LMFDB - Embedded newform 2100.2.ce.e.1657.4

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			1657.4
Character	$\chi$	$=$	2100.1657
Dual form			2100.2.ce.e.493.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{3} +(2.64359 - 0.106918i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{3} +(2.64359 - 0.106918i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(3.02114 + 5.23277i) q^{11} +(-2.18958 - 2.18958i) q^{13} +(-6.21931 - 1.66646i) q^{17} +(-3.37334 + 5.84280i) q^{19} +(-0.580936 + 2.58118i) q^{21} +(1.01552 + 3.78997i) q^{23} +(0.707107 - 0.707107i) q^{27} -2.45965i q^{29} +(-2.81644 + 1.62607i) q^{31} +(-5.83640 + 1.56386i) q^{33} +(0.594521 - 0.159302i) q^{37} +(2.68168 - 1.54827i) q^{39} +6.77442i q^{41} +(5.33519 - 5.33519i) q^{43} +(1.72795 + 6.44881i) q^{47} +(6.97714 - 0.565297i) q^{49} +(3.21935 - 5.57608i) q^{51} +(-3.38093 - 0.905917i) q^{53} +(-4.77063 - 4.77063i) q^{57} +(2.28621 + 3.95983i) q^{59} +(-3.38318 - 1.95328i) q^{61} +(-2.34288 - 1.22920i) q^{63} +(-2.96837 + 11.0781i) q^{67} -3.92366 q^{69} +5.40725 q^{71} +(1.87380 - 6.99311i) q^{73} +(8.54614 + 13.5103i) q^{77} +(-8.00023 - 4.61893i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.451016 + 0.451016i) q^{83} +(2.37584 + 0.636604i) q^{87} +(-6.04716 + 10.4740i) q^{89} +(-6.02246 - 5.55425i) q^{91} +(-0.841717 - 3.14133i) q^{93} +(-9.62431 + 9.62431i) q^{97} -6.04229i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.64359	−	0.106918i	0.999183	−	0.0404114i
$7$	2.64359	−	0.106918i	0.999183	−	0.0404114i
$8$		0			0
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	3.02114	+	5.23277i	0.910909	+	1.57774i	0.812783	+	0.582566i	$0.197951\pi$
$11$	3.02114	+	5.23277i	0.910909	+	1.57774i	0.0981257	+	0.995174i	$0.468715\pi$
$12$		0			0
$13$	−2.18958	−	2.18958i	−0.607280	−	0.607280i	0.334954	−	0.942234i	$-0.391279\pi$
$13$	−2.18958	−	2.18958i	−0.607280	−	0.607280i	−0.942234	+	0.334954i	$0.891279\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.21931	−	1.66646i	−1.50840	−	0.404176i	−0.592499	−	0.805571i	$-0.701859\pi$
$17$	−6.21931	−	1.66646i	−1.50840	−	0.404176i	−0.915905	+	0.401396i	$0.868525\pi$
$18$		0			0
$19$	−3.37334	+	5.84280i	−0.773898	+	1.34043i	0.161514	+	0.986870i	$0.448362\pi$
$19$	−3.37334	+	5.84280i	−0.773898	+	1.34043i	−0.935412	+	0.353560i	$0.884971\pi$
$20$		0			0
$21$	−0.580936	+	2.58118i	−0.126771	+	0.563261i
$22$		0			0
$23$	1.01552	+	3.78997i	0.211750	+	0.790262i	0.987285	+	0.158958i	$0.0508135\pi$
$23$	1.01552	+	3.78997i	0.211750	+	0.790262i	−0.775535	+	0.631304i	$0.782520\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	2.45965i		−	0.456746i	−0.973574	−	0.228373i	$-0.926660\pi$
$29$		−	2.45965i		−	0.456746i	0.973574	−	0.228373i	$-0.0733405\pi$
$30$		0			0
$31$	−2.81644	+	1.62607i	−0.505848	+	0.292051i	−0.731125	−	0.682243i	$-0.761004\pi$
$31$	−2.81644	+	1.62607i	−0.505848	+	0.292051i	0.225277	+	0.974295i	$0.427671\pi$
$32$		0			0
$33$	−5.83640	+	1.56386i	−1.01599	+	0.272233i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.594521	−	0.159302i	0.0977387	−	0.0261890i	−0.209618	−	0.977783i	$-0.567222\pi$
$37$	0.594521	−	0.159302i	0.0977387	−	0.0261890i	0.307357	+	0.951594i	$0.400555\pi$
$38$		0			0
$39$	2.68168	−	1.54827i	0.429412	−	0.247921i
$40$		0			0
$41$			6.77442i			1.05799i	0.848626	+	0.528994i	$0.177430\pi$
$41$			6.77442i			1.05799i	−0.848626	+	0.528994i	$0.822570\pi$
$42$		0			0
$43$	5.33519	−	5.33519i	0.813608	−	0.813608i	−0.171565	−	0.985173i	$-0.554882\pi$
$43$	5.33519	−	5.33519i	0.813608	−	0.813608i	0.985173	+	0.171565i	$0.0548822\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.72795	+	6.44881i	0.252048	+	0.940656i	0.969709	+	0.244263i	$0.0785460\pi$
$47$	1.72795	+	6.44881i	0.252048	+	0.940656i	−0.717661	+	0.696393i	$0.754787\pi$
$48$		0			0
$49$	6.97714	−	0.565297i	0.996734	−	0.0807567i
$50$		0			0
$51$	3.21935	−	5.57608i	0.450799	−	0.780807i
$52$		0			0
$53$	−3.38093	−	0.905917i	−0.464406	−	0.124437i	0.0190261	−	0.999819i	$-0.493943\pi$
$53$	−3.38093	−	0.905917i	−0.464406	−	0.124437i	−0.483432	+	0.875382i	$0.660610\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.77063	−	4.77063i	−0.631885	−	0.631885i
$58$		0			0
$59$	2.28621	+	3.95983i	0.297639	+	0.515526i	0.975595	−	0.219576i	$-0.0704674\pi$
$59$	2.28621	+	3.95983i	0.297639	+	0.515526i	−0.677956	+	0.735102i	$0.737134\pi$
$60$		0			0
$61$	−3.38318	−	1.95328i	−0.433172	−	0.250092i	0.267525	−	0.963551i	$-0.413794\pi$
$61$	−3.38318	−	1.95328i	−0.433172	−	0.250092i	−0.700697	+	0.713459i	$0.747128\pi$
$62$		0			0
$63$	−2.34288	−	1.22920i	−0.295175	−	0.154865i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.96837	+	11.0781i	−0.362644	+	1.35341i	0.507942	+	0.861391i	$0.330406\pi$
$67$	−2.96837	+	11.0781i	−0.362644	+	1.35341i	−0.870586	+	0.492016i	$0.836260\pi$
$68$		0			0
$69$	−3.92366			−0.472353
$70$		0			0
$71$	5.40725			0.641722			0.320861	−	0.947126i	$-0.396028\pi$
$71$	5.40725			0.641722			0.320861	+	0.947126i	$0.396028\pi$
$72$		0			0
$73$	1.87380	−	6.99311i	0.219312	−	0.818482i	−0.765293	−	0.643683i	$-0.777406\pi$
$73$	1.87380	−	6.99311i	0.219312	−	0.818482i	0.984604	−	0.174799i	$-0.0559276\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.54614	+	13.5103i	0.973923	+	1.53964i
$78$		0			0
$79$	−8.00023	−	4.61893i	−0.900096	−	0.519671i	−0.0228646	−	0.999739i	$-0.507279\pi$
$79$	−8.00023	−	4.61893i	−0.900096	−	0.519671i	−0.877231	+	0.480068i	$0.840612\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	0.451016	+	0.451016i	0.0495055	+	0.0495055i	0.731426	−	0.681921i	$-0.238855\pi$
$83$	0.451016	+	0.451016i	0.0495055	+	0.0495055i	−0.681921	+	0.731426i	$0.738855\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.37584	+	0.636604i	0.254717	+	0.0682511i
$88$		0			0
$89$	−6.04716	+	10.4740i	−0.640997	+	1.11024i	0.344213	+	0.938892i	$0.388146\pi$
$89$	−6.04716	+	10.4740i	−0.640997	+	1.11024i	−0.985211	+	0.171348i	$0.945188\pi$
$90$		0			0
$91$	−6.02246	−	5.55425i	−0.631325	−	0.582243i
$92$		0			0
$93$	−0.841717	−	3.14133i	−0.0872820	−	0.325741i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.62431	+	9.62431i	−0.977201	+	0.977201i	−0.999746	−	0.0225452i	$-0.992823\pi$
$97$	−9.62431	+	9.62431i	−0.977201	+	0.977201i	0.0225452	+	0.999746i	$0.492823\pi$
$98$		0			0
$99$		−	6.04229i		−	0.607273i
$100$		0			0
$101$	8.65132	−	4.99484i	0.860838	−	0.497005i	−0.00345474	−	0.999994i	$-0.501100\pi$
$101$	8.65132	−	4.99484i	0.860838	−	0.497005i	0.864293	+	0.502989i	$0.167766\pi$
$102$		0			0
$103$	−9.77343	+	2.61878i	−0.963005	+	0.258036i	−0.705872	−	0.708340i	$-0.749444\pi$
$103$	−9.77343	+	2.61878i	−0.963005	+	0.258036i	−0.257133	+	0.966376i	$0.582778\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.2584	+	2.74873i	−0.991719	+	0.265730i	−0.717972	−	0.696072i	$-0.754930\pi$
$107$	−10.2584	+	2.74873i	−0.991719	+	0.265730i	−0.273746	+	0.961802i	$0.588263\pi$
$108$		0			0
$109$	12.3030	−	7.10312i	1.17841	−	0.680355i	0.222764	−	0.974872i	$-0.428492\pi$
$109$	12.3030	−	7.10312i	1.17841	−	0.680355i	0.955646	+	0.294517i	$0.0951588\pi$
$110$		0			0
$111$			0.615494i			0.0584201i
$112$		0			0
$113$	−2.36172	+	2.36172i	−0.222172	+	0.222172i	−0.809412	−	0.587241i	$-0.800214\pi$
$113$	−2.36172	+	2.36172i	−0.222172	+	0.222172i	0.587241	+	0.809412i	$0.300214\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.801442	+	2.99102i	0.0740933	+	0.276520i
$118$		0			0
$119$	−16.6195	−	3.74047i	−1.52350	−	0.342889i
$120$		0			0
$121$	−12.7546	+	22.0916i	−1.15951	+	2.00833i
$122$		0			0
$123$	−6.54359	−	1.75335i	−0.590016	−	0.158094i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.19418	+	9.19418i	0.815851	+	0.815851i	0.985504	−	0.169653i	$-0.0542646\pi$
$127$	9.19418	+	9.19418i	0.815851	+	0.815851i	−0.169653	+	0.985504i	$0.554265\pi$
$128$		0			0
$129$	3.77255	+	6.53424i	0.332154	+	0.575308i
$130$		0			0
$131$	12.0930	+	6.98191i	1.05657	+	0.610013i	0.924482	−	0.381225i	$-0.124498\pi$
$131$	12.0930	+	6.98191i	1.05657	+	0.610013i	0.132091	+	0.991238i	$0.457831\pi$
$132$		0			0
$133$	−8.29303	+	15.8066i	−0.719097	+	1.37061i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.39004	+	12.6518i	−0.289630	+	1.08092i	0.655758	+	0.754971i	$0.272349\pi$
$137$	−3.39004	+	12.6518i	−0.289630	+	1.08092i	−0.945389	+	0.325945i	$0.894318\pi$
$138$		0			0
$139$	−22.5083			−1.90913			−0.954563	−	0.298010i	$-0.903677\pi$
$139$	−22.5083			−1.90913			−0.954563	+	0.298010i	$0.903677\pi$
$140$		0			0
$141$	−6.67630			−0.562246
$142$		0			0
$143$	4.84254	−	18.0726i	0.404954	−	1.51131i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.25978	+	6.88571i	−0.103905	+	0.567923i
$148$		0			0
$149$	11.1810	+	6.45533i	0.915980	+	0.528841i	0.882350	−	0.470593i	$-0.155960\pi$
$149$	11.1810	+	6.45533i	0.915980	+	0.528841i	0.0336298	+	0.999434i	$0.489293\pi$
$150$		0			0
$151$	−6.64116	−	11.5028i	−0.540450	−	0.936086i	−0.998878	−	0.0473549i	$-0.984921\pi$
$151$	−6.64116	−	11.5028i	−0.540450	−	0.936086i	0.458429	−	0.888731i	$-0.348413\pi$
$152$		0			0
$153$	4.55285	+	4.55285i	0.368076	+	0.368076i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.21969	−	2.47041i	−0.735812	−	0.197160i	−0.128596	−	0.991697i	$-0.541047\pi$
$157$	−9.21969	−	2.47041i	−0.735812	−	0.197160i	−0.607216	+	0.794537i	$0.707714\pi$
$158$		0			0
$159$	1.75010	−	3.03126i	0.138792	−	0.240394i
$160$		0			0
$161$	3.08983	+	9.91054i	0.243513	+	0.781060i
$162$		0			0
$163$	0.258041	+	0.963023i	0.0202113	+	0.0754298i	0.975295	−	0.220907i	$-0.0709017\pi$
$163$	0.258041	+	0.963023i	0.0202113	+	0.0754298i	−0.955084	+	0.296337i	$0.904235\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.32380	−	6.32380i	0.489350	−	0.489350i	−0.418751	−	0.908101i	$-0.637532\pi$
$167$	6.32380	−	6.32380i	0.489350	−	0.489350i	0.908101	+	0.418751i	$0.137532\pi$
$168$		0			0
$169$		−	3.41148i		−	0.262421i
$170$		0			0
$171$	5.84280	−	3.37334i	0.446810	−	0.257966i
$172$		0			0
$173$	13.1650	−	3.52754i	1.00091	−	0.268194i	0.279086	−	0.960266i	$-0.409969\pi$
$173$	13.1650	−	3.52754i	1.00091	−	0.268194i	0.721828	+	0.692072i	$0.243302\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.41662	+	1.18343i	−0.331973	+	0.0889520i
$178$		0			0
$179$	3.14649	−	1.81663i	0.235180	−	0.135781i	−0.377780	−	0.925896i	$-0.623312\pi$
$179$	3.14649	−	1.81663i	0.235180	−	0.135781i	0.612959	+	0.790115i	$0.289979\pi$
$180$		0			0
$181$		−	5.31201i		−	0.394838i	−0.980319	−	0.197419i	$-0.936744\pi$
$181$		−	5.31201i		−	0.394838i	0.980319	−	0.197419i	$-0.0632560\pi$
$182$		0			0
$183$	2.76236	−	2.76236i	0.204199	−	0.204199i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.0692	−	37.5788i	−0.736334	−	2.74804i
$188$		0			0
$189$	1.79370	−	1.94490i	0.130472	−	0.141471i
$190$		0			0
$191$	−4.27281	+	7.40072i	−0.309170	+	0.535497i	−0.978181	−	0.207755i	$-0.933384\pi$
$191$	−4.27281	+	7.40072i	−0.309170	+	0.535497i	0.669011	+	0.743252i	$0.266718\pi$
$192$		0			0
$193$	−2.12384	−	0.569081i	−0.152877	−	0.0409633i	0.181569	−	0.983378i	$-0.441883\pi$
$193$	−2.12384	−	0.569081i	−0.152877	−	0.0409633i	−0.334446	+	0.942415i	$0.608549\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.8683	−	12.8683i	−0.916829	−	0.916829i	0.0799682	−	0.996797i	$-0.474518\pi$
$197$	−12.8683	−	12.8683i	−0.916829	−	0.916829i	−0.996797	+	0.0799682i	$0.974518\pi$
$198$		0			0
$199$	4.20848	+	7.28930i	0.298331	+	0.516725i	0.975754	−	0.218869i	$-0.0702366\pi$
$199$	4.20848	+	7.28930i	0.298331	+	0.516725i	−0.677423	+	0.735594i	$0.736903\pi$
$200$		0			0
$201$	−9.93237	−	5.73445i	−0.700575	−	0.404477i
$202$		0			0
$203$	−0.262982	−	6.50231i	−0.0184577	−	0.456372i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.01552	−	3.78997i	0.0705834	−	0.263421i
$208$		0			0
$209$	−40.7654			−2.81980
$210$		0			0
$211$	26.8727			1.84999			0.924996	−	0.379976i	$-0.124068\pi$
$211$	26.8727			1.84999			0.924996	+	0.379976i	$0.124068\pi$
$212$		0			0
$213$	−1.39950	+	5.22300i	−0.0958921	+	0.357874i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−7.27166	+	4.59980i	−0.493632	+	0.312255i
$218$		0			0
$219$	6.26985	+	3.61990i	0.423677	+	0.244610i
$220$		0			0
$221$	9.96883	+	17.2665i	0.670576	+	1.16147i
$222$		0			0
$223$	−17.1969	−	17.1969i	−1.15159	−	1.15159i	−0.986234	−	0.165358i	$-0.947122\pi$
$223$	−17.1969	−	17.1969i	−1.15159	−	1.15159i	−0.165358	−	0.986234i	$-0.552878\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.90841	+	2.38700i	0.591272	+	0.158431i	0.542035	−	0.840356i	$-0.317654\pi$
$227$	8.90841	+	2.38700i	0.591272	+	0.158431i	0.0492376	+	0.998787i	$0.484321\pi$
$228$		0			0
$229$	3.53248	−	6.11844i	0.233433	−	0.404318i	−0.725383	−	0.688345i	$-0.758337\pi$
$229$	3.53248	−	6.11844i	0.233433	−	0.404318i	0.958816	+	0.284028i	$0.0916708\pi$
$230$		0			0
$231$	−15.2618	+	4.75822i	−1.00416	+	0.313068i
$232$		0			0
$233$	3.57364	+	13.3370i	0.234117	+	0.873736i	0.978545	+	0.206033i	$0.0660556\pi$
$233$	3.57364	+	13.3370i	0.234117	+	0.873736i	−0.744428	+	0.667703i	$0.767278\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.53216	−	6.53216i	0.424309	−	0.424309i
$238$		0			0
$239$			6.83543i			0.442147i	0.975257	+	0.221074i	$0.0709561\pi$
$239$			6.83543i			0.442147i	−0.975257	+	0.221074i	$0.929044\pi$
$240$		0			0
$241$	5.06234	−	2.92274i	0.326094	−	0.188270i	−0.328012	−	0.944674i	$-0.606379\pi$
$241$	5.06234	−	2.92274i	0.326094	−	0.188270i	0.654106	+	0.756403i	$0.273045\pi$
$242$		0			0
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	20.1795	−	5.40708i	1.28399	−	0.344044i
$248$		0			0
$249$	−0.552380	+	0.318917i	−0.0350056	+	0.0202105i
$250$		0			0
$251$		−	14.2887i		−	0.901897i	−0.892550	−	0.450948i	$-0.851086\pi$
$251$		−	14.2887i		−	0.901897i	0.892550	−	0.450948i	$-0.148914\pi$
$252$		0			0
$253$	−16.7640	+	16.7640i	−1.05394	+	1.05394i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.25654	+	4.68946i	0.0783807	+	0.292521i	0.993979	−	0.109574i	$-0.0349488\pi$
$257$	1.25654	+	4.68946i	0.0783807	+	0.292521i	−0.915598	+	0.402095i	$0.868282\pi$
$258$		0			0
$259$	1.55464	−	0.484693i	0.0966005	−	0.0301174i
$260$		0			0
$261$	−1.22982	+	2.13012i	−0.0761243	+	0.131851i
$262$		0			0
$263$	−7.22980	−	1.93722i	−0.445809	−	0.119454i	0.0289290	−	0.999581i	$-0.490790\pi$
$263$	−7.22980	−	1.93722i	−0.445809	−	0.119454i	−0.474738	+	0.880127i	$0.657457\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−8.55197	−	8.55197i	−0.523372	−	0.523372i
$268$		0			0
$269$	4.78143	+	8.28169i	0.291529	+	0.504943i	0.974172	−	0.225809i	$-0.0725026\pi$
$269$	4.78143	+	8.28169i	0.291529	+	0.504943i	−0.682642	+	0.730753i	$0.739169\pi$
$270$		0			0
$271$	21.0069	+	12.1283i	1.27608	+	0.736743i	0.976125	−	0.217211i	$-0.0696961\pi$
$271$	21.0069	+	12.1283i	1.27608	+	0.736743i	0.299952	+	0.953954i	$0.403029\pi$
$272$		0			0
$273$	6.92372	−	4.37970i	0.419042	−	0.265072i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.797887	−	2.97776i	0.0479404	−	0.178916i	−0.937804	−	0.347165i	$-0.887144\pi$
$277$	0.797887	−	2.97776i	0.0479404	−	0.178916i	0.985745	+	0.168249i	$0.0538111\pi$
$278$		0			0
$279$	3.25215			0.194701
$280$		0			0
$281$	5.45417			0.325369			0.162684	−	0.986678i	$-0.447985\pi$
$281$	5.45417			0.325369			0.162684	+	0.986678i	$0.447985\pi$
$282$		0			0
$283$	−1.87133	+	6.98391i	−0.111239	+	0.415150i	−0.998978	−	0.0451971i	$-0.985608\pi$
$283$	−1.87133	+	6.98391i	−0.111239	+	0.415150i	0.887739	+	0.460347i	$0.152275\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.724311	+	17.9088i	0.0427547	+	1.05712i
$288$		0			0
$289$	21.1803	+	12.2284i	1.24590	+	0.719320i
$290$		0			0
$291$	−6.80541	−	11.7873i	−0.398940	−	0.690985i
$292$		0			0
$293$	10.0811	+	10.0811i	0.588942	+	0.588942i	0.937345	−	0.348403i	$-0.113276\pi$
$293$	10.0811	+	10.0811i	0.588942	+	0.588942i	−0.348403	+	0.937345i	$0.613276\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	5.83640	+	1.56386i	0.338662	+	0.0907443i
$298$		0			0
$299$	6.07487	−	10.5220i	0.351319	−	0.608503i
$300$		0			0
$301$	13.5336	−	14.6745i	0.780065	−	0.845823i
$302$		0			0
$303$	2.58552	+	9.64929i	0.148534	+	0.554337i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.65757	+	1.65757i	−0.0946023	+	0.0946023i	−0.752824	−	0.658222i	$-0.771309\pi$
$307$	−1.65757	+	1.65757i	−0.0946023	+	0.0946023i	0.658222	+	0.752824i	$0.271309\pi$
$308$		0			0
$309$		−	10.1182i		−	0.575604i
$310$		0			0
$311$	−11.6703	+	6.73786i	−0.661762	+	0.382069i	−0.792948	−	0.609289i	$-0.791455\pi$
$311$	−11.6703	+	6.73786i	−0.661762	+	0.382069i	0.131186	+	0.991358i	$0.458122\pi$
$312$		0			0
$313$	7.56627	−	2.02738i	0.427671	−	0.114594i	−0.0385618	−	0.999256i	$-0.512278\pi$
$313$	7.56627	−	2.02738i	0.427671	−	0.114594i	0.466233	+	0.884662i	$0.345611\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.1191	−	6.73065i	1.41083	−	0.378031i	0.528609	−	0.848866i	$-0.322714\pi$
$317$	25.1191	−	6.73065i	1.41083	−	0.378031i	0.882221	+	0.470835i	$0.156047\pi$
$318$		0			0
$319$	12.8708	−	7.43095i	0.720626	−	0.416054i
$320$		0			0
$321$		−	10.6203i		−	0.592767i
$322$		0			0
$323$	30.7166	−	30.7166i	1.70912	−	1.70912i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.67684	+	13.7222i	0.203330	+	0.758838i
$328$		0			0
$329$	5.25750	+	16.8633i	0.289855	+	0.929702i
$330$		0			0
$331$	−1.62289	+	2.81093i	−0.0892020	+	0.154502i	−0.907174	−	0.420756i	$-0.861765\pi$
$331$	−1.62289	+	2.81093i	−0.0892020	+	0.154502i	0.817972	+	0.575258i	$0.195098\pi$
$332$		0			0
$333$	−0.594521	−	0.159302i	−0.0325796	−	0.00872967i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.182629	+	0.182629i	0.00994842	+	0.00994842i	0.712063	−	0.702115i	$-0.247761\pi$
$337$	0.182629	+	0.182629i	0.00994842	+	0.00994842i	−0.702115	+	0.712063i	$0.747761\pi$
$338$		0			0
$339$	−1.66999	−	2.89250i	−0.0907013	−	0.157099i
$340$		0			0
$341$	−17.0177	−	9.82520i	−0.921562	−	0.532064i
$342$		0			0
$343$	18.3842	−	2.24040i	0.992656	−	0.120970i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.32084	−	12.3936i	0.178272	−	0.665321i	−0.817699	−	0.575646i	$-0.804751\pi$
$347$	3.32084	−	12.3936i	0.178272	−	0.665321i	0.995971	−	0.0896748i	$-0.0285828\pi$
$348$		0			0
$349$	10.6569			0.570453			0.285226	−	0.958460i	$-0.407931\pi$
$349$	10.6569			0.570453			0.285226	+	0.958460i	$0.407931\pi$
$350$		0			0
$351$	−3.09653			−0.165281
$352$		0			0
$353$	−3.37072	+	12.5797i	−0.179405	+	0.669549i	0.816354	+	0.577552i	$0.195992\pi$
$353$	−3.37072	+	12.5797i	−0.179405	+	0.669549i	−0.995759	+	0.0919975i	$0.970675\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	7.91446	−	15.0851i	0.418877	−	0.798387i
$358$		0			0
$359$	23.1941	+	13.3911i	1.22414	+	0.706757i	0.965798	−	0.259296i	$-0.0834906\pi$
$359$	23.1941	+	13.3911i	1.22414	+	0.706757i	0.258342	+	0.966054i	$0.416824\pi$
$360$		0			0
$361$	−13.2589	−	22.9651i	−0.697836	−	1.20869i
$362$		0			0
$363$	−18.0377	−	18.0377i	−0.946736	−	0.946736i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	21.5660	+	5.77860i	1.12574	+	0.301641i	0.773203	−	0.634158i	$-0.218653\pi$
$367$	21.5660	+	5.77860i	1.12574	+	0.301641i	0.352535	+	0.935799i	$0.385320\pi$
$368$		0			0
$369$	3.38721	−	5.86682i	0.176331	−	0.305415i
$370$		0			0
$371$	−9.03465	−	2.03339i	−0.469056	−	0.105568i
$372$		0			0
$373$	2.72854	+	10.1831i	0.141279	+	0.527259i	0.999893	+	0.0146365i	$0.00465912\pi$
$373$	2.72854	+	10.1831i	0.141279	+	0.527259i	−0.858614	+	0.512622i	$0.828674\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.38560	+	5.38560i	−0.277373	+	0.277373i
$378$		0			0
$379$		−	31.8216i		−	1.63457i	−0.576235	−	0.817284i	$-0.695479\pi$
$379$		−	31.8216i		−	1.63457i	0.576235	−	0.817284i	$-0.304521\pi$
$380$		0			0
$381$	−11.2605	+	6.50126i	−0.576894	+	0.333070i
$382$		0			0
$383$	8.08362	−	2.16600i	0.413054	−	0.110677i	−0.0463068	−	0.998927i	$-0.514745\pi$
$383$	8.08362	−	2.16600i	0.413054	−	0.110677i	0.459361	+	0.888250i	$0.348079\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.28800	+	1.95281i	−0.370470	+	0.0992671i
$388$		0			0
$389$	−16.9925	+	9.81065i	−0.861556	+	0.497420i	−0.864533	−	0.502576i	$-0.832386\pi$
$389$	−16.9925	+	9.81065i	−0.861556	+	0.497420i	0.00297686	+	0.999996i	$0.499052\pi$
$390$		0			0
$391$		−	25.2633i		−	1.27762i
$392$		0			0
$393$	−9.87392	+	9.87392i	−0.498073	+	0.498073i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.10212	−	26.5055i	−0.356445	−	1.33027i	−0.878656	−	0.477456i	$-0.841559\pi$
$397$	−7.10212	−	26.5055i	−0.356445	−	1.33027i	0.522210	−	0.852817i	$-0.325108\pi$
$398$		0			0
$399$	−13.1217	−	12.1015i	−0.656904	−	0.605834i
$400$		0			0
$401$	5.16991	−	8.95454i	0.258173	−	0.447169i	−0.707580	−	0.706634i	$-0.750213\pi$
$401$	5.16991	−	8.95454i	0.258173	−	0.447169i	0.965752	+	0.259465i	$0.0835462\pi$
$402$		0			0
$403$	9.72724	+	2.60641i	0.484548	+	0.129834i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.62972	+	2.62972i	0.130351	+	0.130351i
$408$		0			0
$409$	−5.43985	−	9.42209i	−0.268983	−	0.465893i	0.699616	−	0.714519i	$-0.253354\pi$
$409$	−5.43985	−	9.42209i	−0.268983	−	0.465893i	−0.968600	+	0.248626i	$0.920021\pi$
$410$		0			0
$411$	−11.3433	−	6.54905i	−0.559523	−	0.323041i
$412$		0			0
$413$	6.46718	+	10.2237i	0.318229	+	0.503077i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.82557	−	21.7413i	0.285279	−	1.06468i
$418$		0			0
$419$	22.9080			1.11913			0.559565	−	0.828787i	$-0.310968\pi$
$419$	22.9080			1.11913			0.559565	+	0.828787i	$0.310968\pi$
$420$		0			0
$421$	−35.7174			−1.74076			−0.870379	−	0.492382i	$-0.836126\pi$
$421$	−35.7174			−1.74076			−0.870379	+	0.492382i	$0.836126\pi$
$422$		0			0
$423$	1.72795	−	6.44881i	0.0840160	−	0.313552i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−9.15259	−	4.80195i	−0.442925	−	0.232383i
$428$		0			0
$429$	16.2035	+	9.35507i	0.782310	+	0.451667i
$430$		0			0
$431$	16.7512	+	29.0139i	0.806875	+	1.39755i	0.915018	+	0.403413i	$0.132176\pi$
$431$	16.7512	+	29.0139i	0.806875	+	1.39755i	−0.108143	+	0.994135i	$0.534491\pi$
$432$		0			0
$433$	3.19361	+	3.19361i	0.153475	+	0.153475i	0.779668	−	0.626193i	$-0.215388\pi$
$433$	3.19361	+	3.19361i	0.153475	+	0.153475i	−0.626193	+	0.779668i	$0.715388\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−25.5697	−	6.85138i	−1.22316	−	0.327746i
$438$		0			0
$439$	4.34916	−	7.53297i	0.207574	−	0.359529i	−0.743376	−	0.668874i	$-0.766777\pi$
$439$	4.34916	−	7.53297i	0.207574	−	0.359529i	0.950950	+	0.309345i	$0.100110\pi$
$440$		0			0
$441$	−6.32503	−	2.99901i	−0.301192	−	0.142810i
$442$		0			0
$443$	7.98880	+	29.8146i	0.379559	+	1.41653i	0.846568	+	0.532281i	$0.178665\pi$
$443$	7.98880	+	29.8146i	0.379559	+	1.41653i	−0.467008	+	0.884253i	$0.654668\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−9.12922	+	9.12922i	−0.431797	+	0.431797i
$448$		0			0
$449$		−	20.8515i		−	0.984044i	−0.870583	−	0.492022i	$-0.836258\pi$
$449$		−	20.8515i		−	0.984044i	0.870583	−	0.492022i	$-0.163742\pi$
$450$		0			0
$451$	−35.4490	+	20.4665i	−1.66923	+	0.963730i
$452$		0			0
$453$	12.8297	−	3.43772i	0.602793	−	0.161518i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	26.4789	−	7.09500i	1.23863	−	0.331890i	0.420697	−	0.907201i	$-0.361786\pi$
$457$	26.4789	−	7.09500i	1.23863	−	0.331890i	0.817935	+	0.575311i	$0.195119\pi$
$458$		0			0
$459$	−5.57608	+	3.21935i	−0.260269	+	0.150266i
$460$		0			0
$461$		−	12.7604i		−	0.594309i	−0.954829	−	0.297155i	$-0.903962\pi$
$461$		−	12.7604i		−	0.594309i	0.954829	−	0.297155i	$-0.0960377\pi$
$462$		0			0
$463$	11.3005	−	11.3005i	0.525179	−	0.525179i	−0.393952	−	0.919131i	$-0.628892\pi$
$463$	11.3005	−	11.3005i	0.525179	−	0.525179i	0.919131	+	0.393952i	$0.128892\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.335282	+	1.25129i	0.0155150	+	0.0579028i	0.973249	−	0.229751i	$-0.0737913\pi$
$467$	0.335282	+	1.25129i	0.0155150	+	0.0579028i	−0.957734	+	0.287654i	$0.907125\pi$
$468$		0			0
$469$	−6.66270	+	29.6034i	−0.307655	+	1.36696i
$470$		0			0
$471$	4.77246	−	8.26615i	0.219904	−	0.380884i
$472$		0			0
$473$	44.0362	+	11.7995i	2.02479	+	0.542540i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.47501	+	2.47501i	0.113323	+	0.113323i
$478$		0			0
$479$	−18.9924	−	32.8958i	−0.867785	−	1.50305i	−0.864255	−	0.503054i	$-0.832210\pi$
$479$	−18.9924	−	32.8958i	−0.867785	−	1.50305i	−0.00353033	−	0.999994i	$-0.501124\pi$
$480$		0			0
$481$	−1.65056	−	0.952949i	−0.0752589	−	0.0434507i
$482$		0			0
$483$	−10.3726	+	0.419512i	−0.471967	+	0.0190884i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.99476	−	26.1048i	0.316963	−	1.18292i	−0.605186	−	0.796084i	$-0.706901\pi$
$487$	6.99476	−	26.1048i	0.316963	−	1.18292i	0.922148	−	0.386836i	$-0.126432\pi$
$488$		0			0
$489$	−0.996995			−0.0450857
$490$		0			0
$491$	23.1830			1.04623			0.523117	−	0.852261i	$-0.324769\pi$
$491$	23.1830			1.04623			0.523117	+	0.852261i	$0.324769\pi$
$492$		0			0
$493$	−4.09890	+	15.2973i	−0.184605	+	0.688957i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	14.2945	−	0.578135i	0.641198	−	0.0259329i
$498$		0			0
$499$	0.565265	+	0.326356i	0.0253047	+	0.0146097i	0.512599	−	0.858628i	$-0.328683\pi$
$499$	0.565265	+	0.326356i	0.0253047	+	0.0146097i	−0.487294	+	0.873238i	$0.662016\pi$
$500$		0			0
$501$	4.47160	+	7.74504i	0.199776	+	0.346023i
$502$		0			0
$503$	0.465372	+	0.465372i	0.0207499	+	0.0207499i	0.717406	−	0.696656i	$-0.245329\pi$
$503$	0.465372	+	0.465372i	0.0207499	+	0.0207499i	−0.696656	+	0.717406i	$0.745329\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.29523	+	0.882955i	0.146346	+	0.0392134i
$508$		0			0
$509$	6.93027	−	12.0036i	0.307179	−	0.532050i	−0.670565	−	0.741851i	$-0.733948\pi$
$509$	6.93027	−	12.0036i	0.307179	−	0.532050i	0.977744	+	0.209801i	$0.0672816\pi$
$510$		0			0
$511$	4.20586	−	18.6873i	0.186056	−	0.826676i
$512$		0			0
$513$	1.74617	+	6.51680i	0.0770953	+	0.287724i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−28.5248	+	28.5248i	−1.25452	+	1.25452i
$518$		0			0
$519$			13.6294i			0.598263i
$520$		0			0
$521$	7.39370	−	4.26876i	0.323924	−	0.187018i	−0.329216	−	0.944255i	$-0.606785\pi$
$521$	7.39370	−	4.26876i	0.323924	−	0.187018i	0.653140	+	0.757237i	$0.273451\pi$
$522$		0			0
$523$	−27.5977	+	7.39479i	−1.20677	+	0.323352i	−0.805492	−	0.592607i	$-0.798099\pi$
$523$	−27.5977	+	7.39479i	−1.20677	+	0.323352i	−0.401273	+	0.915958i	$0.631432\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.2261	−	5.41957i	0.881063	−	0.236080i
$528$		0			0
$529$	6.58602	−	3.80244i	0.286349	−	0.165324i
$530$		0			0
$531$		−	4.57242i		−	0.198426i
$532$		0			0
$533$	14.8331	−	14.8331i	0.642495	−	0.642495i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.940355	+	3.50945i	0.0405793	+	0.151444i
$538$		0			0
$539$	24.0370	+	34.8019i	1.03535	+	1.49903i
$540$		0			0
$541$	−8.19049	+	14.1864i	−0.352137	+	0.609919i	−0.986624	−	0.163015i	$-0.947878\pi$
$541$	−8.19049	+	14.1864i	−0.352137	+	0.609919i	0.634487	+	0.772934i	$0.281212\pi$
$542$		0			0
$543$	5.13101	+	1.37485i	0.220193	+	0.0590004i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−31.1848	−	31.1848i	−1.33337	−	1.33337i	−0.902338	−	0.431030i	$-0.858150\pi$
$547$	−31.1848	−	31.1848i	−1.33337	−	1.33337i	−0.431030	−	0.902338i	$-0.641850\pi$
$548$		0			0
$549$	1.95328	+	3.38318i	0.0833640	+	0.144391i
$550$		0			0
$551$	14.3712	+	8.29724i	0.612236	+	0.353474i
$552$		0			0
$553$	−21.6432	−	11.3552i	−0.920361	−	0.482872i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.28447	+	4.79369i	−0.0544245	+	0.203115i	−0.987784	−	0.155827i	$-0.950196\pi$
$557$	−1.28447	+	4.79369i	−0.0544245	+	0.203115i	0.933360	+	0.358942i	$0.116862\pi$
$558$		0			0
$559$	−23.3636			−0.988177
$560$		0			0
$561$	38.9045			1.64255
$562$		0			0
$563$	1.35434	−	5.05448i	0.0570788	−	0.213021i	−0.931496	−	0.363751i	$-0.881496\pi$
$563$	1.35434	−	5.05448i	0.0570788	−	0.213021i	0.988575	+	0.150730i	$0.0481625\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.41439	+	2.23596i	0.0593988	+	0.0939014i
$568$		0			0
$569$	8.66634	+	5.00351i	0.363312	+	0.209758i	0.670533	−	0.741880i	$-0.266066\pi$
$569$	8.66634	+	5.00351i	0.363312	+	0.209758i	−0.307221	+	0.951638i	$0.599399\pi$
$570$		0			0
$571$	−12.1544	−	21.0521i	−0.508646	−	0.881001i	−0.999950	−	0.0100130i	$-0.996813\pi$
$571$	−12.1544	−	21.0521i	−0.508646	−	0.881001i	0.491303	−	0.870988i	$-0.336521\pi$
$572$		0			0
$573$	−6.04266	−	6.04266i	−0.252436	−	0.252436i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	45.4389	+	12.1753i	1.89164	+	0.506865i	0.998352	+	0.0573900i	$0.0182778\pi$
$577$	45.4389	+	12.1753i	1.89164	+	0.506865i	0.893293	+	0.449475i	$0.148389\pi$
$578$		0			0
$579$	1.09938	−	1.90418i	0.0456887	−	0.0791351i
$580$		0			0
$581$	1.24052	+	1.14408i	0.0514656	+	0.0474644i
$582$		0			0
$583$	−5.47381	−	20.4285i	−0.226702	−	0.846064i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.39281	−	9.39281i	0.387683	−	0.387683i	−0.486177	−	0.873860i	$-0.661609\pi$
$587$	9.39281	−	9.39281i	0.387683	−	0.387683i	0.873860	+	0.486177i	$0.161609\pi$
$588$		0			0
$589$		−	21.9412i		−	0.904072i
$590$		0			0
$591$	15.7604	−	9.09927i	0.648296	−	0.374294i
$592$		0			0
$593$	−31.3087	+	8.38913i	−1.28569	+	0.344500i	−0.836023	−	0.548694i	$-0.815125\pi$
$593$	−31.3087	+	8.38913i	−1.28569	+	0.344500i	−0.449670	+	0.893195i	$0.648458\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.13016	+	2.17847i	−0.332745	+	0.0891588i
$598$		0			0
$599$	−11.5175	+	6.64962i	−0.470591	+	0.271696i	−0.716487	−	0.697600i	$-0.754251\pi$
$599$	−11.5175	+	6.64962i	−0.470591	+	0.271696i	0.245896	+	0.969296i	$0.420918\pi$
$600$		0			0
$601$			9.90700i			0.404115i	0.979374	+	0.202058i	$0.0647628\pi$
$601$			9.90700i			0.404115i	−0.979374	+	0.202058i	$0.935237\pi$
$602$		0			0
$603$	8.10974	−	8.10974i	0.330254	−	0.330254i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.78001	+	25.3033i	0.275192	+	1.02703i	0.955713	+	0.294301i	$0.0950870\pi$
$607$	6.78001	+	25.3033i	0.275192	+	1.02703i	−0.680521	+	0.732729i	$0.738246\pi$
$608$		0			0
$609$	6.34881	+	1.42890i	0.257267	+	0.0579019i
$610$		0			0
$611$	10.3367	−	17.9037i	0.418178	−	0.724305i
$612$		0			0
$613$	29.1867	+	7.82055i	1.17884	+	0.315869i	0.794466	−	0.607308i	$-0.207751\pi$
$613$	29.1867	+	7.82055i	1.17884	+	0.315869i	0.384374	+	0.923178i	$0.374417\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.8767	−	17.8767i	−0.719689	−	0.719689i	0.248853	−	0.968541i	$-0.419946\pi$
$617$	−17.8767	−	17.8767i	−0.719689	−	0.719689i	−0.968541	+	0.248853i	$0.919946\pi$
$618$		0			0
$619$	6.13720	+	10.6299i	0.246675	+	0.427253i	0.962601	−	0.270922i	$-0.0873287\pi$
$619$	6.13720	+	10.6299i	0.246675	+	0.427253i	−0.715926	+	0.698176i	$0.753995\pi$
$620$		0			0
$621$	3.39799	+	1.96183i	0.136357	+	0.0787255i
$622$		0			0
$623$	−14.8663	+	28.3355i	−0.595607	+	1.13524i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	10.5509	−	39.3764i	0.421361	−	1.57254i
$628$		0			0
$629$	−3.96298			−0.158014
$630$		0			0
$631$	−31.5840			−1.25734			−0.628670	−	0.777672i	$-0.716400\pi$
$631$	−31.5840			−1.25734			−0.628670	+	0.777672i	$0.716400\pi$
$632$		0			0
$633$	−6.95516	+	25.9570i	−0.276443	+	1.03170i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−16.5148	−	14.0392i	−0.654339	−	0.556255i
$638$		0			0
$639$	−4.68281	−	2.70362i	−0.185249	−	0.106954i
$640$		0			0
$641$	6.20316	+	10.7442i	0.245010	+	0.424370i	0.962134	−	0.272575i	$-0.0878754\pi$
$641$	6.20316	+	10.7442i	0.245010	+	0.424370i	−0.717124	+	0.696945i	$0.754542\pi$
$642$		0			0
$643$	−1.22763	−	1.22763i	−0.0484129	−	0.0484129i	0.682486	−	0.730899i	$-0.260899\pi$
$643$	−1.22763	−	1.22763i	−0.0484129	−	0.0484129i	−0.730899	+	0.682486i	$0.760899\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.5686	+	4.70749i	0.690693	+	0.185070i	0.587058	−	0.809545i	$-0.300286\pi$
$647$	17.5686	+	4.70749i	0.690693	+	0.185070i	0.103635	+	0.994615i	$0.466953\pi$
$648$		0			0
$649$	−13.8139	+	23.9264i	−0.542244	+	0.939195i
$650$		0			0
$651$	−2.56102	−	8.21440i	−0.100374	−	0.321948i
$652$		0			0
$653$	−10.2461	−	38.2391i	−0.400962	−	1.49641i	−0.811383	−	0.584514i	$-0.801285\pi$
$653$	−10.2461	−	38.2391i	−0.400962	−	1.49641i	0.410421	−	0.911896i	$-0.365382\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−5.11931	+	5.11931i	−0.199723	+	0.199723i
$658$		0			0
$659$		−	15.3001i		−	0.596008i	−0.954565	−	0.298004i	$-0.903679\pi$
$659$		−	15.3001i		−	0.596008i	0.954565	−	0.298004i	$-0.0963209\pi$
$660$		0			0
$661$	36.8540	−	21.2777i	1.43346	−	0.827606i	0.436073	−	0.899911i	$-0.356369\pi$
$661$	36.8540	−	21.2777i	1.43346	−	0.827606i	0.997383	+	0.0723057i	$0.0230357\pi$
$662$		0			0
$663$	−19.2583	+	5.16025i	−0.747930	+	0.200407i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.32199	−	2.49782i	0.360949	−	0.0967159i
$668$		0			0
$669$	21.0619	−	12.1601i	0.814298	−	0.470135i
$670$		0			0
$671$		−	23.6046i		−	0.911244i
$672$		0			0
$673$	23.1774	−	23.1774i	0.893422	−	0.893422i	−0.101421	−	0.994844i	$-0.532339\pi$
$673$	23.1774	−	23.1774i	0.893422	−	0.893422i	0.994844	+	0.101421i	$0.0323390\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.02498	−	29.9496i	−0.308425	−	1.15106i	−0.929957	−	0.367669i	$-0.880156\pi$
$677$	−8.02498	−	29.9496i	−0.308425	−	1.15106i	0.621532	−	0.783389i	$-0.286511\pi$
$678$		0			0
$679$	−24.4137	+	26.4717i	−0.936912	+	1.01589i
$680$		0			0
$681$	−4.61133	+	7.98706i	−0.176707	+	0.306065i
$682$		0			0
$683$	−19.1248	−	5.12448i	−0.731790	−	0.196083i	−0.126364	−	0.991984i	$-0.540331\pi$
$683$	−19.1248	−	5.12448i	−0.731790	−	0.196083i	−0.605426	+	0.795901i	$0.706997\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4.99568	+	4.99568i	0.190597	+	0.190597i
$688$		0			0
$689$	5.41924	+	9.38639i	0.206456	+	0.357593i
$690$		0			0
$691$	−2.29096	−	1.32269i	−0.0871524	−	0.0503174i	0.455790	−	0.890087i	$-0.349357\pi$
$691$	−2.29096	−	1.32269i	−0.0871524	−	0.0503174i	−0.542943	+	0.839770i	$0.682690\pi$
$692$		0			0
$693$	−0.646032	−	15.9733i	−0.0245407	−	0.606776i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	11.2893	−	42.1322i	0.427612	−	1.59587i
$698$		0			0
$699$	−13.8075			−0.522247
$700$		0			0
$701$	51.3521			1.93954			0.969772	−	0.244015i	$-0.0784645\pi$
$701$	51.3521			1.93954			0.969772	+	0.244015i	$0.0784645\pi$
$702$		0			0
$703$	−1.07476	+	4.01105i	−0.0405352	+	0.151280i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.3365	−	14.1293i	0.840050	−	0.531387i
$708$		0			0
$709$	−2.96456	−	1.71159i	−0.111337	−	0.0642802i	0.443298	−	0.896374i	$-0.353808\pi$
$709$	−2.96456	−	1.71159i	−0.111337	−	0.0642802i	−0.554634	+	0.832094i	$0.687142\pi$
$710$		0			0
$711$	4.61893	+	8.00023i	0.173224	+	0.300032i
$712$		0			0
$713$	−9.02291	−	9.02291i	−0.337911	−	0.337911i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.60252	−	1.76914i	−0.246576	−	0.0660697i
$718$		0			0
$719$	−12.8855	+	22.3183i	−0.480547	+	0.832333i	−0.999751	−	0.0223181i	$-0.992895\pi$
$719$	−12.8855	+	22.3183i	−0.480547	+	0.832333i	0.519203	+	0.854651i	$0.326229\pi$
$720$		0			0
$721$	−25.5569	+	7.96795i	−0.951790	+	0.296742i
$722$		0			0
$723$	1.51292	+	5.64630i	0.0562662	+	0.209988i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.26918	+	8.26918i	−0.306687	+	0.306687i	−0.843623	−	0.536936i	$-0.819582\pi$
$727$	−8.26918	+	8.26918i	−0.306687	+	0.306687i	0.536936	+	0.843623i	$0.319582\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−42.0720	+	24.2903i	−1.55609	+	0.898409i
$732$		0			0
$733$	29.6885	−	7.95500i	1.09657	−	0.293825i	0.335202	−	0.942146i	$-0.391195\pi$
$733$	29.6885	−	7.95500i	1.09657	−	0.293825i	0.761367	+	0.648322i	$0.224529\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−66.9371	+	17.9358i	−2.46566	+	0.660672i
$738$		0			0
$739$	9.72713	−	5.61596i	0.357818	−	0.206586i	−0.310305	−	0.950637i	$-0.600431\pi$
$739$	9.72713	−	5.61596i	0.357818	−	0.206586i	0.668123	+	0.744051i	$0.267098\pi$
$740$		0			0
$741$			20.8913i			0.767463i
$742$		0			0
$743$	−25.1411	+	25.1411i	−0.922337	+	0.922337i	−0.997194	−	0.0748575i	$-0.976150\pi$
$743$	−25.1411	+	25.1411i	−0.922337	+	0.922337i	0.0748575	+	0.997194i	$0.476150\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.165083	−	0.616100i	−0.00604008	−	0.0225419i
$748$		0			0
$749$	−26.8252	+	8.36334i	−0.980170	+	0.305590i
$750$		0			0
$751$	0.0202455	−	0.0350663i	0.000738769	−	0.00127959i	−0.865656	−	0.500640i	$-0.833098\pi$
$751$	0.0202455	−	0.0350663i	0.000738769	−	0.00127959i	0.866395	+	0.499360i	$0.166432\pi$
$752$		0			0
$753$	13.8019	+	3.69819i	0.502967	+	0.134770i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	10.2352	+	10.2352i	0.372005	+	0.372005i	0.868207	−	0.496202i	$-0.165272\pi$
$757$	10.2352	+	10.2352i	0.372005	+	0.372005i	−0.496202	+	0.868207i	$0.665272\pi$
$758$		0			0
$759$	−11.8539	−	20.5316i	−0.430271	−	0.745251i
$760$		0			0
$761$	−45.7365	−	26.4060i	−1.65795	−	0.957216i	−0.973660	−	0.228003i	$-0.926780\pi$
$761$	−45.7365	−	26.4060i	−1.65795	−	0.957216i	−0.684287	−	0.729213i	$-0.739886\pi$
$762$		0			0
$763$	31.7645	−	20.0931i	1.14995	−	0.727421i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.66453	−	13.6762i	0.132318	−	0.493819i
$768$		0			0
$769$	29.0548			1.04774			0.523872	−	0.851797i	$-0.324487\pi$
$769$	29.0548			1.04774			0.523872	+	0.851797i	$0.324487\pi$
$770$		0			0
$771$	−4.85489			−0.174845
$772$		0			0
$773$	4.55647	−	17.0050i	0.163885	−	0.611627i	−0.834295	−	0.551319i	$-0.814125\pi$
$773$	4.55647	−	17.0050i	0.163885	−	0.611627i	0.998180	−	0.0603084i	$-0.0192084\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.0658076	+	1.62711i	0.00236084	+	0.0583724i
$778$		0			0
$779$	−39.5816	−	22.8525i	−1.41816	−	0.818774i
$780$		0			0
$781$	16.3361	+	28.2949i	0.584551	+	1.01247i
$782$		0			0
$783$	−1.73924	−	1.73924i	−0.0621552	−	0.0621552i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.26224	+	0.338216i	0.0449939	+	0.0120561i	0.281246	−	0.959636i	$-0.409252\pi$
$787$	1.26224	+	0.338216i	0.0449939	+	0.0120561i	−0.236252	+	0.971692i	$0.575919\pi$
$788$		0			0
$789$	3.74242	−	6.48206i	0.133234	−	0.230767i
$790$		0			0
$791$	−5.99091	+	6.49593i	−0.213012	+	0.230969i
$792$		0			0
$793$	3.13088	+	11.6846i	0.111181	+	0.414933i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−35.7992	+	35.7992i	−1.26807	+	1.26807i	−0.320988	+	0.947083i	$0.604015\pi$
$797$	−35.7992	+	35.7992i	−1.26807	+	1.26807i	−0.947083	+	0.320988i	$0.895985\pi$
$798$		0			0
$799$		−	42.9867i		−	1.52076i
$800$		0			0
$801$	10.4740	−	6.04716i	0.370080	−	0.213666i
$802$		0			0
$803$	42.2544	−	11.3220i	1.49112	−	0.399546i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.23702	+	2.47505i	−0.325159	+	0.0871260i
$808$		0			0
$809$	0.814233	−	0.470097i	0.0286269	−	0.0165277i	−0.485618	−	0.874171i	$-0.661405\pi$
$809$	0.814233	−	0.470097i	0.0286269	−	0.0165277i	0.514245	+	0.857643i	$0.328072\pi$
$810$		0			0
$811$		−	19.8145i		−	0.695781i	−0.937535	−	0.347890i	$-0.886898\pi$
$811$		−	19.8145i		−	0.695781i	0.937535	−	0.347890i	$-0.113102\pi$
$812$		0			0
$813$	−17.1520	+	17.1520i	−0.601548	+	0.601548i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	13.1750	+	49.1699i	0.460936	+	1.72024i
$818$		0			0
$819$	2.43848	+	7.82135i	0.0852074	+	0.273300i
$820$		0			0
$821$	−13.4231	+	23.2495i	−0.468469	+	0.811413i	−0.999351	−	0.0360334i	$-0.988528\pi$
$821$	−13.4231	+	23.2495i	−0.468469	+	0.811413i	0.530881	+	0.847446i	$0.321861\pi$
$822$		0			0
$823$	1.09611	+	0.293703i	0.0382081	+	0.0102378i	0.277872	−	0.960618i	$-0.410371\pi$
$823$	1.09611	+	0.293703i	0.0382081	+	0.0102378i	−0.239664	+	0.970856i	$0.577037\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.6331	−	10.6331i	−0.369749	−	0.369749i	0.497636	−	0.867386i	$-0.334201\pi$
$827$	−10.6331	−	10.6331i	−0.369749	−	0.369749i	−0.867386	+	0.497636i	$0.834201\pi$
$828$		0			0
$829$	2.79297	+	4.83757i	0.0970038	+	0.168016i	0.910443	−	0.413634i	$-0.135741\pi$
$829$	2.79297	+	4.83757i	0.0970038	+	0.168016i	−0.813439	+	0.581650i	$0.802407\pi$
$830$		0			0
$831$	2.66978	+	1.54140i	0.0926138	+	0.0534706i
$832$		0			0
$833$	−44.3350	−	8.11135i	−1.53612	−	0.281042i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.841717	+	3.14133i	−0.0290940	+	0.108580i
$838$		0			0
$839$	17.8150			0.615042			0.307521	−	0.951541i	$-0.400500\pi$
$839$	17.8150			0.615042			0.307521	+	0.951541i	$0.400500\pi$
$840$		0			0
$841$	22.9501			0.791384
$842$		0			0
$843$	−1.41164	+	5.26832i	−0.0486196	+	0.181451i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−31.3560	+	59.7649i	−1.07740	+	2.05355i
$848$		0			0
$849$	−6.26160	−	3.61514i	−0.214898	−	0.124071i
$850$		0			0
$851$	1.20749	+	2.09144i	0.0413924	+	0.0716937i
$852$		0			0
$853$	19.9392	+	19.9392i	0.682707	+	0.682707i	0.960609	−	0.277902i	$-0.0896392\pi$
$853$	19.9392	+	19.9392i	0.682707	+	0.682707i	−0.277902	+	0.960609i	$0.589639\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.8413	+	3.97672i	0.506970	+	0.135842i	0.503233	−	0.864151i	$-0.332144\pi$
$857$	14.8413	+	3.97672i	0.506970	+	0.135842i	0.00373690	+	0.999993i	$0.498811\pi$
$858$		0			0
$859$	5.75815	−	9.97341i	0.196465	−	0.340288i	−0.750914	−	0.660399i	$-0.770387\pi$
$859$	5.75815	−	9.97341i	0.196465	−	0.340288i	0.947380	+	0.320111i	$0.103720\pi$
$860$		0			0
$861$	−17.4860	−	3.93551i	−0.595922	−	0.134122i
$862$		0			0
$863$	1.25094	+	4.66858i	0.0425826	+	0.158920i	0.983943	−	0.178482i	$-0.0571185\pi$
$863$	1.25094	+	4.66858i	0.0425826	+	0.158920i	−0.941361	+	0.337402i	$0.890452\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−17.2936	+	17.2936i	−0.587322	+	0.587322i
$868$		0			0
$869$		−	55.8178i		−	1.89349i
$870$		0			0
$871$	30.7559	−	17.7569i	1.04212	−	0.601671i
$872$		0			0
$873$	13.1471	−	3.52274i	0.444960	−	0.119227i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−3.04462	+	0.815805i	−0.102810	+	0.0275478i	−0.309857	−	0.950783i	$-0.600281\pi$
$877$	−3.04462	+	0.815805i	−0.102810	+	0.0275478i	0.207047	+	0.978331i	$0.433615\pi$
$878$		0			0
$879$	−12.3467	+	7.12839i	−0.416445	+	0.240435i
$880$		0			0
$881$		−	29.4612i		−	0.992573i	−0.868159	−	0.496287i	$-0.834697\pi$
$881$		−	29.4612i		−	0.992573i	0.868159	−	0.496287i	$-0.165303\pi$
$882$		0			0
$883$	3.13917	−	3.13917i	0.105641	−	0.105641i	−0.652310	−	0.757952i	$-0.726200\pi$
$883$	3.13917	−	3.13917i	0.105641	−	0.105641i	0.757952	+	0.652310i	$0.226200\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.68563	+	13.7550i	0.123751	+	0.461846i	0.999792	−	0.0203909i	$-0.00649108\pi$
$887$	3.68563	+	13.7550i	0.123751	+	0.461846i	−0.876041	+	0.482237i	$0.839824\pi$
$888$		0			0
$889$	25.2887	+	23.3226i	0.848155	+	0.782215i
$890$		0			0
$891$	−3.02114	+	5.23277i	−0.101212	+	0.175304i
$892$		0			0
$893$	−43.5081	−	11.6580i	−1.45594	−	0.390119i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	8.59117	+	8.59117i	0.286851	+	0.286851i
$898$		0			0
$899$	3.99957	+	6.92746i	0.133393	+	0.231044i
$900$		0			0
$901$	19.5174	+	11.2684i	0.650218	+	0.375403i
$902$		0			0
$903$	10.6717	+	16.8705i	0.355132	+	0.561415i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−11.4313	+	42.6623i	−0.379571	+	1.41658i	0.466979	+	0.884268i	$0.345342\pi$
$907$	−11.4313	+	42.6623i	−0.379571	+	1.41658i	−0.846550	+	0.532309i	$0.821324\pi$
$908$		0			0
$909$	−9.98968			−0.331337
$910$		0			0
$911$	−13.5244			−0.448084			−0.224042	−	0.974580i	$-0.571925\pi$
$911$	−13.5244			−0.448084			−0.224042	+	0.974580i	$0.571925\pi$
$912$		0			0
$913$	−0.997481	+	3.72265i	−0.0330118	+	0.123202i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	32.7155	+	17.1643i	1.08036	+	0.566817i
$918$		0			0
$919$	44.9076	+	25.9274i	1.48137	+	0.855267i	0.999777	−	0.0211294i	$-0.00672620\pi$
$919$	44.9076	+	25.9274i	1.48137	+	0.855267i	0.481590	+	0.876397i	$0.340060\pi$
$920$		0			0
$921$	−1.17208	−	2.03010i	−0.0386212	−	0.0668939i
$922$		0			0
$923$	−11.8396	−	11.8396i	−0.389705	−	0.389705i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	9.77343	+	2.61878i	0.321002	+	0.0860121i
$928$		0			0
$929$	23.9702	−	41.5177i	0.786438	−	1.36215i	−0.141698	−	0.989910i	$-0.545256\pi$
$929$	23.9702	−	41.5177i	0.786438	−	1.36215i	0.928136	−	0.372241i	$-0.121410\pi$
$930$		0			0
$931$	−20.2334	+	42.6730i	−0.663122	+	1.39855i
$932$		0			0
$933$	−3.48777	−	13.0165i	−0.114184	−	0.426142i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.89255	−	3.89255i	0.127164	−	0.127164i	−0.640660	−	0.767824i	$-0.721339\pi$
$937$	3.89255	−	3.89255i	0.127164	−	0.127164i	0.767824	+	0.640660i	$0.221339\pi$
$938$		0			0
$939$			7.83318i			0.255626i
$940$		0			0
$941$	−42.1107	+	24.3126i	−1.37277	+	0.792568i	−0.991276	−	0.131803i	$-0.957923\pi$
$941$	−42.1107	+	24.3126i	−1.37277	+	0.792568i	−0.381493	+	0.924372i	$0.624590\pi$
$942$		0			0
$943$	−25.6748	+	6.87955i	−0.836087	+	0.224029i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	44.2727	−	11.8628i	1.43867	−	0.385490i	0.546601	−	0.837393i	$-0.315921\pi$
$947$	44.2727	−	11.8628i	1.43867	−	0.385490i	0.892067	+	0.451903i	$0.149255\pi$
$948$		0			0
$949$	−19.4148	+	11.2091i	−0.630231	+	0.363864i
$950$		0			0
$951$			26.0052i			0.843277i
$952$		0			0
$953$	−25.2364	+	25.2364i	−0.817488	+	0.817488i	−0.985743	−	0.168255i	$-0.946187\pi$
$953$	−25.2364	+	25.2364i	−0.817488	+	0.817488i	0.168255	+	0.985743i	$0.446187\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	3.84654	+	14.3555i	0.124341	+	0.464047i
$958$		0			0
$959$	−7.60916	+	33.8086i	−0.245713	+	1.09174i
$960$		0			0
$961$	−10.2118	+	17.6873i	−0.329412	+	0.570558i
$962$		0			0
$963$	10.2584	+	2.74873i	0.330573	+	0.0885767i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−9.64834	−	9.64834i	−0.310270	−	0.310270i	0.534744	−	0.845014i	$-0.320408\pi$
$967$	−9.64834	−	9.64834i	−0.310270	−	0.310270i	−0.845014	+	0.534744i	$0.820408\pi$
$968$		0			0
$969$	21.7199	+	37.6201i	0.697745	+	1.20853i
$970$		0			0
$971$	−6.20795	−	3.58416i	−0.199223	−	0.115021i	0.397070	−	0.917788i	$-0.370027\pi$
$971$	−6.20795	−	3.58416i	−0.199223	−	0.115021i	−0.596293	+	0.802767i	$0.703360\pi$
$972$		0			0
$973$	−59.5026	+	2.40655i	−1.90757	+	0.0771504i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.5776	+	39.4761i	−0.338407	+	1.26295i	0.561722	+	0.827326i	$0.310139\pi$
$977$	−10.5776	+	39.4761i	−0.338407	+	1.26295i	−0.900128	+	0.435625i	$0.856528\pi$
$978$		0			0
$979$	−73.0773			−2.33556
$980$		0			0
$981$	−14.2062			−0.453570
$982$		0			0
$983$	−10.1457	+	37.8643i	−0.323598	+	1.20768i	0.592116	+	0.805853i	$0.298293\pi$
$983$	−10.1457	+	37.8643i	−0.323598	+	1.20768i	−0.915714	+	0.401832i	$0.868374\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−17.6494	+	0.713820i	−0.561787	+	0.0227211i
$988$		0			0
$989$	25.6382	+	14.8022i	0.815246	+	0.470682i
$990$		0			0
$991$	15.3183	+	26.5321i	0.486603	+	0.842821i	0.999881	−	0.0154009i	$-0.00490245\pi$
$991$	15.3183	+	26.5321i	0.486603	+	0.842821i	−0.513278	+	0.858222i	$0.671569\pi$
$992$		0			0
$993$	−2.29511	−	2.29511i	−0.0728331	−	0.0728331i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	26.4853	+	7.09671i	0.838797	+	0.224755i	0.652548	−	0.757748i	$-0.273700\pi$
$997$	26.4853	+	7.09671i	0.838797	+	0.224755i	0.186249	+	0.982503i	$0.440367\pi$
$998$		0			0
$999$	0.307747	−	0.533033i	0.00973668	−	0.0168644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.e.1657.4		32
5.2	odd	4		420.2.bo.a.313.8	yes	32
5.3	odd	4	inner	2100.2.ce.e.1993.1		32
5.4	even	2		420.2.bo.a.397.6	yes	32
7.3	odd	6	inner	2100.2.ce.e.157.1		32
15.2	even	4		1260.2.dq.c.1153.2		32
15.14	odd	2		1260.2.dq.c.397.5		32
35.2	odd	12		2940.2.x.c.1273.8		32
35.3	even	12	inner	2100.2.ce.e.493.4		32
35.9	even	6		2940.2.x.c.97.12		32
35.12	even	12		2940.2.x.c.1273.12		32
35.17	even	12		420.2.bo.a.73.6	✓	32
35.19	odd	6		2940.2.x.c.97.8		32
35.24	odd	6		420.2.bo.a.157.8	yes	32
105.17	odd	12		1260.2.dq.c.73.5		32
105.59	even	6		1260.2.dq.c.577.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.6	✓	32	35.17	even	12
420.2.bo.a.157.8	yes	32	35.24	odd	6
420.2.bo.a.313.8	yes	32	5.2	odd	4
420.2.bo.a.397.6	yes	32	5.4	even	2
1260.2.dq.c.73.5		32	105.17	odd	12
1260.2.dq.c.397.5		32	15.14	odd	2
1260.2.dq.c.577.2		32	105.59	even	6
1260.2.dq.c.1153.2		32	15.2	even	4
2100.2.ce.e.157.1		32	7.3	odd	6	inner
2100.2.ce.e.493.4		32	35.3	even	12	inner
2100.2.ce.e.1657.4		32	1.1	even	1	trivial
2100.2.ce.e.1993.1		32	5.3	odd	4	inner
2940.2.x.c.97.8		32	35.19	odd	6
2940.2.x.c.97.12		32	35.9	even	6
2940.2.x.c.1273.8		32	35.2	odd	12
2940.2.x.c.1273.12		32	35.12	even	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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{3} +(2.64359 - 0.106918i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{3} +(2.64359 - 0.106918i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(3.02114 + 5.23277i) q^{11} +(-2.18958 - 2.18958i) q^{13} +(-6.21931 - 1.66646i) q^{17} +(-3.37334 + 5.84280i) q^{19} +(-0.580936 + 2.58118i) q^{21} +(1.01552 + 3.78997i) q^{23} +(0.707107 - 0.707107i) q^{27} -2.45965i q^{29} +(-2.81644 + 1.62607i) q^{31} +(-5.83640 + 1.56386i) q^{33} +(0.594521 - 0.159302i) q^{37} +(2.68168 - 1.54827i) q^{39} +6.77442i q^{41} +(5.33519 - 5.33519i) q^{43} +(1.72795 + 6.44881i) q^{47} +(6.97714 - 0.565297i) q^{49} +(3.21935 - 5.57608i) q^{51} +(-3.38093 - 0.905917i) q^{53} +(-4.77063 - 4.77063i) q^{57} +(2.28621 + 3.95983i) q^{59} +(-3.38318 - 1.95328i) q^{61} +(-2.34288 - 1.22920i) q^{63} +(-2.96837 + 11.0781i) q^{67} -3.92366 q^{69} +5.40725 q^{71} +(1.87380 - 6.99311i) q^{73} +(8.54614 + 13.5103i) q^{77} +(-8.00023 - 4.61893i) q^{79} +(0.500000 + 0.866025i) q^{81} +(0.451016 + 0.451016i) q^{83} +(2.37584 + 0.636604i) q^{87} +(-6.04716 + 10.4740i) q^{89} +(-6.02246 - 5.55425i) q^{91} +(-0.841717 - 3.14133i) q^{93} +(-9.62431 + 9.62431i) q^{97} -6.04229i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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Representations

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Database

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