765800\pi$
$647$	5.35623	−	9.27726i	0.210575	−	0.364727i	0.951895	+	0.306426i	$0.0991330\pi$
$648$	3.83853	+	8.14038i	0.150792	+	0.319784i
$649$	−13.4274	+	7.75229i	−0.527070	+	0.304304i
$650$	−3.33220	−	2.79605i	−0.130700	−	0.109670i
$651$	11.0251	+	8.18286i	0.432109	+	0.320712i
$652$	−3.78252	−	21.4517i	−0.148135	−	0.840114i
$653$	3.78068	−	0.666636i	0.147949	−	0.0260875i	−0.0991829	−	0.995069i	$-0.531623\pi$
$653$	3.78068	−	0.666636i	0.147949	−	0.0260875i	0.247132	+	0.968982i	$0.420512\pi$
$654$	−8.07179	−	9.18422i	−0.315632	−	0.359131i
$655$	−0.484047	−	0.406163i	−0.0189133	−	0.0158701i
$656$	2.82285			0.110214
$657$	−35.2282	+	7.88923i	−1.37438	+	0.307788i
$658$	−17.4288	+	0.640821i	−0.679445	+	0.0249818i
$659$	7.53276	+	20.6961i	0.293434	+	0.806205i	0.995558	+	0.0941495i	$0.0300132\pi$
$659$	7.53276	+	20.6961i	0.293434	+	0.806205i	−0.702124	+	0.712055i	$0.747765\pi$
$660$	−0.145063	−	0.0793820i	−0.00564657	−	0.00308994i
$661$	4.52209	−	0.797367i	0.175889	−	0.0310140i	−0.0850099	−	0.996380i	$-0.527092\pi$
$661$	4.52209	−	0.797367i	0.175889	−	0.0310140i	0.260899	+	0.965366i	$0.415981\pi$
$662$	−13.5233	+	2.38453i	−0.525600	+	0.0926774i
$663$	5.91720	−	3.59934i	0.229805	−	0.139787i
$664$	1.21723	+	3.34431i	0.0472377	+	0.129784i
$665$	−0.383991	+	0.0141186i	−0.0148905	+	0.000547495i
$666$	10.5034	−	6.72312i	0.406998	−	0.260516i
$667$	2.83121			0.109625
$668$	16.2130	+	13.6043i	0.627300	+	0.526367i
$669$	4.15884	−	12.2949i	0.160790	−	0.475347i
$670$	0.474516	−	0.0836700i	0.0183322	−	0.00323246i
$671$	0.314292	+	1.78244i	0.0121331	+	0.0688102i
$672$	4.20513	−	1.82122i	0.162217	−	0.0702551i
$673$	34.3081	+	28.7879i	1.32248	+	1.10969i	0.985773	+	0.168081i	$0.0537570\pi$
$673$	34.3081	+	28.7879i	1.32248	+	1.10969i	0.336705	+	0.941610i	$0.390687\pi$
$674$	15.9842	−	9.22849i	0.615689	−	0.355468i
$675$	−2.74475	+	25.8300i	−0.105646	+	0.994196i
$676$	6.12141	−	10.6026i	0.235439	−	0.407792i
$677$	−8.32152	+	47.1937i	−0.319822	+	1.81380i	0.223987	+	0.974592i	$0.428093\pi$
$677$	−8.32152	+	47.1937i	−0.319822	+	1.81380i	−0.543809	+	0.839209i	$0.683018\pi$
$678$	−7.15067	−	5.72642i	−0.274620	−	0.219922i
$679$	−4.56254	−	21.2720i	−0.175094	−	0.816346i
$680$	−0.0505253	+	0.138817i	−0.00193756	+	0.00532339i
$681$	18.2556	+	6.17511i	0.699556	+	0.236631i
$682$	−5.71963	+	6.81639i	−0.219016	+	0.261013i
$683$	−30.5081	+	17.6139i	−1.16736	+	0.673976i	−0.953057	−	0.302790i	$-0.902082\pi$
$683$	−30.5081	+	17.6139i	−1.16736	+	0.673976i	−0.214304	+	0.976767i	$0.568748\pi$
$684$	−8.22774	+	10.7704i	−0.314595	+	0.411815i
$685$	−0.160330	+	0.0925668i	−0.00612591	+	0.00353680i
$686$	15.4111	+	10.2713i	0.588397	+	0.392159i
$687$	−10.4145	−	5.69906i	−0.397337	−	0.217433i
$688$	−2.94595	−	1.07224i	−0.112313	−	0.0408786i
$689$	−0.780159	−	4.42450i	−0.0297217	−	0.168560i
$690$	0.0122558	+	0.0201481i	0.000466570	+	0.000767026i
$691$	9.21379	−	10.9806i	0.350509	−	0.417720i	−0.561768	−	0.827295i	$-0.689878\pi$
$691$	9.21379	−	10.9806i	0.350509	−	0.417720i	0.912277	+	0.409575i	$0.134323\pi$
$692$	−9.01972	−	15.6226i	−0.342878	−	0.593882i
$693$	−19.2454	−	13.6121i	−0.731072	−	0.517080i
$694$	−8.85844	+	15.3433i	−0.336262	+	0.582422i
$695$	0.113203	+	0.311023i	0.00429404	+	0.0117978i
$696$	2.27094	+	11.3531i	0.0860797	+	0.430339i
$697$	−9.93717	+	8.33827i	−0.376397	+	0.315835i
$698$	−13.2624	+	11.1285i	−0.501989	+	0.421219i
$699$	−12.3441	+	15.4143i	−0.466897	+	0.583022i
$700$	13.1007	+	1.81654i	0.495159	+	0.0686588i
$701$		−	34.0602i		−	1.28643i	−0.765684	−	0.643217i	$-0.777599\pi$
$701$		−	34.0602i		−	1.28643i	0.765684	−	0.643217i	$-0.222401\pi$
$702$	4.51081	−	0.310235i	0.170249	−	0.0117091i
$703$	16.2642	+	9.39017i	0.613418	+	0.354157i
$704$	1.01576	+	2.79078i	0.0382829	+	0.105181i
$705$	0.341938	−	0.133395i	0.0128781	−	0.00502394i
$706$	13.0701	−	2.30462i	0.491902	−	0.0867355i
$707$	−17.7711	−	19.6638i	−0.668353	−	0.739533i
$708$	1.77358	+	8.86669i	0.0666554	+	0.333231i
$709$	2.95115	−	1.07413i	0.110833	−	0.0403399i	−0.286008	−	0.958227i	$-0.592329\pi$
$709$	2.95115	−	1.07413i	0.110833	−	0.0403399i	0.396841	+	0.917887i	$0.370106\pi$
$710$	0.263618	+	0.456600i	0.00989341	+	0.0171359i
$711$	−10.9072	+	21.0627i	−0.409051	+	0.789912i
$712$	−4.08457	−	2.35823i	−0.153076	−	0.0883783i
$713$	1.19246	−	0.434022i	0.0446582	−	0.0162542i
$714$	−9.42355	+	18.8325i	−0.352667	+	0.704788i
$715$	−0.0636397	+	0.0534000i	−0.00237999	+	0.00199705i
$716$	4.17017	−	11.4574i	0.155847	−	0.428185i
$717$	−1.15236	−	50.3359i	−0.0430355	−	1.87983i
$718$	1.25020	−	7.09024i	0.0466571	−	0.264605i
$719$	19.7329	−	34.1785i	0.735914	−	1.27464i	−0.218406	−	0.975858i	$-0.570086\pi$
$719$	19.7329	−	34.1785i	0.735914	−	1.27464i	0.954321	−	0.298783i	$-0.0965808\pi$
$720$	−0.0709632	+	0.0653064i	−0.00264464	+	0.00243383i
$721$	−8.40987	+	0.309214i	−0.313200	+	0.0115157i
$722$	−1.38927	−	0.244965i	−0.0517032	−	0.00911667i
$723$	−29.2993	+	5.86067i	−1.08965	+	0.217961i
$724$	−3.86780	−	4.60947i	−0.143746	−	0.171310i
$725$	−11.4289	+	31.4007i	−0.424460	+	1.16619i
$726$	−2.36000	+	2.94697i	−0.0875879	+	0.109372i
$727$	−15.4429	+	18.4041i	−0.572746	+	0.682572i	−0.972192	−	0.234185i	$-0.924758\pi$
$727$	−15.4429	+	18.4041i	−0.572746	+	0.682572i	0.399446	+	0.916757i	$0.369202\pi$
$728$	−0.0845906	−	2.30066i	−0.00313514	−	0.0852682i
$729$	−16.5741	−	21.3143i	−0.613855	−	0.789419i
$730$	−0.193420	−	0.335014i	−0.00715880	−	0.0123994i
$731$	13.5377	−	4.92732i	0.500710	−	0.182243i
$732$	1.04345	+	0.159456i	0.0385669	+	0.00589368i
$733$	−15.1405	−	18.0437i	−0.559226	−	0.666459i	0.410157	−	0.912015i	$-0.365474\pi$
$733$	−15.1405	−	18.0437i	−0.559226	−	0.666459i	−0.969382	+	0.245556i	$0.921030\pi$
$734$	−15.9831	−	5.81737i	−0.589946	−	0.214723i
$735$	−0.377383	−	0.0974372i	−0.0139200	−	0.00359402i
$736$	0.0735477	−	0.417110i	0.00271101	−	0.0153749i
$737$			44.5146i			1.63972i
$738$	−8.26387	+	1.85067i	−0.304197	+	0.0681239i
$739$	−11.8036			−0.434203			−0.217102	−	0.976149i	$-0.569660\pi$
$739$	−11.8036			−0.434203			−0.217102	+	0.976149i	$0.569660\pi$
$740$	0.102368	+	0.0858971i	0.00376313	+	0.00315764i
$741$	3.53860	+	5.81735i	0.129994	+	0.213706i
$742$	9.15933	+	10.1348i	0.336250	+	0.372060i
$743$	10.7677	+	12.8325i	0.395030	+	0.470778i	0.926498	−	0.376300i	$-0.122804\pi$
$743$	10.7677	+	12.8325i	0.395030	+	0.470778i	−0.531468	+	0.847078i	$0.678359\pi$
$744$	2.69690	+	4.43363i	0.0988733	+	0.162545i
$745$	0.0533349	+	0.00940439i	0.00195404	+	0.000344550i
$746$			4.43951i			0.162542i
$747$	−5.75596	−	8.99241i	−0.210599	−	0.329015i
$748$	−11.8193	−	6.82386i	−0.432155	−	0.249505i
$749$	−33.0935	+	13.4417i	−1.20921	+	0.491149i
$750$	−0.545926	+	0.109200i	−0.0199344	+	0.00398743i
$751$	−2.23563	−	12.6789i	−0.0815794	−	0.462660i	−0.998042	−	0.0625403i	$-0.980080\pi$
$751$	−2.23563	−	12.6789i	−0.0815794	−	0.462660i	0.916463	−	0.400119i	$-0.131031\pi$
$752$	−6.19437	−	2.25457i	−0.225886	−	0.0822156i
$753$	−35.8700	−	28.7255i	−1.30718	−	1.04682i
$754$	5.72825	+	1.01005i	0.208611	+	0.0367837i
$755$	0.336559			0.0122486
$756$	−11.1165	+	8.08849i	−0.404303	+	0.294176i
$757$	−46.0661			−1.67430			−0.837150	−	0.546974i	$-0.815780\pi$
$757$	−46.0661			−1.67430			−0.837150	+	0.546974i	$0.815780\pi$
$758$	−12.2825	−	2.16574i	−0.446121	−	0.0786632i
$759$	−2.02973	+	0.791825i	−0.0736744	+	0.0287414i
$760$	−0.136475	−	0.0496727i	−0.00495045	−	0.00180182i
$761$	5.35611	+	30.3760i	0.194159	+	1.10113i	0.913611	+	0.406588i	$0.133282\pi$
$761$	5.35611	+	30.3760i	0.194159	+	1.10113i	−0.719452	+	0.694542i	$0.755607\pi$
$762$	−22.1368	−	25.1876i	−0.801931	−	0.912450i
$763$	11.4717	−	14.7391i	0.415304	−	0.533591i
$764$	3.04156	+	1.75604i	0.110040	+	0.0635314i
$765$	0.0569036	−	0.439510i	0.00205735	−	0.0158905i
$766$			8.65778i			0.312818i
$767$	4.47372	+	0.788837i	0.161537	+	0.0284833i
$768$	1.73160	−	0.0396420i	0.0624836	−	0.00143046i
$769$	13.1765	+	15.7032i	0.475158	+	0.566271i	0.949378	−	0.314135i	$-0.101714\pi$
$769$	13.1765	+	15.7032i	0.475158	+	0.566271i	−0.474220	+	0.880406i	$0.657270\pi$
$770$	0.0776130	−	0.240376i	0.00279698	−	0.00866256i
$771$	−2.37734	+	4.34436i	−0.0856177	+	0.156458i
$772$	20.4275	+	17.1407i	0.735203	+	0.616909i
$773$	45.7749			1.64641			0.823204	−	0.567745i	$-0.192184\pi$
$773$	45.7749			1.64641			0.823204	+	0.567745i	$0.192184\pi$
$774$	9.32718	+	1.20760i	0.335259	+	0.0434061i
$775$			14.9776i			0.538010i
$776$	1.42790	−	8.09801i	0.0512585	−	0.290702i
$777$	13.0928	+	13.8370i	0.469703	+	0.496399i
$778$	−1.92429	−	0.700384i	−0.0689892	−	0.0251100i
$779$	−8.19757	−	9.76948i	−0.293708	−	0.350028i
$780$	0.0176086	+	0.0451370i	0.000630489	+	0.00161616i
$781$	−45.7714	+	16.6594i	−1.63783	+	0.596121i
$782$	0.973171	+	1.68558i	0.0348005	+	0.0602763i
$783$	−14.0913	−	31.7473i	−0.503581	−	1.13456i
$784$	3.93574	+	5.78878i	0.140562	+	0.206742i
$785$	0.386563	−	0.460687i	0.0137970	−	0.0164426i
$786$	−12.3733	−	31.7172i	−0.441342	−	1.13132i
$787$	0.598314	−	1.64385i	0.0213276	−	0.0585971i	−0.928572	−	0.371152i	$-0.878963\pi$
$787$	0.598314	−	1.64385i	0.0213276	−	0.0585971i	0.949900	+	0.312555i	$0.101185\pi$
$788$	12.3650	+	14.7360i	0.440484	+	0.524949i
$789$	−15.9100	−	18.1027i	−0.566412	−	0.644474i
$790$	−0.250304	−	0.0441353i	−0.00890541	−	0.00157026i
$791$	6.54682	−	12.3678i	0.232778	−	0.439747i
$792$	−4.80327	−	7.50404i	−0.170677	−	0.266645i
$793$	0.265149	−	0.459251i	0.00941571	−	0.0163085i
$794$	−4.13136	+	23.4301i	−0.146616	+	0.831503i
$795$	−0.252193	−	0.138006i	−0.00894435	−	0.00489457i
$796$	−5.76230	+	15.8318i	−0.204239	+	0.561143i
$797$	−3.94462	+	3.30993i	−0.139725	+	0.117244i	−0.709972	−	0.704230i	$-0.751292\pi$
$797$	−3.94462	+	3.30993i	−0.139725	+	0.117244i	0.570246	+	0.821474i	$0.306848\pi$
$798$	−18.5147	−	9.26453i	−0.655412	−	0.327961i
$799$	28.4654	−	10.3606i	1.00703	−	0.366530i
$800$	4.32923	+	2.49948i	0.153061	+	0.0883701i
$801$	13.5036	+	4.22584i	0.477126	+	0.149313i
$802$	−2.68685	−	4.65377i	−0.0948761	−	0.164330i
$803$	33.5831	−	12.2232i	1.18512	−	0.431349i
$804$	24.5923	+	8.31855i	0.867304	+	0.293373i
$805$	−0.0267261	+	0.0241537i	−0.000941971	+	0.000851307i
$806$	2.56749	−	0.452718i	0.0904361	−	0.0159463i
$807$	−26.5207	−	21.2384i	−0.933573	−	0.747627i
$808$	−3.42625	−	9.41354i	−0.120535	−	0.331167i
$809$	−47.6734	−	27.5242i	−1.67611	−	0.967700i	−0.964105	−	0.265522i	$-0.914456\pi$
$809$	−47.6734	−	27.5242i	−1.67611	−	0.967700i	−0.712001	−	0.702178i	$-0.752211\pi$
$810$	0.164929	−	0.237707i	0.00579502	−	0.00835219i
$811$			28.9072i			1.01507i	0.861631	+	0.507535i	$0.169443\pi$
$811$			28.9072i			1.01507i	−0.861631	+	0.507535i	$0.830557\pi$
$812$	−16.3857	+	6.65542i	−0.575024	+	0.233560i
$813$	10.9557	+	28.0834i	0.384235	+	0.984929i
$814$	−9.45732	+	7.93564i	−0.331479	+	0.278144i
$815$	−0.536416	+	0.450106i	−0.0187898	+	0.0157665i
$816$	−5.97857	+	5.25442i	−0.209292	+	0.183941i
$817$	4.84417	+	13.3093i	0.169476	+	0.465632i
$818$	−8.59052	+	14.8792i	−0.300361	+	0.520240i
$819$	1.75595	+	6.67970i	0.0613580	+	0.233408i
$820$	−0.0453728	−	0.0785879i	−0.00158449	−	0.00274441i
$821$	6.76176	−	8.05836i	0.235987	−	0.281239i	−0.635034	−	0.772484i	$-0.719014\pi$
$821$	6.76176	−	8.05836i	0.235987	−	0.281239i	0.871021	+	0.491246i	$0.163458\pi$
$822$	−9.97230	+	0.228299i	−0.347824	+	0.00796283i
$823$	6.27596	+	35.5927i	0.218766	+	1.24069i	0.874250	+	0.485476i	$0.161354\pi$
$823$	6.27596	+	35.5927i	0.218766	+	1.24069i	−0.655484	+	0.755209i	$0.727535\pi$
$824$	−2.98896	−	1.08789i	−0.104125	−	0.0378985i
$825$	−0.588539	−	25.7079i	−0.0204903	−	0.895035i
$826$	−12.7971	+	5.19783i	−0.445267	+	0.180856i
$827$	−45.6020	+	26.3283i	−1.58574	+	0.915525i	−0.591737	+	0.806131i	$0.701558\pi$
$827$	−45.6020	+	26.3283i	−1.58574	+	0.915525i	−0.993999	+	0.109393i	$0.965109\pi$
$828$	0.0581475	+	1.26930i	0.00202077	+	0.0441113i
$829$	−13.2365	+	7.64212i	−0.459724	+	0.265422i	−0.711928	−	0.702252i	$-0.752178\pi$
$829$	−13.2365	+	7.64212i	−0.459724	+	0.265422i	0.252204	+	0.967674i	$0.418844\pi$
$830$	0.0735402	−	0.0876418i	0.00255262	−	0.00304209i
$831$	−3.92337	+	3.44816i	−0.136100	+	0.119615i
$832$	0.297611	−	0.817679i	0.0103178	−	0.0283479i
$833$	−30.9540	−	8.75243i	−1.07249	−	0.303254i
$834$	−2.69395	+	17.6286i	−0.0932838	+	0.610429i
$835$	0.118145	−	0.670036i	0.00408859	−	0.0231875i
$836$	6.70871	−	11.6198i	0.232025	−	0.401880i
$837$	−10.8018	−	11.2113i	−0.373367	−	0.387520i
$838$	−0.464016	+	0.267900i	−0.0160292	+	0.00925444i
$839$	28.4382	+	23.8625i	0.981795	+	0.823824i	0.984359	−	0.176173i	$-0.0563717\pi$
$839$	28.4382	+	23.8625i	0.981795	+	0.823824i	−0.00256404	+	0.999997i	$0.500816\pi$
$840$	−0.118293	−	0.0877973i	−0.00408150	−	0.00302930i
$841$	−2.72341	−	15.4452i	−0.0939107	−	0.532594i
$842$	39.4796	−	6.96132i	1.36056	−	0.239903i
$843$	−25.3929	+	5.07929i	−0.874580	+	0.174940i
$844$	−5.57256	−	4.67594i	−0.191816	−	0.160952i
$845$	−0.393567			−0.0135391
$846$	19.6121	+	2.53918i	0.674276	+	0.0872989i
$847$	−5.09707	−	2.69811i	−0.175137	−	0.0927082i
$848$	1.76590	+	4.85178i	0.0606414	+	0.166611i
$849$	0.799287	+	34.9136i	0.0274315	+	1.19823i
$850$	−22.6231	+	3.98906i	−0.775965	+	0.136824i
$851$	1.73390	−	0.305734i	0.0594374	−	0.0104804i
$852$	0.650165	+	28.3998i	0.0222743	+	0.972961i
$853$	8.60666	+	23.6466i	0.294687	+	0.809645i	0.995365	+	0.0961676i	$0.0306585\pi$
$853$	8.60666	+	23.6466i	0.294687	+	0.809645i	−0.700679	+	0.713477i	$0.747119\pi$
$854$	0.0592444	+	1.61131i	0.00202730	+	0.0551378i
$855$	0.432093	+	0.0559433i	0.0147773	+	0.00191322i
$856$	−13.5006			−0.461440
$857$	16.6267	+	13.9515i	0.567959	+	0.476574i	0.880968	−	0.473176i	$-0.156893\pi$
$857$	16.6267	+	13.9515i	0.567959	+	0.476574i	−0.313009	+	0.949750i	$0.601337\pi$
$858$	−4.38913	+	0.877948i	−0.149843	+	0.0299727i
$859$	−12.4556	+	2.19625i	−0.424978	+	0.0749351i	−0.382047	−	0.924143i	$-0.624781\pi$
$859$	−12.4556	+	2.19625i	−0.424978	+	0.0749351i	−0.0429312	+	0.999078i	$0.513670\pi$
$860$	0.0175003	+	0.0992492i	0.000596756	+	0.00338437i
$861$	−5.14104	−	11.8705i	−0.175206	−	0.404545i
$862$	3.79141	+	3.18137i	0.129136	+	0.108358i
$863$	−35.7533	+	20.6422i	−1.21706	+	0.702668i	−0.964287	−	0.264858i	$-0.914675\pi$
$863$	−35.7533	+	20.6422i	−1.21706	+	0.702668i	−0.252769	+	0.967527i	$0.581341\pi$
$864$	−5.04324	+	1.25129i	−0.171575	+	0.0425697i
$865$	−0.289954	+	0.502216i	−0.00985875	+	0.0170758i
$866$	6.49895	−	36.8574i	0.220843	−	1.25247i
$867$	1.07731	−	7.04969i	0.0365874	−	0.239420i
$868$	−5.88112	+	5.31507i	−0.199618	+	0.180405i
$869$	8.03102	−	22.0651i	0.272434	−	0.748506i
$870$	0.279568	−	0.245706i	0.00947824	−	0.00833020i
$871$	8.38354	−	9.99112i	0.284065	−	0.338536i
$872$	6.11358	−	3.52968i	0.207032	−	0.119530i
$873$	1.12891	+	24.6430i	0.0382078	+	0.834038i
$874$	−1.65714	+	0.956749i	−0.0560535	+	0.0323625i
$875$	−0.320033	−	0.787920i	−0.0108191	−	0.0266366i
$876$	−0.477035	−	20.8373i	−0.0161175	−	0.704028i
$877$	28.0716	+	10.2172i	0.947911	+	0.345011i	0.769285	−	0.638906i	$-0.220613\pi$
$877$	28.0716	+	10.2172i	0.947911	+	0.345011i	0.178626	+	0.983917i	$0.442835\pi$
$878$	4.61284	+	26.1607i	0.155676	+	0.882882i
$879$	32.1947	−	0.737043i	1.08590	−	0.0248598i
$880$	0.0613683	−	0.0731359i	0.00206873	−	0.00246541i
$881$	−8.94029	−	15.4850i	−0.301206	−	0.521704i	0.675203	−	0.737632i	$-0.264056\pi$
$881$	−8.94029	−	15.4850i	−0.301206	−	0.521704i	−0.976409	+	0.215928i	$0.930722\pi$
$882$	−15.3169	−	14.3663i	−0.515748	−	0.483739i
$883$	3.31877	−	5.74828i	0.111686	−	0.193445i	−0.804764	−	0.593594i	$-0.797708\pi$
$883$	3.31877	−	5.74828i	0.111686	−	0.193445i	0.916450	+	0.400149i	$0.131042\pi$
$884$	1.36763	+	3.75754i	0.0459984	+	0.126380i
$885$	0.218340	−	0.191894i	0.00733943	−	0.00645044i
$886$	−22.8328	+	19.1590i	−0.767082	+	0.643658i
$887$	29.2147	−	24.5141i	0.980934	−	0.823102i	−0.00329568	−	0.999995i	$-0.501049\pi$
$887$	29.2147	−	24.5141i	0.980934	−	0.823102i	0.984230	+	0.176893i	$0.0566046\pi$
$888$	2.61677	+	6.70769i	0.0878129	+	0.225095i
$889$	31.4611	−	40.4218i	1.05517	−	1.35570i
$890$			0.151619i			0.00508227i
$891$	18.9812	+	18.8190i	0.635893	+	0.630459i
$892$	6.48961	+	3.74678i	0.217288	+	0.125451i
$893$	10.1857	+	27.9851i	0.340853	+	0.936485i
$894$	2.27765	+	1.82400i	0.0761762	+	0.0610036i
$895$	−0.386003	+	0.0680627i	−0.0129027	+	0.00227509i
$896$	0.554856	+	2.58692i	0.0185364	+	0.0864228i
$897$	0.604690	+	0.204541i	0.0201900	+	0.00682944i
$898$	14.9131	−	5.42793i	0.497657	−	0.181132i
$899$	−10.0139	−	17.3446i	−0.333983	−	0.578475i
$900$	−14.3124	−	4.47896i	−0.477081	−	0.149299i
$901$	−20.5478	−	11.8633i	−0.684548	−	0.395224i
$902$	7.87797	−	2.86735i	0.262308	−	0.0954722i
$903$	0.856315	+	14.3409i	0.0284964	+	0.477234i
$904$	4.05169	−	3.39977i	0.134757	−	0.113075i
$905$	−0.0661585	+	0.181769i	−0.00219918	+	0.00604220i
$906$	15.9076	+	8.70501i	0.528494	+	0.289205i
$907$	−0.572815	+	3.24859i	−0.0190200	+	0.107868i	−0.992840	−	0.119454i	$-0.961886\pi$
$907$	−0.572815	+	3.24859i	−0.0190200	+	0.107868i	0.973820	+	0.227321i	$0.0729968\pi$
$908$	−5.56326	+	9.63586i	−0.184623	+	0.319777i
$909$	16.2018	+	25.3118i	0.537381	+	0.839539i
$910$	−0.0626905	+	0.0393344i	−0.00207817	+	0.00130392i
$911$	−6.04685	−	1.06622i	−0.200341	−	0.0353255i	0.0725770	−	0.997363i	$-0.476878\pi$
$911$	−6.04685	−	1.06622i	−0.200341	−	0.0353255i	−0.272918	+	0.962037i	$0.587989\pi$
$912$	−5.16575	−	5.87768i	−0.171055	−	0.194629i
$913$	6.79404	+	8.09682i	0.224850	+	0.267966i
$914$	−1.00444	+	2.75968i	−0.0332240	+	0.0912823i
$915$	−0.0123325	−	0.0316125i	−0.000407699	−	0.00104508i
$916$	4.40580	−	5.25063i	0.145572	−	0.173486i
$917$	44.0519	−	27.6398i	1.45472	−	0.912746i
$918$	14.0574	−	19.3018i	0.463963	−	0.637054i
$919$	−20.5282	−	35.5559i	−0.677163	−	1.17288i	−0.975832	−	0.218524i	$-0.929876\pi$
$919$	−20.5282	−	35.5559i	−0.677163	−	1.17288i	0.298669	−	0.954357i	$-0.403457\pi$
$920$	−0.0127945	+	0.00465680i	−0.000421821	+	0.000153530i
$921$	18.2379	+	46.7502i	0.600960	+	1.54047i
$922$	−9.75582	−	11.6265i	−0.321291	−	0.382899i
$923$	13.4107	+	4.88110i	0.441419	+	0.160663i
$924$	9.88568	−	9.35404i	0.325215	−	0.307725i
$925$	−3.60848	+	20.4647i	−0.118646	+	0.672876i
$926$		−	18.4843i		−	0.607430i
$927$	9.46336	+	1.22523i	0.310817	+	0.0402417i
$928$	−6.68457			−0.219432
$929$	−6.35982	−	5.33652i	−0.208659	−	0.175086i	0.532469	−	0.846450i	$-0.321264\pi$
$929$	−6.35982	−	5.33652i	−0.208659	−	0.175086i	−0.741128	+	0.671364i	$0.765709\pi$
$930$	0.0800835	−	0.146345i	0.00262604	−	0.00479884i
$931$	8.60474	−	30.4316i	0.282009	−	0.997356i
$932$	−7.32869	−	8.73399i	−0.240059	−	0.286091i
$933$	−37.8602	+	0.866745i	−1.23949	+	0.0283760i
$934$	0.786972	+	0.138764i	0.0257505	+	0.00454051i
$935$			0.438729i			0.0143480i
$936$	−0.335181	+	2.58886i	−0.0109557	+	0.0846196i
$937$	32.1971	+	18.5890i	1.05183	+	0.607277i	0.923162	−	0.384410i	$-0.125595\pi$
$937$	32.1971	+	18.5890i	1.05183	+	0.607277i	0.128672	+	0.991687i	$0.458928\pi$
$938$	−5.44663	+	39.2805i	−0.177839	+	1.28255i
$939$	24.6825	+	28.0841i	0.805481	+	0.916491i
$940$	0.0367975	+	0.208689i	0.00120020	+	0.00680669i
$941$	−37.1956	−	13.5381i	−1.21254	−	0.441329i	−0.344958	−	0.938618i	$-0.612107\pi$
$941$	−37.1956	−	13.5381i	−1.21254	−	0.441329i	−0.867585	+	0.497289i	$0.834329\pi$
$942$	30.1866	−	11.7762i	0.983533	−	0.383690i
$943$	−1.17744	−	0.207615i	−0.0383427	−	0.00676086i
$944$	−5.22059			−0.169916
$945$	0.403862	+	0.179473i	0.0131376	+	0.00583824i
$946$	−9.31062			−0.302714
$947$	−6.18451	−	1.09050i	−0.200970	−	0.0354364i	0.0722571	−	0.997386i	$-0.476980\pi$
$947$	−6.18451	−	1.09050i	−0.200970	−	0.0354364i	−0.273227	+	0.961950i	$0.588091\pi$
$948$	−10.6892	−	8.56013i	−0.347168	−	0.278020i
$949$	−9.83961	−	3.58133i	−0.319407	−	0.116255i
$950$	−3.92175	−	22.2413i	−0.127238	−	0.721604i
$951$	1.84717	−	0.369485i	0.0598986	−	0.0119814i
$952$	−9.59458	−	7.46765i	−0.310962	−	0.242028i
$953$	23.7392	+	13.7058i	0.768987	+	0.443975i	0.832513	−	0.554005i	$-0.186901\pi$
$953$	23.7392	+	13.7058i	0.768987	+	0.443975i	−0.0635260	+	0.997980i	$0.520235\pi$
$954$	−8.35050	−	13.0458i	−0.270357	−	0.422374i
$955$		−	0.112902i		−	0.00365343i
$956$	28.6275	+	5.04779i	0.925878	+	0.163257i
$957$	17.8697	+	29.3773i	0.577647	+	0.949634i
$958$	27.0226	+	32.2043i	0.873061	+	1.04047i
$959$	−3.19543	−	14.8981i	−0.103186	−	0.481085i
$960$	−0.0289362	−	0.0475703i	−0.000933913	−	0.00153532i
$961$	16.8708	+	14.1562i	0.544218	+	0.456653i
$962$	3.61719			0.116623
$963$	39.5228	−	8.85099i	1.27360	−	0.285219i
$964$		−	17.2511i		−	0.555619i
$965$	0.148857	−	0.844210i	0.00479187	−	0.0271761i
$966$	−1.88795	+	0.450371i	−0.0607438	+	0.0144904i
$967$	−44.7224	−	16.2776i	−1.43817	−	0.523453i	−0.498912	−	0.866653i	$-0.666267\pi$
$967$	−44.7224	−	16.2776i	−1.43817	−	0.523453i	−0.939262	+	0.343200i	$0.888489\pi$
$968$	−1.40113	−	1.66980i	−0.0450341	−	0.0536695i
$969$	35.5465	+	5.43210i	1.14192	+	0.174504i
$970$	−0.248399	+	0.0904098i	−0.00797560	+	0.00290288i
$971$	0.720126	+	1.24730i	0.0231100	+	0.0400276i	0.877349	−	0.479853i	$-0.159310\pi$
$971$	0.720126	+	1.24730i	0.0231100	+	0.0400276i	−0.854239	+	0.519880i	$0.825977\pi$
$972$	13.9437	−	6.96948i	0.447244	−	0.223546i
$973$	−27.2224	+	1.00091i	−0.872709	+	0.0320877i
$974$	12.5007	−	14.8978i	0.400549	−	0.477356i
$975$	−4.70954	+	5.88087i	−0.150826	+	0.188339i
$976$	−0.208437	+	0.572675i	−0.00667190	+	0.0183309i
$977$	−17.4331	−	20.7759i	−0.557734	−	0.664681i	0.411332	−	0.911486i	$-0.365064\pi$
$977$	−17.4331	−	20.7759i	−0.557734	−	0.664681i	−0.969065	+	0.246805i	$0.920619\pi$
$978$	−36.9958	+	7.40018i	−1.18299	+	0.236632i
$979$	−13.7945	−	2.43235i	−0.440875	−	0.0777382i
$980$	0.0978985	−	0.202616i	0.00312725	−	0.00647232i
$981$	−15.5834	+	14.3412i	−0.497539	+	0.457878i
$982$	2.57505	−	4.46012i	0.0821732	−	0.142328i
$983$	−1.47568	+	8.36902i	−0.0470670	+	0.266930i	−0.999255	−	0.0385809i	$-0.987716\pi$
$983$	−1.47568	+	8.36902i	−0.0470670	+	0.266930i	0.952188	+	0.305511i	$0.0988274\pi$
$984$	−0.111903	−	4.88805i	−0.00356735	−	0.155825i
$985$	0.211502	−	0.581097i	0.00673902	−	0.0185153i
$986$	23.5314	−	19.7452i	0.749392	−	0.628815i
$987$	1.80055	+	30.1542i	0.0573123	+	0.959820i
$988$	−3.69413	+	1.34455i	−0.117526	+	0.0427759i
$989$	1.14992	+	0.663908i	0.0365654	+	0.0211111i
$990$	−0.131707	+	0.254338i	−0.00418592	+	0.00808338i
$991$	−19.9506	−	34.5555i	−0.633752	−	1.09769i	−0.986778	−	0.162077i	$-0.948181\pi$
$991$	−19.9506	−	34.5555i	−0.633752	−	1.09769i	0.353026	−	0.935614i	$-0.385153\pi$
$992$	−2.81544	+	1.02474i	−0.0893903	+	0.0325354i
$993$	4.66514	+	23.3225i	0.148044	+	0.740116i
$994$	−42.4278	+	9.10015i	−1.34573	+	0.288639i
$995$	0.533375	−	0.0940484i	0.0169091	−	0.00298153i
$996$	5.74274	−	2.24033i	0.181966	−	0.0709874i
$997$	−6.26324	−	17.2081i	−0.198359	−	0.544986i	0.800137	−	0.599818i	$-0.204760\pi$
$997$	−6.26324	−	17.2081i	−0.198359	−	0.544986i	−0.998496	+	0.0548311i	$0.982538\pi$
$998$	−6.45800	−	3.72853i	−0.204424	−	0.118024i
$999$	−12.0581	−	17.9211i	−0.381502	−	0.567000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.227.19	yes	144
7.5	odd	6		378.2.ba.a.173.3	yes	144
27.5	odd	18		378.2.ba.a.59.3	✓	144
189.5	even	18	inner	378.2.bf.a.5.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.59.3	✓	144	27.5	odd	18
378.2.ba.a.173.3	yes	144	7.5	odd	6
378.2.bf.a.5.19	yes	144	189.5	even	18	inner
378.2.bf.a.227.19	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.261649 - 1.71217i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.00558222 - 0.0316584i) q^{5} +(0.554990 - 1.64073i) q^{6} +(2.62068 + 0.363383i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.86308 - 0.895977i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.261649 - 1.71217i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.00558222 - 0.0316584i) q^{5} +(0.554990 - 1.64073i) q^{6} +(2.62068 + 0.363383i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.86308 - 0.895977i) q^{9} -0.0321467i q^{10} +(2.92477 + 0.515715i) q^{11} +(0.831468 - 1.51943i) q^{12} +(-0.559326 - 0.666578i) q^{13} +(2.51776 + 0.812939i) q^{14} +(-0.0556652 + 0.00127436i) q^{15} +(0.766044 + 0.642788i) q^{16} -4.59537 q^{17} +(-2.66400 - 1.37953i) q^{18} -4.51782i q^{19} +(0.00558222 - 0.0316584i) q^{20} +(1.30787 - 4.39198i) q^{21} +(2.79078 + 1.01576i) q^{22} +(-0.272249 - 0.324454i) q^{23} +(1.08268 - 1.35196i) q^{24} +(4.69749 - 1.70975i) q^{25} +(-0.435078 - 0.753577i) q^{26} +(-2.28319 + 4.66766i) q^{27} +(2.33835 + 1.23779i) q^{28} +(-4.29676 + 5.12068i) q^{29} +(-0.0550408 - 0.00841116i) q^{30} +(-1.02474 + 2.81544i) q^{31} +(0.642788 + 0.766044i) q^{32} +(1.64826 - 4.87277i) q^{33} +(-4.52555 - 0.797977i) q^{34} +(-0.00312508 - 0.0849948i) q^{35} +(-2.38397 - 1.82117i) q^{36} +(-2.07847 + 3.60002i) q^{37} +(0.784511 - 4.44918i) q^{38} +(-1.28764 + 0.783253i) q^{39} +(0.0109948 - 0.0302080i) q^{40} +(2.16243 - 1.81450i) q^{41} +(2.05066 - 4.09814i) q^{42} +(-2.94595 + 1.07224i) q^{43} +(2.57200 + 1.48494i) q^{44} +(-0.0123828 + 0.0956419i) q^{45} +(-0.211772 - 0.366800i) q^{46} +(-6.19437 + 2.25457i) q^{47} +(1.30100 - 1.14342i) q^{48} +(6.73590 + 1.90462i) q^{49} +(4.92302 - 0.868061i) q^{50} +(-1.20237 + 7.86807i) q^{51} +(-0.297611 - 0.817679i) q^{52} +(4.47143 + 2.58158i) q^{53} +(-3.05903 + 4.20027i) q^{54} -0.0954721i q^{55} +(2.08788 + 1.62504i) q^{56} +(-7.73529 - 1.18208i) q^{57} +(-5.12068 + 4.29676i) q^{58} +(-3.99921 + 3.35573i) q^{59} +(-0.0527440 - 0.0178411i) q^{60} +(0.208437 + 0.572675i) q^{61} +(-1.49806 + 2.59472i) q^{62} +(-7.17763 - 3.38846i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.0179805 + 0.0214283i) q^{65} +(2.46936 - 4.51253i) q^{66} +(2.60275 + 14.7609i) q^{67} +(-4.31823 - 1.57171i) q^{68} +(-0.626755 + 0.381245i) q^{69} +(0.0116816 - 0.0842462i) q^{70} +(-14.2036 + 8.20047i) q^{71} +(-2.03151 - 2.20748i) q^{72} +(10.4214 - 6.01679i) q^{73} +(-2.67203 + 3.18441i) q^{74} +(-1.69829 - 8.49028i) q^{75} +(1.54519 - 4.24536i) q^{76} +(7.47747 + 2.41434i) q^{77} +(-1.40409 + 0.547757i) q^{78} +(1.37293 - 7.78630i) q^{79} +(0.0160734 - 0.0278399i) q^{80} +(7.39445 + 5.13051i) q^{81} +(2.44466 - 1.41143i) q^{82} +(2.72631 + 2.28764i) q^{83} +(2.73114 - 3.67979i) q^{84} +(0.0256524 + 0.145482i) q^{85} +(-3.08738 + 0.544389i) q^{86} +(7.64325 + 8.69662i) q^{87} +(2.27507 + 1.90901i) q^{88} -4.71645 q^{89} +(-0.0288027 + 0.0920387i) q^{90} +(-1.22359 - 1.95014i) q^{91} +(-0.144861 - 0.398002i) q^{92} +(4.55240 + 2.49119i) q^{93} +(-6.49177 + 1.14467i) q^{94} +(-0.143027 + 0.0252195i) q^{95} +(1.47979 - 0.900129i) q^{96} +(-2.81241 - 7.72703i) q^{97} +(6.30284 + 3.04536i) q^{98} +(-7.91177 - 4.09706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) \) 144 * q + 18 * q^6 - 12 * q^9	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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