LMFDB - Embedded newform 912.2.ci.h.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			751.1
Character	$\chi$	$=$	912.751
Dual form			912.2.ci.h.895.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{3} +(-2.67232 - 0.972646i) q^{5} +(2.07863 + 1.20010i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{3} +(-2.67232 - 0.972646i) q^{5} +(2.07863 + 1.20010i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-0.768651 + 0.443781i) q^{11} +(-1.53207 + 1.82586i) q^{13} +(2.67232 - 0.972646i) q^{15} +(0.112602 + 0.638596i) q^{17} +(0.564339 - 4.32221i) q^{19} +(-2.36373 + 0.416790i) q^{21} +(-1.35012 - 3.70942i) q^{23} +(2.36505 + 1.98452i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-6.77517 - 1.19464i) q^{29} +(3.97662 - 6.88770i) q^{31} +(0.303564 - 0.834035i) q^{33} +(-4.38751 - 5.22883i) q^{35} +5.18757i q^{37} -2.38349i q^{39} +(-4.03637 - 4.81036i) q^{41} +(2.15516 - 5.92127i) q^{43} +(-1.42191 + 2.46283i) q^{45} +(0.153832 + 0.0271248i) q^{47} +(-0.619522 - 1.07304i) q^{49} +(-0.496740 - 0.416814i) q^{51} +(-4.67283 - 12.8385i) q^{53} +(2.48573 - 0.438300i) q^{55} +(2.34596 + 3.67376i) q^{57} +(-0.401320 - 2.27600i) q^{59} +(-7.99995 + 2.91174i) q^{61} +(1.54282 - 1.83866i) q^{63} +(5.87011 - 3.38911i) q^{65} +(1.43913 - 8.16172i) q^{67} +(3.41862 + 1.97374i) q^{69} +(-2.13290 - 0.776313i) q^{71} +(8.89007 - 7.45966i) q^{73} -3.08736 q^{75} -2.13032 q^{77} +(-9.24843 + 7.76036i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(8.09084 + 4.67125i) q^{83} +(0.320220 - 1.81606i) q^{85} +(5.95798 - 3.43984i) q^{87} +(8.44079 - 10.0593i) q^{89} +(-5.37583 + 1.95664i) q^{91} +(1.38106 + 7.83241i) q^{93} +(-5.71208 + 11.0015i) q^{95} +(-2.73079 + 0.481512i) q^{97} +(0.303564 + 0.834035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 9 q^{7}+O(q^{10}) $ 24 * q + 9 * q^7	$ 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$1$	$-1$

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
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$		0			0
$5$	−2.67232	−	0.972646i	−1.19510	−	0.434981i	−0.333588	−	0.942719i	$-0.608260\pi$
$5$	−2.67232	−	0.972646i	−1.19510	−	0.434981i	−0.861511	+	0.507738i	$0.830482\pi$
$6$		0			0
$7$	2.07863	+	1.20010i	0.785650	+	0.453595i	0.838429	−	0.545011i	$-0.183475\pi$
$7$	2.07863	+	1.20010i	0.785650	+	0.453595i	−0.0527792	+	0.998606i	$0.516808\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	−0.768651	+	0.443781i	−0.231757	+	0.133805i	−0.611382	−	0.791335i	$-0.709386\pi$
$11$	−0.768651	+	0.443781i	−0.231757	+	0.133805i	0.379625	+	0.925140i	$0.376053\pi$
$12$		0			0
$13$	−1.53207	+	1.82586i	−0.424921	+	0.506401i	−0.935450	−	0.353459i	$-0.885005\pi$
$13$	−1.53207	+	1.82586i	−0.424921	+	0.506401i	0.510529	+	0.859861i	$0.329450\pi$
$14$		0			0
$15$	2.67232	−	0.972646i	0.689991	−	0.251136i
$16$		0			0
$17$	0.112602	+	0.638596i	0.0273099	+	0.154882i	0.995413	−	0.0956693i	$-0.0304991\pi$
$17$	0.112602	+	0.638596i	0.0273099	+	0.154882i	−0.968103	+	0.250552i	$0.919388\pi$
$18$		0			0
$19$	0.564339	−	4.32221i	0.129468	−	0.991584i
$19$	0.564339	−	4.32221i	0.129468	−	0.991584i
$20$		0			0
$21$	−2.36373	+	0.416790i	−0.515809	+	0.0909511i
$22$		0			0
$23$	−1.35012	−	3.70942i	−0.281519	−	0.773467i	−0.997182	−	0.0750210i	$-0.976098\pi$
$23$	−1.35012	−	3.70942i	−0.281519	−	0.773467i	0.715663	−	0.698446i	$-0.246125\pi$
$24$		0			0
$25$	2.36505	+	1.98452i	0.473011	+	0.396903i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	−6.77517	−	1.19464i	−1.25812	−	0.221840i	−0.495453	−	0.868635i	$-0.664998\pi$
$29$	−6.77517	−	1.19464i	−1.25812	−	0.221840i	−0.762664	+	0.646795i	$0.776109\pi$
$30$		0			0
$31$	3.97662	−	6.88770i	0.714222	−	1.23707i	−0.249037	−	0.968494i	$-0.580114\pi$
$31$	3.97662	−	6.88770i	0.714222	−	1.23707i	0.963259	−	0.268574i	$-0.0865525\pi$
$32$		0			0
$33$	0.303564	−	0.834035i	0.0528437	−	0.145187i
$34$		0			0
$35$	−4.38751	−	5.22883i	−0.741624	−	0.883834i
$36$		0			0
$37$			5.18757i			0.852831i	0.904527	+	0.426415i	$0.140224\pi$
$37$			5.18757i			0.852831i	−0.904527	+	0.426415i	$0.859776\pi$
$38$		0			0
$39$		−	2.38349i		−	0.381663i
$40$		0			0
$41$	−4.03637	−	4.81036i	−0.630376	−	0.751253i	0.352442	−	0.935834i	$-0.385352\pi$
$41$	−4.03637	−	4.81036i	−0.630376	−	0.751253i	−0.982817	+	0.184581i	$0.940907\pi$
$42$		0			0
$43$	2.15516	−	5.92127i	0.328659	−	0.902985i	−0.659792	−	0.751448i	$-0.729356\pi$
$43$	2.15516	−	5.92127i	0.328659	−	0.902985i	0.988452	−	0.151536i	$-0.0484221\pi$
$44$		0			0
$45$	−1.42191	+	2.46283i	−0.211966	+	0.367137i
$46$		0			0
$47$	0.153832	+	0.0271248i	0.0224388	+	0.00395656i	0.184856	−	0.982766i	$-0.440818\pi$
$47$	0.153832	+	0.0271248i	0.0224388	+	0.00395656i	−0.162418	+	0.986722i	$0.551929\pi$
$48$		0			0
$49$	−0.619522	−	1.07304i	−0.0885032	−	0.153292i
$50$		0			0
$51$	−0.496740	−	0.416814i	−0.0695575	−	0.0583657i
$52$		0			0
$53$	−4.67283	−	12.8385i	−0.641863	−	1.76350i	−0.645795	−	0.763511i	$-0.723474\pi$
$53$	−4.67283	−	12.8385i	−0.641863	−	1.76350i	0.00393249	−	0.999992i	$-0.498748\pi$
$54$		0			0
$55$	2.48573	−	0.438300i	0.335175	−	0.0591004i
$56$		0			0
$57$	2.34596	+	3.67376i	0.310729	+	0.486601i
$58$		0			0
$59$	−0.401320	−	2.27600i	−0.0522474	−	0.296310i	0.947476	−	0.319827i	$-0.103625\pi$
$59$	−0.401320	−	2.27600i	−0.0522474	−	0.296310i	−0.999723	+	0.0235171i	$0.992514\pi$
$60$		0			0
$61$	−7.99995	+	2.91174i	−1.02429	+	0.372811i	−0.798904	−	0.601459i	$-0.794586\pi$
$61$	−7.99995	+	2.91174i	−1.02429	+	0.372811i	−0.225385	+	0.974270i	$0.572364\pi$
$62$		0			0
$63$	1.54282	−	1.83866i	0.194377	−	0.231649i
$64$		0			0
$65$	5.87011	−	3.38911i	0.728098	−	0.420367i
$66$		0			0
$67$	1.43913	−	8.16172i	0.175818	−	0.997113i	−0.761377	−	0.648309i	$-0.775477\pi$
$67$	1.43913	−	8.16172i	0.175818	−	0.997113i	0.937195	−	0.348805i	$-0.113412\pi$
$68$		0			0
$69$	3.41862	+	1.97374i	0.411553	+	0.237610i
$70$		0			0
$71$	−2.13290	−	0.776313i	−0.253129	−	0.0921314i	0.212339	−	0.977196i	$-0.431892\pi$
$71$	−2.13290	−	0.776313i	−0.253129	−	0.0921314i	−0.465468	+	0.885065i	$0.654114\pi$
$72$		0			0
$73$	8.89007	−	7.45966i	1.04050	−	0.873087i	0.0484408	−	0.998826i	$-0.484575\pi$
$73$	8.89007	−	7.45966i	1.04050	−	0.873087i	0.992063	+	0.125739i	$0.0401303\pi$
$74$		0			0
$75$	−3.08736			−0.356497
$76$		0			0
$77$	−2.13032			−0.242773
$78$		0			0
$79$	−9.24843	+	7.76036i	−1.04053	+	0.873108i	−0.992066	−	0.125717i	$-0.959877\pi$
$79$	−9.24843	+	7.76036i	−1.04053	+	0.873108i	−0.0484636	+	0.998825i	$0.515433\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	8.09084	+	4.67125i	0.888085	+	0.512736i	0.873316	−	0.487155i	$-0.161965\pi$
$83$	8.09084	+	4.67125i	0.888085	+	0.512736i	0.0147694	+	0.999891i	$0.495299\pi$
$84$		0			0
$85$	0.320220	−	1.81606i	0.0347327	−	0.196979i
$86$		0			0
$87$	5.95798	−	3.43984i	0.638763	−	0.368790i
$88$		0			0
$89$	8.44079	−	10.0593i	0.894722	−	1.06629i	−0.102713	−	0.994711i	$-0.532752\pi$
$89$	8.44079	−	10.0593i	0.894722	−	1.06629i	0.997435	−	0.0715771i	$-0.0228032\pi$
$90$		0			0
$91$	−5.37583	+	1.95664i	−0.563540	+	0.205112i
$92$		0			0
$93$	1.38106	+	7.83241i	0.143210	+	0.812183i
$94$		0			0
$95$	−5.71208	+	11.0015i	−0.586047	+	1.12873i
$96$		0			0
$97$	−2.73079	+	0.481512i	−0.277270	+	0.0488902i	−0.310554	−	0.950556i	$-0.600515\pi$
$97$	−2.73079	+	0.481512i	−0.277270	+	0.0488902i	0.0332839	+	0.999446i	$0.489403\pi$
$98$		0			0
$99$	0.303564	+	0.834035i	0.0305093	+	0.0838237i
$100$		0			0
$101$	−3.27288	−	2.74627i	−0.325663	−	0.273264i	0.465267	−	0.885171i	$-0.345958\pi$
$101$	−3.27288	−	2.74627i	−0.325663	−	0.273264i	−0.790930	+	0.611907i	$0.790403\pi$
$102$		0			0
$103$	1.08954	+	1.88713i	0.107355	+	0.185945i	0.914698	−	0.404138i	$-0.132428\pi$
$103$	1.08954	+	1.88713i	0.107355	+	0.185945i	−0.807343	+	0.590083i	$0.799095\pi$
$104$		0			0
$105$	6.72205	+	1.18528i	0.656005	+	0.115671i
$106$		0			0
$107$	−1.27006	+	2.19980i	−0.122781	+	0.212663i	−0.920863	−	0.389886i	$-0.872515\pi$
$107$	−1.27006	+	2.19980i	−0.122781	+	0.212663i	0.798082	+	0.602548i	$0.205848\pi$
$108$		0			0
$109$	−1.88223	+	5.17140i	−0.180285	+	0.495330i	−0.996611	−	0.0822625i	$-0.973785\pi$
$109$	−1.88223	+	5.17140i	−0.180285	+	0.495330i	0.816325	+	0.577592i	$0.196008\pi$
$110$		0			0
$111$	−3.33450	−	3.97391i	−0.316497	−	0.377187i
$112$		0			0
$113$			8.45569i			0.795444i	0.917506	+	0.397722i	$0.130199\pi$
$113$			8.45569i			0.795444i	−0.917506	+	0.397722i	$0.869801\pi$
$114$		0			0
$115$			11.2259i			1.04683i
$116$		0			0
$117$	1.53207	+	1.82586i	0.141640	+	0.168800i
$118$		0			0
$119$	−0.532321	+	1.46254i	−0.0487978	+	0.134071i
$120$		0			0
$121$	−5.10612	+	8.84405i	−0.464192	+	0.804005i
$122$		0			0
$123$	6.18408	+	1.09042i	0.557600	+	0.0983199i
$124$		0			0
$125$	2.71961	+	4.71051i	0.243250	+	0.421321i
$126$		0			0
$127$	8.12202	+	6.81518i	0.720712	+	0.604750i	0.927582	−	0.373619i	$-0.121883\pi$
$127$	8.12202	+	6.81518i	0.720712	+	0.604750i	−0.206870	+	0.978368i	$0.566328\pi$
$128$		0			0
$129$	2.15516	+	5.92127i	0.189752	+	0.521338i
$130$		0			0
$131$	6.98392	−	1.23145i	0.610188	−	0.107593i	0.139989	−	0.990153i	$-0.455293\pi$
$131$	6.98392	−	1.23145i	0.610188	−	0.107593i	0.470199	+	0.882561i	$0.344182\pi$
$132$		0			0
$133$	6.36014	−	8.30703i	0.551494	−	0.720311i
$134$		0			0
$135$	−0.493826	−	2.80062i	−0.0425017	−	0.241039i
$136$		0			0
$137$	−17.4213	+	6.34083i	−1.48840	+	0.541733i	−0.953028	−	0.302882i	$-0.902051\pi$
$137$	−17.4213	+	6.34083i	−1.48840	+	0.541733i	−0.535373	+	0.844616i	$0.679829\pi$
$138$		0			0
$139$	2.52227	−	3.00593i	0.213937	−	0.254960i	−0.648395	−	0.761304i	$-0.724559\pi$
$139$	2.52227	−	3.00593i	0.213937	−	0.254960i	0.862331	+	0.506345i	$0.169004\pi$
$140$		0			0
$141$	−0.135278	+	0.0781028i	−0.0113925	+	0.00657744i
$142$		0			0
$143$	0.367351	−	2.08335i	0.0307194	−	0.174219i
$144$		0			0
$145$	16.9435	+	9.78232i	1.40708	+	0.812378i
$146$		0			0
$147$	1.16432	+	0.423778i	0.0960316	+	0.0349526i
$148$		0			0
$149$	13.5895	−	11.4029i	1.11329	−	0.934164i	0.115047	−	0.993360i	$-0.463298\pi$
$149$	13.5895	−	11.4029i	1.11329	−	0.934164i	0.998246	+	0.0591962i	$0.0188538\pi$
$150$		0			0
$151$	−5.84439			−0.475610			−0.237805	−	0.971313i	$-0.576428\pi$
$151$	−5.84439			−0.475610			−0.237805	+	0.971313i	$0.576428\pi$
$152$		0			0
$153$	0.648448			0.0524239
$154$		0			0
$155$	−17.3261	+	14.5383i	−1.39167	+	1.16775i
$156$		0			0
$157$	−19.3914	−	7.05788i	−1.54760	−	0.563280i	−0.579747	−	0.814797i	$-0.696849\pi$
$157$	−19.3914	−	7.05788i	−1.54760	−	0.563280i	−0.967853	+	0.251516i	$0.919071\pi$
$158$		0			0
$159$	11.8320	+	6.83122i	0.938340	+	0.541751i
$160$		0			0
$161$	1.64527	−	9.33079i	0.129665	−	0.735369i
$162$		0			0
$163$	6.59464	−	3.80742i	0.516532	−	0.298220i	−0.218982	−	0.975729i	$-0.570274\pi$
$163$	6.59464	−	3.80742i	0.516532	−	0.298220i	0.735515	+	0.677509i	$0.236940\pi$
$164$		0			0
$165$	−1.62244	+	1.93355i	−0.126307	+	0.150527i
$166$		0			0
$167$	−9.00387	+	3.27714i	−0.696741	+	0.253593i	−0.666019	−	0.745935i	$-0.732003\pi$
$167$	−9.00387	+	3.27714i	−0.696741	+	0.253593i	−0.0307221	+	0.999528i	$0.509781\pi$
$168$		0			0
$169$	1.27093	+	7.20781i	0.0977639	+	0.554447i
$170$		0			0
$171$	−4.15855	−	1.30631i	−0.318012	−	0.0998960i
$172$		0			0
$173$	−18.6702	+	3.29207i	−1.41947	+	0.250291i	−0.830120	−	0.557585i	$-0.811728\pi$
$173$	−18.6702	+	3.29207i	−1.41947	+	0.250291i	−0.589352	+	0.807876i	$0.700617\pi$
$174$		0			0
$175$	2.53446	+	6.96338i	0.191587	+	0.526382i
$176$		0			0
$177$	1.77041	+	1.48555i	0.133072	+	0.111661i
$178$		0			0
$179$	−5.66977	−	9.82033i	−0.423778	−	0.734006i	0.572527	−	0.819886i	$-0.305963\pi$
$179$	−5.66977	−	9.82033i	−0.423778	−	0.734006i	−0.996305	+	0.0858801i	$0.972630\pi$
$180$		0			0
$181$	0.179679	+	0.0316822i	0.0133554	+	0.00235492i	0.180322	−	0.983608i	$-0.442286\pi$
$181$	0.179679	+	0.0316822i	0.0133554	+	0.00235492i	−0.166966	+	0.985963i	$0.553397\pi$
$182$		0			0
$183$	4.25669	−	7.37280i	0.314663	−	0.545013i
$184$		0			0
$185$	5.04567	−	13.8629i	0.370965	−	1.01922i
$186$		0			0
$187$	−0.369948	−	0.440887i	−0.0270533	−	0.0322409i
$188$		0			0
$189$			2.40020i			0.174589i
$190$		0			0
$191$			9.97635i			0.721864i	0.932592	+	0.360932i	$0.117541\pi$
$191$			9.97635i			0.721864i	−0.932592	+	0.360932i	$0.882459\pi$
$192$		0			0
$193$	−5.38294	−	6.41513i	−0.387472	−	0.461771i	0.536686	−	0.843782i	$-0.319676\pi$
$193$	−5.38294	−	6.41513i	−0.387472	−	0.461771i	−0.924158	+	0.382011i	$0.875232\pi$
$194$		0			0
$195$	−2.31829	+	6.36945i	−0.166016	+	0.456125i
$196$		0			0
$197$	0.289230	−	0.500961i	0.0206068	−	0.0356920i	−0.855538	−	0.517740i	$-0.826774\pi$
$197$	0.289230	−	0.500961i	0.0206068	−	0.0356920i	0.876145	+	0.482048i	$0.160107\pi$
$198$		0			0
$199$	−10.9200	−	1.92548i	−0.774096	−	0.136494i	−0.227373	−	0.973808i	$-0.573014\pi$
$199$	−10.9200	−	1.92548i	−0.774096	−	0.136494i	−0.546723	+	0.837314i	$0.684125\pi$
$200$		0			0
$201$	4.14382	+	7.17730i	0.292282	+	0.506248i
$202$		0			0
$203$	−12.6494	−	10.6141i	−0.887814	−	0.744964i
$204$		0			0
$205$	6.10772	+	16.7808i	0.426581	+	1.17202i
$206$		0			0
$207$	−3.88751	+	0.685472i	−0.270200	+	0.0476436i
$208$		0			0
$209$	1.48433	+	3.57271i	0.102674	+	0.247130i
$210$		0			0
$211$	3.78830	+	21.4845i	0.260797	+	1.47906i	0.780741	+	0.624855i	$0.214842\pi$
$211$	3.78830	+	21.4845i	0.260797	+	1.47906i	−0.519943	+	0.854201i	$0.674047\pi$
$212$		0			0
$213$	2.13290	−	0.776313i	0.146144	−	0.0531921i
$214$		0			0
$215$	−11.5186	+	13.7273i	−0.785562	+	0.936196i
$216$		0			0
$217$	16.5319	−	9.54467i	1.12226	−	0.647935i
$218$		0			0
$219$	−2.01522	+	11.4289i	−0.136176	+	0.772290i
$220$		0			0
$221$	−1.33850	−	0.772783i	−0.0900372	−	0.0519830i
$222$		0			0
$223$	0.753708	+	0.274327i	0.0504720	+	0.0183703i	0.367133	−	0.930169i	$-0.380339\pi$
$223$	0.753708	+	0.274327i	0.0504720	+	0.0183703i	−0.316661	+	0.948539i	$0.602562\pi$
$224$		0			0
$225$	2.36505	−	1.98452i	0.157670	−	0.132301i
$226$		0			0
$227$	22.8159			1.51435			0.757173	−	0.653214i	$-0.226580\pi$
$227$	22.8159			1.51435			0.757173	+	0.653214i	$0.226580\pi$
$228$		0			0
$229$	8.46974			0.559696			0.279848	−	0.960044i	$-0.409716\pi$
$229$	8.46974			0.559696			0.279848	+	0.960044i	$0.409716\pi$
$230$		0			0
$231$	1.63192	−	1.36935i	0.107373	−	0.0900963i
$232$		0			0
$233$	12.0422	+	4.38299i	0.788909	+	0.287139i	0.704883	−	0.709324i	$-0.251000\pi$
$233$	12.0422	+	4.38299i	0.788909	+	0.287139i	0.0840267	+	0.996464i	$0.473222\pi$
$234$		0			0
$235$	−0.384707	−	0.222111i	−0.0250955	−	0.0144889i
$236$		0			0
$237$	2.09645	−	11.8896i	0.136179	−	0.772310i
$238$		0			0
$239$	−15.7857	+	9.11389i	−1.02109	+	0.589529i	−0.914421	−	0.404765i	$-0.867353\pi$
$239$	−15.7857	+	9.11389i	−1.02109	+	0.589529i	−0.106673	+	0.994294i	$0.534020\pi$
$240$		0			0
$241$	6.08847	−	7.25596i	0.392193	−	0.467397i	−0.533430	−	0.845844i	$-0.679097\pi$
$241$	6.08847	−	7.25596i	0.392193	−	0.467397i	0.925623	+	0.378447i	$0.123542\pi$
$242$		0			0
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$		0			0
$245$	0.611872	+	3.47010i	0.0390911	+	0.221696i
$246$		0			0
$247$	7.02713	+	7.65235i	0.447125	+	0.486908i
$248$		0			0
$249$	−9.20056	+	1.62231i	−0.583062	+	0.102810i
$250$		0			0
$251$	6.08090	+	16.7071i	0.383823	+	1.05454i	0.969733	+	0.244169i	$0.0785150\pi$
$251$	6.08090	+	16.7071i	0.383823	+	1.05454i	−0.585910	+	0.810376i	$0.699263\pi$
$252$		0			0
$253$	2.68394	+	2.25209i	0.168738	+	0.141588i
$254$		0			0
$255$	0.922037	+	1.59702i	0.0577402	+	0.100009i
$256$		0			0
$257$	1.32729	+	0.234037i	0.0827941	+	0.0145988i	0.214892	−	0.976638i	$-0.431060\pi$
$257$	1.32729	+	0.234037i	0.0827941	+	0.0145988i	−0.132098	+	0.991237i	$0.542171\pi$
$258$		0			0
$259$	−6.22560	+	10.7831i	−0.386840	+	0.670026i
$260$		0			0
$261$	−2.35299	+	6.46479i	−0.145646	+	0.400160i
$262$		0			0
$263$	−3.71457	−	4.42685i	−0.229050	−	0.272971i	0.639263	−	0.768989i	$-0.279240\pi$
$263$	−3.71457	−	4.42685i	−0.229050	−	0.272971i	−0.868313	+	0.496017i	$0.834795\pi$
$264$		0			0
$265$			38.8536i			2.38676i
$266$		0			0
$267$			13.1315i			0.803637i
$268$		0			0
$269$	−9.85675	−	11.7468i	−0.600977	−	0.716216i	0.376699	−	0.926336i	$-0.377059\pi$
$269$	−9.85675	−	11.7468i	−0.600977	−	0.716216i	−0.977676	+	0.210120i	$0.932615\pi$
$270$		0			0
$271$	10.6960	−	29.3869i	0.649733	−	1.78513i	0.0310073	−	0.999519i	$-0.490128\pi$
$271$	10.6960	−	29.3869i	0.649733	−	1.78513i	0.618726	−	0.785607i	$-0.287649\pi$
$272$		0			0
$273$	2.86042	−	4.95439i	0.173120	−	0.299853i
$274$		0			0
$275$	−2.69859	−	0.475834i	−0.162731	−	0.0286939i
$276$		0			0
$277$	8.37946	+	14.5136i	0.503473	+	0.872041i	0.999992	+	0.00401481i	$0.00127796\pi$
$277$	8.37946	+	14.5136i	0.503473	+	0.872041i	−0.496519	+	0.868026i	$0.665389\pi$
$278$		0			0
$279$	−6.09253	−	5.11224i	−0.364750	−	0.306062i
$280$		0			0
$281$	−3.85734	−	10.5980i	−0.230110	−	0.632222i	0.769872	−	0.638198i	$-0.220320\pi$
$281$	−3.85734	−	10.5980i	−0.230110	−	0.632222i	−0.999982	+	0.00597641i	$0.998098\pi$
$282$		0			0
$283$	15.8156	−	2.78872i	0.940141	−	0.165772i	0.317481	−	0.948265i	$-0.397163\pi$
$283$	15.8156	−	2.78872i	0.940141	−	0.165772i	0.622660	+	0.782493i	$0.286052\pi$
$284$		0			0
$285$	−2.69589	−	12.0993i	−0.159691	−	0.716698i
$286$		0			0
$287$	−2.61723	−	14.8430i	−0.154490	−	0.876156i
$288$		0			0
$289$	15.5796	−	5.67053i	0.916450	−	0.333560i
$290$		0			0
$291$	1.78240	−	2.12418i	0.104486	−	0.124522i
$292$		0			0
$293$	15.3116	−	8.84018i	0.894515	−	0.516449i	0.0190985	−	0.999818i	$-0.493920\pi$
$293$	15.3116	−	8.84018i	0.894515	−	0.516449i	0.875417	+	0.483369i	$0.160587\pi$
$294$		0			0
$295$	−1.14128	+	6.47255i	−0.0664481	+	0.376846i
$296$		0			0
$297$	−0.768651	−	0.443781i	−0.0446016	−	0.0257508i
$298$		0			0
$299$	8.84134	+	3.21798i	0.511308	+	0.186101i
$300$		0			0
$301$	11.5859	−	9.72173i	0.667800	−	0.560351i
$302$		0			0
$303$	4.27244			0.245445
$304$		0			0
$305$	24.2106			1.38629
$306$		0			0
$307$	−21.5831	+	18.1103i	−1.23181	+	1.03361i	−0.233691	+	0.972311i	$0.575081\pi$
$307$	−21.5831	+	18.1103i	−1.23181	+	1.03361i	−0.998119	+	0.0613011i	$0.980475\pi$
$308$		0			0
$309$	−2.04766	−	0.745288i	−0.116487	−	0.0423979i
$310$		0			0
$311$	24.3439	+	14.0550i	1.38042	+	0.796983i	0.992208	−	0.124589i	$-0.0397613\pi$
$311$	24.3439	+	14.0550i	1.38042	+	0.796983i	0.388207	+	0.921572i	$0.373095\pi$
$312$		0			0
$313$	3.10247	−	17.5950i	0.175362	−	0.994528i	−0.762363	−	0.647150i	$-0.775961\pi$
$313$	3.10247	−	17.5950i	0.175362	−	0.994528i	0.937725	−	0.347378i	$-0.112928\pi$
$314$		0			0
$315$	−5.91128	+	3.41288i	−0.333063	+	0.192294i
$316$		0			0
$317$	−17.6185	+	20.9969i	−0.989551	+	1.17930i	−0.00576012	+	0.999983i	$0.501834\pi$
$317$	−17.6185	+	20.9969i	−0.989551	+	1.17930i	−0.983791	+	0.179318i	$0.942611\pi$
$318$		0			0
$319$	5.73790	−	2.08842i	0.321261	−	0.116929i
$320$		0			0
$321$	−0.441086	−	2.50152i	−0.0246190	−	0.139621i
$322$		0			0
$323$	2.82370	−	0.126304i	0.157115	−	0.00702774i
$324$		0			0
$325$	−7.24688	+	1.27782i	−0.401984	+	0.0708807i
$326$		0			0
$327$	−1.88223	−	5.17140i	−0.104088	−	0.285979i
$328$		0			0
$329$	0.287209	+	0.240997i	0.0158343	+	0.0132866i
$330$		0			0
$331$	−11.4473	−	19.8273i	−0.629202	−	1.08981i	−0.987712	−	0.156284i	$-0.950049\pi$
$331$	−11.4473	−	19.8273i	−0.629202	−	1.08981i	0.358510	−	0.933526i	$-0.383285\pi$
$332$		0			0
$333$	5.10876	+	0.900812i	0.279958	+	0.0493642i
$334$		0			0
$335$	−11.7843	+	20.4110i	−0.643845	+	1.11517i
$336$		0			0
$337$	4.49980	−	12.3631i	0.245120	−	0.673461i	−0.754728	−	0.656037i	$-0.772231\pi$
$337$	4.49980	−	12.3631i	0.245120	−	0.673461i	0.999848	−	0.0174236i	$-0.00554640\pi$
$338$		0			0
$339$	−5.43521	−	6.47743i	−0.295200	−	0.351806i
$340$		0			0
$341$			7.05898i			0.382265i
$342$		0			0
$343$		−	19.7753i		−	1.06777i
$344$		0			0
$345$	−7.21590	−	8.59958i	−0.388491	−	0.462986i
$346$		0			0
$347$	0.649666	−	1.78494i	0.0348759	−	0.0958208i	−0.921033	−	0.389486i	$-0.872653\pi$
$347$	0.649666	−	1.78494i	0.0348759	−	0.0958208i	0.955908	+	0.293665i	$0.0948750\pi$
$348$		0			0
$349$	−10.0718	+	17.4449i	−0.539133	+	0.933806i	0.459818	+	0.888013i	$0.347915\pi$
$349$	−10.0718	+	17.4449i	−0.539133	+	0.933806i	−0.998951	+	0.0457930i	$0.985419\pi$
$350$		0			0
$351$	−2.34727	−	0.413888i	−0.125288	−	0.0220917i
$352$		0			0
$353$	1.93579	+	3.35289i	0.103032	+	0.178456i	0.912932	−	0.408111i	$-0.133812\pi$
$353$	1.93579	+	3.35289i	0.103032	+	0.178456i	−0.809901	+	0.586567i	$0.800479\pi$
$354$		0			0
$355$	4.94473	+	4.14912i	0.262439	+	0.220213i
$356$		0			0
$357$	−0.532321	−	1.46254i	−0.0281734	−	0.0774059i
$358$		0			0
$359$	−29.8374	+	5.26115i	−1.57476	+	0.277673i	−0.891678	−	0.452669i	$-0.850472\pi$
$359$	−29.8374	+	5.26115i	−1.57476	+	0.277673i	−0.683082	+	0.730342i	$0.739361\pi$
$360$		0			0
$361$	−18.3630	−	4.87839i	−0.966476	−	0.256757i
$362$		0			0
$363$	−1.77334	−	10.0571i	−0.0930760	−	0.527860i
$364$		0			0
$365$	−31.0128	+	11.2877i	−1.62328	+	0.590826i
$366$		0			0
$367$	23.3510	−	27.8286i	1.21891	−	1.45264i	0.365979	−	0.930623i	$-0.380734\pi$
$367$	23.3510	−	27.8286i	1.21891	−	1.45264i	0.852933	−	0.522020i	$-0.174821\pi$
$368$		0			0
$369$	−5.43819	+	3.13974i	−0.283101	+	0.163448i
$370$		0			0
$371$	5.69437	−	32.2944i	0.295637	−	1.67664i
$372$		0			0
$373$	−10.7094	−	6.18306i	−0.554510	−	0.320147i	0.196429	−	0.980518i	$-0.437066\pi$
$373$	−10.7094	−	6.18306i	−0.554510	−	0.320147i	−0.750939	+	0.660371i	$0.770399\pi$
$374$		0			0
$375$	−5.11120	−	1.86032i	−0.263941	−	0.0960667i
$376$		0			0
$377$	12.5613	−	10.5402i	0.646941	−	0.542848i
$378$		0			0
$379$	−19.7494			−1.01446			−0.507230	−	0.861810i	$-0.669331\pi$
$379$	−19.7494			−1.01446			−0.507230	+	0.861810i	$0.669331\pi$
$380$		0			0
$381$	−10.6025			−0.543185
$382$		0			0
$383$	19.7580	−	16.5790i	1.00959	−	0.847146i	0.0213052	−	0.999773i	$-0.493218\pi$
$383$	19.7580	−	16.5790i	1.00959	−	0.847146i	0.988284	+	0.152627i	$0.0487734\pi$
$384$		0			0
$385$	5.69292	+	2.07205i	0.290138	+	0.105602i
$386$		0			0
$387$	−5.45707	−	3.15064i	−0.277398	−	0.160156i
$388$		0			0
$389$	−0.963221	+	5.46270i	−0.0488372	+	0.276970i	−0.999441	−	0.0334379i	$-0.989354\pi$
$389$	−0.963221	+	5.46270i	−0.0488372	+	0.276970i	0.950604	+	0.310408i	$0.100466\pi$
$390$		0			0
$391$	2.21679	−	1.27987i	0.112108	−	0.0647256i
$392$		0			0
$393$	−4.55843	+	5.43252i	−0.229942	+	0.274034i
$394$		0			0
$395$	32.2629	−	11.7427i	1.62332	−	0.590841i
$396$		0			0
$397$	−4.44699	−	25.2201i	−0.223188	−	1.26576i	−0.866119	−	0.499838i	$-0.833393\pi$
$397$	−4.44699	−	25.2201i	−0.223188	−	1.26576i	0.642931	−	0.765924i	$-0.277718\pi$
$398$		0			0
$399$	0.467508	+	10.4518i	0.0234047	+	0.523243i
$400$		0			0
$401$	−7.09096	+	1.25033i	−0.354106	+	0.0624384i	−0.347872	−	0.937542i	$-0.613095\pi$
$401$	−7.09096	+	1.25033i	−0.354106	+	0.0624384i	−0.00623405	+	0.999981i	$0.501984\pi$
$402$		0			0
$403$	6.48348	+	17.8132i	0.322965	+	0.887339i
$404$		0			0
$405$	2.17850	+	1.82798i	0.108250	+	0.0908329i
$406$		0			0
$407$	−2.30214	−	3.98743i	−0.114113	−	0.197649i
$408$		0			0
$409$	−24.6981	−	4.35495i	−1.22124	−	0.215338i	−0.474383	−	0.880318i	$-0.657329\pi$
$409$	−24.6981	−	4.35495i	−1.22124	−	0.215338i	−0.746861	+	0.664980i	$0.768440\pi$
$410$		0			0
$411$	9.26967	−	16.0555i	0.457239	−	0.791961i
$412$		0			0
$413$	1.89723	−	5.21259i	0.0933564	−	0.256495i
$414$		0			0
$415$	−17.0779	−	20.3526i	−0.838320	−	0.999071i
$416$		0			0
$417$			3.92396i			0.192157i
$418$		0			0
$419$		−	22.4706i		−	1.09776i	−0.835901	−	0.548880i	$-0.815054\pi$
$419$		−	22.4706i		−	1.09776i	0.835901	−	0.548880i	$-0.184946\pi$
$420$		0			0
$421$	−13.0088	−	15.5033i	−0.634010	−	0.755584i	0.349401	−	0.936973i	$-0.386385\pi$
$421$	−13.0088	−	15.5033i	−0.634010	−	0.755584i	−0.983411	+	0.181389i	$0.941941\pi$
$422$		0			0
$423$	0.0534254	−	0.146785i	0.00259763	−	0.00713694i
$424$		0			0
$425$	−1.00100	+	1.73377i	−0.0485554	+	0.0841004i
$426$		0			0
$427$	−20.1234	−	3.54829i	−0.973837	−	0.171714i
$428$		0			0
$429$	1.05774	+	1.83207i	0.0510684	+	0.0884531i
$430$		0			0
$431$	−3.54690	−	2.97620i	−0.170848	−	0.143359i	0.553354	−	0.832946i	$-0.313348\pi$
$431$	−3.54690	−	2.97620i	−0.170848	−	0.143359i	−0.724203	+	0.689587i	$0.757792\pi$
$432$		0			0
$433$	6.67359	+	18.3355i	0.320712	+	0.881149i	0.990366	+	0.138476i	$0.0442203\pi$
$433$	6.67359	+	18.3355i	0.320712	+	0.881149i	−0.669654	+	0.742673i	$0.733557\pi$
$434$		0			0
$435$	−19.2674	+	3.39736i	−0.923802	+	0.162891i
$436$		0			0
$437$	−16.7948	+	3.74212i	−0.803405	+	0.179010i
$438$		0			0
$439$	4.38676	+	24.8786i	0.209369	+	1.18739i	0.890415	+	0.455149i	$0.150414\pi$
$439$	4.38676	+	24.8786i	0.209369	+	1.18739i	−0.681047	+	0.732240i	$0.738475\pi$
$440$		0			0
$441$	−1.16432	+	0.423778i	−0.0554439	+	0.0201799i
$442$		0			0
$443$	17.6666	−	21.0542i	0.839366	−	1.00032i	−0.160546	−	0.987028i	$-0.551325\pi$
$443$	17.6666	−	21.0542i	0.839366	−	1.00032i	0.999912	−	0.0132891i	$-0.00423017\pi$
$444$		0			0
$445$	−32.3407	+	18.6719i	−1.53310	+	0.885134i
$446$		0			0
$447$	−3.08048	+	17.4703i	−0.145702	+	0.826316i
$448$		0			0
$449$	1.65027	+	0.952786i	0.0778813	+	0.0449648i	0.538435	−	0.842667i	$-0.319016\pi$
$449$	1.65027	+	0.952786i	0.0778813	+	0.0449648i	−0.460554	+	0.887632i	$0.652349\pi$
$450$		0			0
$451$	5.23731	+	1.90622i	0.246615	+	0.0897606i
$452$		0			0
$453$	4.47707	−	3.75670i	0.210351	−	0.176505i
$454$		0			0
$455$	16.2691			0.762706
$456$		0			0
$457$	−25.0138			−1.17010			−0.585049	−	0.810998i	$-0.698925\pi$
$457$	−25.0138			−1.17010			−0.585049	+	0.810998i	$0.698925\pi$
$458$		0			0
$459$	−0.496740	+	0.416814i	−0.0231858	+	0.0194552i
$460$		0			0
$461$	26.8650	+	9.77805i	1.25123	+	0.455409i	0.880816	−	0.473459i	$-0.156995\pi$
$461$	26.8650	+	9.77805i	1.25123	+	0.455409i	0.370410	+	0.928868i	$0.379217\pi$
$462$		0			0
$463$	−20.7424	−	11.9756i	−0.963980	−	0.556554i	−0.0665842	−	0.997781i	$-0.521210\pi$
$463$	−20.7424	−	11.9756i	−0.963980	−	0.556554i	−0.897396	+	0.441227i	$0.854543\pi$
$464$		0			0
$465$	3.92751	−	22.2740i	0.182134	−	1.03293i
$466$		0			0
$467$	36.6138	−	21.1390i	1.69428	−	0.978195i	0.743297	−	0.668962i	$-0.233261\pi$
$467$	36.6138	−	21.1390i	1.69428	−	0.978195i	0.950986	−	0.309233i	$-0.100072\pi$
$468$		0			0
$469$	12.7863	−	15.2381i	0.590417	−	0.703632i
$470$		0			0
$471$	19.3914	−	7.05788i	0.893507	−	0.325210i
$472$		0			0
$473$	0.971175	+	5.50781i	0.0446547	+	0.253249i
$474$		0			0
$475$	9.91219	−	9.10232i	0.454802	−	0.417643i
$476$		0			0
$477$	−13.4549	+	2.37246i	−0.616057	+	0.108627i
$478$		0			0
$479$	2.19142	+	6.02087i	0.100128	+	0.275101i	0.979635	−	0.200786i	$-0.0643495\pi$
$479$	2.19142	+	6.02087i	0.100128	+	0.275101i	−0.879507	+	0.475886i	$0.842127\pi$
$480$		0			0
$481$	−9.47175	−	7.94774i	−0.431875	−	0.362386i
$482$		0			0
$483$	4.73737	+	8.20536i	0.215558	+	0.373357i
$484$		0			0
$485$	7.76591	+	1.36934i	0.352632	+	0.0621785i
$486$		0			0
$487$	2.74378	−	4.75237i	0.124333	−	0.215350i	−0.797139	−	0.603795i	$-0.793654\pi$
$487$	2.74378	−	4.75237i	0.124333	−	0.215350i	0.921472	+	0.388445i	$0.126988\pi$
$488$		0			0
$489$	−2.60443	+	7.15561i	−0.117776	+	0.323588i
$490$		0			0
$491$	5.12899	+	6.11250i	0.231468	+	0.275853i	0.869259	−	0.494356i	$-0.164596\pi$
$491$	5.12899	+	6.11250i	0.231468	+	0.275853i	−0.637791	+	0.770209i	$0.720152\pi$
$492$		0			0
$493$		−	4.46112i		−	0.200919i
$494$		0			0
$495$		−	2.52407i		−	0.113449i
$496$		0			0
$497$	−3.50187	−	4.17337i	−0.157080	−	0.187201i
$498$		0			0
$499$	−10.1552	+	27.9012i	−0.454610	+	1.24903i	0.474836	+	0.880074i	$0.342507\pi$
$499$	−10.1552	+	27.9012i	−0.454610	+	1.24903i	−0.929446	+	0.368957i	$0.879715\pi$
$500$		0			0
$501$	4.79086	−	8.29802i	0.214040	−	0.370728i
$502$		0			0
$503$	−34.9924	−	6.17010i	−1.56023	−	0.275111i	−0.674134	−	0.738609i	$-0.735483\pi$
$503$	−34.9924	−	6.17010i	−1.56023	−	0.275111i	−0.886098	+	0.463498i	$0.846594\pi$
$504$		0			0
$505$	6.07504	+	10.5223i	0.270336	+	0.468235i
$506$		0			0
$507$	−5.60668	−	4.70456i	−0.249001	−	0.208937i
$508$		0			0
$509$	13.8536	+	38.0625i	0.614051	+	1.68709i	0.721094	+	0.692838i	$0.243640\pi$
$509$	13.8536	+	38.0625i	0.614051	+	1.68709i	−0.107042	+	0.994254i	$0.534138\pi$
$510$		0			0
$511$	27.4315	−	4.83692i	1.21350	−	0.213973i
$512$		0			0
$513$	4.02532	−	1.67237i	0.177722	−	0.0738371i
$514$		0			0
$515$	−1.07608	−	6.10277i	−0.0474179	−	0.268920i
$516$		0			0
$517$	−0.130281	+	0.0474184i	−0.00572975	+	0.00208546i
$518$		0			0
$519$	12.1861	−	14.5229i	0.534912	−	0.637483i
$520$		0			0
$521$	−36.8538	+	21.2775i	−1.61459	+	0.932186i	−0.626306	+	0.779577i	$0.715434\pi$
$521$	−36.8538	+	21.2775i	−1.61459	+	0.932186i	−0.988287	+	0.152608i	$0.951233\pi$
$522$		0			0
$523$	5.76481	−	32.6939i	0.252077	−	1.42960i	−0.551387	−	0.834250i	$-0.685901\pi$
$523$	5.76481	−	32.6939i	0.252077	−	1.42960i	0.803464	−	0.595353i	$-0.202988\pi$
$524$		0			0
$525$	−6.41748	−	3.70514i	−0.280082	−	0.161705i
$526$		0			0
$527$	4.84624	+	1.76389i	0.211105	+	0.0768361i
$528$		0			0
$529$	5.68207	−	4.76782i	0.247047	−	0.207297i
$530$		0			0
$531$	−2.31111			−0.100294
$532$		0			0
$533$	14.9671			0.648295
$534$		0			0
$535$	5.53363	−	4.64326i	0.239240	−	0.200746i
$536$		0			0
$537$	10.6557	+	3.87835i	0.459827	+	0.167363i
$538$		0			0
$539$	0.952393	+	0.549864i	0.0410225	+	0.0236843i
$540$		0			0
$541$	5.23800	−	29.7062i	0.225199	−	1.27717i	−0.637105	−	0.770777i	$-0.719868\pi$
$541$	5.23800	−	29.7062i	0.225199	−	1.27717i	0.862304	−	0.506391i	$-0.169021\pi$
$542$		0			0
$543$	−0.158007	+	0.0912253i	−0.00678073	+	0.00391485i
$544$		0			0
$545$	10.0599	−	11.9889i	0.430918	−	0.513548i
$546$		0			0
$547$	−23.0491	+	8.38917i	−0.985507	+	0.358695i	−0.783979	−	0.620788i	$-0.786813\pi$
$547$	−23.0491	+	8.38917i	−0.985507	+	0.358695i	−0.201528	+	0.979483i	$0.564591\pi$
$548$		0			0
$549$	1.47833	+	8.38404i	0.0630937	+	0.357822i
$550$		0			0
$551$	−8.98700	+	28.6095i	−0.382859	+	1.21881i
$552$		0			0
$553$	−28.5373	+	5.03190i	−1.21353	+	0.213978i
$554$		0			0
$555$	5.04567	+	13.8629i	0.214177	+	0.588446i
$556$		0			0
$557$	29.5180	+	24.7685i	1.25072	+	1.04948i	0.996608	+	0.0822999i	$0.0262265\pi$
$557$	29.5180	+	24.7685i	1.25072	+	1.04948i	0.254109	+	0.967176i	$0.418218\pi$
$558$		0			0
$559$	7.50950	+	13.0068i	0.317618	+	0.550131i
$560$		0			0
$561$	0.566794	+	0.0999410i	0.0239300	+	0.00421951i
$562$		0			0
$563$	6.23230	−	10.7947i	0.262660	−	0.454941i	−0.704288	−	0.709915i	$-0.748734\pi$
$563$	6.23230	−	10.7947i	0.262660	−	0.454941i	0.966948	+	0.254974i	$0.0820669\pi$
$564$		0			0
$565$	8.22439	−	22.5963i	0.346003	−	0.950635i
$566$		0			0
$567$	−1.54282	−	1.83866i	−0.0647923	−	0.0772164i
$568$		0			0
$569$			41.8624i			1.75496i	0.479612	+	0.877481i	$0.340777\pi$
$569$			41.8624i			1.75496i	−0.479612	+	0.877481i	$0.659223\pi$
$570$		0			0
$571$			28.2158i			1.18080i	0.807112	+	0.590398i	$0.201029\pi$
$571$			28.2158i			1.18080i	−0.807112	+	0.590398i	$0.798971\pi$
$572$		0			0
$573$	−6.41268	−	7.64233i	−0.267893	−	0.319263i
$574$		0			0
$575$	4.16829	−	11.4523i	0.173830	−	0.477594i
$576$		0			0
$577$	12.8932	−	22.3317i	0.536751	−	0.929680i	−0.462325	−	0.886710i	$-0.652985\pi$
$577$	12.8932	−	22.3317i	0.536751	−	0.929680i	0.999076	−	0.0429699i	$-0.0136820\pi$
$578$		0			0
$579$	8.24714	+	1.45419i	0.342739	+	0.0604342i
$580$		0			0
$581$	11.2119	+	19.4196i	0.465149	+	0.805662i
$582$		0			0
$583$	9.28925	+	7.79461i	0.384721	+	0.322820i
$584$		0			0
$585$	−2.31829	−	6.36945i	−0.0958494	−	0.263344i
$586$		0			0
$587$	−5.55999	+	0.980376i	−0.229485	+	0.0404645i	−0.287208	−	0.957868i	$-0.592727\pi$
$587$	−5.55999	+	0.980376i	−0.229485	+	0.0404645i	0.0577228	+	0.998333i	$0.481616\pi$
$588$		0			0
$589$	−27.5260	−	21.0748i	−1.13419	−	0.868372i
$590$		0			0
$591$	0.100448	+	0.569672i	0.00413190	+	0.0234332i
$592$		0			0
$593$	−28.9620	+	10.5413i	−1.18933	+	0.432879i	−0.859487	−	0.511158i	$-0.829217\pi$
$593$	−28.9620	+	10.5413i	−1.18933	+	0.432879i	−0.329840	+	0.944037i	$0.606995\pi$
$594$		0			0
$595$	2.84507	−	3.39062i	0.116637	−	0.139002i
$596$		0			0
$597$	9.60286	−	5.54421i	0.393019	−	0.226910i
$598$		0			0
$599$	−3.16737	+	17.9630i	−0.129415	+	0.733950i	0.849172	+	0.528116i	$0.177102\pi$
$599$	−3.16737	+	17.9630i	−0.129415	+	0.733950i	−0.978587	+	0.205833i	$0.934010\pi$
$600$		0			0
$601$	−30.8955	−	17.8375i	−1.26025	−	0.727608i	−0.287130	−	0.957892i	$-0.592701\pi$
$601$	−30.8955	−	17.8375i	−1.26025	−	0.727608i	−0.973123	+	0.230284i	$0.926034\pi$
$602$		0			0
$603$	−7.78783	−	2.83454i	−0.317145	−	0.115431i
$604$		0			0
$605$	22.2473	−	18.6677i	0.904483	−	0.758951i
$606$		0			0
$607$	−21.1779			−0.859585			−0.429792	−	0.902928i	$-0.641413\pi$
$607$	−21.1779			−0.859585			−0.429792	+	0.902928i	$0.641413\pi$
$608$		0			0
$609$	16.5126			0.669125
$610$		0			0
$611$	−0.285209	+	0.239319i	−0.0115383	+	0.00968179i
$612$		0			0
$613$	10.0130	+	3.64442i	0.404420	+	0.147197i	0.536218	−	0.844080i	$-0.319853\pi$
$613$	10.0130	+	3.64442i	0.404420	+	0.147197i	−0.131798	+	0.991277i	$0.542075\pi$
$614$		0			0
$615$	−15.4653	−	8.92889i	−0.623620	−	0.360047i
$616$		0			0
$617$	−5.52200	+	31.3168i	−0.222307	+	1.26077i	0.645459	+	0.763795i	$0.276666\pi$
$617$	−5.52200	+	31.3168i	−0.222307	+	1.26077i	−0.867766	+	0.496972i	$0.834445\pi$
$618$		0			0
$619$	10.0717	−	5.81488i	0.404815	−	0.233720i	−0.283745	−	0.958900i	$-0.591577\pi$
$619$	10.0717	−	5.81488i	0.404815	−	0.233720i	0.688559	+	0.725180i	$0.258244\pi$
$620$		0			0
$621$	2.53739	−	3.02394i	0.101822	−	0.121347i
$622$		0			0
$623$	29.6175	−	10.7799i	1.18660	−	0.431887i
$624$		0			0
$625$	−5.36660	−	30.4355i	−0.214664	−	1.21742i
$626$		0			0
$627$	−3.43356	−	1.78275i	−0.137123	−	0.0711960i
$628$		0			0
$629$	−3.31276	+	0.584129i	−0.132088	+	0.0232908i
$630$		0			0
$631$	−1.86228	−	5.11656i	−0.0741361	−	0.203687i	0.897089	−	0.441849i	$-0.145677\pi$
$631$	−1.86228	−	5.11656i	−0.0741361	−	0.203687i	−0.971225	+	0.238162i	$0.923455\pi$
$632$		0			0
$633$	−16.7120	−	14.0230i	−0.664242	−	0.557365i
$634$		0			0
$635$	−15.0759	−	26.1122i	−0.598269	−	1.03623i
$636$		0			0
$637$	2.90838	+	0.512826i	0.115234	+	0.0203189i
$638$		0			0
$639$	−1.13489	+	1.96569i	−0.0448957	+	0.0777617i
$640$		0			0
$641$	10.1240	−	27.8155i	0.399875	−	1.09865i	−0.562470	−	0.826818i	$-0.690149\pi$
$641$	10.1240	−	27.8155i	0.399875	−	1.09865i	0.962345	−	0.271830i	$-0.0876290\pi$
$642$		0			0
$643$	−7.66120	−	9.13027i	−0.302128	−	0.360063i	0.593525	−	0.804816i	$-0.297736\pi$
$643$	−7.66120	−	9.13027i	−0.302128	−	0.360063i	−0.895653	+	0.444753i	$0.853291\pi$
$644$		0			0
$645$		−	17.9198i		−	0.705590i
$646$		0			0
$647$		−	29.8371i		−	1.17302i	−0.809943	−	0.586508i	$-0.800502\pi$
$647$		−	29.8371i		−	1.17302i	0.809943	−	0.586508i	$-0.199498\pi$
$648$		0			0
$649$	1.31852	+	1.57135i	0.0517564	+	0.0616808i
$650$		0			0
$651$	−6.52894	+	17.9381i	−0.255889	+	0.703050i
$652$		0			0
$653$	22.9515	−	39.7531i	0.898160	−	1.55566i	0.0683159	−	0.997664i	$-0.478237\pi$
$653$	22.9515	−	39.7531i	0.898160	−	1.55566i	0.829844	−	0.557995i	$-0.188429\pi$
$654$		0			0
$655$	−19.8611	−	3.50204i	−0.776036	−	0.136836i
$656$		0			0
$657$	−5.80258	−	10.0504i	−0.226380	−	0.392102i
$658$		0			0
$659$	−30.0341	−	25.2016i	−1.16996	−	0.981717i	−0.169971	−	0.985449i	$-0.554367\pi$
$659$	−30.0341	−	25.2016i	−1.16996	−	0.981717i	−0.999993	+	0.00373241i	$0.998812\pi$
$660$		0			0
$661$	9.79645	+	26.9155i	0.381038	+	1.04689i	0.970920	+	0.239403i	$0.0769519\pi$
$661$	9.79645	+	26.9155i	0.381038	+	1.04689i	−0.589882	+	0.807489i	$0.700826\pi$
$662$		0			0
$663$	1.52209	−	0.268385i	0.0591129	−	0.0104232i
$664$		0			0
$665$	−25.0762	+	16.0129i	−0.972412	+	0.620954i
$666$		0			0
$667$	4.71583	+	26.7448i	0.182598	+	1.03556i
$668$		0			0
$669$	−0.753708	+	0.274327i	−0.0291400	+	0.0106061i
$670$		0			0
$671$	4.85699	−	5.78834i	0.187502	−	0.223456i
$672$		0			0
$673$	−4.41605	+	2.54961i	−0.170226	+	0.0982802i	−0.582693	−	0.812693i	$-0.698001\pi$
$673$	−4.41605	+	2.54961i	−0.170226	+	0.0982802i	0.412466	+	0.910973i	$0.364667\pi$
$674$		0			0
$675$	−0.536114	+	3.04045i	−0.0206350	+	0.117027i
$676$		0			0
$677$	−0.0326780	−	0.0188667i	−0.00125592	−	0.000725105i	0.499372	−	0.866388i	$-0.333564\pi$
$677$	−0.0326780	−	0.0188667i	−0.00125592	−	0.000725105i	−0.500628	+	0.865663i	$0.666897\pi$
$678$		0			0
$679$	−6.25418	−	2.27634i	−0.240013	−	0.0873577i
$680$		0			0
$681$	−17.4780	+	14.6658i	−0.669759	+	0.561995i
$682$		0			0
$683$	45.5185			1.74172			0.870858	−	0.491535i	$-0.163564\pi$
$683$	45.5185			1.74172			0.870858	+	0.491535i	$0.163564\pi$
$684$		0			0
$685$	52.7227			2.01443
$686$		0			0
$687$	−6.48820	+	5.44424i	−0.247540	+	0.207711i
$688$		0			0
$689$	30.6004	+	11.1376i	1.16578	+	0.424310i
$690$		0			0
$691$	−39.8831	−	23.0265i	−1.51722	−	0.875970i	−0.999795	−	0.0202443i	$-0.993556\pi$
$691$	−39.8831	−	23.0265i	−1.51722	−	0.875970i	−0.517430	−	0.855726i	$-0.673111\pi$
$692$		0			0
$693$	−0.369927	+	2.09796i	−0.0140524	+	0.0796949i
$694$		0			0
$695$	−9.66404	+	5.57954i	−0.366578	+	0.211644i
$696$		0			0
$697$	2.61738	−	3.11927i	0.0991403	−	0.118151i
$698$		0			0
$699$	−12.0422	+	4.38299i	−0.455477	+	0.165780i
$700$		0			0
$701$	2.50376	+	14.1995i	0.0945658	+	0.536309i	0.994880	+	0.101068i	$0.0322259\pi$
$701$	2.50376	+	14.1995i	0.0945658	+	0.536309i	−0.900314	+	0.435241i	$0.856663\pi$
$702$		0			0
$703$	22.4218	+	2.92755i	0.845653	+	0.110415i
$704$		0			0
$705$	0.437473	−	0.0771383i	0.0164762	−	0.00290520i
$706$		0			0
$707$	−3.50731	−	9.63627i	−0.131906	−	0.362409i
$708$		0			0
$709$	32.5106	+	27.2797i	1.22096	+	1.02451i	0.998774	+	0.0495052i	$0.0157644\pi$
$709$	32.5106	+	27.2797i	1.22096	+	1.02451i	0.222188	+	0.975004i	$0.428680\pi$
$710$		0			0
$711$	6.03648	+	10.4555i	0.226386	+	0.392112i
$712$		0			0
$713$	−30.9183	−	5.45172i	−1.15790	−	0.204169i
$714$		0			0
$715$	−3.00804	+	5.21009i	−0.112494	+	0.194846i
$716$		0			0
$717$	6.23427	−	17.1285i	0.232823	−	0.639676i
$718$		0			0
$719$	14.3800	+	17.1375i	0.536285	+	0.639119i	0.964350	−	0.264628i	$-0.0852493\pi$
$719$	14.3800	+	17.1375i	0.536285	+	0.639119i	−0.428066	+	0.903748i	$0.640805\pi$
$720$		0			0
$721$			5.23021i			0.194783i
$722$		0			0
$723$			9.47198i			0.352267i
$724$		0			0
$725$	−13.6528	−	16.2708i	−0.507054	−	0.604283i
$726$		0			0
$727$	14.7620	−	40.5583i	0.547493	−	1.50422i	−0.289591	−	0.957150i	$-0.593519\pi$
$727$	14.7620	−	40.5583i	0.547493	−	1.50422i	0.837084	−	0.547074i	$-0.184258\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	4.02397	+	0.709535i	0.148832	+	0.0262431i
$732$		0			0
$733$	9.00425	+	15.5958i	0.332580	+	0.576045i	0.983017	−	0.183515i	$-0.0587476\pi$
$733$	9.00425	+	15.5958i	0.332580	+	0.576045i	−0.650437	+	0.759560i	$0.725414\pi$
$734$		0			0
$735$	−2.69926	−	2.26495i	−0.0995636	−	0.0835438i
$736$		0			0
$737$	2.51583	+	6.91217i	0.0926716	+	0.254613i
$738$		0			0
$739$	−25.4986	+	4.49609i	−0.937981	+	0.165391i	−0.621683	−	0.783269i	$-0.713551\pi$
$739$	−25.4986	+	4.49609i	−0.937981	+	0.165391i	−0.316298	+	0.948660i	$0.602440\pi$
$740$		0			0
$741$	−10.3019	−	1.34509i	−0.378451	−	0.0494133i
$742$		0			0
$743$	7.38130	+	41.8614i	0.270794	+	1.53575i	0.752014	+	0.659147i	$0.229083\pi$
$743$	7.38130	+	41.8614i	0.270794	+	1.53575i	−0.481220	+	0.876600i	$0.659806\pi$
$744$		0			0
$745$	−47.4065	+	17.2546i	−1.73684	+	0.632158i
$746$		0			0
$747$	6.00524	−	7.15677i	0.219720	−	0.261852i
$748$		0			0
$749$	−5.27996	+	3.04839i	−0.192925	+	0.111386i
$750$		0			0
$751$	−5.61372	+	31.8370i	−0.204847	+	1.16175i	0.692832	+	0.721099i	$0.256363\pi$
$751$	−5.61372	+	31.8370i	−0.204847	+	1.16175i	−0.897680	+	0.440648i	$0.854749\pi$
$752$		0			0
$753$	−15.3974	−	8.88968i	−0.561112	−	0.323958i
$754$		0			0
$755$	15.6181	+	5.68453i	0.568401	+	0.206881i
$756$		0			0
$757$	29.4600	−	24.7198i	1.07074	−	0.898458i	0.0756209	−	0.997137i	$-0.475906\pi$
$757$	29.4600	−	24.7198i	1.07074	−	0.898458i	0.995119	+	0.0986789i	$0.0314617\pi$
$758$		0			0
$759$	−3.50363			−0.127174
$760$		0			0
$761$	−7.39583			−0.268099			−0.134049	−	0.990975i	$-0.542798\pi$
$761$	−7.39583			−0.268099			−0.134049	+	0.990975i	$0.542798\pi$
$762$		0			0
$763$	−10.1187	+	8.49057i	−0.366320	+	0.307379i
$764$		0			0
$765$	−1.73286	−	0.630711i	−0.0626518	−	0.0228034i
$766$		0			0
$767$	4.77049	+	2.75425i	0.172253	+	0.0994501i
$768$		0			0
$769$	−4.99890	+	28.3502i	−0.180265	+	1.02233i	0.751625	+	0.659591i	$0.229270\pi$
$769$	−4.99890	+	28.3502i	−0.180265	+	1.02233i	−0.931890	+	0.362742i	$0.881841\pi$
$770$		0			0
$771$	−1.16720	+	0.673883i	−0.0420357	+	0.0242693i
$772$		0			0
$773$	5.68552	−	6.77573i	0.204494	−	0.243706i	−0.654044	−	0.756457i	$-0.726929\pi$
$773$	5.68552	−	6.77573i	0.204494	−	0.243706i	0.858538	+	0.512750i	$0.171373\pi$
$774$		0			0
$775$	23.0737	−	8.39813i	0.828831	−	0.301670i
$776$		0			0
$777$	−2.16213	−	12.2620i	−0.0775659	−	0.439898i
$778$		0			0
$779$	−23.0693	+	14.7314i	−0.826543	+	0.527807i
$780$		0			0
$781$	1.98397	−	0.349828i	0.0709920	−	0.0125178i
$782$		0			0
$783$	−2.35299	−	6.46479i	−0.0840890	−	0.231033i
$784$		0			0
$785$	44.9552	+	37.7219i	1.60452	+	1.34635i
$786$		0			0
$787$	19.3024	+	33.4327i	0.688056	+	1.19175i	0.972466	+	0.233045i	$0.0748688\pi$
$787$	19.3024	+	33.4327i	0.688056	+	1.19175i	−0.284410	+	0.958703i	$0.591798\pi$
$788$		0			0
$789$	5.69105	+	1.00349i	0.202607	+	0.0357250i
$790$		0			0
$791$	−10.1477	+	17.5763i	−0.360809	+	0.624940i
$792$		0			0
$793$	6.94010	−	19.0678i	0.246450	−	0.677116i
$794$		0			0
$795$	−24.9746	−	29.7636i	−0.885759	−	1.05561i
$796$		0			0
$797$		−	2.92095i		−	0.103465i	−0.998661	−	0.0517326i	$-0.983526\pi$
$797$		−	2.92095i		−	0.103465i	0.998661	−	0.0517326i	$-0.0164744\pi$
$798$		0			0
$799$			0.101291i			0.00358342i
$800$		0			0
$801$	−8.44079	−	10.0593i	−0.298241	−	0.355429i
$802$		0			0
$803$	−3.52291	+	9.67911i	−0.124321	+	0.341568i
$804$		0			0
$805$	−13.4723	+	23.3346i	−0.474835	+	0.822438i
$806$		0			0
$807$	15.1014	+	2.66279i	0.531595	+	0.0937345i
$808$		0			0
$809$	9.11600	+	15.7894i	0.320502	+	0.555125i	0.980592	−	0.196061i	$-0.0628152\pi$
$809$	9.11600	+	15.7894i	0.320502	+	0.555125i	−0.660090	+	0.751187i	$0.729482\pi$
$810$		0			0
$811$	−11.3781	−	9.54733i	−0.399538	−	0.335252i	0.420777	−	0.907164i	$-0.361757\pi$
$811$	−11.3781	−	9.54733i	−0.399538	−	0.335252i	−0.820315	+	0.571912i	$0.806202\pi$
$812$		0			0
$813$	10.6960	+	29.3869i	0.375123	+	1.03064i
$814$		0			0
$815$	−21.3263	+	3.76040i	−0.747028	+	0.131721i
$816$		0			0
$817$	−24.3767	−	12.6567i	−0.852834	−	0.442801i
$818$		0			0
$819$	0.993413	+	5.63393i	0.0347127	+	0.196865i
$820$		0			0
$821$	36.5594	−	13.3065i	1.27593	−	0.464402i	0.386848	−	0.922143i	$-0.373564\pi$
$821$	36.5594	−	13.3065i	1.27593	−	0.464402i	0.889085	+	0.457742i	$0.151342\pi$
$822$		0			0
$823$	10.7658	−	12.8301i	0.375271	−	0.447231i	−0.545045	−	0.838407i	$-0.683487\pi$
$823$	10.7658	−	12.8301i	0.375271	−	0.447231i	0.920316	+	0.391176i	$0.127932\pi$
$824$		0			0
$825$	2.37310	−	1.37011i	0.0826207	−	0.0477011i
$826$		0			0
$827$	−3.97062	+	22.5185i	−0.138072	+	0.783044i	0.834599	+	0.550857i	$0.185699\pi$
$827$	−3.97062	+	22.5185i	−0.138072	+	0.783044i	−0.972671	+	0.232187i	$0.925412\pi$
$828$		0			0
$829$	13.7157	+	7.91878i	0.476367	+	0.275031i	0.718901	−	0.695112i	$-0.244645\pi$
$829$	13.7157	+	7.91878i	0.476367	+	0.275031i	−0.242534	+	0.970143i	$0.577979\pi$
$830$		0			0
$831$	−15.7482	−	5.73189i	−0.546300	−	0.198837i
$832$		0			0
$833$	0.615483	−	0.516452i	0.0213252	−	0.0178940i
$834$		0			0
$835$	27.2488			0.942983
$836$		0			0
$837$	7.95324			0.274904
$838$		0			0
$839$	3.59854	−	3.01953i	0.124235	−	0.104246i	−0.578553	−	0.815645i	$-0.696382\pi$
$839$	3.59854	−	3.01953i	0.124235	−	0.104246i	0.702788	+	0.711399i	$0.251938\pi$
$840$		0			0
$841$	17.2246	+	6.26926i	0.593953	+	0.216181i
$842$		0			0
$843$	9.76714	+	5.63906i	0.336398	+	0.194220i
$844$		0			0
$845$	3.61431	−	20.4978i	0.124336	−	0.705144i
$846$		0			0
$847$	−21.2275	+	12.2557i	−0.729385	+	0.421111i
$848$		0			0
$849$	−10.3229	+	12.3024i	−0.354281	+	0.422216i
$850$		0			0
$851$	19.2428	−	7.00382i	0.659636	−	0.240088i
$852$		0			0
$853$	−0.481524	−	2.73086i	−0.0164871	−	0.0935028i	0.975454	−	0.220204i	$-0.0706722\pi$
$853$	−0.481524	−	2.73086i	−0.0164871	−	0.0935028i	−0.991941	+	0.126701i	$0.959561\pi$
$854$		0			0
$855$	9.84242	+	7.53568i	0.336604	+	0.257715i
$856$		0			0
$857$	−15.7840	+	2.78315i	−0.539171	+	0.0950704i	−0.436601	−	0.899655i	$-0.643818\pi$
$857$	−15.7840	+	2.78315i	−0.539171	+	0.0950704i	−0.102570	+	0.994726i	$0.532707\pi$
$858$		0			0
$859$	14.2596	+	39.1779i	0.486531	+	1.33673i	0.903802	+	0.427951i	$0.140764\pi$
$859$	14.2596	+	39.1779i	0.486531	+	1.33673i	−0.417271	+	0.908782i	$0.637013\pi$
$860$		0			0
$861$	11.5458	+	9.68810i	0.393481	+	0.330170i
$862$		0			0
$863$	6.20352	+	10.7448i	0.211170	+	0.365757i	0.952081	−	0.305846i	$-0.0989393\pi$
$863$	6.20352	+	10.7448i	0.211170	+	0.365757i	−0.740911	+	0.671603i	$0.765606\pi$
$864$		0			0
$865$	53.0949	+	9.36207i	1.80528	+	0.318320i
$866$		0			0
$867$	−8.28976	+	14.3583i	−0.281535	+	0.487633i
$868$		0			0
$869$	3.66492	−	10.0693i	0.124324	−	0.341577i
$870$		0			0
$871$	12.6973	+	15.1320i	0.430231	+	0.512729i
$872$		0			0
$873$			2.77292i			0.0938491i
$874$		0			0
$875$			13.0552i			0.441347i
$876$		0			0
$877$	−2.13333	−	2.54240i	−0.0720374	−	0.0858508i	0.728822	−	0.684703i	$-0.240068\pi$
$877$	−2.13333	−	2.54240i	−0.0720374	−	0.0858508i	−0.800860	+	0.598852i	$0.795624\pi$
$878$		0			0
$879$	−6.04704	+	16.6141i	−0.203961	+	0.560380i
$880$		0			0
$881$	−3.56517	+	6.17506i	−0.120114	+	0.208043i	−0.919812	−	0.392359i	$-0.871659\pi$
$881$	−3.56517	+	6.17506i	−0.120114	+	0.208043i	0.799699	+	0.600402i	$0.204993\pi$
$882$		0			0
$883$	24.1985	+	4.26685i	0.814345	+	0.143591i	0.565284	−	0.824897i	$-0.308767\pi$
$883$	24.1985	+	4.26685i	0.814345	+	0.143591i	0.249062	+	0.968488i	$0.419878\pi$
$884$		0			0
$885$	−3.28620	−	5.69186i	−0.110464	−	0.191330i
$886$		0			0
$887$	33.0246	+	27.7109i	1.10886	+	0.930441i	0.997989	−	0.0633943i	$-0.0201926\pi$
$887$	33.0246	+	27.7109i	1.10886	+	0.930441i	0.110868	+	0.993835i	$0.464637\pi$
$888$		0			0
$889$	8.70380	+	23.9135i	0.291916	+	0.802033i
$890$		0			0
$891$	0.874077	−	0.154123i	0.0292827	−	0.00516333i
$892$		0			0
$893$	0.204053	−	0.649589i	0.00682837	−	0.0217377i
$894$		0			0
$895$	5.59975	+	31.7578i	0.187179	+	1.06155i
$896$		0			0
$897$	−8.84134	+	3.21798i	−0.295204	+	0.107445i
$898$		0			0
$899$	−35.1706	+	41.9147i	−1.17301	+	1.39793i
$900$		0			0
$901$	7.67245	−	4.42969i	0.255606	−	0.147574i
$902$		0			0
$903$	−2.62631	+	14.8946i	−0.0873982	+	0.495660i
$904$		0			0
$905$	−0.449345	−	0.259429i	−0.0149367	−	0.00862372i
$906$		0			0
$907$	−23.7939	−	8.66028i	−0.790064	−	0.287560i	−0.0847015	−	0.996406i	$-0.526994\pi$
$907$	−23.7939	−	8.66028i	−0.790064	−	0.287560i	−0.705363	+	0.708847i	$0.749216\pi$
$908$		0			0
$909$	−3.27288	+	2.74627i	−0.108554	+	0.0910880i
$910$		0			0
$911$	3.14773			0.104289			0.0521445	−	0.998640i	$-0.483394\pi$
$911$	3.14773			0.104289			0.0521445	+	0.998640i	$0.483394\pi$
$912$		0			0
$913$	−8.29204			−0.274426
$914$		0			0
$915$	−18.5464	+	15.5623i	−0.613124	+	0.514472i
$916$		0			0
$917$	15.9949	+	5.82166i	0.528197	+	0.192248i
$918$		0			0
$919$	−27.7508	−	16.0219i	−0.915414	−	0.528514i	−0.0332448	−	0.999447i	$-0.510584\pi$
$919$	−27.7508	−	16.0219i	−0.915414	−	0.528514i	−0.882169	+	0.470933i	$0.843917\pi$
$920$		0			0
$921$	4.89248	−	27.7467i	0.161213	−	0.914283i
$922$		0			0
$923$	4.68520	−	2.70500i	0.154215	−	0.0890363i
$924$		0			0
$925$	−10.2948	+	12.2689i	−0.338491	+	0.403398i
$926$		0			0
$927$	2.04766	−	0.745288i	0.0672540	−	0.0244785i
$928$		0			0
$929$	−6.30474	−	35.7560i	−0.206852	−	1.17312i	−0.894499	−	0.447070i	$-0.852467\pi$
$929$	−6.30474	−	35.7560i	−0.206852	−	1.17312i	0.687647	−	0.726045i	$-0.258644\pi$
$930$		0			0
$931$	−4.98755	+	2.07215i	−0.163460	+	0.0679119i
$932$		0			0
$933$	−27.6828	+	4.88123i	−0.906296	+	0.159804i
$934$		0			0
$935$	0.559794	+	1.53802i	0.0183072	+	0.0502987i
$936$		0			0
$937$	26.0140	+	21.8283i	0.849839	+	0.713100i	0.959754	−	0.280841i	$-0.0906134\pi$
$937$	26.0140	+	21.8283i	0.849839	+	0.713100i	−0.109915	+	0.993941i	$0.535058\pi$
$938$		0			0
$939$	8.93321	+	15.4728i	0.291524	+	0.504935i
$940$		0			0
$941$	−1.37675	−	0.242757i	−0.0448806	−	0.00791366i	0.151163	−	0.988509i	$-0.451698\pi$
$941$	−1.37675	−	0.242757i	−0.0448806	−	0.00791366i	−0.196043	+	0.980595i	$0.562809\pi$
$942$		0			0
$943$	−12.3941	+	21.4671i	−0.403606	+	0.699066i
$944$		0			0
$945$	2.33455	−	6.41411i	0.0759428	−	0.208651i
$946$		0			0
$947$	3.49145	+	4.16094i	0.113457	+	0.135213i	0.819784	−	0.572673i	$-0.194094\pi$
$947$	3.49145	+	4.16094i	0.113457	+	0.135213i	−0.706327	+	0.707886i	$0.749649\pi$
$948$		0			0
$949$			27.6607i			0.897905i
$950$		0			0
$951$		−	27.4095i		−	0.888813i
$952$		0			0
$953$	−13.8649	−	16.5235i	−0.449127	−	0.535249i	0.493211	−	0.869909i	$-0.335823\pi$
$953$	−13.8649	−	16.5235i	−0.449127	−	0.535249i	−0.942339	+	0.334660i	$0.891378\pi$
$954$		0			0
$955$	9.70347	−	26.6601i	0.313997	−	0.862699i
$956$		0			0
$957$	−3.05307	+	5.28808i	−0.0986918	+	0.170939i
$958$		0			0
$959$	−43.8221	−	7.72701i	−1.41509	−	0.249518i
$960$		0			0
$961$	−16.1270	−	27.9327i	−0.520225	−	0.901056i
$962$		0			0
$963$	1.94584	+	1.63275i	0.0627037	+	0.0526147i
$964$		0			0
$965$	8.14529	+	22.3790i	0.262206	+	0.720406i
$966$		0			0
$967$	−39.6811	+	6.99685i	−1.27606	+	0.225004i	−0.770306	−	0.637675i	$-0.779896\pi$
$967$	−39.6811	+	6.99685i	−1.27606	+	0.225004i	−0.505753	+	0.862678i	$0.668785\pi$
$968$		0			0
$969$	−2.08189	+	1.91179i	−0.0668799	+	0.0614156i
$970$		0			0
$971$	5.73999	+	32.5531i	0.184205	+	1.04468i	0.926972	+	0.375130i	$0.122402\pi$
$971$	5.73999	+	32.5531i	0.184205	+	1.04468i	−0.742767	+	0.669550i	$0.766487\pi$
$972$		0			0
$973$	8.85030	−	3.22125i	0.283728	−	0.103268i
$974$		0			0
$975$	4.73006	−	5.63707i	0.151483	−	0.180531i
$976$		0			0
$977$	−22.0438	+	12.7270i	−0.705245	+	0.407173i	−0.809298	−	0.587398i	$-0.800152\pi$
$977$	−22.0438	+	12.7270i	−0.705245	+	0.407173i	0.104053	+	0.994572i	$0.466819\pi$
$978$		0			0
$979$	−2.02388	+	11.4780i	−0.0646834	+	0.366838i
$980$		0			0
$981$	4.76598	+	2.75164i	0.152166	+	0.0878532i
$982$		0			0
$983$	14.4017	+	5.24180i	0.459344	+	0.167187i	0.561319	−	0.827599i	$-0.310294\pi$
$983$	14.4017	+	5.24180i	0.459344	+	0.167187i	−0.101975	+	0.994787i	$0.532516\pi$
$984$		0			0
$985$	−1.26017	+	1.05741i	−0.0401525	+	0.0336919i
$986$		0			0
$987$	−0.374924			−0.0119340
$988$		0			0
$989$	−24.8742			−0.790952
$990$		0			0
$991$	3.30785	−	2.77561i	0.105077	−	0.0881703i	−0.588735	−	0.808326i	$-0.700374\pi$
$991$	3.30785	−	2.77561i	0.105077	−	0.0881703i	0.693813	+	0.720156i	$0.255930\pi$
$992$		0			0
$993$	21.5139	+	7.83043i	0.682724	+	0.248491i
$994$		0			0
$995$	27.3089	+	15.7668i	0.865750	+	0.499841i
$996$		0			0
$997$	10.6122	−	60.1845i	0.336090	−	1.90606i	−0.0801044	−	0.996786i	$-0.525525\pi$
$997$	10.6122	−	60.1845i	0.336090	−	1.90606i	0.416195	−	0.909276i	$-0.363364\pi$
$998$		0			0
$999$	−4.49257	+	2.59378i	−0.142138	+	0.0820637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.h.751.1	yes	24
4.3	odd	2		912.2.ci.g.751.1	✓	24
19.2	odd	18		912.2.ci.g.895.1	yes	24
76.59	even	18	inner	912.2.ci.h.895.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.751.1	✓	24	4.3	odd	2
912.2.ci.g.895.1	yes	24	19.2	odd	18
912.2.ci.h.751.1	yes	24	1.1	even	1	trivial
912.2.ci.h.895.1	yes	24	76.59	even	18	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{3} +(-2.67232 - 0.972646i) q^{5} +(2.07863 + 1.20010i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{3} +(-2.67232 - 0.972646i) q^{5} +(2.07863 + 1.20010i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-0.768651 + 0.443781i) q^{11} +(-1.53207 + 1.82586i) q^{13} +(2.67232 - 0.972646i) q^{15} +(0.112602 + 0.638596i) q^{17} +(0.564339 - 4.32221i) q^{19} +(-2.36373 + 0.416790i) q^{21} +(-1.35012 - 3.70942i) q^{23} +(2.36505 + 1.98452i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-6.77517 - 1.19464i) q^{29} +(3.97662 - 6.88770i) q^{31} +(0.303564 - 0.834035i) q^{33} +(-4.38751 - 5.22883i) q^{35} +5.18757i q^{37} -2.38349i q^{39} +(-4.03637 - 4.81036i) q^{41} +(2.15516 - 5.92127i) q^{43} +(-1.42191 + 2.46283i) q^{45} +(0.153832 + 0.0271248i) q^{47} +(-0.619522 - 1.07304i) q^{49} +(-0.496740 - 0.416814i) q^{51} +(-4.67283 - 12.8385i) q^{53} +(2.48573 - 0.438300i) q^{55} +(2.34596 + 3.67376i) q^{57} +(-0.401320 - 2.27600i) q^{59} +(-7.99995 + 2.91174i) q^{61} +(1.54282 - 1.83866i) q^{63} +(5.87011 - 3.38911i) q^{65} +(1.43913 - 8.16172i) q^{67} +(3.41862 + 1.97374i) q^{69} +(-2.13290 - 0.776313i) q^{71} +(8.89007 - 7.45966i) q^{73} -3.08736 q^{75} -2.13032 q^{77} +(-9.24843 + 7.76036i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(8.09084 + 4.67125i) q^{83} +(0.320220 - 1.81606i) q^{85} +(5.95798 - 3.43984i) q^{87} +(8.44079 - 10.0593i) q^{89} +(-5.37583 + 1.95664i) q^{91} +(1.38106 + 7.83241i) q^{93} +(-5.71208 + 11.0015i) q^{95} +(-2.73079 + 0.481512i) q^{97} +(0.303564 + 0.834035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 9 q^{7}+O(q^{10}) \) 24 * q + 9 * q^7	\( 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more