LMFDB - Embedded newform 1107.2.e.a.370.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1107,2,Mod(370,1107)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1107, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1107.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1107 = 3^{3} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1107.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.83943950376$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 369)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			370.14
Character	$\chi$	$=$	1107.370
Dual form			1107.2.e.a.739.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.966816 - 1.67457i) q^{2} +(-0.869467 - 1.50596i) q^{4} +(-1.86893 - 3.23707i) q^{5} +(-0.233357 + 0.404186i) q^{7} +0.504807 q^{8} -7.22763 q^{10} +(2.65842 - 4.60453i) q^{11} +(0.558143 + 0.966733i) q^{13} +(0.451226 + 0.781546i) q^{14} +(2.22699 - 3.85726i) q^{16} -3.25843 q^{17} +0.0992768 q^{19} +(-3.24994 + 5.62906i) q^{20} +(-5.14041 - 8.90346i) q^{22} +(-1.79650 - 3.11164i) q^{23} +(-4.48577 + 7.76958i) q^{25} +2.15849 q^{26} +0.811584 q^{28} +(-2.38481 + 4.13061i) q^{29} +(1.55701 + 2.69683i) q^{31} +(-3.80137 - 6.58417i) q^{32} +(-3.15031 + 5.45649i) q^{34} +1.74451 q^{35} -9.77389 q^{37} +(0.0959824 - 0.166246i) q^{38} +(-0.943447 - 1.63410i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(3.19122 - 5.52736i) q^{43} -9.24564 q^{44} -6.94756 q^{46} +(-1.66768 + 2.88851i) q^{47} +(3.39109 + 5.87354i) q^{49} +(8.67383 + 15.0235i) q^{50} +(0.970574 - 1.68108i) q^{52} -6.33395 q^{53} -19.8736 q^{55} +(-0.117800 + 0.204036i) q^{56} +(4.61134 + 7.98708i) q^{58} +(2.20617 + 3.82120i) q^{59} +(4.01831 - 6.95992i) q^{61} +6.02138 q^{62} -5.79295 q^{64} +(2.08626 - 3.61350i) q^{65} +(2.90846 + 5.03759i) q^{67} +(2.83310 + 4.90707i) q^{68} +(1.68662 - 2.92130i) q^{70} +10.1380 q^{71} +8.00974 q^{73} +(-9.44956 + 16.3671i) q^{74} +(-0.0863178 - 0.149507i) q^{76} +(1.24072 + 2.14899i) q^{77} +(6.83258 - 11.8344i) q^{79} -16.6483 q^{80} -1.93363 q^{82} +(3.76329 - 6.51822i) q^{83} +(6.08977 + 10.5478i) q^{85} +(-6.17065 - 10.6879i) q^{86} +(1.34199 - 2.32440i) q^{88} -4.21348 q^{89} -0.520986 q^{91} +(-3.12400 + 5.41093i) q^{92} +(3.22468 + 5.58531i) q^{94} +(-0.185541 - 0.321366i) q^{95} +(9.36425 - 16.2194i) q^{97} +13.1142 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{4} - q^{5} + 13 q^{7} - 16 q^{10} + 2 q^{11} + 5 q^{13} - q^{14} + 8 q^{16} - 2 q^{17} - 38 q^{19} - 11 q^{20} + 14 q^{22} - 2 q^{23} + 3 q^{25} - 30 q^{26} - 48 q^{28} + 10 q^{29} + 39 q^{31}+ \cdots + 96 q^{98}+O(q^{100}) $ 32 * q - 8 * q^4 - q^5 + 13 * q^7 - 16 * q^10 + 2 * q^11 + 5 * q^13 - q^14 + 8 * q^16 - 2 * q^17 - 38 * q^19 - 11 * q^20 + 14 * q^22 - 2 * q^23 + 3 * q^25 - 30 * q^26 - 48 * q^28 + 10 * q^29 + 39 * q^31 + 10 * q^32 + 18 * q^34 - 4 * q^35 - 52 * q^37 + 14 * q^38 + 18 * q^40 - 16 * q^41 + 20 * q^43 + 46 * q^44 - 52 * q^46 - 5 * q^47 + 7 * q^49 - 9 * q^50 + 14 * q^52 - 14 * q^53 - 74 * q^55 + 2 * q^56 + 24 * q^58 - 6 * q^59 + 21 * q^61 + 10 * q^62 - 68 * q^64 - 2 * q^65 + 32 * q^67 + 8 * q^68 + 22 * q^70 + 40 * q^71 - 34 * q^73 - 28 * q^74 + 40 * q^76 + 22 * q^77 + 69 * q^79 - 78 * q^80 - 10 * q^83 + 42 * q^85 + 8 * q^86 + 42 * q^88 - 22 * q^89 - 102 * q^91 + 10 * q^92 + 13 * q^94 + 22 * q^95 + 25 * q^97 + 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1107\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.966816	−	1.67457i	0.683642	−	1.18410i	−0.290219	−	0.956960i	$-0.593728\pi$
$2$	0.966816	−	1.67457i	0.683642	−	1.18410i	0.973861	−	0.227143i	$-0.0729384\pi$
$3$		0			0
$3$		0			0
$4$	−0.869467	−	1.50596i	−0.434733	−	0.752980i
$5$	−1.86893	−	3.23707i	−0.835809	−	1.44766i	−0.893370	−	0.449322i	$-0.851666\pi$
$5$	−1.86893	−	3.23707i	−0.835809	−	1.44766i	0.0575609	−	0.998342i	$-0.481668\pi$
$6$		0			0
$7$	−0.233357	+	0.404186i	−0.0882005	+	0.152768i	−0.906751	−	0.421667i	$-0.861445\pi$
$7$	−0.233357	+	0.404186i	−0.0882005	+	0.152768i	0.818550	+	0.574435i	$0.194778\pi$
$8$	0.504807			0.178476
$9$		0			0
$10$	−7.22763			−2.28558
$11$	2.65842	−	4.60453i	0.801545	−	1.38832i	−0.117054	−	0.993126i	$-0.537345\pi$
$11$	2.65842	−	4.60453i	0.801545	−	1.38832i	0.918599	−	0.395191i	$-0.129322\pi$
$12$		0			0
$13$	0.558143	+	0.966733i	0.154801	+	0.268123i	0.932987	−	0.359911i	$-0.117193\pi$
$13$	0.558143	+	0.966733i	0.154801	+	0.268123i	−0.778185	+	0.628035i	$0.783860\pi$
$14$	0.451226	+	0.781546i	0.120595	+	0.208877i
$15$		0			0
$16$	2.22699	−	3.85726i	0.556747	−	0.964314i
$17$	−3.25843			−0.790286			−0.395143	−	0.918620i	$-0.629305\pi$
$17$	−3.25843			−0.790286			−0.395143	+	0.918620i	$0.629305\pi$
$18$		0			0
$19$	0.0992768			0.0227756			0.0113878	−	0.999935i	$-0.496375\pi$
$19$	0.0992768			0.0227756			0.0113878	+	0.999935i	$0.496375\pi$
$20$	−3.24994	+	5.62906i	−0.726708	+	1.25870i
$21$		0			0
$22$	−5.14041	−	8.90346i	−1.09594	−	1.89822i
$23$	−1.79650	−	3.11164i	−0.374597	−	0.648821i	0.615670	−	0.788004i	$-0.288886\pi$
$23$	−1.79650	−	3.11164i	−0.374597	−	0.648821i	−0.990267	+	0.139183i	$0.955552\pi$
$24$		0			0
$25$	−4.48577	+	7.76958i	−0.897154	+	1.55392i
$26$	2.15849			0.423314
$27$		0			0
$28$	0.811584			0.153375
$29$	−2.38481	+	4.13061i	−0.442848	+	0.767035i	−0.997900	−	0.0647810i	$-0.979365\pi$
$29$	−2.38481	+	4.13061i	−0.442848	+	0.767035i	0.555052	+	0.831816i	$0.312698\pi$
$30$		0			0
$31$	1.55701	+	2.69683i	0.279648	+	0.484364i	0.971297	−	0.237869i	$-0.0764490\pi$
$31$	1.55701	+	2.69683i	0.279648	+	0.484364i	−0.691649	+	0.722233i	$0.743116\pi$
$32$	−3.80137	−	6.58417i	−0.671994	−	1.16393i
$33$		0			0
$34$	−3.15031	+	5.45649i	−0.540273	+	0.935780i
$35$	1.74451			0.294875
$36$		0			0
$37$	−9.77389			−1.60682			−0.803409	−	0.595427i	$-0.796983\pi$
$37$	−9.77389			−1.60682			−0.803409	+	0.595427i	$0.796983\pi$
$38$	0.0959824	−	0.166246i	0.0155704	−	0.0269687i
$39$		0			0
$40$	−0.943447	−	1.63410i	−0.149172	−	0.258373i
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i
$42$		0			0
$43$	3.19122	−	5.52736i	0.486657	−	0.842915i	−0.513225	−	0.858254i	$-0.671549\pi$
$43$	3.19122	−	5.52736i	0.486657	−	0.842915i	0.999882	+	0.0153390i	$0.00488276\pi$
$44$	−9.24564			−1.39383
$45$		0			0
$46$	−6.94756			−1.02436
$47$	−1.66768	+	2.88851i	−0.243256	+	0.421332i	−0.961640	−	0.274315i	$-0.911549\pi$
$47$	−1.66768	+	2.88851i	−0.243256	+	0.421332i	0.718384	+	0.695647i	$0.244882\pi$
$48$		0			0
$49$	3.39109	+	5.87354i	0.484441	+	0.839077i
$50$	8.67383	+	15.0235i	1.22666	+	2.12464i
$51$		0			0
$52$	0.970574	−	1.68108i	0.134594	−	0.233124i
$53$	−6.33395			−0.870035			−0.435017	−	0.900422i	$-0.643258\pi$
$53$	−6.33395			−0.870035			−0.435017	+	0.900422i	$0.643258\pi$
$54$		0			0
$55$	−19.8736			−2.67975
$56$	−0.117800	+	0.204036i	−0.0157417	+	0.0272654i
$57$		0			0
$58$	4.61134	+	7.98708i	0.605499	+	1.04875i
$59$	2.20617	+	3.82120i	0.287219	+	0.497478i	0.973145	−	0.230193i	$-0.0739359\pi$
$59$	2.20617	+	3.82120i	0.287219	+	0.497478i	−0.685926	+	0.727672i	$0.740603\pi$
$60$		0			0
$61$	4.01831	−	6.95992i	0.514492	−	0.891127i	−0.485366	−	0.874311i	$-0.661314\pi$
$61$	4.01831	−	6.95992i	0.514492	−	0.891127i	0.999859	−	0.0168160i	$-0.00535296\pi$
$62$	6.02138			0.764716
$63$		0			0
$64$	−5.79295			−0.724119
$65$	2.08626	−	3.61350i	0.258768	−	0.448200i
$66$		0			0
$67$	2.90846	+	5.03759i	0.355324	+	0.615440i	0.987173	−	0.159652i	$-0.0510370\pi$
$67$	2.90846	+	5.03759i	0.355324	+	0.615440i	−0.631849	+	0.775092i	$0.717704\pi$
$68$	2.83310	+	4.90707i	0.343564	+	0.595070i
$69$		0			0
$70$	1.68662	−	2.92130i	0.201589	−	0.349163i
$71$	10.1380			1.20316			0.601579	−	0.798814i	$-0.294539\pi$
$71$	10.1380			1.20316			0.601579	+	0.798814i	$0.294539\pi$
$72$		0			0
$73$	8.00974			0.937469			0.468735	−	0.883339i	$-0.344710\pi$
$73$	8.00974			0.937469			0.468735	+	0.883339i	$0.344710\pi$
$74$	−9.44956	+	16.3671i	−1.09849	+	1.90264i
$75$		0			0
$76$	−0.0863178	−	0.149507i	−0.00990133	−	0.0171496i
$77$	1.24072	+	2.14899i	0.141393	+	0.244901i
$78$		0			0
$79$	6.83258	−	11.8344i	0.768725	−	1.33147i	−0.169530	−	0.985525i	$-0.554225\pi$
$79$	6.83258	−	11.8344i	0.768725	−	1.33147i	0.938255	−	0.345945i	$-0.112442\pi$
$80$	−16.6483			−1.86134
$81$		0			0
$82$	−1.93363			−0.213534
$83$	3.76329	−	6.51822i	0.413075	−	0.715467i	−0.582149	−	0.813082i	$-0.697788\pi$
$83$	3.76329	−	6.51822i	0.413075	−	0.715467i	0.995224	+	0.0976149i	$0.0311214\pi$
$84$		0			0
$85$	6.08977	+	10.5478i	0.660528	+	1.14407i
$86$	−6.17065	−	10.6879i	−0.665399	−	1.15250i
$87$		0			0
$88$	1.34199	−	2.32440i	0.143057	−	0.247781i
$89$	−4.21348			−0.446628			−0.223314	−	0.974747i	$-0.571688\pi$
$89$	−4.21348			−0.446628			−0.223314	+	0.974747i	$0.571688\pi$
$90$		0			0
$91$	−0.520986			−0.0546142
$92$	−3.12400	+	5.41093i	−0.325700	+	0.564128i
$93$		0			0
$94$	3.22468	+	5.58531i	0.332600	+	0.576081i
$95$	−0.185541	−	0.321366i	−0.0190361	−	0.0329715i
$96$		0			0
$97$	9.36425	−	16.2194i	0.950796	−	1.64683i	0.207087	−	0.978322i	$-0.433602\pi$
$97$	9.36425	−	16.2194i	0.950796	−	1.64683i	0.743708	−	0.668504i	$-0.233065\pi$
$98$	13.1142			1.32474
$99$		0			0
$100$	15.6009			1.56009
$101$	−8.21874	+	14.2353i	−0.817795	+	1.41646i	0.0895085	+	0.995986i	$0.471470\pi$
$101$	−8.21874	+	14.2353i	−0.817795	+	1.41646i	−0.907303	+	0.420476i	$0.861863\pi$
$102$		0			0
$103$	−5.61479	−	9.72509i	−0.553241	−	0.958242i	−0.998038	−	0.0626105i	$-0.980057\pi$
$103$	−5.61479	−	9.72509i	−0.553241	−	0.958242i	0.444797	−	0.895632i	$-0.353276\pi$
$104$	0.281755	+	0.488013i	0.0276283	+	0.0478536i
$105$		0			0
$106$	−6.12376	+	10.6067i	−0.594793	+	1.03021i
$107$	−1.34625			−0.130147			−0.0650737	−	0.997880i	$-0.520728\pi$
$107$	−1.34625			−0.130147			−0.0650737	+	0.997880i	$0.520728\pi$
$108$		0			0
$109$	13.4302			1.28638			0.643191	−	0.765706i	$-0.277610\pi$
$109$	13.4302			1.28638			0.643191	+	0.765706i	$0.277610\pi$
$110$	−19.2141	+	33.2798i	−1.83199	+	3.17311i
$111$		0			0
$112$	1.03937	+	1.80023i	0.0982108	+	0.170106i
$113$	−7.58979	−	13.1459i	−0.713988	−	1.23666i	−0.963349	−	0.268252i	$-0.913554\pi$
$113$	−7.58979	−	13.1459i	−0.713988	−	1.23666i	0.249361	−	0.968411i	$-0.419779\pi$
$114$		0			0
$115$	−6.71507	+	11.6308i	−0.626183	+	1.08458i
$116$	8.29404			0.770083
$117$		0			0
$118$	8.53185			0.785421
$119$	0.760377	−	1.31701i	0.0697037	−	0.120730i
$120$		0			0
$121$	−8.63444	−	14.9553i	−0.784949	−	1.35957i
$122$	−7.76994	−	13.4579i	−0.703457	−	1.21842i
$123$		0			0
$124$	2.70754	−	4.68960i	0.243144	−	0.421139i
$125$	14.8450			1.32778
$126$		0			0
$127$	−16.7423			−1.48564			−0.742821	−	0.669490i	$-0.766513\pi$
$127$	−16.7423			−1.48564			−0.742821	+	0.669490i	$0.766513\pi$
$128$	2.00202	−	3.46761i	0.176956	−	0.306496i
$129$		0			0
$130$	−4.03405	−	6.98719i	−0.353810	−	0.612817i
$131$	7.29501	+	12.6353i	0.637368	+	1.10395i	0.986008	+	0.166697i	$0.0533101\pi$
$131$	7.29501	+	12.6353i	0.637368	+	1.10395i	−0.348640	+	0.937257i	$0.613357\pi$
$132$		0			0
$133$	−0.0231669	+	0.0401262i	−0.00200882	+	0.00347939i
$134$	11.2478			0.971659
$135$		0			0
$136$	−1.64488			−0.141047
$137$	8.92257	−	15.4543i	0.762306	−	1.32035i	−0.179352	−	0.983785i	$-0.557400\pi$
$137$	8.92257	−	15.4543i	0.762306	−	1.32035i	0.941659	−	0.336569i	$-0.109266\pi$
$138$		0			0
$139$	−3.66697	−	6.35137i	−0.311028	−	0.538716i	0.667557	−	0.744558i	$-0.267340\pi$
$139$	−3.66697	−	6.35137i	−0.311028	−	0.538716i	−0.978585	+	0.205842i	$0.934007\pi$
$140$	−1.51679	−	2.62716i	−0.128192	−	0.222035i
$141$		0			0
$142$	9.80157	−	16.9768i	0.822529	−	1.42466i
$143$	5.93513			0.496320
$144$		0			0
$145$	17.8281			1.48054
$146$	7.74395	−	13.4129i	0.640894	−	1.11006i
$147$		0			0
$148$	8.49807	+	14.7191i	0.698537	+	1.20990i
$149$	0.831061	+	1.43944i	0.0680832	+	0.117924i	0.898058	−	0.439878i	$-0.144978\pi$
$149$	0.831061	+	1.43944i	0.0680832	+	0.117924i	−0.829974	+	0.557802i	$0.811645\pi$
$150$		0			0
$151$	1.67072	−	2.89377i	0.135961	−	0.235491i	−0.790003	−	0.613103i	$-0.789921\pi$
$151$	1.67072	−	2.89377i	0.135961	−	0.235491i	0.925964	+	0.377611i	$0.123254\pi$
$152$	0.0501156			0.00406491
$153$		0			0
$154$	4.79820			0.386650
$155$	5.81988	−	10.0803i	0.467464	−	0.809672i
$156$		0			0
$157$	9.91139	+	17.1670i	0.791015	+	1.37008i	0.925339	+	0.379140i	$0.123780\pi$
$157$	9.91139	+	17.1670i	0.791015	+	1.37008i	−0.134324	+	0.990937i	$0.542886\pi$
$158$	−13.2117	−	22.8833i	−1.05107	−	1.82050i
$159$		0			0
$160$	−14.2090	+	24.6106i	−1.12332	+	1.94564i
$161$	1.67691			0.132159
$162$		0			0
$163$	13.9568			1.09318			0.546592	−	0.837399i	$-0.315925\pi$
$163$	13.9568			1.09318			0.546592	+	0.837399i	$0.315925\pi$
$164$	−0.869467	+	1.50596i	−0.0678939	+	0.117596i
$165$		0			0
$166$	−7.27683	−	12.6038i	−0.564791	−	0.978247i
$167$	12.0455	+	20.8635i	0.932110	+	1.61446i	0.779708	+	0.626144i	$0.215368\pi$
$167$	12.0455	+	20.8635i	0.932110	+	1.61446i	0.152403	+	0.988318i	$0.451299\pi$
$168$		0			0
$169$	5.87695	−	10.1792i	0.452073	−	0.783014i
$170$	23.5507			1.80626
$171$		0			0
$172$	−11.0987			−0.846264
$173$	−3.21883	+	5.57517i	−0.244723	+	0.423872i	−0.962054	−	0.272860i	$-0.912030\pi$
$173$	−3.21883	+	5.57517i	−0.244723	+	0.423872i	0.717331	+	0.696733i	$0.245364\pi$
$174$		0			0
$175$	−2.09357	−	3.62617i	−0.158259	−	0.274112i
$176$	−11.8406	−	20.5085i	−0.892516	−	1.54588i
$177$		0			0
$178$	−4.07366	+	7.05579i	−0.305334	+	0.528853i
$179$	1.85372			0.138553			0.0692766	−	0.997597i	$-0.477931\pi$
$179$	1.85372			0.138553			0.0692766	+	0.997597i	$0.477931\pi$
$180$		0			0
$181$	17.1429			1.27422			0.637111	−	0.770772i	$-0.280129\pi$
$181$	17.1429			1.27422			0.637111	+	0.770772i	$0.280129\pi$
$182$	−0.503698	+	0.872430i	−0.0373366	+	0.0646688i
$183$		0			0
$184$	−0.906888	−	1.57078i	−0.0668567	−	0.115799i
$185$	18.2667	+	31.6388i	1.34299	+	2.32613i
$186$		0			0
$187$	−8.66230	+	15.0035i	−0.633450	+	1.09717i
$188$	5.79997			0.423006
$189$		0			0
$190$	−0.717536			−0.0520555
$191$	3.03903	−	5.26376i	0.219897	−	0.380872i	−0.734879	−	0.678198i	$-0.762761\pi$
$191$	3.03903	−	5.26376i	0.219897	−	0.380872i	0.954776	+	0.297325i	$0.0960946\pi$
$192$		0			0
$193$	−1.47310	−	2.55148i	−0.106036	−	0.183659i	0.808125	−	0.589011i	$-0.200482\pi$
$193$	−1.47310	−	2.55148i	−0.106036	−	0.183659i	−0.914161	+	0.405351i	$0.867149\pi$
$194$	−18.1070	−	31.3623i	−1.30001	−	2.25168i
$195$		0			0
$196$	5.89688	−	10.2137i	0.421206	−	0.729549i
$197$	20.7418			1.47779			0.738895	−	0.673820i	$-0.235348\pi$
$197$	20.7418			1.47779			0.738895	+	0.673820i	$0.235348\pi$
$198$		0			0
$199$	−26.3268			−1.86626			−0.933129	−	0.359543i	$-0.882933\pi$
$199$	−26.3268			−1.86626			−0.933129	+	0.359543i	$0.882933\pi$
$200$	−2.26445	+	3.92214i	−0.160121	+	0.277337i
$201$		0			0
$202$	15.8920	+	27.5258i	1.11816	+	1.93671i
$203$	−1.11302	−	1.92781i	−0.0781188	−	0.135306i
$204$		0			0
$205$	−1.86893	+	3.23707i	−0.130531	+	0.226087i
$206$	−21.7139			−1.51288
$207$		0			0
$208$	4.97192			0.344740
$209$	0.263920	−	0.457122i	0.0182557	−	0.0316198i
$210$		0			0
$211$	6.81273	+	11.8000i	0.469008	+	0.812345i	0.999372	−	0.0354246i	$-0.0112783\pi$
$211$	6.81273	+	11.8000i	0.469008	+	0.812345i	−0.530365	+	0.847770i	$0.677945\pi$
$212$	5.50716	+	9.53868i	0.378233	+	0.655119i
$213$		0			0
$214$	−1.30158	+	2.25440i	−0.0889742	+	0.154108i
$215$	−23.8566			−1.62701
$216$		0			0
$217$	−1.45336			−0.0986603
$218$	12.9845	−	22.4899i	0.879425	−	1.52321i
$219$		0			0
$220$	17.2794	+	29.9288i	1.16498	+	2.01780i
$221$	−1.81867	−	3.15003i	−0.122337	−	0.211894i
$222$		0			0
$223$	−5.55500	+	9.62155i	−0.371991	+	0.644307i	−0.989872	−	0.141965i	$-0.954658\pi$
$223$	−5.55500	+	9.62155i	−0.371991	+	0.644307i	0.617881	+	0.786272i	$0.287991\pi$
$224$	3.54830			0.237081
$225$		0			0
$226$	−29.3517			−1.95245
$227$	−2.54210	+	4.40304i	−0.168725	+	0.292240i	−0.937972	−	0.346711i	$-0.887298\pi$
$227$	−2.54210	+	4.40304i	−0.168725	+	0.292240i	0.769247	+	0.638952i	$0.220632\pi$
$228$		0			0
$229$	0.817887	+	1.41662i	0.0540475	+	0.0936130i	0.891783	−	0.452463i	$-0.149454\pi$
$229$	0.817887	+	1.41662i	0.0540475	+	0.0936130i	−0.837736	+	0.546076i	$0.816121\pi$
$230$	12.9845	+	22.4898i	0.856171	+	1.48293i
$231$		0			0
$232$	−1.20387	+	2.08516i	−0.0790378	+	0.136897i
$233$	19.0351			1.24703			0.623515	−	0.781812i	$-0.285704\pi$
$233$	19.0351			1.24703			0.623515	+	0.781812i	$0.285704\pi$
$234$		0			0
$235$	12.4671			0.813263
$236$	3.83639	−	6.64482i	0.249728	−	0.432541i
$237$		0			0
$238$	−1.47029	−	2.54662i	−0.0953047	−	0.165073i
$239$	−0.646142	−	1.11915i	−0.0417954	−	0.0723918i	0.844371	−	0.535759i	$-0.179974\pi$
$239$	−0.646142	−	1.11915i	−0.0417954	−	0.0723918i	−0.886166	+	0.463367i	$0.846641\pi$
$240$		0			0
$241$	−0.647055	+	1.12073i	−0.0416805	+	0.0721927i	−0.886113	−	0.463469i	$-0.846604\pi$
$241$	−0.647055	+	1.12073i	−0.0416805	+	0.0721927i	0.844433	+	0.535662i	$0.179938\pi$
$242$	−33.3916			−2.14650
$243$		0			0
$244$	−13.9752			−0.894668
$245$	12.6754	−	21.9544i	0.809801	−	1.40262i
$246$		0			0
$247$	0.0554107	+	0.0959741i	0.00352570	+	0.00610668i
$248$	0.785991	+	1.36138i	0.0499105	+	0.0864475i
$249$		0			0
$250$	14.3524	−	24.8591i	0.907725	−	1.57223i
$251$	−31.3179			−1.97677			−0.988383	−	0.151982i	$-0.951434\pi$
$251$	−31.3179			−1.97677			−0.988383	+	0.151982i	$0.951434\pi$
$252$		0			0
$253$	−19.1035			−1.20103
$254$	−16.1868	+	28.0363i	−1.01565	+	1.75915i
$255$		0			0
$256$	−9.66413	−	16.7388i	−0.604008	−	1.04617i
$257$	−9.70477	−	16.8092i	−0.605367	−	1.04853i	−0.991993	−	0.126290i	$-0.959693\pi$
$257$	−9.70477	−	16.8092i	−0.605367	−	1.04853i	0.386627	−	0.922236i	$-0.373640\pi$
$258$		0			0
$259$	2.28080	−	3.95047i	0.141722	−	0.245470i
$260$	−7.25572			−0.449981
$261$		0			0
$262$	28.2117			1.74293
$263$	16.0886	−	27.8662i	0.992064	−	1.71830i	0.387140	−	0.922021i	$-0.373463\pi$
$263$	16.0886	−	27.8662i	0.992064	−	1.71830i	0.604924	−	0.796284i	$-0.293204\pi$
$264$		0			0
$265$	11.8377	+	20.5035i	0.727183	+	1.25952i
$266$	0.0447963	+	0.0775894i	0.00274663	+	0.00475731i
$267$		0			0
$268$	5.05761	−	8.76004i	0.308943	−	0.535105i
$269$	13.1228			0.800114			0.400057	−	0.916490i	$-0.368990\pi$
$269$	13.1228			0.800114			0.400057	+	0.916490i	$0.368990\pi$
$270$		0			0
$271$	18.4975			1.12364			0.561821	−	0.827258i	$-0.310101\pi$
$271$	18.4975			1.12364			0.561821	+	0.827258i	$0.310101\pi$
$272$	−7.25649	+	12.5686i	−0.439990	+	0.762084i
$273$		0			0
$274$	−17.2530	−	29.8830i	−1.04229	−	1.80530i
$275$	23.8501	+	41.3097i	1.43822	+	2.49107i
$276$		0			0
$277$	−12.8355	+	22.2317i	−0.771208	+	1.33577i	0.165694	+	0.986177i	$0.447014\pi$
$277$	−12.8355	+	22.2317i	−0.771208	+	1.33577i	−0.936901	+	0.349594i	$0.886320\pi$
$278$	−14.1811			−0.850527
$279$		0			0
$280$	0.880638			0.0526282
$281$	0.873860	−	1.51357i	0.0521301	−	0.0902920i	−0.838783	−	0.544466i	$-0.816732\pi$
$281$	0.873860	−	1.51357i	0.0521301	−	0.0902920i	0.890913	+	0.454174i	$0.150066\pi$
$282$		0			0
$283$	1.38824	+	2.40450i	0.0825223	+	0.142933i	0.904333	−	0.426828i	$-0.140369\pi$
$283$	1.38824	+	2.40450i	0.0825223	+	0.142933i	−0.821810	+	0.569761i	$0.807036\pi$
$284$	−8.81464	−	15.2674i	−0.523053	−	0.905954i
$285$		0			0
$286$	5.73818	−	9.93881i	0.339305	−	0.587694i
$287$	0.466713			0.0275492
$288$		0			0
$289$	−6.38262			−0.375448
$290$	17.2365	−	29.8545i	1.01216	−	1.75312i
$291$		0			0
$292$	−6.96420	−	12.0624i	−0.407549	−	0.705896i
$293$	1.06522	+	1.84502i	0.0622310	+	0.107787i	0.895462	−	0.445137i	$-0.146845\pi$
$293$	1.06522	+	1.84502i	0.0622310	+	0.107787i	−0.833231	+	0.552925i	$0.813512\pi$
$294$		0			0
$295$	8.24635	−	14.2831i	0.480121	−	0.831594i
$296$	−4.93393			−0.286779
$297$		0			0
$298$	3.21393			0.186178
$299$	2.00541	−	3.47348i	0.115976	−	0.200877i
$300$		0			0
$301$	1.48939	+	2.57969i	0.0858469	+	0.148691i
$302$	−3.23055	−	5.59548i	−0.185897	−	0.321984i
$303$		0			0
$304$	0.221088	−	0.382936i	0.0126803	−	0.0219629i
$305$	−30.0397			−1.72007
$306$		0			0
$307$	−5.11496			−0.291926			−0.145963	−	0.989290i	$-0.546628\pi$
$307$	−5.11496			−0.291926			−0.145963	+	0.989290i	$0.546628\pi$
$308$	2.15753	−	3.73696i	0.122937	−	0.212933i
$309$		0			0
$310$	−11.2535	−	19.4917i	−0.639157	−	1.10705i
$311$	−3.04518	−	5.27441i	−0.172677	−	0.299084i	0.766678	−	0.642032i	$-0.221908\pi$
$311$	−3.04518	−	5.27441i	−0.172677	−	0.299084i	−0.939355	+	0.342947i	$0.888575\pi$
$312$		0			0
$313$	−10.8017	+	18.7091i	−0.610547	+	1.05750i	0.380601	+	0.924739i	$0.375717\pi$
$313$	−10.8017	+	18.7091i	−0.610547	+	1.05750i	−0.991148	+	0.132759i	$0.957616\pi$
$314$	38.3300			2.16308
$315$		0			0
$316$	−23.7628			−1.33676
$317$	7.28868	−	12.6244i	0.409373	−	0.709055i	−0.585447	−	0.810711i	$-0.699081\pi$
$317$	7.28868	−	12.6244i	0.409373	−	0.709055i	0.994820	+	0.101656i	$0.0324142\pi$
$318$		0			0
$319$	12.6797	+	21.9618i	0.709925	+	1.22963i
$320$	10.8266	+	18.7522i	0.605225	+	1.04828i
$321$		0			0
$322$	1.62126	−	2.80810i	0.0903493	−	0.156489i
$323$	−0.323487			−0.0179993
$324$		0			0
$325$	−10.0148			−0.555522
$326$	13.4937	−	23.3718i	0.747346	−	1.29444i
$327$		0			0
$328$	−0.252403	−	0.437176i	−0.0139366	−	0.0241390i
$329$	−0.778329	−	1.34810i	−0.0429106	−	0.0743234i
$330$		0			0
$331$	4.44242	−	7.69450i	0.244178	−	0.422928i	−0.717722	−	0.696329i	$-0.754815\pi$
$331$	4.44242	−	7.69450i	0.244178	−	0.422928i	0.961900	+	0.273401i	$0.0881487\pi$
$332$	−13.0882			−0.718310
$333$		0			0
$334$	46.5832			2.54892
$335$	10.8714	−	18.8298i	0.593967	−	1.02878i
$336$		0			0
$337$	6.39247	+	11.0721i	0.348220	+	0.603135i	0.985933	−	0.167139i	$-0.0534529\pi$
$337$	6.39247	+	11.0721i	0.348220	+	0.603135i	−0.637713	+	0.770274i	$0.720120\pi$
$338$	−11.3639	−	19.6828i	−0.618113	−	1.07060i
$339$		0			0
$340$	10.5897	−	18.3419i	0.574307	−	0.994729i
$341$	16.5568			0.896601
$342$		0			0
$343$	−6.43233			−0.347313
$344$	1.61095	−	2.79025i	0.0868567	−	0.150440i
$345$		0			0
$346$	6.22402	+	10.7803i	0.334606	+	0.579554i
$347$	−8.49015	−	14.7054i	−0.455775	−	0.789426i	0.542957	−	0.839760i	$-0.317305\pi$
$347$	−8.49015	−	14.7054i	−0.455775	−	0.789426i	−0.998732	+	0.0503344i	$0.983971\pi$
$348$		0			0
$349$	12.8603	−	22.2746i	0.688393	−	1.19233i	−0.283964	−	0.958835i	$-0.591650\pi$
$349$	12.8603	−	22.2746i	0.688393	−	1.19233i	0.972357	−	0.233498i	$-0.0750171\pi$
$350$	−8.09638			−0.432770
$351$		0			0
$352$	−40.4226			−2.15453
$353$	8.98521	−	15.5628i	0.478234	−	0.828326i	−0.521454	−	0.853279i	$-0.674610\pi$
$353$	8.98521	−	15.5628i	0.478234	−	0.828326i	0.999689	+	0.0249531i	$0.00794364\pi$
$354$		0			0
$355$	−18.9471	−	32.8174i	−1.00561	−	1.74177i
$356$	3.66348	+	6.34533i	0.194164	+	0.336302i
$357$		0			0
$358$	1.79220	−	3.10419i	0.0947209	−	0.164061i
$359$	12.2194			0.644914			0.322457	−	0.946584i	$-0.395491\pi$
$359$	12.2194			0.644914			0.322457	+	0.946584i	$0.395491\pi$
$360$		0			0
$361$	−18.9901			−0.999481
$362$	16.5740	−	28.7071i	0.871112	−	1.50881i
$363$		0			0
$364$	0.452980	+	0.784584i	0.0237426	+	0.0411234i
$365$	−14.9696	−	25.9281i	−0.783545	−	1.35714i
$366$		0			0
$367$	−3.06791	+	5.31378i	−0.160144	+	0.277377i	−0.934920	−	0.354858i	$-0.884529\pi$
$367$	−3.06791	+	5.31378i	−0.160144	+	0.277377i	0.774776	+	0.632235i	$0.217862\pi$
$368$	−16.0032			−0.834224
$369$		0			0
$370$	70.6421			3.67251
$371$	1.47807	−	2.56009i	0.0767375	−	0.132913i
$372$		0			0
$373$	−15.1005	−	26.1549i	−0.781876	−	1.35425i	−0.930848	−	0.365407i	$-0.880930\pi$
$373$	−15.1005	−	26.1549i	−0.781876	−	1.35425i	0.148972	−	0.988841i	$-0.452404\pi$
$374$	16.7497	+	29.0113i	0.866106	+	1.50014i
$375$		0			0
$376$	−0.841856	+	1.45814i	−0.0434154	+	0.0751977i
$377$	−5.32426			−0.274213
$378$		0			0
$379$	−8.34193			−0.428496			−0.214248	−	0.976779i	$-0.568730\pi$
$379$	−8.34193			−0.428496			−0.214248	+	0.976779i	$0.568730\pi$
$380$	−0.322643	+	0.558835i	−0.0165512	+	0.0286676i
$381$		0			0
$382$	−5.87637	−	10.1782i	−0.300661	−	0.520761i
$383$	8.13434	+	14.0891i	0.415645	+	0.719918i	0.995496	−	0.0948042i	$-0.0302225\pi$
$383$	8.13434	+	14.0891i	0.415645	+	0.719918i	−0.579851	+	0.814723i	$0.696889\pi$
$384$		0			0
$385$	4.63764	−	8.03262i	0.236356	−	0.409380i
$386$	−5.69686			−0.289962
$387$		0			0
$388$	−32.5676			−1.65337
$389$	−10.3286	+	17.8897i	−0.523681	+	0.907042i	0.475939	+	0.879478i	$0.342108\pi$
$389$	−10.3286	+	17.8897i	−0.523681	+	0.907042i	−0.999620	+	0.0275635i	$0.991225\pi$
$390$		0			0
$391$	5.85379	+	10.1391i	0.296039	+	0.512754i
$392$	1.71185	+	2.96500i	0.0864612	+	0.149755i
$393$		0			0
$394$	20.0535	−	34.7337i	1.01028	−	1.74986i
$395$	−51.0783			−2.57003
$396$		0			0
$397$	18.1534			0.911091			0.455545	−	0.890213i	$-0.349444\pi$
$397$	18.1534			0.911091			0.455545	+	0.890213i	$0.349444\pi$
$398$	−25.4532	+	44.0862i	−1.27585	+	2.20984i
$399$		0			0
$400$	19.9795	+	34.6055i	0.998975	+	1.73028i
$401$	10.2683	+	17.7852i	0.512774	+	0.888151i	0.999890	+	0.0148136i	$0.00471547\pi$
$401$	10.2683	+	17.7852i	0.512774	+	0.888151i	−0.487116	+	0.873337i	$0.661951\pi$
$402$		0			0
$403$	−1.73807	+	3.01043i	−0.0865796	+	0.149960i
$404$	28.5837			1.42209
$405$		0			0
$406$	−4.30435			−0.213621
$407$	−25.9832	+	45.0041i	−1.28794	+	2.23077i
$408$		0			0
$409$	−0.398407	−	0.690062i	−0.0197000	−	0.0341213i	0.856007	−	0.516964i	$-0.172938\pi$
$409$	−0.398407	−	0.690062i	−0.0197000	−	0.0341213i	−0.875707	+	0.482842i	$0.839604\pi$
$410$	3.61382	+	6.25931i	0.178474	+	0.309125i
$411$		0			0
$412$	−9.76374	+	16.9113i	−0.481025	+	0.833160i
$413$	−2.05930			−0.101332
$414$		0			0
$415$	−28.1333			−1.38101
$416$	4.24342	−	7.34982i	0.208051	−	0.360354i
$417$		0			0
$418$	−0.510324	−	0.883906i	−0.0249607	−	0.0432333i
$419$	16.5814	+	28.7198i	0.810054	+	1.40306i	0.912825	+	0.408350i	$0.133896\pi$
$419$	16.5814	+	28.7198i	0.810054	+	1.40306i	−0.102771	+	0.994705i	$0.532771\pi$
$420$		0			0
$421$	−4.74036	+	8.21055i	−0.231031	+	0.400158i	−0.958112	−	0.286394i	$-0.907543\pi$
$421$	−4.74036	+	8.21055i	−0.231031	+	0.400158i	0.727081	+	0.686552i	$0.240877\pi$
$422$	26.3466			1.28253
$423$		0			0
$424$	−3.19742			−0.155280
$425$	14.6166	−	25.3166i	0.709008	−	1.22804i
$426$		0			0
$427$	1.87540	+	3.24829i	0.0907570	+	0.157196i
$428$	1.17052	+	2.02741i	0.0565794	+	0.0979984i
$429$		0			0
$430$	−23.0650	+	39.9497i	−1.11229	+	1.92655i
$431$	−11.6853			−0.562861			−0.281431	−	0.959582i	$-0.590809\pi$
$431$	−11.6853			−0.562861			−0.281431	+	0.959582i	$0.590809\pi$
$432$		0			0
$433$	2.69870			0.129691			0.0648456	−	0.997895i	$-0.479345\pi$
$433$	2.69870			0.129691			0.0648456	+	0.997895i	$0.479345\pi$
$434$	−1.40513	+	2.43376i	−0.0674484	+	0.116824i
$435$		0			0
$436$	−11.6771	−	20.2254i	−0.559233	−	0.968620i
$437$	−0.178351	−	0.308913i	−0.00853169	−	0.0147773i
$438$		0			0
$439$	−10.6863	+	18.5092i	−0.510029	+	0.883397i	0.489903	+	0.871777i	$0.337032\pi$
$439$	−10.6863	+	18.5092i	−0.510029	+	0.883397i	−0.999932	+	0.0116198i	$0.996301\pi$
$440$	−10.0323			−0.478272
$441$		0			0
$442$	−7.03329			−0.334539
$443$	−8.18051	+	14.1691i	−0.388668	+	0.673192i	−0.992271	−	0.124093i	$-0.960398\pi$
$443$	−8.18051	+	14.1691i	−0.388668	+	0.673192i	0.603603	+	0.797285i	$0.293731\pi$
$444$		0			0
$445$	7.87468	+	13.6393i	0.373296	+	0.646567i
$446$	10.7413	+	18.6045i	0.508617	+	0.880951i
$447$		0			0
$448$	1.35182	−	2.34143i	0.0638677	−	0.110622i
$449$	7.88783			0.372250			0.186125	−	0.982526i	$-0.440407\pi$
$449$	7.88783			0.372250			0.186125	+	0.982526i	$0.440407\pi$
$450$		0			0
$451$	−5.31685			−0.250361
$452$	−13.1981	+	22.8599i	−0.620789	+	1.07524i
$453$		0			0
$454$	4.91548	+	8.51387i	0.230695	+	0.399576i
$455$	0.973684	+	1.68647i	0.0456470	+	0.0790630i
$456$		0			0
$457$	9.48661	−	16.4313i	0.443765	−	0.768624i	−0.554200	−	0.832383i	$-0.686976\pi$
$457$	9.48661	−	16.4313i	0.443765	−	0.768624i	0.997965	+	0.0637598i	$0.0203092\pi$
$458$	3.16299			0.147797
$459$		0			0
$460$	23.3541			1.08889
$461$	−5.06346	+	8.77017i	−0.235829	+	0.408468i	−0.959513	−	0.281663i	$-0.909114\pi$
$461$	−5.06346	+	8.77017i	−0.235829	+	0.408468i	0.723684	+	0.690131i	$0.242447\pi$
$462$		0			0
$463$	7.45758	+	12.9169i	0.346583	+	0.600299i	0.985640	−	0.168860i	$-0.0540085\pi$
$463$	7.45758	+	12.9169i	0.346583	+	0.600299i	−0.639057	+	0.769159i	$0.720675\pi$
$464$	10.6219	+	18.3976i	0.493108	+	0.854089i
$465$		0			0
$466$	18.4034	−	31.8756i	0.852522	−	1.47661i
$467$	2.20817			0.102182			0.0510910	−	0.998694i	$-0.483730\pi$
$467$	2.20817			0.102182			0.0510910	+	0.998694i	$0.483730\pi$
$468$		0			0
$469$	−2.71483			−0.125359
$470$	12.0534	−	20.8771i	0.555981	−	0.962987i
$471$		0			0
$472$	1.11369	+	1.92897i	0.0512618	+	0.0887880i
$473$	−16.9673	−	29.3881i	−0.780155	−	1.35127i
$474$		0			0
$475$	−0.445332	+	0.771339i	−0.0204333	+	0.0353914i
$476$	−2.64449			−0.121210
$477$		0			0
$478$	−2.49880			−0.114292
$479$	−0.584838	+	1.01297i	−0.0267219	+	0.0462837i	−0.879077	−	0.476680i	$-0.841840\pi$
$479$	−0.584838	+	1.01297i	−0.0267219	+	0.0462837i	0.852355	+	0.522963i	$0.175174\pi$
$480$		0			0
$481$	−5.45523	−	9.44874i	−0.248737	−	0.430826i
$482$	1.25117	+	2.16708i	0.0569891	+	0.0987080i
$483$		0			0
$484$	−15.0147	+	26.0062i	−0.682487	+	1.18210i
$485$	−70.0044			−3.17874
$486$		0			0
$487$	−20.3072			−0.920206			−0.460103	−	0.887866i	$-0.652188\pi$
$487$	−20.3072			−0.920206			−0.460103	+	0.887866i	$0.652188\pi$
$488$	2.02847	−	3.51342i	0.0918246	−	0.159045i
$489$		0			0
$490$	−24.5095	−	42.4518i	−1.10723	−	1.91778i
$491$	7.54658	+	13.0711i	0.340572	+	0.589889i	0.984539	−	0.175165i	$-0.0560458\pi$
$491$	7.54658	+	13.0711i	0.340572	+	0.589889i	−0.643967	+	0.765053i	$0.722713\pi$
$492$		0			0
$493$	7.77074	−	13.4593i	0.349976	−	0.606177i
$494$	0.214288			0.00964126
$495$		0			0
$496$	13.8698			0.622772
$497$	−2.36577	+	4.09763i	−0.106119	+	0.183804i
$498$		0			0
$499$	5.09686	+	8.82802i	0.228167	+	0.395196i	0.957265	−	0.289213i	$-0.0933936\pi$
$499$	5.09686	+	8.82802i	0.228167	+	0.395196i	−0.729098	+	0.684409i	$0.760060\pi$
$500$	−12.9072	−	22.3560i	−0.577230	−	0.999791i
$501$		0			0
$502$	−30.2786	+	52.4441i	−1.35140	+	2.34070i
$503$	2.51574			0.112171			0.0560857	−	0.998426i	$-0.482138\pi$
$503$	2.51574			0.112171			0.0560857	+	0.998426i	$0.482138\pi$
$504$		0			0
$505$	61.4408			2.73408
$506$	−18.4696	+	31.9902i	−0.821072	+	1.42214i
$507$		0			0
$508$	14.5569	+	25.2133i	0.645858	+	1.11866i
$509$	3.22953	+	5.59371i	0.143146	+	0.247937i	0.928680	−	0.370882i	$-0.120945\pi$
$509$	3.22953	+	5.59371i	0.143146	+	0.247937i	−0.785534	+	0.618819i	$0.787611\pi$
$510$		0			0
$511$	−1.86913	+	3.23742i	−0.0826853	+	0.143215i
$512$	−29.3656			−1.29779
$513$		0			0
$514$	−37.5309			−1.65542
$515$	−20.9872	+	36.3510i	−0.924808	+	1.60181i
$516$		0			0
$517$	8.86680	+	15.3578i	0.389961	+	0.675433i
$518$	−4.41024	−	7.63875i	−0.193775	−	0.335627i
$519$		0			0
$520$	1.05316	−	1.82412i	0.0461840	−	0.0799930i
$521$	1.31900			0.0577866			0.0288933	−	0.999583i	$-0.490802\pi$
$521$	1.31900			0.0577866			0.0288933	+	0.999583i	$0.490802\pi$
$522$		0			0
$523$	18.1005			0.791482			0.395741	−	0.918362i	$-0.370488\pi$
$523$	18.1005			0.791482			0.395741	+	0.918362i	$0.370488\pi$
$524$	12.6855	−	21.9720i	0.554170	−	0.959851i
$525$		0			0
$526$	−31.1094	−	53.8830i	−1.35643	−	2.34941i
$527$	−5.07342	−	8.78742i	−0.221002	−	0.382786i
$528$		0			0
$529$	5.04514	−	8.73844i	0.219354	−	0.379932i
$530$	45.7794			1.98853
$531$		0			0
$532$	0.0805714			0.00349321
$533$	0.558143	−	0.966733i	0.0241759	−	0.0418738i
$534$		0			0
$535$	2.51605	+	4.35793i	0.108778	+	0.188410i
$536$	1.46821	+	2.54301i	0.0634170	+	0.109841i
$537$		0			0
$538$	12.6874	−	21.9752i	0.546992	−	0.947417i
$539$	36.0598			1.55321
$540$		0			0
$541$	19.2348			0.826968			0.413484	−	0.910511i	$-0.364312\pi$
$541$	19.2348			0.826968			0.413484	+	0.910511i	$0.364312\pi$
$542$	17.8837	−	30.9754i	0.768170	−	1.33051i
$543$		0			0
$544$	12.3865	+	21.4541i	0.531067	+	0.919835i
$545$	−25.1001	−	43.4746i	−1.07517	−	1.86225i
$546$		0			0
$547$	1.78411	−	3.09016i	0.0762828	−	0.132126i	−0.825361	−	0.564606i	$-0.809028\pi$
$547$	1.78411	−	3.09016i	0.0762828	−	0.132126i	0.901643	+	0.432480i	$0.142361\pi$
$548$	−31.0315			−1.32560
$549$		0			0
$550$	92.2348			3.93291
$551$	−0.236756	+	0.410073i	−0.0100861	+	0.0174697i
$552$		0			0
$553$	3.18885	+	5.52326i	0.135604	+	0.234873i
$554$	24.8191	+	42.9879i	1.05446	+	1.82638i
$555$		0			0
$556$	−6.37661	+	11.0446i	−0.270428	+	0.468396i
$557$	−14.5428			−0.616198			−0.308099	−	0.951354i	$-0.599693\pi$
$557$	−14.5428			−0.616198			−0.308099	+	0.951354i	$0.599693\pi$
$558$		0			0
$559$	7.12464			0.301340
$560$	3.88499	−	6.72901i	0.164171	−	0.284352i
$561$		0			0
$562$	−1.68972	−	2.92669i	−0.0712767	−	0.123455i
$563$	5.07032	+	8.78205i	0.213688	+	0.370119i	0.952866	−	0.303391i	$-0.0981190\pi$
$563$	5.07032	+	8.78205i	0.213688	+	0.370119i	−0.739178	+	0.673510i	$0.764786\pi$
$564$		0			0
$565$	−28.3695	+	49.1375i	−1.19351	+	2.06723i
$566$	5.36869			0.225663
$567$		0			0
$568$	5.11772			0.214735
$569$	−17.2441	+	29.8676i	−0.722910	+	1.25212i	0.236919	+	0.971529i	$0.423862\pi$
$569$	−17.2441	+	29.8676i	−0.722910	+	1.25212i	−0.959829	+	0.280587i	$0.909471\pi$
$570$		0			0
$571$	18.5326	+	32.0994i	0.775565	+	1.34332i	0.934476	+	0.356026i	$0.115868\pi$
$571$	18.5326	+	32.0994i	0.775565	+	1.34332i	−0.158911	+	0.987293i	$0.550798\pi$
$572$	−5.16039	−	8.93807i	−0.215767	−	0.373719i
$573$		0			0
$574$	0.451226	−	0.781546i	0.0188338	−	0.0326211i
$575$	32.2348			1.34428
$576$		0			0
$577$	−44.8314			−1.86636			−0.933178	−	0.359415i	$-0.882976\pi$
$577$	−44.8314			−1.86636			−0.933178	+	0.359415i	$0.882976\pi$
$578$	−6.17082	+	10.6882i	−0.256672	+	0.444569i
$579$		0			0
$580$	−15.5010	−	26.8484i	−0.643642	−	1.11482i
$581$	1.75638	+	3.04214i	0.0728669	+	0.126209i
$582$		0			0
$583$	−16.8383	+	29.1648i	−0.697372	+	1.20788i
$584$	4.04337			0.167316
$585$		0			0
$586$	4.11950			0.170175
$587$	−5.92958	+	10.2703i	−0.244740	+	0.423902i	−0.962058	−	0.272843i	$-0.912036\pi$
$587$	−5.92958	+	10.2703i	−0.244740	+	0.423902i	0.717319	+	0.696745i	$0.245369\pi$
$588$		0			0
$589$	0.154575	+	0.267732i	0.00636916	+	0.0110317i
$590$	−15.9454	−	27.6182i	−0.656462	−	1.13703i
$591$		0			0
$592$	−21.7664	+	37.7004i	−0.894591	+	1.54948i
$593$	19.8984			0.817128			0.408564	−	0.912730i	$-0.366030\pi$
$593$	19.8984			0.817128			0.408564	+	0.912730i	$0.366030\pi$
$594$		0			0
$595$	−5.68435			−0.233036
$596$	1.44516	−	2.50309i	0.0591961	−	0.102531i
$597$		0			0
$598$	−3.87773	−	6.71643i	−0.158572	−	0.274655i
$599$	21.4601	+	37.1700i	0.876837	+	1.51873i	0.854793	+	0.518970i	$0.173684\pi$
$599$	21.4601	+	37.1700i	0.876837	+	1.51873i	0.0220446	+	0.999757i	$0.492982\pi$
$600$		0			0
$601$	12.7746	−	22.1263i	0.521087	−	0.902549i	−0.478612	−	0.878026i	$-0.658860\pi$
$601$	12.7746	−	22.1263i	0.521087	−	0.902549i	0.999699	−	0.0245228i	$-0.00780664\pi$
$602$	5.75985			0.234754
$603$		0			0
$604$	−5.81053			−0.236427
$605$	−32.2742	+	55.9006i	−1.31213	+	2.27268i
$606$		0			0
$607$	−2.03717	−	3.52849i	−0.0826863	−	0.143217i	0.821717	−	0.569896i	$-0.193017\pi$
$607$	−2.03717	−	3.52849i	−0.0826863	−	0.143217i	−0.904403	+	0.426679i	$0.859683\pi$
$608$	−0.377388	−	0.653655i	−0.0153051	−	0.0265092i
$609$		0			0
$610$	−29.0429	+	50.3038i	−1.17591	+	2.03674i
$611$	−3.72322			−0.150625
$612$		0			0
$613$	−1.39932			−0.0565182			−0.0282591	−	0.999601i	$-0.508996\pi$
$613$	−1.39932			−0.0565182			−0.0282591	+	0.999601i	$0.508996\pi$
$614$	−4.94523	+	8.56538i	−0.199573	+	0.345671i
$615$		0			0
$616$	0.626325	+	1.08483i	0.0252354	+	0.0437089i
$617$	−15.6753	−	27.1504i	−0.631064	−	1.09303i	−0.987335	−	0.158652i	$-0.949285\pi$
$617$	−15.6753	−	27.1504i	−0.631064	−	1.09303i	0.356271	−	0.934383i	$-0.384048\pi$
$618$		0			0
$619$	−16.7208	+	28.9612i	−0.672065	+	1.16405i	0.305253	+	0.952271i	$0.401259\pi$
$619$	−16.7208	+	28.9612i	−0.672065	+	1.16405i	−0.977318	+	0.211779i	$0.932074\pi$
$620$	−20.2408			−0.812889
$621$		0			0
$622$	−11.7765			−0.472196
$623$	0.983244	−	1.70303i	0.0393928	−	0.0682304i
$624$		0			0
$625$	−5.31539	−	9.20652i	−0.212616	−	0.368261i
$626$	20.8865	+	36.1764i	0.834791	+	1.44590i
$627$		0			0
$628$	17.2352	−	29.8523i	0.687761	−	1.19124i
$629$	31.8476			1.26985
$630$		0			0
$631$	−32.0308			−1.27513			−0.637563	−	0.770398i	$-0.720057\pi$
$631$	−32.0308			−1.27513			−0.637563	+	0.770398i	$0.720057\pi$
$632$	3.44913	−	5.97407i	0.137199	−	0.237636i
$633$		0			0
$634$	−14.0936	−	24.4109i	−0.559729	−	0.969479i
$635$	31.2902	+	54.1962i	1.24171	+	2.15071i
$636$		0			0
$637$	−3.78543	+	6.55655i	−0.149984	+	0.259780i
$638$	49.0356			1.94134
$639$		0			0
$640$	−14.9665			−0.591605
$641$	3.68342	−	6.37987i	0.145486	−	0.251990i	−0.784068	−	0.620675i	$-0.786859\pi$
$641$	3.68342	−	6.37987i	0.145486	−	0.251990i	0.929554	+	0.368685i	$0.120192\pi$
$642$		0			0
$643$	4.23158	+	7.32932i	0.166877	+	0.289040i	0.937320	−	0.348469i	$-0.113298\pi$
$643$	4.23158	+	7.32932i	0.166877	+	0.289040i	−0.770443	+	0.637509i	$0.779965\pi$
$644$	−1.45801	−	2.52535i	−0.0574538	−	0.0995129i
$645$		0			0
$646$	−0.312752	+	0.541702i	−0.0123051	+	0.0213130i
$647$	−20.6282			−0.810980			−0.405490	−	0.914100i	$-0.632899\pi$
$647$	−20.6282			−0.810980			−0.405490	+	0.914100i	$0.632899\pi$
$648$		0			0
$649$	23.4598			0.920876
$650$	−9.68248	+	16.7705i	−0.379778	+	0.657795i
$651$		0			0
$652$	−12.1350	−	21.0184i	−0.475243	−	0.823145i
$653$	−1.20109	−	2.08035i	−0.0470024	−	0.0814105i	0.841567	−	0.540153i	$-0.181634\pi$
$653$	−1.20109	−	2.08035i	−0.0470024	−	0.0814105i	−0.888569	+	0.458742i	$0.848300\pi$
$654$		0			0
$655$	27.2677	−	47.2290i	1.06544	−	1.84539i
$656$	−4.45398			−0.173899
$657$		0			0
$658$	−3.01000			−0.117342
$659$	19.9564	−	34.5655i	0.777390	−	1.34648i	−0.156051	−	0.987749i	$-0.549876\pi$
$659$	19.9564	−	34.5655i	0.777390	−	1.34648i	0.933441	−	0.358731i	$-0.116790\pi$
$660$		0			0
$661$	−8.01611	−	13.8843i	−0.311791	−	0.540037i	0.666959	−	0.745094i	$-0.267595\pi$
$661$	−8.01611	−	13.8843i	−0.311791	−	0.540037i	−0.978750	+	0.205057i	$0.934262\pi$
$662$	−8.59001	−	14.8783i	−0.333860	−	0.578263i
$663$		0			0
$664$	1.89974	−	3.29044i	0.0737241	−	0.127694i
$665$	0.173189			0.00671598
$666$		0			0
$667$	17.1373			0.663558
$668$	20.9464	−	36.2802i	0.810439	−	1.40372i
$669$		0			0
$670$	−21.0212	−	36.4099i	−0.812122	−	1.40664i
$671$	−21.3648	−	37.0049i	−0.824778	−	1.42856i
$672$		0			0
$673$	11.1856	−	19.3740i	0.431174	−	0.746815i	−0.565801	−	0.824542i	$-0.691433\pi$
$673$	11.1856	−	19.3740i	0.431174	−	0.746815i	0.996975	+	0.0777271i	$0.0247663\pi$
$674$	24.7214			0.952232
$675$		0			0
$676$	−20.4393			−0.786125
$677$	−20.0528	+	34.7325i	−0.770692	+	1.33488i	0.166492	+	0.986043i	$0.446756\pi$
$677$	−20.0528	+	34.7325i	−0.770692	+	1.33488i	−0.937184	+	0.348835i	$0.886577\pi$
$678$		0			0
$679$	4.37042	+	7.56979i	0.167721	+	0.290502i
$680$	3.07416	+	5.32460i	0.117889	+	0.204189i
$681$		0			0
$682$	16.0074	−	27.7256i	0.612954	−	1.06167i
$683$	4.42587			0.169351			0.0846755	−	0.996409i	$-0.473015\pi$
$683$	4.42587			0.169351			0.0846755	+	0.996409i	$0.473015\pi$
$684$		0			0
$685$	−66.7025			−2.54857
$686$	−6.21888	+	10.7714i	−0.237438	+	0.411254i
$687$		0			0
$688$	−14.2136	−	24.6188i	−0.541890	−	0.938581i
$689$	−3.53525	−	6.12324i	−0.134682	−	0.233277i
$690$		0			0
$691$	11.9918	−	20.7705i	0.456191	−	0.790146i	−0.542565	−	0.840014i	$-0.682547\pi$
$691$	11.9918	−	20.7705i	0.456191	−	0.790146i	0.998756	+	0.0498680i	$0.0158801\pi$
$692$	11.1946			0.425557
$693$		0			0
$694$	−32.8337			−1.24635
$695$	−13.7066	+	23.7405i	−0.519920	+	0.900528i
$696$		0			0
$697$	1.62922	+	2.82189i	0.0617110	+	0.106887i
$698$	−24.8670	−	43.0709i	−0.941230	−	1.63026i
$699$		0			0
$700$	−3.64058	+	6.30566i	−0.137601	+	0.238332i
$701$	5.86495			0.221516			0.110758	−	0.993847i	$-0.464672\pi$
$701$	5.86495			0.221516			0.110758	+	0.993847i	$0.464672\pi$
$702$		0			0
$703$	−0.970320			−0.0365963
$704$	−15.4001	+	26.6738i	−0.580414	+	1.00531i
$705$		0			0
$706$	−17.3741	−	30.0928i	−0.653882	−	1.13256i
$707$	−3.83580	−	6.64379i	−0.144260	−	0.249866i
$708$		0			0
$709$	−4.27227	+	7.39979i	−0.160449	+	0.277905i	−0.935030	−	0.354570i	$-0.884627\pi$
$709$	−4.27227	+	7.39979i	−0.160449	+	0.277905i	0.774581	+	0.632475i	$0.217961\pi$
$710$	−73.2736			−2.74991
$711$		0			0
$712$	−2.12699			−0.0797124
$713$	5.59436	−	9.68972i	0.209511	−	0.362883i
$714$		0			0
$715$	−11.0923	−	19.2124i	−0.414829	−	0.718505i
$716$	−1.61174	−	2.79162i	−0.0602337	−	0.104328i
$717$		0			0
$718$	11.8139	−	20.4622i	0.440890	−	0.763644i
$719$	40.3054			1.50314			0.751569	−	0.659654i	$-0.229297\pi$
$719$	40.3054			1.50314			0.751569	+	0.659654i	$0.229297\pi$
$720$		0			0
$721$	5.24099			0.195185
$722$	−18.3600	+	31.8004i	−0.683288	+	1.18349i
$723$		0			0
$724$	−14.9052	−	25.8165i	−0.553947	−	0.959464i
$725$	−21.3954	−	37.0579i	−0.794605	−	1.37630i
$726$		0			0
$727$	−4.94520	+	8.56535i	−0.183407	+	0.317671i	−0.943039	−	0.332683i	$-0.892046\pi$
$727$	−4.94520	+	8.56535i	−0.183407	+	0.317671i	0.759631	+	0.650354i	$0.225379\pi$
$728$	−0.262997			−0.00974733
$729$		0			0
$730$	−57.8915			−2.14266
$731$	−10.3984	+	18.0105i	−0.384598	+	0.666144i
$732$		0			0
$733$	7.81582	+	13.5374i	0.288684	+	0.500015i	0.973496	−	0.228705i	$-0.0734490\pi$
$733$	7.81582	+	13.5374i	0.288684	+	0.500015i	−0.684812	+	0.728720i	$0.740116\pi$
$734$	5.93221	+	10.2749i	0.218962	+	0.379253i
$735$		0			0
$736$	−13.6584	+	23.6570i	−0.503454	+	0.872008i
$737$	30.9276			1.13923
$738$		0			0
$739$	−7.50399			−0.276039			−0.138019	−	0.990430i	$-0.544074\pi$
$739$	−7.50399			−0.276039			−0.138019	+	0.990430i	$0.544074\pi$
$740$	31.7645	−	55.0178i	1.16769	−	2.02249i
$741$		0			0
$742$	−2.85804	−	4.95028i	−0.104922	−	0.181730i
$743$	−3.30338	−	5.72162i	−0.121189	−	0.209906i	0.799048	−	0.601268i	$-0.205337\pi$
$743$	−3.30338	−	5.72162i	−0.121189	−	0.209906i	−0.920237	+	0.391362i	$0.872004\pi$
$744$		0			0
$745$	3.10638	−	5.38041i	0.113809	−	0.197123i
$746$	−58.3977			−2.13809
$747$		0			0
$748$	30.1263			1.10153
$749$	0.314158	−	0.544137i	0.0114791	−	0.0198823i
$750$		0			0
$751$	16.6374	+	28.8168i	0.607107	+	1.05154i	0.991715	+	0.128460i	$0.0410035\pi$
$751$	16.6374	+	28.8168i	0.607107	+	1.05154i	−0.384607	+	0.923080i	$0.625663\pi$
$752$	7.42781	+	12.8653i	0.270864	+	0.469151i
$753$		0			0
$754$	−5.14758	+	8.91587i	−0.187464	+	0.324697i
$755$	−12.4898			−0.454550
$756$		0			0
$757$	9.81356			0.356680			0.178340	−	0.983969i	$-0.442927\pi$
$757$	9.81356			0.356680			0.178340	+	0.983969i	$0.442927\pi$
$758$	−8.06512	+	13.9692i	−0.292938	+	0.507384i
$759$		0			0
$760$	−0.0936623	−	0.162228i	−0.00339749	−	0.00588462i
$761$	10.8709	+	18.8289i	0.394069	+	0.682547i	0.992982	−	0.118267i	$-0.0377338\pi$
$761$	10.8709	+	18.8289i	0.394069	+	0.682547i	−0.598913	+	0.800814i	$0.704400\pi$
$762$		0			0
$763$	−3.13403	+	5.42830i	−0.113460	+	0.196518i
$764$	−10.5694			−0.382386
$765$		0			0
$766$	31.4576			1.13661
$767$	−2.46272	+	4.26556i	−0.0889237	+	0.154020i
$768$		0			0
$769$	−6.12950	−	10.6166i	−0.221035	−	0.382844i	0.734087	−	0.679055i	$-0.237610\pi$
$769$	−6.12950	−	10.6166i	−0.221035	−	0.382844i	−0.955123	+	0.296211i	$0.904277\pi$
$770$	−8.96748	−	15.5321i	−0.323166	−	0.559739i
$771$		0			0
$772$	−2.56162	+	4.43685i	−0.0921946	+	0.159686i
$773$	−23.3957			−0.841486			−0.420743	−	0.907180i	$-0.638231\pi$
$773$	−23.3957			−0.841486			−0.420743	+	0.907180i	$0.638231\pi$
$774$		0			0
$775$	−27.9376			−1.00355
$776$	4.72714	−	8.18765i	0.169694	−	0.293919i
$777$		0			0
$778$	19.9717	+	34.5920i	0.716020	+	1.24018i
$779$	−0.0496384	−	0.0859762i	−0.00177848	−	0.00308042i
$780$		0			0
$781$	26.9511	−	46.6806i	0.964385	−	1.67036i
$782$	22.6382			0.809539
$783$		0			0
$784$	30.2077			1.07885
$785$	37.0473	−	64.1678i	1.32227	−	2.29025i
$786$		0			0
$787$	−18.1146	−	31.3754i	−0.645715	−	1.11841i	−0.984136	−	0.177416i	$-0.943226\pi$
$787$	−18.1146	−	31.3754i	−0.645715	−	1.11841i	0.338421	−	0.940995i	$-0.390107\pi$
$788$	−18.0343	−	31.2363i	−0.642445	−	1.11275i
$789$		0			0
$790$	−49.3833	+	85.5344i	−1.75698	+	3.04318i
$791$	7.08452			0.251896
$792$		0			0
$793$	8.97118			0.318576
$794$	17.5510	−	30.3991i	0.622860	−	1.07883i
$795$		0			0
$796$	22.8903	+	39.6471i	0.811324	+	1.40525i
$797$	0.0572616	+	0.0991800i	0.00202831	+	0.00351314i	0.867038	−	0.498242i	$-0.166021\pi$
$797$	0.0572616	+	0.0991800i	0.00202831	+	0.00351314i	−0.865009	+	0.501756i	$0.832688\pi$
$798$		0			0
$799$	5.43402	−	9.41200i	0.192242	−	0.332973i
$800$	68.2083			2.41153
$801$		0			0
$802$	39.7102			1.40222
$803$	21.2933	−	36.8811i	0.751424	−	1.30150i
$804$		0			0
$805$	−3.13401	−	5.42827i	−0.110459	−	0.191321i
$806$	3.36079	+	5.82107i	0.118379	+	0.205038i
$807$		0			0
$808$	−4.14888	+	7.18606i	−0.145957	+	0.252805i
$809$	−20.5034			−0.720861			−0.360431	−	0.932786i	$-0.617370\pi$
$809$	−20.5034			−0.720861			−0.360431	+	0.932786i	$0.617370\pi$
$810$		0			0
$811$	16.6957			0.586264			0.293132	−	0.956072i	$-0.405302\pi$
$811$	16.6957			0.586264			0.293132	+	0.956072i	$0.405302\pi$
$812$	−1.93547	+	3.35233i	−0.0679217	+	0.117644i
$813$		0			0
$814$	50.2419	+	87.0215i	1.76098	+	3.05010i
$815$	−26.0843	−	45.1793i	−0.913693	−	1.58256i
$816$		0			0
$817$	0.316814	−	0.548739i	0.0110839	−	0.0191979i
$818$	−1.54075			−0.0538709
$819$		0			0
$820$	6.49988			0.226985
$821$	−9.68442	+	16.7739i	−0.337989	+	0.585414i	−0.984054	−	0.177868i	$-0.943080\pi$
$821$	−9.68442	+	16.7739i	−0.337989	+	0.585414i	0.646066	+	0.763282i	$0.276413\pi$
$822$		0			0
$823$	−17.1977	−	29.7873i	−0.599475	−	1.03832i	−0.992899	−	0.118964i	$-0.962043\pi$
$823$	−17.1977	−	29.7873i	−0.599475	−	1.03832i	0.393424	−	0.919357i	$-0.371291\pi$
$824$	−2.83438	−	4.90929i	−0.0987404	−	0.171023i
$825$		0			0
$826$	−1.99096	+	3.44845i	−0.0692745	+	0.119987i
$827$	−41.0753			−1.42833			−0.714163	−	0.699979i	$-0.753193\pi$
$827$	−41.0753			−1.42833			−0.714163	+	0.699979i	$0.753193\pi$
$828$		0			0
$829$	−18.2219			−0.632874			−0.316437	−	0.948614i	$-0.602487\pi$
$829$	−18.2219			−0.632874			−0.316437	+	0.948614i	$0.602487\pi$
$830$	−27.1997	+	47.1113i	−0.944115	+	1.63526i
$831$		0			0
$832$	−3.23330	−	5.60023i	−0.112094	−	0.194153i
$833$	−11.0496	−	19.1385i	−0.382847	−	0.663111i
$834$		0			0
$835$	45.0244	−	77.9845i	1.55813	−	2.69876i
$836$	−0.917878			−0.0317455
$837$		0			0
$838$	64.1246			2.21515
$839$	−6.84320	+	11.8528i	−0.236254	+	0.409203i	−0.959636	−	0.281244i	$-0.909253\pi$
$839$	−6.84320	+	11.8528i	−0.236254	+	0.409203i	0.723383	+	0.690447i	$0.242586\pi$
$840$		0			0
$841$	3.12538	+	5.41332i	0.107772	+	0.186666i
$842$	9.16611	+	15.8762i	0.315885	+	0.547129i
$843$		0			0
$844$	11.8469	−	20.5194i	0.407786	−	0.706307i
$845$	−43.9344			−1.51139
$846$		0			0
$847$	8.05961			0.276932
$848$	−14.1056	+	24.4317i	−0.484389	+	0.838987i
$849$		0			0
$850$	−28.2631	−	48.9531i	−0.969416	−	1.67908i
$851$	17.5588	+	30.4128i	0.601909	+	1.04254i
$852$		0			0
$853$	−27.4768	+	47.5911i	−0.940786	+	1.62949i	−0.176810	+	0.984245i	$0.556578\pi$
$853$	−27.4768	+	47.5911i	−0.940786	+	1.62949i	−0.763976	+	0.645244i	$0.776756\pi$
$854$	7.25267			0.248181
$855$		0			0
$856$	−0.679599			−0.0232282
$857$	6.67663	−	11.5643i	0.228069	−	0.395028i	−0.729167	−	0.684336i	$-0.760092\pi$
$857$	6.67663	−	11.5643i	0.228069	−	0.395028i	0.957236	+	0.289309i	$0.0934254\pi$
$858$		0			0
$859$	5.11151	+	8.85340i	0.174402	+	0.302074i	0.939954	−	0.341300i	$-0.110867\pi$
$859$	5.11151	+	8.85340i	0.174402	+	0.302074i	−0.765552	+	0.643374i	$0.777534\pi$
$860$	20.7426	+	35.9272i	0.707315	+	1.22511i
$861$		0			0
$862$	−11.2975	+	19.5679i	−0.384796	+	0.666486i
$863$	−7.53999			−0.256664			−0.128332	−	0.991731i	$-0.540962\pi$
$863$	−7.53999			−0.256664			−0.128332	+	0.991731i	$0.540962\pi$
$864$		0			0
$865$	24.0630			0.818166
$866$	2.60915	−	4.51917i	0.0886624	−	0.153568i
$867$		0			0
$868$	1.26365	+	2.18870i	0.0428909	+	0.0742893i
$869$	−36.3278	−	62.9215i	−1.23234	−	2.13447i
$870$		0			0
$871$	−3.24667	+	5.62340i	−0.110009	+	0.190542i
$872$	6.77967			0.229588
$873$		0			0
$874$	−0.689731			−0.0233305
$875$	−3.46418	+	6.00014i	−0.117111	+	0.202842i
$876$		0			0
$877$	−29.0895	−	50.3845i	−0.982283	−	1.70136i	−0.653438	−	0.756980i	$-0.726674\pi$
$877$	−29.0895	−	50.3845i	−0.982283	−	1.70136i	−0.328845	−	0.944384i	$-0.606659\pi$
$878$	20.6634	+	35.7900i	0.697355	+	1.20785i
$879$		0			0
$880$	−44.2583	+	76.6576i	−1.49195	+	2.58413i
$881$	35.8338			1.20727			0.603636	−	0.797260i	$-0.293718\pi$
$881$	35.8338			1.20727			0.603636	+	0.797260i	$0.293718\pi$
$882$		0			0
$883$	29.7633			1.00161			0.500807	−	0.865559i	$-0.333037\pi$
$883$	29.7633			1.00161			0.500807	+	0.865559i	$0.333037\pi$
$884$	−3.16255	+	5.47770i	−0.106368	+	0.184235i
$885$		0			0
$886$	15.8181	+	27.3977i	0.531419	+	0.920445i
$887$	−13.7075	−	23.7421i	−0.460253	−	0.797181i	0.538720	−	0.842485i	$-0.318908\pi$
$887$	−13.7075	−	23.7421i	−0.460253	−	0.797181i	−0.998973	+	0.0453032i	$0.985575\pi$
$888$		0			0
$889$	3.90694	−	6.76701i	0.131034	−	0.226958i
$890$	30.4535			1.02080
$891$		0			0
$892$	19.3196			0.646867
$893$	−0.165562	+	0.286762i	−0.00554032	+	0.00959611i
$894$		0			0
$895$	−3.46446	−	6.00062i	−0.115804	−	0.200579i
$896$	0.934372	+	1.61838i	0.0312152	+	0.0540663i
$897$		0			0
$898$	7.62608	−	13.2088i	0.254485	−	0.440782i
$899$	−14.8527			−0.495366
$900$		0			0
$901$	20.6387			0.687576
$902$	−5.14041	+	8.90346i	−0.171157	+	0.296453i
$903$		0			0
$904$	−3.83138	−	6.63614i	−0.127430	−	0.220715i
$905$	−32.0388	−	55.4929i	−1.06501	−	1.84464i
$906$		0			0
$907$	−2.74766	+	4.75909i	−0.0912346	+	0.158023i	−0.908031	−	0.418903i	$-0.862415\pi$
$907$	−2.74766	+	4.75909i	−0.0912346	+	0.158023i	0.816796	+	0.576926i	$0.195748\pi$
$908$	8.84108			0.293401
$909$		0			0
$910$	3.76549			0.124825
$911$	−15.0365	+	26.0439i	−0.498180	+	0.862873i	−0.999998	−	0.00210021i	$-0.999331\pi$
$911$	−15.0365	+	26.0439i	−0.498180	+	0.862873i	0.501818	+	0.864973i	$0.332665\pi$
$912$		0			0
$913$	−20.0089	−	34.6564i	−0.662197	−	1.14696i
$914$	−18.3436	−	31.7721i	−0.606753	−	1.05093i
$915$		0			0
$916$	1.42225	−	2.46341i	0.0469925	−	0.0813934i
$917$	−6.80936			−0.224865
$918$		0			0
$919$	7.92860			0.261540			0.130770	−	0.991413i	$-0.458255\pi$
$919$	7.92860			0.261540			0.130770	+	0.991413i	$0.458255\pi$
$920$	−3.38981	+	5.87133i	−0.111759	+	0.193572i
$921$		0			0
$922$	9.79087	+	16.9583i	0.322445	+	0.558492i
$923$	5.65845	+	9.80072i	0.186250	+	0.322595i
$924$		0			0
$925$	43.8434	−	75.9390i	1.44156	−	2.49686i
$926$	28.8404			0.947755
$927$		0			0
$928$	36.2622			1.19036
$929$	22.8882	−	39.6435i	0.750938	−	1.30066i	−0.196431	−	0.980518i	$-0.562935\pi$
$929$	22.8882	−	39.6435i	0.750938	−	1.30066i	0.947369	−	0.320145i	$-0.103732\pi$
$930$		0			0
$931$	0.336656	+	0.583106i	0.0110335	+	0.0191105i
$932$	−16.5504	−	28.6661i	−0.542125	−	0.938988i
$933$		0			0
$934$	2.13490	−	3.69775i	0.0698559	−	0.120994i
$935$	64.7568			2.11777
$936$		0			0
$937$	−1.60857			−0.0525498			−0.0262749	−	0.999655i	$-0.508365\pi$
$937$	−1.60857			−0.0525498			−0.0262749	+	0.999655i	$0.508365\pi$
$938$	−2.62474	+	4.54619i	−0.0857009	+	0.148438i
$939$		0			0
$940$	−10.8397	−	18.7749i	−0.353552	−	0.612371i
$941$	−13.8885	−	24.0556i	−0.452753	−	0.784191i	0.545803	−	0.837914i	$-0.316225\pi$
$941$	−13.8885	−	24.0556i	−0.452753	−	0.784191i	−0.998556	+	0.0537222i	$0.982891\pi$
$942$		0			0
$943$	−1.79650	+	3.11164i	−0.0585022	+	0.101329i
$944$	19.6525			0.639634
$945$		0			0
$946$	−65.6169			−2.13339
$947$	−1.57894	+	2.73481i	−0.0513088	+	0.0888694i	−0.890539	−	0.454907i	$-0.849673\pi$
$947$	−1.57894	+	2.73481i	−0.0513088	+	0.0888694i	0.839230	+	0.543776i	$0.183006\pi$
$948$		0			0
$949$	4.47058	+	7.74328i	0.145121	+	0.251357i
$950$	0.861109	+	1.49148i	0.0279381	+	0.0483902i
$951$		0			0
$952$	0.383844	−	0.664837i	0.0124404	−	0.0215475i
$953$	−17.9816			−0.582483			−0.291241	−	0.956650i	$-0.594068\pi$
$953$	−17.9816			−0.582483			−0.291241	+	0.956650i	$0.594068\pi$
$954$		0			0
$955$	−22.7189			−0.735167
$956$	−1.12360	+	1.94613i	−0.0363397	+	0.0629423i
$957$		0			0
$958$	1.13086	+	1.95871i	0.0365365	+	0.0632830i
$959$	4.16428	+	7.21275i	0.134472	+	0.232912i
$960$		0			0
$961$	10.6514	−	18.4488i	0.343594	−	0.595123i
$962$	−21.0968			−0.680189
$963$		0			0
$964$	2.25037			0.0724796
$965$	−5.50622	+	9.53705i	−0.177251	+	0.307008i
$966$		0			0
$967$	9.74015	+	16.8704i	0.313222	+	0.542517i	0.979058	−	0.203582i	$-0.0652582\pi$
$967$	9.74015	+	16.8704i	0.313222	+	0.542517i	−0.665836	+	0.746098i	$0.731925\pi$
$968$	−4.35872	−	7.54953i	−0.140095	−	0.242651i
$969$		0			0
$970$	−67.6814	+	117.228i	−2.17312	+	3.76395i
$971$	−2.32619			−0.0746509			−0.0373255	−	0.999303i	$-0.511884\pi$
$971$	−2.32619			−0.0746509			−0.0373255	+	0.999303i	$0.511884\pi$
$972$		0			0
$973$	3.42284			0.109731
$974$	−19.6333	+	34.0059i	−0.629092	+	1.08962i
$975$		0			0
$976$	−17.8975	−	30.9993i	−0.572884	−	0.992265i
$977$	27.6827	+	47.9479i	0.885648	+	1.53399i	0.844969	+	0.534816i	$0.179619\pi$
$977$	27.6827	+	47.9479i	0.885648	+	1.53399i	0.0406794	+	0.999172i	$0.487048\pi$
$978$		0			0
$979$	−11.2012	+	19.4011i	−0.357992	+	0.620061i
$980$	−44.0833			−1.40819
$981$		0			0
$982$	29.1846			0.931319
$983$	−11.5448	+	19.9962i	−0.368222	+	0.637779i	−0.989288	−	0.145980i	$-0.953367\pi$
$983$	−11.5448	+	19.9962i	−0.368222	+	0.637779i	0.621066	+	0.783758i	$0.286700\pi$
$984$		0			0
$985$	−38.7648	−	67.1427i	−1.23515	−	2.13934i
$986$	−15.0257	−	26.0254i	−0.478517	−	0.828816i
$987$		0			0
$988$	0.0963554	−	0.166893i	0.00306548	−	0.00530956i
$989$	−22.9322			−0.729202
$990$		0			0
$991$	38.4258			1.22064			0.610318	−	0.792156i	$-0.291042\pi$
$991$	38.4258			1.22064			0.610318	+	0.792156i	$0.291042\pi$
$992$	11.8376	−	20.5033i	0.375843	−	0.650979i
$993$		0			0
$994$	4.57452	+	7.92330i	0.145095	+	0.251312i
$995$	49.2028	+	85.2218i	1.55983	+	2.70171i
$996$		0			0
$997$	−5.61082	+	9.71822i	−0.177696	+	0.307779i	−0.941091	−	0.338153i	$-0.890198\pi$
$997$	−5.61082	+	9.71822i	−0.177696	+	0.307779i	0.763395	+	0.645932i	$0.223531\pi$
$998$	19.7109			0.623937
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1107.2.e.a.370.14		32
3.2	odd	2		369.2.e.a.124.3	✓	32
9.2	odd	6		3321.2.a.i.1.14		16
9.4	even	3	inner	1107.2.e.a.739.14		32
9.5	odd	6		369.2.e.a.247.3	yes	32
9.7	even	3		3321.2.a.j.1.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
369.2.e.a.124.3	✓	32	3.2	odd	2
369.2.e.a.247.3	yes	32	9.5	odd	6
1107.2.e.a.370.14		32	1.1	even	1	trivial
1107.2.e.a.739.14		32	9.4	even	3	inner
3321.2.a.i.1.14		16	9.2	odd	6
3321.2.a.j.1.3		16	9.7	even	3

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:	\( N \)	\(=\)	\( 1107 = 3^{3} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1107.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.966816 - 1.67457i) q^{2} +(-0.869467 - 1.50596i) q^{4} +(-1.86893 - 3.23707i) q^{5} +(-0.233357 + 0.404186i) q^{7} +0.504807 q^{8} -7.22763 q^{10} +(2.65842 - 4.60453i) q^{11} +(0.558143 + 0.966733i) q^{13} +(0.451226 + 0.781546i) q^{14} +(2.22699 - 3.85726i) q^{16} -3.25843 q^{17} +0.0992768 q^{19} +(-3.24994 + 5.62906i) q^{20} +(-5.14041 - 8.90346i) q^{22} +(-1.79650 - 3.11164i) q^{23} +(-4.48577 + 7.76958i) q^{25} +2.15849 q^{26} +0.811584 q^{28} +(-2.38481 + 4.13061i) q^{29} +(1.55701 + 2.69683i) q^{31} +(-3.80137 - 6.58417i) q^{32} +(-3.15031 + 5.45649i) q^{34} +1.74451 q^{35} -9.77389 q^{37} +(0.0959824 - 0.166246i) q^{38} +(-0.943447 - 1.63410i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(3.19122 - 5.52736i) q^{43} -9.24564 q^{44} -6.94756 q^{46} +(-1.66768 + 2.88851i) q^{47} +(3.39109 + 5.87354i) q^{49} +(8.67383 + 15.0235i) q^{50} +(0.970574 - 1.68108i) q^{52} -6.33395 q^{53} -19.8736 q^{55} +(-0.117800 + 0.204036i) q^{56} +(4.61134 + 7.98708i) q^{58} +(2.20617 + 3.82120i) q^{59} +(4.01831 - 6.95992i) q^{61} +6.02138 q^{62} -5.79295 q^{64} +(2.08626 - 3.61350i) q^{65} +(2.90846 + 5.03759i) q^{67} +(2.83310 + 4.90707i) q^{68} +(1.68662 - 2.92130i) q^{70} +10.1380 q^{71} +8.00974 q^{73} +(-9.44956 + 16.3671i) q^{74} +(-0.0863178 - 0.149507i) q^{76} +(1.24072 + 2.14899i) q^{77} +(6.83258 - 11.8344i) q^{79} -16.6483 q^{80} -1.93363 q^{82} +(3.76329 - 6.51822i) q^{83} +(6.08977 + 10.5478i) q^{85} +(-6.17065 - 10.6879i) q^{86} +(1.34199 - 2.32440i) q^{88} -4.21348 q^{89} -0.520986 q^{91} +(-3.12400 + 5.41093i) q^{92} +(3.22468 + 5.58531i) q^{94} +(-0.185541 - 0.321366i) q^{95} +(9.36425 - 16.2194i) q^{97} +13.1142 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{4} - q^{5} + 13 q^{7} - 16 q^{10} + 2 q^{11} + 5 q^{13} - q^{14} + 8 q^{16} - 2 q^{17} - 38 q^{19} - 11 q^{20} + 14 q^{22} - 2 q^{23} + 3 q^{25} - 30 q^{26} - 48 q^{28} + 10 q^{29} + 39 q^{31}+ \cdots + 96 q^{98}+O(q^{100}) \) 32 * q - 8 * q^4 - q^5 + 13 * q^7 - 16 * q^10 + 2 * q^11 + 5 * q^13 - q^14 + 8 * q^16 - 2 * q^17 - 38 * q^19 - 11 * q^20 + 14 * q^22 - 2 * q^23 + 3 * q^25 - 30 * q^26 - 48 * q^28 + 10 * q^29 + 39 * q^31 + 10 * q^32 + 18 * q^34 - 4 * q^35 - 52 * q^37 + 14 * q^38 + 18 * q^40 - 16 * q^41 + 20 * q^43 + 46 * q^44 - 52 * q^46 - 5 * q^47 + 7 * q^49 - 9 * q^50 + 14 * q^52 - 14 * q^53 - 74 * q^55 + 2 * q^56 + 24 * q^58 - 6 * q^59 + 21 * q^61 + 10 * q^62 - 68 * q^64 - 2 * q^65 + 32 * q^67 + 8 * q^68 + 22 * q^70 + 40 * q^71 - 34 * q^73 - 28 * q^74 + 40 * q^76 + 22 * q^77 + 69 * q^79 - 78 * q^80 - 10 * q^83 + 42 * q^85 + 8 * q^86 + 42 * q^88 - 22 * q^89 - 102 * q^91 + 10 * q^92 + 13 * q^94 + 22 * q^95 + 25 * q^97 + 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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