LMFDB - Embedded newform 570.2.bh.b.67.1

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			67.1
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.b.553.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.16408 - 0.562797i) q^{5} +(0.766044 + 0.642788i) q^{6} +(-2.70522 + 0.724862i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.16408 - 0.562797i) q^{5} +(0.766044 + 0.642788i) q^{6} +(-2.70522 + 0.724862i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(1.44991 + 1.70228i) q^{10} +(1.91236 + 3.31230i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(0.00894794 + 0.102275i) q^{13} +(2.63175 + 0.957879i) q^{14} +(2.10680 + 0.749267i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(2.98371 - 4.26118i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-3.83950 + 2.06356i) q^{19} +(-0.211304 - 2.22606i) q^{20} +(2.75810 - 0.486328i) q^{21} +(0.333346 - 3.81017i) q^{22} +(2.62479 - 5.62889i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(4.36652 + 2.43588i) q^{25} +(0.0513331 - 0.0889115i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(-1.60639 - 2.29416i) q^{28} +(1.65611 - 9.39227i) q^{29} +(-1.29603 - 1.82217i) q^{30} +(8.52635 + 4.92269i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-1.61640 - 3.46637i) q^{33} +(-4.88823 + 1.77917i) q^{34} +(6.26228 - 0.0461725i) q^{35} +(0.173648 + 0.984808i) q^{36} +(-3.47087 + 3.47087i) q^{37} +(4.32874 + 0.511879i) q^{38} -0.102666i q^{39} +(-1.10373 + 1.94468i) q^{40} +(-0.496385 - 0.591569i) q^{41} +(-2.53825 - 1.18361i) q^{42} +(6.52970 - 3.04485i) q^{43} +(-2.45848 + 2.92991i) q^{44} +(-2.03348 - 0.930036i) q^{45} +(-5.37870 + 3.10539i) q^{46} +(4.48836 - 3.14278i) q^{47} +(0.819152 - 0.573576i) q^{48} +(0.730618 - 0.421822i) q^{49} +(-2.17968 - 4.49989i) q^{50} +(-3.34375 + 3.98492i) q^{51} +(-0.0930471 + 0.0433886i) q^{52} +(2.57611 + 1.20126i) q^{53} +(0.642788 + 0.766044i) q^{54} +(-2.27435 - 8.24438i) q^{55} +2.80065i q^{56} +(4.00474 - 1.72107i) q^{57} +(-6.74379 + 6.74379i) q^{58} +(1.24462 + 7.05860i) q^{59} +(0.0164863 + 2.23601i) q^{60} +(14.6009 - 5.31428i) q^{61} +(-4.16084 - 8.92295i) q^{62} +(-2.78999 + 0.244093i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.0381962 - 0.226369i) q^{65} +(-0.664156 + 3.76661i) q^{66} +(-6.64318 - 9.48744i) q^{67} +(5.02469 + 1.34636i) q^{68} +(-3.10539 + 5.37870i) q^{69} +(-5.15624 - 3.55407i) q^{70} +(2.14263 - 5.88683i) q^{71} +(0.422618 - 0.906308i) q^{72} +(-0.378621 + 4.32766i) q^{73} +(4.83398 - 0.852360i) q^{74} +(-4.13760 - 2.80718i) q^{75} +(-3.25229 - 2.90217i) q^{76} +(-7.57432 - 7.57432i) q^{77} +(-0.0588869 + 0.0840992i) q^{78} +(7.51264 - 6.30385i) q^{79} +(2.01954 - 0.959919i) q^{80} +(0.939693 + 0.342020i) q^{81} +(0.0673050 + 0.769300i) q^{82} +(3.36658 + 12.5642i) q^{83} +(1.40033 + 2.42543i) q^{84} +(-8.85519 + 7.54234i) q^{85} +(-7.09527 - 1.25109i) q^{86} +(-2.46840 + 9.21219i) q^{87} +(3.69440 - 0.989910i) q^{88} +(-2.24600 - 1.88462i) q^{89} +(1.13228 + 1.92820i) q^{90} +(-0.0983417 - 0.270192i) q^{91} +(6.18715 + 0.541306i) q^{92} +(-8.06486 - 5.64708i) q^{93} -5.47927 q^{94} +(9.47036 - 2.30485i) q^{95} -1.00000 q^{96} +(-3.27599 - 2.29388i) q^{97} +(-0.840434 - 0.0735285i) q^{98} +(1.30813 + 3.59406i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−2.16408	−	0.562797i	−0.967808	−	0.251690i
$5$	−2.16408	−	0.562797i	−0.967808	−	0.251690i
$6$	0.766044	+	0.642788i	0.312736	+	0.262417i
$7$	−2.70522	+	0.724862i	−1.02248	+	0.273972i	−0.730834	−	0.682555i	$-0.760869\pi$
$7$	−2.70522	+	0.724862i	−1.02248	+	0.273972i	−0.291643	+	0.956527i	$0.594202\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	1.44991	+	1.70228i	0.458501	+	0.538309i
$11$	1.91236	+	3.31230i	0.576598	+	0.998697i	0.995866	+	0.0908348i	$0.0289535\pi$
$11$	1.91236	+	3.31230i	0.576598	+	0.998697i	−0.419268	+	0.907863i	$0.637713\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	0.00894794	+	0.102275i	0.00248171	+	0.0283661i	0.997335	−	0.0729639i	$-0.0232458\pi$
$13$	0.00894794	+	0.102275i	0.00248171	+	0.0283661i	−0.994853	+	0.101330i	$0.967690\pi$
$14$	2.63175	+	0.957879i	0.703365	+	0.256004i
$15$	2.10680	+	0.749267i	0.543973	+	0.193460i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	2.98371	−	4.26118i	0.723657	−	1.03349i	−0.273770	−	0.961795i	$-0.588271\pi$
$17$	2.98371	−	4.26118i	0.723657	−	1.03349i	0.997427	−	0.0716939i	$-0.0228405\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−3.83950	+	2.06356i	−0.880841	+	0.473412i
$19$	−3.83950	+	2.06356i	−0.880841	+	0.473412i
$20$	−0.211304	−	2.22606i	−0.0472491	−	0.497763i
$21$	2.75810	−	0.486328i	0.601867	−	0.106125i
$22$	0.333346	−	3.81017i	0.0710697	−	0.812330i
$23$	2.62479	−	5.62889i	0.547307	−	1.17370i	−0.416997	−	0.908908i	$-0.636918\pi$
$23$	2.62479	−	5.62889i	0.547307	−	1.17370i	0.964304	−	0.264796i	$-0.0853047\pi$
$24$	−0.342020	+	0.939693i	−0.0698146	+	0.191814i
$25$	4.36652	+	2.43588i	0.873304	+	0.487176i
$26$	0.0513331	−	0.0889115i	0.0100672	−	0.0174370i
$27$	−0.965926	−	0.258819i	−0.185893	−	0.0498097i
$28$	−1.60639	−	2.29416i	−0.303579	−	0.433555i
$29$	1.65611	−	9.39227i	0.307532	−	1.74410i	−0.303809	−	0.952733i	$-0.598259\pi$
$29$	1.65611	−	9.39227i	0.307532	−	1.74410i	0.611341	−	0.791367i	$-0.290630\pi$
$30$	−1.29603	−	1.82217i	−0.236621	−	0.332682i
$31$	8.52635	+	4.92269i	1.53138	+	0.884141i	0.999299	+	0.0374467i	$0.0119224\pi$
$31$	8.52635	+	4.92269i	1.53138	+	0.884141i	0.532079	+	0.846695i	$0.321411\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$	−1.61640	−	3.46637i	−0.281379	−	0.603418i
$34$	−4.88823	+	1.77917i	−0.838325	+	0.305125i
$35$	6.26228	−	0.0461725i	1.05852	−	0.00780458i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	−3.47087	+	3.47087i	−0.570607	+	0.570607i	−0.932298	−	0.361691i	$-0.882200\pi$
$37$	−3.47087	+	3.47087i	−0.570607	+	0.570607i	0.361691	+	0.932298i	$0.382200\pi$
$38$	4.32874	+	0.511879i	0.702214	+	0.0830378i
$39$		−	0.102666i		−	0.0164397i
$40$	−1.10373	+	1.94468i	−0.174514	+	0.307481i
$41$	−0.496385	−	0.591569i	−0.0775223	−	0.0923875i	0.725889	−	0.687812i	$-0.241428\pi$
$41$	−0.496385	−	0.591569i	−0.0775223	−	0.0923875i	−0.803412	+	0.595424i	$0.796984\pi$
$42$	−2.53825	−	1.18361i	−0.391661	−	0.182634i
$43$	6.52970	−	3.04485i	0.995769	−	0.464335i	0.144749	−	0.989468i	$-0.453762\pi$
$43$	6.52970	−	3.04485i	0.995769	−	0.464335i	0.851020	+	0.525133i	$0.175985\pi$
$44$	−2.45848	+	2.92991i	−0.370630	+	0.441700i
$45$	−2.03348	−	0.930036i	−0.303133	−	0.138642i
$46$	−5.37870	+	3.10539i	−0.793046	+	0.457865i
$47$	4.48836	−	3.14278i	0.654694	−	0.458422i	−0.198440	−	0.980113i	$-0.563588\pi$
$47$	4.48836	−	3.14278i	0.654694	−	0.458422i	0.853134	+	0.521691i	$0.174699\pi$
$48$	0.819152	−	0.573576i	0.118234	−	0.0827886i
$49$	0.730618	−	0.421822i	0.104374	−	0.0602603i
$50$	−2.17968	−	4.49989i	−0.308253	−	0.636380i
$51$	−3.34375	+	3.98492i	−0.468218	+	0.558001i
$52$	−0.0930471	+	0.0433886i	−0.0129033	+	0.00601691i
$53$	2.57611	+	1.20126i	0.353856	+	0.165006i	0.591415	−	0.806367i	$-0.298570\pi$
$53$	2.57611	+	1.20126i	0.353856	+	0.165006i	−0.237559	+	0.971373i	$0.576347\pi$
$54$	0.642788	+	0.766044i	0.0874723	+	0.104245i
$55$	−2.27435	−	8.24438i	−0.306674	−	1.11167i
$56$			2.80065i			0.374253i
$57$	4.00474	−	1.72107i	0.530440	−	0.227961i
$58$	−6.74379	+	6.74379i	−0.885503	+	0.885503i
$59$	1.24462	+	7.05860i	0.162036	+	0.918951i	0.952068	+	0.305886i	$0.0989526\pi$
$59$	1.24462	+	7.05860i	0.162036	+	0.918951i	−0.790032	+	0.613065i	$0.789936\pi$
$60$	0.0164863	+	2.23601i	0.00212838	+	0.288667i
$61$	14.6009	−	5.31428i	1.86945	−	0.680424i	0.899603	−	0.436708i	$-0.143856\pi$
$61$	14.6009	−	5.31428i	1.86945	−	0.680424i	0.969847	−	0.243716i	$-0.0783665\pi$
$62$	−4.16084	−	8.92295i	−0.528427	−	1.13322i
$63$	−2.78999	+	0.244093i	−0.351506	+	0.0307528i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	0.0381962	−	0.226369i	0.00473765	−	0.0280776i
$66$	−0.664156	+	3.76661i	−0.0817519	+	0.463638i
$67$	−6.64318	−	9.48744i	−0.811593	−	1.15908i	−0.984715	−	0.174175i	$-0.944274\pi$
$67$	−6.64318	−	9.48744i	−0.811593	−	1.15908i	0.173122	−	0.984900i	$-0.444615\pi$
$68$	5.02469	+	1.34636i	0.609334	+	0.163270i
$69$	−3.10539	+	5.37870i	−0.373846	+	0.647519i
$70$	−5.15624	−	3.55407i	−0.616288	−	0.424793i
$71$	2.14263	−	5.88683i	0.254283	−	0.698638i	−0.745211	−	0.666829i	$-0.767651\pi$
$71$	2.14263	−	5.88683i	0.254283	−	0.698638i	0.999494	−	0.0318086i	$-0.0101267\pi$
$72$	0.422618	−	0.906308i	0.0498060	−	0.106809i
$73$	−0.378621	+	4.32766i	−0.0443142	+	0.506514i	0.941308	+	0.337549i	$0.109598\pi$
$73$	−0.378621	+	4.32766i	−0.0443142	+	0.506514i	−0.985622	+	0.168965i	$0.945958\pi$
$74$	4.83398	−	0.852360i	0.561938	−	0.0990849i
$75$	−4.13760	−	2.80718i	−0.477769	−	0.324145i
$76$	−3.25229	−	2.90217i	−0.373064	−	0.332902i
$77$	−7.57432	−	7.57432i	−0.863174	−	0.863174i
$78$	−0.0588869	+	0.0840992i	−0.00666763	+	0.00952236i
$79$	7.51264	−	6.30385i	0.845238	−	0.709239i	−0.113498	−	0.993538i	$-0.536206\pi$
$79$	7.51264	−	6.30385i	0.845238	−	0.709239i	0.958735	+	0.284300i	$0.0917611\pi$
$80$	2.01954	−	0.959919i	0.225792	−	0.107322i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	0.0673050	+	0.769300i	0.00743259	+	0.0849549i
$83$	3.36658	+	12.5642i	0.369530	+	1.37910i	0.861175	+	0.508308i	$0.169729\pi$
$83$	3.36658	+	12.5642i	0.369530	+	1.37910i	−0.491645	+	0.870795i	$0.663604\pi$
$84$	1.40033	+	2.42543i	0.152788	+	0.264637i
$85$	−8.85519	+	7.54234i	−0.960480	+	0.818081i
$86$	−7.09527	−	1.25109i	−0.765102	−	0.134908i
$87$	−2.46840	+	9.21219i	−0.264640	+	0.987650i
$88$	3.69440	−	0.989910i	0.393824	−	0.105525i
$89$	−2.24600	−	1.88462i	−0.238076	−	0.199769i	0.515942	−	0.856624i	$-0.327442\pi$
$89$	−2.24600	−	1.88462i	−0.238076	−	0.199769i	−0.754017	+	0.656854i	$0.771887\pi$
$90$	1.13228	+	1.92820i	0.119353	+	0.203250i
$91$	−0.0983417	−	0.270192i	−0.0103090	−	0.0283238i
$92$	6.18715	+	0.541306i	0.645055	+	0.0564350i
$93$	−8.06486	−	5.64708i	−0.836287	−	0.585575i
$94$	−5.47927			−0.565144
$95$	9.47036	−	2.30485i	0.971638	−	0.236473i
$96$	−1.00000			−0.102062
$97$	−3.27599	−	2.29388i	−0.332627	−	0.232908i	0.395317	−	0.918545i	$-0.370635\pi$
$97$	−3.27599	−	2.29388i	−0.332627	−	0.232908i	−0.727944	+	0.685637i	$0.759524\pi$
$98$	−0.840434	−	0.0735285i	−0.0848967	−	0.00742750i
$99$	1.30813	+	3.59406i	0.131472	+	0.361217i
$100$	−0.795539	+	4.93631i	−0.0795539	+	0.493631i
$101$	1.69541	+	1.42262i	0.168700	+	0.141556i	0.723229	−	0.690608i	$-0.242657\pi$
$101$	1.69541	+	1.42262i	0.168700	+	0.141556i	−0.554529	+	0.832164i	$0.687102\pi$
$102$	5.02469	−	1.34636i	0.497519	−	0.133310i
$103$	−4.45255	+	16.6171i	−0.438723	+	1.63734i	0.293275	+	0.956028i	$0.405255\pi$
$103$	−4.45255	+	16.6171i	−0.438723	+	1.63734i	−0.731997	+	0.681307i	$0.761412\pi$
$104$	0.101106	+	0.0178278i	0.00991430	+	0.00174816i
$105$	−6.24247	−	0.499796i	−0.609203	−	0.0487751i
$106$	−1.42121	−	2.46161i	−0.138040	−	0.239093i
$107$	1.30693	+	4.87755i	0.126346	+	0.471530i	0.999884	−	0.0152259i	$-0.00484673\pi$
$107$	1.30693	+	4.87755i	0.126346	+	0.471530i	−0.873538	+	0.486756i	$0.838180\pi$
$108$	−0.0871557	−	0.996195i	−0.00838657	−	0.0958589i
$109$	1.35020	+	0.491433i	0.129326	+	0.0470708i	0.405872	−	0.913930i	$-0.366968\pi$
$109$	1.35020	+	0.491433i	0.129326	+	0.0470708i	−0.276546	+	0.961001i	$0.589190\pi$
$110$	−2.86574	+	8.05791i	−0.273237	+	0.768292i
$111$	3.76017	−	3.15515i	0.356899	−	0.299474i
$112$	1.60639	−	2.29416i	0.151789	−	0.216778i
$113$	−5.68594	−	5.68594i	−0.534888	−	0.534888i	0.387135	−	0.922023i	$-0.373465\pi$
$113$	−5.68594	−	5.68594i	−0.534888	−	0.534888i	−0.922023	+	0.387135i	$0.873465\pi$
$114$	−4.26765	−	0.887206i	−0.399702	−	0.0830945i
$115$	−8.84819	+	10.7042i	−0.825098	+	0.998168i
$116$	9.39227	−	1.65611i	0.872050	−	0.153766i
$117$	−0.00894794	+	0.102275i	−0.000827238	+	0.00945537i
$118$	3.02911	−	6.49595i	0.278852	−	0.598000i
$119$	−4.98283	+	13.6902i	−0.456776	+	1.25498i
$120$	1.26902	−	1.84109i	0.115845	−	0.168067i
$121$	−1.81424	+	3.14236i	−0.164931	+	0.285669i
$122$	−15.0085	−	4.02151i	−1.35880	−	0.364090i
$123$	0.442938	+	0.632580i	0.0399383	+	0.0570379i
$124$	−1.70963	+	9.69581i	−0.153530	+	0.870709i
$125$	−8.07861	−	7.72891i	−0.722573	−	0.691295i
$126$	2.42543	+	1.40033i	0.216075	+	0.124751i
$127$	16.4498	−	1.43917i	1.45968	−	0.127705i	0.670519	−	0.741892i	$-0.266071\pi$
$127$	16.4498	−	1.43917i	1.45968	−	0.127705i	0.789161	+	0.614187i	$0.210516\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$	−6.77022	+	2.46416i	−0.596085	+	0.216957i
$130$	−0.161128	+	0.163522i	−0.0141319	+	0.0143418i
$131$	3.83006	+	21.7214i	0.334634	+	1.89780i	0.430816	+	0.902440i	$0.358226\pi$
$131$	3.83006	+	21.7214i	0.334634	+	1.89780i	−0.0961825	+	0.995364i	$0.530663\pi$
$132$	2.70449	−	2.70449i	0.235395	−	0.235395i
$133$	8.89090	−	8.36548i	0.770938	−	0.725379i
$134$			11.5820i			1.00053i
$135$	1.94468	+	1.10373i	0.167372	+	0.0949936i
$136$	−3.34375	−	3.98492i	−0.286724	−	0.341704i
$137$	−10.1687	−	4.74176i	−0.868773	−	0.405116i	−0.0634736	−	0.997984i	$-0.520218\pi$
$137$	−10.1687	−	4.74176i	−0.868773	−	0.405116i	−0.805300	+	0.592868i	$0.797996\pi$
$138$	5.62889	−	2.62479i	0.479163	−	0.223437i
$139$	−8.37647	+	9.98269i	−0.710483	+	0.846721i	−0.993669	−	0.112344i	$-0.964164\pi$
$139$	−8.37647	+	9.98269i	−0.710483	+	0.846721i	0.283186	+	0.959065i	$0.408609\pi$
$140$	2.18521	+	5.86882i	0.184684	+	0.496006i
$141$	−4.74519	+	2.73964i	−0.399617	+	0.230719i
$142$	−5.13168	+	3.59324i	−0.430641	+	0.301538i
$143$	−0.321656	+	0.225226i	−0.0268982	+	0.0188343i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	−8.86990	+	19.3936i	−0.736605	+	1.61055i
$146$	2.79239	−	3.32784i	0.231100	−	0.275414i
$147$	−0.764602	+	0.356540i	−0.0630633	+	0.0294069i
$148$	−4.44866	−	2.07444i	−0.365677	−	0.170518i
$149$	−1.54103	−	1.83653i	−0.126246	−	0.150455i	0.699218	−	0.714908i	$-0.253531\pi$
$149$	−1.54103	−	1.83653i	−0.126246	−	0.150455i	−0.825465	+	0.564453i	$0.809087\pi$
$150$	1.77920	+	4.67274i	0.145271	+	0.381527i
$151$		−	15.2494i		−	1.24098i	−0.784214	−	0.620490i	$-0.786934\pi$
$151$		−	15.2494i		−	1.24098i	0.784214	−	0.620490i	$-0.213066\pi$
$152$	0.999507	+	4.24276i	0.0810707	+	0.344133i
$153$	3.67833	−	3.67833i	0.297375	−	0.297375i
$154$	1.86007	+	10.5490i	0.149889	+	0.850060i
$155$	−15.6813	−	15.4517i	−1.25955	−	1.24111i
$156$	0.0964746	−	0.0351139i	0.00772415	−	0.00281136i
$157$	1.67213	+	3.58590i	0.133451	+	0.286186i	0.961666	−	0.274225i	$-0.0884212\pi$
$157$	1.67213	+	3.58590i	0.133451	+	0.286186i	−0.828215	+	0.560411i	$0.810643\pi$
$158$	−9.76973	+	0.854741i	−0.777238	+	0.0679995i
$159$	−2.46161	−	1.42121i	−0.195218	−	0.112709i
$160$	−2.20490	−	0.372043i	−0.174313	−	0.0294126i
$161$	−3.02048	+	17.1300i	−0.238047	+	1.35003i
$162$	−0.573576	−	0.819152i	−0.0450644	−	0.0643587i
$163$	5.60304	+	1.50133i	0.438864	+	0.117593i	0.471484	−	0.881874i	$-0.343718\pi$
$163$	5.60304	+	1.50133i	0.438864	+	0.117593i	−0.0326199	+	0.999468i	$0.510385\pi$
$164$	0.386119	−	0.668778i	0.0301508	−	0.0522228i
$165$	1.54715	+	8.41123i	0.120446	+	0.654813i
$166$	4.44881	−	12.2230i	0.345295	−	0.948689i
$167$	−0.176177	+	0.377812i	−0.0136330	+	0.0292360i	−0.913006	−	0.407945i	$-0.866245\pi$
$167$	−0.176177	+	0.377812i	−0.0136330	+	0.0292360i	0.899373	+	0.437181i	$0.144023\pi$
$168$	0.244093	−	2.78999i	0.0188322	−	0.215253i
$169$	12.7921	−	2.25560i	0.984009	−	0.173507i
$170$	11.5799	−	1.09919i	0.888134	−	0.0843044i
$171$	−4.13950	+	1.36548i	−0.316555	+	0.104421i
$172$	5.09451	+	5.09451i	0.388453	+	0.388453i
$173$	5.37388	−	7.67470i	0.408569	−	0.583496i	−0.561152	−	0.827713i	$-0.689642\pi$
$173$	5.37388	−	7.67470i	0.408569	−	0.583496i	0.969721	+	0.244216i	$0.0785307\pi$
$174$	7.30589	−	6.13037i	0.553858	−	0.464742i
$175$	−13.5781	−	3.42447i	−1.02641	−	0.258865i
$176$	−3.59406	−	1.30813i	−0.270913	−	0.0986041i
$177$	−0.624688	−	7.14021i	−0.0469544	−	0.536691i
$178$	0.758844	+	2.83205i	0.0568778	+	0.212271i
$179$	−7.17079	−	12.4202i	−0.535970	−	0.928327i	−0.999116	−	0.0420452i	$-0.986613\pi$
$179$	−7.17079	−	12.4202i	−0.535970	−	0.928327i	0.463146	−	0.886282i	$-0.346721\pi$
$180$	0.178457	−	2.22894i	0.0133014	−	0.166135i
$181$	−9.80554	−	1.72898i	−0.728840	−	0.128514i	−0.203098	−	0.979158i	$-0.565101\pi$
$181$	−9.80554	−	1.72898i	−0.728840	−	0.128514i	−0.525742	+	0.850644i	$0.676212\pi$
$182$	−0.0744187	+	0.277735i	−0.00551628	+	0.0205871i
$183$	−15.0085	+	4.02151i	−1.10946	+	0.297279i
$184$	−4.75774	−	3.99222i	−0.350745	−	0.294310i
$185$	9.46464	−	5.55786i	0.695854	−	0.408622i
$186$	3.36732	+	9.25163i	0.246904	+	0.678363i
$187$	19.8203	+	1.73405i	1.44940	+	0.126806i
$188$	4.48836	+	3.14278i	0.327347	+	0.229211i
$189$	2.80065			0.203717
$190$	−9.07967	−	3.54395i	−0.658709	−	0.257105i
$191$	20.5307			1.48555			0.742773	−	0.669543i	$-0.233510\pi$
$191$	20.5307			1.48555			0.742773	+	0.669543i	$0.233510\pi$
$192$	0.819152	+	0.573576i	0.0591172	+	0.0413943i
$193$	−0.0652082	−	0.00570498i	−0.00469379	−	0.000410653i	0.0848086	−	0.996397i	$-0.472972\pi$
$193$	−0.0652082	−	0.00570498i	−0.00469379	−	0.000410653i	−0.0895024	+	0.995987i	$0.528528\pi$
$194$	1.36782	+	3.75807i	0.0982040	+	0.269813i
$195$	−0.0577802	+	0.222178i	−0.00413772	+	0.0159105i
$196$	0.646269	+	0.542284i	0.0461621	+	0.0387346i
$197$	15.1545	−	4.06064i	1.07971	−	0.289308i	0.325235	−	0.945633i	$-0.394557\pi$
$197$	15.1545	−	4.06064i	1.07971	−	0.289308i	0.754479	+	0.656325i	$0.227890\pi$
$198$	0.989910	−	3.69440i	0.0703499	−	0.262549i
$199$	7.10049	+	1.25201i	0.503341	+	0.0887525i	0.419553	−	0.907731i	$-0.362187\pi$
$199$	7.10049	+	1.25201i	0.503341	+	0.0887525i	0.0837881	+	0.996484i	$0.473298\pi$
$200$	3.48302	−	3.58728i	0.246286	−	0.253659i
$201$	5.79101	+	10.0303i	0.408467	+	0.707485i
$202$	−0.572819	−	2.13779i	−0.0403034	−	0.150414i
$203$	2.32795	+	26.6086i	0.163390	+	1.86756i
$204$	−4.88823	−	1.77917i	−0.342245	−	0.124567i
$205$	0.741286	+	1.55957i	0.0517737	+	0.108925i
$206$	13.1785	−	11.0581i	0.918191	−	0.770453i
$207$	3.56236	−	5.08758i	0.247601	−	0.353611i
$208$	−0.0725959	−	0.0725959i	−0.00503362	−	0.00503362i
$209$	−14.1776	−	8.77132i	−0.980687	−	0.606725i
$210$	4.82686	+	3.98994i	0.333085	+	0.275332i
$211$	−12.3647	+	2.18024i	−0.851223	+	0.150094i	−0.582206	−	0.813042i	$-0.697810\pi$
$211$	−12.3647	+	2.18024i	−0.851223	+	0.150094i	−0.269018	+	0.963135i	$0.586699\pi$
$212$	−0.247734	+	2.83161i	−0.0170144	+	0.194476i
$213$	−2.64755	+	5.67768i	−0.181407	+	0.389028i
$214$	1.72707	−	4.74508i	0.118060	−	0.324367i
$215$	−15.8444	+	2.91441i	−1.08058	+	0.198761i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−26.6339	−	7.13654i	−1.80803	−	0.484460i
$218$	−0.824146	−	1.17700i	−0.0558182	−	0.0797167i
$219$	0.754360	−	4.27819i	0.0509749	−	0.289093i
$220$	6.96930	−	4.95694i	0.469870	−	0.334197i
$221$	0.462513	+	0.267032i	0.0311120	+	0.0179625i
$222$	−4.88987	+	0.427808i	−0.328187	+	0.0287126i
$223$	−2.13371	−	4.57576i	−0.142884	−	0.306415i	0.821822	−	0.569744i	$-0.192958\pi$
$223$	−2.13371	−	4.57576i	−0.142884	−	0.306415i	−0.964706	+	0.263328i	$0.915180\pi$
$224$	−2.63175	+	0.957879i	−0.175841	+	0.0640010i
$225$	3.87720	+	3.15711i	0.258480	+	0.210474i
$226$	1.39633	+	7.91897i	0.0928824	+	0.526762i
$227$	4.01635	−	4.01635i	0.266575	−	0.266575i	−0.561144	−	0.827718i	$-0.689638\pi$
$227$	4.01635	−	4.01635i	0.266575	−	0.266575i	0.827718	+	0.561144i	$0.189638\pi$
$228$	2.98698	+	3.17458i	0.197817	+	0.210242i
$229$		−	28.5998i		−	1.88993i	−0.327170	−	0.944966i	$-0.606095\pi$
$229$		−	28.5998i		−	1.88993i	0.327170	−	0.944966i	$-0.393905\pi$
$230$	13.3877	−	3.69322i	0.882757	−	0.243524i
$231$	6.88535	+	8.20564i	0.453023	+	0.539892i
$232$	−8.64360	−	4.03058i	−0.567480	−	0.264620i
$233$	−1.60400	+	0.747956i	−0.105081	+	0.0490002i	−0.474448	−	0.880283i	$-0.657352\pi$
$233$	−1.60400	+	0.747956i	−0.105081	+	0.0490002i	0.369367	+	0.929284i	$0.379575\pi$
$234$	0.0659925	−	0.0786468i	0.00431407	−	0.00514130i
$235$	−11.4819	+	4.27521i	−0.748999	+	0.278884i
$236$	−6.20722	+	3.58374i	−0.404056	+	0.233282i
$237$	−8.03347	+	5.62509i	−0.521830	+	0.365389i
$238$	11.9341	−	8.35634i	0.773572	−	0.541661i
$239$	−12.1869	+	7.03611i	−0.788305	+	0.455128i	−0.839365	−	0.543568i	$-0.817073\pi$
$239$	−12.1869	+	7.03611i	−0.788305	+	0.455128i	0.0510608	+	0.998696i	$0.483740\pi$
$240$	−2.09552	+	0.780252i	−0.135265	+	0.0503650i
$241$	11.1457	−	13.2830i	0.717961	−	0.855632i	−0.276470	−	0.961022i	$-0.589165\pi$
$241$	11.1457	−	13.2830i	0.717961	−	0.855632i	0.994431	+	0.105390i	$0.0336092\pi$
$242$	3.28852	−	1.53346i	0.211394	−	0.0985747i
$243$	−0.906308	−	0.422618i	−0.0581397	−	0.0271110i
$244$	9.98758	+	11.9027i	0.639390	+	0.761995i
$245$	−1.81852	+	0.501670i	−0.116181	+	0.0320505i
$246$		−	0.772238i		−	0.0492361i
$247$	−0.245407	−	0.374222i	−0.0156149	−	0.0238112i
$248$	6.96174	−	6.96174i	0.442071	−	0.442071i
$249$	−2.25872	−	12.8098i	−0.143141	−	0.811791i
$250$	2.18449	+	10.9649i	0.138159	+	0.693478i
$251$	−3.37759	+	1.22934i	−0.213192	+	0.0775955i	−0.446408	−	0.894829i	$-0.647297\pi$
$251$	−3.37759	+	1.22934i	−0.213192	+	0.0775955i	0.233217	+	0.972425i	$0.425075\pi$
$252$	−1.18361	−	2.53825i	−0.0745602	−	0.159895i
$253$	23.6641	−	2.07034i	1.48775	−	0.130161i
$254$	−14.3003	−	8.25630i	−0.897282	−	0.518046i
$255$	9.47885	−	6.74186i	0.593589	−	0.422191i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.49777	−	2.13904i	−0.0934285	−	0.133430i	0.769717	−	0.638386i	$-0.220398\pi$
$257$	−1.49777	−	2.13904i	−0.0934285	−	0.133430i	−0.863145	+	0.504956i	$0.831509\pi$
$258$	6.95923	+	1.86472i	0.433263	+	0.116092i
$259$	6.87356	−	11.9054i	0.427102	−	0.739763i
$260$	0.225781	−	0.0415299i	0.0140023	−	0.00257558i
$261$	3.26190	−	8.96199i	0.201907	−	0.554734i
$262$	9.32145	−	19.9899i	0.575881	−	1.23498i
$263$	2.08995	−	23.8882i	0.128872	−	1.47301i	−0.606359	−	0.795191i	$-0.707371\pi$
$263$	2.08995	−	23.8882i	0.128872	−	1.47301i	0.735230	−	0.677817i	$-0.237074\pi$
$264$	−3.76661	+	0.664156i	−0.231819	+	0.0408760i
$265$	−4.89885	−	4.04945i	−0.300934	−	0.248756i
$266$	−12.0812	+	1.75299i	−0.740748	+	0.107483i
$267$	2.07320	+	2.07320i	0.126878	+	0.126878i
$268$	6.64318	−	9.48744i	0.405797	−	0.579538i
$269$	5.24657	−	4.40239i	0.319889	−	0.268419i	−0.468676	−	0.883370i	$-0.655269\pi$
$269$	5.24657	−	4.40239i	0.319889	−	0.268419i	0.788565	+	0.614952i	$0.210824\pi$
$270$	−0.959919	−	2.01954i	−0.0584188	−	0.122905i
$271$	6.40213	+	2.33018i	0.388902	+	0.141549i	0.529068	−	0.848579i	$-0.322542\pi$
$271$	6.40213	+	2.33018i	0.388902	+	0.141549i	−0.140167	+	0.990128i	$0.544764\pi$
$272$	0.453379	+	5.18215i	0.0274902	+	0.314214i
$273$	0.0744187	+	0.277735i	0.00450403	+	0.0168093i
$274$	5.60998	+	9.71677i	0.338911	+	0.587011i
$275$	0.281986	+	19.1215i	0.0170044	+	1.15307i
$276$	−6.11643	−	1.07849i	−0.368166	−	0.0649176i
$277$	−4.75250	+	17.7366i	−0.285550	+	1.06569i	0.662886	+	0.748720i	$0.269331\pi$
$277$	−4.75250	+	17.7366i	−0.285550	+	1.06569i	−0.948436	+	0.316968i	$0.897335\pi$
$278$	12.5874	−	3.37279i	0.754944	−	0.202287i
$279$	7.54200	+	6.32849i	0.451528	+	0.378877i
$280$	1.57620	−	6.06084i	0.0941958	−	0.362205i
$281$	−9.82938	−	27.0060i	−0.586372	−	1.61104i	−0.777084	−	0.629397i	$-0.783302\pi$
$281$	−9.82938	−	27.0060i	−0.586372	−	1.61104i	0.190712	−	0.981646i	$-0.438920\pi$
$282$	5.45842	+	0.477550i	0.325044	+	0.0284377i
$283$	−0.189830	−	0.132920i	−0.0112842	−	0.00790128i	0.567921	−	0.823083i	$-0.307748\pi$
$283$	−0.189830	−	0.132920i	−0.0112842	−	0.00790128i	−0.579205	+	0.815182i	$0.696637\pi$
$284$	6.26463			0.371737
$285$	−9.63520	+	1.47068i	−0.570740	+	0.0871159i
$286$	0.392669			0.0232190
$287$	1.77164	+	1.24051i	0.104576	+	0.0732252i
$288$	0.996195	+	0.0871557i	0.0587013	+	0.00513570i
$289$	−3.44081	−	9.45354i	−0.202400	−	0.556090i
$290$	18.3895	−	10.7987i	1.07987	−	0.634124i
$291$	3.06360	+	2.57067i	0.179592	+	0.150695i
$292$	−4.19616	+	1.12436i	−0.245562	+	0.0657981i
$293$	0.782270	−	2.91947i	0.0457007	−	0.170557i	−0.939304	−	0.343087i	$-0.888527\pi$
$293$	0.782270	−	2.91947i	0.0457007	−	0.170557i	0.985004	+	0.172530i	$0.0551941\pi$
$294$	0.830828	+	0.146497i	0.0484549	+	0.00854390i
$295$	1.27909	−	15.9759i	0.0744715	−	0.930151i
$296$	2.45427	+	4.25093i	0.142652	+	0.247080i
$297$	−0.989910	−	3.69440i	−0.0574404	−	0.214371i
$298$	0.208949	+	2.38830i	0.0121041	+	0.138351i
$299$	0.599183	+	0.218085i	0.0346517	+	0.0126122i
$300$	1.22274	−	4.84819i	0.0705949	−	0.279910i
$301$	−15.4572	+	12.9701i	−0.890937	+	0.747585i
$302$	−8.74670	+	12.4916i	−0.503316	+	0.718810i
$303$	−1.56497	−	1.56497i	−0.0899052	−	0.0899052i
$304$	1.61480	−	4.04876i	0.0926150	−	0.232212i
$305$	−34.5884	+	3.28323i	−1.98052	+	0.187997i
$306$	−5.12292	+	0.903308i	−0.292858	+	0.0516387i
$307$	0.683357	−	7.81081i	0.0390012	−	0.445786i	−0.951438	−	0.307839i	$-0.900394\pi$
$307$	0.683357	−	7.81081i	0.0390012	−	0.445786i	0.990440	−	0.137947i	$-0.0440504\pi$
$308$	4.52696	−	9.70810i	0.257948	−	0.553170i
$309$	5.88389	−	16.1658i	0.334723	−	0.919643i
$310$	3.98260	+	21.6517i	0.226196	+	1.22973i
$311$	12.8419	−	22.2429i	0.728199	−	1.26128i	−0.229445	−	0.973322i	$-0.573691\pi$
$311$	12.8419	−	22.2429i	0.728199	−	1.26128i	0.957644	−	0.287956i	$-0.0929756\pi$
$312$	−0.0991679	−	0.0265719i	−0.00561427	−	0.00150434i
$313$	3.35433	+	4.79048i	0.189598	+	0.270774i	0.902685	−	0.430301i	$-0.141593\pi$
$313$	3.35433	+	4.79048i	0.189598	+	0.270774i	−0.713087	+	0.701075i	$0.752704\pi$
$314$	0.687057	−	3.89649i	0.0387729	−	0.219892i
$315$	6.17515	+	1.04196i	0.347931	+	0.0587079i
$316$	8.49315	+	4.90353i	0.477777	+	0.275845i
$317$	−19.0534	+	1.66696i	−1.07015	+	0.0936256i	−0.608589	−	0.793485i	$-0.708264\pi$
$317$	−19.0534	+	1.66696i	−1.07015	+	0.0936256i	−0.461556	+	0.887111i	$0.652709\pi$
$318$	1.20126	+	2.57611i	0.0673633	+	0.144461i
$319$	34.2771	−	12.4759i	1.91915	−	0.698514i
$320$	1.59275	+	1.56944i	0.0890376	+	0.0877343i
$321$	−0.876855	−	4.97289i	−0.0489413	−	0.277560i
$322$	12.2996	−	12.2996i	0.685429	−	0.685429i
$323$	−2.66277	+	22.5179i	−0.148160	+	1.25293i
$324$			1.00000i			0.0555556i
$325$	−0.210059	+	0.468384i	−0.0116520	+	0.0259813i
$326$	−3.72862	−	4.44359i	−0.206509	−	0.246108i
$327$	−1.30223	−	0.607241i	−0.0720136	−	0.0335805i
$328$	−0.699885	+	0.326362i	−0.0386447	+	0.0180203i
$329$	−9.86392	+	11.7554i	−0.543815	+	0.648094i
$330$	3.55713	−	7.77748i	0.195813	−	0.428136i
$331$	−1.65952	+	0.958126i	−0.0912156	+	0.0526633i	−0.544914	−	0.838492i	$-0.683438\pi$
$331$	−1.65952	+	0.958126i	−0.0912156	+	0.0526633i	0.453698	+	0.891155i	$0.350104\pi$
$332$	−10.6551	+	7.46077i	−0.584773	+	0.409463i
$333$	−4.02085	+	2.81543i	−0.220341	+	0.154284i
$334$	0.361020	−	0.208435i	0.0197541	−	0.0114050i
$335$	9.03689	+	24.2704i	0.493738	+	1.32603i
$336$	−1.80022	+	2.14542i	−0.0982102	+	0.117042i
$337$	27.2341	−	12.6995i	1.48353	−	0.691783i	0.498940	−	0.866637i	$-0.333723\pi$
$337$	27.2341	−	12.6995i	1.48353	−	0.691783i	0.984594	+	0.174853i	$0.0559451\pi$
$338$	−11.7724	−	5.48958i	−0.640337	−	0.298594i
$339$	5.16874	+	6.15987i	0.280728	+	0.334558i
$340$	−10.1161	−	5.74152i	−0.548624	−	0.311378i
$341$			37.6558i			2.03918i
$342$	4.17409	+	1.25578i	0.225709	+	0.0679048i
$343$	12.1918	−	12.1918i	0.658295	−	0.658295i
$344$	−1.25109	−	7.09527i	−0.0674541	−	0.382551i
$345$	9.74745	−	9.89226i	0.524785	−	0.532581i
$346$	−8.80405	+	3.20441i	−0.473309	+	0.172270i
$347$	11.8915	+	25.5015i	0.638371	+	1.36899i	0.913205	+	0.407499i	$0.133599\pi$
$347$	11.8915	+	25.5015i	0.638371	+	1.36899i	−0.274835	+	0.961492i	$0.588623\pi$
$348$	−9.50086	+	0.831218i	−0.509300	+	0.0445580i
$349$	21.4679	+	12.3945i	1.14915	+	0.663462i	0.948680	−	0.316238i	$-0.102420\pi$
$349$	21.4679	+	12.3945i	1.14915	+	0.663462i	0.200470	+	0.979700i	$0.435753\pi$
$350$	9.15832	+	10.5932i	0.489533	+	0.566232i
$351$	0.0178278	−	0.101106i	0.000951577	−	0.00539666i
$352$	2.19377	+	3.13303i	0.116928	+	0.166991i
$353$	12.4782	+	3.34351i	0.664145	+	0.177957i	0.575116	−	0.818072i	$-0.304957\pi$
$353$	12.4782	+	3.34351i	0.664145	+	0.177957i	0.0890291	+	0.996029i	$0.471624\pi$
$354$	−3.58374	+	6.20722i	−0.190474	+	0.329910i
$355$	−7.94992	+	11.5337i	−0.421938	+	0.612146i
$356$	1.00279	−	2.75513i	0.0531475	−	0.146022i
$357$	6.15706	−	13.2038i	0.325866	−	0.698822i
$358$	−1.24995	+	14.2870i	−0.0660620	+	0.755092i
$359$	−22.5744	+	3.98048i	−1.19143	+	0.210082i	−0.733992	−	0.679158i	$-0.762345\pi$
$359$	−22.5744	+	3.98048i	−1.19143	+	0.210082i	−0.457441	+	0.889240i	$0.651234\pi$
$360$	−1.42465	+	1.72348i	−0.0750856	+	0.0908353i
$361$	10.4835	−	15.8460i	0.551762	−	0.834002i
$362$	7.04053	+	7.04053i	0.370042	+	0.370042i
$363$	2.08121	−	2.97228i	0.109235	−	0.156004i
$364$	0.220262	−	0.184822i	0.0115449	−	0.00968730i
$365$	3.25496	−	9.15232i	0.170372	−	0.479054i
$366$	14.6009	+	5.31428i	0.763200	+	0.277782i
$367$	1.77115	+	20.2443i	0.0924532	+	1.05674i	0.890754	+	0.454486i	$0.150177\pi$
$367$	1.77115	+	20.2443i	0.0924532	+	1.05674i	−0.798301	+	0.602259i	$0.794268\pi$
$368$	1.60747	+	5.99916i	0.0837952	+	0.312728i
$369$	−0.386119	−	0.668778i	−0.0201006	−	0.0348152i
$370$	−10.9408	−	0.875966i	−0.568787	−	0.0455393i
$371$	−7.83970	−	1.38235i	−0.407017	−	0.0717680i
$372$	2.54817	−	9.50991i	0.132117	−	0.493066i
$373$	−10.6042	+	2.84139i	−0.549065	+	0.147121i	−0.522678	−	0.852530i	$-0.675067\pi$
$373$	−10.6042	+	2.84139i	−0.549065	+	0.147121i	−0.0263870	+	0.999652i	$0.508400\pi$
$374$	−15.2412	−	12.7889i	−0.788104	−	0.661298i
$375$	7.37425	+	8.40360i	0.380805	+	0.433960i
$376$	−1.87402	−	5.14883i	−0.0966453	−	0.265531i
$377$	0.975417	+	0.0853379i	0.0502365	+	0.00439513i
$378$	−2.29416	−	1.60639i	−0.117999	−	0.0826236i
$379$	22.9480			1.17876			0.589381	−	0.807855i	$-0.299372\pi$
$379$	22.9480			1.17876			0.589381	+	0.807855i	$0.299372\pi$
$380$	5.40490	+	8.11092i	0.277266	+	0.416081i
$381$	−16.5126			−0.845966
$382$	−16.8177	−	11.7759i	−0.860470	−	0.602507i
$383$	−23.4275	−	2.04964i	−1.19709	−	0.104732i	−0.528874	−	0.848700i	$-0.677386\pi$
$383$	−23.4275	−	2.04964i	−1.19709	−	0.104732i	−0.668215	+	0.743969i	$0.732941\pi$
$384$	−0.342020	−	0.939693i	−0.0174536	−	0.0479535i
$385$	12.1287	+	20.6543i	0.618134	+	1.05264i
$386$	0.0501432	+	0.0420751i	0.00255222	+	0.00214157i
$387$	6.95923	−	1.86472i	0.353757	−	0.0947890i
$388$	1.03508	−	3.86298i	0.0525483	−	0.196113i
$389$	7.07981	+	1.24836i	0.358961	+	0.0632945i	0.350220	−	0.936667i	$-0.386107\pi$
$389$	7.07981	+	1.24836i	0.358961	+	0.0632945i	0.00874035	+	0.999962i	$0.497218\pi$
$390$	0.174767	−	0.148856i	0.00884966	−	0.00753763i
$391$	−16.1541	−	27.9797i	−0.816948	−	1.41499i
$392$	−0.218351	−	0.814898i	−0.0110284	−	0.0411586i
$393$	−1.92235	−	21.9725i	−0.0969695	−	1.10837i
$394$	−14.7429	−	5.36599i	−0.742738	−	0.270335i
$395$	−19.8058	+	9.41398i	−0.996536	+	0.473669i
$396$	−2.92991	+	2.45848i	−0.147233	+	0.123543i
$397$	−18.8611	+	26.9364i	−0.946611	+	1.35190i	−0.0105950	+	0.999944i	$0.503373\pi$
$397$	−18.8611	+	26.9364i	−0.946611	+	1.35190i	−0.936016	+	0.351957i	$0.885516\pi$
$398$	−5.09826	−	5.09826i	−0.255553	−	0.255553i
$399$	−9.58616	+	7.55875i	−0.479908	+	0.378411i
$400$	−4.91070	+	0.940754i	−0.245535	+	0.0470377i
$401$	15.6711	−	2.76324i	0.782579	−	0.137990i	0.231937	−	0.972731i	$-0.425494\pi$
$401$	15.6711	−	2.76324i	0.782579	−	0.137990i	0.550643	+	0.834741i	$0.314383\pi$
$402$	1.00944	−	11.5380i	0.0503463	−	0.575461i
$403$	−0.427177	+	0.916084i	−0.0212792	+	0.0456334i
$404$	−0.756960	+	2.07973i	−0.0376601	+	0.103470i
$405$	−1.84109	−	1.26902i	−0.0914843	−	0.0630579i
$406$	13.3551	−	23.1317i	0.662804	−	1.14801i
$407$	−18.1341	−	4.85902i	−0.898875	−	0.240853i
$408$	2.98371	+	4.26118i	0.147716	+	0.210960i
$409$	3.02022	−	17.1285i	0.149340	−	0.846950i	−0.814439	−	0.580249i	$-0.802955\pi$
$409$	3.02022	−	17.1285i	0.149340	−	0.846950i	0.963779	−	0.266701i	$-0.0859336\pi$
$410$	0.287306	−	1.70271i	0.0141890	−	0.0840907i
$411$	9.71677	+	5.60998i	0.479293	+	0.276720i
$412$	−17.1379	+	1.49937i	−0.844322	+	0.0738686i
$413$	−8.48348	−	18.1929i	−0.417445	−	0.895213i
$414$	−5.83623	+	2.12421i	−0.286835	+	0.104399i
$415$	−0.214445	−	29.0848i	−0.0105267	−	1.42771i
$416$	0.0178278	+	0.101106i	0.000874079	+	0.00495715i
$417$	9.21464	−	9.21464i	0.451243	−	0.451243i
$418$	6.58261	+	15.3170i	0.321966	+	0.749179i
$419$		−	19.8034i		−	0.967460i	−0.875217	−	0.483730i	$-0.839282\pi$
$419$		−	19.8034i		−	0.967460i	0.875217	−	0.483730i	$-0.160718\pi$
$420$	−1.66540	−	6.03694i	−0.0812630	−	0.294573i
$421$	−15.4323	−	18.3915i	−0.752123	−	0.896346i	0.245199	−	0.969473i	$-0.421147\pi$
$421$	−15.4323	−	18.3915i	−0.752123	−	0.896346i	−0.997323	+	0.0731270i	$0.976702\pi$
$422$	11.3791	+	5.30617i	0.553927	+	0.258300i
$423$	4.96591	−	2.31564i	0.241451	−	0.112590i
$424$	1.82707	−	2.17742i	0.0887306	−	0.105745i
$425$	23.4082	−	11.3386i	1.13546	−	0.550002i
$426$	5.42533	−	3.13231i	0.262858	−	0.151761i
$427$	−35.6465	+	24.9599i	−1.72505	+	1.20790i
$428$	−4.13640	+	2.89634i	−0.199940	+	0.140000i
$429$	0.340061	−	0.196335i	0.0164183	−	0.00947912i
$430$	14.6506	+	6.70065i	0.706517	+	0.323134i
$431$	−10.6657	+	12.7109i	−0.513751	+	0.612264i	−0.959091	−	0.283097i	$-0.908638\pi$
$431$	−10.6657	+	12.7109i	−0.513751	+	0.612264i	0.445341	+	0.895361i	$0.353083\pi$
$432$	0.906308	−	0.422618i	0.0436048	−	0.0203332i
$433$	4.89547	+	2.28279i	0.235261	+	0.109704i	0.536674	−	0.843790i	$-0.319680\pi$
$433$	4.89547	+	2.28279i	0.235261	+	0.109704i	−0.301413	+	0.953494i	$0.597458\pi$
$434$	17.7239	+	21.1225i	0.850774	+	1.01391i
$435$	10.5264	−	18.5467i	0.504703	−	0.889248i
$436$			1.43685i			0.0688129i
$437$	1.53763	+	27.0285i	0.0735551	+	1.29295i
$438$	−3.07180	+	3.07180i	−0.146776	+	0.146776i
$439$	1.33423	+	7.56677i	0.0636791	+	0.361142i	0.999951	+	0.00986686i	$0.00314077\pi$
$439$	1.33423	+	7.56677i	0.0636791	+	0.361142i	−0.936272	+	0.351275i	$0.885748\pi$
$440$	−8.55210	+	0.0630557i	−0.407705	+	0.00300606i
$441$	0.792767	−	0.288543i	0.0377508	−	0.0137402i
$442$	−0.225705	−	0.484026i	−0.0107357	−	0.0230228i
$443$	−11.0343	+	0.965373i	−0.524254	+	0.0458662i	−0.346211	−	0.938157i	$-0.612532\pi$
$443$	−11.0343	+	0.965373i	−0.524254	+	0.0458662i	−0.178042	+	0.984023i	$0.556976\pi$
$444$	4.25093	+	2.45427i	0.201740	+	0.116475i
$445$	3.79988	+	5.34252i	0.180132	+	0.253260i
$446$	−0.876713	+	4.97209i	−0.0415136	+	0.235435i
$447$	1.37511	+	1.96386i	0.0650403	+	0.0928872i
$448$	2.70522	+	0.724862i	0.127810	+	0.0342465i
$449$	2.19033	−	3.79375i	0.103368	−	0.179038i	−0.809702	−	0.586841i	$-0.800371\pi$
$449$	2.19033	−	3.79375i	0.103368	−	0.179038i	0.913070	+	0.407802i	$0.133705\pi$
$450$	−1.36517	−	4.81002i	−0.0643547	−	0.226747i
$451$	1.01019	−	2.77547i	0.0475679	−	0.130692i
$452$	3.39833	−	7.28774i	0.159844	−	0.342787i
$453$	−1.32907	+	15.1914i	−0.0624453	+	0.713754i
$454$	−5.59369	+	0.986319i	−0.262525	+	0.0462902i
$455$	0.0607568	+	0.640064i	0.00284832	+	0.0300067i
$456$	−0.625923	−	4.31372i	−0.0293115	−	0.202009i
$457$	18.9544	+	18.9544i	0.886651	+	0.886651i	0.994200	−	0.107549i	$-0.0343002\pi$
$457$	18.9544	+	18.9544i	0.886651	+	0.886651i	−0.107549	+	0.994200i	$0.534300\pi$
$458$	−16.4042	+	23.4276i	−0.766518	+	1.09470i
$459$	−3.98492	+	3.34375i	−0.186000	+	0.156073i
$460$	−13.0849	−	4.65354i	−0.610086	−	0.216972i
$461$	−19.7436	−	7.18608i	−0.919550	−	0.334689i	−0.161491	−	0.986874i	$-0.551630\pi$
$461$	−19.7436	−	7.18608i	−0.919550	−	0.334689i	−0.758060	+	0.652185i	$0.773852\pi$
$462$	−0.933587	−	10.6709i	−0.0434344	−	0.496457i
$463$	4.62278	+	17.2524i	0.214839	+	0.801789i	0.986223	+	0.165420i	$0.0528978\pi$
$463$	4.62278	+	17.2524i	0.214839	+	0.801789i	−0.771385	+	0.636369i	$0.780436\pi$
$464$	4.76858	+	8.25942i	0.221376	+	0.383434i
$465$	14.2749	+	16.7596i	0.661982	+	0.777209i
$466$	1.74293	+	0.307325i	0.0807395	+	0.0142366i
$467$	8.64005	−	32.2451i	0.399814	−	1.49213i	−0.413610	−	0.910454i	$-0.635732\pi$
$467$	8.64005	−	32.2451i	0.399814	−	1.49213i	0.813424	−	0.581672i	$-0.197601\pi$
$468$	−0.0991679	+	0.0265719i	−0.00458404	+	0.00122829i
$469$	24.8483	+	20.8502i	1.14739	+	0.962774i
$470$	11.8576	+	3.08372i	0.546951	+	0.142241i
$471$	−1.35324	−	3.71799i	−0.0623539	−	0.171316i
$472$	7.14021	+	0.624688i	0.328655	+	0.0287536i
$473$	22.5726	+	15.8055i	1.03789	+	0.726738i
$474$	9.80705			0.450453
$475$	−21.7918	−	0.341993i	−0.999877	−	0.0156917i
$476$	−14.5688			−0.667761
$477$	2.32838	+	1.63035i	0.106609	+	0.0746485i
$478$	14.0187	+	1.22647i	0.641199	+	0.0560976i
$479$	3.56092	+	9.78356i	0.162703	+	0.447022i	0.994075	−	0.108693i	$-0.0346666\pi$
$479$	3.56092	+	9.78356i	0.162703	+	0.447022i	−0.831373	+	0.555715i	$0.812444\pi$
$480$	2.16408	+	0.562797i	0.0987765	+	0.0256880i
$481$	−0.386042	−	0.323927i	−0.0176020	−	0.0147698i
$482$	−16.7489	+	4.48785i	−0.762890	+	0.204416i
$483$	4.50196	−	16.8016i	0.204846	−	0.764497i
$484$	−3.57336	−	0.630079i	−0.162425	−	0.0286400i
$485$	5.79854	+	6.80786i	0.263298	+	0.309129i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	3.01441	+	11.2499i	0.136596	+	0.509783i	0.999986	+	0.00524653i	$0.00167003\pi$
$487$	3.01441	+	11.2499i	0.136596	+	0.509783i	−0.863390	+	0.504537i	$0.831663\pi$
$488$	−1.35422	−	15.4788i	−0.0613026	−	0.700692i
$489$	−5.45087	−	1.98396i	−0.246497	−	0.0897176i
$490$	1.77739	+	0.632115i	0.0802942	+	0.0285561i
$491$	18.5272	−	15.5462i	0.836121	−	0.701589i	−0.120567	−	0.992705i	$-0.538471\pi$
$491$	18.5272	−	15.5462i	0.836121	−	0.701589i	0.956688	+	0.291117i	$0.0940268\pi$
$492$	−0.442938	+	0.632580i	−0.0199692	+	0.0285189i
$493$	−35.0808	−	35.0808i	−1.57996	−	1.57996i
$494$	−0.0136194	+	0.447304i	−0.000612765	+	0.0201252i
$495$	−0.808180	−	8.51406i	−0.0363250	−	0.382679i
$496$	−9.69581	+	1.70963i	−0.435355	+	0.0767648i
$497$	−1.52915	+	17.4783i	−0.0685918	+	0.784008i
$498$	−5.49719	+	11.7888i	−0.246335	+	0.528267i
$499$	−8.06092	+	22.1472i	−0.360857	+	0.991445i	0.617871	+	0.786280i	$0.287995\pi$
$499$	−8.06092	+	22.1472i	−0.360857	+	0.991445i	−0.978727	+	0.205166i	$0.934227\pi$
$500$	4.49975	−	10.2349i	0.201235	−	0.457717i
$501$	0.208435	−	0.361020i	0.00931218	−	0.0161292i
$502$	3.47189	+	0.930289i	0.154958	+	0.0415208i
$503$	−8.57341	−	12.2441i	−0.382269	−	0.545937i	0.581198	−	0.813762i	$-0.302584\pi$
$503$	−8.57341	−	12.2441i	−0.382269	−	0.545937i	−0.963468	+	0.267825i	$0.913695\pi$
$504$	−0.486328	+	2.75810i	−0.0216628	+	0.122856i
$505$	−2.86837	−	4.03284i	−0.127641	−	0.179459i
$506$	−20.5720	−	11.8773i	−0.914538	−	0.528009i
$507$	−12.9400	+	1.13211i	−0.574687	+	0.0502786i
$508$	6.97852	+	14.9655i	0.309622	+	0.663986i
$509$	−4.97101	+	1.80930i	−0.220336	+	0.0801959i	−0.449830	−	0.893114i	$-0.648515\pi$
$509$	−4.97101	+	1.80930i	−0.220336	+	0.0801959i	0.229493	+	0.973310i	$0.426293\pi$
$510$	−11.6316	+	0.0857611i	−0.515055	+	0.00379756i
$511$	−2.11270	−	11.9817i	−0.0934603	−	0.530040i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.24276	−	0.999507i	0.187322	−	0.0441293i
$514$			2.61129i			0.115179i
$515$	18.9878	−	33.4550i	0.836701	−	1.47420i
$516$	−4.63111	−	5.51914i	−0.203873	−	0.242966i
$517$	18.9932	+	8.85668i	0.835320	+	0.389516i
$518$	−12.4591	+	5.80979i	−0.547423	+	0.255267i
$519$	−6.02233	+	7.17713i	−0.264351	+	0.315041i
$520$	−0.208769	−	0.0954832i	−0.00915514	−	0.00418721i
$521$	−24.8182	+	14.3288i	−1.08730	+	0.627755i	−0.932857	−	0.360246i	$-0.882693\pi$
$521$	−24.8182	+	14.3288i	−1.08730	+	0.627755i	−0.154447	+	0.988001i	$0.549360\pi$
$522$	−7.81238	+	5.47029i	−0.341939	+	0.239428i
$523$	−26.4053	+	18.4892i	−1.15462	+	0.808476i	−0.984229	−	0.176900i	$-0.943393\pi$
$523$	−26.4053	+	18.4892i	−1.15462	+	0.808476i	−0.170395	+	0.985376i	$0.554504\pi$
$524$	−19.1014	+	11.0282i	−0.834450	+	0.481770i
$525$	13.2279	+	4.59484i	0.577315	+	0.200535i
$526$	−15.4137	+	18.3693i	−0.672068	+	0.800940i
$527$	46.4167	−	21.6445i	2.02194	−	0.942847i
$528$	3.46637	+	1.61640i	0.150855	+	0.0703446i
$529$	−10.0107	−	11.9303i	−0.435248	−	0.518709i
$530$	1.69024	+	6.12699i	0.0734191	+	0.266139i
$531$			7.16749i			0.311042i
$532$	10.9018	+	5.49355i	0.472655	+	0.238175i
$533$	0.0560613	−	0.0560613i	0.00242829	−	0.00242829i
$534$	−0.509128	−	2.88741i	−0.0220321	−	0.124950i
$535$	−0.0832496	−	11.2910i	−0.00359919	−	0.488151i
$536$	−10.8835	+	3.96129i	−0.470097	+	0.171101i
$537$	6.06101	+	12.9979i	0.261552	+	0.560900i
$538$	−6.82284	+	0.596921i	−0.294154	+	0.0257351i
$539$	2.79441	+	1.61335i	0.120364	+	0.0694920i
$540$	−0.372043	+	2.20490i	−0.0160102	+	0.0948838i
$541$	−6.50746	+	36.9056i	−0.279778	+	1.58670i	0.443587	+	0.896231i	$0.353706\pi$
$541$	−6.50746	+	36.9056i	−0.279778	+	1.58670i	−0.723364	+	0.690466i	$0.757405\pi$
$542$	−3.90778	−	5.58089i	−0.167853	−	0.239720i
$543$	9.61754	+	2.57701i	0.412728	+	0.110590i
$544$	2.60097	−	4.50502i	0.111516	−	0.193151i
$545$	−2.64537	−	1.82339i	−0.113315	−	0.0781055i
$546$	0.0983417	−	0.270192i	0.00420864	−	0.0115631i
$547$	−4.29460	+	9.20980i	−0.183624	+	0.393783i	−0.976474	−	0.215634i	$-0.930818\pi$
$547$	−4.29460	+	9.20980i	−0.183624	+	0.393783i	0.792850	+	0.609416i	$0.208596\pi$
$548$	0.977883	−	11.1773i	0.0417731	−	0.477469i
$549$	15.3019	−	2.69813i	0.653068	−	0.115153i
$550$	10.7367	−	15.8252i	0.457813	−	0.674788i
$551$	13.0228	+	39.4790i	0.554791	+	1.68186i
$552$	4.39169	+	4.39169i	0.186923	+	0.186923i
$553$	−15.7539	+	22.4989i	−0.669925	+	0.956752i
$554$	14.0663	−	11.8030i	0.597620	−	0.501463i
$555$	−9.91303	+	4.71181i	−0.420784	+	0.200005i
$556$	−12.2456	−	4.45703i	−0.519328	−	0.189020i
$557$	3.40978	+	38.9740i	0.144477	+	1.65138i	0.629589	+	0.776929i	$0.283223\pi$
$557$	3.40978	+	38.9740i	0.144477	+	1.65138i	−0.485112	+	0.874452i	$0.661221\pi$
$558$	−2.54817	−	9.50991i	−0.107873	−	0.402587i
$559$	0.369840	+	0.640583i	0.0156426	+	0.0270938i
$560$	−4.76750	+	4.06068i	−0.201464	+	0.171595i
$561$	−19.5937	−	3.45490i	−0.827248	−	0.145866i
$562$	−7.43825	+	27.7599i	−0.313764	+	1.17098i
$563$	−43.2062	+	11.5771i	−1.82092	+	0.487915i	−0.996903	−	0.0786437i	$-0.974941\pi$
$563$	−43.2062	+	11.5771i	−1.82092	+	0.487915i	−0.824021	+	0.566559i	$0.808274\pi$
$564$	−4.19737	−	3.52201i	−0.176741	−	0.148303i
$565$	9.10483	+	15.5049i	0.383043	+	0.652295i
$566$	0.0792595	+	0.217764i	0.00333153	+	0.00915329i
$567$	−2.78999	−	0.244093i	−0.117169	−	0.0102509i
$568$	−5.13168	−	3.59324i	−0.215321	−	0.150769i
$569$	19.9297			0.835498			0.417749	−	0.908562i	$-0.362819\pi$
$569$	19.9297			0.835498			0.417749	+	0.908562i	$0.362819\pi$
$570$	8.73624	+	4.32181i	0.365921	+	0.181021i
$571$	−15.5434			−0.650472			−0.325236	−	0.945633i	$-0.605444\pi$
$571$	−15.5434			−0.650472			−0.325236	+	0.945633i	$0.605444\pi$
$572$	−0.321656	−	0.225226i	−0.0134491	−	0.00941716i
$573$	−20.4525	−	1.78936i	−0.854417	−	0.0747518i
$574$	−0.739711	−	2.03234i	−0.0308749	−	0.0848282i
$575$	25.1725	−	18.1850i	1.04977	−	0.758366i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−5.50726	+	1.47567i	−0.229270	+	0.0614328i	−0.371625	−	0.928383i	$-0.621199\pi$
$577$	−5.50726	+	1.47567i	−0.229270	+	0.0614328i	0.142355	+	0.989816i	$0.454533\pi$
$578$	−2.60378	+	9.71745i	−0.108303	+	0.404193i
$579$	0.0644629	+	0.0113665i	0.00267898	+	0.000472377i
$580$	−21.2577	−	1.70197i	−0.882678	−	0.0706707i
$581$	−18.2147	−	31.5487i	−0.755672	−	1.30886i
$582$	−1.03508	−	3.86298i	−0.0429055	−	0.160126i
$583$	0.947511	+	10.8301i	0.0392419	+	0.448537i
$584$	4.08220	+	1.48580i	0.168923	+	0.0614828i
$585$	0.0769244	−	0.216297i	0.00318043	−	0.00894277i
$586$	−2.31534	+	1.94280i	−0.0956458	+	0.0802563i
$587$	6.11022	−	8.72630i	0.252196	−	0.360173i	−0.673013	−	0.739630i	$-0.735000\pi$
$587$	6.11022	−	8.72630i	0.252196	−	0.360173i	0.925209	+	0.379457i	$0.123889\pi$
$588$	−0.596547	−	0.596547i	−0.0246012	−	0.0246012i
$589$	−42.8951	−	1.30606i	−1.76746	−	0.0538152i
$590$	−10.2111	+	12.3530i	−0.420386	+	0.508565i
$591$	−15.4507	+	2.72438i	−0.635559	+	0.112066i
$592$	0.427808	−	4.88987i	0.0175828	−	0.200972i
$593$	−0.523861	+	1.12342i	−0.0215124	+	0.0461335i	−0.916770	−	0.399415i	$-0.869213\pi$
$593$	−0.523861	+	1.12342i	−0.0215124	+	0.0461335i	0.895258	+	0.445548i	$0.146991\pi$
$594$	−1.30813	+	3.59406i	−0.0536733	+	0.147466i
$595$	18.4881	−	26.8225i	0.757938	−	1.09961i
$596$	1.19871	−	2.07623i	0.0491012	−	0.0850457i
$597$	−6.96436	−	1.86609i	−0.285032	−	0.0763741i
$598$	−0.365734	−	0.522322i	−0.0149560	−	0.0213593i
$599$	1.28714	−	7.29972i	0.0525910	−	0.298258i	−0.947155	−	0.320775i	$-0.896057\pi$
$599$	1.28714	−	7.29972i	0.0525910	−	0.298258i	0.999746	+	0.0225165i	$0.00716782\pi$
$600$	−3.78241	+	3.27007i	−0.154416	+	0.133500i
$601$	26.1153	+	15.0777i	1.06527	+	0.615032i	0.926884	−	0.375347i	$-0.122477\pi$
$601$	26.1153	+	15.0777i	1.06527	+	0.615032i	0.138382	+	0.990379i	$0.455810\pi$
$602$	20.1011	−	1.75862i	0.819261	−	0.0716760i
$603$	−4.89478	−	10.4969i	−0.199331	−	0.427466i
$604$	14.3298	−	5.21561i	0.583070	−	0.212220i
$605$	5.69468	−	5.77928i	0.231522	−	0.234961i
$606$	0.384318	+	2.17958i	0.0156119	+	0.0885393i
$607$	−3.14753	+	3.14753i	−0.127754	+	0.127754i	−0.768093	−	0.640339i	$-0.778794\pi$
$607$	−3.14753	+	3.14753i	−0.127754	+	0.127754i	0.640339	+	0.768093i	$0.278794\pi$
$608$	−3.64504	+	2.39034i	−0.147826	+	0.0969410i
$609$		−	26.7102i		−	1.08235i
$610$	30.2163	+	17.1496i	1.22342	+	0.694367i
$611$	0.361591	+	0.430927i	0.0146284	+	0.0174335i
$612$	4.71456	+	2.19844i	0.190575	+	0.0888666i
$613$	−0.0917616	+	0.0427891i	−0.00370621	+	0.00172824i	−0.424470	−	0.905442i	$-0.639540\pi$
$613$	−0.0917616	+	0.0427891i	−0.00370621	+	0.00172824i	0.420764	+	0.907170i	$0.361762\pi$
$614$	−5.03987	+	6.00628i	−0.203393	+	0.242394i
$615$	−0.602540	−	1.61824i	−0.0242968	−	0.0652538i
$616$	−9.27661	+	5.35585i	−0.373765	+	0.215793i
$617$	24.4104	−	17.0924i	0.982728	−	0.688113i	0.0324358	−	0.999474i	$-0.489674\pi$
$617$	24.4104	−	17.0924i	0.982728	−	0.688113i	0.950292	+	0.311360i	$0.100785\pi$
$618$	−14.0921	+	9.86743i	−0.566869	+	0.396926i
$619$	0.182242	−	0.105217i	0.00732491	−	0.00422904i	−0.496333	−	0.868132i	$-0.665321\pi$
$619$	0.182242	−	0.105217i	0.00732491	−	0.00422904i	0.503658	+	0.863903i	$0.331987\pi$
$620$	9.15656	−	20.0204i	0.367736	−	0.804037i
$621$	−3.99222	+	4.75774i	−0.160202	+	0.190922i
$622$	−23.2775	+	10.8545i	−0.933342	+	0.435224i
$623$	7.44203	+	3.47027i	0.298158	+	0.139034i
$624$	0.0659925	+	0.0786468i	0.00264181	+	0.00314839i
$625$	13.1330	+	21.2726i	0.525320	+	0.850905i
$626$		−	5.84809i		−	0.233737i
$627$	13.3592	+	9.97361i	0.533515	+	0.398308i
$628$	−2.79774	+	2.79774i	−0.111642	+	0.111642i
$629$	4.43393	+	25.1461i	0.176792	+	1.00264i
$630$	−4.46075	−	4.39545i	−0.177720	−	0.175119i
$631$	6.18910	−	2.25265i	0.246384	−	0.0896765i	−0.215876	−	0.976421i	$-0.569261\pi$
$631$	6.18910	−	2.25265i	0.246384	−	0.0896765i	0.462260	+	0.886744i	$0.347039\pi$
$632$	−4.14464	−	8.88821i	−0.164865	−	0.353554i
$633$	12.5077	−	1.09428i	0.497136	−	0.0434938i
$634$	16.5638	+	9.56309i	0.657831	+	0.379799i
$635$	−36.4086	−	6.14339i	−1.44483	−	0.243793i
$636$	0.493582	−	2.79924i	0.0195718	−	0.110997i
$637$	0.0496796	+	0.0709498i	0.00196838	+	0.00281113i
$638$	−35.2340	−	9.44093i	−1.39493	−	0.373770i
$639$	3.13231	−	5.42533i	0.123912	−	0.214623i
$640$	−0.404514	−	2.19917i	−0.0159898	−	0.0869300i
$641$	−14.3451	+	39.4129i	−0.566598	+	1.55672i	0.243181	+	0.969981i	$0.421809\pi$
$641$	−14.3451	+	39.4129i	−0.566598	+	1.55672i	−0.809779	+	0.586735i	$0.800413\pi$
$642$	−2.13406	+	4.57650i	−0.0842245	+	0.180620i
$643$	−1.19669	+	13.6782i	−0.0471928	+	0.539416i	0.935393	+	0.353609i	$0.115046\pi$
$643$	−1.19669	+	13.6782i	−0.0471928	+	0.539416i	−0.982586	+	0.185807i	$0.940510\pi$
$644$	−17.1300	+	3.02048i	−0.675016	+	0.119024i
$645$	16.0382	−	1.52239i	0.631502	−	0.0599441i
$646$	15.0969	−	16.9183i	0.593981	−	0.665640i
$647$	−30.7518	−	30.7518i	−1.20898	−	1.20898i	−0.971358	−	0.237619i	$-0.923633\pi$
$647$	−30.7518	−	30.7518i	−1.20898	−	1.20898i	−0.237619	−	0.971358i	$-0.576367\pi$
$648$	0.573576	−	0.819152i	0.0225322	−	0.0321793i
$649$	−21.0001	+	17.6211i	−0.824324	+	0.691690i
$650$	0.440724	−	0.263193i	0.0172866	−	0.0103233i
$651$	25.9106	+	9.43068i	1.01552	+	0.369618i
$652$	0.505564	+	5.77863i	0.0197994	+	0.226308i
$653$	−5.19857	−	19.4013i	−0.203436	−	0.759232i	−0.989921	−	0.141623i	$-0.954768\pi$
$653$	−5.19857	−	19.4013i	−0.203436	−	0.759232i	0.786485	−	0.617609i	$-0.211899\pi$
$654$	0.718427	+	1.24435i	0.0280927	+	0.0486580i
$655$	3.93613	−	49.1624i	0.153797	−	1.92093i
$656$	0.760506	+	0.134098i	0.0296928	+	0.00523564i
$657$	−1.12436	+	4.19616i	−0.0438654	+	0.163708i
$658$	14.8226	−	3.97172i	0.577847	−	0.154834i
$659$	−2.40942	−	2.02174i	−0.0938577	−	0.0787559i	0.594651	−	0.803984i	$-0.297290\pi$
$659$	−2.40942	−	2.02174i	−0.0938577	−	0.0787559i	−0.688509	+	0.725228i	$0.741734\pi$
$660$	−7.37481	+	4.33066i	−0.287064	+	0.168571i
$661$	−9.91031	−	27.2283i	−0.385466	−	1.05906i	−0.969019	−	0.246985i	$-0.920560\pi$
$661$	−9.91031	−	27.2283i	−0.385466	−	1.05906i	0.583553	−	0.812075i	$-0.301662\pi$
$662$	1.90896	+	0.167012i	0.0741938	+	0.00649112i
$663$	−0.437479	−	0.306326i	−0.0169903	−	0.0118967i
$664$	13.0075			0.504787
$665$	−23.9487	+	13.0998i	−0.928691	+	0.507990i
$666$	4.90855			0.190202
$667$	−48.5210	−	33.9748i	−1.87874	−	1.31551i
$668$	−0.415283	−	0.0363326i	−0.0160678	−	0.00140575i
$669$	1.72679	+	4.74431i	0.0667615	+	0.183426i
$670$	6.51832	−	25.0645i	0.251825	−	0.968325i
$671$	45.5246	+	38.1997i	1.75746	+	1.47468i
$672$	2.70522	−	0.724862i	0.104356	−	0.0279621i
$673$	3.18220	−	11.8761i	0.122665	−	0.457791i	−0.877081	−	0.480343i	$-0.840512\pi$
$673$	3.18220	−	11.8761i	0.122665	−	0.457791i	0.999746	+	0.0225515i	$0.00717897\pi$
$674$	−29.5929	−	5.21804i	−1.13988	−	0.200991i
$675$	−3.58728	−	3.48302i	−0.138075	−	0.134061i
$676$	6.49473	+	11.2492i	0.249797	+	0.432662i
$677$	5.56521	+	20.7696i	0.213888	+	0.798242i	0.986555	+	0.163430i	$0.0522559\pi$
$677$	5.56521	+	20.7696i	0.213888	+	0.798242i	−0.772666	+	0.634812i	$0.781077\pi$
$678$	−0.700831	−	8.01054i	−0.0269153	−	0.307643i
$679$	10.5250	+	3.83080i	0.403914	+	0.147013i
$680$	4.99345	+	10.5056i	0.191490	+	0.402870i
$681$	−4.35112	+	3.65102i	−0.166735	+	0.139907i
$682$	21.5985	−	30.8458i	0.827049	−	1.18115i
$683$	22.3922	+	22.3922i	0.856812	+	0.856812i	0.990961	−	0.134149i	$-0.0428301\pi$
$683$	22.3922	+	22.3922i	0.856812	+	0.856812i	−0.134149	+	0.990961i	$0.542830\pi$
$684$	−2.69893	−	3.42283i	−0.103196	−	0.130875i
$685$	19.3373	+	15.9845i	0.738842	+	0.610736i
$686$	−16.9799	+	2.99401i	−0.648294	+	0.114312i
$687$	−2.49264	+	28.4910i	−0.0951002	+	1.08700i
$688$	−3.04485	+	6.52970i	−0.116084	+	0.248942i
$689$	−0.0998085	+	0.274222i	−0.00380240	+	0.0104470i
$690$	−13.6586	+	2.51235i	−0.519974	+	0.0956437i
$691$	11.8088	−	20.4534i	0.449227	−	0.778084i	−0.549109	−	0.835751i	$-0.685033\pi$
$691$	11.8088	−	20.4534i	0.449227	−	0.778084i	0.998336	+	0.0576665i	$0.0183660\pi$
$692$	9.04983	+	2.42490i	0.344023	+	0.0921807i
$693$	−6.14398	−	8.77451i	−0.233391	−	0.333316i
$694$	4.88607	−	27.7103i	0.185473	−	1.05187i
$695$	23.7456	−	16.8891i	0.900722	−	0.640641i
$696$	8.25942	+	4.76858i	0.313072	+	0.180752i
$697$	−4.00185	+	0.350117i	−0.151581	+	0.0132616i
$698$	−10.4763	−	22.4664i	−0.396533	−	0.850368i
$699$	1.66308	−	0.605312i	0.0629035	−	0.0228950i
$700$	−1.42603	−	13.9305i	−0.0538989	−	0.526522i
$701$	−0.00163464	−	0.00927049i	−6.17394e−5	−	0.000350142i	0.984777	−	0.173823i	$-0.0556121\pi$
$701$	−0.00163464	−	0.00927049i	−6.17394e−5	−	0.000350142i	−0.984839	+	0.173473i	$0.944501\pi$
$702$	−0.0725959	+	0.0725959i	−0.00273996	+	0.00273996i
$703$	6.16406	−	20.4887i	0.232482	−	0.772746i
$704$		−	3.82472i		−	0.144150i
$705$	11.8109	−	3.25823i	0.444822	−	0.122712i
$706$	−8.30375	−	9.89602i	−0.312516	−	0.372442i
$707$	−5.61766	−	2.61956i	−0.211274	−	0.0985187i
$708$	6.49595	−	3.02911i	0.244133	−	0.113841i
$709$	16.1426	−	19.2380i	0.606247	−	0.722497i	−0.372394	−	0.928075i	$-0.621463\pi$
$709$	16.1426	−	19.2380i	0.606247	−	0.722497i	0.978641	+	0.205578i	$0.0659074\pi$
$710$	13.1277	−	4.88799i	0.492672	−	0.183443i
$711$	8.49315	−	4.90353i	0.318518	−	0.183897i
$712$	−2.40171	+	1.68170i	−0.0900080	+	0.0630243i
$713$	50.0892	−	35.0728i	1.87585	−	1.31349i
$714$	−12.6170	+	7.28442i	−0.472179	+	0.272612i
$715$	0.822846	−	0.306381i	0.0307727	−	0.0114580i
$716$	9.21859	−	10.9863i	0.344515	−	0.410577i
$717$	12.7538	−	5.94717i	0.476298	−	0.222101i
$718$	20.7750	+	9.68755i	0.775317	+	0.361536i
$719$	−0.466501	−	0.555954i	−0.0173976	−	0.0207336i	0.757276	−	0.653096i	$-0.226530\pi$
$719$	−0.466501	−	0.555954i	−0.0173976	−	0.0207336i	−0.774673	+	0.632362i	$0.782086\pi$
$720$	2.15555	−	0.594646i	0.0803326	−	0.0221611i
$721$		−	48.1805i		−	1.79434i
$722$	−17.6765	+	6.96723i	−0.657850	+	0.259294i
$723$	−12.2610	+	12.2610i	−0.455992	+	0.455992i
$724$	−1.72898	−	9.80554i	−0.0642571	−	0.364420i
$725$	30.1099	−	36.9774i	1.11825	−	1.37331i
$726$	−3.40966	+	1.24101i	−0.126544	+	0.0460584i
$727$	2.93541	+	6.29501i	0.108868	+	0.233469i	0.953193	−	0.302363i	$-0.0977756\pi$
$727$	2.93541	+	6.29501i	0.108868	+	0.233469i	−0.844324	+	0.535832i	$0.819998\pi$
$728$	−0.286438	+	0.0250601i	−0.0106161	+	0.000928788i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	−7.91586	+	5.63018i	−0.292979	+	0.208382i
$731$	6.50809	−	36.9092i	0.240710	−	1.36514i
$732$	−8.91219	−	12.7279i	−0.329404	−	0.470437i
$733$	20.6697	+	5.53842i	0.763451	+	0.204566i	0.619476	−	0.785015i	$-0.287345\pi$
$733$	20.6697	+	5.53842i	0.763451	+	0.204566i	0.143975	+	0.989581i	$0.454012\pi$
$734$	10.1608	−	17.5991i	0.375043	−	0.649593i
$735$	1.85532	−	0.341266i	0.0684346	−	0.0125878i
$736$	2.12421	−	5.83623i	0.0782996	−	0.215126i
$737$	18.7211	−	40.1476i	0.689602	−	1.47886i
$738$	−0.0673050	+	0.769300i	−0.00247753	+	0.0283183i
$739$	−17.0220	+	3.00144i	−0.626164	+	0.110410i	−0.477721	−	0.878511i	$-0.658537\pi$
$739$	−17.0220	+	3.00144i	−0.626164	+	0.110410i	−0.148443	+	0.988921i	$0.547426\pi$
$740$	8.45977	+	6.99296i	0.310988	+	0.257066i
$741$	0.211857	+	0.394186i	0.00778277	+	0.0144808i
$742$	5.62902	+	5.62902i	0.206648	+	0.206648i
$743$	9.37197	−	13.3846i	0.343824	−	0.491032i	−0.609581	−	0.792724i	$-0.708662\pi$
$743$	9.37197	−	13.3846i	0.343824	−	0.491032i	0.953406	+	0.301692i	$0.0975513\pi$
$744$	−7.54200	+	6.32849i	−0.276503	+	0.232014i
$745$	2.30133	+	4.84170i	0.0843143	+	0.177386i
$746$	10.3162	+	3.75479i	0.377703	+	0.137473i
$747$	1.13367	+	12.9580i	0.0414790	+	0.474107i
$748$	5.14946	+	19.2180i	0.188283	+	0.702681i
$749$	−7.07109	−	12.2475i	−0.258372	−	0.447514i
$750$	−1.22053	−	11.1135i	−0.0445674	−	0.405808i
$751$	−31.4941	−	5.55326i	−1.14924	−	0.202641i	−0.433593	−	0.901109i	$-0.642755\pi$
$751$	−31.4941	−	5.55326i	−1.14924	−	0.202641i	−0.715642	+	0.698467i	$0.753866\pi$
$752$	−1.41814	+	5.29257i	−0.0517143	+	0.193000i
$753$	3.47189	−	0.930289i	0.126523	−	0.0339016i
$754$	−0.750067	−	0.629381i	−0.0273158	−	0.0229207i
$755$	−8.58232	+	33.0010i	−0.312343	+	1.20103i
$756$	0.957879	+	2.63175i	0.0348377	+	0.0957159i
$757$	34.7726	+	3.04221i	1.26383	+	0.110571i	0.699294	−	0.714835i	$-0.253498\pi$
$757$	34.7726	+	3.04221i	1.26383	+	0.110571i	0.564540	+	0.825406i	$0.309054\pi$
$758$	−18.7979	−	13.1625i	−0.682772	−	0.478082i
$759$	−23.7545			−0.862235
$760$	0.224793	−	9.74420i	0.00815410	−	0.353459i
$761$	11.5270			0.417852			0.208926	−	0.977931i	$-0.433003\pi$
$761$	11.5270			0.417852			0.208926	+	0.977931i	$0.433003\pi$
$762$	13.5263	+	9.47123i	0.490007	+	0.343107i
$763$	−4.00881	−	0.350726i	−0.145129	−	0.0126971i
$764$	7.02190	+	19.2925i	0.254043	+	0.697978i
$765$	−10.0304	+	5.89007i	−0.362649	+	0.212956i
$766$	18.0151	+	15.1164i	0.650910	+	0.546179i
$767$	−0.710784	+	0.190454i	−0.0256649	+	0.00687690i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	−17.9060	−	3.15731i	−0.645706	−	0.113855i	−0.158801	−	0.987311i	$-0.550763\pi$
$769$	−17.9060	−	3.15731i	−0.645706	−	0.113855i	−0.486905	+	0.873455i	$0.661874\pi$
$770$	1.91158	−	23.8757i	0.0688886	−	0.860420i
$771$	1.30564	+	2.26144i	0.0470216	+	0.0814438i
$772$	−0.0169416	−	0.0632269i	−0.000609741	−	0.00227559i
$773$	−0.739828	−	8.45628i	−0.0266098	−	0.304151i	−0.997824	−	0.0659413i	$-0.978995\pi$
$773$	−0.739828	−	8.45628i	−0.0266098	−	0.304151i	0.971214	−	0.238210i	$-0.0765606\pi$
$774$	−6.77022	−	2.46416i	−0.243351	−	0.0885724i
$775$	25.2394	+	42.2642i	0.906626	+	1.51817i
$776$	−3.06360	+	2.57067i	−0.109977	+	0.0922816i
$777$	−7.88503	+	11.2610i	−0.282874	+	0.403986i
$778$	−5.08341	−	5.08341i	−0.182249	−	0.182249i
$779$	3.12660	+	1.24701i	0.112022	+	0.0446787i
$780$	−0.228541	+	0.0216938i	−0.00818308	+	0.000776763i
$781$	23.5964	−	4.16069i	0.844347	−	0.148881i
$782$	−2.81584	+	32.1852i	−0.100694	+	1.15094i
$783$	−4.03058	+	8.64360i	−0.144041	+	0.308897i
$784$	−0.288543	+	0.792767i	−0.0103051	+	0.0283131i
$785$	−1.60050	−	8.70126i	−0.0571244	−	0.310561i
$786$	−11.0282	+	19.1014i	−0.393364	+	0.681326i
$787$	−16.6467	−	4.46046i	−0.593389	−	0.158998i	−0.0503874	−	0.998730i	$-0.516046\pi$
$787$	−16.6467	−	4.46046i	−0.593389	−	0.158998i	−0.543002	+	0.839732i	$0.682712\pi$
$788$	8.99890	+	12.8518i	0.320572	+	0.457825i
$789$	−4.16398	+	23.6151i	−0.148242	+	0.840721i
$790$	21.6236	+	3.64864i	0.769332	+	0.129813i
$791$	19.5032	+	11.2602i	0.693456	+	0.400367i
$792$	3.81017	−	0.333346i	0.135388	−	0.0118449i
$793$	0.674168	+	1.44576i	0.0239404	+	0.0513404i
$794$	30.9002	−	11.2468i	1.09661	−	0.399132i
$795$	4.52728	+	4.46101i	0.160566	+	0.158216i
$796$	1.25201	+	7.10049i	0.0443763	+	0.251670i
$797$	−5.04838	+	5.04838i	−0.178823	+	0.178823i	−0.790842	−	0.612020i	$-0.790357\pi$
$797$	−5.04838	+	5.04838i	−0.178823	+	0.178823i	0.612020	+	0.790842i	$0.290357\pi$
$798$	12.1880	−	0.693371i	0.431452	−	0.0245451i
$799$		−	28.5029i		−	1.00836i
$800$	4.56220	+	2.04604i	0.161298	+	0.0723385i
$801$	−1.88462	−	2.24600i	−0.0665898	−	0.0793586i
$802$	−14.4220	−	6.72508i	−0.509258	−	0.237471i
$803$	−15.0586	+	7.02193i	−0.531405	+	0.247798i
$804$	−7.44478	+	8.87235i	−0.262557	+	0.312903i
$805$	16.1773	−	35.3708i	0.570174	−	1.24666i
$806$	0.875367	−	0.505394i	0.0308335	−	0.0178017i
$807$	−5.61029	+	3.92837i	−0.197492	+	0.138285i
$808$	1.81295	−	1.26944i	0.0637793	−	0.0446588i
$809$	−32.9263	+	19.0100i	−1.15763	+	0.668356i	−0.950734	−	0.310008i	$-0.899668\pi$
$809$	−32.9263	+	19.0100i	−1.15763	+	0.668356i	−0.206893	+	0.978364i	$0.566335\pi$
$810$	0.780252	+	2.09552i	0.0274152	+	0.0736291i
$811$	15.8116	−	18.8436i	0.555222	−	0.661687i	−0.413306	−	0.910592i	$-0.635626\pi$
$811$	15.8116	−	18.8436i	0.555222	−	0.661687i	0.968528	+	0.248905i	$0.0800706\pi$
$812$	−24.2077	+	11.2882i	−0.849524	+	0.396139i
$813$	−6.17468	−	2.87930i	−0.216555	−	0.100981i
$814$	12.0676	+	14.3816i	0.422968	+	0.504074i
$815$	−11.2805	−	6.40238i	−0.395139	−	0.224266i
$816$		−	5.20195i		−	0.182105i
$817$	−18.7875	+	25.1651i	−0.657293	+	0.880414i
$818$	−12.2985	+	12.2985i	−0.430008	+	0.430008i
$819$	−0.0499294	−	0.283164i	−0.00174467	−	0.00989454i
$820$	−1.21198	+	1.22998i	−0.0423242	+	0.0429529i
$821$	9.87744	−	3.59509i	0.344725	−	0.125470i	−0.163855	−	0.986484i	$-0.552393\pi$
$821$	9.87744	−	3.59509i	0.344725	−	0.125470i	0.508580	+	0.861015i	$0.330171\pi$
$822$	−4.74176	−	10.1687i	−0.165388	−	0.354675i
$823$	−19.1117	+	1.67206i	−0.666193	+	0.0582844i	−0.415236	−	0.909714i	$-0.636301\pi$
$823$	−19.1117	+	1.67206i	−0.666193	+	0.0582844i	−0.250957	+	0.967998i	$0.580745\pi$
$824$	14.8985	+	8.60167i	0.519015	+	0.299653i
$825$	1.38564	−	19.0733i	0.0482417	−	0.664048i
$826$	−3.48575	+	19.7687i	−0.121285	+	0.687840i
$827$	4.97713	+	7.10808i	0.173072	+	0.247172i	0.896312	−	0.443425i	$-0.146237\pi$
$827$	4.97713	+	7.10808i	0.173072	+	0.247172i	−0.723240	+	0.690597i	$0.757348\pi$
$828$	5.99916	+	1.60747i	0.208485	+	0.0558635i
$829$	4.79700	−	8.30865i	0.166607	−	0.288571i	−0.770618	−	0.637297i	$-0.780052\pi$
$829$	4.79700	−	8.30865i	0.166607	−	0.288571i	0.937225	+	0.348726i	$0.113386\pi$
$830$	−16.5067	+	23.9478i	−0.572955	+	0.831242i
$831$	6.28026	−	17.2549i	0.217860	−	0.598565i
$832$	0.0433886	−	0.0930471i	0.00150423	−	0.00322583i
$833$	0.382491	−	4.37189i	0.0132525	−	0.151477i
$834$	−12.8335	+	2.26289i	−0.444388	+	0.0783575i
$835$	0.593893	−	0.718466i	0.0205525	−	0.0248635i
$836$	3.39331	−	16.3226i	0.117360	−	0.564528i
$837$	−6.96174	−	6.96174i	−0.240633	−	0.240633i
$838$	−11.3588	+	16.2220i	−0.392382	+	0.560380i
$839$	−7.98253	+	6.69814i	−0.275587	+	0.231245i	−0.770097	−	0.637927i	$-0.779792\pi$
$839$	−7.98253	+	6.69814i	−0.275587	+	0.231245i	0.494509	+	0.869172i	$0.335348\pi$
$840$	−2.09844	+	5.90041i	−0.0724029	+	0.203583i
$841$	−58.2209	−	21.1907i	−2.00762	−	0.730712i
$842$	2.09247	+	23.9170i	0.0721112	+	0.824234i
$843$	7.43825	+	27.7599i	0.256187	+	0.956103i
$844$	−6.27774	−	10.8734i	−0.216089	−	0.374277i
$845$	−28.9527	−	2.31806i	−0.996002	−	0.0797438i
$846$	−5.39603	−	0.951466i	−0.185519	−	0.0327121i
$847$	2.63015	−	9.81585i	0.0903730	−	0.337276i
$848$	−2.74557	+	0.735673i	−0.0942833	+	0.0252631i
$849$	0.177523	+	0.148959i	0.00609256	+	0.00511226i
$850$	−25.6784	−	4.13835i	−0.880762	−	0.141944i
$851$	10.4268	+	28.6474i	0.357426	+	0.982021i
$852$	−6.24079	−	0.545998i	−0.213806	−	0.0187056i
$853$	17.0995	+	11.9732i	0.585475	+	0.409954i	0.828438	−	0.560081i	$-0.189230\pi$
$853$	17.0995	+	11.9732i	0.585475	+	0.409954i	−0.242962	+	0.970036i	$0.578119\pi$
$854$	43.5163			1.48910
$855$	9.72671	−	0.625325i	0.332647	−	0.0213857i
$856$	5.04961			0.172592
$857$	12.5129	+	8.76164i	0.427433	+	0.299292i	0.767428	−	0.641136i	$-0.221536\pi$
$857$	12.5129	+	8.76164i	0.427433	+	0.299292i	−0.339995	+	0.940427i	$0.610425\pi$
$858$	−0.391175	−	0.0342234i	−0.0133545	−	0.00116837i
$859$	4.43889	+	12.1958i	0.151453	+	0.416114i	0.992097	−	0.125475i	$-0.0400454\pi$
$859$	4.43889	+	12.1958i	0.151453	+	0.416114i	−0.840644	+	0.541588i	$0.817823\pi$
$860$	−8.15777	−	13.8921i	−0.278178	−	0.473717i
$861$	−1.65678	−	1.39020i	−0.0564628	−	0.0473779i
$862$	16.0276	−	4.29457i	0.545901	−	0.146274i
$863$	−9.18543	+	34.2805i	−0.312676	+	1.16692i	0.613459	+	0.789727i	$0.289778\pi$
$863$	−9.18543	+	34.2805i	−0.312676	+	1.16692i	−0.926134	+	0.377194i	$0.876889\pi$
$864$	−0.984808	−	0.173648i	−0.0335038	−	0.00590763i
$865$	−15.9488	+	13.5843i	−0.542276	+	0.461880i
$866$	−2.70077	−	4.67788i	−0.0917761	−	0.158961i
$867$	2.60378	+	9.71745i	0.0884291	+	0.330022i
$868$	−2.40319	−	27.4685i	−0.0815695	−	0.932343i
$869$	35.2471	+	12.8289i	1.19568	+	0.435191i
$870$	−19.2607	+	9.15490i	−0.652999	+	0.310380i
$871$	0.910889	−	0.764327i	0.0308643	−	0.0258982i
$872$	0.824146	−	1.17700i	0.0279091	−	0.0398583i
$873$	−2.82790	−	2.82790i	−0.0957098	−	0.0957098i
$874$	14.2434	−	23.0224i	0.481789	−	0.778744i
$875$	27.4568	+	15.0525i	0.928210	+	0.508868i
$876$	4.27819	−	0.754360i	0.144547	−	0.0254875i
$877$	−3.01329	+	34.4420i	−0.101752	+	1.16303i	0.757980	+	0.652278i	$0.226187\pi$
$877$	−3.01329	+	34.4420i	−0.101752	+	1.16303i	−0.859731	+	0.510747i	$0.829369\pi$
$878$	3.24719	−	6.96361i	0.109587	−	0.235011i
$879$	−1.03374	+	2.84018i	−0.0348673	+	0.0957970i
$880$	7.04164	+	4.85363i	0.237374	+	0.163616i
$881$	10.9872	−	19.0305i	0.370170	−	0.641153i	−0.619422	−	0.785059i	$-0.712633\pi$
$881$	10.9872	−	19.0305i	0.370170	−	0.641153i	0.989591	+	0.143906i	$0.0459662\pi$
$882$	−0.814898	−	0.218351i	−0.0274390	−	0.00735227i
$883$	−10.1221	−	14.4559i	−0.340636	−	0.486479i	0.611887	−	0.790945i	$-0.290411\pi$
$883$	−10.1221	−	14.4559i	−0.340636	−	0.486479i	−0.952523	+	0.304466i	$0.901522\pi$
$884$	−0.0927392	+	0.525950i	−0.00311916	+	0.0176896i
$885$	−2.66661	+	15.8036i	−0.0896371	+	0.531232i
$886$	9.59245	+	5.53821i	0.322265	+	0.186060i
$887$	41.1249	−	3.59797i	1.38084	−	0.120808i	0.627591	−	0.778543i	$-0.284041\pi$
$887$	41.1249	−	3.59797i	1.38084	−	0.120808i	0.753249	+	0.657735i	$0.228485\pi$
$888$	−2.07444	−	4.44866i	−0.0696137	−	0.149287i
$889$	−43.4570	+	15.8171i	−1.45750	+	0.530487i
$890$	−0.0483371	−	6.55586i	−0.00162026	−	0.219753i
$891$	0.664156	+	3.76661i	0.0222501	+	0.126186i
$892$	3.57003	−	3.57003i	0.119534	−	0.119534i
$893$	−10.7477	+	21.3287i	−0.359659	+	0.713737i
$894$		−	2.39742i		−	0.0801819i
$895$	8.52816	+	30.9140i	0.285065	+	1.03334i
$896$	−1.80022	−	2.14542i	−0.0601412	−	0.0716735i
$897$	−0.577896	−	0.269477i	−0.0192954	−	0.00899759i
$898$	−3.97022	+	1.85134i	−0.132488	+	0.0617801i
$899$	60.3558	−	71.9292i	2.01298	−	2.39897i
$900$	−1.64063	+	4.72317i	−0.0546878	+	0.157439i
$901$	12.8052	−	7.39307i	0.426602	−	0.246299i
$902$	−2.41944	+	1.69411i	−0.0805586	+	0.0564078i
$903$	16.5288	−	11.5736i	0.550043	−	0.385144i
$904$	−6.96383	+	4.02057i	−0.231613	+	0.133722i
$905$	20.2470	+	9.26019i	0.673032	+	0.307819i
$906$	9.80213	−	11.6817i	0.325654	−	0.388099i
$907$	26.8985	−	12.5430i	0.893149	−	0.416482i	0.0788219	−	0.996889i	$-0.474884\pi$
$907$	26.8985	−	12.5430i	0.893149	−	0.416482i	0.814327	+	0.580407i	$0.197106\pi$
$908$	5.14781	+	2.40046i	0.170836	+	0.0796622i
$909$	1.42262	+	1.69541i	0.0471853	+	0.0562332i
$910$	0.317357	−	0.559158i	0.0105203	−	0.0185359i
$911$			24.8396i			0.822971i	0.911416	+	0.411486i	$0.134990\pi$
$911$			24.8396i			0.822971i	−0.911416	+	0.411486i	$0.865010\pi$
$912$	−1.96153	+	3.89261i	−0.0649526	+	0.128897i
$913$	−35.1785	+	35.1785i	−1.16424	+	1.16424i
$914$	−4.65475	−	26.3984i	−0.153965	−	0.873181i
$915$	34.7429	−	0.256164i	1.14857	−	0.00846851i
$916$	26.8751	−	9.78172i	0.887977	−	0.323197i
$917$	−26.1061	−	55.9848i	−0.862101	−	1.84878i
$918$	5.18215	−	0.453379i	0.171036	−	0.0149638i
$919$	−27.0957	−	15.6437i	−0.893806	−	0.516039i	−0.0186206	−	0.999827i	$-0.505927\pi$
$919$	−27.0957	−	15.6437i	−0.893806	−	0.516039i	−0.875186	+	0.483787i	$0.839261\pi$
$920$	8.04934	+	11.3171i	0.265379	+	0.373115i
$921$	−1.36151	+	7.72153i	−0.0448634	+	0.254433i
$922$	12.0512	+	17.2109i	0.396886	+	0.566812i
$923$	0.621250	+	0.166463i	0.0204487	+	0.00547921i
$924$	−5.35585	+	9.27661i	−0.176195	+	0.305178i
$925$	−23.6102	+	6.70100i	−0.776299	+	0.220328i
$926$	6.10883	−	16.7839i	0.200749	−	0.551553i
$927$	−7.27044	+	15.5915i	−0.238793	+	0.512092i
$928$	0.831218	−	9.50086i	0.0272861	−	0.311881i
$929$	23.6303	−	4.16666i	0.775285	−	0.136704i	0.228013	−	0.973658i	$-0.426777\pi$
$929$	23.6303	−	4.16666i	0.775285	−	0.136704i	0.547273	+	0.836954i	$0.315666\pi$
$930$	−2.08037	−	21.9164i	−0.0682181	−	0.718668i
$931$	−1.93475	+	3.12726i	−0.0634089	+	0.102492i
$932$	−1.25145	−	1.25145i	−0.0409925	−	0.0409925i
$933$	−14.7317	+	21.0390i	−0.482293	+	0.688785i
$934$	−25.5726	+	21.4579i	−0.836760	+	0.702125i
$935$	−41.9168	−	14.9074i	−1.37083	−	0.487525i
$936$	0.0964746	+	0.0351139i	0.00315337	+	0.00114773i
$937$	1.11895	+	12.7897i	0.0365546	+	0.417821i	0.992321	+	0.123693i	$0.0394737\pi$
$937$	1.11895	+	12.7897i	0.0365546	+	0.417821i	−0.955766	+	0.294128i	$0.904971\pi$
$938$	−8.39537	−	31.3319i	−0.274118	−	1.02302i
$939$	−2.92405	−	5.06460i	−0.0954227	−	0.165277i
$940$	−7.94444	−	9.32728i	−0.259119	−	0.304222i
$941$	−18.1751	−	3.20476i	−0.592492	−	0.104472i	−0.130641	−	0.991430i	$-0.541703\pi$
$941$	−18.1751	−	3.20476i	−0.592492	−	0.104472i	−0.461851	+	0.886957i	$0.652815\pi$
$942$	−1.02404	+	3.82178i	−0.0333652	+	0.124520i
$943$	−4.63278	+	1.24135i	−0.150864	+	0.0404239i
$944$	−5.49061	−	4.60717i	−0.178704	−	0.149951i
$945$	−6.06084	−	1.57620i	−0.197159	−	0.0512737i
$946$	−9.42472	−	25.8942i	−0.306424	−	0.841893i
$947$	4.07320	+	0.356359i	0.132361	+	0.0115801i	0.153144	−	0.988204i	$-0.451060\pi$
$947$	4.07320	+	0.356359i	0.132361	+	0.0115801i	−0.0207825	+	0.999784i	$0.506616\pi$
$948$	−8.03347	−	5.62509i	−0.260915	−	0.182695i
$949$	−0.446001			−0.0144778
$950$	17.6546	+	12.7794i	0.572792	+	0.414619i
$951$	19.1262			0.620209
$952$	11.9341	+	8.35634i	0.386786	+	0.270831i
$953$	50.0836	+	4.38175i	1.62237	+	0.141939i	0.861775	−	0.507291i	$-0.169353\pi$
$953$	50.0836	+	4.38175i	1.62237	+	0.141939i	0.760592	+	0.649230i	$0.224909\pi$
$954$	−0.972166	−	2.67100i	−0.0314750	−	0.0864770i
$955$	−44.4301	−	11.5546i	−1.43772	−	0.373898i
$956$	−10.7799	−	9.04544i	−0.348648	−	0.292551i
$957$	−35.2340	+	9.44093i	−1.13895	+	0.305182i
$958$	2.69468	−	10.0567i	0.0870611	−	0.324917i
$959$	30.9458	+	5.45658i	0.999292	+	0.176202i
$960$	−1.44991	−	1.70228i	−0.0467955	−	0.0549410i
$961$	32.9658	+	57.0984i	1.06341	+	1.84188i
$962$	0.130430	+	0.486770i	0.00420522	+	0.0156941i
$963$	0.440102	+	5.03039i	0.0141821	+	0.162102i
$964$	16.2940	+	5.93053i	0.524794	+	0.191009i
$965$	0.137905	+	0.0490450i	0.00443933	+	0.00157882i
$966$	−13.3248	+	11.1808i	−0.428717	+	0.359737i
$967$	22.8392	−	32.6178i	0.734459	−	1.04892i	−0.262019	−	0.965063i	$-0.584388\pi$
$967$	22.8392	−	32.6178i	0.734459	−	1.04892i	0.996478	−	0.0838539i	$-0.0267229\pi$
$968$	2.56572	+	2.56572i	0.0824655	+	0.0824655i
$969$	4.61520	−	22.2001i	0.148262	−	0.713170i
$970$	−0.845059	−	8.90258i	−0.0271332	−	0.285845i
$971$	27.2392	−	4.80300i	0.874147	−	0.154136i	0.281464	−	0.959572i	$-0.409180\pi$
$971$	27.2392	−	4.80300i	0.874147	−	0.154136i	0.592683	+	0.805436i	$0.298069\pi$
$972$	0.0871557	−	0.996195i	0.00279552	−	0.0319530i
$973$	15.4241	−	33.0772i	0.494475	−	1.06041i
$974$	3.98344	−	10.9444i	0.127638	−	0.350681i
$975$	0.250082	−	0.448294i	0.00800904	−	0.0143569i
$976$	−7.76896	+	13.4562i	−0.248678	+	0.430724i
$977$	2.10314	+	0.563535i	0.0672854	+	0.0180291i	0.292305	−	0.956325i	$-0.405578\pi$
$977$	2.10314	+	0.563535i	0.0672854	+	0.0180291i	−0.225019	+	0.974354i	$0.572245\pi$
$978$	3.32714	+	4.75165i	0.106390	+	0.151941i
$979$	1.94727	−	11.0435i	0.0622351	−	0.352953i
$980$	−1.09339	−	1.53727i	−0.0349269	−	0.0491062i
$981$	1.24435	+	0.718427i	0.0397291	+	0.0229376i
$982$	−24.0935	+	2.10791i	−0.768855	+	0.0672661i
$983$	−19.8371	−	42.5408i	−0.632705	−	1.35684i	−0.917302	−	0.398192i	$-0.869638\pi$
$983$	−19.8371	−	42.5408i	−0.632705	−	1.35684i	0.284597	−	0.958647i	$-0.408140\pi$
$984$	0.725666	−	0.264121i	0.0231334	−	0.00841987i
$985$	−35.0809	+	0.258656i	−1.11777	+	0.00824146i
$986$	8.61499	+	48.8581i	0.274357	+	1.55596i
$987$	10.8509	−	10.8509i	0.345389	−	0.345389i
$988$	0.267719	−	0.358598i	0.00851729	−	0.0114085i
$989$		−	44.7470i		−	1.42287i
$990$	−4.22144	+	7.43786i	−0.134166	+	0.236391i
$991$	−3.45790	−	4.12097i	−0.109844	−	0.130907i	0.708321	−	0.705890i	$-0.249453\pi$
$991$	−3.45790	−	4.12097i	−0.109844	−	0.130907i	−0.818165	+	0.574983i	$0.805008\pi$
$992$	8.92295	+	4.16084i	0.283304	+	0.132107i
$993$	1.73671	−	0.809843i	0.0551129	−	0.0256996i
$994$	11.2777	−	13.4403i	0.357708	−	0.426300i
$995$	−14.6614	−	6.70559i	−0.464799	−	0.212581i
$996$	11.2648	−	6.50373i	0.356938	−	0.206078i
$997$	22.1705	−	15.5239i	0.702146	−	0.491648i	−0.167155	−	0.985931i	$-0.553458\pi$
$997$	22.1705	−	15.5239i	0.702146	−	0.491648i	0.869301	+	0.494283i	$0.164569\pi$
$998$	19.3062	−	13.5184i	0.611128	−	0.427917i
$999$	4.25093	−	2.45427i	0.134493	−	0.0776498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.67.1	✓	120
5.3	odd	4	inner	570.2.bh.b.523.1	yes	120
19.2	odd	18	inner	570.2.bh.b.97.1	yes	120
95.78	even	36	inner	570.2.bh.b.553.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.67.1	✓	120	1.1	even	1	trivial
570.2.bh.b.97.1	yes	120	19.2	odd	18	inner
570.2.bh.b.523.1	yes	120	5.3	odd	4	inner
570.2.bh.b.553.1	yes	120	95.78	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)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.16408 - 0.562797i) q^{5} +(0.766044 + 0.642788i) q^{6} +(-2.70522 + 0.724862i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.16408 - 0.562797i) q^{5} +(0.766044 + 0.642788i) q^{6} +(-2.70522 + 0.724862i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(1.44991 + 1.70228i) q^{10} +(1.91236 + 3.31230i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(0.00894794 + 0.102275i) q^{13} +(2.63175 + 0.957879i) q^{14} +(2.10680 + 0.749267i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(2.98371 - 4.26118i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-3.83950 + 2.06356i) q^{19} +(-0.211304 - 2.22606i) q^{20} +(2.75810 - 0.486328i) q^{21} +(0.333346 - 3.81017i) q^{22} +(2.62479 - 5.62889i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(4.36652 + 2.43588i) q^{25} +(0.0513331 - 0.0889115i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(-1.60639 - 2.29416i) q^{28} +(1.65611 - 9.39227i) q^{29} +(-1.29603 - 1.82217i) q^{30} +(8.52635 + 4.92269i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-1.61640 - 3.46637i) q^{33} +(-4.88823 + 1.77917i) q^{34} +(6.26228 - 0.0461725i) q^{35} +(0.173648 + 0.984808i) q^{36} +(-3.47087 + 3.47087i) q^{37} +(4.32874 + 0.511879i) q^{38} -0.102666i q^{39} +(-1.10373 + 1.94468i) q^{40} +(-0.496385 - 0.591569i) q^{41} +(-2.53825 - 1.18361i) q^{42} +(6.52970 - 3.04485i) q^{43} +(-2.45848 + 2.92991i) q^{44} +(-2.03348 - 0.930036i) q^{45} +(-5.37870 + 3.10539i) q^{46} +(4.48836 - 3.14278i) q^{47} +(0.819152 - 0.573576i) q^{48} +(0.730618 - 0.421822i) q^{49} +(-2.17968 - 4.49989i) q^{50} +(-3.34375 + 3.98492i) q^{51} +(-0.0930471 + 0.0433886i) q^{52} +(2.57611 + 1.20126i) q^{53} +(0.642788 + 0.766044i) q^{54} +(-2.27435 - 8.24438i) q^{55} +2.80065i q^{56} +(4.00474 - 1.72107i) q^{57} +(-6.74379 + 6.74379i) q^{58} +(1.24462 + 7.05860i) q^{59} +(0.0164863 + 2.23601i) q^{60} +(14.6009 - 5.31428i) q^{61} +(-4.16084 - 8.92295i) q^{62} +(-2.78999 + 0.244093i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.0381962 - 0.226369i) q^{65} +(-0.664156 + 3.76661i) q^{66} +(-6.64318 - 9.48744i) q^{67} +(5.02469 + 1.34636i) q^{68} +(-3.10539 + 5.37870i) q^{69} +(-5.15624 - 3.55407i) q^{70} +(2.14263 - 5.88683i) q^{71} +(0.422618 - 0.906308i) q^{72} +(-0.378621 + 4.32766i) q^{73} +(4.83398 - 0.852360i) q^{74} +(-4.13760 - 2.80718i) q^{75} +(-3.25229 - 2.90217i) q^{76} +(-7.57432 - 7.57432i) q^{77} +(-0.0588869 + 0.0840992i) q^{78} +(7.51264 - 6.30385i) q^{79} +(2.01954 - 0.959919i) q^{80} +(0.939693 + 0.342020i) q^{81} +(0.0673050 + 0.769300i) q^{82} +(3.36658 + 12.5642i) q^{83} +(1.40033 + 2.42543i) q^{84} +(-8.85519 + 7.54234i) q^{85} +(-7.09527 - 1.25109i) q^{86} +(-2.46840 + 9.21219i) q^{87} +(3.69440 - 0.989910i) q^{88} +(-2.24600 - 1.88462i) q^{89} +(1.13228 + 1.92820i) q^{90} +(-0.0983417 - 0.270192i) q^{91} +(6.18715 + 0.541306i) q^{92} +(-8.06486 - 5.64708i) q^{93} -5.47927 q^{94} +(9.47036 - 2.30485i) q^{95} -1.00000 q^{96} +(-3.27599 - 2.29388i) q^{97} +(-0.840434 - 0.0735285i) q^{98} +(1.30813 + 3.59406i) 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

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Representations

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Database

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