LMFDB - Embedded newform 378.2.bf.a.227.12

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			227.12
Character	$\chi$	$=$	378.227
Dual form			378.2.bf.a.5.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(1.73169 - 0.0354625i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.334523 - 1.89717i) q^{5} +(-1.71154 - 0.265781i) q^{6} +(2.15385 - 1.53653i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.99748 - 0.122820i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(1.73169 - 0.0354625i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.334523 - 1.89717i) q^{5} +(-1.71154 - 0.265781i) q^{6} +(2.15385 - 1.53653i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.99748 - 0.122820i) q^{9} +1.92644i q^{10} +(-1.95364 - 0.344480i) q^{11} +(1.63938 + 0.558948i) q^{12} +(-0.332627 - 0.396409i) q^{13} +(-2.38795 + 1.13917i) q^{14} +(-0.646568 - 3.27345i) q^{15} +(0.766044 + 0.642788i) q^{16} -2.62195 q^{17} +(-2.97327 - 0.399554i) q^{18} -2.64927i q^{19} +(0.334523 - 1.89717i) q^{20} +(3.67531 - 2.73717i) q^{21} +(1.86414 + 0.678492i) q^{22} +(0.904765 + 1.07826i) q^{23} +(-1.51742 - 0.835132i) q^{24} +(1.21110 - 0.440805i) q^{25} +(0.258738 + 0.448147i) q^{26} +(5.18635 - 0.318984i) q^{27} +(2.54948 - 0.707201i) q^{28} +(1.24439 - 1.48301i) q^{29} +(0.0683165 + 3.33599i) q^{30} +(-3.14896 + 8.65171i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-3.39531 - 0.527250i) q^{33} +(2.58212 + 0.455297i) q^{34} +(-3.63557 - 3.57223i) q^{35} +(2.85872 + 0.909787i) q^{36} +(-2.52634 + 4.37575i) q^{37} +(-0.460041 + 2.60902i) q^{38} +(-0.590063 - 0.674661i) q^{39} +(-0.658881 + 1.81026i) q^{40} +(4.09818 - 3.43878i) q^{41} +(-4.09478 + 2.05737i) q^{42} +(10.5080 - 3.82460i) q^{43} +(-1.71800 - 0.991889i) q^{44} +(-1.23574 - 5.64566i) q^{45} +(-0.703782 - 1.21899i) q^{46} +(-1.15580 + 0.420678i) q^{47} +(1.34934 + 1.08594i) q^{48} +(2.27817 - 6.61891i) q^{49} +(-1.26925 + 0.223803i) q^{50} +(-4.54040 + 0.0929811i) q^{51} +(-0.176987 - 0.486268i) q^{52} +(2.98015 + 1.72059i) q^{53} +(-5.16295 - 0.586462i) q^{54} +3.82163i q^{55} +(-2.63356 + 0.253744i) q^{56} +(-0.0939498 - 4.58771i) q^{57} +(-1.48301 + 1.24439i) q^{58} +(-3.01598 + 2.53071i) q^{59} +(0.512011 - 3.29717i) q^{60} +(0.959994 + 2.63756i) q^{61} +(4.60348 - 7.97345i) q^{62} +(6.26743 - 4.87025i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.640785 + 0.763658i) q^{65} +(3.25217 + 1.10883i) q^{66} +(-0.405899 - 2.30197i) q^{67} +(-2.46383 - 0.896760i) q^{68} +(1.60501 + 1.83512i) q^{69} +(2.96003 + 4.14927i) q^{70} +(-7.92127 + 4.57335i) q^{71} +(-2.65731 - 1.39238i) q^{72} +(-13.9043 + 8.02766i) q^{73} +(3.24780 - 3.87058i) q^{74} +(2.08162 - 0.806286i) q^{75} +(0.906103 - 2.48950i) q^{76} +(-4.73716 + 2.25986i) q^{77} +(0.463945 + 0.766875i) q^{78} +(-1.00582 + 5.70432i) q^{79} +(0.963220 - 1.66835i) q^{80} +(8.96983 - 0.736303i) q^{81} +(-4.63306 + 2.67490i) q^{82} +(11.7457 + 9.85582i) q^{83} +(4.38983 - 1.31506i) q^{84} +(0.877103 + 4.97430i) q^{85} +(-11.0125 + 1.94180i) q^{86} +(2.10230 - 2.61223i) q^{87} +(1.51966 + 1.27515i) q^{88} -12.4027 q^{89} +(0.236606 + 5.77448i) q^{90} +(-1.32552 - 0.342717i) q^{91} +(0.481415 + 1.32268i) q^{92} +(-5.14621 + 15.0937i) q^{93} +(1.21130 - 0.213584i) q^{94} +(-5.02612 + 0.886241i) q^{95} +(-1.14027 - 1.30375i) q^{96} +(0.655092 + 1.79985i) q^{97} +(-3.39292 + 6.12275i) q^{98} +(-5.89832 - 0.792626i) 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
$3$	1.73169	−	0.0354625i	0.999790	−	0.0204743i
$3$	1.73169	−	0.0354625i	0.999790	−	0.0204743i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−0.334523	−	1.89717i	−0.149603	−	0.848442i	−0.963555	−	0.267510i	$-0.913799\pi$
$5$	−0.334523	−	1.89717i	−0.149603	−	0.848442i	0.813952	−	0.580932i	$-0.197312\pi$
$6$	−1.71154	−	0.265781i	−0.698732	−	0.108504i
$7$	2.15385	−	1.53653i	0.814080	−	0.580752i
$7$	2.15385	−	1.53653i	0.814080	−	0.580752i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	2.99748	−	0.122820i	0.999162	−	0.0409400i
$10$			1.92644i			0.609194i
$11$	−1.95364	−	0.344480i	−0.589045	−	0.103864i	−0.128822	−	0.991668i	$-0.541119\pi$
$11$	−1.95364	−	0.344480i	−0.589045	−	0.103864i	−0.460223	+	0.887803i	$0.652231\pi$
$12$	1.63938	+	0.558948i	0.473249	+	0.161354i
$13$	−0.332627	−	0.396409i	−0.0922540	−	0.109944i	0.717942	−	0.696102i	$-0.245084\pi$
$13$	−0.332627	−	0.396409i	−0.0922540	−	0.109944i	−0.810196	+	0.586158i	$0.800640\pi$
$14$	−2.38795	+	1.13917i	−0.638206	+	0.304456i
$15$	−0.646568	−	3.27345i	−0.166943	−	0.845201i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.62195			−0.635917			−0.317958	−	0.948105i	$-0.602997\pi$
$17$	−2.62195			−0.635917			−0.317958	+	0.948105i	$0.602997\pi$
$18$	−2.97327	−	0.399554i	−0.700807	−	0.0941757i
$19$		−	2.64927i		−	0.607784i	−0.952707	−	0.303892i	$-0.901714\pi$
$19$		−	2.64927i		−	0.607784i	0.952707	−	0.303892i	$-0.0982862\pi$
$20$	0.334523	−	1.89717i	0.0748016	−	0.424221i
$21$	3.67531	−	2.73717i	0.802019	−	0.597298i
$22$	1.86414	+	0.678492i	0.397436	+	0.144655i
$23$	0.904765	+	1.07826i	0.188657	+	0.224832i	0.852079	−	0.523413i	$-0.175341\pi$
$23$	0.904765	+	1.07826i	0.188657	+	0.224832i	−0.663423	+	0.748245i	$0.730897\pi$
$24$	−1.51742	−	0.835132i	−0.309741	−	0.170471i
$25$	1.21110	−	0.440805i	0.242220	−	0.0881610i
$26$	0.258738	+	0.448147i	0.0507426	+	0.0878888i
$27$	5.18635	−	0.318984i	0.998114	−	0.0613886i
$28$	2.54948	−	0.707201i	0.481807	−	0.133648i
$29$	1.24439	−	1.48301i	0.231077	−	0.275387i	−0.638029	−	0.770012i	$-0.720250\pi$
$29$	1.24439	−	1.48301i	0.231077	−	0.275387i	0.869107	+	0.494625i	$0.164695\pi$
$30$	0.0683165	+	3.33599i	0.0124728	+	0.609066i
$31$	−3.14896	+	8.65171i	−0.565570	+	1.55389i	0.245776	+	0.969327i	$0.420957\pi$
$31$	−3.14896	+	8.65171i	−0.565570	+	1.55389i	−0.811347	+	0.584565i	$0.801265\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	−3.39531	−	0.527250i	−0.591048	−	0.0917824i
$34$	2.58212	+	0.455297i	0.442830	+	0.0780828i
$35$	−3.63557	−	3.57223i	−0.614524	−	0.603817i
$36$	2.85872	+	0.909787i	0.476454	+	0.151631i
$37$	−2.52634	+	4.37575i	−0.415328	+	0.719368i	−0.995463	−	0.0951518i	$-0.969666\pi$
$37$	−2.52634	+	4.37575i	−0.415328	+	0.719368i	0.580135	+	0.814520i	$0.303000\pi$
$38$	−0.460041	+	2.60902i	−0.0746284	+	0.423239i
$39$	−0.590063	−	0.674661i	−0.0944857	−	0.108032i
$40$	−0.658881	+	1.81026i	−0.104178	+	0.286228i
$41$	4.09818	−	3.43878i	0.640028	−	0.537047i	−0.263999	−	0.964523i	$-0.585042\pi$
$41$	4.09818	−	3.43878i	0.640028	−	0.537047i	0.904027	+	0.427476i	$0.140597\pi$
$42$	−4.09478	+	2.05737i	−0.631838	+	0.317459i
$43$	10.5080	−	3.82460i	1.60246	−	0.583246i	0.622528	−	0.782597i	$-0.286106\pi$
$43$	10.5080	−	3.82460i	1.60246	−	0.583246i	0.979928	+	0.199351i	$0.0638833\pi$
$44$	−1.71800	−	0.991889i	−0.258999	−	0.149533i
$45$	−1.23574	−	5.64566i	−0.184213	−	0.841606i
$46$	−0.703782	−	1.21899i	−0.103767	−	0.179730i
$47$	−1.15580	+	0.420678i	−0.168591	+	0.0613622i	−0.424937	−	0.905223i	$-0.639704\pi$
$47$	−1.15580	+	0.420678i	−0.168591	+	0.0613622i	0.256346	+	0.966585i	$0.417482\pi$
$48$	1.34934	+	1.08594i	0.194761	+	0.156742i
$49$	2.27817	−	6.61891i	0.325453	−	0.945558i
$50$	−1.26925	+	0.223803i	−0.179499	+	0.0316505i
$51$	−4.54040	+	0.0929811i	−0.635783	+	0.0130200i
$52$	−0.176987	−	0.486268i	−0.0245437	−	0.0674332i
$53$	2.98015	+	1.72059i	0.409355	+	0.236341i	0.690512	−	0.723321i	$-0.257385\pi$
$53$	2.98015	+	1.72059i	0.409355	+	0.236341i	−0.281158	+	0.959662i	$0.590718\pi$
$54$	−5.16295	−	0.586462i	−0.702589	−	0.0798074i
$55$			3.82163i			0.515309i
$56$	−2.63356	+	0.253744i	−0.351924	+	0.0339080i
$57$	−0.0939498	−	4.58771i	−0.0124440	−	0.607656i
$58$	−1.48301	+	1.24439i	−0.194728	+	0.163396i
$59$	−3.01598	+	2.53071i	−0.392647	+	0.329470i	−0.817643	−	0.575725i	$-0.804720\pi$
$59$	−3.01598	+	2.53071i	−0.392647	+	0.329470i	0.424996	+	0.905195i	$0.360275\pi$
$60$	0.512011	−	3.29717i	0.0661003	−	0.425663i
$61$	0.959994	+	2.63756i	0.122915	+	0.337705i	0.985855	−	0.167601i	$-0.0536019\pi$
$61$	0.959994	+	2.63756i	0.122915	+	0.337705i	−0.862940	+	0.505306i	$0.831380\pi$
$62$	4.60348	−	7.97345i	0.584642	−	1.01263i
$63$	6.26743	−	4.87025i	0.789622	−	0.613594i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.640785	+	0.763658i	−0.0794796	+	0.0947201i
$66$	3.25217	+	1.10883i	0.400315	+	0.136487i
$67$	−0.405899	−	2.30197i	−0.0495884	−	0.281230i	0.949923	−	0.312484i	$-0.101161\pi$
$67$	−0.405899	−	2.30197i	−0.0495884	−	0.281230i	−0.999511	+	0.0312541i	$0.990050\pi$
$68$	−2.46383	−	0.896760i	−0.298783	−	0.108748i
$69$	1.60501	+	1.83512i	0.193220	+	0.220922i
$70$	2.96003	+	4.14927i	0.353791	+	0.495933i
$71$	−7.92127	+	4.57335i	−0.940082	+	0.542757i	−0.889986	−	0.455988i	$-0.849286\pi$
$71$	−7.92127	+	4.57335i	−0.940082	+	0.542757i	−0.0500960	+	0.998744i	$0.515953\pi$
$72$	−2.65731	−	1.39238i	−0.313167	−	0.164093i
$73$	−13.9043	+	8.02766i	−1.62738	+	0.939566i	−0.642504	+	0.766282i	$0.722105\pi$
$73$	−13.9043	+	8.02766i	−1.62738	+	0.939566i	−0.984872	+	0.173284i	$0.944562\pi$
$74$	3.24780	−	3.87058i	0.377549	−	0.449945i
$75$	2.08162	−	0.806286i	0.240365	−	0.0931018i
$76$	0.906103	−	2.48950i	0.103937	−	0.285565i
$77$	−4.73716	+	2.25986i	−0.539849	+	0.257535i
$78$	0.463945	+	0.766875i	0.0525314	+	0.0868314i
$79$	−1.00582	+	5.70432i	−0.113164	+	0.641786i	0.874479	+	0.485064i	$0.161204\pi$
$79$	−1.00582	+	5.70432i	−0.113164	+	0.641786i	−0.987643	+	0.156722i	$0.949907\pi$
$80$	0.963220	−	1.66835i	0.107691	−	0.186527i
$81$	8.96983	−	0.736303i	0.996648	−	0.0818114i
$82$	−4.63306	+	2.67490i	−0.511635	+	0.295393i
$83$	11.7457	+	9.85582i	1.28926	+	1.08182i	0.991896	+	0.127052i	$0.0405514\pi$
$83$	11.7457	+	9.85582i	1.28926	+	1.08182i	0.297362	+	0.954765i	$0.403893\pi$
$84$	4.38983	−	1.31506i	0.478970	−	0.143485i
$85$	0.877103	+	4.97430i	0.0951352	+	0.539538i
$86$	−11.0125	+	1.94180i	−1.18751	+	0.209390i
$87$	2.10230	−	2.61223i	0.225390	−	0.280061i
$88$	1.51966	+	1.27515i	0.161997	+	0.135931i
$89$	−12.4027			−1.31469			−0.657344	−	0.753591i	$-0.728320\pi$
$89$	−12.4027			−1.31469			−0.657344	+	0.753591i	$0.728320\pi$
$90$	0.236606	+	5.77448i	0.0249404	+	0.608683i
$91$	−1.32552	−	0.342717i	−0.138952	−	0.0359265i
$92$	0.481415	+	1.32268i	0.0501910	+	0.137899i
$93$	−5.14621	+	15.0937i	−0.533637	+	1.56515i
$94$	1.21130	−	0.213584i	0.124936	−	0.0220295i
$95$	−5.02612	+	0.886241i	−0.515669	+	0.0909264i
$96$	−1.14027	−	1.30375i	−0.116379	−	0.133064i
$97$	0.655092	+	1.79985i	0.0665145	+	0.182747i	0.968497	−	0.249026i	$-0.0801104\pi$
$97$	0.655092	+	1.79985i	0.0665145	+	0.182747i	−0.901982	+	0.431773i	$0.857888\pi$
$98$	−3.39292	+	6.12275i	−0.342737	+	0.618491i
$99$	−5.89832	−	0.792626i	−0.592803	−	0.0796619i
$100$	1.28883			0.128883
$101$	8.48955	+	7.12358i	0.844742	+	0.708822i	0.958625	−	0.284672i	$-0.0918846\pi$
$101$	8.48955	+	7.12358i	0.844742	+	0.708822i	−0.113883	+	0.993494i	$0.536329\pi$
$102$	4.48757	+	0.696864i	0.444336	+	0.0689998i
$103$	−6.50597	+	1.14718i	−0.641053	+	0.113035i	−0.484720	−	0.874670i	$-0.661078\pi$
$103$	−6.50597	+	1.14718i	−0.641053	+	0.113035i	−0.156333	+	0.987704i	$0.549967\pi$
$104$	0.0898586	+	0.509614i	0.00881136	+	0.0499717i
$105$	−6.42235	−	6.05706i	−0.626758	−	0.591109i
$106$	−2.63610	−	2.21195i	−0.256040	−	0.214843i
$107$	3.81047	−	2.19998i	0.368372	−	0.212680i	−0.304375	−	0.952552i	$-0.598448\pi$
$107$	3.81047	−	2.19998i	0.368372	−	0.212680i	0.672747	+	0.739872i	$0.265114\pi$
$108$	4.98268	+	1.47409i	0.479458	+	0.141844i
$109$	−7.65735	+	13.2629i	−0.733441	+	1.27036i	0.221963	+	0.975055i	$0.428754\pi$
$109$	−7.65735	+	13.2629i	−0.733441	+	1.27036i	−0.955404	+	0.295302i	$0.904580\pi$
$110$	0.663619	−	3.76357i	0.0632736	−	0.358842i
$111$	−4.21965	+	7.66702i	−0.400512	+	0.727721i
$112$	2.63761	+	0.207423i	0.249231	+	0.0195996i
$113$	−6.41396	+	17.6222i	−0.603375	+	1.65776i	0.141010	+	0.990008i	$0.454965\pi$
$113$	−6.41396	+	17.6222i	−0.603375	+	1.65776i	−0.744385	+	0.667751i	$0.767257\pi$
$114$	−0.704124	+	4.53432i	−0.0659473	+	0.424678i
$115$	1.74298	−	2.07720i	0.162533	−	0.193700i
$116$	1.67656	−	0.967963i	0.155665	−	0.0898731i
$117$	−1.04573	−	1.14738i	−0.0966778	−	0.106075i
$118$	3.40961	−	1.96854i	0.313880	−	0.181219i
$119$	−5.64730	+	4.02870i	−0.517687	+	0.369310i
$120$	−1.07678	+	3.15817i	−0.0982961	+	0.288300i
$121$	−6.63857	−	2.41624i	−0.603507	−	0.219658i
$122$	−0.487402	−	2.76419i	−0.0441273	−	0.250258i
$123$	6.97482	−	6.10023i	0.628898	−	0.550039i
$124$	−5.91811	+	7.05293i	−0.531462	+	0.633372i
$125$	−6.05753	−	10.4919i	−0.541802	−	0.938428i
$126$	−7.01792	+	3.70793i	−0.625206	+	0.330329i
$127$	2.37008	−	4.10510i	0.210311	−	0.364269i	−0.741501	−	0.670952i	$-0.765886\pi$
$127$	2.37008	−	4.10510i	0.210311	−	0.364269i	0.951812	+	0.306683i	$0.0992191\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	18.0610	−	6.99566i	1.59018	−	0.615933i
$130$	0.763658	−	0.640785i	0.0669773	−	0.0562006i
$131$	10.7859	−	9.05044i	0.942368	−	0.790740i	−0.0356282	−	0.999365i	$-0.511343\pi$
$131$	10.7859	−	9.05044i	0.942368	−	0.790740i	0.977996	+	0.208625i	$0.0668988\pi$
$132$	−3.01022	−	1.65672i	−0.262006	−	0.144199i
$133$	−4.07067	−	5.70614i	−0.352972	−	0.494785i
$134$			2.33748i			0.201927i
$135$	−2.34012	−	9.73270i	−0.201406	−	0.837658i
$136$	2.27068	+	1.31098i	0.194709	+	0.112415i
$137$	5.69916	+	15.6583i	0.486912	+	1.33778i	0.903462	+	0.428668i	$0.141017\pi$
$137$	5.69916	+	15.6583i	0.486912	+	1.33778i	−0.416550	+	0.909113i	$0.636761\pi$
$138$	−1.26196	−	2.08595i	−0.107425	−	0.177568i
$139$	6.07497	−	1.07118i	0.515272	−	0.0908564i	0.0900355	−	0.995939i	$-0.471302\pi$
$139$	6.07497	−	1.07118i	0.515272	−	0.0908564i	0.425237	+	0.905082i	$0.360191\pi$
$140$	−2.19454	−	4.60024i	−0.185473	−	0.388791i
$141$	−1.98657	+	0.769471i	−0.167300	+	0.0648012i
$142$	8.59508	−	3.12835i	0.721283	−	0.262526i
$143$	0.513278	+	0.889024i	0.0429225	+	0.0743439i
$144$	2.37515	+	1.83266i	0.197929	+	0.152722i
$145$	−3.22979	−	1.86472i	−0.268220	−	0.154857i
$146$	15.0871	−	5.49124i	1.24861	−	0.454458i
$147$	3.71036	−	11.5427i	0.306025	−	0.952023i
$148$	−3.87058	+	3.24780i	−0.318159	+	0.266967i
$149$	−3.74487	+	10.2890i	−0.306792	+	0.842904i	0.686485	+	0.727144i	$0.259153\pi$
$149$	−3.74487	+	10.2890i	−0.306792	+	0.842904i	−0.993277	+	0.115760i	$0.963070\pi$
$150$	−2.19000	+	0.432567i	−0.178813	+	0.0353189i
$151$	3.68979	−	20.9259i	0.300271	−	1.70292i	−0.344698	−	0.938713i	$-0.612019\pi$
$151$	3.68979	−	20.9259i	0.300271	−	1.70292i	0.644970	−	0.764208i	$-0.276870\pi$
$152$	−1.32463	+	2.29433i	−0.107442	+	0.186095i
$153$	−7.85926	+	0.322028i	−0.635384	+	0.0260345i
$154$	5.05761	−	1.40293i	0.407554	−	0.113051i
$155$	17.4672	+	3.07994i	1.40300	+	0.247386i
$156$	−0.323730	−	0.835787i	−0.0259192	−	0.0669165i
$157$	−13.0047	−	15.4984i	−1.03789	−	1.23690i	−0.970984	−	0.239144i	$-0.923133\pi$
$157$	−13.0047	−	15.4984i	−1.03789	−	1.23690i	−0.0669012	−	0.997760i	$-0.521311\pi$
$158$	1.98109	−	5.44299i	0.157607	−	0.433021i
$159$	5.22170	+	2.87384i	0.414108	+	0.227910i
$160$	−1.23829	+	1.47574i	−0.0978956	+	0.116667i
$161$	3.60550	+	0.932212i	0.284153	+	0.0734686i
$162$	−8.96142	−	0.832478i	−0.704075	−	0.0654057i
$163$	8.59373	+	14.8848i	0.673113	+	1.16587i	0.977017	+	0.213163i	$0.0683767\pi$
$163$	8.59373	+	14.8848i	0.673113	+	1.16587i	−0.303903	+	0.952703i	$0.598290\pi$
$164$	5.02716	−	1.82974i	0.392555	−	0.142878i
$165$	0.135525	+	6.61787i	0.0105506	+	0.515201i
$166$	−9.85582	−	11.7457i	−0.764960	−	0.911643i
$167$	−7.66854	−	2.79112i	−0.593409	−	0.215983i	0.0278189	−	0.999613i	$-0.491144\pi$
$167$	−7.66854	−	2.79112i	−0.593409	−	0.215983i	−0.621228	+	0.783630i	$0.713366\pi$
$168$	−4.55150	+	0.532798i	−0.351156	+	0.0411063i
$169$	2.21093	−	12.5388i	0.170071	−	0.964522i
$170$		−	5.05103i		−	0.387397i
$171$	−0.325383	−	7.94114i	−0.0248827	−	0.607274i
$172$	11.1824			0.852649
$173$	−8.08548	−	6.78453i	−0.614728	−	0.515818i	0.281413	−	0.959587i	$-0.409197\pi$
$173$	−8.08548	−	6.78453i	−0.614728	−	0.515818i	−0.896141	+	0.443769i	$0.853641\pi$
$174$	−2.52397	+	2.20748i	−0.191342	+	0.167349i
$175$	1.93123	−	2.81032i	0.145987	−	0.212440i
$176$	−1.27515	−	1.51966i	−0.0961179	−	0.114549i
$177$	−5.13299	+	4.48935i	−0.385819	+	0.337440i
$178$	12.2143	+	2.15371i	0.915502	+	0.161428i
$179$		−	12.9636i		−	0.968944i	−0.874807	−	0.484472i	$-0.839012\pi$
$179$		−	12.9636i		−	0.968944i	0.874807	−	0.484472i	$-0.160988\pi$
$180$	0.769716	−	5.72783i	0.0573713	−	0.426928i
$181$	−22.1974	−	12.8157i	−1.64992	−	0.952581i	−0.977102	−	0.212771i	$-0.931751\pi$
$181$	−22.1974	−	12.8157i	−1.64992	−	0.952581i	−0.672816	−	0.739810i	$-0.734916\pi$
$182$	1.24587	+	0.567685i	0.0923502	+	0.0420796i
$183$	1.75594	+	4.53339i	0.129803	+	0.335118i
$184$	−0.244421	−	1.38618i	−0.0180190	−	0.102191i
$185$	9.14667	+	3.32912i	0.672476	+	0.244761i
$186$	7.68902	−	13.9708i	0.563787	−	1.02439i
$187$	5.12235	+	0.903209i	0.374583	+	0.0660492i
$188$	−1.22998			−0.0897056
$189$	10.6805	−	8.65601i	0.776893	−	0.629632i
$190$	5.10366			0.370258
$191$	19.9688	+	3.52104i	1.44489	+	0.254773i	0.840456	−	0.541881i	$-0.182287\pi$
$191$	19.9688	+	3.52104i	1.44489	+	0.254773i	0.604436	+	0.796654i	$0.293399\pi$
$192$	0.896555	+	1.48195i	0.0647033	+	0.106951i
$193$	3.53518	+	1.28670i	0.254468	+	0.0926186i	0.466104	−	0.884730i	$-0.345657\pi$
$193$	3.53518	+	1.28670i	0.254468	+	0.0926186i	−0.211637	+	0.977348i	$0.567879\pi$
$194$	−0.332599	−	1.88626i	−0.0238792	−	0.135426i
$195$	−1.08256	+	1.34514i	−0.0775236	+	0.0963276i
$196$	4.40458	−	5.44056i	0.314613	−	0.388611i
$197$	9.88793	+	5.70880i	0.704486	+	0.406735i	0.809016	−	0.587787i	$-0.200001\pi$
$197$	9.88793	+	5.70880i	0.704486	+	0.406735i	−0.104530	+	0.994522i	$0.533334\pi$
$198$	5.67107	+	1.80482i	0.403025	+	0.128263i
$199$			2.74733i			0.194753i	0.995248	+	0.0973764i	$0.0310451\pi$
$199$			2.74733i			0.194753i	−0.995248	+	0.0973764i	$0.968955\pi$
$200$	−1.26925	−	0.223803i	−0.0897494	−	0.0158252i
$201$	−0.784523	−	3.97189i	−0.0553360	−	0.280156i
$202$	−7.12358	−	8.48955i	−0.501213	−	0.597323i
$203$	0.401555	−	5.10621i	0.0281837	−	0.358386i
$204$	−4.29838	−	1.46554i	−0.300947	−	0.102608i
$205$	−7.89490	−	6.62460i	−0.551403	−	0.462682i
$206$	6.60634			0.460285
$207$	2.84445	+	3.12094i	0.197703	+	0.216920i
$208$		−	0.517475i		−	0.0358804i
$209$	−0.912619	+	5.17572i	−0.0631272	+	0.358012i
$210$	5.27299	+	7.08027i	0.363871	+	0.488585i
$211$	4.90289	+	1.78451i	0.337529	+	0.122850i	0.505224	−	0.862989i	$-0.331410\pi$
$211$	4.90289	+	1.78451i	0.337529	+	0.122850i	−0.167695	+	0.985839i	$0.553632\pi$
$212$	2.21195	+	2.63610i	0.151917	+	0.181048i
$213$	−13.5550	+	8.20052i	−0.928772	+	0.561890i
$214$	−4.13461	+	1.50487i	−0.282636	+	0.102871i
$215$	−10.7711	−	18.6561i	−0.734583	−	1.27234i
$216$	−4.65100	−	2.31693i	−0.316461	−	0.157647i
$217$	6.51117	+	23.4730i	0.442007	+	1.59345i
$218$	9.84410	−	11.7317i	0.666727	−	0.794574i
$219$	−23.7932	+	14.3945i	−1.60780	+	0.972689i
$220$	−1.30707	+	3.59116i	−0.0881230	+	0.242116i
$221$	0.872131	+	1.03937i	0.0586659	+	0.0699153i
$222$	5.48691	−	6.81780i	0.368257	−	0.457581i
$223$	−5.50892	−	0.971370i	−0.368904	−	0.0650478i	−0.0138770	−	0.999904i	$-0.504417\pi$
$223$	−5.50892	−	0.971370i	−0.368904	−	0.0650478i	−0.355027	+	0.934856i	$0.615528\pi$
$224$	−2.56152	−	0.662287i	−0.171149	−	0.0442509i
$225$	3.57612	−	1.47005i	0.238408	−	0.0980036i
$226$	9.37659	−	16.2407i	0.623721	−	1.08032i
$227$	2.33961	−	13.2686i	0.155286	−	0.880668i	−0.803239	−	0.595657i	$-0.796892\pi$
$227$	2.33961	−	13.2686i	0.155286	−	0.880668i	0.958524	−	0.285011i	$-0.0919972\pi$
$228$	1.48080	−	4.34317i	0.0980686	−	0.287633i
$229$	−5.56476	+	15.2891i	−0.367730	+	1.01033i	0.608493	+	0.793559i	$0.291774\pi$
$229$	−5.56476	+	15.2891i	−0.367730	+	1.01033i	−0.976223	+	0.216770i	$0.930448\pi$
$230$	−2.07720	+	1.74298i	−0.136966	+	0.114928i
$231$	−8.12314	+	4.08137i	−0.534463	+	0.268534i
$232$	−1.81918	+	0.662126i	−0.119435	+	0.0434707i
$233$	14.4177	+	8.32408i	0.944537	+	0.545329i	0.891380	−	0.453257i	$-0.149738\pi$
$233$	14.4177	+	8.32408i	0.944537	+	0.545329i	0.0531575	+	0.998586i	$0.483071\pi$
$234$	0.830603	+	1.31153i	0.0542982	+	0.0857377i
$235$	1.18474	+	2.05203i	0.0772841	+	0.133860i
$236$	−3.69965	+	1.34656i	−0.240827	+	0.0876537i
$237$	−1.53948	+	9.91376i	−0.100000	+	0.643968i
$238$	6.26108	−	2.98685i	0.405846	−	0.193609i
$239$	18.0220	−	3.17776i	1.16574	−	0.205552i	0.442905	−	0.896568i	$-0.353948\pi$
$239$	18.0220	−	3.17776i	1.16574	−	0.205552i	0.722839	+	0.691016i	$0.242837\pi$
$240$	1.60883	−	2.92321i	0.103850	−	0.188693i
$241$	−9.42896	−	25.9059i	−0.607373	−	1.66874i	−0.735943	−	0.677043i	$-0.763261\pi$
$241$	−9.42896	−	25.9059i	−0.607373	−	1.66874i	0.128570	−	0.991700i	$-0.458961\pi$
$242$	6.11814	+	3.53231i	0.393289	+	0.227066i
$243$	15.5068	−	1.59314i	0.994764	−	0.102200i
$244$			2.80683i			0.179689i
$245$	−13.3193	−	2.10791i	−0.850940	−	0.134670i
$246$	−7.92815	+	4.79638i	−0.505480	+	0.305806i
$247$	−1.05019	+	0.881217i	−0.0668222	+	0.0560705i
$248$	7.05293	−	5.91811i	0.447862	−	0.375801i
$249$	20.6894	+	16.6507i	1.31114	+	1.05519i
$250$	4.14359	+	11.3844i	0.262064	+	0.720014i
$251$	12.3534	−	21.3967i	0.779740	−	1.35055i	−0.152352	−	0.988326i	$-0.548685\pi$
$251$	12.3534	−	21.3967i	0.779740	−	1.35055i	0.932092	−	0.362222i	$-0.117982\pi$
$252$	7.55518	−	2.43295i	0.475932	−	0.153262i
$253$	−1.39615	−	2.41820i	−0.0877751	−	0.152031i
$254$	−3.04692	+	3.63118i	−0.191181	+	0.227840i
$255$	1.69527	+	8.58283i	0.106162	+	0.537477i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−1.38484	−	0.504041i	−0.0863841	−	0.0314412i	0.298467	−	0.954420i	$-0.403525\pi$
$257$	−1.38484	−	0.504041i	−0.0863841	−	0.0314412i	−0.384851	+	0.922979i	$0.625747\pi$
$258$	−19.0014	+	3.75313i	−1.18297	+	0.233659i
$259$	1.28209	+	13.3065i	0.0796650	+	0.826826i
$260$	−0.863328	+	0.498442i	−0.0535413	+	0.0309121i
$261$	3.54789	−	4.59812i	0.219609	−	0.284617i
$262$	−12.1936	+	7.03999i	−0.753324	+	0.434932i
$263$	−17.0172	+	20.2803i	−1.04933	+	1.25054i	−0.0820984	+	0.996624i	$0.526162\pi$
$263$	−17.0172	+	20.2803i	−1.04933	+	1.25054i	−0.967227	+	0.253913i	$0.918282\pi$
$264$	2.67680	+	2.15427i	0.164746	+	0.132586i
$265$	2.26733	−	6.22943i	0.139281	−	0.382671i
$266$	3.01797	+	6.32631i	0.185044	+	0.387891i
$267$	−21.4777	+	0.439833i	−1.31441	+	0.0269173i
$268$	0.405899	−	2.30197i	0.0247942	−	0.140615i
$269$	−0.447870	+	0.775733i	−0.0273071	+	0.0472973i	−0.879356	−	0.476165i	$-0.842027\pi$
$269$	−0.447870	+	0.775733i	−0.0273071	+	0.0472973i	0.852049	+	0.523462i	$0.175360\pi$
$270$	0.614505	+	9.99120i	0.0373976	+	0.608045i
$271$	8.65540	−	4.99720i	0.525778	−	0.303558i	−0.213517	−	0.976939i	$-0.568492\pi$
$271$	8.65540	−	4.99720i	0.525778	−	0.303558i	0.739296	+	0.673381i	$0.235159\pi$
$272$	−2.00853	−	1.68536i	−0.121785	−	0.102190i
$273$	−2.30754	−	0.546473i	−0.139659	−	0.0330740i
$274$	−2.89354	−	16.4101i	−0.174805	−	0.991370i
$275$	−2.51791	+	0.443975i	−0.151835	+	0.0267727i
$276$	0.880567	+	2.27339i	0.0530039	+	0.136842i
$277$	−2.57824	−	2.16340i	−0.154911	−	0.129986i	0.562038	−	0.827112i	$-0.310018\pi$
$277$	−2.57824	−	2.16340i	−0.154911	−	0.129986i	−0.716949	+	0.697126i	$0.754462\pi$
$278$	−6.16869			−0.369973
$279$	−8.37637	+	26.3201i	−0.501480	+	1.57574i
$280$	1.36238	+	4.91143i	0.0814178	+	0.293514i
$281$	0.911317	+	2.50382i	0.0543646	+	0.149366i	0.963902	−	0.266255i	$-0.0857865\pi$
$281$	0.911317	+	2.50382i	0.0543646	+	0.149366i	−0.909538	+	0.415621i	$0.863564\pi$
$282$	2.09001	−	0.412816i	0.124458	−	0.0245829i
$283$	−18.1841	+	3.20635i	−1.08093	+	0.190598i	−0.685628	−	0.727952i	$-0.740472\pi$
$283$	−18.1841	+	3.20635i	−1.08093	+	0.190598i	−0.395305	+	0.918550i	$0.629361\pi$
$284$	−9.00774	+	1.58831i	−0.534511	+	0.0942487i
$285$	−8.67224	+	1.71293i	−0.513699	+	0.101465i
$286$	−0.351103	−	0.964647i	−0.0207611	−	0.0570408i
$287$	3.54310	−	13.7036i	0.209143	−	0.808897i
$288$	−2.02083	−	2.21726i	−0.119079	−	0.130653i
$289$	−10.1254			−0.595610
$290$	2.85692	+	2.39724i	0.167764	+	0.140771i
$291$	1.19824	+	3.09355i	0.0702422	+	0.181347i
$292$	−15.8114	+	2.78798i	−0.925292	+	0.163154i
$293$	1.93369	+	10.9665i	0.112967	+	0.640670i	0.987737	+	0.156130i	$0.0499019\pi$
$293$	1.93369	+	10.9665i	0.112967	+	0.640670i	−0.874769	+	0.484540i	$0.838987\pi$
$294$	−5.65835	+	10.7230i	−0.330002	+	0.625379i
$295$	5.81011	+	4.87526i	0.338278	+	0.283849i
$296$	4.37575	−	2.52634i	0.254335	−	0.146840i
$297$	−10.2422	−	1.16341i	−0.594310	−	0.0675080i
$298$	5.47464	−	9.48235i	0.317137	−	0.549298i
$299$	0.126482	−	0.717314i	0.00731463	−	0.0414833i
$300$	2.23185	−	0.0457051i	0.128856	−	0.00263879i
$301$	16.7561	−	24.3835i	0.965806	−	1.40544i
$302$	−7.26747	+	19.9672i	−0.418196	+	1.14898i
$303$	14.9539	+	12.0347i	0.859077	+	0.691378i
$304$	1.70292	−	2.02946i	0.0976690	−	0.116397i
$305$	4.68277	−	2.70360i	0.268135	−	0.154808i
$306$	7.79578	+	1.04761i	0.445655	+	0.0598879i
$307$	9.80089	−	5.65855i	0.559367	−	0.322950i	−0.193525	−	0.981095i	$-0.561992\pi$
$307$	9.80089	−	5.65855i	0.559367	−	0.322950i	0.752891	+	0.658145i	$0.228659\pi$
$308$	−5.22439	+	0.503372i	−0.297687	+	0.0286823i
$309$	−11.2256	+	2.21727i	−0.638604	+	0.126136i
$310$	−16.6670	−	6.06629i	−0.946622	−	0.344542i
$311$	−3.89239	−	22.0748i	−0.220717	−	1.25175i	−0.870706	−	0.491804i	$-0.836337\pi$
$311$	−3.89239	−	22.0748i	−0.220717	−	1.25175i	0.649989	−	0.759944i	$-0.274774\pi$
$312$	0.173679	+	0.879305i	0.00983265	+	0.0497808i
$313$	−13.7961	+	16.4415i	−0.779800	+	0.929329i	−0.998924	−	0.0463678i	$-0.985235\pi$
$313$	−13.7961	+	16.4415i	−0.779800	+	0.929329i	0.219125	+	0.975697i	$0.429680\pi$
$314$	10.1158	+	17.5211i	0.570870	+	0.988775i
$315$	−11.3363	−	10.2612i	−0.638729	−	0.578152i
$316$	−2.89616	+	5.01629i	−0.162922	+	0.282188i
$317$	−4.31829	−	11.8644i	−0.242540	−	0.666372i	−0.999910	−	0.0133869i	$-0.995739\pi$
$317$	−4.31829	−	11.8644i	−0.242540	−	0.666372i	0.757371	−	0.652985i	$-0.226484\pi$
$318$	−4.64333	−	3.73692i	−0.260385	−	0.209556i
$319$	−2.94195	+	2.46859i	−0.164718	+	0.138215i
$320$	1.47574	−	1.23829i	0.0824963	−	0.0692226i
$321$	6.52053	−	3.94480i	0.363941	−	0.220177i
$322$	−3.38885	−	1.54414i	−0.188853	−	0.0860515i
$323$			6.94625i			0.386500i
$324$	8.68071	+	2.37596i	0.482262	+	0.131998i
$325$	−0.577584	−	0.333468i	−0.0320386	−	0.0184975i
$326$	−5.87846	−	16.1509i	−0.325578	−	0.894518i
$327$	−12.7898	+	23.2388i	−0.707278	+	1.28511i
$328$	−5.26852	+	0.928982i	−0.290905	+	0.0512944i
$329$	−1.84305	+	2.68200i	−0.101611	+	0.147864i
$330$	1.01572	−	6.54086i	0.0559133	−	0.360063i
$331$	9.38948	−	3.41749i	0.516092	−	0.187842i	−0.0708256	−	0.997489i	$-0.522563\pi$
$331$	9.38948	−	3.41749i	0.516092	−	0.187842i	0.586918	+	0.809646i	$0.300341\pi$
$332$	7.66646	+	13.2787i	0.420752	+	0.728764i
$333$	−7.03523	+	13.4265i	−0.385528	+	0.735769i
$334$	7.06737	+	4.08035i	0.386709	+	0.223267i
$335$	−4.23144	+	1.54012i	−0.231189	+	0.0841457i
$336$	4.57487	+	0.265655i	0.249580	+	0.0144927i
$337$	19.9744	−	16.7605i	1.08807	−	0.913003i	0.0915080	−	0.995804i	$-0.470831\pi$
$337$	19.9744	−	16.7605i	1.08807	−	0.913003i	0.996566	+	0.0828018i	$0.0263869\pi$
$338$	−4.35468	+	11.9644i	−0.236863	+	0.650776i
$339$	−10.4821	+	30.7436i	−0.569307	+	1.66977i
$340$	−0.877103	+	4.97430i	−0.0475676	+	0.269769i
$341$	9.13228	−	15.8176i	0.494541	−	0.856569i
$342$	−1.05852	+	7.87700i	−0.0572385	+	0.425939i
$343$	−5.26328	−	17.7566i	−0.284190	−	0.958768i
$344$	−11.0125	−	1.94180i	−0.593754	−	0.104695i
$345$	2.94463	−	3.65887i	0.158533	−	0.196987i
$346$	6.78453	+	8.08548i	0.364738	+	0.434678i
$347$	−6.68949	+	18.3792i	−0.359111	+	0.986649i	0.620228	+	0.784422i	$0.287040\pi$
$347$	−6.68949	+	18.3792i	−0.359111	+	0.986649i	−0.979339	+	0.202227i	$0.935182\pi$
$348$	2.86895	−	1.73566i	0.153792	−	0.0930414i
$349$	11.4133	−	13.6019i	0.610941	−	0.728091i	−0.368543	−	0.929611i	$-0.620143\pi$
$349$	11.4133	−	13.6019i	0.610941	−	0.728091i	0.979485	+	0.201519i	$0.0645878\pi$
$350$	−2.38990	+	2.43227i	−0.127745	+	0.130010i
$351$	−1.85157	−	1.94981i	−0.0988293	−	0.104073i
$352$	0.991889	+	1.71800i	0.0528679	+	0.0915698i
$353$	−15.7637	+	5.73751i	−0.839016	+	0.305377i	−0.725554	−	0.688165i	$-0.758416\pi$
$353$	−15.7637	+	5.73751i	−0.839016	+	0.305377i	−0.113462	+	0.993542i	$0.536194\pi$
$354$	5.83458	−	3.52981i	0.310104	−	0.187607i
$355$	11.3263	+	13.4981i	0.601137	+	0.716407i
$356$	−11.6548	−	4.24199i	−0.617701	−	0.224825i
$357$	−9.63649	+	7.17672i	−0.510017	+	0.379832i
$358$	−2.25110	+	12.7666i	−0.118975	+	0.674738i
$359$		−	5.36965i		−	0.283400i	−0.989910	−	0.141700i	$-0.954743\pi$
$359$		−	5.36965i		−	0.283400i	0.989910	−	0.141700i	$-0.0452568\pi$
$360$	−1.75265	+	5.50716i	−0.0923728	+	0.290253i
$361$	11.9814			0.630599
$362$	19.6347	+	16.4755i	1.03198	+	0.865933i
$363$	−11.5816	−	3.94876i	−0.607878	−	0.207256i
$364$	−1.12837	−	0.775404i	−0.0591425	−	0.0406422i
$365$	19.8812	+	23.6934i	1.04063	+	1.24017i
$366$	−0.942053	−	4.76943i	−0.0492419	−	0.249302i
$367$	13.6476	+	2.40645i	0.712401	+	0.125616i	0.518092	−	0.855325i	$-0.326642\pi$
$367$	13.6476	+	2.40645i	0.712401	+	0.125616i	0.194309	+	0.980940i	$0.437754\pi$
$368$			1.40756i			0.0733744i
$369$	11.8619	−	10.8110i	0.617505	−	0.562800i
$370$	−8.42962	−	4.86684i	−0.438235	−	0.253015i
$371$	9.06253	−	0.873179i	0.470503	−	0.0453332i
$372$	−9.99821	+	12.4234i	−0.518383	+	0.644121i
$373$	2.74178	+	15.5494i	0.141964	+	0.805118i	0.969755	+	0.244081i	$0.0784862\pi$
$373$	2.74178	+	15.5494i	0.141964	+	0.805118i	−0.827791	+	0.561037i	$0.810403\pi$
$374$	−4.88769	−	1.77897i	−0.252736	−	0.0919886i
$375$	−10.8618	−	17.9540i	−0.560902	−	0.927138i
$376$	1.21130	+	0.213584i	0.0624678	+	0.0110148i
$377$	−1.00179			−0.0515950
$378$	−12.0214	+	6.66986i	−0.618312	+	0.343060i
$379$	−6.91993			−0.355453			−0.177727	−	0.984080i	$-0.556874\pi$
$379$	−6.91993			−0.355453			−0.177727	+	0.984080i	$0.556874\pi$
$380$	−5.02612	−	0.886241i	−0.257835	−	0.0454632i
$381$	3.95866	−	7.19280i	0.202808	−	0.368498i
$382$	−19.0540	−	6.93509i	−0.974888	−	0.354830i
$383$	1.45390	+	8.24546i	0.0742907	+	0.421324i	0.999158	+	0.0410330i	$0.0130649\pi$
$383$	1.45390	+	8.24546i	0.0742907	+	0.421324i	−0.924867	+	0.380291i	$0.875824\pi$
$384$	−0.625596	−	1.61513i	−0.0319248	−	0.0824215i
$385$	5.87204	+	8.23123i	0.299267	+	0.419503i
$386$	−3.25804	−	1.88103i	−0.165830	−	0.0957418i
$387$	31.0279	−	12.7548i	1.57723	−	0.648362i
$388$			1.91536i			0.0972377i
$389$	−13.3299	−	2.35043i	−0.675854	−	0.119171i	−0.174822	−	0.984600i	$-0.555935\pi$
$389$	−13.3299	−	2.35043i	−0.675854	−	0.119171i	−0.501032	+	0.865429i	$0.667046\pi$
$390$	1.29969	−	1.13672i	0.0658125	−	0.0575601i
$391$	−2.37225	−	2.82714i	−0.119970	−	0.142974i
$392$	−5.28241	+	4.59306i	−0.266802	+	0.231984i
$393$	18.3568	−	16.0550i	0.925980	−	0.809869i
$394$	−8.74639	−	7.33909i	−0.440637	−	0.369738i
$395$	11.1585			0.561447
$396$	−5.27151	−	2.76217i	−0.264903	−	0.138804i
$397$		−	5.58324i		−	0.280215i	−0.990136	−	0.140107i	$-0.955255\pi$
$397$		−	5.58324i		−	0.280215i	0.990136	−	0.140107i	$-0.0447448\pi$
$398$	0.477068	−	2.70559i	0.0239133	−	0.135619i
$399$	−7.25149	−	9.73689i	−0.363028	−	0.487454i
$400$	1.21110	+	0.440805i	0.0605551	+	0.0220403i
$401$	−18.5861	−	22.1500i	−0.928145	−	1.10612i	−0.994118	−	0.108298i	$-0.965460\pi$
$401$	−18.5861	−	22.1500i	−0.928145	−	1.10612i	0.0659739	−	0.997821i	$-0.478985\pi$
$402$	0.0828929	+	4.04778i	0.00413432	+	0.201885i
$403$	4.47704	−	1.62951i	0.223017	−	0.0811717i
$404$	5.54116	+	9.59757i	0.275683	+	0.477497i
$405$	−4.39751	−	16.7710i	−0.218514	−	0.833358i
$406$	−1.28214	+	4.95891i	−0.0636315	+	0.246107i
$407$	6.44291	−	7.67836i	0.319363	−	0.380602i
$408$	3.97859	+	2.18968i	0.196970	+	0.108405i
$409$	7.55158	−	20.7478i	0.373402	−	1.02591i	−0.600635	−	0.799523i	$-0.705086\pi$
$409$	7.55158	−	20.7478i	0.373402	−	1.02591i	0.974037	−	0.226390i	$-0.0726922\pi$
$410$	6.62460	+	7.89490i	0.327166	+	0.389901i
$411$	10.4245	+	26.9132i	0.514200	+	1.32753i
$412$	−6.50597	−	1.14718i	−0.320526	−	0.0565174i
$413$	−2.60748	+	10.0849i	−0.128306	+	0.496246i
$414$	−2.25929	−	3.56745i	−0.111038	−	0.175331i
$415$	14.7690	−	25.5806i	0.724981	−	1.25570i
$416$	−0.0898586	+	0.509614i	−0.00440568	+	0.0249859i
$417$	10.4820	−	2.07039i	0.513304	−	0.101387i
$418$	1.79751	−	4.93861i	0.0879190	−	0.241555i
$419$	27.4128	−	23.0021i	1.33920	−	1.12373i	0.357375	−	0.933961i	$-0.383672\pi$
$419$	27.4128	−	23.0021i	1.33920	−	1.12373i	0.981830	−	0.189765i	$-0.0607725\pi$
$420$	−3.96340	−	7.88835i	−0.193394	−	0.384912i
$421$	−13.3926	+	4.87451i	−0.652716	+	0.237569i	−0.647089	−	0.762415i	$-0.724014\pi$
$421$	−13.3926	+	4.87451i	−0.652716	+	0.237569i	−0.00562773	+	0.999984i	$0.501791\pi$
$422$	−4.51853	−	2.60877i	−0.219958	−	0.126993i
$423$	−3.41284	+	1.40293i	−0.165938	+	0.0682129i
$424$	−1.72059	−	2.98015i	−0.0835592	−	0.144729i
$425$	−3.17545	+	1.15577i	−0.154032	+	0.0560631i
$426$	14.7731	−	5.72214i	0.715757	−	0.277238i
$427$	6.12037	+	4.20587i	0.296185	+	0.203536i
$428$	4.33311	−	0.764044i	0.209449	−	0.0369315i
$429$	0.920364	+	1.52131i	0.0444356	+	0.0734495i
$430$	7.36787	+	20.2431i	0.355310	+	0.976207i
$431$	−20.1509	−	11.6341i	−0.970633	−	0.560395i	−0.0712041	−	0.997462i	$-0.522684\pi$
$431$	−20.1509	−	11.6341i	−0.970633	−	0.560395i	−0.899429	+	0.437066i	$0.856017\pi$
$432$	4.17802	+	3.08937i	0.201015	+	0.148637i
$433$			1.61264i			0.0774985i	0.999249	+	0.0387493i	$0.0123374\pi$
$433$			1.61264i			0.0774985i	−0.999249	+	0.0387493i	$0.987663\pi$
$434$	−2.33621	−	24.2470i	−0.112142	−	1.16389i
$435$	−5.65912	−	3.11458i	−0.271334	−	0.149333i
$436$	−11.7317	+	9.84410i	−0.561849	+	0.471447i
$437$	2.85659	−	2.39697i	0.136649	−	0.114662i
$438$	25.9313	−	10.0441i	1.23905	−	0.479928i
$439$	7.48881	+	20.5753i	0.357421	+	0.982007i	0.979921	+	0.199387i	$0.0638950\pi$
$439$	7.48881	+	20.5753i	0.357421	+	0.982007i	−0.622500	+	0.782620i	$0.713883\pi$
$440$	1.91082	−	3.30963i	0.0910945	−	0.157780i
$441$	6.01585	−	20.1199i	0.286469	−	0.958089i
$442$	−0.678397	−	1.17502i	−0.0322681	−	0.0558900i
$443$	23.2286	−	27.6828i	1.10362	−	1.31525i	0.158932	−	0.987289i	$-0.449195\pi$
$443$	23.2286	−	27.6828i	1.10362	−	1.31525i	0.944692	−	0.327959i	$-0.106361\pi$
$444$	−6.58745	+	5.76143i	−0.312627	+	0.273426i
$445$	4.14900	+	23.5301i	0.196681	+	1.11544i
$446$	5.25655	+	1.91323i	0.248905	+	0.0905939i
$447$	−6.12008	+	17.9501i	−0.289470	+	0.849009i
$448$	2.40760	+	1.09703i	0.113748	+	0.0518297i
$449$	−30.7375	+	17.7463i	−1.45059	+	0.837501i	−0.998515	−	0.0544772i	$-0.982651\pi$
$449$	−30.7375	+	17.7463i	−1.45059	+	0.837501i	−0.452079	+	0.891978i	$0.649317\pi$
$450$	−3.77706	+	0.826734i	−0.178052	+	0.0389726i
$451$	−9.19096	+	5.30640i	−0.432785	+	0.249869i
$452$	−12.0543	+	14.3658i	−0.566987	+	0.675709i
$453$	5.64748	−	36.3679i	0.265342	−	1.70871i
$454$	−4.60814	+	12.6608i	−0.216271	+	0.594199i
$455$	−0.206777	+	2.62939i	−0.00969384	+	0.123268i
$456$	−2.21249	+	4.02004i	−0.103609	+	0.188256i
$457$	−2.02818	+	11.5024i	−0.0948741	+	0.538058i	0.899912	+	0.436072i	$0.143631\pi$
$457$	−2.02818	+	11.5024i	−0.0948741	+	0.538058i	−0.994786	+	0.101986i	$0.967480\pi$
$458$	8.13514	−	14.0905i	0.380130	−	0.658405i
$459$	−13.5984	+	0.836362i	−0.634717	+	0.0390380i
$460$	2.34830	−	1.35579i	0.109490	−	0.0632142i
$461$	−5.08810	−	4.26943i	−0.236977	−	0.198847i	0.516564	−	0.856249i	$-0.327211\pi$
$461$	−5.08810	−	4.26943i	−0.236977	−	0.198847i	−0.753540	+	0.657402i	$0.771655\pi$
$462$	8.70845	−	2.60879i	0.405154	−	0.121372i
$463$	2.45481	+	13.9219i	0.114085	+	0.647007i	0.987199	+	0.159492i	$0.0509855\pi$
$463$	2.45481	+	13.9219i	0.114085	+	0.647007i	−0.873115	+	0.487515i	$0.837903\pi$
$464$	1.90651	−	0.336170i	0.0885077	−	0.0156063i
$465$	30.3569	+	4.71406i	1.40777	+	0.218609i
$466$	−12.7532	−	10.7012i	−0.590782	−	0.495725i
$467$	−22.7958			−1.05486			−0.527432	−	0.849597i	$-0.676845\pi$
$467$	−22.7958			−1.05486			−0.527432	+	0.849597i	$0.676845\pi$
$468$	−0.590239	−	1.43584i	−0.0272838	−	0.0663718i
$469$	−4.41128	−	4.33442i	−0.203694	−	0.200145i
$470$	−0.810412	−	2.22659i	−0.0373815	−	0.102705i
$471$	−23.0696	−	26.3771i	−1.06299	−	1.21539i
$472$	3.87727	−	0.683667i	0.178466	−	0.0314683i
$473$	−21.8464	+	3.85210i	−1.00450	+	0.177120i
$474$	3.23760	−	9.49582i	0.148708	−	0.436157i
$475$	−1.16781	−	3.20853i	−0.0535828	−	0.147218i
$476$	−6.68462	+	1.85425i	−0.306389	+	0.0849893i
$477$	9.14427	+	4.79142i	0.418687	+	0.219384i
$478$	−18.3000			−0.837022
$479$	−19.7410	−	16.5647i	−0.901990	−	0.756859i	0.0685886	−	0.997645i	$-0.478150\pi$
$479$	−19.7410	−	16.5647i	−0.901990	−	0.756859i	−0.970578	+	0.240786i	$0.922595\pi$
$480$	−2.09200	+	2.59943i	−0.0954864	+	0.118647i
$481$	2.57491	−	0.454027i	0.117406	−	0.0207018i
$482$	4.78721	+	27.1496i	0.218051	+	1.23663i
$483$	6.27666	+	1.48644i	0.285598	+	0.0676354i
$484$	−5.41182	−	4.54105i	−0.245992	−	0.206411i
$485$	3.19548	−	1.84491i	0.145099	−	0.0837732i
$486$	−15.5479	−	1.12380i	−0.705267	−	0.0509765i
$487$	−20.2952	+	35.1523i	−0.919663	+	1.59290i	−0.119736	+	0.992806i	$0.538205\pi$
$487$	−20.2952	+	35.1523i	−0.919663	+	1.59290i	−0.799927	+	0.600098i	$0.795128\pi$
$488$	0.487402	−	2.76419i	0.0220636	−	0.125129i
$489$	15.4095	+	25.4710i	0.696842	+	1.15184i
$490$	12.7509	+	4.38876i	0.576028	+	0.198264i
$491$	−9.69311	+	26.6316i	−0.437444	+	1.20187i	0.503705	+	0.863876i	$0.331970\pi$
$491$	−9.69311	+	26.6316i	−0.437444	+	1.20187i	−0.941149	+	0.337992i	$0.890252\pi$
$492$	8.64058	−	3.34681i	0.389548	−	0.150886i
$493$	−3.26273	+	3.88837i	−0.146946	+	0.175123i
$494$	1.18726	−	0.685465i	0.0534174	−	0.0308405i
$495$	0.469373	+	11.4553i	0.0210967	+	0.514877i
$496$	−7.97345	+	4.60348i	−0.358019	+	0.206702i
$497$	−10.0342	+	22.0216i	−0.450095	+	0.987802i
$498$	−17.4837	−	19.9904i	−0.783465	−	0.895790i
$499$	19.0592	+	6.93699i	0.853208	+	0.310542i	0.731347	−	0.682005i	$-0.238892\pi$
$499$	19.0592	+	6.93699i	0.853208	+	0.310542i	0.121860	+	0.992547i	$0.461114\pi$
$500$	−2.10376	−	11.9310i	−0.0940829	−	0.533570i
$501$	−13.3785	−	4.56140i	−0.597707	−	0.203788i
$502$	−15.8812	+	18.9265i	−0.708814	+	0.844731i
$503$	6.65996	+	11.5354i	0.296953	+	0.514338i	0.975437	−	0.220277i	$-0.0706962\pi$
$503$	6.65996	+	11.5354i	0.296953	+	0.514338i	−0.678484	+	0.734615i	$0.737363\pi$
$504$	−7.86288	+	1.08405i	−0.350240	+	0.0482873i
$505$	10.6747	−	18.4891i	0.475018	−	0.822756i
$506$	0.955021	+	2.62390i	0.0424559	+	0.116647i
$507$	3.38398	−	21.7917i	0.150288	−	0.967802i
$508$	3.63118	−	3.04692i	0.161107	−	0.135185i
$509$	17.9086	−	15.0271i	0.793784	−	0.666064i	−0.152895	−	0.988242i	$-0.548860\pi$
$509$	17.9086	−	15.0271i	0.793784	−	0.666064i	0.946679	+	0.322178i	$0.104415\pi$
$510$	−0.179122	−	8.74681i	−0.00793168	−	0.387315i
$511$	−17.6131	+	38.6547i	−0.779159	+	1.70998i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.845076	−	13.7400i	−0.0373110	−	0.606638i
$514$	1.27628	+	0.736859i	0.0562942	+	0.0325015i
$515$	4.35279	+	11.9592i	0.191807	+	0.526985i
$516$	19.3644	−	0.396556i	0.852471	−	0.0174574i
$517$	2.40294	−	0.423703i	0.105681	−	0.0186345i
$518$	1.04804	−	13.3270i	0.0460483	−	0.585554i
$519$	−14.2421	−	11.4620i	−0.625160	−	0.503124i
$520$	0.936765	−	0.340955i	0.0410799	−	0.0149519i
$521$	12.9930	+	22.5045i	0.569233	+	0.985940i	0.996642	+	0.0818815i	$0.0260929\pi$
$521$	12.9930	+	22.5045i	0.569233	+	0.985940i	−0.427410	+	0.904058i	$0.640574\pi$
$522$	−4.29245	+	3.91218i	−0.187875	+	0.171231i
$523$	20.7771	+	11.9956i	0.908518	+	0.524533i	0.879954	−	0.475059i	$-0.157573\pi$
$523$	20.7771	+	11.9956i	0.908518	+	0.524533i	0.0285636	+	0.999592i	$0.490907\pi$
$524$	13.2309	−	4.81564i	0.577992	−	0.210372i
$525$	3.24462	−	4.93508i	0.141607	−	0.215385i
$526$	20.2803	−	17.0172i	0.884263	−	0.741985i
$527$	8.25643	−	22.6844i	0.359656	−	0.988146i
$528$	−2.26205	−	2.58636i	−0.0984431	−	0.112557i
$529$	3.64987	−	20.6994i	0.158690	−	0.899976i
$530$	−3.31461	+	5.74108i	−0.143978	+	0.249376i
$531$	−8.72954	+	7.95618i	−0.378830	+	0.345269i
$532$	−1.87357	−	6.75427i	−0.0812294	−	0.292835i
$533$	−2.72633	−	0.480725i	−0.118090	−	0.0208225i
$534$	21.2278	+	3.29641i	0.918615	+	0.142650i
$535$	−5.44843	−	6.49319i	−0.235556	−	0.280725i
$536$	−0.799464	+	2.19651i	−0.0345316	+	0.0948748i
$537$	−0.459722	−	22.4489i	−0.0198385	−	0.968741i
$538$	0.575770	−	0.686176i	0.0248232	−	0.0295831i
$539$	−6.73081	+	12.1462i	−0.289916	+	0.523173i
$540$	1.12978	−	9.94612i	0.0486182	−	0.428013i
$541$	3.83161	+	6.63655i	0.164734	+	0.285328i	0.936561	−	0.350505i	$-0.113990\pi$
$541$	3.83161	+	6.63655i	0.164734	+	0.285328i	−0.771827	+	0.635833i	$0.780657\pi$
$542$	−9.39166	+	3.41828i	−0.403406	+	0.146828i
$543$	−38.8934	−	21.4056i	−1.66908	−	0.918600i
$544$	1.68536	+	2.00853i	0.0722591	+	0.0861151i
$545$	27.7236	+	10.0906i	1.18755	+	0.432233i
$546$	2.17759	+	0.938872i	0.0931924	+	0.0401800i
$547$	1.83339	−	10.3977i	0.0783901	−	0.444572i	−0.920198	−	0.391453i	$-0.871973\pi$
$547$	1.83339	−	10.3977i	0.0783901	−	0.444572i	0.998588	−	0.0531193i	$-0.0169164\pi$
$548$			16.6632i			0.711818i
$549$	3.20151	+	7.78814i	0.136637	+	0.332390i
$550$	2.55675			0.109020
$551$	−3.92888	−	3.29672i	−0.167376	−	0.140445i
$552$	−0.472418	−	2.39176i	−0.0201075	−	0.101800i
$553$	6.59843	+	13.8317i	0.280594	+	0.588185i
$554$	2.16340	+	2.57824i	0.0919139	+	0.109539i
$555$	15.9572	+	5.44062i	0.677347	+	0.230942i
$556$	6.07497	+	1.07118i	0.257636	+	0.0454282i
$557$		−	36.5344i		−	1.54801i	−0.633177	−	0.774007i	$-0.718250\pi$
$557$		−	36.5344i		−	1.54801i	0.633177	−	0.774007i	$-0.281750\pi$
$558$	12.8195	−	24.4657i	0.542695	−	1.03572i
$559$	−5.01135	−	2.89330i	−0.211958	−	0.122374i
$560$	−0.488823	−	5.07339i	−0.0206565	−	0.214390i
$561$	8.90234	+	1.38242i	0.375857	+	0.0583660i
$562$	−0.462688	−	2.62403i	−0.0195173	−	0.110688i
$563$	−39.7083	−	14.4527i	−1.67351	−	0.609107i	−0.681110	−	0.732181i	$-0.738502\pi$
$563$	−39.7083	−	14.4527i	−1.67351	−	0.609107i	−0.992397	+	0.123074i	$0.960725\pi$
$564$	−2.12994	+	0.0436183i	−0.0896868	+	0.00183666i
$565$	35.5780	+	6.27336i	1.49678	+	0.263922i
$566$	18.4646			0.776127
$567$	18.1884	−	15.3683i	0.763839	−	0.645407i
$568$	9.14670			0.383787
$569$	−11.9082	−	2.09974i	−0.499219	−	0.0880258i	−0.0816318	−	0.996663i	$-0.526013\pi$
$569$	−11.9082	−	2.09974i	−0.499219	−	0.0880258i	−0.417587	+	0.908637i	$0.637124\pi$
$570$	8.83794	−	0.180989i	0.370181	−	0.00758078i
$571$	−23.2779	−	8.47248i	−0.974152	−	0.354562i	−0.194588	−	0.980885i	$-0.562337\pi$
$571$	−23.2779	−	8.47248i	−0.974152	−	0.354562i	−0.779564	+	0.626323i	$0.784559\pi$
$572$	0.178260	+	1.01096i	0.00745341	+	0.0422704i
$573$	34.7046	+	5.38919i	1.44980	+	0.225137i
$574$	−5.86888	+	12.8801i	−0.244962	+	0.537607i
$575$	1.57106	+	0.907054i	0.0655179	+	0.0378268i
$576$	1.60511	+	2.53449i	0.0668795	+	0.105604i
$577$			11.5414i			0.480473i	0.970714	+	0.240237i	$0.0772250\pi$
$577$			11.5414i			0.480473i	−0.970714	+	0.240237i	$0.922775\pi$
$578$	9.97154	+	1.75825i	0.414761	+	0.0731336i
$579$	6.16745	+	2.10279i	0.256311	+	0.0873892i
$580$	−2.39724	−	2.85692i	−0.0995400	−	0.118627i
$581$	40.4422	+	3.18040i	1.67783	+	0.131945i
$582$	−0.642849	−	3.25462i	−0.0266470	−	0.134908i
$583$	−5.22943	−	4.38801i	−0.216581	−	0.181733i
$584$	16.0553			0.664374
$585$	−1.82695	+	2.36776i	−0.0755352	+	0.0978946i
$586$		−	11.1357i		−	0.460011i
$587$	−1.93467	+	10.9720i	−0.0798523	+	0.452865i	0.918497	+	0.395428i	$0.129404\pi$
$587$	−1.93467	+	10.9720i	−0.0798523	+	0.452865i	−0.998349	+	0.0574366i	$0.981707\pi$
$588$	7.43442	−	9.57754i	0.306590	−	0.394971i
$589$	22.9207	+	8.34245i	0.944431	+	0.343745i
$590$	−4.87526	−	5.81011i	−0.200711	−	0.239198i
$591$	17.3253	+	9.53521i	0.712666	+	0.392226i
$592$	−4.74796	+	1.72812i	−0.195140	+	0.0710252i
$593$	−3.66922	−	6.35528i	−0.150677	−	0.260980i	0.780800	−	0.624782i	$-0.214812\pi$
$593$	−3.66922	−	6.35528i	−0.150677	−	0.260980i	−0.931477	+	0.363801i	$0.881479\pi$
$594$	9.88453	+	2.92427i	0.405567	+	0.119984i
$595$	9.53229	+	9.36622i	0.390786	+	0.383977i
$596$	−7.03806	+	8.38763i	−0.288290	+	0.343571i
$597$	0.0974272	+	4.75751i	0.00398743	+	0.194712i
$598$	−0.249120	+	0.684453i	−0.0101873	+	0.0279894i
$599$	−17.6589	−	21.0451i	−0.721524	−	0.859879i	0.273254	−	0.961942i	$-0.411900\pi$
$599$	−17.6589	−	21.0451i	−0.721524	−	0.859879i	−0.994778	+	0.102063i	$0.967456\pi$
$600$	−2.20588	−	0.342545i	−0.0900546	−	0.0139844i
$601$	−38.3533	−	6.76273i	−1.56447	−	0.275858i	−0.676737	−	0.736225i	$-0.736607\pi$
$601$	−38.3533	−	6.76273i	−1.56447	−	0.275858i	−0.887729	+	0.460367i	$0.847718\pi$
$602$	−20.7357	+	21.1034i	−0.845124	+	0.860109i
$603$	−1.49940	−	6.85025i	−0.0610604	−	0.278964i
$604$	10.6243	−	18.4019i	0.432298	−	0.748762i
$605$	−2.36328	+	13.4028i	−0.0960809	+	0.544902i
$606$	−12.6369	−	14.4486i	−0.513338	−	0.586935i
$607$	7.71106	−	21.1860i	0.312982	−	0.859911i	−0.679069	−	0.734075i	$-0.737616\pi$
$607$	7.71106	−	21.1860i	0.312982	−	0.859911i	0.992051	−	0.125837i	$-0.0401616\pi$
$608$	−2.02946	+	1.70292i	−0.0823054	+	0.0690624i
$609$	0.514289	−	8.85661i	0.0208400	−	0.358888i
$610$	−5.08110	+	1.84937i	−0.205728	+	0.0748788i
$611$	0.551212	+	0.318242i	0.0222996	+	0.0128747i
$612$	−7.49543	−	2.38542i	−0.302985	−	0.0964248i
$613$	8.49818	+	14.7193i	0.343238	+	0.594506i	0.985032	−	0.172371i	$-0.0551429\pi$
$613$	8.49818	+	14.7193i	0.343238	+	0.594506i	−0.641794	+	0.766877i	$0.721810\pi$
$614$	−10.6346	+	3.87068i	−0.429177	+	0.156208i
$615$	−13.9064	−	11.1918i	−0.560761	−	0.451296i
$616$	5.23243	+	0.411481i	0.210821	+	0.0165790i
$617$	12.3868	−	2.18412i	0.498672	−	0.0879294i	0.0813457	−	0.996686i	$-0.474078\pi$
$617$	12.3868	−	2.18412i	0.498672	−	0.0879294i	0.417327	+	0.908757i	$0.362967\pi$
$618$	11.4401	−	0.234278i	0.460189	−	0.00942402i
$619$	−1.38251	−	3.79842i	−0.0555679	−	0.152671i	0.908803	−	0.417226i	$-0.136997\pi$
$619$	−1.38251	−	3.79842i	−0.0555679	−	0.152671i	−0.964371	+	0.264554i	$0.914775\pi$
$620$	15.3604	+	8.86832i	0.616888	+	0.356160i
$621$	5.03638	+	5.30361i	0.202103	+	0.212827i
$622$			22.4154i			0.898774i
$623$	−26.7137	+	19.0571i	−1.07026	+	0.763508i
$624$	−0.0183510	−	0.896105i	−0.000734627	−	0.0358729i
$625$	−12.9422	+	10.8598i	−0.517686	+	0.434390i
$626$	16.4415	−	13.7961i	0.657135	−	0.551402i
$627$	−1.39683	+	8.99509i	−0.0557839	+	0.359229i
$628$	−6.91964	−	19.0115i	−0.276124	−	0.758643i
$629$	6.62394	−	11.4730i	0.264114	−	0.457458i
$630$	9.38225	+	12.0738i	0.373798	+	0.481033i
$631$	−21.8576	−	37.8585i	−0.870138	−	1.50712i	−0.861853	−	0.507158i	$-0.830696\pi$
$631$	−21.8576	−	37.8585i	−0.870138	−	1.50712i	−0.00828527	−	0.999966i	$-0.502637\pi$
$632$	3.72323	−	4.43717i	0.148102	−	0.176501i
$633$	8.55356	+	2.91634i	0.339973	+	0.115914i
$634$	2.19245	+	12.4340i	0.0870735	+	0.493818i
$635$	−8.58093	−	3.12320i	−0.340524	−	0.123941i
$636$	3.92388	+	4.48645i	0.155592	+	0.177899i
$637$	−3.38157	+	1.29854i	−0.133983	+	0.0514499i
$638$	3.32593	−	1.92022i	0.131675	−	0.0760224i
$639$	−23.1822	+	14.6814i	−0.917073	+	0.580789i
$640$	−1.66835	+	0.963220i	−0.0659472	+	0.0380746i
$641$	25.3255	−	30.1818i	1.00030	−	1.19211i	0.0189607	−	0.999820i	$-0.493964\pi$
$641$	25.3255	−	30.1818i	1.00030	−	1.19211i	0.981338	−	0.192290i	$-0.0615913\pi$
$642$	−7.10648	+	2.75259i	−0.280470	+	0.108636i
$643$	−0.0804737	+	0.221100i	−0.00317357	+	0.00871932i	−0.941269	−	0.337657i	$-0.890366\pi$
$643$	−0.0804737	+	0.221100i	−0.00317357	+	0.00871932i	0.938096	+	0.346376i	$0.112588\pi$
$644$	3.06923	+	2.10915i	0.120945	+	0.0831120i
$645$	−19.3138	−	31.9246i	−0.760479	−	1.25703i
$646$	1.20620	−	6.84073i	0.0474575	−	0.269145i
$647$	−17.5267	+	30.3572i	−0.689047	+	1.19347i	0.283099	+	0.959091i	$0.408638\pi$
$647$	−17.5267	+	30.3572i	−0.689047	+	1.19347i	−0.972146	+	0.234375i	$0.924696\pi$
$648$	−8.13625	−	3.84726i	−0.319622	−	0.151135i
$649$	6.76392	−	3.90515i	0.265507	−	0.153291i
$650$	0.510903	+	0.428698i	0.0200393	+	0.0168149i
$651$	12.1077	+	40.4170i	0.474539	+	1.58407i
$652$	2.98457	+	16.9264i	0.116885	+	0.662887i
$653$	12.1538	−	2.14305i	0.475616	−	0.0838640i	0.0692988	−	0.997596i	$-0.477924\pi$
$653$	12.1538	−	2.14305i	0.475616	−	0.0838640i	0.406317	+	0.913732i	$0.366813\pi$
$654$	16.6309	−	20.6648i	0.650319	−	0.808058i
$655$	−20.7784	−	17.4351i	−0.811878	−	0.681247i
$656$	5.34979			0.208874
$657$	−40.6920	+	25.7705i	−1.58755	+	1.00540i
$658$	2.28077	−	2.32122i	0.0889139	−	0.0904904i
$659$	−9.39906	−	25.8237i	−0.366135	−	1.00595i	−0.976818	−	0.214073i	$-0.931327\pi$
$659$	−9.39906	−	25.8237i	−0.366135	−	1.00595i	0.610683	−	0.791876i	$-0.290895\pi$
$660$	−2.13609	+	6.26512i	−0.0831473	+	0.243869i
$661$	9.89161	−	1.74416i	0.384739	−	0.0678399i	0.0220666	−	0.999757i	$-0.492975\pi$
$661$	9.89161	−	1.74416i	0.384739	−	0.0678399i	0.362673	+	0.931917i	$0.381864\pi$
$662$	−9.84027	+	1.73510i	−0.382453	+	0.0674368i
$663$	1.54712	+	1.76893i	0.0600850	+	0.0686995i
$664$	−5.24417	−	14.4082i	−0.203513	−	0.559148i
$665$	−9.46380	+	9.63160i	−0.366990	+	0.373498i
$666$	9.25984	−	12.0009i	0.358812	−	0.465025i
$667$	2.72494			0.105510
$668$	−6.25145	−	5.24559i	−0.241876	−	0.202958i
$669$	−9.57417	−	1.48675i	−0.370159	−	0.0574811i
$670$	4.43460	−	0.781939i	0.171323	−	0.0302090i
$671$	−0.966897	−	5.48354i	−0.0373266	−	0.211690i
$672$	−4.45924	−	1.05604i	−0.172019	−	0.0407375i
$673$	−2.89418	−	2.42851i	−0.111563	−	0.0936121i	0.585300	−	0.810817i	$-0.300977\pi$
$673$	−2.89418	−	2.42851i	−0.111563	−	0.0936121i	−0.696862	+	0.717205i	$0.745421\pi$
$674$	−22.5814	+	13.0374i	−0.869801	+	0.502180i
$675$	6.14059	−	2.67249i	0.236351	−	0.102864i
$676$	6.36611	−	11.0264i	0.244850	−	0.424093i
$677$	0.154389	−	0.875583i	0.00593365	−	0.0336514i	−0.981697	−	0.190449i	$-0.939006\pi$
$677$	0.154389	−	0.875583i	0.00593365	−	0.0336514i	0.987631	+	0.156797i	$0.0501169\pi$
$678$	15.6614	−	28.4564i	0.601472	−	1.09286i
$679$	4.17649	+	2.87005i	0.160279	+	0.110142i
$680$	1.72756	−	4.74642i	0.0662487	−	0.182017i
$681$	3.58094	−	23.0600i	0.137222	−	0.883663i
$682$	−11.7402	+	13.9915i	−0.449557	+	0.535761i
$683$	7.65790	−	4.42129i	0.293021	−	0.169176i	−0.346282	−	0.938130i	$-0.612556\pi$
$683$	7.65790	−	4.42129i	0.293021	−	0.169176i	0.639304	+	0.768954i	$0.279223\pi$
$684$	2.41027	−	7.57352i	0.0921590	−	0.289581i
$685$	27.8001	−	16.0504i	1.06219	−	0.613253i
$686$	2.09991	+	18.4008i	0.0801749	+	0.702547i
$687$	−9.09424	+	26.6732i	−0.346967	+	1.01765i
$688$	10.5080	+	3.82460i	0.400614	+	0.145812i
$689$	−0.309219	−	1.75367i	−0.0117803	−	0.0668095i
$690$	−3.53525	+	3.09195i	−0.134585	+	0.117709i
$691$	−2.52699	+	3.01155i	−0.0961313	+	0.114565i	−0.811965	−	0.583706i	$-0.801602\pi$
$691$	−2.52699	+	3.01155i	−0.0961313	+	0.114565i	0.715834	+	0.698270i	$0.246047\pi$
$692$	−5.27743	−	9.14077i	−0.200618	−	0.347480i
$693$	−13.9220	+	7.35572i	−0.528853	+	0.279421i
$694$	9.77938	−	16.9384i	0.371220	−	0.642972i
$695$	−4.06443	−	11.1669i	−0.154173	−	0.423586i
$696$	−3.12676	+	1.21111i	−0.118520	+	0.0459069i
$697$	−10.7452	+	9.01632i	−0.407005	+	0.341517i
$698$	−13.6019	+	11.4133i	−0.514838	+	0.432001i
$699$	25.2622	+	13.9034i	0.955504	+	0.525876i
$700$	2.77595	−	1.98032i	0.104921	−	0.0748490i
$701$		−	13.6174i		−	0.514323i	−0.966368	−	0.257162i	$-0.917213\pi$
$701$		−	13.6174i		−	0.514323i	0.966368	−	0.257162i	$-0.0827873\pi$
$702$	1.48486	+	2.24171i	0.0560423	+	0.0846080i
$703$	11.5925	+	6.69295i	0.437221	+	0.252429i
$704$	−0.678492	−	1.86414i	−0.0255716	−	0.0702575i
$705$	2.12437	+	3.51147i	0.0800086	+	0.132250i
$706$	16.5205	−	2.91301i	0.621757	−	0.109633i
$707$	29.2308	+	2.29873i	1.09934	+	0.0864525i
$708$	−6.35888	+	2.46302i	−0.238981	+	0.0925661i
$709$	−18.0211	+	6.55915i	−0.676797	+	0.246334i	−0.657472	−	0.753479i	$-0.728374\pi$
$709$	−18.0211	+	6.55915i	−0.676797	+	0.246334i	−0.0193255	+	0.999813i	$0.506152\pi$
$710$	−8.81028	−	15.2599i	−0.330644	−	0.572692i
$711$	−2.31434	+	17.2221i	−0.0867945	+	0.645880i
$712$	10.7411	+	6.20137i	0.402539	+	0.232406i
$713$	−12.1778	+	4.43237i	−0.456063	+	0.165993i
$714$	10.7363	−	5.39433i	0.401797	−	0.201878i
$715$	1.51493	−	1.27118i	0.0566551	−	0.0475393i
$716$	4.43381	−	12.1818i	0.165699	−	0.455255i
$717$	31.0957	−	6.14199i	1.16129	−	0.229377i
$718$	−0.932431	+	5.28808i	−0.0347980	+	0.197349i
$719$	−23.3797	+	40.4948i	−0.871915	+	1.51020i	−0.0119017	+	0.999929i	$0.503789\pi$
$719$	−23.3797	+	40.4948i	−0.871915	+	1.51020i	−0.860013	+	0.510272i	$0.829545\pi$
$720$	2.68233	−	5.11915i	0.0999646	−	0.190779i
$721$	−12.2502	+	12.4675i	−0.456223	+	0.464312i
$722$	−11.7994	−	2.08054i	−0.439126	−	0.0774298i
$723$	−17.2467	−	44.5265i	−0.641412	−	1.65596i
$724$	−16.4755	−	19.6347i	−0.612307	−	0.729719i
$725$	0.853366	−	2.34460i	0.0316932	−	0.0870764i
$726$	10.7200	+	5.89990i	0.397856	+	0.218966i
$727$	−5.66253	+	6.74834i	−0.210012	+	0.250282i	−0.860760	−	0.509012i	$-0.830011\pi$
$727$	−5.66253	+	6.74834i	−0.210012	+	0.250282i	0.650748	+	0.759294i	$0.274455\pi$
$728$	0.976577	+	0.959563i	0.0361944	+	0.0355638i
$729$	26.7965	−	3.30873i	0.992463	−	0.122546i
$730$	−15.4648	−	26.7858i	−0.572378	−	0.991388i
$731$	−27.5515	+	10.0279i	−1.01903	+	0.370896i
$732$	0.0995375	+	4.86056i	0.00367901	+	0.179651i
$733$	6.82787	+	8.13714i	0.252193	+	0.300552i	0.877256	−	0.480022i	$-0.159371\pi$
$733$	6.82787	+	8.13714i	0.252193	+	0.300552i	−0.625063	+	0.780574i	$0.714927\pi$
$734$	−13.0224	−	4.73978i	−0.480667	−	0.174948i
$735$	−23.1396	−	3.17791i	−0.853519	−	0.117219i
$736$	0.244421	−	1.38618i	0.00900948	−	0.0510953i
$737$			4.63704i			0.170807i
$738$	−13.5590	+	8.58699i	−0.499113	+	0.316092i
$739$	44.6002			1.64064			0.820322	−	0.571902i	$-0.193794\pi$
$739$	44.6002			1.64064			0.820322	+	0.571902i	$0.193794\pi$
$740$	7.45643	+	6.25669i	0.274104	+	0.230000i
$741$	−1.78736	+	1.56324i	−0.0656602	+	0.0574269i
$742$	−9.07648	−	0.713779i	−0.333208	−	0.0262036i
$743$	−30.2182	−	36.0126i	−1.10860	−	1.32117i	−0.942176	−	0.335120i	$-0.891223\pi$
$743$	−30.2182	−	36.0126i	−1.10860	−	1.32117i	−0.166421	−	0.986055i	$-0.553221\pi$
$744$	12.0036	−	10.4984i	0.440074	−	0.384892i
$745$	20.7727	+	3.66278i	0.761052	+	0.134194i
$746$		−	15.7893i		−	0.578087i
$747$	36.4181	+	28.1000i	1.33247	+	1.02813i
$748$	4.50452	+	2.60069i	0.164702	+	0.0950905i
$749$	4.82688	−	10.5933i	0.176370	−	0.387072i
$750$	7.57913	+	19.5673i	0.276751	+	0.714498i
$751$	5.89208	+	33.4156i	0.215005	+	1.21935i	0.880898	+	0.473306i	$0.156940\pi$
$751$	5.89208	+	33.4156i	0.215005	+	1.21935i	−0.665893	+	0.746047i	$0.731949\pi$
$752$	−1.15580	−	0.420678i	−0.0421478	−	0.0153406i
$753$	20.6334	−	37.4905i	0.751925	−	1.36623i
$754$	0.986574	+	0.173960i	0.0359289	+	0.00633524i
$755$	−40.9343			−1.48975
$756$	12.9969	−	4.48104i	0.472694	−	0.162974i
$757$	−23.4247			−0.851384			−0.425692	−	0.904868i	$-0.639969\pi$
$757$	−23.4247			−0.851384			−0.425692	+	0.904868i	$0.639969\pi$
$758$	6.81480	+	1.20163i	0.247525	+	0.0436453i
$759$	−2.50345	−	4.13805i	−0.0908694	−	0.150202i
$760$	4.79587	+	1.74555i	0.173964	+	0.0633179i
$761$	−7.68387	−	43.5774i	−0.278540	−	1.57968i	−0.727487	−	0.686121i	$-0.759312\pi$
$761$	−7.68387	−	43.5774i	−0.278540	−	1.57968i	0.448947	−	0.893558i	$-0.351799\pi$
$762$	−5.14754	+	6.39611i	−0.186476	+	0.231707i
$763$	3.88602	+	40.3321i	0.140683	+	1.46012i
$764$	17.5603	+	10.1384i	0.635308	+	0.366795i
$765$	3.24005	+	14.8027i	0.117144	+	0.535191i
$766$		−	8.37266i		−	0.302517i
$767$	2.00639	+	0.353781i	0.0724466	+	0.0127743i
$768$	0.335628	+	1.69922i	0.0121109	+	0.0613154i
$769$	−1.27575	−	1.52038i	−0.0460048	−	0.0548264i	0.742551	−	0.669789i	$-0.233615\pi$
$769$	−1.27575	−	1.52038i	−0.0460048	−	0.0548264i	−0.788556	+	0.614963i	$0.789171\pi$
$770$	−4.35349	−	9.12585i	−0.156889	−	0.328873i
$771$	−2.41599	−	0.823732i	−0.0870097	−	0.0296660i
$772$	2.88190	+	2.41820i	0.103722	+	0.0870330i
$773$	22.1679			0.797323			0.398662	−	0.917098i	$-0.369475\pi$
$773$	22.1679			0.797323			0.398662	+	0.917098i	$0.369475\pi$
$774$	−32.7713	+	7.17308i	−1.17794	+	0.257831i
$775$			11.8662i			0.426246i
$776$	0.332599	−	1.88626i	0.0119396	−	0.0677129i
$777$	2.69206	+	22.9972i	0.0965770	+	0.825022i
$778$	12.7193	+	4.62943i	0.456008	+	0.165973i
$779$	−9.11025	−	10.8572i	−0.326409	−	0.388999i
$780$	−1.47734	+	0.893763i	−0.0528972	+	0.0320018i
$781$	17.0507	−	6.20596i	0.610123	−	0.222067i
$782$	1.84528	+	3.19612i	0.0659872	+	0.114293i
$783$	5.98078	−	8.08833i	0.213736	−	0.289053i
$784$	5.99973	−	3.60600i	0.214276	−	0.128786i
$785$	−25.0527	+	29.8567i	−0.894170	+	1.06563i
$786$	−20.8659	+	12.6235i	−0.744261	+	0.450265i
$787$	−1.66810	+	4.58307i	−0.0594613	+	0.163369i	−0.965866	−	0.259041i	$-0.916593\pi$
$787$	−1.66810	+	4.58307i	−0.0594613	+	0.163369i	0.906405	+	0.422410i	$0.138816\pi$
$788$	7.33909	+	8.74639i	0.261444	+	0.311577i
$789$	−28.7493	+	35.7226i	−1.02350	+	1.27176i
$790$	−10.9890	−	1.93766i	−0.390972	−	0.0689389i
$791$	13.2623	+	47.8109i	0.471552	+	1.69996i
$792$	4.71178	+	3.63559i	0.167426	+	0.129185i
$793$	0.726233	−	1.25787i	0.0257893	−	0.0446684i
$794$	−0.969519	+	5.49842i	−0.0344069	+	0.195131i
$795$	3.70539	−	10.8678i	0.131417	−	0.385442i
$796$	−0.939641	+	2.58164i	−0.0333047	+	0.0915039i
$797$	−12.6293	+	10.5972i	−0.447353	+	0.375374i	−0.838452	−	0.544975i	$-0.816539\pi$
$797$	−12.6293	+	10.5972i	−0.447353	+	0.375374i	0.391100	+	0.920348i	$0.372095\pi$
$798$	5.45053	+	10.8482i	0.192947	+	0.384021i
$799$	3.03046	−	1.10300i	0.107210	−	0.0390213i
$800$	−1.11616	−	0.644414i	−0.0394621	−	0.0227835i
$801$	−37.1770	+	1.52331i	−1.31359	+	0.0538234i
$802$	14.4574	+	25.0410i	0.510509	+	0.884227i
$803$	29.9294	−	10.8934i	1.05618	−	0.384420i
$804$	0.621256	−	4.00068i	0.0219100	−	0.141093i
$805$	0.562445	−	7.15211i	0.0198236	−	0.252079i
$806$	−4.69199	+	0.827324i	−0.165268	+	0.0291412i
$807$	−0.748061	+	1.35921i	−0.0263330	+	0.0478464i
$808$	−3.79038	−	10.4140i	−0.133345	−	0.366362i
$809$	38.5579	+	22.2614i	1.35562	+	0.782669i	0.989030	−	0.147712i	$-0.0471910\pi$
$809$	38.5579	+	22.2614i	1.35562	+	0.782669i	0.366593	+	0.930382i	$0.380524\pi$
$810$	1.41844	+	17.2798i	0.0498390	+	0.607152i
$811$		−	8.10998i		−	0.284780i	−0.989811	−	0.142390i	$-0.954521\pi$
$811$		−	8.10998i		−	0.284780i	0.989811	−	0.142390i	$-0.0454787\pi$
$812$	2.12377	−	4.66093i	0.0745296	−	0.163567i
$813$	14.8112	−	8.96053i	0.519453	−	0.314259i
$814$	−7.67836	+	6.44291i	−0.269127	+	0.225824i
$815$	25.3642	−	21.2831i	0.888470	−	0.745515i
$816$	−3.53792	−	2.84729i	−0.123852	−	0.0996750i
$817$	−10.1324	−	27.8385i	−0.354488	−	0.973947i
$818$	−11.0397	+	19.1213i	−0.385993	+	0.668560i
$819$	−4.01532	−	0.864489i	−0.140307	−	0.0302077i
$820$	−5.15303	−	8.92531i	−0.179952	−	0.311685i
$821$	−6.28035	+	7.48463i	−0.219186	+	0.261215i	−0.864421	−	0.502768i	$-0.832315\pi$
$821$	−6.28035	+	7.48463i	−0.219186	+	0.261215i	0.645235	+	0.763984i	$0.276759\pi$
$822$	−5.59265	−	28.3145i	−0.195066	−	0.987583i
$823$	7.74400	+	43.9184i	0.269939	+	1.53090i	0.754593	+	0.656193i	$0.227834\pi$
$823$	7.74400	+	43.9184i	0.269939	+	1.53090i	−0.484654	+	0.874706i	$0.661054\pi$
$824$	6.20793	+	2.25950i	0.216263	+	0.0787134i
$825$	−4.34448	+	0.858117i	−0.151255	+	0.0298758i
$826$	4.31909	−	9.47891i	0.150280	−	0.329814i
$827$	−0.332182	+	0.191785i	−0.0115511	+	0.00666903i	−0.505764	−	0.862672i	$-0.668790\pi$
$827$	−0.332182	+	0.191785i	−0.0115511	+	0.00666903i	0.494213	+	0.869341i	$0.335456\pi$
$828$	1.60549	+	3.90558i	0.0557945	+	0.135728i
$829$	−11.1763	+	6.45264i	−0.388169	+	0.224109i	−0.681367	−	0.731942i	$-0.738614\pi$
$829$	−11.1763	+	6.45264i	−0.388169	+	0.224109i	0.293197	+	0.956052i	$0.405281\pi$
$830$	−18.9866	+	22.6274i	−0.659036	+	0.785408i
$831$	−4.54142	−	3.65490i	−0.157540	−	0.126787i
$832$	0.176987	−	0.486268i	0.00613592	−	0.0168583i
$833$	−5.97326	+	17.3545i	−0.206961	+	0.601296i
$834$	−10.6822	+	0.218757i	−0.369896	+	0.00757495i
$835$	−2.72994	+	15.4822i	−0.0944734	+	0.535785i
$836$	−2.62778	+	4.55145i	−0.0908837	+	0.157415i
$837$	−13.5719	+	45.8753i	−0.469113	+	1.58568i
$838$	−30.9906	+	17.8925i	−1.07055	+	0.618084i
$839$	−7.39096	−	6.20176i	−0.255164	−	0.214108i	0.506228	−	0.862400i	$-0.331039\pi$
$839$	−7.39096	−	6.20176i	−0.255164	−	0.214108i	−0.761392	+	0.648291i	$0.775484\pi$
$840$	2.53339	+	8.45675i	0.0874103	+	0.291785i
$841$	4.38500	+	24.8686i	0.151207	+	0.857536i
$842$	14.0356	−	2.47486i	0.483699	−	0.0852892i
$843$	1.66691	+	4.30352i	0.0574114	+	0.148221i
$844$	3.99687	+	3.35377i	0.137578	+	0.115442i
$845$	−24.5279			−0.843784
$846$	3.60461	−	0.788986i	0.123929	−	0.0271259i
$847$	−18.0111	+	4.99611i	−0.618870	+	0.171668i
$848$	1.17695	+	3.23365i	0.0404167	+	0.111044i
$849$	−31.3755	+	6.19725i	−1.07680	+	0.212689i
$850$	3.32791	−	0.586800i	0.114146	−	0.0201271i
$851$	−7.00392	+	1.23498i	−0.240091	+	0.0423346i
$852$	−15.5423	+	3.06989i	−0.532469	+	0.105173i
$853$	−6.63676	−	18.2343i	−0.227238	−	0.624332i	0.772707	−	0.634762i	$-0.218902\pi$
$853$	−6.63676	−	18.2343i	−0.227238	−	0.624332i	−0.999946	+	0.0104305i	$0.996680\pi$
$854$	−5.29705	−	5.20476i	−0.181261	−	0.178103i
$855$	−14.9569	+	3.27380i	−0.511514	+	0.111962i
$856$	−4.39996			−0.150387
$857$	−18.3882	−	15.4296i	−0.628131	−	0.527064i	0.272217	−	0.962236i	$-0.412243\pi$
$857$	−18.3882	−	15.4296i	−0.628131	−	0.527064i	−0.900347	+	0.435172i	$0.856688\pi$
$858$	−0.642209	−	1.65802i	−0.0219247	−	0.0566038i
$859$	14.6084	−	2.57585i	0.498431	−	0.0878868i	0.0812195	−	0.996696i	$-0.474119\pi$
$859$	14.6084	−	2.57585i	0.498431	−	0.0878868i	0.417212	+	0.908809i	$0.363007\pi$
$860$	−3.74077	−	21.2149i	−0.127559	−	0.723423i
$861$	5.64958	−	23.8560i	0.192537	−	0.813010i
$862$	17.8245	+	14.9565i	0.607105	+	0.509421i
$863$	−9.41678	+	5.43678i	−0.320551	+	0.185070i	−0.651638	−	0.758530i	$-0.725918\pi$
$863$	−9.41678	+	5.43678i	−0.320551	+	0.185070i	0.331087	+	0.943600i	$0.392585\pi$
$864$	−3.57808	−	3.76794i	−0.121729	−	0.128188i
$865$	−10.1666	+	17.6091i	−0.345676	+	0.598729i
$866$	0.280032	−	1.58814i	0.00951587	−	0.0539672i
$867$	−17.5340	+	0.359071i	−0.595485	+	0.0121947i
$868$	−1.90973	+	24.2843i	−0.0648205	+	0.824264i
$869$	3.93004	−	10.7977i	0.133317	−	0.366287i
$870$	5.03231	+	4.04996i	0.170611	+	0.137306i
$871$	−0.777507	+	0.926597i	−0.0263448	+	0.0313965i
$872$	13.2629	−	7.65735i	0.449139	−	0.259311i
$873$	2.18469	+	5.31457i	0.0739404	+	0.179871i
$874$	−3.22942	+	1.86451i	−0.109237	+	0.0630679i
$875$	−29.1682	−	13.2906i	−0.986064	−	0.449303i
$876$	−27.2815	+	5.38862i	−0.921758	+	0.182064i
$877$	28.3648	+	10.3239i	0.957810	+	0.348614i	0.773175	−	0.634193i	$-0.218667\pi$
$877$	28.3648	+	10.3239i	0.957810	+	0.348614i	0.184635	+	0.982807i	$0.440890\pi$
$878$	−3.80217	−	21.5632i	−0.128317	−	0.727721i
$879$	3.73745	+	18.9220i	0.126061	+	0.638223i
$880$	−2.45650	+	2.92754i	−0.0828085	+	0.0986873i
$881$	13.1018	+	22.6929i	0.441409	+	0.764543i	0.997794	−	0.0663813i	$-0.0211454\pi$
$881$	13.1018	+	22.6929i	0.441409	+	0.764543i	−0.556385	+	0.830925i	$0.687812\pi$
$882$	−9.41824	+	18.7696i	−0.317129	+	0.632004i
$883$	0.563982	−	0.976845i	0.0189795	−	0.0328735i	−0.856380	−	0.516347i	$-0.827292\pi$
$883$	0.563982	−	0.976845i	0.0189795	−	0.0328735i	0.875359	+	0.483473i	$0.160625\pi$
$884$	0.464051	+	1.27497i	0.0156077	+	0.0428819i
$885$	10.2342	+	8.23638i	0.344018	+	0.276863i
$886$	−27.6828	+	23.2286i	−0.930021	+	0.780380i
$887$	−7.60866	+	6.38442i	−0.255474	+	0.214368i	−0.761525	−	0.648135i	$-0.775549\pi$
$887$	−7.60866	+	6.38442i	−0.255474	+	0.214368i	0.506051	+	0.862503i	$0.331105\pi$
$888$	7.48784	−	4.53000i	0.251275	−	0.152017i
$889$	−1.20279	−	12.4835i	−0.0403402	−	0.418682i
$890$		−	23.8931i		−	0.800900i
$891$	−17.7775	−	1.65145i	−0.595567	−	0.0553257i
$892$	−4.84446	−	2.79695i	−0.162204	−	0.0936488i
$893$	1.11449	+	3.06204i	0.0372950	+	0.102467i
$894$	9.14410	−	16.6146i	0.305824	−	0.555676i
$895$	−24.5942	+	4.33662i	−0.822093	+	0.144957i
$896$	−2.18052	−	1.49844i	−0.0728462	−	0.0500593i
$897$	0.193589	−	1.24665i	0.00646375	−	0.0416244i
$898$	33.3522	−	12.1392i	1.11298	−	0.405090i
$899$	8.91199	+	15.4360i	0.297231	+	0.514820i
$900$	3.86324	−	0.158294i	0.128775	−	0.00527647i
$901$	−7.81380	−	4.51130i	−0.260316	−	0.150293i
$902$	9.97277	−	3.62979i	0.332057	−	0.120859i
$903$	28.1517	−	42.8188i	0.936828	−	1.42492i
$904$	14.3658	−	12.0543i	0.477798	−	0.400920i
$905$	−16.8880	+	46.3994i	−0.561376	+	1.54237i
$906$	−11.8769	+	34.8347i	−0.394584	+	1.15731i
$907$	1.69373	−	9.60560i	0.0562393	−	0.318949i	−0.943690	−	0.330831i	$-0.892671\pi$
$907$	1.69373	−	9.60560i	0.0562393	−	0.318949i	0.999929	+	0.0118819i	$0.00378220\pi$
$908$	6.73665	−	11.6682i	0.223563	−	0.387223i
$909$	26.3222	+	20.3101i	0.873053	+	0.673644i
$910$	0.660224	−	2.55354i	0.0218862	−	0.0846490i
$911$	37.9915	+	6.69892i	1.25871	+	0.221945i	0.762919	−	0.646494i	$-0.223766\pi$
$911$	37.9915	+	6.69892i	1.25871	+	0.221945i	0.495795	+	0.868439i	$0.334877\pi$
$912$	2.87695	−	3.57478i	0.0952654	−	0.118373i
$913$	−19.5518	−	23.3009i	−0.647069	−	0.771146i
$914$	3.99473	−	10.9754i	0.132134	−	0.363035i
$915$	8.01322	−	4.84785i	0.264909	−	0.160265i
$916$	−10.4583	+	12.4638i	−0.345553	+	0.411814i
$917$	9.32499	−	36.0661i	0.307938	−	1.19101i
$918$	13.5370	+	1.53768i	0.446788	+	0.0507509i
$919$	−21.9714	−	38.0555i	−0.724768	−	1.25534i	−0.959069	−	0.283172i	$-0.908613\pi$
$919$	−21.9714	−	38.0555i	−0.724768	−	1.25534i	0.234301	−	0.972164i	$-0.424720\pi$
$920$	−2.54806	+	0.927418i	−0.0840070	+	0.0305761i
$921$	16.7714	−	10.1464i	0.552637	−	0.334335i
$922$	4.26943	+	5.08810i	0.140606	+	0.167568i
$923$	4.44774	+	1.61885i	0.146399	+	0.0532850i
$924$	−9.02916	+	1.05695i	−0.297038	+	0.0347712i
$925$	−1.13080	+	6.41310i	−0.0371806	+	0.210861i
$926$		−	14.1367i		−	0.464560i
$927$	−19.3607	+	4.23771i	−0.635887	+	0.139185i
$928$	−1.93593			−0.0635499
$929$	−5.38479	−	4.51838i	−0.176669	−	0.148243i	0.550165	−	0.835056i	$-0.314565\pi$
$929$	−5.38479	−	4.51838i	−0.176669	−	0.148243i	−0.726834	+	0.686813i	$0.759009\pi$
$930$	−29.0772	−	9.91387i	−0.953477	−	0.325088i
$931$	−17.5353	−	6.03549i	−0.574695	−	0.197805i
$932$	10.7012	+	12.7532i	0.350531	+	0.417746i
$933$	−7.52323	−	38.0887i	−0.246299	−	1.24697i
$934$	22.4495	+	3.95845i	0.734569	+	0.129524i
$935$		−	10.0201i		−	0.327693i
$936$	0.331941	+	1.51652i	0.0108498	+	0.0495691i
$937$	−21.8124	−	12.5934i	−0.712581	−	0.411409i	0.0994350	−	0.995044i	$-0.468296\pi$
$937$	−21.8124	−	12.5934i	−0.712581	−	0.411409i	−0.812016	+	0.583635i	$0.801630\pi$
$938$	3.59160	+	5.03458i	0.117270	+	0.164385i
$939$	−23.3074	+	28.9608i	−0.760609	+	0.945100i
$940$	0.411457	+	2.33349i	0.0134202	+	0.0761100i
$941$	29.0388	+	10.5692i	0.946637	+	0.344548i	0.768783	−	0.639509i	$-0.220862\pi$
$941$	29.0388	+	10.5692i	0.946637	+	0.344548i	0.177853	+	0.984057i	$0.443085\pi$
$942$	18.1388	+	29.9824i	0.590994	+	0.976880i
$943$	7.41578	+	1.30760i	0.241491	+	0.0425814i
$944$	−3.93708			−0.128141
$945$	−19.9948	−	17.3672i	−0.650432	−	0.564954i
$946$	22.1834			0.721244
$947$	54.8640	+	9.67400i	1.78284	+	0.314363i	0.965228	−	0.261408i	$-0.0841868\pi$
$947$	54.8640	+	9.67400i	1.78284	+	0.314363i	0.817611	+	0.575771i	$0.195298\pi$
$948$	−4.83735	+	8.78935i	−0.157110	+	0.285465i
$949$	7.80718	+	2.84158i	0.253432	+	0.0922416i
$950$	0.592913	+	3.36258i	0.0192366	+	0.109096i
$951$	−7.89868	−	20.3923i	−0.256132	−	0.661266i
$952$	6.90506	−	0.665305i	0.223794	−	0.0215627i
$953$	−40.2498	−	23.2382i	−1.30382	−	0.752760i	−0.322762	−	0.946480i	$-0.604611\pi$
$953$	−40.2498	−	23.2382i	−1.30382	−	0.752760i	−0.981057	+	0.193720i	$0.937945\pi$
$954$	−8.17333	−	6.30651i	−0.264621	−	0.204181i
$955$		−	39.0621i		−	1.26402i
$956$	18.0220	+	3.17776i	0.582872	+	0.102776i
$957$	−5.00700	+	4.37916i	−0.161853	+	0.141558i
$958$	16.5647	+	19.7410i	0.535180	+	0.637803i
$959$	36.3346	+	24.9688i	1.17331	+	0.806285i
$960$	2.51161	−	2.19667i	0.0810617	−	0.0708972i
$961$	−41.1887	−	34.5614i	−1.32867	−	1.11488i
$962$	−2.61463			−0.0842992
$963$	11.1516	−	7.06240i	0.359356	−	0.227583i
$964$		−	27.5684i		−	0.887920i
$965$	1.25849	−	7.13727i	0.0405123	−	0.229757i
$966$	−5.92319	−	2.55379i	−0.190575	−	0.0821668i
$967$	30.5627	+	11.1239i	0.982832	+	0.357721i	0.782940	−	0.622097i	$-0.213719\pi$
$967$	30.5627	+	11.1239i	0.982832	+	0.357721i	0.199891	+	0.979818i	$0.435941\pi$
$968$	4.54105	+	5.41182i	0.145955	+	0.173942i
$969$	0.246332	+	12.0287i	0.00791332	+	0.386419i
$970$	−3.46730	+	1.26200i	−0.111328	+	0.0405202i
$971$	22.0578	+	38.2053i	0.707869	+	1.22607i	0.965646	+	0.259861i	$0.0836766\pi$
$971$	22.0578	+	38.2053i	0.707869	+	1.22607i	−0.257777	+	0.966204i	$0.582990\pi$
$972$	15.1165	+	3.80659i	0.484863	+	0.122096i
$973$	11.4387	−	11.6415i	0.366708	−	0.373210i
$974$	26.0910	−	31.0940i	0.836010	−	0.996317i
$975$	−1.01202	−	0.556980i	−0.0324106	−	0.0178376i
$976$	−0.959994	+	2.63756i	−0.0307287	+	0.0844263i
$977$	−4.28896	−	5.11139i	−0.137216	−	0.163528i	0.693060	−	0.720880i	$-0.256262\pi$
$977$	−4.28896	−	5.11139i	−0.137216	−	0.163528i	−0.830276	+	0.557352i	$0.811817\pi$
$978$	−10.7524	−	27.7599i	−0.343824	−	0.887664i
$979$	24.2305	+	4.27249i	0.774410	+	0.136549i
$980$	−11.7951	−	6.53626i	−0.376781	−	0.208793i
$981$	−21.3238	+	40.6959i	−0.680818	+	1.29932i
$982$	14.1704	−	24.5438i	0.452195	−	0.783225i
$983$	−4.17110	+	23.6555i	−0.133037	+	0.754492i	0.843169	+	0.537649i	$0.180687\pi$
$983$	−4.17110	+	23.6555i	−0.133037	+	0.754492i	−0.976206	+	0.216844i	$0.930424\pi$
$984$	−9.09048	+	1.79554i	−0.289794	+	0.0572398i
$985$	7.52284	−	20.6688i	0.239698	−	0.658564i
$986$	3.88837	−	3.26273i	0.123831	−	0.103906i
$987$	−3.09648	+	4.70975i	−0.0985619	+	0.149913i
$988$	−1.28825	+	0.468886i	−0.0409848	+	0.0149172i
$989$	13.6312	+	7.86997i	0.433446	+	0.250250i
$990$	1.52695	−	11.3628i	0.0485295	−	0.361132i
$991$	−1.21651	−	2.10706i	−0.0386438	−	0.0669330i	0.846057	−	0.533093i	$-0.178970\pi$
$991$	−1.21651	−	2.10706i	−0.0386438	−	0.0669330i	−0.884700	+	0.466160i	$0.845637\pi$
$992$	8.65171	−	3.14896i	0.274692	−	0.0999797i
$993$	16.1384	−	6.25100i	0.512138	−	0.198369i
$994$	13.7058	−	19.9446i	0.434720	−	0.632604i
$995$	5.21215	−	0.919044i	0.165236	−	0.0291356i
$996$	13.7468	+	22.7227i	0.435585	+	0.719996i
$997$	−0.464421	−	1.27599i	−0.0147084	−	0.0404109i	0.932121	−	0.362147i	$-0.117956\pi$
$997$	−0.464421	−	1.27599i	−0.0147084	−	0.0404109i	−0.946830	+	0.321736i	$0.895734\pi$
$998$	−17.5651	−	10.1412i	−0.556013	−	0.321014i
$999$	−11.7067	+	23.5000i	−0.370383	+	0.743508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.227.12	yes	144
7.5	odd	6		378.2.ba.a.173.20	yes	144
27.5	odd	18		378.2.ba.a.59.20	✓	144
189.5	even	18	inner	378.2.bf.a.5.12	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.59.20	✓	144	27.5	odd	18
378.2.ba.a.173.20	yes	144	7.5	odd	6
378.2.bf.a.5.12	yes	144	189.5	even	18	inner
378.2.bf.a.227.12	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)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(1.73169 - 0.0354625i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.334523 - 1.89717i) q^{5} +(-1.71154 - 0.265781i) q^{6} +(2.15385 - 1.53653i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.99748 - 0.122820i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(1.73169 - 0.0354625i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.334523 - 1.89717i) q^{5} +(-1.71154 - 0.265781i) q^{6} +(2.15385 - 1.53653i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.99748 - 0.122820i) q^{9} +1.92644i q^{10} +(-1.95364 - 0.344480i) q^{11} +(1.63938 + 0.558948i) q^{12} +(-0.332627 - 0.396409i) q^{13} +(-2.38795 + 1.13917i) q^{14} +(-0.646568 - 3.27345i) q^{15} +(0.766044 + 0.642788i) q^{16} -2.62195 q^{17} +(-2.97327 - 0.399554i) q^{18} -2.64927i q^{19} +(0.334523 - 1.89717i) q^{20} +(3.67531 - 2.73717i) q^{21} +(1.86414 + 0.678492i) q^{22} +(0.904765 + 1.07826i) q^{23} +(-1.51742 - 0.835132i) q^{24} +(1.21110 - 0.440805i) q^{25} +(0.258738 + 0.448147i) q^{26} +(5.18635 - 0.318984i) q^{27} +(2.54948 - 0.707201i) q^{28} +(1.24439 - 1.48301i) q^{29} +(0.0683165 + 3.33599i) q^{30} +(-3.14896 + 8.65171i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-3.39531 - 0.527250i) q^{33} +(2.58212 + 0.455297i) q^{34} +(-3.63557 - 3.57223i) q^{35} +(2.85872 + 0.909787i) q^{36} +(-2.52634 + 4.37575i) q^{37} +(-0.460041 + 2.60902i) q^{38} +(-0.590063 - 0.674661i) q^{39} +(-0.658881 + 1.81026i) q^{40} +(4.09818 - 3.43878i) q^{41} +(-4.09478 + 2.05737i) q^{42} +(10.5080 - 3.82460i) q^{43} +(-1.71800 - 0.991889i) q^{44} +(-1.23574 - 5.64566i) q^{45} +(-0.703782 - 1.21899i) q^{46} +(-1.15580 + 0.420678i) q^{47} +(1.34934 + 1.08594i) q^{48} +(2.27817 - 6.61891i) q^{49} +(-1.26925 + 0.223803i) q^{50} +(-4.54040 + 0.0929811i) q^{51} +(-0.176987 - 0.486268i) q^{52} +(2.98015 + 1.72059i) q^{53} +(-5.16295 - 0.586462i) q^{54} +3.82163i q^{55} +(-2.63356 + 0.253744i) q^{56} +(-0.0939498 - 4.58771i) q^{57} +(-1.48301 + 1.24439i) q^{58} +(-3.01598 + 2.53071i) q^{59} +(0.512011 - 3.29717i) q^{60} +(0.959994 + 2.63756i) q^{61} +(4.60348 - 7.97345i) q^{62} +(6.26743 - 4.87025i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.640785 + 0.763658i) q^{65} +(3.25217 + 1.10883i) q^{66} +(-0.405899 - 2.30197i) q^{67} +(-2.46383 - 0.896760i) q^{68} +(1.60501 + 1.83512i) q^{69} +(2.96003 + 4.14927i) q^{70} +(-7.92127 + 4.57335i) q^{71} +(-2.65731 - 1.39238i) q^{72} +(-13.9043 + 8.02766i) q^{73} +(3.24780 - 3.87058i) q^{74} +(2.08162 - 0.806286i) q^{75} +(0.906103 - 2.48950i) q^{76} +(-4.73716 + 2.25986i) q^{77} +(0.463945 + 0.766875i) q^{78} +(-1.00582 + 5.70432i) q^{79} +(0.963220 - 1.66835i) q^{80} +(8.96983 - 0.736303i) q^{81} +(-4.63306 + 2.67490i) q^{82} +(11.7457 + 9.85582i) q^{83} +(4.38983 - 1.31506i) q^{84} +(0.877103 + 4.97430i) q^{85} +(-11.0125 + 1.94180i) q^{86} +(2.10230 - 2.61223i) q^{87} +(1.51966 + 1.27515i) q^{88} -12.4027 q^{89} +(0.236606 + 5.77448i) q^{90} +(-1.32552 - 0.342717i) q^{91} +(0.481415 + 1.32268i) q^{92} +(-5.14621 + 15.0937i) q^{93} +(1.21130 - 0.213584i) q^{94} +(-5.02612 + 0.886241i) q^{95} +(-1.14027 - 1.30375i) q^{96} +(0.655092 + 1.79985i) q^{97} +(-3.39292 + 6.12275i) q^{98} +(-5.89832 - 0.792626i) 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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