LMFDB - Embedded newform 475.2.l.f.351.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.2
Character	$\chi$	$=$	475.351
Dual form			475.2.l.f.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.256855 - 1.45670i) q^{2} +(1.90225 - 1.59617i) q^{3} +(-0.176607 + 0.0642796i) q^{4} +(-2.81374 - 2.36101i) q^{6} +(1.62494 - 2.81448i) q^{7} +(-1.34017 - 2.32124i) q^{8} +(0.549824 - 3.11821i) q^{9} +O(q^{10})$	\(q+(-0.256855 - 1.45670i) q^{2} +(1.90225 - 1.59617i) q^{3} +(-0.176607 + 0.0642796i) q^{4} +(-2.81374 - 2.36101i) q^{6} +(1.62494 - 2.81448i) q^{7} +(-1.34017 - 2.32124i) q^{8} +(0.549824 - 3.11821i) q^{9} +(2.09200 + 3.62344i) q^{11} +(-0.233348 + 0.404171i) q^{12} +(1.36673 + 1.14682i) q^{13} +(-4.51721 - 1.64413i) q^{14} +(-3.32506 + 2.79006i) q^{16} +(1.09959 + 6.23606i) q^{17} -4.68351 q^{18} +(-4.09399 + 1.49640i) q^{19} +(-1.40136 - 7.94751i) q^{21} +(4.74092 - 3.97810i) q^{22} +(-1.34721 + 0.490346i) q^{23} +(-6.25444 - 2.27643i) q^{24} +(1.31952 - 2.28547i) q^{26} +(-0.206494 - 0.357658i) q^{27} +(-0.106062 + 0.601506i) q^{28} +(-0.0589345 + 0.334234i) q^{29} +(1.38932 - 2.40638i) q^{31} +(0.811808 + 0.681187i) q^{32} +(9.76313 + 3.55349i) q^{33} +(8.80161 - 3.20352i) q^{34} +(0.103335 + 0.586040i) q^{36} -2.70482 q^{37} +(3.23137 + 5.57935i) q^{38} +4.43037 q^{39} +(-5.46819 + 4.58835i) q^{41} +(-11.2172 + 4.08271i) q^{42} +(-9.29755 - 3.38403i) q^{43} +(-0.602374 - 0.505452i) q^{44} +(1.06032 + 1.83654i) q^{46} +(-0.0773501 + 0.438674i) q^{47} +(-1.87167 + 10.6148i) q^{48} +(-1.78085 - 3.08452i) q^{49} +(12.0455 + 10.1074i) q^{51} +(-0.315090 - 0.114683i) q^{52} +(6.80087 - 2.47532i) q^{53} +(-0.467960 + 0.392665i) q^{54} -8.71078 q^{56} +(-5.39926 + 9.38125i) q^{57} +0.502015 q^{58} +(0.545712 + 3.09489i) q^{59} +(2.88074 - 1.04850i) q^{61} +(-3.86222 - 1.40573i) q^{62} +(-7.88269 - 6.61436i) q^{63} +(-3.55679 + 6.16055i) q^{64} +(2.66865 - 15.1347i) q^{66} +(1.48513 - 8.42261i) q^{67} +(-0.595046 - 1.03065i) q^{68} +(-1.78006 + 3.08315i) q^{69} +(-12.1153 - 4.40959i) q^{71} +(-7.97498 + 2.90266i) q^{72} +(-1.39594 + 1.17133i) q^{73} +(0.694747 + 3.94011i) q^{74} +(0.626839 - 0.527435i) q^{76} +13.5974 q^{77} +(-1.13796 - 6.45371i) q^{78} +(0.535235 - 0.449116i) q^{79} +(7.96239 + 2.89807i) q^{81} +(8.08837 + 6.78695i) q^{82} +(0.276493 - 0.478899i) q^{83} +(0.758353 + 1.31351i) q^{84} +(-2.54139 + 14.4129i) q^{86} +(0.421388 + 0.729865i) q^{87} +(5.60726 - 9.71206i) q^{88} +(5.23109 + 4.38940i) q^{89} +(5.44854 - 1.98311i) q^{91} +(0.206408 - 0.173197i) q^{92} +(-1.19816 - 6.79513i) q^{93} +0.658883 q^{94} +2.63155 q^{96} +(-2.29226 - 13.0001i) q^{97} +(-4.03579 + 3.38643i) q^{98} +(12.4489 - 4.53102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.256855	−	1.45670i	−0.181624	−	1.03004i	−0.930217	−	0.367010i	$-0.880381\pi$
$2$	−0.256855	−	1.45670i	−0.181624	−	1.03004i	0.748593	−	0.663030i	$-0.230730\pi$
$3$	1.90225	−	1.59617i	1.09826	−	0.921552i	0.100955	−	0.994891i	$-0.467810\pi$
$3$	1.90225	−	1.59617i	1.09826	−	0.921552i	0.997307	+	0.0733394i	$0.0233656\pi$
$4$	−0.176607	+	0.0642796i	−0.0883034	+	0.0321398i
$5$		0			0
$5$		0			0
$6$	−2.81374	−	2.36101i	−1.14871	−	0.963879i
$7$	1.62494	−	2.81448i	0.614169	−	1.06377i	−0.376361	−	0.926473i	$-0.622825\pi$
$7$	1.62494	−	2.81448i	0.614169	−	1.06377i	0.990530	−	0.137298i	$-0.0438419\pi$
$8$	−1.34017	−	2.32124i	−0.473822	−	0.820684i
$9$	0.549824	−	3.11821i	0.183275	−	1.03940i
$10$		0			0
$11$	2.09200	+	3.62344i	0.630760	+	1.09251i	0.987397	+	0.158265i	$0.0505902\pi$
$11$	2.09200	+	3.62344i	0.630760	+	1.09251i	−0.356636	+	0.934243i	$0.616076\pi$
$12$	−0.233348	+	0.404171i	−0.0673618	+	0.116674i
$13$	1.36673	+	1.14682i	0.379062	+	0.318070i	0.812334	−	0.583193i	$-0.198197\pi$
$13$	1.36673	+	1.14682i	0.379062	+	0.318070i	−0.433272	+	0.901263i	$0.642641\pi$
$14$	−4.51721	−	1.64413i	−1.20728	−	0.439412i
$15$		0			0
$16$	−3.32506	+	2.79006i	−0.831266	+	0.697515i
$17$	1.09959	+	6.23606i	0.266689	+	1.51247i	0.764183	+	0.644999i	$0.223142\pi$
$17$	1.09959	+	6.23606i	0.266689	+	1.51247i	−0.497495	+	0.867467i	$0.665747\pi$
$18$	−4.68351			−1.10391
$19$	−4.09399	+	1.49640i	−0.939226	+	0.343298i
$19$	−4.09399	+	1.49640i	−0.939226	+	0.343298i
$20$		0			0
$21$	−1.40136	−	7.94751i	−0.305802	−	1.73429i
$22$	4.74092	−	3.97810i	1.01077	−	0.848134i
$23$	−1.34721	+	0.490346i	−0.280914	+	0.102244i	−0.478635	−	0.878014i	$-0.658868\pi$
$23$	−1.34721	+	0.490346i	−0.280914	+	0.102244i	0.197721	+	0.980258i	$0.436646\pi$
$24$	−6.25444	−	2.27643i	−1.27668	−	0.464675i
$25$		0			0
$26$	1.31952	−	2.28547i	0.258779	−	0.448218i
$27$	−0.206494	−	0.357658i	−0.0397398	−	0.0688313i
$28$	−0.106062	+	0.601506i	−0.0200438	+	0.113674i
$29$	−0.0589345	+	0.334234i	−0.0109439	+	0.0620657i	−0.989791	−	0.142529i	$-0.954477\pi$
$29$	−0.0589345	+	0.334234i	−0.0109439	+	0.0620657i	0.978847	+	0.204595i	$0.0655877\pi$
$30$		0			0
$31$	1.38932	−	2.40638i	0.249530	−	0.432199i	−0.713866	−	0.700283i	$-0.753057\pi$
$31$	1.38932	−	2.40638i	0.249530	−	0.432199i	0.963395	+	0.268084i	$0.0863906\pi$
$32$	0.811808	+	0.681187i	0.143509	+	0.120418i
$33$	9.76313	+	3.55349i	1.69954	+	0.618583i
$34$	8.80161	−	3.20352i	1.50946	−	0.549400i
$35$		0			0
$36$	0.103335	+	0.586040i	0.0172224	+	0.0976733i
$37$	−2.70482			−0.444670			−0.222335	−	0.974970i	$-0.571368\pi$
$37$	−2.70482			−0.444670			−0.222335	+	0.974970i	$0.571368\pi$
$38$	3.23137	+	5.57935i	0.524197	+	0.905090i
$39$	4.43037			0.709427
$40$		0			0
$41$	−5.46819	+	4.58835i	−0.853987	+	0.716581i	−0.960664	−	0.277713i	$-0.910423\pi$
$41$	−5.46819	+	4.58835i	−0.853987	+	0.716581i	0.106677	+	0.994294i	$0.465979\pi$
$42$	−11.2172	+	4.08271i	−1.73085	+	0.629977i
$43$	−9.29755	−	3.38403i	−1.41786	−	0.516060i	−0.484436	−	0.874827i	$-0.660975\pi$
$43$	−9.29755	−	3.38403i	−1.41786	−	0.516060i	−0.933427	+	0.358767i	$0.883197\pi$
$44$	−0.602374	−	0.505452i	−0.0908113	−	0.0761997i
$45$		0			0
$46$	1.06032	+	1.83654i	0.156336	+	0.270782i
$47$	−0.0773501	+	0.438674i	−0.0112827	+	0.0639872i	−0.989929	−	0.141563i	$-0.954787\pi$
$47$	−0.0773501	+	0.438674i	−0.0112827	+	0.0639872i	0.978647	+	0.205550i	$0.0658984\pi$
$48$	−1.87167	+	10.6148i	−0.270152	+	1.53211i
$49$	−1.78085	−	3.08452i	−0.254407	−	0.440645i
$50$		0			0
$51$	12.0455	+	10.1074i	1.68671	+	1.41532i
$52$	−0.315090	−	0.114683i	−0.0436952	−	0.0159037i
$53$	6.80087	−	2.47532i	0.934172	−	0.340011i	0.170310	−	0.985391i	$-0.445523\pi$
$53$	6.80087	−	2.47532i	0.934172	−	0.340011i	0.763862	+	0.645380i	$0.223301\pi$
$54$	−0.467960	+	0.392665i	−0.0636813	+	0.0534350i
$55$		0			0
$56$	−8.71078			−1.16403
$57$	−5.39926	+	9.38125i	−0.715150	+	1.24258i
$58$	0.502015			0.0659178
$59$	0.545712	+	3.09489i	0.0710457	+	0.402920i	0.999504	+	0.0314842i	$0.0100234\pi$
$59$	0.545712	+	3.09489i	0.0710457	+	0.402920i	−0.928459	+	0.371436i	$0.878866\pi$
$60$		0			0
$61$	2.88074	−	1.04850i	0.368841	−	0.134247i	−0.150948	−	0.988542i	$-0.548233\pi$
$61$	2.88074	−	1.04850i	0.368841	−	0.134247i	0.519789	+	0.854295i	$0.326010\pi$
$62$	−3.86222	−	1.40573i	−0.490503	−	0.178528i
$63$	−7.88269	−	6.61436i	−0.993126	−	0.833331i
$64$	−3.55679	+	6.16055i	−0.444599	+	0.770068i
$65$		0			0
$66$	2.66865	−	15.1347i	0.328488	−	1.86295i
$67$	1.48513	−	8.42261i	0.181438	−	1.02899i	−0.749009	−	0.662559i	$-0.769470\pi$
$67$	1.48513	−	8.42261i	0.181438	−	1.02899i	0.930447	−	0.366426i	$-0.119419\pi$
$68$	−0.595046	−	1.03065i	−0.0721599	−	0.124985i
$69$	−1.78006	+	3.08315i	−0.214294	+	0.371167i
$70$		0			0
$71$	−12.1153	−	4.40959i	−1.43782	−	0.523322i	−0.498656	−	0.866800i	$-0.666173\pi$
$71$	−12.1153	−	4.40959i	−1.43782	−	0.523322i	−0.939161	+	0.343478i	$0.888395\pi$
$72$	−7.97498	+	2.90266i	−0.939861	+	0.342081i
$73$	−1.39594	+	1.17133i	−0.163382	+	0.137094i	−0.720813	−	0.693129i	$-0.756232\pi$
$73$	−1.39594	+	1.17133i	−0.163382	+	0.137094i	0.557431	+	0.830223i	$0.311787\pi$
$74$	0.694747	+	3.94011i	0.0807627	+	0.458028i
$75$		0			0
$76$	0.626839	−	0.527435i	0.0719034	−	0.0605010i
$77$	13.5974			1.54957
$78$	−1.13796	−	6.45371i	−0.128849	−	0.730739i
$79$	0.535235	−	0.449116i	0.0602187	−	0.0505295i	−0.612182	−	0.790717i	$-0.709708\pi$
$79$	0.535235	−	0.449116i	0.0602187	−	0.0505295i	0.672400	+	0.740188i	$0.265263\pi$
$80$		0			0
$81$	7.96239	+	2.89807i	0.884710	+	0.322008i
$82$	8.08837	+	6.78695i	0.893211	+	0.749493i
$83$	0.276493	−	0.478899i	0.0303490	−	0.0525660i	−0.850452	−	0.526053i	$-0.823671\pi$
$83$	0.276493	−	0.478899i	0.0303490	−	0.0525660i	0.880801	+	0.473487i	$0.157005\pi$
$84$	0.758353	+	1.31351i	0.0827431	+	0.143315i
$85$		0			0
$86$	−2.54139	+	14.4129i	−0.274045	+	1.55419i
$87$	0.421388	+	0.729865i	0.0451775	+	0.0782497i
$88$	5.60726	−	9.71206i	0.597736	−	1.03531i
$89$	5.23109	+	4.38940i	0.554494	+	0.465276i	0.876459	−	0.481476i	$-0.159899\pi$
$89$	5.23109	+	4.38940i	0.554494	+	0.465276i	−0.321965	+	0.946751i	$0.604343\pi$
$90$		0			0
$91$	5.44854	−	1.98311i	0.571162	−	0.207886i
$92$	0.206408	−	0.173197i	0.0215195	−	0.0180570i
$93$	−1.19816	−	6.79513i	−0.124244	−	0.704622i
$94$	0.658883			0.0679586
$95$		0			0
$96$	2.63155			0.268582
$97$	−2.29226	−	13.0001i	−0.232744	−	1.31996i	−0.847313	−	0.531094i	$-0.821781\pi$
$97$	−2.29226	−	13.0001i	−0.232744	−	1.31996i	0.614569	−	0.788863i	$-0.289330\pi$
$98$	−4.03579	+	3.38643i	−0.407676	+	0.342081i
$99$	12.4489	−	4.53102i	1.25116	−	0.455385i
$100$		0			0
$101$	13.2339	+	11.1046i	1.31683	+	1.10495i	0.986968	+	0.160916i	$0.0514450\pi$
$101$	13.2339	+	11.1046i	1.31683	+	1.10495i	0.329857	+	0.944031i	$0.392999\pi$
$102$	11.6294	−	20.1428i	1.15149	−	1.99443i
$103$	−6.91430	−	11.9759i	−0.681286	−	1.18002i	−0.974589	−	0.224003i	$-0.928088\pi$
$103$	−6.91430	−	11.9759i	−0.681286	−	1.18002i	0.293302	−	0.956020i	$-0.405246\pi$
$104$	0.830401	−	4.70944i	0.0814275	−	0.461798i
$105$		0			0
$106$	−5.35262	−	9.27101i	−0.519893	−	0.900481i
$107$	1.63230	−	2.82722i	0.157800	−	0.273318i	−0.776275	−	0.630394i	$-0.782893\pi$
$107$	1.63230	−	2.82722i	0.157800	−	0.273318i	0.934075	+	0.357077i	$0.116226\pi$
$108$	0.0594584	+	0.0498915i	0.00572138	+	0.00480081i
$109$	3.02669	+	1.10163i	0.289905	+	0.105517i	0.482879	−	0.875687i	$-0.339591\pi$
$109$	3.02669	+	1.10163i	0.289905	+	0.105517i	−0.192974	+	0.981204i	$0.561813\pi$
$110$		0			0
$111$	−5.14524	+	4.31737i	−0.488364	+	0.409786i
$112$	2.44953	+	13.8920i	0.231459	+	1.31267i
$113$	4.71007			0.443086			0.221543	−	0.975151i	$-0.428891\pi$
$113$	4.71007			0.443086			0.221543	+	0.975151i	$0.428891\pi$
$114$	15.0525	+	5.45547i	1.40979	+	0.510952i
$115$		0			0
$116$	−0.0110762	−	0.0628163i	−0.00102840	−	0.00583234i
$117$	4.32748	−	3.63119i	0.400076	−	0.335704i
$118$	4.36815	−	1.58988i	0.402121	−	0.146360i
$119$	19.3380	+	7.03845i	1.77271	+	0.645214i
$120$		0			0
$121$	−3.25289	+	5.63416i	−0.295717	+	0.512197i
$122$	−2.26729	−	3.92705i	−0.205270	−	0.355539i
$123$	−3.07803	+	17.4564i	−0.277536	+	1.57399i
$124$	−0.0906829	+	0.514288i	−0.00814356	+	0.0461844i
$125$		0			0
$126$	−7.61042	+	13.1816i	−0.677990	+	1.17431i
$127$	0.453507	+	0.380538i	0.0402423	+	0.0337673i	0.662687	−	0.748897i	$-0.269416\pi$
$127$	0.453507	+	0.380538i	0.0402423	+	0.0337673i	−0.622445	+	0.782664i	$0.713860\pi$
$128$	11.8793	+	4.32371i	1.04999	+	0.382165i
$129$	−23.0877	+	8.40325i	−2.03276	+	0.739865i
$130$		0			0
$131$	−3.56830	−	20.2369i	−0.311764	−	1.76810i	−0.589817	−	0.807537i	$-0.700800\pi$
$131$	−3.56830	−	20.2369i	−0.311764	−	1.76810i	0.278053	−	0.960566i	$-0.410311\pi$
$132$	−1.95265			−0.169957
$133$	−2.44090	+	13.9540i	−0.211653	+	1.20997i
$134$	−12.6507			−1.09285
$135$		0			0
$136$	13.0018	−	10.9098i	1.11489	−	0.935506i
$137$	−8.22613	+	2.99407i	−0.702806	+	0.255800i	−0.668608	−	0.743615i	$-0.733110\pi$
$137$	−8.22613	+	2.99407i	−0.702806	+	0.255800i	−0.0341973	+	0.999415i	$0.510887\pi$
$138$	4.94843	+	1.80108i	0.421238	+	0.153318i
$139$	5.89041	+	4.94264i	0.499618	+	0.419229i	0.857458	−	0.514553i	$-0.172042\pi$
$139$	5.89041	+	4.94264i	0.499618	+	0.419229i	−0.357840	+	0.933783i	$0.616487\pi$
$140$		0			0
$141$	0.553061	+	0.957930i	0.0465762	+	0.0806723i
$142$	−3.31158	+	18.7809i	−0.277901	+	1.57606i
$143$	−1.29625	+	7.35139i	−0.108398	+	0.614754i
$144$	6.87178	+	11.9023i	0.572649	+	0.991857i
$145$		0			0
$146$	2.06483	+	1.73260i	0.170887	+	0.143391i
$147$	−8.31104	−	3.02497i	−0.685483	−	0.249495i
$148$	0.477690	−	0.173865i	0.0392659	−	0.0142916i
$149$	−11.4457	+	9.60412i	−0.937672	+	0.786800i	−0.977179	−	0.212419i	$-0.931866\pi$
$149$	−11.4457	+	9.60412i	−0.937672	+	0.786800i	0.0395067	+	0.999219i	$0.487421\pi$
$150$		0			0
$151$	13.1424			1.06951			0.534757	−	0.845006i	$-0.320403\pi$
$151$	13.1424			1.06951			0.534757	+	0.845006i	$0.320403\pi$
$152$	8.96017	+	7.49772i	0.726765	+	0.608145i
$153$	20.0499			1.62094
$154$	−3.49257	−	19.8074i	−0.281440	−	1.59612i
$155$		0			0
$156$	−0.782434	+	0.284783i	−0.0626449	+	0.0228009i
$157$	−10.1836	−	3.70654i	−0.812742	−	0.295814i	−0.0979861	−	0.995188i	$-0.531240\pi$
$157$	−10.1836	−	3.70654i	−0.812742	−	0.295814i	−0.714756	+	0.699374i	$0.753462\pi$
$158$	−0.791704	−	0.664318i	−0.0629846	−	0.0528503i
$159$	8.98590	−	15.5640i	0.712628	−	1.23431i
$160$		0			0
$161$	−0.809073	+	4.58848i	−0.0637639	+	0.361623i
$162$	2.17644	−	12.3432i	0.170997	−	0.969772i
$163$	−4.22277	−	7.31405i	−0.330753	−	0.572881i	0.651907	−	0.758299i	$-0.273969\pi$
$163$	−4.22277	−	7.31405i	−0.330753	−	0.572881i	−0.982660	+	0.185418i	$0.940636\pi$
$164$	0.670782	−	1.16183i	0.0523792	−	0.0907235i
$165$		0			0
$166$	−0.768630	−	0.279758i	−0.0596573	−	0.0217135i
$167$	18.7011	−	6.80663i	1.44713	−	0.526713i	0.505343	−	0.862919i	$-0.331366\pi$
$167$	18.7011	−	6.80663i	1.44713	−	0.526713i	0.941788	+	0.336206i	$0.109144\pi$
$168$	−16.5700	+	13.9039i	−1.27841	+	1.07271i
$169$	−1.70468	−	9.66772i	−0.131129	−	0.743671i
$170$		0			0
$171$	2.41512	+	13.5887i	0.184689	+	1.03915i
$172$	1.85954			0.141788
$173$	2.03534	+	11.5430i	0.154744	+	0.877597i	0.959019	+	0.283340i	$0.0914426\pi$
$173$	2.03534	+	11.5430i	0.154744	+	0.877597i	−0.804275	+	0.594257i	$0.797446\pi$
$174$	0.954956	−	0.801304i	0.0723951	−	0.0607467i
$175$		0			0
$176$	−17.0656	−	6.21138i	−1.28637	−	0.468200i
$177$	5.97806	+	5.01619i	0.449339	+	0.377040i
$178$	5.05040	−	8.74755i	0.378544	−	0.655657i
$179$	−3.54189	−	6.13473i	−0.264733	−	0.458532i	0.702760	−	0.711427i	$-0.251951\pi$
$179$	−3.54189	−	6.13473i	−0.264733	−	0.458532i	−0.967494	+	0.252895i	$0.918617\pi$
$180$		0			0
$181$	1.61176	−	9.14076i	0.119801	−	0.679427i	−0.864459	−	0.502703i	$-0.832339\pi$
$181$	1.61176	−	9.14076i	0.119801	−	0.679427i	0.984260	−	0.176724i	$-0.0565500\pi$
$182$	−4.28827	−	7.42750i	−0.317868	−	0.550563i
$183$	3.80628	−	6.59268i	0.281369	−	0.487345i
$184$	2.94371	+	2.47007i	0.217013	+	0.182096i
$185$		0			0
$186$	−9.59069	+	3.49073i	−0.703224	+	0.255952i
$187$	−20.2957	+	17.0301i	−1.48417	+	1.24536i
$188$	−0.0145373	−	0.0824448i	−0.00106024	−	0.00601291i
$189$	−1.34216			−0.0976277
$190$		0			0
$191$	8.12426			0.587850			0.293925	−	0.955828i	$-0.405038\pi$
$191$	8.12426			0.587850			0.293925	+	0.955828i	$0.405038\pi$
$192$	3.06741	+	17.3961i	0.221371	+	1.25546i
$193$	5.91649	−	4.96452i	0.425878	−	0.357354i	−0.404516	−	0.914531i	$-0.632560\pi$
$193$	5.91649	−	4.96452i	0.425878	−	0.357354i	0.830394	+	0.557177i	$0.188115\pi$
$194$	−18.3484	+	6.67827i	−1.31734	+	0.479472i
$195$		0			0
$196$	0.512781	+	0.430275i	0.0366272	+	0.0307339i
$197$	−1.78381	+	3.08965i	−0.127091	+	0.220129i	−0.922548	−	0.385881i	$-0.873897\pi$
$197$	−1.78381	+	3.08965i	−0.127091	+	0.220129i	0.795457	+	0.606010i	$0.207231\pi$
$198$	−9.79788	−	16.9704i	−0.696305	−	1.20604i
$199$	−1.52279	+	8.63615i	−0.107947	+	0.612201i	0.882055	+	0.471147i	$0.156160\pi$
$199$	−1.52279	+	8.63615i	−0.107947	+	0.612201i	−0.990002	+	0.141053i	$0.954951\pi$
$200$		0			0
$201$	−10.6189	−	18.3924i	−0.748997	−	1.29730i
$202$	12.7768	−	22.1301i	0.898974	−	1.55707i
$203$	0.844928	+	0.708979i	0.0593023	+	0.0497606i
$204$	−2.77702	−	1.01075i	−0.194430	−	0.0707668i
$205$		0			0
$206$	−15.6693	+	13.1481i	−1.09173	+	0.916073i
$207$	0.788270	+	4.47050i	0.0547885	+	0.310721i
$208$	−7.74414			−0.536960
$209$	−13.9867	−	11.7039i	−0.967483	−	0.809574i
$210$		0			0
$211$	2.05203	+	11.6376i	0.141267	+	0.801167i	0.970289	+	0.241950i	$0.0777870\pi$
$211$	2.05203	+	11.6376i	0.141267	+	0.801167i	−0.829021	+	0.559217i	$0.811102\pi$
$212$	−1.04197	+	0.874315i	−0.0715627	+	0.0600482i
$213$	−30.0847	+	10.9499i	−2.06137	+	0.750277i
$214$	−4.53767	−	1.65158i	−0.310189	−	0.112899i
$215$		0			0
$216$	−0.553474	+	0.958646i	−0.0376592	+	0.0652276i
$217$	−4.51513	−	7.82043i	−0.306507	−	0.530886i
$218$	0.827314	−	4.69193i	0.0560328	−	0.317778i
$219$	−0.785770	+	4.45633i	−0.0530974	+	0.301131i
$220$		0			0
$221$	−5.64880	+	9.78401i	−0.379979	+	0.658144i
$222$	7.61067	+	6.38611i	0.510795	+	0.428608i
$223$	−8.36101	−	3.04316i	−0.559895	−	0.203785i	0.0465426	−	0.998916i	$-0.485180\pi$
$223$	−8.36101	−	3.04316i	−0.559895	−	0.203785i	−0.606437	+	0.795131i	$0.707402\pi$
$224$	3.23632	−	1.17792i	0.216236	−	0.0787034i
$225$		0			0
$226$	−1.20980	−	6.86114i	−0.0804750	−	0.456396i
$227$	−26.4080			−1.75276			−0.876380	−	0.481620i	$-0.840049\pi$
$227$	−26.4080			−1.75276			−0.876380	+	0.481620i	$0.840049\pi$
$228$	0.350523	−	2.00386i	0.0232140	−	0.132709i
$229$	21.7852			1.43961			0.719804	−	0.694177i	$-0.244232\pi$
$229$	21.7852			1.43961			0.719804	+	0.694177i	$0.244232\pi$
$230$		0			0
$231$	25.8657	−	21.7039i	1.70184	−	1.42801i
$232$	0.854821	−	0.311129i	0.0561217	−	0.0204266i
$233$	−9.39780	−	3.42052i	−0.615670	−	0.224086i	0.0153122	−	0.999883i	$-0.495126\pi$
$233$	−9.39780	−	3.42052i	−0.615670	−	0.224086i	−0.630982	+	0.775797i	$0.717348\pi$
$234$	−6.40108	−	5.37114i	−0.418452	−	0.351123i
$235$		0			0
$236$	−0.295315	−	0.511500i	−0.0192234	−	0.0332958i
$237$	0.301282	−	1.70866i	0.0195704	−	0.110989i
$238$	5.28583	−	29.9774i	0.342630	−	1.94315i
$239$	−8.91823	−	15.4468i	−0.576872	−	0.999172i	−0.995835	−	0.0911689i	$-0.970940\pi$
$239$	−8.91823	−	15.4468i	−0.576872	−	0.999172i	0.418963	−	0.908003i	$-0.362394\pi$
$240$		0			0
$241$	−13.1332	−	11.0201i	−0.845984	−	0.709864i	0.112918	−	0.993604i	$-0.463980\pi$
$241$	−13.1332	−	11.0201i	−0.845984	−	0.709864i	−0.958901	+	0.283740i	$0.908425\pi$
$242$	9.04279	+	3.29131i	0.581293	+	0.211573i
$243$	20.9365	−	7.62027i	1.34308	−	0.488840i
$244$	−0.441361	+	0.370346i	−0.0282552	+	0.0237090i
$245$		0			0
$246$	26.2192			1.67168
$247$	−7.31147	−	2.64990i	−0.465218	−	0.168609i
$248$	−7.44772			−0.472931
$249$	−0.238450	−	1.35232i	−0.0151111	−	0.0856995i
$250$		0			0
$251$	−9.11112	+	3.31618i	−0.575089	+	0.209315i	−0.613159	−	0.789960i	$-0.710101\pi$
$251$	−9.11112	+	3.31618i	−0.575089	+	0.209315i	0.0380697	+	0.999275i	$0.487879\pi$
$252$	1.81731	+	0.661445i	0.114480	+	0.0416671i
$253$	−4.59511	−	3.85575i	−0.288892	−	0.242409i
$254$	0.437843	−	0.758366i	0.0274727	−	0.0475841i
$255$		0			0
$256$	0.776555	−	4.40406i	0.0485347	−	0.275254i
$257$	−1.74528	+	9.89795i	−0.108867	+	0.617417i	0.880738	+	0.473605i	$0.157047\pi$
$257$	−1.74528	+	9.89795i	−0.108867	+	0.617417i	−0.989605	+	0.143813i	$0.954064\pi$
$258$	18.1712	+	31.4734i	1.13129	+	1.95945i
$259$	−4.39517	+	7.61265i	−0.273102	+	0.473027i
$260$		0			0
$261$	1.00981	+	0.367540i	0.0625055	+	0.0227501i
$262$	−28.5624	+	10.3959i	−1.76459	+	0.642259i
$263$	−16.7232	+	14.0324i	−1.03120	+	0.865276i	−0.990993	−	0.133916i	$-0.957245\pi$
$263$	−16.7232	+	14.0324i	−1.03120	+	0.865276i	−0.0402026	+	0.999192i	$0.512800\pi$
$264$	−4.83575	−	27.4249i	−0.297620	−	1.68789i
$265$		0			0
$266$	20.9537	−	0.0285081i	1.28475	−	0.00174794i
$267$	16.9571			1.03776
$268$	0.279117	+	1.58295i	0.0170498	+	0.0966943i
$269$	11.8393	−	9.93433i	0.721853	−	0.605707i	−0.206044	−	0.978543i	$-0.566059\pi$
$269$	11.8393	−	9.93433i	0.721853	−	0.605707i	0.927897	+	0.372836i	$0.121615\pi$
$270$		0			0
$271$	−4.85182	−	1.76592i	−0.294727	−	0.107272i	0.190425	−	0.981702i	$-0.439013\pi$
$271$	−4.85182	−	1.76592i	−0.294727	−	0.107272i	−0.485152	+	0.874430i	$0.661236\pi$
$272$	−21.0552	−	17.6674i	−1.27666	−	1.07124i
$273$	7.19908	−	12.4692i	0.435708	−	0.754669i
$274$	6.47437	+	11.2139i	0.391131	+	0.677459i
$275$		0			0
$276$	0.116186	−	0.658926i	0.00699360	−	0.0396627i
$277$	2.78515	+	4.82402i	0.167343	+	0.289847i	0.937485	−	0.348026i	$-0.113148\pi$
$277$	2.78515	+	4.82402i	0.167343	+	0.289847i	−0.770142	+	0.637873i	$0.779814\pi$
$278$	5.68695	−	9.85009i	0.341081	−	0.590769i
$279$	−6.73971	−	5.65529i	−0.403496	−	0.338573i
$280$		0			0
$281$	−25.6282	+	9.32789i	−1.52885	+	0.556455i	−0.963339	−	0.268287i	$-0.913542\pi$
$281$	−25.6282	+	9.32789i	−1.52885	+	0.556455i	−0.565509	+	0.824742i	$0.691320\pi$
$282$	1.25336	−	1.05169i	0.0746363	−	0.0626273i
$283$	2.61267	+	14.8172i	0.155307	+	0.880792i	0.958504	+	0.285078i	$0.0920196\pi$
$283$	2.61267	+	14.8172i	0.155307	+	0.880792i	−0.803197	+	0.595714i	$0.796869\pi$
$284$	2.42308			0.143784
$285$		0			0
$286$	11.0417			0.652910
$287$	4.02834	+	22.8459i	0.237786	+	1.34855i
$288$	2.57044	−	2.15685i	0.151464	−	0.127094i
$289$	−21.7045	+	7.89981i	−1.27674	+	0.464694i
$290$		0			0
$291$	−25.1108	−	21.0705i	−1.47202	−	1.23517i
$292$	0.171240	−	0.296596i	0.0100210	−	0.0173570i
$293$	−3.91441	−	6.77995i	−0.228682	−	0.396089i	0.728736	−	0.684795i	$-0.240108\pi$
$293$	−3.91441	−	6.77995i	−0.228682	−	0.396089i	−0.957418	+	0.288706i	$0.906775\pi$
$294$	−2.27173	+	12.8836i	−0.132490	+	0.751389i
$295$		0			0
$296$	3.62492	+	6.27855i	0.210694	+	0.364933i
$297$	0.863969	−	1.49644i	0.0501325	−	0.0868321i
$298$	16.9302	+	14.2061i	0.980740	+	0.822938i
$299$	−2.40361	−	0.874843i	−0.139004	−	0.0505935i
$300$		0			0
$301$	−24.6322	+	20.6689i	−1.41978	+	1.19133i
$302$	−3.37569	−	19.1445i	−0.194249	−	1.10164i
$303$	42.8990			2.46449
$304$	9.43773	−	16.3981i	0.541291	−	0.940496i
$305$		0			0
$306$	−5.14992	−	29.2066i	−0.294401	−	1.66963i
$307$	12.0381	−	10.1011i	0.687049	−	0.576503i	−0.231008	−	0.972952i	$-0.574202\pi$
$307$	12.0381	−	10.1011i	0.687049	−	0.576503i	0.918057	+	0.396449i	$0.129758\pi$
$308$	−2.40140	+	0.874039i	−0.136833	+	0.0498030i
$309$	−32.2684	−	11.7447i	−1.83568	−	0.668134i
$310$		0			0
$311$	−8.99061	+	15.5722i	−0.509810	+	0.883018i	0.490125	+	0.871652i	$0.336951\pi$
$311$	−8.99061	+	15.5722i	−0.509810	+	0.883018i	−0.999935	+	0.0113654i	$0.996382\pi$
$312$	−5.93746	−	10.2840i	−0.336142	−	0.582216i
$313$	−3.68143	+	20.8784i	−0.208087	+	1.18012i	0.684422	+	0.729087i	$0.260055\pi$
$313$	−3.68143	+	20.8784i	−0.208087	+	1.18012i	−0.892508	+	0.451031i	$0.851056\pi$
$314$	−2.78359	+	15.7865i	−0.157087	+	0.890884i
$315$		0			0
$316$	−0.0656572	+	0.113722i	−0.00369351	+	0.00639734i
$317$	−2.34748	−	1.96977i	−0.131848	−	0.110633i	0.574479	−	0.818519i	$-0.305205\pi$
$317$	−2.34748	−	1.96977i	−0.131848	−	0.110633i	−0.706327	+	0.707886i	$0.749649\pi$
$318$	−24.9802	−	9.09203i	−1.40082	−	0.509856i
$319$	−1.33437	+	0.485670i	−0.0747102	+	0.0271923i
$320$		0			0
$321$	−1.40771	−	7.98350i	−0.0785706	−	0.445596i
$322$	6.89184			0.384067
$323$	−13.8333	−	23.8850i	−0.769708	−	1.32899i
$324$	−1.59250			−0.0884722
$325$		0			0
$326$	−9.56972	+	8.02995i	−0.530018	+	0.444738i
$327$	7.51590	−	2.73556i	0.415630	−	0.151277i
$328$	17.9790	+	6.54382i	0.992724	+	0.361322i
$329$	1.10895	+	0.930518i	0.0611383	+	0.0513011i
$330$		0			0
$331$	12.9754	+	22.4741i	0.713195	+	1.23529i	0.963652	+	0.267162i	$0.0860858\pi$
$331$	12.9754	+	22.4741i	0.713195	+	1.23529i	−0.250457	+	0.968128i	$0.580581\pi$
$332$	−0.0180470	+	0.102350i	−0.000990459	+	0.00561717i
$333$	−1.48718	+	8.43420i	−0.0814968	+	0.462191i
$334$	−14.7187	−	25.4935i	−0.805369	−	1.39494i
$335$		0			0
$336$	26.8336	+	22.5161i	1.46389	+	1.22835i
$337$	9.45093	+	3.43986i	0.514825	+	0.187381i	0.586350	−	0.810058i	$-0.300564\pi$
$337$	9.45093	+	3.43986i	0.514825	+	0.187381i	−0.0715252	+	0.997439i	$0.522787\pi$
$338$	−13.6451	+	4.96641i	−0.742195	+	0.270137i
$339$	8.95971	−	7.51809i	0.486624	−	0.408326i
$340$		0			0
$341$	11.6258			0.629574
$342$	19.1743	−	7.00842i	1.03683	−	0.378972i
$343$	11.1741			0.603343
$344$	4.60514	+	26.1171i	0.248293	+	1.40814i
$345$		0			0
$346$	16.2918	−	5.92975i	0.875855	−	0.318785i
$347$	6.40683	+	2.33190i	0.343937	+	0.125183i	0.508213	−	0.861232i	$-0.330306\pi$
$347$	6.40683	+	2.33190i	0.343937	+	0.125183i	−0.164276	+	0.986414i	$0.552529\pi$
$348$	−0.121335	−	0.101812i	−0.00650426	−	0.00545772i
$349$	−15.7983	+	27.3634i	−0.845663	+	1.46473i	0.0393817	+	0.999224i	$0.487461\pi$
$349$	−15.7983	+	27.3634i	−0.845663	+	1.46473i	−0.885044	+	0.465507i	$0.845872\pi$
$350$		0			0
$351$	0.127948	−	0.725632i	0.00682938	−	0.0387314i
$352$	−0.769945	+	4.36658i	−0.0410382	+	0.232739i
$353$	−3.15328	−	5.46165i	−0.167832	−	0.290694i	0.769825	−	0.638255i	$-0.220343\pi$
$353$	−3.15328	−	5.46165i	−0.167832	−	0.290694i	−0.937658	+	0.347561i	$0.887010\pi$
$354$	5.77157	−	9.99666i	0.306756	−	0.531316i
$355$		0			0
$356$	−1.20600	−	0.438946i	−0.0639176	−	0.0232641i
$357$	48.0202	−	17.4779i	2.54150	−	0.925030i
$358$	−8.02670	+	6.73520i	−0.424224	+	0.355966i
$359$	0.725269	+	4.11321i	0.0382782	+	0.217087i	0.997947	−	0.0640469i	$-0.0204007\pi$
$359$	0.725269	+	4.11321i	0.0382782	+	0.217087i	−0.959669	+	0.281134i	$0.909290\pi$
$360$		0			0
$361$	14.5216	−	12.2525i	0.764293	−	0.644870i
$362$	−13.7293			−0.721596
$363$	2.80532	+	15.9097i	0.147241	+	0.835045i
$364$	−0.834776	+	0.700460i	−0.0437542	+	0.0367141i
$365$		0			0
$366$	−10.5812	−	3.85124i	−0.553088	−	0.201308i
$367$	12.6941	+	10.6516i	0.662627	+	0.556010i	0.910873	−	0.412687i	$-0.135410\pi$
$367$	12.6941	+	10.6516i	0.662627	+	0.556010i	−0.248246	+	0.968697i	$0.579854\pi$
$368$	3.11148	−	5.38924i	0.162197	−	0.280933i
$369$	11.3009	+	19.5737i	0.588302	+	1.01897i
$370$		0			0
$371$	4.08428	−	23.1631i	0.212045	−	1.20257i
$372$	0.648392	+	1.12305i	0.0336176	+	0.0582274i
$373$	−18.5002	+	32.0433i	−0.957905	+	1.65914i	−0.230330	+	0.973113i	$0.573980\pi$
$373$	−18.5002	+	32.0433i	−0.957905	+	1.65914i	−0.727576	+	0.686028i	$0.759353\pi$
$374$	30.0207	+	25.1904i	1.55233	+	1.30256i
$375$		0			0
$376$	1.12193	−	0.408350i	0.0578592	−	0.0210590i
$377$	−0.463853	+	0.389219i	−0.0238897	+	0.0200458i
$378$	0.344740	+	1.95512i	0.0177315	+	0.100561i
$379$	31.5147			1.61880			0.809400	−	0.587257i	$-0.199792\pi$
$379$	31.5147			1.61880			0.809400	+	0.587257i	$0.199792\pi$
$380$		0			0
$381$	1.47009			0.0753148
$382$	−2.08676	−	11.8346i	−0.106768	−	0.605510i
$383$	2.37331	−	1.99144i	0.121270	−	0.101758i	−0.580136	−	0.814520i	$-0.697000\pi$
$383$	2.37331	−	1.99144i	0.121270	−	0.101758i	0.701406	+	0.712762i	$0.252556\pi$
$384$	29.4987	−	10.7367i	1.50535	−	0.547903i
$385$		0			0
$386$	−8.75148	−	7.34337i	−0.445439	−	0.373768i
$387$	−15.6641	+	27.1311i	−0.796253	+	1.37915i
$388$	1.24047	+	2.14856i	0.0629753	+	0.109076i
$389$	4.52037	−	25.6363i	0.229192	−	1.29981i	−0.625316	−	0.780372i	$-0.715030\pi$
$389$	4.52037	−	25.6363i	0.229192	−	1.29981i	0.854507	−	0.519439i	$-0.173859\pi$
$390$		0			0
$391$	−4.53920	−	7.86213i	−0.229557	−	0.397605i
$392$	−4.77328	+	8.26756i	−0.241087	+	0.417575i
$393$	−39.0893	−	32.7999i	−1.97180	−	1.65453i
$394$	4.95887	+	1.80488i	0.249824	+	0.0909285i
$395$		0			0
$396$	−1.90730	+	1.60042i	−0.0958457	+	0.0804241i
$397$	−2.19851	−	12.4684i	−0.110340	−	0.625770i	−0.988952	−	0.148234i	$-0.952641\pi$
$397$	−2.19851	−	12.4684i	−0.110340	−	0.625770i	0.878612	−	0.477536i	$-0.158470\pi$
$398$	12.9714			0.650197
$399$	17.6298	+	30.4400i	0.882595	+	1.52391i
$400$		0			0
$401$	−1.60135	−	9.08170i	−0.0799675	−	0.453518i	−0.998330	−	0.0577770i	$-0.981599\pi$
$401$	−1.60135	−	9.08170i	−0.0799675	−	0.453518i	0.918362	−	0.395741i	$-0.129512\pi$
$402$	−24.0647	+	20.1926i	−1.20024	+	1.00712i
$403$	4.65851	−	1.69556i	0.232057	−	0.0844618i
$404$	−3.05100	−	1.11047i	−0.151793	−	0.0552481i
$405$		0			0
$406$	0.815744	−	1.41291i	0.0404847	−	0.0701215i
$407$	−5.65847	−	9.80076i	−0.280480	−	0.485806i
$408$	7.31866	−	41.5062i	0.362328	−	2.05486i
$409$	5.98343	−	33.9337i	0.295861	−	1.67791i	−0.367819	−	0.929897i	$-0.619895\pi$
$409$	5.98343	−	33.9337i	0.295861	−	1.67791i	0.663680	−	0.748016i	$-0.268993\pi$
$410$		0			0
$411$	−10.8691	+	18.8258i	−0.536132	+	0.928607i
$412$	1.99092	+	1.67058i	0.0980856	+	0.0823036i
$413$	9.59724	+	3.49311i	0.472249	+	0.171885i
$414$	6.30969	−	2.29654i	0.310104	−	0.112869i
$415$		0			0
$416$	0.328320	+	1.86199i	0.0160972	+	0.0912917i
$417$	19.0943			0.935053
$418$	−13.4564	+	23.3806i	−0.658176	+	1.14358i
$419$	−7.86047			−0.384009			−0.192005	−	0.981394i	$-0.561499\pi$
$419$	−7.86047			−0.384009			−0.192005	+	0.981394i	$0.561499\pi$
$420$		0			0
$421$	8.03752	−	6.74428i	0.391725	−	0.328696i	−0.425560	−	0.904930i	$-0.639923\pi$
$421$	8.03752	−	6.74428i	0.391725	−	0.328696i	0.817285	+	0.576234i	$0.195478\pi$
$422$	16.4254	−	5.97836i	0.799577	−	0.291022i
$423$	1.32535	+	0.482387i	0.0644406	+	0.0234545i
$424$	−14.8601	−	12.4691i	−0.721672	−	0.605555i
$425$		0			0
$426$	23.6781	+	41.0117i	1.14721	+	1.98702i
$427$	1.73004	−	9.81153i	0.0837223	−	0.474813i
$428$	−0.106542	+	0.604230i	−0.00514991	+	0.0292066i
$429$	9.26832	+	16.0532i	0.447479	+	0.775056i
$430$		0			0
$431$	22.8988	+	19.2144i	1.10300	+	0.925525i	0.997623	−	0.0689073i	$-0.0219513\pi$
$431$	22.8988	+	19.2144i	1.10300	+	0.925525i	0.105375	+	0.994433i	$0.466396\pi$
$432$	1.68449	+	0.613105i	0.0810452	+	0.0294980i
$433$	6.38969	−	2.32566i	0.307069	−	0.111764i	−0.183890	−	0.982947i	$-0.558869\pi$
$433$	6.38969	−	2.32566i	0.307069	−	0.111764i	0.490959	+	0.871183i	$0.336647\pi$
$434$	−10.2323	+	8.58589i	−0.491165	+	0.412136i
$435$		0			0
$436$	−0.605347			−0.0289908
$437$	4.78173	−	4.02345i	0.228741	−	0.192468i
$438$	6.69335			0.319820
$439$	1.38329	+	7.84504i	0.0660209	+	0.374423i	0.999860	+	0.0167300i	$0.00532558\pi$
$439$	1.38329	+	7.84504i	0.0660209	+	0.374423i	−0.933839	+	0.357693i	$0.883563\pi$
$440$		0			0
$441$	−10.5973	+	3.85711i	−0.504634	+	0.183672i
$442$	15.7033	+	5.71552i	0.746928	+	0.271859i
$443$	16.6916	+	14.0059i	0.793041	+	0.665440i	0.946496	−	0.322715i	$-0.104596\pi$
$443$	16.6916	+	14.0059i	0.793041	+	0.665440i	−0.153455	+	0.988156i	$0.549040\pi$
$444$	0.631165	−	1.09321i	0.0299538	−	0.0518815i
$445$		0			0
$446$	−2.28539	+	12.9611i	−0.108217	+	0.613726i
$447$	−6.44278	+	36.5388i	−0.304733	+	1.72823i
$448$	11.5591	+	20.0210i	0.546118	+	0.945904i
$449$	−9.39185	+	16.2672i	−0.443229	+	0.767695i	−0.997927	−	0.0643569i	$-0.979500\pi$
$449$	−9.39185	+	16.2672i	−0.443229	+	0.767695i	0.554698	+	0.832052i	$0.312834\pi$
$450$		0			0
$451$	−28.0651	−	10.2148i	−1.32153	−	0.480998i
$452$	−0.831830	+	0.302761i	−0.0391260	+	0.0142407i
$453$	25.0001	−	20.9776i	1.17461	−	0.985612i
$454$	6.78303	+	38.4685i	0.318343	+	1.80541i
$455$		0			0
$456$	29.0121	−	0.0394717i	1.35862	−	0.00184843i
$457$	−28.2368			−1.32086			−0.660431	−	0.750887i	$-0.729627\pi$
$457$	−28.2368			−1.32086			−0.660431	+	0.750887i	$0.729627\pi$
$458$	−5.59564	−	31.7345i	−0.261467	−	1.48285i
$459$	2.00332	−	1.68098i	0.0935069	−	0.0784616i
$460$		0			0
$461$	0.184187	+	0.0670386i	0.00857845	+	0.00312230i	0.346306	−	0.938122i	$-0.387436\pi$
$461$	0.184187	+	0.0670386i	0.00857845	+	0.00312230i	−0.337727	+	0.941244i	$0.609658\pi$
$462$	−38.2597	−	32.1037i	−1.78000	−	1.49360i
$463$	6.98206	−	12.0933i	0.324484	−	0.562022i	−0.656924	−	0.753957i	$-0.728143\pi$
$463$	6.98206	−	12.0933i	0.324484	−	0.562022i	0.981408	+	0.191935i	$0.0614761\pi$
$464$	−0.736571	−	1.27578i	−0.0341945	−	0.0592266i
$465$		0			0
$466$	−2.56879	+	14.5683i	−0.118997	+	0.674865i
$467$	−16.0512	−	27.8016i	−0.742763	−	1.28650i	−0.951233	−	0.308474i	$-0.900182\pi$
$467$	−16.0512	−	27.8016i	−0.742763	−	1.28650i	0.208470	−	0.978029i	$-0.433152\pi$
$468$	−0.530851	+	0.919462i	−0.0245386	+	0.0425021i
$469$	−21.2920	−	17.8661i	−0.983172	−	0.824979i
$470$		0			0
$471$	−25.2881	+	9.20410i	−1.16521	+	0.424102i
$472$	6.45264	−	5.41441i	0.297007	−	0.249218i
$473$	−7.18859	−	40.7685i	−0.330532	−	1.87454i
$474$	−2.56638			−0.117878
$475$		0			0
$476$	−3.86765			−0.177273
$477$	−3.97926	−	22.5675i	−0.182198	−	1.03330i
$478$	−20.2107	+	16.9588i	−0.924414	+	0.775675i
$479$	1.86271	−	0.677972i	0.0851095	−	0.0309773i	−0.299114	−	0.954217i	$-0.596691\pi$
$479$	1.86271	−	0.677972i	0.0851095	−	0.0309773i	0.384224	+	0.923240i	$0.374469\pi$
$480$		0			0
$481$	−3.69675	−	3.10194i	−0.168557	−	0.141436i
$482$	−12.6796	+	21.9616i	−0.577538	+	1.00033i
$483$	5.78496	+	10.0198i	0.263225	+	0.455919i
$484$	0.212320	−	1.20413i	0.00965091	−	0.0547330i
$485$		0			0
$486$	−16.4781	−	28.5409i	−0.747460	−	1.29464i
$487$	4.29458	−	7.43843i	0.194606	−	0.337068i	−0.752165	−	0.658975i	$-0.770990\pi$
$487$	4.29458	−	7.43843i	0.194606	−	0.337068i	0.946771	+	0.321907i	$0.104324\pi$
$488$	−6.29452	−	5.28173i	−0.284939	−	0.239093i
$489$	−19.7072	−	7.17285i	−0.891192	−	0.324367i
$490$		0			0
$491$	19.8407	−	16.6483i	0.895398	−	0.751328i	−0.0738874	−	0.997267i	$-0.523541\pi$
$491$	19.8407	−	16.6483i	0.895398	−	0.751328i	0.969285	+	0.245938i	$0.0790961\pi$
$492$	−0.578488	−	3.28077i	−0.0260802	−	0.147908i
$493$	−2.14910			−0.0967908
$494$	−1.98211	+	11.3312i	−0.0891794	+	0.509817i
$495$		0			0
$496$	2.09435	+	11.8777i	0.0940391	+	0.533322i
$497$	−32.0972	+	26.9328i	−1.43976	+	1.20810i
$498$	−1.90867	+	0.694698i	−0.0855294	+	0.0311302i
$499$	19.9251	+	7.25214i	0.891970	+	0.324650i	0.747030	−	0.664790i	$-0.231479\pi$
$499$	19.9251	+	7.25214i	0.891970	+	0.324650i	0.144939	+	0.989441i	$0.453701\pi$
$500$		0			0
$501$	24.7094	−	42.7980i	1.10394	−	1.91207i
$502$	7.17090	+	12.4204i	0.320053	+	0.554348i
$503$	−4.43084	+	25.1285i	−0.197561	+	1.12043i	0.711162	+	0.703028i	$0.248169\pi$
$503$	−4.43084	+	25.1285i	−0.197561	+	1.12043i	−0.908724	+	0.417398i	$0.862942\pi$
$504$	−4.78940	+	27.1620i	−0.213337	+	1.20989i
$505$		0			0
$506$	−4.43639	+	7.68405i	−0.197221	+	0.341597i
$507$	−18.6741	−	15.6694i	−0.829346	−	0.695904i
$508$	−0.104553	−	0.0380543i	−0.00463880	−	0.00168839i
$509$	16.0130	−	5.82825i	0.709763	−	0.258333i	0.0381894	−	0.999271i	$-0.487841\pi$
$509$	16.0130	−	5.82825i	0.709763	−	0.258333i	0.671574	+	0.740938i	$0.265619\pi$
$510$		0			0
$511$	1.02837	+	5.83218i	0.0454924	+	0.258000i
$512$	18.6685			0.825039
$513$	1.38059	+	1.15525i	0.0609543	+	0.0510056i
$514$	14.8666			0.655738
$515$		0			0
$516$	3.53729	−	2.96814i	0.155721	−	0.130665i
$517$	−1.75133	+	0.637430i	−0.0770232	+	0.0280342i
$518$	12.2183	+	4.44708i	0.536839	+	0.195393i
$519$	22.2963	+	18.7088i	0.978700	+	0.821227i
$520$		0			0
$521$	−10.8909	−	18.8635i	−0.477137	−	0.826426i	0.522520	−	0.852627i	$-0.324992\pi$
$521$	−10.8909	−	18.8635i	−0.477137	−	0.826426i	−0.999657	+	0.0262016i	$0.991659\pi$
$522$	0.276020	−	1.56539i	0.0120811	−	0.0685152i
$523$	3.03633	−	17.2199i	0.132769	−	0.752973i	−0.843618	−	0.536944i	$-0.819578\pi$
$523$	3.03633	−	17.2199i	0.132769	−	0.752973i	0.976387	−	0.216028i	$-0.0693104\pi$
$524$	1.93100	+	3.34460i	0.0843563	+	0.146109i
$525$		0			0
$526$	24.7364	+	20.7563i	1.07856	+	0.905018i
$527$	16.5340	+	6.01788i	0.720232	+	0.262143i
$528$	−42.3775	+	15.4241i	−1.84424	+	0.671249i
$529$	−16.0445	+	13.4629i	−0.697586	+	0.585344i
$530$		0			0
$531$	9.95056			0.431817
$532$	−0.465879	−	2.62127i	−0.0201984	−	0.113647i
$533$	−12.7355			−0.551637
$534$	−4.35551	−	24.7013i	−0.188481	−	1.06893i
$535$		0			0
$536$	−21.5413	+	7.84038i	−0.930441	+	0.338653i
$537$	−16.5297	−	6.01630i	−0.713307	−	0.259623i
$538$	−17.5123	−	14.6945i	−0.755008	−	0.633527i
$539$	7.45104	−	12.9056i	0.320939	−	0.555883i
$540$		0			0
$541$	2.57157	−	14.5841i	0.110560	−	0.627018i	−0.878293	−	0.478123i	$-0.841317\pi$
$541$	2.57157	−	14.5841i	0.110560	−	0.627018i	0.988853	−	0.148895i	$-0.0475717\pi$
$542$	−1.32619	+	7.52121i	−0.0569648	+	0.323064i
$543$	−11.5243	−	19.9606i	−0.494554	−	0.856592i
$544$	−3.35527	+	5.81150i	−0.143856	+	0.249166i
$545$		0			0
$546$	−20.0129	−	7.28411i	−0.856474	−	0.311731i
$547$	−24.9709	+	9.08867i	−1.06768	+	0.388603i	−0.815308	−	0.579027i	$-0.803433\pi$
$547$	−24.9709	+	9.08867i	−1.06768	+	0.388603i	−0.252371	+	0.967631i	$0.581210\pi$
$548$	1.26033	−	1.05754i	0.0538388	−	0.0451761i
$549$	−1.68555	−	9.55924i	−0.0719376	−	0.407979i
$550$		0			0
$551$	−0.258871	−	1.45654i	−0.0110283	−	0.0620507i
$552$	9.54231			0.406148
$553$	−0.394301	−	2.23619i	−0.0167674	−	0.0950926i
$554$	6.31176	−	5.29619i	0.268161	−	0.225014i
$555$		0			0
$556$	−1.35800	−	0.494271i	−0.0575919	−	0.0209618i
$557$	12.3143	+	10.3330i	0.521775	+	0.437821i	0.865250	−	0.501340i	$-0.167160\pi$
$557$	12.3143	+	10.3330i	0.521775	+	0.437821i	−0.343475	+	0.939162i	$0.611604\pi$
$558$	−6.50691	+	11.2703i	−0.275460	+	0.477110i
$559$	−8.82633	−	15.2877i	−0.373314	−	0.646599i
$560$		0			0
$561$	−11.4244	+	64.7908i	−0.482337	+	2.73547i
$562$	20.1706	+	34.9365i	0.850847	+	1.47371i
$563$	−1.01573	+	1.75929i	−0.0428078	+	0.0741452i	−0.886635	−	0.462469i	$-0.846964\pi$
$563$	−1.01573	+	1.75929i	−0.0428078	+	0.0741452i	0.843828	+	0.536614i	$0.180297\pi$
$564$	−0.159250	−	0.133626i	−0.00670562	−	0.00562669i
$565$		0			0
$566$	20.9131	−	7.61175i	0.879044	−	0.319946i
$567$	21.0950	−	17.7008i	0.885905	−	0.743362i
$568$	6.00077	+	34.0321i	0.251787	+	1.42795i
$569$	−12.8224			−0.537543			−0.268772	−	0.963204i	$-0.586618\pi$
$569$	−12.8224			−0.537543			−0.268772	+	0.963204i	$0.586618\pi$
$570$		0			0
$571$	12.9168			0.540551			0.270276	−	0.962783i	$-0.412885\pi$
$571$	12.9168			0.540551			0.270276	+	0.962783i	$0.412885\pi$
$572$	−0.243618	−	1.38163i	−0.0101862	−	0.0577688i
$573$	15.4543	−	12.9677i	0.645614	−	0.541735i
$574$	32.2448	−	11.7362i	1.34587	−	0.489858i
$575$		0			0
$576$	17.2543	+	14.4780i	0.718928	+	0.603252i
$577$	−4.05680	+	7.02658i	−0.168887	+	0.292520i	−0.938029	−	0.346558i	$-0.887351\pi$
$577$	−4.05680	+	7.02658i	−0.168887	+	0.292520i	0.769142	+	0.639078i	$0.220684\pi$
$578$	17.0825	+	29.5878i	0.710540	+	1.23069i
$579$	3.33037	−	18.8875i	0.138406	−	0.784937i
$580$		0			0
$581$	−0.898567	−	1.55636i	−0.0372788	−	0.0645689i
$582$	−24.2435	+	41.9909i	−1.00492	+	1.74058i
$583$	23.1966	+	19.4642i	0.960703	+	0.806126i
$584$	4.58975	+	1.67053i	0.189925	+	0.0691271i
$585$		0			0
$586$	−8.87090	+	7.44357i	−0.366454	+	0.307491i
$587$	−5.65427	−	32.0670i	−0.233377	−	1.32355i	−0.846005	−	0.533174i	$-0.820999\pi$
$587$	−5.65427	−	32.0670i	−0.233377	−	1.32355i	0.612629	−	0.790371i	$-0.290112\pi$
$588$	1.66223			0.0685492
$589$	−2.08697	+	11.9307i	−0.0859921	+	0.491595i
$590$		0			0
$591$	1.53837	+	8.72455i	0.0632802	+	0.358880i
$592$	8.99370	−	7.54661i	0.369639	−	0.310164i
$593$	10.7832	−	3.92476i	0.442812	−	0.161171i	−0.110985	−	0.993822i	$-0.535401\pi$
$593$	10.7832	−	3.92476i	0.442812	−	0.161171i	0.553797	+	0.832652i	$0.313178\pi$
$594$	−2.40177	−	0.874173i	−0.0985459	−	0.0358678i
$595$		0			0
$596$	1.40405	−	2.43188i	0.0575120	−	0.0996138i
$597$	10.8881	+	18.8587i	0.445620	+	0.771836i
$598$	−0.657002	+	3.72604i	−0.0268668	+	0.152369i
$599$	5.76684	−	32.7054i	0.235627	−	1.33631i	−0.605663	−	0.795721i	$-0.707092\pi$
$599$	5.76684	−	32.7054i	0.235627	−	1.33631i	0.841290	−	0.540584i	$-0.181797\pi$
$600$		0			0
$601$	−13.6590	+	23.6581i	−0.557163	+	0.965034i	0.440569	+	0.897719i	$0.354777\pi$
$601$	−13.6590	+	23.6581i	−0.557163	+	0.965034i	−0.997732	+	0.0673154i	$0.978557\pi$
$602$	36.4352	+	30.5728i	1.48499	+	1.24605i
$603$	−25.4469	−	9.26191i	−1.03628	−	0.377174i
$604$	−2.32104	+	0.844789i	−0.0944417	+	0.0343740i
$605$		0			0
$606$	−11.0188	−	62.4909i	−0.447609	−	2.53852i
$607$	25.7405			1.04478			0.522388	−	0.852708i	$-0.325041\pi$
$607$	25.7405			1.04478			0.522388	+	0.852708i	$0.325041\pi$
$608$	−4.34286	−	1.57399i	−0.176126	−	0.0638335i
$609$	2.73892			0.110986
$610$		0			0
$611$	−0.608796	+	0.510841i	−0.0246293	+	0.0206664i
$612$	−3.54095	+	1.28880i	−0.143134	+	0.0520967i
$613$	−38.1551	−	13.8873i	−1.54107	−	0.560904i	−0.574770	−	0.818315i	$-0.694908\pi$
$613$	−38.1551	−	13.8873i	−1.54107	−	0.560904i	−0.966302	+	0.257411i	$0.917131\pi$
$614$	−17.8063	−	14.9413i	−0.718606	−	0.602982i
$615$		0			0
$616$	−18.2229	−	31.5630i	−0.734222	−	1.27171i
$617$	2.46776	−	13.9954i	0.0993485	−	0.563433i	−0.893979	−	0.448108i	$-0.852098\pi$
$617$	2.46776	−	13.9954i	0.0993485	−	0.563433i	0.993328	−	0.115325i	$-0.0367910\pi$
$618$	−8.82021	+	50.0219i	−0.354801	+	2.01218i
$619$	14.7818	+	25.6028i	0.594129	+	1.02906i	0.993669	+	0.112346i	$0.0358364\pi$
$619$	14.7818	+	25.6028i	0.594129	+	1.02906i	−0.399540	+	0.916716i	$0.630830\pi$
$620$		0			0
$621$	0.453568	+	0.380589i	0.0182010	+	0.0152725i
$622$	24.9932	+	9.09680i	1.00214	+	0.364748i
$623$	20.8541	−	7.59026i	0.835500	−	0.304097i
$624$	−14.7313	+	12.3610i	−0.589723	+	0.494836i
$625$		0			0
$626$	31.3591			1.25336
$627$	−45.2877	+	0.0616150i	−1.80861	+	0.00246067i
$628$	2.03675			0.0812753
$629$	−2.97418	−	16.8674i	−0.118588	−	0.672548i
$630$		0			0
$631$	1.60465	−	0.584045i	0.0638801	−	0.0232505i	−0.309882	−	0.950775i	$-0.600290\pi$
$631$	1.60465	−	0.584045i	0.0638801	−	0.0232505i	0.373763	+	0.927524i	$0.378067\pi$
$632$	−1.75981	−	0.640520i	−0.0700017	−	0.0254785i
$633$	22.4791	+	18.8622i	0.893465	+	0.749706i
$634$	−2.26640	+	3.92552i	−0.0900102	+	0.155902i
$635$		0			0
$636$	−0.586521	+	3.32633i	−0.0232571	+	0.131897i
$637$	1.10345	−	6.25800i	0.0437204	−	0.247951i
$638$	1.05021	+	1.81902i	0.0415783	+	0.0720158i
$639$	−20.4113	+	35.3534i	−0.807459	+	1.39856i
$640$		0			0
$641$	−2.59543	−	0.944659i	−0.102513	−	0.0373118i	0.290254	−	0.956950i	$-0.406260\pi$
$641$	−2.59543	−	0.944659i	−0.102513	−	0.0373118i	−0.392768	+	0.919638i	$0.628482\pi$
$642$	−11.2680	+	4.10121i	−0.444711	+	0.161862i
$643$	16.6209	−	13.9466i	0.655465	−	0.550000i	−0.253259	−	0.967398i	$-0.581503\pi$
$643$	16.6209	−	13.9466i	0.655465	−	0.550000i	0.908724	+	0.417398i	$0.137058\pi$
$644$	−0.152058	−	0.862364i	−0.00599193	−	0.0339819i
$645$		0			0
$646$	−31.2400	+	26.2860i	−1.22912	+	1.03421i
$647$	−28.0268			−1.10185			−0.550923	−	0.834556i	$-0.685724\pi$
$647$	−28.0268			−1.10185			−0.550923	+	0.834556i	$0.685724\pi$
$648$	−3.94383	−	22.3666i	−0.154928	−	0.878642i
$649$	−10.0725	+	8.45185i	−0.395381	+	0.331764i
$650$		0			0
$651$	−21.0717	−	7.66946i	−0.825864	−	0.300590i
$652$	1.21591	+	1.02027i	0.0476189	+	0.0399570i
$653$	−3.79654	+	6.57580i	−0.148570	+	0.257331i	−0.930699	−	0.365785i	$-0.880800\pi$
$653$	−3.79654	+	6.57580i	−0.148570	+	0.257331i	0.782129	+	0.623116i	$0.214134\pi$
$654$	−5.91538	−	10.2457i	−0.231310	−	0.400640i
$655$		0			0
$656$	5.38029	−	30.5131i	0.210065	−	1.19134i
$657$	2.88494	+	4.99686i	0.112552	+	0.194946i
$658$	1.07064	−	1.85441i	0.0417380	−	0.0722924i
$659$	5.50322	+	4.61775i	0.214375	+	0.179882i	0.743652	−	0.668567i	$-0.233092\pi$
$659$	5.50322	+	4.61775i	0.214375	+	0.179882i	−0.529277	+	0.848449i	$0.677537\pi$
$660$		0			0
$661$	27.1268	−	9.87335i	1.05511	−	0.384029i	0.244521	−	0.969644i	$-0.421369\pi$
$661$	27.1268	−	9.87335i	1.05511	−	0.384029i	0.810589	+	0.585615i	$0.199147\pi$
$662$	29.4052	−	24.6739i	1.14287	−	0.958978i
$663$	4.87157	+	27.6281i	0.189196	+	1.07298i
$664$	−1.48219			−0.0575201
$665$		0			0
$666$	12.6681			0.490877
$667$	−0.0844929	−	0.479183i	−0.00327158	−	0.0185540i
$668$	−2.86521	+	2.40419i	−0.110858	+	0.0930210i
$669$	−20.7621	+	7.55679i	−0.802710	+	0.292162i
$670$		0			0
$671$	9.82569	+	8.24473i	0.379316	+	0.318284i
$672$	4.27611	−	7.40644i	0.164954	−	0.285709i
$673$	11.6595	+	20.1949i	0.449442	+	0.778457i	0.998350	−	0.0574263i	$-0.0182894\pi$
$673$	11.6595	+	20.1949i	0.449442	+	0.778457i	−0.548907	+	0.835883i	$0.684956\pi$
$674$	2.58331	−	14.6507i	0.0995054	−	0.564323i
$675$		0			0
$676$	0.922496	+	1.59781i	0.0354806	+	0.0614542i
$677$	−8.75493	+	15.1640i	−0.336479	+	0.582799i	−0.983768	−	0.179446i	$-0.942570\pi$
$677$	−8.75493	+	15.1640i	−0.336479	+	0.582799i	0.647289	+	0.762245i	$0.275903\pi$
$678$	−13.2529	−	11.1205i	−0.508975	−	0.427081i
$679$	−40.3132	−	14.6728i	−1.54708	−	0.563090i
$680$		0			0
$681$	−50.2345	+	42.1518i	−1.92499	+	1.61526i
$682$	−2.98615	−	16.9353i	−0.114346	−	0.648487i
$683$	−22.0114			−0.842243			−0.421122	−	0.907004i	$-0.638363\pi$
$683$	−22.0114			−0.842243			−0.421122	+	0.907004i	$0.638363\pi$
$684$	−1.30000	−	2.24461i	−0.0497068	−	0.0858249i
$685$		0			0
$686$	−2.87012	−	16.2772i	−0.109582	−	0.621468i
$687$	41.4409	−	34.7730i	1.58107	−	1.32667i
$688$	40.3566	−	14.6886i	1.53858	−	0.559997i
$689$	12.1337	+	4.41629i	0.462256	+	0.168247i
$690$		0			0
$691$	1.32811	−	2.30036i	0.0505238	−	0.0875098i	−0.839657	−	0.543116i	$-0.817244\pi$
$691$	1.32811	−	2.30036i	0.0505238	−	0.0875098i	0.890181	+	0.455607i	$0.150578\pi$
$692$	−1.10143	−	1.90774i	−0.0418702	−	0.0725214i
$693$	7.47621	−	42.3997i	0.283998	−	1.61063i
$694$	1.75124	−	9.93178i	0.0664762	−	0.377005i
$695$		0			0
$696$	1.12946	−	1.95629i	0.0428122	−	0.0741529i
$697$	−34.6260	−	29.0546i	−1.31155	−	1.10052i
$698$	43.9181	+	15.9849i	1.66232	+	0.605037i
$699$	−23.3367	+	8.49385i	−0.882674	+	0.321267i
$700$		0			0
$701$	−1.27931	−	7.25535i	−0.0483190	−	0.274031i	0.951070	−	0.308975i	$-0.0999859\pi$
$701$	−1.27931	−	7.25535i	−0.0483190	−	0.274031i	−0.999389	+	0.0349439i	$0.988875\pi$
$702$	−1.08989			−0.0411352
$703$	11.0735	−	4.04750i	0.417646	−	0.152654i
$704$	−29.7632			−1.12174
$705$		0			0
$706$	−7.14603	+	5.99623i	−0.268944	+	0.225671i
$707$	52.7579	−	19.2023i	1.98416	−	0.722177i
$708$	−1.37821	−	0.501626i	−0.0517961	−	0.0188522i
$709$	−4.58997	−	3.85144i	−0.172380	−	0.144644i	0.552516	−	0.833502i	$-0.313668\pi$
$709$	−4.58997	−	3.85144i	−0.172380	−	0.144644i	−0.724896	+	0.688858i	$0.758112\pi$
$710$		0			0
$711$	−1.10615	−	1.91591i	−0.0414839	−	0.0718523i
$712$	3.17833	−	18.0252i	0.119113	−	0.675522i
$713$	−0.691759	+	3.92316i	−0.0259066	+	0.146923i
$714$	−37.7943	−	65.4616i	−1.41441	−	2.44984i
$715$		0			0
$716$	1.01986	+	0.855765i	0.0381140	+	0.0319814i
$717$	−41.6205	−	15.1486i	−1.55435	−	0.565736i
$718$	5.80541	−	2.11300i	0.216656	−	0.0788563i
$719$	10.4040	−	8.73002i	0.388005	−	0.325575i	−0.427831	−	0.903859i	$-0.640722\pi$
$719$	10.4040	−	8.73002i	0.388005	−	0.325575i	0.815835	+	0.578284i	$0.196278\pi$
$720$		0			0
$721$	−44.9412			−1.67370
$722$	−21.5782	−	18.0064i	−0.803056	−	0.670128i
$723$	−42.5725			−1.58329
$724$	0.302916	+	1.71792i	0.0112578	+	0.0638461i
$725$		0			0
$726$	22.4551	−	8.17299i	0.833387	−	0.303328i
$727$	38.7574	+	14.1065i	1.43743	+	0.523183i	0.939052	−	0.343776i	$-0.111706\pi$
$727$	38.7574	+	14.1065i	1.43743	+	0.523183i	0.498381	+	0.866958i	$0.333928\pi$
$728$	−11.9052	−	9.98969i	−0.441238	−	0.370242i
$729$	14.9530	−	25.8994i	0.553816	−	0.959237i
$730$		0			0
$731$	10.8796	−	61.7011i	0.402395	−	2.28210i
$732$	−0.248441	+	1.40898i	−0.00918264	+	0.0520773i
$733$	0.0619240	+	0.107256i	0.00228722	+	0.00396158i	0.867167	−	0.498018i	$-0.165939\pi$
$733$	0.0619240	+	0.107256i	0.00228722	+	0.00396158i	−0.864880	+	0.501979i	$0.832605\pi$
$734$	12.2556	−	21.2274i	0.452364	−	0.783517i
$735$		0			0
$736$	−1.42770	−	0.519639i	−0.0526256	−	0.0191541i
$737$	33.6257	−	12.2388i	1.23862	−	0.450821i
$738$	25.6103	−	21.4896i	0.942729	−	0.791043i
$739$	−6.34049	−	35.9587i	−0.233239	−	1.32276i	−0.846291	−	0.532720i	$-0.821170\pi$
$739$	−6.34049	−	35.9587i	−0.233239	−	1.32276i	0.613053	−	0.790042i	$-0.289941\pi$
$740$		0			0
$741$	−18.1379	+	6.62962i	−0.666313	+	0.243545i
$742$	−34.7907			−1.27721
$743$	1.57359	+	8.92430i	0.0577296	+	0.327401i	0.999972	−	0.00753195i	$-0.00239752\pi$
$743$	1.57359	+	8.92430i	0.0577296	+	0.327401i	−0.942242	+	0.334933i	$0.891286\pi$
$744$	−14.1674	+	11.8879i	−0.519402	+	0.435830i
$745$		0			0
$746$	51.4293	+	18.7187i	1.88296	+	0.685341i
$747$	−1.34129	−	1.12547i	−0.0490751	−	0.0411789i
$748$	2.48967	−	4.31223i	0.0910312	−	0.157671i
$749$	−5.30476	−	9.18812i	−0.193832	−	0.335727i
$750$		0			0
$751$	−0.709544	+	4.02402i	−0.0258916	+	0.146839i	−0.995013	−	0.0997456i	$-0.968197\pi$
$751$	−0.709544	+	4.02402i	−0.0258916	+	0.146839i	0.969121	+	0.246584i	$0.0793082\pi$
$752$	−0.966732	−	1.67443i	−0.0352531	−	0.0610602i
$753$	−12.0384	+	20.8511i	−0.438704	+	0.759857i
$754$	0.686117	+	0.575721i	0.0249869	+	0.0209665i
$755$		0			0
$756$	0.237035	−	0.0862735i	0.00862086	−	0.00313774i
$757$	−26.3977	+	22.1503i	−0.959441	+	0.805066i	−0.980862	−	0.194704i	$-0.937625\pi$
$757$	−26.3977	+	22.1503i	−0.959441	+	0.805066i	0.0214214	+	0.999771i	$0.493181\pi$
$758$	−8.09470	−	45.9073i	−0.294013	−	1.66743i
$759$	−14.8955			−0.540671
$760$		0			0
$761$	20.5813			0.746072			0.373036	−	0.927817i	$-0.378317\pi$
$761$	20.5813			0.746072			0.373036	+	0.927817i	$0.378317\pi$
$762$	−0.377599	−	2.14147i	−0.0136790	−	0.0775773i
$763$	8.01868	−	6.72848i	0.290296	−	0.243587i
$764$	−1.43480	+	0.522224i	−0.0519092	+	0.0188934i
$765$		0			0
$766$	−3.51052	−	2.94568i	−0.126840	−	0.106432i
$767$	−2.80344	+	4.85570i	−0.101226	+	0.175329i
$768$	−5.55245	−	9.61713i	−0.200357	−	0.347028i
$769$	−5.27109	+	29.8939i	−0.190081	+	1.07800i	0.729172	+	0.684331i	$0.239906\pi$
$769$	−5.27109	+	29.8939i	−0.190081	+	1.07800i	−0.919252	+	0.393669i	$0.871206\pi$
$770$		0			0
$771$	12.4789	+	21.6141i	0.449417	+	0.778413i
$772$	−0.725774	+	1.25708i	−0.0261212	+	0.0452432i
$773$	14.9551	+	12.5488i	0.537898	+	0.451350i	0.870818	−	0.491605i	$-0.163590\pi$
$773$	14.9551	+	12.5488i	0.537898	+	0.451350i	−0.332921	+	0.942955i	$0.608034\pi$
$774$	43.5452	+	15.8491i	1.56520	+	0.569686i
$775$		0			0
$776$	−27.1043	+	22.7432i	−0.972988	+	0.816434i
$777$	3.79043	+	21.4966i	0.135981	+	0.771186i
$778$	−38.5054			−1.38048
$779$	15.5207	−	26.9673i	0.556087	−	0.966204i
$780$		0			0
$781$	−9.36716	−	53.1238i	−0.335183	−	1.90092i
$782$	−10.2868	+	8.63167i	−0.367856	+	0.308668i
$783$	0.131711	−	0.0479389i	0.00470697	−	0.00171320i
$784$	14.5274	+	5.28754i	0.518836	+	0.188841i
$785$		0			0
$786$	−37.7392	+	65.3661i	−1.34611	+	2.33153i
$787$	17.6118	+	30.5046i	0.627793	+	1.08737i	0.987994	+	0.154495i	$0.0493750\pi$
$787$	17.6118	+	30.5046i	0.627793	+	1.08737i	−0.360200	+	0.932875i	$0.617292\pi$
$788$	0.116432	−	0.660316i	0.00414770	−	0.0235228i
$789$	−9.41343	+	53.3862i	−0.335127	+	1.90060i
$790$		0			0
$791$	7.65357	−	13.2564i	0.272129	−	0.471342i
$792$	−27.2012	−	22.8245i	−0.966554	−	0.811035i
$793$	5.13963	+	1.87067i	0.182514	+	0.0664295i
$794$	−17.5979	+	6.40513i	−0.624528	+	0.227309i
$795$		0			0
$796$	−0.286194	−	1.62309i	−0.0101439	−	0.0575288i
$797$	28.7940			1.01994			0.509969	−	0.860193i	$-0.329657\pi$
$797$	28.7940			1.01994			0.509969	+	0.860193i	$0.329657\pi$
$798$	39.8136	−	33.5000i	1.40939	−	1.18589i
$799$	−2.82065			−0.0997874
$800$		0			0
$801$	16.5633	−	13.8982i	0.585234	−	0.491070i
$802$	−12.8180	+	4.66536i	−0.452618	+	0.164740i
$803$	−7.16455	−	2.60768i	−0.252832	−	0.0920232i
$804$	3.05762	+	2.56565i	0.107834	+	0.0904834i
$805$		0			0
$806$	−3.66648	−	6.35052i	−0.129146	−	0.223688i
$807$	6.66429	−	37.7951i	0.234594	−	1.33045i
$808$	8.04072	−	45.6012i	0.282872	−	1.60425i
$809$	24.0034	+	41.5751i	0.843915	+	1.46170i	0.886560	+	0.462613i	$0.153088\pi$
$809$	24.0034	+	41.5751i	0.843915	+	1.46170i	−0.0426458	+	0.999090i	$0.513579\pi$
$810$		0			0
$811$	−7.37613	−	6.18931i	−0.259011	−	0.217336i	0.504030	−	0.863686i	$-0.331850\pi$
$811$	−7.37613	−	6.18931i	−0.259011	−	0.217336i	−0.763041	+	0.646350i	$0.776295\pi$
$812$	−0.194793	−	0.0708988i	−0.00683589	−	0.00248806i
$813$	−12.0481	+	4.38513i	−0.422544	+	0.153793i
$814$	−12.8233	+	10.7601i	−0.449458	+	0.377140i
$815$		0			0
$816$	−68.2523			−2.38931
$817$	43.1280	−	0.0586768i	1.50886	−	0.00205284i
$818$	−50.9680			−1.78205
$819$	−3.18800	−	18.0800i	−0.111398	−	0.631768i
$820$		0			0
$821$	24.1743	−	8.79872i	0.843688	−	0.307077i	0.116224	−	0.993223i	$-0.462921\pi$
$821$	24.1743	−	8.79872i	0.843688	−	0.307077i	0.727464	+	0.686146i	$0.240699\pi$
$822$	30.2152	+	10.9974i	1.05388	+	0.383580i
$823$	−10.3098	−	8.65091i	−0.359376	−	0.301552i	0.445166	−	0.895448i	$-0.353145\pi$
$823$	−10.3098	−	8.65091i	−0.359376	−	0.301552i	−0.804542	+	0.593896i	$0.797589\pi$
$824$	−18.5327	+	32.0996i	−0.645617	+	1.11824i
$825$		0			0
$826$	2.62330	−	14.8775i	0.0912764	−	0.517654i
$827$	0.0299383	−	0.169788i	0.00104106	−	0.00590412i	−0.984283	−	0.176599i	$-0.943490\pi$
$827$	0.0299383	−	0.169788i	0.00104106	−	0.00590412i	0.985324	+	0.170695i	$0.0546014\pi$
$828$	−0.426576	−	0.738851i	−0.0148245	−	0.0256769i
$829$	21.1895	−	36.7014i	0.735943	−	1.27469i	−0.218365	−	0.975867i	$-0.570072\pi$
$829$	21.1895	−	36.7014i	0.735943	−	1.27469i	0.954308	−	0.298824i	$-0.0965942\pi$
$830$		0			0
$831$	12.9980	+	4.73089i	0.450896	+	0.164113i
$832$	−11.9262	+	4.34078i	−0.413467	+	0.150490i
$833$	17.2770	−	14.4971i	0.598614	−	0.502296i
$834$	−4.90447	−	27.8147i	−0.169828	−	0.963143i
$835$		0			0
$836$	3.22247	+	1.16792i	0.111452	+	0.0403934i
$837$	−1.14755			−0.0396651
$838$	2.01900	+	11.4503i	0.0697452	+	0.395545i
$839$	34.5791	−	29.0153i	1.19380	−	1.00172i	0.194019	−	0.980998i	$-0.437848\pi$
$839$	34.5791	−	29.0153i	1.19380	−	1.00172i	0.999785	−	0.0207231i	$-0.00659684\pi$
$840$		0			0
$841$	27.1428	+	9.87919i	0.935960	+	0.340662i
$842$	−11.8888	−	9.97593i	−0.409717	−	0.343793i
$843$	−33.8621	+	58.6509i	−1.16627	+	2.02005i
$844$	−1.11046	−	1.92338i	−0.0382237	−	0.0662055i
$845$		0			0
$846$	0.362270	−	2.05453i	0.0124551	−	0.0706363i
$847$	10.5715	+	18.3103i	0.363240	+	0.629151i
$848$	−15.7070	+	27.2054i	−0.539382	+	0.934238i
$849$	28.6208	+	24.0157i	0.982263	+	0.824217i
$850$		0			0
$851$	3.64397	−	1.32630i	0.124914	−	0.0454649i
$852$	4.60930	−	3.86766i	0.157912	−	0.132504i
$853$	−8.04694	−	45.6364i	−0.275522	−	1.56256i	−0.737299	−	0.675566i	$-0.763899\pi$
$853$	−8.04694	−	45.6364i	−0.275522	−	1.56256i	0.461778	−	0.886996i	$-0.347212\pi$
$854$	−14.7368			−0.504283
$855$		0			0
$856$	−8.75023			−0.299077
$857$	3.80174	+	21.5607i	0.129865	+	0.736501i	0.978299	+	0.207199i	$0.0664349\pi$
$857$	3.80174	+	21.5607i	0.129865	+	0.736501i	−0.848434	+	0.529302i	$0.822454\pi$
$858$	21.0040	−	17.6245i	0.717066	−	0.601690i
$859$	−31.3876	+	11.4242i	−1.07093	+	0.389787i	−0.816525	−	0.577310i	$-0.804102\pi$
$859$	−31.3876	+	11.4242i	−1.07093	+	0.389787i	−0.254406	+	0.967097i	$0.581880\pi$
$860$		0			0
$861$	44.1289	+	37.0285i	1.50391	+	1.26193i
$862$	22.1079	−	38.2920i	0.752998	−	1.30423i
$863$	13.5627	+	23.4913i	0.461680	+	0.799653i	0.999045	−	0.0436971i	$-0.0139137\pi$
$863$	13.5627	+	23.4913i	0.461680	+	0.799653i	−0.537365	+	0.843350i	$0.680580\pi$
$864$	0.0759988	−	0.431011i	0.00258553	−	0.0146633i
$865$		0			0
$866$	−5.02900	−	8.71049i	−0.170892	−	0.295994i
$867$	−28.6779	+	49.6716i	−0.973953	+	1.68694i
$868$	1.30010	+	1.09091i	0.0441282	+	0.0370279i
$869$	2.74705	+	0.999846i	0.0931875	+	0.0339175i
$870$		0			0
$871$	11.6890	−	9.80822i	0.396066	−	0.332339i
$872$	−1.49914	−	8.50206i	−0.0507674	−	0.287916i
$873$	−41.7973			−1.41462
$874$	−7.08916	−	5.93209i	−0.239794	−	0.200656i
$875$		0			0
$876$	−0.147679	−	0.837527i	−0.00498960	−	0.0282974i
$877$	−37.5992	+	31.5495i	−1.26963	+	1.06535i	−0.275049	+	0.961430i	$0.588694\pi$
$877$	−37.5992	+	31.5495i	−1.26963	+	1.06535i	−0.994586	+	0.103920i	$0.966861\pi$
$878$	11.0725	−	4.03008i	0.373680	−	0.136008i
$879$	−18.2682	−	6.64906i	−0.616169	−	0.224267i
$880$		0			0
$881$	−18.9889	+	32.8898i	−0.639753	+	1.10808i	0.345734	+	0.938332i	$0.387630\pi$
$881$	−18.9889	+	32.8898i	−0.639753	+	1.10808i	−0.985487	+	0.169751i	$0.945704\pi$
$882$	8.34062	+	14.4464i	0.280843	+	0.486435i
$883$	5.76686	−	32.7055i	0.194070	−	1.10063i	−0.719666	−	0.694320i	$-0.755705\pi$
$883$	5.76686	−	32.7055i	0.194070	−	1.10063i	0.913737	−	0.406307i	$-0.133184\pi$
$884$	0.368704	−	2.09103i	0.0124009	−	0.0703288i
$885$		0			0
$886$	16.1150	−	27.9121i	0.541395	−	0.937724i
$887$	20.1106	+	16.8748i	0.675248	+	0.566601i	0.914614	−	0.404329i	$-0.132495\pi$
$887$	20.1106	+	16.8748i	0.675248	+	0.566601i	−0.239365	+	0.970930i	$0.576939\pi$
$888$	16.9172	+	6.15734i	0.567703	+	0.206627i
$889$	1.80794	−	0.658035i	0.0606362	−	0.0220698i
$890$		0			0
$891$	6.15629	+	34.9140i	0.206243	+	1.16966i
$892$	1.67222			0.0559902
$893$	−0.339762	−	1.91167i	−0.0113697	−	0.0639718i
$894$	54.8808			1.83549
$895$		0			0
$896$	31.4721	−	26.4082i	1.05141	−	0.882236i
$897$	−5.96866	+	2.17242i	−0.199288	+	0.0725348i
$898$	26.1087	+	9.50278i	0.871258	+	0.317112i
$899$	0.722415	+	0.606178i	0.0240939	+	0.0202172i
$900$		0			0
$901$	22.9143	+	39.6888i	0.763387	+	1.32223i
$902$	−7.67129	+	43.5060i	−0.255426	+	1.44859i
$903$	−13.8654	+	78.6346i	−0.461412	+	2.61680i
$904$	−6.31229	−	10.9332i	−0.209944	−	0.363633i
$905$		0			0
$906$	−36.9793	−	31.0294i	−1.22856	−	1.03088i
$907$	−7.44950	−	2.71140i	−0.247357	−	0.0900305i	0.215366	−	0.976533i	$-0.430905\pi$
$907$	−7.44950	−	2.71140i	−0.247357	−	0.0900305i	−0.462723	+	0.886503i	$0.653128\pi$
$908$	4.66383	−	1.69750i	0.154775	−	0.0563334i
$909$	41.9027	−	35.1606i	1.38983	−	1.16620i
$910$		0			0
$911$	−0.619746			−0.0205331			−0.0102665	−	0.999947i	$-0.503268\pi$
$911$	−0.619746			−0.0205331			−0.0102665	+	0.999947i	$0.503268\pi$
$912$	−8.22135	−	46.2575i	−0.272236	−	1.53174i
$913$	2.31369			0.0765718
$914$	7.25277	+	41.1325i	0.239900	+	1.36054i
$915$		0			0
$916$	−3.84742	+	1.40035i	−0.127122	+	0.0462687i
$917$	−62.7544	−	22.8407i	−2.07233	−	0.754268i
$918$	−2.96325	−	2.48646i	−0.0978017	−	0.0820654i
$919$	17.5287	−	30.3606i	0.578219	−	1.00150i	−0.417465	−	0.908693i	$-0.637081\pi$
$919$	17.5287	−	30.3606i	0.578219	−	1.00150i	0.995684	−	0.0928113i	$-0.0295853\pi$
$920$		0			0
$921$	6.77620	−	38.4297i	0.223283	−	1.26630i
$922$	0.0503456	−	0.285524i	0.00165804	−	0.00940324i
$923$	−11.5012	−	19.9207i	−0.378568	−	0.655699i
$924$	−3.17294	+	5.49569i	−0.104382	+	0.180795i
$925$		0			0
$926$	−19.4096	−	7.06452i	−0.637840	−	0.232155i
$927$	−41.1451	+	14.9756i	−1.35138	+	0.491863i
$928$	−0.275519	+	0.231188i	−0.00904437	+	0.00758912i
$929$	2.09132	+	11.8605i	0.0686140	+	0.389129i	0.999704	+	0.0243392i	$0.00774816\pi$
$929$	2.09132	+	11.8605i	0.0686140	+	0.389129i	−0.931090	+	0.364790i	$0.881141\pi$
$930$		0			0
$931$	11.9065	+	9.96313i	0.390218	+	0.326528i
$932$	1.87959			0.0615679
$933$	7.75357	+	43.9727i	0.253841	+	1.43960i
$934$	−36.3756	+	30.5228i	−1.19025	+	0.998735i
$935$		0			0
$936$	−14.2284	−	5.17873i	−0.465071	−	0.169272i
$937$	11.4374	+	9.59711i	0.373643	+	0.313524i	0.810201	−	0.586152i	$-0.199358\pi$
$937$	11.4374	+	9.59711i	0.373643	+	0.313524i	−0.436558	+	0.899676i	$0.643802\pi$
$938$	−20.5565	+	35.6049i	−0.671194	+	1.16254i
$939$	26.3226	+	45.5921i	0.859006	+	1.48784i
$940$		0			0
$941$	3.37221	−	19.1248i	0.109931	−	0.623450i	−0.879205	−	0.476444i	$-0.841925\pi$
$941$	3.37221	−	19.1248i	0.109931	−	0.623450i	0.989136	−	0.147006i	$-0.0469635\pi$
$942$	19.9029	+	34.4729i	0.648473	+	1.12319i
$943$	5.11694	−	8.86280i	0.166630	−	0.288612i
$944$	−10.4494	−	8.76813i	−0.340101	−	0.285378i
$945$		0			0
$946$	−57.5409	+	20.9432i	−1.87082	+	0.680922i
$947$	12.8212	−	10.7583i	0.416634	−	0.349598i	−0.410247	−	0.911975i	$-0.634557\pi$
$947$	12.8212	−	10.7583i	0.416634	−	0.349598i	0.826881	+	0.562377i	$0.190113\pi$
$948$	0.0566233	+	0.321127i	0.00183904	+	0.0104297i
$949$	−3.25117			−0.105538
$950$		0			0
$951$	−7.60959			−0.246758
$952$	−9.57824	−	54.3209i	−0.310433	−	1.76055i
$953$	−40.7361	+	34.1817i	−1.31957	+	1.10725i	−0.333177	+	0.942864i	$0.608121\pi$
$953$	−40.7361	+	34.1817i	−1.31957	+	1.10725i	−0.986396	+	0.164389i	$0.947435\pi$
$954$	−31.8520	+	11.5932i	−1.03125	+	0.375343i
$955$		0			0
$956$	2.56794	+	2.15475i	0.0830530	+	0.0696897i
$957$	−1.76308	+	3.05375i	−0.0569923	+	0.0987136i
$958$	−1.46605	−	2.53927i	−0.0473658	−	0.0820400i
$959$	−4.94022	+	28.0174i	−0.159528	+	0.904729i
$960$		0			0
$961$	11.6396	+	20.1603i	0.375470	+	0.650332i
$962$	−3.56906	+	6.18179i	−0.115071	+	0.199309i
$963$	−7.91839	−	6.64432i	−0.255167	−	0.214110i
$964$	3.02778	+	1.10202i	0.0975181	+	0.0354937i
$965$		0			0
$966$	13.1100	−	11.0006i	0.421807	−	0.353938i
$967$	5.21432	+	29.5719i	0.167681	+	0.950967i	0.946257	+	0.323416i	$0.104831\pi$
$967$	5.21432	+	29.5719i	0.167681	+	0.950967i	−0.778576	+	0.627551i	$0.784057\pi$
$968$	17.4377			0.560469
$969$	−64.4390	−	23.3546i	−2.07008	−	0.750259i
$970$		0			0
$971$	4.19210	+	23.7746i	0.134531	+	0.762962i	0.975185	+	0.221390i	$0.0710595\pi$
$971$	4.19210	+	23.7746i	0.134531	+	0.762962i	−0.840654	+	0.541572i	$0.817829\pi$
$972$	−3.20770	+	2.69158i	−0.102887	+	0.0863325i
$973$	23.4825	−	8.54693i	0.752814	−	0.274002i
$974$	−11.9386	−	4.34531i	−0.382538	−	0.139233i
$975$		0			0
$976$	−6.65325	+	11.5238i	−0.212965	+	0.368867i
$977$	4.78840	+	8.29375i	0.153195	+	0.265341i	0.932400	−	0.361428i	$-0.117711\pi$
$977$	4.78840	+	8.29375i	0.153195	+	0.265341i	−0.779206	+	0.626768i	$0.784377\pi$
$978$	−5.38677	+	30.5499i	−0.172250	+	0.976877i
$979$	−4.96134	+	28.1372i	−0.158565	+	0.899267i
$980$		0			0
$981$	5.09925	−	8.83216i	0.162806	−	0.281989i
$982$	−29.3477	−	24.6257i	−0.936524	−	0.785837i
$983$	−29.2916	−	10.6613i	−0.934257	−	0.340042i	−0.170362	−	0.985382i	$-0.554494\pi$
$983$	−29.2916	−	10.6613i	−0.934257	−	0.340042i	−0.763896	+	0.645340i	$0.776716\pi$
$984$	44.6455	−	16.2497i	1.42325	−	0.518020i
$985$		0			0
$986$	0.552008	+	3.13060i	0.0175795	+	0.0996985i
$987$	3.59476			0.114422
$988$	1.46159	−	0.00198853i	0.0464994	−	6.32636e-5i
$989$	14.1851			0.451061
$990$		0			0
$991$	−37.2791	+	31.2808i	−1.18421	+	0.993669i	−0.184266	+	0.982876i	$0.558991\pi$
$991$	−37.2791	+	31.2808i	−1.18421	+	0.993669i	−0.999942	+	0.0107922i	$0.996565\pi$
$992$	2.76706	−	1.00713i	0.0878542	−	0.0319763i
$993$	60.5551	+	22.0403i	1.92166	+	0.699426i
$994$	47.4772	+	39.8381i	1.50589	+	1.26359i
$995$		0			0
$996$	0.129038	+	0.223501i	0.00408873	+	0.00708189i
$997$	5.53857	−	31.4108i	0.175408	−	0.994790i	−0.762263	−	0.647267i	$-0.775912\pi$
$997$	5.53857	−	31.4108i	0.175408	−	0.994790i	0.937672	−	0.347523i	$-0.112977\pi$
$998$	5.44631	−	30.8876i	0.172400	−	0.977729i
$999$	0.558529	+	0.967401i	0.0176711	+	0.0306072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.351.2		48
5.2	odd	4		95.2.p.a.9.7	yes	48
5.3	odd	4		95.2.p.a.9.2	✓	48
5.4	even	2	inner	475.2.l.f.351.7		48
15.2	even	4		855.2.da.b.199.2		48
15.8	even	4		855.2.da.b.199.7		48
19.6	even	9		9025.2.a.cu.1.7		24
19.13	odd	18		9025.2.a.ct.1.18		24
19.17	even	9	inner	475.2.l.f.226.2		48
95.13	even	36		1805.2.b.l.1084.7		24
95.17	odd	36		95.2.p.a.74.2	yes	48
95.32	even	36		1805.2.b.l.1084.18		24
95.44	even	18		9025.2.a.cu.1.18		24
95.63	odd	36		1805.2.b.k.1084.18		24
95.74	even	18	inner	475.2.l.f.226.7		48
95.82	odd	36		1805.2.b.k.1084.7		24
95.89	odd	18		9025.2.a.ct.1.7		24
95.93	odd	36		95.2.p.a.74.7	yes	48
285.17	even	36		855.2.da.b.739.7		48
285.188	even	36		855.2.da.b.739.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.2	✓	48	5.3	odd	4
95.2.p.a.9.7	yes	48	5.2	odd	4
95.2.p.a.74.2	yes	48	95.17	odd	36
95.2.p.a.74.7	yes	48	95.93	odd	36
475.2.l.f.226.2		48	19.17	even	9	inner
475.2.l.f.226.7		48	95.74	even	18	inner
475.2.l.f.351.2		48	1.1	even	1	trivial
475.2.l.f.351.7		48	5.4	even	2	inner
855.2.da.b.199.2		48	15.2	even	4
855.2.da.b.199.7		48	15.8	even	4
855.2.da.b.739.2		48	285.188	even	36
855.2.da.b.739.7		48	285.17	even	36
1805.2.b.k.1084.7		24	95.82	odd	36
1805.2.b.k.1084.18		24	95.63	odd	36
1805.2.b.l.1084.7		24	95.13	even	36
1805.2.b.l.1084.18		24	95.32	even	36
9025.2.a.ct.1.7		24	95.89	odd	18
9025.2.a.ct.1.18		24	19.13	odd	18
9025.2.a.cu.1.7		24	19.6	even	9
9025.2.a.cu.1.18		24	95.44	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.256855 - 1.45670i) q^{2} +(1.90225 - 1.59617i) q^{3} +(-0.176607 + 0.0642796i) q^{4} +(-2.81374 - 2.36101i) q^{6} +(1.62494 - 2.81448i) q^{7} +(-1.34017 - 2.32124i) q^{8} +(0.549824 - 3.11821i) q^{9} +O(q^{10})\)	\(q+(-0.256855 - 1.45670i) q^{2} +(1.90225 - 1.59617i) q^{3} +(-0.176607 + 0.0642796i) q^{4} +(-2.81374 - 2.36101i) q^{6} +(1.62494 - 2.81448i) q^{7} +(-1.34017 - 2.32124i) q^{8} +(0.549824 - 3.11821i) q^{9} +(2.09200 + 3.62344i) q^{11} +(-0.233348 + 0.404171i) q^{12} +(1.36673 + 1.14682i) q^{13} +(-4.51721 - 1.64413i) q^{14} +(-3.32506 + 2.79006i) q^{16} +(1.09959 + 6.23606i) q^{17} -4.68351 q^{18} +(-4.09399 + 1.49640i) q^{19} +(-1.40136 - 7.94751i) q^{21} +(4.74092 - 3.97810i) q^{22} +(-1.34721 + 0.490346i) q^{23} +(-6.25444 - 2.27643i) q^{24} +(1.31952 - 2.28547i) q^{26} +(-0.206494 - 0.357658i) q^{27} +(-0.106062 + 0.601506i) q^{28} +(-0.0589345 + 0.334234i) q^{29} +(1.38932 - 2.40638i) q^{31} +(0.811808 + 0.681187i) q^{32} +(9.76313 + 3.55349i) q^{33} +(8.80161 - 3.20352i) q^{34} +(0.103335 + 0.586040i) q^{36} -2.70482 q^{37} +(3.23137 + 5.57935i) q^{38} +4.43037 q^{39} +(-5.46819 + 4.58835i) q^{41} +(-11.2172 + 4.08271i) q^{42} +(-9.29755 - 3.38403i) q^{43} +(-0.602374 - 0.505452i) q^{44} +(1.06032 + 1.83654i) q^{46} +(-0.0773501 + 0.438674i) q^{47} +(-1.87167 + 10.6148i) q^{48} +(-1.78085 - 3.08452i) q^{49} +(12.0455 + 10.1074i) q^{51} +(-0.315090 - 0.114683i) q^{52} +(6.80087 - 2.47532i) q^{53} +(-0.467960 + 0.392665i) q^{54} -8.71078 q^{56} +(-5.39926 + 9.38125i) q^{57} +0.502015 q^{58} +(0.545712 + 3.09489i) q^{59} +(2.88074 - 1.04850i) q^{61} +(-3.86222 - 1.40573i) q^{62} +(-7.88269 - 6.61436i) q^{63} +(-3.55679 + 6.16055i) q^{64} +(2.66865 - 15.1347i) q^{66} +(1.48513 - 8.42261i) q^{67} +(-0.595046 - 1.03065i) q^{68} +(-1.78006 + 3.08315i) q^{69} +(-12.1153 - 4.40959i) q^{71} +(-7.97498 + 2.90266i) q^{72} +(-1.39594 + 1.17133i) q^{73} +(0.694747 + 3.94011i) q^{74} +(0.626839 - 0.527435i) q^{76} +13.5974 q^{77} +(-1.13796 - 6.45371i) q^{78} +(0.535235 - 0.449116i) q^{79} +(7.96239 + 2.89807i) q^{81} +(8.08837 + 6.78695i) q^{82} +(0.276493 - 0.478899i) q^{83} +(0.758353 + 1.31351i) q^{84} +(-2.54139 + 14.4129i) q^{86} +(0.421388 + 0.729865i) q^{87} +(5.60726 - 9.71206i) q^{88} +(5.23109 + 4.38940i) q^{89} +(5.44854 - 1.98311i) q^{91} +(0.206408 - 0.173197i) q^{92} +(-1.19816 - 6.79513i) q^{93} +0.658883 q^{94} +2.63155 q^{96} +(-2.29226 - 13.0001i) q^{97} +(-4.03579 + 3.38643i) q^{98} +(12.4489 - 4.53102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more