LMFDB - Embedded newform 552.2.t.a.19.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.19
Character	$\chi$	$=$	552.19
Dual form			552.2.t.a.523.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17115 - 0.792724i) q^{2} +(0.959493 - 0.281733i) q^{3} +(0.743177 - 1.85679i) q^{4} +(0.824449 + 0.529841i) q^{5} +(0.900373 - 1.09056i) q^{6} +(0.536086 + 3.72856i) q^{7} +(-0.601555 - 2.76372i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(1.17115 - 0.792724i) q^{2} +(0.959493 - 0.281733i) q^{3} +(0.743177 - 1.85679i) q^{4} +(0.824449 + 0.529841i) q^{5} +(0.900373 - 1.09056i) q^{6} +(0.536086 + 3.72856i) q^{7} +(-0.601555 - 2.76372i) q^{8} +(0.841254 - 0.540641i) q^{9} +(1.38557 - 0.0330378i) q^{10} +(2.79329 + 1.27565i) q^{11} +(0.189954 - 1.99096i) q^{12} +(1.96450 + 0.282452i) q^{13} +(3.58356 + 3.94173i) q^{14} +(0.940327 + 0.276105i) q^{15} +(-2.89537 - 2.75986i) q^{16} +(-0.726462 + 0.629483i) q^{17} +(0.556654 - 1.30005i) q^{18} +(-5.54449 - 4.80433i) q^{19} +(1.59652 - 1.13707i) q^{20} +(1.56483 + 3.42650i) q^{21} +(4.28260 - 0.720329i) q^{22} +(-3.39143 + 3.39090i) q^{23} +(-1.35582 - 2.48229i) q^{24} +(-1.67809 - 3.67451i) q^{25} +(2.52463 - 1.22651i) q^{26} +(0.654861 - 0.755750i) q^{27} +(7.32158 + 1.77558i) q^{28} +(3.85883 - 3.34370i) q^{29} +(1.32014 - 0.422060i) q^{30} +(1.57929 - 5.37857i) q^{31} +(-5.57872 - 0.936969i) q^{32} +(3.03954 + 0.437019i) q^{33} +(-0.351789 + 1.31310i) q^{34} +(-1.53357 + 3.35805i) q^{35} +(-0.378658 - 1.96383i) q^{36} +(-9.08706 + 5.83990i) q^{37} +(-10.3019 - 1.23133i) q^{38} +(1.96450 - 0.282452i) q^{39} +(0.968380 - 2.59727i) q^{40} +(-9.00665 - 5.78823i) q^{41} +(4.54891 + 2.77246i) q^{42} +(1.59145 + 5.41997i) q^{43} +(4.44454 - 4.23853i) q^{44} +0.980025 q^{45} +(-1.28382 + 6.65972i) q^{46} +10.4088i q^{47} +(-3.55563 - 1.83234i) q^{48} +(-6.89834 + 2.02554i) q^{49} +(-4.87816 - 2.97313i) q^{50} +(-0.519690 + 0.808653i) q^{51} +(1.98443 - 3.43776i) q^{52} +(-0.102462 - 0.712638i) q^{53} +(0.167838 - 1.40422i) q^{54} +(1.62703 + 2.53171i) q^{55} +(9.98221 - 3.72453i) q^{56} +(-6.67344 - 3.04766i) q^{57} +(1.86864 - 6.97495i) q^{58} +(-0.0209618 + 0.145793i) q^{59} +(1.21150 - 1.54080i) q^{60} +(2.08979 + 0.613618i) q^{61} +(-2.41414 - 7.55105i) q^{62} +(2.46680 + 2.84684i) q^{63} +(-7.27626 + 3.32505i) q^{64} +(1.46998 + 1.27374i) q^{65} +(3.90618 - 1.89770i) q^{66} +(10.1579 - 4.63894i) q^{67} +(0.628931 + 1.81671i) q^{68} +(-2.29873 + 4.20902i) q^{69} +(0.865969 + 5.14847i) q^{70} +(-3.62012 + 1.65325i) q^{71} +(-2.00024 - 1.99976i) q^{72} +(9.88976 - 11.4134i) q^{73} +(-6.01287 + 14.0429i) q^{74} +(-2.64534 - 3.05289i) q^{75} +(-13.0412 + 6.72452i) q^{76} +(-3.25891 + 11.0988i) q^{77} +(2.07681 - 1.88810i) q^{78} +(0.297379 - 2.06831i) q^{79} +(-0.924803 - 3.80945i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-15.1366 + 0.360920i) q^{82} +(6.75956 + 10.5181i) q^{83} +(7.52525 - 0.359071i) q^{84} +(-0.932458 + 0.134067i) q^{85} +(6.16036 + 5.08601i) q^{86} +(2.76049 - 4.29541i) q^{87} +(1.84523 - 8.48724i) q^{88} +(-0.0222747 - 0.0758606i) q^{89} +(1.14775 - 0.776889i) q^{90} +7.47618i q^{91} +(3.77577 + 8.81723i) q^{92} -5.60564i q^{93} +(8.25133 + 12.1903i) q^{94} +(-2.02562 - 6.89863i) q^{95} +(-5.61671 + 0.672692i) q^{96} +(-0.0735896 + 0.114508i) q^{97} +(-6.47329 + 7.84068i) q^{98} +(3.03954 - 0.437019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{15}{22}\right)$	$1$	$-1$	$-1$

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 $

$2$	1.17115	−	0.792724i	0.828127	−	0.560540i
$2$	1.17115	−	0.792724i	0.828127	−	0.560540i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	0.743177	−	1.85679i	0.371589	−	0.928397i
$5$	0.824449	+	0.529841i	0.368705	+	0.236952i	0.711852	−	0.702329i	$-0.247857\pi$
$5$	0.824449	+	0.529841i	0.368705	+	0.236952i	−0.343147	+	0.939282i	$0.611493\pi$
$6$	0.900373	−	1.09056i	0.367576	−	0.445221i
$7$	0.536086	+	3.72856i	0.202622	+	1.40926i	0.796466	+	0.604684i	$0.206701\pi$
$7$	0.536086	+	3.72856i	0.202622	+	1.40926i	−0.593844	+	0.804580i	$0.702390\pi$
$8$	−0.601555	−	2.76372i	−0.212682	−	0.977122i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	1.38557	−	0.0330378i	0.438156	−	0.0104475i
$11$	2.79329	+	1.27565i	0.842209	+	0.384624i	0.789324	−	0.613977i	$-0.210431\pi$
$11$	2.79329	+	1.27565i	0.842209	+	0.384624i	0.0528846	+	0.998601i	$0.483158\pi$
$12$	0.189954	−	1.99096i	0.0548350	−	0.574740i
$13$	1.96450	+	0.282452i	0.544854	+	0.0783382i	0.409246	−	0.912424i	$-0.365792\pi$
$13$	1.96450	+	0.282452i	0.544854	+	0.0783382i	0.135609	+	0.990762i	$0.456701\pi$
$14$	3.58356	+	3.94173i	0.957746	+	1.05347i
$15$	0.940327	+	0.276105i	0.242791	+	0.0712900i
$16$	−2.89537	−	2.75986i	−0.723844	−	0.689964i
$17$	−0.726462	+	0.629483i	−0.176193	+	0.152672i	−0.738493	−	0.674261i	$-0.764462\pi$
$17$	−0.726462	+	0.629483i	−0.176193	+	0.152672i	0.562300	+	0.826933i	$0.309917\pi$
$18$	0.556654	−	1.30005i	0.131205	−	0.306425i
$19$	−5.54449	−	4.80433i	−1.27199	−	1.10219i	−0.989745	−	0.142848i	$-0.954374\pi$
$19$	−5.54449	−	4.80433i	−1.27199	−	1.10219i	−0.282249	−	0.959341i	$-0.591081\pi$
$20$	1.59652	−	1.13707i	0.356992	−	0.254256i
$21$	1.56483	+	3.42650i	0.341474	+	0.747723i
$22$	4.28260	−	0.720329i	0.913053	−	0.153575i
$23$	−3.39143	+	3.39090i	−0.707162	+	0.707052i
$23$	−3.39143	+	3.39090i	−0.707162	+	0.707052i
$24$	−1.35582	−	2.48229i	−0.276755	−	0.506695i
$25$	−1.67809	−	3.67451i	−0.335618	−	0.734901i
$26$	2.52463	−	1.22651i	0.495120	−	0.240539i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	7.32158	+	1.77558i	1.38365	+	0.335553i
$29$	3.85883	−	3.34370i	0.716567	−	0.620909i	−0.218311	−	0.975879i	$-0.570055\pi$
$29$	3.85883	−	3.34370i	0.716567	−	0.620909i	0.934877	+	0.354971i	$0.115509\pi$
$30$	1.32014	−	0.422060i	0.241023	−	0.0770572i
$31$	1.57929	−	5.37857i	0.283649	−	0.966020i	−0.687228	−	0.726442i	$-0.741173\pi$
$31$	1.57929	−	5.37857i	0.283649	−	0.966020i	0.970877	−	0.239578i	$-0.0770092\pi$
$32$	−5.57872	−	0.936969i	−0.986187	−	0.165634i
$33$	3.03954	+	0.437019i	0.529115	+	0.0760753i
$34$	−0.351789	+	1.31310i	−0.0603313	+	0.225195i
$35$	−1.53357	+	3.35805i	−0.259221	+	0.567614i
$36$	−0.378658	−	1.96383i	−0.0631097	−	0.327305i
$37$	−9.08706	+	5.83990i	−1.49390	+	0.960074i	−0.498241	+	0.867038i	$0.666021\pi$
$37$	−9.08706	+	5.83990i	−1.49390	+	0.960074i	−0.995663	+	0.0930354i	$0.970343\pi$
$38$	−10.3019	−	1.23133i	−1.67119	−	0.199748i
$39$	1.96450	−	0.282452i	0.314572	−	0.0452286i
$40$	0.968380	−	2.59727i	0.153114	−	0.410665i
$41$	−9.00665	−	5.78823i	−1.40660	−	0.903969i	−0.406649	−	0.913584i	$-0.633303\pi$
$41$	−9.00665	−	5.78823i	−1.40660	−	0.903969i	−0.999954	+	0.00961533i	$0.996939\pi$
$42$	4.54891	+	2.77246i	0.701912	+	0.427800i
$43$	1.59145	+	5.41997i	0.242693	+	0.826537i	0.987277	+	0.159009i	$0.0508297\pi$
$43$	1.59145	+	5.41997i	0.242693	+	0.826537i	−0.744584	+	0.667529i	$0.767352\pi$
$44$	4.44454	−	4.23853i	0.670039	−	0.638983i
$45$	0.980025			0.146093
$46$	−1.28382	+	6.65972i	−0.189289	+	0.981921i
$47$			10.4088i			1.51828i	0.650925	+	0.759142i	$0.274381\pi$
$47$			10.4088i			1.51828i	−0.650925	+	0.759142i	$0.725619\pi$
$48$	−3.55563	−	1.83234i	−0.513211	−	0.264476i
$49$	−6.89834	+	2.02554i	−0.985477	+	0.289362i
$50$	−4.87816	−	2.97313i	−0.689876	−	0.420464i
$51$	−0.519690	+	0.808653i	−0.0727711	+	0.113234i
$52$	1.98443	−	3.43776i	0.275191	−	0.476732i
$53$	−0.102462	−	0.712638i	−0.0140742	−	0.0978883i	0.981574	−	0.191085i	$-0.0612006\pi$
$53$	−0.102462	−	0.712638i	−0.0140742	−	0.0978883i	−0.995648	+	0.0931966i	$0.970291\pi$
$54$	0.167838	−	1.40422i	0.0228399	−	0.191090i
$55$	1.62703	+	2.53171i	0.219389	+	0.341376i
$56$	9.98221	−	3.72453i	1.33393	−	0.497711i
$57$	−6.67344	−	3.04766i	−0.883918	−	0.403672i
$58$	1.86864	−	6.97495i	0.245364	−	0.915856i
$59$	−0.0209618	+	0.145793i	−0.00272900	+	0.0189806i	−0.991140	−	0.132818i	$-0.957597\pi$
$59$	−0.0209618	+	0.145793i	−0.00272900	+	0.0189806i	0.988411	+	0.151799i	$0.0485065\pi$
$60$	1.21150	−	1.54080i	0.156404	−	0.198916i
$61$	2.08979	+	0.613618i	0.267570	+	0.0785657i	0.412766	−	0.910837i	$-0.364563\pi$
$61$	2.08979	+	0.613618i	0.267570	+	0.0785657i	−0.145195	+	0.989403i	$0.546381\pi$
$62$	−2.41414	−	7.55105i	−0.306596	−	0.958984i
$63$	2.46680	+	2.84684i	0.310787	+	0.358668i
$64$	−7.27626	+	3.32505i	−0.909533	+	0.415632i
$65$	1.46998	+	1.27374i	0.182328	+	0.157988i
$66$	3.90618	−	1.89770i	0.480818	−	0.233590i
$67$	10.1579	−	4.63894i	1.24098	−	0.566736i	0.316726	−	0.948517i	$-0.397416\pi$
$67$	10.1579	−	4.63894i	1.24098	−	0.566736i	0.924253	+	0.381781i	$0.124689\pi$
$68$	0.628931	+	1.81671i	0.0762691	+	0.220308i
$69$	−2.29873	+	4.20902i	−0.276734	+	0.506707i
$70$	0.865969	+	5.14847i	0.103503	+	0.615360i
$71$	−3.62012	+	1.65325i	−0.429629	+	0.196205i	−0.618479	−	0.785801i	$-0.712251\pi$
$71$	−3.62012	+	1.65325i	−0.429629	+	0.196205i	0.188851	+	0.982006i	$0.439524\pi$
$72$	−2.00024	−	1.99976i	−0.235730	−	0.235674i
$73$	9.88976	−	11.4134i	1.15751	−	1.33584i	0.225140	−	0.974326i	$-0.427716\pi$
$73$	9.88976	−	11.4134i	1.15751	−	1.33584i	0.932368	−	0.361510i	$-0.117739\pi$
$74$	−6.01287	+	14.0429i	−0.698982	+	1.63246i
$75$	−2.64534	−	3.05289i	−0.305458	−	0.352517i
$76$	−13.0412	+	6.72452i	−1.49593	+	0.771355i
$77$	−3.25891	+	11.0988i	−0.371387	+	1.26483i
$78$	2.07681	−	1.88810i	0.235153	−	0.213785i
$79$	0.297379	−	2.06831i	0.0334577	−	0.232703i	−0.966230	−	0.257680i	$-0.917042\pi$
$79$	0.297379	−	2.06831i	0.0334577	−	0.232703i	0.999688	+	0.0249765i	$0.00795109\pi$
$80$	−0.924803	−	3.80945i	−0.103396	−	0.425909i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−15.1366	+	0.360920i	−1.67156	+	0.0398569i
$83$	6.75956	+	10.5181i	0.741958	+	1.15451i	0.982930	+	0.183978i	$0.0588974\pi$
$83$	6.75956	+	10.5181i	0.741958	+	1.15451i	−0.240972	+	0.970532i	$0.577466\pi$
$84$	7.52525	−	0.359071i	0.821072	−	0.0391778i
$85$	−0.932458	+	0.134067i	−0.101139	+	0.0145416i
$86$	6.16036	+	5.08601i	0.664289	+	0.548439i
$87$	2.76049	−	4.29541i	0.295956	−	0.460516i
$88$	1.84523	−	8.48724i	0.196702	−	0.904743i
$89$	−0.0222747	−	0.0758606i	−0.00236111	−	0.00804121i	0.958304	−	0.285751i	$-0.0922429\pi$
$89$	−0.0222747	−	0.0758606i	−0.00236111	−	0.00804121i	−0.960665	+	0.277709i	$0.910425\pi$
$90$	1.14775	−	0.776889i	0.120984	−	0.0818913i
$91$			7.47618i			0.783717i
$92$	3.77577	+	8.81723i	0.393651	+	0.919260i
$93$		−	5.60564i		−	0.581278i
$94$	8.25133	+	12.1903i	0.851060	+	1.25733i
$95$	−2.02562	−	6.89863i	−0.207824	−	0.707784i
$96$	−5.61671	+	0.672692i	−0.573254	+	0.0686563i
$97$	−0.0735896	+	0.114508i	−0.00747190	+	0.0116265i	−0.844969	−	0.534815i	$-0.820381\pi$
$97$	−0.0735896	+	0.114508i	−0.00747190	+	0.0116265i	0.837497	+	0.546441i	$0.184018\pi$
$98$	−6.47329	+	7.84068i	−0.653901	+	0.792029i
$99$	3.03954	−	0.437019i	0.305485	−	0.0439221i
$100$	−8.06992	+	0.385060i	−0.806992	+	0.0385060i
$101$	6.94706	+	10.8098i	0.691258	+	1.07562i	0.992521	+	0.122077i	$0.0389555\pi$
$101$	6.94706	+	10.8098i	0.691258	+	1.07562i	−0.301263	+	0.953541i	$0.597408\pi$
$102$	0.0324048	+	1.35902i	0.00320855	+	0.134563i
$103$	1.62454	−	3.55726i	0.160071	−	0.350507i	−0.812554	−	0.582885i	$-0.801924\pi$
$103$	1.62454	−	3.55726i	0.160071	−	0.350507i	0.972625	+	0.232379i	$0.0746509\pi$
$104$	−0.401135	−	5.59923i	−0.0393346	−	0.549050i
$105$	−0.525378	+	3.65408i	−0.0512716	+	0.356602i
$106$	−0.684923	−	0.753381i	−0.0665256	−	0.0731748i
$107$	−4.45368	+	15.1678i	−0.430554	+	1.46633i	0.403670	+	0.914905i	$0.367734\pi$
$107$	−4.45368	+	15.1678i	−0.430554	+	1.46633i	−0.834224	+	0.551426i	$0.814084\pi$
$108$	−0.916594	−	1.77760i	−0.0881993	−	0.171049i
$109$	−9.99429	−	11.5340i	−0.957280	−	1.10476i	−0.994425	−	0.105450i	$-0.966372\pi$
$109$	−9.99429	−	11.5340i	−0.957280	−	1.10476i	0.0371449	−	0.999310i	$-0.488174\pi$
$110$	3.91244	+	1.67522i	0.373037	+	0.159726i
$111$	−7.07368	+	8.16347i	−0.671404	+	0.774842i
$112$	8.73813	−	12.2751i	0.825675	−	1.15989i
$113$	−6.34601	+	2.89812i	−0.596982	+	0.272633i	−0.690903	−	0.722947i	$-0.742787\pi$
$113$	−6.34601	+	2.89812i	−0.596982	+	0.272633i	0.0939214	+	0.995580i	$0.470060\pi$
$114$	−10.2315	+	1.72094i	−0.958271	+	0.161180i
$115$	−4.59270	+	0.998705i	−0.428272	+	0.0931297i
$116$	−3.34076	−	9.65001i	−0.310182	−	0.895981i
$117$	1.80535	−	0.824475i	0.166904	−	0.0762227i
$118$	0.0910240	+	0.187362i	0.00837944	+	0.0172481i
$119$	−2.73651	−	2.37120i	−0.250856	−	0.217368i
$120$	0.197418	−	2.76489i	0.0180217	−	0.252399i
$121$	−1.02829	−	1.18671i	−0.0934808	−	0.107883i
$122$	2.93389	−	0.937990i	0.265621	−	0.0849216i
$123$	−10.2726	−	3.01629i	−0.926245	−	0.271970i
$124$	−8.81321	−	6.92965i	−0.791450	−	0.622301i
$125$	1.26076	−	8.76881i	0.112766	−	0.784306i
$126$	5.14574	+	1.37858i	0.458419	+	0.122814i
$127$	−8.27273	−	3.77803i	−0.734086	−	0.335246i	0.0130522	−	0.999915i	$-0.495845\pi$
$127$	−8.27273	−	3.77803i	−0.734086	−	0.335246i	−0.747138	+	0.664669i	$0.768573\pi$
$128$	−5.88574	+	9.66220i	−0.520230	+	0.854026i
$129$	3.05396	+	4.75206i	0.268886	+	0.418395i
$130$	2.73128	+	0.326455i	0.239549	+	0.0286320i
$131$	2.31349	+	16.0906i	0.202130	+	1.40585i	0.797948	+	0.602727i	$0.205919\pi$
$131$	2.31349	+	16.0906i	0.202130	+	1.40585i	−0.595818	+	0.803120i	$0.703172\pi$
$132$	3.07037	−	5.31901i	0.267241	−	0.462960i
$133$	14.9409	−	23.2485i	1.29554	−	2.01590i
$134$	8.21896	−	13.4853i	0.710010	−	1.16495i
$135$	0.940327	−	0.276105i	0.0809304	−	0.0237633i
$136$	2.17672	+	1.62907i	0.186652	+	0.139691i
$137$		−	7.33306i		−	0.626506i	−0.949670	−	0.313253i	$-0.898581\pi$
$137$		−	7.33306i		−	0.626506i	0.949670	−	0.313253i	$-0.101419\pi$
$138$	0.644442	+	6.75164i	0.0548586	+	0.574738i
$139$	10.0889			0.855727			0.427864	−	0.903843i	$-0.359266\pi$
$139$	10.0889			0.855727			0.427864	+	0.903843i	$0.359266\pi$
$140$	5.09550	+	5.34315i	0.430648	+	0.451579i
$141$	2.93251	+	9.98720i	0.246962	+	0.841074i
$142$	−2.92912	+	4.80595i	−0.245806	+	0.403307i
$143$	5.12711	+	3.29499i	0.428750	+	0.275541i
$144$	−3.92783	−	0.756381i	−0.327320	−	0.0630318i
$145$	4.95304	−	0.712139i	0.411327	−	0.0591399i
$146$	2.53471	−	21.2066i	0.209774	−	1.75507i
$147$	−6.04825	+	3.88697i	−0.498851	+	0.320592i
$148$	4.09020	+	21.2129i	0.336212	+	1.74369i
$149$	2.17408	−	4.76056i	0.178107	−	0.390001i	−0.799431	−	0.600758i	$-0.794866\pi$
$149$	2.17408	−	4.76056i	0.178107	−	0.390001i	0.977538	+	0.210757i	$0.0675929\pi$
$150$	−5.51819	−	1.47836i	−0.450558	−	0.120708i
$151$	−12.1076	−	1.74081i	−0.985302	−	0.141665i	−0.369216	−	0.929344i	$-0.620374\pi$
$151$	−12.1076	−	1.74081i	−0.985302	−	0.141665i	−0.616086	+	0.787679i	$0.711283\pi$
$152$	−9.94249	+	18.2135i	−0.806443	+	1.47731i
$153$	−0.270815	+	0.922310i	−0.0218941	+	0.0745644i
$154$	4.98163	+	15.5818i	0.401432	+	1.25562i
$155$	4.15184	−	3.59759i	0.333483	−	0.288965i
$156$	0.935516	−	3.85759i	0.0749012	−	0.308854i
$157$	−5.07367	+	5.85533i	−0.404923	+	0.467306i	−0.921185	−	0.389125i	$-0.872778\pi$
$157$	−5.07367	+	5.85533i	−0.404923	+	0.467306i	0.516262	+	0.856431i	$0.327323\pi$
$158$	−1.29133	−	2.65804i	−0.102732	−	0.211462i
$159$	−0.299085	−	0.654904i	−0.0237190	−	0.0519373i
$160$	−4.10292	−	3.72832i	−0.324365	−	0.294749i
$161$	−14.4613	−	10.8273i	−1.13971	−	0.853314i
$162$	−0.234574	−	1.39462i	−0.0184299	−	0.109572i
$163$	4.86139	+	10.6450i	0.380774	+	0.833778i	0.998863	+	0.0476705i	$0.0151797\pi$
$163$	4.86139	+	10.6450i	0.380774	+	0.833778i	−0.618089	+	0.786108i	$0.712093\pi$
$164$	−17.4411	+	12.4218i	−1.36192	+	0.969982i
$165$	2.27439	+	1.97077i	0.177061	+	0.153424i
$166$	16.2544	+	6.95977i	1.26159	+	0.540183i
$167$	−6.26748	+	5.43080i	−0.484992	+	0.420248i	−0.862730	−	0.505665i	$-0.831247\pi$
$167$	−6.26748	+	5.43080i	−0.484992	+	0.420248i	0.377738	+	0.925912i	$0.376702\pi$
$168$	8.52854	−	6.38597i	0.657991	−	0.492688i
$169$	−8.69393	−	2.55277i	−0.668764	−	0.196367i
$170$	−0.985768	+	0.896194i	−0.0756050	+	0.0687349i
$171$	−7.26174	−	1.04408i	−0.555319	−	0.0798429i
$172$	11.2465	+	1.07301i	0.857537	+	0.0818162i
$173$	−0.813558	−	0.371540i	−0.0618537	−	0.0282476i	0.384248	−	0.923230i	$-0.374461\pi$
$173$	−0.813558	−	0.371540i	−0.0618537	−	0.0282476i	−0.446102	+	0.894982i	$0.647188\pi$
$174$	−0.172128	−	7.21887i	−0.0130490	−	0.547261i
$175$	12.8010	−	8.22672i	0.967666	−	0.621881i
$176$	−4.56700	−	11.4026i	−0.344251	−	0.859501i
$177$	0.0209618	+	0.145793i	0.00157559	+	0.0109585i
$178$	−0.0862235	−	0.0711863i	−0.00646272	−	0.00533564i
$179$	11.6684	+	7.49884i	0.872139	+	0.560490i	0.898406	−	0.439165i	$-0.144726\pi$
$179$	11.6684	+	7.49884i	0.872139	+	0.560490i	−0.0262674	+	0.999655i	$0.508362\pi$
$180$	0.728332	−	1.81970i	0.0542867	−	0.135633i
$181$	14.5813	−	4.28145i	1.08382	−	0.318238i	0.309413	−	0.950928i	$-0.399867\pi$
$181$	14.5813	−	4.28145i	1.08382	−	0.318238i	0.774405	+	0.632690i	$0.218049\pi$
$182$	5.92655	+	8.75572i	0.439305	+	0.649017i
$183$	2.17802			0.161004
$184$	11.4116	+	7.33314i	0.841276	+	0.540606i
$185$	−10.5860			−0.778301
$186$	−4.44373	−	6.56504i	−0.325830	−	0.481372i
$187$	−2.83222	+	0.831616i	−0.207113	+	0.0608138i
$188$	19.3271	+	7.73561i	1.40957	+	0.564177i
$189$	3.16892	+	2.03654i	0.230505	+	0.148137i
$190$	−7.84101	−	6.47356i	−0.568847	−	0.469641i
$191$	−2.26290	−	15.7388i	−0.163738	−	1.13882i	−0.891509	−	0.453002i	$-0.850353\pi$
$191$	−2.26290	−	15.7388i	−0.163738	−	1.13882i	0.727771	−	0.685820i	$-0.240556\pi$
$192$	−6.04475	+	5.24033i	−0.436242	+	0.378188i
$193$	−7.54936	+	4.85168i	−0.543415	+	0.349232i	−0.783373	−	0.621552i	$-0.786503\pi$
$193$	−7.54936	+	4.85168i	−0.543415	+	0.349232i	0.239958	+	0.970783i	$0.422866\pi$
$194$	0.00458862	+	0.192442i	0.000329443	+	0.0138165i
$195$	1.76929	+	0.808005i	0.126701	+	0.0578625i
$196$	−1.36569	+	14.3141i	−0.0975491	+	1.02244i
$197$	−15.6394	−	2.24861i	−1.11426	−	0.160207i	−0.439501	−	0.898242i	$-0.644845\pi$
$197$	−15.6394	−	2.24861i	−1.11426	−	0.160207i	−0.674762	+	0.738035i	$0.735754\pi$
$198$	3.21331	−	2.92133i	0.228360	−	0.207610i
$199$	−15.4116	−	4.52526i	−1.09250	−	0.320787i	−0.314631	−	0.949214i	$-0.601881\pi$
$199$	−15.4116	−	4.52526i	−1.09250	−	0.320787i	−0.777868	+	0.628427i	$0.783699\pi$
$200$	−9.14583	+	6.84818i	−0.646708	+	0.484240i
$201$	8.43945	−	7.31283i	0.595273	−	0.515807i
$202$	16.7052	+	7.15282i	1.17538	+	0.503271i
$203$	14.5358	+	12.5954i	1.02022	+	0.884022i
$204$	1.11528	+	1.56593i	0.0780853	+	0.109637i
$205$	−4.35869	−	9.54420i	−0.304424	−	0.666596i
$206$	−0.917339	−	5.45389i	−0.0639140	−	0.379990i
$207$	−1.01979	+	4.68615i	−0.0708805	+	0.325710i
$208$	−4.90843	−	6.23954i	−0.340339	−	0.432634i
$209$	−9.35872	−	20.4927i	−0.647356	−	1.41751i
$210$	2.28138	+	4.69595i	0.157430	+	0.324052i
$211$	9.04908	−	10.4432i	0.622965	−	0.718939i	−0.353303	−	0.935509i	$-0.614941\pi$
$211$	9.04908	−	10.4432i	0.622965	−	0.718939i	0.976267	+	0.216570i	$0.0694869\pi$
$212$	−1.39937	−	0.339366i	−0.0961091	−	0.0233077i
$213$	−3.00770	+	2.60619i	−0.206084	+	0.178573i
$214$	6.80799	+	21.2943i	0.465385	+	1.45565i
$215$	−1.55966	+	5.31170i	−0.106368	+	0.362255i
$216$	−2.48261	−	1.35523i	−0.168920	−	0.0922114i
$217$	20.9010	+	3.00511i	1.41885	+	0.204000i
$218$	−20.8481	−	5.58535i	−1.41201	−	0.378287i
$219$	6.27363	−	13.7373i	0.423933	−	0.928283i
$220$	5.91004	−	1.13955i	0.398455	−	0.0768287i
$221$	−1.60493	+	1.03143i	−0.107960	+	0.0693814i
$222$	−1.81296	+	15.1681i	−0.121678	+	1.01802i
$223$	9.94294	−	1.42958i	0.665829	−	0.0957317i	0.198891	−	0.980022i	$-0.436266\pi$
$223$	9.94294	−	1.42958i	0.665829	−	0.0957317i	0.466938	+	0.884290i	$0.345357\pi$
$224$	0.502872	−	21.3029i	0.0335995	−	1.42336i
$225$	−3.39829	−	2.18395i	−0.226552	−	0.145596i
$226$	−5.13470	+	8.42476i	−0.341555	+	0.560407i
$227$	−3.85207	−	13.1189i	−0.255671	−	0.870734i	−0.982869	−	0.184307i	$-0.940996\pi$
$227$	−3.85207	−	13.1189i	−0.255671	−	0.870734i	0.727198	−	0.686428i	$-0.240822\pi$
$228$	−10.6184	+	10.1263i	−0.703222	+	0.670628i
$229$	14.5577			0.962002			0.481001	−	0.876720i	$-0.340273\pi$
$229$	14.5577			0.962002			0.481001	+	0.876720i	$0.340273\pi$
$230$	−4.58704	+	4.81038i	−0.302460	+	0.317187i
$231$			11.5674i			0.761078i
$232$	−11.5623	−	8.65330i	−0.759104	−	0.568117i
$233$	3.59168	−	1.05461i	0.235299	−	0.0690899i	−0.161957	−	0.986798i	$-0.551781\pi$
$233$	3.59168	−	1.05461i	0.235299	−	0.0690899i	0.397256	+	0.917708i	$0.369963\pi$
$234$	1.46075	−	2.39672i	0.0954922	−	0.156679i
$235$	−5.51503	+	8.58155i	−0.359761	+	0.559799i
$236$	0.255129	+	0.147272i	0.0166075	+	0.00958657i
$237$	−0.297379	−	2.06831i	−0.0193168	−	0.134351i
$238$	−5.08457	−	0.607731i	−0.329584	−	0.0393933i
$239$	16.5678	+	25.7799i	1.07168	+	1.66757i	0.647702	+	0.761894i	$0.275730\pi$
$239$	16.5678	+	25.7799i	1.07168	+	1.66757i	0.423978	+	0.905673i	$0.360633\pi$
$240$	−1.96059	−	3.39459i	−0.126555	−	0.219120i
$241$	23.7316	+	10.8378i	1.52869	+	0.698127i	0.989563	−	0.144101i	$-0.0460289\pi$
$241$	23.7316	+	10.8378i	1.52869	+	0.698127i	0.539122	+	0.842228i	$0.318756\pi$
$242$	−2.14501	−	0.574662i	−0.137886	−	0.0369407i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	2.69245	−	3.42429i	0.172366	−	0.219217i
$245$	−6.76054	−	1.98507i	−0.431915	−	0.126822i
$246$	−14.4218	+	4.61077i	−0.919499	+	0.293972i
$247$	−9.53516	−	11.0042i	−0.606708	−	0.700178i
$248$	−15.8149	−	1.12921i	−1.00425	−	0.0717049i
$249$	9.44904	+	8.18764i	0.598808	+	0.518870i
$250$	−5.47470	−	11.2690i	−0.346251	−	0.712715i
$251$	12.4542	−	5.68764i	0.786102	−	0.359001i	0.0184186	−	0.999830i	$-0.494137\pi$
$251$	12.4542	−	5.68764i	0.786102	−	0.359001i	0.767683	+	0.640830i	$0.221410\pi$
$252$	7.11926	−	2.46463i	0.448471	−	0.155257i
$253$	−13.7989	+	5.14548i	−0.867527	+	0.323494i
$254$	−12.6835	+	2.13336i	−0.795835	+	0.133859i
$255$	−0.856915	+	0.391340i	−0.0536621	+	0.0245067i
$256$	0.766387	+	15.9816i	0.0478992	+	0.998852i
$257$	6.50631	−	7.50868i	0.405852	−	0.468378i	−0.515623	−	0.856816i	$-0.672439\pi$
$257$	6.50631	−	7.50868i	0.405852	−	0.468378i	0.921475	+	0.388437i	$0.126985\pi$
$258$	7.34371	+	3.14442i	0.457200	+	0.195763i
$259$	−26.6459	−	30.7510i	−1.65569	−	1.91077i
$260$	3.45753	−	1.78283i	0.214427	−	0.110566i
$261$	1.43852	−	4.89914i	0.0890419	−	0.303249i
$262$	15.4649	+	17.0106i	0.955423	+	1.05092i
$263$	0.742776	−	5.16612i	0.0458016	−	0.318557i	−0.954021	−	0.299739i	$-0.903101\pi$
$263$	0.742776	−	5.16612i	0.0458016	−	0.318557i	0.999823	−	0.0188182i	$-0.00599037\pi$
$264$	−0.620649	−	8.66331i	−0.0381983	−	0.533190i
$265$	0.293110	−	0.641822i	0.0180056	−	0.0394268i
$266$	−0.931627	−	39.0715i	−0.0571217	−	2.39563i
$267$	−0.0427448	−	0.0665122i	−0.00261594	−	0.00407048i
$268$	−1.06447	−	22.3086i	−0.0650226	−	1.36272i
$269$	−8.50673	+	1.22308i	−0.518664	+	0.0745727i	−0.396676	−	0.917959i	$-0.629836\pi$
$269$	−8.50673	+	1.22308i	−0.518664	+	0.0745727i	−0.121989	+	0.992531i	$0.538927\pi$
$270$	0.882387	−	1.06878i	0.0537004	−	0.0650438i
$271$	5.86094	−	9.11981i	0.356027	−	0.553989i	−0.616330	−	0.787488i	$-0.711381\pi$
$271$	5.86094	−	9.11981i	0.356027	−	0.553989i	0.972357	+	0.233499i	$0.0750176\pi$
$272$	3.84066	+	0.182342i	0.232874	+	0.0110561i
$273$	2.10628	+	7.17334i	0.127478	+	0.434150i
$274$	−5.81309	−	8.58810i	−0.351182	−	0.518826i
$275$		−	12.4046i		−	0.748027i
$276$	6.10693	+	7.39631i	0.367594	+	0.445206i
$277$		−	12.6045i		−	0.757330i	−0.925534	−	0.378665i	$-0.876383\pi$
$277$		−	12.6045i		−	0.757330i	0.925534	−	0.378665i	$-0.123617\pi$
$278$	11.8156	−	7.99769i	0.708651	−	0.479670i
$279$	−1.57929	−	5.37857i	−0.0945497	−	0.322007i
$280$	10.2032	+	2.21830i	0.609760	+	0.132569i
$281$	11.7605	−	18.2997i	0.701574	−	1.09167i	−0.289347	−	0.957224i	$-0.593438\pi$
$281$	11.7605	−	18.2997i	0.701574	−	1.09167i	0.990921	−	0.134446i	$-0.0429255\pi$
$282$	11.3515	+	9.37183i	0.675972	+	0.558084i
$283$	−18.2167	+	2.61916i	−1.08287	+	0.155693i	−0.660571	−	0.750764i	$-0.729686\pi$
$283$	−18.2167	+	2.61916i	−1.08287	+	0.155693i	−0.422299	+	0.906457i	$0.638777\pi$
$284$	0.379360	+	7.95047i	0.0225109	+	0.471774i
$285$	−3.88714	−	6.04850i	−0.230254	−	0.358282i
$286$	8.61662	−	0.205456i	0.509512	−	0.0121489i
$287$	16.7534	−	36.6849i	0.988923	−	2.16544i
$288$	−5.19968	+	2.22785i	−0.306394	+	0.131278i
$289$	−2.28785	+	15.9124i	−0.134580	+	0.936022i
$290$	5.23621	−	4.76041i	0.307481	−	0.279541i
$291$	−0.0383482	+	0.130602i	−0.00224801	+	0.00765602i
$292$	−13.8425	−	26.8454i	−0.810070	−	1.57101i
$293$	9.63976	+	11.1249i	0.563161	+	0.649922i	0.963898	−	0.266271i	$-0.0857916\pi$
$293$	9.63976	+	11.1249i	0.563161	+	0.649922i	−0.400738	+	0.916193i	$0.631246\pi$
$294$	−4.00210	+	9.34682i	−0.233407	+	0.545117i
$295$	−0.0945290	+	0.109092i	−0.00550369	+	0.00635160i
$296$	21.6062	+	21.6011i	1.25583	+	1.25554i
$297$	2.79329	−	1.27565i	0.162083	−	0.0740209i
$298$	−1.22765	−	7.29877i	−0.0711156	−	0.422806i
$299$	−7.62023	+	5.70351i	−0.440689	+	0.329842i
$300$	−7.63455	+	2.64302i	−0.440781	+	0.152595i
$301$	−19.3555	+	8.83938i	−1.11563	+	0.509493i
$302$	−15.5598	+	7.55923i	−0.895364	+	0.434985i
$303$	9.71113	+	8.41474i	0.557890	+	0.483414i
$304$	2.79412	+	29.2123i	0.160254	+	1.67544i
$305$	1.39781	+	1.61315i	0.0800382	+	0.0923690i
$306$	0.413973	+	1.29484i	0.0236653	+	0.0740213i
$307$	9.00611	+	2.64443i	0.514006	+	0.150926i	0.528441	−	0.848970i	$-0.322777\pi$
$307$	9.00611	+	2.64443i	0.514006	+	0.150926i	−0.0144351	+	0.999896i	$0.504595\pi$
$308$	18.1863	+	14.2995i	1.03626	+	0.814790i
$309$	0.556544	−	3.87085i	0.0316607	−	0.220205i
$310$	2.01052	−	7.50457i	0.114190	−	0.426231i
$311$	14.4930	+	6.61875i	0.821824	+	0.375315i	0.781526	−	0.623873i	$-0.214442\pi$
$311$	14.4930	+	6.61875i	0.821824	+	0.375315i	0.0402987	+	0.999188i	$0.487169\pi$
$312$	−1.96237	−	5.25941i	−0.111097	−	0.297756i
$313$	−7.32210	−	11.3934i	−0.413869	−	0.643993i	0.570256	−	0.821467i	$-0.306844\pi$
$313$	−7.32210	−	11.3934i	−0.413869	−	0.643993i	−0.984126	+	0.177474i	$0.943208\pi$
$314$	−1.30036	+	10.8795i	−0.0733837	+	0.613964i
$315$	0.525378	+	3.65408i	0.0296017	+	0.205884i
$316$	−3.61943	−	2.08929i	−0.203609	−	0.117532i
$317$	1.20500	−	1.87502i	0.0676796	−	0.105312i	−0.805764	−	0.592237i	$-0.798245\pi$
$317$	1.20500	−	1.87502i	0.0676796	−	0.105312i	0.873444	+	0.486925i	$0.161881\pi$
$318$	−0.869431	−	0.529898i	−0.0487553	−	0.0297152i
$319$	15.0442	−	4.41738i	0.842315	−	0.247326i
$320$	−7.76066	−	1.11393i	−0.433834	−	0.0622704i
$321$			15.8082i			0.882327i
$322$	−25.5194	−	1.21662i	−1.42214	−	0.0677996i
$323$	7.05211			0.392390
$324$	−1.38027	−	1.44736i	−0.0766818	−	0.0804088i
$325$	−2.25874	−	7.69255i	−0.125292	−	0.426706i
$326$	14.1319	+	8.61310i	0.782696	+	0.477035i
$327$	−12.8390	−	8.25110i	−0.709996	−	0.456287i
$328$	−10.5790	+	28.3738i	−0.584129	+	1.56668i
$329$	−38.8100	+	5.58003i	−2.13966	+	0.307637i
$330$	4.22593	+	0.505101i	0.232630	+	0.0278049i
$331$	25.6600	−	16.4907i	1.41040	−	0.906410i	0.410417	−	0.911898i	$-0.365383\pi$
$331$	25.6600	−	16.4907i	1.41040	−	0.906410i	0.999985	+	0.00548794i	$0.00174687\pi$
$332$	24.5535	−	4.73432i	1.34755	−	0.259829i
$333$	−4.48724	+	9.82567i	−0.245899	+	0.538444i
$334$	−3.03502	+	11.3287i	−0.166069	+	0.619876i
$335$	10.8325	+	1.55748i	0.591845	+	0.0850944i
$336$	4.92587	−	14.2397i	0.268728	−	0.776839i
$337$	4.97171	−	16.9321i	0.270826	−	0.922350i	−0.705981	−	0.708231i	$-0.749494\pi$
$337$	4.97171	−	16.9321i	0.270826	−	0.922350i	0.976807	−	0.214119i	$-0.0686882\pi$
$338$	−12.2055	+	3.90222i	−0.663893	+	0.212253i
$339$	−5.27245	+	4.56861i	−0.286360	+	0.248133i
$340$	−0.444046	+	1.83102i	−0.0240818	+	0.0993009i
$341$	11.2726	−	13.0093i	0.610446	−	0.704492i
$342$	−9.33225	+	4.53378i	−0.504630	+	0.245159i
$343$	−0.296643	−	0.649557i	−0.0160172	−	0.0350728i
$344$	14.0219	−	7.65871i	0.756011	−	0.412930i
$345$	−4.12530	+	2.25216i	−0.222098	+	0.121252i
$346$	−1.24733	+	0.209799i	−0.0670567	+	0.0112789i
$347$	−8.34939	−	18.2826i	−0.448219	−	0.981462i	−0.990016	−	0.140953i	$-0.954983\pi$
$347$	−8.34939	−	18.2826i	−0.448219	−	0.981462i	0.541798	−	0.840509i	$-0.317744\pi$
$348$	−5.92416	−	8.31792i	−0.317568	−	0.445887i
$349$	7.47836	+	6.48004i	0.400308	+	0.346868i	0.831631	−	0.555329i	$-0.187408\pi$
$349$	7.47836	+	6.48004i	0.400308	+	0.346868i	−0.431323	+	0.902197i	$0.641953\pi$
$350$	8.47038	−	19.7824i	0.452761	−	1.05741i
$351$	1.49994	−	1.29970i	0.0800607	−	0.0693730i
$352$	−14.3877	−	9.73373i	−0.766869	−	0.518810i
$353$	25.5959	+	7.51565i	1.36233	+	0.400017i	0.879585	−	0.475741i	$-0.157820\pi$
$353$	25.5959	+	7.51565i	1.36233	+	0.400017i	0.482749	+	0.875759i	$0.339638\pi$
$354$	0.140123	+	0.154128i	0.00744745	+	0.00819181i
$355$	−3.86056	−	0.555065i	−0.204897	−	0.0294598i
$356$	−0.157412	−	0.0150184i	−0.00834280	−	0.000795972i
$357$	−3.29371	−	1.50419i	−0.174322	−	0.0796101i
$358$	19.6100	−	0.467583i	1.03642	−	0.0247125i
$359$	−8.69371	+	5.58711i	−0.458836	+	0.294876i	−0.749567	−	0.661929i	$-0.769738\pi$
$359$	−8.69371	+	5.58711i	−0.458836	+	0.294876i	0.290730	+	0.956805i	$0.406102\pi$
$360$	−0.589538	−	2.70851i	−0.0310714	−	0.142751i
$361$	4.95583	+	34.4685i	0.260833	+	1.81413i
$362$	13.6828	−	16.5732i	0.719154	−	0.871066i
$363$	−1.32097	−	0.848936i	−0.0693329	−	0.0445576i
$364$	13.8817	+	5.55613i	0.727600	+	0.291220i
$365$	14.2009	−	4.16976i	0.743308	−	0.218255i
$366$	2.55078	−	1.72657i	0.133331	−	0.0902490i
$367$	−32.4592			−1.69436			−0.847179	−	0.531308i	$-0.821701\pi$
$367$	−32.4592			−1.69436			−0.847179	+	0.531308i	$0.821701\pi$
$368$	19.1779	−	0.458067i	0.999715	−	0.0238784i
$369$	−10.7062			−0.557344
$370$	−12.3978	+	8.39181i	−0.644532	+	0.436269i
$371$	2.60219	−	0.764071i	0.135099	−	0.0396686i
$372$	−10.4085	−	4.16599i	−0.539657	−	0.215996i
$373$	−9.50790	−	6.11036i	−0.492301	−	0.316382i	0.270829	−	0.962627i	$-0.412702\pi$
$373$	−9.50790	−	6.11036i	−0.492301	−	0.316382i	−0.763130	+	0.646245i	$0.776338\pi$
$374$	−2.65771	+	3.21912i	−0.137427	+	0.166457i
$375$	−1.26076	−	8.76881i	−0.0651056	−	0.452819i
$376$	28.7671	−	6.26148i	1.48355	−	0.322911i
$377$	8.52511	−	5.47875i	0.439065	−	0.282170i
$378$	5.32569	−	0.126987i	0.273924	−	0.00653149i
$379$	−19.8615	−	9.07044i	−1.02022	−	0.465917i	−0.166161	−	0.986099i	$-0.553137\pi$
$379$	−19.8615	−	9.07044i	−1.02022	−	0.465917i	−0.854056	+	0.520181i	$0.825864\pi$
$380$	−14.3147	−	1.36574i	−0.734330	−	0.0700612i
$381$	−9.00202	−	1.29429i	−0.461187	−	0.0663087i
$382$	−15.1267	−	16.6387i	−0.773952	−	0.851308i
$383$	27.8226	+	8.16945i	1.42167	+	0.417439i	0.900067	−	0.435751i	$-0.143517\pi$
$383$	27.8226	+	8.16945i	1.42167	+	0.417439i	0.521600	+	0.853190i	$0.325335\pi$
$384$	−2.92517	+	10.9290i	−0.149274	+	0.557719i
$385$	−8.56741	+	7.42371i	−0.436636	+	0.378347i
$386$	−4.99538	+	11.6666i	−0.254258	+	0.593814i
$387$	4.26907	+	3.69917i	0.217009	+	0.188039i
$388$	0.157927	+	0.221740i	0.00801754	+	0.0112572i
$389$	2.57207	+	5.63204i	0.130409	+	0.285556i	0.963561	−	0.267488i	$-0.0861935\pi$
$389$	2.57207	+	5.63204i	0.130409	+	0.285556i	−0.833152	+	0.553044i	$0.813466\pi$
$390$	2.71262	−	0.456260i	0.137359	−	0.0231036i
$391$	0.329231	−	4.59821i	0.0166499	−	0.232541i
$392$	9.74774	+	17.8466i	0.492335	+	0.901389i
$393$	6.75303	+	14.7871i	0.340645	+	0.745909i
$394$	−20.0986	+	9.76430i	−1.01255	+	0.491918i
$395$	1.34105	−	1.54766i	0.0674756	−	0.0778710i
$396$	1.44746	−	5.96858i	0.0727376	−	0.299932i
$397$	−0.642158	+	0.556433i	−0.0322290	+	0.0279266i	−0.670826	−	0.741614i	$-0.734060\pi$
$397$	−0.642158	+	0.556433i	−0.0322290	+	0.0279266i	0.638597	+	0.769541i	$0.279515\pi$
$398$	−21.6366	+	6.91740i	−1.08454	+	0.346738i
$399$	7.78584	−	26.5161i	0.389780	−	1.32747i
$400$	−5.28241	+	15.2704i	−0.264120	+	0.763518i
$401$	4.85132	+	0.697515i	0.242264	+	0.0348322i	0.262377	−	0.964965i	$-0.415494\pi$
$401$	4.85132	+	0.697515i	0.242264	+	0.0348322i	−0.0201134	+	0.999798i	$0.506403\pi$
$402$	4.08680	−	15.2546i	0.203831	−	0.760828i
$403$	4.62171	−	10.1201i	0.230224	−	0.504120i
$404$	25.2345	−	4.86564i	1.25546	−	0.242074i
$405$	0.824449	−	0.529841i	0.0409672	−	0.0263280i
$406$	27.0083	+	3.22815i	1.34040	+	0.160210i
$407$	−32.8325	+	4.72060i	−1.62745	+	0.233991i
$408$	2.54751	+	0.949826i	0.126121	+	0.0470234i
$409$	5.35307	+	3.44021i	0.264692	+	0.170107i	0.666255	−	0.745724i	$-0.267896\pi$
$409$	5.35307	+	3.44021i	0.264692	+	0.170107i	−0.401562	+	0.915832i	$0.631533\pi$
$410$	−12.6706	−	7.72243i	−0.625755	−	0.381384i
$411$	−2.06596	−	7.03602i	−0.101906	−	0.347061i
$412$	−5.39777	−	5.66012i	−0.265929	−	0.278854i
$413$	−0.554835			−0.0273016
$414$	2.52050	+	6.29659i	0.123876	+	0.309461i
$415$			12.2531i			0.601482i
$416$	−10.6947	−	3.41640i	−0.524353	−	0.167503i
$417$	9.68021	−	2.84237i	0.474042	−	0.139191i
$418$	−27.2055	−	16.5812i	−1.33067	−	0.811011i
$419$	−2.33645	+	3.63559i	−0.114143	+	0.177610i	−0.893625	−	0.448815i	$-0.851846\pi$
$419$	−2.33645	+	3.63559i	−0.114143	+	0.177610i	0.779482	+	0.626425i	$0.215483\pi$
$420$	6.39443	+	3.69115i	0.312016	+	0.180110i
$421$	2.15063	+	14.9580i	0.104815	+	0.729006i	0.972671	+	0.232189i	$0.0745889\pi$
$421$	2.15063	+	14.9580i	0.104815	+	0.729006i	−0.867855	+	0.496817i	$0.834502\pi$
$422$	2.31925	−	19.4040i	0.112899	−	0.944570i
$423$	5.62744	+	8.75647i	0.273616	+	0.425754i
$424$	−1.90789	+	0.711866i	−0.0926555	+	0.0345713i
$425$	3.53211	+	1.61306i	0.171332	+	0.0782449i
$426$	−1.45648	+	5.43651i	−0.0705665	+	0.263400i
$427$	−1.16760	+	8.12087i	−0.0565044	+	0.392996i
$428$	24.8537	+	19.5420i	1.20135	+	0.944597i
$429$	5.84773	+	1.71705i	0.282331	+	0.0828999i
$430$	2.38412	+	7.45717i	0.114973	+	0.359617i
$431$	−22.4265	−	25.8815i	−1.08024	−	1.24667i	−0.967453	−	0.253050i	$-0.918566\pi$
$431$	−22.4265	−	25.8815i	−1.08024	−	1.24667i	−0.112791	−	0.993619i	$-0.535979\pi$
$432$	−3.98183	+	0.380857i	−0.191576	+	0.0183240i
$433$	25.9222	+	22.4617i	1.24574	+	1.07944i	0.993740	+	0.111715i	$0.0356345\pi$
$433$	25.9222	+	22.4617i	1.24574	+	1.07944i	0.252002	+	0.967727i	$0.418911\pi$
$434$	26.8604	−	13.0493i	1.28934	−	0.626386i
$435$	4.55177	−	2.07872i	0.218241	−	0.0996672i
$436$	−28.8439	+	9.98552i	−1.38137	+	0.478220i
$437$	35.0948	−	2.50727i	1.67881	−	0.119939i
$438$	−3.54256	−	21.0617i	−0.169270	−	1.00637i
$439$	−3.60684	+	1.64719i	−0.172145	+	0.0786161i	−0.499624	−	0.866243i	$-0.666528\pi$
$439$	−3.60684	+	1.64719i	−0.172145	+	0.0786161i	0.327479	+	0.944859i	$0.393801\pi$
$440$	6.01819	−	6.01962i	0.286906	−	0.286974i
$441$	−4.70817	+	5.43351i	−0.224198	+	0.258739i
$442$	−1.06198	+	2.48023i	−0.0505132	+	0.117972i
$443$	−9.59320	−	11.0711i	−0.455787	−	0.526006i	0.480617	−	0.876931i	$-0.340413\pi$
$443$	−9.59320	−	11.0711i	−0.455787	−	0.526006i	−0.936404	+	0.350925i	$0.885867\pi$
$444$	9.90088	+	19.2013i	0.469875	+	0.911253i
$445$	0.0218297	−	0.0743452i	0.00103483	−	0.00352430i
$446$	10.5114	−	9.55626i	0.497729	−	0.452502i
$447$	0.744805	−	5.18023i	0.0352281	−	0.245017i
$448$	−16.2984	−	25.3475i	−0.770026	−	1.19756i
$449$	−0.318820	+	0.698119i	−0.0150461	+	0.0329463i	−0.917006	−	0.398874i	$-0.869401\pi$
$449$	−0.318820	+	0.698119i	−0.0150461	+	0.0329463i	0.901960	+	0.431820i	$0.142128\pi$
$450$	−5.71117	+	0.136178i	−0.269227	+	0.00641949i
$451$	−17.7744	−	27.6576i	−0.836965	−	1.30234i
$452$	0.665013	+	13.9371i	0.0312796	+	0.655544i
$453$	−12.1076	+	1.74081i	−0.568864	+	0.0817904i
$454$	−14.9110	−	12.3106i	−0.699810	−	0.577765i
$455$	−3.96119	+	6.16373i	−0.185703	+	0.288960i
$456$	−4.40842	+	20.2768i	−0.206443	+	0.949549i
$457$	5.96984	+	20.3314i	0.279257	+	0.951063i	0.972993	+	0.230834i	$0.0741453\pi$
$457$	5.96984	+	20.3314i	0.279257	+	0.951063i	−0.693736	+	0.720229i	$0.744037\pi$
$458$	17.0493	−	11.5403i	0.796660	−	0.539241i
$459$			0.961248i			0.0448672i
$460$	−1.55880	+	9.26992i	−0.0726795	+	0.432212i
$461$		−	17.7722i		−	0.827736i	−0.910337	−	0.413868i	$-0.864178\pi$
$461$		−	17.7722i		−	0.827736i	0.910337	−	0.413868i	$-0.135822\pi$
$462$	9.16974	+	13.5471i	0.426615	+	0.630269i
$463$	6.62304	+	22.5560i	0.307799	+	1.04827i	0.957585	+	0.288150i	$0.0930401\pi$
$463$	6.62304	+	22.5560i	0.307799	+	1.04827i	−0.649786	+	0.760117i	$0.725142\pi$
$464$	−20.4009	−	0.968566i	−0.947087	−	0.0449645i
$465$	2.97010	−	4.62157i	0.137735	−	0.214320i
$466$	3.37037	−	4.08232i	0.156129	−	0.189110i
$467$	21.9690	−	3.15867i	1.01660	−	0.146166i	0.386186	−	0.922421i	$-0.373792\pi$
$467$	21.9690	−	3.15867i	1.01660	−	0.146166i	0.630419	+	0.776255i	$0.282883\pi$
$468$	−0.189187	−	3.96489i	−0.00874516	−	0.183277i
$469$	22.7421	+	35.3873i	1.05013	+	1.63404i
$470$	0.343885	+	14.4222i	0.0158622	+	0.665245i
$471$	−3.21851	+	7.04756i	−0.148301	+	0.324735i
$472$	0.415540	−	0.0297697i	0.0191268	−	0.00137026i
$473$	−2.46863	+	17.1697i	−0.113508	+	0.789463i
$474$	−1.98788	−	2.18656i	−0.0913062	−	0.100432i
$475$	−8.34938	+	28.4354i	−0.383096	+	1.30470i
$476$	−6.43655	+	3.31892i	−0.295019	+	0.152123i
$477$	−0.471478	−	0.544114i	−0.0215875	−	0.0249133i
$478$	39.8397	+	17.0585i	1.82223	+	0.780237i
$479$	−15.5130	+	17.9029i	−0.708806	+	0.818005i	−0.989914	−	0.141671i	$-0.954753\pi$
$479$	−15.5130	+	17.9029i	−0.708806	+	0.818005i	0.281108	+	0.959676i	$0.409298\pi$
$480$	−4.98712	−	2.42137i	−0.227630	−	0.110520i
$481$	−19.5010	+	8.90582i	−0.889170	+	0.406071i
$482$	36.3846	−	6.11986i	1.65727	−	0.278752i
$483$	−16.9259	−	6.31455i	−0.770156	−	0.287322i
$484$	−2.96767	+	1.02739i	−0.134894	+	0.0466994i
$485$	−0.121342	+	0.0554150i	−0.00550985	+	0.00251626i
$486$	−0.617983	−	1.27204i	−0.0280323	−	0.0577011i
$487$	9.86312	+	8.54644i	0.446941	+	0.387276i	0.849048	−	0.528316i	$-0.177177\pi$
$487$	9.86312	+	8.54644i	0.446941	+	0.387276i	−0.402107	+	0.915593i	$0.631722\pi$
$488$	0.438743	−	6.14472i	0.0198610	−	0.278158i
$489$	7.66351	+	8.84416i	0.346556	+	0.399947i
$490$	−9.49122	+	3.03443i	−0.428769	+	0.137081i
$491$	−1.78189	−	0.523211i	−0.0804157	−	0.0236122i	0.241277	−	0.970456i	$-0.422434\pi$
$491$	−1.78189	−	0.523211i	−0.0804157	−	0.0236122i	−0.321693	+	0.946844i	$0.604252\pi$
$492$	−13.2350	+	16.8324i	−0.596679	+	0.758862i
$493$	−0.698495	+	4.85814i	−0.0314586	+	0.218800i
$494$	−19.8904	−	5.32876i	−0.894909	−	0.239752i
$495$	2.73749	+	1.25017i	0.123041	+	0.0561910i
$496$	−19.4167	+	11.2144i	−0.871837	+	0.503540i
$497$	−8.10495	−	12.6115i	−0.363556	−	0.565705i
$498$	17.5568	+	2.09846i	0.786737	+	0.0940343i
$499$	2.07557	+	14.4359i	0.0929152	+	0.646240i	0.982054	+	0.188601i	$0.0603954\pi$
$499$	2.07557	+	14.4359i	0.0929152	+	0.646240i	−0.889138	+	0.457638i	$0.848695\pi$
$500$	−15.3449	−	8.85776i	−0.686245	−	0.396131i
$501$	−4.48357	+	6.97657i	−0.200311	+	0.311690i
$502$	10.0770	−	16.5338i	0.449758	−	0.737940i
$503$	−12.9071	+	3.78987i	−0.575499	+	0.168982i	−0.556514	−	0.830838i	$-0.687862\pi$
$503$	−12.9071	+	3.78987i	−0.575499	+	0.168982i	−0.0189848	+	0.999820i	$0.506043\pi$
$504$	6.38394	−	8.53006i	0.284363	−	0.379959i
$505$			12.5930i			0.560381i
$506$	−12.0816	+	16.9648i	−0.537091	+	0.754178i
$507$	−9.06096			−0.402411
$508$	−13.1631	+	12.5530i	−0.584019	+	0.556950i
$509$	−3.20865	−	10.9277i	−0.142221	−	0.484361i	0.857316	−	0.514791i	$-0.172130\pi$
$509$	−3.20865	−	10.9277i	−0.142221	−	0.484361i	−0.999537	+	0.0304303i	$0.990312\pi$
$510$	−0.693350	+	1.13761i	−0.0307021	+	0.0503744i
$511$	47.8573	+	30.7560i	2.11708	+	1.36057i
$512$	13.5666	+	18.1093i	0.599564	+	0.800327i
$513$	−7.26174	+	1.04408i	−0.320614	+	0.0460973i
$514$	1.66754	−	13.9515i	0.0735521	−	0.615373i
$515$	3.22413	−	2.07203i	0.142072	−	0.0913043i
$516$	11.0932	−	2.13896i	0.488352	−	0.0941624i
$517$	−13.2781	+	29.0749i	−0.583968	+	1.27871i
$518$	−55.5833	−	14.8911i	−2.44219	−	0.654279i
$519$	−0.885278	−	0.127284i	−0.0388594	−	0.00558714i
$520$	2.63599	−	4.82882i	0.115596	−	0.211758i
$521$	−6.77182	+	23.0627i	−0.296679	+	1.01040i	0.667383	+	0.744715i	$0.267415\pi$
$521$	−6.77182	+	23.0627i	−0.296679	+	1.01040i	−0.964061	+	0.265680i	$0.914404\pi$
$522$	−2.19895	−	6.87796i	−0.0962453	−	0.301040i
$523$	7.75578	−	6.72042i	0.339137	−	0.293864i	−0.468596	−	0.883413i	$-0.655240\pi$
$523$	7.75578	−	6.72042i	0.339137	−	0.293864i	0.807733	+	0.589549i	$0.200695\pi$
$524$	31.5964	+	7.66254i	1.38029	+	0.334740i
$525$	9.96476	−	11.4999i	0.434898	−	0.501899i
$526$	−3.22541	−	6.63911i	−0.140634	−	0.289479i
$527$	2.23843	+	4.90147i	0.0975074	+	0.213511i
$528$	−7.59448	−	9.65401i	−0.330507	−	0.420137i
$529$	0.00359257	−	23.0000i	0.000156199	−	1.00000i
$530$	−0.165512	−	0.984025i	−0.00718939	−	0.0427433i
$531$	0.0611873	+	0.133982i	0.00265530	+	0.00581430i
$532$	−32.0640	−	45.0200i	−1.39015	−	1.95186i
$533$	−16.0587	−	13.9149i	−0.695578	−	0.602722i
$534$	−0.102786	−	0.0440108i	−0.00444800	−	0.00190454i
$535$	−11.7084	+	10.1454i	−0.506197	+	0.438623i
$536$	−18.9312	−	25.2829i	−0.817704	−	1.09205i
$537$	13.3084	+	3.90771i	0.574301	+	0.168630i
$538$	−8.99307	+	8.17590i	−0.387719	+	0.352488i
$539$	−21.8529	−	3.14198i	−0.941273	−	0.135335i
$540$	0.186160	−	1.95119i	0.00801103	−	0.0839658i
$541$	9.09777	+	4.15481i	0.391144	+	0.178629i	0.601272	−	0.799045i	$-0.294661\pi$
$541$	9.09777	+	4.15481i	0.391144	+	0.178629i	−0.210128	+	0.977674i	$0.567388\pi$
$542$	−0.365454	−	15.3268i	−0.0156976	−	0.658341i
$543$	12.7844	−	8.21605i	0.548632	−	0.352584i
$544$	4.64254	−	2.83104i	0.199047	−	0.121380i
$545$	−2.12858	−	14.8046i	−0.0911784	−	0.634160i
$546$	8.15325	+	6.73135i	0.348927	+	0.288075i
$547$	−29.9520	−	19.2490i	−1.28066	−	0.823027i	−0.289687	−	0.957122i	$-0.593551\pi$
$547$	−29.9520	−	19.2490i	−1.28066	−	0.823027i	−0.990969	+	0.134094i	$0.957187\pi$
$548$	−13.6160	−	5.44976i	−0.581646	−	0.232802i
$549$	2.08979	−	0.613618i	0.0891901	−	0.0261886i
$550$	−9.83344	−	14.5277i	−0.419299	−	0.619461i
$551$	−37.4595			−1.59583
$552$	13.0154	+	3.82107i	0.553970	+	0.162636i
$553$	7.87126			0.334720
$554$	−9.99188	−	14.7617i	−0.424514	−	0.627165i
$555$	−10.1572	+	2.98243i	−0.431151	+	0.126597i
$556$	7.49783	−	18.7330i	0.317979	−	0.794455i
$557$	11.6676	+	7.49833i	0.494373	+	0.317714i	0.763962	−	0.645261i	$-0.223251\pi$
$557$	11.6676	+	7.49833i	0.494373	+	0.317714i	−0.269589	+	0.962976i	$0.586888\pi$
$558$	−6.11331	−	5.04716i	−0.258797	−	0.213664i
$559$	1.59551	+	11.0970i	0.0674830	+	0.469355i
$560$	13.7080	−	5.49038i	0.579269	−	0.232011i
$561$	−2.48320	+	1.59586i	−0.104841	+	0.0673772i
$562$	−0.733317	−	30.7546i	−0.0309331	−	1.29730i
$563$	7.73084	+	3.53056i	0.325816	+	0.148795i	0.571607	−	0.820528i	$-0.306320\pi$
$563$	7.73084	+	3.53056i	0.325816	+	0.148795i	−0.245791	+	0.969323i	$0.579048\pi$
$564$	20.7236	+	1.97720i	0.872619	+	0.0832551i
$565$	−6.76750	−	0.973020i	−0.284711	−	0.0409353i
$566$	−19.2582	+	17.5082i	−0.809481	+	0.735926i
$567$	3.61432	+	1.06126i	0.151787	+	0.0445687i
$568$	6.74682	+	9.01045i	0.283090	+	0.378070i
$569$	−27.5505	+	23.8726i	−1.15498	+	1.00079i	−0.155060	+	0.987905i	$0.549557\pi$
$569$	−27.5505	+	23.8726i	−1.15498	+	1.00079i	−0.999917	+	0.0128880i	$0.995898\pi$
$570$	−9.34721	−	4.00227i	−0.391511	−	0.167637i
$571$	−12.8226	−	11.1108i	−0.536609	−	0.464974i	0.343898	−	0.939007i	$-0.388252\pi$
$571$	−12.8226	−	11.1108i	−0.536609	−	0.464974i	−0.880507	+	0.474033i	$0.842798\pi$
$572$	9.92847	−	7.07122i	0.415130	−	0.295663i
$573$	−6.60538	−	14.4638i	−0.275944	−	0.604233i
$574$	−9.46023	−	56.2443i	−0.394863	−	2.34759i
$575$	18.1510	+	6.77159i	0.756949	+	0.282395i
$576$	−4.32352	+	6.73106i	−0.180147	+	0.280461i
$577$	−4.25684	−	9.32118i	−0.177215	−	0.388046i	0.800091	−	0.599878i	$-0.204784\pi$
$577$	−4.25684	−	9.32118i	−0.177215	−	0.388046i	−0.977306	+	0.211832i	$0.932057\pi$
$578$	9.93470	+	20.4494i	0.413229	+	0.850582i
$579$	−5.87669	+	6.78206i	−0.244227	+	0.281853i
$580$	2.35869	−	9.72602i	0.0979392	−	0.403851i
$581$	−35.5936	+	30.8420i	−1.47667	+	1.27954i
$582$	0.0586199	+	0.183354i	0.00242987	+	0.00760026i
$583$	0.622873	−	2.12131i	0.0257968	−	0.0878557i
$584$	−37.4926	−	20.4667i	−1.55146	−	0.846919i
$585$	1.92526	+	0.276810i	0.0795996	+	0.0114447i
$586$	20.1085	+	5.38721i	0.830676	+	0.222544i
$587$	12.7049	−	27.8198i	0.524386	−	1.14824i	−0.443367	−	0.896340i	$-0.646216\pi$
$587$	12.7049	−	27.8198i	0.524386	−	1.14824i	0.967752	−	0.251904i	$-0.0810567\pi$
$588$	2.72239	+	14.1191i	0.112270	+	0.582261i
$589$	−34.5968	+	22.2340i	−1.42554	+	0.916137i
$590$	−0.0242274	+	0.202699i	−0.000997428	+	0.00834497i
$591$	−15.6394	+	2.24861i	−0.643320	+	0.0924955i
$592$	42.4277	+	8.17029i	1.74377	+	0.335797i
$593$	−20.9869	−	13.4875i	−0.861828	−	0.553863i	0.0334147	−	0.999442i	$-0.489362\pi$
$593$	−20.9869	−	13.4875i	−0.861828	−	0.553863i	−0.895243	+	0.445578i	$0.852998\pi$
$594$	2.26012	−	3.70829i	0.0927337	−	0.152153i
$595$	−0.999756	−	3.40486i	−0.0409860	−	0.139585i
$596$	−7.22366	−	7.57476i	−0.295893	−	0.310274i
$597$	−16.0622			−0.657384
$598$	−4.40312	+	12.7204i	−0.180057	+	0.520175i
$599$		−	14.9992i		−	0.612849i	−0.951895	−	0.306425i	$-0.900867\pi$
$599$		−	14.9992i		−	0.612849i	0.951895	−	0.306425i	$-0.0991328\pi$
$600$	−6.84600	+	9.14746i	−0.279487	+	0.373444i
$601$	−30.8005	+	9.04384i	−1.25638	+	0.368906i	−0.841145	−	0.540809i	$-0.818118\pi$
$601$	−30.8005	+	9.04384i	−1.25638	+	0.368906i	−0.415233	+	0.909715i	$0.636300\pi$
$602$	−15.6610	+	25.6958i	−0.638296	+	1.04728i
$603$	6.03733	−	9.39427i	0.245859	−	0.382564i
$604$	−12.2304	+	21.1876i	−0.497649	+	0.862111i
$605$	−0.219005	−	1.52321i	−0.00890380	−	0.0619273i
$606$	18.0437	+	2.15667i	0.732977	+	0.0876086i
$607$	−22.6982	−	35.3190i	−0.921290	−	1.43356i	−0.901028	−	0.433761i	$-0.857186\pi$
$607$	−22.6982	−	35.3190i	−0.921290	−	1.43356i	−0.0202622	−	0.999795i	$-0.506450\pi$
$608$	26.4297	+	31.9970i	1.07186	+	1.29765i
$609$	17.4956	+	7.98996i	0.708956	+	0.323769i
$610$	2.91582	+	0.781169i	0.118058	+	0.0316286i
$611$	−2.94000	+	20.4482i	−0.118940	+	0.827244i
$612$	1.51128	+	1.18829i	0.0610898	+	0.0480337i
$613$	−16.7994	−	4.93276i	−0.678523	−	0.199232i	−0.0757279	−	0.997129i	$-0.524128\pi$
$613$	−16.7994	−	4.93276i	−0.678523	−	0.199232i	−0.602795	+	0.797896i	$0.705946\pi$
$614$	12.6438	−	4.04234i	0.510262	−	0.163135i
$615$	−6.87104	−	7.92960i	−0.277067	−	0.319752i
$616$	32.6344	+	2.33015i	1.31488	+	0.0938845i
$617$	21.9130	+	18.9877i	0.882185	+	0.764418i	0.972843	−	0.231464i	$-0.0743517\pi$
$617$	21.9130	+	18.9877i	0.882185	+	0.764418i	−0.0906584	+	0.995882i	$0.528897\pi$
$618$	−2.41672	−	4.97452i	−0.0972147	−	0.200105i
$619$	5.79950	−	2.64854i	0.233102	−	0.106454i	−0.295440	−	0.955361i	$-0.595466\pi$
$619$	5.79950	−	2.64854i	0.233102	−	0.106454i	0.528542	+	0.848907i	$0.322739\pi$
$620$	−3.59443	−	10.3828i	−0.144356	−	0.416981i
$621$	0.341757	+	4.78364i	0.0137142	+	0.191961i
$622$	22.2203	−	3.73744i	0.890954	−	0.149858i
$623$	0.270910	−	0.123720i	0.0108538	−	0.00495675i
$624$	−6.46749	−	4.60393i	−0.258907	−	0.184305i
$625$	−7.54120	+	8.70301i	−0.301648	+	0.348121i
$626$	−17.6071	−	7.53897i	−0.703721	−	0.301318i
$627$	−14.7531	−	17.0260i	−0.589182	−	0.679952i
$628$	7.10151	+	13.7723i	0.283381	+	0.549575i
$629$	2.92529	−	9.96262i	0.116639	−	0.397236i
$630$	3.51197	+	3.86299i	0.139920	+	0.153905i
$631$	−2.39996	+	16.6921i	−0.0955410	+	0.664502i	0.884622	+	0.466309i	$0.154416\pi$
$631$	−2.39996	+	16.6921i	−0.0955410	+	0.664502i	−0.980163	+	0.198193i	$0.936493\pi$
$632$	−5.89512	+	0.422333i	−0.234495	+	0.0167995i
$633$	5.74034	−	12.5696i	0.228158	−	0.499597i
$634$	−0.0751368	−	3.15116i	−0.00298406	−	0.125149i
$635$	−4.81869	−	7.49802i	−0.191224	−	0.297550i
$636$	−1.43830	+	0.0686290i	−0.0570321	+	0.00272132i
$637$	−14.1239	+	2.03071i	−0.559610	+	0.0804597i
$638$	14.1173	−	17.0993i	0.558908	−	0.676969i
$639$	−2.15162	+	3.34799i	−0.0851168	+	0.132444i
$640$	−9.97192	+	4.84749i	−0.394175	+	0.191614i
$641$	1.56660	+	5.33535i	0.0618770	+	0.210734i	0.984628	−	0.174662i	$-0.0558832\pi$
$641$	1.56660	+	5.33535i	0.0618770	+	0.210734i	−0.922752	+	0.385395i	$0.874065\pi$
$642$	12.5315	+	18.5137i	0.494580	+	0.730679i
$643$			11.7024i			0.461498i	0.973013	+	0.230749i	$0.0741176\pi$
$643$			11.7024i			0.461498i	−0.973013	+	0.230749i	$0.925882\pi$
$644$	−30.8515	+	18.8050i	−1.21572	+	0.741021i
$645$			5.53595i			0.217978i
$646$	8.25907	−	5.59038i	0.324949	−	0.219950i
$647$	9.56977	+	32.5917i	0.376227	+	1.28131i	0.902388	+	0.430925i	$0.141813\pi$
$647$	9.56977	+	32.5917i	0.376227	+	1.28131i	−0.526161	+	0.850385i	$0.676369\pi$
$648$	−2.76386	−	0.600896i	−0.108575	−	0.0236054i
$649$	−0.244533	+	0.380502i	−0.00959878	+	0.0149360i
$650$	−8.74338	−	7.21856i	−0.342944	−	0.283135i
$651$	20.9010	−	3.00511i	0.819174	−	0.117779i
$652$	23.3784	−	1.11551i	0.915569	−	0.0436868i
$653$	22.4237	+	34.8920i	0.877508	+	1.36543i	0.930291	+	0.366824i	$0.119555\pi$
$653$	22.4237	+	34.8920i	0.877508	+	1.36543i	−0.0527822	+	0.998606i	$0.516809\pi$
$654$	−21.5772	+	0.514490i	−0.843735	+	0.0201181i
$655$	−6.61814	+	14.4917i	−0.258592	+	0.566238i
$656$	10.1030	+	41.6162i	0.394455	+	1.62484i
$657$	2.14925	−	14.9484i	0.0838502	−	0.583191i
$658$	−41.0288	+	37.3007i	−1.59947	+	1.45413i
$659$	−11.5710	+	39.4073i	−0.450743	+	1.53509i	0.350389	+	0.936604i	$0.386049\pi$
$659$	−11.5710	+	39.4073i	−0.450743	+	1.53509i	−0.801133	+	0.598487i	$0.795769\pi$
$660$	5.34959	−	2.75845i	0.208233	−	0.107372i
$661$	20.1239	+	23.2242i	0.782728	+	0.903317i	0.997303	−	0.0733909i	$-0.0233821\pi$
$661$	20.1239	+	23.2242i	0.782728	+	0.903317i	−0.214575	+	0.976708i	$0.568837\pi$
$662$	16.9791	−	39.6543i	0.659912	−	1.54121i
$663$	−1.24934	+	1.44181i	−0.0485202	+	0.0559953i
$664$	25.0028	−	25.0087i	0.970295	−	0.970526i
$665$	24.6361	−	11.2509i	0.955345	−	0.436292i
$666$	2.53383	+	15.0645i	0.0981839	+	0.583736i
$667$	−1.74881	+	24.4248i	−0.0677144	+	0.945733i
$668$	5.42603	+	15.6735i	0.209940	+	0.606425i
$669$	9.13742	−	4.17292i	0.353273	−	0.161334i
$670$	13.9212	−	6.76317i	0.537821	−	0.261284i
$671$	5.05463	+	4.37986i	0.195132	+	0.169083i
$672$	−5.51922	−	20.5817i	−0.212908	−	0.793955i
$673$	−26.2038	−	30.2408i	−1.01008	−	1.16570i	−0.986129	−	0.165983i	$-0.946920\pi$
$673$	−26.2038	−	30.2408i	−1.01008	−	1.16570i	−0.0239532	−	0.999713i	$-0.507625\pi$
$674$	−7.59987	−	23.7712i	−0.292736	−	0.915632i
$675$	−3.87592	−	1.13807i	−0.149184	−	0.0438045i
$676$	−11.2011	+	14.2457i	−0.430811	+	0.547911i
$677$	0.423385	−	2.94471i	0.0162720	−	0.113174i	−0.980067	−	0.198669i	$-0.936338\pi$
$677$	0.423385	−	2.94471i	0.0162720	−	0.113174i	0.996339	+	0.0854950i	$0.0272472\pi$
$678$	−2.55318	+	9.53012i	−0.0980543	+	0.366002i
$679$	−0.466400	−	0.212998i	−0.0178988	−	0.00817410i
$680$	0.931448	+	2.49640i	0.0357194	+	0.0957326i
$681$	−7.39206	−	11.5023i	−0.283264	−	0.440768i
$682$	2.88913	−	24.1719i	0.110630	−	0.925589i
$683$	−3.12682	−	21.7475i	−0.119644	−	0.832145i	−0.957948	−	0.286942i	$-0.907361\pi$
$683$	−3.12682	−	21.7475i	−0.119644	−	0.832145i	0.838304	−	0.545204i	$-0.183548\pi$
$684$	−7.33541	+	12.7076i	−0.280476	+	0.485888i
$685$	3.88536	−	6.04573i	0.148452	−	0.230996i
$686$	−0.862332	−	0.525572i	−0.0329240	−	0.0200664i
$687$	13.9680	−	4.10139i	0.532914	−	0.156478i
$688$	10.3505	−	20.0850i	0.394609	−	0.765733i
$689$		−	1.42892i		−	0.0544374i
$690$	−3.04599	+	5.90784i	−0.115959	+	0.224908i
$691$	−19.1248			−0.727542			−0.363771	−	0.931488i	$-0.618511\pi$
$691$	−19.1248			−0.727542			−0.363771	+	0.931488i	$0.618511\pi$
$692$	−1.29449	+	1.23449i	−0.0492092	+	0.0469283i
$693$	3.25891	+	11.0988i	0.123796	+	0.421609i
$694$	−24.2714	−	14.7929i	−0.921331	−	0.561530i
$695$	8.31777	+	5.34550i	0.315511	+	0.202767i
$696$	−13.5319	−	5.04530i	−0.512925	−	0.191241i
$697$	10.1866	−	1.46461i	0.385845	−	0.0554761i
$698$	13.8952	+	1.66081i	0.525939	+	0.0628626i
$699$	3.14907	−	2.02378i	0.119109	−	0.0765466i
$700$	−5.76190	−	29.8828i	−0.217779	−	1.12946i
$701$	−4.05786	+	8.88548i	−0.153263	+	0.335600i	−0.970653	−	0.240486i	$-0.922693\pi$
$701$	−4.05786	+	8.88548i	−0.153263	+	0.335600i	0.817389	+	0.576086i	$0.195421\pi$
$702$	0.726343	−	2.71118i	0.0274141	−	0.102327i
$703$	78.4400	+	11.2780i	2.95842	+	0.425357i
$704$	−24.5663	+	0.00585280i	−0.925878	+	0.000220586i
$705$	−2.87393	+	9.78770i	−0.108238	+	0.368626i
$706$	35.9345	−	11.4886i	1.35241	−	0.432378i
$707$	−36.5809	+	31.6975i	−1.37577	+	1.19211i
$708$	0.286286	+	0.0694281i	0.0107593	+	0.00260927i
$709$	20.1770	−	23.2855i	0.757762	−	0.874504i	−0.237535	−	0.971379i	$-0.576339\pi$
$709$	20.1770	−	23.2855i	0.757762	−	0.874504i	0.995297	+	0.0968752i	$0.0308848\pi$
$710$	−4.96130	+	2.41030i	−0.186194	+	0.0904568i
$711$	−0.868044	−	1.90075i	−0.0325542	−	0.0712837i
$712$	−0.196258	+	0.107195i	−0.00735507	+	0.00401731i
$713$	12.8821	+	23.5963i	0.482440	+	0.883687i
$714$	−5.04983	+	0.849377i	−0.188985	+	0.0317871i
$715$	2.48122	+	5.43311i	0.0927922	+	0.203187i
$716$	22.5955	−	16.0929i	0.844434	−	0.601420i
$717$	23.1597	+	20.0680i	0.864915	+	0.749453i
$718$	−5.75259	+	13.4350i	−0.214685	+	0.501391i
$719$	38.2034	−	33.1034i	1.42475	−	1.23455i	0.493708	−	0.869628i	$-0.335641\pi$
$719$	38.2034	−	33.1034i	1.42475	−	1.23455i	0.931038	−	0.364922i	$-0.118904\pi$
$720$	−2.83754	−	2.70473i	−0.105749	−	0.100799i
$721$	14.1343	+	4.15022i	0.526390	+	0.154562i
$722$	33.1281	+	36.4392i	1.23290	+	1.35613i
$723$	25.8237	+	3.71288i	0.960392	+	0.138084i
$724$	2.88671	−	30.2563i	0.107284	−	1.12447i
$725$	−18.7619	−	8.56827i	−0.696799	−	0.318218i
$726$	−2.22002	+	0.0529346i	−0.0823928	+	0.00196459i
$727$	−3.13911	+	2.01738i	−0.116423	+	0.0748206i	−0.597557	−	0.801827i	$-0.703862\pi$
$727$	−3.13911	+	2.01738i	−0.116423	+	0.0748206i	0.481133	+	0.876647i	$0.340225\pi$
$728$	20.6620	−	4.49733i	0.765786	−	0.166682i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	13.3259	−	16.1408i	0.493213	−	0.597397i
$731$	−4.56791	−	2.93561i	−0.168950	−	0.108578i
$732$	1.61865	−	4.04413i	0.0598271	−	0.149475i
$733$	24.8697	−	7.30240i	0.918583	−	0.269720i	0.211934	−	0.977284i	$-0.432024\pi$
$733$	24.8697	−	7.30240i	0.918583	−	0.269720i	0.706650	+	0.707564i	$0.250206\pi$
$734$	−38.0146	+	25.7312i	−1.40314	+	0.949756i
$735$	−7.04595			−0.259894
$736$	22.0970	−	15.7392i	0.814506	−	0.580155i
$737$	34.2915			1.26314
$738$	−12.5386	+	8.48709i	−0.461552	+	0.312414i
$739$	13.7252	−	4.03007i	0.504888	−	0.148248i	−0.0193627	−	0.999813i	$-0.506164\pi$
$739$	13.7252	−	4.03007i	0.504888	−	0.148248i	0.524251	+	0.851564i	$0.324346\pi$
$740$	−7.86731	+	19.6561i	−0.289208	+	0.722573i
$741$	−12.2492	−	7.87205i	−0.449984	−	0.289187i
$742$	2.44185	−	2.95766i	0.0896431	−	0.108579i
$743$	1.12510	+	7.82521i	0.0412758	+	0.287079i	0.999996	+	0.00272911i	$0.000868703\pi$
$743$	1.12510	+	7.82521i	0.0412758	+	0.287079i	−0.958721	+	0.284350i	$0.908222\pi$
$744$	−15.4924	+	3.37210i	−0.567979	+	0.123627i
$745$	4.31476	−	2.77293i	0.158081	−	0.101592i
$746$	−15.9790	+	0.381006i	−0.585033	+	0.0139496i
$747$	11.3730	+	5.19388i	0.416117	+	0.190034i
$748$	−0.560704	+	5.87689i	−0.0205014	+	0.214881i
$749$	−58.9418	−	8.47455i	−2.15369	−	0.309653i
$750$	−8.42779	−	9.27014i	−0.307739	−	0.338498i
$751$	4.07472	+	1.19644i	0.148688	+	0.0436589i	0.355230	−	0.934779i	$-0.384403\pi$
$751$	4.07472	+	1.19644i	0.148688	+	0.0436589i	−0.206541	+	0.978438i	$0.566221\pi$
$752$	28.7269	−	30.1375i	1.04756	−	1.09900i
$753$	10.3473	−	8.96600i	0.377077	−	0.326739i
$754$	5.64103	−	13.1745i	0.205434	−	0.479787i
$755$	−9.05974	−	7.85031i	−0.329718	−	0.285702i
$756$	6.13651	−	4.37053i	0.223183	−	0.158954i
$757$	3.03500	+	6.64572i	0.110309	+	0.241543i	0.956733	−	0.290966i	$-0.0939766\pi$
$757$	3.03500	+	6.64572i	0.110309	+	0.241543i	−0.846424	+	0.532509i	$0.821249\pi$
$758$	−30.4511	+	5.12185i	−1.10603	+	0.186034i
$759$	−11.7903	+	8.82464i	−0.427959	+	0.320314i
$760$	−17.8473	+	9.74814i	−0.647391	+	0.353602i
$761$	−0.494366	−	1.08251i	−0.0179208	−	0.0392410i	0.900460	−	0.434939i	$-0.143230\pi$
$761$	−0.494366	−	1.08251i	−0.0179208	−	0.0392410i	−0.918381	+	0.395698i	$0.870503\pi$
$762$	−11.5687	+	5.62030i	−0.419090	+	0.203602i
$763$	37.6475	−	43.4476i	1.36293	−	1.57291i
$764$	−30.9055	−	7.49500i	−1.11812	−	0.271160i
$765$	−0.711951	+	0.616909i	−0.0257406	+	0.0223044i
$766$	39.0605	−	12.4880i	1.41131	−	0.451209i
$767$	−0.0823591	+	0.280489i	−0.00297381	+	0.0101279i
$768$	5.23789	+	15.1183i	0.189006	+	0.545536i
$769$	−21.0758	−	3.03024i	−0.760012	−	0.109273i	−0.248597	−	0.968607i	$-0.579970\pi$
$769$	−21.0758	−	3.03024i	−0.760012	−	0.109273i	−0.511415	+	0.859334i	$0.670879\pi$
$770$	−4.14876	+	15.4859i	−0.149511	+	0.558072i
$771$	4.12732	−	9.03756i	0.148642	−	0.325480i
$772$	3.39806	+	17.6233i	0.122299	+	0.634276i
$773$	10.4347	−	6.70600i	0.375311	−	0.241198i	−0.339363	−	0.940656i	$-0.610211\pi$
$773$	10.4347	−	6.70600i	0.375311	−	0.241198i	0.714674	+	0.699458i	$0.246575\pi$
$774$	7.93213	+	0.948082i	0.285114	+	0.0340781i
$775$	−22.4138	+	3.22262i	−0.805127	+	0.115760i
$776$	0.360735	+	0.134498i	0.0129496	+	0.00482821i
$777$	−34.2301	−	21.9983i	−1.22800	−	0.789186i
$778$	7.47693	+	4.55702i	0.268061	+	0.163377i
$779$	22.1288	+	75.3637i	0.792846	+	2.70019i
$780$	2.81519	−	2.68471i	0.100800	−	0.0961280i
$781$	−12.2210			−0.437302
$782$	−3.25953	−	5.64618i	−0.116561	−	0.201907i
$783$		−	5.10596i		−	0.182472i
$784$	25.5635	+	13.1737i	0.912981	+	0.470491i
$785$	−7.28538	+	2.13918i	−0.260026	+	0.0763506i
$786$	19.6309	+	11.9646i	0.700210	+	0.426762i
$787$	−5.42166	+	8.43626i	−0.193261	+	0.300720i	−0.924338	−	0.381575i	$-0.875382\pi$
$787$	−5.42166	+	8.43626i	−0.193261	+	0.300720i	0.731077	+	0.682295i	$0.239018\pi$
$788$	−15.7981	+	27.3681i	−0.562784	+	0.974948i
$789$	−0.742776	−	5.16612i	−0.0264435	−	0.183919i
$790$	0.343706	−	2.87562i	0.0122285	−	0.102310i
$791$	−14.2078	−	22.1078i	−0.505173	−	0.786064i
$792$	−3.03624	−	8.13752i	−0.107888	−	0.289154i
$793$	3.93208	+	1.79572i	0.139632	+	0.0637679i
$794$	−0.310964	+	1.16072i	−0.0110357	+	0.0411924i
$795$	0.100415	−	0.698403i	0.00356136	−	0.0247698i
$796$	−19.8560	+	25.2531i	−0.703778	+	0.895073i
$797$	12.4333	+	3.65076i	0.440411	+	0.129316i	0.494418	−	0.869224i	$-0.335381\pi$
$797$	12.4333	+	3.65076i	0.440411	+	0.129316i	−0.0540069	+	0.998541i	$0.517199\pi$
$798$	−11.9016	−	37.2264i	−0.421312	−	1.31780i
$799$	−6.55219	−	7.56163i	−0.231800	−	0.267511i
$800$	5.91870	+	22.0713i	0.209258	+	0.780340i
$801$	−0.0597520	−	0.0517754i	−0.00211123	−	0.00182939i
$802$	6.23456	−	3.02887i	0.220150	−	0.106953i
$803$	42.1845	−	19.2650i	1.48866	−	0.679847i
$804$	−7.30641	−	21.1051i	−0.257677	−	0.744318i
$805$	−6.18582	−	16.5888i	−0.218021	−	0.584678i
$806$	−2.60976	−	15.5159i	−0.0919250	−	0.546525i
$807$	−7.81756	+	3.57016i	−0.275191	+	0.125676i
$808$	25.6963	−	25.7024i	0.903992	−	0.904207i
$809$	17.6286	−	20.3445i	0.619790	−	0.715276i	−0.355877	−	0.934533i	$-0.615818\pi$
$809$	17.6286	−	20.3445i	0.619790	−	0.715276i	0.975667	+	0.219257i	$0.0703632\pi$
$810$	0.545534	−	1.27408i	0.0191681	−	0.0447667i
$811$	18.6203	+	21.4889i	0.653846	+	0.754578i	0.981759	−	0.190129i	$-0.0608908\pi$
$811$	18.6203	+	21.4889i	0.653846	+	0.754578i	−0.327913	+	0.944708i	$0.606345\pi$
$812$	34.1897	−	17.6295i	1.19982	−	0.618673i
$813$	3.05419	−	10.4016i	0.107115	−	0.364800i
$814$	−34.7096	+	31.5556i	−1.21657	+	1.10602i
$815$	−1.63217	+	11.3520i	−0.0571725	+	0.397643i
$816$	3.73646	−	0.907084i	0.130802	−	0.0317543i
$817$	17.2156	−	37.6968i	0.602296	−	1.31884i
$818$	8.99637	−	0.214511i	0.314551	−	0.00750020i
$819$	4.04193	+	6.28936i	0.141236	+	0.219768i
$820$	−20.9609	+	1.00016i	−0.731986	+	0.0349271i
$821$	4.32034	−	0.621172i	0.150781	−	0.0216790i	−0.0665109	−	0.997786i	$-0.521187\pi$
$821$	4.32034	−	0.621172i	0.150781	−	0.0216790i	0.217292	+	0.976107i	$0.430278\pi$
$822$	−7.99717	−	6.60249i	−0.278933	−	0.230288i
$823$	8.03194	−	12.4979i	0.279976	−	0.435651i	−0.672576	−	0.740028i	$-0.734812\pi$
$823$	8.03194	−	12.4979i	0.279976	−	0.435651i	0.952552	+	0.304377i	$0.0984484\pi$
$824$	−10.8085	−	2.34990i	−0.376532	−	0.0818625i
$825$	−3.49479	−	11.9021i	−0.121673	−	0.414380i
$826$	−0.649794	+	0.439831i	−0.0226092	+	0.0153037i
$827$		−	3.97545i		−	0.138240i	−0.997608	−	0.0691200i	$-0.977981\pi$
$827$		−	3.97545i		−	0.138240i	0.997608	−	0.0691200i	$-0.0220191\pi$
$828$	7.94334	+	5.37619i	0.276050	+	0.186836i
$829$		−	9.43457i		−	0.327676i	−0.986487	−	0.163838i	$-0.947613\pi$
$829$		−	9.43457i		−	0.327676i	0.986487	−	0.163838i	$-0.0523875\pi$
$830$	9.71334	+	14.3502i	0.337155	+	0.498103i
$831$	−3.55109	−	12.0939i	−0.123186	−	0.419533i
$832$	−15.2334	+	4.47687i	−0.528123	+	0.155208i
$833$	3.73634	−	5.81387i	0.129457	−	0.201439i
$834$	9.08375	−	11.0026i	0.314544	−	0.380988i
$835$	−8.04468	+	1.15665i	−0.278398	+	0.0400275i
$836$	−45.0060	+	2.14748i	−1.55657	+	0.0742722i
$837$	−3.03064	−	4.71576i	−0.104754	−	0.163001i
$838$	0.145687	+	6.10997i	0.00503268	+	0.211065i
$839$	17.4865	−	38.2902i	0.603702	−	1.32192i	−0.323097	−	0.946366i	$-0.604724\pi$
$839$	17.4865	−	38.2902i	0.603702	−	1.32192i	0.926799	−	0.375557i	$-0.122549\pi$
$840$	10.4149	−	0.746135i	0.359348	−	0.0257441i
$841$	−0.416860	+	2.89932i	−0.0143745	+	0.0999766i
$842$	14.3762	+	15.8131i	0.495438	+	0.544957i
$843$	6.12851	−	20.8718i	0.211077	−	0.718863i
$844$	−12.6658	−	24.5634i	−0.435975	−	0.845508i
$845$	−5.81514	−	6.71103i	−0.200047	−	0.230866i
$846$	13.5320	+	5.79412i	0.465241	+	0.199206i
$847$	3.87346	−	4.47022i	0.133094	−	0.153598i
$848$	−1.67011	+	2.34613i	−0.0573519	+	0.0805666i
$849$	−16.7409	+	7.64530i	−0.574545	+	0.262386i
$850$	5.41534	−	0.910855i	0.185745	−	0.0312421i
$851$	11.0156	−	50.6189i	0.377610	−	1.73519i
$852$	2.60390	+	7.52154i	0.0892081	+	0.257684i
$853$	45.5989	−	20.8243i	1.56128	−	0.713011i	0.567393	−	0.823447i	$-0.307952\pi$
$853$	45.5989	−	20.8243i	1.56128	−	0.713011i	0.993883	+	0.110436i	$0.0352248\pi$
$854$	5.07017	+	10.4363i	0.173498	+	0.357124i
$855$	−5.43374	−	4.70836i	−0.185830	−	0.161023i
$856$	44.5988	+	3.18443i	1.52435	+	0.108841i
$857$	−33.5202	−	38.6843i	−1.14503	−	1.32143i	−0.939409	−	0.342799i	$-0.888625\pi$
$857$	−33.5202	−	38.6843i	−1.14503	−	1.32143i	−0.205618	−	0.978632i	$-0.565920\pi$
$858$	8.20970	−	2.62472i	0.280275	−	0.0896064i
$859$	17.1602	+	5.03869i	0.585498	+	0.171918i	0.561048	−	0.827783i	$-0.310398\pi$
$859$	17.1602	+	5.03869i	0.585498	+	0.171918i	0.0244503	+	0.999701i	$0.492216\pi$
$860$	8.70364	+	6.84350i	0.296792	+	0.233361i
$861$	5.73946	−	39.9189i	0.195600	−	1.36043i
$862$	−46.7816	−	12.5331i	−1.59339	−	0.426879i
$863$	−25.9435	−	11.8480i	−0.883127	−	0.403311i	−0.0783765	−	0.996924i	$-0.524974\pi$
$863$	−25.9435	−	11.8480i	−0.883127	−	0.403311i	−0.804750	+	0.593613i	$0.797701\pi$
$864$	−4.36140	+	3.60253i	−0.148378	+	0.122561i
$865$	−0.473880	−	0.737372i	−0.0161124	−	0.0250714i
$866$	48.1647	+	5.75686i	1.63670	+	0.195626i
$867$	2.28785	+	15.9124i	0.0776996	+	0.540413i
$868$	21.1130	−	36.5755i	0.716622	−	1.24145i
$869$	3.46911	−	5.39805i	0.117682	−	0.183116i
$870$	3.68295	−	6.04279i	0.124864	−	0.204870i
$871$	21.2654	−	6.24408i	0.720550	−	0.211573i
$872$	−25.8647	+	34.5597i	−0.875889	+	1.17034i
$873$			0.136116i			0.00460681i
$874$	39.1136	−	30.7568i	1.32304	−	1.04037i
$875$	33.3709			1.12814
$876$	−20.8450	−	21.8581i	−0.704287	−	0.738517i
$877$	4.97418	+	16.9405i	0.167966	+	0.572040i	0.999854	+	0.0170958i	$0.00544204\pi$
$877$	4.97418	+	16.9405i	0.167966	+	0.572040i	−0.831888	+	0.554944i	$0.812740\pi$
$878$	−2.91838	+	4.78833i	−0.0984906	+	0.161598i
$879$	12.3835	+	7.95840i	0.417686	+	0.268430i
$880$	2.27629	−	11.8206i	0.0767338	−	0.398473i
$881$	2.12678	−	0.305784i	0.0716529	−	0.0103021i	−0.106395	−	0.994324i	$-0.533931\pi$
$881$	2.12678	−	0.305784i	0.0716529	−	0.0103021i	0.178048	+	0.984022i	$0.443022\pi$
$882$	−1.20669	+	10.0957i	−0.0406312	+	0.339941i
$883$	−38.4372	+	24.7021i	−1.29351	+	0.831291i	−0.992490	−	0.122325i	$-0.960965\pi$
$883$	−38.4372	+	24.7021i	−1.29351	+	0.831291i	−0.301024	+	0.953616i	$0.597329\pi$
$884$	0.722401	+	3.74657i	0.0242970	+	0.126011i
$885$	−0.0599651	+	0.131305i	−0.00201570	+	0.00441378i
$886$	−20.0114	−	5.36119i	−0.672297	−	0.180113i
$887$	−27.9361	−	4.01660i	−0.938002	−	0.134864i	−0.343676	−	0.939088i	$-0.611672\pi$
$887$	−27.9361	−	4.01660i	−0.938002	−	0.134864i	−0.594326	+	0.804224i	$0.702581\pi$
$888$	26.8167	+	14.6389i	0.899910	+	0.491249i
$889$	9.65172	−	32.8707i	0.323708	−	1.10245i
$890$	−0.0333694	−	0.104374i	−0.00111854	−	0.00349863i
$891$	2.32075	−	2.01094i	0.0777480	−	0.0673691i
$892$	4.73493	−	19.5244i	0.158537	−	0.653726i
$893$	50.0075	−	57.7117i	1.67344	−	1.93125i
$894$	−3.23422	−	6.65725i	−0.108168	−	0.222652i
$895$	5.64683	+	12.3648i	0.188753	+	0.413311i
$896$	−39.1814	−	16.7656i	−1.30896	−	0.560098i
$897$	−5.70470	+	7.61934i	−0.190474	+	0.254402i
$898$	0.180030	+	1.07034i	0.00600767	+	0.0357176i
$899$	−11.8901	−	26.0357i	−0.396557	−	0.868338i
$900$	−6.58067	+	4.68686i	−0.219356	+	0.156229i
$901$	0.523028	+	0.453207i	0.0174246	+	0.0150985i
$902$	−42.7413	−	18.3009i	−1.42313	−	0.609353i
$903$	−16.0812	+	13.9344i	−0.535148	+	0.463708i
$904$	11.8271	+	15.7952i	0.393362	+	0.525340i
$905$	14.2900	+	4.19593i	0.475017	+	0.139477i
$906$	−12.7998	+	11.6367i	−0.425245	+	0.386604i
$907$	−31.1020	−	4.47180i	−1.03273	−	0.148484i	−0.394948	−	0.918704i	$-0.629237\pi$
$907$	−31.1020	−	4.47180i	−1.03273	−	0.148484i	−0.637778	+	0.770220i	$0.720146\pi$
$908$	−27.2219	−	2.59720i	−0.903392	−	0.0861911i
$909$	11.6885	+	5.33795i	0.387682	+	0.177048i
$910$	0.246996	+	10.3588i	0.00818785	+	0.343390i
$911$	0.437471	−	0.281145i	0.0144941	−	0.00931476i	−0.533374	−	0.845880i	$-0.679076\pi$
$911$	0.437471	−	0.281145i	0.0144941	−	0.00931476i	0.547868	+	0.836565i	$0.315440\pi$
$912$	10.9110	+	27.2418i	0.361300	+	0.902067i
$913$	5.46399	+	38.0029i	0.180832	+	1.25771i
$914$	23.1088	+	19.0787i	0.764370	+	0.631066i
$915$	1.79566	+	1.15400i	0.0593628	+	0.0381502i
$916$	10.8190	−	27.0307i	0.357469	−	0.893120i
$917$	−58.7548	+	17.2520i	−1.94025	+	0.569710i
$918$	0.762004	+	1.12576i	0.0251499	+	0.0371557i
$919$	−44.3163			−1.46186			−0.730929	−	0.682453i	$-0.760913\pi$
$919$	−44.3163			−1.46186			−0.730929	+	0.682453i	$0.760913\pi$
$920$	5.52290	+	12.0921i	0.182085	+	0.398666i
$921$	9.38632			0.309290
$922$	−14.0885	−	20.8139i	−0.463979	−	0.685470i
$923$	−7.57868	+	2.22530i	−0.249455	+	0.0732467i
$924$	21.4782	+	8.59661i	0.706582	+	0.282808i
$925$	36.7077	+	23.5906i	1.20694	+	0.775654i
$926$	25.6373	+	21.1662i	0.842492	+	0.695564i
$927$	−0.556544	−	3.87085i	−0.0182793	−	0.127135i
$928$	−24.6603	+	15.0379i	−0.809513	+	0.493644i
$929$	−1.92086	+	1.23446i	−0.0630214	+	0.0405014i	−0.571772	−	0.820412i	$-0.693744\pi$
$929$	−1.92086	+	1.23446i	−0.0630214	+	0.0405014i	0.508751	+	0.860914i	$0.330107\pi$
$930$	−0.185198	−	7.76701i	−0.00607288	−	0.254690i
$931$	47.9791	+	21.9113i	1.57245	+	0.718115i
$932$	0.711056	−	7.45277i	0.0232914	−	0.244124i
$933$	15.7707	+	2.26748i	0.516309	+	0.0742340i
$934$	23.2250	−	21.1146i	0.759946	−	0.690892i
$935$	−2.77565	−	0.815004i	−0.0907734	−	0.0266535i
$936$	−3.36463	−	4.49350i	−0.109976	−	0.146875i
$937$	−9.48420	+	8.21810i	−0.309835	+	0.268474i	−0.795872	−	0.605464i	$-0.792987\pi$
$937$	−9.48420	+	8.21810i	−0.309835	+	0.268474i	0.486037	+	0.873938i	$0.338442\pi$
$938$	54.6867	+	23.4156i	1.78558	+	0.764548i
$939$	−10.2354	−	8.86902i	−0.334019	−	0.289429i
$940$	11.8355	+	16.6179i	0.386033	+	0.542016i
$941$	15.9528	+	34.9318i	0.520047	+	1.13874i	0.969422	+	0.245401i	$0.0789197\pi$
$941$	15.9528	+	34.9318i	0.520047	+	1.13874i	−0.449374	+	0.893344i	$0.648353\pi$
$942$	1.81741	+	10.8051i	0.0592146	+	0.352050i
$943$	50.1727	−	10.9103i	1.63385	−	0.355288i
$944$	0.463060	−	0.364273i	0.0150713	−	0.0118561i
$945$	1.53357	+	3.35805i	0.0498871	+	0.109237i
$946$	10.7197	+	22.0652i	0.348527	+	0.717401i
$947$	−36.2464	+	41.8305i	−1.17785	+	1.35931i	−0.258430	+	0.966030i	$0.583205\pi$
$947$	−36.2464	+	41.8305i	−1.17785	+	1.35931i	−0.919419	+	0.393280i	$0.871340\pi$
$948$	−4.06144	−	0.984953i	−0.131909	−	0.0319898i
$949$	22.6522	−	19.6282i	0.735320	−	0.637159i
$950$	12.7630	+	39.9208i	0.414088	+	1.29520i
$951$	0.627937	−	2.13856i	0.0203622	−	0.0693474i
$952$	−4.90717	+	8.98936i	−0.159042	+	0.291347i
$953$	−10.8728	−	1.56327i	−0.352205	−	0.0506394i	−0.0360579	−	0.999350i	$-0.511480\pi$
$953$	−10.8728	−	1.56327i	−0.352205	−	0.0506394i	−0.316147	+	0.948710i	$0.602389\pi$
$954$	−0.983503	−	0.263487i	−0.0318421	−	0.00853070i
$955$	6.47344	−	14.1748i	0.209476	−	0.458687i
$956$	60.1809	−	11.6039i	1.94639	−	0.375296i
$957$	13.1903	−	8.47690i	0.426382	−	0.274019i
$958$	−3.97592	+	33.2645i	−0.128456	+	1.07473i
$959$	27.3418	−	3.93115i	0.882912	−	0.126944i
$960$	−7.76013	+	1.11763i	−0.250457	+	0.0360712i
$961$	−0.356021	−	0.228801i	−0.0114845	−	0.00738067i
$962$	−15.7787	+	25.8890i	−0.508727	+	0.834694i
$963$	4.45368	+	15.1678i	0.143518	+	0.488777i
$964$	37.7604	−	36.0102i	1.21618	−	1.15981i
$965$	−8.79469			−0.283111
$966$	−24.8285	+	6.02231i	−0.798842	+	0.193765i
$967$			47.8013i			1.53719i	0.639737	+	0.768593i	$0.279043\pi$
$967$			47.8013i			1.53719i	−0.639737	+	0.768593i	$0.720957\pi$
$968$	−2.66115	+	3.55577i	−0.0855327	+	0.114287i
$969$	6.76645	−	1.98681i	0.217370	−	0.0638255i
$970$	−0.0981805	+	0.161090i	−0.00315239	+	0.00517228i
$971$	20.2889	−	31.5702i	0.651102	−	1.01313i	−0.346086	−	0.938203i	$-0.612490\pi$
$971$	20.2889	−	31.5702i	0.651102	−	1.01313i	0.997189	−	0.0749322i	$-0.0238740\pi$
$972$	−1.73213	−	0.999862i	−0.0555581	−	0.0320706i
$973$	5.40851	+	37.6170i	0.173389	+	1.20595i
$974$	18.3261	+	2.19042i	0.587208	+	0.0701856i
$975$	−4.33448	−	6.74459i	−0.138815	−	0.216000i
$976$	−4.35723	−	7.54418i	−0.139472	−	0.241483i
$977$	−4.62883	−	2.11391i	−0.148089	−	0.0676301i	0.339992	−	0.940428i	$-0.389576\pi$
$977$	−4.62883	−	2.11391i	−0.148089	−	0.0676301i	−0.488081	+	0.872798i	$0.662303\pi$
$978$	15.9861	+	4.28278i	0.511179	+	0.136948i
$979$	0.0345521	−	0.240315i	0.00110429	−	0.00768051i
$980$	−8.71016	+	11.0777i	−0.278236	+	0.353864i
$981$	−14.6435	−	4.29972i	−0.467531	−	0.137279i
$982$	−2.50162	+	0.799792i	−0.0798300	+	0.0255224i
$983$	−35.2898	−	40.7266i	−1.12557	−	1.29898i	−0.949207	−	0.314652i	$-0.898112\pi$
$983$	−35.2898	−	40.7266i	−1.12557	−	1.29898i	−0.176364	−	0.984325i	$-0.556433\pi$
$984$	−2.15668	+	30.2049i	−0.0687525	+	0.962897i
$985$	−11.7025	−	10.1403i	−0.372873	−	0.323096i
$986$	3.03312	+	6.24331i	0.0965943	+	0.198828i
$987$	−35.6658	+	16.2880i	−1.13526	+	0.518454i
$988$	−27.5188	+	9.52679i	−0.875489	+	0.303088i
$989$	−23.7758	−	12.9850i	−0.756028	−	0.412899i
$990$	4.19705	−	0.705940i	0.133391	−	0.0224363i
$991$	−29.9216	+	13.6648i	−0.950492	+	0.434075i	−0.829456	−	0.558573i	$-0.811349\pi$
$991$	−29.9216	+	13.6648i	−0.950492	+	0.434075i	−0.121037	+	0.992648i	$0.538622\pi$
$992$	−13.8500	+	28.5258i	−0.439737	+	0.905695i
$993$	19.9746	−	23.0520i	0.633876	−	0.731532i
$994$	−19.4896	−	8.34500i	−0.618171	−	0.264687i
$995$	−10.3084	−	11.8965i	−0.326799	−	0.377146i
$996$	22.2251	−	11.4601i	0.704228	−	0.363126i
$997$	12.5022	−	42.5785i	0.395947	−	1.34847i	−0.484691	−	0.874685i	$-0.661068\pi$
$997$	12.5022	−	42.5785i	0.395947	−	1.34847i	0.880639	−	0.473788i	$-0.157114\pi$
$998$	13.8745	+	15.2612i	0.439189	+	0.483086i
$999$	−1.53726	+	10.6919i	−0.0486367	+	0.338276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.19.19	yes	240
8.3	odd	2	inner	552.2.t.a.19.3	✓	240
23.17	odd	22	inner	552.2.t.a.523.3	yes	240
184.155	even	22	inner	552.2.t.a.523.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.19.3	✓	240	8.3	odd	2	inner
552.2.t.a.19.19	yes	240	1.1	even	1	trivial
552.2.t.a.523.3	yes	240	23.17	odd	22	inner
552.2.t.a.523.19	yes	240	184.155	even	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17115 - 0.792724i) q^{2} +(0.959493 - 0.281733i) q^{3} +(0.743177 - 1.85679i) q^{4} +(0.824449 + 0.529841i) q^{5} +(0.900373 - 1.09056i) q^{6} +(0.536086 + 3.72856i) q^{7} +(-0.601555 - 2.76372i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(1.17115 - 0.792724i) q^{2} +(0.959493 - 0.281733i) q^{3} +(0.743177 - 1.85679i) q^{4} +(0.824449 + 0.529841i) q^{5} +(0.900373 - 1.09056i) q^{6} +(0.536086 + 3.72856i) q^{7} +(-0.601555 - 2.76372i) q^{8} +(0.841254 - 0.540641i) q^{9} +(1.38557 - 0.0330378i) q^{10} +(2.79329 + 1.27565i) q^{11} +(0.189954 - 1.99096i) q^{12} +(1.96450 + 0.282452i) q^{13} +(3.58356 + 3.94173i) q^{14} +(0.940327 + 0.276105i) q^{15} +(-2.89537 - 2.75986i) q^{16} +(-0.726462 + 0.629483i) q^{17} +(0.556654 - 1.30005i) q^{18} +(-5.54449 - 4.80433i) q^{19} +(1.59652 - 1.13707i) q^{20} +(1.56483 + 3.42650i) q^{21} +(4.28260 - 0.720329i) q^{22} +(-3.39143 + 3.39090i) q^{23} +(-1.35582 - 2.48229i) q^{24} +(-1.67809 - 3.67451i) q^{25} +(2.52463 - 1.22651i) q^{26} +(0.654861 - 0.755750i) q^{27} +(7.32158 + 1.77558i) q^{28} +(3.85883 - 3.34370i) q^{29} +(1.32014 - 0.422060i) q^{30} +(1.57929 - 5.37857i) q^{31} +(-5.57872 - 0.936969i) q^{32} +(3.03954 + 0.437019i) q^{33} +(-0.351789 + 1.31310i) q^{34} +(-1.53357 + 3.35805i) q^{35} +(-0.378658 - 1.96383i) q^{36} +(-9.08706 + 5.83990i) q^{37} +(-10.3019 - 1.23133i) q^{38} +(1.96450 - 0.282452i) q^{39} +(0.968380 - 2.59727i) q^{40} +(-9.00665 - 5.78823i) q^{41} +(4.54891 + 2.77246i) q^{42} +(1.59145 + 5.41997i) q^{43} +(4.44454 - 4.23853i) q^{44} +0.980025 q^{45} +(-1.28382 + 6.65972i) q^{46} +10.4088i q^{47} +(-3.55563 - 1.83234i) q^{48} +(-6.89834 + 2.02554i) q^{49} +(-4.87816 - 2.97313i) q^{50} +(-0.519690 + 0.808653i) q^{51} +(1.98443 - 3.43776i) q^{52} +(-0.102462 - 0.712638i) q^{53} +(0.167838 - 1.40422i) q^{54} +(1.62703 + 2.53171i) q^{55} +(9.98221 - 3.72453i) q^{56} +(-6.67344 - 3.04766i) q^{57} +(1.86864 - 6.97495i) q^{58} +(-0.0209618 + 0.145793i) q^{59} +(1.21150 - 1.54080i) q^{60} +(2.08979 + 0.613618i) q^{61} +(-2.41414 - 7.55105i) q^{62} +(2.46680 + 2.84684i) q^{63} +(-7.27626 + 3.32505i) q^{64} +(1.46998 + 1.27374i) q^{65} +(3.90618 - 1.89770i) q^{66} +(10.1579 - 4.63894i) q^{67} +(0.628931 + 1.81671i) q^{68} +(-2.29873 + 4.20902i) q^{69} +(0.865969 + 5.14847i) q^{70} +(-3.62012 + 1.65325i) q^{71} +(-2.00024 - 1.99976i) q^{72} +(9.88976 - 11.4134i) q^{73} +(-6.01287 + 14.0429i) q^{74} +(-2.64534 - 3.05289i) q^{75} +(-13.0412 + 6.72452i) q^{76} +(-3.25891 + 11.0988i) q^{77} +(2.07681 - 1.88810i) q^{78} +(0.297379 - 2.06831i) q^{79} +(-0.924803 - 3.80945i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-15.1366 + 0.360920i) q^{82} +(6.75956 + 10.5181i) q^{83} +(7.52525 - 0.359071i) q^{84} +(-0.932458 + 0.134067i) q^{85} +(6.16036 + 5.08601i) q^{86} +(2.76049 - 4.29541i) q^{87} +(1.84523 - 8.48724i) q^{88} +(-0.0222747 - 0.0758606i) q^{89} +(1.14775 - 0.776889i) q^{90} +7.47618i q^{91} +(3.77577 + 8.81723i) q^{92} -5.60564i q^{93} +(8.25133 + 12.1903i) q^{94} +(-2.02562 - 6.89863i) q^{95} +(-5.61671 + 0.672692i) q^{96} +(-0.0735896 + 0.114508i) q^{97} +(-6.47329 + 7.84068i) q^{98} +(3.03954 - 0.437019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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