LMFDB - Embedded newform 560.2.cp.a.221.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(221,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 0, 8]))

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

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

chi := DirichletCharacter("560.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cp (of order $12$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			221.8
Character	$\chi$	$=$	560.221
Dual form			560.2.cp.a.261.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31828 + 0.511983i) q^{2} +(-0.0714125 + 0.0191349i) q^{3} +(1.47575 - 1.34988i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(0.0843453 - 0.0617872i) q^{6} +(1.28741 - 2.31140i) q^{7} +(-1.25434 + 2.53508i) q^{8} +(-2.59334 + 1.49727i) q^{9} +(1.40588 - 0.153340i) q^{10} +(0.200747 + 0.749199i) q^{11} +(-0.0795571 + 0.124636i) q^{12} +(3.55535 + 3.55535i) q^{13} +(-0.513781 + 3.70621i) q^{14} +0.0739317 q^{15} +(0.355663 - 3.98416i) q^{16} +(2.94108 - 5.09409i) q^{17} +(2.65219 - 3.30157i) q^{18} +(0.576876 - 2.15293i) q^{19} +(-1.77484 + 0.921930i) q^{20} +(-0.0477089 + 0.189697i) q^{21} +(-0.648219 - 0.884878i) q^{22} +(0.800962 - 0.462436i) q^{23} +(0.0410671 - 0.205038i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-6.50724 - 2.86668i) q^{26} +(0.313380 - 0.313380i) q^{27} +(-1.22021 - 5.14889i) q^{28} +(-6.32528 - 6.32528i) q^{29} +(-0.0974630 + 0.0378517i) q^{30} +(3.30314 - 5.72120i) q^{31} +(1.57095 + 5.43434i) q^{32} +(-0.0286717 - 0.0496609i) q^{33} +(-1.26909 + 8.22124i) q^{34} +(-1.84178 + 1.89943i) q^{35} +(-1.80599 + 5.71028i) q^{36} +(7.46881 + 2.00126i) q^{37} +(0.341776 + 3.13353i) q^{38} +(-0.321928 - 0.185865i) q^{39} +(1.86773 - 2.12405i) q^{40} -4.60176i q^{41} +(-0.0342278 - 0.274501i) q^{42} +(7.39440 - 7.39440i) q^{43} +(1.30758 + 0.834644i) q^{44} +(2.89250 - 0.775042i) q^{45} +(-0.819137 + 1.01970i) q^{46} +(3.78888 + 6.56253i) q^{47} +(0.0508377 + 0.291324i) q^{48} +(-3.68513 - 5.95145i) q^{49} +(-1.39766 - 0.215752i) q^{50} +(-0.112555 + 0.420059i) q^{51} +(10.0461 + 0.447514i) q^{52} +(-1.34908 - 5.03484i) q^{53} +(-0.252679 + 0.573569i) q^{54} -0.775628i q^{55} +(4.24472 + 6.16298i) q^{56} +0.164785i q^{57} +(11.5770 + 5.10009i) q^{58} +(1.91388 + 7.14271i) q^{59} +(0.109104 - 0.0997987i) q^{60} +(-1.04444 + 3.89791i) q^{61} +(-1.42532 + 9.23332i) q^{62} +(0.122079 + 7.92185i) q^{63} +(-4.85325 - 6.35971i) q^{64} +(-2.51401 - 4.35439i) q^{65} +(0.0632230 + 0.0507877i) q^{66} +(15.2216 - 4.07861i) q^{67} +(-2.53611 - 11.4877i) q^{68} +(-0.0483500 + 0.0483500i) q^{69} +(1.45551 - 3.44695i) q^{70} -7.90648i q^{71} +(-0.542753 - 8.45241i) q^{72} +(-12.9123 - 7.45489i) q^{73} +(-10.8706 + 1.18567i) q^{74} +(-0.0714125 - 0.0191349i) q^{75} +(-2.05487 - 3.95590i) q^{76} +(1.99014 + 0.500521i) q^{77} +(0.519552 + 0.0802016i) q^{78} +(4.96382 + 8.59759i) q^{79} +(-1.37472 + 3.75635i) q^{80} +(4.47542 - 7.75165i) q^{81} +(2.35602 + 6.06643i) q^{82} +(4.47941 + 4.47941i) q^{83} +(0.185662 + 0.344347i) q^{84} +(-4.15931 + 4.15931i) q^{85} +(-5.96212 + 13.5337i) q^{86} +(0.572738 + 0.330671i) q^{87} +(-2.15108 - 0.430841i) q^{88} +(-4.74867 + 2.74164i) q^{89} +(-3.41633 + 2.50263i) q^{90} +(12.7950 - 3.64063i) q^{91} +(0.557787 - 1.76364i) q^{92} +(-0.126411 + 0.471771i) q^{93} +(-8.35472 - 6.71144i) q^{94} +(-1.11444 + 1.93027i) q^{95} +(-0.216172 - 0.358020i) q^{96} -2.86704 q^{97} +(7.90510 + 5.95898i) q^{98} +(-1.64236 - 1.64236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.31828	+	0.511983i	−0.932168	+	0.362026i
$2$	−1.31828	+	0.511983i	−0.932168	+	0.362026i
$3$	−0.0714125	+	0.0191349i	−0.0412300	+	0.0110476i	−0.279375	−	0.960182i	$-0.590127\pi$
$3$	−0.0714125	+	0.0191349i	−0.0412300	+	0.0110476i	0.238145	+	0.971230i	$0.423461\pi$
$4$	1.47575	−	1.34988i	0.737874	−	0.674939i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	0.0843453	−	0.0617872i	0.0344338	−	0.0252245i
$7$	1.28741	−	2.31140i	0.486596	−	0.873627i
$7$	1.28741	−	2.31140i	0.486596	−	0.873627i
$8$	−1.25434	+	2.53508i	−0.443477	+	0.896286i
$9$	−2.59334	+	1.49727i	−0.864448	+	0.499089i
$10$	1.40588	−	0.153340i	0.444577	−	0.0484904i
$11$	0.200747	+	0.749199i	0.0605276	+	0.225892i	0.989563	−	0.144098i	$-0.0460279\pi$
$11$	0.200747	+	0.749199i	0.0605276	+	0.225892i	−0.929036	+	0.369990i	$0.879361\pi$
$12$	−0.0795571	+	0.124636i	−0.0229661	+	0.0359794i
$13$	3.55535	+	3.55535i	0.986076	+	0.986076i	0.999904	−	0.0138282i	$-0.00440178\pi$
$13$	3.55535	+	3.55535i	0.986076	+	0.986076i	−0.0138282	+	0.999904i	$0.504402\pi$
$14$	−0.513781	+	3.70621i	−0.137314	+	0.990528i
$15$	0.0739317			0.0190891
$16$	0.355663	−	3.98416i	0.0889158	−	0.996039i
$17$	2.94108	−	5.09409i	0.713316	−	1.23550i	−0.250290	−	0.968171i	$-0.580526\pi$
$17$	2.94108	−	5.09409i	0.713316	−	1.23550i	0.963606	−	0.267328i	$-0.0861408\pi$
$18$	2.65219	−	3.30157i	0.625127	−	0.778188i
$19$	0.576876	−	2.15293i	0.132344	−	0.493916i	−0.867650	−	0.497175i	$-0.834371\pi$
$19$	0.576876	−	2.15293i	0.132344	−	0.493916i	0.999995	+	0.00325877i	$0.00103730\pi$
$20$	−1.77484	+	0.921930i	−0.396866	+	0.206150i
$21$	−0.0477089	+	0.189697i	−0.0104109	+	0.0413954i
$22$	−0.648219	−	0.884878i	−0.138201	−	0.188657i
$23$	0.800962	−	0.462436i	0.167012	−	0.0964245i	−0.414164	−	0.910202i	$-0.635926\pi$
$23$	0.800962	−	0.462436i	0.167012	−	0.0964245i	0.581176	+	0.813778i	$0.302593\pi$
$24$	0.0410671	−	0.205038i	0.00838280	−	0.0418532i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−6.50724	−	2.86668i	−1.27617	−	0.562203i
$27$	0.313380	−	0.313380i	0.0603100	−	0.0603100i
$28$	−1.22021	−	5.14889i	−0.230598	−	0.973049i
$29$	−6.32528	−	6.32528i	−1.17458	−	1.17458i	−0.981106	−	0.193469i	$-0.938026\pi$
$29$	−6.32528	−	6.32528i	−1.17458	−	1.17458i	−0.193469	−	0.981106i	$-0.561974\pi$
$30$	−0.0974630	+	0.0378517i	−0.0177942	+	0.00691075i
$31$	3.30314	−	5.72120i	0.593261	−	1.02756i	−0.400529	−	0.916284i	$-0.631173\pi$
$31$	3.30314	−	5.72120i	0.593261	−	1.02756i	0.993790	−	0.111274i	$-0.0354932\pi$
$32$	1.57095	+	5.43434i	0.277708	+	0.960666i
$33$	−0.0286717	−	0.0496609i	−0.00499111	−	0.00864485i
$34$	−1.26909	+	8.22124i	−0.217647	+	1.40993i
$35$	−1.84178	+	1.89943i	−0.311318	+	0.321063i
$36$	−1.80599	+	5.71028i	−0.300999	+	0.951714i
$37$	7.46881	+	2.00126i	1.22786	+	0.329005i	0.813748	−	0.581218i	$-0.197424\pi$
$37$	7.46881	+	2.00126i	1.22786	+	0.329005i	0.414117	+	0.910224i	$0.364090\pi$
$38$	0.341776	+	3.13353i	0.0554434	+	0.508325i
$39$	−0.321928	−	0.185865i	−0.0515497	−	0.0297622i
$40$	1.86773	−	2.12405i	0.295314	−	0.335842i
$41$		−	4.60176i		−	0.718675i	−0.933208	−	0.359337i	$-0.883003\pi$
$41$		−	4.60176i		−	0.718675i	0.933208	−	0.359337i	$-0.116997\pi$
$42$	−0.0342278	−	0.274501i	−0.00528146	−	0.0423565i
$43$	7.39440	−	7.39440i	1.12764	−	1.12764i	0.137075	−	0.990561i	$-0.456230\pi$
$43$	7.39440	−	7.39440i	1.12764	−	1.12764i	0.990561	−	0.137075i	$-0.0437701\pi$
$44$	1.30758	+	0.834644i	0.197125	+	0.125827i
$45$	2.89250	−	0.775042i	0.431188	−	0.115537i
$46$	−0.819137	+	1.01970i	−0.120775	+	0.150347i
$47$	3.78888	+	6.56253i	0.552665	+	0.957244i	0.998081	+	0.0619200i	$0.0197224\pi$
$47$	3.78888	+	6.56253i	0.552665	+	0.957244i	−0.445416	+	0.895324i	$0.646944\pi$
$48$	0.0508377	+	0.291324i	0.00733780	+	0.0420490i
$49$	−3.68513	−	5.95145i	−0.526448	−	0.850207i
$50$	−1.39766	−	0.215752i	−0.197659	−	0.0305120i
$51$	−0.112555	+	0.420059i	−0.0157608	+	0.0588201i
$52$	10.0461	+	0.447514i	1.39314	+	0.0620590i
$53$	−1.34908	−	5.03484i	−0.185311	−	0.691589i	−0.994564	−	0.104129i	$-0.966795\pi$
$53$	−1.34908	−	5.03484i	−0.185311	−	0.691589i	0.809253	−	0.587460i	$-0.199872\pi$
$54$	−0.252679	+	0.573569i	−0.0343852	+	0.0780528i
$55$		−	0.775628i		−	0.104586i
$56$	4.24472	+	6.16298i	0.567225	+	0.823563i
$57$			0.164785i			0.0218263i
$58$	11.5770	+	5.10009i	1.52013	+	0.669674i
$59$	1.91388	+	7.14271i	0.249166	+	0.929902i	0.971243	+	0.238089i	$0.0765210\pi$
$59$	1.91388	+	7.14271i	0.249166	+	0.929902i	−0.722077	+	0.691813i	$0.756812\pi$
$60$	0.109104	−	0.0997987i	0.0140853	−	0.0128840i
$61$	−1.04444	+	3.89791i	−0.133727	+	0.499076i	−1.00000		0.000495316i	$-0.999842\pi$
$61$	−1.04444	+	3.89791i	−0.133727	+	0.499076i	0.866273	+	0.499571i	$0.166509\pi$
$62$	−1.42532	+	9.23332i	−0.181016	+	1.17263i
$63$	0.122079	+	7.92185i	0.0153805	+	0.998060i
$64$	−4.85325	−	6.35971i	−0.606657	−	0.794964i
$65$	−2.51401	−	4.35439i	−0.311825	−	0.540096i
$66$	0.0632230	+	0.0507877i	0.00778221	+	0.00625154i
$67$	15.2216	−	4.07861i	1.85961	−	0.498281i	0.859690	−	0.510816i	$-0.170657\pi$
$67$	15.2216	−	4.07861i	1.85961	−	0.498281i	0.999921	+	0.0125342i	$0.00398987\pi$
$68$	−2.53611	−	11.4877i	−0.307549	−	1.39309i
$69$	−0.0483500	+	0.0483500i	−0.00582066	+	0.00582066i
$70$	1.45551	−	3.44695i	0.173967	−	0.411990i
$71$		−	7.90648i		−	0.938327i	−0.883111	−	0.469163i	$-0.844556\pi$
$71$		−	7.90648i		−	0.938327i	0.883111	−	0.469163i	$-0.155444\pi$
$72$	−0.542753	−	8.45241i	−0.0639640	−	0.996126i
$73$	−12.9123	−	7.45489i	−1.51126	−	0.872529i	−0.999913	−	0.0131572i	$-0.995812\pi$
$73$	−12.9123	−	7.45489i	−1.51126	−	0.872529i	−0.511351	−	0.859372i	$-0.670855\pi$
$74$	−10.8706	+	1.18567i	−1.26368	+	0.137831i
$75$	−0.0714125	−	0.0191349i	−0.00824601	−	0.00220951i
$76$	−2.05487	−	3.95590i	−0.235710	−	0.453772i
$77$	1.99014	+	0.500521i	0.226798	+	0.0570397i
$78$	0.519552	+	0.0802016i	0.0588277	+	0.00908105i
$79$	4.96382	+	8.59759i	0.558473	+	0.967304i	0.997624	+	0.0688907i	$0.0219460\pi$
$79$	4.96382	+	8.59759i	0.558473	+	0.967304i	−0.439151	+	0.898413i	$0.644721\pi$
$80$	−1.37472	+	3.75635i	−0.153698	+	0.419972i
$81$	4.47542	−	7.75165i	0.497269	−	0.861295i
$82$	2.35602	+	6.06643i	0.260179	+	0.669926i
$83$	4.47941	+	4.47941i	0.491679	+	0.491679i	0.908835	−	0.417156i	$-0.136973\pi$
$83$	4.47941	+	4.47941i	0.491679	+	0.491679i	−0.417156	+	0.908835i	$0.636973\pi$
$84$	0.185662	+	0.344347i	0.0202574	+	0.0375713i
$85$	−4.15931	+	4.15931i	−0.451141	+	0.451141i
$86$	−5.96212	+	13.5337i	−0.642912	+	1.45938i
$87$	0.572738	+	0.330671i	0.0614040	+	0.0354516i
$88$	−2.15108	−	0.430841i	−0.229306	−	0.0459278i
$89$	−4.74867	+	2.74164i	−0.503358	+	0.290614i	−0.730099	−	0.683341i	$-0.760526\pi$
$89$	−4.74867	+	2.74164i	−0.503358	+	0.290614i	0.226741	+	0.973955i	$0.427193\pi$
$90$	−3.41633	+	2.50263i	−0.360112	+	0.263801i
$91$	12.7950	−	3.64063i	1.34128	−	0.381642i
$92$	0.557787	−	1.76364i	0.0581533	−	0.183872i
$93$	−0.126411	+	0.471771i	−0.0131082	+	0.0489204i
$94$	−8.35472	−	6.71144i	−0.861724	−	0.692233i
$95$	−1.11444	+	1.93027i	−0.114339	+	0.198041i
$96$	−0.216172	−	0.358020i	−0.0220629	−	0.0365403i
$97$	−2.86704			−0.291103			−0.145552	−	0.989351i	$-0.546496\pi$
$97$	−2.86704			−0.291103			−0.145552	+	0.989351i	$0.546496\pi$
$98$	7.90510	+	5.95898i	0.798535	+	0.601948i
$99$	−1.64236	−	1.64236i	−0.165063	−	0.165063i
$100$	1.95297	−	0.431154i	0.195297	−	0.0431154i
$101$	4.93821	+	18.4296i	0.491370	+	1.83382i	0.549480	+	0.835507i	$0.314826\pi$
$101$	4.93821	+	18.4296i	0.491370	+	1.83382i	−0.0581097	+	0.998310i	$0.518507\pi$
$102$	−0.0666841	−	0.611384i	−0.00660271	−	0.0605360i
$103$	−9.31271	+	5.37670i	−0.917609	+	0.529782i	−0.882871	−	0.469615i	$-0.844393\pi$
$103$	−9.31271	+	5.37670i	−0.917609	+	0.529782i	−0.0347373	+	0.999396i	$0.511059\pi$
$104$	−13.4727	+	4.55347i	−1.32111	+	0.446504i
$105$	0.0951806	−	0.170886i	0.00928868	−	0.0166767i
$106$	4.35623	+	5.94665i	0.423114	+	0.577590i
$107$	11.0622	+	2.96411i	1.06942	+	0.286552i	0.750257	−	0.661147i	$-0.229930\pi$
$107$	11.0622	+	2.96411i	1.06942	+	0.286552i	0.319168	+	0.947698i	$0.396597\pi$
$108$	0.0394453	−	0.885494i	0.00379562	−	0.0852067i
$109$	−6.45351	+	1.72921i	−0.618134	+	0.165629i	−0.554279	−	0.832331i	$-0.687006\pi$
$109$	−6.45351	+	1.72921i	−0.618134	+	0.165629i	−0.0638546	+	0.997959i	$0.520339\pi$
$110$	0.397108	+	1.02250i	0.0378627	+	0.0974913i
$111$	−0.571660			−0.0542596
$112$	−8.75109	−	5.95133i	−0.826900	−	0.562348i
$113$	−0.281386			−0.0264705			−0.0132353	−	0.999912i	$-0.504213\pi$
$113$	−0.281386			−0.0264705			−0.0132353	+	0.999912i	$0.504213\pi$
$114$	−0.0843669	−	0.217233i	−0.00790168	−	0.0203457i
$115$	−0.893357	+	0.239374i	−0.0833060	+	0.0223218i
$116$	−17.8729	−	0.796167i	−1.65945	−	0.0739222i
$117$	−14.5435	−	3.89693i	−1.34455	−	0.360271i
$118$	−6.17999	−	8.43625i	−0.568914	−	0.776620i
$119$	−7.98811	−	13.3562i	−0.732268	−	1.22436i
$120$	−0.0927356	+	0.187423i	−0.00846556	+	0.0171093i
$121$	9.00528	−	5.19920i	0.818662	−	0.472655i
$122$	−0.618790	−	5.67328i	−0.0560226	−	0.513635i
$123$	0.0880544	+	0.328623i	0.00793960	+	0.0296310i
$124$	−2.84832	−	12.9019i	−0.255787	−	1.15862i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−4.21678	−	10.3808i	−0.375661	−	0.924791i
$127$	−19.3562			−1.71759			−0.858794	−	0.512321i	$-0.828786\pi$
$127$	−19.3562			−1.71759			−0.858794	+	0.512321i	$0.828786\pi$
$128$	9.65403	+	5.89913i	0.853304	+	0.521414i
$129$	−0.386561	+	0.669544i	−0.0340348	+	0.0589501i
$130$	5.54356	+	4.45320i	0.486202	+	0.390572i
$131$	2.46148	−	9.18636i	0.215060	−	0.802616i	−0.771085	−	0.636732i	$-0.780286\pi$
$131$	2.46148	−	9.18636i	0.215060	−	0.802616i	0.986145	−	0.165884i	$-0.0530477\pi$
$132$	−0.109348	−	0.0345836i	−0.00951755	−	0.00301012i
$133$	−4.23361	−	4.10510i	−0.367100	−	0.355958i
$134$	−17.9782	+	13.1699i	−1.55308	+	1.13771i
$135$	−0.383810	+	0.221593i	−0.0330331	+	0.0190717i
$136$	9.22482	+	13.8456i	0.791021	+	1.18725i
$137$	−4.36248	−	2.51868i	−0.372712	−	0.215185i	0.301931	−	0.953330i	$-0.402369\pi$
$137$	−4.36248	−	2.51868i	−0.372712	−	0.215185i	−0.674642	+	0.738145i	$0.735702\pi$
$138$	0.0389847	−	0.0884935i	0.00331860	−	0.00753306i
$139$	−6.50997	+	6.50997i	−0.552168	+	0.552168i	−0.927066	−	0.374898i	$-0.877678\pi$
$139$	−6.50997	+	6.50997i	−0.552168	+	0.552168i	0.374898	+	0.927066i	$0.377678\pi$
$140$	−0.154001	+	5.28926i	−0.0130154	+	0.447024i
$141$	−0.396147	−	0.396147i	−0.0333616	−	0.0333616i
$142$	4.04798	+	10.4230i	0.339699	+	0.874678i
$143$	−1.94994	+	3.37739i	−0.163062	+	0.282431i
$144$	5.04299	+	10.8648i	0.420249	+	0.905400i
$145$	4.47265	+	7.74686i	0.371433	+	0.643342i
$146$	20.8388	+	3.21682i	1.72463	+	0.266226i
$147$	0.377045	+	0.354493i	0.0310982	+	0.0292381i
$148$	13.7235	−	7.12862i	1.12807	−	0.585969i
$149$	−7.65993	−	2.05247i	−0.627526	−	0.168145i	−0.0689793	−	0.997618i	$-0.521974\pi$
$149$	−7.65993	−	2.05247i	−0.627526	−	0.168145i	−0.558547	+	0.829473i	$0.688641\pi$
$150$	0.103939	−	0.0113367i	0.00848656	−	0.000925636i
$151$	−12.2432	−	7.06862i	−0.996338	−	0.575236i	−0.0891750	−	0.996016i	$-0.528423\pi$
$151$	−12.2432	−	7.06862i	−0.996338	−	0.575236i	−0.907163	+	0.420780i	$0.861756\pi$
$152$	4.73425	+	4.16294i	0.383999	+	0.337659i
$153$			17.6143i			1.42403i
$154$	−2.87983	+	0.359089i	−0.232063	+	0.0289362i
$155$	−4.67134	+	4.67134i	−0.375211	+	0.375211i
$156$	−0.725979	+	0.160273i	−0.0581248	+	0.0128321i
$157$	−14.6202	+	3.91747i	−1.16682	+	0.312648i	−0.789686	−	0.613511i	$-0.789757\pi$
$157$	−14.6202	+	3.91747i	−1.16682	+	0.312648i	−0.377133	+	0.926159i	$0.623090\pi$
$158$	−10.9455	−	8.79267i	−0.870780	−	0.699508i
$159$	0.192683	+	0.333736i	0.0152807	+	0.0264670i
$160$	−0.110913	−	5.65577i	−0.00876841	−	0.447128i
$161$	−0.0377045	−	2.44669i	−0.00297153	−	0.192826i
$162$	−1.93116	+	12.5102i	−0.151727	+	0.982896i
$163$	−1.81449	+	6.77175i	−0.142121	+	0.530404i	0.857745	+	0.514075i	$0.171865\pi$
$163$	−1.81449	+	6.77175i	−0.142121	+	0.530404i	−0.999867	+	0.0163294i	$0.994802\pi$
$164$	−6.21182	−	6.79104i	−0.485061	−	0.530291i
$165$	0.0148416	+	0.0553895i	0.00115542	+	0.00431207i
$166$	−8.19852	−	3.61176i	−0.636328	−	0.280327i
$167$		−	3.57827i		−	0.276895i	−0.990370	−	0.138447i	$-0.955789\pi$
$167$		−	3.57827i		−	0.276895i	0.990370	−	0.138447i	$-0.0442112\pi$
$168$	−0.421055	−	0.358891i	−0.0324851	−	0.0276891i
$169$			12.2810i			0.944693i
$170$	3.35366	−	7.61265i	0.257214	−	0.583863i
$171$	1.72748	+	6.44703i	0.132103	+	0.493016i
$172$	0.930737	−	20.8938i	0.0709681	−	1.59314i
$173$	−0.0405441	+	0.151313i	−0.00308251	+	0.0115041i	−0.967450	−	0.253062i	$-0.918562\pi$
$173$	−0.0405441	+	0.151313i	−0.00308251	+	0.0115041i	0.964367	+	0.264567i	$0.0852289\pi$
$174$	−0.924329	−	0.142686i	−0.0700732	−	0.0108170i
$175$	2.27063	−	1.35802i	0.171644	−	0.102657i
$176$	3.05632	−	0.533346i	0.230379	−	0.0402025i
$177$	−0.273350	−	0.473457i	−0.0205463	−	0.0355872i
$178$	4.85642	−	6.04550i	0.364004	−	0.453129i
$179$	3.07295	−	0.823395i	0.229683	−	0.0615434i	−0.142142	−	0.989846i	$-0.545399\pi$
$179$	3.07295	−	0.823395i	0.229683	−	0.0615434i	0.371825	+	0.928303i	$0.378732\pi$
$180$	3.22239	−	5.04828i	0.240182	−	0.376277i
$181$	−7.79249	+	7.79249i	−0.579211	+	0.579211i	−0.934686	−	0.355475i	$-0.884319\pi$
$181$	−7.79249	+	7.79249i	−0.579211	+	0.579211i	0.355475	+	0.934686i	$0.384319\pi$
$182$	−15.0036	+	11.3502i	−1.11214	+	0.841334i
$183$		−	0.298345i		−	0.0220543i
$184$	0.167631	+	2.61055i	0.0123579	+	0.192453i
$185$	−6.69635	−	3.86614i	−0.492325	−	0.284244i
$186$	−0.0748933	−	0.686648i	−0.00549144	−	0.0503475i
$187$	4.40690	+	1.18083i	0.322265	+	0.0863505i
$188$	14.4500	+	4.57012i	1.05388	+	0.333310i
$189$	−0.320897	−	1.12780i	−0.0233418	−	0.0820350i
$190$	0.480886	−	3.11521i	0.0348871	−	0.226001i
$191$	5.67045	+	9.82151i	0.410300	+	0.710660i	0.994922	−	0.100646i	$-0.0320908\pi$
$191$	5.67045	+	9.82151i	0.410300	+	0.710660i	−0.584623	+	0.811305i	$0.698757\pi$
$192$	0.468276	+	0.361296i	0.0337949	+	0.0260743i
$193$	6.76922	−	11.7246i	0.487259	−	0.843958i	−0.512634	−	0.858607i	$-0.671330\pi$
$193$	6.76922	−	11.7246i	0.487259	−	0.843958i	0.999893	+	0.0146500i	$0.00466340\pi$
$194$	3.77957	−	1.46787i	0.271357	−	0.105387i
$195$	0.262853	+	0.262853i	0.0188233	+	0.0188233i
$196$	−13.4721	−	3.80836i	−0.962290	−	0.272026i
$197$	−5.37009	+	5.37009i	−0.382603	+	0.382603i	−0.872039	−	0.489436i	$-0.837203\pi$
$197$	−5.37009	+	5.37009i	−0.382603	+	0.382603i	0.489436	+	0.872039i	$0.337203\pi$
$198$	3.00595	+	1.32424i	0.213624	+	0.0941093i
$199$	13.9774	+	8.06987i	0.990833	+	0.572058i	0.905523	−	0.424297i	$-0.139479\pi$
$199$	13.9774	+	8.06987i	0.990833	+	0.572058i	0.0853101	+	0.996354i	$0.472812\pi$
$200$	−2.35383	+	1.56827i	−0.166441	+	0.110894i
$201$	−1.00897	+	0.582527i	−0.0711671	+	0.0410883i
$202$	−15.9456	−	21.7672i	−1.12193	−	1.53154i
$203$	−22.7635	+	6.47700i	−1.59768	+	0.454597i
$204$	0.400926	+	0.771836i	0.0280705	+	0.0540394i
$205$	−1.19102	+	4.44496i	−0.0831847	+	0.310450i
$206$	9.52403	−	11.8560i	0.663570	−	0.826044i
$207$	−1.38478	+	2.39851i	−0.0962488	+	0.166708i
$208$	15.4296	−	12.9006i	1.06985	−	0.894493i
$209$	1.72878			0.119582
$210$	−0.0379847	+	0.274007i	−0.00262119	+	0.0189083i
$211$	−3.74525	−	3.74525i	−0.257834	−	0.257834i	0.566339	−	0.824172i	$-0.308359\pi$
$211$	−3.74525	−	3.74525i	−0.257834	−	0.257834i	−0.824172	+	0.566339i	$0.808359\pi$
$212$	−8.78732	−	5.60906i	−0.603516	−	0.385232i
$213$	0.151290	+	0.564622i	0.0103662	+	0.0386872i
$214$	−16.1007	+	1.75612i	−1.10062	+	0.120046i
$215$	−9.05625	+	5.22863i	−0.617631	+	0.356590i
$216$	0.401357	+	1.18753i	0.0273089	+	0.0808010i
$217$	−8.97148	−	15.0004i	−0.609024	−	1.01830i
$218$	7.62223	−	5.58368i	0.516243	−	0.378174i
$219$	1.06475	+	0.285298i	0.0719488	+	0.0192786i
$220$	−1.04700	−	1.14463i	−0.0705889	−	0.0771710i
$221$	28.5678	−	7.65473i	1.92168	−	0.514913i
$222$	0.753611	−	0.292680i	0.0505791	−	0.0196434i
$223$	19.3384			1.29499			0.647497	−	0.762068i	$-0.275816\pi$
$223$	19.3384			1.29499			0.647497	+	0.762068i	$0.275816\pi$
$224$	14.5834	+	3.36515i	0.974395	+	0.224843i
$225$	−2.99453			−0.199636
$226$	0.370947	−	0.144065i	0.0246750	−	0.00958304i
$227$	22.6274	−	6.06299i	1.50183	−	0.402415i	0.588119	−	0.808774i	$-0.299869\pi$
$227$	22.6274	−	6.06299i	1.50183	−	0.402415i	0.913713	+	0.406359i	$0.133202\pi$
$228$	0.222439	+	0.243181i	0.0147314	+	0.0161050i
$229$	16.4598	+	4.41038i	1.08769	+	0.291446i	0.757743	−	0.652553i	$-0.226302\pi$
$229$	16.4598	+	4.41038i	1.08769	+	0.291446i	0.329949	+	0.943999i	$0.392969\pi$
$230$	1.05514	−	0.772947i	0.0695741	−	0.0509666i
$231$	−0.151698	+	0.00233774i	−0.00998103	+	0.000153812i
$232$	23.9692	−	8.10103i	1.57365	−	0.531858i
$233$	2.45055	−	1.41483i	0.160541	−	0.0926884i	−0.417577	−	0.908642i	$-0.637121\pi$
$233$	2.45055	−	1.41483i	0.160541	−	0.0926884i	0.578118	+	0.815953i	$0.303787\pi$
$234$	21.1677	−	2.30878i	1.38377	−	0.150929i
$235$	−1.96127	−	7.31955i	−0.127939	−	0.477475i
$236$	12.4662	+	7.95733i	0.811480	+	0.517978i
$237$	−0.518993	−	0.518993i	−0.0337122	−	0.0337122i
$238$	17.3687	+	13.5175i	1.12585	+	0.876210i
$239$	−16.8240			−1.08825			−0.544127	−	0.839003i	$-0.683139\pi$
$239$	−16.8240			−1.08825			−0.544127	+	0.839003i	$0.683139\pi$
$240$	0.0262948	−	0.294555i	0.00169732	−	0.0190135i
$241$	1.46799	−	2.54263i	0.0945613	−	0.163785i	−0.814864	−	0.579652i	$-0.803188\pi$
$241$	1.46799	−	2.54263i	0.0945613	−	0.163785i	0.909425	+	0.415867i	$0.136522\pi$
$242$	−9.20962	+	11.4646i	−0.592017	+	0.736971i
$243$	−0.515388	+	1.92346i	−0.0330622	+	0.123390i
$244$	3.72036	+	7.16219i	0.238172	+	0.458512i
$245$	2.01922	+	6.70244i	0.129003	+	0.428203i
$246$	−0.284330	−	0.388137i	−0.0181282	−	0.0247467i
$247$	9.70542	−	5.60343i	0.617541	−	0.356537i
$248$	10.3604	+	15.5501i	0.657889	+	0.987430i
$249$	−0.405599	−	0.234173i	−0.0257038	−	0.0148401i
$250$	1.29419	+	0.570142i	0.0818520	+	0.0360589i
$251$	−2.40005	+	2.40005i	−0.151490	+	0.151490i	−0.778783	−	0.627293i	$-0.784163\pi$
$251$	−2.40005	+	2.40005i	−0.151490	+	0.151490i	0.627293	+	0.778783i	$0.284163\pi$
$252$	10.8737	+	11.5259i	0.684978	+	0.726061i
$253$	0.507247	+	0.507247i	0.0318904	+	0.0318904i
$254$	25.5170	−	9.91005i	1.60108	−	0.621812i
$255$	0.217439	−	0.376615i	0.0136165	−	0.0235845i
$256$	−15.7470	−	2.83403i	−0.984188	−	0.177127i
$257$	−4.66252	−	8.07572i	−0.290840	−	0.503750i	0.683169	−	0.730261i	$-0.260601\pi$
$257$	−4.66252	−	8.07572i	−0.290840	−	0.503750i	−0.974009	+	0.226511i	$0.927268\pi$
$258$	0.166803	−	1.08056i	0.0103847	−	0.0672729i
$259$	14.2412	−	14.6870i	0.884902	−	0.912603i
$260$	−9.58794	−	3.03238i	−0.594619	−	0.188060i
$261$	25.8743	+	6.93299i	1.60158	+	0.429141i
$262$	1.45833	+	13.3705i	0.0900959	+	0.826031i
$263$	7.95015	+	4.59002i	0.490227	+	0.283033i	0.724669	−	0.689097i	$-0.241993\pi$
$263$	7.95015	+	4.59002i	0.490227	+	0.283033i	−0.234442	+	0.972130i	$0.575326\pi$
$264$	0.161858	−	0.0103934i	0.00996170	−	0.000639668i
$265$			5.21245i			0.320198i
$266$	7.68284	+	3.24416i	0.471065	+	0.198912i
$267$	0.286653	−	0.286653i	0.0175429	−	0.0175429i
$268$	16.9576	−	26.5663i	1.03585	−	1.62279i
$269$	1.38706	−	0.371661i	0.0845703	−	0.0226605i	−0.216286	−	0.976330i	$-0.569394\pi$
$269$	1.38706	−	0.371661i	0.0845703	−	0.0226605i	0.300856	+	0.953670i	$0.402728\pi$
$270$	0.392519	−	0.488627i	0.0238880	−	0.0297369i
$271$	4.28327	+	7.41884i	0.260190	+	0.450662i	0.966292	−	0.257447i	$-0.0828814\pi$
$271$	4.28327	+	7.41884i	0.260190	+	0.450662i	−0.706102	+	0.708110i	$0.749548\pi$
$272$	−19.2496	−	13.5295i	−1.16718	−	0.820346i
$273$	−0.844062	+	0.504818i	−0.0510850	+	0.0305530i
$274$	7.04051	+	1.08682i	0.425333	+	0.0656573i
$275$	−0.200747	+	0.749199i	−0.0121055	+	0.0451784i
$276$	−0.00608585	+	0.136619i	−0.000366325	+	0.00822350i
$277$	1.11314	+	4.15430i	0.0668822	+	0.249608i	0.991270	−	0.131846i	$-0.0420903\pi$
$277$	1.11314	+	4.15430i	0.0668822	+	0.249608i	−0.924388	+	0.381454i	$0.875424\pi$
$278$	5.24900	−	11.9150i	0.314814	−	0.714613i
$279$			19.7827i			1.18436i
$280$	−2.50499	−	7.05160i	−0.149702	−	0.421413i
$281$			6.90383i			0.411848i	0.978568	+	0.205924i	$0.0660199\pi$
$281$			6.90383i			0.411848i	−0.978568	+	0.205924i	$0.933980\pi$
$282$	0.725055	+	0.319414i	0.0431764	+	0.0190208i
$283$	1.31577	+	4.91053i	0.0782146	+	0.291901i	0.993943	−	0.109897i	$-0.0350521\pi$
$283$	1.31577	+	4.91053i	0.0782146	+	0.291901i	−0.915728	+	0.401798i	$0.868385\pi$
$284$	−10.6728	−	11.6680i	−0.633313	−	0.692367i
$285$	0.0426494	−	0.159170i	0.00252633	−	0.00942841i
$286$	0.841407	−	5.45069i	0.0497534	−	0.322306i
$287$	−10.6365	−	5.92437i	−0.627854	−	0.349705i
$288$	−12.2107	−	11.7410i	−0.719522	−	0.691844i
$289$	−8.79986	−	15.2418i	−0.517639	−	0.896577i
$290$	−9.86248	−	7.92264i	−0.579145	−	0.465234i
$291$	0.204742	−	0.0548605i	0.0120022	−	0.00321598i
$292$	−29.1184	+	6.42841i	−1.70403	+	0.376194i
$293$	−15.7921	+	15.7921i	−0.922585	+	0.922585i	−0.997212	−	0.0746264i	$-0.976224\pi$
$293$	−15.7921	+	15.7921i	−0.922585	+	0.922585i	0.0746264	+	0.997212i	$0.476224\pi$
$294$	−0.678547	−	0.274282i	−0.0395737	−	0.0159965i
$295$		−	7.39468i		−	0.430535i
$296$	−14.4418	+	16.4238i	−0.839412	+	0.954611i
$297$	0.297694	+	0.171874i	0.0172739	+	0.00997312i
$298$	11.1488	−	1.21601i	0.645833	−	0.0704415i
$299$	4.49182	+	1.20358i	0.259769	+	0.0696048i
$300$	−0.131217	+	0.0681598i	−0.00757580	+	0.00393521i
$301$	−7.57176	−	26.6111i	−0.436429	−	1.53384i
$302$	19.7590	+	3.05014i	1.13700	+	0.175516i
$303$	−0.705299	−	1.22161i	−0.0405184	−	0.0701799i
$304$	−8.37244	−	3.06408i	−0.480193	−	0.175737i
$305$	2.01770	−	3.49477i	0.115533	−	0.200110i
$306$	−9.01822	−	23.2207i	−0.515537	−	1.32744i
$307$	15.2503	+	15.2503i	0.870381	+	0.870381i	0.992514	−	0.122133i	$-0.0389733\pi$
$307$	15.2503	+	15.2503i	0.870381	+	0.870381i	−0.122133	+	0.992514i	$0.538973\pi$
$308$	3.61259	−	1.94780i	0.205846	−	0.110986i
$309$	0.562161	−	0.562161i	0.0319802	−	0.0319802i
$310$	3.76651	−	8.54981i	0.213924	−	0.485596i
$311$	−8.56501	−	4.94501i	−0.485677	−	0.280406i	0.237102	−	0.971485i	$-0.423802\pi$
$311$	−8.56501	−	4.94501i	−0.485677	−	0.280406i	−0.722779	+	0.691079i	$0.757136\pi$
$312$	0.874990	−	0.582974i	0.0495365	−	0.0330044i
$313$	−23.8636	+	13.7777i	−1.34885	+	0.778760i	−0.988087	−	0.153896i	$-0.950818\pi$
$313$	−23.8636	+	13.7777i	−1.34885	+	0.778760i	−0.360766	+	0.932657i	$0.617485\pi$
$314$	17.2679	−	12.6496i	0.974485	−	0.713860i
$315$	1.93241	−	7.68352i	0.108879	−	0.432917i
$316$	18.9310	+	5.98732i	1.06495	+	0.336813i
$317$	1.82241	−	6.80134i	0.102357	−	0.382001i	−0.895675	−	0.444709i	$-0.853307\pi$
$317$	1.82241	−	6.80134i	0.102357	−	0.382001i	0.998032	+	0.0627080i	$0.0199737\pi$
$318$	−0.424878	−	0.341309i	−0.0238260	−	0.0191397i
$319$	3.46911	−	6.00868i	0.194233	−	0.336421i
$320$	3.04187	+	7.39912i	0.170046	+	0.413624i
$321$	−0.846699			−0.0472581
$322$	1.30237	+	3.20613i	0.0725781	+	0.178671i
$323$	−9.27060	−	9.27060i	−0.515830	−	0.515830i
$324$	−3.85919	−	17.4807i	−0.214399	−	0.971153i
$325$	1.30135	+	4.85670i	0.0721858	+	0.269401i
$326$	−1.07501	−	9.85608i	−0.0595393	−	0.545878i
$327$	0.427773	−	0.246975i	0.0236559	−	0.0136577i
$328$	11.6658	+	5.77218i	0.644138	+	0.318716i
$329$	20.0465	−	0.308925i	1.10520	−	0.0170316i
$330$	−0.0479239	−	0.0654205i	−0.00263812	−	0.00360128i
$331$	−30.8890	−	8.27670i	−1.69782	−	0.454928i	−0.725428	−	0.688298i	$-0.758358\pi$
$331$	−30.8890	−	8.27670i	−1.69782	−	0.454928i	−0.972388	+	0.233370i	$0.925025\pi$
$332$	12.6571	+	0.563826i	0.694651	+	0.0309440i
$333$	−22.3656	+	5.99285i	−1.22563	+	0.328406i
$334$	1.83201	+	4.71718i	0.100243	+	0.258113i
$335$	−15.7585			−0.860981
$336$	0.738816	+	0.257548i	0.0403057	+	0.0140504i
$337$	33.3088			1.81445			0.907224	−	0.420649i	$-0.138198\pi$
$337$	33.3088			1.81445			0.907224	+	0.420649i	$0.138198\pi$
$338$	−6.28766	−	16.1899i	−0.342004	−	0.880612i
$339$	0.0200945	−	0.00538430i	0.00109138	−	0.000292435i
$340$	−0.523535	+	11.7527i	−0.0283927	+	0.637377i
$341$	4.94942	+	1.32619i	0.268026	+	0.0718173i
$342$	−5.57807	−	7.61458i	−0.301627	−	0.411749i
$343$	−18.5005	+	0.855842i	−0.998932	+	0.0462111i
$344$	9.47029	+	28.0205i	0.510604	+	1.51076i
$345$	0.0592165	−	0.0341886i	0.00318811	−	0.00184065i
$346$	−0.0240208	−	0.220231i	−0.00129137	−	0.0118397i
$347$	1.60395	+	5.98603i	0.0861046	+	0.321347i	0.995521	−	0.0945398i	$-0.0301380\pi$
$347$	1.60395	+	5.98603i	0.0861046	+	0.321347i	−0.909416	+	0.415887i	$0.863471\pi$
$348$	1.29158	−	0.285140i	0.0692360	−	0.0152851i
$349$	0.506566	+	0.506566i	0.0271158	+	0.0271158i	0.720535	−	0.693419i	$-0.243896\pi$
$349$	0.506566	+	0.506566i	0.0271158	+	0.0271158i	−0.693419	+	0.720535i	$0.743896\pi$
$350$	−2.29805	+	2.95279i	−0.122836	+	0.157833i
$351$	2.22835			0.118940
$352$	−3.75604	+	2.26789i	−0.200198	+	0.120879i
$353$	−5.48817	+	9.50579i	−0.292106	+	0.505942i	−0.974307	−	0.225222i	$-0.927689\pi$
$353$	−5.48817	+	9.50579i	−0.292106	+	0.505942i	0.682202	+	0.731164i	$0.261023\pi$
$354$	0.602755	+	0.484200i	0.0320361	+	0.0257350i
$355$	−2.04635	+	7.63707i	−0.108609	+	0.405334i
$356$	−3.30695	+	10.4561i	−0.175268	+	0.554172i
$357$	0.826021	+	0.800948i	0.0437176	+	0.0423907i
$358$	−3.62946	+	2.65877i	−0.191823	+	0.140520i
$359$	−5.15629	+	2.97699i	−0.272139	+	0.157119i	−0.629859	−	0.776709i	$-0.716887\pi$
$359$	−5.15629	+	2.97699i	−0.272139	+	0.157119i	0.357720	+	0.933829i	$0.383554\pi$
$360$	−1.66339	+	8.30488i	−0.0876682	+	0.437706i
$361$	12.1522	+	7.01605i	0.639587	+	0.369266i
$362$	6.28310	−	14.2623i	0.330232	−	0.749612i
$363$	−0.543603	+	0.543603i	−0.0285318	+	0.0285318i
$364$	13.9678	−	22.6444i	0.732114	−	1.18689i
$365$	10.5428	+	10.5428i	0.551836	+	0.551836i
$366$	0.152747	+	0.393303i	0.00798422	+	0.0205583i
$367$	−12.1622	+	21.0656i	−0.634862	+	1.09961i	0.351682	+	0.936119i	$0.385610\pi$
$367$	−12.1622	+	21.0656i	−0.634862	+	1.09961i	−0.986544	+	0.163494i	$0.947724\pi$
$368$	−1.55754	−	3.35563i	−0.0811926	−	0.174924i
$369$	6.89007	+	11.9339i	0.358683	+	0.621257i
$370$	10.8071	+	1.66826i	0.561834	+	0.0867286i
$371$	−13.3744	−	3.36365i	−0.694362	−	0.174632i
$372$	0.450283	+	0.866854i	0.0233461	+	0.0449443i
$373$	25.4540	+	6.82038i	1.31796	+	0.353146i	0.848213	−	0.529656i	$-0.177679\pi$
$373$	25.4540	+	6.82038i	1.31796	+	0.353146i	0.469746	+	0.882802i	$0.344346\pi$
$374$	−6.41411	+	0.699592i	−0.331666	+	0.0361751i
$375$	0.0640267	+	0.0369658i	0.00330632	+	0.00190891i
$376$	−21.3891	+	1.37345i	−1.10306	+	0.0708304i
$377$		−	44.9772i		−	2.31644i
$378$	1.00044	+	1.32246i	0.0514573	+	0.0680201i
$379$	−6.49600	+	6.49600i	−0.333677	+	0.333677i	−0.853981	−	0.520304i	$-0.825819\pi$
$379$	−6.49600	+	6.49600i	−0.333677	+	0.333677i	0.520304	+	0.853981i	$0.325819\pi$
$380$	0.960990	+	4.35294i	0.0492978	+	0.223301i
$381$	1.38228	−	0.370380i	0.0708162	−	0.0189751i
$382$	−12.5037	−	10.0444i	−0.639746	−	0.513915i
$383$	−10.9886	−	19.0328i	−0.561491	−	0.972531i	−0.997367	−	0.0725243i	$-0.976895\pi$
$383$	−10.9886	−	19.0328i	−0.561491	−	0.972531i	0.435875	−	0.900007i	$-0.356439\pi$
$384$	−0.802298	−	0.236542i	−0.0409421	−	0.0120710i
$385$	−1.79279	−	0.998553i	−0.0913688	−	0.0508910i
$386$	−2.92095	+	18.9221i	−0.148672	+	0.963111i
$387$	−8.10482	+	30.2476i	−0.411991	+	1.53757i
$388$	−4.23102	+	3.87015i	−0.214798	+	0.196477i
$389$	4.13894	+	15.4467i	0.209852	+	0.783180i	0.987915	+	0.154994i	$0.0495357\pi$
$389$	4.13894	+	15.4467i	0.209852	+	0.783180i	−0.778063	+	0.628186i	$0.783798\pi$
$390$	−0.481091	−	0.211939i	−0.0243610	−	0.0107319i
$391$		−	5.44023i		−	0.275124i
$392$	19.7098	−	1.87695i	0.995496	−	0.0948005i
$393$			0.703122i			0.0354678i
$394$	4.32991	−	9.82870i	0.218138	−	0.495163i
$395$	−2.56946	−	9.58936i	−0.129284	−	0.482493i
$396$	−4.64068	−	0.206724i	−0.233203	−	0.0103883i
$397$	−6.20050	+	23.1406i	−0.311194	+	1.16139i	0.616286	+	0.787522i	$0.288636\pi$
$397$	−6.20050	+	23.1406i	−0.311194	+	1.16139i	−0.927481	+	0.373871i	$0.878030\pi$
$398$	−22.5579	−	3.48219i	−1.13072	−	0.174546i
$399$	0.380883	+	0.212146i	0.0190680	+	0.0106206i
$400$	2.30009	−	3.27255i	0.115005	−	0.163627i
$401$	−14.0977	−	24.4178i	−0.704003	−	1.21937i	−0.967050	−	0.254586i	$-0.918061\pi$
$401$	−14.0977	−	24.4178i	−0.704003	−	1.21937i	0.263047	−	0.964783i	$-0.415273\pi$
$402$	1.03186	−	1.28451i	0.0514646	−	0.0640656i
$403$	32.0847	−	8.59706i	1.59825	−	0.428250i
$404$	32.1653	+	20.5315i	1.60028	+	1.02148i
$405$	−6.32920	+	6.32920i	−0.314500	+	0.314500i
$406$	26.6927	−	20.1931i	1.32473	−	1.00216i
$407$			5.99737i			0.297279i
$408$	−0.923702	−	0.812233i	−0.0457300	−	0.0402115i
$409$	−26.6420	−	15.3818i	−1.31736	−	0.760580i	−0.334059	−	0.942552i	$-0.608418\pi$
$409$	−26.6420	−	15.3818i	−1.31736	−	0.760580i	−0.983304	+	0.181972i	$0.941752\pi$
$410$	−0.705635	−	6.46951i	−0.0348488	−	0.319506i
$411$	0.359730	+	0.0963894i	0.0177442	+	0.00475454i
$412$	−6.48533	+	20.5057i	−0.319509	+	1.01024i
$413$	18.9736	+	4.77187i	0.933631	+	0.234808i
$414$	0.597539	−	3.87090i	0.0293674	−	0.190244i
$415$	−3.16742	−	5.48614i	−0.155483	−	0.269304i
$416$	−13.7357	+	24.9063i	−0.673448	+	1.22113i
$417$	0.340325	−	0.589461i	0.0166658	−	0.0288660i
$418$	−2.27902	+	0.885105i	−0.111471	+	0.0432919i
$419$	−8.58559	−	8.58559i	−0.419433	−	0.419433i	0.465575	−	0.885008i	$-0.345848\pi$
$419$	−8.58559	−	8.58559i	−0.419433	−	0.419433i	−0.885008	+	0.465575i	$0.845848\pi$
$420$	−0.0902120	−	0.380666i	−0.00440190	−	0.0185746i
$421$	−0.954514	+	0.954514i	−0.0465202	+	0.0465202i	−0.729984	−	0.683464i	$-0.760473\pi$
$421$	−0.954514	+	0.954514i	−0.0465202	+	0.0465202i	0.683464	+	0.729984i	$0.260473\pi$
$422$	6.85481	+	3.01980i	0.333687	+	0.147002i
$423$	−19.6517	−	11.3459i	−0.955500	−	0.551658i
$424$	14.4559	+	2.89538i	0.702042	+	0.140612i
$425$	5.09409	−	2.94108i	0.247100	−	0.142663i
$426$	−0.488520	−	0.666874i	−0.0236688	−	0.0323102i
$427$	7.66499	+	7.43233i	0.370935	+	0.359676i
$428$	20.3262	−	10.5584i	0.982505	−	0.510357i
$429$	0.0746238	−	0.278500i	0.00360287	−	0.0134461i
$430$	9.26175	−	11.5295i	0.446641	−	0.556000i
$431$	12.6594	−	21.9267i	0.609781	−	1.05617i	−0.381495	−	0.924371i	$-0.624591\pi$
$431$	12.6594	−	21.9267i	0.609781	−	1.05617i	0.991276	−	0.131801i	$-0.0420759\pi$
$432$	−1.13710	−	1.36001i	−0.0547086	−	0.0654336i
$433$	11.6962			0.562086			0.281043	−	0.959695i	$-0.409320\pi$
$433$	11.6962			0.562086			0.281043	+	0.959695i	$0.409320\pi$
$434$	19.5069	+	15.1816i	0.936362	+	0.728739i
$435$	−0.467639	−	0.467639i	−0.0224216	−	0.0224216i
$436$	−7.18953	+	11.2633i	−0.344316	+	0.539415i
$437$	−0.533536	−	1.99118i	−0.0255225	−	0.0952513i
$438$	−1.54970	+	0.169027i	−0.0740477	+	0.00807645i
$439$	7.86644	−	4.54169i	0.375445	−	0.216763i	−0.300390	−	0.953817i	$-0.597117\pi$
$439$	7.86644	−	4.54169i	0.375445	−	0.216763i	0.675834	+	0.737053i	$0.263783\pi$
$440$	1.96628	+	0.972902i	0.0937386	+	0.0463813i
$441$	18.4677	+	9.91652i	0.879416	+	0.472215i
$442$	−33.7414	+	24.7173i	−1.60492	+	1.17568i
$443$	−1.83199	−	0.490881i	−0.0870405	−	0.0233224i	0.215036	−	0.976606i	$-0.431013\pi$
$443$	−1.83199	−	0.490881i	−0.0870405	−	0.0233224i	−0.302076	+	0.953284i	$0.597680\pi$
$444$	−0.843626	+	0.771671i	−0.0400367	+	0.0366219i
$445$	5.29645	−	1.41918i	0.251076	−	0.0672755i
$446$	−25.4935	+	9.90092i	−1.20715	+	0.468822i
$447$	0.586289			0.0277305
$448$	−20.9480	+	3.03023i	−0.989699	+	0.143165i
$449$	4.22607			0.199441			0.0997203	−	0.995016i	$-0.468205\pi$
$449$	4.22607			0.199441			0.0997203	+	0.995016i	$0.468205\pi$
$450$	3.94765	−	1.53315i	0.186094	−	0.0722733i
$451$	3.44764	−	0.923791i	0.162343	−	0.0434996i
$452$	−0.415254	+	0.379836i	−0.0195319	+	0.0178660i
$453$	1.00958	+	0.270515i	0.0474340	+	0.0127099i
$454$	−26.7252	+	19.5776i	−1.25428	+	0.918821i
$455$	−13.3013	+	0.204979i	−0.623575	+	0.00960955i
$456$	−0.417742	−	0.206696i	−0.0195626	−	0.00967944i
$457$	−10.8272	+	6.25111i	−0.506477	+	0.292415i	−0.731384	−	0.681965i	$-0.761125\pi$
$457$	−10.8272	+	6.25111i	−0.506477	+	0.292415i	0.224907	+	0.974380i	$0.427792\pi$
$458$	−23.9567	+	2.61298i	−1.11942	+	0.122096i
$459$	−0.674712	−	2.51806i	−0.0314929	−	0.117533i
$460$	−0.995244	+	1.55918i	−0.0464035	+	0.0726971i
$461$	−6.47006	−	6.47006i	−0.301341	−	0.301341i	0.540198	−	0.841538i	$-0.318349\pi$
$461$	−6.47006	−	6.47006i	−0.301341	−	0.301341i	−0.841538	+	0.540198i	$0.818349\pi$
$462$	0.198785	−	0.0807488i	0.00924831	−	0.00375677i
$463$	7.95132			0.369529			0.184765	−	0.982783i	$-0.440848\pi$
$463$	7.95132			0.369529			0.184765	+	0.982783i	$0.440848\pi$
$464$	−27.4506	+	22.9512i	−1.27436	+	1.06548i
$465$	0.244207	−	0.422978i	0.0113248	−	0.0196151i
$466$	−2.50616	+	3.11979i	−0.116096	+	0.144521i
$467$	3.19649	−	11.9295i	0.147916	−	0.552029i	−0.851692	−	0.524042i	$-0.824423\pi$
$467$	3.19649	−	11.9295i	0.147916	−	0.552029i	0.999608	−	0.0279875i	$-0.00890985\pi$
$468$	−26.7230	+	13.8811i	−1.23527	+	0.641655i
$469$	10.1692	−	40.4340i	0.469568	−	1.86707i
$470$	6.33299	+	8.64512i	0.292119	+	0.398770i
$471$	0.969105	−	0.559513i	0.0446540	−	0.0257810i
$472$	−20.5080	−	4.10755i	−0.943957	−	0.189066i
$473$	7.02428	+	4.05547i	0.322977	+	0.186471i
$474$	0.949895	+	0.418465i	0.0436301	+	0.0192207i
$475$	1.57606	−	1.57606i	0.0723144	−	0.0723144i
$476$	−29.8177	−	8.92743i	−1.36669	−	0.409188i
$477$	11.0371	+	11.0371i	0.505356	+	0.505356i
$478$	22.1788	−	8.61359i	1.01443	−	0.393976i
$479$	12.6954	−	21.9891i	0.580068	−	1.00471i	−0.415402	−	0.909638i	$-0.636359\pi$
$479$	12.6954	−	21.9891i	0.580068	−	1.00471i	0.995471	−	0.0950700i	$-0.0303075\pi$
$480$	0.116143	+	0.401770i	0.00530119	+	0.0183382i
$481$	19.4390	+	33.6694i	0.886344	+	1.53519i
$482$	−0.633443	+	4.10349i	−0.0288525	+	0.186909i
$483$	0.0495098	+	0.174003i	0.00225277	+	0.00791740i
$484$	6.27124	−	19.8287i	0.285056	−	0.901306i
$485$	2.76934	+	0.742044i	0.125749	+	0.0336945i
$486$	−0.305347	−	2.79953i	−0.0138508	−	0.126989i
$487$	7.26564	+	4.19482i	0.329238	+	0.190086i	0.655503	−	0.755193i	$-0.272457\pi$
$487$	7.26564	+	4.19482i	0.329238	+	0.190086i	−0.326265	+	0.945278i	$0.605790\pi$
$488$	−8.57141	−	7.53705i	−0.388010	−	0.341186i
$489$		−	0.518308i		−	0.0234387i
$490$	−6.09344	−	7.80192i	−0.275273	−	0.352455i
$491$	19.9226	−	19.9226i	0.899097	−	0.899097i	−0.0962597	−	0.995356i	$-0.530688\pi$
$491$	19.9226	−	19.9226i	0.899097	−	0.899097i	0.995356	+	0.0962597i	$0.0306879\pi$
$492$	0.573547	+	0.366103i	0.0258575	+	0.0165052i
$493$	−50.8247	+	13.6184i	−2.28903	+	0.613344i
$494$	−9.92565	+	12.3559i	−0.446576	+	0.555919i
$495$	1.16132	+	2.01147i	0.0521975	+	0.0904088i
$496$	−21.6194	−	15.1950i	−0.970738	−	0.682278i
$497$	−18.2750	−	10.1789i	−0.819747	−	0.456586i
$498$	0.654587	+	0.101047i	0.0293328	+	0.00452801i
$499$	−2.05496	+	7.66920i	−0.0919925	+	0.343321i	−0.996546	−	0.0830389i	$-0.973537\pi$
$499$	−2.05496	+	7.66920i	−0.0919925	+	0.343321i	0.904554	+	0.426359i	$0.140204\pi$
$500$	−1.99802	−	0.0890039i	−0.0893541	−	0.00398038i
$501$	0.0684699	+	0.255533i	0.00305901	+	0.0114164i
$502$	1.93516	−	4.39273i	0.0863706	−	0.196057i
$503$			26.1413i			1.16558i	0.812622	+	0.582792i	$0.198040\pi$
$503$			26.1413i			1.16558i	−0.812622	+	0.582792i	$0.801960\pi$
$504$	−20.2357	−	9.62723i	−0.901368	−	0.428831i
$505$		−	19.0798i		−	0.849038i
$506$	−0.928398	−	0.408994i	−0.0412723	−	0.0181820i
$507$	−0.234996	−	0.877017i	−0.0104365	−	0.0389497i
$508$	−28.5649	+	26.1285i	−1.26736	+	1.15927i
$509$	−5.68320	+	21.2100i	−0.251903	+	0.940116i	0.717884	+	0.696163i	$0.245111\pi$
$509$	−5.68320	+	21.2100i	−0.251903	+	0.940116i	−0.969787	+	0.243953i	$0.921556\pi$
$510$	−0.0938258	+	0.607810i	−0.00415468	+	0.0269143i
$511$	−33.8546	+	20.2478i	−1.49764	+	0.895712i
$512$	22.2100	−	4.32613i	0.981553	−	0.191190i
$513$	−0.493904	−	0.855467i	−0.0218064	−	0.0377698i
$514$	10.2812	+	8.25897i	0.453482	+	0.364287i
$515$	10.3870	−	2.78318i	0.457705	−	0.122642i
$516$	0.333335	+	1.50989i	0.0146743	+	0.0664691i
$517$	−4.15603	+	4.15603i	−0.182782	+	0.182782i
$518$	−11.2544	+	26.6528i	−0.494491	+	1.17106i
$519$		−	0.0115814i		−	0.000508368i
$520$	14.1922	−	0.911318i	0.622368	−	0.0399639i
$521$	31.0809	+	17.9446i	1.36168	+	0.786165i	0.989847	−	0.142135i	$-0.0453967\pi$
$521$	31.0809	+	17.9446i	1.36168	+	0.786165i	0.371831	+	0.928300i	$0.378730\pi$
$522$	−37.6592	+	4.10752i	−1.64830	+	0.179781i
$523$	2.34242	+	0.627650i	0.102427	+	0.0274452i	0.309668	−	0.950845i	$-0.399782\pi$
$523$	2.34242	+	0.627650i	0.102427	+	0.0274452i	−0.207242	+	0.978290i	$0.566449\pi$
$524$	−8.76794	−	16.8795i	−0.383029	−	0.737382i
$525$	−0.136166	+	0.140428i	−0.00594277	+	0.00612879i
$526$	−12.8306	−	1.98061i	−0.559439	−	0.0863589i
$527$	−19.4296	−	33.6530i	−0.846365	−	1.46595i
$528$	−0.208054	+	0.0965701i	−0.00905440	+	0.00420267i
$529$	−11.0723	+	19.1778i	−0.481405	+	0.833817i
$530$	−2.66868	−	6.87150i	−0.115920	−	0.298479i
$531$	−15.6579	−	15.6579i	−0.679495	−	0.679495i
$532$	−11.7891	−	0.343249i	−0.511123	−	0.0148817i
$533$	16.3609	−	16.3609i	0.708668	−	0.708668i
$534$	−0.231129	+	0.524651i	−0.0100019	+	0.0227039i
$535$	−9.91811	−	5.72622i	−0.428797	−	0.247566i
$536$	−8.75346	+	43.7039i	−0.378092	+	1.88772i
$537$	−0.203692	+	0.117601i	−0.00878994	+	0.00507487i
$538$	−1.63825	+	1.20010i	−0.0706300	+	0.0517401i
$539$	3.71904	−	3.95564i	0.160190	−	0.170381i
$540$	−0.267284	+	0.845112i	−0.0115021	+	0.0363678i
$541$	−0.516629	+	1.92809i	−0.0222116	+	0.0828949i	−0.976142	−	0.217133i	$-0.930329\pi$
$541$	−0.516629	+	1.92809i	−0.0222116	+	0.0828949i	0.953930	+	0.300028i	$0.0969961\pi$
$542$	−9.44488	−	7.58718i	−0.405692	−	0.325897i
$543$	0.407373	−	0.705590i	0.0174820	−	0.0302798i
$544$	32.3034	+	7.98024i	1.38500	+	0.342150i
$545$	6.68116			0.286190
$546$	0.854256	−	1.09764i	0.0365588	−	0.0469746i
$547$	−23.7662	−	23.7662i	−1.01617	−	1.01617i	−0.999867	−	0.0163036i	$-0.994810\pi$
$547$	−23.7662	−	23.7662i	−1.01617	−	1.01617i	−0.0163036	−	0.999867i	$-0.505190\pi$
$548$	−9.83783	+	2.17188i	−0.420251	+	0.0927780i
$549$	−3.12761	−	11.6724i	−0.133483	−	0.498166i
$550$	−0.118935	−	1.09044i	−0.00507140	−	0.0464964i
$551$	−17.2668	+	9.96900i	−0.735591	+	0.424693i
$552$	−0.0619237	−	0.183219i	−0.00263565	−	0.00779830i
$553$	26.2629	−	0.404723i	1.11681	−	0.0172106i
$554$	−3.59437	−	4.90665i	−0.152710	−	0.208463i
$555$	0.552182	+	0.147957i	0.0234388	+	0.00628041i
$556$	−0.819413	+	18.3947i	−0.0347509	+	0.780110i
$557$	12.2756	−	3.28924i	0.520135	−	0.139370i	0.0108060	−	0.999942i	$-0.496560\pi$
$557$	12.2756	−	3.28924i	0.520135	−	0.139370i	0.509329	+	0.860572i	$0.329894\pi$
$558$	−10.1284	−	26.0793i	−0.428770	−	1.10402i
$559$	52.5793			2.22387
$560$	6.91259	+	8.01350i	0.292110	+	0.338632i
$561$	−0.337303			−0.0142409
$562$	−3.53464	−	9.10121i	−0.149100	−	0.383911i
$563$	−22.0889	+	5.91870i	−0.930936	+	0.249444i	−0.692254	−	0.721654i	$-0.743382\pi$
$563$	−22.0889	+	5.91870i	−0.930936	+	0.249444i	−0.238682	+	0.971098i	$0.576715\pi$
$564$	−1.11936	−	0.0498632i	−0.0471337	−	0.00209962i
$565$	0.271798	+	0.0728280i	0.0114346	+	0.00306390i
$566$	−4.24867	−	5.79983i	−0.178585	−	0.243785i
$567$	−12.1555	−	20.3241i	−0.510481	−	0.853530i
$568$	20.0436	+	9.91743i	0.841009	+	0.416126i
$569$	−2.11785	+	1.22274i	−0.0887848	+	0.0512599i	−0.543735	−	0.839257i	$-0.682990\pi$
$569$	−2.11785	+	1.22274i	−0.0887848	+	0.0512599i	0.454950	+	0.890517i	$0.349657\pi$
$570$	0.0252681	+	0.231667i	0.00105836	+	0.00970346i
$571$	−3.80725	−	14.2088i	−0.159328	−	0.594622i	−0.998696	−	0.0510572i	$-0.983741\pi$
$571$	−3.80725	−	14.2088i	−0.159328	−	0.594622i	0.839367	−	0.543565i	$-0.182926\pi$
$572$	1.68145	+	7.61635i	0.0703048	+	0.318456i
$573$	−0.592875	−	0.592875i	−0.0247677	−	0.0247677i
$574$	17.0551	+	2.36430i	0.711867	+	0.0986838i
$575$	0.924871			0.0385698
$576$	22.1083	+	9.22629i	0.921181	+	0.384429i
$577$	−20.7412	+	35.9248i	−0.863466	+	1.49557i	0.00509632	+	0.999987i	$0.498378\pi$
$577$	−20.7412	+	35.9248i	−0.863466	+	1.49557i	−0.868562	+	0.495580i	$0.834956\pi$
$578$	19.4043	+	15.5877i	0.807111	+	0.648361i
$579$	−0.259057	+	0.966814i	−0.0107660	+	0.0401794i
$580$	17.0578	+	5.39488i	0.708287	+	0.224010i
$581$	16.1206	−	4.58686i	0.668794	−	0.190295i
$582$	−0.241821	+	0.177146i	−0.0100238	+	0.00734295i
$583$	3.50127	−	2.02146i	0.145008	−	0.0837204i
$584$	35.0951	−	23.3826i	1.45225	−	0.967579i
$585$	13.0394	+	7.52829i	0.539112	+	0.311257i
$586$	12.7332	−	28.9038i	0.526004	−	1.19400i
$587$	10.8150	−	10.8150i	0.446383	−	0.446383i	−0.447767	−	0.894150i	$-0.647781\pi$
$587$	10.8150	−	10.8150i	0.446383	−	0.446383i	0.894150	+	0.447767i	$0.147781\pi$
$588$	1.03495	+	0.0141779i	0.0426805	+	0.000584686i
$589$	−10.4119	−	10.4119i	−0.429013	−	0.429013i
$590$	3.78595	+	9.74829i	0.155865	+	0.401331i
$591$	0.280735	−	0.486248i	0.0115479	−	0.0200016i
$592$	10.6297	−	29.0451i	0.436879	−	1.19375i
$593$	2.49234	+	4.31686i	0.102348	+	0.177272i	0.912652	−	0.408738i	$-0.134031\pi$
$593$	2.49234	+	4.31686i	0.102348	+	0.177272i	−0.810304	+	0.586010i	$0.800698\pi$
$594$	−0.480441	−	0.0741643i	−0.0197128	−	0.00304300i
$595$	4.25908	+	14.9686i	0.174605	+	0.613652i
$596$	−14.0747	+	7.31104i	−0.576523	+	0.299472i
$597$	−1.15258	−	0.308833i	−0.0471719	−	0.0126397i
$598$	−6.53771	+	0.713073i	−0.267347	+	0.0291597i
$599$	10.0637	+	5.81025i	0.411190	+	0.237401i	0.691301	−	0.722567i	$-0.257038\pi$
$599$	10.0637	+	5.81025i	0.411190	+	0.237401i	−0.280111	+	0.959968i	$0.590371\pi$
$600$	0.138084	−	0.157035i	0.00563727	−	0.00641091i
$601$		−	18.6238i		−	0.759680i	−0.925052	−	0.379840i	$-0.875979\pi$
$601$		−	18.6238i		−	0.759680i	0.925052	−	0.379840i	$-0.124021\pi$
$602$	23.6061	+	31.2043i	0.962114	+	1.27179i
$603$	−33.3680	+	33.3680i	−1.35885	+	1.35885i
$604$	−27.6096	+	6.09532i	−1.12342	+	0.248015i
$605$	−10.0441	+	2.69130i	−0.408350	+	0.109417i
$606$	1.55523	+	1.24933i	0.0631769	+	0.0507507i
$607$	−0.807813	−	1.39917i	−0.0327881	−	0.0567907i	0.849166	−	0.528127i	$-0.177105\pi$
$607$	−0.807813	−	1.39917i	−0.0327881	−	0.0567907i	−0.881954	+	0.471336i	$0.843772\pi$
$608$	12.6060	−	0.247211i	0.511242	−	0.0100257i
$609$	1.50166	−	0.898117i	0.0608504	−	0.0363935i
$610$	−0.870649	+	5.64013i	−0.0352515	+	0.228362i
$611$	−9.86130	+	36.8029i	−0.398945	+	1.48888i
$612$	23.7772	+	25.9943i	0.961134	+	1.05076i
$613$	−4.93419	−	18.4147i	−0.199290	−	0.743761i	−0.991114	−	0.133012i	$-0.957535\pi$
$613$	−4.93419	−	18.4147i	−0.199290	−	0.743761i	0.791824	−	0.610749i	$-0.209132\pi$
$614$	−27.9121	−	12.2964i	−1.12644	−	0.496241i
$615$		−	0.340216i		−	0.0137188i
$616$	−3.76518	+	4.41734i	−0.151703	+	0.177980i
$617$		−	42.3750i		−	1.70595i	−0.521948	−	0.852977i	$-0.674795\pi$
$617$		−	42.3750i		−	1.70595i	0.521948	−	0.852977i	$-0.325205\pi$
$618$	−0.453272	+	1.02891i	−0.0182333	+	0.0413886i
$619$	1.47559	+	5.50696i	0.0593088	+	0.221343i	0.989219	−	0.146443i	$-0.0467825\pi$
$619$	1.47559	+	5.50696i	0.0593088	+	0.221343i	−0.929910	+	0.367786i	$0.880116\pi$
$620$	−0.587985	+	13.1995i	−0.0236140	+	0.530103i
$621$	0.106087	−	0.395923i	0.00425714	−	0.0158879i
$622$	13.8229	+	2.13380i	0.554247	+	0.0855574i
$623$	0.223539	+	14.5057i	0.00895589	+	0.581158i
$624$	−0.855013	+	1.21650i	−0.0342279	+	0.0486992i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	24.4051	−	30.3807i	0.975425	−	1.21426i
$627$	−0.123457	+	0.0330801i	−0.00493038	+	0.00132109i
$628$	−16.2876	+	25.5167i	−0.649947	+	1.01823i
$629$	32.1610	−	32.1610i	1.28234	−	1.28234i
$630$	1.38636	+	11.1184i	0.0552341	+	0.442968i
$631$		−	20.5258i		−	0.817119i	−0.912732	−	0.408559i	$-0.866031\pi$
$631$		−	20.5258i		−	0.817119i	0.912732	−	0.408559i	$-0.133969\pi$
$632$	−28.0219	+	1.79936i	−1.11465	+	0.0715748i
$633$	0.339123	+	0.195793i	0.0134789	+	0.00778206i
$634$	1.07971	+	9.89914i	0.0428807	+	0.393145i
$635$	18.6967	+	5.00976i	0.741955	+	0.198806i
$636$	0.734854	+	0.232412i	0.0291389	+	0.00921575i
$637$	8.05755	−	34.2614i	0.319252	−	1.35749i
$638$	−1.49694	+	9.69727i	−0.0592643	+	0.383919i
$639$	11.8381	+	20.5042i	0.468309	+	0.811134i
$640$	−7.79827	−	8.19677i	−0.308254	−	0.324006i
$641$	−19.3154	+	33.4552i	−0.762911	+	1.32140i	0.178433	+	0.983952i	$0.442897\pi$
$641$	−19.3154	+	33.4552i	−0.762911	+	1.32140i	−0.941344	+	0.337448i	$0.890436\pi$
$642$	1.11619	−	0.433495i	0.0440525	−	0.0171087i
$643$	−21.2128	−	21.2128i	−0.836551	−	0.836551i	0.151852	−	0.988403i	$-0.451476\pi$
$643$	−21.2128	−	21.2128i	−0.836551	−	0.836551i	−0.988403	+	0.151852i	$0.951476\pi$
$644$	−3.35837	−	3.55980i	−0.132338	−	0.140276i
$645$	0.546680	−	0.546680i	0.0215255	−	0.0215255i
$646$	16.9677	+	7.47490i	0.667584	+	0.294096i
$647$	41.0314	+	23.6895i	1.61311	+	0.931330i	0.988644	+	0.150279i	$0.0480171\pi$
$647$	41.0314	+	23.6895i	1.61311	+	0.931330i	0.624467	+	0.781051i	$0.285316\pi$
$648$	14.0373	+	21.0688i	0.551439	+	0.827659i
$649$	−4.96710	+	2.86776i	−0.194976	+	0.112569i
$650$	−4.20209	−	5.73624i	−0.164820	−	0.224994i
$651$	0.927708	+	0.899549i	0.0363597	+	0.0352561i
$652$	6.46331	+	12.4427i	0.253123	+	0.487295i
$653$	6.06445	−	22.6328i	0.237320	−	0.885691i	−0.739769	−	0.672861i	$-0.765065\pi$
$653$	6.06445	−	22.6328i	0.237320	−	0.885691i	0.977089	−	0.212830i	$-0.0682680\pi$
$654$	−0.437480	+	0.544595i	−0.0171068	+	0.0212954i
$655$	−4.75521	+	8.23627i	−0.185802	+	0.321818i
$656$	−18.3341	−	1.63668i	−0.715828	−	0.0639015i
$657$	44.6479			1.74188
$658$	−26.2688	+	10.6707i	−1.02406	+	0.415987i
$659$	−28.8922	−	28.8922i	−1.12548	−	1.12548i	−0.990903	−	0.134578i	$-0.957032\pi$
$659$	−28.8922	−	28.8922i	−1.12548	−	1.12548i	−0.134578	−	0.990903i	$-0.542968\pi$
$660$	0.0966715	+	0.0617067i	0.00376293	+	0.00240193i
$661$	−0.278577	−	1.03966i	−0.0108354	−	0.0404382i	0.960296	−	0.278981i	$-0.0899968\pi$
$661$	−0.278577	−	1.03966i	−0.0108354	−	0.0404382i	−0.971132	+	0.238543i	$0.923330\pi$
$662$	44.9581	−	4.90361i	1.74735	−	0.190584i
$663$	−1.89363	+	1.09329i	−0.0735424	+	0.0424597i
$664$	−16.9744	+	5.73695i	−0.658734	+	0.222637i
$665$	3.02687	+	5.06096i	0.117377	+	0.196256i
$666$	26.4160	−	19.3511i	1.02360	−	0.749839i
$667$	−7.99135	−	2.14127i	−0.309426	−	0.0829105i
$668$	−4.83023	−	5.28062i	−0.186887	−	0.204314i
$669$	−1.38100	+	0.370039i	−0.0533927	+	0.0143065i
$670$	20.7742	−	8.06810i	0.802579	−	0.311698i
$671$	−3.12997			−0.120831
$672$	−1.10583	+	0.0387389i	−0.0426583	+	0.00149439i
$673$	−5.30245			−0.204394			−0.102197	−	0.994764i	$-0.532587\pi$
$673$	−5.30245			−0.204394			−0.102197	+	0.994764i	$0.532587\pi$
$674$	−43.9105	+	17.0535i	−1.69137	+	0.656878i
$675$	0.428085	−	0.114705i	0.0164770	−	0.00441500i
$676$	16.5778	+	18.1237i	0.637610	+	0.697064i
$677$	−8.42519	−	2.25752i	−0.323806	−	0.0867637i	0.0932542	−	0.995642i	$-0.470273\pi$
$677$	−8.42519	−	2.25752i	−0.323806	−	0.0867637i	−0.417061	+	0.908879i	$0.636940\pi$
$678$	−0.0237336	+	0.0173860i	−0.000911482	+	0.000667707i
$679$	−3.69106	+	6.62687i	−0.141650	+	0.254316i
$680$	−5.32698	−	15.7614i	−0.204281	−	0.604421i
$681$	−1.49986	+	0.865947i	−0.0574749	+	0.0331831i
$682$	−7.20372	+	0.785716i	−0.275845	+	0.0300866i
$683$	−1.01182	−	3.77615i	−0.0387160	−	0.144490i	0.943862	−	0.330339i	$-0.107163\pi$
$683$	−1.01182	−	3.77615i	−0.0387160	−	0.144490i	−0.982578	+	0.185849i	$0.940496\pi$
$684$	11.2520	+	7.18231i	0.430231	+	0.274622i
$685$	3.56195	+	3.56195i	0.136095	+	0.136095i
$686$	23.9507	−	10.6002i	0.914442	−	0.404716i
$687$	−1.25983			−0.0480653
$688$	−26.8305	−	32.0904i	−1.02290	−	1.22343i
$689$	13.1042	−	22.6971i	0.499229	−	0.864690i
$690$	−0.0605601	+	0.0753881i	−0.00230549	+	0.00286998i
$691$	−2.89379	+	10.7998i	−0.110085	+	0.410843i	−0.998872	−	0.0474770i	$-0.984882\pi$
$691$	−2.89379	+	10.7998i	−0.110085	+	0.410843i	0.888787	+	0.458320i	$0.151549\pi$
$692$	0.144421	+	0.278029i	0.00549005	+	0.0105691i
$693$	−5.91053	+	1.68175i	−0.224523	+	0.0638844i
$694$	−5.17921	−	7.07009i	−0.196600	−	0.268377i
$695$	7.97305	−	4.60324i	0.302435	−	0.174611i
$696$	−1.55669	+	1.03716i	−0.0590060	+	0.0393135i
$697$	−23.4418	−	13.5341i	−0.887922	−	0.512642i
$698$	−0.927150	−	0.408445i	−0.0350931	−	0.0154599i
$699$	−0.147928	+	0.147928i	−0.00559513	+	0.00559513i
$700$	1.51771	−	5.06918i	0.0573642	−	0.191597i
$701$	34.7748	+	34.7748i	1.31343	+	1.31343i	0.918873	+	0.394553i	$0.129100\pi$
$701$	34.7748	+	34.7748i	1.31343	+	1.31343i	0.394553	+	0.918873i	$0.370900\pi$
$702$	−2.93760	+	1.14088i	−0.110872	+	0.0430596i
$703$	8.61716	−	14.9254i	0.325002	−	0.562920i
$704$	3.79041	−	4.91275i	0.142856	−	0.185156i
$705$	0.280118	+	0.485179i	0.0105499	+	0.0182729i
$706$	2.36817	−	15.3412i	0.0891273	−	0.577373i
$707$	48.9558	+	12.3124i	1.84117	+	0.463055i
$708$	−1.04251	−	0.329713i	−0.0391797	−	0.0123914i
$709$	14.5380	+	3.89545i	0.545986	+	0.146297i	0.521260	−	0.853398i	$-0.325462\pi$
$709$	14.5380	+	3.89545i	0.545986	+	0.146297i	0.0247259	+	0.999694i	$0.492129\pi$
$710$	−1.21238	−	11.1155i	−0.0454998	−	0.417158i
$711$	−25.7458	−	14.8643i	−0.965542	−	0.557456i
$712$	−0.993833	−	15.4772i	−0.0372455	−	0.580033i
$713$		−	6.10996i		−	0.228820i
$714$	−1.49900	−	0.632970i	−0.0560987	−	0.0236883i
$715$	2.75763	−	2.75763i	0.103129	−	0.103129i
$716$	3.42342	−	5.36323i	0.127939	−	0.200433i
$717$	1.20144	−	0.321926i	0.0448687	−	0.0120225i
$718$	5.27330	−	6.56445i	0.196798	−	0.244983i
$719$	5.42619	+	9.39843i	0.202363	+	0.350502i	0.949289	−	0.314404i	$-0.101805\pi$
$719$	5.42619	+	9.39843i	0.202363	+	0.350502i	−0.746927	+	0.664907i	$0.768471\pi$
$720$	−2.05914	−	11.7998i	−0.0767395	−	0.439753i
$721$	0.438387	+	28.4474i	0.0163264	+	1.05944i
$722$	−19.6121	−	3.02746i	−0.729886	−	0.112670i
$723$	−0.0561796	+	0.209665i	−0.00208934	+	0.00779753i
$724$	−0.980845	+	22.0187i	−0.0364528	+	0.818317i
$725$	−2.31521	−	8.64050i	−0.0859849	−	0.320900i
$726$	0.438308	−	0.994939i	0.0162672	−	0.0369257i
$727$			39.3655i			1.45999i	0.683454	+	0.729993i	$0.260477\pi$
$727$			39.3655i			1.45999i	−0.683454	+	0.729993i	$0.739523\pi$
$728$	−6.82006	+	37.0030i	−0.252768	+	1.37142i
$729$			26.7053i			0.989085i
$730$	−19.2962	−	8.50069i	−0.714183	−	0.314625i
$731$	−15.9203	−	59.4153i	−0.588833	−	2.19755i
$732$	−0.402728	−	0.440281i	−0.0148853	−	0.0162733i
$733$	7.27692	−	27.1578i	0.268779	−	1.00310i	−0.691117	−	0.722743i	$-0.742881\pi$
$733$	7.27692	−	27.1578i	0.268779	−	1.00310i	0.959896	−	0.280355i	$-0.0904522\pi$
$734$	5.24805	−	33.9972i	0.193709	−	1.25486i
$735$	−0.272448	−	0.440001i	−0.0100494	−	0.0162297i
$736$	3.77131	+	3.62624i	0.139012	+	0.133665i
$737$	6.11138	+	10.5852i	0.225116	+	0.389912i
$738$	−15.1930	−	12.2047i	−0.559264	−	0.449263i
$739$	12.8707	−	3.44869i	0.473456	−	0.126862i	−0.0141979	−	0.999899i	$-0.504519\pi$
$739$	12.8707	−	3.44869i	0.473456	−	0.126862i	0.487654	+	0.873037i	$0.337853\pi$
$740$	−15.1009	+	3.33380i	−0.555122	+	0.122553i
$741$	−0.585867	+	0.585867i	−0.0215224	+	0.0215224i
$742$	19.3533	−	2.41318i	0.710483	−	0.0885908i
$743$		−	38.6194i		−	1.41681i	−0.705807	−	0.708404i	$-0.749416\pi$
$743$		−	38.6194i		−	1.41681i	0.705807	−	0.708404i	$-0.250584\pi$
$744$	−1.03741	−	0.912223i	−0.0380335	−	0.0334437i
$745$	6.86771	+	3.96507i	0.251613	+	0.145269i
$746$	−37.0475	+	4.04081i	−1.35641	+	0.147944i
$747$	−18.3235	−	4.90977i	−0.670423	−	0.179639i
$748$	8.09745	−	4.20618i	0.296072	−	0.153793i
$749$	21.0929	−	21.7532i	0.770717	−	0.794843i
$750$	−0.103331	−	0.0159509i	−0.00377312	−	0.000582446i
$751$	−17.8461	−	30.9104i	−0.651215	−	1.12794i	−0.982828	−	0.184522i	$-0.940926\pi$
$751$	−17.8461	−	30.9104i	−0.651215	−	1.12794i	0.331614	−	0.943415i	$-0.392407\pi$
$752$	27.4937	−	12.7614i	1.00259	−	0.465362i
$753$	0.125469	−	0.217318i	0.00457234	−	0.00791952i
$754$	23.0275	+	59.2927i	0.838613	+	2.15931i
$755$	9.99653	+	9.99653i	0.363811	+	0.363811i
$756$	−1.99595	−	1.23117i	−0.0725919	−	0.0447772i
$757$	−33.9775	+	33.9775i	−1.23493	+	1.23493i	−0.272888	+	0.962046i	$0.587979\pi$
$757$	−33.9775	+	33.9775i	−1.23493	+	1.23493i	−0.962046	+	0.272888i	$0.912021\pi$
$758$	5.23774	−	11.8894i	0.190243	−	0.431843i
$759$	−0.0459299	−	0.0265177i	−0.00166715	−	0.000962530i
$760$	−3.49549	−	5.24641i	−0.126795	−	0.190307i
$761$	14.8691	−	8.58469i	0.539005	−	0.311195i	−0.205670	−	0.978621i	$-0.565937\pi$
$761$	14.8691	−	8.58469i	0.539005	−	0.311195i	0.744676	+	0.667426i	$0.232604\pi$
$762$	−1.63261	+	1.19597i	−0.0591431	+	0.0433253i
$763$	−4.31143	+	17.1428i	−0.156084	+	0.620613i
$764$	21.6260	+	6.83966i	0.782401	+	0.247450i
$765$	4.55892	−	17.0141i	0.164828	−	0.615147i
$766$	24.2306	+	19.4647i	0.875486	+	0.703288i
$767$	−18.5903	+	32.1994i	−0.671257	+	1.16265i
$768$	1.17876	−	0.0989323i	0.0425349	−	0.00356991i
$769$	17.9657			0.647860			0.323930	−	0.946081i	$-0.394996\pi$
$769$	17.9657			0.647860			0.323930	+	0.946081i	$0.394996\pi$
$770$	2.87464	+	0.398502i	0.103595	+	0.0143610i
$771$	0.487490	+	0.487490i	0.0175565	+	0.0175565i
$772$	−5.83715	−	26.4402i	−0.210084	−	0.951604i
$773$	−2.45207	−	9.15126i	−0.0881949	−	0.329148i	0.907705	−	0.419609i	$-0.137833\pi$
$773$	−2.45207	−	9.15126i	−0.0881949	−	0.329148i	−0.995900	+	0.0904608i	$0.971166\pi$
$774$	−4.80179	−	44.0245i	−0.172597	−	1.58243i
$775$	5.72120	−	3.30314i	0.205512	−	0.118652i
$776$	3.59624	−	7.26817i	0.129098	−	0.260912i
$777$	−0.735963	+	1.32134i	−0.0264025	+	0.0474026i
$778$	−13.3647	−	18.2441i	−0.479149	−	0.654083i
$779$	−9.90728	−	2.65465i	−0.354965	−	0.0951126i
$780$	0.742724	+	0.0330854i	0.0265938	+	0.00118465i
$781$	5.92353	−	1.58720i	0.211960	−	0.0567946i
$782$	2.78530	+	7.17178i	0.0996023	+	0.256462i
$783$	−3.96443			−0.141677
$784$	−25.0222	+	12.5654i	−0.893649	+	0.448766i
$785$	15.1360			0.540225
$786$	−0.359986	−	0.926914i	−0.0128403	−	0.0330619i
$787$	32.3953	−	8.68030i	1.15477	−	0.309419i	0.369894	−	0.929074i	$-0.379394\pi$
$787$	32.3953	−	8.68030i	1.15477	−	0.309419i	0.784875	+	0.619655i	$0.212727\pi$
$788$	−0.675936	+	15.1739i	−0.0240792	+	0.540546i
$789$	−0.655570	−	0.175659i	−0.0233389	−	0.00625364i
$790$	8.29687	+	11.3260i	0.295189	+	0.402960i
$791$	−0.362260	+	0.650395i	−0.0128805	+	0.0231254i
$792$	6.22358	−	2.10343i	0.221145	−	0.0747421i
$793$	−17.5718	+	10.1451i	−0.623992	+	0.360262i
$794$	−3.67355	−	33.6804i	−0.130370	−	1.19527i
$795$	−0.0997399	−	0.372234i	−0.00353741	−	0.0132018i
$796$	31.5205	−	6.95871i	1.11721	−	0.246645i
$797$	18.7740	+	18.7740i	0.665010	+	0.665010i	0.956557	−	0.291547i	$-0.0941698\pi$
$797$	18.7740	+	18.7740i	0.665010	+	0.665010i	−0.291547	+	0.956557i	$0.594170\pi$
$798$	−0.610728	−	0.0846632i	−0.0216195	−	0.00299704i
$799$	44.5735			1.57690
$800$	−1.35669	+	5.49176i	−0.0479661	+	0.194163i
$801$	8.20994	−	14.2200i	0.290084	−	0.502440i
$802$	31.0862	+	24.9719i	1.09769	+	0.881789i
$803$	2.99310	−	11.1704i	0.105624	−	0.394195i
$804$	−0.702641	+	2.22165i	−0.0247802	+	0.0783514i
$805$	−0.596830	+	2.37308i	−0.0210355	+	0.0836400i
$806$	−37.8952	+	27.7602i	−1.33480	+	0.977810i
$807$	−0.0919415	+	0.0530824i	−0.00323649	+	0.00186859i
$808$	−52.9148	−	10.5983i	−1.86154	−	0.372848i
$809$	19.7919	+	11.4268i	0.695845	+	0.401746i	0.805798	−	0.592190i	$-0.201737\pi$
$809$	19.7919	+	11.4268i	0.695845	+	0.401746i	−0.109953	+	0.993937i	$0.535070\pi$
$810$	5.10324	−	11.5841i	0.179310	−	0.407025i
$811$	−14.4326	+	14.4326i	−0.506799	+	0.506799i	−0.913542	−	0.406744i	$-0.866664\pi$
$811$	−14.4326	+	14.4326i	−0.506799	+	0.506799i	0.406744	+	0.913542i	$0.366664\pi$
$812$	−24.8500	+	40.2864i	−0.872065	+	1.41377i
$813$	−0.447838	−	0.447838i	−0.0157064	−	0.0157064i
$814$	−3.07055	−	7.90624i	−0.107623	−	0.277114i
$815$	3.50532	−	6.07139i	0.122786	−	0.212671i
$816$	1.63355	+	0.597834i	0.0571857	+	0.0209284i
$817$	−11.6540	−	20.1853i	−0.407721	−	0.706194i
$818$	42.9969	+	6.63731i	1.50335	+	0.232068i
$819$	−27.7309	+	28.5990i	−0.968996	+	0.999329i
$820$	4.24250	+	8.16738i	0.148155	+	0.285217i
$821$	−22.9775	−	6.15681i	−0.801921	−	0.214874i	−0.165494	−	0.986211i	$-0.552922\pi$
$821$	−22.9775	−	6.15681i	−0.801921	−	0.214874i	−0.636427	+	0.771337i	$0.719588\pi$
$822$	−0.523577	+	0.0571069i	−0.0182618	+	0.00199183i
$823$	24.7415	+	14.2845i	0.862435	+	0.497927i	0.864827	−	0.502070i	$-0.167428\pi$
$823$	24.7415	+	14.2845i	0.862435	+	0.497927i	−0.00239183	+	0.999997i	$0.500761\pi$
$824$	−1.94903	−	30.3527i	−0.0678976	−	1.05739i
$825$		−	0.0573434i		−	0.00199644i
$826$	−27.4557	+	3.42348i	−0.955307	+	0.119118i
$827$	16.0030	−	16.0030i	0.556479	−	0.556479i	−0.371824	−	0.928303i	$-0.621268\pi$
$827$	16.0030	−	16.0030i	0.556479	−	0.556479i	0.928303	+	0.371824i	$0.121268\pi$
$828$	1.19411	+	5.40887i	0.0414981	+	0.187971i
$829$	−7.31466	+	1.95996i	−0.254048	+	0.0680721i	−0.383596	−	0.923501i	$-0.625314\pi$
$829$	−7.31466	+	1.95996i	−0.254048	+	0.0680721i	0.129547	+	0.991573i	$0.458648\pi$
$830$	6.98437	+	5.61062i	0.242431	+	0.194748i
$831$	−0.158985	−	0.275369i	−0.00551511	−	0.00955246i
$832$	5.35598	−	39.8660i	0.185685	−	1.38210i
$833$	−41.1555	+	1.26875i	−1.42595	+	0.0439595i
$834$	−0.146852	+	0.951317i	−0.00508507	+	0.0329414i
$835$	−0.926125	+	3.45634i	−0.0320499	+	0.119612i
$836$	2.55124	−	2.33364i	0.0882366	−	0.0807107i
$837$	−0.757773	−	2.82805i	−0.0261925	−	0.0977516i
$838$	15.7139	+	6.92257i	0.542828	+	0.239136i
$839$		−	5.18217i		−	0.178908i	−0.995991	−	0.0894542i	$-0.971488\pi$
$839$		−	5.18217i		−	0.178908i	0.995991	−	0.0894542i	$-0.0285123\pi$
$840$	0.313820	+	0.455639i	0.0108278	+	0.0157211i
$841$			51.0184i			1.75926i
$842$	0.769626	−	1.74702i	0.0265231	−	0.0602061i
$843$	−0.132104	−	0.493020i	−0.00454991	−	0.0169805i
$844$	−10.5827	−	0.471417i	−0.364271	−	0.0162268i
$845$	3.17856	−	11.8625i	0.109346	−	0.408084i
$846$	31.7155	+	4.89582i	1.09040	+	0.168322i
$847$	−0.423915	−	27.5083i	−0.0145659	−	0.945197i
$848$	−20.5394	+	3.58425i	−0.705327	+	0.123084i
$849$	−0.187925	−	0.325496i	−0.00644958	−	0.0111710i
$850$	−5.20968	+	6.48526i	−0.178691	+	0.222443i
$851$	6.90769	−	1.85091i	0.236792	−	0.0634483i
$852$	0.985436	+	0.629016i	0.0337605	+	0.0215497i
$853$	1.48271	−	1.48271i	0.0507670	−	0.0507670i	−0.681268	−	0.732035i	$-0.738571\pi$
$853$	1.48271	−	1.48271i	0.0507670	−	0.0507670i	0.732035	+	0.681268i	$0.238571\pi$
$854$	−13.9099	−	5.87359i	−0.475986	−	0.200990i
$855$		−	6.67445i		−	0.228262i
$856$	−21.3901	+	24.3256i	−0.731097	+	0.831431i
$857$	−30.1043	−	17.3807i	−1.02834	−	0.593714i	−0.111833	−	0.993727i	$-0.535672\pi$
$857$	−30.1043	−	17.3807i	−1.02834	−	0.593714i	−0.916509	+	0.400013i	$0.869006\pi$
$858$	0.0442116	+	0.405348i	0.00150936	+	0.0138383i
$859$	−31.7926	−	8.51880i	−1.08475	−	0.290658i	−0.328209	−	0.944605i	$-0.606445\pi$
$859$	−31.7926	−	8.51880i	−1.08475	−	0.290658i	−0.756540	+	0.653948i	$0.773112\pi$
$860$	−6.30674	+	19.9410i	−0.215058	+	0.679981i
$861$	0.872943	+	0.219545i	0.0297498	+	0.00748208i
$862$	−5.46258	+	35.3870i	−0.186056	+	1.20529i
$863$	1.32489	+	2.29478i	0.0450999	+	0.0781153i	0.887694	−	0.460434i	$-0.152306\pi$
$863$	1.32489	+	2.29478i	0.0450999	+	0.0781153i	−0.842594	+	0.538549i	$0.818973\pi$
$864$	2.19532	+	1.21071i	0.0746863	+	0.0411891i
$865$	0.0783252	−	0.135663i	0.00266314	−	0.00461269i
$866$	−15.4190	+	5.98827i	−0.523958	+	0.203490i
$867$	0.920071	+	0.920071i	0.0312472	+	0.0312472i
$868$	−33.4884	−	10.0264i	−1.13667	−	0.340320i
$869$	−5.44483	+	5.44483i	−0.184703	+	0.184703i
$870$	0.855904	+	0.377058i	0.0290179	+	0.0127835i
$871$	68.6189	+	39.6171i	2.32506	+	1.34238i
$872$	3.71121	−	18.5292i	0.125678	−	0.627477i
$873$	7.43521	−	4.29272i	0.251644	−	0.145287i
$874$	1.72280	+	2.35179i	0.0582747	+	0.0795504i
$875$	−2.54474	+	0.724068i	−0.0860281	+	0.0244780i
$876$	1.95641	−	1.01625i	0.0661010	−	0.0343358i
$877$	−11.5178	+	42.9849i	−0.388927	+	1.45150i	0.442955	+	0.896544i	$0.353930\pi$
$877$	−11.5178	+	42.9849i	−0.388927	+	1.45150i	−0.831882	+	0.554953i	$0.812736\pi$
$878$	−8.04494	+	10.0147i	−0.271504	+	0.337980i
$879$	0.825574	−	1.42994i	0.0278459	−	0.0482305i
$880$	−3.09022	−	0.275862i	−0.104171	−	0.00929931i
$881$	−42.5936			−1.43501			−0.717507	−	0.696551i	$-0.754717\pi$
$881$	−42.5936			−1.43501			−0.717507	+	0.696551i	$0.754717\pi$
$882$	−29.4228	−	3.61764i	−0.990717	−	0.121812i
$883$	−13.6042	−	13.6042i	−0.457818	−	0.457818i	0.440121	−	0.897939i	$-0.354936\pi$
$883$	−13.6042	−	13.6042i	−0.457818	−	0.457818i	−0.897939	+	0.440121i	$0.854936\pi$
$884$	31.8260	−	49.8595i	1.07042	−	1.67696i
$885$	0.141497	+	0.528073i	0.00475636	+	0.0177510i
$886$	2.66641	−	0.290827i	0.0895797	−	0.00977053i
$887$	44.9161	−	25.9323i	1.50813	−	0.870722i	0.508179	−	0.861251i	$-0.330319\pi$
$887$	44.9161	−	25.9323i	1.50813	−	0.870722i	0.999955	−	0.00947056i	$-0.00301462\pi$
$888$	0.717057	−	1.44920i	0.0240629	−	0.0486321i
$889$	−24.9195	+	44.7400i	−0.835772	+	1.50053i
$890$	−6.25563	+	4.58257i	−0.209689	+	0.153608i
$891$	6.70596	+	1.79686i	0.224658	+	0.0601969i
$892$	28.5386	−	26.1045i	0.955543	−	0.874042i
$893$	16.3144	−	4.37143i	0.545940	−	0.146284i
$894$	−0.772896	+	0.300170i	−0.0258495	+	0.0100392i
$895$	−3.18135			−0.106341
$896$	26.0640	−	14.7197i	0.870736	−	0.491751i
$897$	−0.343802			−0.0114792
$898$	−5.57116	+	2.16367i	−0.185912	+	0.0722027i
$899$	−57.0815	+	15.2949i	−1.90378	+	0.510115i
$900$	−4.41918	+	4.04225i	−0.147306	+	0.134742i
$901$	−29.6157	−	7.93551i	−0.986642	−	0.264370i
$902$	−4.07200	+	2.98295i	−0.135583	+	0.0993213i
$903$	1.04992	+	1.75548i	0.0349391	+	0.0584186i
$904$	0.352954	−	0.713335i	0.0117391	−	0.0237252i
$905$	9.54381	−	5.51012i	0.317247	−	0.183163i
$906$	−1.46941	+	0.160269i	−0.0488177	+	0.00532459i
$907$	9.07283	+	33.8603i	0.301258	+	1.12431i	0.936119	+	0.351685i	$0.114391\pi$
$907$	9.07283	+	33.8603i	0.301258	+	1.12431i	−0.634860	+	0.772627i	$0.718942\pi$
$908$	25.2080	−	39.4916i	0.836558	−	1.31058i
$909$	−40.4005	−	40.4005i	−1.34000	−	1.34000i
$910$	17.4300	−	7.08026i	0.577798	−	0.234708i
$911$	−20.5421			−0.680591			−0.340295	−	0.940319i	$-0.610527\pi$
$911$	−20.5421			−0.680591			−0.340295	+	0.940319i	$0.610527\pi$
$912$	0.656528	+	0.0586078i	0.0217398	+	0.00194070i
$913$	−2.45674	+	4.25520i	−0.0813062	+	0.140827i
$914$	11.0729	−	13.7841i	0.366260	−	0.455938i
$915$	−0.0772172	+	0.288179i	−0.00255272	+	0.00952689i
$916$	30.2439	−	15.7101i	0.999288	−	0.519075i
$917$	−18.0644	−	17.5161i	−0.596540	−	0.578433i
$918$	2.17867	+	2.97408i	0.0719067	+	0.0981592i
$919$	17.4248	−	10.0602i	0.574790	−	0.331855i	−0.184270	−	0.982876i	$-0.558992\pi$
$919$	17.4248	−	10.0602i	0.574790	−	0.331855i	0.759060	+	0.651020i	$0.225659\pi$
$920$	0.513742	−	2.56499i	0.0169376	−	0.0845651i
$921$	−1.38088	−	0.797249i	−0.0455014	−	0.0262703i
$922$	11.8419	+	5.21682i	0.389993	+	0.171807i
$923$	28.1103	−	28.1103i	0.925262	−	0.925262i
$924$	−0.220713	+	0.208224i	−0.00726093	+	0.00685007i
$925$	5.46755	+	5.46755i	0.179772	+	0.179772i
$926$	−10.4821	+	4.07094i	−0.344463	+	0.133779i
$927$	16.1007	−	27.8872i	0.528816	−	0.915937i
$928$	24.4370	−	44.3105i	0.802185	−	1.45456i
$929$	12.7891	+	22.1514i	0.419597	+	0.726763i	0.995899	−	0.0904737i	$-0.0288381\pi$
$929$	12.7891	+	22.1514i	0.419597	+	0.726763i	−0.576302	+	0.817237i	$0.695505\pi$
$930$	−0.105376	+	0.682635i	−0.00345542	+	0.0223845i
$931$	−14.9389	+	4.50059i	−0.489604	+	0.147501i
$932$	1.70655	−	5.39587i	0.0559001	−	0.176748i
$933$	0.706271	+	0.189245i	0.0231223	+	0.00619560i
$934$	1.89379	+	17.3630i	0.0619668	+	0.568134i
$935$	−3.95112	−	2.28118i	−0.129215	−	0.0746026i
$936$	28.1216	−	31.9809i	0.919183	−	1.04533i
$937$		−	6.49360i		−	0.212137i	−0.994359	−	0.106068i	$-0.966174\pi$
$937$		−	6.49360i		−	0.212137i	0.994359	−	0.106068i	$-0.0338262\pi$
$938$	7.29565	+	58.5100i	0.238212	+	1.91042i
$939$	1.44053	−	1.44053i	0.0470098	−	0.0470098i
$940$	−12.7748	−	8.15434i	−0.416669	−	0.265965i
$941$	−19.9876	+	5.35567i	−0.651578	+	0.174590i	−0.569442	−	0.822031i	$-0.692841\pi$
$941$	−19.9876	+	5.35567i	−0.651578	+	0.174590i	−0.0821358	+	0.996621i	$0.526174\pi$
$942$	−0.991095	+	1.23376i	−0.0322916	+	0.0401981i
$943$	−2.12802	−	3.68584i	−0.0692978	−	0.120027i
$944$	29.1384	−	5.08481i	0.948373	−	0.165497i
$945$	0.0180675	+	1.17242i	0.000587735	+	0.0381388i
$946$	−11.3363	−	1.74995i	−0.368576	−	0.0568959i
$947$	−9.53830	+	35.5974i	−0.309953	+	1.15676i	0.618644	+	0.785672i	$0.287682\pi$
$947$	−9.53830	+	35.5974i	−0.309953	+	1.15676i	−0.928597	+	0.371090i	$0.878984\pi$
$948$	−1.46648	−	0.0653259i	−0.0476290	−	0.00212169i
$949$	−19.4028	−	72.4123i	−0.629842	−	2.35060i
$950$	−1.27078	+	2.88460i	−0.0412294	+	0.0935888i
$951$			0.520572i			0.0168807i
$952$	43.8789	−	3.49723i	1.42212	−	0.113346i
$953$			1.60311i			0.0519298i	0.999663	+	0.0259649i	$0.00826581\pi$
$953$			1.60311i			0.0519298i	−0.999663	+	0.0259649i	$0.991734\pi$
$954$	−20.2009	−	8.89926i	−0.654028	−	0.288124i
$955$	−2.93524	−	10.9545i	−0.0949822	−	0.354478i
$956$	−24.8280	+	22.7103i	−0.802994	+	0.734504i
$957$	−0.132762	+	0.495476i	−0.00429160	+	0.0160165i
$958$	−5.47813	+	35.4877i	−0.176990	+	1.14656i
$959$	−11.4380	+	6.84085i	−0.369352	+	0.220903i
$960$	−0.358809	−	0.470184i	−0.0115805	−	0.0151751i
$961$	−6.32145	−	10.9491i	−0.203918	−	0.353196i
$962$	−42.8643	−	34.4334i	−1.38200	−	1.11018i
$963$	−33.1262	+	8.87613i	−1.06748	+	0.286029i
$964$	−1.26586	−	5.73388i	−0.0407705	−	0.184676i
$965$	−9.57312	+	9.57312i	−0.308170	+	0.308170i
$966$	−0.154354	−	0.204037i	−0.00496627	−	0.00656478i
$967$			3.66250i			0.117778i	0.998265	+	0.0588890i	$0.0187558\pi$
$967$			3.66250i			0.117778i	−0.998265	+	0.0588890i	$0.981244\pi$
$968$	1.88469	+	29.3507i	0.0605761	+	0.943366i
$969$	0.839429	+	0.484644i	0.0269663	+	0.0155690i
$970$	−4.03070	+	0.439631i	−0.129418	+	0.0141157i
$971$	7.80590	+	2.09159i	0.250503	+	0.0671222i	0.381886	−	0.924210i	$-0.375275\pi$
$971$	7.80590	+	2.09159i	0.250503	+	0.0671222i	−0.131382	+	0.991332i	$0.541942\pi$
$972$	1.83585	+	3.53425i	0.0588848	+	0.113361i
$973$	6.66612	+	23.4281i	0.213706	+	0.751072i
$974$	−11.7259	−	1.81009i	−0.375721	−	0.0579989i
$975$	−0.185865	−	0.321928i	−0.00595244	−	0.0103099i
$976$	15.1584	+	5.54756i	0.485208	+	0.177573i
$977$	−0.0525672	+	0.0910490i	−0.00168177	+	0.00291292i	−0.866865	−	0.498543i	$-0.833869\pi$
$977$	−0.0525672	+	0.0910490i	−0.00168177	+	0.00291292i	0.865183	+	0.501456i	$0.167202\pi$
$978$	0.265364	+	0.683277i	0.00848542	+	0.0218488i
$979$	−3.00732	−	3.00732i	−0.0961143	−	0.0961143i
$980$	12.0273	+	7.16542i	0.384199	+	0.228891i
$981$	14.1471	−	14.1471i	0.451681	−	0.451681i
$982$	−16.0637	+	36.4638i	−0.512612	+	1.16361i
$983$	44.1248	+	25.4755i	1.40736	+	0.812541i	0.995133	−	0.0985395i	$-0.0314171\pi$
$983$	44.1248	+	25.4755i	1.40736	+	0.812541i	0.412229	+	0.911080i	$0.364750\pi$
$984$	−0.943537	−	0.188981i	−0.0300789	−	0.00602450i
$985$	6.57699	−	3.79723i	0.209560	−	0.120990i
$986$	60.0290	−	43.9744i	1.91171	−	1.40043i
$987$	−1.42566	+	0.405649i	−0.0453792	+	0.0129120i
$988$	6.75881	−	21.3704i	0.215026	−	0.679882i
$989$	2.50320	−	9.34207i	0.0795971	−	0.297060i
$990$	−2.56079	−	2.05711i	−0.0813872	−	0.0653793i
$991$	19.7841	−	34.2670i	0.628461	−	1.08853i	−0.359399	−	0.933184i	$-0.617018\pi$
$991$	19.7841	−	34.2670i	0.628461	−	1.08853i	0.987861	−	0.155343i	$-0.0496483\pi$
$992$	36.2801	+	8.96265i	1.15189	+	0.284564i
$993$	2.36424			0.0750268
$994$	29.3031	+	4.06220i	0.929438	+	0.128845i
$995$	−11.4125	−	11.4125i	−0.361801	−	0.361801i
$996$	−0.914667	+	0.201929i	−0.0289823	+	0.00639837i
$997$	7.24471	+	27.0376i	0.229442	+	0.856290i	0.980576	+	0.196140i	$0.0628406\pi$
$997$	7.24471	+	27.0376i	0.229442	+	0.856290i	−0.751134	+	0.660150i	$0.770493\pi$
$998$	−1.21748	−	11.1623i	−0.0385387	−	0.353336i
$999$	2.96773	−	1.71342i	0.0938948	−	0.0542102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.221.8	✓	256
7.2	even	3	inner	560.2.cp.a.541.49	yes	256
16.5	even	4	inner	560.2.cp.a.501.49	yes	256
112.37	even	12	inner	560.2.cp.a.261.8	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.8	✓	256	1.1	even	1	trivial
560.2.cp.a.261.8	yes	256	112.37	even	12	inner
560.2.cp.a.501.49	yes	256	16.5	even	4	inner
560.2.cp.a.541.49	yes	256	7.2	even	3	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31828 + 0.511983i) q^{2} +(-0.0714125 + 0.0191349i) q^{3} +(1.47575 - 1.34988i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(0.0843453 - 0.0617872i) q^{6} +(1.28741 - 2.31140i) q^{7} +(-1.25434 + 2.53508i) q^{8} +(-2.59334 + 1.49727i) q^{9} +(1.40588 - 0.153340i) q^{10} +(0.200747 + 0.749199i) q^{11} +(-0.0795571 + 0.124636i) q^{12} +(3.55535 + 3.55535i) q^{13} +(-0.513781 + 3.70621i) q^{14} +0.0739317 q^{15} +(0.355663 - 3.98416i) q^{16} +(2.94108 - 5.09409i) q^{17} +(2.65219 - 3.30157i) q^{18} +(0.576876 - 2.15293i) q^{19} +(-1.77484 + 0.921930i) q^{20} +(-0.0477089 + 0.189697i) q^{21} +(-0.648219 - 0.884878i) q^{22} +(0.800962 - 0.462436i) q^{23} +(0.0410671 - 0.205038i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-6.50724 - 2.86668i) q^{26} +(0.313380 - 0.313380i) q^{27} +(-1.22021 - 5.14889i) q^{28} +(-6.32528 - 6.32528i) q^{29} +(-0.0974630 + 0.0378517i) q^{30} +(3.30314 - 5.72120i) q^{31} +(1.57095 + 5.43434i) q^{32} +(-0.0286717 - 0.0496609i) q^{33} +(-1.26909 + 8.22124i) q^{34} +(-1.84178 + 1.89943i) q^{35} +(-1.80599 + 5.71028i) q^{36} +(7.46881 + 2.00126i) q^{37} +(0.341776 + 3.13353i) q^{38} +(-0.321928 - 0.185865i) q^{39} +(1.86773 - 2.12405i) q^{40} -4.60176i q^{41} +(-0.0342278 - 0.274501i) q^{42} +(7.39440 - 7.39440i) q^{43} +(1.30758 + 0.834644i) q^{44} +(2.89250 - 0.775042i) q^{45} +(-0.819137 + 1.01970i) q^{46} +(3.78888 + 6.56253i) q^{47} +(0.0508377 + 0.291324i) q^{48} +(-3.68513 - 5.95145i) q^{49} +(-1.39766 - 0.215752i) q^{50} +(-0.112555 + 0.420059i) q^{51} +(10.0461 + 0.447514i) q^{52} +(-1.34908 - 5.03484i) q^{53} +(-0.252679 + 0.573569i) q^{54} -0.775628i q^{55} +(4.24472 + 6.16298i) q^{56} +0.164785i q^{57} +(11.5770 + 5.10009i) q^{58} +(1.91388 + 7.14271i) q^{59} +(0.109104 - 0.0997987i) q^{60} +(-1.04444 + 3.89791i) q^{61} +(-1.42532 + 9.23332i) q^{62} +(0.122079 + 7.92185i) q^{63} +(-4.85325 - 6.35971i) q^{64} +(-2.51401 - 4.35439i) q^{65} +(0.0632230 + 0.0507877i) q^{66} +(15.2216 - 4.07861i) q^{67} +(-2.53611 - 11.4877i) q^{68} +(-0.0483500 + 0.0483500i) q^{69} +(1.45551 - 3.44695i) q^{70} -7.90648i q^{71} +(-0.542753 - 8.45241i) q^{72} +(-12.9123 - 7.45489i) q^{73} +(-10.8706 + 1.18567i) q^{74} +(-0.0714125 - 0.0191349i) q^{75} +(-2.05487 - 3.95590i) q^{76} +(1.99014 + 0.500521i) q^{77} +(0.519552 + 0.0802016i) q^{78} +(4.96382 + 8.59759i) q^{79} +(-1.37472 + 3.75635i) q^{80} +(4.47542 - 7.75165i) q^{81} +(2.35602 + 6.06643i) q^{82} +(4.47941 + 4.47941i) q^{83} +(0.185662 + 0.344347i) q^{84} +(-4.15931 + 4.15931i) q^{85} +(-5.96212 + 13.5337i) q^{86} +(0.572738 + 0.330671i) q^{87} +(-2.15108 - 0.430841i) q^{88} +(-4.74867 + 2.74164i) q^{89} +(-3.41633 + 2.50263i) q^{90} +(12.7950 - 3.64063i) q^{91} +(0.557787 - 1.76364i) q^{92} +(-0.126411 + 0.471771i) q^{93} +(-8.35472 - 6.71144i) q^{94} +(-1.11444 + 1.93027i) q^{95} +(-0.216172 - 0.358020i) q^{96} -2.86704 q^{97} +(7.90510 + 5.95898i) q^{98} +(-1.64236 - 1.64236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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