LMFDB - Embedded newform 637.2.bl.a.53.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.17
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500003 + 0.340896i) q^{2} +(-1.93585 - 1.79621i) q^{3} +(-0.596889 - 1.52085i) q^{4} +(-4.16664 + 1.28524i) q^{5} +(-0.355611 - 1.55803i) q^{6} +(-2.59900 - 0.495162i) q^{7} +(0.489325 - 2.14387i) q^{8} +(0.296968 + 3.96277i) q^{9} +O(q^{10})$	\(q+(0.500003 + 0.340896i) q^{2} +(-1.93585 - 1.79621i) q^{3} +(-0.596889 - 1.52085i) q^{4} +(-4.16664 + 1.28524i) q^{5} +(-0.355611 - 1.55803i) q^{6} +(-2.59900 - 0.495162i) q^{7} +(0.489325 - 2.14387i) q^{8} +(0.296968 + 3.96277i) q^{9} +(-2.52146 - 0.777768i) q^{10} +(0.169052 - 2.25584i) q^{11} +(-1.57627 + 4.01627i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-1.13071 - 1.13357i) q^{14} +(10.3745 + 4.99611i) q^{15} +(-1.41980 + 1.31738i) q^{16} +(1.97466 - 0.297632i) q^{17} +(-1.20241 + 2.08263i) q^{18} +(1.12938 + 1.95615i) q^{19} +(4.44167 + 5.56968i) q^{20} +(4.14187 + 5.62691i) q^{21} +(0.853536 - 1.07030i) q^{22} +(2.09860 + 0.316314i) q^{23} +(-4.79810 + 3.27129i) q^{24} +(11.5778 - 7.89362i) q^{25} +(0.598396 + 0.0901938i) q^{26} +(1.60351 - 2.01074i) q^{27} +(0.798250 + 4.24825i) q^{28} +(-6.29530 - 7.89405i) q^{29} +(3.48414 + 6.03471i) q^{30} +(-4.60842 + 7.98202i) q^{31} +(-5.50788 + 0.830180i) q^{32} +(-4.37922 + 4.06333i) q^{33} +(1.08880 + 0.524338i) q^{34} +(11.4655 - 1.27717i) q^{35} +(5.84951 - 2.81698i) q^{36} +(2.07098 - 5.27677i) q^{37} +(-0.102149 + 1.36308i) q^{38} +(-2.52349 - 0.778392i) q^{39} +(0.716545 + 9.56163i) q^{40} +(0.111805 - 0.489852i) q^{41} +(0.152755 + 4.22542i) q^{42} +(0.842763 + 3.69238i) q^{43} +(-3.53170 + 1.08939i) q^{44} +(-6.33045 - 16.1297i) q^{45} +(0.941478 + 0.873564i) q^{46} +(-0.981281 - 0.669026i) q^{47} +5.11481 q^{48} +(6.50963 + 2.57386i) q^{49} +8.47985 q^{50} +(-4.35726 - 2.97073i) q^{51} +(-1.19765 - 1.11126i) q^{52} +(3.78258 + 9.63787i) q^{53} +(1.48721 - 0.458744i) q^{54} +(2.19492 + 9.61655i) q^{55} +(-2.33332 + 5.32964i) q^{56} +(1.32733 - 5.81541i) q^{57} +(-0.456614 - 6.09309i) q^{58} +(-2.85480 - 0.880590i) q^{59} +(1.40588 - 18.7602i) q^{60} +(0.389204 - 0.991676i) q^{61} +(-5.02527 + 2.42004i) q^{62} +(1.19039 - 10.4463i) q^{63} +(0.453088 + 0.218196i) q^{64} +(-3.19637 + 2.96579i) q^{65} +(-3.57480 + 0.538814i) q^{66} +(-3.63962 + 6.30401i) q^{67} +(-1.63131 - 2.82551i) q^{68} +(-3.49442 - 4.38186i) q^{69} +(6.16817 + 3.26995i) q^{70} +(-10.2591 + 12.8645i) q^{71} +(8.64098 + 1.30242i) q^{72} +(5.36845 - 3.66015i) q^{73} +(2.83433 - 1.93241i) q^{74} +(-36.5915 - 5.51528i) q^{75} +(2.30089 - 2.88522i) q^{76} +(-1.55638 + 5.77924i) q^{77} +(-0.996400 - 1.24945i) q^{78} +(-1.10639 - 1.91633i) q^{79} +(4.22264 - 7.31382i) q^{80} +(5.07263 - 0.764575i) q^{81} +(0.222892 - 0.206813i) q^{82} +(-6.20892 - 2.99006i) q^{83} +(6.08544 - 9.65780i) q^{84} +(-7.84517 + 3.77803i) q^{85} +(-0.837336 + 2.13350i) q^{86} +(-1.99260 + 26.5894i) q^{87} +(-4.75352 - 1.46627i) q^{88} +(-0.325480 - 4.34323i) q^{89} +(2.33332 - 10.2229i) q^{90} +(-2.55646 + 0.681539i) q^{91} +(-0.771569 - 3.38046i) q^{92} +(23.2586 - 7.17432i) q^{93} +(-0.262575 - 0.669030i) q^{94} +(-7.21983 - 6.69902i) q^{95} +(12.1536 + 8.28620i) q^{96} +0.654532 q^{97} +(2.37742 + 3.50604i) q^{98} +8.98959 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	0.500003	+	0.340896i	0.353556	+	0.241050i	0.727053	−	0.686581i	$-0.240889\pi$
$2$	0.500003	+	0.340896i	0.353556	+	0.241050i	−0.373498	+	0.927631i	$0.621842\pi$
$3$	−1.93585	−	1.79621i	−1.11766	−	1.03704i	−0.999027	−	0.0441030i	$-0.985957\pi$
$3$	−1.93585	−	1.79621i	−1.11766	−	1.03704i	−0.118637	−	0.992938i	$-0.537852\pi$
$4$	−0.596889	−	1.52085i	−0.298445	−	0.760425i
$5$	−4.16664	+	1.28524i	−1.86338	+	0.574775i	−0.866198	+	0.499701i	$0.833443\pi$
$5$	−4.16664	+	1.28524i	−1.86338	+	0.574775i	−0.997178	+	0.0750743i	$0.976081\pi$
$6$	−0.355611	−	1.55803i	−0.145178	−	0.636064i
$7$	−2.59900	−	0.495162i	−0.982331	−	0.187154i
$7$	−2.59900	−	0.495162i	−0.982331	−	0.187154i
$8$	0.489325	−	2.14387i	0.173002	−	0.757973i
$9$	0.296968	+	3.96277i	0.0989894	+	1.32092i
$10$	−2.52146	−	0.777768i	−0.797356	−	0.245952i
$11$	0.169052	−	2.25584i	0.0509712	−	0.680163i	−0.911936	−	0.410331i	$-0.865413\pi$
$11$	0.169052	−	2.25584i	0.0509712	−	0.680163i	0.962908	−	0.269831i	$-0.0869679\pi$
$12$	−1.57627	+	4.01627i	−0.455030	+	1.15940i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	−1.13071	−	1.13357i	−0.302195	−	0.302960i
$15$	10.3745	+	4.99611i	2.67869	+	1.28999i
$16$	−1.41980	+	1.31738i	−0.354950	+	0.329345i
$17$	1.97466	−	0.297632i	0.478926	−	0.0721864i	0.0948569	−	0.995491i	$-0.469761\pi$
$17$	1.97466	−	0.297632i	0.478926	−	0.0721864i	0.384069	+	0.923304i	$0.374523\pi$
$18$	−1.20241	+	2.08263i	−0.283410	+	0.490881i
$19$	1.12938	+	1.95615i	0.259098	+	0.448771i	0.966001	−	0.258540i	$-0.0832414\pi$
$19$	1.12938	+	1.95615i	0.259098	+	0.448771i	−0.706903	+	0.707311i	$0.749908\pi$
$20$	4.44167	+	5.56968i	0.993188	+	1.24542i
$21$	4.14187	+	5.62691i	0.903830	+	1.22789i
$22$	0.853536	−	1.07030i	0.181974	−	0.228189i
$23$	2.09860	+	0.316314i	0.437589	+	0.0659559i	0.364143	−	0.931343i	$-0.381362\pi$
$23$	2.09860	+	0.316314i	0.437589	+	0.0659559i	0.0734465	+	0.997299i	$0.476600\pi$
$24$	−4.79810	+	3.27129i	−0.979408	+	0.667749i
$25$	11.5778	−	7.89362i	2.31556	−	1.57872i
$26$	0.598396	+	0.0901938i	0.117355	+	0.0176885i
$27$	1.60351	−	2.01074i	0.308595	−	0.386966i
$28$	0.798250	+	4.24825i	0.150855	+	0.802843i
$29$	−6.29530	−	7.89405i	−1.16901	−	1.46589i	−0.856631	−	0.515930i	$-0.827446\pi$
$29$	−6.29530	−	7.89405i	−1.16901	−	1.46589i	−0.312376	−	0.949958i	$-0.601125\pi$
$30$	3.48414	+	6.03471i	0.636114	+	1.10178i
$31$	−4.60842	+	7.98202i	−0.827697	+	1.43361i	0.0721433	+	0.997394i	$0.477016\pi$
$31$	−4.60842	+	7.98202i	−0.827697	+	1.43361i	−0.899840	+	0.436219i	$0.856317\pi$
$32$	−5.50788	+	0.830180i	−0.973666	+	0.146756i
$33$	−4.37922	+	4.06333i	−0.762325	+	0.707334i
$34$	1.08880	+	0.524338i	0.186727	+	0.0899232i
$35$	11.4655	−	1.27717i	1.93802	−	0.215882i
$36$	5.84951	−	2.81698i	0.974919	−	0.469496i
$37$	2.07098	−	5.27677i	0.340467	−	0.867496i	−0.653410	−	0.757004i	$-0.726662\pi$
$37$	2.07098	−	5.27677i	0.340467	−	0.867496i	0.993877	−	0.110491i	$-0.0352425\pi$
$38$	−0.102149	+	1.36308i	−0.0165707	+	0.221121i
$39$	−2.52349	−	0.778392i	−0.404081	−	0.124643i
$40$	0.716545	+	9.56163i	0.113296	+	1.51183i
$41$	0.111805	−	0.489852i	0.0174611	−	0.0765020i	−0.965447	−	0.260601i	$-0.916079\pi$
$41$	0.111805	−	0.489852i	0.0174611	−	0.0765020i	0.982908	+	0.184099i	$0.0589366\pi$
$42$	0.152755	+	4.22542i	0.0235706	+	0.651996i
$43$	0.842763	+	3.69238i	0.128520	+	0.563083i	0.997651	+	0.0685012i	$0.0218217\pi$
$43$	0.842763	+	3.69238i	0.128520	+	0.563083i	−0.869131	+	0.494582i	$0.835321\pi$
$44$	−3.53170	+	1.08939i	−0.532425	+	0.164231i
$45$	−6.33045	−	16.1297i	−0.943688	−	2.40448i
$46$	0.941478	+	0.873564i	0.138813	+	0.128800i
$47$	−0.981281	−	0.669026i	−0.143135	−	0.0975875i	0.489636	−	0.871927i	$-0.337130\pi$
$47$	−0.981281	−	0.669026i	−0.143135	−	0.0975875i	−0.632770	+	0.774340i	$0.718082\pi$
$48$	5.11481			0.738259
$49$	6.50963	+	2.57386i	0.929947	+	0.367694i
$50$	8.47985			1.19923
$51$	−4.35726	−	2.97073i	−0.610138	−	0.415985i
$52$	−1.19765	−	1.11126i	−0.166084	−	0.154104i
$53$	3.78258	+	9.63787i	0.519578	+	1.32386i	0.914291	+	0.405058i	$0.132749\pi$
$53$	3.78258	+	9.63787i	0.519578	+	1.32386i	−0.394713	+	0.918805i	$0.629156\pi$
$54$	1.48721	−	0.458744i	0.202384	−	0.0624272i
$55$	2.19492	+	9.61655i	0.295962	+	1.29670i
$56$	−2.33332	+	5.32964i	−0.311803	+	0.712202i
$57$	1.32733	−	5.81541i	0.175809	−	0.770270i
$58$	−0.456614	−	6.09309i	−0.0599564	−	0.800062i
$59$	−2.85480	−	0.880590i	−0.371664	−	0.114643i	0.103296	−	0.994651i	$-0.467061\pi$
$59$	−2.85480	−	0.880590i	−0.371664	−	0.114643i	−0.474960	+	0.880008i	$0.657537\pi$
$60$	1.40588	−	18.7602i	0.181499	−	2.42194i
$61$	0.389204	−	0.991676i	0.0498325	−	0.126971i	−0.903790	−	0.427976i	$-0.859227\pi$
$61$	0.389204	−	0.991676i	0.0498325	−	0.126971i	0.953623	+	0.301005i	$0.0973220\pi$
$62$	−5.02527	+	2.42004i	−0.638209	+	0.307345i
$63$	1.19039	−	10.4463i	0.149975	−	1.31611i
$64$	0.453088	+	0.218196i	0.0566360	+	0.0272745i
$65$	−3.19637	+	2.96579i	−0.396460	+	0.367861i
$66$	−3.57480	+	0.538814i	−0.440027	+	0.0663234i
$67$	−3.63962	+	6.30401i	−0.444650	+	0.770157i	−0.998028	−	0.0627737i	$-0.980005\pi$
$67$	−3.63962	+	6.30401i	−0.444650	+	0.770157i	0.553378	+	0.832931i	$0.313339\pi$
$68$	−1.63131	−	2.82551i	−0.197825	−	0.342643i
$69$	−3.49442	−	4.38186i	−0.420678	−	0.527514i
$70$	6.16817	+	3.26995i	0.737237	+	0.390834i
$71$	−10.2591	+	12.8645i	−1.21753	+	1.52674i	−0.439862	+	0.898065i	$0.644973\pi$
$71$	−10.2591	+	12.8645i	−1.21753	+	1.52674i	−0.777670	+	0.628673i	$0.783599\pi$
$72$	8.64098	+	1.30242i	1.01835	+	0.153491i
$73$	5.36845	−	3.66015i	0.628330	−	0.428388i	−0.206844	−	0.978374i	$-0.566319\pi$
$73$	5.36845	−	3.66015i	0.628330	−	0.428388i	0.835174	+	0.549986i	$0.185367\pi$
$74$	2.83433	−	1.93241i	0.329484	−	0.224638i
$75$	−36.5915	−	5.51528i	−4.22522	−	0.636850i
$76$	2.30089	−	2.88522i	0.263930	−	0.330958i
$77$	−1.55638	+	5.77924i	−0.177365	+	0.658605i
$78$	−0.996400	−	1.24945i	−0.112820	−	0.141472i
$79$	−1.10639	−	1.91633i	−0.124479	−	0.215603i	0.797050	−	0.603913i	$-0.206393\pi$
$79$	−1.10639	−	1.91633i	−0.124479	−	0.215603i	−0.921529	+	0.388309i	$0.873059\pi$
$80$	4.22264	−	7.31382i	0.472105	−	0.817710i
$81$	5.07263	−	0.764575i	0.563625	−	0.0849528i
$82$	0.222892	−	0.206813i	0.0246143	−	0.0228387i
$83$	−6.20892	−	2.99006i	−0.681517	−	0.328201i	0.0608956	−	0.998144i	$-0.480604\pi$
$83$	−6.20892	−	2.99006i	−0.681517	−	0.328201i	−0.742413	+	0.669943i	$0.766319\pi$
$84$	6.08544	−	9.65780i	0.663976	−	1.05375i
$85$	−7.84517	+	3.77803i	−0.850928	+	0.409785i
$86$	−0.837336	+	2.13350i	−0.0902923	+	0.230061i
$87$	−1.99260	+	26.5894i	−0.213629	+	2.85068i
$88$	−4.75352	−	1.46627i	−0.506727	−	0.156305i
$89$	−0.325480	−	4.34323i	−0.0345008	−	0.460382i	−0.987522	−	0.157479i	$-0.949663\pi$
$89$	−0.325480	−	4.34323i	−0.0345008	−	0.460382i	0.953022	−	0.302903i	$-0.0979557\pi$
$90$	2.33332	−	10.2229i	0.245953	−	1.07759i
$91$	−2.55646	+	0.681539i	−0.267990	+	0.0714447i
$92$	−0.771569	−	3.38046i	−0.0804416	−	0.352438i
$93$	23.2586	−	7.17432i	2.41180	−	0.743943i
$94$	−0.262575	−	0.669030i	−0.0270825	−	0.0690052i
$95$	−7.21983	−	6.69902i	−0.740739	−	0.687305i
$96$	12.1536	+	8.28620i	1.24042	+	0.845706i
$97$	0.654532			0.0664577			0.0332288	−	0.999448i	$-0.489421\pi$
$97$	0.654532			0.0664577			0.0332288	+	0.999448i	$0.489421\pi$
$98$	2.37742	+	3.50604i	0.240155	+	0.354164i
$99$	8.98959			0.903488
$100$	−18.9157	−	12.8965i	−1.89157	−	1.28965i
$101$	−12.4561	−	11.5576i	−1.23943	−	1.15002i	−0.983029	−	0.183448i	$-0.941274\pi$
$101$	−12.4561	−	11.5576i	−1.23943	−	1.15002i	−0.256397	−	0.966572i	$-0.582536\pi$
$102$	−1.16593	−	2.97075i	−0.115444	−	0.294148i
$103$	15.2556	−	4.70573i	1.50318	−	0.463669i	0.569563	−	0.821948i	$-0.307112\pi$
$103$	15.2556	−	4.70573i	1.50318	−	0.463669i	0.933615	+	0.358279i	$0.116636\pi$
$104$	−0.489325	−	2.14387i	−0.0479823	−	0.210224i
$105$	−24.4896	−	18.1220i	−2.38994	−	1.76852i
$106$	−1.39421	+	6.10843i	−0.135418	+	0.593303i
$107$	0.459253	+	6.12830i	0.0443976	+	0.592445i	0.974390	+	0.224866i	$0.0721943\pi$
$107$	0.459253	+	6.12830i	0.0443976	+	0.592445i	−0.929992	+	0.367579i	$0.880187\pi$
$108$	−4.01515	−	1.23851i	−0.386358	−	0.119176i
$109$	−0.255729	+	3.41246i	−0.0244944	+	0.326855i	0.971474	+	0.237147i	$0.0762123\pi$
$109$	−0.255729	+	3.41246i	−0.0244944	+	0.326855i	−0.995968	+	0.0897077i	$0.971407\pi$
$110$	−2.18078	+	5.55654i	−0.207929	+	0.529796i
$111$	−13.4873	+	6.49513i	−1.28016	+	0.616491i
$112$	4.34238	−	2.72085i	0.410316	−	0.257096i
$113$	1.85194	+	0.891847i	0.174216	+	0.0838979i	0.518959	−	0.854799i	$-0.326320\pi$
$113$	1.85194	+	0.891847i	0.174216	+	0.0838979i	−0.344743	+	0.938697i	$0.612034\pi$
$114$	2.64612	−	2.45524i	0.247832	−	0.229954i
$115$	−9.15065	+	1.37924i	−0.853303	+	0.128615i
$116$	−8.24807	+	14.2861i	−0.765814	+	1.32643i
$117$	1.98694	+	3.44148i	0.183693	+	0.318165i
$118$	−1.12722	−	1.41349i	−0.103769	−	0.130122i
$119$	−5.27953	−	0.204230i	−0.483973	−	0.0187218i
$120$	15.7875	−	19.7970i	1.44120	−	1.80721i
$121$	5.81688	+	0.876754i	0.528808	+	0.0797049i
$122$	0.532662	−	0.363163i	0.0482249	−	0.0328792i
$123$	−1.09631	+	0.747454i	−0.0988513	+	0.0673957i
$124$	14.8902	+	2.24433i	1.33718	+	0.201547i
$125$	−24.5022	+	30.7248i	−2.19154	+	2.74811i
$126$	4.15630	−	4.81738i	0.370273	−	0.429166i
$127$	12.3530	+	15.4902i	1.09615	+	1.37453i	0.920804	+	0.390026i	$0.127534\pi$
$127$	12.3530	+	15.4902i	1.09615	+	1.37453i	0.175350	+	0.984506i	$0.443894\pi$
$128$	5.72226	+	9.91125i	0.505781	+	0.876039i
$129$	5.00082	−	8.66168i	0.440298	−	0.762619i
$130$	−2.60922	+	0.393277i	−0.228844	+	0.0344926i
$131$	0.470867	−	0.436901i	0.0411398	−	0.0381722i	−0.659335	−	0.751849i	$-0.729162\pi$
$131$	0.470867	−	0.436901i	0.0411398	−	0.0381722i	0.700475	+	0.713677i	$0.252972\pi$
$132$	8.79362	+	4.23478i	0.765386	+	0.368591i
$133$	−1.96666	−	5.64326i	−0.170531	−	0.489332i
$134$	−3.96883	+	1.91129i	−0.342855	+	0.165110i
$135$	−4.09696	+	10.4389i	−0.352611	+	0.898437i
$136$	0.328165	−	4.37906i	0.0281399	−	0.375501i
$137$	−13.3994	−	4.13318i	−1.14479	−	0.353122i	−0.336373	−	0.941729i	$-0.609200\pi$
$137$	−13.3994	−	4.13318i	−1.14479	−	0.353122i	−0.808419	+	0.588607i	$0.799676\pi$
$138$	−0.253459	−	3.38218i	−0.0215759	−	0.287910i
$139$	−2.70625	+	11.8569i	−0.229541	+	1.00569i	0.720474	+	0.693482i	$0.243924\pi$
$139$	−2.70625	+	11.8569i	−0.229541	+	1.00569i	−0.950015	+	0.312204i	$0.898933\pi$
$140$	−8.78602	−	16.6750i	−0.742554	−	1.40929i
$141$	0.697904	+	3.05772i	0.0587741	+	0.257506i
$142$	−9.51505	+	2.93501i	−0.798486	+	0.246300i
$143$	−0.826464	−	2.10579i	−0.0691124	−	0.176095i
$144$	−5.64211	−	5.23511i	−0.470176	−	0.436259i
$145$	36.3759	+	24.8007i	3.02086	+	2.05958i
$146$	3.93197			0.325412
$147$	−7.97849	−	16.6752i	−0.658055	−	1.37535i
$148$	−9.26132			−0.761276
$149$	−7.87081	−	5.36623i	−0.644802	−	0.439618i	0.196264	−	0.980551i	$-0.437119\pi$
$149$	−7.87081	−	5.36623i	−0.644802	−	0.439618i	−0.841066	+	0.540933i	$0.818071\pi$
$150$	−16.4157	−	15.2316i	−1.34034	−	1.24365i
$151$	−0.301093	−	0.767171i	−0.0245026	−	0.0624315i	0.918099	−	0.396351i	$-0.129724\pi$
$151$	−0.301093	−	0.767171i	−0.0245026	−	0.0624315i	−0.942601	+	0.333920i	$0.891629\pi$
$152$	4.74636	−	1.46406i	0.384981	−	0.118751i
$153$	1.76586	+	7.73674i	0.142761	+	0.625478i
$154$	−2.74831	+	2.35907i	−0.221465	+	0.190100i
$155$	8.94283	−	39.1811i	0.718305	−	3.14710i
$156$	0.322425	+	4.30246i	0.0258146	+	0.344472i
$157$	−3.78235	−	1.16670i	−0.301865	−	0.0931129i	0.140123	−	0.990134i	$-0.455250\pi$
$157$	−3.78235	−	1.16670i	−0.301865	−	0.0931129i	−0.441987	+	0.897021i	$0.645726\pi$
$158$	0.100069	−	1.33533i	0.00796109	−	0.106233i
$159$	9.98909	−	25.4518i	0.792186	−	2.01846i
$160$	21.8824	−	10.5380i	1.72995	−	0.833101i
$161$	−5.29765	−	1.86125i	−0.417513	−	0.146687i
$162$	2.79697	+	1.34695i	0.219751	+	0.105826i
$163$	2.53604	−	2.35310i	0.198638	−	0.184309i	−0.574582	−	0.818447i	$-0.694835\pi$
$163$	2.53604	−	2.35310i	0.198638	−	0.184309i	0.773220	+	0.634138i	$0.218645\pi$
$164$	−0.811726	+	0.122348i	−0.0633852	+	0.00955378i
$165$	13.0243	−	22.5587i	1.01394	−	1.75620i
$166$	−2.08518	−	3.61163i	−0.161841	−	0.280317i
$167$	6.73684	+	8.44773i	0.521312	+	0.653705i	0.970887	−	0.239538i	$-0.0769959\pi$
$167$	6.73684	+	8.44773i	0.521312	+	0.653705i	−0.449575	+	0.893243i	$0.648424\pi$
$168$	14.0901	−	6.12625i	1.08707	−	0.472651i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	−5.21052	−	0.785360i	−0.399629	−	0.0602344i
$171$	−7.41636	+	5.05639i	−0.567143	+	0.386672i
$172$	5.11252	−	3.48566i	0.389826	−	0.265779i
$173$	12.5524	+	1.89197i	0.954344	+	0.143844i	0.607712	−	0.794157i	$-0.292087\pi$
$173$	12.5524	+	1.89197i	0.954344	+	0.143844i	0.346631	+	0.938001i	$0.387325\pi$
$174$	−10.0605	+	12.6155i	−0.762686	+	0.956378i
$175$	−33.9994	+	14.7827i	−2.57011	+	1.11746i
$176$	2.73179	+	3.42555i	0.205916	+	0.258211i
$177$	3.94475	+	6.83251i	0.296506	+	0.513563i
$178$	1.31785	−	2.28258i	0.0987771	−	0.171087i
$179$	22.3042	−	3.36181i	1.66709	−	0.251274i	0.753365	−	0.657602i	$-0.228429\pi$
$179$	22.3042	−	3.36181i	1.66709	−	0.251274i	0.913727	+	0.406328i	$0.133191\pi$
$180$	−20.7523	+	19.2553i	−1.54679	+	1.43521i
$181$	−19.4418	−	9.36269i	−1.44510	−	0.695923i	−0.463363	−	0.886169i	$-0.653357\pi$
$181$	−19.4418	−	9.36269i	−1.44510	−	0.695923i	−0.981737	+	0.190246i	$0.939072\pi$
$182$	−1.51057	−	0.530717i	−0.111971	−	0.0393394i
$183$	−2.53470	+	1.22065i	−0.187370	+	0.0902327i
$184$	1.70503	−	4.34436i	0.125697	−	0.320270i
$185$	−1.84712	+	24.6481i	−0.135803	+	1.81216i
$186$	14.0751	+	4.34158i	1.03203	+	0.318340i
$187$	−0.337591	−	4.50484i	−0.0246871	−	0.329427i
$188$	−0.431771	+	1.89171i	−0.0314902	+	0.137967i
$189$	−5.16317	+	4.43191i	−0.375565	+	0.322374i
$190$	−1.32626	−	5.81075i	−0.0962174	−	0.421556i
$191$	−15.3593	+	4.73772i	−1.11136	+	0.342810i	−0.795474	−	0.605987i	$-0.792778\pi$
$191$	−15.3593	+	4.73772i	−1.11136	+	0.342810i	−0.315887	+	0.948797i	$0.602302\pi$
$192$	−0.485186	−	1.23623i	−0.0350153	−	0.0892175i
$193$	5.99879	+	5.56607i	0.431803	+	0.400654i	0.865904	−	0.500210i	$-0.166744\pi$
$193$	5.99879	+	5.56607i	0.431803	+	0.400654i	−0.434102	+	0.900864i	$0.642934\pi$
$194$	0.327268	+	0.223128i	0.0234965	+	0.0160196i
$195$	11.5149			0.824597
$196$	0.0289173	−	11.4365i	0.00206552	−	0.816891i
$197$	15.6090			1.11209			0.556047	−	0.831151i	$-0.312318\pi$
$197$	15.6090			1.11209			0.556047	+	0.831151i	$0.312318\pi$
$198$	4.49482	+	3.06452i	0.319433	+	0.217786i
$199$	−14.6239	−	13.5690i	−1.03666	−	0.961878i	−0.0373588	−	0.999302i	$-0.511894\pi$
$199$	−14.6239	−	13.5690i	−1.03666	−	0.961878i	−0.999299	+	0.0374236i	$0.988085\pi$
$200$	−11.2576	−	28.6839i	−0.796033	−	2.02826i
$201$	18.3691	−	5.66610i	1.29565	−	0.399656i
$202$	−2.28815	−	10.0250i	−0.160994	−	0.705360i
$203$	12.4527	+	23.6339i	0.874005	+	1.65877i
$204$	−1.91723	+	8.39993i	−0.134233	+	0.588113i
$205$	0.163723	+	2.18473i	0.0114349	+	0.152588i
$206$	9.23200	+	2.84770i	0.643224	+	0.198408i
$207$	−0.630258	+	8.41021i	−0.0438060	+	0.584550i
$208$	−0.707604	+	1.80295i	−0.0490635	+	0.125012i
$209$	4.60369	−	2.21702i	0.318444	−	0.153354i
$210$	−6.06714	−	17.4094i	−0.418672	−	1.20137i
$211$	14.7510	+	7.10369i	1.01550	+	0.489038i	0.866170	−	0.499750i	$-0.166575\pi$
$211$	14.7510	+	7.10369i	1.01550	+	0.489038i	0.149328	+	0.988788i	$0.452289\pi$
$212$	12.4000	−	11.5055i	0.851633	−	0.790200i
$213$	42.9675	−	6.47630i	2.94408	−	0.443749i
$214$	−1.85949	+	3.22073i	−0.127112	+	0.220164i
$215$	−8.25707	−	14.3017i	−0.563128	−	0.975366i
$216$	−3.52613	−	4.42162i	−0.239923	−	0.300853i
$217$	15.9297	−	18.4634i	1.08138	−	1.25338i
$218$	−1.29116	+	1.61907i	−0.0874485	+	0.109657i
$219$	−16.9669	−	2.55735i	−1.14652	−	0.172810i
$220$	13.3152	−	9.07815i	0.897711	−	0.612049i
$221$	1.64997	−	1.12493i	0.110989	−	0.0756710i
$222$	−8.95785	−	1.35018i	−0.601211	−	0.0906180i
$223$	−12.3798	+	15.5238i	−0.829012	+	1.03955i	0.169528	+	0.985525i	$0.445776\pi$
$223$	−12.3798	+	15.5238i	−0.829012	+	1.03955i	−0.998540	+	0.0540226i	$0.982796\pi$
$224$	14.7261	+	0.569655i	0.983928	+	0.0380617i
$225$	34.7188	+	43.5361i	2.31459	+	2.90240i
$226$	0.621948	+	1.07725i	0.0413714	+	0.0716573i
$227$	−0.465477	+	0.806229i	−0.0308948	+	0.0535113i	−0.881059	−	0.473006i	$-0.843169\pi$
$227$	−0.465477	+	0.806229i	−0.0308948	+	0.0535113i	0.850165	+	0.526517i	$0.176502\pi$
$228$	−9.63663	+	1.45249i	−0.638201	+	0.0961934i
$229$	7.86940	−	7.30173i	0.520024	−	0.482512i	−0.375936	−	0.926645i	$-0.622679\pi$
$229$	7.86940	−	7.30173i	0.520024	−	0.482512i	0.895961	+	0.444133i	$0.146488\pi$
$230$	−5.04553	−	2.42980i	−0.332692	−	0.160216i
$231$	13.3936	−	8.39217i	0.881235	−	0.552164i
$232$	−20.0043	+	9.63356i	−1.31335	+	0.632474i
$233$	−6.61251	+	16.8484i	−0.433200	+	1.10377i	0.533031	+	0.846096i	$0.321053\pi$
$233$	−6.61251	+	16.8484i	−0.433200	+	1.10377i	−0.966231	+	0.257679i	$0.917042\pi$
$234$	−0.179712	+	2.39809i	−0.0117481	+	0.156768i
$235$	4.94850	+	1.52641i	0.322804	+	0.0995719i
$236$	0.364757	+	4.86734i	0.0237436	+	0.316837i
$237$	−1.30031	+	5.69703i	−0.0844642	+	0.370062i
$238$	−2.57016	−	1.90189i	−0.166599	−	0.123281i
$239$	1.61648	+	7.08224i	0.104561	+	0.458112i	0.999919	+	0.0127639i	$0.00406299\pi$
$239$	1.61648	+	7.08224i	0.104561	+	0.458112i	−0.895357	+	0.445348i	$0.853080\pi$
$240$	−21.3115	+	6.57374i	−1.37565	+	0.424333i
$241$	3.70773	+	9.44714i	0.238836	+	0.608544i	0.999159	−	0.0410012i	$-0.0130548\pi$
$241$	3.70773	+	9.44714i	0.238836	+	0.608544i	−0.760323	+	0.649545i	$0.774960\pi$
$242$	2.60958	+	2.42133i	0.167750	+	0.155649i
$243$	−17.5680	−	11.9777i	−1.12699	−	0.768368i
$244$	−1.74050			−0.111424
$245$	−30.4313	−	2.35790i	−1.94418	−	0.150641i
$246$	−0.802965			−0.0511952
$247$	1.86628	+	1.27241i	0.118748	+	0.0809613i
$248$	14.8574	+	13.7857i	0.943447	+	0.875391i
$249$	6.64878	+	16.9408i	0.421349	+	1.07358i
$250$	−22.7251	+	7.00978i	−1.43726	+	0.443337i
$251$	−2.59828	−	11.3838i	−0.164002	−	0.718540i	−0.988317	−	0.152409i	$-0.951297\pi$
$251$	−2.59828	−	11.3838i	−0.164002	−	0.718540i	0.824315	−	0.566131i	$-0.191560\pi$
$252$	−16.5978	+	4.42487i	−1.04556	+	0.278741i
$253$	1.06833	−	4.68065i	0.0671652	−	0.294270i
$254$	0.895997	+	11.9562i	0.0562198	+	0.750201i
$255$	21.9732	+	6.77783i	1.37602	+	0.424444i
$256$	−0.442397	+	5.90338i	−0.0276498	+	0.368961i
$257$	−7.23241	+	18.4279i	−0.451146	+	1.14950i	0.506676	+	0.862137i	$0.330874\pi$
$257$	−7.23241	+	18.4279i	−0.451146	+	1.14950i	−0.957822	+	0.287364i	$0.907221\pi$
$258$	5.45316	−	2.62610i	0.339499	−	0.163494i
$259$	−7.99534	+	12.6889i	−0.496806	+	0.788448i
$260$	6.41840	+	3.09094i	0.398052	+	0.191692i
$261$	29.4128	−	27.2911i	1.82061	−	1.68928i
$262$	0.384373	−	0.0579348i	0.0237466	−	0.00357923i
$263$	6.07769	−	10.5269i	0.374766	−	0.649114i	−0.615526	−	0.788117i	$-0.711056\pi$
$263$	6.07769	−	10.5269i	0.374766	−	0.649114i	0.990292	+	0.139003i	$0.0443896\pi$
$264$	6.56839	+	11.3768i	0.404256	+	0.700193i
$265$	−28.1476	−	35.2960i	−1.72909	−	2.16821i
$266$	0.940431	−	3.49207i	0.0576615	−	0.214113i
$267$	−7.17126	+	8.99248i	−0.438874	+	0.550331i
$268$	11.7599	+	1.77252i	0.718350	+	0.108274i
$269$	−18.6078	+	12.6866i	−1.13454	+	0.773515i	−0.976840	−	0.213973i	$-0.931360\pi$
$269$	−18.6078	+	12.6866i	−1.13454	+	0.773515i	−0.157698	+	0.987487i	$0.550407\pi$
$270$	−5.60708	+	3.82284i	−0.341236	+	0.232651i
$271$	6.35788	+	0.958296i	0.386214	+	0.0582123i	0.339279	−	0.940686i	$-0.389817\pi$
$271$	6.35788	+	0.958296i	0.386214	+	0.0582123i	0.0469342	+	0.998898i	$0.485055\pi$
$272$	−2.41153	+	3.02396i	−0.146220	+	0.183354i
$273$	6.17312	+	3.27258i	0.373614	+	0.198065i
$274$	−5.29078	−	6.63443i	−0.319628	−	0.400800i
$275$	−15.8495	−	27.4522i	−0.955763	−	1.65543i
$276$	−4.57837	+	7.92997i	−0.275585	+	0.477328i
$277$	−19.9636	+	3.00903i	−1.19950	+	0.180795i	−0.718248	−	0.695788i	$-0.755055\pi$
$277$	−19.9636	+	3.00903i	−1.19950	+	0.180795i	−0.481251	+	0.876583i	$0.659817\pi$
$278$	−5.39510	+	5.00592i	−0.323576	+	0.300235i
$279$	−32.9994	−	15.8917i	−1.97563	−	0.951411i
$280$	2.87225	−	25.2055i	0.171650	−	1.50632i
$281$	−14.9850	+	7.21642i	−0.893933	+	0.430495i	−0.823694	−	0.567035i	$-0.808090\pi$
$281$	−14.9850	+	7.21642i	−0.893933	+	0.430495i	−0.0702391	+	0.997530i	$0.522376\pi$
$282$	−0.693410	+	1.76678i	−0.0412920	+	0.105210i
$283$	1.19745	−	15.9789i	0.0711812	−	0.949848i	−0.841258	−	0.540635i	$-0.818184\pi$
$283$	1.19745	−	15.9789i	0.0711812	−	0.949848i	0.912439	−	0.409213i	$-0.134197\pi$
$284$	25.6885	+	7.92387i	1.52433	+	0.470195i
$285$	1.94368	+	25.9366i	0.115134	+	1.53635i
$286$	0.304623	−	1.33464i	0.0180128	−	0.0789190i
$287$	−0.533139	+	1.21776i	−0.0314702	+	0.0718823i
$288$	−4.92548	−	21.5799i	−0.290237	−	1.27161i
$289$	−12.4340	+	3.83539i	−0.731414	+	0.225611i
$290$	9.73361	+	24.8008i	0.571577	+	1.45636i
$291$	−1.26708	−	1.17568i	−0.0742774	−	0.0689193i
$292$	−8.77090	−	5.97990i	−0.513278	−	0.349947i
$293$	19.4509			1.13634			0.568168	−	0.822913i	$-0.307653\pi$
$293$	19.4509			1.13634			0.568168	+	0.822913i	$0.307653\pi$
$294$	1.69526	−	11.0575i	0.0988694	−	0.644887i
$295$	13.0267			0.758443
$296$	−10.2993	−	7.02197i	−0.598637	−	0.408144i
$297$	−4.26483	−	3.95719i	−0.247471	−	0.229619i
$298$	−2.10610	−	5.36626i	−0.122003	−	0.310859i
$299$	2.02802	−	0.625561i	0.117283	−	0.0361771i
$300$	13.4532	+	58.9422i	0.776719	+	3.40303i
$301$	−0.362014	−	10.0138i	−0.0208661	−	0.577187i
$302$	0.110979	−	0.486229i	0.00638610	−	0.0279793i
$303$	3.35335	+	44.7474i	0.192645	+	2.57067i
$304$	−4.18048	−	1.28951i	−0.239767	−	0.0739584i
$305$	−0.347133	+	4.63217i	−0.0198768	+	0.265237i
$306$	−1.75449	+	4.47037i	−0.100297	+	0.255554i
$307$	−0.753487	+	0.362860i	−0.0430038	+	0.0207095i	−0.455262	−	0.890357i	$-0.650454\pi$
$307$	−0.753487	+	0.362860i	−0.0430038	+	0.0207095i	0.412258	+	0.911067i	$0.364740\pi$
$308$	9.71833	−	1.08255i	0.553753	−	0.0616842i
$309$	−37.9850	−	18.2926i	−2.16089	−	1.04063i
$310$	17.8281	−	16.5421i	1.01257	−	0.939527i
$311$	−4.61753	+	0.695981i	−0.261836	+	0.0394655i	−0.278648	−	0.960393i	$-0.589886\pi$
$311$	−4.61753	+	0.695981i	−0.261836	+	0.0394655i	0.0168121	+	0.999859i	$0.494648\pi$
$312$	−2.90358	+	5.02915i	−0.164383	+	0.284719i
$313$	6.27589	+	10.8702i	0.354734	+	0.614418i	0.987072	−	0.160275i	$-0.0512380\pi$
$313$	6.27589	+	10.8702i	0.354734	+	0.614418i	−0.632338	+	0.774693i	$0.717905\pi$
$314$	−1.49346	−	1.87274i	−0.0842810	−	0.105685i
$315$	8.46603	+	45.0558i	0.477007	+	2.53861i
$316$	−2.25405	+	2.82649i	−0.126800	+	0.159002i
$317$	−18.8716	−	2.84443i	−1.05993	−	0.159759i	−0.404138	−	0.914698i	$-0.632429\pi$
$317$	−18.8716	−	2.84443i	−1.05993	−	0.159759i	−0.655795	+	0.754939i	$0.727667\pi$
$318$	13.6710	−	9.32072i	0.766631	−	0.522680i
$319$	−18.8720	+	12.8667i	−1.05663	+	0.720397i
$320$	−2.16829	−	0.326816i	−0.121211	−	0.0182696i
$321$	10.1187	−	12.6884i	0.564768	−	0.708197i
$322$	−2.01435	−	2.73658i	−0.112255	−	0.152504i
$323$	2.81236	+	3.52659i	0.156484	+	0.196224i
$324$	−4.19060	−	7.25833i	−0.232811	−	0.403241i
$325$	7.00634	−	12.1353i	0.388642	−	0.673147i
$326$	2.07019	−	0.312032i	0.114657	−	0.0172818i
$327$	6.62455	−	6.14668i	0.366338	−	0.339912i
$328$	−0.995471	−	0.479393i	−0.0549657	−	0.0264701i
$329$	2.21908	+	2.22469i	0.122342	+	0.122651i
$330$	14.2024	−	6.83950i	0.781815	−	0.376502i
$331$	−6.07091	+	15.4684i	−0.333687	+	0.850221i	0.661291	+	0.750129i	$0.270009\pi$
$331$	−6.07091	+	15.4684i	−0.333687	+	0.850221i	−0.994978	+	0.100092i	$0.968086\pi$
$332$	−0.841389	+	11.2276i	−0.0461772	+	0.616192i
$333$	21.5256	+	6.63978i	1.17960	+	0.363857i
$334$	0.488640	+	6.52045i	0.0267372	+	0.356783i
$335$	7.06283	−	30.9443i	0.385883	−	1.69067i
$336$	−13.2934	−	2.53266i	−0.725214	−	0.138168i
$337$	2.57361	+	11.2757i	0.140194	+	0.614228i	0.995389	+	0.0959223i	$0.0305800\pi$
$337$	2.57361	+	11.2757i	0.140194	+	0.614228i	−0.855195	+	0.518306i	$0.826563\pi$
$338$	0.578270	−	0.178373i	0.0314538	−	0.00970220i
$339$	−1.98314	−	5.05295i	−0.107709	−	0.274439i
$340$	10.4285	+	9.67625i	0.565566	+	0.524768i
$341$	17.2271	+	11.7453i	0.932902	+	0.636042i
$342$	−5.43191			−0.293724
$343$	−15.6441	−	9.91278i	−0.844700	−	0.535240i
$344$	8.32839			0.449036
$345$	20.1917	+	13.7665i	1.08708	+	0.741162i
$346$	5.63129	+	5.22507i	0.302740	+	0.280902i
$347$	−10.9720	−	27.9561i	−0.589007	−	1.50076i	−0.845369	−	0.534183i	$-0.820619\pi$
$347$	−10.9720	−	27.9561i	−0.589007	−	1.50076i	0.256362	−	0.966581i	$-0.417476\pi$
$348$	41.6278	−	12.8405i	2.23148	−	0.688321i
$349$	6.29063	+	27.5610i	0.336730	+	1.47531i	0.805821	+	0.592159i	$0.201724\pi$
$349$	6.29063	+	27.5610i	0.336730	+	1.47531i	−0.469091	+	0.883150i	$0.655418\pi$
$350$	−22.0392	−	4.19890i	−1.17804	−	0.224441i
$351$	0.572286	−	2.50735i	0.0305464	−	0.133832i
$352$	0.941637	+	12.5653i	0.0501894	+	0.669731i
$353$	3.79655	+	1.17108i	0.202070	+	0.0623303i	0.394138	−	0.919051i	$-0.371043\pi$
$353$	3.79655	+	1.17108i	0.202070	+	0.0623303i	−0.192068	+	0.981382i	$0.561519\pi$
$354$	−0.356789	+	4.76102i	−0.0189631	+	0.253046i
$355$	26.2120	−	66.7871i	1.39119	−	3.54469i
$356$	−6.41112	+	3.08743i	−0.339789	+	0.163634i
$357$	9.85354	+	9.87848i	0.521504	+	0.522825i
$358$	12.2982	+	5.92249i	0.649979	+	0.313014i
$359$	−16.5987	+	15.4014i	−0.876047	+	0.812853i	−0.983416	−	0.181367i	$-0.941948\pi$
$359$	−16.5987	+	15.4014i	−0.876047	+	0.812853i	0.107369	+	0.994219i	$0.465757\pi$
$360$	−37.6777	+	5.67900i	−1.98579	+	0.299310i
$361$	6.94899	−	12.0360i	0.365737	−	0.633474i
$362$	−6.52926	−	11.3090i	−0.343170	−	0.594389i
$363$	−9.68579	−	12.1456i	−0.508372	−	0.637478i
$364$	2.56244	+	3.48119i	0.134309	+	0.182464i
$365$	−17.6642	+	22.1502i	−0.924587	+	1.15940i
$366$	−1.68347	−	0.253742i	−0.0879964	−	0.0132633i
$367$	−15.7662	+	10.7492i	−0.822990	+	0.561105i	−0.899982	−	0.435927i	$-0.856421\pi$
$367$	−15.7662	+	10.7492i	−0.822990	+	0.561105i	0.0769923	+	0.997032i	$0.475468\pi$
$368$	−3.39630	+	2.31556i	−0.177044	+	0.120707i
$369$	1.97437	+	0.297589i	0.102782	+	0.0154918i
$370$	−9.32600	+	11.6944i	−0.484836	+	0.607965i
$371$	−5.05864	−	26.9218i	−0.262632	−	1.39771i
$372$	−24.7939	−	31.0905i	−1.28550	−	1.61197i
$373$	−3.54874	−	6.14660i	−0.183747	−	0.318259i	0.759407	−	0.650616i	$-0.225489\pi$
$373$	−3.54874	−	6.14660i	−0.183747	−	0.318259i	−0.943154	+	0.332357i	$0.892156\pi$
$374$	1.36689	−	2.36752i	0.0706801	−	0.122422i
$375$	102.621	−	15.4676i	5.29931	−	0.798742i
$376$	−1.91447	+	1.77637i	−0.0987313	+	0.0916093i
$377$	−9.09697	−	4.38087i	−0.468518	−	0.225626i
$378$	−4.09242	+	0.455866i	−0.210491	+	0.0234472i
$379$	−27.3923	+	13.1914i	−1.40705	+	0.677599i	−0.974578	−	0.224049i	$-0.928072\pi$
$379$	−27.3923	+	13.1914i	−1.40705	+	0.677599i	−0.432471	+	0.901648i	$0.642358\pi$
$380$	−5.87877	+	14.9789i	−0.301574	+	0.768399i
$381$	3.91000	−	52.1753i	0.200315	−	2.67302i
$382$	−9.29478	−	2.86706i	−0.475562	−	0.146692i
$383$	0.980164	+	13.0794i	0.0500841	+	0.668325i	0.964590	+	0.263753i	$0.0849605\pi$
$383$	0.980164	+	13.0794i	0.0500841	+	0.668325i	−0.914506	+	0.404572i	$0.867420\pi$
$384$	6.72521	−	29.4651i	0.343194	−	1.50363i
$385$	−0.942839	−	26.0803i	−0.0480515	−	1.32917i
$386$	1.10196	+	4.82802i	0.0560884	+	0.245740i
$387$	−14.3818	+	4.43619i	−0.731067	+	0.225504i
$388$	−0.390683	−	0.995445i	−0.0198339	−	0.0505361i
$389$	6.47422	+	6.00720i	0.328256	+	0.304577i	0.827033	−	0.562153i	$-0.190027\pi$
$389$	6.47422	+	6.00720i	0.328256	+	0.304577i	−0.498777	+	0.866730i	$0.666217\pi$
$390$	5.75747	+	3.92537i	0.291541	+	0.198769i
$391$	4.23818			0.214334
$392$	8.70334	−	12.6964i	0.439585	−	0.641263i
$393$	−1.69629			−0.0855666
$394$	7.80454	+	5.32104i	0.393187	+	0.268070i
$395$	7.07286	+	6.56265i	0.355874	+	0.330203i
$396$	−5.36579	−	13.6718i	−0.269641	−	0.687034i
$397$	12.1570	−	3.74992i	0.610140	−	0.188203i	0.0257397	−	0.999669i	$-0.491806\pi$
$397$	12.1570	−	3.74992i	0.610140	−	0.188203i	0.584401	+	0.811465i	$0.301330\pi$
$398$	−2.68637	−	11.7697i	−0.134655	−	0.589964i
$399$	−6.32930	+	14.4570i	−0.316861	+	0.723756i
$400$	−6.03927	+	26.4598i	−0.301963	+	1.32299i
$401$	0.968155	+	12.9191i	0.0483473	+	0.645150i	0.967763	+	0.251863i	$0.0810432\pi$
$401$	0.968155	+	12.9191i	0.0483473	+	0.645150i	−0.919416	+	0.393287i	$0.871338\pi$
$402$	11.1161	+	3.42887i	0.554423	+	0.171017i
$403$	−0.688776	+	9.19107i	−0.0343104	+	0.457840i
$404$	−10.1424	+	25.8424i	−0.504603	+	1.28571i
$405$	−20.1531	+	9.70523i	−1.00142	+	0.482257i
$406$	−1.83033	+	16.0621i	−0.0908376	+	0.797147i
$407$	−11.5535	−	5.56386i	−0.572684	−	0.275790i
$408$	−8.50098	+	7.88776i	−0.420861	+	0.390502i
$409$	−4.28731	+	0.646208i	−0.211994	+	0.0319529i	−0.254180	−	0.967157i	$-0.581806\pi$
$409$	−4.28731	+	0.646208i	−0.211994	+	0.0319529i	0.0421865	+	0.999110i	$0.486568\pi$
$410$	−0.662904	+	1.14818i	−0.0327385	+	0.0567048i
$411$	18.5153	+	32.0694i	0.913292	+	1.58187i
$412$	−16.2626	−	20.3926i	−0.801201	−	1.00467i
$413$	6.98360	+	3.70225i	0.343641	+	0.182176i
$414$	−3.18214	+	3.99028i	−0.156394	+	0.196111i
$415$	29.7132	+	4.47855i	1.45856	+	0.219843i
$416$	−4.60223	+	3.13775i	−0.225643	+	0.153841i
$417$	26.5363	−	18.0921i	1.29949	−	0.885976i
$418$	3.05763	+	0.460864i	0.149554	+	0.0225416i
$419$	−3.46062	+	4.33948i	−0.169062	+	0.211998i	−0.859144	−	0.511734i	$-0.829003\pi$
$419$	−3.46062	+	4.33948i	−0.169062	+	0.211998i	0.690081	+	0.723732i	$0.257575\pi$
$420$	−12.9433	+	48.0617i	−0.631566	+	2.34517i
$421$	8.27542	+	10.3770i	0.403319	+	0.505746i	0.941467	−	0.337104i	$-0.109447\pi$
$421$	8.27542	+	10.3770i	0.403319	+	0.505746i	−0.538148	+	0.842850i	$0.680876\pi$
$422$	4.95390	+	8.58041i	0.241152	+	0.417688i
$423$	2.35978	−	4.08727i	0.114737	−	0.198730i
$424$	22.5133	−	3.39333i	1.09334	−	0.164795i
$425$	20.5129	−	19.0332i	0.995021	−	0.923244i
$426$	23.6916	+	11.4093i	1.14786	+	0.552781i
$427$	−1.50258	+	2.38465i	−0.0727151	+	0.115401i
$428$	9.04610	−	4.35637i	0.437260	−	0.210573i
$429$	−2.18253	+	5.56100i	−0.105374	+	0.268488i
$430$	0.746825	−	9.96568i	0.0360151	−	0.480588i
$431$	−8.30992	−	2.56327i	−0.400275	−	0.123468i	0.0880805	−	0.996113i	$-0.471927\pi$
$431$	−8.30992	−	2.56327i	−0.400275	−	0.123468i	−0.488355	+	0.872645i	$0.662403\pi$
$432$	0.372246	+	4.96727i	0.0179097	+	0.238988i
$433$	0.530838	−	2.32575i	0.0255105	−	0.111769i	−0.960570	−	0.278039i	$-0.910315\pi$
$433$	0.530838	−	2.32575i	0.0255105	−	0.111769i	0.986080	+	0.166271i	$0.0531726\pi$
$434$	14.2590	−	3.80137i	0.684454	−	0.182472i
$435$	−25.8712	−	113.349i	−1.24043	−	5.43467i
$436$	5.34249	−	1.64794i	0.255859	−	0.0789219i
$437$	1.75137	+	4.46241i	0.0837793	+	0.213466i
$438$	−7.61171	−	7.06264i	−0.363702	−	0.337466i
$439$	1.55426	+	1.05968i	0.0741809	+	0.0505757i	0.599843	−	0.800118i	$-0.295230\pi$
$439$	1.55426	+	1.05968i	0.0741809	+	0.0505757i	−0.525662	+	0.850694i	$0.676182\pi$
$440$	21.6907			1.03406
$441$	−8.26643	+	26.5605i	−0.393640	+	1.26479i
$442$	1.20847			0.0574813
$443$	−2.25805	−	1.53951i	−0.107283	−	0.0731445i	0.508490	−	0.861068i	$-0.330204\pi$
$443$	−2.25805	−	1.53951i	−0.107283	−	0.0731445i	−0.615773	+	0.787923i	$0.711156\pi$
$444$	17.9285	+	16.6352i	0.850850	+	0.789474i
$445$	6.93824	+	17.6783i	0.328904	+	0.838034i
$446$	−11.4819	+	3.54170i	−0.543685	+	0.167705i
$447$	5.59786	+	24.5258i	0.264770	+	1.16003i
$448$	−1.06953	−	0.791443i	−0.0505308	−	0.0373922i
$449$	5.66143	−	24.8044i	0.267180	−	1.17059i	−0.646099	−	0.763254i	$-0.723601\pi$
$449$	5.66143	−	24.8044i	0.267180	−	1.17059i	0.913278	−	0.407336i	$-0.133542\pi$
$450$	2.51825	+	33.6037i	0.118711	+	1.58409i
$451$	−1.08613	−	0.335026i	−0.0511438	−	0.0157758i
$452$	0.250962	−	3.34885i	0.0118043	−	0.157517i
$453$	−0.795128	+	2.02595i	−0.0373584	+	0.0951876i
$454$	−0.507580	+	0.244438i	−0.0238219	+	0.0114720i
$455$	9.77591	−	6.12539i	0.458302	−	0.287163i
$456$	−11.8180	−	5.69125i	−0.553429	−	0.266517i
$457$	7.02769	−	6.52075i	0.328742	−	0.305028i	−0.498482	−	0.866900i	$-0.666109\pi$
$457$	7.02769	−	6.52075i	0.328742	−	0.305028i	0.827224	+	0.561872i	$0.189919\pi$
$458$	6.42385	−	0.968240i	0.300167	−	0.0452429i
$459$	2.56793	−	4.44778i	0.119861	−	0.207605i
$460$	7.55954	+	13.0935i	0.352465	+	0.610488i
$461$	−11.4460	−	14.3528i	−0.533092	−	0.668476i	0.440240	−	0.897880i	$-0.354894\pi$
$461$	−11.4460	−	14.3528i	−0.533092	−	0.668476i	−0.973331	+	0.229405i	$0.926322\pi$
$462$	9.55771	+	0.369725i	0.444665	+	0.0172012i
$463$	2.14424	−	2.68879i	0.0996512	−	0.124959i	−0.729505	−	0.683975i	$-0.760250\pi$
$463$	2.14424	−	2.68879i	0.0996512	−	0.124959i	0.829157	+	0.559016i	$0.188821\pi$
$464$	19.3375	+	2.91466i	0.897722	+	0.135310i
$465$	−87.6893	+	59.7856i	−4.06650	+	2.77249i
$466$	−9.04983	+	6.17007i	−0.419225	+	0.285823i
$467$	−4.43184	−	0.667992i	−0.205081	−	0.0309110i	0.0456983	−	0.998955i	$-0.485449\pi$
$467$	−4.43184	−	0.667992i	−0.205081	−	0.0309110i	−0.250779	+	0.968044i	$0.580687\pi$
$468$	4.04799	−	5.07602i	0.187118	−	0.234639i
$469$	12.5809	−	14.5819i	0.580931	−	0.673331i
$470$	1.95392	+	2.45013i	0.0901274	+	0.113016i
$471$	5.22643	+	9.05245i	0.240821	+	0.417115i
$472$	−3.28480	+	5.68944i	−0.151195	+	0.261878i
$473$	8.47192	−	1.27694i	0.389539	−	0.0587136i
$474$	−2.59225	+	2.40526i	−0.119066	+	0.110477i
$475$	28.5169	+	13.7330i	1.30844	+	0.630113i
$476$	2.84069	+	8.15127i	0.130203	+	0.373613i
$477$	−37.0693	+	17.8516i	−1.69729	+	0.817371i
$478$	−1.60607	+	4.09219i	−0.0734598	+	0.187173i
$479$	0.0707931	−	0.944668i	0.00323462	−	0.0431630i	−0.995353	−	0.0962941i	$-0.969301\pi$
$479$	0.0707931	−	0.944668i	0.00323462	−	0.0431630i	0.998588	+	0.0531311i	$0.0169201\pi$
$480$	−61.2894	−	18.9053i	−2.79747	−	0.862904i
$481$	−0.423617	−	5.65277i	−0.0193152	−	0.257744i
$482$	−1.36662	+	5.98755i	−0.0622478	+	0.272725i
$483$	6.91227	+	13.1188i	0.314519	+	0.596925i
$484$	−2.13862	−	9.36993i	−0.0972102	−	0.425906i
$485$	−2.72720	+	0.841229i	−0.123836	+	0.0381982i
$486$	−4.70092	−	11.9777i	−0.213238	−	0.543322i
$487$	14.3124	+	13.2800i	0.648557	+	0.601773i	0.934280	−	0.356539i	$-0.116043\pi$
$487$	14.3124	+	13.2800i	0.648557	+	0.601773i	−0.285723	+	0.958312i	$0.592234\pi$
$488$	−1.93558	−	1.31966i	−0.0876196	−	0.0597380i
$489$	−9.13606			−0.413147
$490$	−14.4119	−	11.5529i	−0.651064	−	0.521905i
$491$	11.5943			0.523242			0.261621	−	0.965171i	$-0.415743\pi$
$491$	11.5943			0.523242			0.261621	+	0.965171i	$0.415743\pi$
$492$	1.79114	+	1.22118i	0.0807510	+	0.0550551i
$493$	−14.7806	−	13.7144i	−0.665685	−	0.617665i
$494$	0.499386	+	1.27241i	0.0224684	+	0.0572486i
$495$	−37.4563	+	11.5538i	−1.68354	+	0.519302i
$496$	−3.97233	−	17.4039i	−0.178363	−	0.781459i
$497$	33.0335	−	28.3550i	1.48175	−	1.27190i
$498$	−2.45065	+	10.7370i	−0.109816	+	0.481136i
$499$	0.327825	+	4.37452i	0.0146755	+	0.195831i	0.999723	+	0.0235463i	$0.00749573\pi$
$499$	0.327825	+	4.37452i	0.0146755	+	0.195831i	−0.985047	+	0.172284i	$0.944885\pi$
$500$	61.3529	+	18.9249i	2.74378	+	0.846345i
$501$	2.13236	−	28.4543i	0.0952666	−	1.27124i
$502$	2.58155	−	6.57769i	0.115220	−	0.293576i
$503$	−5.52082	+	2.65869i	−0.246161	+	0.118545i	−0.552897	−	0.833250i	$-0.686478\pi$
$503$	−5.52082	+	2.65869i	−0.246161	+	0.118545i	0.306736	+	0.951795i	$0.400763\pi$
$504$	−21.8130	−	7.66368i	−0.971629	−	0.341367i
$505$	66.7541	+	32.1471i	2.97052	+	1.43053i
$506$	2.12978	−	1.97615i	0.0946804	−	0.0878506i
$507$	−2.61131	+	0.393592i	−0.115973	+	0.0174800i
$508$	16.1849	−	28.0330i	0.718087	−	1.24376i
$509$	−12.2498	−	21.2173i	−0.542963	−	0.940439i	−0.998732	−	0.0503409i	$-0.983969\pi$
$509$	−12.2498	−	21.2173i	−0.542963	−	0.940439i	0.455770	−	0.890098i	$-0.349364\pi$
$510$	8.67613	+	10.8795i	0.384185	+	0.481753i
$511$	−15.7650	+	6.85448i	−0.697402	+	0.303224i
$512$	12.0374	−	15.0945i	0.531985	−	0.667088i
$513$	5.74427	+	0.865809i	0.253616	+	0.0382264i
$514$	−9.89823	+	6.74850i	−0.436592	+	0.297663i
$515$	−57.5165	+	39.2141i	−2.53448	+	1.72798i
$516$	−16.1580	−	2.43543i	−0.711318	−	0.107214i
$517$	−1.67511	+	2.10052i	−0.0736711	+	0.0923806i
$518$	−8.32328	+	3.61889i	−0.365704	+	0.159005i
$519$	−20.9013	−	26.2093i	−0.917463	−	1.15046i
$520$	4.79422	+	8.30384i	0.210241	+	0.364147i
$521$	5.35194	−	9.26983i	0.234473	−	0.406118i	−0.724647	−	0.689121i	$-0.757997\pi$
$521$	5.35194	−	9.26983i	0.234473	−	0.406118i	0.959119	+	0.283002i	$0.0913304\pi$
$522$	24.0099	−	3.61891i	1.05088	−	0.158395i
$523$	5.20048	−	4.82534i	0.227401	−	0.210997i	−0.558241	−	0.829679i	$-0.688523\pi$
$523$	5.20048	−	4.82534i	0.227401	−	0.210997i	0.785642	+	0.618682i	$0.212333\pi$
$524$	−0.945515	−	0.455336i	−0.0413050	−	0.0198915i
$525$	92.3705	+	32.4530i	4.03138	+	1.41636i
$526$	6.62743	−	3.19160i	0.288970	−	0.139160i
$527$	−6.72437	+	17.1334i	−0.292918	+	0.746343i
$528$	0.864669	−	11.5382i	0.0376299	−	0.502136i
$529$	−17.6741	−	5.45174i	−0.768439	−	0.237032i
$530$	−2.04162	−	27.2435i	−0.0886822	−	1.18338i
$531$	2.64179	−	11.5744i	0.114644	−	0.502287i
$532$	−7.40866	+	6.35939i	−0.321206	+	0.275714i
$533$	−0.111805	−	0.489852i	−0.00484283	−	0.0212178i
$534$	−6.65115	+	2.05161i	−0.287824	+	0.0887818i
$535$	−9.78985	−	24.9441i	−0.423252	−	1.07843i
$536$	11.7340	+	10.8876i	0.506833	+	0.470272i
$537$	−49.2161	−	33.5550i	−2.12383	−	1.44800i
$538$	−13.6288			−0.587578
$539$	6.90668	−	14.2496i	0.297492	−	0.613774i
$540$	18.3214			0.788428
$541$	13.1812	+	8.98678i	0.566704	+	0.386372i	0.812510	−	0.582947i	$-0.198100\pi$
$541$	13.1812	+	8.98678i	0.566704	+	0.386372i	−0.245807	+	0.969319i	$0.579053\pi$
$542$	2.85228	+	2.64653i	0.122516	+	0.113678i
$543$	20.8191	+	53.0463i	0.893435	+	2.27643i
$544$	−10.6291	+	3.27865i	−0.455720	+	0.140571i
$545$	−3.32030	−	14.5472i	−0.142226	−	0.623132i
$546$	1.97097	+	3.74069i	0.0843496	+	0.160087i
$547$	8.05244	−	35.2801i	0.344298	−	1.50847i	−0.445603	−	0.895231i	$-0.647011\pi$
$547$	8.05244	−	35.2801i	0.344298	−	1.50847i	0.789900	−	0.613235i	$-0.210132\pi$
$548$	1.71204	+	22.8456i	0.0731347	+	0.975915i
$549$	4.04536	+	1.24783i	0.172652	+	0.0532560i
$550$	1.43354	−	19.1292i	0.0611262	−	0.815673i
$551$	8.33213	−	21.2299i	0.354961	−	0.904425i
$552$	−11.1041	+	5.34743i	−0.472620	+	0.227602i
$553$	1.92662	+	5.52838i	0.0819283	+	0.235091i
$554$	−11.0076	−	5.30100i	−0.467670	−	0.225218i
$555$	47.8488	−	44.3972i	2.03107	−	1.88456i
$556$	19.6478	−	2.96144i	0.833254	−	0.125593i
$557$	−19.5984	+	33.9455i	−0.830413	+	1.43832i	0.0672989	+	0.997733i	$0.478562\pi$
$557$	−19.5984	+	33.9455i	−0.830413	+	1.43832i	−0.897711	+	0.440584i	$0.854771\pi$
$558$	−11.0824	−	19.1953i	−0.469156	−	0.812601i
$559$	2.36137	+	2.96106i	0.0998752	+	0.125240i
$560$	−14.5962	+	16.9178i	−0.616801	+	0.714906i
$561$	−7.43811	+	9.32709i	−0.314037	+	0.393790i
$562$	−9.95262	−	1.50012i	−0.419826	−	0.0632786i
$563$	−31.9684	+	21.7957i	−1.34731	+	0.918578i	−0.999817	−	0.0191067i	$-0.993918\pi$
$563$	−31.9684	+	21.7957i	−1.34731	+	0.918578i	−0.347488	+	0.937684i	$0.612965\pi$
$564$	4.23376	−	2.88653i	0.178273	−	0.121545i
$565$	−8.86259	−	1.33582i	−0.372852	−	0.0561984i
$566$	6.04588	−	7.58130i	0.254127	−	0.318666i
$567$	−13.5624	−	0.524639i	−0.569566	−	0.0220328i
$568$	22.5599	+	28.2892i	0.946590	+	1.18699i
$569$	6.60823	+	11.4458i	0.277031	+	0.479832i	0.970646	−	0.240514i	$-0.0773161\pi$
$569$	6.60823	+	11.4458i	0.277031	+	0.479832i	−0.693614	+	0.720347i	$0.743983\pi$
$570$	−7.86985	+	13.6310i	−0.329632	+	0.570939i
$571$	−36.7057	+	5.53250i	−1.53609	+	0.231528i	−0.861917	−	0.507049i	$-0.830736\pi$
$571$	−36.7057	+	5.53250i	−1.53609	+	0.231528i	−0.674170	+	0.738576i	$0.735498\pi$
$572$	−2.70929	+	2.51385i	−0.113281	+	0.105109i
$573$	38.2433	+	18.4170i	1.59764	+	0.769381i
$574$	−0.681702	+	0.427141i	−0.0284537	+	0.0178285i
$575$	26.7941	−	12.9034i	1.11739	−	0.538107i
$576$	−0.730106	+	1.86028i	−0.0304211	+	0.0775116i
$577$	−0.387695	+	5.17343i	−0.0161400	+	0.215373i	0.983302	+	0.181980i	$0.0582505\pi$
$577$	−0.387695	+	5.17343i	−0.0161400	+	0.215373i	−0.999442	+	0.0333933i	$0.989369\pi$
$578$	−7.52453	−	2.32101i	−0.312979	−	0.0965412i
$579$	−1.61496	−	21.5501i	−0.0671155	−	0.895594i
$580$	16.0057	−	70.1256i	0.664601	−	2.91181i
$581$	14.6564	+	10.8456i	0.608051	+	0.449951i
$582$	−0.232759	−	1.01978i	−0.00964816	−	0.0422714i
$583$	22.3810	−	6.90362i	0.926926	−	0.285919i
$584$	−5.21997	−	13.3003i	−0.216004	−	0.550369i
$585$	−12.7020	−	11.7857i	−0.525162	−	0.487279i
$586$	9.72552	+	6.63075i	0.401758	+	0.273914i
$587$	−16.3800			−0.676073			−0.338037	−	0.941133i	$-0.609763\pi$
$587$	−16.3800			−0.676073			−0.338037	+	0.941133i	$0.609763\pi$
$588$	−20.5982	+	22.0874i	−0.849458	+	0.910867i
$589$	−20.8187			−0.857818
$590$	6.51338	+	4.44075i	0.268152	+	0.182823i
$591$	−30.2167	−	28.0370i	−1.24295	−	1.15329i
$592$	4.01114	+	10.2202i	0.164857	+	0.420048i
$593$	30.8583	−	9.51853i	1.26720	−	0.390879i	0.412956	−	0.910751i	$-0.364496\pi$
$593$	30.8583	−	9.51853i	1.26720	−	0.390879i	0.854244	+	0.519872i	$0.174020\pi$
$594$	−0.783439	−	3.43247i	−0.0321449	−	0.140836i
$595$	22.2603	−	5.93449i	0.912585	−	0.243290i
$596$	−3.46322	+	15.1734i	−0.141859	+	0.621525i
$597$	3.93695	+	52.5350i	0.161129	+	2.15011i
$598$	1.22727	+	0.378562i	0.0501867	+	0.0154805i
$599$	−0.718960	+	9.59386i	−0.0293759	+	0.391994i	0.963065	+	0.269270i	$0.0867823\pi$
$599$	−0.718960	+	9.59386i	−0.0293759	+	0.391994i	−0.992441	+	0.122725i	$0.960837\pi$
$600$	−29.7292	+	75.7488i	−1.21369	+	3.09243i
$601$	16.3070	−	7.85302i	0.665175	−	0.320331i	−0.0706522	−	0.997501i	$-0.522508\pi$
$601$	16.3070	−	7.85302i	0.665175	−	0.320331i	0.735827	+	0.677170i	$0.236794\pi$
$602$	3.23267	−	5.13035i	0.131754	−	0.209097i
$603$	−26.0622	−	12.5509i	−1.06133	−	0.511111i
$604$	−0.987033	+	0.915833i	−0.0401618	+	0.0372647i
$605$	−25.3637	+	3.82296i	−1.03118	+	0.155425i
$606$	−13.5775	+	23.5170i	−0.551550	+	0.955312i
$607$	0.215718	+	0.373635i	0.00875574	+	0.0151654i	0.870370	−	0.492398i	$-0.163880\pi$
$607$	0.215718	+	0.373635i	0.00875574	+	0.0151654i	−0.861614	+	0.507564i	$0.830546\pi$
$608$	−7.84446	−	9.83664i	−0.318135	−	0.398928i
$609$	18.3448	−	68.1192i	0.743369	−	2.76033i
$610$	−1.75266	+	2.19776i	−0.0709630	+	0.0889848i
$611$	−1.17438	−	0.177010i	−0.0475104	−	0.00716105i
$612$	10.7124	−	7.30358i	0.433022	−	0.295230i
$613$	14.8536	−	10.1270i	0.599931	−	0.409026i	−0.224919	−	0.974377i	$-0.572212\pi$
$613$	14.8536	−	10.1270i	0.599931	−	0.409026i	0.824850	+	0.565351i	$0.191259\pi$
$614$	−0.500444	−	0.0754297i	−0.0201963	−	0.00304410i
$615$	3.60728	−	4.52339i	0.145460	−	0.182401i
$616$	11.6284	+	6.16460i	0.468521	+	0.248379i
$617$	−9.33457	−	11.7052i	−0.375796	−	0.471233i	0.557585	−	0.830120i	$-0.311728\pi$
$617$	−9.33457	−	11.7052i	−0.375796	−	0.471233i	−0.933381	+	0.358887i	$0.883156\pi$
$618$	−12.7567	−	22.0953i	−0.513151	−	0.888803i
$619$	19.0002	−	32.9093i	0.763683	−	1.32274i	−0.177257	−	0.984165i	$-0.556722\pi$
$619$	19.0002	−	32.9093i	0.763683	−	1.32274i	0.940940	−	0.338573i	$-0.109944\pi$
$620$	−64.9264	+	9.78608i	−2.60751	+	0.393018i
$621$	4.00115	−	3.71253i	0.160561	−	0.148979i
$622$	−2.54604	−	1.22611i	−0.102087	−	0.0491624i
$623$	−1.30468	+	11.4492i	−0.0522709	+	0.458704i
$624$	4.60828	−	2.21923i	0.184479	−	0.0888404i
$625$	37.0061	−	94.2899i	1.48024	−	3.77160i
$626$	−0.567633	+	7.57454i	−0.0226872	+	0.302740i
$627$	−12.8943	−	3.97736i	−0.514948	−	0.158840i
$628$	0.483269	+	6.44878i	0.0192845	+	0.257334i
$629$	2.51895	−	11.0362i	0.100437	−	0.440043i
$630$	−11.1263	+	25.4141i	−0.443283	+	1.01252i
$631$	−5.16523	−	22.6304i	−0.205625	−	0.900901i	−0.967439	−	0.253105i	$-0.918548\pi$
$631$	−5.16523	−	22.6304i	−0.205625	−	0.900901i	0.761814	−	0.647796i	$-0.224309\pi$
$632$	−4.64974	+	1.43426i	−0.184957	+	0.0570516i
$633$	−15.7960	−	40.2475i	−0.627833	−	1.59969i
$634$	−8.46619	−	7.85548i	−0.336235	−	0.311981i
$635$	−71.3791	−	48.6654i	−2.83259	−	1.93123i
$636$	−44.6707			−1.77131
$637$	6.98173	−	0.505459i	0.276626	−	0.0200270i
$638$	−13.8223			−0.547229
$639$	−54.0257	−	36.8341i	−2.13722	−	1.45714i
$640$	−36.5809	−	33.9421i	−1.44599	−	1.34168i
$641$	−15.6435	−	39.8590i	−0.617882	−	1.57434i	−0.805823	−	0.592157i	$-0.798277\pi$
$641$	−15.6435	−	39.8590i	−0.617882	−	1.57434i	0.187941	−	0.982180i	$-0.439819\pi$
$642$	9.38478	−	2.89482i	0.370388	−	0.114249i
$643$	3.33350	+	14.6050i	0.131461	+	0.575967i	0.997154	+	0.0753919i	$0.0240208\pi$
$643$	3.33350	+	14.6050i	0.131461	+	0.575967i	−0.865693	+	0.500575i	$0.833122\pi$
$644$	0.331432	+	9.16788i	0.0130602	+	0.361265i
$645$	−9.70430	+	42.5173i	−0.382106	+	1.67412i
$646$	0.203988	+	2.72203i	0.00802579	+	0.107097i
$647$	−27.2498	−	8.40546i	−1.07130	−	0.330453i	−0.291559	−	0.956553i	$-0.594174\pi$
$647$	−27.2498	−	8.40546i	−1.07130	−	0.330453i	−0.779743	+	0.626100i	$0.784650\pi$
$648$	0.843010	−	11.2492i	0.0331166	−	0.441910i
$649$	−2.46908	+	6.29112i	−0.0969200	+	0.246948i
$650$	7.64008	−	3.67927i	0.299669	−	0.144313i
$651$	−64.0016	+	7.12932i	−2.50842	+	0.279420i
$652$	−5.09245	−	2.45240i	−0.199436	−	0.0960433i
$653$	29.6203	−	27.4837i	1.15913	−	1.07552i	0.163094	−	0.986611i	$-0.447853\pi$
$653$	29.6203	−	27.4837i	1.15913	−	1.07552i	0.996040	−	0.0889081i	$-0.0283378\pi$
$654$	5.40767	−	0.815076i	0.211457	−	0.0318720i
$655$	−1.40041	+	2.42558i	−0.0547185	+	0.0947753i
$656$	0.486580	+	0.842781i	0.0189978	+	0.0329051i
$657$	16.0986	+	20.1870i	0.628065	+	0.787569i
$658$	0.351155	+	1.86883i	0.0136894	+	0.0728545i
$659$	−29.6117	+	37.1319i	−1.15351	+	1.44645i	−0.279762	+	0.960069i	$0.590256\pi$
$659$	−29.6117	+	37.1319i	−1.15351	+	1.44645i	−0.873745	+	0.486383i	$0.838316\pi$
$660$	−42.0825	−	6.34292i	−1.63806	−	0.246898i
$661$	1.66597	−	1.13584i	0.0647988	−	0.0441791i	−0.530487	−	0.847693i	$-0.677991\pi$
$661$	1.66597	−	1.13584i	0.0647988	−	0.0441791i	0.595286	+	0.803514i	$0.297039\pi$
$662$	−8.30860	+	5.66470i	−0.322923	+	0.220165i
$663$	−5.21471	−	0.785990i	−0.202522	−	0.0305253i
$664$	−9.44848	+	11.8480i	−0.366672	+	0.459792i
$665$	15.4473	+	20.9858i	0.599019	+	0.813793i
$666$	8.49940	+	10.6579i	0.329345	+	0.412986i
$667$	−10.7143	−	18.5578i	−0.414861	−	0.718560i
$668$	8.82658	−	15.2881i	0.341510	−	0.591513i
$669$	51.8493	−	7.81503i	2.00461	−	0.302146i
$670$	14.0802	−	13.0645i	0.543966	−	0.504727i
$671$	−2.17127	−	1.04563i	−0.0838210	−	0.0403661i
$672$	−27.4843	−	27.5539i	−1.06023	−	1.06291i
$673$	8.95309	−	4.31158i	0.345116	−	0.166199i	−0.253293	−	0.967389i	$-0.581514\pi$
$673$	8.95309	−	4.31158i	0.345116	−	0.166199i	0.598410	+	0.801190i	$0.295800\pi$
$674$	−2.55704	+	6.51523i	−0.0984935	+	0.250957i
$675$	2.69314	−	35.9375i	0.103659	−	1.38323i
$676$	−1.56120	−	0.481567i	−0.0600462	−	0.0185218i
$677$	0.451059	+	6.01897i	0.0173356	+	0.231328i	0.999141	+	0.0414382i	$0.0131940\pi$
$677$	0.451059	+	6.01897i	0.0173356	+	0.231328i	−0.981805	+	0.189890i	$0.939187\pi$
$678$	0.730957	−	3.20253i	0.0280722	−	0.122993i
$679$	−1.70113	−	0.324100i	−0.0652834	−	0.0124378i
$680$	4.26079	+	18.6677i	0.163394	+	0.715874i
$681$	2.34925	−	0.724647i	0.0900234	−	0.0277685i
$682$	4.60970	+	11.7453i	0.176515	+	0.449752i
$683$	17.1538	+	15.9164i	0.656374	+	0.609026i	0.936387	−	0.350971i	$-0.114148\pi$
$683$	17.1538	+	15.9164i	0.656374	+	0.609026i	−0.280013	+	0.959996i	$0.590339\pi$
$684$	12.1168	+	8.26106i	0.463296	+	0.315870i
$685$	61.1427			2.33614
$686$	−4.44285	−	10.2894i	−0.169629	−	0.392852i
$687$	−28.3494			−1.08160
$688$	−6.06083	−	4.13220i	−0.231067	−	0.157539i
$689$	7.58971	+	7.04222i	0.289145	+	0.268287i
$690$	5.40297	+	13.7665i	0.205688	+	0.524083i
$691$	10.3162	−	3.18212i	0.392446	−	0.121054i	−0.0922508	−	0.995736i	$-0.529406\pi$
$691$	10.3162	−	3.18212i	0.392446	−	0.121054i	0.484697	+	0.874682i	$0.338930\pi$
$692$	−4.61500	−	20.2197i	−0.175436	−	0.768636i
$693$	−23.3640	−	4.45130i	−0.887524	−	0.169091i
$694$	4.04412	−	17.7185i	0.153513	−	0.672584i
$695$	−3.96291	−	52.8814i	−0.150322	−	2.00591i
$696$	56.0292	+	17.2827i	2.12378	+	0.655099i
$697$	0.0749822	−	1.00057i	0.00284015	−	0.0378992i
$698$	−6.25012	+	15.9251i	−0.236571	+	0.602772i
$699$	43.0640	−	20.7385i	1.62883	−	0.784404i
$700$	42.7761	+	42.8844i	1.61678	+	1.62088i
$701$	13.8334	+	6.66182i	0.522481	+	0.251614i	0.676485	−	0.736457i	$-0.263503\pi$
$701$	13.8334	+	6.66182i	0.522481	+	0.251614i	−0.154004	+	0.988070i	$0.549217\pi$
$702$	1.14089	−	1.05859i	0.0430601	−	0.0399540i
$703$	12.6611	−	1.90835i	0.477521	−	0.0719747i
$704$	0.568811	−	0.985210i	0.0214379	−	0.0371315i
$705$	−6.83780	−	11.8434i	−0.257527	−	0.446049i
$706$	1.49907	+	1.87977i	0.0564182	+	0.0707462i
$707$	26.6505	+	36.2059i	1.00230	+	1.36166i
$708$	8.03663	−	10.0776i	0.302035	−	0.378740i
$709$	−32.9058	−	4.95976i	−1.23581	−	0.186268i	−0.501542	−	0.865133i	$-0.667234\pi$
$709$	−32.9058	−	4.95976i	−1.23581	−	0.186268i	−0.734263	+	0.678865i	$0.762472\pi$
$710$	35.8736	−	24.4582i	1.34631	−	0.917900i
$711$	7.26539	−	4.95346i	0.272473	−	0.185769i
$712$	−9.47060	−	1.42746i	−0.354926	−	0.0534965i
$713$	−12.1961	+	15.2934i	−0.456746	+	0.572742i
$714$	1.55926	+	8.29830i	0.0583538	+	0.310556i
$715$	6.15002	+	7.71188i	0.229998	+	0.288408i
$716$	−18.4259	−	31.9147i	−0.688610	−	1.19271i
$717$	9.59192	−	16.6137i	0.358217	−	0.620450i
$718$	−13.5497	+	2.04229i	−0.505669	+	0.0762174i
$719$	−24.2056	+	22.4596i	−0.902718	+	0.837600i	−0.987308	−	0.158816i	$-0.949232\pi$
$719$	−24.2056	+	22.4596i	−0.902718	+	0.837600i	0.0845901	+	0.996416i	$0.473042\pi$
$720$	30.2370	+	14.5614i	1.12687	+	0.542670i
$721$	−41.9794	+	4.67620i	−1.56339	+	0.174151i
$722$	7.57755	−	3.64916i	0.282007	−	0.135808i
$723$	9.79140	−	24.9481i	0.364146	−	0.927830i
$724$	−2.63462	+	35.1566i	−0.0979149	+	1.30658i
$725$	−135.198	−	41.7032i	−5.02115	−	1.54882i
$726$	−0.702535	−	9.37468i	−0.0260735	−	0.347927i
$727$	−3.70820	+	16.2467i	−0.137529	+	0.602556i	0.858444	+	0.512907i	$0.171432\pi$
$727$	−3.70820	+	16.2467i	−0.137529	+	0.602556i	−0.995973	+	0.0896485i	$0.971426\pi$
$728$	0.210192	+	5.81423i	0.00779025	+	0.215490i
$729$	9.07014	+	39.7389i	0.335931	+	1.47181i
$730$	−16.3831	+	5.05351i	−0.606365	+	0.187039i
$731$	2.76314	+	7.04037i	0.102199	+	0.260398i
$732$	3.36935	+	3.12630i	0.124535	+	0.115551i
$733$	−12.0927	−	8.24467i	−0.446654	−	0.304524i	0.319025	−	0.947746i	$-0.396645\pi$
$733$	−12.0927	−	8.24467i	−0.446654	−	0.304524i	−0.765679	+	0.643223i	$0.777597\pi$
$734$	−11.5475			−0.426227
$735$	54.6751	+	59.2254i	2.01672	+	2.18456i
$736$	−11.8215			−0.435745
$737$	13.6056	+	9.27612i	0.501168	+	0.341690i
$738$	0.885745	+	0.821851i	0.0326047	+	0.0302527i
$739$	−16.0172	−	40.8112i	−0.589203	−	1.50126i	−0.845126	−	0.534567i	$-0.820475\pi$
$739$	−16.0172	−	40.8112i	−0.589203	−	1.50126i	0.255924	−	0.966697i	$-0.417620\pi$
$740$	38.5885	−	11.9030i	1.41854	−	0.437562i
$741$	−1.32733	−	5.81541i	−0.0487607	−	0.213634i
$742$	6.64822	−	15.1855i	0.244064	−	0.557476i
$743$	4.24806	−	18.6120i	0.155846	−	0.682807i	−0.835273	−	0.549835i	$-0.814691\pi$
$743$	4.24806	−	18.6120i	0.155846	−	0.682807i	0.991120	−	0.132972i	$-0.0424522\pi$
$744$	−3.99983	−	53.3740i	−0.146641	−	1.95679i
$745$	39.6917	+	12.2433i	1.45419	+	0.448558i
$746$	0.320972	−	4.28307i	0.0117516	−	0.156814i
$747$	10.0050	−	25.4924i	0.366065	−	0.932720i
$748$	−6.64968	+	3.20232i	−0.243137	+	0.117088i
$749$	1.84090	−	16.1549i	0.0672651	−	0.590286i
$750$	56.5835	+	27.2492i	2.06614	+	0.994999i
$751$	−1.84328	+	1.71032i	−0.0672624	+	0.0624104i	−0.713088	−	0.701075i	$-0.752704\pi$
$751$	−1.84328	+	1.71032i	−0.0672624	+	0.0624104i	0.645825	+	0.763485i	$0.276513\pi$
$752$	2.27458	−	0.342838i	0.0829455	−	0.0125020i
$753$	−15.4178	+	26.7044i	−0.561856	+	0.973163i
$754$	−3.05509	−	5.29157i	−0.111260	−	0.192708i
$755$	2.24054	+	2.80955i	0.0815416	+	0.102250i
$756$	9.82211	+	5.20703i	0.357227	+	0.189378i
$757$	−31.0547	+	38.9414i	−1.12870	+	1.41535i	−0.231999	+	0.972716i	$0.574527\pi$
$757$	−31.0547	+	38.9414i	−1.12870	+	1.41535i	−0.896703	+	0.442632i	$0.854045\pi$
$758$	−18.1931	−	2.74218i	−0.660805	−	0.0996003i
$759$	−10.4755	+	7.14210i	−0.380238	+	0.259242i
$760$	−17.8947	+	12.2004i	−0.649109	+	0.442555i
$761$	35.8857	+	5.40890i	1.30086	+	0.196072i	0.762689	−	0.646766i	$-0.223879\pi$
$761$	35.8857	+	5.40890i	1.30086	+	0.196072i	0.538167	+	0.842838i	$0.319117\pi$
$762$	19.7414	−	24.7549i	0.715154	−	0.896775i
$763$	2.35436	−	8.74238i	0.0852337	−	0.316495i
$764$	16.3732	+	20.5313i	0.592361	+	0.742797i
$765$	−17.3012	−	29.9666i	−0.625527	−	1.08344i
$766$	−3.96863	+	6.87386i	−0.143392	+	0.248363i
$767$	−2.95416	+	0.445268i	−0.106669	+	0.0160777i
$768$	11.4601	−	10.6334i	0.413531	−	0.383701i
$769$	40.7603	+	19.6291i	1.46986	+	0.707845i	0.985914	−	0.167255i	$-0.0534905\pi$
$769$	40.7603	+	19.6291i	1.46986	+	0.707845i	0.483941	+	0.875100i	$0.339205\pi$
$770$	8.41925	−	13.3616i	0.303409	−	0.481520i
$771$	47.1012	−	22.6827i	1.69631	−	0.816899i
$772$	4.88453	−	12.4456i	0.175798	−	0.447926i
$773$	−2.15130	+	28.7071i	−0.0773770	+	1.03252i	0.814476	+	0.580198i	$0.197025\pi$
$773$	−2.15130	+	28.7071i	−0.0773770	+	1.03252i	−0.891853	+	0.452326i	$0.850594\pi$
$774$	−8.70322	−	2.68459i	−0.312831	−	0.0964955i
$775$	9.65159	+	128.792i	0.346696	+	4.62633i
$776$	0.320279	−	1.40323i	0.0114973	−	0.0503732i
$777$	38.2696	−	10.2025i	1.37291	−	0.366012i
$778$	1.18930	+	5.21065i	0.0426384	+	0.186811i
$779$	1.08449	−	0.334522i	0.0388560	−	0.0119855i
$780$	−6.87310	−	17.5124i	−0.246096	−	0.627044i
$781$	27.2860	+	25.3177i	0.976371	+	0.905940i
$782$	2.11910	+	1.44478i	0.0757789	+	0.0516652i
$783$	−25.9674			−0.928000
$784$	−12.6331	+	4.92130i	−0.451183	+	0.175761i
$785$	17.2592			0.616006
$786$	−0.848151	−	0.578260i	−0.0302525	−	0.0206258i
$787$	24.3506	+	22.5940i	0.868005	+	0.805391i	0.982155	−	0.188073i	$-0.0602241\pi$
$787$	24.3506	+	22.5940i	0.868005	+	0.805391i	−0.114150	+	0.993463i	$0.536415\pi$
$788$	−9.31683	−	23.7389i	−0.331898	−	0.845663i
$789$	−30.6739	+	9.46165i	−1.09202	+	0.336844i
$790$	1.29927	+	5.69246i	0.0462258	+	0.202529i
$791$	−4.37159	−	3.23492i	−0.155436	−	0.115021i
$792$	4.39883	−	19.2725i	0.156306	−	0.684820i
$793$	−0.0796113	−	1.06234i	−0.00282708	−	0.0377248i
$794$	7.35685	+	2.26929i	0.261085	+	0.0805340i
$795$	−8.90932	+	118.887i	−0.315981	+	4.21647i
$796$	−11.9075	+	30.3399i	−0.422051	+	1.07537i
$797$	0.804861	−	0.387601i	0.0285096	−	0.0137295i	−0.419575	−	0.907721i	$-0.637821\pi$
$797$	0.804861	−	0.387601i	0.0285096	−	0.0137295i	0.448084	+	0.893991i	$0.352106\pi$
$798$	−8.09302	+	5.07092i	−0.286490	+	0.179509i
$799$	−2.13682	−	1.02904i	−0.0755953	−	0.0364048i
$800$	−57.2162	+	53.0888i	−2.02290	+	1.87697i
$801$	17.1146	−	2.57960i	0.604713	−	0.0911458i
$802$	−3.92000	+	6.78964i	−0.138420	+	0.239751i
$803$	−7.34918	−	12.7291i	−0.259347	−	0.449202i
$804$	−19.5816	−	24.5545i	−0.690589	−	0.865972i
$805$	24.4655	+	0.946410i	0.862296	+	0.0333566i
$806$	−3.47759	+	4.36076i	−0.122493	+	0.153601i
$807$	58.8097	+	8.86413i	2.07020	+	0.312032i
$808$	−30.8730	+	21.0489i	−1.08611	+	0.740496i
$809$	−32.3701	+	22.0696i	−1.13807	+	0.775924i	−0.977466	−	0.211094i	$-0.932297\pi$
$809$	−32.3701	+	22.0696i	−1.13807	+	0.775924i	−0.160606	+	0.987019i	$0.551345\pi$
$810$	−13.3851	−	2.01748i	−0.470304	−	0.0708870i
$811$	−26.1917	+	32.8433i	−0.919715	+	1.15329i	0.0681043	+	0.997678i	$0.478305\pi$
$811$	−26.1917	+	32.8433i	−0.919715	+	1.15329i	−0.987819	+	0.155607i	$0.950266\pi$
$812$	28.5107	−	33.0454i	1.00053	−	1.15967i
$813$	−10.5866	−	13.2752i	−0.371289	−	0.465581i
$814$	−3.88007	−	6.72048i	−0.135996	−	0.235553i
$815$	−7.54247	+	13.0639i	−0.264201	+	0.457610i
$816$	10.1000	−	1.52233i	0.353571	−	0.0532923i
$817$	−6.27104	+	5.81868i	−0.219396	+	0.203570i
$818$	−2.36396	−	1.13842i	−0.0826539	−	0.0398040i
$819$	−3.45997	−	9.92827i	−0.120901	−	0.346922i
$820$	3.22492	−	1.55304i	0.112619	−	0.0542345i
$821$	0.617936	−	1.57448i	0.0215661	−	0.0549496i	−0.919685	−	0.392657i	$-0.871556\pi$
$821$	0.617936	−	1.57448i	0.0215661	−	0.0549496i	0.941251	+	0.337707i	$0.109651\pi$
$822$	−1.67465	+	22.3466i	−0.0584100	+	0.779427i
$823$	42.6910	+	13.1684i	1.48811	+	0.459022i	0.929004	−	0.370071i	$-0.120666\pi$
$823$	42.6910	+	13.1684i	1.48811	+	0.459022i	0.559111	+	0.829093i	$0.311143\pi$
$824$	−2.62354	−	35.0087i	−0.0913952	−	1.21958i
$825$	−18.6275	+	81.6124i	−0.648526	+	2.84138i
$826$	2.22974	+	4.23182i	0.0775826	+	0.147244i
$827$	−0.00583585	−	0.0255686i	−0.000202933	−	0.000889106i	0.974826	−	0.222965i	$-0.0715737\pi$
$827$	−0.00583585	−	0.0255686i	−0.000202933	−	0.000889106i	−0.975029	+	0.222076i	$0.928717\pi$
$828$	13.1669	−	4.06144i	0.457580	−	0.141145i
$829$	−7.22682	−	18.4136i	−0.250998	−	0.639532i	0.748730	−	0.662875i	$-0.230664\pi$
$829$	−7.22682	−	18.4136i	−0.250998	−	0.639532i	−0.999728	+	0.0233435i	$0.992569\pi$
$830$	13.3300	+	12.3684i	0.462690	+	0.429314i
$831$	44.0515	+	30.0338i	1.52813	+	1.04186i
$832$	0.502890			0.0174346
$833$	13.6204	+	3.14502i	0.471918	+	0.108968i
$834$	19.4358			0.673005
$835$	−38.9273	−	26.5402i	−1.34713	−	0.918461i
$836$	−6.11964	−	5.67820i	−0.211652	−	0.196385i
$837$	8.66010	+	22.0656i	0.299337	+	0.762698i
$838$	−3.20963	+	0.990041i	−0.110875	+	0.0342004i
$839$	5.16461	+	22.6276i	0.178302	+	0.781192i	0.982414	+	0.186715i	$0.0597840\pi$
$839$	5.16461	+	22.6276i	0.178302	+	0.781192i	−0.804112	+	0.594478i	$0.797359\pi$
$840$	−50.8346	+	43.6350i	−1.75396	+	1.50555i
$841$	−16.2322	+	71.1179i	−0.559731	+	2.45234i
$842$	0.600238	+	8.00962i	0.0206856	+	0.276030i
$843$	41.9710	+	12.9463i	1.44556	+	0.445896i
$844$	1.99895	−	26.6741i	0.0688066	−	0.918160i
$845$	−1.59302	+	4.05894i	−0.0548014	+	0.139632i
$846$	2.57323	−	1.23920i	0.0884696	−	0.0426047i
$847$	−14.6840	−	5.15899i	−0.504547	−	0.177265i
$848$	−18.0673	−	8.70073i	−0.620432	−	0.298784i
$849$	−31.0195	+	28.7819i	−1.06459	+	0.987793i
$850$	16.7448	−	2.52388i	0.574343	−	0.0865683i
$851$	6.01528	−	10.4188i	0.206201	−	0.357151i
$852$	−35.4963	−	61.4814i	−1.21608	−	2.10632i
$853$	−16.4809	−	20.6664i	−0.564296	−	0.707605i	0.415050	−	0.909799i	$-0.363764\pi$
$853$	−16.4809	−	20.6664i	−0.564296	−	0.707605i	−0.979345	+	0.202194i	$0.935193\pi$
$854$	−1.56421	+	0.680107i	−0.0535263	+	0.0232728i
$855$	24.4026	−	30.5999i	0.834552	−	1.04649i
$856$	13.3630	+	2.01415i	0.456738	+	0.0688423i
$857$	−19.3501	+	13.1927i	−0.660987	+	0.450653i	−0.846785	−	0.531935i	$-0.821465\pi$
$857$	−19.3501	+	13.1927i	−0.660987	+	0.450653i	0.185798	+	0.982588i	$0.440513\pi$
$858$	−2.98700	+	2.03650i	−0.101974	+	0.0695250i
$859$	8.56248	+	1.29059i	0.292148	+	0.0440342i	0.293481	−	0.955965i	$-0.405186\pi$
$859$	8.56248	+	1.29059i	0.292148	+	0.0440342i	−0.00133299	+	0.999999i	$0.500424\pi$
$860$	−16.8221	+	21.0943i	−0.573630	+	0.719309i
$861$	3.21943	−	1.39978i	0.109718	−	0.0477045i
$862$	−3.28117	−	4.11446i	−0.111757	−	0.140139i
$863$	8.24017	+	14.2724i	0.280499	+	0.485838i	0.971508	−	0.237008i	$-0.0761668\pi$
$863$	8.24017	+	14.2724i	0.280499	+	0.485838i	−0.691009	+	0.722846i	$0.742833\pi$
$864$	−7.16267	+	12.4061i	−0.243679	+	0.422064i
$865$	−54.7330	+	8.24968i	−1.86098	+	0.280497i
$866$	1.05826	−	0.981923i	0.0359612	−	0.0333671i
$867$	30.9596	+	14.9094i	1.05144	+	0.506348i
$868$	−37.5883	−	13.2061i	−1.27583	−	0.448243i
$869$	−4.50997	+	2.17189i	−0.152990	+	0.0736762i
$870$	25.7046	−	65.4943i	0.871468	−	2.22046i
$871$	−0.543978	+	7.25888i	−0.0184320	+	0.245958i
$872$	7.19075	+	2.21805i	0.243510	+	0.0751128i
$873$	0.194375	+	2.59376i	0.00657861	+	0.0877854i
$874$	−0.645531	+	2.82825i	−0.0218354	+	0.0956671i
$875$	78.8950	−	67.7212i	2.66714	−	2.28940i
$876$	6.23802	+	27.3306i	0.210763	+	0.923414i
$877$	−2.81889	+	0.869513i	−0.0951872	+	0.0293614i	−0.341983	−	0.939706i	$-0.611099\pi$
$877$	−2.81889	+	0.869513i	−0.0951872	+	0.0293614i	0.246796	+	0.969068i	$0.420622\pi$
$878$	0.415896	+	1.05968i	0.0140358	+	0.0357626i
$879$	−37.6541	−	34.9379i	−1.27004	−	1.17843i
$880$	−15.7850	−	10.7620i	−0.532112	−	0.362788i
$881$	32.0771			1.08070			0.540352	−	0.841439i	$-0.318291\pi$
$881$	32.0771			1.08070			0.540352	+	0.841439i	$0.318291\pi$
$882$	−13.1876	+	10.4623i	−0.444050	+	0.352285i
$883$	−6.44985			−0.217055			−0.108527	−	0.994093i	$-0.534614\pi$
$883$	−6.44985			−0.217055			−0.108527	+	0.994093i	$0.534614\pi$
$884$	−2.69570	−	1.83790i	−0.0906662	−	0.0618152i
$885$	−25.2177	−	23.3986i	−0.847684	−	0.786536i
$886$	−0.604218	−	1.53952i	−0.0202991	−	0.0517213i
$887$	34.0097	−	10.4906i	1.14193	−	0.352240i	0.334615	−	0.942355i	$-0.391394\pi$
$887$	34.0097	−	10.4906i	1.14193	−	0.352240i	0.807319	+	0.590115i	$0.200917\pi$
$888$	7.32507	+	32.0932i	0.245813	+	1.07698i
$889$	−24.4354	−	46.3758i	−0.819536	−	1.55539i
$890$	−2.55734	+	11.2044i	−0.0857223	+	0.375574i
$891$	−0.867225	−	11.5723i	−0.0290531	−	0.387687i
$892$	30.9987	+	9.56182i	1.03791	+	0.320153i
$893$	0.200472	−	2.67511i	0.00670854	−	0.0895193i
$894$	−5.56181	+	14.1713i	−0.186015	+	0.473958i
$895$	−88.6126	+	42.6736i	−2.96199	+	1.42642i
$896$	−9.96450	−	28.5928i	−0.332890	−	0.955218i
$897$	−5.04958	−	2.43175i	−0.168601	−	0.0811938i
$898$	11.2864	−	10.4723i	0.376634	−	0.349465i
$899$	92.0219	−	13.8701i	3.06910	−	0.462593i
$900$	45.4885	−	78.7883i	1.51628	−	2.62628i
$901$	10.3379	+	17.9057i	0.344404	+	0.596526i
$902$	−0.428858	−	0.537771i	−0.0142794	−	0.0179058i
$903$	−17.2861	+	20.0355i	−0.575245	+	0.666740i
$904$	2.81821	−	3.53392i	0.0937321	−	0.117536i
$905$	93.0402	+	14.0236i	3.09276	+	0.466159i
$906$	−1.08821	+	0.741927i	−0.0361532	+	0.0246489i
$907$	34.8585	−	23.7661i	1.15746	−	0.789141i	0.176680	−	0.984268i	$-0.443464\pi$
$907$	34.8585	−	23.7661i	1.15746	−	0.789141i	0.980778	+	0.195127i	$0.0625119\pi$
$908$	1.50399	+	0.226690i	0.0499117	+	0.00752298i
$909$	42.1008	−	52.7928i	1.39640	−	1.75103i
$910$	6.97611	+	0.269860i	0.231256	+	0.00894577i
$911$	−10.9689	−	13.7546i	−0.363416	−	0.455710i	0.566184	−	0.824279i	$-0.308419\pi$
$911$	−10.9689	−	13.7546i	−0.363416	−	0.455710i	−0.929600	+	0.368569i	$0.879848\pi$
$912$	5.77657	+	10.0053i	0.191281	+	0.331309i
$913$	−7.79473	+	13.5009i	−0.257968	+	0.446814i
$914$	5.73677	−	0.864678i	0.189755	−	0.0286010i
$915$	8.99234	−	8.34367i	0.297278	−	0.275833i
$916$	−15.8020	−	7.60984i	−0.522112	−	0.251436i
$917$	−1.44012	+	0.902350i	−0.0475570	+	0.0297982i
$918$	2.80020	−	1.34851i	0.0924205	−	0.0445074i
$919$	−12.4311	+	31.6740i	−0.410065	+	1.04483i	0.565428	+	0.824798i	$0.308711\pi$
$919$	−12.4311	+	31.6740i	−0.410065	+	1.04483i	−0.975493	+	0.220031i	$0.929384\pi$
$920$	−1.52073	+	20.2927i	−0.0501370	+	0.669031i
$921$	2.11041	+	0.650976i	0.0695404	+	0.0214504i
$922$	−0.830205	−	11.0783i	−0.0273414	−	0.364845i
$923$	−3.66143	+	16.0418i	−0.120518	+	0.528022i
$924$	−20.7577	−	15.3605i	−0.682879	−	0.505323i
$925$	−17.6754	−	77.4410i	−0.581164	−	2.54625i
$926$	1.98872	−	0.613440i	0.0653535	−	0.0201589i
$927$	23.1781	+	59.0569i	0.761269	+	1.93968i
$928$	41.2272	+	38.2533i	1.35335	+	1.25573i
$929$	22.5352	+	15.3643i	0.739358	+	0.504085i	0.873468	−	0.486881i	$-0.161865\pi$
$929$	22.5352	+	15.3643i	0.739358	+	0.504085i	−0.134111	+	0.990966i	$0.542818\pi$
$930$	−64.2256			−2.10604
$931$	2.31702	+	15.6406i	0.0759372	+	0.512602i
$932$	29.5708			0.968624
$933$	10.1890	+	6.94673i	0.333572	+	0.227426i
$934$	−1.98822	−	1.84479i	−0.0650564	−	0.0603635i
$935$	7.19641	+	18.3362i	0.235348	+	0.599656i
$936$	8.35035	−	2.57574i	0.272940	−	0.0841908i
$937$	−2.57284	−	11.2724i	−0.0840511	−	0.368252i	0.915357	−	0.402642i	$-0.131908\pi$
$937$	−2.57284	−	11.2724i	−0.0840511	−	0.368252i	−0.999408	+	0.0343905i	$0.989051\pi$
$938$	11.2614	−	3.00223i	0.367698	−	0.0980263i
$939$	7.37587	−	32.3158i	0.240703	−	1.05459i
$940$	−0.632267	−	8.43701i	−0.0206223	−	0.275185i
$941$	−14.5529	−	4.48897i	−0.474411	−	0.146336i	0.0483240	−	0.998832i	$-0.484612\pi$
$941$	−14.5529	−	4.48897i	−0.474411	−	0.146336i	−0.522735	+	0.852495i	$0.675088\pi$
$942$	−0.472713	+	6.30792i	−0.0154018	+	0.205523i
$943$	0.389582	−	0.992639i	0.0126865	−	0.0323248i
$944$	5.21332	−	2.51060i	0.169679	−	0.0817131i
$945$	15.8170	−	25.1021i	0.514526	−	0.816570i
$946$	4.67129	+	2.24957i	0.151877	+	0.0731399i
$947$	17.9080	−	16.6162i	0.581933	−	0.539955i	−0.333331	−	0.942810i	$-0.608173\pi$
$947$	17.9080	−	16.6162i	0.581933	−	0.539955i	0.915264	+	0.402855i	$0.131982\pi$
$948$	9.44046	−	1.42292i	0.306612	−	0.0462143i
$949$	3.24873	−	5.62696i	0.105458	−	0.182659i
$950$	9.57699	+	16.5878i	0.310719	+	0.538180i
$951$	31.4234	+	39.4037i	1.01897	+	1.27775i
$952$	−3.02125	+	11.2187i	−0.0979192	+	0.363600i
$953$	−19.5761	+	24.5477i	−0.634134	+	0.795178i	−0.990256	−	0.139261i	$-0.955527\pi$
$953$	−19.5761	+	24.5477i	−0.634134	+	0.795178i	0.356122	+	0.934439i	$0.384099\pi$
$954$	−24.6203	−	3.71092i	−0.797113	−	0.120145i
$955$	57.9076	−	39.4807i	1.87385	−	1.27757i
$956$	9.80617	−	6.68573i	0.317154	−	0.216232i
$957$	59.6446	+	8.98998i	1.92804	+	0.290605i
$958$	0.357431	−	0.448204i	0.0115481	−	0.0144808i
$959$	32.7786	+	17.3771i	1.05848	+	0.561134i
$960$	3.61045	+	4.52736i	0.116527	+	0.146120i
$961$	−26.9751	−	46.7223i	−0.870165	−	1.50717i
$962$	1.71520	−	2.97081i	0.0553002	−	0.0957828i
$963$	−24.1486	+	3.63982i	−0.778179	+	0.117292i
$964$	12.1546	−	11.2778i	0.391472	−	0.363233i
$965$	−32.1485	−	15.4819i	−1.03490	−	0.498380i
$966$	−1.01599	+	8.91579i	−0.0326888	+	0.286861i
$967$	13.5083	−	6.50526i	0.434398	−	0.209195i	−0.203888	−	0.978994i	$-0.565358\pi$
$967$	13.5083	−	6.50526i	0.434398	−	0.209195i	0.638286	+	0.769799i	$0.279644\pi$
$968$	4.72599	−	12.0416i	0.151899	−	0.387033i
$969$	0.890172	−	11.8785i	0.0285964	−	0.381593i
$970$	−1.65038	−	0.509074i	−0.0529905	−	0.0163454i
$971$	−1.46536	−	19.5539i	−0.0470257	−	0.627514i	−0.970071	−	0.242822i	$-0.921927\pi$
$971$	−1.46536	−	19.5539i	−0.0470257	−	0.627514i	0.923045	−	0.384692i	$-0.125692\pi$
$972$	−7.73007	+	33.8677i	−0.247942	+	1.08631i
$973$	12.9046	−	29.4760i	0.413703	−	0.944957i
$974$	2.62915	+	11.5191i	0.0842435	+	0.369095i
$975$	−35.3608	+	10.9074i	−1.13245	+	0.349315i
$976$	0.753823	+	1.92071i	0.0241293	+	0.0614804i
$977$	−35.2511	−	32.7082i	−1.12778	−	1.04643i	−0.998496	−	0.0548207i	$-0.982541\pi$
$977$	−35.2511	−	32.7082i	−1.12778	−	1.04643i	−0.129285	−	0.991607i	$-0.541268\pi$
$978$	−4.56806	−	3.11445i	−0.146070	−	0.0995891i
$979$	−9.85268			−0.314893
$980$	14.5781	+	47.6888i	0.465680	+	1.52336i
$981$	−13.5987			−0.434175
$982$	5.79717	+	3.95245i	0.184995	+	0.126128i
$983$	−22.6085	−	20.9776i	−0.721099	−	0.669082i	0.231665	−	0.972796i	$-0.425583\pi$
$983$	−22.6085	−	20.9776i	−0.721099	−	0.669082i	−0.952763	+	0.303714i	$0.901773\pi$
$984$	1.06599	+	2.71611i	0.0339826	+	0.0865863i
$985$	−65.0369	+	20.0612i	−2.07225	+	0.639204i
$986$	−2.71516	−	11.8959i	−0.0864683	−	0.378842i
$987$	−0.299789	−	8.29259i	−0.00954238	−	0.263956i
$988$	0.821177	−	3.59781i	0.0261251	−	0.114462i
$989$	0.600673	+	8.01543i	0.0191003	+	0.254876i
$990$	−22.6669	−	6.99182i	−0.720402	−	0.222215i
$991$	−4.04962	+	54.0385i	−0.128641	+	1.71659i	0.443367	+	0.896340i	$0.353784\pi$
$991$	−4.04962	+	54.0385i	−0.128641	+	1.71659i	−0.572007	+	0.820248i	$0.693835\pi$
$992$	18.7561	−	47.7899i	0.595508	−	1.51733i
$993$	39.5368	−	19.0399i	1.25466	−	0.604214i
$994$	26.1830	−	2.91659i	0.830473	−	0.0925087i
$995$	78.3716	+	37.7418i	2.48455	+	1.19650i
$996$	21.7958	−	20.2236i	0.690627	−	0.640808i
$997$	−14.9648	+	2.25557i	−0.473938	+	0.0714347i	−0.381668	−	0.924299i	$-0.624650\pi$
$997$	−14.9648	+	2.25557i	−0.473938	+	0.0714347i	−0.0922700	+	0.995734i	$0.529412\pi$
$998$	−1.32735	+	2.29903i	−0.0420164	+	0.0727745i
$999$	−7.28936	−	12.6255i	−0.230625	−	0.399454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.17	✓	324
49.37	even	21	inner	637.2.bl.a.625.17	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.17	✓	324	1.1	even	1	trivial
637.2.bl.a.625.17	yes	324	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500003 + 0.340896i) q^{2} +(-1.93585 - 1.79621i) q^{3} +(-0.596889 - 1.52085i) q^{4} +(-4.16664 + 1.28524i) q^{5} +(-0.355611 - 1.55803i) q^{6} +(-2.59900 - 0.495162i) q^{7} +(0.489325 - 2.14387i) q^{8} +(0.296968 + 3.96277i) q^{9} +O(q^{10})\)	\(q+(0.500003 + 0.340896i) q^{2} +(-1.93585 - 1.79621i) q^{3} +(-0.596889 - 1.52085i) q^{4} +(-4.16664 + 1.28524i) q^{5} +(-0.355611 - 1.55803i) q^{6} +(-2.59900 - 0.495162i) q^{7} +(0.489325 - 2.14387i) q^{8} +(0.296968 + 3.96277i) q^{9} +(-2.52146 - 0.777768i) q^{10} +(0.169052 - 2.25584i) q^{11} +(-1.57627 + 4.01627i) q^{12} +(0.900969 - 0.433884i) q^{13} +(-1.13071 - 1.13357i) q^{14} +(10.3745 + 4.99611i) q^{15} +(-1.41980 + 1.31738i) q^{16} +(1.97466 - 0.297632i) q^{17} +(-1.20241 + 2.08263i) q^{18} +(1.12938 + 1.95615i) q^{19} +(4.44167 + 5.56968i) q^{20} +(4.14187 + 5.62691i) q^{21} +(0.853536 - 1.07030i) q^{22} +(2.09860 + 0.316314i) q^{23} +(-4.79810 + 3.27129i) q^{24} +(11.5778 - 7.89362i) q^{25} +(0.598396 + 0.0901938i) q^{26} +(1.60351 - 2.01074i) q^{27} +(0.798250 + 4.24825i) q^{28} +(-6.29530 - 7.89405i) q^{29} +(3.48414 + 6.03471i) q^{30} +(-4.60842 + 7.98202i) q^{31} +(-5.50788 + 0.830180i) q^{32} +(-4.37922 + 4.06333i) q^{33} +(1.08880 + 0.524338i) q^{34} +(11.4655 - 1.27717i) q^{35} +(5.84951 - 2.81698i) q^{36} +(2.07098 - 5.27677i) q^{37} +(-0.102149 + 1.36308i) q^{38} +(-2.52349 - 0.778392i) q^{39} +(0.716545 + 9.56163i) q^{40} +(0.111805 - 0.489852i) q^{41} +(0.152755 + 4.22542i) q^{42} +(0.842763 + 3.69238i) q^{43} +(-3.53170 + 1.08939i) q^{44} +(-6.33045 - 16.1297i) q^{45} +(0.941478 + 0.873564i) q^{46} +(-0.981281 - 0.669026i) q^{47} +5.11481 q^{48} +(6.50963 + 2.57386i) q^{49} +8.47985 q^{50} +(-4.35726 - 2.97073i) q^{51} +(-1.19765 - 1.11126i) q^{52} +(3.78258 + 9.63787i) q^{53} +(1.48721 - 0.458744i) q^{54} +(2.19492 + 9.61655i) q^{55} +(-2.33332 + 5.32964i) q^{56} +(1.32733 - 5.81541i) q^{57} +(-0.456614 - 6.09309i) q^{58} +(-2.85480 - 0.880590i) q^{59} +(1.40588 - 18.7602i) q^{60} +(0.389204 - 0.991676i) q^{61} +(-5.02527 + 2.42004i) q^{62} +(1.19039 - 10.4463i) q^{63} +(0.453088 + 0.218196i) q^{64} +(-3.19637 + 2.96579i) q^{65} +(-3.57480 + 0.538814i) q^{66} +(-3.63962 + 6.30401i) q^{67} +(-1.63131 - 2.82551i) q^{68} +(-3.49442 - 4.38186i) q^{69} +(6.16817 + 3.26995i) q^{70} +(-10.2591 + 12.8645i) q^{71} +(8.64098 + 1.30242i) q^{72} +(5.36845 - 3.66015i) q^{73} +(2.83433 - 1.93241i) q^{74} +(-36.5915 - 5.51528i) q^{75} +(2.30089 - 2.88522i) q^{76} +(-1.55638 + 5.77924i) q^{77} +(-0.996400 - 1.24945i) q^{78} +(-1.10639 - 1.91633i) q^{79} +(4.22264 - 7.31382i) q^{80} +(5.07263 - 0.764575i) q^{81} +(0.222892 - 0.206813i) q^{82} +(-6.20892 - 2.99006i) q^{83} +(6.08544 - 9.65780i) q^{84} +(-7.84517 + 3.77803i) q^{85} +(-0.837336 + 2.13350i) q^{86} +(-1.99260 + 26.5894i) q^{87} +(-4.75352 - 1.46627i) q^{88} +(-0.325480 - 4.34323i) q^{89} +(2.33332 - 10.2229i) q^{90} +(-2.55646 + 0.681539i) q^{91} +(-0.771569 - 3.38046i) q^{92} +(23.2586 - 7.17432i) q^{93} +(-0.262575 - 0.669030i) q^{94} +(-7.21983 - 6.69902i) q^{95} +(12.1536 + 8.28620i) q^{96} +0.654532 q^{97} +(2.37742 + 3.50604i) q^{98} +8.98959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

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