LMFDB - Embedded newform 76.8.e.a.45.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(45,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("76.45");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.e (of order $3$, degree $2$, 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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.10
Character	$\chi$	$=$	76.45
Dual form			76.8.e.a.49.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(36.8075 + 63.7525i) q^{3} +(-206.713 - 358.037i) q^{5} +601.253 q^{7} +(-1616.09 + 2799.14i) q^{9} +O(q^{10})$	\(q+(36.8075 + 63.7525i) q^{3} +(-206.713 - 358.037i) q^{5} +601.253 q^{7} +(-1616.09 + 2799.14i) q^{9} +3731.62 q^{11} +(5827.71 - 10093.9i) q^{13} +(15217.2 - 26356.9i) q^{15} +(2898.95 + 5021.12i) q^{17} +(26782.0 + 13289.0i) q^{19} +(22130.6 + 38331.4i) q^{21} +(8207.55 - 14215.9i) q^{23} +(-46397.9 + 80363.5i) q^{25} -76940.5 q^{27} +(-71206.7 + 123334. i) q^{29} +32380.4 q^{31} +(137352. + 237900. i) q^{33} +(-124287. - 215271. i) q^{35} +513418. q^{37} +858014. q^{39} +(277124. + 479993. i) q^{41} +(-345365. - 598190. i) q^{43} +1.33626e6 q^{45} +(321391. - 556666. i) q^{47} -462038. q^{49} +(-213406. + 369630. i) q^{51} +(-54614.1 + 94594.4i) q^{53} +(-771374. - 1.33606e6i) q^{55} +(138572. + 2.19655e6i) q^{57} +(1.46307e6 + 2.53412e6i) q^{59} +(559090. - 968372. i) q^{61} +(-971677. + 1.68299e6i) q^{63} -4.81865e6 q^{65} +(1.54690e6 - 2.67932e6i) q^{67} +1.20840e6 q^{69} +(228472. + 395725. i) q^{71} +(-3.18133e6 - 5.51023e6i) q^{73} -6.83116e6 q^{75} +2.24365e6 q^{77} +(1.45650e6 + 2.52273e6i) q^{79} +(702392. + 1.21658e6i) q^{81} -1.61367e6 q^{83} +(1.19850e6 - 2.07586e6i) q^{85} -1.04838e7 q^{87} +(105438. - 182624. i) q^{89} +(3.50393e6 - 6.06898e6i) q^{91} +(1.19184e6 + 2.06433e6i) q^{93} +(-778229. - 1.23359e7i) q^{95} +(2.28074e6 + 3.95035e6i) q^{97} +(-6.03062e6 + 1.04453e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 13 q^{3} + q^{5} + 560 q^{7} - 6002 q^{9}+O(q^{10}) $ 22 * q + 13 * q^3 + q^5 + 560 * q^7 - 6002 * q^9	$ 22 q + 13 q^{3} + q^{5} + 560 q^{7} - 6002 q^{9} + 472 q^{11} - 567 q^{13} + 2995 q^{15} + 5589 q^{17} + 80912 q^{19} + 44412 q^{21} - 15425 q^{23} - 32806 q^{25} + 50290 q^{27} - 18919 q^{29} + 150296 q^{31} + 314618 q^{33} + 92808 q^{35} + 350100 q^{37} + 948810 q^{39} + 698891 q^{41} + 402545 q^{43} + 1477508 q^{45} - 653621 q^{47} - 1938490 q^{49} - 1386401 q^{51} - 106763 q^{53} + 414508 q^{55} + 1267563 q^{57} + 3136737 q^{59} + 2004581 q^{61} + 1465000 q^{63} - 7397638 q^{65} + 4344391 q^{67} + 1732238 q^{69} - 133823 q^{71} - 8349685 q^{73} - 12136824 q^{75} + 9147480 q^{77} - 94679 q^{79} - 838595 q^{81} - 2884080 q^{83} - 1421409 q^{85} - 31740598 q^{87} - 7039347 q^{89} + 1520096 q^{91} - 1993628 q^{93} + 1707587 q^{95} + 13308115 q^{97} + 6011488 q^{99}+O(q^{100}) $ 22 * q + 13 * q^3 + q^5 + 560 * q^7 - 6002 * q^9 + 472 * q^11 - 567 * q^13 + 2995 * q^15 + 5589 * q^17 + 80912 * q^19 + 44412 * q^21 - 15425 * q^23 - 32806 * q^25 + 50290 * q^27 - 18919 * q^29 + 150296 * q^31 + 314618 * q^33 + 92808 * q^35 + 350100 * q^37 + 948810 * q^39 + 698891 * q^41 + 402545 * q^43 + 1477508 * q^45 - 653621 * q^47 - 1938490 * q^49 - 1386401 * q^51 - 106763 * q^53 + 414508 * q^55 + 1267563 * q^57 + 3136737 * q^59 + 2004581 * q^61 + 1465000 * q^63 - 7397638 * q^65 + 4344391 * q^67 + 1732238 * q^69 - 133823 * q^71 - 8349685 * q^73 - 12136824 * q^75 + 9147480 * q^77 - 94679 * q^79 - 838595 * q^81 - 2884080 * q^83 - 1421409 * q^85 - 31740598 * q^87 - 7039347 * q^89 + 1520096 * q^91 - 1993628 * q^93 + 1707587 * q^95 + 13308115 * q^97 + 6011488 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	36.8075	+	63.7525i	0.787068	+	1.36324i	0.927756	+	0.373188i	$0.121735\pi$
$3$	36.8075	+	63.7525i	0.787068	+	1.36324i	−0.140688	+	0.990054i	$0.544931\pi$
$4$		0			0
$5$	−206.713	−	358.037i	−0.739558	−	1.28095i	−0.952694	−	0.303930i	$-0.901701\pi$
$5$	−206.713	−	358.037i	−0.739558	−	1.28095i	0.213136	−	0.977023i	$-0.431632\pi$
$6$		0			0
$7$	601.253			0.662543			0.331272	−	0.943535i	$-0.392522\pi$
$7$	601.253			0.662543			0.331272	+	0.943535i	$0.392522\pi$
$8$		0			0
$9$	−1616.09	+	2799.14i	−0.738952	+	1.27990i
$10$		0			0
$11$	3731.62			0.845324			0.422662	−	0.906287i	$-0.361096\pi$
$11$	3731.62			0.845324			0.422662	+	0.906287i	$0.361096\pi$
$12$		0			0
$13$	5827.71	−	10093.9i	0.735692	−	1.27426i	−0.218727	−	0.975786i	$-0.570190\pi$
$13$	5827.71	−	10093.9i	0.735692	−	1.27426i	0.954419	−	0.298470i	$-0.0964764\pi$
$14$		0			0
$15$	15217.2	−	26356.9i	1.16417	−	2.01639i
$16$		0			0
$17$	2898.95	+	5021.12i	0.143110	+	0.247873i	0.928666	−	0.370917i	$-0.120957\pi$
$17$	2898.95	+	5021.12i	0.143110	+	0.247873i	−0.785556	+	0.618790i	$0.787623\pi$
$18$		0			0
$19$	26782.0	+	13289.0i	0.895788	+	0.444482i
$19$	26782.0	+	13289.0i	0.895788	+	0.444482i
$20$		0			0
$21$	22130.6	+	38331.4i	0.521466	+	0.903206i
$22$		0			0
$23$	8207.55	−	14215.9i	0.140659	−	0.243628i	−0.787086	−	0.616843i	$-0.788411\pi$
$23$	8207.55	−	14215.9i	0.140659	−	0.243628i	0.927745	+	0.373215i	$0.121745\pi$
$24$		0			0
$25$	−46397.9	+	80363.5i	−0.593893	+	1.02865i
$26$		0			0
$27$	−76940.5			−0.752284
$28$		0			0
$29$	−71206.7	+	123334.i	−0.542161	+	0.939050i	0.456619	+	0.889662i	$0.349060\pi$
$29$	−71206.7	+	123334.i	−0.542161	+	0.939050i	−0.998780	+	0.0493876i	$0.984273\pi$
$30$		0			0
$31$	32380.4			0.195217			0.0976083	−	0.995225i	$-0.468881\pi$
$31$	32380.4			0.195217			0.0976083	+	0.995225i	$0.468881\pi$
$32$		0			0
$33$	137352.	+	237900.i	0.665327	+	1.15238i
$34$		0			0
$35$	−124287.	−	215271.i	−0.489989	−	0.848686i
$36$		0			0
$37$	513418.			1.66634			0.833172	−	0.553013i	$-0.186522\pi$
$37$	513418.			1.66634			0.833172	+	0.553013i	$0.186522\pi$
$38$		0			0
$39$	858014.			2.31616
$40$		0			0
$41$	277124.	+	479993.i	0.627958	+	1.08765i	0.987961	+	0.154704i	$0.0494423\pi$
$41$	277124.	+	479993.i	0.627958	+	1.08765i	−0.360003	+	0.932951i	$0.617224\pi$
$42$		0			0
$43$	−345365.	−	598190.i	−0.662428	−	1.14736i	−0.979976	−	0.199117i	$-0.936193\pi$
$43$	−345365.	−	598190.i	−0.662428	−	1.14736i	0.317547	−	0.948242i	$-0.397141\pi$
$44$		0			0
$45$	1.33626e6			2.18599
$46$		0			0
$47$	321391.	−	556666.i	0.451535	−	0.782082i	−0.546947	−	0.837167i	$-0.684210\pi$
$47$	321391.	−	556666.i	0.451535	−	0.782082i	0.998482	+	0.0550859i	$0.0175433\pi$
$48$		0			0
$49$	−462038.			−0.561037
$50$		0			0
$51$	−213406.	+	369630.i	−0.225274	+	0.390186i
$52$		0			0
$53$	−54614.1	+	94594.4i	−0.0503894	+	0.0872771i	−0.890120	−	0.455726i	$-0.849380\pi$
$53$	−54614.1	+	94594.4i	−0.0503894	+	0.0872771i	0.839731	+	0.543003i	$0.182713\pi$
$54$		0			0
$55$	−771374.	−	1.33606e6i	−0.625166	−	1.08282i
$56$		0			0
$57$	138572.	+	2.19655e6i	0.0991093	+	1.57101i
$58$		0			0
$59$	1.46307e6	+	2.53412e6i	0.927436	+	1.60637i	0.787596	+	0.616191i	$0.211325\pi$
$59$	1.46307e6	+	2.53412e6i	0.927436	+	1.60637i	0.139839	+	0.990174i	$0.455341\pi$
$60$		0			0
$61$	559090.	−	968372.i	0.315375	−	0.546245i	−0.664142	−	0.747606i	$-0.731203\pi$
$61$	559090.	−	968372.i	0.315375	−	0.546245i	0.979517	+	0.201361i	$0.0645364\pi$
$62$		0			0
$63$	−971677.	+	1.68299e6i	−0.489587	+	0.847990i
$64$		0			0
$65$	−4.81865e6			−2.17635
$66$		0			0
$67$	1.54690e6	−	2.67932e6i	0.628350	−	1.08833i	−0.359533	−	0.933132i	$-0.617064\pi$
$67$	1.54690e6	−	2.67932e6i	0.628350	−	1.08833i	0.987883	−	0.155201i	$-0.0496026\pi$
$68$		0			0
$69$	1.20840e6			0.442831
$70$		0			0
$71$	228472.	+	395725.i	0.0757581	+	0.131217i	0.901416	−	0.432955i	$-0.142529\pi$
$71$	228472.	+	395725.i	0.0757581	+	0.131217i	−0.825658	+	0.564172i	$0.809196\pi$
$72$		0			0
$73$	−3.18133e6	−	5.51023e6i	−0.957148	−	1.65783i	−0.729374	−	0.684116i	$-0.760188\pi$
$73$	−3.18133e6	−	5.51023e6i	−0.957148	−	1.65783i	−0.227775	−	0.973714i	$-0.573145\pi$
$74$		0			0
$75$	−6.83116e6			−1.86974
$76$		0			0
$77$	2.24365e6			0.560064
$78$		0			0
$79$	1.45650e6	+	2.52273e6i	0.332365	+	0.575673i	0.982975	−	0.183739i	$-0.0588200\pi$
$79$	1.45650e6	+	2.52273e6i	0.332365	+	0.575673i	−0.650610	+	0.759412i	$0.725487\pi$
$80$		0			0
$81$	702392.	+	1.21658e6i	0.146853	+	0.254356i
$82$		0			0
$83$	−1.61367e6			−0.309771			−0.154885	−	0.987932i	$-0.549501\pi$
$83$	−1.61367e6			−0.309771			−0.154885	+	0.987932i	$0.549501\pi$
$84$		0			0
$85$	1.19850e6	−	2.07586e6i	0.211676	−	0.366633i
$86$		0			0
$87$	−1.04838e7			−1.70687
$88$		0			0
$89$	105438.	−	182624.i	0.0158538	−	0.0274596i	−0.857990	−	0.513667i	$-0.828287\pi$
$89$	105438.	−	182624.i	0.0158538	−	0.0274596i	0.873843	+	0.486207i	$0.161620\pi$
$90$		0			0
$91$	3.50393e6	−	6.06898e6i	0.487428	−	0.844250i
$92$		0			0
$93$	1.19184e6	+	2.06433e6i	0.153649	+	0.266127i
$94$		0			0
$95$	−778229.	−	1.23359e7i	−0.0931268	−	1.47618i
$96$		0			0
$97$	2.28074e6	+	3.95035e6i	0.253731	+	0.439475i	0.964550	−	0.263900i	$-0.0850088\pi$
$97$	2.28074e6	+	3.95035e6i	0.253731	+	0.439475i	−0.710819	+	0.703375i	$0.751675\pi$
$98$		0			0
$99$	−6.03062e6	+	1.04453e7i	−0.624653	+	1.08193i
$100$		0			0
$101$	3.94086e6	−	6.82577e6i	0.380598	−	0.659215i	−0.610550	−	0.791978i	$-0.709052\pi$
$101$	3.94086e6	−	6.82577e6i	0.380598	−	0.659215i	0.991148	+	0.132763i	$0.0423849\pi$
$102$		0			0
$103$	−1.07590e7			−0.970157			−0.485078	−	0.874471i	$-0.661209\pi$
$103$	−1.07590e7			−0.970157			−0.485078	+	0.874471i	$0.661209\pi$
$104$		0			0
$105$	9.14937e6	−	1.58472e7i	0.771310	−	1.33595i
$106$		0			0
$107$	9.38681e6			0.740755			0.370378	−	0.928881i	$-0.379228\pi$
$107$	9.38681e6			0.740755			0.370378	+	0.928881i	$0.379228\pi$
$108$		0			0
$109$	−1.13818e7	−	1.97139e7i	−0.841821	−	1.45808i	−0.888354	−	0.459159i	$-0.848151\pi$
$109$	−1.13818e7	−	1.97139e7i	−0.841821	−	1.45808i	0.0465332	−	0.998917i	$-0.485183\pi$
$110$		0			0
$111$	1.88976e7	+	3.27317e7i	1.31153	+	2.27163i
$112$		0			0
$113$	−2.93609e7			−1.91423			−0.957117	−	0.289701i	$-0.906444\pi$
$113$	−2.93609e7			−1.91423			−0.957117	+	0.289701i	$0.906444\pi$
$114$		0			0
$115$	−6.78643e6			−0.416101
$116$		0			0
$117$	1.88362e7	+	3.26252e7i	1.08728	+	1.88323i
$118$		0			0
$119$	1.74300e6	+	3.01896e6i	0.0948163	+	0.164227i
$120$		0			0
$121$	−5.56217e6			−0.285427
$122$		0			0
$123$	−2.04005e7	+	3.53347e7i	−0.988491	+	1.71212i
$124$		0			0
$125$	6.06527e6			0.277757
$126$		0			0
$127$	2.74085e6	−	4.74730e6i	0.118733	−	0.205652i	−0.800533	−	0.599289i	$-0.795450\pi$
$127$	2.74085e6	−	4.74730e6i	0.118733	−	0.205652i	0.919266	+	0.393637i	$0.128783\pi$
$128$		0			0
$129$	2.54241e7	−	4.40358e7i	1.04275	−	1.80610i
$130$		0			0
$131$	−8.42108e6	−	1.45857e7i	−0.327279	−	0.566864i	0.654692	−	0.755896i	$-0.272798\pi$
$131$	−8.42108e6	−	1.45857e7i	−0.327279	−	0.566864i	−0.981971	+	0.189032i	$0.939465\pi$
$132$		0			0
$133$	1.61027e7	+	7.99004e6i	0.593498	+	0.294489i
$134$		0			0
$135$	1.59046e7	+	2.75476e7i	0.556358	+	0.963641i
$136$		0			0
$137$	1.26119e7	−	2.18445e7i	0.419043	−	0.725804i	−0.576800	−	0.816885i	$-0.695699\pi$
$137$	1.26119e7	−	2.18445e7i	0.419043	−	0.725804i	0.995843	+	0.0910810i	$0.0290322\pi$
$138$		0			0
$139$	−2.79447e7	+	4.84017e7i	−0.882568	+	1.52865i	−0.0340921	+	0.999419i	$0.510854\pi$
$139$	−2.79447e7	+	4.84017e7i	−0.882568	+	1.52865i	−0.848476	+	0.529234i	$0.822479\pi$
$140$		0			0
$141$	4.73184e7			1.42155
$142$		0			0
$143$	2.17468e7	−	3.76666e7i	0.621898	−	1.07716i
$144$		0			0
$145$	5.88774e7			1.60384
$146$		0			0
$147$	−1.70065e7	−	2.94561e7i	−0.441574	−	0.764828i
$148$		0			0
$149$	2.42533e7	+	4.20080e7i	0.600647	+	1.04035i	0.992723	+	0.120418i	$0.0384235\pi$
$149$	2.42533e7	+	4.20080e7i	0.600647	+	1.04035i	−0.392076	+	0.919933i	$0.628243\pi$
$150$		0			0
$151$	6.27480e7			1.48313			0.741567	−	0.670879i	$-0.234083\pi$
$151$	6.27480e7			1.48313			0.741567	+	0.670879i	$0.234083\pi$
$152$		0			0
$153$	−1.87398e7			−0.423004
$154$		0			0
$155$	−6.69345e6	−	1.15934e7i	−0.144374	−	0.250063i
$156$		0			0
$157$	−2.34795e7	−	4.06677e7i	−0.484217	−	0.838688i	0.515619	−	0.856818i	$-0.327562\pi$
$157$	−2.34795e7	−	4.06677e7i	−0.484217	−	0.838688i	−0.999836	+	0.0181299i	$0.994229\pi$
$158$		0			0
$159$	−8.04084e6			−0.158640
$160$		0			0
$161$	4.93482e6	−	8.54735e6i	0.0931924	−	0.161414i
$162$		0			0
$163$	3.85645e7			0.697478			0.348739	−	0.937220i	$-0.386610\pi$
$163$	3.85645e7			0.697478			0.348739	+	0.937220i	$0.386610\pi$
$164$		0			0
$165$	5.67847e7	−	9.83540e7i	0.984097	−	1.70451i
$166$		0			0
$167$	−3.02675e7	+	5.24248e7i	−0.502885	+	0.871023i	0.497109	+	0.867688i	$0.334395\pi$
$167$	−3.02675e7	+	5.24248e7i	−0.502885	+	0.871023i	−0.999994	+	0.00333465i	$0.998939\pi$
$168$		0			0
$169$	−3.65502e7	−	6.33067e7i	−0.582486	−	1.00890i
$170$		0			0
$171$	−8.04798e7	+	5.34905e7i	−1.23084	+	0.818069i
$172$		0			0
$173$	3.81759e7	+	6.61227e7i	0.560568	+	0.970932i	0.997447	+	0.0714120i	$0.0227505\pi$
$173$	3.81759e7	+	6.61227e7i	0.560568	+	0.970932i	−0.436879	+	0.899520i	$0.643916\pi$
$174$		0			0
$175$	−2.78969e7	+	4.83188e7i	−0.393480	+	0.681527i
$176$		0			0
$177$	−1.07704e8	+	1.86549e8i	−1.45991	+	2.52864i
$178$		0			0
$179$	−1.35644e8			−1.76773			−0.883865	−	0.467742i	$-0.845068\pi$
$179$	−1.35644e8			−1.76773			−0.883865	+	0.467742i	$0.845068\pi$
$180$		0			0
$181$	−4.86084e7	+	8.41921e7i	−0.609307	+	1.05535i	0.382048	+	0.924142i	$0.375219\pi$
$181$	−4.86084e7	+	8.41921e7i	−0.609307	+	1.05535i	−0.991355	+	0.131208i	$0.958115\pi$
$182$		0			0
$183$	8.23148e7			0.992886
$184$		0			0
$185$	−1.06130e8	−	1.83823e8i	−1.23236	−	2.13451i
$186$		0			0
$187$	1.08178e7	+	1.87369e7i	0.120974	+	0.209533i
$188$		0			0
$189$	−4.62607e7			−0.498421
$190$		0			0
$191$	−1.10884e8			−1.15147			−0.575733	−	0.817638i	$-0.695283\pi$
$191$	−1.10884e8			−1.15147			−0.575733	+	0.817638i	$0.695283\pi$
$192$		0			0
$193$	6.18556e7	+	1.07137e8i	0.619339	+	1.07273i	0.989606	+	0.143802i	$0.0459329\pi$
$193$	6.18556e7	+	1.07137e8i	0.619339	+	1.07273i	−0.370267	+	0.928925i	$0.620734\pi$
$194$		0			0
$195$	−1.77363e8	−	3.07201e8i	−1.71293	−	2.96689i
$196$		0			0
$197$	−1.48210e7			−0.138116			−0.0690581	−	0.997613i	$-0.521999\pi$
$197$	−1.48210e7			−0.138116			−0.0690581	+	0.997613i	$0.521999\pi$
$198$		0			0
$199$	4.04662e7	−	7.00895e7i	0.364004	−	0.630474i	−0.624612	−	0.780936i	$-0.714743\pi$
$199$	4.04662e7	−	7.00895e7i	0.364004	−	0.630474i	0.988616	+	0.150462i	$0.0480760\pi$
$200$		0			0
$201$	2.27751e8			1.97822
$202$		0			0
$203$	−4.28133e7	+	7.41548e7i	−0.359205	+	0.622161i
$204$		0			0
$205$	1.14570e8	−	1.98441e8i	0.928823	−	1.60877i
$206$		0			0
$207$	2.65282e7	+	4.59483e7i	0.207880	+	0.360058i
$208$		0			0
$209$	9.99402e7	+	4.95895e7i	0.757231	+	0.375731i
$210$		0			0
$211$	−8.43487e7	−	1.46096e8i	−0.618144	−	1.07066i	−0.989824	−	0.142296i	$-0.954551\pi$
$211$	−8.43487e7	−	1.46096e8i	−0.618144	−	1.07066i	0.371680	−	0.928361i	$-0.378782\pi$
$212$		0			0
$213$	−1.68190e7	+	2.91313e7i	−0.119254	+	0.206553i
$214$		0			0
$215$	−1.42783e8	+	2.47307e8i	−0.979809	+	1.69708i
$216$		0			0
$217$	1.94688e7			0.129339
$218$		0			0
$219$	2.34194e8	−	4.05636e8i	1.50668	−	2.60965i
$220$		0			0
$221$	6.75768e7			0.421139
$222$		0			0
$223$	6.83025e7	+	1.18303e8i	0.412448	+	0.714382i	0.995157	−	0.0982997i	$-0.0313404\pi$
$223$	6.83025e7	+	1.18303e8i	0.412448	+	0.714382i	−0.582708	+	0.812681i	$0.698007\pi$
$224$		0			0
$225$	−1.49966e8	−	2.59749e8i	−0.877716	−	1.52025i
$226$		0			0
$227$	1.33074e7			0.0755097			0.0377549	−	0.999287i	$-0.487979\pi$
$227$	1.33074e7			0.0755097			0.0377549	+	0.999287i	$0.487979\pi$
$228$		0			0
$229$	−2.78054e8			−1.53005			−0.765024	−	0.644002i	$-0.777273\pi$
$229$	−2.78054e8			−1.53005			−0.765024	+	0.644002i	$0.777273\pi$
$230$		0			0
$231$	8.25831e7	+	1.43038e8i	0.440808	+	0.763502i
$232$		0			0
$233$	9.18937e7	+	1.59164e8i	0.475926	+	0.824329i	0.999620	−	0.0275781i	$-0.00877951\pi$
$233$	9.18937e7	+	1.59164e8i	0.475926	+	0.824329i	−0.523693	+	0.851907i	$0.675446\pi$
$234$		0			0
$235$	−2.65743e8			−1.33575
$236$		0			0
$237$	−1.07220e8	+	1.85711e8i	−0.523188	+	0.906188i
$238$		0			0
$239$	1.36523e8			0.646866			0.323433	−	0.946251i	$-0.395163\pi$
$239$	1.36523e8			0.646866			0.323433	+	0.946251i	$0.395163\pi$
$240$		0			0
$241$	−8.48172e7	+	1.46908e8i	−0.390323	+	0.676059i	−0.992492	−	0.122309i	$-0.960970\pi$
$241$	−8.48172e7	+	1.46908e8i	−0.390323	+	0.676059i	0.602169	+	0.798369i	$0.294303\pi$
$242$		0			0
$243$	−1.35841e8	+	2.35284e8i	−0.607308	+	1.05189i
$244$		0			0
$245$	9.55091e7	+	1.65427e8i	0.414919	+	0.718661i
$246$		0			0
$247$	2.90215e8	−	1.92890e8i	1.22541	−	0.814461i
$248$		0			0
$249$	−5.93951e7	−	1.02875e8i	−0.243811	−	0.422293i
$250$		0			0
$251$	−1.93343e8	+	3.34879e8i	−0.771738	+	1.33669i	0.164872	+	0.986315i	$0.447279\pi$
$251$	−1.93343e8	+	3.34879e8i	−0.771738	+	1.33669i	−0.936610	+	0.350374i	$0.886054\pi$
$252$		0			0
$253$	3.06275e7	−	5.30484e7i	0.118902	−	0.205944i
$254$		0			0
$255$	1.76455e8			0.666413
$256$		0			0
$257$	1.19660e8	−	2.07257e8i	0.439726	−	0.761627i	−0.557942	−	0.829880i	$-0.688409\pi$
$257$	1.19660e8	−	2.07257e8i	0.439726	−	0.761627i	0.997668	+	0.0682525i	$0.0217424\pi$
$258$		0			0
$259$	3.08694e8			1.10403
$260$		0			0
$261$	−2.30153e8	−	3.98636e8i	−0.801261	−	1.38782i
$262$		0			0
$263$	4.31787e6	+	7.47878e6i	0.0146361	+	0.0253504i	0.873251	−	0.487271i	$-0.162008\pi$
$263$	4.31787e6	+	7.47878e6i	0.0146361	+	0.0253504i	−0.858615	+	0.512622i	$0.828674\pi$
$264$		0			0
$265$	4.51578e7			0.149064
$266$		0			0
$267$	1.55237e7			0.0499120
$268$		0			0
$269$	1.36030e8	+	2.35611e8i	0.426090	+	0.738010i	0.996522	−	0.0833352i	$-0.0265572\pi$
$269$	1.36030e8	+	2.35611e8i	0.426090	+	0.738010i	−0.570431	+	0.821345i	$0.693224\pi$
$270$		0			0
$271$	9.21018e7	+	1.59525e8i	0.281110	+	0.486896i	0.971658	−	0.236390i	$-0.0759642\pi$
$271$	9.21018e7	+	1.59525e8i	0.281110	+	0.486896i	−0.690549	+	0.723286i	$0.742631\pi$
$272$		0			0
$273$	5.15884e8			1.53456
$274$		0			0
$275$	−1.73139e8	+	2.99886e8i	−0.502032	+	0.869545i
$276$		0			0
$277$	1.27753e8			0.361154			0.180577	−	0.983561i	$-0.442204\pi$
$277$	1.27753e8			0.361154			0.180577	+	0.983561i	$0.442204\pi$
$278$		0			0
$279$	−5.23296e7	+	9.06375e7i	−0.144256	+	0.249858i
$280$		0			0
$281$	−1.11377e8	+	1.92910e8i	−0.299449	+	0.518660i	−0.976010	−	0.217726i	$-0.930136\pi$
$281$	−1.11377e8	+	1.92910e8i	−0.299449	+	0.518660i	0.676561	+	0.736386i	$0.263469\pi$
$282$		0			0
$283$	2.96369e8	+	5.13327e8i	0.777286	+	1.34630i	0.933501	+	0.358575i	$0.116737\pi$
$283$	2.96369e8	+	5.13327e8i	0.777286	+	1.34630i	−0.156215	+	0.987723i	$0.549929\pi$
$284$		0			0
$285$	7.57803e8	−	5.03670e8i	1.93910	−	1.28881i
$286$		0			0
$287$	1.66622e8	+	2.88597e8i	0.416049	+	0.720618i
$288$		0			0
$289$	1.88362e8	−	3.26252e8i	0.459039	−	0.795079i
$290$		0			0
$291$	−1.67896e8	+	2.90805e8i	−0.399407	+	0.691794i
$292$		0			0
$293$	−8.00352e8			−1.85885			−0.929425	−	0.369011i	$-0.879696\pi$
$293$	−8.00352e8			−1.85885			−0.929425	+	0.369011i	$0.879696\pi$
$294$		0			0
$295$	6.04872e8	−	1.04767e9i	1.37179	−	2.37600i
$296$		0			0
$297$	−2.87113e8			−0.635924
$298$		0			0
$299$	−9.56625e7	−	1.65692e8i	−0.206963	−	0.358470i
$300$		0			0
$301$	−2.07652e8	−	3.59664e8i	−0.438887	−	0.760175i
$302$		0			0
$303$	5.80213e8			1.19823
$304$		0			0
$305$	−4.62284e8			−0.932952
$306$		0			0
$307$	−1.03504e8	−	1.79275e8i	−0.204162	−	0.353618i	0.745704	−	0.666278i	$-0.232113\pi$
$307$	−1.03504e8	−	1.79275e8i	−0.204162	−	0.353618i	−0.949865	+	0.312660i	$0.898780\pi$
$308$		0			0
$309$	−3.96012e8	−	6.85914e8i	−0.763579	−	1.32256i
$310$		0			0
$311$	−1.18238e8			−0.222892			−0.111446	−	0.993770i	$-0.535548\pi$
$311$	−1.18238e8			−0.222892			−0.111446	+	0.993770i	$0.535548\pi$
$312$		0			0
$313$	−2.88478e8	+	4.99659e8i	−0.531751	+	0.921019i	0.467562	+	0.883960i	$0.345132\pi$
$313$	−2.88478e8	+	4.99659e8i	−0.531751	+	0.921019i	−0.999313	+	0.0370592i	$0.988201\pi$
$314$		0			0
$315$	8.03433e8			1.44831
$316$		0			0
$317$	−3.85567e8	+	6.67822e8i	−0.679818	+	1.17748i	0.295218	+	0.955430i	$0.404608\pi$
$317$	−3.85567e8	+	6.67822e8i	−0.679818	+	1.17748i	−0.975036	+	0.222049i	$0.928726\pi$
$318$		0			0
$319$	−2.65717e8	+	4.60235e8i	−0.458301	+	0.793801i
$320$		0			0
$321$	3.45505e8	+	5.98432e8i	0.583024	+	1.00983i
$322$		0			0
$323$	1.09139e7	+	1.73000e8i	0.0180207	+	0.285651i
$324$		0			0
$325$	5.40787e8	+	9.36670e8i	0.873845	+	1.51354i
$326$		0			0
$327$	8.37874e8	−	1.45124e9i	1.32514	−	2.29521i
$328$		0			0
$329$	1.93237e8	−	3.34697e8i	0.299161	−	0.518163i
$330$		0			0
$331$	1.61558e8			0.244867			0.122434	−	0.992477i	$-0.460930\pi$
$331$	1.61558e8			0.244867			0.122434	+	0.992477i	$0.460930\pi$
$332$		0			0
$333$	−8.29728e8	+	1.43713e9i	−1.23135	+	2.13276i
$334$		0			0
$335$	−1.27906e9			−1.85881
$336$		0			0
$337$	−2.71000e8	−	4.69386e8i	−0.385714	−	0.668076i	0.606154	−	0.795347i	$-0.292711\pi$
$337$	−2.71000e8	−	4.69386e8i	−0.385714	−	0.668076i	−0.991868	+	0.127271i	$0.959378\pi$
$338$		0			0
$339$	−1.08070e9	−	1.87183e9i	−1.50663	−	2.60956i
$340$		0			0
$341$	1.20832e8			0.165021
$342$		0			0
$343$	−7.72959e8			−1.03425
$344$		0			0
$345$	−2.49792e8	−	4.32652e8i	−0.327500	−	0.567246i
$346$		0			0
$347$	−2.60755e8	−	4.51642e8i	−0.335027	−	0.580284i	0.648463	−	0.761246i	$-0.275412\pi$
$347$	−2.60755e8	−	4.51642e8i	−0.335027	−	0.580284i	−0.983490	+	0.180962i	$0.942079\pi$
$348$		0			0
$349$	−3.06680e8			−0.386186			−0.193093	−	0.981180i	$-0.561852\pi$
$349$	−3.06680e8			−0.386186			−0.193093	+	0.981180i	$0.561852\pi$
$350$		0			0
$351$	−4.48387e8	+	7.76629e8i	−0.553450	+	0.958603i
$352$		0			0
$353$	4.54510e8			0.549961			0.274980	−	0.961450i	$-0.411329\pi$
$353$	4.54510e8			0.549961			0.274980	+	0.961450i	$0.411329\pi$
$354$		0			0
$355$	9.44563e7	−	1.63603e8i	0.112055	−	0.194085i
$356$		0			0
$357$	−1.28311e8	+	2.22241e8i	−0.149254	+	0.258515i
$358$		0			0
$359$	−7.41126e8	−	1.28367e9i	−0.845398	−	1.46427i	−0.885275	−	0.465068i	$-0.846030\pi$
$359$	−7.41126e8	−	1.28367e9i	−0.845398	−	1.46427i	0.0398768	−	0.999205i	$-0.487303\pi$
$360$		0			0
$361$	5.40677e8	+	7.11811e8i	0.604871	+	0.796323i
$362$		0			0
$363$	−2.04730e8	−	3.54602e8i	−0.224651	−	0.389107i
$364$		0			0
$365$	−1.31524e9	+	2.27807e9i	−1.41573	+	2.45212i
$366$		0			0
$367$	1.59412e8	−	2.76109e8i	0.168341	−	0.291574i	−0.769496	−	0.638652i	$-0.779493\pi$
$367$	1.59412e8	−	2.76109e8i	0.168341	−	0.291574i	0.937837	+	0.347077i	$0.112826\pi$
$368$		0			0
$369$	−1.79143e9			−1.85612
$370$		0			0
$371$	−3.28369e7	+	5.68752e7i	−0.0333852	+	0.0578248i
$372$		0			0
$373$	−1.47989e7			−0.0147655			−0.00738275	−	0.999973i	$-0.502350\pi$
$373$	−1.47989e7			−0.0147655			−0.00738275	+	0.999973i	$0.502350\pi$
$374$		0			0
$375$	2.23247e8	+	3.86676e8i	0.218614	+	0.378650i
$376$		0			0
$377$	8.29944e8	+	1.43751e9i	0.797727	+	1.38170i
$378$		0			0
$379$	1.57908e9			1.48993			0.744966	−	0.667102i	$-0.232466\pi$
$379$	1.57908e9			1.48993			0.744966	+	0.667102i	$0.232466\pi$
$380$		0			0
$381$	4.03536e8			0.373805
$382$		0			0
$383$	−8.95363e8	−	1.55081e9i	−0.814335	−	1.41047i	−0.909804	−	0.415037i	$-0.863768\pi$
$383$	−8.95363e8	−	1.55081e9i	−0.814335	−	1.41047i	0.0954691	−	0.995432i	$-0.469565\pi$
$384$		0			0
$385$	−4.63791e8	−	8.03309e8i	−0.414200	−	0.717415i
$386$		0			0
$387$	2.23256e9			1.95801
$388$		0			0
$389$	3.54888e8	−	6.14685e8i	0.305681	−	0.529455i	−0.671732	−	0.740794i	$-0.734449\pi$
$389$	3.54888e8	−	6.14685e8i	0.305681	−	0.529455i	0.977413	+	0.211340i	$0.0677826\pi$
$390$		0			0
$391$	9.51730e7			0.0805184
$392$		0			0
$393$	6.19918e8	−	1.07373e9i	0.515181	−	0.892320i
$394$		0			0
$395$	6.02154e8	−	1.04296e9i	0.491607	−	0.851488i
$396$		0			0
$397$	−1.87108e7	−	3.24081e7i	−0.0150081	−	0.0259948i	0.858424	−	0.512941i	$-0.171444\pi$
$397$	−1.87108e7	−	3.24081e7i	−0.0150081	−	0.0259948i	−0.873432	+	0.486946i	$0.838111\pi$
$398$		0			0
$399$	8.33170e7	+	1.32068e9i	0.0656642	+	1.04086i
$400$		0			0
$401$	−5.15148e8	−	8.92263e8i	−0.398958	−	0.691015i	0.594640	−	0.803992i	$-0.297295\pi$
$401$	−5.15148e8	−	8.92263e8i	−0.398958	−	0.691015i	−0.993598	+	0.112977i	$0.963961\pi$
$402$		0			0
$403$	1.88704e8	−	3.26845e8i	0.143619	−	0.248756i
$404$		0			0
$405$	2.90387e8	−	5.02965e8i	0.217212	−	0.376223i
$406$		0			0
$407$	1.91588e9			1.40860
$408$		0			0
$409$	8.23931e8	−	1.42709e9i	0.595469	−	1.03138i	−0.398012	−	0.917380i	$-0.630300\pi$
$409$	8.23931e8	−	1.42709e9i	0.595469	−	1.03138i	0.993481	−	0.114002i	$-0.0363670\pi$
$410$		0			0
$411$	1.85685e9			1.31926
$412$		0			0
$413$	8.79677e8	+	1.52364e9i	0.614466	+	1.06429i
$414$		0			0
$415$	3.33566e8	+	5.77753e8i	0.229094	+	0.396802i
$416$		0			0
$417$	−4.11431e9			−2.77856
$418$		0			0
$419$	−2.00439e9			−1.33117			−0.665584	−	0.746323i	$-0.731817\pi$
$419$	−2.00439e9			−1.33117			−0.665584	+	0.746323i	$0.731817\pi$
$420$		0			0
$421$	−1.46471e8	−	2.53696e8i	−0.0956677	−	0.165701i	0.814219	−	0.580557i	$-0.197165\pi$
$421$	−1.46471e8	−	2.53696e8i	−0.0956677	−	0.165701i	−0.909887	+	0.414856i	$0.863832\pi$
$422$		0			0
$423$	1.03879e9	+	1.79924e9i	0.667325	+	1.15584i
$424$		0			0
$425$	−5.38020e8			−0.339967
$426$		0			0
$427$	3.36154e8	−	5.82236e8i	0.208949	−	0.361911i
$428$		0			0
$429$	3.20178e9			1.95790
$430$		0			0
$431$	−8.85166e8	+	1.53315e9i	−0.532542	+	0.922390i	0.466736	+	0.884397i	$0.345430\pi$
$431$	−8.85166e8	+	1.53315e9i	−0.532542	+	0.922390i	−0.999278	+	0.0379935i	$0.987903\pi$
$432$		0			0
$433$	5.52897e8	−	9.57647e8i	0.327293	−	0.566888i	−0.654681	−	0.755906i	$-0.727197\pi$
$433$	5.52897e8	−	9.57647e8i	0.327293	−	0.566888i	0.981974	+	0.189017i	$0.0605302\pi$
$434$		0			0
$435$	2.16713e9	+	3.75358e9i	1.26233	+	2.18642i
$436$		0			0
$437$	4.08729e8	−	2.71660e8i	0.234288	−	0.155719i
$438$		0			0
$439$	−1.40638e9	−	2.43592e9i	−0.793370	−	1.37416i	−0.923869	−	0.382709i	$-0.874991\pi$
$439$	−1.40638e9	−	2.43592e9i	−0.793370	−	1.37416i	0.130499	−	0.991448i	$-0.458342\pi$
$440$		0			0
$441$	7.46693e8	−	1.29331e9i	0.414579	−	0.718072i
$442$		0			0
$443$	−1.17505e9	+	2.03525e9i	−0.642161	+	1.11226i	0.342788	+	0.939413i	$0.388629\pi$
$443$	−1.17505e9	+	2.03525e9i	−0.642161	+	1.11226i	−0.984949	+	0.172843i	$0.944705\pi$
$444$		0			0
$445$	−8.71817e7			−0.0468992
$446$		0			0
$447$	−1.78541e9	+	3.09242e9i	−0.945500	+	1.63765i
$448$		0			0
$449$	−2.52724e9			−1.31760			−0.658802	−	0.752316i	$-0.728936\pi$
$449$	−2.52724e9			−1.31760			−0.658802	+	0.752316i	$0.728936\pi$
$450$		0			0
$451$	1.03412e9	+	1.79115e9i	0.530828	+	0.919421i
$452$		0			0
$453$	2.30960e9	+	4.00034e9i	1.16733	+	2.02187i
$454$		0			0
$455$	−2.89723e9			−1.44193
$456$		0			0
$457$	2.08311e9			1.02095			0.510476	−	0.859892i	$-0.329469\pi$
$457$	2.08311e9			1.02095			0.510476	+	0.859892i	$0.329469\pi$
$458$		0			0
$459$	−2.23046e8	−	3.86328e8i	−0.107659	−	0.186471i
$460$		0			0
$461$	1.17925e9	+	2.04252e9i	0.560599	+	0.970986i	0.997444	+	0.0714493i	$0.0227624\pi$
$461$	1.17925e9	+	2.04252e9i	0.560599	+	0.970986i	−0.436845	+	0.899537i	$0.643904\pi$
$462$		0			0
$463$	−2.20948e9			−1.03456			−0.517282	−	0.855815i	$-0.673056\pi$
$463$	−2.20948e9			−1.03456			−0.517282	+	0.855815i	$0.673056\pi$
$464$		0			0
$465$	4.92739e8	−	8.53448e8i	0.227264	−	0.393633i
$466$		0			0
$467$	−6.83713e8			−0.310646			−0.155323	−	0.987864i	$-0.549642\pi$
$467$	−6.83713e8			−0.310646			−0.155323	+	0.987864i	$0.549642\pi$
$468$		0			0
$469$	9.30081e8	−	1.61095e9i	0.416309	−	0.721068i
$470$		0			0
$471$	1.72844e9	−	2.99375e9i	0.762223	−	1.32021i
$472$		0			0
$473$	−1.28877e9	−	2.23222e9i	−0.559967	−	0.969890i
$474$		0			0
$475$	−2.31058e9	+	1.53571e9i	−0.989220	+	0.657480i
$476$		0			0
$477$	−1.76522e8	−	3.05746e8i	−0.0744707	−	0.128987i
$478$		0			0
$479$	1.57356e9	−	2.72549e9i	0.654198	−	1.13310i	−0.327896	−	0.944714i	$-0.606339\pi$
$479$	1.57356e9	−	2.72549e9i	0.654198	−	1.13310i	0.982094	−	0.188391i	$-0.0603272\pi$
$480$		0			0
$481$	2.99205e9	−	5.18238e9i	1.22592	−	2.12335i
$482$		0			0
$483$	7.26554e8			0.293395
$484$		0			0
$485$	9.42915e8	−	1.63318e9i	0.375298	−	0.650035i
$486$		0			0
$487$	2.60761e8			0.102304			0.0511518	−	0.998691i	$-0.483711\pi$
$487$	2.60761e8			0.102304			0.0511518	+	0.998691i	$0.483711\pi$
$488$		0			0
$489$	1.41946e9	+	2.45858e9i	0.548963	+	0.950831i
$490$		0			0
$491$	8.77196e8	+	1.51935e9i	0.334435	+	0.579258i	0.983376	−	0.181581i	$-0.0581213\pi$
$491$	8.77196e8	+	1.51935e9i	0.334435	+	0.579258i	−0.648941	+	0.760838i	$0.724788\pi$
$492$		0			0
$493$	−8.25698e8			−0.310354
$494$		0			0
$495$	4.98643e9			1.84787
$496$		0			0
$497$	1.37370e8	+	2.37931e8i	0.0501930	+	0.0869368i
$498$		0			0
$499$	1.25972e9	+	2.18189e9i	0.453859	+	0.786106i	0.998622	−	0.0524836i	$-0.0167137\pi$
$499$	1.25972e9	+	2.18189e9i	0.453859	+	0.786106i	−0.544763	+	0.838590i	$0.683380\pi$
$500$		0			0
$501$	−4.45629e9			−1.58322
$502$		0			0
$503$	−1.93307e8	+	3.34818e8i	−0.0677268	+	0.117306i	−0.897900	−	0.440199i	$-0.854908\pi$
$503$	−1.93307e8	+	3.34818e8i	−0.0677268	+	0.117306i	0.830174	+	0.557505i	$0.188241\pi$
$504$		0			0
$505$	−3.25851e9			−1.12590
$506$		0			0
$507$	2.69064e9	−	4.66033e9i	0.916912	−	1.58814i
$508$		0			0
$509$	9.37381e8	−	1.62359e9i	0.315068	−	0.545713i	−0.664384	−	0.747391i	$-0.731306\pi$
$509$	9.37381e8	−	1.62359e9i	0.315068	−	0.545713i	0.979452	+	0.201678i	$0.0646394\pi$
$510$		0			0
$511$	−1.91279e9	−	3.31304e9i	−0.634152	−	1.09838i
$512$		0			0
$513$	−2.06062e9	−	1.02246e9i	−0.673887	−	0.334377i
$514$		0			0
$515$	2.22403e9	+	3.85212e9i	0.717488	+	1.24272i
$516$		0			0
$517$	1.19931e9	−	2.07727e9i	0.381693	−	0.661112i
$518$		0			0
$519$	−2.81032e9	+	4.86762e9i	−0.882410	+	1.52838i
$520$		0			0
$521$	1.39695e9			0.432760			0.216380	−	0.976309i	$-0.430575\pi$
$521$	1.39695e9			0.432760			0.216380	+	0.976309i	$0.430575\pi$
$522$		0			0
$523$	8.32397e8	−	1.44175e9i	0.254434	−	0.440692i	−0.710308	−	0.703891i	$-0.751444\pi$
$523$	8.32397e8	−	1.44175e9i	0.254434	−	0.440692i	0.964742	+	0.263199i	$0.0847776\pi$
$524$		0			0
$525$	−4.10726e9			−1.23878
$526$		0			0
$527$	9.38691e7	+	1.62586e8i	0.0279374	+	0.0483890i
$528$		0			0
$529$	1.56768e9	+	2.71531e9i	0.460430	+	0.797489i
$530$		0			0
$531$	−9.45781e9			−2.74132
$532$		0			0
$533$	6.45999e9			1.84793
$534$		0			0
$535$	−1.94037e9	−	3.36082e9i	−0.547832	−	0.948872i
$536$		0			0
$537$	−4.99273e9	−	8.64766e9i	−1.39132	−	2.40984i
$538$		0			0
$539$	−1.72415e9			−0.474258
$540$		0			0
$541$	−6.39585e8	+	1.10779e9i	−0.173663	+	0.300794i	−0.939698	−	0.342006i	$-0.888894\pi$
$541$	−6.39585e8	+	1.10779e9i	−0.173663	+	0.300794i	0.766035	+	0.642799i	$0.222227\pi$
$542$		0			0
$543$	−7.15661e9			−1.91826
$544$		0			0
$545$	−4.70554e9	+	8.15024e9i	−1.24515	+	2.15666i
$546$		0			0
$547$	−1.72875e9	+	2.99429e9i	−0.451624	+	0.782237i	−0.998487	−	0.0549858i	$-0.982489\pi$
$547$	−1.72875e9	+	2.99429e9i	−0.451624	+	0.782237i	0.546863	+	0.837222i	$0.315822\pi$
$548$		0			0
$549$	1.80708e9	+	3.12995e9i	0.466093	+	0.807298i
$550$		0			0
$551$	−3.54604e9	+	2.35686e9i	−0.903052	+	0.600209i
$552$		0			0
$553$	8.75725e8	+	1.51680e9i	0.220206	+	0.381408i
$554$		0			0
$555$	7.81277e9	−	1.35321e10i	1.93990	−	3.36001i
$556$		0			0
$557$	−1.94324e9	+	3.36578e9i	−0.476466	+	0.825264i	−0.999636	−	0.0269644i	$-0.991416\pi$
$557$	−1.94324e9	+	3.36578e9i	−0.476466	+	0.825264i	0.523170	+	0.852228i	$0.324749\pi$
$558$		0			0
$559$	−8.05075e9			−1.94937
$560$		0			0
$561$	−7.96350e8	+	1.37932e9i	−0.190429	+	0.329833i
$562$		0			0
$563$	−1.81193e9			−0.427919			−0.213959	−	0.976843i	$-0.568636\pi$
$563$	−1.81193e9			−0.427919			−0.213959	+	0.976843i	$0.568636\pi$
$564$		0			0
$565$	6.06928e9	+	1.05123e10i	1.41569	+	2.45204i
$566$		0			0
$567$	4.22315e8	+	7.31472e8i	0.0972963	+	0.168522i
$568$		0			0
$569$	8.58649e8			0.195399			0.0976996	−	0.995216i	$-0.468852\pi$
$569$	8.58649e8			0.195399			0.0976996	+	0.995216i	$0.468852\pi$
$570$		0			0
$571$	2.73775e9			0.615415			0.307708	−	0.951481i	$-0.400438\pi$
$571$	2.73775e9			0.615415			0.307708	+	0.951481i	$0.400438\pi$
$572$		0			0
$573$	−4.08135e9	−	7.06911e9i	−0.906281	−	1.56973i
$574$		0			0
$575$	7.61626e8	+	1.31918e9i	0.167072	+	0.289378i
$576$		0			0
$577$	−4.93214e8			−0.106886			−0.0534429	−	0.998571i	$-0.517020\pi$
$577$	−4.93214e8			−0.106886			−0.0534429	+	0.998571i	$0.517020\pi$
$578$		0			0
$579$	−4.55351e9	+	7.88690e9i	−0.974924	+	1.68862i
$580$		0			0
$581$	−9.70223e8			−0.205237
$582$		0			0
$583$	−2.03799e8	+	3.52991e8i	−0.0425954	+	0.0737774i
$584$		0			0
$585$	7.78736e9	−	1.34881e10i	1.60822	−	2.78551i
$586$		0			0
$587$	−2.40386e9	−	4.16360e9i	−0.490541	−	0.849642i	0.509400	−	0.860530i	$-0.329868\pi$
$587$	−2.40386e9	−	4.16360e9i	−0.490541	−	0.849642i	−0.999941	+	0.0108880i	$0.996534\pi$
$588$		0			0
$589$	8.67212e8	+	4.30303e8i	0.174873	+	0.0867703i
$590$		0			0
$591$	−5.45523e8	−	9.44873e8i	−0.108707	−	0.188286i
$592$		0			0
$593$	3.46949e9	−	6.00933e9i	0.683241	−	1.18341i	−0.290746	−	0.956800i	$-0.593903\pi$
$593$	3.46949e9	−	6.00933e9i	0.683241	−	1.18341i	0.973986	−	0.226607i	$-0.0727633\pi$
$594$		0			0
$595$	7.20601e8	−	1.24812e9i	0.140244	−	0.242910i
$596$		0			0
$597$	5.95784e9			1.14598
$598$		0			0
$599$	−8.08925e7	+	1.40110e8i	−0.0153785	+	0.0266364i	−0.873612	−	0.486623i	$-0.838229\pi$
$599$	−8.08925e7	+	1.40110e8i	−0.0153785	+	0.0266364i	0.858234	+	0.513259i	$0.171562\pi$
$600$		0			0
$601$	3.54890e9			0.666857			0.333429	−	0.942775i	$-0.391794\pi$
$601$	3.54890e9			0.666857			0.333429	+	0.942775i	$0.391794\pi$
$602$		0			0
$603$	4.99986e9	+	8.66002e9i	0.928640	+	1.60845i
$604$		0			0
$605$	1.14977e9	+	1.99146e9i	0.211090	+	0.365619i
$606$		0			0
$607$	4.11398e8			0.0746623			0.0373311	−	0.999303i	$-0.488114\pi$
$607$	4.11398e8			0.0746623			0.0373311	+	0.999303i	$0.488114\pi$
$608$		0			0
$609$	−6.30340e9			−1.13087
$610$		0			0
$611$	−3.74595e9	−	6.48817e9i	−0.664382	−	1.15074i
$612$		0			0
$613$	2.16884e9	+	3.75653e9i	0.380290	+	0.658682i	0.991104	−	0.133093i	$-0.0424908\pi$
$613$	2.16884e9	+	3.75653e9i	0.380290	+	0.658682i	−0.610814	+	0.791775i	$0.709157\pi$
$614$		0			0
$615$	1.68682e10			2.92419
$616$		0			0
$617$	4.98824e9	−	8.63989e9i	0.854967	−	1.48085i	−0.0217079	−	0.999764i	$-0.506910\pi$
$617$	4.98824e9	−	8.63989e9i	0.854967	−	1.48085i	0.876675	−	0.481083i	$-0.159756\pi$
$618$		0			0
$619$	−1.78058e9			−0.301748			−0.150874	−	0.988553i	$-0.548209\pi$
$619$	−1.78058e9			−0.301748			−0.150874	+	0.988553i	$0.548209\pi$
$620$		0			0
$621$	−6.31494e8	+	1.09378e9i	−0.105815	+	0.183277i
$622$		0			0
$623$	6.33950e7	−	1.09803e8i	0.0105038	−	0.0181931i
$624$		0			0
$625$	2.37107e9	+	4.10681e9i	0.388475	+	0.672859i
$626$		0			0
$627$	5.17099e8	+	8.19670e9i	0.0837795	+	1.32801i
$628$		0			0
$629$	1.48837e9	+	2.57793e9i	0.238470	+	0.413042i
$630$		0			0
$631$	−8.45777e8	+	1.46493e9i	−0.134015	+	0.232121i	−0.925221	−	0.379429i	$-0.876120\pi$
$631$	−8.45777e8	+	1.46493e9i	−0.134015	+	0.232121i	0.791206	+	0.611550i	$0.209454\pi$
$632$		0			0
$633$	6.20933e9	−	1.07549e10i	0.973043	−	1.68536i
$634$		0			0
$635$	−2.26628e9			−0.351241
$636$		0			0
$637$	−2.69262e9	+	4.66376e9i	−0.412750	+	0.714904i
$638$		0			0
$639$	−1.47692e9			−0.223926
$640$		0			0
$641$	3.06578e9	+	5.31009e9i	0.459767	+	0.796340i	0.998948	−	0.0458498i	$-0.0145996\pi$
$641$	3.06578e9	+	5.31009e9i	0.459767	+	0.796340i	−0.539181	+	0.842190i	$0.681266\pi$
$642$		0			0
$643$	−1.04009e9	−	1.80149e9i	−0.154288	−	0.267235i	0.778511	−	0.627631i	$-0.215975\pi$
$643$	−1.04009e9	−	1.80149e9i	−0.154288	−	0.267235i	−0.932800	+	0.360395i	$0.882642\pi$
$644$		0			0
$645$	−2.10219e10			−3.08470
$646$		0			0
$647$	1.00635e10			1.46078			0.730389	−	0.683031i	$-0.239339\pi$
$647$	1.00635e10			1.46078			0.730389	+	0.683031i	$0.239339\pi$
$648$		0			0
$649$	5.45963e9	+	9.45636e9i	0.783983	+	1.35790i
$650$		0			0
$651$	7.16600e8	+	1.24119e9i	0.101799	+	0.176321i
$652$		0			0
$653$	−1.22027e10			−1.71498			−0.857491	−	0.514500i	$-0.827978\pi$
$653$	−1.22027e10			−1.71498			−0.857491	+	0.514500i	$0.827978\pi$
$654$		0			0
$655$	−3.48149e9	+	6.03011e9i	−0.484084	+	0.838457i
$656$		0			0
$657$	2.05653e10			2.82914
$658$		0			0
$659$	6.48030e8	−	1.12242e9i	0.0882056	−	0.152777i	−0.818547	−	0.574439i	$-0.805220\pi$
$659$	6.48030e8	−	1.12242e9i	0.0882056	−	0.152777i	0.906753	+	0.421663i	$0.138553\pi$
$660$		0			0
$661$	3.69894e9	−	6.40675e9i	0.498163	−	0.862844i	−0.501834	−	0.864964i	$-0.667341\pi$
$661$	3.69894e9	−	6.40675e9i	0.498163	−	0.862844i	0.999998	+	0.00211932i	$0.000674602\pi$
$662$		0			0
$663$	2.48734e9	+	4.30819e9i	0.331465	+	0.574114i
$664$		0			0
$665$	−4.67913e8	−	7.41703e9i	−0.0617005	−	0.978034i
$666$		0			0
$667$	1.16887e9	+	2.02454e9i	0.152519	+	0.264171i
$668$		0			0
$669$	−5.02809e9	+	8.70891e9i	−0.649250	+	1.12453i
$670$		0			0
$671$	2.08631e9	−	3.61360e9i	0.266594	−	0.461754i
$672$		0			0
$673$	−4.44870e9			−0.562574			−0.281287	−	0.959624i	$-0.590761\pi$
$673$	−4.44870e9			−0.562574			−0.281287	+	0.959624i	$0.590761\pi$
$674$		0			0
$675$	3.56988e9	−	6.18321e9i	0.446776	−	0.773839i
$676$		0			0
$677$	8.12099e9			1.00589			0.502943	−	0.864320i	$-0.332251\pi$
$677$	8.12099e9			1.00589			0.502943	+	0.864320i	$0.332251\pi$
$678$		0			0
$679$	1.37130e9	+	2.37516e9i	0.168108	+	0.291171i
$680$		0			0
$681$	4.89813e8	+	8.48380e8i	0.0594313	+	0.102938i
$682$		0			0
$683$	1.14142e9			0.137080			0.0685400	−	0.997648i	$-0.478166\pi$
$683$	1.14142e9			0.137080			0.0685400	+	0.997648i	$0.478166\pi$
$684$		0			0
$685$	−1.04282e10			−1.23963
$686$		0			0
$687$	−1.02345e10	−	1.77266e10i	−1.20425	−	2.08582i
$688$		0			0
$689$	6.36551e8	+	1.10254e9i	0.0741422	+	0.128418i
$690$		0			0
$691$	−2.04621e9			−0.235927			−0.117963	−	0.993018i	$-0.537637\pi$
$691$	−2.04621e9			−0.235927			−0.117963	+	0.993018i	$0.537637\pi$
$692$		0			0
$693$	−3.62593e9	+	6.28030e9i	−0.413860	+	0.716826i
$694$		0			0
$695$	2.31061e10			2.61084
$696$		0			0
$697$	−1.60673e9	+	2.78294e9i	−0.179734	+	0.311308i
$698$		0			0
$699$	−6.76476e9	+	1.17169e10i	−0.749173	+	1.29761i
$700$		0			0
$701$	5.80331e9	+	1.00516e10i	0.636301	+	1.10211i	0.986238	+	0.165333i	$0.0528697\pi$
$701$	5.80331e9	+	1.00516e10i	0.636301	+	1.10211i	−0.349937	+	0.936773i	$0.613797\pi$
$702$		0			0
$703$	1.37503e10	+	6.82280e9i	1.49269	+	0.740660i
$704$		0			0
$705$	−9.78133e9	−	1.69418e10i	−1.05132	−	1.82094i
$706$		0			0
$707$	2.36946e9	−	4.10402e9i	0.252163	−	0.436758i
$708$		0			0
$709$	−1.70531e9	+	2.95368e9i	−0.179697	+	0.311244i	−0.941777	−	0.336239i	$-0.890845\pi$
$709$	−1.70531e9	+	2.95368e9i	−0.179697	+	0.311244i	0.762080	+	0.647483i	$0.224178\pi$
$710$		0			0
$711$	−9.41532e9			−0.982407
$712$		0			0
$713$	2.65764e8	−	4.60317e8i	0.0274589	−	0.0475602i
$714$		0			0
$715$	−1.79814e10			−1.83972
$716$		0			0
$717$	5.02508e9	+	8.70370e9i	0.509127	+	0.881834i
$718$		0			0
$719$	8.30817e9	+	1.43902e10i	0.833593	+	1.44383i	0.895171	+	0.445723i	$0.147053\pi$
$719$	8.30817e9	+	1.43902e10i	0.833593	+	1.44383i	−0.0615779	+	0.998102i	$0.519613\pi$
$720$		0			0
$721$	−6.46889e9			−0.642771
$722$		0			0
$723$	−1.24876e10			−1.22884
$724$		0			0
$725$	−6.60768e9	−	1.14448e10i	−0.643971	−	1.11539i
$726$		0			0
$727$	−4.66717e9	−	8.08377e9i	−0.450488	−	0.780267i	0.547929	−	0.836525i	$-0.315417\pi$
$727$	−4.66717e9	−	8.08377e9i	−0.450488	−	0.780267i	−0.998416	+	0.0562576i	$0.982083\pi$
$728$		0			0
$729$	−1.69276e10			−1.61827
$730$		0			0
$731$	2.00239e9	−	3.46824e9i	0.189600	−	0.328396i
$732$		0			0
$733$	4.64186e9			0.435340			0.217670	−	0.976022i	$-0.430154\pi$
$733$	4.64186e9			0.435340			0.217670	+	0.976022i	$0.430154\pi$
$734$		0			0
$735$	−7.03091e9	+	1.21779e10i	−0.653139	+	1.13127i
$736$		0			0
$737$	5.77246e9	−	9.99819e9i	0.531159	−	0.919995i
$738$		0			0
$739$	2.09701e9	+	3.63212e9i	0.191137	+	0.331058i	0.945627	−	0.325252i	$-0.105449\pi$
$739$	2.09701e9	+	3.63212e9i	0.191137	+	0.331058i	−0.754491	+	0.656311i	$0.772116\pi$
$740$		0			0
$741$	2.29793e10	+	1.14021e10i	2.07479	+	1.02949i
$742$		0			0
$743$	−4.76920e9	−	8.26049e9i	−0.426564	−	0.738831i	0.570001	−	0.821644i	$-0.306943\pi$
$743$	−4.76920e9	−	8.26049e9i	−0.426564	−	0.738831i	−0.996565	+	0.0828133i	$0.973609\pi$
$744$		0			0
$745$	1.00269e10	−	1.73672e10i	0.888427	−	1.53880i
$746$		0			0
$747$	2.60783e9	−	4.51689e9i	0.228906	−	0.396476i
$748$		0			0
$749$	5.64385e9			0.490782
$750$		0			0
$751$	3.05462e9	−	5.29075e9i	0.263158	−	0.455803i	−0.703921	−	0.710278i	$-0.748569\pi$
$751$	3.05462e9	−	5.29075e9i	0.263158	−	0.455803i	0.967079	+	0.254475i	$0.0819026\pi$
$752$		0			0
$753$	−2.84659e10			−2.42964
$754$		0			0
$755$	−1.29708e10	−	2.24661e10i	−1.09686	−	1.89982i
$756$		0			0
$757$	−9.60392e9	−	1.66345e10i	−0.804661	−	1.39371i	−0.916520	−	0.399990i	$-0.869014\pi$
$757$	−9.60392e9	−	1.66345e10i	−0.804661	−	1.39371i	0.111858	−	0.993724i	$-0.464320\pi$
$758$		0			0
$759$	4.50929e9			0.374336
$760$		0			0
$761$	−1.91142e10			−1.57221			−0.786104	−	0.618095i	$-0.787905\pi$
$761$	−1.91142e10			−1.57221			−0.786104	+	0.618095i	$0.787905\pi$
$762$		0			0
$763$	−6.84336e9	−	1.18531e10i	−0.557743	−	0.966038i
$764$		0			0
$765$	3.87376e9	+	6.70954e9i	0.312836	+	0.541848i
$766$		0			0
$767$	3.41054e10			2.72923
$768$		0			0
$769$	−7.34074e9	+	1.27145e10i	−0.582100	+	1.00823i	0.413130	+	0.910672i	$0.364435\pi$
$769$	−7.34074e9	+	1.27145e10i	−0.582100	+	1.00823i	−0.995230	+	0.0975549i	$0.968898\pi$
$770$		0			0
$771$	1.76175e10			1.38438
$772$		0			0
$773$	1.21542e10	−	2.10517e10i	0.946450	−	1.63930i	0.193630	−	0.981075i	$-0.437974\pi$
$773$	1.21542e10	−	2.10517e10i	0.946450	−	1.63930i	0.752821	−	0.658226i	$-0.228693\pi$
$774$		0			0
$775$	−1.50238e9	+	2.60220e9i	−0.115938	+	0.200810i
$776$		0			0
$777$	1.13623e10	+	1.96800e10i	0.868943	+	1.50505i
$778$		0			0
$779$	1.04331e9	+	1.65378e10i	0.0790738	+	1.25342i
$780$		0			0
$781$	8.52572e8	+	1.47670e9i	0.0640401	+	0.110921i
$782$		0			0
$783$	5.47868e9	−	9.48936e9i	0.407859	−	0.706433i
$784$		0			0
$785$	−9.70702e9	+	1.68131e10i	−0.716213	+	1.24052i
$786$		0			0
$787$	−1.61259e10			−1.17926			−0.589632	−	0.807672i	$-0.700727\pi$
$787$	−1.61259e10			−1.17926			−0.589632	+	0.807672i	$0.700727\pi$
$788$		0			0
$789$	−3.17860e8	+	5.50550e8i	−0.0230392	+	0.0399050i
$790$		0			0
$791$	−1.76533e10			−1.26826
$792$		0			0
$793$	−6.51643e9	−	1.12868e10i	−0.464038	−	0.803737i
$794$		0			0
$795$	1.66215e9	+	2.87892e9i	0.117323	+	0.203210i
$796$		0			0
$797$	2.65281e9			0.185610			0.0928050	−	0.995684i	$-0.470417\pi$
$797$	2.65281e9			0.185610			0.0928050	+	0.995684i	$0.470417\pi$
$798$		0			0
$799$	3.72678e9			0.258476
$800$		0			0
$801$	3.40794e8	+	5.90273e8i	0.0234303	+	0.0405826i
$802$		0			0
$803$	−1.18715e10	−	2.05621e10i	−0.809100	−	1.40140i
$804$		0			0
$805$	−4.08036e9			−0.275685
$806$		0			0
$807$	−1.00139e10	+	1.73445e10i	−0.670724	+	1.16173i
$808$		0			0
$809$	4.94007e9			0.328030			0.164015	−	0.986458i	$-0.447556\pi$
$809$	4.94007e9			0.328030			0.164015	+	0.986458i	$0.447556\pi$
$810$		0			0
$811$	6.06540e9	−	1.05056e10i	0.399288	−	0.691587i	−0.594350	−	0.804206i	$-0.702591\pi$
$811$	6.06540e9	−	1.05056e10i	0.399288	−	0.691587i	0.993638	+	0.112619i	$0.0359240\pi$
$812$		0			0
$813$	−6.78008e9	+	1.17434e10i	−0.442505	+	0.766441i
$814$		0			0
$815$	−7.97177e9	−	1.38075e10i	−0.515826	−	0.893437i
$816$		0			0
$817$	−1.30022e9	−	2.06103e10i	−0.0834144	−	1.32223i
$818$		0			0
$819$	1.13253e10	+	1.96160e10i	0.720371	+	1.24772i
$820$		0			0
$821$	−2.92018e9	+	5.05790e9i	−0.184165	+	0.318984i	−0.943295	−	0.331956i	$-0.892292\pi$
$821$	−2.92018e9	+	5.05790e9i	−0.184165	+	0.318984i	0.759130	+	0.650940i	$0.225625\pi$
$822$		0			0
$823$	−1.29461e10	+	2.24233e10i	−0.809543	+	1.40217i	0.103638	+	0.994615i	$0.466952\pi$
$823$	−1.29461e10	+	2.24233e10i	−0.809543	+	1.40217i	−0.913181	+	0.407554i	$0.866382\pi$
$824$		0			0
$825$	−2.54913e10			−1.58053
$826$		0			0
$827$	7.47818e9	−	1.29526e10i	0.459755	−	0.796319i	−0.539193	−	0.842183i	$-0.681270\pi$
$827$	7.47818e9	−	1.29526e10i	0.459755	−	0.796319i	0.998948	+	0.0458631i	$0.0146038\pi$
$828$		0			0
$829$	−9.72077e9			−0.592597			−0.296299	−	0.955095i	$-0.595752\pi$
$829$	−9.72077e9			−0.592597			−0.296299	+	0.955095i	$0.595752\pi$
$830$		0			0
$831$	4.70227e9	+	8.14457e9i	0.284252	+	0.492339i
$832$		0			0
$833$	−1.33942e9	−	2.31995e9i	−0.0802897	−	0.139066i
$834$		0			0
$835$	2.50267e10			1.48765
$836$		0			0
$837$	−2.49137e9			−0.146858
$838$		0			0
$839$	3.46965e9	+	6.00962e9i	0.202824	+	0.351301i	0.949437	−	0.313957i	$-0.101655\pi$
$839$	3.46965e9	+	6.00962e9i	0.202824	+	0.351301i	−0.746613	+	0.665258i	$0.768321\pi$
$840$		0			0
$841$	−1.51586e9	−	2.62555e9i	−0.0878766	−	0.152207i
$842$		0			0
$843$	−1.63980e10			−0.942745
$844$		0			0
$845$	−1.51108e10	+	2.61726e10i	−0.861565	+	1.49227i
$846$		0			0
$847$	−3.34427e9			−0.189108
$848$		0			0
$849$	−2.18172e10	+	3.77886e10i	−1.22355	+	2.11926i
$850$		0			0
$851$	4.21390e9	−	7.29870e9i	0.234386	−	0.405968i
$852$		0			0
$853$	9.94780e9	+	1.72301e10i	0.548789	+	0.950530i	0.998358	+	0.0572846i	$0.0182443\pi$
$853$	9.94780e9	+	1.72301e10i	0.548789	+	0.950530i	−0.449569	+	0.893246i	$0.648422\pi$
$854$		0			0
$855$	3.57878e10	+	1.77576e10i	1.95818	+	0.971634i
$856$		0			0
$857$	−5.69195e9	−	9.85875e9i	−0.308907	−	0.535043i	0.669216	−	0.743068i	$-0.266630\pi$
$857$	−5.69195e9	−	9.85875e9i	−0.308907	−	0.535043i	−0.978124	+	0.208024i	$0.933297\pi$
$858$		0			0
$859$	1.32860e10	−	2.30121e10i	0.715187	−	1.23874i	−0.247700	−	0.968837i	$-0.579675\pi$
$859$	1.32860e10	−	2.30121e10i	0.715187	−	1.23874i	0.962887	−	0.269903i	$-0.0869918\pi$
$860$		0			0
$861$	−1.22659e10	+	2.12451e10i	−0.654918	+	1.13435i
$862$		0			0
$863$	2.16347e10			1.14581			0.572906	−	0.819621i	$-0.305816\pi$
$863$	2.16347e10			1.14581			0.572906	+	0.819621i	$0.305816\pi$
$864$		0			0
$865$	1.57829e10	−	2.73368e10i	0.829145	−	1.43612i
$866$		0			0
$867$	2.77325e10			1.44518
$868$		0			0
$869$	5.43510e9	+	9.41388e9i	0.280956	+	0.486630i
$870$		0			0
$871$	−1.80298e10	−	3.12286e10i	−0.924544	−	1.60136i
$872$		0			0
$873$	−1.47435e10			−0.749980
$874$		0			0
$875$	3.64676e9			0.184026
$876$		0			0
$877$	5.98069e9	+	1.03589e10i	0.299401	+	0.518577i	0.975999	−	0.217775i	$-0.0698799\pi$
$877$	5.98069e9	+	1.03589e10i	0.299401	+	0.518577i	−0.676598	+	0.736352i	$0.736547\pi$
$878$		0			0
$879$	−2.94590e10	−	5.10244e10i	−1.46304	−	2.53406i
$880$		0			0
$881$	1.11039e10			0.547093			0.273547	−	0.961859i	$-0.411803\pi$
$881$	1.11039e10			0.547093			0.273547	+	0.961859i	$0.411803\pi$
$882$		0			0
$883$	−8.66973e9	+	1.50164e10i	−0.423783	+	0.734013i	−0.996306	−	0.0858753i	$-0.972631\pi$
$883$	−8.66973e9	+	1.50164e10i	−0.423783	+	0.734013i	0.572523	+	0.819889i	$0.305965\pi$
$884$		0			0
$885$	8.90553e10			4.31875
$886$		0			0
$887$	7.51460e9	−	1.30157e10i	0.361554	−	0.626230i	−0.626663	−	0.779291i	$-0.715580\pi$
$887$	7.51460e9	−	1.30157e10i	0.361554	−	0.626230i	0.988217	+	0.153060i	$0.0489129\pi$
$888$		0			0
$889$	1.64795e9	−	2.85433e9i	0.0786659	−	0.136253i
$890$		0			0
$891$	2.62106e9	+	4.53981e9i	0.124138	+	0.215014i
$892$		0			0
$893$	1.60050e10	−	1.06377e10i	0.752101	−	0.499880i
$894$		0			0
$895$	2.80394e10	+	4.85657e10i	1.30734	+	2.26438i
$896$		0			0
$897$	7.04220e9	−	1.21974e10i	0.325788	−	0.564281i
$898$		0			0
$899$	−2.30571e9	+	3.99360e9i	−0.105839	+	0.183318i
$900$		0			0
$901$	−6.33293e8			−0.0288448
$902$		0			0
$903$	1.52863e10	−	2.64766e10i	0.690868	−	1.19662i
$904$		0			0
$905$	4.01919e10			1.80247
$906$		0			0
$907$	8.60886e9	+	1.49110e10i	0.383107	+	0.663561i	0.991505	−	0.130071i	$-0.0415207\pi$
$907$	8.60886e9	+	1.49110e10i	0.383107	+	0.663561i	−0.608398	+	0.793632i	$0.708187\pi$
$908$		0			0
$909$	1.27376e10	+	2.20621e10i	0.562487	+	0.974256i
$910$		0			0
$911$	−2.53737e10			−1.11191			−0.555955	−	0.831212i	$-0.687647\pi$
$911$	−2.53737e10			−1.11191			−0.555955	+	0.831212i	$0.687647\pi$
$912$		0			0
$913$	−6.02160e9			−0.261857
$914$		0			0
$915$	−1.70155e10	−	2.94718e10i	−0.734297	−	1.27184i
$916$		0			0
$917$	−5.06320e9	−	8.76972e9i	−0.216836	−	0.375572i
$918$		0			0
$919$	1.12319e10			0.477361			0.238681	−	0.971098i	$-0.423285\pi$
$919$	1.12319e10			0.477361			0.238681	+	0.971098i	$0.423285\pi$
$920$		0			0
$921$	7.61947e9	−	1.31973e10i	0.321378	−	0.556643i
$922$		0			0
$923$	5.32588e9			0.222939
$924$		0			0
$925$	−2.38215e10	+	4.12600e10i	−0.989630	+	1.71409i
$926$		0			0
$927$	1.73875e10	−	3.01160e10i	0.716899	−	1.24171i
$928$		0			0
$929$	1.40320e10	+	2.43042e10i	0.574202	+	0.994548i	0.996128	+	0.0879173i	$0.0280211\pi$
$929$	1.40320e10	+	2.43042e10i	0.574202	+	0.994548i	−0.421925	+	0.906631i	$0.638646\pi$
$930$		0			0
$931$	−1.23743e10	−	6.14001e9i	−0.502570	−	0.249371i
$932$		0			0
$933$	−4.35203e9	−	7.53795e9i	−0.175431	−	0.303856i
$934$		0			0
$935$	4.47234e9	−	7.74632e9i	0.178935	−	0.309924i
$936$		0			0
$937$	2.25001e10	−	3.89713e10i	0.893503	−	1.54759i	0.0578566	−	0.998325i	$-0.481573\pi$
$937$	2.25001e10	−	3.89713e10i	0.893503	−	1.54759i	0.835646	−	0.549268i	$-0.185093\pi$
$938$		0			0
$939$	−4.24727e10			−1.67410
$940$		0			0
$941$	6.40797e9	−	1.10989e10i	0.250702	−	0.434228i	−0.713018	−	0.701146i	$-0.752672\pi$
$941$	6.40797e9	−	1.10989e10i	0.250702	−	0.434228i	0.963719	+	0.266918i	$0.0860054\pi$
$942$		0			0
$943$	9.09804e9			0.353311
$944$		0			0
$945$	9.56269e9	+	1.65631e10i	0.368611	+	0.638453i
$946$		0			0
$947$	−8.26947e8	−	1.43231e9i	−0.0316412	−	0.0548041i	0.849771	−	0.527152i	$-0.176740\pi$
$947$	−8.26947e8	−	1.43231e9i	−0.0316412	−	0.0548041i	−0.881412	+	0.472348i	$0.843407\pi$
$948$		0			0
$949$	−7.41596e10			−2.81667
$950$		0			0
$951$	−5.67671e10			−2.14025
$952$		0			0
$953$	2.14215e10	+	3.71032e10i	0.801725	+	1.38863i	0.918480	+	0.395468i	$0.129418\pi$
$953$	2.14215e10	+	3.71032e10i	0.801725	+	1.38863i	−0.116754	+	0.993161i	$0.537249\pi$
$954$		0			0
$955$	2.29211e10	+	3.97005e10i	0.851576	+	1.47497i
$956$		0			0
$957$	−3.91215e10			−1.44286
$958$		0			0
$959$	7.58295e9	−	1.31341e10i	0.277634	−	0.480877i
$960$		0			0
$961$	−2.64641e10			−0.961890
$962$		0			0
$963$	−1.51699e10	+	2.62750e10i	−0.547382	+	0.948094i
$964$		0			0
$965$	2.55727e10	−	4.42932e10i	0.916075	−	1.58669i
$966$		0			0
$967$	1.27574e10	+	2.20965e10i	0.453702	+	0.785836i	0.998613	−	0.0526587i	$-0.0167695\pi$
$967$	1.27574e10	+	2.20965e10i	0.453702	+	0.785836i	−0.544910	+	0.838494i	$0.683436\pi$
$968$		0			0
$969$	−1.06274e10	+	7.06347e9i	−0.375228	+	0.249394i
$970$		0			0
$971$	9.26560e9	+	1.60485e10i	0.324793	+	0.562557i	0.981470	−	0.191614i	$-0.0613722\pi$
$971$	9.26560e9	+	1.60485e10i	0.324793	+	0.562557i	−0.656678	+	0.754171i	$0.728039\pi$
$972$		0			0
$973$	−1.68019e10	+	2.91017e10i	−0.584739	+	1.01280i
$974$		0			0
$975$	−3.98100e10	+	6.89530e10i	−1.37555	+	2.38252i
$976$		0			0
$977$	−4.29083e10			−1.47201			−0.736005	−	0.676976i	$-0.763290\pi$
$977$	−4.29083e10			−1.47201			−0.736005	+	0.676976i	$0.763290\pi$
$978$		0			0
$979$	3.93455e8	−	6.81485e8i	0.0134016	−	0.0232122i
$980$		0			0
$981$	7.35762e10			2.48826
$982$		0			0
$983$	−1.53186e10	−	2.65326e10i	−0.514377	−	0.890927i	−0.999861	−	0.0166811i	$-0.994690\pi$
$983$	−1.53186e10	−	2.65326e10i	−0.514377	−	0.890927i	0.485484	−	0.874245i	$-0.338643\pi$
$984$		0			0
$985$	3.06368e9	+	5.30645e9i	0.102145	+	0.176920i
$986$		0			0
$987$	2.84504e10			0.941841
$988$		0			0
$989$	−1.13384e10			−0.372705
$990$		0			0
$991$	1.29655e10	+	2.24568e10i	0.423185	+	0.732978i	0.996249	−	0.0865328i	$-0.0275787\pi$
$991$	1.29655e10	+	2.24568e10i	0.423185	+	0.732978i	−0.573064	+	0.819511i	$0.694245\pi$
$992$		0			0
$993$	5.94655e9	+	1.02997e10i	0.192727	+	0.333813i
$994$		0			0
$995$	−3.34595e10			−1.07681
$996$		0			0
$997$	−2.26789e10	+	3.92811e10i	−0.724753	+	1.25531i	0.234323	+	0.972159i	$0.424713\pi$
$997$	−2.26789e10	+	3.92811e10i	−0.724753	+	1.25531i	−0.959076	+	0.283150i	$0.908621\pi$
$998$		0			0
$999$	−3.95026e10			−1.25356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.e.a.45.10	✓	22
19.11	even	3	inner	76.8.e.a.49.10	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.e.a.45.10	✓	22	1.1	even	1	trivial
76.8.e.a.49.10	yes	22	19.11	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(36.8075 + 63.7525i) q^{3} +(-206.713 - 358.037i) q^{5} +601.253 q^{7} +(-1616.09 + 2799.14i) q^{9} +O(q^{10})\)	\(q+(36.8075 + 63.7525i) q^{3} +(-206.713 - 358.037i) q^{5} +601.253 q^{7} +(-1616.09 + 2799.14i) q^{9} +3731.62 q^{11} +(5827.71 - 10093.9i) q^{13} +(15217.2 - 26356.9i) q^{15} +(2898.95 + 5021.12i) q^{17} +(26782.0 + 13289.0i) q^{19} +(22130.6 + 38331.4i) q^{21} +(8207.55 - 14215.9i) q^{23} +(-46397.9 + 80363.5i) q^{25} -76940.5 q^{27} +(-71206.7 + 123334. i) q^{29} +32380.4 q^{31} +(137352. + 237900. i) q^{33} +(-124287. - 215271. i) q^{35} +513418. q^{37} +858014. q^{39} +(277124. + 479993. i) q^{41} +(-345365. - 598190. i) q^{43} +1.33626e6 q^{45} +(321391. - 556666. i) q^{47} -462038. q^{49} +(-213406. + 369630. i) q^{51} +(-54614.1 + 94594.4i) q^{53} +(-771374. - 1.33606e6i) q^{55} +(138572. + 2.19655e6i) q^{57} +(1.46307e6 + 2.53412e6i) q^{59} +(559090. - 968372. i) q^{61} +(-971677. + 1.68299e6i) q^{63} -4.81865e6 q^{65} +(1.54690e6 - 2.67932e6i) q^{67} +1.20840e6 q^{69} +(228472. + 395725. i) q^{71} +(-3.18133e6 - 5.51023e6i) q^{73} -6.83116e6 q^{75} +2.24365e6 q^{77} +(1.45650e6 + 2.52273e6i) q^{79} +(702392. + 1.21658e6i) q^{81} -1.61367e6 q^{83} +(1.19850e6 - 2.07586e6i) q^{85} -1.04838e7 q^{87} +(105438. - 182624. i) q^{89} +(3.50393e6 - 6.06898e6i) q^{91} +(1.19184e6 + 2.06433e6i) q^{93} +(-778229. - 1.23359e7i) q^{95} +(2.28074e6 + 3.95035e6i) q^{97} +(-6.03062e6 + 1.04453e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 13 q^{3} + q^{5} + 560 q^{7} - 6002 q^{9}+O(q^{10}) \) 22 * q + 13 * q^3 + q^5 + 560 * q^7 - 6002 * q^9	\( 22 q + 13 q^{3} + q^{5} + 560 q^{7} - 6002 q^{9} + 472 q^{11} - 567 q^{13} + 2995 q^{15} + 5589 q^{17} + 80912 q^{19} + 44412 q^{21} - 15425 q^{23} - 32806 q^{25} + 50290 q^{27} - 18919 q^{29} + 150296 q^{31} + 314618 q^{33} + 92808 q^{35} + 350100 q^{37} + 948810 q^{39} + 698891 q^{41} + 402545 q^{43} + 1477508 q^{45} - 653621 q^{47} - 1938490 q^{49} - 1386401 q^{51} - 106763 q^{53} + 414508 q^{55} + 1267563 q^{57} + 3136737 q^{59} + 2004581 q^{61} + 1465000 q^{63} - 7397638 q^{65} + 4344391 q^{67} + 1732238 q^{69} - 133823 q^{71} - 8349685 q^{73} - 12136824 q^{75} + 9147480 q^{77} - 94679 q^{79} - 838595 q^{81} - 2884080 q^{83} - 1421409 q^{85} - 31740598 q^{87} - 7039347 q^{89} + 1520096 q^{91} - 1993628 q^{93} + 1707587 q^{95} + 13308115 q^{97} + 6011488 q^{99}+O(q^{100}) \) 22 * q + 13 * q^3 + q^5 + 560 * q^7 - 6002 * q^9 + 472 * q^11 - 567 * q^13 + 2995 * q^15 + 5589 * q^17 + 80912 * q^19 + 44412 * q^21 - 15425 * q^23 - 32806 * q^25 + 50290 * q^27 - 18919 * q^29 + 150296 * q^31 + 314618 * q^33 + 92808 * q^35 + 350100 * q^37 + 948810 * q^39 + 698891 * q^41 + 402545 * q^43 + 1477508 * q^45 - 653621 * q^47 - 1938490 * q^49 - 1386401 * q^51 - 106763 * q^53 + 414508 * q^55 + 1267563 * q^57 + 3136737 * q^59 + 2004581 * q^61 + 1465000 * q^63 - 7397638 * q^65 + 4344391 * q^67 + 1732238 * q^69 - 133823 * q^71 - 8349685 * q^73 - 12136824 * q^75 + 9147480 * q^77 - 94679 * q^79 - 838595 * q^81 - 2884080 * q^83 - 1421409 * q^85 - 31740598 * q^87 - 7039347 * q^89 + 1520096 * q^91 - 1993628 * q^93 + 1707587 * q^95 + 13308115 * q^97 + 6011488 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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