LMFDB - Embedded newform 392.2.z.a.109.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$392 = 2^{3} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	392.z (of order $42$ , degree $12$ , 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			109.32
Character	$\chi$	$=$	392.109
Dual form			392.2.z.a.205.32

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.402179 - 1.35582i) q^{2} +(0.480822 + 3.19005i) q^{3} +(-1.67650 - 1.09057i) q^{4} +(3.18290 + 1.24920i) q^{5} +(4.51851 + 0.631060i) q^{6} +(2.64002 + 0.174060i) q^{7} +(-2.15287 + 1.83444i) q^{8} +(-7.07848 + 2.18342i) q^{9} +(2.97378 - 3.81304i) q^{10} +(0.905502 - 2.93557i) q^{11} +(2.67285 - 5.87249i) q^{12} +(-4.15301 + 0.947897i) q^{13} +(1.29775 - 3.50939i) q^{14} +(-2.45458 + 10.7542i) q^{15} +(1.62133 + 3.65668i) q^{16} +(0.121679 - 0.0829593i) q^{17} +(0.113516 + 10.4753i) q^{18} +(1.42532 - 0.822906i) q^{19} +(-3.97382 - 5.56544i) q^{20} +(0.714121 + 8.50547i) q^{21} +(-3.61593 - 2.40832i) q^{22} +(-0.949454 - 0.647327i) q^{23} +(-6.88709 - 5.98570i) q^{24} +(4.90510 + 4.55127i) q^{25} +(-0.385072 + 6.01196i) q^{26} +(-6.16947 - 12.8110i) q^{27} +(-4.23618 - 3.17093i) q^{28} +(-1.72310 + 3.57804i) q^{29} +(13.5936 + 7.65310i) q^{30} +(3.54658 - 6.14285i) q^{31} +(5.60987 - 0.727603i) q^{32} +(9.79997 + 1.47711i) q^{33} +(-0.0635413 - 0.198339i) q^{34} +(8.18548 + 3.85192i) q^{35} +(14.2483 + 4.05903i) q^{36} +(6.09583 - 0.456819i) q^{37} +(-0.542483 - 2.26343i) q^{38} +(-5.02069 - 12.7925i) q^{39} +(-9.14393 + 3.14948i) q^{40} +(-1.33803 - 1.67783i) q^{41} +(11.8191 + 2.45250i) q^{42} +(-0.298217 - 0.237820i) q^{43} +(-4.71950 + 3.93398i) q^{44} +(-25.2576 - 1.89280i) q^{45} +(-1.25951 + 1.02695i) q^{46} +(-2.35300 + 2.18327i) q^{47} +(-10.8854 + 6.93034i) q^{48} +(6.93941 + 0.919042i) q^{49} +(8.14344 - 4.82002i) q^{50} +(0.323150 + 0.348273i) q^{51} +(7.99628 + 2.93997i) q^{52} +(-11.4314 - 0.856667i) q^{53} +(-19.8507 + 3.21238i) q^{54} +(6.54922 - 8.21246i) q^{55} +(-6.00291 + 4.46823i) q^{56} +(3.31043 + 4.15115i) q^{57} +(4.15820 + 3.77522i) q^{58} +(13.6553 - 5.35931i) q^{59} +(15.8433 - 15.3526i) q^{60} +(-6.74860 + 0.505737i) q^{61} +(-6.90225 - 7.27905i) q^{62} +(-19.0674 + 4.53220i) q^{63} +(1.26967 - 7.89860i) q^{64} +(-14.4027 - 2.17086i) q^{65} +(5.94404 - 12.6930i) q^{66} +(-13.1568 - 7.59607i) q^{67} +(-0.294468 + 0.00638280i) q^{68} +(1.60848 - 3.34005i) q^{69} +(8.51454 - 9.54890i) q^{70} +(4.09407 - 1.97160i) q^{71} +(11.2337 - 17.6857i) q^{72} +(-1.25891 - 1.16809i) q^{73} +(1.83225 - 8.44858i) q^{74} +(-12.1603 + 17.8358i) q^{75} +(-3.28698 - 0.174794i) q^{76} +(2.90151 - 7.59234i) q^{77} +(-19.3636 + 1.66228i) q^{78} +(1.61189 + 2.79188i) q^{79} +(0.592641 + 13.6642i) q^{80} +(19.5401 - 13.3222i) q^{81} +(-2.81297 + 1.13934i) q^{82} +(6.80280 + 1.55269i) q^{83} +(8.07855 - 15.0383i) q^{84} +(0.490924 - 0.112050i) q^{85} +(-0.442379 + 0.308683i) q^{86} +(-12.2426 - 3.77635i) q^{87} +(3.43569 + 7.98097i) q^{88} +(10.9484 - 3.37713i) q^{89} +(-12.7244 + 33.4836i) q^{90} +(-11.1290 + 1.77960i) q^{91} +(0.885812 + 2.12069i) q^{92} +(21.3012 + 8.36012i) q^{93} +(2.01379 + 4.06831i) q^{94} +(5.56461 - 0.838730i) q^{95} +(5.01843 + 17.5459i) q^{96} -9.85703 q^{97} +(4.03694 - 9.03898i) q^{98} +22.7564i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25}+ \cdots + 151 q^{98}+O(q^{100})$ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$ .

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.402179	−	1.35582i	0.284383	−	0.958711i
$2$	0.402179	−	1.35582i	0.284383	−	0.958711i
$3$	0.480822	+	3.19005i	0.277603	+	1.84177i	0.499015	+	0.866593i	$0.333695\pi$
$3$	0.480822	+	3.19005i	0.277603	+	1.84177i	−0.221413	+	0.975180i	$0.571067\pi$
$4$	−1.67650	−	1.09057i	−0.838252	−	0.545283i
$5$	3.18290	+	1.24920i	1.42344	+	0.558657i	0.947195	−	0.320657i	$-0.103904\pi$
$5$	3.18290	+	1.24920i	1.42344	+	0.558657i	0.476241	+	0.879315i	$0.341999\pi$
$6$	4.51851	+	0.631060i	1.84467	+	0.257629i
$7$	2.64002	+	0.174060i	0.997834	+	0.0657884i
$7$	2.64002	+	0.174060i	0.997834	+	0.0657884i
$8$	−2.15287	+	1.83444i	−0.761153	+	0.648572i
$9$	−7.07848	+	2.18342i	−2.35949	+	0.727807i
$10$	2.97378	−	3.81304i	0.940392	−	1.20579i
$11$	0.905502	−	2.93557i	0.273019	−	0.885106i	−0.710406	−	0.703792i	$-0.751489\pi$
$11$	0.905502	−	2.93557i	0.273019	−	0.885106i	0.983425	−	0.181314i	$-0.0580351\pi$
$12$	2.67285	−	5.87249i	0.771586	−	1.69524i
$13$	−4.15301	+	0.947897i	−1.15184	+	0.262899i	−0.755464	−	0.655190i	$-0.772589\pi$
$13$	−4.15301	+	0.947897i	−1.15184	+	0.262899i	−0.396373	+	0.918089i	$0.629731\pi$
$14$	1.29775	−	3.50939i	0.346839	−	0.937925i
$15$	−2.45458	+	10.7542i	−0.633771	+	2.77673i
$16$	1.62133	+	3.65668i	0.405334	+	0.914169i
$17$	0.121679	−	0.0829593i	0.0295115	−	0.0201206i	−0.548474	−	0.836167i	$-0.684791\pi$
$17$	0.121679	−	0.0829593i	0.0295115	−	0.0201206i	0.577986	+	0.816047i	$0.303839\pi$
$18$	0.113516	+	10.4753i	0.0267560	+	2.46905i
$19$	1.42532	−	0.822906i	0.326990	−	0.188788i	−0.327514	−	0.944846i	$-0.606211\pi$
$19$	1.42532	−	0.822906i	0.326990	−	0.188788i	0.654504	+	0.756059i	$0.272878\pi$
$20$	−3.97382	−	5.56544i	−0.888572	−	1.24447i
$21$	0.714121	+	8.50547i	0.155834	+	1.85605i
$22$	−3.61593	−	2.40832i	−0.770919	−	0.513456i
$23$	−0.949454	−	0.647327i	−0.197975	−	0.134977i	0.460275	−	0.887776i	$-0.347751\pi$
$23$	−0.949454	−	0.647327i	−0.197975	−	0.134977i	−0.658250	+	0.752799i	$0.728703\pi$
$24$	−6.88709	−	5.98570i	−1.40582	−	1.22183i
$25$	4.90510	+	4.55127i	0.981020	+	0.910254i
$26$	−0.385072	+	6.01196i	−0.0755189	+	1.17904i
$27$	−6.16947	−	12.8110i	−1.18732	−	2.46549i
$28$	−4.23618	−	3.17093i	−0.800563	−	0.599249i
$29$	−1.72310	+	3.57804i	−0.319971	+	0.664426i	−0.997469	−	0.0710979i	$-0.977350\pi$
$29$	−1.72310	+	3.57804i	−0.319971	+	0.664426i	0.677499	+	0.735524i	$0.263064\pi$
$30$	13.5936	+	7.65310i	2.48185	+	1.39726i
$31$	3.54658	−	6.14285i	0.636984	−	1.10329i	−0.349107	−	0.937083i	$-0.613515\pi$
$31$	3.54658	−	6.14285i	0.636984	−	1.10329i	0.986091	−	0.166206i	$-0.0531516\pi$
$32$	5.60987	−	0.727603i	0.991694	−	0.128623i
$33$	9.79997	+	1.47711i	1.70596	+	0.257131i
$34$	−0.0635413	−	0.198339i	−0.0108973	−	0.0340149i
$35$	8.18548	+	3.85192i	1.38360	+	0.651093i
$36$	14.2483	+	4.05903i	2.37471	+	0.676505i
$37$	6.09583	−	0.456819i	1.00215	−	0.0751006i	0.436463	−	0.899722i	$-0.356231\pi$
$37$	6.09583	−	0.456819i	1.00215	−	0.0751006i	0.565685	+	0.824621i	$0.308612\pi$
$38$	−0.542483	−	2.26343i	−0.0880023	−	0.367177i
$39$	−5.02069	−	12.7925i	−0.803954	−	2.04844i
$40$	−9.14393	+	3.14948i	−1.44578	+	0.497977i
$41$	−1.33803	−	1.67783i	−0.208965	−	0.262034i	0.666293	−	0.745690i	$-0.267880\pi$
$41$	−1.33803	−	1.67783i	−0.208965	−	0.262034i	−0.875258	+	0.483656i	$0.839309\pi$
$42$	11.8191	+	2.45250i	1.82373	+	0.378429i
$43$	−0.298217	−	0.237820i	−0.0454777	−	0.0362673i	0.600487	−	0.799634i	$-0.294973\pi$
$43$	−0.298217	−	0.237820i	−0.0454777	−	0.0362673i	−0.645965	+	0.763367i	$0.723545\pi$
$44$	−4.71950	+	3.93398i	−0.711492	+	0.593070i
$45$	−25.2576	−	1.89280i	−3.76518	−	0.282161i
$46$	−1.25951	+	1.02695i	−0.185705	+	0.151415i
$47$	−2.35300	+	2.18327i	−0.343220	+	0.318462i	−0.832882	−	0.553451i	$-0.813311\pi$
$47$	−2.35300	+	2.18327i	−0.343220	+	0.318462i	0.489662	+	0.871913i	$0.337120\pi$
$48$	−10.8854	+	6.93034i	−1.57117	+	1.00031i
$49$	6.93941	+	0.919042i	0.991344	+	0.131292i
$50$	8.14344	−	4.82002i	1.15166	−	0.681653i
$51$	0.323150	+	0.348273i	0.0452500	+	0.0487679i
$52$	7.99628	+	2.93997i	1.10888	+	0.407701i
$53$	−11.4314	−	0.856667i	−1.57023	−	0.117672i	−0.739038	−	0.673663i	$-0.764720\pi$
$53$	−11.4314	−	0.856667i	−1.57023	−	0.117672i	−0.831188	+	0.555991i	$0.812339\pi$
$54$	−19.8507	+	3.21238i	−2.70134	+	0.437149i
$55$	6.54922	−	8.21246i	0.883096	−	1.10737i
$56$	−6.00291	+	4.46823i	−0.802173	+	0.597092i
$57$	3.31043	+	4.15115i	0.438477	+	0.549833i
$58$	4.15820	+	3.77522i	0.545998	+	0.495711i
$59$	13.6553	−	5.35931i	1.77777	−	0.697722i	0.780395	−	0.625287i	$-0.215018\pi$
$59$	13.6553	−	5.35931i	1.77777	−	0.697722i	0.997373	−	0.0724349i	$-0.0230770\pi$
$60$	15.8433	−	15.3526i	2.04536	−	1.98202i
$61$	−6.74860	+	0.505737i	−0.864069	+	0.0647530i	−0.499387	−	0.866379i	$-0.666441\pi$
$61$	−6.74860	+	0.505737i	−0.864069	+	0.0647530i	−0.364682	+	0.931132i	$0.618822\pi$
$62$	−6.90225	−	7.27905i	−0.876587	−	0.924440i
$63$	−19.0674	+	4.53220i	−2.40226	+	0.571003i
$64$	1.26967	−	7.89860i	0.158709	−	0.987325i
$65$	−14.4027	−	2.17086i	−1.78644	−	0.269262i
$66$	5.94404	−	12.6930i	0.731660	−	1.56239i
$67$	−13.1568	−	7.59607i	−1.60736	−	0.928008i	−0.989959	−	0.141356i	$-0.954854\pi$
$67$	−13.1568	−	7.59607i	−1.60736	−	0.928008i	−0.617398	−	0.786651i	$-0.711813\pi$
$68$	−0.294468	+	0.00638280i	−0.0357095	+	0.000774029i
$69$	1.60848	−	3.34005i	0.193639	−	0.402095i
$70$	8.51454	−	9.54890i	1.01768	−	1.14131i
$71$	4.09407	−	1.97160i	0.485877	−	0.233986i	−0.174875	−	0.984591i	$-0.555952\pi$
$71$	4.09407	−	1.97160i	0.485877	−	0.233986i	0.660751	+	0.750605i	$0.270238\pi$
$72$	11.2337	−	17.6857i	1.32390	−	2.08427i
$73$	−1.25891	−	1.16809i	−0.147344	−	0.136715i	0.603057	−	0.797698i	$-0.293949\pi$
$73$	−1.25891	−	1.16809i	−0.147344	−	0.136715i	−0.750401	+	0.660983i	$0.770140\pi$
$74$	1.83225	−	8.44858i	0.212994	−	0.982128i
$75$	−12.1603	+	17.8358i	−1.40415	+	2.05951i
$76$	−3.28698	−	0.174794i	−0.377043	−	0.0200502i
$77$	2.90151	−	7.59234i	0.330657	−	0.865227i
$78$	−19.3636	+	1.66228i	−2.19249	+	0.188217i
$79$	1.61189	+	2.79188i	0.181352	+	0.314111i	0.942341	−	0.334654i	$-0.108619\pi$
$79$	1.61189	+	2.79188i	0.181352	+	0.314111i	−0.760989	+	0.648764i	$0.775286\pi$
$80$	0.592641	+	13.6642i	0.0662593	+	1.52770i
$81$	19.5401	−	13.3222i	2.17112	−	1.48025i
$82$	−2.81297	+	1.13934i	−0.310641	+	0.125819i
$83$	6.80280	+	1.55269i	0.746704	+	0.170430i	0.578910	−	0.815392i	$-0.303478\pi$
$83$	6.80280	+	1.55269i	0.746704	+	0.170430i	0.167795	+	0.985822i	$0.446335\pi$
$84$	8.07855	−	15.0383i	0.881442	−	1.64081i
$85$	0.490924	−	0.112050i	0.0532482	−	0.0121536i
$86$	−0.442379	+	0.308683i	−0.0477029	+	0.0332862i
$87$	−12.2426	−	3.77635i	−1.31255	−	0.404867i
$88$	3.43569	+	7.98097i	0.366246	+	0.850774i
$89$	10.9484	−	3.37713i	1.16053	−	0.357976i	0.346076	−	0.938206i	$-0.387514\pi$
$89$	10.9484	−	3.37713i	1.16053	−	0.357976i	0.814452	+	0.580231i	$0.197038\pi$
$90$	−12.7244	+	33.4836i	−1.34127	+	3.52948i
$91$	−11.1290	+	1.77960i	−1.16664	+	0.186552i
$92$	0.885812	+	2.12069i	0.0923523	+	0.221097i
$93$	21.3012	+	8.36012i	2.20884	+	0.866904i
$94$	2.01379	+	4.06831i	0.207707	+	0.419614i
$95$	5.56461	−	0.838730i	0.570917	−	0.0860519i
$96$	5.01843	+	17.5459i	0.512192	+	1.79077i
$97$	−9.85703			−1.00083			−0.500415	−	0.865786i	$-0.666819\pi$
$97$	−9.85703			−1.00083			−0.500415	+	0.865786i	$0.666819\pi$
$98$	4.03694	−	9.03898i	0.407792	−	0.913075i
$99$			22.7564i			2.28711i
$100$	−3.25997	−	12.9796i	−0.325997	−	1.29796i
$101$	−1.19842	−	7.95098i	−0.119247	−	0.791152i	−0.965883	−	0.258980i	$-0.916614\pi$
$101$	−1.19842	−	7.95098i	−0.119247	−	0.791152i	0.846636	−	0.532173i	$-0.178624\pi$
$102$	0.602160	−	0.298066i	0.0596227	−	0.0295129i
$103$	−5.30939	+	13.5281i	−0.523150	+	1.33296i	0.388292	+	0.921536i	$0.373065\pi$
$103$	−5.30939	+	13.5281i	−0.523150	+	1.33296i	−0.911442	+	0.411428i	$0.865030\pi$
$104$	7.20201	−	9.65914i	0.706216	−	0.947156i
$105$	−8.35203	+	27.9641i	−0.815074	+	2.72902i
$106$	−5.75896	+	15.1544i	−0.559360	+	1.47193i
$107$	−4.80927	−	15.5913i	−0.464929	−	1.50726i	−0.819966	−	0.572412i	$-0.806008\pi$
$107$	−4.80927	−	15.5913i	−0.464929	−	1.50726i	0.355037	−	0.934852i	$-0.384468\pi$
$108$	−3.62813	+	28.2060i	−0.349117	+	2.71412i
$109$	−1.40599	+	4.55810i	−0.134669	+	0.436587i	−0.997640	−	0.0686675i	$-0.978125\pi$
$109$	−1.40599	+	4.55810i	−0.134669	+	0.436587i	0.862970	+	0.505255i	$0.168601\pi$
$110$	−8.50067	−	12.1824i	−0.810508	−	1.16155i
$111$	4.38828	+	19.2263i	0.416517	+	1.82488i
$112$	3.64388	+	9.93590i	0.344314	+	0.938855i
$113$	0.510297	−	2.23576i	0.0480047	−	0.210323i	−0.945237	−	0.326384i	$-0.894170\pi$
$113$	0.510297	−	2.23576i	0.0480047	−	0.210323i	0.993242	+	0.116061i	$0.0370269\pi$
$114$	6.95960	−	2.81885i	0.651827	−	0.264010i
$115$	−2.21338	−	3.24643i	−0.206399	−	0.302731i
$116$	6.79087	−	4.11946i	0.630516	−	0.382482i
$117$	27.3273	−	15.7774i	2.52641	−	1.45862i
$118$	−1.77440	−	20.6695i	−0.163346	−	1.90279i
$119$	0.335675	−	0.197835i	0.0307713	−	0.0181355i
$120$	−14.4436	−	27.6552i	−1.31851	−	2.52456i
$121$	1.29102	+	0.880200i	0.117365	+	0.0800182i
$122$	−2.02845	+	9.35329i	−0.183647	+	0.846807i
$123$	4.70902	−	5.07511i	0.424598	−	0.457607i
$124$	−12.6450	+	6.43074i	−1.13556	+	0.577498i
$125$	2.50921	+	5.21043i	0.224431	+	0.466035i
$126$	−1.52364	+	27.6747i	−0.135737	+	2.46546i
$127$	−5.79468	−	2.79057i	−0.514195	−	0.247623i	0.158746	−	0.987319i	$-0.449255\pi$
$127$	−5.79468	−	2.79057i	−0.514195	−	0.247623i	−0.672941	+	0.739696i	$0.734969\pi$
$128$	−10.1985	−	4.89809i	−0.901425	−	0.432935i
$129$	0.615268	−	1.06568i	0.0541714	−	0.0938275i
$130$	−8.73577	+	18.6544i	−0.766177	+	1.63610i
$131$	1.27805	−	8.47929i	0.111663	−	0.740839i	−0.860998	−	0.508609i	$-0.830160\pi$
$131$	1.27805	−	8.47929i	0.111663	−	0.740839i	0.972661	−	0.232230i	$-0.0746021\pi$
$132$	−14.8188	−	13.1639i	−1.28981	−	1.14577i
$133$	3.90610	−	1.92440i	0.338701	−	0.166867i
$134$	−15.5903	+	14.7833i	−1.34680	+	1.27708i
$135$	−3.63331	−	48.4832i	−0.312706	−	4.17277i
$136$	−0.109775	+	0.401813i	−0.00941311	+	0.0344552i
$137$	1.43454	+	3.65515i	0.122561	+	0.312280i	0.978966	−	0.204025i	$-0.0654023\pi$
$137$	1.43454	+	3.65515i	0.122561	+	0.312280i	−0.856405	+	0.516305i	$0.827307\pi$
$138$	−3.88162	−	3.52411i	−0.330425	−	0.299993i
$139$	11.5363	−	9.19986i	0.978492	−	0.780322i	0.00291913	−	0.999996i	$-0.499071\pi$
$139$	11.5363	−	9.19986i	0.978492	−	0.780322i	0.975573	+	0.219674i	$0.0704994\pi$
$140$	−9.52223	−	15.3846i	−0.804775	−	1.30023i
$141$	−8.09609	−	6.45642i	−0.681814	−	0.543728i
$142$	−1.02659	−	6.34376i	−0.0861495	−	0.532357i
$143$	−0.977944	+	13.0497i	−0.0817797	+	1.09127i
$144$	−19.4606	−	22.3436i	−1.62172	−	1.86197i
$145$	−9.95412	+	9.23607i	−0.826645	+	0.767014i
$146$	−2.09003	+	1.23707i	−0.172972	+	0.102381i
$147$	0.404833	+	22.5789i	0.0333901	+	1.86228i
$148$	−10.7179	−	5.88204i	−0.881004	−	0.483501i
$149$	5.42767	+	5.84963i	0.444652	+	0.479221i	0.915111	−	0.403201i	$-0.132102\pi$
$149$	5.42767	+	5.84963i	0.444652	+	0.479221i	−0.470460	+	0.882421i	$0.655912\pi$
$150$	19.2916	+	23.6604i	1.57515	+	1.93186i
$151$	−0.571244	+	7.62272i	−0.0464872	+	0.620328i	0.924498	+	0.381187i	$0.124485\pi$
$151$	−0.571244	+	7.62272i	−0.0464872	+	0.620328i	−0.970985	+	0.239141i	$0.923134\pi$
$152$	−1.55894	+	4.38626i	−0.126447	+	0.355773i
$153$	−0.680167	+	0.852902i	−0.0549882	+	0.0689531i
$154$	−9.12693	−	6.98740i	−0.735469	−	0.563061i
$155$	18.9620	−	15.1217i	1.52307	−	1.21460i
$156$	−5.53386	+	26.9221i	−0.443063	+	2.15549i
$157$	−11.6913	+	4.58848i	−0.933065	+	0.366201i	−0.782678	−	0.622426i	$-0.786147\pi$
$157$	−11.6913	+	4.58848i	−0.933065	+	0.366201i	−0.150386	+	0.988627i	$0.548052\pi$
$158$	4.43355	−	1.06260i	0.352715	−	0.0845361i
$159$	−2.76367	−	36.8787i	−0.219174	−	2.92467i
$160$	18.7646	+	4.69193i	1.48347	+	0.370930i
$161$	−2.39390	−	1.87422i	−0.188666	−	0.147709i
$162$	−10.2039	−	31.8508i	−0.801697	−	2.50244i
$163$	−1.83312	+	12.1620i	−0.143581	+	0.952599i	0.794769	+	0.606912i	$0.207592\pi$
$163$	−1.83312	+	12.1620i	−0.143581	+	0.952599i	−0.938350	+	0.345687i	$0.887646\pi$
$164$	0.413423	+	4.27211i	0.0322829	+	0.333595i
$165$	29.3471	+	16.9436i	2.28467	+	1.31906i
$166$	4.84112	−	8.59892i	0.375744	−	0.667406i
$167$	13.6413	+	6.56933i	1.05560	+	0.508350i	0.879439	−	0.476012i	$-0.157918\pi$
$167$	13.6413	+	6.56933i	1.05560	+	0.508350i	0.176160	+	0.984361i	$0.443632\pi$
$168$	−17.1402	−	17.0011i	−1.32239	−	1.31167i
$169$	4.63637	−	2.23276i	0.356644	−	0.171751i
$170$	0.0455192	−	0.710670i	0.00349116	−	0.0545059i
$171$	−8.29232	+	8.93699i	−0.634129	+	0.683429i
$172$	0.240604	+	0.723932i	0.0183459	+	0.0551993i
$173$	0.954859	−	1.40052i	0.0725966	−	0.106480i	−0.788223	−	0.615389i	$-0.788999\pi$
$173$	0.954859	−	1.40052i	0.0725966	−	0.106480i	0.860820	+	0.508910i	$0.169951\pi$
$174$	−10.0438	+	15.0800i	−0.761417	+	1.14322i
$175$	12.1574	+	12.8692i	0.919011	+	0.972821i
$176$	12.2025	−	1.44841i	0.919800	−	0.109178i
$177$	23.6622	+	40.9841i	1.77856	+	3.08056i
$178$	−0.175578	−	16.2023i	−0.0131601	−	1.21441i
$179$	5.41810	+	7.94689i	0.404968	+	0.593979i	0.973501	−	0.228681i	$-0.0734414\pi$
$179$	5.41810	+	7.94689i	0.404968	+	0.593979i	−0.568534	+	0.822660i	$0.692489\pi$
$180$	40.2803	+	30.7184i	3.00232	+	2.28961i
$181$	2.65486	+	0.605954i	0.197334	+	0.0450402i	0.320045	−	0.947402i	$-0.396302\pi$
$181$	2.65486	+	0.605954i	0.197334	+	0.0450402i	−0.122711	+	0.992442i	$0.539159\pi$
$182$	−2.06304	+	15.8047i	−0.152923	+	1.17152i
$183$	−4.85820	−	21.2852i	−0.359128	−	1.57344i
$184$	3.23153	−	0.348107i	0.238232	−	0.0256628i
$185$	19.9731	+	6.16088i	1.46845	+	0.452957i
$186$	19.9017	−	25.5184i	1.45927	−	1.87110i
$187$	−0.133352	−	0.432316i	−0.00975166	−	0.0316141i
$188$	6.32581	−	1.09415i	0.461357	−	0.0797993i
$189$	−14.0576	−	34.8953i	−1.02254	−	2.53826i
$190$	1.10080	−	7.88194i	0.0798604	−	0.571816i
$191$	−2.98549	+	7.60690i	−0.216022	+	0.550416i	−0.997273	−	0.0738014i	$-0.976487\pi$
$191$	−2.98549	+	7.60690i	−0.216022	+	0.550416i	0.781251	+	0.624218i	$0.214582\pi$
$192$	25.8074	+	0.252478i	1.86249	+	0.0182210i
$193$	−19.9425	+	3.00585i	−1.43550	+	0.216366i	−0.820266	−	0.571982i	$-0.806175\pi$
$193$	−19.9425	+	3.00585i	−1.43550	+	0.216366i	−0.615229	+	0.788348i	$0.710937\pi$
$194$	−3.96429	+	13.3644i	−0.284619	+	0.959507i
$195$		−	46.9891i		−	3.36496i
$196$	−10.6317	−	9.10865i	−0.759405	−	0.650618i
$197$			10.9486i			0.780052i	0.920804	+	0.390026i	$0.127534\pi$
$197$			10.9486i			0.780052i	−0.920804	+	0.390026i	$0.872466\pi$
$198$	30.8537	+	9.15215i	2.19267	+	0.650415i
$199$	−16.1384	+	2.43247i	−1.14402	+	0.172433i	−0.693583	−	0.720376i	$-0.743969\pi$
$199$	−16.1384	+	2.43247i	−1.14402	+	0.172433i	−0.450435	+	0.892809i	$0.648731\pi$
$200$	−18.9090	−	0.800166i	−1.33707	−	0.0565803i
$201$	17.9057	−	45.6231i	1.26297	−	3.21800i
$202$	−11.2621	−	1.57288i	−0.792398	−	0.110667i
$203$	−5.17180	+	9.14619i	−0.362989	+	0.641936i
$204$	−0.161948	−	0.936297i	−0.0113386	−	0.0655539i
$205$	−2.16287	−	7.01184i	−0.151061	−	0.489728i
$206$	16.2064	+	12.6393i	1.12915	+	0.880622i
$207$	8.13408	+	2.50903i	0.565358	+	0.174390i
$208$	−10.1996	−	13.6493i	−0.707213	−	0.946412i
$209$	−1.12507	−	4.92925i	−0.0778227	−	0.340963i
$210$	34.5554	+	22.5704i	2.38455	+	1.55751i
$211$	0.274900	+	0.0627442i	0.0189249	+	0.00431949i	0.231973	−	0.972722i	$-0.425482\pi$
$211$	0.274900	+	0.0627442i	0.0189249	+	0.00431949i	−0.213048	+	0.977042i	$0.568339\pi$
$212$	18.2306	+	13.9029i	1.25208	+	0.954856i
$213$	8.25801	+	12.1123i	0.565830	+	0.829920i
$214$	−23.0732	+	0.250034i	−1.57725	+	0.0170920i
$215$	−0.652112	−	1.12949i	−0.0444736	−	0.0770306i
$216$	36.7831	+	16.2629i	2.50278	+	1.10655i
$217$	10.4323	−	15.5999i	0.708188	−	1.05899i
$218$	5.61452	+	3.73944i	0.380263	+	0.253267i
$219$	3.12096	−	4.57761i	0.210895	−	0.309326i
$220$	−19.9360	+	6.62588i	−1.34409	+	0.446716i
$221$	−0.426697	+	0.459870i	−0.0287027	+	0.0309342i
$222$	27.8323	+	1.78269i	1.86798	+	0.119646i
$223$	−4.87927	+	2.34973i	−0.326740	+	0.157350i	−0.590061	−	0.807359i	$-0.700896\pi$
$223$	−4.87927	+	2.34973i	−0.326740	+	0.157350i	0.263321	+	0.964708i	$0.415182\pi$
$224$	14.9368	−	0.944435i	0.998007	−	0.0631027i
$225$	−44.6580	−	21.5062i	−2.97720	−	1.43374i
$226$	−2.82606	−	1.59105i	−0.187987	−	0.105835i
$227$	−6.37040	−	3.67795i	−0.422818	−	0.244114i	0.273464	−	0.961882i	$-0.411831\pi$
$227$	−6.37040	−	3.67795i	−0.422818	−	0.244114i	−0.696282	+	0.717768i	$0.745164\pi$
$228$	−1.02285	−	10.5697i	−0.0677401	−	0.699993i
$229$	−2.67414	+	17.7418i	−0.176712	+	1.17241i	0.707979	+	0.706233i	$0.249607\pi$
$229$	−2.67414	+	17.7418i	−0.176712	+	1.17241i	−0.884692	+	0.466177i	$0.845631\pi$
$230$	−5.29176	+	1.69530i	−0.348928	+	0.111785i
$231$	25.6150	+	5.60537i	1.68534	+	0.368807i
$232$	−2.85411	−	10.8640i	−0.187381	−	0.713254i
$233$	−1.93529	−	25.8246i	−0.126785	−	1.69183i	−0.591452	−	0.806340i	$-0.701445\pi$
$233$	−1.93529	−	25.8246i	−0.126785	−	1.69183i	0.464667	−	0.885485i	$-0.346174\pi$
$234$	−10.4009	−	43.3963i	−0.679930	−	2.83691i
$235$	−10.2167	+	4.00976i	−0.666463	+	0.261568i
$236$	−28.7378	−	5.90709i	−1.87067	−	0.384519i
$237$	−8.13118	+	6.48440i	−0.528177	+	0.421207i
$238$	−0.133227	−	0.534680i	−0.00863586	−	0.0346582i
$239$	1.50485	−	1.88702i	0.0973404	−	0.122061i	−0.730776	−	0.682618i	$-0.760841\pi$
$239$	1.50485	−	1.88702i	0.0973404	−	0.122061i	0.828116	+	0.560557i	$0.189413\pi$
$240$	−43.3044	+	8.46060i	−2.79529	+	0.546129i
$241$	1.17623	−	15.6957i	0.0757676	−	1.01105i	−0.821686	−	0.569940i	$-0.806966\pi$
$241$	1.17623	−	15.6957i	0.0757676	−	1.01105i	0.897454	−	0.441108i	$-0.145415\pi$
$242$	1.71261	−	1.39639i	0.110091	−	0.0897634i
$243$	22.8793	+	24.6580i	1.46771	+	1.58181i
$244$	11.8656	+	6.51191i	0.759617	+	0.416883i
$245$	20.9394	+	11.5939i	1.33777	+	0.740707i
$246$	−4.98708	−	8.42569i	−0.317965	−	0.537202i
$247$	−5.13932	+	4.76859i	−0.327007	+	0.303418i
$248$	3.63338	+	19.7307i	0.230720	+	1.25290i
$249$	−1.68223	+	22.4478i	−0.106607	+	1.42257i
$250$	8.07356	−	1.30652i	0.510617	−	0.0826314i
$251$	5.76923	+	4.60081i	0.364150	+	0.290400i	0.788422	−	0.615135i	$-0.210898\pi$
$251$	5.76923	+	4.60081i	0.364150	+	0.290400i	−0.424272	+	0.905535i	$0.639470\pi$
$252$	36.9092	+	13.1960i	2.32506	+	0.831267i
$253$	−2.76000	+	2.20103i	−0.173520	+	0.138378i
$254$	−6.11401	+	6.73424i	−0.383627	+	0.422544i
$255$	0.593493	+	1.51220i	0.0371660	+	0.0946973i
$256$	−10.7425	+	11.8574i	−0.671409	+	0.741087i
$257$	0.443766	+	5.92165i	0.0276814	+	0.369382i	0.993792	+	0.111254i	$0.0354867\pi$
$257$	0.443766	+	5.92165i	0.0276814	+	0.369382i	−0.966111	+	0.258128i	$0.916894\pi$
$258$	−1.19742	−	1.26279i	−0.0745480	−	0.0786177i
$259$	16.1726	−	0.144974i	1.00492	−	0.00900822i
$260$	21.7788	+	19.3466i	1.35066	+	1.19982i
$261$	4.38452	−	29.0894i	0.271395	−	1.80059i
$262$	−10.9824	−	5.14299i	−0.678495	−	0.317735i
$263$	−5.32000	+	9.21451i	−0.328045	+	0.568191i	−0.982124	−	0.188235i	$-0.939723\pi$
$263$	−5.32000	+	9.21451i	−0.328045	+	0.568191i	0.654079	+	0.756427i	$0.273057\pi$
$264$	−23.8077	+	14.7974i	−1.46526	+	0.910719i
$265$	−35.3149	−	17.0068i	−2.16938	−	1.04472i
$266$	−1.03819	−	6.06992i	−0.0636557	−	0.372171i
$267$	16.0374	+	33.3021i	0.981476	+	2.03806i
$268$	13.7734	+	27.0832i	0.841344	+	1.65437i
$269$	−1.03117	+	1.11134i	−0.0628715	+	0.0677593i	−0.763704	−	0.645566i	$-0.776621\pi$
$269$	−1.03117	+	1.11134i	−0.0628715	+	0.0677593i	0.700833	+	0.713326i	$0.252812\pi$
$270$	−67.1958	−	14.5728i	−4.08940	−	0.886871i
$271$	6.62790	+	4.51882i	0.402616	+	0.274499i	0.747652	−	0.664090i	$-0.231181\pi$
$271$	6.62790	+	4.51882i	0.402616	+	0.274499i	−0.345036	+	0.938589i	$0.612133\pi$
$272$	0.500638	+	0.310436i	0.0303556	+	0.0188229i
$273$	−11.0281	−	34.6464i	−0.667449	−	2.09689i
$274$	5.53267	−	0.474957i	0.334241	−	0.0286932i
$275$	17.8021	−	10.2781i	1.07351	−	0.619790i
$276$	−6.33917	+	3.84545i	−0.381573	+	0.231469i
$277$	−0.592255	−	0.868678i	−0.0355851	−	0.0521938i	0.808034	−	0.589136i	$-0.200532\pi$
$277$	−0.592255	−	0.868678i	−0.0355851	−	0.0521938i	−0.843619	+	0.536942i	$0.819579\pi$
$278$	−7.83373	−	19.3411i	−0.469836	−	1.16000i
$279$	−11.6919	+	51.2257i	−0.699978	+	3.06680i
$280$	−24.6884	+	6.72310i	−1.47541	+	0.401782i
$281$	1.04100	+	4.56094i	0.0621011	+	0.272083i	0.996440	−	0.0843026i	$-0.0268662\pi$
$281$	1.04100	+	4.56094i	0.0621011	+	0.272083i	−0.934339	+	0.356385i	$0.884009\pi$
$282$	−12.0098	+	8.38022i	−0.715175	+	0.499035i
$283$	1.63915	−	5.31400i	0.0974376	−	0.315885i	−0.893711	−	0.448643i	$-0.851907\pi$
$283$	1.63915	−	5.31400i	0.0974376	−	0.315885i	0.991148	+	0.132759i	$0.0423835\pi$
$284$	−9.01388	−	1.15945i	−0.534876	−	0.0688009i
$285$	5.35117	+	17.3481i	0.316976	+	1.02761i
$286$	17.2998	+	6.57425i	1.02296	+	0.388743i
$287$	−3.24038	−	4.66241i	−0.191274	−	0.275214i
$288$	−38.1207	+	17.3990i	−2.24628	+	1.02525i
$289$	−6.20287	+	15.8047i	−0.364875	+	0.929686i
$290$	8.51913	+	17.2106i	0.500261	+	1.01064i
$291$	−4.73948	−	31.4444i	−0.277833	−	1.84330i
$292$	0.836679	+	3.33124i	0.0489629	+	0.194946i
$293$			13.4515i			0.785846i	0.919571	+	0.392923i	$0.128536\pi$
$293$			13.4515i			0.785846i	−0.919571	+	0.392923i	$0.871464\pi$
$294$	30.7758	+	8.53188i	1.79488	+	0.497589i
$295$	50.1583			2.92033
$296$	−12.2855	+	12.1659i	−0.714080	+	0.707128i
$297$	−43.1941	+	6.51047i	−2.50638	+	0.377776i
$298$	10.1139	−	5.00635i	0.585885	−	0.290010i
$299$	4.55669	+	1.78837i	0.263520	+	0.103424i
$300$	39.8379	−	16.6403i	2.30004	−	0.960728i
$301$	−0.745905	−	0.679758i	−0.0429932	−	0.0391806i
$302$	10.1053	+	3.84020i	0.581495	+	0.220979i
$303$	24.7878	−	7.64601i	1.42402	−	0.439252i
$304$	5.32002	+	3.87771i	0.305124	+	0.222402i
$305$	−22.1119	−	6.82061i	−1.26612	−	0.390547i
$306$	0.882835	+	1.26520i	0.0504683	+	0.0723269i
$307$	−30.6068	+	6.98581i	−1.74682	+	0.398701i	−0.972280	−	0.233820i	$-0.924877\pi$
$307$	−30.6068	+	6.98581i	−1.74682	+	0.398701i	−0.774544	+	0.632521i	$0.782020\pi$
$308$	−13.1443	+	9.56431i	−0.748968	+	0.544977i
$309$	−45.7082	−	10.4326i	−2.60025	−	0.593489i
$310$	−12.8762	−	31.7908i	−0.731320	−	1.80559i
$311$	−13.5236	+	9.22025i	−0.766854	+	0.522832i	−0.882417	−	0.470468i	$-0.844085\pi$
$311$	−13.5236	+	9.22025i	−0.766854	+	0.522832i	0.115563	+	0.993300i	$0.463133\pi$
$312$	34.2760	+	18.3304i	1.94049	+	1.03776i
$313$	5.43562	+	9.41477i	0.307239	+	0.532154i	0.977757	−	0.209739i	$-0.0672614\pi$
$313$	5.43562	+	9.41477i	0.307239	+	0.532154i	−0.670518	+	0.741893i	$0.733928\pi$
$314$	1.51919	+	17.6967i	0.0857327	+	0.998681i
$315$	−66.3511	−	9.39335i	−3.73846	−	0.529255i
$316$	0.342382	−	6.43846i	0.0192605	−	0.362192i
$317$	−5.23553	+	7.67911i	−0.294056	+	0.431302i	−0.944628	−	0.328143i	$-0.893577\pi$
$317$	−5.23553	+	7.67911i	−0.294056	+	0.431302i	0.650571	+	0.759445i	$0.274529\pi$
$318$	−51.1124	−	11.0848i	−2.86624	−	0.621603i
$319$	8.94332	+	8.29819i	0.500730	+	0.464609i
$320$	13.9081	−	23.5544i	0.777488	−	1.31673i
$321$	47.4244	−	22.8384i	2.64697	−	1.27472i
$322$	−3.50388	+	2.49194i	−0.195264	+	0.138870i
$323$	0.105163	−	0.218374i	0.00585144	−	0.0121506i
$324$	−47.2878	+	1.02500i	−2.62710	+	0.0569443i
$325$	−24.6851	−	14.2519i	−1.36928	−	0.790554i
$326$	15.7522	+	7.37667i	0.872435	+	0.408556i
$327$	−15.2166	−	2.29353i	−0.841479	−	0.126833i
$328$	5.95848	+	1.15762i	0.329002	+	0.0639190i
$329$	−6.59199	+	5.35430i	−0.363428	+	0.295192i
$330$	34.7753	−	32.9751i	1.91431	−	1.81522i
$331$	16.8913	−	1.26583i	0.928432	−	0.0695764i	0.398077	−	0.917352i	$-0.369678\pi$
$331$	16.8913	−	1.26583i	0.928432	−	0.0695764i	0.530355	+	0.847776i	$0.322059\pi$
$332$	−9.71161	−	10.0220i	−0.532994	−	0.550029i
$333$	−42.1518	+	16.5434i	−2.30990	+	0.906570i
$334$	14.3931	−	15.8532i	0.787555	−	0.867448i
$335$	−32.3877	−	40.6129i	−1.76953	−	2.21892i
$336$	−29.9439	+	16.4015i	−1.63358	+	0.894777i
$337$	−13.9442	+	17.4855i	−0.759591	+	0.952498i	−0.999834	−	0.0182153i	$-0.994202\pi$
$337$	−13.9442	+	17.4855i	−0.759591	+	0.952498i	0.240243	+	0.970713i	$0.422773\pi$
$338$	−1.16257	−	7.18406i	−0.0632356	−	0.390762i
$339$	7.37753	+	0.552870i	0.400693	+	0.0300278i
$340$	−0.945235	−	0.347532i	−0.0512626	−	0.0188476i
$341$	−14.8213	−	15.9736i	−0.802619	−	0.865017i
$342$	8.78197	+	14.8372i	0.474875	+	0.802302i
$343$	18.1602	+	3.63416i	0.980559	+	0.196226i
$344$	1.07829	−	0.0350659i	0.0581375	−	0.00189063i
$345$	9.29202	−	8.62174i	0.500266	−	0.464179i
$346$	−1.51483	−	1.85788i	−0.0814379	−	0.0998802i
$347$	32.6811	+	2.44911i	1.75441	+	0.131475i	0.912747	−	0.408525i	$-0.133957\pi$
$347$	32.6811	+	2.44911i	1.75441	+	0.131475i	0.841665	+	0.540000i	$0.181576\pi$
$348$	16.4065	+	19.6825i	0.879479	+	1.05509i
$349$	−28.0313	−	22.3542i	−1.50048	−	1.19659i	−0.925684	−	0.378297i	$-0.876510\pi$
$349$	−28.0313	−	22.3542i	−1.50048	−	1.19659i	−0.574796	−	0.818297i	$-0.694919\pi$
$350$	22.3378	−	11.3075i	1.19401	−	0.604411i
$351$	37.7654	+	47.3564i	2.01577	+	2.52770i
$352$	2.94382	−	17.1270i	0.156906	−	0.912871i
$353$	6.82947	+	17.4012i	0.363496	+	0.926173i	0.989261	+	0.146161i	$0.0466918\pi$
$353$	6.82947	+	17.4012i	0.363496	+	0.926173i	−0.625765	+	0.780012i	$0.715213\pi$
$354$	65.0836	−	15.5988i	3.45915	−	0.829065i
$355$	15.4939	−	1.16111i	0.822332	−	0.0616253i
$356$	−22.0380	−	6.27817i	−1.16801	−	0.332742i
$357$	0.792502	+	0.975694i	0.0419436	+	0.0516392i
$358$	12.9536	−	4.14990i	0.684620	−	0.219329i
$359$	16.8795	+	2.54418i	0.890868	+	0.134277i	0.578498	−	0.815684i	$-0.303639\pi$
$359$	16.8795	+	2.54418i	0.890868	+	0.134277i	0.312370	+	0.949961i	$0.398877\pi$
$360$	57.8485	−	42.2586i	3.04888	−	2.22722i
$361$	−8.14565	+	14.1087i	−0.428718	+	0.742562i
$362$	1.88929	−	3.35581i	0.0992990	−	0.176378i
$363$	−2.18713	+	4.54162i	−0.114795	+	0.238373i
$364$	20.5986	+	9.15342i	1.07966	+	0.479769i
$365$	−2.54779	−	5.29055i	−0.133358	−	0.276920i
$366$	−30.8127	−	1.97359i	−1.61061	−	0.103161i
$367$	5.20108	+	4.82589i	0.271494	+	0.251910i	0.804156	−	0.594419i	$-0.202618\pi$
$367$	5.20108	+	4.82589i	0.271494	+	0.251910i	−0.532662	+	0.846328i	$0.678808\pi$
$368$	0.827682	−	4.52138i	0.0431459	−	0.235693i
$369$	13.1346	+	8.95504i	0.683762	+	0.466181i
$370$	16.3858	−	24.6021i	0.851857	−	1.27900i
$371$	−30.0301	−	4.25137i	−1.55908	−	0.220720i
$372$	−26.5944	−	37.2462i	−1.37885	−	1.93112i
$373$	22.6051	−	13.0511i	1.17045	−	0.675759i	0.216663	−	0.976247i	$-0.430483\pi$
$373$	22.6051	−	13.0511i	1.17045	−	0.675759i	0.953786	+	0.300488i	$0.0971495\pi$
$374$	−0.639775	+	0.00693298i	−0.0330820	+	0.000358496i
$375$	−15.4150	+	10.5098i	−0.796028	+	0.542723i
$376$	1.06063	−	9.01671i	0.0546978	−	0.465002i
$377$	3.76441	−	16.4930i	0.193877	−	0.849431i
$378$	−52.9654	+	5.02553i	−2.72425	+	0.258485i
$379$	−22.6378	+	5.16694i	−1.16283	+	0.265408i	−0.760034	−	0.649883i	$-0.774818\pi$
$379$	−22.6378	+	5.16694i	−1.16283	+	0.265408i	−0.402793	+	0.915291i	$0.631961\pi$
$380$	−10.2438	−	4.66243i	−0.525495	−	0.239178i
$381$	6.11584	−	19.8271i	0.313324	−	1.01577i
$382$	9.11290	+	7.10713i	0.466257	+	0.363632i
$383$	−19.8119	+	6.11115i	−1.01234	+	0.312265i	−0.756176	−	0.654368i	$-0.772935\pi$
$383$	−19.8119	+	6.11115i	−1.01234	+	0.312265i	−0.256163	+	0.966634i	$0.582458\pi$
$384$	10.7215	−	34.8887i	0.547129	−	1.78041i
$385$	18.7195	−	20.5411i	0.954035	−	1.04687i
$386$	−3.94506	+	28.2474i	−0.200798	+	1.43776i
$387$	2.63019	+	1.03227i	0.133700	+	0.0524734i
$388$	16.5254	+	10.7497i	0.838948	+	0.545735i
$389$	1.36490	+	9.05549i	0.0692030	+	0.459132i	0.996415	+	0.0845957i	$0.0269599\pi$
$389$	1.36490	+	9.05549i	0.0692030	+	0.459132i	−0.927212	+	0.374536i	$0.877802\pi$
$390$	−63.7089	−	18.8980i	−3.22602	−	0.956939i
$391$	−0.169230			−0.00855835
$392$	−16.6255	+	10.7513i	−0.839717	+	0.543025i
$393$	27.6638			1.39545
$394$	14.8443	+	4.40327i	0.747844	+	0.221834i
$395$	1.64288	+	10.8998i	0.0826625	+	0.548430i
$396$	24.8174	−	38.1513i	1.24712	−	1.91717i
$397$	26.7020	+	10.4798i	1.34013	+	0.525964i	0.923670	−	0.383188i	$-0.125174\pi$
$397$	26.7020	+	10.4798i	1.34013	+	0.525964i	0.416464	+	0.909152i	$0.363269\pi$
$398$	−3.19252	+	22.8590i	−0.160026	+	1.14582i
$399$	8.01706	+	11.5353i	0.401355	+	0.577489i
$400$	−8.68970	+	25.3155i	−0.434485	+	1.26577i
$401$	−7.87289	+	2.42846i	−0.393153	+	0.121272i	−0.485028	−	0.874499i	$-0.661190\pi$
$401$	−7.87289	+	2.42846i	−0.393153	+	0.121272i	0.0918742	+	0.995771i	$0.470714\pi$
$402$	−54.6554	−	42.6256i	−2.72597	−	2.12597i
$403$	−8.90617	+	28.8731i	−0.443648	+	1.43827i
$404$	−6.66191	+	14.6368i	−0.331443	+	0.728209i
$405$	78.8363	−	17.9939i	3.91741	−	0.894122i
$406$	10.3206	+	10.6904i	0.512203	+	0.530558i
$407$	4.17876	−	18.3084i	0.207134	−	0.907512i
$408$	−1.33458	−	0.156986i	−0.0660717	−	0.00777197i
$409$	−4.18943	+	2.85630i	−0.207154	+	0.141235i	−0.662453	−	0.749103i	$-0.730485\pi$
$409$	−4.18943	+	2.85630i	−0.207154	+	0.141235i	0.455299	+	0.890338i	$0.349532\pi$
$410$	−10.3767	+	0.112448i	−0.512467	+	0.00555339i
$411$	−10.9703	+	6.33372i	−0.541126	+	0.312419i
$412$	23.6545	−	16.8897i	1.16537	−	0.832096i
$413$	36.9831	−	11.7718i	1.81982	−	0.579254i
$414$	6.67315	−	10.0193i	0.327968	−	0.492421i
$415$	19.7130	+	13.4401i	0.967674	+	0.659749i
$416$	−22.6081	+	8.33932i	−1.10845	+	0.408869i
$417$	34.8948	+	32.3777i	1.70881	+	1.58554i
$418$	−7.13566	−	0.457047i	−0.349017	−	0.0223549i
$419$	0.871311	+	1.80930i	0.0425663	+	0.0883899i	0.921167	−	0.389166i	$-0.127237\pi$
$419$	0.871311	+	1.80930i	0.0425663	+	0.0883899i	−0.878601	+	0.477556i	$0.841523\pi$
$420$	44.4989	−	37.7736i	2.17133	−	1.84316i
$421$	−9.85422	+	20.4625i	−0.480265	+	0.997281i	0.510269	+	0.860015i	$0.329546\pi$
$421$	−9.85422	+	20.4625i	−0.480265	+	0.997281i	−0.990534	+	0.137266i	$0.956168\pi$
$422$	0.195629	−	0.347481i	0.00952307	−	0.0169151i
$423$	11.8887	−	20.5918i	0.578047	−	1.00121i
$424$	26.1818	−	19.1260i	1.27150	−	0.928839i
$425$	0.974418	+	0.146870i	0.0472662	+	0.00712423i
$426$	19.7433	−	6.32509i	0.956565	−	0.306452i
$427$	−17.9045	+	0.160498i	−0.866457	+	0.00776704i
$428$	−8.94053	+	31.3836i	−0.432157	+	1.51699i
$429$	−42.0995	+	3.15492i	−2.03258	+	0.152321i
$430$	−1.79365	+	0.429890i	−0.0864976	+	0.0207311i
$431$	−9.58070	−	24.4112i	−0.461486	−	1.17585i	−0.952457	−	0.304672i	$-0.901453\pi$
$431$	−9.58070	−	24.4112i	−0.461486	−	1.17585i	0.490971	−	0.871176i	$-0.336642\pi$
$432$	36.8431	−	43.3308i	1.77261	−	2.08475i
$433$	11.2393	+	14.0936i	0.540124	+	0.677294i	0.974745	−	0.223319i	$-0.0716892\pi$
$433$	11.2393	+	14.0936i	0.540124	+	0.677294i	−0.434621	+	0.900613i	$0.643118\pi$
$434$	−16.9551	−	20.4182i	−0.813870	−	0.980107i
$435$	−34.2497	−	27.3132i	−1.64215	−	1.30957i
$436$	7.32806	−	6.10836i	0.350950	−	0.292537i
$437$	−1.88596	−	0.141333i	−0.0902178	−	0.00676089i
$438$	−4.95124	−	6.07249i	−0.236580	−	0.290155i
$439$	−10.1152	+	9.38549i	−0.482770	+	0.447945i	−0.883624	−	0.468197i	$-0.844904\pi$
$439$	−10.1152	+	9.38549i	−0.482770	+	0.447945i	0.400854	+	0.916142i	$0.368713\pi$
$440$	0.965662	+	29.6945i	0.0460361	+	1.41563i
$441$	−51.1271	+	8.64623i	−2.43462	+	0.411725i
$442$	0.451893	+	0.763475i	0.0214944	+	0.0363148i
$443$	−17.3351	−	18.6827i	−0.823613	−	0.887644i	0.171620	−	0.985163i	$-0.445100\pi$
$443$	−17.3351	−	18.6827i	−0.823613	−	0.887644i	−0.995234	+	0.0975191i	$0.968909\pi$
$444$	13.6106	−	37.0187i	0.645930	−	1.75683i
$445$	39.0664	+	2.92762i	1.85192	+	0.138782i
$446$	1.22348	+	7.56043i	0.0579334	+	0.357997i
$447$	−16.0508	+	20.1271i	−0.759179	+	0.951981i
$448$	4.72678	−	20.6315i	0.223319	−	0.974745i
$449$	−11.4473	−	14.3544i	−0.540230	−	0.677427i	0.434537	−	0.900654i	$-0.356912\pi$
$449$	−11.4473	−	14.3544i	−0.540230	−	0.677427i	−0.974766	+	0.223227i	$0.928341\pi$
$450$	−47.1190	+	51.8990i	−2.22121	+	2.44654i
$451$	−6.13698	+	2.40859i	−0.288979	+	0.113416i
$452$	−3.29376	+	3.19175i	−0.154925	+	0.150127i
$453$	−24.5915	+	1.84288i	−1.15541	+	0.0865859i
$454$	−7.54868	+	7.15793i	−0.354277	+	0.335938i
$455$	−37.6456	−	8.23805i	−1.76485	−	0.386206i
$456$	−14.7419	−	2.86409i	−0.690355	−	0.134123i
$457$	−24.7112	−	3.72462i	−1.15594	−	0.174230i	−0.457039	−	0.889447i	$-0.651090\pi$
$457$	−24.7112	−	3.72462i	−1.15594	−	0.174230i	−0.698903	+	0.715217i	$0.746328\pi$
$458$	22.9792	+	10.7610i	1.07375	+	0.502830i
$459$	−1.81349	−	1.04702i	−0.0846465	−	0.0488707i
$460$	0.170295	+	7.85649i	0.00794005	+	0.366311i
$461$	6.84382	−	14.2113i	0.318749	−	0.661888i	−0.678612	−	0.734497i	$-0.737418\pi$
$461$	6.84382	−	14.2113i	0.318749	−	0.661888i	0.997361	+	0.0726087i	$0.0231324\pi$
$462$	17.9017	−	32.4750i	0.832862	−	1.51087i
$463$	14.7868	−	7.12095i	0.687201	−	0.330939i	−0.0574918	−	0.998346i	$-0.518310\pi$
$463$	14.7868	−	7.12095i	0.687201	−	0.330939i	0.744693	+	0.667407i	$0.232596\pi$
$464$	−15.8775	−	0.499593i	−0.737093	−	0.0231930i
$465$	57.3563	+	53.2189i	2.65983	+	2.46797i
$466$	−35.7919	−	7.76220i	−1.65803	−	0.359577i
$467$	9.67045	−	14.1839i	0.447495	−	0.656355i	−0.534520	−	0.845156i	$-0.679508\pi$
$467$	9.67045	−	14.1839i	0.447495	−	0.656355i	0.982015	+	0.188801i	$0.0604601\pi$
$468$	−63.0207	−	3.35129i	−2.91313	−	0.154913i
$469$	−33.4120	−	22.3438i	−1.54282	−	1.03174i
$470$	1.32758	+	15.4646i	0.0612366	+	0.713331i
$471$	−20.2589	−	35.0894i	−0.933480	−	1.61684i
$472$	−19.5667	+	36.5877i	−0.900630	+	1.68408i
$473$	−0.968174	+	0.660090i	−0.0445167	+	0.0303510i
$474$	5.52150	+	13.6323i	0.253611	+	0.626153i
$475$	10.7366	+	2.45056i	0.492628	+	0.112439i
$476$	−0.778512	−	0.0344043i	−0.0356830	−	0.00157692i
$477$	82.7876	−	18.8957i	3.79058	−	0.865176i
$478$	−1.95324	−	2.79922i	−0.0893392	−	0.128033i
$479$	28.4846	+	8.78634i	1.30150	+	0.401458i	0.866591	−	0.499018i	$-0.166306\pi$
$479$	28.4846	+	8.78634i	1.30150	+	0.401458i	0.434905	+	0.900477i	$0.356782\pi$
$480$	−5.94507	+	62.1158i	−0.271354	+	2.83518i
$481$	−24.8830	+	7.67539i	−1.13457	+	0.349968i
$482$	−20.8075	−	7.90723i	−0.947756	−	0.360165i
$483$	4.82780	−	8.53783i	0.219672	−	0.388485i
$484$	−1.20448	−	2.88360i	−0.0547491	−	0.131073i
$485$	−31.3740	−	12.3134i	−1.42462	−	0.559121i
$486$	42.6334	−	21.1033i	1.93389	−	0.957266i
$487$	2.39319	−	0.360715i	0.108446	−	0.0163455i	−0.0945952	−	0.995516i	$-0.530156\pi$
$487$	2.39319	−	0.360715i	0.108446	−	0.0163455i	0.203041	+	0.979170i	$0.434918\pi$
$488$	13.6011	−	13.4687i	0.615692	−	0.609698i
$489$	−39.6786			−1.79433
$490$	24.1406	−	23.7272i	1.09056	−	1.07189i
$491$		−	0.646345i		−	0.0291691i	−0.999894	−	0.0145846i	$-0.995357\pi$
$491$		−	0.646345i		−	0.0291691i	0.999894	−	0.0145846i	$-0.00464257\pi$
$492$	−13.4294	+	3.37296i	−0.605445	+	0.152065i
$493$	0.0871677	+	0.578320i	0.00392583	+	0.0260462i
$494$	4.39843	+	8.88582i	0.197895	+	0.399792i
$495$	−28.4272	+	72.4314i	−1.27771	+	3.25555i
$496$	28.2126	+	3.00906i	1.26678	+	0.135111i
$497$	11.1516	−	4.49245i	0.500218	−	0.201514i
$498$	29.7587	+	11.3088i	1.33352	+	0.506761i
$499$	7.51111	+	24.3504i	0.336244	+	1.09008i	0.953013	+	0.302931i	$0.0979651\pi$
$499$	7.51111	+	24.3504i	0.336244	+	1.09008i	−0.616769	+	0.787144i	$0.711559\pi$
$500$	1.47561	−	11.4718i	0.0659913	−	0.513033i
$501$	−14.3974	+	46.6752i	−0.643228	+	2.08529i
$502$	8.55813	−	5.97170i	0.381968	−	0.266530i
$503$	−8.26929	−	36.2301i	−0.368710	−	1.61542i	−0.730328	−	0.683096i	$-0.760633\pi$
$503$	−8.26929	−	36.2301i	−0.368710	−	1.61542i	0.361619	−	0.932326i	$-0.382224\pi$
$504$	32.7355	−	44.7351i	1.45815	−	1.99266i
$505$	6.11789	−	26.8042i	0.272243	−	1.19277i
$506$	1.87419	+	4.62728i	0.0833178	+	0.205708i
$507$	9.35187	+	13.7167i	0.415331	+	0.609179i
$508$	6.67151	+	10.9979i	0.296000	+	0.487952i
$509$	7.13381	−	4.11871i	0.316200	−	0.182558i	−0.333497	−	0.942751i	$-0.608229\pi$
$509$	7.13381	−	4.11871i	0.316200	−	0.182558i	0.649698	+	0.760193i	$0.274895\pi$
$510$	2.28896	−	0.196498i	0.101357	−	0.00870106i
$511$	−3.12022	−	3.30292i	−0.138030	−	0.146112i
$512$	11.7561	+	19.3338i	0.519550	+	0.854440i
$513$	−19.3357	−	13.1829i	−0.853694	−	0.582039i
$514$	8.20717	+	1.77989i	0.362003	+	0.0785077i
$515$	−33.7985	+	36.4262i	−1.48934	+	1.60513i
$516$	−2.19369	+	1.11562i	−0.0965718	+	0.0491124i
$517$	4.27847	+	8.88434i	0.188167	+	0.390733i
$518$	6.30773	−	21.9855i	0.277146	−	0.965987i
$519$	4.92684	+	2.37264i	0.216264	+	0.104147i
$520$	34.9894	−	21.7473i	1.53439	−	0.953684i
$521$	−7.61780	+	13.1944i	−0.333742	+	0.578058i	−0.983242	−	0.182303i	$-0.941645\pi$
$521$	−7.61780	+	13.1944i	−0.333742	+	0.578058i	0.649500	+	0.760361i	$0.274978\pi$
$522$	−37.6766	−	17.6437i	−1.64906	−	0.772246i
$523$	2.32974	−	15.4568i	0.101873	−	0.675880i	−0.878355	−	0.478008i	$-0.841359\pi$
$523$	2.32974	−	15.4568i	0.101873	−	0.675880i	0.980228	−	0.197872i	$-0.0634030\pi$
$524$	−11.3899	+	12.8218i	−0.497569	+	0.560122i
$525$	−35.2079	+	44.9704i	−1.53660	+	1.96267i
$526$	10.3536	+	10.9189i	0.451440	+	0.476085i
$527$	−0.0780629	−	1.04168i	−0.00340048	−	0.0453762i
$528$	10.4877	+	38.2302i	0.456420	+	1.66376i
$529$	−7.92041	−	20.1809i	−0.344366	−	0.877430i
$530$	−37.2611	+	41.0410i	−1.61852	+	1.78271i
$531$	−84.9571	+	67.7510i	−3.68682	+	2.94014i
$532$	−8.64727	−	1.03359i	−0.374907	−	0.0448118i
$533$	7.14726	+	5.69975i	0.309582	+	0.246884i
$534$	51.6016	−	8.35052i	2.23302	−	0.361362i
$535$	4.16913	−	55.6331i	0.180247	−	2.40523i
$536$	42.2593	−	7.78198i	1.82532	−	0.336130i
$537$	−22.7458	+	21.1050i	−0.981554	+	0.910749i
$538$	1.09206	+	1.84504i	0.0470820	+	0.0795452i
$539$	8.98155	−	19.5389i	0.386863	−	0.841599i
$540$	−46.7828	+	85.2446i	−2.01321	+	3.66834i
$541$	−3.88442	−	4.18640i	−0.167004	−	0.179988i	0.644005	−	0.765021i	$-0.277272\pi$
$541$	−3.88442	−	4.18640i	−0.167004	−	0.179988i	−0.811009	+	0.585034i	$0.801081\pi$
$542$	8.79232	−	7.16887i	0.377662	−	0.307929i
$543$	−0.656506	+	8.76047i	−0.0281734	+	0.375948i
$544$	0.622241	−	0.553925i	0.0266784	−	0.0237493i
$545$	−10.1691	+	12.7516i	−0.435596	+	0.546220i
$546$	−51.4096	+	1.01805i	−2.20013	+	0.0435683i
$547$	5.90158	−	4.70635i	0.252333	−	0.201229i	−0.489151	−	0.872199i	$-0.662693\pi$
$547$	5.90158	−	4.70635i	0.252333	−	0.201229i	0.741485	+	0.670970i	$0.234122\pi$
$548$	1.58116	−	7.69233i	0.0675440	−	0.328600i
$549$	46.6656	−	18.3149i	1.99164	−	0.781660i
$550$	−6.77558	−	28.2701i	−0.288912	−	1.20544i
$551$	0.488441	+	6.51779i	0.0208083	+	0.277667i
$552$	2.66427	+	10.1413i	0.113399	+	0.431644i
$553$	3.76947	+	7.65117i	0.160294	+	0.325361i
$554$	−1.41596	+	0.453628i	−0.0601586	+	0.0192728i
$555$	−10.0500	+	66.6773i	−0.426598	+	2.83029i
$556$	−29.3736	+	2.84256i	−1.24572	+	0.120551i
$557$	6.23661	+	3.60071i	0.264254	+	0.152567i	0.626273	−	0.779604i	$-0.284579\pi$
$557$	6.23661	+	3.60071i	0.264254	+	0.152567i	−0.362020	+	0.932170i	$0.617913\pi$
$558$	64.7507	+	36.4541i	2.74112	+	1.54322i
$559$	1.46393	+	0.704991i	0.0619176	+	0.0298179i
$560$	−0.813802	+	36.1769i	−0.0343894	+	1.52875i
$561$	1.31499	−	0.633266i	0.0555189	−	0.0267365i
$562$	6.60249	+	0.422896i	0.278509	+	0.0178388i
$563$	16.8555	−	18.1659i	0.710374	−	0.765602i	−0.269976	−	0.962867i	$-0.587016\pi$
$563$	16.8555	−	18.1659i	0.710374	−	0.765602i	0.980350	+	0.197266i	$0.0632061\pi$
$564$	6.53199	+	19.6535i	0.275046	+	0.827563i
$565$	4.41713	−	6.47874i	0.185830	−	0.272562i
$566$	−6.54561	−	4.35958i	−0.275132	−	0.183247i
$567$	53.9051	−	31.7698i	2.26380	−	1.33421i
$568$	−5.19721	+	11.7549i	−0.218070	+	0.493225i
$569$	16.6345	+	28.8119i	0.697356	+	1.20786i	0.969380	+	0.245566i	$0.0789737\pi$
$569$	16.6345	+	28.8119i	0.697356	+	1.20786i	−0.272024	+	0.962291i	$0.587693\pi$
$570$	25.6730	−	0.278208i	1.07532	−	0.0116528i
$571$	−15.0130	−	22.0200i	−0.628274	−	0.921508i	0.371703	−	0.928352i	$-0.378774\pi$
$571$	−15.0130	−	22.0200i	−0.628274	−	0.921508i	−0.999977	+	0.00684353i	$0.997822\pi$
$572$	15.8711	−	20.8115i	0.663605	−	0.870171i
$573$	−25.7019	−	5.86628i	−1.07371	−	0.245067i
$574$	−7.62461	+	2.51825i	−0.318245	+	0.105110i
$575$	−1.71101	−	7.49643i	−0.0713541	−	0.312623i
$576$	8.25866	+	58.6823i	0.344111	+	2.44510i
$577$	−10.0495	−	3.09985i	−0.418365	−	0.129049i	0.0784235	−	0.996920i	$-0.475011\pi$
$577$	−10.0495	−	3.09985i	−0.418365	−	0.129049i	−0.496789	+	0.867872i	$0.665488\pi$
$578$	18.9336	+	14.7663i	0.787536	+	0.614197i
$579$	−19.1776	−	62.1723i	−0.796995	−	2.58379i
$580$	26.7607	−	4.62870i	1.11118	−	0.192196i
$581$	17.6893	+	5.28324i	0.733874	+	0.219186i
$582$	−44.5391	−	6.22038i	−1.84620	−	0.257843i
$583$	−12.8660	+	32.7820i	−0.532854	+	1.35769i
$584$	4.85306	+	0.205365i	0.200821	+	0.00849805i
$585$	106.689	−	16.0808i	4.41106	−	0.664860i
$586$	18.2379	+	5.40992i	0.753399	+	0.223482i
$587$			30.9244i			1.27638i	0.769877	+	0.638192i	$0.220318\pi$
$587$			30.9244i			1.27638i	−0.769877	+	0.638192i	$0.779682\pi$
$588$	23.9451	−	38.2951i	0.987478	−	1.57927i
$589$		−	11.6740i		−	0.481019i
$590$	20.1726	−	68.0056i	0.830492	−	2.79975i
$591$	−34.9264	+	5.26430i	−1.43668	+	0.216544i
$592$	11.5538	+	21.5498i	0.474859	+	0.885692i
$593$	13.0018	−	33.1279i	0.533918	−	1.36040i	−0.368535	−	0.929614i	$-0.620141\pi$
$593$	13.0018	−	33.1279i	0.533918	−	1.36040i	0.902453	−	0.430787i	$-0.141764\pi$
$594$	−8.54473	+	61.1819i	−0.350595	+	2.51032i
$595$	1.31555	−	0.210365i	0.0539324	−	0.00862412i
$596$	−2.72010	−	15.7262i	−0.111420	−	0.644169i
$597$	−15.5194	−	50.3125i	−0.635165	−	2.05915i
$598$	4.25731	−	5.45882i	0.174095	−	0.223228i
$599$	−25.3262	−	7.81208i	−1.03480	−	0.319193i	−0.269590	−	0.962975i	$-0.586888\pi$
$599$	−25.3262	−	7.81208i	−1.03480	−	0.319193i	−0.765209	+	0.643782i	$0.777364\pi$
$600$	−6.53932	−	60.7055i	−0.266967	−	2.47829i
$601$	−9.54453	−	41.8173i	−0.389330	−	1.70576i	−0.666975	−	0.745080i	$-0.732411\pi$
$601$	−9.54453	−	41.8173i	−0.389330	−	1.70576i	0.277645	−	0.960684i	$-0.410446\pi$
$602$	−1.22162	+	0.737929i	−0.0497894	+	0.0300758i
$603$	109.715	+	25.0418i	4.46796	+	1.01978i
$604$	9.27077	−	12.1565i	0.377222	−	0.494643i
$605$	3.00963	+	4.41432i	0.122359	+	0.179468i
$606$	−0.397517	−	36.6829i	−0.0161480	−	1.49014i
$607$	1.58042	+	2.73737i	0.0641474	+	0.111107i	0.896315	−	0.443417i	$-0.146234\pi$
$607$	1.58042	+	2.73737i	0.0641474	+	0.111107i	−0.832168	+	0.554523i	$0.812901\pi$
$608$	7.39708	−	5.65346i	0.299991	−	0.229278i
$609$	−31.6635	−	12.1006i	−1.28307	−	0.490340i
$610$	−18.1405	+	27.2366i	−0.734485	+	1.10278i
$611$	7.70252	−	11.2975i	0.311611	−	0.457049i
$612$	2.07045	−	0.688128i	0.0836929	−	0.0278159i
$613$	12.3440	−	13.3037i	0.498570	−	0.537331i	−0.432759	−	0.901510i	$-0.642460\pi$
$613$	12.3440	−	13.3037i	0.498570	−	0.537331i	0.931329	+	0.364179i	$0.118650\pi$
$614$	−2.83791	+	44.3069i	−0.114529	+	1.78808i
$615$	21.3281	−	10.2711i	0.860033	−	0.414170i
$616$	7.68112	+	21.6679i	0.309481	+	0.873026i
$617$	37.8730	+	18.2387i	1.52471	+	0.734262i	0.993591	−	0.113035i	$-0.0360573\pi$
$617$	37.8730	+	18.2387i	1.52471	+	0.734262i	0.531119	+	0.847297i	$0.321772\pi$
$618$	−32.5276	+	57.7764i	−1.30845	+	2.32411i
$619$	−13.2493	−	7.64952i	−0.532536	−	0.307460i	0.209512	−	0.977806i	$-0.432812\pi$
$619$	−13.2493	−	7.64952i	−0.532536	−	0.307460i	−0.742049	+	0.670346i	$0.766146\pi$
$620$	−48.2811	+	4.67229i	−1.93902	+	0.187644i
$621$	−2.43530	+	16.1572i	−0.0977253	+	0.648365i
$622$	7.06210	+	22.0438i	0.283164	+	0.883876i
$623$	29.4918	−	7.01003i	1.18156	−	0.280851i
$624$	38.6378	−	39.1000i	1.54675	−	1.56525i
$625$	−1.02251	−	13.6444i	−0.0409002	−	0.545776i
$626$	14.9508	−	3.58331i	0.597556	−	0.143218i
$627$	15.1836	−	5.95911i	0.606374	−	0.237984i
$628$	24.6045	+	5.05748i	0.981827	+	0.201815i
$629$	0.703837	−	0.561291i	0.0280638	−	0.0223801i
$630$	−39.4207	+	86.1825i	−1.57056	+	3.43359i
$631$	9.72213	−	12.1912i	0.387032	−	0.485323i	−0.549704	−	0.835359i	$-0.685260\pi$
$631$	9.72213	−	12.1912i	0.387032	−	0.485323i	0.936736	+	0.350037i	$0.113831\pi$
$632$	−8.59171	−	3.05362i	−0.341760	−	0.121467i
$633$	−0.0679787	+	0.907113i	−0.00270191	+	0.0360545i
$634$	8.30588	+	10.1868i	0.329869	+	0.404570i
$635$	−14.9579	−	16.1208i	−0.593587	−	0.639734i
$636$	−35.5853	+	64.8412i	−1.41105	+	2.57112i
$637$	−29.6906	+	2.76105i	−1.17638	+	0.109397i
$638$	14.8477	−	8.78819i	0.587825	−	0.347928i
$639$	−24.6750	+	22.8950i	−0.976126	+	0.905713i
$640$	−26.3420	−	28.3300i	−1.04126	−	1.11984i
$641$	0.973886	−	12.9956i	0.0384662	−	0.513296i	−0.944378	−	0.328861i	$-0.893335\pi$
$641$	0.973886	−	12.9956i	0.0384662	−	0.513296i	0.982845	−	0.184435i	$-0.0590456\pi$
$642$	−11.8917	−	73.4842i	−0.469328	−	2.90019i
$643$	30.0919	+	23.9975i	1.18671	+	0.946370i	0.999355	−	0.0359220i	$-0.0114368\pi$
$643$	30.0919	+	23.9975i	1.18671	+	0.946370i	0.187356	+	0.982292i	$0.440008\pi$
$644$	1.96943	+	5.75284i	0.0776066	+	0.226694i
$645$	3.28958	−	2.62335i	0.129527	−	0.103294i
$646$	−0.253781	−	0.230408i	−0.00998489	−	0.00906527i
$647$	−11.4494	−	29.1725i	−0.450121	−	1.14689i	−0.958332	−	0.285657i	$-0.907788\pi$
$647$	−11.4494	−	29.1725i	−0.450121	−	1.14689i	0.508211	−	0.861233i	$-0.330307\pi$
$648$	−17.6285	+	64.5261i	−0.692511	+	2.53482i
$649$	−3.36770	−	44.9389i	−0.132194	−	1.76400i
$650$	−29.2509	+	27.7367i	−1.14731	+	1.08792i
$651$	54.7805	+	25.7786i	2.14702	+	1.01034i
$652$	16.3367	−	18.3905i	0.639793	−	0.720226i
$653$	−5.56920	+	36.9492i	−0.217940	+	1.44593i	0.565645	+	0.824649i	$0.308627\pi$
$653$	−5.56920	+	36.9492i	−0.217940	+	1.44593i	−0.783584	+	0.621286i	$0.786611\pi$
$654$	−9.22941	+	19.7086i	−0.360898	+	0.770666i
$655$	14.6602	−	25.3922i	0.572821	−	0.992155i
$656$	3.96591	−	7.61307i	0.154843	−	0.297240i
$657$	11.4616	+	5.51961i	0.447159	+	0.215340i
$658$	4.60832	+	11.0909i	0.179651	+	0.432370i
$659$	−18.7748	−	38.9863i	−0.731363	−	1.51869i	−0.850594	−	0.525823i	$-0.823757\pi$
$659$	−18.7748	−	38.9863i	−0.731363	−	1.51869i	0.119231	−	0.992867i	$-0.461957\pi$
$660$	−30.7225	−	60.4109i	−1.19587	−	2.35149i
$661$	16.2074	−	17.4675i	0.630396	−	0.679405i	−0.334392	−	0.942434i	$-0.608531\pi$
$661$	16.2074	−	17.4675i	0.630396	−	0.679405i	0.964788	+	0.263029i	$0.0847215\pi$
$662$	5.07710	−	23.4107i	0.197327	−	0.909884i
$663$	−1.67217	−	1.14007i	−0.0649417	−	0.0442765i
$664$	−17.4938	+	9.13658i	−0.678893	+	0.354568i
$665$	14.8367	−	1.24569i	0.575341	−	0.0483057i
$666$	5.47729	+	63.8037i	0.212241	+	2.47234i
$667$	3.95217	−	2.28178i	0.153028	−	0.0883510i
$668$	−15.7055	−	25.8903i	−0.607664	−	1.00173i
$669$	−9.84181	−	14.4353i	−0.380506	−	0.558100i
$670$	−68.0895	+	27.5783i	−2.63053	+	1.06544i
$671$	−4.62624	+	20.2689i	−0.178594	+	0.782472i
$672$	10.1947	+	47.1950i	0.393270	+	1.82059i
$673$	3.03308	+	13.2888i	0.116917	+	0.512246i	0.999142	+	0.0414180i	$0.0131875\pi$
$673$	3.03308	+	13.2888i	0.116917	+	0.512246i	−0.882225	+	0.470828i	$0.843955\pi$
$674$	18.0992	+	25.9382i	0.697154	+	0.999103i
$675$	28.0446	−	90.9184i	1.07944	−	3.49945i
$676$	−10.2079	−	1.31304i	−0.392610	−	0.0505014i
$677$	7.34279	+	23.8047i	0.282206	+	0.914891i	0.980069	+	0.198659i	$0.0636586\pi$
$677$	7.34279	+	23.8047i	0.282206	+	0.914891i	−0.697862	+	0.716232i	$0.745865\pi$
$678$	3.71668	−	9.78027i	0.142738	−	0.375609i
$679$	−26.0228	−	1.71571i	−0.998662	−	0.0658430i
$680$	−0.851345	+	1.14180i	−0.0326476	+	0.0437860i
$681$	8.66980	−	22.0903i	0.332228	−	0.846502i
$682$	−27.6181	+	13.6708i	−1.05755	+	0.523483i
$683$	2.19074	+	14.5346i	0.0838263	+	0.556151i	0.990839	+	0.135048i	$0.0431189\pi$
$683$	2.19074	+	14.5346i	0.0838263	+	0.556151i	−0.907013	+	0.421103i	$0.861643\pi$
$684$	23.6485	−	5.93959i	0.904222	−	0.227106i
$685$			13.4260i			0.512980i
$686$	12.2309	−	23.1604i	0.466979	−	0.884269i
$687$	−57.8829			−2.20837
$688$	0.386122	−	1.47607i	0.0147208	−	0.0562747i
$689$	48.2868	−	7.27807i	1.83958	−	0.277272i
$690$	−7.95248	−	16.0658i	−0.302746	−	0.611615i
$691$	24.6396	+	9.67031i	0.937333	+	0.367876i	0.784326	−	0.620349i	$-0.213009\pi$
$691$	24.6396	+	9.67031i	0.937333	+	0.367876i	0.153007	+	0.988225i	$0.451104\pi$
$692$	−3.12819	+	1.30664i	−0.118916	+	0.0496711i
$693$	−3.96098	+	60.0774i	−0.150465	+	2.28215i
$694$	16.4642	−	43.3247i	0.624972	−	1.64458i
$695$	48.2112	−	14.8712i	1.82875	−	0.564096i
$696$	33.2842	−	14.3284i	1.26164	−	0.543116i
$697$	−0.302002	−	0.0931553i	−0.0114391	−	0.00352851i
$698$	−41.5819	+	29.0150i	−1.57390	+	1.09824i
$699$	81.4511	−	18.5907i	3.08076	−	0.703164i
$700$	−6.34716	−	34.8337i	−0.239900	−	1.31659i
$701$	30.9041	+	7.05367i	1.16723	+	0.266413i	0.761862	−	0.647739i	$-0.224285\pi$
$701$	30.9041	+	7.05367i	1.16723	+	0.266413i	0.405371	+	0.914152i	$0.367142\pi$
$702$	79.3952	−	32.1575i	2.99658	−	1.21371i
$703$	8.31256	−	5.66741i	0.313514	−	0.213750i
$704$	−22.0372	−	10.8794i	−0.830557	−	0.410033i
$705$	−17.7037	−	30.6637i	−0.666760	−	1.15486i
$706$	26.3396	−	2.26115i	0.991304	−	0.0850995i
$707$	−1.77990	−	21.1993i	−0.0669401	−	0.797284i
$708$	5.02609	−	94.5152i	0.188892	−	3.55210i
$709$	−29.3190	+	43.0031i	−1.10110	+	1.61502i	−0.375617	+	0.926775i	$0.622569\pi$
$709$	−29.3190	+	43.0031i	−1.10110	+	1.61502i	−0.725483	+	0.688241i	$0.758383\pi$
$710$	4.65707	−	21.4740i	0.174777	−	0.805904i
$711$	−17.5056	−	16.2428i	−0.656510	−	0.609153i
$712$	−17.3753	+	27.3547i	−0.651167	+	1.02516i
$713$	−7.34375	+	3.53656i	−0.275025	+	0.132445i
$714$	1.64159	−	0.682088i	0.0614351	−	0.0255265i
$715$	−19.4144	+	40.3144i	−0.726057	+	1.50767i
$716$	−0.416863	−	19.2318i	−0.0155789	−	0.718726i
$717$	6.74323	+	3.89321i	0.251831	+	0.145394i
$718$	10.2380	−	21.8624i	0.382081	−	0.815899i
$719$	49.4325	+	7.45074i	1.84352	+	0.277866i	0.975716	−	0.219041i	$-0.0702929\pi$
$719$	49.4325	+	7.45074i	1.84352	+	0.277866i	0.867804	+	0.496907i	$0.165531\pi$
$720$	−34.0297	−	95.4277i	−1.26821	−	3.55638i
$721$	−16.3716	+	34.7903i	−0.609710	+	1.29566i
$722$	15.8528	+	16.7183i	0.589982	+	0.622189i
$723$	50.6355	−	3.79461i	1.88316	−	0.141123i
$724$	−3.79005	−	3.91118i	−0.140856	−	0.145358i
$725$	−24.7366	+	9.70840i	−0.918694	+	0.360561i
$726$	5.27801	+	4.79190i	0.195885	+	0.177844i
$727$	−4.33400	−	5.43466i	−0.160739	−	0.201560i	0.694939	−	0.719068i	$-0.255431\pi$
$727$	−4.33400	−	5.43466i	−0.160739	−	0.201560i	−0.855678	+	0.517508i	$0.826860\pi$
$728$	20.6947	−	24.2467i	0.766997	−	0.898643i
$729$	−23.4237	+	29.3724i	−0.867544	+	1.08787i
$730$	−8.19771	+	1.32661i	−0.303411	+	0.0491000i
$731$	−0.0560162	−	0.00419783i	−0.00207183	−	0.000155263i
$732$	−15.0681	+	40.9828i	−0.556932	+	1.51477i
$733$	8.17257	+	8.80794i	0.301861	+	0.325329i	0.865707	−	0.500551i	$-0.166869\pi$
$733$	8.17257	+	8.80794i	0.301861	+	0.325329i	−0.563846	+	0.825880i	$0.690679\pi$
$734$	8.63482	−	5.11086i	0.318717	−	0.188645i
$735$	−26.9169	+	72.3721i	−0.992847	+	2.66949i
$736$	−5.79731	−	2.94059i	−0.213692	−	0.108392i
$737$	−34.2122	+	31.7443i	−1.26022	+	1.16932i
$738$	17.4239	−	14.2067i	0.641383	−	0.522955i
$739$	7.70780	+	0.577620i	0.283536	+	0.0212481i	0.215739	−	0.976451i	$-0.430784\pi$
$739$	7.70780	+	0.577620i	0.283536	+	0.0212481i	0.0677970	+	0.997699i	$0.478403\pi$
$740$	−26.7661	−	32.1107i	−0.983942	−	1.18041i
$741$	−17.6831	−	14.1018i	−0.649605	−	0.518043i
$742$	−17.8416	+	39.0056i	−0.654984	+	1.43194i
$743$	−27.1585	−	34.0557i	−0.996349	−	1.24938i	−0.968304	−	0.249775i	$-0.919643\pi$
$743$	−27.1585	−	34.0557i	−0.996349	−	1.24938i	−0.0280446	−	0.999607i	$-0.508928\pi$
$744$	−61.1949	+	21.0776i	−2.24351	+	0.772742i
$745$	9.96838	+	25.3990i	0.365213	+	0.930548i
$746$	−8.60362	−	35.8974i	−0.315001	−	1.31430i
$747$	−51.5437	+	3.86266i	−1.88588	+	0.141327i
$748$	−0.247904	+	0.870209i	−0.00906427	+	0.0318180i
$749$	−9.98275	−	41.9983i	−0.364762	−	1.53459i
$750$	8.04979	+	25.1268i	0.293937	+	0.917502i
$751$	−35.0874	−	5.28858i	−1.28036	−	0.192983i	−0.526588	−	0.850121i	$-0.676529\pi$
$751$	−35.0874	−	5.28858i	−1.28036	−	0.192983i	−0.753771	+	0.657138i	$0.771767\pi$
$752$	−11.7985	−	5.06435i	−0.430247	−	0.184678i
$753$	−11.9028	+	20.6163i	−0.433762	+	0.751299i
$754$	−20.8476	−	11.7370i	−0.759223	−	0.427436i
$755$	−11.3405	+	23.5488i	−0.412722	+	0.857027i
$756$	−14.4879	+	73.8329i	−0.526918	+	2.68527i
$757$	−11.6136	−	24.1159i	−0.422104	−	0.876508i	−0.998249	−	0.0591600i	$-0.981158\pi$
$757$	−11.6136	−	24.1159i	−0.422104	−	0.876508i	0.576145	−	0.817348i	$-0.304557\pi$
$758$	−2.09901	+	32.7709i	−0.0762395	+	1.19029i
$759$	−8.34845	−	7.74623i	−0.303030	−	0.281170i
$760$	−10.4413	+	12.0136i	−0.378744	+	0.435779i
$761$	−6.42506	−	4.38053i	−0.232908	−	0.158794i	0.441243	−	0.897388i	$-0.354538\pi$
$761$	−6.42506	−	4.38053i	−0.232908	−	0.158794i	−0.674151	+	0.738594i	$0.735490\pi$
$762$	−24.4223	−	16.2660i	−0.884726	−	0.589255i
$763$	−4.50522	+	11.7888i	−0.163100	+	0.426782i
$764$	13.3010	−	9.49714i	0.481214	−	0.343594i
$765$	−3.23035	+	1.86504i	−0.116793	+	0.0674307i
$766$	0.317719	+	29.3191i	0.0114797	+	1.05934i
$767$	−51.6305	+	35.2011i	−1.86427	+	1.27104i
$768$	−42.9909	−	28.5679i	−1.55130	−	1.03086i
$769$	6.97178	−	30.5454i	0.251409	−	1.10149i	−0.678759	−	0.734361i	$-0.737482\pi$
$769$	6.97178	−	30.5454i	0.251409	−	1.10149i	0.930168	−	0.367134i	$-0.119661\pi$
$770$	−20.3215	−	33.6415i	−0.732335	−	1.21236i
$771$	−18.6770	+	4.26289i	−0.672634	+	0.153524i
$772$	36.7118	+	16.7093i	1.32129	+	0.601381i
$773$	1.04676	−	3.39353i	0.0376495	−	0.122057i	−0.934797	−	0.355182i	$-0.884419\pi$
$773$	1.04676	−	3.39353i	0.0376495	−	0.122057i	0.972447	+	0.233125i	$0.0748952\pi$
$774$	2.45738	−	3.15091i	0.0883288	−	0.113257i
$775$	45.3541	−	13.9899i	1.62917	−	0.502531i
$776$	21.2209	−	18.0821i	0.761785	−	0.649111i
$777$	8.23862	+	51.5217i	0.295559	+	1.84833i
$778$	12.8266	+	1.79137i	0.459855	+	0.0642238i
$779$	−3.28781	−	1.29037i	−0.117798	−	0.0462324i
$780$	−51.2447	+	78.7775i	−1.83485	+	2.82069i
$781$	−2.08057	−	13.8037i	−0.0744487	−	0.493935i
$782$	−0.0680609	+	0.229446i	−0.00243385	+	0.00820498i
$783$	56.4691			2.01804
$784$	7.89046	+	26.8652i	0.281802	+	0.959473i
$785$	−42.9441			−1.53274
$786$	11.1258	−	37.5072i	0.396844	−	1.33784i
$787$	0.262435	+	1.74114i	0.00935480	+	0.0620650i	0.993021	−	0.117936i	$-0.0376279\pi$
$787$	0.262435	+	1.74114i	0.00935480	+	0.0620650i	−0.983666	+	0.180001i	$0.942390\pi$
$788$	11.9401	−	18.3553i	0.425349	−	0.653880i
$789$	−31.9527	−	12.5405i	−1.13755	−	0.446454i
$790$	15.4390	+	2.15622i	0.549293	+	0.0767149i
$791$	1.73635	−	5.81363i	0.0617375	−	0.206709i
$792$	−41.7453	−	48.9916i	−1.48335	−	1.74084i
$793$	27.5476	−	8.49731i	0.978243	−	0.301748i
$794$	24.9477	−	31.9884i	0.885359	−	1.13523i
$795$	37.2722	−	120.833i	1.32191	−	4.28552i
$796$	29.7088	+	13.5219i	1.05300	+	0.479271i
$797$	35.6006	−	8.12560i	1.26104	−	0.287823i	0.460798	−	0.887505i	$-0.347563\pi$
$797$	35.6006	−	8.12560i	1.26104	−	0.287823i	0.800239	+	0.599682i	$0.204706\pi$
$798$	18.8641	−	6.23043i	0.667783	−	0.220555i
$799$	−0.105188	+	0.460861i	−0.00372130	+	0.0163041i
$800$	30.8285	+	21.9630i	1.08995	+	0.776511i
$801$	−70.1243	+	47.8100i	−2.47772	+	1.68928i
$802$	0.126256	+	11.6509i	0.00445826	+	0.411408i
$803$	−4.56896	+	2.63789i	−0.161235	+	0.0930891i
$804$	−79.7740	+	56.9599i	−2.81341	+	2.00882i
$805$	−5.27829	−	8.95590i	−0.186035	−	0.315654i
$806$	35.5649	+	23.6873i	1.25272	+	0.834351i
$807$	−4.04102	−	2.75512i	−0.142251	−	0.0969848i
$808$	17.1656	+	14.9190i	0.603885	+	0.524848i
$809$	−6.17105	−	5.72590i	−0.216963	−	0.201312i	0.564202	−	0.825637i	$-0.309184\pi$
$809$	−6.17105	−	5.72590i	−0.216963	−	0.201312i	−0.781165	+	0.624325i	$0.785374\pi$
$810$	7.30981	−	114.125i	0.256840	−	4.00993i
$811$	−3.48582	−	7.23838i	−0.122404	−	0.254174i	0.830759	−	0.556633i	$-0.187907\pi$
$811$	−3.48582	−	7.23838i	−0.122404	−	0.254174i	−0.953163	+	0.302459i	$0.902193\pi$
$812$	18.6451	−	9.69344i	0.654313	−	0.340173i
$813$	−11.2284	+	23.3160i	−0.393798	+	0.817729i
$814$	−23.1423	−	13.0289i	−0.811136	−	0.456662i
$815$	−21.0273	+	36.4204i	−0.736555	+	1.27575i
$816$	−0.749586	+	1.74632i	−0.0262408	+	0.0611335i
$817$	−0.620758	−	0.0935642i	−0.0217176	−	0.00327340i
$818$	2.18774	+	6.82886i	0.0764925	+	0.238765i
$819$	74.8909	−	36.8962i	2.61690	−	1.28926i
$820$	−4.02082	+	14.1141i	−0.140413	+	0.492887i
$821$	−20.9463	+	1.56971i	−0.731031	+	0.0547832i	−0.435045	−	0.900409i	$-0.643267\pi$
$821$	−20.9463	+	1.56971i	−0.731031	+	0.0547832i	−0.295986	+	0.955192i	$0.595648\pi$
$822$	4.17536	+	17.4211i	0.145632	+	0.607630i
$823$	1.35484	+	3.45208i	0.0472268	+	0.120332i	0.952541	−	0.304411i	$-0.0984597\pi$
$823$	1.35484	+	3.45208i	0.0472268	+	0.120332i	−0.905314	+	0.424743i	$0.860364\pi$
$824$	−13.3861	−	38.8640i	−0.466326	−	1.35389i
$825$	41.3471	+	51.8477i	1.43952	+	1.80510i
$826$	−1.08671	−	54.8768i	−0.0378114	−	1.90941i
$827$	−29.7467	−	23.7222i	−1.03439	−	0.824902i	−0.0496251	−	0.998768i	$-0.515803\pi$
$827$	−29.7467	−	23.7222i	−1.03439	−	0.824902i	−0.984769	+	0.173866i	$0.944374\pi$
$828$	−10.9006	−	13.0771i	−0.378821	−	0.454462i
$829$	23.4817	+	1.75971i	0.815552	+	0.0611172i	0.475972	−	0.879460i	$-0.342096\pi$
$829$	23.4817	+	1.75971i	0.815552	+	0.0611172i	0.339579	+	0.940577i	$0.389715\pi$
$830$	26.1505	−	21.3220i	0.907698	−	0.740097i
$831$	2.48635	−	2.30700i	0.0862506	−	0.0800289i
$832$	2.21412	+	34.0065i	0.0767608	+	1.17896i
$833$	0.920623	−	0.463860i	0.0318977	−	0.0160718i
$834$	57.9323	−	34.2896i	2.00603	−	1.18735i
$835$	35.2127	+	37.9502i	1.21858	+	1.31332i
$836$	−3.48949	+	9.49087i	−0.120686	+	0.328249i
$837$	−100.577	−	7.53719i	−3.47644	−	0.260524i
$838$	2.80351	−	0.453682i	0.0968455	−	0.0156722i
$839$	−6.31349	+	7.91687i	−0.217966	+	0.273321i	−0.878778	−	0.477231i	$-0.841641\pi$
$839$	−6.31349	+	7.91687i	−0.217966	+	0.273321i	0.660812	+	0.750551i	$0.270212\pi$
$840$	−33.3177	−	75.5244i	−1.14957	−	2.60584i
$841$	8.24786	+	10.3425i	0.284409	+	0.356637i
$842$	23.7803	+	21.5901i	0.819525	+	0.744046i
$843$	−14.0491	+	5.51385i	−0.483875	+	0.189907i
$844$	−0.392445	−	0.404987i	−0.0135085	−	0.0139402i
$845$	17.5463	−	1.31491i	0.603610	−	0.0452343i
$846$	−23.1374	−	24.4005i	−0.795481	−	0.838907i
$847$	3.25510	+	2.54846i	0.111847	+	0.0875661i
$848$	−15.4016	−	43.1899i	−0.528893	−	1.48315i
$849$	17.7401	+	2.67388i	0.608837	+	0.0917674i
$850$	0.591019	−	1.26207i	0.0202718	−	0.0432886i
$851$	−6.08342	−	3.51227i	−0.208537	−	0.120399i
$852$	−0.635363	−	29.3122i	−0.0217672	−	1.00422i
$853$	23.1098	−	47.9880i	0.791264	−	1.64308i	0.0257405	−	0.999669i	$-0.491806\pi$
$853$	23.1098	−	47.9880i	0.791264	−	1.64308i	0.765523	−	0.643408i	$-0.222480\pi$
$854$	−6.98318	+	24.3398i	−0.238960	+	0.832891i
$855$	−37.5577	+	18.0868i	−1.28445	+	0.618556i
$856$	38.9549	+	24.7436i	1.33145	+	0.845719i
$857$	−20.9796	−	19.4663i	−0.716651	−	0.664955i	0.235049	−	0.971983i	$-0.424475\pi$
$857$	−20.9796	−	19.4663i	−0.716651	−	0.664955i	−0.951700	+	0.307029i	$0.900665\pi$
$858$	−12.6540	+	58.3483i	−0.432001	+	1.99198i
$859$	9.23965	−	13.5521i	0.315253	−	0.462391i	−0.635607	−	0.772013i	$-0.719250\pi$
$859$	9.23965	−	13.5521i	0.315253	−	0.462391i	0.950860	+	0.309622i	$0.100202\pi$
$860$	−0.138515	+	2.60477i	−0.00472332	+	0.0888218i
$861$	13.3153	−	12.5787i	0.453783	−	0.428682i
$862$	−36.9504	+	3.17204i	−1.25854	+	0.108040i
$863$	9.99629	+	17.3141i	0.340278	+	0.589378i	0.984484	−	0.175473i	$-0.0561456\pi$
$863$	9.99629	+	17.3141i	0.340278	+	0.589378i	−0.644206	+	0.764852i	$0.722812\pi$
$864$	−43.9313	−	67.3793i	−1.49457	−	2.29229i
$865$	4.78875	−	3.26491i	0.162822	−	0.111010i
$866$	23.6286	−	9.57029i	0.802931	−	0.325212i
$867$	−53.4001	−	12.1882i	−1.81356	−	0.413934i
$868$	−34.5025	+	14.7763i	−1.17109	+	0.501540i
$869$	9.65530	−	2.20376i	0.327534	−	0.0747574i
$870$	−50.8063	+	35.4516i	−1.72249	+	1.20192i
$871$	61.8405	+	19.0753i	2.09539	+	0.646341i
$872$	−5.33466	−	12.3922i	−0.180654	−	0.419653i
$873$	69.7728	−	21.5221i	2.36145	−	0.728412i
$874$	−0.950116	+	2.50019i	−0.0321382	+	0.0845701i
$875$	5.71744	+	14.1924i	0.193285	+	0.479790i
$876$	−10.2245	+	4.27077i	−0.345454	+	0.144296i
$877$	48.0696	+	18.8659i	1.62319	+	0.637057i	0.990521	−	0.137361i	$-0.0438622\pi$
$877$	48.0696	+	18.8659i	1.62319	+	0.637057i	0.632674	+	0.774418i	$0.281957\pi$
$878$	8.65695	+	17.4890i	0.292158	+	0.590225i
$879$	−42.9110	+	6.46779i	−1.44735	+	0.218153i
$880$	40.6488	+	10.6332i	1.37027	+	0.358446i
$881$	58.4334			1.96867			0.984336	−	0.176300i	$-0.0564129\pi$
$881$	58.4334			1.96867			0.984336	+	0.176300i	$0.0564129\pi$
$882$	−8.83949	+	72.7966i	−0.297641	+	2.45119i
$883$			8.40675i			0.282910i	0.989945	+	0.141455i	$0.0451780\pi$
$883$			8.40675i			0.282910i	−0.989945	+	0.141455i	$0.954822\pi$
$884$	1.21688	−	0.305633i	0.0409280	−	0.0102796i
$885$	24.1172	+	160.007i	0.810690	+	5.37858i
$886$	−32.3023	+	15.9894i	−1.08522	+	0.537176i
$887$	13.8839	−	35.3755i	0.466174	−	1.18779i	−0.483720	−	0.875223i	$-0.660715\pi$
$887$	13.8839	−	35.3755i	0.466174	−	1.18779i	0.949895	−	0.312570i	$-0.101190\pi$
$888$	−44.7169	−	33.3417i	−1.50060	−	1.11887i
$889$	−14.8123	−	8.37578i	−0.496790	−	0.280915i
$890$	19.6810	−	51.7896i	0.659708	−	1.73599i
$891$	−21.4146	−	69.4246i	−0.717418	−	2.32581i
$892$	10.7426	+	1.38182i	0.359690	+	0.0462669i
$893$	−1.55715	+	5.04814i	−0.0521079	+	0.168930i
$894$	20.8335	+	29.8568i	0.696776	+	0.998561i
$895$	7.31804	+	32.0624i	0.244615	+	1.07173i
$896$	−26.0716	−	14.7062i	−0.870990	−	0.491300i
$897$	−3.51402	+	15.3959i	−0.117330	+	0.514055i
$898$	−24.0659	+	9.74741i	−0.803089	+	0.325275i
$899$	15.8683	+	23.2745i	0.529238	+	0.776249i
$900$	51.4155	+	84.7576i	1.71385	+	2.82525i
$901$	−1.46203	+	0.844105i	−0.0487074	+	0.0281212i
$902$	0.797452	+	9.28934i	0.0265522	+	0.309301i
$903$	1.80981	−	2.70631i	0.0602268	−	0.0900604i
$904$	3.00276	+	5.74940i	0.0998703	+	0.191222i
$905$	7.69319	+	5.24513i	0.255730	+	0.174354i
$906$	−7.39156	+	34.0828i	−0.245568	+	1.13233i
$907$	−19.6901	+	21.2208i	−0.653797	+	0.704626i	−0.969737	−	0.244153i	$-0.921490\pi$
$907$	−19.6901	+	21.2208i	−0.653797	+	0.704626i	0.315939	+	0.948779i	$0.397680\pi$
$908$	6.66896	+	13.1134i	0.221317	+	0.435185i
$909$	25.8433	+	53.6642i	0.857169	+	1.77993i
$910$	−26.3096	+	47.7275i	−0.872154	+	1.58215i
$911$	16.8252	+	8.10257i	0.557442	+	0.268450i	0.691321	−	0.722548i	$-0.257029\pi$
$911$	16.8252	+	8.10257i	0.557442	+	0.268450i	−0.133879	+	0.990998i	$0.542743\pi$
$912$	−9.81209	+	18.8356i	−0.324911	+	0.623708i
$913$	10.7180	−	18.5641i	0.354714	−	0.614382i
$914$	−14.9882	+	32.0060i	−0.495767	+	1.05867i
$915$	11.1262	−	73.8174i	0.367820	−	2.44033i
$916$	23.8318	−	26.8279i	0.787425	−	0.886417i
$917$	4.84997	−	22.1630i	0.160160	−	0.731888i
$918$	−2.14892	+	2.03768i	−0.0709249	+	0.0672535i
$919$	0.539153	+	7.19450i	0.0177850	+	0.237325i	0.999011	+	0.0444632i	$0.0141578\pi$
$919$	0.539153	+	7.19450i	0.0177850	+	0.237325i	−0.981226	+	0.192861i	$0.938223\pi$
$920$	10.7205	+	2.92882i	0.353444	+	0.0965605i
$921$	−37.0015	−	94.2782i	−1.21924	−	3.10657i
$922$	−16.5156	−	14.9945i	−0.543913	−	0.493818i
$923$	−15.1338	+	12.0688i	−0.498136	+	0.397250i
$924$	−36.8307	−	37.3323i	−1.21164	−	1.22814i
$925$	31.9798	+	25.5030i	1.05149	+	0.838534i
$926$	−3.70780	−	22.9122i	−0.121846	−	0.752940i
$927$	8.04485	−	107.351i	0.264228	−	3.52587i
$928$	−7.06294	+	21.3261i	−0.231852	+	0.700063i
$929$	33.8015	−	31.3632i	1.10899	−	1.02899i	0.109606	−	0.993975i	$-0.465041\pi$
$929$	33.8015	−	31.3632i	1.10899	−	1.02899i	0.999387	−	0.0350195i	$-0.0111493\pi$
$930$	95.2228	−	56.3614i	3.12248	−	1.84816i
$931$	10.6471	−	4.40056i	0.348946	−	0.144222i
$932$	−24.9189	+	45.4056i	−0.816245	+	1.48731i
$933$	−35.9155	−	38.7077i	−1.17582	−	1.26723i
$934$	−15.3417	−	18.8159i	−0.501994	−	0.615675i
$935$	0.115602	−	1.54260i	0.00378059	−	0.0504485i
$936$	−29.8893	+	84.0970i	−0.976964	+	2.74880i
$937$	2.31121	−	2.89817i	0.0755040	−	0.0946790i	−0.742645	−	0.669685i	$-0.766429\pi$
$937$	2.31121	−	2.89817i	0.0755040	−	0.0946790i	0.818149	+	0.575006i	$0.195000\pi$
$938$	−43.7318	+	36.3145i	−1.42790	+	1.18571i
$939$	−27.4200	+	21.8667i	−0.894817	+	0.713593i
$940$	21.5012	+	4.41960i	0.701293	+	0.144151i
$941$	−39.4650	+	15.4889i	−1.28652	+	0.504922i	−0.907339	−	0.420400i	$-0.861890\pi$
$941$	−39.4650	+	15.4889i	−1.28652	+	0.504922i	−0.379182	+	0.925322i	$0.623795\pi$
$942$	−55.7227	+	13.3552i	−1.81554	+	0.435137i
$943$	0.184289	+	2.45917i	0.00600129	+	0.0800816i
$944$	41.7370	+	41.2437i	1.35843	+	1.34237i
$945$	−1.15305	−	128.629i	−0.0375086	−	4.18430i
$946$	0.505585	+	1.57814i	0.0164380	+	0.0513099i
$947$	−1.57613	+	10.4569i	−0.0512174	+	0.339805i	0.948516	+	0.316728i	$0.102584\pi$
$947$	−1.57613	+	10.4569i	−0.0512174	+	0.339805i	−0.999734	+	0.0230767i	$0.992654\pi$
$948$	20.7036	−	2.00354i	0.672422	−	0.0650720i
$949$	6.33548	+	3.65779i	0.205658	+	0.118737i
$950$	7.64054	−	13.5713i	0.247892	−	0.440312i
$951$	−27.0141	−	13.0093i	−0.875991	−	0.421855i
$952$	−0.359747	+	1.04169i	−0.0116595	+	0.0337613i
$953$	−53.8495	+	25.9326i	−1.74436	+	0.840038i	−0.763370	+	0.645961i	$0.776457\pi$
$953$	−53.8495	+	25.9326i	−1.74436	+	0.840038i	−0.980986	+	0.194077i	$0.937829\pi$
$954$	7.67617	−	119.845i	0.248525	−	3.88011i
$955$	−19.0050	+	20.4825i	−0.614988	+	0.662800i
$956$	−4.58080	+	1.52246i	−0.148154	+	0.0492399i
$957$	−22.1714	+	32.5195i	−0.716701	+	1.05121i
$958$	23.3686	−	35.0864i	0.755006	−	1.13359i
$959$	3.15100	+	9.89935i	0.101751	+	0.319667i
$960$	81.8269	+	33.0421i	2.64095	+	1.06643i
$961$	−9.65641	−	16.7254i	−0.311497	−	0.539529i
$962$	0.399044	+	36.8238i	0.0128657	+	1.18725i
$963$	68.0846	+	99.8618i	2.19400	+	3.21800i
$964$	−19.0891	+	25.0311i	−0.614820	+	0.806199i
$965$	−67.2300	−	15.3448i	−2.16421	−	0.493967i
$966$	−9.63413	−	9.97936i	−0.309973	−	0.321081i
$967$	4.23572	+	18.5579i	0.136211	+	0.596781i	0.996248	+	0.0865483i	$0.0275837\pi$
$967$	4.23572	+	18.5579i	0.136211	+	0.596781i	−0.860036	+	0.510233i	$0.829559\pi$
$968$	−4.39406	+	0.473337i	−0.141230	+	0.0152136i
$969$	0.747187	+	0.230477i	0.0240031	+	0.00740397i
$970$	−29.3127	+	37.5853i	−0.941173	+	1.20679i
$971$	1.57923	+	5.11975i	0.0506801	+	0.164301i	0.977375	−	0.211514i	$-0.0678393\pi$
$971$	1.57923	+	5.11975i	0.0506801	+	0.164301i	−0.926695	+	0.375814i	$0.877363\pi$
$972$	−11.4661	−	66.2906i	−0.367774	−	2.12627i
$973$	32.0573	−	22.2798i	1.02771	−	0.714258i
$974$	0.473424	−	3.38980i	0.0151695	−	0.108616i
$975$	33.5952	−	85.5991i	1.07591	−	2.74136i
$976$	−12.7910	−	23.8575i	−0.409431	−	0.763658i
$977$	40.1683	−	6.05439i	1.28510	−	0.193697i	0.529261	−	0.848459i	$-0.322469\pi$
$977$	40.1683	−	6.05439i	1.28510	−	0.193697i	0.755835	+	0.654762i	$0.227231\pi$
$978$	−15.9579	+	53.7972i	−0.510278	+	1.72024i
$979$		−	35.1978i		−	1.12493i
$980$	−22.4610	−	42.2730i	−0.717492	−	1.35036i
$981$		−	35.3343i		−	1.12814i
$982$	−0.876328	−	0.259946i	−0.0279648	−	0.00829521i
$983$	−22.7532	+	3.42949i	−0.725713	+	0.109384i	−0.501502	−	0.865157i	$-0.667219\pi$
$983$	−22.7532	+	3.42949i	−0.725713	+	0.109384i	−0.224212	+	0.974540i	$0.571981\pi$
$984$	−0.827900	+	19.5644i	−0.0263925	+	0.623692i
$985$	−13.6769	+	34.8481i	−0.435782	+	1.11035i
$986$	0.819155	+	0.114404i	0.0260872	+	0.00364337i
$987$	−20.2500	−	18.4543i	−0.644566	−	0.587406i
$988$	13.8165	−	2.38980i	0.439563	−	0.0760297i
$989$	0.129196	+	0.418844i	0.00410820	+	0.0133185i
$990$	86.7713	+	67.6727i	2.75777	+	2.15078i
$991$	−33.5984	−	10.3637i	−1.06729	−	0.329215i	−0.289135	−	0.957288i	$-0.593368\pi$
$991$	−33.5984	−	10.3637i	−1.06729	−	0.329215i	−0.778154	+	0.628073i	$0.783844\pi$
$992$	15.4263	−	37.0411i	0.489784	−	1.17606i
$993$	12.1598	+	53.2755i	0.385879	+	1.69065i
$994$	−1.60602	−	16.9263i	−0.0509400	−	0.536871i
$995$	−54.4054	−	12.4177i	−1.72477	−	0.393667i
$996$	27.3011	−	35.7993i	0.865067	−	1.13434i
$997$	−26.8913	−	39.4424i	−0.851657	−	1.24915i	−0.966731	−	0.255795i	$-0.917663\pi$
$997$	−26.8913	−	39.4424i	−0.851657	−	1.24915i	0.115074	−	0.993357i	$-0.463290\pi$
$998$	36.0357	−	0.390503i	1.14069	−	0.0123612i
$999$	−43.4604	−	75.2756i	−1.37503	−	2.38162i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.109.32	✓	648
8.5	even	2	inner	392.2.z.a.109.51	yes	648
49.9	even	21	inner	392.2.z.a.205.51	yes	648
392.205	even	42	inner	392.2.z.a.205.32	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.109.32	✓	648	1.1	even	1	trivial
392.2.z.a.109.51	yes	648	8.5	even	2	inner
392.2.z.a.205.32	yes	648	392.205	even	42	inner
392.2.z.a.205.51	yes	648	49.9	even	21	inner

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

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	392.2.z.a.109.32

Level	$392$
Weight	$2$
Character	392.109
Analytic conductor	$3.130$
Analytic rank	$0$
Dimension	$648$
Inner twists	$4$