LMFDB - Embedded newform 2100.2.ce.a.1993.1

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			1993.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2100.1993
Dual form			2100.2.ce.a.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{3} +(2.38014 - 1.15539i) q^{7} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{3} +(2.38014 - 1.15539i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-1.36603 - 2.36603i) q^{11} +(-0.707107 + 0.707107i) q^{13} +(-1.74238 + 6.50266i) q^{17} +(-4.23205 + 7.33013i) q^{19} +(-2.59808 + 0.500000i) q^{21} +(7.20977 - 1.93185i) q^{23} +(-0.707107 - 0.707107i) q^{27} +6.92820i q^{29} +(-1.73205 + 1.00000i) q^{31} +(0.707107 + 2.63896i) q^{33} +(-2.89778 - 10.8147i) q^{37} +(0.866025 - 0.500000i) q^{39} +4.19615i q^{41} +(0.378937 + 0.378937i) q^{43} +(9.84873 - 2.63896i) q^{47} +(4.33013 - 5.50000i) q^{49} +(3.36603 - 5.83013i) q^{51} +(-2.26002 + 8.43451i) q^{53} +(5.98502 - 5.98502i) q^{57} +(4.63397 + 8.02628i) q^{59} +(-8.42820 - 4.86603i) q^{61} +(2.63896 + 0.189469i) q^{63} +(6.76148 + 1.81173i) q^{67} -7.46410 q^{69} -8.00000 q^{71} +(14.8678 + 3.98382i) q^{73} +(-5.98502 - 4.05317i) q^{77} +(-1.96410 - 1.13397i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-3.34607 + 3.34607i) q^{83} +(1.79315 - 6.69213i) q^{87} +(-3.63397 + 6.29423i) q^{89} +(-0.866025 + 2.50000i) q^{91} +(1.93185 - 0.517638i) q^{93} +(2.50026 + 2.50026i) q^{97} -2.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.38014	−	1.15539i	0.899608	−	0.436698i
$7$	2.38014	−	1.15539i	0.899608	−	0.436698i
$8$		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	$-0.794284\pi$
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i	0.602217	+	0.798333i	$0.294284\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.74238	+	6.50266i	−0.422590	+	1.57713i	0.346540	+	0.938035i	$0.387356\pi$
$17$	−1.74238	+	6.50266i	−0.422590	+	1.57713i	−0.769130	+	0.639092i	$0.779310\pi$
$18$		0			0
$19$	−4.23205	+	7.33013i	−0.970899	+	1.68165i	−0.278046	+	0.960568i	$0.589687\pi$
$19$	−4.23205	+	7.33013i	−0.970899	+	1.68165i	−0.692853	+	0.721079i	$0.743647\pi$
$20$		0			0
$21$	−2.59808	+	0.500000i	−0.566947	+	0.109109i
$22$		0			0
$23$	7.20977	−	1.93185i	1.50334	−	0.402819i	0.589123	−	0.808043i	$-0.299473\pi$
$23$	7.20977	−	1.93185i	1.50334	−	0.402819i	0.914217	+	0.405224i	$0.132807\pi$
$24$		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	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$		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
$33$	0.707107	+	2.63896i	0.123091	+	0.459384i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.89778	−	10.8147i	−0.476392	−	1.77792i	−0.616038	−	0.787717i	$-0.711263\pi$
$37$	−2.89778	−	10.8147i	−0.476392	−	1.77792i	0.139646	−	0.990201i	$-0.455403\pi$
$38$		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	0.735410	−	0.677623i	$-0.236990\pi$
$43$	0.378937	+	0.378937i	0.0577874	+	0.0577874i	−0.677623	+	0.735410i	$0.736990\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.84873	−	2.63896i	1.43658	−	0.384932i	0.545248	−	0.838275i	$-0.316435\pi$
$47$	9.84873	−	2.63896i	1.43658	−	0.384932i	0.891336	+	0.453343i	$0.149769\pi$
$48$		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
$53$	−2.26002	+	8.43451i	−0.310438	+	1.15857i	0.617725	+	0.786394i	$0.288055\pi$
$53$	−2.26002	+	8.43451i	−0.310438	+	1.15857i	−0.928163	+	0.372175i	$0.878612\pi$
$54$		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	$0.0394780\pi$
$59$	4.63397	+	8.02628i	0.603292	+	1.04493i	−0.389027	+	0.921226i	$0.627189\pi$
$60$		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
$63$	2.63896	+	0.189469i	0.332478	+	0.0238708i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.76148	+	1.81173i	0.826046	+	0.221338i	0.646988	−	0.762500i	$-0.276028\pi$
$67$	6.76148	+	1.81173i	0.826046	+	0.221338i	0.179058	+	0.983838i	$0.442695\pi$
$68$		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
$73$	14.8678	+	3.98382i	1.74015	+	0.466271i	0.982480	−	0.186370i	$-0.0596722\pi$
$73$	14.8678	+	3.98382i	1.74015	+	0.466271i	0.757668	+	0.652641i	$0.226339\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.98502	−	4.05317i	−0.682057	−	0.461902i
$78$		0			0
$79$	−1.96410	−	1.13397i	−0.220979	−	0.127582i	0.385425	−	0.922739i	$-0.374055\pi$
$79$	−1.96410	−	1.13397i	−0.220979	−	0.127582i	−0.606403	+	0.795157i	$0.707388\pi$
$80$		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	$-0.833625\pi$
$83$	−3.34607	+	3.34607i	−0.367278	+	0.367278i	0.499205	+	0.866484i	$0.333625\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.79315	−	6.69213i	0.192246	−	0.717472i
$88$		0			0
$89$	−3.63397	+	6.29423i	−0.385201	+	0.667187i	−0.991797	−	0.127823i	$-0.959201\pi$
$89$	−3.63397	+	6.29423i	−0.385201	+	0.667187i	0.606596	+	0.795010i	$0.292534\pi$
$90$		0			0
$91$	−0.866025	+	2.50000i	−0.0907841	+	0.262071i
$92$		0			0
$93$	1.93185	−	0.517638i	0.200324	−	0.0536766i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.50026	+	2.50026i	0.253863	+	0.253863i	0.822552	−	0.568690i	$-0.192549\pi$
$97$	2.50026	+	2.50026i	0.253863	+	0.253863i	−0.568690	+	0.822552i	$0.692549\pi$
$98$		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
$103$	1.20616	+	4.50146i	0.118847	+	0.443542i	0.999546	−	0.0301341i	$-0.00959342\pi$
$103$	1.20616	+	4.50146i	0.118847	+	0.443542i	−0.880699	+	0.473676i	$0.842927\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.81294	+	14.2301i	0.368610	+	1.37567i	0.862460	+	0.506125i	$0.168923\pi$
$107$	3.81294	+	14.2301i	0.368610	+	1.37567i	−0.493850	+	0.869547i	$0.664411\pi$
$108$		0			0
$109$	−12.0622	+	6.96410i	−1.15535	+	0.667040i	−0.950185	−	0.311688i	$-0.899106\pi$
$109$	−12.0622	+	6.96410i	−1.15535	+	0.667040i	−0.205163	+	0.978728i	$0.565772\pi$
$110$		0			0
$111$			11.1962i			1.06269i
$112$		0			0
$113$	6.03579	+	6.03579i	0.567800	+	0.567800i	0.931511	−	0.363712i	$-0.118491\pi$
$113$	6.03579	+	6.03579i	0.567800	+	0.567800i	−0.363712	+	0.931511i	$0.618491\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.965926	+	0.258819i	−0.0892999	+	0.0239278i
$118$		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
$123$	1.08604	−	4.05317i	0.0979253	−	0.365462i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.0507680	−	0.0507680i	0.00450493	−	0.00450493i	−0.704851	−	0.709356i	$-0.748986\pi$
$127$	0.0507680	−	0.0507680i	0.00450493	−	0.00450493i	0.709356	+	0.704851i	$0.248986\pi$
$128$		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
$133$	−1.60368	+	22.3364i	−0.139057	+	1.93681i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.79555	−	1.55291i	−0.495148	−	0.132674i	0.00259945	−	0.999997i	$-0.499173\pi$
$137$	−5.79555	−	1.55291i	−0.495148	−	0.132674i	−0.497747	+	0.867322i	$0.665839\pi$
$138$		0			0
$139$	16.8564			1.42974			0.714871	−	0.699256i	$-0.246485\pi$
$139$	16.8564			1.42974			0.714871	+	0.699256i	$0.246485\pi$
$140$		0			0
$141$	−10.1962			−0.858671
$142$		0			0
$143$	2.63896	+	0.707107i	0.220681	+	0.0591312i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.60609	+	4.19187i	−0.462382	+	0.345740i
$148$		0			0
$149$	7.90192	+	4.56218i	0.647351	+	0.373748i	0.787441	−	0.616391i	$-0.211406\pi$
$149$	7.90192	+	4.56218i	0.647351	+	0.373748i	−0.140090	+	0.990139i	$0.544739\pi$
$150$		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
$157$	3.32748	−	12.4183i	0.265562	−	0.991091i	−0.696343	−	0.717709i	$-0.745191\pi$
$157$	3.32748	−	12.4183i	0.265562	−	0.991091i	0.961905	−	0.273382i	$-0.0881424\pi$
$158$		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
$163$	2.89778	−	0.776457i	0.226971	−	0.0608168i	−0.143541	−	0.989644i	$-0.545849\pi$
$163$	2.89778	−	0.776457i	0.226971	−	0.0608168i	0.370512	+	0.928828i	$0.379182\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.240237	−	0.240237i	−0.0185901	−	0.0185901i	0.697751	−	0.716341i	$-0.254184\pi$
$167$	−0.240237	−	0.240237i	−0.0185901	−	0.0185901i	−0.716341	+	0.697751i	$0.754184\pi$
$168$		0			0
$169$			12.0000i			0.923077i
$170$		0			0
$171$	−7.33013	+	4.23205i	−0.560549	+	0.323633i
$172$		0			0
$173$	−3.24453	−	12.1087i	−0.246677	−	0.920611i	−0.972533	−	0.232765i	$-0.925223\pi$
$173$	−3.24453	−	12.1087i	−0.246677	−	0.920611i	0.725856	−	0.687847i	$-0.241444\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.39872	−	8.95215i	−0.180299	−	0.672885i
$178$		0			0
$179$	−8.19615	+	4.73205i	−0.612609	+	0.353690i	−0.773986	−	0.633203i	$-0.781740\pi$
$179$	−8.19615	+	4.73205i	−0.612609	+	0.353690i	0.161377	+	0.986893i	$0.448407\pi$
$180$		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
$187$	17.7656	−	4.76028i	1.29915	−	0.348106i
$188$		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
$193$	3.44760	−	12.8666i	0.248164	−	0.926160i	−0.723603	−	0.690216i	$-0.757515\pi$
$193$	3.44760	−	12.8666i	0.248164	−	0.926160i	0.971767	−	0.235943i	$-0.0758180\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.58630	+	3.58630i	−0.255513	+	0.255513i	−0.823226	−	0.567713i	$-0.807828\pi$
$197$	−3.58630	+	3.58630i	−0.255513	+	0.255513i	0.567713	+	0.823226i	$0.307828\pi$
$198$		0			0
$199$	−4.23205	−	7.33013i	−0.300002	−	0.519619i	0.676134	−	0.736779i	$-0.263654\pi$
$199$	−4.23205	−	7.33013i	−0.300002	−	0.519619i	−0.976136	+	0.217160i	$0.930321\pi$
$200$		0			0
$201$	−6.06218	−	3.50000i	−0.427593	−	0.246871i
$202$		0			0
$203$	8.00481	+	16.4901i	0.561827	+	1.15738i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.20977	+	1.93185i	0.501114	+	0.134273i
$208$		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
$213$	7.72741	+	2.07055i	0.529473	+	0.141872i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.96713	+	4.38134i	−0.201422	+	0.297425i
$218$		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	$-0.764284\pi$
$223$	−0.947343	+	0.947343i	−0.0634388	+	0.0634388i	0.674676	+	0.738114i	$0.264284\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.58630	+	13.3843i	−0.238031	+	0.888345i	0.738728	+	0.674004i	$0.235427\pi$
$227$	−3.58630	+	13.3843i	−0.238031	+	0.888345i	−0.976759	+	0.214341i	$0.931240\pi$
$228$		0			0
$229$	5.86603	−	10.1603i	0.387638	−	0.671408i	−0.604493	−	0.796610i	$-0.706624\pi$
$229$	5.86603	−	10.1603i	0.387638	−	0.671408i	0.992131	+	0.125202i	$0.0399578\pi$
$230$		0			0
$231$	4.73205	+	5.46410i	0.311346	+	0.359511i
$232$		0			0
$233$	−10.3664	+	2.77766i	−0.679123	+	0.181971i	−0.581861	−	0.813288i	$-0.697675\pi$
$233$	−10.3664	+	2.77766i	−0.679123	+	0.181971i	−0.0972622	+	0.995259i	$0.531009\pi$
$234$		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	$0.271994\pi$
$239$			23.3205i			1.50848i	−0.656600	+	0.754239i	$0.728006\pi$
$240$		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
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.19067	−	8.17569i	−0.139389	−	0.520207i
$248$		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
$257$	−20.7835	+	5.56892i	−1.29644	+	0.347380i	−0.840103	−	0.542428i	$-0.817505\pi$
$257$	−20.7835	+	5.56892i	−1.29644	+	0.347380i	−0.456336	+	0.889807i	$0.650839\pi$
$258$		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
$263$	2.34795	−	8.76268i	0.144781	−	0.540330i	−0.854984	−	0.518654i	$-0.826433\pi$
$263$	2.34795	−	8.76268i	0.144781	−	0.540330i	0.999765	−	0.0216758i	$-0.00690017\pi$
$264$		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	0.704903	−	0.709304i	$-0.250991\pi$
$269$	−4.29423	−	7.43782i	−0.261824	−	0.453492i	−0.966727	+	0.255812i	$0.917657\pi$
$270$		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
$273$	1.48356	−	2.19067i	0.0897894	−	0.132585i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−20.4739	−	5.48597i	−1.23016	−	0.329620i	−0.415517	−	0.909585i	$-0.636399\pi$
$277$	−20.4739	−	5.48597i	−1.23016	−	0.329620i	−0.814641	+	0.579966i	$0.803066\pi$
$278$		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
$283$	7.08965	+	1.89967i	0.421436	+	0.112923i	0.463303	−	0.886200i	$-0.346664\pi$
$283$	7.08965	+	1.89967i	0.421436	+	0.112923i	−0.0418674	+	0.999123i	$0.513331\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.84821	+	9.98743i	0.286181	+	0.589539i
$288$		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	$-0.908937\pi$
$293$	−11.5911	+	11.5911i	−0.677160	+	0.677160i	0.282197	+	0.959357i	$0.408937\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.707107	+	2.63896i	−0.0410305	+	0.153128i
$298$		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
$303$	−6.50266	+	1.74238i	−0.373568	+	0.100097i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.79315	−	1.79315i	−0.102341	−	0.102341i	0.654083	−	0.756423i	$-0.273055\pi$
$307$	−1.79315	−	1.79315i	−0.102341	−	0.102341i	−0.756423	+	0.654083i	$0.773055\pi$
$308$		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
$313$	0.656339	+	2.44949i	0.0370985	+	0.138453i	0.981991	−	0.188927i	$-0.0605009\pi$
$313$	0.656339	+	2.44949i	0.0370985	+	0.138453i	−0.944893	+	0.327380i	$0.893834\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.619174	−	2.31079i	−0.0347763	−	0.129787i	0.946355	−	0.323128i	$-0.104734\pi$
$317$	−0.619174	−	2.31079i	−0.0347763	−	0.129787i	−0.981132	+	0.193341i	$0.938068\pi$
$318$		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
$327$	13.4536	−	3.60488i	0.743986	−	0.199351i
$328$		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
$333$	2.89778	−	10.8147i	0.158797	−	0.592639i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.656339	−	0.656339i	0.0357531	−	0.0357531i	−0.689004	−	0.724757i	$-0.741952\pi$
$337$	0.656339	−	0.656339i	0.0357531	−	0.0357531i	0.724757	+	0.689004i	$0.241952\pi$
$338$		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
$343$	3.95164	−	18.0938i	0.213368	−	0.976972i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	34.3065	+	9.19239i	1.84167	+	0.493473i	0.998989	−	0.0449449i	$-0.0143112\pi$
$347$	34.3065	+	9.19239i	1.84167	+	0.493473i	0.842678	+	0.538418i	$0.180978\pi$
$348$		0			0
$349$	−12.9282			−0.692031			−0.346015	−	0.938229i	$-0.612466\pi$
$349$	−12.9282			−0.692031			−0.346015	+	0.938229i	$0.612466\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$		0			0
$353$	−11.2629	−	3.01790i	−0.599466	−	0.160626i	−0.0536901	−	0.998558i	$-0.517098\pi$
$353$	−11.2629	−	3.01790i	−0.599466	−	0.160626i	−0.545776	+	0.837931i	$0.683765\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.27551	−	17.7656i	0.0675073	−	0.940255i
$358$		0			0
$359$	24.2942	+	14.0263i	1.28220	+	0.740279i	0.977250	−	0.212090i	$-0.0680269\pi$
$359$	24.2942	+	14.0263i	1.28220	+	0.740279i	0.304950	+	0.952368i	$0.401360\pi$
$360$		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
$367$	−1.93185	+	7.20977i	−0.100842	+	0.376347i	−0.997840	−	0.0656868i	$-0.979076\pi$
$367$	−1.93185	+	7.20977i	−0.100842	+	0.376347i	0.896998	+	0.442034i	$0.145743\pi$
$368$		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
$373$	14.5397	−	3.89589i	0.752835	−	0.201721i	0.138060	−	0.990424i	$-0.455913\pi$
$373$	14.5397	−	3.89589i	0.752835	−	0.201721i	0.614775	+	0.788702i	$0.289247\pi$
$374$		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	$-0.794315\pi$
$379$		−	23.4449i		−	1.20428i	0.798390	−	0.602141i	$-0.205685\pi$
$380$		0			0
$381$	−0.0621778	+	0.0358984i	−0.00318547	+	0.00183913i
$382$		0			0
$383$	−7.69024	−	28.7004i	−0.392953	−	1.46652i	−0.825239	−	0.564784i	$-0.808960\pi$
$383$	−7.69024	−	28.7004i	−0.392953	−	1.46652i	0.432286	−	0.901737i	$-0.357707\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.138701	+	0.517638i	0.00705055	+	0.0263130i
$388$		0			0
$389$	−15.4186	+	8.90192i	−0.781753	+	0.451345i	−0.837051	−	0.547124i	$-0.815722\pi$
$389$	−15.4186	+	8.90192i	−0.781753	+	0.451345i	0.0552980	+	0.998470i	$0.482389\pi$
$390$		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
$397$	6.31319	−	1.69161i	0.316850	−	0.0848997i	−0.0968891	−	0.995295i	$-0.530889\pi$
$397$	6.31319	−	1.69161i	0.316850	−	0.0848997i	0.413739	+	0.910395i	$0.364223\pi$
$398$		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
$403$	0.517638	−	1.93185i	0.0257854	−	0.0962324i
$404$		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	0.972973	−	0.230918i	$-0.0741728\pi$
$409$	5.79423	+	10.0359i	0.286506	+	0.496243i	−0.686467	+	0.727161i	$0.740839\pi$
$410$		0			0
$411$	5.19615	+	3.00000i	0.256307	+	0.147979i
$412$		0			0
$413$	20.3030	+	13.7496i	0.999047	+	0.676573i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−16.2820	−	4.36276i	−0.797335	−	0.213645i
$418$		0			0
$419$	0.0525589			0.00256767			0.00128383	−	0.999999i	$-0.499591\pi$
$419$	0.0525589			0.00256767			0.00128383	+	0.999999i	$0.499591\pi$
$420$		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
$423$	9.84873	+	2.63896i	0.478861	+	0.128311i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−25.6825	−	1.84392i	−1.24286	−	0.0892335i
$428$		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	−0.0383892	+	0.999263i	$0.512223\pi$
$433$	−21.5921	+	21.5921i	−1.03765	+	1.03765i	−0.999263	+	0.0383892i	$0.987777\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.3514	+	61.0242i	−0.782193	+	2.91918i
$438$		0			0
$439$	−6.89230	+	11.9378i	−0.328952	+	0.569761i	−0.982304	−	0.187293i	$-0.940029\pi$
$439$	−6.89230	+	11.9378i	−0.328952	+	0.569761i	0.653352	+	0.757054i	$0.273362\pi$
$440$		0			0
$441$	6.50000	−	2.59808i	0.309524	−	0.123718i
$442$		0			0
$443$	22.3872	−	5.99863i	1.06365	−	0.285003i	0.315767	−	0.948837i	$-0.397738\pi$
$443$	22.3872	−	5.99863i	1.06365	−	0.285003i	0.747880	+	0.663834i	$0.231072\pi$
$444$		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	$0.0784536\pi$
$449$			10.3397i			0.487963i	−0.969780	+	0.243981i	$0.921546\pi$
$450$		0			0
$451$	9.92820	−	5.73205i	0.467501	−	0.269912i
$452$		0			0
$453$	−2.75908	−	10.2970i	−0.129633	−	0.483796i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.17329	+	15.5749i	0.195218	+	0.728565i	0.992210	+	0.124575i	$0.0397566\pi$
$457$	4.17329	+	15.5749i	0.195218	+	0.728565i	−0.796992	+	0.603990i	$0.793577\pi$
$458$		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	−0.999628	−	0.0272682i	$-0.991319\pi$
$463$	−22.0962	−	22.0962i	−1.02690	−	1.02690i	−0.0272682	−	0.999628i	$-0.508681\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−26.9072	+	7.20977i	−1.24512	+	0.333628i	−0.820449	−	0.571720i	$-0.806276\pi$
$467$	−26.9072	+	7.20977i	−1.24512	+	0.333628i	−0.424669	+	0.905349i	$0.639610\pi$
$468$		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
$473$	0.378937	−	1.41421i	0.0174236	−	0.0650256i
$474$		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	$-0.960180\pi$
$479$	−13.2224	−	22.9019i	−0.604148	−	1.04642i	0.388037	−	0.921644i	$-0.373153\pi$
$480$		0			0
$481$	9.69615	+	5.59808i	0.442106	+	0.255250i
$482$		0			0
$483$	−17.7656	+	8.62398i	−0.808363	+	0.392405i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	24.4577	+	6.55343i	1.10829	+	0.296964i	0.766134	−	0.642681i	$-0.222178\pi$
$487$	24.4577	+	6.55343i	1.10829	+	0.296964i	0.342151	+	0.939645i	$0.388844\pi$
$488$		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
$493$	−45.0518	−	12.0716i	−2.02903	−	0.543677i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−19.0411	+	9.24316i	−0.854111	+	0.414612i
$498$		0			0
$499$	−1.03590	−	0.598076i	−0.0463732	−	0.0267736i	0.476634	−	0.879102i	$-0.341857\pi$
$499$	−1.03590	−	0.598076i	−0.0463732	−	0.0267736i	−0.523007	+	0.852328i	$0.675190\pi$
$500$		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	$-0.596640\pi$
$503$	14.6969	−	14.6969i	0.655304	−	0.655304i	0.954265	+	0.298961i	$0.0966401\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.10583	−	11.5911i	0.137935	−	0.514779i
$508$		0			0
$509$	10.7321	−	18.5885i	0.475690	−	0.823919i	−0.523922	−	0.851766i	$-0.675532\pi$
$509$	10.7321	−	18.5885i	0.475690	−	0.823919i	0.999612	+	0.0278471i	$0.00886516\pi$
$510$		0			0
$511$	39.9904	−	7.69615i	1.76907	−	0.340458i
$512$		0			0
$513$	8.17569	−	2.19067i	0.360966	−	0.0967205i
$514$		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
$523$	−5.00052	−	18.6622i	−0.218657	−	0.816040i	−0.984847	−	0.173426i	$-0.944516\pi$
$523$	−5.00052	−	18.6622i	−0.218657	−	0.816040i	0.766190	−	0.642614i	$-0.222150\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.48477	−	13.0053i	−0.151799	−	0.566521i
$528$		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
$537$	9.14162	−	2.44949i	0.394490	−	0.105703i
$538$		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
$543$	1.65445	−	6.17449i	0.0709993	−	0.264973i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	20.3538	−	20.3538i	0.870265	−	0.870265i	−0.122236	−	0.992501i	$-0.539006\pi$
$547$	20.3538	−	20.3538i	0.870265	−	0.870265i	0.992501	+	0.122236i	$0.0390064\pi$
$548$		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
$553$	−5.98502	−	0.429705i	−0.254509	−	0.0182729i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.24264	+	1.13681i	0.179766	+	0.0481683i	0.347579	−	0.937651i	$-0.387004\pi$
$557$	4.24264	+	1.13681i	0.179766	+	0.0481683i	−0.167813	+	0.985819i	$0.553670\pi$
$558$		0			0
$559$	−0.535898			−0.0226661
$560$		0			0
$561$	−18.3923			−0.776524
$562$		0			0
$563$	−38.1702	−	10.2277i	−1.60868	−	0.431045i	−0.661031	−	0.750358i	$-0.729881\pi$
$563$	−38.1702	−	10.2277i	−1.60868	−	0.431045i	−0.947649	+	0.319314i	$0.896548\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.19067	+	1.48356i	0.0919995	+	0.0623038i
$568$		0			0
$569$	−33.4186	−	19.2942i	−1.40098	−	0.808856i	−0.406487	−	0.913657i	$-0.633246\pi$
$569$	−33.4186	−	19.2942i	−1.40098	−	0.808856i	−0.994493	+	0.104801i	$0.966580\pi$
$570$		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
$577$	2.58819	−	9.65926i	0.107748	−	0.402120i	−0.890895	−	0.454210i	$-0.849922\pi$
$577$	2.58819	−	9.65926i	0.107748	−	0.402120i	0.998642	+	0.0520899i	$0.0165882\pi$
$578$		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
$583$	23.0435	−	6.17449i	0.954365	−	0.255721i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.0101	+	21.0101i	0.867181	+	0.867181i	0.992159	−	0.124979i	$-0.0398862\pi$
$587$	21.0101	+	21.0101i	0.867181	+	0.867181i	−0.124979	+	0.992159i	$0.539886\pi$
$588$		0			0
$589$		−	16.9282i		−	0.697514i
$590$		0			0
$591$	4.39230	−	2.53590i	0.180675	−	0.104313i
$592$		0			0
$593$	9.10446	+	33.9783i	0.373875	+	1.39532i	0.854981	+	0.518659i	$0.173568\pi$
$593$	9.10446	+	33.9783i	0.373875	+	1.39532i	−0.481106	+	0.876662i	$0.659765\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.19067	+	8.17569i	0.0896582	+	0.334609i
$598$		0			0
$599$	−11.9545	+	6.90192i	−0.488447	+	0.282005i	−0.723930	−	0.689874i	$-0.757666\pi$
$599$	−11.9545	+	6.90192i	−0.488447	+	0.282005i	0.235483	+	0.971878i	$0.424333\pi$
$600$		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
$607$	−14.1607	+	3.79435i	−0.574766	+	0.154008i	−0.534481	−	0.845180i	$-0.679493\pi$
$607$	−14.1607	+	3.79435i	−0.574766	+	0.154008i	−0.0402844	+	0.999188i	$0.512826\pi$
$608$		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
$613$	7.20977	−	26.9072i	0.291200	−	1.08677i	−0.652989	−	0.757367i	$-0.726485\pi$
$613$	7.20977	−	26.9072i	0.291200	−	1.08677i	0.944189	−	0.329405i	$-0.106848\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.14110	−	4.14110i	0.166715	−	0.166715i	−0.618819	−	0.785534i	$-0.712389\pi$
$617$	4.14110	−	4.14110i	0.166715	−	0.166715i	0.785534	+	0.618819i	$0.212389\pi$
$618$		0			0
$619$	−19.1962	−	33.2487i	−0.771559	−	1.33638i	−0.936709	−	0.350110i	$-0.886144\pi$
$619$	−19.1962	−	33.2487i	−0.771559	−	1.33638i	0.165150	−	0.986268i	$-0.447189\pi$
$620$		0			0
$621$	−6.46410	−	3.73205i	−0.259395	−	0.149762i
$622$		0			0
$623$	−1.37705	+	19.1798i	−0.0551703	+	0.768423i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−22.3364	−	5.98502i	−0.892030	−	0.239019i
$628$		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
$633$	15.1960	+	4.07175i	0.603987	+	0.161838i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.827225	+	6.95095i	0.0327759	+	0.275407i
$638$		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	−0.411714	+	0.911313i	$0.635070\pi$
$643$	−33.5486	+	33.5486i	−1.32303	+	1.32303i	−0.911313	+	0.411714i	$0.864930\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.19239	−	34.3065i	0.361390	−	1.34873i	−0.510859	−	0.859664i	$-0.670673\pi$
$647$	9.19239	−	34.3065i	0.361390	−	1.34873i	0.872249	−	0.489062i	$-0.162661\pi$
$648$		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
$653$	0.568406	−	0.152304i	0.0222434	−	0.00596011i	−0.247680	−	0.968842i	$-0.579668\pi$
$653$	0.568406	−	0.152304i	0.0222434	−	0.00596011i	0.269924	+	0.962882i	$0.413002\pi$
$654$		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	$-0.964836\pi$
$659$		−	5.66025i		−	0.220492i	0.993904	−	0.110246i	$-0.0351639\pi$
$660$		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
$663$	1.74238	+	6.50266i	0.0676685	+	0.252542i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.3843	+	49.9507i	0.518241	+	1.93410i
$668$		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	0.848683	−	0.528903i	$-0.177396\pi$
$673$	8.29581	+	8.29581i	0.319780	+	0.319780i	−0.528903	+	0.848683i	$0.677396\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.34607	−	0.896575i	0.128600	−	0.0344582i	−0.193945	−	0.981012i	$-0.562128\pi$
$677$	3.34607	−	0.896575i	0.128600	−	0.0344582i	0.322545	+	0.946554i	$0.395462\pi$
$678$		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
$683$	2.91636	−	10.8840i	0.111591	−	0.416465i	−0.887418	−	0.460966i	$-0.847503\pi$
$683$	2.91636	−	10.8840i	0.111591	−	0.416465i	0.999009	+	0.0445009i	$0.0141698\pi$
$684$		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
$693$	−3.15660	−	6.50266i	−0.119909	−	0.247016i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−27.2862	−	7.31130i	−1.03354	−	0.276935i
$698$		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
$703$	91.5363	+	24.5271i	3.45236	+	0.925056i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.98743	−	14.7477i	0.375616	−	0.554645i
$708$		0			0
$709$	−4.45448	−	2.57180i	−0.167292	−	0.0965859i	0.414017	−	0.910269i	$-0.364126\pi$
$709$	−4.45448	−	2.57180i	−0.167292	−	0.0965859i	−0.581308	+	0.813684i	$0.697459\pi$
$710$		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
$717$	6.03579	−	22.5259i	0.225411	−	0.841244i
$718$		0			0
$719$	4.75833	−	8.24167i	0.177456	−	0.307362i	−0.763553	−	0.645746i	$-0.776547\pi$
$719$	4.75833	−	8.24167i	0.177456	−	0.307362i	0.941008	+	0.338383i	$0.109880\pi$
$720$		0			0
$721$	8.07180	+	9.32051i	0.300609	+	0.347114i
$722$		0			0
$723$	10.8147	−	2.89778i	0.402201	−	0.107770i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	0.568406	+	0.568406i	0.0210810	+	0.0210810i	0.717569	−	0.696488i	$-0.245255\pi$
$727$	0.568406	+	0.568406i	0.0210810	+	0.0210810i	−0.696488	+	0.717569i	$0.745255\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−3.12436	+	1.80385i	−0.115558	+	0.0667177i
$732$		0			0
$733$	−4.26122	−	15.9031i	−0.157392	−	0.587394i	−0.998889	−	0.0471323i	$-0.984992\pi$
$733$	−4.26122	−	15.9031i	−0.157392	−	0.587394i	0.841497	−	0.540262i	$-0.181675\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.94975	−	18.4727i	−0.182326	−	0.680451i
$738$		0			0
$739$	−25.0359	+	14.4545i	−0.920960	+	0.531717i	−0.883941	−	0.467598i	$-0.845120\pi$
$739$	−25.0359	+	14.4545i	−0.920960	+	0.531717i	−0.0370191	+	0.999315i	$0.511786\pi$
$740$		0			0
$741$			8.46410i			0.310937i
$742$		0			0
$743$	−24.1160	−	24.1160i	−0.884729	−	0.884729i	0.109282	−	0.994011i	$-0.465145\pi$
$743$	−24.1160	−	24.1160i	−0.884729	−	0.884729i	−0.994011	+	0.109282i	$0.965145\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.57081	+	1.22474i	−0.167237	+	0.0448111i
$748$		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
$753$	2.74049	−	10.2277i	0.0998692	−	0.372717i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.74479	−	5.74479i	0.208798	−	0.208798i	−0.594959	−	0.803756i	$-0.702832\pi$
$757$	5.74479	−	5.74479i	0.208798	−	0.208798i	0.803756	+	0.594959i	$0.202832\pi$
$758$		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
$763$	−20.6634	+	30.5121i	−0.748065	+	1.10461i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.95215	−	2.39872i	−0.323243	−	0.0866128i
$768$		0			0
$769$	−21.3205			−0.768837			−0.384419	−	0.923159i	$-0.625598\pi$
$769$	−21.3205			−0.768837			−0.384419	+	0.923159i	$0.625598\pi$
$770$		0			0
$771$	21.5167			0.774904
$772$		0			0
$773$	−3.10583	−	0.832204i	−0.111709	−	0.0299323i	0.202532	−	0.979276i	$-0.435083\pi$
$773$	−3.10583	−	0.832204i	−0.111709	−	0.0299323i	−0.314240	+	0.949343i	$0.601750\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	12.9360	+	26.6484i	0.464075	+	0.956006i
$778$		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
$787$	0.106515	−	0.397520i	0.00379685	−	0.0141700i	−0.964001	−	0.265897i	$-0.914332\pi$
$787$	0.106515	−	0.397520i	0.00379685	−	0.0141700i	0.967798	+	0.251727i	$0.0809985\pi$
$788$		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
$793$	9.40044	−	2.51884i	0.333819	−	0.0894466i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−29.9759	−	29.9759i	−1.06180	−	1.06180i	−0.997960	−	0.0638402i	$-0.979665\pi$
$797$	−29.9759	−	29.9759i	−1.06180	−	1.06180i	−0.0638402	−	0.997960i	$-0.520335\pi$
$798$		0			0
$799$			68.6410i			2.42834i
$800$		0			0
$801$	−6.29423	+	3.63397i	−0.222396	+	0.128400i
$802$		0			0
$803$	−10.8840	−	40.6197i	−0.384088	−	1.43344i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.22286	+	8.29581i	0.0782482	+	0.292026i
$808$		0			0
$809$	−44.5692	+	25.7321i	−1.56697	+	0.904691i	−0.570451	+	0.821332i	$0.693231\pi$
$809$	−44.5692	+	25.7321i	−1.56697	+	0.904691i	−0.996520	+	0.0833589i	$0.973435\pi$
$810$		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
$817$	−4.38134	+	1.17398i	−0.153284	+	0.0410723i
$818$		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
$823$	0.0829536	−	0.309587i	0.00289158	−	0.0107915i	−0.964465	−	0.264211i	$-0.914889\pi$
$823$	0.0829536	−	0.309587i	0.00289158	−	0.0107915i	0.967357	+	0.253419i	$0.0815552\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.2784	−	10.2784i	0.357416	−	0.357416i	−0.505444	−	0.862860i	$-0.668671\pi$
$827$	10.2784	−	10.2784i	0.357416	−	0.357416i	0.862860	+	0.505444i	$0.168671\pi$
$828$		0			0
$829$	22.7224	+	39.3564i	0.789183	+	1.36690i	0.926468	+	0.376373i	$0.122829\pi$
$829$	22.7224	+	39.3564i	0.789183	+	1.36690i	−0.137286	+	0.990532i	$0.543838\pi$
$830$		0			0
$831$	18.3564	+	10.5981i	0.636777	+	0.367643i
$832$		0			0
$833$	28.2199	+	37.7405i	0.977762	+	1.30763i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.93185	+	0.517638i	0.0667746	+	0.0178922i
$838$		0			0
$839$	51.9615			1.79391			0.896956	−	0.442121i	$-0.145774\pi$
$839$	51.9615			1.79391			0.896956	+	0.442121i	$0.145774\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$		0			0
$843$	8.57321	+	2.29719i	0.295277	+	0.0791193i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.669942	−	9.33109i	0.0230195	−	0.320620i
$848$		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	$-0.872918\pi$
$853$	−15.5563	+	15.5563i	−0.532639	+	0.532639i	0.388718	+	0.921357i	$0.372918\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.37756	−	23.8014i	0.217853	−	0.813040i	−0.767289	−	0.641301i	$-0.778395\pi$
$857$	6.37756	−	23.8014i	0.217853	−	0.813040i	0.985143	−	0.171739i	$-0.0549385\pi$
$858$		0			0
$859$	−0.464102	+	0.803848i	−0.0158349	+	0.0274269i	−0.873834	−	0.486224i	$-0.838374\pi$
$859$	−0.464102	+	0.803848i	−0.0158349	+	0.0274269i	0.857999	+	0.513651i	$0.171707\pi$
$860$		0			0
$861$	−2.09808	−	10.9019i	−0.0715022	−	0.371537i
$862$		0			0
$863$	43.0691	−	11.5403i	1.46609	−	0.392838i	0.564502	−	0.825432i	$-0.309068\pi$
$863$	43.0691	−	11.5403i	1.46609	−	0.392838i	0.901589	+	0.432594i	$0.142402\pi$
$864$		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
$873$	0.915158	+	3.41542i	0.0309734	+	0.115594i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.72191	+	10.1583i	0.0919124	+	0.343022i	0.996533	−	0.0831954i	$-0.0265126\pi$
$877$	2.72191	+	10.1583i	0.0919124	+	0.343022i	−0.904621	+	0.426217i	$0.859846\pi$
$878$		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	0.703283	−	0.710910i	$-0.251717\pi$
$883$	−0.226633	−	0.226633i	−0.00762682	−	0.00762682i	−0.710910	+	0.703283i	$0.751717\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.0740	−	4.30701i	0.539712	−	0.144615i	0.0213425	−	0.999772i	$-0.493206\pi$
$887$	16.0740	−	4.30701i	0.539712	−	0.144615i	0.518369	+	0.855157i	$0.326539\pi$
$888$		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
$893$	−22.3364	+	83.3606i	−0.747460	+	2.78956i
$894$		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
$903$	−1.17398	−	0.795040i	−0.0390675	−	0.0264573i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−15.7644	−	4.22406i	−0.523448	−	0.140258i	−0.0125871	−	0.999921i	$-0.504007\pi$
$907$	−15.7644	−	4.22406i	−0.523448	−	0.140258i	−0.510861	+	0.859663i	$0.670673\pi$
$908$		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
$913$	12.4877	+	3.34607i	0.413282	+	0.110739i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	44.6728	+	3.20736i	1.47523	+	0.105917i
$918$		0			0
$919$	−10.3923	−	6.00000i	−0.342811	−	0.197922i	0.318704	−	0.947854i	$-0.396753\pi$
$919$	−10.3923	−	6.00000i	−0.342811	−	0.197922i	−0.661514	+	0.749933i	$0.730086\pi$
$920$		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
$927$	−1.20616	+	4.50146i	−0.0396156	+	0.147847i
$928$		0			0
$929$	6.09808	−	10.5622i	0.200071	−	0.346534i	−0.748480	−	0.663158i	$-0.769216\pi$
$929$	6.09808	−	10.5622i	0.200071	−	0.346534i	0.948551	+	0.316624i	$0.102549\pi$
$930$		0			0
$931$	21.9904	+	55.0167i	0.720706	+	1.80310i
$932$		0			0
$933$	−5.79555	+	1.55291i	−0.189738	+	0.0508401i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.8685	+	11.8685i	0.387727	+	0.387727i	0.873876	−	0.486149i	$-0.161599\pi$
$937$	11.8685	+	11.8685i	0.387727	+	0.387727i	−0.486149	+	0.873876i	$0.661599\pi$
$938$		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
$943$	8.10634	+	30.2533i	0.263979	+	0.985183i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.44812	+	31.5288i	0.274527	+	1.02455i	0.956158	+	0.292852i	$0.0946044\pi$
$947$	8.44812	+	31.5288i	0.274527	+	1.02455i	−0.681631	+	0.731696i	$0.738729\pi$
$948$		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	0.745098	−	0.666955i	$-0.232403\pi$
$953$	2.41233	+	2.41233i	0.0781429	+	0.0781429i	−0.666955	+	0.745098i	$0.732403\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−18.2832	+	4.89898i	−0.591013	+	0.158362i
$958$		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
$963$	−3.81294	+	14.2301i	−0.122870	+	0.458558i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.50026	−	2.50026i	0.0804029	−	0.0804029i	−0.665762	−	0.746164i	$-0.731893\pi$
$967$	2.50026	−	2.50026i	0.0804029	−	0.0804029i	0.746164	+	0.665762i	$0.231893\pi$
$968$		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
$973$	40.1206	−	19.4758i	1.28621	−	0.624365i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.7506	+	6.36396i	0.759850	+	0.203601i	0.617883	−	0.786270i	$-0.287991\pi$
$977$	23.7506	+	6.36396i	0.759850	+	0.203601i	0.141967	+	0.989871i	$0.454657\pi$
$978$		0			0
$979$	19.8564			0.634614
$980$		0			0
$981$	−13.9282			−0.444693
$982$		0			0
$983$	−2.39872	−	0.642736i	−0.0765073	−	0.0205001i	0.220362	−	0.975418i	$-0.429276\pi$
$983$	−2.39872	−	0.642736i	−0.0765073	−	0.0205001i	−0.296870	+	0.954918i	$0.595943\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−24.2683	+	11.7806i	−0.772467	+	0.374980i
$988$		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
$997$	−9.02150	+	33.6687i	−0.285714	+	1.06630i	0.662602	+	0.748971i	$0.269452\pi$
$997$	−9.02150	+	33.6687i	−0.285714	+	1.06630i	−0.948316	+	0.317327i	$0.897215\pi$
$998$		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.a.1993.1	yes	8
5.2	odd	4		2100.2.ce.b.1657.1	yes	8
5.3	odd	4		2100.2.ce.b.1657.2	yes	8
5.4	even	2	inner	2100.2.ce.a.1993.2	yes	8
7.3	odd	6		2100.2.ce.b.493.1	yes	8
35.3	even	12	inner	2100.2.ce.a.157.2	yes	8
35.17	even	12	inner	2100.2.ce.a.157.1	✓	8
35.24	odd	6		2100.2.ce.b.493.2	yes	8

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

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)

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