LMFDB - Embedded newform 2100.2.ce.e.493.3

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			493.3
Character	$\chi$	$=$	2100.493
Dual form			2100.2.ce.e.1657.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{3} +(-2.20765 + 1.45817i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{3} +(-2.20765 + 1.45817i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(0.803071 - 1.39096i) q^{11} +(-0.275509 + 0.275509i) q^{13} +(0.633566 - 0.169763i) q^{17} +(-1.05775 - 1.83208i) q^{19} +(1.97987 + 1.75503i) q^{21} +(0.622978 - 2.32498i) q^{23} +(0.707107 + 0.707107i) q^{27} +7.02768i q^{29} +(-2.35930 - 1.36214i) q^{31} +(-1.55141 - 0.415700i) q^{33} +(-2.43129 - 0.651463i) q^{37} +(0.337428 + 0.194814i) q^{39} +9.88678i q^{41} +(2.73843 + 2.73843i) q^{43} +(-1.44856 + 5.40610i) q^{47} +(2.74747 - 6.43828i) q^{49} +(-0.327958 - 0.568039i) q^{51} +(-0.439427 + 0.117744i) q^{53} +(-1.49588 + 1.49588i) q^{57} +(-2.85833 + 4.95077i) q^{59} +(-11.0916 + 6.40371i) q^{61} +(1.18280 - 2.36664i) q^{63} +(3.94670 + 14.7293i) q^{67} -2.40700 q^{69} -12.6729 q^{71} +(3.70676 + 13.8338i) q^{73} +(0.255355 + 4.24177i) q^{77} +(7.64128 - 4.41169i) q^{79} +(0.500000 - 0.866025i) q^{81} +(5.09559 - 5.09559i) q^{83} +(6.78822 - 1.81890i) q^{87} +(4.64627 + 8.04757i) q^{89} +(0.206489 - 1.00997i) q^{91} +(-0.705096 + 2.63145i) q^{93} +(-5.40643 - 5.40643i) q^{97} +1.60614i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) $ 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.20765	+	1.45817i	−0.834415	+	0.551137i
$7$	−2.20765	+	1.45817i	−0.834415	+	0.551137i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	0.803071	−	1.39096i	0.242135	−	0.419390i	−0.719187	−	0.694816i	$-0.755486\pi$
$11$	0.803071	−	1.39096i	0.242135	−	0.419390i	0.961322	+	0.275426i	$0.0888190\pi$
$12$		0			0
$13$	−0.275509	+	0.275509i	−0.0764123	+	0.0764123i	−0.744280	−	0.667868i	$-0.767207\pi$
$13$	−0.275509	+	0.275509i	−0.0764123	+	0.0764123i	0.667868	+	0.744280i	$0.267207\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.633566	−	0.169763i	0.153662	−	0.0411737i	−0.181168	−	0.983452i	$-0.557988\pi$
$17$	0.633566	−	0.169763i	0.153662	−	0.0411737i	0.334830	+	0.942279i	$0.391321\pi$
$18$		0			0
$19$	−1.05775	−	1.83208i	−0.242664	−	0.420307i	0.718808	−	0.695209i	$-0.244688\pi$
$19$	−1.05775	−	1.83208i	−0.242664	−	0.420307i	−0.961472	+	0.274902i	$0.911355\pi$
$20$		0			0
$21$	1.97987	+	1.75503i	0.432043	+	0.382978i
$22$		0			0
$23$	0.622978	−	2.32498i	0.129900	−	0.484793i	−0.870067	−	0.492933i	$-0.835925\pi$
$23$	0.622978	−	2.32498i	0.129900	−	0.484793i	0.999967	+	0.00814070i	$0.00259129\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			7.02768i			1.30501i	0.757785	+	0.652504i	$0.226281\pi$
$29$			7.02768i			1.30501i	−0.757785	+	0.652504i	$0.773719\pi$
$30$		0			0
$31$	−2.35930	−	1.36214i	−0.423742	−	0.244648i	0.272935	−	0.962033i	$-0.412006\pi$
$31$	−2.35930	−	1.36214i	−0.423742	−	0.244648i	−0.696677	+	0.717385i	$0.745339\pi$
$32$		0			0
$33$	−1.55141	−	0.415700i	−0.270066	−	0.0723641i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.43129	−	0.651463i	−0.399702	−	0.107100i	0.0533678	−	0.998575i	$-0.483004\pi$
$37$	−2.43129	−	0.651463i	−0.399702	−	0.107100i	−0.453070	+	0.891475i	$0.649671\pi$
$38$		0			0
$39$	0.337428	+	0.194814i	0.0540317	+	0.0311952i
$40$		0			0
$41$			9.88678i			1.54406i	0.635589	+	0.772028i	$0.280757\pi$
$41$			9.88678i			1.54406i	−0.635589	+	0.772028i	$0.719243\pi$
$42$		0			0
$43$	2.73843	+	2.73843i	0.417607	+	0.417607i	0.884378	−	0.466771i	$-0.154583\pi$
$43$	2.73843	+	2.73843i	0.417607	+	0.417607i	−0.466771	+	0.884378i	$0.654583\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.44856	+	5.40610i	−0.211294	+	0.788561i	0.776144	+	0.630556i	$0.217173\pi$
$47$	−1.44856	+	5.40610i	−0.211294	+	0.788561i	−0.987438	+	0.158005i	$0.949494\pi$
$48$		0			0
$49$	2.74747	−	6.43828i	0.392496	−	0.919754i
$50$		0			0
$51$	−0.327958	−	0.568039i	−0.0459233	−	0.0795414i
$52$		0			0
$53$	−0.439427	+	0.117744i	−0.0603600	+	0.0161734i	−0.288873	−	0.957368i	$-0.593280\pi$
$53$	−0.439427	+	0.117744i	−0.0603600	+	0.0161734i	0.228513	+	0.973541i	$0.426614\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.49588	+	1.49588i	−0.198135	+	0.198135i
$58$		0			0
$59$	−2.85833	+	4.95077i	−0.372123	+	0.644536i	−0.989892	−	0.141824i	$-0.954703\pi$
$59$	−2.85833	+	4.95077i	−0.372123	+	0.644536i	0.617769	+	0.786360i	$0.288037\pi$
$60$		0			0
$61$	−11.0916	+	6.40371i	−1.42013	+	0.819911i	−0.996309	−	0.0858361i	$-0.972644\pi$
$61$	−11.0916	+	6.40371i	−1.42013	+	0.819911i	−0.423818	+	0.905747i	$0.639311\pi$
$62$		0			0
$63$	1.18280	−	2.36664i	0.149019	−	0.298169i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.94670	+	14.7293i	0.482166	+	1.79947i	0.592496	+	0.805573i	$0.298142\pi$
$67$	3.94670	+	14.7293i	0.482166	+	1.79947i	−0.110330	+	0.993895i	$0.535191\pi$
$68$		0			0
$69$	−2.40700			−0.289769
$70$		0			0
$71$	−12.6729			−1.50400			−0.752000	−	0.659163i	$-0.770911\pi$
$71$	−12.6729			−1.50400			−0.752000	+	0.659163i	$0.770911\pi$
$72$		0			0
$73$	3.70676	+	13.8338i	0.433843	+	1.61912i	0.743820	+	0.668380i	$0.233012\pi$
$73$	3.70676	+	13.8338i	0.433843	+	1.61912i	−0.309977	+	0.950744i	$0.600321\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.255355	+	4.24177i	0.0291004	+	0.483395i
$78$		0			0
$79$	7.64128	−	4.41169i	0.859711	−	0.496354i	−0.00420460	−	0.999991i	$-0.501338\pi$
$79$	7.64128	−	4.41169i	0.859711	−	0.496354i	0.863915	+	0.503637i	$0.168005\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	5.09559	−	5.09559i	0.559313	−	0.559313i	−0.369799	−	0.929112i	$-0.620573\pi$
$83$	5.09559	−	5.09559i	0.559313	−	0.559313i	0.929112	+	0.369799i	$0.120573\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.78822	−	1.81890i	0.727773	−	0.195006i
$88$		0			0
$89$	4.64627	+	8.04757i	0.492503	+	0.853041i	0.999963	−	0.00863479i	$-0.00274857\pi$
$89$	4.64627	+	8.04757i	0.492503	+	0.853041i	−0.507459	+	0.861676i	$0.669415\pi$
$90$		0			0
$91$	0.206489	−	1.00997i	0.0216459	−	0.105873i
$92$		0			0
$93$	−0.705096	+	2.63145i	−0.0731151	+	0.272869i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.40643	−	5.40643i	−0.548939	−	0.548939i	0.377195	−	0.926134i	$-0.376889\pi$
$97$	−5.40643	−	5.40643i	−0.548939	−	0.548939i	−0.926134	+	0.377195i	$0.876889\pi$
$98$		0			0
$99$			1.60614i			0.161423i
$100$		0			0
$101$	−12.7053	−	7.33544i	−1.26423	−	0.729903i	−0.290339	−	0.956924i	$-0.593768\pi$
$101$	−12.7053	−	7.33544i	−1.26423	−	0.729903i	−0.973890	+	0.227021i	$0.927102\pi$
$102$		0			0
$103$	14.2799	+	3.82630i	1.40705	+	0.377017i	0.880869	−	0.473359i	$-0.156959\pi$
$103$	14.2799	+	3.82630i	1.40705	+	0.377017i	0.526176	+	0.850376i	$0.323625\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.37101	−	1.43916i	−0.519235	−	0.139129i	−0.0103222	−	0.999947i	$-0.503286\pi$
$107$	−5.37101	−	1.43916i	−0.519235	−	0.139129i	−0.508913	+	0.860818i	$0.669952\pi$
$108$		0			0
$109$	1.50497	+	0.868898i	0.144150	+	0.0832253i	0.570341	−	0.821408i	$-0.306811\pi$
$109$	1.50497	+	0.868898i	0.144150	+	0.0832253i	−0.426190	+	0.904634i	$0.640145\pi$
$110$		0			0
$111$			2.51706i			0.238909i
$112$		0			0
$113$	3.09316	+	3.09316i	0.290980	+	0.290980i	0.837467	−	0.546487i	$-0.184035\pi$
$113$	3.09316	+	3.09316i	0.290980	+	0.290980i	−0.546487	+	0.837467i	$0.684035\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.100843	−	0.376352i	0.00932295	−	0.0347937i
$118$		0			0
$119$	−1.15115	+	1.29863i	−0.105526	+	0.119045i
$120$		0			0
$121$	4.21015	+	7.29220i	0.382741	+	0.662927i
$122$		0			0
$123$	9.54990	−	2.55889i	0.861085	−	0.230727i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.38575	+	6.38575i	−0.566644	+	0.566644i	−0.931187	−	0.364543i	$-0.881225\pi$
$127$	−6.38575	+	6.38575i	−0.566644	+	0.566644i	0.364543	+	0.931187i	$0.381225\pi$
$128$		0			0
$129$	1.93637	−	3.35388i	0.170487	−	0.295293i
$130$		0			0
$131$	−9.12578	+	5.26877i	−0.797323	+	0.460335i	−0.842534	−	0.538643i	$-0.818937\pi$
$131$	−9.12578	+	5.26877i	−0.797323	+	0.460335i	0.0452109	+	0.998977i	$0.485604\pi$
$132$		0			0
$133$	5.00663	+	2.50221i	0.434130	+	0.216969i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.44289	+	20.3131i	0.465017	+	1.73547i	0.656832	+	0.754037i	$0.271896\pi$
$137$	5.44289	+	20.3131i	0.465017	+	1.73547i	−0.191815	+	0.981431i	$0.561437\pi$
$138$		0			0
$139$	−2.13678			−0.181240			−0.0906198	−	0.995886i	$-0.528885\pi$
$139$	−2.13678			−0.181240			−0.0906198	+	0.995886i	$0.528885\pi$
$140$		0			0
$141$	5.59681			0.471336
$142$		0			0
$143$	0.161968	+	0.604474i	0.0135445	+	0.0505487i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.93000	−	0.987506i	−0.571576	−	0.0814481i
$148$		0			0
$149$	8.35637	−	4.82455i	0.684580	−	0.395243i	−0.116998	−	0.993132i	$-0.537327\pi$
$149$	8.35637	−	4.82455i	0.684580	−	0.395243i	0.801579	+	0.597889i	$0.203994\pi$
$150$		0			0
$151$	9.35287	−	16.1997i	0.761126	−	1.31831i	−0.181145	−	0.983456i	$-0.557980\pi$
$151$	9.35287	−	16.1997i	0.761126	−	1.31831i	0.942271	−	0.334852i	$-0.108686\pi$
$152$		0			0
$153$	−0.463802	+	0.463802i	−0.0374962	+	0.0374962i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	16.5466	−	4.43366i	1.32057	−	0.353845i	0.471376	−	0.881932i	$-0.343757\pi$
$157$	16.5466	−	4.43366i	1.32057	−	0.353845i	0.849190	+	0.528088i	$0.177091\pi$
$158$		0			0
$159$	0.227464	+	0.393980i	0.0180391	+	0.0312446i
$160$		0			0
$161$	2.01491	+	6.04117i	0.158797	+	0.476111i
$162$		0			0
$163$	5.42844	−	20.2592i	0.425188	−	1.58682i	−0.338324	−	0.941030i	$-0.609860\pi$
$163$	5.42844	−	20.2592i	0.425188	−	1.58682i	0.763512	−	0.645794i	$-0.223473\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.29940	−	4.29940i	−0.332698	−	0.332698i	0.520912	−	0.853610i	$-0.325592\pi$
$167$	−4.29940	−	4.29940i	−0.332698	−	0.332698i	−0.853610	+	0.520912i	$0.825592\pi$
$168$		0			0
$169$			12.8482i			0.988322i
$170$		0			0
$171$	1.83208	+	1.05775i	0.140102	+	0.0808882i
$172$		0			0
$173$	−17.9755	−	4.81651i	−1.36665	−	0.366193i	−0.500396	−	0.865797i	$-0.666812\pi$
$173$	−17.9755	−	4.81651i	−1.36665	−	0.366193i	−0.866254	+	0.499604i	$0.833479\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.52187	+	1.47958i	0.415049	+	0.111212i
$178$		0			0
$179$	2.26571	+	1.30811i	0.169347	+	0.0977726i	0.582278	−	0.812990i	$-0.302162\pi$
$179$	2.26571	+	1.30811i	0.169347	+	0.0977726i	−0.412931	+	0.910762i	$0.635495\pi$
$180$		0			0
$181$			7.26604i			0.540081i	0.962849	+	0.270040i	$0.0870370\pi$
$181$			7.26604i			0.540081i	−0.962849	+	0.270040i	$0.912963\pi$
$182$		0			0
$183$	9.05621	+	9.05621i	0.669455	+	0.669455i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.272664	−	1.01760i	0.0199392	−	0.0744140i
$188$		0			0
$189$	−2.59213	−	0.529964i	−0.188550	−	0.0385492i
$190$		0			0
$191$	−10.0833	−	17.4647i	−0.729599	−	1.26370i	−0.957053	−	0.289913i	$-0.906374\pi$
$191$	−10.0833	−	17.4647i	−0.729599	−	1.26370i	0.227454	−	0.973789i	$-0.426960\pi$
$192$		0			0
$193$	−9.39610	+	2.51768i	−0.676346	+	0.181226i	−0.580612	−	0.814181i	$-0.697187\pi$
$193$	−9.39610	+	2.51768i	−0.676346	+	0.181226i	−0.0957343	+	0.995407i	$0.530520\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−13.8585	+	13.8585i	−0.987378	+	0.987378i	−0.999921	−	0.0125433i	$-0.996007\pi$
$197$	−13.8585	+	13.8585i	−0.987378	+	0.987378i	0.0125433	+	0.999921i	$0.496007\pi$
$198$		0			0
$199$	−3.97162	+	6.87905i	−0.281541	+	0.487643i	−0.971764	−	0.235953i	$-0.924179\pi$
$199$	−3.97162	+	6.87905i	−0.281541	+	0.487643i	0.690224	+	0.723596i	$0.257512\pi$
$200$		0			0
$201$	13.2059	−	7.62444i	0.931473	−	0.537786i
$202$		0			0
$203$	−10.2476	−	15.5147i	−0.719238	−	1.08892i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.622978	+	2.32498i	0.0432999	+	0.161598i
$208$		0			0
$209$	−3.39779			−0.235030
$210$		0			0
$211$	24.7491			1.70380			0.851900	−	0.523704i	$-0.175450\pi$
$211$	24.7491			1.70380			0.851900	+	0.523704i	$0.175450\pi$
$212$		0			0
$213$	3.28000	+	12.2411i	0.224742	+	0.838747i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	7.19475	−	0.433124i	0.488411	−	0.0294024i
$218$		0			0
$219$	12.4030	−	7.16090i	0.838120	−	0.483889i
$220$		0			0
$221$	−0.127782	+	0.221324i	−0.00859552	+	0.0148879i
$222$		0			0
$223$	−7.69489	+	7.69489i	−0.515288	+	0.515288i	−0.916142	−	0.400854i	$-0.868713\pi$
$223$	−7.69489	+	7.69489i	−0.515288	+	0.515288i	0.400854	+	0.916142i	$0.368713\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.13119	+	0.303102i	−0.0750799	+	0.0201176i	−0.296163	−	0.955137i	$-0.595707\pi$
$227$	−1.13119	+	0.303102i	−0.0750799	+	0.0201176i	0.221084	+	0.975255i	$0.429041\pi$
$228$		0			0
$229$	−2.42787	−	4.20519i	−0.160438	−	0.277887i	0.774588	−	0.632466i	$-0.217957\pi$
$229$	−2.42787	−	4.20519i	−0.160438	−	0.277887i	−0.935026	+	0.354580i	$0.884624\pi$
$230$		0			0
$231$	4.03115	−	1.34451i	0.265230	−	0.0884619i
$232$		0			0
$233$	3.75475	−	14.0129i	0.245982	−	0.918016i	−0.726906	−	0.686737i	$-0.759042\pi$
$233$	3.75475	−	14.0129i	0.245982	−	0.918016i	0.972887	−	0.231279i	$-0.0742910\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.23908	−	6.23908i	−0.405272	−	0.405272i
$238$		0			0
$239$			11.8194i			0.764533i	0.924052	+	0.382266i	$0.124856\pi$
$239$			11.8194i			0.764533i	−0.924052	+	0.382266i	$0.875144\pi$
$240$		0			0
$241$	7.38360	+	4.26292i	0.475619	+	0.274599i	0.718589	−	0.695435i	$-0.244788\pi$
$241$	7.38360	+	4.26292i	0.475619	+	0.274599i	−0.242970	+	0.970034i	$0.578122\pi$
$242$		0			0
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.796172	+	0.213334i	0.0506592	+	0.0135741i
$248$		0			0
$249$	−6.24079	−	3.60312i	−0.395494	−	0.228339i
$250$		0			0
$251$			25.8739i			1.63315i	0.577241	+	0.816574i	$0.304129\pi$
$251$			25.8739i			1.63315i	−0.577241	+	0.816574i	$0.695871\pi$
$252$		0			0
$253$	−2.73366	−	2.73366i	−0.171864	−	0.171864i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.28353	+	15.9864i	−0.267199	+	0.997202i	0.693691	+	0.720273i	$0.255983\pi$
$257$	−4.28353	+	15.9864i	−0.267199	+	0.997202i	−0.960890	+	0.276929i	$0.910683\pi$
$258$		0			0
$259$	6.31739	−	2.10704i	0.392544	−	0.130925i
$260$		0			0
$261$	−3.51384	−	6.08615i	−0.217501	−	0.376723i
$262$		0			0
$263$	−10.9532	+	2.93489i	−0.675402	+	0.180973i	−0.580187	−	0.814483i	$-0.697020\pi$
$263$	−10.9532	+	2.93489i	−0.675402	+	0.180973i	−0.0952148	+	0.995457i	$0.530354\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	6.57082	−	6.57082i	0.402127	−	0.402127i
$268$		0			0
$269$	−3.87003	+	6.70309i	−0.235960	+	0.408695i	−0.959551	−	0.281534i	$-0.909157\pi$
$269$	−3.87003	+	6.70309i	−0.235960	+	0.408695i	0.723591	+	0.690229i	$0.242490\pi$
$270$		0			0
$271$	2.25229	−	1.30036i	0.136817	−	0.0789912i	−0.430029	−	0.902815i	$-0.641497\pi$
$271$	2.25229	−	1.30036i	0.136817	−	0.0789912i	0.566846	+	0.823824i	$0.308163\pi$
$272$		0			0
$273$	−1.02900	+	0.0619456i	−0.0622777	+	0.00374912i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.0555290	+	0.207237i	0.00333642	+	0.0124517i	0.967574	−	0.252588i	$-0.0812817\pi$
$277$	0.0555290	+	0.207237i	0.00333642	+	0.0124517i	−0.964238	+	0.265040i	$0.914615\pi$
$278$		0			0
$279$	2.72428			0.163099
$280$		0			0
$281$	−3.87306			−0.231048			−0.115524	−	0.993305i	$-0.536855\pi$
$281$	−3.87306			−0.231048			−0.115524	+	0.993305i	$0.536855\pi$
$282$		0			0
$283$	−8.31641	−	31.0373i	−0.494360	−	1.84497i	−0.533588	−	0.845745i	$-0.679157\pi$
$283$	−8.31641	−	31.0373i	−0.494360	−	1.84497i	0.0392282	−	0.999230i	$-0.487510\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.4166	−	21.8266i	−0.850986	−	1.28838i
$288$		0			0
$289$	−14.3498	+	8.28489i	−0.844109	+	0.487346i
$290$		0			0
$291$	−3.82292	+	6.62149i	−0.224104	+	0.388159i
$292$		0			0
$293$	−15.2585	+	15.2585i	−0.891413	+	0.891413i	−0.994656	−	0.103243i	$-0.967078\pi$
$293$	−15.2585	+	15.2585i	−0.891413	+	0.891413i	0.103243	+	0.994656i	$0.467078\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.55141	−	0.415700i	0.0900221	−	0.0241214i
$298$		0			0
$299$	0.468917	+	0.812189i	0.0271182	+	0.0469701i
$300$		0			0
$301$	−10.0386	−	2.05241i	−0.578617	−	0.118299i
$302$		0			0
$303$	−3.79710	+	14.1710i	−0.218138	+	0.814101i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−14.0431	−	14.0431i	−0.801481	−	0.801481i	0.181846	−	0.983327i	$-0.441793\pi$
$307$	−14.0431	−	14.0431i	−0.801481	−	0.801481i	−0.983327	+	0.181846i	$0.941793\pi$
$308$		0			0
$309$		−	14.7837i		−	0.841015i
$310$		0			0
$311$	−24.3736	−	14.0721i	−1.38210	−	0.797955i	−0.389690	−	0.920946i	$-0.627418\pi$
$311$	−24.3736	−	14.0721i	−1.38210	−	0.797955i	−0.992408	+	0.122991i	$0.960751\pi$
$312$		0			0
$313$	5.28563	+	1.41628i	0.298761	+	0.0800529i	0.405086	−	0.914279i	$-0.367242\pi$
$313$	5.28563	+	1.41628i	0.298761	+	0.0800529i	−0.106325	+	0.994331i	$0.533908\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	27.3676	+	7.33313i	1.53712	+	0.411870i	0.925334	−	0.379154i	$-0.123785\pi$
$317$	27.3676	+	7.33313i	1.53712	+	0.411870i	0.611785	+	0.791024i	$0.290452\pi$
$318$		0			0
$319$	9.77522	+	5.64373i	0.547307	+	0.315988i
$320$		0			0
$321$			5.56048i			0.310355i
$322$		0			0
$323$	−0.981174	−	0.981174i	−0.0545940	−	0.0545940i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.449774	−	1.67858i	0.0248726	−	0.0928258i
$328$		0			0
$329$	−4.68510	−	14.0470i	−0.258298	−	0.774439i
$330$		0			0
$331$	2.48800	+	4.30934i	0.136753	+	0.236863i	0.926266	−	0.376871i	$-0.123000\pi$
$331$	2.48800	+	4.30934i	0.136753	+	0.236863i	−0.789513	+	0.613734i	$0.789667\pi$
$332$		0			0
$333$	2.43129	−	0.651463i	0.133234	−	0.0356999i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	14.0207	−	14.0207i	0.763757	−	0.763757i	−0.213243	−	0.976999i	$-0.568403\pi$
$337$	14.0207	−	14.0207i	0.763757	−	0.763757i	0.976999	+	0.213243i	$0.0684025\pi$
$338$		0			0
$339$	2.18719	−	3.78833i	0.118792	−	0.205754i
$340$		0			0
$341$	−3.78937	+	2.18779i	−0.205206	+	0.118476i
$342$		0			0
$343$	3.32264	+	18.2198i	0.179406	+	0.983775i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.41425	−	35.1344i	−0.505383	−	1.88612i	−0.461628	−	0.887073i	$-0.652735\pi$
$347$	−9.41425	−	35.1344i	−0.505383	−	1.88612i	−0.0437548	−	0.999042i	$-0.513932\pi$
$348$		0			0
$349$	−35.4056			−1.89522			−0.947610	−	0.319431i	$-0.896508\pi$
$349$	−35.4056			−1.89522			−0.947610	+	0.319431i	$0.896508\pi$
$350$		0			0
$351$	−0.389628			−0.0207968
$352$		0			0
$353$	4.40400	+	16.4359i	0.234401	+	0.874797i	0.978418	+	0.206636i	$0.0662516\pi$
$353$	4.40400	+	16.4359i	0.234401	+	0.874797i	−0.744017	+	0.668161i	$0.767082\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.55232	+	0.775816i	0.0821573	+	0.0410605i
$358$		0			0
$359$	24.3468	−	14.0566i	1.28497	−	0.741879i	0.307220	−	0.951639i	$-0.400601\pi$
$359$	24.3468	−	14.0566i	1.28497	−	0.741879i	0.977753	+	0.209759i	$0.0672680\pi$
$360$		0			0
$361$	7.26233	−	12.5787i	0.382228	−	0.662038i
$362$		0			0
$363$	5.95406	−	5.95406i	0.312507	−	0.312507i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.31505	−	1.69211i	0.329643	−	0.0883276i	−0.0902017	−	0.995924i	$-0.528751\pi$
$367$	6.31505	−	1.69211i	0.329643	−	0.0883276i	0.419845	+	0.907596i	$0.362084\pi$
$368$		0			0
$369$	−4.94339	−	8.56220i	−0.257343	−	0.445730i
$370$		0			0
$371$	0.798412	−	0.900699i	0.0414515	−	0.0467619i
$372$		0			0
$373$	4.89631	−	18.2733i	0.253521	−	0.946155i	−0.715386	−	0.698730i	$-0.753749\pi$
$373$	4.89631	−	18.2733i	0.253521	−	0.946155i	0.968907	−	0.247425i	$-0.0795844\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.93619	−	1.93619i	−0.0997187	−	0.0997187i
$378$		0			0
$379$			6.56543i			0.337243i	0.985681	+	0.168622i	$0.0539316\pi$
$379$			6.56543i			0.337243i	−0.985681	+	0.168622i	$0.946068\pi$
$380$		0			0
$381$	7.82092	+	4.51541i	0.400678	+	0.231331i
$382$		0			0
$383$	0.465275	+	0.124670i	0.0237745	+	0.00637035i	0.270687	−	0.962668i	$-0.412749\pi$
$383$	0.465275	+	0.124670i	0.0237745	+	0.00637035i	−0.246912	+	0.969038i	$0.579416\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.74077	−	1.00234i	−0.190154	−	0.0509516i
$388$		0			0
$389$	−7.04917	−	4.06984i	−0.357407	−	0.206349i	0.310536	−	0.950562i	$-0.399492\pi$
$389$	−7.04917	−	4.06984i	−0.357407	−	0.206349i	−0.667943	+	0.744213i	$0.732825\pi$
$390$		0			0
$391$		−	1.57879i		−	0.0798428i
$392$		0			0
$393$	7.45117	+	7.45117i	0.375862	+	0.375862i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.24409	−	15.8391i	0.213005	−	0.794944i	−0.773855	−	0.633363i	$-0.781674\pi$
$397$	4.24409	−	15.8391i	0.213005	−	0.794944i	0.986859	−	0.161581i	$-0.0516593\pi$
$398$		0			0
$399$	1.12114	−	5.48365i	0.0561272	−	0.274526i
$400$		0			0
$401$	−8.21670	−	14.2318i	−0.410323	−	0.710700i	0.584602	−	0.811320i	$-0.301251\pi$
$401$	−8.21670	−	14.2318i	−0.410323	−	0.710700i	−0.994925	+	0.100620i	$0.967917\pi$
$402$		0			0
$403$	1.02529	−	0.274725i	0.0510733	−	0.0136850i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.85866	+	2.85866i	−0.141698	+	0.141698i
$408$		0			0
$409$	14.2130	−	24.6176i	0.702786	−	1.21726i	−0.264698	−	0.964331i	$-0.585272\pi$
$409$	14.2130	−	24.6176i	0.702786	−	1.21726i	0.967485	−	0.252930i	$-0.0813942\pi$
$410$		0			0
$411$	18.2123	−	10.5148i	0.898344	−	0.518659i
$412$		0			0
$413$	−0.908872	−	15.0975i	−0.0447227	−	0.742901i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.553040	+	2.06397i	0.0270825	+	0.101073i
$418$		0			0
$419$	−29.6713			−1.44954			−0.724768	−	0.688993i	$-0.758053\pi$
$419$	−29.6713			−1.44954			−0.724768	+	0.688993i	$0.758053\pi$
$420$		0			0
$421$	16.5789			0.808008			0.404004	−	0.914757i	$-0.367618\pi$
$421$	16.5789			0.808008			0.404004	+	0.914757i	$0.367618\pi$
$422$		0			0
$423$	−1.44856	−	5.40610i	−0.0704314	−	0.262854i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.1486	−	30.3106i	0.733092	−	1.46683i
$428$		0			0
$429$	0.541957	−	0.312899i	0.0261659	−	0.0151069i
$430$		0			0
$431$	−8.74180	+	15.1412i	−0.421078	+	0.729328i	−0.996045	−	0.0888482i	$-0.971681\pi$
$431$	−8.74180	+	15.1412i	−0.421078	+	0.729328i	0.574967	+	0.818176i	$0.305015\pi$
$432$		0			0
$433$	−21.8490	+	21.8490i	−1.05000	+	1.05000i	−0.0513140	+	0.998683i	$0.516341\pi$
$433$	−21.8490	+	21.8490i	−1.05000	+	1.05000i	−0.998683	+	0.0513140i	$0.983659\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.91850	+	1.31791i	−0.235284	+	0.0630441i
$438$		0			0
$439$	−10.7878	−	18.6849i	−0.514872	−	0.891784i	−0.999851	−	0.0172583i	$-0.994506\pi$
$439$	−10.7878	−	18.6849i	−0.514872	−	0.891784i	0.484979	−	0.874526i	$-0.338827\pi$
$440$		0			0
$441$	0.839757	+	6.94945i	0.0399884	+	0.330926i
$442$		0			0
$443$	−4.38976	+	16.3828i	−0.208564	+	0.778370i	0.779770	+	0.626066i	$0.215336\pi$
$443$	−4.38976	+	16.3828i	−0.208564	+	0.778370i	−0.988334	+	0.152304i	$0.951331\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−6.82295	−	6.82295i	−0.322714	−	0.322714i
$448$		0			0
$449$			23.2940i			1.09931i	0.835392	+	0.549655i	$0.185241\pi$
$449$			23.2940i			1.09931i	−0.835392	+	0.549655i	$0.814759\pi$
$450$		0			0
$451$	13.7521	+	7.93978i	0.647561	+	0.373870i
$452$		0			0
$453$	−18.0684	−	4.84140i	−0.848926	−	0.227469i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.00277	−	2.41228i	−0.421132	−	0.112842i	0.0420287	−	0.999116i	$-0.486618\pi$
$457$	−9.00277	−	2.41228i	−0.421132	−	0.112842i	−0.463160	+	0.886275i	$0.653285\pi$
$458$		0			0
$459$	0.568039	+	0.327958i	0.0265138	+	0.0153078i
$460$		0			0
$461$		−	28.9183i		−	1.34686i	−0.739251	−	0.673430i	$-0.764820\pi$
$461$		−	28.9183i		−	1.34686i	0.739251	−	0.673430i	$-0.235180\pi$
$462$		0			0
$463$	0.489997	+	0.489997i	0.0227721	+	0.0227721i	0.718401	−	0.695629i	$-0.244874\pi$
$463$	0.489997	+	0.489997i	0.0227721	+	0.0227721i	−0.695629	+	0.718401i	$0.744874\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.34437	−	12.4814i	0.154759	−	0.577569i	−0.844367	−	0.535766i	$-0.820023\pi$
$467$	3.34437	−	12.4814i	0.154759	−	0.577569i	0.999126	−	0.0418035i	$-0.0133103\pi$
$468$		0			0
$469$	−30.1908	−	26.7622i	−1.39408	−	1.23576i
$470$		0			0
$471$	−8.56518	−	14.8353i	−0.394662	−	0.683575i
$472$		0			0
$473$	6.00821	−	1.60989i	0.276258	−	0.0740230i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.321683	−	0.321683i	0.0147289	−	0.0147289i
$478$		0			0
$479$	0.0272496	−	0.0471978i	0.00124507	−	0.00215652i	−0.865402	−	0.501078i	$-0.832937\pi$
$479$	0.0272496	−	0.0471978i	0.00124507	−	0.00215652i	0.866647	+	0.498921i	$0.166270\pi$
$480$		0			0
$481$	0.849325	−	0.490358i	0.0387259	−	0.0223584i
$482$		0			0
$483$	5.31382	−	3.50982i	0.241787	−	0.159702i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.495369	+	1.84874i	0.0224473	+	0.0837746i	0.976241	−	0.216688i	$-0.0695255\pi$
$487$	0.495369	+	1.84874i	0.0224473	+	0.0837746i	−0.953794	+	0.300463i	$0.902859\pi$
$488$		0			0
$489$	−20.9739			−0.948471
$490$		0			0
$491$	23.6163			1.06579			0.532894	−	0.846182i	$-0.321105\pi$
$491$	23.6163			1.06579			0.532894	+	0.846182i	$0.321105\pi$
$492$		0			0
$493$	1.19304	+	4.45250i	0.0537320	+	0.200530i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	27.9774	−	18.4793i	1.25496	−	0.828910i
$498$		0			0
$499$	35.4989	−	20.4953i	1.58915	−	0.917496i	0.595703	−	0.803205i	$-0.296874\pi$
$499$	35.4989	−	20.4953i	1.58915	−	0.917496i	0.993447	−	0.114291i	$-0.0364596\pi$
$500$		0			0
$501$	−3.04014	+	5.26567i	−0.135823	+	0.235253i
$502$		0			0
$503$	12.7642	−	12.7642i	0.569127	−	0.569127i	−0.362757	−	0.931884i	$-0.618165\pi$
$503$	12.7642	−	12.7642i	0.569127	−	0.569127i	0.931884	+	0.362757i	$0.118165\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.4104	−	3.32536i	0.551165	−	0.147684i
$508$		0			0
$509$	13.2181	+	22.8944i	0.585881	+	1.01478i	0.994765	+	0.102189i	$0.0325847\pi$
$509$	13.2181	+	22.8944i	0.585881	+	1.01478i	−0.408884	+	0.912586i	$0.634082\pi$
$510$		0			0
$511$	−28.3553	−	25.1352i	−1.25436	−	1.11191i
$512$		0			0
$513$	0.547532	−	2.04342i	0.0241741	−	0.0902190i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.35637	+	6.35637i	0.279553	+	0.279553i
$518$		0			0
$519$			18.6096i			0.816870i
$520$		0			0
$521$	13.5413	+	7.81808i	0.593255	+	0.342516i	0.766384	−	0.642383i	$-0.222054\pi$
$521$	13.5413	+	7.81808i	0.593255	+	0.342516i	−0.173128	+	0.984899i	$0.555388\pi$
$522$		0			0
$523$	3.74349	+	1.00306i	0.163691	+	0.0438609i	0.339734	−	0.940522i	$-0.389663\pi$
$523$	3.74349	+	1.00306i	0.163691	+	0.0438609i	−0.176043	+	0.984383i	$0.556330\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.72601	−	0.462484i	−0.0751863	−	0.0201461i
$528$		0			0
$529$	14.9011	+	8.60317i	0.647875	+	0.374051i
$530$		0			0
$531$		−	5.71666i		−	0.248082i
$532$		0			0
$533$	−2.72389	−	2.72389i	−0.117985	−	0.117985i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.677127	−	2.52707i	0.0292202	−	0.109051i
$538$		0			0
$539$	−6.74897	−	8.99201i	−0.290699	−	0.387313i
$540$		0			0
$541$	8.96813	+	15.5332i	0.385570	+	0.667827i	0.991848	−	0.127426i	$-0.0406716\pi$
$541$	8.96813	+	15.5332i	0.385570	+	0.667827i	−0.606278	+	0.795253i	$0.707338\pi$
$542$		0			0
$543$	7.01846	−	1.88059i	0.301191	−	0.0807038i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−15.3881	+	15.3881i	−0.657948	+	0.657948i	−0.954894	−	0.296946i	$-0.904032\pi$
$547$	−15.3881	+	15.3881i	−0.657948	+	0.657948i	0.296946	+	0.954894i	$0.404032\pi$
$548$		0			0
$549$	6.40371	−	11.0916i	0.273304	−	0.473376i
$550$		0			0
$551$	12.8753	−	7.43353i	0.548504	−	0.316679i
$552$		0			0
$553$	−10.4363	+	20.8818i	−0.443796	+	0.887984i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.19616	−	34.3205i	−0.389654	−	1.45421i	−0.830698	−	0.556723i	$-0.812059\pi$
$557$	−9.19616	−	34.3205i	−0.389654	−	1.45421i	0.441045	−	0.897485i	$-0.354608\pi$
$558$		0			0
$559$	−1.50892			−0.0638207
$560$		0			0
$561$	−1.05349			−0.0444785
$562$		0			0
$563$	−8.32762	−	31.0791i	−0.350967	−	1.30983i	−0.885484	−	0.464670i	$-0.846173\pi$
$563$	−8.32762	−	31.0791i	−0.350967	−	1.30983i	0.534516	−	0.845158i	$-0.320494\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.158987	+	2.64097i	0.00667681	+	0.110910i
$568$		0			0
$569$	−14.5946	+	8.42618i	−0.611836	+	0.353244i	−0.773684	−	0.633572i	$-0.781588\pi$
$569$	−14.5946	+	8.42618i	−0.611836	+	0.353244i	0.161848	+	0.986816i	$0.448255\pi$
$570$		0			0
$571$	0.919768	−	1.59309i	0.0384911	−	0.0666685i	−0.846138	−	0.532964i	$-0.821078\pi$
$571$	0.919768	−	1.59309i	0.0384911	−	0.0666685i	0.884629	+	0.466295i	$0.154412\pi$
$572$		0			0
$573$	−14.2599	+	14.2599i	−0.595715	+	0.595715i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−26.2695	+	7.03890i	−1.09361	+	0.293033i	−0.760162	−	0.649734i	$-0.774880\pi$
$577$	−26.2695	+	7.03890i	−1.09361	+	0.293033i	−0.333453	+	0.942767i	$0.608214\pi$
$578$		0			0
$579$	4.86378	+	8.42431i	0.202132	+	0.350102i
$580$		0			0
$581$	−3.81905	+	18.6795i	−0.158441	+	0.774957i
$582$		0			0
$583$	−0.189114	+	0.705782i	−0.00783229	+	0.0292305i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.2565	+	17.2565i	0.712252	+	0.712252i	0.967006	−	0.254754i	$-0.0819945\pi$
$587$	17.2565	+	17.2565i	0.712252	+	0.712252i	−0.254754	+	0.967006i	$0.581994\pi$
$588$		0			0
$589$			5.76322i			0.237469i
$590$		0			0
$591$	16.9731	+	9.79945i	0.698182	+	0.403095i
$592$		0			0
$593$	−32.1148	−	8.60512i	−1.31879	−	0.353370i	−0.470269	−	0.882523i	$-0.655843\pi$
$593$	−32.1148	−	8.60512i	−1.31879	−	0.353370i	−0.848526	+	0.529153i	$0.822510\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.67259	+	2.05586i	0.314018	+	0.0841409i
$598$		0			0
$599$	16.4156	+	9.47753i	0.670722	+	0.387241i	0.796350	−	0.604836i	$-0.206761\pi$
$599$	16.4156	+	9.47753i	0.670722	+	0.387241i	−0.125628	+	0.992077i	$0.540095\pi$
$600$		0			0
$601$		−	19.6156i		−	0.800138i	−0.916485	−	0.400069i	$-0.868986\pi$
$601$		−	19.6156i		−	0.800138i	0.916485	−	0.400069i	$-0.131014\pi$
$602$		0			0
$603$	−10.7826	−	10.7826i	−0.439101	−	0.439101i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	0.535137	−	1.99716i	0.0217205	−	0.0810622i	−0.954215	−	0.299122i	$-0.903306\pi$
$607$	0.535137	−	1.99716i	0.0217205	−	0.0810622i	0.975935	+	0.218060i	$0.0699729\pi$
$608$		0			0
$609$	−12.3338	+	13.9139i	−0.499790	+	0.563819i
$610$		0			0
$611$	−1.09034	−	1.88852i	−0.0441103	−	0.0764013i
$612$		0			0
$613$	−5.83045	+	1.56227i	−0.235490	+	0.0630993i	−0.374634	−	0.927173i	$-0.622232\pi$
$613$	−5.83045	+	1.56227i	−0.235490	+	0.0630993i	0.139144	+	0.990272i	$0.455565\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.39249	+	9.39249i	−0.378127	+	0.378127i	−0.870426	−	0.492299i	$-0.836157\pi$
$617$	−9.39249	+	9.39249i	−0.378127	+	0.378127i	0.492299	+	0.870426i	$0.336157\pi$
$618$		0			0
$619$	6.82928	−	11.8287i	0.274492	−	0.475434i	−0.695515	−	0.718512i	$-0.744824\pi$
$619$	6.82928	−	11.8287i	0.274492	−	0.475434i	0.970007	+	0.243078i	$0.0781570\pi$
$620$		0			0
$621$	2.08452	−	1.20350i	0.0836491	−	0.0482948i
$622$		0			0
$623$	−21.9921	−	10.9912i	−0.881095	−	0.440353i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.879413	+	3.28202i	0.0351204	+	0.131071i
$628$		0			0
$629$	−1.65098			−0.0658288
$630$		0			0
$631$	32.9192			1.31049			0.655246	−	0.755416i	$-0.272565\pi$
$631$	32.9192			1.31049			0.655246	+	0.755416i	$0.272565\pi$
$632$		0			0
$633$	−6.40555	−	23.9058i	−0.254598	−	0.950171i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.01685	+	2.53075i	0.0402890	+	0.100272i
$638$		0			0
$639$	10.9751	−	6.33647i	0.434168	−	0.250667i
$640$		0			0
$641$	14.5479	−	25.1978i	0.574609	−	0.995253i	−0.421475	−	0.906840i	$-0.638487\pi$
$641$	14.5479	−	25.1978i	0.574609	−	0.995253i	0.996084	−	0.0884125i	$-0.0281794\pi$
$642$		0			0
$643$	−0.849619	+	0.849619i	−0.0335057	+	0.0335057i	−0.723661	−	0.690155i	$-0.757542\pi$
$643$	−0.849619	+	0.849619i	−0.0335057	+	0.0335057i	0.690155	+	0.723661i	$0.257542\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−36.5394	+	9.79070i	−1.43651	+	0.384912i	−0.891311	−	0.453393i	$-0.850213\pi$
$647$	−36.5394	+	9.79070i	−1.43651	+	0.384912i	−0.545201	+	0.838305i	$0.683547\pi$
$648$		0			0
$649$	4.59088	+	7.95164i	0.180208	+	0.312129i
$650$		0			0
$651$	−2.28050	−	6.83749i	−0.0893800	−	0.267982i
$652$		0			0
$653$	1.79838	−	6.71164i	0.0703760	−	0.262647i	−0.921769	−	0.387739i	$-0.873256\pi$
$653$	1.79838	−	6.71164i	0.0703760	−	0.262647i	0.992145	+	0.125092i	$0.0399228\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−10.1270	−	10.1270i	−0.395094	−	0.395094i
$658$		0			0
$659$			23.0532i			0.898024i	0.893526	+	0.449012i	$0.148224\pi$
$659$			23.0532i			0.898024i	−0.893526	+	0.449012i	$0.851776\pi$
$660$		0			0
$661$	16.9212	+	9.76947i	0.658159	+	0.379988i	0.791575	−	0.611072i	$-0.209261\pi$
$661$	16.9212	+	9.76947i	0.658159	+	0.379988i	−0.133416	+	0.991060i	$0.542595\pi$
$662$		0			0
$663$	0.246855	+	0.0661446i	0.00958705	+	0.00256884i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	16.3392	+	4.37809i	0.632658	+	0.169520i
$668$		0			0
$669$	9.42428	+	5.44111i	0.364364	+	0.210365i
$670$		0			0
$671$			20.5705i			0.794116i
$672$		0			0
$673$	−2.66575	−	2.66575i	−0.102757	−	0.102757i	0.653859	−	0.756616i	$-0.273149\pi$
$673$	−2.66575	−	2.66575i	−0.102757	−	0.102757i	−0.756616	+	0.653859i	$0.773149\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.19820	+	26.8640i	−0.276649	+	1.03247i	0.678079	+	0.734989i	$0.262813\pi$
$677$	−7.19820	+	26.8640i	−0.276649	+	1.03247i	−0.954728	+	0.297480i	$0.903854\pi$
$678$		0			0
$679$	19.8190	+	4.05202i	0.760584	+	0.155502i
$680$		0			0
$681$	0.585548	+	1.01420i	0.0224383	+	0.0388642i
$682$		0			0
$683$	1.78756	−	0.478976i	0.0683992	−	0.0183275i	−0.224457	−	0.974484i	$-0.572061\pi$
$683$	1.78756	−	0.478976i	0.0683992	−	0.0183275i	0.292856	+	0.956156i	$0.405394\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.43352	+	3.43352i	−0.130997	+	0.130997i
$688$		0			0
$689$	0.0886265	−	0.153506i	0.00337640	−	0.00584810i
$690$		0			0
$691$	5.19942	−	3.00188i	0.197795	−	0.114197i	−0.397832	−	0.917458i	$-0.630237\pi$
$691$	5.19942	−	3.00188i	0.197795	−	0.114197i	0.595627	+	0.803261i	$0.296904\pi$
$692$		0			0
$693$	−2.34203	−	3.54580i	−0.0889663	−	0.134694i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.67841	+	6.26392i	0.0635744	+	0.237263i
$698$		0			0
$699$	−14.5072			−0.548714
$700$		0			0
$701$	4.65445			0.175796			0.0878981	−	0.996129i	$-0.471985\pi$
$701$	4.65445			0.175796			0.0878981	+	0.996129i	$0.471985\pi$
$702$		0			0
$703$	1.37817	+	5.14340i	0.0519786	+	0.193987i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	38.7453	−	2.33247i	1.45717	−	0.0877216i
$708$		0			0
$709$	−0.743926	+	0.429506i	−0.0279387	+	0.0161304i	−0.513904	−	0.857848i	$-0.671801\pi$
$709$	−0.743926	+	0.429506i	−0.0279387	+	0.0161304i	0.485966	+	0.873978i	$0.338468\pi$
$710$		0			0
$711$	−4.41169	+	7.64128i	−0.165451	+	0.286570i
$712$		0			0
$713$	−4.63675	+	4.63675i	−0.173648	+	0.173648i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	11.4167	−	3.05908i	0.426363	−	0.114244i
$718$		0			0
$719$	−12.1602	−	21.0621i	−0.453500	−	0.785485i	0.545101	−	0.838371i	$-0.316491\pi$
$719$	−12.1602	−	21.0621i	−0.453500	−	0.785485i	−0.998601	+	0.0528857i	$0.983158\pi$
$720$		0			0
$721$	−37.1046	+	12.3755i	−1.38185	+	0.460886i
$722$		0			0
$723$	2.20665	−	8.23533i	0.0820662	−	0.306275i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.12079	−	8.12079i	−0.301183	−	0.301183i	0.540293	−	0.841477i	$-0.318313\pi$
$727$	−8.12079	−	8.12079i	−0.301183	−	0.301183i	−0.841477	+	0.540293i	$0.818313\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	2.19986	+	1.27009i	0.0813649	+	0.0469761i
$732$		0			0
$733$	20.1200	+	5.39113i	0.743148	+	0.199126i	0.610477	−	0.792034i	$-0.290978\pi$
$733$	20.1200	+	5.39113i	0.743148	+	0.199126i	0.132671	+	0.991160i	$0.457645\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	23.6573	+	6.33896i	0.871428	+	0.233498i
$738$		0			0
$739$	17.6831	+	10.2094i	0.650485	+	0.375558i	0.788642	−	0.614853i	$-0.210785\pi$
$739$	17.6831	+	10.2094i	0.650485	+	0.375558i	−0.138157	+	0.990410i	$0.544118\pi$
$740$		0			0
$741$		−	0.824258i		−	0.0302799i
$742$		0			0
$743$	10.7038	+	10.7038i	0.392683	+	0.392683i	0.875643	−	0.482960i	$-0.160438\pi$
$743$	10.7038	+	10.7038i	0.392683	+	0.392683i	−0.482960	+	0.875643i	$0.660438\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.86511	+	6.96070i	−0.0682409	+	0.254679i
$748$		0			0
$749$	13.9559	−	4.65469i	0.509936	−	0.170079i
$750$		0			0
$751$	−18.2185	−	31.5554i	−0.664803	−	1.15147i	−0.979339	−	0.202227i	$-0.935182\pi$
$751$	−18.2185	−	31.5554i	−0.664803	−	1.15147i	0.314535	−	0.949246i	$-0.398151\pi$
$752$		0			0
$753$	24.9923	−	6.69666i	0.910769	−	0.244040i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−19.9653	+	19.9653i	−0.725651	+	0.725651i	−0.969750	−	0.244099i	$-0.921508\pi$
$757$	−19.9653	+	19.9653i	−0.725651	+	0.725651i	0.244099	+	0.969750i	$0.421508\pi$
$758$		0			0
$759$	−1.93299	+	3.34804i	−0.0701632	+	0.121526i
$760$		0			0
$761$	14.5349	−	8.39176i	0.526892	−	0.304201i	−0.212858	−	0.977083i	$-0.568277\pi$
$761$	14.5349	−	8.39176i	0.526892	−	0.304201i	0.739750	+	0.672882i	$0.234944\pi$
$762$		0			0
$763$	−4.58946	+	0.276286i	−0.166150	+	0.0100022i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.576486	−	2.15147i	−0.0208157	−	0.0776853i
$768$		0			0
$769$	−12.9268			−0.466151			−0.233076	−	0.972459i	$-0.574879\pi$
$769$	−12.9268			−0.466151			−0.233076	+	0.972459i	$0.574879\pi$
$770$		0			0
$771$	16.5503			0.596045
$772$		0			0
$773$	3.29374	+	12.2924i	0.118468	+	0.442127i	0.999523	−	0.0308862i	$-0.00983295\pi$
$773$	3.29374	+	12.2924i	0.118468	+	0.442127i	−0.881055	+	0.473013i	$0.843166\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.67030	−	5.55679i	−0.131671	−	0.199349i
$778$		0			0
$779$	18.1133	−	10.4577i	0.648978	−	0.374687i
$780$		0			0
$781$	−10.1773	+	17.6275i	−0.364171	+	0.630763i
$782$		0			0
$783$	−4.96932	+	4.96932i	−0.177589	+	0.177589i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	23.3269	−	6.25043i	0.831514	−	0.222804i	0.182140	−	0.983273i	$-0.441698\pi$
$787$	23.3269	−	6.25043i	0.831514	−	0.222804i	0.649374	+	0.760469i	$0.275031\pi$
$788$		0			0
$789$	5.66978	+	9.82035i	0.201850	+	0.349614i
$790$		0			0
$791$	−11.3390	−	2.31827i	−0.403168	−	0.0824281i
$792$		0			0
$793$	1.29154	−	4.82010i	0.0458640	−	0.171167i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.46616	−	6.46616i	−0.229043	−	0.229043i	0.583250	−	0.812293i	$-0.301781\pi$
$797$	−6.46616	−	6.46616i	−0.229043	−	0.229043i	−0.812293	+	0.583250i	$0.801781\pi$
$798$		0			0
$799$			3.67103i			0.129872i
$800$		0			0
$801$	−8.04757	−	4.64627i	−0.284347	−	0.164168i
$802$		0			0
$803$	22.2190	+	5.95357i	0.784093	+	0.210097i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	7.47632	+	2.00328i	0.263179	+	0.0705186i
$808$		0			0
$809$	9.32249	+	5.38234i	0.327761	+	0.189233i	0.654847	−	0.755762i	$-0.272733\pi$
$809$	9.32249	+	5.38234i	0.327761	+	0.189233i	−0.327085	+	0.944995i	$0.606067\pi$
$810$		0			0
$811$			2.55216i			0.0896184i	0.998996	+	0.0448092i	$0.0142680\pi$
$811$			2.55216i			0.0896184i	−0.998996	+	0.0448092i	$0.985732\pi$
$812$		0			0
$813$	−1.83899	−	1.83899i	−0.0644961	−	0.0644961i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	2.12044	−	7.91360i	0.0741849	−	0.276862i
$818$		0			0
$819$	0.326159	+	0.977901i	0.0113969	+	0.0341706i
$820$		0			0
$821$	−11.1868	−	19.3762i	−0.390423	−	0.676233i	0.602082	−	0.798434i	$-0.294338\pi$
$821$	−11.1868	−	19.3762i	−0.390423	−	0.676233i	−0.992505	+	0.122201i	$0.961005\pi$
$822$		0			0
$823$	24.3190	−	6.51626i	0.847707	−	0.227142i	0.191283	−	0.981535i	$-0.438735\pi$
$823$	24.3190	−	6.51626i	0.847707	−	0.227142i	0.656424	+	0.754392i	$0.272068\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.16960	+	3.16960i	−0.110218	+	0.110218i	−0.760065	−	0.649847i	$-0.774833\pi$
$827$	−3.16960	+	3.16960i	−0.110218	+	0.110218i	0.649847	+	0.760065i	$0.274833\pi$
$828$		0			0
$829$	8.68023	−	15.0346i	0.301477	−	0.522173i	−0.674994	−	0.737823i	$-0.735854\pi$
$829$	8.68023	−	15.0346i	0.301477	−	0.522173i	0.976471	+	0.215650i	$0.0691871\pi$
$830$		0			0
$831$	0.185804	−	0.107274i	0.00644546	−	0.00372129i
$832$		0			0
$833$	0.647720	−	4.54549i	0.0224422	−	0.157492i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.705096	−	2.63145i	−0.0243717	−	0.0909564i
$838$		0			0
$839$	−27.6873			−0.955870			−0.477935	−	0.878395i	$-0.658615\pi$
$839$	−27.6873			−0.955870			−0.477935	+	0.878395i	$0.658615\pi$
$840$		0			0
$841$	−20.3883			−0.703045
$842$		0			0
$843$	1.00242	+	3.74109i	0.0345253	+	0.128850i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−19.9278	−	9.95953i	−0.684729	−	0.342214i
$848$		0			0
$849$	−27.8273	+	16.0661i	−0.955029	+	0.551386i
$850$		0			0
$851$	−3.02928	+	5.24687i	−0.103842	+	0.179860i
$852$		0			0
$853$	−6.70940	+	6.70940i	−0.229725	+	0.229725i	−0.812578	−	0.582853i	$-0.801937\pi$
$853$	−6.70940	+	6.70940i	−0.229725	+	0.229725i	0.582853	+	0.812578i	$0.301937\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−31.9194	+	8.55278i	−1.09035	+	0.292157i	−0.758828	−	0.651291i	$-0.774228\pi$
$857$	−31.9194	+	8.55278i	−1.09035	+	0.292157i	−0.331519	+	0.943449i	$0.607561\pi$
$858$		0			0
$859$	−9.46364	−	16.3915i	−0.322895	−	0.559271i	0.658189	−	0.752853i	$-0.271323\pi$
$859$	−9.46364	−	16.3915i	−0.322895	−	0.559271i	−0.981084	+	0.193582i	$0.937990\pi$
$860$		0			0
$861$	−17.3516	+	19.5745i	−0.591340	+	0.667098i
$862$		0			0
$863$	−1.14153	+	4.26026i	−0.0388583	+	0.145021i	−0.982629	−	0.185578i	$-0.940584\pi$
$863$	−1.14153	+	4.26026i	−0.0388583	+	0.145021i	0.943771	+	0.330599i	$0.107251\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	11.7166	+	11.7166i	0.397917	+	0.397917i
$868$		0			0
$869$		−	14.1716i		−	0.480739i
$870$		0			0
$871$	−5.14539	−	2.97069i	−0.174345	−	0.100658i
$872$		0			0
$873$	7.38531	+	1.97889i	0.249955	+	0.0669752i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.0297	+	3.22334i	0.406213	+	0.108844i	0.456139	−	0.889909i	$-0.349232\pi$
$877$	12.0297	+	3.22334i	0.406213	+	0.108844i	−0.0499262	+	0.998753i	$0.515899\pi$
$878$		0			0
$879$	18.6878	+	10.7894i	0.630324	+	0.363918i
$880$		0			0
$881$			55.0306i			1.85403i	0.375026	+	0.927014i	$0.377634\pi$
$881$			55.0306i			1.85403i	−0.375026	+	0.927014i	$0.622366\pi$
$882$		0			0
$883$	30.2918	+	30.2918i	1.01940	+	1.01940i	0.999808	+	0.0195926i	$0.00623691\pi$
$883$	30.2918	+	30.2918i	1.01940	+	1.01940i	0.0195926	+	0.999808i	$0.493763\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.66980	+	24.8920i	−0.223950	+	0.835793i	0.758872	+	0.651239i	$0.225751\pi$
$887$	−6.66980	+	24.8920i	−0.223950	+	0.835793i	−0.982822	+	0.184554i	$0.940916\pi$
$888$		0			0
$889$	4.78601	−	23.4091i	0.160518	−	0.785114i
$890$		0			0
$891$	−0.803071	−	1.39096i	−0.0269039	−	0.0465989i
$892$		0			0
$893$	11.4366	−	3.06443i	0.382711	−	0.102547i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.663149	−	0.663149i	0.0221419	−	0.0221419i
$898$		0			0
$899$	9.57270	−	16.5804i	0.319267	−	0.552987i
$900$		0			0
$901$	−0.258417	+	0.149197i	−0.00860913	+	0.00497048i
$902$		0			0
$903$	0.615712	+	10.2278i	0.0204896	+	0.340359i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4.59270	+	17.1402i	0.152498	+	0.569130i	0.999307	+	0.0372326i	$0.0118542\pi$
$907$	4.59270	+	17.1402i	0.152498	+	0.569130i	−0.846809	+	0.531898i	$0.821479\pi$
$908$		0			0
$909$	14.6709			0.486602
$910$		0			0
$911$	−14.8454			−0.491850			−0.245925	−	0.969289i	$-0.579092\pi$
$911$	−14.8454			−0.491850			−0.245925	+	0.969289i	$0.579092\pi$
$912$		0			0
$913$	−2.99564	−	11.1799i	−0.0991411	−	0.370000i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.4638	−	24.9386i	0.411591	−	0.823545i
$918$		0			0
$919$	−40.7286	+	23.5147i	−1.34351	+	0.775677i	−0.987321	−	0.158737i	$-0.949258\pi$
$919$	−40.7286	+	23.5147i	−1.34351	+	0.775677i	−0.356191	+	0.934413i	$0.615925\pi$
$920$		0			0
$921$	−9.92995	+	17.1992i	−0.327203	+	0.566732i
$922$		0			0
$923$	3.49150	−	3.49150i	0.114924	−	0.114924i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−14.2799	+	3.82630i	−0.469015	+	0.125672i
$928$		0			0
$929$	8.46604	+	14.6636i	0.277762	+	0.481098i	0.970828	−	0.239776i	$-0.0770741\pi$
$929$	8.46604	+	14.6636i	0.277762	+	0.481098i	−0.693066	+	0.720874i	$0.743741\pi$
$930$		0			0
$931$	−14.7016	+	1.77651i	−0.481824	+	0.0582226i
$932$		0			0
$933$	−7.28425	+	27.1852i	−0.238476	+	0.890003i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−22.2245	−	22.2245i	−0.726043	−	0.726043i	0.243786	−	0.969829i	$-0.421610\pi$
$937$	−22.2245	−	22.2245i	−0.726043	−	0.726043i	−0.969829	+	0.243786i	$0.921610\pi$
$938$		0			0
$939$		−	5.47209i		−	0.178575i
$940$		0			0
$941$	−21.7380	−	12.5504i	−0.708638	−	0.409133i	0.101918	−	0.994793i	$-0.467502\pi$
$941$	−21.7380	−	12.5504i	−0.708638	−	0.409133i	−0.810557	+	0.585660i	$0.800835\pi$
$942$		0			0
$943$	22.9866	+	6.15924i	0.748547	+	0.200573i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	38.2299	+	10.2437i	1.24231	+	0.332875i	0.819359	−	0.573280i	$-0.194329\pi$
$947$	38.2299	+	10.2437i	1.24231	+	0.332875i	0.422946	+	0.906155i	$0.360996\pi$
$948$		0			0
$949$	−4.83257	−	2.79009i	−0.156872	−	0.0905701i
$950$		0			0
$951$		−	28.3331i		−	0.918762i
$952$		0			0
$953$	24.0270	+	24.0270i	0.778311	+	0.778311i	0.979543	−	0.201233i	$-0.0644948\pi$
$953$	24.0270	+	24.0270i	0.778311	+	0.778311i	−0.201233	+	0.979543i	$0.564495\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.92141	−	10.9028i	0.0944357	−	0.352439i
$958$		0			0
$959$	−41.6360	−	36.9077i	−1.34450	−	1.19181i
$960$		0			0
$961$	−11.7891	−	20.4194i	−0.380295	−	0.658690i
$962$		0			0
$963$	5.37101	−	1.43916i	0.173078	−	0.0463762i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−29.9647	+	29.9647i	−0.963598	+	0.963598i	−0.999360	−	0.0357620i	$-0.988614\pi$
$967$	−29.9647	+	29.9647i	−0.963598	+	0.963598i	0.0357620	+	0.999360i	$0.488614\pi$
$968$		0			0
$969$	−0.693795	+	1.20169i	−0.0222879	+	0.0386038i
$970$		0			0
$971$	3.68533	−	2.12773i	0.118268	−	0.0682820i	−0.439699	−	0.898145i	$-0.644915\pi$
$971$	3.68533	−	2.12773i	0.118268	−	0.0682820i	0.557967	+	0.829863i	$0.311582\pi$
$972$		0			0
$973$	4.71728	−	3.11580i	0.151229	−	0.0998879i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.63062	−	13.5497i	−0.116154	−	0.433493i	0.883217	−	0.468965i	$-0.155373\pi$
$977$	−3.63062	−	13.5497i	−0.116154	−	0.433493i	−0.999371	+	0.0354726i	$0.988706\pi$
$978$		0			0
$979$	14.9251			0.477009
$980$		0			0
$981$	−1.73780			−0.0554835
$982$		0			0
$983$	4.11293	+	15.3497i	0.131182	+	0.489578i	0.999984	−	0.00558070i	$-0.00177640\pi$
$983$	4.11293	+	15.3497i	0.131182	+	0.489578i	−0.868802	+	0.495159i	$0.835110\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−12.3558	+	8.16110i	−0.393290	+	0.259771i
$988$		0			0
$989$	8.07280	−	4.66083i	0.256700	−	0.148206i
$990$		0			0
$991$	−24.1558	+	41.8391i	−0.767335	+	1.32906i	0.171669	+	0.985155i	$0.445084\pi$
$991$	−24.1558	+	41.8391i	−0.767335	+	1.32906i	−0.939003	+	0.343908i	$0.888249\pi$
$992$		0			0
$993$	3.51856	−	3.51856i	0.111658	−	0.111658i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	28.5349	−	7.64591i	0.903710	−	0.242148i	0.223101	−	0.974795i	$-0.428382\pi$
$997$	28.5349	−	7.64591i	0.903710	−	0.242148i	0.680609	+	0.732647i	$0.261715\pi$
$998$		0			0
$999$	−1.25853	−	2.17984i	−0.0398181	−	0.0689670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.e.493.3		32
5.2	odd	4	inner	2100.2.ce.e.157.3		32
5.3	odd	4		420.2.bo.a.157.7	yes	32
5.4	even	2		420.2.bo.a.73.8	✓	32
7.5	odd	6	inner	2100.2.ce.e.1993.3		32
15.8	even	4		1260.2.dq.c.577.3		32
15.14	odd	2		1260.2.dq.c.73.1		32
35.3	even	12		2940.2.x.c.97.14		32
35.4	even	6		2940.2.x.c.1273.14		32
35.12	even	12	inner	2100.2.ce.e.1657.3		32
35.18	odd	12		2940.2.x.c.97.5		32
35.19	odd	6		420.2.bo.a.313.7	yes	32
35.24	odd	6		2940.2.x.c.1273.5		32
35.33	even	12		420.2.bo.a.397.8	yes	32
105.68	odd	12		1260.2.dq.c.397.1		32
105.89	even	6		1260.2.dq.c.1153.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.8	✓	32	5.4	even	2
420.2.bo.a.157.7	yes	32	5.3	odd	4
420.2.bo.a.313.7	yes	32	35.19	odd	6
420.2.bo.a.397.8	yes	32	35.33	even	12
1260.2.dq.c.73.1		32	15.14	odd	2
1260.2.dq.c.397.1		32	105.68	odd	12
1260.2.dq.c.577.3		32	15.8	even	4
1260.2.dq.c.1153.3		32	105.89	even	6
2100.2.ce.e.157.3		32	5.2	odd	4	inner
2100.2.ce.e.493.3		32	1.1	even	1	trivial
2100.2.ce.e.1657.3		32	35.12	even	12	inner
2100.2.ce.e.1993.3		32	7.5	odd	6	inner
2940.2.x.c.97.5		32	35.18	odd	12
2940.2.x.c.97.14		32	35.3	even	12
2940.2.x.c.1273.5		32	35.24	odd	6
2940.2.x.c.1273.14		32	35.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{3} +(-2.20765 + 1.45817i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{3} +(-2.20765 + 1.45817i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(0.803071 - 1.39096i) q^{11} +(-0.275509 + 0.275509i) q^{13} +(0.633566 - 0.169763i) q^{17} +(-1.05775 - 1.83208i) q^{19} +(1.97987 + 1.75503i) q^{21} +(0.622978 - 2.32498i) q^{23} +(0.707107 + 0.707107i) q^{27} +7.02768i q^{29} +(-2.35930 - 1.36214i) q^{31} +(-1.55141 - 0.415700i) q^{33} +(-2.43129 - 0.651463i) q^{37} +(0.337428 + 0.194814i) q^{39} +9.88678i q^{41} +(2.73843 + 2.73843i) q^{43} +(-1.44856 + 5.40610i) q^{47} +(2.74747 - 6.43828i) q^{49} +(-0.327958 - 0.568039i) q^{51} +(-0.439427 + 0.117744i) q^{53} +(-1.49588 + 1.49588i) q^{57} +(-2.85833 + 4.95077i) q^{59} +(-11.0916 + 6.40371i) q^{61} +(1.18280 - 2.36664i) q^{63} +(3.94670 + 14.7293i) q^{67} -2.40700 q^{69} -12.6729 q^{71} +(3.70676 + 13.8338i) q^{73} +(0.255355 + 4.24177i) q^{77} +(7.64128 - 4.41169i) q^{79} +(0.500000 - 0.866025i) q^{81} +(5.09559 - 5.09559i) q^{83} +(6.78822 - 1.81890i) q^{87} +(4.64627 + 8.04757i) q^{89} +(0.206489 - 1.00997i) q^{91} +(-0.705096 + 2.63145i) q^{93} +(-5.40643 - 5.40643i) q^{97} +1.60614i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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

Varieties

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Database

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