LMFDB - Embedded newform 920.2.bb.a.11.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))

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

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

chi := DirichletCharacter("920.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.662561 + 1.24940i) q^{2} +(0.121688 - 0.846359i) q^{3} +(-1.12203 - 1.65561i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.976819 + 0.712802i) q^{6} +(2.94177 + 3.39498i) q^{7} +(2.81194 - 0.304917i) q^{8} +(2.17696 + 0.639214i) q^{9} +(0.283725 - 1.38546i) q^{10} +(0.120792 - 0.187956i) q^{11} +(-1.53778 + 0.748167i) q^{12} +(-3.17005 - 2.74686i) q^{13} +(-6.19081 + 1.42608i) q^{14} +(0.121688 + 0.846359i) q^{15} +(-1.48212 + 3.71528i) q^{16} +(2.41671 - 1.10368i) q^{17} +(-2.24101 + 2.29639i) q^{18} +(-0.528965 - 0.241570i) q^{19} +(1.54302 + 1.27244i) q^{20} +(3.23135 - 2.07666i) q^{21} +(0.154801 + 0.275450i) q^{22} +(0.892936 + 4.71197i) q^{23} +(0.0841103 - 2.41702i) q^{24} +(0.841254 - 0.540641i) q^{25} +(5.53229 - 2.14071i) q^{26} +(1.87153 - 4.09808i) q^{27} +(2.32004 - 8.67969i) q^{28} +(-7.80202 + 3.56306i) q^{29} +(-1.13807 - 0.408727i) q^{30} +(4.52833 - 0.651076i) q^{31} +(-3.65990 - 4.31337i) q^{32} +(-0.144379 - 0.125105i) q^{33} +(-0.222283 + 3.75071i) q^{34} +(-3.77908 - 2.42867i) q^{35} +(-1.38432 - 4.32143i) q^{36} +(8.78628 + 2.57989i) q^{37} +(0.652291 - 0.500836i) q^{38} +(-2.71059 + 2.34874i) q^{39} +(-2.61213 + 1.08478i) q^{40} +(3.06298 - 0.899372i) q^{41} +(0.453625 + 5.41318i) q^{42} +(2.41571 + 0.347327i) q^{43} +(-0.446714 + 0.0109063i) q^{44} -2.26887 q^{45} +(-6.47878 - 2.00633i) q^{46} -0.401020i q^{47} +(2.96411 + 1.70651i) q^{48} +(-1.87570 + 13.0458i) q^{49} +(0.118097 + 1.40927i) q^{50} +(-0.640021 - 2.17971i) q^{51} +(-0.990872 + 8.33043i) q^{52} +(6.00018 + 6.92457i) q^{53} +(3.88016 + 5.05353i) q^{54} +(-0.0629457 + 0.214373i) q^{55} +(9.30728 + 8.64950i) q^{56} +(-0.268824 + 0.418298i) q^{57} +(0.717608 - 12.1086i) q^{58} +(-3.94981 + 4.55833i) q^{59} +(1.26471 - 1.15110i) q^{60} +(1.39010 + 9.66837i) q^{61} +(-2.18684 + 6.08910i) q^{62} +(4.23400 + 9.27117i) q^{63} +(7.81405 - 1.71482i) q^{64} +(3.81552 + 1.74249i) q^{65} +(0.251967 - 0.0974981i) q^{66} +(3.87276 + 6.02613i) q^{67} +(-4.53887 - 2.76279i) q^{68} +(4.09668 - 0.182354i) q^{69} +(5.53827 - 3.11246i) q^{70} +(3.96281 + 6.16625i) q^{71} +(6.31641 + 1.13364i) q^{72} +(-0.914458 + 2.00238i) q^{73} +(-9.04477 + 9.26829i) q^{74} +(-0.355206 - 0.777792i) q^{75} +(0.193565 + 1.14681i) q^{76} +(0.993448 - 0.142836i) q^{77} +(-1.13859 - 4.94281i) q^{78} +(5.71857 - 6.59958i) q^{79} +(0.375367 - 3.98235i) q^{80} +(2.48537 + 1.59725i) q^{81} +(-0.905732 + 4.42279i) q^{82} +(2.61189 - 8.89527i) q^{83} +(-7.06381 - 3.01980i) q^{84} +(-2.00788 + 1.73984i) q^{85} +(-2.03451 + 2.78808i) q^{86} +(2.06622 + 7.03689i) q^{87} +(0.282349 - 0.565353i) q^{88} +(-8.03553 - 1.15534i) q^{89} +(1.50326 - 2.83474i) q^{90} -18.8429i q^{91} +(6.79931 - 6.76531i) q^{92} -3.91182i q^{93} +(0.501036 + 0.265700i) q^{94} +(0.575596 + 0.0827582i) q^{95} +(-4.09602 + 2.57270i) q^{96} +(-4.27542 - 14.5608i) q^{97} +(-15.0567 - 10.9871i) q^{98} +(0.383103 - 0.331961i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.662561	+	1.24940i	−0.468502	+	0.883463i
$2$	−0.662561	+	1.24940i	−0.468502	+	0.883463i
$3$	0.121688	−	0.846359i	0.0702566	−	0.488646i	−0.924066	−	0.382234i	$-0.875155\pi$
$3$	0.121688	−	0.846359i	0.0702566	−	0.488646i	0.994322	−	0.106412i	$-0.0339361\pi$
$4$	−1.12203	−	1.65561i	−0.561013	−	0.827807i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	0.976819	+	0.712802i	0.398785	+	0.291000i
$7$	2.94177	+	3.39498i	1.11188	+	1.28318i	0.955339	+	0.295512i	$0.0954902\pi$
$7$	2.94177	+	3.39498i	1.11188	+	1.28318i	0.156545	+	0.987671i	$0.449964\pi$
$8$	2.81194	−	0.304917i	0.994172	−	0.107805i
$9$	2.17696	+	0.639214i	0.725655	+	0.213071i
$10$	0.283725	−	1.38546i	0.0897217	−	0.438121i
$11$	0.120792	−	0.187956i	0.0364201	−	0.0566708i	−0.822566	−	0.568669i	$-0.807458\pi$
$11$	0.120792	−	0.187956i	0.0364201	−	0.0566708i	0.858986	+	0.511999i	$0.171095\pi$
$12$	−1.53778	+	0.748167i	−0.443919	+	0.215977i
$13$	−3.17005	−	2.74686i	−0.879213	−	0.761843i	0.0930674	−	0.995660i	$-0.470333\pi$
$13$	−3.17005	−	2.74686i	−0.879213	−	0.761843i	−0.972281	+	0.233817i	$0.924878\pi$
$14$	−6.19081	+	1.42608i	−1.65456	+	0.381135i
$15$	0.121688	+	0.846359i	0.0314197	+	0.218529i
$16$	−1.48212	+	3.71528i	−0.370530	+	0.928821i
$17$	2.41671	−	1.10368i	0.586139	−	0.267681i	−0.100194	−	0.994968i	$-0.531946\pi$
$17$	2.41671	−	1.10368i	0.586139	−	0.267681i	0.686333	+	0.727287i	$0.259219\pi$
$18$	−2.24101	+	2.29639i	−0.528211	+	0.541264i
$19$	−0.528965	−	0.241570i	−0.121353	−	0.0554200i	0.353813	−	0.935316i	$-0.384885\pi$
$19$	−0.528965	−	0.241570i	−0.121353	−	0.0554200i	−0.475166	+	0.879896i	$0.657612\pi$
$20$	1.54302	+	1.27244i	0.345029	+	0.284526i
$21$	3.23135	−	2.07666i	0.705139	−	0.453165i
$22$	0.154801	+	0.275450i	0.0330037	+	0.0587262i
$23$	0.892936	+	4.71197i	0.186190	+	0.982514i
$23$	0.892936	+	4.71197i	0.186190	+	0.982514i
$24$	0.0841103	−	2.41702i	0.0171690	−	0.493372i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	5.53229	−	2.14071i	1.08497	−	0.419828i
$27$	1.87153	−	4.09808i	0.360177	−	0.788677i
$28$	2.32004	−	8.67969i	0.438447	−	1.64031i
$29$	−7.80202	+	3.56306i	−1.44880	+	0.661644i	−0.975649	−	0.219339i	$-0.929610\pi$
$29$	−7.80202	+	3.56306i	−1.44880	+	0.661644i	−0.473149	+	0.880982i	$0.656883\pi$
$30$	−1.13807	−	0.408727i	−0.207782	−	0.0746230i
$31$	4.52833	−	0.651076i	0.813312	−	0.116937i	0.276907	−	0.960897i	$-0.410691\pi$
$31$	4.52833	−	0.651076i	0.813312	−	0.116937i	0.536406	+	0.843960i	$0.319782\pi$
$32$	−3.65990	−	4.31337i	−0.646984	−	0.762503i
$33$	−0.144379	−	0.125105i	−0.0251332	−	0.0217780i
$34$	−0.222283	+	3.75071i	−0.0381211	+	0.643241i
$35$	−3.77908	−	2.42867i	−0.638782	−	0.410520i
$36$	−1.38432	−	4.32143i	−0.230719	−	0.720238i
$37$	8.78628	+	2.57989i	1.44446	+	0.424131i	0.907705	−	0.419610i	$-0.137833\pi$
$37$	8.78628	+	2.57989i	1.44446	+	0.424131i	0.536751	+	0.843740i	$0.319651\pi$
$38$	0.652291	−	0.500836i	0.105815	−	0.0812464i
$39$	−2.71059	+	2.34874i	−0.434042	+	0.376099i
$40$	−2.61213	+	1.08478i	−0.413015	+	0.171519i
$41$	3.06298	−	0.899372i	0.478357	−	0.140458i	−0.0336603	−	0.999433i	$-0.510716\pi$
$41$	3.06298	−	0.899372i	0.478357	−	0.140458i	0.512018	+	0.858975i	$0.328898\pi$
$42$	0.453625	+	5.41318i	0.0699959	+	0.835272i
$43$	2.41571	+	0.347327i	0.368393	+	0.0529669i	0.324025	−	0.946048i	$-0.394964\pi$
$43$	2.41571	+	0.347327i	0.368393	+	0.0529669i	0.0443675	+	0.999015i	$0.485873\pi$
$44$	−0.446714	+	0.0109063i	−0.0673447	+	0.00164419i
$45$	−2.26887			−0.338223
$46$	−6.47878	−	2.00633i	−0.955245	−	0.295817i
$47$		−	0.401020i		−	0.0584948i	−0.999572	−	0.0292474i	$-0.990689\pi$
$47$		−	0.401020i		−	0.0584948i	0.999572	−	0.0292474i	$-0.00931106\pi$
$48$	2.96411	+	1.70651i	0.427832	+	0.246314i
$49$	−1.87570	+	13.0458i	−0.267957	+	1.86368i
$50$	0.118097	+	1.40927i	0.0167015	+	0.199301i
$51$	−0.640021	−	2.17971i	−0.0896208	−	0.305221i
$52$	−0.990872	+	8.33043i	−0.137409	+	1.15522i
$53$	6.00018	+	6.92457i	0.824188	+	0.951163i	0.999443	−	0.0333597i	$-0.0106207\pi$
$53$	6.00018	+	6.92457i	0.824188	+	0.951163i	−0.175256	+	0.984523i	$0.556075\pi$
$54$	3.88016	+	5.05353i	0.528023	+	0.687699i
$55$	−0.0629457	+	0.214373i	−0.00848759	+	0.0289061i
$56$	9.30728	+	8.64950i	1.24374	+	1.15584i
$57$	−0.268824	+	0.418298i	−0.0356066	+	0.0554049i
$58$	0.717608	−	12.1086i	0.0942265	−	1.58994i
$59$	−3.94981	+	4.55833i	−0.514222	+	0.593444i	−0.952175	−	0.305554i	$-0.901158\pi$
$59$	−3.94981	+	4.55833i	−0.514222	+	0.593444i	0.437953	+	0.898998i	$0.355704\pi$
$60$	1.26471	−	1.15110i	0.163273	−	0.148607i
$61$	1.39010	+	9.66837i	0.177984	+	1.23791i	0.861419	+	0.507896i	$0.169577\pi$
$61$	1.39010	+	9.66837i	0.177984	+	1.23791i	−0.683434	+	0.730012i	$0.739514\pi$
$62$	−2.18684	+	6.08910i	−0.277729	+	0.773316i
$63$	4.23400	+	9.27117i	0.533434	+	1.16806i
$64$	7.81405	−	1.71482i	0.976756	−	0.214353i
$65$	3.81552	+	1.74249i	0.473257	+	0.216129i
$66$	0.251967	−	0.0974981i	0.0310150	−	0.0120012i
$67$	3.87276	+	6.02613i	0.473132	+	0.736209i	0.993010	−	0.118032i	$-0.0376587\pi$
$67$	3.87276	+	6.02613i	0.473132	+	0.736209i	−0.519877	+	0.854241i	$0.674022\pi$
$68$	−4.53887	−	2.76279i	−0.550419	−	0.335038i
$69$	4.09668	−	0.182354i	0.493182	−	0.0219528i
$70$	5.53827	−	3.11246i	0.661949	−	0.372011i
$71$	3.96281	+	6.16625i	0.470299	+	0.731800i	0.992662	−	0.120924i	$-0.0385857\pi$
$71$	3.96281	+	6.16625i	0.470299	+	0.731800i	−0.522363	+	0.852723i	$0.674949\pi$
$72$	6.31641	+	1.13364i	0.744396	+	0.133601i
$73$	−0.914458	+	2.00238i	−0.107029	+	0.234361i	−0.955567	−	0.294773i	$-0.904756\pi$
$73$	−0.914458	+	2.00238i	−0.107029	+	0.234361i	0.848538	+	0.529134i	$0.177483\pi$
$74$	−9.04477	+	9.26829i	−1.05143	+	1.07742i
$75$	−0.355206	−	0.777792i	−0.0410156	−	0.0898117i
$76$	0.193565	+	1.14681i	0.0222034	+	0.131548i
$77$	0.993448	−	0.142836i	0.113214	−	0.0162777i
$78$	−1.13859	−	4.94281i	−0.128920	−	0.559663i
$79$	5.71857	−	6.59958i	0.643390	−	0.742511i	−0.336581	−	0.941655i	$-0.609270\pi$
$79$	5.71857	−	6.59958i	0.643390	−	0.742511i	0.979970	+	0.199143i	$0.0638160\pi$
$80$	0.375367	−	3.98235i	0.0419673	−	0.445240i
$81$	2.48537	+	1.59725i	0.276153	+	0.177473i
$82$	−0.905732	+	4.42279i	−0.100021	+	0.488416i
$83$	2.61189	−	8.89527i	0.286692	−	0.976383i	−0.682666	−	0.730730i	$-0.739180\pi$
$83$	2.61189	−	8.89527i	0.286692	−	0.976383i	0.969358	−	0.245652i	$-0.0790022\pi$
$84$	−7.06381	−	3.01980i	−0.770725	−	0.329488i
$85$	−2.00788	+	1.73984i	−0.217785	+	0.188712i
$86$	−2.03451	+	2.78808i	−0.219387	+	0.300646i
$87$	2.06622	+	7.03689i	0.221522	+	0.754433i
$88$	0.282349	−	0.565353i	0.0300985	−	0.0602668i
$89$	−8.03553	−	1.15534i	−0.851765	−	0.122465i	−0.297414	−	0.954749i	$-0.596124\pi$
$89$	−8.03553	−	1.15534i	−0.851765	−	0.122465i	−0.554351	+	0.832283i	$0.687033\pi$
$90$	1.50326	−	2.83474i	0.158458	−	0.298807i
$91$		−	18.8429i		−	1.97527i
$92$	6.79931	−	6.76531i	0.708877	−	0.705332i
$93$		−	3.91182i		−	0.405637i
$94$	0.501036	+	0.265700i	0.0516780	+	0.0274049i
$95$	0.575596	+	0.0827582i	0.0590549	+	0.00849082i
$96$	−4.09602	+	2.57270i	−0.418049	+	0.262575i
$97$	−4.27542	−	14.5608i	−0.434104	−	1.47842i	−0.828766	−	0.559595i	$-0.810957\pi$
$97$	−4.27542	−	14.5608i	−0.434104	−	1.47842i	0.394663	−	0.918826i	$-0.370861\pi$
$98$	−15.0567	−	10.9871i	−1.52095	−	1.10987i
$99$	0.383103	−	0.331961i	0.0385033	−	0.0333633i
$100$	−1.83900	−	0.786179i	−0.183900	−	0.0786179i
$101$	−3.71555	+	12.6540i	−0.369711	+	1.25912i	0.539217	+	0.842167i	$0.318720\pi$
$101$	−3.71555	+	12.6540i	−0.369711	+	1.25912i	−0.908928	+	0.416953i	$0.863098\pi$
$102$	3.14739	+	0.644547i	0.311638	+	0.0638196i
$103$	−13.1986	−	8.48221i	−1.30049	−	0.835777i	−0.307228	−	0.951636i	$-0.599401\pi$
$103$	−13.1986	−	8.48221i	−1.30049	−	0.835777i	−0.993266	+	0.115859i	$0.963038\pi$
$104$	−9.75156	−	6.75742i	−0.956219	−	0.662619i
$105$	−2.51540	+	2.90292i	−0.245477	+	0.283296i
$106$	−12.6271	+	2.90870i	−1.22645	+	0.282518i
$107$	9.48311	−	1.36347i	0.916767	−	0.131811i	0.332249	−	0.943192i	$-0.392193\pi$
$107$	9.48311	−	1.36347i	0.916767	−	0.131811i	0.584518	+	0.811381i	$0.301284\pi$
$108$	−8.88475	+	1.49962i	−0.854936	+	0.144301i
$109$	6.01194	+	13.1643i	0.575839	+	1.26091i	0.943629	+	0.331004i	$0.107387\pi$
$109$	6.01194	+	13.1643i	0.575839	+	1.26091i	−0.367790	+	0.929909i	$0.619885\pi$
$110$	−0.226134	−	0.220680i	−0.0215610	−	0.0210410i
$111$	3.25269	−	7.12241i	0.308732	−	0.676029i
$112$	−16.9734	+	5.89773i	−1.60383	+	0.557283i
$113$	−6.59651	−	10.2644i	−0.620548	−	0.965591i	−0.999198	−	0.0400509i	$-0.987248\pi$
$113$	−6.59651	−	10.2644i	−0.620548	−	0.965591i	0.378650	−	0.925540i	$-0.376388\pi$
$114$	−0.344511	−	0.613018i	−0.0322664	−	0.0574144i
$115$	−2.18428	−	4.26953i	−0.203685	−	0.398136i
$116$	14.6531	+	8.91929i	1.36051	+	0.828135i
$117$	−5.14525	−	8.00616i	−0.475678	−	0.740170i
$118$	−3.07820	−	7.95508i	−0.283371	−	0.732325i
$119$	10.8564	+	4.95794i	0.995202	+	0.454493i
$120$	0.600249	+	2.34281i	0.0547950	+	0.213868i
$121$	4.54883	+	9.96054i	0.413530	+	0.905504i
$122$	−13.0007	−	4.66909i	−1.17703	−	0.422719i
$123$	−0.388464	−	2.70182i	−0.0350266	−	0.243615i
$124$	−6.15883	−	6.76665i	−0.553079	−	0.607663i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−14.3887	−	0.852737i	−1.28185	−	0.0759678i
$127$	9.15891	−	14.2515i	0.812722	−	1.26462i	−0.148519	−	0.988910i	$-0.547451\pi$
$127$	9.15891	−	14.2515i	0.812722	−	1.26462i	0.961241	−	0.275710i	$-0.0889131\pi$
$128$	−3.03478	+	10.8991i	−0.268239	+	0.963352i
$129$	0.587927	−	2.00230i	0.0517641	−	0.176292i
$130$	−4.70509	+	3.61262i	−0.412664	+	0.316848i
$131$	−8.14717	−	9.40233i	−0.711821	−	0.821485i	0.278477	−	0.960443i	$-0.410170\pi$
$131$	−8.14717	−	9.40233i	−0.711821	−	0.821485i	−0.990298	+	0.138957i	$0.955625\pi$
$132$	−0.0451291	+	0.379407i	−0.00392798	+	0.0330232i
$133$	−0.735966	−	2.50647i	−0.0638163	−	0.217338i
$134$	−10.0950	+	0.845962i	−0.872076	+	0.0730800i
$135$	−0.641158	+	4.45935i	−0.0551821	+	0.383800i
$136$	6.45913	−	3.84037i	0.553866	−	0.329309i
$137$			16.6969i			1.42651i	0.700903	+	0.713256i	$0.252780\pi$
$137$			16.6969i			1.42651i	−0.700903	+	0.713256i	$0.747220\pi$
$138$	−2.48647	+	5.23923i	−0.211662	+	0.445993i
$139$	16.9137			1.43460			0.717301	−	0.696764i	$-0.245377\pi$
$139$	16.9137			1.43460			0.717301	+	0.696764i	$0.245377\pi$
$140$	0.219286	+	8.98173i	0.0185330	+	0.759095i
$141$	−0.339407	−	0.0487993i	−0.0285832	−	0.00410965i
$142$	−10.3298	+	0.865634i	−0.866853	+	0.0726424i
$143$	−0.899205	+	0.264030i	−0.0751953	+	0.0220793i
$144$	−5.60138	+	7.14064i	−0.466782	+	0.595053i
$145$	6.48215	−	5.61681i	0.538313	−	0.466451i
$146$	−1.89590	−	2.46923i	−0.156906	−	0.204355i
$147$	10.8131	+	3.17503i	0.891853	+	0.261872i
$148$	−5.58713	−	17.4414i	−0.459260	−	1.43367i
$149$	−15.5219	−	9.97530i	−1.27160	−	0.817208i	−0.281773	−	0.959481i	$-0.590923\pi$
$149$	−15.5219	−	9.97530i	−1.27160	−	0.817208i	−0.989827	+	0.142273i	$0.954559\pi$
$150$	1.20712	+	0.0715391i	0.0985611	+	0.00584115i
$151$	−5.50344	−	4.76876i	−0.447863	−	0.388076i	0.401522	−	0.915850i	$-0.368481\pi$
$151$	−5.50344	−	4.76876i	−0.447863	−	0.388076i	−0.849385	+	0.527774i	$0.823027\pi$
$152$	−1.56108	−	0.517991i	−0.126620	−	0.0420146i
$153$	5.96658	−	0.857865i	0.482369	−	0.0693543i
$154$	−0.479760	+	1.33586i	−0.0386602	+	0.107646i
$155$	−4.16147	+	1.90048i	−0.334258	+	0.152650i
$156$	6.92995	+	1.85235i	0.554840	+	0.148306i
$157$	4.46637	−	9.77998i	0.356455	−	0.780527i	−0.643432	−	0.765503i	$-0.722490\pi$
$157$	4.46637	−	9.77998i	0.356455	−	0.780527i	0.999887	−	0.0150242i	$-0.00478252\pi$
$158$	4.45665	+	11.5174i	0.354552	+	0.916278i
$159$	6.59082	−	4.23567i	0.522686	−	0.335910i
$160$	4.72686	+	3.10754i	0.373691	+	0.245672i
$161$	−13.3702	+	16.8930i	−1.05372	+	1.33136i
$162$	−3.64233	+	2.04696i	−0.286168	+	0.160824i
$163$	6.12698	−	3.93757i	0.479902	−	0.308414i	−0.278231	−	0.960514i	$-0.589748\pi$
$163$	6.12698	−	3.93757i	0.479902	−	0.308414i	0.758133	+	0.652100i	$0.226112\pi$
$164$	−4.92576	−	4.06200i	−0.384637	−	0.317189i
$165$	0.173777	+	0.0793613i	0.0135285	+	0.00617827i
$166$	9.38326	+	9.15697i	0.728282	+	0.710719i
$167$	−19.5850	+	8.94418i	−1.51553	+	0.692121i	−0.987575	−	0.157148i	$-0.949770\pi$
$167$	−19.5850	+	8.94418i	−1.51553	+	0.692121i	−0.527959	+	0.849270i	$0.677043\pi$
$168$	8.45317	−	6.82476i	0.652176	−	0.526541i
$169$	0.653860	+	4.54769i	0.0502969	+	0.349823i
$170$	−0.843417	−	3.66140i	−0.0646872	−	0.280817i
$171$	−0.997122	−	0.864011i	−0.0762518	−	0.0660726i
$172$	−2.13545	−	4.38920i	−0.162827	−	0.334673i
$173$	−2.61646	+	4.07130i	−0.198926	+	0.309535i	−0.926358	−	0.376645i	$-0.877078\pi$
$173$	−2.61646	+	4.07130i	−0.198926	+	0.309535i	0.727431	+	0.686180i	$0.240714\pi$
$174$	−10.1609	−	2.08083i	−0.770297	−	0.157747i
$175$	4.31024	+	1.26560i	0.325824	+	0.0956704i
$176$	0.519281	+	0.727349i	0.0391423	+	0.0548260i
$177$	3.37733	+	3.89765i	0.253856	+	0.292965i
$178$	6.76751	−	9.27415i	0.507247	−	0.695127i
$179$	8.94337	−	2.62601i	0.668459	−	0.196277i	0.0701423	−	0.997537i	$-0.477655\pi$
$179$	8.94337	−	2.62601i	0.668459	−	0.196277i	0.598317	+	0.801260i	$0.295836\pi$
$180$	2.54573	+	3.75637i	0.189747	+	0.279983i
$181$	0.661890	−	4.60355i	0.0491979	−	0.342179i	−0.950324	−	0.311262i	$-0.899248\pi$
$181$	0.661890	−	4.60355i	0.0491979	−	0.342179i	0.999522	−	0.0309168i	$-0.00984268\pi$
$182$	23.5424	+	12.4846i	1.74508	+	0.925418i
$183$	8.35207			0.617403
$184$	3.94765	+	12.9775i	0.291024	+	0.956716i
$185$	−9.15721			−0.673252
$186$	4.88745	+	2.59182i	0.358365	+	0.190042i
$187$	0.0844770	−	0.587550i	0.00617757	−	0.0429659i
$188$	−0.663935	+	0.449955i	−0.0484224	+	0.0328163i
$189$	19.4185	−	5.70180i	1.41249	−	0.414745i
$190$	−0.484766	+	0.664320i	−0.0351686	+	0.0481949i
$191$	2.84886	+	3.28776i	0.206136	+	0.237894i	0.849398	−	0.527752i	$-0.176965\pi$
$191$	2.84886	+	3.28776i	0.206136	+	0.237894i	−0.643262	+	0.765646i	$0.722420\pi$
$192$	−0.500477	−	6.82216i	−0.0361188	−	0.492347i
$193$	−1.40460	−	0.412426i	−0.101105	−	0.0296871i	0.230789	−	0.973004i	$-0.425869\pi$
$193$	−1.40460	−	0.412426i	−0.101105	−	0.0296871i	−0.331894	+	0.943317i	$0.607688\pi$
$194$	21.0250	+	4.30566i	1.50951	+	0.309128i
$195$	1.93907	−	3.01726i	0.138860	−	0.216070i
$196$	23.7033	−	11.5322i	1.69309	−	0.823731i
$197$	−17.5878	−	15.2399i	−1.25308	−	1.08580i	−0.992740	−	0.120281i	$-0.961620\pi$
$197$	−17.5878	−	15.2399i	−1.25308	−	1.08580i	−0.260339	−	0.965517i	$-0.583834\pi$
$198$	0.160924	+	0.698596i	0.0114364	+	0.0496471i
$199$	−2.25077	−	15.6544i	−0.159553	−	1.10971i	−0.899460	−	0.437004i	$-0.856040\pi$
$199$	−2.25077	−	15.6544i	−0.159553	−	1.10971i	0.739907	−	0.672709i	$-0.234869\pi$
$200$	2.20071	−	1.77676i	0.155613	−	0.125636i
$201$	5.57153	−	2.54443i	0.392986	−	0.179471i
$202$	−13.3482	−	13.0263i	−0.939175	−	0.916525i
$203$	−35.0483	−	16.0060i	−2.45991	−	1.12340i
$204$	−2.89064	+	3.50532i	−0.202385	+	0.245421i
$205$	−2.68553	+	1.72588i	−0.187565	+	0.120541i
$206$	19.3426	−	10.8704i	1.34766	−	0.757375i
$207$	−1.06807	+	10.8286i	−0.0742360	+	0.752637i
$208$	14.9038	−	7.70645i	1.03339	−	0.534346i
$209$	−0.109299	+	0.0702423i	−0.00756038	+	0.00485876i
$210$	−1.96032	−	5.06611i	−0.135275	−	0.349595i
$211$	−4.85578	+	10.6327i	−0.334286	+	0.731983i	−0.999898	−	0.0143147i	$-0.995443\pi$
$211$	−4.85578	+	10.6327i	−0.334286	+	0.731983i	0.665612	+	0.746298i	$0.268171\pi$
$212$	4.73208	−	17.7035i	0.325000	−	1.21588i
$213$	5.70109	−	2.60360i	0.390632	−	0.178396i
$214$	−4.57962	+	12.7516i	−0.313057	+	0.871683i
$215$	−2.41571	+	0.347327i	−0.164750	+	0.0236875i
$216$	4.01307	−	12.0942i	0.273054	−	0.822909i
$217$	15.5317	+	13.4583i	1.05436	+	0.913608i
$218$	−20.4308	−	1.21082i	−1.38375	−	0.0820069i
$219$	1.58346	+	1.01763i	0.107000	+	0.0687648i
$220$	0.425546	−	0.136318i	0.0286903	−	0.00919059i
$221$	−10.6927	−	3.13967i	−0.719272	−	0.211197i
$222$	6.74366	+	8.78296i	0.452605	+	0.589474i
$223$	15.0624	−	13.0516i	1.00865	−	0.874001i	0.0166034	−	0.999862i	$-0.494715\pi$
$223$	15.0624	−	13.0516i	1.00865	−	0.874001i	0.992048	+	0.125861i	$0.0401693\pi$
$224$	3.87724	−	25.1142i	0.259059	−	1.67801i
$225$	2.17696	−	0.639214i	0.145131	−	0.0426143i
$226$	17.1949	−	1.44094i	1.14379	−	0.0958497i
$227$	−3.69054	−	0.530620i	−0.244950	−	0.0352185i	0.0187463	−	0.999824i	$-0.494033\pi$
$227$	−3.69054	−	0.530620i	−0.244950	−	0.0352185i	−0.263696	+	0.964606i	$0.584942\pi$
$228$	0.994167	−	0.0242722i	0.0658403	−	0.00160747i
$229$	−5.80906			−0.383873			−0.191937	−	0.981407i	$-0.561477\pi$
$229$	−5.80906			−0.383873			−0.191937	+	0.981407i	$0.561477\pi$
$230$	6.78160	+	0.0997761i	0.447165	+	0.00657904i
$231$		−	0.858195i		−	0.0564651i
$232$	−20.8524	+	12.3981i	−1.36903	+	0.813975i
$233$	2.02759	−	14.1022i	0.132832	−	0.923867i	−0.809006	−	0.587800i	$-0.799994\pi$
$233$	2.02759	−	14.1022i	0.132832	−	0.923867i	0.941838	−	0.336067i	$-0.109097\pi$
$234$	13.4120	−	1.12392i	0.876768	−	0.0734732i
$235$	0.112980	+	0.384776i	0.00737003	+	0.0251000i
$236$	11.9786	+	1.42481i	0.779742	+	0.0927473i
$237$	−4.88973	−	5.64305i	−0.317622	−	0.366556i
$238$	−13.3875	+	10.2791i	−0.867782	+	0.666293i
$239$	0.0196672	−	0.0669804i	0.00127217	−	0.00433260i	−0.958854	−	0.283898i	$-0.908372\pi$
$239$	0.0196672	−	0.0669804i	0.00127217	−	0.00433260i	0.960127	+	0.279566i	$0.0901904\pi$
$240$	−3.32482	−	0.802300i	−0.214616	−	0.0517882i
$241$	−11.1630	+	17.3700i	−0.719072	+	1.11890i	0.268734	+	0.963214i	$0.413395\pi$
$241$	−11.1630	+	17.3700i	−0.719072	+	1.11890i	−0.987807	+	0.155684i	$0.950242\pi$
$242$	−15.4586	−	0.916143i	−0.993718	−	0.0588919i
$243$	10.5051	−	12.1236i	0.673905	−	0.777728i
$244$	14.4474	−	13.1496i	0.924898	−	0.841819i
$245$	−1.87570	−	13.0458i	−0.119834	−	0.833463i
$246$	3.63305	+	1.30478i	0.231635	+	0.0831895i
$247$	1.01328	+	2.21878i	0.0644737	+	0.141178i
$248$	12.5349	−	3.21156i	0.795966	−	0.203934i
$249$	−7.21076	−	3.29304i	−0.456963	−	0.208688i
$250$	−0.510352	−	1.31892i	−0.0322775	−	0.0834156i
$251$	0.00164652	+	0.00256203i	0.000103927	+	0.000161714i	0.841305	−	0.540560i	$-0.181788\pi$
$251$	0.00164652	+	0.00256203i	0.000103927	+	0.000161714i	−0.841202	+	0.540722i	$0.818151\pi$
$252$	10.5988	−	17.4124i	0.667664	−	1.09688i
$253$	0.993502	+	0.401335i	0.0624609	+	0.0252317i
$254$	11.7376	+	20.8857i	0.736483	+	1.31049i
$255$	1.22819	+	1.91110i	0.0769123	+	0.119678i
$256$	−11.6066	−	11.0130i	−0.725415	−	0.688312i
$257$	−6.81165	+	14.9154i	−0.424899	+	0.930399i	0.569228	+	0.822180i	$0.307242\pi$
$257$	−6.81165	+	14.9154i	−0.424899	+	0.930399i	−0.994127	+	0.108220i	$0.965485\pi$
$258$	2.11214	+	2.06120i	0.131496	+	0.128325i
$259$	17.0885	+	37.4187i	1.06183	+	2.32509i
$260$	−1.39622	−	8.27215i	−0.0865897	−	0.513017i
$261$	−19.2623	+	2.76950i	−1.19230	+	0.171427i
$262$	17.1453	−	3.94949i	1.05924	−	0.244000i
$263$	8.54935	−	9.86648i	0.527176	−	0.608393i	−0.428237	−	0.903666i	$-0.640865\pi$
$263$	8.54935	−	9.86648i	0.527176	−	0.608393i	0.955413	+	0.295273i	$0.0954107\pi$
$264$	−0.444133	−	0.307765i	−0.0273345	−	0.0189416i
$265$	−7.70800	−	4.95363i	−0.473499	−	0.304299i
$266$	3.61922	+	0.741170i	0.221909	+	0.0454441i
$267$	−1.95566	+	6.66035i	−0.119684	+	0.407607i
$268$	5.63161	−	13.1733i	0.344006	−	0.804685i
$269$	1.35159	−	1.17116i	0.0824078	−	0.0714068i	−0.612683	−	0.790329i	$-0.709910\pi$
$269$	1.35159	−	1.17116i	0.0824078	−	0.0714068i	0.695091	+	0.718922i	$0.255364\pi$
$270$	−5.14673	−	3.75566i	−0.313220	−	0.228562i
$271$	−3.37576	−	11.4968i	−0.205063	−	0.698379i	−0.996228	−	0.0867765i	$-0.972343\pi$
$271$	−3.37576	−	11.4968i	−0.205063	−	0.698379i	0.791165	−	0.611602i	$-0.209475\pi$
$272$	0.518609	+	10.6145i	0.0314453	+	0.643602i
$273$	−15.9479	−	2.29295i	−0.965208	−	0.138776i
$274$	−20.8612	−	11.0627i	−1.26027	−	0.668324i
$275$		−	0.223424i		−	0.0134729i
$276$	−4.89848	−	6.57791i	−0.294854	−	0.395944i
$277$		−	8.75292i		−	0.525912i	−0.964808	−	0.262956i	$-0.915303\pi$
$277$		−	8.75292i		−	0.525912i	0.964808	−	0.262956i	$-0.0846974\pi$
$278$	−11.2064	+	21.1321i	−0.672113	+	1.26742i
$279$	10.2742	+	1.47721i	0.615100	+	0.0884380i
$280$	−11.3671	−	5.67697i	−0.679315	−	0.339264i
$281$	−2.86593	−	9.76046i	−0.170967	−	0.582260i	−0.999743	−	0.0226795i	$-0.992780\pi$
$281$	−2.86593	−	9.76046i	−0.170967	−	0.582260i	0.828776	−	0.559581i	$-0.189038\pi$
$282$	0.285848	−	0.391724i	0.0170220	−	0.0233268i
$283$	12.5623	−	10.8853i	0.746749	−	0.647061i	−0.195985	−	0.980607i	$-0.562791\pi$
$283$	12.5623	−	10.8853i	0.746749	−	0.647061i	0.942734	+	0.333545i	$0.108245\pi$
$284$	5.76257	−	13.4796i	0.341945	−	0.799866i
$285$	0.140086	−	0.477090i	0.00829800	−	0.0282604i
$286$	0.265897	−	1.29841i	0.0157228	−	0.0767764i
$287$	12.0639	+	7.75302i	0.712112	+	0.457646i
$288$	−5.21029	−	11.7295i	−0.307020	−	0.691168i
$289$	−6.51023	+	7.51321i	−0.382955	+	0.441953i
$290$	2.72285	+	11.8203i	0.159891	+	0.694113i
$291$	−12.8439	+	1.84667i	−0.752923	+	0.108254i
$292$	4.34122	−	0.732735i	0.254051	−	0.0428801i
$293$	−1.09320	−	2.39377i	−0.0638653	−	0.139845i	0.875008	−	0.484109i	$-0.160856\pi$
$293$	−1.09320	−	2.39377i	−0.0638653	−	0.139845i	−0.938873	+	0.344263i	$0.888129\pi$
$294$	−11.1313	+	11.4063i	−0.649188	+	0.665232i
$295$	2.50559	−	5.48647i	0.145881	−	0.319435i
$296$	25.4932	+	4.57540i	1.48176	+	0.265940i
$297$	−0.544193	−	0.846780i	−0.0315773	−	0.0491352i
$298$	22.7474	−	12.7838i	1.31772	−	0.740548i
$299$	10.1125	−	17.3899i	0.584820	−	1.00569i
$300$	−0.889174	+	1.46079i	−0.0513365	+	0.0843385i
$301$	5.92730	+	9.22306i	0.341644	+	0.531609i
$302$	9.60447	−	3.71643i	0.552675	−	0.213856i
$303$	10.2577	+	4.68453i	0.589289	+	0.269119i
$304$	1.68149	−	1.60722i	0.0964401	−	0.0921803i
$305$	−4.05769	−	8.88510i	−0.232343	−	0.508759i
$306$	−2.88140	+	8.02306i	−0.164719	+	0.458648i
$307$	−1.84975	−	12.8653i	−0.105571	−	0.734260i	−0.972004	−	0.234966i	$-0.924502\pi$
$307$	−1.84975	−	12.8653i	−0.105571	−	0.734260i	0.866433	−	0.499293i	$-0.166407\pi$
$308$	−1.35116	−	1.48450i	−0.0769893	−	0.0845873i
$309$	−8.78510	+	10.1385i	−0.499767	+	0.576762i
$310$	0.382761	−	6.45855i	0.0217393	−	0.366821i
$311$	−14.9531	+	23.2675i	−0.847913	+	1.31938i	0.0980762	+	0.995179i	$0.468731\pi$
$311$	−14.9531	+	23.2675i	−0.847913	+	1.31938i	−0.945989	+	0.324199i	$0.894905\pi$
$312$	−6.90585	+	7.43102i	−0.390967	+	0.420699i
$313$	−4.74373	+	16.1557i	−0.268131	+	0.913172i	0.709828	+	0.704375i	$0.248773\pi$
$313$	−4.74373	+	16.1557i	−0.268131	+	0.913172i	−0.977959	+	0.208796i	$0.933045\pi$
$314$	9.25991	+	12.0601i	0.522567	+	0.680593i
$315$	−6.67449	−	7.70277i	−0.376065	−	0.434002i
$316$	−17.3427	−	2.06285i	−0.975606	−	0.116045i
$317$	−5.78406	−	19.6987i	−0.324865	−	1.10639i	−0.946399	−	0.323001i	$-0.895308\pi$
$317$	−5.78406	−	19.6987i	−0.324865	−	1.10639i	0.621534	−	0.783388i	$-0.286510\pi$
$318$	0.925236	+	11.0410i	0.0518847	+	0.619148i
$319$	−0.272722	+	1.89682i	−0.0152695	+	0.106202i
$320$	−7.01441	+	3.84683i	−0.392117	+	0.215044i
$321$		−	8.19204i		−	0.457235i
$322$	−12.2476	−	27.8975i	−0.682534	−	1.55467i
$323$	−1.54497			−0.0859645
$324$	−0.144217	−	5.90698i	−0.00801204	−	0.328166i
$325$	−4.15188	−	0.596950i	−0.230305	−	0.0331128i
$326$	0.860121	+	10.2640i	0.0476377	+	0.568468i
$327$	11.8733	−	3.48632i	0.656596	−	0.192794i
$328$	8.33869	−	3.46294i	0.460427	−	0.191209i
$329$	1.36146	−	1.17971i	0.0750595	−	0.0650394i
$330$	−0.214292	+	0.164536i	−0.0117964	+	0.00905741i
$331$	3.89433	+	1.14348i	0.214051	+	0.0628512i	0.387000	−	0.922080i	$-0.373511\pi$
$331$	3.89433	+	1.14348i	0.214051	+	0.0628512i	−0.172949	+	0.984931i	$0.555329\pi$
$332$	−17.6577	+	5.65644i	−0.969095	+	0.310437i
$333$	17.4783	+	11.2326i	0.957806	+	0.615544i
$334$	1.80138	−	30.3957i	0.0985669	−	1.66318i
$335$	−5.41364	−	4.69094i	−0.295779	−	0.256294i
$336$	2.92614	+	15.0832i	0.159634	+	0.822859i
$337$	26.8580	−	3.86159i	1.46305	−	0.210354i	0.635652	−	0.771976i	$-0.280731\pi$
$337$	26.8580	−	3.86159i	1.46305	−	0.210354i	0.827394	+	0.561622i	$0.189822\pi$
$338$	−6.11513	−	2.19619i	−0.332619	−	0.119457i
$339$	−9.49006	+	4.33396i	−0.515429	+	0.235389i
$340$	5.13339	+	1.37213i	0.278397	+	0.0744143i
$341$	0.424612	−	0.929771i	0.0229940	−	0.0503499i
$342$	1.74015	−	0.673349i	0.0940968	−	0.0364105i
$343$	−23.3544	+	15.0090i	−1.26102	+	0.810408i
$344$	6.89876	+	0.240071i	0.371956	+	0.0129438i
$345$	−3.87936	+	1.32913i	−0.208858	+	0.0715582i
$346$	−3.35313	−	5.96651i	−0.180265	−	0.320761i
$347$	2.53169	−	1.62702i	0.135908	−	0.0873430i	−0.470920	−	0.882176i	$-0.656078\pi$
$347$	2.53169	−	1.62702i	0.135908	−	0.0873430i	0.606828	+	0.794833i	$0.292442\pi$
$348$	9.33203	−	11.3164i	0.500249	−	0.606624i
$349$	−15.9944	−	7.30438i	−0.856159	−	0.390995i	−0.0615409	−	0.998105i	$-0.519601\pi$
$349$	−15.9944	−	7.30438i	−0.856159	−	0.390995i	−0.794618	+	0.607110i	$0.792329\pi$
$350$	−4.43705	+	4.54670i	−0.237170	+	0.243031i
$351$	−17.1897	+	7.85028i	−0.917519	+	0.419017i
$352$	−1.25281	+	0.166879i	−0.0667749	+	0.00889467i
$353$	3.95737	+	27.5241i	0.210630	+	1.46496i	0.771061	+	0.636761i	$0.219726\pi$
$353$	3.95737	+	27.5241i	0.210630	+	1.46496i	−0.560431	+	0.828201i	$0.689365\pi$
$354$	−7.10744	+	1.63723i	−0.377756	+	0.0870175i
$355$	−5.53952	−	4.80002i	−0.294007	−	0.254759i
$356$	7.10328	+	14.6001i	0.376473	+	0.773802i
$357$	5.51729	−	8.58506i	0.292006	−	0.454370i
$358$	−2.64458	+	12.9138i	−0.139770	+	0.682515i
$359$	−25.6426	−	7.52934i	−1.35336	−	0.397383i	−0.476945	−	0.878933i	$-0.658256\pi$
$359$	−25.6426	−	7.52934i	−1.35336	−	0.397383i	−0.876419	+	0.481550i	$0.840074\pi$
$360$	−6.37993	+	0.691817i	−0.336252	+	0.0364620i
$361$	−12.2209	−	14.1037i	−0.643206	−	0.742299i
$362$	5.31315	+	3.87710i	0.279253	+	0.203776i
$363$	8.98373	−	2.63786i	0.471524	−	0.138452i
$364$	−31.1966	+	21.1422i	−1.63514	+	1.10815i
$365$	0.313279	−	2.17891i	0.0163978	−	0.114049i
$366$	−5.53376	+	10.4351i	−0.289254	+	0.545452i
$367$	−17.2680			−0.901380			−0.450690	−	0.892680i	$-0.648822\pi$
$367$	−17.2680			−0.901380			−0.450690	+	0.892680i	$0.648822\pi$
$368$	−18.8297	−	3.66620i	−0.981568	−	0.191114i
$369$	7.24289			0.377050
$370$	6.06722	−	11.4411i	0.315420	−	0.594793i
$371$	−5.85767	+	40.7410i	−0.304115	+	2.11517i
$372$	−6.47647	+	4.38916i	−0.335789	+	0.227567i
$373$	23.6065	−	6.93149i	1.22230	−	0.358899i	0.393960	−	0.919128i	$-0.371105\pi$
$373$	23.6065	−	6.93149i	1.22230	−	0.358899i	0.828338	+	0.560229i	$0.189287\pi$
$374$	0.678117	+	0.494834i	0.0350646	+	0.0255873i
$375$	0.559947	+	0.646213i	0.0289155	+	0.0333703i
$376$	−0.122278	−	1.12765i	−0.00630601	−	0.0581539i
$377$	34.5200	+	10.1360i	1.77787	+	0.522030i
$378$	−5.74212	+	28.0394i	−0.295343	+	1.44219i
$379$	2.72658	−	4.24265i	0.140055	−	0.217930i	−0.764139	−	0.645051i	$-0.776836\pi$
$379$	2.72658	−	4.24265i	0.140055	−	0.217930i	0.904194	+	0.427121i	$0.140472\pi$
$380$	−0.508818	−	1.04582i	−0.0261018	−	0.0536496i
$381$	−10.9474	−	9.48597i	−0.560852	−	0.485981i
$382$	−5.99528	+	1.38104i	−0.306745	+	0.0706599i
$383$	−1.19607	−	8.31888i	−0.0611165	−	0.425075i	−0.997292	−	0.0735421i	$-0.976570\pi$
$383$	−1.19607	−	8.31888i	−0.0611165	−	0.425075i	0.936176	−	0.351533i	$-0.114339\pi$
$384$	8.85524	+	3.89480i	0.451892	+	0.198756i
$385$	−0.912965	+	0.416937i	−0.0465290	+	0.0212491i
$386$	1.44592	−	1.48165i	0.0735953	−	0.0754140i
$387$	5.03690	+	2.30028i	0.256040	+	0.116930i
$388$	−19.3099	+	23.4160i	−0.980310	+	1.18877i
$389$	−7.84862	+	5.04400i	−0.397941	+	0.255741i	−0.724272	−	0.689514i	$-0.757824\pi$
$389$	−7.84862	+	5.04400i	−0.397941	+	0.255741i	0.326331	+	0.945256i	$0.394188\pi$
$390$	2.48502	+	4.42181i	0.125834	+	0.223907i
$391$	7.35846	+	10.4020i	0.372133	+	0.526050i
$392$	−1.29648	+	37.2559i	−0.0654819	+	1.88171i
$393$	−8.94916	+	5.75128i	−0.451425	+	0.290113i
$394$	30.6938	−	11.8769i	1.54633	−	0.598350i
$395$	−3.62761	+	7.94336i	−0.182525	+	0.399674i
$396$	−0.979451	−	0.261803i	−0.0492193	−	0.0131561i
$397$	23.0852	−	10.5426i	1.15861	−	0.529120i	0.259029	−	0.965870i	$-0.416598\pi$
$397$	23.0852	−	10.5426i	1.15861	−	0.529120i	0.899583	+	0.436749i	$0.143870\pi$
$398$	21.0500	+	7.55990i	1.05514	+	0.378943i
$399$	−2.21093	+	0.317884i	−0.110685	+	0.0159141i
$400$	0.761795	+	3.92679i	0.0380897	+	0.196339i
$401$	6.54989	+	5.67551i	0.327086	+	0.283422i	0.802887	−	0.596131i	$-0.203296\pi$
$401$	6.54989	+	5.67551i	0.327086	+	0.283422i	−0.475801	+	0.879553i	$0.657842\pi$
$402$	−0.512454	+	8.64695i	−0.0255589	+	0.431270i
$403$	−16.1434	−	10.3748i	−0.804162	−	0.516804i
$404$	25.1191	−	8.04658i	1.24972	−	0.400333i
$405$	−2.83470	−	0.832342i	−0.140857	−	0.0413594i
$406$	43.2196	−	33.1845i	2.14495	−	1.64692i
$407$	1.54622	−	1.33980i	0.0766431	−	0.0664116i
$408$	−2.46433	−	5.93407i	−0.122003	−	0.293780i
$409$	30.1128	−	8.84192i	1.48898	−	0.437205i	0.566767	−	0.823878i	$-0.308194\pi$
$409$	30.1128	−	8.84192i	1.48898	−	0.437205i	0.922217	+	0.386673i	$0.126376\pi$
$410$	−0.377001	−	4.49881i	−0.0186187	−	0.222181i
$411$	14.1316	+	2.03181i	0.697059	+	0.100222i
$412$	0.765862	+	31.3690i	0.0377313	+	1.54544i
$413$	−27.0949			−1.33325
$414$	−12.8216	−	8.50904i	−0.630147	−	0.418196i
$415$			9.27080i			0.455086i
$416$	−0.246184	+	23.7268i	−0.0120702	+	1.16330i
$417$	2.05819	−	14.3151i	0.100790	−	0.701012i
$418$	−0.0153437	−	0.183099i	−0.000750484	−	0.00895565i
$419$	0.296774	+	1.01072i	0.0144983	+	0.0493768i	0.966424	−	0.256951i	$-0.0827179\pi$
$419$	0.296774	+	1.01072i	0.0144983	+	0.0493768i	−0.951926	+	0.306328i	$0.900900\pi$
$420$	7.62846	+	0.907375i	0.372231	+	0.0442754i
$421$	−8.89244	−	10.2624i	−0.433391	−	0.500160i	0.496479	−	0.868049i	$-0.334626\pi$
$421$	−8.89244	−	10.2624i	−0.433391	−	0.500160i	−0.929870	+	0.367889i	$0.880081\pi$
$422$	−10.0673	−	13.1116i	−0.490067	−	0.638264i
$423$	0.256338	−	0.873006i	0.0124636	−	0.0424470i
$424$	18.9836	+	17.6419i	0.921924	+	0.856769i
$425$	1.43638	−	2.23504i	0.0696745	−	0.108416i
$426$	−0.524370	+	8.84801i	−0.0254058	+	0.428688i
$427$	−28.7346	+	33.1615i	−1.39056	+	1.60480i
$428$	−12.8977	−	14.1705i	−0.623432	−	0.684959i
$429$	0.114042	+	0.793179i	0.00550600	+	0.0382951i
$430$	1.16661	−	3.24833i	0.0562587	−	0.156648i
$431$	2.28995	+	5.01429i	0.110303	+	0.241530i	0.956731	−	0.290973i	$-0.0939789\pi$
$431$	2.28995	+	5.01429i	0.110303	+	0.241530i	−0.846428	+	0.532503i	$0.821252\pi$
$432$	12.4517	+	13.0271i	0.599083	+	0.626768i
$433$	−19.5139	−	8.91168i	−0.937776	−	0.428268i	−0.112916	−	0.993605i	$-0.536019\pi$
$433$	−19.5139	−	8.91168i	−0.937776	−	0.428268i	−0.824860	+	0.565337i	$0.808746\pi$
$434$	−27.1056	+	10.4884i	−1.30111	+	0.503461i
$435$	−3.96504	−	6.16972i	−0.190109	−	0.295816i
$436$	15.0495	−	24.7241i	0.720739	−	1.18407i
$437$	0.665940	−	2.70817i	0.0318562	−	0.129549i
$438$	−2.32056	+	1.30414i	−0.110881	+	0.0623142i
$439$	−2.30026	−	3.57927i	−0.109785	−	0.170829i	0.782013	−	0.623262i	$-0.214193\pi$
$439$	−2.30026	−	3.57927i	−0.109785	−	0.170829i	−0.891799	+	0.452432i	$0.850556\pi$
$440$	−0.111634	+	0.621999i	−0.00532192	+	0.0296526i
$441$	−12.4224	+	27.2012i	−0.591541	+	1.29529i
$442$	11.0073	−	11.2793i	0.523565	−	0.536503i
$443$	13.1004	+	28.6858i	0.622416	+	1.36290i	0.913749	+	0.406280i	$0.133174\pi$
$443$	13.1004	+	28.6858i	0.622416	+	1.36290i	−0.291332	+	0.956622i	$0.594098\pi$
$444$	−15.4416	+	2.60631i	−0.732824	+	0.123690i
$445$	8.03553	−	1.15534i	0.380921	−	0.0547681i
$446$	6.32701	+	27.4665i	0.299593	+	1.30058i
$447$	−10.3315	+	11.9232i	−0.488664	+	0.563948i
$448$	28.8089	+	21.4840i	1.36109	+	1.01502i
$449$	−24.3699	−	15.6616i	−1.15009	−	0.739115i	−0.180430	−	0.983588i	$-0.557749\pi$
$449$	−24.3699	−	15.6616i	−1.15009	−	0.739115i	−0.969656	+	0.244473i	$0.921385\pi$
$450$	−0.643734	+	3.14343i	−0.0303459	+	0.148183i
$451$	0.200941	−	0.684342i	0.00946194	−	0.0322244i
$452$	−9.59239	+	22.4382i	−0.451188	+	1.05540i
$453$	−4.70578	+	4.07758i	−0.221097	+	0.191582i
$454$	3.10817	−	4.25941i	0.145874	−	0.199904i
$455$	5.30866	+	18.0796i	0.248874	+	0.847586i
$456$	−0.628371	+	1.25820i	−0.0294262	+	0.0589206i
$457$	−3.01183	−	0.433036i	−0.140888	−	0.0202566i	0.0715102	−	0.997440i	$-0.477218\pi$
$457$	−3.01183	−	0.433036i	−0.140888	−	0.0202566i	−0.212398	+	0.977183i	$0.568127\pi$
$458$	3.84886	−	7.25786i	0.179845	−	0.339138i
$459$		−	11.9695i		−	0.558686i
$460$	−4.61788	+	8.40685i	−0.215310	+	0.391971i
$461$			21.1681i			0.985898i	0.870058	+	0.492949i	$0.164081\pi$
$461$			21.1681i			0.985898i	−0.870058	+	0.492949i	$0.835919\pi$
$462$	1.07223	+	0.568607i	0.0498848	+	0.0264540i
$463$	−35.7645	−	5.14216i	−1.66212	−	0.238976i	−0.753754	−	0.657157i	$-0.771759\pi$
$463$	−35.7645	−	5.14216i	−1.66212	−	0.238976i	−0.908364	+	0.418180i	$0.862668\pi$
$464$	−1.67426	−	34.2676i	−0.0777254	−	1.59083i
$465$	1.10209	+	3.75337i	0.0511081	+	0.174058i
$466$	16.2760	+	11.8769i	0.753970	+	0.550185i
$467$	−2.86227	+	2.48017i	−0.132450	+	0.114768i	−0.718567	−	0.695458i	$-0.755201\pi$
$467$	−2.86227	+	2.48017i	−0.132450	+	0.114768i	0.586117	+	0.810227i	$0.300656\pi$
$468$	−7.48202	+	17.5017i	−0.345856	+	0.809014i
$469$	−9.06584	+	30.8754i	−0.418622	+	1.42569i
$470$	−0.555597	−	0.113779i	−0.0256278	−	0.00524825i
$471$	−7.73387	−	4.97025i	−0.356358	−	0.229017i
$472$	−9.71673	+	14.0221i	−0.447249	+	0.645420i
$473$	0.357081	−	0.412093i	0.0164186	−	0.0189481i
$474$	10.2902	−	2.37039i	0.472645	−	0.108876i
$475$	−0.575596	+	0.0827582i	−0.0264102	+	0.00379721i
$476$	−3.97268	−	23.5369i	−0.182088	−	1.07881i
$477$	8.63588	+	18.9099i	0.395410	+	0.865827i
$478$	0.0706549	+	0.0689509i	0.00323168	+	0.00315374i
$479$	17.8211	−	39.0227i	0.814265	−	1.78299i	0.226395	−	0.974036i	$-0.427306\pi$
$479$	17.8211	−	39.0227i	0.814265	−	1.78299i	0.587870	−	0.808955i	$-0.299967\pi$
$480$	3.20529	−	3.62247i	0.146301	−	0.165342i
$481$	−20.7663	−	32.3131i	−0.946864	−	1.47335i
$482$	−14.3060	−	25.4558i	−0.651618	−	1.15948i
$483$	12.6706	+	13.3717i	0.576531	+	0.608434i
$484$	11.3869	−	18.7071i	0.517587	−	0.850322i
$485$	8.20448	+	12.7664i	0.372546	+	0.579693i
$486$	8.18696	+	21.1578i	0.371368	+	0.959737i
$487$	9.52386	+	4.34940i	0.431567	+	0.197090i	0.619341	−	0.785122i	$-0.287400\pi$
$487$	9.52386	+	4.34940i	0.431567	+	0.197090i	−0.187774	+	0.982212i	$0.560127\pi$
$488$	6.85694	+	26.7630i	0.310399	+	1.21151i
$489$	−2.58702	−	5.66478i	−0.116989	−	0.256170i
$490$	17.5422	+	6.30011i	0.792476	+	0.284610i
$491$	−5.28468	−	36.7558i	−0.238494	−	1.65876i	−0.659499	−	0.751706i	$-0.729231\pi$
$491$	−5.28468	−	36.7558i	−0.238494	−	1.65876i	0.421005	−	0.907059i	$-0.361678\pi$
$492$	−4.03731	+	3.67466i	−0.182016	+	0.165666i
$493$	−14.9228	+	17.2218i	−0.672088	+	0.775630i
$494$	−3.44352	−	0.204077i	−0.154931	−	0.00918188i
$495$	−0.274061	+	0.426447i	−0.0123181	+	0.0191674i
$496$	−4.29260	+	17.7890i	−0.192743	+	0.798750i
$497$	−9.27665	+	31.5934i	−0.416115	+	1.41716i
$498$	8.89191	−	6.82731i	0.398456	−	0.305939i
$499$	−12.7066	−	14.6642i	−0.568827	−	0.656461i	0.396338	−	0.918105i	$-0.370281\pi$
$499$	−12.7066	−	14.6642i	−0.568827	−	0.656461i	−0.965165	+	0.261644i	$0.915736\pi$
$500$	1.98600	+	0.236227i	0.0888166	+	0.0105644i
$501$	5.18672	+	17.6644i	0.231726	+	0.789185i
$502$	−0.00429193		0.000359664i	−0.000191558		1.60526e-5i
$503$	5.58479	−	38.8431i	0.249013	−	1.73193i	−0.354924	−	0.934895i	$-0.615493\pi$
$503$	5.58479	−	38.8431i	0.249013	−	1.73193i	0.603938	−	0.797032i	$-0.293598\pi$
$504$	14.7327	+	24.7790i	0.656247	+	1.10374i
$505$		−	13.1882i		−	0.586868i
$506$	−1.15969	+	0.975377i	−0.0515543	+	0.0433608i
$507$	3.92855			0.174473
$508$	−33.8716	+	0.826962i	−1.50281	+	0.0366905i
$509$	28.9837	+	4.16723i	1.28468	+	0.184709i	0.750618	−	0.660736i	$-0.229756\pi$
$509$	28.9837	+	4.16723i	1.28468	+	0.184709i	0.534062	+	0.845445i	$0.320665\pi$
$510$	−3.20149	+	0.268285i	−0.141764	+	0.0118799i
$511$	−9.48818	+	2.78598i	−0.419732	+	0.123245i
$512$	21.4498	−	7.20462i	0.947956	−	0.318402i
$513$	−1.97995	+	1.71564i	−0.0874169	+	0.0757472i
$514$	−14.1223	−	18.3929i	−0.622907	−	0.811276i
$515$	15.0536	+	4.42015i	0.663343	+	0.194775i
$516$	−3.97470	+	1.27325i	−0.174976	+	0.0560515i
$517$	−0.0753741	−	0.0484400i	−0.00331495	−	0.00213039i
$518$	−58.0733	−	3.44167i	−2.55160	−	0.151218i
$519$	3.12739	+	2.70990i	0.137277	+	0.118951i
$520$	11.2603	+	3.73636i	0.493799	+	0.163850i
$521$	−14.3484	+	2.06299i	−0.628616	+	0.0903814i	−0.449257	−	0.893402i	$-0.648311\pi$
$521$	−14.3484	+	2.06299i	−0.628616	+	0.0903814i	−0.179359	+	0.983784i	$0.557402\pi$
$522$	9.30221	−	25.9013i	0.407147	−	1.13367i
$523$	−23.3850	+	10.6796i	−1.02255	+	0.466984i	−0.854862	−	0.518855i	$-0.826358\pi$
$523$	−23.3850	+	10.6796i	−1.02255	+	0.466984i	−0.167691	+	0.985840i	$0.553631\pi$
$524$	−6.42531	+	24.0382i	−0.280691	+	1.05011i
$525$	1.59566	−	3.49400i	0.0696402	−	0.152491i
$526$	6.66276	+	17.2187i	0.290510	+	0.750773i
$527$	10.2251	−	6.57127i	0.445412	−	0.286249i
$528$	0.678788	−	0.350988i	0.0295405	−	0.0152748i
$529$	−21.4053	+	8.41497i	−0.930667	+	0.365868i
$530$	11.2961	−	6.34833i	0.490672	−	0.275754i
$531$	−11.5123	+	7.39853i	−0.499593	+	0.321069i
$532$	−3.32398	+	4.03080i	−0.144113	+	0.174757i
$533$	−12.1802	−	5.56253i	−0.527585	−	0.240940i
$534$	−7.02574	−	6.85630i	−0.304033	−	0.296701i
$535$	−8.71485	+	3.97994i	−0.376776	+	0.172068i
$536$	12.7274	+	15.7643i	0.549742	+	0.680912i
$537$	−1.13425	−	7.88886i	−0.0489463	−	0.340429i
$538$	0.567740	+	2.46465i	0.0244770	+	0.106258i
$539$	2.22546	+	1.92837i	0.0958572	+	0.0830608i
$540$	8.10237	−	3.94200i	0.348670	−	0.169636i
$541$	6.35336	−	9.88603i	0.273152	−	0.425033i	−0.677392	−	0.735622i	$-0.736890\pi$
$541$	6.35336	−	9.88603i	0.273152	−	0.425033i	0.950544	+	0.310589i	$0.100526\pi$
$542$	16.6008	+	3.39963i	0.713064	+	0.146027i
$543$	−3.81571	−	1.12039i	−0.163748	−	0.0480807i
$544$	−13.6055	−	6.38484i	−0.583330	−	0.273748i
$545$	−9.47723	−	10.9373i	−0.405960	−	0.468503i
$546$	13.4313	−	18.4061i	0.574805	−	0.787708i
$547$	−11.4048	+	3.34876i	−0.487635	+	0.143183i	−0.516302	−	0.856406i	$-0.672692\pi$
$547$	−11.4048	+	3.34876i	−0.487635	+	0.143183i	0.0286673	+	0.999589i	$0.490874\pi$
$548$	27.6436	−	18.7343i	1.18088	−	0.800292i
$549$	−3.15396	+	21.9363i	−0.134608	+	0.936217i
$550$	0.279146	+	0.148032i	0.0119028	+	0.00631210i
$551$	4.98772			0.212484
$552$	11.4640	−	1.76192i	0.487941	−	0.0749922i
$553$	39.2282			1.66815
$554$	10.9359	+	5.79935i	0.464624	+	0.246391i
$555$	−1.11432	+	7.75029i	−0.0473004	+	0.328981i
$556$	−18.9776	−	28.0026i	−0.804829	−	1.18757i
$557$	−24.5259	+	7.20144i	−1.03919	+	0.305135i	−0.756444	−	0.654059i	$-0.773065\pi$
$557$	−24.5259	+	7.20144i	−1.03919	+	0.305135i	−0.282750	+	0.959194i	$0.591247\pi$
$558$	−8.65291	+	11.8579i	−0.366307	+	0.501984i
$559$	−6.70387	−	7.73668i	−0.283543	−	0.327227i
$560$	14.6242	−	10.4408i	0.617987	−	0.441204i
$561$	−0.486999	−	0.142996i	−0.0205611	−	0.00603728i
$562$	14.0936	+	2.88620i	0.594504	+	0.121747i
$563$	13.8070	−	21.4841i	0.581897	−	0.905449i	−0.418099	−	0.908401i	$-0.637303\pi$
$563$	13.8070	−	21.4841i	0.581897	−	0.905449i	0.999996	+	0.00295255i	$0.000939827\pi$
$564$	0.300030	+	0.616681i	0.0126335	+	0.0259670i
$565$	9.22111	+	7.99014i	0.387935	+	0.336148i
$566$	5.27683	+	22.9075i	0.221802	+	0.962874i
$567$	1.88875	+	13.1366i	0.0793201	+	0.551683i
$568$	13.0234	+	16.1308i	0.546449	+	0.676834i
$569$	16.3154	−	7.45098i	0.683976	−	0.312361i	−0.0429501	−	0.999077i	$-0.513676\pi$
$569$	16.3154	−	7.45098i	0.683976	−	0.312361i	0.726926	+	0.686716i	$0.240948\pi$
$570$	0.503263	+	0.491126i	0.0210794	+	0.0205710i
$571$	−13.5632	−	6.19409i	−0.567601	−	0.259215i	0.110879	−	0.993834i	$-0.464634\pi$
$571$	−13.5632	−	6.19409i	−0.567601	−	0.259215i	−0.678480	+	0.734619i	$0.737361\pi$
$572$	1.44606	+	1.19249i	0.0604629	+	0.0498604i
$573$	3.12929	−	2.01108i	0.130728	−	0.0840139i
$574$	−17.6798	+	9.93589i	−0.737939	+	0.414716i
$575$	3.29867	+	3.48120i	0.137564	+	0.145176i
$576$	18.1070	+	1.26175i	0.754460	+	0.0525729i
$577$	24.5798	−	15.7965i	1.02327	−	0.657615i	0.0824750	−	0.996593i	$-0.473718\pi$
$577$	24.5798	−	15.7965i	1.02327	−	0.657615i	0.940794	+	0.338978i	$0.110081\pi$
$578$	−5.07361	−	13.1119i	−0.211034	−	0.545382i
$579$	−0.519983	+	1.13860i	−0.0216098	+	0.0473188i
$580$	−16.5724	−	4.42973i	−0.688132	−	0.183935i
$581$	37.8829	−	17.3005i	1.57165	−	0.717747i
$582$	6.20263	−	17.2708i	0.257107	−	0.715896i
$583$	2.02629	−	0.291336i	0.0839202	−	0.0120659i
$584$	−1.96084	+	5.90942i	−0.0811402	+	0.244534i
$585$	7.19242	+	6.23227i	0.297370	+	0.257673i
$586$	3.71510	+	0.220172i	0.153469	+	0.00909523i
$587$	12.4192	+	7.98135i	0.512596	+	0.329426i	0.771237	−	0.636548i	$-0.219638\pi$
$587$	12.4192	+	7.98135i	0.512596	+	0.329426i	−0.258641	+	0.965974i	$0.583275\pi$
$588$	−6.87600	−	21.4649i	−0.283561	−	0.885196i
$589$	−2.55261	−	0.749513i	−0.105178	−	0.0308832i
$590$	5.19472	+	6.76562i	0.213863	+	0.278536i
$591$	−15.0387	+	13.0311i	−0.618608	+	0.536027i
$592$	−22.6073	+	28.8198i	−0.929155	+	1.18449i
$593$	−10.5802	+	3.10663i	−0.434477	+	0.127574i	−0.491655	−	0.870790i	$-0.663608\pi$
$593$	−10.5802	+	3.10663i	−0.434477	+	0.127574i	0.0571783	+	0.998364i	$0.481790\pi$
$594$	1.41853	−	0.118873i	0.0582031	−	0.00487742i
$595$	−11.8134	−	1.69851i	−0.484303	−	0.0696323i
$596$	0.900674	+	36.8908i	0.0368930	+	1.51110i
$597$	−13.5232			−0.553466
$598$	15.0269	+	24.1565i	0.614497	+	0.987832i
$599$		−	14.8975i		−	0.608694i	−0.952561	−	0.304347i	$-0.901562\pi$
$599$		−	14.8975i		−	0.608694i	0.952561	−	0.304347i	$-0.0984382\pi$
$600$	−1.23598	−	2.07880i	−0.0504587	−	0.0848666i
$601$	3.11996	−	21.6998i	0.127266	−	0.885152i	−0.821733	−	0.569873i	$-0.806993\pi$
$601$	3.11996	−	21.6998i	0.127266	−	0.885152i	0.948999	−	0.315280i	$-0.102098\pi$
$602$	−15.4505	+	1.29476i	−0.629717	+	0.0527703i
$603$	4.57886	+	15.5942i	0.186466	+	0.635044i
$604$	−1.72023	+	14.4622i	−0.0699950	+	0.588460i
$605$	−7.17078	−	8.27552i	−0.291534	−	0.336448i
$606$	−12.6492	+	9.71221i	−0.513839	+	0.394532i
$607$	3.78602	−	12.8940i	0.153670	−	0.523351i	−0.846286	−	0.532728i	$-0.821167\pi$
$607$	3.78602	−	12.8940i	0.153670	−	0.523351i	0.999956	+	0.00937751i	$0.00298500\pi$
$608$	0.893975	+	3.16574i	0.0362555	+	0.128388i
$609$	−17.8118	+	27.7157i	−0.721770	+	1.12310i
$610$	13.7895	+	0.817226i	0.558323	+	0.0330885i
$611$	−1.10155	+	1.27125i	−0.0445638	+	0.0514294i
$612$	−8.11495	−	8.91581i	−0.328027	−	0.360400i
$613$	4.45104	+	30.9577i	0.179776	+	1.25037i	0.857280	+	0.514850i	$0.172152\pi$
$613$	4.45104	+	30.9577i	0.179776	+	1.25037i	−0.677504	+	0.735519i	$0.736938\pi$
$614$	17.2995	+	6.21295i	0.698151	+	0.250734i
$615$	1.13392	+	2.48294i	0.0457241	+	0.100122i
$616$	2.74997	−	0.704567i	0.110799	−	0.0283878i
$617$	36.8832	+	16.8440i	1.48486	+	0.678114i	0.982452	−	0.186515i	$-0.0597194\pi$
$617$	36.8832	+	16.8440i	1.48486	+	0.678114i	0.502410	+	0.864629i	$0.332447\pi$
$618$	−6.84648	−	17.6936i	−0.275406	−	0.711739i
$619$	−14.7270	−	22.9157i	−0.591930	−	0.921061i	−0.999967	−	0.00809566i	$-0.997423\pi$
$619$	−14.7270	−	22.9157i	−0.591930	−	0.921061i	0.408037	−	0.912965i	$-0.366213\pi$
$620$	7.81574	+	4.75741i	0.313888	+	0.191062i
$621$	20.9812	+	5.15928i	0.841947	+	0.207035i
$622$	−19.1632	−	34.0986i	−0.768373	−	1.36723i
$623$	−19.7163	−	30.6792i	−0.789918	−	1.22914i
$624$	−4.70881	−	13.5517i	−0.188503	−	0.542503i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−17.0419	−	16.6310i	−0.681133	−	0.664707i
$627$	0.0461498	+	0.101054i	0.00184305	+	0.00403571i
$628$	−21.2032	+	3.57880i	−0.846102	+	0.142810i
$629$	24.0813	−	3.46236i	0.960183	−	0.138054i
$630$	14.0461	−	3.23558i	0.559611	−	0.128909i
$631$	−19.2823	+	22.2529i	−0.767614	+	0.885874i	−0.996150	−	0.0876612i	$-0.972061\pi$
$631$	−19.2823	+	22.2529i	−0.767614	+	0.885874i	0.228536	+	0.973535i	$0.426606\pi$
$632$	14.0680	−	20.3013i	0.559594	−	0.807544i
$633$	8.40817	+	5.40360i	0.334195	+	0.214774i
$634$	28.4439	+	5.82496i	1.12965	+	0.231339i
$635$	−4.77279	+	16.2546i	−0.189402	+	0.645045i
$636$	−14.4077	−	6.15934i	−0.571302	−	0.244234i
$637$	41.7810	−	36.2034i	1.65542	−	1.43443i
$638$	−2.18920	−	1.59750i	−0.0866714	−	0.0632457i
$639$	4.68534	+	15.9568i	0.185349	+	0.631241i
$640$	−0.158775	−	11.3126i	−0.00627615	−	0.447170i
$641$	−27.3406	−	3.93099i	−1.07989	−	0.155265i	−0.420669	−	0.907214i	$-0.638205\pi$
$641$	−27.3406	−	3.93099i	−1.07989	−	0.155265i	−0.659221	+	0.751949i	$0.729114\pi$
$642$	10.2352	+	5.42773i	0.403950	+	0.214215i
$643$			13.9730i			0.551040i	0.961295	+	0.275520i	$0.0888500\pi$
$643$			13.9730i			0.551040i	−0.961295	+	0.275520i	$0.911150\pi$
$644$	42.9701	+	3.18157i	1.69326	+	0.125371i
$645$			2.08683i			0.0821687i
$646$	1.02364	−	1.93029i	0.0402745	−	0.0759464i
$647$	−5.04376	−	0.725183i	−0.198291	−	0.0285099i	0.0424538	−	0.999098i	$-0.486482\pi$
$647$	−5.04376	−	0.725183i	−0.198291	−	0.0285099i	−0.240744	+	0.970589i	$0.577392\pi$
$648$	7.47576	+	3.73355i	0.293676	+	0.146668i
$649$	0.379659	+	1.29300i	0.0149029	+	0.0507546i
$650$	3.49671	−	4.79186i	0.137152	−	0.187952i
$651$	13.2806	−	11.5077i	0.520506	−	0.451021i
$652$	−13.3937	−	5.72586i	−0.524539	−	0.224242i
$653$	−0.0606476	+	0.206547i	−0.00237332	+	0.00808279i	−0.960671	−	0.277689i	$-0.910432\pi$
$653$	−0.0606476	+	0.206547i	−0.00237332	+	0.00808279i	0.958298	+	0.285771i	$0.0922498\pi$
$654$	−3.51097	+	17.1445i	−0.137290	+	0.670402i
$655$	10.4661	+	6.72615i	0.408944	+	0.262812i
$656$	−1.19828	+	12.7128i	−0.0467851	+	0.496352i
$657$	−3.27069	+	3.77458i	−0.127602	+	0.147260i
$658$	0.571885	+	2.48264i	0.0222944	+	0.0967834i
$659$	39.8198	−	5.72522i	1.55116	−	0.223023i	0.687155	−	0.726511i	$-0.258859\pi$
$659$	39.8198	−	5.72522i	1.55116	−	0.223023i	0.864002	+	0.503488i	$0.167950\pi$
$660$	−0.0635904	−	0.376753i	−0.00247525	−	0.0146651i
$661$	−4.57382	−	10.0153i	−0.177901	−	0.389549i	0.799584	−	0.600555i	$-0.205053\pi$
$661$	−4.57382	−	10.0153i	−0.177901	−	0.389549i	−0.977485	+	0.211006i	$0.932326\pi$
$662$	−4.00890	+	4.10797i	−0.155810	+	0.159661i
$663$	−3.95847	+	8.66784i	−0.153734	+	0.336631i
$664$	4.63216	−	25.8094i	0.179763	−	1.00160i
$665$	1.41231	+	2.19759i	0.0547670	+	0.0852191i
$666$	−25.6146	+	14.3952i	−0.992544	+	0.557802i
$667$	−23.7557	−	33.5813i	−0.919826	−	1.30027i
$668$	36.7830	+	22.3897i	1.42318	+	0.866282i
$669$	−9.21345	−	14.3364i	−0.356212	−	0.554277i
$670$	9.44776	−	3.65579i	0.364999	−	0.141235i
$671$	1.98514	+	0.906583i	0.0766355	+	0.0349982i
$672$	−20.7838	−	6.33764i	−0.801754	−	0.244480i
$673$	−7.40927	−	16.2240i	−0.285606	−	0.625391i	0.711394	−	0.702794i	$-0.248064\pi$
$673$	−7.40927	−	16.2240i	−0.285606	−	0.625391i	−0.997000	+	0.0774032i	$0.975337\pi$
$674$	−12.9704	+	36.1150i	−0.499599	+	1.39110i
$675$	−0.641158	−	4.45935i	−0.0246782	−	0.171641i
$676$	6.79558	−	6.18517i	0.261369	−	0.237891i
$677$	7.30641	−	8.43204i	0.280808	−	0.324070i	−0.597771	−	0.801667i	$-0.703947\pi$
$677$	7.30641	−	8.43204i	0.280808	−	0.324070i	0.878579	+	0.477597i	$0.158492\pi$
$678$	0.872869	−	14.7284i	0.0335223	−	0.565642i
$679$	36.8562	−	57.3494i	1.41441	−	2.20087i
$680$	−5.11553	+	5.50456i	−0.196172	+	0.211090i
$681$	−0.898189	+	3.05895i	−0.0344187	+	0.117219i
$682$	0.880329	+	1.14654i	0.0337095	+	0.0439034i
$683$	25.1561	+	29.0317i	0.962573	+	1.11087i	0.993781	+	0.111355i	$0.0355192\pi$
$683$	25.1561	+	29.0317i	0.962573	+	1.11087i	−0.0312078	+	0.999513i	$0.509935\pi$
$684$	−0.311674	+	2.62029i	−0.0119171	+	0.100189i
$685$	−4.70406	−	16.0206i	−0.179733	−	0.612114i
$686$	−3.27855	−	39.1235i	−0.125176	−	1.49374i
$687$	−0.706893	+	4.91655i	−0.0269696	+	0.187578i
$688$	−4.87080	+	8.46028i	−0.185697	+	0.322545i
$689$		−	38.4329i		−	1.46418i
$690$	0.909686	−	5.72752i	0.0346311	−	0.218043i
$691$	−11.2143			−0.426611			−0.213306	−	0.976986i	$-0.568423\pi$
$691$	−11.2143			−0.426611			−0.213306	+	0.976986i	$0.568423\pi$
$692$	9.67624	−	0.236242i	0.367835	−	0.00898056i
$693$	2.25400	+	0.324077i	0.0856225	+	0.0123107i
$694$	0.355405	+	4.24111i	0.0134910	+	0.160990i
$695$	−16.2286	+	4.76514i	−0.615585	+	0.180752i
$696$	7.95575	+	19.1573i	0.301562	+	0.726156i
$697$	6.40973	−	5.55406i	0.242786	−	0.210375i
$698$	19.7234	−	15.1438i	0.746541	−	0.573203i
$699$	−11.6888	−	3.43214i	−0.442111	−	0.129816i
$700$	−2.74085	−	8.55613i	−0.103594	−	0.323391i
$701$	−22.6654	−	14.5662i	−0.856062	−	0.550157i	0.0373983	−	0.999300i	$-0.488093\pi$
$701$	−22.6654	−	14.5662i	−0.856062	−	0.550157i	−0.893460	+	0.449143i	$0.851729\pi$
$702$	1.58106	−	26.6782i	0.0596734	−	1.00690i
$703$	−4.02441	−	3.48717i	−0.151784	−	0.131521i
$704$	0.621563	−	1.67583i	0.0234260	−	0.0631603i
$705$	0.339407	−	0.0487993i	0.0127828	−	0.00183789i
$706$	−37.0108	−	13.2921i	−1.39292	−	0.500254i
$707$	−53.8904	+	24.6109i	−2.02676	+	0.925589i
$708$	2.66356	−	9.96483i	0.100103	−	0.374501i
$709$	−13.3411	+	29.2130i	−0.501036	+	1.09712i	0.475095	+	0.879935i	$0.342414\pi$
$709$	−13.3411	+	29.2130i	−0.501036	+	1.09712i	−0.976131	+	0.217182i	$0.930313\pi$
$710$	9.66745	−	3.74080i	0.362813	−	0.140390i
$711$	16.6677	−	10.7117i	0.625086	−	0.401719i
$712$	−22.9477	−	0.798564i	−0.860003	−	0.0299274i
$713$	7.11136	+	20.7560i	0.266323	+	0.777318i
$714$	7.07068	+	12.5815i	0.264614	+	0.470849i
$715$	0.788395	−	0.506671i	0.0294843	−	0.0189484i
$716$	−14.3823	−	11.8603i	−0.537494	−	0.443241i
$717$	−0.0542962	−	0.0247962i	−0.00202773	−	0.000926032i
$718$	26.3970	−	27.0493i	0.985126	−	1.00947i
$719$	16.3932	−	7.48651i	0.611362	−	0.279200i	−0.0855754	−	0.996332i	$-0.527273\pi$
$719$	16.3932	−	7.48651i	0.611362	−	0.279200i	0.696937	+	0.717132i	$0.254546\pi$
$720$	3.36273	−	8.42949i	0.125322	−	0.314148i
$721$	−10.0302	−	69.7616i	−0.373544	−	2.59806i
$722$	25.7183	−	5.92431i	0.957136	−	0.220480i
$723$	13.3428	+	11.5616i	0.496225	+	0.429982i
$724$	−8.36436	+	4.06946i	−0.310859	+	0.151240i
$725$	−4.63714	+	7.21553i	−0.172219	+	0.267978i
$726$	−2.65652	+	12.9721i	−0.0985926	+	0.481439i
$727$	30.9338	+	9.08299i	1.14727	+	0.336869i	0.799474	−	0.600700i	$-0.205112\pi$
$727$	30.9338	+	9.08299i	1.14727	+	0.336869i	0.347797	+	0.937570i	$0.386930\pi$
$728$	−5.74553	−	52.9851i	−0.212943	−	1.96376i
$729$	−3.17845	−	3.66813i	−0.117720	−	0.135857i
$730$	2.51477	+	1.83507i	0.0930758	+	0.0679190i
$731$	6.22142	−	1.82677i	0.230108	−	0.0675657i
$732$	−9.37123	−	13.8278i	−0.346371	−	0.511091i
$733$	0.150402	−	1.04607i	0.00555522	−	0.0386374i	−0.986855	−	0.161606i	$-0.948332\pi$
$733$	0.150402	−	1.04607i	0.00555522	−	0.0386374i	0.992411	+	0.122969i	$0.0392416\pi$
$734$	11.4411	−	21.5747i	0.422298	−	0.796336i
$735$	−11.2696			−0.415687
$736$	17.0564	−	21.0969i	0.628708	−	0.777642i
$737$	1.60044			0.0589531
$738$	−4.79886	+	9.04930i	−0.176648	+	0.333109i
$739$	−3.81586	+	26.5399i	−0.140369	+	0.976286i	0.790898	+	0.611948i	$0.209614\pi$
$739$	−3.81586	+	26.5399i	−0.140369	+	0.976286i	−0.931267	+	0.364338i	$0.881295\pi$
$740$	10.2746	+	15.1608i	0.377703	+	0.557323i
$741$	2.00119	−	0.587603i	0.0735156	−	0.0215861i
$742$	−47.0209	−	34.3120i	−1.72619	−	1.25963i
$743$	−22.6316	−	26.1183i	−0.830273	−	0.958187i	0.169352	−	0.985556i	$-0.445833\pi$
$743$	−22.6316	−	26.1183i	−0.830273	−	0.958187i	−0.999625	+	0.0273691i	$0.991287\pi$
$744$	−1.19278	−	10.9998i	−0.0437295	−	0.403273i
$745$	17.7035	+	5.19821i	0.648606	+	0.190448i
$746$	−6.98051	+	34.0866i	−0.255575	+	1.24800i
$747$	11.3720	−	17.6951i	0.416079	−	0.647431i
$748$	−1.06754	+	0.519385i	−0.0390332	+	0.0189906i
$749$	32.5261	+	28.1840i	1.18848	+	1.02982i
$750$	−1.17838	+	0.271444i	−0.0430284	+	0.00991175i
$751$	2.83766	+	19.7363i	0.103548	+	0.720189i	0.973771	+	0.227531i	$0.0730655\pi$
$751$	2.83766	+	19.7363i	0.103548	+	0.720189i	−0.870223	+	0.492658i	$0.836025\pi$
$752$	1.48990	+	0.594360i	0.0543312	+	0.0216741i
$753$	0.00236876	−	0.00108178i	8.63224e−5	−	3.94221e-5i
$754$	−35.5356	+	36.4137i	−1.29413	+	1.32611i
$755$	6.62402	+	3.02509i	0.241073	+	0.110094i
$756$	−31.2281	−	25.7521i	−1.13575	−	0.936593i
$757$	−37.2600	+	23.9456i	−1.35424	+	0.870317i	−0.997946	−	0.0640574i	$-0.979596\pi$
$757$	−37.2600	+	23.9456i	−1.35424	+	0.870317i	−0.356293	+	0.934374i	$0.615960\pi$
$758$	3.49425	+	6.21762i	0.126917	+	0.225834i
$759$	0.460571	−	0.792021i	0.0167177	−	0.0287485i
$760$	1.64378	+	0.0572022i	0.0596261	+	0.00207494i
$761$	14.1378	−	9.08580i	0.512494	−	0.329360i	−0.258702	−	0.965957i	$-0.583295\pi$
$761$	14.1378	−	9.08580i	0.512494	−	0.329360i	0.771197	+	0.636597i	$0.219658\pi$
$762$	19.1051	−	7.39269i	0.692106	−	0.267809i
$763$	−27.0069	+	59.1368i	−0.977714	+	2.14090i
$764$	2.24677	−	8.40556i	0.0812852	−	0.304102i
$765$	−5.48320	+	2.50410i	−0.198246	+	0.0905358i
$766$	11.1861	+	4.01739i	0.404171	+	0.145154i
$767$	25.0422	−	3.60052i	0.904221	−	0.130007i
$768$	−10.7333	+	8.48324i	−0.387306	+	0.306112i
$769$	26.7806	+	23.2055i	0.965733	+	0.836813i	0.986631	−	0.162969i	$-0.0521070\pi$
$769$	26.7806	+	23.2055i	0.965733	+	0.836813i	−0.0208979	+	0.999782i	$0.506652\pi$
$770$	0.0839720	−	1.41691i	0.00302614	−	0.0510619i
$771$	11.7949	+	7.58013i	0.424784	+	0.272992i
$772$	0.893172	+	2.78822i	0.0321460	+	0.100350i
$773$	5.27224	+	1.54807i	0.189629	+	0.0556802i	0.375168	−	0.926957i	$-0.377585\pi$
$773$	5.27224	+	1.54807i	0.189629	+	0.0556802i	−0.185539	+	0.982637i	$0.559403\pi$
$774$	−6.21124	+	4.76906i	−0.223258	+	0.171420i
$775$	3.45748	−	2.99592i	0.124196	−	0.107617i
$776$	−16.4621	−	39.6404i	−0.590954	−	1.42301i
$777$	33.7491	−	9.90964i	1.21074	−	0.355506i
$778$	−1.10181	−	13.1481i	−0.0395018	−	0.471381i
$779$	−1.83747	−	0.264188i	−0.0658342	−	0.00946553i
$780$	−7.17111	+	0.175080i	−0.256767	+	0.00626886i
$781$	1.63766			0.0586000
$782$	−17.8717	+	2.30175i	−0.639091	+	0.0823104i
$783$			38.6417i			1.38094i
$784$	−45.6887	−	26.3041i	−1.63174	−	0.939433i
$785$	−1.53011	+	10.6421i	−0.0546119	+	0.379834i
$786$	−1.25630	−	14.9917i	−0.0448109	−	0.534736i
$787$	4.96991	+	16.9260i	0.177158	+	0.603345i	0.999414	+	0.0342272i	$0.0108970\pi$
$787$	4.96991	+	16.9260i	0.177158	+	0.603345i	−0.822256	+	0.569118i	$0.807285\pi$
$788$	−5.49747	+	46.2182i	−0.195839	+	1.64645i
$789$	−7.31023	−	8.43645i	−0.260251	−	0.300346i
$790$	−7.52096	−	9.79532i	−0.267584	−	0.348502i
$791$	15.4419	−	52.5904i	0.549052	−	1.86990i
$792$	0.976045	−	1.05027i	0.0346822	−	0.0373197i
$793$	22.1510	−	34.4676i	0.786605	−	1.22398i
$794$	−2.12331	+	35.8279i	−0.0753535	+	1.27148i
$795$	−5.13052	+	5.92094i	−0.181961	+	0.209994i
$796$	−23.3923	+	21.2911i	−0.829117	+	0.754641i
$797$	−2.96860	−	20.6471i	−0.105153	−	0.731356i	−0.972373	−	0.233431i	$-0.925005\pi$
$797$	−2.96860	−	20.6471i	−0.105153	−	0.731356i	0.867220	−	0.497925i	$-0.165905\pi$
$798$	1.06771	−	2.97297i	0.0377966	−	0.105242i
$799$	−0.442596	−	0.969150i	−0.0156579	−	0.0342861i
$800$	−5.41088	−	1.64995i	−0.191304	−	0.0583345i
$801$	−16.7546	−	7.65155i	−0.591993	−	0.270354i
$802$	−11.4307	+	4.42309i	−0.403633	+	0.156185i
$803$	0.265901	+	0.413749i	0.00938343	+	0.0146009i
$804$	−10.4640	−	6.36939i	−0.369037	−	0.224631i
$805$	8.06934	−	19.9756i	0.284407	−	0.704047i
$806$	23.6583	−	13.2958i	0.833328	−	0.468324i
$807$	−0.826748	−	1.28644i	−0.0291029	−	0.0452850i
$808$	−6.58949	+	36.7153i	−0.231817	+	1.29164i
$809$	6.01664	−	13.1746i	0.211534	−	0.463195i	−0.773888	−	0.633322i	$-0.781691\pi$
$809$	6.01664	−	13.1746i	0.211534	−	0.463195i	0.985422	+	0.170128i	$0.0544180\pi$
$810$	2.91809	−	2.99021i	0.102531	−	0.105065i
$811$	8.89382	+	19.4748i	0.312304	+	0.683851i	0.999074	−	0.0430239i	$-0.0136991\pi$
$811$	8.89382	+	19.4748i	0.312304	+	0.683851i	−0.686770	+	0.726875i	$0.740972\pi$
$812$	12.8253	+	75.9855i	0.450078	+	2.66657i
$813$	−10.1412	+	1.45808i	−0.355667	+	0.0511372i
$814$	0.649494	+	2.81955i	0.0227648	+	0.0988252i
$815$	−4.76945	+	5.50424i	−0.167067	+	0.192805i
$816$	9.04683	+	0.852734i	0.316702	+	0.0298517i
$817$	−1.19392	−	0.767288i	−0.0417701	−	0.0268440i
$818$	−8.90445	+	43.4814i	−0.311337	+	1.52029i
$819$	12.0446	−	41.0203i	0.420874	−	1.43336i
$820$	5.87062	+	2.50971i	0.205011	+	0.0876430i
$821$	21.0945	−	18.2785i	0.736203	−	0.637924i	−0.203830	−	0.979006i	$-0.565339\pi$
$821$	21.0945	−	18.2785i	0.736203	−	0.637924i	0.940033	+	0.341083i	$0.110794\pi$
$822$	−11.9016	+	16.3099i	−0.415116	+	0.568872i
$823$	13.2285	+	45.0523i	0.461118	+	1.57042i	0.781984	+	0.623299i	$0.214208\pi$
$823$	13.2285	+	45.0523i	0.461118	+	1.57042i	−0.320866	+	0.947125i	$0.603974\pi$
$824$	−39.7000	−	19.8270i	−1.38302	−	0.690707i
$825$	−0.189096	−	0.0271880i	−0.00658349	−	0.000946564i
$826$	17.9520	−	33.8525i	0.624630	−	1.17788i
$827$		−	30.5136i		−	1.06106i	−0.847666	−	0.530531i	$-0.821993\pi$
$827$		−	30.5136i		−	1.06106i	0.847666	−	0.530531i	$-0.178007\pi$
$828$	19.1263	−	10.3816i	0.664686	−	0.360786i
$829$		−	28.5806i		−	0.992644i	−0.868138	−	0.496322i	$-0.834683\pi$
$829$		−	28.5806i		−	0.992644i	0.868138	−	0.496322i	$-0.165317\pi$
$830$	−11.5830	−	6.14248i	−0.402051	−	0.213208i
$831$	−7.40811	−	1.06513i	−0.256985	−	0.0369488i
$832$	−29.4813	−	16.0281i	−1.02208	−	0.555673i
$833$	9.86527	+	33.5980i	0.341811	+	1.16410i
$834$	16.5216	+	12.0561i	0.572097	+	0.417469i
$835$	16.2718	−	14.0996i	0.563110	−	0.487937i
$836$	0.238931	+	0.102144i	0.00826359	+	0.00353271i
$837$	5.80675	−	19.7760i	0.200711	−	0.683558i
$838$	−1.45943	−	0.298872i	−0.0504151	−	0.0103244i
$839$	−10.9224	−	7.01941i	−0.377084	−	0.242337i	0.338346	−	0.941022i	$-0.390133\pi$
$839$	−10.9224	−	7.01941i	−0.377084	−	0.242337i	−0.715430	+	0.698685i	$0.753769\pi$
$840$	−6.18800	+	8.92984i	−0.213506	+	0.308109i
$841$	29.1851	−	33.6814i	1.00638	−	1.16143i
$842$	18.7137	−	4.31078i	0.644917	−	0.148559i
$843$	−8.60961	+	1.23787i	−0.296531	+	0.0426347i
$844$	23.0519	−	3.89083i	0.793480	−	0.133928i
$845$	−1.90861	−	4.17927i	−0.0656581	−	0.143771i
$846$	0.920899	+	0.898690i	0.0316611	+	0.0308976i
$847$	−20.4343	+	44.7448i	−0.702130	+	1.53745i
$848$	−34.6197	+	12.0293i	−1.18885	+	0.413088i
$849$	−7.68416	−	11.9568i	−0.263720	−	0.410356i
$850$	1.84079	+	3.27547i	0.0631385	+	0.112348i
$851$	−4.31076	+	43.7044i	−0.147771	+	1.49817i
$852$	−10.7073	−	6.51750i	−0.366827	−	0.223286i
$853$	−20.3293	−	31.6330i	−0.696062	−	1.08309i	−0.991797	−	0.127824i	$-0.959201\pi$
$853$	−20.3293	−	31.6330i	−0.696062	−	1.08309i	0.295735	−	0.955270i	$-0.404436\pi$
$854$	−22.3937	−	57.8726i	−0.766296	−	1.98036i
$855$	1.20015	+	0.548091i	0.0410443	+	0.0187443i
$856$	26.2502	−	6.72556i	0.897215	−	0.229875i
$857$	−1.81637	−	3.97730i	−0.0620461	−	0.135862i	0.876069	−	0.482186i	$-0.160157\pi$
$857$	−1.81637	−	3.97730i	−0.0620461	−	0.135862i	−0.938115	+	0.346324i	$0.887430\pi$
$858$	−1.06656	−	0.383045i	−0.0364118	−	0.0130770i
$859$	7.50946	+	52.2294i	0.256219	+	1.78204i	0.559184	+	0.829043i	$0.311114\pi$
$859$	7.50946	+	52.2294i	0.256219	+	1.78204i	−0.302965	+	0.953002i	$0.597977\pi$
$860$	3.28553	+	3.60978i	0.112036	+	0.123093i
$861$	8.02988	−	9.26697i	0.273657	−	0.315817i
$862$	−7.78210	−	0.461200i	−0.265060	−	0.0157085i
$863$	3.04602	−	4.73970i	0.103688	−	0.161341i	−0.785533	−	0.618820i	$-0.787611\pi$
$863$	3.04602	−	4.73970i	0.103688	−	0.161341i	0.889221	+	0.457479i	$0.151247\pi$
$864$	−24.5262	+	6.92595i	−0.834397	+	0.235626i
$865$	1.36346	−	4.64352i	0.0463591	−	0.157885i
$866$	24.0634	−	18.4762i	0.817708	−	0.627846i
$867$	5.56665	+	6.42426i	0.189053	+	0.218179i
$868$	4.85479	−	40.8150i	0.164782	−	1.38535i
$869$	−0.549673	−	1.87201i	−0.0186464	−	0.0635038i
$870$	10.3356	−	0.866121i	0.350408	−	0.0293642i
$871$	4.27612	−	29.7410i	0.144891	−	1.00774i
$872$	20.9193	+	35.1842i	0.708416	+	1.19149i
$873$		−	34.4312i		−	1.16532i
$874$	2.94238	+	2.62636i	0.0995275	+	0.0888379i
$875$	−4.49221			−0.151864
$876$	−0.0918819	−	3.76340i	−0.00310440	−	0.127153i
$877$	24.1726	+	3.47550i	0.816251	+	0.117359i	0.537780	−	0.843085i	$-0.319263\pi$
$877$	24.1726	+	3.47550i	0.816251	+	0.117359i	0.278471	+	0.960445i	$0.410172\pi$
$878$	5.99602	−	0.502467i	0.202356	−	0.0169574i
$879$	−2.15902	+	0.633944i	−0.0728218	+	0.0213824i
$880$	−0.703164	−	0.551588i	−0.0237037	−	0.0185940i
$881$	12.4487	−	10.7869i	0.419408	−	0.363419i	−0.419442	−	0.907782i	$-0.637774\pi$
$881$	12.4487	−	10.7869i	0.419408	−	0.363419i	0.838850	+	0.544363i	$0.183229\pi$
$882$	−25.7547	−	33.5430i	−0.867206	−	1.12945i
$883$	23.3121	+	6.84505i	0.784514	+	0.230354i	0.649371	−	0.760472i	$-0.275032\pi$
$883$	23.3121	+	6.84505i	0.784514	+	0.230354i	0.135143	+	0.990826i	$0.456850\pi$
$884$	6.79944	+	21.2258i	0.228690	+	0.713903i
$885$	−4.33862	−	2.78826i	−0.145841	−	0.0937265i
$886$	−44.5199	−	2.63844i	−1.49568	−	0.0886400i
$887$	37.6969	+	32.6646i	1.26574	+	1.09677i	0.990804	+	0.135307i	$0.0432019\pi$
$887$	37.6969	+	32.6646i	1.26574	+	1.09677i	0.274935	+	0.961463i	$0.411344\pi$
$888$	6.97465	−	21.0196i	0.234054	−	0.705372i
$889$	75.3271	−	10.8304i	2.52639	−	0.363240i
$890$	−3.88055	+	10.8051i	−0.130076	+	0.362188i
$891$	0.600426	−	0.274205i	0.0201150	−	0.00918623i
$892$	−38.5088	−	10.2932i	−1.28937	−	0.344643i
$893$	−0.0968745	+	0.212126i	−0.00324178	+	0.00709851i
$894$	−8.05164	−	20.8081i	−0.269287	−	0.695926i
$895$	−7.84127	+	5.03928i	−0.262105	+	0.168444i
$896$	−45.9298	+	21.7596i	−1.53441	+	0.726936i
$897$	−13.4876	−	10.6749i	−0.450337	−	0.356426i
$898$	35.7142	−	20.0711i	1.19180	−	0.669781i
$899$	−33.0103	+	21.2144i	−1.10095	+	0.707541i
$900$	−3.50090	−	2.88700i	−0.116697	−	0.0962333i
$901$	22.1432	+	10.1125i	0.737696	+	0.336895i
$902$	0.721884	+	0.704475i	0.0240361	+	0.0234565i
$903$	8.52730	−	3.89429i	0.283771	−	0.129594i
$904$	−21.6788	−	26.8514i	−0.721026	−	0.893066i
$905$	0.661890	+	4.60355i	0.0220020	+	0.153027i
$906$	−1.97668	−	8.58107i	−0.0656709	−	0.285087i
$907$	8.39354	+	7.27304i	0.278703	+	0.241497i	0.782984	−	0.622042i	$-0.213697\pi$
$907$	8.39354	+	7.27304i	0.278703	+	0.241497i	−0.504281	+	0.863540i	$0.668242\pi$
$908$	3.26238	+	6.70548i	0.108266	+	0.222529i
$909$	−16.1772	+	25.1723i	−0.536565	+	0.834911i
$910$	−26.1061	−	5.34620i	−0.865408	−	0.177225i
$911$	−6.60035	−	1.93804i	−0.218679	−	0.0642100i	0.170558	−	0.985348i	$-0.445443\pi$
$911$	−6.60035	−	1.93804i	−0.218679	−	0.0642100i	−0.389237	+	0.921138i	$0.627261\pi$
$912$	−1.15567	−	1.61872i	−0.0382679	−	0.0536013i
$913$	−1.35642	−	1.56540i	−0.0448911	−	0.0518070i
$914$	2.53656	−	3.47609i	0.0839020	−	0.114979i
$915$	−8.01375	+	2.35305i	−0.264926	+	0.0777894i
$916$	6.51791	+	9.61756i	0.215358	+	0.317773i
$917$	7.95367	−	55.3190i	0.262653	−	1.82679i
$918$	14.9547	+	7.93050i	0.493578	+	0.261745i
$919$	−46.6766			−1.53972			−0.769859	−	0.638214i	$-0.779674\pi$
$919$	−46.6766			−1.53972			−0.769859	+	0.638214i	$0.779674\pi$
$920$	−7.44393	−	11.3397i	−0.245419	−	0.373858i
$921$	−11.1137			−0.366210
$922$	−26.4476	−	14.0252i	−0.871004	−	0.461895i
$923$	4.37555	−	30.4326i	0.144023	−	1.00170i
$924$	−1.42084	+	0.962917i	−0.0467422	+	0.0316776i
$925$	8.78628	−	2.57989i	0.288891	−	0.0848261i
$926$	30.1208	−	41.2774i	0.989832	−	1.35646i
$927$	−23.3109	−	26.9022i	−0.765629	−	0.883583i
$928$	43.9234	+	20.6125i	1.44186	+	0.676640i
$929$	−28.2894	−	8.30651i	−0.928144	−	0.272528i	−0.217485	−	0.976064i	$-0.569785\pi$
$929$	−28.2894	−	8.30651i	−0.928144	−	0.272528i	−0.710660	+	0.703536i	$0.751603\pi$
$930$	−5.41967	−	1.10988i	−0.177718	−	0.0363944i
$931$	4.14364	−	6.44764i	0.135802	−	0.211313i
$932$	−25.6228	+	12.4661i	−0.839304	+	0.408342i
$933$	17.8730	+	15.4871i	0.585137	+	0.507024i
$934$	−1.20231	−	5.21939i	−0.0393407	−	0.170784i
$935$	0.0844770	+	0.587550i	0.00276269	+	0.0192149i
$936$	−16.9094	−	20.9440i	−0.552700	−	0.684576i
$937$	−39.4234	+	18.0041i	−1.28791	+	0.588168i	−0.937355	−	0.348376i	$-0.886733\pi$
$937$	−39.4234	+	18.0041i	−1.28791	+	0.588168i	−0.350552	+	0.936543i	$0.614006\pi$
$938$	−32.5692	−	31.7838i	−1.06342	−	1.03778i
$939$	13.0962	+	5.98085i	0.427379	+	0.195178i
$940$	0.510274	−	0.618780i	0.0166433	−	0.0201824i
$941$	−47.4459	+	30.4916i	−1.54669	+	0.993999i	−0.560546	+	0.828123i	$0.689409\pi$
$941$	−47.4459	+	30.4916i	−1.54669	+	0.993999i	−0.986147	+	0.165876i	$0.946955\pi$
$942$	11.3340	−	6.36963i	0.369282	−	0.207534i
$943$	6.97286	+	13.6296i	0.227068	+	0.443841i
$944$	−11.0814	−	21.4307i	−0.360668	−	0.697508i
$945$	−17.0256	+	10.9417i	−0.553842	+	0.355932i
$946$	0.278283	+	0.719175i	0.00904777	+	0.0233824i
$947$	−16.7172	+	36.6055i	−0.543236	+	1.18952i	0.416634	+	0.909074i	$0.363210\pi$
$947$	−16.7172	+	36.6055i	−0.543236	+	1.18952i	−0.959870	+	0.280446i	$0.909518\pi$
$948$	−3.85632	+	14.4272i	−0.125247	+	0.468573i
$949$	8.39915	−	3.83576i	0.272648	−	0.124514i
$950$	0.277969	−	0.773985i	0.00901851	−	0.0251114i
$951$	−17.3760	+	2.49829i	−0.563456	+	0.0810127i
$952$	32.0393	+	10.6311i	1.03840	+	0.344557i
$953$	24.3207	+	21.0740i	0.787825	+	0.682654i	0.952785	−	0.303646i	$-0.0982041\pi$
$953$	24.3207	+	21.0740i	0.787825	+	0.682654i	−0.164960	+	0.986300i	$0.552750\pi$
$954$	−29.3480	−	1.73928i	−0.950176	−	0.0563114i
$955$	−3.65973	−	2.35196i	−0.118426	−	0.0761078i
$956$	−0.132961	+	0.0425923i	−0.00430026	+	0.00137753i
$957$	1.57221	+	0.461641i	0.0508222	+	0.0149227i
$958$	36.9476	+	48.1206i	1.19372	+	1.55471i
$959$	−56.6857	+	49.1184i	−1.83048	+	1.58612i
$960$	2.40223	+	6.40482i	0.0775317	+	0.206715i
$961$	−9.66240	+	2.83714i	−0.311690	+	0.0915205i
$962$	54.1311	−	4.53619i	1.74526	−	0.146253i
$963$	21.5159	+	3.09353i	0.693341	+	0.0996875i
$964$	41.2832	−	1.00791i	1.32964	−	0.0324627i
$965$	1.46389			0.0471244
$966$	−25.1017	+	6.97109i	−0.807634	+	0.224291i
$967$			23.3377i			0.750491i	0.926925	+	0.375246i	$0.122442\pi$
$967$			23.3377i			0.750491i	−0.926925	+	0.375246i	$0.877558\pi$
$968$	15.8282	+	26.6215i	0.508737	+	0.855646i
$969$	−0.188004	+	1.30760i	−0.00603957	+	0.0420062i
$970$	−21.3864	+	1.79218i	−0.686676	+	0.0575435i
$971$	−9.90075	−	33.7189i	−0.317730	−	1.08209i	−0.951265	−	0.308375i	$-0.900215\pi$
$971$	−9.90075	−	33.7189i	−0.317730	−	1.08209i	0.633535	−	0.773714i	$-0.281603\pi$
$972$	−31.8590	−	3.78951i	−1.02188	−	0.121549i
$973$	49.7562	+	57.4217i	1.59511	+	1.84086i
$974$	−11.7443	+	9.01741i	−0.376312	+	0.288936i
$975$	−1.01047	+	3.44134i	−0.0323609	+	0.110211i
$976$	−37.9810	−	9.16506i	−1.21574	−	0.293366i
$977$	6.57158	−	10.2256i	0.210244	−	0.327145i	−0.720076	−	0.693895i	$-0.755893\pi$
$977$	6.57158	−	10.2256i	0.210244	−	0.327145i	0.930320	+	0.366750i	$0.119529\pi$
$978$	8.79166	+	0.521031i	0.281126	+	0.0166607i
$979$	−1.18778	+	1.37077i	−0.0379616	+	0.0438100i
$980$	−19.4942	+	17.7431i	−0.622718	+	0.566783i
$981$	4.67296	+	32.5011i	0.149196	+	1.03768i
$982$	49.4242	+	17.7502i	1.57719	+	0.566433i
$983$	−7.95399	−	17.4168i	−0.253693	−	0.555510i	0.739342	−	0.673330i	$-0.235137\pi$
$983$	−7.95399	−	17.4168i	−0.253693	−	0.555510i	−0.993035	+	0.117820i	$0.962409\pi$
$984$	−1.91617	−	7.47893i	−0.0610853	−	0.238419i
$985$	21.1689	+	9.66753i	0.674499	+	0.308033i
$986$	−11.6297	−	30.0551i	−0.370366	−	0.957148i
$987$	−0.832784	−	1.29584i	−0.0265078	−	0.0412469i
$988$	2.53652	−	4.16714i	0.0806974	−	0.132574i
$989$	0.520482	+	11.6929i	0.0165504	+	0.371813i
$990$	−0.351223	−	0.624960i	−0.0111626	−	0.0198625i
$991$	10.8487	+	16.8810i	0.344622	+	0.536242i	0.969693	−	0.244326i	$-0.0785666\pi$
$991$	10.8487	+	16.8810i	0.344622	+	0.536242i	−0.625072	+	0.780567i	$0.714930\pi$
$992$	−19.3816	−	17.1495i	−0.615365	−	0.544497i
$993$	1.44168	−	3.15685i	0.0457505	−	0.100180i
$994$	−33.3266	−	32.5228i	−1.05705	−	1.03156i
$995$	6.56995	+	14.3862i	0.208282	+	0.456073i
$996$	2.63864	+	15.6331i	0.0836085	+	0.495354i
$997$	29.2402	−	4.20411i	0.926047	−	0.133145i	0.337239	−	0.941419i	$-0.390507\pi$
$997$	29.2402	−	4.20411i	0.926047	−	0.133145i	0.588807	+	0.808274i	$0.299598\pi$
$998$	26.7405	−	6.15977i	0.846455	−	0.194984i
$999$	27.0164	−	31.1786i	0.854761	−	0.986447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.17	✓	480
8.3	odd	2		920.2.bb.b.11.1	yes	480
23.21	odd	22		920.2.bb.b.251.1	yes	480
184.67	even	22	inner	920.2.bb.a.251.17	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.17	✓	480	1.1	even	1	trivial
920.2.bb.a.251.17	yes	480	184.67	even	22	inner
920.2.bb.b.11.1	yes	480	8.3	odd	2
920.2.bb.b.251.1	yes	480	23.21	odd	22

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.662561 + 1.24940i) q^{2} +(0.121688 - 0.846359i) q^{3} +(-1.12203 - 1.65561i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.976819 + 0.712802i) q^{6} +(2.94177 + 3.39498i) q^{7} +(2.81194 - 0.304917i) q^{8} +(2.17696 + 0.639214i) q^{9} +(0.283725 - 1.38546i) q^{10} +(0.120792 - 0.187956i) q^{11} +(-1.53778 + 0.748167i) q^{12} +(-3.17005 - 2.74686i) q^{13} +(-6.19081 + 1.42608i) q^{14} +(0.121688 + 0.846359i) q^{15} +(-1.48212 + 3.71528i) q^{16} +(2.41671 - 1.10368i) q^{17} +(-2.24101 + 2.29639i) q^{18} +(-0.528965 - 0.241570i) q^{19} +(1.54302 + 1.27244i) q^{20} +(3.23135 - 2.07666i) q^{21} +(0.154801 + 0.275450i) q^{22} +(0.892936 + 4.71197i) q^{23} +(0.0841103 - 2.41702i) q^{24} +(0.841254 - 0.540641i) q^{25} +(5.53229 - 2.14071i) q^{26} +(1.87153 - 4.09808i) q^{27} +(2.32004 - 8.67969i) q^{28} +(-7.80202 + 3.56306i) q^{29} +(-1.13807 - 0.408727i) q^{30} +(4.52833 - 0.651076i) q^{31} +(-3.65990 - 4.31337i) q^{32} +(-0.144379 - 0.125105i) q^{33} +(-0.222283 + 3.75071i) q^{34} +(-3.77908 - 2.42867i) q^{35} +(-1.38432 - 4.32143i) q^{36} +(8.78628 + 2.57989i) q^{37} +(0.652291 - 0.500836i) q^{38} +(-2.71059 + 2.34874i) q^{39} +(-2.61213 + 1.08478i) q^{40} +(3.06298 - 0.899372i) q^{41} +(0.453625 + 5.41318i) q^{42} +(2.41571 + 0.347327i) q^{43} +(-0.446714 + 0.0109063i) q^{44} -2.26887 q^{45} +(-6.47878 - 2.00633i) q^{46} -0.401020i q^{47} +(2.96411 + 1.70651i) q^{48} +(-1.87570 + 13.0458i) q^{49} +(0.118097 + 1.40927i) q^{50} +(-0.640021 - 2.17971i) q^{51} +(-0.990872 + 8.33043i) q^{52} +(6.00018 + 6.92457i) q^{53} +(3.88016 + 5.05353i) q^{54} +(-0.0629457 + 0.214373i) q^{55} +(9.30728 + 8.64950i) q^{56} +(-0.268824 + 0.418298i) q^{57} +(0.717608 - 12.1086i) q^{58} +(-3.94981 + 4.55833i) q^{59} +(1.26471 - 1.15110i) q^{60} +(1.39010 + 9.66837i) q^{61} +(-2.18684 + 6.08910i) q^{62} +(4.23400 + 9.27117i) q^{63} +(7.81405 - 1.71482i) q^{64} +(3.81552 + 1.74249i) q^{65} +(0.251967 - 0.0974981i) q^{66} +(3.87276 + 6.02613i) q^{67} +(-4.53887 - 2.76279i) q^{68} +(4.09668 - 0.182354i) q^{69} +(5.53827 - 3.11246i) q^{70} +(3.96281 + 6.16625i) q^{71} +(6.31641 + 1.13364i) q^{72} +(-0.914458 + 2.00238i) q^{73} +(-9.04477 + 9.26829i) q^{74} +(-0.355206 - 0.777792i) q^{75} +(0.193565 + 1.14681i) q^{76} +(0.993448 - 0.142836i) q^{77} +(-1.13859 - 4.94281i) q^{78} +(5.71857 - 6.59958i) q^{79} +(0.375367 - 3.98235i) q^{80} +(2.48537 + 1.59725i) q^{81} +(-0.905732 + 4.42279i) q^{82} +(2.61189 - 8.89527i) q^{83} +(-7.06381 - 3.01980i) q^{84} +(-2.00788 + 1.73984i) q^{85} +(-2.03451 + 2.78808i) q^{86} +(2.06622 + 7.03689i) q^{87} +(0.282349 - 0.565353i) q^{88} +(-8.03553 - 1.15534i) q^{89} +(1.50326 - 2.83474i) q^{90} -18.8429i q^{91} +(6.79931 - 6.76531i) q^{92} -3.91182i q^{93} +(0.501036 + 0.265700i) q^{94} +(0.575596 + 0.0827582i) q^{95} +(-4.09602 + 2.57270i) q^{96} +(-4.27542 - 14.5608i) q^{97} +(-15.0567 - 10.9871i) q^{98} +(0.383103 - 0.331961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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