LMFDB - Embedded newform 260.2.p.d.207.10

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			207.10
Character	$\chi$	$=$	260.207
Dual form			260.2.p.d.103.10

$q$-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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

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

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	0.998488	−	0.0549669i	$-0.0175053\pi$
$3$	1.63423	+	1.63423i	0.943521	+	0.943521i	−0.0549669	+	0.998488i	$0.517505\pi$
$4$	−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	0.960230	−	0.279210i	$-0.0900727\pi$
$7$	1.80181	+	1.80181i	0.681020	+	0.681020i	−0.279210	+	0.960230i	$0.590073\pi$
$8$	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	0.972530	−	0.232776i	$-0.0747810\pi$
$17$	3.05008	+	3.05008i	0.739754	+	0.739754i	−0.232776	+	0.972530i	$0.574781\pi$
$18$	−2.87337	−	1.64560i	−0.677260	−	0.387872i
$19$		−	5.05926i		−	1.16067i	−0.814376	−	0.580337i	$-0.802921\pi$
$19$		−	5.05926i		−	1.16067i	0.814376	−	0.580337i	$-0.197079\pi$
$20$	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	0.407161	−	0.913356i	$-0.366519\pi$
$23$	−2.42763	−	2.42763i	−0.506196	−	0.506196i	−0.913356	+	0.407161i	$0.866519\pi$
$24$	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	$0.217348\pi$
$29$			6.79589i			1.26197i	−0.775797	+	0.630983i	$0.782652\pi$
$30$	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	−0.478197	−	0.878253i	$-0.658710\pi$
$37$	2.43344	−	2.43344i	0.400055	−	0.400055i	0.878253	+	0.478197i	$0.158710\pi$
$38$	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	$0.0942721\pi$
$41$			3.73755i			0.583708i	−0.956463	+	0.291854i	$0.905728\pi$
$42$	−7.22717	−	4.13905i	−1.11518	−	0.638670i
$43$	−1.36253	−	1.36253i	−0.207785	−	0.207785i	0.595541	−	0.803325i	$-0.296938\pi$
$43$	−1.36253	−	1.36253i	−0.207785	−	0.207785i	−0.803325	+	0.595541i	$0.796938\pi$
$44$	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	0.999269	+	0.0382282i	$0.0121714\pi$
$47$	7.11272	+	7.11272i	1.03750	+	1.03750i	0.0382282	+	0.999269i	$0.487829\pi$
$48$	−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	−0.849082	−	0.528262i	$-0.822844\pi$
$53$	−2.33561	+	2.33561i	−0.320820	+	0.320820i	0.528262	+	0.849082i	$0.322844\pi$
$54$	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	$-0.900683\pi$
$59$		−	4.71586i		−	0.613953i	0.951717	−	0.306976i	$-0.0993172\pi$
$60$	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	0.614980	−	0.788542i	$-0.289164\pi$
$67$	−1.42067	−	1.42067i	−0.173562	−	0.173562i	−0.788542	+	0.614980i	$0.789164\pi$
$68$	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	0.952572	−	0.304314i	$-0.0984272\pi$
$73$	5.53872	+	5.53872i	0.648258	+	0.648258i	−0.304314	+	0.952572i	$0.598427\pi$
$74$	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	−0.503172	−	0.864186i	$-0.667834\pi$
$83$	3.28900	−	3.28900i	0.361014	−	0.361014i	0.864186	+	0.503172i	$0.167834\pi$
$84$	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	−0.675368	−	0.737481i	$-0.736015\pi$
$97$	0.611740	−	0.611740i	0.0621128	−	0.0621128i	0.737481	+	0.675368i	$0.236015\pi$
$98$	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	0.239705	−	0.970846i	$-0.422949\pi$
$103$	−7.42027	−	7.42027i	−0.731141	−	0.731141i	−0.970846	+	0.239705i	$0.922949\pi$
$104$	−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	0.152258	−	0.988341i	$-0.451346\pi$
$107$	11.7984	−	11.7984i	1.14060	−	1.14060i	0.988341	−	0.152258i	$-0.0486545\pi$
$108$	−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	−0.888675	−	0.458537i	$-0.848374\pi$
$113$	−4.57244	+	4.57244i	−0.430139	+	0.430139i	0.458537	+	0.888675i	$0.348374\pi$
$114$	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	−0.796772	−	0.604280i	$-0.793461\pi$
$127$	−2.16928	+	2.16928i	−0.192492	+	0.192492i	0.604280	+	0.796772i	$0.293461\pi$
$128$	−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	$-0.656885\pi$
$131$		−	20.1665i		−	1.76196i	0.473156	−	0.880979i	$-0.343115\pi$
$132$	−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	−0.126771	−	0.991932i	$-0.540461\pi$
$137$	10.1264	−	10.1264i	0.865160	−	0.865160i	0.991932	+	0.126771i	$0.0404615\pi$
$138$	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	0.550819	−	0.834625i	$-0.314315\pi$
$157$	−3.55608	−	3.55608i	−0.283806	−	0.283806i	−0.834625	+	0.550819i	$0.814315\pi$
$158$	−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	−0.797381	−	0.603476i	$-0.793782\pi$
$163$	−2.47561	+	2.47561i	−0.193905	+	0.193905i	0.603476	+	0.797381i	$0.293782\pi$
$164$	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	−0.979817	−	0.199896i	$-0.935940\pi$
$167$	−15.2453	−	15.2453i	−1.17971	−	1.17971i	−0.199896	−	0.979817i	$-0.564060\pi$
$168$	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	−0.337095	−	0.941471i	$-0.609444\pi$
$173$	7.94933	−	7.94933i	0.604376	−	0.604376i	0.941471	+	0.337095i	$0.109444\pi$
$174$	−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	$-0.886365\pi$
$191$		−	9.65925i		−	0.698919i	0.936951	−	0.349460i	$-0.113635\pi$
$192$	13.3446	+	12.7973i	0.963065	+	0.923564i
$193$	8.33730	+	8.33730i	0.600132	+	0.600132i	0.940347	−	0.340216i	$-0.110500\pi$
$193$	8.33730	+	8.33730i	0.600132	+	0.600132i	−0.340216	+	0.940347i	$0.610500\pi$
$194$	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	−0.867255	−	0.497865i	$-0.834118\pi$
$197$	−5.18463	+	5.18463i	−0.369390	+	0.369390i	0.497865	+	0.867255i	$0.334118\pi$
$198$	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	$0.271385\pi$
$211$			21.8754i			1.50596i	−0.658041	+	0.752982i	$0.728615\pi$
$212$	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	−0.350190	−	0.936679i	$-0.613883\pi$
$223$	8.75815	−	8.75815i	0.586489	−	0.586489i	0.936679	+	0.350190i	$0.113883\pi$
$224$	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	0.963605	−	0.267330i	$-0.0861414\pi$
$227$	10.4904	+	10.4904i	0.696275	+	0.696275i	−0.267330	+	0.963605i	$0.586141\pi$
$228$	−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	−0.875311	−	0.483561i	$-0.839343\pi$
$233$	−5.97980	+	5.97980i	−0.391750	+	0.391750i	0.483561	+	0.875311i	$0.339343\pi$
$234$	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	$0.0261976\pi$
$239$			2.54185i			0.164419i	−0.996615	+	0.0822094i	$0.973802\pi$
$240$	13.3526	−	15.7804i	0.861904	−	1.01862i
$241$		−	0.873299i		−	0.0562542i	−0.999604	−	0.0281271i	$-0.991046\pi$
$241$		−	0.873299i		−	0.0562542i	0.999604	−	0.0281271i	$-0.00895431\pi$
$242$	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	$0.145752\pi$
$251$			14.0071i			0.884120i	−0.896985	+	0.442060i	$0.854248\pi$
$252$	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	0.405974	−	0.913885i	$-0.366932\pi$
$257$	−8.14242	−	8.14242i	−0.507910	−	0.507910i	−0.913885	+	0.405974i	$0.866932\pi$
$258$	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	0.904129	−	0.427260i	$-0.140521\pi$
$263$	7.73352	+	7.73352i	0.476869	+	0.476869i	−0.427260	+	0.904129i	$0.640521\pi$
$264$	−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	$0.000661326\pi$
$269$			0.0681509i			0.00415523i	−0.999998	+	0.00207762i	$0.999339\pi$
$270$	−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	0.974713	−	0.223459i	$-0.0717348\pi$
$277$	12.5034	+	12.5034i	0.751255	+	0.751255i	−0.223459	+	0.974713i	$0.571735\pi$
$278$	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	$-0.771820\pi$
$281$		−	22.0270i		−	1.31402i	0.753881	−	0.657012i	$-0.228180\pi$
$282$	−28.5296	−	16.3391i	−1.69891	−	0.972979i
$283$	5.03687	+	5.03687i	0.299411	+	0.299411i	0.840783	−	0.541372i	$-0.182095\pi$
$283$	5.03687	+	5.03687i	0.299411	+	0.299411i	−0.541372	+	0.840783i	$0.682095\pi$
$284$	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	0.821232	−	0.570594i	$-0.193287\pi$
$293$	4.29024	+	4.29024i	0.250638	+	0.250638i	−0.570594	+	0.821232i	$0.693287\pi$
$294$	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	0.997833	−	0.0657965i	$-0.0209588\pi$
$307$	16.3306	+	16.3306i	0.932037	+	0.932037i	−0.0657965	+	0.997833i	$0.520959\pi$
$308$	−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	$-0.921875\pi$
$311$		−	8.57004i		−	0.485962i	0.970031	−	0.242981i	$-0.0781253\pi$
$312$	−22.9179	+	5.50243i	−1.29747	+	0.311514i
$313$	3.62652	−	3.62652i	0.204983	−	0.204983i	−0.597148	−	0.802131i	$-0.703700\pi$
$313$	3.62652	−	3.62652i	0.204983	−	0.204983i	0.802131	+	0.597148i	$0.203700\pi$
$314$	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	−0.333942	−	0.942594i	$-0.608379\pi$
$317$	10.8367	−	10.8367i	0.608652	−	0.608652i	0.942594	+	0.333942i	$0.108379\pi$
$318$	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	0.555155	−	0.831747i	$-0.312659\pi$
$337$	−5.07755	−	5.07755i	−0.276592	−	0.276592i	−0.831747	+	0.555155i	$0.812659\pi$
$338$	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	−0.787021	−	0.616926i	$-0.788378\pi$
$347$	−3.16853	+	3.16853i	−0.170096	+	0.170096i	0.616926	+	0.787021i	$0.288378\pi$
$348$	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	0.213501	−	0.976943i	$-0.431513\pi$
$353$	−14.3438	−	14.3438i	−0.763442	−	0.763442i	−0.976943	+	0.213501i	$0.931513\pi$
$354$	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	$-0.789194\pi$
$359$		−	23.3016i		−	1.22981i	0.788600	−	0.614906i	$-0.210806\pi$
$360$	−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	−0.465491	+	0.885052i	$0.654122\pi$
$367$	−25.8727	+	25.8727i	−1.35054	+	1.35054i	−0.885052	+	0.465491i	$0.845878\pi$
$368$	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	−0.500069	−	0.865986i	$-0.666692\pi$
$373$	7.06704	−	7.06704i	0.365917	−	0.365917i	0.865986	+	0.500069i	$0.166692\pi$
$374$	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	$0.0853335\pi$
$379$			10.3135i			0.529767i	−0.964280	+	0.264884i	$0.914666\pi$
$380$	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	−0.543522	−	0.839395i	$-0.682909\pi$
$383$	5.79036	−	5.79036i	0.295873	−	0.295873i	0.839395	+	0.543522i	$0.182909\pi$
$384$	−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	$-0.914180\pi$
$389$		−	10.5068i		−	0.532715i	0.963874	−	0.266357i	$-0.0858201\pi$
$390$	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	−0.995833	−	0.0911976i	$-0.970930\pi$
$397$	−18.0247	+	18.0247i	−0.904635	+	0.904635i	0.0911976	+	0.995833i	$0.470930\pi$
$398$	−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	$0.256694\pi$
$401$			28.9089i			1.44364i	−0.692080	+	0.721820i	$0.743306\pi$
$402$	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	$0.182570\pi$
$421$			22.2675i			1.08525i	−0.839974	+	0.542626i	$0.817430\pi$
$422$	−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	−0.961682	−	0.274167i	$-0.911598\pi$
$433$	−14.3063	+	14.3063i	−0.687515	+	0.687515i	0.274167	+	0.961682i	$0.411598\pi$
$434$	−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	0.587911	−	0.808926i	$-0.299951\pi$
$443$	−4.65182	−	4.65182i	−0.221015	−	0.221015i	−0.808926	+	0.587911i	$0.799951\pi$
$444$	−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	−0.462367	−	0.886689i	$-0.653000\pi$
$457$	9.07097	−	9.07097i	0.424322	−	0.424322i	0.886689	+	0.462367i	$0.153000\pi$
$458$	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	$-0.763225\pi$
$461$		−	29.0770i		−	1.35425i	0.735867	−	0.677126i	$-0.236775\pi$
$462$	20.7291	+	11.8717i	0.964407	+	0.552323i
$463$	−16.7239	+	16.7239i	−0.777227	+	0.777227i	−0.979358	−	0.202132i	$-0.935213\pi$
$463$	−16.7239	+	16.7239i	−0.777227	+	0.777227i	0.202132	+	0.979358i	$0.435213\pi$
$464$	−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	0.0688934	−	0.997624i	$-0.478053\pi$
$467$	23.0476	−	23.0476i	1.06652	−	1.06652i	0.997624	−	0.0688934i	$-0.0219468\pi$
$468$	−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	$-0.867979\pi$
$479$		−	17.6387i		−	0.805934i	0.915215	−	0.402967i	$-0.132021\pi$
$480$	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	0.229847	−	0.973227i	$-0.426177\pi$
$487$	−16.4050	−	16.4050i	−0.743380	−	0.743380i	−0.973227	+	0.229847i	$0.926177\pi$
$488$	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	$0.136941\pi$
$491$			18.4831i			0.834130i	−0.908877	+	0.417065i	$0.863059\pi$
$492$	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	$-0.904878\pi$
$499$		−	13.1530i		−	0.588810i	0.955681	−	0.294405i	$-0.0951215\pi$
$500$	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	0.760427	−	0.649423i	$-0.224989\pi$
$503$	2.48957	+	2.48957i	0.111005	+	0.111005i	−0.649423	+	0.760427i	$0.724989\pi$
$504$	−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	0.686976	−	0.726681i	$-0.258938\pi$
$523$	−0.908020	−	0.908020i	−0.0397050	−	0.0397050i	−0.726681	+	0.686976i	$0.758938\pi$
$524$	−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	$-0.957858\pi$
$541$		−	6.14081i		−	0.264014i	0.991249	−	0.132007i	$-0.0421421\pi$
$542$	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	−0.820190	−	0.572091i	$-0.806132\pi$
$547$	−5.80253	+	5.80253i	−0.248098	+	0.248098i	0.572091	+	0.820190i	$0.306132\pi$
$548$	−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	−0.497378	−	0.867534i	$-0.665704\pi$
$557$	8.73598	−	8.73598i	0.370155	−	0.370155i	0.867534	+	0.497378i	$0.165704\pi$
$558$	−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	0.999433	−	0.0336711i	$-0.0107199\pi$
$563$	22.9152	+	22.9152i	0.965762	+	0.965762i	−0.0336711	+	0.999433i	$0.510720\pi$
$564$	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	$0.283467\pi$
$569$			37.0883i			1.55482i	−0.628993	+	0.777411i	$0.716533\pi$
$570$	−27.9751	−	24.1781i	−1.17175	−	1.01271i
$571$		−	19.8776i		−	0.831850i	−0.909399	−	0.415925i	$-0.863458\pi$
$571$		−	19.8776i		−	0.831850i	0.909399	−	0.415925i	$-0.136542\pi$
$572$	−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	−0.992787	−	0.119889i	$-0.961746\pi$
$577$	−20.9677	+	20.9677i	−0.872898	+	0.872898i	0.119889	+	0.992787i	$0.461746\pi$
$578$	−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	0.223021	−	0.974814i	$-0.428408\pi$
$587$	−18.2145	−	18.2145i	−0.751793	−	0.751793i	−0.974814	+	0.223021i	$0.928408\pi$
$588$	−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	−0.999981	−	0.00621080i	$-0.998023\pi$
$593$	−24.5024	−	24.5024i	−1.00619	−	1.00619i	−0.00621080	−	0.999981i	$-0.501977\pi$
$594$	−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	0.222933	−	0.974834i	$-0.428437\pi$
$607$	29.5098	−	29.5098i	1.19777	−	1.19777i	0.974834	−	0.222933i	$-0.0715632\pi$
$608$	−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	0.999126	+	0.0417992i	$0.0133090\pi$
$613$	25.7721	+	25.7721i	1.04093	+	1.04093i	0.0417992	+	0.999126i	$0.486691\pi$
$614$	−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	−0.997157	−	0.0753568i	$-0.975990\pi$
$617$	−22.8970	+	22.8970i	−0.921800	+	0.921800i	0.0753568	+	0.997157i	$0.475990\pi$
$618$	29.7631	+	17.0456i	1.19725	+	0.685674i
$619$		−	24.6592i		−	0.991136i	−0.868569	−	0.495568i	$-0.834960\pi$
$619$		−	24.6592i		−	0.991136i	0.868569	−	0.495568i	$-0.165040\pi$
$620$	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	−0.955745	−	0.294195i	$-0.904948\pi$
$643$	−16.7752	+	16.7752i	−0.661550	+	0.661550i	0.294195	+	0.955745i	$0.404948\pi$
$644$	−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	−0.917805	−	0.397032i	$-0.870040\pi$
$647$	−13.2465	+	13.2465i	−0.520773	+	0.520773i	0.397032	+	0.917805i	$0.370040\pi$
$648$	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	−0.788791	−	0.614662i	$-0.789293\pi$
$653$	−4.44968	+	4.44968i	−0.174129	+	0.174129i	0.614662	+	0.788791i	$0.289293\pi$
$654$	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	$-0.596488\pi$
$661$		−	49.0755i		−	1.90882i	0.298506	−	0.954408i	$-0.403512\pi$
$662$	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	−0.659872	−	0.751378i	$-0.729389\pi$
$673$	2.37388	−	2.37388i	0.0915062	−	0.0915062i	0.751378	+	0.659872i	$0.229389\pi$
$674$	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	0.938329	−	0.345744i	$-0.112373\pi$
$677$	15.4186	+	15.4186i	0.592585	+	0.592585i	−0.345744	+	0.938329i	$0.612373\pi$
$678$	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	−0.0383091	−	0.999266i	$-0.512197\pi$
$683$	25.1139	−	25.1139i	0.960957	−	0.960957i	0.999266	+	0.0383091i	$0.0121971\pi$
$684$	−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	−0.853833	−	0.520546i	$-0.825728\pi$
$727$	−8.98640	+	8.98640i	−0.333287	+	0.333287i	0.520546	+	0.853833i	$0.325728\pi$
$728$	−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	0.628361	−	0.777922i	$-0.283726\pi$
$733$	−4.04919	−	4.04919i	−0.149560	−	0.149560i	−0.777922	+	0.628361i	$0.783726\pi$
$734$	−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	$0.0522310\pi$
$739$			8.88137i			0.326707i	−0.986568	+	0.163353i	$0.947769\pi$
$740$	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	−0.876810	−	0.480837i	$-0.840333\pi$
$743$	−10.7934	+	10.7934i	−0.395972	+	0.395972i	0.480837	+	0.876810i	$0.340333\pi$
$744$	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	$-0.913768\pi$
$751$		−	14.6670i		−	0.535208i	0.963529	−	0.267604i	$-0.0862319\pi$
$752$	−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	0.908911	−	0.416991i	$-0.136915\pi$
$757$	13.5345	+	13.5345i	0.491920	+	0.491920i	−0.416991	+	0.908911i	$0.636915\pi$
$758$	−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	$0.157212\pi$
$761$			26.1550i			0.948120i	−0.880493	+	0.474060i	$0.842788\pi$
$762$	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	0.823371	−	0.567504i	$-0.192091\pi$
$773$	7.11384	+	7.11384i	0.255867	+	0.255867i	−0.567504	+	0.823371i	$0.692091\pi$
$774$	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	0.0982642	−	0.995160i	$-0.468671\pi$
$787$	−25.1611	−	25.1611i	−0.896896	−	0.896896i	−0.995160	+	0.0982642i	$0.968671\pi$
$788$	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	0.667287	−	0.744801i	$-0.267455\pi$
$797$	−2.18831	−	2.18831i	−0.0775139	−	0.0775139i	−0.744801	+	0.667287i	$0.767455\pi$
$798$	−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	$0.244381\pi$
$809$			39.5081i			1.38903i	−0.719478	+	0.694515i	$0.755619\pi$
$810$	−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	$-0.868020\pi$
$821$		−	23.0858i		−	0.805700i	0.915266	−	0.402850i	$-0.131980\pi$
$822$	−23.2621	+	40.6178i	−0.811359	+	1.41671i
$823$	33.1841	+	33.1841i	1.15672	+	1.15672i	0.985176	+	0.171549i	$0.0548773\pi$
$823$	33.1841	+	33.1841i	1.15672	+	1.15672i	0.171549	+	0.985176i	$0.445123\pi$
$824$	−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	0.928418	−	0.371536i	$-0.121169\pi$
$827$	16.0146	+	16.0146i	0.556882	+	0.556882i	−0.371536	+	0.928418i	$0.621169\pi$
$828$	−15.5577	−	4.05254i	−0.540669	−	0.140835i
$829$			14.1917i			0.492899i	0.969156	+	0.246450i	$0.0792640\pi$
$829$			14.1917i			0.492899i	−0.969156	+	0.246450i	$0.920736\pi$
$830$	−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	$0.0376719\pi$
$839$			6.84013i			0.236148i	−0.993005	+	0.118074i	$0.962328\pi$
$840$	−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	0.288427	−	0.957502i	$-0.406868\pi$
$853$	−19.5411	−	19.5411i	−0.669074	−	0.669074i	−0.957502	+	0.288427i	$0.906868\pi$
$854$	−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	−0.924707	−	0.380680i	$-0.875690\pi$
$857$	−38.2146	−	38.2146i	−1.30539	−	1.30539i	−0.380680	−	0.924707i	$-0.624310\pi$
$858$	−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	−0.889150	−	0.457615i	$-0.848704\pi$
$863$	−12.6771	+	12.6771i	−0.431535	+	0.431535i	0.457615	+	0.889150i	$0.348704\pi$
$864$	−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	−0.793729	−	0.608272i	$-0.791863\pi$
$877$	−5.49214	+	5.49214i	−0.185456	+	0.185456i	0.608272	+	0.793729i	$0.291863\pi$
$878$	−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	0.808537	−	0.588445i	$-0.200260\pi$
$883$	6.54013	+	6.54013i	0.220093	+	0.220093i	−0.588445	+	0.808537i	$0.700260\pi$
$884$	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	−0.431993	−	0.901877i	$-0.642190\pi$
$887$	13.9943	−	13.9943i	0.469883	−	0.469883i	0.901877	+	0.431993i	$0.142190\pi$
$888$	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	−0.433540	−	0.901134i	$-0.642736\pi$
$907$	14.0823	−	14.0823i	0.467594	−	0.467594i	0.901134	+	0.433540i	$0.142736\pi$
$908$	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	$-0.921085\pi$
$911$		−	14.8128i		−	0.490771i	0.969426	−	0.245386i	$-0.0789145\pi$
$912$	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	0.960260	−	0.279107i	$-0.0900386\pi$
$937$	20.8504	+	20.8504i	0.681152	+	0.681152i	−0.279107	+	0.960260i	$0.590039\pi$
$938$	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	$0.258716\pi$
$941$			44.5535i			1.45240i	−0.687483	+	0.726201i	$0.741284\pi$
$942$	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	0.999923	+	0.0124091i	$0.00395004\pi$
$947$	31.1529	+	31.1529i	1.01233	+	1.01233i	0.0124091	+	0.999923i	$0.496050\pi$
$948$	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	−0.456606	−	0.889669i	$-0.650935\pi$
$953$	13.3690	−	13.3690i	0.433064	−	0.433064i	0.889669	+	0.456606i	$0.150935\pi$
$954$	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	0.0427873	−	0.999084i	$-0.486376\pi$
$967$	−29.7376	−	29.7376i	−0.956297	−	0.956297i	−0.999084	+	0.0427873i	$0.986376\pi$
$968$	−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	$0.0604966\pi$
$971$			11.7734i			0.377827i	−0.981994	+	0.188913i	$0.939503\pi$
$972$	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	−0.757072	−	0.653331i	$-0.773371\pi$
$977$	−3.24264	+	3.24264i	−0.103741	+	0.103741i	0.653331	+	0.757072i	$0.273371\pi$
$978$	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	−0.699944	−	0.714198i	$-0.746792\pi$
$983$	0.446909	−	0.446909i	0.0142542	−	0.0142542i	0.714198	+	0.699944i	$0.246792\pi$
$984$	−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	$-0.705693\pi$
$991$		−	50.2660i		−	1.59675i	0.602159	−	0.798376i	$-0.294307\pi$
$992$	−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	0.179268	−	0.983800i	$-0.442627\pi$
$997$	−25.4034	−	25.4034i	−0.804532	−	0.804532i	−0.983800	+	0.179268i	$0.942627\pi$
$998$	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.207.10	yes	64
4.3	odd	2	inner	260.2.p.d.207.7	yes	64
5.3	odd	4	inner	260.2.p.d.103.26	yes	64
13.12	even	2	inner	260.2.p.d.207.23	yes	64
20.3	even	4	inner	260.2.p.d.103.23	yes	64
52.51	odd	2	inner	260.2.p.d.207.26	yes	64
65.38	odd	4	inner	260.2.p.d.103.7	✓	64
260.103	even	4	inner	260.2.p.d.103.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.p.d.103.7	✓	64	65.38	odd	4	inner
260.2.p.d.103.10	yes	64	260.103	even	4	inner
260.2.p.d.103.23	yes	64	20.3	even	4	inner
260.2.p.d.103.26	yes	64	5.3	odd	4	inner
260.2.p.d.207.7	yes	64	4.3	odd	2	inner
260.2.p.d.207.10	yes	64	1.1	even	1	trivial
260.2.p.d.207.23	yes	64	13.12	even	2	inner
260.2.p.d.207.26	yes	64	52.51	odd	2	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