LMFDB - Embedded newform 2100.2.ce.b.1657.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1657.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2100.1657
Dual form			2100.2.ce.b.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{3} +(1.15539 + 2.38014i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{3} +(1.15539 + 2.38014i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(0.707107 + 0.707107i) q^{13} +(-6.50266 - 1.74238i) q^{17} +(4.23205 - 7.33013i) q^{19} +(-2.59808 + 0.500000i) q^{21} +(-1.93185 - 7.20977i) q^{23} +(0.707107 - 0.707107i) q^{27} -6.92820i q^{29} +(-1.73205 + 1.00000i) q^{31} +(2.63896 - 0.707107i) q^{33} +(10.8147 - 2.89778i) q^{37} +(-0.866025 + 0.500000i) q^{39} +4.19615i q^{41} +(0.378937 - 0.378937i) q^{43} +(2.63896 + 9.84873i) q^{47} +(-4.33013 + 5.50000i) q^{49} +(3.36603 - 5.83013i) q^{51} +(8.43451 + 2.26002i) q^{53} +(5.98502 + 5.98502i) q^{57} +(-4.63397 - 8.02628i) q^{59} +(-8.42820 - 4.86603i) q^{61} +(0.189469 - 2.63896i) q^{63} +(-1.81173 + 6.76148i) q^{67} +7.46410 q^{69} -8.00000 q^{71} +(3.98382 - 14.8678i) q^{73} +(4.05317 - 5.98502i) q^{77} +(1.96410 + 1.13397i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.34607 + 3.34607i) q^{83} +(6.69213 + 1.79315i) q^{87} +(3.63397 - 6.29423i) q^{89} +(-0.866025 + 2.50000i) q^{91} +(-0.517638 - 1.93185i) q^{93} +(-2.50026 + 2.50026i) q^{97} +2.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{11} + 20 q^{19} + 20 q^{51} - 44 q^{59} - 12 q^{61} + 32 q^{69} - 64 q^{71} - 12 q^{79} + 4 q^{81} + 36 q^{89}+O(q^{100}) $ 8 * q - 4 * q^11 + 20 * q^19 + 20 * q^51 - 44 * q^59 - 12 * q^61 + 32 * q^69 - 64 * q^71 - 12 * q^79 + 4 * q^81 + 36 * q^89

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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
$7$	1.15539	+	2.38014i	0.436698	+	0.899608i
$7$	1.15539	+	2.38014i	0.436698	+	0.899608i
$8$		0			0
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	0.583222	−	0.812313i	$-0.301792\pi$
$11$	−1.36603	−	2.36603i	−0.411872	−	0.713384i	−0.995094	+	0.0989291i	$0.968458\pi$
$12$		0			0
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i	0.798333	−	0.602217i	$-0.205716\pi$
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i	−0.602217	+	0.798333i	$0.705716\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.50266	−	1.74238i	−1.57713	−	0.422590i	−0.639092	−	0.769130i	$-0.720690\pi$
$17$	−6.50266	−	1.74238i	−1.57713	−	0.422590i	−0.938035	+	0.346540i	$0.887356\pi$
$18$		0			0
$19$	4.23205	−	7.33013i	0.970899	−	1.68165i	0.278046	−	0.960568i	$-0.410313\pi$
$19$	4.23205	−	7.33013i	0.970899	−	1.68165i	0.692853	−	0.721079i	$-0.256353\pi$
$20$		0			0
$21$	−2.59808	+	0.500000i	−0.566947	+	0.109109i
$22$		0			0
$23$	−1.93185	−	7.20977i	−0.402819	−	1.50334i	−0.808043	−	0.589123i	$-0.799473\pi$
$23$	−1.93185	−	7.20977i	−0.402819	−	1.50334i	0.405224	−	0.914217i	$-0.367193\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	6.92820i		−	1.28654i	−0.765641	−	0.643268i	$-0.777578\pi$
$29$		−	6.92820i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$30$		0			0
$31$	−1.73205	+	1.00000i	−0.311086	+	0.179605i	−0.647412	−	0.762140i	$-0.724149\pi$
$31$	−1.73205	+	1.00000i	−0.311086	+	0.179605i	0.336327	+	0.941745i	$0.390815\pi$
$32$		0			0
$33$	2.63896	−	0.707107i	0.459384	−	0.123091i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	10.8147	−	2.89778i	1.77792	−	0.476392i	0.787717	−	0.616038i	$-0.211263\pi$
$37$	10.8147	−	2.89778i	1.77792	−	0.476392i	0.990201	+	0.139646i	$0.0445965\pi$
$38$		0			0
$39$	−0.866025	+	0.500000i	−0.138675	+	0.0800641i
$40$		0			0
$41$			4.19615i			0.655329i	0.944794	+	0.327664i	$0.106262\pi$
$41$			4.19615i			0.655329i	−0.944794	+	0.327664i	$0.893738\pi$
$42$		0			0
$43$	0.378937	−	0.378937i	0.0577874	−	0.0577874i	−0.677623	−	0.735410i	$-0.736990\pi$
$43$	0.378937	−	0.378937i	0.0577874	−	0.0577874i	0.735410	+	0.677623i	$0.236990\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.63896	+	9.84873i	0.384932	+	1.43658i	0.838275	+	0.545248i	$0.183565\pi$
$47$	2.63896	+	9.84873i	0.384932	+	1.43658i	−0.453343	+	0.891336i	$0.649769\pi$
$48$		0			0
$49$	−4.33013	+	5.50000i	−0.618590	+	0.785714i
$50$		0			0
$51$	3.36603	−	5.83013i	0.471338	−	0.816381i
$52$		0			0
$53$	8.43451	+	2.26002i	1.15857	+	0.310438i	0.786394	−	0.617725i	$-0.211945\pi$
$53$	8.43451	+	2.26002i	1.15857	+	0.310438i	0.372175	+	0.928163i	$0.378612\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.98502	+	5.98502i	0.792736	+	0.792736i
$58$		0			0
$59$	−4.63397	−	8.02628i	−0.603292	−	1.04493i	−0.992319	−	0.123706i	$-0.960522\pi$
$59$	−4.63397	−	8.02628i	−0.603292	−	1.04493i	0.389027	−	0.921226i	$-0.372811\pi$
$60$		0			0
$61$	−8.42820	−	4.86603i	−1.07912	−	0.623031i	−0.148462	−	0.988918i	$-0.547432\pi$
$61$	−8.42820	−	4.86603i	−1.07912	−	0.623031i	−0.930659	+	0.365887i	$0.880766\pi$
$62$		0			0
$63$	0.189469	−	2.63896i	0.0238708	−	0.332478i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.81173	+	6.76148i	−0.221338	+	0.826046i	0.762500	+	0.646988i	$0.223972\pi$
$67$	−1.81173	+	6.76148i	−0.221338	+	0.826046i	−0.983838	+	0.179058i	$0.942695\pi$
$68$		0			0
$69$	7.46410			0.898572
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	3.98382	−	14.8678i	0.466271	−	1.74015i	−0.186370	−	0.982480i	$-0.559672\pi$
$73$	3.98382	−	14.8678i	0.466271	−	1.74015i	0.652641	−	0.757668i	$-0.273661\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.05317	−	5.98502i	0.461902	−	0.682057i
$78$		0			0
$79$	1.96410	+	1.13397i	0.220979	+	0.127582i	0.606403	−	0.795157i	$-0.292612\pi$
$79$	1.96410	+	1.13397i	0.220979	+	0.127582i	−0.385425	+	0.922739i	$0.625945\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	3.34607	+	3.34607i	0.367278	+	0.367278i	0.866484	−	0.499205i	$-0.166375\pi$
$83$	3.34607	+	3.34607i	0.367278	+	0.367278i	−0.499205	+	0.866484i	$0.666375\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.69213	+	1.79315i	0.717472	+	0.192246i
$88$		0			0
$89$	3.63397	−	6.29423i	0.385201	−	0.667187i	−0.606596	−	0.795010i	$-0.707466\pi$
$89$	3.63397	−	6.29423i	0.385201	−	0.667187i	0.991797	+	0.127823i	$0.0407989\pi$
$90$		0			0
$91$	−0.866025	+	2.50000i	−0.0907841	+	0.262071i
$92$		0			0
$93$	−0.517638	−	1.93185i	−0.0536766	−	0.200324i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.50026	+	2.50026i	−0.253863	+	0.253863i	−0.822552	−	0.568690i	$-0.807451\pi$
$97$	−2.50026	+	2.50026i	−0.253863	+	0.253863i	0.568690	+	0.822552i	$0.307451\pi$
$98$		0			0
$99$			2.73205i			0.274581i
$100$		0			0
$101$	5.83013	−	3.36603i	0.580119	−	0.334932i	−0.181061	−	0.983472i	$-0.557953\pi$
$101$	5.83013	−	3.36603i	0.580119	−	0.334932i	0.761181	+	0.648540i	$0.224620\pi$
$102$		0			0
$103$	4.50146	−	1.20616i	0.443542	−	0.118847i	−0.0301341	−	0.999546i	$-0.509593\pi$
$103$	4.50146	−	1.20616i	0.443542	−	0.118847i	0.473676	+	0.880699i	$0.342927\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.2301	+	3.81294i	−1.37567	+	0.368610i	−0.869547	−	0.493850i	$-0.835589\pi$
$107$	−14.2301	+	3.81294i	−1.37567	+	0.368610i	−0.506125	+	0.862460i	$0.668923\pi$
$108$		0			0
$109$	12.0622	−	6.96410i	1.15535	−	0.667040i	0.205163	−	0.978728i	$-0.434228\pi$
$109$	12.0622	−	6.96410i	1.15535	−	0.667040i	0.950185	+	0.311688i	$0.100894\pi$
$110$		0			0
$111$			11.1962i			1.06269i
$112$		0			0
$113$	6.03579	−	6.03579i	0.567800	−	0.567800i	−0.363712	−	0.931511i	$-0.618491\pi$
$113$	6.03579	−	6.03579i	0.567800	−	0.567800i	0.931511	+	0.363712i	$0.118491\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.258819	−	0.965926i	−0.0239278	−	0.0892999i
$118$		0			0
$119$	−3.36603	−	17.4904i	−0.308563	−	1.60334i
$120$		0			0
$121$	1.76795	−	3.06218i	0.160723	−	0.278380i
$122$		0			0
$123$	−4.05317	−	1.08604i	−0.365462	−	0.0979253i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.0507680	+	0.0507680i	0.00450493	+	0.00450493i	0.709356	−	0.704851i	$-0.248986\pi$
$127$	0.0507680	+	0.0507680i	0.00450493	+	0.00450493i	−0.704851	+	0.709356i	$0.748986\pi$
$128$		0			0
$129$	0.267949	+	0.464102i	0.0235916	+	0.0408619i
$130$		0			0
$131$	14.6603	+	8.46410i	1.28087	+	0.739512i	0.977008	−	0.213203i	$-0.0683897\pi$
$131$	14.6603	+	8.46410i	1.28087	+	0.739512i	0.303864	+	0.952715i	$0.401723\pi$
$132$		0			0
$133$	22.3364	+	1.60368i	1.93681	+	0.139057i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.55291	−	5.79555i	0.132674	−	0.495148i	−0.867322	−	0.497747i	$-0.834161\pi$
$137$	1.55291	−	5.79555i	0.132674	−	0.495148i	0.999997	+	0.00259945i	$0.000827431\pi$
$138$		0			0
$139$	−16.8564			−1.42974			−0.714871	−	0.699256i	$-0.753515\pi$
$139$	−16.8564			−1.42974			−0.714871	+	0.699256i	$0.753515\pi$
$140$		0			0
$141$	−10.1962			−0.858671
$142$		0			0
$143$	0.707107	−	2.63896i	0.0591312	−	0.220681i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.19187	−	5.60609i	−0.345740	−	0.462382i
$148$		0			0
$149$	−7.90192	−	4.56218i	−0.647351	−	0.373748i	0.140090	−	0.990139i	$-0.455261\pi$
$149$	−7.90192	−	4.56218i	−0.647351	−	0.373748i	−0.787441	+	0.616391i	$0.788594\pi$
$150$		0			0
$151$	5.33013	+	9.23205i	0.433760	+	0.751294i	0.997193	−	0.0748675i	$-0.0238534\pi$
$151$	5.33013	+	9.23205i	0.433760	+	0.751294i	−0.563434	+	0.826161i	$0.690520\pi$
$152$		0			0
$153$	4.76028	+	4.76028i	0.384846	+	0.384846i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.4183	+	3.32748i	0.991091	+	0.265562i	0.717709	−	0.696343i	$-0.245191\pi$
$157$	12.4183	+	3.32748i	0.991091	+	0.265562i	0.273382	+	0.961905i	$0.411858\pi$
$158$		0			0
$159$	−4.36603	+	7.56218i	−0.346248	+	0.599720i
$160$		0			0
$161$	14.9282	−	12.9282i	1.17651	−	1.01889i
$162$		0			0
$163$	−0.776457	−	2.89778i	−0.0608168	−	0.226971i	0.928828	−	0.370512i	$-0.120818\pi$
$163$	−0.776457	−	2.89778i	−0.0608168	−	0.226971i	−0.989644	+	0.143541i	$0.954151\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.240237	−	0.240237i	0.0185901	−	0.0185901i	−0.697751	−	0.716341i	$-0.745816\pi$
$167$	0.240237	−	0.240237i	0.0185901	−	0.0185901i	0.716341	+	0.697751i	$0.245816\pi$
$168$		0			0
$169$		−	12.0000i		−	0.923077i
$170$		0			0
$171$	−7.33013	+	4.23205i	−0.560549	+	0.323633i
$172$		0			0
$173$	−12.1087	+	3.24453i	−0.920611	+	0.246677i	−0.687847	−	0.725856i	$-0.741444\pi$
$173$	−12.1087	+	3.24453i	−0.920611	+	0.246677i	−0.232765	+	0.972533i	$0.574777\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.95215	−	2.39872i	0.672885	−	0.180299i
$178$		0			0
$179$	8.19615	−	4.73205i	0.612609	−	0.353690i	−0.161377	−	0.986893i	$-0.551593\pi$
$179$	8.19615	−	4.73205i	0.612609	−	0.353690i	0.773986	+	0.633203i	$0.218260\pi$
$180$		0			0
$181$			6.39230i			0.475136i	0.971371	+	0.237568i	$0.0763503\pi$
$181$			6.39230i			0.475136i	−0.971371	+	0.237568i	$0.923650\pi$
$182$		0			0
$183$	6.88160	−	6.88160i	0.508702	−	0.508702i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.76028	+	17.7656i	0.348106	+	1.29915i
$188$		0			0
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$		0			0
$191$	12.0981	−	20.9545i	0.875386	−	1.51621i	0.0190352	−	0.999819i	$-0.493941\pi$
$191$	12.0981	−	20.9545i	0.875386	−	1.51621i	0.856351	−	0.516394i	$-0.172726\pi$
$192$		0			0
$193$	−12.8666	−	3.44760i	−0.926160	−	0.248164i	−0.235943	−	0.971767i	$-0.575818\pi$
$193$	−12.8666	−	3.44760i	−0.926160	−	0.248164i	−0.690216	+	0.723603i	$0.742485\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.58630	−	3.58630i	−0.255513	−	0.255513i	0.567713	−	0.823226i	$-0.307828\pi$
$197$	−3.58630	−	3.58630i	−0.255513	−	0.255513i	−0.823226	+	0.567713i	$0.807828\pi$
$198$		0			0
$199$	4.23205	+	7.33013i	0.300002	+	0.519619i	0.976136	−	0.217160i	$-0.0696793\pi$
$199$	4.23205	+	7.33013i	0.300002	+	0.519619i	−0.676134	+	0.736779i	$0.736346\pi$
$200$		0			0
$201$	−6.06218	−	3.50000i	−0.427593	−	0.246871i
$202$		0			0
$203$	16.4901	−	8.00481i	1.15738	−	0.561827i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.93185	+	7.20977i	−0.134273	+	0.501114i
$208$		0			0
$209$	−23.1244			−1.59955
$210$		0			0
$211$	−15.7321			−1.08304			−0.541520	−	0.840688i	$-0.682151\pi$
$211$	−15.7321			−1.08304			−0.541520	+	0.840688i	$0.682151\pi$
$212$		0			0
$213$	2.07055	−	7.72741i	0.141872	−	0.529473i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.38134	−	2.96713i	−0.297425	−	0.201422i
$218$		0			0
$219$	13.3301	+	7.69615i	0.900767	+	0.520058i
$220$		0			0
$221$	−3.36603	−	5.83013i	−0.226423	−	0.392177i
$222$		0			0
$223$	0.947343	+	0.947343i	0.0634388	+	0.0634388i	0.738114	−	0.674676i	$-0.235716\pi$
$223$	0.947343	+	0.947343i	0.0634388	+	0.0634388i	−0.674676	+	0.738114i	$0.735716\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.3843	−	3.58630i	−0.888345	−	0.238031i	−0.214341	−	0.976759i	$-0.568760\pi$
$227$	−13.3843	−	3.58630i	−0.888345	−	0.238031i	−0.674004	+	0.738728i	$0.735427\pi$
$228$		0			0
$229$	−5.86603	+	10.1603i	−0.387638	+	0.671408i	−0.992131	−	0.125202i	$-0.960042\pi$
$229$	−5.86603	+	10.1603i	−0.387638	+	0.671408i	0.604493	+	0.796610i	$0.293376\pi$
$230$		0			0
$231$	4.73205	+	5.46410i	0.311346	+	0.359511i
$232$		0			0
$233$	2.77766	+	10.3664i	0.181971	+	0.679123i	0.995259	+	0.0972622i	$0.0310085\pi$
$233$	2.77766	+	10.3664i	0.181971	+	0.679123i	−0.813288	+	0.581861i	$0.802325\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.60368	+	1.60368i	−0.104170	+	0.104170i
$238$		0			0
$239$		−	23.3205i		−	1.50848i	−0.656600	−	0.754239i	$-0.728006\pi$
$239$		−	23.3205i		−	1.50848i	0.656600	−	0.754239i	$-0.271994\pi$
$240$		0			0
$241$	−9.69615	+	5.59808i	−0.624584	+	0.360604i	−0.778652	−	0.627457i	$-0.784096\pi$
$241$	−9.69615	+	5.59808i	−0.624584	+	0.360604i	0.154068	+	0.988060i	$0.450763\pi$
$242$		0			0
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.17569	−	2.19067i	0.520207	−	0.139389i
$248$		0			0
$249$	−4.09808	+	2.36603i	−0.259705	+	0.149941i
$250$		0			0
$251$			10.5885i			0.668337i	0.942513	+	0.334169i	$0.108456\pi$
$251$			10.5885i			0.668337i	−0.942513	+	0.334169i	$0.891544\pi$
$252$		0			0
$253$	−14.4195	+	14.4195i	−0.906549	+	0.906549i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.56892	−	20.7835i	−0.347380	−	1.29644i	−0.889807	−	0.456336i	$-0.849161\pi$
$257$	−5.56892	−	20.7835i	−0.347380	−	1.29644i	0.542428	−	0.840103i	$-0.317505\pi$
$258$		0			0
$259$	19.3923	+	22.3923i	1.20498	+	1.39139i
$260$		0			0
$261$	−3.46410	+	6.00000i	−0.214423	+	0.371391i
$262$		0			0
$263$	−8.76268	−	2.34795i	−0.540330	−	0.144781i	−0.0216758	−	0.999765i	$-0.506900\pi$
$263$	−8.76268	−	2.34795i	−0.540330	−	0.144781i	−0.518654	+	0.854984i	$0.673567\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	5.13922	+	5.13922i	0.314515	+	0.314515i
$268$		0			0
$269$	4.29423	+	7.43782i	0.261824	+	0.453492i	0.966727	−	0.255812i	$-0.0823428\pi$
$269$	4.29423	+	7.43782i	0.261824	+	0.453492i	−0.704903	+	0.709304i	$0.749009\pi$
$270$		0			0
$271$	12.9282	+	7.46410i	0.785332	+	0.453412i	0.838317	−	0.545183i	$-0.183540\pi$
$271$	12.9282	+	7.46410i	0.785332	+	0.453412i	−0.0529843	+	0.998595i	$0.516873\pi$
$272$		0			0
$273$	−2.19067	−	1.48356i	−0.132585	−	0.0897894i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.48597	−	20.4739i	0.329620	−	1.23016i	−0.579966	−	0.814641i	$-0.696934\pi$
$277$	5.48597	−	20.4739i	0.329620	−	1.23016i	0.909585	−	0.415517i	$-0.136399\pi$
$278$		0			0
$279$	2.00000			0.119737
$280$		0			0
$281$	−8.87564			−0.529477			−0.264738	−	0.964320i	$-0.585286\pi$
$281$	−8.87564			−0.529477			−0.264738	+	0.964320i	$0.585286\pi$
$282$		0			0
$283$	1.89967	−	7.08965i	0.112923	−	0.421436i	−0.886200	−	0.463303i	$-0.846664\pi$
$283$	1.89967	−	7.08965i	0.112923	−	0.421436i	0.999123	+	0.0418674i	$0.0133307\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.98743	+	4.84821i	−0.589539	+	0.286181i
$288$		0			0
$289$	24.5263	+	14.1603i	1.44272	+	0.832956i
$290$		0			0
$291$	−1.76795	−	3.06218i	−0.103639	−	0.179508i
$292$		0			0
$293$	11.5911	+	11.5911i	0.677160	+	0.677160i	0.959357	−	0.282197i	$-0.0910631\pi$
$293$	11.5911	+	11.5911i	0.677160	+	0.677160i	−0.282197	+	0.959357i	$0.591063\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.63896	−	0.707107i	−0.153128	−	0.0410305i
$298$		0			0
$299$	3.73205	−	6.46410i	0.215830	−	0.373829i
$300$		0			0
$301$	1.33975	+	0.464102i	0.0772217	+	0.0267504i
$302$		0			0
$303$	1.74238	+	6.50266i	0.100097	+	0.373568i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.79315	−	1.79315i	0.102341	−	0.102341i	−0.654083	−	0.756423i	$-0.726945\pi$
$307$	1.79315	−	1.79315i	0.102341	−	0.102341i	0.756423	+	0.654083i	$0.226945\pi$
$308$		0			0
$309$			4.66025i			0.265113i
$310$		0			0
$311$	5.19615	−	3.00000i	0.294647	−	0.170114i	−0.345389	−	0.938460i	$-0.612253\pi$
$311$	5.19615	−	3.00000i	0.294647	−	0.170114i	0.640036	+	0.768345i	$0.278920\pi$
$312$		0			0
$313$	2.44949	−	0.656339i	0.138453	−	0.0370985i	−0.188927	−	0.981991i	$-0.560501\pi$
$313$	2.44949	−	0.656339i	0.138453	−	0.0370985i	0.327380	+	0.944893i	$0.393834\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.31079	−	0.619174i	0.129787	−	0.0347763i	−0.193341	−	0.981132i	$-0.561932\pi$
$317$	2.31079	−	0.619174i	0.129787	−	0.0347763i	0.323128	+	0.946355i	$0.395266\pi$
$318$		0			0
$319$	−16.3923	+	9.46410i	−0.917793	+	0.529888i
$320$		0			0
$321$		−	14.7321i		−	0.822263i
$322$		0			0
$323$	−40.2915	+	40.2915i	−2.24188	+	2.24188i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.60488	+	13.4536i	0.199351	+	0.743986i
$328$		0			0
$329$	−20.3923	+	17.6603i	−1.12426	+	0.973641i
$330$		0			0
$331$	6.66987	−	11.5526i	0.366609	−	0.634986i	−0.622424	−	0.782681i	$-0.713852\pi$
$331$	6.66987	−	11.5526i	0.366609	−	0.634986i	0.989033	+	0.147694i	$0.0471852\pi$
$332$		0			0
$333$	−10.8147	−	2.89778i	−0.592639	−	0.158797i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.656339	+	0.656339i	0.0357531	+	0.0357531i	0.724757	−	0.689004i	$-0.241952\pi$
$337$	0.656339	+	0.656339i	0.0357531	+	0.0357531i	−0.689004	+	0.724757i	$0.741952\pi$
$338$		0			0
$339$	4.26795	+	7.39230i	0.231803	+	0.401495i
$340$		0			0
$341$	4.73205	+	2.73205i	0.256255	+	0.147949i
$342$		0			0
$343$	−18.0938	−	3.95164i	−0.976972	−	0.213368i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.19239	+	34.3065i	−0.493473	+	1.84167i	0.0449449	+	0.998989i	$0.485689\pi$
$347$	−9.19239	+	34.3065i	−0.493473	+	1.84167i	−0.538418	+	0.842678i	$0.680978\pi$
$348$		0			0
$349$	12.9282			0.692031			0.346015	−	0.938229i	$-0.387534\pi$
$349$	12.9282			0.692031			0.346015	+	0.938229i	$0.387534\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$		0			0
$353$	−3.01790	+	11.2629i	−0.160626	+	0.599466i	0.837931	+	0.545776i	$0.183765\pi$
$353$	−3.01790	+	11.2629i	−0.160626	+	0.599466i	−0.998558	+	0.0536901i	$0.982902\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	17.7656	+	1.27551i	0.940255	+	0.0675073i
$358$		0			0
$359$	−24.2942	−	14.0263i	−1.28220	−	0.740279i	−0.304950	−	0.952368i	$-0.598640\pi$
$359$	−24.2942	−	14.0263i	−1.28220	−	0.740279i	−0.977250	+	0.212090i	$0.931973\pi$
$360$		0			0
$361$	−26.3205	−	45.5885i	−1.38529	−	2.39939i
$362$		0			0
$363$	2.50026	+	2.50026i	0.131229	+	0.131229i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.20977	−	1.93185i	−0.376347	−	0.100842i	0.0656868	−	0.997840i	$-0.479076\pi$
$367$	−7.20977	−	1.93185i	−0.376347	−	0.100842i	−0.442034	+	0.896998i	$0.645743\pi$
$368$		0			0
$369$	2.09808	−	3.63397i	0.109221	−	0.189177i
$370$		0			0
$371$	4.36603	+	22.6865i	0.226673	+	1.17783i
$372$		0			0
$373$	−3.89589	−	14.5397i	−0.201721	−	0.752835i	−0.990424	−	0.138060i	$-0.955913\pi$
$373$	−3.89589	−	14.5397i	−0.201721	−	0.752835i	0.788702	−	0.614775i	$-0.210753\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.89898	−	4.89898i	0.252310	−	0.252310i
$378$		0			0
$379$			23.4449i			1.20428i	0.798390	+	0.602141i	$0.205685\pi$
$379$			23.4449i			1.20428i	−0.798390	+	0.602141i	$0.794315\pi$
$380$		0			0
$381$	−0.0621778	+	0.0358984i	−0.00318547	+	0.00183913i
$382$		0			0
$383$	−28.7004	+	7.69024i	−1.46652	+	0.392953i	−0.901737	−	0.432286i	$-0.857707\pi$
$383$	−28.7004	+	7.69024i	−1.46652	+	0.392953i	−0.564784	+	0.825239i	$0.691040\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.517638	+	0.138701i	−0.0263130	+	0.00705055i
$388$		0			0
$389$	15.4186	−	8.90192i	0.781753	−	0.451345i	−0.0552980	−	0.998470i	$-0.517611\pi$
$389$	15.4186	−	8.90192i	0.781753	−	0.451345i	0.837051	+	0.547124i	$0.184278\pi$
$390$		0			0
$391$			50.2487i			2.54119i
$392$		0			0
$393$	−11.9700	+	11.9700i	−0.603809	+	0.603809i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.69161	+	6.31319i	0.0848997	+	0.316850i	0.995295	−	0.0968891i	$-0.0308892\pi$
$397$	1.69161	+	6.31319i	0.0848997	+	0.316850i	−0.910395	+	0.413739i	$0.864223\pi$
$398$		0			0
$399$	−7.33013	+	21.1603i	−0.366965	+	1.05934i
$400$		0			0
$401$	13.2942	−	23.0263i	0.663882	−	1.14988i	−0.315705	−	0.948857i	$-0.602241\pi$
$401$	13.2942	−	23.0263i	0.663882	−	1.14988i	0.979587	−	0.201020i	$-0.0644257\pi$
$402$		0			0
$403$	−1.93185	−	0.517638i	−0.0962324	−	0.0257854i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−21.6293	−	21.6293i	−1.07212	−	1.07212i
$408$		0			0
$409$	−5.79423	−	10.0359i	−0.286506	−	0.496243i	0.686467	−	0.727161i	$-0.259161\pi$
$409$	−5.79423	−	10.0359i	−0.286506	−	0.496243i	−0.972973	+	0.230918i	$0.925827\pi$
$410$		0			0
$411$	5.19615	+	3.00000i	0.256307	+	0.147979i
$412$		0			0
$413$	13.7496	−	20.3030i	0.676573	−	0.999047i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.36276	−	16.2820i	0.213645	−	0.797335i
$418$		0			0
$419$	−0.0525589			−0.00256767			−0.00128383	−	0.999999i	$-0.500409\pi$
$419$	−0.0525589			−0.00256767			−0.00128383	+	0.999999i	$0.500409\pi$
$420$		0			0
$421$	−31.3923			−1.52997			−0.764984	−	0.644050i	$-0.777253\pi$
$421$	−31.3923			−1.52997			−0.764984	+	0.644050i	$0.777253\pi$
$422$		0			0
$423$	2.63896	−	9.84873i	0.128311	−	0.478861i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.84392	−	25.6825i	0.0892335	−	1.24286i
$428$		0			0
$429$	2.36603	+	1.36603i	0.114233	+	0.0659523i
$430$		0			0
$431$	−5.53590	−	9.58846i	−0.266655	−	0.461860i	0.701341	−	0.712826i	$-0.252585\pi$
$431$	−5.53590	−	9.58846i	−0.266655	−	0.461860i	−0.967996	+	0.250966i	$0.919252\pi$
$432$		0			0
$433$	21.5921	+	21.5921i	1.03765	+	1.03765i	0.999263	+	0.0383892i	$0.0122227\pi$
$433$	21.5921	+	21.5921i	1.03765	+	1.03765i	0.0383892	+	0.999263i	$0.487777\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−61.0242	−	16.3514i	−2.91918	−	0.782193i
$438$		0			0
$439$	6.89230	−	11.9378i	0.328952	−	0.569761i	−0.653352	−	0.757054i	$-0.726638\pi$
$439$	6.89230	−	11.9378i	0.328952	−	0.569761i	0.982304	+	0.187293i	$0.0599713\pi$
$440$		0			0
$441$	6.50000	−	2.59808i	0.309524	−	0.123718i
$442$		0			0
$443$	−5.99863	−	22.3872i	−0.285003	−	1.06365i	−0.948837	−	0.315767i	$-0.897738\pi$
$443$	−5.99863	−	22.3872i	−0.285003	−	1.06365i	0.663834	−	0.747880i	$-0.268928\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	6.45189	−	6.45189i	0.305164	−	0.305164i
$448$		0			0
$449$		−	10.3397i		−	0.487963i	−0.969780	−	0.243981i	$-0.921546\pi$
$449$		−	10.3397i		−	0.487963i	0.969780	−	0.243981i	$-0.0784536\pi$
$450$		0			0
$451$	9.92820	−	5.73205i	0.467501	−	0.269912i
$452$		0			0
$453$	−10.2970	+	2.75908i	−0.483796	+	0.129633i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.5749	+	4.17329i	−0.728565	+	0.195218i	−0.603990	−	0.796992i	$-0.706423\pi$
$457$	−15.5749	+	4.17329i	−0.728565	+	0.195218i	−0.124575	+	0.992210i	$0.539757\pi$
$458$		0			0
$459$	−5.83013	+	3.36603i	−0.272127	+	0.157113i
$460$		0			0
$461$			17.7128i			0.824968i	0.910965	+	0.412484i	$0.135339\pi$
$461$			17.7128i			0.824968i	−0.910965	+	0.412484i	$0.864661\pi$
$462$		0			0
$463$	−22.0962	+	22.0962i	−1.02690	+	1.02690i	−0.0272682	+	0.999628i	$0.508681\pi$
$463$	−22.0962	+	22.0962i	−1.02690	+	1.02690i	−0.999628	+	0.0272682i	$0.991319\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.20977	−	26.9072i	−0.333628	−	1.24512i	−0.905349	−	0.424669i	$-0.860390\pi$
$467$	−7.20977	−	26.9072i	−0.333628	−	1.24512i	0.571720	−	0.820449i	$-0.306276\pi$
$468$		0			0
$469$	−18.1865	+	3.50000i	−0.839776	+	0.161615i
$470$		0			0
$471$	−6.42820	+	11.1340i	−0.296196	+	0.513026i
$472$		0			0
$473$	−1.41421	−	0.378937i	−0.0650256	−	0.0174236i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−6.17449	−	6.17449i	−0.282711	−	0.282711i
$478$		0			0
$479$	13.2224	+	22.9019i	0.604148	+	1.04642i	0.992185	+	0.124772i	$0.0398199\pi$
$479$	13.2224	+	22.9019i	0.604148	+	1.04642i	−0.388037	+	0.921644i	$0.626847\pi$
$480$		0			0
$481$	9.69615	+	5.59808i	0.442106	+	0.255250i
$482$		0			0
$483$	8.62398	+	17.7656i	0.392405	+	0.808363i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−6.55343	+	24.4577i	−0.296964	+	1.10829i	0.642681	+	0.766134i	$0.277822\pi$
$487$	−6.55343	+	24.4577i	−0.296964	+	1.10829i	−0.939645	+	0.342151i	$0.888844\pi$
$488$		0			0
$489$	3.00000			0.135665
$490$		0			0
$491$	14.3923			0.649516			0.324758	−	0.945797i	$-0.394717\pi$
$491$	14.3923			0.649516			0.324758	+	0.945797i	$0.394717\pi$
$492$		0			0
$493$	−12.0716	+	45.0518i	−0.543677	+	2.02903i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.24316	−	19.0411i	−0.414612	−	0.854111i
$498$		0			0
$499$	1.03590	+	0.598076i	0.0463732	+	0.0267736i	0.523007	−	0.852328i	$-0.324810\pi$
$499$	1.03590	+	0.598076i	0.0463732	+	0.0267736i	−0.476634	+	0.879102i	$0.658143\pi$
$500$		0			0
$501$	0.169873	+	0.294229i	0.00758937	+	0.0131452i
$502$		0			0
$503$	−14.6969	−	14.6969i	−0.655304	−	0.655304i	0.298961	−	0.954265i	$-0.403360\pi$
$503$	−14.6969	−	14.6969i	−0.655304	−	0.655304i	−0.954265	+	0.298961i	$0.903360\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	11.5911	+	3.10583i	0.514779	+	0.137935i
$508$		0			0
$509$	−10.7321	+	18.5885i	−0.475690	+	0.823919i	−0.999612	−	0.0278471i	$-0.991135\pi$
$509$	−10.7321	+	18.5885i	−0.475690	+	0.823919i	0.523922	+	0.851766i	$0.324468\pi$
$510$		0			0
$511$	39.9904	−	7.69615i	1.76907	−	0.340458i
$512$		0			0
$513$	−2.19067	−	8.17569i	−0.0967205	−	0.360966i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	19.6975	−	19.6975i	0.866293	−	0.866293i
$518$		0			0
$519$		−	12.5359i		−	0.550265i
$520$		0			0
$521$	32.3205	−	18.6603i	1.41599	−	0.817521i	0.420044	−	0.907504i	$-0.362015\pi$
$521$	32.3205	−	18.6603i	1.41599	−	0.817521i	0.995943	+	0.0899832i	$0.0286813\pi$
$522$		0			0
$523$	−18.6622	+	5.00052i	−0.816040	+	0.218657i	−0.642614	−	0.766190i	$-0.722150\pi$
$523$	−18.6622	+	5.00052i	−0.816040	+	0.218657i	−0.173426	+	0.984847i	$0.555484\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.0053	−	3.48477i	0.566521	−	0.151799i
$528$		0			0
$529$	−28.3301	+	16.3564i	−1.23174	+	0.711148i
$530$		0			0
$531$			9.26795i			0.402195i
$532$		0			0
$533$	−2.96713	+	2.96713i	−0.128521	+	0.128521i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.44949	+	9.14162i	0.105703	+	0.394490i
$538$		0			0
$539$	18.9282	+	2.73205i	0.815295	+	0.117678i
$540$		0			0
$541$	19.1603	−	33.1865i	0.823764	−	1.42680i	−0.0790969	−	0.996867i	$-0.525204\pi$
$541$	19.1603	−	33.1865i	0.823764	−	1.42680i	0.902861	−	0.429934i	$-0.141463\pi$
$542$		0			0
$543$	−6.17449	−	1.65445i	−0.264973	−	0.0709993i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	20.3538	+	20.3538i	0.870265	+	0.870265i	0.992501	−	0.122236i	$-0.0390064\pi$
$547$	20.3538	+	20.3538i	0.870265	+	0.870265i	−0.122236	+	0.992501i	$0.539006\pi$
$548$		0			0
$549$	4.86603	+	8.42820i	0.207677	+	0.359707i
$550$		0			0
$551$	−50.7846	−	29.3205i	−2.16350	−	1.24910i
$552$		0			0
$553$	−0.429705	+	5.98502i	−0.0182729	+	0.254509i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.13681	+	4.24264i	−0.0481683	+	0.179766i	−0.985819	−	0.167813i	$-0.946330\pi$
$557$	−1.13681	+	4.24264i	−0.0481683	+	0.179766i	0.937651	+	0.347579i	$0.112996\pi$
$558$		0			0
$559$	0.535898			0.0226661
$560$		0			0
$561$	−18.3923			−0.776524
$562$		0			0
$563$	−10.2277	+	38.1702i	−0.431045	+	1.60868i	0.319314	+	0.947649i	$0.396548\pi$
$563$	−10.2277	+	38.1702i	−0.431045	+	1.60868i	−0.750358	+	0.661031i	$0.770119\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.48356	+	2.19067i	−0.0623038	+	0.0919995i
$568$		0			0
$569$	33.4186	+	19.2942i	1.40098	+	0.808856i	0.994493	−	0.104801i	$-0.0334204\pi$
$569$	33.4186	+	19.2942i	1.40098	+	0.808856i	0.406487	+	0.913657i	$0.366754\pi$
$570$		0			0
$571$	13.4545	+	23.3038i	0.563053	+	0.975236i	0.997228	+	0.0744073i	$0.0237065\pi$
$571$	13.4545	+	23.3038i	0.563053	+	0.975236i	−0.434175	+	0.900828i	$0.642960\pi$
$572$		0			0
$573$	17.1093	+	17.1093i	0.714750	+	0.714750i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.65926	+	2.58819i	0.402120	+	0.107748i	0.454210	−	0.890895i	$-0.349922\pi$
$577$	9.65926	+	2.58819i	0.402120	+	0.107748i	−0.0520899	+	0.998642i	$0.516588\pi$
$578$		0			0
$579$	6.66025	−	11.5359i	0.276791	−	0.479416i
$580$		0			0
$581$	−4.09808	+	11.8301i	−0.170017	+	0.490796i
$582$		0			0
$583$	−6.17449	−	23.0435i	−0.255721	−	0.954365i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−21.0101	+	21.0101i	−0.867181	+	0.867181i	−0.992159	−	0.124979i	$-0.960114\pi$
$587$	−21.0101	+	21.0101i	−0.867181	+	0.867181i	0.124979	+	0.992159i	$0.460114\pi$
$588$		0			0
$589$			16.9282i			0.697514i
$590$		0			0
$591$	4.39230	−	2.53590i	0.180675	−	0.104313i
$592$		0			0
$593$	33.9783	−	9.10446i	1.39532	−	0.373875i	0.518659	−	0.854981i	$-0.326432\pi$
$593$	33.9783	−	9.10446i	1.39532	−	0.373875i	0.876662	+	0.481106i	$0.159765\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.17569	+	2.19067i	−0.334609	+	0.0896582i
$598$		0			0
$599$	11.9545	−	6.90192i	0.488447	−	0.282005i	−0.235483	−	0.971878i	$-0.575667\pi$
$599$	11.9545	−	6.90192i	0.488447	−	0.282005i	0.723930	+	0.689874i	$0.242334\pi$
$600$		0			0
$601$			12.5167i			0.510565i	0.966866	+	0.255283i	$0.0821685\pi$
$601$			12.5167i			0.510565i	−0.966866	+	0.255283i	$0.917831\pi$
$602$		0			0
$603$	4.94975	−	4.94975i	0.201569	−	0.201569i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−3.79435	−	14.1607i	−0.154008	−	0.574766i	−0.999188	−	0.0402844i	$-0.987174\pi$
$607$	−3.79435	−	14.1607i	−0.154008	−	0.574766i	0.845180	−	0.534481i	$-0.179493\pi$
$608$		0			0
$609$	3.46410	+	18.0000i	0.140372	+	0.729397i
$610$		0			0
$611$	−5.09808	+	8.83013i	−0.206246	+	0.357229i
$612$		0			0
$613$	−26.9072	−	7.20977i	−1.08677	−	0.291200i	−0.329405	−	0.944189i	$-0.606848\pi$
$613$	−26.9072	−	7.20977i	−1.08677	−	0.291200i	−0.757367	+	0.652989i	$0.773515\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.14110	+	4.14110i	0.166715	+	0.166715i	0.785534	−	0.618819i	$-0.212389\pi$
$617$	4.14110	+	4.14110i	0.166715	+	0.166715i	−0.618819	+	0.785534i	$0.712389\pi$
$618$		0			0
$619$	19.1962	+	33.2487i	0.771559	+	1.33638i	0.936709	+	0.350110i	$0.113856\pi$
$619$	19.1962	+	33.2487i	0.771559	+	1.33638i	−0.165150	+	0.986268i	$0.552811\pi$
$620$		0			0
$621$	−6.46410	−	3.73205i	−0.259395	−	0.149762i
$622$		0			0
$623$	19.1798	+	1.37705i	0.768423	+	0.0551703i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	5.98502	−	22.3364i	0.239019	−	0.892030i
$628$		0			0
$629$	−75.3731			−3.00532
$630$		0			0
$631$	−26.8038			−1.06704			−0.533522	−	0.845786i	$-0.679132\pi$
$631$	−26.8038			−1.06704			−0.533522	+	0.845786i	$0.679132\pi$
$632$		0			0
$633$	4.07175	−	15.1960i	0.161838	−	0.603987i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−6.95095	+	0.827225i	−0.275407	+	0.0327759i
$638$		0			0
$639$	6.92820	+	4.00000i	0.274075	+	0.158238i
$640$		0			0
$641$	22.5885	+	39.1244i	0.892190	+	1.54532i	0.837244	+	0.546830i	$0.184166\pi$
$641$	22.5885	+	39.1244i	0.892190	+	1.54532i	0.0549467	+	0.998489i	$0.482501\pi$
$642$		0			0
$643$	33.5486	+	33.5486i	1.32303	+	1.32303i	0.911313	+	0.411714i	$0.135070\pi$
$643$	33.5486	+	33.5486i	1.32303	+	1.32303i	0.411714	+	0.911313i	$0.364930\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	34.3065	+	9.19239i	1.34873	+	0.361390i	0.859664	−	0.510859i	$-0.170673\pi$
$647$	34.3065	+	9.19239i	1.34873	+	0.361390i	0.489062	+	0.872249i	$0.337339\pi$
$648$		0			0
$649$	−12.6603	+	21.9282i	−0.496958	+	0.860757i
$650$		0			0
$651$	4.00000	−	3.46410i	0.156772	−	0.135769i
$652$		0			0
$653$	−0.152304	−	0.568406i	−0.00596011	−	0.0222434i	0.962882	−	0.269924i	$-0.0869985\pi$
$653$	−0.152304	−	0.568406i	−0.00596011	−	0.0222434i	−0.968842	+	0.247680i	$0.920332\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−10.8840	+	10.8840i	−0.424625	+	0.424625i
$658$		0			0
$659$			5.66025i			0.220492i	0.993904	+	0.110246i	$0.0351639\pi$
$659$			5.66025i			0.220492i	−0.993904	+	0.110246i	$0.964836\pi$
$660$		0			0
$661$	1.37564	−	0.794229i	0.0535064	−	0.0308919i	−0.473008	−	0.881058i	$-0.656832\pi$
$661$	1.37564	−	0.794229i	0.0535064	−	0.0308919i	0.526515	+	0.850166i	$0.323499\pi$
$662$		0			0
$663$	6.50266	−	1.74238i	0.252542	−	0.0676685i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−49.9507	+	13.3843i	−1.93410	+	0.518241i
$668$		0			0
$669$	−1.16025	+	0.669873i	−0.0448580	+	0.0258988i
$670$		0			0
$671$			26.5885i			1.02644i
$672$		0			0
$673$	8.29581	−	8.29581i	0.319780	−	0.319780i	−0.528903	−	0.848683i	$-0.677396\pi$
$673$	8.29581	−	8.29581i	0.319780	−	0.319780i	0.848683	+	0.528903i	$0.177396\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.896575	+	3.34607i	0.0344582	+	0.128600i	0.981012	−	0.193945i	$-0.0621284\pi$
$677$	0.896575	+	3.34607i	0.0344582	+	0.128600i	−0.946554	+	0.322545i	$0.895462\pi$
$678$		0			0
$679$	−8.83975	−	3.06218i	−0.339238	−	0.117516i
$680$		0			0
$681$	6.92820	−	12.0000i	0.265489	−	0.459841i
$682$		0			0
$683$	−10.8840	−	2.91636i	−0.416465	−	0.111591i	0.0445009	−	0.999009i	$-0.485830\pi$
$683$	−10.8840	−	2.91636i	−0.416465	−	0.111591i	−0.460966	+	0.887418i	$0.652497\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.29581	−	8.29581i	−0.316505	−	0.316505i
$688$		0			0
$689$	4.36603	+	7.56218i	0.166332	+	0.288096i
$690$		0			0
$691$	−11.4737	−	6.62436i	−0.436481	−	0.252002i	0.265623	−	0.964077i	$-0.414422\pi$
$691$	−11.4737	−	6.62436i	−0.436481	−	0.252002i	−0.702104	+	0.712075i	$0.747756\pi$
$692$		0			0
$693$	−6.50266	+	3.15660i	−0.247016	+	0.119909i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	7.31130	−	27.2862i	0.276935	−	1.03354i
$698$		0			0
$699$	−10.7321			−0.405923
$700$		0			0
$701$	−18.3397			−0.692683			−0.346341	−	0.938109i	$-0.612576\pi$
$701$	−18.3397			−0.692683			−0.346341	+	0.938109i	$0.612576\pi$
$702$		0			0
$703$	24.5271	−	91.5363i	0.925056	−	3.45236i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	14.7477	+	9.98743i	0.554645	+	0.375616i
$708$		0			0
$709$	4.45448	+	2.57180i	0.167292	+	0.0965859i	0.581308	−	0.813684i	$-0.302541\pi$
$709$	4.45448	+	2.57180i	0.167292	+	0.0965859i	−0.414017	+	0.910269i	$0.635874\pi$
$710$		0			0
$711$	−1.13397	−	1.96410i	−0.0425274	−	0.0736596i
$712$		0			0
$713$	10.5558	+	10.5558i	0.395319	+	0.395319i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	22.5259	+	6.03579i	0.841244	+	0.225411i
$718$		0			0
$719$	−4.75833	+	8.24167i	−0.177456	+	0.307362i	−0.941008	−	0.338383i	$-0.890120\pi$
$719$	−4.75833	+	8.24167i	−0.177456	+	0.307362i	0.763553	+	0.645746i	$0.223453\pi$
$720$		0			0
$721$	8.07180	+	9.32051i	0.300609	+	0.347114i
$722$		0			0
$723$	−2.89778	−	10.8147i	−0.107770	−	0.402201i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.568406	+	0.568406i	−0.0210810	+	0.0210810i	−0.717569	−	0.696488i	$-0.754745\pi$
$727$	−0.568406	+	0.568406i	−0.0210810	+	0.0210810i	0.696488	+	0.717569i	$0.254745\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−3.12436	+	1.80385i	−0.115558	+	0.0667177i
$732$		0			0
$733$	−15.9031	+	4.26122i	−0.587394	+	0.157392i	−0.540262	−	0.841497i	$-0.681675\pi$
$733$	−15.9031	+	4.26122i	−0.587394	+	0.157392i	−0.0471323	+	0.998889i	$0.515008\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18.4727	−	4.94975i	0.680451	−	0.182326i
$738$		0			0
$739$	25.0359	−	14.4545i	0.920960	−	0.531717i	0.0370191	−	0.999315i	$-0.488214\pi$
$739$	25.0359	−	14.4545i	0.920960	−	0.531717i	0.883941	+	0.467598i	$0.154880\pi$
$740$		0			0
$741$			8.46410i			0.310937i
$742$		0			0
$743$	−24.1160	+	24.1160i	−0.884729	+	0.884729i	−0.994011	−	0.109282i	$-0.965145\pi$
$743$	−24.1160	+	24.1160i	−0.884729	+	0.884729i	0.109282	+	0.994011i	$0.465145\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.22474	−	4.57081i	−0.0448111	−	0.167237i
$748$		0			0
$749$	−25.5167	−	29.4641i	−0.932358	−	1.07659i
$750$		0			0
$751$	−0.0621778	+	0.107695i	−0.00226890	+	0.00392985i	−0.867158	−	0.498034i	$-0.834056\pi$
$751$	−0.0621778	+	0.107695i	−0.00226890	+	0.00392985i	0.864889	+	0.501964i	$0.167389\pi$
$752$		0			0
$753$	−10.2277	−	2.74049i	−0.372717	−	0.0998692i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.74479	+	5.74479i	0.208798	+	0.208798i	0.803756	−	0.594959i	$-0.202832\pi$
$757$	5.74479	+	5.74479i	0.208798	+	0.208798i	−0.594959	+	0.803756i	$0.702832\pi$
$758$		0			0
$759$	−10.1962	−	17.6603i	−0.370097	−	0.641027i
$760$		0			0
$761$	20.4904	+	11.8301i	0.742776	+	0.428842i	0.823078	−	0.567929i	$-0.192255\pi$
$761$	20.4904	+	11.8301i	0.742776	+	0.428842i	−0.0803019	+	0.996771i	$0.525588\pi$
$762$		0			0
$763$	30.5121	+	20.6634i	1.10461	+	0.748065i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.39872	−	8.95215i	0.0866128	−	0.323243i
$768$		0			0
$769$	21.3205			0.768837			0.384419	−	0.923159i	$-0.374402\pi$
$769$	21.3205			0.768837			0.384419	+	0.923159i	$0.374402\pi$
$770$		0			0
$771$	21.5167			0.774904
$772$		0			0
$773$	−0.832204	+	3.10583i	−0.0299323	+	0.111709i	−0.979276	−	0.202532i	$-0.935083\pi$
$773$	−0.832204	+	3.10583i	−0.0299323	+	0.111709i	0.949343	+	0.314240i	$0.101750\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−26.6484	+	12.9360i	−0.956006	+	0.464075i
$778$		0			0
$779$	30.7583	+	17.7583i	1.10203	+	0.636258i
$780$		0			0
$781$	10.9282	+	18.9282i	0.391042	+	0.677304i
$782$		0			0
$783$	−4.89898	−	4.89898i	−0.175075	−	0.175075i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.397520	+	0.106515i	0.0141700	+	0.00379685i	0.265897	−	0.964001i	$-0.414332\pi$
$787$	0.397520	+	0.106515i	0.0141700	+	0.00379685i	−0.251727	+	0.967798i	$0.580999\pi$
$788$		0			0
$789$	4.53590	−	7.85641i	0.161482	−	0.279695i
$790$		0			0
$791$	21.3397	+	7.39230i	0.758754	+	0.262840i
$792$		0			0
$793$	−2.51884	−	9.40044i	−0.0894466	−	0.333819i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	29.9759	−	29.9759i	1.06180	−	1.06180i	0.0638402	−	0.997960i	$-0.479665\pi$
$797$	29.9759	−	29.9759i	1.06180	−	1.06180i	0.997960	−	0.0638402i	$-0.0203348\pi$
$798$		0			0
$799$		−	68.6410i		−	2.42834i
$800$		0			0
$801$	−6.29423	+	3.63397i	−0.222396	+	0.128400i
$802$		0			0
$803$	−40.6197	+	10.8840i	−1.43344	+	0.384088i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8.29581	+	2.22286i	−0.292026	+	0.0782482i
$808$		0			0
$809$	44.5692	−	25.7321i	1.56697	−	0.904691i	0.570451	−	0.821332i	$-0.306769\pi$
$809$	44.5692	−	25.7321i	1.56697	−	0.904691i	0.996520	−	0.0833589i	$-0.0265648\pi$
$810$		0			0
$811$		−	27.1436i		−	0.953140i	−0.879136	−	0.476570i	$-0.841880\pi$
$811$		−	27.1436i		−	0.953140i	0.879136	−	0.476570i	$-0.158120\pi$
$812$		0			0
$813$	−10.5558	+	10.5558i	−0.370209	+	0.370209i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.17398	−	4.38134i	−0.0410723	−	0.153284i
$818$		0			0
$819$	2.00000	−	1.73205i	0.0698857	−	0.0605228i
$820$		0			0
$821$	25.8301	−	44.7391i	0.901478	−	1.56141i	0.0759008	−	0.997115i	$-0.475817\pi$
$821$	25.8301	−	44.7391i	0.901478	−	1.56141i	0.825577	−	0.564290i	$-0.190850\pi$
$822$		0			0
$823$	−0.309587	−	0.0829536i	−0.0107915	−	0.00289158i	0.253419	−	0.967357i	$-0.418445\pi$
$823$	−0.309587	−	0.0829536i	−0.0107915	−	0.00289158i	−0.264211	+	0.964465i	$0.585111\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.2784	+	10.2784i	0.357416	+	0.357416i	0.862860	−	0.505444i	$-0.168671\pi$
$827$	10.2784	+	10.2784i	0.357416	+	0.357416i	−0.505444	+	0.862860i	$0.668671\pi$
$828$		0			0
$829$	−22.7224	−	39.3564i	−0.789183	−	1.36690i	−0.926468	−	0.376373i	$-0.877171\pi$
$829$	−22.7224	−	39.3564i	−0.789183	−	1.36690i	0.137286	−	0.990532i	$-0.456162\pi$
$830$		0			0
$831$	18.3564	+	10.5981i	0.636777	+	0.367643i
$832$		0			0
$833$	37.7405	−	28.2199i	1.30763	−	0.977762i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.517638	+	1.93185i	−0.0178922	+	0.0667746i
$838$		0			0
$839$	−51.9615			−1.79391			−0.896956	−	0.442121i	$-0.854226\pi$
$839$	−51.9615			−1.79391			−0.896956	+	0.442121i	$0.854226\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$		0			0
$843$	2.29719	−	8.57321i	0.0791193	−	0.295277i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	9.33109	+	0.669942i	0.320620	+	0.0230195i
$848$		0			0
$849$	6.35641	+	3.66987i	0.218151	+	0.125950i
$850$		0			0
$851$	−41.7846	−	72.3731i	−1.43236	−	2.48092i
$852$		0			0
$853$	15.5563	+	15.5563i	0.532639	+	0.532639i	0.921357	−	0.388718i	$-0.127082\pi$
$853$	15.5563	+	15.5563i	0.532639	+	0.532639i	−0.388718	+	0.921357i	$0.627082\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.8014	+	6.37756i	0.813040	+	0.217853i	0.641301	−	0.767289i	$-0.278395\pi$
$857$	23.8014	+	6.37756i	0.813040	+	0.217853i	0.171739	+	0.985143i	$0.445062\pi$
$858$		0			0
$859$	0.464102	−	0.803848i	0.0158349	−	0.0274269i	−0.857999	−	0.513651i	$-0.828293\pi$
$859$	0.464102	−	0.803848i	0.0158349	−	0.0274269i	0.873834	+	0.486224i	$0.161626\pi$
$860$		0			0
$861$	−2.09808	−	10.9019i	−0.0715022	−	0.371537i
$862$		0			0
$863$	−11.5403	−	43.0691i	−0.392838	−	1.46609i	−0.825432	−	0.564502i	$-0.809068\pi$
$863$	−11.5403	−	43.0691i	−0.392838	−	1.46609i	0.432594	−	0.901589i	$-0.357598\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−20.0256	+	20.0256i	−0.680106	+	0.680106i
$868$		0			0
$869$		−	6.19615i		−	0.210190i
$870$		0			0
$871$	−6.06218	+	3.50000i	−0.205409	+	0.118593i
$872$		0			0
$873$	3.41542	−	0.915158i	0.115594	−	0.0309734i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.1583	+	2.72191i	−0.343022	+	0.0919124i	−0.426217	−	0.904621i	$-0.640154\pi$
$877$	−10.1583	+	2.72191i	−0.343022	+	0.0919124i	0.0831954	+	0.996533i	$0.473487\pi$
$878$		0			0
$879$	−14.1962	+	8.19615i	−0.478824	+	0.276449i
$880$		0			0
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$		0			0
$883$	−0.226633	+	0.226633i	−0.00762682	+	0.00762682i	−0.710910	−	0.703283i	$-0.751717\pi$
$883$	−0.226633	+	0.226633i	−0.00762682	+	0.00762682i	0.703283	+	0.710910i	$0.251717\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.30701	+	16.0740i	0.144615	+	0.539712i	0.999772	+	0.0213425i	$0.00679403\pi$
$887$	4.30701	+	16.0740i	0.144615	+	0.539712i	−0.855157	+	0.518369i	$0.826539\pi$
$888$		0			0
$889$	−0.0621778	+	0.179492i	−0.00208538	+	0.00601997i
$890$		0			0
$891$	1.36603	−	2.36603i	0.0457636	−	0.0792648i
$892$		0			0
$893$	83.3606	+	22.3364i	2.78956	+	0.747460i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	5.27792	+	5.27792i	0.176225	+	0.176225i
$898$		0			0
$899$	6.92820	+	12.0000i	0.231069	+	0.400222i
$900$		0			0
$901$	−50.9090	−	29.3923i	−1.69602	−	0.979200i
$902$		0			0
$903$	−0.795040	+	1.17398i	−0.0264573	+	0.0390675i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4.22406	−	15.7644i	0.140258	−	0.523448i	−0.859663	−	0.510861i	$-0.829327\pi$
$907$	4.22406	−	15.7644i	0.140258	−	0.523448i	0.999921	−	0.0125871i	$-0.00400672\pi$
$908$		0			0
$909$	−6.73205			−0.223288
$910$		0			0
$911$	−9.71281			−0.321800			−0.160900	−	0.986971i	$-0.551440\pi$
$911$	−9.71281			−0.321800			−0.160900	+	0.986971i	$0.551440\pi$
$912$		0			0
$913$	3.34607	−	12.4877i	0.110739	−	0.413282i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.20736	+	44.6728i	−0.105917	+	1.47523i
$918$		0			0
$919$	10.3923	+	6.00000i	0.342811	+	0.197922i	0.661514	−	0.749933i	$-0.269914\pi$
$919$	10.3923	+	6.00000i	0.342811	+	0.197922i	−0.318704	+	0.947854i	$0.603247\pi$
$920$		0			0
$921$	1.26795	+	2.19615i	0.0417803	+	0.0723657i
$922$		0			0
$923$	−5.65685	−	5.65685i	−0.186198	−	0.186198i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.50146	−	1.20616i	−0.147847	−	0.0396156i
$928$		0			0
$929$	−6.09808	+	10.5622i	−0.200071	+	0.346534i	−0.948551	−	0.316624i	$-0.897451\pi$
$929$	−6.09808	+	10.5622i	−0.200071	+	0.346534i	0.748480	+	0.663158i	$0.230784\pi$
$930$		0			0
$931$	21.9904	+	55.0167i	0.720706	+	1.80310i
$932$		0			0
$933$	1.55291	+	5.79555i	0.0508401	+	0.189738i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−11.8685	+	11.8685i	−0.387727	+	0.387727i	−0.873876	−	0.486149i	$-0.838401\pi$
$937$	−11.8685	+	11.8685i	−0.387727	+	0.387727i	0.486149	+	0.873876i	$0.338401\pi$
$938$		0			0
$939$			2.53590i			0.0827559i
$940$		0			0
$941$	−0.124356	+	0.0717968i	−0.00405388	+	0.00234051i	−0.502026	−	0.864853i	$-0.667412\pi$
$941$	−0.124356	+	0.0717968i	−0.00405388	+	0.00234051i	0.497972	+	0.867193i	$0.334078\pi$
$942$		0			0
$943$	30.2533	−	8.10634i	0.985183	−	0.263979i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−31.5288	+	8.44812i	−1.02455	+	0.274527i	−0.731696	−	0.681631i	$-0.761271\pi$
$947$	−31.5288	+	8.44812i	−1.02455	+	0.274527i	−0.292852	+	0.956158i	$0.594604\pi$
$948$		0			0
$949$	13.3301	−	7.69615i	0.432714	−	0.249828i
$950$		0			0
$951$			2.39230i			0.0775758i
$952$		0			0
$953$	2.41233	−	2.41233i	0.0781429	−	0.0781429i	−0.666955	−	0.745098i	$-0.732403\pi$
$953$	2.41233	−	2.41233i	0.0781429	−	0.0781429i	0.745098	+	0.666955i	$0.232403\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−4.89898	−	18.2832i	−0.158362	−	0.591013i
$958$		0			0
$959$	15.5885	−	3.00000i	0.503378	−	0.0968751i
$960$		0			0
$961$	−13.5000	+	23.3827i	−0.435484	+	0.754280i
$962$		0			0
$963$	14.2301	+	3.81294i	0.458558	+	0.122870i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.50026	+	2.50026i	0.0804029	+	0.0804029i	0.746164	−	0.665762i	$-0.231893\pi$
$967$	2.50026	+	2.50026i	0.0804029	+	0.0804029i	−0.665762	+	0.746164i	$0.731893\pi$
$968$		0			0
$969$	−28.4904	−	49.3468i	−0.915243	−	1.58525i
$970$		0			0
$971$	−1.22243	−	0.705771i	−0.0392297	−	0.0226493i	0.480257	−	0.877128i	$-0.340543\pi$
$971$	−1.22243	−	0.705771i	−0.0392297	−	0.0226493i	−0.519487	+	0.854479i	$0.673877\pi$
$972$		0			0
$973$	−19.4758	−	40.1206i	−0.624365	−	1.28621i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.36396	+	23.7506i	−0.203601	+	0.759850i	0.786270	+	0.617883i	$0.212009\pi$
$977$	−6.36396	+	23.7506i	−0.203601	+	0.759850i	−0.989871	+	0.141967i	$0.954657\pi$
$978$		0			0
$979$	−19.8564			−0.634614
$980$		0			0
$981$	−13.9282			−0.444693
$982$		0			0
$983$	−0.642736	+	2.39872i	−0.0205001	+	0.0765073i	−0.975418	−	0.220362i	$-0.929276\pi$
$983$	−0.642736	+	2.39872i	−0.0205001	+	0.0765073i	0.954918	+	0.296870i	$0.0959427\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−11.7806	−	24.2683i	−0.374980	−	0.772467i
$988$		0			0
$989$	−3.46410	−	2.00000i	−0.110152	−	0.0635963i
$990$		0			0
$991$	−10.6603	−	18.4641i	−0.338634	−	0.586532i	0.645542	−	0.763725i	$-0.276632\pi$
$991$	−10.6603	−	18.4641i	−0.338634	−	0.586532i	−0.984176	+	0.177193i	$0.943298\pi$
$992$		0			0
$993$	9.43262	+	9.43262i	0.299335	+	0.299335i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−33.6687	−	9.02150i	−1.06630	−	0.285714i	−0.317327	−	0.948316i	$-0.602785\pi$
$997$	−33.6687	−	9.02150i	−1.06630	−	0.285714i	−0.748971	+	0.662602i	$0.769452\pi$
$998$		0			0
$999$	5.59808	−	9.69615i	0.177115	−	0.306773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.b.1657.1	yes	8
5.2	odd	4		2100.2.ce.a.1993.2	yes	8
5.3	odd	4		2100.2.ce.a.1993.1	yes	8
5.4	even	2	inner	2100.2.ce.b.1657.2	yes	8
7.3	odd	6		2100.2.ce.a.157.1	✓	8
35.3	even	12	inner	2100.2.ce.b.493.1	yes	8
35.17	even	12	inner	2100.2.ce.b.493.2	yes	8
35.24	odd	6		2100.2.ce.a.157.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.a.157.1	✓	8	7.3	odd	6
2100.2.ce.a.157.2	yes	8	35.24	odd	6
2100.2.ce.a.1993.1	yes	8	5.3	odd	4
2100.2.ce.a.1993.2	yes	8	5.2	odd	4
2100.2.ce.b.493.1	yes	8	35.3	even	12	inner
2100.2.ce.b.493.2	yes	8	35.17	even	12	inner
2100.2.ce.b.1657.1	yes	8	1.1	even	1	trivial
2100.2.ce.b.1657.2	yes	8	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{3} +(1.15539 + 2.38014i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{3} +(1.15539 + 2.38014i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(0.707107 + 0.707107i) q^{13} +(-6.50266 - 1.74238i) q^{17} +(4.23205 - 7.33013i) q^{19} +(-2.59808 + 0.500000i) q^{21} +(-1.93185 - 7.20977i) q^{23} +(0.707107 - 0.707107i) q^{27} -6.92820i q^{29} +(-1.73205 + 1.00000i) q^{31} +(2.63896 - 0.707107i) q^{33} +(10.8147 - 2.89778i) q^{37} +(-0.866025 + 0.500000i) q^{39} +4.19615i q^{41} +(0.378937 - 0.378937i) q^{43} +(2.63896 + 9.84873i) q^{47} +(-4.33013 + 5.50000i) q^{49} +(3.36603 - 5.83013i) q^{51} +(8.43451 + 2.26002i) q^{53} +(5.98502 + 5.98502i) q^{57} +(-4.63397 - 8.02628i) q^{59} +(-8.42820 - 4.86603i) q^{61} +(0.189469 - 2.63896i) q^{63} +(-1.81173 + 6.76148i) q^{67} +7.46410 q^{69} -8.00000 q^{71} +(3.98382 - 14.8678i) q^{73} +(4.05317 - 5.98502i) q^{77} +(1.96410 + 1.13397i) q^{79} +(0.500000 + 0.866025i) q^{81} +(3.34607 + 3.34607i) q^{83} +(6.69213 + 1.79315i) q^{87} +(3.63397 - 6.29423i) q^{89} +(-0.866025 + 2.50000i) q^{91} +(-0.517638 - 1.93185i) q^{93} +(-2.50026 + 2.50026i) q^{97} +2.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{11} + 20 q^{19} + 20 q^{51} - 44 q^{59} - 12 q^{61} + 32 q^{69} - 64 q^{71} - 12 q^{79} + 4 q^{81} + 36 q^{89}+O(q^{100}) \) 8 * q - 4 * q^11 + 20 * q^19 + 20 * q^51 - 44 * q^59 - 12 * q^61 + 32 * q^69 - 64 * q^71 - 12 * q^79 + 4 * q^81 + 36 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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