LMFDB - Embedded newform 570.2.bh.b.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.b.307.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.02568 + 0.946899i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-1.23745 - 4.61822i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.02568 + 0.946899i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-1.23745 - 4.61822i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(1.93544 + 1.11985i) q^{10} +(2.99982 + 5.19583i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(1.52397 - 3.26817i) q^{13} +(-0.830236 - 4.70850i) q^{14} +(-2.23607 - 0.00209206i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.165257 - 1.88890i) q^{17} +(0.707107 - 0.707107i) q^{18} +(2.35193 - 3.66993i) q^{19} +(1.83048 + 1.28427i) q^{20} +(3.07326 + 3.66256i) q^{21} +(2.53555 + 5.43751i) q^{22} +(-4.76200 + 3.33439i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(3.20677 + 3.83623i) q^{25} +(1.80302 - 3.12292i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(-0.416704 - 4.76294i) q^{28} +(5.62951 + 4.72372i) q^{29} +(-2.22738 - 0.196970i) q^{30} +(-3.11739 - 1.79982i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-4.91461 - 3.44125i) q^{33} +(0.329257 - 1.86731i) q^{34} +(1.86631 - 10.5268i) q^{35} +(0.766044 - 0.642788i) q^{36} +(4.85524 + 4.85524i) q^{37} +(2.66284 - 3.45098i) q^{38} +3.60603i q^{39} +(1.71158 + 1.43892i) q^{40} +(0.946293 - 2.59992i) q^{41} +(2.74235 + 3.91648i) q^{42} +(-1.92825 + 2.75383i) q^{43} +(2.05199 + 5.63781i) q^{44} +(2.02745 - 0.943107i) q^{45} +(-5.03449 + 2.90666i) q^{46} +(2.30921 - 0.202029i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(-13.7345 + 7.92964i) q^{49} +(2.86021 + 4.10112i) q^{50} +(0.648509 + 1.78176i) q^{51} +(2.06833 - 2.95389i) q^{52} +(-5.15086 - 7.35620i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(1.15674 + 13.3656i) q^{55} -4.78114i q^{56} +(-0.580597 + 4.32006i) q^{57} +(5.19639 + 5.19639i) q^{58} +(-7.15578 + 6.00441i) q^{59} +(-2.20173 - 0.390349i) q^{60} +(0.697407 - 3.95519i) q^{61} +(-2.94866 - 2.06467i) q^{62} +(-4.33318 - 2.02060i) q^{63} +(0.866025 + 0.500000i) q^{64} +(6.18172 - 5.17723i) q^{65} +(-4.59598 - 3.85649i) q^{66} +(-0.816771 - 9.33574i) q^{67} +(0.490751 - 1.83151i) q^{68} +(2.90666 - 5.03449i) q^{69} +(2.77668 - 10.3241i) q^{70} +(-3.87366 + 0.683031i) q^{71} +(0.819152 - 0.573576i) q^{72} +(1.92323 + 4.12439i) q^{73} +(4.41360 + 5.25993i) q^{74} +(-4.52758 - 2.12157i) q^{75} +(2.95348 - 3.20577i) q^{76} +(20.2834 - 20.2834i) q^{77} +(-0.314286 + 3.59231i) q^{78} +(-14.4916 - 5.27450i) q^{79} +(1.57966 + 1.58262i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(1.16929 - 2.50755i) q^{82} +(-2.42104 + 0.648717i) q^{83} +(2.39057 + 4.14059i) q^{84} +(2.12335 - 3.66982i) q^{85} +(-2.16093 + 2.57529i) q^{86} +(-7.09840 - 1.90201i) q^{87} +(1.55282 + 5.79520i) q^{88} +(-2.34063 + 0.851920i) q^{89} +(2.10193 - 0.762814i) q^{90} +(-16.9790 - 2.99386i) q^{91} +(-5.26866 + 2.45682i) q^{92} +(3.58595 + 0.313730i) q^{93} +2.31803 q^{94} +(8.23932 - 5.20707i) q^{95} -1.00000 q^{96} +(-5.11749 - 0.447723i) q^{97} +(-14.3734 + 6.70242i) q^{98} +(5.90848 + 1.04183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^5 + 12 * q^7	$ 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	2.02568	+	0.946899i	0.905912	+	0.423466i
$5$	2.02568	+	0.946899i	0.905912	+	0.423466i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	−1.23745	−	4.61822i	−0.467712	−	1.74552i	−0.647738	−	0.761863i	$-0.724285\pi$
$7$	−1.23745	−	4.61822i	−0.467712	−	1.74552i	0.180026	−	0.983662i	$-0.442382\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	1.93544	+	1.11985i	0.612041	+	0.354126i
$11$	2.99982	+	5.19583i	0.904479	+	1.56660i	0.821616	+	0.570042i	$0.193073\pi$
$11$	2.99982	+	5.19583i	0.904479	+	1.56660i	0.0828628	+	0.996561i	$0.473594\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	1.52397	−	3.26817i	0.422675	−	0.906429i	−0.573513	−	0.819196i	$-0.694420\pi$
$13$	1.52397	−	3.26817i	0.422675	−	0.906429i	0.996188	−	0.0872324i	$-0.0278023\pi$
$14$	−0.830236	−	4.70850i	−0.221890	−	1.25840i
$15$	−2.23607	−	0.00209206i	−0.577350	−	0.000540169i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	0.165257	−	1.88890i	0.0400808	−	0.458125i	−0.949462	−	0.313883i	$-0.898370\pi$
$17$	0.165257	−	1.88890i	0.0400808	−	0.458125i	0.989542	−	0.144242i	$-0.0460745\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	2.35193	−	3.66993i	0.539571	−	0.841940i
$19$	2.35193	−	3.66993i	0.539571	−	0.841940i
$20$	1.83048	+	1.28427i	0.409308	+	0.287171i
$21$	3.07326	+	3.66256i	0.670640	+	0.799237i
$22$	2.53555	+	5.43751i	0.540582	+	1.15928i
$23$	−4.76200	+	3.33439i	−0.992945	+	0.695267i	−0.952697	−	0.303922i	$-0.901704\pi$
$23$	−4.76200	+	3.33439i	−0.992945	+	0.695267i	−0.0402479	+	0.999190i	$0.512815\pi$
$24$	−0.984808	+	0.173648i	−0.201023	+	0.0354458i
$25$	3.20677	+	3.83623i	0.641353	+	0.767246i
$26$	1.80302	−	3.12292i	0.353600	−	0.612454i
$27$	−0.258819	+	0.965926i	−0.0498097	+	0.185893i
$28$	−0.416704	−	4.76294i	−0.0787496	−	0.900112i
$29$	5.62951	+	4.72372i	1.04537	+	0.877173i	0.992600	−	0.121433i	$-0.0387491\pi$
$29$	5.62951	+	4.72372i	1.04537	+	0.877173i	0.0527746	+	0.998606i	$0.483194\pi$
$30$	−2.22738	−	0.196970i	−0.406661	−	0.0359617i
$31$	−3.11739	−	1.79982i	−0.559899	−	0.323258i	0.193206	−	0.981158i	$-0.438111\pi$
$31$	−3.11739	−	1.79982i	−0.559899	−	0.323258i	−0.753105	+	0.657900i	$0.771445\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$	−4.91461	−	3.44125i	−0.855524	−	0.599044i
$34$	0.329257	−	1.86731i	0.0564671	−	0.320241i
$35$	1.86631	−	10.5268i	0.315465	−	1.77935i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	4.85524	+	4.85524i	0.798197	+	0.798197i	0.982811	−	0.184614i	$-0.0591036\pi$
$37$	4.85524	+	4.85524i	0.798197	+	0.798197i	−0.184614	+	0.982811i	$0.559104\pi$
$38$	2.66284	−	3.45098i	0.431970	−	0.559823i
$39$			3.60603i			0.577427i
$40$	1.71158	+	1.43892i	0.270625	+	0.227513i
$41$	0.946293	−	2.59992i	0.147786	−	0.406039i	−0.843606	−	0.536962i	$-0.819572\pi$
$41$	0.946293	−	2.59992i	0.147786	−	0.406039i	0.991393	+	0.130923i	$0.0417940\pi$
$42$	2.74235	+	3.91648i	0.423154	+	0.604326i
$43$	−1.92825	+	2.75383i	−0.294056	+	0.419955i	−0.938810	−	0.344435i	$-0.888071\pi$
$43$	−1.92825	+	2.75383i	−0.294056	+	0.419955i	0.644755	+	0.764390i	$0.276960\pi$
$44$	2.05199	+	5.63781i	0.309350	+	0.849932i
$45$	2.02745	−	0.943107i	0.302234	−	0.140590i
$46$	−5.03449	+	2.90666i	−0.742294	+	0.428564i
$47$	2.30921	−	0.202029i	0.336832	−	0.0294690i	0.0825150	−	0.996590i	$-0.473705\pi$
$47$	2.30921	−	0.202029i	0.336832	−	0.0294690i	0.254317	+	0.967121i	$0.418149\pi$
$48$	−0.996195	+	0.0871557i	−0.143788	+	0.0125798i
$49$	−13.7345	+	7.92964i	−1.96208	+	1.13281i
$50$	2.86021	+	4.10112i	0.404495	+	0.579986i
$51$	0.648509	+	1.78176i	0.0908095	+	0.249497i
$52$	2.06833	−	2.95389i	0.286826	−	0.409631i
$53$	−5.15086	−	7.35620i	−0.707526	−	1.01045i	−0.998555	−	0.0537371i	$-0.982887\pi$
$53$	−5.15086	−	7.35620i	−0.707526	−	1.01045i	0.291030	−	0.956714i	$-0.406002\pi$
$54$	−0.342020	+	0.939693i	−0.0465430	+	0.127876i
$55$	1.15674	+	13.3656i	0.155975	+	1.80222i
$56$		−	4.78114i		−	0.638906i
$57$	−0.580597	+	4.32006i	−0.0769019	+	0.572206i
$58$	5.19639	+	5.19639i	0.682320	+	0.682320i
$59$	−7.15578	+	6.00441i	−0.931603	+	0.781707i	−0.976104	−	0.217302i	$-0.930274\pi$
$59$	−7.15578	+	6.00441i	−0.931603	+	0.781707i	0.0445018	+	0.999009i	$0.485830\pi$
$60$	−2.20173	−	0.390349i	−0.284242	−	0.0503939i
$61$	0.697407	−	3.95519i	0.0892938	−	0.506410i	−0.907053	−	0.421015i	$-0.861674\pi$
$61$	0.697407	−	3.95519i	0.0892938	−	0.506410i	0.996347	−	0.0853946i	$-0.0272151\pi$
$62$	−2.94866	−	2.06467i	−0.374480	−	0.262214i
$63$	−4.33318	−	2.02060i	−0.545930	−	0.254571i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	6.18172	−	5.17723i	0.766748	−	0.642156i
$66$	−4.59598	−	3.85649i	−0.565727	−	0.474701i
$67$	−0.816771	−	9.33574i	−0.0997845	−	1.14054i	−0.866712	−	0.498809i	$-0.833771\pi$
$67$	−0.816771	−	9.33574i	−0.0997845	−	1.14054i	0.766928	−	0.641733i	$-0.221784\pi$
$68$	0.490751	−	1.83151i	0.0595122	−	0.222103i
$69$	2.90666	−	5.03449i	0.349921	−	0.606081i
$70$	2.77668	−	10.3241i	0.331877	−	1.23396i
$71$	−3.87366	+	0.683031i	−0.459719	+	0.0810608i	−0.398711	−	0.917076i	$-0.630542\pi$
$71$	−3.87366	+	0.683031i	−0.459719	+	0.0810608i	−0.0610074	+	0.998137i	$0.519431\pi$
$72$	0.819152	−	0.573576i	0.0965380	−	0.0675966i
$73$	1.92323	+	4.12439i	0.225098	+	0.482723i	0.986127	−	0.165994i	$-0.0530834\pi$
$73$	1.92323	+	4.12439i	0.225098	+	0.482723i	−0.761029	+	0.648718i	$0.775306\pi$
$74$	4.41360	+	5.25993i	0.513071	+	0.611454i
$75$	−4.52758	−	2.12157i	−0.522800	−	0.244977i
$76$	2.95348	−	3.20577i	0.338787	−	0.367727i
$77$	20.2834	−	20.2834i	2.31151	−	2.31151i
$78$	−0.314286	+	3.59231i	−0.0355859	+	0.406749i
$79$	−14.4916	−	5.27450i	−1.63043	−	0.593428i	−0.645101	−	0.764097i	$-0.723185\pi$
$79$	−14.4916	−	5.27450i	−1.63043	−	0.593428i	−0.985328	+	0.170669i	$0.945407\pi$
$80$	1.57966	+	1.58262i	0.176611	+	0.176942i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	1.16929	−	2.50755i	0.129126	−	0.276913i
$83$	−2.42104	+	0.648717i	−0.265744	+	0.0712059i	−0.389231	−	0.921140i	$-0.627259\pi$
$83$	−2.42104	+	0.648717i	−0.265744	+	0.0712059i	0.123487	+	0.992346i	$0.460592\pi$
$84$	2.39057	+	4.14059i	0.260832	+	0.451775i
$85$	2.12335	−	3.66982i	0.230310	−	0.398048i
$86$	−2.16093	+	2.57529i	−0.233019	+	0.277701i
$87$	−7.09840	−	1.90201i	−0.761029	−	0.203917i
$88$	1.55282	+	5.79520i	0.165531	+	0.617770i
$89$	−2.34063	+	0.851920i	−0.248106	+	0.0903034i	−0.463080	−	0.886317i	$-0.653256\pi$
$89$	−2.34063	+	0.851920i	−0.248106	+	0.0903034i	0.214973	+	0.976620i	$0.431033\pi$
$90$	2.10193	−	0.762814i	0.221563	−	0.0804077i
$91$	−16.9790	−	2.99386i	−1.77988	−	0.313841i
$92$	−5.26866	+	2.45682i	−0.549296	+	0.256141i
$93$	3.58595	+	0.313730i	0.371846	+	0.0325323i
$94$	2.31803			0.239086
$95$	8.23932	−	5.20707i	0.845337	−	0.534234i
$96$	−1.00000			−0.102062
$97$	−5.11749	−	0.447723i	−0.519603	−	0.0454593i	−0.175662	−	0.984451i	$-0.556206\pi$
$97$	−5.11749	−	0.447723i	−0.519603	−	0.0454593i	−0.343941	+	0.938991i	$0.611762\pi$
$98$	−14.3734	+	6.70242i	−1.45193	+	0.677047i
$99$	5.90848	+	1.04183i	0.593825	+	0.104707i
$100$	2.49189	+	4.33480i	0.249189	+	0.433480i
$101$	−1.30965	+	0.476675i	−0.130315	+	0.0474310i	−0.406355	−	0.913715i	$-0.633200\pi$
$101$	−1.30965	+	0.476675i	−0.130315	+	0.0474310i	0.276039	+	0.961146i	$0.410978\pi$
$102$	0.490751	+	1.83151i	0.0485915	+	0.181346i
$103$	2.89661	+	0.776145i	0.285412	+	0.0764758i	0.398685	−	0.917088i	$-0.369467\pi$
$103$	2.89661	+	0.776145i	0.285412	+	0.0764758i	−0.113273	+	0.993564i	$0.536133\pi$
$104$	2.31791	−	2.76238i	0.227290	−	0.270874i
$105$	2.75736	+	10.3292i	0.269091	+	1.00803i
$106$	−4.49013	−	7.77713i	−0.436120	−	0.755382i
$107$	−9.50888	+	2.54790i	−0.919258	+	0.246314i	−0.687268	−	0.726404i	$-0.741190\pi$
$107$	−9.50888	+	2.54790i	−0.919258	+	0.246314i	−0.231990	+	0.972718i	$0.574524\pi$
$108$	−0.422618	+	0.906308i	−0.0406665	+	0.0872095i
$109$	−0.0855656	−	0.485267i	−0.00819570	−	0.0464801i	0.980436	−	0.196840i	$-0.0630679\pi$
$109$	−0.0855656	−	0.485267i	−0.00819570	−	0.0464801i	−0.988631	+	0.150360i	$0.951957\pi$
$110$	−0.0125516	+	13.4156i	−0.00119675	+	1.27913i
$111$	−6.45226	−	2.34843i	−0.612421	−	0.222903i
$112$	0.416704	−	4.76294i	0.0393748	−	0.450056i
$113$	−7.93133	+	7.93133i	−0.746117	+	0.746117i	−0.973748	−	0.227631i	$-0.926902\pi$
$113$	−7.93133	+	7.93133i	−0.746117	+	0.746117i	0.227631	+	0.973748i	$0.426902\pi$
$114$	−0.954905	+	4.25302i	−0.0894351	+	0.398332i
$115$	−12.8036	+	2.24527i	−1.19394	+	0.209373i
$116$	4.72372	+	5.62951i	0.438587	+	0.522687i
$117$	−1.52397	−	3.26817i	−0.140892	−	0.302143i
$118$	−7.65186	+	5.35789i	−0.704411	+	0.493234i
$119$	−8.92786	+	1.57422i	−0.818415	+	0.144309i
$120$	−2.15933	−	0.580758i	−0.197119	−	0.0530157i
$121$	−12.4978	+	21.6468i	−1.13616	+	1.96789i
$122$	1.03947	−	3.87936i	0.0941092	−	0.351220i
$123$	0.241140	+	2.75625i	0.0217429	+	0.248522i
$124$	−2.75749	−	2.31381i	−0.247630	−	0.207786i
$125$	2.86336	+	10.8075i	0.256107	+	0.966648i
$126$	−4.14059	−	2.39057i	−0.368873	−	0.212969i
$127$	−1.25235	−	0.583980i	−0.111128	−	0.0518199i	0.366259	−	0.930513i	$-0.380638\pi$
$127$	−1.25235	−	0.583980i	−0.111128	−	0.0518199i	−0.477387	+	0.878693i	$0.658416\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$	0.583771	−	3.31073i	0.0513982	−	0.291494i
$130$	6.60942	−	4.61876i	0.579684	−	0.405092i
$131$	2.03837	−	1.71039i	0.178093	−	0.149438i	−0.549384	−	0.835570i	$-0.685137\pi$
$131$	2.03837	−	1.71039i	0.178093	−	0.149438i	0.727477	+	0.686132i	$0.240693\pi$
$132$	−4.24238	−	4.24238i	−0.369252	−	0.369252i
$133$	−19.8590	−	6.32041i	−1.72199	−	0.548049i
$134$		−	9.37140i		−	0.809566i
$135$	−1.43892	+	1.71158i	−0.123842	+	0.147310i
$136$	0.648509	−	1.78176i	0.0556092	−	0.152785i
$137$	−7.54568	−	10.7763i	−0.644671	−	0.920685i	0.355230	−	0.934779i	$-0.384403\pi$
$137$	−7.54568	−	10.7763i	−0.644671	−	0.920685i	−0.999901	+	0.0140938i	$0.995514\pi$
$138$	3.33439	−	4.76200i	0.283842	−	0.405368i
$139$	6.30400	+	17.3201i	0.534698	+	1.46907i	0.853421	+	0.521223i	$0.174524\pi$
$139$	6.30400	+	17.3201i	0.534698	+	1.46907i	−0.318722	+	0.947848i	$0.603254\pi$
$140$	3.66592	−	10.0428i	0.309827	−	0.848770i
$141$	−2.00747	+	1.15901i	−0.169060	+	0.0976066i
$142$	−3.91845	+	0.342820i	−0.328829	+	0.0287688i
$143$	21.5525	−	1.88560i	1.80231	−	0.157682i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	6.93071	+	14.8993i	0.575564	+	1.23732i
$146$	1.55645	+	4.27631i	0.128813	+	0.353910i
$147$	9.09651	−	12.9912i	0.750268	−	1.07149i
$148$	3.93838	+	5.62458i	0.323733	+	0.462338i
$149$	−4.94059	+	13.5741i	−0.404749	+	1.11204i	0.555165	+	0.831740i	$0.312655\pi$
$149$	−4.94059	+	13.5741i	−0.404749	+	1.11204i	−0.959913	+	0.280297i	$0.909567\pi$
$150$	−4.32544	−	2.50810i	−0.353171	−	0.204785i
$151$		−	21.9602i		−	1.78710i	−0.448965	−	0.893549i	$-0.648207\pi$
$151$		−	21.9602i		−	1.78710i	0.448965	−	0.893549i	$-0.351793\pi$
$152$	3.22164	−	2.93616i	0.261310	−	0.238154i
$153$	−1.34076	−	1.34076i	−0.108394	−	0.108394i
$154$	21.9740	−	18.4384i	1.77072	−	1.48581i
$155$	−4.61058	−	6.59772i	−0.370331	−	0.529942i
$156$	−0.626181	+	3.55125i	−0.0501346	+	0.284327i
$157$	3.56867	+	2.49881i	0.284810	+	0.199426i	0.707248	−	0.706966i	$-0.249936\pi$
$157$	3.56867	+	2.49881i	0.284810	+	0.199426i	−0.422437	+	0.906392i	$0.638825\pi$
$158$	−13.9767	−	6.51745i	−1.11193	−	0.518501i
$159$	7.77713	+	4.49013i	0.616767	+	0.356090i
$160$	1.43571	+	1.71427i	0.113503	+	0.135525i
$161$	21.2917	+	17.8658i	1.67802	+	1.40802i
$162$	−0.0871557	−	0.996195i	−0.00684760	−	0.0782684i
$163$	−3.14122	+	11.7232i	−0.246039	+	0.918231i	0.726819	+	0.686829i	$0.240998\pi$
$163$	−3.14122	+	11.7232i	−0.246039	+	0.918231i	−0.972858	+	0.231402i	$0.925669\pi$
$164$	1.38339	−	2.39610i	0.108024	−	0.187104i
$165$	−6.69692	−	11.6245i	−0.521354	−	0.904967i
$166$	−2.46837	+	0.435240i	−0.191583	+	0.0337812i
$167$	1.50190	−	1.05164i	0.116220	−	0.0813782i	−0.514021	−	0.857777i	$-0.671845\pi$
$167$	1.50190	−	1.05164i	0.116220	−	0.0813782i	0.630241	+	0.776399i	$0.282956\pi$
$168$	2.02060	+	4.33318i	0.155892	+	0.334312i
$169$	−0.00222671	−	0.00265370i	−0.000171286	−	0.000204130i
$170$	2.43512	−	3.47080i	0.186765	−	0.266198i
$171$	−1.29954	−	4.16067i	−0.0993780	−	0.318175i
$172$	−2.37715	+	2.37715i	−0.181256	+	0.181256i
$173$	0.452652	−	5.17383i	0.0344145	−	0.393359i	−0.959379	−	0.282120i	$-0.908962\pi$
$173$	0.452652	−	5.17383i	0.0344145	−	0.393359i	0.993794	−	0.111239i	$-0.0354821\pi$
$174$	−6.90562	−	2.51344i	−0.523514	−	0.190543i
$175$	13.7484	−	19.5567i	1.03928	−	1.47835i
$176$	1.04183	+	5.90848i	0.0785305	+	0.445369i
$177$	3.94776	−	8.46600i	0.296732	−	0.636344i
$178$	−2.40597	+	0.644679i	−0.180335	+	0.0483207i
$179$	−7.21635	−	12.4991i	−0.539375	−	0.934225i	−0.998938	−	0.0460797i	$-0.985327\pi$
$179$	−7.21635	−	12.4991i	−0.539375	−	0.934225i	0.459563	−	0.888145i	$-0.348006\pi$
$180$	2.16042	−	0.576716i	0.161028	−	0.0429859i
$181$	14.9053	−	17.7635i	1.10790	−	1.32035i	0.165370	−	0.986232i	$-0.447118\pi$
$181$	14.9053	−	17.7635i	1.10790	−	1.32035i	0.942532	−	0.334115i	$-0.108438\pi$
$182$	−16.6535	−	4.46228i	−1.23444	−	0.330766i
$183$	1.03947	+	3.87936i	0.0768398	+	0.286770i
$184$	−5.46274	+	1.98827i	−0.402718	+	0.146577i
$185$	5.23775	+	14.4326i	0.385087	+	1.06111i
$186$	3.54496	+	0.625072i	0.259929	+	0.0458325i
$187$	10.3101	−	4.80770i	0.753953	−	0.351574i
$188$	2.30921	+	0.202029i	0.168416	+	0.0147345i
$189$	4.78114			0.347777
$190$	8.66180	−	4.46915i	0.628393	−	0.324226i
$191$	4.36343			0.315726			0.157863	−	0.987461i	$-0.449539\pi$
$191$	4.36343			0.315726			0.157863	+	0.987461i	$0.449539\pi$
$192$	−0.996195	−	0.0871557i	−0.0718942	−	0.00628992i
$193$	−15.8599	+	7.39558i	−1.14162	+	0.532345i	−0.899075	−	0.437795i	$-0.855759\pi$
$193$	−15.8599	+	7.39558i	−1.14162	+	0.532345i	−0.242543	+	0.970141i	$0.577982\pi$
$194$	−5.05900	−	0.892038i	−0.363215	−	0.0640446i
$195$	−3.41455	+	7.30467i	−0.244521	+	0.523098i
$196$	−14.9028	+	5.42419i	−1.06449	+	0.387442i
$197$	4.43037	+	16.5344i	0.315651	+	1.17802i	0.923382	+	0.383882i	$0.125413\pi$
$197$	4.43037	+	16.5344i	0.315651	+	1.17802i	−0.607732	+	0.794142i	$0.707920\pi$
$198$	5.79520	+	1.55282i	0.411847	+	0.110354i
$199$	−6.93494	+	8.26474i	−0.491605	+	0.585872i	−0.953625	−	0.300997i	$-0.902680\pi$
$199$	−6.93494	+	8.26474i	−0.491605	+	0.585872i	0.462020	+	0.886870i	$0.347125\pi$
$200$	2.10461	+	4.53549i	0.148818	+	0.320707i
$201$	4.68570	+	8.11587i	0.330504	+	0.572449i
$202$	−1.34622	+	0.360717i	−0.0947194	+	0.0253800i
$203$	14.8490	−	31.8437i	1.04219	−	2.23499i
$204$	0.329257	+	1.86731i	0.0230526	+	0.130738i
$205$	4.37875	−	4.37056i	0.305825	−	0.305253i
$206$	2.81794	+	1.02565i	0.196335	+	0.0714603i
$207$	−0.506665	+	5.79120i	−0.0352156	+	0.402516i
$208$	2.54985	−	2.54985i	0.176800	−	0.176800i
$209$	26.1237	+	1.21114i	1.80702	+	0.0837764i
$210$	1.84661	+	10.5303i	0.127428	+	0.726657i
$211$	3.80827	+	4.53851i	0.262172	+	0.312444i	0.881032	−	0.473057i	$-0.156850\pi$
$211$	3.80827	+	4.53851i	0.262172	+	0.312444i	−0.618860	+	0.785501i	$0.712405\pi$
$212$	−3.79522	−	8.13888i	−0.260657	−	0.558980i
$213$	3.22207	−	2.25612i	0.220772	−	0.154586i
$214$	−9.69476	+	1.70945i	−0.662720	+	0.116855i
$215$	−6.51362	+	3.75252i	−0.444225	+	0.255920i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−4.45438	+	16.6240i	−0.302383	+	1.12851i
$218$	−0.0429462	−	0.490878i	−0.00290869	−	0.0332464i
$219$	−3.48608	−	2.92517i	−0.235568	−	0.197665i
$220$	−1.18175	+	13.3634i	−0.0796735	+	0.900963i
$221$	−5.92140	−	3.41872i	−0.398317	−	0.229968i
$222$	−6.22303	−	2.90184i	−0.417662	−	0.194759i
$223$	19.8791	+	13.9195i	1.33120	+	0.932117i	0.999935	−	0.0114210i	$-0.00363551\pi$
$223$	19.8791	+	13.9195i	1.33120	+	0.932117i	0.331266	+	0.943538i	$0.392524\pi$
$224$	0.830236	−	4.70850i	0.0554725	−	0.314600i
$225$	4.99999	+	0.00935599i	0.333333	+	0.000623733i
$226$	−8.59241	+	7.20989i	−0.571559	+	0.479595i
$227$	10.0629	+	10.0629i	0.667900	+	0.667900i	0.957230	−	0.289330i	$-0.0934323\pi$
$227$	10.0629	+	10.0629i	0.667900	+	0.667900i	−0.289330	+	0.957230i	$0.593432\pi$
$228$	−1.32195	+	4.15361i	−0.0875480	+	0.275079i
$229$			14.7107i			0.972109i	0.873928	+	0.486055i	$0.161564\pi$
$229$			14.7107i			0.972109i	−0.873928	+	0.486055i	$0.838436\pi$
$230$	−12.9506	+	1.12082i	−0.853936	+	0.0739047i
$231$	−9.81087	+	26.9551i	−0.645508	+	1.77352i
$232$	4.21510	+	6.01979i	0.276735	+	0.395219i
$233$	11.4829	−	16.3993i	0.752269	−	1.07435i	−0.242293	−	0.970203i	$-0.577900\pi$
$233$	11.4829	−	16.3993i	0.752269	−	1.07435i	0.994562	−	0.104148i	$-0.0332115\pi$
$234$	−1.23334	−	3.38856i	−0.0806257	−	0.221517i
$235$	4.86902	+	1.77734i	0.317620	+	0.115941i
$236$	−8.08972	+	4.67060i	−0.526596	+	0.304030i
$237$	15.3629	−	1.34408i	0.997929	−	0.0873075i
$238$	−9.03109	+	0.790118i	−0.585398	+	0.0512157i
$239$	23.1199	−	13.3483i	1.49550	−	0.863430i	0.495517	−	0.868598i	$-0.334979\pi$
$239$	23.1199	−	13.3483i	1.49550	−	0.863430i	0.999987	+	0.00516865i	$0.00164524\pi$
$240$	−2.10050	−	0.766746i	−0.135587	−	0.0494932i
$241$	−1.37527	−	3.77853i	−0.0885891	−	0.243396i	0.887484	−	0.460838i	$-0.152451\pi$
$241$	−1.37527	−	3.77853i	−0.0885891	−	0.243396i	−0.976073	+	0.217442i	$0.930229\pi$
$242$	−14.3369	+	20.4752i	−0.921609	+	1.31619i
$243$	0.573576	+	0.819152i	0.0367949	+	0.0525486i
$244$	1.37362	−	3.77400i	0.0879372	−	0.241605i
$245$	−35.3304	+	3.05770i	−2.25717	+	0.195349i
$246$			2.76678i			0.176403i
$247$	−8.40969	−	13.2794i	−0.535096	−	0.844949i
$248$	−2.54534	−	2.54534i	−0.161629	−	0.161629i
$249$	1.92005	−	1.61111i	0.121678	−	0.102100i
$250$	1.91053	+	11.0159i	0.120833	+	0.696706i
$251$	2.11170	−	11.9760i	0.133289	−	0.755921i	−0.842746	−	0.538311i	$-0.819063\pi$
$251$	2.11170	−	11.9760i	0.133289	−	0.755921i	0.976036	−	0.217611i	$-0.0698263\pi$
$252$	−3.91648	−	2.74235i	−0.246715	−	0.172752i
$253$	−31.6100	−	14.7400i	−1.98730	−	0.926696i
$254$	−1.19669	−	0.690908i	−0.0750868	−	0.0433514i
$255$	−0.373478	+	4.22336i	−0.0233881	+	0.264477i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.433268	+	4.95228i	0.0270265	+	0.308915i	0.997661	+	0.0683556i	$0.0217752\pi$
$257$	0.433268	+	4.95228i	0.0270265	+	0.308915i	−0.970634	+	0.240559i	$0.922669\pi$
$258$	0.870099	−	3.24725i	0.0541700	−	0.202165i
$259$	16.4145	−	28.4307i	1.01995	−	1.76660i
$260$	6.98682	−	4.02513i	0.433304	−	0.249628i
$261$	7.23716	−	1.27611i	0.447969	−	0.0789890i
$262$	2.17968	−	1.52623i	0.134661	−	0.0942908i
$263$	−9.78987	−	20.9945i	−0.603670	−	1.29457i	−0.936196	−	0.351479i	$-0.885679\pi$
$263$	−9.78987	−	20.9945i	−0.603670	−	1.29457i	0.332526	−	0.943094i	$-0.392099\pi$
$264$	−3.85649	−	4.59598i	−0.237350	−	0.282863i
$265$	−3.46843	−	19.7787i	−0.213064	−	1.21499i
$266$	−19.2325	−	8.02718i	−1.17922	−	0.492178i
$267$	1.76130	−	1.76130i	0.107790	−	0.107790i
$268$	0.816771	−	9.33574i	0.0498922	−	0.570271i
$269$	3.06186	+	1.11443i	0.186685	+	0.0679477i	0.433671	−	0.901071i	$-0.357218\pi$
$269$	3.06186	+	1.11443i	0.186685	+	0.0679477i	−0.246986	+	0.969019i	$0.579440\pi$
$270$	−1.58262	+	1.57966i	−0.0963150	+	0.0961350i
$271$	−1.21728	−	6.90353i	−0.0739444	−	0.419359i	−0.999199	−	0.0400131i	$-0.987260\pi$
$271$	−1.21728	−	6.90353i	−0.0739444	−	0.419359i	0.925255	−	0.379346i	$-0.123851\pi$
$272$	0.801333	−	1.71846i	0.0485879	−	0.104197i
$273$	16.6535	−	4.46228i	1.00791	−	0.270070i
$274$	−6.57774	−	11.3930i	−0.397376	−	0.688275i
$275$	−10.3127	+	28.1698i	−0.621879	+	1.69870i
$276$	3.73673	−	4.45326i	0.224925	−	0.268055i
$277$	19.7895	+	5.30259i	1.18904	+	0.318602i	0.798506	−	0.601987i	$-0.205624\pi$
$277$	19.7895	+	5.30259i	1.18904	+	0.318602i	0.390532	+	0.920589i	$0.372291\pi$
$278$	4.77046	+	17.8036i	0.286113	+	1.06779i
$279$	−3.38256	+	1.23115i	−0.202509	+	0.0737072i
$280$	4.52725	−	9.68506i	0.270555	−	0.578793i
$281$	5.00382	+	0.882308i	0.298503	+	0.0526341i	0.320894	−	0.947115i	$-0.396017\pi$
$281$	5.00382	+	0.882308i	0.298503	+	0.0526341i	−0.0223910	+	0.999749i	$0.507128\pi$
$282$	−2.10085	+	0.979641i	−0.125104	+	0.0583368i
$283$	−12.2671	−	1.07323i	−0.729202	−	0.0637969i	−0.283493	−	0.958974i	$-0.591493\pi$
$283$	−12.2671	−	1.07323i	−0.729202	−	0.0637969i	−0.445710	+	0.895178i	$0.647049\pi$
$284$	−3.93342			−0.233405
$285$	−5.26676	+	8.20129i	−0.311976	+	0.485803i
$286$	21.6349			1.27930
$287$	−13.1780	−	1.15293i	−0.777873	−	0.0680551i
$288$	0.906308	−	0.422618i	0.0534047	−	0.0249030i
$289$	13.2011	+	2.32771i	0.776535	+	0.136924i
$290$	5.60577	+	15.4467i	0.329182	+	0.907061i
$291$	4.82724	−	1.75697i	0.282978	−	0.102995i
$292$	1.17782	+	4.39570i	0.0689269	+	0.257239i
$293$	2.65477	+	0.711344i	0.155093	+	0.0415572i	0.335530	−	0.942029i	$-0.391084\pi$
$293$	2.65477	+	0.711344i	0.155093	+	0.0415572i	−0.180437	+	0.983587i	$0.557751\pi$
$294$	10.1941	−	12.1489i	0.594535	−	0.708539i
$295$	−20.1809	+	5.38722i	−1.17498	+	0.313656i
$296$	3.43317	+	5.94643i	0.199549	+	0.345629i
$297$	−5.79520	+	1.55282i	−0.336272	+	0.0901037i
$298$	−6.10485	+	13.0919i	−0.353644	+	0.758393i
$299$	3.64019	+	20.6446i	0.210518	+	1.19391i
$300$	−4.09039	−	2.87554i	−0.236159	−	0.166019i
$301$	15.1039	+	5.49737i	0.870575	+	0.316863i
$302$	1.91396	−	21.8767i	0.110136	−	1.25886i
$303$	0.985498	−	0.985498i	0.0566154	−	0.0566154i
$304$	3.46529	−	2.64420i	0.198748	−	0.151655i
$305$	5.15789	−	7.35158i	0.295340	−	0.420950i
$306$	−1.21880	−	1.45251i	−0.0696741	−	0.0830344i
$307$	3.43362	+	7.36343i	0.195967	+	0.420253i	0.979596	−	0.200976i	$-0.0644114\pi$
$307$	3.43362	+	7.36343i	0.195967	+	0.420253i	−0.783629	+	0.621229i	$0.786634\pi$
$308$	23.4974	−	16.4531i	1.33889	−	0.937501i
$309$	−2.95324	+	0.520735i	−0.168004	+	0.0296236i
$310$	−4.01801	−	6.97445i	−0.228207	−	0.396122i
$311$	−16.2043	+	28.0667i	−0.918864	+	1.59152i	−0.117721	+	0.993047i	$0.537559\pi$
$311$	−16.2043	+	28.0667i	−0.918864	+	1.59152i	−0.801143	+	0.598473i	$0.795775\pi$
$312$	−0.933310	+	3.48316i	−0.0528383	+	0.197195i
$313$	−0.109335	−	1.24971i	−0.00617998	−	0.0706375i	0.992478	−	0.122420i	$-0.0390654\pi$
$313$	−0.109335	−	1.24971i	−0.00617998	−	0.0706375i	−0.998658	+	0.0517822i	$0.983510\pi$
$314$	3.33730	+	2.80033i	0.188335	+	0.158032i
$315$	−6.86434	−	8.19617i	−0.386762	−	0.461802i
$316$	−13.3555	−	7.71081i	−0.751306	−	0.433767i
$317$	−27.0551	−	12.6160i	−1.51957	−	0.708586i	−0.529388	−	0.848380i	$-0.677578\pi$
$317$	−27.0551	−	12.6160i	−1.51957	−	0.708586i	−0.990181	+	0.139793i	$0.955356\pi$
$318$	7.35620	+	5.15086i	0.412515	+	0.288846i
$319$	−7.65617	+	43.4203i	−0.428663	+	2.43107i
$320$	1.28084	+	1.83288i	0.0716012	+	0.102461i
$321$	7.54118	−	6.32781i	0.420908	−	0.353184i
$322$	19.6535	+	19.6535i	1.09525	+	1.09525i
$323$	−6.54346	−	5.04905i	−0.364088	−	0.280937i
$324$		−	1.00000i		−	0.0555556i
$325$	17.4245	−	4.63395i	0.966537	−	0.257045i
$326$	−4.15101	+	11.4048i	−0.229903	+	0.631654i
$327$	0.282631	+	0.403639i	0.0156295	+	0.0223213i
$328$	1.58696	−	2.26641i	0.0876251	−	0.125142i
$329$	−3.79054	−	10.4144i	−0.208979	−	0.574166i
$330$	−5.65829	−	12.1639i	−0.311479	−	0.669603i
$331$	−4.40443	+	2.54290i	−0.242089	+	0.139770i	−0.616137	−	0.787639i	$-0.711303\pi$
$331$	−4.40443	+	2.54290i	−0.242089	+	0.139770i	0.374047	+	0.927410i	$0.377970\pi$
$332$	−2.49691	+	0.218451i	−0.137036	+	0.0119891i
$333$	6.84022	−	0.598442i	0.374842	−	0.0327944i
$334$	1.58784	−	0.916738i	0.0868826	−	0.0501617i
$335$	7.18548	−	19.6846i	0.392585	−	1.07549i
$336$	1.63525	+	4.49280i	0.0892100	+	0.245102i
$337$	4.85243	−	6.92999i	0.264329	−	0.377501i	−0.664945	−	0.746892i	$-0.731545\pi$
$337$	4.85243	−	6.92999i	0.264329	−	0.377501i	0.929274	+	0.369392i	$0.120434\pi$
$338$	−0.00198696	−	0.00283767i	−0.000108076	−	0.000154349i
$339$	3.83630	−	10.5402i	0.208359	−	0.572463i
$340$	2.72835	−	3.24536i	0.147966	−	0.176004i
$341$		−	21.5966i		−	1.16952i
$342$	−0.931965	−	4.25810i	−0.0503949	−	0.230252i
$343$	29.9512	+	29.9512i	1.61721	+	1.61721i
$344$	−2.57529	+	2.16093i	−0.138850	+	0.116509i
$345$	10.6551	−	7.44595i	0.573652	−	0.400876i
$346$	0.901859	−	5.11470i	0.0484842	−	0.274968i
$347$	6.68861	+	4.68342i	0.359063	+	0.251419i	0.739163	−	0.673527i	$-0.235221\pi$
$347$	6.68861	+	4.68342i	0.359063	+	0.251419i	−0.380099	+	0.924946i	$0.624110\pi$
$348$	−6.66028	−	3.10574i	−0.357029	−	0.166485i
$349$	7.20916	+	4.16221i	0.385898	+	0.222798i	0.680381	−	0.732858i	$-0.261814\pi$
$349$	7.20916	+	4.16221i	0.385898	+	0.222798i	−0.294484	+	0.955657i	$0.595148\pi$
$350$	15.4005	−	18.2840i	0.823193	−	0.977323i
$351$	2.76238	+	2.31791i	0.147445	+	0.123721i
$352$	0.522902	+	5.97680i	0.0278708	+	0.318565i
$353$	−7.67745	+	28.6526i	−0.408629	+	1.52503i	0.388633	+	0.921393i	$0.372948\pi$
$353$	−7.67745	+	28.6526i	−0.408629	+	1.52503i	−0.797262	+	0.603633i	$0.793719\pi$
$354$	4.67060	−	8.08972i	0.248240	−	0.429964i
$355$	−8.49356	−	2.28436i	−0.450791	−	0.121241i
$356$	−2.45301	+	0.432531i	−0.130009	+	0.0229241i
$357$	7.42609	−	5.19981i	0.393030	−	0.275203i
$358$	−6.09952	−	13.0805i	−0.322370	−	0.691324i
$359$	13.1576	+	15.6806i	0.694430	+	0.827590i	0.991884	−	0.127146i	$-0.0405818\pi$
$359$	13.1576	+	15.6806i	0.694430	+	0.827590i	−0.297453	+	0.954736i	$0.596137\pi$
$360$	2.20246	−	0.386229i	0.116080	−	0.0203560i
$361$	−7.93680	−	17.2629i	−0.417727	−	0.908573i
$362$	16.3968	−	16.3968i	0.861795	−	0.861795i
$363$	2.17851	−	24.9005i	0.114342	−	1.30694i
$364$	−16.2012	−	5.89675i	−0.849173	−	0.309074i
$365$	−0.00952048	+	10.1758i	−0.000498325	+	0.532626i
$366$	0.697407	+	3.95519i	0.0364540	+	0.206741i
$367$	7.22988	−	15.5045i	0.377397	−	0.809330i	−0.622252	−	0.782817i	$-0.713782\pi$
$367$	7.22988	−	15.5045i	0.377397	−	0.809330i	0.999648	−	0.0265128i	$-0.00844027\pi$
$368$	−5.61524	+	1.50460i	−0.292715	+	0.0784326i
$369$	−1.38339	−	2.39610i	−0.0720163	−	0.124736i
$370$	3.95993	+	14.8342i	0.205867	+	0.771192i
$371$	−27.5986	+	32.8908i	−1.43285	+	1.70760i
$372$	3.47699	+	0.931657i	0.180274	+	0.0483042i
$373$	1.15000	+	4.29185i	0.0595446	+	0.222223i	0.989286	−	0.145989i	$-0.0466365\pi$
$373$	1.15000	+	4.29185i	0.0595446	+	0.222223i	−0.929742	+	0.368213i	$0.879970\pi$
$374$	10.6899	−	3.89082i	0.552763	−	0.201189i
$375$	−7.16252	−	8.58477i	−0.369871	−	0.443316i
$376$	2.28281	+	0.402521i	0.117727	+	0.0207585i
$377$	24.0172	−	11.1994i	1.23695	−	0.576798i
$378$	4.76294	+	0.416704i	0.244979	+	0.0214329i
$379$	11.1082			0.570589			0.285295	−	0.958440i	$-0.407909\pi$
$379$	11.1082			0.570589			0.285295	+	0.958440i	$0.407909\pi$
$380$	9.01835	−	3.69722i	0.462631	−	0.189663i
$381$	1.38182			0.0707926
$382$	4.34682	+	0.380298i	0.222403	+	0.0194577i
$383$	−4.07711	+	1.90119i	−0.208330	+	0.0971461i	−0.523983	−	0.851729i	$-0.675554\pi$
$383$	−4.07711	+	1.90119i	−0.208330	+	0.0971461i	0.315652	+	0.948875i	$0.397777\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	60.2940	−	21.8814i	3.07287	−	1.11518i
$386$	−16.4441	+	5.98516i	−0.836982	+	0.304636i
$387$	0.870099	+	3.24725i	0.0442296	+	0.165067i
$388$	−4.96200	−	1.32956i	−0.251907	−	0.0674984i
$389$	−15.9139	+	18.9655i	−0.806869	+	0.961589i	−0.999807	−	0.0196217i	$-0.993754\pi$
$389$	−15.9139	+	18.9655i	−0.806869	+	0.961589i	0.192938	+	0.981211i	$0.438198\pi$
$390$	−4.03820	+	6.97928i	−0.204482	+	0.353409i
$391$	5.51136	+	9.54596i	0.278722	+	0.482760i
$392$	−15.3189	+	4.10468i	−0.773721	+	0.207318i
$393$	−1.12454	+	2.41159i	−0.0567258	+	0.121649i
$394$	2.97244	+	16.8576i	0.149750	+	0.849272i
$395$	−24.3609	−	24.4065i	−1.22573	−	1.22802i
$396$	5.63781	+	2.05199i	0.283311	+	0.103117i
$397$	2.69506	−	30.8047i	0.135261	−	1.54604i	−0.560735	−	0.827996i	$-0.689481\pi$
$397$	2.69506	−	30.8047i	0.135261	−	1.54604i	0.695996	−	0.718046i	$-0.254963\pi$
$398$	−7.62887	+	7.62887i	−0.382401	+	0.382401i
$399$	20.6695	−	2.66453i	1.03477	−	0.133393i
$400$	1.70131	+	4.70165i	0.0850653	+	0.235083i
$401$	−5.64387	−	6.72610i	−0.281841	−	0.335886i	0.606488	−	0.795093i	$-0.292578\pi$
$401$	−5.64387	−	6.72610i	−0.281841	−	0.335886i	−0.888329	+	0.459207i	$0.848133\pi$
$402$	3.96052	+	8.49337i	0.197533	+	0.423611i
$403$	−10.6330	+	7.44528i	−0.529665	+	0.370876i
$404$	−1.37253	+	0.242014i	−0.0682860	+	0.0120407i
$405$	0.580758	−	2.15933i	0.0288581	−	0.107298i
$406$	17.5678	−	30.4284i	0.871877	−	1.51013i
$407$	−10.6622	+	39.7919i	−0.528505	+	1.97241i
$408$	0.165257	+	1.88890i	0.00818145	+	0.0935144i
$409$	−23.7888	−	19.9612i	−1.17628	−	0.987015i	−0.999996	−	0.00267577i	$-0.999148\pi$
$409$	−23.7888	−	19.9612i	−1.17628	−	0.987015i	−0.176283	−	0.984340i	$-0.556407\pi$
$410$	4.74301	−	3.97230i	0.234240	−	0.196178i
$411$	11.3930	+	6.57774i	0.561975	+	0.324456i
$412$	2.71783	+	1.26734i	0.133898	+	0.0624376i
$413$	36.5846	+	25.6168i	1.80021	+	1.26052i
$414$	−1.00947	+	5.72501i	−0.0496129	+	0.281369i
$415$	−5.51853	−	0.978390i	−0.270894	−	0.0480273i
$416$	2.76238	−	2.31791i	0.135437	−	0.113645i
$417$	−13.0331	−	13.0331i	−0.638236	−	0.638236i
$418$	25.9188	+	3.48337i	1.26773	+	0.170377i
$419$			28.5642i			1.39545i	0.716365	+	0.697726i	$0.245805\pi$
$419$			28.5642i			1.39545i	−0.716365	+	0.697726i	$0.754195\pi$
$420$	0.921813	+	10.6511i	0.0449799	+	0.519722i
$421$	−6.90877	+	18.9817i	−0.336713	+	0.925112i	0.649607	+	0.760270i	$0.274933\pi$
$421$	−6.90877	+	18.9817i	−0.336713	+	0.925112i	−0.986320	+	0.164841i	$0.947289\pi$
$422$	3.39822	+	4.85316i	0.165423	+	0.236248i
$423$	1.32957	−	1.89882i	0.0646457	−	0.0923237i
$424$	−3.07143	−	8.43868i	−0.149162	−	0.409819i
$425$	7.77619	−	5.42329i	0.377201	−	0.263068i
$426$	3.40644	−	1.96671i	0.165042	−	0.0952873i
$427$	−19.1290	+	1.67357i	−0.925715	+	0.0809896i
$428$	−9.80686	+	0.857989i	−0.474032	+	0.0414725i
$429$	−18.7363	+	10.8174i	−0.904599	+	0.522270i
$430$	−6.81589	+	3.17054i	−0.328691	+	0.152897i
$431$	8.34384	+	22.9245i	0.401909	+	1.10424i	0.961341	+	0.275360i	$0.0887969\pi$
$431$	8.34384	+	22.9245i	0.401909	+	1.10424i	−0.559432	+	0.828876i	$0.688981\pi$
$432$	−0.573576	+	0.819152i	−0.0275962	+	0.0394115i
$433$	−13.9006	−	19.8522i	−0.668022	−	0.954034i	−0.999942	−	0.0107265i	$-0.996586\pi$
$433$	−13.9006	−	19.8522i	−0.668022	−	0.954034i	0.331921	−	0.943307i	$-0.392303\pi$
$434$	−5.88631	+	16.1725i	−0.282552	+	0.776305i
$435$	−12.5781	−	10.5743i	−0.603073	−	0.507001i
$436$		−	0.492753i		−	0.0235986i
$437$	1.03706	+	25.3185i	0.0496095	+	1.21115i
$438$	−3.21787	−	3.21787i	−0.153756	−	0.153756i
$439$	12.6575	−	10.6209i	0.604108	−	0.506907i	−0.288655	−	0.957433i	$-0.593208\pi$
$439$	12.6575	−	10.6209i	0.604108	−	0.506907i	0.892763	+	0.450526i	$0.148764\pi$
$440$	−2.34195	+	13.2096i	−0.111648	+	0.629742i
$441$	−2.75394	+	15.6183i	−0.131140	+	0.743731i
$442$	−5.60091	−	3.92180i	−0.266408	−	0.186541i
$443$	−4.02146	−	1.87524i	−0.191065	−	0.0890952i	0.324731	−	0.945806i	$-0.394726\pi$
$443$	−4.02146	−	1.87524i	−0.191065	−	0.0890952i	−0.515796	+	0.856711i	$0.672504\pi$
$444$	−5.94643	−	3.43317i	−0.282205	−	0.162931i
$445$	−5.54806	−	0.490623i	−0.263003	−	0.0232578i
$446$	18.5903	+	15.5991i	0.880274	+	0.738638i
$447$	−1.25899	−	14.3903i	−0.0595482	−	0.680640i
$448$	1.23745	−	4.61822i	0.0584640	−	0.218191i
$449$	5.51788	−	9.55725i	0.260405	−	0.451034i	−0.705945	−	0.708267i	$-0.749477\pi$
$449$	5.51788	−	9.55725i	0.260405	−	0.451034i	0.966350	+	0.257233i	$0.0828106\pi$
$450$	4.98015	+	0.445098i	0.234766	+	0.0209821i
$451$	16.3475	−	2.88250i	0.769771	−	0.135731i
$452$	−9.18810	+	6.43358i	−0.432172	+	0.302610i
$453$	9.28080	+	19.9027i	0.436050	+	0.935112i
$454$	9.14759	+	10.9017i	0.429318	+	0.511641i
$455$	−31.5592	−	22.1420i	−1.47952	−	1.03803i
$456$	−1.67893	+	4.02259i	−0.0786229	+	0.188375i
$457$	1.48063	−	1.48063i	0.0692609	−	0.0692609i	−0.671628	−	0.740889i	$-0.734405\pi$
$457$	1.48063	−	1.48063i	0.0692609	−	0.0692609i	0.740889	+	0.671628i	$0.234405\pi$
$458$	−1.28212	+	14.6547i	−0.0599096	+	0.684769i
$459$	1.78176	+	0.648509i	0.0831657	+	0.0302698i
$460$	−12.9990	−	0.0121618i	−0.606081	−	0.000567049i
$461$	−6.46765	−	36.6799i	−0.301228	−	1.70835i	−0.640747	−	0.767752i	$-0.721375\pi$
$461$	−6.46765	−	36.6799i	−0.301228	−	1.70835i	0.339519	−	0.940599i	$-0.389736\pi$
$462$	−12.1228	+	25.9975i	−0.564005	+	1.20951i
$463$	33.6966	−	9.02897i	1.56601	−	0.419612i	0.631451	−	0.775415i	$-0.282460\pi$
$463$	33.6966	−	9.02897i	1.56601	−	0.419612i	0.934561	+	0.355804i	$0.115793\pi$
$464$	3.67440	+	6.36425i	0.170580	+	0.295453i
$465$	6.96692	+	4.03105i	0.323083	+	0.186935i
$466$	12.8685	−	15.3361i	0.596121	−	0.710429i
$467$	−31.4488	−	8.42667i	−1.45528	−	0.389940i	−0.557420	−	0.830230i	$-0.688209\pi$
$467$	−31.4488	−	8.42667i	−1.45528	−	0.389940i	−0.897855	+	0.440290i	$0.854876\pi$
$468$	−0.933310	−	3.48316i	−0.0431423	−	0.161009i
$469$	−42.1038	+	15.3245i	−1.94417	+	0.707621i
$470$	4.69558	+	2.19494i	0.216591	+	0.101245i
$471$	−4.29035	−	0.756504i	−0.197689	−	0.0348579i
$472$	−8.46600	+	3.94776i	−0.389679	+	0.181710i
$473$	−20.0928	−	1.75790i	−0.923869	−	0.0808281i
$474$	15.4216			0.708338
$475$	21.6208	−	2.74605i	0.992031	−	0.125997i
$476$	−9.06559			−0.415520
$477$	−8.94608	−	0.782681i	−0.409613	−	0.0358365i
$478$	24.1953	−	11.2825i	1.10667	−	0.516048i
$479$	−26.1079	−	4.60352i	−1.19290	−	0.210340i	−0.458272	−	0.888812i	$-0.651531\pi$
$479$	−26.1079	−	4.60352i	−1.19290	−	0.210340i	−0.734626	+	0.678472i	$0.762643\pi$
$480$	−2.02568	−	0.946899i	−0.0924593	−	0.0432198i
$481$	23.2670	−	8.46851i	1.06089	−	0.386131i
$482$	−1.04072	−	3.88401i	−0.0474034	−	0.176912i
$483$	−26.8472	−	7.19369i	−1.22159	−	0.327324i
$484$	−16.0668	+	19.1477i	−0.730311	+	0.870351i
$485$	−9.94246	−	5.75269i	−0.451464	−	0.261216i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	32.6572	−	8.75046i	1.47984	−	0.396521i	0.573545	−	0.819174i	$-0.305568\pi$
$487$	32.6572	−	8.75046i	1.47984	−	0.396521i	0.906292	+	0.422653i	$0.138901\pi$
$488$	1.69732	−	3.63992i	0.0768341	−	0.164771i
$489$	−2.10752	−	11.9524i	−0.0953055	−	0.540504i
$490$	−35.4624	−	0.0331786i	−1.60203	−	0.00149886i
$491$	15.3572	+	5.58956i	0.693061	+	0.252253i	0.664445	−	0.747337i	$-0.268668\pi$
$491$	15.3572	+	5.58956i	0.693061	+	0.252253i	0.0286155	+	0.999590i	$0.490890\pi$
$492$	−0.241140	+	2.75625i	−0.0108714	+	0.124261i
$493$	9.85295	−	9.85295i	0.443755	−	0.443755i
$494$	−7.22031	−	13.9618i	−0.324857	−	0.628173i
$495$	10.9822	+	7.70514i	0.493613	+	0.346320i
$496$	−2.31381	−	2.75749i	−0.103893	−	0.123815i
$497$	7.94785	+	17.0442i	0.356510	+	0.764537i
$498$	2.05316	−	1.43764i	0.0920044	−	0.0644222i
$499$	−12.3039	+	2.16950i	−0.550797	+	0.0971204i	−0.442119	−	0.896957i	$-0.645773\pi$
$499$	−12.3039	+	2.16950i	−0.550797	+	0.0971204i	−0.108678	+	0.994077i	$0.534662\pi$
$500$	0.943165	+	11.1405i	0.0421796	+	0.498218i
$501$	−0.916738	+	1.58784i	−0.0409568	+	0.0709393i
$502$	3.14745	−	11.7464i	0.140477	−	0.524269i
$503$	−2.98110	−	34.0742i	−0.132921	−	1.51929i	−0.710931	−	0.703262i	$-0.751726\pi$
$503$	−2.98110	−	34.0742i	−0.132921	−	1.51929i	0.578010	−	0.816030i	$-0.303829\pi$
$504$	−3.66256	−	3.07326i	−0.163144	−	0.136894i
$505$	−3.10430	−	0.274518i	−0.138140	−	0.0122159i
$506$	−30.2051	−	17.4389i	−1.34278	−	0.775254i
$507$	0.00313959	+	0.00146401i	0.000139434	+	6.50192e-5i
$508$	−1.13192	−	0.792577i	−0.0502207	−	0.0351649i
$509$	5.54574	−	31.4514i	0.245811	−	1.39406i	−0.572792	−	0.819701i	$-0.694140\pi$
$509$	5.54574	−	31.4514i	0.245811	−	1.39406i	0.818603	−	0.574360i	$-0.194749\pi$
$510$	−0.740147	+	4.17474i	−0.0327743	+	0.184860i
$511$	16.6674	−	13.9857i	0.737325	−	0.618689i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.93616	+	3.22164i	0.129634	+	0.142239i
$514$			4.97120i			0.219270i
$515$	5.13268	+	4.31502i	0.226173	+	0.190143i
$516$	1.14980	−	3.15906i	0.0506173	−	0.139070i
$517$	7.97691	+	11.3922i	0.350824	+	0.501029i
$518$	18.8299	−	26.8919i	0.827339	−	1.18156i
$519$	1.77632	+	4.88039i	0.0779716	+	0.214225i
$520$	7.31105	−	3.40087i	0.320611	−	0.149138i
$521$	9.20471	−	5.31434i	0.403266	−	0.232826i	−0.284626	−	0.958639i	$-0.591870\pi$
$521$	9.20471	−	5.31434i	0.403266	−	0.232826i	0.687892	+	0.725813i	$0.258536\pi$
$522$	7.32084	−	0.640491i	0.320425	−	0.0280335i
$523$	−25.8564	+	2.26214i	−1.13062	+	0.0989166i	−0.637075	−	0.770802i	$-0.719856\pi$
$523$	−25.8564	+	2.26214i	−1.13062	+	0.0989166i	−0.493548	+	0.869719i	$0.664300\pi$
$524$	2.30441	−	1.33045i	0.100668	−	0.0581210i
$525$	−4.19523	+	23.5347i	−0.183095	+	1.02714i
$526$	−7.92283	−	21.7678i	−0.345452	−	0.949122i
$527$	−3.91486	+	5.59100i	−0.170534	+	0.243548i
$528$	−3.44125	−	4.91461i	−0.149761	−	0.213881i
$529$	3.69201	−	10.1437i	0.160522	−	0.441032i
$530$	−1.73141	−	20.0057i	−0.0752077	−	0.868991i
$531$			9.34120i			0.405374i
$532$	−18.4597	−	9.67286i	−0.800331	−	0.419372i
$533$	−7.05486	−	7.05486i	−0.305580	−	0.305580i
$534$	1.90810	−	1.60109i	0.0825716	−	0.0692858i
$535$	−21.6746	−	3.84272i	−0.937073	−	0.166135i
$536$	1.62733	−	9.22903i	0.0702898	−	0.398633i
$537$	11.8226	+	8.27825i	0.510182	+	0.357233i
$538$	2.95308	+	1.37704i	0.127316	+	0.0593685i
$539$	−82.4022	−	47.5749i	−3.54931	−	2.04920i
$540$	−1.71427	+	1.43571i	−0.0737705	+	0.0617833i
$541$	−13.6262	−	11.4337i	−0.585835	−	0.491574i	0.301022	−	0.953617i	$-0.402672\pi$
$541$	−13.6262	−	11.4337i	−0.585835	−	0.491574i	−0.886858	+	0.462043i	$0.847117\pi$
$542$	−0.610964	−	6.98335i	−0.0262431	−	0.299961i
$543$	−6.00164	+	22.3984i	−0.257555	+	0.961208i
$544$	0.948057	−	1.64208i	0.0406476	−	0.0704037i
$545$	0.286170	−	1.06402i	0.0122582	−	0.0455775i
$546$	16.9790	−	2.99386i	0.726634	−	0.128125i
$547$	−15.7662	+	11.0396i	−0.674112	+	0.472018i	−0.859827	−	0.510585i	$-0.829429\pi$
$547$	−15.7662	+	11.0396i	−0.674112	+	0.472018i	0.185715	+	0.982604i	$0.440540\pi$
$548$	−5.55975	−	11.9229i	−0.237501	−	0.509322i
$549$	−2.58157	−	3.07659i	−0.110179	−	0.131306i
$550$	−12.7286	+	27.1638i	−0.542750	+	1.15827i
$551$	30.5760	−	9.55004i	1.30258	−	0.406845i
$552$	4.11064	−	4.11064i	0.174960	−	0.174960i
$553$	−6.42624	+	73.4523i	−0.273272	+	3.12351i
$554$	19.2521	+	7.00718i	0.817943	+	0.297707i
$555$	−10.8465	−	10.8668i	−0.460408	−	0.461270i
$556$	3.20062	+	18.1516i	0.135737	+	0.769801i
$557$	−18.0716	+	38.7547i	−0.765719	+	1.64209i	0.000910344		1.00000i	$0.499710\pi$
$557$	−18.0716	+	38.7547i	−0.765719	+	1.64209i	−0.766629	+	0.642090i	$0.778068\pi$
$558$	−3.47699	+	0.931657i	−0.147193	+	0.0394402i
$559$	6.06139	+	10.4986i	0.256369	+	0.444045i
$560$	5.35413	−	9.25363i	0.226253	−	0.391037i
$561$	−7.31234	+	8.71451i	−0.308727	+	0.367927i
$562$	4.90788	+	1.31506i	0.207026	+	0.0554725i
$563$	1.22048	+	4.55491i	0.0514373	+	0.191966i	0.986864	−	0.161555i	$-0.0516509\pi$
$563$	1.22048	+	4.55491i	0.0514373	+	0.191966i	−0.935426	+	0.353521i	$0.884984\pi$
$564$	−2.17823	+	0.792812i	−0.0917202	+	0.0333834i
$565$	−23.5765	+	8.55618i	−0.991872	+	0.359961i
$566$	−12.1269	−	2.13829i	−0.509730	−	0.0898792i
$567$	−4.33318	+	2.02060i	−0.181977	+	0.0848571i
$568$	−3.91845	−	0.342820i	−0.164414	−	0.0143844i
$569$	8.90748			0.373421			0.186711	−	0.982415i	$-0.440217\pi$
$569$	8.90748			0.373421			0.186711	+	0.982415i	$0.440217\pi$
$570$	−5.96151	+	7.71106i	−0.249700	+	0.322981i
$571$	17.5685			0.735218			0.367609	−	0.929980i	$-0.380176\pi$
$571$	17.5685			0.735218			0.367609	+	0.929980i	$0.380176\pi$
$572$	21.5525	+	1.88560i	0.901157	+	0.0788410i
$573$	−3.95461	+	1.84406i	−0.165206	+	0.0770369i
$574$	−13.0274	−	2.29708i	−0.543752	−	0.0958781i
$575$	−28.0621	−	7.57552i	−1.17027	−	0.315921i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	−1.93982	−	7.23950i	−0.0807557	−	0.301384i	0.913721	−	0.406342i	$-0.133196\pi$
$577$	−1.93982	−	7.23950i	−0.0807557	−	0.301384i	−0.994477	+	0.104958i	$0.966529\pi$
$578$	12.9480	+	3.46940i	0.538566	+	0.144308i
$579$	11.2484	−	13.4053i	0.467468	−	0.557107i
$580$	4.23817	+	15.8765i	0.175981	+	0.659235i
$581$	5.99184	+	10.3782i	0.248583	+	0.430559i
$582$	4.96200	−	1.32956i	0.205682	−	0.0551122i
$583$	22.7699	−	48.8303i	0.943034	−	2.02234i
$584$	0.790231	+	4.48162i	0.0327000	+	0.185451i
$585$	0.00754405	−	8.06333i	0.000311908	−	0.333378i
$586$	2.58267	+	0.940016i	0.106689	+	0.0388317i
$587$	0.516005	−	5.89796i	0.0212978	−	0.243435i	−0.978082	−	0.208220i	$-0.933233\pi$
$587$	0.516005	−	5.89796i	0.0212978	−	0.243435i	0.999380	−	0.0352147i	$-0.0112115\pi$
$588$	11.2142	−	11.2142i	0.462466	−	0.462466i
$589$	−13.9371	+	7.20753i	−0.574269	+	0.296981i
$590$	−20.5736	+	3.60784i	−0.847002	+	0.148532i
$591$	−11.0030	−	13.1129i	−0.452603	−	0.539391i
$592$	2.90184	+	6.22303i	0.119265	+	0.255765i
$593$	5.21965	−	3.65484i	0.214345	−	0.150086i	−0.461474	−	0.887154i	$-0.652679\pi$
$593$	5.21965	−	3.65484i	0.214345	−	0.150086i	0.675819	+	0.737068i	$0.263790\pi$
$594$	−5.90848	+	1.04183i	−0.242428	+	0.0427466i
$595$	−19.5756	−	5.26491i	−0.802522	−	0.215840i
$596$	−7.22265	+	12.5100i	−0.295851	+	0.512430i
$597$	2.79236	−	10.4212i	0.114284	−	0.426513i
$598$	1.82705	+	20.8833i	0.0747136	+	0.853980i
$599$	4.07669	+	3.42075i	0.166569	+	0.139768i	0.722262	−	0.691620i	$-0.243103\pi$
$599$	4.07669	+	3.42075i	0.166569	+	0.139768i	−0.555693	+	0.831388i	$0.687547\pi$
$600$	−3.82420	−	3.22110i	−0.156122	−	0.131501i
$601$	−33.5183	−	19.3518i	−1.36724	−	0.789376i	−0.376665	−	0.926350i	$-0.622929\pi$
$601$	−33.5183	−	19.3518i	−1.36724	−	0.789376i	−0.990575	+	0.136973i	$0.956263\pi$
$602$	14.5673	+	6.79285i	0.593719	+	0.276856i
$603$	−7.67660	−	5.37521i	−0.312615	−	0.218896i
$604$	3.81335	−	21.6266i	0.155163	−	0.879974i
$605$	−45.8139	+	32.0154i	−1.86260	+	1.30161i
$606$	1.06764	−	0.895856i	0.0433699	−	0.0363917i
$607$	17.2307	+	17.2307i	0.699371	+	0.699371i	0.964275	−	0.264904i	$-0.0853402\pi$
$607$	17.2307	+	17.2307i	0.699371	+	0.699371i	−0.264904	+	0.964275i	$0.585340\pi$
$608$	3.68256	−	2.33212i	0.149347	−	0.0945799i
$609$			35.1357i			1.42377i
$610$	5.77899	−	6.87406i	0.233985	−	0.278323i
$611$	2.85891	−	7.85478i	0.115659	−	0.317770i
$612$	−1.08757	−	1.55321i	−0.0439623	−	0.0627846i
$613$	−4.74367	+	6.77467i	−0.191595	+	0.273626i	−0.903444	−	0.428707i	$-0.858969\pi$
$613$	−4.74367	+	6.77467i	−0.191595	+	0.273626i	0.711849	+	0.702333i	$0.247858\pi$
$614$	2.77879	+	7.63467i	0.112143	+	0.308110i
$615$	−2.12141	+	5.81161i	−0.0855437	+	0.234347i
$616$	24.8420	−	14.3425i	1.00091	−	0.577877i
$617$	0.893196	−	0.0781446i	0.0359587	−	0.00314598i	−0.0691622	−	0.997605i	$-0.522033\pi$
$617$	0.893196	−	0.0781446i	0.0359587	−	0.00314598i	0.105121	+	0.994459i	$0.466477\pi$
$618$	−2.98738	+	0.261362i	−0.120170	+	0.0105135i
$619$	38.4733	−	22.2126i	1.54637	−	0.892799i	0.547958	−	0.836506i	$-0.315405\pi$
$619$	38.4733	−	22.2126i	1.54637	−	0.892799i	0.998414	−	0.0562932i	$-0.0179282\pi$
$620$	−3.39485	−	7.29810i	−0.136341	−	0.293099i
$621$	−1.98827	−	5.46274i	−0.0797867	−	0.219212i
$622$	−18.5889	+	26.5476i	−0.745345	+	1.06446i
$623$	6.83077	+	9.75536i	0.273669	+	0.390840i
$624$	−1.23334	+	3.38856i	−0.0493729	+	0.135651i
$625$	−4.43331	+	24.6038i	−0.177332	+	0.984151i
$626$		−	1.25448i		−	0.0501391i
$627$	−24.1880	+	9.94270i	−0.965975	+	0.397073i
$628$	3.08054	+	3.08054i	0.122927	+	0.122927i
$629$	9.97343	−	8.36870i	0.397667	−	0.333682i
$630$	−6.12388	−	8.76325i	−0.243981	−	0.349136i
$631$	−1.26810	+	7.19174i	−0.0504822	+	0.286299i	−0.999589	−	0.0286546i	$-0.990878\pi$
$631$	−1.26810	+	7.19174i	−0.0504822	+	0.286299i	0.949107	+	0.314953i	$0.101989\pi$
$632$	−12.6326	−	8.84547i	−0.502500	−	0.351854i
$633$	−5.36952	−	2.50385i	−0.213419	−	0.0995190i
$634$	−25.8526	−	14.9260i	−1.02674	−	0.592788i
$635$	−1.98389	−	2.36881i	−0.0787283	−	0.0940032i
$636$	6.87928	+	5.77240i	0.272781	+	0.228890i
$637$	4.98436	+	56.9714i	0.197487	+	2.25729i
$638$	−11.4114	+	42.5878i	−0.451780	+	1.68607i
$639$	−1.96671	+	3.40644i	−0.0778018	+	0.134757i
$640$	1.11622	+	1.93754i	0.0441225	+	0.0765879i
$641$	17.7190	−	3.12433i	0.699858	−	0.123404i	0.187613	−	0.982243i	$-0.439925\pi$
$641$	17.7190	−	3.12433i	0.699858	−	0.123404i	0.512245	+	0.858839i	$0.328814\pi$
$642$	8.06399	−	5.64647i	0.318260	−	0.222848i
$643$	19.8709	+	42.6133i	0.783632	+	1.68050i	0.731478	+	0.681865i	$0.238831\pi$
$643$	19.8709	+	42.6133i	0.783632	+	1.68050i	0.0521538	+	0.998639i	$0.483391\pi$
$644$	17.8658	+	21.2917i	0.704012	+	0.839009i
$645$	4.31746	−	6.15371i	0.170000	−	0.242302i
$646$	−6.07850	−	5.60014i	−0.239156	−	0.220334i
$647$	−14.5380	+	14.5380i	−0.571547	+	0.571547i	−0.932561	−	0.361013i	$-0.882431\pi$
$647$	−14.5380	+	14.5380i	−0.571547	+	0.571547i	0.361013	+	0.932561i	$0.382431\pi$
$648$	0.0871557	−	0.996195i	0.00342380	−	0.0391342i
$649$	−52.6639	−	19.1681i	−2.06724	−	0.752414i
$650$	17.7621	−	3.09767i	0.696686	−	0.121501i
$651$	−2.98856	−	16.9489i	−0.117131	−	0.664282i
$652$	−5.12921	+	10.9996i	−0.200875	+	0.430779i
$653$	−6.31398	+	1.69183i	−0.247085	+	0.0662063i	−0.380236	−	0.924890i	$-0.624157\pi$
$653$	−6.31398	+	1.69183i	−0.247085	+	0.0662063i	0.133151	+	0.991096i	$0.457491\pi$
$654$	0.246376	+	0.426736i	0.00963408	+	0.0166867i
$655$	5.74865	−	1.53458i	0.224618	−	0.0599611i
$656$	1.77845	−	2.11947i	0.0694368	−	0.0827515i
$657$	4.39570	+	1.17782i	0.171492	+	0.0459513i
$658$	−2.86844	−	10.7052i	−0.111824	−	0.417331i
$659$	29.0304	−	10.5662i	1.13086	−	0.411601i	0.292259	−	0.956339i	$-0.405593\pi$
$659$	29.0304	−	10.5662i	1.13086	−	0.411601i	0.838606	+	0.544738i	$0.183371\pi$
$660$	−4.57660	−	12.6108i	−0.178144	−	0.490875i
$661$	−20.9654	−	3.69676i	−0.815458	−	0.143787i	−0.249662	−	0.968333i	$-0.580320\pi$
$661$	−20.9654	−	3.69676i	−0.815458	−	0.143787i	−0.565795	+	0.824546i	$0.691431\pi$
$662$	−4.60929	+	2.14935i	−0.179145	+	0.0835368i
$663$	6.81143	+	0.595923i	0.264534	+	0.0231437i
$664$	−2.50645			−0.0972691
$665$	−34.2432	−	31.6076i	−1.32789	−	1.22569i
$666$	6.86635			0.266066
$667$	−42.5584	−	3.72338i	−1.64787	−	0.144170i
$668$	1.66169	−	0.774860i	0.0642929	−	0.0299802i
$669$	−23.8992	−	4.21407i	−0.923995	−	0.162925i
$670$	8.87377	−	18.9835i	0.342824	−	0.733395i
$671$	22.6426	−	8.24123i	0.874108	−	0.318149i
$672$	1.23745	+	4.61822i	0.0477357	+	0.178152i
$673$	−43.1314	−	11.5570i	−1.66259	−	0.445491i	−0.699495	−	0.714638i	$-0.746592\pi$
$673$	−43.1314	−	11.5570i	−1.66259	−	0.445491i	−0.963099	+	0.269147i	$0.913258\pi$
$674$	5.43796	−	6.48070i	0.209462	−	0.249627i
$675$	−4.53549	+	2.10461i	−0.174571	+	0.0810064i
$676$	−0.00173208	−	0.00300004i	−6.66183e−5	−	0.000115386i
$677$	22.6284	−	6.06327i	0.869681	−	0.233030i	0.203731	−	0.979027i	$-0.434693\pi$
$677$	22.6284	−	6.06327i	0.869681	−	0.233030i	0.665950	+	0.745997i	$0.268026\pi$
$678$	4.74034	−	10.1657i	0.182052	−	0.390411i
$679$	4.26496	+	24.1878i	0.163674	+	0.928241i
$680$	3.00082	−	2.99521i	0.115076	−	0.114861i
$681$	−13.3729	−	4.86733i	−0.512450	−	0.186517i
$682$	1.88226	−	21.5144i	0.0720756	−	0.823828i
$683$	−4.46188	+	4.46188i	−0.170729	+	0.170729i	−0.787300	−	0.616571i	$-0.788521\pi$
$683$	−4.46188	+	4.46188i	−0.170729	+	0.170729i	0.616571	+	0.787300i	$0.288521\pi$
$684$	−0.557300	−	4.32313i	−0.0213089	−	0.165299i
$685$	−5.08103	−	28.9744i	−0.194136	−	1.10706i
$686$	27.2268	+	32.4477i	1.03953	+	1.23886i
$687$	−6.21700	−	13.3324i	−0.237193	−	0.508663i
$688$	−2.75383	+	1.92825i	−0.104989	+	0.0735139i
$689$	−31.8911	+	5.62326i	−1.21495	+	0.214229i
$690$	11.2635	−	6.48896i	0.428795	−	0.247030i
$691$	−2.79108	+	4.83430i	−0.106178	+	0.183905i	−0.914219	−	0.405221i	$-0.867195\pi$
$691$	−2.79108	+	4.83430i	−0.106178	+	0.183905i	0.808041	+	0.589126i	$0.200528\pi$
$692$	1.34420	−	5.01663i	0.0510989	−	0.190704i
$693$	−2.50007	−	28.5759i	−0.0949697	−	1.08551i
$694$	6.25497	+	5.24855i	0.237436	+	0.199232i
$695$	−3.63049	+	41.0542i	−0.137712	+	1.55728i
$696$	−6.36425	−	3.67440i	−0.241236	−	0.139278i
$697$	−4.75460	−	2.21711i	−0.180093	−	0.0839789i
$698$	6.81897	+	4.77469i	0.258102	+	0.180725i
$699$	−3.47640	+	19.7156i	−0.131490	+	0.745714i
$700$	16.9355	−	16.8722i	0.640101	−	0.637710i
$701$	33.9975	−	28.5273i	1.28407	−	1.07746i	0.291397	−	0.956602i	$-0.405880\pi$
$701$	33.9975	−	28.5273i	1.28407	−	1.07746i	0.992670	−	0.120857i	$-0.0385644\pi$
$702$	2.54985	+	2.54985i	0.0962379	+	0.0962379i
$703$	29.2376	−	6.39920i	1.10272	−	0.241350i
$704$			5.99963i			0.226120i
$705$	−5.16396	+	0.446920i	−0.194486	+	0.0168320i
$706$	−10.1455	+	27.8745i	−0.381830	+	1.04907i
$707$	3.82202	+	5.45842i	0.143742	+	0.205285i
$708$	5.35789	−	7.65186i	0.201362	−	0.287575i
$709$	−12.4546	−	34.2188i	−0.467743	−	1.28511i	−0.919541	−	0.392993i	$-0.871440\pi$
$709$	−12.4546	−	34.2188i	−0.467743	−	1.28511i	0.451798	−	0.892120i	$-0.350783\pi$
$710$	−8.26214	−	3.01593i	−0.310073	−	0.113186i
$711$	−13.3555	+	7.71081i	−0.500871	+	0.289178i
$712$	−2.48137	+	0.217092i	−0.0929933	+	0.00813586i
$713$	20.8463	−	1.82381i	0.780700	−	0.0683024i
$714$	7.85103	−	4.53279i	0.293817	−	0.169635i
$715$	45.4440	+	16.5884i	1.69951	+	0.620372i
$716$	−4.93627	−	13.5623i	−0.184477	−	0.506847i
$717$	−15.3125	+	21.8686i	−0.571857	+	0.816697i
$718$	11.7409	+	16.7677i	0.438165	+	0.625764i
$719$	10.6696	−	29.3145i	0.397909	−	1.09325i	−0.565391	−	0.824823i	$-0.691275\pi$
$719$	10.6696	−	29.3145i	0.397909	−	1.09325i	0.963301	−	0.268424i	$-0.0865029\pi$
$720$	2.22774	−	0.192802i	0.0830230	−	0.00718531i
$721$		−	14.3376i		−	0.533962i
$722$	−6.40204	−	17.8889i	−0.238259	−	0.665757i
$723$	2.84330	+	2.84330i	0.105743	+	0.105743i
$724$	17.7635	−	14.9053i	0.660173	−	0.553951i
$725$	−0.0687554	+	36.7440i	−0.00255351	+	1.36464i
$726$	4.34044	−	24.6158i	0.161089	−	0.913580i
$727$	−28.0798	−	19.6617i	−1.04142	−	0.729212i	−0.0779331	−	0.996959i	$-0.524832\pi$
$727$	−28.0798	−	19.6617i	−1.04142	−	0.729212i	−0.963489	+	0.267747i	$0.913721\pi$
$728$	−15.6256	−	7.28633i	−0.579123	−	0.270050i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	−0.896364	+	10.1363i	−0.0331759	+	0.375159i
$731$	4.88305	+	4.09736i	0.180606	+	0.151546i
$732$	0.350035	+	4.00092i	0.0129377	+	0.147878i
$733$	−1.66281	+	6.20570i	−0.0614174	+	0.229213i	−0.989811	−	0.142384i	$-0.954523\pi$
$733$	−1.66281	+	6.20570i	−0.0614174	+	0.229213i	0.928394	+	0.371597i	$0.121190\pi$
$734$	8.55368	−	14.8154i	0.315722	−	0.546847i
$735$	30.7279	−	17.7025i	1.13342	−	0.652966i
$736$	−5.72501	+	1.00947i	−0.211027	+	0.0372097i
$737$	46.0568	−	32.2493i	1.69652	−	1.18792i
$738$	−1.16929	−	2.50755i	−0.0430422	−	0.0923042i
$739$	7.57976	+	9.03321i	0.278826	+	0.332292i	0.887223	−	0.461341i	$-0.152632\pi$
$739$	7.57976	+	9.03321i	0.278826	+	0.332292i	−0.608397	+	0.793633i	$0.708187\pi$
$740$	2.65198	+	15.1229i	0.0974888	+	0.555927i
$741$	13.2339	+	8.48115i	0.486159	+	0.311563i
$742$	−30.3602	+	30.3602i	−1.11456	+	1.11456i
$743$	0.0574319	−	0.656449i	0.00210697	−	0.0240828i	−0.995068	−	0.0991908i	$-0.968375\pi$
$743$	0.0574319	−	0.656449i	0.00210697	−	0.0240828i	0.997175	+	0.0751080i	$0.0239301\pi$
$744$	3.38256	+	1.23115i	0.124011	+	0.0451362i
$745$	−22.8614	+	22.8187i	−0.837577	+	0.836011i
$746$	0.771562	+	4.37574i	0.0282489	+	0.160207i
$747$	−1.05927	+	2.27161i	−0.0387567	+	0.0831140i
$748$	10.9884	−	2.94432i	0.401774	−	0.107655i
$749$	23.5335	+	40.7613i	0.859896	+	1.48938i
$750$	−6.38705	−	9.17636i	−0.233222	−	0.335073i
$751$	21.1845	−	25.2467i	0.773033	−	0.921265i	−0.225564	−	0.974228i	$-0.572422\pi$
$751$	21.1845	−	25.2467i	0.773033	−	0.921265i	0.998596	+	0.0529639i	$0.0168668\pi$
$752$	2.23904	+	0.599950i	0.0816495	+	0.0218779i
$753$	3.14745	+	11.7464i	0.114699	+	0.428064i
$754$	24.9019	−	9.06354i	0.906873	−	0.330075i
$755$	20.7941	−	44.4844i	0.756776	−	1.61895i
$756$	4.70850	+	0.830236i	0.171247	+	0.0301954i
$757$	17.3592	−	8.09474i	0.630932	−	0.294208i	−0.0807242	−	0.996736i	$-0.525723\pi$
$757$	17.3592	−	8.09474i	0.630932	−	0.294208i	0.711656	+	0.702528i	$0.247946\pi$
$758$	11.0659	+	0.968142i	0.401932	+	0.0351645i
$759$	34.8778			1.26598
$760$	9.30626	−	2.89715i	0.337574	−	0.105091i
$761$	12.1467			0.440318			0.220159	−	0.975464i	$-0.429342\pi$
$761$	12.1467			0.440318			0.220159	+	0.975464i	$0.429342\pi$
$762$	1.37656	+	0.120433i	0.0498674	+	0.00436283i
$763$	−2.13519	+	0.995654i	−0.0772990	+	0.0360451i
$764$	4.29714	+	0.757701i	0.155465	+	0.0274127i
$765$	−1.44638	−	3.98550i	−0.0522941	−	0.144096i
$766$	−4.22729	+	1.53861i	−0.152738	+	0.0555922i
$767$	8.71823	+	32.5369i	0.314797	+	1.17484i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	20.4310	−	24.3487i	0.736761	−	0.878038i	−0.259383	−	0.965775i	$-0.583519\pi$
$769$	20.4310	−	24.3487i	0.736761	−	0.878038i	0.996144	+	0.0877370i	$0.0279635\pi$
$770$	61.9717	−	16.5431i	2.23330	−	0.596173i
$771$	−2.48560	−	4.30518i	−0.0895166	−	0.155047i
$772$	−16.9031	+	4.52918i	−0.608358	+	0.163009i
$773$	3.47142	−	7.44449i	0.124858	−	0.267760i	−0.833936	−	0.551862i	$-0.813918\pi$
$773$	3.47142	−	7.44449i	0.124858	−	0.267760i	0.958794	+	0.284102i	$0.0916954\pi$
$774$	0.583771	+	3.31073i	0.0209832	+	0.119002i
$775$	−3.09219	−	17.7306i	−0.111075	−	0.636903i
$776$	−4.82724	−	1.75697i	−0.173288	−	0.0630716i
$777$	−2.86123	+	32.7040i	−0.102646	+	1.17325i
$778$	−17.5063	+	17.5063i	−0.627633	+	0.627633i
$779$	−7.31591	−	9.58767i	−0.262120	−	0.343514i
$780$	−4.63111	+	6.60076i	−0.165821	+	0.236345i
$781$	−15.1692	−	18.0779i	−0.542796	−	0.646879i
$782$	4.65841	+	9.98998i	0.166584	+	0.357241i
$783$	−6.01979	+	4.21510i	−0.215130	+	0.150635i
$784$	−15.6183	+	2.75394i	−0.557798	+	0.0983548i
$785$	4.86286	+	8.44095i	0.173563	+	0.301270i
$786$	−1.33045	+	2.30441i	−0.0474556	+	0.0821955i
$787$	6.04329	−	22.5539i	0.215420	−	0.803958i	−0.770598	−	0.637321i	$-0.780042\pi$
$787$	6.04329	−	22.5539i	0.215420	−	0.803958i	0.986018	−	0.166637i	$-0.0532908\pi$
$788$	1.49190	+	17.0525i	0.0531467	+	0.607470i
$789$	17.7453	+	14.8901i	0.631749	+	0.530100i
$790$	−22.1410	−	26.4368i	−0.787742	−	0.940580i
$791$	46.4433	+	26.8141i	1.65133	+	0.953398i
$792$	5.43751	+	2.53555i	0.193214	+	0.0900970i
$793$	−11.8634	−	8.30685i	−0.421282	−	0.294985i
$794$	5.36961	−	30.4526i	0.190560	−	1.08072i
$795$	11.5023	+	16.4597i	0.407944	+	0.583766i
$796$	−8.26474	+	6.93494i	−0.292936	+	0.245803i
$797$	−18.3729	−	18.3729i	−0.650802	−	0.650802i	0.302384	−	0.953186i	$-0.402217\pi$
$797$	−18.3729	−	18.3729i	−0.650802	−	0.650802i	−0.953186	+	0.302384i	$0.902217\pi$
$798$	20.8230	−	0.852928i	0.737128	−	0.0301933i
$799$		−	4.39525i		−	0.155493i
$800$	1.28506	+	4.83204i	0.0454336	+	0.170838i
$801$	−0.851920	+	2.34063i	−0.0301011	+	0.0827022i
$802$	−5.03618	−	7.19240i	−0.177834	−	0.253973i
$803$	−15.6603	+	22.3652i	−0.552640	+	0.789251i
$804$	3.20521	+	8.80624i	0.113039	+	0.310572i
$805$	26.2130	+	56.3515i	0.923887	+	1.98613i
$806$	−11.2414	+	6.49022i	−0.395961	+	0.228608i
$807$	−3.24596	+	0.283985i	−0.114263	+	0.00999674i
$808$	−1.38840	+	0.121469i	−0.0488438	+	0.00427328i
$809$	14.2177	−	8.20858i	0.499867	−	0.288598i	−0.228792	−	0.973475i	$-0.573477\pi$
$809$	14.2177	−	8.20858i	0.499867	−	0.288598i	0.728659	+	0.684877i	$0.240144\pi$
$810$	0.766746	−	2.10050i	0.0269407	−	0.0738041i
$811$	−7.57222	−	20.8045i	−0.265896	−	0.730545i	−0.998742	−	0.0501492i	$-0.984030\pi$
$811$	−7.57222	−	20.8045i	−0.265896	−	0.730545i	0.732845	−	0.680395i	$-0.238192\pi$
$812$	20.1530	−	28.7814i	0.707231	−	1.01003i
$813$	4.02078	+	5.74228i	0.141015	+	0.201390i
$814$	−14.0897	+	38.7112i	−0.493844	+	1.35683i
$815$	−17.4638	+	20.7730i	−0.611730	+	0.727648i
$816$			1.89611i			0.0663773i
$817$	5.57124	+	13.5534i	0.194913	+	0.474173i
$818$	−21.9585	−	21.9585i	−0.767762	−	0.767762i
$819$	−13.2073	+	11.0823i	−0.461501	+	0.387245i
$820$	5.07117	−	3.54380i	0.177093	−	0.123755i
$821$	7.65544	−	43.4161i	0.267177	−	1.51523i	−0.495588	−	0.868558i	$-0.665048\pi$
$821$	7.65544	−	43.4161i	0.267177	−	1.51523i	0.762765	−	0.646676i	$-0.223841\pi$
$822$	10.7763	+	7.54568i	0.375868	+	0.263186i
$823$	−43.8275	−	20.4371i	−1.52773	−	0.712393i	−0.536422	−	0.843950i	$-0.680225\pi$
$823$	−43.8275	−	20.4371i	−1.52773	−	0.712393i	−0.991309	+	0.131557i	$0.958002\pi$
$824$	2.59703	+	1.49940i	0.0904719	+	0.0522340i
$825$	−2.55859	−	29.8888i	−0.0890786	−	1.04060i
$826$	34.2128	+	28.7079i	1.19041	+	0.998876i
$827$	1.19942	+	13.7095i	0.0417080	+	0.476725i	0.988112	+	0.153739i	$0.0491313\pi$
$827$	1.19942	+	13.7095i	0.0417080	+	0.476725i	−0.946404	+	0.322987i	$0.895313\pi$
$828$	−1.50460	+	5.61524i	−0.0522884	+	0.195143i
$829$	−5.07115	+	8.78348i	−0.176128	+	0.305063i	−0.940551	−	0.339652i	$-0.889691\pi$
$829$	−5.07115	+	8.78348i	−0.176128	+	0.305063i	0.764423	+	0.644715i	$0.223024\pi$
$830$	−5.41226	−	1.45564i	−0.187862	−	0.0505260i
$831$	−20.1764	+	3.55764i	−0.699911	+	0.123413i
$832$	2.95389	−	2.06833i	0.102408	−	0.0717066i
$833$	12.7086	+	27.2536i	0.440325	+	0.944281i
$834$	−11.8476	−	14.1195i	−0.410250	−	0.488917i
$835$	4.03816	−	0.708141i	0.139746	−	0.0245062i
$836$	25.5165	+	5.72908i	0.882508	+	0.198144i
$837$	2.54534	−	2.54534i	0.0879797	−	0.0879797i
$838$	−2.48953	+	28.4555i	−0.0859995	+	0.982979i
$839$	47.6880	+	17.3570i	1.64637	+	0.599231i	0.988136	−	0.153579i	$-0.0490800\pi$
$839$	47.6880	+	17.3570i	1.64637	+	0.599231i	0.658238	+	0.752810i	$0.271302\pi$
$840$	−0.0100025	+	10.6909i	−0.000345117	+	0.368873i
$841$	4.34207	+	24.6251i	0.149726	+	0.849141i
$842$	−8.53685	+	18.3073i	−0.294199	+	0.630912i
$843$	−4.90788	+	1.31506i	−0.169036	+	0.0452931i
$844$	2.96230	+	5.13086i	0.101967	+	0.176612i
$845$	−0.00199783	−	0.00748401i	−6.87275e−5	−	0.000257458i
$846$	1.49000	−	1.77571i	0.0512272	−	0.0610502i
$847$	115.435	+	30.9308i	3.96640	+	1.06279i
$848$	−2.32426	−	8.67426i	−0.0798155	−	0.297875i
$849$	11.5713	−	4.21162i	0.397127	−	0.144542i
$850$	8.21927	−	4.72491i	0.281919	−	0.162063i
$851$	−39.3099	−	6.93139i	−1.34753	−	0.237605i
$852$	3.56489	−	1.66233i	0.122131	−	0.0569506i
$853$	43.8924	+	3.84009i	1.50285	+	0.131482i	0.808644	−	0.588298i	$-0.200202\pi$
$853$	43.8924	+	3.84009i	1.50285	+	0.131482i	0.694202	+	0.719780i	$0.255757\pi$
$854$	−19.2020			−0.657080
$855$	1.30729	−	9.65873i	0.0447084	−	0.330321i
$856$	−9.84432			−0.336472
$857$	−14.9499	−	1.30794i	−0.510677	−	0.0446785i	−0.171094	−	0.985255i	$-0.554730\pi$
$857$	−14.9499	−	1.30794i	−0.510677	−	0.0446785i	−0.339583	+	0.940576i	$0.610286\pi$
$858$	−19.6078	+	9.14329i	−0.669401	+	0.312147i
$859$	−39.4770	−	6.96086i	−1.34694	−	0.237501i	−0.546773	−	0.837281i	$-0.684144\pi$
$859$	−39.4770	−	6.96086i	−1.34694	−	0.237501i	−0.800165	+	0.599780i	$0.795255\pi$
$860$	−7.06628	+	2.56443i	−0.240958	+	0.0874464i
$861$	12.4306	−	4.52436i	0.423633	−	0.154190i
$862$	6.31409	+	23.5645i	0.215059	+	0.802610i
$863$	50.5014	+	13.5318i	1.71909	+	0.460628i	0.977623	−	0.210366i	$-0.0674655\pi$
$863$	50.5014	+	13.5318i	1.71909	+	0.460628i	0.741463	+	0.670993i	$0.234132\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	5.81603	−	10.0519i	0.197751	−	0.341776i
$866$	−12.1175	−	20.9881i	−0.411770	−	0.713206i
$867$	−12.9480	+	3.46940i	−0.439737	+	0.117827i
$868$	−7.27344	+	15.5979i	−0.246876	+	0.529428i
$869$	−16.0666	−	91.1183i	−0.545023	−	3.09098i
$870$	−11.6086	−	11.6303i	−0.393569	−	0.394306i
$871$	−31.7556	−	11.5581i	−1.07600	−	0.391631i
$872$	0.0429462	−	0.490878i	0.00145434	−	0.0166232i
$873$	−3.63244	+	3.63244i	−0.122939	+	0.122939i
$874$	−1.17353	+	25.3125i	−0.0396953	+	0.856208i
$875$	46.3680	−	26.5973i	1.56752	−	0.899154i
$876$	−2.92517	−	3.48608i	−0.0988324	−	0.117784i
$877$	11.9582	+	25.6444i	0.403798	+	0.865949i	0.998095	+	0.0617023i	$0.0196529\pi$
$877$	11.9582	+	25.6444i	0.403798	+	0.865949i	−0.594296	+	0.804246i	$0.702569\pi$
$878$	13.5350	−	9.47729i	0.456783	−	0.319843i
$879$	−2.70667	+	0.477259i	−0.0912936	+	0.0160975i
$880$	−3.48433	+	12.9552i	−0.117457	+	0.436720i
$881$	−16.8050	+	29.1071i	−0.566174	+	0.980642i	0.430765	+	0.902464i	$0.358244\pi$
$881$	−16.8050	+	29.1071i	−0.566174	+	0.980642i	−0.996939	+	0.0781782i	$0.975090\pi$
$882$	−4.10468	+	15.3189i	−0.138212	+	0.515814i
$883$	−2.37230	−	27.1155i	−0.0798343	−	0.912510i	−0.925488	−	0.378778i	$-0.876344\pi$
$883$	−2.37230	−	27.1155i	−0.0798343	−	0.912510i	0.845653	−	0.533733i	$-0.179211\pi$
$884$	−5.23779	−	4.39503i	−0.176166	−	0.147821i
$885$	16.0134	−	13.4113i	0.538283	−	0.450816i
$886$	−3.84272	−	2.21859i	−0.129099	−	0.0745351i
$887$	24.9113	+	11.6163i	0.836440	+	0.390039i	0.793152	−	0.609024i	$-0.208439\pi$
$887$	24.9113	+	11.6163i	0.836440	+	0.390039i	0.0432886	+	0.999063i	$0.486217\pi$
$888$	−5.62458	−	3.93838i	−0.188749	−	0.132163i
$889$	−1.14723	+	6.50628i	−0.0384770	+	0.218214i
$890$	−5.48418	−	0.972301i	−0.183830	−	0.0325916i
$891$	4.59598	−	3.85649i	0.153971	−	0.129197i
$892$	17.1600	+	17.1600i	0.574558	+	0.574558i
$893$	4.68967	−	8.94979i	0.156934	−	0.299493i
$894$		−	14.4453i		−	0.483123i
$895$	−2.78265	−	32.1523i	−0.0930138	−	1.07473i
$896$	1.63525	−	4.49280i	0.0546297	−	0.150094i
$897$	−12.0239	−	17.1719i	−0.401466	−	0.573353i
$898$	6.32985	−	9.03997i	0.211230	−	0.301668i
$899$	−9.04750	−	24.8578i	−0.301751	−	0.829054i
$900$	4.92241	+	0.877453i	0.164080	+	0.0292484i
$901$	−14.7463	+	8.51380i	−0.491271	+	0.283636i
$902$	16.5365	−	1.44675i	0.550604	−	0.0481716i
$903$	−16.0121	+	1.40088i	−0.532849	+	0.0466182i
$904$	−9.71386	+	5.60830i	−0.323078	+	0.186529i
$905$	47.0136	−	21.8693i	1.56278	−	0.726959i
$906$	7.51084	+	20.6359i	0.249531	+	0.685581i
$907$	21.1021	−	30.1369i	0.700684	−	1.00068i	−0.298249	−	0.954488i	$-0.596403\pi$
$907$	21.1021	−	30.1369i	0.700684	−	1.00068i	0.998933	−	0.0461918i	$-0.0147085\pi$
$908$	8.16264	+	11.6575i	0.270887	+	0.386866i
$909$	−0.476675	+	1.30965i	−0.0158103	+	0.0434385i
$910$	−29.5093	−	24.8083i	−0.978223	−	0.822387i
$911$			8.55862i			0.283560i	0.989898	+	0.141780i	$0.0452825\pi$
$911$			8.55862i			0.283560i	−0.989898	+	0.141780i	$0.954717\pi$
$912$	−2.02313	+	3.86095i	−0.0669925	+	0.127849i
$913$	−10.6333	−	10.6333i	−0.351911	−	0.351911i
$914$	1.60404	−	1.34595i	0.0530569	−	0.0445200i
$915$	−1.56772	+	8.84261i	−0.0518273	+	0.292328i
$916$	−2.55448	+	14.4872i	−0.0844025	+	0.478670i
$917$	−10.4214	−	7.29711i	−0.344144	−	0.240972i
$918$	1.71846	+	0.801333i	0.0567177	+	0.0264479i
$919$	21.2368	+	12.2611i	0.700537	+	0.404455i	0.807547	−	0.589803i	$-0.200795\pi$
$919$	21.2368	+	12.2611i	0.700537	+	0.404455i	−0.107011	+	0.994258i	$0.534128\pi$
$920$	−12.9485	−	1.14505i	−0.426898	−	0.0377512i
$921$	−6.22384	−	5.22242i	−0.205082	−	0.172085i
$922$	−3.24618	−	37.1040i	−0.106907	−	1.22195i
$923$	−3.67110	+	13.7007i	−0.120836	+	0.450965i
$924$	−14.3425	+	24.8420i	−0.471835	+	0.817242i
$925$	−3.05620	+	34.1954i	−0.100487	+	1.12434i
$926$	34.3553	−	6.05776i	1.12898	−	0.199070i
$927$	2.45647	−	1.72004i	0.0806810	−	0.0564934i
$928$	3.10574	+	6.66028i	0.101951	+	0.218634i
$929$	2.33087	+	2.77782i	0.0764733	+	0.0911373i	0.802925	−	0.596081i	$-0.203276\pi$
$929$	2.33087	+	2.77782i	0.0764733	+	0.0911373i	−0.726451	+	0.687218i	$0.758832\pi$
$930$	6.58908	+	4.62292i	0.216064	+	0.151591i
$931$	−3.20150	+	69.0548i	−0.104925	+	2.26318i
$932$	14.1561	−	14.1561i	0.463700	−	0.463700i
$933$	2.82460	−	32.2854i	0.0924734	−	1.05698i
$934$	−30.5947	−	11.1356i	−1.00109	−	0.364366i
$935$	25.4375	+	0.0237993i	0.831894	+	0.000778320i
$936$	−0.626181	−	3.55125i	−0.0204674	−	0.116076i
$937$	−3.18274	+	6.82541i	−0.103976	+	0.222976i	−0.951412	−	0.307920i	$-0.900367\pi$
$937$	−3.18274	+	6.82541i	−0.103976	+	0.222976i	0.847437	+	0.530897i	$0.178145\pi$
$938$	−43.2792	+	11.5966i	−1.41312	+	0.378644i
$939$	0.627239	+	1.08641i	0.0204692	+	0.0354537i
$940$	4.48641	+	2.59583i	0.146331	+	0.0846667i
$941$	0.600360	−	0.715481i	0.0195712	−	0.0233240i	−0.756170	−	0.654375i	$-0.772932\pi$
$941$	0.600360	−	0.715481i	0.0195712	−	0.0233240i	0.775741	+	0.631051i	$0.217376\pi$
$942$	−4.20809	−	1.12755i	−0.137107	−	0.0367377i
$943$	4.16289	+	15.5361i	0.135562	+	0.505925i
$944$	−8.77786	+	3.19488i	−0.285695	+	0.103984i
$945$	9.68506	+	4.52725i	0.315055	+	0.147272i
$946$	−19.8632	−	3.50241i	−0.645807	−	0.113873i
$947$	33.7422	−	15.7343i	1.09648	−	0.511295i	0.211710	−	0.977332i	$-0.432097\pi$
$947$	33.7422	−	15.7343i	1.09648	−	0.511295i	0.884765	+	0.466038i	$0.154319\pi$
$948$	15.3629	+	1.34408i	0.498965	+	0.0436538i
$949$	16.4102			0.532697
$950$	21.7779	−	0.851222i	0.706567	−	0.0276173i
$951$	29.8521			0.968019
$952$	−9.03109	−	0.790118i	−0.292699	−	0.0256079i
$953$	5.17351	−	2.41245i	0.167586	−	0.0781469i	−0.337015	−	0.941499i	$-0.609417\pi$
$953$	5.17351	−	2.41245i	0.167586	−	0.0781469i	0.504601	+	0.863352i	$0.331639\pi$
$954$	−8.84383	−	1.55941i	−0.286329	−	0.0504876i
$955$	8.83891	+	4.13172i	0.286020	+	0.133699i
$956$	25.0866	−	9.13077i	0.811358	−	0.295310i
$957$	−11.4114	−	42.5878i	−0.368877	−	1.37667i
$958$	−25.6073	−	6.86145i	−0.827334	−	0.221683i
$959$	−40.4302	+	48.1828i	−1.30556	+	1.55590i
$960$	−1.93544	−	1.11985i	−0.0624662	−	0.0361429i
$961$	−9.02127	−	15.6253i	−0.291009	−	0.504042i
$962$	23.9166	−	6.40843i	0.771102	−	0.206616i
$963$	−4.16039	+	8.92198i	−0.134067	+	0.287507i
$964$	−0.698244	−	3.95994i	−0.0224889	−	0.127541i
$965$	−39.1299	−	0.0366099i	−1.25964	−	0.00117852i
$966$	−26.1181	−	9.50621i	−0.840336	−	0.305857i
$967$	−0.154094	+	1.76130i	−0.00495533	+	0.0566397i	−0.998270	−	0.0588007i	$-0.981272\pi$
$967$	−0.154094	+	1.76130i	−0.00495533	+	0.0566397i	0.993314	+	0.115440i	$0.0368279\pi$
$968$	−17.6745	+	17.6745i	−0.568081	+	0.568081i
$969$	8.06421	+	1.81061i	0.259060	+	0.0581652i
$970$	−9.40324	−	6.59734i	−0.301920	−	0.211828i
$971$	−31.5069	−	37.5485i	−1.01110	−	1.20499i	−0.978654	−	0.205514i	$-0.934113\pi$
$971$	−31.5069	−	37.5485i	−1.01110	−	1.20499i	−0.0324500	−	0.999473i	$-0.510331\pi$
$972$	0.422618	+	0.906308i	0.0135555	+	0.0290698i
$973$	72.1872	−	50.5460i	2.31422	−	1.62043i
$974$	33.2955	−	5.87090i	1.06686	−	0.188116i
$975$	−13.8336	+	11.5637i	−0.443029	+	0.370335i
$976$	2.00810	−	3.47813i	0.0642778	−	0.111332i
$977$	−4.11559	+	15.3596i	−0.131669	+	0.491397i	−0.999989	−	0.00460743i	$-0.998533\pi$
$977$	−4.11559	+	15.3596i	−0.131669	+	0.491397i	0.868320	+	0.496005i	$0.165200\pi$
$978$	−1.05779	−	12.0906i	−0.0338243	−	0.386613i
$979$	−11.4479	−	9.60593i	−0.365876	−	0.307007i
$980$	−35.3246	−	3.12381i	−1.12840	−	0.0997863i
$981$	−0.426736	−	0.246376i	−0.0136246	−	0.00786619i
$982$	14.8116	+	6.90676i	0.472657	+	0.220404i
$983$	3.47700	+	2.43462i	0.110899	+	0.0776523i	0.627710	−	0.778447i	$-0.283992\pi$
$983$	3.47700	+	2.43462i	0.110899	+	0.0776523i	−0.516811	+	0.856099i	$0.672881\pi$
$984$	−0.480446	+	2.72474i	−0.0153160	+	0.0868616i
$985$	−6.68185	+	37.6884i	−0.212901	+	1.20085i
$986$	10.6742	−	8.95672i	0.339936	−	0.285240i
$987$	7.83673	+	7.83673i	0.249446	+	0.249446i
$988$	−5.97598	−	14.5380i	−0.190121	−	0.462515i
$989$		−	19.5433i		−	0.621439i
$990$	10.2689	+	8.63298i	0.326366	+	0.274374i
$991$	−1.15274	+	3.16712i	−0.0366179	+	0.100607i	−0.956654	−	0.291226i	$-0.905937\pi$
$991$	−1.15274	+	3.16712i	−0.0366179	+	0.100607i	0.920036	+	0.391833i	$0.128159\pi$
$992$	−2.06467	−	2.94866i	−0.0655534	−	0.0936200i
$993$	2.91709	−	4.16604i	0.0925711	−	0.132205i
$994$	6.43210	+	17.6721i	0.204014	+	0.560524i
$995$	−21.8739	+	10.1750i	−0.693448	+	0.322570i
$996$	2.17065	−	1.25322i	0.0687796	−	0.0397099i
$997$	−2.30629	+	0.201775i	−0.0730410	+	0.00639026i	−0.123618	−	0.992330i	$-0.539450\pi$
$997$	−2.30629	+	0.201775i	−0.0730410	+	0.00639026i	0.0505766	+	0.998720i	$0.483894\pi$
$998$	−12.4461	+	1.08890i	−0.393976	+	0.0344684i
$999$	−5.94643	+	3.43317i	−0.188137	+	0.108621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.13.10	✓	120
5.2	odd	4	inner	570.2.bh.b.127.2	yes	120
19.3	odd	18	inner	570.2.bh.b.193.2	yes	120
95.22	even	36	inner	570.2.bh.b.307.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.13.10	✓	120	1.1	even	1	trivial
570.2.bh.b.127.2	yes	120	5.2	odd	4	inner
570.2.bh.b.193.2	yes	120	19.3	odd	18	inner
570.2.bh.b.307.10	yes	120	95.22	even	36	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.02568 + 0.946899i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-1.23745 - 4.61822i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.02568 + 0.946899i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-1.23745 - 4.61822i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(1.93544 + 1.11985i) q^{10} +(2.99982 + 5.19583i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(1.52397 - 3.26817i) q^{13} +(-0.830236 - 4.70850i) q^{14} +(-2.23607 - 0.00209206i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.165257 - 1.88890i) q^{17} +(0.707107 - 0.707107i) q^{18} +(2.35193 - 3.66993i) q^{19} +(1.83048 + 1.28427i) q^{20} +(3.07326 + 3.66256i) q^{21} +(2.53555 + 5.43751i) q^{22} +(-4.76200 + 3.33439i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(3.20677 + 3.83623i) q^{25} +(1.80302 - 3.12292i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(-0.416704 - 4.76294i) q^{28} +(5.62951 + 4.72372i) q^{29} +(-2.22738 - 0.196970i) q^{30} +(-3.11739 - 1.79982i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-4.91461 - 3.44125i) q^{33} +(0.329257 - 1.86731i) q^{34} +(1.86631 - 10.5268i) q^{35} +(0.766044 - 0.642788i) q^{36} +(4.85524 + 4.85524i) q^{37} +(2.66284 - 3.45098i) q^{38} +3.60603i q^{39} +(1.71158 + 1.43892i) q^{40} +(0.946293 - 2.59992i) q^{41} +(2.74235 + 3.91648i) q^{42} +(-1.92825 + 2.75383i) q^{43} +(2.05199 + 5.63781i) q^{44} +(2.02745 - 0.943107i) q^{45} +(-5.03449 + 2.90666i) q^{46} +(2.30921 - 0.202029i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(-13.7345 + 7.92964i) q^{49} +(2.86021 + 4.10112i) q^{50} +(0.648509 + 1.78176i) q^{51} +(2.06833 - 2.95389i) q^{52} +(-5.15086 - 7.35620i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(1.15674 + 13.3656i) q^{55} -4.78114i q^{56} +(-0.580597 + 4.32006i) q^{57} +(5.19639 + 5.19639i) q^{58} +(-7.15578 + 6.00441i) q^{59} +(-2.20173 - 0.390349i) q^{60} +(0.697407 - 3.95519i) q^{61} +(-2.94866 - 2.06467i) q^{62} +(-4.33318 - 2.02060i) q^{63} +(0.866025 + 0.500000i) q^{64} +(6.18172 - 5.17723i) q^{65} +(-4.59598 - 3.85649i) q^{66} +(-0.816771 - 9.33574i) q^{67} +(0.490751 - 1.83151i) q^{68} +(2.90666 - 5.03449i) q^{69} +(2.77668 - 10.3241i) q^{70} +(-3.87366 + 0.683031i) q^{71} +(0.819152 - 0.573576i) q^{72} +(1.92323 + 4.12439i) q^{73} +(4.41360 + 5.25993i) q^{74} +(-4.52758 - 2.12157i) q^{75} +(2.95348 - 3.20577i) q^{76} +(20.2834 - 20.2834i) q^{77} +(-0.314286 + 3.59231i) q^{78} +(-14.4916 - 5.27450i) q^{79} +(1.57966 + 1.58262i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(1.16929 - 2.50755i) q^{82} +(-2.42104 + 0.648717i) q^{83} +(2.39057 + 4.14059i) q^{84} +(2.12335 - 3.66982i) q^{85} +(-2.16093 + 2.57529i) q^{86} +(-7.09840 - 1.90201i) q^{87} +(1.55282 + 5.79520i) q^{88} +(-2.34063 + 0.851920i) q^{89} +(2.10193 - 0.762814i) q^{90} +(-16.9790 - 2.99386i) q^{91} +(-5.26866 + 2.45682i) q^{92} +(3.58595 + 0.313730i) q^{93} +2.31803 q^{94} +(8.23932 - 5.20707i) q^{95} -1.00000 q^{96} +(-5.11749 - 0.447723i) q^{97} +(-14.3734 + 6.70242i) q^{98} +(5.90848 + 1.04183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^5 + 12 * q^7	\( 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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