LMFDB - Embedded newform 672.2.bo.a.125.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(125,672)]

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([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("672.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bo (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:	$496$
Relative dimension:	$124$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			125.12
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33124 + 0.477276i) q^{2} +(1.25546 - 1.19324i) q^{3} +(1.54442 - 1.27074i) q^{4} +(1.54647 + 3.73351i) q^{5} +(-1.10181 + 2.18770i) q^{6} +(2.10482 - 1.60304i) q^{7} +(-1.44950 + 2.42878i) q^{8} +(0.152341 - 2.99613i) q^{9} +O(q^{10})$	\(q+(-1.33124 + 0.477276i) q^{2} +(1.25546 - 1.19324i) q^{3} +(1.54442 - 1.27074i) q^{4} +(1.54647 + 3.73351i) q^{5} +(-1.10181 + 2.18770i) q^{6} +(2.10482 - 1.60304i) q^{7} +(-1.44950 + 2.42878i) q^{8} +(0.152341 - 2.99613i) q^{9} +(-3.84065 - 4.23212i) q^{10} +(-1.84430 - 4.45254i) q^{11} +(0.422645 - 3.43822i) q^{12} +(2.04801 + 0.848312i) q^{13} +(-2.03693 + 3.13862i) q^{14} +(6.39652 + 2.84195i) q^{15} +(0.770440 - 3.92510i) q^{16} -5.92062i q^{17} +(1.22718 + 4.06129i) q^{18} +(2.98948 + 1.23828i) q^{19} +(7.13272 + 3.80093i) q^{20} +(0.729688 - 4.52411i) q^{21} +(4.58030 + 5.04717i) q^{22} +(2.51595 - 2.51595i) q^{23} +(1.07834 + 4.77883i) q^{24} +(-8.01201 + 8.01201i) q^{25} +(-3.13127 - 0.151846i) q^{26} +(-3.38385 - 3.94329i) q^{27} +(1.21366 - 5.15044i) q^{28} +(-3.18572 + 7.69100i) q^{29} +(-9.87171 - 0.730417i) q^{30} -1.79497i q^{31} +(0.847712 + 5.59298i) q^{32} +(-7.62840 - 3.38926i) q^{33} +(2.82577 + 7.88178i) q^{34} +(9.24002 + 5.37931i) q^{35} +(-3.57202 - 4.82086i) q^{36} +(2.33828 + 5.64512i) q^{37} +(-4.57072 - 0.221649i) q^{38} +(3.58343 - 1.37875i) q^{39} +(-11.3095 - 1.65569i) q^{40} +(1.96174 + 1.96174i) q^{41} +(1.18786 + 6.37095i) q^{42} +(1.44691 - 0.599330i) q^{43} +(-8.50638 - 4.53294i) q^{44} +(11.4217 - 4.06466i) q^{45} +(-2.14854 + 4.55015i) q^{46} +1.75294i q^{47} +(-3.71635 - 5.84712i) q^{48} +(1.86051 - 6.74822i) q^{49} +(6.84200 - 14.4899i) q^{50} +(-7.06474 - 7.43307i) q^{51} +(4.24096 - 1.29234i) q^{52} +(-1.14206 - 2.75717i) q^{53} +(6.38677 + 3.63444i) q^{54} +(13.7714 - 13.7714i) q^{55} +(0.842496 + 7.43574i) q^{56} +(5.23073 - 2.01256i) q^{57} +(0.570235 - 11.7591i) q^{58} +(2.21830 + 5.35544i) q^{59} +(13.4903 - 3.73916i) q^{60} +(-2.98452 + 7.20526i) q^{61} +(0.856694 + 2.38954i) q^{62} +(-4.48227 - 6.55051i) q^{63} +(-3.79790 - 7.04102i) q^{64} +8.95815i q^{65} +(11.7729 + 0.871086i) q^{66} +(-5.28456 - 2.18894i) q^{67} +(-7.52356 - 9.14389i) q^{68} +(0.156525 - 6.16081i) q^{69} +(-14.8681 - 2.75113i) q^{70} +(5.27683 + 5.27683i) q^{71} +(7.05611 + 4.71289i) q^{72} +(0.317731 - 0.317731i) q^{73} +(-5.80710 - 6.39902i) q^{74} +(-0.498451 + 19.6190i) q^{75} +(6.19053 - 1.88642i) q^{76} +(-11.0195 - 6.41529i) q^{77} +(-4.11237 + 3.54574i) q^{78} +1.64462i q^{79} +(15.8459 - 3.19361i) q^{80} +(-8.95358 - 0.912865i) q^{81} +(-3.54783 - 1.67526i) q^{82} +(-2.78649 + 6.72718i) q^{83} +(-4.62202 - 7.91435i) q^{84} +(22.1047 - 9.15607i) q^{85} +(-1.64014 + 1.48843i) q^{86} +(5.17770 + 13.4570i) q^{87} +(13.4875 + 1.97456i) q^{88} +(9.92232 - 9.92232i) q^{89} +(-13.2651 + 10.8623i) q^{90} +(5.67056 - 1.49750i) q^{91} +(0.688556 - 7.08280i) q^{92} +(-2.14183 - 2.25350i) q^{93} +(-0.836634 - 2.33358i) q^{94} +13.0762i q^{95} +(7.73805 + 6.01021i) q^{96} +13.0232i q^{97} +(0.743964 + 9.87150i) q^{98} +(-13.6213 + 4.84746i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.33124	+	0.477276i	−0.941331	+	0.337485i
$2$	−1.33124	+	0.477276i	−0.941331	+	0.337485i
$3$	1.25546	−	1.19324i	0.724838	−	0.688919i
$3$	1.25546	−	1.19324i	0.724838	−	0.688919i
$4$	1.54442	−	1.27074i	0.772208	−	0.635370i
$5$	1.54647	+	3.73351i	0.691603	+	1.66968i	0.741525	+	0.670925i	$0.234103\pi$
$5$	1.54647	+	3.73351i	0.691603	+	1.66968i	−0.0499221	+	0.998753i	$0.515897\pi$
$6$	−1.10181	+	2.18770i	−0.449813	+	0.893123i
$7$	2.10482	−	1.60304i	0.795546	−	0.605893i
$7$	2.10482	−	1.60304i	0.795546	−	0.605893i
$8$	−1.44950	+	2.42878i	−0.512475	+	0.858702i
$9$	0.152341	−	2.99613i	0.0507802	−	0.998710i
$10$	−3.84065	−	4.23212i	−1.21452	−	1.33831i
$11$	−1.84430	−	4.45254i	−0.556078	−	1.34249i	−0.912849	−	0.408298i	$-0.866122\pi$
$11$	−1.84430	−	4.45254i	−0.556078	−	1.34249i	0.356771	−	0.934192i	$-0.383878\pi$
$12$	0.422645	−	3.43822i	0.122007	−	0.992529i
$13$	2.04801	+	0.848312i	0.568015	+	0.235279i	0.648161	−	0.761504i	$-0.275539\pi$
$13$	2.04801	+	0.848312i	0.568015	+	0.235279i	−0.0801457	+	0.996783i	$0.525539\pi$
$14$	−2.03693	+	3.13862i	−0.544393	+	0.838830i
$15$	6.39652	+	2.84195i	1.65157	+	0.733787i
$16$	0.770440	−	3.92510i	0.192610	−	0.981275i
$17$		−	5.92062i		−	1.43596i	−0.696064	−	0.717980i	$-0.745067\pi$
$17$		−	5.92062i		−	1.43596i	0.696064	−	0.717980i	$-0.254933\pi$
$18$	1.22718	+	4.06129i	0.289248	+	0.957254i
$19$	2.98948	+	1.23828i	0.685833	+	0.284081i	0.698263	−	0.715842i	$-0.253957\pi$
$19$	2.98948	+	1.23828i	0.685833	+	0.284081i	−0.0124301	+	0.999923i	$0.503957\pi$
$20$	7.13272	+	3.80093i	1.59492	+	0.849915i
$21$	0.729688	−	4.52411i	0.159231	−	0.987241i
$22$	4.58030	+	5.04717i	0.976523	+	1.07606i
$23$	2.51595	−	2.51595i	0.524613	−	0.524613i	−0.394348	−	0.918961i	$-0.629030\pi$
$23$	2.51595	−	2.51595i	0.524613	−	0.524613i	0.918961	+	0.394348i	$0.129030\pi$
$24$	1.07834	+	4.77883i	0.220115	+	0.975474i
$25$	−8.01201	+	8.01201i	−1.60240	+	1.60240i
$26$	−3.13127	−	0.151846i	−0.614093	−	0.0297794i
$27$	−3.38385	−	3.94329i	−0.651223	−	0.758886i
$28$	1.21366	−	5.15044i	0.229361	−	0.973341i
$29$	−3.18572	+	7.69100i	−0.591572	+	1.42818i	0.290411	+	0.956902i	$0.406208\pi$
$29$	−3.18572	+	7.69100i	−0.591572	+	1.42818i	−0.881984	+	0.471280i	$0.843792\pi$
$30$	−9.87171	−	0.730417i	−1.80232	−	0.133355i
$31$		−	1.79497i		−	0.322385i	−0.986923	−	0.161193i	$-0.948466\pi$
$31$		−	1.79497i		−	0.322385i	0.986923	−	0.161193i	$-0.0515341\pi$
$32$	0.847712	+	5.59298i	0.149856	+	0.988708i
$33$	−7.62840	−	3.38926i	−1.32793	−	0.589995i
$34$	2.82577	+	7.88178i	0.484615	+	1.35171i
$35$	9.24002	+	5.37931i	1.56185	+	0.909269i
$36$	−3.57202	−	4.82086i	−0.595337	−	0.803476i
$37$	2.33828	+	5.64512i	0.384412	+	0.928051i	0.991101	+	0.133113i	$0.0424972\pi$
$37$	2.33828	+	5.64512i	0.384412	+	0.928051i	−0.606689	+	0.794939i	$0.707503\pi$
$38$	−4.57072	−	0.221649i	−0.741469	−	0.0359563i
$39$	3.58343	−	1.37875i	0.573807	−	0.220777i
$40$	−11.3095	−	1.65569i	−1.78819	−	0.261788i
$41$	1.96174	+	1.96174i	0.306372	+	0.306372i	0.843500	−	0.537129i	$-0.180491\pi$
$41$	1.96174	+	1.96174i	0.306372	+	0.306372i	−0.537129	+	0.843500i	$0.680491\pi$
$42$	1.18786	+	6.37095i	0.183290	+	0.983059i
$43$	1.44691	−	0.599330i	0.220652	−	0.0913969i	−0.269619	−	0.962967i	$-0.586898\pi$
$43$	1.44691	−	0.599330i	0.220652	−	0.0913969i	0.490271	+	0.871570i	$0.336898\pi$
$44$	−8.50638	−	4.53294i	−1.28239	−	0.683367i
$45$	11.4217	−	4.06466i	1.70264	−	0.605924i
$46$	−2.14854	+	4.55015i	−0.316785	+	0.670883i
$47$			1.75294i			0.255692i	0.991794	+	0.127846i	$0.0408063\pi$
$47$			1.75294i			0.255692i	−0.991794	+	0.127846i	$0.959194\pi$
$48$	−3.71635	−	5.84712i	−0.536408	−	0.843959i
$49$	1.86051	−	6.74822i	0.265788	−	0.964032i
$50$	6.84200	−	14.4899i	0.967605	−	2.04918i
$51$	−7.06474	−	7.43307i	−0.989261	−	1.04084i
$52$	4.24096	−	1.29234i	0.588115	−	0.179215i
$53$	−1.14206	−	2.75717i	−0.156874	−	0.378726i	0.825828	−	0.563922i	$-0.190708\pi$
$53$	−1.14206	−	2.75717i	−0.156874	−	0.378726i	−0.982702	+	0.185196i	$0.940708\pi$
$54$	6.38677	+	3.63444i	0.869129	+	0.494585i
$55$	13.7714	−	13.7714i	1.85694	−	1.85694i
$56$	0.842496	+	7.43574i	0.112583	+	0.993642i
$57$	5.23073	−	2.01256i	0.692827	−	0.266571i
$58$	0.570235	−	11.7591i	0.0748755	−	1.54404i
$59$	2.21830	+	5.35544i	0.288798	+	0.697219i	0.999983	−	0.00578511i	$-0.00184147\pi$
$59$	2.21830	+	5.35544i	0.288798	+	0.697219i	−0.711186	+	0.703004i	$0.751841\pi$
$60$	13.4903	−	3.73916i	1.74158	−	0.482724i
$61$	−2.98452	+	7.20526i	−0.382128	+	0.922539i	0.609426	+	0.792843i	$0.291400\pi$
$61$	−2.98452	+	7.20526i	−0.382128	+	0.922539i	−0.991554	+	0.129696i	$0.958600\pi$
$62$	0.856694	+	2.38954i	0.108800	+	0.303471i
$63$	−4.48227	−	6.55051i	−0.564713	−	0.825287i
$64$	−3.79790	−	7.04102i	−0.474738	−	0.880127i
$65$			8.95815i			1.11112i
$66$	11.7729	+	0.871086i	1.44914	+	0.107223i
$67$	−5.28456	−	2.18894i	−0.645612	−	0.267421i	0.0357581	−	0.999360i	$-0.488615\pi$
$67$	−5.28456	−	2.18894i	−0.645612	−	0.267421i	−0.681370	+	0.731939i	$0.738615\pi$
$68$	−7.52356	−	9.14389i	−0.912366	−	1.10886i
$69$	0.156525	−	6.16081i	0.0188434	−	0.741675i
$70$	−14.8681	−	2.75113i	−1.77708	−	0.328823i
$71$	5.27683	+	5.27683i	0.626245	+	0.626245i	0.947121	−	0.320876i	$-0.103977\pi$
$71$	5.27683	+	5.27683i	0.626245	+	0.626245i	−0.320876	+	0.947121i	$0.603977\pi$
$72$	7.05611	+	4.71289i	0.831570	+	0.555419i
$73$	0.317731	−	0.317731i	0.0371876	−	0.0371876i	−0.688268	−	0.725456i	$-0.741629\pi$
$73$	0.317731	−	0.317731i	0.0371876	−	0.0371876i	0.725456	+	0.688268i	$0.241629\pi$
$74$	−5.80710	−	6.39902i	−0.675062	−	0.743871i
$75$	−0.498451	+	19.6190i	−0.0575561	+	2.26541i
$76$	6.19053	−	1.88642i	0.710102	−	0.216388i
$77$	−11.0195	−	6.41529i	−1.25579	−	0.731090i
$78$	−4.11237	+	3.54574i	−0.465634	+	0.401475i
$79$			1.64462i			0.185034i	0.995711	+	0.0925172i	$0.0294913\pi$
$79$			1.64462i			0.185034i	−0.995711	+	0.0925172i	$0.970509\pi$
$80$	15.8459	−	3.19361i	1.77162	−	0.357056i
$81$	−8.95358	−	0.912865i	−0.994843	−	0.101429i
$82$	−3.54783	−	1.67526i	−0.391793	−	0.185001i
$83$	−2.78649	+	6.72718i	−0.305857	+	0.738404i	0.693974	+	0.720000i	$0.255858\pi$
$83$	−2.78649	+	6.72718i	−0.305857	+	0.738404i	−0.999831	+	0.0184034i	$0.994142\pi$
$84$	−4.62202	−	7.91435i	−0.504304	−	0.863526i
$85$	22.1047	−	9.15607i	2.39759	−	0.993115i
$86$	−1.64014	+	1.48843i	−0.176861	+	0.160501i
$87$	5.17770	+	13.4570i	0.555108	+	1.44275i
$88$	13.4875	+	1.97456i	1.43778	+	0.210488i
$89$	9.92232	−	9.92232i	1.05176	−	1.05176i	0.0531783	−	0.998585i	$-0.483065\pi$
$89$	9.92232	−	9.92232i	1.05176	−	1.05176i	0.998585	−	0.0531783i	$-0.0169352\pi$
$90$	−13.2651	+	10.8623i	−1.39826	+	1.14499i
$91$	5.67056	−	1.49750i	0.594436	−	0.156980i
$92$	0.688556	−	7.08280i	0.0717869	−	0.738433i
$93$	−2.14183	−	2.25350i	−0.222098	−	0.233677i
$94$	−0.836634	−	2.33358i	−0.0862922	−	0.240691i
$95$			13.0762i			1.34159i
$96$	7.73805	+	6.01021i	0.789761	+	0.613415i
$97$			13.0232i			1.32230i	0.750253	+	0.661151i	$0.229932\pi$
$97$			13.0232i			1.32230i	−0.750253	+	0.661151i	$0.770068\pi$
$98$	0.743964	+	9.87150i	0.0751517	+	0.997172i
$99$	−13.6213	+	4.84746i	−1.36900	+	0.487188i
$100$	−2.19270	+	22.5551i	−0.219270	+	2.25551i
$101$	−6.18477	−	14.9314i	−0.615408	−	1.48573i	−0.856983	−	0.515344i	$-0.827664\pi$
$101$	−6.18477	−	14.9314i	−0.615408	−	1.48573i	0.241575	−	0.970382i	$-0.422336\pi$
$102$	12.9525	+	6.52340i	1.28249	+	0.645913i
$103$	−5.27256	−	5.27256i	−0.519521	−	0.519521i	0.397906	−	0.917426i	$-0.369737\pi$
$103$	−5.27256	−	5.27256i	−0.519521	−	0.519521i	−0.917426	+	0.397906i	$0.869737\pi$
$104$	−5.02894	+	3.74452i	−0.493129	+	0.367181i
$105$	18.0193	−	4.27211i	1.75850	−	0.416915i
$106$	2.83629	+	3.12539i	0.275484	+	0.303564i
$107$	0.645688	+	1.55883i	0.0624210	+	0.150698i	0.952012	−	0.306060i	$-0.0990107\pi$
$107$	0.645688	+	1.55883i	0.0624210	+	0.150698i	−0.889591	+	0.456757i	$0.849011\pi$
$108$	−10.2370	−	1.79008i	−0.985053	−	0.172250i
$109$	−2.38787	+	5.76482i	−0.228716	+	0.552170i	−0.996022	−	0.0891121i	$-0.971597\pi$
$109$	−2.38787	+	5.76482i	−0.228716	+	0.552170i	0.767305	+	0.641282i	$0.221597\pi$
$110$	−11.7604	+	24.9059i	−1.12131	+	2.37469i
$111$	9.67161	+	4.29706i	0.917989	+	0.407858i
$112$	−4.67046	−	9.49667i	−0.441317	−	0.897351i
$113$	0.300039			0.0282253			0.0141126	−	0.999900i	$-0.495508\pi$
$113$	0.300039			0.0282253			0.0141126	+	0.999900i	$0.495508\pi$
$114$	−6.00282	+	5.17571i	−0.562216	+	0.484750i
$115$	13.2842	+	5.50249i	1.23876	+	0.513110i
$116$	4.85319	+	15.9263i	0.450607	+	1.47872i
$117$	2.85365	−	6.00686i	0.263820	−	0.555335i
$118$	−5.50911	−	6.07066i	−0.507155	−	0.558849i
$119$	−9.49099	−	12.4618i	−0.870038	−	1.14237i
$120$	−16.1742	+	11.4163i	−1.47650	+	1.04216i
$121$	−8.64546	+	8.64546i	−0.785951	+	0.785951i
$122$	0.534221	−	11.0164i	0.0483661	−	0.997377i
$123$	4.80370	+	0.122045i	0.433135	+	0.0110045i
$124$	−2.28093	−	2.77217i	−0.204834	−	0.248949i
$125$	−23.6357	−	9.79025i	−2.11405	−	0.875666i
$126$	9.09339	+	6.58105i	0.810104	+	0.586286i
$127$	−21.4788			−1.90593			−0.952966	−	0.303076i	$-0.901986\pi$
$127$	−21.4788			−1.90593			−0.952966	+	0.303076i	$0.901986\pi$
$128$	8.41644	+	7.56066i	0.743915	+	0.668274i
$129$	1.10139	−	2.47895i	0.0969716	−	0.218259i
$130$	−4.27551	−	11.9255i	−0.374987	−	1.04593i
$131$	6.40447	+	2.65282i	0.559561	+	0.231778i	0.644495	−	0.764609i	$-0.277068\pi$
$131$	6.40447	+	2.65282i	0.559561	+	0.231778i	−0.0849335	+	0.996387i	$0.527068\pi$
$132$	−16.0883	+	4.45928i	−1.40031	+	0.388130i
$133$	8.27732	−	2.18590i	0.717734	−	0.189541i
$134$	8.07976	+	0.391814i	0.697985	+	0.0338476i
$135$	9.48929	−	18.7319i	0.816708	−	1.61218i
$136$	14.3798	+	8.58193i	1.23306	+	0.735894i
$137$	−6.08033	+	6.08033i	−0.519478	+	0.519478i	−0.917413	−	0.397936i	$-0.869727\pi$
$137$	−6.08033	+	6.08033i	−0.519478	+	0.519478i	0.397936	+	0.917413i	$0.369727\pi$
$138$	2.73203	+	8.27625i	0.232566	+	0.704521i
$139$	0.286916	+	0.692676i	0.0243359	+	0.0587520i	0.935580	−	0.353114i	$-0.114877\pi$
$139$	0.286916	+	0.692676i	0.0243359	+	0.0587520i	−0.911244	+	0.411866i	$0.864877\pi$
$140$	21.1061	−	3.43377i	1.78379	−	0.290207i
$141$	2.09168	+	2.20074i	0.176151	+	0.185335i
$142$	−9.54325	−	4.50624i	−0.800852	−	0.378156i
$143$		−	10.6834i		−	0.893388i
$144$	−11.6427	−	2.90629i	−0.970229	−	0.242191i
$145$	−33.6411			−2.79374
$146$	−0.271332	+	0.574622i	−0.0224556	+	0.0475561i
$147$	−5.71647	−	10.6921i	−0.471487	−	0.881873i
$148$	10.7848	+	5.74706i	0.886502	+	0.472405i
$149$	−2.32807	−	5.62047i	−0.190723	−	0.460447i	0.799373	−	0.600835i	$-0.205165\pi$
$149$	−2.32807	−	5.62047i	−0.190723	−	0.460447i	−0.990097	+	0.140388i	$0.955165\pi$
$150$	−8.70012	−	26.3556i	−0.710362	−	2.15192i
$151$	−0.796485	−	0.796485i	−0.0648171	−	0.0648171i	0.673955	−	0.738772i	$-0.264594\pi$
$151$	−0.796485	−	0.796485i	−0.0648171	−	0.0648171i	−0.738772	+	0.673955i	$0.764594\pi$
$152$	−7.34075	+	5.46588i	−0.595414	+	0.443341i
$153$	−17.7389	−	0.901951i	−1.43411	−	0.0729184i
$154$	17.7315	+	3.28096i	1.42885	+	0.264387i
$155$	6.70153	−	2.77586i	0.538280	−	0.222963i
$156$	3.78226	−	6.68297i	0.302824	−	0.535066i
$157$	5.49649	−	13.2697i	0.438668	−	1.05904i	−0.537742	−	0.843110i	$-0.680722\pi$
$157$	5.49649	−	13.2697i	0.438668	−	1.05904i	0.976409	−	0.215928i	$-0.0692776\pi$
$158$	−0.784938	−	2.18939i	−0.0624463	−	0.174179i
$159$	−4.72378	−	2.09875i	−0.374620	−	0.166442i
$160$	−19.5705	+	11.8143i	−1.54718	+	0.934004i
$161$	1.26245	−	9.32880i	0.0994946	−	0.735212i
$162$	12.3551	−	3.05808i	0.970707	−	0.240266i
$163$	9.80977	+	4.06334i	0.768360	+	0.318265i	0.732208	−	0.681081i	$-0.238490\pi$
$163$	9.80977	+	4.06334i	0.768360	+	0.318265i	0.0361523	+	0.999346i	$0.488490\pi$
$164$	5.52259	+	0.536880i	0.431242	+	0.0419233i
$165$	0.856762	−	33.7221i	0.0666988	−	2.62526i
$166$	0.498775	−	10.2854i	0.0387124	−	0.798304i
$167$	−16.3290	+	16.3290i	−1.26357	+	1.26357i	−0.314227	+	0.949348i	$0.601745\pi$
$167$	−16.3290	+	16.3290i	−1.26357	+	1.26357i	−0.949348	+	0.314227i	$0.898255\pi$
$168$	9.93036	+	8.32994i	0.766144	+	0.642669i
$169$	−5.71769	−	5.71769i	−0.439822	−	0.439822i
$170$	−25.0568	+	22.7390i	−1.92177	+	1.74400i
$171$	4.16547	−	8.76822i	0.318541	−	0.670522i
$172$	1.47304	−	2.76426i	0.112318	−	0.210773i
$173$	−4.33175	+	10.4578i	−0.329337	+	0.795090i	0.669305	+	0.742988i	$0.266592\pi$
$173$	−4.33175	+	10.4578i	−0.329337	+	0.795090i	−0.998642	+	0.0521022i	$0.983408\pi$
$174$	−13.3155	−	15.4434i	−1.00945	−	1.17076i
$175$	−4.02024	+	29.7074i	−0.303901	+	2.24567i
$176$	−18.8976	+	3.80865i	−1.42446	+	0.287088i
$177$	9.17532	+	4.07656i	0.689659	+	0.306413i
$178$	−8.47333	+	17.9447i	−0.635103	+	1.34501i
$179$	−15.2085	−	6.29958i	−1.13674	−	0.470852i	−0.266672	−	0.963787i	$-0.585924\pi$
$179$	−15.2085	−	6.29958i	−1.13674	−	0.470852i	−0.870066	+	0.492935i	$0.835924\pi$
$180$	12.4747	−	20.7915i	0.929809	−	1.54971i
$181$	6.28963	+	15.1845i	0.467505	+	1.12866i	0.965249	+	0.261332i	$0.0841618\pi$
$181$	6.28963	+	15.1845i	0.467505	+	1.12866i	−0.497744	+	0.867324i	$0.665838\pi$
$182$	−6.83418	+	4.69995i	−0.506583	+	0.348384i
$183$	4.85070	+	12.6071i	0.358574	+	0.931947i
$184$	2.46381	+	9.75756i	0.181635	+	0.719337i
$185$	−17.4600	+	17.4600i	−1.28369	+	1.28369i
$186$	3.92684	+	1.97771i	0.287930	+	0.145013i
$187$	−26.3618	+	10.9194i	−1.92776	+	0.798506i
$188$	2.22753	+	2.70726i	0.162459	+	0.197447i
$189$	−13.4437	−	2.87544i	−0.977882	−	0.209158i
$190$	−6.24096	−	17.4076i	−0.452767	−	1.26288i
$191$		−	19.5225i		−	1.41260i	−0.707914	−	0.706299i	$-0.750363\pi$
$191$		−	19.5225i		−	1.41260i	0.707914	−	0.706299i	$-0.249637\pi$
$192$	−13.1697	−	4.30787i	−0.950445	−	0.310894i
$193$	4.76967			0.343328			0.171664	−	0.985156i	$-0.445086\pi$
$193$	4.76967			0.343328			0.171664	+	0.985156i	$0.445086\pi$
$194$	−6.21564	−	17.3370i	−0.446257	−	1.24472i
$195$	10.6893	+	11.2466i	0.765473	+	0.805383i
$196$	−5.70182	−	12.7863i	−0.407273	−	0.913306i
$197$	−0.688749	+	0.285289i	−0.0490713	+	0.0203260i	−0.407084	−	0.913391i	$-0.633454\pi$
$197$	−0.688749	+	0.285289i	−0.0490713	+	0.0203260i	0.358013	+	0.933717i	$0.383454\pi$
$198$	15.8197	−	12.9543i	1.12426	−	0.920621i
$199$	9.27027	+	9.27027i	0.657152	+	0.657152i	0.954705	−	0.297553i	$-0.0961705\pi$
$199$	9.27027	+	9.27027i	0.657152	+	0.657152i	−0.297553	+	0.954705i	$0.596171\pi$
$200$	−7.84597	−	31.0728i	−0.554794	−	2.19718i
$201$	−9.24647	+	3.55765i	−0.652195	+	0.250937i
$202$	15.3598	+	16.9254i	1.08071	+	1.19087i
$203$	5.62364	+	21.2950i	0.394702	+	1.49461i
$204$	−20.3564	−	2.50232i	−1.42523	−	0.175197i
$205$	−4.29040	+	10.3579i	−0.299654	+	0.723429i
$206$	9.53552	+	4.50259i	0.664371	+	0.313710i
$207$	−7.15484	−	7.92140i	−0.497296	−	0.550576i
$208$	4.90758	−	7.38506i	0.340279	−	0.512062i
$209$		−	15.5945i		−	1.07869i
$210$	−21.9490	+	14.2874i	−1.51463	+	0.985922i
$211$	−1.27989	+	3.08993i	−0.0881113	+	0.212719i	−0.961793	−	0.273779i	$-0.911726\pi$
$211$	−1.27989	+	3.08993i	−0.0881113	+	0.212719i	0.873681	+	0.486499i	$0.161726\pi$
$212$	−5.26746	−	2.80696i	−0.361771	−	0.192783i
$213$	12.9214	+	0.328287i	0.885358	+	0.0224939i
$214$	−1.60356	−	1.76701i	−0.109617	−	0.120790i
$215$	4.47521	+	4.47521i	0.305207	+	0.305207i
$216$	14.4823	−	2.50283i	0.985393	−	0.170296i
$217$	−2.87741	−	3.77808i	−0.195331	−	0.256473i
$218$	0.427422	−	8.81405i	0.0289487	−	0.596963i
$219$	0.0197670	−	0.778027i	0.00133573	−	0.0525742i
$220$	3.76891	−	38.7688i	0.254100	−	2.61379i
$221$	5.02253	−	12.1255i	0.337852	−	0.815647i
$222$	−14.9261	−	1.10440i	−1.00178	−	0.0741225i
$223$		−	5.07368i		−	0.339759i	−0.985465	−	0.169879i	$-0.945662\pi$
$223$		−	5.07368i		−	0.339759i	0.985465	−	0.169879i	$-0.0543378\pi$
$224$	10.7501	+	10.4133i	0.718268	+	0.695766i
$225$	22.7845	+	25.2256i	1.51896	+	1.68171i
$226$	−0.399425	+	0.143201i	−0.0265693	+	0.00952560i
$227$	8.73117	+	3.61657i	0.579508	+	0.240040i	0.653130	−	0.757246i	$-0.273456\pi$
$227$	8.73117	+	3.61657i	0.579508	+	0.240040i	−0.0736216	+	0.997286i	$0.523456\pi$
$228$	5.52097	−	9.75513i	0.365635	−	0.646049i
$229$	17.4113	−	7.21201i	1.15057	−	0.476583i	0.275848	−	0.961201i	$-0.411041\pi$
$229$	17.4113	−	7.21201i	1.15057	−	0.476583i	0.874726	+	0.484618i	$0.161041\pi$
$230$	−20.3107	−	0.984933i	−1.33925	−	0.0649445i
$231$	−21.4895	+	5.09486i	−1.41391	+	0.335217i
$232$	−14.0620	−	18.8855i	−0.923216	−	1.23989i
$233$	−6.23946	+	6.23946i	−0.408760	+	0.408760i	−0.881306	−	0.472546i	$-0.843335\pi$
$233$	−6.23946	+	6.23946i	−0.408760	+	0.408760i	0.472546	+	0.881306i	$0.343335\pi$
$234$	−0.931970	+	9.35857i	−0.0609248	+	0.611789i
$235$	−6.54461	+	2.71087i	−0.426923	+	0.176837i
$236$	10.2313	+	5.45215i	0.666004	+	0.354905i
$237$	1.96243	+	2.06475i	0.127474	+	0.134120i
$238$	18.5825	+	12.0599i	1.20453	+	0.781726i
$239$	−13.3137			−0.861194			−0.430597	−	0.902544i	$-0.641697\pi$
$239$	−13.3137			−0.861194			−0.430597	+	0.902544i	$0.641697\pi$
$240$	16.0831	−	22.9174i	1.03816	−	1.47931i
$241$	−24.3441			−1.56814			−0.784071	−	0.620671i	$-0.786860\pi$
$241$	−24.3441			−1.56814			−0.784071	+	0.620671i	$0.786860\pi$
$242$	7.38294	−	15.6355i	0.474593	−	1.00509i
$243$	−12.3301	+	9.53774i	−0.790977	+	0.611846i
$244$	4.54668	+	14.9205i	0.291071	+	0.955185i
$245$	28.0718	−	3.48968i	1.79344	−	0.222947i
$246$	−6.45314	+	2.13022i	−0.411437	+	0.135818i
$247$	5.07202	+	5.07202i	0.322725	+	0.322725i
$248$	4.35957	+	2.60180i	0.276833	+	0.165215i
$249$	4.52885	+	11.7706i	0.287004	+	0.745934i
$250$	36.1376	+	1.75243i	2.28554	+	0.110833i
$251$	−1.77107	−	4.27574i	−0.111789	−	0.269882i	0.858077	−	0.513521i	$-0.171659\pi$
$251$	−1.77107	−	4.27574i	−0.111789	−	0.269882i	−0.969866	+	0.243638i	$0.921659\pi$
$252$	−15.2465	−	4.42092i	−0.960439	−	0.278492i
$253$	−15.8425	−	6.56220i	−0.996013	−	0.412562i
$254$	28.5935	−	10.2513i	1.79411	−	0.643223i
$255$	16.8261	−	37.8713i	1.05369	−	2.37159i
$256$	−14.8128	−	6.04811i	−0.925803	−	0.378007i
$257$	8.52098			0.531524			0.265762	−	0.964039i	$-0.414376\pi$
$257$	8.52098			0.531524			0.265762	+	0.964039i	$0.414376\pi$
$258$	−0.283071	+	3.82575i	−0.0176232	+	0.238181i
$259$	13.9710	+	8.13358i	0.868117	+	0.505396i
$260$	11.3835	+	13.8351i	0.705974	+	0.858017i
$261$	22.5579	+	10.7165i	1.39630	+	0.663333i
$262$	−9.79203	−	0.474848i	−0.604954	−	0.0293362i
$263$	12.3540	+	12.3540i	0.761779	+	0.761779i	0.976644	−	0.214864i	$-0.0689310\pi$
$263$	12.3540	+	12.3540i	0.761779	+	0.761779i	−0.214864	+	0.976644i	$0.568931\pi$
$264$	19.2891	−	13.6149i	1.18716	−	0.837941i
$265$	8.52777	−	8.52777i	0.523857	−	0.523857i
$266$	−9.97585	+	6.86052i	−0.611658	+	0.420646i
$267$	0.617296	−	24.2968i	0.0377779	−	1.48694i
$268$	−10.9431	+	3.33467i	−0.668458	+	0.203698i
$269$	−2.39235	+	5.77565i	−0.145864	+	0.352148i	−0.979878	−	0.199596i	$-0.936037\pi$
$269$	−2.39235	+	5.77565i	−0.145864	+	0.352148i	0.834014	+	0.551743i	$0.186037\pi$
$270$	−3.69229	+	29.4657i	−0.224706	+	1.79322i
$271$	−2.36363			−0.143580			−0.0717900	−	0.997420i	$-0.522871\pi$
$271$	−2.36363			−0.143580			−0.0717900	+	0.997420i	$0.522871\pi$
$272$	−23.2390	−	4.56148i	−1.40907	−	0.276580i
$273$	5.33226	−	8.64640i	0.322723	−	0.523304i
$274$	5.19240	−	10.9964i	0.313685	−	0.664316i
$275$	50.4503	+	20.8972i	3.04227	+	1.26015i
$276$	−7.58705	−	9.71376i	−0.456687	−	0.584700i
$277$	−25.2636	+	10.4645i	−1.51794	+	0.628751i	−0.977178	−	0.212424i	$-0.931864\pi$
$277$	−25.2636	+	10.4645i	−1.51794	+	0.628751i	−0.540763	+	0.841175i	$0.681864\pi$
$278$	−0.712552	−	0.785182i	−0.0427360	−	0.0470921i
$279$	−5.37795	−	0.273446i	−0.321969	−	0.0163708i
$280$	−26.4585	+	14.6446i	−1.58120	+	0.875184i
$281$	−14.2112	−	14.2112i	−0.847769	−	0.847769i	0.142086	−	0.989854i	$-0.454619\pi$
$281$	−14.2112	−	14.2112i	−0.847769	−	0.847769i	−0.989854	+	0.142086i	$0.954619\pi$
$282$	−3.83489	−	1.93141i	−0.228364	−	0.115014i
$283$	−3.47129	+	1.43786i	−0.206347	+	0.0854716i	−0.483463	−	0.875365i	$-0.660621\pi$
$283$	−3.47129	+	1.43786i	−0.206347	+	0.0854716i	0.277116	+	0.960836i	$0.410621\pi$
$284$	14.8551	+	1.44414i	0.881489	+	0.0856941i
$285$	15.6031	+	16.4166i	0.924248	+	0.972436i
$286$	5.09891	+	14.2222i	0.301505	+	0.840974i
$287$	7.27384	+	0.984352i	0.429361	+	0.0581044i
$288$	16.8864	−	1.68782i	0.995042	−	0.0994556i
$289$	−18.0537			−1.06198
$290$	44.7844	−	16.0561i	2.62983	−	0.942844i
$291$	15.5398	+	16.3500i	0.910959	+	0.958454i
$292$	0.0869553	−	0.894462i	0.00508867	−	0.0523444i
$293$	3.88526	+	9.37985i	0.226979	+	0.547977i	0.995807	−	0.0914794i	$-0.0291596\pi$
$293$	3.88526	+	9.37985i	0.226979	+	0.547977i	−0.768828	+	0.639456i	$0.779160\pi$
$294$	12.7131	+	11.5055i	0.741444	+	0.671015i
$295$	−16.5641	+	16.5641i	−0.964398	+	0.964398i
$296$	−17.1001	−	2.50343i	−0.993921	−	0.145509i
$297$	−11.3168	+	22.3393i	−0.656667	+	1.29626i
$298$	5.78175	+	6.37108i	0.334928	+	0.369067i
$299$	7.28700	−	3.01838i	0.421418	−	0.174557i
$300$	24.1608	+	30.9333i	1.39493	+	1.78594i
$301$	2.08473	−	3.58094i	0.120162	−	0.206402i
$302$	1.44046	+	0.680172i	0.0828891	+	0.0391395i
$303$	−25.5815	−	11.3657i	−1.46962	−	0.652944i
$304$	7.16359	−	10.7800i	0.410860	−	0.618274i
$305$	−31.5164			−1.80462
$306$	24.0453	−	7.26565i	1.37458	−	0.415349i
$307$	4.96585	+	2.05692i	0.283416	+	0.117395i	0.519863	−	0.854250i	$-0.325983\pi$
$307$	4.96585	+	2.05692i	0.283416	+	0.117395i	−0.236447	+	0.971644i	$0.575983\pi$
$308$	−25.1709	+	4.09507i	−1.43424	+	0.233338i
$309$	−12.9109	−	0.328021i	−0.734476	−	0.0186605i
$310$	−7.59651	+	6.89383i	−0.431453	+	0.391543i
$311$	15.8363	+	15.8363i	0.897994	+	0.897994i	0.995259	−	0.0972644i	$-0.0310092\pi$
$311$	15.8363	+	15.8363i	0.897994	+	0.897994i	−0.0972644	+	0.995259i	$0.531009\pi$
$312$	−1.84550	+	10.7018i	−0.104481	+	0.605872i
$313$	21.8990	+	21.8990i	1.23781	+	1.23781i	0.960896	+	0.276909i	$0.0893102\pi$
$313$	21.8990	+	21.8990i	1.23781	+	1.23781i	0.276909	+	0.960896i	$0.410690\pi$
$314$	−0.983858	+	20.2885i	−0.0555223	+	1.14495i
$315$	17.5247	−	26.8648i	0.987407	−	1.51366i
$316$	2.08989	+	2.53998i	0.117565	+	0.142885i
$317$	−4.76529	+	11.5044i	−0.267645	+	0.646153i	−0.999372	−	0.0354458i	$-0.988715\pi$
$317$	−4.76529	+	11.5044i	−0.267645	+	0.646153i	0.731726	+	0.681598i	$0.238715\pi$
$318$	7.29018	+	0.539408i	0.408813	+	0.0302485i
$319$	40.1199			2.24628
$320$	20.4144	−	25.0683i	1.14120	−	1.40136i
$321$	2.67070	+	1.18658i	0.149064	+	0.0662284i
$322$	2.77179	+	13.0214i	0.154466	+	0.725656i
$323$	7.33139	−	17.6995i	0.407929	−	0.984829i
$324$	−14.9881	+	9.96783i	−0.832671	+	0.553769i
$325$	−23.2053	+	9.61197i	−1.28720	+	0.533176i
$326$	−14.9985	−	0.727328i	−0.830691	−	0.0402829i
$327$	3.88097	+	10.0868i	0.214618	+	0.557801i
$328$	−7.60815	+	1.92108i	−0.420090	+	0.106074i
$329$	2.81003	+	3.68961i	0.154922	+	0.203415i
$330$	14.9542	+	45.3013i	0.823201	+	2.49375i
$331$	14.8530	−	6.15229i	0.816392	−	0.338161i	0.0648909	−	0.997892i	$-0.479330\pi$
$331$	14.8530	−	6.15229i	0.816392	−	0.338161i	0.751501	+	0.659732i	$0.229330\pi$
$332$	4.24500	+	13.9305i	0.232974	+	0.764533i
$333$	17.2697	−	6.14582i	0.946375	−	0.336789i
$334$	13.9444	−	29.5313i	0.763005	−	1.61588i
$335$		−	23.1151i		−	1.26291i
$336$	−17.1954	−	6.34965i	−0.938086	−	0.346402i
$337$			31.7230i			1.72806i	0.503440	+	0.864030i	$0.332067\pi$
$337$			31.7230i			1.72806i	−0.503440	+	0.864030i	$0.667933\pi$
$338$	10.3405	+	4.88272i	0.562452	+	0.265585i
$339$	0.376686	−	0.358019i	0.0204588	−	0.0194449i
$340$	22.5039	−	42.2301i	1.22044	−	2.29025i
$341$	−7.99215	+	3.31046i	−0.432799	+	0.179271i
$342$	−1.36040	+	13.6607i	−0.0735618	+	0.738686i
$343$	−6.90163	−	17.1863i	−0.372653	−	0.927971i
$344$	−0.641658	+	4.38295i	−0.0345959	+	0.236313i
$345$	23.2435	−	8.94314i	1.25139	−	0.481482i
$346$	0.775373	−	15.9893i	0.0416843	−	0.859590i
$347$	13.3893	−	5.54602i	0.718774	−	0.297726i	0.00684449	−	0.999977i	$-0.497821\pi$
$347$	13.3893	−	5.54602i	0.718774	−	0.297726i	0.711930	+	0.702250i	$0.247821\pi$
$348$	25.0969	+	14.2038i	1.34534	+	0.761401i
$349$	8.15731	−	19.6935i	0.436651	−	1.05417i	−0.540447	−	0.841378i	$-0.681745\pi$
$349$	8.15731	−	19.6935i	0.436651	−	1.05417i	0.977098	−	0.212791i	$-0.0682552\pi$
$350$	−8.82672	−	41.4666i	−0.471808	−	2.21648i
$351$	−3.58502	−	10.9464i	−0.191354	−	0.584278i
$352$	23.3395	−	14.0896i	1.24400	−	0.750978i
$353$	−12.5119			−0.665939			−0.332970	−	0.942938i	$-0.608051\pi$
$353$	−12.5119			−0.665939			−0.332970	+	0.942938i	$0.608051\pi$
$354$	−14.1602	−	1.04773i	−0.752607	−	0.0556861i
$355$	−11.5407	+	27.8616i	−0.612514	+	1.47874i
$356$	2.71550	−	27.9329i	0.143921	−	1.48044i
$357$	−26.7855	−	4.32020i	−1.41764	−	0.228649i
$358$	23.2529	+	1.12761i	1.22895	+	0.0595960i
$359$	−15.0675	−	15.0675i	−0.795232	−	0.795232i	0.187107	−	0.982339i	$-0.440089\pi$
$359$	−15.0675	−	15.0675i	−0.795232	−	0.795232i	−0.982339	+	0.187107i	$0.940089\pi$
$360$	−6.68356	+	33.6324i	−0.352255	+	1.77258i
$361$	−6.03141	−	6.03141i	−0.317442	−	0.317442i
$362$	−15.6202	−	17.2124i	−0.820981	−	0.904663i
$363$	−0.537859	+	21.1701i	−0.0282303	+	1.11114i
$364$	6.85477	−	9.51857i	0.359288	−	0.498908i
$365$	1.67761	+	0.694891i	0.0878103	+	0.0363722i
$366$	−12.4745	−	14.4681i	−0.652055	−	0.756257i
$367$	−22.3430			−1.16629			−0.583146	−	0.812367i	$-0.698179\pi$
$367$	−22.3430			−1.16629			−0.583146	+	0.812367i	$0.698179\pi$
$368$	−7.93698	−	11.8138i	−0.413744	−	0.615835i
$369$	6.17647	−	5.57876i	0.321534	−	0.290419i
$370$	14.9103	−	31.5768i	0.775149	−	1.64160i
$371$	−6.82368	−	3.97258i	−0.354268	−	0.206246i
$372$	−6.17149	−	0.758633i	−0.319977	−	0.0393333i
$373$	8.20536	−	3.39877i	0.424857	−	0.175982i	−0.160001	−	0.987117i	$-0.551150\pi$
$373$	8.20536	−	3.39877i	0.424857	−	0.175982i	0.584859	+	0.811135i	$0.301150\pi$
$374$	29.8823	−	27.1182i	1.54518	−	1.40225i
$375$	−41.3558	+	15.9120i	−2.13560	+	0.821691i
$376$	−4.25749	−	2.54088i	−0.219563	−	0.131036i
$377$	−13.0487	+	13.0487i	−0.672044	+	0.672044i
$378$	19.2691	−	2.58841i	0.991098	−	0.133134i
$379$	−12.4330	−	30.0160i	−0.638643	−	1.54182i	−0.828488	−	0.560006i	$-0.810799\pi$
$379$	−12.4330	−	30.0160i	−0.638643	−	1.54182i	0.189846	−	0.981814i	$-0.439201\pi$
$380$	16.6165	+	20.1951i	0.852407	+	1.03599i
$381$	−26.9657	+	25.6294i	−1.38149	+	1.31303i
$382$	9.31761	+	25.9892i	0.476730	+	1.32972i
$383$	−16.3973			−0.837860			−0.418930	−	0.908018i	$-0.637595\pi$
$383$	−16.3973			−0.837860			−0.418930	+	0.908018i	$0.637595\pi$
$384$	19.5882	−	0.550781i	0.999605	−	0.0281069i
$385$	6.91018	−	51.0626i	0.352175	−	2.60239i
$386$	−6.34959	+	2.27645i	−0.323186	+	0.115868i
$387$	−1.57525	−	4.42643i	−0.0800742	−	0.225008i
$388$	16.5490	+	20.1132i	0.840151	+	1.02109i
$389$	13.2005	−	5.46781i	0.669290	−	0.277229i	−0.0220516	−	0.999757i	$-0.507020\pi$
$389$	13.2005	−	5.46781i	0.669290	−	0.277229i	0.691342	+	0.722528i	$0.257020\pi$
$390$	−19.5977	−	9.87019i	−0.992369	−	0.499797i
$391$	−14.8960	−	14.8960i	−0.753323	−	0.753323i
$392$	13.6931	+	14.3003i	0.691606	+	0.722275i
$393$	11.2060	−	4.31159i	0.565268	−	0.217491i
$394$	0.780731	−	0.708513i	0.0393327	−	0.0356943i
$395$	−6.14022	+	2.54336i	−0.308948	+	0.127970i
$396$	−14.8771	+	24.7957i	−0.747605	+	1.24603i
$397$	−3.51259	−	1.45496i	−0.176292	−	0.0730224i	0.292792	−	0.956176i	$-0.405416\pi$
$397$	−3.51259	−	1.45496i	−0.176292	−	0.0730224i	−0.469084	+	0.883154i	$0.655416\pi$
$398$	−16.7655	−	7.91651i	−0.840377	−	0.396819i
$399$	7.78350	−	12.6212i	0.389662	−	0.631848i
$400$	25.2752	+	37.6207i	1.26376	+	1.88104i
$401$	24.2428			1.21063			0.605313	−	0.795988i	$-0.293048\pi$
$401$	24.2428			1.21063			0.605313	+	0.795988i	$0.293048\pi$
$402$	10.6113	−	9.14921i	0.529244	−	0.456321i
$403$	1.52269	−	3.67610i	0.0758507	−	0.183120i
$404$	−28.5257	−	15.2010i	−1.41921	−	0.756278i
$405$	−10.4383	−	34.8400i	−0.518682	−	1.73122i
$406$	−17.6500	−	25.6648i	−0.875955	−	1.27372i
$407$	20.8226	−	20.8226i	1.03214	−	1.03214i
$408$	28.2936	−	6.38442i	1.40074	−	0.316076i
$409$	−27.8713	−	27.8713i	−1.37815	−	1.37815i	−0.847746	−	0.530403i	$-0.822041\pi$
$409$	−27.8713	−	27.8713i	−1.37815	−	1.37815i	−0.530403	−	0.847746i	$-0.677959\pi$
$410$	0.767970	−	15.8366i	0.0379274	−	0.782115i
$411$	−0.378275	+	14.8889i	−0.0186589	+	0.734415i
$412$	−14.8431	−	1.44297i	−0.731266	−	0.0710901i
$413$	13.2541	+	7.71621i	0.652192	+	0.379690i
$414$	13.3055	+	7.13048i	0.653931	+	0.350444i
$415$	−29.4252			−1.44443
$416$	−3.00847	+	12.1736i	−0.147502	+	0.596859i
$417$	1.18674	+	0.527264i	0.0581150	+	0.0258202i
$418$	7.44288	+	20.7601i	0.364043	+	1.01541i
$419$	21.5079	+	8.90885i	1.05073	+	0.435226i	0.840152	−	0.542352i	$-0.182466\pi$
$419$	21.5079	+	8.90885i	1.05073	+	0.435226i	0.210576	+	0.977577i	$0.432466\pi$
$420$	22.4005	−	29.4957i	1.09303	−	1.43924i
$421$	0.152458	+	0.368065i	0.00743033	+	0.0179384i	0.927551	−	0.373696i	$-0.121910\pi$
$421$	0.152458	+	0.368065i	0.00743033	+	0.0179384i	−0.920121	+	0.391635i	$0.871910\pi$
$422$	0.229097	−	4.72431i	0.0111523	−	0.229976i
$423$	5.25203	+	0.267044i	0.255362	+	0.0129841i
$424$	8.35196	+	1.22272i	0.405607	+	0.0593803i
$425$	47.4361	+	47.4361i	2.30099	+	2.30099i
$426$	−17.3582	+	5.73003i	−0.841007	+	0.277621i
$427$	5.26847	+	19.9501i	0.254959	+	0.965451i
$428$	2.97808	+	1.58698i	0.143951	+	0.0767095i
$429$	−12.7479	−	13.4125i	−0.615472	−	0.647562i
$430$	−8.09350	−	3.82168i	−0.390303	−	0.184298i
$431$	27.0998			1.30535			0.652675	−	0.757638i	$-0.273647\pi$
$431$	27.0998			1.30535			0.652675	+	0.757638i	$0.273647\pi$
$432$	−18.0849	+	10.2439i	−0.870109	+	0.492860i
$433$	9.68673			0.465515			0.232757	−	0.972535i	$-0.425225\pi$
$433$	9.68673			0.465515			0.232757	+	0.972535i	$0.425225\pi$
$434$	5.63371	+	3.65622i	0.270427	+	0.175504i
$435$	−42.2349	+	40.1420i	−2.02501	+	1.92466i
$436$	3.63773	+	11.9376i	0.174216	+	0.571709i
$437$	10.6368	−	4.40592i	0.508829	−	0.210764i
$438$	0.345019	+	1.04518i	0.0164856	+	0.0499405i
$439$	6.10283	−	6.10283i	0.291272	−	0.291272i	−0.546311	−	0.837583i	$-0.683968\pi$
$439$	6.10283	−	6.10283i	0.291272	−	0.291272i	0.837583	+	0.546311i	$0.183968\pi$
$440$	13.4860	+	53.4095i	0.642922	+	2.54620i
$441$	−19.9351	−	6.60237i	−0.949291	−	0.314399i
$442$	−0.899021	+	18.5391i	−0.0427621	+	0.881814i
$443$	−14.5181	+	6.01360i	−0.689776	+	0.285715i	−0.699907	−	0.714234i	$-0.746775\pi$
$443$	−14.5181	+	6.01360i	−0.689776	+	0.285715i	0.0101307	+	0.999949i	$0.496775\pi$
$444$	20.3974	−	5.65366i	0.968019	−	0.268311i
$445$	52.3897	+	21.7005i	2.48351	+	1.02870i
$446$	2.42155	+	6.75430i	0.114663	+	0.319826i
$447$	−9.62938	−	4.27829i	−0.455454	−	0.202356i
$448$	−19.2809	−	8.73186i	−0.910939	−	0.412542i
$449$		−	36.8532i		−	1.73921i	−0.493749	−	0.869604i	$-0.664374\pi$
$449$		−	36.8532i		−	1.73921i	0.493749	−	0.869604i	$-0.335626\pi$
$450$	−42.3712	−	22.7069i	−1.99740	−	1.07041i
$451$	5.11667	−	12.3527i	0.240934	−	0.581667i
$452$	0.463385	−	0.381271i	0.0217958	−	0.0179335i
$453$	−1.95035	−	0.0495517i	−0.0916356	−	0.00232814i
$454$	−13.3494	−	0.647357i	−0.626519	−	0.0303820i
$455$	14.3603	+	18.8553i	0.673221	+	0.883949i
$456$	−2.69387	+	15.6215i	−0.126152	+	0.731542i
$457$	−13.8249	−	13.8249i	−0.646700	−	0.646700i	0.305494	−	0.952194i	$-0.401179\pi$
$457$	−13.8249	−	13.8249i	−0.646700	−	0.646700i	−0.952194	+	0.305494i	$0.901179\pi$
$458$	−19.7366	+	17.9110i	−0.922231	+	0.836924i
$459$	−23.3467	+	20.0345i	−1.08973	+	0.935131i
$460$	27.5086	−	8.38262i	1.28259	−	0.390842i
$461$	−4.69409	+	11.3325i	−0.218626	+	0.527809i	−0.994699	−	0.102834i	$-0.967209\pi$
$461$	−4.69409	+	11.3325i	−0.218626	+	0.527809i	0.776073	+	0.630643i	$0.217209\pi$
$462$	26.1761	−	17.0389i	1.21782	−	0.792722i
$463$		−	35.7374i		−	1.66086i	−0.557125	−	0.830429i	$-0.688096\pi$
$463$		−	35.7374i		−	1.66086i	0.557125	−	0.830429i	$-0.311904\pi$
$464$	27.7335	+	18.4297i	1.28750	+	0.855578i
$465$	5.10120	−	11.4815i	0.236562	−	0.532443i
$466$	5.32829	−	11.2842i	0.246828	−	0.522729i
$467$	2.10193	−	5.07450i	0.0972657	−	0.234820i	−0.867756	−	0.496991i	$-0.834438\pi$
$467$	2.10193	−	5.07450i	0.0972657	−	0.234820i	0.965022	+	0.262171i	$0.0844383\pi$
$468$	−3.22594	−	12.9033i	−0.149119	−	0.596457i
$469$	−14.6320	+	3.86406i	−0.675643	+	0.178426i
$470$	7.41864	−	6.73241i	0.342196	−	0.310543i
$471$	−8.93338	−	23.2182i	−0.411628	−	1.06984i
$472$	−16.2226	−	2.37497i	−0.746705	−	0.109317i
$473$	−5.33707	−	5.33707i	−0.245399	−	0.245399i
$474$	−3.59793	−	1.81206i	−0.165259	−	0.0832308i
$475$	−33.8728	+	14.0306i	−1.55419	+	0.643768i
$476$	−30.4938	−	7.18564i	−1.39768	−	0.329353i
$477$	−8.43482	+	3.00172i	−0.386204	+	0.137439i
$478$	17.7238	−	6.35432i	0.810669	−	0.290640i
$479$	14.1328			0.645743			0.322871	−	0.946443i	$-0.395352\pi$
$479$	14.1328			0.645743			0.322871	+	0.946443i	$0.395352\pi$
$480$	−10.4725	+	38.1847i	−0.478003	+	1.74289i
$481$			13.5448i			0.617591i
$482$	32.4079	−	11.6189i	1.47614	−	0.529224i
$483$	−9.54658	−	13.2183i	−0.434385	−	0.601454i
$484$	−2.36605	+	24.3383i	−0.107548	+	1.10629i
$485$	−48.6221	+	20.1400i	−2.20782	+	0.914508i
$486$	11.8622	−	18.5819i	0.538082	−	0.842893i
$487$	−9.14130	+	9.14130i	−0.414232	+	0.414232i	−0.883210	−	0.468978i	$-0.844622\pi$
$487$	−9.14130	+	9.14130i	−0.414232	+	0.414232i	0.468978	+	0.883210i	$0.344622\pi$
$488$	−13.1739	−	17.6927i	−0.596355	−	0.800913i
$489$	17.1643	−	6.60410i	0.776196	−	0.298648i
$490$	−35.7049	+	18.0436i	−1.61298	+	0.815127i
$491$	−10.7789	−	26.0226i	−0.486446	−	1.17438i	−0.956496	−	0.291745i	$-0.905764\pi$
$491$	−10.7789	−	26.0226i	−0.486446	−	1.17438i	0.470050	−	0.882640i	$-0.344236\pi$
$492$	7.57400	−	5.91576i	0.341462	−	0.266703i
$493$	45.5354	+	18.8614i	2.05081	+	0.849475i
$494$	−9.17284	−	4.33134i	−0.412705	−	0.194876i
$495$	−39.1631	−	43.3590i	−1.76025	−	1.94884i
$496$	−7.04542	−	1.38291i	−0.316349	−	0.0620947i
$497$	19.5658	+	2.64779i	0.877644	+	0.118770i
$498$	−11.6468	−	13.5081i	−0.521907	−	0.605311i
$499$	−4.20424	+	10.1499i	−0.188207	+	0.454373i	−0.989615	−	0.143746i	$-0.954085\pi$
$499$	−4.20424	+	10.1499i	−0.188207	+	0.454373i	0.801407	+	0.598119i	$0.204085\pi$
$500$	−48.9443	+	14.9147i	−2.18885	+	0.667004i
$501$	−1.01587	+	39.9848i	−0.0453859	+	1.78639i
$502$	4.39843	+	4.84676i	0.196312	+	0.216322i
$503$	−21.2822	−	21.2822i	−0.948925	−	0.948925i	0.0498330	−	0.998758i	$-0.484131\pi$
$503$	−21.2822	−	21.2822i	−0.948925	−	0.948925i	−0.998758	+	0.0498330i	$0.984131\pi$
$504$	22.4068	−	1.39146i	0.998077	−	0.0619807i
$505$	46.1819	−	46.1819i	2.05507	−	2.05507i
$506$	24.2223	+	1.17462i	1.07681	+	0.0522181i
$507$	−14.0009	−	0.355714i	−0.621802	−	0.0157978i
$508$	−33.1721	+	27.2939i	−1.47178	+	1.21097i
$509$	13.5364	+	5.60697i	0.599992	+	0.248525i	0.661943	−	0.749554i	$-0.269732\pi$
$509$	13.5364	+	5.60697i	0.599992	+	0.248525i	−0.0619509	+	0.998079i	$0.519732\pi$
$510$	−4.32452	+	58.4466i	−0.191493	+	2.58806i
$511$	0.159430	−	1.17810i	0.00705276	−	0.0521161i
$512$	22.6061	+	0.981699i	0.999058	+	0.0433854i
$513$	−5.23305	−	15.9785i	−0.231045	−	0.705469i
$514$	−11.3435	+	4.06686i	−0.500340	+	0.179381i
$515$	11.5313	−	27.8390i	0.508130	−	1.22673i
$516$	−1.44910	−	5.22810i	−0.0637931	−	0.230154i
$517$	7.80501	−	3.23294i	0.343264	−	0.142185i
$518$	−22.4808	−	4.15974i	−0.987749	−	0.182768i
$519$	7.04035	+	18.2981i	0.309037	+	0.803199i
$520$	−21.7573	−	12.9848i	−0.954123	−	0.569423i
$521$	−2.56181	−	2.56181i	−0.112235	−	0.112235i	0.648759	−	0.760994i	$-0.275288\pi$
$521$	−2.56181	−	2.56181i	−0.112235	−	0.112235i	−0.760994	+	0.648759i	$0.775288\pi$
$522$	−35.1448	−	3.49988i	−1.53824	−	0.153186i
$523$	−6.73643	−	16.2632i	−0.294563	−	0.711139i	−0.999997	−	0.00236328i	$-0.999248\pi$
$523$	−6.73643	−	16.2632i	−0.294563	−	0.711139i	0.705434	−	0.708776i	$-0.250752\pi$
$524$	13.2622	−	4.04136i	0.579362	−	0.176548i
$525$	30.4009	+	42.0935i	1.32681	+	1.83711i
$526$	−22.3424	−	10.5499i	−0.974176	−	0.459997i
$527$	−10.6273			−0.462933
$528$	−19.1804	+	27.3310i	−0.834721	+	1.18943i
$529$			10.3400i			0.449563i
$530$	−7.28244	+	15.4226i	−0.316329	+	0.669917i
$531$	16.3835	−	5.83045i	0.710985	−	0.253020i
$532$	10.0059	−	13.8943i	0.433811	−	0.602392i
$533$	2.35348	+	5.68181i	0.101941	+	0.246107i
$534$	10.7745	+	32.6395i	0.466258	+	1.41245i
$535$	−4.82137	+	4.82137i	−0.208446	+	0.208446i
$536$	12.9764	−	9.66215i	0.560495	−	0.417341i
$537$	−26.6106	+	10.2386i	−1.14833	+	0.441829i
$538$	0.428225	−	8.83060i	0.0184621	−	0.380714i
$539$	−33.4780	+	4.16174i	−1.44200	+	0.179259i
$540$	−9.14791	−	40.9882i	−0.393663	−	1.76385i
$541$	28.3964	+	11.7622i	1.22086	+	0.505696i	0.897682	−	0.440644i	$-0.145250\pi$
$541$	28.3964	+	11.7622i	1.22086	+	0.505696i	0.323175	+	0.946339i	$0.395250\pi$
$542$	3.14656	−	1.12810i	0.135156	−	0.0484561i
$543$	26.0152	+	11.5584i	1.11642	+	0.496020i
$544$	33.1139	−	5.01898i	1.41975	−	0.215187i
$545$	−25.2158			−1.08013
$546$	−2.97182	+	14.0554i	−0.127182	+	0.601516i
$547$	−14.3475	−	5.94294i	−0.613456	−	0.254102i	0.0542495	−	0.998527i	$-0.482723\pi$
$547$	−14.3475	−	5.94294i	−0.613456	−	0.254102i	−0.667705	+	0.744426i	$0.732723\pi$
$548$	−1.66404	+	17.1171i	−0.0710843	+	0.731205i
$549$	21.1332	+	10.0397i	0.901944	+	0.428482i
$550$	−77.1354	−	3.74055i	−3.28906	−	0.159498i
$551$	−19.0472	+	19.0472i	−0.811440	+	0.811440i
$552$	14.7364	+	9.31026i	0.627221	+	0.396271i
$553$	2.63640	+	3.46163i	0.112111	+	0.147203i
$554$	28.6375	−	25.9885i	1.21669	−	1.10414i
$555$	−1.08624	+	42.7544i	−0.0461083	+	1.81482i
$556$	1.32333	+	0.705184i	0.0561216	+	0.0299065i
$557$	22.2731	+	9.22580i	0.943739	+	0.390910i	0.800874	−	0.598832i	$-0.204368\pi$
$557$	22.2731	+	9.22580i	0.943739	+	0.390910i	0.142865	+	0.989742i	$0.454368\pi$
$558$	7.28987	−	2.20274i	0.308605	−	0.0932495i
$559$	3.47170			0.146837
$560$	28.2332	−	32.1236i	1.19307	−	1.35747i
$561$	−20.0665	+	45.1648i	−0.847210	+	1.90686i
$562$	25.7012	+	12.1359i	1.08414	+	0.511922i
$563$	8.30361	−	20.0467i	0.349956	−	0.844867i	−0.646669	−	0.762771i	$-0.723838\pi$
$563$	8.30361	−	20.0467i	0.349956	−	0.844867i	0.996624	−	0.0820965i	$-0.0261616\pi$
$564$	6.02699	+	0.740869i	0.253782	+	0.0311962i
$565$	0.464002	+	1.12020i	0.0195207	+	0.0471271i
$566$	3.93488	−	3.57090i	0.165395	−	0.150096i
$567$	−20.3090	+	12.4316i	−0.852899	+	0.522076i
$568$	−20.4650	+	5.16748i	−0.858693	+	0.216823i
$569$	−12.4485	−	12.4485i	−0.521869	−	0.521869i	0.396266	−	0.918136i	$-0.370306\pi$
$569$	−12.4485	−	12.4485i	−0.521869	−	0.521869i	−0.918136	+	0.396266i	$0.870306\pi$
$570$	−28.6068	−	14.4075i	−1.19821	−	0.603465i
$571$	−1.63836	−	3.95535i	−0.0685632	−	0.165526i	0.885883	−	0.463908i	$-0.153553\pi$
$571$	−1.63836	−	3.95535i	−0.0685632	−	0.165526i	−0.954447	+	0.298382i	$0.903553\pi$
$572$	−13.5758	−	16.4996i	−0.567632	−	0.689881i
$573$	−23.2951	−	24.5096i	−0.973166	−	1.02390i
$574$	−10.1531	+	2.16121i	−0.423780	+	0.0902074i
$575$			40.3157i			1.68128i
$576$	−21.6744	+	10.3064i	−0.903099	+	0.429432i
$577$			31.1610i			1.29725i	0.761109	+	0.648625i	$0.224655\pi$
$577$			31.1610i			1.29725i	−0.761109	+	0.648625i	$0.775345\pi$
$578$	24.0339	−	8.61659i	0.999677	−	0.358403i
$579$	5.98811	−	5.69138i	0.248857	−	0.236526i
$580$	−51.9558	+	42.7490i	−2.15735	+	1.77506i
$581$	4.91890	+	18.6263i	0.204070	+	0.772751i
$582$	−28.4907	−	14.3491i	−1.18098	−	0.594788i
$583$	−10.1701	+	10.1701i	−0.421203	+	0.421203i
$584$	0.311146	+	1.23225i	0.0128753	+	0.0509908i
$585$	26.8398	+	1.36469i	1.10969	+	0.0564230i
$586$	−9.64900	−	10.6325i	−0.398597	−	0.439225i
$587$	−25.7742	+	10.6760i	−1.06382	+	0.440647i	−0.844805	−	0.535075i	$-0.820283\pi$
$587$	−25.7742	+	10.6760i	−1.06382	+	0.440647i	−0.219012	+	0.975722i	$0.570283\pi$
$588$	−22.4155	−	9.24896i	−0.924402	−	0.381421i
$589$	2.22267	−	5.36601i	0.0915836	−	0.221102i
$590$	14.1452	−	29.9564i	0.582348	−	1.23329i
$591$	−0.524275	+	1.18001i	−0.0215658	+	0.0485393i
$592$	23.9592	−	4.82878i	0.984716	−	0.198461i
$593$		−	14.8502i		−	0.609823i	−0.952381	−	0.304911i	$-0.901373\pi$
$593$		−	14.8502i		−	0.609823i	0.952381	−	0.304911i	$-0.0986269\pi$
$594$	4.40337	−	35.1403i	0.180673	−	1.44183i
$595$	31.8488	−	54.7066i	1.30567	−	2.24275i
$596$	−10.7377	−	5.72197i	−0.439832	−	0.234381i
$597$	22.7001	+	0.576731i	0.929054	+	0.0236040i
$598$	−8.26017	+	7.49610i	−0.337784	+	0.306538i
$599$	15.8395	−	15.8395i	0.647185	−	0.647185i	−0.305127	−	0.952312i	$-0.598699\pi$
$599$	15.8395	−	15.8395i	0.647185	−	0.647185i	0.952312	+	0.305127i	$0.0986988\pi$
$600$	−46.9277	−	29.6484i	−1.91581	−	1.21039i
$601$	31.3594	+	31.3594i	1.27918	+	1.27918i	0.941128	+	0.338050i	$0.109767\pi$
$601$	31.3594	+	31.3594i	1.27918	+	1.27918i	0.338050	+	0.941128i	$0.390233\pi$
$602$	−1.06619	+	5.76209i	−0.0434546	+	0.234845i
$603$	−7.36339	+	15.4998i	−0.299860	+	0.631199i
$604$	−2.24223	−	0.217979i	−0.0912350	−	0.00886943i
$605$	−45.6479	−	18.9080i	−1.85585	−	0.768719i
$606$	39.4797	+	2.92114i	1.60375	+	0.118663i
$607$			23.0811i			0.936834i	0.883508	+	0.468417i	$0.155175\pi$
$607$			23.0811i			0.936834i	−0.883508	+	0.468417i	$0.844825\pi$
$608$	−4.39146	+	17.7698i	−0.178097	+	0.720659i
$609$	32.4703	+	20.0245i	1.31576	+	0.811436i
$610$	41.9560	−	15.0420i	1.69875	−	0.609033i
$611$	−1.48704	+	3.59003i	−0.0601591	+	0.145237i
$612$	−28.5424	+	21.1486i	−1.15376	+	0.854881i
$613$	1.40417	+	3.38996i	0.0567138	+	0.136919i	0.949697	−	0.313172i	$-0.101392\pi$
$613$	1.40417	+	3.38996i	0.0567138	+	0.136919i	−0.892983	+	0.450091i	$0.851392\pi$
$614$	−7.59247	−	0.368184i	−0.306407	−	0.0148587i
$615$	6.97313	+	18.1234i	0.281184	+	0.730807i
$616$	31.5541	−	17.4650i	1.27135	−	0.703684i
$617$	−12.2100	+	12.2100i	−0.491555	+	0.491555i	−0.908796	−	0.417241i	$-0.862997\pi$
$617$	−12.2100	+	12.2100i	−0.491555	+	0.491555i	0.417241	+	0.908796i	$0.362997\pi$
$618$	17.3441	−	5.72539i	0.697683	−	0.230309i
$619$	2.53977	+	6.13155i	0.102082	+	0.246448i	0.966666	−	0.256040i	$-0.0824180\pi$
$619$	2.53977	+	6.13155i	0.102082	+	0.246448i	−0.864584	+	0.502488i	$0.832418\pi$
$620$	6.82255	−	12.8030i	0.274000	−	0.514180i
$621$	−18.4348	−	1.40751i	−0.739761	−	0.0564815i
$622$	−28.6402	−	13.5237i	−1.14837	−	0.542250i
$623$	4.97878	−	36.7905i	0.199471	−	1.47398i
$624$	−2.65092	−	15.1276i	−0.106122	−	0.605587i
$625$		−	46.7312i		−	1.86925i
$626$	−39.6048	−	18.7010i	−1.58293	−	0.747444i
$627$	−18.6080	−	19.5782i	−0.743134	−	0.781879i
$628$	−8.37347	−	27.4785i	−0.334138	−	1.09651i
$629$	33.4226	−	13.8441i	1.33265	−	0.552000i
$630$	−10.5078	+	44.1277i	−0.418639	+	1.75809i
$631$	27.7925	+	27.7925i	1.10640	+	1.10640i	0.993620	+	0.112784i	$0.0359768\pi$
$631$	27.7925	+	27.7925i	1.10640	+	1.10640i	0.112784	+	0.993620i	$0.464023\pi$
$632$	−3.99442	−	2.38388i	−0.158889	−	0.0948256i
$633$	2.08019	+	5.40649i	0.0826801	+	0.214889i
$634$	0.852975	−	17.5895i	0.0338759	−	0.698570i
$635$	−33.2163	−	80.1913i	−1.31815	−	3.18229i
$636$	−9.96245	+	2.76134i	−0.395037	+	0.109494i
$637$	9.53495	−	12.2421i	0.377788	−	0.485050i
$638$	−53.4093	+	19.1482i	−2.11449	+	0.758086i
$639$	16.6140	−	15.0062i	0.657238	−	0.593636i
$640$	−15.2120	+	43.1152i	−0.601309	+	1.70428i
$641$		−	5.78369i		−	0.228442i	−0.993455	−	0.114221i	$-0.963563\pi$
$641$		−	5.78369i		−	0.228442i	0.993455	−	0.114221i	$-0.0364372\pi$
$642$	−4.12167	−	0.304966i	−0.162669	−	0.0120361i
$643$	17.9708	−	43.3854i	0.708700	−	1.71095i	0.00547659	−	0.999985i	$-0.498257\pi$
$643$	17.9708	−	43.3854i	0.708700	−	1.71095i	0.703224	−	0.710969i	$-0.251743\pi$
$644$	−9.90474	−	16.0118i	−0.390301	−	0.630953i
$645$	10.9584	+	0.278416i	0.431488	+	0.0109626i
$646$	−1.31230	+	27.0615i	−0.0516318	+	1.06472i
$647$	−13.8409	+	13.8409i	−0.544142	+	0.544142i	−0.924741	−	0.380598i	$-0.875718\pi$
$647$	−13.8409	+	13.8409i	−0.544142	+	0.544142i	0.380598	+	0.924741i	$0.375718\pi$
$648$	15.1954	−	20.4231i	0.596930	−	0.802293i
$649$	19.7541	−	19.7541i	0.775416	−	0.775416i
$650$	26.3044	−	23.8712i	1.03174	−	0.936306i
$651$	−8.12062	−	1.30976i	−0.318272	−	0.0513337i
$652$	20.3138	−	6.19018i	0.795550	−	0.242426i
$653$	12.5602	+	5.20261i	0.491519	+	0.203594i	0.614655	−	0.788796i	$-0.289295\pi$
$653$	12.5602	+	5.20261i	0.491519	+	0.203594i	−0.123136	+	0.992390i	$0.539295\pi$
$654$	−9.98069	−	11.5757i	−0.390276	−	0.452645i
$655$			28.0137i			1.09459i
$656$	9.21141	−	6.18861i	0.359645	−	0.241625i
$657$	−0.903559	−	1.00037i	−0.0352512	−	0.0390280i
$658$	−5.50180	−	3.57061i	−0.214482	−	0.139197i
$659$	28.5918	+	11.8431i	1.11378	+	0.461343i	0.862238	−	0.506504i	$-0.169062\pi$
$659$	28.5918	+	11.8431i	1.11378	+	0.461343i	0.251542	+	0.967846i	$0.419062\pi$
$660$	−41.5289	−	53.1697i	−1.61651	−	2.06963i
$661$	−0.104102	−	0.251323i	−0.00404908	−	0.00977534i	0.921842	−	0.387566i	$-0.126684\pi$
$661$	−0.104102	−	0.251323i	−0.00404908	−	0.00977534i	−0.925891	+	0.377790i	$0.876684\pi$
$662$	−16.8365	+	15.2792i	−0.654371	+	0.593841i
$663$	−8.16306	−	21.2161i	−0.317027	−	0.823965i
$664$	−12.2998	−	16.5188i	−0.477325	−	0.641054i
$665$	20.9617	+	27.5230i	0.812860	+	1.06730i
$666$	−20.0569	+	16.4240i	−0.777191	+	0.636417i
$667$	11.3351	+	27.3653i	0.438896	+	1.05959i
$668$	−4.46885	+	45.9686i	−0.172905	+	1.77858i
$669$	−6.05414	−	6.36979i	−0.234066	−	0.246270i
$670$	11.0323	+	30.7718i	0.426214	+	1.18882i
$671$	37.5860			1.45099
$672$	25.9218	+	0.245985i	0.999955	+	0.00948907i
$673$	−37.5660			−1.44806			−0.724031	−	0.689768i	$-0.757713\pi$
$673$	−37.5660			−1.44806			−0.724031	+	0.689768i	$0.757713\pi$
$674$	−15.1406	−	42.2310i	−0.583194	−	1.62668i
$675$	58.7052	+	4.48220i	2.25956	+	0.172520i
$676$	−16.0962	−	1.56479i	−0.619084	−	0.0601844i
$677$	−3.25480	−	7.85779i	−0.125092	−	0.301999i	0.848910	−	0.528537i	$-0.177259\pi$
$677$	−3.25480	−	7.85779i	−0.125092	−	0.301999i	−0.974002	+	0.226538i	$0.927259\pi$
$678$	−0.330586	+	0.656394i	−0.0126961	+	0.0252086i
$679$	20.8767	+	27.4114i	0.801173	+	1.05195i
$680$	−9.80272	+	66.9591i	−0.375917	+	2.56776i
$681$	15.2770	−	5.87796i	0.585418	−	0.225244i
$682$	9.05949	−	8.22148i	0.346906	−	0.314817i
$683$	−6.14501	−	14.8354i	−0.235132	−	0.567659i	0.761635	−	0.648007i	$-0.224397\pi$
$683$	−6.14501	−	14.8354i	−0.235132	−	0.567659i	−0.996767	+	0.0803473i	$0.974397\pi$
$684$	−4.70890	−	18.8350i	−0.180049	−	0.720174i
$685$	−32.1041	−	13.2979i	−1.22663	−	0.508088i
$686$	17.3903	+	19.5851i	0.663966	+	0.747763i
$687$	13.2535	−	29.8303i	0.505652	−	1.13810i
$688$	−1.23767	−	6.14101i	−0.0471858	−	0.234124i
$689$		−	6.61553i		−	0.252031i
$690$	−26.6745	+	22.9991i	−1.01548	+	0.875560i
$691$	21.8932	+	9.06848i	0.832858	+	0.344981i	0.758034	−	0.652216i	$-0.226160\pi$
$691$	21.8932	+	9.06848i	0.832858	+	0.344981i	0.0748246	+	0.997197i	$0.476160\pi$
$692$	6.59909	+	21.6557i	0.250860	+	0.823226i
$693$	−20.8998	+	32.0386i	−0.793916	+	1.21705i
$694$	−15.1774	+	13.7735i	−0.576127	+	0.522834i
$695$	−2.14241	+	2.14241i	−0.0812662	+	0.0812662i
$696$	−40.1892	−	6.93049i	−1.52337	−	0.262700i
$697$	11.6147	−	11.6147i	0.439937	−	0.439937i
$698$	−1.46014	+	30.1101i	−0.0552671	+	1.13968i
$699$	−0.388175	+	15.2786i	−0.0146821	+	0.577888i
$700$	31.5415	+	50.9893i	1.19216	+	1.92721i
$701$	−13.7735	+	33.2523i	−0.520219	+	1.25592i	0.417547	+	0.908655i	$0.362890\pi$
$701$	−13.7735	+	33.2523i	−0.520219	+	1.25592i	−0.937767	+	0.347266i	$0.887110\pi$
$702$	9.99700	+	12.8613i	0.377313	+	0.485420i
$703$			19.7714i			0.745692i
$704$	−24.3459	+	29.8961i	−0.917571	+	1.12675i
$705$	−4.98175	+	11.2127i	−0.187624	+	0.422294i
$706$	16.6563	−	5.97161i	0.626869	−	0.224744i
$707$	−36.9534	−	21.5134i	−1.38978	−	0.809093i
$708$	19.3508	−	5.36355i	0.727246	−	0.201574i
$709$	−0.562810	−	1.35874i	−0.0211368	−	0.0510287i	0.912959	−	0.408052i	$-0.133792\pi$
$709$	−0.562810	−	1.35874i	−0.0211368	−	0.0510287i	−0.934096	+	0.357023i	$0.883792\pi$
$710$	2.06575	−	42.5986i	0.0775262	−	1.59870i
$711$	4.92750	+	0.250543i	0.184796	+	0.00939609i
$712$	9.71669	+	38.4815i	0.364148	+	1.44215i
$713$	−4.51605	−	4.51605i	−0.169127	−	0.169127i
$714$	37.7199	−	7.03284i	1.41163	−	0.263197i
$715$	39.8865	−	16.5215i	1.49167	−	0.617870i
$716$	−31.4934	+	9.59691i	−1.17696	+	0.358653i
$717$	−16.7148	+	15.8865i	−0.624226	+	0.593293i
$718$	27.2498	+	12.8671i	1.01696	+	0.480198i
$719$		−	8.32879i		−	0.310611i	−0.987866	−	0.155306i	$-0.950364\pi$
$719$		−	8.32879i		−	0.310611i	0.987866	−	0.155306i	$-0.0496362\pi$
$720$	−7.15449	−	47.9628i	−0.266632	−	1.78747i
$721$	−19.5499	−	2.64564i	−0.728076	−	0.0985289i
$722$	10.9079	+	5.15062i	0.405950	+	0.191686i
$723$	−30.5630	+	29.0484i	−1.13665	+	1.08032i
$724$	29.0094	+	15.4587i	1.07812	+	0.574519i
$725$	−36.0964	−	87.1444i	−1.34059	−	3.23646i
$726$	−9.38797	−	28.4393i	−0.348420	−	1.05548i
$727$	30.5210	−	30.5210i	1.13196	−	1.13196i	0.142110	−	0.989851i	$-0.454611\pi$
$727$	30.5210	−	30.5210i	1.13196	−	1.13196i	0.989851	−	0.142110i	$-0.0453887\pi$
$728$	−4.58239	+	15.9431i	−0.169835	+	0.590892i
$729$	−4.09906	+	26.6870i	−0.151817	+	0.988409i
$730$	−2.56497	−	0.124384i	−0.0949337	−	0.00460365i
$731$	−3.54840	−	8.56660i	−0.131242	−	0.316847i
$732$	23.5119	+	13.3067i	0.869025	+	0.491830i
$733$	−9.25903	+	22.3533i	−0.341990	+	0.825637i	0.655524	+	0.755174i	$0.272448\pi$
$733$	−9.25903	+	22.3533i	−0.341990	+	0.825637i	−0.997514	+	0.0704632i	$0.977552\pi$
$734$	29.7439	−	10.6637i	1.09787	−	0.393606i
$735$	31.0789	−	37.8776i	1.14636	−	1.39714i
$736$	16.2045	+	11.9389i	0.597305	+	0.440072i
$737$			27.5668i			1.01543i
$738$	−5.55977	+	10.3746i	−0.204658	+	0.381893i
$739$	30.1353	+	12.4824i	1.10854	+	0.459174i	0.860436	−	0.509558i	$-0.170191\pi$
$739$	30.1353	+	12.4824i	1.10854	+	0.459174i	0.248108	+	0.968732i	$0.420191\pi$
$740$	−4.77839	+	49.1527i	−0.175657	+	1.80689i
$741$	12.4198	+	0.315545i	0.456254	+	0.0115918i
$742$	10.9800	+	2.03169i	0.403088	+	0.0745855i
$743$	−14.6702	−	14.6702i	−0.538196	−	0.538196i	0.384803	−	0.922999i	$-0.374270\pi$
$743$	−14.6702	−	14.6702i	−0.538196	−	0.538196i	−0.922999	+	0.384803i	$0.874270\pi$
$744$	8.57783	−	1.93558i	0.314479	−	0.0709618i
$745$	17.3838	−	17.3838i	0.636893	−	0.636893i
$746$	−9.30118	+	8.44081i	−0.340540	+	0.309040i
$747$	19.7310	+	9.37350i	0.721920	+	0.342959i
$748$	−26.8378	+	50.3630i	−0.981287	+	1.84145i
$749$	3.85792	+	2.24599i	0.140965	+	0.0820665i
$750$	47.4602	−	40.9208i	1.73300	−	1.49422i
$751$		−	13.0083i		−	0.474680i	−0.971427	−	0.237340i	$-0.923725\pi$
$751$		−	13.0083i		−	0.474680i	0.971427	−	0.237340i	$-0.0762755\pi$
$752$	6.88045	+	1.35053i	0.250904	+	0.0492489i
$753$	−7.32550	−	3.25469i	−0.266956	−	0.118607i
$754$	11.1432	−	23.5989i	0.405811	−	0.859420i
$755$	1.74195	−	4.20543i	0.0633959	−	0.153051i
$756$	−24.4165	+	12.6425i	−0.888021	+	0.459803i
$757$	2.85258	−	1.18158i	0.103679	−	0.0429451i	−0.330241	−	0.943897i	$-0.607130\pi$
$757$	2.85258	−	1.18158i	0.103679	−	0.0429451i	0.433920	+	0.900951i	$0.357130\pi$
$758$	30.8773	+	34.0246i	1.12152	+	1.23583i
$759$	−27.7199	+	10.6655i	−1.00617	+	0.387132i
$760$	−31.7592	−	18.9540i	−1.15203	−	0.687533i
$761$	−29.1020	+	29.1020i	−1.05495	+	1.05495i	−0.0565482	+	0.998400i	$0.518009\pi$
$761$	−29.1020	+	29.1020i	−1.05495	+	1.05495i	−0.998400	+	0.0565482i	$0.981991\pi$
$762$	23.6655	−	46.9890i	0.857312	−	1.70223i
$763$	4.21522	+	15.9617i	0.152601	+	0.577854i
$764$	−24.8080	−	30.1508i	−0.897522	−	1.09082i
$765$	−24.0653	−	67.6234i	−0.870083	−	2.44493i
$766$	21.8287	−	7.82601i	0.788704	−	0.282765i
$767$			12.8498i			0.463979i
$768$	−25.8137	+	10.0822i	−0.931473	+	0.363809i
$769$			46.5819i			1.67979i	0.542751	+	0.839894i	$0.317383\pi$
$769$			46.5819i			1.67979i	−0.542751	+	0.839894i	$0.682617\pi$
$770$	15.1718	+	71.2748i	0.546754	+	2.56856i
$771$	10.6977	−	10.1676i	0.385269	−	0.366177i
$772$	7.36635	−	6.06101i	0.265121	−	0.218140i
$773$	5.80523	+	14.0151i	0.208800	+	0.504087i	0.993235	−	0.116124i	$-0.0370471\pi$
$773$	5.80523	+	14.0151i	0.208800	+	0.504087i	−0.784435	+	0.620211i	$0.787047\pi$
$774$	4.20966	+	5.14083i	0.151313	+	0.184783i
$775$	14.3813	+	14.3813i	0.516591	+	0.516591i
$776$	−31.6303	−	18.8771i	−1.13546	−	0.677647i
$777$	27.2453	−	6.45948i	0.977421	−	0.231732i
$778$	−14.9634	+	13.5793i	−0.536463	+	0.486840i
$779$	3.43538	+	8.29374i	0.123085	+	0.297154i
$780$	30.8001	+	3.78611i	1.10282	+	0.135565i
$781$	13.7632	−	33.2274i	0.492487	−	1.18897i
$782$	26.9397	+	12.7207i	0.963361	+	0.454891i
$783$	41.1078	−	13.4630i	1.46907	−	0.481129i
$784$	−25.0540	−	12.5018i	−0.894787	−	0.446493i
$785$	58.0428			2.07164
$786$	−12.8601	+	11.0881i	−0.458704	+	0.395500i
$787$	−35.5471	−	14.7241i	−1.26712	−	0.524857i	−0.355030	−	0.934855i	$-0.615529\pi$
$787$	−35.5471	−	14.7241i	−1.26712	−	0.524857i	−0.912086	+	0.409998i	$0.865529\pi$
$788$	−0.701187	+	1.31583i	−0.0249787	+	0.0468744i
$789$	30.2512	+	0.768577i	1.07697	+	0.0273621i
$790$	6.96024	−	6.31641i	0.247634	−	0.224728i
$791$	0.631527	−	0.480975i	0.0224545	−	0.0171015i
$792$	7.97072	−	40.1096i	0.283227	−	1.42523i
$793$	−12.2246	+	12.2246i	−0.434109	+	0.434109i
$794$	5.37052	+	0.260434i	0.190593	+	0.00924247i
$795$	0.530538	−	20.8820i	0.0188162	−	0.740607i
$796$	26.0973	+	2.53705i	0.924993	+	0.0899234i
$797$	16.3229	+	6.76115i	0.578186	+	0.239492i	0.652559	−	0.757738i	$-0.273696\pi$
$797$	16.3229	+	6.76115i	0.578186	+	0.239492i	−0.0743731	+	0.997230i	$0.523696\pi$
$798$	−4.33796	+	20.5167i	−0.153562	+	0.726283i
$799$	10.3785			0.367164
$800$	−51.6029	−	38.0191i	−1.82444	−	1.34418i
$801$	−28.2170	−	31.2401i	−0.996998	−	1.10382i
$802$	−32.2730	+	11.5705i	−1.13960	+	0.408568i
$803$	−2.00070	−	0.828717i	−0.0706032	−	0.0292448i
$804$	−9.75954	+	17.2443i	−0.344192	+	0.608161i
$805$	36.7815	−	9.71337i	1.29638	−	0.342351i
$806$	−0.272558	+	5.62053i	−0.00960045	+	0.197975i
$807$	3.88826	+	10.1057i	0.136873	+	0.355739i
$808$	45.2298	+	6.62158i	1.59118	+	0.232946i
$809$	−3.29677	+	3.29677i	−0.115908	+	0.115908i	−0.762682	−	0.646774i	$-0.776118\pi$
$809$	−3.29677	+	3.29677i	−0.115908	+	0.115908i	0.646774	+	0.762682i	$0.276118\pi$
$810$	30.5242	+	41.3986i	1.07251	+	1.45460i
$811$	0.0856246	+	0.206716i	0.00300669	+	0.00725879i	0.925376	−	0.379051i	$-0.123750\pi$
$811$	0.0856246	+	0.206716i	0.00300669	+	0.00725879i	−0.922369	+	0.386310i	$0.873750\pi$
$812$	35.7456	+	25.7421i	1.25443	+	0.903371i
$813$	−2.96743	+	2.82038i	−0.104072	+	0.0989151i
$814$	−17.7818	+	37.6580i	−0.623252	+	1.31991i
$815$			42.9087i			1.50303i
$816$	−34.6185	+	22.0031i	−1.21189	+	0.770261i
$817$	5.06764			0.177294
$818$	50.4058	+	23.8012i	1.76240	+	0.832190i
$819$	−3.62284	−	17.2179i	−0.126592	−	0.601641i
$820$	6.53608	+	21.4489i	0.228250	+	0.749029i
$821$	−8.48321	−	20.4803i	−0.296066	−	0.714767i	−0.999990	−	0.00449149i	$-0.998570\pi$
$821$	−8.48321	−	20.4803i	−0.296066	−	0.714767i	0.703924	−	0.710276i	$-0.251430\pi$
$822$	−6.60254	−	20.0013i	−0.230290	−	0.697625i
$823$	−8.90456	−	8.90456i	−0.310393	−	0.310393i	0.534669	−	0.845062i	$-0.320436\pi$
$823$	−8.90456	−	8.90456i	−0.310393	−	0.310393i	−0.845062	+	0.534669i	$0.820436\pi$
$824$	20.4484	−	5.16329i	0.712355	−	0.179872i
$825$	88.2737	−	33.9640i	3.07329	−	1.18247i
$826$	−21.3272	−	3.94628i	−0.742068	−	0.137309i
$827$	−42.7428	+	17.7046i	−1.48631	+	0.615651i	−0.970511	−	0.241057i	$-0.922506\pi$
$827$	−42.7428	+	17.7046i	−1.48631	+	0.615651i	−0.515802	+	0.856708i	$0.672506\pi$
$828$	−21.1161	−	3.14200i	−0.733835	−	0.109192i
$829$	−10.2143	+	24.6595i	−0.354758	+	0.856461i	0.641261	+	0.767323i	$0.278411\pi$
$829$	−10.2143	+	24.6595i	−0.354758	+	0.856461i	−0.996019	+	0.0891387i	$0.971589\pi$
$830$	39.1721	−	14.0439i	1.35968	−	0.487473i
$831$	−19.2306	+	43.2833i	−0.667102	+	1.50148i
$832$	−1.80515	−	17.6419i	−0.0625823	−	0.611621i
$833$	−39.9536	−	11.0154i	−1.38431	−	0.381661i
$834$	−1.83149	−	0.135514i	−0.0634194	−	0.00469246i
$835$	−86.2168	−	35.7122i	−2.98366	−	1.23587i
$836$	−19.8166	−	24.0844i	−0.685370	−	0.832977i
$837$	−7.07807	+	6.07390i	−0.244654	+	0.209945i
$838$	−32.8842	−	1.59466i	−1.13597	−	0.0550867i
$839$	37.8386	−	37.8386i	1.30633	−	1.30633i	0.382293	−	0.924041i	$-0.375135\pi$
$839$	37.8386	−	37.8386i	1.30633	−	1.30633i	0.924041	−	0.382293i	$-0.124865\pi$
$840$	−15.7429	+	49.9572i	−0.543182	+	1.72369i
$841$	−28.4966	−	28.4966i	−0.982640	−	0.982640i
$842$	−0.378627	−	0.417220i	−0.0130483	−	0.0143783i
$843$	−34.7989	−	0.884120i	−1.19854	−	0.0304507i
$844$	1.94981	+	6.39854i	0.0671153	+	0.220247i
$845$	12.5048	−	30.1893i	0.430179	−	1.03854i
$846$	−7.11918	+	2.15116i	−0.244762	+	0.0739585i
$847$	−4.33809	+	32.0562i	−0.149058	+	1.10146i
$848$	−11.7021	+	2.35846i	−0.401850	+	0.0809897i
$849$	−2.64234	+	5.94726i	−0.0906849	+	0.204109i
$850$	−85.7890	−	40.5088i	−2.94254	−	1.38944i
$851$	20.0859	+	8.31984i	0.688534	+	0.285200i
$852$	20.3732	−	15.9127i	0.697973	−	0.545160i
$853$	−17.2771	−	41.7105i	−0.591555	−	1.42814i	−0.882000	−	0.471249i	$-0.843803\pi$
$853$	−17.2771	−	41.7105i	−0.591555	−	1.42814i	0.290445	−	0.956892i	$-0.406197\pi$
$854$	−16.5353	−	24.0439i	−0.565826	−	0.822764i
$855$	39.1780	+	1.99204i	1.33986	+	0.0681263i
$856$	−4.72197	−	0.691290i	−0.161394	−	0.0236278i
$857$	8.08200	−	8.08200i	0.276076	−	0.276076i	−0.555465	−	0.831540i	$-0.687460\pi$
$857$	8.08200	−	8.08200i	0.276076	−	0.276076i	0.831540	+	0.555465i	$0.187460\pi$
$858$	23.3720	+	11.7711i	0.797905	+	0.401857i
$859$	12.3710	−	5.12424i	0.422093	−	0.174837i	−0.161518	−	0.986870i	$-0.551639\pi$
$859$	12.3710	−	5.12424i	0.422093	−	0.174837i	0.583612	+	0.812033i	$0.301639\pi$
$860$	12.5984	+	1.22476i	0.429602	+	0.0417639i
$861$	10.3066	−	7.44365i	0.351247	−	0.253679i
$862$	−36.0764	+	12.9341i	−1.22877	+	0.440536i
$863$			17.2356i			0.586706i	0.956004	+	0.293353i	$0.0947711\pi$
$863$			17.2356i			0.586706i	−0.956004	+	0.293353i	$0.905229\pi$
$864$	19.1862	−	22.2686i	0.652727	−	0.757593i
$865$	−45.7432			−1.55532
$866$	−12.8954	+	4.62324i	−0.438203	+	0.157104i
$867$	−22.6656	+	21.5425i	−0.769765	+	0.731620i
$868$	−9.24486	−	2.17849i	−0.313791	−	0.0739427i
$869$	7.32274	−	3.03318i	0.248407	−	0.102894i
$870$	37.0661	−	73.5964i	1.25666	−	2.49515i
$871$	−8.96591	−	8.96591i	−0.303798	−	0.303798i
$872$	−10.5402	−	14.1557i	−0.356938	−	0.479372i
$873$	39.0191	+	1.98396i	1.32060	+	0.0671468i
$874$	−12.0574	+	10.9421i	−0.407847	+	0.370121i
$875$	−65.4431	+	17.2824i	−2.21238	+	0.584252i
$876$	−0.958142	−	1.22672i	−0.0323726	−	0.0414469i
$877$	5.79116	−	13.9811i	0.195554	−	0.472108i	−0.795438	−	0.606036i	$-0.792759\pi$
$877$	5.79116	−	13.9811i	0.195554	−	0.472108i	0.990991	+	0.133927i	$0.0427589\pi$
$878$	−5.21161	+	11.0371i	−0.175883	+	0.372483i
$879$	16.0702	+	7.13993i	0.542035	+	0.240824i
$880$	−43.4442	−	64.6644i	−1.46451	−	2.17984i
$881$		−	5.06833i		−	0.170756i	−0.996349	−	0.0853782i	$-0.972790\pi$
$881$		−	5.06833i		−	0.170756i	0.996349	−	0.0853782i	$-0.0272098\pi$
$882$	29.6896	−	0.725182i	0.999702	−	0.0244181i
$883$	18.9145	−	45.6637i	0.636525	−	1.53671i	−0.194754	−	0.980852i	$-0.562391\pi$
$883$	18.9145	−	45.6637i	0.636525	−	1.53671i	0.831279	−	0.555855i	$-0.187609\pi$
$884$	−7.65143	−	25.1091i	−0.257346	−	0.844510i
$885$	−1.03050	+	40.5605i	−0.0346399	+	1.36342i
$886$	16.4570	−	14.9347i	0.552883	−	0.501741i
$887$	29.6244	+	29.6244i	0.994691	+	0.994691i	0.999986	−	0.00529486i	$-0.00168541\pi$
$887$	29.6244	+	29.6244i	0.994691	+	0.994691i	−0.00529486	+	0.999986i	$0.501685\pi$
$888$	−24.4556	+	17.2616i	−0.820675	+	0.579261i
$889$	−45.2089	+	34.4314i	−1.51626	+	1.15479i
$890$	−80.1005	−	3.88434i	−2.68498	−	0.130203i
$891$	12.4485	+	41.5498i	0.417042	+	1.39197i
$892$	−6.44733	−	7.83588i	−0.215873	−	0.262365i
$893$	−2.17063	+	5.24036i	−0.0726373	+	0.175362i
$894$	14.8610	+	1.09958i	0.497025	+	0.0367754i
$895$		−	66.5233i		−	2.22363i
$896$	29.8351	+	2.42191i	0.996721	+	0.0809103i
$897$	5.54686	−	12.4846i	0.185204	−	0.416849i
$898$	17.5891	+	49.0605i	0.586957	+	1.63717i
$899$	13.8051	+	5.71825i	0.460425	+	0.190714i
$900$	67.2439	+	10.0057i	2.24146	+	0.333522i
$901$	−16.3241	+	6.76168i	−0.543836	+	0.225264i
$902$	−0.915871	+	18.8865i	−0.0304952	+	0.628853i
$903$	−1.65564	−	6.98330i	−0.0550962	−	0.232390i
$904$	−0.434906	+	0.728727i	−0.0144648	+	0.0242371i
$905$	−46.9648	+	46.9648i	−1.56116	+	1.56116i
$906$	2.62004	−	0.864891i	0.0870451	−	0.0287341i
$907$	−23.7170	+	9.82390i	−0.787510	+	0.326197i	−0.739942	−	0.672671i	$-0.765147\pi$
$907$	−23.7170	+	9.82390i	−0.787510	+	0.326197i	−0.0475680	+	0.998868i	$0.515147\pi$
$908$	18.0803	−	5.50956i	0.600015	−	0.182841i
$909$	−45.6785	+	16.2557i	−1.51506	+	0.539168i
$910$	−28.1162	−	18.2471i	−0.932043	−	0.604887i
$911$	−13.5552			−0.449102			−0.224551	−	0.974462i	$-0.572092\pi$
$911$	−13.5552			−0.449102			−0.224551	+	0.974462i	$0.572092\pi$
$912$	−3.86955	−	22.0817i	−0.128134	−	0.731198i
$913$	35.0921			1.16138
$914$	25.0025	+	11.8060i	0.827011	+	0.390508i
$915$	−39.5675	+	37.6067i	−1.30806	+	1.24324i
$916$	17.7258	−	33.2636i	0.585676	−	1.09906i
$917$	17.7328	−	4.68293i	0.585589	−	0.154644i
$918$	21.5182	−	37.8136i	0.710205	−	1.24803i
$919$	12.0181	+	12.0181i	0.396442	+	0.396442i	0.876976	−	0.480534i	$-0.159557\pi$
$919$	12.0181	+	12.0181i	0.396442	+	0.396442i	−0.480534	+	0.876976i	$0.659557\pi$
$920$	−32.6198	+	24.2885i	−1.07544	+	0.800767i
$921$	8.68881	−	3.34309i	0.286306	−	0.110159i
$922$	0.840231	−	17.3267i	0.0276715	−	0.570626i
$923$	6.33059	+	15.2834i	0.208374	+	0.503059i
$924$	−26.7145	+	35.1762i	−0.878843	+	1.15721i
$925$	−63.9631	−	26.4944i	−2.10309	−	0.871130i
$926$	17.0566	+	47.5752i	0.560514	+	1.56342i
$927$	−16.6005	+	14.9940i	−0.545232	+	0.492469i
$928$	−45.7161	−	11.2979i	−1.50071	−	0.370871i
$929$	52.1055			1.70953			0.854763	−	0.519019i	$-0.173702\pi$
$929$	52.1055			1.70953			0.854763	+	0.519019i	$0.173702\pi$
$930$	−1.31107	+	17.7194i	−0.0429918	+	0.581042i
$931$	13.9182	−	17.8698i	0.456149	−	0.585659i
$932$	−1.70759	+	17.5650i	−0.0559340	+	0.575362i
$933$	38.7783	+	0.985222i	1.26955	+	0.0322547i
$934$	−0.376240	+	7.75860i	−0.0123110	+	0.253869i
$935$	−81.5354	−	81.5354i	−2.66649	−	2.66649i
$936$	10.4530	+	15.6378i	0.341666	+	0.511138i
$937$	−24.3231	+	24.3231i	−0.794601	+	0.794601i	−0.982238	−	0.187637i	$-0.939917\pi$
$937$	−24.3231	+	24.3231i	−0.794601	+	0.794601i	0.187637	+	0.982238i	$0.439917\pi$
$938$	17.6345	−	12.1275i	0.575787	−	0.395977i
$939$	53.6241	+	1.36240i	1.74996	+	0.0444603i
$940$	−6.66280	+	12.5032i	−0.217316	+	0.407810i
$941$	6.13673	−	14.8154i	0.200052	−	0.482967i	−0.791736	−	0.610863i	$-0.790822\pi$
$941$	6.13673	−	14.8154i	0.200052	−	0.482967i	0.991788	+	0.127896i	$0.0408225\pi$
$942$	22.9740	+	26.6454i	0.748533	+	0.868153i
$943$	9.87127			0.321453
$944$	22.7297	−	4.58099i	0.739789	−	0.149099i
$945$	−10.0547	−	54.6389i	−0.327080	−	1.77740i
$946$	9.65220	+	4.55769i	0.313820	+	0.148183i
$947$	20.2507	+	8.38813i	0.658061	+	0.272578i	0.686622	−	0.727014i	$-0.259093\pi$
$947$	20.2507	+	8.38813i	0.658061	+	0.272578i	−0.0285615	+	0.999592i	$0.509093\pi$
$948$	5.65458	+	0.695091i	0.183652	+	0.0225755i
$949$	0.920250	−	0.381180i	0.0298726	−	0.0123736i
$950$	38.3965	−	34.8448i	1.24575	−	1.13051i
$951$	7.74496	+	20.1294i	0.251148	+	0.652742i
$952$	44.0242	−	4.98810i	1.42683	−	0.161665i
$953$	5.38791	+	5.38791i	0.174531	+	0.174531i	0.788967	−	0.614436i	$-0.210616\pi$
$953$	5.38791	+	5.38791i	0.174531	+	0.174531i	−0.614436	+	0.788967i	$0.710616\pi$
$954$	9.79615	−	8.02176i	0.317162	−	0.259714i
$955$	72.8875	−	30.1910i	2.35858	−	0.976957i
$956$	−20.5619	+	16.9183i	−0.665021	+	0.547177i
$957$	50.3687	−	47.8728i	1.62819	−	1.54751i
$958$	−18.8141	+	6.74523i	−0.607857	+	0.217928i
$959$	−3.05096	+	22.5450i	−0.0985208	+	0.728016i
$960$	−4.28316	−	55.8314i	−0.138238	−	1.80195i
$961$	27.7781			0.896068
$962$	−6.46462	−	18.0315i	−0.208428	−	0.581358i
$963$	4.76882	−	1.69709i	0.153673	−	0.0546880i
$964$	−37.5974	+	30.9350i	−1.21093	+	0.996350i
$965$	7.37616	+	17.8076i	0.237447	+	0.573248i
$966$	19.0176	+	13.0404i	0.611881	+	0.419569i
$967$	26.0066	−	26.0066i	0.836315	−	0.836315i	−0.152057	−	0.988372i	$-0.548590\pi$
$967$	26.0066	−	26.0066i	0.836315	−	0.836315i	0.988372	+	0.152057i	$0.0485896\pi$
$968$	−8.46629	−	33.5295i	−0.272117	−	1.07768i
$969$	−11.9156	−	30.9691i	−0.382785	−	0.994872i
$970$	55.1156	−	50.0173i	1.76965	−	1.60596i
$971$	8.35933	−	3.46255i	0.268264	−	0.111118i	−0.244497	−	0.969650i	$-0.578623\pi$
$971$	8.35933	−	3.46255i	0.268264	−	0.111118i	0.512761	+	0.858532i	$0.328623\pi$
$972$	−6.92282	+	30.3986i	−0.222049	+	0.975035i
$973$	1.71429	+	0.998019i	0.0549577	+	0.0319950i
$974$	7.80637	−	16.5322i	0.250132	−	0.529726i
$975$	−17.6639	+	39.7570i	−0.565697	+	1.27324i
$976$	25.9820	+	17.2658i	0.831663	+	0.552663i
$977$	−27.4735			−0.878955			−0.439477	−	0.898254i	$-0.644836\pi$
$977$	−27.4735			−0.878955			−0.439477	+	0.898254i	$0.644836\pi$
$978$	−19.6979	+	16.9838i	−0.629868	+	0.543081i
$979$	−62.4792	−	25.8797i	−1.99684	−	0.827120i
$980$	38.9201	−	41.0615i	1.24326	−	1.31166i
$981$	16.9084	+	8.03258i	0.539843	+	0.256460i
$982$	26.7693	+	29.4979i	0.854244	+	0.941316i
$983$	22.5675	+	22.5675i	0.719790	+	0.719790i	0.968562	−	0.248772i	$-0.0800270\pi$
$983$	22.5675	+	22.5675i	0.719790	+	0.719790i	−0.248772	+	0.968562i	$0.580027\pi$
$984$	−7.25938	+	11.4902i	−0.231421	+	0.366294i
$985$	−2.13026	−	2.13026i	−0.0678758	−	0.0678758i
$986$	−69.6208	−	3.37614i	−2.21718	−	0.107518i
$987$	7.93048	+	1.27910i	0.252430	+	0.0407141i
$988$	14.2785	+	1.38809i	0.454260	+	0.0441610i
$989$	2.13247	−	5.14824i	0.0678086	−	0.163705i
$990$	72.8298	+	39.0298i	2.31468	+	1.24045i
$991$	−4.44589			−0.141228			−0.0706142	−	0.997504i	$-0.522496\pi$
$991$	−4.44589			−0.141228			−0.0706142	+	0.997504i	$0.522496\pi$
$992$	10.0392	−	1.52161i	0.318745	−	0.0483113i
$993$	11.3060	−	25.4471i	0.358787	−	0.807540i
$994$	−27.3105	+	5.81341i	−0.866237	+	0.184390i
$995$	−20.2745	+	48.9469i	−0.642744	+	1.55172i
$996$	21.9518	+	12.4238i	0.695571	+	0.393662i
$997$	−27.2441	+	11.2849i	−0.862831	+	0.357396i	−0.769814	−	0.638268i	$-0.779651\pi$
$997$	−27.2441	+	11.2849i	−0.862831	+	0.357396i	−0.0930168	+	0.995665i	$0.529651\pi$
$998$	0.752548	−	15.5186i	0.0238215	−	0.491233i
$999$	14.3479	−	28.3228i	0.453948	−	0.896093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bo.a.125.12	yes	496
3.2	odd	2	inner	672.2.bo.a.125.113	yes	496
7.6	odd	2	inner	672.2.bo.a.125.11	✓	496
21.20	even	2	inner	672.2.bo.a.125.114	yes	496
32.21	even	8	inner	672.2.bo.a.629.114	yes	496
96.53	odd	8	inner	672.2.bo.a.629.11	yes	496
224.181	odd	8	inner	672.2.bo.a.629.113	yes	496
672.629	even	8	inner	672.2.bo.a.629.12	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bo.a.125.11	✓	496	7.6	odd	2	inner
672.2.bo.a.125.12	yes	496	1.1	even	1	trivial
672.2.bo.a.125.113	yes	496	3.2	odd	2	inner
672.2.bo.a.125.114	yes	496	21.20	even	2	inner
672.2.bo.a.629.11	yes	496	96.53	odd	8	inner
672.2.bo.a.629.12	yes	496	672.629	even	8	inner
672.2.bo.a.629.113	yes	496	224.181	odd	8	inner
672.2.bo.a.629.114	yes	496	32.21	even	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.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33124 + 0.477276i) q^{2} +(1.25546 - 1.19324i) q^{3} +(1.54442 - 1.27074i) q^{4} +(1.54647 + 3.73351i) q^{5} +(-1.10181 + 2.18770i) q^{6} +(2.10482 - 1.60304i) q^{7} +(-1.44950 + 2.42878i) q^{8} +(0.152341 - 2.99613i) q^{9} +O(q^{10})\)	\(q+(-1.33124 + 0.477276i) q^{2} +(1.25546 - 1.19324i) q^{3} +(1.54442 - 1.27074i) q^{4} +(1.54647 + 3.73351i) q^{5} +(-1.10181 + 2.18770i) q^{6} +(2.10482 - 1.60304i) q^{7} +(-1.44950 + 2.42878i) q^{8} +(0.152341 - 2.99613i) q^{9} +(-3.84065 - 4.23212i) q^{10} +(-1.84430 - 4.45254i) q^{11} +(0.422645 - 3.43822i) q^{12} +(2.04801 + 0.848312i) q^{13} +(-2.03693 + 3.13862i) q^{14} +(6.39652 + 2.84195i) q^{15} +(0.770440 - 3.92510i) q^{16} -5.92062i q^{17} +(1.22718 + 4.06129i) q^{18} +(2.98948 + 1.23828i) q^{19} +(7.13272 + 3.80093i) q^{20} +(0.729688 - 4.52411i) q^{21} +(4.58030 + 5.04717i) q^{22} +(2.51595 - 2.51595i) q^{23} +(1.07834 + 4.77883i) q^{24} +(-8.01201 + 8.01201i) q^{25} +(-3.13127 - 0.151846i) q^{26} +(-3.38385 - 3.94329i) q^{27} +(1.21366 - 5.15044i) q^{28} +(-3.18572 + 7.69100i) q^{29} +(-9.87171 - 0.730417i) q^{30} -1.79497i q^{31} +(0.847712 + 5.59298i) q^{32} +(-7.62840 - 3.38926i) q^{33} +(2.82577 + 7.88178i) q^{34} +(9.24002 + 5.37931i) q^{35} +(-3.57202 - 4.82086i) q^{36} +(2.33828 + 5.64512i) q^{37} +(-4.57072 - 0.221649i) q^{38} +(3.58343 - 1.37875i) q^{39} +(-11.3095 - 1.65569i) q^{40} +(1.96174 + 1.96174i) q^{41} +(1.18786 + 6.37095i) q^{42} +(1.44691 - 0.599330i) q^{43} +(-8.50638 - 4.53294i) q^{44} +(11.4217 - 4.06466i) q^{45} +(-2.14854 + 4.55015i) q^{46} +1.75294i q^{47} +(-3.71635 - 5.84712i) q^{48} +(1.86051 - 6.74822i) q^{49} +(6.84200 - 14.4899i) q^{50} +(-7.06474 - 7.43307i) q^{51} +(4.24096 - 1.29234i) q^{52} +(-1.14206 - 2.75717i) q^{53} +(6.38677 + 3.63444i) q^{54} +(13.7714 - 13.7714i) q^{55} +(0.842496 + 7.43574i) q^{56} +(5.23073 - 2.01256i) q^{57} +(0.570235 - 11.7591i) q^{58} +(2.21830 + 5.35544i) q^{59} +(13.4903 - 3.73916i) q^{60} +(-2.98452 + 7.20526i) q^{61} +(0.856694 + 2.38954i) q^{62} +(-4.48227 - 6.55051i) q^{63} +(-3.79790 - 7.04102i) q^{64} +8.95815i q^{65} +(11.7729 + 0.871086i) q^{66} +(-5.28456 - 2.18894i) q^{67} +(-7.52356 - 9.14389i) q^{68} +(0.156525 - 6.16081i) q^{69} +(-14.8681 - 2.75113i) q^{70} +(5.27683 + 5.27683i) q^{71} +(7.05611 + 4.71289i) q^{72} +(0.317731 - 0.317731i) q^{73} +(-5.80710 - 6.39902i) q^{74} +(-0.498451 + 19.6190i) q^{75} +(6.19053 - 1.88642i) q^{76} +(-11.0195 - 6.41529i) q^{77} +(-4.11237 + 3.54574i) q^{78} +1.64462i q^{79} +(15.8459 - 3.19361i) q^{80} +(-8.95358 - 0.912865i) q^{81} +(-3.54783 - 1.67526i) q^{82} +(-2.78649 + 6.72718i) q^{83} +(-4.62202 - 7.91435i) q^{84} +(22.1047 - 9.15607i) q^{85} +(-1.64014 + 1.48843i) q^{86} +(5.17770 + 13.4570i) q^{87} +(13.4875 + 1.97456i) q^{88} +(9.92232 - 9.92232i) q^{89} +(-13.2651 + 10.8623i) q^{90} +(5.67056 - 1.49750i) q^{91} +(0.688556 - 7.08280i) q^{92} +(-2.14183 - 2.25350i) q^{93} +(-0.836634 - 2.33358i) q^{94} +13.0762i q^{95} +(7.73805 + 6.01021i) q^{96} +13.0232i q^{97} +(0.743964 + 9.87150i) q^{98} +(-13.6213 + 4.84746i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

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