LMFDB - Embedded newform 416.2.z.a.113.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(81,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("416.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.z (of order $6$, degree $2$, not 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			113.6
Character	$\chi$	$=$	416.113
Dual form			416.2.z.a.81.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.509400 - 0.294102i) q^{3} +1.78237i q^{5} +(-1.65832 - 2.87229i) q^{7} +(-1.32701 - 2.29844i) q^{9} +(-2.13570 - 1.23305i) q^{11} +(3.57591 - 0.461374i) q^{13} +(0.524200 - 0.907941i) q^{15} +(-2.79947 - 4.84883i) q^{17} +(2.54173 - 1.46747i) q^{19} +1.95086i q^{21} +(1.21868 - 2.11082i) q^{23} +1.82314 q^{25} +3.32572i q^{27} +(-6.28420 - 3.62819i) q^{29} +4.42876 q^{31} +(0.725283 + 1.25623i) q^{33} +(5.11949 - 2.95574i) q^{35} +(-3.62746 - 2.09432i) q^{37} +(-1.95726 - 0.816660i) q^{39} +(1.19018 - 2.06145i) q^{41} +(-9.41391 + 5.43512i) q^{43} +(4.09669 - 2.36522i) q^{45} -8.82426 q^{47} +(-2.00003 + 3.46415i) q^{49} +3.29333i q^{51} -1.32698i q^{53} +(2.19775 - 3.80661i) q^{55} -1.72634 q^{57} +(4.50116 - 2.59874i) q^{59} +(-1.38839 + 0.801590i) q^{61} +(-4.40120 + 7.62310i) q^{63} +(0.822340 + 6.37361i) q^{65} +(10.0039 + 5.77577i) q^{67} +(-1.24159 + 0.716834i) q^{69} +(5.07044 + 8.78227i) q^{71} +12.1620 q^{73} +(-0.928710 - 0.536191i) q^{75} +8.17912i q^{77} +7.72073 q^{79} +(-3.00292 + 5.20121i) q^{81} -6.77111i q^{83} +(8.64243 - 4.98971i) q^{85} +(2.13412 + 3.69640i) q^{87} +(-5.89082 + 10.2032i) q^{89} +(-7.25519 - 9.50594i) q^{91} +(-2.25601 - 1.30251i) q^{93} +(2.61558 + 4.53031i) q^{95} +(-3.17980 - 5.50758i) q^{97} +6.54505i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{7} + 6 q^{9} - 4 q^{15} + 14 q^{23} - 12 q^{25} + 8 q^{31} - 14 q^{33} + 34 q^{39} - 4 q^{41} + 8 q^{47} + 6 q^{49} - 8 q^{55} - 52 q^{57} - 32 q^{63} + 30 q^{65} - 30 q^{71} - 12 q^{73} + 48 q^{79}+ \cdots + 2 q^{97}+O(q^{100}) $ 24 * q + 2 * q^7 + 6 * q^9 - 4 * q^15 + 14 * q^23 - 12 * q^25 + 8 * q^31 - 14 * q^33 + 34 * q^39 - 4 * q^41 + 8 * q^47 + 6 * q^49 - 8 * q^55 - 52 * q^57 - 32 * q^63 + 30 * q^65 - 30 * q^71 - 12 * q^73 + 48 * q^79 + 8 * q^81 + 26 * q^87 - 22 * q^89 - 60 * q^95 + 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	−0.509400	−	0.294102i	−0.294102	−	0.169800i	0.345688	−	0.938349i	$-0.387646\pi$
$3$	−0.509400	−	0.294102i	−0.294102	−	0.169800i	−0.639790	+	0.768549i	$0.720979\pi$
$4$		0			0
$5$			1.78237i			0.797102i	0.917146	+	0.398551i	$0.130487\pi$
$5$			1.78237i			0.797102i	−0.917146	+	0.398551i	$0.869513\pi$
$6$		0			0
$7$	−1.65832	−	2.87229i	−0.626785	−	1.08562i	−0.988193	−	0.153215i	$-0.951037\pi$
$7$	−1.65832	−	2.87229i	−0.626785	−	1.08562i	0.361408	−	0.932408i	$-0.382296\pi$
$8$		0			0
$9$	−1.32701	−	2.29844i	−0.442336	−	0.766148i
$10$		0			0
$11$	−2.13570	−	1.23305i	−0.643937	−	0.371777i	0.142192	−	0.989839i	$-0.454585\pi$
$11$	−2.13570	−	1.23305i	−0.643937	−	0.371777i	−0.786130	+	0.618062i	$0.787918\pi$
$12$		0			0
$13$	3.57591	−	0.461374i	0.991779	−	0.127962i
$13$	3.57591	−	0.461374i	0.991779	−	0.127962i
$14$		0			0
$15$	0.524200	−	0.907941i	0.135348	−	0.234429i
$16$		0			0
$17$	−2.79947	−	4.84883i	−0.678972	−	1.17601i	−0.975291	−	0.220925i	$-0.929092\pi$
$17$	−2.79947	−	4.84883i	−0.678972	−	1.17601i	0.296319	−	0.955089i	$-0.404241\pi$
$18$		0			0
$19$	2.54173	−	1.46747i	0.583113	−	0.336660i	−0.179257	−	0.983802i	$-0.557369\pi$
$19$	2.54173	−	1.46747i	0.583113	−	0.336660i	0.762369	+	0.647142i	$0.224036\pi$
$20$		0			0
$21$			1.95086i			0.425712i
$22$		0			0
$23$	1.21868	−	2.11082i	0.254112	−	0.440136i	−0.710542	−	0.703655i	$-0.751550\pi$
$23$	1.21868	−	2.11082i	0.254112	−	0.440136i	0.964654	+	0.263519i	$0.0848833\pi$
$24$		0			0
$25$	1.82314			0.364629
$26$		0			0
$27$			3.32572i			0.640035i
$28$		0			0
$29$	−6.28420	−	3.62819i	−1.16695	−	0.673737i	−0.213988	−	0.976836i	$-0.568645\pi$
$29$	−6.28420	−	3.62819i	−1.16695	−	0.673737i	−0.952959	+	0.303099i	$0.901979\pi$
$30$		0			0
$31$	4.42876			0.795429			0.397714	−	0.917509i	$-0.369804\pi$
$31$	4.42876			0.795429			0.397714	+	0.917509i	$0.369804\pi$
$32$		0			0
$33$	0.725283	+	1.25623i	0.126256	+	0.218681i
$34$		0			0
$35$	5.11949	−	2.95574i	0.865352	−	0.499611i
$36$		0			0
$37$	−3.62746	−	2.09432i	−0.596351	−	0.344303i	0.171254	−	0.985227i	$-0.445218\pi$
$37$	−3.62746	−	2.09432i	−0.596351	−	0.344303i	−0.767605	+	0.640924i	$0.778552\pi$
$38$		0			0
$39$	−1.95726	−	0.816660i	−0.313412	−	0.130770i
$40$		0			0
$41$	1.19018	−	2.06145i	0.185875	−	0.321945i	−0.757996	−	0.652259i	$-0.773821\pi$
$41$	1.19018	−	2.06145i	0.185875	−	0.321945i	0.943871	+	0.330314i	$0.107155\pi$
$42$		0			0
$43$	−9.41391	+	5.43512i	−1.43561	+	0.828848i	−0.997540	−	0.0700937i	$-0.977670\pi$
$43$	−9.41391	+	5.43512i	−1.43561	+	0.828848i	−0.438067	+	0.898942i	$0.644337\pi$
$44$		0			0
$45$	4.09669	−	2.36522i	0.610698	−	0.352587i
$46$		0			0
$47$	−8.82426			−1.28715			−0.643575	−	0.765383i	$-0.722550\pi$
$47$	−8.82426			−1.28715			−0.643575	+	0.765383i	$0.722550\pi$
$48$		0			0
$49$	−2.00003	+	3.46415i	−0.285718	+	0.494878i
$50$		0			0
$51$			3.29333i			0.461158i
$52$		0			0
$53$		−	1.32698i		−	0.182274i	−0.995838	−	0.0911371i	$-0.970950\pi$
$53$		−	1.32698i		−	0.182274i	0.995838	−	0.0911371i	$-0.0290501\pi$
$54$		0			0
$55$	2.19775	−	3.80661i	0.296344	−	0.513283i
$56$		0			0
$57$	−1.72634			−0.228660
$58$		0			0
$59$	4.50116	−	2.59874i	0.586001	−	0.338328i	−0.177514	−	0.984118i	$-0.556805\pi$
$59$	4.50116	−	2.59874i	0.586001	−	0.338328i	0.763514	+	0.645791i	$0.223472\pi$
$60$		0			0
$61$	−1.38839	+	0.801590i	−0.177766	+	0.102633i	−0.586242	−	0.810136i	$-0.699393\pi$
$61$	−1.38839	+	0.801590i	−0.177766	+	0.102633i	0.408477	+	0.912769i	$0.366060\pi$
$62$		0			0
$63$	−4.40120	+	7.62310i	−0.554499	+	0.960420i
$64$		0			0
$65$	0.822340	+	6.37361i	0.101999	+	0.790549i
$66$		0			0
$67$	10.0039	+	5.77577i	1.22217	+	0.705622i	0.965381	−	0.260844i	$-0.0840008\pi$
$67$	10.0039	+	5.77577i	1.22217	+	0.705622i	0.256793	+	0.966466i	$0.417334\pi$
$68$		0			0
$69$	−1.24159	+	0.716834i	−0.149470	+	0.0862966i
$70$		0			0
$71$	5.07044	+	8.78227i	0.601751	+	1.04226i	0.992556	+	0.121790i	$0.0388634\pi$
$71$	5.07044	+	8.78227i	0.601751	+	1.04226i	−0.390805	+	0.920474i	$0.627803\pi$
$72$		0			0
$73$	12.1620			1.42345			0.711727	−	0.702456i	$-0.247913\pi$
$73$	12.1620			1.42345			0.711727	+	0.702456i	$0.247913\pi$
$74$		0			0
$75$	−0.928710	−	0.536191i	−0.107238	−	0.0619140i
$76$		0			0
$77$			8.17912i			0.932097i
$78$		0			0
$79$	7.72073			0.868650			0.434325	−	0.900756i	$-0.356987\pi$
$79$	7.72073			0.868650			0.434325	+	0.900756i	$0.356987\pi$
$80$		0			0
$81$	−3.00292	+	5.20121i	−0.333658	+	0.577913i
$82$		0			0
$83$		−	6.77111i		−	0.743225i	−0.928388	−	0.371613i	$-0.878805\pi$
$83$		−	6.77111i		−	0.743225i	0.928388	−	0.371613i	$-0.121195\pi$
$84$		0			0
$85$	8.64243	−	4.98971i	0.937403	−	0.541210i
$86$		0			0
$87$	2.13412	+	3.69640i	0.228801	+	0.396295i
$88$		0			0
$89$	−5.89082	+	10.2032i	−0.624426	+	1.08154i	0.364226	+	0.931311i	$0.381334\pi$
$89$	−5.89082	+	10.2032i	−0.624426	+	1.08154i	−0.988652	+	0.150227i	$0.952000\pi$
$90$		0			0
$91$	−7.25519	−	9.50594i	−0.760550	−	0.996493i
$92$		0			0
$93$	−2.25601	−	1.30251i	−0.233937	−	0.135064i
$94$		0			0
$95$	2.61558	+	4.53031i	0.268353	+	0.464800i
$96$		0			0
$97$	−3.17980	−	5.50758i	−0.322860	−	0.559210i	0.658217	−	0.752828i	$-0.271311\pi$
$97$	−3.17980	−	5.50758i	−0.322860	−	0.559210i	−0.981077	+	0.193618i	$0.937978\pi$
$98$		0			0
$99$			6.54505i			0.657802i
$100$		0			0
$101$	10.0401	+	5.79665i	0.999027	+	0.576788i	0.907960	−	0.419056i	$-0.137639\pi$
$101$	10.0401	+	5.79665i	0.999027	+	0.576788i	0.0910665	+	0.995845i	$0.470972\pi$
$102$		0			0
$103$	−2.03907			−0.200915			−0.100458	−	0.994941i	$-0.532031\pi$
$103$	−2.03907			−0.200915			−0.100458	+	0.994941i	$0.532031\pi$
$104$		0			0
$105$	−3.47716			−0.339336
$106$		0			0
$107$	−10.5701	−	6.10265i	−1.02185	−	0.589965i	−0.107210	−	0.994236i	$-0.534192\pi$
$107$	−10.5701	−	6.10265i	−1.02185	−	0.589965i	−0.914639	+	0.404271i	$0.867525\pi$
$108$		0			0
$109$			7.39858i			0.708656i	0.935121	+	0.354328i	$0.115290\pi$
$109$			7.39858i			0.708656i	−0.935121	+	0.354328i	$0.884710\pi$
$110$		0			0
$111$	1.23189	+	2.13369i	0.116925	+	0.202521i
$112$		0			0
$113$	4.78047	+	8.28002i	0.449709	+	0.778918i	0.998367	−	0.0571285i	$-0.0181945\pi$
$113$	4.78047	+	8.28002i	0.449709	+	0.778918i	−0.548658	+	0.836047i	$0.684861\pi$
$114$		0			0
$115$	3.76226	+	2.17214i	0.350833	+	0.202553i
$116$		0			0
$117$	−5.80570	−	7.60679i	−0.536737	−	0.703248i
$118$		0			0
$119$	−9.28482	+	16.0818i	−0.851138	+	1.47421i
$120$		0			0
$121$	−2.45920	−	4.25945i	−0.223563	−	0.387223i
$122$		0			0
$123$	−1.21255	+	0.700069i	−0.109332	+	0.0631231i
$124$		0			0
$125$			12.1614i			1.08775i
$126$		0			0
$127$	7.87951	−	13.6477i	0.699193	−	1.21104i	−0.269553	−	0.962985i	$-0.586876\pi$
$127$	7.87951	−	13.6477i	0.699193	−	1.21104i	0.968747	−	0.248053i	$-0.0797906\pi$
$128$		0			0
$129$	6.39393			0.562954
$130$		0			0
$131$		−	11.1215i		−	0.971688i	−0.874045	−	0.485844i	$-0.838512\pi$
$131$		−	11.1215i		−	0.971688i	0.874045	−	0.485844i	$-0.161488\pi$
$132$		0			0
$133$	−8.42998	−	4.86705i	−0.730972	−	0.422027i
$134$		0			0
$135$	−5.92767			−0.510173
$136$		0			0
$137$	−0.0304295	−	0.0527055i	−0.00259977	−	0.00450293i	0.864723	−	0.502250i	$-0.167494\pi$
$137$	−0.0304295	−	0.0527055i	−0.00259977	−	0.00450293i	−0.867322	+	0.497747i	$0.834161\pi$
$138$		0			0
$139$	−13.1191	+	7.57434i	−1.11275	+	0.642447i	−0.939540	−	0.342438i	$-0.888747\pi$
$139$	−13.1191	+	7.57434i	−1.11275	+	0.642447i	−0.173210	+	0.984885i	$0.555414\pi$
$140$		0			0
$141$	4.49508	+	2.59523i	0.378554	+	0.218558i
$142$		0			0
$143$	−8.20596	−	3.42391i	−0.686217	−	0.286321i
$144$		0			0
$145$	6.46678	−	11.2008i	0.537037	−	0.930176i
$146$		0			0
$147$	2.03763	−	1.17643i	0.168061	−	0.0970299i
$148$		0			0
$149$	0.971793	−	0.561065i	0.0796123	−	0.0459642i	−0.459665	−	0.888092i	$-0.652031\pi$
$149$	0.971793	−	0.561065i	0.0796123	−	0.0459642i	0.539278	+	0.842128i	$0.318697\pi$
$150$		0			0
$151$	2.07494			0.168856			0.0844281	−	0.996430i	$-0.473094\pi$
$151$	2.07494			0.168856			0.0844281	+	0.996430i	$0.473094\pi$
$152$		0			0
$153$	−7.42984	+	12.8689i	−0.600667	+	1.04039i
$154$		0			0
$155$			7.89370i			0.634038i
$156$		0			0
$157$		−	23.8908i		−	1.90669i	−0.301875	−	0.953347i	$-0.597613\pi$
$157$		−	23.8908i		−	1.90669i	0.301875	−	0.953347i	$-0.402387\pi$
$158$		0			0
$159$	−0.390267	+	0.675962i	−0.0309502	+	0.0536072i
$160$		0			0
$161$	−8.08383			−0.637095
$162$		0			0
$163$	19.7876	−	11.4244i	1.54988	−	0.894825i	0.551732	−	0.834022i	$-0.313967\pi$
$163$	19.7876	−	11.4244i	1.54988	−	0.894825i	0.998150	−	0.0608031i	$-0.0193662\pi$
$164$		0			0
$165$	−2.23907	+	1.29273i	−0.174311	+	0.100639i
$166$		0			0
$167$	8.93203	−	15.4707i	0.691181	−	1.19716i	−0.280270	−	0.959921i	$-0.590424\pi$
$167$	8.93203	−	15.4707i	0.691181	−	1.19716i	0.971451	−	0.237239i	$-0.0762426\pi$
$168$		0			0
$169$	12.5743	−	3.29966i	0.967251	−	0.253820i
$170$		0			0
$171$	−6.74579	−	3.89468i	−0.515863	−	0.297834i
$172$		0			0
$173$	−9.62750	+	5.55844i	−0.731965	+	0.422600i	−0.819141	−	0.573593i	$-0.805549\pi$
$173$	−9.62750	+	5.55844i	−0.731965	+	0.422600i	0.0871756	+	0.996193i	$0.472216\pi$
$174$		0			0
$175$	−3.02335	−	5.23660i	−0.228544	−	0.395849i
$176$		0			0
$177$	−3.05719			−0.229792
$178$		0			0
$179$	20.1700	+	11.6452i	1.50758	+	0.870400i	0.999961	+	0.00881628i	$0.00280635\pi$
$179$	20.1700	+	11.6452i	1.50758	+	0.870400i	0.507616	+	0.861584i	$0.330527\pi$
$180$		0			0
$181$			6.40510i			0.476088i	0.971254	+	0.238044i	$0.0765062\pi$
$181$			6.40510i			0.476088i	−0.971254	+	0.238044i	$0.923494\pi$
$182$		0			0
$183$	0.942997			0.0697084
$184$		0			0
$185$	3.73285	−	6.46549i	0.274445	−	0.475352i
$186$		0			0
$187$			13.8075i			1.00971i
$188$		0			0
$189$	9.55242	−	5.51509i	0.694836	−	0.401164i
$190$		0			0
$191$	−4.09795	−	7.09786i	−0.296517	−	0.513583i	0.678819	−	0.734305i	$-0.262492\pi$
$191$	−4.09795	−	7.09786i	−0.296517	−	0.513583i	−0.975337	+	0.220722i	$0.929159\pi$
$192$		0			0
$193$	8.77012	−	15.1903i	0.631287	−	1.09342i	−0.356002	−	0.934485i	$-0.615860\pi$
$193$	8.77012	−	15.1903i	0.631287	−	1.09342i	0.987289	−	0.158936i	$-0.0508064\pi$
$194$		0			0
$195$	1.45559	−	3.48857i	0.104237	−	0.249822i
$196$		0			0
$197$	3.84294	+	2.21872i	0.273798	+	0.158078i	0.630612	−	0.776098i	$-0.282804\pi$
$197$	3.84294	+	2.21872i	0.273798	+	0.158078i	−0.356814	+	0.934175i	$0.616137\pi$
$198$		0			0
$199$	6.11231	+	10.5868i	0.433290	+	0.750480i	0.997154	−	0.0753871i	$-0.0240192\pi$
$199$	6.11231	+	10.5868i	0.433290	+	0.750480i	−0.563864	+	0.825867i	$0.690686\pi$
$200$		0			0
$201$	−3.39733	−	5.88435i	−0.239629	−	0.415050i
$202$		0			0
$203$			24.0667i			1.68915i
$204$		0			0
$205$	3.67428	+	2.12134i	0.256623	+	0.148161i
$206$		0			0
$207$	−6.46879			−0.449612
$208$		0			0
$209$	−7.23782			−0.500651
$210$		0			0
$211$	−9.32352	−	5.38294i	−0.641858	−	0.370577i	0.143472	−	0.989654i	$-0.454173\pi$
$211$	−9.32352	−	5.38294i	−0.641858	−	0.370577i	−0.785330	+	0.619078i	$0.787507\pi$
$212$		0			0
$213$		−	5.96492i		−	0.408709i
$214$		0			0
$215$	−9.68742	−	16.7791i	−0.660677	−	1.14433i
$216$		0			0
$217$	−7.34428	−	12.7207i	−0.498562	−	0.863536i
$218$		0			0
$219$	−6.19533	−	3.57687i	−0.418641	−	0.241703i
$220$		0			0
$221$	−12.2478	−	16.0474i	−0.823875	−	1.07946i
$222$		0			0
$223$	3.59038	−	6.21873i	0.240430	−	0.416437i	−0.720407	−	0.693552i	$-0.756045\pi$
$223$	3.59038	−	6.21873i	0.240430	−	0.416437i	0.960837	+	0.277115i	$0.0893783\pi$
$224$		0			0
$225$	−2.41933	−	4.19040i	−0.161288	−	0.279360i
$226$		0			0
$227$	−0.276361	+	0.159557i	−0.0183427	+	0.0105902i	−0.509143	−	0.860682i	$-0.670038\pi$
$227$	−0.276361	+	0.159557i	−0.0183427	+	0.0105902i	0.490801	+	0.871272i	$0.336704\pi$
$228$		0			0
$229$			9.18620i			0.607041i	0.952825	+	0.303521i	$0.0981622\pi$
$229$			9.18620i			0.607041i	−0.952825	+	0.303521i	$0.901838\pi$
$230$		0			0
$231$	2.40550	−	4.16645i	0.158270	−	0.274132i
$232$		0			0
$233$	−21.0081			−1.37628			−0.688142	−	0.725576i	$-0.741573\pi$
$233$	−21.0081			−1.37628			−0.688142	+	0.725576i	$0.741573\pi$
$234$		0			0
$235$		−	15.7281i		−	1.02599i
$236$		0			0
$237$	−3.93294	−	2.27069i	−0.255472	−	0.147497i
$238$		0			0
$239$	14.3918			0.930929			0.465464	−	0.885067i	$-0.345887\pi$
$239$	14.3918			0.930929			0.465464	+	0.885067i	$0.345887\pi$
$240$		0			0
$241$	1.04373	+	1.80780i	0.0672328	+	0.116451i	0.897682	−	0.440643i	$-0.145250\pi$
$241$	1.04373	+	1.80780i	0.0672328	+	0.116451i	−0.830449	+	0.557094i	$0.811916\pi$
$242$		0			0
$243$	11.6998	−	6.75491i	0.750545	−	0.433328i
$244$		0			0
$245$	−6.17441	−	3.56480i	−0.394468	−	0.227746i
$246$		0			0
$247$	8.41195	−	6.42022i	0.535239	−	0.408509i
$248$		0			0
$249$	−1.99140	+	3.44920i	−0.126200	+	0.218584i
$250$		0			0
$251$	−6.27541	+	3.62311i	−0.396100	+	0.228688i	−0.684800	−	0.728731i	$-0.740110\pi$
$251$	−6.27541	+	3.62311i	−0.396100	+	0.228688i	0.288700	+	0.957420i	$0.406777\pi$
$252$		0			0
$253$	−5.20547	+	3.00538i	−0.327265	+	0.188947i
$254$		0			0
$255$	−5.86994			−0.367590
$256$		0			0
$257$	9.08570	−	15.7369i	0.566750	−	0.981640i	−0.430134	−	0.902765i	$-0.641534\pi$
$257$	9.08570	−	15.7369i	0.566750	−	0.981640i	0.996885	−	0.0788752i	$-0.0251328\pi$
$258$		0			0
$259$			13.8922i			0.863216i
$260$		0			0
$261$			19.2585i			1.19207i
$262$		0			0
$263$	−3.91017	+	6.77261i	−0.241111	+	0.417617i	−0.961031	−	0.276440i	$-0.910845\pi$
$263$	−3.91017	+	6.77261i	−0.241111	+	0.417617i	0.719920	+	0.694057i	$0.244179\pi$
$264$		0			0
$265$	2.36517			0.145291
$266$		0			0
$267$	6.00157	−	3.46501i	0.367290	−	0.212055i
$268$		0			0
$269$	10.5009	−	6.06272i	0.640253	−	0.369650i	−0.144459	−	0.989511i	$-0.546144\pi$
$269$	10.5009	−	6.06272i	0.640253	−	0.369650i	0.784712	+	0.619860i	$0.212811\pi$
$270$		0			0
$271$	−2.50994	+	4.34734i	−0.152468	+	0.264082i	−0.932134	−	0.362113i	$-0.882055\pi$
$271$	−2.50994	+	4.34734i	−0.152468	+	0.264082i	0.779666	+	0.626195i	$0.215389\pi$
$272$		0			0
$273$	0.900075	+	6.97610i	0.0544750	+	0.422213i
$274$		0			0
$275$	−3.89369	−	2.24802i	−0.234798	−	0.135561i
$276$		0			0
$277$	−24.9286	+	14.3925i	−1.49781	+	0.864762i	−0.999997	−	0.00252032i	$-0.999198\pi$
$277$	−24.9286	+	14.3925i	−1.49781	+	0.864762i	−0.497816	+	0.867283i	$0.665864\pi$
$278$		0			0
$279$	−5.87700	−	10.1793i	−0.351847	−	0.609416i
$280$		0			0
$281$	13.5594			0.808884			0.404442	−	0.914564i	$-0.367466\pi$
$281$	13.5594			0.808884			0.404442	+	0.914564i	$0.367466\pi$
$282$		0			0
$283$	−18.4454	−	10.6494i	−1.09646	−	0.633043i	−0.161173	−	0.986926i	$-0.551528\pi$
$283$	−18.4454	−	10.6494i	−1.09646	−	0.633043i	−0.935290	+	0.353883i	$0.884861\pi$
$284$		0			0
$285$		−	3.07699i		−	0.182265i
$286$		0			0
$287$	−7.89478			−0.466014
$288$		0			0
$289$	−7.17410	+	12.4259i	−0.422006	+	0.730935i
$290$		0			0
$291$			3.74075i			0.219287i
$292$		0			0
$293$	23.7670	−	13.7219i	1.38848	−	0.801640i	0.395337	−	0.918536i	$-0.370628\pi$
$293$	23.7670	−	13.7219i	1.38848	−	0.801640i	0.993144	+	0.116896i	$0.0372944\pi$
$294$		0			0
$295$	4.63193	+	8.02274i	0.269681	+	0.467102i
$296$		0			0
$297$	4.10076	−	7.10273i	0.237950	−	0.412142i
$298$		0			0
$299$	3.38402	−	8.11036i	0.195703	−	0.469034i
$300$		0			0
$301$	31.2225	+	18.0263i	1.79963	+	1.03902i
$302$		0			0
$303$	−3.40962	−	5.90563i	−0.195877	−	0.339270i
$304$		0			0
$305$	−1.42873	−	2.47464i	−0.0818090	−	0.141697i
$306$		0			0
$307$			4.96158i			0.283173i	0.989926	+	0.141586i	$0.0452203\pi$
$307$			4.96158i			0.283173i	−0.989926	+	0.141586i	$0.954780\pi$
$308$		0			0
$309$	1.03870	+	0.599694i	0.0590896	+	0.0341154i
$310$		0			0
$311$	−1.03478			−0.0586768			−0.0293384	−	0.999570i	$-0.509340\pi$
$311$	−1.03478			−0.0586768			−0.0293384	+	0.999570i	$0.509340\pi$
$312$		0			0
$313$	6.17484			0.349023			0.174511	−	0.984655i	$-0.444165\pi$
$313$	6.17484			0.349023			0.174511	+	0.984655i	$0.444165\pi$
$314$		0			0
$315$	−13.5872	−	7.84458i	−0.765552	−	0.441992i
$316$		0			0
$317$		−	11.6534i		−	0.654523i	−0.944934	−	0.327261i	$-0.893874\pi$
$317$		−	11.6534i		−	0.654523i	0.944934	−	0.327261i	$-0.106126\pi$
$318$		0			0
$319$	8.94744	+	15.4974i	0.500961	+	0.867689i
$320$		0			0
$321$	3.58960	+	6.21738i	0.200352	+	0.347020i
$322$		0			0
$323$	−14.2310	−	8.21628i	−0.791834	−	0.457166i
$324$		0			0
$325$	6.51940	−	0.841151i	0.361631	−	0.0466587i
$326$		0			0
$327$	2.17594	−	3.76884i	0.120330	−	0.208417i
$328$		0			0
$329$	14.6334	+	25.3458i	0.806766	+	1.39736i
$330$		0			0
$331$	26.0340	−	15.0307i	1.43096	−	0.826163i	0.433762	−	0.901028i	$-0.357186\pi$
$331$	26.0340	−	15.0307i	1.43096	−	0.826163i	0.997194	+	0.0748651i	$0.0238526\pi$
$332$		0			0
$333$			11.1167i			0.609191i
$334$		0			0
$335$	−10.2946	+	17.8307i	−0.562453	+	0.974197i
$336$		0			0
$337$	17.7875			0.968946			0.484473	−	0.874806i	$-0.339011\pi$
$337$	17.7875			0.968946			0.484473	+	0.874806i	$0.339011\pi$
$338$		0			0
$339$		−	5.62379i		−	0.305442i
$340$		0			0
$341$	−9.45849	−	5.46086i	−0.512206	−	0.295722i
$342$		0			0
$343$	−9.94972			−0.537234
$344$		0			0
$345$	−1.27767	−	2.21298i	−0.0687872	−	0.119143i
$346$		0			0
$347$	1.27962	−	0.738791i	0.0686938	−	0.0396604i	−0.465260	−	0.885174i	$-0.654039\pi$
$347$	1.27962	−	0.738791i	0.0686938	−	0.0396604i	0.533954	+	0.845514i	$0.320706\pi$
$348$		0			0
$349$	−12.1744	−	7.02888i	−0.651679	−	0.376247i	0.137420	−	0.990513i	$-0.456119\pi$
$349$	−12.1744	−	7.02888i	−0.651679	−	0.376247i	−0.789099	+	0.614266i	$0.789452\pi$
$350$		0			0
$351$	1.53440	+	11.8925i	0.0819002	+	0.634773i
$352$		0			0
$353$	−7.52945	+	13.0414i	−0.400752	+	0.694123i	−0.993817	−	0.111032i	$-0.964585\pi$
$353$	−7.52945	+	13.0414i	−0.400752	+	0.694123i	0.593065	+	0.805155i	$0.297918\pi$
$354$		0			0
$355$	−15.6533	+	9.03743i	−0.830790	+	0.479657i
$356$		0			0
$357$	9.45938	−	5.46138i	0.500644	−	0.289047i
$358$		0			0
$359$	0.213296			0.0112573			0.00562866	−	0.999984i	$-0.498208\pi$
$359$	0.213296			0.0112573			0.00562866	+	0.999984i	$0.498208\pi$
$360$		0			0
$361$	−5.19307	+	8.99467i	−0.273320	+	0.473404i
$362$		0			0
$363$			2.89302i			0.151844i
$364$		0			0
$365$			21.6772i			1.13464i
$366$		0			0
$367$	5.55712	−	9.62522i	0.290079	−	0.502432i	−0.683749	−	0.729717i	$-0.739652\pi$
$367$	5.55712	−	9.62522i	0.290079	−	0.502432i	0.973828	+	0.227285i	$0.0729850\pi$
$368$		0			0
$369$	−6.31751			−0.328876
$370$		0			0
$371$	−3.81146	+	2.20055i	−0.197881	+	0.114247i
$372$		0			0
$373$	6.29802	−	3.63616i	0.326099	−	0.188273i	−0.328009	−	0.944675i	$-0.606378\pi$
$373$	6.29802	−	3.63616i	0.326099	−	0.188273i	0.654108	+	0.756401i	$0.273044\pi$
$374$		0			0
$375$	3.57669	−	6.19502i	0.184700	−	0.319909i
$376$		0			0
$377$	−24.1457	−	10.0747i	−1.24357	−	0.518874i
$378$		0			0
$379$	8.29446	+	4.78881i	0.426058	+	0.245984i	0.697666	−	0.716423i	$-0.254222\pi$
$379$	8.29446	+	4.78881i	0.426058	+	0.245984i	−0.271608	+	0.962408i	$0.587555\pi$
$380$		0			0
$381$	−8.02765	+	4.63476i	−0.411269	+	0.237446i
$382$		0			0
$383$	13.7992	+	23.9008i	0.705104	+	1.22128i	0.966654	+	0.256086i	$0.0824329\pi$
$383$	13.7992	+	23.9008i	0.705104	+	1.22128i	−0.261550	+	0.965190i	$0.584234\pi$
$384$		0			0
$385$	−14.5783			−0.742976
$386$		0			0
$387$	24.9847	+	14.4249i	1.27004	+	0.733259i
$388$		0			0
$389$			3.20160i			0.162328i	0.996701	+	0.0811638i	$0.0258637\pi$
$389$			3.20160i			0.162328i	−0.996701	+	0.0811638i	$0.974136\pi$
$390$		0			0
$391$	−13.6467			−0.690141
$392$		0			0
$393$	−3.27085	+	5.66528i	−0.164993	+	0.285776i
$394$		0			0
$395$			13.7612i			0.692403i
$396$		0			0
$397$	−2.89755	+	1.67290i	−0.145424	+	0.0839605i	−0.570946	−	0.820987i	$-0.693424\pi$
$397$	−2.89755	+	1.67290i	−0.145424	+	0.0839605i	0.425523	+	0.904948i	$0.360090\pi$
$398$		0			0
$399$	2.86282	+	4.95856i	0.143320	+	0.248238i
$400$		0			0
$401$	−3.35071	+	5.80359i	−0.167326	+	0.289818i	−0.937479	−	0.348042i	$-0.886847\pi$
$401$	−3.35071	+	5.80359i	−0.167326	+	0.289818i	0.770153	+	0.637860i	$0.220180\pi$
$402$		0			0
$403$	15.8368	−	2.04331i	0.788889	−	0.101785i
$404$		0			0
$405$	−9.27050	−	5.35233i	−0.460655	−	0.265959i
$406$		0			0
$407$	5.16477	+	8.94565i	0.256008	+	0.443419i
$408$		0			0
$409$	10.5468	+	18.2676i	0.521506	+	0.903274i	0.999687	+	0.0250132i	$0.00796277\pi$
$409$	10.5468	+	18.2676i	0.521506	+	0.903274i	−0.478182	+	0.878261i	$0.658704\pi$
$410$		0			0
$411$			0.0357976i			0.00176576i
$412$		0			0
$413$	−14.9287	−	8.61908i	−0.734592	−	0.424117i
$414$		0			0
$415$	12.0686			0.592426
$416$		0			0
$417$	8.91052			0.436350
$418$		0			0
$419$	−26.6905	−	15.4098i	−1.30392	−	0.752817i	−0.322843	−	0.946453i	$-0.604639\pi$
$419$	−26.6905	−	15.4098i	−1.30392	−	0.752817i	−0.981073	+	0.193636i	$0.937972\pi$
$420$		0			0
$421$			5.77781i			0.281593i	0.990039	+	0.140796i	$0.0449663\pi$
$421$			5.77781i			0.281593i	−0.990039	+	0.140796i	$0.955034\pi$
$422$		0			0
$423$	11.7099	+	20.2821i	0.569353	+	0.986148i
$424$		0			0
$425$	−5.10384	−	8.84011i	−0.247573	−	0.428809i
$426$		0			0
$427$	4.60479	+	2.65858i	0.222842	+	0.128658i
$428$		0			0
$429$	3.17314	+	4.15753i	0.153201	+	0.200727i
$430$		0			0
$431$	3.25712	−	5.64150i	0.156890	−	0.271741i	−0.776856	−	0.629679i	$-0.783187\pi$
$431$	3.25712	−	5.64150i	0.156890	−	0.271741i	0.933746	+	0.357937i	$0.116520\pi$
$432$		0			0
$433$	0.570484	+	0.988107i	0.0274157	+	0.0474854i	0.879408	−	0.476069i	$-0.157939\pi$
$433$	0.570484	+	0.988107i	0.0274157	+	0.0474854i	−0.851992	+	0.523555i	$0.824606\pi$
$434$		0			0
$435$	−6.58836	+	3.80379i	−0.315888	+	0.182378i
$436$		0			0
$437$		−	7.15350i		−	0.342198i
$438$		0			0
$439$	−11.9751	+	20.7415i	−0.571540	+	0.989936i	0.424868	+	0.905255i	$0.360320\pi$
$439$	−11.9751	+	20.7415i	−0.571540	+	0.989936i	−0.996408	+	0.0846810i	$0.973013\pi$
$440$		0			0
$441$	10.6162			0.505534
$442$		0			0
$443$			24.5182i			1.16489i	0.812868	+	0.582447i	$0.197905\pi$
$443$			24.5182i			1.16489i	−0.812868	+	0.582447i	$0.802095\pi$
$444$		0			0
$445$	−18.1859	−	10.4996i	−0.862095	−	0.497731i
$446$		0			0
$447$	−0.660042			−0.0312189
$448$		0			0
$449$	9.86244	+	17.0822i	0.465437	+	0.806161i	0.999221	−	0.0394599i	$-0.0125637\pi$
$449$	9.86244	+	17.0822i	0.465437	+	0.806161i	−0.533784	+	0.845621i	$0.679230\pi$
$450$		0			0
$451$	−5.08373	+	2.93509i	−0.239383	+	0.138208i
$452$		0			0
$453$	−1.05697	−	0.610244i	−0.0496610	−	0.0286718i
$454$		0			0
$455$	16.9431	−	12.9315i	0.794307	−	0.606236i
$456$		0			0
$457$	−5.33778	+	9.24531i	−0.249691	+	0.432477i	−0.963440	−	0.267924i	$-0.913662\pi$
$457$	−5.33778	+	9.24531i	−0.249691	+	0.432477i	0.713749	+	0.700401i	$0.246996\pi$
$458$		0			0
$459$	16.1258	−	9.31026i	0.752690	−	0.434566i
$460$		0			0
$461$	22.4467	−	12.9596i	1.04545	−	0.603590i	0.124077	−	0.992273i	$-0.460403\pi$
$461$	22.4467	−	12.9596i	1.04545	−	0.603590i	0.921372	+	0.388683i	$0.127070\pi$
$462$		0			0
$463$	20.4817			0.951867			0.475933	−	0.879481i	$-0.342110\pi$
$463$	20.4817			0.951867			0.475933	+	0.879481i	$0.342110\pi$
$464$		0			0
$465$	2.32156	−	4.02105i	0.107660	−	0.186472i
$466$		0			0
$467$			2.02585i			0.0937453i	0.998901	+	0.0468726i	$0.0149255\pi$
$467$			2.02585i			0.0937453i	−0.998901	+	0.0468726i	$0.985075\pi$
$468$		0			0
$469$		−	38.3122i		−	1.76909i
$470$		0			0
$471$	−7.02635	+	12.1700i	−0.323757	+	0.560763i
$472$		0			0
$473$	26.8070			1.23259
$474$		0			0
$475$	4.63394	−	2.67541i	0.212620	−	0.122756i
$476$		0			0
$477$	−3.04998	+	1.76091i	−0.139649	+	0.0806264i
$478$		0			0
$479$	−9.72335	+	16.8413i	−0.444271	+	0.769500i	−0.998001	−	0.0631961i	$-0.979871\pi$
$479$	−9.72335	+	16.8413i	−0.444271	+	0.769500i	0.553730	+	0.832696i	$0.313204\pi$
$480$		0			0
$481$	−13.9377	−	5.81547i	−0.635506	−	0.265163i
$482$		0			0
$483$	4.11791	+	2.37747i	0.187371	+	0.108179i
$484$		0			0
$485$	9.81657	−	5.66760i	0.445748	−	0.257352i
$486$		0			0
$487$	−14.9615	−	25.9141i	−0.677971	−	1.17428i	−0.975591	−	0.219596i	$-0.929526\pi$
$487$	−14.9615	−	25.9141i	−0.677971	−	1.17428i	0.297620	−	0.954685i	$-0.403807\pi$
$488$		0			0
$489$	−13.4397			−0.607765
$490$		0			0
$491$	11.5127	+	6.64683i	0.519559	+	0.299967i	0.736754	−	0.676161i	$-0.236358\pi$
$491$	11.5127	+	6.64683i	0.519559	+	0.299967i	−0.217195	+	0.976128i	$0.569691\pi$
$492$		0			0
$493$			40.6280i			1.82979i
$494$		0			0
$495$	−11.6657			−0.524335
$496$		0			0
$497$	16.8168	−	29.1276i	0.754337	−	1.30655i
$498$		0			0
$499$			4.06334i			0.181900i	0.995855	+	0.0909501i	$0.0289904\pi$
$499$			4.06334i			0.181900i	−0.995855	+	0.0909501i	$0.971010\pi$
$500$		0			0
$501$	−9.09995	+	5.25386i	−0.406556	+	0.234725i
$502$		0			0
$503$	0.391329	+	0.677801i	0.0174485	+	0.0302217i	0.874618	−	0.484813i	$-0.161112\pi$
$503$	0.391329	+	0.677801i	0.0174485	+	0.0302217i	−0.857169	+	0.515035i	$0.827779\pi$
$504$		0			0
$505$	−10.3318	+	17.8952i	−0.459759	+	0.796326i
$506$		0			0
$507$	−7.37577	−	2.01727i	−0.327570	−	0.0895902i
$508$		0			0
$509$	−16.5487	−	9.55438i	−0.733507	−	0.423491i	0.0861967	−	0.996278i	$-0.472529\pi$
$509$	−16.5487	−	9.55438i	−0.733507	−	0.423491i	−0.819704	+	0.572788i	$0.805862\pi$
$510$		0			0
$511$	−20.1685	−	34.9328i	−0.892200	−	1.54534i
$512$		0			0
$513$	4.88039	+	8.45308i	0.215474	+	0.373212i
$514$		0			0
$515$		−	3.63438i		−	0.160150i
$516$		0			0
$517$	18.8459	+	10.8807i	0.828844	+	0.478533i
$518$		0			0
$519$	6.53900			0.287030
$520$		0			0
$521$	−3.23410			−0.141688			−0.0708441	−	0.997487i	$-0.522569\pi$
$521$	−3.23410			−0.141688			−0.0708441	+	0.997487i	$0.522569\pi$
$522$		0			0
$523$	16.6431	+	9.60888i	0.727750	+	0.420167i	0.817599	−	0.575789i	$-0.195305\pi$
$523$	16.6431	+	9.60888i	0.727750	+	0.420167i	−0.0898482	+	0.995955i	$0.528638\pi$
$524$		0			0
$525$			3.55670i			0.155227i
$526$		0			0
$527$	−12.3982	−	21.4743i	−0.540074	−	0.935435i
$528$		0			0
$529$	8.52964	+	14.7738i	0.370854	+	0.642337i
$530$		0			0
$531$	−11.9461	−	6.89710i	−0.518418	−	0.299309i
$532$		0			0
$533$	3.30487	−	7.92068i	0.143150	−	0.343083i
$534$		0			0
$535$	10.8772	−	18.8399i	0.470262	−	0.814518i
$536$		0			0
$537$	−6.84974	−	11.8641i	−0.295588	−	0.511973i
$538$		0			0
$539$	8.54291	−	4.93225i	0.367969	−	0.212447i
$540$		0			0
$541$		−	17.5473i		−	0.754417i	−0.926128	−	0.377208i	$-0.876884\pi$
$541$		−	17.5473i		−	0.754417i	0.926128	−	0.377208i	$-0.123116\pi$
$542$		0			0
$543$	1.88376	−	3.26276i	0.0808397	−	0.140018i
$544$		0			0
$545$	−13.1870			−0.564871
$546$		0			0
$547$		−	10.8081i		−	0.462121i	−0.972939	−	0.231061i	$-0.925780\pi$
$547$		−	10.8081i		−	0.462121i	0.972939	−	0.231061i	$-0.0742196\pi$
$548$		0			0
$549$	3.68482	+	2.12743i	0.157264	+	0.0907965i
$550$		0			0
$551$	−21.2970			−0.907283
$552$		0			0
$553$	−12.8034	−	22.1762i	−0.544457	−	0.943027i
$554$		0			0
$555$	−3.80303	+	2.19568i	−0.161430	+	0.0932015i
$556$		0			0
$557$	8.61540	+	4.97411i	0.365046	+	0.210760i	0.671292	−	0.741193i	$-0.265740\pi$
$557$	8.61540	+	4.97411i	0.365046	+	0.210760i	−0.306246	+	0.951952i	$0.599073\pi$
$558$		0			0
$559$	−31.1557	+	23.7788i	−1.31774	+	1.00574i
$560$		0			0
$561$	4.06082	−	7.03355i	0.171448	−	0.296957i
$562$		0			0
$563$	−7.22674	+	4.17236i	−0.304571	+	0.175844i	−0.644494	−	0.764609i	$-0.722932\pi$
$563$	−7.22674	+	4.17236i	−0.304571	+	0.175844i	0.339924	+	0.940453i	$0.389599\pi$
$564$		0			0
$565$	−14.7581	+	8.52058i	−0.620877	+	0.358464i
$566$		0			0
$567$	19.9192			0.836527
$568$		0			0
$569$	17.5793	−	30.4482i	0.736961	−	1.27645i	−0.216896	−	0.976195i	$-0.569593\pi$
$569$	17.5793	−	30.4482i	0.736961	−	1.27645i	0.953858	−	0.300260i	$-0.0970733\pi$
$570$		0			0
$571$		−	19.3907i		−	0.811474i	−0.913990	−	0.405737i	$-0.867015\pi$
$571$		−	19.3907i		−	0.811474i	0.913990	−	0.405737i	$-0.132985\pi$
$572$		0			0
$573$			4.82087i			0.201395i
$574$		0			0
$575$	2.22183	−	3.84832i	0.0926567	−	0.160486i
$576$		0			0
$577$	5.44279			0.226586			0.113293	−	0.993562i	$-0.463860\pi$
$577$	5.44279			0.226586			0.113293	+	0.993562i	$0.463860\pi$
$578$		0			0
$579$	−8.93500	+	5.15863i	−0.371326	+	0.214385i
$580$		0			0
$581$	−19.4486	+	11.2286i	−0.806863	+	0.465842i
$582$		0			0
$583$	−1.63622	+	2.83402i	−0.0677654	+	0.117373i
$584$		0			0
$585$	13.5581	−	10.3479i	0.560560	−	0.427834i
$586$		0			0
$587$	6.70704	+	3.87231i	0.276829	+	0.159827i	0.631987	−	0.774979i	$-0.282240\pi$
$587$	6.70704	+	3.87231i	0.276829	+	0.159827i	−0.355158	+	0.934806i	$0.615573\pi$
$588$		0			0
$589$	11.2567	−	6.49906i	0.463825	−	0.267789i
$590$		0			0
$591$	−1.30506	−	2.26044i	−0.0536831	−	0.0929819i
$592$		0			0
$593$	−41.9381			−1.72219			−0.861095	−	0.508444i	$-0.830221\pi$
$593$	−41.9381			−1.72219			−0.861095	+	0.508444i	$0.830221\pi$
$594$		0			0
$595$	−28.6638	−	16.5490i	−1.17510	−	0.678444i
$596$		0			0
$597$		−	7.19058i		−	0.294291i
$598$		0			0
$599$	28.4843			1.16384			0.581919	−	0.813246i	$-0.302302\pi$
$599$	28.4843			1.16384			0.581919	+	0.813246i	$0.302302\pi$
$600$		0			0
$601$	10.3349	−	17.9005i	0.421569	−	0.730178i	−0.574525	−	0.818487i	$-0.694813\pi$
$601$	10.3349	−	17.9005i	0.421569	−	0.730178i	0.996093	+	0.0883092i	$0.0281464\pi$
$602$		0			0
$603$		−	30.6580i		−	1.24849i
$604$		0			0
$605$	7.59194	−	4.38321i	0.308656	−	0.178203i
$606$		0			0
$607$	−21.0555	−	36.4693i	−0.854618	−	1.48024i	−0.876999	−	0.480492i	$-0.840458\pi$
$607$	−21.0555	−	36.4693i	−0.854618	−	1.48024i	0.0223811	−	0.999750i	$-0.492875\pi$
$608$		0			0
$609$	7.07808	−	12.2596i	0.286818	−	0.496784i
$610$		0			0
$611$	−31.5547	+	4.07128i	−1.27657	+	0.164706i
$612$		0			0
$613$	−2.45743	−	1.41880i	−0.0992548	−	0.0573048i	0.449551	−	0.893255i	$-0.351584\pi$
$613$	−2.45743	−	1.41880i	−0.0992548	−	0.0573048i	−0.548806	+	0.835950i	$0.684917\pi$
$614$		0			0
$615$	−1.24778	−	2.16123i	−0.0503155	−	0.0871490i
$616$		0			0
$617$	4.20136	+	7.27696i	0.169140	+	0.292960i	0.938118	−	0.346316i	$-0.112568\pi$
$617$	4.20136	+	7.27696i	0.169140	+	0.292960i	−0.768978	+	0.639276i	$0.779234\pi$
$618$		0			0
$619$		−	20.3468i		−	0.817806i	−0.912578	−	0.408903i	$-0.865911\pi$
$619$		−	20.3468i		−	0.817806i	0.912578	−	0.408903i	$-0.134089\pi$
$620$		0			0
$621$	7.01998	+	4.05299i	0.281702	+	0.162641i
$622$		0			0
$623$	39.0754			1.56552
$624$		0			0
$625$	−12.5604			−0.502417
$626$		0			0
$627$	3.68695	+	2.12866i	0.147243	+	0.0850105i
$628$		0			0
$629$			23.4519i			0.935089i
$630$		0			0
$631$	9.63472	+	16.6878i	0.383552	+	0.664332i	0.991567	−	0.129594i	$-0.0413673\pi$
$631$	9.63472	+	16.6878i	0.383552	+	0.664332i	−0.608015	+	0.793925i	$0.708034\pi$
$632$		0			0
$633$	3.16627	+	5.48414i	0.125848	+	0.217975i
$634$		0			0
$635$	24.3253	+	14.0442i	0.965321	+	0.557328i
$636$		0			0
$637$	−5.55365	+	13.3102i	−0.220044	+	0.527371i
$638$		0			0
$639$	13.4570	−	23.3083i	0.532352	−	0.922061i
$640$		0			0
$641$	6.64940	+	11.5171i	0.262636	+	0.454898i	0.966941	−	0.254998i	$-0.0820750\pi$
$641$	6.64940	+	11.5171i	0.262636	+	0.454898i	−0.704306	+	0.709897i	$0.748742\pi$
$642$		0			0
$643$	−29.9292	+	17.2797i	−1.18029	+	0.681443i	−0.956083	−	0.293097i	$-0.905314\pi$
$643$	−29.9292	+	17.2797i	−1.18029	+	0.681443i	−0.224212	+	0.974540i	$0.571981\pi$
$644$		0			0
$645$			11.3964i			0.448732i
$646$		0			0
$647$	2.33433	−	4.04318i	0.0917721	−	0.158954i	−0.816485	−	0.577367i	$-0.804080\pi$
$647$	2.33433	−	4.04318i	0.0917721	−	0.158954i	0.908257	+	0.418413i	$0.137414\pi$
$648$		0			0
$649$	−12.8175			−0.503130
$650$		0			0
$651$			8.63988i			0.338624i
$652$		0			0
$653$	16.4329	+	9.48755i	0.643069	+	0.371276i	0.785796	−	0.618486i	$-0.212254\pi$
$653$	16.4329	+	9.48755i	0.643069	+	0.371276i	−0.142726	+	0.989762i	$0.545587\pi$
$654$		0			0
$655$	19.8226			0.774534
$656$		0			0
$657$	−16.1391	−	27.9537i	−0.629645	−	1.09058i
$658$		0			0
$659$	−7.64797	+	4.41556i	−0.297923	+	0.172006i	−0.641509	−	0.767115i	$-0.721691\pi$
$659$	−7.64797	+	4.41556i	−0.297923	+	0.172006i	0.343587	+	0.939121i	$0.388358\pi$
$660$		0			0
$661$	26.5464	+	15.3266i	1.03254	+	0.596135i	0.917710	−	0.397250i	$-0.130035\pi$
$661$	26.5464	+	15.3266i	1.03254	+	0.596135i	0.114826	+	0.993386i	$0.463369\pi$
$662$		0			0
$663$	1.51945	+	11.7766i	0.0590107	+	0.457367i
$664$		0			0
$665$	8.67491	−	15.0254i	0.336398	−	0.582659i
$666$		0			0
$667$	−15.3169	+	8.84320i	−0.593072	+	0.342410i
$668$		0			0
$669$	−3.65788	+	2.11188i	−0.141422	+	0.0816500i
$670$		0			0
$671$	3.95359			0.152627
$672$		0			0
$673$	−0.586586	+	1.01600i	−0.0226112	+	0.0391638i	−0.877110	−	0.480290i	$-0.840531\pi$
$673$	−0.586586	+	1.01600i	−0.0226112	+	0.0391638i	0.854498	+	0.519454i	$0.173865\pi$
$674$		0			0
$675$			6.06326i			0.233375i
$676$		0			0
$677$			5.90986i			0.227134i	0.993530	+	0.113567i	$0.0362277\pi$
$677$			5.90986i			0.227134i	−0.993530	+	0.113567i	$0.963772\pi$
$678$		0			0
$679$	−10.5462	+	18.2666i	−0.404728	+	0.701009i
$680$		0			0
$681$	0.187705			0.00719286
$682$		0			0
$683$	22.0262	−	12.7169i	0.842811	−	0.486597i	−0.0154080	−	0.999881i	$-0.504905\pi$
$683$	22.0262	−	12.7169i	0.842811	−	0.486597i	0.858219	+	0.513284i	$0.171571\pi$
$684$		0			0
$685$	0.0939408	−	0.0542368i	0.00358929	−	0.00207228i
$686$		0			0
$687$	2.70168	−	4.67945i	0.103076	−	0.178532i
$688$		0			0
$689$	−0.612232	−	4.74515i	−0.0233242	−	0.180776i
$690$		0			0
$691$	2.50444	+	1.44594i	0.0952733	+	0.0550061i	0.546880	−	0.837211i	$-0.315816\pi$
$691$	2.50444	+	1.44594i	0.0952733	+	0.0550061i	−0.451606	+	0.892217i	$0.649149\pi$
$692$		0			0
$693$	18.7993	−	10.8538i	0.714125	−	0.412300i
$694$		0			0
$695$	−13.5003	−	23.3832i	−0.512096	−	0.886976i
$696$		0			0
$697$	−13.3275			−0.504815
$698$		0			0
$699$	10.7015	+	6.17852i	0.404768	+	0.233693i
$700$		0			0
$701$		−	44.2006i		−	1.66943i	−0.550679	−	0.834717i	$-0.685631\pi$
$701$		−	44.2006i		−	1.66943i	0.550679	−	0.834717i	$-0.314369\pi$
$702$		0			0
$703$	−12.2934			−0.463653
$704$		0			0
$705$	−4.62568	+	8.01191i	−0.174213	+	0.301746i
$706$		0			0
$707$		−	38.4507i		−	1.44609i
$708$		0			0
$709$	−24.1216	+	13.9266i	−0.905904	+	0.523024i	−0.879111	−	0.476617i	$-0.841863\pi$
$709$	−24.1216	+	13.9266i	−0.905904	+	0.523024i	−0.0267929	+	0.999641i	$0.508529\pi$
$710$		0			0
$711$	−10.2455	−	17.7457i	−0.384235	−	0.665515i
$712$		0			0
$713$	5.39724	−	9.34830i	0.202128	−	0.350097i
$714$		0			0
$715$	6.10268	−	14.6261i	0.228227	−	0.546985i
$716$		0			0
$717$	−7.33119	−	4.23266i	−0.273788	−	0.158072i
$718$		0			0
$719$	−24.2128	−	41.9378i	−0.902984	−	1.56401i	−0.823601	−	0.567170i	$-0.808038\pi$
$719$	−24.2128	−	41.9378i	−0.902984	−	1.56401i	−0.0793833	−	0.996844i	$-0.525295\pi$
$720$		0			0
$721$	3.38142	+	5.85679i	0.125931	+	0.218118i
$722$		0			0
$723$		−	1.22786i		−	0.0456645i
$724$		0			0
$725$	−11.4570	−	6.61471i	−0.425503	−	0.245664i
$726$		0			0
$727$	−46.8805			−1.73870			−0.869351	−	0.494195i	$-0.835463\pi$
$727$	−46.8805			−1.73870			−0.869351	+	0.494195i	$0.835463\pi$
$728$		0			0
$729$	10.0710			0.373000
$730$		0			0
$731$	52.7080	+	30.4310i	1.94947	+	1.12553i
$732$		0			0
$733$		−	27.5679i		−	1.01824i	−0.860694	−	0.509122i	$-0.829970\pi$
$733$		−	27.5679i		−	1.01824i	0.860694	−	0.509122i	$-0.170030\pi$
$734$		0			0
$735$	2.09683	+	3.63181i	0.0773427	+	0.133961i
$736$		0			0
$737$	−14.2436	−	24.6706i	−0.524669	−	0.908753i
$738$		0			0
$739$	28.2348	+	16.3014i	1.03863	+	0.599655i	0.919446	−	0.393216i	$-0.128638\pi$
$739$	28.2348	+	16.3014i	1.03863	+	0.599655i	0.119188	+	0.992872i	$0.461971\pi$
$740$		0			0
$741$	−6.17325	+	0.796489i	−0.226780	+	0.0292598i
$742$		0			0
$743$	−12.2924	+	21.2910i	−0.450963	+	0.781091i	−0.998446	−	0.0557256i	$-0.982253\pi$
$743$	−12.2924	+	21.2910i	−0.450963	+	0.781091i	0.547483	+	0.836817i	$0.315586\pi$
$744$		0			0
$745$	1.00003	+	1.73210i	0.0366382	+	0.0634591i
$746$		0			0
$747$	−15.5630	+	8.98531i	−0.569421	+	0.328755i
$748$		0			0
$749$			40.4805i			1.47912i
$750$		0			0
$751$	−22.5199	+	39.0057i	−0.821764	+	1.42334i	0.0826041	+	0.996582i	$0.473676\pi$
$751$	−22.5199	+	39.0057i	−0.821764	+	1.42334i	−0.904368	+	0.426754i	$0.859657\pi$
$752$		0			0
$753$	4.26226			0.155325
$754$		0			0
$755$			3.69832i			0.134596i
$756$		0			0
$757$	10.4986	+	6.06138i	0.381579	+	0.220305i	0.678505	−	0.734596i	$-0.262628\pi$
$757$	10.4986	+	6.06138i	0.381579	+	0.220305i	−0.296926	+	0.954900i	$0.595962\pi$
$758$		0			0
$759$	3.53555			0.128333
$760$		0			0
$761$	12.0876	+	20.9363i	0.438174	+	0.758940i	0.997549	−	0.0699753i	$-0.0222921\pi$
$761$	12.0876	+	20.9363i	0.438174	+	0.758940i	−0.559375	+	0.828915i	$0.688959\pi$
$762$		0			0
$763$	21.2509	−	12.2692i	0.769333	−	0.444175i
$764$		0			0
$765$	−22.9371	−	13.2428i	−0.829294	−	0.478793i
$766$		0			0
$767$	14.8967	−	11.3696i	0.537890	−	0.410532i
$768$		0			0
$769$	−17.0904	+	29.6015i	−0.616296	+	1.06746i	0.373859	+	0.927485i	$0.378034\pi$
$769$	−17.0904	+	29.6015i	−0.616296	+	1.06746i	−0.990156	+	0.139971i	$0.955299\pi$
$770$		0			0
$771$	−9.25651	+	5.34425i	−0.333365	+	0.192468i
$772$		0			0
$773$	−14.7695	+	8.52716i	−0.531221	+	0.306701i	−0.741514	−	0.670938i	$-0.765892\pi$
$773$	−14.7695	+	8.52716i	−0.531221	+	0.306701i	0.210292	+	0.977639i	$0.432558\pi$
$774$		0			0
$775$	8.07427			0.290036
$776$		0			0
$777$	4.08571	−	7.07666i	0.146574	−	0.253874i
$778$		0			0
$779$		−	6.98620i		−	0.250307i
$780$		0			0
$781$		−	25.0084i		−	0.894870i
$782$		0			0
$783$	12.0663	−	20.8995i	0.431215	−	0.746887i
$784$		0			0
$785$	42.5824			1.51983
$786$		0			0
$787$	−33.3134	+	19.2335i	−1.18749	+	0.685600i	−0.957736	−	0.287648i	$-0.907127\pi$
$787$	−33.3134	+	19.2335i	−1.18749	+	0.685600i	−0.229757	+	0.973248i	$0.573793\pi$
$788$		0			0
$789$	3.98368	−	2.29998i	0.141823	−	0.0818814i
$790$		0			0
$791$	15.8551	−	27.4618i	0.563741	−	0.976428i
$792$		0			0
$793$	−4.59494	+	3.50698i	−0.163171	+	0.124537i
$794$		0			0
$795$	−1.20482	−	0.695601i	−0.0427304	−	0.0246704i
$796$		0			0
$797$	38.4730	−	22.2124i	1.36278	−	0.786804i	0.372791	−	0.927915i	$-0.378401\pi$
$797$	38.4730	−	22.2124i	1.36278	−	0.786804i	0.989994	+	0.141111i	$0.0450675\pi$
$798$		0			0
$799$	24.7033	+	42.7873i	0.873939	+	1.51371i
$800$		0			0
$801$	31.2687			1.10482
$802$		0			0
$803$	−25.9744	−	14.9963i	−0.916616	−	0.529208i
$804$		0			0
$805$		−	14.4084i		−	0.507830i
$806$		0			0
$807$	−7.13224			−0.251067
$808$		0			0
$809$	−15.4545	+	26.7681i	−0.543353	+	0.941115i	0.455356	+	0.890310i	$0.349512\pi$
$809$	−15.4545	+	26.7681i	−0.543353	+	0.941115i	−0.998709	+	0.0508052i	$0.983821\pi$
$810$		0			0
$811$			32.1542i			1.12909i	0.825403	+	0.564544i	$0.190948\pi$
$811$			32.1542i			1.12909i	−0.825403	+	0.564544i	$0.809052\pi$
$812$		0			0
$813$	2.55712	−	1.47636i	0.0896823	−	0.0517781i
$814$		0			0
$815$	20.3625	+	35.2688i	0.713266	+	1.23541i
$816$		0			0
$817$	−15.9517	+	27.6292i	−0.558081	+	0.966624i
$818$		0			0
$819$	−12.2212	+	29.2901i	−0.427043	+	1.02348i
$820$		0			0
$821$	−10.3465	−	5.97353i	−0.361094	−	0.208478i	0.308466	−	0.951235i	$-0.400184\pi$
$821$	−10.3465	−	5.97353i	−0.361094	−	0.208478i	−0.669561	+	0.742757i	$0.733518\pi$
$822$		0			0
$823$	19.2125	+	33.2770i	0.669706	+	1.15996i	0.977986	+	0.208669i	$0.0669130\pi$
$823$	19.2125	+	33.2770i	0.669706	+	1.15996i	−0.308281	+	0.951295i	$0.599754\pi$
$824$		0			0
$825$	1.32230	+	2.29028i	0.0460364	+	0.0797374i
$826$		0			0
$827$		−	13.1098i		−	0.455872i	−0.973676	−	0.227936i	$-0.926802\pi$
$827$		−	13.1098i		−	0.455872i	0.973676	−	0.227936i	$-0.0731977\pi$
$828$		0			0
$829$	−11.4829	−	6.62967i	−0.398818	−	0.230258i	0.287156	−	0.957884i	$-0.407290\pi$
$829$	−11.4829	−	6.62967i	−0.398818	−	0.230258i	−0.685974	+	0.727626i	$0.740624\pi$
$830$		0			0
$831$	16.9315			0.587347
$832$		0			0
$833$	22.3961			0.775978
$834$		0			0
$835$	27.5746	+	15.9202i	0.954259	+	0.550942i
$836$		0			0
$837$			14.7288i			0.509102i
$838$		0			0
$839$	−2.06865	−	3.58301i	−0.0714179	−	0.123699i	0.828105	−	0.560573i	$-0.189419\pi$
$839$	−2.06865	−	3.58301i	−0.0714179	−	0.123699i	−0.899523	+	0.436874i	$0.856086\pi$
$840$		0			0
$841$	11.8275	+	20.4858i	0.407844	+	0.706407i
$842$		0			0
$843$	−6.90715	−	3.98784i	−0.237895	−	0.137349i
$844$		0			0
$845$	5.88123	+	22.4120i	0.202321	+	0.770998i
$846$		0			0
$847$	−8.15625	+	14.1270i	−0.280252	+	0.485411i
$848$		0			0
$849$	6.26405	+	10.8497i	0.214982	+	0.372359i
$850$		0			0
$851$	−8.84143	+	5.10460i	−0.303080	+	0.174984i
$852$		0			0
$853$		−	38.2871i		−	1.31093i	−0.755227	−	0.655463i	$-0.772473\pi$
$853$		−	38.2871i		−	1.31093i	0.755227	−	0.655463i	$-0.227527\pi$
$854$		0			0
$855$	6.94178	−	12.0235i	0.237404	−	0.411196i
$856$		0			0
$857$	4.33857			0.148203			0.0741014	−	0.997251i	$-0.476391\pi$
$857$	4.33857			0.148203			0.0741014	+	0.997251i	$0.476391\pi$
$858$		0			0
$859$		−	13.0557i		−	0.445453i	−0.974881	−	0.222727i	$-0.928504\pi$
$859$		−	13.0557i		−	0.445453i	0.974881	−	0.222727i	$-0.0714958\pi$
$860$		0			0
$861$	4.02160	+	2.32187i	0.137056	+	0.0791292i
$862$		0			0
$863$	−40.9955			−1.39550			−0.697751	−	0.716340i	$-0.745816\pi$
$863$	−40.9955			−1.39550			−0.697751	+	0.716340i	$0.745816\pi$
$864$		0			0
$865$	−9.90721	−	17.1598i	−0.336855	−	0.583451i
$866$		0			0
$867$	7.30897	−	4.21984i	0.248226	−	0.143313i
$868$		0			0
$869$	−16.4892	−	9.52002i	−0.559356	−	0.322944i
$870$		0			0
$871$	38.4379	+	16.0381i	1.30242	+	0.543430i
$872$		0			0
$873$	−8.43925	+	14.6172i	−0.285625	+	0.494718i
$874$		0			0
$875$	34.9310	−	20.1674i	1.18088	−	0.681784i
$876$		0			0
$877$	−26.9990	+	15.5879i	−0.911690	+	0.526365i	−0.880975	−	0.473164i	$-0.843112\pi$
$877$	−26.9990	+	15.5879i	−0.911690	+	0.526365i	−0.0307156	+	0.999528i	$0.509779\pi$
$878$		0			0
$879$	−16.1425			−0.544474
$880$		0			0
$881$	2.45718	−	4.25595i	0.0827844	−	0.143387i	−0.821661	−	0.569977i	$-0.806952\pi$
$881$	2.45718	−	4.25595i	0.0827844	−	0.143387i	0.904445	+	0.426590i	$0.140285\pi$
$882$		0			0
$883$		−	2.14194i		−	0.0720821i	−0.999350	−	0.0360411i	$-0.988525\pi$
$883$		−	2.14194i		−	0.0720821i	0.999350	−	0.0360411i	$-0.0114747\pi$
$884$		0			0
$885$		−	5.44905i		−	0.183168i
$886$		0			0
$887$	−2.61724	+	4.53319i	−0.0878783	+	0.152210i	−0.906614	−	0.421961i	$-0.861342\pi$
$887$	−2.61724	+	4.53319i	−0.0878783	+	0.152210i	0.818736	+	0.574170i	$0.194675\pi$
$888$		0			0
$889$	−52.2669			−1.75297
$890$		0			0
$891$	12.8267	−	7.40548i	0.429710	−	0.248093i
$892$		0			0
$893$	−22.4289	+	12.9493i	−0.750554	+	0.433332i
$894$		0			0
$895$	−20.7560	+	35.9505i	−0.693797	+	1.20169i
$896$		0			0
$897$	−4.10909	+	3.13617i	−0.137199	+	0.104714i
$898$		0			0
$899$	−27.8312	−	16.0684i	−0.928223	−	0.535910i
$900$		0			0
$901$	−6.43428	+	3.71483i	−0.214357	+	0.123759i
$902$		0			0
$903$	−10.6032	−	18.3652i	−0.352851	−	0.611156i
$904$		0			0
$905$	−11.4163			−0.379490
$906$		0			0
$907$	−13.8926	−	8.02088i	−0.461296	−	0.266329i	0.251293	−	0.967911i	$-0.419144\pi$
$907$	−13.8926	−	8.02088i	−0.461296	−	0.266329i	−0.712589	+	0.701582i	$0.752477\pi$
$908$		0			0
$909$		−	30.7688i		−	1.02054i
$910$		0			0
$911$	43.9693			1.45677			0.728384	−	0.685170i	$-0.240272\pi$
$911$	43.9693			1.45677			0.728384	+	0.685170i	$0.240272\pi$
$912$		0			0
$913$	−8.34908	+	14.4610i	−0.276314	+	0.478590i
$914$		0			0
$915$			1.68077i			0.0555647i
$916$		0			0
$917$	−31.9441	+	18.4429i	−1.05489	+	0.609039i
$918$		0			0
$919$	14.9889	+	25.9615i	0.494437	+	0.856390i	0.999979	−	0.00641145i	$-0.00204084\pi$
$919$	14.9889	+	25.9615i	0.494437	+	0.856390i	−0.505542	+	0.862802i	$0.668708\pi$
$920$		0			0
$921$	1.45921	−	2.52743i	0.0480827	−	0.0832817i
$922$		0			0
$923$	22.1834	+	29.0652i	0.730174	+	0.956694i
$924$		0			0
$925$	−6.61338	−	3.81824i	−0.217447	−	0.125543i
$926$		0			0
$927$	2.70586	+	4.68668i	0.0888720	+	0.153931i
$928$		0			0
$929$	−6.63588	−	11.4937i	−0.217716	−	0.377095i	0.736393	−	0.676554i	$-0.236527\pi$
$929$	−6.63588	−	11.4937i	−0.217716	−	0.377095i	−0.954109	+	0.299458i	$0.903194\pi$
$930$		0			0
$931$			11.7399i			0.384760i
$932$		0			0
$933$	0.527115	+	0.304330i	0.0172570	+	0.00996332i
$934$		0			0
$935$	−24.6101			−0.804838
$936$		0			0
$937$	2.64444			0.0863903			0.0431951	−	0.999067i	$-0.486246\pi$
$937$	2.64444			0.0863903			0.0431951	+	0.999067i	$0.486246\pi$
$938$		0			0
$939$	−3.14547	−	1.81604i	−0.102648	−	0.0592641i
$940$		0			0
$941$			28.1115i			0.916408i	0.888847	+	0.458204i	$0.151507\pi$
$941$			28.1115i			0.916408i	−0.888847	+	0.458204i	$0.848493\pi$
$942$		0			0
$943$	−2.90090	−	5.02450i	−0.0944662	−	0.163620i
$944$		0			0
$945$	9.82996	+	17.0260i	0.319768	+	0.553855i
$946$		0			0
$947$	−39.4200	−	22.7591i	−1.28098	−	0.739573i	−0.303951	−	0.952688i	$-0.598306\pi$
$947$	−39.4200	−	22.7591i	−1.28098	−	0.739573i	−0.977027	+	0.213115i	$0.931639\pi$
$948$		0			0
$949$	43.4902	−	5.61123i	1.41175	−	0.182148i
$950$		0			0
$951$	−3.42731	+	5.93627i	−0.111138	+	0.192497i
$952$		0			0
$953$	3.59780	+	6.23157i	0.116544	+	0.201860i	0.918396	−	0.395663i	$-0.129485\pi$
$953$	3.59780	+	6.23157i	0.116544	+	0.201860i	−0.801852	+	0.597523i	$0.796152\pi$
$954$		0			0
$955$	12.6510	−	7.30408i	0.409378	−	0.236355i
$956$		0			0
$957$		−	10.5259i		−	0.340253i
$958$		0			0
$959$	−0.100924	+	0.174805i	−0.00325899	+	0.00564474i
$960$		0			0
$961$	−11.3861			−0.367293
$962$		0			0
$963$			32.3930i			1.04385i
$964$		0			0
$965$	27.0748	+	15.6316i	0.871568	+	0.503200i
$966$		0			0
$967$	−10.5233			−0.338408			−0.169204	−	0.985581i	$-0.554120\pi$
$967$	−10.5233			−0.338408			−0.169204	+	0.985581i	$0.554120\pi$
$968$		0			0
$969$	4.83285	+	8.37074i	0.155254	+	0.268907i
$970$		0			0
$971$	5.96165	−	3.44196i	0.191319	−	0.110458i	−0.401281	−	0.915955i	$-0.631435\pi$
$971$	5.96165	−	3.44196i	0.191319	−	0.110458i	0.592600	+	0.805497i	$0.298102\pi$
$972$		0			0
$973$	43.5114	+	25.1213i	1.39491	+	0.805352i
$974$		0			0
$975$	−3.56837	−	1.48889i	−0.114279	−	0.0476826i
$976$		0			0
$977$	4.89362	−	8.47599i	0.156561	−	0.271171i	−0.777066	−	0.629420i	$-0.783293\pi$
$977$	4.89362	−	8.47599i	0.156561	−	0.271171i	0.933626	+	0.358249i	$0.116626\pi$
$978$		0			0
$979$	25.1620	−	14.5273i	0.804182	−	0.464295i
$980$		0			0
$981$	17.0052	−	9.81798i	0.542935	−	0.313464i
$982$		0			0
$983$	19.2063			0.612586			0.306293	−	0.951937i	$-0.400911\pi$
$983$	19.2063			0.612586			0.306293	+	0.951937i	$0.400911\pi$
$984$		0			0
$985$	−3.95459	+	6.84956i	−0.126004	+	0.218245i
$986$		0			0
$987$		−	17.2149i		−	0.547956i
$988$		0			0
$989$			26.4947i			0.842483i
$990$		0			0
$991$	−11.1847	+	19.3725i	−0.355295	+	0.615389i	−0.987168	−	0.159683i	$-0.948953\pi$
$991$	−11.1847	+	19.3725i	−0.355295	+	0.615389i	0.631873	+	0.775072i	$0.282286\pi$
$992$		0			0
$993$	−17.6823			−0.561130
$994$		0			0
$995$	−18.8697	+	10.8944i	−0.598209	+	0.345376i
$996$		0			0
$997$	39.2759	−	22.6759i	1.24388	−	0.718154i	0.273998	−	0.961730i	$-0.411654\pi$
$997$	39.2759	−	22.6759i	1.24388	−	0.718154i	0.969882	+	0.243576i	$0.0783206\pi$
$998$		0			0
$999$	6.96510	−	12.0639i	0.220366	−	0.381685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.z.a.113.6		24
4.3	odd	2		104.2.r.a.61.3	yes	24
8.3	odd	2		104.2.r.a.61.11	yes	24
8.5	even	2	inner	416.2.z.a.113.7		24
12.11	even	2		936.2.be.a.685.10		24
13.3	even	3	inner	416.2.z.a.81.7		24
24.11	even	2		936.2.be.a.685.2		24
52.3	odd	6		104.2.r.a.29.11	yes	24
104.3	odd	6		104.2.r.a.29.3	✓	24
104.29	even	6	inner	416.2.z.a.81.6		24
156.107	even	6		936.2.be.a.757.2		24
312.107	even	6		936.2.be.a.757.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.3	✓	24	104.3	odd	6
104.2.r.a.29.11	yes	24	52.3	odd	6
104.2.r.a.61.3	yes	24	4.3	odd	2
104.2.r.a.61.11	yes	24	8.3	odd	2
416.2.z.a.81.6		24	104.29	even	6	inner
416.2.z.a.81.7		24	13.3	even	3	inner
416.2.z.a.113.6		24	1.1	even	1	trivial
416.2.z.a.113.7		24	8.5	even	2	inner
936.2.be.a.685.2		24	24.11	even	2
936.2.be.a.685.10		24	12.11	even	2
936.2.be.a.757.2		24	156.107	even	6
936.2.be.a.757.10		24	312.107	even	6

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.509400 - 0.294102i) q^{3} +1.78237i q^{5} +(-1.65832 - 2.87229i) q^{7} +(-1.32701 - 2.29844i) q^{9} +(-2.13570 - 1.23305i) q^{11} +(3.57591 - 0.461374i) q^{13} +(0.524200 - 0.907941i) q^{15} +(-2.79947 - 4.84883i) q^{17} +(2.54173 - 1.46747i) q^{19} +1.95086i q^{21} +(1.21868 - 2.11082i) q^{23} +1.82314 q^{25} +3.32572i q^{27} +(-6.28420 - 3.62819i) q^{29} +4.42876 q^{31} +(0.725283 + 1.25623i) q^{33} +(5.11949 - 2.95574i) q^{35} +(-3.62746 - 2.09432i) q^{37} +(-1.95726 - 0.816660i) q^{39} +(1.19018 - 2.06145i) q^{41} +(-9.41391 + 5.43512i) q^{43} +(4.09669 - 2.36522i) q^{45} -8.82426 q^{47} +(-2.00003 + 3.46415i) q^{49} +3.29333i q^{51} -1.32698i q^{53} +(2.19775 - 3.80661i) q^{55} -1.72634 q^{57} +(4.50116 - 2.59874i) q^{59} +(-1.38839 + 0.801590i) q^{61} +(-4.40120 + 7.62310i) q^{63} +(0.822340 + 6.37361i) q^{65} +(10.0039 + 5.77577i) q^{67} +(-1.24159 + 0.716834i) q^{69} +(5.07044 + 8.78227i) q^{71} +12.1620 q^{73} +(-0.928710 - 0.536191i) q^{75} +8.17912i q^{77} +7.72073 q^{79} +(-3.00292 + 5.20121i) q^{81} -6.77111i q^{83} +(8.64243 - 4.98971i) q^{85} +(2.13412 + 3.69640i) q^{87} +(-5.89082 + 10.2032i) q^{89} +(-7.25519 - 9.50594i) q^{91} +(-2.25601 - 1.30251i) q^{93} +(2.61558 + 4.53031i) q^{95} +(-3.17980 - 5.50758i) q^{97} +6.54505i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{7} + 6 q^{9} - 4 q^{15} + 14 q^{23} - 12 q^{25} + 8 q^{31} - 14 q^{33} + 34 q^{39} - 4 q^{41} + 8 q^{47} + 6 q^{49} - 8 q^{55} - 52 q^{57} - 32 q^{63} + 30 q^{65} - 30 q^{71} - 12 q^{73} + 48 q^{79}+ \cdots + 2 q^{97}+O(q^{100}) \) 24 * q + 2 * q^7 + 6 * q^9 - 4 * q^15 + 14 * q^23 - 12 * q^25 + 8 * q^31 - 14 * q^33 + 34 * q^39 - 4 * q^41 + 8 * q^47 + 6 * q^49 - 8 * q^55 - 52 * q^57 - 32 * q^63 + 30 * q^65 - 30 * q^71 - 12 * q^73 + 48 * q^79 + 8 * q^81 + 26 * q^87 - 22 * q^89 - 60 * q^95 + 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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