LMFDB - Embedded newform 2100.2.ce.e.493.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.5
Character	$\chi$	$=$	2100.493
Dual form			2100.2.ce.e.1657.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{3} +(-1.80016 - 1.93892i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{3} +(-1.80016 - 1.93892i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(2.59908 - 4.50174i) q^{11} +(-4.04593 + 4.04593i) q^{13} +(-1.22333 + 0.327789i) q^{17} +(3.15056 + 5.45692i) q^{19} +(1.40694 - 2.24065i) q^{21} +(-0.650490 + 2.42766i) q^{23} +(-0.707107 - 0.707107i) q^{27} -6.75763i q^{29} +(-8.26714 - 4.77304i) q^{31} +(5.02104 + 1.34538i) q^{33} +(-5.80126 - 1.55444i) q^{37} +(-4.95523 - 2.86090i) q^{39} +8.93326i q^{41} +(-2.26710 - 2.26710i) q^{43} +(-0.418520 + 1.56194i) q^{47} +(-0.518842 + 6.98075i) q^{49} +(-0.633240 - 1.09680i) q^{51} +(-9.35687 + 2.50717i) q^{53} +(-4.45556 + 4.45556i) q^{57} +(-5.58668 + 9.67641i) q^{59} +(1.32114 - 0.762763i) q^{61} +(2.52845 + 0.779076i) q^{63} +(-0.699229 - 2.60956i) q^{67} -2.51330 q^{69} -11.6584 q^{71} +(2.03522 + 7.59553i) q^{73} +(-13.4073 + 3.06444i) q^{77} +(1.49223 - 0.861538i) q^{79} +(0.500000 - 0.866025i) q^{81} +(5.17905 - 5.17905i) q^{83} +(6.52737 - 1.74900i) q^{87} +(-3.44514 - 5.96716i) q^{89} +(15.1281 + 0.561420i) q^{91} +(2.47070 - 9.22080i) q^{93} +(-12.2173 - 12.2173i) q^{97} +5.19816i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) $ 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.80016	−	1.93892i	−0.680397	−	0.732844i
$7$	−1.80016	−	1.93892i	−0.680397	−	0.732844i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	2.59908	−	4.50174i	0.783653	−	1.35733i	−0.146148	−	0.989263i	$-0.546688\pi$
$11$	2.59908	−	4.50174i	0.783653	−	1.35733i	0.929801	−	0.368064i	$-0.119979\pi$
$12$		0			0
$13$	−4.04593	+	4.04593i	−1.12214	+	1.12214i	−0.130719	+	0.991419i	$0.541729\pi$
$13$	−4.04593	+	4.04593i	−1.12214	+	1.12214i	−0.991419	+	0.130719i	$0.958271\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.22333	+	0.327789i	−0.296700	+	0.0795005i	−0.404098	−	0.914716i	$-0.632415\pi$
$17$	−1.22333	+	0.327789i	−0.296700	+	0.0795005i	0.107398	+	0.994216i	$0.465748\pi$
$18$		0			0
$19$	3.15056	+	5.45692i	0.722787	+	1.25190i	0.959878	+	0.280417i	$0.0904726\pi$
$19$	3.15056	+	5.45692i	0.722787	+	1.25190i	−0.237091	+	0.971487i	$0.576194\pi$
$20$		0			0
$21$	1.40694	−	2.24065i	0.307019	−	0.488950i
$22$		0			0
$23$	−0.650490	+	2.42766i	−0.135636	+	0.506202i	0.864358	+	0.502877i	$0.167725\pi$
$23$	−0.650490	+	2.42766i	−0.135636	+	0.506202i	−0.999994	+	0.00332527i	$0.998942\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	6.75763i		−	1.25486i	−0.778673	−	0.627430i	$-0.784107\pi$
$29$		−	6.75763i		−	1.25486i	0.778673	−	0.627430i	$-0.215893\pi$
$30$		0			0
$31$	−8.26714	−	4.77304i	−1.48482	−	0.857262i	−0.484971	−	0.874530i	$-0.661170\pi$
$31$	−8.26714	−	4.77304i	−1.48482	−	0.857262i	−0.999851	+	0.0172678i	$0.994503\pi$
$32$		0			0
$33$	5.02104	+	1.34538i	0.874051	+	0.234201i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.80126	−	1.55444i	−0.953722	−	0.255549i	−0.251781	−	0.967784i	$-0.581016\pi$
$37$	−5.80126	−	1.55444i	−0.953722	−	0.255549i	−0.701941	+	0.712235i	$0.747683\pi$
$38$		0			0
$39$	−4.95523	−	2.86090i	−0.793472	−	0.458111i
$40$		0			0
$41$			8.93326i			1.39514i	0.716516	+	0.697570i	$0.245735\pi$
$41$			8.93326i			1.39514i	−0.716516	+	0.697570i	$0.754265\pi$
$42$		0			0
$43$	−2.26710	−	2.26710i	−0.345729	−	0.345729i	0.512787	−	0.858516i	$-0.328613\pi$
$43$	−2.26710	−	2.26710i	−0.345729	−	0.345729i	−0.858516	+	0.512787i	$0.828613\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.418520	+	1.56194i	−0.0610474	+	0.227832i	−0.989709	−	0.143097i	$-0.954294\pi$
$47$	−0.418520	+	1.56194i	−0.0610474	+	0.227832i	0.928661	+	0.370929i	$0.120961\pi$
$48$		0			0
$49$	−0.518842	+	6.98075i	−0.0741202	+	0.997249i
$50$		0			0
$51$	−0.633240	−	1.09680i	−0.0886713	−	0.153583i
$52$		0			0
$53$	−9.35687	+	2.50717i	−1.28526	+	0.344386i	−0.835860	−	0.548943i	$-0.815031\pi$
$53$	−9.35687	+	2.50717i	−1.28526	+	0.344386i	−0.449405	+	0.893328i	$0.648364\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.45556	+	4.45556i	−0.590153	+	0.590153i
$58$		0			0
$59$	−5.58668	+	9.67641i	−0.727324	+	1.25976i	0.230687	+	0.973028i	$0.425903\pi$
$59$	−5.58668	+	9.67641i	−0.727324	+	1.25976i	−0.958010	+	0.286734i	$0.907431\pi$
$60$		0			0
$61$	1.32114	−	0.762763i	0.169155	−	0.0976618i	−0.413032	−	0.910716i	$-0.635530\pi$
$61$	1.32114	−	0.762763i	0.169155	−	0.0976618i	0.582187	+	0.813055i	$0.302197\pi$
$62$		0			0
$63$	2.52845	+	0.779076i	0.318554	+	0.0981543i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.699229	−	2.60956i	−0.0854245	−	0.318808i	0.909970	−	0.414675i	$-0.136105\pi$
$67$	−0.699229	−	2.60956i	−0.0854245	−	0.318808i	−0.995394	+	0.0958661i	$0.969438\pi$
$68$		0			0
$69$	−2.51330			−0.302566
$70$		0			0
$71$	−11.6584			−1.38359			−0.691797	−	0.722092i	$-0.743181\pi$
$71$	−11.6584			−1.38359			−0.691797	+	0.722092i	$0.743181\pi$
$72$		0			0
$73$	2.03522	+	7.59553i	0.238204	+	0.888990i	0.976678	+	0.214708i	$0.0688801\pi$
$73$	2.03522	+	7.59553i	0.238204	+	0.888990i	−0.738474	+	0.674282i	$0.764453\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−13.4073	+	3.06444i	−1.52790	+	0.349225i
$78$		0			0
$79$	1.49223	−	0.861538i	0.167889	−	0.0969307i	−0.413701	−	0.910413i	$-0.635764\pi$
$79$	1.49223	−	0.861538i	0.167889	−	0.0969307i	0.581590	+	0.813482i	$0.302431\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	5.17905	−	5.17905i	0.568475	−	0.568475i	−0.363226	−	0.931701i	$-0.618325\pi$
$83$	5.17905	−	5.17905i	0.568475	−	0.568475i	0.931701	+	0.363226i	$0.118325\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.52737	−	1.74900i	0.699808	−	0.187513i
$88$		0			0
$89$	−3.44514	−	5.96716i	−0.365184	−	0.632517i	0.623622	−	0.781726i	$-0.285661\pi$
$89$	−3.44514	−	5.96716i	−0.365184	−	0.632517i	−0.988806	+	0.149209i	$0.952327\pi$
$90$		0			0
$91$	15.1281	+	0.561420i	1.58585	+	0.0588528i
$92$		0			0
$93$	2.47070	−	9.22080i	0.256200	−	0.956152i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−12.2173	−	12.2173i	−1.24048	−	1.24048i	−0.959802	−	0.280677i	$-0.909441\pi$
$97$	−12.2173	−	12.2173i	−1.24048	−	1.24048i	−0.280677	−	0.959802i	$-0.590559\pi$
$98$		0			0
$99$			5.19816i			0.522435i
$100$		0			0
$101$	−1.98176	−	1.14417i	−0.197193	−	0.113849i	0.398153	−	0.917319i	$-0.369651\pi$
$101$	−1.98176	−	1.14417i	−0.197193	−	0.113849i	−0.595345	+	0.803470i	$0.702985\pi$
$102$		0			0
$103$	1.47620	+	0.395546i	0.145454	+	0.0389743i	0.330811	−	0.943697i	$-0.392678\pi$
$103$	1.47620	+	0.395546i	0.145454	+	0.0389743i	−0.185357	+	0.982671i	$0.559344\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.46463	−	0.392445i	−0.141591	−	0.0379391i	0.187328	−	0.982298i	$-0.440017\pi$
$107$	−1.46463	−	0.392445i	−0.141591	−	0.0379391i	−0.328918	+	0.944358i	$0.606684\pi$
$108$		0			0
$109$	−9.00437	−	5.19868i	−0.862462	−	0.497943i	0.00237373	−	0.999997i	$-0.499244\pi$
$109$	−9.00437	−	5.19868i	−0.862462	−	0.497943i	−0.864836	+	0.502054i	$0.832578\pi$
$110$		0			0
$111$		−	6.00591i		−	0.570056i
$112$		0			0
$113$	2.57700	+	2.57700i	0.242423	+	0.242423i	0.817852	−	0.575429i	$-0.195165\pi$
$113$	2.57700	+	2.57700i	0.242423	+	0.242423i	−0.575429	+	0.817852i	$0.695165\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.48091	−	5.52684i	0.136910	−	0.510957i
$118$		0			0
$119$	2.83774	+	1.78186i	0.260135	+	0.163343i
$120$		0			0
$121$	−8.01046	−	13.8745i	−0.728223	−	1.26132i
$122$		0			0
$123$	−8.62886	+	2.31210i	−0.778038	+	0.208475i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.56921	−	8.56921i	0.760395	−	0.760395i	−0.215999	−	0.976394i	$-0.569301\pi$
$127$	8.56921	−	8.56921i	0.760395	−	0.760395i	0.976394	+	0.215999i	$0.0693008\pi$
$128$		0			0
$129$	1.60308	−	2.77662i	0.141143	−	0.244468i
$130$		0			0
$131$	−9.84058	+	5.68146i	−0.859776	+	0.496392i	−0.863937	−	0.503600i	$-0.832009\pi$
$131$	−9.84058	+	5.68146i	−0.859776	+	0.496392i	0.00416145	+	0.999991i	$0.498675\pi$
$132$		0			0
$133$	4.90904	−	15.9320i	0.425668	−	1.38148i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.994902	+	3.71302i	0.0850002	+	0.317225i	0.995314	−	0.0966933i	$-0.0308266\pi$
$137$	0.994902	+	3.71302i	0.0850002	+	0.317225i	−0.910314	+	0.413918i	$0.864160\pi$
$138$		0			0
$139$	−9.20204			−0.780507			−0.390254	−	0.920707i	$-0.627613\pi$
$139$	−9.20204			−0.780507			−0.390254	+	0.920707i	$0.627613\pi$
$140$		0			0
$141$	−1.61704			−0.136179
$142$		0			0
$143$	7.69803	+	28.7294i	0.643741	+	2.40248i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.87717	+	1.30559i	−0.567219	+	0.107683i
$148$		0			0
$149$	−0.487962	+	0.281725i	−0.0399754	+	0.0230798i	−0.519855	−	0.854255i	$-0.674014\pi$
$149$	−0.487962	+	0.281725i	−0.0399754	+	0.0230798i	0.479879	+	0.877335i	$0.340681\pi$
$150$		0			0
$151$	0.896891	−	1.55346i	0.0729880	−	0.126419i	−0.827222	−	0.561876i	$-0.810080\pi$
$151$	0.896891	−	1.55346i	0.0729880	−	0.126419i	0.900210	+	0.435457i	$0.143413\pi$
$152$		0			0
$153$	0.895536	−	0.895536i	0.0723998	−	0.0723998i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.25420	−	0.336061i	0.100096	−	0.0268206i	−0.208423	−	0.978039i	$-0.566833\pi$
$157$	1.25420	−	0.336061i	0.100096	−	0.0268206i	0.308519	+	0.951218i	$0.400167\pi$
$158$		0			0
$159$	−4.84347	−	8.38914i	−0.384112	−	0.665302i
$160$		0			0
$161$	5.87803	−	3.10893i	0.463254	−	0.245018i
$162$		0			0
$163$	−3.14467	+	11.7361i	−0.246310	+	0.919241i	0.726411	+	0.687261i	$0.241187\pi$
$163$	−3.14467	+	11.7361i	−0.246310	+	0.919241i	−0.972721	+	0.231980i	$0.925480\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.32502	+	8.32502i	0.644210	+	0.644210i	0.951588	−	0.307378i	$-0.0994516\pi$
$167$	8.32502	+	8.32502i	0.644210	+	0.644210i	−0.307378	+	0.951588i	$0.599452\pi$
$168$		0			0
$169$		−	19.7391i		−	1.51839i
$170$		0			0
$171$	−5.45692	−	3.15056i	−0.417301	−	0.240929i
$172$		0			0
$173$	−17.9699	−	4.81501i	−1.36622	−	0.366079i	−0.500126	−	0.865953i	$-0.666713\pi$
$173$	−17.9699	−	4.81501i	−1.36622	−	0.366079i	−0.866098	+	0.499874i	$0.833380\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.7926	−	2.89188i	−0.811224	−	0.217367i
$178$		0			0
$179$	16.6929	+	9.63766i	1.24769	+	0.720353i	0.970648	−	0.240506i	$-0.0773133\pi$
$179$	16.6929	+	9.63766i	1.24769	+	0.720353i	0.277040	+	0.960858i	$0.410647\pi$
$180$		0			0
$181$		−	16.4279i		−	1.22108i	−0.791986	−	0.610539i	$-0.790953\pi$
$181$		−	16.4279i		−	1.22108i	0.791986	−	0.610539i	$-0.209047\pi$
$182$		0			0
$183$	1.07871	+	1.07871i	0.0797405	+	0.0797405i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.70390	+	6.35905i	−0.124602	+	0.465020i
$188$		0			0
$189$	−0.0981194	+	2.64393i	−0.00713713	+	0.192318i
$190$		0			0
$191$	12.5756	+	21.7815i	0.909937	+	1.57606i	0.814150	+	0.580655i	$0.197204\pi$
$191$	12.5756	+	21.7815i	0.909937	+	1.57606i	0.0957872	+	0.995402i	$0.469463\pi$
$192$		0			0
$193$	−1.15548	+	0.309610i	−0.0831732	+	0.0222862i	−0.300166	−	0.953887i	$-0.597042\pi$
$193$	−1.15548	+	0.309610i	−0.0831732	+	0.0222862i	0.216992	+	0.976173i	$0.430375\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.5844	−	12.5844i	0.896604	−	0.896604i	−0.0985305	−	0.995134i	$-0.531414\pi$
$197$	12.5844	−	12.5844i	0.896604	−	0.896604i	0.995134	+	0.0985305i	$0.0314142\pi$
$198$		0			0
$199$	0.359578	−	0.622808i	0.0254898	−	0.0441497i	−0.852999	−	0.521912i	$-0.825219\pi$
$199$	0.359578	−	0.622808i	0.0254898	−	0.0441497i	0.878489	+	0.477763i	$0.158552\pi$
$200$		0			0
$201$	2.33967	−	1.35081i	0.165027	−	0.0952786i
$202$		0			0
$203$	−13.1025	+	12.1648i	−0.919617	+	0.853803i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.650490	−	2.42766i	−0.0452122	−	0.168734i
$208$		0			0
$209$	32.7542			2.26566
$210$		0			0
$211$	−5.57873			−0.384056			−0.192028	−	0.981389i	$-0.561506\pi$
$211$	−5.57873			−0.384056			−0.192028	+	0.981389i	$0.561506\pi$
$212$		0			0
$213$	−3.01741	−	11.2611i	−0.206750	−	0.771600i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.62764	+	24.6216i	0.382029	+	1.67142i
$218$		0			0
$219$	−6.80997	+	3.93174i	−0.460175	+	0.265682i
$220$		0			0
$221$	3.62328	−	6.27570i	0.243728	−	0.422149i
$222$		0			0
$223$	15.5509	−	15.5509i	1.04136	−	1.04136i	0.0422554	−	0.999107i	$-0.486546\pi$
$223$	15.5509	−	15.5509i	1.04136	−	1.04136i	0.999107	−	0.0422554i	$-0.0134543\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.87684	+	0.502898i	−0.124570	+	0.0333785i	−0.320566	−	0.947226i	$-0.603873\pi$
$227$	−1.87684	+	0.502898i	−0.124570	+	0.0333785i	0.195995	+	0.980605i	$0.437206\pi$
$228$		0			0
$229$	−1.89220	−	3.27738i	−0.125040	−	0.216575i	0.796709	−	0.604364i	$-0.206573\pi$
$229$	−1.89220	−	3.27738i	−0.125040	−	0.216575i	−0.921749	+	0.387788i	$0.873239\pi$
$230$		0			0
$231$	−6.43009	−	12.1573i	−0.423069	−	0.799893i
$232$		0			0
$233$	2.60704	−	9.72959i	0.170793	−	0.637407i	−0.826437	−	0.563029i	$-0.809636\pi$
$233$	2.60704	−	9.72959i	0.170793	−	0.637407i	0.997230	−	0.0743783i	$-0.0236972\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.21840	+	1.21840i	0.0791435	+	0.0791435i
$238$		0			0
$239$			13.1578i			0.851110i	0.904933	+	0.425555i	$0.139921\pi$
$239$			13.1578i			0.851110i	−0.904933	+	0.425555i	$0.860079\pi$
$240$		0			0
$241$	−8.94291	−	5.16319i	−0.576063	−	0.332590i	0.183504	−	0.983019i	$-0.441256\pi$
$241$	−8.94291	−	5.16319i	−0.576063	−	0.332590i	−0.759567	+	0.650429i	$0.774589\pi$
$242$		0			0
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−34.8252	−	9.33140i	−2.21588	−	0.593742i
$248$		0			0
$249$	6.34302	+	3.66214i	0.401973	+	0.232079i
$250$		0			0
$251$			4.72936i			0.298515i	0.988798	+	0.149257i	$0.0476883\pi$
$251$			4.72936i			0.298515i	−0.988798	+	0.149257i	$0.952312\pi$
$252$		0			0
$253$	9.23803	+	9.23803i	0.580790	+	0.580790i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.63076	−	6.08609i	0.101724	−	0.379640i	−0.896229	−	0.443592i	$-0.853704\pi$
$257$	1.63076	−	6.08609i	0.101724	−	0.379640i	0.997953	+	0.0639523i	$0.0203705\pi$
$258$		0			0
$259$	7.42926	+	14.0465i	0.461632	+	0.872804i
$260$		0			0
$261$	3.37882	+	5.85228i	0.209143	+	0.362247i
$262$		0			0
$263$	−19.8204	+	5.31086i	−1.22218	+	0.327482i	−0.811530	−	0.584311i	$-0.801365\pi$
$263$	−19.8204	+	5.31086i	−1.22218	+	0.327482i	−0.410650	+	0.911793i	$0.634698\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	4.87216	−	4.87216i	0.298171	−	0.298171i
$268$		0			0
$269$	0.296005	−	0.512696i	0.0180478	−	0.0312596i	−0.856860	−	0.515548i	$-0.827588\pi$
$269$	0.296005	−	0.512696i	0.0180478	−	0.0312596i	0.874908	+	0.484289i	$0.160922\pi$
$270$		0			0
$271$	0.538407	−	0.310849i	0.0327059	−	0.0188827i	−0.483558	−	0.875312i	$-0.660656\pi$
$271$	0.538407	−	0.310849i	0.0327059	−	0.0188827i	0.516264	+	0.856430i	$0.327322\pi$
$272$		0			0
$273$	3.37314	+	14.7579i	0.204152	+	0.893188i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.79167	+	21.6148i	0.347988	+	1.29871i	0.889083	+	0.457747i	$0.151343\pi$
$277$	5.79167	+	21.6148i	0.347988	+	1.29871i	−0.541095	+	0.840962i	$0.681990\pi$
$278$		0			0
$279$	9.54607			0.571508
$280$		0			0
$281$	1.43896			0.0858411			0.0429205	−	0.999078i	$-0.486334\pi$
$281$	1.43896			0.0858411			0.0429205	+	0.999078i	$0.486334\pi$
$282$		0			0
$283$	0.290720	+	1.08498i	0.0172815	+	0.0644955i	0.974028	−	0.226427i	$-0.0727045\pi$
$283$	0.290720	+	1.08498i	0.0172815	+	0.0644955i	−0.956747	+	0.290923i	$0.906038\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	17.3209	−	16.0813i	1.02242	−	0.949249i
$288$		0			0
$289$	−13.3334	+	7.69801i	−0.784315	+	0.452824i
$290$		0			0
$291$	8.63894	−	14.9631i	0.506423	−	0.877151i
$292$		0			0
$293$	−8.66246	+	8.66246i	−0.506066	+	0.506066i	−0.913317	−	0.407250i	$-0.866488\pi$
$293$	−8.66246	+	8.66246i	−0.506066	+	0.506066i	0.407250	+	0.913317i	$0.366488\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.02104	+	1.34538i	−0.291350	+	0.0780671i
$298$		0			0
$299$	−7.19031	−	12.4540i	−0.415826	−	0.720232i
$300$		0			0
$301$	−0.314587	+	8.47687i	−0.0181325	+	0.488599i
$302$		0			0
$303$	0.592267	−	2.21037i	0.0340248	−	0.126982i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	13.9680	+	13.9680i	0.797193	+	0.797193i	0.982652	−	0.185459i	$-0.0593772\pi$
$307$	13.9680	+	13.9680i	0.797193	+	0.797193i	−0.185459	+	0.982652i	$0.559377\pi$
$308$		0			0
$309$			1.52827i			0.0869405i
$310$		0			0
$311$	20.3864	+	11.7701i	1.15601	+	0.667422i	0.950344	−	0.311200i	$-0.100731\pi$
$311$	20.3864	+	11.7701i	1.15601	+	0.667422i	0.205665	+	0.978622i	$0.434064\pi$
$312$		0			0
$313$	−29.6273	−	7.93861i	−1.67463	−	0.448717i	−0.708280	−	0.705932i	$-0.750529\pi$
$313$	−29.6273	−	7.93861i	−1.67463	−	0.448717i	−0.966354	+	0.257215i	$0.917195\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.809115	−	0.216802i	−0.0454444	−	0.0121768i	0.236025	−	0.971747i	$-0.424155\pi$
$317$	−0.809115	−	0.216802i	−0.0454444	−	0.0121768i	−0.281470	+	0.959570i	$0.590822\pi$
$318$		0			0
$319$	−30.4211	−	17.5636i	−1.70326	−	0.983375i
$320$		0			0
$321$		−	1.51629i		−	0.0846312i
$322$		0			0
$323$	−5.64287	−	5.64287i	−0.313978	−	0.313978i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.69103	−	10.0431i	0.148814	−	0.555383i
$328$		0			0
$329$	3.78188	−	2.00026i	0.208502	−	0.110278i
$330$		0			0
$331$	4.40849	+	7.63572i	0.242312	+	0.419697i	0.961373	−	0.275250i	$-0.0887608\pi$
$331$	4.40849	+	7.63572i	0.242312	+	0.419697i	−0.719060	+	0.694948i	$0.755427\pi$
$332$		0			0
$333$	5.80126	−	1.55444i	0.317907	−	0.0851830i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	10.4683	−	10.4683i	0.570242	−	0.570242i	−0.361954	−	0.932196i	$-0.617890\pi$
$337$	10.4683	−	10.4683i	0.570242	−	0.570242i	0.932196	+	0.361954i	$0.117890\pi$
$338$		0			0
$339$	−1.82221	+	3.15616i	−0.0989689	+	0.171419i
$340$		0			0
$341$	−42.9739	+	24.8110i	−2.32717	+	1.34359i
$342$		0			0
$343$	14.4691	−	11.5605i	0.781259	−	0.624207i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.146801	−	0.547869i	−0.00788069	−	0.0294111i	0.961874	−	0.273495i	$-0.0881796\pi$
$347$	−0.146801	−	0.547869i	−0.00788069	−	0.0294111i	−0.969754	+	0.244083i	$0.921513\pi$
$348$		0			0
$349$	9.59993			0.513873			0.256936	−	0.966428i	$-0.417287\pi$
$349$	9.59993			0.513873			0.256936	+	0.966428i	$0.417287\pi$
$350$		0			0
$351$	5.72181			0.305407
$352$		0			0
$353$	−4.70650	−	17.5649i	−0.250502	−	0.934886i	−0.970538	−	0.240949i	$-0.922541\pi$
$353$	−4.70650	−	17.5649i	−0.250502	−	0.934886i	0.720036	−	0.693937i	$-0.244125\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.986684	+	3.20223i	−0.0522208	+	0.169480i
$358$		0			0
$359$	−5.96221	+	3.44229i	−0.314674	+	0.181677i	−0.649016	−	0.760775i	$-0.724819\pi$
$359$	−5.96221	+	3.44229i	−0.314674	+	0.181677i	0.334342	+	0.942452i	$0.391486\pi$
$360$		0			0
$361$	−10.3520	+	17.9302i	−0.544842	+	0.943695i
$362$		0			0
$363$	11.3285	−	11.3285i	0.594592	−	0.594592i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	14.2065	−	3.80662i	0.741574	−	0.198704i	0.131796	−	0.991277i	$-0.457925\pi$
$367$	14.2065	−	3.80662i	0.741574	−	0.198704i	0.609777	+	0.792573i	$0.291259\pi$
$368$		0			0
$369$	−4.46663	−	7.73643i	−0.232523	−	0.402742i
$370$		0			0
$371$	21.7051	+	13.6289i	1.12687	+	0.707580i
$372$		0			0
$373$	0.340696	−	1.27150i	0.0176406	−	0.0658356i	−0.956544	−	0.291586i	$-0.905817\pi$
$373$	0.340696	−	1.27150i	0.0176406	−	0.0658356i	0.974185	+	0.225751i	$0.0724836\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	27.3409	+	27.3409i	1.40813	+	1.40813i
$378$		0			0
$379$			3.14027i			0.161305i	0.996742	+	0.0806524i	$0.0257004\pi$
$379$			3.14027i			0.161305i	−0.996742	+	0.0806524i	$0.974300\pi$
$380$		0			0
$381$	10.4951	+	6.05935i	0.537680	+	0.310430i
$382$		0			0
$383$	31.1388	+	8.34361i	1.59112	+	0.426339i	0.942345	−	0.334643i	$-0.108616\pi$
$383$	31.1388	+	8.34361i	1.59112	+	0.426339i	0.648773	+	0.760982i	$0.275283\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.09692	+	0.829816i	0.157425	+	0.0421819i
$388$		0			0
$389$	−2.87408	−	1.65935i	−0.145721	−	0.0841323i	0.425367	−	0.905021i	$-0.360145\pi$
$389$	−2.87408	−	1.65935i	−0.145721	−	0.0841323i	−0.571088	+	0.820889i	$0.693479\pi$
$390$		0			0
$391$		−	3.18304i		−	0.160973i
$392$		0			0
$393$	−8.03480	−	8.03480i	−0.405302	−	0.405302i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.628000	−	2.34373i	0.0315184	−	0.117628i	−0.948374	−	0.317153i	$-0.897273\pi$
$397$	0.628000	−	2.34373i	0.0315184	−	0.117628i	0.979893	+	0.199525i	$0.0639398\pi$
$398$		0			0
$399$	16.6597	+	0.618261i	0.834029	+	0.0309518i
$400$		0			0
$401$	13.1560	+	22.7868i	0.656978	+	1.13792i	0.981394	+	0.192005i	$0.0614988\pi$
$401$	13.1560	+	22.7868i	0.656978	+	1.13792i	−0.324416	+	0.945914i	$0.605168\pi$
$402$		0			0
$403$	52.7596	−	14.1369i	2.62814	−	0.704209i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−22.0757	+	22.0757i	−1.09425	+	1.09425i
$408$		0			0
$409$	−7.74497	+	13.4147i	−0.382964	+	0.663313i	−0.991484	−	0.130225i	$-0.958430\pi$
$409$	−7.74497	+	13.4147i	−0.382964	+	0.663313i	0.608521	+	0.793538i	$0.291763\pi$
$410$		0			0
$411$	−3.32901	+	1.92200i	−0.164208	+	0.0948054i
$412$		0			0
$413$	28.8187	−	6.58696i	1.41808	−	0.324123i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.38166	−	8.88849i	−0.116631	−	0.435271i
$418$		0			0
$419$	26.9269			1.31547			0.657734	−	0.753251i	$-0.271515\pi$
$419$	26.9269			1.31547			0.657734	+	0.753251i	$0.271515\pi$
$420$		0			0
$421$	1.69272			0.0824983			0.0412492	−	0.999149i	$-0.486866\pi$
$421$	1.69272			0.0824983			0.0412492	+	0.999149i	$0.486866\pi$
$422$		0			0
$423$	−0.418520	−	1.56194i	−0.0203491	−	0.0759440i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.85721	−	1.18850i	−0.186663	−	0.0575156i
$428$		0			0
$429$	−25.7581	+	14.8714i	−1.24361	+	0.718000i
$430$		0			0
$431$	−11.0126	+	19.0744i	−0.530460	+	0.918783i	0.468909	+	0.883247i	$0.344647\pi$
$431$	−11.0126	+	19.0744i	−0.530460	+	0.918783i	−0.999368	+	0.0355363i	$0.988686\pi$
$432$		0			0
$433$	16.5222	−	16.5222i	0.794005	−	0.794005i	−0.188138	−	0.982143i	$-0.560245\pi$
$433$	16.5222	−	16.5222i	0.794005	−	0.794005i	0.982143	+	0.188138i	$0.0602452\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−15.2970	+	4.09881i	−0.731753	+	0.196073i
$438$		0			0
$439$	−5.41387	−	9.37709i	−0.258390	−	0.447544i	0.707421	−	0.706792i	$-0.249859\pi$
$439$	−5.41387	−	9.37709i	−0.258390	−	0.447544i	−0.965811	+	0.259248i	$0.916525\pi$
$440$		0			0
$441$	−3.04104	−	6.30492i	−0.144812	−	0.300234i
$442$		0			0
$443$	0.708791	−	2.64524i	0.0336757	−	0.125679i	−0.947042	−	0.321110i	$-0.895944\pi$
$443$	0.708791	−	2.64524i	0.0336757	−	0.125679i	0.980717	+	0.195431i	$0.0626106\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.398420	−	0.398420i	−0.0188446	−	0.0188446i
$448$		0			0
$449$		−	34.2818i		−	1.61786i	−0.587906	−	0.808929i	$-0.700048\pi$
$449$		−	34.2818i		−	1.61786i	0.587906	−	0.808929i	$-0.299952\pi$
$450$		0			0
$451$	40.2152	+	23.2183i	1.89366	+	1.09331i
$452$		0			0
$453$	1.73266	+	0.464265i	0.0814075	+	0.0218131i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	36.0303	+	9.65429i	1.68543	+	0.451609i	0.969203	−	0.246263i	$-0.0792027\pi$
$457$	36.0303	+	9.65429i	1.68543	+	0.451609i	0.716223	+	0.697871i	$0.245869\pi$
$458$		0			0
$459$	1.09680	+	0.633240i	0.0511944	+	0.0295571i
$460$		0			0
$461$			3.36145i			0.156559i	0.996931	+	0.0782793i	$0.0249426\pi$
$461$			3.36145i			0.156559i	−0.996931	+	0.0782793i	$0.975057\pi$
$462$		0			0
$463$	−2.21431	−	2.21431i	−0.102907	−	0.102907i	0.653778	−	0.756686i	$-0.273183\pi$
$463$	−2.21431	−	2.21431i	−0.102907	−	0.102907i	−0.756686	+	0.653778i	$0.773183\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.67588	+	17.4506i	−0.216374	+	0.807518i	0.769305	+	0.638882i	$0.220603\pi$
$467$	−4.67588	+	17.4506i	−0.216374	+	0.807518i	−0.985678	+	0.168636i	$0.946064\pi$
$468$		0			0
$469$	−3.80101	+	6.05338i	−0.175514	+	0.279519i
$470$		0			0
$471$	0.649221	+	1.12448i	0.0299145	+	0.0518134i
$472$		0			0
$473$	−16.0983	+	4.31352i	−0.740199	+	0.198336i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	6.84970	−	6.84970i	0.313626	−	0.313626i
$478$		0			0
$479$	−8.73071	+	15.1220i	−0.398917	+	0.690944i	−0.993593	−	0.113022i	$-0.963947\pi$
$479$	−8.73071	+	15.1220i	−0.398917	+	0.690944i	0.594676	+	0.803965i	$0.297280\pi$
$480$		0			0
$481$	29.7607	−	17.1823i	1.35697	−	0.783447i
$482$		0			0
$483$	4.52434	+	4.87309i	0.205865	+	0.221733i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−6.87867	−	25.6715i	−0.311702	−	1.16329i	−0.927021	−	0.375010i	$-0.877639\pi$
$487$	−6.87867	−	25.6715i	−0.311702	−	1.16329i	0.615319	−	0.788278i	$-0.289027\pi$
$488$		0			0
$489$	−12.1501			−0.549446
$490$		0			0
$491$	−16.0019			−0.722155			−0.361078	−	0.932536i	$-0.617591\pi$
$491$	−16.0019			−0.722155			−0.361078	+	0.932536i	$0.617591\pi$
$492$		0			0
$493$	2.21508	+	8.26678i	0.0997621	+	0.372317i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.9870	+	22.6047i	0.941393	+	1.01396i
$498$		0			0
$499$	23.9884	−	13.8497i	1.07387	−	0.619999i	0.144634	−	0.989485i	$-0.453800\pi$
$499$	23.9884	−	13.8497i	1.07387	−	0.619999i	0.929236	+	0.369486i	$0.120466\pi$
$500$		0			0
$501$	−5.88668	+	10.1960i	−0.262997	+	0.455525i
$502$		0			0
$503$	−10.3020	+	10.3020i	−0.459343	+	0.459343i	−0.898440	−	0.439097i	$-0.855299\pi$
$503$	−10.3020	+	10.3020i	−0.459343	+	0.459343i	0.439097	+	0.898440i	$0.355299\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	19.0665	−	5.10885i	0.846772	−	0.226892i
$508$		0			0
$509$	10.9166	+	18.9080i	0.483868	+	0.838084i	0.999828	−	0.0185286i	$-0.00589818\pi$
$509$	10.9166	+	18.9080i	0.483868	+	0.838084i	−0.515960	+	0.856612i	$0.672565\pi$
$510$		0			0
$511$	11.0634	−	17.6193i	0.489418	−	0.779433i
$512$		0			0
$513$	1.63085	−	6.08641i	0.0720037	−	0.268721i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.94367	+	5.94367i	0.261402	+	0.261402i
$518$		0			0
$519$		−	18.6038i		−	0.816616i
$520$		0			0
$521$	−15.4830	−	8.93914i	−0.678324	−	0.391631i	0.120899	−	0.992665i	$-0.461422\pi$
$521$	−15.4830	−	8.93914i	−0.678324	−	0.391631i	−0.799223	+	0.601034i	$0.794756\pi$
$522$		0			0
$523$	−30.3206	−	8.12438i	−1.32583	−	0.355254i	−0.474670	−	0.880164i	$-0.657432\pi$
$523$	−30.3206	−	8.12438i	−1.32583	−	0.355254i	−0.851158	+	0.524910i	$0.824099\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	11.6779	+	3.12910i	0.508699	+	0.136306i
$528$		0			0
$529$	14.4482	+	8.34166i	0.628182	+	0.362681i
$530$		0			0
$531$		−	11.1734i		−	0.484883i
$532$		0			0
$533$	−36.1433	−	36.1433i	−1.56554	−	1.56554i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.98882	+	18.6185i	−0.215284	+	0.803449i
$538$		0			0
$539$	30.0770	+	20.4792i	1.29551	+	0.882103i
$540$		0			0
$541$	−9.96889	−	17.2666i	−0.428596	−	0.742350i	0.568153	−	0.822923i	$-0.307658\pi$
$541$	−9.96889	−	17.2666i	−0.428596	−	0.742350i	−0.996749	+	0.0805732i	$0.974325\pi$
$542$		0			0
$543$	15.8682	−	4.25186i	0.680968	−	0.182465i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	17.0663	−	17.0663i	0.729704	−	0.729704i	−0.240857	−	0.970561i	$-0.577428\pi$
$547$	17.0663	−	17.0663i	0.729704	−	0.729704i	0.970561	+	0.240857i	$0.0774283\pi$
$548$		0			0
$549$	−0.762763	+	1.32114i	−0.0325539	+	0.0563851i
$550$		0			0
$551$	36.8759	−	21.2903i	1.57097	−	0.906997i
$552$		0			0
$553$	−4.35671	−	1.34241i	−0.185266	−	0.0570850i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.35137	−	31.1677i	−0.353859	−	1.32062i	−0.881914	−	0.471409i	$-0.843745\pi$
$557$	−8.35137	−	31.1677i	−0.353859	−	1.32062i	0.528056	−	0.849210i	$-0.322921\pi$
$558$		0			0
$559$	18.3450			0.775913
$560$		0			0
$561$	−6.58337			−0.277950
$562$		0			0
$563$	−3.05585	−	11.4046i	−0.128789	−	0.480647i	0.871158	−	0.491004i	$-0.163370\pi$
$563$	−3.05585	−	11.4046i	−0.128789	−	0.480647i	−0.999946	+	0.0103571i	$0.996703\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.57924	+	0.589524i	−0.108318	+	0.0247577i
$568$		0			0
$569$	3.89920	−	2.25121i	0.163463	−	0.0943755i	−0.416037	−	0.909348i	$-0.636581\pi$
$569$	3.89920	−	2.25121i	0.163463	−	0.0943755i	0.579500	+	0.814972i	$0.303248\pi$
$570$		0			0
$571$	−11.0095	+	19.0691i	−0.460734	+	0.798016i	−0.998998	−	0.0447613i	$-0.985747\pi$
$571$	−11.0095	+	19.0691i	−0.460734	+	0.798016i	0.538263	+	0.842777i	$0.319081\pi$
$572$		0			0
$573$	−17.7846	+	17.7846i	−0.742960	+	0.742960i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−23.2242	+	6.22291i	−0.966836	+	0.259063i	−0.707491	−	0.706722i	$-0.750173\pi$
$577$	−23.2242	+	6.22291i	−0.966836	+	0.259063i	−0.259345	+	0.965785i	$0.583507\pi$
$578$		0			0
$579$	−0.598120	−	1.03597i	−0.0248570	−	0.0430536i
$580$		0			0
$581$	−19.3649	−	0.718654i	−0.803392	−	0.0298148i
$582$		0			0
$583$	−13.0327	+	48.6385i	−0.539758	+	2.01440i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.4300	+	21.4300i	0.884511	+	0.884511i	0.993989	−	0.109478i	$-0.0349179\pi$
$587$	21.4300	+	21.4300i	0.884511	+	0.884511i	−0.109478	+	0.993989i	$0.534918\pi$
$588$		0			0
$589$		−	60.1509i		−	2.47847i
$590$		0			0
$591$	15.4127	+	8.89854i	0.633994	+	0.366037i
$592$		0			0
$593$	9.60091	+	2.57256i	0.394262	+	0.105642i	0.450503	−	0.892775i	$-0.351245\pi$
$593$	9.60091	+	2.57256i	0.394262	+	0.105642i	−0.0562407	+	0.998417i	$0.517911\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.694652	+	0.186132i	0.0284302	+	0.00761786i
$598$		0			0
$599$	−39.7393	−	22.9435i	−1.62371	−	0.937447i	−0.985917	−	0.167235i	$-0.946516\pi$
$599$	−39.7393	−	22.9435i	−1.62371	−	0.937447i	−0.637789	−	0.770211i	$-0.720151\pi$
$600$		0			0
$601$		−	8.34994i		−	0.340601i	−0.985392	−	0.170301i	$-0.945526\pi$
$601$		−	8.34994i		−	0.340601i	0.985392	−	0.170301i	$-0.0544739\pi$
$602$		0			0
$603$	1.91033	+	1.91033i	0.0777947	+	0.0777947i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	5.24785	−	19.5852i	0.213003	−	0.794940i	−0.773856	−	0.633361i	$-0.781675\pi$
$607$	5.24785	−	19.5852i	0.213003	−	0.794940i	0.986860	−	0.161579i	$-0.0516586\pi$
$608$		0			0
$609$	−15.1415	−	9.50758i	−0.613565	−	0.385267i
$610$		0			0
$611$	−4.62618	−	8.01278i	−0.187155	−	0.324163i
$612$		0			0
$613$	2.87553	−	0.770497i	0.116142	−	0.0311201i	−0.200280	−	0.979739i	$-0.564185\pi$
$613$	2.87553	−	0.770497i	0.116142	−	0.0311201i	0.316422	+	0.948619i	$0.397519\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.0772	−	25.0772i	1.00957	−	1.00957i	0.00961576	−	0.999954i	$-0.496939\pi$
$617$	25.0772	−	25.0772i	1.00957	−	1.00957i	0.999954	−	0.00961576i	$-0.00306084\pi$
$618$		0			0
$619$	3.61388	−	6.25942i	0.145254	−	0.251587i	−0.784214	−	0.620491i	$-0.786933\pi$
$619$	3.61388	−	6.25942i	0.145254	−	0.251587i	0.929468	+	0.368904i	$0.120267\pi$
$620$		0			0
$621$	2.17658	−	1.25665i	0.0873432	−	0.0504276i
$622$		0			0
$623$	−5.36805	+	17.4217i	−0.215066	+	0.697986i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	8.47742	+	31.6381i	0.338555	+	1.26351i
$628$		0			0
$629$	7.60636			0.303286
$630$		0			0
$631$	−39.7178			−1.58114			−0.790570	−	0.612372i	$-0.790215\pi$
$631$	−39.7178			−1.58114			−0.790570	+	0.612372i	$0.790215\pi$
$632$		0			0
$633$	−1.44388	−	5.38864i	−0.0573892	−	0.214179i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−26.1444	−	30.3428i	−1.03588	−	1.20223i
$638$		0			0
$639$	10.0964	−	5.82919i	0.399409	−	0.230599i
$640$		0			0
$641$	−12.3608	+	21.4095i	−0.488222	+	0.845626i	−0.999908	−	0.0135467i	$-0.995688\pi$
$641$	−12.3608	+	21.4095i	−0.488222	+	0.845626i	0.511686	+	0.859173i	$0.329021\pi$
$642$		0			0
$643$	−16.2892	+	16.2892i	−0.642382	+	0.642382i	−0.951141	−	0.308758i	$-0.900087\pi$
$643$	−16.2892	+	16.2892i	−0.642382	+	0.642382i	0.308758	+	0.951141i	$0.400087\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.23612	−	1.13507i	0.166539	−	0.0446240i	−0.174586	−	0.984642i	$-0.555859\pi$
$647$	4.23612	−	1.13507i	0.166539	−	0.0446240i	0.341125	+	0.940018i	$0.389192\pi$
$648$		0			0
$649$	29.0405	+	50.2996i	1.13994	+	1.97443i
$650$		0			0
$651$	−22.3261	+	11.8084i	−0.875028	+	0.462808i
$652$		0			0
$653$	1.53282	−	5.72056i	0.0599839	−	0.223863i	−0.929427	−	0.369007i	$-0.879698\pi$
$653$	1.53282	−	5.72056i	0.0599839	−	0.223863i	0.989411	+	0.145144i	$0.0463646\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−5.56032	−	5.56032i	−0.216929	−	0.216929i
$658$		0			0
$659$		−	11.9537i		−	0.465650i	−0.972519	−	0.232825i	$-0.925203\pi$
$659$		−	11.9537i		−	0.465650i	0.972519	−	0.232825i	$-0.0747969\pi$
$660$		0			0
$661$	12.9816	+	7.49494i	0.504927	+	0.291520i	0.730746	−	0.682650i	$-0.239172\pi$
$661$	12.9816	+	7.49494i	0.504927	+	0.291520i	−0.225819	+	0.974169i	$0.572506\pi$
$662$		0			0
$663$	6.99963	+	1.87555i	0.271843	+	0.0728401i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	16.4052	+	4.39577i	0.635213	+	0.170205i
$668$		0			0
$669$	19.0458	+	10.9961i	0.736354	+	0.425134i
$670$		0			0
$671$		−	7.92993i		−	0.306132i
$672$		0			0
$673$	−27.7618	−	27.7618i	−1.07014	−	1.07014i	−0.997347	−	0.0727904i	$-0.976810\pi$
$673$	−27.7618	−	27.7618i	−1.07014	−	1.07014i	−0.0727904	−	0.997347i	$-0.523190\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.65538	+	24.8382i	−0.255787	+	0.954610i	0.711864	+	0.702317i	$0.247851\pi$
$677$	−6.65538	+	24.8382i	−0.255787	+	0.954610i	−0.967651	+	0.252292i	$0.918816\pi$
$678$		0			0
$679$	−1.69529	+	45.6815i	−0.0650594	+	1.75310i
$680$		0			0
$681$	−0.971524	−	1.68273i	−0.0372289	−	0.0644823i
$682$		0			0
$683$	−6.35372	+	1.70247i	−0.243118	+	0.0651434i	−0.378321	−	0.925675i	$-0.623498\pi$
$683$	−6.35372	+	1.70247i	−0.243118	+	0.0651434i	0.135202	+	0.990818i	$0.456832\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	2.67597	−	2.67597i	0.102095	−	0.102095i
$688$		0			0
$689$	27.7134	−	48.0010i	1.05580	−	1.82869i
$690$		0			0
$691$	5.96472	−	3.44373i	0.226909	−	0.131006i	−0.382236	−	0.924065i	$-0.624846\pi$
$691$	5.96472	−	3.44373i	0.226909	−	0.131006i	0.609145	+	0.793059i	$0.291513\pi$
$692$		0			0
$693$	10.0788	−	9.35753i	0.382863	−	0.355463i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.92822	−	10.9283i	−0.110914	−	0.413938i
$698$		0			0
$699$	10.0728			0.380989
$700$		0			0
$701$	14.2273			0.537357			0.268678	−	0.963230i	$-0.413413\pi$
$701$	14.2273			0.537357			0.268678	+	0.963230i	$0.413413\pi$
$702$		0			0
$703$	−9.79473	−	36.5544i	−0.369415	−	1.37868i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.34903	+	5.90218i	0.0507356	+	0.221974i
$708$		0			0
$709$	−13.0747	+	7.54867i	−0.491030	+	0.283496i	−0.725002	−	0.688747i	$-0.758161\pi$
$709$	−13.0747	+	7.54867i	−0.491030	+	0.283496i	0.233972	+	0.972243i	$0.424828\pi$
$710$		0			0
$711$	−0.861538	+	1.49223i	−0.0323102	+	0.0559629i
$712$		0			0
$713$	16.9650	−	16.9650i	0.635344	−	0.635344i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−12.7095	+	3.40550i	−0.474645	+	0.127181i
$718$		0			0
$719$	−0.324132	−	0.561413i	−0.0120881	−	0.0209372i	0.859918	−	0.510432i	$-0.170515\pi$
$719$	−0.324132	−	0.561413i	−0.0120881	−	0.0209372i	−0.872006	+	0.489495i	$0.837181\pi$
$720$		0			0
$721$	−1.89046	−	3.57428i	−0.0704045	−	0.133113i
$722$		0			0
$723$	2.67266	−	9.97452i	0.0993975	−	0.370956i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	31.2375	+	31.2375i	1.15853	+	1.15853i	0.984791	+	0.173742i	$0.0555860\pi$
$727$	31.2375	+	31.2375i	1.15853	+	1.15853i	0.173742	+	0.984791i	$0.444414\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	3.51653	+	2.03027i	0.130064	+	0.0750922i
$732$		0			0
$733$	2.60368	+	0.697653i	0.0961690	+	0.0257684i	0.306583	−	0.951844i	$-0.400814\pi$
$733$	2.60368	+	0.697653i	0.0961690	+	0.0257684i	−0.210414	+	0.977612i	$0.567481\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13.5649	−	3.63471i	−0.499670	−	0.133886i
$738$		0			0
$739$	32.5445	+	18.7896i	1.19717	+	0.691185i	0.959923	−	0.280264i	$-0.0904221\pi$
$739$	32.5445	+	18.7896i	1.19717	+	0.691185i	0.237245	+	0.971450i	$0.423755\pi$
$740$		0			0
$741$		−	36.0537i		−	1.32447i
$742$		0			0
$743$	8.93242	+	8.93242i	0.327699	+	0.327699i	0.851711	−	0.524012i	$-0.175565\pi$
$743$	8.93242	+	8.93242i	0.327699	+	0.327699i	−0.524012	+	0.851711i	$0.675565\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.89567	+	7.07472i	−0.0693588	+	0.258850i
$748$		0			0
$749$	1.87564	+	3.54626i	0.0685344	+	0.129578i
$750$		0			0
$751$	−5.52178	−	9.56400i	−0.201492	−	0.348995i	0.747517	−	0.664243i	$-0.231246\pi$
$751$	−5.52178	−	9.56400i	−0.201492	−	0.348995i	−0.949010	+	0.315247i	$0.897912\pi$
$752$		0			0
$753$	−4.56821	+	1.22405i	−0.166475	+	0.0446068i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−34.2461	+	34.2461i	−1.24469	+	1.24469i	−0.286663	+	0.958032i	$0.592546\pi$
$757$	−34.2461	+	34.2461i	−1.24469	+	1.24469i	−0.958032	+	0.286663i	$0.907454\pi$
$758$		0			0
$759$	−6.53227	+	11.3142i	−0.237106	+	0.410680i
$760$		0			0
$761$	16.0161	−	9.24688i	0.580582	−	0.335199i	−0.180783	−	0.983523i	$-0.557863\pi$
$761$	16.0161	−	9.24688i	0.580582	−	0.335199i	0.761365	+	0.648324i	$0.224530\pi$
$762$		0			0
$763$	6.12949	+	26.8172i	0.221902	+	0.970849i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.5468	−	61.7534i	−0.597469	−	2.22979i
$768$		0			0
$769$	36.3966			1.31249			0.656247	−	0.754546i	$-0.272143\pi$
$769$	36.3966			1.31249			0.656247	+	0.754546i	$0.272143\pi$
$770$		0			0
$771$	6.30078			0.226917
$772$		0			0
$773$	7.40466	+	27.6346i	0.266327	+	0.993946i	0.961433	+	0.275039i	$0.0886907\pi$
$773$	7.40466	+	27.6346i	0.266327	+	0.993946i	−0.695106	+	0.718907i	$0.744643\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−11.6450	+	10.8116i	−0.417762	+	0.387864i
$778$		0			0
$779$	−48.7481	+	28.1447i	−1.74658	+	1.00839i
$780$		0			0
$781$	−30.3011	+	52.4830i	−1.08426	+	1.87799i
$782$		0			0
$783$	−4.77837	+	4.77837i	−0.170765	+	0.170765i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	15.5011	−	4.15351i	0.552555	−	0.148057i	0.0282710	−	0.999600i	$-0.491000\pi$
$787$	15.5011	−	4.15351i	0.552555	−	0.148057i	0.524284	+	0.851544i	$0.324333\pi$
$788$		0			0
$789$	−10.2598	−	17.7705i	−0.365259	−	0.632647i
$790$		0			0
$791$	0.357588	−	9.63560i	0.0127144	−	0.342603i
$792$		0			0
$793$	−2.25917	+	8.43134i	−0.0802255	+	0.299406i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	30.3610	+	30.3610i	1.07544	+	1.07544i	0.996912	+	0.0785284i	$0.0250221\pi$
$797$	30.3610	+	30.3610i	1.07544	+	1.07544i	0.0785284	+	0.996912i	$0.474978\pi$
$798$		0			0
$799$		−	2.04794i		−	0.0724510i
$800$		0			0
$801$	5.96716	+	3.44514i	0.210839	+	0.121728i
$802$		0			0
$803$	39.4828	+	10.5794i	1.39332	+	0.373339i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.571838	+	0.153224i	0.0201297	+	0.00539373i
$808$		0			0
$809$	−37.4222	−	21.6057i	−1.31569	−	0.759617i	−0.332662	−	0.943046i	$-0.607947\pi$
$809$	−37.4222	−	21.6057i	−1.31569	−	0.759617i	−0.983033	+	0.183429i	$0.941280\pi$
$810$		0			0
$811$		−	43.7498i		−	1.53626i	−0.640293	−	0.768131i	$-0.721187\pi$
$811$		−	43.7498i		−	1.53626i	0.640293	−	0.768131i	$-0.278813\pi$
$812$		0			0
$813$	0.439607	+	0.439607i	0.0154177	+	0.0154177i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	5.22876	−	19.5140i	0.182931	−	0.682709i
$818$		0			0
$819$	−13.3820	+	7.07783i	−0.467605	+	0.247319i
$820$		0			0
$821$	12.4677	+	21.5947i	0.435126	+	0.753660i	0.997306	−	0.0733551i	$-0.0233706\pi$
$821$	12.4677	+	21.5947i	0.435126	+	0.753660i	−0.562180	+	0.827015i	$0.690037\pi$
$822$		0			0
$823$	0.0153231	−	0.00410583i	0.000534131	−	0.000143120i	−0.258552	−	0.965997i	$-0.583245\pi$
$823$	0.0153231	−	0.00410583i	0.000534131	−	0.000143120i	0.259086	+	0.965854i	$0.416579\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.6569	−	13.6569i	0.474895	−	0.474895i	−0.428599	−	0.903495i	$-0.640993\pi$
$827$	13.6569	−	13.6569i	0.474895	−	0.474895i	0.903495	+	0.428599i	$0.140993\pi$
$828$		0			0
$829$	1.69427	−	2.93457i	0.0588446	−	0.101922i	−0.835102	−	0.550094i	$-0.814592\pi$
$829$	1.69427	−	2.93457i	0.0588446	−	0.101922i	0.893947	+	0.448173i	$0.147925\pi$
$830$		0			0
$831$	−19.3793	+	11.1887i	−0.672261	+	0.388130i
$832$		0			0
$833$	−1.65350	−	8.70979i	−0.0572904	−	0.301776i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.47070	+	9.22080i	0.0854000	+	0.318717i
$838$		0			0
$839$	−5.25634			−0.181469			−0.0907344	−	0.995875i	$-0.528921\pi$
$839$	−5.25634			−0.181469			−0.0907344	+	0.995875i	$0.528921\pi$
$840$		0			0
$841$	−16.6656			−0.574675
$842$		0			0
$843$	0.372430	+	1.38993i	0.0128272	+	0.0478716i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.4815	+	40.5080i	−0.428870	+	1.39187i
$848$		0			0
$849$	−0.972769	+	0.561628i	−0.0333853	+	0.0192750i
$850$		0			0
$851$	7.54733	−	13.0724i	0.258719	−	0.448114i
$852$		0			0
$853$	−7.80756	+	7.80756i	−0.267326	+	0.267326i	−0.828022	−	0.560696i	$-0.810534\pi$
$853$	−7.80756	+	7.80756i	−0.267326	+	0.267326i	0.560696	+	0.828022i	$0.310534\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−49.3412	+	13.2209i	−1.68546	+	0.451619i	−0.969213	−	0.246224i	$-0.920810\pi$
$857$	−49.3412	+	13.2209i	−1.68546	+	0.451619i	−0.716251	+	0.697843i	$0.754143\pi$
$858$		0			0
$859$	−17.7613	−	30.7635i	−0.606009	−	1.04964i	−0.991891	−	0.127090i	$-0.959436\pi$
$859$	−17.7613	−	30.7635i	−0.606009	−	1.04964i	0.385883	−	0.922548i	$-0.373897\pi$
$860$		0			0
$861$	20.0163	+	12.5686i	0.682154	+	0.428335i
$862$		0			0
$863$	−0.665257	+	2.48277i	−0.0226456	+	0.0845146i	−0.976324	−	0.216314i	$-0.930597\pi$
$863$	−0.665257	+	2.48277i	−0.0226456	+	0.0845146i	0.953678	+	0.300829i	$0.0972632\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−10.8866	−	10.8866i	−0.369730	−	0.369730i
$868$		0			0
$869$		−	8.95684i		−	0.303840i
$870$		0			0
$871$	13.3871	+	7.72906i	0.453605	+	0.261889i
$872$		0			0
$873$	16.6891	+	4.47184i	0.564842	+	0.151349i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−43.4798	−	11.6504i	−1.46821	−	0.393405i	−0.565892	−	0.824479i	$-0.691468\pi$
$877$	−43.4798	−	11.6504i	−1.46821	−	0.393405i	−0.902317	+	0.431074i	$0.858135\pi$
$878$		0			0
$879$	−10.6093	−	6.12528i	−0.357843	−	0.206601i
$880$		0			0
$881$		−	33.9524i		−	1.14389i	−0.820294	−	0.571943i	$-0.806190\pi$
$881$		−	33.9524i		−	1.14389i	0.820294	−	0.571943i	$-0.193810\pi$
$882$		0			0
$883$	13.0249	+	13.0249i	0.438324	+	0.438324i	0.891448	−	0.453123i	$-0.149690\pi$
$883$	13.0249	+	13.0249i	0.438324	+	0.438324i	−0.453123	+	0.891448i	$0.649690\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.08993	−	30.1920i	0.271633	−	1.01375i	−0.686431	−	0.727195i	$-0.740823\pi$
$887$	8.08993	−	30.1920i	0.271633	−	1.01375i	0.958064	−	0.286554i	$-0.0925098\pi$
$888$		0			0
$889$	−32.0410	−	1.18908i	−1.07462	−	0.0398804i
$890$		0			0
$891$	−2.59908	−	4.50174i	−0.0870725	−	0.150814i
$892$		0			0
$893$	−9.84194	+	2.63714i	−0.329348	+	0.0882485i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	10.1686	−	10.1686i	0.339521	−	0.339521i
$898$		0			0
$899$	−32.2544	+	55.8663i	−1.07574	+	1.86324i
$900$		0			0
$901$	10.6247	−	6.13416i	0.353959	−	0.204358i
$902$		0			0
$903$	−8.26945	+	1.89011i	−0.275190	+	0.0628989i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.540204	+	2.01607i	0.0179372	+	0.0669425i	0.974314	−	0.225192i	$-0.0723011\pi$
$907$	0.540204	+	2.01607i	0.0179372	+	0.0669425i	−0.956377	+	0.292135i	$0.905634\pi$
$908$		0			0
$909$	2.28834			0.0758995
$910$		0			0
$911$	31.8693			1.05588			0.527939	−	0.849282i	$-0.322965\pi$
$911$	31.8693			1.05588			0.527939	+	0.849282i	$0.322965\pi$
$912$		0			0
$913$	−9.85398	−	36.7756i	−0.326119	−	1.21709i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.7305	+	8.85258i	0.948766	+	0.292338i
$918$		0			0
$919$	−4.15764	+	2.40041i	−0.137148	+	0.0791823i	−0.567004	−	0.823715i	$-0.691898\pi$
$919$	−4.15764	+	2.40041i	−0.137148	+	0.0791823i	0.429856	+	0.902897i	$0.358564\pi$
$920$		0			0
$921$	−9.87683	+	17.1072i	−0.325453	+	0.563701i
$922$		0			0
$923$	47.1689	−	47.1689i	1.55258	−	1.55258i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.47620	+	0.395546i	−0.0484847	+	0.0129914i
$928$		0			0
$929$	10.4131	+	18.0360i	0.341642	+	0.591742i	0.984738	−	0.174044i	$-0.0556836\pi$
$929$	10.4131	+	18.0360i	0.341642	+	0.591742i	−0.643096	+	0.765786i	$0.722350\pi$
$930$		0			0
$931$	−39.7280	+	19.1619i	−1.30203	+	0.628008i
$932$		0			0
$933$	−6.09266	+	22.7381i	−0.199465	+	0.744413i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−31.7620	−	31.7620i	−1.03762	−	1.03762i	−0.999264	−	0.0383539i	$-0.987789\pi$
$937$	−31.7620	−	31.7620i	−1.03762	−	1.03762i	−0.0383539	−	0.999264i	$-0.512211\pi$
$938$		0			0
$939$		−	30.6724i		−	1.00096i
$940$		0			0
$941$	−41.3643	−	23.8817i	−1.34844	−	0.778522i	−0.360410	−	0.932794i	$-0.617363\pi$
$941$	−41.3643	−	23.8817i	−1.34844	−	0.778522i	−0.988028	+	0.154272i	$0.950697\pi$
$942$		0			0
$943$	−21.6869	−	5.81099i	−0.706223	−	0.189232i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−34.6650	−	9.28845i	−1.12646	−	0.301834i	−0.352965	−	0.935637i	$-0.614827\pi$
$947$	−34.6650	−	9.28845i	−1.12646	−	0.301834i	−0.773495	+	0.633803i	$0.781493\pi$
$948$		0			0
$949$	−38.9653	−	22.4966i	−1.26487	−	0.730272i
$950$		0			0
$951$		−	0.837658i		−	0.0271629i
$952$		0			0
$953$	34.7317	+	34.7317i	1.12507	+	1.12507i	0.990967	+	0.134104i	$0.0428157\pi$
$953$	34.7317	+	34.7317i	1.12507	+	1.12507i	0.134104	+	0.990967i	$0.457184\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	9.09161	−	33.9303i	0.293890	−	1.09681i
$958$		0			0
$959$	5.40828	−	8.61308i	0.174643	−	0.278131i
$960$		0			0
$961$	30.0637	+	52.0719i	0.969798	+	1.67974i
$962$		0			0
$963$	1.46463	−	0.392445i	0.0471969	−	0.0126464i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	23.6646	−	23.6646i	0.761004	−	0.761004i	−0.215500	−	0.976504i	$-0.569138\pi$
$967$	23.6646	−	23.6646i	0.761004	−	0.761004i	0.976504	+	0.215500i	$0.0691382\pi$
$968$		0			0
$969$	3.99012	−	6.91108i	0.128181	−	0.222016i
$970$		0			0
$971$	−16.9353	+	9.77759i	−0.543479	+	0.313778i	−0.746488	−	0.665399i	$-0.768261\pi$
$971$	−16.9353	+	9.77759i	−0.543479	+	0.313778i	0.203009	+	0.979177i	$0.434928\pi$
$972$		0			0
$973$	16.5652	+	17.8420i	0.531055	+	0.571990i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.73533	−	28.8686i	−0.247475	−	0.923589i	−0.972123	−	0.234470i	$-0.924664\pi$
$977$	−7.73533	−	28.8686i	−0.247475	−	0.923589i	0.724648	−	0.689119i	$-0.242002\pi$
$978$		0			0
$979$	−35.8168			−1.14471
$980$		0			0
$981$	10.3974			0.331962
$982$		0			0
$983$	−0.375999	−	1.40325i	−0.0119925	−	0.0447567i	0.959670	−	0.281128i	$-0.0907085\pi$
$983$	−0.375999	−	1.40325i	−0.0119925	−	0.0447567i	−0.971663	+	0.236371i	$0.924042\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.91092	+	3.13531i	0.0926558	+	0.0997979i
$988$		0			0
$989$	6.97847	−	4.02902i	0.221903	−	0.128115i
$990$		0			0
$991$	26.9478	−	46.6750i	0.856026	−	1.48268i	−0.0196634	−	0.999807i	$-0.506259\pi$
$991$	26.9478	−	46.6750i	0.856026	−	1.48268i	0.875690	−	0.482874i	$-0.160407\pi$
$992$		0			0
$993$	−6.23454	+	6.23454i	−0.197847	+	0.197847i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−17.4928	+	4.68717i	−0.554002	+	0.148444i	−0.524949	−	0.851134i	$-0.675916\pi$
$997$	−17.4928	+	4.68717i	−0.554002	+	0.148444i	−0.0290525	+	0.999578i	$0.509249\pi$
$998$		0			0
$999$	3.00296	+	5.20127i	0.0950093	+	0.164561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.e.493.5		32
5.2	odd	4	inner	2100.2.ce.e.157.8		32
5.3	odd	4		420.2.bo.a.157.2	yes	32
5.4	even	2		420.2.bo.a.73.1	✓	32
7.5	odd	6	inner	2100.2.ce.e.1993.8		32
15.8	even	4		1260.2.dq.c.577.6		32
15.14	odd	2		1260.2.dq.c.73.8		32
35.3	even	12		2940.2.x.c.97.2		32
35.4	even	6		2940.2.x.c.1273.2		32
35.12	even	12	inner	2100.2.ce.e.1657.5		32
35.18	odd	12		2940.2.x.c.97.16		32
35.19	odd	6		420.2.bo.a.313.2	yes	32
35.24	odd	6		2940.2.x.c.1273.16		32
35.33	even	12		420.2.bo.a.397.1	yes	32
105.68	odd	12		1260.2.dq.c.397.8		32
105.89	even	6		1260.2.dq.c.1153.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.1	✓	32	5.4	even	2
420.2.bo.a.157.2	yes	32	5.3	odd	4
420.2.bo.a.313.2	yes	32	35.19	odd	6
420.2.bo.a.397.1	yes	32	35.33	even	12
1260.2.dq.c.73.8		32	15.14	odd	2
1260.2.dq.c.397.8		32	105.68	odd	12
1260.2.dq.c.577.6		32	15.8	even	4
1260.2.dq.c.1153.6		32	105.89	even	6
2100.2.ce.e.157.8		32	5.2	odd	4	inner
2100.2.ce.e.493.5		32	1.1	even	1	trivial
2100.2.ce.e.1657.5		32	35.12	even	12	inner
2100.2.ce.e.1993.8		32	7.5	odd	6	inner
2940.2.x.c.97.2		32	35.3	even	12
2940.2.x.c.97.16		32	35.18	odd	12
2940.2.x.c.1273.2		32	35.4	even	6
2940.2.x.c.1273.16		32	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{3} +(-1.80016 - 1.93892i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{3} +(-1.80016 - 1.93892i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(2.59908 - 4.50174i) q^{11} +(-4.04593 + 4.04593i) q^{13} +(-1.22333 + 0.327789i) q^{17} +(3.15056 + 5.45692i) q^{19} +(1.40694 - 2.24065i) q^{21} +(-0.650490 + 2.42766i) q^{23} +(-0.707107 - 0.707107i) q^{27} -6.75763i q^{29} +(-8.26714 - 4.77304i) q^{31} +(5.02104 + 1.34538i) q^{33} +(-5.80126 - 1.55444i) q^{37} +(-4.95523 - 2.86090i) q^{39} +8.93326i q^{41} +(-2.26710 - 2.26710i) q^{43} +(-0.418520 + 1.56194i) q^{47} +(-0.518842 + 6.98075i) q^{49} +(-0.633240 - 1.09680i) q^{51} +(-9.35687 + 2.50717i) q^{53} +(-4.45556 + 4.45556i) q^{57} +(-5.58668 + 9.67641i) q^{59} +(1.32114 - 0.762763i) q^{61} +(2.52845 + 0.779076i) q^{63} +(-0.699229 - 2.60956i) q^{67} -2.51330 q^{69} -11.6584 q^{71} +(2.03522 + 7.59553i) q^{73} +(-13.4073 + 3.06444i) q^{77} +(1.49223 - 0.861538i) q^{79} +(0.500000 - 0.866025i) q^{81} +(5.17905 - 5.17905i) q^{83} +(6.52737 - 1.74900i) q^{87} +(-3.44514 - 5.96716i) q^{89} +(15.1281 + 0.561420i) q^{91} +(2.47070 - 9.22080i) q^{93} +(-12.2173 - 12.2173i) q^{97} +5.19816i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) \) 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Introduction

L-functions

Modular forms

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