LMFDB - Embedded newform 260.2.p.d.103.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(103,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("260.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			103.10
Character	$\chi$	$=$	260.103
Dual form			260.2.p.d.207.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.702829 - 1.22720i) q^{2} +(1.63423 - 1.63423i) q^{3} +(-1.01206 + 1.72503i) q^{4} +(-1.85457 - 1.24923i) q^{5} +(-3.15411 - 0.856948i) q^{6} +(1.80181 - 1.80181i) q^{7} +(2.82827 + 0.0296052i) q^{8} -2.34139i q^{9} +O(q^{10})$	\(q+(-0.702829 - 1.22720i) q^{2} +(1.63423 - 1.63423i) q^{3} +(-1.01206 + 1.72503i) q^{4} +(-1.85457 - 1.24923i) q^{5} +(-3.15411 - 0.856948i) q^{6} +(1.80181 - 1.80181i) q^{7} +(2.82827 + 0.0296052i) q^{8} -2.34139i q^{9} +(-0.229622 + 3.15393i) q^{10} -2.86823 q^{11} +(1.16515 + 4.47303i) q^{12} +(-1.91593 - 3.05438i) q^{13} +(-3.47755 - 0.944824i) q^{14} +(-5.07231 + 0.989250i) q^{15} +(-1.95146 - 3.49168i) q^{16} +(3.05008 - 3.05008i) q^{17} +(-2.87337 + 1.64560i) q^{18} +5.05926i q^{19} +(4.03190 - 1.93488i) q^{20} -5.88913i q^{21} +(2.01587 + 3.51990i) q^{22} +(-2.42763 + 2.42763i) q^{23} +(4.67042 - 4.57366i) q^{24} +(1.87883 + 4.63357i) q^{25} +(-2.40178 + 4.49794i) q^{26} +(1.07631 + 1.07631i) q^{27} +(1.28463 + 4.93172i) q^{28} -6.79589i q^{29} +(4.77898 + 5.52949i) q^{30} +7.49990 q^{31} +(-2.91346 + 4.84889i) q^{32} +(-4.68733 + 4.68733i) q^{33} +(-5.88676 - 1.59939i) q^{34} +(-5.59245 + 1.09069i) q^{35} +(4.03898 + 2.36964i) q^{36} +(2.43344 + 2.43344i) q^{37} +(6.20875 - 3.55580i) q^{38} +(-8.12261 - 1.86048i) q^{39} +(-5.20823 - 3.58808i) q^{40} -3.73755i q^{41} +(-7.22717 + 4.13905i) q^{42} +(-1.36253 + 1.36253i) q^{43} +(2.90282 - 4.94778i) q^{44} +(-2.92495 + 4.34227i) q^{45} +(4.68541 + 1.27299i) q^{46} +(7.11272 - 7.11272i) q^{47} +(-8.89532 - 2.51706i) q^{48} +0.506970i q^{49} +(4.36585 - 5.56232i) q^{50} -9.96906i q^{51} +(7.20793 - 0.213815i) q^{52} +(-2.33561 - 2.33561i) q^{53} +(0.564390 - 2.07732i) q^{54} +(5.31931 + 3.58309i) q^{55} +(5.14935 - 5.04266i) q^{56} +(8.26798 + 8.26798i) q^{57} +(-8.33995 + 4.77635i) q^{58} +4.71586i q^{59} +(3.42701 - 9.75108i) q^{60} +9.15507 q^{61} +(-5.27115 - 9.20391i) q^{62} +(-4.21875 - 4.21875i) q^{63} +(7.99825 + 0.167463i) q^{64} +(-0.262417 + 8.05799i) q^{65} +(9.04671 + 2.45792i) q^{66} +(-1.42067 + 1.42067i) q^{67} +(2.17461 + 8.34836i) q^{68} +7.93459i q^{69} +(5.26904 + 6.09651i) q^{70} -2.80652 q^{71} +(0.0693174 - 6.62210i) q^{72} +(5.53872 - 5.53872i) q^{73} +(1.27604 - 4.69662i) q^{74} +(10.6427 + 4.50188i) q^{75} +(-8.72738 - 5.12029i) q^{76} +(-5.16800 + 5.16800i) q^{77} +(3.42561 + 11.2757i) q^{78} +16.7129 q^{79} +(-0.742807 + 8.91337i) q^{80} +10.5421 q^{81} +(-4.58674 + 2.62686i) q^{82} +(3.28900 + 3.28900i) q^{83} +(10.1589 + 5.96016i) q^{84} +(-9.46685 + 1.84631i) q^{85} +(2.62974 + 0.714479i) q^{86} +(-11.1060 - 11.1060i) q^{87} +(-8.11213 - 0.0849143i) q^{88} -0.690019 q^{89} +(7.38460 + 0.537637i) q^{90} +(-8.95554 - 2.05127i) q^{91} +(-1.73082 - 6.64464i) q^{92} +(12.2565 - 12.2565i) q^{93} +(-13.7278 - 3.72974i) q^{94} +(6.32020 - 9.38273i) q^{95} +(3.16294 + 12.6854i) q^{96} +(0.611740 + 0.611740i) q^{97} +(0.622156 - 0.356314i) q^{98} +6.71565i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) $ 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.702829	−	1.22720i	−0.496975	−	0.867765i
$2$	−0.702829	−	1.22720i	−0.496975	−	0.867765i
$3$	1.63423	−	1.63423i	0.943521	−	0.943521i	−0.0549669	−	0.998488i	$-0.517505\pi$
$3$	1.63423	−	1.63423i	0.943521	−	0.943521i	0.998488	+	0.0549669i	$0.0175053\pi$
$4$	−1.01206	+	1.72503i	−0.506031	+	0.862515i
$5$	−1.85457	−	1.24923i	−0.829387	−	0.558674i
$5$	−1.85457	−	1.24923i	−0.829387	−	0.558674i
$6$	−3.15411	−	0.856948i	−1.28766	−	0.349848i
$7$	1.80181	−	1.80181i	0.681020	−	0.681020i	−0.279210	−	0.960230i	$-0.590073\pi$
$7$	1.80181	−	1.80181i	0.681020	−	0.681020i	0.960230	+	0.279210i	$0.0900727\pi$
$8$	2.82827	+	0.0296052i	0.999945	+	0.0104670i
$9$		−	2.34139i		−	0.780465i
$10$	−0.229622	+	3.15393i	−0.0726130	+	0.997360i
$11$	−2.86823			−0.864803			−0.432401	−	0.901681i	$-0.642334\pi$
$11$	−2.86823			−0.864803			−0.432401	+	0.901681i	$0.642334\pi$
$12$	1.16515	+	4.47303i	0.336351	+	1.29125i
$13$	−1.91593	−	3.05438i	−0.531383	−	0.847132i
$13$	−1.91593	−	3.05438i	−0.531383	−	0.847132i
$14$	−3.47755	−	0.944824i	−0.929415	−	0.252515i
$15$	−5.07231	+	0.989250i	−1.30967	+	0.255423i
$16$	−1.95146	−	3.49168i	−0.487865	−	0.872919i
$17$	3.05008	−	3.05008i	0.739754	−	0.739754i	−0.232776	−	0.972530i	$-0.574781\pi$
$17$	3.05008	−	3.05008i	0.739754	−	0.739754i	0.972530	+	0.232776i	$0.0747810\pi$
$18$	−2.87337	+	1.64560i	−0.677260	+	0.387872i
$19$			5.05926i			1.16067i	0.814376	+	0.580337i	$0.197079\pi$
$19$			5.05926i			1.16067i	−0.814376	+	0.580337i	$0.802921\pi$
$20$	4.03190	−	1.93488i	0.901561	−	0.432652i
$21$		−	5.88913i		−	1.28511i
$22$	2.01587	+	3.51990i	0.429786	+	0.750445i
$23$	−2.42763	+	2.42763i	−0.506196	+	0.506196i	−0.913356	−	0.407161i	$-0.866519\pi$
$23$	−2.42763	+	2.42763i	−0.506196	+	0.506196i	0.407161	+	0.913356i	$0.366519\pi$
$24$	4.67042	−	4.57366i	0.953345	−	0.933594i
$25$	1.87883	+	4.63357i	0.375766	+	0.926715i
$26$	−2.40178	+	4.49794i	−0.471027	+	0.882119i
$27$	1.07631	+	1.07631i	0.207136	+	0.207136i
$28$	1.28463	+	4.93172i	0.242773	+	0.932007i
$29$		−	6.79589i		−	1.26197i	−0.775797	−	0.630983i	$-0.782652\pi$
$29$		−	6.79589i		−	1.26197i	0.775797	−	0.630983i	$-0.217348\pi$
$30$	4.77898	+	5.52949i	0.872519	+	1.00954i
$31$	7.49990			1.34702			0.673511	−	0.739178i	$-0.264786\pi$
$31$	7.49990			1.34702			0.673511	+	0.739178i	$0.264786\pi$
$32$	−2.91346	+	4.84889i	−0.515031	+	0.857171i
$33$	−4.68733	+	4.68733i	−0.815960	+	0.815960i
$34$	−5.88676	−	1.59939i	−1.00957	−	0.274293i
$35$	−5.59245	+	1.09069i	−0.945297	+	0.184361i
$36$	4.03898	+	2.36964i	0.673163	+	0.394939i
$37$	2.43344	+	2.43344i	0.400055	+	0.400055i	0.878253	−	0.478197i	$-0.158710\pi$
$37$	2.43344	+	2.43344i	0.400055	+	0.400055i	−0.478197	+	0.878253i	$0.658710\pi$
$38$	6.20875	−	3.55580i	1.00719	−	0.576826i
$39$	−8.12261	−	1.86048i	−1.30066	−	0.297916i
$40$	−5.20823	−	3.58808i	−0.823494	−	0.567325i
$41$		−	3.73755i		−	0.583708i	−0.956463	−	0.291854i	$-0.905728\pi$
$41$		−	3.73755i		−	0.583708i	0.956463	−	0.291854i	$-0.0942721\pi$
$42$	−7.22717	+	4.13905i	−1.11518	+	0.638670i
$43$	−1.36253	+	1.36253i	−0.207785	+	0.207785i	−0.803325	−	0.595541i	$-0.796938\pi$
$43$	−1.36253	+	1.36253i	−0.207785	+	0.207785i	0.595541	+	0.803325i	$0.296938\pi$
$44$	2.90282	−	4.94778i	0.437617	−	0.745906i
$45$	−2.92495	+	4.34227i	−0.436026	+	0.647308i
$46$	4.68541	+	1.27299i	0.690825	+	0.187692i
$47$	7.11272	−	7.11272i	1.03750	−	1.03750i	0.0382282	−	0.999269i	$-0.487829\pi$
$47$	7.11272	−	7.11272i	1.03750	−	1.03750i	0.999269	−	0.0382282i	$-0.0121714\pi$
$48$	−8.89532	−	2.51706i	−1.28393	−	0.363306i
$49$			0.506970i			0.0724243i
$50$	4.36585	−	5.56232i	0.617424	−	0.786631i
$51$		−	9.96906i		−	1.39595i
$52$	7.20793	−	0.213815i	0.999560	−	0.0296509i
$53$	−2.33561	−	2.33561i	−0.320820	−	0.320820i	0.528262	−	0.849082i	$-0.322844\pi$
$53$	−2.33561	−	2.33561i	−0.320820	−	0.320820i	−0.849082	+	0.528262i	$0.822844\pi$
$54$	0.564390	−	2.07732i	0.0768038	−	0.282687i
$55$	5.31931	+	3.58309i	0.717256	+	0.483143i
$56$	5.14935	−	5.04266i	0.688111	−	0.673854i
$57$	8.26798	+	8.26798i	1.09512	+	1.09512i
$58$	−8.33995	+	4.77635i	−1.09509	+	0.627166i
$59$			4.71586i			0.613953i	0.951717	+	0.306976i	$0.0993172\pi$
$59$			4.71586i			0.613953i	−0.951717	+	0.306976i	$0.900683\pi$
$60$	3.42701	−	9.75108i	0.442425	−	1.25886i
$61$	9.15507			1.17219			0.586093	−	0.810244i	$-0.300665\pi$
$61$	9.15507			1.17219			0.586093	+	0.810244i	$0.300665\pi$
$62$	−5.27115	−	9.20391i	−0.669436	−	1.16890i
$63$	−4.21875	−	4.21875i	−0.531512	−	0.531512i
$64$	7.99825	+	0.167463i	0.999781	+	0.0209329i
$65$	−0.262417	+	8.05799i	−0.0325488	+	0.999470i
$66$	9.04671	+	2.45792i	1.11357	+	0.302549i
$67$	−1.42067	+	1.42067i	−0.173562	+	0.173562i	−0.788542	−	0.614980i	$-0.789164\pi$
$67$	−1.42067	+	1.42067i	−0.173562	+	0.173562i	0.614980	+	0.788542i	$0.289164\pi$
$68$	2.17461	+	8.34836i	0.263711	+	1.01239i
$69$			7.93459i			0.955213i
$70$	5.26904	+	6.09651i	0.629771	+	0.728673i
$71$	−2.80652			−0.333073			−0.166536	−	0.986035i	$-0.553258\pi$
$71$	−2.80652			−0.333073			−0.166536	+	0.986035i	$0.553258\pi$
$72$	0.0693174	−	6.62210i	0.00816913	−	0.780422i
$73$	5.53872	−	5.53872i	0.648258	−	0.648258i	−0.304314	−	0.952572i	$-0.598427\pi$
$73$	5.53872	−	5.53872i	0.648258	−	0.648258i	0.952572	+	0.304314i	$0.0984272\pi$
$74$	1.27604	−	4.69662i	0.148336	−	0.545972i
$75$	10.6427	+	4.50188i	1.22892	+	0.519832i
$76$	−8.72738	−	5.12029i	−1.00110	−	0.587337i
$77$	−5.16800	+	5.16800i	−0.588948	+	0.588948i
$78$	3.42561	+	11.2757i	0.387874	+	1.27672i
$79$	16.7129			1.88034			0.940172	−	0.340700i	$-0.110664\pi$
$79$	16.7129			1.88034			0.940172	+	0.340700i	$0.110664\pi$
$80$	−0.742807	+	8.91337i	−0.0830484	+	0.996546i
$81$	10.5421			1.17134
$82$	−4.58674	+	2.62686i	−0.506521	+	0.290088i
$83$	3.28900	+	3.28900i	0.361014	+	0.361014i	0.864186	−	0.503172i	$-0.167834\pi$
$83$	3.28900	+	3.28900i	0.361014	+	0.361014i	−0.503172	+	0.864186i	$0.667834\pi$
$84$	10.1589	+	5.96016i	1.10843	+	0.650307i
$85$	−9.46685	+	1.84631i	−1.02682	+	0.200261i
$86$	2.62974	+	0.714479i	0.283572	+	0.0770443i
$87$	−11.1060	−	11.1060i	−1.19069	−	1.19069i
$88$	−8.11213	−	0.0849143i	−0.864755	−	0.00905189i
$89$	−0.690019			−0.0731419			−0.0365709	−	0.999331i	$-0.511643\pi$
$89$	−0.690019			−0.0731419			−0.0365709	+	0.999331i	$0.511643\pi$
$90$	7.38460	+	0.537637i	0.778405	+	0.0566719i
$91$	−8.95554	−	2.05127i	−0.938796	−	0.215031i
$92$	−1.73082	−	6.64464i	−0.180451	−	0.692752i
$93$	12.2565	−	12.2565i	1.27094	−	1.27094i
$94$	−13.7278	−	3.72974i	−1.41591	−	0.384693i
$95$	6.32020	−	9.38273i	0.648439	−	0.962648i
$96$	3.16294	+	12.6854i	0.322817	+	1.29470i
$97$	0.611740	+	0.611740i	0.0621128	+	0.0621128i	0.737481	−	0.675368i	$-0.236015\pi$
$97$	0.611740	+	0.611740i	0.0621128	+	0.0621128i	−0.675368	+	0.737481i	$0.736015\pi$
$98$	0.622156	−	0.356314i	0.0628473	−	0.0359931i
$99$			6.71565i			0.674948i
$100$	−9.89455	−	1.44843i	−0.989455	−	0.144843i
$101$	−19.5821			−1.94849			−0.974247	−	0.225482i	$-0.927604\pi$
$101$	−19.5821			−1.94849			−0.974247	+	0.225482i	$0.927604\pi$
$102$	−12.2341	+	7.00654i	−1.21135	+	0.693751i
$103$	−7.42027	+	7.42027i	−0.731141	+	0.731141i	−0.970846	−	0.239705i	$-0.922949\pi$
$103$	−7.42027	+	7.42027i	−0.731141	+	0.731141i	0.239705	+	0.970846i	$0.422949\pi$
$104$	−5.32834	−	8.69533i	−0.522487	−	0.852647i
$105$	−7.35690	+	10.9218i	−0.717960	+	1.06586i
$106$	−1.22473	+	4.50780i	−0.118957	+	0.437836i
$107$	11.7984	+	11.7984i	1.14060	+	1.14060i	0.988341	+	0.152258i	$0.0486545\pi$
$107$	11.7984	+	11.7984i	1.14060	+	1.14060i	0.152258	+	0.988341i	$0.451346\pi$
$108$	−2.94596	+	0.767375i	−0.283475	+	0.0738407i
$109$	−17.0037			−1.62866			−0.814329	−	0.580403i	$-0.802895\pi$
$109$	−17.0037			−1.62866			−0.814329	+	0.580403i	$0.802895\pi$
$110$	0.658609	−	9.04619i	0.0627959	−	0.862520i
$111$	7.95359			0.754922
$112$	−9.80749	−	2.77517i	−0.926721	−	0.262229i
$113$	−4.57244	−	4.57244i	−0.430139	−	0.430139i	0.458537	−	0.888675i	$-0.348374\pi$
$113$	−4.57244	−	4.57244i	−0.430139	−	0.430139i	−0.888675	+	0.458537i	$0.848374\pi$
$114$	4.33552	−	15.9575i	0.406059	−	1.49456i
$115$	7.53487	−	1.46952i	0.702631	−	0.137034i
$116$	11.7231	+	6.87786i	1.08846	+	0.638593i
$117$	−7.15150	+	4.48594i	−0.661157	+	0.414726i
$118$	5.78732	−	3.31444i	0.532766	−	0.305119i
$119$		−	10.9913i		−	1.00757i
$120$	−14.3752	+	2.64770i	−1.31227	+	0.241701i
$121$	−2.77328			−0.252116
$122$	−6.43445	−	11.2351i	−0.582548	−	1.01718i
$123$	−6.10801	−	6.10801i	−0.550741	−	0.550741i
$124$	−7.59036	+	12.9376i	−0.681634	+	1.16183i
$125$	2.30400	−	10.9404i	0.206076	−	0.978536i
$126$	−2.21221	+	8.14232i	−0.197079	+	0.725376i
$127$	−2.16928	−	2.16928i	−0.192492	−	0.192492i	0.604280	−	0.796772i	$-0.293461\pi$
$127$	−2.16928	−	2.16928i	−0.192492	−	0.192492i	−0.796772	+	0.604280i	$0.793461\pi$
$128$	−5.41589	−	9.93318i	−0.478702	−	0.877978i
$129$			4.45338i			0.392098i
$130$	10.0732	−	5.34135i	0.883481	−	0.468467i
$131$			20.1665i			1.76196i	0.473156	+	0.880979i	$0.343115\pi$
$131$			20.1665i			1.76196i	−0.473156	+	0.880979i	$0.656885\pi$
$132$	−3.34192	−	12.8297i	−0.290877	−	1.11668i
$133$	9.11582	+	9.11582i	0.790442	+	0.790442i
$134$	2.74193	+	0.744962i	0.236867	+	0.0643550i
$135$	−0.651525	−	3.34065i	−0.0560743	−	0.287517i
$136$	8.71676	−	8.53617i	0.747456	−	0.731970i
$137$	10.1264	+	10.1264i	0.865160	+	0.865160i	0.991932	−	0.126771i	$-0.0404615\pi$
$137$	10.1264	+	10.1264i	0.865160	+	0.865160i	−0.126771	+	0.991932i	$0.540461\pi$
$138$	9.73737	−	5.57666i	0.828900	−	0.474717i
$139$	−6.95427			−0.589854			−0.294927	−	0.955520i	$-0.595295\pi$
$139$	−6.95427			−0.589854			−0.294927	+	0.955520i	$0.595295\pi$
$140$	3.77843	−	10.7510i	0.319336	−	0.908626i
$141$		−	23.2476i		−	1.95780i
$142$	1.97250	+	3.44417i	0.165529	+	0.289029i
$143$	5.49532	+	8.76065i	0.459541	+	0.732602i
$144$	−8.17539	+	4.56914i	−0.681283	+	0.380762i
$145$	−8.48966	+	12.6034i	−0.705028	+	1.04666i
$146$	−10.6899	−	2.90437i	−0.884703	−	0.240367i
$147$	0.828504	+	0.828504i	0.0683339	+	0.0683339i
$148$	−6.66056	+	1.73497i	−0.547494	+	0.142613i
$149$	4.62642			0.379011			0.189506	−	0.981880i	$-0.439311\pi$
$149$	4.62642			0.379011			0.189506	+	0.981880i	$0.439311\pi$
$150$	−1.95531	−	16.2249i	−0.159650	−	1.32476i
$151$	−21.8510			−1.77821			−0.889106	−	0.457701i	$-0.848673\pi$
$151$	−21.8510			−1.77821			−0.889106	+	0.457701i	$0.848673\pi$
$152$	−0.149780	+	14.3090i	−0.0121488	+	1.16061i
$153$	−7.14145	−	7.14145i	−0.577352	−	0.577352i
$154$	9.97441	+	2.70997i	0.803761	+	0.218376i
$155$	−13.9091	−	9.36913i	−1.11720	−	0.752546i
$156$	11.4300	−	12.1288i	0.915130	−	0.971083i
$157$	−3.55608	+	3.55608i	−0.283806	+	0.283806i	−0.834625	−	0.550819i	$-0.814315\pi$
$157$	−3.55608	+	3.55608i	−0.283806	+	0.283806i	0.550819	+	0.834625i	$0.314315\pi$
$158$	−11.7463	−	20.5101i	−0.934485	−	1.63170i
$159$	−7.63382			−0.605401
$160$	11.4606	−	5.35300i	0.906040	−	0.423192i
$161$			8.74824i			0.689458i
$162$	−7.40926	−	12.9373i	−0.582127	−	1.01645i
$163$	−2.47561	−	2.47561i	−0.193905	−	0.193905i	0.603476	−	0.797381i	$-0.293782\pi$
$163$	−2.47561	−	2.47561i	−0.193905	−	0.193905i	−0.797381	+	0.603476i	$0.793782\pi$
$164$	6.44740	+	3.78264i	0.503457	+	0.295374i
$165$	14.5485	−	2.83739i	1.13260	−	0.220891i
$166$	1.72467	−	6.34788i	0.133860	−	0.492691i
$167$	−15.2453	+	15.2453i	−1.17971	+	1.17971i	−0.199896	+	0.979817i	$0.564060\pi$
$167$	−15.2453	+	15.2453i	−1.17971	+	1.17971i	−0.979817	+	0.199896i	$0.935940\pi$
$168$	0.174349	−	16.6561i	0.0134513	−	1.28504i
$169$	−5.65844	+	11.7039i	−0.435265	+	0.900303i
$170$	8.91938	+	10.3201i	0.684085	+	0.791517i
$171$	11.8457			0.905865
$172$	−0.971444	−	3.72938i	−0.0740719	−	0.284363i
$173$	7.94933	+	7.94933i	0.604376	+	0.604376i	0.941471	−	0.337095i	$-0.109444\pi$
$173$	7.94933	+	7.94933i	0.604376	+	0.604376i	−0.337095	+	0.941471i	$0.609444\pi$
$174$	−5.82373	+	21.4350i	−0.441495	+	1.62498i
$175$	11.7341	+	4.96352i	0.887015	+	0.375207i
$176$	5.59723	+	10.0149i	0.421907	+	0.754903i
$177$	7.70678	+	7.70678i	0.579277	+	0.579277i
$178$	0.484966	+	0.846795i	0.0363497	+	0.0634699i
$179$	−4.23086			−0.316230			−0.158115	−	0.987421i	$-0.550542\pi$
$179$	−4.23086			−0.316230			−0.158115	+	0.987421i	$0.550542\pi$
$180$	−4.53032	−	9.44028i	−0.337670	−	0.703637i
$181$	4.89410			0.363776			0.181888	−	0.983319i	$-0.441779\pi$
$181$	4.89410			0.363776			0.181888	+	0.983319i	$0.441779\pi$
$182$	3.77689	+	12.4320i	0.279962	+	0.921519i
$183$	14.9615	−	14.9615i	1.10598	−	1.10598i
$184$	−6.93786	+	6.79412i	−0.511466	+	0.500869i
$185$	−1.47304	−	7.55292i	−0.108300	−	0.555301i
$186$	−23.6555	−	6.42702i	−1.73451	−	0.471252i
$187$	−8.74833	+	8.74833i	−0.639741	+	0.639741i
$188$	5.07115	+	19.4682i	0.369851	+	1.41986i
$189$	3.87861			0.282127
$190$	−15.9566	−	1.16172i	−1.15761	−	0.0842800i
$191$			9.65925i			0.698919i	0.936951	+	0.349460i	$0.113635\pi$
$191$			9.65925i			0.698919i	−0.936951	+	0.349460i	$0.886365\pi$
$192$	13.3446	−	12.7973i	0.963065	−	0.923564i
$193$	8.33730	−	8.33730i	0.600132	−	0.600132i	−0.340216	−	0.940347i	$-0.610500\pi$
$193$	8.33730	−	8.33730i	0.600132	−	0.600132i	0.940347	+	0.340216i	$0.110500\pi$
$194$	0.320781	−	1.18068i	0.0230308	−	0.0847678i
$195$	12.7397	+	13.5974i	0.912311	+	0.973732i
$196$	−0.874539	−	0.513085i	−0.0624671	−	0.0366490i
$197$	−5.18463	−	5.18463i	−0.369390	−	0.369390i	0.497865	−	0.867255i	$-0.334118\pi$
$197$	−5.18463	−	5.18463i	−0.369390	−	0.369390i	−0.867255	+	0.497865i	$0.834118\pi$
$198$	8.24148	−	4.71996i	0.585696	−	0.335433i
$199$	2.05260			0.145505			0.0727526	−	0.997350i	$-0.476822\pi$
$199$	2.05260			0.145505			0.0727526	+	0.997350i	$0.476822\pi$
$200$	5.17666	+	13.1606i	0.366045	+	0.930597i
$201$			4.64338i			0.327519i
$202$	13.7629	+	24.0313i	0.968354	+	1.69083i
$203$	−12.2449	−	12.2449i	−0.859423	−	0.859423i
$204$	17.1969	+	10.0893i	1.20403	+	0.706393i
$205$	−4.66908	+	6.93154i	−0.326103	+	0.484120i
$206$	14.3214	+	3.89100i	0.997817	+	0.271099i
$207$	5.68404	+	5.68404i	0.395068	+	0.395068i
$208$	−6.92604	+	12.6503i	−0.480234	+	0.877140i
$209$		−	14.5111i		−	1.00375i
$210$	18.5739	+	1.35228i	1.28172	+	0.0933159i
$211$		−	21.8754i		−	1.50596i	−0.658041	−	0.752982i	$-0.728615\pi$
$211$		−	21.8754i		−	1.50596i	0.658041	−	0.752982i	$-0.271385\pi$
$212$	6.39277	−	1.66521i	0.439057	−	0.114367i
$213$	−4.58649	+	4.58649i	−0.314261	+	0.314261i
$214$	6.18681	−	22.7714i	0.422922	−	1.55662i
$215$	4.22903	−	0.824786i	0.288418	−	0.0562499i
$216$	3.01223	+	3.07596i	0.204957	+	0.209293i
$217$	13.5134	−	13.5134i	0.917348	−	0.917348i
$218$	11.9507	+	20.8670i	0.809403	+	1.41329i
$219$		−	18.1030i		−	1.22329i
$220$	−11.5644	+	5.54968i	−0.779672	+	0.374159i
$221$	−15.1598	−	3.47236i	−1.01976	−	0.233577i
$222$	−5.59002	−	9.76068i	−0.375177	−	0.655094i
$223$	8.75815	+	8.75815i	0.586489	+	0.586489i	0.936679	−	0.350190i	$-0.113883\pi$
$223$	8.75815	+	8.75815i	0.586489	+	0.586489i	−0.350190	+	0.936679i	$0.613883\pi$
$224$	3.48729	+	13.9863i	0.233004	+	0.934497i
$225$	10.8490	−	4.39908i	0.723268	−	0.293272i
$226$	−2.39767	+	8.82496i	−0.159491	+	0.587028i
$227$	10.4904	−	10.4904i	0.696275	−	0.696275i	−0.267330	−	0.963605i	$-0.586141\pi$
$227$	10.4904	−	10.4904i	0.696275	−	0.696275i	0.963605	+	0.267330i	$0.0861414\pi$
$228$	−22.6302	+	5.89481i	−1.49872	+	0.390393i
$229$	−16.8561			−1.11389			−0.556943	−	0.830551i	$-0.688026\pi$
$229$	−16.8561			−1.11389			−0.556943	+	0.830551i	$0.688026\pi$
$230$	−7.09913	−	8.21401i	−0.468103	−	0.541616i
$231$			16.8914i			1.11137i
$232$	0.201193	−	19.2206i	0.0132090	−	1.26190i
$233$	−5.97980	−	5.97980i	−0.391750	−	0.391750i	0.483561	−	0.875311i	$-0.339343\pi$
$233$	−5.97980	−	5.97980i	−0.391750	−	0.391750i	−0.875311	+	0.483561i	$0.839343\pi$
$234$	10.5315	+	5.62350i	0.688463	+	0.367620i
$235$	−22.0765	+	4.30556i	−1.44011	+	0.280864i
$236$	−8.13500	−	4.77274i	−0.529543	−	0.310679i
$237$	27.3126	−	27.3126i	1.77414	−	1.77414i
$238$	−13.4886	+	7.72503i	−0.874337	+	0.500739i
$239$		−	2.54185i		−	0.164419i	−0.996615	−	0.0822094i	$-0.973802\pi$
$239$		−	2.54185i		−	0.164419i	0.996615	−	0.0822094i	$-0.0261976\pi$
$240$	13.3526	+	15.7804i	0.861904	+	1.01862i
$241$			0.873299i			0.0562542i	0.999604	+	0.0281271i	$0.00895431\pi$
$241$			0.873299i			0.0562542i	−0.999604	+	0.0281271i	$0.991046\pi$
$242$	1.94914	+	3.40338i	0.125295	+	0.218777i
$243$	13.9992	−	13.9992i	0.898048	−	0.898048i
$244$	−9.26550	+	15.7928i	−0.593163	+	1.01103i
$245$	0.633324	−	0.940210i	0.0404616	−	0.0600678i
$246$	−3.20289	+	11.7887i	−0.204209	+	0.751618i
$247$	15.4529	−	9.69318i	0.983244	−	0.616762i
$248$	21.2117	+	0.222036i	1.34695	+	0.0140993i
$249$	10.7499			0.681249
$250$	−15.0454	+	4.86172i	−0.951554	+	0.307482i
$251$		−	14.0071i		−	0.884120i	−0.896985	−	0.442060i	$-0.854248\pi$
$251$		−	14.0071i		−	0.884120i	0.896985	−	0.442060i	$-0.145752\pi$
$252$	11.5471	−	3.00783i	0.727399	−	0.189476i
$253$	6.96299	−	6.96299i	0.437759	−	0.437759i
$254$	−1.13752	+	4.18678i	−0.0713741	+	0.262702i
$255$	−12.4537	+	18.4883i	−0.779880	+	1.15778i
$256$	−8.38360	+	13.6277i	−0.523975	+	0.851734i
$257$	−8.14242	+	8.14242i	−0.507910	+	0.507910i	−0.913885	−	0.405974i	$-0.866932\pi$
$257$	−8.14242	+	8.14242i	−0.507910	+	0.507910i	0.405974	+	0.913885i	$0.366932\pi$
$258$	5.46521	−	3.12997i	0.340249	−	0.194863i
$259$	8.76919			0.544891
$260$	−13.6347	−	8.60786i	−0.845588	−	0.533837i
$261$	−15.9119			−0.984920
$262$	24.7485	−	14.1736i	1.52896	−	0.875650i
$263$	7.73352	−	7.73352i	0.476869	−	0.476869i	−0.427260	−	0.904129i	$-0.640521\pi$
$263$	7.73352	−	7.73352i	0.476869	−	0.476869i	0.904129	+	0.427260i	$0.140521\pi$
$264$	−13.3958	+	13.1183i	−0.824456	+	0.807375i
$265$	1.41382	+	7.24925i	0.0868501	+	0.445318i
$266$	4.78011	−	17.5938i	0.293087	−	1.07875i
$267$	−1.12765	+	1.12765i	−0.0690109	+	0.0690109i
$268$	−1.01289	−	3.88850i	−0.0618721	−	0.237528i
$269$		−	0.0681509i		−	0.00415523i	−0.999998	−	0.00207762i	$-0.999339\pi$
$269$		−	0.0681509i		−	0.00415523i	0.999998	−	0.00207762i	$-0.000661326\pi$
$270$	−3.64175	+	3.14746i	−0.221630	+	0.191548i
$271$	−4.89920			−0.297605			−0.148803	−	0.988867i	$-0.547542\pi$
$271$	−4.89920			−0.297605			−0.148803	+	0.988867i	$0.547542\pi$
$272$	−16.6020	−	4.69778i	−1.00665	−	0.284845i
$273$	−17.9876	+	11.2831i	−1.08866	+	0.682887i
$274$	5.31006	−	19.5444i	0.320792	−	1.18072i
$275$	−5.38891	−	13.2901i	−0.324963	−	0.801425i
$276$	−13.6874	−	8.03030i	−0.823885	−	0.483367i
$277$	12.5034	−	12.5034i	0.751255	−	0.751255i	−0.223459	−	0.974713i	$-0.571735\pi$
$277$	12.5034	−	12.5034i	0.751255	−	0.751255i	0.974713	+	0.223459i	$0.0717348\pi$
$278$	4.88767	+	8.53432i	0.293143	+	0.511854i
$279$		−	17.5602i		−	1.05130i
$280$	−15.8493	+	2.91921i	−0.947175	+	0.174456i
$281$			22.0270i			1.31402i	0.753881	+	0.657012i	$0.228180\pi$
$281$			22.0270i			1.31402i	−0.753881	+	0.657012i	$0.771820\pi$
$282$	−28.5296	+	16.3391i	−1.69891	+	0.972979i
$283$	5.03687	−	5.03687i	0.299411	−	0.299411i	−0.541372	−	0.840783i	$-0.682095\pi$
$283$	5.03687	−	5.03687i	0.299411	−	0.299411i	0.840783	+	0.541372i	$0.182095\pi$
$284$	2.84037	−	4.84133i	0.168545	−	0.287280i
$285$	−5.00487	−	25.6622i	−0.296463	−	1.52009i
$286$	6.88884	−	12.9011i	0.407345	−	0.762859i
$287$	−6.73436	−	6.73436i	−0.397517	−	0.397517i
$288$	11.3532	+	6.82155i	0.668992	+	0.401964i
$289$		−	1.60602i		−	0.0944717i
$290$	21.4338	+	1.56049i	1.25863	+	0.0916350i
$291$	1.99944			0.117209
$292$	3.94893	+	15.1600i	0.231094	+	0.887171i
$293$	4.29024	−	4.29024i	0.250638	−	0.250638i	−0.570594	−	0.821232i	$-0.693287\pi$
$293$	4.29024	−	4.29024i	0.250638	−	0.250638i	0.821232	+	0.570594i	$0.193287\pi$
$294$	0.434447	−	1.59904i	0.0253375	−	0.0932580i
$295$	5.89121	−	8.74587i	0.343000	−	0.509204i
$296$	6.81039	+	6.95448i	0.395846	+	0.404221i
$297$	−3.08710	−	3.08710i	−0.179132	−	0.179132i
$298$	−3.25158	−	5.67756i	−0.188359	−	0.328892i
$299$	12.0661	+	2.76373i	0.697798	+	0.159831i
$300$	−18.5370	+	13.8029i	−1.07023	+	0.796910i
$301$			4.91005i			0.283011i
$302$	15.3576	+	26.8157i	0.883728	+	1.54307i
$303$	−32.0016	+	32.0016i	−1.83845	+	1.83845i
$304$	17.6653	−	9.87295i	1.01317	−	0.566252i
$305$	−16.9787	−	11.4368i	−0.972197	−	0.654871i
$306$	−3.74480	+	13.7832i	−0.214076	+	0.787935i
$307$	16.3306	−	16.3306i	0.932037	−	0.932037i	−0.0657965	−	0.997833i	$-0.520959\pi$
$307$	16.3306	−	16.3306i	0.932037	−	0.932037i	0.997833	+	0.0657965i	$0.0209588\pi$
$308$	−3.68462	−	14.1453i	−0.209951	−	0.806002i
$309$			24.2528i			1.37969i
$310$	−1.72214	+	23.6541i	−0.0978112	+	1.34347i
$311$			8.57004i			0.485962i	0.970031	+	0.242981i	$0.0781253\pi$
$311$			8.57004i			0.485962i	−0.970031	+	0.242981i	$0.921875\pi$
$312$	−22.9179	−	5.50243i	−1.29747	−	0.311514i
$313$	3.62652	+	3.62652i	0.204983	+	0.204983i	0.802131	−	0.597148i	$-0.203700\pi$
$313$	3.62652	+	3.62652i	0.204983	+	0.204983i	−0.597148	+	0.802131i	$0.703700\pi$
$314$	6.86335	+	1.86472i	0.387321	+	0.105232i
$315$	2.55374	+	13.0941i	0.143887	+	0.737771i
$316$	−16.9145	+	28.8302i	−0.951512	+	1.62183i
$317$	10.8367	+	10.8367i	0.608652	+	0.608652i	0.942594	−	0.333942i	$-0.108379\pi$
$317$	10.8367	+	10.8367i	0.608652	+	0.608652i	−0.333942	+	0.942594i	$0.608379\pi$
$318$	5.36527	+	9.36826i	0.300870	+	0.525346i
$319$			19.4922i			1.09135i
$320$	−14.6241	−	10.3023i	−0.817511	−	0.575913i
$321$	38.5627			2.15236
$322$	10.7359	−	6.14852i	0.598288	−	0.342644i
$323$	15.4312	+	15.4312i	0.858613	+	0.858613i
$324$	−10.6692	+	18.1854i	−0.592734	+	1.01030i
$325$	10.5530	−	14.6162i	0.585374	−	0.810763i
$326$	−1.29815	+	4.77802i	−0.0718979	+	0.264630i
$327$	−27.7879	+	27.7879i	−1.53667	+	1.53667i
$328$	0.110651	−	10.5708i	0.00610967	−	0.583676i
$329$		−	25.6315i		−	1.41311i
$330$	−13.7072	−	15.8598i	−0.754557	−	0.873055i
$331$	−9.27419			−0.509756			−0.254878	−	0.966973i	$-0.582035\pi$
$331$	−9.27419			−0.509756			−0.254878	+	0.966973i	$0.582035\pi$
$332$	−9.00229	+	2.34495i	−0.494065	+	0.128696i
$333$	5.69765	−	5.69765i	0.312229	−	0.312229i
$334$	29.4239	+	7.99423i	1.61000	+	0.437425i
$335$	4.40946	−	0.859975i	0.240915	−	0.0469854i
$336$	−20.5629	+	11.4924i	−1.12180	+	0.626962i
$337$	−5.07755	+	5.07755i	−0.276592	+	0.276592i	−0.831747	−	0.555155i	$-0.812659\pi$
$337$	−5.07755	+	5.07755i	−0.276592	+	0.276592i	0.555155	+	0.831747i	$0.312659\pi$
$338$	18.3400	−	1.28180i	0.997567	−	0.0697210i
$339$	−14.9448			−0.811690
$340$	6.39609	−	18.1992i	0.346877	−	0.986989i
$341$	−21.5114			−1.16491
$342$	−8.32552	−	14.5371i	−0.450193	−	0.786078i
$343$	13.5261	+	13.5261i	0.730342	+	0.730342i
$344$	−3.89396	+	3.81328i	−0.209948	+	0.205598i
$345$	9.91216	−	14.7152i	0.533653	−	0.792241i
$346$	4.16843	−	15.3425i	0.224096	−	0.824816i
$347$	−3.16853	−	3.16853i	−0.170096	−	0.170096i	0.616926	−	0.787021i	$-0.288378\pi$
$347$	−3.16853	−	3.16853i	−0.170096	−	0.170096i	−0.787021	+	0.616926i	$0.788378\pi$
$348$	30.3982	−	7.91825i	1.62952	−	0.424463i
$349$	16.3474			0.875059			0.437529	−	0.899204i	$-0.355854\pi$
$349$	16.3474			0.875059			0.437529	+	0.899204i	$0.355854\pi$
$350$	−2.15581	−	17.8887i	−0.115233	−	0.956189i
$351$	1.22532	−	5.34959i	0.0654030	−	0.285540i
$352$	8.35645	−	13.9077i	0.445400	−	0.741284i
$353$	−14.3438	+	14.3438i	−0.763442	+	0.763442i	−0.976943	−	0.213501i	$-0.931513\pi$
$353$	−14.3438	+	14.3438i	−0.763442	+	0.763442i	0.213501	+	0.976943i	$0.431513\pi$
$354$	4.04125	−	14.8744i	0.214790	−	0.790563i
$355$	5.20488	+	3.50600i	0.276246	+	0.186079i
$356$	0.698342	−	1.19030i	0.0370121	−	0.0630860i
$357$	−17.9623	−	17.9623i	−0.950668	−	0.950668i
$358$	2.97357	+	5.19214i	0.157158	+	0.274413i
$359$			23.3016i			1.22981i	0.788600	+	0.614906i	$0.210806\pi$
$359$			23.3016i			1.22981i	−0.788600	+	0.614906i	$0.789194\pi$
$360$	−8.40111	+	12.1945i	−0.442777	+	0.642708i
$361$	−6.59612			−0.347164
$362$	−3.43972	−	6.00607i	−0.180788	−	0.315672i
$363$	−4.53216	+	4.53216i	−0.237877	+	0.237877i
$364$	12.6021	−	13.3726i	0.660527	−	0.700913i
$365$	−17.1911	+	3.35276i	−0.899821	+	0.175492i
$366$	−28.8761	−	7.84542i	−1.50938	−	0.410087i
$367$	−25.8727	−	25.8727i	−1.35054	−	1.35054i	−0.885052	−	0.465491i	$-0.845878\pi$
$367$	−25.8727	−	25.8727i	−1.35054	−	1.35054i	−0.465491	−	0.885052i	$-0.654122\pi$
$368$	13.2139	+	3.73907i	0.688823	+	0.194912i
$369$	−8.75109			−0.455564
$370$	−8.23368	+	7.11613i	−0.428048	+	0.369950i
$371$	−8.41663			−0.436970
$372$	8.73852	+	33.5473i	0.453071	+	1.73934i
$373$	7.06704	+	7.06704i	0.365917	+	0.365917i	0.865986	−	0.500069i	$-0.166692\pi$
$373$	7.06704	+	7.06704i	0.365917	+	0.365917i	−0.500069	+	0.865986i	$0.666692\pi$
$374$	16.8846	+	4.58741i	0.873080	+	0.237209i
$375$	−14.1138	−	21.6443i	−0.728832	−	1.11771i
$376$	20.3273	−	19.9061i	1.04830	−	1.02658i
$377$	−20.7572	+	13.0204i	−1.06905	+	0.670587i
$378$	−2.72600	−	4.75985i	−0.140210	−	0.244820i
$379$		−	10.3135i		−	0.529767i	−0.964280	−	0.264884i	$-0.914666\pi$
$379$		−	10.3135i		−	0.529767i	0.964280	−	0.264884i	$-0.0853335\pi$
$380$	9.78907	+	20.3984i	0.502168	+	1.04642i
$381$	−7.09019			−0.363241
$382$	11.8539	−	6.78881i	0.606497	−	0.347346i
$383$	5.79036	+	5.79036i	0.295873	+	0.295873i	0.839395	−	0.543522i	$-0.182909\pi$
$383$	5.79036	+	5.79036i	0.295873	+	0.295873i	−0.543522	+	0.839395i	$0.682909\pi$
$384$	−25.0839	−	7.38228i	−1.28006	−	0.376725i
$385$	16.0404	−	3.12835i	0.817496	−	0.159436i
$386$	−16.0913	−	4.37187i	−0.819024	−	0.222522i
$387$	3.19023	+	3.19023i	0.162169	+	0.162169i
$388$	−1.67439	+	0.436151i	−0.0850042	+	0.0221422i
$389$			10.5068i			0.532715i	0.963874	+	0.266357i	$0.0858201\pi$
$389$			10.5068i			0.532715i	−0.963874	+	0.266357i	$0.914180\pi$
$390$	7.73297	−	25.1909i	0.391574	−	1.27559i
$391$			14.8089i			0.748920i
$392$	−0.0150089	+	1.43385i	−0.000758066	+	0.0724204i
$393$	32.9567	+	32.9567i	1.66244	+	1.66244i
$394$	−2.71869	+	10.0065i	−0.136966	+	0.504121i
$395$	−30.9951	−	20.8783i	−1.55953	−	1.05050i
$396$	−11.5847	−	6.79666i	−0.582153	−	0.341545i
$397$	−18.0247	−	18.0247i	−0.904635	−	0.904635i	0.0911976	−	0.995833i	$-0.470930\pi$
$397$	−18.0247	−	18.0247i	−0.904635	−	0.904635i	−0.995833	+	0.0911976i	$0.970930\pi$
$398$	−1.44263	−	2.51896i	−0.0723125	−	0.126264i
$399$	29.7946			1.49160
$400$	12.5125	−	15.6025i	0.625624	−	0.780125i
$401$		−	28.9089i		−	1.44364i	−0.692080	−	0.721820i	$-0.743306\pi$
$401$		−	28.9089i		−	1.44364i	0.692080	−	0.721820i	$-0.256694\pi$
$402$	5.69838	−	3.26351i	0.284209	−	0.162769i
$403$	−14.3693	−	22.9075i	−0.715784	−	1.14110i
$404$	19.8183	−	33.7798i	0.985999	−	1.68061i
$405$	−19.5509	−	13.1695i	−0.971494	−	0.654397i
$406$	−6.42092	+	23.6331i	−0.318665	+	1.17289i
$407$	−6.97966	−	6.97966i	−0.345969	−	0.345969i
$408$	0.295135	−	28.1952i	0.0146114	−	1.39587i
$409$	33.8248			1.67253			0.836266	−	0.548325i	$-0.184734\pi$
$409$	33.8248			1.67253			0.836266	+	0.548325i	$0.184734\pi$
$410$	11.7880	+	0.858226i	0.582167	+	0.0423848i
$411$	33.0978			1.63259
$412$	−5.29042	−	20.3100i	−0.260640	−	1.00060i
$413$	8.49708	+	8.49708i	0.418114	+	0.418114i
$414$	2.98057	−	10.9704i	0.146487	−	0.539165i
$415$	−1.99093	−	10.2084i	−0.0977312	−	0.501110i
$416$	20.3923	−	0.391336i	0.999816	−	0.0191868i
$417$	−11.3649	+	11.3649i	−0.556540	+	0.556540i
$418$	−17.8081	+	10.1988i	−0.871022	+	0.498841i
$419$	−29.8088			−1.45626			−0.728128	−	0.685441i	$-0.759609\pi$
$419$	−29.8088			−1.45626			−0.728128	+	0.685441i	$0.759609\pi$
$420$	−11.3948	−	23.7444i	−0.556007	−	1.15861i
$421$		−	22.2675i		−	1.08525i	−0.839974	−	0.542626i	$-0.817430\pi$
$421$		−	22.2675i		−	1.08525i	0.839974	−	0.542626i	$-0.182570\pi$
$422$	−26.8456	+	15.3747i	−1.30682	+	0.748427i
$423$	−16.6537	−	16.6537i	−0.809730	−	0.809730i
$424$	−6.53658	−	6.67488i	−0.317445	−	0.324161i
$425$	19.8634	+	8.40220i	0.963515	+	0.407567i
$426$	8.85208	+	2.40504i	0.428885	+	0.116525i
$427$	16.4957	−	16.4957i	0.798282	−	0.798282i
$428$	−32.2934	+	8.41192i	−1.56096	+	0.406606i
$429$	23.2975	+	5.33629i	1.12481	+	0.257638i
$430$	−3.98447	−	4.61021i	−0.192148	−	0.222324i
$431$	16.6731			0.803116			0.401558	−	0.915834i	$-0.368469\pi$
$431$	16.6731			0.803116			0.401558	+	0.915834i	$0.368469\pi$
$432$	1.65775	−	5.85850i	0.0797585	−	0.281867i
$433$	−14.3063	−	14.3063i	−0.687515	−	0.687515i	0.274167	−	0.961682i	$-0.411598\pi$
$433$	−14.3063	−	14.3063i	−0.687515	−	0.687515i	−0.961682	+	0.274167i	$0.911598\pi$
$434$	−26.0813	−	7.08608i	−1.25194	−	0.340143i
$435$	6.72283	+	34.4709i	0.322335	+	1.65275i
$436$	17.2088	−	29.3319i	0.824152	−	1.40474i
$437$	−12.2820	−	12.2820i	−0.587528	−	0.587528i
$438$	−22.2161	+	12.7233i	−1.06153	+	0.607945i
$439$	1.27466			0.0608361			0.0304181	−	0.999537i	$-0.490316\pi$
$439$	1.27466			0.0608361			0.0304181	+	0.999537i	$0.490316\pi$
$440$	14.9384	+	10.2914i	0.712160	+	0.490624i
$441$	1.18702			0.0565246
$442$	6.39348	+	21.0447i	0.304107	+	1.00099i
$443$	−4.65182	+	4.65182i	−0.221015	+	0.221015i	−0.808926	−	0.587911i	$-0.799951\pi$
$443$	−4.65182	+	4.65182i	−0.221015	+	0.221015i	0.587911	+	0.808926i	$0.299951\pi$
$444$	−8.04953	+	13.7202i	−0.382014	+	0.651131i
$445$	1.27969	+	0.861995i	0.0606629	+	0.0408625i
$446$	4.59256	−	16.9035i	0.217464	−	0.800405i
$447$	7.56062	−	7.56062i	0.357605	−	0.357605i
$448$	14.7130	−	14.1096i	0.695126	−	0.666615i
$449$	−4.97674			−0.234867			−0.117434	−	0.993081i	$-0.537467\pi$
$449$	−4.97674			−0.234867			−0.117434	+	0.993081i	$0.537467\pi$
$450$	−13.0236	−	10.2222i	−0.613938	−	0.481878i
$451$			10.7202i			0.504792i
$452$	12.5152	−	3.26000i	0.588665	−	0.153338i
$453$	−35.7096	+	35.7096i	−1.67778	+	1.67778i
$454$	−20.2469	−	5.50093i	−0.950234	−	0.258171i
$455$	14.0461	+	14.9918i	0.658493	+	0.702825i
$456$	23.1393	+	23.6289i	1.08360	+	1.10652i
$457$	9.07097	+	9.07097i	0.424322	+	0.424322i	0.886689	−	0.462367i	$-0.153000\pi$
$457$	9.07097	+	9.07097i	0.424322	+	0.424322i	−0.462367	+	0.886689i	$0.653000\pi$
$458$	11.8470	+	20.6859i	0.553574	+	0.966591i
$459$	6.56567			0.306459
$460$	−5.09079	+	14.4851i	−0.237359	+	0.675373i
$461$			29.0770i			1.35425i	0.735867	+	0.677126i	$0.236775\pi$
$461$			29.0770i			1.35425i	−0.735867	+	0.677126i	$0.763225\pi$
$462$	20.7291	−	11.8717i	0.964407	−	0.552323i
$463$	−16.7239	−	16.7239i	−0.777227	−	0.777227i	0.202132	−	0.979358i	$-0.435213\pi$
$463$	−16.7239	−	16.7239i	−0.777227	−	0.777227i	−0.979358	+	0.202132i	$0.935213\pi$
$464$	−23.7290	+	13.2619i	−1.10159	+	0.615669i
$465$	−38.0418	+	7.41927i	−1.76415	+	0.344060i
$466$	−3.13566	+	11.5412i	−0.145257	+	0.534637i
$467$	23.0476	+	23.0476i	1.06652	+	1.06652i	0.997624	+	0.0688934i	$0.0219468\pi$
$467$	23.0476	+	23.0476i	1.06652	+	1.06652i	0.0688934	+	0.997624i	$0.478053\pi$
$468$	−0.500626	−	16.8766i	−0.0231415	−	0.780122i
$469$			5.11954i			0.236398i
$470$	20.7998	+	24.0663i	0.959423	+	1.11009i
$471$			11.6229i			0.535554i
$472$	−0.139614	+	13.3377i	−0.00642624	+	0.613919i
$473$	3.90806	−	3.90806i	0.179693	−	0.179693i
$474$	−52.7143	−	14.3221i	−2.42125	−	0.657834i
$475$	−23.4425	+	9.50549i	−1.07561	+	0.436142i
$476$	18.9604	+	11.1239i	0.869048	+	0.509864i
$477$	−5.46858	+	5.46858i	−0.250389	+	0.250389i
$478$	−3.11937	+	1.78649i	−0.142677	+	0.0817121i
$479$			17.6387i			0.805934i	0.915215	+	0.402967i	$0.132021\pi$
$479$			17.6387i			0.805934i	−0.915215	+	0.402967i	$0.867979\pi$
$480$	9.98120	−	27.4772i	0.455577	−	1.25416i
$481$	2.77035	−	12.0949i	0.126317	−	0.551482i
$482$	1.07172	−	0.613780i	0.0488154	−	0.0279569i
$483$	14.2966	+	14.2966i	0.650519	+	0.650519i
$484$	2.80673	−	4.78399i	0.127579	−	0.217454i
$485$	−0.370306	−	1.89872i	−0.0168147	−	0.0862163i
$486$	−27.0189	−	7.34082i	−1.22560	−	0.332986i
$487$	−16.4050	+	16.4050i	−0.743380	+	0.743380i	−0.973227	−	0.229847i	$-0.926177\pi$
$487$	−16.4050	+	16.4050i	−0.743380	+	0.743380i	0.229847	+	0.973227i	$0.426177\pi$
$488$	25.8930	+	0.271037i	1.17212	+	0.0122693i
$489$	−8.09142			−0.365907
$490$	−1.59895	−	0.116412i	−0.0722331	−	0.00525895i
$491$		−	18.4831i		−	0.834130i	−0.908877	−	0.417065i	$-0.863059\pi$
$491$		−	18.4831i		−	0.834130i	0.908877	−	0.417065i	$-0.136941\pi$
$492$	16.7182	−	4.35482i	0.753714	−	0.196330i
$493$	−20.7280	−	20.7280i	−0.933544	−	0.933544i
$494$	−22.7563	−	12.1512i	−1.02385	−	0.546709i
$495$	8.38942	−	12.4546i	0.377076	−	0.559793i
$496$	−14.6358	−	26.1872i	−0.657165	−	1.17584i
$497$	−5.05681	+	5.05681i	−0.226829	+	0.226829i
$498$	−7.55537	−	13.1924i	−0.338564	−	0.591164i
$499$			13.1530i			0.588810i	0.955681	+	0.294405i	$0.0951215\pi$
$499$			13.1530i			0.588810i	−0.955681	+	0.294405i	$0.904878\pi$
$500$	16.5407	+	15.0468i	0.739721	+	0.672914i
$501$			49.8284i			2.22617i
$502$	−17.1896	+	9.84460i	−0.767208	+	0.439386i
$503$	2.48957	−	2.48957i	0.111005	−	0.111005i	−0.649423	−	0.760427i	$-0.724989\pi$
$503$	2.48957	−	2.48957i	0.111005	−	0.111005i	0.760427	+	0.649423i	$0.224989\pi$
$504$	−11.8069	−	12.0567i	−0.525920	−	0.537046i
$505$	36.3163	+	24.4627i	1.61606	+	1.08857i
$506$	−13.4388	−	3.65122i	−0.597428	−	0.162316i
$507$	9.87971	+	28.3741i	0.438773	+	1.26014i
$508$	5.93752	−	1.54663i	0.263435	−	0.0686205i
$509$	5.04310			0.223532			0.111766	−	0.993735i	$-0.464349\pi$
$509$	5.04310			0.223532			0.111766	+	0.993735i	$0.464349\pi$
$510$	31.4417	+	2.28912i	1.39226	+	0.101364i
$511$		−	19.9594i		−	0.882952i
$512$	22.6163	+	0.710420i	0.999507	+	0.0313964i
$513$	−5.44533	+	5.44533i	−0.240417	+	0.240417i
$514$	15.7152	+	4.26969i	0.693166	+	0.188328i
$515$	23.0310	−	4.49172i	1.01487	−	0.197929i
$516$	−7.68222	−	4.50710i	−0.338191	−	0.198414i
$517$	−20.4009	+	20.4009i	−0.897231	+	0.897231i
$518$	−6.16325	−	10.7616i	−0.270797	−	0.472837i
$519$	25.9820			1.14048
$520$	−0.980744	+	22.7824i	−0.0430085	+	0.999075i
$521$	−8.86981			−0.388593			−0.194297	−	0.980943i	$-0.562242\pi$
$521$	−8.86981			−0.388593			−0.194297	+	0.980943i	$0.562242\pi$
$522$	11.1833	+	19.5271i	0.489481	+	0.854678i
$523$	−0.908020	+	0.908020i	−0.0397050	+	0.0397050i	−0.726681	−	0.686976i	$-0.758938\pi$
$523$	−0.908020	+	0.908020i	−0.0397050	+	0.0397050i	0.686976	+	0.726681i	$0.258938\pi$
$524$	−34.7879	−	20.4098i	−1.51972	−	0.891605i
$525$	27.2877	−	11.0647i	1.19093	−	0.482902i
$526$	−14.9259	−	4.05526i	−0.650802	−	0.176818i
$527$	22.8753	−	22.8753i	0.996464	−	0.996464i
$528$	25.5138	+	7.21950i	1.11035	+	0.314188i
$529$			11.2132i			0.487532i
$530$	7.90265	−	6.83003i	0.343269	−	0.296678i
$531$	11.0417			0.479168
$532$	−24.9508	+	6.49929i	−1.08176	+	0.281780i
$533$	−11.4159	+	7.16088i	−0.494478	+	0.310172i
$534$	2.17640	+	0.591311i	0.0941820	+	0.0255885i
$535$	−7.14198	−	36.6200i	−0.308775	−	1.58322i
$536$	−4.06009	+	3.97597i	−0.175369	+	0.171736i
$537$	−6.91419	+	6.91419i	−0.298369	+	0.298369i
$538$	−0.0836351	+	0.0478984i	−0.00360576	+	0.00206505i
$539$		−	1.45411i		−	0.0626328i
$540$	6.42211	+	2.25705i	0.276364	+	0.0971278i
$541$			6.14081i			0.264014i	0.991249	+	0.132007i	$0.0421421\pi$
$541$			6.14081i			0.264014i	−0.991249	+	0.132007i	$0.957858\pi$
$542$	3.44330	+	6.01232i	0.147903	+	0.258251i
$543$	7.99808	−	7.99808i	0.343230	−	0.343230i
$544$	5.90324	+	23.6758i	0.253100	+	1.01509i
$545$	31.5345	+	21.2416i	1.35079	+	0.909890i
$546$	26.4890	+	14.1444i	1.13362	+	0.605323i
$547$	−5.80253	−	5.80253i	−0.248098	−	0.248098i	0.572091	−	0.820190i	$-0.306132\pi$
$547$	−5.80253	−	5.80253i	−0.248098	−	0.248098i	−0.820190	+	0.572091i	$0.806132\pi$
$548$	−27.7170	+	7.21984i	−1.18401	+	0.308416i
$549$		−	21.4356i		−	0.914851i
$550$	−12.5222	+	15.9540i	−0.533950	+	0.680280i
$551$	34.3822			1.46473
$552$	−0.234905	+	22.4412i	−0.00999821	+	0.955160i
$553$	30.1134	−	30.1134i	1.28055	−	1.28055i
$554$	−24.1319	−	6.55646i	−1.02527	−	0.278557i
$555$	−14.7505	−	9.93590i	−0.626122	−	0.421755i
$556$	7.03816	−	11.9963i	0.298484	−	0.508758i
$557$	8.73598	+	8.73598i	0.370155	+	0.370155i	0.867534	−	0.497378i	$-0.165704\pi$
$557$	8.73598	+	8.73598i	0.370155	+	0.370155i	−0.497378	+	0.867534i	$0.665704\pi$
$558$	−21.5500	+	12.3418i	−0.912283	+	0.522472i
$559$	6.77221	+	1.55118i	0.286434	+	0.0656078i
$560$	14.7218	+	17.3986i	0.622110	+	0.735225i
$561$			28.5935i			1.20722i
$562$	27.0317	−	15.4812i	1.14026	−	0.653037i
$563$	22.9152	−	22.9152i	0.965762	−	0.965762i	−0.0336711	−	0.999433i	$-0.510720\pi$
$563$	22.9152	−	22.9152i	0.965762	−	0.965762i	0.999433	+	0.0336711i	$0.0107199\pi$
$564$	40.1028	+	23.5280i	1.68863	+	0.990708i
$565$	2.76784	+	14.1919i	0.116444	+	0.597059i
$566$	−9.72134	−	2.64121i	−0.408618	−	0.111018i
$567$	18.9948	−	18.9948i	0.797705	−	0.797705i
$568$	−7.93760	−	0.0830875i	−0.333054	−	0.00348627i
$569$		−	37.0883i		−	1.55482i	−0.628993	−	0.777411i	$-0.716533\pi$
$569$		−	37.0883i		−	1.55482i	0.628993	−	0.777411i	$-0.283467\pi$
$570$	−27.9751	+	24.1781i	−1.17175	+	1.01271i
$571$			19.8776i			0.831850i	0.909399	+	0.415925i	$0.136542\pi$
$571$			19.8776i			0.831850i	−0.909399	+	0.415925i	$0.863458\pi$
$572$	−20.6740	+	0.613271i	−0.864423	+	0.0256421i
$573$	15.7854	+	15.7854i	0.659445	+	0.659445i
$574$	−3.53133	+	12.9975i	−0.147395	+	0.542507i
$575$	−15.8097	−	6.68750i	−0.659310	−	0.278888i
$576$	0.392097	−	18.7271i	0.0163374	−	0.780294i
$577$	−20.9677	−	20.9677i	−0.872898	−	0.872898i	0.119889	−	0.992787i	$-0.461746\pi$
$577$	−20.9677	−	20.9677i	−0.872898	−	0.872898i	−0.992787	+	0.119889i	$0.961746\pi$
$578$	−1.97091	+	1.12876i	−0.0819792	+	0.0469501i
$579$		−	27.2501i		−	1.13247i
$580$	−13.1492	−	27.4004i	−0.545992	−	1.13774i
$581$	11.8523			0.491716
$582$	−1.40527	−	2.45373i	−0.0582502	−	0.101710i
$583$	6.69905	+	6.69905i	0.277446	+	0.277446i
$584$	15.8290	−	15.5010i	0.655007	−	0.641437i
$585$	18.8669	+	0.614421i	0.780051	+	0.0254032i
$586$	−8.28031	−	2.24970i	−0.342056	−	0.0929341i
$587$	−18.2145	+	18.2145i	−0.751793	+	0.751793i	−0.974814	−	0.223021i	$-0.928408\pi$
$587$	−18.2145	+	18.2145i	−0.751793	+	0.751793i	0.223021	+	0.974814i	$0.428408\pi$
$588$	−2.26769	+	0.590698i	−0.0935181	+	0.0243600i
$589$			37.9439i			1.56345i
$590$	−14.8735	−	1.08287i	−0.612332	−	0.0445809i
$591$	−16.9457			−0.697054
$592$	3.74802	−	13.2456i	0.154043	−	0.544389i
$593$	−24.5024	+	24.5024i	−1.00619	+	1.00619i	−0.00621080	+	0.999981i	$0.501977\pi$
$593$	−24.5024	+	24.5024i	−1.00619	+	1.00619i	−0.999981	+	0.00621080i	$0.998023\pi$
$594$	−1.61880	+	5.95821i	−0.0664202	+	0.244468i
$595$	−13.7307	+	20.3842i	−0.562906	+	0.835669i
$596$	−4.68222	+	7.98072i	−0.191791	+	0.326903i
$597$	3.35442	−	3.35442i	0.137287	−	0.137287i
$598$	−5.08871	−	16.7499i	−0.208093	−	0.684956i
$599$	−35.5348			−1.45191			−0.725955	−	0.687742i	$-0.758602\pi$
$599$	−35.5348			−1.45191			−0.725955	+	0.687742i	$0.758602\pi$
$600$	29.9673	+	13.0476i	1.22341	+	0.532667i
$601$	29.2793			1.19433			0.597165	−	0.802119i	$-0.296294\pi$
$601$	29.2793			1.19433			0.597165	+	0.802119i	$0.296294\pi$
$602$	6.02564	−	3.45093i	0.245587	−	0.140649i
$603$	3.32634	+	3.32634i	0.135459	+	0.135459i
$604$	22.1146	−	37.6937i	0.899831	−	1.53374i
$605$	5.14323	+	3.46447i	0.209102	+	0.140851i
$606$	61.7642	+	16.7809i	2.50900	+	0.681676i
$607$	29.5098	+	29.5098i	1.19777	+	1.19777i	0.974834	+	0.222933i	$0.0715632\pi$
$607$	29.5098	+	29.5098i	1.19777	+	1.19777i	0.222933	+	0.974834i	$0.428437\pi$
$608$	−24.5318	−	14.7399i	−0.994897	−	0.597783i
$609$	−40.0219			−1.62177
$610$	−2.10221	+	28.8745i	−0.0851160	+	1.16909i
$611$	−35.3524	−	8.09747i	−1.43021	−	0.327589i
$612$	19.5468	−	5.09163i	0.790133	−	0.205817i
$613$	25.7721	−	25.7721i	1.04093	−	1.04093i	0.0417992	−	0.999126i	$-0.486691\pi$
$613$	25.7721	−	25.7721i	1.04093	−	1.04093i	0.999126	−	0.0417992i	$-0.0133090\pi$
$614$	−31.5186	−	8.56336i	−1.27199	−	0.345589i
$615$	3.69737	+	18.9580i	0.149093	+	0.764462i
$616$	−14.7695	+	14.4635i	−0.595080	+	0.582751i
$617$	−22.8970	−	22.8970i	−0.921800	−	0.921800i	0.0753568	−	0.997157i	$-0.475990\pi$
$617$	−22.8970	−	22.8970i	−0.921800	−	0.921800i	−0.997157	+	0.0753568i	$0.975990\pi$
$618$	29.7631	−	17.0456i	1.19725	−	0.685674i
$619$			24.6592i			0.991136i	0.868569	+	0.495568i	$0.165040\pi$
$619$			24.6592i			0.991136i	−0.868569	+	0.495568i	$0.834960\pi$
$620$	30.2389	−	14.5114i	1.21442	−	0.582792i
$621$	−5.22576			−0.209703
$622$	10.5172	−	6.02327i	0.421701	−	0.241511i
$623$	−1.24328	+	1.24328i	−0.0498111	+	0.0498111i
$624$	9.35474	+	31.9922i	0.374489	+	1.28071i
$625$	−17.9400	+	17.4114i	−0.717600	+	0.696455i
$626$	1.90166	−	6.99930i	0.0760054	−	0.279748i
$627$	−23.7144	−	23.7144i	−0.947063	−	0.947063i
$628$	−2.53537	−	9.73331i	−0.101172	−	0.388401i
$629$	14.8444			0.591885
$630$	14.2743	−	12.3369i	0.568704	−	0.491514i
$631$	23.6013			0.939553			0.469777	−	0.882785i	$-0.344334\pi$
$631$	23.6013			0.939553			0.469777	+	0.882785i	$0.344334\pi$
$632$	47.2685	+	0.494787i	1.88024	+	0.0196816i
$633$	−35.7494	−	35.7494i	−1.42091	−	1.42091i
$634$	5.68252	−	20.9153i	0.225682	−	0.830652i
$635$	1.31313	+	6.73301i	0.0521101	+	0.267191i
$636$	7.72590	−	13.1686i	0.306352	−	0.522168i
$637$	1.54848	−	0.971319i	0.0613529	−	0.0384850i
$638$	23.9209	−	13.6997i	0.947036	−	0.542375i
$639$			6.57117i			0.259952i
$640$	−2.36474	+	25.1875i	−0.0934747	+	0.995622i
$641$	36.2451			1.43160			0.715798	−	0.698307i	$-0.246063\pi$
$641$	36.2451			1.43160			0.715798	+	0.698307i	$0.246063\pi$
$642$	−27.1030	−	47.3243i	−1.06967	−	1.86774i
$643$	−16.7752	−	16.7752i	−0.661550	−	0.661550i	0.294195	−	0.955745i	$-0.404948\pi$
$643$	−16.7752	−	16.7752i	−0.661550	−	0.661550i	−0.955745	+	0.294195i	$0.904948\pi$
$644$	−15.0910	−	8.85377i	−0.594668	−	0.348887i
$645$	5.56331	−	8.25909i	0.219055	−	0.325201i
$646$	8.09172	−	29.7827i	0.318365	−	1.17178i
$647$	−13.2465	−	13.2465i	−0.520773	−	0.520773i	0.397032	−	0.917805i	$-0.370040\pi$
$647$	−13.2465	−	13.2465i	−0.520773	−	0.520773i	−0.917805	+	0.397032i	$0.870040\pi$
$648$	29.8158	+	0.312099i	1.17128	+	0.0122604i
$649$		−	13.5262i		−	0.530948i
$650$	−25.3541	−	2.67794i	−0.994468	−	0.105037i
$651$		−	44.1679i		−	1.73107i
$652$	6.77598	−	1.76503i	0.265368	−	0.0691241i
$653$	−4.44968	−	4.44968i	−0.174129	−	0.174129i	0.614662	−	0.788791i	$-0.289293\pi$
$653$	−4.44968	−	4.44968i	−0.174129	−	0.174129i	−0.788791	+	0.614662i	$0.789293\pi$
$654$	53.6316	+	14.5713i	2.09716	+	0.569782i
$655$	25.1927	−	37.4002i	0.984361	−	1.46134i
$656$	−13.0503	+	7.29369i	−0.509530	+	0.284771i
$657$	−12.9683	−	12.9683i	−0.505942	−	0.505942i
$658$	−31.4551	+	18.0146i	−1.22625	+	0.702282i
$659$	5.67561			0.221090			0.110545	−	0.993871i	$-0.464740\pi$
$659$	5.67561			0.221090			0.110545	+	0.993871i	$0.464740\pi$
$660$	−9.82944	+	27.9683i	−0.382610	+	1.08866i
$661$			49.0755i			1.90882i	0.298506	+	0.954408i	$0.403512\pi$
$661$			49.0755i			1.90882i	−0.298506	+	0.954408i	$0.596488\pi$
$662$	6.51817	+	11.3813i	0.253336	+	0.442348i
$663$	−30.4493	+	19.1000i	−1.18255	+	0.741782i
$664$	9.20481	+	9.39955i	0.357216	+	0.364773i
$665$	−5.51810	−	28.2937i	−0.213983	−	1.09718i
$666$	−10.9967	−	2.98771i	−0.426112	−	0.115771i
$667$	16.4979	+	16.4979i	0.638801	+	0.638801i
$668$	−10.8694	−	41.7277i	−0.420549	−	1.61449i
$669$	28.6256			1.10673
$670$	−4.15447	−	4.80690i	−0.160501	−	0.185707i
$671$	−26.2588			−1.01371
$672$	28.5558	+	17.1577i	1.10156	+	0.661873i
$673$	2.37388	+	2.37388i	0.0915062	+	0.0915062i	0.751378	−	0.659872i	$-0.229389\pi$
$673$	2.37388	+	2.37388i	0.0915062	+	0.0915062i	−0.659872	+	0.751378i	$0.729389\pi$
$674$	9.79984	+	2.66254i	0.377476	+	0.102557i
$675$	−2.96496	+	7.00937i	−0.114121	+	0.269791i
$676$	−14.4630	−	21.6061i	−0.556267	−	0.831003i
$677$	15.4186	−	15.4186i	0.592585	−	0.592585i	−0.345744	−	0.938329i	$-0.612373\pi$
$677$	15.4186	−	15.4186i	0.592585	−	0.592585i	0.938329	+	0.345744i	$0.112373\pi$
$678$	10.5036	+	18.3403i	0.403390	+	0.704356i
$679$	2.20448			0.0846000
$680$	−26.8295	+	4.94161i	−1.02886	+	0.189502i
$681$		−	34.2875i		−	1.31390i
$682$	15.1188	+	26.3989i	0.578930	+	1.01087i
$683$	25.1139	+	25.1139i	0.960957	+	0.960957i	0.999266	−	0.0383091i	$-0.0121971\pi$
$683$	25.1139	+	25.1139i	0.960957	+	0.960957i	−0.0383091	+	0.999266i	$0.512197\pi$
$684$	−11.9886	+	20.4342i	−0.458396	+	0.781323i
$685$	−6.12986	−	31.4305i	−0.234210	−	1.20090i
$686$	7.09277	−	26.1059i	0.270803	−	0.996727i
$687$	−27.5468	+	27.5468i	−1.05097	+	1.05097i
$688$	7.41646	+	2.09860i	0.282750	+	0.0800082i
$689$	−2.65897	+	11.6087i	−0.101299	+	0.442255i
$690$	−25.0251	−	1.82196i	−0.952691	−	0.0693608i
$691$	13.9179			0.529461			0.264730	−	0.964322i	$-0.414717\pi$
$691$	13.9179			0.529461			0.264730	+	0.964322i	$0.414717\pi$
$692$	−21.7580	+	5.66762i	−0.827117	+	0.215451i
$693$	12.1003	+	12.1003i	0.459653	+	0.459653i
$694$	−1.66150	+	6.11537i	−0.0630697	+	0.232136i
$695$	12.8972	+	8.68752i	0.489217	+	0.329536i
$696$	−31.0821	−	31.7397i	−1.17816	−	1.20309i
$697$	−11.3999	−	11.3999i	−0.431800	−	0.431800i
$698$	−11.4895	−	20.0617i	−0.434883	−	0.759345i
$699$	−19.5447			−0.739249
$700$	−20.4379	+	15.2183i	−0.772479	+	0.575198i
$701$	16.3609			0.617941			0.308971	−	0.951072i	$-0.400016\pi$
$701$	16.3609			0.617941			0.308971	+	0.951072i	$0.400016\pi$
$702$	−7.42624	+	2.25612i	−0.280285	+	0.0851520i
$703$	−12.3114	+	12.3114i	−0.464334	+	0.464334i
$704$	−22.9408	−	0.480321i	−0.864613	−	0.0181028i
$705$	−29.0417	+	43.1142i	−1.09377	+	1.62378i
$706$	27.6840	+	7.52152i	1.04190	+	0.283076i
$707$	−35.2833	+	35.2833i	−1.32696	+	1.32696i
$708$	−21.0942	+	5.49469i	−0.792768	+	0.206503i
$709$	−43.9222			−1.64953			−0.824766	−	0.565474i	$-0.808693\pi$
$709$	−43.9222			−1.64953			−0.824766	+	0.565474i	$0.808693\pi$
$710$	0.644440	−	8.85157i	0.0241854	−	0.332193i
$711$		−	39.1314i		−	1.46754i
$712$	−1.95156	−	0.0204281i	−0.0731379	−	0.000765576i
$713$	−18.2070	+	18.2070i	−0.681856	+	0.681856i
$714$	−9.41900	+	34.6679i	−0.352497	+	1.29741i
$715$	0.752671	−	23.1121i	0.0281483	−	0.864345i
$716$	4.28190	−	7.29837i	0.160022	−	0.272753i
$717$	−4.15396	−	4.15396i	−0.155133	−	0.155133i
$718$	28.5958	−	16.3771i	1.06719	−	0.611186i
$719$	−31.4906			−1.17440			−0.587200	−	0.809442i	$-0.699770\pi$
$719$	−31.4906			−1.17440			−0.587200	+	0.809442i	$0.699770\pi$
$720$	20.8697	+	1.73920i	0.777769	+	0.0648163i
$721$			26.7398i			0.995842i
$722$	4.63595	+	8.09479i	0.172532	+	0.301257i
$723$	1.42717	+	1.42717i	0.0530770	+	0.0530770i
$724$	−4.95314	+	8.44248i	−0.184082	+	0.313762i
$725$	31.4893	−	12.7683i	1.16948	−	0.474203i
$726$	8.74723	+	2.37655i	0.324640	+	0.0882022i
$727$	−8.98640	−	8.98640i	−0.333287	−	0.333287i	0.520546	−	0.853833i	$-0.325728\pi$
$727$	−8.98640	−	8.98640i	−0.333287	−	0.333287i	−0.853833	+	0.520546i	$0.825728\pi$
$728$	−25.2680	−	6.06667i	−0.936493	−	0.224846i
$729$		−	14.1295i		−	0.523315i
$730$	16.1969	+	18.7405i	0.599474	+	0.693618i
$731$			8.31169i			0.307419i
$732$	10.6671	+	40.9509i	0.394266	+	1.51359i
$733$	−4.04919	+	4.04919i	−0.149560	+	0.149560i	−0.777922	−	0.628361i	$-0.783726\pi$
$733$	−4.04919	+	4.04919i	−0.149560	+	0.149560i	0.628361	+	0.777922i	$0.283726\pi$
$734$	−13.5670	+	49.9352i	−0.500767	+	1.84314i
$735$	−0.501520	−	2.57151i	−0.0184989	−	0.0948516i
$736$	−4.69852	−	18.8441i	−0.173190	−	0.694603i
$737$	4.07479	−	4.07479i	0.150097	−	0.150097i
$738$	6.15052	+	10.7394i	0.226404	+	0.395322i
$739$		−	8.88137i		−	0.326707i	−0.986568	−	0.163353i	$-0.947769\pi$
$739$		−	8.88137i		−	0.326707i	0.986568	−	0.163353i	$-0.0522310\pi$
$740$	14.5198	+	5.10298i	0.533759	+	0.187589i
$741$	9.41267	−	41.0944i	0.345783	−	1.50964i
$742$	5.91546	+	10.3289i	0.217163	+	0.379187i
$743$	−10.7934	−	10.7934i	−0.395972	−	0.395972i	0.480837	−	0.876810i	$-0.340333\pi$
$743$	−10.7934	−	10.7934i	−0.395972	−	0.395972i	−0.876810	+	0.480837i	$0.840333\pi$
$744$	35.0277	−	34.3020i	1.28418	−	1.25757i
$745$	−8.58000	−	5.77948i	−0.314347	−	0.211744i
$746$	3.70578	−	13.6396i	0.135678	−	0.499382i
$747$	7.70084	−	7.70084i	0.281759	−	0.281759i
$748$	−6.23728	−	23.9450i	−0.228058	−	0.875516i
$749$	42.5171			1.55354
$750$	−16.6424	+	32.5327i	−0.607695	+	1.18793i
$751$			14.6670i			0.535208i	0.963529	+	0.267604i	$0.0862319\pi$
$751$			14.6670i			0.535208i	−0.963529	+	0.267604i	$0.913768\pi$
$752$	−38.7155	−	10.9551i	−1.41181	−	0.399492i
$753$	−22.8908	−	22.8908i	−0.834186	−	0.834186i
$754$	30.5675	+	16.3222i	1.11320	+	0.594419i
$755$	40.5242	+	27.2971i	1.47483	+	0.993442i
$756$	−3.92539	+	6.69072i	−0.142765	+	0.243339i
$757$	13.5345	−	13.5345i	0.491920	−	0.491920i	−0.416991	−	0.908911i	$-0.636915\pi$
$757$	13.5345	−	13.5345i	0.491920	−	0.491920i	0.908911	+	0.416991i	$0.136915\pi$
$758$	−12.6567	+	7.24861i	−0.459713	+	0.263281i
$759$		−	22.7582i		−	0.826071i
$760$	18.1530	−	26.3498i	0.658479	−	0.955808i
$761$		−	26.1550i		−	0.948120i	−0.880493	−	0.474060i	$-0.842788\pi$
$761$		−	26.1550i		−	0.948120i	0.880493	−	0.474060i	$-0.157212\pi$
$762$	4.98319	+	8.70111i	0.180522	+	0.315208i
$763$	−30.6374	+	30.6374i	−1.10915	+	1.10915i
$764$	−16.6625	−	9.77576i	−0.602828	−	0.353675i
$765$	4.32295	+	22.1656i	0.156297	+	0.801400i
$766$	3.03632	−	11.1756i	0.109707	−	0.403790i
$767$	14.4040	−	9.03525i	0.520099	−	0.326244i
$768$	8.57011	+	35.9715i	0.309247	+	1.29801i
$769$	−1.57519			−0.0568028			−0.0284014	−	0.999597i	$-0.509042\pi$
$769$	−1.57519			−0.0568028			−0.0284014	+	0.999597i	$0.509042\pi$
$770$	−15.1128	−	17.4862i	−0.544628	−	0.630158i
$771$			26.6131i			0.958449i
$772$	5.94423	+	22.8200i	0.213938	+	0.821308i
$773$	7.11384	−	7.11384i	0.255867	−	0.255867i	−0.567504	−	0.823371i	$-0.692091\pi$
$773$	7.11384	−	7.11384i	0.255867	−	0.255867i	0.823371	+	0.567504i	$0.192091\pi$
$774$	1.67288	−	6.15725i	0.0601304	−	0.221318i
$775$	14.0910	+	34.7513i	0.506165	+	1.24830i
$776$	1.71206	+	1.74828i	0.0614592	+	0.0627595i
$777$	14.3309	−	14.3309i	0.514116	−	0.514116i
$778$	12.8940	−	7.38447i	0.462271	−	0.264746i
$779$	18.9093			0.677495
$780$	−36.3494	+	8.21498i	−1.30152	+	0.294144i
$781$	8.04974			0.288042
$782$	18.1736	−	10.4082i	0.649887	−	0.372195i
$783$	7.31449	−	7.31449i	0.261398	−	0.261398i
$784$	1.77018	−	0.989333i	0.0632206	−	0.0353333i
$785$	11.0374	−	2.15261i	0.393940	−	0.0768298i
$786$	17.2817	−	63.6075i	0.616417	−	2.26880i
$787$	−25.1611	+	25.1611i	−0.896896	+	0.896896i	−0.995160	−	0.0982642i	$-0.968671\pi$
$787$	−25.1611	+	25.1611i	−0.896896	+	0.896896i	0.0982642	+	0.995160i	$0.468671\pi$
$788$	14.1908	−	3.69648i	0.505527	−	0.131682i
$789$		−	25.2766i		−	0.899872i
$790$	−3.83765	+	52.7112i	−0.136537	+	1.87538i
$791$	−16.4773			−0.585866
$792$	−0.198818	+	18.9937i	−0.00706469	+	0.674911i
$793$	−17.5405	−	27.9630i	−0.622880	−	0.992997i
$794$	−9.45172	+	34.7883i	−0.335429	+	1.23459i
$795$	14.1574	+	9.53643i	0.502112	+	0.338222i
$796$	−2.07736	+	3.54080i	−0.0736301	+	0.125500i
$797$	−2.18831	+	2.18831i	−0.0775139	+	0.0775139i	−0.744801	−	0.667287i	$-0.767455\pi$
$797$	−2.18831	+	2.18831i	−0.0775139	+	0.0775139i	0.667287	+	0.744801i	$0.267455\pi$
$798$	−20.9405	−	36.5641i	−0.741287	−	1.29436i
$799$		−	43.3888i		−	1.53499i
$800$	−27.9416	−	4.38947i	−0.987884	−	0.155191i
$801$			1.61561i			0.0570847i
$802$	−35.4771	+	20.3180i	−1.25274	+	0.717454i
$803$	−15.8863	+	15.8863i	−0.560615	+	0.560615i
$804$	−8.00998	−	4.69939i	−0.282490	−	0.165735i
$805$	10.9286	−	16.2242i	0.385183	−	0.571828i
$806$	−18.0131	+	33.7341i	−0.634483	+	1.18823i
$807$	−0.111374	−	0.111374i	−0.00392055	−	0.00392055i
$808$	−55.3836	−	0.579732i	−1.94839	−	0.0203949i
$809$		−	39.5081i		−	1.38903i	−0.719478	−	0.694515i	$-0.755619\pi$
$809$		−	39.5081i		−	1.38903i	0.719478	−	0.694515i	$-0.244381\pi$
$810$	−2.42069	+	33.2489i	−0.0850544	+	1.16825i
$811$	−34.9250			−1.22638			−0.613192	−	0.789934i	$-0.710115\pi$
$811$	−34.9250			−1.22638			−0.613192	+	0.789934i	$0.710115\pi$
$812$	33.5154	−	8.73022i	1.17616	−	0.306371i
$813$	−8.00641	+	8.00641i	−0.280797	+	0.280797i
$814$	−3.65996	+	13.4710i	−0.128282	+	0.472158i
$815$	1.49857	+	7.68380i	0.0524925	+	0.269152i
$816$	−34.8087	+	19.4542i	−1.21855	+	0.681034i
$817$	−6.89342	−	6.89342i	−0.241170	−	0.241170i
$818$	−23.7731	−	41.5100i	−0.831207	−	1.45136i
$819$	−4.80283	+	20.9685i	−0.167824	+	0.732697i
$820$	−7.23172	−	15.0695i	−0.252543	−	0.526248i
$821$			23.0858i			0.805700i	0.915266	+	0.402850i	$0.131980\pi$
$821$			23.0858i			0.805700i	−0.915266	+	0.402850i	$0.868020\pi$
$822$	−23.2621	−	40.6178i	−0.811359	−	1.41671i
$823$	33.1841	−	33.1841i	1.15672	−	1.15672i	0.171549	−	0.985176i	$-0.445123\pi$
$823$	33.1841	−	33.1841i	1.15672	−	1.15672i	0.985176	−	0.171549i	$-0.0548773\pi$
$824$	−21.2062	+	20.7669i	−0.738753	+	0.723448i
$825$	−30.5258	−	12.9124i	−1.06277	−	0.449552i
$826$	4.45566	−	16.3996i	0.155032	−	0.570617i
$827$	16.0146	−	16.0146i	0.556882	−	0.556882i	−0.371536	−	0.928418i	$-0.621169\pi$
$827$	16.0146	−	16.0146i	0.556882	−	0.556882i	0.928418	+	0.371536i	$0.121169\pi$
$828$	−15.5577	+	4.05254i	−0.540669	+	0.140835i
$829$		−	14.1917i		−	0.492899i	−0.969156	−	0.246450i	$-0.920736\pi$
$829$		−	14.1917i		−	0.492899i	0.969156	−	0.246450i	$-0.0792640\pi$
$830$	−11.1285	+	9.61804i	−0.386276	+	0.333847i
$831$		−	40.8667i		−	1.41765i
$832$	−14.8126	−	24.7505i	−0.513534	−	0.858070i
$833$	1.54630	+	1.54630i	0.0535762	+	0.0535762i
$834$	21.9346	+	5.95945i	0.759532	+	0.206359i
$835$	47.3182	−	9.22844i	1.63751	−	0.319363i
$836$	25.0321	+	14.6861i	0.865753	+	0.507931i
$837$	8.07221	+	8.07221i	0.279017	+	0.279017i
$838$	20.9505	+	36.5815i	0.723723	+	1.26369i
$839$		−	6.84013i		−	0.236148i	−0.993005	−	0.118074i	$-0.962328\pi$
$839$		−	6.84013i		−	0.236148i	0.993005	−	0.118074i	$-0.0376719\pi$
$840$	−21.1307	+	30.6720i	−0.729077	+	1.05828i
$841$	−17.1841			−0.592556
$842$	−27.3268	+	15.6503i	−0.941743	+	0.539343i
$843$	35.9972	+	35.9972i	1.23981	+	1.23981i
$844$	37.7357	+	22.1393i	1.29892	+	0.762065i
$845$	25.1149	−	14.6370i	0.863979	−	0.503528i
$846$	−8.73278	+	32.1422i	−0.300239	+	1.10507i
$847$	−4.99692	+	4.99692i	−0.171696	+	0.171696i
$848$	−3.59734	+	12.7130i	−0.123533	+	0.436567i
$849$		−	16.4628i		−	0.565001i
$850$	−3.64934	−	30.2817i	−0.125171	−	1.03865i
$851$	−11.8150			−0.405012
$852$	−3.27002	−	12.5536i	−0.112029	−	0.430081i
$853$	−19.5411	+	19.5411i	−0.669074	+	0.669074i	−0.957502	−	0.288427i	$-0.906868\pi$
$853$	−19.5411	+	19.5411i	−0.669074	+	0.669074i	0.288427	+	0.957502i	$0.406868\pi$
$854$	−31.8372	−	8.64993i	−1.08945	−	0.295995i
$855$	−21.9687	−	14.7981i	−0.751313	−	0.506084i
$856$	33.0199	+	33.7185i	1.12860	+	1.15248i
$857$	−38.2146	+	38.2146i	−1.30539	+	1.30539i	−0.380680	+	0.924707i	$0.624310\pi$
$857$	−38.2146	+	38.2146i	−1.30539	+	1.30539i	−0.924707	+	0.380680i	$0.875690\pi$
$858$	−9.82543	−	32.3413i	−0.335435	−	1.10411i
$859$	5.27198			0.179878			0.0899389	−	0.995947i	$-0.471333\pi$
$859$	5.27198			0.179878			0.0899389	+	0.995947i	$0.471333\pi$
$860$	−2.85726	+	8.12995i	−0.0974319	+	0.277229i
$861$	−22.0109			−0.750131
$862$	−11.7184	−	20.4613i	−0.399129	−	0.696916i
$863$	−12.6771	−	12.6771i	−0.431535	−	0.431535i	0.457615	−	0.889150i	$-0.348704\pi$
$863$	−12.6771	−	12.6771i	−0.431535	−	0.431535i	−0.889150	+	0.457615i	$0.848704\pi$
$864$	−8.35470	+	2.08313i	−0.284233	+	0.0708695i
$865$	−4.81198	−	24.6731i	−0.163612	−	0.838911i
$866$	−7.50185	+	27.6116i	−0.254923	+	0.938279i
$867$	−2.62460	−	2.62460i	−0.0891360	−	0.0891360i
$868$	9.63461	+	36.9874i	0.327020	+	1.25543i
$869$	−47.9363			−1.62613
$870$	37.5778	−	32.4774i	1.27401	−	1.10109i
$871$	7.06115	+	1.61736i	0.239258	+	0.0548020i
$872$	−48.0911	−	0.503397i	−1.62857	−	0.0170472i
$873$	1.43232	−	1.43232i	0.0484768	−	0.0484768i
$874$	−6.44038	+	23.7047i	−0.217849	+	0.801823i
$875$	−15.5611	−	23.8638i	−0.526060	−	0.806744i
$876$	31.2283	+	18.3214i	1.05511	+	0.619023i
$877$	−5.49214	−	5.49214i	−0.185456	−	0.185456i	0.608272	−	0.793729i	$-0.291863\pi$
$877$	−5.49214	−	5.49214i	−0.185456	−	0.185456i	−0.793729	+	0.608272i	$0.791863\pi$
$878$	−0.895867	−	1.56427i	−0.0302340	−	0.0527914i
$879$		−	14.0224i		−	0.472965i
$880$	2.13054	−	25.5656i	0.0718205	−	0.861815i
$881$	12.2190			0.411670			0.205835	−	0.978587i	$-0.434009\pi$
$881$	12.2190			0.411670			0.205835	+	0.978587i	$0.434009\pi$
$882$	−0.834271	−	1.45671i	−0.0280914	−	0.0490501i
$883$	6.54013	−	6.54013i	0.220093	−	0.220093i	−0.588445	−	0.808537i	$-0.700260\pi$
$883$	6.54013	−	6.54013i	0.220093	−	0.220093i	0.808537	+	0.588445i	$0.200260\pi$
$884$	21.3326	−	22.6369i	0.717494	−	0.761363i
$885$	−4.66516	−	23.9203i	−0.156818	−	0.804072i
$886$	8.97818	+	2.43930i	0.301628	+	0.0819499i
$887$	13.9943	+	13.9943i	0.469883	+	0.469883i	0.901877	−	0.431993i	$-0.142190\pi$
$887$	13.9943	+	13.9943i	0.469883	+	0.469883i	−0.431993	+	0.901877i	$0.642190\pi$
$888$	22.4949	+	0.235467i	0.754880	+	0.00790177i
$889$	−7.81725			−0.262182
$890$	0.158444	−	2.17627i	0.00531105	−	0.0729488i
$891$	−30.2370			−1.01298
$892$	−23.9719	+	6.24429i	−0.802638	+	0.209074i
$893$	35.9851	+	35.9851i	1.20420	+	1.20420i
$894$	−14.5923	−	3.96460i	−0.488038	−	0.132596i
$895$	7.84642	+	5.28534i	0.262277	+	0.176669i
$896$	−27.6561	−	8.13930i	−0.923925	−	0.271915i
$897$	24.2352	−	15.2021i	0.809191	−	0.507584i
$898$	3.49780	+	6.10748i	0.116723	+	0.203809i
$899$		−	50.9685i		−	1.69989i
$900$	−3.39134	+	23.1670i	−0.113045	+	0.772235i
$901$	−14.2476			−0.474656
$902$	13.1558	−	7.53444i	0.438041	−	0.250869i
$903$	8.02414	+	8.02414i	0.267027	+	0.267027i
$904$	−12.7967	−	13.0675i	−0.425613	−	0.434617i
$905$	−9.07644	−	6.11388i	−0.301711	−	0.203232i
$906$	68.9207	+	18.7252i	2.28974	+	0.622103i
$907$	14.0823	+	14.0823i	0.467594	+	0.467594i	0.901134	−	0.433540i	$-0.142736\pi$
$907$	14.0823	+	14.0823i	0.467594	+	0.467594i	−0.433540	+	0.901134i	$0.642736\pi$
$908$	7.47935	+	28.7133i	0.248211	+	0.952884i
$909$			45.8495i			1.52073i
$910$	8.52595	−	27.7741i	0.282632	−	0.920703i
$911$			14.8128i			0.490771i	0.969426	+	0.245386i	$0.0789145\pi$
$911$			14.8128i			0.490771i	−0.969426	+	0.245386i	$0.921085\pi$
$912$	12.7345	−	45.0037i	0.421680	−	1.49022i
$913$	−9.43359	−	9.43359i	−0.312206	−	0.312206i
$914$	4.75659	−	17.5073i	0.157334	−	0.579089i
$915$	−46.4374	+	9.05665i	−1.53517	+	0.299404i
$916$	17.0595	−	29.0774i	0.563661	−	0.960743i
$917$	36.3362	+	36.3362i	1.19993	+	1.19993i
$918$	−4.61455	−	8.05742i	−0.152303	−	0.265935i
$919$	−51.3334			−1.69333			−0.846666	−	0.532125i	$-0.821394\pi$
$919$	−51.3334			−1.69333			−0.846666	+	0.532125i	$0.821394\pi$
$920$	21.3542	−	3.93313i	0.704026	−	0.129672i
$921$		−	53.3758i		−	1.75879i
$922$	35.6835	−	20.4362i	1.17517	−	0.673030i
$923$	5.37709	+	8.57217i	0.176989	+	0.282156i
$924$	−29.1381	−	17.0951i	−0.958573	−	0.562387i
$925$	−6.70351	+	15.8476i	−0.220410	+	0.521064i
$926$	−8.76961	+	32.2777i	−0.288187	+	1.06071i
$927$	17.3738	+	17.3738i	0.570630	+	0.570630i
$928$	32.9525	+	19.7995i	1.08172	+	0.649951i
$929$	22.5337			0.739306			0.369653	−	0.929170i	$-0.379477\pi$
$929$	22.5337			0.739306			0.369653	+	0.929170i	$0.379477\pi$
$930$	35.8419	+	41.4706i	1.17530	+	1.35988i
$931$	−2.56489			−0.0840610
$932$	16.3673	−	4.26341i	0.536128	−	0.139653i
$933$	14.0054	+	14.0054i	0.458516	+	0.458516i
$934$	12.0856	−	44.4827i	0.395453	−	1.45552i
$935$	27.1531	−	5.29564i	0.888000	−	0.173186i
$936$	−20.3592	+	12.4757i	−0.665461	+	0.407783i
$937$	20.8504	−	20.8504i	0.681152	−	0.681152i	−0.279107	−	0.960260i	$-0.590039\pi$
$937$	20.8504	−	20.8504i	0.681152	−	0.681152i	0.960260	+	0.279107i	$0.0900386\pi$
$938$	6.28272	−	3.59816i	0.205138	−	0.117484i
$939$	11.8531			0.386811
$940$	14.9155	−	42.4401i	0.486491	−	1.38424i
$941$		−	44.5535i		−	1.45240i	−0.687483	−	0.726201i	$-0.741284\pi$
$941$		−	44.5535i		−	1.45240i	0.687483	−	0.726201i	$-0.258716\pi$
$942$	14.2636	−	8.16890i	0.464735	−	0.266157i
$943$	9.07339	+	9.07339i	0.295470	+	0.295470i
$944$	16.4662	−	9.20281i	0.535931	−	0.299526i
$945$	−7.19314	−	4.84529i	−0.233993	−	0.157617i
$946$	−7.54268	−	2.04929i	−0.245234	−	0.0666281i
$947$	31.1529	−	31.1529i	1.01233	−	1.01233i	0.0124091	−	0.999923i	$-0.496050\pi$
$947$	31.1529	−	31.1529i	1.01233	−	1.01233i	0.999923	−	0.0124091i	$-0.00395004\pi$
$948$	19.4730	+	74.7571i	0.632455	+	2.42800i
$949$	−27.5291	−	6.30555i	−0.893633	−	0.204687i
$950$	28.1412	+	22.0880i	0.913022	+	0.716628i
$951$	35.4194			1.14855
$952$	0.325400	−	31.0865i	0.0105463	−	1.00752i
$953$	13.3690	+	13.3690i	0.433064	+	0.433064i	0.889669	−	0.456606i	$-0.150935\pi$
$953$	13.3690	+	13.3690i	0.433064	+	0.433064i	−0.456606	+	0.889669i	$0.650935\pi$
$954$	10.5545	+	2.86759i	0.341716	+	0.0928415i
$955$	12.0667	−	17.9137i	0.390468	−	0.579674i
$956$	4.38477	+	2.57251i	0.141814	+	0.0832010i
$957$	31.8546	+	31.8546i	1.02971	+	1.02971i
$958$	21.6463	−	12.3970i	0.699361	−	0.400529i
$959$	36.4918			1.17838
$960$	−40.7353	+	7.06284i	−1.31473	+	0.227952i
$961$	25.2484			0.814466
$962$	−16.7901	+	5.10090i	−0.541333	+	0.164460i
$963$	27.6248	−	27.6248i	0.890197	−	0.890197i
$964$	−1.50647	−	0.883833i	−0.0485201	−	0.0284663i
$965$	−25.8773	+	5.04683i	−0.833020	+	0.162463i
$966$	7.49679	−	27.5930i	0.241205	−	0.887789i
$967$	−29.7376	+	29.7376i	−0.956297	+	0.956297i	−0.999084	−	0.0427873i	$-0.986376\pi$
$967$	−29.7376	+	29.7376i	−0.956297	+	0.956297i	0.0427873	+	0.999084i	$0.486376\pi$
$968$	−7.84358	−	0.0821033i	−0.252102	−	0.00263890i
$969$	50.4361			1.62024
$970$	−2.06985	+	1.78892i	−0.0664590	+	0.0574386i
$971$		−	11.7734i		−	0.377827i	−0.981994	−	0.188913i	$-0.939503\pi$
$971$		−	11.7734i		−	0.377827i	0.981994	−	0.188913i	$-0.0604966\pi$
$972$	9.98097	+	38.3170i	0.320140	+	1.22902i
$973$	−12.5303	+	12.5303i	−0.401702	+	0.401702i
$974$	31.6621	+	8.60236i	1.01452	+	0.275637i
$975$	−6.64030	−	41.1322i	−0.212660	−	1.31729i
$976$	−17.8658	−	31.9665i	−0.571869	−	1.02322i
$977$	−3.24264	−	3.24264i	−0.103741	−	0.103741i	0.653331	−	0.757072i	$-0.273371\pi$
$977$	−3.24264	−	3.24264i	−0.103741	−	0.103741i	−0.757072	+	0.653331i	$0.773371\pi$
$978$	5.68689	+	9.92983i	0.181847	+	0.317521i
$979$	1.97913			0.0632533
$980$	0.980927	+	2.04405i	0.0313346	+	0.0652949i
$981$			39.8124i			1.27111i
$982$	−22.6825	+	12.9905i	−0.723829	+	0.414542i
$983$	0.446909	+	0.446909i	0.0142542	+	0.0142542i	0.714198	−	0.699944i	$-0.246792\pi$
$983$	0.446909	+	0.446909i	0.0142542	+	0.0142542i	−0.699944	+	0.714198i	$0.746792\pi$
$984$	−17.0943	−	17.4559i	−0.544946	−	0.556475i
$985$	3.13842	+	16.0921i	0.0999985	+	0.512736i
$986$	−10.8693	+	40.0058i	−0.346148	+	1.27404i
$987$	−41.8877	−	41.8877i	−1.33330	−	1.33330i
$988$	1.08175	+	36.4668i	0.0344150	+	1.16016i
$989$		−	6.61546i		−	0.210359i
$990$	−21.1807	−	1.54206i	−0.673167	−	0.0490100i
$991$			50.2660i			1.59675i	0.602159	+	0.798376i	$0.294307\pi$
$991$			50.2660i			1.59675i	−0.602159	+	0.798376i	$0.705693\pi$
$992$	−21.8506	+	36.3662i	−0.693758	+	1.15463i
$993$	−15.1561	+	15.1561i	−0.480965	+	0.480965i
$994$	9.75982	+	2.65167i	0.309563	+	0.0841058i
$995$	−3.80669	−	2.56418i	−0.120680	−	0.0812900i
$996$	−10.8796	+	18.5440i	−0.344733	+	0.587588i
$997$	−25.4034	+	25.4034i	−0.804532	+	0.804532i	−0.983800	−	0.179268i	$-0.942627\pi$
$997$	−25.4034	+	25.4034i	−0.804532	+	0.804532i	0.179268	+	0.983800i	$0.442627\pi$
$998$	16.1415	−	9.24433i	0.510949	−	0.292624i
$999$			5.23828i			0.165732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.p.d.103.10	yes	64
4.3	odd	2	inner	260.2.p.d.103.7	✓	64
5.2	odd	4	inner	260.2.p.d.207.26	yes	64
13.12	even	2	inner	260.2.p.d.103.23	yes	64
20.7	even	4	inner	260.2.p.d.207.23	yes	64
52.51	odd	2	inner	260.2.p.d.103.26	yes	64
65.12	odd	4	inner	260.2.p.d.207.7	yes	64
260.207	even	4	inner	260.2.p.d.207.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.p.d.103.7	✓	64	4.3	odd	2	inner
260.2.p.d.103.10	yes	64	1.1	even	1	trivial
260.2.p.d.103.23	yes	64	13.12	even	2	inner
260.2.p.d.103.26	yes	64	52.51	odd	2	inner
260.2.p.d.207.7	yes	64	65.12	odd	4	inner
260.2.p.d.207.10	yes	64	260.207	even	4	inner
260.2.p.d.207.23	yes	64	20.7	even	4	inner
260.2.p.d.207.26	yes	64	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.702829 - 1.22720i) q^{2} +(1.63423 - 1.63423i) q^{3} +(-1.01206 + 1.72503i) q^{4} +(-1.85457 - 1.24923i) q^{5} +(-3.15411 - 0.856948i) q^{6} +(1.80181 - 1.80181i) q^{7} +(2.82827 + 0.0296052i) q^{8} -2.34139i q^{9} +O(q^{10})\)	\(q+(-0.702829 - 1.22720i) q^{2} +(1.63423 - 1.63423i) q^{3} +(-1.01206 + 1.72503i) q^{4} +(-1.85457 - 1.24923i) q^{5} +(-3.15411 - 0.856948i) q^{6} +(1.80181 - 1.80181i) q^{7} +(2.82827 + 0.0296052i) q^{8} -2.34139i q^{9} +(-0.229622 + 3.15393i) q^{10} -2.86823 q^{11} +(1.16515 + 4.47303i) q^{12} +(-1.91593 - 3.05438i) q^{13} +(-3.47755 - 0.944824i) q^{14} +(-5.07231 + 0.989250i) q^{15} +(-1.95146 - 3.49168i) q^{16} +(3.05008 - 3.05008i) q^{17} +(-2.87337 + 1.64560i) q^{18} +5.05926i q^{19} +(4.03190 - 1.93488i) q^{20} -5.88913i q^{21} +(2.01587 + 3.51990i) q^{22} +(-2.42763 + 2.42763i) q^{23} +(4.67042 - 4.57366i) q^{24} +(1.87883 + 4.63357i) q^{25} +(-2.40178 + 4.49794i) q^{26} +(1.07631 + 1.07631i) q^{27} +(1.28463 + 4.93172i) q^{28} -6.79589i q^{29} +(4.77898 + 5.52949i) q^{30} +7.49990 q^{31} +(-2.91346 + 4.84889i) q^{32} +(-4.68733 + 4.68733i) q^{33} +(-5.88676 - 1.59939i) q^{34} +(-5.59245 + 1.09069i) q^{35} +(4.03898 + 2.36964i) q^{36} +(2.43344 + 2.43344i) q^{37} +(6.20875 - 3.55580i) q^{38} +(-8.12261 - 1.86048i) q^{39} +(-5.20823 - 3.58808i) q^{40} -3.73755i q^{41} +(-7.22717 + 4.13905i) q^{42} +(-1.36253 + 1.36253i) q^{43} +(2.90282 - 4.94778i) q^{44} +(-2.92495 + 4.34227i) q^{45} +(4.68541 + 1.27299i) q^{46} +(7.11272 - 7.11272i) q^{47} +(-8.89532 - 2.51706i) q^{48} +0.506970i q^{49} +(4.36585 - 5.56232i) q^{50} -9.96906i q^{51} +(7.20793 - 0.213815i) q^{52} +(-2.33561 - 2.33561i) q^{53} +(0.564390 - 2.07732i) q^{54} +(5.31931 + 3.58309i) q^{55} +(5.14935 - 5.04266i) q^{56} +(8.26798 + 8.26798i) q^{57} +(-8.33995 + 4.77635i) q^{58} +4.71586i q^{59} +(3.42701 - 9.75108i) q^{60} +9.15507 q^{61} +(-5.27115 - 9.20391i) q^{62} +(-4.21875 - 4.21875i) q^{63} +(7.99825 + 0.167463i) q^{64} +(-0.262417 + 8.05799i) q^{65} +(9.04671 + 2.45792i) q^{66} +(-1.42067 + 1.42067i) q^{67} +(2.17461 + 8.34836i) q^{68} +7.93459i q^{69} +(5.26904 + 6.09651i) q^{70} -2.80652 q^{71} +(0.0693174 - 6.62210i) q^{72} +(5.53872 - 5.53872i) q^{73} +(1.27604 - 4.69662i) q^{74} +(10.6427 + 4.50188i) q^{75} +(-8.72738 - 5.12029i) q^{76} +(-5.16800 + 5.16800i) q^{77} +(3.42561 + 11.2757i) q^{78} +16.7129 q^{79} +(-0.742807 + 8.91337i) q^{80} +10.5421 q^{81} +(-4.58674 + 2.62686i) q^{82} +(3.28900 + 3.28900i) q^{83} +(10.1589 + 5.96016i) q^{84} +(-9.46685 + 1.84631i) q^{85} +(2.62974 + 0.714479i) q^{86} +(-11.1060 - 11.1060i) q^{87} +(-8.11213 - 0.0849143i) q^{88} -0.690019 q^{89} +(7.38460 + 0.537637i) q^{90} +(-8.95554 - 2.05127i) q^{91} +(-1.73082 - 6.64464i) q^{92} +(12.2565 - 12.2565i) q^{93} +(-13.7278 - 3.72974i) q^{94} +(6.32020 - 9.38273i) q^{95} +(3.16294 + 12.6854i) q^{96} +(0.611740 + 0.611740i) q^{97} +(0.622156 - 0.356314i) q^{98} +6.71565i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) \) 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more