LMFDB - Embedded newform 280.2.w.a.43.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.33
Character	$\chi$	$=$	280.43
Dual form			280.2.w.a.267.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39133 + 0.253372i) q^{2} +(-0.161197 - 0.161197i) q^{3} +(1.87161 + 0.705048i) q^{4} +(-0.0283969 - 2.23589i) q^{5} +(-0.183435 - 0.265120i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.42538 + 1.45517i) q^{8} -2.94803i q^{9} +O(q^{10})$	\(q+(1.39133 + 0.253372i) q^{2} +(-0.161197 - 0.161197i) q^{3} +(1.87161 + 0.705048i) q^{4} +(-0.0283969 - 2.23589i) q^{5} +(-0.183435 - 0.265120i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.42538 + 1.45517i) q^{8} -2.94803i q^{9} +(0.527001 - 3.11806i) q^{10} +4.93386 q^{11} +(-0.188045 - 0.415348i) q^{12} +(-4.05315 + 4.05315i) q^{13} +(-0.804659 - 1.16298i) q^{14} +(-0.355840 + 0.364995i) q^{15} +(3.00582 + 2.63914i) q^{16} +(-0.793172 + 0.793172i) q^{17} +(0.746947 - 4.10169i) q^{18} +5.81519i q^{19} +(1.52326 - 4.20472i) q^{20} +0.227966i q^{21} +(6.86463 + 1.25010i) q^{22} +(0.565908 - 0.565908i) q^{23} +(-0.156396 - 0.625532i) q^{24} +(-4.99839 + 0.126984i) q^{25} +(-6.66623 + 4.61233i) q^{26} +(-0.958802 + 0.958802i) q^{27} +(-0.824881 - 1.82197i) q^{28} -8.34882 q^{29} +(-0.587571 + 0.417669i) q^{30} -6.01380i q^{31} +(3.51340 + 4.43351i) q^{32} +(-0.795321 - 0.795321i) q^{33} +(-1.30453 + 0.902597i) q^{34} +(-1.56093 + 1.60109i) q^{35} +(2.07850 - 5.51755i) q^{36} +(3.79589 + 3.79589i) q^{37} +(-1.47340 + 8.09086i) q^{38} +1.30671 q^{39} +(3.18472 - 5.46421i) q^{40} +1.53295 q^{41} +(-0.0577602 + 0.317177i) q^{42} +(-3.41409 - 3.41409i) q^{43} +(9.23424 + 3.47860i) q^{44} +(-6.59147 + 0.0837149i) q^{45} +(0.930751 - 0.643981i) q^{46} +(3.43120 + 3.43120i) q^{47} +(-0.0591065 - 0.909948i) q^{48} +1.00000i q^{49} +(-6.98659 - 1.08977i) q^{50} +0.255713 q^{51} +(-10.4436 + 4.72824i) q^{52} +(-3.22442 + 3.22442i) q^{53} +(-1.57694 + 1.09108i) q^{54} +(-0.140106 - 11.0316i) q^{55} +(-0.686048 - 2.74396i) q^{56} +(0.937389 - 0.937389i) q^{57} +(-11.6160 - 2.11535i) q^{58} -1.96633i q^{59} +(-0.923331 + 0.432242i) q^{60} -5.27850i q^{61} +(1.52373 - 8.36719i) q^{62} +(-2.08457 + 2.08457i) q^{63} +(3.76498 + 7.05868i) q^{64} +(9.17749 + 8.94730i) q^{65} +(-0.905043 - 1.30807i) q^{66} +(-5.02471 + 5.02471i) q^{67} +(-2.04373 + 0.925281i) q^{68} -0.182445 q^{69} +(-2.57744 + 1.83215i) q^{70} +6.02581i q^{71} +(4.28988 - 7.15011i) q^{72} +(-10.7665 - 10.7665i) q^{73} +(4.31957 + 6.24311i) q^{74} +(0.826192 + 0.785253i) q^{75} +(-4.09999 + 10.8837i) q^{76} +(-3.48876 - 3.48876i) q^{77} +(1.81807 + 0.331083i) q^{78} +8.60880 q^{79} +(5.81547 - 6.79561i) q^{80} -8.53498 q^{81} +(2.13284 + 0.388405i) q^{82} +(10.2290 + 10.2290i) q^{83} +(-0.160727 + 0.426663i) q^{84} +(1.79597 + 1.75092i) q^{85} +(-3.88509 - 5.61516i) q^{86} +(1.34580 + 1.34580i) q^{87} +(11.9665 + 7.17958i) q^{88} -0.308629i q^{89} +(-9.19213 - 1.55362i) q^{90} +5.73203 q^{91} +(1.45815 - 0.660165i) q^{92} +(-0.969404 + 0.969404i) q^{93} +(3.90457 + 5.64331i) q^{94} +(13.0021 - 0.165133i) q^{95} +(0.148318 - 1.28101i) q^{96} +(3.04108 - 3.04108i) q^{97} +(-0.253372 + 1.39133i) q^{98} -14.5452i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.39133	+	0.253372i	0.983820	+	0.179161i
$2$	1.39133	+	0.253372i	0.983820	+	0.179161i
$3$	−0.161197	−	0.161197i	−0.0930669	−	0.0930669i	0.659041	−	0.752107i	$-0.270963\pi$
$3$	−0.161197	−	0.161197i	−0.0930669	−	0.0930669i	−0.752107	+	0.659041i	$0.770963\pi$
$4$	1.87161	+	0.705048i	0.935803	+	0.352524i
$5$	−0.0283969	−	2.23589i	−0.0126995	−	0.999919i
$5$	−0.0283969	−	2.23589i	−0.0126995	−	0.999919i
$6$	−0.183435	−	0.265120i	−0.0748871	−	0.108235i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	2.42538	+	1.45517i	0.857503	+	0.514479i
$9$		−	2.94803i		−	0.982677i
$10$	0.527001	−	3.11806i	0.166652	−	0.986016i
$11$	4.93386			1.48761			0.743807	−	0.668394i	$-0.233018\pi$
$11$	4.93386			1.48761			0.743807	+	0.668394i	$0.233018\pi$
$12$	−0.188045	−	0.415348i	−0.0542840	−	0.119901i
$13$	−4.05315	+	4.05315i	−1.12414	+	1.12414i	−0.133031	+	0.991112i	$0.542471\pi$
$13$	−4.05315	+	4.05315i	−1.12414	+	1.12414i	−0.991112	+	0.133031i	$0.957529\pi$
$14$	−0.804659	−	1.16298i	−0.215054	−	0.310820i
$15$	−0.355840	+	0.364995i	−0.0918775	+	0.0942413i
$16$	3.00582	+	2.63914i	0.751454	+	0.659786i
$17$	−0.793172	+	0.793172i	−0.192372	+	0.192372i	−0.796720	−	0.604348i	$-0.793434\pi$
$17$	−0.793172	+	0.793172i	−0.192372	+	0.192372i	0.604348	+	0.796720i	$0.293434\pi$
$18$	0.746947	−	4.10169i	0.176057	−	0.966777i
$19$			5.81519i			1.33410i	0.745015	+	0.667048i	$0.232442\pi$
$19$			5.81519i			1.33410i	−0.745015	+	0.667048i	$0.767558\pi$
$20$	1.52326	−	4.20472i	0.340611	−	0.940204i
$21$			0.227966i			0.0497463i
$22$	6.86463	+	1.25010i	1.46354	+	0.266522i
$23$	0.565908	−	0.565908i	0.118000	−	0.118000i	−0.645641	−	0.763641i	$-0.723410\pi$
$23$	0.565908	−	0.565908i	0.118000	−	0.118000i	0.763641	+	0.645641i	$0.223410\pi$
$24$	−0.156396	−	0.625532i	−0.0319242	−	0.127686i
$25$	−4.99839	+	0.126984i	−0.999677	+	0.0253969i
$26$	−6.66623	+	4.61233i	−1.30736	+	0.904552i
$27$	−0.958802	+	0.958802i	−0.184522	+	0.184522i
$28$	−0.824881	−	1.82197i	−0.155888	−	0.344320i
$29$	−8.34882			−1.55034			−0.775169	−	0.631754i	$-0.782335\pi$
$29$	−8.34882			−1.55034			−0.775169	+	0.631754i	$0.782335\pi$
$30$	−0.587571	+	0.417669i	−0.107275	+	0.0762556i
$31$		−	6.01380i		−	1.08011i	−0.841629	−	0.540055i	$-0.818403\pi$
$31$		−	6.01380i		−	1.08011i	0.841629	−	0.540055i	$-0.181597\pi$
$32$	3.51340	+	4.43351i	0.621088	+	0.783741i
$33$	−0.795321	−	0.795321i	−0.138448	−	0.138448i
$34$	−1.30453	+	0.902597i	−0.223725	+	0.154794i
$35$	−1.56093	+	1.60109i	−0.263846	+	0.270634i
$36$	2.07850	−	5.51755i	0.346417	−	0.919592i
$37$	3.79589	+	3.79589i	0.624040	+	0.624040i	0.946562	−	0.322522i	$-0.104531\pi$
$37$	3.79589	+	3.79589i	0.624040	+	0.624040i	−0.322522	+	0.946562i	$0.604531\pi$
$38$	−1.47340	+	8.09086i	−0.239018	+	1.31251i
$39$	1.30671			0.209241
$40$	3.18472	−	5.46421i	0.503548	−	0.863967i
$41$	1.53295			0.239406			0.119703	−	0.992810i	$-0.461806\pi$
$41$	1.53295			0.239406			0.119703	+	0.992810i	$0.461806\pi$
$42$	−0.0577602	+	0.317177i	−0.00891259	+	0.0489414i
$43$	−3.41409	−	3.41409i	−0.520643	−	0.520643i	0.397122	−	0.917766i	$-0.370009\pi$
$43$	−3.41409	−	3.41409i	−0.520643	−	0.520643i	−0.917766	+	0.397122i	$0.870009\pi$
$44$	9.23424	+	3.47860i	1.39211	+	0.524419i
$45$	−6.59147	+	0.0837149i	−0.982598	+	0.0124795i
$46$	0.930751	−	0.643981i	0.137232	−	0.0949498i
$47$	3.43120	+	3.43120i	0.500492	+	0.500492i	0.911591	−	0.411099i	$-0.134855\pi$
$47$	3.43120	+	3.43120i	0.500492	+	0.500492i	−0.411099	+	0.911591i	$0.634855\pi$
$48$	−0.0591065	−	0.909948i	−0.00853129	−	0.131340i
$49$			1.00000i			0.142857i
$50$	−6.98659	−	1.08977i	−0.988053	−	0.154117i
$51$	0.255713			0.0358070
$52$	−10.4436	+	4.72824i	−1.44826	+	0.655689i
$53$	−3.22442	+	3.22442i	−0.442909	+	0.442909i	−0.892988	−	0.450080i	$-0.851396\pi$
$53$	−3.22442	+	3.22442i	−0.442909	+	0.442909i	0.450080	+	0.892988i	$0.351396\pi$
$54$	−1.57694	+	1.09108i	−0.214595	+	0.148477i
$55$	−0.140106	−	11.0316i	−0.0188919	−	1.48749i
$56$	−0.686048	−	2.74396i	−0.0916770	−	0.366678i
$57$	0.937389	−	0.937389i	0.124160	−	0.124160i
$58$	−11.6160	−	2.11535i	−1.52525	−	0.277760i
$59$		−	1.96633i		−	0.255994i	−0.991775	−	0.127997i	$-0.959145\pi$
$59$		−	1.96633i		−	0.255994i	0.991775	−	0.127997i	$-0.0408548\pi$
$60$	−0.923331	+	0.432242i	−0.119201	+	0.0558023i
$61$		−	5.27850i		−	0.675843i	−0.941174	−	0.337922i	$-0.890276\pi$
$61$		−	5.27850i		−	0.675843i	0.941174	−	0.337922i	$-0.109724\pi$
$62$	1.52373	−	8.36719i	0.193513	−	1.06263i
$63$	−2.08457	+	2.08457i	−0.262632	+	0.262632i
$64$	3.76498	+	7.05868i	0.470623	+	0.882335i
$65$	9.17749	+	8.94730i	1.13833	+	1.10978i
$66$	−0.905043	−	1.30807i	−0.111403	−	0.161012i
$67$	−5.02471	+	5.02471i	−0.613866	+	0.613866i	−0.943951	−	0.330085i	$-0.892923\pi$
$67$	−5.02471	+	5.02471i	−0.613866	+	0.613866i	0.330085	+	0.943951i	$0.392923\pi$
$68$	−2.04373	+	0.925281i	−0.247838	+	0.112207i
$69$	−0.182445			−0.0219638
$70$	−2.57744	+	1.83215i	−0.308063	+	0.218984i
$71$			6.02581i			0.715132i	0.933888	+	0.357566i	$0.116393\pi$
$71$			6.02581i			0.715132i	−0.933888	+	0.357566i	$0.883607\pi$
$72$	4.28988	−	7.15011i	0.505567	−	0.842649i
$73$	−10.7665	−	10.7665i	−1.26013	−	1.26013i	−0.951030	−	0.309098i	$-0.899973\pi$
$73$	−10.7665	−	10.7665i	−1.26013	−	1.26013i	−0.309098	−	0.951030i	$-0.600027\pi$
$74$	4.31957	+	6.24311i	0.502139	+	0.725746i
$75$	0.826192	+	0.785253i	0.0954005	+	0.0906733i
$76$	−4.09999	+	10.8837i	−0.470301	+	1.24845i
$77$	−3.48876	−	3.48876i	−0.397582	−	0.397582i
$78$	1.81807	+	0.331083i	0.205855	+	0.0374878i
$79$	8.60880			0.968565			0.484283	−	0.874912i	$-0.339081\pi$
$79$	8.60880			0.968565			0.484283	+	0.874912i	$0.339081\pi$
$80$	5.81547	−	6.79561i	0.650189	−	0.759772i
$81$	−8.53498			−0.948331
$82$	2.13284	+	0.388405i	0.235533	+	0.0428922i
$83$	10.2290	+	10.2290i	1.12277	+	1.12277i	0.991323	+	0.131451i	$0.0419635\pi$
$83$	10.2290	+	10.2290i	1.12277	+	1.12277i	0.131451	+	0.991323i	$0.458036\pi$
$84$	−0.160727	+	0.426663i	−0.0175368	+	0.0465528i
$85$	1.79597	+	1.75092i	0.194800	+	0.189914i
$86$	−3.88509	−	5.61516i	−0.418940	−	0.605498i
$87$	1.34580	+	1.34580i	0.144285	+	0.144285i
$88$	11.9665	+	7.17958i	1.27563	+	0.765346i
$89$		−	0.308629i		−	0.0327146i	−0.999866	−	0.0163573i	$-0.994793\pi$
$89$		−	0.308629i		−	0.0327146i	0.999866	−	0.0163573i	$-0.00520692\pi$
$90$	−9.19213	−	1.55362i	−0.968935	−	0.163765i
$91$	5.73203			0.600880
$92$	1.45815	−	0.660165i	0.152023	−	0.0688269i
$93$	−0.969404	+	0.969404i	−0.100523	+	0.100523i
$94$	3.90457	+	5.64331i	0.402726	+	0.582063i
$95$	13.0021	−	0.165133i	1.33399	−	0.0169423i
$96$	0.148318	−	1.28101i	0.0151377	−	0.130743i
$97$	3.04108	−	3.04108i	0.308775	−	0.308775i	−0.535659	−	0.844434i	$-0.679937\pi$
$97$	3.04108	−	3.04108i	0.308775	−	0.308775i	0.844434	+	0.535659i	$0.179937\pi$
$98$	−0.253372	+	1.39133i	−0.0255944	+	0.140546i
$99$		−	14.5452i		−	1.46184i
$100$	−9.44454	−	3.28644i	−0.944454	−	0.328644i
$101$		−	3.91032i		−	0.389091i	−0.980893	−	0.194546i	$-0.937677\pi$
$101$		−	3.91032i		−	0.389091i	0.980893	−	0.194546i	$-0.0623232\pi$
$102$	0.355782	+	0.0647904i	0.0352276	+	0.00641521i
$103$	4.13590	−	4.13590i	0.407522	−	0.407522i	−0.473352	−	0.880874i	$-0.656956\pi$
$103$	4.13590	−	4.13590i	0.407522	−	0.407522i	0.880874	+	0.473352i	$0.156956\pi$
$104$	−15.7285	+	3.93244i	−1.54230	+	0.385608i
$105$	0.509707	−	0.00647353i	0.0497423	−	0.000631752i
$106$	−5.30322	+	3.66926i	−0.515094	+	0.356390i
$107$	−9.50203	+	9.50203i	−0.918596	+	0.918596i	−0.996927	−	0.0783311i	$-0.975041\pi$
$107$	−9.50203	+	9.50203i	−0.918596	+	0.918596i	0.0783311	+	0.996927i	$0.475041\pi$
$108$	−2.47050	+	1.11850i	−0.237724	+	0.107628i
$109$	16.9042			1.61913			0.809563	−	0.587032i	$-0.199704\pi$
$109$	16.9042			1.61913			0.809563	+	0.587032i	$0.199704\pi$
$110$	2.60015	−	15.3840i	0.247914	−	1.46681i
$111$		−	1.22377i		−	0.116155i
$112$	−0.259277	−	3.99159i	−0.0244994	−	0.377170i
$113$	−10.7566	−	10.7566i	−1.01190	−	1.01190i	−0.999928	−	0.0119714i	$-0.996189\pi$
$113$	−10.7566	−	10.7566i	−1.01190	−	1.01190i	−0.0119714	−	0.999928i	$-0.503811\pi$
$114$	1.54173	−	1.06671i	0.144396	−	0.0999066i
$115$	−1.28138	−	1.24924i	−0.119489	−	0.116492i
$116$	−15.6257	−	5.88632i	−1.45081	−	0.546531i
$117$	11.9488	+	11.9488i	1.10467	+	1.10467i
$118$	0.498212	−	2.73581i	0.0458641	−	0.251852i
$119$	1.12171			0.102827
$120$	−1.39418	+	0.367447i	−0.127270	+	0.0335431i
$121$	13.3429			1.21300
$122$	1.33742	−	7.34415i	0.121085	−	0.664908i
$123$	−0.247106	−	0.247106i	−0.0222808	−	0.0222808i
$124$	4.24002	−	11.2555i	0.380765	−	1.01077i
$125$	0.425862	+	11.1722i	0.0380902	+	0.999274i
$126$	−3.42850	+	2.37216i	−0.305435	+	0.211329i
$127$	−7.44595	−	7.44595i	−0.660722	−	0.660722i	0.294829	−	0.955550i	$-0.404737\pi$
$127$	−7.44595	−	7.44595i	−0.660722	−	0.660722i	−0.955550	+	0.294829i	$0.904737\pi$
$128$	3.44987	+	10.7749i	0.304928	+	0.952375i
$129$			1.10068i			0.0969093i
$130$	10.5019	+	14.7740i	0.921081	+	1.29576i
$131$	19.2815			1.68464			0.842318	−	0.538981i	$-0.181191\pi$
$131$	19.2815			1.68464			0.842318	+	0.538981i	$0.181191\pi$
$132$	−0.927788	−	2.04927i	−0.0807536	−	0.178366i
$133$	4.11196	−	4.11196i	0.356552	−	0.356552i
$134$	−8.26416	+	5.71792i	−0.713915	+	0.493953i
$135$	2.17100	+	2.11655i	0.186850	+	0.182163i
$136$	−3.07794	+	0.769550i	−0.263931	+	0.0659883i
$137$	8.17817	−	8.17817i	0.698708	−	0.698708i	−0.265424	−	0.964132i	$-0.585512\pi$
$137$	8.17817	−	8.17817i	0.698708	−	0.698708i	0.964132	+	0.265424i	$0.0855118\pi$
$138$	−0.253841	−	0.0462264i	−0.0216084	−	0.00393505i
$139$		−	9.23438i		−	0.783250i	−0.920125	−	0.391625i	$-0.871913\pi$
$139$		−	9.23438i		−	0.783250i	0.920125	−	0.391625i	$-0.128087\pi$
$140$	−4.05029	+	1.89608i	−0.342312	+	0.160248i
$141$		−	1.10620i		−	0.0931585i
$142$	−1.52677	+	8.38390i	−0.128124	+	0.703561i
$143$	−19.9977	+	19.9977i	−1.67229	+	1.67229i
$144$	7.78027	−	8.86124i	0.648356	−	0.738437i
$145$	0.237080	+	18.6670i	0.0196885	+	1.55021i
$146$	−12.2519	−	17.7078i	−1.01397	−	1.46550i
$147$	0.161197	−	0.161197i	0.0132953	−	0.0132953i
$148$	4.42812	+	9.78069i	0.363989	+	0.803967i
$149$	−4.94060			−0.404750			−0.202375	−	0.979308i	$-0.564866\pi$
$149$	−4.94060			−0.404750			−0.202375	+	0.979308i	$0.564866\pi$
$150$	0.950546	+	1.30188i	0.0776118	+	0.106298i
$151$			8.15959i			0.664018i	0.943276	+	0.332009i	$0.107726\pi$
$151$			8.15959i			0.664018i	−0.943276	+	0.332009i	$0.892274\pi$
$152$	−8.46207	+	14.1041i	−0.686365	+	1.14399i
$153$	2.33829	+	2.33829i	0.189040	+	0.189040i
$154$	−3.97007	−	5.73798i	−0.319918	−	0.462380i
$155$	−13.4462	+	0.170773i	−1.08002	+	0.0137168i
$156$	2.44564	+	0.921292i	0.195808	+	0.0737624i
$157$	0.893861	+	0.893861i	0.0713379	+	0.0713379i	0.741876	−	0.670538i	$-0.233937\pi$
$157$	0.893861	+	0.893861i	0.0713379	+	0.0713379i	−0.670538	+	0.741876i	$0.733937\pi$
$158$	11.9777	+	2.18122i	0.952894	+	0.173529i
$159$	1.03953			0.0824403
$160$	9.81306	−	7.98147i	0.775790	−	0.630991i
$161$	−0.800315			−0.0630737
$162$	−11.8750	−	2.16252i	−0.932987	−	0.169904i
$163$	−14.3530	−	14.3530i	−1.12422	−	1.12422i	−0.991101	−	0.133114i	$-0.957502\pi$
$163$	−14.3530	−	14.3530i	−1.12422	−	1.12422i	−0.133114	−	0.991101i	$-0.542498\pi$
$164$	2.86907	+	1.08080i	0.224037	+	0.0843964i
$165$	−1.75566	+	1.80083i	−0.136678	+	0.140195i
$166$	11.6401	+	16.8236i	0.903450	+	1.30576i
$167$	4.02024	+	4.02024i	0.311095	+	0.311095i	0.845334	−	0.534239i	$-0.179402\pi$
$167$	4.02024	+	4.02024i	0.311095	+	0.311095i	−0.534239	+	0.845334i	$0.679402\pi$
$168$	−0.331729	+	0.552906i	−0.0255934	+	0.0426576i
$169$		−	19.8561i		−	1.52739i
$170$	2.05515	+	2.89116i	0.157623	+	0.221741i
$171$	17.1434			1.31099
$172$	−3.98273	−	8.79692i	−0.303680	−	0.670759i
$173$	11.2339	−	11.2339i	0.854097	−	0.854097i	−0.136538	−	0.990635i	$-0.543598\pi$
$173$	11.2339	−	11.2339i	0.854097	−	0.854097i	0.990635	+	0.136538i	$0.0435975\pi$
$174$	1.53147	+	2.21344i	0.116100	+	0.167801i
$175$	3.62419	+	3.44460i	0.273963	+	0.260387i
$176$	14.8303	+	13.0212i	1.11787	+	0.981506i
$177$	−0.316965	+	0.316965i	−0.0238246	+	0.0238246i
$178$	0.0781978	−	0.429405i	0.00586117	−	0.0321853i
$179$		−	9.06992i		−	0.677917i	−0.940801	−	0.338959i	$-0.889925\pi$
$179$		−	9.06992i		−	0.677917i	0.940801	−	0.338959i	$-0.110075\pi$
$180$	−12.3956	−	4.49062i	−0.923917	−	0.334711i
$181$		−	15.8706i		−	1.17965i	−0.807531	−	0.589826i	$-0.799196\pi$
$181$		−	15.8706i		−	1.17965i	0.807531	−	0.589826i	$-0.200804\pi$
$182$	7.97515	+	1.45233i	0.591157	+	0.107654i
$183$	−0.850877	+	0.850877i	−0.0628986	+	0.0628986i
$184$	2.19604	−	0.549054i	0.161894	−	0.0404768i
$185$	8.37939	−	8.59497i	0.616065	−	0.631915i
$186$	−1.59438	+	1.10314i	−0.116906	+	0.0808864i
$187$	−3.91340	+	3.91340i	−0.286176	+	0.286176i
$188$	4.00270	+	8.84102i	0.291927	+	0.644797i
$189$	1.35595			0.0986309
$190$	18.1321	+	3.06461i	1.31544	+	0.222330i
$191$		−	15.0376i		−	1.08809i	−0.839057	−	0.544043i	$-0.816893\pi$
$191$		−	15.0376i		−	1.08809i	0.839057	−	0.544043i	$-0.183107\pi$
$192$	0.530932	−	1.74474i	0.0383167	−	0.125916i
$193$	5.19746	+	5.19746i	0.374121	+	0.374121i	0.868976	−	0.494854i	$-0.164779\pi$
$193$	5.19746	+	5.19746i	0.374121	+	0.374121i	−0.494854	+	0.868976i	$0.664779\pi$
$194$	5.00167	−	3.46063i	0.359099	−	0.248459i
$195$	−0.0371065	−	2.92165i	−0.00265725	−	0.209224i
$196$	−0.705048	+	1.87161i	−0.0503605	+	0.133686i
$197$	4.61388	+	4.61388i	0.328725	+	0.328725i	0.852102	−	0.523376i	$-0.175328\pi$
$197$	4.61388	+	4.61388i	0.328725	+	0.328725i	−0.523376	+	0.852102i	$0.675328\pi$
$198$	3.68533	−	20.2371i	0.261905	−	1.43819i
$199$	4.66360			0.330594			0.165297	−	0.986244i	$-0.447142\pi$
$199$	4.66360			0.330594			0.165297	+	0.986244i	$0.447142\pi$
$200$	−12.3078	−	6.96550i	−0.870293	−	0.492535i
$201$	1.61993			0.114261
$202$	0.990764	−	5.44055i	0.0697099	−	0.382796i
$203$	5.90351	+	5.90351i	0.414345	+	0.414345i
$204$	0.478594	+	0.180290i	0.0335083	+	0.0126228i
$205$	−0.0435309	−	3.42750i	−0.00304033	−	0.239387i
$206$	6.80232	−	4.70649i	0.473940	−	0.327916i
$207$	−1.66832	−	1.66832i	−0.115956	−	0.115956i
$208$	−22.8799	+	1.48619i	−1.58643	+	0.103048i
$209$			28.6913i			1.98462i
$210$	0.710812	+	0.120138i	0.0490507	+	0.00829034i
$211$	−5.48822			−0.377824			−0.188912	−	0.981994i	$-0.560496\pi$
$211$	−5.48822			−0.377824			−0.188912	+	0.981994i	$0.560496\pi$
$212$	−8.30822	+	3.76148i	−0.570611	+	0.258339i
$213$	0.971340	−	0.971340i	0.0665551	−	0.0665551i
$214$	−15.6280	+	10.8129i	−1.06831	+	0.739157i
$215$	−7.53656	+	7.73046i	−0.513989	+	0.527213i
$216$	−3.72068	+	0.930247i	−0.253160	+	0.0632953i
$217$	−4.25240	+	4.25240i	−0.288672	+	0.288672i
$218$	23.5193	+	4.28304i	1.59293	+	0.290084i
$219$			3.47106i			0.234552i
$220$	7.51554	−	20.7455i	0.506698	−	1.39866i
$221$		−	6.42969i		−	0.432508i
$222$	0.310068	−	1.70267i	0.0208104	−	0.114276i
$223$	5.41097	−	5.41097i	0.362346	−	0.362346i	−0.502330	−	0.864676i	$-0.667524\pi$
$223$	5.41097	−	5.41097i	0.362346	−	0.362346i	0.864676	+	0.502330i	$0.167524\pi$
$224$	0.650614	−	5.61932i	0.0434710	−	0.375456i
$225$	0.374354	+	14.7354i	0.0249569	+	0.982360i
$226$	−12.2406	−	17.6915i	−0.814234	−	1.17682i
$227$	−0.614111	+	0.614111i	−0.0407600	+	0.0407600i	−0.727193	−	0.686433i	$-0.759175\pi$
$227$	−0.614111	+	0.614111i	−0.0407600	+	0.0407600i	0.686433	+	0.727193i	$0.259175\pi$
$228$	2.41533	−	1.09352i	0.159959	−	0.0724200i
$229$	−18.2039			−1.20295			−0.601475	−	0.798892i	$-0.705420\pi$
$229$	−18.2039			−1.20295			−0.601475	+	0.798892i	$0.705420\pi$
$230$	−1.46630	−	2.06277i	−0.0966849	−	0.136015i
$231$			1.12475i			0.0740034i
$232$	−20.2491	−	12.1489i	−1.32942	−	0.797616i
$233$	11.7656	+	11.7656i	0.770789	+	0.770789i	0.978245	−	0.207455i	$-0.0665181\pi$
$233$	11.7656	+	11.7656i	0.770789	+	0.770789i	−0.207455	+	0.978245i	$0.566518\pi$
$234$	13.5973	+	19.6523i	0.888882	+	1.28471i
$235$	7.57435	−	7.76922i	0.494096	−	0.506808i
$236$	1.38635	−	3.68019i	0.0902440	−	0.239560i
$237$	−1.38771	−	1.38771i	−0.0901413	−	0.0901413i
$238$	1.56068	+	0.284210i	0.101164	+	0.0184226i
$239$	−8.80908			−0.569812			−0.284906	−	0.958555i	$-0.591962\pi$
$239$	−8.80908			−0.569812			−0.284906	+	0.958555i	$0.591962\pi$
$240$	−2.03286	+	0.157995i	−0.131221	+	0.0101986i
$241$	−21.3908			−1.37791			−0.688953	−	0.724806i	$-0.741929\pi$
$241$	−21.3908			−1.37791			−0.688953	+	0.724806i	$0.741929\pi$
$242$	18.5645	+	3.38072i	1.19337	+	0.217321i
$243$	4.25222	+	4.25222i	0.272780	+	0.272780i
$244$	3.72160	−	9.87928i	0.238251	−	0.632456i
$245$	2.23589	−	0.0283969i	0.142846	−	0.00181421i
$246$	−0.281197	−	0.406416i	−0.0179284	−	0.0259121i
$247$	−23.5699	−	23.5699i	−1.49971	−	1.49971i
$248$	8.75108	−	14.5858i	0.555694	−	0.926198i
$249$		−	3.29774i		−	0.208986i
$250$	−2.23821	+	15.6522i	−0.141557	+	0.989930i
$251$	−31.3913			−1.98140			−0.990701	−	0.136057i	$-0.956557\pi$
$251$	−31.3913			−1.98140			−0.990701	+	0.136057i	$0.956557\pi$
$252$	−5.37122	+	2.43178i	−0.338355	+	0.153187i
$253$	2.79211	−	2.79211i	0.175538	−	0.175538i
$254$	−8.47320	−	12.2464i	−0.531656	−	0.768406i
$255$	−0.00726145	−	0.571746i	−0.000454730	−	0.0358041i
$256$	2.06986	+	15.8656i	0.129366	+	0.991597i
$257$	−2.22517	+	2.22517i	−0.138802	+	0.138802i	−0.773094	−	0.634292i	$-0.781292\pi$
$257$	−2.22517	+	2.22517i	−0.138802	+	0.138802i	0.634292	+	0.773094i	$0.281292\pi$
$258$	−0.278881	+	1.53141i	−0.0173623	+	0.0953413i
$259$		−	5.36820i		−	0.333563i
$260$	10.8684	+	23.2164i	0.674028	+	1.43982i
$261$			24.6126i			1.52348i
$262$	26.8270	+	4.88539i	1.65738	+	0.301821i
$263$	−5.98405	+	5.98405i	−0.368993	+	0.368993i	−0.867110	−	0.498117i	$-0.834025\pi$
$263$	−5.98405	+	5.98405i	−0.368993	+	0.368993i	0.498117	+	0.867110i	$0.334025\pi$
$264$	−0.771635	−	3.08628i	−0.0474908	−	0.189948i
$265$	7.30101	+	7.11789i	0.448498	+	0.437248i
$266$	6.76295	−	4.67925i	0.414663	−	0.286903i
$267$	−0.0497499	+	0.0497499i	−0.00304465	+	0.00304465i
$268$	−12.9469	+	5.86162i	−0.790860	+	0.358055i
$269$	0.590188			0.0359844			0.0179922	−	0.999838i	$-0.494273\pi$
$269$	0.590188			0.0359844			0.0179922	+	0.999838i	$0.494273\pi$
$270$	2.48431	+	3.49489i	0.151190	+	0.212692i
$271$			16.0576i			0.975431i	0.873003	+	0.487715i	$0.162170\pi$
$271$			16.0576i			0.975431i	−0.873003	+	0.487715i	$0.837830\pi$
$272$	−4.47742	+	0.290835i	−0.271484	+	0.0176345i
$273$	−0.923983	−	0.923983i	−0.0559220	−	0.0559220i
$274$	13.4507	−	9.30643i	0.812584	−	0.562222i
$275$	−24.6613	+	0.626523i	−1.48713	+	0.0377808i
$276$	−0.341465	−	0.128632i	−0.0205538	−	0.00774276i
$277$	−10.0221	−	10.0221i	−0.602172	−	0.602172i	0.338716	−	0.940889i	$-0.390007\pi$
$277$	−10.0221	−	10.0221i	−0.602172	−	0.602172i	−0.940889	+	0.338716i	$0.890007\pi$
$278$	2.33973	−	12.8481i	0.140328	−	0.770577i
$279$	−17.7289			−1.06140
$280$	−6.11571	+	1.61185i	−0.365484	+	0.0963262i
$281$	3.54046			0.211206			0.105603	−	0.994408i	$-0.466323\pi$
$281$	3.54046			0.211206			0.105603	+	0.994408i	$0.466323\pi$
$282$	0.280279	−	1.53909i	0.0166903	−	0.0916512i
$283$	−1.18755	−	1.18755i	−0.0705928	−	0.0705928i	0.670929	−	0.741522i	$-0.265896\pi$
$283$	−1.18755	−	1.18755i	−0.0705928	−	0.0705928i	−0.741522	+	0.670929i	$0.765896\pi$
$284$	−4.24848	+	11.2779i	−0.252101	+	0.669223i
$285$	−2.12251	−	2.06928i	−0.125727	−	0.122573i
$286$	−32.8902	+	22.7566i	−1.94484	+	1.34562i
$287$	−1.08396	−	1.08396i	−0.0639840	−	0.0639840i
$288$	13.0701	−	10.3576i	0.770164	−	0.610329i
$289$			15.7418i			0.925986i
$290$	−4.39984	+	26.0321i	−0.258367	+	1.52866i
$291$	−0.980423			−0.0574734
$292$	−12.5598	−	27.7416i	−0.735007	−	1.62346i
$293$	10.7306	−	10.7306i	0.626889	−	0.626889i	−0.320395	−	0.947284i	$-0.603816\pi$
$293$	10.7306	−	10.7306i	0.626889	−	0.626889i	0.947284	+	0.320395i	$0.103816\pi$
$294$	0.265120	−	0.183435i	0.0154621	−	0.0106982i
$295$	−4.39649	+	0.0558376i	−0.255973	+	0.00325099i
$296$	3.68284	+	14.7301i	0.214061	+	0.856172i
$297$	−4.73059	+	4.73059i	−0.274497	+	0.274497i
$298$	−6.87401	−	1.25181i	−0.398201	−	0.0725153i
$299$			4.58743i			0.265298i
$300$	0.992665	+	2.05219i	0.0573116	+	0.118483i
$301$			4.82825i			0.278296i
$302$	−2.06741	+	11.3527i	−0.118966	+	0.653274i
$303$	−0.630330	+	0.630330i	−0.0362115	+	0.0362115i
$304$	−15.3471	+	17.4794i	−0.880217	+	1.00251i
$305$	−11.8021	+	0.149893i	−0.675789	+	0.00858285i
$306$	2.66089	+	3.84580i	0.152113	+	0.219850i
$307$	−6.20070	+	6.20070i	−0.353893	+	0.353893i	−0.861556	−	0.507663i	$-0.830509\pi$
$307$	−6.20070	+	6.20070i	−0.353893	+	0.353893i	0.507663	+	0.861556i	$0.330509\pi$
$308$	−4.06985	−	8.98934i	−0.231901	−	0.512215i
$309$	−1.33339			−0.0758536
$310$	−18.7514	−	3.16928i	−1.06501	−	0.180003i
$311$			22.9744i			1.30276i	0.758752	+	0.651380i	$0.225809\pi$
$311$			22.9744i			1.30276i	−0.758752	+	0.651380i	$0.774191\pi$
$312$	3.16927	+	1.90148i	0.179425	+	0.107650i
$313$	−15.3383	−	15.3383i	−0.866974	−	0.866974i	0.125162	−	0.992136i	$-0.460055\pi$
$313$	−15.3383	−	15.3383i	−0.866974	−	0.866974i	−0.992136	+	0.125162i	$0.960055\pi$
$314$	1.01718	+	1.47014i	0.0574027	+	0.0829645i
$315$	4.72007	+	4.60168i	0.265946	+	0.259275i
$316$	16.1123	+	6.06961i	0.906386	+	0.341442i
$317$	1.54114	+	1.54114i	0.0865589	+	0.0865589i	0.749060	−	0.662502i	$-0.230505\pi$
$317$	1.54114	+	1.54114i	0.0865589	+	0.0865589i	−0.662502	+	0.749060i	$0.730505\pi$
$318$	1.44633	+	0.263388i	0.0811064	+	0.0147701i
$319$	−41.1919			−2.30630
$320$	15.6755	−	8.61852i	0.876287	−	0.481790i
$321$	3.06339			0.170982
$322$	−1.11350	−	0.202777i	−0.0620531	−	0.0113003i
$323$	−4.61244	−	4.61244i	−0.256643	−	0.256643i
$324$	−15.9741	−	6.01757i	−0.887451	−	0.334309i
$325$	19.7445	−	20.7739i	1.09523	−	1.15233i
$326$	−16.3332	−	23.6064i	−0.904610	−	1.30744i
$327$	−2.72490	−	2.72490i	−0.150687	−	0.150687i
$328$	3.71799	+	2.23069i	0.205292	+	0.123170i
$329$		−	4.85245i		−	0.267524i
$330$	−2.89899	+	2.06072i	−0.159584	+	0.113439i
$331$	23.1716			1.27363			0.636814	−	0.771017i	$-0.280252\pi$
$331$	23.1716			1.27363			0.636814	+	0.771017i	$0.280252\pi$
$332$	11.9327	+	26.3565i	0.654890	+	1.44650i
$333$	11.1904	−	11.1904i	0.613230	−	0.613230i
$334$	4.57487	+	6.61209i	0.250326	+	0.361798i
$335$	11.3774	+	11.0920i	0.621613	+	0.606021i
$336$	−0.601636	+	0.685225i	−0.0328219	+	0.0373821i
$337$	8.31200	−	8.31200i	0.452783	−	0.452783i	−0.443494	−	0.896277i	$-0.646261\pi$
$337$	8.31200	−	8.31200i	0.452783	−	0.452783i	0.896277	+	0.443494i	$0.146261\pi$
$338$	5.03097	−	27.6264i	0.273649	−	1.50268i
$339$			3.46787i			0.188349i
$340$	2.12686	+	4.54327i	0.115345	+	0.246394i
$341$		−	29.6712i		−	1.60679i
$342$	23.8521	+	4.34364i	1.28977	+	0.234877i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−3.31241	−	13.2485i	−0.178593	−	0.714313i
$345$	0.00518087	+	0.407926i	0.000278928	+	0.0219620i
$346$	18.4764	−	12.7837i	0.993298	−	0.687257i
$347$	2.43072	−	2.43072i	0.130488	−	0.130488i	−0.638846	−	0.769334i	$-0.720588\pi$
$347$	2.43072	−	2.43072i	0.130488	−	0.130488i	0.769334	+	0.638846i	$0.220588\pi$
$348$	1.56996	+	3.46766i	0.0841585	+	0.185886i
$349$	4.27164			0.228656			0.114328	−	0.993443i	$-0.463529\pi$
$349$	4.27164			0.228656			0.114328	+	0.993443i	$0.463529\pi$
$350$	4.16968	+	5.71085i	0.222879	+	0.305258i
$351$		−	7.77235i		−	0.414857i
$352$	17.3346	+	21.8743i	0.923939	+	1.16590i
$353$	1.56759	+	1.56759i	0.0834343	+	0.0834343i	0.747592	−	0.664158i	$-0.231210\pi$
$353$	1.56759	+	1.56759i	0.0834343	+	0.0834343i	−0.664158	+	0.747592i	$0.731210\pi$
$354$	−0.521314	+	0.360694i	−0.0277075	+	0.0191707i
$355$	13.4730	−	0.171114i	0.715075	−	0.00908180i
$356$	0.217598	−	0.577632i	0.0115327	−	0.0306144i
$357$	−0.180816	−	0.180816i	−0.00956982	−	0.00956982i
$358$	2.29806	−	12.6193i	0.121456	−	0.666949i
$359$	14.1532			0.746975			0.373488	−	0.927635i	$-0.378162\pi$
$359$	14.1532			0.746975			0.373488	+	0.927635i	$0.378162\pi$
$360$	−16.1087	−	9.38864i	−0.849001	−	0.494825i
$361$	−14.8164			−0.779813
$362$	4.02116	−	22.0812i	0.211347	−	1.16056i
$363$	−2.15084	−	2.15084i	−0.112890	−	0.112890i
$364$	10.7281	+	4.04135i	0.562305	+	0.211824i
$365$	−23.7670	+	24.3785i	−1.24402	+	1.27603i
$366$	−1.39944	+	0.968264i	−0.0731499	+	0.0506120i
$367$	−13.0374	−	13.0374i	−0.680544	−	0.680544i	0.279578	−	0.960123i	$-0.409805\pi$
$367$	−13.0374	−	13.0374i	−0.680544	−	0.680544i	−0.960123	+	0.279578i	$0.909805\pi$
$368$	3.19453	−	0.207504i	0.166526	−	0.0108169i
$369$		−	4.51918i		−	0.235259i
$370$	13.8362	−	9.83535i	0.719311	−	0.511316i
$371$	4.56002			0.236745
$372$	−2.49782	+	1.13087i	−0.129506	+	0.0586327i
$373$	−8.98073	+	8.98073i	−0.465004	+	0.465004i	−0.900292	−	0.435287i	$-0.856647\pi$
$373$	−8.98073	+	8.98073i	−0.465004	+	0.465004i	0.435287	+	0.900292i	$0.356647\pi$
$374$	−6.43637	+	4.45329i	−0.332817	+	0.230274i
$375$	1.73228	−	1.86957i	0.0894544	−	0.0965443i
$376$	3.32901	+	13.3150i	0.171681	+	0.686666i
$377$	33.8391	−	33.8391i	1.74280	−	1.74280i
$378$	1.88658	+	0.343559i	0.0970351	+	0.0176708i
$379$		−	10.9173i		−	0.560785i	−0.959885	−	0.280392i	$-0.909535\pi$
$379$		−	10.9173i		−	0.560785i	0.959885	−	0.280392i	$-0.0904646\pi$
$380$	24.4513	+	8.85804i	1.25432	+	0.454408i
$381$			2.40052i			0.122983i
$382$	3.81011	−	20.9223i	0.194942	−	1.07048i
$383$	−3.00460	+	3.00460i	−0.153528	+	0.153528i	−0.779692	−	0.626164i	$-0.784624\pi$
$383$	−3.00460	+	3.00460i	−0.153528	+	0.153528i	0.626164	+	0.779692i	$0.284624\pi$
$384$	1.18077	−	2.29298i	0.0602559	−	0.117013i
$385$	−7.70141	+	7.89955i	−0.392500	+	0.402599i
$386$	5.91450	+	8.54828i	0.301040	+	0.435096i
$387$	−10.0648	+	10.0648i	−0.511624	+	0.511624i
$388$	7.83581	−	3.54760i	0.397803	−	0.180102i
$389$	−25.6455			−1.30028			−0.650140	−	0.759814i	$-0.725290\pi$
$389$	−25.6455			−1.30028			−0.650140	+	0.759814i	$0.725290\pi$
$390$	0.688637	−	4.07439i	0.0348705	−	0.206315i
$391$			0.897725i			0.0453999i
$392$	−1.45517	+	2.42538i	−0.0734970	+	0.122500i
$393$	−3.10812	−	3.10812i	−0.156784	−	0.156784i
$394$	5.25041	+	7.58847i	0.264512	+	0.382301i
$395$	−0.244463	−	19.2483i	−0.0123003	−	0.968487i
$396$	10.2550	−	27.2228i	0.515335	−	1.36800i
$397$	6.63522	+	6.63522i	0.333012	+	0.333012i	0.853729	−	0.520717i	$-0.174335\pi$
$397$	6.63522	+	6.63522i	0.333012	+	0.333012i	−0.520717	+	0.853729i	$0.674335\pi$
$398$	6.48861	+	1.18162i	0.325245	+	0.0592294i
$399$	−1.32567			−0.0663664
$400$	−15.3594	−	12.8098i	−0.767968	−	0.640488i
$401$	19.7675			0.987141			0.493570	−	0.869706i	$-0.335692\pi$
$401$	19.7675			0.987141			0.493570	+	0.869706i	$0.335692\pi$
$402$	2.25386	+	0.410445i	0.112412	+	0.0204711i
$403$	24.3749	+	24.3749i	1.21420	+	1.21420i
$404$	2.75696	−	7.31858i	0.137164	−	0.364113i
$405$	0.242367	+	19.0833i	0.0120433	+	0.948255i
$406$	6.71795	+	9.70952i	0.333407	+	0.481875i
$407$	18.7284	+	18.7284i	0.928331	+	0.928331i
$408$	0.620203	+	0.372105i	0.0307046	+	0.0184219i
$409$		−	7.16001i		−	0.354040i	−0.984207	−	0.177020i	$-0.943354\pi$
$409$		−	7.16001i		−	0.354040i	0.984207	−	0.177020i	$-0.0566457\pi$
$410$	0.807865	−	4.77982i	0.0398976	−	0.236058i
$411$	−2.63659			−0.130053
$412$	10.6568	−	4.82477i	0.525022	−	0.237699i
$413$	−1.39040	+	1.39040i	−0.0684173	+	0.0684173i
$414$	−1.89848	−	2.74388i	−0.0933050	−	0.134854i
$415$	22.5803	−	23.1613i	1.10842	−	1.13694i
$416$	−32.2101	−	3.72934i	−1.57923	−	0.182846i
$417$	−1.48855	+	1.48855i	−0.0728946	+	0.0728946i
$418$	−7.26956	+	39.9191i	−0.355566	+	1.95251i
$419$			27.2101i			1.32930i	0.747156	+	0.664649i	$0.231419\pi$
$419$			27.2101i			1.32930i	−0.747156	+	0.664649i	$0.768581\pi$
$420$	0.958535	+	0.347252i	0.0467717	+	0.0169442i
$421$		−	7.10155i		−	0.346108i	−0.984912	−	0.173054i	$-0.944636\pi$
$421$		−	7.10155i		−	0.346108i	0.984912	−	0.173054i	$-0.0553636\pi$
$422$	−7.63593	−	1.39056i	−0.371711	−	0.0676913i
$423$	10.1153	−	10.1153i	0.491822	−	0.491822i
$424$	−12.5125	+	3.12839i	−0.607663	+	0.151928i
$425$	3.86386	−	4.06530i	0.187425	−	0.197196i
$426$	1.59757	−	1.10535i	0.0774023	−	0.0535542i
$427$	−3.73247	+	3.73247i	−0.180627	+	0.180627i
$428$	−24.4834	+	11.0847i	−1.18345	+	0.535798i
$429$	6.44712			0.311270
$430$	−12.4445	+	8.84608i	−0.600129	+	0.426596i
$431$			30.0783i			1.44882i	0.689369	+	0.724410i	$0.257888\pi$
$431$			30.0783i			1.44882i	−0.689369	+	0.724410i	$0.742112\pi$
$432$	−5.41240	+	0.351568i	−0.260404	+	0.0169148i
$433$	23.6663	+	23.6663i	1.13733	+	1.13733i	0.988927	+	0.148403i	$0.0474133\pi$
$433$	23.6663	+	23.6663i	1.13733	+	1.13733i	0.148403	+	0.988927i	$0.452587\pi$
$434$	−6.99394	+	4.83906i	−0.335720	+	0.232282i
$435$	2.97084	−	3.04728i	0.142441	−	0.146106i
$436$	31.6380	+	11.9183i	1.51518	+	0.570781i
$437$	3.29086	+	3.29086i	0.157423	+	0.157423i
$438$	−0.879468	+	4.82939i	−0.0420226	+	0.230757i
$439$	11.9778			0.571670			0.285835	−	0.958279i	$-0.407729\pi$
$439$	11.9778			0.571670			0.285835	+	0.958279i	$0.407729\pi$
$440$	15.7129	−	26.9596i	0.749085	−	1.28525i
$441$	2.94803			0.140382
$442$	1.62910	−	8.94583i	0.0774885	−	0.425510i
$443$	−7.85823	−	7.85823i	−0.373356	−	0.373356i	0.495342	−	0.868698i	$-0.335043\pi$
$443$	−7.85823	−	7.85823i	−0.373356	−	0.373356i	−0.868698	+	0.495342i	$0.835043\pi$
$444$	0.862815	−	2.29041i	0.0409474	−	0.108698i
$445$	−0.690059	+	0.00876410i	−0.0327120	+	0.000415458i
$446$	8.89945	−	6.15747i	0.421401	−	0.291565i
$447$	0.796408	+	0.796408i	0.0376688	+	0.0376688i
$448$	2.32899	−	7.65348i	0.110035	−	0.361593i
$449$			30.5279i			1.44070i	0.693609	+	0.720351i	$0.256019\pi$
$449$			30.5279i			1.44070i	−0.693609	+	0.720351i	$0.743981\pi$
$450$	−3.21268	+	20.5967i	−0.151447	+	0.970937i
$451$	7.56335			0.356144
$452$	−12.5482	−	27.7161i	−0.590220	−	1.30366i
$453$	1.31530	−	1.31530i	0.0617981	−	0.0617981i
$454$	−1.01003	+	0.698833i	−0.0474030	+	0.0327979i
$455$	−0.162772	−	12.8162i	−0.00763085	−	0.600831i
$456$	3.63758	−	0.909472i	0.170346	−	0.0425899i
$457$	15.9007	−	15.9007i	0.743805	−	0.743805i	−0.229503	−	0.973308i	$-0.573710\pi$
$457$	15.9007	−	15.9007i	0.743805	−	0.743805i	0.973308	+	0.229503i	$0.0737100\pi$
$458$	−25.3277	−	4.61236i	−1.18349	−	0.215521i
$459$		−	1.52099i		−	0.0709937i
$460$	−1.51746	−	3.24151i	−0.0707520	−	0.151136i
$461$			10.3015i			0.479789i	0.970799	+	0.239895i	$0.0771129\pi$
$461$			10.3015i			0.479789i	−0.970799	+	0.239895i	$0.922887\pi$
$462$	−0.284981	+	1.56490i	−0.0132585	+	0.0728060i
$463$	29.5149	−	29.5149i	1.37167	−	1.37167i	0.513708	−	0.857965i	$-0.328271\pi$
$463$	29.5149	−	29.5149i	1.37167	−	1.37167i	0.857965	−	0.513708i	$-0.171729\pi$
$464$	−25.0950	−	22.0337i	−1.16501	−	1.02289i
$465$	2.19501	+	2.13995i	0.101791	+	0.0992379i
$466$	13.3888	+	19.3509i	0.620223	+	0.896413i
$467$	12.4119	−	12.4119i	0.574357	−	0.574357i	−0.358986	−	0.933343i	$-0.616878\pi$
$467$	12.4119	−	12.4119i	0.574357	−	0.574357i	0.933343	+	0.358986i	$0.116878\pi$
$468$	13.9390	+	30.7880i	0.644330	+	1.42317i
$469$	7.10602			0.328125
$470$	12.5069	−	8.89043i	0.576901	−	0.410085i
$471$		−	0.288175i		−	0.0132784i
$472$	2.86133	−	4.76910i	0.131704	−	0.219516i
$473$	−16.8446	−	16.8446i	−0.774516	−	0.774516i
$474$	−1.57916	−	2.28237i	−0.0725330	−	0.104833i
$475$	−0.738439	−	29.0666i	−0.0338819	−	1.33367i
$476$	2.09941	+	0.790862i	0.0962261	+	0.0362491i
$477$	9.50570	+	9.50570i	0.435236	+	0.435236i
$478$	−12.2563	−	2.23197i	−0.560592	−	0.102088i
$479$	38.2100			1.74586			0.872929	−	0.487848i	$-0.162218\pi$
$479$	38.2100			1.74586			0.872929	+	0.487848i	$0.162218\pi$
$480$	−2.86842	−	0.295246i	−0.130925	−	0.0134761i
$481$	−30.7706			−1.40302
$482$	−29.7617	−	5.41983i	−1.35561	−	0.246867i
$483$	0.129008	+	0.129008i	0.00587007	+	0.00587007i
$484$	24.9727	+	9.40741i	1.13512	+	0.427610i
$485$	−6.88587	−	6.71316i	−0.312671	−	0.304829i
$486$	4.83885	+	6.99363i	0.219495	+	0.317238i
$487$	−10.0740	−	10.0740i	−0.456496	−	0.456496i	0.441007	−	0.897503i	$-0.354621\pi$
$487$	−10.0740	−	10.0740i	−0.456496	−	0.456496i	−0.897503	+	0.441007i	$0.854621\pi$
$488$	7.68110	−	12.8024i	0.347707	−	0.579538i
$489$			4.62731i			0.209254i
$490$	3.11806	+	0.527001i	0.140859	+	0.0238075i
$491$	1.05766			0.0477314			0.0238657	−	0.999715i	$-0.492403\pi$
$491$	1.05766			0.0477314			0.0238657	+	0.999715i	$0.492403\pi$
$492$	−0.288263	−	0.636706i	−0.0129959	−	0.0287049i
$493$	6.62205	−	6.62205i	0.298242	−	0.298242i
$494$	−26.8216	−	38.7654i	−1.20676	−	1.74414i
$495$	−32.5214	+	0.413037i	−1.46173	+	0.0185646i
$496$	15.8713	−	18.0764i	0.712642	−	0.811654i
$497$	4.26089	−	4.26089i	0.191127	−	0.191127i
$498$	0.835555	−	4.58825i	0.0374421	−	0.205605i
$499$		−	27.3238i		−	1.22318i	−0.791175	−	0.611590i	$-0.790530\pi$
$499$		−	27.3238i		−	1.22318i	0.791175	−	0.611590i	$-0.209470\pi$
$500$	−7.07991	+	21.2103i	−0.316623	+	0.948551i
$501$		−	1.29610i		−	0.0579053i
$502$	−43.6757	−	7.95367i	−1.94934	−	0.354989i
$503$	4.15122	−	4.15122i	0.185094	−	0.185094i	−0.608477	−	0.793571i	$-0.708219\pi$
$503$	4.15122	−	4.15122i	0.185094	−	0.185094i	0.793571	+	0.608477i	$0.208219\pi$
$504$	−8.08929	+	2.02249i	−0.360326	+	0.0900889i
$505$	−8.74303	+	0.111041i	−0.389060	+	0.00494125i
$506$	4.59219	−	3.17731i	0.204148	−	0.141249i
$507$	−3.20074	+	3.20074i	−0.142150	+	0.142150i
$508$	−8.68614	−	19.1856i	−0.385385	−	0.851225i
$509$	1.69580			0.0751651			0.0375826	−	0.999294i	$-0.488034\pi$
$509$	1.69580			0.0751651			0.0375826	+	0.999294i	$0.488034\pi$
$510$	0.134761	−	0.797328i	0.00596732	−	0.0353063i
$511$			15.2262i			0.673567i
$512$	−1.14002	+	22.5987i	−0.0503823	+	0.998730i
$513$	−5.57562	−	5.57562i	−0.246170	−	0.246170i
$514$	−3.65974	+	2.53215i	−0.161424	+	0.111689i
$515$	−9.36485	−	9.12996i	−0.412665	−	0.402314i
$516$	−0.776030	+	2.06004i	−0.0341628	+	0.0906880i
$517$	16.9291	+	16.9291i	0.744539	+	0.744539i
$518$	1.36015	−	7.46894i	0.0597615	−	0.328166i
$519$	−3.62173			−0.158976
$520$	9.23914	+	35.0554i	0.405163	+	1.53728i
$521$	−17.5802			−0.770204			−0.385102	−	0.922874i	$-0.625834\pi$
$521$	−17.5802			−0.770204			−0.385102	+	0.922874i	$0.625834\pi$
$522$	−6.23613	+	34.2443i	−0.272948	+	1.49883i
$523$	17.3356	+	17.3356i	0.758034	+	0.758034i	0.975964	−	0.217931i	$-0.0699307\pi$
$523$	17.3356	+	17.3356i	0.758034	+	0.758034i	−0.217931	+	0.975964i	$0.569931\pi$
$524$	36.0874	+	13.5944i	1.57649	+	0.593874i
$525$	−0.0289482	−	1.13946i	−0.00126340	−	0.0497303i
$526$	−9.84199	+	6.80961i	−0.429131	+	0.296913i
$527$	4.76998	+	4.76998i	0.207784	+	0.207784i
$528$	−0.291623	−	4.48955i	−0.0126913	−	0.195383i
$529$			22.3595i			0.972152i
$530$	8.35466	+	11.7532i	0.362903	+	0.510527i
$531$	−5.79680			−0.251560
$532$	10.5951	−	4.79684i	0.459356	−	0.207969i
$533$	−6.21327	+	6.21327i	−0.269127	+	0.269127i
$534$	−0.0818238	+	0.0566134i	−0.00354086	+	0.00244990i
$535$	21.5153	+	20.9757i	0.930188	+	0.906857i
$536$	−19.4987	+	4.87507i	−0.842214	+	0.210571i
$537$	−1.46204	+	1.46204i	−0.0630917	+	0.0630917i
$538$	0.821147	+	0.149537i	0.0354022	+	0.00644699i
$539$			4.93386i			0.212516i
$540$	2.57099	+	5.49200i	0.110638	+	0.236338i
$541$			40.8275i			1.75531i	0.479292	+	0.877655i	$0.340893\pi$
$541$			40.8275i			1.75531i	−0.479292	+	0.877655i	$0.659107\pi$
$542$	−4.06854	+	22.3415i	−0.174759	+	0.959648i
$543$	−2.55828	+	2.55828i	−0.109786	+	0.109786i
$544$	−6.30326	−	0.729803i	−0.270250	−	0.0312900i
$545$	−0.480026	−	37.7959i	−0.0205621	−	1.61900i
$546$	−1.05146	−	1.51968i	−0.0449981	−	0.0650362i
$547$	−9.45318	+	9.45318i	−0.404189	+	0.404189i	−0.879706	−	0.475518i	$-0.842261\pi$
$547$	−9.45318	+	9.45318i	−0.404189	+	0.404189i	0.475518	+	0.879706i	$0.342261\pi$
$548$	21.0723	−	9.54031i	0.900165	−	0.407542i
$549$	−15.5612			−0.664136
$550$	−34.4708	−	5.37678i	−1.46984	−	0.229267i
$551$		−	48.5500i		−	2.06830i
$552$	−0.442499	−	0.265488i	−0.0188340	−	0.0112999i
$553$	−6.08734	−	6.08734i	−0.258860	−	0.258860i
$554$	−11.4048	−	16.4835i	−0.484544	−	0.700315i
$555$	−2.73621	+	0.0347512i	−0.116146	+	0.00147511i
$556$	6.51068	−	17.2831i	0.276114	−	0.732968i
$557$	−19.2588	−	19.2588i	−0.816023	−	0.816023i	0.169507	−	0.985529i	$-0.445783\pi$
$557$	−19.2588	−	19.2588i	−0.816023	−	0.816023i	−0.985529	+	0.169507i	$0.945783\pi$
$558$	−24.6667	−	4.49199i	−1.04423	−	0.190161i
$559$	27.6756			1.17055
$560$	−8.91738	+	0.693064i	−0.376828	+	0.0292873i
$561$	1.26165			0.0532670
$562$	4.92596	+	0.897053i	0.207789	+	0.0378399i
$563$	22.4254	+	22.4254i	0.945119	+	0.945119i	0.998570	−	0.0534519i	$-0.0170224\pi$
$563$	22.4254	+	22.4254i	0.945119	+	0.945119i	−0.0534519	+	0.998570i	$0.517022\pi$
$564$	0.779921	−	2.07036i	0.0328406	−	0.0871780i
$565$	−23.7452	+	24.3561i	−0.998968	+	1.02467i
$566$	−1.35139	−	1.95317i	−0.0568031	−	0.0820980i
$567$	6.03514	+	6.03514i	0.253452	+	0.253452i
$568$	−8.76856	+	14.6149i	−0.367921	+	0.613228i
$569$		−	31.3785i		−	1.31545i	−0.753256	−	0.657727i	$-0.771518\pi$
$569$		−	31.3785i		−	1.31545i	0.753256	−	0.657727i	$-0.228482\pi$
$570$	−2.42883	−	3.41683i	−0.101732	−	0.143115i
$571$	−15.2261			−0.637194			−0.318597	−	0.947890i	$-0.603212\pi$
$571$	−15.2261			−0.637194			−0.318597	+	0.947890i	$0.603212\pi$
$572$	−51.5271	+	23.3285i	−2.15446	+	0.975412i
$573$	−2.42402	+	2.42402i	−0.101265	+	0.101265i
$574$	−1.23350	−	1.78279i	−0.0514853	−	0.0744122i
$575$	−2.75677	+	2.90049i	−0.114965	+	0.120959i
$576$	20.8092	−	11.0993i	0.867050	−	0.462470i
$577$	−23.1621	+	23.1621i	−0.964252	+	0.964252i	−0.999383	−	0.0351312i	$-0.988815\pi$
$577$	−23.1621	+	23.1621i	−0.964252	+	0.964252i	0.0351312	+	0.999383i	$0.488815\pi$
$578$	−3.98851	+	21.9020i	−0.165900	+	0.911003i
$579$		−	1.67563i		−	0.0696366i
$580$	−12.7174	+	35.1045i	−0.528062	+	1.45763i
$581$		−	14.4659i		−	0.600148i
$582$	−1.36409	−	0.248411i	−0.0565435	−	0.0102970i
$583$	−15.9088	+	15.9088i	−0.658877	+	0.658877i
$584$	−10.4459	−	41.7801i	−0.432254	−	1.72887i
$585$	26.3769	−	27.0555i	1.09055	−	1.11861i
$586$	17.6487	−	12.2110i	0.729060	−	0.504432i
$587$	6.02231	−	6.02231i	0.248567	−	0.248567i	−0.571815	−	0.820382i	$-0.693761\pi$
$587$	6.02231	−	6.02231i	0.248567	−	0.248567i	0.820382	+	0.571815i	$0.193761\pi$
$588$	0.415348	−	0.188045i	0.0171286	−	0.00775485i
$589$	34.9714			1.44097
$590$	−6.13112	−	1.03626i	−0.252414	−	0.0426620i
$591$		−	1.48748i		−	0.0611869i
$592$	1.39185	+	21.4276i	0.0572048	+	0.880670i
$593$	−5.40684	−	5.40684i	−0.222032	−	0.222032i	0.587321	−	0.809354i	$-0.300182\pi$
$593$	−5.40684	−	5.40684i	−0.222032	−	0.222032i	−0.809354	+	0.587321i	$0.800182\pi$
$594$	−7.78042	+	5.38322i	−0.319235	+	0.220876i
$595$	−0.0318532	−	2.50803i	−0.00130585	−	0.102819i
$596$	−9.24686	−	3.48336i	−0.378766	−	0.142684i
$597$	−0.751756	−	0.751756i	−0.0307673	−	0.0307673i
$598$	−1.16232	+	6.38263i	−0.0475309	+	0.261005i
$599$	47.4665			1.93943			0.969715	−	0.244240i	$-0.0785384\pi$
$599$	47.4665			1.93943			0.969715	+	0.244240i	$0.0785384\pi$
$600$	0.861160	+	3.10679i	0.0351567	+	0.126834i
$601$	−47.1229			−1.92218			−0.961092	−	0.276227i	$-0.910916\pi$
$601$	−47.1229			−1.92218			−0.961092	+	0.276227i	$0.910916\pi$
$602$	−1.22334	+	6.71769i	−0.0498596	+	0.273793i
$603$	14.8130	+	14.8130i	0.603232	+	0.603232i
$604$	−5.75290	+	15.2715i	−0.234082	+	0.621390i
$605$	−0.378898	−	29.8333i	−0.0154044	−	1.21290i
$606$	−1.03671	+	0.717290i	−0.0421133	+	0.0291379i
$607$	20.6362	+	20.6362i	0.837599	+	0.837599i	0.988542	−	0.150943i	$-0.0482311\pi$
$607$	20.6362	+	20.6362i	0.837599	+	0.837599i	−0.150943	+	0.988542i	$0.548231\pi$
$608$	−25.7817	+	20.4311i	−1.04559	+	0.828591i
$609$		−	1.90325i		−	0.0771236i
$610$	−16.4587	−	2.78178i	−0.666392	−	0.112631i
$611$	−27.8144			−1.12525
$612$	2.72776	+	6.02498i	0.110263	+	0.243545i
$613$	−15.1404	+	15.1404i	−0.611514	+	0.611514i	−0.943340	−	0.331827i	$-0.892335\pi$
$613$	−15.1404	+	15.1404i	−0.611514	+	0.611514i	0.331827	+	0.943340i	$0.392335\pi$
$614$	−10.1983	+	7.05615i	−0.411570	+	0.284763i
$615$	−0.545484	+	0.559518i	−0.0219960	+	0.0225620i
$616$	−3.38486	−	13.5383i	−0.136380	−	0.545475i
$617$	14.1397	−	14.1397i	0.569242	−	0.569242i	−0.362674	−	0.931916i	$-0.618136\pi$
$617$	14.1397	−	14.1397i	0.569242	−	0.569242i	0.931916	+	0.362674i	$0.118136\pi$
$618$	−1.85518	−	0.337842i	−0.0746263	−	0.0135900i
$619$			41.2646i			1.65857i	0.558829	+	0.829283i	$0.311251\pi$
$619$			41.2646i			1.65857i	−0.558829	+	0.829283i	$0.688749\pi$
$620$	−25.2864	−	9.16058i	−1.01552	−	0.367898i
$621$			1.08519i			0.0435471i
$622$	−5.82106	+	31.9650i	−0.233403	+	1.28168i
$623$	−0.218234	+	0.218234i	−0.00874334	+	0.00874334i
$624$	3.92773	+	3.44859i	0.157235	+	0.138054i
$625$	24.9677	−	1.26944i	0.998710	−	0.0507774i
$626$	−17.4544	−	25.2270i	−0.697618	−	1.00827i
$627$	4.62494	−	4.62494i	0.184702	−	0.184702i
$628$	1.04274	+	2.30317i	0.0416099	+	0.0919065i
$629$	−6.02158			−0.240096
$630$	5.40124	+	7.59839i	0.215191	+	0.302727i
$631$			0.491483i			0.0195656i	0.999952	+	0.00978281i	$0.00311401\pi$
$631$			0.491483i			0.0195656i	−0.999952	+	0.00978281i	$0.996886\pi$
$632$	20.8796	+	12.5272i	0.830547	+	0.498306i
$633$	0.884682	+	0.884682i	0.0351629	+	0.0351629i
$634$	1.75375	+	2.53471i	0.0696504	+	0.100666i
$635$	−16.4369	+	16.8598i	−0.652277	+	0.669059i
$636$	1.94559	+	0.732920i	0.0771478	+	0.0290622i
$637$	−4.05315	−	4.05315i	−0.160592	−	0.160592i
$638$	−57.3116	−	10.4369i	−2.26899	−	0.413199i
$639$	17.7643			0.702744
$640$	23.9935	−	8.01949i	0.948426	−	0.316998i
$641$	18.4768			0.729791			0.364896	−	0.931048i	$-0.381105\pi$
$641$	18.4768			0.729791			0.364896	+	0.931048i	$0.381105\pi$
$642$	4.26219	+	0.776176i	0.168215	+	0.0306332i
$643$	−0.743869	−	0.743869i	−0.0293353	−	0.0293353i	0.692287	−	0.721622i	$-0.256603\pi$
$643$	−0.743869	−	0.743869i	−0.0293353	−	0.0293353i	−0.721622	+	0.692287i	$0.756603\pi$
$644$	−1.49787	−	0.564260i	−0.0590245	−	0.0222350i
$645$	2.46099	−	0.0312558i	0.0969015	−	0.00123070i
$646$	−5.24878	−	7.58610i	−0.206510	−	0.298471i
$647$	−17.5707	−	17.5707i	−0.690777	−	0.690777i	0.271626	−	0.962403i	$-0.412439\pi$
$647$	−17.5707	−	17.5707i	−0.690777	−	0.690777i	−0.962403	+	0.271626i	$0.912439\pi$
$648$	−20.7006	−	12.4198i	−0.813197	−	0.487897i
$649$		−	9.70158i		−	0.380820i
$650$	32.7347	−	23.9007i	1.28396	−	0.937463i
$651$	1.37094			0.0537316
$652$	−16.7436	−	36.9827i	−0.655731	−	1.44836i
$653$	−5.81323	+	5.81323i	−0.227489	+	0.227489i	−0.811643	−	0.584154i	$-0.801426\pi$
$653$	−5.81323	+	5.81323i	−0.227489	+	0.227489i	0.584154	+	0.811643i	$0.301426\pi$
$654$	−3.10082	−	4.48164i	−0.121252	−	0.175246i
$655$	−0.547535	−	43.1113i	−0.0213940	−	1.68450i
$656$	4.60776	+	4.04567i	0.179903	+	0.157957i
$657$	−31.7401	+	31.7401i	−1.23830	+	1.23830i
$658$	1.22947	−	6.75137i	0.0479299	−	0.263196i
$659$			9.18508i			0.357800i	0.983867	+	0.178900i	$0.0572539\pi$
$659$			9.18508i			0.357800i	−0.983867	+	0.178900i	$0.942746\pi$
$660$	−4.55558	+	2.13262i	−0.177326	+	0.0830122i
$661$			17.3173i			0.673563i	0.941583	+	0.336782i	$0.109338\pi$
$661$			17.3173i			0.673563i	−0.941583	+	0.336782i	$0.890662\pi$
$662$	32.2394	+	5.87103i	1.25302	+	0.228184i
$663$	−1.03644	+	1.03644i	−0.0402522	+	0.0402522i
$664$	9.92432	+	39.6940i	0.385138	+	1.54042i
$665$	−9.31065	−	9.07712i	−0.361051	−	0.351995i
$666$	18.4049	−	12.7342i	0.713174	−	0.493441i
$667$	−4.72467	+	4.72467i	−0.182940	+	0.182940i
$668$	4.68984	+	10.3588i	0.181455	+	0.400792i
$669$	−1.74446			−0.0674448
$670$	13.0193	+	18.3154i	0.502980	+	0.707584i
$671$		−	26.0434i		−	1.00539i
$672$	−1.01069	+	0.800938i	−0.0389883	+	0.0308968i
$673$	14.5702	+	14.5702i	0.561639	+	0.561639i	0.929773	−	0.368134i	$-0.120003\pi$
$673$	14.5702	+	14.5702i	0.561639	+	0.561639i	−0.368134	+	0.929773i	$0.620003\pi$
$674$	13.6708	−	9.45872i	0.526578	−	0.364336i
$675$	4.67071	−	4.91422i	0.179776	−	0.189148i
$676$	13.9995	−	37.1628i	0.538443	−	1.42934i
$677$	0.273066	+	0.273066i	0.0104948	+	0.0104948i	0.712335	−	0.701840i	$-0.247638\pi$
$677$	0.273066	+	0.273066i	0.0104948	+	0.0104948i	−0.701840	+	0.712335i	$0.747638\pi$
$678$	−0.878659	+	4.82495i	−0.0337447	+	0.185301i
$679$	−4.30074			−0.165047
$680$	1.80803	+	6.86008i	0.0693348	+	0.263072i
$681$	0.197985			0.00758681
$682$	7.51785	−	41.2825i	0.287873	−	1.58079i
$683$	4.61975	+	4.61975i	0.176770	+	0.176770i	0.789946	−	0.613176i	$-0.210108\pi$
$683$	4.61975	+	4.61975i	0.176770	+	0.176770i	−0.613176	+	0.789946i	$0.710108\pi$
$684$	32.0856	+	12.0869i	1.22682	+	0.462154i
$685$	−18.5177	−	18.0532i	−0.707525	−	0.689779i
$686$	1.16298	−	0.804659i	0.0444028	−	0.0307220i
$687$	2.93441	+	2.93441i	0.111955	+	0.111955i
$688$	−1.25186	−	19.2724i	−0.0477266	−	0.734752i
$689$		−	26.1382i		−	0.995785i
$690$	−0.0961486	+	0.568873i	−0.00366032	+	0.0216566i
$691$	−21.8634			−0.831722			−0.415861	−	0.909428i	$-0.636520\pi$
$691$	−21.8634			−0.831722			−0.415861	+	0.909428i	$0.636520\pi$
$692$	28.9458	−	13.1050i	1.10036	−	0.498177i
$693$	−10.2850	+	10.2850i	−0.390694	+	0.390694i
$694$	3.99781	−	2.76606i	0.151755	−	0.104998i
$695$	−20.6470	+	0.262228i	−0.783187	+	0.00994686i
$696$	1.30572	+	5.22245i	0.0494932	+	0.197956i
$697$	−1.21589	+	1.21589i	−0.0460552	+	0.0460552i
$698$	5.94327	+	1.08231i	0.224956	+	0.0409661i
$699$		−	3.79314i		−	0.143470i
$700$	4.35444	+	9.00216i	0.164582	+	0.340250i
$701$		−	13.2692i		−	0.501170i	−0.968095	−	0.250585i	$-0.919377\pi$
$701$		−	13.2692i		−	0.501170i	0.968095	−	0.250585i	$-0.0806229\pi$
$702$	1.96929	−	10.8139i	0.0743261	−	0.408145i
$703$	−22.0738	+	22.0738i	−0.832529	+	0.832529i
$704$	18.5759	+	34.8265i	0.700105	+	1.31257i
$705$	−2.47333	+	0.0314125i	−0.0931510	+	0.00118306i
$706$	1.78385	+	2.57822i	0.0671362	+	0.0970325i
$707$	−2.76501	+	2.76501i	−0.103989	+	0.103989i
$708$	−0.816710	+	0.369759i	−0.0306938	+	0.0138964i
$709$	−15.1247			−0.568020			−0.284010	−	0.958821i	$-0.591665\pi$
$709$	−15.1247			−0.568020			−0.284010	+	0.958821i	$0.591665\pi$
$710$	18.7888	+	3.17561i	0.705132	+	0.119178i
$711$		−	25.3790i		−	0.951787i
$712$	0.449106	−	0.748544i	0.0168310	−	0.0280529i
$713$	−3.40326	−	3.40326i	−0.127453	−	0.127453i
$714$	−0.205762	−	0.297389i	−0.00770044	−	0.0111295i
$715$	45.2804	+	44.1447i	1.69339	+	1.65092i
$716$	6.39472	−	16.9753i	0.238982	−	0.634397i
$717$	1.41999	+	1.41999i	0.0530306	+	0.0530306i
$718$	19.6917	+	3.58601i	0.734889	+	0.133829i
$719$	−22.8933			−0.853776			−0.426888	−	0.904304i	$-0.640390\pi$
$719$	−22.8933			−0.853776			−0.426888	+	0.904304i	$0.640390\pi$
$720$	−20.0337	−	17.1442i	−0.746611	−	0.638926i
$721$	−5.84904			−0.217830
$722$	−20.6146	−	3.75406i	−0.767195	−	0.139712i
$723$	3.44813	+	3.44813i	0.128237	+	0.128237i
$724$	11.1895	−	29.7035i	0.415855	−	1.10392i
$725$	41.7306	−	1.06017i	1.54984	−	0.0393737i
$726$	−2.44757	−	3.53749i	−0.0908377	−	0.131289i
$727$	0.712383	+	0.712383i	0.0264208	+	0.0264208i	0.720194	−	0.693773i	$-0.244053\pi$
$727$	0.712383	+	0.712383i	0.0264208	+	0.0264208i	−0.693773	+	0.720194i	$0.744053\pi$
$728$	13.9024	+	8.34105i	0.515256	+	0.309140i
$729$			24.2341i			0.897558i
$730$	−39.2447	+	27.8967i	−1.45251	+	1.03250i
$731$	5.41591			0.200315
$732$	−2.19241	+	0.992597i	−0.0810340	+	0.0366875i
$733$	13.0673	−	13.0673i	0.482653	−	0.482653i	−0.423325	−	0.905978i	$-0.639137\pi$
$733$	13.0673	−	13.0673i	0.482653	−	0.482653i	0.905978	+	0.423325i	$0.139137\pi$
$734$	−14.8360	−	21.4426i	−0.547606	−	0.791460i
$735$	−0.364995	−	0.355840i	−0.0134630	−	0.0131254i
$736$	4.49722	+	0.520696i	0.165770	+	0.0191931i
$737$	−24.7912	+	24.7912i	−0.913196	+	0.913196i
$738$	1.14503	−	6.28768i	0.0421492	−	0.231453i
$739$			13.0130i			0.478692i	0.970934	+	0.239346i	$0.0769330\pi$
$739$			13.0130i			0.478692i	−0.970934	+	0.239346i	$0.923067\pi$
$740$	21.7428	−	10.1785i	0.799280	−	0.374170i
$741$			7.59876i			0.279147i
$742$	6.34450	+	1.15538i	0.232914	+	0.0424153i
$743$	−3.95133	+	3.95133i	−0.144960	+	0.144960i	−0.775862	−	0.630902i	$-0.782685\pi$
$743$	−3.95133	+	3.95133i	−0.144960	+	0.144960i	0.630902	+	0.775862i	$0.282685\pi$
$744$	−3.76182	+	0.940534i	−0.137915	+	0.0344816i
$745$	0.140298	+	11.0466i	0.00514011	+	0.404717i
$746$	−14.7706	+	10.2197i	−0.540791	+	0.374170i
$747$	30.1553	−	30.1553i	1.10332	−	1.10332i
$748$	−10.0835	+	4.56520i	−0.368688	+	0.166920i
$749$	13.4379			0.491010
$750$	2.88387	−	2.16228i	0.105304	−	0.0789555i
$751$			10.6694i			0.389333i	0.980869	+	0.194666i	$0.0623625\pi$
$751$			10.6694i			0.389333i	−0.980869	+	0.194666i	$0.937638\pi$
$752$	1.25813	+	19.3690i	0.0458793	+	0.706314i
$753$	5.06017	+	5.06017i	0.184403	+	0.184403i
$754$	55.6552	−	38.5075i	2.02684	−	1.40236i
$755$	18.2439	−	0.231707i	0.663965	−	0.00843268i
$756$	2.53781	+	0.956010i	0.0922991	+	0.0347697i
$757$	−19.7518	−	19.7518i	−0.717890	−	0.717890i	0.250283	−	0.968173i	$-0.419476\pi$
$757$	−19.7518	−	19.7518i	−0.717890	−	0.717890i	−0.968173	+	0.250283i	$0.919476\pi$
$758$	2.76614	−	15.1896i	0.100471	−	0.551711i
$759$	−0.900157			−0.0326736
$760$	31.7754	+	18.5197i	1.15262	+	0.671781i
$761$	5.08452			0.184314			0.0921568	−	0.995745i	$-0.470624\pi$
$761$	5.08452			0.184314			0.0921568	+	0.995745i	$0.470624\pi$
$762$	−0.608225	+	3.33992i	−0.0220337	+	0.120993i
$763$	−11.9531	−	11.9531i	−0.432730	−	0.432730i
$764$	10.6023	−	28.1445i	0.383576	−	1.01823i
$765$	5.16176	−	5.29456i	0.186624	−	0.191425i
$766$	−4.94167	+	3.41911i	−0.178550	+	0.123537i
$767$	7.96983	+	7.96983i	0.287774	+	0.287774i
$768$	2.22382	−	2.89113i	0.0802451	−	0.104325i
$769$		−	41.2578i		−	1.48780i	−0.668293	−	0.743898i	$-0.732975\pi$
$769$		−	41.2578i		−	1.48780i	0.668293	−	0.743898i	$-0.267025\pi$
$770$	−12.7167	+	9.03958i	−0.458280	+	0.325764i
$771$	0.717380			0.0258358
$772$	6.06314	+	13.3921i	0.218217	+	0.481991i
$773$	−5.76976	+	5.76976i	−0.207524	+	0.207524i	−0.803214	−	0.595690i	$-0.796879\pi$
$773$	−5.76976	+	5.76976i	−0.207524	+	0.207524i	0.595690	+	0.803214i	$0.296879\pi$
$774$	−16.5537	+	11.4534i	−0.595009	+	0.411683i
$775$	0.763660	+	30.0593i	0.0274315	+	1.07976i
$776$	11.8011	−	2.95051i	0.423634	−	0.105917i
$777$	−0.865335	+	0.865335i	−0.0310437	+	0.0310437i
$778$	−35.6814	−	6.49785i	−1.27924	−	0.232959i
$779$			8.91439i			0.319391i
$780$	1.99046	−	5.49435i	0.0712698	−	0.196729i
$781$			29.7305i			1.06384i
$782$	−0.227458	+	1.24903i	−0.00813388	+	0.0446653i
$783$	8.00487	−	8.00487i	0.286071	−	0.286071i
$784$	−2.63914	+	3.00582i	−0.0942551	+	0.107351i
$785$	1.97319	−	2.02396i	0.0704261	−	0.0722381i
$786$	−3.53691	−	5.11193i	−0.126157	−	0.182336i
$787$	35.7523	−	35.7523i	1.27443	−	1.27443i	0.330692	−	0.943739i	$-0.392718\pi$
$787$	35.7523	−	35.7523i	1.27443	−	1.27443i	0.943739	−	0.330692i	$-0.107282\pi$
$788$	5.38236	+	11.8884i	0.191739	+	0.423506i
$789$	1.92922			0.0686820
$790$	4.53684	−	26.8427i	0.161414	−	0.955020i
$791$			15.2122i			0.540883i
$792$	21.1656	−	35.2776i	0.752088	−	1.25354i
$793$	21.3946	+	21.3946i	0.759744	+	0.759744i
$794$	7.55061	+	10.9130i	0.267961	+	0.387287i
$795$	−0.0295195	−	2.32428i	−0.00104695	−	0.0824336i
$796$	8.72842	+	3.28806i	0.309371	+	0.116542i
$797$	−5.97318	−	5.97318i	−0.211581	−	0.211581i	0.593358	−	0.804939i	$-0.297802\pi$
$797$	−5.97318	−	5.97318i	−0.211581	−	0.211581i	−0.804939	+	0.593358i	$0.797802\pi$
$798$	−1.84444	−	0.335887i	−0.0652926	−	0.0118903i
$799$	−5.44306			−0.192562
$800$	−18.1243	−	21.7142i	−0.640792	−	0.767715i
$801$	−0.909848			−0.0321479
$802$	27.5031	+	5.00852i	0.971168	+	0.176857i
$803$	−53.1206	−	53.1206i	−1.87458	−	1.87458i
$804$	3.03188	+	1.14213i	0.106926	+	0.0402798i
$805$	0.0227264	+	1.78941i	0.000801002	+	0.0630686i
$806$	27.7376	+	40.0894i	0.977016	+	1.41209i
$807$	−0.0951363	−	0.0951363i	−0.00334896	−	0.00334896i
$808$	5.69017	−	9.48403i	0.200179	−	0.333647i
$809$			36.5735i			1.28586i	0.765927	+	0.642928i	$0.222281\pi$
$809$			36.5735i			1.28586i	−0.765927	+	0.642928i	$0.777719\pi$
$810$	−4.49794	+	26.6125i	−0.158042	+	0.935070i
$811$	−0.603322			−0.0211855			−0.0105928	−	0.999944i	$-0.503372\pi$
$811$	−0.603322			−0.0211855			−0.0105928	+	0.999944i	$0.503372\pi$
$812$	6.88679	+	15.2113i	0.241679	+	0.533812i
$813$	2.58843	−	2.58843i	0.0907803	−	0.0907803i
$814$	21.3121	+	30.8026i	0.746990	+	1.07963i
$815$	−31.6842	+	32.4993i	−1.10985	+	1.13840i
$816$	0.768626	+	0.674863i	0.0269073	+	0.0236249i
$817$	19.8536	−	19.8536i	0.694588	−	0.694588i
$818$	1.81414	−	9.96195i	0.0634300	−	0.348311i
$819$		−	16.8982i		−	0.590471i
$820$	2.33508	−	6.44562i	0.0815444	−	0.225091i
$821$		−	33.2259i		−	1.15959i	−0.814762	−	0.579796i	$-0.803132\pi$
$821$		−	33.2259i		−	1.15959i	0.814762	−	0.579796i	$-0.196868\pi$
$822$	−3.66837	−	0.668036i	−0.127949	−	0.0233004i
$823$	−9.06126	+	9.06126i	−0.315856	+	0.315856i	−0.847173	−	0.531317i	$-0.821697\pi$
$823$	−9.06126	+	9.06126i	−0.315856	+	0.315856i	0.531317	+	0.847173i	$0.321697\pi$
$824$	16.0496	−	4.01272i	0.559113	−	0.139790i
$825$	4.07632	+	3.87433i	0.141919	+	0.134887i
$826$	−2.28680	+	1.58222i	−0.0795680	+	0.0550526i
$827$	−21.4284	+	21.4284i	−0.745140	+	0.745140i	−0.973562	−	0.228422i	$-0.926643\pi$
$827$	−21.4284	+	21.4284i	−0.745140	+	0.745140i	0.228422	+	0.973562i	$0.426643\pi$
$828$	−1.94619	−	4.29867i	−0.0676347	−	0.149389i
$829$	−24.1876			−0.840071			−0.420036	−	0.907508i	$-0.637982\pi$
$829$	−24.1876			−0.840071			−0.420036	+	0.907508i	$0.637982\pi$
$830$	37.2851	−	26.5038i	1.29419	−	0.919959i
$831$			3.23107i			0.112085i
$832$	−43.8700	−	13.3499i	−1.52092	−	0.462823i
$833$	−0.793172	−	0.793172i	−0.0274818	−	0.0274818i
$834$	−2.44822	+	1.69391i	−0.0847750	+	0.0586553i
$835$	8.87463	−	9.10296i	0.307119	−	0.315021i
$836$	−20.2287	+	53.6988i	−0.699626	+	1.85721i
$837$	5.76605	+	5.76605i	0.199304	+	0.199304i
$838$	−6.89425	+	37.8582i	−0.238158	+	1.30779i
$839$	−34.0386			−1.17514			−0.587571	−	0.809172i	$-0.699916\pi$
$839$	−34.0386			−1.17514			−0.587571	+	0.809172i	$0.699916\pi$
$840$	1.24566	+	0.726008i	0.0429792	+	0.0250497i
$841$	40.7028			1.40355
$842$	1.79933	−	9.88061i	0.0620090	−	0.340508i
$843$	−0.570711	−	0.570711i	−0.0196563	−	0.0196563i
$844$	−10.2718	−	3.86945i	−0.353569	−	0.133192i
$845$	−44.3960	+	0.563852i	−1.52727	+	0.0193971i
$846$	16.6366	−	11.5108i	0.571980	−	0.395749i
$847$	−9.43489	−	9.43489i	−0.324187	−	0.324187i
$848$	−18.2017	+	1.18231i	−0.625050	+	0.0406007i
$849$			0.382859i			0.0131397i
$850$	6.40594	−	4.67719i	0.219722	−	0.160426i
$851$	4.29625			0.147273
$852$	2.50281	−	1.13312i	0.0857447	−	0.0388202i
$853$	−36.0811	+	36.0811i	−1.23539	+	1.23539i	−0.273530	+	0.961863i	$0.588191\pi$
$853$	−36.0811	+	36.0811i	−1.23539	+	1.23539i	−0.961863	+	0.273530i	$0.911809\pi$
$854$	−6.13880	+	4.24740i	−0.210065	+	0.145343i
$855$	−0.486818	−	38.3306i	−0.0166488	−	1.31088i
$856$	−36.8731	+	9.21905i	−1.26030	+	0.315101i
$857$	20.0497	−	20.0497i	0.684885	−	0.684885i	−0.276212	−	0.961097i	$-0.589079\pi$
$857$	20.0497	−	20.0497i	0.684885	−	0.684885i	0.961097	+	0.276212i	$0.0890792\pi$
$858$	8.97007	+	1.63352i	0.306233	+	0.0557673i
$859$		−	11.0584i		−	0.377306i	−0.982044	−	0.188653i	$-0.939588\pi$
$859$		−	11.0584i		−	0.377306i	0.982044	−	0.188653i	$-0.0604122\pi$
$860$	−19.5558	+	9.15474i	−0.666848	+	0.312174i
$861$			0.349461i			0.0119096i
$862$	−7.62098	+	41.8489i	−0.259572	+	1.42538i
$863$	24.9568	−	24.9568i	0.849539	−	0.849539i	−0.140536	−	0.990076i	$-0.544883\pi$
$863$	24.9568	−	24.9568i	0.849539	−	0.849539i	0.990076	+	0.140536i	$0.0448827\pi$
$864$	−7.61952	−	0.882201i	−0.259221	−	0.0300131i
$865$	−25.4367	−	24.7987i	−0.864875	−	0.843182i
$866$	26.9313	+	38.9240i	0.915163	+	1.32269i
$867$	2.53752	−	2.53752i	0.0861786	−	0.0861786i
$868$	−10.9570	+	4.96067i	−0.371904	+	0.168376i
$869$	42.4746			1.44085
$870$	4.90552	−	3.48704i	0.166313	−	0.118222i
$871$		−	40.7319i		−	1.38015i
$872$	40.9991	+	24.5984i	1.38841	+	0.833007i
$873$	−8.96520	−	8.96520i	−0.303426	−	0.303426i
$874$	3.74487	+	5.41249i	0.126672	+	0.183080i
$875$	7.59883	−	8.20109i	0.256887	−	0.277247i
$876$	−2.44726	+	6.49645i	−0.0826853	+	0.219495i
$877$	−23.6400	−	23.6400i	−0.798265	−	0.798265i	0.184557	−	0.982822i	$-0.440915\pi$
$877$	−23.6400	−	23.6400i	−0.798265	−	0.798265i	−0.982822	+	0.184557i	$0.940915\pi$
$878$	16.6651	+	3.03484i	0.562420	+	0.102421i
$879$	−3.45947			−0.116685
$880$	28.6927	−	33.5286i	0.967231	−	1.13025i
$881$	−2.61767			−0.0881914			−0.0440957	−	0.999027i	$-0.514041\pi$
$881$	−2.61767			−0.0881914			−0.0440957	+	0.999027i	$0.514041\pi$
$882$	4.10169	+	0.746947i	0.138111	+	0.0251510i
$883$	−14.2779	−	14.2779i	−0.480488	−	0.480488i	0.424799	−	0.905288i	$-0.360345\pi$
$883$	−14.2779	−	14.2779i	−0.480488	−	0.480488i	−0.905288	+	0.424799i	$0.860345\pi$
$884$	4.53324	−	12.0339i	0.152469	−	0.404742i
$885$	0.717700	+	0.699698i	0.0241252	+	0.0235201i
$886$	−8.94235	−	12.9245i	−0.300424	−	0.434206i
$887$	36.9666	+	36.9666i	1.24122	+	1.24122i	0.959496	+	0.281723i	$0.0909058\pi$
$887$	36.9666	+	36.9666i	1.24122	+	1.24122i	0.281723	+	0.959496i	$0.409094\pi$
$888$	1.78079	−	2.96811i	0.0597593	−	0.0996032i
$889$			10.5302i			0.353171i
$890$	−0.962322	−	0.162648i	−0.0322571	−	0.00545196i
$891$	−42.1104			−1.41075
$892$	13.9422	−	6.31222i	0.466820	−	0.211349i
$893$	−19.9531	+	19.9531i	−0.667705	+	0.667705i
$894$	0.906280	+	1.30985i	0.0303105	+	0.0438081i
$895$	−20.2793	+	0.257557i	−0.677863	+	0.00860919i
$896$	5.17958	−	10.0584i	0.173038	−	0.336029i
$897$	0.739477	−	0.739477i	0.0246904	−	0.0246904i
$898$	−7.73491	+	42.4745i	−0.258117	+	1.41739i
$899$			50.2082i			1.67454i
$900$	−9.68852	+	27.8428i	−0.322951	+	0.928093i
$901$		−	5.11504i		−	0.170407i
$902$	10.5231	+	1.91634i	0.350382	+	0.0638070i
$903$	0.778297	−	0.778297i	0.0259001	−	0.0259001i
$904$	−10.4363	−	41.7417i	−0.347106	−	1.38831i
$905$	−35.4848	+	0.450675i	−1.17956	+	0.0149809i
$906$	2.16327	−	1.49676i	0.0718700	−	0.0497264i
$907$	−7.40975	+	7.40975i	−0.246037	+	0.246037i	−0.819342	−	0.573305i	$-0.805661\pi$
$907$	−7.40975	+	7.40975i	−0.246037	+	0.246037i	0.573305	+	0.819342i	$0.305661\pi$
$908$	−1.58235	+	0.716396i	−0.0525121	+	0.0237744i
$909$	−11.5277			−0.382351
$910$	3.02078	−	17.8728i	0.100138	−	0.592477i
$911$			12.4164i			0.411374i	0.978618	+	0.205687i	$0.0659428\pi$
$911$			12.4164i			0.411374i	−0.978618	+	0.205687i	$0.934057\pi$
$912$	5.29152	−	0.343716i	0.175220	−	0.0113816i
$913$	50.4682	+	50.4682i	1.67025	+	1.67025i
$914$	26.1520	−	18.0944i	0.865031	−	0.598509i
$915$	1.92663	+	1.87830i	0.0636923	+	0.0620948i
$916$	−34.0706	−	12.8346i	−1.12572	−	0.424068i
$917$	−13.6341	−	13.6341i	−0.450238	−	0.450238i
$918$	0.385375	−	2.11620i	0.0127193	−	0.0698450i
$919$	−47.8744			−1.57923			−0.789616	−	0.613602i	$-0.789720\pi$
$919$	−47.8744			−1.57923			−0.789616	+	0.613602i	$0.789720\pi$
$920$	−1.28998	−	4.89450i	−0.0425295	−	0.161367i
$921$	1.99906			0.0658714
$922$	−2.61011	+	14.3328i	−0.0859594	+	0.472026i
$923$	−24.4235	−	24.4235i	−0.803911	−	0.803911i
$924$	−0.793005	+	2.10510i	−0.0260879	+	0.0692525i
$925$	−19.4553	−	18.4913i	−0.639687	−	0.607990i
$926$	48.5432	−	33.5868i	1.59523	−	1.10373i
$927$	−12.1928	−	12.1928i	−0.400463	−	0.400463i
$928$	−29.3328	−	37.0146i	−0.962895	−	1.21506i
$929$			26.0603i			0.855009i	0.904013	+	0.427505i	$0.140607\pi$
$929$			26.0603i			0.855009i	−0.904013	+	0.427505i	$0.859393\pi$
$930$	2.51178	+	3.53353i	0.0823645	+	0.115869i
$931$	−5.81519			−0.190585
$932$	13.7252	+	30.3158i	0.449585	+	0.993028i
$933$	3.70340	−	3.70340i	0.121244	−	0.121244i
$934$	20.4140	−	14.1243i	0.667965	−	0.462161i
$935$	8.86104	+	8.63879i	0.289787	+	0.282518i
$936$	11.5930	+	46.3680i	0.378928	+	1.51559i
$937$	19.5860	−	19.5860i	0.639848	−	0.639848i	−0.310670	−	0.950518i	$-0.600553\pi$
$937$	19.5860	−	19.5860i	0.639848	−	0.639848i	0.950518	+	0.310670i	$0.100553\pi$
$938$	9.88682	+	1.80046i	0.322816	+	0.0587872i
$939$			4.94497i			0.161373i
$940$	19.6539	−	9.20064i	0.641038	−	0.300092i
$941$			36.3757i			1.18581i	0.805271	+	0.592907i	$0.202020\pi$
$941$			36.3757i			1.18581i	−0.805271	+	0.592907i	$0.797980\pi$
$942$	0.0730152	−	0.400946i	0.00237897	−	0.0130635i
$943$	0.867508	−	0.867508i	0.0282499	−	0.0282499i
$944$	5.18942	−	5.91042i	0.168901	−	0.192368i
$945$	−0.0385048	−	3.03175i	−0.00125256	−	0.0986230i
$946$	−19.1685	−	27.7044i	−0.623222	−	0.900747i
$947$	26.4642	−	26.4642i	0.859970	−	0.859970i	−0.131364	−	0.991334i	$-0.541936\pi$
$947$	26.4642	−	26.4642i	0.859970	−	0.859970i	0.991334	+	0.131364i	$0.0419357\pi$
$948$	−1.61884	−	3.57564i	−0.0525776	−	0.116131i
$949$	87.2769			2.83313
$950$	6.33723	−	40.6283i	0.205607	−	1.31816i
$951$		−	0.496852i		−	0.0161115i
$952$	2.72059	+	1.63228i	0.0881748	+	0.0529025i
$953$	10.8801	+	10.8801i	0.352441	+	0.352441i	0.861017	−	0.508576i	$-0.169828\pi$
$953$	10.8801	+	10.8801i	0.352441	+	0.352441i	−0.508576	+	0.861017i	$0.669828\pi$
$954$	10.8171	+	15.6341i	0.350217	+	0.506171i
$955$	−33.6225	+	0.427022i	−1.08800	+	0.0138181i
$956$	−16.4871	−	6.21082i	−0.533232	−	0.200872i
$957$	6.63999	+	6.63999i	0.214640	+	0.214640i
$958$	53.1627	+	9.68132i	1.71761	+	0.312789i
$959$	−11.5657			−0.373475
$960$	−3.91611	−	1.13756i	−0.126392	−	0.0367146i
$961$	−5.16583			−0.166640
$962$	−42.8121	−	7.79640i	−1.38032	−	0.251366i
$963$	28.0123	+	28.0123i	0.902684	+	0.902684i
$964$	−40.0352	−	15.0816i	−1.28945	−	0.485744i
$965$	11.4733	−	11.7685i	0.369340	−	0.378842i
$966$	0.146806	+	0.212180i	0.00472340	+	0.00682678i
$967$	24.6020	+	24.6020i	0.791148	+	0.791148i	0.981681	−	0.190532i	$-0.0610214\pi$
$967$	24.6020	+	24.6020i	0.791148	+	0.791148i	−0.190532	+	0.981681i	$0.561021\pi$
$968$	32.3618	+	19.4162i	1.04015	+	0.624061i
$969$			1.48702i			0.0477700i
$970$	−7.87960	−	11.0849i	−0.252999	−	0.355915i
$971$	27.2265			0.873739			0.436869	−	0.899525i	$-0.356087\pi$
$971$	27.2265			0.873739			0.436869	+	0.899525i	$0.356087\pi$
$972$	4.96046	+	10.9565i	0.159107	+	0.351430i
$973$	−6.52969	+	6.52969i	−0.209332	+	0.209332i
$974$	−11.4638	−	16.5687i	−0.367324	−	0.530896i
$975$	−6.53144	+	0.165932i	−0.209173	+	0.00531407i
$976$	13.9307	−	15.8662i	0.445912	−	0.507865i
$977$	−33.1217	+	33.1217i	−1.05966	+	1.05966i	−0.0615547	+	0.998104i	$0.519606\pi$
$977$	−33.1217	+	33.1217i	−1.05966	+	1.05966i	−0.998104	+	0.0615547i	$0.980394\pi$
$978$	−1.17243	+	6.43813i	−0.0374902	+	0.205869i
$979$		−	1.52273i		−	0.0486667i
$980$	4.20472	+	1.52326i	0.134315	+	0.0486587i
$981$		−	49.8341i		−	1.59108i
$982$	1.47155	+	0.267980i	0.0469591	+	0.00855160i
$983$	18.9409	−	18.9409i	0.604120	−	0.604120i	−0.337283	−	0.941403i	$-0.609508\pi$
$983$	18.9409	−	18.9409i	0.604120	−	0.604120i	0.941403	+	0.337283i	$0.109508\pi$
$984$	−0.239747	−	0.958907i	−0.00764285	−	0.0305689i
$985$	10.1851	−	10.4471i	0.324524	−	0.332874i
$986$	10.8913	−	7.53562i	0.346850	−	0.239983i
$987$	−0.782199	+	0.782199i	−0.0248977	+	0.0248977i
$988$	−27.4956	−	60.7314i	−0.874752	−	1.93212i
$989$	−3.86412			−0.122872
$990$	−45.3526	−	7.66532i	−1.44140	−	0.243620i
$991$			47.4907i			1.50859i	0.656535	+	0.754296i	$0.272021\pi$
$991$			47.4907i			1.50859i	−0.656535	+	0.754296i	$0.727979\pi$
$992$	26.6623	−	21.1289i	0.846527	−	0.670844i
$993$	−3.73519	−	3.73519i	−0.118533	−	0.118533i
$994$	7.00790	−	4.84872i	0.222277	−	0.153792i
$995$	−0.132432	−	10.4273i	−0.00419837	−	0.330567i
$996$	2.32507	−	6.17208i	0.0736726	−	0.195570i
$997$	23.6086	+	23.6086i	0.747690	+	0.747690i	0.974045	−	0.226355i	$-0.0726808\pi$
$997$	23.6086	+	23.6086i	0.747690	+	0.747690i	−0.226355	+	0.974045i	$0.572681\pi$
$998$	6.92307	−	38.0164i	0.219146	−	1.20339i
$999$	−7.27901			−0.230298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.43.33	yes	72
4.3	odd	2		1120.2.bi.a.463.20		72
5.2	odd	4	inner	280.2.w.a.267.16	yes	72
8.3	odd	2	inner	280.2.w.a.43.16	✓	72
8.5	even	2		1120.2.bi.a.463.19		72
20.7	even	4		1120.2.bi.a.687.19		72
40.27	even	4	inner	280.2.w.a.267.33	yes	72
40.37	odd	4		1120.2.bi.a.687.20		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.16	✓	72	8.3	odd	2	inner
280.2.w.a.43.33	yes	72	1.1	even	1	trivial
280.2.w.a.267.16	yes	72	5.2	odd	4	inner
280.2.w.a.267.33	yes	72	40.27	even	4	inner
1120.2.bi.a.463.19		72	8.5	even	2
1120.2.bi.a.463.20		72	4.3	odd	2
1120.2.bi.a.687.19		72	20.7	even	4
1120.2.bi.a.687.20		72	40.37	odd	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39133 + 0.253372i) q^{2} +(-0.161197 - 0.161197i) q^{3} +(1.87161 + 0.705048i) q^{4} +(-0.0283969 - 2.23589i) q^{5} +(-0.183435 - 0.265120i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.42538 + 1.45517i) q^{8} -2.94803i q^{9} +O(q^{10})\)	\(q+(1.39133 + 0.253372i) q^{2} +(-0.161197 - 0.161197i) q^{3} +(1.87161 + 0.705048i) q^{4} +(-0.0283969 - 2.23589i) q^{5} +(-0.183435 - 0.265120i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.42538 + 1.45517i) q^{8} -2.94803i q^{9} +(0.527001 - 3.11806i) q^{10} +4.93386 q^{11} +(-0.188045 - 0.415348i) q^{12} +(-4.05315 + 4.05315i) q^{13} +(-0.804659 - 1.16298i) q^{14} +(-0.355840 + 0.364995i) q^{15} +(3.00582 + 2.63914i) q^{16} +(-0.793172 + 0.793172i) q^{17} +(0.746947 - 4.10169i) q^{18} +5.81519i q^{19} +(1.52326 - 4.20472i) q^{20} +0.227966i q^{21} +(6.86463 + 1.25010i) q^{22} +(0.565908 - 0.565908i) q^{23} +(-0.156396 - 0.625532i) q^{24} +(-4.99839 + 0.126984i) q^{25} +(-6.66623 + 4.61233i) q^{26} +(-0.958802 + 0.958802i) q^{27} +(-0.824881 - 1.82197i) q^{28} -8.34882 q^{29} +(-0.587571 + 0.417669i) q^{30} -6.01380i q^{31} +(3.51340 + 4.43351i) q^{32} +(-0.795321 - 0.795321i) q^{33} +(-1.30453 + 0.902597i) q^{34} +(-1.56093 + 1.60109i) q^{35} +(2.07850 - 5.51755i) q^{36} +(3.79589 + 3.79589i) q^{37} +(-1.47340 + 8.09086i) q^{38} +1.30671 q^{39} +(3.18472 - 5.46421i) q^{40} +1.53295 q^{41} +(-0.0577602 + 0.317177i) q^{42} +(-3.41409 - 3.41409i) q^{43} +(9.23424 + 3.47860i) q^{44} +(-6.59147 + 0.0837149i) q^{45} +(0.930751 - 0.643981i) q^{46} +(3.43120 + 3.43120i) q^{47} +(-0.0591065 - 0.909948i) q^{48} +1.00000i q^{49} +(-6.98659 - 1.08977i) q^{50} +0.255713 q^{51} +(-10.4436 + 4.72824i) q^{52} +(-3.22442 + 3.22442i) q^{53} +(-1.57694 + 1.09108i) q^{54} +(-0.140106 - 11.0316i) q^{55} +(-0.686048 - 2.74396i) q^{56} +(0.937389 - 0.937389i) q^{57} +(-11.6160 - 2.11535i) q^{58} -1.96633i q^{59} +(-0.923331 + 0.432242i) q^{60} -5.27850i q^{61} +(1.52373 - 8.36719i) q^{62} +(-2.08457 + 2.08457i) q^{63} +(3.76498 + 7.05868i) q^{64} +(9.17749 + 8.94730i) q^{65} +(-0.905043 - 1.30807i) q^{66} +(-5.02471 + 5.02471i) q^{67} +(-2.04373 + 0.925281i) q^{68} -0.182445 q^{69} +(-2.57744 + 1.83215i) q^{70} +6.02581i q^{71} +(4.28988 - 7.15011i) q^{72} +(-10.7665 - 10.7665i) q^{73} +(4.31957 + 6.24311i) q^{74} +(0.826192 + 0.785253i) q^{75} +(-4.09999 + 10.8837i) q^{76} +(-3.48876 - 3.48876i) q^{77} +(1.81807 + 0.331083i) q^{78} +8.60880 q^{79} +(5.81547 - 6.79561i) q^{80} -8.53498 q^{81} +(2.13284 + 0.388405i) q^{82} +(10.2290 + 10.2290i) q^{83} +(-0.160727 + 0.426663i) q^{84} +(1.79597 + 1.75092i) q^{85} +(-3.88509 - 5.61516i) q^{86} +(1.34580 + 1.34580i) q^{87} +(11.9665 + 7.17958i) q^{88} -0.308629i q^{89} +(-9.19213 - 1.55362i) q^{90} +5.73203 q^{91} +(1.45815 - 0.660165i) q^{92} +(-0.969404 + 0.969404i) q^{93} +(3.90457 + 5.64331i) q^{94} +(13.0021 - 0.165133i) q^{95} +(0.148318 - 1.28101i) q^{96} +(3.04108 - 3.04108i) q^{97} +(-0.253372 + 1.39133i) q^{98} -14.5452i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more