LMFDB - Embedded newform 228.2.v.a.23.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(23,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 2]))

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

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

chi := DirichletCharacter("228.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.v (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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.18
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.243359 + 1.39312i) q^{2} +(-1.68017 + 0.420760i) q^{3} +(-1.88155 - 0.678056i) q^{4} +(-2.09742 - 2.49961i) q^{5} +(-0.177284 - 2.44307i) q^{6} +(2.63219 + 1.51969i) q^{7} +(1.40250 - 2.45621i) q^{8} +(2.64592 - 1.41389i) q^{9} +O(q^{10})$	\(q+(-0.243359 + 1.39312i) q^{2} +(-1.68017 + 0.420760i) q^{3} +(-1.88155 - 0.678056i) q^{4} +(-2.09742 - 2.49961i) q^{5} +(-0.177284 - 2.44307i) q^{6} +(2.63219 + 1.51969i) q^{7} +(1.40250 - 2.45621i) q^{8} +(2.64592 - 1.41389i) q^{9} +(3.99268 - 2.31366i) q^{10} +(0.326657 + 0.565787i) q^{11} +(3.44662 + 0.347565i) q^{12} +(0.487847 - 2.76672i) q^{13} +(-2.75768 + 3.29711i) q^{14} +(4.57576 + 3.31726i) q^{15} +(3.08048 + 2.55160i) q^{16} +(1.31571 - 3.61488i) q^{17} +(1.32581 + 4.03016i) q^{18} +(1.88049 - 3.93240i) q^{19} +(2.25154 + 6.12533i) q^{20} +(-5.06194 - 1.44582i) q^{21} +(-0.867702 + 0.317382i) q^{22} +(-5.40830 - 4.53810i) q^{23} +(-1.32297 + 4.71697i) q^{24} +(-0.980636 + 5.56146i) q^{25} +(3.73564 + 1.35293i) q^{26} +(-3.85068 + 3.48887i) q^{27} +(-3.92216 - 4.64415i) q^{28} +(-0.771141 - 2.11869i) q^{29} +(-5.73488 + 5.56729i) q^{30} +(2.94846 + 1.70229i) q^{31} +(-4.30433 + 3.67052i) q^{32} +(-0.786899 - 0.813172i) q^{33} +(4.71577 + 2.71265i) q^{34} +(-1.72217 - 9.76689i) q^{35} +(-5.93714 + 0.866232i) q^{36} +2.89778 q^{37} +(5.02066 + 3.57673i) q^{38} +(0.344459 + 4.85381i) q^{39} +(-9.08123 + 1.64600i) q^{40} +(10.3840 - 1.83098i) q^{41} +(3.24607 - 6.70002i) q^{42} +(-7.58372 - 9.03792i) q^{43} +(-0.230988 - 1.28605i) q^{44} +(-9.08381 - 3.64825i) q^{45} +(7.63826 - 6.43000i) q^{46} +(1.83801 - 0.668980i) q^{47} +(-6.24933 - 2.99096i) q^{48} +(1.11894 + 1.93805i) q^{49} +(-7.50913 - 2.71957i) q^{50} +(-0.689615 + 6.62721i) q^{51} +(-2.79390 + 4.87493i) q^{52} +(-5.81935 + 6.93523i) q^{53} +(-3.92331 - 6.21350i) q^{54} +(0.729109 - 2.00321i) q^{55} +(7.42434 - 4.33383i) q^{56} +(-1.50495 + 7.39832i) q^{57} +(3.13925 - 0.558687i) q^{58} +(8.69888 + 3.16613i) q^{59} +(-6.36025 - 9.34421i) q^{60} +(-4.97808 - 4.17711i) q^{61} +(-3.08903 + 3.69328i) q^{62} +(9.11324 + 0.299360i) q^{63} +(-4.06596 - 6.88970i) q^{64} +(-7.93894 + 4.58355i) q^{65} +(1.32434 - 0.898350i) q^{66} +(2.95870 + 8.12896i) q^{67} +(-4.92667 + 5.90947i) q^{68} +(10.9963 + 5.34917i) q^{69} +(14.0255 - 0.0223180i) q^{70} +(-4.41322 + 3.70313i) q^{71} +(0.238095 - 8.48194i) q^{72} +(0.0225042 + 0.127627i) q^{73} +(-0.705201 + 4.03694i) q^{74} +(-0.692408 - 9.75680i) q^{75} +(-6.20463 + 6.12393i) q^{76} +1.98567i q^{77} +(-6.84576 - 0.701348i) q^{78} +(-13.9125 + 2.45315i) q^{79} +(-0.0830752 - 13.0518i) q^{80} +(5.00181 - 7.48210i) q^{81} +(0.0237281 + 14.9117i) q^{82} +(-1.37681 + 2.38470i) q^{83} +(8.54396 + 6.15266i) q^{84} +(-11.7954 + 4.29318i) q^{85} +(14.4365 - 8.36555i) q^{86} +(2.18711 + 3.23529i) q^{87} +(1.84783 - 0.00882109i) q^{88} +(1.45226 + 0.256073i) q^{89} +(7.29307 - 11.7670i) q^{90} +(5.48866 - 6.54113i) q^{91} +(7.09891 + 12.2058i) q^{92} +(-5.67016 - 1.61954i) q^{93} +(0.484672 + 2.72336i) q^{94} +(-13.7737 + 3.54740i) q^{95} +(5.68760 - 7.97817i) q^{96} +(3.69157 + 1.34362i) q^{97} +(-2.97224 + 1.08717i) q^{98} +(1.66427 + 1.03517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−0.243359	+	1.39312i	−0.172081	+	0.985083i
$2$	−0.243359	+	1.39312i	−0.172081	+	0.985083i
$3$	−1.68017	+	0.420760i	−0.970045	+	0.242926i
$3$	−1.68017	+	0.420760i	−0.970045	+	0.242926i
$4$	−1.88155	−	0.678056i	−0.940776	−	0.339028i
$5$	−2.09742	−	2.49961i	−0.937997	−	1.11786i	−0.992850	−	0.119367i	$-0.961914\pi$
$5$	−2.09742	−	2.49961i	−0.937997	−	1.11786i	0.0548534	−	0.998494i	$-0.482531\pi$
$6$	−0.177284	−	2.44307i	−0.0723758	−	0.997377i
$7$	2.63219	+	1.51969i	0.994873	+	0.574390i	0.906727	−	0.421718i	$-0.138573\pi$
$7$	2.63219	+	1.51969i	0.994873	+	0.574390i	0.0881455	+	0.996108i	$0.471906\pi$
$8$	1.40250	−	2.45621i	0.495860	−	0.868402i
$9$	2.64592	−	1.41389i	0.881974	−	0.471298i
$10$	3.99268	−	2.31366i	1.26260	−	0.731642i
$11$	0.326657	+	0.565787i	0.0984908	+	0.170591i	0.911060	−	0.412273i	$-0.135265\pi$
$11$	0.326657	+	0.565787i	0.0984908	+	0.170591i	−0.812569	+	0.582865i	$0.801932\pi$
$12$	3.44662	+	0.347565i	0.994954	+	0.100333i
$13$	0.487847	−	2.76672i	0.135304	−	0.767349i	−0.839343	−	0.543602i	$-0.817060\pi$
$13$	0.487847	−	2.76672i	0.135304	−	0.767349i	0.974647	−	0.223747i	$-0.0718288\pi$
$14$	−2.75768	+	3.29711i	−0.737020	+	0.881191i
$15$	4.57576	+	3.31726i	1.18146	+	0.856512i
$16$	3.08048	+	2.55160i	0.770120	+	0.637899i
$17$	1.31571	−	3.61488i	0.319107	−	0.876738i	−0.671624	−	0.740893i	$-0.734403\pi$
$17$	1.31571	−	3.61488i	0.319107	−	0.876738i	0.990730	−	0.135845i	$-0.0433750\pi$
$18$	1.32581	+	4.03016i	0.312496	+	0.949919i
$19$	1.88049	−	3.93240i	0.431415	−	0.902154i
$19$	1.88049	−	3.93240i	0.431415	−	0.902154i
$20$	2.25154	+	6.12533i	0.503459	+	1.36966i
$21$	−5.06194	−	1.44582i	−1.10461	−	0.315504i
$22$	−0.867702	+	0.317382i	−0.184995	+	0.0676662i
$23$	−5.40830	−	4.53810i	−1.12771	−	0.946259i	−0.128740	−	0.991678i	$-0.541093\pi$
$23$	−5.40830	−	4.53810i	−1.12771	−	0.946259i	−0.998968	+	0.0454194i	$0.985538\pi$
$24$	−1.32297	+	4.71697i	−0.270049	+	0.962846i
$25$	−0.980636	+	5.56146i	−0.196127	+	1.11229i
$26$	3.73564	+	1.35293i	0.732619	+	0.265332i
$27$	−3.85068	+	3.48887i	−0.741064	+	0.671434i
$28$	−3.92216	−	4.64415i	−0.741219	−	0.877662i
$29$	−0.771141	−	2.11869i	−0.143197	−	0.393431i	0.847273	−	0.531158i	$-0.178243\pi$
$29$	−0.771141	−	2.11869i	−0.143197	−	0.393431i	−0.990470	+	0.137726i	$0.956021\pi$
$30$	−5.73488	+	5.56729i	−1.04704	+	1.01644i
$31$	2.94846	+	1.70229i	0.529559	+	0.305741i	0.740837	−	0.671685i	$-0.234429\pi$
$31$	2.94846	+	1.70229i	0.529559	+	0.305741i	−0.211278	+	0.977426i	$0.567763\pi$
$32$	−4.30433	+	3.67052i	−0.760906	+	0.648862i
$33$	−0.786899	−	0.813172i	−0.136982	−	0.141555i
$34$	4.71577	+	2.71265i	0.808747	+	0.465216i
$35$	−1.72217	−	9.76689i	−0.291099	−	1.65091i
$36$	−5.93714	+	0.866232i	−0.989523	+	0.144372i
$37$	2.89778			0.476392			0.238196	−	0.971217i	$-0.423444\pi$
$37$	2.89778			0.476392			0.238196	+	0.971217i	$0.423444\pi$
$38$	5.02066	+	3.57673i	0.814458	+	0.580222i
$39$	0.344459	+	4.85381i	0.0551576	+	0.777232i
$40$	−9.08123	+	1.64600i	−1.43587	+	0.260256i
$41$	10.3840	−	1.83098i	1.62171	−	0.285950i	0.712304	−	0.701871i	$-0.247652\pi$
$41$	10.3840	−	1.83098i	1.62171	−	0.285950i	0.909401	+	0.415920i	$0.136541\pi$
$42$	3.24607	−	6.70002i	0.500879	−	1.03384i
$43$	−7.58372	−	9.03792i	−1.15651	−	1.37827i	−0.912793	−	0.408423i	$-0.866079\pi$
$43$	−7.58372	−	9.03792i	−1.15651	−	1.37827i	−0.243713	−	0.969847i	$-0.578366\pi$
$44$	−0.230988	−	1.28605i	−0.0348227	−	0.193879i
$45$	−9.08381	−	3.64825i	−1.35413	−	0.543849i
$46$	7.63826	−	6.43000i	1.12620	−	0.948052i
$47$	1.83801	−	0.668980i	0.268101	−	0.0975808i	−0.204472	−	0.978872i	$-0.565548\pi$
$47$	1.83801	−	0.668980i	0.268101	−	0.0975808i	0.472573	+	0.881292i	$0.343325\pi$
$48$	−6.24933	−	2.99096i	−0.902013	−	0.431708i
$49$	1.11894	+	1.93805i	0.159848	+	0.276865i
$50$	−7.50913	−	2.71957i	−1.06195	−	0.384606i
$51$	−0.689615	+	6.62721i	−0.0965654	+	0.927994i
$52$	−2.79390	+	4.87493i	−0.387444	+	0.676032i
$53$	−5.81935	+	6.93523i	−0.799349	+	0.952628i	−0.999632	−	0.0271105i	$-0.991369\pi$
$53$	−5.81935	+	6.93523i	−0.799349	+	0.952628i	0.200283	+	0.979738i	$0.435814\pi$
$54$	−3.92331	−	6.21350i	−0.533895	−	0.845551i
$55$	0.729109	−	2.00321i	0.0983131	−	0.270113i
$56$	7.42434	−	4.33383i	0.992119	−	0.579133i
$57$	−1.50495	+	7.39832i	−0.199335	+	0.979931i
$58$	3.13925	−	0.558687i	0.412204	−	0.0733592i
$59$	8.69888	+	3.16613i	1.13250	+	0.412195i	0.839198	−	0.543825i	$-0.183025\pi$
$59$	8.69888	+	3.16613i	1.13250	+	0.412195i	0.293299	+	0.956021i	$0.405247\pi$
$60$	−6.36025	−	9.34421i	−0.821105	−	1.20633i
$61$	−4.97808	−	4.17711i	−0.637378	−	0.534824i	0.265834	−	0.964019i	$-0.414353\pi$
$61$	−4.97808	−	4.17711i	−0.637378	−	0.534824i	−0.903212	+	0.429195i	$0.858797\pi$
$62$	−3.08903	+	3.69328i	−0.392307	+	0.469047i
$63$	9.11324	+	0.299360i	1.14816	+	0.0377159i
$64$	−4.06596	−	6.88970i	−0.508245	−	0.861212i
$65$	−7.93894	+	4.58355i	−0.984704	+	0.568519i
$66$	1.32434	−	0.898350i	0.163015	−	0.110579i
$67$	2.95870	+	8.12896i	0.361463	+	0.993110i	0.978513	+	0.206187i	$0.0661054\pi$
$67$	2.95870	+	8.12896i	0.361463	+	0.993110i	−0.617050	+	0.786924i	$0.711672\pi$
$68$	−4.92667	+	5.90947i	−0.597446	+	0.716628i
$69$	10.9963	+	5.34917i	1.32380	+	0.643964i
$70$	14.0255	−	0.0223180i	1.67637	−	0.00266751i
$71$	−4.41322	+	3.70313i	−0.523753	+	0.439481i	−0.865938	−	0.500152i	$-0.833278\pi$
$71$	−4.41322	+	3.70313i	−0.523753	+	0.439481i	0.342185	+	0.939633i	$0.388833\pi$
$72$	0.238095	−	8.48194i	0.0280597	−	0.999606i
$73$	0.0225042	+	0.127627i	0.00263391	+	0.0149377i	0.986096	−	0.166174i	$-0.0531415\pi$
$73$	0.0225042	+	0.127627i	0.00263391	+	0.0149377i	−0.983462	+	0.181112i	$0.942030\pi$
$74$	−0.705201	+	4.03694i	−0.0819779	+	0.469285i
$75$	−0.692408	−	9.75680i	−0.0799523	−	1.12662i
$76$	−6.20463	+	6.12393i	−0.711720	+	0.702463i
$77$			1.98567i			0.226289i
$78$	−6.84576	−	0.701348i	−0.775129	−	0.0794120i
$79$	−13.9125	+	2.45315i	−1.56528	+	0.276001i	−0.888041	−	0.459765i	$-0.847934\pi$
$79$	−13.9125	+	2.45315i	−1.56528	+	0.276001i	−0.677237	+	0.735765i	$0.736823\pi$
$80$	−0.0830752	−	13.0518i	−0.00928809	−	1.45923i
$81$	5.00181	−	7.48210i	0.555757	−	0.831345i
$82$	0.0237281	+	14.9117i	0.00262033	+	1.64672i
$83$	−1.37681	+	2.38470i	−0.151124	+	0.261755i	−0.931641	−	0.363380i	$-0.881623\pi$
$83$	−1.37681	+	2.38470i	−0.151124	+	0.261755i	0.780517	+	0.625135i	$0.214956\pi$
$84$	8.54396	+	6.15266i	0.932222	+	0.671311i
$85$	−11.7954	+	4.29318i	−1.27939	+	0.465661i
$86$	14.4365	−	8.36555i	1.55672	−	0.902080i
$87$	2.18711	+	3.23529i	0.234482	+	0.346860i
$88$	1.84783	−	0.00882109i	0.196979	−	0.000940331i
$89$	1.45226	+	0.256073i	0.153939	+	0.0271437i	0.250087	−	0.968223i	$-0.419541\pi$
$89$	1.45226	+	0.256073i	0.153939	+	0.0271437i	−0.0961473	+	0.995367i	$0.530652\pi$
$90$	7.29307	−	11.7670i	0.768757	−	1.24035i
$91$	5.48866	−	6.54113i	0.575368	−	0.685697i
$92$	7.09891	+	12.2058i	0.740112	+	1.27254i
$93$	−5.67016	−	1.61954i	−0.587968	−	0.167939i
$94$	0.484672	+	2.72336i	0.0499901	+	0.280893i
$95$	−13.7737	+	3.54740i	−1.41315	+	0.363956i
$96$	5.68760	−	7.97817i	0.580488	−	0.814269i
$97$	3.69157	+	1.34362i	0.374822	+	0.136424i	0.522560	−	0.852603i	$-0.324977\pi$
$97$	3.69157	+	1.34362i	0.374822	+	0.136424i	−0.147738	+	0.989027i	$0.547199\pi$
$98$	−2.97224	+	1.08717i	−0.300241	+	0.109820i
$99$	1.66427	+	1.03517i	0.167266	+	0.104038i
$100$	5.61610	−	9.79926i	0.561610	−	0.979926i
$101$	13.9725	+	2.46373i	1.39032	+	0.245151i	0.818159	−	0.574992i	$-0.194995\pi$
$101$	13.9725	+	2.46373i	1.39032	+	0.245151i	0.572159	+	0.820142i	$0.306106\pi$
$102$	−9.06465	−	2.57351i	−0.897534	−	0.254815i
$103$	3.43677	−	1.98422i	0.338635	−	0.195511i	−0.321033	−	0.947068i	$-0.604030\pi$
$103$	3.43677	−	1.98422i	0.338635	−	0.195511i	0.659668	+	0.751557i	$0.270697\pi$
$104$	−6.11144	−	5.07859i	−0.599276	−	0.497996i
$105$	7.00304	+	15.6854i	0.683427	+	1.53074i
$106$	−8.24540	−	9.79479i	−0.800864	−	0.951354i
$107$	4.46115	−	7.72694i	0.431276	−	0.746991i	−0.565708	−	0.824606i	$-0.691397\pi$
$107$	4.46115	−	7.72694i	0.431276	−	0.746991i	0.996983	+	0.0776145i	$0.0247303\pi$
$108$	9.61091	−	3.95352i	0.924811	−	0.380428i
$109$	6.48936	−	5.44522i	0.621568	−	0.521557i	−0.276728	−	0.960948i	$-0.589250\pi$
$109$	6.48936	−	5.44522i	0.621568	−	0.521557i	0.898296	+	0.439391i	$0.144806\pi$
$110$	2.61327	+	1.50323i	0.249166	+	0.143328i
$111$	−4.86875	+	1.21927i	−0.462121	+	0.115728i
$112$	4.23076	+	11.3977i	0.399769	+	1.07698i
$113$			10.5767i			0.994974i	0.867472	+	0.497487i	$0.165744\pi$
$113$			10.5767i			0.994974i	−0.867472	+	0.497487i	$0.834256\pi$
$114$	−9.94049	−	3.89702i	−0.931012	−	0.364989i
$115$			23.0370i			2.14821i
$116$	0.0143508	+	4.50931i	0.00133244	+	0.418679i
$117$	−2.62104	−	8.01028i	−0.242315	−	0.740550i
$118$	−6.52775	+	11.3481i	−0.600928	+	1.04467i
$119$	8.95671	−	7.51557i	0.821060	−	0.688951i
$120$	14.5654	−	6.58658i	1.32963	−	0.601269i
$121$	5.28659	−	9.15664i	0.480599	−	0.832422i
$122$	7.03066	−	5.91851i	0.636526	−	0.535837i
$123$	−16.6764	+	7.44551i	−1.50366	+	0.671339i
$124$	−4.39343	−	5.20217i	−0.394542	−	0.467169i
$125$	1.82906	−	1.05601i	0.163596	−	0.0944520i
$126$	−2.63484	+	12.6230i	−0.234730	+	1.12454i
$127$	−0.305126	−	0.0538019i	−0.0270755	−	0.00477414i	0.160094	−	0.987102i	$-0.448820\pi$
$127$	−0.305126	−	0.0538019i	−0.0270755	−	0.00477414i	−0.187170	+	0.982328i	$0.559931\pi$
$128$	10.5876	−	3.98769i	0.935825	−	0.352466i
$129$	16.5447	+	11.9943i	1.45668	+	1.05604i
$130$	−4.45341	−	12.1753i	−0.390590	−	1.06785i
$131$	−9.19231	−	3.34573i	−0.803136	−	0.292318i	−0.0923506	−	0.995727i	$-0.529438\pi$
$131$	−9.19231	−	3.34573i	−0.803136	−	0.292318i	−0.710785	+	0.703409i	$0.751660\pi$
$132$	0.929216	+	2.06359i	0.0808778	+	0.179612i
$133$	10.9258	−	7.49303i	0.947391	−	0.649728i
$134$	−12.0446	+	2.14356i	−1.04050	+	0.185175i
$135$	16.7974	+	2.30757i	1.44569	+	0.198604i
$136$	−7.03363	−	8.30155i	−0.603129	−	0.711852i
$137$	−12.3749	+	14.7479i	−1.05726	+	1.26000i	−0.0928254	+	0.995682i	$0.529590\pi$
$137$	−12.3749	+	14.7479i	−1.05726	+	1.26000i	−0.964437	+	0.264314i	$0.914855\pi$
$138$	−10.1281	+	14.0174i	−0.862159	+	1.19324i
$139$	7.24624	+	1.27771i	0.614618	+	0.108374i	0.472286	−	0.881445i	$-0.343429\pi$
$139$	7.24624	+	1.27771i	0.614618	+	0.108374i	0.142332	+	0.989819i	$0.454540\pi$
$140$	−3.38215	+	19.5446i	−0.285844	+	1.65182i
$141$	−2.80668	+	1.89736i	−0.236365	+	0.159786i
$142$	−4.08490	−	7.04933i	−0.342797	−	0.591566i
$143$	1.72473	−	0.627750i	0.144229	−	0.0524951i
$144$	11.7584	+	2.39585i	0.979866	+	0.199654i
$145$	−3.67850	+	6.37135i	−0.305483	+	0.529112i
$146$	−0.183277		0.000291637i	−0.0151681		2.41361e-5i
$147$	−2.69545	−	2.78545i	−0.222317	−	0.229740i
$148$	−5.45232	−	1.96485i	−0.448178	−	0.161510i
$149$	15.1969	−	2.67962i	1.24498	−	0.219523i	0.487929	−	0.872883i	$-0.337752\pi$
$149$	15.1969	−	2.67962i	1.24498	−	0.219523i	0.757047	+	0.653360i	$0.226641\pi$
$150$	13.7609	+	1.40980i	1.12357	+	0.115110i
$151$		−	7.69823i		−	0.626473i	−0.949675	−	0.313237i	$-0.898587\pi$
$151$		−	7.69823i		−	0.626473i	0.949675	−	0.313237i	$-0.101413\pi$
$152$	−7.02141	−	10.1341i	−0.569511	−	0.821984i
$153$	−1.62979	−	11.4250i	−0.131761	−	0.923654i
$154$	−2.76628	−	0.483232i	−0.222913	−	0.0389399i
$155$	−1.92909	−	10.9404i	−0.154949	−	0.878757i
$156$	2.64304	−	9.36626i	0.211612	−	0.749901i
$157$	−5.46726	+	4.58757i	−0.436335	+	0.366128i	−0.834336	−	0.551257i	$-0.814148\pi$
$157$	−5.46726	+	4.58757i	−0.436335	+	0.366128i	0.398001	+	0.917385i	$0.369704\pi$
$158$	−0.0317910	−	19.9787i	−0.00252915	−	1.58942i
$159$	6.85942	−	14.1009i	0.543987	−	1.11827i
$160$	18.2029	+	3.06054i	1.43907	+	0.241957i
$161$	−7.33912	−	20.1641i	−0.578404	−	1.58915i
$162$	9.20621	+	8.78895i	0.723308	+	0.690525i
$163$	6.04489	−	3.49002i	0.473473	−	0.273359i	−0.244220	−	0.969720i	$-0.578532\pi$
$163$	6.04489	−	3.49002i	0.473473	−	0.273359i	0.717692	+	0.696360i	$0.245198\pi$
$164$	−20.7795	−	3.59584i	−1.62261	−	0.280788i
$165$	−0.382155	+	3.67251i	−0.0297507	+	0.285905i
$166$	−2.98711	−	2.49840i	−0.231845	−	0.193913i
$167$	−7.26672	−	6.09750i	−0.562316	−	0.471839i	0.316770	−	0.948502i	$-0.397402\pi$
$167$	−7.26672	−	6.09750i	−0.562316	−	0.471839i	−0.879086	+	0.476663i	$0.841846\pi$
$168$	−10.6506	+	10.4054i	−0.821714	+	0.802796i
$169$	4.79928	+	1.74680i	0.369176	+	0.134369i
$170$	−3.11038	−	17.4772i	−0.238555	−	1.34044i
$171$	−0.584354	−	13.0636i	−0.0446866	−	0.999001i
$172$	8.14095	+	22.1475i	0.620742	+	1.68873i
$173$	2.73008	−	7.50083i	0.207564	−	0.570278i	−0.791605	−	0.611033i	$-0.790754\pi$
$173$	2.73008	−	7.50083i	0.207564	−	0.570278i	0.999169	+	0.0407554i	$0.0129764\pi$
$174$	−5.03939	+	2.25956i	−0.382035	+	0.171297i
$175$	−11.0329	+	13.1485i	−0.834011	+	0.993936i
$176$	−0.437398	+	2.57639i	−0.0329701	+	0.194203i
$177$	−15.9477	−	1.65949i	−1.19871	−	0.124735i
$178$	−0.710160	+	1.96085i	−0.0532288	+	0.146972i
$179$	11.8117	+	20.4584i	0.882846	+	1.52913i	0.848163	+	0.529736i	$0.177709\pi$
$179$	11.8117	+	20.4584i	0.882846	+	1.52913i	0.0346836	+	0.999398i	$0.488958\pi$
$180$	14.6180	+	13.0237i	1.08956	+	0.970729i
$181$	−6.00583	+	2.18594i	−0.446410	+	0.162480i	−0.555437	−	0.831559i	$-0.687449\pi$
$181$	−6.00583	+	2.18594i	−0.446410	+	0.162480i	0.109027	+	0.994039i	$0.465227\pi$
$182$	7.77685	+	9.23820i	0.576459	+	0.684781i
$183$	10.1216	+	4.92366i	0.748208	+	0.363967i
$184$	−18.7317	+	6.91922i	−1.38092	+	0.510092i
$185$	−6.07787	−	7.24332i	−0.446854	−	0.532540i
$186$	3.63610	−	7.50506i	0.266612	−	0.550298i
$187$	2.47504	−	0.436416i	0.180993	−	0.0319139i
$188$	−3.91191	+	0.0124496i	−0.285306	+	0.000907982i
$189$	−15.4377	+	3.33151i	−1.12293	+	0.242332i
$190$	−1.59000	−	20.0516i	−0.115351	−	1.45470i
$191$	−2.34872			−0.169948			−0.0849739	−	0.996383i	$-0.527081\pi$
$191$	−2.34872			−0.169948			−0.0849739	+	0.996383i	$0.527081\pi$
$192$	9.73041	+	9.86505i	0.702232	+	0.711949i
$193$	2.26613	+	12.8519i	0.163120	+	0.925098i	0.950982	+	0.309247i	$0.100077\pi$
$193$	2.26613	+	12.8519i	0.163120	+	0.925098i	−0.787862	+	0.615852i	$0.788812\pi$
$194$	−2.77020	+	4.81580i	−0.198889	+	0.345755i
$195$	11.4102	−	11.0415i	0.817100	−	0.790699i
$196$	−0.791228	−	4.40525i	−0.0565163	−	0.314661i
$197$	−4.00455	−	2.31203i	−0.285313	−	0.164725i	0.350513	−	0.936558i	$-0.386007\pi$
$197$	−4.00455	−	2.31203i	−0.285313	−	0.164725i	−0.635826	+	0.771832i	$0.719340\pi$
$198$	−1.84713	+	2.06661i	−0.131270	+	0.146867i
$199$	−4.29933	−	11.8123i	−0.304772	−	0.837353i	−0.993654	−	0.112480i	$-0.964121\pi$
$199$	−4.29933	−	11.8123i	−0.304772	−	0.837353i	0.688882	−	0.724873i	$-0.258102\pi$
$200$	12.2848	+	10.2086i	0.868666	+	0.721859i
$201$	−8.39145	−	12.4131i	−0.591887	−	0.875553i
$202$	−6.83261	+	18.8658i	−0.480741	+	1.32739i
$203$	1.18998	−	6.74869i	0.0835199	−	0.473665i
$204$	5.79116	−	12.0018i	0.405462	−	0.840297i
$205$	−26.3563	−	22.1156i	−1.84081	−	1.54462i
$206$	1.92788	+	5.27071i	0.134322	+	0.367227i
$207$	−20.7263	−	4.36070i	−1.44058	−	0.303090i
$208$	8.56234	−	7.27803i	0.593691	−	0.504640i
$209$	2.83917	−	0.220588i	0.196390	−	0.0152584i
$210$	−23.5558	+	5.93888i	−1.62551	+	0.409821i
$211$	−4.22389	+	11.6050i	−0.290785	+	0.798924i	0.705168	+	0.709041i	$0.250872\pi$
$211$	−4.22389	+	11.6050i	−0.290785	+	0.798924i	−0.995952	+	0.0898835i	$0.971351\pi$
$212$	15.6519	−	9.10316i	1.07498	−	0.625208i
$213$	5.85682	−	8.07879i	0.401303	−	0.553549i
$214$	9.67887	+	8.09533i	0.661634	+	0.553385i
$215$	−6.68504	+	37.9127i	−0.455916	+	2.58563i
$216$	3.16882	+	14.3513i	0.215611	+	0.976479i
$217$	5.17393	+	8.96150i	0.351229	+	0.608346i
$218$	6.00659	+	10.3656i	0.406817	+	0.702046i
$219$	−0.0915113	−	0.204967i	−0.00618376	−	0.0138504i
$220$	−2.73015	+	3.27477i	−0.184066	+	0.220785i
$221$	−9.35949	−	5.40370i	−0.629587	−	0.363492i
$222$	−0.513729	−	7.07946i	−0.0344792	−	0.475142i
$223$	−10.0855	−	12.0194i	−0.675373	−	0.804879i	0.314131	−	0.949380i	$-0.398287\pi$
$223$	−10.0855	−	12.0194i	−0.675373	−	0.804879i	−0.989505	+	0.144501i	$0.953842\pi$
$224$	−16.9079	+	3.12022i	−1.12970	+	0.208478i
$225$	5.26863	+	16.1017i	0.351242	+	1.07345i
$226$	−14.7346	−	2.57394i	−0.980131	−	0.171216i
$227$	2.67764			0.177721			0.0888606	−	0.996044i	$-0.471677\pi$
$227$	2.67764			0.177721			0.0888606	+	0.996044i	$0.471677\pi$
$228$	7.84811	−	12.8999i	0.519754	−	0.854316i
$229$	−18.6821			−1.23455			−0.617273	−	0.786749i	$-0.711762\pi$
$229$	−18.6821			−1.23455			−0.617273	+	0.786749i	$0.711762\pi$
$230$	−32.0932	−	5.60626i	−2.11616	−	0.369666i
$231$	−0.835492	−	3.33626i	−0.0549713	−	0.219510i
$232$	−6.28549	−	1.07739i	−0.412662	−	0.0707340i
$233$	7.52375	+	8.96645i	0.492897	+	0.587412i	0.953952	−	0.299960i	$-0.0969732\pi$
$233$	7.52375	+	8.96645i	0.492897	+	0.587412i	−0.461055	+	0.887372i	$0.652529\pi$
$234$	11.7971	−	1.70204i	0.771201	−	0.111266i
$235$	−5.52727	−	3.19117i	−0.360560	−	0.208169i
$236$	−14.2206	−	11.8556i	−0.925681	−	0.771732i
$237$	22.3431	−	9.97551i	1.45134	−	0.647979i
$238$	8.29038	+	14.3067i	0.537385	+	0.927367i
$239$	4.10165	+	7.10426i	0.265313	+	0.459536i	0.967646	−	0.252313i	$-0.0811912\pi$
$239$	4.10165	+	7.10426i	0.265313	+	0.459536i	−0.702332	+	0.711849i	$0.747858\pi$
$240$	5.63125	+	21.8942i	0.363496	+	1.41327i
$241$	−1.07046	+	6.07088i	−0.0689544	+	0.391060i	0.930725	+	0.365721i	$0.119178\pi$
$241$	−1.07046	+	6.07088i	−0.0689544	+	0.391060i	−0.999679	+	0.0253388i	$0.991934\pi$
$242$	11.4697	+	9.59319i	0.737303	+	0.616674i
$243$	−5.25571	+	14.6757i	−0.337154	+	0.941450i
$244$	6.53421	+	11.2349i	0.418310	+	0.719238i
$245$	2.49750	−	6.86183i	0.159559	−	0.438386i
$246$	−6.31411	−	25.0441i	−0.402573	−	1.59676i
$247$	−9.96243	−	7.12119i	−0.633894	−	0.453111i
$248$	8.31642	−	4.85457i	0.528093	−	0.308265i
$249$	1.30988	−	4.58601i	0.0830104	−	0.290626i
$250$	1.02602	+	2.80508i	0.0648914	+	0.177409i
$251$	19.7949	+	16.6099i	1.24944	+	1.04841i	0.996725	+	0.0808687i	$0.0257694\pi$
$251$	19.7949	+	16.6099i	1.24944	+	1.04841i	0.252720	+	0.967540i	$0.418675\pi$
$252$	−16.9441	−	6.74255i	−1.06738	−	0.424741i
$253$	0.800938	−	4.54234i	0.0503545	−	0.285575i
$254$	0.149207	−	0.411983i	0.00936210	−	0.0258501i
$255$	18.0119	−	12.1763i	1.12795	−	0.762509i
$256$	2.97872	+	15.7203i	0.186170	+	0.982517i
$257$	−7.23134	−	19.8679i	−0.451078	−	1.23933i	−0.931966	−	0.362546i	$-0.881908\pi$
$257$	−7.23134	−	19.8679i	−0.451078	−	1.23933i	0.480888	−	0.876782i	$-0.340315\pi$
$258$	−20.7358	+	20.1298i	−1.29095	+	1.25323i
$259$	7.62749	+	4.40373i	0.473949	+	0.273635i
$260$	18.0454	−	3.24115i	1.11913	−	0.201007i
$261$	−5.03598	−	4.51558i	−0.311720	−	0.279508i
$262$	6.89802	−	11.9918i	0.426161	−	0.740853i
$263$	−2.79554	−	15.8543i	−0.172381	−	0.977619i	−0.941124	−	0.338062i	$-0.890229\pi$
$263$	−2.79554	−	15.8543i	−0.172381	−	0.977619i	0.768743	−	0.639557i	$-0.220882\pi$
$264$	−3.10095	+	0.792314i	−0.190850	+	0.0487635i
$265$	29.5411			1.81469
$266$	7.77977	+	17.0445i	0.477008	+	1.04506i
$267$	−2.54779	+	0.180808i	−0.155922	+	0.0110653i
$268$	−0.0550610	−	17.3012i	−0.00336338	−	1.05684i
$269$	−11.6194	+	2.04881i	−0.708446	+	0.124918i	−0.516249	−	0.856438i	$-0.672672\pi$
$269$	−11.6194	+	2.04881i	−0.708446	+	0.124918i	−0.192196	+	0.981356i	$0.561561\pi$
$270$	−7.30250	+	22.8391i	−0.444416	+	1.38994i
$271$	11.0698	+	13.1924i	0.672440	+	0.801383i	0.989114	−	0.147152i	$-0.0470105\pi$
$271$	11.0698	+	13.1924i	0.672440	+	0.801383i	−0.316674	+	0.948535i	$0.602566\pi$
$272$	13.2767	−	7.77842i	0.805020	−	0.471636i
$273$	−6.46962	+	13.2996i	−0.391559	+	0.804929i
$274$	−17.5340	−	20.8288i	−1.05927	−	1.25831i
$275$	−3.46693	+	1.26186i	−0.209064	+	0.0760931i
$276$	−17.0631	−	17.5208i	−1.02708	−	1.05463i
$277$	12.7567	+	22.0953i	0.766479	+	1.32758i	0.939461	+	0.342655i	$0.111326\pi$
$277$	12.7567	+	22.0953i	0.766479	+	1.32758i	−0.172983	+	0.984925i	$0.555340\pi$
$278$	−3.54344	+	9.78392i	−0.212521	+	0.586801i
$279$	10.2082	+	0.335330i	0.611152	+	0.0200757i
$280$	−26.4049	−	9.46810i	−1.57799	−	0.565827i
$281$	8.74766	−	10.4251i	0.521842	−	0.621907i	−0.439174	−	0.898402i	$-0.644729\pi$
$281$	8.74766	−	10.4251i	0.521842	−	0.621907i	0.961015	+	0.276496i	$0.0891731\pi$
$282$	−1.96021	−	4.37177i	−0.116729	−	0.260335i
$283$	−8.24218	+	22.6452i	−0.489947	+	1.34612i	0.410782	+	0.911734i	$0.365256\pi$
$283$	−8.24218	+	22.6452i	−0.489947	+	1.34612i	−0.900728	+	0.434383i	$0.856966\pi$
$284$	10.8146	−	3.97523i	0.641731	−	0.235886i
$285$	21.6495	−	11.7556i	1.28240	−	0.696344i
$286$	0.454801	+	2.55552i	0.0268930	+	0.151111i
$287$	30.1151	+	10.9610i	1.77764	+	0.647007i
$288$	−6.19922	+	15.7978i	−0.365292	+	0.930893i
$289$	1.68647	+	1.41511i	0.0992039	+	0.0832420i
$290$	−7.98084	−	6.67511i	−0.468651	−	0.391976i
$291$	−6.76779	−	0.704244i	−0.396735	−	0.0412835i
$292$	0.0441958	−	0.255397i	0.00258636	−	0.0149460i
$293$	−10.5221	+	6.07496i	−0.614710	+	0.354903i	−0.774807	−	0.632198i	$-0.782153\pi$
$293$	−10.5221	+	6.07496i	−0.614710	+	0.354903i	0.160096	+	0.987101i	$0.448820\pi$
$294$	4.53642	−	3.07722i	0.264569	−	0.179467i
$295$	−10.3311	−	28.3846i	−0.601502	−	1.65261i
$296$	4.06415	−	7.11756i	0.236224	−	0.413700i
$297$	−3.23181	−	1.03900i	−0.187529	−	0.0602888i
$298$	0.0347259	+	21.8231i	0.00201161	+	1.26418i
$299$	−15.1940	+	12.7493i	−0.878694	+	0.737312i
$300$	−5.31285	+	18.8274i	−0.306738	+	1.08700i
$301$	−6.22689	−	35.3144i	−0.358912	−	2.03549i
$302$	10.7245	+	1.87343i	0.617128	+	0.107804i
$303$	−24.5128	+	1.73959i	−1.40822	+	0.0999370i
$304$	15.8267	−	7.31542i	0.907724	−	0.419568i
$305$			21.2044i			1.21416i
$306$	16.3130	+	0.509879i	0.932550	+	0.0291478i
$307$	8.33133	−	1.46904i	0.475494	−	0.0838424i	0.0692349	−	0.997600i	$-0.477944\pi$
$307$	8.33133	−	1.46904i	0.475494	−	0.0838424i	0.406259	+	0.913758i	$0.366833\pi$
$308$	1.34640	−	3.73615i	0.0767181	−	0.212887i
$309$	−4.93947	+	4.77988i	−0.280997	+	0.271918i
$310$	15.7108	−	0.0249996i	0.892312	−	0.00141988i
$311$	12.7885	−	22.1504i	0.725172	−	1.25603i	−0.233731	−	0.972301i	$-0.575094\pi$
$311$	12.7885	−	22.1504i	0.725172	−	1.25603i	0.958903	−	0.283733i	$-0.0915730\pi$
$312$	12.4051	+	5.96143i	0.702300	+	0.337499i
$313$	8.56333	−	3.11680i	0.484028	−	0.176172i	−0.0884683	−	0.996079i	$-0.528197\pi$
$313$	8.56333	−	3.11680i	0.484028	−	0.176172i	0.572497	+	0.819907i	$0.305975\pi$
$314$	−5.06052	−	8.73296i	−0.285582	−	0.492829i
$315$	−18.3661	−	23.4075i	−1.03481	−	1.31886i
$316$	27.8405	+	4.81772i	1.56615	+	0.271018i
$317$	−16.6909	−	2.94305i	−0.937452	−	0.165298i	−0.316008	−	0.948757i	$-0.602343\pi$
$317$	−16.6909	−	2.94305i	−0.937452	−	0.165298i	−0.621444	+	0.783458i	$0.713454\pi$
$318$	17.9749	+	12.9876i	1.00798	+	0.728306i
$319$	0.946829	−	1.12839i	0.0530123	−	0.0631775i
$320$	−8.69353	+	24.6140i	−0.485983	+	1.37596i
$321$	−4.24429	+	14.8596i	−0.236893	+	0.829383i
$322$	29.8770	−	5.31715i	1.66498	−	0.296313i
$323$	−11.7410	−	11.9717i	−0.653285	−	0.666121i
$324$	−14.4845	+	10.6865i	−0.804692	+	0.593693i
$325$	14.9086	+	5.42628i	0.826980	+	0.300996i
$326$	3.39093	+	9.27057i	0.187806	+	0.513450i
$327$	−8.61208	+	11.8793i	−0.476249	+	0.656929i
$328$	10.0663	−	28.0732i	0.555819	−	1.55008i
$329$	5.85462	+	1.03233i	0.322776	+	0.0569141i
$330$	−5.02324	−	1.42613i	−0.276520	−	0.0785056i
$331$	27.7909	−	16.0451i	1.52753	−	0.881917i	0.528060	−	0.849207i	$-0.322920\pi$
$331$	27.7909	−	16.0451i	1.52753	−	0.881917i	0.999465	−	0.0327101i	$-0.0104138\pi$
$332$	4.20750	−	3.55339i	0.230917	−	0.195018i
$333$	7.66730	−	4.09715i	0.420165	−	0.224522i
$334$	10.2630	−	8.63951i	0.561564	−	0.472733i
$335$	14.1136	−	24.4455i	0.771109	−	1.33560i
$336$	−11.9041	−	17.3698i	−0.649419	−	0.947602i
$337$	−12.2571	+	10.2850i	−0.667689	+	0.560258i	−0.912381	−	0.409343i	$-0.865758\pi$
$337$	−12.2571	+	10.2850i	−0.667689	+	0.560258i	0.244691	+	0.969601i	$0.421313\pi$
$338$	−3.60144	+	6.26087i	−0.195893	+	0.340546i
$339$	−4.45026	−	17.7706i	−0.241705	−	0.965169i
$340$	25.1047	−	0.0798955i	1.36149	−	0.00433294i
$341$			2.22426i			0.120451i
$342$	18.3414	+	2.36508i	0.991788	+	0.127889i
$343$		−	14.4740i		−	0.781520i
$344$	−32.8353	+	5.95150i	−1.77036	+	0.320883i
$345$	−9.69303	−	38.7060i	−0.521855	−	2.08386i
$346$	9.78515	+	5.62872i	0.526053	+	0.302602i
$347$	−3.18422	+	2.67188i	−0.170938	+	0.143434i	−0.724243	−	0.689544i	$-0.757811\pi$
$347$	−3.18422	+	2.67188i	−0.170938	+	0.143434i	0.553305	+	0.832979i	$0.313366\pi$
$348$	−1.92145	−	7.57035i	−0.103000	−	0.405813i
$349$	5.11063	−	8.85188i	0.273566	−	0.473830i	−0.696206	−	0.717842i	$-0.745130\pi$
$349$	5.11063	−	8.85188i	0.273566	−	0.473830i	0.969772	+	0.244012i	$0.0784635\pi$
$350$	−15.6325	−	18.5700i	−0.835592	−	0.992608i
$351$	7.77418	+	12.3558i	0.414955	+	0.659503i
$352$	−3.48277	−	1.23633i	−0.185632	−	0.0658969i
$353$	12.9925	−	7.50122i	0.691521	−	0.399250i	−0.112661	−	0.993634i	$-0.535937\pi$
$353$	12.9925	−	7.50122i	0.691521	−	0.399250i	0.804182	+	0.594384i	$0.202604\pi$
$354$	6.19290	−	21.8132i	0.329149	−	1.15936i
$355$	18.5128	+	3.26431i	0.982557	+	0.173251i
$356$	−2.55887	−	1.46653i	−0.135620	−	0.0777258i
$357$	−11.8865	+	16.3960i	−0.629101	+	0.867770i
$358$	−31.3755	+	11.4763i	−1.65824	+	0.606542i
$359$	4.93808	+	1.79731i	0.260622	+	0.0948586i	0.469027	−	0.883184i	$-0.344605\pi$
$359$	4.93808	+	1.79731i	0.260622	+	0.0948586i	−0.208405	+	0.978043i	$0.566827\pi$
$360$	−21.7010	+	17.1951i	−1.14374	+	0.906261i
$361$	−11.9275	−	14.7897i	−0.627763	−	0.778405i
$362$	−1.58370	−	8.89880i	−0.0832376	−	0.467710i
$363$	−5.02961	+	17.6091i	−0.263986	+	0.924237i
$364$	−14.7625	+	8.58587i	−0.773763	+	0.450022i
$365$	0.271819	−	0.323941i	0.0142276	−	0.0169558i
$366$	−9.32241	+	12.9023i	−0.487290	+	0.674415i
$367$	16.6854	+	2.94209i	0.870971	+	0.153576i	0.591233	−	0.806501i	$-0.298641\pi$
$367$	16.6854	+	2.94209i	0.870971	+	0.153576i	0.279738	+	0.960076i	$0.409752\pi$
$368$	−5.08076	−	27.7793i	−0.264853	−	1.44810i
$369$	24.8864	−	19.5265i	1.29553	−	1.01651i
$370$	11.5699	−	6.70446i	0.601491	−	0.348548i
$371$	−25.8570	+	9.41119i	−1.34243	+	0.488605i
$372$	9.57056	+	6.89194i	0.496210	+	0.357330i
$373$	−5.90873	+	10.2342i	−0.305942	+	0.529908i	−0.977471	−	0.211071i	$-0.932305\pi$
$373$	−5.90873	+	10.2342i	−0.305942	+	0.529908i	0.671528	+	0.740979i	$0.265638\pi$
$374$	0.00565563	+	3.55423i	0.000292446	+	0.183785i
$375$	−2.62879	+	2.54386i	−0.135750	+	0.131364i
$376$	0.934656	−	5.45279i	0.0482012	−	0.281206i
$377$	−6.23802	+	1.09993i	−0.321274	+	0.0566493i
$378$	−0.884273	−	22.3173i	−0.0454821	−	1.14788i
$379$			9.39554i			0.482617i	0.970448	+	0.241308i	$0.0775765\pi$
$379$			9.39554i			0.482617i	−0.970448	+	0.241308i	$0.922423\pi$
$380$	28.3212	+	2.66469i	1.45285	+	0.136695i
$381$	0.535300	−	0.0379884i	0.0274242	−	0.00194621i
$382$	0.571584	−	3.27205i	0.0292448	−	0.167413i
$383$	5.78100	+	32.7857i	0.295396	+	1.67527i	0.665590	+	0.746317i	$0.268180\pi$
$383$	5.78100	+	32.7857i	0.295396	+	1.67527i	−0.370195	+	0.928954i	$0.620709\pi$
$384$	−16.1112	+	11.1548i	−0.822169	+	0.569243i
$385$	4.96342	−	4.16480i	0.252959	−	0.212258i
$386$	−18.4557	+	0.0293674i	−0.939368	+	0.00149476i
$387$	−32.8446	−	13.1911i	−1.66958	−	0.670540i
$388$	−6.03483	−	5.03118i	−0.306372	−	0.255420i
$389$	4.73715	+	13.0152i	0.240183	+	0.659898i	0.999953	+	0.00970576i	$0.00308949\pi$
$389$	4.73715	+	13.0152i	0.240183	+	0.659898i	−0.759770	+	0.650192i	$0.774688\pi$
$390$	12.6054	+	18.5828i	0.638297	+	0.940975i
$391$	−23.5204	+	13.5795i	−1.18948	+	0.686747i
$392$	6.32958	−	0.0302159i	0.319692	−	0.00152613i
$393$	16.8524	+	1.75363i	0.850089	+	0.0884588i
$394$	4.19547	−	5.01616i	0.211365	−	0.252710i
$395$	35.3123	+	29.6306i	1.77676	+	1.49087i
$396$	−2.42951	−	3.07619i	−0.122088	−	0.154585i
$397$	0.932247	+	0.339310i	0.0467881	+	0.0170295i	0.365308	−	0.930887i	$-0.380964\pi$
$397$	0.932247	+	0.339310i	0.0467881	+	0.0170295i	−0.318520	+	0.947916i	$0.603186\pi$
$398$	17.5022	−	3.11484i	0.877308	−	0.156133i
$399$	−15.2045	+	17.1867i	−0.761176	+	0.860411i
$400$	−17.2114	+	14.6298i	−0.860572	+	0.731490i
$401$	−5.98274	+	16.4374i	−0.298764	+	0.820846i	0.695944	+	0.718096i	$0.254986\pi$
$401$	−5.98274	+	16.4374i	−0.298764	+	0.820846i	−0.994707	+	0.102750i	$0.967236\pi$
$402$	19.3351	−	8.66943i	0.964345	−	0.432392i
$403$	6.14815	−	7.32709i	0.306261	−	0.364988i
$404$	−24.6195	−	14.1098i	−1.22487	−	0.701989i
$405$	−29.1933	+	3.19056i	−1.45063	+	0.158540i
$406$	9.11212	+	3.30013i	0.452227	+	0.163783i
$407$	0.946580	+	1.63952i	0.0469202	+	0.0812682i
$408$	15.3106	+	10.9885i	0.757990	+	0.544013i
$409$	4.35134	−	1.58376i	0.215160	−	0.0783117i	−0.232192	−	0.972670i	$-0.574590\pi$
$409$	4.35134	−	1.58376i	0.215160	−	0.0783117i	0.447351	+	0.894358i	$0.352367\pi$
$410$	37.2237	−	31.3355i	1.83835	−	1.54755i
$411$	14.5866	−	29.9858i	0.719506	−	1.47909i
$412$	−7.81188	+	1.40309i	−0.384864	+	0.0691255i
$413$	18.0855	+	21.5535i	0.889930	+	1.06058i
$414$	11.1189	−	27.8130i	0.546465	−	1.36693i
$415$	8.84859	−	1.56025i	0.434360	−	0.0765894i
$416$	8.05542	+	13.6995i	0.394950	+	0.671674i
$417$	−12.7125	+	0.902164i	−0.622534	+	0.0441792i
$418$	−0.383634	+	4.00899i	−0.0187642	+	0.196086i
$419$	−8.40525			−0.410623			−0.205312	−	0.978697i	$-0.565821\pi$
$419$	−8.40525			−0.410623			−0.205312	+	0.978697i	$0.565821\pi$
$420$	−2.54102	−	34.2613i	−0.123989	−	1.67178i
$421$	5.22059	+	29.6074i	0.254436	+	1.44298i	0.797516	+	0.603298i	$0.206147\pi$
$421$	5.22059	+	29.6074i	0.254436	+	1.44298i	−0.543080	+	0.839681i	$0.682742\pi$
$422$	−15.1393	−	8.70857i	−0.736968	−	0.423926i
$423$	3.91736	−	4.36882i	0.190469	−	0.212419i
$424$	8.87274	+	24.0203i	0.430899	+	1.16653i
$425$	18.8138	+	10.8622i	0.912604	+	0.526892i
$426$	9.82939	+	10.1253i	0.476235	+	0.490572i
$427$	−6.75531	−	18.5601i	−0.326913	−	0.898185i
$428$	−13.6332	+	11.5137i	−0.658985	+	0.556537i
$429$	−2.63370	+	1.78042i	−0.127156	+	0.0859596i
$430$	−51.1900	−	18.5395i	−2.46860	−	0.894052i
$431$	−2.28945	+	12.9841i	−0.110279	+	0.625423i	0.878701	+	0.477373i	$0.158411\pi$
$431$	−2.28945	+	12.9841i	−0.110279	+	0.625423i	−0.988980	+	0.148050i	$0.952700\pi$
$432$	−20.7641	+	0.922029i	−0.999016	+	0.0443612i
$433$	10.7374	+	9.00974i	0.516006	+	0.432980i	0.863237	−	0.504799i	$-0.168434\pi$
$433$	10.7374	+	9.00974i	0.516006	+	0.432980i	−0.347231	+	0.937780i	$0.612878\pi$
$434$	−13.7435	+	5.02702i	−0.659711	+	0.241305i
$435$	3.49969	−	12.2527i	0.167797	−	0.587472i
$436$	−15.9022	+	5.84532i	−0.761579	+	0.279940i
$437$	−28.0159	+	12.7337i	−1.34018	+	0.609136i
$438$	0.307813	−	0.0776054i	0.0147079	−	0.00370813i
$439$	2.46668	−	6.77715i	0.117728	−	0.323456i	−0.866807	−	0.498644i	$-0.833831\pi$
$439$	2.46668	−	6.77715i	0.117728	−	0.323456i	0.984535	+	0.175189i	$0.0560535\pi$
$440$	−3.89774	−	4.60036i	−0.185817	−	0.219314i
$441$	5.70082	+	3.54588i	0.271467	+	0.168852i
$442$	9.80571	−	11.7238i	0.466410	−	0.557646i
$443$	−3.36520	+	19.0850i	−0.159886	+	0.906756i	0.794297	+	0.607530i	$0.207840\pi$
$443$	−3.36520	+	19.0850i	−0.159886	+	0.906756i	−0.954182	+	0.299226i	$0.903272\pi$
$444$	9.98754	+	1.00717i	0.473988	+	0.0477980i
$445$	−2.40592	−	4.16718i	−0.114052	−	0.197543i
$446$	19.1988	−	11.1252i	0.909091	−	0.526794i
$447$	−24.4058	+	10.8964i	−1.15435	+	0.515384i
$448$	−0.232143	−	24.3140i	−0.0109677	−	1.14873i
$449$	24.5079	+	14.1497i	1.15660	+	0.667764i	0.950487	−	0.310764i	$-0.100585\pi$
$449$	24.5079	+	14.1497i	1.15660	+	0.667764i	0.206114	+	0.978528i	$0.433918\pi$
$450$	−23.7138	+	3.42132i	−1.11788	+	0.161283i
$451$	4.42794	+	5.27702i	0.208504	+	0.248485i
$452$	7.17160	−	19.9006i	0.337324	−	0.936048i
$453$	3.23911	+	12.9343i	0.152186	+	0.607707i
$454$	−0.651628	+	3.73027i	−0.0305824	+	0.175070i
$455$	−27.8624			−1.30621
$456$	16.0612	+	14.0726i	0.752132	+	0.659012i
$457$	0.227042			0.0106206			0.00531030	−	0.999986i	$-0.498310\pi$
$457$	0.227042			0.0106206			0.00531030	+	0.999986i	$0.498310\pi$
$458$	4.54645	−	26.0263i	0.212442	−	1.21613i
$459$	7.54549	+	18.5101i	0.352193	+	0.863978i
$460$	15.6203	−	43.3453i	0.728303	−	2.02098i
$461$	19.4833	+	23.2193i	0.907427	+	1.08143i	0.996348	+	0.0853910i	$0.0272139\pi$
$461$	19.4833	+	23.2193i	0.907427	+	1.08143i	−0.0889202	+	0.996039i	$0.528342\pi$
$462$	4.85113	−	0.352028i	0.225695	−	0.0163778i
$463$	−11.6413	−	6.72110i	−0.541016	−	0.312356i	0.204474	−	0.978872i	$-0.434451\pi$
$463$	−11.6413	−	6.72110i	−0.541016	−	0.312356i	−0.745491	+	0.666516i	$0.767785\pi$
$464$	3.03056	−	8.49423i	0.140690	−	0.394335i
$465$	7.84449	+	17.5701i	0.363780	+	0.814793i
$466$	−14.3223	+	8.29940i	−0.663468	+	0.384462i
$467$	−8.48758	−	14.7009i	−0.392759	−	0.680278i	0.600054	−	0.799960i	$-0.295146\pi$
$467$	−8.48758	−	14.7009i	−0.392759	−	0.680278i	−0.992812	+	0.119682i	$0.961813\pi$
$468$	−0.499797	+	16.8490i	−0.0231031	+	0.778844i
$469$	−4.56568	+	25.8932i	−0.210823	+	1.19564i
$470$	5.79079	−	6.92354i	0.267109	−	0.319359i
$471$	7.25564	−	10.0083i	0.334322	−	0.461158i
$472$	19.9769	−	16.9258i	0.919512	−	0.779072i
$473$	2.63626	−	7.24307i	0.121215	−	0.333037i
$474$	8.45966	+	33.5542i	0.388565	+	1.54120i
$475$	20.0258	+	14.3145i	0.918847	+	0.656796i
$476$	−21.9485	+	8.06779i	−1.00601	+	0.369787i
$477$	−5.59187	+	26.5780i	−0.256034	+	1.21692i
$478$	−10.8952	+	3.98519i	−0.498337	+	0.182278i
$479$	−17.5568	−	14.7319i	−0.802189	−	0.673117i	0.146541	−	0.989205i	$-0.453186\pi$
$479$	−17.5568	−	14.7319i	−0.802189	−	0.673117i	−0.948730	+	0.316088i	$0.897631\pi$
$480$	−31.8717	+	2.51683i	−1.45474	+	0.114877i
$481$	1.41367	−	8.01733i	0.0644579	−	0.365559i
$482$	−8.19695	−	2.96868i	−0.373361	−	0.135220i
$483$	20.8152	+	30.7910i	0.947123	+	1.40104i
$484$	−16.1557	+	13.6441i	−0.734351	+	0.620187i
$485$	−4.38425	−	12.0456i	−0.199079	−	0.546964i
$486$	−19.1660	−	10.8933i	−0.869388	−	0.494130i
$487$	−3.45229	−	1.99318i	−0.156438	−	0.0903195i	0.419737	−	0.907646i	$-0.362122\pi$
$487$	−3.45229	−	1.99318i	−0.156438	−	0.0903195i	−0.576175	+	0.817326i	$0.695455\pi$
$488$	−17.2416	+	6.36882i	−0.780492	+	0.288303i
$489$	−8.68797	+	8.40726i	−0.392884	+	0.380190i
$490$	8.95154	+	5.14920i	0.404389	+	0.232617i
$491$	−3.94193	−	22.3558i	−0.177897	−	1.00890i	−0.934747	−	0.355315i	$-0.884374\pi$
$491$	−3.94193	−	22.3558i	−0.177897	−	1.00890i	0.756850	−	0.653589i	$-0.226737\pi$
$492$	36.4260	−	2.70157i	1.64221	−	0.121796i
$493$	−8.67342			−0.390631
$494$	12.3451	−	12.1458i	0.555433	−	0.546467i
$495$	−0.903161	−	6.33123i	−0.0405941	−	0.284567i
$496$	4.73910	+	12.7671i	0.212792	+	0.573262i
$497$	−17.2440	+	3.04059i	−0.773501	+	0.136389i
$498$	6.07007	+	2.94087i	0.272007	+	0.131783i
$499$	11.1830	+	13.3274i	0.500620	+	0.596616i	0.955885	−	0.293740i	$-0.0948999\pi$
$499$	11.1830	+	13.3274i	0.500620	+	0.596616i	−0.455265	+	0.890356i	$0.650455\pi$
$500$	−4.15749	+	0.746729i	−0.185929	+	0.0333947i
$501$	14.7749	+	7.18728i	0.660093	+	0.321104i
$502$	−27.9568	+	23.5345i	−1.24777	+	1.05040i
$503$	15.5356	−	5.65449i	0.692697	−	0.252121i	0.0284077	−	0.999596i	$-0.490956\pi$
$503$	15.5356	−	5.65449i	0.692697	−	0.252121i	0.664290	+	0.747475i	$0.268734\pi$
$504$	13.5167	−	21.9642i	0.602080	−	0.978364i
$505$	−23.1479	−	40.0934i	−1.03007	−	1.78413i
$506$	6.13310	+	2.22122i	0.272650	+	0.0987453i
$507$	−8.79858	−	0.915564i	−0.390759	−	0.0406616i
$508$	0.537629	+	0.308123i	0.0238534	+	0.0136708i
$509$	25.1975	−	30.0292i	1.11686	−	1.33102i	0.179061	−	0.983838i	$-0.442694\pi$
$509$	25.1975	−	30.0292i	1.11686	−	1.33102i	0.937798	−	0.347182i	$-0.112861\pi$
$510$	12.5797	+	28.0559i	0.557036	+	1.24233i
$511$	−0.134719	+	0.370139i	−0.00595964	+	0.0163740i
$512$	−22.6251	+	0.324040i	−0.999897	+	0.0143207i
$513$	6.47846	+	21.7032i	0.286031	+	0.958220i
$514$	29.4382	−	5.23906i	1.29846	−	0.231085i
$515$	−12.1682	−	4.42885i	−0.536193	−	0.195158i
$516$	−22.9969	−	33.7861i	−1.01238	−	1.48735i
$517$	0.978898	+	0.821393i	0.0430519	+	0.0361248i
$518$	−7.99114	+	9.55430i	−0.351110	+	0.419792i
$519$	−1.43094	+	13.7514i	−0.0628114	+	0.603618i
$520$	0.123775	+	25.9282i	0.00542788	+	1.13703i
$521$	−13.5099	+	7.79995i	−0.591880	+	0.341722i	−0.765840	−	0.643031i	$-0.777677\pi$
$521$	−13.5099	+	7.79995i	−0.591880	+	0.341722i	0.173961	+	0.984753i	$0.444343\pi$
$522$	7.51629	−	5.91681i	0.328979	−	0.258972i
$523$	−1.23099	−	3.38212i	−0.0538275	−	0.147890i	0.909865	−	0.414905i	$-0.136185\pi$
$523$	−1.23099	−	3.38212i	−0.0538275	−	0.147890i	−0.963692	+	0.267015i	$0.913963\pi$
$524$	15.0272	+	12.5281i	0.656467	+	0.547291i
$525$	13.0048	−	26.7340i	0.567576	−	1.16677i
$526$	22.7673	−	0.0362282i	0.992699	−	0.00157962i
$527$	10.0329	−	8.41861i	0.437040	−	0.366720i
$528$	−0.349141	−	4.51281i	−0.0151944	−	0.196395i
$529$	4.66141	+	26.4362i	0.202670	+	1.14940i
$530$	−7.18909	+	41.1542i	−0.312274	+	1.78762i
$531$	27.4931	−	3.92194i	1.19310	−	0.170198i
$532$	−25.6382	+	6.69020i	−1.11156	+	0.290057i
$533$		−	29.6228i		−	1.28310i
$534$	0.368140	−	3.59337i	0.0159310	−	0.155500i
$535$	−28.6713	+	5.05552i	−1.23957	+	0.218569i
$536$	24.1160	+	4.13371i	1.04165	+	0.178549i
$537$	−28.4537	−	29.4037i	−1.22787	−	1.26886i
$538$	−0.0265510	−	16.6857i	−0.00114470	−	0.719374i
$539$	−0.731016	+	1.26616i	−0.0314871	+	0.0545373i
$540$	−30.0404	−	15.7313i	−1.29274	−	0.676969i
$541$	−36.4567	+	13.2692i	−1.56740	+	0.570485i	−0.972416	−	0.233255i	$-0.925062\pi$
$541$	−36.4567	+	13.2692i	−1.56740	+	0.570485i	−0.594980	+	0.803740i	$0.702840\pi$
$542$	−21.0725	+	12.2110i	−0.905143	+	0.524507i
$543$	9.17104	−	6.19976i	0.393567	−	0.266057i
$544$	7.60524	+	20.3890i	0.326072	+	0.874171i
$545$	−27.2219	−	4.79995i	−1.16606	−	0.205607i
$546$	−16.9535	−	12.2495i	−0.725541	−	0.524231i
$547$	−4.86216	+	5.79450i	−0.207891	+	0.247755i	−0.859907	−	0.510450i	$-0.829479\pi$
$547$	−4.86216	+	5.79450i	−0.207891	+	0.247755i	0.652016	+	0.758205i	$0.273923\pi$
$548$	33.2840	−	19.3580i	1.42182	−	0.826933i
$549$	−19.0776	−	4.01382i	−0.814212	−	0.171306i
$550$	−0.914210	−	5.13693i	−0.0389821	−	0.219039i
$551$	−9.78166	−	0.951752i	−0.416713	−	0.0405460i
$552$	28.5610	−	19.5070i	1.21564	−	0.830273i
$553$	−40.3483	−	14.6856i	−1.71578	−	0.624494i
$554$	−33.8859	+	12.3945i	−1.43967	+	0.526594i
$555$	13.2595	+	9.61267i	0.562836	+	0.408035i
$556$	−12.7678	−	7.31743i	−0.541477	−	0.310328i
$557$	4.94767	+	0.872407i	0.209639	+	0.0369651i	0.277481	−	0.960731i	$-0.410500\pi$
$557$	4.94767	+	0.872407i	0.209639	+	0.0369651i	−0.0678421	+	0.997696i	$0.521611\pi$
$558$	−2.95143	+	14.1397i	−0.124944	+	0.598581i
$559$	−28.7051	+	16.5729i	−1.21409	+	0.700958i
$560$	19.6160	−	34.4810i	0.828929	−	1.45709i
$561$	−3.97485	+	1.77465i	−0.167818	+	0.0749257i
$562$	12.3945	+	14.7235i	0.522831	+	0.621075i
$563$	20.1435	−	34.8895i	0.848947	−	1.47042i	−0.0332020	−	0.999449i	$-0.510570\pi$
$563$	20.1435	−	34.8895i	0.848947	−	1.47042i	0.882149	−	0.470971i	$-0.156096\pi$
$564$	6.56743	−	1.66689i	0.276539	−	0.0701889i
$565$	26.4377	−	22.1839i	1.11224	−	0.933282i
$566$	−29.5416	−	16.9932i	−1.24173	−	0.714279i
$567$	24.5362	−	12.0931i	1.03042	−	0.507861i
$568$	2.90612	+	16.0335i	0.121938	+	0.672750i
$569$		−	37.3623i		−	1.56631i	−0.621827	−	0.783154i	$-0.713609\pi$
$569$		−	37.3623i		−	1.56631i	0.621827	−	0.783154i	$-0.286391\pi$
$570$	11.1084	+	33.0211i	0.465279	+	1.38310i
$571$		−	14.6286i		−	0.612190i	−0.952001	−	0.306095i	$-0.900977\pi$
$571$		−	14.6286i		−	0.612190i	0.952001	−	0.306095i	$-0.0990225\pi$
$572$	−3.67082	+	0.0116823i	−0.153485	+	0.000488463i
$573$	3.94625	−	0.988249i	0.164857	−	0.0412847i
$574$	−22.5987	+	39.2864i	−0.943253	+	1.63978i
$575$	30.5420	−	25.6278i	1.27369	−	1.06875i
$576$	−20.4995	−	12.4808i	−0.854147	−	0.520032i
$577$	−0.860500	+	1.49043i	−0.0358231	+	0.0620474i	−0.883381	−	0.468655i	$-0.844739\pi$
$577$	−0.860500	+	1.49043i	−0.0358231	+	0.0620474i	0.847558	+	0.530703i	$0.178072\pi$
$578$	−2.38184	+	2.00507i	−0.0990713	+	0.0833997i
$579$	−9.21503	−	20.6398i	−0.382964	−	0.857761i
$580$	11.2414	−	9.49380i	0.466775	−	0.394209i
$581$	−7.24804	+	4.18466i	−0.300699	+	0.173609i
$582$	2.62810	−	9.25694i	0.108938	−	0.383713i
$583$	−5.82480	−	1.02707i	−0.241238	−	0.0425368i
$584$	0.345042	+	0.123723i	0.0142780	+	0.00511970i
$585$	−14.5252	+	23.3525i	−0.600542	+	0.965508i
$586$	−5.90248	−	16.1370i	−0.243829	−	0.666613i
$587$	−38.8181	−	14.1286i	−1.60219	−	0.583151i	−0.622318	−	0.782764i	$-0.713809\pi$
$587$	−38.8181	−	14.1286i	−1.60219	−	0.583151i	−0.979875	+	0.199614i	$0.936031\pi$
$588$	3.18295	+	7.06864i	0.131263	+	0.291506i
$589$	12.2386	−	8.39336i	0.504284	−	0.345842i
$590$	42.0572	−	7.48484i	1.73147	−	0.308146i
$591$	7.70113	+	2.19964i	0.316782	+	0.0904811i
$592$	8.92655	+	7.39396i	0.366879	+	0.303890i
$593$	19.0591	−	22.7138i	0.782665	−	0.932744i	−0.216385	−	0.976308i	$-0.569427\pi$
$593$	19.0591	−	22.7138i	0.782665	−	0.932744i	0.999051	+	0.0435638i	$0.0138712\pi$
$594$	2.23394	−	4.24944i	0.0916596	−	0.174357i
$595$	−37.5720	−	6.62496i	−1.54030	−	0.271597i
$596$	−30.4106	−	5.26248i	−1.24567	−	0.215560i
$597$	12.1937	+	18.0377i	0.499057	+	0.738233i
$598$	−14.0637	−	24.2698i	−0.575107	−	0.992464i
$599$	−20.0137	+	7.28438i	−0.817736	+	0.297632i	−0.716815	−	0.697263i	$-0.754401\pi$
$599$	−20.0137	+	7.28438i	−0.817736	+	0.297632i	−0.100920	+	0.994894i	$0.532179\pi$
$600$	−24.9359	−	11.9833i	−1.01800	−	0.489214i
$601$	−8.75979	+	15.1724i	−0.357319	+	0.618895i	−0.987512	−	0.157544i	$-0.949642\pi$
$601$	−8.75979	+	15.1724i	−0.357319	+	0.618895i	0.630193	+	0.776439i	$0.282976\pi$
$602$	50.7125	−	0.0806958i	2.06689	−	0.00328892i
$603$	19.3220	+	17.3253i	0.786851	+	0.705541i
$604$	−5.21983	+	14.4846i	−0.212392	+	0.589371i
$605$	−33.9763	+	5.99094i	−1.38133	+	0.243566i
$606$	3.54196	−	34.5726i	0.143882	−	1.40442i
$607$			2.97897i			0.120913i	0.998171	+	0.0604564i	$0.0192556\pi$
$607$			2.97897i			0.120913i	−0.998171	+	0.0604564i	$0.980744\pi$
$608$	6.33967	+	23.8287i	0.257107	+	0.966383i
$609$	0.840218	+	11.8396i	0.0340474	+	0.479765i
$610$	−29.5403	−	5.16029i	−1.19605	−	0.208934i
$611$	−0.954212	−	5.41160i	−0.0386033	−	0.218930i
$612$	−4.68023	+	22.6018i	−0.189187	+	0.913623i
$613$	16.1979	−	13.5917i	0.654228	−	0.548963i	−0.254122	−	0.967172i	$-0.581787\pi$
$613$	16.1979	−	13.5917i	0.654228	−	0.548963i	0.908351	+	0.418209i	$0.137342\pi$
$614$	0.0190376	+	11.9640i	0.000768296	+	0.482829i
$615$	53.5884	+	26.0682i	2.16089	+	1.05117i
$616$	4.87724	+	2.78492i	0.196510	+	0.112208i
$617$	8.90497	+	24.4662i	0.358501	+	0.984973i	0.979550	+	0.201201i	$0.0644845\pi$
$617$	8.90497	+	24.4662i	0.358501	+	0.984973i	−0.621049	+	0.783772i	$0.713293\pi$
$618$	−5.45687	−	8.04449i	−0.219507	−	0.323597i
$619$	−0.493499	+	0.284922i	−0.0198354	+	0.0114520i	−0.509885	−	0.860243i	$-0.670312\pi$
$619$	−0.493499	+	0.284922i	−0.0198354	+	0.0114520i	0.490050	+	0.871695i	$0.336979\pi$
$620$	−3.78853	+	21.8930i	−0.152151	+	0.879245i
$621$	36.6585	−	1.39409i	1.47105	−	0.0559428i
$622$	27.7459	+	23.2064i	1.11251	+	0.930494i
$623$	3.43347	+	2.88102i	0.137559	+	0.115426i
$624$	−11.3239	+	15.8310i	−0.453317	+	0.633747i
$625$	20.0575	+	7.30034i	0.802301	+	0.292014i
$626$	2.25810	+	12.6882i	0.0902519	+	0.507124i
$627$	−4.67747	+	1.56524i	−0.186800	+	0.0625095i
$628$	13.3976	−	4.92466i	0.534621	−	0.196515i
$629$	3.81263	−	10.4751i	0.152020	−	0.417671i
$630$	37.0789	−	19.8897i	1.47726	−	0.792423i
$631$	13.3954	−	15.9640i	0.533263	−	0.635518i	−0.430400	−	0.902638i	$-0.641628\pi$
$631$	13.3954	−	15.9640i	0.533263	−	0.635518i	0.963663	+	0.267120i	$0.0860720\pi$
$632$	−13.4869	+	37.6126i	−0.536479	+	1.49615i
$633$	2.21391	−	21.2757i	0.0879949	−	0.845631i
$634$	8.16189	−	22.5361i	0.324150	−	0.895023i
$635$	0.505494	+	0.875541i	0.0200599	+	0.0347448i
$636$	−22.4675	+	21.8805i	−0.890896	+	0.867619i
$637$	5.90791	−	2.15030i	0.234080	−	0.0851981i
$638$	1.34156	+	1.59365i	0.0531127	+	0.0630931i
$639$	−6.44121	+	16.0380i	−0.254810	+	0.634455i
$640$	−32.1745	−	18.1011i	−1.27181	−	0.715510i
$641$	−4.51590	−	5.38184i	−0.178367	−	0.212570i	0.669452	−	0.742856i	$-0.266529\pi$
$641$	−4.51590	−	5.38184i	−0.178367	−	0.212570i	−0.847819	+	0.530286i	$0.822085\pi$
$642$	−19.6683	−	9.52902i	−0.776246	−	0.376080i
$643$	−7.97336	+	1.40592i	−0.314439	+	0.0554440i	−0.328640	−	0.944455i	$-0.606590\pi$
$643$	−7.97336	+	1.40592i	−0.314439	+	0.0554440i	0.0142018	+	0.999899i	$0.495479\pi$
$644$	0.136580	+	42.9161i	0.00538201	+	1.69113i
$645$	−4.72017	−	66.5125i	−0.185857	−	2.61893i
$646$	19.5352	−	13.4431i	0.768602	−	0.528914i
$647$	−4.63787			−0.182333			−0.0911667	−	0.995836i	$-0.529060\pi$
$647$	−4.63787			−0.182333			−0.0911667	+	0.995836i	$0.529060\pi$
$648$	−11.3626	−	22.7792i	−0.446364	−	0.894851i
$649$	1.05019	+	5.95595i	0.0412237	+	0.233791i
$650$	−11.1876	+	19.4489i	−0.438813	+	0.762848i
$651$	−12.4637	−	12.8798i	−0.488491	−	0.504801i
$652$	−13.7402	+	2.46788i	−0.538108	+	0.0966498i
$653$	20.0746	+	11.5901i	0.785580	+	0.453555i	0.838404	−	0.545049i	$-0.183489\pi$
$653$	20.0746	+	11.5901i	0.785580	+	0.453555i	−0.0528245	+	0.998604i	$0.516822\pi$
$654$	−14.4535	−	14.8886i	−0.565176	−	0.582190i
$655$	10.9172	+	29.9946i	0.426569	+	1.17199i
$656$	36.6596	+	20.8554i	1.43132	+	0.814268i
$657$	0.239996	+	0.305874i	0.00936313	+	0.0119333i
$658$	−2.86293	+	7.90495i	−0.111609	+	0.308167i
$659$	1.05533	−	5.98510i	0.0411100	−	0.233146i	−0.957329	−	0.289001i	$-0.906677\pi$
$659$	1.05533	−	5.98510i	0.0411100	−	0.233146i	0.998439	+	0.0558541i	$0.0177882\pi$
$660$	3.20921	−	6.65090i	0.124918	−	0.258886i
$661$	16.7794	+	14.0796i	0.652643	+	0.547633i	0.907872	−	0.419248i	$-0.137706\pi$
$661$	16.7794	+	14.0796i	0.652643	+	0.547633i	−0.255228	+	0.966881i	$0.582151\pi$
$662$	15.5895	+	42.6207i	0.605903	+	1.65650i
$663$	17.9992	+	5.14103i	0.699030	+	0.199661i
$664$	3.92636	+	6.72629i	0.152372	+	0.261031i
$665$	−41.6458	−	11.5943i	−1.61496	−	0.449608i
$666$	3.84190	+	11.6785i	0.148871	+	0.452534i
$667$	−5.44428	+	14.9580i	−0.210803	+	0.579177i
$668$	9.53827	+	16.4000i	0.369047	+	0.634536i
$669$	22.0026	+	15.9510i	0.850668	+	0.616703i
$670$	30.6208	+	25.6109i	1.18298	+	0.989437i
$671$	0.737225	−	4.18101i	0.0284603	−	0.161406i
$672$	27.0952	−	12.3566i	1.04522	−	0.476668i
$673$	−16.7726	−	29.0509i	−0.646535	−	1.11983i	−0.983945	−	0.178474i	$-0.942884\pi$
$673$	−16.7726	−	29.0509i	−0.646535	−	1.11983i	0.337409	−	0.941358i	$-0.390449\pi$
$674$	−11.3453	−	19.5786i	−0.437004	−	0.754139i
$675$	−15.6271	−	24.8367i	−0.601489	−	0.955967i
$676$	−7.84568	−	6.54087i	−0.301757	−	0.251572i
$677$	−2.79478	−	1.61357i	−0.107412	−	0.0620144i	0.445332	−	0.895366i	$-0.353086\pi$
$677$	−2.79478	−	1.61357i	−0.107412	−	0.0620144i	−0.552744	+	0.833351i	$0.686419\pi$
$678$	25.8396	−	1.87508i	0.992364	−	0.0720120i
$679$	7.67500	+	9.14671i	0.294539	+	0.351018i
$680$	−5.99816	+	34.9932i	−0.230019	+	1.34193i
$681$	−4.49888	+	1.12664i	−0.172398	+	0.0431731i
$682$	−3.09866	−	0.541295i	−0.118654	−	0.0207273i
$683$	6.83061			0.261366			0.130683	−	0.991424i	$-0.458283\pi$
$683$	6.83061			0.261366			0.130683	+	0.991424i	$0.458283\pi$
$684$	−7.75838	+	24.9761i	−0.296649	+	0.954987i
$685$	62.8195			2.40021
$686$	20.1639	+	3.52237i	0.769862	+	0.134485i
$687$	31.3890	−	7.86066i	1.19756	−	0.299903i
$688$	−0.300377	−	47.1917i	−0.0114518	−	1.79917i
$689$	16.3489	+	19.4838i	0.622842	+	0.742275i
$690$	56.2808	−	4.08408i	2.14257	−	0.155478i
$691$	15.0091	+	8.66552i	0.570974	+	0.329652i	0.757538	−	0.652791i	$-0.226402\pi$
$691$	15.0091	+	8.66552i	0.570974	+	0.329652i	−0.186564	+	0.982443i	$0.559735\pi$
$692$	−10.2228	+	12.2621i	−0.388611	+	0.466134i
$693$	2.80753	+	5.25394i	0.106649	+	0.199581i
$694$	−2.94733	−	5.08622i	−0.111879	−	0.193070i
$695$	−12.0047	−	20.7927i	−0.455363	−	0.788712i
$696$	11.0140	−	0.834487i	0.417484	−	0.0316311i
$697$	7.04354	−	39.9459i	0.266793	−	1.51306i
$698$	11.0880	+	9.27390i	0.419686	+	0.351022i
$699$	−16.4139	−	11.8995i	−0.620830	−	0.450079i
$700$	29.6745	−	17.2587i	1.12159	−	0.652319i
$701$	8.96391	−	24.6281i	0.338562	−	0.930192i	−0.647241	−	0.762286i	$-0.724077\pi$
$701$	8.96391	−	24.6281i	0.338562	−	0.930192i	0.985803	−	0.167906i	$-0.0537006\pi$
$702$	−19.1050	+	7.82346i	−0.721071	+	0.295277i
$703$	5.44925	−	11.3952i	0.205522	−	0.429779i
$704$	2.56992	−	4.55104i	0.0968577	−	0.171524i
$705$	10.6295	+	3.03605i	0.400329	+	0.114344i
$706$	7.28824	+	19.9256i	0.274297	+	0.749909i
$707$	33.0342	+	27.7190i	1.24238	+	1.04248i
$708$	28.8813	+	13.9359i	1.08543	+	0.523743i
$709$	−3.23370	+	18.3392i	−0.121444	+	0.688745i	0.861912	+	0.507058i	$0.169267\pi$
$709$	−3.23370	+	18.3392i	−0.121444	+	0.688745i	−0.983356	+	0.181687i	$0.941844\pi$
$710$	−9.05282	+	24.9961i	−0.339746	+	0.938087i
$711$	−33.3429	+	26.1616i	−1.25046	+	0.981137i
$712$	2.66577	−	3.20792i	0.0999040	−	0.120222i
$713$	−8.22096	−	22.5869i	−0.307877	−	0.845886i
$714$	−19.9489	−	20.5494i	−0.746569	−	0.769043i
$715$	−5.18662	−	2.99450i	−0.193969	−	0.111988i
$716$	−8.35234	−	46.5026i	−0.312142	−	1.73788i
$717$	−9.88064	−	10.2105i	−0.368999	−	0.381319i
$718$	−3.70560	+	6.44193i	−0.138292	+	0.240411i
$719$	4.28932	+	24.3259i	0.159965	+	0.907205i	0.954105	+	0.299471i	$0.0968101\pi$
$719$	4.28932	+	24.3259i	0.159965	+	0.907205i	−0.794141	+	0.607734i	$0.792079\pi$
$720$	−18.6736	−	34.4166i	−0.695926	−	1.28263i
$721$	12.0616			0.449199
$722$	23.5064	−	13.0172i	0.874819	−	0.484450i
$723$	−0.755831	−	10.6505i	−0.0281096	−	0.396096i
$724$	12.7825	−	0.0406801i	0.475057	−	0.00151186i
$725$	12.5392	−	2.21101i	0.465695	−	0.0821147i
$726$	−23.3075	−	11.2922i	−0.865023	−	0.419091i
$727$	−8.93073	−	10.6432i	−0.331223	−	0.394736i	0.574571	−	0.818455i	$-0.305169\pi$
$727$	−8.93073	−	10.6432i	−0.331223	−	0.394736i	−0.905794	+	0.423719i	$0.860724\pi$
$728$	−8.36854	−	22.6553i	−0.310159	−	0.839661i
$729$	2.65551	−	26.8691i	0.0983521	−	0.995152i
$730$	0.385138	+	0.457509i	0.0142546	+	0.0169332i
$731$	−42.6490	+	15.5230i	−1.57743	+	0.574138i
$732$	−15.7057	−	16.1271i	−0.580501	−	0.596075i
$733$	16.5298	+	28.6304i	0.610540	+	1.05749i	0.991149	+	0.132751i	$0.0423810\pi$
$733$	16.5298	+	28.6304i	0.610540	+	1.05749i	−0.380609	+	0.924736i	$0.624286\pi$
$734$	−8.15922	+	22.5287i	−0.301162	+	0.831551i
$735$	−1.30904	+	12.5799i	−0.0482846	+	0.464015i
$736$	39.9363	−	0.317748i	1.47207	−	0.0117123i
$737$	−3.63278	+	4.32938i	−0.133815	+	0.159475i
$738$	21.1463	+	39.4216i	0.778407	+	1.45113i
$739$	12.1086	−	33.2681i	0.445423	−	1.22379i	−0.490456	−	0.871466i	$-0.663170\pi$
$739$	12.1086	−	33.2681i	0.445423	−	1.22379i	0.935879	−	0.352323i	$-0.114608\pi$
$740$	6.52446	+	17.7498i	0.239844	+	0.652497i
$741$	19.7349	+	7.77300i	0.724978	+	0.285548i
$742$	−6.81835	−	38.3122i	−0.250310	−	1.40649i
$743$	36.0519	+	13.1218i	1.32262	+	0.481393i	0.904296	−	0.426907i	$-0.140397\pi$
$743$	36.0519	+	13.1218i	1.32262	+	0.481393i	0.418320	+	0.908300i	$0.362619\pi$
$744$	−11.9304	+	11.6557i	−0.437388	+	0.427319i
$745$	−38.5723	−	32.3660i	−1.41318	−	1.18580i
$746$	−12.8195	−	10.7221i	−0.469356	−	0.392566i
$747$	−0.271214	+	8.25640i	−0.00992320	+	0.302086i
$748$	−4.95283	−	0.857074i	−0.181093	−	0.0313377i
$749$	23.4852	−	13.5592i	0.858129	−	0.495441i
$750$	−2.90415	−	4.28129i	−0.106045	−	0.156331i
$751$	15.9279	+	43.7615i	0.581216	+	1.59688i	0.786105	+	0.618093i	$0.212095\pi$
$751$	15.9279	+	43.7615i	0.581216	+	1.59688i	−0.204889	+	0.978785i	$0.565683\pi$
$752$	7.36891	+	2.62907i	0.268717	+	0.0958724i
$753$	−40.2476	−	19.5785i	−1.46670	−	0.713481i
$754$	−0.0142543	−	8.95797i	−0.000519110	−	0.326230i
$755$	−19.2426	+	16.1465i	−0.700310	+	0.587630i
$756$	31.3059	+	4.19923i	1.13858	+	0.152724i
$757$	−6.05933	−	34.3642i	−0.220230	−	1.24899i	−0.871597	−	0.490224i	$-0.836915\pi$
$757$	−6.05933	−	34.3642i	−0.220230	−	1.24899i	0.651366	−	0.758763i	$-0.274196\pi$
$758$	−13.0891	−	2.28649i	−0.475417	−	0.0830491i
$759$	0.565526	+	7.96890i	0.0205273	+	0.289253i
$760$	−10.6044	+	38.8063i	−0.384664	+	1.40765i
$761$		−	30.6269i		−	1.11022i	−0.831776	−	0.555111i	$-0.812676\pi$
$761$		−	30.6269i		−	1.11022i	0.831776	−	0.555111i	$-0.187324\pi$
$762$	−0.0773477	+	0.754980i	−0.00280201	+	0.0273500i
$763$	25.3563	−	4.47099i	0.917959	−	0.161861i
$764$	4.41925	+	1.59257i	0.159883	+	0.0576170i
$765$	−25.1397	+	28.0369i	−0.908926	+	1.01368i
$766$	−47.0812	+	0.0749175i	−1.70111	+	0.00270688i
$767$	13.0035	−	22.5227i	0.469529	−	0.813249i
$768$	−11.6192	−	25.1594i	−0.419272	−	0.907861i
$769$	−9.16571	+	3.33605i	−0.330524	+	0.120301i	−0.501951	−	0.864896i	$-0.667384\pi$
$769$	−9.16571	+	3.33605i	−0.330524	+	0.120301i	0.171427	+	0.985197i	$0.445162\pi$
$770$	4.59417	+	7.92817i	0.165562	+	0.285711i
$771$	20.5095	+	30.3388i	0.738631	+	1.09263i
$772$	4.45044	−	25.7181i	0.160175	−	0.925613i
$773$	5.56522	+	0.981298i	0.200167	+	0.0352948i	0.272833	−	0.962062i	$-0.412039\pi$
$773$	5.56522	+	0.981298i	0.200167	+	0.0352948i	−0.0726656	+	0.997356i	$0.523151\pi$
$774$	26.3697	−	42.5462i	0.947841	−	1.52929i
$775$	−12.3586	+	14.7284i	−0.443934	+	0.529060i
$776$	8.47766	−	7.18284i	0.304330	−	0.257849i
$777$	−14.6684	−	4.18967i	−0.526225	−	0.150303i
$778$	−19.2846	+	3.43204i	−0.691385	+	0.123045i
$779$	12.3269	−	44.2771i	0.441656	−	1.58639i
$780$	−28.9556	+	13.0385i	−1.03678	+	0.466852i
$781$	−3.53679	−	1.28729i	−0.126556	−	0.0460628i
$782$	−13.1940	−	36.0714i	−0.471816	−	1.28991i
$783$	10.3613	+	5.46800i	0.370282	+	0.195410i
$784$	−1.49827	+	8.82521i	−0.0535096	+	0.315186i
$785$	22.9343	+	4.04394i	0.818561	+	0.144334i
$786$	−6.54418	+	23.0506i	−0.233423	+	0.822186i
$787$	−28.6722	+	16.5539i	−1.02205	+	0.590083i	−0.914698	−	0.404138i	$-0.867572\pi$
$787$	−28.6722	+	16.5539i	−1.02205	+	0.590083i	−0.107355	+	0.994221i	$0.534238\pi$
$788$	5.96709	+	7.06551i	0.212569	+	0.251699i
$789$	11.3678	+	25.4617i	0.404706	+	0.906459i
$790$	−49.8724	+	41.9833i	−1.77438	+	1.49370i
$791$	−16.0734	+	27.8399i	−0.571503	+	0.989872i
$792$	4.87674	−	2.63598i	0.173288	−	0.0936653i
$793$	−13.9854	+	11.7351i	−0.496636	+	0.416727i
$794$	−0.699570	+	1.21616i	−0.0248268	+	0.0431597i
$795$	−49.6339	+	12.4297i	−1.76033	+	0.440836i
$796$	0.0800100	+	25.1407i	0.00283588	+	0.891088i
$797$			29.5333i			1.04612i	0.852295	+	0.523061i	$0.175210\pi$
$797$			29.5333i			1.04612i	−0.852295	+	0.523061i	$0.824790\pi$
$798$	−20.2429	−	25.3642i	−0.716592	−	0.897882i
$799$		−	7.52437i		−	0.266193i
$800$	−16.1925	−	27.5378i	−0.572490	−	0.973610i
$801$	4.20463	−	1.37579i	0.148563	−	0.0486113i
$802$	−21.4433	−	12.3349i	−0.757190	−	0.435559i
$803$	−0.0648588	+	0.0544230i	−0.00228882	+	0.00192055i
$804$	7.37217	+	29.0458i	0.259996	+	1.02437i
$805$	−35.0091	+	60.6376i	−1.23391	+	2.13719i
$806$	8.71128	+	10.3482i	0.306842	+	0.364500i
$807$	18.6604	−	8.33131i	0.656878	−	0.293276i
$808$	25.6480	−	30.8641i	0.902293	−	1.08580i
$809$	−28.4311	+	16.4147i	−0.999585	+	0.577111i	−0.908125	−	0.418698i	$-0.862486\pi$
$809$	−28.4311	+	16.4147i	−0.999585	+	0.577111i	−0.0914593	+	0.995809i	$0.529153\pi$
$810$	2.65964	−	41.4461i	0.0934501	−	1.45627i
$811$	−30.5273	−	5.38278i	−1.07196	−	0.189015i	−0.390301	−	0.920687i	$-0.627629\pi$
$811$	−30.5273	−	5.38278i	−1.07196	−	0.189015i	−0.681657	+	0.731672i	$0.738740\pi$
$812$	−6.81499	+	11.8911i	−0.239159	+	0.417297i
$813$	−24.1499	−	17.5078i	−0.846974	−	0.614024i
$814$	−2.51441	+	0.919704i	−0.0881300	+	0.0322356i
$815$	−21.4024	−	7.78984i	−0.749694	−	0.272866i
$816$	−19.0343	+	18.6554i	−0.666333	+	0.653068i
$817$	−49.8018	+	12.8264i	−1.74235	+	0.448741i
$818$	1.14742	+	6.44734i	0.0401187	+	0.225426i
$819$	5.27411	−	25.0677i	0.184292	−	0.875937i
$820$	34.5952	+	59.4827i	1.20812	+	2.07723i
$821$	−32.0878	+	38.2408i	−1.11987	+	1.33461i	−0.183736	+	0.982976i	$0.558819\pi$
$821$	−32.0878	+	38.2408i	−1.11987	+	1.33461i	−0.936137	+	0.351637i	$0.885625\pi$
$822$	38.2239	+	27.6182i	1.33321	+	0.963296i
$823$	−7.61161	−	1.34213i	−0.265324	−	0.0467838i	0.0394033	−	0.999223i	$-0.487454\pi$
$823$	−7.61161	−	1.34213i	−0.265324	−	0.0467838i	−0.304728	+	0.952440i	$0.598565\pi$
$824$	−0.0535822	−	11.2243i	−0.00186662	−	0.391018i
$825$	5.29409	−	3.57888i	0.184316	−	0.124601i
$826$	−34.4278	+	19.9500i	−1.19790	+	0.694150i
$827$	50.3256	−	18.3170i	1.74999	−	0.636946i	0.750286	−	0.661113i	$-0.229916\pi$
$827$	50.3256	−	18.3170i	1.74999	−	0.636946i	0.999708	+	0.0241671i	$0.00769339\pi$
$828$	36.0409	+	22.2585i	1.25251	+	0.773536i
$829$	11.3383	−	19.6386i	0.393796	−	0.682075i	−0.599150	−	0.800637i	$-0.704495\pi$
$829$	11.3383	−	19.6386i	0.393796	−	0.682075i	0.992947	+	0.118561i	$0.0378282\pi$
$830$	0.0202196	+	12.7068i	0.000701833	+	0.441060i
$831$	−30.7303	−	31.7563i	−1.06602	−	1.10161i
$832$	−21.0454	+	7.88825i	−0.729618	+	0.273476i
$833$	8.47803	−	1.49491i	0.293746	−	0.0517954i
$834$	1.83688	−	17.9296i	0.0636061	−	0.620850i
$835$			30.9530i			1.07117i
$836$	−5.49163	−	1.51007i	−0.189932	−	0.0522269i
$837$	−17.2927	+	3.73181i	−0.597722	+	0.128990i
$838$	2.04549	−	11.7095i	0.0706604	−	0.404498i
$839$	−2.15188	−	12.2039i	−0.0742910	−	0.421325i	−0.999158	−	0.0410340i	$-0.986935\pi$
$839$	−2.15188	−	12.2039i	−0.0742910	−	0.421325i	0.924867	−	0.380291i	$-0.124176\pi$
$840$	48.3484	+	4.79786i	1.66818	+	0.165542i
$841$	18.3211	−	15.3732i	0.631762	−	0.530111i
$842$	−42.5171	+	0.0676550i	−1.46524	+	0.00233154i
$843$	−10.3111	+	21.1965i	−0.355133	+	0.730046i
$844$	15.8163	−	18.9715i	0.544421	−	0.653025i
$845$	−5.69982	−	15.6601i	−0.196080	−	0.538725i
$846$	5.13295	+	6.52053i	0.176474	+	0.224181i
$847$	27.8306	−	16.0680i	0.956270	−	0.552103i
$848$	−35.6223	+	6.51522i	−1.22328	+	0.223734i
$849$	4.32005	−	41.5157i	0.148264	−	1.42481i
$850$	−19.7108	+	23.5664i	−0.676074	+	0.808322i
$851$	−15.6720	−	13.1504i	−0.537231	−	0.450790i
$852$	−16.4978	+	11.2294i	−0.565205	+	0.384713i
$853$	17.8293	+	6.48933i	0.610463	+	0.222190i	0.628706	−	0.777643i	$-0.283585\pi$
$853$	17.8293	+	6.48933i	0.610463	+	0.222190i	−0.0182428	+	0.999834i	$0.505807\pi$
$854$	27.5003	−	4.89418i	0.941042	−	0.167476i
$855$	−31.4284	+	28.8606i	−1.07483	+	0.987013i
$856$	−12.7222	−	21.7946i	−0.434837	−	0.744924i
$857$	−4.46342	+	12.2632i	−0.152468	+	0.418901i	−0.992287	−	0.123965i	$-0.960439\pi$
$857$	−4.46342	+	12.2632i	−0.152468	+	0.418901i	0.839819	+	0.542867i	$0.182661\pi$
$858$	−1.83940	−	4.10234i	−0.0627961	−	0.140052i
$859$	12.5117	−	14.9109i	0.426894	−	0.508753i	−0.509129	−	0.860690i	$-0.670032\pi$
$859$	12.5117	−	14.9109i	0.426894	−	0.508753i	0.936024	+	0.351937i	$0.114477\pi$
$860$	38.2852	−	66.8020i	1.30551	−	2.27793i
$861$	−55.2103	−	5.74509i	−1.88156	−	0.195792i
$862$	−17.5313	−	6.34928i	−0.597117	−	0.216257i
$863$	−13.5776	−	23.5171i	−0.462188	−	0.800532i	0.536882	−	0.843657i	$-0.319602\pi$
$863$	−13.5776	−	23.5171i	−0.462188	−	0.800532i	−0.999070	+	0.0431249i	$0.986269\pi$
$864$	3.76865	−	29.1513i	0.128212	−	0.991747i
$865$	−24.4753	+	8.90829i	−0.832186	+	0.302891i
$866$	−15.1647	+	12.7658i	−0.515316	+	0.433801i
$867$	−3.42897	−	1.66803i	−0.116454	−	0.0566493i
$868$	−3.65862	−	20.3697i	−0.124182	−	0.691394i
$869$	−5.93257	−	7.07016i	−0.201249	−	0.239839i
$870$	16.2178	+	7.85728i	0.549834	+	0.266387i
$871$	23.9339	−	4.22019i	0.810970	−	0.142996i
$872$	−4.27326	−	23.5762i	−0.144711	−	0.798391i
$873$	11.6673	−	1.66437i	0.394880	−	0.0563303i
$874$	−10.9216	−	42.1283i	−0.369430	−	1.42501i
$875$	6.41922			0.217009
$876$	0.0332045	+	0.447705i	0.00112187	+	0.0151266i
$877$	−1.15649	−	6.55877i	−0.0390519	−	0.221474i	0.959036	−	0.283284i	$-0.0914239\pi$
$877$	−1.15649	−	6.55877i	−0.0390519	−	0.221474i	−0.998088	+	0.0618098i	$0.980313\pi$
$878$	8.84108	+	5.08566i	0.298372	+	0.171633i
$879$	15.1229	−	14.6342i	0.510081	−	0.493601i
$880$	7.35739	−	4.31046i	0.248018	−	0.145306i
$881$	24.4643	+	14.1245i	0.824223	+	0.475865i	0.851870	−	0.523753i	$-0.175468\pi$
$881$	24.4643	+	14.1245i	0.824223	+	0.475865i	−0.0276479	+	0.999618i	$0.508802\pi$
$882$	−6.32718	+	7.07898i	−0.213047	+	0.238362i
$883$	3.65339	+	10.0376i	0.122946	+	0.337793i	0.985863	−	0.167554i	$-0.0535869\pi$
$883$	3.65339	+	10.0376i	0.122946	+	0.337793i	−0.862916	+	0.505347i	$0.831365\pi$
$884$	13.9464	+	16.5136i	0.469067	+	0.555413i
$885$	29.3011	+	43.3439i	0.984946	+	1.45699i
$886$	−25.7687	−	9.33263i	−0.865717	−	0.313536i
$887$	6.21498	−	35.2469i	0.208679	−	1.18348i	−0.682866	−	0.730543i	$-0.739267\pi$
$887$	6.21498	−	35.2469i	0.208679	−	1.18348i	0.891545	−	0.452932i	$-0.149622\pi$
$888$	−3.83366	+	13.6687i	−0.128649	+	0.458692i
$889$	−0.721385	−	0.605314i	−0.0241945	−	0.0203016i
$890$	6.39088	−	2.33761i	0.214223	−	0.0783570i
$891$	5.86715	+	0.385876i	0.196557	+	0.0129273i
$892$	10.8265	+	29.4536i	0.362499	+	0.986181i
$893$	0.825664	−	8.48579i	0.0276298	−	0.283966i
$894$	−9.24064	−	36.6519i	−0.309053	−	1.22582i
$895$	26.3640	−	72.4346i	0.881253	−	2.42122i
$896$	33.9287	+	5.59363i	1.13348	+	0.186870i
$897$	20.1641	−	27.8140i	0.673261	−	0.928683i
$898$	−25.6764	+	30.6990i	−0.856831	+	1.02444i
$899$	1.33296	−	7.55958i	0.0444566	−	0.252126i
$900$	1.00466	−	33.8686i	0.0334886	−	1.12895i
$901$	17.4135	+	30.1610i	0.580127	+	1.00481i
$902$	−8.42908	+	4.88443i	−0.280658	+	0.162634i
$903$	25.3211	+	56.7141i	0.842633	+	1.88733i
$904$	25.9787	+	14.8339i	0.864037	+	0.493368i
$905$	18.0608	+	10.4274i	0.600361	+	0.346619i
$906$	−18.8073	+	1.36477i	−0.624830	+	0.0453415i
$907$	19.7743	+	23.5661i	0.656596	+	0.782501i	0.986893	−	0.161376i	$-0.0515933\pi$
$907$	19.7743	+	23.5661i	0.656596	+	0.782501i	−0.330297	+	0.943877i	$0.607149\pi$
$908$	−5.03812	−	1.81559i	−0.167196	−	0.0602525i
$909$	40.4537	−	13.2368i	1.34176	−	0.439037i
$910$	6.78056	−	38.8155i	0.224773	−	1.28672i
$911$	−22.5055			−0.745639			−0.372820	−	0.927904i	$-0.621609\pi$
$911$	−22.5055			−0.745639			−0.372820	+	0.927904i	$0.621609\pi$
$912$	−23.5135	+	18.9504i	−0.778609	+	0.627509i
$913$	−1.79898			−0.0595375
$914$	−0.0552529	+	0.316297i	−0.00182760	+	0.0104622i
$915$	−8.92198	−	35.6270i	−0.294951	−	1.17779i
$916$	35.1513	+	12.6675i	1.16143	+	0.418545i
$917$	−19.1114	−	22.7761i	−0.631114	−	0.752132i
$918$	−27.6230	+	6.00715i	−0.911696	+	0.198266i
$919$	26.5104	+	15.3058i	0.874499	+	0.504892i	0.868841	−	0.495092i	$-0.164866\pi$
$919$	26.5104	+	15.3058i	0.874499	+	0.504892i	0.00565818	+	0.999984i	$0.498199\pi$
$920$	56.5837	+	32.3094i	1.86551	+	1.06521i
$921$	−13.3799	+	5.97372i	−0.440883	+	0.196841i
$922$	−37.0886	+	21.4919i	−1.22145	+	0.707798i
$923$	8.09254	+	14.0167i	0.266369	+	0.461365i
$924$	−0.690151	+	6.84387i	−0.0227043	+	0.225147i
$925$	−2.84167	+	16.1159i	−0.0934334	+	0.529887i
$926$	12.1963	−	14.5820i	0.400795	−	0.479195i
$927$	6.28796	−	10.1093i	0.206524	−	0.332034i
$928$	11.0959	+	6.28907i	0.364242	+	0.206449i
$929$	6.13485	−	16.8554i	0.201278	−	0.553006i	−0.797452	−	0.603382i	$-0.793820\pi$
$929$	6.13485	−	16.8554i	0.201278	−	0.553006i	0.998730	+	0.0503753i	$0.0160417\pi$
$930$	−26.3862	+	6.65246i	−0.865238	+	0.218143i
$931$	9.72534	−	0.755605i	0.318735	−	0.0247640i
$932$	−8.07657	−	21.9724i	−0.264557	−	0.719729i
$933$	−12.1669	+	42.5973i	−0.398326	+	1.39457i
$934$	22.5456	−	8.24660i	0.737716	−	0.269837i
$935$	−6.28208	−	5.27129i	−0.205446	−	0.172390i
$936$	−23.3510	−	4.79663i	−0.763250	−	0.156783i
$937$	−3.92460	+	22.2575i	−0.128211	+	0.727121i	0.851138	+	0.524943i	$0.175913\pi$
$937$	−3.92460	+	22.2575i	−0.128211	+	0.727121i	−0.979349	+	0.202179i	$0.935198\pi$
$938$	−34.9612	−	12.6619i	−1.14152	−	0.413425i
$939$	−13.0764	+	8.83985i	−0.426732	+	0.288478i
$940$	8.23606	+	9.75216i	0.268631	+	0.318080i
$941$	2.86540	+	7.87263i	0.0934094	+	0.256640i	0.977595	−	0.210496i	$-0.0675079\pi$
$941$	2.86540	+	7.87263i	0.0934094	+	0.256640i	−0.884185	+	0.467136i	$0.845286\pi$
$942$	12.1770	+	12.5436i	0.396748	+	0.408692i
$943$	−64.4688	−	37.2211i	−2.09939	−	1.21208i
$944$	18.7180	+	31.9492i	0.609220	+	1.03986i
$945$	40.7070	+	31.6008i	1.32420	+	1.02797i
$946$	9.44889	+	5.43529i	0.307210	+	0.176716i
$947$	−3.26107	−	18.4944i	−0.105970	−	0.600988i	−0.990828	−	0.135127i	$-0.956856\pi$
$947$	−3.26107	−	18.4944i	−0.105970	−	0.600988i	0.884858	−	0.465861i	$-0.154255\pi$
$948$	−48.8037	+	3.61957i	−1.58507	+	0.117558i
$949$	0.364087			0.0118188
$950$	−24.8153	+	24.4147i	−0.805115	+	0.792118i
$951$	29.2817	−	2.07803i	0.949526	−	0.0673847i
$952$	−5.89802	−	32.5402i	−0.191156	−	1.05463i
$953$	−5.06668	+	0.893392i	−0.164126	+	0.0289398i	−0.255107	−	0.966913i	$-0.582111\pi$
$953$	−5.06668	+	0.893392i	−0.164126	+	0.0289398i	0.0909813	+	0.995853i	$0.471000\pi$
$954$	−35.6655	−	14.2581i	−1.15471	−	0.461624i
$955$	4.92627	+	5.87090i	0.159410	+	0.189978i
$956$	−2.90038	−	16.1482i	−0.0938050	−	0.522269i
$957$	−1.11605	+	2.29427i	−0.0360768	+	0.0741631i
$958$	24.7958	−	20.8735i	0.801117	−	0.674392i
$959$	−54.9854	+	20.0130i	−1.77557	+	0.646255i
$960$	4.25002	−	45.0135i	0.137169	−	1.45280i
$961$	−9.70440	−	16.8085i	−0.313045	−	0.542210i
$962$	10.8250	+	3.92050i	0.349014	+	0.126402i
$963$	0.878790	−	26.7525i	0.0283186	−	0.862086i
$964$	6.13052	−	10.6969i	0.197451	−	0.344522i
$965$	27.3717	−	32.6203i	0.881126	−	1.05008i
$966$	−47.9610	+	21.5047i	−1.54312	+	0.691903i
$967$	1.25521	−	3.44866i	0.0403648	−	0.110901i	−0.917873	−	0.396875i	$-0.870095\pi$
$967$	1.25521	−	3.44866i	0.0403648	−	0.110901i	0.958238	+	0.285974i	$0.0923169\pi$
$968$	−15.0762	−	25.8272i	−0.484567	−	0.830118i
$969$	24.7640	+	15.1742i	0.795534	+	0.487467i
$970$	17.8479	−	3.17636i	0.573063	−	0.101987i
$971$	−8.41235	−	3.06185i	−0.269965	−	0.0982593i	0.203490	−	0.979077i	$-0.434771\pi$
$971$	−8.41235	−	3.06185i	−0.269965	−	0.0982593i	−0.473456	+	0.880818i	$0.656994\pi$
$972$	19.8399	−	24.0495i	0.636364	−	0.771389i
$973$	17.1317	+	14.3752i	0.549218	+	0.460849i
$974$	3.61688	−	4.32438i	0.115892	−	0.138562i
$975$	−27.3321	−	2.84413i	−0.875327	−	0.0910849i
$976$	−4.67660	−	25.5695i	−0.149694	−	0.818461i
$977$	−19.6548	+	11.3477i	−0.628813	+	0.363046i	−0.780292	−	0.625415i	$-0.784930\pi$
$977$	−19.6548	+	11.3477i	−0.628813	+	0.363046i	0.151479	+	0.988460i	$0.451596\pi$
$978$	−9.59801	−	14.1493i	−0.306911	−	0.452446i
$979$	0.329509	+	0.905318i	0.0105311	+	0.0289341i
$980$	−9.35188	+	11.2174i	−0.298735	+	0.358328i
$981$	9.47138	−	23.5829i	0.302398	−	0.752944i
$982$	32.1036	−	0.0510845i	1.02447	−	0.00163017i
$983$	6.87084	−	5.76532i	0.219146	−	0.183885i	−0.526605	−	0.850110i	$-0.676535\pi$
$983$	6.87084	−	5.76532i	0.219146	−	0.183885i	0.745751	+	0.666225i	$0.232091\pi$
$984$	−5.10100	+	51.4032i	−0.162614	+	1.63867i
$985$	2.62007	+	14.8591i	0.0834823	+	0.473452i
$986$	2.11076	−	12.0831i	0.0672202	−	0.384804i
$987$	−10.2711	+	0.728906i	−0.326933	+	0.0232013i
$988$	13.9163	+	20.1540i	0.442736	+	0.641184i
$989$			83.2954i			2.64864i
$990$	9.03993	+	0.282553i	0.287308	+	0.00898012i
$991$	−11.1764	+	1.97069i	−0.355029	+	0.0626011i	−0.348318	−	0.937376i	$-0.613247\pi$
$991$	−11.1764	+	1.97069i	−0.355029	+	0.0626011i	−0.00671047	+	0.999977i	$0.502136\pi$
$992$	−18.9394	+	3.49513i	−0.601328	+	0.110970i
$993$	−39.9422	+	38.6517i	−1.26753	+	1.22657i
$994$	−0.0394038	−	24.7629i	−0.00124981	−	0.785433i
$995$	−20.5087	+	35.5221i	−0.650170	+	1.12613i
$996$	−5.57418	+	7.74064i	−0.176625	+	0.245272i
$997$	36.8274	−	13.4041i	1.16634	−	0.424511i	0.314979	−	0.949099i	$-0.398003\pi$
$997$	36.8274	−	13.4041i	1.16634	−	0.424511i	0.851357	+	0.524587i	$0.175780\pi$
$998$	−21.2881	+	12.3359i	−0.673864	+	0.390486i
$999$	−11.1584	+	10.1100i	−0.353037	+	0.319866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.v.a.23.18	yes	216
3.2	odd	2	inner	228.2.v.a.23.19	yes	216
4.3	odd	2	inner	228.2.v.a.23.11	✓	216
12.11	even	2	inner	228.2.v.a.23.26	yes	216
19.5	even	9	inner	228.2.v.a.119.26	yes	216
57.5	odd	18	inner	228.2.v.a.119.11	yes	216
76.43	odd	18	inner	228.2.v.a.119.19	yes	216
228.119	even	18	inner	228.2.v.a.119.18	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.v.a.23.11	✓	216	4.3	odd	2	inner
228.2.v.a.23.18	yes	216	1.1	even	1	trivial
228.2.v.a.23.19	yes	216	3.2	odd	2	inner
228.2.v.a.23.26	yes	216	12.11	even	2	inner
228.2.v.a.119.11	yes	216	57.5	odd	18	inner
228.2.v.a.119.18	yes	216	228.119	even	18	inner
228.2.v.a.119.19	yes	216	76.43	odd	18	inner
228.2.v.a.119.26	yes	216	19.5	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.243359 + 1.39312i) q^{2} +(-1.68017 + 0.420760i) q^{3} +(-1.88155 - 0.678056i) q^{4} +(-2.09742 - 2.49961i) q^{5} +(-0.177284 - 2.44307i) q^{6} +(2.63219 + 1.51969i) q^{7} +(1.40250 - 2.45621i) q^{8} +(2.64592 - 1.41389i) q^{9} +O(q^{10})\)	\(q+(-0.243359 + 1.39312i) q^{2} +(-1.68017 + 0.420760i) q^{3} +(-1.88155 - 0.678056i) q^{4} +(-2.09742 - 2.49961i) q^{5} +(-0.177284 - 2.44307i) q^{6} +(2.63219 + 1.51969i) q^{7} +(1.40250 - 2.45621i) q^{8} +(2.64592 - 1.41389i) q^{9} +(3.99268 - 2.31366i) q^{10} +(0.326657 + 0.565787i) q^{11} +(3.44662 + 0.347565i) q^{12} +(0.487847 - 2.76672i) q^{13} +(-2.75768 + 3.29711i) q^{14} +(4.57576 + 3.31726i) q^{15} +(3.08048 + 2.55160i) q^{16} +(1.31571 - 3.61488i) q^{17} +(1.32581 + 4.03016i) q^{18} +(1.88049 - 3.93240i) q^{19} +(2.25154 + 6.12533i) q^{20} +(-5.06194 - 1.44582i) q^{21} +(-0.867702 + 0.317382i) q^{22} +(-5.40830 - 4.53810i) q^{23} +(-1.32297 + 4.71697i) q^{24} +(-0.980636 + 5.56146i) q^{25} +(3.73564 + 1.35293i) q^{26} +(-3.85068 + 3.48887i) q^{27} +(-3.92216 - 4.64415i) q^{28} +(-0.771141 - 2.11869i) q^{29} +(-5.73488 + 5.56729i) q^{30} +(2.94846 + 1.70229i) q^{31} +(-4.30433 + 3.67052i) q^{32} +(-0.786899 - 0.813172i) q^{33} +(4.71577 + 2.71265i) q^{34} +(-1.72217 - 9.76689i) q^{35} +(-5.93714 + 0.866232i) q^{36} +2.89778 q^{37} +(5.02066 + 3.57673i) q^{38} +(0.344459 + 4.85381i) q^{39} +(-9.08123 + 1.64600i) q^{40} +(10.3840 - 1.83098i) q^{41} +(3.24607 - 6.70002i) q^{42} +(-7.58372 - 9.03792i) q^{43} +(-0.230988 - 1.28605i) q^{44} +(-9.08381 - 3.64825i) q^{45} +(7.63826 - 6.43000i) q^{46} +(1.83801 - 0.668980i) q^{47} +(-6.24933 - 2.99096i) q^{48} +(1.11894 + 1.93805i) q^{49} +(-7.50913 - 2.71957i) q^{50} +(-0.689615 + 6.62721i) q^{51} +(-2.79390 + 4.87493i) q^{52} +(-5.81935 + 6.93523i) q^{53} +(-3.92331 - 6.21350i) q^{54} +(0.729109 - 2.00321i) q^{55} +(7.42434 - 4.33383i) q^{56} +(-1.50495 + 7.39832i) q^{57} +(3.13925 - 0.558687i) q^{58} +(8.69888 + 3.16613i) q^{59} +(-6.36025 - 9.34421i) q^{60} +(-4.97808 - 4.17711i) q^{61} +(-3.08903 + 3.69328i) q^{62} +(9.11324 + 0.299360i) q^{63} +(-4.06596 - 6.88970i) q^{64} +(-7.93894 + 4.58355i) q^{65} +(1.32434 - 0.898350i) q^{66} +(2.95870 + 8.12896i) q^{67} +(-4.92667 + 5.90947i) q^{68} +(10.9963 + 5.34917i) q^{69} +(14.0255 - 0.0223180i) q^{70} +(-4.41322 + 3.70313i) q^{71} +(0.238095 - 8.48194i) q^{72} +(0.0225042 + 0.127627i) q^{73} +(-0.705201 + 4.03694i) q^{74} +(-0.692408 - 9.75680i) q^{75} +(-6.20463 + 6.12393i) q^{76} +1.98567i q^{77} +(-6.84576 - 0.701348i) q^{78} +(-13.9125 + 2.45315i) q^{79} +(-0.0830752 - 13.0518i) q^{80} +(5.00181 - 7.48210i) q^{81} +(0.0237281 + 14.9117i) q^{82} +(-1.37681 + 2.38470i) q^{83} +(8.54396 + 6.15266i) q^{84} +(-11.7954 + 4.29318i) q^{85} +(14.4365 - 8.36555i) q^{86} +(2.18711 + 3.23529i) q^{87} +(1.84783 - 0.00882109i) q^{88} +(1.45226 + 0.256073i) q^{89} +(7.29307 - 11.7670i) q^{90} +(5.48866 - 6.54113i) q^{91} +(7.09891 + 12.2058i) q^{92} +(-5.67016 - 1.61954i) q^{93} +(0.484672 + 2.72336i) q^{94} +(-13.7737 + 3.54740i) q^{95} +(5.68760 - 7.97817i) q^{96} +(3.69157 + 1.34362i) q^{97} +(-2.97224 + 1.08717i) q^{98} +(1.66427 + 1.03517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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