LMFDB - Embedded newform 672.2.bs.a.155.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (of order $8$, degree $4$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.19
Character	$\chi$	$=$	672.155
Dual form			672.2.bs.a.659.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422431 + 1.34965i) q^{2} +(1.42128 + 0.989935i) q^{3} +(-1.64310 - 1.14027i) q^{4} +(-0.956738 + 2.30977i) q^{5} +(-1.93646 + 1.50004i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.23306 - 1.73593i) q^{8} +(1.04006 + 2.81394i) q^{9} +O(q^{10})$	\(q+(-0.422431 + 1.34965i) q^{2} +(1.42128 + 0.989935i) q^{3} +(-1.64310 - 1.14027i) q^{4} +(-0.956738 + 2.30977i) q^{5} +(-1.93646 + 1.50004i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.23306 - 1.73593i) q^{8} +(1.04006 + 2.81394i) q^{9} +(-2.71322 - 2.26698i) q^{10} +(-0.113313 + 0.273562i) q^{11} +(-1.20651 - 3.24720i) q^{12} +(-2.72770 + 1.12985i) q^{13} +(-0.655642 - 1.25305i) q^{14} +(-3.64631 + 2.33571i) q^{15} +(1.39958 + 3.74716i) q^{16} +0.0768131 q^{17} +(-4.23719 + 0.215012i) q^{18} +(-0.698312 - 1.68587i) q^{19} +(4.20578 - 2.70425i) q^{20} +(-1.70498 + 0.305005i) q^{21} +(-0.321346 - 0.268494i) q^{22} +(-3.80139 + 3.80139i) q^{23} +(4.89225 - 0.256649i) q^{24} +(-0.884156 - 0.884156i) q^{25} +(-0.372635 - 4.15872i) q^{26} +(-1.30741 + 5.02898i) q^{27} +(1.96814 - 0.355558i) q^{28} +(-0.290098 + 0.120163i) q^{29} +(-1.61208 - 5.90792i) q^{30} -9.32333i q^{31} +(-5.64857 + 0.306020i) q^{32} +(-0.431858 + 0.276635i) q^{33} +(-0.0324483 + 0.103671i) q^{34} +(-0.956738 - 2.30977i) q^{35} +(1.49973 - 5.80954i) q^{36} +(-0.158672 - 0.0657241i) q^{37} +(2.57033 - 0.230310i) q^{38} +(-4.99529 - 1.09442i) q^{39} +(1.87314 + 6.81868i) q^{40} +(1.97377 + 1.97377i) q^{41} +(0.308590 - 2.42997i) q^{42} +(0.443573 + 0.183734i) q^{43} +(0.498119 - 0.320283i) q^{44} +(-7.49463 - 0.289916i) q^{45} +(-3.52471 - 6.73637i) q^{46} +3.76906i q^{47} +(-1.72026 + 6.71124i) q^{48} -1.00000i q^{49} +(1.56680 - 0.819805i) q^{50} +(0.109173 + 0.0760400i) q^{51} +(5.77022 + 1.25385i) q^{52} +(-12.2843 - 5.08832i) q^{53} +(-6.23507 - 3.88895i) q^{54} +(-0.523455 - 0.523455i) q^{55} +(-0.351526 + 2.80650i) q^{56} +(0.676412 - 3.08738i) q^{57} +(-0.0396307 - 0.442291i) q^{58} +(8.54736 + 3.54043i) q^{59} +(8.65461 + 0.319954i) q^{60} +(5.41310 + 13.0684i) q^{61} +(12.5832 + 3.93847i) q^{62} +(-2.72519 - 1.25433i) q^{63} +(1.97311 - 7.75286i) q^{64} -7.38133i q^{65} +(-0.190929 - 0.699716i) q^{66} +(-6.15696 + 2.55030i) q^{67} +(-0.126212 - 0.0875876i) q^{68} +(-9.16596 + 1.63970i) q^{69} +(3.52153 - 0.315541i) q^{70} +(11.0876 + 11.0876i) q^{71} +(7.20731 + 4.47824i) q^{72} +(7.31988 - 7.31988i) q^{73} +(0.155733 - 0.186388i) q^{74} +(-0.381373 - 2.13189i) q^{75} +(-0.774950 + 3.56633i) q^{76} +(-0.113313 - 0.273562i) q^{77} +(3.58725 - 6.27958i) q^{78} +1.28386 q^{79} +(-9.99410 - 0.352346i) q^{80} +(-6.83657 + 5.85332i) q^{81} +(-3.49769 + 1.83012i) q^{82} +(4.95770 - 2.05355i) q^{83} +(3.14925 + 1.44299i) q^{84} +(-0.0734901 + 0.177421i) q^{85} +(-0.435355 + 0.521052i) q^{86} +(-0.531263 - 0.116394i) q^{87} +(0.221849 + 0.807584i) q^{88} +(-1.14675 + 1.14675i) q^{89} +(3.55725 - 9.99264i) q^{90} +(1.12985 - 2.72770i) q^{91} +(10.5807 - 1.91147i) q^{92} +(9.22950 - 13.2510i) q^{93} +(-5.08690 - 1.59217i) q^{94} +4.56208 q^{95} +(-8.33112 - 5.15678i) q^{96} -0.165586 q^{97} +(1.34965 + 0.422431i) q^{98} +(-0.887641 - 0.0343368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{4}+O(q^{10}) $ 192 * q - 16 * q^4	$ 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.422431	+	1.34965i	−0.298704	+	0.954346i
$2$	−0.422431	+	1.34965i	−0.298704	+	0.954346i
$3$	1.42128	+	0.989935i	0.820575	+	0.571539i
$3$	1.42128	+	0.989935i	0.820575	+	0.571539i
$4$	−1.64310	−	1.14027i	−0.821552	−	0.570134i
$5$	−0.956738	+	2.30977i	−0.427866	+	1.03296i	0.552097	+	0.833780i	$0.313828\pi$
$5$	−0.956738	+	2.30977i	−0.427866	+	1.03296i	−0.979963	+	0.199180i	$0.936172\pi$
$6$	−1.93646	+	1.50004i	−0.790555	+	0.612391i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	2.23306	−	1.73593i	0.789506	−	0.613743i
$9$	1.04006	+	2.81394i	0.346685	+	0.937981i
$10$	−2.71322	−	2.26698i	−0.857996	−	0.716882i
$11$	−0.113313	+	0.273562i	−0.0341652	+	0.0824821i	−0.940041	−	0.341061i	$-0.889214\pi$
$11$	−0.113313	+	0.273562i	−0.0341652	+	0.0824821i	0.905876	+	0.423543i	$0.139214\pi$
$12$	−1.20651	−	3.24720i	−0.348290	−	0.937387i
$13$	−2.72770	+	1.12985i	−0.756527	+	0.313364i	−0.727402	−	0.686212i	$-0.759272\pi$
$13$	−2.72770	+	1.12985i	−0.756527	+	0.313364i	−0.0291257	+	0.999576i	$0.509272\pi$
$14$	−0.655642	−	1.25305i	−0.175228	−	0.334892i
$15$	−3.64631	+	2.33571i	−0.941474	+	0.603079i
$16$	1.39958	+	3.74716i	0.349894	+	0.936789i
$17$	0.0768131			0.0186299			0.00931496	−	0.999957i	$-0.497035\pi$
$17$	0.0768131			0.0186299			0.00931496	+	0.999957i	$0.497035\pi$
$18$	−4.23719	+	0.215012i	−0.998715	+	0.0506789i
$19$	−0.698312	−	1.68587i	−0.160204	−	0.386766i	0.823312	−	0.567589i	$-0.192124\pi$
$19$	−0.698312	−	1.68587i	−0.160204	−	0.386766i	−0.983516	+	0.180823i	$0.942124\pi$
$20$	4.20578	−	2.70425i	0.940440	−	0.604689i
$21$	−1.70498	+	0.305005i	−0.372058	+	0.0665575i
$22$	−0.321346	−	0.268494i	−0.0685111	−	0.0572431i
$23$	−3.80139	+	3.80139i	−0.792645	+	0.792645i	−0.981923	−	0.189279i	$-0.939385\pi$
$23$	−3.80139	+	3.80139i	−0.792645	+	0.792645i	0.189279	+	0.981923i	$0.439385\pi$
$24$	4.89225	−	0.256649i	0.998627	−	0.0523882i
$25$	−0.884156	−	0.884156i	−0.176831	−	0.176831i
$26$	−0.372635	−	4.15872i	−0.0730796	−	0.815592i
$27$	−1.30741	+	5.02898i	−0.251612	+	0.967828i
$28$	1.96814	−	0.355558i	0.371944	−	0.0671942i
$29$	−0.290098	+	0.120163i	−0.0538699	+	0.0223136i	−0.409456	−	0.912330i	$-0.634281\pi$
$29$	−0.290098	+	0.120163i	−0.0538699	+	0.0223136i	0.355586	+	0.934644i	$0.384281\pi$
$30$	−1.61208	−	5.90792i	−0.294324	−	1.07863i
$31$		−	9.32333i		−	1.67452i	−0.546805	−	0.837260i	$-0.684156\pi$
$31$		−	9.32333i		−	1.67452i	0.546805	−	0.837260i	$-0.315844\pi$
$32$	−5.64857	+	0.306020i	−0.998536	+	0.0540973i
$33$	−0.431858	+	0.276635i	−0.0751768	+	0.0481559i
$34$	−0.0324483	+	0.103671i	−0.00556484	+	0.0177794i
$35$	−0.956738	−	2.30977i	−0.161718	−	0.390422i
$36$	1.49973	−	5.80954i	0.249955	−	0.968257i
$37$	−0.158672	−	0.0657241i	−0.0260855	−	0.0108050i	0.369603	−	0.929190i	$-0.379494\pi$
$37$	−0.158672	−	0.0657241i	−0.0260855	−	0.0108050i	−0.395688	+	0.918385i	$0.629494\pi$
$38$	2.57033	−	0.230310i	0.416962	−	0.0373611i
$39$	−4.99529	−	1.09442i	−0.799887	−	0.175247i
$40$	1.87314	+	6.81868i	0.296169	+	1.07813i
$41$	1.97377	+	1.97377i	0.308252	+	0.308252i	0.844231	−	0.535979i	$-0.180058\pi$
$41$	1.97377	+	1.97377i	0.308252	+	0.308252i	−0.535979	+	0.844231i	$0.680058\pi$
$42$	0.308590	−	2.42997i	0.0476165	−	0.374953i
$43$	0.443573	+	0.183734i	0.0676442	+	0.0280191i	0.416249	−	0.909251i	$-0.363344\pi$
$43$	0.443573	+	0.183734i	0.0676442	+	0.0280191i	−0.348605	+	0.937270i	$0.613344\pi$
$44$	0.498119	−	0.320283i	0.0750943	−	0.0482845i
$45$	−7.49463	−	0.289916i	−1.11723	−	0.0432182i
$46$	−3.52471	−	6.73637i	−0.519691	−	0.993223i
$47$			3.76906i			0.549773i	0.961477	+	0.274887i	$0.0886403\pi$
$47$			3.76906i			0.549773i	−0.961477	+	0.274887i	$0.911360\pi$
$48$	−1.72026	+	6.71124i	−0.248298	+	0.968684i
$49$		−	1.00000i		−	0.142857i
$50$	1.56680	−	0.819805i	0.221578	−	0.115938i
$51$	0.109173	+	0.0760400i	0.0152872	+	0.0106477i
$52$	5.77022	+	1.25385i	0.800186	+	0.173877i
$53$	−12.2843	−	5.08832i	−1.68738	−	0.698935i	−0.687742	−	0.725955i	$-0.741398\pi$
$53$	−12.2843	−	5.08832i	−1.68738	−	0.698935i	−0.999635	+	0.0270204i	$0.991398\pi$
$54$	−6.23507	−	3.88895i	−0.848485	−	0.529219i
$55$	−0.523455	−	0.523455i	−0.0705826	−	0.0705826i
$56$	−0.351526	+	2.80650i	−0.0469746	+	0.375034i
$57$	0.676412	−	3.08738i	0.0895929	−	0.408933i
$58$	−0.0396307	−	0.442291i	−0.00520377	−	0.0580757i
$59$	8.54736	+	3.54043i	1.11277	+	0.460925i	0.861891	−	0.507093i	$-0.169280\pi$
$59$	8.54736	+	3.54043i	1.11277	+	0.460925i	0.250880	+	0.968018i	$0.419280\pi$
$60$	8.65461	+	0.319954i	1.11731	+	0.0413059i
$61$	5.41310	+	13.0684i	0.693076	+	1.67323i	0.738489	+	0.674266i	$0.235540\pi$
$61$	5.41310	+	13.0684i	0.693076	+	1.67323i	−0.0454124	+	0.998968i	$0.514460\pi$
$62$	12.5832	+	3.93847i	1.59807	+	0.500186i
$63$	−2.72519	−	1.25433i	−0.343342	−	0.158030i
$64$	1.97311	−	7.75286i	0.246639	−	0.969107i
$65$		−	7.38133i		−	0.915541i
$66$	−0.190929	−	0.699716i	−0.0235018	−	0.0861291i
$67$	−6.15696	+	2.55030i	−0.752193	+	0.311568i	−0.725636	−	0.688079i	$-0.758454\pi$
$67$	−6.15696	+	2.55030i	−0.752193	+	0.311568i	−0.0265568	+	0.999647i	$0.508454\pi$
$68$	−0.126212	−	0.0875876i	−0.0153054	−	0.0106216i
$69$	−9.16596	+	1.63970i	−1.10345	+	0.197396i
$70$	3.52153	−	0.315541i	0.420904	−	0.0377143i
$71$	11.0876	+	11.0876i	1.31586	+	1.31586i	0.917021	+	0.398840i	$0.130587\pi$
$71$	11.0876	+	11.0876i	1.31586	+	1.31586i	0.398840	+	0.917021i	$0.369413\pi$
$72$	7.20731	+	4.47824i	0.849390	+	0.527766i
$73$	7.31988	−	7.31988i	0.856727	−	0.856727i	−0.134224	−	0.990951i	$-0.542854\pi$
$73$	7.31988	−	7.31988i	0.856727	−	0.856727i	0.990951	+	0.134224i	$0.0428540\pi$
$74$	0.155733	−	0.186388i	0.0181035	−	0.0216671i
$75$	−0.381373	−	2.13189i	−0.0440372	−	0.246169i
$76$	−0.774950	+	3.56633i	−0.0888929	+	0.409086i
$77$	−0.113313	−	0.273562i	−0.0129132	−	0.0311753i
$78$	3.58725	−	6.27958i	0.406176	−	0.711022i
$79$	1.28386			0.144445			0.0722226	−	0.997389i	$-0.476991\pi$
$79$	1.28386			0.144445			0.0722226	+	0.997389i	$0.476991\pi$
$80$	−9.99410	−	0.352346i	−1.11737	−	0.0393935i
$81$	−6.83657	+	5.85332i	−0.759618	+	0.650369i
$82$	−3.49769	+	1.83012i	−0.386255	+	0.202103i
$83$	4.95770	−	2.05355i	0.544178	−	0.225406i	−0.0936220	−	0.995608i	$-0.529845\pi$
$83$	4.95770	−	2.05355i	0.544178	−	0.225406i	0.637800	+	0.770202i	$0.279845\pi$
$84$	3.14925	+	1.44299i	0.343612	+	0.157443i
$85$	−0.0734901	+	0.177421i	−0.00797112	+	0.0192440i
$86$	−0.435355	+	0.521052i	−0.0469455	+	0.0561865i
$87$	−0.531263	−	0.116394i	−0.0569574	−	0.0124788i
$88$	0.221849	+	0.807584i	0.0236492	+	0.0860887i
$89$	−1.14675	+	1.14675i	−0.121555	+	0.121555i	−0.765268	−	0.643712i	$-0.777393\pi$
$89$	−1.14675	+	1.14675i	−0.121555	+	0.121555i	0.643712	+	0.765268i	$0.277393\pi$
$90$	3.55725	−	9.99264i	0.374967	−	1.05332i
$91$	1.12985	−	2.72770i	0.118440	−	0.285940i
$92$	10.5807	−	1.91147i	1.10311	−	0.199285i
$93$	9.22950	−	13.2510i	0.957054	−	1.37407i
$94$	−5.08690	−	1.59217i	−0.524674	−	0.164220i
$95$	4.56208			0.468060
$96$	−8.33112	−	5.15678i	−0.850292	−	0.526312i
$97$	−0.165586			−0.0168127			−0.00840637	−	0.999965i	$-0.502676\pi$
$97$	−0.165586			−0.0168127			−0.00840637	+	0.999965i	$0.502676\pi$
$98$	1.34965	+	0.422431i	0.136335	+	0.0426720i
$99$	−0.887641	−	0.0343368i	−0.0892112	−	0.00345098i
$100$	0.444585	+	2.46094i	0.0444585	+	0.246094i
$101$	−5.05042	+	12.1928i	−0.502536	+	1.21323i	0.445562	+	0.895251i	$0.353004\pi$
$101$	−5.05042	+	12.1928i	−0.502536	+	1.21323i	−0.948098	+	0.317978i	$0.896996\pi$
$102$	−0.148745	+	0.115223i	−0.0147280	+	0.0114088i
$103$	10.4935	−	10.4935i	1.03395	−	1.03395i	0.0345506	−	0.999403i	$-0.489000\pi$
$103$	10.4935	−	10.4935i	1.03395	−	1.03395i	0.999403	−	0.0345506i	$-0.0110000\pi$
$104$	−4.12978	+	7.25811i	−0.404958	+	0.711716i
$105$	0.926733	−	4.22993i	0.0904399	−	0.412799i
$106$	12.0567	−	14.4300i	1.17105	−	1.40157i
$107$	0.330787	−	0.798590i	0.0319784	−	0.0772026i	−0.907084	−	0.420951i	$-0.861697\pi$
$107$	0.330787	−	0.798590i	0.0319784	−	0.0772026i	0.939062	+	0.343748i	$0.111697\pi$
$108$	7.88261	−	6.77234i	0.758504	−	0.651668i
$109$	−13.8475	+	5.73581i	−1.32635	+	0.549391i	−0.929611	−	0.368542i	$-0.879857\pi$
$109$	−13.8475	+	5.73581i	−1.32635	+	0.549391i	−0.396736	+	0.917933i	$0.629857\pi$
$110$	0.927603	−	0.485356i	0.0884435	−	0.0462769i
$111$	−0.160454	−	0.250487i	−0.0152297	−	0.0237752i
$112$	−3.63929	−	1.65999i	−0.343881	−	0.156854i
$113$	−2.20010			−0.206968			−0.103484	−	0.994631i	$-0.532999\pi$
$113$	−2.20010			−0.206968			−0.103484	+	0.994631i	$0.532999\pi$
$114$	3.88114	+	2.21712i	0.363502	+	0.207653i
$115$	−5.14340	−	12.4173i	−0.479625	−	1.15792i
$116$	0.613679	+	0.133350i	0.0569787	+	0.0123813i
$117$	−6.01629	−	6.50048i	−0.556207	−	0.600970i
$118$	−8.38902	+	10.0403i	−0.772271	+	0.924289i
$119$	−0.0543151	+	0.0543151i	−0.00497906	+	0.00497906i
$120$	−4.08781	+	11.5455i	−0.373164	+	1.05396i
$121$	7.71618	+	7.71618i	0.701471	+	0.701471i
$122$	−19.9244	+	1.78529i	−1.80387	+	0.161632i
$123$	0.851371	+	4.75919i	0.0767656	+	0.429122i
$124$	−10.6311	+	15.3192i	−0.954701	+	1.37570i
$125$	−8.66075	+	3.58740i	−0.774641	+	0.320867i
$126$	2.84411	−	3.14818i	0.253373	−	0.280462i
$127$		−	7.95298i		−	0.705712i	−0.935678	−	0.352856i	$-0.885210\pi$
$127$		−	7.95298i		−	0.705712i	0.935678	−	0.352856i	$-0.114790\pi$
$128$	9.63013	+	5.93806i	0.851191	+	0.524856i
$129$	0.448555	+	0.700245i	0.0394931	+	0.0616531i
$130$	9.96220	+	3.11810i	0.873743	+	0.273476i
$131$	0.972913	+	2.34882i	0.0850038	+	0.205217i	0.960666	−	0.277707i	$-0.0895745\pi$
$131$	0.972913	+	2.34882i	0.0850038	+	0.205217i	−0.875662	+	0.482925i	$0.839575\pi$
$132$	1.02503	+	0.0378944i	0.0892170	+	0.00329828i
$133$	1.68587	+	0.698312i	0.146184	+	0.0605513i
$134$	−0.841111	−	9.38706i	−0.0726609	−	0.810919i
$135$	−10.3649	−	7.83125i	−0.892072	−	0.674006i
$136$	0.171528	−	0.133342i	0.0147084	−	0.0114340i
$137$	3.75801	+	3.75801i	0.321069	+	0.321069i	0.849177	−	0.528108i	$-0.177098\pi$
$137$	3.75801	+	3.75801i	0.321069	+	0.321069i	−0.528108	+	0.849177i	$0.677098\pi$
$138$	1.65897	−	13.0635i	0.141221	−	1.11204i
$139$	16.6055	+	6.87823i	1.40846	+	0.583404i	0.951933	−	0.306306i	$-0.0990930\pi$
$139$	16.6055	+	6.87823i	1.40846	+	0.583404i	0.456528	+	0.889709i	$0.349093\pi$
$140$	−1.06174	+	4.88613i	−0.0897332	+	0.412953i
$141$	−3.73112	+	5.35687i	−0.314217	+	0.451130i
$142$	−19.6482	+	10.2806i	−1.64884	+	0.862733i
$143$		−	0.874222i		−	0.0731061i
$144$	−9.08865	+	7.83559i	−0.757388	+	0.652966i
$145$		−	0.785025i		−	0.0651927i
$146$	6.78712	+	12.9714i	0.561706	+	1.07352i
$147$	0.989935	−	1.42128i	0.0816485	−	0.117225i
$148$	0.185772	+	0.288920i	0.0152703	+	0.0237491i
$149$	3.82095	+	1.58269i	0.313024	+	0.129659i	0.533664	−	0.845696i	$-0.320815\pi$
$149$	3.82095	+	1.58269i	0.313024	+	0.129659i	−0.220640	+	0.975355i	$0.570815\pi$
$150$	3.03840	+	0.385856i	0.248085	+	0.0315050i
$151$	12.3859	+	12.3859i	1.00795	+	1.00795i	0.999968	+	0.00798169i	$0.00254068\pi$
$151$	12.3859	+	12.3859i	1.00795	+	1.00795i	0.00798169	+	0.999968i	$0.497459\pi$
$152$	−4.48593	−	2.55244i	−0.363857	−	0.207030i
$153$	0.0798900	+	0.216148i	0.00645872	+	0.0174745i
$154$	0.417080	−	0.0373717i	0.0336092	−	0.00301150i
$155$	21.5348	+	8.91999i	1.72971	+	0.716471i
$156$	6.95986	+	7.49421i	0.557234	+	0.600017i
$157$	3.05830	+	7.38338i	0.244079	+	0.589258i	0.997680	−	0.0680734i	$-0.0216852\pi$
$157$	3.05830	+	7.38338i	0.244079	+	0.589258i	−0.753602	+	0.657331i	$0.771685\pi$
$158$	−0.542341	+	1.73276i	−0.0431464	+	0.137851i
$159$	−12.4223	−	19.3926i	−0.985150	−	1.53793i
$160$	4.69737	−	13.3397i	0.371359	−	1.05459i
$161$		−	5.37598i		−	0.423686i
$162$	−5.01195	−	11.6996i	−0.393776	−	0.919206i
$163$	2.18964	−	0.906977i	0.171505	−	0.0710399i	−0.295279	−	0.955411i	$-0.595412\pi$
$163$	2.18964	−	0.906977i	0.171505	−	0.0710399i	0.466784	+	0.884371i	$0.345412\pi$
$164$	−0.992483	−	5.49375i	−0.0774999	−	0.428990i
$165$	−0.225788	−	1.26216i	−0.0175776	−	0.0982590i
$166$	0.677278	+	7.55864i	0.0525670	+	0.586664i
$167$	11.5946	+	11.5946i	0.897217	+	0.897217i	0.995189	−	0.0979718i	$-0.0312355\pi$
$167$	11.5946	+	11.5946i	0.897217	+	0.897217i	−0.0979718	+	0.995189i	$0.531235\pi$
$168$	−3.27787	+	3.64082i	−0.252893	+	0.280896i
$169$	−3.02861	+	3.02861i	−0.232970	+	0.232970i
$170$	−0.208411	−	0.174134i	−0.0159844	−	0.0133555i
$171$	4.01767	−	3.71842i	0.307239	−	0.284354i
$172$	−0.519330	−	0.807685i	−0.0395985	−	0.0615854i
$173$	4.38255	+	10.5804i	0.333199	+	0.804414i	0.998334	+	0.0576914i	$0.0183739\pi$
$173$	4.38255	+	10.5804i	0.333199	+	0.804414i	−0.665135	+	0.746723i	$0.731626\pi$
$174$	0.381514	−	0.667850i	0.0289225	−	0.0506296i
$175$	1.25039			0.0945203
$176$	−1.18367	−	0.0417308i	−0.0892225	−	0.00314558i
$177$	8.64337	+	13.4933i	0.649675	+	1.01422i
$178$	−1.06329	−	2.03213i	−0.0796967	−	0.152315i
$179$	11.4614	−	4.74746i	0.856663	−	0.354842i	0.0892617	−	0.996008i	$-0.471549\pi$
$179$	11.4614	−	4.74746i	0.856663	−	0.354842i	0.767402	+	0.641167i	$0.221549\pi$
$180$	11.9839	+	9.02225i	0.893224	+	0.672479i
$181$	5.12748	−	12.3788i	0.381123	−	0.920112i	−0.610626	−	0.791919i	$-0.709082\pi$
$181$	5.12748	−	12.3788i	0.381123	−	0.920112i	0.991749	−	0.128193i	$-0.0409177\pi$
$182$	3.20415	+	2.67717i	0.237507	+	0.198445i
$183$	−5.24333	+	23.9324i	−0.387598	+	1.76913i
$184$	−1.88980	+	15.0877i	−0.139318	+	1.11228i
$185$	0.303615	−	0.303615i	0.0223222	−	0.0223222i
$186$	13.9854	+	18.0542i	1.02546	+	1.32380i
$187$	−0.00870394	+	0.0210132i	−0.000636495	+	0.00153663i
$188$	4.29773	−	6.19295i	0.313444	−	0.451667i
$189$	−2.63155	−	4.48051i	−0.191417	−	0.325909i
$190$	−1.92717	+	6.15721i	−0.139811	+	0.446691i
$191$	−13.7676			−0.996190			−0.498095	−	0.867122i	$-0.665967\pi$
$191$	−13.7676			−0.996190			−0.498095	+	0.867122i	$0.665967\pi$
$192$	10.4792	−	9.06570i	0.756269	−	0.654261i
$193$	−14.3048			−1.02968			−0.514841	−	0.857286i	$-0.672149\pi$
$193$	−14.3048			−1.02968			−0.514841	+	0.857286i	$0.672149\pi$
$194$	0.0699489	−	0.223483i	0.00502204	−	0.0160452i
$195$	7.30704	−	10.4909i	0.523268	−	0.751270i
$196$	−1.14027	+	1.64310i	−0.0814477	+	0.117365i
$197$	−9.86475	+	23.8156i	−0.702834	+	1.69679i	0.0143392	+	0.999897i	$0.495436\pi$
$197$	−9.86475	+	23.8156i	−0.702834	+	1.69679i	−0.717173	+	0.696895i	$0.754564\pi$
$198$	0.421310	−	1.18350i	0.0299412	−	0.0841075i
$199$	14.1629	−	14.1629i	1.00398	−	1.00398i	0.00398960	−	0.999992i	$-0.498730\pi$
$199$	14.1629	−	14.1629i	1.00398	−	1.00398i	0.999992	−	0.00398960i	$-0.00126993\pi$
$200$	−3.50920	−	0.439543i	−0.248138	−	0.0310804i
$201$	−11.2754	−	2.47032i	−0.795304	−	0.174243i
$202$	−14.3225	−	11.9669i	−1.00773	−	0.841990i
$203$	0.120163	−	0.290098i	0.00843376	−	0.0203609i
$204$	−0.0926761	−	0.249428i	−0.00648862	−	0.0174634i
$205$	−6.44735	+	2.67058i	−0.450302	+	0.186521i
$206$	9.72974	+	18.5953i	0.677903	+	1.29560i
$207$	−14.6506	−	6.74324i	−1.01828	−	0.468688i
$208$	−8.05135	−	8.63980i	−0.558261	−	0.599062i
$209$	0.540319			0.0373747
$210$	5.31744	+	3.03762i	0.366938	+	0.209616i
$211$	6.10523	+	14.7393i	0.420301	+	1.01470i	0.982259	+	0.187531i	$0.0600484\pi$
$211$	6.10523	+	14.7393i	0.420301	+	1.01470i	−0.561958	+	0.827166i	$0.689952\pi$
$212$	14.3823	+	22.3680i	0.987781	+	1.53624i
$213$	4.78256	+	26.7346i	0.327696	+	1.83183i
$214$	0.938081	+	0.783795i	0.0641259	+	0.0535792i
$215$	−0.848765	+	0.848765i	−0.0578853	+	0.0578853i
$216$	5.81041	+	13.4996i	0.395349	+	0.918531i
$217$	6.59259	+	6.59259i	0.447534	+	0.447534i
$218$	−1.89172	−	21.1122i	−0.128124	−	1.42990i
$219$	17.6498	−	3.15737i	1.19266	−	0.213355i
$220$	0.263211	+	1.45697i	0.0177457	+	0.0982288i
$221$	−0.209523	+	0.0867873i	−0.0140940	+	0.00583795i
$222$	0.405851	−	0.110743i	0.0272389	−	0.00743261i
$223$		−	16.3618i		−	1.09567i	−0.836588	−	0.547833i	$-0.815453\pi$
$223$		−	16.3618i		−	1.09567i	0.836588	−	0.547833i	$-0.184547\pi$
$224$	3.77775	−	4.21053i	0.252412	−	0.281328i
$225$	1.56839	−	3.40754i	0.104560	−	0.227169i
$226$	0.929390	−	2.96936i	0.0618221	−	0.197519i
$227$	−1.25898	−	3.03945i	−0.0835614	−	0.201735i	0.876576	−	0.481263i	$-0.159822\pi$
$227$	−1.25898	−	3.03945i	−0.0835614	−	0.201735i	−0.960137	+	0.279528i	$0.909822\pi$
$228$	−4.63185	+	4.30159i	−0.306752	+	0.284880i
$229$	12.7035	+	5.26196i	0.839470	+	0.347720i	0.760645	−	0.649169i	$-0.224883\pi$
$229$	12.7035	+	5.26196i	0.839470	+	0.347720i	0.0788254	+	0.996888i	$0.474883\pi$
$230$	18.9317	−	1.69634i	1.24832	−	0.111853i
$231$	0.109759	−	0.500980i	0.00722164	−	0.0329621i
$232$	−0.439213	+	0.771920i	−0.0288358	+	0.0506790i
$233$	−15.2266	−	15.2266i	−0.997529	−	0.997529i	0.00246796	−	0.999997i	$-0.499214\pi$
$233$	−15.2266	−	15.2266i	−0.997529	−	0.997529i	−0.999997	+	0.00246796i	$0.999214\pi$
$234$	11.3148	−	5.37388i	0.739674	−	0.351301i
$235$	−8.70565	−	3.60600i	−0.567894	−	0.235229i
$236$	−10.0072	−	15.5636i	−0.651410	−	1.01310i
$237$	1.82472	+	1.27093i	0.118528	+	0.0825561i
$238$	−0.0503619	−	0.0962507i	−0.00326448	−	0.00623901i
$239$		−	6.09194i		−	0.394055i	−0.980398	−	0.197028i	$-0.936871\pi$
$239$		−	6.09194i		−	0.394055i	0.980398	−	0.197028i	$-0.0631288\pi$
$240$	−13.8556	−	10.3943i	−0.894374	−	0.670949i
$241$			25.3965i			1.63593i	0.575265	+	0.817967i	$0.304899\pi$
$241$			25.3965i			1.63593i	−0.575265	+	0.817967i	$0.695101\pi$
$242$	−13.6737	+	7.15457i	−0.878978	+	0.459913i
$243$	−15.5111	+	1.55143i	−0.995035	+	0.0995246i
$244$	6.00717	−	27.6451i	0.384570	−	1.76979i
$245$	2.30977	+	0.956738i	0.147566	+	0.0611238i
$246$	−6.78288	−	0.861379i	−0.432461	−	0.0549195i
$247$	3.80957	+	3.80957i	0.242397	+	0.242397i
$248$	−16.1846	−	20.8196i	−1.02772	−	1.32204i
$249$	9.07914	+	1.98914i	0.575367	+	0.126057i
$250$	−1.18316	−	13.2044i	−0.0748294	−	0.835119i
$251$	−11.1487	−	4.61793i	−0.703698	−	0.291481i	0.00199596	−	0.999998i	$-0.499365\pi$
$251$	−11.1487	−	4.61793i	−0.703698	−	0.291481i	−0.705694	+	0.708517i	$0.749365\pi$
$252$	3.04750	+	5.16844i	0.191974	+	0.325581i
$253$	−0.609169	−	1.47066i	−0.0382981	−	0.0924598i
$254$	10.7337	+	3.35959i	0.673494	+	0.210799i
$255$	−0.280085	+	0.179414i	−0.0175396	+	0.0112353i
$256$	−12.0824	+	10.4889i	−0.755148	+	0.655554i
$257$		−	27.6266i		−	1.72330i	−0.507502	−	0.861650i	$-0.669431\pi$
$257$		−	27.6266i		−	1.72330i	0.507502	−	0.861650i	$-0.330569\pi$
$258$	−1.13457	+	0.309586i	−0.0706351	+	0.0192740i
$259$	0.158672	−	0.0657241i	0.00985941	−	0.00408390i
$260$	−8.41669	+	12.1283i	−0.521981	+	0.752164i
$261$	−0.639850	−	0.691345i	−0.0396057	−	0.0427932i
$262$	−3.58107	+	0.320875i	−0.221239	+	0.0198237i
$263$	−12.3241	−	12.3241i	−0.759938	−	0.759938i	0.216373	−	0.976311i	$-0.430577\pi$
$263$	−12.3241	−	12.3241i	−0.759938	−	0.759938i	−0.976311	+	0.216373i	$0.930577\pi$
$264$	−0.484147	+	1.36742i	−0.0297972	+	0.0841587i
$265$	23.5057	−	23.5057i	1.44394	−	1.44394i
$266$	−1.65464	+	1.98035i	−0.101453	+	0.121423i
$267$	−2.76506	+	0.494641i	−0.169219	+	0.0302715i
$268$	13.0245	+	2.83019i	0.795601	+	0.172881i
$269$	−5.36948	−	12.9631i	−0.327383	−	0.790372i	−0.998785	−	0.0492791i	$-0.984308\pi$
$269$	−5.36948	−	12.9631i	−0.327383	−	0.790372i	0.671402	−	0.741093i	$-0.265692\pi$
$270$	14.9479	−	10.6809i	0.909701	−	0.650017i
$271$	21.2718			1.29217			0.646084	−	0.763266i	$-0.276406\pi$
$271$	21.2718			1.29217			0.646084	+	0.763266i	$0.276406\pi$
$272$	0.107506	+	0.287831i	0.00651850	+	0.0174523i
$273$	4.30607	−	2.75834i	0.260615	−	0.166942i
$274$	−6.65950	+	3.48450i	−0.402315	+	0.210506i
$275$	0.342058	−	0.141685i	0.0206269	−	0.00854393i
$276$	16.9303	+	7.75746i	1.01909	+	0.466944i
$277$	−1.48207	+	3.57803i	−0.0890488	+	0.214983i	−0.962129	−	0.272593i	$-0.912119\pi$
$277$	−1.48207	+	3.57803i	−0.0890488	+	0.214983i	0.873081	+	0.487576i	$0.162119\pi$
$278$	−16.2979	+	19.5060i	−0.977482	+	1.16989i
$279$	26.2353	−	9.69679i	1.57067	−	0.580532i
$280$	−6.14605	−	3.49703i	−0.367297	−	0.208987i
$281$	20.7690	−	20.7690i	1.23897	−	1.23897i	0.278554	−	0.960421i	$-0.410145\pi$
$281$	20.7690	−	20.7690i	1.23897	−	1.23897i	0.960421	−	0.278554i	$-0.0898550\pi$
$282$	−5.65375	−	7.29861i	−0.336676	−	0.434626i
$283$	6.67831	−	16.1229i	0.396984	−	0.958405i	−0.591393	−	0.806384i	$-0.701422\pi$
$283$	6.67831	−	16.1229i	0.396984	−	0.958405i	0.988377	−	0.152021i	$-0.0485783\pi$
$284$	−5.57525	−	30.8610i	−0.330830	−	1.83126i
$285$	6.48398	+	4.51617i	0.384078	+	0.267515i
$286$	1.17989	+	0.369299i	0.0697685	+	0.0218371i
$287$	−2.79134			−0.164768
$288$	−6.73596	−	15.5765i	−0.396920	−	0.917853i
$289$	−16.9941			−0.999653
$290$	1.05951	+	0.331619i	0.0622164	+	0.0194733i
$291$	−0.235344	−	0.163920i	−0.0137961	−	0.00960915i
$292$	−20.3740	+	3.68069i	−1.19230	+	0.215396i
$293$	3.15978	−	7.62839i	0.184597	−	0.445655i	−0.804307	−	0.594214i	$-0.797463\pi$
$293$	3.15978	−	7.62839i	0.184597	−	0.445655i	0.988904	+	0.148558i	$0.0474633\pi$
$294$	1.50004	+	1.93646i	0.0874844	+	0.112936i
$295$	−16.3552	+	16.3552i	−0.952235	+	0.952235i
$296$	−0.468417	+	0.128677i	−0.0272262	+	0.00747922i
$297$	−1.22759	−	0.927509i	−0.0712321	−	0.0538195i
$298$	−3.75016	+	4.48836i	−0.217241	+	0.260004i
$299$	6.07405	−	14.6640i	0.351271	−	0.848044i
$300$	−1.80429	+	3.93778i	−0.104171	+	0.227348i
$301$	−0.443573	+	0.183734i	−0.0255671	+	0.0105902i
$302$	−21.9488	+	11.4844i	−1.26301	+	0.660854i
$303$	−19.2481	+	12.3298i	−1.10578	+	0.708326i
$304$	5.33989	−	4.97620i	0.306264	−	0.285404i
$305$	−35.3639			−2.02493
$306$	−0.325472	+	0.0165158i	−0.0186060	+	0.000944144i
$307$	1.36656	+	3.29916i	0.0779936	+	0.188293i	0.958067	−	0.286545i	$-0.0925067\pi$
$307$	1.36656	+	3.29916i	0.0779936	+	0.188293i	−0.880073	+	0.474838i	$0.842507\pi$
$308$	−0.125749	+	0.578698i	−0.00716521	+	0.0329744i
$309$	25.3020	−	4.52628i	1.43938	−	0.257491i
$310$	−21.1358	+	25.2963i	−1.20043	+	1.43673i
$311$	−5.07179	+	5.07179i	−0.287595	+	0.287595i	−0.836128	−	0.548534i	$-0.815186\pi$
$311$	−5.07179	+	5.07179i	−0.287595	+	0.287595i	0.548534	+	0.836128i	$0.315186\pi$
$312$	−13.0546	+	6.22757i	−0.739072	+	0.352567i
$313$	−12.8966	−	12.8966i	−0.728960	−	0.728960i	0.241452	−	0.970413i	$-0.422376\pi$
$313$	−12.8966	−	12.8966i	−0.728960	−	0.728960i	−0.970413	+	0.241452i	$0.922376\pi$
$314$	−11.2569	+	1.00865i	−0.635263	+	0.0569216i
$315$	5.50450	−	5.09450i	0.310144	−	0.287043i
$316$	−2.10951	−	1.46394i	−0.118669	−	0.0823531i
$317$	−1.94162	+	0.804245i	−0.109052	+	0.0451709i	−0.436542	−	0.899684i	$-0.643797\pi$
$317$	−1.94162	+	0.804245i	−0.109052	+	0.0451709i	0.327490	+	0.944855i	$0.393797\pi$
$318$	31.4207	−	8.57368i	1.76199	−	0.480788i
$319$		−	0.0929759i		−	0.00520565i
$320$	16.0196	+	11.9749i	0.895521	+	0.669417i
$321$	1.26069	−	0.807560i	0.0703650	−	0.0450736i
$322$	7.25568	+	2.27098i	0.404343	+	0.126557i
$323$	−0.0536395	−	0.129497i	−0.00298458	−	0.00720542i
$324$	17.9075	−	1.82210i	0.994863	−	0.101228i
$325$	3.41068	+	1.41275i	0.189190	+	0.0783652i
$326$	0.299129	+	3.33837i	0.0165672	+	0.184895i
$327$	−25.3592	−	5.55592i	−1.40237	−	0.307243i
$328$	7.83389	+	0.981228i	0.432554	+	0.0541793i
$329$	−2.66512	−	2.66512i	−0.146933	−	0.146933i
$330$	1.79885	+	0.228442i	0.0990236	+	0.0125753i
$331$	13.4299	+	5.56283i	0.738172	+	0.305761i	0.719905	−	0.694072i	$-0.244185\pi$
$331$	13.4299	+	5.56283i	0.738172	+	0.305761i	0.0182665	+	0.999833i	$0.494185\pi$
$332$	−10.4876	−	2.27892i	−0.575582	−	0.125072i
$333$	0.0199161	−	0.514851i	0.00109140	−	0.0282137i
$334$	−20.5466	+	10.7507i	−1.12426	+	0.588253i
$335$		−	16.6611i		−	0.910295i
$336$	−3.52916	−	5.96197i	−0.192531	−	0.325252i
$337$			2.34915i			0.127966i	0.997951	+	0.0639831i	$0.0203804\pi$
$337$			2.34915i			0.127966i	−0.997951	+	0.0639831i	$0.979620\pi$
$338$	−2.80818	−	5.36694i	−0.152745	−	0.291923i
$339$	−3.12695	−	2.17795i	−0.169832	−	0.118290i
$340$	0.323059	−	0.207722i	0.0175203	−	0.0112653i
$341$	2.55051	+	1.05646i	0.138118	+	0.0572103i
$342$	3.32136	+	6.99322i	0.179599	+	0.378150i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	1.30947	−	0.359721i	0.0706020	−	0.0193949i
$345$	4.98210	−	22.7400i	0.268227	−	1.22428i
$346$	−16.1312	+	1.44541i	−0.867218	+	0.0777055i
$347$	12.4095	+	5.14020i	0.666179	+	0.275940i	0.690036	−	0.723775i	$-0.257595\pi$
$347$	12.4095	+	5.14020i	0.666179	+	0.275940i	−0.0238573	+	0.999715i	$0.507595\pi$
$348$	0.740200	+	0.797030i	0.0396789	+	0.0427253i
$349$	−3.74765	−	9.04763i	−0.200607	−	0.484309i	0.791276	−	0.611459i	$-0.209417\pi$
$349$	−3.74765	−	9.04763i	−0.200607	−	0.484309i	−0.991883	+	0.127150i	$0.959417\pi$
$350$	−0.528202	+	1.68758i	−0.0282336	+	0.0902050i
$351$	−2.11576	−	15.1947i	−0.112931	−	0.811035i
$352$	0.556342	−	1.57991i	0.0296531	−	0.0842095i
$353$			6.42750i			0.342101i	0.985262	+	0.171051i	$0.0547162\pi$
$353$			6.42750i			0.342101i	−0.985262	+	0.171051i	$0.945284\pi$
$354$	−21.8624	+	5.96553i	−1.16197	+	0.317064i
$355$	−36.2179	+	15.0019i	−1.92224	+	0.796220i
$356$	3.19183	−	0.576626i	0.169167	−	0.0305611i
$357$	−0.130965	+	0.0234284i	−0.00693141	+	0.00123996i
$358$	1.56575	+	17.4743i	0.0827527	+	0.923546i
$359$	−25.2504	−	25.2504i	−1.33267	−	1.33267i	−0.902976	−	0.429691i	$-0.858622\pi$
$359$	−25.2504	−	25.2504i	−1.33267	−	1.33267i	−0.429691	−	0.902976i	$-0.641378\pi$
$360$	−17.2392	+	12.3627i	−0.908587	+	0.651573i
$361$	11.0805	−	11.0805i	0.583184	−	0.583184i
$362$	14.5411	+	12.1495i	0.764262	+	0.638564i
$363$	3.32831	+	18.6053i	0.174691	+	0.976527i
$364$	−4.96677	+	3.19356i	−0.260329	+	0.167388i
$365$	9.90404	+	23.9105i	0.518401	+	1.25153i
$366$	−30.0854	−	17.1865i	−1.57259	−	0.898351i
$367$	−17.6923			−0.923532			−0.461766	−	0.887002i	$-0.652784\pi$
$367$	−17.6923			−0.923532			−0.461766	+	0.887002i	$0.652784\pi$
$368$	−19.5647	−	8.92407i	−1.01988	−	0.465199i
$369$	−3.50125	+	7.60693i	−0.182268	+	0.396001i
$370$	0.281517	+	0.538031i	0.0146354	+	0.0279709i
$371$	12.2843	−	5.08832i	0.637769	−	0.264172i
$372$	−30.2748	+	11.2487i	−1.56967	+	0.583219i
$373$	0.998242	−	2.40997i	0.0516870	−	0.124784i	−0.895927	−	0.444202i	$-0.853487\pi$
$373$	0.998242	−	2.40997i	0.0516870	−	0.124784i	0.947614	+	0.319418i	$0.103487\pi$
$374$	−0.0246836	−	0.0206239i	−0.00127636	−	0.00106644i
$375$	−15.8606	−	3.47489i	−0.819039	−	0.179443i
$376$	6.54281	+	8.41653i	0.337419	+	0.434049i
$377$	0.655535	−	0.655535i	0.0337618	−	0.0337618i
$378$	7.15876	−	1.65895i	0.368207	−	0.0853274i
$379$	−6.36628	+	15.3696i	−0.327014	+	0.789481i	0.671797	+	0.740735i	$0.265523\pi$
$379$	−6.36628	+	15.3696i	−0.327014	+	0.789481i	−0.998811	+	0.0487463i	$0.984477\pi$
$380$	−7.49598	−	5.20200i	−0.384535	−	0.266857i
$381$	7.87293	−	11.3034i	0.403342	−	0.579090i
$382$	5.81588	−	18.5815i	0.297566	−	0.950710i
$383$	19.0154			0.971640			0.485820	−	0.874059i	$-0.338521\pi$
$383$	19.0154			0.971640			0.485820	+	0.874059i	$0.338521\pi$
$384$	7.80879	+	17.9728i	0.398490	+	0.917172i
$385$	0.740277			0.0377280
$386$	6.04280	−	19.3065i	0.307570	−	0.982673i
$387$	−0.0556761	+	1.43928i	−0.00283017	+	0.0731628i
$388$	0.272075	+	0.188813i	0.0138125	+	0.00958552i
$389$	12.8488	−	31.0198i	0.651460	−	1.57276i	−0.159199	−	0.987246i	$-0.550891\pi$
$389$	12.8488	−	31.0198i	0.651460	−	1.57276i	0.810659	−	0.585518i	$-0.199109\pi$
$390$	11.0723	+	14.2936i	0.560669	+	0.723786i
$391$	−0.291997	+	0.291997i	−0.0147669	+	0.0147669i
$392$	−1.73593	−	2.23306i	−0.0876776	−	0.112787i
$393$	−0.942400	+	4.30144i	−0.0475378	+	0.216979i
$394$	−27.9755	−	23.3744i	−1.40939	−	1.17759i
$395$	−1.22831	+	2.96541i	−0.0618032	+	0.149206i
$396$	1.41933	+	1.06857i	0.0713241	+	0.0536975i
$397$	−2.55269	+	1.05736i	−0.128116	+	0.0530672i	−0.445820	−	0.895122i	$-0.647088\pi$
$397$	−2.55269	+	1.05736i	−0.128116	+	0.0530672i	0.317705	+	0.948190i	$0.397088\pi$
$398$	13.1321	+	25.0978i	0.658252	+	1.25804i
$399$	1.70481	+	2.66140i	0.0853473	+	0.133237i
$400$	2.07563	−	4.55052i	0.103781	−	0.227526i
$401$	−13.6027			−0.679288			−0.339644	−	0.940554i	$-0.610307\pi$
$401$	−13.6027			−0.679288			−0.339644	+	0.940554i	$0.610307\pi$
$402$	8.09713	−	14.1743i	0.403848	−	0.706948i
$403$	10.5340	+	25.4312i	0.524734	+	1.26682i
$404$	22.2014	−	14.2752i	1.10456	−	0.710218i
$405$	−6.97903	−	21.3910i	−0.346791	−	1.06293i
$406$	0.340770	+	0.284724i	0.0169121	+	0.0141306i
$407$	0.0359593	−	0.0359593i	0.00178243	−	0.00178243i
$408$	0.375789	−	0.0197140i	0.0186043	−	0.000975987i
$409$	3.03239	+	3.03239i	0.149942	+	0.149942i	0.778092	−	0.628150i	$-0.216188\pi$
$409$	3.03239	+	3.03239i	0.149942	+	0.149942i	−0.628150	+	0.778092i	$0.716188\pi$
$410$	−0.880781	−	9.82980i	−0.0434987	−	0.485459i
$411$	1.62099	+	9.06137i	0.0799575	+	0.446964i
$412$	−29.2073	+	5.27649i	−1.43894	+	0.259954i
$413$	−8.54736	+	3.54043i	−0.420588	+	0.174213i
$414$	15.2899	−	16.9246i	0.751456	−	0.831796i
$415$			13.4159i			0.658558i
$416$	15.0618	−	7.21677i	0.738467	−	0.353831i
$417$	16.7920	+	26.2142i	0.822309	+	1.28372i
$418$	−0.228248	+	0.729241i	−0.0111640	+	0.0356683i
$419$	−9.97914	−	24.0918i	−0.487513	−	1.17696i	−0.955968	−	0.293473i	$-0.905189\pi$
$419$	−9.97914	−	24.0918i	−0.487513	−	1.17696i	0.468455	−	0.883488i	$-0.344811\pi$
$420$	−6.34597	+	5.89349i	−0.309652	+	0.287573i
$421$	18.4447	+	7.64003i	0.898938	+	0.372352i	0.783812	−	0.620999i	$-0.213273\pi$
$421$	18.4447	+	7.64003i	0.898938	+	0.372352i	0.115126	+	0.993351i	$0.463273\pi$
$422$	−22.4719	+	2.01356i	−1.09392	+	0.0980185i
$423$	−10.6059	+	3.92003i	−0.515677	+	0.190598i
$424$	−36.2645	+	9.96211i	−1.76116	+	0.483803i
$425$	−0.0679148	−	0.0679148i	−0.00329435	−	0.00329435i
$426$	−38.1027	−	4.83878i	−1.84608	−	0.234440i
$427$	−13.0684	−	5.41310i	−0.632423	−	0.261958i
$428$	−1.45412	+	0.934980i	−0.0702877	+	0.0451940i
$429$	0.865423	−	1.24251i	0.0417830	−	0.0599890i
$430$	−0.786990	−	1.50408i	−0.0379520	−	0.0725332i
$431$		−	18.4543i		−	0.888913i	−0.895800	−	0.444457i	$-0.853397\pi$
$431$		−	18.4543i		−	0.888913i	0.895800	−	0.444457i	$-0.146603\pi$
$432$	−20.6742	+	2.13936i	−0.994689	+	0.102930i
$433$		−	17.7498i		−	0.853002i	−0.904487	−	0.426501i	$-0.859746\pi$
$433$		−	17.7498i		−	0.853002i	0.904487	−	0.426501i	$-0.140254\pi$
$434$	−11.6826	+	6.11277i	−0.560783	+	0.293422i
$435$	0.777124	−	1.11574i	0.0372602	−	0.0534955i
$436$	29.2932	+	6.36530i	1.40289	+	0.304843i
$437$	9.06322	+	3.75411i	0.433553	+	0.179583i
$438$	−3.19449	+	25.1548i	−0.152638	+	1.20194i
$439$	−11.1631	−	11.1631i	−0.532786	−	0.532786i	0.388615	−	0.921400i	$-0.372954\pi$
$439$	−11.1631	−	11.1631i	−0.532786	−	0.532786i	−0.921400	+	0.388615i	$0.872954\pi$
$440$	−2.07758	−	0.260226i	−0.0990449	−	0.0124058i
$441$	2.81394	−	1.04006i	0.133997	−	0.0495265i
$442$	−0.0286232	−	0.319444i	−0.00136147	−	0.0151944i
$443$	−12.7490	−	5.28081i	−0.605723	−	0.250899i	0.0586754	−	0.998277i	$-0.481312\pi$
$443$	−12.7490	−	5.28081i	−0.605723	−	0.250899i	−0.664399	+	0.747378i	$0.731312\pi$
$444$	−0.0219796	+	0.594538i	−0.00104311	+	0.0282155i
$445$	−1.55159	−	3.74587i	−0.0735524	−	0.177571i
$446$	22.0827	+	6.91173i	1.04564	+	0.327280i
$447$	3.86387	+	6.03193i	0.182755	+	0.285301i
$448$	4.08690	+	6.87730i	0.193088	+	0.324922i
$449$			5.64720i			0.266508i	0.991082	+	0.133254i	$0.0425426\pi$
$449$			5.64720i			0.266508i	−0.991082	+	0.133254i	$0.957457\pi$
$450$	3.93644	+	3.55623i	0.185566	+	0.167642i
$451$	−0.763604	+	0.316295i	−0.0359567	+	0.0148938i
$452$	3.61499	+	2.50870i	0.170035	+	0.117999i
$453$	5.34255	+	29.8650i	0.251015	+	1.40318i
$454$	4.63402	−	0.415223i	0.217485	−	0.0194874i
$455$	5.21939	+	5.21939i	0.244689	+	0.244689i
$456$	−3.84900	−	8.06850i	−0.180246	−	0.377842i
$457$	27.4388	−	27.4388i	1.28353	−	1.28353i	0.344890	−	0.938643i	$-0.387916\pi$
$457$	27.4388	−	27.4388i	1.28353	−	1.28353i	0.938643	−	0.344890i	$-0.112084\pi$
$458$	−12.4681	+	14.9224i	−0.582598	+	0.697279i
$459$	−0.100427	+	0.386292i	−0.00468751	+	0.0180306i
$460$	−5.70788	+	26.2677i	−0.266131	+	1.22474i
$461$	−10.8098	−	26.0971i	−0.503461	−	1.21546i	−0.947587	−	0.319497i	$-0.896486\pi$
$461$	−10.8098	−	26.0971i	−0.503461	−	1.21546i	0.444126	−	0.895964i	$-0.353514\pi$
$462$	0.629781	+	0.359766i	0.0293001	+	0.0167378i
$463$	−6.67663			−0.310289			−0.155145	−	0.987892i	$-0.549584\pi$
$463$	−6.67663			−0.310289			−0.155145	+	0.987892i	$0.549584\pi$
$464$	−0.856283	−	0.918867i	−0.0397520	−	0.0426573i
$465$	21.7766	+	33.9958i	1.00987	+	1.57652i
$466$	26.9828	−	14.1184i	1.24995	−	0.654022i
$467$	23.8266	−	9.86930i	1.10256	−	0.456697i	0.244193	−	0.969727i	$-0.421477\pi$
$467$	23.8266	−	9.86930i	1.10256	−	0.456697i	0.858371	+	0.513030i	$0.171477\pi$
$468$	2.47310	+	17.5412i	0.114319	+	0.810840i
$469$	2.55030	−	6.15696i	0.117762	−	0.284302i
$470$	8.54437	−	10.2263i	0.394123	−	0.471703i
$471$	−2.96238	+	13.5213i	−0.136499	+	0.623031i
$472$	25.2327	−	6.93160i	1.16143	−	0.319053i
$473$	−0.100525	+	0.100525i	−0.00462215	+	0.00462215i
$474$	−2.48613	+	1.92584i	−0.114192	+	0.0884569i
$475$	−0.873159	+	2.10799i	−0.0400633	+	0.0967214i
$476$	0.151179	−	0.0273115i	0.00692928	−	0.00125182i
$477$	1.54189	−	39.8595i	0.0705984	−	1.82504i
$478$	8.22198	+	2.57343i	0.376065	+	0.117706i
$479$	41.1853			1.88181			0.940903	−	0.338676i	$-0.109979\pi$
$479$	41.1853			1.88181			0.940903	+	0.338676i	$0.109979\pi$
$480$	19.8817	−	14.3093i	0.907470	−	0.653127i
$481$	0.507068			0.0231203
$482$	−34.2764	−	10.7283i	−1.56125	−	0.488660i
$483$	5.32187	−	7.64075i	0.242153	−	0.347666i
$484$	−3.87997	−	21.4770i	−0.176362	−	0.976227i
$485$	0.158423	−	0.382466i	0.00719361	−	0.0173669i
$486$	4.45847	−	21.5899i	0.202240	−	0.979336i
$487$	14.3418	−	14.3418i	0.649889	−	0.649889i	−0.303077	−	0.952966i	$-0.598014\pi$
$487$	14.3418	−	14.3418i	0.649889	−	0.649889i	0.952966	+	0.303077i	$0.0980140\pi$
$488$	34.7735	+	19.7857i	1.57412	+	0.895658i
$489$	4.00993	+	0.878532i	0.181335	+	0.0397286i
$490$	−2.26698	+	2.71322i	−0.102412	+	0.122571i
$491$	−8.15481	+	19.6874i	−0.368021	+	0.888482i	0.626053	+	0.779780i	$0.284669\pi$
$491$	−8.15481	+	19.6874i	−0.368021	+	0.888482i	−0.994074	+	0.108702i	$0.965331\pi$
$492$	4.02786	−	8.79063i	0.181590	−	0.396312i
$493$	−0.0222834	+	0.00923007i	−0.00100359	+	0.000415701i
$494$	−6.75086	+	3.53230i	−0.303736	+	0.158926i
$495$	0.928550	−	2.01739i	0.0417352	−	0.0906751i
$496$	34.9360	−	13.0487i	1.56867	−	0.585905i
$497$	−15.6803			−0.703357
$498$	−6.51996	+	11.4134i	−0.292166	+	0.511446i
$499$	7.52319	+	18.1626i	0.336784	+	0.813069i	0.998020	+	0.0628914i	$0.0200322\pi$
$499$	7.52319	+	18.1626i	0.336784	+	0.813069i	−0.661236	+	0.750178i	$0.729968\pi$
$500$	18.3211	+	3.98111i	0.819344	+	0.178041i
$501$	5.00124	+	27.9571i	0.223439	+	1.24903i
$502$	10.9421	−	13.0960i	0.488371	−	0.584505i
$503$	−10.8395	+	10.8395i	−0.483309	+	0.483309i	−0.906187	−	0.422878i	$-0.861020\pi$
$503$	−10.8395	+	10.8395i	−0.483309	+	0.483309i	0.422878	+	0.906187i	$0.361020\pi$
$504$	−8.26294	+	1.92974i	−0.368060	+	0.0859575i
$505$	−23.3306	−	23.3306i	−1.03820	−	1.03820i
$506$	2.24221	−	0.200909i	0.0996785	−	0.00893151i
$507$	−7.30262	+	1.30637i	−0.324321	+	0.0580177i
$508$	−9.06853	+	13.0676i	−0.402351	+	0.579779i
$509$	3.43809	−	1.42411i	0.152391	−	0.0631224i	−0.305184	−	0.952293i	$-0.598718\pi$
$509$	3.43809	−	1.42411i	0.152391	−	0.0631224i	0.457575	+	0.889171i	$0.348718\pi$
$510$	−0.123829	−	0.453806i	−0.00548323	−	0.0200949i
$511$			10.3519i			0.457940i
$512$	−9.05232	−	20.7378i	−0.400060	−	0.916489i
$513$	9.39122	−	1.30766i	0.414632	−	0.0577347i
$514$	37.2862	+	11.6703i	1.64462	+	0.514757i
$515$	14.1980	+	34.2770i	0.625639	+	1.51043i
$516$	0.0614446	−	1.66205i	0.00270495	−	0.0731675i
$517$	−1.03107	−	0.427083i	−0.0453464	−	0.0187831i
$518$	0.0216764	+	0.241916i	0.000952407	+	0.0106292i
$519$	−4.24511	+	19.3762i	−0.186340	+	0.850519i
$520$	−12.8134	−	16.4829i	−0.561907	−	0.722825i
$521$	2.23318	+	2.23318i	0.0978372	+	0.0978372i	0.754331	−	0.656494i	$-0.227961\pi$
$521$	2.23318	+	2.23318i	0.0978372	+	0.0978372i	−0.656494	+	0.754331i	$0.727961\pi$
$522$	1.20336	−	0.571527i	0.0526699	−	0.0250150i
$523$	39.3271	+	16.2898i	1.71965	+	0.712304i	0.999835	+	0.0181404i	$0.00577458\pi$
$523$	39.3271	+	16.2898i	1.71965	+	0.712304i	0.719818	+	0.694163i	$0.244225\pi$
$524$	1.07969	−	4.96873i	0.0471664	−	0.217060i
$525$	1.77714	+	1.23780i	0.0775609	+	0.0540221i
$526$	21.8393	−	11.4271i	0.952240	−	0.498247i
$527$		−	0.716154i		−	0.0311962i
$528$	−1.64101	−	1.23107i	−0.0714159	−	0.0535754i
$529$		−	5.90114i		−	0.256571i
$530$	21.7949	+	41.6540i	0.946710	+	1.80933i
$531$	−1.07284	+	27.7340i	−0.0465574	+	1.20356i
$532$	−1.97380	−	3.06975i	−0.0855752	−	0.133090i
$533$	−7.61393	−	3.15379i	−0.329796	−	0.136606i
$534$	0.500455	−	3.94081i	0.0216568	−	0.170535i
$535$	1.52808	+	1.52808i	0.0660648	+	0.0660648i
$536$	−9.32174	+	16.3830i	−0.402638	+	0.707638i
$537$	20.9895	+	4.59857i	0.905762	+	0.198443i
$538$	19.7638	−	1.77090i	0.852079	−	0.0763490i
$539$	0.273562	+	0.113313i	0.0117832	+	0.00488074i
$540$	8.10095	+	24.6864i	0.348609	+	1.06233i
$541$	−14.7446	−	35.5967i	−0.633921	−	1.53042i	−0.834654	−	0.550774i	$-0.814332\pi$
$541$	−14.7446	−	35.5967i	−0.633921	−	1.53042i	0.200733	−	0.979646i	$-0.435668\pi$
$542$	−8.98586	+	28.7094i	−0.385976	+	1.23317i
$543$	19.5418	−	12.5179i	0.838620	−	0.537194i
$544$	−0.433884	+	0.0235064i	−0.0186026	+	0.00100783i
$545$		−	37.4721i		−	1.60513i
$546$	1.90376	+	6.97690i	0.0814736	+	0.298584i
$547$	−36.4138	+	15.0831i	−1.55694	+	0.644906i	−0.984554	−	0.175079i	$-0.943982\pi$
$547$	−36.4138	+	15.0831i	−1.55694	+	0.644906i	−0.572386	+	0.819985i	$0.693982\pi$
$548$	−1.88966	−	10.4600i	−0.0807224	−	0.446827i
$549$	−31.1438	+	28.8240i	−1.32918	+	1.23018i
$550$	0.0467290	+	0.521511i	0.00199253	+	0.0222373i
$551$	0.405158	+	0.405158i	0.0172603	+	0.0172603i
$552$	−17.6217	+	19.5730i	−0.750031	+	0.833081i
$553$	−0.907824	+	0.907824i	−0.0386046	+	0.0386046i
$554$	−4.20301	−	3.51174i	−0.178569	−	0.149200i
$555$	0.732081	−	0.130962i	0.0310751	−	0.00555903i
$556$	−19.4415	−	30.2364i	−0.824505	−	1.28231i
$557$	6.59965	+	15.9330i	0.279636	+	0.675101i	0.999826	−	0.0186762i	$-0.00594518\pi$
$557$	6.59965	+	15.9330i	0.279636	+	0.675101i	−0.720190	+	0.693777i	$0.755945\pi$
$558$	2.00463	+	39.5047i	0.0848628	+	1.67237i
$559$	−1.41752			−0.0599549
$560$	7.31604	−	6.81775i	0.309159	−	0.288102i
$561$	−0.0331724	+	0.0212492i	−0.00140054	+	0.000897141i
$562$	19.2574	+	36.8043i	0.812323	+	1.55250i
$563$	−10.6053	+	4.39284i	−0.446958	+	0.185136i	−0.594798	−	0.803875i	$-0.702768\pi$
$563$	−10.6053	+	4.39284i	−0.446958	+	0.185136i	0.147840	+	0.989011i	$0.452768\pi$
$564$	12.2389	−	4.54742i	0.515350	−	0.191481i
$565$	2.10492	−	5.08172i	0.0885545	−	0.213790i
$566$	18.9391	+	15.8242i	0.796069	+	0.665140i
$567$	0.695258	−	8.97311i	0.0291981	−	0.376835i
$568$	44.0067	+	5.51203i	1.84648	+	0.231280i
$569$	−12.1719	+	12.1719i	−0.510273	+	0.510273i	−0.914610	−	0.404337i	$-0.867502\pi$
$569$	−12.1719	+	12.1719i	−0.510273	+	0.510273i	0.404337	+	0.914610i	$0.367502\pi$
$570$	−8.83428	+	6.84333i	−0.370027	+	0.286636i
$571$	−5.19422	+	12.5400i	−0.217372	+	0.524781i	−0.994521	−	0.104534i	$-0.966665\pi$
$571$	−5.19422	+	12.5400i	−0.217372	+	0.524781i	0.777150	+	0.629316i	$0.216665\pi$
$572$	−0.996847	+	1.43644i	−0.0416803	+	0.0600604i
$573$	−19.5676	−	13.6291i	−0.817449	−	0.569362i
$574$	1.17915	−	3.76733i	0.0492167	−	0.157245i
$575$	6.72205			0.280329
$576$	23.8683	−	2.51118i	0.994511	−	0.104632i
$577$	21.8231			0.908505			0.454253	−	0.890873i	$-0.349906\pi$
$577$	21.8231			0.908505			0.454253	+	0.890873i	$0.349906\pi$
$578$	7.17884	−	22.9361i	0.298600	−	0.954015i
$579$	−20.3311	−	14.1608i	−0.844931	−	0.588504i
$580$	−0.895139	+	1.28988i	−0.0371686	+	0.0535592i
$581$	−2.05355	+	4.95770i	−0.0851955	+	0.205680i
$582$	0.320651	−	0.248387i	0.0132914	−	0.0102960i
$583$	2.78394	−	2.78394i	0.115299	−	0.115299i
$584$	3.63895	−	29.0525i	0.150581	−	1.20220i
$585$	20.7706	−	7.67700i	0.858760	−	0.317405i
$586$	8.96086	+	7.48707i	0.370170	+	0.309288i
$587$	−16.5755	+	40.0168i	−0.684143	+	1.65167i	0.0721161	+	0.997396i	$0.477025\pi$
$587$	−16.5755	+	40.0168i	−0.684143	+	1.65167i	−0.756259	+	0.654272i	$0.772975\pi$
$588$	−3.24720	+	1.20651i	−0.133912	+	0.0497558i
$589$	−15.7180	+	6.51060i	−0.647648	+	0.268264i
$590$	−15.1648	−	28.9827i	−0.624325	−	1.19320i
$591$	−37.5965	+	24.0831i	−1.54651	+	0.990647i
$592$	0.0242048	−	0.686555i	0.000994812	−	0.0282173i
$593$	−38.6108			−1.58556			−0.792778	−	0.609511i	$-0.791366\pi$
$593$	−38.6108			−1.58556			−0.792778	+	0.609511i	$0.791366\pi$
$594$	1.77038	−	1.26501i	0.0726398	−	0.0519039i
$595$	−0.0734901	−	0.177421i	−0.00301280	−	0.00727354i
$596$	−4.47352	−	6.95743i	−0.183243	−	0.284987i
$597$	34.1498	−	6.10905i	1.39766	−	0.250027i
$598$	17.2254	+	14.3924i	0.704401	+	0.588548i
$599$	−6.48060	+	6.48060i	−0.264790	+	0.264790i	−0.826997	−	0.562207i	$-0.809953\pi$
$599$	−6.48060	+	6.48060i	−0.264790	+	0.264790i	0.562207	+	0.826997i	$0.309953\pi$
$600$	−4.55243	−	4.09860i	−0.185852	−	0.167325i
$601$	2.75312	+	2.75312i	0.112302	+	0.112302i	0.761025	−	0.648723i	$-0.224696\pi$
$601$	2.75312	+	2.75312i	0.112302	+	0.112302i	−0.648723	+	0.761025i	$0.724696\pi$
$602$	−0.0605970	−	0.676282i	−0.00246975	−	0.0275632i
$603$	−13.5800	−	14.6729i	−0.553020	−	0.597526i
$604$	−6.22806	−	34.4745i	−0.253416	−	1.40275i
$605$	−25.2050	+	10.4402i	−1.02473	+	0.424456i
$606$	−8.50982	−	31.1867i	−0.345688	−	1.26687i
$607$		−	40.5740i		−	1.64685i	−0.567427	−	0.823424i	$-0.692061\pi$
$607$		−	40.5740i		−	1.64685i	0.567427	−	0.823424i	$-0.307939\pi$
$608$	4.46038	+	9.30908i	0.180892	+	0.377533i
$609$	0.457963	−	0.293357i	0.0185576	−	0.0118874i
$610$	14.9388	−	47.7288i	0.604855	−	1.93248i
$611$	−4.25847	−	10.2808i	−0.172279	−	0.415919i
$612$	0.115199	−	0.446249i	0.00465664	−	0.0180386i
$613$	20.5018	+	8.49211i	0.828059	+	0.342993i	0.756134	−	0.654417i	$-0.227086\pi$
$613$	20.5018	+	8.49211i	0.828059	+	0.342993i	0.0719247	+	0.997410i	$0.477086\pi$
$614$	−5.02999	+	0.450703i	−0.202994	+	0.0181889i
$615$	−11.8072	−	2.58683i	−0.476111	−	0.104311i
$616$	−0.727919	−	0.414177i	−0.0293287	−	0.0166877i
$617$	21.6790	+	21.6790i	0.872762	+	0.872762i	0.992773	−	0.120011i	$-0.0382929\pi$
$617$	21.6790	+	21.6790i	0.872762	+	0.872762i	−0.120011	+	0.992773i	$0.538293\pi$
$618$	−4.57948	+	36.0609i	−0.184214	+	1.45058i
$619$	−30.7990	−	12.7574i	−1.23792	−	0.512762i	−0.334854	−	0.942270i	$-0.608687\pi$
$619$	−30.7990	−	12.7574i	−1.23792	−	0.512762i	−0.903063	+	0.429508i	$0.858687\pi$
$620$	−25.2127	−	39.2119i	−1.01256	−	1.57479i
$621$	−14.1471	−	24.0871i	−0.567705	−	0.966583i
$622$	−4.70265	−	8.98761i	−0.188559	−	0.360370i
$623$		−	1.62175i		−	0.0649740i
$624$	−2.89035	−	20.2499i	−0.115707	−	0.810643i
$625$		−	29.6885i		−	1.18754i
$626$	22.8538	−	11.9580i	0.913423	−	0.477937i
$627$	0.767943	+	0.534881i	0.0306687	+	0.0213611i
$628$	3.39394	−	15.6189i	0.135433	−	0.623263i
$629$	−0.0121881	−	0.00504848i	−0.000485972	−	0.000201296i
$630$	4.55051	+	9.58122i	0.181297	+	0.381725i
$631$	22.5598	+	22.5598i	0.898090	+	0.898090i	0.995267	−	0.0971767i	$-0.0309812\pi$
$631$	22.5598	+	22.5598i	0.898090	+	0.898090i	−0.0971767	+	0.995267i	$0.530981\pi$
$632$	2.86693	−	2.22868i	0.114040	−	0.0886522i
$633$	−5.91376	+	26.9924i	−0.235051	+	1.07285i
$634$	−0.265247	−	2.96024i	−0.0105343	−	0.117566i
$635$	18.3695	+	7.60891i	0.728973	+	0.301951i
$636$	−1.70165	+	46.0287i	−0.0674747	+	1.82516i
$637$	1.12985	+	2.72770i	0.0447663	+	0.108075i
$638$	0.125485	+	0.0392759i	0.00496799	+	0.00155495i
$639$	−19.6682	+	42.7318i	−0.778063	+	1.69044i
$640$	−22.9291	+	16.5622i	−0.906351	+	0.654679i
$641$			44.9148i			1.77403i	0.461744	+	0.887013i	$0.347224\pi$
$641$			44.9148i			1.77403i	−0.461744	+	0.887013i	$0.652776\pi$
$642$	0.557366	+	2.04263i	0.0219975	+	0.0806162i
$643$	−41.2462	+	17.0847i	−1.62659	+	0.673756i	−0.994844	−	0.101418i	$-0.967662\pi$
$643$	−41.2462	+	17.0847i	−1.62659	+	0.673756i	−0.631748	+	0.775174i	$0.717662\pi$
$644$	−6.13006	+	8.83329i	−0.241558	+	0.348080i
$645$	−2.04655	+	0.366108i	−0.0805830	+	0.0144155i
$646$	0.197435	−	0.0176908i	0.00776797	−	0.000696035i
$647$	−3.42881	−	3.42881i	−0.134800	−	0.134800i	0.636487	−	0.771287i	$-0.280387\pi$
$647$	−3.42881	−	3.42881i	−0.134800	−	0.134800i	−0.771287	+	0.636487i	$0.780387\pi$
$648$	−5.10552	+	24.9386i	−0.200564	+	0.979681i
$649$	−1.93706	+	1.93706i	−0.0760361	+	0.0760361i
$650$	−3.34749	+	4.00642i	−0.131299	+	0.157145i
$651$	2.84366	+	15.8961i	0.111452	+	0.623019i
$652$	−4.63199	−	1.00652i	−0.181403	−	0.0394182i
$653$	−5.06942	−	12.2387i	−0.198382	−	0.478936i	0.793114	−	0.609073i	$-0.208458\pi$
$653$	−5.06942	−	12.2387i	−0.198382	−	0.478936i	−0.991496	+	0.130137i	$0.958458\pi$
$654$	18.2111	−	31.8790i	0.712109	−	1.24657i
$655$	−6.35606			−0.248352
$656$	−4.63359	+	10.1585i	−0.180911	+	0.396622i
$657$	28.2108	+	12.9847i	1.10061	+	0.506579i
$658$	4.72281	−	2.47115i	0.184114	−	0.0963354i
$659$	34.7498	−	14.3938i	1.35366	−	0.560704i	0.416351	−	0.909204i	$-0.363309\pi$
$659$	34.7498	−	14.3938i	1.35366	−	0.560704i	0.937309	+	0.348500i	$0.113309\pi$
$660$	−1.06821	+	2.33132i	−0.0415799	+	0.0907464i
$661$	−5.20221	+	12.5593i	−0.202343	+	0.488498i	−0.992180	−	0.124819i	$-0.960165\pi$
$661$	−5.20221	+	12.5593i	−0.202343	+	0.488498i	0.789837	+	0.613317i	$0.210165\pi$
$662$	−13.1811	+	15.7757i	−0.512296	+	0.613139i
$663$	−0.383704	−	0.0840655i	−0.0149018	−	0.00326483i
$664$	7.50604	−	13.1919i	0.291291	−	0.511945i
$665$	−3.22588	+	3.22588i	−0.125094	+	0.125094i
$666$	0.686455	+	0.244369i	0.0265996	+	0.00946911i
$667$	0.645992	−	1.55956i	0.0250129	−	0.0603865i
$668$	−5.83017	−	32.2721i	−0.225576	−	1.24864i
$669$	16.1971	−	23.2546i	0.626216	−	0.899076i
$670$	22.4867	+	7.03819i	0.868736	+	0.271909i
$671$	−4.18839			−0.161691
$672$	9.53739	−	2.24460i	0.367913	−	0.0865873i
$673$	8.89681			0.342947			0.171473	−	0.985189i	$-0.445147\pi$
$673$	8.89681			0.342947			0.171473	+	0.985189i	$0.445147\pi$
$674$	−3.17052	−	0.992353i	−0.122124	−	0.0382240i
$675$	5.60236	−	3.29045i	0.215635	−	0.126649i
$676$	8.42975	−	1.52289i	0.324221	−	0.0585728i
$677$	2.87418	−	6.93889i	0.110464	−	0.266683i	−0.858975	−	0.512018i	$-0.828898\pi$
$677$	2.87418	−	6.93889i	0.110464	−	0.266683i	0.969438	+	0.245335i	$0.0788980\pi$
$678$	4.26039	−	3.30024i	0.163619	−	0.126745i
$679$	0.117087	−	0.117087i	0.00449340	−	0.00449340i
$680$	0.143882	+	0.523764i	0.00551761	+	0.0200854i
$681$	1.21950	−	5.56620i	0.0467312	−	0.213297i
$682$	−2.50326	+	2.99601i	−0.0958548	+	0.114723i
$683$	−12.1386	+	29.3053i	−0.464472	+	1.12134i	0.502070	+	0.864827i	$0.332572\pi$
$683$	−12.1386	+	29.3053i	−0.464472	+	1.12134i	−0.966542	+	0.256508i	$0.917428\pi$
$684$	−10.8414	+	1.52852i	−0.414533	+	0.0584443i
$685$	−12.2756	+	5.08471i	−0.469026	+	0.194277i
$686$	−1.25305	+	0.655642i	−0.0478417	+	0.0250325i
$687$	12.8462	+	20.0543i	0.490112	+	0.765120i
$688$	−0.0676653	+	1.91929i	−0.00257971	+	0.0731721i
$689$	39.2569			1.49557
$690$	28.5864	+	16.3302i	1.08827	+	0.621679i
$691$	−6.31202	−	15.2386i	−0.240120	−	0.579702i	0.757174	−	0.653213i	$-0.226580\pi$
$691$	−6.31202	−	15.2386i	−0.240120	−	0.579702i	−0.997294	+	0.0735113i	$0.976580\pi$
$692$	4.86353	−	22.3820i	0.184884	−	0.850836i
$693$	0.651936	−	0.603377i	0.0247650	−	0.0229204i
$694$	−12.1796	+	14.5771i	−0.462333	+	0.553340i
$695$	−31.7742	+	31.7742i	−1.20527	+	1.20527i
$696$	−1.38839	+	0.662319i	−0.0526270	+	0.0251051i
$697$	0.151612	+	0.151612i	0.00574271	+	0.00574271i
$698$	13.7943	−	1.23601i	0.522120	−	0.0467836i
$699$	−6.56788	−	36.7146i	−0.248420	−	1.38867i
$700$	−2.05451	−	1.42578i	−0.0776533	−	0.0538892i
$701$	−5.32672	+	2.20640i	−0.201188	+	0.0833346i	−0.481002	−	0.876719i	$-0.659727\pi$
$701$	−5.32672	+	2.20640i	−0.201188	+	0.0833346i	0.279814	+	0.960054i	$0.409727\pi$
$702$	21.4013	+	3.56320i	0.807740	+	0.134484i
$703$			0.313397i			0.0118200i
$704$	1.89731	+	1.41827i	0.0715075	+	0.0534531i
$705$	−8.80344	−	13.7432i	−0.331557	−	0.517597i
$706$	−8.67487	−	2.71518i	−0.326483	−	0.102187i
$707$	−5.05042	−	12.1928i	−0.189941	−	0.458558i
$708$	1.18400	−	32.0266i	0.0444974	−	1.20363i
$709$	8.45768	+	3.50328i	0.317635	+	0.131569i	0.535804	−	0.844342i	$-0.320009\pi$
$709$	8.45768	+	3.50328i	0.317635	+	0.131569i	−0.218169	+	0.975911i	$0.570009\pi$
$710$	−4.94777	−	55.2187i	−0.185686	−	2.07232i
$711$	1.33528	+	3.61270i	0.0500770	+	0.135487i
$712$	−0.570087	+	4.55144i	−0.0213649	+	0.170572i
$713$	35.4416	+	35.4416i	1.32730	+	1.32730i
$714$	0.0237038	−	0.186654i	0.000887091	−	0.00698535i
$715$	2.01925	+	0.836401i	0.0755157	+	0.0312796i
$716$	−24.2456	−	5.26848i	−0.906101	−	0.196892i
$717$	6.03063	−	8.65834i	0.225218	−	0.323352i
$718$	44.7458	−	23.4126i	1.66990	−	0.873752i
$719$		−	28.8352i		−	1.07537i	−0.843146	−	0.537685i	$-0.819299\pi$
$719$		−	28.8352i		−	1.07537i	0.843146	−	0.537685i	$-0.180701\pi$
$720$	−9.40294	−	28.4893i	−0.350427	−	1.06173i
$721$			14.8400i			0.552671i
$722$	10.2740	+	19.6355i	0.382360	+	0.730759i
$723$	−25.1409	+	36.0955i	−0.935001	+	1.34241i
$724$	−22.5402	+	14.4930i	−0.837699	+	0.538628i
$725$	0.362735	+	0.150250i	0.0134716	+	0.00558013i
$726$	−26.5167	−	3.36743i	−0.984126	−	0.124977i
$727$	−7.14622	−	7.14622i	−0.265039	−	0.265039i	0.562059	−	0.827097i	$-0.310009\pi$
$727$	−7.14622	−	7.14622i	−0.265039	−	0.265039i	−0.827097	+	0.562059i	$0.810009\pi$
$728$	−2.21206	−	8.05245i	−0.0819845	−	0.298444i
$729$	−23.5813	−	13.1499i	−0.873383	−	0.487034i
$730$	−36.4545	+	3.26644i	−1.34924	+	0.120896i
$731$	0.0340722	+	0.0141132i	0.00126021	+	0.000521994i
$732$	35.9047	−	33.3446i	1.32708	−	1.23245i
$733$	17.0489	+	41.1596i	0.629714	+	1.52026i	0.839978	+	0.542620i	$0.182568\pi$
$733$	17.0489	+	41.1596i	0.629714	+	1.52026i	−0.210264	+	0.977645i	$0.567432\pi$
$734$	7.47380	−	23.8784i	0.275863	−	0.881369i
$735$	2.33571	+	3.64631i	0.0861541	+	0.134496i
$736$	20.3091	−	22.6357i	0.748604	−	0.834364i
$737$		−	1.97329i		−	0.0726872i
$738$	−8.78764	−	7.93887i	−0.323478	−	0.292234i
$739$	−4.45751	+	1.84636i	−0.163972	+	0.0679196i	−0.463160	−	0.886275i	$-0.653284\pi$
$739$	−4.45751	+	1.84636i	−0.163972	+	0.0679196i	0.299187	+	0.954194i	$0.403284\pi$
$740$	−0.845074	+	0.152668i	−0.0310655	+	0.00561220i
$741$	1.64323	+	9.18568i	0.0603654	+	0.337444i
$742$	1.67817	+	18.7289i	0.0616077	+	0.687561i
$743$	4.95310	+	4.95310i	0.181712	+	0.181712i	0.792101	−	0.610390i	$-0.208987\pi$
$743$	4.95310	+	4.95310i	0.181712	+	0.181712i	−0.610390	+	0.792101i	$0.708987\pi$
$744$	−2.39282	−	45.6121i	−0.0877250	−	1.67222i
$745$	−7.31129	+	7.31129i	−0.267865	+	0.267865i
$746$	2.83092	+	2.36532i	0.103647	+	0.0866006i
$747$	10.9349	+	11.8149i	0.400085	+	0.432284i
$748$	0.0382621	−	0.0246020i	0.00139900	−	0.000899537i
$749$	0.330787	+	0.798590i	0.0120867	+	0.0291798i
$750$	11.3899	−	19.9384i	0.415900	−	0.728046i
$751$	51.2421			1.86985			0.934926	−	0.354843i	$-0.115466\pi$
$751$	51.2421			1.86985			0.934926	+	0.354843i	$0.115466\pi$
$752$	−14.1232	+	5.27508i	−0.515022	+	0.192362i
$753$	−11.2739	−	17.5998i	−0.410844	−	0.641373i
$754$	0.607823	+	1.16166i	0.0221356	+	0.0423052i
$755$	−40.4586	+	16.7585i	−1.47244	+	0.609905i
$756$	−0.785080	+	10.3626i	−0.0285531	+	0.376884i
$757$	−12.8258	+	30.9643i	−0.466162	+	1.12542i	0.499662	+	0.866220i	$0.333457\pi$
$757$	−12.8258	+	30.9643i	−0.466162	+	1.12542i	−0.965825	+	0.259196i	$0.916543\pi$
$758$	−18.0542	−	15.0848i	−0.655758	−	0.547906i
$759$	0.590064	−	2.69326i	0.0214180	−	0.0977591i
$760$	10.1874	−	7.91945i	0.369536	−	0.287268i
$761$	−23.8013	+	23.8013i	−0.862797	+	0.862797i	−0.991662	−	0.128865i	$-0.958867\pi$
$761$	−23.8013	+	23.8013i	−0.862797	+	0.862797i	0.128865	+	0.991662i	$0.458867\pi$
$762$	11.9298	+	15.4006i	0.432172	+	0.557905i
$763$	5.73581	−	13.8475i	0.207650	−	0.501312i
$764$	22.6216	+	15.6988i	0.818422	+	0.567962i
$765$	−0.575686	−	0.0222694i	−0.0208140	−	0.000805151i
$766$	−8.03269	+	25.6641i	−0.290233	+	0.927281i
$767$	−27.3148			−0.986280
$768$	−27.5557	+	2.94683i	−0.994330	+	0.106334i
$769$	3.45869			0.124724			0.0623619	−	0.998054i	$-0.480137\pi$
$769$	3.45869			0.124724			0.0623619	+	0.998054i	$0.480137\pi$
$770$	−0.312716	+	0.999113i	−0.0112695	+	0.0360055i
$771$	27.3486	−	39.2651i	0.984934	−	1.41410i
$772$	23.5043	+	16.3113i	0.845937	+	0.587057i
$773$	−5.56893	+	13.4446i	−0.200301	+	0.483569i	−0.991831	−	0.127562i	$-0.959285\pi$
$773$	−5.56893	+	13.4446i	−0.200301	+	0.483569i	0.791530	+	0.611130i	$0.209285\pi$
$774$	−1.91901	−	0.683141i	−0.0689772	−	0.0245550i
$775$	−8.24328	+	8.24328i	−0.296107	+	0.296107i
$776$	−0.369764	+	0.287446i	−0.0132738	+	0.0103187i
$777$	0.290580	+	0.0636629i	0.0104245	+	0.00228389i
$778$	36.4380	+	30.4451i	1.30637	+	1.09151i
$779$	1.94923	−	4.70585i	0.0698382	−	0.168604i
$780$	−23.9687	+	8.90567i	−0.858216	+	0.318874i
$781$	−4.28953	+	1.77678i	−0.153492	+	0.0635783i
$782$	−0.270744	−	0.517442i	−0.00968180	−	0.0185037i
$783$	−0.225017	−	1.61600i	−0.00804146	−	0.0577512i
$784$	3.74716	−	1.39958i	0.133827	−	0.0499849i
$785$	−19.9799			−0.713113
$786$	−5.40734	−	3.08897i	−0.192873	−	0.110180i
$787$	−3.36321	−	8.11950i	−0.119885	−	0.289429i	0.852533	−	0.522674i	$-0.175066\pi$
$787$	−3.36321	−	8.11950i	−0.119885	−	0.289429i	−0.972418	+	0.233245i	$0.925066\pi$
$788$	43.3650	−	27.8830i	1.54481	−	0.993292i
$789$	−5.31591	−	29.7161i	−0.189251	−	1.05792i
$790$	−3.48339	−	2.91048i	−0.123933	−	0.103550i
$791$	1.55570	−	1.55570i	0.0553145	−	0.0553145i
$792$	−2.04176	+	1.46420i	−0.0725508	+	0.0520282i
$793$	−29.5306	−	29.5306i	−1.04866	−	1.04866i
$794$	−0.348726	−	3.89189i	−0.0123758	−	0.138118i
$795$	56.6772	−	10.1390i	2.01013	−	0.359593i
$796$	−39.4206	+	7.12161i	−1.39723	+	0.252419i
$797$	23.5067	−	9.73679i	0.832649	−	0.344895i	0.0746984	−	0.997206i	$-0.476201\pi$
$797$	23.5067	−	9.73679i	0.832649	−	0.344895i	0.757951	+	0.652312i	$0.226201\pi$
$798$	−4.31212	+	1.17664i	−0.152647	+	0.0416525i
$799$			0.289513i			0.0102422i
$800$	5.26479	+	4.72365i	0.186138	+	0.167006i
$801$	−4.41957	−	2.03421i	−0.156158	−	0.0718751i
$802$	5.74622	−	18.3589i	0.202906	−	0.648275i
$803$	1.17300	+	2.83188i	0.0413944	+	0.0999349i
$804$	15.7098	+	16.9159i	0.554042	+	0.596579i
$805$	12.4173	+	5.14340i	0.437651	+	0.181281i
$806$	−38.7731	+	3.47420i	−1.36572	+	0.122373i
$807$	5.20108	−	23.7395i	0.183087	−	0.835672i
$808$	9.88792	+	35.9944i	0.347856	+	1.26628i
$809$	18.6761	+	18.6761i	0.656615	+	0.656615i	0.954578	−	0.297962i	$-0.0963070\pi$
$809$	18.6761	+	18.6761i	0.656615	+	0.656615i	−0.297962	+	0.954578i	$0.596307\pi$
$810$	31.8185	−	0.383006i	1.11799	−	0.0134575i
$811$	−10.8348	−	4.48792i	−0.380461	−	0.157592i	0.184253	−	0.982879i	$-0.441013\pi$
$811$	−10.8348	−	4.48792i	−0.380461	−	0.157592i	−0.564714	+	0.825287i	$0.691013\pi$
$812$	−0.528230	+	0.339644i	−0.0185372	+	0.0119192i
$813$	30.2331	+	21.0577i	1.06032	+	0.738525i
$814$	0.0333421	+	0.0637227i	0.00116864	+	0.00223348i
$815$			5.92529i			0.207554i
$816$	−0.132138	+	0.515511i	−0.00462576	+	0.0180465i
$817$		−	0.876111i		−	0.0306512i
$818$	−5.37363	+	2.81168i	−0.187885	+	0.0983081i
$819$	8.85070	+	0.342374i	0.309268	+	0.0119635i
$820$	13.6388	+	2.96367i	0.476289	+	0.103496i
$821$	32.8006	+	13.5865i	1.14475	+	0.474170i	0.872769	−	0.488133i	$-0.162322\pi$
$821$	32.8006	+	13.5865i	1.14475	+	0.474170i	0.271979	+	0.962303i	$0.412322\pi$
$822$	−12.9144	−	1.64004i	−0.450442	−	0.0572031i
$823$	−8.86241	−	8.86241i	−0.308924	−	0.308924i	0.535568	−	0.844492i	$-0.320098\pi$
$823$	−8.86241	−	8.86241i	−0.308924	−	0.308924i	−0.844492	+	0.535568i	$0.820098\pi$
$824$	5.21665	−	41.6485i	0.181731	−	1.45089i
$825$	0.626418	+	0.137242i	0.0218091	+	0.00477814i
$826$	−1.16767	−	13.0315i	−0.0406283	−	0.453425i
$827$	−35.5497	−	14.7252i	−1.23618	−	0.512044i	−0.333663	−	0.942692i	$-0.608285\pi$
$827$	−35.5497	−	14.7252i	−1.23618	−	0.512044i	−0.902520	+	0.430648i	$0.858285\pi$
$828$	16.3833	+	27.7854i	0.569358	+	0.965610i
$829$	−11.2940	−	27.2662i	−0.392258	−	0.946995i	−0.989447	−	0.144895i	$-0.953716\pi$
$829$	−11.2940	−	27.2662i	−0.392258	−	0.946995i	0.597189	−	0.802101i	$-0.296284\pi$
$830$	−18.1067	−	5.66728i	−0.628492	−	0.196714i
$831$	−5.64844	+	3.61822i	−0.195942	+	0.125515i
$832$	3.37751	+	23.3768i	0.117094	+	0.810444i
$833$		−	0.0768131i		−	0.00266142i
$834$	−42.4735	+	11.5896i	−1.47074	+	0.401316i
$835$	−37.8739	+	15.6879i	−1.31068	+	0.542901i
$836$	−0.887800	−	0.616109i	−0.0307052	−	0.0213086i
$837$	46.8869	+	12.1895i	1.62065	+	0.421329i
$838$	36.7309	−	3.29121i	1.26885	−	0.113693i
$839$	31.1741	+	31.1741i	1.07625	+	1.07625i	0.996842	+	0.0794079i	$0.0253030\pi$
$839$	31.1741	+	31.1741i	1.07625	+	1.07625i	0.0794079	+	0.996842i	$0.474697\pi$
$840$	−5.27340	−	11.0544i	−0.181950	−	0.381414i
$841$	−20.4364	+	20.4364i	−0.704703	+	0.704703i
$842$	−18.1030	+	21.6664i	−0.623869	+	0.746675i
$843$	50.0785	−	8.95853i	1.72479	−	0.308548i
$844$	6.77526	−	31.1798i	0.233214	−	1.07325i
$845$	−4.09781	−	9.89298i	−0.140969	−	0.340329i
$846$	−0.810393	−	15.9702i	−0.0278619	−	0.549067i
$847$	−10.9123			−0.374952
$848$	1.87392	−	53.1527i	0.0643507	−	1.82527i
$849$	25.4523	−	16.3040i	0.873521	−	0.559551i
$850$	0.120350	−	0.0629718i	0.00412799	−	0.00215991i
$851$	0.853018	−	0.353332i	0.0292411	−	0.0121120i
$852$	22.6264	−	49.3812i	0.775168	−	1.69177i
$853$	−12.7425	+	30.7632i	−0.436296	+	1.05331i	0.540921	+	0.841073i	$0.318076\pi$
$853$	−12.7425	+	30.7632i	−0.436296	+	1.05331i	−0.977218	+	0.212239i	$0.931924\pi$
$854$	12.8263	−	15.3511i	0.438906	−	0.525302i
$855$	4.74482	+	12.8374i	0.162270	+	0.439032i
$856$	−0.647627	−	2.35752i	−0.0221354	−	0.0805784i
$857$	7.33214	−	7.33214i	0.250461	−	0.250461i	−0.570698	−	0.821160i	$-0.693327\pi$
$857$	7.33214	−	7.33214i	0.250461	−	0.250461i	0.821160	+	0.570698i	$0.193327\pi$
$858$	1.31137	+	1.69289i	0.0447695	+	0.0577944i
$859$	13.9039	−	33.5670i	0.474395	−	1.14529i	−0.487807	−	0.872951i	$-0.662203\pi$
$859$	13.9039	−	33.5670i	0.474395	−	1.14529i	0.962202	−	0.272338i	$-0.0877970\pi$
$860$	2.36243	−	0.426789i	0.0805582	−	0.0145534i
$861$	−3.96727	−	2.76324i	−0.135204	−	0.0941711i
$862$	24.9068	+	7.79568i	0.848330	+	0.265522i
$863$	22.0877			0.751873			0.375937	−	0.926645i	$-0.377321\pi$
$863$	22.0877			0.751873			0.375937	+	0.926645i	$0.377321\pi$
$864$	5.84605	−	28.8067i	0.198887	−	0.980022i
$865$	−28.6313			−0.973493
$866$	23.9560	+	7.49809i	0.814059	+	0.254795i
$867$	−24.1533	−	16.8231i	−0.820290	−	0.571341i
$868$	−3.31499	−	18.3496i	−0.112518	−	0.622827i
$869$	−0.145478	+	0.351214i	−0.00493500	+	0.0119141i
$870$	1.17757	+	1.52017i	0.0399234	+	0.0515385i
$871$	13.9129	−	13.9129i	0.471420	−	0.471420i
$872$	−20.9653	+	36.8466i	−0.709974	+	1.24778i
$873$	−0.172219	−	0.465951i	−0.00582874	−	0.0157700i
$874$	−8.89532	+	10.6463i	−0.300889	+	0.360117i
$875$	3.58740	−	8.66075i	0.121276	−	0.292787i
$876$	−32.6007	−	14.9376i	−1.10147	−	0.504695i
$877$	33.4549	−	13.8575i	1.12969	−	0.467933i	0.262015	−	0.965064i	$-0.415613\pi$
$877$	33.4549	−	13.8575i	1.12969	−	0.467933i	0.867676	+	0.497131i	$0.165613\pi$
$878$	19.7819	−	10.3506i	0.667607	−	0.349316i
$879$	12.0425	−	7.71408i	0.406185	−	0.260189i
$880$	1.22885	−	2.69408i	0.0414246	−	0.0908175i
$881$	−2.60233			−0.0876747			−0.0438373	−	0.999039i	$-0.513958\pi$
$881$	−2.60233			−0.0876747			−0.0438373	+	0.999039i	$0.513958\pi$
$882$	0.215012	+	4.23719i	0.00723984	+	0.142674i
$883$	−13.0581	−	31.5251i	−0.439441	−	1.06090i	−0.976142	−	0.217132i	$-0.930330\pi$
$883$	−13.0581	−	31.5251i	−0.439441	−	1.06090i	0.536702	−	0.843772i	$-0.319670\pi$
$884$	0.443229	+	0.0963120i	0.0149074	+	0.00323932i
$885$	−39.4358	+	7.05467i	−1.32562	+	0.237140i
$886$	12.5128	−	14.9759i	0.420376	−	0.503125i
$887$	8.36335	−	8.36335i	0.280814	−	0.280814i	−0.552620	−	0.833433i	$-0.686372\pi$
$887$	8.36335	−	8.36335i	0.280814	−	0.280814i	0.833433	+	0.552620i	$0.186372\pi$
$888$	−0.793132	−	0.280816i	−0.0266158	−	0.00942357i
$889$	5.62360	+	5.62360i	0.188610	+	0.188610i
$890$	5.71105	−	0.511728i	0.191435	−	0.0171532i
$891$	−0.826574	−	2.53348i	−0.0276913	−	0.0848749i
$892$	−18.6568	+	26.8841i	−0.624677	+	0.900147i
$893$	6.35415	−	2.63198i	0.212634	−	0.0880757i
$894$	−9.77321	+	2.66679i	−0.326865	+	0.0891907i
$895$			31.0152i			1.03672i
$896$	−11.0084	+	2.61069i	−0.367764	+	0.0872169i
$897$	23.1494	−	14.8288i	0.772935	−	0.495118i
$898$	−7.62173	−	2.38555i	−0.254341	−	0.0796070i
$899$	1.12032	+	2.70468i	0.0373646	+	0.0902062i
$900$	−6.46254	+	3.81055i	−0.215418	+	0.127018i
$901$	−0.943595	−	0.390850i	−0.0314357	−	0.0130211i
$902$	−0.104317	−	1.16421i	−0.00347338	−	0.0387640i
$903$	−0.812324	−	0.177972i	−0.0270324	−	0.00592252i
$904$	−4.91295	+	3.81921i	−0.163402	+	0.127025i
$905$	23.6866	+	23.6866i	0.787370	+	0.787370i
$906$	−42.5642	−	5.40535i	−1.41410	−	0.179581i
$907$	−39.0474	−	16.1740i	−1.29655	−	0.537048i	−0.375617	−	0.926775i	$-0.622569\pi$
$907$	−39.0474	−	16.1740i	−1.29655	−	0.537048i	−0.920930	+	0.389727i	$0.872569\pi$
$908$	−1.39715	+	6.42970i	−0.0463660	+	0.213377i
$909$	−39.5626	−	1.53041i	−1.31221	−	0.0507605i
$910$	−9.24917	+	4.83950i	−0.306607	+	0.160428i
$911$		−	33.7710i		−	1.11888i	−0.828869	−	0.559442i	$-0.811015\pi$
$911$		−	33.7710i		−	1.11888i	0.828869	−	0.559442i	$-0.188985\pi$
$912$	12.5156	−	1.78640i	0.414432	−	0.0591537i
$913$			1.58893i			0.0525860i
$914$	25.4417	+	48.6238i	0.841538	+	1.60833i
$915$	−50.2618	−	35.0079i	−1.66161	−	1.15733i
$916$	−14.8731	−	23.1313i	−0.491421	−	0.764280i
$917$	−2.34882	−	0.972913i	−0.0775648	−	0.0321284i
$918$	−0.478935	−	0.298722i	−0.0158072	−	0.00985931i
$919$	26.7729	+	26.7729i	0.883155	+	0.883155i	0.993854	−	0.110699i	$-0.0353090\pi$
$919$	26.7729	+	26.7729i	0.883155	+	0.883155i	−0.110699	+	0.993854i	$0.535309\pi$
$920$	−33.0410	−	18.7999i	−1.08933	−	0.619816i
$921$	−1.32370	+	6.04183i	−0.0436174	+	0.199085i
$922$	39.7883	−	3.56516i	1.31036	−	0.117412i
$923$	−42.7711	−	17.7164i	−1.40783	−	0.583141i
$924$	−0.751598	+	0.698007i	−0.0247258	+	0.0229627i
$925$	0.0821805	+	0.198401i	0.00270208	+	0.00652340i
$926$	2.82042	−	9.01111i	0.0926847	−	0.296123i
$927$	40.4419	+	18.6143i	1.32829	+	0.611373i
$928$	1.60187	−	0.767523i	0.0525839	−	0.0251952i
$929$			18.6736i			0.612660i	0.951925	+	0.306330i	$0.0991011\pi$
$929$			18.6736i			0.612660i	−0.951925	+	0.306330i	$0.900899\pi$
$930$	−55.0815	+	15.0299i	−1.80619	+	0.492851i
$931$	−1.68587	+	0.698312i	−0.0552523	+	0.0228863i
$932$	7.65648	+	42.3813i	0.250796	+	1.38825i
$933$	−12.2292	+	2.18767i	−0.400365	+	0.0716212i
$934$	3.25498	+	36.3266i	0.106506	+	1.18864i
$935$	−0.0402082	−	0.0402082i	−0.00131495	−	0.00131495i
$936$	−24.7191	−	4.07212i	−0.807969	−	0.133101i
$937$	−19.8185	+	19.8185i	−0.647443	+	0.647443i	−0.952374	−	0.304931i	$-0.901367\pi$
$937$	−19.8185	+	19.8185i	−0.647443	+	0.647443i	0.304931	+	0.952374i	$0.401367\pi$
$938$	7.23241	+	6.04290i	0.236147	+	0.197308i
$939$	−5.56285	−	31.0965i	−0.181537	−	1.01480i
$940$	10.1925	+	15.8518i	0.332442	+	0.517029i
$941$	−2.42271	−	5.84894i	−0.0789781	−	0.190670i	0.879459	−	0.475976i	$-0.157905\pi$
$941$	−2.42271	−	5.84894i	−0.0789781	−	0.190670i	−0.958437	+	0.285306i	$0.907905\pi$
$942$	−16.9977	−	9.71002i	−0.553814	−	0.316369i
$943$	−15.0062			−0.488668
$944$	−1.30387	+	36.9834i	−0.0424373	+	1.20371i
$945$	12.8666	−	1.79159i	0.418552	−	0.0582805i
$946$	−0.0932087	−	0.178139i	−0.00303048	−	0.00579179i
$947$	45.2420	−	18.7399i	1.47017	−	0.608964i	0.503271	−	0.864128i	$-0.332130\pi$
$947$	45.2420	−	18.7399i	1.47017	−	0.608964i	0.966898	+	0.255164i	$0.0821296\pi$
$948$	−1.54899	−	4.16894i	−0.0503089	−	0.135401i
$949$	−11.6961	+	28.2368i	−0.379670	+	0.916605i
$950$	−2.47620	−	2.06894i	−0.0803385	−	0.0671253i
$951$	−3.55573	−	0.779023i	−0.115302	−	0.0252615i
$952$	−0.0270018	+	0.215576i	−0.000875134	+	0.00698685i
$953$	5.61838	−	5.61838i	0.181997	−	0.181997i	−0.610228	−	0.792226i	$-0.708922\pi$
$953$	5.61838	−	5.61838i	0.181997	−	0.181997i	0.792226	+	0.610228i	$0.208922\pi$
$954$	53.1449	+	18.9189i	1.72063	+	0.612522i
$955$	13.1720	−	31.8001i	0.426236	−	1.02903i
$956$	−6.94645	+	10.0097i	−0.224664	+	0.323737i
$957$	0.0920401	−	0.132145i	0.00297523	−	0.00427163i
$958$	−17.3980	+	55.5857i	−0.562103	+	1.79589i
$959$	−5.31464			−0.171619
$960$	10.9139	+	32.8780i	0.352244	+	1.06113i
$961$	−55.9245			−1.80402
$962$	−0.214202	+	0.684364i	−0.00690613	+	0.0220648i
$963$	2.59122	+	0.100237i	0.0835010	+	0.00323009i
$964$	28.9588	−	41.7291i	0.932702	−	1.34400i
$965$	13.6860	−	33.0408i	0.440566	−	1.06362i
$966$	8.06421	+	10.4103i	0.259462	+	0.334948i
$967$	−33.9111	+	33.9111i	−1.09051	+	1.09051i	−0.0950334	+	0.995474i	$0.530296\pi$
$967$	−33.9111	+	33.9111i	−1.09051	+	1.09051i	−0.995474	+	0.0950334i	$0.969704\pi$
$968$	30.6254	+	3.83597i	0.984338	+	0.123293i
$969$	0.0519573	−	0.237151i	0.00166911	−	0.00761839i
$970$	0.449273	+	0.375381i	0.0144253	+	0.0120528i
$971$	20.2369	−	48.8561i	0.649432	−	1.56787i	−0.164161	−	0.986433i	$-0.552492\pi$
$971$	20.2369	−	48.8561i	0.649432	−	1.56787i	0.813593	−	0.581434i	$-0.197508\pi$
$972$	27.2553	+	15.1376i	0.874215	+	0.485539i
$973$	−16.6055	+	6.87823i	−0.532348	+	0.220506i
$974$	13.2980	+	25.4148i	0.426094	+	0.814343i
$975$	3.44899	+	5.38425i	0.110456	+	0.172434i
$976$	−41.3932	+	38.5739i	−1.32496	+	1.23472i
$977$	−1.59721			−0.0510991			−0.0255496	−	0.999674i	$-0.508134\pi$
$977$	−1.59721			−0.0510991			−0.0255496	+	0.999674i	$0.508134\pi$
$978$	−2.87963	+	5.04087i	−0.0920804	+	0.161189i
$979$	−0.183765	−	0.443649i	−0.00587317	−	0.0141791i
$980$	−2.70425	−	4.20578i	−0.0863842	−	0.134349i
$981$	−30.5424	−	33.0004i	−0.975144	−	1.05362i
$982$	−23.1263	−	19.3227i	−0.737989	−	0.616613i
$983$	−7.61268	+	7.61268i	−0.242807	+	0.242807i	−0.818010	−	0.575203i	$-0.804923\pi$
$983$	−7.61268	+	7.61268i	−0.242807	+	0.242807i	0.575203	+	0.818010i	$0.304923\pi$
$984$	10.1628	+	9.14964i	0.323977	+	0.291680i
$985$	−45.5706	−	45.5706i	−1.45200	−	1.45200i
$986$	−0.00304416	−	0.0339738i	−9.69458e−5	−	0.00108195i
$987$	−1.14958	−	6.42618i	−0.0365915	−	0.204548i
$988$	−1.91559	−	10.6034i	−0.0609429	−	0.337341i
$989$	−2.38464	+	0.987749i	−0.0758270	+	0.0314086i
$990$	2.33052	+	2.10543i	0.0740689	+	0.0669149i
$991$		−	25.6078i		−	0.813458i	−0.913549	−	0.406729i	$-0.866669\pi$
$991$		−	25.6078i		−	0.813458i	0.913549	−	0.406729i	$-0.133331\pi$
$992$	2.85313	+	52.6635i	0.0905870	+	1.67207i
$993$	13.5807	+	21.2010i	0.430971	+	0.672794i
$994$	6.62385	−	21.1629i	0.210096	−	0.671246i
$995$	19.1629	+	46.2632i	0.607504	+	1.46664i
$996$	−12.6498	−	13.6210i	−0.400825	−	0.431599i
$997$	22.7762	+	9.43423i	0.721331	+	0.298785i	0.712984	−	0.701180i	$-0.247343\pi$
$997$	22.7762	+	9.43423i	0.721331	+	0.298785i	0.00834671	+	0.999965i	$0.497343\pi$
$998$	−27.6912	+	2.48122i	−0.876548	+	0.0785415i
$999$	0.537976	−	0.712031i	0.0170208	−	0.0225277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.a.155.19	✓	192
3.2	odd	2	inner	672.2.bs.a.155.30	yes	192
32.19	odd	8	inner	672.2.bs.a.659.30	yes	192
96.83	even	8	inner	672.2.bs.a.659.19	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.a.155.19	✓	192	1.1	even	1	trivial
672.2.bs.a.155.30	yes	192	3.2	odd	2	inner
672.2.bs.a.659.19	yes	192	96.83	even	8	inner
672.2.bs.a.659.30	yes	192	32.19	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.422431 + 1.34965i) q^{2} +(1.42128 + 0.989935i) q^{3} +(-1.64310 - 1.14027i) q^{4} +(-0.956738 + 2.30977i) q^{5} +(-1.93646 + 1.50004i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.23306 - 1.73593i) q^{8} +(1.04006 + 2.81394i) q^{9} +O(q^{10})\)	\(q+(-0.422431 + 1.34965i) q^{2} +(1.42128 + 0.989935i) q^{3} +(-1.64310 - 1.14027i) q^{4} +(-0.956738 + 2.30977i) q^{5} +(-1.93646 + 1.50004i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.23306 - 1.73593i) q^{8} +(1.04006 + 2.81394i) q^{9} +(-2.71322 - 2.26698i) q^{10} +(-0.113313 + 0.273562i) q^{11} +(-1.20651 - 3.24720i) q^{12} +(-2.72770 + 1.12985i) q^{13} +(-0.655642 - 1.25305i) q^{14} +(-3.64631 + 2.33571i) q^{15} +(1.39958 + 3.74716i) q^{16} +0.0768131 q^{17} +(-4.23719 + 0.215012i) q^{18} +(-0.698312 - 1.68587i) q^{19} +(4.20578 - 2.70425i) q^{20} +(-1.70498 + 0.305005i) q^{21} +(-0.321346 - 0.268494i) q^{22} +(-3.80139 + 3.80139i) q^{23} +(4.89225 - 0.256649i) q^{24} +(-0.884156 - 0.884156i) q^{25} +(-0.372635 - 4.15872i) q^{26} +(-1.30741 + 5.02898i) q^{27} +(1.96814 - 0.355558i) q^{28} +(-0.290098 + 0.120163i) q^{29} +(-1.61208 - 5.90792i) q^{30} -9.32333i q^{31} +(-5.64857 + 0.306020i) q^{32} +(-0.431858 + 0.276635i) q^{33} +(-0.0324483 + 0.103671i) q^{34} +(-0.956738 - 2.30977i) q^{35} +(1.49973 - 5.80954i) q^{36} +(-0.158672 - 0.0657241i) q^{37} +(2.57033 - 0.230310i) q^{38} +(-4.99529 - 1.09442i) q^{39} +(1.87314 + 6.81868i) q^{40} +(1.97377 + 1.97377i) q^{41} +(0.308590 - 2.42997i) q^{42} +(0.443573 + 0.183734i) q^{43} +(0.498119 - 0.320283i) q^{44} +(-7.49463 - 0.289916i) q^{45} +(-3.52471 - 6.73637i) q^{46} +3.76906i q^{47} +(-1.72026 + 6.71124i) q^{48} -1.00000i q^{49} +(1.56680 - 0.819805i) q^{50} +(0.109173 + 0.0760400i) q^{51} +(5.77022 + 1.25385i) q^{52} +(-12.2843 - 5.08832i) q^{53} +(-6.23507 - 3.88895i) q^{54} +(-0.523455 - 0.523455i) q^{55} +(-0.351526 + 2.80650i) q^{56} +(0.676412 - 3.08738i) q^{57} +(-0.0396307 - 0.442291i) q^{58} +(8.54736 + 3.54043i) q^{59} +(8.65461 + 0.319954i) q^{60} +(5.41310 + 13.0684i) q^{61} +(12.5832 + 3.93847i) q^{62} +(-2.72519 - 1.25433i) q^{63} +(1.97311 - 7.75286i) q^{64} -7.38133i q^{65} +(-0.190929 - 0.699716i) q^{66} +(-6.15696 + 2.55030i) q^{67} +(-0.126212 - 0.0875876i) q^{68} +(-9.16596 + 1.63970i) q^{69} +(3.52153 - 0.315541i) q^{70} +(11.0876 + 11.0876i) q^{71} +(7.20731 + 4.47824i) q^{72} +(7.31988 - 7.31988i) q^{73} +(0.155733 - 0.186388i) q^{74} +(-0.381373 - 2.13189i) q^{75} +(-0.774950 + 3.56633i) q^{76} +(-0.113313 - 0.273562i) q^{77} +(3.58725 - 6.27958i) q^{78} +1.28386 q^{79} +(-9.99410 - 0.352346i) q^{80} +(-6.83657 + 5.85332i) q^{81} +(-3.49769 + 1.83012i) q^{82} +(4.95770 - 2.05355i) q^{83} +(3.14925 + 1.44299i) q^{84} +(-0.0734901 + 0.177421i) q^{85} +(-0.435355 + 0.521052i) q^{86} +(-0.531263 - 0.116394i) q^{87} +(0.221849 + 0.807584i) q^{88} +(-1.14675 + 1.14675i) q^{89} +(3.55725 - 9.99264i) q^{90} +(1.12985 - 2.72770i) q^{91} +(10.5807 - 1.91147i) q^{92} +(9.22950 - 13.2510i) q^{93} +(-5.08690 - 1.59217i) q^{94} +4.56208 q^{95} +(-8.33112 - 5.15678i) q^{96} -0.165586 q^{97} +(1.34965 + 0.422431i) q^{98} +(-0.887641 - 0.0343368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{4}+O(q^{10}) \) 192 * q - 16 * q^4	\( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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