LMFDB - Embedded newform 2100.2.ce.e.493.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.ce (of order $12$, degree $4$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.7
Character	$\chi$	$=$	2100.493
Dual form			2100.2.ce.e.1657.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{3} +(-2.42432 + 1.05955i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{3} +(-2.42432 + 1.05955i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-1.30656 + 2.26302i) q^{11} +(-2.50064 + 2.50064i) q^{13} +(1.07121 - 0.287031i) q^{17} +(-3.66827 - 6.35364i) q^{19} +(-1.65091 - 2.06749i) q^{21} +(0.398771 - 1.48823i) q^{23} +(-0.707107 - 0.707107i) q^{27} -3.81626i q^{29} +(6.66074 + 3.84558i) q^{31} +(-2.52408 - 0.676324i) q^{33} +(-3.25263 - 0.871539i) q^{37} +(-3.06264 - 1.76822i) q^{39} -8.65223i q^{41} +(-0.817775 - 0.817775i) q^{43} +(2.71712 - 10.1404i) q^{47} +(4.75470 - 5.13740i) q^{49} +(0.554501 + 0.960424i) q^{51} +(0.0300539 - 0.00805292i) q^{53} +(5.18772 - 5.18772i) q^{57} +(-6.72313 + 11.6448i) q^{59} +(8.32607 - 4.80706i) q^{61} +(1.56975 - 2.12976i) q^{63} +(-2.42631 - 9.05510i) q^{67} +1.54073 q^{69} -3.73088 q^{71} +(-2.12557 - 7.93274i) q^{73} +(0.769727 - 6.87067i) q^{77} +(-6.44965 + 3.72371i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-9.33753 + 9.33753i) q^{83} +(3.68622 - 0.987720i) q^{87} +(5.56421 + 9.63750i) q^{89} +(3.41280 - 8.71192i) q^{91} +(-1.99062 + 7.42909i) q^{93} +(-1.97130 - 1.97130i) q^{97} -2.61312i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) $ 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.42432	+	1.05955i	−0.916309	+	0.400473i
$7$	−2.42432	+	1.05955i	−0.916309	+	0.400473i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	−1.30656	+	2.26302i	−0.393942	+	0.682327i	−0.992966	−	0.118404i	$-0.962222\pi$
$11$	−1.30656	+	2.26302i	−0.393942	+	0.682327i	0.599024	+	0.800731i	$0.295556\pi$
$12$		0			0
$13$	−2.50064	+	2.50064i	−0.693552	+	0.693552i	−0.963012	−	0.269459i	$-0.913155\pi$
$13$	−2.50064	+	2.50064i	−0.693552	+	0.693552i	0.269459	+	0.963012i	$0.413155\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.07121	−	0.287031i	0.259808	−	0.0696152i	−0.126564	−	0.991958i	$-0.540395\pi$
$17$	1.07121	−	0.287031i	0.259808	−	0.0696152i	0.386372	+	0.922343i	$0.373728\pi$
$18$		0			0
$19$	−3.66827	−	6.35364i	−0.841560	−	1.45762i	−0.888576	−	0.458730i	$-0.848305\pi$
$19$	−3.66827	−	6.35364i	−0.841560	−	1.45762i	0.0470160	−	0.998894i	$-0.485029\pi$
$20$		0			0
$21$	−1.65091	−	2.06749i	−0.360258	−	0.451162i
$22$		0			0
$23$	0.398771	−	1.48823i	0.0831494	−	0.310318i	−0.911808	−	0.410617i	$-0.865313\pi$
$23$	0.398771	−	1.48823i	0.0831494	−	0.310318i	0.994957	+	0.100299i	$0.0319800\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	3.81626i		−	0.708661i	−0.935120	−	0.354330i	$-0.884709\pi$
$29$		−	3.81626i		−	0.708661i	0.935120	−	0.354330i	$-0.115291\pi$
$30$		0			0
$31$	6.66074	+	3.84558i	1.19630	+	0.690687i	0.959729	−	0.280927i	$-0.0906418\pi$
$31$	6.66074	+	3.84558i	1.19630	+	0.690687i	0.236575	+	0.971613i	$0.423975\pi$
$32$		0			0
$33$	−2.52408	−	0.676324i	−0.439385	−	0.117733i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.25263	−	0.871539i	−0.534729	−	0.143280i	−0.0186576	−	0.999826i	$-0.505939\pi$
$37$	−3.25263	−	0.871539i	−0.534729	−	0.143280i	−0.516071	+	0.856546i	$0.672606\pi$
$38$		0			0
$39$	−3.06264	−	1.76822i	−0.490416	−	0.283142i
$40$		0			0
$41$		−	8.65223i		−	1.35125i	−0.737245	−	0.675626i	$-0.763874\pi$
$41$		−	8.65223i		−	1.35125i	0.737245	−	0.675626i	$-0.236126\pi$
$42$		0			0
$43$	−0.817775	−	0.817775i	−0.124709	−	0.124709i	0.641997	−	0.766707i	$-0.278106\pi$
$43$	−0.817775	−	0.817775i	−0.124709	−	0.124709i	−0.766707	+	0.641997i	$0.778106\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.71712	−	10.1404i	0.396333	−	1.47913i	−0.423166	−	0.906052i	$-0.639081\pi$
$47$	2.71712	−	10.1404i	0.396333	−	1.47913i	0.819498	−	0.573081i	$-0.194252\pi$
$48$		0			0
$49$	4.75470	−	5.13740i	0.679243	−	0.733914i
$50$		0			0
$51$	0.554501	+	0.960424i	0.0776457	+	0.134486i
$52$		0			0
$53$	0.0300539	−	0.00805292i	0.00412822	−	0.00110615i	−0.256754	−	0.966477i	$-0.582653\pi$
$53$	0.0300539	−	0.00805292i	0.00412822	−	0.00110615i	0.260883	+	0.965371i	$0.415986\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.18772	−	5.18772i	0.687131	−	0.687131i
$58$		0			0
$59$	−6.72313	+	11.6448i	−0.875276	+	1.51602i	−0.0188084	+	0.999823i	$0.505987\pi$
$59$	−6.72313	+	11.6448i	−0.875276	+	1.51602i	−0.856468	+	0.516200i	$0.827346\pi$
$60$		0			0
$61$	8.32607	−	4.80706i	1.06604	−	0.615481i	0.138946	−	0.990300i	$-0.455629\pi$
$61$	8.32607	−	4.80706i	1.06604	−	0.615481i	0.927098	+	0.374819i	$0.122295\pi$
$62$		0			0
$63$	1.56975	−	2.12976i	0.197770	−	0.268325i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.42631	−	9.05510i	−0.296420	−	1.10626i	−0.940083	−	0.340947i	$-0.889252\pi$
$67$	−2.42631	−	9.05510i	−0.296420	−	1.10626i	0.643662	−	0.765310i	$-0.277414\pi$
$68$		0			0
$69$	1.54073			0.185482
$70$		0			0
$71$	−3.73088			−0.442774			−0.221387	−	0.975186i	$-0.571058\pi$
$71$	−3.73088			−0.442774			−0.221387	+	0.975186i	$0.571058\pi$
$72$		0			0
$73$	−2.12557	−	7.93274i	−0.248779	−	0.928457i	−0.971446	−	0.237261i	$-0.923750\pi$
$73$	−2.12557	−	7.93274i	−0.248779	−	0.928457i	0.722667	−	0.691197i	$-0.242916\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.769727	−	6.87067i	0.0877186	−	0.782986i
$78$		0			0
$79$	−6.44965	+	3.72371i	−0.725642	+	0.418950i	−0.816826	−	0.576885i	$-0.804268\pi$
$79$	−6.44965	+	3.72371i	−0.725642	+	0.418950i	0.0911838	+	0.995834i	$0.470935\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	−9.33753	+	9.33753i	−1.02493	+	1.02493i	−0.0252460	+	0.999681i	$0.508037\pi$
$83$	−9.33753	+	9.33753i	−1.02493	+	1.02493i	−0.999681	+	0.0252460i	$0.991963\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.68622	−	0.987720i	0.395204	−	0.105895i
$88$		0			0
$89$	5.56421	+	9.63750i	0.589805	+	1.02157i	0.994258	+	0.107014i	$0.0341289\pi$
$89$	5.56421	+	9.63750i	0.589805	+	1.02157i	−0.404452	+	0.914559i	$0.632538\pi$
$90$		0			0
$91$	3.41280	−	8.71192i	0.357759	−	0.913257i
$92$		0			0
$93$	−1.99062	+	7.42909i	−0.206418	+	0.770361i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.97130	−	1.97130i	−0.200155	−	0.200155i	0.599912	−	0.800066i	$-0.295202\pi$
$97$	−1.97130	−	1.97130i	−0.200155	−	0.200155i	−0.800066	+	0.599912i	$0.795202\pi$
$98$		0			0
$99$		−	2.61312i		−	0.262628i
$100$		0			0
$101$	−1.86548	−	1.07703i	−0.185622	−	0.107169i	0.404309	−	0.914622i	$-0.367512\pi$
$101$	−1.86548	−	1.07703i	−0.185622	−	0.107169i	−0.589931	+	0.807453i	$0.700845\pi$
$102$		0			0
$103$	−12.2633	−	3.28595i	−1.20834	−	0.323775i	−0.402232	−	0.915538i	$-0.631765\pi$
$103$	−12.2633	−	3.28595i	−1.20834	−	0.323775i	−0.806112	+	0.591763i	$0.798432\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.2247	−	2.73970i	−0.988458	−	0.264857i	−0.271856	−	0.962338i	$-0.587637\pi$
$107$	−10.2247	−	2.73970i	−0.988458	−	0.264857i	−0.716603	+	0.697481i	$0.754304\pi$
$108$		0			0
$109$	−7.14879	−	4.12735i	−0.684730	−	0.395329i	0.116905	−	0.993143i	$-0.462703\pi$
$109$	−7.14879	−	4.12735i	−0.684730	−	0.395329i	−0.801635	+	0.597814i	$0.796036\pi$
$110$		0			0
$111$		−	3.36737i		−	0.319616i
$112$		0			0
$113$	−11.1237	−	11.1237i	−1.04643	−	1.04643i	−0.998868	−	0.0475601i	$-0.984855\pi$
$113$	−11.1237	−	11.1237i	−1.04643	−	1.04643i	−0.0475601	−	0.998868i	$-0.515145\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.915297	−	3.41594i	0.0846193	−	0.315803i
$118$		0			0
$119$	−2.29285	+	1.83086i	−0.210185	+	0.167835i
$120$		0			0
$121$	2.08581	+	3.61274i	0.189619	+	0.328431i
$122$		0			0
$123$	8.35741	−	2.23936i	0.753563	−	0.201917i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	6.38248	−	6.38248i	0.566354	−	0.566354i	−0.364751	−	0.931105i	$-0.618846\pi$
$127$	6.38248	−	6.38248i	0.566354	−	0.566354i	0.931105	+	0.364751i	$0.118846\pi$
$128$		0			0
$129$	0.578254	−	1.00157i	0.0509124	−	0.0881829i
$130$		0			0
$131$	−10.1238	+	5.84497i	−0.884519	+	0.510677i	−0.872146	−	0.489246i	$-0.837272\pi$
$131$	−10.1238	+	5.84497i	−0.884519	+	0.510677i	−0.0123735	+	0.999923i	$0.503939\pi$
$132$		0			0
$133$	15.6251	+	11.5165i	1.35487	+	0.998611i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.23864	+	8.35471i	0.191260	+	0.713791i	0.993203	+	0.116391i	$0.0371326\pi$
$137$	2.23864	+	8.35471i	0.191260	+	0.713791i	−0.801944	+	0.597399i	$0.796201\pi$
$138$		0			0
$139$	17.9935			1.52619			0.763096	−	0.646285i	$-0.223678\pi$
$139$	17.9935			1.52619			0.763096	+	0.646285i	$0.223678\pi$
$140$		0			0
$141$	10.4981			0.884103
$142$		0			0
$143$	−2.39178	−	8.92623i	−0.200010	−	0.746449i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.19295	+	3.26303i	0.510786	+	0.269130i
$148$		0			0
$149$	13.3414	−	7.70268i	1.09297	−	0.631028i	0.158606	−	0.987342i	$-0.449300\pi$
$149$	13.3414	−	7.70268i	1.09297	−	0.631028i	0.934366	+	0.356314i	$0.115967\pi$
$150$		0			0
$151$	0.518779	−	0.898552i	0.0422177	−	0.0731231i	−0.844144	−	0.536116i	$-0.819891\pi$
$151$	0.518779	−	0.898552i	0.0422177	−	0.0731231i	0.886362	+	0.462993i	$0.153224\pi$
$152$		0			0
$153$	−0.784183	+	0.784183i	−0.0633974	+	0.0633974i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.3036	−	3.29675i	0.981936	−	0.263109i	0.268076	−	0.963398i	$-0.413612\pi$
$157$	12.3036	−	3.29675i	0.981936	−	0.263109i	0.713860	+	0.700289i	$0.246945\pi$
$158$		0			0
$159$	0.0155570	+	0.0269456i	0.00123375	+	0.00213692i
$160$		0			0
$161$	0.610110	+	4.03048i	0.0480834	+	0.317646i
$162$		0			0
$163$	−1.44743	+	5.40188i	−0.113371	+	0.423108i	−0.999160	−	0.0409812i	$-0.986952\pi$
$163$	−1.44743	+	5.40188i	−0.113371	+	0.423108i	0.885788	+	0.464089i	$0.153618\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.50030	+	9.50030i	0.735155	+	0.735155i	0.971636	−	0.236481i	$-0.0759940\pi$
$167$	9.50030	+	9.50030i	0.735155	+	0.735155i	−0.236481	+	0.971636i	$0.575994\pi$
$168$		0			0
$169$			0.493616i			0.0379704i
$170$		0			0
$171$	6.35364	+	3.66827i	0.485875	+	0.280520i
$172$		0			0
$173$	−18.1595	−	4.86581i	−1.38064	−	0.369941i	−0.509286	−	0.860598i	$-0.670090\pi$
$173$	−18.1595	−	4.86581i	−1.38064	−	0.369941i	−0.871353	+	0.490656i	$0.836757\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.9881	−	3.48015i	−0.976244	−	0.261584i
$178$		0			0
$179$	−20.7684	−	11.9907i	−1.55230	−	0.896223i	−0.997954	−	0.0639403i	$-0.979633\pi$
$179$	−20.7684	−	11.9907i	−1.55230	−	0.896223i	−0.554351	−	0.832283i	$-0.687033\pi$
$180$		0			0
$181$		−	11.7552i		−	0.873760i	−0.899520	−	0.436880i	$-0.856083\pi$
$181$		−	11.7552i		−	0.873760i	0.899520	−	0.436880i	$-0.143917\pi$
$182$		0			0
$183$	6.79821	+	6.79821i	0.502538	+	0.502538i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.750045	+	2.79921i	−0.0548487	+	0.204698i
$188$		0			0
$189$	2.46347	+	0.965040i	0.179191	+	0.0701963i
$190$		0			0
$191$	−6.06853	−	10.5110i	−0.439103	−	0.760549i	0.558517	−	0.829493i	$-0.311370\pi$
$191$	−6.06853	−	10.5110i	−0.439103	−	0.760549i	−0.997621	+	0.0689439i	$0.978037\pi$
$192$		0			0
$193$	8.56799	−	2.29578i	0.616737	−	0.165254i	0.0630931	−	0.998008i	$-0.479903\pi$
$193$	8.56799	−	2.29578i	0.616737	−	0.165254i	0.553644	+	0.832753i	$0.313237\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.23024	−	3.23024i	0.230145	−	0.230145i	−0.582608	−	0.812753i	$-0.697968\pi$
$197$	3.23024	−	3.23024i	0.230145	−	0.230145i	0.812753	+	0.582608i	$0.197968\pi$
$198$		0			0
$199$	−7.49827	+	12.9874i	−0.531538	+	0.920651i	0.467784	+	0.883843i	$0.345052\pi$
$199$	−7.49827	+	12.9874i	−0.531538	+	0.920651i	−0.999322	+	0.0368085i	$0.988281\pi$
$200$		0			0
$201$	8.11858	−	4.68726i	0.572640	−	0.330614i
$202$		0			0
$203$	4.04352	+	9.25184i	0.283800	+	0.649352i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.398771	+	1.48823i	0.0277165	+	0.103439i
$208$		0			0
$209$	19.1712			1.32610
$210$		0			0
$211$	2.45975			0.169336			0.0846680	−	0.996409i	$-0.473017\pi$
$211$	2.45975			0.169336			0.0846680	+	0.996409i	$0.473017\pi$
$212$		0			0
$213$	−0.965623	−	3.60375i	−0.0661634	−	0.246925i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−20.2224	−	2.26553i	−1.37279	−	0.153794i
$218$		0			0
$219$	7.11230	−	4.10629i	0.480605	−	0.277477i
$220$		0			0
$221$	−1.96096	+	3.39648i	−0.131908	+	0.228472i
$222$		0			0
$223$	3.17528	−	3.17528i	0.212632	−	0.212632i	−0.592752	−	0.805385i	$-0.701959\pi$
$223$	3.17528	−	3.17528i	0.212632	−	0.212632i	0.805385	+	0.592752i	$0.201959\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−25.0688	+	6.71717i	−1.66388	+	0.445834i	−0.963449	−	0.267891i	$-0.913673\pi$
$227$	−25.0688	+	6.71717i	−1.66388	+	0.445834i	−0.700426	+	0.713725i	$0.747007\pi$
$228$		0			0
$229$	−12.6016	−	21.8266i	−0.832735	−	1.44234i	−0.895861	−	0.444334i	$-0.853440\pi$
$229$	−12.6016	−	21.8266i	−0.832735	−	1.44234i	0.0631257	−	0.998006i	$-0.479893\pi$
$230$		0			0
$231$	6.83578	−	1.03476i	0.449761	−	0.0680823i
$232$		0			0
$233$	2.01386	−	7.51582i	0.131932	−	0.492378i	−0.868059	−	0.496460i	$-0.834633\pi$
$233$	2.01386	−	7.51582i	0.131932	−	0.492378i	0.999992	+	0.00408254i	$0.00129952\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−5.26611	−	5.26611i	−0.342071	−	0.342071i
$238$		0			0
$239$		−	9.67330i		−	0.625714i	−0.949800	−	0.312857i	$-0.898714\pi$
$239$		−	9.67330i		−	0.625714i	0.949800	−	0.312857i	$-0.101286\pi$
$240$		0			0
$241$	0.558157	+	0.322252i	0.0359541	+	0.0207581i	0.517869	−	0.855460i	$-0.326725\pi$
$241$	0.558157	+	0.322252i	0.0359541	+	0.0207581i	−0.481915	+	0.876218i	$0.660059\pi$
$242$		0			0
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	25.0612	+	6.71512i	1.59460	+	0.427273i
$248$		0			0
$249$	−11.4361	−	6.60263i	−0.724733	−	0.418425i
$250$		0			0
$251$			15.2157i			0.960405i	0.877158	+	0.480202i	$0.159437\pi$
$251$			15.2157i			0.960405i	−0.877158	+	0.480202i	$0.840563\pi$
$252$		0			0
$253$	2.84689	+	2.84689i	0.178982	+	0.178982i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.98383	+	26.0640i	−0.435639	+	1.62583i	0.303893	+	0.952706i	$0.401714\pi$
$257$	−6.98383	+	26.0640i	−0.435639	+	1.62583i	−0.739532	+	0.673122i	$0.764953\pi$
$258$		0			0
$259$	8.80886	−	1.33344i	0.547356	−	0.0828556i
$260$		0			0
$261$	1.90813	+	3.30497i	0.118110	+	0.204573i
$262$		0			0
$263$	−12.9653	+	3.47405i	−0.799476	+	0.214219i	−0.635354	−	0.772221i	$-0.719146\pi$
$263$	−12.9653	+	3.47405i	−0.799476	+	0.214219i	−0.164122	+	0.986440i	$0.552479\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−7.86899	+	7.86899i	−0.481574	+	0.481574i
$268$		0			0
$269$	−7.71133	+	13.3564i	−0.470168	+	0.814355i	−0.999418	−	0.0341109i	$-0.989140\pi$
$269$	−7.71133	+	13.3564i	−0.470168	+	0.814355i	0.529250	+	0.848466i	$0.322473\pi$
$270$		0			0
$271$	−0.584881	+	0.337681i	−0.0355290	+	0.0205127i	−0.517659	−	0.855587i	$-0.673197\pi$
$271$	−0.584881	+	0.337681i	−0.0355290	+	0.0205127i	0.482130	+	0.876100i	$0.339863\pi$
$272$		0			0
$273$	9.29836	+	1.04170i	0.562762	+	0.0630468i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.35789	−	12.5318i	−0.201756	−	0.752963i	−0.990414	−	0.138131i	$-0.955890\pi$
$277$	−3.35789	−	12.5318i	−0.201756	−	0.752963i	0.788658	−	0.614832i	$-0.210776\pi$
$278$		0			0
$279$	−7.69116			−0.460458
$280$		0			0
$281$	−21.2425			−1.26722			−0.633610	−	0.773653i	$-0.718428\pi$
$281$	−21.2425			−1.26722			−0.633610	+	0.773653i	$0.718428\pi$
$282$		0			0
$283$	3.97222	+	14.8245i	0.236124	+	0.881227i	0.977639	+	0.210291i	$0.0674410\pi$
$283$	3.97222	+	14.8245i	0.236124	+	0.881227i	−0.741515	+	0.670936i	$0.765892\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.16749	+	20.9758i	0.541140	+	1.23816i
$288$		0			0
$289$	−13.6573	+	7.88506i	−0.803372	+	0.463827i
$290$		0			0
$291$	1.39392	−	2.41434i	0.0817129	−	0.141531i
$292$		0			0
$293$	17.4898	−	17.4898i	1.02176	−	1.02176i	0.0220045	−	0.999758i	$-0.492995\pi$
$293$	17.4898	−	17.4898i	1.02176	−	1.02176i	0.999758	−	0.0220045i	$-0.00700482\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.52408	−	0.676324i	0.146462	−	0.0392443i
$298$		0			0
$299$	2.72435	+	4.71871i	0.157553	+	0.272890i
$300$		0			0
$301$	2.84903	+	1.11608i	0.164215	+	0.0643296i
$302$		0			0
$303$	0.557514	−	2.08067i	0.0320283	−	0.119531i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	5.10251	+	5.10251i	0.291216	+	0.291216i	0.837560	−	0.546345i	$-0.183981\pi$
$307$	5.10251	+	5.10251i	0.291216	+	0.291216i	−0.546345	+	0.837560i	$0.683981\pi$
$308$		0			0
$309$		−	12.6960i		−	0.722248i
$310$		0			0
$311$	1.03506	+	0.597590i	0.0586927	+	0.0338862i	0.529059	−	0.848585i	$-0.322545\pi$
$311$	1.03506	+	0.597590i	0.0586927	+	0.0338862i	−0.470367	+	0.882471i	$0.655878\pi$
$312$		0			0
$313$	24.9485	+	6.68492i	1.41017	+	0.377854i	0.881986	−	0.471275i	$-0.156206\pi$
$313$	24.9485	+	6.68492i	1.41017	+	0.377854i	0.528185	+	0.849129i	$0.322873\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.8556	−	5.85619i	−1.22753	−	0.328916i	−0.413914	−	0.910316i	$-0.635839\pi$
$317$	−21.8556	−	5.85619i	−1.22753	−	0.328916i	−0.813618	+	0.581400i	$0.802505\pi$
$318$		0			0
$319$	8.63628	+	4.98616i	0.483539	+	0.279171i
$320$		0			0
$321$		−	10.5854i		−	0.590818i
$322$		0			0
$323$	−5.75320	−	5.75320i	−0.320116	−	0.320116i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.13648	−	7.97344i	0.118147	−	0.440932i
$328$		0			0
$329$	4.15713	+	27.4626i	0.229190	+	1.51406i
$330$		0			0
$331$	−7.57802	−	13.1255i	−0.416525	−	0.721443i	0.579062	−	0.815284i	$-0.303419\pi$
$331$	−7.57802	−	13.1255i	−0.416525	−	0.721443i	−0.995587	+	0.0938404i	$0.970086\pi$
$332$		0			0
$333$	3.25263	−	0.871539i	0.178243	−	0.0477600i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	21.1099	−	21.1099i	1.14993	−	1.14993i	0.163362	−	0.986566i	$-0.447766\pi$
$337$	21.1099	−	21.1099i	1.14993	−	1.14993i	0.986566	−	0.163362i	$-0.0522338\pi$
$338$		0			0
$339$	7.86564	−	13.6237i	0.427203	−	0.739937i
$340$		0			0
$341$	−17.4053	+	10.0489i	−0.942549	+	0.544181i
$342$		0			0
$343$	−6.08359	+	17.4926i	−0.328483	+	0.944510i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.19756	−	11.9334i	−0.171654	−	0.640621i	−0.997097	−	0.0761364i	$-0.975742\pi$
$347$	−3.19756	−	11.9334i	−0.171654	−	0.640621i	0.825443	−	0.564485i	$-0.190925\pi$
$348$		0			0
$349$	5.27965			0.282613			0.141307	−	0.989966i	$-0.454870\pi$
$349$	5.27965			0.282613			0.141307	+	0.989966i	$0.454870\pi$
$350$		0			0
$351$	3.53644			0.188761
$352$		0			0
$353$	4.78521	+	17.8586i	0.254691	+	0.950519i	0.968262	+	0.249937i	$0.0804098\pi$
$353$	4.78521	+	17.8586i	0.254691	+	0.950519i	−0.713571	+	0.700583i	$0.752924\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−2.36191	−	1.74086i	−0.125006	−	0.0921359i
$358$		0			0
$359$	−26.0976	+	15.0675i	−1.37738	+	0.795231i	−0.991844	−	0.127462i	$-0.959317\pi$
$359$	−26.0976	+	15.0675i	−1.37738	+	0.795231i	−0.385537	+	0.922692i	$0.625984\pi$
$360$		0			0
$361$	−17.4125	+	30.1593i	−0.916445	+	1.58733i
$362$		0			0
$363$	−2.94979	+	2.94979i	−0.154824	+	0.154824i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	25.0035	−	6.69965i	1.30517	−	0.349719i	0.461767	−	0.887001i	$-0.347216\pi$
$367$	25.0035	−	6.69965i	1.30517	−	0.349719i	0.843403	+	0.537282i	$0.180549\pi$
$368$		0			0
$369$	4.32612	+	7.49305i	0.225209	+	0.390073i
$370$		0			0
$371$	−0.0643279	+	0.0513666i	−0.00333974	+	0.00266682i
$372$		0			0
$373$	8.14929	−	30.4136i	0.421954	−	1.57475i	−0.348532	−	0.937297i	$-0.613320\pi$
$373$	8.14929	−	30.4136i	0.421954	−	1.57475i	0.770486	−	0.637457i	$-0.220014\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.54308	+	9.54308i	0.491493	+	0.491493i
$378$		0			0
$379$			2.34759i			0.120588i	0.998181	+	0.0602939i	$0.0192038\pi$
$379$			2.34759i			0.120588i	−0.998181	+	0.0602939i	$0.980796\pi$
$380$		0			0
$381$	7.81691	+	4.51310i	0.400472	+	0.231213i
$382$		0			0
$383$	−19.5369	−	5.23489i	−0.998287	−	0.267490i	−0.277560	−	0.960708i	$-0.589526\pi$
$383$	−19.5369	−	5.23489i	−0.998287	−	0.267490i	−0.720728	+	0.693218i	$0.756192\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.11710	+	0.299326i	0.0567854	+	0.0152156i
$388$		0			0
$389$	20.6731	+	11.9356i	1.04817	+	0.605160i	0.922136	−	0.386866i	$-0.126442\pi$
$389$	20.6731	+	11.9356i	1.04817	+	0.605160i	0.126032	+	0.992026i	$0.459776\pi$
$390$		0			0
$391$		−	1.70867i		−	0.0864114i
$392$		0			0
$393$	−8.26604	−	8.26604i	−0.416966	−	0.416966i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.61891	+	17.2380i	−0.231816	+	0.865150i	0.747742	+	0.663989i	$0.231138\pi$
$397$	−4.61891	+	17.2380i	−0.231816	+	0.865150i	−0.979558	+	0.201161i	$0.935529\pi$
$398$		0			0
$399$	−7.08006	+	18.0734i	−0.354446	+	0.904801i
$400$		0			0
$401$	13.2374	+	22.9278i	0.661043	+	1.14496i	0.980342	+	0.197305i	$0.0632191\pi$
$401$	13.2374	+	22.9278i	0.661043	+	1.14496i	−0.319299	+	0.947654i	$0.603448\pi$
$402$		0			0
$403$	−26.2725	+	7.03970i	−1.30873	+	0.350672i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.22206	−	6.22206i	0.308416	−	0.308416i
$408$		0			0
$409$	3.48825	−	6.04182i	0.172483	−	0.298749i	−0.766805	−	0.641881i	$-0.778154\pi$
$409$	3.48825	−	6.04182i	0.172483	−	0.298749i	0.939287	+	0.343132i	$0.111488\pi$
$410$		0			0
$411$	−7.49062	+	4.32471i	−0.369485	+	0.213322i
$412$		0			0
$413$	3.96077	−	35.3543i	0.194897	−	1.73967i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.65707	+	17.3804i	0.228058	+	0.851123i
$418$		0			0
$419$	20.2560			0.989568			0.494784	−	0.869016i	$-0.335247\pi$
$419$	20.2560			0.989568			0.494784	+	0.869016i	$0.335247\pi$
$420$		0			0
$421$	−33.7473			−1.64474			−0.822372	−	0.568950i	$-0.807350\pi$
$421$	−33.7473			−1.64474			−0.822372	+	0.568950i	$0.807350\pi$
$422$		0			0
$423$	2.71712	+	10.1404i	0.132111	+	0.493045i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−15.0918	+	20.4758i	−0.730341	+	0.990892i
$428$		0			0
$429$	8.00304	−	4.62056i	0.386390	−	0.223083i
$430$		0			0
$431$	−4.62323	+	8.00768i	−0.222693	+	0.385716i	−0.955625	−	0.294586i	$-0.904818\pi$
$431$	−4.62323	+	8.00768i	−0.222693	+	0.385716i	0.732932	+	0.680302i	$0.238152\pi$
$432$		0			0
$433$	−0.163149	+	0.163149i	−0.00784046	+	0.00784046i	−0.711016	−	0.703176i	$-0.751765\pi$
$433$	−0.163149	+	0.163149i	−0.00784046	+	0.00784046i	0.703176	+	0.711016i	$0.251765\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.9185	+	2.92560i	−0.522302	+	0.139950i
$438$		0			0
$439$	−1.13372	−	1.96367i	−0.0541097	−	0.0937207i	0.837702	−	0.546128i	$-0.183899\pi$
$439$	−1.13372	−	1.96367i	−0.0541097	−	0.0937207i	−0.891812	+	0.452407i	$0.850565\pi$
$440$		0			0
$441$	−1.54899	+	6.82647i	−0.0737615	+	0.325070i
$442$		0			0
$443$	−7.81659	+	29.1719i	−0.371377	+	1.38600i	0.487189	+	0.873297i	$0.338022\pi$
$443$	−7.81659	+	29.1719i	−0.371377	+	1.38600i	−0.858566	+	0.512703i	$0.828644\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	10.8932	+	10.8932i	0.515232	+	0.515232i
$448$		0			0
$449$			0.665009i			0.0313837i	0.999877	+	0.0156919i	$0.00499508\pi$
$449$			0.665009i			0.0313837i	−0.999877	+	0.0156919i	$0.995005\pi$
$450$		0			0
$451$	19.5802	+	11.3046i	0.921996	+	0.532315i
$452$		0			0
$453$	1.00220	+	0.268540i	0.0470877	+	0.0126171i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−24.0850	−	6.45356i	−1.12665	−	0.301885i	−0.353078	−	0.935594i	$-0.614865\pi$
$457$	−24.0850	−	6.45356i	−1.12665	−	0.301885i	−0.773571	+	0.633709i	$0.781532\pi$
$458$		0			0
$459$	−0.960424	−	0.554501i	−0.0448288	−	0.0258819i
$460$		0			0
$461$		−	8.67924i		−	0.404232i	−0.979362	−	0.202116i	$-0.935218\pi$
$461$		−	8.67924i		−	0.404232i	0.979362	−	0.202116i	$-0.0647819\pi$
$462$		0			0
$463$	−4.17474	−	4.17474i	−0.194017	−	0.194017i	0.603413	−	0.797429i	$-0.293807\pi$
$463$	−4.17474	−	4.17474i	−0.194017	−	0.194017i	−0.797429	+	0.603413i	$0.793807\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.275985	+	1.02999i	−0.0127711	+	0.0476623i	−0.972017	−	0.234909i	$-0.924521\pi$
$467$	−0.275985	+	1.02999i	−0.0127711	+	0.0476623i	0.959246	+	0.282571i	$0.0911874\pi$
$468$		0			0
$469$	15.4765	+	19.3817i	0.714638	+	0.894964i
$470$		0			0
$471$	6.36883	+	11.0311i	0.293460	+	0.508288i
$472$		0			0
$473$	2.91911	−	0.782174i	0.134221	−	0.0359644i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.0220010	+	0.0220010i	−0.00100736	+	0.00100736i
$478$		0			0
$479$	2.52994	−	4.38198i	0.115596	−	0.200218i	−0.802422	−	0.596757i	$-0.796456\pi$
$479$	2.52994	−	4.38198i	0.115596	−	0.200218i	0.918018	+	0.396539i	$0.129789\pi$
$480$		0			0
$481$	10.3130	−	5.95424i	0.470234	−	0.271490i
$482$		0			0
$483$	−3.73523	+	1.63248i	−0.169959	+	0.0742806i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	3.50758	+	13.0905i	0.158944	+	0.593186i	0.998735	+	0.0502772i	$0.0160105\pi$
$487$	3.50758	+	13.0905i	0.158944	+	0.593186i	−0.839792	+	0.542909i	$0.817323\pi$
$488$		0			0
$489$	−5.59244			−0.252899
$490$		0			0
$491$	−36.2774			−1.63718			−0.818588	−	0.574381i	$-0.805243\pi$
$491$	−36.2774			−1.63718			−0.818588	+	0.574381i	$0.805243\pi$
$492$		0			0
$493$	−1.09538	−	4.08803i	−0.0493336	−	0.184115i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.04486	−	3.95306i	0.405717	−	0.177319i
$498$		0			0
$499$	−33.8072	+	19.5186i	−1.51342	+	0.873772i	−0.513541	+	0.858065i	$0.671666\pi$
$499$	−33.8072	+	19.5186i	−1.51342	+	0.873772i	−0.999877	+	0.0157065i	$0.995000\pi$
$500$		0			0
$501$	−6.71773	+	11.6354i	−0.300126	+	0.519833i
$502$		0			0
$503$	20.9666	−	20.9666i	0.934854	−	0.934854i	−0.0631500	−	0.998004i	$-0.520115\pi$
$503$	20.9666	−	20.9666i	0.934854	−	0.934854i	0.998004	+	0.0631500i	$0.0201147\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.476796	+	0.127757i	−0.0211753	+	0.00567389i
$508$		0			0
$509$	2.33286	+	4.04063i	0.103402	+	0.179098i	0.913084	−	0.407771i	$-0.133694\pi$
$509$	2.33286	+	4.04063i	0.103402	+	0.179098i	−0.809682	+	0.586869i	$0.800360\pi$
$510$		0			0
$511$	13.5582	+	16.9794i	0.599781	+	0.751124i
$512$		0			0
$513$	−1.89884	+	7.08656i	−0.0838358	+	0.312879i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	19.3980	+	19.3980i	0.853121	+	0.853121i
$518$		0			0
$519$		−	18.8001i		−	0.825231i
$520$		0			0
$521$	−32.2184	−	18.6013i	−1.41152	−	0.814939i	−0.415984	−	0.909372i	$-0.636563\pi$
$521$	−32.2184	−	18.6013i	−1.41152	−	0.814939i	−0.995531	+	0.0944334i	$0.969896\pi$
$522$		0			0
$523$	33.0011	+	8.84263i	1.44304	+	0.386661i	0.893597	−	0.448871i	$-0.148174\pi$
$523$	33.0011	+	8.84263i	1.44304	+	0.386661i	0.549442	+	0.835532i	$0.314840\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.23888	+	2.20760i	0.358891	+	0.0961646i
$528$		0			0
$529$	17.8628	+	10.3131i	0.776642	+	0.448395i
$530$		0			0
$531$		−	13.4463i		−	0.583518i
$532$		0			0
$533$	21.6361	+	21.6361i	0.937164	+	0.937164i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.20682	−	23.1642i	0.267844	−	0.999607i
$538$		0			0
$539$	5.41377	+	17.4723i	0.233187	+	0.752585i
$540$		0			0
$541$	13.9932	+	24.2369i	0.601614	+	1.04203i	0.992577	+	0.121620i	$0.0388089\pi$
$541$	13.9932	+	24.2369i	0.601614	+	1.04203i	−0.390962	+	0.920407i	$0.627858\pi$
$542$		0			0
$543$	11.3547	−	3.04248i	0.487276	−	0.130565i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−24.9817	+	24.9817i	−1.06814	+	1.06814i	−0.0706379	+	0.997502i	$0.522503\pi$
$547$	−24.9817	+	24.9817i	−1.06814	+	1.06814i	−0.997502	+	0.0706379i	$0.977497\pi$
$548$		0			0
$549$	−4.80706	+	8.32607i	−0.205160	+	0.355348i
$550$		0			0
$551$	−24.2471	+	13.9991i	−1.03296	+	0.596380i
$552$		0			0
$553$	11.6906	−	15.8612i	0.497134	−	0.674487i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.28033	−	4.77825i	−0.0542492	−	0.202461i	0.933482	−	0.358624i	$-0.116754\pi$
$557$	−1.28033	−	4.77825i	−0.0542492	−	0.202461i	−0.987731	+	0.156163i	$0.950087\pi$
$558$		0			0
$559$	4.08992			0.172985
$560$		0			0
$561$	−2.89795			−0.122352
$562$		0			0
$563$	9.16492	+	34.2039i	0.386255	+	1.44152i	0.836179	+	0.548457i	$0.184784\pi$
$563$	9.16492	+	34.2039i	0.386255	+	1.44152i	−0.449924	+	0.893067i	$0.648549\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.294563	+	2.62930i	−0.0123705	+	0.110420i
$568$		0			0
$569$	20.8668	−	12.0475i	0.874784	−	0.505057i	0.00584864	−	0.999983i	$-0.498138\pi$
$569$	20.8668	−	12.0475i	0.874784	−	0.505057i	0.868935	+	0.494926i	$0.164805\pi$
$570$		0			0
$571$	9.60115	−	16.6297i	0.401796	−	0.695931i	−0.592147	−	0.805830i	$-0.701719\pi$
$571$	9.60115	−	16.6297i	0.401796	−	0.695931i	0.993943	+	0.109899i	$0.0350528\pi$
$572$		0			0
$573$	8.58219	−	8.58219i	0.358526	−	0.358526i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−43.1731	+	11.5682i	−1.79732	+	0.481591i	−0.993555	−	0.113355i	$-0.963840\pi$
$577$	−43.1731	+	11.5682i	−1.79732	+	0.481591i	−0.803766	+	0.594945i	$0.797174\pi$
$578$		0			0
$579$	4.43512	+	7.68185i	0.184317	+	0.319247i
$580$		0			0
$581$	12.7436	−	32.5308i	0.528694	−	1.34961i
$582$		0			0
$583$	−0.0210432	+	0.0785343i	−0.000871520	+	0.00325256i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	31.3904	+	31.3904i	1.29562	+	1.29562i	0.931258	+	0.364361i	$0.118713\pi$
$587$	31.3904	+	31.3904i	1.29562	+	1.29562i	0.364361	+	0.931258i	$0.381287\pi$
$588$		0			0
$589$		−	56.4266i		−	2.32502i
$590$		0			0
$591$	3.95622	+	2.28413i	0.162737	+	0.0939564i
$592$		0			0
$593$	23.6695	+	6.34221i	0.971988	+	0.260443i	0.709667	−	0.704537i	$-0.248845\pi$
$593$	23.6695	+	6.34221i	0.971988	+	0.260443i	0.262321	+	0.964981i	$0.415512\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−14.4855	−	3.88139i	−0.592854	−	0.158855i
$598$		0			0
$599$	−19.6337	−	11.3355i	−0.802209	−	0.463156i	0.0420338	−	0.999116i	$-0.486616\pi$
$599$	−19.6337	−	11.3355i	−0.802209	−	0.463156i	−0.844243	+	0.535960i	$0.819950\pi$
$600$		0			0
$601$		−	19.4984i		−	0.795358i	−0.917525	−	0.397679i	$-0.869816\pi$
$601$		−	19.4984i		−	0.795358i	0.917525	−	0.397679i	$-0.130184\pi$
$602$		0			0
$603$	6.62879	+	6.62879i	0.269945	+	0.269945i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−1.91320	+	7.14016i	−0.0776544	+	0.289810i	−0.993822	−	0.110985i	$-0.964599\pi$
$607$	−1.91320	+	7.14016i	−0.0776544	+	0.289810i	0.916168	+	0.400795i	$0.131266\pi$
$608$		0			0
$609$	−7.89005	+	6.30030i	−0.319721	+	0.255301i
$610$		0			0
$611$	18.5630	+	32.1521i	0.750979	+	1.30073i
$612$		0			0
$613$	−4.89323	+	1.31114i	−0.197636	+	0.0529563i	−0.356279	−	0.934380i	$-0.615955\pi$
$613$	−4.89323	+	1.31114i	−0.197636	+	0.0529563i	0.158643	+	0.987336i	$0.449288\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.0610	+	12.0610i	−0.485559	+	0.485559i	−0.906902	−	0.421342i	$-0.861559\pi$
$617$	−12.0610	+	12.0610i	−0.485559	+	0.485559i	0.421342	+	0.906902i	$0.361559\pi$
$618$		0			0
$619$	15.5699	−	26.9679i	0.625808	−	1.08393i	−0.362577	−	0.931954i	$-0.618103\pi$
$619$	15.5699	−	26.9679i	0.625808	−	1.08393i	0.988384	−	0.151976i	$-0.0485638\pi$
$620$		0			0
$621$	−1.33431	+	0.770366i	−0.0535441	+	0.0309137i
$622$		0			0
$623$	−23.7009	−	17.4689i	−0.949556	−	0.699875i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	4.96188	+	18.5180i	0.198159	+	0.739538i
$628$		0			0
$629$	−3.73442			−0.148901
$630$		0			0
$631$	15.8402			0.630589			0.315295	−	0.948994i	$-0.397897\pi$
$631$	15.8402			0.630589			0.315295	+	0.948994i	$0.397897\pi$
$632$		0			0
$633$	0.636630	+	2.37593i	0.0253038	+	0.0944349i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.956989	+	24.7366i	0.0379173	+	0.980098i
$638$		0			0
$639$	3.23104	−	1.86544i	0.127818	−	0.0737956i
$640$		0			0
$641$	19.7449	−	34.1992i	0.779878	−	1.35079i	−0.152133	−	0.988360i	$-0.548614\pi$
$641$	19.7449	−	34.1992i	0.779878	−	1.35079i	0.932012	−	0.362429i	$-0.118052\pi$
$642$		0			0
$643$	14.0810	−	14.0810i	0.555301	−	0.555301i	−0.372665	−	0.927966i	$-0.621556\pi$
$643$	14.0810	−	14.0810i	0.555301	−	0.555301i	0.927966	+	0.372665i	$0.121556\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.3226	+	4.90953i	−0.720336	+	0.193014i	−0.600322	−	0.799759i	$-0.704961\pi$
$647$	−18.3226	+	4.90953i	−0.720336	+	0.193014i	−0.120015	+	0.992772i	$0.538294\pi$
$648$		0			0
$649$	−17.5683	−	30.4292i	−0.689616	−	1.19445i
$650$		0			0
$651$	−3.04560	−	20.1197i	−0.119367	−	0.788553i
$652$		0			0
$653$	2.87547	−	10.7314i	0.112526	−	0.419953i	−0.886564	−	0.462606i	$-0.846914\pi$
$653$	2.87547	−	10.7314i	0.112526	−	0.419953i	0.999090	+	0.0426535i	$0.0135811\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	5.80717	+	5.80717i	0.226559	+	0.226559i
$658$		0			0
$659$		−	1.30248i		−	0.0507373i	−0.999678	−	0.0253687i	$-0.991924\pi$
$659$		−	1.30248i		−	0.0507373i	0.999678	−	0.0253687i	$-0.00807596\pi$
$660$		0			0
$661$	−22.4023	−	12.9340i	−0.871347	−	0.503073i	−0.00355158	−	0.999994i	$-0.501131\pi$
$661$	−22.4023	−	12.9340i	−0.871347	−	0.503073i	−0.867796	+	0.496921i	$0.834464\pi$
$662$		0			0
$663$	−3.78828	−	1.01507i	−0.147125	−	0.0394219i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.67947	−	1.52181i	−0.219910	−	0.0589247i
$668$		0			0
$669$	3.88890	+	2.24526i	0.150354	+	0.0868068i
$670$		0			0
$671$			25.1228i			0.969854i
$672$		0			0
$673$	−16.5969	−	16.5969i	−0.639764	−	0.639764i	0.310734	−	0.950497i	$-0.399425\pi$
$673$	−16.5969	−	16.5969i	−0.639764	−	0.639764i	−0.950497	+	0.310734i	$0.899425\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.85119	+	10.6408i	−0.109580	+	0.408959i	−0.998824	−	0.0484737i	$-0.984564\pi$
$677$	−2.85119	+	10.6408i	−0.109580	+	0.408959i	0.889244	+	0.457433i	$0.151231\pi$
$678$		0			0
$679$	6.86775	+	2.69037i	0.263560	+	0.103247i
$680$		0			0
$681$	−12.9766	−	22.4761i	−0.497263	−	0.861285i
$682$		0			0
$683$	−8.16904	+	2.18889i	−0.312580	+	0.0837555i	−0.411698	−	0.911320i	$-0.635064\pi$
$683$	−8.16904	+	2.18889i	−0.312580	+	0.0837555i	0.0991188	+	0.995076i	$0.468398\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	17.8213	−	17.8213i	0.679926	−	0.679926i
$688$		0			0
$689$	−0.0550165	+	0.0952914i	−0.00209596	+	0.00363031i
$690$		0			0
$691$	−11.8344	+	6.83258i	−0.450201	+	0.259924i	−0.707915	−	0.706298i	$-0.750364\pi$
$691$	−11.8344	+	6.83258i	−0.450201	+	0.259924i	0.257714	+	0.966221i	$0.417031\pi$
$692$		0			0
$693$	2.76873	+	6.33504i	0.105175	+	0.240648i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.48346	−	9.26839i	−0.0940677	−	0.351065i
$698$		0			0
$699$	7.78095			0.294303
$700$		0			0
$701$	7.38773			0.279031			0.139515	−	0.990220i	$-0.455446\pi$
$701$	7.38773			0.279031			0.139515	+	0.990220i	$0.455446\pi$
$702$		0			0
$703$	6.39409	+	23.8631i	0.241157	+	0.900012i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.66370	+	0.634509i	0.213005	+	0.0238632i
$708$		0			0
$709$	−22.5859	+	13.0400i	−0.848233	+	0.489727i	−0.860054	−	0.510203i	$-0.829570\pi$
$709$	−22.5859	+	13.0400i	−0.848233	+	0.489727i	0.0118214	+	0.999930i	$0.496237\pi$
$710$		0			0
$711$	3.72371	−	6.44965i	0.139650	−	0.241881i
$712$		0			0
$713$	8.37922	−	8.37922i	0.313804	−	0.313804i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	9.34369	−	2.50364i	0.348947	−	0.0935000i
$718$		0			0
$719$	0.125473	+	0.217326i	0.00467937	+	0.00810490i	0.868356	−	0.495942i	$-0.165177\pi$
$719$	0.125473	+	0.217326i	0.00467937	+	0.00810490i	−0.863676	+	0.504047i	$0.831844\pi$
$720$		0			0
$721$	33.2120	−	5.02744i	1.23688	−	0.187232i
$722$		0			0
$723$	−0.166810	+	0.622543i	−0.00620373	+	0.0231526i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−9.99550	−	9.99550i	−0.370712	−	0.370712i	0.497024	−	0.867737i	$-0.334426\pi$
$727$	−9.99550	−	9.99550i	−0.370712	−	0.370712i	−0.867737	+	0.497024i	$0.834426\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−1.11074	−	0.641285i	−0.0410821	−	0.0237188i
$732$		0			0
$733$	−19.8818	−	5.32732i	−0.734352	−	0.196769i	−0.127786	−	0.991802i	$-0.540787\pi$
$733$	−19.8818	−	5.32732i	−0.734352	−	0.196769i	−0.606567	+	0.795033i	$0.707454\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	23.6620	+	6.34022i	0.871602	+	0.233545i
$738$		0			0
$739$	19.2594	+	11.1194i	0.708468	+	0.409034i	0.810494	−	0.585748i	$-0.199199\pi$
$739$	19.2594	+	11.1194i	0.708468	+	0.409034i	−0.102026	+	0.994782i	$0.532532\pi$
$740$		0			0
$741$			25.9452i			0.953122i
$742$		0			0
$743$	−11.2211	−	11.2211i	−0.411662	−	0.411662i	0.470655	−	0.882317i	$-0.344017\pi$
$743$	−11.2211	−	11.2211i	−0.411662	−	0.411662i	−0.882317	+	0.470655i	$0.844017\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.41777	−	12.7553i	0.125050	−	0.466692i
$748$		0			0
$749$	27.6908	−	4.19168i	1.01180	−	0.153161i
$750$		0			0
$751$	−4.85963	−	8.41712i	−0.177330	−	0.307145i	0.763635	−	0.645648i	$-0.223413\pi$
$751$	−4.85963	−	8.41712i	−0.177330	−	0.307145i	−0.940965	+	0.338503i	$0.890079\pi$
$752$		0			0
$753$	−14.6972	+	3.93811i	−0.535596	+	0.143513i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	33.1884	−	33.1884i	1.20625	−	1.20625i	0.234024	−	0.972231i	$-0.424811\pi$
$757$	33.1884	−	33.1884i	1.20625	−	1.20625i	0.972231	−	0.234024i	$-0.0751893\pi$
$758$		0			0
$759$	−2.01305	+	3.48671i	−0.0730692	+	0.126560i
$760$		0			0
$761$	0.886119	−	0.511601i	0.0321218	−	0.0185455i	−0.483853	−	0.875149i	$-0.660763\pi$
$761$	0.886119	−	0.511601i	0.0321218	−	0.0185455i	0.515975	+	0.856604i	$0.327430\pi$
$762$		0			0
$763$	21.7041	+	2.43153i	0.785742	+	0.0880274i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.3073	−	45.9315i	−0.444391	−	1.65849i
$768$		0			0
$769$	43.5377			1.57001			0.785005	−	0.619489i	$-0.212660\pi$
$769$	43.5377			1.57001			0.785005	+	0.619489i	$0.212660\pi$
$770$		0			0
$771$	−26.9834			−0.971785
$772$		0			0
$773$	−1.62096	−	6.04952i	−0.0583020	−	0.217586i	0.930629	−	0.365965i	$-0.119261\pi$
$773$	−1.62096	−	6.04952i	−0.0583020	−	0.217586i	−0.988931	+	0.148379i	$0.952594\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	3.56790	+	8.16359i	0.127998	+	0.292867i
$778$		0			0
$779$	−54.9731	+	31.7388i	−1.96962	+	1.13716i
$780$		0			0
$781$	4.87461	−	8.44307i	0.174427	−	0.302117i
$782$		0			0
$783$	−2.69850	+	2.69850i	−0.0964365	+	0.0964365i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−6.03236	+	1.61637i	−0.215030	+	0.0576172i	−0.364726	−	0.931115i	$-0.618837\pi$
$787$	−6.03236	+	1.61637i	−0.215030	+	0.0576172i	0.149696	+	0.988732i	$0.452171\pi$
$788$		0			0
$789$	−6.71135	−	11.6244i	−0.238930	−	0.413839i
$790$		0			0
$791$	38.7536	+	15.1813i	1.37792	+	0.539785i
$792$		0			0
$793$	−8.79977	+	32.8412i	−0.312489	+	1.16622i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	19.3409	+	19.3409i	0.685089	+	0.685089i	0.961142	−	0.276054i	$-0.0890268\pi$
$797$	19.3409	+	19.3409i	0.685089	+	0.685089i	−0.276054	+	0.961142i	$0.589027\pi$
$798$		0			0
$799$		−	11.6425i		−	0.411881i
$800$		0			0
$801$	−9.63750	−	5.56421i	−0.340524	−	0.196602i
$802$		0			0
$803$	20.7292	+	5.55436i	0.731517	+	0.196009i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−14.8971	−	3.99168i	−0.524404	−	0.140514i
$808$		0			0
$809$	−11.5898	−	6.69139i	−0.407477	−	0.235257i	0.282228	−	0.959347i	$-0.408926\pi$
$809$	−11.5898	−	6.69139i	−0.407477	−	0.235257i	−0.689705	+	0.724090i	$0.742260\pi$
$810$		0			0
$811$			22.6255i			0.794490i	0.917713	+	0.397245i	$0.130034\pi$
$811$			22.6255i			0.794490i	−0.917713	+	0.397245i	$0.869966\pi$
$812$		0			0
$813$	−0.477554	−	0.477554i	−0.0167485	−	0.0167485i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.19602	+	8.19567i	−0.0768291	+	0.286730i
$818$		0			0
$819$	1.40038	+	9.25114i	0.0489334	+	0.323261i
$820$		0			0
$821$	0.945055	+	1.63688i	0.0329827	+	0.0571276i	0.882046	−	0.471164i	$-0.156166\pi$
$821$	0.945055	+	1.63688i	0.0329827	+	0.0571276i	−0.849063	+	0.528292i	$0.822833\pi$
$822$		0			0
$823$	12.4134	−	3.32617i	0.432705	−	0.115943i	−0.0358905	−	0.999356i	$-0.511427\pi$
$823$	12.4134	−	3.32617i	0.432705	−	0.115943i	0.468596	+	0.883413i	$0.344760\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.57643	+	6.57643i	−0.228685	+	0.228685i	−0.812143	−	0.583458i	$-0.801699\pi$
$827$	−6.57643	+	6.57643i	−0.228685	+	0.228685i	0.583458	+	0.812143i	$0.301699\pi$
$828$		0			0
$829$	−25.7054	+	44.5230i	−0.892785	+	1.54635i	−0.0562634	+	0.998416i	$0.517919\pi$
$829$	−25.7054	+	44.5230i	−0.892785	+	1.54635i	−0.836522	+	0.547933i	$0.815415\pi$
$830$		0			0
$831$	11.2357	−	6.48694i	0.389762	−	0.225029i
$832$		0			0
$833$	3.61871	−	6.86800i	0.125381	−	0.237962i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.99062	−	7.42909i	−0.0688058	−	0.256787i
$838$		0			0
$839$	11.0847			0.382685			0.191342	−	0.981523i	$-0.438716\pi$
$839$	11.0847			0.382685			0.191342	+	0.981523i	$0.438716\pi$
$840$		0			0
$841$	14.4362			0.497800
$842$		0			0
$843$	−5.49796	−	20.5187i	−0.189360	−	0.706700i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.88457	−	6.54842i	−0.305278	−	0.225006i
$848$		0			0
$849$	−13.2913	+	7.67374i	−0.456157	+	0.263362i
$850$		0			0
$851$	−2.59410	+	4.49312i	−0.0889247	+	0.154022i
$852$		0			0
$853$	−12.4523	+	12.4523i	−0.426359	+	0.426359i	−0.887386	−	0.461027i	$-0.847481\pi$
$853$	−12.4523	+	12.4523i	−0.426359	+	0.426359i	0.461027	+	0.887386i	$0.347481\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.28129	+	1.68307i	−0.214565	+	0.0574925i	−0.364500	−	0.931203i	$-0.618760\pi$
$857$	−6.28129	+	1.68307i	−0.214565	+	0.0574925i	0.149935	+	0.988696i	$0.452093\pi$
$858$		0			0
$859$	−0.159908	−	0.276969i	−0.00545599	−	0.00945005i	0.863285	−	0.504718i	$-0.168403\pi$
$859$	−0.159908	−	0.276969i	−0.00545599	−	0.00945005i	−0.868741	+	0.495268i	$0.835070\pi$
$860$		0			0
$861$	−17.8884	+	14.2841i	−0.609634	+	0.486799i
$862$		0			0
$863$	−3.82517	+	14.2757i	−0.130210	+	0.485951i	−0.999972	−	0.00752126i	$-0.997606\pi$
$863$	−3.82517	+	14.2757i	−0.130210	+	0.485951i	0.869762	+	0.493472i	$0.164273\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−11.1512	−	11.1512i	−0.378713	−	0.378713i
$868$		0			0
$869$		−	19.4609i		−	0.660167i
$870$		0			0
$871$	28.7108	+	16.5762i	0.972830	+	0.561663i
$872$		0			0
$873$	2.69284	+	0.721545i	0.0911389	+	0.0244206i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.98971	−	0.533141i	−0.0671877	−	0.0180029i	0.225069	−	0.974343i	$-0.427739\pi$
$877$	−1.98971	−	0.533141i	−0.0671877	−	0.0180029i	−0.292256	+	0.956340i	$0.594406\pi$
$878$		0			0
$879$	21.4205	+	12.3671i	0.722495	+	0.417133i
$880$		0			0
$881$		−	28.5054i		−	0.960372i	−0.877167	−	0.480186i	$-0.840569\pi$
$881$		−	28.5054i		−	0.960372i	0.877167	−	0.480186i	$-0.159431\pi$
$882$		0			0
$883$	−22.8816	−	22.8816i	−0.770028	−	0.770028i	0.208083	−	0.978111i	$-0.433277\pi$
$883$	−22.8816	−	22.8816i	−0.770028	−	0.770028i	−0.978111	+	0.208083i	$0.933277\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.0294	−	52.3584i	0.471061	−	1.75802i	−0.164910	−	0.986309i	$-0.552733\pi$
$887$	14.0294	−	52.3584i	0.471061	−	1.75802i	0.635971	−	0.771713i	$-0.280600\pi$
$888$		0			0
$889$	−8.71063	+	22.2358i	−0.292145	+	0.745764i
$890$		0			0
$891$	1.30656	+	2.26302i	0.0437713	+	0.0758142i
$892$		0			0
$893$	−74.3957	+	19.9343i	−2.48956	+	0.667075i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−3.85281	+	3.85281i	−0.128642	+	0.128642i
$898$		0			0
$899$	14.6757	−	25.4191i	0.489463	−	0.847774i
$900$		0			0
$901$	0.0298827	−	0.0172528i	0.000995538	−	0.000574774i
$902$		0			0
$903$	−0.340665	+	3.04081i	−0.0113366	+	0.101192i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.597697	−	2.23064i	−0.0198462	−	0.0740670i	0.955293	−	0.295662i	$-0.0955403\pi$
$907$	−0.597697	−	2.23064i	−0.0198462	−	0.0740670i	−0.975139	+	0.221595i	$0.928874\pi$
$908$		0			0
$909$	2.15407			0.0714459
$910$		0			0
$911$	−8.82541			−0.292399			−0.146199	−	0.989255i	$-0.546704\pi$
$911$	−8.82541			−0.292399			−0.146199	+	0.989255i	$0.546704\pi$
$912$		0			0
$913$	−8.93104	−	33.3311i	−0.295574	−	1.10310i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	18.3503	−	24.8968i	0.605980	−	0.822164i
$918$		0			0
$919$	3.73429	−	2.15599i	0.123183	−	0.0711197i	−0.437142	−	0.899392i	$-0.644009\pi$
$919$	3.73429	−	2.15599i	0.123183	−	0.0711197i	0.560325	+	0.828273i	$0.310676\pi$
$920$		0			0
$921$	−3.60802	+	6.24928i	−0.118888	+	0.205921i
$922$		0			0
$923$	9.32958	−	9.32958i	0.307087	−	0.307087i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	12.2633	−	3.28595i	0.402781	−	0.107925i
$928$		0			0
$929$	−3.18089	−	5.50946i	−0.104362	−	0.180760i	0.809116	−	0.587650i	$-0.199947\pi$
$929$	−3.18089	−	5.50946i	−0.104362	−	0.180760i	−0.913477	+	0.406890i	$0.866613\pi$
$930$		0			0
$931$	−50.0827	−	11.3642i	−1.64139	−	0.372448i
$932$		0			0
$933$	−0.309335	+	1.15446i	−0.0101272	+	0.0377952i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−25.2849	−	25.2849i	−0.826020	−	0.826020i	0.160943	−	0.986964i	$-0.448546\pi$
$937$	−25.2849	−	25.2849i	−0.826020	−	0.826020i	−0.986964	+	0.160943i	$0.948546\pi$
$938$		0			0
$939$			25.8286i			0.842883i
$940$		0			0
$941$	−48.9931	−	28.2862i	−1.59713	−	0.922104i	−0.992037	−	0.125949i	$-0.959802\pi$
$941$	−48.9931	−	28.2862i	−1.59713	−	0.922104i	−0.605094	−	0.796154i	$-0.706864\pi$
$942$		0			0
$943$	−12.8765	−	3.45025i	−0.419317	−	0.112356i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.9164	−	4.26478i	−0.517212	−	0.138587i	−0.00923540	−	0.999957i	$-0.502940\pi$
$947$	−15.9164	−	4.26478i	−0.517212	−	0.138587i	−0.507977	+	0.861371i	$0.669606\pi$
$948$		0			0
$949$	25.1522	+	14.5216i	0.816475	+	0.471392i
$950$		0			0
$951$		−	22.6266i		−	0.733717i
$952$		0			0
$953$	−6.25650	−	6.25650i	−0.202668	−	0.202668i	0.598474	−	0.801142i	$-0.295774\pi$
$953$	−6.25650	−	6.25650i	−0.202668	−	0.202668i	−0.801142	+	0.598474i	$0.795774\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.58103	+	9.63252i	−0.0834327	+	0.311375i
$958$		0			0
$959$	−14.2794	−	17.8826i	−0.461107	−	0.577458i
$960$		0			0
$961$	14.0770	+	24.3820i	0.454096	+	0.786517i
$962$		0			0
$963$	10.2247	−	2.73970i	0.329486	−	0.0882855i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	41.6676	−	41.6676i	1.33994	−	1.33994i	0.443828	−	0.896112i	$-0.353620\pi$
$967$	41.6676	−	41.6676i	1.33994	−	1.33994i	0.896112	−	0.443828i	$-0.146380\pi$
$968$		0			0
$969$	4.06812	−	7.04620i	0.130687	−	0.226356i
$970$		0			0
$971$	22.4033	−	12.9346i	0.718957	−	0.415090i	−0.0954119	−	0.995438i	$-0.530417\pi$
$971$	22.4033	−	12.9346i	0.718957	−	0.415090i	0.814369	+	0.580348i	$0.197083\pi$
$972$		0			0
$973$	−43.6222	+	19.0651i	−1.39846	+	0.611199i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.3375	−	38.5800i	−0.330726	−	1.23428i	−0.908429	−	0.418038i	$-0.862718\pi$
$977$	−10.3375	−	38.5800i	−0.330726	−	1.23428i	0.577704	−	0.816246i	$-0.303949\pi$
$978$		0			0
$979$	−29.0799			−0.929396
$980$		0			0
$981$	8.25471			0.263553
$982$		0			0
$983$	−1.32838	−	4.95757i	−0.0423687	−	0.158122i	0.941500	−	0.337012i	$-0.109416\pi$
$983$	−1.32838	−	4.95757i	−0.0423687	−	0.158122i	−0.983869	+	0.178890i	$0.942749\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−25.4509	+	11.1233i	−0.810111	+	0.354060i
$988$		0			0
$989$	−1.54314	+	0.890934i	−0.0490691	+	0.0283301i
$990$		0			0
$991$	−5.68862	+	9.85297i	−0.180705	+	0.312990i	−0.942121	−	0.335274i	$-0.891171\pi$
$991$	−5.68862	+	9.85297i	−0.180705	+	0.312990i	0.761416	+	0.648264i	$0.224505\pi$
$992$		0			0
$993$	10.7169	−	10.7169i	0.340092	−	0.340092i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	23.5455	−	6.30900i	0.745693	−	0.199808i	0.134086	−	0.990970i	$-0.457190\pi$
$997$	23.5455	−	6.30900i	0.745693	−	0.199808i	0.611607	+	0.791162i	$0.290523\pi$
$998$		0			0
$999$	1.68368	+	2.91623i	0.0532694	+	0.0922653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.e.493.7		32
5.2	odd	4	inner	2100.2.ce.e.157.7		32
5.3	odd	4		420.2.bo.a.157.4	yes	32
5.4	even	2		420.2.bo.a.73.3	✓	32
7.5	odd	6	inner	2100.2.ce.e.1993.7		32
15.8	even	4		1260.2.dq.c.577.1		32
15.14	odd	2		1260.2.dq.c.73.3		32
35.3	even	12		2940.2.x.c.97.1		32
35.4	even	6		2940.2.x.c.1273.1		32
35.12	even	12	inner	2100.2.ce.e.1657.7		32
35.18	odd	12		2940.2.x.c.97.13		32
35.19	odd	6		420.2.bo.a.313.4	yes	32
35.24	odd	6		2940.2.x.c.1273.13		32
35.33	even	12		420.2.bo.a.397.3	yes	32
105.68	odd	12		1260.2.dq.c.397.3		32
105.89	even	6		1260.2.dq.c.1153.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.3	✓	32	5.4	even	2
420.2.bo.a.157.4	yes	32	5.3	odd	4
420.2.bo.a.313.4	yes	32	35.19	odd	6
420.2.bo.a.397.3	yes	32	35.33	even	12
1260.2.dq.c.73.3		32	15.14	odd	2
1260.2.dq.c.397.3		32	105.68	odd	12
1260.2.dq.c.577.1		32	15.8	even	4
1260.2.dq.c.1153.1		32	105.89	even	6
2100.2.ce.e.157.7		32	5.2	odd	4	inner
2100.2.ce.e.493.7		32	1.1	even	1	trivial
2100.2.ce.e.1657.7		32	35.12	even	12	inner
2100.2.ce.e.1993.7		32	7.5	odd	6	inner
2940.2.x.c.97.1		32	35.3	even	12
2940.2.x.c.97.13		32	35.18	odd	12
2940.2.x.c.1273.1		32	35.4	even	6
2940.2.x.c.1273.13		32	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{3} +(-2.42432 + 1.05955i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{3} +(-2.42432 + 1.05955i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-1.30656 + 2.26302i) q^{11} +(-2.50064 + 2.50064i) q^{13} +(1.07121 - 0.287031i) q^{17} +(-3.66827 - 6.35364i) q^{19} +(-1.65091 - 2.06749i) q^{21} +(0.398771 - 1.48823i) q^{23} +(-0.707107 - 0.707107i) q^{27} -3.81626i q^{29} +(6.66074 + 3.84558i) q^{31} +(-2.52408 - 0.676324i) q^{33} +(-3.25263 - 0.871539i) q^{37} +(-3.06264 - 1.76822i) q^{39} -8.65223i q^{41} +(-0.817775 - 0.817775i) q^{43} +(2.71712 - 10.1404i) q^{47} +(4.75470 - 5.13740i) q^{49} +(0.554501 + 0.960424i) q^{51} +(0.0300539 - 0.00805292i) q^{53} +(5.18772 - 5.18772i) q^{57} +(-6.72313 + 11.6448i) q^{59} +(8.32607 - 4.80706i) q^{61} +(1.56975 - 2.12976i) q^{63} +(-2.42631 - 9.05510i) q^{67} +1.54073 q^{69} -3.73088 q^{71} +(-2.12557 - 7.93274i) q^{73} +(0.769727 - 6.87067i) q^{77} +(-6.44965 + 3.72371i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-9.33753 + 9.33753i) q^{83} +(3.68622 - 0.987720i) q^{87} +(5.56421 + 9.63750i) q^{89} +(3.41280 - 8.71192i) q^{91} +(-1.99062 + 7.42909i) q^{93} +(-1.97130 - 1.97130i) q^{97} -2.61312i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) \) 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Introduction

L-functions

Modular forms

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