LMFDB - Embedded newform 2100.2.ce.e.157.3

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			157.3
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.e.1993.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{3} +(-1.45817 - 2.20765i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{3} +(-1.45817 - 2.20765i) q^{7} +(0.866025 - 0.500000i) q^{9} +(0.803071 - 1.39096i) q^{11} +(0.275509 + 0.275509i) q^{13} +(0.169763 + 0.633566i) q^{17} +(1.05775 + 1.83208i) q^{19} +(1.97987 + 1.75503i) q^{21} +(-2.32498 - 0.622978i) q^{23} +(-0.707107 + 0.707107i) q^{27} -7.02768i q^{29} +(-2.35930 - 1.36214i) q^{31} +(-0.415700 + 1.55141i) q^{33} +(0.651463 - 2.43129i) q^{37} +(-0.337428 - 0.194814i) q^{39} +9.88678i q^{41} +(2.73843 - 2.73843i) q^{43} +(-5.40610 - 1.44856i) q^{47} +(-2.74747 + 6.43828i) q^{49} +(-0.327958 - 0.568039i) q^{51} +(0.117744 + 0.439427i) q^{53} +(-1.49588 - 1.49588i) q^{57} +(2.85833 - 4.95077i) q^{59} +(-11.0916 + 6.40371i) q^{61} +(-2.36664 - 1.18280i) q^{63} +(-14.7293 + 3.94670i) q^{67} +2.40700 q^{69} -12.6729 q^{71} +(13.8338 - 3.70676i) q^{73} +(-4.24177 + 0.255355i) q^{77} +(-7.64128 + 4.41169i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-5.09559 - 5.09559i) q^{83} +(1.81890 + 6.78822i) q^{87} +(-4.64627 - 8.04757i) q^{89} +(0.206489 - 1.00997i) q^{91} +(2.63145 + 0.705096i) q^{93} +(5.40643 - 5.40643i) q^{97} -1.60614i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.45817	−	2.20765i	−0.551137	−	0.834415i
$7$	−1.45817	−	2.20765i	−0.551137	−	0.834415i
$8$		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	$-0.232793\pi$
$13$	0.275509	+	0.275509i	0.0764123	+	0.0764123i	−0.667868	+	0.744280i	$0.732793\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.169763	+	0.633566i	0.0411737	+	0.153662i	0.983452	−	0.181168i	$-0.0579877\pi$
$17$	0.169763	+	0.633566i	0.0411737	+	0.153662i	−0.942279	+	0.334830i	$0.891321\pi$
$18$		0			0
$19$	1.05775	+	1.83208i	0.242664	+	0.420307i	0.961472	−	0.274902i	$-0.0886453\pi$
$19$	1.05775	+	1.83208i	0.242664	+	0.420307i	−0.718808	+	0.695209i	$0.755312\pi$
$20$		0			0
$21$	1.97987	+	1.75503i	0.432043	+	0.382978i
$22$		0			0
$23$	−2.32498	−	0.622978i	−0.484793	−	0.129900i	0.00814070	−	0.999967i	$-0.497409\pi$
$23$	−2.32498	−	0.622978i	−0.484793	−	0.129900i	−0.492933	+	0.870067i	$0.664075\pi$
$24$		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	$-0.773719\pi$
$29$		−	7.02768i		−	1.30501i	0.757785	−	0.652504i	$-0.226281\pi$
$30$		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
$33$	−0.415700	+	1.55141i	−0.0723641	+	0.270066i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.651463	−	2.43129i	0.107100	−	0.399702i	−0.891475	−	0.453070i	$-0.850329\pi$
$37$	0.651463	−	2.43129i	0.107100	−	0.399702i	0.998575	+	0.0533678i	$0.0169956\pi$
$38$		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	−0.466771	−	0.884378i	$-0.654583\pi$
$43$	2.73843	−	2.73843i	0.417607	−	0.417607i	0.884378	+	0.466771i	$0.154583\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.40610	−	1.44856i	−0.788561	−	0.211294i	−0.158005	−	0.987438i	$-0.550506\pi$
$47$	−5.40610	−	1.44856i	−0.788561	−	0.211294i	−0.630556	+	0.776144i	$0.717173\pi$
$48$		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
$53$	0.117744	+	0.439427i	0.0161734	+	0.0603600i	0.973541	−	0.228513i	$-0.0733862\pi$
$53$	0.117744	+	0.439427i	0.0161734	+	0.0603600i	−0.957368	+	0.288873i	$0.906720\pi$
$54$		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	−0.617769	−	0.786360i	$-0.711963\pi$
$59$	2.85833	−	4.95077i	0.372123	−	0.644536i	0.989892	+	0.141824i	$0.0452967\pi$
$60$		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
$63$	−2.36664	−	1.18280i	−0.298169	−	0.149019i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−14.7293	+	3.94670i	−1.79947	+	0.482166i	−0.993895	−	0.110330i	$-0.964809\pi$
$67$	−14.7293	+	3.94670i	−1.79947	+	0.482166i	−0.805573	+	0.592496i	$0.798142\pi$
$68$		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
$73$	13.8338	−	3.70676i	1.61912	−	0.433843i	0.668380	−	0.743820i	$-0.266988\pi$
$73$	13.8338	−	3.70676i	1.61912	−	0.433843i	0.950744	+	0.309977i	$0.100321\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.24177	+	0.255355i	−0.483395	+	0.0291004i
$78$		0			0
$79$	−7.64128	+	4.41169i	−0.859711	+	0.496354i	−0.863915	−	0.503637i	$-0.831995\pi$
$79$	−7.64128	+	4.41169i	−0.859711	+	0.496354i	0.00420460	+	0.999991i	$0.498662\pi$
$80$		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	$-0.379427\pi$
$83$	−5.09559	−	5.09559i	−0.559313	−	0.559313i	−0.929112	+	0.369799i	$0.879427\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.81890	+	6.78822i	0.195006	+	0.727773i
$88$		0			0
$89$	−4.64627	−	8.04757i	−0.492503	−	0.853041i	0.507459	−	0.861676i	$-0.330585\pi$
$89$	−4.64627	−	8.04757i	−0.492503	−	0.853041i	−0.999963	+	0.00863479i	$0.997251\pi$
$90$		0			0
$91$	0.206489	−	1.00997i	0.0216459	−	0.105873i
$92$		0			0
$93$	2.63145	+	0.705096i	0.272869	+	0.0731151i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.40643	−	5.40643i	0.548939	−	0.548939i	−0.377195	−	0.926134i	$-0.623111\pi$
$97$	5.40643	−	5.40643i	0.548939	−	0.548939i	0.926134	+	0.377195i	$0.123111\pi$
$98$		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
$103$	3.82630	−	14.2799i	0.377017	−	1.40705i	−0.473359	−	0.880869i	$-0.656959\pi$
$103$	3.82630	−	14.2799i	0.377017	−	1.40705i	0.850376	−	0.526176i	$-0.176375\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.43916	−	5.37101i	0.139129	−	0.519235i	−0.860818	−	0.508913i	$-0.830048\pi$
$107$	1.43916	−	5.37101i	0.139129	−	0.519235i	0.999947	−	0.0103222i	$-0.00328572\pi$
$108$		0			0
$109$	−1.50497	−	0.868898i	−0.144150	−	0.0832253i	0.426190	−	0.904634i	$-0.359855\pi$
$109$	−1.50497	−	0.868898i	−0.144150	−	0.0832253i	−0.570341	+	0.821408i	$0.693189\pi$
$110$		0			0
$111$			2.51706i			0.238909i
$112$		0			0
$113$	3.09316	−	3.09316i	0.290980	−	0.290980i	−0.546487	−	0.837467i	$-0.684035\pi$
$113$	3.09316	−	3.09316i	0.290980	−	0.290980i	0.837467	+	0.546487i	$0.184035\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.376352	+	0.100843i	0.0347937	+	0.00932295i
$118$		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
$123$	−2.55889	−	9.54990i	−0.230727	−	0.861085i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.38575	−	6.38575i	−0.566644	−	0.566644i	0.364543	−	0.931187i	$-0.381225\pi$
$127$	−6.38575	−	6.38575i	−0.566644	−	0.566644i	−0.931187	+	0.364543i	$0.881225\pi$
$128$		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
$133$	2.50221	−	5.00663i	0.216969	−	0.434130i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−20.3131	+	5.44289i	−1.73547	+	0.465017i	−0.981431	−	0.191815i	$-0.938563\pi$
$137$	−20.3131	+	5.44289i	−1.73547	+	0.465017i	−0.754037	+	0.656832i	$0.771896\pi$
$138$		0			0
$139$	2.13678			0.181240			0.0906198	−	0.995886i	$-0.471115\pi$
$139$	2.13678			0.181240			0.0906198	+	0.995886i	$0.471115\pi$
$140$		0			0
$141$	5.59681			0.471336
$142$		0			0
$143$	0.604474	−	0.161968i	0.0505487	−	0.0135445i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.987506	−	6.93000i	0.0814481	−	0.571576i
$148$		0			0
$149$	−8.35637	+	4.82455i	−0.684580	+	0.395243i	−0.801579	−	0.597889i	$-0.796006\pi$
$149$	−8.35637	+	4.82455i	−0.684580	+	0.395243i	0.116998	+	0.993132i	$0.462673\pi$
$150$		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
$157$	4.43366	+	16.5466i	0.353845	+	1.32057i	0.881932	+	0.471376i	$0.156243\pi$
$157$	4.43366	+	16.5466i	0.353845	+	1.32057i	−0.528088	+	0.849190i	$0.677091\pi$
$158$		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
$163$	−20.2592	−	5.42844i	−1.58682	−	0.425188i	−0.645794	−	0.763512i	$-0.723473\pi$
$163$	−20.2592	−	5.42844i	−1.58682	−	0.425188i	−0.941030	+	0.338324i	$0.890140\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.29940	−	4.29940i	0.332698	−	0.332698i	−0.520912	−	0.853610i	$-0.674408\pi$
$167$	4.29940	−	4.29940i	0.332698	−	0.332698i	0.853610	+	0.520912i	$0.174408\pi$
$168$		0			0
$169$		−	12.8482i		−	0.988322i
$170$		0			0
$171$	1.83208	+	1.05775i	0.140102	+	0.0808882i
$172$		0			0
$173$	−4.81651	+	17.9755i	−0.366193	+	1.36665i	0.499604	+	0.866254i	$0.333479\pi$
$173$	−4.81651	+	17.9755i	−0.366193	+	1.36665i	−0.865797	+	0.500396i	$0.833188\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.47958	+	5.52187i	−0.111212	+	0.415049i
$178$		0			0
$179$	−2.26571	−	1.30811i	−0.169347	−	0.0977726i	0.412931	−	0.910762i	$-0.364505\pi$
$179$	−2.26571	−	1.30811i	−0.169347	−	0.0977726i	−0.582278	+	0.812990i	$0.697838\pi$
$180$		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
$187$	1.01760	+	0.272664i	0.0744140	+	0.0199392i
$188$		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
$193$	2.51768	+	9.39610i	0.181226	+	0.676346i	0.995407	+	0.0957343i	$0.0305199\pi$
$193$	2.51768	+	9.39610i	0.181226	+	0.676346i	−0.814181	+	0.580612i	$0.802813\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−13.8585	−	13.8585i	−0.987378	−	0.987378i	0.0125433	−	0.999921i	$-0.496007\pi$
$197$	−13.8585	−	13.8585i	−0.987378	−	0.987378i	−0.999921	+	0.0125433i	$0.996007\pi$
$198$		0			0
$199$	3.97162	−	6.87905i	0.281541	−	0.487643i	−0.690224	−	0.723596i	$-0.742488\pi$
$199$	3.97162	−	6.87905i	0.281541	−	0.487643i	0.971764	+	0.235953i	$0.0758211\pi$
$200$		0			0
$201$	13.2059	−	7.62444i	0.931473	−	0.537786i
$202$		0			0
$203$	−15.5147	+	10.2476i	−1.08892	+	0.719238i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.32498	+	0.622978i	−0.161598	+	0.0432999i
$208$		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
$213$	12.2411	−	3.28000i	0.838747	−	0.224742i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.433124	+	7.19475i	0.0294024	+	0.488411i
$218$		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	$-0.131287\pi$
$223$	7.69489	+	7.69489i	0.515288	+	0.515288i	−0.400854	+	0.916142i	$0.631287\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.303102	−	1.13119i	−0.0201176	−	0.0750799i	0.955137	−	0.296163i	$-0.0957073\pi$
$227$	−0.303102	−	1.13119i	−0.0201176	−	0.0750799i	−0.975255	+	0.221084i	$0.929041\pi$
$228$		0			0
$229$	2.42787	+	4.20519i	0.160438	+	0.277887i	0.935026	−	0.354580i	$-0.115376\pi$
$229$	2.42787	+	4.20519i	0.160438	+	0.277887i	−0.774588	+	0.632466i	$0.782043\pi$
$230$		0			0
$231$	4.03115	−	1.34451i	0.265230	−	0.0884619i
$232$		0			0
$233$	−14.0129	−	3.75475i	−0.918016	−	0.245982i	−0.231279	−	0.972887i	$-0.574291\pi$
$233$	−14.0129	−	3.75475i	−0.918016	−	0.245982i	−0.686737	+	0.726906i	$0.740958\pi$
$234$		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	$-0.875144\pi$
$239$		−	11.8194i		−	0.764533i	0.924052	−	0.382266i	$-0.124856\pi$
$240$		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
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.213334	+	0.796172i	−0.0135741	+	0.0506592i
$248$		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
$257$	−15.9864	−	4.28353i	−0.997202	−	0.267199i	−0.276929	−	0.960890i	$-0.589317\pi$
$257$	−15.9864	−	4.28353i	−0.997202	−	0.267199i	−0.720273	+	0.693691i	$0.755983\pi$
$258$		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
$263$	2.93489	+	10.9532i	0.180973	+	0.675402i	0.995457	+	0.0952148i	$0.0303538\pi$
$263$	2.93489	+	10.9532i	0.180973	+	0.675402i	−0.814483	+	0.580187i	$0.802980\pi$
$264$		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	−0.723591	−	0.690229i	$-0.757510\pi$
$269$	3.87003	−	6.70309i	0.235960	−	0.408695i	0.959551	+	0.281534i	$0.0908433\pi$
$270$		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
$273$	0.0619456	+	1.02900i	0.00374912	+	0.0622777i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.207237	+	0.0555290i	−0.0124517	+	0.00333642i	−0.265040	−	0.964238i	$-0.585385\pi$
$277$	−0.207237	+	0.0555290i	−0.0124517	+	0.00333642i	0.252588	+	0.967574i	$0.418718\pi$
$278$		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
$283$	−31.0373	+	8.31641i	−1.84497	+	0.494360i	−0.999230	−	0.0392282i	$-0.987510\pi$
$283$	−31.0373	+	8.31641i	−1.84497	+	0.494360i	−0.845745	+	0.533588i	$0.820843\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	21.8266	−	14.4166i	1.28838	−	0.850986i
$288$		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	$-0.0329220\pi$
$293$	15.2585	+	15.2585i	0.891413	+	0.891413i	−0.103243	+	0.994656i	$0.532922\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.415700	+	1.55141i	0.0241214	+	0.0900221i
$298$		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
$303$	14.1710	+	3.79710i	0.814101	+	0.218138i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	14.0431	−	14.0431i	0.801481	−	0.801481i	−0.181846	−	0.983327i	$-0.558207\pi$
$307$	14.0431	−	14.0431i	0.801481	−	0.801481i	0.983327	+	0.181846i	$0.0582073\pi$
$308$		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
$313$	1.41628	−	5.28563i	0.0800529	−	0.298761i	−0.914279	−	0.405086i	$-0.867242\pi$
$313$	1.41628	−	5.28563i	0.0800529	−	0.298761i	0.994331	+	0.106325i	$0.0339082\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.33313	+	27.3676i	−0.411870	+	1.53712i	0.379154	+	0.925334i	$0.376215\pi$
$317$	−7.33313	+	27.3676i	−0.411870	+	1.53712i	−0.791024	+	0.611785i	$0.790452\pi$
$318$		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
$327$	1.67858	+	0.449774i	0.0928258	+	0.0248726i
$328$		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
$333$	−0.651463	−	2.43129i	−0.0356999	−	0.133234i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	14.0207	+	14.0207i	0.763757	+	0.763757i	0.976999	−	0.213243i	$-0.0684025\pi$
$337$	14.0207	+	14.0207i	0.763757	+	0.763757i	−0.213243	+	0.976999i	$0.568403\pi$
$338$		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
$343$	18.2198	−	3.32264i	0.983775	−	0.179406i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	35.1344	−	9.41425i	1.88612	−	0.505383i	0.887073	−	0.461628i	$-0.152735\pi$
$347$	35.1344	−	9.41425i	1.88612	−	0.505383i	0.999042	−	0.0437548i	$-0.0139320\pi$
$348$		0			0
$349$	35.4056			1.89522			0.947610	−	0.319431i	$-0.103492\pi$
$349$	35.4056			1.89522			0.947610	+	0.319431i	$0.103492\pi$
$350$		0			0
$351$	−0.389628			−0.0207968
$352$		0			0
$353$	16.4359	−	4.40400i	0.874797	−	0.234401i	0.206636	−	0.978418i	$-0.433748\pi$
$353$	16.4359	−	4.40400i	0.874797	−	0.234401i	0.668161	+	0.744017i	$0.267082\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.775816	+	1.55232i	−0.0410605	+	0.0821573i
$358$		0			0
$359$	−24.3468	+	14.0566i	−1.28497	+	0.741879i	−0.977753	−	0.209759i	$-0.932732\pi$
$359$	−24.3468	+	14.0566i	−1.28497	+	0.741879i	−0.307220	+	0.951639i	$0.599399\pi$
$360$		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
$367$	1.69211	+	6.31505i	0.0883276	+	0.329643i	0.995924	−	0.0902017i	$-0.0287512\pi$
$367$	1.69211	+	6.31505i	0.0883276	+	0.329643i	−0.907596	+	0.419845i	$0.862084\pi$
$368$		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
$373$	−18.2733	−	4.89631i	−0.946155	−	0.253521i	−0.247425	−	0.968907i	$-0.579584\pi$
$373$	−18.2733	−	4.89631i	−0.946155	−	0.253521i	−0.698730	+	0.715386i	$0.746251\pi$
$374$		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	$-0.946068\pi$
$379$		−	6.56543i		−	0.337243i	0.985681	−	0.168622i	$-0.0539316\pi$
$380$		0			0
$381$	7.82092	+	4.51541i	0.400678	+	0.231331i
$382$		0			0
$383$	0.124670	−	0.465275i	0.00637035	−	0.0237745i	−0.962668	−	0.270687i	$-0.912749\pi$
$383$	0.124670	−	0.465275i	0.00637035	−	0.0237745i	0.969038	+	0.246912i	$0.0794159\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.00234	−	3.74077i	0.0509516	−	0.190154i
$388$		0			0
$389$	7.04917	+	4.06984i	0.357407	+	0.206349i	0.667943	−	0.744213i	$-0.267175\pi$
$389$	7.04917	+	4.06984i	0.357407	+	0.206349i	−0.310536	+	0.950562i	$0.600508\pi$
$390$		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
$397$	15.8391	+	4.24409i	0.794944	+	0.213005i	0.633363	−	0.773855i	$-0.281674\pi$
$397$	15.8391	+	4.24409i	0.794944	+	0.213005i	0.161581	+	0.986859i	$0.448341\pi$
$398$		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
$403$	−0.274725	−	1.02529i	−0.0136850	−	0.0510733i
$404$		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	$0.414728\pi$
$409$	−14.2130	+	24.6176i	−0.702786	+	1.21726i	−0.967485	+	0.252930i	$0.918606\pi$
$410$		0			0
$411$	18.2123	−	10.5148i	0.898344	−	0.518659i
$412$		0			0
$413$	−15.0975	+	0.908872i	−0.742901	+	0.0447227i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.06397	+	0.553040i	−0.101073	+	0.0270825i
$418$		0			0
$419$	29.6713			1.44954			0.724768	−	0.688993i	$-0.241947\pi$
$419$	29.6713			1.44954			0.724768	+	0.688993i	$0.241947\pi$
$420$		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
$423$	−5.40610	+	1.44856i	−0.262854	+	0.0704314i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	30.3106	+	15.1486i	1.46683	+	0.733092i
$428$		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	0.998683	+	0.0513140i	$0.0163409\pi$
$433$	21.8490	+	21.8490i	1.05000	+	1.05000i	0.0513140	+	0.998683i	$0.483659\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.31791	−	4.91850i	−0.0630441	−	0.235284i
$438$		0			0
$439$	10.7878	+	18.6849i	0.514872	+	0.891784i	0.999851	+	0.0172583i	$0.00549377\pi$
$439$	10.7878	+	18.6849i	0.514872	+	0.891784i	−0.484979	+	0.874526i	$0.661173\pi$
$440$		0			0
$441$	0.839757	+	6.94945i	0.0399884	+	0.330926i
$442$		0			0
$443$	16.3828	+	4.38976i	0.778370	+	0.208564i	0.626066	−	0.779770i	$-0.284664\pi$
$443$	16.3828	+	4.38976i	0.778370	+	0.208564i	0.152304	+	0.988334i	$0.451331\pi$
$444$		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	$-0.814759\pi$
$449$		−	23.2940i		−	1.09931i	0.835392	−	0.549655i	$-0.185241\pi$
$450$		0			0
$451$	13.7521	+	7.93978i	0.647561	+	0.373870i
$452$		0			0
$453$	−4.84140	+	18.0684i	−0.227469	+	0.848926i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.41228	−	9.00277i	0.112842	−	0.421132i	−0.886275	−	0.463160i	$-0.846715\pi$
$457$	2.41228	−	9.00277i	0.112842	−	0.421132i	0.999116	+	0.0420287i	$0.0133821\pi$
$458$		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	−0.695629	−	0.718401i	$-0.744874\pi$
$463$	0.489997	−	0.489997i	0.0227721	−	0.0227721i	0.718401	+	0.695629i	$0.244874\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.4814	+	3.34437i	0.577569	+	0.154759i	0.535766	−	0.844367i	$-0.320023\pi$
$467$	12.4814	+	3.34437i	0.577569	+	0.154759i	0.0418035	+	0.999126i	$0.486690\pi$
$468$		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
$473$	−1.60989	−	6.00821i	−0.0740230	−	0.276258i
$474$		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	−0.866647	−	0.498921i	$-0.833730\pi$
$479$	−0.0272496	+	0.0471978i	−0.00124507	+	0.00215652i	0.865402	+	0.501078i	$0.167063\pi$
$480$		0			0
$481$	0.849325	−	0.490358i	0.0387259	−	0.0223584i
$482$		0			0
$483$	−3.50982	−	5.31382i	−0.159702	−	0.241787i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.84874	+	0.495369i	−0.0837746	+	0.0224473i	−0.300463	−	0.953794i	$-0.597141\pi$
$487$	−1.84874	+	0.495369i	−0.0837746	+	0.0224473i	0.216688	+	0.976241i	$0.430474\pi$
$488$		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
$493$	4.45250	−	1.19304i	0.200530	−	0.0537320i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.4793	+	27.9774i	0.828910	+	1.25496i
$498$		0			0
$499$	−35.4989	+	20.4953i	−1.58915	+	0.917496i	−0.595703	+	0.803205i	$0.703126\pi$
$499$	−35.4989	+	20.4953i	−1.58915	+	0.917496i	−0.993447	+	0.114291i	$0.963540\pi$
$500$		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	$-0.381835\pi$
$503$	−12.7642	−	12.7642i	−0.569127	−	0.569127i	−0.931884	+	0.362757i	$0.881835\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.32536	+	12.4104i	0.147684	+	0.551165i
$508$		0			0
$509$	−13.2181	−	22.8944i	−0.585881	−	1.01478i	−0.994765	−	0.102189i	$-0.967415\pi$
$509$	−13.2181	−	22.8944i	−0.585881	−	1.01478i	0.408884	−	0.912586i	$-0.365918\pi$
$510$		0			0
$511$	−28.3553	−	25.1352i	−1.25436	−	1.11191i
$512$		0			0
$513$	−2.04342	−	0.547532i	−0.0902190	−	0.0241741i
$514$		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
$523$	1.00306	−	3.74349i	0.0438609	−	0.163691i	−0.940522	−	0.339734i	$-0.889663\pi$
$523$	1.00306	−	3.74349i	0.0438609	−	0.163691i	0.984383	+	0.176043i	$0.0563297\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.462484	−	1.72601i	0.0201461	−	0.0751863i
$528$		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
$537$	2.52707	+	0.677127i	0.109051	+	0.0292202i
$538$		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
$543$	−1.88059	−	7.01846i	−0.0807038	−	0.301191i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−15.3881	−	15.3881i	−0.657948	−	0.657948i	0.296946	−	0.954894i	$-0.404032\pi$
$547$	−15.3881	−	15.3881i	−0.657948	−	0.657948i	−0.954894	+	0.296946i	$0.904032\pi$
$548$		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
$553$	20.8818	+	10.4363i	0.887984	+	0.443796i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	34.3205	−	9.19616i	1.45421	−	0.389654i	0.556723	−	0.830698i	$-0.312059\pi$
$557$	34.3205	−	9.19616i	1.45421	−	0.389654i	0.897485	+	0.441045i	$0.145392\pi$
$558$		0			0
$559$	1.50892			0.0638207
$560$		0			0
$561$	−1.05349			−0.0444785
$562$		0			0
$563$	−31.0791	+	8.32762i	−1.30983	+	0.350967i	−0.845158	−	0.534516i	$-0.820494\pi$
$563$	−31.0791	+	8.32762i	−1.30983	+	0.350967i	−0.464670	+	0.885484i	$0.653827\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.64097	+	0.158987i	−0.110910	+	0.00667681i
$568$		0			0
$569$	14.5946	−	8.42618i	0.611836	−	0.353244i	−0.161848	−	0.986816i	$-0.551745\pi$
$569$	14.5946	−	8.42618i	0.611836	−	0.353244i	0.773684	+	0.633572i	$0.218412\pi$
$570$		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
$577$	−7.03890	−	26.2695i	−0.293033	−	1.09361i	−0.942767	−	0.333453i	$-0.891786\pi$
$577$	−7.03890	−	26.2695i	−0.293033	−	1.09361i	0.649734	−	0.760162i	$-0.274880\pi$
$578$		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
$583$	0.705782	+	0.189114i	0.0292305	+	0.00783229i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.2565	+	17.2565i	−0.712252	+	0.712252i	−0.967006	−	0.254754i	$-0.918006\pi$
$587$	−17.2565	+	17.2565i	−0.712252	+	0.712252i	0.254754	+	0.967006i	$0.418006\pi$
$588$		0			0
$589$		−	5.76322i		−	0.237469i
$590$		0			0
$591$	16.9731	+	9.79945i	0.698182	+	0.403095i
$592$		0			0
$593$	−8.60512	+	32.1148i	−0.353370	+	1.31879i	0.529153	+	0.848526i	$0.322510\pi$
$593$	−8.60512	+	32.1148i	−0.353370	+	1.31879i	−0.882523	+	0.470269i	$0.844157\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.05586	+	7.67259i	−0.0841409	+	0.314018i
$598$		0			0
$599$	−16.4156	−	9.47753i	−0.670722	−	0.387241i	0.125628	−	0.992077i	$-0.459905\pi$
$599$	−16.4156	−	9.47753i	−0.670722	−	0.387241i	−0.796350	+	0.604836i	$0.793239\pi$
$600$		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
$607$	1.99716	+	0.535137i	0.0810622	+	0.0217205i	0.299122	−	0.954215i	$-0.403306\pi$
$607$	1.99716	+	0.535137i	0.0810622	+	0.0217205i	−0.218060	+	0.975935i	$0.569973\pi$
$608$		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
$613$	1.56227	+	5.83045i	0.0630993	+	0.235490i	0.990272	−	0.139144i	$-0.0444351\pi$
$613$	1.56227	+	5.83045i	0.0630993	+	0.235490i	−0.927173	+	0.374634i	$0.877768\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.39249	−	9.39249i	−0.378127	−	0.378127i	0.492299	−	0.870426i	$-0.336157\pi$
$617$	−9.39249	−	9.39249i	−0.378127	−	0.378127i	−0.870426	+	0.492299i	$0.836157\pi$
$618$		0			0
$619$	−6.82928	+	11.8287i	−0.274492	+	0.475434i	−0.970007	−	0.243078i	$-0.921843\pi$
$619$	−6.82928	+	11.8287i	−0.274492	+	0.475434i	0.695515	+	0.718512i	$0.255176\pi$
$620$		0			0
$621$	2.08452	−	1.20350i	0.0836491	−	0.0482948i
$622$		0			0
$623$	−10.9912	+	21.9921i	−0.440353	+	0.881095i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−3.28202	+	0.879413i	−0.131071	+	0.0351204i
$628$		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
$633$	−23.9058	+	6.40555i	−0.950171	+	0.254598i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.53075	+	1.01685i	−0.100272	+	0.0402890i
$638$		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	$-0.242458\pi$
$643$	0.849619	+	0.849619i	0.0335057	+	0.0335057i	−0.690155	+	0.723661i	$0.742458\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.79070	−	36.5394i	−0.384912	−	1.43651i	−0.838305	−	0.545201i	$-0.816453\pi$
$647$	−9.79070	−	36.5394i	−0.384912	−	1.43651i	0.453393	−	0.891311i	$-0.350213\pi$
$648$		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
$653$	−6.71164	−	1.79838i	−0.262647	−	0.0703760i	0.125092	−	0.992145i	$-0.460077\pi$
$653$	−6.71164	−	1.79838i	−0.262647	−	0.0703760i	−0.387739	+	0.921769i	$0.626744\pi$
$654$		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	$-0.851776\pi$
$659$		−	23.0532i		−	0.898024i	0.893526	−	0.449012i	$-0.148224\pi$
$660$		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
$663$	0.0661446	−	0.246855i	0.00256884	−	0.00958705i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.37809	+	16.3392i	−0.169520	+	0.632658i
$668$		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	−0.756616	−	0.653859i	$-0.773149\pi$
$673$	−2.66575	+	2.66575i	−0.102757	+	0.102757i	0.653859	+	0.756616i	$0.273149\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−26.8640	−	7.19820i	−1.03247	−	0.276649i	−0.297480	−	0.954728i	$-0.596146\pi$
$677$	−26.8640	−	7.19820i	−1.03247	−	0.276649i	−0.734989	+	0.678079i	$0.762813\pi$
$678$		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
$683$	−0.478976	−	1.78756i	−0.0183275	−	0.0683992i	0.956156	−	0.292856i	$-0.0946058\pi$
$683$	−0.478976	−	1.78756i	−0.0183275	−	0.0683992i	−0.974484	+	0.224457i	$0.927939\pi$
$684$		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
$693$	−3.54580	+	2.34203i	−0.134694	+	0.0889663i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−6.26392	+	1.67841i	−0.237263	+	0.0635744i
$698$		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
$703$	5.14340	−	1.37817i	0.193987	−	0.0519786i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.33247	+	38.7453i	0.0877216	+	1.45717i
$708$		0			0
$709$	0.743926	−	0.429506i	0.0279387	−	0.0161304i	−0.485966	−	0.873978i	$-0.661532\pi$
$709$	0.743926	−	0.429506i	0.0279387	−	0.0161304i	0.513904	+	0.857848i	$0.328199\pi$
$710$		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
$717$	3.05908	+	11.4167i	0.114244	+	0.426363i
$718$		0			0
$719$	12.1602	+	21.0621i	0.453500	+	0.785485i	0.998601	−	0.0528857i	$-0.0168419\pi$
$719$	12.1602	+	21.0621i	0.453500	+	0.785485i	−0.545101	+	0.838371i	$0.683509\pi$
$720$		0			0
$721$	−37.1046	+	12.3755i	−1.38185	+	0.460886i
$722$		0			0
$723$	−8.23533	−	2.20665i	−0.306275	−	0.0820662i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	8.12079	−	8.12079i	0.301183	−	0.301183i	−0.540293	−	0.841477i	$-0.681687\pi$
$727$	8.12079	−	8.12079i	0.301183	−	0.301183i	0.841477	+	0.540293i	$0.181687\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	2.19986	+	1.27009i	0.0813649	+	0.0469761i
$732$		0			0
$733$	5.39113	−	20.1200i	0.199126	−	0.743148i	−0.792034	−	0.610477i	$-0.790978\pi$
$733$	5.39113	−	20.1200i	0.199126	−	0.743148i	0.991160	−	0.132671i	$-0.0423555\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.33896	+	23.6573i	−0.233498	+	0.871428i
$738$		0			0
$739$	−17.6831	−	10.2094i	−0.650485	−	0.375558i	0.138157	−	0.990410i	$-0.455882\pi$
$739$	−17.6831	−	10.2094i	−0.650485	−	0.375558i	−0.788642	+	0.614853i	$0.789215\pi$
$740$		0			0
$741$		−	0.824258i		−	0.0302799i
$742$		0			0
$743$	10.7038	−	10.7038i	0.392683	−	0.392683i	−0.482960	−	0.875643i	$-0.660438\pi$
$743$	10.7038	−	10.7038i	0.392683	−	0.392683i	0.875643	+	0.482960i	$0.160438\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−6.96070	−	1.86511i	−0.254679	−	0.0682409i
$748$		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
$753$	−6.69666	−	24.9923i	−0.244040	−	0.910769i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−19.9653	−	19.9653i	−0.725651	−	0.725651i	0.244099	−	0.969750i	$-0.421508\pi$
$757$	−19.9653	−	19.9653i	−0.725651	−	0.725651i	−0.969750	+	0.244099i	$0.921508\pi$
$758$		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
$763$	0.276286	+	4.58946i	0.0100022	+	0.166150i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.15147	−	0.576486i	0.0776853	−	0.0208157i
$768$		0			0
$769$	12.9268			0.466151			0.233076	−	0.972459i	$-0.425121\pi$
$769$	12.9268			0.466151			0.233076	+	0.972459i	$0.425121\pi$
$770$		0			0
$771$	16.5503			0.596045
$772$		0			0
$773$	12.2924	−	3.29374i	0.442127	−	0.118468i	−0.0308862	−	0.999523i	$-0.509833\pi$
$773$	12.2924	−	3.29374i	0.442127	−	0.118468i	0.473013	+	0.881055i	$0.343166\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5.55679	−	3.67030i	0.199349	−	0.131671i
$778$		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
$787$	6.25043	+	23.3269i	0.222804	+	0.831514i	0.983273	+	0.182140i	$0.0583025\pi$
$787$	6.25043	+	23.3269i	0.222804	+	0.831514i	−0.760469	+	0.649374i	$0.775031\pi$
$788$		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
$793$	−4.82010	−	1.29154i	−0.171167	−	0.0458640i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.46616	−	6.46616i	0.229043	−	0.229043i	−0.583250	−	0.812293i	$-0.698219\pi$
$797$	6.46616	−	6.46616i	0.229043	−	0.229043i	0.812293	+	0.583250i	$0.198219\pi$
$798$		0			0
$799$		−	3.67103i		−	0.129872i
$800$		0			0
$801$	−8.04757	−	4.64627i	−0.284347	−	0.164168i
$802$		0			0
$803$	5.95357	−	22.2190i	0.210097	−	0.784093i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.00328	+	7.47632i	−0.0705186	+	0.263179i
$808$		0			0
$809$	−9.32249	−	5.38234i	−0.327761	−	0.189233i	0.327085	−	0.944995i	$-0.393933\pi$
$809$	−9.32249	−	5.38234i	−0.327761	−	0.189233i	−0.654847	+	0.755762i	$0.727267\pi$
$810$		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
$817$	7.91360	+	2.12044i	0.276862	+	0.0741849i
$818$		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
$823$	−6.51626	−	24.3190i	−0.227142	−	0.847707i	−0.981535	−	0.191283i	$-0.938735\pi$
$823$	−6.51626	−	24.3190i	−0.227142	−	0.847707i	0.754392	−	0.656424i	$-0.227932\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.16960	−	3.16960i	−0.110218	−	0.110218i	0.649847	−	0.760065i	$-0.274833\pi$
$827$	−3.16960	−	3.16960i	−0.110218	−	0.110218i	−0.760065	+	0.649847i	$0.774833\pi$
$828$		0			0
$829$	−8.68023	+	15.0346i	−0.301477	+	0.522173i	−0.976471	−	0.215650i	$-0.930813\pi$
$829$	−8.68023	+	15.0346i	−0.301477	+	0.522173i	0.674994	+	0.737823i	$0.264146\pi$
$830$		0			0
$831$	0.185804	−	0.107274i	0.00644546	−	0.00372129i
$832$		0			0
$833$	−4.54549	−	0.647720i	−0.157492	−	0.0224422i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.63145	−	0.705096i	0.0909564	−	0.0243717i
$838$		0			0
$839$	27.6873			0.955870			0.477935	−	0.878395i	$-0.341385\pi$
$839$	27.6873			0.955870			0.477935	+	0.878395i	$0.341385\pi$
$840$		0			0
$841$	−20.3883			−0.703045
$842$		0			0
$843$	3.74109	−	1.00242i	0.128850	−	0.0345253i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	9.95953	−	19.9278i	0.342214	−	0.684729i
$848$		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	$-0.198063\pi$
$853$	6.70940	+	6.70940i	0.229725	+	0.229725i	−0.582853	+	0.812578i	$0.698063\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.55278	−	31.9194i	−0.292157	−	1.09035i	−0.943449	−	0.331519i	$-0.892439\pi$
$857$	−8.55278	−	31.9194i	−0.292157	−	1.09035i	0.651291	−	0.758828i	$-0.274228\pi$
$858$		0			0
$859$	9.46364	+	16.3915i	0.322895	+	0.559271i	0.981084	−	0.193582i	$-0.0620105\pi$
$859$	9.46364	+	16.3915i	0.322895	+	0.559271i	−0.658189	+	0.752853i	$0.728677\pi$
$860$		0			0
$861$	−17.3516	+	19.5745i	−0.591340	+	0.667098i
$862$		0			0
$863$	4.26026	+	1.14153i	0.145021	+	0.0388583i	0.330599	−	0.943771i	$-0.392749\pi$
$863$	4.26026	+	1.14153i	0.145021	+	0.0388583i	−0.185578	+	0.982629i	$0.559416\pi$
$864$		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
$873$	1.97889	−	7.38531i	0.0669752	−	0.249955i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−3.22334	+	12.0297i	−0.108844	+	0.406213i	−0.998753	−	0.0499262i	$-0.984101\pi$
$877$	−3.22334	+	12.0297i	−0.108844	+	0.406213i	0.889909	+	0.456139i	$0.150768\pi$
$878$		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	0.0195926	−	0.999808i	$-0.493763\pi$
$883$	30.2918	−	30.2918i	1.01940	−	1.01940i	0.999808	−	0.0195926i	$-0.00623691\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.8920	−	6.66980i	−0.835793	−	0.223950i	−0.184554	−	0.982822i	$-0.559084\pi$
$887$	−24.8920	−	6.66980i	−0.835793	−	0.223950i	−0.651239	+	0.758872i	$0.725751\pi$
$888$		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
$893$	−3.06443	−	11.4366i	−0.102547	−	0.382711i
$894$		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
$903$	10.2278	−	0.615712i	0.340359	−	0.0204896i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−17.1402	+	4.59270i	−0.569130	+	0.152498i	−0.531898	−	0.846809i	$-0.678521\pi$
$907$	−17.1402	+	4.59270i	−0.569130	+	0.152498i	−0.0372326	+	0.999307i	$0.511854\pi$
$908$		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
$913$	−11.1799	+	2.99564i	−0.370000	+	0.0991411i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.9386	+	12.4638i	0.823545	+	0.411591i
$918$		0			0
$919$	40.7286	−	23.5147i	1.34351	−	0.775677i	0.356191	−	0.934413i	$-0.384075\pi$
$919$	40.7286	−	23.5147i	1.34351	−	0.775677i	0.987321	+	0.158737i	$0.0507420\pi$
$920$		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
$927$	−3.82630	−	14.2799i	−0.125672	−	0.469015i
$928$		0			0
$929$	−8.46604	−	14.6636i	−0.277762	−	0.481098i	0.693066	−	0.720874i	$-0.256259\pi$
$929$	−8.46604	−	14.6636i	−0.277762	−	0.481098i	−0.970828	+	0.239776i	$0.922926\pi$
$930$		0			0
$931$	−14.7016	+	1.77651i	−0.481824	+	0.0582226i
$932$		0			0
$933$	27.1852	+	7.28425i	0.890003	+	0.238476i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	22.2245	−	22.2245i	0.726043	−	0.726043i	−0.243786	−	0.969829i	$-0.578390\pi$
$937$	22.2245	−	22.2245i	0.726043	−	0.726043i	0.969829	+	0.243786i	$0.0783895\pi$
$938$		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
$943$	6.15924	−	22.9866i	0.200573	−	0.748547i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.2437	+	38.2299i	−0.332875	+	1.24231i	0.573280	+	0.819359i	$0.305671\pi$
$947$	−10.2437	+	38.2299i	−0.332875	+	1.24231i	−0.906155	+	0.422946i	$0.860996\pi$
$948$		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	−0.201233	−	0.979543i	$-0.564495\pi$
$953$	24.0270	−	24.0270i	0.778311	−	0.778311i	0.979543	+	0.201233i	$0.0644948\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	10.9028	+	2.92141i	0.352439	+	0.0944357i
$958$		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
$963$	−1.43916	−	5.37101i	−0.0463762	−	0.173078i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−29.9647	−	29.9647i	−0.963598	−	0.963598i	0.0357620	−	0.999360i	$-0.488614\pi$
$967$	−29.9647	−	29.9647i	−0.963598	−	0.963598i	−0.999360	+	0.0357620i	$0.988614\pi$
$968$		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
$973$	−3.11580	−	4.71728i	−0.0998879	−	0.151229i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.5497	−	3.63062i	0.433493	−	0.116154i	−0.0354726	−	0.999371i	$-0.511294\pi$
$977$	13.5497	−	3.63062i	0.433493	−	0.116154i	0.468965	+	0.883217i	$0.344627\pi$
$978$		0			0
$979$	−14.9251			−0.477009
$980$		0			0
$981$	−1.73780			−0.0554835
$982$		0			0
$983$	15.3497	−	4.11293i	0.489578	−	0.131182i	−0.00558070	−	0.999984i	$-0.501776\pi$
$983$	15.3497	−	4.11293i	0.489578	−	0.131182i	0.495159	+	0.868802i	$0.335110\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−8.16110	−	12.3558i	−0.259771	−	0.393290i
$988$		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
$997$	7.64591	+	28.5349i	0.242148	+	0.903710i	0.974795	+	0.223101i	$0.0716180\pi$
$997$	7.64591	+	28.5349i	0.242148	+	0.903710i	−0.732647	+	0.680609i	$0.761715\pi$
$998$		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.157.3		32
5.2	odd	4		420.2.bo.a.73.8	✓	32
5.3	odd	4	inner	2100.2.ce.e.493.3		32
5.4	even	2		420.2.bo.a.157.7	yes	32
7.5	odd	6	inner	2100.2.ce.e.1657.3		32
15.2	even	4		1260.2.dq.c.73.1		32
15.14	odd	2		1260.2.dq.c.577.3		32
35.4	even	6		2940.2.x.c.97.5		32
35.12	even	12		420.2.bo.a.313.7	yes	32
35.17	even	12		2940.2.x.c.1273.5		32
35.19	odd	6		420.2.bo.a.397.8	yes	32
35.24	odd	6		2940.2.x.c.97.14		32
35.32	odd	12		2940.2.x.c.1273.14		32
35.33	even	12	inner	2100.2.ce.e.1993.3		32
105.47	odd	12		1260.2.dq.c.1153.3		32
105.89	even	6		1260.2.dq.c.397.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.8	✓	32	5.2	odd	4
420.2.bo.a.157.7	yes	32	5.4	even	2
420.2.bo.a.313.7	yes	32	35.12	even	12
420.2.bo.a.397.8	yes	32	35.19	odd	6
1260.2.dq.c.73.1		32	15.2	even	4
1260.2.dq.c.397.1		32	105.89	even	6
1260.2.dq.c.577.3		32	15.14	odd	2
1260.2.dq.c.1153.3		32	105.47	odd	12
2100.2.ce.e.157.3		32	1.1	even	1	trivial
2100.2.ce.e.493.3		32	5.3	odd	4	inner
2100.2.ce.e.1657.3		32	7.5	odd	6	inner
2100.2.ce.e.1993.3		32	35.33	even	12	inner
2940.2.x.c.97.5		32	35.4	even	6
2940.2.x.c.97.14		32	35.24	odd	6
2940.2.x.c.1273.5		32	35.17	even	12
2940.2.x.c.1273.14		32	35.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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