LMFDB - Embedded newform 700.2.k.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(43,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("700.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.k (of order $4$, degree $2$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	700.43
Dual form			700.2.k.b.407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35755 - 0.396294i) q^{2} +(-0.945787 + 0.945787i) q^{3} +(1.68590 + 1.07598i) q^{4} +(1.65877 - 0.909146i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-1.86230 - 2.12881i) q^{8} +1.21097i q^{9} +O(q^{10})$	\(q+(-1.35755 - 0.396294i) q^{2} +(-0.945787 + 0.945787i) q^{3} +(1.68590 + 1.07598i) q^{4} +(1.65877 - 0.909146i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-1.86230 - 2.12881i) q^{8} +1.21097i q^{9} -5.00376i q^{11} +(-2.61215 + 0.576855i) q^{12} +(3.27438 + 3.27438i) q^{13} +(-0.679713 - 1.24016i) q^{14} +(1.68453 + 3.62800i) q^{16} +(2.38623 - 2.38623i) q^{17} +(0.479902 - 1.64396i) q^{18} +0.428759 q^{19} -1.33754 q^{21} +(-1.98296 + 6.79287i) q^{22} +(2.54453 - 2.54453i) q^{23} +(3.77474 + 0.252069i) q^{24} +(-3.14753 - 5.74276i) q^{26} +(-3.98268 - 3.98268i) q^{27} +(0.431279 + 1.95295i) q^{28} +7.51811i q^{29} -0.407938i q^{31} +(-0.849085 - 5.59277i) q^{32} +(4.73249 + 4.73249i) q^{33} +(-4.18508 + 2.29378i) q^{34} +(-1.30298 + 2.04158i) q^{36} +(-3.17476 + 3.17476i) q^{37} +(-0.582063 - 0.169915i) q^{38} -6.19373 q^{39} +5.67429 q^{41} +(1.81579 + 0.530061i) q^{42} +(-4.01233 + 4.01233i) q^{43} +(5.38395 - 8.43584i) q^{44} +(-4.46271 + 2.44595i) q^{46} +(7.13029 + 7.13029i) q^{47} +(-5.02452 - 1.83811i) q^{48} +1.00000i q^{49} +4.51373i q^{51} +(1.99711 + 9.04345i) q^{52} +(0.811260 + 0.811260i) q^{53} +(3.82839 + 6.98502i) q^{54} +(0.188457 - 2.82214i) q^{56} +(-0.405515 + 0.405515i) q^{57} +(2.97938 - 10.2062i) q^{58} +3.87524 q^{59} +12.2345 q^{61} +(-0.161663 + 0.553797i) q^{62} +(-0.856288 + 0.856288i) q^{63} +(-1.06370 + 7.92897i) q^{64} +(-4.54915 - 8.30006i) q^{66} +(8.29609 + 8.29609i) q^{67} +(6.59048 - 1.45541i) q^{68} +4.81316i q^{69} +12.2700i q^{71} +(2.57794 - 2.25519i) q^{72} +(-3.78692 - 3.78692i) q^{73} +(5.56805 - 3.05177i) q^{74} +(0.722846 + 0.461337i) q^{76} +(3.53819 - 3.53819i) q^{77} +(8.40832 + 2.45454i) q^{78} +0.197543 q^{79} +3.90062 q^{81} +(-7.70315 - 2.24869i) q^{82} +(-1.86715 + 1.86715i) q^{83} +(-2.25497 - 1.43917i) q^{84} +(7.03702 - 3.85689i) q^{86} +(-7.11053 - 7.11053i) q^{87} +(-10.6521 + 9.31848i) q^{88} +7.05881i q^{89} +4.63067i q^{91} +(7.02768 - 1.55196i) q^{92} +(0.385822 + 0.385822i) q^{93} +(-6.85406 - 12.5054i) q^{94} +(6.09262 + 4.48651i) q^{96} +(5.24949 - 5.24949i) q^{97} +(0.396294 - 1.35755i) q^{98} +6.05942 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{6}+O(q^{10}) $ 36 * q - 8 * q^6	$ 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) $ 36 * q - 8 * q^6 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 - 28 * q^18 - 4 * q^22 - 32 * q^26 - 20 * q^37 + 20 * q^42 + 16 * q^46 + 24 * q^48 - 16 * q^52 + 44 * q^53 - 24 * q^56 + 16 * q^57 + 4 * q^58 - 64 * q^61 - 40 * q^62 + 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 8 * q^76 + 76 * q^78 - 36 * q^81 - 56 * q^82 + 56 * q^86 + 40 * q^88 + 56 * q^92 - 32 * q^93 + 120 * q^96 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.35755	−	0.396294i	−0.959935	−	0.280222i
$2$	−1.35755	−	0.396294i	−0.959935	−	0.280222i
$3$	−0.945787	+	0.945787i	−0.546050	+	0.546050i	−0.925296	−	0.379246i	$-0.876184\pi$
$3$	−0.945787	+	0.945787i	−0.546050	+	0.546050i	0.379246	+	0.925296i	$0.376184\pi$
$4$	1.68590	+	1.07598i	0.842951	+	0.537990i
$5$		0			0
$5$		0			0
$6$	1.65877	−	0.909146i	0.677188	−	0.371157i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−1.86230	−	2.12881i	−0.658421	−	0.752650i
$9$			1.21097i			0.403658i
$10$		0			0
$11$		−	5.00376i		−	1.50869i	−0.656479	−	0.754345i	$-0.727955\pi$
$11$		−	5.00376i		−	1.50869i	0.656479	−	0.754345i	$-0.272045\pi$
$12$	−2.61215	+	0.576855i	−0.754064	+	0.166524i
$13$	3.27438	+	3.27438i	0.908150	+	0.908150i	0.996123	−	0.0879732i	$-0.0280390\pi$
$13$	3.27438	+	3.27438i	0.908150	+	0.908150i	−0.0879732	+	0.996123i	$0.528039\pi$
$14$	−0.679713	−	1.24016i	−0.181661	−	0.331446i
$15$		0			0
$16$	1.68453	+	3.62800i	0.421133	+	0.906999i
$17$	2.38623	−	2.38623i	0.578745	−	0.578745i	−0.355812	−	0.934557i	$-0.615796\pi$
$17$	2.38623	−	2.38623i	0.578745	−	0.578745i	0.934557	+	0.355812i	$0.115796\pi$
$18$	0.479902	−	1.64396i	0.113114	−	0.387485i
$19$	0.428759			0.0983641			0.0491820	−	0.998790i	$-0.484339\pi$
$19$	0.428759			0.0983641			0.0491820	+	0.998790i	$0.484339\pi$
$20$		0			0
$21$	−1.33754			−0.291876
$22$	−1.98296	+	6.79287i	−0.422768	+	1.44824i
$23$	2.54453	−	2.54453i	0.530570	−	0.530570i	−0.390172	−	0.920742i	$-0.627584\pi$
$23$	2.54453	−	2.54453i	0.530570	−	0.530570i	0.920742	+	0.390172i	$0.127584\pi$
$24$	3.77474	+	0.252069i	0.770516	+	0.0514534i
$25$		0			0
$26$	−3.14753	−	5.74276i	−0.617281	−	1.12625i
$27$	−3.98268	−	3.98268i	−0.766468	−	0.766468i
$28$	0.431279	+	1.95295i	0.0815041	+	0.369072i
$29$			7.51811i			1.39608i	0.716060	+	0.698039i	$0.245944\pi$
$29$			7.51811i			1.39608i	−0.716060	+	0.698039i	$0.754056\pi$
$30$		0			0
$31$		−	0.407938i		−	0.0732678i	−0.999329	−	0.0366339i	$-0.988336\pi$
$31$		−	0.407938i		−	0.0732678i	0.999329	−	0.0366339i	$-0.0116635\pi$
$32$	−0.849085	−	5.59277i	−0.150099	−	0.988671i
$33$	4.73249	+	4.73249i	0.823820	+	0.823820i
$34$	−4.18508	+	2.29378i	−0.717735	+	0.393381i
$35$		0			0
$36$	−1.30298	+	2.04158i	−0.217164	+	0.340264i
$37$	−3.17476	+	3.17476i	−0.521928	+	0.521928i	−0.918153	−	0.396226i	$-0.870320\pi$
$37$	−3.17476	+	3.17476i	−0.521928	+	0.521928i	0.396226	+	0.918153i	$0.370320\pi$
$38$	−0.582063	−	0.169915i	−0.0944231	−	0.0275638i
$39$	−6.19373			−0.991791
$40$		0			0
$41$	5.67429			0.886176			0.443088	−	0.896478i	$-0.353883\pi$
$41$	5.67429			0.886176			0.443088	+	0.896478i	$0.353883\pi$
$42$	1.81579	+	0.530061i	0.280182	+	0.0817902i
$43$	−4.01233	+	4.01233i	−0.611875	+	0.611875i	−0.943434	−	0.331560i	$-0.892425\pi$
$43$	−4.01233	+	4.01233i	−0.611875	+	0.611875i	0.331560	+	0.943434i	$0.392425\pi$
$44$	5.38395	−	8.43584i	0.811660	−	1.27175i
$45$		0			0
$46$	−4.46271	+	2.44595i	−0.657991	+	0.360636i
$47$	7.13029	+	7.13029i	1.04006	+	1.04006i	0.999163	+	0.0408970i	$0.0130216\pi$
$47$	7.13029	+	7.13029i	1.04006	+	1.04006i	0.0408970	+	0.999163i	$0.486978\pi$
$48$	−5.02452	−	1.83811i	−0.725227	−	0.265308i
$49$			1.00000i			0.142857i
$50$		0			0
$51$			4.51373i			0.632048i
$52$	1.99711	+	9.04345i	0.276950	+	1.25410i
$53$	0.811260	+	0.811260i	0.111435	+	0.111435i	0.760626	−	0.649191i	$-0.224892\pi$
$53$	0.811260	+	0.811260i	0.111435	+	0.111435i	−0.649191	+	0.760626i	$0.724892\pi$
$54$	3.82839	+	6.98502i	0.520978	+	0.950541i
$55$		0			0
$56$	0.188457	−	2.82214i	0.0251836	−	0.377125i
$57$	−0.405515	+	0.405515i	−0.0537117	+	0.0537117i
$58$	2.97938	−	10.2062i	0.391212	−	1.34014i
$59$	3.87524			0.504513			0.252257	−	0.967660i	$-0.418827\pi$
$59$	3.87524			0.504513			0.252257	+	0.967660i	$0.418827\pi$
$60$		0			0
$61$	12.2345			1.56646			0.783231	−	0.621730i	$-0.213570\pi$
$61$	12.2345			1.56646			0.783231	+	0.621730i	$0.213570\pi$
$62$	−0.161663	+	0.553797i	−0.0205313	+	0.0703323i
$63$	−0.856288	+	0.856288i	−0.107882	+	0.107882i
$64$	−1.06370	+	7.92897i	−0.132963	+	0.991121i
$65$		0			0
$66$	−4.54915	−	8.30006i	−0.559961	−	1.02167i
$67$	8.29609	+	8.29609i	1.01353	+	1.01353i	0.999907	+	0.0136218i	$0.00433607\pi$
$67$	8.29609	+	8.29609i	1.01353	+	1.01353i	0.0136218	+	0.999907i	$0.495664\pi$
$68$	6.59048	−	1.45541i	0.799213	−	0.176494i
$69$			4.81316i			0.579436i
$70$		0			0
$71$			12.2700i			1.45618i	0.685482	+	0.728090i	$0.259592\pi$
$71$			12.2700i			1.45618i	−0.685482	+	0.728090i	$0.740408\pi$
$72$	2.57794	−	2.25519i	0.303813	−	0.265777i
$73$	−3.78692	−	3.78692i	−0.443226	−	0.443226i	0.449869	−	0.893095i	$-0.351471\pi$
$73$	−3.78692	−	3.78692i	−0.443226	−	0.443226i	−0.893095	+	0.449869i	$0.851471\pi$
$74$	5.56805	−	3.05177i	0.647273	−	0.354761i
$75$		0			0
$76$	0.722846	+	0.461337i	0.0829161	+	0.0529189i
$77$	3.53819	−	3.53819i	0.403214	−	0.403214i
$78$	8.40832	+	2.45454i	0.952055	+	0.277922i
$79$	0.197543			0.0222254			0.0111127	−	0.999938i	$-0.496463\pi$
$79$	0.197543			0.0222254			0.0111127	+	0.999938i	$0.496463\pi$
$80$		0			0
$81$	3.90062			0.433402
$82$	−7.70315	−	2.24869i	−0.850671	−	0.248326i
$83$	−1.86715	+	1.86715i	−0.204946	+	0.204946i	−0.802115	−	0.597169i	$-0.796292\pi$
$83$	−1.86715	+	1.86715i	−0.204946	+	0.204946i	0.597169	+	0.802115i	$0.296292\pi$
$84$	−2.25497	−	1.43917i	−0.246037	−	0.157027i
$85$		0			0
$86$	7.03702	−	3.85689i	0.758821	−	0.415899i
$87$	−7.11053	−	7.11053i	−0.762329	−	0.762329i
$88$	−10.6521	+	9.31848i	−1.13551	+	0.993353i
$89$			7.05881i			0.748232i	0.927382	+	0.374116i	$0.122054\pi$
$89$			7.05881i			0.748232i	−0.927382	+	0.374116i	$0.877946\pi$
$90$		0			0
$91$			4.63067i			0.485426i
$92$	7.02768	−	1.55196i	0.732687	−	0.161803i
$93$	0.385822	+	0.385822i	0.0400079	+	0.0400079i
$94$	−6.85406	−	12.5054i	−0.706942	−	1.28984i
$95$		0			0
$96$	6.09262	+	4.48651i	0.621826	+	0.457903i
$97$	5.24949	−	5.24949i	0.533005	−	0.533005i	−0.388460	−	0.921465i	$-0.626993\pi$
$97$	5.24949	−	5.24949i	0.533005	−	0.533005i	0.921465	+	0.388460i	$0.126993\pi$
$98$	0.396294	−	1.35755i	0.0400318	−	0.137134i
$99$	6.05942			0.608994
$100$		0			0
$101$	−9.71515			−0.966694			−0.483347	−	0.875429i	$-0.660579\pi$
$101$	−9.71515			−0.966694			−0.483347	+	0.875429i	$0.660579\pi$
$102$	1.78876	−	6.12763i	0.177114	−	0.606725i
$103$	−0.0876770	+	0.0876770i	−0.00863907	+	0.00863907i	−0.711413	−	0.702774i	$-0.751944\pi$
$103$	−0.0876770	+	0.0876770i	−0.00863907	+	0.00863907i	0.702774	+	0.711413i	$0.251944\pi$
$104$	0.872681	−	13.0684i	0.0855734	−	1.28146i
$105$		0			0
$106$	−0.779831	−	1.42283i	−0.0757439	−	0.138197i
$107$	−1.67616	−	1.67616i	−0.162041	−	0.162041i	0.621429	−	0.783470i	$-0.286552\pi$
$107$	−1.67616	−	1.67616i	−0.162041	−	0.162041i	−0.783470	+	0.621429i	$0.786552\pi$
$108$	−2.42912	−	10.9997i	−0.233742	−	1.05845i
$109$		−	10.1145i		−	0.968789i	−0.874850	−	0.484395i	$-0.839040\pi$
$109$		−	10.1145i		−	0.968789i	0.874850	−	0.484395i	$-0.160960\pi$
$110$		0			0
$111$		−	6.00530i		−	0.569998i
$112$	−1.37424	+	3.75652i	−0.129853	+	0.354958i
$113$	7.67087	+	7.67087i	0.721614	+	0.721614i	0.968934	−	0.247320i	$-0.0795498\pi$
$113$	7.67087	+	7.67087i	0.721614	+	0.721614i	−0.247320	+	0.968934i	$0.579550\pi$
$114$	0.711211	−	0.389805i	0.0666110	−	0.0365086i
$115$		0			0
$116$	−8.08934	+	12.6748i	−0.751076	+	1.17682i
$117$	−3.96519	+	3.96519i	−0.366582	+	0.366582i
$118$	−5.26084	−	1.53574i	−0.484300	−	0.141376i
$119$	3.37464			0.309352
$120$		0			0
$121$	−14.0376			−1.27614
$122$	−16.6089	−	4.84845i	−1.50370	−	0.438958i
$123$	−5.36667	+	5.36667i	−0.483897	+	0.483897i
$124$	0.438933	−	0.687743i	0.0394174	−	0.0617612i
$125$		0			0
$126$	1.50180	−	0.823114i	0.133791	−	0.0733289i
$127$	6.81065	+	6.81065i	0.604347	+	0.604347i	0.941463	−	0.337116i	$-0.109451\pi$
$127$	6.81065	+	6.81065i	0.604347	+	0.604347i	−0.337116	+	0.941463i	$0.609451\pi$
$128$	4.58624	−	10.3425i	0.405370	−	0.914153i
$129$		−	7.58962i		−	0.668229i
$130$		0			0
$131$		−	2.17187i		−	0.189757i	−0.995489	−	0.0948786i	$-0.969754\pi$
$131$		−	2.17187i		−	0.189757i	0.995489	−	0.0948786i	$-0.0302463\pi$
$132$	2.88644	+	13.0706i	0.251233	+	1.13765i
$133$	0.303178	+	0.303178i	0.0262889	+	0.0262889i
$134$	−7.97469	−	14.5501i	−0.688909	−	1.25694i
$135$		0			0
$136$	−9.52370	−	0.635973i	−0.816651	−	0.0545342i
$137$	8.24845	−	8.24845i	0.704712	−	0.704712i	−0.260706	−	0.965418i	$-0.583955\pi$
$137$	8.24845	−	8.24845i	0.704712	−	0.704712i	0.965418	+	0.260706i	$0.0839553\pi$
$138$	1.90743	−	6.53412i	0.162371	−	0.556221i
$139$	−15.0008			−1.27235			−0.636175	−	0.771545i	$-0.719484\pi$
$139$	−15.0008			−1.27235			−0.636175	+	0.771545i	$0.719484\pi$
$140$		0			0
$141$	−13.4875			−1.13585
$142$	4.86253	−	16.6572i	0.408054	−	1.39784i
$143$	16.3842	−	16.3842i	1.37012	−	1.37012i
$144$	−4.39341	+	2.03992i	−0.366117	+	0.169993i
$145$		0			0
$146$	3.64021	+	6.64168i	0.301266	+	0.549669i
$147$	−0.945787	−	0.945787i	−0.0780072	−	0.0780072i
$148$	−8.76832	+	1.93635i	−0.720752	+	0.159167i
$149$		−	8.99644i		−	0.737017i	−0.929624	−	0.368509i	$-0.879868\pi$
$149$		−	8.99644i		−	0.737017i	0.929624	−	0.368509i	$-0.120132\pi$
$150$		0			0
$151$		−	0.634873i		−	0.0516652i	−0.999666	−	0.0258326i	$-0.991776\pi$
$151$		−	0.634873i		−	0.0516652i	0.999666	−	0.0258326i	$-0.00822369\pi$
$152$	−0.798477	−	0.912749i	−0.0647650	−	0.0740337i
$153$	2.88966	+	2.88966i	0.233615	+	0.233615i
$154$	−6.20545	+	3.40112i	−0.500049	+	0.274070i
$155$		0			0
$156$	−10.4420	−	6.66434i	−0.836031	−	0.533574i
$157$	6.04319	−	6.04319i	0.482299	−	0.482299i	−0.423566	−	0.905865i	$-0.639222\pi$
$157$	6.04319	−	6.04319i	0.482299	−	0.482299i	0.905865	+	0.423566i	$0.139222\pi$
$158$	−0.268176	−	0.0782853i	−0.0213349	−	0.00622804i
$159$	−1.53456			−0.121698
$160$		0			0
$161$	3.59850			0.283602
$162$	−5.29530	−	1.54579i	−0.416038	−	0.121449i
$163$	−13.9323	+	13.9323i	−1.09126	+	1.09126i	−0.0958704	+	0.995394i	$0.530563\pi$
$163$	−13.9323	+	13.9323i	−1.09126	+	1.09126i	−0.995394	+	0.0958704i	$0.969437\pi$
$164$	9.56630	+	6.10543i	0.747003	+	0.476754i
$165$		0			0
$166$	3.27469	−	1.79481i	0.254165	−	0.139305i
$167$	−8.56192	−	8.56192i	−0.662541	−	0.662541i	0.293437	−	0.955978i	$-0.405201\pi$
$167$	−8.56192	−	8.56192i	−0.662541	−	0.662541i	−0.955978	+	0.293437i	$0.905201\pi$
$168$	2.49091	+	2.84738i	0.192178	+	0.219681i
$169$			8.44313i			0.649471i
$170$		0			0
$171$			0.519216i			0.0397054i
$172$	−11.0816	+	2.44720i	−0.844963	+	0.186598i
$173$	−13.0965	−	13.0965i	−0.995708	−	0.995708i	0.00428297	−	0.999991i	$-0.498637\pi$
$173$	−13.0965	−	13.0965i	−0.995708	−	0.995708i	−0.999991	+	0.00428297i	$0.998637\pi$
$174$	6.83506	+	12.4708i	0.518165	+	0.945407i
$175$		0			0
$176$	18.1536	−	8.42898i	1.36838	−	0.635358i
$177$	−3.66515	+	3.66515i	−0.275490	+	0.275490i
$178$	2.79736	−	9.58271i	0.209671	−	0.718254i
$179$	−23.6288			−1.76610			−0.883050	−	0.469279i	$-0.844514\pi$
$179$	−23.6288			−1.76610			−0.883050	+	0.469279i	$0.844514\pi$
$180$		0			0
$181$	−0.943069			−0.0700978			−0.0350489	−	0.999386i	$-0.511159\pi$
$181$	−0.943069			−0.0700978			−0.0350489	+	0.999386i	$0.511159\pi$
$182$	1.83511	−	6.28638i	0.136027	−	0.465978i
$183$	−11.5712	+	11.5712i	−0.855368	+	0.855368i
$184$	−10.1555	−	0.678162i	−0.748672	−	0.0499948i
$185$		0			0
$186$	−0.370875	−	0.676673i	−0.0271939	−	0.0496161i
$187$	−11.9401	−	11.9401i	−0.873147	−	0.873147i
$188$	4.34892	+	19.6930i	0.317177	+	1.43626i
$189$		−	5.63237i		−	0.409694i
$190$		0			0
$191$		−	17.2673i		−	1.24942i	−0.780857	−	0.624710i	$-0.785217\pi$
$191$		−	17.2673i		−	1.24942i	0.780857	−	0.624710i	$-0.214783\pi$
$192$	−6.49308	−	8.50515i	−0.468598	−	0.613806i
$193$	4.22030	+	4.22030i	0.303784	+	0.303784i	0.842492	−	0.538708i	$-0.181087\pi$
$193$	4.22030	+	4.22030i	0.303784	+	0.303784i	−0.538708	+	0.842492i	$0.681087\pi$
$194$	−9.20681	+	5.04612i	−0.661010	+	0.362290i
$195$		0			0
$196$	−1.07598	+	1.68590i	−0.0768558	+	0.120422i
$197$	−5.72538	+	5.72538i	−0.407917	+	0.407917i	−0.881012	−	0.473095i	$-0.843137\pi$
$197$	−5.72538	+	5.72538i	−0.407917	+	0.407917i	0.473095	+	0.881012i	$0.343137\pi$
$198$	−8.22598	−	2.40131i	−0.584595	−	0.170654i
$199$	19.9405			1.41355			0.706773	−	0.707440i	$-0.250150\pi$
$199$	19.9405			1.41355			0.706773	+	0.707440i	$0.250150\pi$
$200$		0			0
$201$	−15.6927			−1.10688
$202$	13.1888	+	3.85006i	0.927963	+	0.270889i
$203$	−5.31610	+	5.31610i	−0.373117	+	0.373117i
$204$	−4.85668	+	7.60970i	−0.340036	+	0.532786i
$205$		0			0
$206$	0.153772	−	0.0842803i	0.0107138	−	0.00587209i
$207$	3.08135	+	3.08135i	0.214169	+	0.214169i
$208$	−6.36365	+	17.3952i	−0.441240	+	1.20614i
$209$		−	2.14541i		−	0.148401i
$210$		0			0
$211$			7.74837i			0.533420i	0.963777	+	0.266710i	$0.0859365\pi$
$211$			7.74837i			0.533420i	−0.963777	+	0.266710i	$0.914063\pi$
$212$	0.494804	+	2.24061i	0.0339833	+	0.153885i
$213$	−11.6048	−	11.6048i	−0.795148	−	0.795148i
$214$	1.61123	+	2.93973i	0.110141	+	0.200956i
$215$		0			0
$216$	−1.06146	+	15.8953i	−0.0722230	+	1.08154i
$217$	0.288456	−	0.288456i	0.0195816	−	0.0195816i
$218$	−4.00830	+	13.7309i	−0.271476	+	0.929975i
$219$	7.16324			0.484047
$220$		0			0
$221$	15.6268			1.05117
$222$	−2.37986	+	8.15251i	−0.159726	+	0.547161i
$223$	11.1091	−	11.1091i	0.743923	−	0.743923i	−0.229407	−	0.973331i	$-0.573679\pi$
$223$	11.1091	−	11.1091i	0.743923	−	0.743923i	0.973331	+	0.229407i	$0.0736787\pi$
$224$	3.35429	−	4.55508i	0.224118	−	0.304349i
$225$		0			0
$226$	−7.37369	−	13.4535i	−0.490491	−	0.894915i
$227$	−4.87903	−	4.87903i	−0.323833	−	0.323833i	0.526403	−	0.850235i	$-0.323540\pi$
$227$	−4.87903	−	4.87903i	−0.323833	−	0.323833i	−0.850235	+	0.526403i	$0.823540\pi$
$228$	−1.11998	+	0.247332i	−0.0741728	+	0.0163800i
$229$		−	5.04967i		−	0.333692i	−0.985983	−	0.166846i	$-0.946642\pi$
$229$		−	5.04967i		−	0.333692i	0.985983	−	0.166846i	$-0.0533582\pi$
$230$		0			0
$231$			6.69275i			0.440351i
$232$	16.0047	−	14.0009i	1.05076	−	0.919207i
$233$	−2.45508	−	2.45508i	−0.160837	−	0.160837i	0.622100	−	0.782938i	$-0.286280\pi$
$233$	−2.45508	−	2.45508i	−0.160837	−	0.160837i	−0.782938	+	0.622100i	$0.786280\pi$
$234$	6.95434	−	3.81157i	0.454619	−	0.249170i
$235$		0			0
$236$	6.53327	+	4.16968i	0.425280	+	0.271423i
$237$	−0.186834	+	0.186834i	−0.0121362	+	0.0121362i
$238$	−4.58125	−	1.33735i	−0.296958	−	0.0866874i
$239$	−11.2814			−0.729734			−0.364867	−	0.931060i	$-0.618886\pi$
$239$	−11.2814			−0.729734			−0.364867	+	0.931060i	$0.618886\pi$
$240$		0			0
$241$	26.1136			1.68212			0.841062	−	0.540939i	$-0.181931\pi$
$241$	26.1136			1.68212			0.841062	+	0.540939i	$0.181931\pi$
$242$	19.0568	+	5.56301i	1.22501	+	0.357604i
$243$	8.25890	−	8.25890i	0.529808	−	0.529808i
$244$	20.6261	+	13.1641i	1.32045	+	0.842742i
$245$		0			0
$246$	9.41232	−	5.15876i	0.600108	−	0.328911i
$247$	1.40392	+	1.40392i	0.0893293	+	0.0893293i
$248$	−0.868424	+	0.759701i	−0.0551450	+	0.0482411i
$249$		−	3.53185i		−	0.223822i
$250$		0			0
$251$		−	26.0311i		−	1.64307i	−0.570157	−	0.821536i	$-0.693118\pi$
$251$		−	26.0311i		−	1.64307i	0.570157	−	0.821536i	$-0.306882\pi$
$252$	−2.36497	+	0.522268i	−0.148979	+	0.0328998i
$253$	−12.7322	−	12.7322i	−0.800466	−	0.800466i
$254$	−6.54680	−	11.9448i	−0.410783	−	0.749486i
$255$		0			0
$256$	−10.3247	+	12.2229i	−0.645295	+	0.763934i
$257$	−3.91601	+	3.91601i	−0.244274	+	0.244274i	−0.818616	−	0.574342i	$-0.805258\pi$
$257$	−3.91601	+	3.91601i	−0.244274	+	0.244274i	0.574342	+	0.818616i	$0.305258\pi$
$258$	−3.00772	+	10.3033i	−0.187253	+	0.641456i
$259$	−4.48979			−0.278982
$260$		0			0
$261$	−9.10423			−0.563538
$262$	−0.860700	+	2.94843i	−0.0531742	+	0.182155i
$263$	10.3499	−	10.3499i	0.638203	−	0.638203i	−0.311909	−	0.950112i	$-0.600968\pi$
$263$	10.3499	−	10.3499i	0.638203	−	0.638203i	0.950112	+	0.311909i	$0.100968\pi$
$264$	1.26129	−	18.8879i	0.0776272	−	1.16247i
$265$		0			0
$266$	−0.291433	−	0.531729i	−0.0178689	−	0.0326024i
$267$	−6.67613	−	6.67613i	−0.408572	−	0.408572i
$268$	5.05996	+	22.9128i	0.309086	+	1.39962i
$269$		−	19.6523i		−	1.19822i	−0.800666	−	0.599112i	$-0.795521\pi$
$269$		−	19.6523i		−	1.19822i	0.800666	−	0.599112i	$-0.204479\pi$
$270$		0			0
$271$			13.7114i			0.832908i	0.909157	+	0.416454i	$0.136727\pi$
$271$			13.7114i			0.832908i	−0.909157	+	0.416454i	$0.863273\pi$
$272$	12.6769	+	4.63755i	0.768650	+	0.281193i
$273$	−4.37963	−	4.37963i	−0.265067	−	0.265067i
$274$	−14.4665	+	7.92889i	−0.873954	+	0.479002i
$275$		0			0
$276$	−5.17887	+	8.11452i	−0.311731	+	0.488436i
$277$	−4.99126	+	4.99126i	−0.299896	+	0.299896i	−0.840973	−	0.541077i	$-0.818017\pi$
$277$	−4.99126	+	4.99126i	−0.299896	+	0.299896i	0.541077	+	0.840973i	$0.318017\pi$
$278$	20.3644	+	5.94472i	1.22137	+	0.356541i
$279$	0.494002			0.0295751
$280$		0			0
$281$	15.9701			0.952697			0.476348	−	0.879257i	$-0.341960\pi$
$281$	15.9701			0.952697			0.476348	+	0.879257i	$0.341960\pi$
$282$	18.3100	+	5.34501i	1.09034	+	0.318291i
$283$	15.2448	−	15.2448i	0.906212	−	0.906212i	−0.0897520	−	0.995964i	$-0.528607\pi$
$283$	15.2448	−	15.2448i	0.906212	−	0.906212i	0.995964	+	0.0897520i	$0.0286074\pi$
$284$	−13.2023	+	20.6860i	−0.783411	+	1.22749i
$285$		0			0
$286$	−28.7354	+	15.7495i	−1.69916	+	0.931285i
$287$	4.01233	+	4.01233i	0.236840	+	0.236840i
$288$	6.77270	−	1.02822i	0.399085	−	0.0605885i
$289$			5.61183i			0.330108i
$290$		0			0
$291$			9.92980i			0.582095i
$292$	−2.30972	−	10.4590i	−0.135166	−	0.612068i
$293$	19.8931	+	19.8931i	1.16217	+	1.16217i	0.984000	+	0.178170i	$0.0570177\pi$
$293$	19.8931	+	19.8931i	1.16217	+	1.16217i	0.178170	+	0.984000i	$0.442982\pi$
$294$	0.909146	+	1.65877i	0.0530225	+	0.0967412i
$295$		0			0
$296$	12.6708	+	0.846131i	0.736477	+	0.0491804i
$297$	−19.9284	+	19.9284i	−1.15636	+	1.15636i
$298$	−3.56524	+	12.2132i	−0.206529	+	0.707489i
$299$	16.6635			0.963675
$300$		0			0
$301$	−5.67429			−0.327061
$302$	−0.251596	+	0.861873i	−0.0144777	+	0.0495952i
$303$	9.18846	−	9.18846i	0.527863	−	0.527863i
$304$	0.722258	+	1.55554i	0.0414243	+	0.0892161i
$305$		0			0
$306$	−2.77771	−	5.06802i	−0.158791	−	0.289720i
$307$	14.1084	+	14.1084i	0.805207	+	0.805207i	0.983904	−	0.178697i	$-0.0571882\pi$
$307$	14.1084	+	14.1084i	0.805207	+	0.805207i	−0.178697	+	0.983904i	$0.557188\pi$
$308$	9.77207	−	2.15802i	0.556815	−	0.122964i
$309$		−	0.165847i		−	0.00943473i
$310$		0			0
$311$		−	16.7271i		−	0.948506i	−0.880389	−	0.474253i	$-0.842718\pi$
$311$		−	16.7271i		−	0.948506i	0.880389	−	0.474253i	$-0.157282\pi$
$312$	11.5346	+	13.1853i	0.653016	+	0.746471i
$313$	−5.72746	−	5.72746i	−0.323735	−	0.323735i	0.526463	−	0.850198i	$-0.323518\pi$
$313$	−5.72746	−	5.72746i	−0.323735	−	0.323735i	−0.850198	+	0.526463i	$0.823518\pi$
$314$	−10.5988	+	5.80907i	−0.598127	+	0.327825i
$315$		0			0
$316$	0.333039	+	0.212553i	0.0187349	+	0.0119570i
$317$	−4.33172	+	4.33172i	−0.243293	+	0.243293i	−0.818211	−	0.574918i	$-0.805034\pi$
$317$	−4.33172	+	4.33172i	−0.243293	+	0.243293i	0.574918	+	0.818211i	$0.305034\pi$
$318$	2.08324	+	0.608137i	0.116823	+	0.0341026i
$319$	37.6188			2.10625
$320$		0			0
$321$	3.17059			0.176965
$322$	−4.88516	−	1.42607i	−0.272239	−	0.0794716i
$323$	1.02312	−	1.02312i	0.0569278	−	0.0569278i
$324$	6.57606	+	4.19699i	0.365337	+	0.233166i
$325$		0			0
$326$	24.4352	−	13.3926i	1.35334	−	0.741746i
$327$	9.56612	+	9.56612i	0.529008	+	0.529008i
$328$	−10.5672	−	12.0795i	−0.583477	−	0.666980i
$329$			10.0838i			0.555936i
$330$		0			0
$331$			31.0994i			1.70938i	0.519141	+	0.854689i	$0.326252\pi$
$331$			31.0994i			1.70938i	−0.519141	+	0.854689i	$0.673748\pi$
$332$	−5.15684	+	1.13881i	−0.283019	+	0.0625005i
$333$	−3.84455	−	3.84455i	−0.210680	−	0.210680i
$334$	8.23022	+	15.0163i	0.450338	+	0.821655i
$335$		0			0
$336$	−2.25313	−	4.85261i	−0.122919	−	0.264731i
$337$	9.43123	−	9.43123i	0.513752	−	0.513752i	−0.401922	−	0.915674i	$-0.631658\pi$
$337$	9.43123	−	9.43123i	0.513752	−	0.513752i	0.915674	+	0.401922i	$0.131658\pi$
$338$	3.34596	−	11.4620i	0.181996	−	0.623450i
$339$	−14.5100			−0.788076
$340$		0			0
$341$	−2.04122			−0.110538
$342$	0.205762	−	0.704863i	0.0111264	−	0.0381147i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	16.0137	+	1.06936i	0.863399	+	0.0576559i
$345$		0			0
$346$	12.5891	+	22.9692i	0.676795	+	1.23483i
$347$	−22.4192	−	22.4192i	−1.20352	−	1.20352i	−0.973087	−	0.230436i	$-0.925985\pi$
$347$	−22.4192	−	22.4192i	−1.20352	−	1.20352i	−0.230436	−	0.973087i	$-0.574015\pi$
$348$	−4.33686	−	19.6384i	−0.232480	−	1.05273i
$349$		−	13.8389i		−	0.740778i	−0.928877	−	0.370389i	$-0.879224\pi$
$349$		−	13.8389i		−	0.740778i	0.928877	−	0.370389i	$-0.120776\pi$
$350$		0			0
$351$		−	26.0816i		−	1.39214i
$352$	−27.9848	+	4.24862i	−1.49160	+	0.226452i
$353$	1.22430	+	1.22430i	0.0651627	+	0.0651627i	0.738937	−	0.673774i	$-0.235328\pi$
$353$	1.22430	+	1.22430i	0.0651627	+	0.0651627i	−0.673774	+	0.738937i	$0.735328\pi$
$354$	6.42812	−	3.52316i	0.341651	−	0.187254i
$355$		0			0
$356$	−7.59514	+	11.9005i	−0.402542	+	0.630723i
$357$	−3.19169	+	3.19169i	−0.168922	+	0.168922i
$358$	32.0774	+	9.36396i	1.69534	+	0.494901i
$359$	30.9232			1.63206			0.816031	−	0.578008i	$-0.196170\pi$
$359$	30.9232			1.63206			0.816031	+	0.578008i	$0.196170\pi$
$360$		0			0
$361$	−18.8162			−0.990325
$362$	1.28027	+	0.373733i	0.0672893	+	0.0196430i
$363$	13.2766	−	13.2766i	0.696839	−	0.696839i
$364$	−4.98252	+	7.80686i	−0.261155	+	0.409191i
$365$		0			0
$366$	20.2941	−	11.1229i	1.06079	−	0.581404i
$367$	8.77487	+	8.77487i	0.458045	+	0.458045i	0.898013	−	0.439969i	$-0.145010\pi$
$367$	8.77487	+	8.77487i	0.458045	+	0.458045i	−0.439969	+	0.898013i	$0.645010\pi$
$368$	13.5179	+	4.94520i	0.704667	+	0.257786i
$369$			6.87142i			0.357712i
$370$		0			0
$371$			1.14730i			0.0595646i
$372$	0.235321	+	1.06560i	0.0122008	+	0.0552486i
$373$	−15.8590	−	15.8590i	−0.821147	−	0.821147i	0.165126	−	0.986273i	$-0.447197\pi$
$373$	−15.8590	−	15.8590i	−0.821147	−	0.821147i	−0.986273	+	0.165126i	$0.947197\pi$
$374$	11.4775	+	20.9411i	0.593489	+	1.08284i
$375$		0			0
$376$	1.90035	−	28.4578i	0.0980031	−	1.46760i
$377$	−24.6171	+	24.6171i	−1.26785	+	1.26785i
$378$	−2.23207	+	7.64624i	−0.114805	+	0.393280i
$379$	−6.09622			−0.313142			−0.156571	−	0.987667i	$-0.550044\pi$
$379$	−6.09622			−0.313142			−0.156571	+	0.987667i	$0.550044\pi$
$380$		0			0
$381$	−12.8828			−0.660008
$382$	−6.84294	+	23.4413i	−0.350115	+	1.19936i
$383$	−19.5052	+	19.5052i	−0.996670	+	0.996670i	−0.999994	−	0.00332492i	$-0.998942\pi$
$383$	−19.5052	+	19.5052i	−0.996670	+	0.996670i	0.00332492	+	0.999994i	$0.498942\pi$
$384$	5.44416	+	14.1194i	0.277821	+	0.720526i
$385$		0			0
$386$	−4.05681	−	7.40177i	−0.206486	−	0.376740i
$387$	−4.85883	−	4.85883i	−0.246988	−	0.246988i
$388$	14.4985	−	3.20177i	0.736049	−	0.162545i
$389$			21.0957i			1.06959i	0.844981	+	0.534797i	$0.179612\pi$
$389$			21.0957i			1.06959i	−0.844981	+	0.534797i	$0.820388\pi$
$390$		0			0
$391$		−	12.1436i		−	0.614130i
$392$	2.12881	−	1.86230i	0.107521	−	0.0940602i
$393$	2.05413	+	2.05413i	0.103617	+	0.103617i
$394$	10.0415	−	5.50358i	0.505881	−	0.277266i
$395$		0			0
$396$	10.2156	+	6.51982i	0.513352	+	0.327633i
$397$	3.68009	−	3.68009i	0.184698	−	0.184698i	−0.608701	−	0.793400i	$-0.708309\pi$
$397$	3.68009	−	3.68009i	0.184698	−	0.184698i	0.793400	+	0.608701i	$0.208309\pi$
$398$	−27.0703	−	7.90231i	−1.35691	−	0.396107i
$399$	−0.573485			−0.0287101
$400$		0			0
$401$	−11.5701			−0.577782			−0.288891	−	0.957362i	$-0.593287\pi$
$401$	−11.5701			−0.577782			−0.288891	+	0.957362i	$0.593287\pi$
$402$	21.3036	+	6.21891i	1.06253	+	0.310171i
$403$	1.33574	−	1.33574i	0.0665381	−	0.0665381i
$404$	−16.3788	−	10.4533i	−0.814875	−	0.520072i
$405$		0			0
$406$	9.32364	−	5.11015i	0.462724	−	0.253613i
$407$	15.8857	+	15.8857i	0.787427	+	0.787427i
$408$	9.60889	−	8.40590i	0.475711	−	0.416154i
$409$			4.46748i			0.220903i	0.993882	+	0.110451i	$0.0352296\pi$
$409$			4.46748i			0.220903i	−0.993882	+	0.110451i	$0.964770\pi$
$410$		0			0
$411$			15.6025i			0.769617i
$412$	−0.242153	+	0.0534760i	−0.0119300	+	0.00263457i
$413$	2.74021	+	2.74021i	0.134837	+	0.134837i
$414$	−2.96198	−	5.40423i	−0.145573	−	0.265603i
$415$		0			0
$416$	15.5326	−	21.0931i	0.761549	−	1.03417i
$417$	14.1875	−	14.1875i	0.694767	−	0.694767i
$418$	−0.850212	+	2.91250i	−0.0415852	+	0.142455i
$419$	−25.3590			−1.23887			−0.619433	−	0.785049i	$-0.712638\pi$
$419$	−25.3590			−1.23887			−0.619433	+	0.785049i	$0.712638\pi$
$420$		0			0
$421$	−11.7614			−0.573218			−0.286609	−	0.958048i	$-0.592528\pi$
$421$	−11.7614			−0.573218			−0.286609	+	0.958048i	$0.592528\pi$
$422$	3.07063	−	10.5188i	0.149476	−	0.512048i
$423$	−8.63460	+	8.63460i	−0.419829	+	0.419829i
$424$	0.216215	−	3.23783i	0.0105003	−	0.157243i
$425$		0			0
$426$	11.1552	+	20.3530i	0.540472	+	0.986108i
$427$	8.65107	+	8.65107i	0.418655	+	0.418655i
$428$	−1.02233	−	4.62937i	−0.0494160	−	0.223769i
$429$			30.9919i			1.49630i
$430$		0			0
$431$		−	16.6321i		−	0.801141i	−0.916266	−	0.400571i	$-0.868812\pi$
$431$		−	16.6321i		−	0.801141i	0.916266	−	0.400571i	$-0.131188\pi$
$432$	7.74021	−	21.1581i	0.372401	−	1.01797i
$433$	−25.8715	−	25.8715i	−1.24330	−	1.24330i	−0.958623	−	0.284680i	$-0.908113\pi$
$433$	−25.8715	−	25.8715i	−1.24330	−	1.24330i	−0.284680	−	0.958623i	$-0.591887\pi$
$434$	−0.505907	+	0.277281i	−0.0242843	+	0.0133099i
$435$		0			0
$436$	10.8830	−	17.0520i	0.521200	−	0.816642i
$437$	1.09099	−	1.09099i	0.0521891	−	0.0521891i
$438$	−9.72448	−	2.83875i	−0.464654	−	0.135641i
$439$	25.4267			1.21355			0.606775	−	0.794873i	$-0.292463\pi$
$439$	25.4267			1.21355			0.606775	+	0.794873i	$0.292463\pi$
$440$		0			0
$441$	−1.21097			−0.0576654
$442$	−21.2143	−	6.19282i	−1.00906	−	0.294563i
$443$	−1.27365	+	1.27365i	−0.0605127	+	0.0605127i	−0.736716	−	0.676203i	$-0.763624\pi$
$443$	−1.27365	+	1.27365i	−0.0605127	+	0.0605127i	0.676203	+	0.736716i	$0.263624\pi$
$444$	6.46159	−	10.1243i	0.306653	−	0.480480i
$445$		0			0
$446$	−19.4837	+	10.6788i	−0.922582	+	0.505654i
$447$	8.50872	+	8.50872i	0.402449	+	0.402449i
$448$	−6.35878	+	4.85448i	−0.300424	+	0.229352i
$449$		−	27.3838i		−	1.29232i	−0.763202	−	0.646160i	$-0.776374\pi$
$449$		−	27.3838i		−	1.29232i	0.763202	−	0.646160i	$-0.223626\pi$
$450$		0			0
$451$		−	28.3928i		−	1.33696i
$452$	4.67862	+	21.1860i	0.220064	+	0.996507i
$453$	0.600454	+	0.600454i	0.0282118	+	0.0282118i
$454$	4.69001	+	8.55708i	0.220113	+	0.401604i
$455$		0			0
$456$	1.61845	+	0.108077i	0.0757911	+	0.00506117i
$457$	−2.70508	+	2.70508i	−0.126538	+	0.126538i	−0.767540	−	0.641001i	$-0.778519\pi$
$457$	−2.70508	+	2.70508i	−0.126538	+	0.126538i	0.641001	+	0.767540i	$0.278519\pi$
$458$	−2.00115	+	6.85519i	−0.0935078	+	0.320322i
$459$	−19.0072			−0.887180
$460$		0			0
$461$	24.8145			1.15573			0.577864	−	0.816133i	$-0.303886\pi$
$461$	24.8145			1.15573			0.577864	+	0.816133i	$0.303886\pi$
$462$	2.65230	−	9.08576i	0.123396	−	0.422708i
$463$	−10.3704	+	10.3704i	−0.481955	+	0.481955i	−0.905755	−	0.423801i	$-0.860696\pi$
$463$	−10.3704	+	10.3704i	−0.481955	+	0.481955i	0.423801	+	0.905755i	$0.360696\pi$
$464$	−27.2757	+	12.6645i	−1.26624	+	0.587934i
$465$		0			0
$466$	2.35996	+	4.30583i	0.109323	+	0.199464i
$467$	−3.62962	−	3.62962i	−0.167959	−	0.167959i	0.618123	−	0.786082i	$-0.287893\pi$
$467$	−3.62962	−	3.62962i	−0.167959	−	0.167959i	−0.786082	+	0.618123i	$0.787893\pi$
$468$	−10.9514	+	2.41845i	−0.506228	+	0.111793i
$469$			11.7324i			0.541754i
$470$		0			0
$471$			11.4311i			0.526719i
$472$	−7.21685	−	8.24967i	−0.332182	−	0.379722i
$473$	20.0767	+	20.0767i	0.923129	+	0.923129i
$474$	0.327678	−	0.179596i	0.0150508	−	0.00824911i
$475$		0			0
$476$	5.68931	+	3.63104i	0.260769	+	0.166429i
$477$	−0.982415	+	0.982415i	−0.0449817	+	0.0449817i
$478$	15.3151	+	4.47076i	0.700498	+	0.204488i
$479$	−4.22349			−0.192976			−0.0964882	−	0.995334i	$-0.530761\pi$
$479$	−4.22349			−0.192976			−0.0964882	+	0.995334i	$0.530761\pi$
$480$		0			0
$481$	−20.7908			−0.947977
$482$	−35.4506	−	10.3487i	−1.61473	−	0.471369i
$483$	−3.40342	+	3.40342i	−0.154861	+	0.154861i
$484$	−23.6660	−	15.1042i	−1.07573	−	0.686553i
$485$		0			0
$486$	−14.4848	+	7.93894i	−0.657046	+	0.360118i
$487$	−16.5752	−	16.5752i	−0.751095	−	0.751095i	0.223589	−	0.974684i	$-0.428223\pi$
$487$	−16.5752	−	16.5752i	−0.751095	−	0.751095i	−0.974684	+	0.223589i	$0.928223\pi$
$488$	−22.7842	−	26.0449i	−1.03139	−	1.17900i
$489$		−	26.3540i		−	1.19177i
$490$		0			0
$491$			43.0124i			1.94112i	0.240851	+	0.970562i	$0.422573\pi$
$491$			43.0124i			1.94112i	−0.240851	+	0.970562i	$0.577427\pi$
$492$	−14.8221	+	3.27325i	−0.668233	+	0.147569i
$493$	17.9399	+	17.9399i	0.807973	+	0.807973i
$494$	−1.34953	−	2.46226i	−0.0607183	−	0.110782i
$495$		0			0
$496$	1.48000	−	0.687184i	0.0664538	−	0.0308555i
$497$	−8.67619	+	8.67619i	−0.389180	+	0.389180i
$498$	−1.39965	+	4.79467i	−0.0627199	+	0.214854i
$499$	0.561951			0.0251564			0.0125782	−	0.999921i	$-0.495996\pi$
$499$	0.561951			0.0251564			0.0125782	+	0.999921i	$0.495996\pi$
$500$		0			0
$501$	16.1955			0.723562
$502$	−10.3160	+	35.3387i	−0.460425	+	1.57724i
$503$	−9.37781	+	9.37781i	−0.418136	+	0.418136i	−0.884561	−	0.466425i	$-0.845542\pi$
$503$	−9.37781	+	9.37781i	−0.418136	+	0.418136i	0.466425	+	0.884561i	$0.345542\pi$
$504$	3.41754	+	0.228216i	0.152229	+	0.0101656i
$505$		0			0
$506$	12.2389	+	22.3303i	0.544087	+	0.992704i
$507$	−7.98540	−	7.98540i	−0.354644	−	0.354644i
$508$	4.15396	+	18.8102i	0.184302	+	0.834568i
$509$		−	18.4455i		−	0.817583i	−0.912628	−	0.408791i	$-0.865950\pi$
$509$		−	18.4455i		−	0.817583i	0.912628	−	0.408791i	$-0.134050\pi$
$510$		0			0
$511$		−	5.35551i		−	0.236914i
$512$	18.8602	−	12.5017i	0.833512	−	0.552501i
$513$	−1.70761	−	1.70761i	−0.0753929	−	0.0753929i
$514$	6.86808	−	3.76430i	0.302938	−	0.166036i
$515$		0			0
$516$	8.16629	−	12.7954i	0.359501	−	0.563284i
$517$	35.6783	−	35.6783i	1.56913	−	1.56913i
$518$	6.09513	+	1.77928i	0.267805	+	0.0781770i
$519$	24.7730			1.08741
$520$		0			0
$521$	−13.8088			−0.604976			−0.302488	−	0.953153i	$-0.597817\pi$
$521$	−13.8088			−0.604976			−0.302488	+	0.953153i	$0.597817\pi$
$522$	12.3595	+	3.60795i	0.540960	+	0.157916i
$523$	8.97547	−	8.97547i	0.392470	−	0.392470i	−0.483097	−	0.875567i	$-0.660488\pi$
$523$	8.97547	−	8.97547i	0.392470	−	0.392470i	0.875567	+	0.483097i	$0.160488\pi$
$524$	2.33689	−	3.66156i	0.102088	−	0.159956i
$525$		0			0
$526$	−18.1522	+	9.94896i	−0.791473	+	0.433795i
$527$	−0.973433	−	0.973433i	−0.0424034	−	0.0424034i
$528$	−9.19743	+	25.1415i	−0.400267	+	1.09414i
$529$			10.0508i			0.436990i
$530$		0			0
$531$			4.69281i			0.203651i
$532$	0.184915	+	0.837343i	0.00801708	+	0.0363034i
$533$	18.5798	+	18.5798i	0.804780	+	0.804780i
$534$	6.41749	+	11.7089i	0.277712	+	0.506694i
$535$		0			0
$536$	2.21106	−	33.1106i	0.0955031	−	1.43016i
$537$	22.3478	−	22.3478i	0.964380	−	0.964380i
$538$	−7.78810	+	26.6791i	−0.335769	+	1.15022i
$539$	5.00376			0.215527
$540$		0			0
$541$	23.3643			1.00451			0.502254	−	0.864720i	$-0.332504\pi$
$541$	23.3643			1.00451			0.502254	+	0.864720i	$0.332504\pi$
$542$	5.43375	−	18.6140i	0.233399	−	0.799538i
$543$	0.891942	−	0.891942i	0.0382769	−	0.0382769i
$544$	−15.3717	−	11.3195i	−0.659058	−	0.485320i
$545$		0			0
$546$	4.20996	+	7.68120i	0.180170	+	0.328725i
$547$	5.99240	+	5.99240i	0.256216	+	0.256216i	0.823513	−	0.567297i	$-0.192011\pi$
$547$	5.99240	+	5.99240i	0.256216	+	0.256216i	−0.567297	+	0.823513i	$0.692011\pi$
$548$	22.7812	−	5.03090i	0.973166	−	0.214909i
$549$			14.8156i			0.632315i
$550$		0			0
$551$			3.22346i			0.137324i
$552$	10.2463	−	8.96353i	0.436113	−	0.381513i
$553$	0.139684	+	0.139684i	0.00593998	+	0.00593998i
$554$	8.75392	−	4.79790i	0.371918	−	0.203843i
$555$		0			0
$556$	−25.2898	−	16.1406i	−1.07253	−	0.684512i
$557$	−16.5270	+	16.5270i	−0.700272	+	0.700272i	−0.964469	−	0.264197i	$-0.914893\pi$
$557$	−16.5270	+	16.5270i	−0.700272	+	0.700272i	0.264197	+	0.964469i	$0.414893\pi$
$558$	−0.670634	−	0.195770i	−0.0283902	−	0.00828761i
$559$	−26.2758			−1.11135
$560$		0			0
$561$	22.5856			0.953564
$562$	−21.6803	−	6.32886i	−0.914527	−	0.266967i
$563$	−6.57698	+	6.57698i	−0.277187	+	0.277187i	−0.831985	−	0.554798i	$-0.812795\pi$
$563$	−6.57698	+	6.57698i	−0.277187	+	0.277187i	0.554798	+	0.831985i	$0.312795\pi$
$564$	−22.7386	−	14.5123i	−0.957466	−	0.611077i
$565$		0			0
$566$	−26.7371	+	14.6542i	−1.12385	+	0.615964i
$567$	2.75816	+	2.75816i	0.115832	+	0.115832i
$568$	26.1205	−	22.8504i	1.09599	−	0.958780i
$569$			3.00520i			0.125984i	0.998014	+	0.0629922i	$0.0200643\pi$
$569$			3.00520i			0.125984i	−0.998014	+	0.0629922i	$0.979936\pi$
$570$		0			0
$571$		−	18.3018i		−	0.765909i	−0.923767	−	0.382954i	$-0.874907\pi$
$571$		−	18.3018i		−	0.765909i	0.923767	−	0.382954i	$-0.125093\pi$
$572$	45.2512	−	9.99307i	1.89205	−	0.417831i
$573$	16.3312	+	16.3312i	0.682246	+	0.682246i
$574$	−3.85689	−	7.03702i	−0.160983	−	0.293719i
$575$		0			0
$576$	−9.60177	−	1.28812i	−0.400074	−	0.0536715i
$577$	0.746129	−	0.746129i	0.0310618	−	0.0310618i	−0.691405	−	0.722467i	$-0.743008\pi$
$577$	0.746129	−	0.746129i	0.0310618	−	0.0310618i	0.722467	+	0.691405i	$0.243008\pi$
$578$	2.22394	−	7.61836i	0.0925035	−	0.316882i
$579$	−7.98302			−0.331763
$580$		0			0
$581$	−2.64055			−0.109548
$582$	3.93512	−	13.4802i	0.163116	−	0.558774i
$583$	4.05935	−	4.05935i	0.168121	−	0.168121i
$584$	−1.00928	+	15.1140i	−0.0417644	+	0.625423i
$585$		0			0
$586$	−19.1225	−	34.8895i	−0.789942	−	1.44127i
$587$	−29.5589	−	29.5589i	−1.22003	−	1.22003i	−0.967621	−	0.252406i	$-0.918778\pi$
$587$	−29.5589	−	29.5589i	−1.22003	−	1.22003i	−0.252406	−	0.967621i	$-0.581222\pi$
$588$	−0.576855	−	2.61215i	−0.0237891	−	0.107723i
$589$		−	0.174907i		−	0.00720692i
$590$		0			0
$591$		−	10.8300i		−	0.445486i
$592$	−16.8660	−	6.17004i	−0.693189	−	0.253587i
$593$	2.25040	+	2.25040i	0.0924127	+	0.0924127i	0.751802	−	0.659389i	$-0.229185\pi$
$593$	2.25040	+	2.25040i	0.0924127	+	0.0924127i	−0.659389	+	0.751802i	$0.729185\pi$
$594$	34.9513	−	19.1563i	1.43407	−	0.785994i
$595$		0			0
$596$	9.68000	−	15.1671i	0.396508	−	0.621269i
$597$	−18.8595	+	18.8595i	−0.771868	+	0.771868i
$598$	−22.6216	−	6.60365i	−0.925065	−	0.270043i
$599$	−1.98589			−0.0811413			−0.0405707	−	0.999177i	$-0.512918\pi$
$599$	−1.98589			−0.0811413			−0.0405707	+	0.999177i	$0.512918\pi$
$600$		0			0
$601$	29.8474			1.21750			0.608750	−	0.793362i	$-0.291671\pi$
$601$	29.8474			1.21750			0.608750	+	0.793362i	$0.291671\pi$
$602$	7.70315	+	2.24869i	0.313957	+	0.0916497i
$603$	−10.0464	+	10.0464i	−0.409119	+	0.409119i
$604$	0.683111	−	1.07033i	0.0277954	−	0.0435512i
$605$		0			0
$606$	−16.1152	+	8.83249i	−0.654634	+	0.358796i
$607$	−5.34562	−	5.34562i	−0.216972	−	0.216972i	0.590249	−	0.807221i	$-0.299030\pi$
$607$	−5.34562	−	5.34562i	−0.216972	−	0.216972i	−0.807221	+	0.590249i	$0.799030\pi$
$608$	−0.364053	−	2.39795i	−0.0147643	−	0.0972497i
$609$		−	10.0558i		−	0.407482i
$610$		0			0
$611$			46.6946i			1.88906i
$612$	1.76246	+	7.98090i	0.0712434	+	0.322609i
$613$	−14.9757	−	14.9757i	−0.604862	−	0.604862i	0.336737	−	0.941599i	$-0.390677\pi$
$613$	−14.9757	−	14.9757i	−0.604862	−	0.604862i	−0.941599	+	0.336737i	$0.890677\pi$
$614$	−13.5618	−	24.7439i	−0.547310	−	0.998584i
$615$		0			0
$616$	−14.1213	−	0.942991i	−0.568964	−	0.0379942i
$617$	−3.15050	+	3.15050i	−0.126835	+	0.126835i	−0.767675	−	0.640840i	$-0.778586\pi$
$617$	−3.15050	+	3.15050i	−0.126835	+	0.126835i	0.640840	+	0.767675i	$0.278586\pi$
$618$	−0.0657244	+	0.225147i	−0.00264382	+	0.00905673i
$619$	−47.6102			−1.91362			−0.956808	−	0.290722i	$-0.906105\pi$
$619$	−47.6102			−1.91362			−0.956808	+	0.290722i	$0.906105\pi$
$620$		0			0
$621$	−20.2681			−0.813330
$622$	−6.62884	+	22.7079i	−0.265792	+	0.910504i
$623$	−4.99133	+	4.99133i	−0.199973	+	0.199973i
$624$	−10.4335	−	22.4708i	−0.417675	−	0.899553i
$625$		0			0
$626$	5.50557	+	10.0451i	0.220047	+	0.401482i
$627$	2.02910	+	2.02910i	0.0810343	+	0.0810343i
$628$	16.6906	−	3.68587i	0.666026	−	0.147082i
$629$			15.1514i			0.604126i
$630$		0			0
$631$			22.2381i			0.885285i	0.896698	+	0.442643i	$0.145959\pi$
$631$			22.2381i			0.885285i	−0.896698	+	0.442643i	$0.854041\pi$
$632$	−0.367884	−	0.420533i	−0.0146336	−	0.0167279i
$633$	−7.32831	−	7.32831i	−0.291274	−	0.291274i
$634$	7.59717	−	4.16390i	0.301722	−	0.165370i
$635$		0			0
$636$	−2.58712	−	1.65116i	−0.102586	−	0.0654726i
$637$	−3.27438	+	3.27438i	−0.129736	+	0.129736i
$638$	−51.0695	−	14.9081i	−2.02186	−	0.590217i
$639$	−14.8586			−0.587799
$640$		0			0
$641$	−23.4027			−0.924352			−0.462176	−	0.886788i	$-0.652931\pi$
$641$	−23.4027			−0.924352			−0.462176	+	0.886788i	$0.652931\pi$
$642$	−4.30424	−	1.25648i	−0.169875	−	0.0495895i
$643$	16.9251	−	16.9251i	0.667460	−	0.667460i	−0.289668	−	0.957127i	$-0.593545\pi$
$643$	16.9251	−	16.9251i	0.667460	−	0.667460i	0.957127	+	0.289668i	$0.0935447\pi$
$644$	6.06672	+	3.87192i	0.239062	+	0.152575i
$645$		0			0
$646$	−1.79439	+	0.983481i	−0.0705994	+	0.0386945i
$647$	6.33786	+	6.33786i	0.249167	+	0.249167i	0.820629	−	0.571462i	$-0.193623\pi$
$647$	6.33786	+	6.33786i	0.249167	+	0.249167i	−0.571462	+	0.820629i	$0.693623\pi$
$648$	−7.26411	−	8.30370i	−0.285361	−	0.326200i
$649$		−	19.3908i		−	0.761154i
$650$		0			0
$651$			0.545635i			0.0213851i
$652$	−38.4795	+	8.49762i	−1.50697	+	0.332792i
$653$	−14.5231	−	14.5231i	−0.568332	−	0.568332i	0.363329	−	0.931661i	$-0.381640\pi$
$653$	−14.5231	−	14.5231i	−0.568332	−	0.568332i	−0.931661	+	0.363329i	$0.881640\pi$
$654$	−9.19552	−	16.7775i	−0.359573	−	0.656053i
$655$		0			0
$656$	9.55852	+	20.5863i	0.373197	+	0.803761i
$657$	4.58586	−	4.58586i	0.178911	−	0.178911i
$658$	3.99614	−	13.6892i	0.155786	−	0.533662i
$659$	−6.31956			−0.246175			−0.123088	−	0.992396i	$-0.539280\pi$
$659$	−6.31956			−0.246175			−0.123088	+	0.992396i	$0.539280\pi$
$660$		0			0
$661$	30.0317			1.16810			0.584049	−	0.811718i	$-0.301467\pi$
$661$	30.0317			1.16810			0.584049	+	0.811718i	$0.301467\pi$
$662$	12.3245	−	42.2191i	0.479006	−	1.64089i
$663$	−14.7797	+	14.7797i	−0.573994	+	0.573994i
$664$	7.45200	+	0.497628i	0.289193	+	0.0193117i
$665$		0			0
$666$	3.69561	+	6.74276i	0.143202	+	0.261277i
$667$	19.1300	+	19.1300i	0.740717	+	0.740717i
$668$	−5.22209	−	23.6470i	−0.202049	−	0.914931i
$669$			21.0138i			0.812439i
$670$		0			0
$671$		−	61.2183i		−	2.36331i
$672$	1.13569	+	7.48058i	0.0438102	+	0.288570i
$673$	−29.5868	−	29.5868i	−1.14049	−	1.14049i	−0.988361	−	0.152127i	$-0.951388\pi$
$673$	−29.5868	−	29.5868i	−1.14049	−	1.14049i	−0.152127	−	0.988361i	$-0.548612\pi$
$674$	−16.5409	+	9.06585i	−0.637133	+	0.349204i
$675$		0			0
$676$	−9.08465	+	14.2343i	−0.349409	+	0.547473i
$677$	−7.19716	+	7.19716i	−0.276609	+	0.276609i	−0.831754	−	0.555145i	$-0.812663\pi$
$677$	−7.19716	+	7.19716i	−0.276609	+	0.276609i	0.555145	+	0.831754i	$0.312663\pi$
$678$	19.6981	+	5.75023i	0.756501	+	0.220836i
$679$	7.42390			0.284903
$680$		0			0
$681$	9.22905			0.353658
$682$	2.77107	+	0.808924i	0.106110	+	0.0309753i
$683$	2.35531	−	2.35531i	0.0901236	−	0.0901236i	−0.660608	−	0.750731i	$-0.729701\pi$
$683$	2.35531	−	2.35531i	0.0901236	−	0.0901236i	0.750731	+	0.660608i	$0.229701\pi$
$684$	−0.558667	+	0.875347i	−0.0213612	+	0.0334697i
$685$		0			0
$686$	1.24016	−	0.679713i	0.0473494	−	0.0259516i
$687$	4.77591	+	4.77591i	0.182212	+	0.182212i
$688$	−21.3156	−	7.79783i	−0.812650	−	0.297289i
$689$			5.31275i			0.202400i
$690$		0			0
$691$			2.74496i			0.104423i	0.998636	+	0.0522116i	$0.0166270\pi$
$691$			2.74496i			0.104423i	−0.998636	+	0.0522116i	$0.983373\pi$
$692$	−7.98782	−	36.1710i	−0.303652	−	1.37501i
$693$	4.28466	+	4.28466i	0.162761	+	0.162761i
$694$	21.5506	+	39.3198i	0.818050	+	1.49256i
$695$		0			0
$696$	−1.89508	+	28.3789i	−0.0718329	+	1.07570i
$697$	13.5402	−	13.5402i	0.512870	−	0.512870i
$698$	−5.48426	+	18.7870i	−0.207582	+	0.711099i
$699$	4.64396			0.175651
$700$		0			0
$701$	−45.4380			−1.71617			−0.858085	−	0.513508i	$-0.828346\pi$
$701$	−45.4380			−1.71617			−0.858085	+	0.513508i	$0.828346\pi$
$702$	−10.3360	+	35.4072i	−0.390107	+	1.33636i
$703$	−1.36121	+	1.36121i	−0.0513389	+	0.0513389i
$704$	39.6746	+	5.32251i	1.49529	+	0.200600i
$705$		0			0
$706$	−1.17687	−	2.14723i	−0.0442919	−	0.0808120i
$707$	−6.86965	−	6.86965i	−0.258360	−	0.258360i
$708$	−10.1227	+	2.23545i	−0.380435	+	0.0840135i
$709$		−	43.0494i		−	1.61675i	−0.588665	−	0.808377i	$-0.700346\pi$
$709$		−	43.0494i		−	1.61675i	0.588665	−	0.808377i	$-0.299654\pi$
$710$		0			0
$711$			0.239220i			0.00897144i
$712$	15.0269	−	13.1456i	0.563157	−	0.492652i
$713$	−1.03801	−	1.03801i	−0.0388737	−	0.0388737i
$714$	5.59773	−	3.06804i	0.209490	−	0.114818i
$715$		0			0
$716$	−39.8359	−	25.4242i	−1.48874	−	0.950145i
$717$	10.6698	−	10.6698i	0.398472	−	0.398472i
$718$	−41.9798	−	12.2547i	−1.56667	−	0.457340i
$719$	−17.9081			−0.667860			−0.333930	−	0.942598i	$-0.608375\pi$
$719$	−17.9081			−0.667860			−0.333930	+	0.942598i	$0.608375\pi$
$720$		0			0
$721$	−0.123994			−0.00461778
$722$	25.5439	+	7.45674i	0.950647	+	0.277511i
$723$	−24.6979	+	24.6979i	−0.918524	+	0.918524i
$724$	−1.58992	−	1.01472i	−0.0590890	−	0.0377119i
$725$		0			0
$726$	−23.2851	+	12.7622i	−0.864190	+	0.473650i
$727$	−9.20391	−	9.20391i	−0.341354	−	0.341354i	0.515522	−	0.856876i	$-0.327598\pi$
$727$	−9.20391	−	9.20391i	−0.341354	−	0.341354i	−0.856876	+	0.515522i	$0.827598\pi$
$728$	9.85784	−	8.62369i	0.365356	−	0.319615i
$729$			27.3242i			1.01201i
$730$		0			0
$731$			19.1487i			0.708239i
$732$	−31.9583	+	7.05752i	−1.18121	+	0.260853i
$733$	13.1462	+	13.1462i	0.485567	+	0.485567i	0.906904	−	0.421337i	$-0.138439\pi$
$733$	13.1462	+	13.1462i	0.485567	+	0.485567i	−0.421337	+	0.906904i	$0.638439\pi$
$734$	−8.43492	−	15.3898i	−0.311339	−	0.568047i
$735$		0			0
$736$	−16.3915	−	12.0704i	−0.604197	−	0.444922i
$737$	41.5116	−	41.5116i	1.52910	−	1.52910i
$738$	2.72310	−	9.32832i	0.100239	−	0.343380i
$739$	7.07544			0.260274			0.130137	−	0.991496i	$-0.458458\pi$
$739$	7.07544			0.260274			0.130137	+	0.991496i	$0.458458\pi$
$740$		0			0
$741$	−2.65562			−0.0975566
$742$	0.454666	−	1.55751i	0.0166913	−	0.0571781i
$743$	34.5013	−	34.5013i	1.26573	−	1.26573i	0.317456	−	0.948273i	$-0.397172\pi$
$743$	34.5013	−	34.5013i	1.26573	−	1.26573i	0.948273	−	0.317456i	$-0.102828\pi$
$744$	0.102829	−	1.53986i	0.00376988	−	0.0564540i
$745$		0			0
$746$	15.2446	+	27.8142i	0.558144	+	1.01835i
$747$	−2.26107	−	2.26107i	−0.0827281	−	0.0827281i
$748$	−7.28252	−	32.9772i	−0.266275	−	1.20576i
$749$		−	2.37045i		−	0.0866144i
$750$		0			0
$751$		−	8.42098i		−	0.307286i	−0.988126	−	0.153643i	$-0.950899\pi$
$751$		−	8.42098i		−	0.307286i	0.988126	−	0.153643i	$-0.0491006\pi$
$752$	−13.8575	+	37.8799i	−0.505331	+	1.38134i
$753$	24.6199	+	24.6199i	0.897200	+	0.897200i
$754$	43.1747	−	23.6634i	1.57233	−	0.861772i
$755$		0			0
$756$	6.06032	−	9.49562i	0.220412	−	0.345352i
$757$	−0.487957	+	0.487957i	−0.0177351	+	0.0177351i	−0.715919	−	0.698184i	$-0.753992\pi$
$757$	−0.487957	+	0.487957i	−0.0177351	+	0.0177351i	0.698184	+	0.715919i	$0.253992\pi$
$758$	8.27594	+	2.41590i	0.300596	+	0.0877493i
$759$	24.0839			0.874189
$760$		0			0
$761$	4.36990			0.158409			0.0792044	−	0.996858i	$-0.474762\pi$
$761$	4.36990			0.158409			0.0792044	+	0.996858i	$0.474762\pi$
$762$	17.4892	+	5.10540i	0.633565	+	0.184949i
$763$	7.15200	−	7.15200i	0.258920	−	0.258920i
$764$	18.5793	−	29.1110i	0.672176	−	1.05320i
$765$		0			0
$766$	34.2092	−	18.7496i	1.23603	−	0.677449i
$767$	12.6890	+	12.6890i	0.458174	+	0.458174i
$768$	−1.79531	−	21.3253i	−0.0647828	−	0.769510i
$769$		−	9.02388i		−	0.325409i	−0.986675	−	0.162705i	$-0.947978\pi$
$769$		−	9.02388i		−	0.325409i	0.986675	−	0.162705i	$-0.0520218\pi$
$770$		0			0
$771$		−	7.40742i		−	0.266772i
$772$	2.57405	+	11.6560i	0.0926422	+	0.419508i
$773$	24.6869	+	24.6869i	0.887926	+	0.887926i	0.994324	−	0.106397i	$-0.0339316\pi$
$773$	24.6869	+	24.6869i	0.887926	+	0.887926i	−0.106397	+	0.994324i	$0.533932\pi$
$774$	4.67059	+	8.52164i	0.167881	+	0.306304i
$775$		0			0
$776$	−20.9513	−	1.39908i	−0.752108	−	0.0502242i
$777$	4.24639	−	4.24639i	0.152338	−	0.152338i
$778$	8.36010	−	28.6385i	0.299724	−	1.02674i
$779$	2.43290			0.0871679
$780$		0			0
$781$	61.3960			2.19692
$782$	−4.81245	+	16.4856i	−0.172093	+	0.589525i
$783$	29.9422	−	29.9422i	1.07005	−	1.07005i
$784$	−3.62800	+	1.68453i	−0.129571	+	0.0601618i
$785$		0			0
$786$	−1.97455	−	3.60263i	−0.0704298	−	0.128501i
$787$	2.73452	+	2.73452i	0.0974751	+	0.0974751i	0.754163	−	0.656688i	$-0.228043\pi$
$787$	2.73452	+	2.73452i	0.0974751	+	0.0974751i	−0.656688	+	0.754163i	$0.728043\pi$
$788$	−15.8128	+	3.49203i	−0.563309	+	0.124398i
$789$			19.5776i			0.696983i
$790$		0			0
$791$			10.8482i			0.385719i
$792$	−11.2844	−	12.8994i	−0.400975	−	0.458359i
$793$	40.0603	+	40.0603i	1.42258	+	1.42258i
$794$	−6.45432	+	3.53752i	−0.229055	+	0.125542i
$795$		0			0
$796$	33.6178	+	21.4556i	1.19155	+	0.760474i
$797$	34.6913	−	34.6913i	1.22883	−	1.22883i	0.264420	−	0.964408i	$-0.414819\pi$
$797$	34.6913	−	34.6913i	1.22883	−	1.22883i	0.964408	−	0.264420i	$-0.0851806\pi$
$798$	0.778536	+	0.227269i	0.0275599	+	0.00804522i
$799$	34.0290			1.20386
$800$		0			0
$801$	−8.54803			−0.302030
$802$	15.7070	+	4.58516i	0.554634	+	0.161907i
$803$	−18.9488	+	18.9488i	−0.668690	+	0.668690i
$804$	−26.4563	−	16.8850i	−0.933042	−	0.595489i
$805$		0			0
$806$	−2.34269	+	1.28400i	−0.0825177	+	0.0452268i
$807$	18.5869	+	18.5869i	0.654290	+	0.654290i
$808$	18.0925	+	20.6818i	0.636492	+	0.727582i
$809$		−	36.7269i		−	1.29125i	−0.763655	−	0.645624i	$-0.776597\pi$
$809$		−	36.7269i		−	1.29125i	0.763655	−	0.645624i	$-0.223403\pi$
$810$		0			0
$811$			9.04068i			0.317461i	0.987322	+	0.158731i	$0.0507401\pi$
$811$			9.04068i			0.317461i	−0.987322	+	0.158731i	$0.949260\pi$
$812$	−14.6825	+	3.24240i	−0.515253	+	0.113786i
$813$	−12.9681	−	12.9681i	−0.454810	−	0.454810i
$814$	−15.2703	−	27.8612i	−0.535224	−	0.976533i
$815$		0			0
$816$	−16.3758	+	7.60351i	−0.573267	+	0.266176i
$817$	−1.72032	+	1.72032i	−0.0601865	+	0.0601865i
$818$	1.77044	−	6.06484i	0.0619019	−	0.212052i
$819$	−5.60762			−0.195946
$820$		0			0
$821$	−0.570761			−0.0199197			−0.00995984	−	0.999950i	$-0.503170\pi$
$821$	−0.570761			−0.0199197			−0.00995984	+	0.999950i	$0.503170\pi$
$822$	6.18320	−	21.1813i	0.215664	−	0.738782i
$823$	−4.64286	+	4.64286i	−0.161840	+	0.161840i	−0.783381	−	0.621541i	$-0.786507\pi$
$823$	−4.64286	+	4.64286i	−0.161840	+	0.161840i	0.621541	+	0.783381i	$0.286507\pi$
$824$	0.349929	+	0.0233675i	0.0121903	+	0.000814045i
$825$		0			0
$826$	−2.63405	−	4.80591i	−0.0916503	−	0.167219i
$827$	6.28320	+	6.28320i	0.218488	+	0.218488i	0.807861	−	0.589373i	$-0.200625\pi$
$827$	6.28320	+	6.28320i	0.218488	+	0.218488i	−0.589373	+	0.807861i	$0.700625\pi$
$828$	1.87938	+	8.51034i	0.0653131	+	0.295755i
$829$			25.1880i			0.874816i	0.899263	+	0.437408i	$0.144103\pi$
$829$			25.1880i			0.874816i	−0.899263	+	0.437408i	$0.855897\pi$
$830$		0			0
$831$		−	9.44134i		−	0.327517i
$832$	−29.4454	+	22.4795i	−1.02084	+	0.779336i
$833$	2.38623	+	2.38623i	0.0826779	+	0.0826779i
$834$	−24.8828	+	13.6379i	−0.861621	+	0.472242i
$835$		0			0
$836$	2.30842	−	3.61694i	0.0798382	−	0.125095i
$837$	−1.62469	+	1.62469i	−0.0561574	+	0.0561574i
$838$	34.4262	+	10.0496i	1.18923	+	0.347158i
$839$	−0.275469			−0.00951026			−0.00475513	−	0.999989i	$-0.501514\pi$
$839$	−0.275469			−0.00951026			−0.00475513	+	0.999989i	$0.501514\pi$
$840$		0			0
$841$	−27.5219			−0.949032
$842$	15.9668	+	4.66099i	0.550252	+	0.160628i
$843$	−15.1043	+	15.1043i	−0.520221	+	0.520221i
$844$	−8.33710	+	13.0630i	−0.286975	+	0.449647i
$845$		0			0
$846$	15.1438	−	8.30009i	0.520654	−	0.285363i
$847$	−9.92607	−	9.92607i	−0.341064	−	0.341064i
$848$	−1.57666	+	4.30984i	−0.0541426	+	0.148001i
$849$			28.8368i			0.989675i
$850$		0			0
$851$			16.1565i			0.553839i
$852$	−7.07801	−	32.0511i	−0.242489	−	1.09805i
$853$	20.8769	+	20.8769i	0.714813	+	0.714813i	0.967538	−	0.252725i	$-0.0813269\pi$
$853$	20.8769	+	20.8769i	0.714813	+	0.714813i	−0.252725	+	0.967538i	$0.581327\pi$
$854$	−8.31592	−	15.1727i	−0.284565	−	0.519198i
$855$		0			0
$856$	−0.446727	+	6.68975i	−0.0152688	+	0.228651i
$857$	−17.2312	+	17.2312i	−0.588607	+	0.588607i	−0.937254	−	0.348647i	$-0.886641\pi$
$857$	−17.2312	+	17.2312i	−0.588607	+	0.588607i	0.348647	+	0.937254i	$0.386641\pi$
$858$	12.2819	−	42.0732i	0.419298	−	1.43636i
$859$	−56.3316			−1.92201			−0.961004	−	0.276534i	$-0.910814\pi$
$859$	−56.3316			−1.92201			−0.961004	+	0.276534i	$0.910814\pi$
$860$		0			0
$861$	−7.58962			−0.258654
$862$	−6.59121	+	22.5790i	−0.224498	+	0.769044i
$863$	−10.5264	+	10.5264i	−0.358323	+	0.358323i	−0.863195	−	0.504871i	$-0.831540\pi$
$863$	−10.5264	+	10.5264i	−0.358323	+	0.358323i	0.504871	+	0.863195i	$0.331540\pi$
$864$	−18.8926	+	25.6559i	−0.642739	+	0.872830i
$865$		0			0
$866$	24.8692	+	45.3746i	0.845089	+	1.54189i
$867$	−5.30760	−	5.30760i	−0.180255	−	0.180255i
$868$	0.796681	−	0.175935i	0.0270411	−	0.00597163i
$869$		−	0.988459i		−	0.0335312i
$870$		0			0
$871$			54.3291i			1.84087i
$872$	−21.5318	+	18.8361i	−0.729159	+	0.637872i
$873$	6.35700	+	6.35700i	0.215152	+	0.215152i
$874$	−1.91343	+	1.04872i	−0.0647227	+	0.0354736i
$875$		0			0
$876$	12.0765	+	7.70751i	0.408028	+	0.260413i
$877$	33.1677	−	33.1677i	1.11999	−	1.11999i	0.128251	−	0.991742i	$-0.459064\pi$
$877$	33.1677	−	33.1677i	1.11999	−	1.11999i	0.991742	−	0.128251i	$-0.0409362\pi$
$878$	−34.5181	−	10.0765i	−1.16493	−	0.340064i
$879$	−37.6294			−1.26921
$880$		0			0
$881$	−8.94374			−0.301322			−0.150661	−	0.988585i	$-0.548140\pi$
$881$	−8.94374			−0.301322			−0.150661	+	0.988585i	$0.548140\pi$
$882$	1.64396	+	0.479902i	0.0553551	+	0.0161591i
$883$	−13.6439	+	13.6439i	−0.459153	+	0.459153i	−0.898377	−	0.439224i	$-0.855253\pi$
$883$	−13.6439	+	13.6439i	−0.459153	+	0.459153i	0.439224	+	0.898377i	$0.355253\pi$
$884$	26.3453	+	16.8142i	0.886089	+	0.565522i
$885$		0			0
$886$	2.23378	−	1.22430i	0.0750453	−	0.0411313i
$887$	23.2799	+	23.2799i	0.781664	+	0.781664i	0.980111	−	0.198448i	$-0.0635900\pi$
$887$	23.2799	+	23.2799i	0.781664	+	0.781664i	−0.198448	+	0.980111i	$0.563590\pi$
$888$	−12.7842	+	11.1836i	−0.429009	+	0.375299i
$889$			9.63171i			0.323037i
$890$		0			0
$891$		−	19.5178i		−	0.653869i
$892$	30.6822	−	6.77570i	1.02731	−	0.226867i
$893$	3.05718	+	3.05718i	0.102305	+	0.102305i
$894$	−8.17908	−	14.9230i	−0.273549	−	0.499100i
$895$		0			0
$896$	10.5562	−	4.07026i	0.352657	−	0.135978i
$897$	−15.7601	+	15.7601i	−0.526215	+	0.526215i
$898$	−10.8520	+	37.1749i	−0.362137	+	1.24054i
$899$	3.06692			0.102288
$900$		0			0
$901$	3.87170			0.128985
$902$	−11.2519	+	38.5447i	−0.374647	+	1.28340i
$903$	5.36667	−	5.36667i	0.178592	−	0.178592i
$904$	2.04442	−	30.6153i	0.0679965	−	1.01825i
$905$		0			0
$906$	−0.577192	−	1.05311i	−0.0191759	−	0.0349871i
$907$	10.1283	+	10.1283i	0.336304	+	0.336304i	0.854974	−	0.518670i	$-0.173573\pi$
$907$	10.1283	+	10.1283i	0.336304	+	0.336304i	−0.518670	+	0.854974i	$0.673573\pi$
$908$	−2.97582	−	13.4753i	−0.0987562	−	0.447194i
$909$		−	11.7648i		−	0.390214i
$910$		0			0
$911$		−	1.96705i		−	0.0651712i	−0.999469	−	0.0325856i	$-0.989626\pi$
$911$		−	1.96705i		−	0.0651712i	0.999469	−	0.0325856i	$-0.0103742\pi$
$912$	−2.15431	−	0.788104i	−0.0713363	−	0.0260967i
$913$	9.34275	+	9.34275i	0.309200	+	0.309200i
$914$	4.74429	−	2.60028i	0.156927	−	0.0860096i
$915$		0			0
$916$	5.43335	−	8.51325i	0.179523	−	0.281286i
$917$	1.53574	−	1.53574i	0.0507148	−	0.0507148i
$918$	25.8033	+	7.53244i	0.851635	+	0.248607i
$919$	8.51566			0.280906			0.140453	−	0.990087i	$-0.455144\pi$
$919$	8.51566			0.280906			0.140453	+	0.990087i	$0.455144\pi$
$920$		0			0
$921$	−26.6870			−0.879367
$922$	−33.6871	−	9.83386i	−1.10942	−	0.323861i
$923$	−40.1766	+	40.1766i	−1.32243	+	1.32243i
$924$	−7.20127	+	11.2833i	−0.236904	+	0.371194i
$925$		0			0
$926$	18.1881	−	9.96867i	0.597700	−	0.327591i
$927$	−0.106175	−	0.106175i	−0.00348723	−	0.00348723i
$928$	42.0470	−	6.38351i	1.38026	−	0.209549i
$929$			35.5258i			1.16556i	0.812629	+	0.582781i	$0.198036\pi$
$929$			35.5258i			1.16556i	−0.812629	+	0.582781i	$0.801964\pi$
$930$		0			0
$931$			0.428759i			0.0140520i
$932$	−1.49740	−	6.78063i	−0.0490490	−	0.222107i
$933$	15.8203	+	15.8203i	0.517932	+	0.517932i
$934$	3.48900	+	6.36580i	0.114164	+	0.208295i
$935$		0			0
$936$	15.8255	+	1.05679i	0.517273	+	0.0345424i
$937$	−23.8007	+	23.8007i	−0.777536	+	0.777536i	−0.979411	−	0.201876i	$-0.935296\pi$
$937$	−23.8007	+	23.8007i	−0.777536	+	0.777536i	0.201876	+	0.979411i	$0.435296\pi$
$938$	4.64950	−	15.9274i	0.151812	−	0.520049i
$939$	10.8339			0.353551
$940$		0			0
$941$	−13.5960			−0.443217			−0.221609	−	0.975136i	$-0.571131\pi$
$941$	−13.5960			−0.443217			−0.221609	+	0.975136i	$0.571131\pi$
$942$	4.53009	−	15.5184i	0.147598	−	0.505616i
$943$	14.4384	−	14.4384i	0.470179	−	0.470179i
$944$	6.52796	+	14.0594i	0.212467	+	0.457593i
$945$		0			0
$946$	−19.2989	−	35.2115i	−0.627463	−	1.14483i
$947$	25.8348	+	25.8348i	0.839518	+	0.839518i	0.988795	−	0.149277i	$-0.0476946\pi$
$947$	25.8348	+	25.8348i	0.839518	+	0.839518i	−0.149277	+	0.988795i	$0.547695\pi$
$948$	−0.516013	+	0.113954i	−0.0167593	+	0.00370105i
$949$		−	24.7996i		−	0.805030i
$950$		0			0
$951$		−	8.19376i		−	0.265701i
$952$	−6.28457	−	7.18397i	−0.203684	−	0.232834i
$953$	−4.64369	−	4.64369i	−0.150424	−	0.150424i	0.627883	−	0.778307i	$-0.283921\pi$
$953$	−4.64369	−	4.64369i	−0.150424	−	0.150424i	−0.778307	+	0.627883i	$0.783921\pi$
$954$	1.72301	−	0.944355i	0.0557844	−	0.0305746i
$955$		0			0
$956$	−19.0194	−	12.1386i	−0.615130	−	0.392590i
$957$	−35.5793	+	35.5793i	−1.15012	+	1.15012i
$958$	5.73362	+	1.67375i	0.185245	+	0.0540763i
$959$	11.6651			0.376685
$960$		0			0
$961$	30.8336			0.994632
$962$	28.2246	+	8.23926i	0.909996	+	0.265644i
$963$	2.02979	−	2.02979i	0.0654090	−	0.0654090i
$964$	44.0249	+	28.0977i	1.41795	+	0.904967i
$965$		0			0
$966$	5.96908	−	3.27157i	0.192052	−	0.105261i
$967$	−24.8629	−	24.8629i	−0.799538	−	0.799538i	0.183485	−	0.983023i	$-0.441262\pi$
$967$	−24.8629	−	24.8629i	−0.799538	−	0.799538i	−0.983023	+	0.183485i	$0.941262\pi$
$968$	26.1421	+	29.8834i	0.840240	+	0.960489i
$969$			1.93530i			0.0621708i
$970$		0			0
$971$		−	38.8694i		−	1.24738i	−0.781672	−	0.623689i	$-0.785633\pi$
$971$		−	38.8694i		−	1.24738i	0.781672	−	0.623689i	$-0.214367\pi$
$972$	22.8101	−	5.03727i	0.731634	−	0.161571i
$973$	−10.6072	−	10.6072i	−0.340050	−	0.340050i
$974$	15.9331	+	29.0704i	0.510529	+	0.931476i
$975$		0			0
$976$	20.6093	+	44.3866i	0.659688	+	1.42078i
$977$	−37.7523	+	37.7523i	−1.20780	+	1.20780i	−0.236067	+	0.971737i	$0.575859\pi$
$977$	−37.7523	+	37.7523i	−1.20780	+	1.20780i	−0.971737	+	0.236067i	$0.924141\pi$
$978$	−10.4439	+	35.7770i	−0.333961	+	1.14402i
$979$	35.3206			1.12885
$980$		0			0
$981$	12.2483			0.391060
$982$	17.0456	−	58.3917i	0.543946	−	1.86335i
$983$	−28.2170	+	28.2170i	−0.899983	+	0.899983i	−0.995434	−	0.0954508i	$-0.969571\pi$
$983$	−28.2170	+	28.2170i	−0.899983	+	0.899983i	0.0954508	+	0.995434i	$0.469571\pi$
$984$	21.4190	+	1.43031i	0.682812	+	0.0455968i
$985$		0			0
$986$	−17.2449	−	31.4639i	−0.549190	−	1.00201i
$987$	−9.53709	−	9.53709i	−0.303569	−	0.303569i
$988$	0.856280	+	3.87746i	0.0272419	+	0.123359i
$989$			20.4190i			0.649285i
$990$		0			0
$991$		−	23.5273i		−	0.747370i	−0.927556	−	0.373685i	$-0.878094\pi$
$991$		−	23.5273i		−	0.747370i	0.927556	−	0.373685i	$-0.121906\pi$
$992$	−2.28150	+	0.346374i	−0.0724378	+	0.0109974i
$993$	−29.4134	−	29.4134i	−0.933406	−	0.933406i
$994$	15.2167	−	8.34007i	0.482645	−	0.264531i
$995$		0			0
$996$	3.80020	−	5.95435i	0.120414	−	0.188671i
$997$	23.7351	−	23.7351i	0.751699	−	0.751699i	−0.223097	−	0.974796i	$-0.571617\pi$
$997$	23.7351	−	23.7351i	0.751699	−	0.751699i	0.974796	+	0.223097i	$0.0716168\pi$
$998$	−0.762878	−	0.222698i	−0.0241485	−	0.00704937i
$999$	25.2882			0.800082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.k.b.43.1		36
4.3	odd	2	inner	700.2.k.b.43.11		36
5.2	odd	4	inner	700.2.k.b.407.11		36
5.3	odd	4		140.2.k.a.127.8	yes	36
5.4	even	2		140.2.k.a.43.18	yes	36
20.3	even	4		140.2.k.a.127.18	yes	36
20.7	even	4	inner	700.2.k.b.407.1		36
20.19	odd	2		140.2.k.a.43.8	✓	36
35.3	even	12		980.2.x.l.667.5		72
35.4	even	6		980.2.x.k.863.5		72
35.9	even	6		980.2.x.k.263.7		72
35.13	even	4		980.2.k.l.687.8		36
35.18	odd	12		980.2.x.k.667.5		72
35.19	odd	6		980.2.x.l.263.7		72
35.23	odd	12		980.2.x.k.67.17		72
35.24	odd	6		980.2.x.l.863.5		72
35.33	even	12		980.2.x.l.67.17		72
35.34	odd	2		980.2.k.l.883.18		36
140.3	odd	12		980.2.x.l.667.7		72
140.19	even	6		980.2.x.l.263.5		72
140.23	even	12		980.2.x.k.67.5		72
140.39	odd	6		980.2.x.k.863.17		72
140.59	even	6		980.2.x.l.863.17		72
140.79	odd	6		980.2.x.k.263.5		72
140.83	odd	4		980.2.k.l.687.18		36
140.103	odd	12		980.2.x.l.67.5		72
140.123	even	12		980.2.x.k.667.7		72
140.139	even	2		980.2.k.l.883.8		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.8	✓	36	20.19	odd	2
140.2.k.a.43.18	yes	36	5.4	even	2
140.2.k.a.127.8	yes	36	5.3	odd	4
140.2.k.a.127.18	yes	36	20.3	even	4
700.2.k.b.43.1		36	1.1	even	1	trivial
700.2.k.b.43.11		36	4.3	odd	2	inner
700.2.k.b.407.1		36	20.7	even	4	inner
700.2.k.b.407.11		36	5.2	odd	4	inner
980.2.k.l.687.8		36	35.13	even	4
980.2.k.l.687.18		36	140.83	odd	4
980.2.k.l.883.8		36	140.139	even	2
980.2.k.l.883.18		36	35.34	odd	2
980.2.x.k.67.5		72	140.23	even	12
980.2.x.k.67.17		72	35.23	odd	12
980.2.x.k.263.5		72	140.79	odd	6
980.2.x.k.263.7		72	35.9	even	6
980.2.x.k.667.5		72	35.18	odd	12
980.2.x.k.667.7		72	140.123	even	12
980.2.x.k.863.5		72	35.4	even	6
980.2.x.k.863.17		72	140.39	odd	6
980.2.x.l.67.5		72	140.103	odd	12
980.2.x.l.67.17		72	35.33	even	12
980.2.x.l.263.5		72	140.19	even	6
980.2.x.l.263.7		72	35.19	odd	6
980.2.x.l.667.5		72	35.3	even	12
980.2.x.l.667.7		72	140.3	odd	12
980.2.x.l.863.5		72	35.24	odd	6
980.2.x.l.863.17		72	140.59	even	6

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35755 - 0.396294i) q^{2} +(-0.945787 + 0.945787i) q^{3} +(1.68590 + 1.07598i) q^{4} +(1.65877 - 0.909146i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-1.86230 - 2.12881i) q^{8} +1.21097i q^{9} +O(q^{10})\)	\(q+(-1.35755 - 0.396294i) q^{2} +(-0.945787 + 0.945787i) q^{3} +(1.68590 + 1.07598i) q^{4} +(1.65877 - 0.909146i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-1.86230 - 2.12881i) q^{8} +1.21097i q^{9} -5.00376i q^{11} +(-2.61215 + 0.576855i) q^{12} +(3.27438 + 3.27438i) q^{13} +(-0.679713 - 1.24016i) q^{14} +(1.68453 + 3.62800i) q^{16} +(2.38623 - 2.38623i) q^{17} +(0.479902 - 1.64396i) q^{18} +0.428759 q^{19} -1.33754 q^{21} +(-1.98296 + 6.79287i) q^{22} +(2.54453 - 2.54453i) q^{23} +(3.77474 + 0.252069i) q^{24} +(-3.14753 - 5.74276i) q^{26} +(-3.98268 - 3.98268i) q^{27} +(0.431279 + 1.95295i) q^{28} +7.51811i q^{29} -0.407938i q^{31} +(-0.849085 - 5.59277i) q^{32} +(4.73249 + 4.73249i) q^{33} +(-4.18508 + 2.29378i) q^{34} +(-1.30298 + 2.04158i) q^{36} +(-3.17476 + 3.17476i) q^{37} +(-0.582063 - 0.169915i) q^{38} -6.19373 q^{39} +5.67429 q^{41} +(1.81579 + 0.530061i) q^{42} +(-4.01233 + 4.01233i) q^{43} +(5.38395 - 8.43584i) q^{44} +(-4.46271 + 2.44595i) q^{46} +(7.13029 + 7.13029i) q^{47} +(-5.02452 - 1.83811i) q^{48} +1.00000i q^{49} +4.51373i q^{51} +(1.99711 + 9.04345i) q^{52} +(0.811260 + 0.811260i) q^{53} +(3.82839 + 6.98502i) q^{54} +(0.188457 - 2.82214i) q^{56} +(-0.405515 + 0.405515i) q^{57} +(2.97938 - 10.2062i) q^{58} +3.87524 q^{59} +12.2345 q^{61} +(-0.161663 + 0.553797i) q^{62} +(-0.856288 + 0.856288i) q^{63} +(-1.06370 + 7.92897i) q^{64} +(-4.54915 - 8.30006i) q^{66} +(8.29609 + 8.29609i) q^{67} +(6.59048 - 1.45541i) q^{68} +4.81316i q^{69} +12.2700i q^{71} +(2.57794 - 2.25519i) q^{72} +(-3.78692 - 3.78692i) q^{73} +(5.56805 - 3.05177i) q^{74} +(0.722846 + 0.461337i) q^{76} +(3.53819 - 3.53819i) q^{77} +(8.40832 + 2.45454i) q^{78} +0.197543 q^{79} +3.90062 q^{81} +(-7.70315 - 2.24869i) q^{82} +(-1.86715 + 1.86715i) q^{83} +(-2.25497 - 1.43917i) q^{84} +(7.03702 - 3.85689i) q^{86} +(-7.11053 - 7.11053i) q^{87} +(-10.6521 + 9.31848i) q^{88} +7.05881i q^{89} +4.63067i q^{91} +(7.02768 - 1.55196i) q^{92} +(0.385822 + 0.385822i) q^{93} +(-6.85406 - 12.5054i) q^{94} +(6.09262 + 4.48651i) q^{96} +(5.24949 - 5.24949i) q^{97} +(0.396294 - 1.35755i) q^{98} +6.05942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{6}+O(q^{10}) \) 36 * q - 8 * q^6	\( 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) \) 36 * q - 8 * q^6 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 - 28 * q^18 - 4 * q^22 - 32 * q^26 - 20 * q^37 + 20 * q^42 + 16 * q^46 + 24 * q^48 - 16 * q^52 + 44 * q^53 - 24 * q^56 + 16 * q^57 + 4 * q^58 - 64 * q^61 - 40 * q^62 + 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 8 * q^76 + 76 * q^78 - 36 * q^81 - 56 * q^82 + 56 * q^86 + 40 * q^88 + 56 * q^92 - 32 * q^93 + 120 * q^96 - 20 * q^97

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