LMFDB - Embedded newform 756.2.bq.a.277.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(25,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10, 12]))

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

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

chi := DirichletCharacter("756.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bq (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			277.9
Character	$\chi$	$=$	756.277
Dual form			756.2.bq.a.625.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.740435 + 1.56581i) q^{3} +(0.924734 - 0.775944i) q^{5} +(-0.000647530 - 2.64575i) q^{7} +(-1.90351 - 2.31876i) q^{9} +O(q^{10})$	\(q+(-0.740435 + 1.56581i) q^{3} +(0.924734 - 0.775944i) q^{5} +(-0.000647530 - 2.64575i) q^{7} +(-1.90351 - 2.31876i) q^{9} +(-0.935772 - 0.785206i) q^{11} +(-1.33860 - 0.487212i) q^{13} +(0.530273 + 2.02249i) q^{15} -2.54169 q^{17} -6.59414 q^{19} +(4.14322 + 1.95799i) q^{21} +(-8.05868 - 2.93312i) q^{23} +(-0.615197 + 3.48896i) q^{25} +(5.04016 - 1.26364i) q^{27} +(-3.96187 + 1.44200i) q^{29} +(-1.23676 - 7.01400i) q^{31} +(1.92236 - 0.883845i) q^{33} +(-2.05355 - 2.44611i) q^{35} +(5.69795 - 9.86913i) q^{37} +(1.75403 - 1.73525i) q^{39} +(10.2365 + 3.72579i) q^{41} +(0.269511 - 1.52847i) q^{43} +(-3.55947 - 0.667218i) q^{45} +(-1.93628 + 10.9812i) q^{47} +(-7.00000 + 0.00342640i) q^{49} +(1.88196 - 3.97980i) q^{51} +(6.20454 - 10.7466i) q^{53} -1.47462 q^{55} +(4.88254 - 10.3252i) q^{57} +(5.52412 + 2.01061i) q^{59} +(1.15759 - 6.56500i) q^{61} +(-6.13363 + 5.03772i) q^{63} +(-1.61590 + 0.588140i) q^{65} +(1.50594 - 1.26363i) q^{67} +(10.5596 - 10.4466i) q^{69} +(0.665025 + 1.15186i) q^{71} +(5.69772 + 9.86873i) q^{73} +(-5.00752 - 3.54663i) q^{75} +(-2.07685 + 2.47633i) q^{77} +(-12.7656 - 10.7116i) q^{79} +(-1.75329 + 8.82757i) q^{81} +(-9.56572 + 3.48164i) q^{83} +(-2.35039 + 1.97221i) q^{85} +(0.675610 - 7.27124i) q^{87} -4.13364 q^{89} +(-1.28818 + 3.54193i) q^{91} +(11.8983 + 3.25689i) q^{93} +(-6.09783 + 5.11668i) q^{95} +(1.44888 - 8.21701i) q^{97} +(-0.0394521 + 3.66448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.740435	+	1.56581i	−0.427491	+	0.904020i
$3$	−0.740435	+	1.56581i	−0.427491	+	0.904020i
$4$		0			0
$5$	0.924734	−	0.775944i	0.413553	−	0.347013i	−0.412151	−	0.911116i	$-0.635222\pi$
$5$	0.924734	−	0.775944i	0.413553	−	0.347013i	0.825704	+	0.564103i	$0.190778\pi$
$6$		0			0
$7$	−0.000647530	−	2.64575i	−0.000244743	−	1.00000i
$7$	−0.000647530	−	2.64575i	−0.000244743	−	1.00000i
$8$		0			0
$9$	−1.90351	−	2.31876i	−0.634504	−	0.772920i
$10$		0			0
$11$	−0.935772	−	0.785206i	−0.282146	−	0.236749i	0.490721	−	0.871317i	$-0.336733\pi$
$11$	−0.935772	−	0.785206i	−0.282146	−	0.236749i	−0.772867	+	0.634568i	$0.781178\pi$
$12$		0			0
$13$	−1.33860	−	0.487212i	−0.371262	−	0.135128i	0.149649	−	0.988739i	$-0.452186\pi$
$13$	−1.33860	−	0.487212i	−0.371262	−	0.135128i	−0.520911	+	0.853611i	$0.674408\pi$
$14$		0			0
$15$	0.530273	+	2.02249i	0.136916	+	0.522205i
$16$		0			0
$17$	−2.54169			−0.616451			−0.308225	−	0.951313i	$-0.599735\pi$
$17$	−2.54169			−0.616451			−0.308225	+	0.951313i	$0.599735\pi$
$18$		0			0
$19$	−6.59414			−1.51280			−0.756400	−	0.654109i	$-0.773044\pi$
$19$	−6.59414			−1.51280			−0.756400	+	0.654109i	$0.773044\pi$
$20$		0			0
$21$	4.14322	+	1.95799i	0.904124	+	0.427269i
$22$		0			0
$23$	−8.05868	−	2.93312i	−1.68035	−	0.611598i	−0.686994	−	0.726663i	$-0.741070\pi$
$23$	−8.05868	−	2.93312i	−1.68035	−	0.611598i	−0.993358	+	0.115065i	$0.963292\pi$
$24$		0			0
$25$	−0.615197	+	3.48896i	−0.123039	+	0.697791i
$26$		0			0
$27$	5.04016	−	1.26364i	0.969979	−	0.243188i
$28$		0			0
$29$	−3.96187	+	1.44200i	−0.735701	+	0.267773i	−0.682576	−	0.730814i	$-0.739140\pi$
$29$	−3.96187	+	1.44200i	−0.735701	+	0.267773i	−0.0531252	+	0.998588i	$0.516918\pi$
$30$		0			0
$31$	−1.23676	−	7.01400i	−0.222128	−	1.25975i	−0.868100	−	0.496390i	$-0.834659\pi$
$31$	−1.23676	−	7.01400i	−0.222128	−	1.25975i	0.645971	−	0.763362i	$-0.276452\pi$
$32$		0			0
$33$	1.92236	−	0.883845i	0.334640	−	0.153858i
$34$		0			0
$35$	−2.05355	−	2.44611i	−0.347114	−	0.413468i
$36$		0			0
$37$	5.69795	−	9.86913i	0.936736	−	1.62248i	0.165229	−	0.986255i	$-0.447164\pi$
$37$	5.69795	−	9.86913i	0.936736	−	1.62248i	0.771508	−	0.636220i	$-0.219503\pi$
$38$		0			0
$39$	1.75403	−	1.73525i	0.280870	−	0.277862i
$40$		0			0
$41$	10.2365	+	3.72579i	1.59867	+	0.581870i	0.979156	−	0.203112i	$-0.0651055\pi$
$41$	10.2365	+	3.72579i	1.59867	+	0.581870i	0.619519	+	0.784982i	$0.287328\pi$
$42$		0			0
$43$	0.269511	−	1.52847i	0.0411000	−	0.233090i	−0.957337	−	0.288973i	$-0.906686\pi$
$43$	0.269511	−	1.52847i	0.0411000	−	0.233090i	0.998437	+	0.0558830i	$0.0177974\pi$
$44$		0			0
$45$	−3.55947	−	0.667218i	−0.530614	−	0.0994630i
$46$		0			0
$47$	−1.93628	+	10.9812i	−0.282436	+	1.60177i	0.431868	+	0.901937i	$0.357855\pi$
$47$	−1.93628	+	10.9812i	−0.282436	+	1.60177i	−0.714304	+	0.699836i	$0.753256\pi$
$48$		0			0
$49$	−7.00000	+	0.00342640i	−1.00000	+	0.000489486i
$50$		0			0
$51$	1.88196	−	3.97980i	0.263527	−	0.557284i
$52$		0			0
$53$	6.20454	−	10.7466i	0.852260	−	1.47616i	−0.0269043	−	0.999638i	$-0.508565\pi$
$53$	6.20454	−	10.7466i	0.852260	−	1.47616i	0.879164	−	0.476519i	$-0.158102\pi$
$54$		0			0
$55$	−1.47462			−0.198837
$56$		0			0
$57$	4.88254	−	10.3252i	0.646708	−	1.36760i
$58$		0			0
$59$	5.52412	+	2.01061i	0.719179	+	0.261760i	0.675577	−	0.737289i	$-0.263895\pi$
$59$	5.52412	+	2.01061i	0.719179	+	0.261760i	0.0436016	+	0.999049i	$0.486117\pi$
$60$		0			0
$61$	1.15759	−	6.56500i	0.148214	−	0.840562i	−0.816516	−	0.577322i	$-0.804098\pi$
$61$	1.15759	−	6.56500i	0.148214	−	0.840562i	0.964730	−	0.263240i	$-0.0847912\pi$
$62$		0			0
$63$	−6.13363	+	5.03772i	−0.772765	+	0.634693i
$64$		0			0
$65$	−1.61590	+	0.588140i	−0.200428	+	0.0729498i
$66$		0			0
$67$	1.50594	−	1.26363i	0.183980	−	0.154377i	−0.546146	−	0.837690i	$-0.683906\pi$
$67$	1.50594	−	1.26363i	0.183980	−	0.154377i	0.730126	+	0.683312i	$0.239461\pi$
$68$		0			0
$69$	10.5596	−	10.4466i	1.27123	−	1.25762i
$70$		0			0
$71$	0.665025	+	1.15186i	0.0789240	+	0.136700i	0.902786	−	0.430090i	$-0.141518\pi$
$71$	0.665025	+	1.15186i	0.0789240	+	0.136700i	−0.823862	+	0.566791i	$0.808185\pi$
$72$		0			0
$73$	5.69772	+	9.86873i	0.666867	+	1.15505i	0.978775	+	0.204936i	$0.0656985\pi$
$73$	5.69772	+	9.86873i	0.666867	+	1.15505i	−0.311908	+	0.950112i	$0.600968\pi$
$74$		0			0
$75$	−5.00752	−	3.54663i	−0.578219	−	0.409529i
$76$		0			0
$77$	−2.07685	+	2.47633i	−0.236680	+	0.282204i
$78$		0			0
$79$	−12.7656	−	10.7116i	−1.43625	−	1.20515i	−0.941902	−	0.335889i	$-0.890963\pi$
$79$	−12.7656	−	10.7116i	−1.43625	−	1.20515i	−0.494346	−	0.869265i	$-0.664592\pi$
$80$		0			0
$81$	−1.75329	+	8.82757i	−0.194811	+	0.980841i
$82$		0			0
$83$	−9.56572	+	3.48164i	−1.04997	+	0.382159i	−0.808653	−	0.588286i	$-0.799803\pi$
$83$	−9.56572	+	3.48164i	−1.04997	+	0.382159i	−0.241321	+	0.970445i	$0.577581\pi$
$84$		0			0
$85$	−2.35039	+	1.97221i	−0.254935	+	0.213916i
$86$		0			0
$87$	0.675610	−	7.27124i	0.0724330	−	0.779559i
$88$		0			0
$89$	−4.13364			−0.438165			−0.219082	−	0.975706i	$-0.570306\pi$
$89$	−4.13364			−0.438165			−0.219082	+	0.975706i	$0.570306\pi$
$90$		0			0
$91$	−1.28818	+	3.54193i	−0.135038	+	0.371295i
$92$		0			0
$93$	11.8983	+	3.25689i	1.23380	+	0.337724i
$94$		0			0
$95$	−6.09783	+	5.11668i	−0.625624	+	0.524961i
$96$		0			0
$97$	1.44888	−	8.21701i	0.147111	−	0.834311i	−0.818536	−	0.574455i	$-0.805214\pi$
$97$	1.44888	−	8.21701i	0.147111	−	0.834311i	0.965648	−	0.259855i	$-0.0836749\pi$
$98$		0			0
$99$	−0.0394521	+	3.66448i	−0.00396509	+	0.368294i
$100$		0			0
$101$	−7.58133	+	2.75938i	−0.754371	+	0.274568i	−0.690444	−	0.723386i	$-0.742585\pi$
$101$	−7.58133	+	2.75938i	−0.754371	+	0.274568i	−0.0639269	+	0.997955i	$0.520362\pi$
$102$		0			0
$103$	9.18737	−	7.70912i	0.905259	−	0.759602i	−0.0659523	−	0.997823i	$-0.521009\pi$
$103$	9.18737	−	7.70912i	0.905259	−	0.759602i	0.971211	+	0.238220i	$0.0765641\pi$
$104$		0			0
$105$	5.35067	−	1.40428i	0.522172	−	0.137044i
$106$		0			0
$107$	1.40726	+	2.43744i	0.136045	+	0.235636i	0.925996	−	0.377533i	$-0.123228\pi$
$107$	1.40726	+	2.43744i	0.136045	+	0.235636i	−0.789951	+	0.613170i	$0.789894\pi$
$108$		0			0
$109$	−0.123885	+	0.214575i	−0.0118660	+	0.0205526i	−0.871897	−	0.489689i	$-0.837110\pi$
$109$	−0.123885	+	0.214575i	−0.0118660	+	0.0205526i	0.860031	+	0.510241i	$0.170444\pi$
$110$		0			0
$111$	11.2342	+	16.2293i	1.06630	+	1.54042i
$112$		0			0
$113$	2.76266	+	15.6678i	0.259889	+	1.47390i	0.783204	+	0.621765i	$0.213584\pi$
$113$	2.76266	+	15.6678i	0.259889	+	1.47390i	−0.523315	+	0.852139i	$0.675305\pi$
$114$		0			0
$115$	−9.72807	+	3.54073i	−0.907147	+	0.330175i
$116$		0			0
$117$	1.41832	+	4.03132i	0.131124	+	0.372695i
$118$		0			0
$119$	0.00164582	+	6.72468i	0.000150872	+	0.616451i
$120$		0			0
$121$	−1.65101	−	9.36334i	−0.150092	−	0.851212i
$122$		0			0
$123$	−13.4133	+	13.2697i	−1.20944	+	1.19649i
$124$		0			0
$125$	5.15622	+	8.93084i	0.461187	+	0.798799i
$126$		0			0
$127$	−3.23555	+	5.60414i	−0.287109	+	0.497287i	−0.973118	−	0.230305i	$-0.926027\pi$
$127$	−3.23555	+	5.60414i	−0.287109	+	0.497287i	0.686010	+	0.727593i	$0.259361\pi$
$128$		0			0
$129$	2.19374	+	1.55374i	0.193148	+	0.136799i
$130$		0			0
$131$	3.32363	+	1.20970i	0.290387	+	0.105692i	0.483106	−	0.875562i	$-0.339509\pi$
$131$	3.32363	+	1.20970i	0.290387	+	0.105692i	−0.192720	+	0.981254i	$0.561731\pi$
$132$		0			0
$133$	0.00426990	+	17.4465i	0.000370248	+	1.51280i
$134$		0			0
$135$	3.68029	−	5.07941i	0.316749	−	0.437166i
$136$		0			0
$137$	−0.883662	+	5.01150i	−0.0754964	+	0.428161i	0.923509	+	0.383576i	$0.125308\pi$
$137$	−0.883662	+	5.01150i	−0.0754964	+	0.428161i	−0.999006	+	0.0445850i	$0.985803\pi$
$138$		0			0
$139$	9.60142	−	8.05655i	0.814382	−	0.683348i	−0.137267	−	0.990534i	$-0.543832\pi$
$139$	9.60142	−	8.05655i	0.814382	−	0.683348i	0.951649	+	0.307186i	$0.0993875\pi$
$140$		0			0
$141$	−15.7608	−	11.1627i	−1.32730	−	0.940070i
$142$		0			0
$143$	0.870067	+	1.50700i	0.0727587	+	0.126022i
$144$		0			0
$145$	−2.54476	+	4.40766i	−0.211331	+	0.366036i
$146$		0			0
$147$	5.17768	−	10.9632i	0.427048	−	0.904229i
$148$		0			0
$149$	−1.07563	−	6.10019i	−0.0881189	−	0.499747i	−0.996640	−	0.0819079i	$-0.973899\pi$
$149$	−1.07563	−	6.10019i	−0.0881189	−	0.499747i	0.908521	−	0.417839i	$-0.137212\pi$
$150$		0			0
$151$	2.37899	+	1.99621i	0.193599	+	0.162449i	0.734435	−	0.678679i	$-0.237447\pi$
$151$	2.37899	+	1.99621i	0.193599	+	0.162449i	−0.540835	+	0.841128i	$0.681892\pi$
$152$		0			0
$153$	4.83814	+	5.89357i	0.391140	+	0.476467i
$154$		0			0
$155$	−6.58614	−	5.52643i	−0.529011	−	0.443893i
$156$		0			0
$157$	2.40188	+	0.874214i	0.191691	+	0.0697698i	0.436082	−	0.899907i	$-0.356366\pi$
$157$	2.40188	+	0.874214i	0.191691	+	0.0697698i	−0.244391	+	0.969677i	$0.578588\pi$
$158$		0			0
$159$	12.2330	+	17.6723i	0.970142	+	1.40150i
$160$		0			0
$161$	−7.75509	+	21.3232i	−0.611187	+	1.68050i
$162$		0			0
$163$	−1.93202	−	3.34636i	−0.151328	−	0.262108i	0.780388	−	0.625296i	$-0.215022\pi$
$163$	−1.93202	−	3.34636i	−0.151328	−	0.262108i	−0.931716	+	0.363188i	$0.881688\pi$
$164$		0			0
$165$	1.09186	−	2.30897i	0.0850010	−	0.179753i
$166$		0			0
$167$	2.37370	+	13.4619i	0.183683	+	1.04172i	0.927636	+	0.373485i	$0.121837\pi$
$167$	2.37370	+	13.4619i	0.183683	+	1.04172i	−0.743954	+	0.668231i	$0.767052\pi$
$168$		0			0
$169$	−8.40409	−	7.05187i	−0.646469	−	0.542451i
$170$		0			0
$171$	12.5520	+	15.2902i	0.959877	+	1.16927i
$172$		0			0
$173$	15.2439	−	5.54834i	1.15898	−	0.421833i	0.310244	−	0.950657i	$-0.399589\pi$
$173$	15.2439	−	5.54834i	1.15898	−	0.421833i	0.848731	+	0.528824i	$0.177367\pi$
$174$		0			0
$175$	9.23131	+	1.62540i	0.697821	+	0.122869i
$176$		0			0
$177$	−7.23849	+	7.16098i	−0.544078	+	0.538252i
$178$		0			0
$179$	−19.0006			−1.42017			−0.710087	−	0.704114i	$-0.751344\pi$
$179$	−19.0006			−1.42017			−0.710087	+	0.704114i	$0.751344\pi$
$180$		0			0
$181$	−1.42054	+	2.46045i	−0.105588	+	0.182884i	−0.913978	−	0.405763i	$-0.867006\pi$
$181$	−1.42054	+	2.46045i	−0.105588	+	0.182884i	0.808390	+	0.588647i	$0.200339\pi$
$182$		0			0
$183$	9.42242	+	6.67352i	0.696525	+	0.493321i
$184$		0			0
$185$	−2.38881	−	13.5476i	−0.175629	−	0.996039i
$186$		0			0
$187$	2.37844	+	1.99575i	0.173929	+	0.145944i
$188$		0			0
$189$	−3.34654	−	13.3342i	−0.243425	−	0.969920i
$190$		0			0
$191$	−14.6340	−	12.2794i	−1.05888	−	0.888506i	−0.0648810	−	0.997893i	$-0.520667\pi$
$191$	−14.6340	−	12.2794i	−1.05888	−	0.888506i	−0.993999	+	0.109387i	$0.965111\pi$
$192$		0			0
$193$	−0.901837	−	5.11457i	−0.0649157	−	0.368155i	−0.999909	−	0.0134898i	$-0.995706\pi$
$193$	−0.901837	−	5.11457i	−0.0649157	−	0.368155i	0.934993	−	0.354665i	$-0.115405\pi$
$194$		0			0
$195$	0.275556	−	2.96567i	0.0197330	−	0.212376i
$196$		0			0
$197$	12.8017	−	22.1732i	0.912085	−	1.57978i	0.100971	−	0.994889i	$-0.467805\pi$
$197$	12.8017	−	22.1732i	0.912085	−	1.57978i	0.811114	−	0.584888i	$-0.198862\pi$
$198$		0			0
$199$	12.3581			0.876040			0.438020	−	0.898965i	$-0.355680\pi$
$199$	12.3581			0.876040			0.438020	+	0.898965i	$0.355680\pi$
$200$		0			0
$201$	0.863556	+	3.29365i	0.0609106	+	0.232316i
$202$		0			0
$203$	3.81775	+	10.4812i	0.267953	+	0.735636i
$204$		0			0
$205$	12.3570	−	4.49760i	0.863053	−	0.314126i
$206$		0			0
$207$	8.53859	+	24.2694i	0.593473	+	1.68684i
$208$		0			0
$209$	6.17062	+	5.17776i	0.426831	+	0.358153i
$210$		0			0
$211$	1.34718	+	7.64025i	0.0927439	+	0.525977i	0.995415	+	0.0956464i	$0.0304918\pi$
$211$	1.34718	+	7.64025i	0.0927439	+	0.525977i	−0.902672	+	0.430330i	$0.858397\pi$
$212$		0			0
$213$	−2.29600	+	0.188426i	−0.157319	+	0.0129107i
$214$		0			0
$215$	−0.936782	−	1.62255i	−0.0638880	−	0.110657i
$216$		0			0
$217$	−18.5565	+	3.27669i	−1.25970	+	0.222436i
$218$		0			0
$219$	−19.6713	+	1.61437i	−1.32927	+	0.109089i
$220$		0			0
$221$	3.40232	+	1.23834i	0.228865	+	0.0833000i
$222$		0			0
$223$	−5.87637	−	4.93086i	−0.393511	−	0.330195i	0.424468	−	0.905443i	$-0.360461\pi$
$223$	−5.87637	−	4.93086i	−0.393511	−	0.330195i	−0.817979	+	0.575248i	$0.804905\pi$
$224$		0			0
$225$	9.26109	−	5.21477i	0.617406	−	0.347651i
$226$		0			0
$227$	0.455680	+	0.382361i	0.0302445	+	0.0253782i	0.657785	−	0.753206i	$-0.271494\pi$
$227$	0.455680	+	0.382361i	0.0302445	+	0.0253782i	−0.627540	+	0.778584i	$0.715938\pi$
$228$		0			0
$229$	0.927307	+	5.25902i	0.0612782	+	0.347526i	0.999996	+	0.00283906i	$0.000903702\pi$
$229$	0.927307	+	5.25902i	0.0612782	+	0.347526i	−0.938718	+	0.344687i	$0.887985\pi$
$230$		0			0
$231$	−2.33968	−	5.08552i	−0.153940	−	0.334603i
$232$		0			0
$233$	1.58141	−	2.73907i	0.103601	−	0.179443i	−0.809565	−	0.587031i	$-0.800297\pi$
$233$	1.58141	−	2.73907i	0.103601	−	0.179443i	0.913166	+	0.407588i	$0.133630\pi$
$234$		0			0
$235$	6.73025	+	11.6571i	0.439033	+	0.760427i
$236$		0			0
$237$	26.2245	−	12.0573i	1.70347	−	0.783204i
$238$		0			0
$239$	1.27452	−	1.06945i	0.0824421	−	0.0691772i	−0.600635	−	0.799523i	$-0.705086\pi$
$239$	1.27452	−	1.06945i	0.0824421	−	0.0691772i	0.683077	+	0.730346i	$0.260641\pi$
$240$		0			0
$241$	1.83122	−	10.3854i	0.117959	−	0.668981i	−0.867283	−	0.497816i	$-0.834136\pi$
$241$	1.83122	−	10.3854i	0.117959	−	0.668981i	0.985242	−	0.171165i	$-0.0547533\pi$
$242$		0			0
$243$	−12.5241	−	9.28157i	−0.803420	−	0.595413i
$244$		0			0
$245$	−6.47048	+	5.43477i	−0.413384	+	0.347215i
$246$		0			0
$247$	8.82695	+	3.21275i	0.561646	+	0.204422i
$248$		0			0
$249$	1.63122	−	17.5560i	0.103374	−	1.11257i
$250$		0			0
$251$	1.73221	−	3.00028i	0.109336	−	0.189376i	−0.806165	−	0.591690i	$-0.798461\pi$
$251$	1.73221	−	3.00028i	0.109336	−	0.189376i	0.915502	+	0.402314i	$0.131794\pi$
$252$		0			0
$253$	5.23799	+	9.07246i	0.329310	+	0.570381i
$254$		0			0
$255$	−1.34779	−	5.14055i	−0.0844019	−	0.321914i
$256$		0			0
$257$	2.94471	+	16.7003i	0.183686	+	1.04174i	0.927632	+	0.373496i	$0.121841\pi$
$257$	2.94471	+	16.7003i	0.183686	+	1.04174i	−0.743945	+	0.668240i	$0.767048\pi$
$258$		0			0
$259$	−26.1150	−	15.0690i	−1.62270	−	0.936339i
$260$		0			0
$261$	10.8851	+	6.44176i	0.673772	+	0.398735i
$262$		0			0
$263$	−0.752997	+	0.274068i	−0.0464318	+	0.0168998i	−0.365132	−	0.930956i	$-0.618976\pi$
$263$	−0.752997	+	0.274068i	−0.0464318	+	0.0168998i	0.318700	+	0.947856i	$0.396754\pi$
$264$		0			0
$265$	−2.60119	−	14.7521i	−0.159790	−	0.906215i
$266$		0			0
$267$	3.06069	−	6.47249i	0.187311	−	0.396110i
$268$		0			0
$269$	12.1374	−	21.0225i	0.740029	−	1.28177i	−0.212453	−	0.977171i	$-0.568145\pi$
$269$	12.1374	−	21.0225i	0.740029	−	1.28177i	0.952482	−	0.304596i	$-0.0985214\pi$
$270$		0			0
$271$	10.7864	+	18.6826i	0.655227	+	1.13489i	0.981837	+	0.189727i	$0.0607603\pi$
$271$	10.7864	+	18.6826i	0.655227	+	1.13489i	−0.326610	+	0.945159i	$0.605906\pi$
$272$		0			0
$273$	−4.59217	−	4.63961i	−0.277931	−	0.280802i
$274$		0			0
$275$	3.31524	−	2.78181i	0.199916	−	0.167750i
$276$		0			0
$277$	−24.7090	+	8.99332i	−1.48462	+	0.540356i	−0.952026	−	0.306017i	$-0.901004\pi$
$277$	−24.7090	+	8.99332i	−1.48462	+	0.540356i	−0.532591	+	0.846373i	$0.678781\pi$
$278$		0			0
$279$	−13.9096	+	16.2190i	−0.832746	+	0.971004i
$280$		0			0
$281$	−1.74183	+	9.87843i	−0.103909	+	0.589298i	0.887741	+	0.460343i	$0.152273\pi$
$281$	−1.74183	+	9.87843i	−0.103909	+	0.589298i	−0.991650	+	0.128955i	$0.958838\pi$
$282$		0			0
$283$	13.8453	−	11.6176i	0.823020	−	0.690596i	−0.130657	−	0.991428i	$-0.541709\pi$
$283$	13.8453	−	11.6176i	0.823020	−	0.690596i	0.953677	+	0.300832i	$0.0972643\pi$
$284$		0			0
$285$	−3.49670	−	13.3366i	−0.207127	−	0.789992i
$286$		0			0
$287$	9.85087	−	27.0857i	0.581479	−	1.59882i
$288$		0			0
$289$	−10.5398			−0.619989
$290$		0			0
$291$	11.7935	+	8.35283i	0.691345	+	0.489652i
$292$		0			0
$293$	−10.0250	+	8.41200i	−0.585668	+	0.491434i	−0.886803	−	0.462147i	$-0.847079\pi$
$293$	−10.0250	+	8.41200i	−0.585668	+	0.491434i	0.301135	+	0.953582i	$0.402635\pi$
$294$		0			0
$295$	6.66846	−	2.42712i	0.388253	−	0.141312i
$296$		0			0
$297$	−5.70866	−	2.77509i	−0.331250	−	0.161027i
$298$		0			0
$299$	9.35834	+	7.85258i	0.541207	+	0.454126i
$300$		0			0
$301$	−4.04413	−	0.712069i	−0.233100	−	0.0410430i
$302$		0			0
$303$	1.29283	−	13.9141i	0.0742711	−	0.799341i
$304$		0			0
$305$	−4.02361	−	6.96910i	−0.230391	−	0.399049i
$306$		0			0
$307$	−3.12591	−	5.41424i	−0.178405	−	0.309007i	0.762929	−	0.646482i	$-0.223760\pi$
$307$	−3.12591	−	5.41424i	−0.178405	−	0.309007i	−0.941334	+	0.337475i	$0.890427\pi$
$308$		0			0
$309$	5.26835	+	20.0938i	0.299706	+	1.14309i
$310$		0			0
$311$	0.883493	−	0.741339i	0.0500983	−	0.0420375i	−0.617395	−	0.786654i	$-0.711812\pi$
$311$	0.883493	−	0.741339i	0.0500983	−	0.0420375i	0.667493	+	0.744616i	$0.267367\pi$
$312$		0			0
$313$	−22.4130	+	8.15765i	−1.26686	+	0.461098i	−0.886064	−	0.463563i	$-0.846571\pi$
$313$	−22.4130	+	8.15765i	−1.26686	+	0.461098i	−0.380792	+	0.924661i	$0.624349\pi$
$314$		0			0
$315$	−1.76299	+	9.41790i	−0.0993332	+	0.530638i
$316$		0			0
$317$	1.68911	−	9.57944i	0.0948701	−	0.538035i	−0.899917	−	0.436061i	$-0.856373\pi$
$317$	1.68911	−	9.57944i	0.0948701	−	0.538035i	0.994787	−	0.101974i	$-0.0325158\pi$
$318$		0			0
$319$	4.83968	+	1.76150i	0.270970	+	0.0986251i
$320$		0			0
$321$	−4.85855	+	0.398727i	−0.271178	+	0.0222548i
$322$		0			0
$323$	16.7603			0.932567
$324$		0			0
$325$	2.52337	−	4.37060i	0.139971	−	0.242437i
$326$		0			0
$327$	−0.244254	−	0.352859i	−0.0135073	−	0.0195131i
$328$		0			0
$329$	29.0548	+	5.11581i	1.60184	+	0.282044i
$330$		0			0
$331$	2.30729	−	13.0853i	0.126820	−	0.719233i	−0.853390	−	0.521273i	$-0.825457\pi$
$331$	2.30729	−	13.0853i	0.126820	−	0.719233i	0.980210	−	0.197960i	$-0.0634315\pi$
$332$		0			0
$333$	−33.7302	+	5.57383i	−1.84841	+	0.305444i
$334$		0			0
$335$	0.412085	−	2.33705i	0.0225146	−	0.127687i
$336$		0			0
$337$	22.9087	+	8.33807i	1.24791	+	0.454203i	0.879696	−	0.475536i	$-0.157746\pi$
$337$	22.9087	+	8.33807i	1.24791	+	0.454203i	0.368218	+	0.929740i	$0.379968\pi$
$338$		0			0
$339$	−26.5784	−	7.27521i	−1.44354	−	0.395135i
$340$		0			0
$341$	−4.35011	+	7.53462i	−0.235572	+	0.408022i
$342$		0			0
$343$	0.0135981	+	18.5203i	0.000734230	+	1.00000i
$344$		0			0
$345$	1.65891	−	17.8540i	0.0893126	−	0.961226i
$346$		0			0
$347$	−4.61971	−	26.1997i	−0.247999	−	1.40647i	−0.813423	−	0.581672i	$-0.802399\pi$
$347$	−4.61971	−	26.1997i	−0.247999	−	1.40647i	0.565424	−	0.824800i	$-0.308712\pi$
$348$		0			0
$349$	−25.2893	+	9.20456i	−1.35371	+	0.492709i	−0.914102	−	0.405483i	$-0.867103\pi$
$349$	−25.2893	+	9.20456i	−1.35371	+	0.492709i	−0.439603	+	0.898192i	$0.644881\pi$
$350$		0			0
$351$	−7.36244	−	0.764113i	−0.392978	−	0.0407853i
$352$		0			0
$353$	−1.60900	+	9.12509i	−0.0856384	+	0.485679i	0.911579	+	0.411126i	$0.134864\pi$
$353$	−1.60900	+	9.12509i	−0.0856384	+	0.485679i	−0.997217	+	0.0745537i	$0.976247\pi$
$354$		0			0
$355$	1.50875	+	0.549139i	0.0800760	+	0.0291453i
$356$		0			0
$357$	−10.5308	−	4.97662i	−0.557348	−	0.263390i
$358$		0			0
$359$	−27.2347			−1.43739			−0.718695	−	0.695325i	$-0.755260\pi$
$359$	−27.2347			−1.43739			−0.718695	+	0.695325i	$0.755260\pi$
$360$		0			0
$361$	24.4827			1.28856
$362$		0			0
$363$	15.8837	+	4.34778i	0.833676	+	0.228199i
$364$		0			0
$365$	12.9264	+	4.70484i	0.676601	+	0.246263i
$366$		0			0
$367$	9.50537	+	7.97595i	0.496176	+	0.416341i	0.856234	−	0.516589i	$-0.172798\pi$
$367$	9.50537	+	7.97595i	0.496176	+	0.416341i	−0.360057	+	0.932930i	$0.617243\pi$
$368$		0			0
$369$	−10.8461	−	30.8281i	−0.564626	−	1.60485i
$370$		0			0
$371$	−28.4368	−	16.4087i	−1.47637	−	0.851898i
$372$		0			0
$373$	−0.806179	+	0.676464i	−0.0417423	+	0.0350260i	−0.663420	−	0.748247i	$-0.730896\pi$
$373$	−0.806179	+	0.676464i	−0.0417423	+	0.0350260i	0.621678	+	0.783273i	$0.286451\pi$
$374$		0			0
$375$	−17.8018	+	1.46095i	−0.919283	+	0.0754429i
$376$		0			0
$377$	6.00594			0.309322
$378$		0			0
$379$	1.75486			0.0901411			0.0450705	−	0.998984i	$-0.485649\pi$
$379$	1.75486			0.0901411			0.0450705	+	0.998984i	$0.485649\pi$
$380$		0			0
$381$	−6.37929	−	9.21576i	−0.326821	−	0.472138i
$382$		0			0
$383$	14.4461	−	12.1217i	0.738160	−	0.619389i	−0.194183	−	0.980965i	$-0.562206\pi$
$383$	14.4461	−	12.1217i	0.738160	−	0.619389i	0.932343	+	0.361576i	$0.117761\pi$
$384$		0			0
$385$	0.000954858		3.90147i	4.86640e−5		0.198837i
$386$		0			0
$387$	−4.05718	+	2.28453i	−0.206238	+	0.116129i
$388$		0			0
$389$	−14.8638	−	12.4722i	−0.753624	−	0.632366i	0.182834	−	0.983144i	$-0.441473\pi$
$389$	−14.8638	−	12.4722i	−0.753624	−	0.632366i	−0.936459	+	0.350778i	$0.885917\pi$
$390$		0			0
$391$	20.4827	+	7.45509i	1.03585	+	0.377020i
$392$		0			0
$393$	−4.35509	+	4.30846i	−0.219685	+	0.217333i
$394$		0			0
$395$	−20.1165			−1.01217
$396$		0			0
$397$	−16.6131			−0.833788			−0.416894	−	0.908955i	$-0.636881\pi$
$397$	−16.6131			−0.833788			−0.416894	+	0.908955i	$0.636881\pi$
$398$		0			0
$399$	−27.3210	−	12.9113i	−1.36776	−	0.646373i
$400$		0			0
$401$	5.77872	+	2.10328i	0.288576	+	0.105033i	0.482252	−	0.876033i	$-0.339819\pi$
$401$	5.77872	+	2.10328i	0.288576	+	0.105033i	−0.193676	+	0.981065i	$0.562041\pi$
$402$		0			0
$403$	−1.76178	+	9.99154i	−0.0877604	+	0.497714i
$404$		0			0
$405$	5.22836	+	9.52361i	0.259800	+	0.473232i
$406$		0			0
$407$	−13.0813	+	4.76120i	−0.648415	+	0.236004i
$408$		0			0
$409$	−2.65941	−	15.0823i	−0.131499	−	0.745770i	−0.977234	−	0.212166i	$-0.931948\pi$
$409$	−2.65941	−	15.0823i	−0.131499	−	0.745770i	0.845734	−	0.533604i	$-0.179163\pi$
$410$		0			0
$411$	−7.19275	−	5.09434i	−0.354792	−	0.251285i
$412$		0			0
$413$	5.31601	−	14.6167i	0.261584	−	0.719243i
$414$		0			0
$415$	−6.14419	+	10.6420i	−0.301606	+	0.522397i
$416$		0			0
$417$	5.50578	+	20.9993i	0.269619	+	1.02834i
$418$		0			0
$419$	−21.9431	−	7.98663i	−1.07199	−	0.390172i	−0.255069	−	0.966923i	$-0.582098\pi$
$419$	−21.9431	−	7.98663i	−1.07199	−	0.390172i	−0.816920	+	0.576750i	$0.804320\pi$
$420$		0			0
$421$	1.90088	−	10.7804i	0.0926431	−	0.525405i	−0.902801	−	0.430058i	$-0.858493\pi$
$421$	1.90088	−	10.7804i	0.0926431	−	0.525405i	0.995444	−	0.0953466i	$-0.0303959\pi$
$422$		0			0
$423$	29.1485	−	16.4131i	1.41725	−	0.798030i
$424$		0			0
$425$	1.56364	−	8.86785i	0.0758477	−	0.430154i
$426$		0			0
$427$	−17.3701	−	3.05844i	−0.840599	−	0.148008i
$428$		0			0
$429$	−3.00390	+	0.246522i	−0.145030	+	0.0119022i
$430$		0			0
$431$	−2.23273	+	3.86721i	−0.107547	+	0.186277i	−0.914776	−	0.403962i	$-0.867633\pi$
$431$	−2.23273	+	3.86721i	−0.107547	+	0.186277i	0.807229	+	0.590238i	$0.200966\pi$
$432$		0			0
$433$	19.1320			0.919423			0.459712	−	0.888068i	$-0.347953\pi$
$433$	19.1320			0.919423			0.459712	+	0.888068i	$0.347953\pi$
$434$		0			0
$435$	−5.01732	−	7.24820i	−0.240562	−	0.347524i
$436$		0			0
$437$	53.1401	+	19.3414i	2.54204	+	0.925226i
$438$		0			0
$439$	−5.51656	+	31.2860i	−0.263291	+	1.49320i	0.510567	+	0.859838i	$0.329435\pi$
$439$	−5.51656	+	31.2860i	−0.263291	+	1.49320i	−0.773858	+	0.633359i	$0.781676\pi$
$440$		0			0
$441$	13.3325	+	16.2248i	0.634882	+	0.772609i
$442$		0			0
$443$	−3.42069	+	1.24503i	−0.162522	+	0.0591532i	−0.422000	−	0.906596i	$-0.638672\pi$
$443$	−3.42069	+	1.24503i	−0.162522	+	0.0591532i	0.259478	+	0.965749i	$0.416450\pi$
$444$		0			0
$445$	−3.82251	+	3.20747i	−0.181205	+	0.152049i
$446$		0			0
$447$	10.3482	+	2.83257i	0.489451	+	0.133976i
$448$		0			0
$449$	−6.66096	−	11.5371i	−0.314350	−	0.544470i	0.664949	−	0.746889i	$-0.268453\pi$
$449$	−6.66096	−	11.5371i	−0.314350	−	0.544470i	−0.979299	+	0.202418i	$0.935120\pi$
$450$		0			0
$451$	−6.65353	−	11.5243i	−0.313303	−	0.542656i
$452$		0			0
$453$	−4.88717	+	2.24698i	−0.229619	+	0.105572i
$454$		0			0
$455$	1.55712	+	4.27489i	0.0729989	+	0.200410i
$456$		0			0
$457$	11.3245	+	9.50242i	0.529740	+	0.444504i	0.868011	−	0.496544i	$-0.165398\pi$
$457$	11.3245	+	9.50242i	0.529740	+	0.444504i	−0.338272	+	0.941048i	$0.609842\pi$
$458$		0			0
$459$	−12.8105	+	3.21178i	−0.597944	+	0.149913i
$460$		0			0
$461$	−12.7289	+	4.63295i	−0.592846	+	0.215778i	−0.620981	−	0.783826i	$-0.713265\pi$
$461$	−12.7289	+	4.63295i	−0.592846	+	0.215778i	0.0281350	+	0.999604i	$0.491043\pi$
$462$		0			0
$463$	21.8512	−	18.3354i	1.01551	−	0.852117i	0.0264563	−	0.999650i	$-0.491578\pi$
$463$	21.8512	−	18.3354i	1.01551	−	0.852117i	0.989057	+	0.147533i	$0.0471333\pi$
$464$		0			0
$465$	13.5299	−	6.22067i	0.627436	−	0.288477i
$466$		0			0
$467$	39.8915			1.84596			0.922980	−	0.384848i	$-0.125746\pi$
$467$	39.8915			1.84596			0.922980	+	0.384848i	$0.125746\pi$
$468$		0			0
$469$	−3.34423	−	3.98352i	−0.154422	−	0.183942i
$470$		0			0
$471$	−3.14729	+	3.11359i	−0.145019	+	0.143467i
$472$		0			0
$473$	−1.45237	+	1.21868i	−0.0667799	+	0.0560350i
$474$		0			0
$475$	4.05670	−	23.0067i	0.186134	−	1.05562i
$476$		0			0
$477$	−36.7292	+	6.06939i	−1.68171	+	0.277898i
$478$		0			0
$479$	6.55313	−	2.38514i	0.299420	−	0.108980i	−0.187942	−	0.982180i	$-0.560182\pi$
$479$	6.55313	−	2.38514i	0.299420	−	0.108980i	0.487362	+	0.873200i	$0.337959\pi$
$480$		0			0
$481$	−12.4357	+	10.4348i	−0.567017	+	0.475784i
$482$		0			0
$483$	−27.6459	−	27.9314i	−1.25793	−	1.27092i
$484$		0			0
$485$	−5.03611	−	8.72279i	−0.228678	−	0.396082i
$486$		0			0
$487$	20.1799	−	34.9526i	0.914438	−	1.58385i	0.106715	−	0.994290i	$-0.465967\pi$
$487$	20.1799	−	34.9526i	0.914438	−	1.58385i	0.807722	−	0.589563i	$-0.200700\pi$
$488$		0			0
$489$	6.67031	−	0.547413i	0.301642	−	0.0247549i
$490$		0			0
$491$	−3.51327	−	19.9247i	−0.158551	−	0.899190i	−0.955467	−	0.295099i	$-0.904647\pi$
$491$	−3.51327	−	19.9247i	−0.158551	−	0.899190i	0.796915	−	0.604091i	$-0.206464\pi$
$492$		0			0
$493$	10.0699	−	3.66513i	0.453523	−	0.165069i
$494$		0			0
$495$	2.80695	+	3.41928i	0.126163	+	0.153685i
$496$		0			0
$497$	3.04710	−	1.76024i	0.136681	−	0.0789575i
$498$		0			0
$499$	−1.65001	−	9.35767i	−0.0738646	−	0.418907i	−0.999209	−	0.0397783i	$-0.987335\pi$
$499$	−1.65001	−	9.35767i	−0.0738646	−	0.418907i	0.925344	−	0.379129i	$-0.123776\pi$
$500$		0			0
$501$	−22.8364	−	6.25093i	−1.02025	−	0.279271i
$502$		0			0
$503$	−7.67986	−	13.3019i	−0.342428	−	0.593103i	0.642455	−	0.766324i	$-0.277916\pi$
$503$	−7.67986	−	13.3019i	−0.342428	−	0.593103i	−0.984883	+	0.173220i	$0.944583\pi$
$504$		0			0
$505$	−4.86959	+	8.43438i	−0.216694	+	0.375325i
$506$		0			0
$507$	17.2646	−	7.93774i	0.766746	−	0.352527i
$508$		0			0
$509$	−31.6463	−	11.5183i	−1.40270	−	0.510540i	−0.473719	−	0.880676i	$-0.657089\pi$
$509$	−31.6463	−	11.5183i	−1.40270	−	0.510540i	−0.928978	+	0.370136i	$0.879311\pi$
$510$		0			0
$511$	26.1065	−	15.0811i	1.15488	−	0.667150i
$512$		0			0
$513$	−33.2355	+	8.33263i	−1.46738	+	0.367894i
$514$		0			0
$515$	2.51403	−	14.2578i	0.110781	−	0.628272i
$516$		0			0
$517$	10.4344	−	8.75552i	0.458906	−	0.385068i
$518$		0			0
$519$	−2.59952	+	27.9773i	−0.114106	+	1.22807i
$520$		0			0
$521$	−18.1693	−	31.4701i	−0.796010	−	1.37873i	−0.922196	−	0.386723i	$-0.873607\pi$
$521$	−18.1693	−	31.4701i	−0.796010	−	1.37873i	0.126186	−	0.992007i	$-0.459726\pi$
$522$		0			0
$523$	−8.35451	+	14.4704i	−0.365317	+	0.632748i	−0.988827	−	0.149068i	$-0.952373\pi$
$523$	−8.35451	+	14.4704i	−0.365317	+	0.632748i	0.623510	+	0.781815i	$0.285706\pi$
$524$		0			0
$525$	−9.38025	+	13.2510i	−0.409388	+	0.578319i
$526$		0			0
$527$	3.14345	+	17.8274i	0.136931	+	0.776575i
$528$		0			0
$529$	38.7202	+	32.4901i	1.68348	+	1.41261i
$530$		0			0
$531$	−5.85308	−	16.6363i	−0.254002	−	0.721955i
$532$		0			0
$533$	−11.8874	−	9.97471i	−0.514900	−	0.432053i
$534$		0			0
$535$	3.19266	+	1.16203i	0.138031	+	0.0502390i
$536$		0			0
$537$	14.0687	−	29.7513i	0.607111	−	1.28387i
$538$		0			0
$539$	6.55310	+	5.49324i	0.282262	+	0.236610i
$540$		0			0
$541$	7.18915	+	12.4520i	0.309086	+	0.535352i	0.978163	−	0.207841i	$-0.0666437\pi$
$541$	7.18915	+	12.4520i	0.309086	+	0.535352i	−0.669077	+	0.743193i	$0.733310\pi$
$542$		0			0
$543$	−2.80078	−	4.04611i	−0.120193	−	0.173635i
$544$		0			0
$545$	0.0519375	+	0.294552i	0.00222476	+	0.0126172i
$546$		0			0
$547$	5.21279	+	4.37405i	0.222883	+	0.187021i	0.747391	−	0.664385i	$-0.231306\pi$
$547$	5.21279	+	4.37405i	0.222883	+	0.187021i	−0.524508	+	0.851405i	$0.675751\pi$
$548$		0			0
$549$	−17.4261	+	9.81238i	−0.743730	+	0.418782i
$550$		0			0
$551$	26.1252	−	9.50878i	1.11297	−	0.405088i
$552$		0			0
$553$	−28.3321	+	33.7817i	−1.20480	+	1.43654i
$554$		0			0
$555$	22.9817	+	6.29071i	0.975519	+	0.267026i
$556$		0			0
$557$	32.6579			1.38376			0.691881	−	0.722012i	$-0.256782\pi$
$557$	32.6579			1.38376			0.691881	+	0.722012i	$0.256782\pi$
$558$		0			0
$559$	−1.10546	+	1.91471i	−0.0467559	+	0.0809837i
$560$		0			0
$561$	−4.88605	+	2.24646i	−0.206289	+	0.0948457i
$562$		0			0
$563$	−3.05022	−	17.2986i	−0.128551	−	0.729051i	−0.979135	−	0.203211i	$-0.934862\pi$
$563$	−3.05022	−	17.2986i	−0.128551	−	0.729051i	0.850584	−	0.525840i	$-0.176249\pi$
$564$		0			0
$565$	14.7121	+	12.3449i	0.618941	+	0.519353i
$566$		0			0
$567$	23.3567	+	4.63307i	0.980889	+	0.194570i
$568$		0			0
$569$	32.9774	+	27.6713i	1.38248	+	1.16004i	0.968283	+	0.249856i	$0.0803832\pi$
$569$	32.9774	+	27.6713i	1.38248	+	1.16004i	0.414201	+	0.910186i	$0.364061\pi$
$570$		0			0
$571$	−1.24773	−	7.07620i	−0.0522157	−	0.296130i	0.947506	−	0.319739i	$-0.103595\pi$
$571$	−1.24773	−	7.07620i	−0.0522157	−	0.296130i	−0.999721	+	0.0236094i	$0.992484\pi$
$572$		0			0
$573$	30.0627	−	13.8220i	1.25589	−	0.577421i
$574$		0			0
$575$	15.1912	−	26.3119i	0.633517	−	1.09728i
$576$		0			0
$577$	−0.368099			−0.0153241			−0.00766207	−	0.999971i	$-0.502439\pi$
$577$	−0.368099			−0.0153241			−0.00766207	+	0.999971i	$0.502439\pi$
$578$		0			0
$579$	8.67619	+	2.37491i	0.360570	+	0.0986978i
$580$		0			0
$581$	9.21774	+	25.3062i	0.382416	+	1.04988i
$582$		0			0
$583$	−14.2443	+	5.18451i	−0.589940	+	0.214721i
$584$		0			0
$585$	4.43964	+	2.62736i	0.183557	+	0.108628i
$586$		0			0
$587$	−4.89969	−	4.11133i	−0.202232	−	0.169693i	0.536047	−	0.844188i	$-0.319917\pi$
$587$	−4.89969	−	4.11133i	−0.202232	−	0.169693i	−0.738279	+	0.674495i	$0.764361\pi$
$588$		0			0
$589$	8.15536	+	46.2513i	0.336036	+	1.90575i
$590$		0			0
$591$	25.2402	+	36.4629i	1.03824	+	1.49988i
$592$		0			0
$593$	−12.8441	−	22.2467i	−0.527444	−	0.913561i	−0.999488	−	0.0319856i	$-0.989817\pi$
$593$	−12.8441	−	22.2467i	−0.527444	−	0.913561i	0.472044	−	0.881575i	$-0.343516\pi$
$594$		0			0
$595$	5.21950	+	6.21726i	0.213978	+	0.254883i
$596$		0			0
$597$	−9.15035	+	19.3504i	−0.374499	+	0.791957i
$598$		0			0
$599$	−3.45802	−	1.25862i	−0.141291	−	0.0514256i	0.270407	−	0.962746i	$-0.412842\pi$
$599$	−3.45802	−	1.25862i	−0.141291	−	0.0514256i	−0.411698	+	0.911321i	$0.635064\pi$
$600$		0			0
$601$	−20.8118	−	17.4631i	−0.848930	−	0.712336i	0.110624	−	0.993862i	$-0.464715\pi$
$601$	−20.8118	−	17.4631i	−0.848930	−	0.712336i	−0.959554	+	0.281526i	$0.909159\pi$
$602$		0			0
$603$	−5.79663	−	1.08657i	−0.236057	−	0.0442487i
$604$		0			0
$605$	−8.79216	−	7.37750i	−0.357452	−	0.299938i
$606$		0			0
$607$	0.617370	+	3.50128i	0.0250583	+	0.142113i	0.994770	−	0.102139i	$-0.0325687\pi$
$607$	0.617370	+	3.50128i	0.0250583	+	0.142113i	−0.969712	+	0.244252i	$0.921458\pi$
$608$		0			0
$609$	−19.2383	−	1.78279i	−0.779577	−	0.0722422i
$610$		0			0
$611$	7.94209	−	13.7561i	0.321303	−	0.556513i
$612$		0			0
$613$	13.2899	+	23.0187i	0.536773	+	0.929717i	0.999075	+	0.0429953i	$0.0136900\pi$
$613$	13.2899	+	23.0187i	0.536773	+	0.929717i	−0.462303	+	0.886722i	$0.652977\pi$
$614$		0			0
$615$	−2.10722	+	22.6789i	−0.0849713	+	0.914503i
$616$		0			0
$617$	16.6754	−	13.9923i	0.671326	−	0.563309i	−0.242132	−	0.970243i	$-0.577847\pi$
$617$	16.6754	−	13.9923i	0.671326	−	0.563309i	0.913458	+	0.406934i	$0.133402\pi$
$618$		0			0
$619$	1.47950	−	8.39065i	0.0594660	−	0.337249i	−0.940531	−	0.339708i	$-0.889672\pi$
$619$	1.47950	−	8.39065i	0.0594660	−	0.337249i	0.999997	+	0.00245942i	$0.000782857\pi$
$620$		0			0
$621$	−44.3235	−	4.60012i	−1.77864	−	0.184596i
$622$		0			0
$623$	0.00267665	+	10.9366i	0.000107238	+	0.438165i
$624$		0			0
$625$	−4.94765	−	1.80080i	−0.197906	−	0.0720319i
$626$		0			0
$627$	−12.6763	+	5.82820i	−0.506244	+	0.232756i
$628$		0			0
$629$	−14.4824	+	25.0843i	−0.577452	+	1.00018i
$630$		0			0
$631$	8.98748	+	15.5668i	0.357786	+	0.619703i	0.987591	−	0.157050i	$-0.0501984\pi$
$631$	8.98748	+	15.5668i	0.357786	+	0.619703i	−0.629805	+	0.776754i	$0.716865\pi$
$632$		0			0
$633$	−12.9607	−	3.54768i	−0.515140	−	0.141008i
$634$		0			0
$635$	1.35647	+	7.69294i	0.0538300	+	0.305285i
$636$		0			0
$637$	9.37190	+	3.40590i	0.371328	+	0.134947i
$638$		0			0
$639$	1.40500	−	3.73461i	0.0555809	−	0.147739i
$640$		0			0
$641$	−18.7225	+	6.81445i	−0.739496	+	0.269155i	−0.684179	−	0.729314i	$-0.739839\pi$
$641$	−18.7225	+	6.81445i	−0.739496	+	0.269155i	−0.0553171	+	0.998469i	$0.517617\pi$
$642$		0			0
$643$	−3.93605	−	22.3225i	−0.155223	−	0.880312i	−0.958582	−	0.284817i	$-0.908067\pi$
$643$	−3.93605	−	22.3225i	−0.155223	−	0.880312i	0.803359	−	0.595495i	$-0.203044\pi$
$644$		0			0
$645$	3.23424	−	0.265424i	0.127348	−	0.0104511i
$646$		0			0
$647$	−8.75034	+	15.1560i	−0.344011	+	0.595845i	−0.985174	−	0.171560i	$-0.945119\pi$
$647$	−8.75034	+	15.1560i	−0.344011	+	0.595845i	0.641162	+	0.767405i	$0.278453\pi$
$648$		0			0
$649$	−3.59057	−	6.21905i	−0.140942	−	0.244119i
$650$		0			0
$651$	8.60921	−	31.4821i	0.337422	−	1.23388i
$652$		0			0
$653$	30.1349	−	25.2862i	1.17927	−	0.989524i	0.179285	−	0.983797i	$-0.442621\pi$
$653$	30.1349	−	25.2862i	1.17927	−	0.989524i	0.999984	−	0.00572696i	$-0.00182296\pi$
$654$		0			0
$655$	4.01213	−	1.46030i	0.156767	−	0.0570585i
$656$		0			0
$657$	12.0376	−	31.9969i	0.469630	−	1.24832i
$658$		0			0
$659$	1.59405	−	9.04031i	0.0620954	−	0.352161i	−0.937891	−	0.346930i	$-0.887224\pi$
$659$	1.59405	−	9.04031i	0.0620954	−	0.352161i	0.999986	−	0.00523031i	$-0.00166487\pi$
$660$		0			0
$661$	−7.80272	+	6.54726i	−0.303491	+	0.254659i	−0.781795	−	0.623535i	$-0.785696\pi$
$661$	−7.80272	+	6.54726i	−0.303491	+	0.254659i	0.478305	+	0.878194i	$0.341251\pi$
$662$		0			0
$663$	−4.45821	+	4.41047i	−0.173142	+	0.171288i
$664$		0			0
$665$	13.5414	+	16.1300i	0.525114	+	0.625495i
$666$		0			0
$667$	36.1570			1.40001
$668$		0			0
$669$	12.0718	−	5.55028i	0.466724	−	0.214586i
$670$		0			0
$671$	−6.23812	+	5.23440i	−0.240820	+	0.202072i
$672$		0			0
$673$	−33.3067	+	12.1226i	−1.28388	+	0.467294i	−0.891713	−	0.452601i	$-0.850496\pi$
$673$	−33.3067	+	12.1226i	−1.28388	+	0.467294i	−0.392166	+	0.919895i	$0.628274\pi$
$674$		0			0
$675$	1.30809	+	18.3623i	0.0503486	+	0.706765i
$676$		0			0
$677$	33.7867	+	28.3504i	1.29853	+	1.08960i	0.990397	+	0.138252i	$0.0441484\pi$
$677$	33.7867	+	28.3504i	1.29853	+	1.08960i	0.308132	+	0.951343i	$0.400296\pi$
$678$		0			0
$679$	−21.7411	−	3.82806i	−0.834347	−	0.146907i
$680$		0			0
$681$	−0.936106	+	0.430394i	−0.0358716	+	0.0164927i
$682$		0			0
$683$	14.4869	+	25.0921i	0.554327	+	0.960123i	0.997956	+	0.0639122i	$0.0203578\pi$
$683$	14.4869	+	25.0921i	0.554327	+	0.960123i	−0.443628	+	0.896211i	$0.646309\pi$
$684$		0			0
$685$	3.07149	+	5.31997i	0.117356	+	0.203266i
$686$		0			0
$687$	−8.92122	−	2.44198i	−0.340366	−	0.0931673i
$688$		0			0
$689$	−13.5413	+	11.3625i	−0.515883	+	0.432877i
$690$		0			0
$691$	−21.3452	+	7.76901i	−0.812009	+	0.295547i	−0.714453	−	0.699683i	$-0.753325\pi$
$691$	−21.3452	+	7.76901i	−0.812009	+	0.295547i	−0.0975555	+	0.995230i	$0.531102\pi$
$692$		0			0
$693$	9.69533	+	0.102008i	0.368295	+	0.00387495i
$694$		0			0
$695$	2.62733	−	14.9003i	0.0996603	−	0.565201i
$696$		0			0
$697$	−26.0180	−	9.46979i	−0.985504	−	0.358694i
$698$		0			0
$699$	3.11794	+	4.50429i	0.117931	+	0.170368i
$700$		0			0
$701$	−7.95748			−0.300550			−0.150275	−	0.988644i	$-0.548016\pi$
$701$	−7.95748			−0.300550			−0.150275	+	0.988644i	$0.548016\pi$
$702$		0			0
$703$	−37.5731	+	65.0785i	−1.41710	+	2.45448i
$704$		0			0
$705$	−23.2361	+	1.90692i	−0.875124	+	0.0718189i
$706$		0			0
$707$	7.30554	+	20.0565i	0.274753	+	0.754303i
$708$		0			0
$709$	0.920464	−	5.22021i	0.0345688	−	0.196049i	−0.962633	−	0.270810i	$-0.912708\pi$
$709$	0.920464	−	5.22021i	0.0345688	−	0.196049i	0.997201	+	0.0747612i	$0.0238195\pi$
$710$		0			0
$711$	−0.538199	+	49.9902i	−0.0201840	+	1.87478i
$712$		0			0
$713$	−10.6063	+	60.1512i	−0.397208	+	2.25268i
$714$		0			0
$715$	1.97393	+	0.718451i	0.0738207	+	0.0268685i
$716$		0			0
$717$	0.730855	+	2.78752i	0.0272943	+	0.104102i
$718$		0			0
$719$	−11.6977	+	20.2609i	−0.436249	+	0.755606i	−0.997397	−	0.0721102i	$-0.977027\pi$
$719$	−11.6977	+	20.2609i	−0.436249	+	0.755606i	0.561148	+	0.827716i	$0.310360\pi$
$720$		0			0
$721$	−20.4024	−	24.3025i	−0.759824	−	0.905073i
$722$		0			0
$723$	14.9056	+	10.5570i	0.554346	+	0.392621i
$724$		0			0
$725$	−2.59376	−	14.7099i	−0.0963297	−	0.546313i
$726$		0			0
$727$	3.94940	−	1.43746i	0.146475	−	0.0533126i	−0.267742	−	0.963491i	$-0.586278\pi$
$727$	3.94940	−	1.43746i	0.146475	−	0.0533126i	0.414217	+	0.910178i	$0.364055\pi$
$728$		0			0
$729$	23.8064	−	12.7379i	0.881719	−	0.471774i
$730$		0			0
$731$	−0.685013	+	3.88490i	−0.0253361	+	0.143688i
$732$		0			0
$733$	22.9198	+	8.34213i	0.846563	+	0.308124i	0.728638	−	0.684899i	$-0.240154\pi$
$733$	22.9198	+	8.34213i	0.846563	+	0.308124i	0.117925	+	0.993023i	$0.462376\pi$
$734$		0			0
$735$	−3.71884	−	14.1556i	−0.137172	−	0.522138i
$736$		0			0
$737$	−2.40143			−0.0884578
$738$		0			0
$739$	23.4592			0.862960			0.431480	−	0.902123i	$-0.357992\pi$
$739$	23.4592			0.862960			0.431480	+	0.902123i	$0.357992\pi$
$740$		0			0
$741$	−11.5663	+	11.4425i	−0.424900	+	0.420350i
$742$		0			0
$743$	17.2444	+	6.27646i	0.632636	+	0.230261i	0.638378	−	0.769723i	$-0.279606\pi$
$743$	17.2444	+	6.27646i	0.632636	+	0.230261i	−0.00574196	+	0.999984i	$0.501828\pi$
$744$		0			0
$745$	−5.72807	−	4.80642i	−0.209860	−	0.176094i
$746$		0			0
$747$	26.2815	+	15.5533i	0.961590	+	0.569064i
$748$		0			0
$749$	6.44796	−	3.72483i	0.235603	−	0.136102i
$750$		0			0
$751$	25.0851	−	21.0489i	0.915369	−	0.768086i	−0.0577640	−	0.998330i	$-0.518397\pi$
$751$	25.0851	−	21.0489i	0.915369	−	0.768086i	0.973133	+	0.230245i	$0.0739526\pi$
$752$		0			0
$753$	3.41527	+	4.93382i	0.124459	+	0.179799i
$754$		0			0
$755$	3.74888			0.136436
$756$		0			0
$757$	−40.9371			−1.48789			−0.743943	−	0.668243i	$-0.767047\pi$
$757$	−40.9371			−1.48789			−0.743943	+	0.668243i	$0.767047\pi$
$758$		0			0
$759$	−18.0841	+	1.48411i	−0.656412	+	0.0538699i
$760$		0			0
$761$	36.7910	−	30.8713i	1.33367	−	1.11908i	0.350469	−	0.936574i	$-0.386022\pi$
$761$	36.7910	−	30.8713i	1.33367	−	1.11908i	0.983204	−	0.182510i	$-0.0584223\pi$
$762$		0			0
$763$	0.567792	+	0.327630i	0.0205555	+	0.0118610i
$764$		0			0
$765$	9.04706	+	1.69586i	0.327097	+	0.0613140i
$766$		0			0
$767$	−6.41501	−	5.38284i	−0.231633	−	0.194363i
$768$		0			0
$769$	−28.9757	−	10.5463i	−1.04489	−	0.380309i	−0.238158	−	0.971226i	$-0.576544\pi$
$769$	−28.9757	−	10.5463i	−1.04489	−	0.380309i	−0.806732	+	0.590917i	$0.798766\pi$
$770$		0			0
$771$	−28.3299	−	7.75464i	−1.02027	−	0.279277i
$772$		0			0
$773$	−2.12813			−0.0765434			−0.0382717	−	0.999267i	$-0.512185\pi$
$773$	−2.12813			−0.0765434			−0.0382717	+	0.999267i	$0.512185\pi$
$774$		0			0
$775$	25.2324			0.906374
$776$		0			0
$777$	42.9315	−	29.7334i	1.54016	−	1.06668i
$778$		0			0
$779$	−67.5010	−	24.5684i	−2.41848	−	0.880253i
$780$		0			0
$781$	0.282134	−	1.60006i	0.0100955	−	0.0572546i
$782$		0			0
$783$	−18.1463	+	12.2743i	−0.648496	+	0.438648i
$784$		0			0
$785$	2.89944	−	1.05531i	0.103486	−	0.0376656i
$786$		0			0
$787$	6.53641	+	37.0698i	0.232998	+	1.32140i	0.846789	+	0.531929i	$0.178533\pi$
$787$	6.53641	+	37.0698i	0.232998	+	1.32140i	−0.613791	+	0.789469i	$0.710356\pi$
$788$		0			0
$789$	0.128407	−	1.38198i	0.00457141	−	0.0491997i
$790$		0			0
$791$	41.4514	−	7.31945i	1.47384	−	0.260250i
$792$		0			0
$793$	−4.74810	+	8.22395i	−0.168610	+	0.292041i
$794$		0			0
$795$	25.0250	+	6.85001i	0.887545	+	0.242945i
$796$		0			0
$797$	−6.16107	−	2.24245i	−0.218236	−	0.0794315i	0.230588	−	0.973051i	$-0.425935\pi$
$797$	−6.16107	−	2.24245i	−0.218236	−	0.0794315i	−0.448825	+	0.893620i	$0.648157\pi$
$798$		0			0
$799$	4.92143	−	27.9108i	0.174108	−	0.987414i
$800$		0			0
$801$	7.86843	+	9.58492i	0.278017	+	0.338666i
$802$		0			0
$803$	2.41723	−	13.7088i	0.0853020	−	0.483772i
$804$		0			0
$805$	9.37419	+	25.7358i	0.330397	+	0.907066i
$806$		0			0
$807$	23.9303	+	34.5706i	0.842388	+	1.21694i
$808$		0			0
$809$	3.29662	−	5.70991i	0.115903	−	0.200750i	−0.802237	−	0.597005i	$-0.796357\pi$
$809$	3.29662	−	5.70991i	0.115903	−	0.200750i	0.918140	+	0.396255i	$0.129690\pi$
$810$		0			0
$811$	−3.35495			−0.117808			−0.0589041	−	0.998264i	$-0.518761\pi$
$811$	−3.35495			−0.117808			−0.0589041	+	0.998264i	$0.518761\pi$
$812$		0			0
$813$	−37.2400	+	3.05618i	−1.30606	+	0.107185i
$814$		0			0
$815$	−4.38320	−	1.59535i	−0.153537	−	0.0558828i
$816$		0			0
$817$	−1.77719	+	10.0790i	−0.0621761	+	0.352618i
$818$		0			0
$819$	10.6649	−	3.75513i	0.372663	−	0.131215i
$820$		0			0
$821$	−37.4583	+	13.6337i	−1.30730	+	0.475819i	−0.899368	−	0.437192i	$-0.855973\pi$
$821$	−37.4583	+	13.6337i	−1.30730	+	0.475819i	−0.407935	+	0.913011i	$0.633751\pi$
$822$		0			0
$823$	41.3265	−	34.6770i	1.44055	−	1.20877i	0.501421	−	0.865203i	$-0.332811\pi$
$823$	41.3265	−	34.6770i	1.44055	−	1.20877i	0.939130	−	0.343563i	$-0.111634\pi$
$824$		0			0
$825$	1.90107	+	7.25077i	0.0661867	+	0.252440i
$826$		0			0
$827$	−7.30251	−	12.6483i	−0.253933	−	0.439825i	0.710672	−	0.703523i	$-0.248391\pi$
$827$	−7.30251	−	12.6483i	−0.253933	−	0.439825i	−0.964605	+	0.263698i	$0.915058\pi$
$828$		0			0
$829$	10.5421	+	18.2595i	0.366143	+	0.634178i	0.988959	−	0.148190i	$-0.0473448\pi$
$829$	10.5421	+	18.2595i	0.366143	+	0.634178i	−0.622816	+	0.782368i	$0.714011\pi$
$830$		0			0
$831$	4.21357	−	45.3485i	0.146167	−	1.57312i
$832$		0			0
$833$	17.7918	−	0.00870886i	0.616450	−	0.000301744i
$834$		0			0
$835$	12.6407	+	10.6068i	0.437451	+	0.367065i
$836$		0			0
$837$	−15.0966	−	33.7889i	−0.521816	−	1.16791i
$838$		0			0
$839$	−2.21902	+	0.807659i	−0.0766092	+	0.0278835i	−0.380040	−	0.924970i	$-0.624090\pi$
$839$	−2.21902	+	0.807659i	−0.0766092	+	0.0278835i	0.303431	+	0.952853i	$0.401868\pi$
$840$		0			0
$841$	−8.59823	+	7.21477i	−0.296491	+	0.248785i
$842$		0			0
$843$	−14.1780	−	10.0417i	−0.488317	−	0.345855i
$844$		0			0
$845$	−13.2434			−0.455587
$846$		0			0
$847$	−24.7720	+	4.37422i	−0.851176	+	0.150300i
$848$		0			0
$849$	7.93938	+	30.2812i	0.272479	+	1.03925i
$850$		0			0
$851$	−74.8653	+	62.8194i	−2.56635	+	2.15342i
$852$		0			0
$853$	0.460804	−	2.61335i	0.0157776	−	0.0894793i	−0.975902	−	0.218209i	$-0.929979\pi$
$853$	0.460804	−	2.61335i	0.0157776	−	0.0894793i	0.991680	+	0.128729i	$0.0410898\pi$
$854$		0			0
$855$	23.4716	+	4.39973i	0.802713	+	0.150468i
$856$		0			0
$857$	−15.7390	+	5.72854i	−0.537635	+	0.195683i	−0.596544	−	0.802580i	$-0.703460\pi$
$857$	−15.7390	+	5.72854i	−0.537635	+	0.195683i	0.0589093	+	0.998263i	$0.481238\pi$
$858$		0			0
$859$	9.30366	−	7.80670i	0.317437	−	0.266361i	−0.470121	−	0.882602i	$-0.655790\pi$
$859$	9.30366	−	7.80670i	0.317437	−	0.266361i	0.787558	+	0.616241i	$0.211345\pi$
$860$		0			0
$861$	35.1170	+	35.4798i	1.19679	+	1.20915i
$862$		0			0
$863$	20.6817	+	35.8218i	0.704015	+	1.21939i	0.967046	+	0.254602i	$0.0819445\pi$
$863$	20.6817	+	35.8218i	0.704015	+	1.21939i	−0.263031	+	0.964787i	$0.584722\pi$
$864$		0			0
$865$	9.79139	−	16.9592i	0.332917	−	0.576629i
$866$		0			0
$867$	7.80405	−	16.5033i	0.265039	−	0.560482i
$868$		0			0
$869$	3.53488	+	20.0473i	0.119913	+	0.680059i
$870$		0			0
$871$	−2.63152	+	0.957793i	−0.0891655	+	0.0324536i
$872$		0			0
$873$	−21.8112	+	12.2816i	−0.738198	+	0.415668i
$874$		0			0
$875$	23.6255	−	13.6479i	0.798686	−	0.461382i
$876$		0			0
$877$	3.04685	+	17.2796i	0.102885	+	0.583489i	0.992044	+	0.125891i	$0.0401790\pi$
$877$	3.04685	+	17.2796i	0.102885	+	0.583489i	−0.889159	+	0.457598i	$0.848710\pi$
$878$		0			0
$879$	−5.74869	−	21.9258i	−0.193898	−	0.739539i
$880$		0			0
$881$	−4.99602	−	8.65336i	−0.168320	−	0.291539i	0.769509	−	0.638636i	$-0.220501\pi$
$881$	−4.99602	−	8.65336i	−0.168320	−	0.291539i	−0.937829	+	0.347097i	$0.887168\pi$
$882$		0			0
$883$	17.9754	−	31.1343i	0.604920	−	1.04775i	−0.387144	−	0.922019i	$-0.626538\pi$
$883$	17.9754	−	31.1343i	0.604920	−	1.04775i	0.992064	−	0.125733i	$-0.0401284\pi$
$884$		0			0
$885$	−1.13716	+	12.2387i	−0.0382252	+	0.411398i
$886$		0			0
$887$	14.3325	+	5.21660i	0.481238	+	0.175156i	0.571237	−	0.820785i	$-0.306464\pi$
$887$	14.3325	+	5.21660i	0.481238	+	0.175156i	−0.0899982	+	0.995942i	$0.528686\pi$
$888$		0			0
$889$	14.8293	+	8.55684i	0.497357	+	0.286987i
$890$		0			0
$891$	8.57215	−	6.88390i	0.287178	−	0.230619i
$892$		0			0
$893$	12.7681	−	72.4116i	0.427269	−	2.42316i
$894$		0			0
$895$	−17.5705	+	14.7434i	−0.587318	+	0.492818i
$896$		0			0
$897$	−19.2249	+	8.83904i	−0.641900	+	0.295127i
$898$		0			0
$899$	15.0141	+	26.0052i	0.500748	+	0.867321i
$900$		0			0
$901$	−15.7700	+	27.3145i	−0.525376	+	0.909978i
$902$		0			0
$903$	4.10938	−	5.80509i	0.136752	−	0.193181i
$904$		0			0
$905$	0.595549	+	3.37753i	0.0197967	+	0.112273i
$906$		0			0
$907$	7.25181	+	6.08499i	0.240792	+	0.202049i	0.755195	−	0.655500i	$-0.227542\pi$
$907$	7.25181	+	6.08499i	0.240792	+	0.202049i	−0.514403	+	0.857549i	$0.671986\pi$
$908$		0			0
$909$	20.8295	+	12.3268i	0.690870	+	0.408853i
$910$		0			0
$911$	26.0760	+	21.8804i	0.863937	+	0.724930i	0.962813	−	0.270170i	$-0.0870800\pi$
$911$	26.0760	+	21.8804i	0.863937	+	0.724930i	−0.0988751	+	0.995100i	$0.531524\pi$
$912$		0			0
$913$	11.6851	+	4.25304i	0.386722	+	0.140755i
$914$		0			0
$915$	13.8915	−	1.14004i	0.459239	−	0.0376884i
$916$		0			0
$917$	3.19842	−	8.79427i	0.105621	−	0.290412i
$918$		0			0
$919$	−13.0898	−	22.6722i	−0.431793	−	0.747888i	0.565234	−	0.824930i	$-0.308786\pi$
$919$	−13.0898	−	22.6722i	−0.431793	−	0.747888i	−0.997028	+	0.0770422i	$0.975452\pi$
$920$		0			0
$921$	10.7922	−	0.885684i	0.355615	−	0.0291843i
$922$		0			0
$923$	−0.329007	−	1.86589i	−0.0108294	−	0.0614166i
$924$		0			0
$925$	30.9276	+	25.9513i	1.01689	+	0.853275i
$926$		0			0
$927$	−35.3639	−	6.62892i	−1.16150	−	0.217722i
$928$		0			0
$929$	−11.5820	+	4.21550i	−0.379993	+	0.138306i	−0.524953	−	0.851131i	$-0.675917\pi$
$929$	−11.5820	+	4.21550i	−0.379993	+	0.138306i	0.144960	+	0.989438i	$0.453695\pi$
$930$		0			0
$931$	46.1590	−	0.0225942i	1.51280	−	0.000740495i
$932$		0			0
$933$	0.506625	+	1.93229i	0.0165861	+	0.0632605i
$934$		0			0
$935$	3.74802			0.122573
$936$		0			0
$937$	16.7156	−	28.9523i	0.546075	−	0.945830i	−0.452463	−	0.891783i	$-0.649455\pi$
$937$	16.7156	−	28.9523i	0.546075	−	0.945830i	0.998538	−	0.0540471i	$-0.0172121\pi$
$938$		0			0
$939$	3.82204	−	41.1346i	0.124727	−	1.34238i
$940$		0			0
$941$	−7.40199	−	41.9788i	−0.241298	−	1.36847i	−0.828935	−	0.559345i	$-0.811053\pi$
$941$	−7.40199	−	41.9788i	−0.241298	−	1.36847i	0.587637	−	0.809125i	$-0.300058\pi$
$942$		0			0
$943$	−71.5646	−	60.0498i	−2.33046	−	1.95549i
$944$		0			0
$945$	−13.4412	−	9.73385i	−0.437244	−	0.316642i
$946$		0			0
$947$	−28.6269	−	24.0208i	−0.930248	−	0.780571i	0.0456137	−	0.998959i	$-0.485476\pi$
$947$	−28.6269	−	24.0208i	−0.930248	−	0.780571i	−0.975862	+	0.218388i	$0.929920\pi$
$948$		0			0
$949$	−2.81882	−	15.9863i	−0.0915028	−	0.518938i
$950$		0			0
$951$	13.7489	+	9.73779i	0.445838	+	0.315769i
$952$		0			0
$953$	−17.9054	+	31.0130i	−0.580012	+	1.00461i	0.415465	+	0.909609i	$0.363619\pi$
$953$	−17.9054	+	31.0130i	−0.580012	+	1.00461i	−0.995477	+	0.0950012i	$0.969715\pi$
$954$		0			0
$955$	−23.0607			−0.746226
$956$		0			0
$957$	−6.34164	+	6.27374i	−0.204996	+	0.202801i
$958$		0			0
$959$	13.2598	+	2.33471i	0.428180	+	0.0753916i
$960$		0			0
$961$	−18.5361	+	6.74661i	−0.597940	+	0.217632i
$962$		0			0
$963$	2.97311	−	7.90279i	0.0958072	−	0.254664i
$964$		0			0
$965$	−4.80258	−	4.02984i	−0.154601	−	0.129725i
$966$		0			0
$967$	−0.0727281	−	0.412461i	−0.00233878	−	0.0132639i	0.983616	−	0.180276i	$-0.0576991\pi$
$967$	−0.0727281	−	0.412461i	−0.00233878	−	0.0132639i	−0.985955	+	0.167012i	$0.946588\pi$
$968$		0			0
$969$	−12.4099	+	26.2434i	−0.398663	+	0.843059i
$970$		0			0
$971$	−12.1008	−	20.9592i	−0.388334	−	0.672614i	0.603892	−	0.797066i	$-0.293616\pi$
$971$	−12.1008	−	20.9592i	−0.388334	−	0.672614i	−0.992226	+	0.124453i	$0.960283\pi$
$972$		0			0
$973$	−21.3218	−	25.3978i	−0.683547	−	0.814215i
$974$		0			0
$975$	4.97513	+	7.18726i	0.159332	+	0.230177i
$976$		0			0
$977$	−18.3749	−	6.68792i	−0.587865	−	0.213966i	0.0309249	−	0.999522i	$-0.490155\pi$
$977$	−18.3749	−	6.68792i	−0.587865	−	0.213966i	−0.618790	+	0.785556i	$0.712377\pi$
$978$		0			0
$979$	3.86815	+	3.24576i	0.123626	+	0.103735i
$980$		0			0
$981$	0.733364	−	0.121186i	0.0234145	−	0.00386918i
$982$		0			0
$983$	2.30952	+	1.93792i	0.0736622	+	0.0618099i	0.678875	−	0.734254i	$-0.262468\pi$
$983$	2.30952	+	1.93792i	0.0736622	+	0.0618099i	−0.605213	+	0.796063i	$0.706912\pi$
$984$		0			0
$985$	−5.36700	−	30.4377i	−0.171007	−	0.969827i
$986$		0			0
$987$	−29.5236	+	41.7063i	−0.939746	+	1.32753i
$988$		0			0
$989$	−6.65510	+	11.5270i	−0.211620	+	0.366536i
$990$		0			0
$991$	−8.75917	−	15.1713i	−0.278244	−	0.481933i	0.692704	−	0.721222i	$-0.256419\pi$
$991$	−8.75917	−	15.1713i	−0.278244	−	0.481933i	−0.970948	+	0.239289i	$0.923086\pi$
$992$		0			0
$993$	18.7807	+	13.3016i	0.595986	+	0.422113i
$994$		0			0
$995$	11.4279	−	9.58916i	0.362289	−	0.303997i
$996$		0			0
$997$	3.09531	−	17.5544i	0.0980293	−	0.555952i	−0.895748	−	0.444563i	$-0.853359\pi$
$997$	3.09531	−	17.5544i	0.0980293	−	0.555952i	0.993777	−	0.111389i	$-0.0355299\pi$
$998$		0			0
$999$	16.2475	−	56.9422i	0.514049	−	1.80157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.277.9	yes	144
7.2	even	3		756.2.bp.a.709.7	yes	144
27.4	even	9		756.2.bp.a.193.7	✓	144
189.58	even	9	inner	756.2.bq.a.625.9	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.7	✓	144	27.4	even	9
756.2.bp.a.709.7	yes	144	7.2	even	3
756.2.bq.a.277.9	yes	144	1.1	even	1	trivial
756.2.bq.a.625.9	yes	144	189.58	even	9	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.740435 + 1.56581i) q^{3} +(0.924734 - 0.775944i) q^{5} +(-0.000647530 - 2.64575i) q^{7} +(-1.90351 - 2.31876i) q^{9} +O(q^{10})\)	\(q+(-0.740435 + 1.56581i) q^{3} +(0.924734 - 0.775944i) q^{5} +(-0.000647530 - 2.64575i) q^{7} +(-1.90351 - 2.31876i) q^{9} +(-0.935772 - 0.785206i) q^{11} +(-1.33860 - 0.487212i) q^{13} +(0.530273 + 2.02249i) q^{15} -2.54169 q^{17} -6.59414 q^{19} +(4.14322 + 1.95799i) q^{21} +(-8.05868 - 2.93312i) q^{23} +(-0.615197 + 3.48896i) q^{25} +(5.04016 - 1.26364i) q^{27} +(-3.96187 + 1.44200i) q^{29} +(-1.23676 - 7.01400i) q^{31} +(1.92236 - 0.883845i) q^{33} +(-2.05355 - 2.44611i) q^{35} +(5.69795 - 9.86913i) q^{37} +(1.75403 - 1.73525i) q^{39} +(10.2365 + 3.72579i) q^{41} +(0.269511 - 1.52847i) q^{43} +(-3.55947 - 0.667218i) q^{45} +(-1.93628 + 10.9812i) q^{47} +(-7.00000 + 0.00342640i) q^{49} +(1.88196 - 3.97980i) q^{51} +(6.20454 - 10.7466i) q^{53} -1.47462 q^{55} +(4.88254 - 10.3252i) q^{57} +(5.52412 + 2.01061i) q^{59} +(1.15759 - 6.56500i) q^{61} +(-6.13363 + 5.03772i) q^{63} +(-1.61590 + 0.588140i) q^{65} +(1.50594 - 1.26363i) q^{67} +(10.5596 - 10.4466i) q^{69} +(0.665025 + 1.15186i) q^{71} +(5.69772 + 9.86873i) q^{73} +(-5.00752 - 3.54663i) q^{75} +(-2.07685 + 2.47633i) q^{77} +(-12.7656 - 10.7116i) q^{79} +(-1.75329 + 8.82757i) q^{81} +(-9.56572 + 3.48164i) q^{83} +(-2.35039 + 1.97221i) q^{85} +(0.675610 - 7.27124i) q^{87} -4.13364 q^{89} +(-1.28818 + 3.54193i) q^{91} +(11.8983 + 3.25689i) q^{93} +(-6.09783 + 5.11668i) q^{95} +(1.44888 - 8.21701i) q^{97} +(-0.0394521 + 3.66448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more