LMFDB - Embedded newform 228.2.v.a.23.19

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			23.19
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.243359 - 1.39312i) q^{2} +(-1.72275 + 0.179266i) q^{3} +(-1.88155 - 0.678056i) q^{4} +(2.09742 + 2.49961i) q^{5} +(-0.169508 + 2.44362i) q^{6} +(2.63219 + 1.51969i) q^{7} +(-1.40250 + 2.45621i) q^{8} +(2.93573 - 0.617661i) q^{9} +O(q^{10})$	\(q+(0.243359 - 1.39312i) q^{2} +(-1.72275 + 0.179266i) q^{3} +(-1.88155 - 0.678056i) q^{4} +(2.09742 + 2.49961i) q^{5} +(-0.169508 + 2.44362i) q^{6} +(2.63219 + 1.51969i) q^{7} +(-1.40250 + 2.45621i) q^{8} +(2.93573 - 0.617661i) q^{9} +(3.99268 - 2.31366i) q^{10} +(-0.326657 - 0.565787i) q^{11} +(3.36300 + 0.830821i) q^{12} +(0.487847 - 2.76672i) q^{13} +(2.75768 - 3.29711i) q^{14} +(-4.06143 - 3.93021i) q^{15} +(3.08048 + 2.55160i) q^{16} +(-1.31571 + 3.61488i) q^{17} +(-0.146038 - 4.24013i) q^{18} +(1.88049 - 3.93240i) q^{19} +(-2.25154 - 6.12533i) q^{20} +(-4.80702 - 2.14619i) q^{21} +(-0.867702 + 0.317382i) q^{22} +(5.40830 + 4.53810i) q^{23} +(1.97585 - 4.48286i) q^{24} +(-0.980636 + 5.56146i) q^{25} +(-3.73564 - 1.35293i) q^{26} +(-4.94680 + 1.59035i) q^{27} +(-3.92216 - 4.64415i) q^{28} +(0.771141 + 2.11869i) q^{29} +(-6.46363 + 4.70160i) q^{30} +(2.94846 + 1.70229i) q^{31} +(4.30433 - 3.67052i) q^{32} +(0.664175 + 0.916150i) q^{33} +(4.71577 + 2.71265i) q^{34} +(1.72217 + 9.76689i) q^{35} +(-5.94253 - 0.828425i) 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} +(-4.15973 + 6.17446i) q^{42} +(-7.58372 - 9.03792i) q^{43} +(0.230988 + 1.28605i) q^{44} +(7.70138 + 6.04269i) q^{45} +(7.63826 - 6.43000i) q^{46} +(-1.83801 + 0.668980i) q^{47} +(-5.76431 - 3.84353i) q^{48} +(1.11894 + 1.93805i) q^{49} +(7.50913 + 2.71957i) q^{50} +(1.61861 - 6.46340i) q^{51} +(-2.79390 + 4.87493i) q^{52} +(5.81935 - 6.93523i) q^{53} +(1.01170 + 7.27849i) q^{54} +(0.729109 - 2.00321i) q^{55} +(-7.42434 + 4.33383i) q^{56} +(-2.53467 + 7.11164i) q^{57} +(3.13925 - 0.558687i) q^{58} +(-8.69888 - 3.16613i) q^{59} +(4.97690 + 10.1488i) q^{60} +(-4.97808 - 4.17711i) q^{61} +(3.08903 - 3.69328i) q^{62} +(8.66604 + 2.83561i) q^{63} +(-4.06596 - 6.88970i) q^{64} +(7.93894 - 4.58355i) q^{65} +(1.43794 - 0.702320i) q^{66} +(2.95870 + 8.12896i) q^{67} +(4.92667 - 5.90947i) q^{68} +(-10.1307 - 6.84848i) q^{69} +(14.0255 - 0.0223180i) q^{70} +(4.41322 - 3.70313i) q^{71} +(-2.60026 + 8.07704i) 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} +(6.67810 + 1.66109i) q^{78} +(-13.9125 + 2.45315i) q^{79} +(0.0830752 + 13.0518i) q^{80} +(8.23699 - 3.62657i) q^{81} +(0.0237281 + 14.9117i) q^{82} +(1.37681 - 2.38470i) q^{83} +(7.58944 + 7.29760i) q^{84} +(-11.7954 + 4.29318i) q^{85} +(-14.4365 + 8.36555i) q^{86} +(-1.70829 - 3.51173i) q^{87} +(1.84783 - 0.00882109i) q^{88} +(-1.45226 - 0.256073i) q^{89} +(10.2924 - 9.25839i) q^{90} +(5.48866 - 6.54113i) q^{91} +(-7.09891 - 12.2058i) q^{92} +(-5.38461 - 2.40406i) q^{93} +(0.484672 + 2.72336i) q^{94} +(13.7737 - 3.54740i) q^{95} +(-6.75729 + 7.09500i) q^{96} +(3.69157 + 1.34362i) q^{97} +(2.97224 - 1.08717i) q^{98} +(-1.30844 - 1.45923i) 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
$3$	−1.72275	+	0.179266i	−0.994630	+	0.103499i
$3$	−1.72275	+	0.179266i	−0.994630	+	0.103499i
$4$	−1.88155	−	0.678056i	−0.940776	−	0.339028i
$5$	2.09742	+	2.49961i	0.937997	+	1.11786i	0.992850	+	0.119367i	$0.0380864\pi$
$5$	2.09742	+	2.49961i	0.937997	+	1.11786i	−0.0548534	+	0.998494i	$0.517469\pi$
$6$	−0.169508	+	2.44362i	−0.0692013	+	0.997603i
$7$	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
$9$	2.93573	−	0.617661i	0.978576	−	0.205887i
$10$	3.99268	−	2.31366i	1.26260	−	0.731642i
$11$	−0.326657	−	0.565787i	−0.0984908	−	0.170591i	0.812569	−	0.582865i	$-0.198068\pi$
$11$	−0.326657	−	0.565787i	−0.0984908	−	0.170591i	−0.911060	+	0.412273i	$0.864735\pi$
$12$	3.36300	+	0.830821i	0.970813	+	0.239837i
$13$	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
$15$	−4.06143	−	3.93021i	−1.04866	−	1.01478i
$16$	3.08048	+	2.55160i	0.770120	+	0.637899i
$17$	−1.31571	+	3.61488i	−0.319107	+	0.876738i	0.671624	+	0.740893i	$0.265597\pi$
$17$	−1.31571	+	3.61488i	−0.319107	+	0.876738i	−0.990730	+	0.135845i	$0.956625\pi$
$18$	−0.146038	−	4.24013i	−0.0344216	−	0.999407i
$19$	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
$21$	−4.80702	−	2.14619i	−1.04898	−	0.468337i
$22$	−0.867702	+	0.317382i	−0.184995	+	0.0676662i
$23$	5.40830	+	4.53810i	1.12771	+	0.946259i	0.998968	−	0.0454194i	$-0.0144624\pi$
$23$	5.40830	+	4.53810i	1.12771	+	0.946259i	0.128740	+	0.991678i	$0.458907\pi$
$24$	1.97585	−	4.48286i	0.403318	−	0.915060i
$25$	−0.980636	+	5.56146i	−0.196127	+	1.11229i
$26$	−3.73564	−	1.35293i	−0.732619	−	0.265332i
$27$	−4.94680	+	1.59035i	−0.952011	+	0.306063i
$28$	−3.92216	−	4.64415i	−0.741219	−	0.877662i
$29$	0.771141	+	2.11869i	0.143197	+	0.393431i	0.990470	−	0.137726i	$-0.0439795\pi$
$29$	0.771141	+	2.11869i	0.143197	+	0.393431i	−0.847273	+	0.531158i	$0.821757\pi$
$30$	−6.46363	+	4.70160i	−1.18009	+	0.858391i
$31$	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
$33$	0.664175	+	0.916150i	0.115618	+	0.159481i
$34$	4.71577	+	2.71265i	0.808747	+	0.465216i
$35$	1.72217	+	9.76689i	0.291099	+	1.65091i
$36$	−5.94253	−	0.828425i	−0.990422	−	0.138071i
$37$	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	−0.909401	−	0.415920i	$-0.863459\pi$
$41$	−10.3840	+	1.83098i	−1.62171	+	0.285950i	−0.712304	+	0.701871i	$0.752348\pi$
$42$	−4.15973	+	6.17446i	−0.641860	+	0.952739i
$43$	−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
$45$	7.70138	+	6.04269i	1.14805	+	0.900790i
$46$	7.63826	−	6.43000i	1.12620	−	0.948052i
$47$	−1.83801	+	0.668980i	−0.268101	+	0.0975808i	−0.472573	−	0.881292i	$-0.656675\pi$
$47$	−1.83801	+	0.668980i	−0.268101	+	0.0975808i	0.204472	+	0.978872i	$0.434452\pi$
$48$	−5.76431	−	3.84353i	−0.832006	−	0.554766i
$49$	1.11894	+	1.93805i	0.159848	+	0.276865i
$50$	7.50913	+	2.71957i	1.06195	+	0.384606i
$51$	1.61861	−	6.46340i	0.226651	−	0.905057i
$52$	−2.79390	+	4.87493i	−0.387444	+	0.676032i
$53$	5.81935	−	6.93523i	0.799349	−	0.952628i	−0.200283	−	0.979738i	$-0.564186\pi$
$53$	5.81935	−	6.93523i	0.799349	−	0.952628i	0.999632	+	0.0271105i	$0.00863059\pi$
$54$	1.01170	+	7.27849i	0.137675	+	0.990477i
$55$	0.729109	−	2.00321i	0.0983131	−	0.270113i
$56$	−7.42434	+	4.33383i	−0.992119	+	0.579133i
$57$	−2.53467	+	7.11164i	−0.335725	+	0.941960i
$58$	3.13925	−	0.558687i	0.412204	−	0.0733592i
$59$	−8.69888	−	3.16613i	−1.13250	−	0.412195i	−0.293299	−	0.956021i	$-0.594753\pi$
$59$	−8.69888	−	3.16613i	−1.13250	−	0.412195i	−0.839198	+	0.543825i	$0.816975\pi$
$60$	4.97690	+	10.1488i	0.642515	+	1.31020i
$61$	−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
$63$	8.66604	+	2.83561i	1.09182	+	0.357253i
$64$	−4.06596	−	6.88970i	−0.508245	−	0.861212i
$65$	7.93894	−	4.58355i	0.984704	−	0.568519i
$66$	1.43794	−	0.702320i	0.176998	−	0.0864496i
$67$	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
$69$	−10.1307	−	6.84848i	−1.21959	−	0.824460i
$70$	14.0255	−	0.0223180i	1.67637	−	0.00266751i
$71$	4.41322	−	3.70313i	0.523753	−	0.439481i	−0.342185	−	0.939633i	$-0.611167\pi$
$71$	4.41322	−	3.70313i	0.523753	−	0.439481i	0.865938	+	0.500152i	$0.166722\pi$
$72$	−2.60026	+	8.07704i	−0.306444	+	0.951889i
$73$	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
$78$	6.67810	+	1.66109i	0.756146	+	0.188081i
$79$	−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
$81$	8.23699	−	3.62657i	0.915221	−	0.402952i
$82$	0.0237281	+	14.9117i	0.00262033	+	1.64672i
$83$	1.37681	−	2.38470i	0.151124	−	0.261755i	−0.780517	−	0.625135i	$-0.785044\pi$
$83$	1.37681	−	2.38470i	0.151124	−	0.261755i	0.931641	+	0.363380i	$0.118377\pi$
$84$	7.58944	+	7.29760i	0.828075	+	0.796233i
$85$	−11.7954	+	4.29318i	−1.27939	+	0.465661i
$86$	−14.4365	+	8.36555i	−1.55672	+	0.902080i
$87$	−1.70829	−	3.51173i	−0.183148	−	0.376497i
$88$	1.84783	−	0.00882109i	0.196979	−	0.000940331i
$89$	−1.45226	−	0.256073i	−0.153939	−	0.0271437i	0.0961473	−	0.995367i	$-0.469348\pi$
$89$	−1.45226	−	0.256073i	−0.153939	−	0.0271437i	−0.250087	+	0.968223i	$0.580459\pi$
$90$	10.2924	−	9.25839i	1.08491	−	0.975920i
$91$	5.48866	−	6.54113i	0.575368	−	0.685697i
$92$	−7.09891	−	12.2058i	−0.740112	−	1.27254i
$93$	−5.38461	−	2.40406i	−0.558359	−	0.249290i
$94$	0.484672	+	2.72336i	0.0499901	+	0.280893i
$95$	13.7737	−	3.54740i	1.41315	−	0.363956i
$96$	−6.75729	+	7.09500i	−0.689663	+	0.724131i
$97$	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
$99$	−1.30844	−	1.45923i	−0.131503	−	0.146658i
$100$	5.61610	−	9.79926i	0.561610	−	0.979926i
$101$	−13.9725	−	2.46373i	−1.39032	−	0.245151i	−0.572159	−	0.820142i	$-0.693894\pi$
$101$	−13.9725	−	2.46373i	−1.39032	−	0.245151i	−0.818159	+	0.574992i	$0.805005\pi$
$102$	−8.61037	−	3.82784i	−0.852554	−	0.379013i
$103$	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
$105$	−4.71773	−	16.5172i	−0.460404	−	1.61191i
$106$	−8.24540	−	9.79479i	−0.800864	−	0.951354i
$107$	−4.46115	+	7.72694i	−0.431276	+	0.746991i	−0.996983	−	0.0776145i	$-0.975270\pi$
$107$	−4.46115	+	7.72694i	−0.431276	+	0.746991i	0.565708	+	0.824606i	$0.308603\pi$
$108$	10.3860	+	0.361873i	0.999394	+	0.0348212i
$109$	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
$111$	−4.99214	+	0.519473i	−0.473833	+	0.0493062i
$112$	4.23076	+	11.3977i	0.399769	+	1.07698i
$113$		−	10.5767i		−	0.994974i	−0.867472	−	0.497487i	$-0.834256\pi$
$113$		−	10.5767i		−	0.994974i	0.867472	−	0.497487i	$-0.165744\pi$
$114$	9.29052	+	5.26178i	0.870137	+	0.492811i
$115$			23.0370i			2.14821i
$116$	−0.0143508	−	4.50931i	−0.00133244	−	0.418679i
$117$	−0.276708	−	8.42365i	−0.0255816	−	0.778766i
$118$	−6.52775	+	11.3481i	−0.600928	+	1.04467i
$119$	−8.95671	+	7.51557i	−0.821060	+	0.688951i
$120$	15.3496	−	4.46361i	1.40122	−	0.407470i
$121$	5.28659	−	9.15664i	0.480599	−	0.832422i
$122$	−7.03066	+	5.91851i	−0.636526	+	0.535837i
$123$	17.5608	−	5.01581i	1.58340	−	0.452260i
$124$	−4.39343	−	5.20217i	−0.394542	−	0.467169i
$125$	−1.82906	+	1.05601i	−0.163596	+	0.0944520i
$126$	6.05929	−	11.3827i	0.539805	−	1.01405i
$127$	−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
$129$	14.6850	+	14.2106i	1.29295	+	1.25117i
$130$	−4.45341	−	12.1753i	−0.390590	−	1.06785i
$131$	9.19231	+	3.34573i	0.803136	+	0.292318i	0.710785	−	0.703409i	$-0.248340\pi$
$131$	9.19231	+	3.34573i	0.803136	+	0.292318i	0.0923506	+	0.995727i	$0.470562\pi$
$132$	−0.628479	−	2.17413i	−0.0547021	−	0.189234i
$133$	10.9258	−	7.49303i	0.947391	−	0.649728i
$134$	12.0446	−	2.14356i	1.04050	−	0.185175i
$135$	−14.3508	−	9.02943i	−1.23512	−	0.777130i
$136$	−7.03363	−	8.30155i	−0.603129	−	0.711852i
$137$	12.3749	−	14.7479i	1.05726	−	1.26000i	0.0928254	−	0.995682i	$-0.470410\pi$
$137$	12.3749	−	14.7479i	1.05726	−	1.26000i	0.964437	−	0.264314i	$-0.0851454\pi$
$138$	−12.0061	+	12.4466i	−1.02203	+	1.05952i
$139$	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
$141$	3.04650	−	1.48198i	0.256562	−	0.124805i
$142$	−4.08490	−	7.04933i	−0.342797	−	0.591566i
$143$	−1.72473	+	0.627750i	−0.144229	+	0.0524951i
$144$	10.6195	+	5.58809i	0.884956	+	0.465675i
$145$	−3.67850	+	6.37135i	−0.305483	+	0.529112i
$146$	0.183277		0.000291637i	0.0151681		2.41361e-5i
$147$	−2.27507	−	3.13819i	−0.187645	−	0.258834i
$148$	−5.45232	−	1.96485i	−0.448178	−	0.161510i
$149$	−15.1969	+	2.67962i	−1.24498	+	0.219523i	−0.757047	−	0.653360i	$-0.773359\pi$
$149$	−15.1969	+	2.67962i	−1.24498	+	0.219523i	−0.487929	+	0.872883i	$0.662248\pi$
$150$	−13.4239	−	3.33901i	−1.09605	−	0.272629i
$151$		−	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
$156$	3.93927	−	8.89914i	0.315394	−	0.712501i
$157$	−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
$159$	−8.78203	+	12.9909i	−0.696460	+	1.03024i
$160$	18.2029	+	3.06054i	1.43907	+	0.241957i
$161$	7.33912	+	20.1641i	0.578404	+	1.58915i
$162$	−3.04769	−	12.3577i	−0.239449	−	0.970909i
$163$	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
$165$	−0.896964	+	3.58174i	−0.0698286	+	0.278838i
$166$	−2.98711	−	2.49840i	−0.231845	−	0.193913i
$167$	7.26672	+	6.09750i	0.562316	+	0.471839i	0.879086	−	0.476663i	$-0.158154\pi$
$167$	7.26672	+	6.09750i	0.562316	+	0.471839i	−0.316770	+	0.948502i	$0.602598\pi$
$168$	12.0134	−	8.79704i	0.926851	−	0.678706i
$169$	4.79928	+	1.74680i	0.369176	+	0.134369i
$170$	3.11038	+	17.4772i	0.238555	+	1.34044i
$171$	3.09172	−	12.7060i	0.236430	−	0.971649i
$172$	8.14095	+	22.1475i	0.620742	+	1.68873i
$173$	−2.73008	+	7.50083i	−0.207564	+	0.570278i	−0.999169	−	0.0407554i	$-0.987024\pi$
$173$	−2.73008	+	7.50083i	−0.207564	+	0.570278i	0.791605	+	0.611033i	$0.209246\pi$
$174$	−5.30799	+	1.52524i	−0.402397	+	0.115628i
$175$	−11.0329	+	13.1485i	−0.834011	+	0.993936i
$176$	0.437398	−	2.57639i	0.0329701	−	0.194203i
$177$	15.5536	+	3.89504i	1.16908	+	0.292769i
$178$	−0.710160	+	1.96085i	−0.0532288	+	0.146972i
$179$	−11.8117	−	20.4584i	−0.882846	−	1.52913i	−0.848163	−	0.529736i	$-0.822291\pi$
$179$	−11.8117	−	20.4584i	−0.882846	−	1.52913i	−0.0346836	−	0.999398i	$-0.511042\pi$
$180$	−10.3933	−	16.5916i	−0.774669	−	1.23666i
$181$	−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
$183$	9.32480	+	6.30370i	0.689309	+	0.465983i
$184$	−18.7317	+	6.91922i	−1.38092	+	0.510092i
$185$	6.07787	+	7.24332i	0.446854	+	0.532540i
$186$	−4.65954	+	6.91635i	−0.341654	+	0.507131i
$187$	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	$-0.472919\pi$
$191$	2.34872			0.169948			0.0849739	+	0.996383i	$0.472919\pi$
$192$	8.23972	+	11.1403i	0.594651	+	0.803984i
$193$	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
$195$	−12.8551	+	9.31949i	−0.920575	+	0.667382i
$196$	−0.791228	−	4.40525i	−0.0565163	−	0.314661i
$197$	4.00455	+	2.31203i	0.285313	+	0.164725i	0.635826	−	0.771832i	$-0.280660\pi$
$197$	4.00455	+	2.31203i	0.285313	+	0.164725i	−0.350513	+	0.936558i	$0.613993\pi$
$198$	−2.35130	+	1.46769i	−0.167100	+	0.104304i
$199$	−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
$201$	−6.55434	−	13.4738i	−0.462308	−	0.950366i
$202$	−6.83261	+	18.8658i	−0.480741	+	1.32739i
$203$	−1.18998	+	6.74869i	−0.0835199	+	0.473665i
$204$	−7.42805	+	11.0637i	−0.520067	+	0.774615i
$205$	−26.3563	−	22.1156i	−1.84081	−	1.54462i
$206$	−1.92788	−	5.27071i	−0.134322	−	0.367227i
$207$	18.6803	+	9.98213i	1.29837	+	0.693806i
$208$	8.56234	−	7.27803i	0.593691	−	0.504640i
$209$	−2.83917	+	0.220588i	−0.196390	+	0.0152584i
$210$	−24.1585	+	2.55275i	−1.66709	+	0.176157i
$211$	−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
$213$	−6.93903	+	7.17071i	−0.475454	+	0.491329i
$214$	9.67887	+	8.09533i	0.661634	+	0.553385i
$215$	6.68504	−	37.9127i	0.455916	−	2.58563i
$216$	3.03166	−	14.3809i	0.206278	−	0.978493i
$217$	5.17393	+	8.96150i	0.351229	+	0.608346i
$218$	−6.00659	−	10.3656i	−0.406817	−	0.702046i
$219$	−0.0616483	−	0.215836i	−0.00416581	−	0.0145848i
$220$	−2.73015	+	3.27477i	−0.184066	+	0.220785i
$221$	9.35949	+	5.40370i	0.629587	+	0.363492i
$222$	−0.491196	+	7.08106i	−0.0329669	+	0.475250i
$223$	−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
$225$	0.556219	+	16.9326i	0.0370813	+	1.12884i
$226$	−14.7346	−	2.57394i	−0.980131	−	0.171216i
$227$	−2.67764			−0.177721			−0.0888606	−	0.996044i	$-0.528323\pi$
$227$	−2.67764			−0.177721			−0.0888606	+	0.996044i	$0.528323\pi$
$228$	9.59121	−	11.6623i	0.635193	−	0.772353i
$229$	−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
$231$	0.355964	+	3.42082i	0.0234207	+	0.225073i
$232$	−6.28549	−	1.07739i	−0.412662	−	0.0707340i
$233$	−7.52375	−	8.96645i	−0.492897	−	0.587412i	0.461055	−	0.887372i	$-0.347471\pi$
$233$	−7.52375	−	8.96645i	−0.492897	−	0.587412i	−0.953952	+	0.299960i	$0.903027\pi$
$234$	−11.8025	−	1.66448i	−0.771552	−	0.108811i
$235$	−5.52727	−	3.19117i	−0.360560	−	0.208169i
$236$	14.2206	+	11.8556i	0.925681	+	0.771732i
$237$	23.5280	−	6.72019i	1.52831	−	0.436524i
$238$	8.29038	+	14.3067i	0.537385	+	0.927367i
$239$	−4.10165	−	7.10426i	−0.265313	−	0.459536i	0.702332	−	0.711849i	$-0.252142\pi$
$239$	−4.10165	−	7.10426i	−0.265313	−	0.459536i	−0.967646	+	0.252313i	$0.918809\pi$
$240$	−2.48286	−	22.4701i	−0.160268	−	1.45044i
$241$	−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
$243$	−13.5401	+	7.72428i	−0.868601	+	0.495513i
$244$	6.53421	+	11.2349i	0.418310	+	0.719238i
$245$	−2.49750	+	6.86183i	−0.159559	+	0.438386i
$246$	−2.71404	−	25.6848i	−0.173041	−	1.63761i
$247$	−9.96243	−	7.12119i	−0.633894	−	0.453111i
$248$	−8.31642	+	4.85457i	−0.528093	+	0.308265i
$249$	−1.94440	+	4.35506i	−0.123221	+	0.275991i
$250$	1.02602	+	2.80508i	0.0648914	+	0.177409i
$251$	−19.7949	−	16.6099i	−1.24944	−	1.04841i	−0.996725	−	0.0808687i	$-0.974231\pi$
$251$	−19.7949	−	16.6099i	−1.24944	−	1.04841i	−0.252720	−	0.967540i	$-0.581325\pi$
$252$	−14.3829	−	11.2114i	−0.906038	−	0.706252i
$253$	0.800938	−	4.54234i	0.0503545	−	0.285575i
$254$	−0.149207	+	0.411983i	−0.00936210	+	0.0258501i
$255$	19.5509	−	9.51059i	1.22433	−	0.595576i
$256$	2.97872	+	15.7203i	0.186170	+	0.982517i
$257$	7.23134	+	19.8679i	0.451078	+	1.23933i	0.931966	+	0.362546i	$0.118092\pi$
$257$	7.23134	+	19.8679i	0.451078	+	1.23933i	−0.480888	+	0.876782i	$0.659685\pi$
$258$	23.3707	−	16.9997i	1.45500	−	1.05836i
$259$	7.62749	+	4.40373i	0.473949	+	0.273635i
$260$	−18.0454	+	3.24115i	−1.11913	+	0.201007i
$261$	3.57249	+	5.74360i	0.221132	+	0.355520i
$262$	6.89802	−	11.9918i	0.426161	−	0.740853i
$263$	2.79554	+	15.8543i	0.172381	+	0.977619i	0.941124	+	0.338062i	$0.109771\pi$
$263$	2.79554	+	15.8543i	0.172381	+	0.977619i	−0.768743	+	0.639557i	$0.779118\pi$
$264$	−3.18177	+	0.346450i	−0.195824	+	0.0213225i
$265$	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	0.192196	−	0.981356i	$-0.438439\pi$
$269$	11.6194	−	2.04881i	0.708446	−	0.124918i	0.516249	+	0.856438i	$0.327328\pi$
$270$	−16.0715	+	17.7949i	−0.978078	+	1.08297i
$271$	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
$273$	−8.28298	+	12.2527i	−0.501309	+	0.741565i
$274$	−17.5340	−	20.8288i	−1.05927	−	1.25831i
$275$	3.46693	−	1.26186i	0.209064	−	0.0760931i
$276$	14.4177	+	19.7549i	0.867845	+	1.18911i
$277$	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
$279$	9.70731	+	3.17632i	0.581161	+	0.190161i
$280$	−26.4049	−	9.46810i	−1.57799	−	0.565827i
$281$	−8.74766	+	10.4251i	−0.521842	+	0.621907i	−0.961015	−	0.276496i	$-0.910827\pi$
$281$	−8.74766	+	10.4251i	−0.521842	+	0.621907i	0.439174	+	0.898402i	$0.355271\pi$
$282$	−1.32317	−	4.60479i	−0.0787939	−	0.274211i
$283$	−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
$285$	−23.0926	+	8.58044i	−1.36789	+	0.508261i
$286$	0.454801	+	2.55552i	0.0268930	+	0.151111i
$287$	−30.1151	−	10.9610i	−1.77764	−	0.647007i
$288$	10.3692	−	13.4343i	0.611012	−	0.791621i
$289$	1.68647	+	1.41511i	0.0992039	+	0.0832420i
$290$	7.98084	+	6.67511i	0.468651	+	0.391976i
$291$	−6.60051	−	1.65295i	−0.386929	−	0.0968975i
$292$	0.0441958	−	0.255397i	0.00258636	−	0.0149460i
$293$	10.5221	−	6.07496i	0.614710	−	0.354903i	−0.160096	−	0.987101i	$-0.551180\pi$
$293$	10.5221	−	6.07496i	0.614710	−	0.354903i	0.774807	+	0.632198i	$0.217847\pi$
$294$	−4.92553	+	2.40573i	−0.287263	+	0.140305i
$295$	−10.3311	−	28.3846i	−0.601502	−	1.65261i
$296$	−4.06415	+	7.11756i	−0.236224	+	0.413700i
$297$	2.51571	+	2.27933i	0.145976	+	0.132260i
$298$	0.0347259	+	21.8231i	0.00201161	+	1.26418i
$299$	15.1940	−	12.7493i	0.878694	−	0.737312i
$300$	−7.91846	+	17.8884i	−0.457172	+	1.03279i
$301$	−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
$306$	15.5197	+	5.05086i	0.887203	+	0.288739i
$307$	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
$309$	−5.56499	+	4.03441i	−0.316581	+	0.229510i
$310$	15.7108	−	0.0249996i	0.892312	−	0.00141988i
$311$	−12.7885	+	22.1504i	−0.725172	+	1.25603i	0.233731	+	0.972301i	$0.424906\pi$
$311$	−12.7885	+	22.1504i	−0.725172	+	1.25603i	−0.958903	+	0.283733i	$0.908427\pi$
$312$	−11.4389	−	7.65355i	−0.647599	−	0.433297i
$313$	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
$315$	11.0884	+	27.6092i	0.624763	+	1.55560i
$316$	27.8405	+	4.81772i	1.56615	+	0.271018i
$317$	16.6909	+	2.94305i	0.937452	+	0.165298i	0.621444	−	0.783458i	$-0.286546\pi$
$317$	16.6909	+	2.94305i	0.937452	+	0.165298i	0.316008	+	0.948757i	$0.397657\pi$
$318$	15.9606	+	15.3958i	0.895028	+	0.863356i
$319$	0.946829	−	1.12839i	0.0530123	−	0.0631775i
$320$	8.69353	−	24.6140i	0.485983	−	1.37596i
$321$	6.30026	−	14.1113i	0.351646	−	0.787616i
$322$	29.8770	−	5.31715i	1.66498	−	0.296313i
$323$	11.7410	+	11.9717i	0.653285	+	0.666121i
$324$	−17.9573	+	1.23844i	−0.997630	+	0.0688023i
$325$	14.9086	+	5.42628i	0.826980	+	0.300996i
$326$	−3.39093	−	9.27057i	−0.187806	−	0.513450i
$327$	−10.2034	+	10.5441i	−0.564249	+	0.583088i
$328$	10.0663	−	28.0732i	0.555819	−	1.55008i
$329$	−5.85462	−	1.03233i	−0.322776	−	0.0569141i
$330$	4.77149	+	2.12122i	0.262662	+	0.116770i
$331$	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
$333$	8.50709	−	1.78984i	0.466185	−	0.0980829i
$334$	10.2630	−	8.63951i	0.561564	−	0.472733i
$335$	−14.1136	+	24.4455i	−0.771109	+	1.33560i
$336$	−9.33175	−	18.8769i	−0.509088	−	1.02982i
$337$	−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
$339$	1.89605	+	18.2210i	0.102979	+	0.989630i
$340$	25.1047	−	0.0798955i	1.36149	−	0.00433294i
$341$		−	2.22426i		−	0.120451i
$342$	−16.9485	−	7.39924i	−0.916469	−	0.400105i
$343$		−	14.4740i		−	0.781520i
$344$	32.8353	−	5.95150i	1.77036	−	0.320883i
$345$	−4.12975	−	39.6869i	−0.222338	−	2.13667i
$346$	9.78515	+	5.62872i	0.526053	+	0.302602i
$347$	3.18422	−	2.67188i	0.170938	−	0.143434i	−0.553305	−	0.832979i	$-0.686634\pi$
$347$	3.18422	−	2.67188i	0.170938	−	0.143434i	0.724243	+	0.689544i	$0.242189\pi$
$348$	0.833089	+	7.76583i	0.0446582	+	0.416292i
$349$	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
$351$	1.98677	+	14.4622i	0.106046	+	0.771936i
$352$	−3.48277	−	1.23633i	−0.185632	−	0.0658969i
$353$	−12.9925	+	7.50122i	−0.691521	+	0.399250i	−0.804182	−	0.594384i	$-0.797396\pi$
$353$	−12.9925	+	7.50122i	−0.691521	+	0.399250i	0.112661	+	0.993634i	$0.464063\pi$
$354$	9.21135	−	20.7200i	0.489577	−	1.10126i
$355$	18.5128	+	3.26431i	0.982557	+	0.173251i
$356$	2.55887	+	1.46653i	0.135620	+	0.0777258i
$357$	14.0829	−	14.5531i	0.745345	−	0.770230i
$358$	−31.3755	+	11.4763i	−1.65824	+	0.606542i
$359$	−4.93808	−	1.79731i	−0.260622	−	0.0948586i	0.208405	−	0.978043i	$-0.433173\pi$
$359$	−4.93808	−	1.79731i	−0.260622	−	0.0948586i	−0.469027	+	0.883184i	$0.655395\pi$
$360$	−25.6433	+	10.4413i	−1.35152	+	0.550307i
$361$	−11.9275	−	14.7897i	−0.627763	−	0.778405i
$362$	1.58370	+	8.89880i	0.0832376	+	0.467710i
$363$	−7.46599	+	16.7223i	−0.391863	+	0.877693i
$364$	−14.7625	+	8.58587i	−0.773763	+	0.450022i
$365$	−0.271819	+	0.323941i	−0.0142276	+	0.0169558i
$366$	11.0511	−	11.4565i	0.577649	−	0.598839i
$367$	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
$369$	−29.3536	+	11.7890i	−1.52809	+	0.613712i
$370$	11.5699	−	6.70446i	0.601491	−	0.348548i
$371$	25.8570	−	9.41119i	1.34243	−	0.488605i
$372$	8.50135	+	8.17444i	0.440774	+	0.423825i
$373$	−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
$375$	2.96170	−	2.14712i	0.152941	−	0.110877i
$376$	0.934656	−	5.45279i	0.0482012	−	0.281206i
$377$	6.23802	−	1.09993i	0.321274	−	0.0566493i
$378$	−8.39810	+	20.6958i	−0.431952	+	1.06448i
$379$			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	$-0.731820\pi$
$383$	−5.78100	−	32.7857i	−0.295396	−	1.67527i	0.370195	−	0.928954i	$-0.379291\pi$
$384$	17.5250	−	8.76780i	0.894319	−	0.447430i
$385$	4.96342	−	4.16480i	0.252959	−	0.212258i
$386$	18.4557	−	0.0293674i	0.939368	−	0.00149476i
$387$	−27.8461	−	21.8487i	−1.41550	−	1.11063i
$388$	−6.03483	−	5.03118i	−0.306372	−	0.255420i
$389$	−4.73715	−	13.0152i	−0.240183	−	0.659898i	−0.999953	−	0.00970576i	$-0.996911\pi$
$389$	−4.73715	−	13.0152i	−0.240183	−	0.659898i	0.759770	−	0.650192i	$-0.225312\pi$
$390$	9.85473	+	20.1767i	0.499014	+	1.02169i
$391$	−23.5204	+	13.5795i	−1.18948	+	0.686747i
$392$	−6.32958	+	0.0302159i	−0.319692	+	0.00152613i
$393$	−16.4358	−	4.11598i	−0.829077	−	0.207624i
$394$	4.19547	−	5.01616i	0.211365	−	0.252710i
$395$	−35.3123	−	29.6306i	−1.77676	−	1.49087i
$396$	1.47246	+	3.63282i	0.0739939	+	0.182556i
$397$	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
$399$	−17.4792	+	14.8672i	−0.875056	+	0.744293i
$400$	−17.2114	+	14.6298i	−0.860572	+	0.731490i
$401$	5.98274	−	16.4374i	0.298764	−	0.820846i	−0.695944	−	0.718096i	$-0.745014\pi$
$401$	5.98274	−	16.4374i	0.298764	−	0.820846i	0.994707	−	0.102750i	$-0.0327641\pi$
$402$	−20.3656	+	5.85201i	−1.01574	+	0.291872i
$403$	6.14815	−	7.32709i	0.306261	−	0.364988i
$404$	24.6195	+	14.1098i	1.22487	+	0.701989i
$405$	26.3415	+	12.9828i	1.30892	+	0.645122i
$406$	9.11212	+	3.30013i	0.452227	+	0.163783i
$407$	−0.946580	−	1.63952i	−0.0469202	−	0.0812682i
$408$	13.6054	+	13.0406i	0.673566	+	0.645606i
$409$	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
$411$	−18.6751	+	27.6253i	−0.921175	+	1.36266i
$412$	−7.81188	+	1.40309i	−0.384864	+	0.0691255i
$413$	−18.0855	−	21.5535i	−0.889930	−	1.06058i
$414$	18.4523	−	23.5946i	0.906881	−	1.15961i
$415$	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	$-0.434179\pi$
$419$	8.40525			0.410623			0.205312	+	0.978697i	$0.434179\pi$
$420$	−2.32290	+	34.2768i	−0.113346	+	1.67254i
$421$	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
$423$	−4.98269	+	3.09921i	−0.242267	+	0.150689i
$424$	8.87274	+	24.0203i	0.430899	+	1.16653i
$425$	−18.8138	−	10.8622i	−0.912604	−	0.526892i
$426$	8.30096	+	11.4119i	0.402183	+	0.552910i
$427$	−6.75531	−	18.5601i	−0.326913	−	0.898185i
$428$	13.6332	−	11.5137i	0.658985	−	0.556537i
$429$	2.85874	−	1.39064i	0.138021	−	0.0671408i
$430$	−51.1900	−	18.5395i	−2.46860	−	0.894052i
$431$	2.28945	−	12.9841i	0.110279	−	0.625423i	−0.878701	−	0.477373i	$-0.841589\pi$
$431$	2.28945	−	12.9841i	0.110279	−	0.625423i	0.988980	−	0.148050i	$-0.0472998\pi$
$432$	−19.2964	−	7.72317i	−0.928400	−	0.371581i
$433$	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
$435$	5.19497	−	11.6357i	0.249080	−	0.557888i
$436$	−15.9022	+	5.84532i	−0.761579	+	0.279940i
$437$	28.0159	−	12.7337i	1.34018	−	0.609136i
$438$	−0.315687	+	0.0333577i	−0.0150841	+	0.00159389i
$439$	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
$441$	4.48195	+	4.99847i	0.213426	+	0.238022i
$442$	9.80571	−	11.7238i	0.466410	−	0.557646i
$443$	3.36520	−	19.0850i	0.159886	−	0.906756i	−0.794297	−	0.607530i	$-0.792160\pi$
$443$	3.36520	−	19.0850i	0.159886	−	0.906756i	0.954182	−	0.299226i	$-0.0967285\pi$
$444$	9.74521	+	2.40753i	0.462487	+	0.114257i
$445$	−2.40592	−	4.16718i	−0.114052	−	0.197543i
$446$	−19.1988	+	11.1252i	−0.909091	+	0.526794i
$447$	25.7000	−	7.34059i	1.21557	−	0.347198i
$448$	−0.232143	−	24.3140i	−0.0109677	−	1.14873i
$449$	−24.5079	−	14.1497i	−1.15660	−	0.667764i	−0.206114	−	0.978528i	$-0.566082\pi$
$449$	−24.5079	−	14.1497i	−1.15660	−	0.667764i	−0.950487	+	0.310764i	$0.899415\pi$
$450$	23.7245	+	3.34583i	1.11838	+	0.157724i
$451$	4.42794	+	5.27702i	0.208504	+	0.248485i
$452$	−7.17160	+	19.9006i	−0.337324	+	0.936048i
$453$	1.38003	+	13.2621i	0.0648396	+	0.623109i
$454$	−0.651628	+	3.73027i	−0.0305824	+	0.175070i
$455$	27.8624			1.30621
$456$	−13.9128	−	16.1998i	−0.651527	−	0.758625i
$457$	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
$459$	0.759613	−	19.9745i	0.0354557	−	0.932331i
$460$	15.6203	−	43.3453i	0.728303	−	2.02098i
$461$	−19.4833	−	23.2193i	−0.907427	−	1.08143i	−0.996348	−	0.0853910i	$-0.972786\pi$
$461$	−19.4833	−	23.2193i	−0.907427	−	1.08143i	0.0889202	−	0.996039i	$-0.471658\pi$
$462$	4.85223	+	0.336588i	0.225746	+	0.0156595i
$463$	−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
$465$	−5.28459	−	18.5018i	−0.245067	−	0.858000i
$466$	−14.3223	+	8.29940i	−0.663468	+	0.384462i
$467$	8.48758	+	14.7009i	0.392759	+	0.680278i	0.992812	−	0.119682i	$-0.0381875\pi$
$467$	8.48758	+	14.7009i	0.392759	+	0.680278i	−0.600054	+	0.799960i	$0.704854\pi$
$468$	−5.19106	+	16.0372i	−0.239957	+	0.741318i
$469$	−4.56568	+	25.8932i	−0.210823	+	1.19564i
$470$	−5.79079	+	6.92354i	−0.267109	+	0.319359i
$471$	8.59632	−	8.88333i	0.396097	−	0.409322i
$472$	19.9769	−	16.9258i	0.919512	−	0.779072i
$473$	−2.63626	+	7.24307i	−0.121215	+	0.333037i
$474$	−3.63628	−	34.4126i	−0.167020	−	1.58062i
$475$	20.0258	+	14.3145i	0.918847	+	0.656796i
$476$	21.9485	−	8.06779i	1.00601	−	0.369787i
$477$	12.8004	−	23.9543i	0.586090	−	1.09679i
$478$	−10.8952	+	3.98519i	−0.498337	+	0.182278i
$479$	17.5568	+	14.7319i	0.802189	+	0.673117i	0.948730	−	0.316088i	$-0.102369\pi$
$479$	17.5568	+	14.7319i	0.802189	+	0.673117i	−0.146541	+	0.989205i	$0.546814\pi$
$480$	−31.9077	−	2.00938i	−1.45638	−	0.0917151i
$481$	1.41367	−	8.01733i	0.0644579	−	0.365559i
$482$	8.19695	+	2.96868i	0.373361	+	0.135220i
$483$	−16.2582	−	33.4220i	−0.739774	−	1.52075i
$484$	−16.1557	+	13.6441i	−0.734351	+	0.620187i
$485$	4.38425	+	12.0456i	0.199079	+	0.546964i
$486$	7.46571	+	20.7428i	0.338652	+	0.940912i
$487$	−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
$489$	−9.78819	+	7.09607i	−0.442637	+	0.320896i
$490$	8.95154	+	5.14920i	0.404389	+	0.232617i
$491$	3.94193	+	22.3558i	0.177897	+	1.00890i	0.934747	+	0.355315i	$0.115626\pi$
$491$	3.94193	+	22.3558i	0.177897	+	1.00890i	−0.756850	+	0.653589i	$0.773263\pi$
$492$	−36.4425	−	2.46967i	−1.64295	−	0.111341i
$493$	−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
$498$	5.59392	+	3.76862i	0.250670	+	0.168876i
$499$	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
$501$	−13.6118	−	9.20179i	−0.608131	−	0.411106i
$502$	−27.9568	+	23.5345i	−1.24777	+	1.05040i
$503$	−15.5356	+	5.65449i	−0.692697	+	0.252121i	−0.664290	−	0.747475i	$-0.731266\pi$
$503$	−15.5356	+	5.65449i	−0.692697	+	0.252121i	−0.0284077	+	0.999596i	$0.509044\pi$
$504$	−19.1190	+	17.3087i	−0.851628	+	0.770990i
$505$	−23.1479	−	40.0934i	−1.03007	−	1.78413i
$506$	−6.13310	−	2.22122i	−0.272650	−	0.0987453i
$507$	−8.58110	−	2.14894i	−0.381100	−	0.0954379i
$508$	0.537629	+	0.308123i	0.0238534	+	0.0136708i
$509$	−25.1975	+	30.0292i	−1.11686	+	1.33102i	−0.179061	+	0.983838i	$0.557306\pi$
$509$	−25.1975	+	30.0292i	−1.11686	+	1.33102i	−0.937798	+	0.347182i	$0.887139\pi$
$510$	−8.49147	−	29.5512i	−0.376009	−	1.30855i
$511$	−0.134719	+	0.370139i	−0.00595964	+	0.0163740i
$512$	22.6251	−	0.324040i	0.999897	−	0.0143207i
$513$	−3.04852	+	22.4434i	−0.134595	+	0.990901i
$514$	29.4382	−	5.23906i	1.29846	−	0.231085i
$515$	12.1682	+	4.42885i	0.536193	+	0.195158i
$516$	−17.9951	−	36.6952i	−0.792191	−	1.61542i
$517$	0.978898	+	0.821393i	0.0430519	+	0.0361248i
$518$	7.99114	−	9.55430i	0.351110	−	0.419792i
$519$	3.35860	−	13.4115i	0.147426	−	0.588698i
$520$	0.123775	+	25.9282i	0.00542788	+	1.13703i
$521$	13.5099	−	7.79995i	0.591880	−	0.341722i	−0.173961	−	0.984753i	$-0.555657\pi$
$521$	13.5099	−	7.79995i	0.591880	−	0.341722i	0.765840	+	0.643031i	$0.222323\pi$
$522$	8.87090	−	3.57914i	0.388269	−	0.156655i
$523$	−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
$525$	16.6499	−	24.6295i	0.726661	−	1.07492i
$526$	22.7673	−	0.0362282i	0.992699	−	0.00157962i
$527$	−10.0329	+	8.41861i	−0.437040	+	0.366720i
$528$	−0.291667	+	4.51689i	−0.0126932	+	0.196572i
$529$	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
$534$	0.871914	−	3.50536i	0.0377314	−	0.151692i
$535$	−28.6713	+	5.05552i	−1.23957	+	0.218569i
$536$	−24.1160	−	4.13371i	−1.04165	−	0.178549i
$537$	24.0161	+	33.1273i	1.03637	+	1.42955i
$538$	−0.0265510	−	16.6857i	−0.00114470	−	0.719374i
$539$	0.731016	−	1.26616i	0.0314871	−	0.0545373i
$540$	20.8793	+	26.7200i	0.898503	+	1.14985i
$541$	−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
$543$	9.95467	−	4.84247i	0.427196	−	0.207810i
$544$	7.60524	+	20.3890i	0.326072	+	0.874171i
$545$	27.2219	+	4.79995i	1.16606	+	0.205607i
$546$	15.0537	+	14.5210i	0.644237	+	0.621440i
$547$	−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
$549$	−17.1943	−	9.18808i	−0.733836	−	0.392138i
$550$	−0.914210	−	5.13693i	−0.0389821	−	0.219039i
$551$	9.78166	+	0.951752i	0.416713	+	0.0405460i
$552$	31.0296	−	15.2780i	1.32071	−	0.650277i
$553$	−40.3483	−	14.6856i	−1.71578	−	0.624494i
$554$	33.8859	−	12.3945i	1.43967	−	0.526594i
$555$	−11.7691	−	11.3889i	−0.499572	−	0.483431i
$556$	−12.7678	−	7.31743i	−0.541477	−	0.310328i
$557$	−4.94767	−	0.872407i	−0.209639	−	0.0369651i	0.0678421	−	0.997696i	$-0.478389\pi$
$557$	−4.94767	−	0.872407i	−0.209639	−	0.0369651i	−0.277481	+	0.960731i	$0.589500\pi$
$558$	6.78735	−	12.7504i	0.287331	−	0.539769i
$559$	−28.7051	+	16.5729i	−1.21409	+	0.700958i
$560$	−19.6160	+	34.4810i	−0.828929	+	1.45709i
$561$	−4.18564	+	1.19553i	−0.176718	+	0.0504752i
$562$	12.3945	+	14.7235i	0.522831	+	0.621075i
$563$	−20.1435	+	34.8895i	−0.848947	+	1.47042i	0.0332020	+	0.999449i	$0.489430\pi$
$563$	−20.1435	+	34.8895i	−0.848947	+	1.47042i	−0.882149	+	0.470971i	$0.843904\pi$
$564$	−6.73701	+	0.722721i	−0.283679	+	0.0304321i
$565$	26.4377	−	22.1839i	1.11224	−	0.933282i
$566$	29.5416	+	16.9932i	1.24173	+	0.714279i
$567$	27.1926	+	2.97189i	1.14198	+	0.124808i
$568$	2.90612	+	16.0335i	0.121938	+	0.672750i
$569$			37.3623i			1.56631i	0.621827	+	0.783154i	$0.286391\pi$
$569$			37.3623i			1.56631i	−0.621827	+	0.783154i	$0.713609\pi$
$570$	6.33375	+	34.2589i	0.265292	+	1.43495i
$571$		−	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
$573$	−4.04626	+	0.421047i	−0.169035	+	0.0175895i
$574$	−22.5987	+	39.2864i	−0.943253	+	1.63978i
$575$	−30.5420	+	25.6278i	−1.27369	+	1.06875i
$576$	−16.1921	−	17.7149i	−0.674669	−	0.738120i
$577$	−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
$579$	−6.20788	−	21.7343i	−0.257991	−	0.903247i
$580$	11.2414	−	9.49380i	0.466775	−	0.394209i
$581$	7.24804	−	4.18466i	0.300699	−	0.173609i
$582$	−3.90904	+	8.79302i	−0.162035	+	0.364483i
$583$	−5.82480	−	1.02707i	−0.241238	−	0.0425368i
$584$	−0.345042	−	0.123723i	−0.0142780	−	0.00511970i
$585$	20.4755	−	18.3596i	0.846557	−	0.759077i
$586$	−5.90248	−	16.1370i	−0.243829	−	0.666613i
$587$	38.8181	+	14.1286i	1.60219	+	0.583151i	0.979875	−	0.199614i	$-0.0639687\pi$
$587$	38.8181	+	14.1286i	1.60219	+	0.583151i	0.622318	+	0.782764i	$0.286191\pi$
$588$	2.15280	+	7.44730i	0.0887799	+	0.307121i
$589$	12.2386	−	8.39336i	0.504284	−	0.345842i
$590$	−42.0572	+	7.48484i	−1.73147	+	0.308146i
$591$	−7.31331	−	3.26517i	−0.300829	−	0.134311i
$592$	8.92655	+	7.39396i	0.366879	+	0.303890i
$593$	−19.0591	+	22.7138i	−0.782665	+	0.932744i	−0.999051	−	0.0435638i	$-0.986129\pi$
$593$	−19.0591	+	22.7138i	−0.782665	+	0.932744i	0.216385	+	0.976308i	$0.430573\pi$
$594$	3.78760	−	2.94998i	0.155407	−	0.121039i
$595$	−37.5720	−	6.62496i	−1.54030	−	0.271597i
$596$	30.4106	+	5.26248i	1.24567	+	0.215560i
$597$	9.52422	+	19.5789i	0.389800	+	0.801313i
$598$	−14.0637	−	24.2698i	−0.575107	−	0.992464i
$599$	20.0137	−	7.28438i	0.817736	−	0.297632i	0.100920	−	0.994894i	$-0.467821\pi$
$599$	20.0137	−	7.28438i	0.817736	−	0.297632i	0.716815	+	0.697263i	$0.245599\pi$
$600$	22.9937	+	15.3847i	0.938713	+	0.628076i
$601$	−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
$603$	13.7069	+	22.0369i	0.558187	+	0.897413i
$604$	−5.21983	+	14.4846i	−0.212392	+	0.589371i
$605$	33.9763	−	5.99094i	1.38133	−	0.243566i
$606$	8.38888	−	33.7259i	0.340775	−	1.37002i
$607$			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
$612$	10.8133	−	20.3916i	0.437102	−	0.824282i
$613$	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
$615$	49.3699	+	33.3748i	1.99079	+	1.34580i
$616$	4.87724	+	2.78492i	0.196510	+	0.112208i
$617$	−8.90497	−	24.4662i	−0.358501	−	0.984973i	−0.979550	−	0.201201i	$-0.935516\pi$
$617$	−8.90497	−	24.4662i	−0.358501	−	0.984973i	0.621049	−	0.783772i	$-0.286707\pi$
$618$	4.26612	+	8.73450i	0.171608	+	0.351353i
$619$	−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
$621$	−33.9709	−	13.8480i	−1.36321	−	0.555699i
$622$	27.7459	+	23.2064i	1.11251	+	0.930494i
$623$	−3.43347	−	2.88102i	−0.137559	−	0.115426i
$624$	−13.4461	+	14.0732i	−0.538273	+	0.563377i
$625$	20.0575	+	7.30034i	0.802301	+	0.292014i
$626$	−2.25810	−	12.6882i	−0.0902519	−	0.507124i
$627$	4.85164	−	0.888986i	0.193756	−	0.0355027i
$628$	13.3976	−	4.92466i	0.534621	−	0.196515i
$629$	−3.81263	+	10.4751i	−0.152020	+	0.417671i
$630$	41.1613	−	8.72854i	1.63991	−	0.347753i
$631$	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
$633$	5.19631	−	20.7498i	0.206535	−	0.824730i
$634$	8.16189	−	22.5361i	0.324150	−	0.895023i
$635$	−0.505494	−	0.875541i	−0.0200599	−	0.0347448i
$636$	25.3324	−	18.4883i	1.00449	−	0.733109i
$637$	5.90791	−	2.15030i	0.234080	−	0.0851981i
$638$	−1.34156	−	1.59365i	−0.0531127	−	0.0630931i
$639$	10.6687	−	13.5973i	0.422049	−	0.537899i
$640$	−32.1745	−	18.1011i	−1.27181	−	0.715510i
$641$	4.51590	+	5.38184i	0.178367	+	0.212570i	0.847819	−	0.530286i	$-0.177915\pi$
$641$	4.51590	+	5.38184i	0.178367	+	0.212570i	−0.669452	+	0.742856i	$0.733471\pi$
$642$	−18.1255	−	12.2111i	−0.715356	−	0.481934i
$643$	−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	$-0.470940\pi$
$647$	4.63787			0.182333			0.0911667	+	0.995836i	$0.470940\pi$
$648$	−2.64479	+	25.3181i	−0.103897	+	0.994588i
$649$	1.05019	+	5.95595i	0.0412237	+	0.233791i
$650$	11.1876	−	19.4489i	0.438813	−	0.762848i
$651$	−10.5199	−	14.5109i	−0.412306	−	0.568727i
$652$	−13.7402	+	2.46788i	−0.538108	+	0.0966498i
$653$	−20.0746	−	11.5901i	−0.785580	−	0.453555i	0.0528245	−	0.998604i	$-0.483178\pi$
$653$	−20.0746	−	11.5901i	−0.785580	−	0.453555i	−0.838404	+	0.545049i	$0.816511\pi$
$654$	12.2060	+	16.7805i	0.477294	+	0.656170i
$655$	10.9172	+	29.9946i	0.426569	+	1.17199i
$656$	−36.6596	−	20.8554i	−1.43132	−	0.814268i
$657$	0.144897	+	0.360779i	0.00565296	+	0.0140753i
$658$	−2.86293	+	7.90495i	−0.111609	+	0.308167i
$659$	−1.05533	+	5.98510i	−0.0411100	+	0.233146i	−0.998439	−	0.0558541i	$-0.982212\pi$
$659$	−1.05533	+	5.98510i	−0.0411100	+	0.233146i	0.957329	+	0.289001i	$0.0933229\pi$
$660$	4.11630	−	6.13103i	0.160227	−	0.238650i
$661$	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
$663$	−17.0928	−	7.63139i	−0.663827	−	0.296378i
$664$	3.92636	+	6.72629i	0.152372	+	0.261031i
$665$	41.6458	+	11.5943i	1.61496	+	0.449608i
$666$	−0.423187	−	12.2869i	−0.0163982	−	0.476109i
$667$	−5.44428	+	14.9580i	−0.210803	+	0.579177i
$668$	−9.53827	−	16.4000i	−0.369047	−	0.634536i
$669$	19.5294	+	18.8984i	0.755051	+	0.730655i
$670$	30.6208	+	25.6109i	1.18298	+	0.989437i
$671$	−0.737225	+	4.18101i	−0.0284603	+	0.161406i
$672$	−28.5687	+	8.40636i	−1.10206	+	0.324282i
$673$	−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
$675$	−3.99368	−	29.0710i	−0.153717	−	1.11894i
$676$	−7.84568	−	6.54087i	−0.301757	−	0.251572i
$677$	2.79478	+	1.61357i	0.107412	+	0.0620144i	0.552744	−	0.833351i	$-0.313581\pi$
$677$	2.79478	+	1.61357i	0.107412	+	0.0620144i	−0.445332	+	0.895366i	$0.646914\pi$
$678$	25.8454	+	1.79284i	0.992588	+	0.0688535i
$679$	7.67500	+	9.14671i	0.294539	+	0.351018i
$680$	5.99816	−	34.9932i	0.230019	−	1.34193i
$681$	4.61290	−	0.480010i	0.176767	−	0.0183940i
$682$	−3.09866	−	0.541295i	−0.118654	−	0.0207273i
$683$	−6.83061			−0.261366			−0.130683	−	0.991424i	$-0.541717\pi$
$683$	−6.83061			−0.261366			−0.130683	+	0.991424i	$0.541717\pi$
$684$	−14.4326	+	21.8106i	−0.551844	+	0.833948i
$685$	62.8195			2.40021
$686$	−20.1639	−	3.52237i	−0.769862	−	0.134485i
$687$	32.1845	−	3.34906i	1.22792	−	0.127775i
$688$	−0.300377	−	47.1917i	−0.0114518	−	1.79917i
$689$	−16.3489	−	19.4838i	−0.622842	−	0.742275i
$690$	−56.2935	−	3.90495i	−2.14306	−	0.148659i
$691$	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
$693$	−1.22647	−	5.82940i	−0.0465899	−	0.221441i
$694$	−2.94733	−	5.08622i	−0.111879	−	0.193070i
$695$	12.0047	+	20.7927i	0.455363	+	0.788712i
$696$	11.0215	+	0.729295i	0.417767	+	0.0276439i
$697$	7.04354	−	39.9459i	0.266793	−	1.51306i
$698$	−11.0880	−	9.27390i	−0.419686	−	0.351022i
$699$	14.5689	+	14.0982i	0.551047	+	0.533243i
$700$	29.6745	−	17.2587i	1.12159	−	0.652319i
$701$	−8.96391	+	24.6281i	−0.338562	+	0.930192i	0.647241	+	0.762286i	$0.275923\pi$
$701$	−8.96391	+	24.6281i	−0.338562	+	0.930192i	−0.985803	+	0.167906i	$0.946299\pi$
$702$	20.6311	+	0.751706i	0.778670	+	0.0283713i
$703$	5.44925	−	11.3952i	0.205522	−	0.429779i
$704$	−2.56992	+	4.55104i	−0.0968577	+	0.171524i
$705$	10.0942	+	4.50674i	0.380169	+	0.169734i
$706$	7.28824	+	19.9256i	0.274297	+	0.749909i
$707$	−33.0342	−	27.7190i	−1.24238	−	1.04248i
$708$	−26.6238	−	17.8749i	−1.00058	−	0.671780i
$709$	−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
$711$	−39.3281	+	15.7950i	−1.47492	+	0.592358i
$712$	2.66577	−	3.20792i	0.0999040	−	0.120222i
$713$	8.22096	+	22.5869i	0.307877	+	0.845886i
$714$	−16.8469	−	23.1607i	−0.630481	−	0.866768i
$715$	−5.18662	−	2.99450i	−0.193969	−	0.111988i
$716$	8.35234	+	46.5026i	0.312142	+	1.73788i
$717$	8.33966	+	11.5036i	0.311450	+	0.429609i
$718$	−3.70560	+	6.44193i	−0.138292	+	0.240411i
$719$	−4.28932	−	24.3259i	−0.159965	−	0.907205i	−0.954105	−	0.299471i	$-0.903190\pi$
$719$	−4.28932	−	24.3259i	−0.159965	−	0.907205i	0.794141	−	0.607734i	$-0.207921\pi$
$720$	8.30547	+	38.2652i	0.309527	+	1.42606i
$721$	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
$726$	21.4792	+	14.4705i	0.797168	+	0.537052i
$727$	−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
$729$	21.9416	−	15.7343i	0.812651	−	0.582751i
$730$	0.385138	+	0.457509i	0.0142546	+	0.0169332i
$731$	42.6490	−	15.5230i	1.57743	−	0.574138i
$732$	−13.2708	−	18.1835i	−0.490504	−	0.672081i
$733$	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
$735$	3.07247	−	12.2689i	0.113330	−	0.452546i
$736$	39.9363	−	0.317748i	1.47207	−	0.0117123i
$737$	3.63278	−	4.32938i	0.133815	−	0.159475i
$738$	9.28003	+	43.7620i	0.341603	+	1.61090i
$739$	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
$741$	18.4394	+	10.4821i	0.677387	+	0.385070i
$742$	−6.81835	−	38.3122i	−0.250310	−	1.40649i
$743$	−36.0519	−	13.1218i	−1.32262	−	0.481393i	−0.418320	−	0.908300i	$-0.637381\pi$
$743$	−36.0519	−	13.1218i	−1.32262	−	0.481393i	−0.904296	+	0.426907i	$0.859603\pi$
$744$	13.4568	−	9.85405i	0.493352	−	0.361267i
$745$	−38.5723	−	32.3660i	−1.41318	−	1.18580i
$746$	12.8195	+	10.7221i	0.469356	+	0.392566i
$747$	2.56900	−	7.85124i	0.0939947	−	0.287262i
$748$	−4.95283	−	0.857074i	−0.181093	−	0.0313377i
$749$	−23.4852	+	13.5592i	−0.858129	+	0.495441i
$750$	−2.27043	−	4.64851i	−0.0829045	−	0.169740i
$751$	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
$753$	37.0793	+	25.0661i	1.35124	+	0.913461i
$754$	−0.0142543	−	8.95797i	−0.000519110	−	0.326230i
$755$	19.2426	−	16.1465i	0.700310	−	0.587630i
$756$	26.7880	+	16.7361i	0.974268	+	0.608684i
$757$	−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	$0.187324\pi$
$761$			30.6269i			1.11022i	−0.831776	+	0.555111i	$0.812676\pi$
$762$	0.183192	−	0.736490i	0.00663636	−	0.0266802i
$763$	25.3563	−	4.47099i	0.917959	−	0.161861i
$764$	−4.41925	−	1.59257i	−0.159883	−	0.0576170i
$765$	−31.9764	+	19.8892i	−1.15611	+	0.719095i
$766$	−47.0812	+	0.0749175i	−1.70111	+	0.00270688i
$767$	−13.0035	+	22.5227i	−0.469529	+	0.813249i
$768$	−7.94971	−	26.5481i	−0.286860	−	0.957972i
$769$	−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
$771$	−16.0194	−	32.9311i	−0.576926	−	1.18599i
$772$	4.45044	−	25.7181i	0.160175	−	0.925613i
$773$	−5.56522	−	0.981298i	−0.200167	−	0.0352948i	0.0726656	−	0.997356i	$-0.476849\pi$
$773$	−5.56522	−	0.981298i	−0.200167	−	0.0352948i	−0.272833	+	0.962062i	$0.587961\pi$
$774$	−37.2144	+	33.4758i	−1.33764	+	1.20326i
$775$	−12.3586	+	14.7284i	−0.443934	+	0.529060i
$776$	−8.47766	+	7.18284i	−0.304330	+	0.257849i
$777$	−13.9297	−	6.21918i	−0.499725	−	0.223112i
$778$	−19.2846	+	3.43204i	−0.691385	+	0.123045i
$779$	−12.3269	+	44.2771i	−0.441656	+	1.58639i
$780$	30.5067	−	8.81862i	1.09232	−	0.315757i
$781$	−3.53679	−	1.28729i	−0.126556	−	0.0460628i
$782$	13.1940	+	36.0714i	0.471816	+	1.28991i
$783$	−7.18414	−	9.25435i	−0.256740	−	0.330723i
$784$	−1.49827	+	8.82521i	−0.0535096	+	0.315186i
$785$	−22.9343	−	4.04394i	−0.818561	−	0.144334i
$786$	−9.73385	+	21.8954i	−0.347195	+	0.780982i
$787$	−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
$789$	−7.65816	−	26.8119i	−0.272638	−	0.954528i
$790$	−49.8724	+	41.9833i	−1.77438	+	1.49370i
$791$	16.0734	−	27.8399i	0.571503	−	0.989872i
$792$	5.41928	−	1.16723i	0.192566	−	0.0414757i
$793$	−13.9854	+	11.7351i	−0.496636	+	0.416727i
$794$	0.699570	−	1.21616i	0.0248268	−	0.0431597i
$795$	−50.8918	+	5.29571i	−1.80495	+	0.187820i
$796$	0.0800100	+	25.1407i	0.00283588	+	0.891088i
$797$		−	29.5333i		−	1.04612i	−0.852295	−	0.523061i	$-0.824790\pi$
$797$		−	29.5333i		−	1.04612i	0.852295	−	0.523061i	$-0.175210\pi$
$798$	16.4581	+	27.9687i	0.582610	+	0.990082i
$799$		−	7.52437i		−	0.266193i
$800$	16.1925	+	27.5378i	0.572490	+	0.973610i
$801$	−4.42161	+	0.145245i	−0.156230	+	0.00513198i
$802$	−21.4433	−	12.3349i	−0.757190	−	0.435559i
$803$	0.0648588	−	0.0544230i	0.00228882	−	0.00192055i
$804$	3.19638	+	29.7958i	0.112728	+	1.05082i
$805$	−35.0091	+	60.6376i	−1.23391	+	2.13719i
$806$	−8.71128	−	10.3482i	−0.306842	−	0.364500i
$807$	−19.6500	+	5.61254i	−0.691712	+	0.197571i
$808$	25.6480	−	30.8641i	0.902293	−	1.08580i
$809$	28.4311	−	16.4147i	0.999585	−	0.577111i	0.0914593	−	0.995809i	$-0.470847\pi$
$809$	28.4311	−	16.4147i	0.999585	−	0.577111i	0.908125	+	0.418698i	$0.137514\pi$
$810$	24.4971	−	33.5373i	0.860739	−	1.17838i
$811$	−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
$813$	−21.4354	−	20.7428i	−0.751771	−	0.727482i
$814$	−2.51441	+	0.919704i	−0.0881300	+	0.0322356i
$815$	21.4024	+	7.78984i	0.749694	+	0.272866i
$816$	21.4781	−	15.7803i	0.751883	−	0.552422i
$817$	−49.8018	+	12.8264i	−1.74235	+	0.448741i
$818$	−1.14742	−	6.44734i	−0.0401187	−	0.225426i
$819$	12.0730	−	22.5931i	0.421865	−	0.789467i
$820$	34.5952	+	59.4827i	1.20812	+	2.07723i
$821$	32.0878	−	38.2408i	1.11987	−	1.33461i	0.183736	−	0.982976i	$-0.441181\pi$
$821$	32.0878	−	38.2408i	1.11987	−	1.33461i	0.936137	−	0.351637i	$-0.114375\pi$
$822$	33.9405	+	32.7395i	1.18381	+	1.14192i
$823$	−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
$825$	−5.74645	+	2.79537i	−0.200066	+	0.0973224i
$826$	−34.4278	+	19.9500i	−1.19790	+	0.694150i
$827$	−50.3256	+	18.3170i	−1.74999	+	0.636946i	−0.999708	−	0.0241671i	$-0.992307\pi$
$827$	−50.3256	+	18.3170i	−1.74999	+	0.636946i	−0.750286	+	0.661113i	$0.770084\pi$
$828$	−28.3795	−	31.4482i	−0.986256	−	1.09290i
$829$	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
$831$	−25.9376	−	35.7779i	−0.899766	−	1.24112i
$832$	−21.0454	+	7.88825i	−0.729618	+	0.273476i
$833$	−8.47803	+	1.49491i	−0.293746	+	0.0517954i
$834$	−4.35052	+	17.4905i	−0.150646	+	0.605645i
$835$			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	$0.0130652\pi$
$839$	2.15188	+	12.2039i	0.0742910	+	0.421325i	−0.924867	+	0.380291i	$0.875824\pi$
$840$	47.1863	+	11.5777i	1.62808	+	0.399467i
$841$	18.3211	−	15.3732i	0.631762	−	0.530111i
$842$	42.5171	−	0.0676550i	1.46524	−	0.00233154i
$843$	13.2012	−	19.5279i	0.454672	−	0.672577i
$844$	15.8163	−	18.9715i	0.544421	−	0.653025i
$845$	5.69982	+	15.6601i	0.196080	+	0.538725i
$846$	3.10498	+	7.69569i	0.106751	+	0.264583i
$847$	27.8306	−	16.0680i	0.956270	−	0.552103i
$848$	35.6223	−	6.51522i	1.22328	−	0.223734i
$849$	10.1397	−	40.4895i	0.347993	−	1.38960i
$850$	−19.7108	+	23.5664i	−0.676074	+	0.808322i
$851$	15.6720	+	13.1504i	0.537231	+	0.450790i
$852$	17.9183	−	8.78702i	0.613870	−	0.301038i
$853$	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
$855$	38.2446	−	18.9217i	1.30794	−	0.647107i
$856$	−12.7222	−	21.7946i	−0.434837	−	0.744924i
$857$	4.46342	−	12.2632i	0.152468	−	0.418901i	−0.839819	−	0.542867i	$-0.817339\pi$
$857$	4.46342	−	12.2632i	0.152468	−	0.418901i	0.992287	+	0.123965i	$0.0395612\pi$
$858$	−1.24163	−	4.32099i	−0.0423884	−	0.147516i
$859$	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
$861$	53.8457	+	13.4844i	1.83506	+	0.459548i
$862$	−17.5313	−	6.34928i	−0.597117	−	0.216257i
$863$	13.5776	+	23.5171i	0.462188	+	0.800532i	0.999070	−	0.0431249i	$-0.0137313\pi$
$863$	13.5776	+	23.5171i	0.462188	+	0.800532i	−0.536882	+	0.843657i	$0.680398\pi$
$864$	−15.4553	+	25.0027i	−0.525798	+	0.850609i
$865$	−24.4753	+	8.90829i	−0.832186	+	0.302891i
$866$	15.1647	−	12.7658i	0.515316	−	0.433801i
$867$	−3.15904	−	2.13556i	−0.107287	−	0.0725274i
$868$	−3.65862	−	20.3697i	−0.124182	−	0.691394i
$869$	5.93257	+	7.07016i	0.201249	+	0.239839i
$870$	−14.9456	−	10.0688i	−0.506704	−	0.341366i
$871$	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
$876$	−0.0303542	+	0.447907i	−0.00102557	+	0.0151334i
$877$	−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
$879$	−17.0380	+	12.3519i	−0.574677	+	0.416619i
$880$	7.35739	−	4.31046i	0.248018	−	0.145306i
$881$	−24.4643	−	14.1245i	−0.824223	−	0.475865i	0.0276479	−	0.999618i	$-0.491198\pi$
$881$	−24.4643	−	14.1245i	−0.824223	−	0.475865i	−0.851870	+	0.523753i	$0.824532\pi$
$882$	8.05418	−	5.02746i	0.271198	−	0.169283i
$883$	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
$885$	22.8863	+	47.0474i	0.769316	+	1.58148i
$886$	−25.7687	−	9.33263i	−0.865717	−	0.313536i
$887$	−6.21498	+	35.2469i	−0.208679	+	1.18348i	0.682866	+	0.730543i	$0.260733\pi$
$887$	−6.21498	+	35.2469i	−0.208679	+	1.18348i	−0.891545	+	0.452932i	$0.850378\pi$
$888$	5.72557	−	12.9903i	0.192137	−	0.435927i
$889$	−0.721385	−	0.605314i	−0.0241945	−	0.0203016i
$890$	−6.39088	+	2.33761i	−0.214223	+	0.0783570i
$891$	−4.74254	−	3.47573i	−0.158881	−	0.116442i
$892$	10.8265	+	29.4536i	0.362499	+	0.986181i
$893$	−0.825664	+	8.48579i	−0.0276298	+	0.283966i
$894$	−3.97197	−	37.5896i	−0.132843	−	1.25718i
$895$	26.3640	−	72.4346i	0.881253	−	2.42122i
$896$	−33.9287	−	5.59363i	−1.13348	−	0.186870i
$897$	−23.8900	+	24.6877i	−0.797664	+	0.824297i
$898$	−25.6764	+	30.6990i	−0.856831	+	1.02444i
$899$	−1.33296	+	7.55958i	−0.0444566	+	0.252126i
$900$	10.4347	−	32.2368i	0.347824	−	1.07456i
$901$	17.4135	+	30.1610i	0.580127	+	1.00481i
$902$	8.42908	−	4.88443i	0.280658	−	0.162634i
$903$	17.0580	+	59.7216i	0.567656	+	1.98741i
$904$	25.9787	+	14.8339i	0.864037	+	0.493368i
$905$	−18.0608	−	10.4274i	−0.600361	−	0.346619i
$906$	18.8115	+	1.30491i	0.624971	+	0.0433528i
$907$	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
$909$	−42.5413	+	1.39744i	−1.41101	+	0.0463500i
$910$	6.78056	−	38.8155i	0.224773	−	1.28672i
$911$	22.5055			0.745639			0.372820	−	0.927904i	$-0.378391\pi$
$911$	22.5055			0.745639			0.372820	+	0.927904i	$0.378391\pi$
$912$	−25.9540	+	15.4398i	−0.859424	+	0.511264i
$913$	−1.79898			−0.0595375
$914$	0.0552529	−	0.316297i	0.00182760	−	0.0104622i
$915$	3.80124	+	36.5299i	0.125665	+	1.20764i
$916$	35.1513	+	12.6675i	1.16143	+	0.418545i
$917$	19.1114	+	22.7761i	0.631114	+	0.752132i
$918$	−27.6420	−	5.91921i	−0.912322	−	0.195363i
$919$	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
$921$	−14.0894	+	4.02431i	−0.464263	+	0.132605i
$922$	−37.0886	+	21.4919i	−1.22145	+	0.707798i
$923$	−8.09254	−	14.0167i	−0.266369	−	0.461365i
$924$	1.64974	−	6.67781i	0.0542725	−	0.219684i
$925$	−2.84167	+	16.1159i	−0.0934334	+	0.529887i
$926$	−12.1963	+	14.5820i	−0.400795	+	0.479195i
$927$	8.86385	−	7.94789i	0.291127	−	0.261043i
$928$	11.0959	+	6.28907i	0.364242	+	0.206449i
$929$	−6.13485	+	16.8554i	−0.201278	+	0.553006i	−0.998730	−	0.0503753i	$-0.983958\pi$
$929$	−6.13485	+	16.8554i	−0.201278	+	0.553006i	0.797452	+	0.603382i	$0.206180\pi$
$930$	−27.0612	+	2.85948i	−0.887373	+	0.0937660i
$931$	9.72534	−	0.755605i	0.318735	−	0.0247640i
$932$	8.07657	+	21.9724i	0.264557	+	0.719729i
$933$	18.0606	−	40.4521i	0.591279	−	1.32434i
$934$	22.5456	−	8.24660i	0.737716	−	0.269837i
$935$	6.28208	+	5.27129i	0.205446	+	0.172390i
$936$	21.0784	+	11.1345i	0.688968	+	0.363944i
$937$	−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
$939$	−14.1937	+	6.90458i	−0.463195	+	0.225322i
$940$	8.23606	+	9.75216i	0.268631	+	0.318080i
$941$	−2.86540	−	7.87263i	−0.0934094	−	0.256640i	0.884185	−	0.467136i	$-0.154714\pi$
$941$	−2.86540	−	7.87263i	−0.0934094	−	0.256640i	−0.977595	+	0.210496i	$0.932492\pi$
$942$	−10.2835	−	14.1375i	−0.335056	−	0.460625i
$943$	−64.4688	−	37.2211i	−2.09939	−	1.21208i
$944$	−18.7180	−	31.9492i	−0.609220	−	1.03986i
$945$	−24.0520	−	45.5760i	−0.782411	−	1.48259i
$946$	9.44889	+	5.43529i	0.307210	+	0.176716i
$947$	3.26107	+	18.4944i	0.105970	+	0.600988i	0.990828	+	0.135127i	$0.0431442\pi$
$947$	3.26107	+	18.4944i	0.105970	+	0.600988i	−0.884858	+	0.465861i	$0.845745\pi$
$948$	−48.8258	−	3.30887i	−1.58579	−	0.107467i
$949$	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	−0.0909813	−	0.995853i	$-0.529000\pi$
$953$	5.06668	−	0.893392i	0.164126	−	0.0289398i	0.255107	+	0.966913i	$0.417889\pi$
$954$	−30.2561	−	23.6620i	−0.979578	−	0.766085i
$955$	4.92627	+	5.87090i	0.159410	+	0.189978i
$956$	2.90038	+	16.1482i	0.0938050	+	0.522269i
$957$	−1.42887	+	2.11366i	−0.0461887	+	0.0683250i
$958$	24.7958	−	20.8735i	0.801117	−	0.674392i
$959$	54.9854	−	20.0130i	1.77557	−	0.646255i
$960$	−10.5643	+	43.9621i	−0.340962	+	1.41887i
$961$	−9.70440	−	16.8085i	−0.313045	−	0.542210i
$962$	−10.8250	−	3.92050i	−0.349014	−	0.126402i
$963$	−8.32409	+	25.4397i	−0.268240	+	0.819782i
$964$	6.13052	−	10.6969i	0.197451	−	0.344522i
$965$	−27.3717	+	32.6203i	−0.881126	+	1.05008i
$966$	−50.5173	+	14.5160i	−1.62537	+	0.467046i
$967$	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
$969$	−22.3729	−	18.5194i	−0.718720	−	0.594929i
$970$	17.8479	−	3.17636i	0.573063	−	0.101987i
$971$	8.41235	+	3.06185i	0.269965	+	0.0982593i	0.473456	−	0.880818i	$-0.343006\pi$
$971$	8.41235	+	3.06185i	0.269965	+	0.0982593i	−0.203490	+	0.979077i	$0.565229\pi$
$972$	30.7140	−	5.35267i	0.985152	−	0.171687i
$973$	17.1317	+	14.3752i	0.549218	+	0.460849i
$974$	−3.61688	+	4.32438i	−0.115892	+	0.138562i
$975$	−26.6565	−	6.67552i	−0.853691	−	0.213788i
$976$	−4.67660	−	25.5695i	−0.149694	−	0.818461i
$977$	19.6548	−	11.3477i	0.628813	−	0.363046i	−0.151479	−	0.988460i	$-0.548404\pi$
$977$	19.6548	−	11.3477i	0.628813	−	0.363046i	0.780292	+	0.625415i	$0.215070\pi$
$978$	7.50362	+	15.3630i	0.239939	+	0.491254i
$979$	0.329509	+	0.905318i	0.0105311	+	0.0289341i
$980$	9.35188	−	11.2174i	0.298735	−	0.358328i
$981$	15.6877	−	19.9939i	0.500869	−	0.638356i
$982$	32.1036	−	0.0510845i	1.02447	−	0.00163017i
$983$	−6.87084	+	5.76532i	−0.219146	+	0.183885i	−0.745751	−	0.666225i	$-0.767909\pi$
$983$	−6.87084	+	5.76532i	−0.219146	+	0.183885i	0.526605	+	0.850110i	$0.323465\pi$
$984$	−12.3091	+	50.1677i	−0.392401	+	1.59929i
$985$	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
$990$	−8.60035	−	2.79897i	−0.273337	−	0.0889571i
$991$	−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
$993$	−45.0004	+	32.6236i	−1.42804	+	1.03528i
$994$	−0.0394038	−	24.7629i	−0.00124981	−	0.785433i
$995$	20.5087	−	35.5221i	0.650170	−	1.12613i
$996$	6.61147	−	6.87587i	0.209492	−	0.217870i
$997$	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
$999$	−14.3347	+	4.60848i	−0.453530	+	0.145806i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.243359 - 1.39312i) q^{2} +(-1.72275 + 0.179266i) q^{3} +(-1.88155 - 0.678056i) q^{4} +(2.09742 + 2.49961i) q^{5} +(-0.169508 + 2.44362i) q^{6} +(2.63219 + 1.51969i) q^{7} +(-1.40250 + 2.45621i) q^{8} +(2.93573 - 0.617661i) q^{9} +O(q^{10})\)	\(q+(0.243359 - 1.39312i) q^{2} +(-1.72275 + 0.179266i) q^{3} +(-1.88155 - 0.678056i) q^{4} +(2.09742 + 2.49961i) q^{5} +(-0.169508 + 2.44362i) q^{6} +(2.63219 + 1.51969i) q^{7} +(-1.40250 + 2.45621i) q^{8} +(2.93573 - 0.617661i) q^{9} +(3.99268 - 2.31366i) q^{10} +(-0.326657 - 0.565787i) q^{11} +(3.36300 + 0.830821i) q^{12} +(0.487847 - 2.76672i) q^{13} +(2.75768 - 3.29711i) q^{14} +(-4.06143 - 3.93021i) q^{15} +(3.08048 + 2.55160i) q^{16} +(-1.31571 + 3.61488i) q^{17} +(-0.146038 - 4.24013i) q^{18} +(1.88049 - 3.93240i) q^{19} +(-2.25154 - 6.12533i) q^{20} +(-4.80702 - 2.14619i) q^{21} +(-0.867702 + 0.317382i) q^{22} +(5.40830 + 4.53810i) q^{23} +(1.97585 - 4.48286i) q^{24} +(-0.980636 + 5.56146i) q^{25} +(-3.73564 - 1.35293i) q^{26} +(-4.94680 + 1.59035i) q^{27} +(-3.92216 - 4.64415i) q^{28} +(0.771141 + 2.11869i) q^{29} +(-6.46363 + 4.70160i) q^{30} +(2.94846 + 1.70229i) q^{31} +(4.30433 - 3.67052i) q^{32} +(0.664175 + 0.916150i) q^{33} +(4.71577 + 2.71265i) q^{34} +(1.72217 + 9.76689i) q^{35} +(-5.94253 - 0.828425i) 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} +(-4.15973 + 6.17446i) q^{42} +(-7.58372 - 9.03792i) q^{43} +(0.230988 + 1.28605i) q^{44} +(7.70138 + 6.04269i) q^{45} +(7.63826 - 6.43000i) q^{46} +(-1.83801 + 0.668980i) q^{47} +(-5.76431 - 3.84353i) q^{48} +(1.11894 + 1.93805i) q^{49} +(7.50913 + 2.71957i) q^{50} +(1.61861 - 6.46340i) q^{51} +(-2.79390 + 4.87493i) q^{52} +(5.81935 - 6.93523i) q^{53} +(1.01170 + 7.27849i) q^{54} +(0.729109 - 2.00321i) q^{55} +(-7.42434 + 4.33383i) q^{56} +(-2.53467 + 7.11164i) q^{57} +(3.13925 - 0.558687i) q^{58} +(-8.69888 - 3.16613i) q^{59} +(4.97690 + 10.1488i) q^{60} +(-4.97808 - 4.17711i) q^{61} +(3.08903 - 3.69328i) q^{62} +(8.66604 + 2.83561i) q^{63} +(-4.06596 - 6.88970i) q^{64} +(7.93894 - 4.58355i) q^{65} +(1.43794 - 0.702320i) q^{66} +(2.95870 + 8.12896i) q^{67} +(4.92667 - 5.90947i) q^{68} +(-10.1307 - 6.84848i) q^{69} +(14.0255 - 0.0223180i) q^{70} +(4.41322 - 3.70313i) q^{71} +(-2.60026 + 8.07704i) 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} +(6.67810 + 1.66109i) q^{78} +(-13.9125 + 2.45315i) q^{79} +(0.0830752 + 13.0518i) q^{80} +(8.23699 - 3.62657i) q^{81} +(0.0237281 + 14.9117i) q^{82} +(1.37681 - 2.38470i) q^{83} +(7.58944 + 7.29760i) q^{84} +(-11.7954 + 4.29318i) q^{85} +(-14.4365 + 8.36555i) q^{86} +(-1.70829 - 3.51173i) q^{87} +(1.84783 - 0.00882109i) q^{88} +(-1.45226 - 0.256073i) q^{89} +(10.2924 - 9.25839i) q^{90} +(5.48866 - 6.54113i) q^{91} +(-7.09891 - 12.2058i) q^{92} +(-5.38461 - 2.40406i) q^{93} +(0.484672 + 2.72336i) q^{94} +(13.7737 - 3.54740i) q^{95} +(-6.75729 + 7.09500i) q^{96} +(3.69157 + 1.34362i) q^{97} +(2.97224 - 1.08717i) q^{98} +(-1.30844 - 1.45923i) 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

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