LMFDB - Embedded newform 2100.2.ce.e.157.4

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			157.4
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.e.1993.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{3} +(2.02043 + 1.70817i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{3} +(2.02043 + 1.70817i) q^{7} +(0.866025 - 0.500000i) q^{9} +(1.21556 - 2.10542i) q^{11} +(-0.728866 - 0.728866i) q^{13} +(1.96555 + 7.33552i) q^{17} +(-1.84965 - 3.20369i) q^{19} +(-2.39370 - 1.12704i) q^{21} +(2.83634 + 0.759994i) q^{23} +(-0.707107 + 0.707107i) q^{27} -1.99120i q^{29} +(6.02262 + 3.47716i) q^{31} +(-0.629222 + 2.34829i) q^{33} +(2.20273 - 8.22068i) q^{37} +(0.892675 + 0.515386i) q^{39} -1.08701i q^{41} +(-5.91785 + 5.91785i) q^{43} +(4.81085 + 1.28906i) q^{47} +(1.16431 + 6.90249i) q^{49} +(-3.79715 - 6.57685i) q^{51} +(-1.76035 - 6.56972i) q^{53} +(2.61580 + 2.61580i) q^{57} +(1.39403 - 2.41454i) q^{59} +(0.217574 - 0.125616i) q^{61} +(2.60383 + 0.469102i) q^{63} +(-7.79096 + 2.08758i) q^{67} -2.93639 q^{69} +14.5737 q^{71} +(-6.46450 + 1.73216i) q^{73} +(6.05238 - 2.17747i) q^{77} +(-9.54459 + 5.51057i) q^{79} +(0.500000 - 0.866025i) q^{81} +(9.90994 + 9.90994i) q^{83} +(0.515361 + 1.92335i) q^{87} +(5.81468 + 10.0713i) q^{89} +(-0.227598 - 2.71765i) q^{91} +(-6.71736 - 1.79991i) q^{93} +(10.8833 - 10.8833i) q^{97} -2.43113i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	2.02043	+	1.70817i	0.763652	+	0.645628i
$7$	2.02043	+	1.70817i	0.763652	+	0.645628i
$8$		0			0
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	1.21556	−	2.10542i	0.366506	−	0.634808i	−0.622510	−	0.782612i	$-0.713887\pi$
$11$	1.21556	−	2.10542i	0.366506	−	0.634808i	0.989017	+	0.147804i	$0.0472204\pi$
$12$		0			0
$13$	−0.728866	−	0.728866i	−0.202151	−	0.202151i	0.598770	−	0.800921i	$-0.295656\pi$
$13$	−0.728866	−	0.728866i	−0.202151	−	0.202151i	−0.800921	+	0.598770i	$0.795656\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.96555	+	7.33552i	0.476715	+	1.77913i	0.614776	+	0.788702i	$0.289247\pi$
$17$	1.96555	+	7.33552i	0.476715	+	1.77913i	−0.138060	+	0.990424i	$0.544087\pi$
$18$		0			0
$19$	−1.84965	−	3.20369i	−0.424339	−	0.734977i	0.572019	−	0.820240i	$-0.306160\pi$
$19$	−1.84965	−	3.20369i	−0.424339	−	0.734977i	−0.996358	+	0.0852629i	$0.972827\pi$
$20$		0			0
$21$	−2.39370	−	1.12704i	−0.522347	−	0.245940i
$22$		0			0
$23$	2.83634	+	0.759994i	0.591417	+	0.158470i	0.542101	−	0.840313i	$-0.317629\pi$
$23$	2.83634	+	0.759994i	0.591417	+	0.158470i	0.0493165	+	0.998783i	$0.484296\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	1.99120i		−	0.369757i	−0.982761	−	0.184878i	$-0.940811\pi$
$29$		−	1.99120i		−	0.369757i	0.982761	−	0.184878i	$-0.0591891\pi$
$30$		0			0
$31$	6.02262	+	3.47716i	1.08169	+	0.624517i	0.931353	−	0.364117i	$-0.118629\pi$
$31$	6.02262	+	3.47716i	1.08169	+	0.624517i	0.150342	+	0.988634i	$0.451963\pi$
$32$		0			0
$33$	−0.629222	+	2.34829i	−0.109534	+	0.408785i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.20273	−	8.22068i	0.362126	−	1.35147i	−0.509150	−	0.860678i	$-0.670040\pi$
$37$	2.20273	−	8.22068i	0.362126	−	1.35147i	0.871276	−	0.490794i	$-0.163293\pi$
$38$		0			0
$39$	0.892675	+	0.515386i	0.142942	+	0.0825278i
$40$		0			0
$41$		−	1.08701i		−	0.169762i	−0.996391	−	0.0848810i	$-0.972949\pi$
$41$		−	1.08701i		−	0.169762i	0.996391	−	0.0848810i	$-0.0270510\pi$
$42$		0			0
$43$	−5.91785	+	5.91785i	−0.902464	+	0.902464i	−0.995649	−	0.0931848i	$-0.970295\pi$
$43$	−5.91785	+	5.91785i	−0.902464	+	0.902464i	0.0931848	+	0.995649i	$0.470295\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.81085	+	1.28906i	0.701735	+	0.188029i	0.592007	−	0.805932i	$-0.298336\pi$
$47$	4.81085	+	1.28906i	0.701735	+	0.188029i	0.109727	+	0.993962i	$0.465002\pi$
$48$		0			0
$49$	1.16431	+	6.90249i	0.166329	+	0.986070i
$50$		0			0
$51$	−3.79715	−	6.57685i	−0.531707	−	0.920943i
$52$		0			0
$53$	−1.76035	−	6.56972i	−0.241803	−	0.902420i	−0.974964	−	0.222365i	$-0.928622\pi$
$53$	−1.76035	−	6.56972i	−0.241803	−	0.902420i	0.733161	−	0.680055i	$-0.238044\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.61580	+	2.61580i	0.346472	+	0.346472i
$58$		0			0
$59$	1.39403	−	2.41454i	0.181488	−	0.314346i	−0.760900	−	0.648870i	$-0.775242\pi$
$59$	1.39403	−	2.41454i	0.181488	−	0.314346i	0.942387	+	0.334523i	$0.108575\pi$
$60$		0			0
$61$	0.217574	−	0.125616i	0.0278575	−	0.0160835i	−0.486007	−	0.873955i	$-0.661547\pi$
$61$	0.217574	−	0.125616i	0.0278575	−	0.0160835i	0.513864	+	0.857872i	$0.328214\pi$
$62$		0			0
$63$	2.60383	+	0.469102i	0.328052	+	0.0591013i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.79096	+	2.08758i	−0.951818	+	0.255039i	−0.701133	−	0.713030i	$-0.747322\pi$
$67$	−7.79096	+	2.08758i	−0.951818	+	0.255039i	−0.250684	+	0.968069i	$0.580656\pi$
$68$		0			0
$69$	−2.93639			−0.353500
$70$		0			0
$71$	14.5737			1.72958			0.864790	−	0.502133i	$-0.167451\pi$
$71$	14.5737			1.72958			0.864790	+	0.502133i	$0.167451\pi$
$72$		0			0
$73$	−6.46450	+	1.73216i	−0.756612	+	0.202734i	−0.616449	−	0.787395i	$-0.711429\pi$
$73$	−6.46450	+	1.73216i	−0.756612	+	0.202734i	−0.140163	+	0.990128i	$0.544763\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.05238	−	2.17747i	0.689733	−	0.248146i
$78$		0			0
$79$	−9.54459	+	5.51057i	−1.07385	+	0.619987i	−0.929231	−	0.369500i	$-0.879529\pi$
$79$	−9.54459	+	5.51057i	−1.07385	+	0.619987i	−0.144619	+	0.989487i	$0.546196\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	9.90994	+	9.90994i	1.08776	+	1.08776i	0.995759	+	0.0919976i	$0.0293252\pi$
$83$	9.90994	+	9.90994i	1.08776	+	1.08776i	0.0919976	+	0.995759i	$0.470675\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.515361	+	1.92335i	0.0552525	+	0.206205i
$88$		0			0
$89$	5.81468	+	10.0713i	0.616354	+	1.06756i	0.990145	+	0.140044i	$0.0447244\pi$
$89$	5.81468	+	10.0713i	0.616354	+	1.06756i	−0.373791	+	0.927513i	$0.621942\pi$
$90$		0			0
$91$	−0.227598	−	2.71765i	−0.0238587	−	0.284887i
$92$		0			0
$93$	−6.71736	−	1.79991i	−0.696558	−	0.186642i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	10.8833	−	10.8833i	1.10503	−	1.10503i	0.111236	−	0.993794i	$-0.464519\pi$
$97$	10.8833	−	10.8833i	1.10503	−	1.10503i	0.993794	−	0.111236i	$-0.0354808\pi$
$98$		0			0
$99$		−	2.43113i		−	0.244338i
$100$		0			0
$101$	5.44655	+	3.14457i	0.541952	+	0.312896i	0.745870	−	0.666092i	$-0.232034\pi$
$101$	5.44655	+	3.14457i	0.541952	+	0.312896i	−0.203918	+	0.978988i	$0.565367\pi$
$102$		0			0
$103$	−3.90512	+	14.5741i	−0.384782	+	1.43603i	0.453727	+	0.891141i	$0.350094\pi$
$103$	−3.90512	+	14.5741i	−0.384782	+	1.43603i	−0.838510	+	0.544887i	$0.816573\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.78551	+	14.1277i	−0.365960	+	1.36578i	0.500156	+	0.865935i	$0.333276\pi$
$107$	−3.78551	+	14.1277i	−0.365960	+	1.36578i	−0.866115	+	0.499844i	$0.833391\pi$
$108$		0			0
$109$	10.3565	+	5.97935i	0.991976	+	0.572718i	0.905864	−	0.423568i	$-0.139222\pi$
$109$	10.3565	+	5.97935i	0.991976	+	0.572718i	0.0861118	+	0.996285i	$0.472556\pi$
$110$		0			0
$111$			8.51068i			0.807798i
$112$		0			0
$113$	5.10715	−	5.10715i	0.480441	−	0.480441i	−0.424832	−	0.905272i	$-0.639667\pi$
$113$	5.10715	−	5.10715i	0.480441	−	0.480441i	0.905272	+	0.424832i	$0.139667\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.995650	−	0.266783i	−0.0920478	−	0.0246641i
$118$		0			0
$119$	−8.55907	+	18.1784i	−0.784609	+	1.66641i
$120$		0			0
$121$	2.54481	+	4.40773i	0.231346	+	0.400703i
$122$		0			0
$123$	0.281338	+	1.04997i	0.0253674	+	0.0946724i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.0263367	+	0.0263367i	0.00233701	+	0.00233701i	0.708274	−	0.705937i	$-0.249474\pi$
$127$	0.0263367	+	0.0263367i	0.00233701	+	0.00233701i	−0.705937	+	0.708274i	$0.749474\pi$
$128$		0			0
$129$	4.18455	−	7.24786i	0.368429	−	0.638138i
$130$		0			0
$131$	8.58485	−	4.95646i	0.750062	−	0.433048i	−0.0756546	−	0.997134i	$-0.524105\pi$
$131$	8.58485	−	4.95646i	0.750062	−	0.433048i	0.825716	+	0.564086i	$0.190771\pi$
$132$		0			0
$133$	1.73535	−	9.63237i	0.150474	−	0.835232i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.8828	−	3.71987i	1.18608	−	0.317810i	0.388747	−	0.921345i	$-0.372908\pi$
$137$	13.8828	−	3.71987i	1.18608	−	0.317810i	0.797337	+	0.603535i	$0.206241\pi$
$138$		0			0
$139$	11.0917			0.940787			0.470394	−	0.882457i	$-0.344112\pi$
$139$	11.0917			0.940787			0.470394	+	0.882457i	$0.344112\pi$
$140$		0			0
$141$	−4.98056			−0.419439
$142$		0			0
$143$	−2.42055	+	0.648585i	−0.202417	+	0.0542374i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.91113	−	6.36595i	−0.240106	−	0.525055i
$148$		0			0
$149$	−7.66332	+	4.42442i	−0.627804	+	0.362463i	−0.779901	−	0.625903i	$-0.784731\pi$
$149$	−7.66332	+	4.42442i	−0.627804	+	0.362463i	0.152097	+	0.988366i	$0.451397\pi$
$150$		0			0
$151$	−0.901062	+	1.56068i	−0.0733274	+	0.127007i	−0.900358	−	0.435151i	$-0.856695\pi$
$151$	−0.901062	+	1.56068i	−0.0733274	+	0.127007i	0.827030	+	0.562157i	$0.190028\pi$
$152$		0			0
$153$	5.36998	+	5.36998i	0.434137	+	0.434137i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.96972	+	11.0832i	0.237010	+	0.884532i	0.977233	+	0.212171i	$0.0680533\pi$
$157$	2.96972	+	11.0832i	0.237010	+	0.884532i	−0.740223	+	0.672361i	$0.765280\pi$
$158$		0			0
$159$	3.40074	+	5.89025i	0.269696	+	0.467127i
$160$		0			0
$161$	4.43243	+	6.38047i	0.349325	+	0.502851i
$162$		0			0
$163$	−0.303489	−	0.0813198i	−0.0237711	−	0.00636946i	0.246914	−	0.969037i	$-0.420584\pi$
$163$	−0.303489	−	0.0813198i	−0.0237711	−	0.00636946i	−0.270685	+	0.962668i	$0.587250\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.10159	−	2.10159i	0.162626	−	0.162626i	−0.621103	−	0.783729i	$-0.713315\pi$
$167$	2.10159	−	2.10159i	0.162626	−	0.162626i	0.783729	+	0.621103i	$0.213315\pi$
$168$		0			0
$169$		−	11.9375i		−	0.918270i
$170$		0			0
$171$	−3.20369	−	1.84965i	−0.244992	−	0.141446i
$172$		0			0
$173$	−2.54209	+	9.48720i	−0.193271	+	0.721298i	0.799436	+	0.600751i	$0.205132\pi$
$173$	−2.54209	+	9.48720i	−0.193271	+	0.721298i	−0.992708	+	0.120547i	$0.961535\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.721606	+	2.69307i	−0.0542392	+	0.202423i
$178$		0			0
$179$	15.8512	+	9.15169i	1.18477	+	0.684030i	0.957114	−	0.289711i	$-0.0935592\pi$
$179$	15.8512	+	9.15169i	1.18477	+	0.684030i	0.227660	+	0.973741i	$0.426893\pi$
$180$		0			0
$181$		−	20.1817i		−	1.50009i	−0.661387	−	0.750045i	$-0.730032\pi$
$181$		−	20.1817i		−	1.50009i	0.661387	−	0.750045i	$-0.269968\pi$
$182$		0			0
$183$	−0.177648	+	0.177648i	−0.0131321	+	0.0131321i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	17.8336	+	4.77850i	1.30412	+	0.349439i
$188$		0			0
$189$	−2.63652	+	0.220803i	−0.191779	+	0.0160611i
$190$		0			0
$191$	−1.24147	−	2.15029i	−0.0898297	−	0.155590i	0.817609	−	0.575773i	$-0.195299\pi$
$191$	−1.24147	−	2.15029i	−0.0898297	−	0.155590i	−0.907439	+	0.420184i	$0.861966\pi$
$192$		0			0
$193$	−3.44019	−	12.8390i	−0.247630	−	0.924169i	−0.972043	−	0.234802i	$-0.924556\pi$
$193$	−3.44019	−	12.8390i	−0.247630	−	0.924169i	0.724413	−	0.689366i	$-0.242111\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.45204	+	5.45204i	0.388442	+	0.388442i	0.874131	−	0.485690i	$-0.161431\pi$
$197$	5.45204	+	5.45204i	0.388442	+	0.388442i	−0.485690	+	0.874131i	$0.661431\pi$
$198$		0			0
$199$	6.32953	−	10.9631i	0.448689	−	0.777152i	−0.549612	−	0.835420i	$-0.685224\pi$
$199$	6.32953	−	10.9631i	0.448689	−	0.777152i	0.998301	+	0.0582681i	$0.0185578\pi$
$200$		0			0
$201$	6.98519	−	4.03290i	0.492697	−	0.284459i
$202$		0			0
$203$	3.40131	−	4.02309i	0.238725	−	0.282366i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.83634	−	0.759994i	0.197139	−	0.0528233i
$208$		0			0
$209$	−8.99349			−0.622093
$210$		0			0
$211$	−5.37636			−0.370124			−0.185062	−	0.982727i	$-0.559249\pi$
$211$	−5.37636			−0.370124			−0.185062	+	0.982727i	$0.559249\pi$
$212$		0			0
$213$	−14.0771	+	3.77195i	−0.964548	+	0.258450i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	6.22872	+	17.3130i	0.422833	+	1.17529i
$218$		0			0
$219$	5.79591	−	3.34627i	0.391651	−	0.226120i
$220$		0			0
$221$	3.91399	−	6.77924i	0.263284	−	0.456021i
$222$		0			0
$223$	17.2847	+	17.2847i	1.15747	+	1.15747i	0.985018	+	0.172452i	$0.0551689\pi$
$223$	17.2847	+	17.2847i	1.15747	+	1.15747i	0.172452	+	0.985018i	$0.444831\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.487401	+	1.81901i	0.0323499	+	0.120732i	0.980213	−	0.197947i	$-0.0634275\pi$
$227$	0.487401	+	1.81901i	0.0323499	+	0.120732i	−0.947863	+	0.318679i	$0.896761\pi$
$228$		0			0
$229$	−12.5383	−	21.7171i	−0.828557	−	1.43510i	−0.899170	−	0.437600i	$-0.855829\pi$
$229$	−12.5383	−	21.7171i	−0.828557	−	1.43510i	0.0706123	−	0.997504i	$-0.477505\pi$
$230$		0			0
$231$	−5.28258	+	3.66975i	−0.347568	+	0.241452i
$232$		0			0
$233$	−21.6669	−	5.80563i	−1.41945	−	0.380340i	−0.534159	−	0.845384i	$-0.679372\pi$
$233$	−21.6669	−	5.80563i	−1.41945	−	0.380340i	−0.885287	+	0.465044i	$0.846038\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	7.79312	−	7.79312i	0.506218	−	0.506218i
$238$		0			0
$239$		−	6.38917i		−	0.413281i	−0.978417	−	0.206641i	$-0.933747\pi$
$239$		−	6.38917i		−	0.413281i	0.978417	−	0.206641i	$-0.0662531\pi$
$240$		0			0
$241$	−16.1337	−	9.31479i	−1.03926	−	0.600018i	−0.119638	−	0.992818i	$-0.538173\pi$
$241$	−16.1337	−	9.31479i	−1.03926	−	0.600018i	−0.919624	+	0.392799i	$0.871507\pi$
$242$		0			0
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.986914	+	3.68321i	−0.0627958	+	0.234357i
$248$		0			0
$249$	−12.1371	−	7.00738i	−0.769160	−	0.444075i
$250$		0			0
$251$			31.5776i			1.99316i	0.0826181	+	0.996581i	$0.473672\pi$
$251$			31.5776i			1.99316i	−0.0826181	+	0.996581i	$0.526328\pi$
$252$		0			0
$253$	5.04786	−	5.04786i	0.317356	−	0.317356i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−17.9559	−	4.81126i	−1.12006	−	0.300118i	−0.349150	−	0.937067i	$-0.613530\pi$
$257$	−17.9559	−	4.81126i	−1.12006	−	0.300118i	−0.770906	+	0.636949i	$0.780196\pi$
$258$		0			0
$259$	18.4928	−	12.8467i	1.14909	−	0.798256i
$260$		0			0
$261$	−0.995601	−	1.72443i	−0.0616261	−	0.106740i
$262$		0			0
$263$	1.47956	+	5.52178i	0.0912334	+	0.340488i	0.996421	−	0.0845235i	$-0.0269368\pi$
$263$	1.47956	+	5.52178i	0.0912334	+	0.340488i	−0.905188	+	0.425011i	$0.860270\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−8.22319	−	8.22319i	−0.503251	−	0.503251i
$268$		0			0
$269$	−1.22482	+	2.12145i	−0.0746785	+	0.129347i	−0.900946	−	0.433930i	$-0.857126\pi$
$269$	−1.22482	+	2.12145i	−0.0746785	+	0.129347i	0.826268	+	0.563277i	$0.190460\pi$
$270$		0			0
$271$	−21.9156	+	12.6530i	−1.33128	+	0.768613i	−0.985495	−	0.169702i	$-0.945720\pi$
$271$	−21.9156	+	12.6530i	−1.33128	+	0.768613i	−0.345782	+	0.938315i	$0.612386\pi$
$272$		0			0
$273$	0.923223	+	2.56614i	0.0558760	+	0.155310i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−30.8901	+	8.27697i	−1.85600	+	0.497315i	−0.999813	−	0.0193451i	$-0.993842\pi$
$277$	−30.8901	+	8.27697i	−1.85600	+	0.497315i	−0.856191	+	0.516660i	$0.827175\pi$
$278$		0			0
$279$	6.95433			0.416345
$280$		0			0
$281$	12.3044			0.734020			0.367010	−	0.930217i	$-0.380382\pi$
$281$	12.3044			0.734020			0.367010	+	0.930217i	$0.380382\pi$
$282$		0			0
$283$	−2.18325	+	0.584999i	−0.129780	+	0.0347746i	−0.323125	−	0.946356i	$-0.604733\pi$
$283$	−2.18325	+	0.584999i	−0.129780	+	0.0347746i	0.193344	+	0.981131i	$0.438067\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.85679	−	2.19623i	0.109603	−	0.129639i
$288$		0			0
$289$	−35.2241	+	20.3366i	−2.07201	+	1.19627i
$290$		0			0
$291$	−7.69564	+	13.3292i	−0.451126	+	0.781374i
$292$		0			0
$293$	−3.19458	−	3.19458i	−0.186629	−	0.186629i	0.607608	−	0.794237i	$-0.292129\pi$
$293$	−3.19458	−	3.19458i	−0.186629	−	0.186629i	−0.794237	+	0.607608i	$0.792129\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.629222	+	2.34829i	0.0365112	+	0.136262i
$298$		0			0
$299$	−1.51338	−	2.62124i	−0.0875208	−	0.151590i
$300$		0			0
$301$	−22.0653	+	1.84793i	−1.27182	+	0.106513i
$302$		0			0
$303$	−6.07484	−	1.62775i	−0.348990	−	0.0935117i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−5.74597	+	5.74597i	−0.327940	+	0.327940i	−0.851803	−	0.523863i	$-0.824490\pi$
$307$	−5.74597	+	5.74597i	−0.327940	+	0.327940i	0.523863	+	0.851803i	$0.324490\pi$
$308$		0			0
$309$		−	15.0882i		−	0.858338i
$310$		0			0
$311$	12.5238	+	7.23064i	0.710161	+	0.410012i	0.811121	−	0.584879i	$-0.198858\pi$
$311$	12.5238	+	7.23064i	0.710161	+	0.410012i	−0.100959	+	0.994891i	$0.532191\pi$
$312$		0			0
$313$	0.305958	−	1.14185i	0.0172938	−	0.0645412i	−0.956740	−	0.290945i	$-0.906030\pi$
$313$	0.305958	−	1.14185i	0.0172938	−	0.0645412i	0.974033	+	0.226404i	$0.0726969\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.28828	−	8.53996i	0.128522	−	0.479652i	−0.871418	−	0.490541i	$-0.836799\pi$
$317$	2.28828	−	8.53996i	0.128522	−	0.479652i	0.999941	+	0.0108885i	$0.00346598\pi$
$318$		0			0
$319$	−4.19231	−	2.42043i	−0.234725	−	0.135518i
$320$		0			0
$321$		−	14.6261i		−	0.816350i
$322$		0			0
$323$	19.8652	−	19.8652i	1.10533	−	1.10533i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−11.5512	−	3.09514i	−0.638784	−	0.171162i
$328$		0			0
$329$	7.51807	+	10.8222i	0.414484	+	0.596649i
$330$		0			0
$331$	−10.9304	−	18.9320i	−0.600789	−	1.04060i	−0.992702	−	0.120595i	$-0.961520\pi$
$331$	−10.9304	−	18.9320i	−0.600789	−	1.04060i	0.391913	−	0.920002i	$-0.371814\pi$
$332$		0			0
$333$	−2.20273	−	8.22068i	−0.120709	−	0.450491i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−18.0987	−	18.0987i	−0.985900	−	0.985900i	0.0140019	−	0.999902i	$-0.495543\pi$
$337$	−18.0987	−	18.0987i	−0.985900	−	0.985900i	−0.999902	+	0.0140019i	$0.995543\pi$
$338$		0			0
$339$	−3.61130	+	6.25496i	−0.196139	+	0.339723i
$340$		0			0
$341$	14.6418	−	8.45343i	0.792896	−	0.457779i
$342$		0			0
$343$	−9.43823	+	15.9349i	−0.509617	+	0.860402i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.04711	+	1.08442i	−0.217261	+	0.0582148i	−0.365807	−	0.930691i	$-0.619207\pi$
$347$	−4.04711	+	1.08442i	−0.217261	+	0.0582148i	0.148547	+	0.988905i	$0.452540\pi$
$348$		0			0
$349$	33.8258			1.81065			0.905327	−	0.424715i	$-0.139626\pi$
$349$	33.8258			1.81065			0.905327	+	0.424715i	$0.139626\pi$
$350$		0			0
$351$	1.03077			0.0550186
$352$		0			0
$353$	32.4911	−	8.70598i	1.72933	−	0.463372i	0.749301	−	0.662230i	$-0.230390\pi$
$353$	32.4911	−	8.70598i	1.72933	−	0.463372i	0.980028	+	0.198857i	$0.0637231\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	3.56250	−	19.7743i	0.188548	−	1.04657i
$358$		0			0
$359$	−14.0177	+	8.09313i	−0.739826	+	0.427139i	−0.822006	−	0.569479i	$-0.807145\pi$
$359$	−14.0177	+	8.09313i	−0.739826	+	0.427139i	0.0821800	+	0.996618i	$0.473812\pi$
$360$		0			0
$361$	2.65757	−	4.60305i	0.139872	−	0.242266i
$362$		0			0
$363$	−3.59890	−	3.59890i	−0.188893	−	0.188893i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.18786	−	15.6293i	−0.218604	−	0.815842i	−0.984867	−	0.173314i	$-0.944552\pi$
$367$	−4.18786	−	15.6293i	−0.218604	−	0.815842i	0.766262	−	0.642528i	$-0.222114\pi$
$368$		0			0
$369$	−0.543504	−	0.941376i	−0.0282937	−	0.0490061i
$370$		0			0
$371$	7.66553	−	16.2807i	0.397974	−	0.845250i
$372$		0			0
$373$	−3.59216	−	0.962517i	−0.185995	−	0.0498372i	0.164619	−	0.986357i	$-0.447360\pi$
$373$	−3.59216	−	0.962517i	−0.185995	−	0.0498372i	−0.350614	+	0.936520i	$0.614027\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.45132	+	1.45132i	−0.0747467	+	0.0747467i
$378$		0			0
$379$		−	0.149127i		−	0.00766015i	−0.999993	−	0.00383007i	$-0.998781\pi$
$379$		−	0.149127i		−	0.00766015i	0.999993	−	0.00383007i	$-0.00121915\pi$
$380$		0			0
$381$	−0.0322558	−	0.0186229i	−0.00165251	−	0.000954080i
$382$		0			0
$383$	8.97006	−	33.4767i	0.458349	−	1.71058i	−0.219703	−	0.975567i	$-0.570509\pi$
$383$	8.97006	−	33.4767i	0.458349	−	1.71058i	0.678052	−	0.735014i	$-0.262824\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.16608	+	8.08394i	−0.110108	+	0.410930i
$388$		0			0
$389$	−28.3146	−	16.3474i	−1.43561	−	0.828847i	−0.438065	−	0.898943i	$-0.644336\pi$
$389$	−28.3146	−	16.3474i	−1.43561	−	0.828847i	−0.997540	+	0.0700961i	$0.977669\pi$
$390$		0			0
$391$			22.2998i			1.12775i
$392$		0			0
$393$	−7.00950	+	7.00950i	−0.353582	+	0.353582i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−17.6559	−	4.73087i	−0.886122	−	0.237436i	−0.213076	−	0.977036i	$-0.568348\pi$
$397$	−17.6559	−	4.73087i	−0.886122	−	0.237436i	−0.673047	+	0.739600i	$0.735015\pi$
$398$		0			0
$399$	0.816819	+	9.75330i	0.0408921	+	0.488276i
$400$		0			0
$401$	−0.590882	−	1.02344i	−0.0295072	−	0.0511080i	0.850895	−	0.525336i	$-0.176060\pi$
$401$	−0.590882	−	1.02344i	−0.0295072	−	0.0511080i	−0.880402	+	0.474228i	$0.842727\pi$
$402$		0			0
$403$	−1.85530	−	6.92407i	−0.0924190	−	0.344913i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−14.6304	−	14.6304i	−0.725203	−	0.725203i
$408$		0			0
$409$	−8.11235	+	14.0510i	−0.401130	+	0.694777i	−0.993863	−	0.110622i	$-0.964716\pi$
$409$	−8.11235	+	14.0510i	−0.401130	+	0.694777i	0.592733	+	0.805399i	$0.298049\pi$
$410$		0			0
$411$	−12.4469	+	7.18624i	−0.613962	+	0.354471i
$412$		0			0
$413$	6.94100	−	2.49717i	0.341544	−	0.122878i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−10.7138	+	2.87075i	−0.524656	+	0.140581i
$418$		0			0
$419$	15.4289			0.753750			0.376875	−	0.926264i	$-0.376999\pi$
$419$	15.4289			0.753750			0.376875	+	0.926264i	$0.376999\pi$
$420$		0			0
$421$	26.6085			1.29682			0.648409	−	0.761292i	$-0.275435\pi$
$421$	26.6085			1.29682			0.648409	+	0.761292i	$0.275435\pi$
$422$		0			0
$423$	4.81085	−	1.28906i	0.233912	−	0.0626764i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.654167	+	0.117854i	0.0316574	+	0.00570335i
$428$		0			0
$429$	2.17021	−	1.25297i	0.104779	−	0.0604940i
$430$		0			0
$431$	−1.83304	+	3.17492i	−0.0882944	+	0.152930i	−0.906790	−	0.421582i	$-0.861475\pi$
$431$	−1.83304	+	3.17492i	−0.0882944	+	0.152930i	0.818496	+	0.574512i	$0.194808\pi$
$432$		0			0
$433$	−9.74318	−	9.74318i	−0.468227	−	0.468227i	0.433112	−	0.901340i	$-0.357415\pi$
$433$	−9.74318	−	9.74318i	−0.468227	−	0.468227i	−0.901340	+	0.433112i	$0.857415\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.81145	−	10.4925i	−0.134490	−	0.501923i
$438$		0			0
$439$	−3.00918	−	5.21204i	−0.143620	−	0.248757i	0.785237	−	0.619195i	$-0.212541\pi$
$439$	−3.00918	−	5.21204i	−0.143620	−	0.248757i	−0.928857	+	0.370438i	$0.879208\pi$
$440$		0			0
$441$	4.45956	+	5.39558i	0.212360	+	0.256932i
$442$		0			0
$443$	19.6065	+	5.25355i	0.931534	+	0.249604i	0.692509	−	0.721410i	$-0.256505\pi$
$443$	19.6065	+	5.25355i	0.931534	+	0.249604i	0.239025	+	0.971013i	$0.423172\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	6.25708	−	6.25708i	0.295950	−	0.295950i
$448$		0			0
$449$		−	12.7251i		−	0.600534i	−0.953855	−	0.300267i	$-0.902924\pi$
$449$		−	12.7251i		−	0.600534i	0.953855	−	0.300267i	$-0.0970758\pi$
$450$		0			0
$451$	−2.28861	−	1.32133i	−0.107766	−	0.0622189i
$452$		0			0
$453$	0.466424	−	1.74072i	0.0219145	−	0.0817860i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.08197	−	30.1623i	0.378058	−	1.41093i	−0.470766	−	0.882258i	$-0.656022\pi$
$457$	8.08197	−	30.1623i	0.378058	−	1.41093i	0.848824	−	0.528675i	$-0.177311\pi$
$458$		0			0
$459$	−6.57685	−	3.79715i	−0.306981	−	0.177236i
$460$		0			0
$461$			23.4059i			1.09012i	0.838397	+	0.545060i	$0.183493\pi$
$461$			23.4059i			1.09012i	−0.838397	+	0.545060i	$0.816507\pi$
$462$		0			0
$463$	16.8382	−	16.8382i	0.782539	−	0.782539i	−0.197720	−	0.980259i	$-0.563354\pi$
$463$	16.8382	−	16.8382i	0.782539	−	0.782539i	0.980259	+	0.197720i	$0.0633537\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−37.6898	−	10.0990i	−1.74408	−	0.467324i	−0.760730	−	0.649068i	$-0.775159\pi$
$467$	−37.6898	−	10.0990i	−1.74408	−	0.467324i	−0.983346	+	0.181744i	$0.941826\pi$
$468$		0			0
$469$	−19.3071	−	9.09048i	−0.891518	−	0.419759i
$470$		0			0
$471$	−5.73706	−	9.93688i	−0.264350	−	0.457867i
$472$		0			0
$473$	5.26603	+	19.6531i	0.242132	+	0.903650i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−4.80937	−	4.80937i	−0.220206	−	0.220206i
$478$		0			0
$479$	−7.66084	+	13.2690i	−0.350033	+	0.606275i	−0.986255	−	0.165231i	$-0.947163\pi$
$479$	−7.66084	+	13.2690i	−0.350033	+	0.606275i	0.636222	+	0.771506i	$0.280496\pi$
$480$		0			0
$481$	−7.59727	+	4.38628i	−0.346406	+	0.199997i
$482$		0			0
$483$	−5.93279	−	5.01586i	−0.269951	−	0.228230i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−16.1398	+	4.32465i	−0.731364	+	0.195968i	−0.605237	−	0.796046i	$-0.706921\pi$
$487$	−16.1398	+	4.32465i	−0.731364	+	0.195968i	−0.126127	+	0.992014i	$0.540255\pi$
$488$		0			0
$489$	0.314195			0.0142084
$490$		0			0
$491$	0.188878			0.00852393			0.00426196	−	0.999991i	$-0.498643\pi$
$491$	0.188878			0.00852393			0.00426196	+	0.999991i	$0.498643\pi$
$492$		0			0
$493$	14.6065	−	3.91380i	0.657844	−	0.176269i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	29.4452	+	24.8944i	1.32080	+	1.11667i
$498$		0			0
$499$	12.1410	−	7.00959i	0.543504	−	0.313792i	−0.202994	−	0.979180i	$-0.565067\pi$
$499$	12.1410	−	7.00959i	0.543504	−	0.313792i	0.746498	+	0.665388i	$0.231734\pi$
$500$		0			0
$501$	−1.48605	+	2.57391i	−0.0663917	+	0.114994i
$502$		0			0
$503$	−20.0052	−	20.0052i	−0.891989	−	0.891989i	0.102721	−	0.994710i	$-0.467245\pi$
$503$	−20.0052	−	20.0052i	−0.891989	−	0.891989i	−0.994710	+	0.102721i	$0.967245\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.08965	+	11.5307i	0.137216	+	0.512098i
$508$		0			0
$509$	6.58364	+	11.4032i	0.291815	+	0.505438i	0.974239	−	0.225518i	$-0.0724076\pi$
$509$	6.58364	+	11.4032i	0.291815	+	0.505438i	−0.682424	+	0.730956i	$0.739074\pi$
$510$		0			0
$511$	−16.0199	−	7.54276i	−0.708679	−	0.333672i
$512$		0			0
$513$	3.57325	+	0.957451i	0.157763	+	0.0422725i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	8.56192	−	8.56192i	0.376553	−	0.376553i
$518$		0			0
$519$		−	9.82187i		−	0.431132i
$520$		0			0
$521$	−22.6255	−	13.0628i	−0.991242	−	0.572294i	−0.0855965	−	0.996330i	$-0.527280\pi$
$521$	−22.6255	−	13.0628i	−0.991242	−	0.572294i	−0.905645	+	0.424036i	$0.860613\pi$
$522$		0			0
$523$	1.48330	−	5.53573i	0.0648600	−	0.242061i	−0.925883	−	0.377810i	$-0.876677\pi$
$523$	1.48330	−	5.53573i	0.0648600	−	0.242061i	0.990743	+	0.135749i	$0.0433440\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.6691	+	51.0136i	−0.595434	+	2.22219i
$528$		0			0
$529$	−12.4514	−	7.18880i	−0.541364	−	0.312556i
$530$		0			0
$531$		−	2.78807i		−	0.120992i
$532$		0			0
$533$	−0.792283	+	0.792283i	−0.0343176	+	0.0343176i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−17.6797	−	4.73727i	−0.762936	−	0.204428i
$538$		0			0
$539$	15.9479	+	5.93907i	0.686926	+	0.255814i
$540$		0			0
$541$	−14.1293	−	24.4727i	−0.607468	−	1.05217i	−0.991656	−	0.128910i	$-0.958852\pi$
$541$	−14.1293	−	24.4727i	−0.607468	−	1.05217i	0.384188	−	0.923255i	$-0.374481\pi$
$542$		0			0
$543$	5.22340	+	19.4940i	0.224157	+	0.836567i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−20.0515	−	20.0515i	−0.857341	−	0.857341i	0.133683	−	0.991024i	$-0.457320\pi$
$547$	−20.0515	−	20.0515i	−0.857341	−	0.857341i	−0.991024	+	0.133683i	$0.957320\pi$
$548$		0			0
$549$	0.125616	−	0.217574i	0.00536117	−	0.00928582i
$550$		0			0
$551$	−6.37920	+	3.68303i	−0.271763	+	0.156902i
$552$		0			0
$553$	−28.6972	−	5.17004i	−1.22033	−	0.219853i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	21.3952	−	5.73283i	0.906544	−	0.242908i	0.224720	−	0.974423i	$-0.427853\pi$
$557$	21.3952	−	5.73283i	0.906544	−	0.242908i	0.681825	+	0.731516i	$0.261187\pi$
$558$		0			0
$559$	8.62664			0.364868
$560$		0			0
$561$	−18.4627			−0.779496
$562$		0			0
$563$	1.26083	−	0.337839i	0.0531378	−	0.0142382i	−0.232152	−	0.972679i	$-0.574577\pi$
$563$	1.26083	−	0.337839i	0.0531378	−	0.0142382i	0.285290	+	0.958441i	$0.407910\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.48954	−	0.895662i	0.104551	−	0.0376143i
$568$		0			0
$569$	0.426999	−	0.246528i	0.0179007	−	0.0103350i	−0.491023	−	0.871147i	$-0.663377\pi$
$569$	0.426999	−	0.246528i	0.0179007	−	0.0103350i	0.508924	+	0.860812i	$0.330044\pi$
$570$		0			0
$571$	−1.79895	+	3.11588i	−0.0752839	+	0.130395i	−0.901210	−	0.433383i	$-0.857320\pi$
$571$	−1.79895	+	3.11588i	−0.0752839	+	0.130395i	0.825926	+	0.563779i	$0.190653\pi$
$572$		0			0
$573$	1.75571	+	1.75571i	0.0733456	+	0.0733456i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	3.27724	+	12.2308i	0.136433	+	0.509177i	0.999988	+	0.00492102i	$0.00156642\pi$
$577$	3.27724	+	12.2308i	0.136433	+	0.509177i	−0.863554	+	0.504256i	$0.831767\pi$
$578$		0			0
$579$	6.64594	+	11.5111i	0.276196	+	0.478385i
$580$		0			0
$581$	3.09451	+	36.9502i	0.128382	+	1.53295i
$582$		0			0
$583$	−15.9718	−	4.27964i	−0.661486	−	0.177245i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.84683	−	2.84683i	0.117501	−	0.117501i	−0.645911	−	0.763413i	$-0.723522\pi$
$587$	2.84683	−	2.84683i	0.117501	−	0.117501i	0.763413	+	0.645911i	$0.223522\pi$
$588$		0			0
$589$		−	25.7262i		−	1.06003i
$590$		0			0
$591$	−6.67736	−	3.85517i	−0.274670	−	0.158581i
$592$		0			0
$593$	8.23903	−	30.7485i	0.338336	−	1.26269i	−0.561870	−	0.827226i	$-0.689918\pi$
$593$	8.23903	−	30.7485i	0.338336	−	1.26269i	0.900206	−	0.435463i	$-0.143415\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.27641	+	12.2277i	−0.134094	+	0.500447i
$598$		0			0
$599$	−33.3274	−	19.2416i	−1.36172	−	0.786191i	−0.371869	−	0.928285i	$-0.621283\pi$
$599$	−33.3274	−	19.2416i	−1.36172	−	0.786191i	−0.989853	+	0.142095i	$0.954616\pi$
$600$		0			0
$601$			45.6842i			1.86350i	0.363102	+	0.931750i	$0.381718\pi$
$601$			45.6842i			1.86350i	−0.363102	+	0.931750i	$0.618282\pi$
$602$		0			0
$603$	−5.70338	+	5.70338i	−0.232260	+	0.232260i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	23.9680	+	6.42220i	0.972831	+	0.260669i	0.710023	−	0.704179i	$-0.248685\pi$
$607$	23.9680	+	6.42220i	0.972831	+	0.260669i	0.262808	+	0.964848i	$0.415351\pi$
$608$		0			0
$609$	−2.24416	+	4.76633i	−0.0909381	+	0.193141i
$610$		0			0
$611$	−2.56691	−	4.44602i	−0.103846	−	0.179867i
$612$		0			0
$613$	−0.286436	−	1.06899i	−0.0115690	−	0.0431762i	0.959900	−	0.280343i	$-0.0904480\pi$
$613$	−0.286436	−	1.06899i	−0.0115690	−	0.0431762i	−0.971469	+	0.237166i	$0.923781\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.353089	+	0.353089i	0.0142148	+	0.0142148i	0.714178	−	0.699964i	$-0.246800\pi$
$617$	0.353089	+	0.353089i	0.0142148	+	0.0142148i	−0.699964	+	0.714178i	$0.746800\pi$
$618$		0			0
$619$	−11.6067	+	20.1034i	−0.466513	+	0.808024i	−0.999268	−	0.0382453i	$-0.987823\pi$
$619$	−11.6067	+	20.1034i	−0.466513	+	0.808024i	0.532756	+	0.846269i	$0.321156\pi$
$620$		0			0
$621$	−2.54299	+	1.46820i	−0.102047	+	0.0589167i
$622$		0			0
$623$	−5.45536	+	30.2809i	−0.218564	+	1.21318i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	8.68704	−	2.32769i	0.346927	−	0.0929588i
$628$		0			0
$629$	64.6326			2.57707
$630$		0			0
$631$	18.8761			0.751445			0.375723	−	0.926732i	$-0.377395\pi$
$631$	18.8761			0.751445			0.375723	+	0.926732i	$0.377395\pi$
$632$		0			0
$633$	5.19316	−	1.39150i	0.206410	−	0.0553073i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	4.18237	−	5.87961i	0.165712	−	0.232959i
$638$		0			0
$639$	12.6212	−	7.28685i	0.499287	−	0.288263i
$640$		0			0
$641$	18.7675	−	32.5062i	0.741271	−	1.28392i	−0.210646	−	0.977562i	$-0.567557\pi$
$641$	18.7675	−	32.5062i	0.741271	−	1.28392i	0.951917	−	0.306356i	$-0.0991099\pi$
$642$		0			0
$643$	12.0570	+	12.0570i	0.475483	+	0.475483i	0.903684	−	0.428201i	$-0.140852\pi$
$643$	12.0570	+	12.0570i	0.475483	+	0.475483i	−0.428201	+	0.903684i	$0.640852\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.82656	−	18.0130i	−0.189752	−	0.708163i	−0.993563	−	0.113279i	$-0.963865\pi$
$647$	−4.82656	−	18.0130i	−0.189752	−	0.708163i	0.803812	−	0.594884i	$-0.202802\pi$
$648$		0			0
$649$	−3.38908	−	5.87006i	−0.133033	−	0.230420i
$650$		0			0
$651$	−10.4974	−	15.1110i	−0.411427	−	0.592247i
$652$		0			0
$653$	−16.2195	−	4.34601i	−0.634719	−	0.170073i	−0.0729090	−	0.997339i	$-0.523228\pi$
$653$	−16.2195	−	4.34601i	−0.634719	−	0.170073i	−0.561810	+	0.827266i	$0.689895\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−4.73234	+	4.73234i	−0.184626	+	0.184626i
$658$		0			0
$659$		−	47.4270i		−	1.84749i	−0.383005	−	0.923746i	$-0.625111\pi$
$659$		−	47.4270i		−	1.84749i	0.383005	−	0.923746i	$-0.374889\pi$
$660$		0			0
$661$	10.5554	+	6.09418i	0.410558	+	0.237036i	0.691030	−	0.722826i	$-0.257157\pi$
$661$	10.5554	+	6.09418i	0.410558	+	0.237036i	−0.280471	+	0.959862i	$0.590491\pi$
$662$		0			0
$663$	−2.02603	+	7.56125i	−0.0786846	+	0.293655i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.51330	−	5.64772i	0.0585953	−	0.218681i
$668$		0			0
$669$	−21.1694	−	12.2221i	−0.818455	−	0.472535i
$670$		0			0
$671$		−	0.610779i		−	0.0235789i
$672$		0			0
$673$	−1.19597	+	1.19597i	−0.0461011	+	0.0461011i	−0.729782	−	0.683680i	$-0.760378\pi$
$673$	−1.19597	+	1.19597i	−0.0461011	+	0.0461011i	0.683680	+	0.729782i	$0.260378\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.14780	+	2.45115i	0.351578	+	0.0942052i	0.430286	−	0.902693i	$-0.358413\pi$
$677$	9.14780	+	2.45115i	0.351578	+	0.0942052i	−0.0787076	+	0.996898i	$0.525079\pi$
$678$		0			0
$679$	40.5794	−	3.39845i	1.55730	−	0.130420i
$680$		0			0
$681$	−0.941587	−	1.63088i	−0.0360817	−	0.0624953i
$682$		0			0
$683$	5.56809	+	20.7804i	0.213057	+	0.795139i	0.986842	+	0.161690i	$0.0516946\pi$
$683$	5.56809	+	20.7804i	0.213057	+	0.795139i	−0.773785	+	0.633449i	$0.781639\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	17.7319	+	17.7319i	0.676514	+	0.676514i
$688$		0			0
$689$	−3.50538	+	6.07150i	−0.133544	+	0.231306i
$690$		0			0
$691$	5.42242	−	3.13064i	0.206279	−	0.119095i	−0.393302	−	0.919409i	$-0.628667\pi$
$691$	5.42242	−	3.13064i	0.206279	−	0.119095i	0.599581	+	0.800314i	$0.295334\pi$
$692$		0			0
$693$	4.15278	−	4.91193i	0.157751	−	0.186589i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	7.97377	−	2.13656i	0.302028	−	0.0809281i
$698$		0			0
$699$	22.4312			0.848427
$700$		0			0
$701$	−41.6155			−1.57180			−0.785899	−	0.618355i	$-0.787799\pi$
$701$	−41.6155			−1.57180			−0.785899	+	0.618355i	$0.787799\pi$
$702$		0			0
$703$	−30.4108	+	8.14855i	−1.14697	+	0.307328i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.63294	+	15.6570i	0.211848	+	0.588843i
$708$		0			0
$709$	−0.279672	+	0.161469i	−0.0105033	+	0.00606409i	−0.505242	−	0.862977i	$-0.668597\pi$
$709$	−0.279672	+	0.161469i	−0.0105033	+	0.00606409i	0.494739	+	0.869042i	$0.335264\pi$
$710$		0			0
$711$	−5.51057	+	9.54459i	−0.206662	+	0.357950i
$712$		0			0
$713$	14.4396	+	14.4396i	0.540766	+	0.540766i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.65364	+	6.17147i	0.0617563	+	0.230478i
$718$		0			0
$719$	−10.1034	−	17.4996i	−0.376792	−	0.652623i	0.613801	−	0.789460i	$-0.289640\pi$
$719$	−10.1034	−	17.4996i	−0.376792	−	0.652623i	−0.990594	+	0.136837i	$0.956306\pi$
$720$		0			0
$721$	−32.7851	+	22.7754i	−1.22098	+	0.848199i
$722$		0			0
$723$	17.9948	+	4.82169i	0.669234	+	0.179321i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−3.29844	+	3.29844i	−0.122332	+	0.122332i	−0.765622	−	0.643290i	$-0.777569\pi$
$727$	−3.29844	+	3.29844i	−0.122332	+	0.122332i	0.643290	+	0.765622i	$0.277569\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−55.0424	−	31.7787i	−2.03582	−	1.17538i
$732$		0			0
$733$	−3.93084	+	14.6701i	−0.145189	+	0.541852i	0.854558	+	0.519356i	$0.173828\pi$
$733$	−3.93084	+	14.6701i	−0.145189	+	0.541852i	−0.999747	+	0.0224964i	$0.992839\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.07518	+	18.9408i	−0.186947	+	0.697695i
$738$		0			0
$739$	−15.6624	−	9.04272i	−0.576153	−	0.332642i	0.183450	−	0.983029i	$-0.441273\pi$
$739$	−15.6624	−	9.04272i	−0.576153	−	0.332642i	−0.759603	+	0.650387i	$0.774607\pi$
$740$		0			0
$741$		−	3.81314i		−	0.140079i
$742$		0			0
$743$	4.73236	−	4.73236i	0.173613	−	0.173613i	−0.614952	−	0.788565i	$-0.710824\pi$
$743$	4.73236	−	4.73236i	0.173613	−	0.173613i	0.788565	+	0.614952i	$0.210824\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	13.5372	+	3.62729i	0.495301	+	0.132716i
$748$		0			0
$749$	−31.7810	+	22.0778i	−1.16125	+	0.806707i
$750$		0			0
$751$	22.6070	+	39.1564i	0.824940	+	1.42884i	0.901965	+	0.431809i	$0.142124\pi$
$751$	22.6070	+	39.1564i	0.824940	+	1.42884i	−0.0770253	+	0.997029i	$0.524542\pi$
$752$		0			0
$753$	−8.17289	−	30.5017i	−0.297837	−	1.11154i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−13.8934	−	13.8934i	−0.504964	−	0.504964i	0.408012	−	0.912976i	$-0.366222\pi$
$757$	−13.8934	−	13.8934i	−0.504964	−	0.504964i	−0.912976	+	0.408012i	$0.866222\pi$
$758$		0			0
$759$	−3.56938	+	6.18234i	−0.129560	+	0.224405i
$760$		0			0
$761$	−22.4013	+	12.9334i	−0.812046	+	0.468835i	−0.847666	−	0.530531i	$-0.821993\pi$
$761$	−22.4013	+	12.9334i	−0.812046	+	0.468835i	0.0356201	+	0.999365i	$0.488659\pi$
$762$		0			0
$763$	10.7109	+	29.7716i	0.387762	+	1.07780i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.77594	+	0.743811i	−0.100233	+	0.0268575i
$768$		0			0
$769$	3.97934			0.143499			0.0717493	−	0.997423i	$-0.477142\pi$
$769$	3.97934			0.143499			0.0717493	+	0.997423i	$0.477142\pi$
$770$		0			0
$771$	18.5893			0.669476
$772$		0			0
$773$	28.1147	−	7.53332i	1.01122	−	0.270955i	0.285079	−	0.958504i	$-0.407980\pi$
$773$	28.1147	−	7.53332i	1.01122	−	0.270955i	0.726138	+	0.687549i	$0.241314\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−14.5377	+	17.1953i	−0.521537	+	0.616876i
$778$		0			0
$779$	−3.48244	+	2.01059i	−0.124771	+	0.0720367i
$780$		0			0
$781$	17.7153	−	30.6838i	0.633903	−	1.09795i
$782$		0			0
$783$	1.40799	+	1.40799i	0.0503175	+	0.0503175i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.87190	−	29.3783i	−0.280603	−	1.04722i	−0.951993	−	0.306120i	$-0.900969\pi$
$787$	−7.87190	−	29.3783i	−0.280603	−	1.04722i	0.671390	−	0.741104i	$-0.265698\pi$
$788$		0			0
$789$	−2.85829	−	4.95070i	−0.101758	−	0.176249i
$790$		0			0
$791$	19.0426	−	1.59477i	0.677075	−	0.0567037i
$792$		0			0
$793$	−0.250140	−	0.0670247i	−0.00888272	−	0.00238012i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.04054	−	4.04054i	0.143123	−	0.143123i	−0.631915	−	0.775038i	$-0.717731\pi$
$797$	4.04054	−	4.04054i	0.143123	−	0.143123i	0.775038	+	0.631915i	$0.217731\pi$
$798$		0			0
$799$			37.8238i			1.33811i
$800$		0			0
$801$	10.0713	+	5.81468i	0.355852	+	0.205451i
$802$		0			0
$803$	−4.21110	+	15.7160i	−0.148606	+	0.554607i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.634013	−	2.36617i	0.0223183	−	0.0832931i
$808$		0			0
$809$	37.9488	+	21.9098i	1.33421	+	0.770306i	0.985942	−	0.167089i	$-0.0534366\pi$
$809$	37.9488	+	21.9098i	1.33421	+	0.770306i	0.348268	+	0.937395i	$0.386770\pi$
$810$		0			0
$811$			1.74791i			0.0613774i	0.999529	+	0.0306887i	$0.00977005\pi$
$811$			1.74791i			0.0613774i	−0.999529	+	0.0306887i	$0.990230\pi$
$812$		0			0
$813$	17.8940	−	17.8940i	0.627570	−	0.627570i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	29.9049	+	8.01301i	1.04624	+	0.280340i
$818$		0			0
$819$	−1.55593	−	2.23976i	−0.0543687	−	0.0782635i
$820$		0			0
$821$	13.5210	+	23.4191i	0.471886	+	0.817331i	0.999483	−	0.0321643i	$-0.0102400\pi$
$821$	13.5210	+	23.4191i	0.471886	+	0.817331i	−0.527596	+	0.849495i	$0.676907\pi$
$822$		0			0
$823$	0.670043	+	2.50063i	0.0233562	+	0.0871667i	0.976620	−	0.214972i	$-0.0689661\pi$
$823$	0.670043	+	2.50063i	0.0233562	+	0.0871667i	−0.953264	+	0.302139i	$0.902299\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−37.3013	−	37.3013i	−1.29709	−	1.29709i	−0.930305	−	0.366787i	$-0.880458\pi$
$827$	−37.3013	−	37.3013i	−1.29709	−	1.29709i	−0.366787	−	0.930305i	$-0.619542\pi$
$828$		0			0
$829$	−19.0559	+	33.0057i	−0.661837	+	1.14634i	0.318295	+	0.947992i	$0.396890\pi$
$829$	−19.0559	+	33.0057i	−0.661837	+	1.14634i	−0.980132	+	0.198344i	$0.936444\pi$
$830$		0			0
$831$	27.6953	−	15.9899i	0.960738	−	0.554682i
$832$		0			0
$833$	−48.3449	+	22.1080i	−1.67505	+	0.765996i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−6.71736	+	1.79991i	−0.232186	+	0.0622141i
$838$		0			0
$839$	−27.2101			−0.939398			−0.469699	−	0.882827i	$-0.655638\pi$
$839$	−27.2101			−0.939398			−0.469699	+	0.882827i	$0.655638\pi$
$840$		0			0
$841$	25.0351			0.863280
$842$		0			0
$843$	−11.8852	+	3.18462i	−0.409346	+	0.109684i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.38755	+	13.2525i	−0.0820372	+	0.455361i
$848$		0			0
$849$	1.95744	−	1.13013i	0.0671793	−	0.0387860i
$850$		0			0
$851$	12.4953	−	21.6426i	0.428335	−	0.741898i
$852$		0			0
$853$	−12.1745	−	12.1745i	−0.416848	−	0.416848i	0.467268	−	0.884116i	$-0.345238\pi$
$853$	−12.1745	−	12.1745i	−0.416848	−	0.416848i	−0.884116	+	0.467268i	$0.845238\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.99840	−	33.5825i	−0.307379	−	1.14716i	−0.930878	−	0.365331i	$-0.880956\pi$
$857$	−8.99840	−	33.5825i	−0.307379	−	1.14716i	0.623498	−	0.781825i	$-0.285711\pi$
$858$		0			0
$859$	16.7607	+	29.0304i	0.571869	+	0.990506i	0.996374	+	0.0850805i	$0.0271148\pi$
$859$	16.7607	+	29.0304i	0.571869	+	0.990506i	−0.424505	+	0.905426i	$0.639552\pi$
$860$		0			0
$861$	−1.22510	+	2.60196i	−0.0417513	+	0.0886747i
$862$		0			0
$863$	−32.8275	−	8.79609i	−1.11746	−	0.299422i	−0.347605	−	0.937641i	$-0.613005\pi$
$863$	−32.8275	−	8.79609i	−1.11746	−	0.299422i	−0.769855	+	0.638219i	$0.779671\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	28.7604	−	28.7604i	0.976753	−	0.976753i
$868$		0			0
$869$			26.7938i			0.908918i
$870$		0			0
$871$	7.20014	+	4.15700i	0.243967	+	0.140855i
$872$		0			0
$873$	3.98356	−	14.8668i	0.134823	−	0.503166i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.74085	+	17.6931i	−0.160087	+	0.597454i	0.838529	+	0.544858i	$0.183416\pi$
$877$	−4.74085	+	17.6931i	−0.160087	+	0.597454i	−0.998616	+	0.0525963i	$0.983250\pi$
$878$		0			0
$879$	3.91255	+	2.25891i	0.131967	+	0.0761911i
$880$		0			0
$881$		−	17.5109i		−	0.589956i	−0.955504	−	0.294978i	$-0.904688\pi$
$881$		−	17.5109i		−	0.589956i	0.955504	−	0.294978i	$-0.0953123\pi$
$882$		0			0
$883$	33.5448	−	33.5448i	1.12887	−	1.12887i	0.138510	−	0.990361i	$-0.455769\pi$
$883$	33.5448	−	33.5448i	1.12887	−	1.12887i	0.990361	−	0.138510i	$-0.0442312\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.5015	+	7.10104i	0.889832	+	0.238430i	0.674644	−	0.738143i	$-0.264297\pi$
$887$	26.5015	+	7.10104i	0.889832	+	0.238430i	0.215188	+	0.976573i	$0.430964\pi$
$888$		0			0
$889$	0.00822399	+	0.0981993i	0.000275824	+	0.00329350i
$890$		0			0
$891$	−1.21556	−	2.10542i	−0.0407229	−	0.0705342i
$892$		0			0
$893$	−4.76864	−	17.7968i	−0.159576	−	0.595547i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.14024	+	2.14024i	0.0714604	+	0.0714604i
$898$		0			0
$899$	6.92373	−	11.9923i	0.230919	−	0.399964i
$900$		0			0
$901$	44.7323	−	25.8262i	1.49025	−	0.860395i
$902$		0			0
$903$	20.8352	−	7.49589i	0.693352	−	0.249448i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.09623	+	0.829631i	−0.102809	+	0.0275475i	−0.309857	−	0.950783i	$-0.600281\pi$
$907$	−3.09623	+	0.829631i	−0.102809	+	0.0275475i	0.207048	+	0.978331i	$0.433614\pi$
$908$		0			0
$909$	6.28914			0.208597
$910$		0			0
$911$	51.5087			1.70656			0.853279	−	0.521454i	$-0.174610\pi$
$911$	51.5087			1.70656			0.853279	+	0.521454i	$0.174610\pi$
$912$		0			0
$913$	32.9107	−	8.81841i	1.08919	−	0.291847i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	25.8116	+	4.65018i	0.852374	+	0.153562i
$918$		0			0
$919$	−41.7186	+	24.0862i	−1.37617	+	0.794531i	−0.991696	−	0.128605i	$-0.958950\pi$
$919$	−41.7186	+	24.0862i	−1.37617	+	0.794531i	−0.384473	+	0.923136i	$0.625617\pi$
$920$		0			0
$921$	4.06301	−	7.03734i	0.133881	−	0.231888i
$922$		0			0
$923$	−10.6223	−	10.6223i	−0.349637	−	0.349637i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.90512	+	14.5741i	0.128261	+	0.478676i
$928$		0			0
$929$	14.4707	+	25.0639i	0.474767	+	0.822321i	0.999582	−	0.0288955i	$-0.00919901\pi$
$929$	14.4707	+	25.0639i	0.474767	+	0.822321i	−0.524815	+	0.851216i	$0.675866\pi$
$930$		0			0
$931$	19.9599	−	16.4973i	0.654159	−	0.540677i
$932$		0			0
$933$	−13.9685	−	3.74285i	−0.457309	−	0.122536i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	9.57644	−	9.57644i	0.312849	−	0.312849i	−0.533164	−	0.846012i	$-0.678997\pi$
$937$	9.57644	−	9.57644i	0.312849	−	0.312849i	0.846012	+	0.533164i	$0.178997\pi$
$938$		0			0
$939$			1.18213i			0.0385774i
$940$		0			0
$941$	13.8414	+	7.99136i	0.451218	+	0.260511i	0.708344	−	0.705867i	$-0.249442\pi$
$941$	13.8414	+	7.99136i	0.451218	+	0.260511i	−0.257127	+	0.966378i	$0.582776\pi$
$942$		0			0
$943$	0.826119	−	3.08312i	0.0269021	−	0.100400i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.13572	+	7.97060i	−0.0694015	+	0.259010i	−0.991906	−	0.126977i	$-0.959472\pi$
$947$	−2.13572	+	7.97060i	−0.0694015	+	0.259010i	0.922504	+	0.385987i	$0.126139\pi$
$948$		0			0
$949$	5.97426	+	3.44924i	0.193933	+	0.111967i
$950$		0			0
$951$			8.84122i			0.286696i
$952$		0			0
$953$	−25.2246	+	25.2246i	−0.817104	+	0.817104i	−0.985687	−	0.168584i	$-0.946081\pi$
$953$	−25.2246	+	25.2246i	−0.817104	+	0.817104i	0.168584	+	0.985687i	$0.446081\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	4.67592	+	1.25291i	0.151151	+	0.0405008i
$958$		0			0
$959$	34.4034	+	16.1984i	1.11094	+	0.523072i
$960$		0			0
$961$	8.68132	+	15.0365i	0.280043	+	0.485048i
$962$		0			0
$963$	3.78551	+	14.1277i	0.121987	+	0.455260i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	16.3072	+	16.3072i	0.524405	+	0.524405i	0.918899	−	0.394494i	$-0.129080\pi$
$967$	16.3072	+	16.3072i	0.524405	+	0.524405i	−0.394494	+	0.918899i	$0.629080\pi$
$968$		0			0
$969$	−14.0468	+	24.3298i	−0.451248	+	0.781585i
$970$		0			0
$971$	−3.80744	+	2.19823i	−0.122187	+	0.0705445i	−0.559848	−	0.828596i	$-0.689140\pi$
$971$	−3.80744	+	2.19823i	−0.122187	+	0.0705445i	0.437661	+	0.899140i	$0.355807\pi$
$972$		0			0
$973$	22.4101	+	18.9466i	0.718434	+	0.607399i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	39.6743	−	10.6307i	1.26929	−	0.340106i	0.439534	−	0.898226i	$-0.355144\pi$
$977$	39.6743	−	10.6307i	1.26929	−	0.340106i	0.829760	+	0.558120i	$0.188477\pi$
$978$		0			0
$979$	28.2725			0.903592
$980$		0			0
$981$	11.9587			0.381812
$982$		0			0
$983$	−2.54704	+	0.682478i	−0.0812380	+	0.0217677i	−0.299209	−	0.954188i	$-0.596723\pi$
$983$	−2.54704	+	0.682478i	−0.0812380	+	0.0217677i	0.217971	+	0.975955i	$0.430056\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−10.0629	−	8.50765i	−0.320305	−	0.270801i
$988$		0			0
$989$	−21.2826	+	12.2875i	−0.676746	+	0.390720i
$990$		0			0
$991$	0.658365	−	1.14032i	0.0209136	−	0.0362235i	−0.855379	−	0.518002i	$-0.826676\pi$
$991$	0.658365	−	1.14032i	0.0209136	−	0.0362235i	0.876293	+	0.481779i	$0.160009\pi$
$992$		0			0
$993$	15.4579	+	15.4579i	0.490542	+	0.490542i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	13.2647	+	49.5044i	0.420096	+	1.56782i	0.774404	+	0.632692i	$0.218050\pi$
$997$	13.2647	+	49.5044i	0.420096	+	1.56782i	−0.354307	+	0.935129i	$0.615283\pi$
$998$		0			0
$999$	4.25534	+	7.37046i	0.134633	+	0.233191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.e.157.4		32
5.2	odd	4		420.2.bo.a.73.7	✓	32
5.3	odd	4	inner	2100.2.ce.e.493.2		32
5.4	even	2		420.2.bo.a.157.5	yes	32
7.5	odd	6	inner	2100.2.ce.e.1657.2		32
15.2	even	4		1260.2.dq.c.73.4		32
15.14	odd	2		1260.2.dq.c.577.7		32
35.4	even	6		2940.2.x.c.97.4		32
35.12	even	12		420.2.bo.a.313.5	yes	32
35.17	even	12		2940.2.x.c.1273.4		32
35.19	odd	6		420.2.bo.a.397.7	yes	32
35.24	odd	6		2940.2.x.c.97.15		32
35.32	odd	12		2940.2.x.c.1273.15		32
35.33	even	12	inner	2100.2.ce.e.1993.4		32
105.47	odd	12		1260.2.dq.c.1153.7		32
105.89	even	6		1260.2.dq.c.397.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.7	✓	32	5.2	odd	4
420.2.bo.a.157.5	yes	32	5.4	even	2
420.2.bo.a.313.5	yes	32	35.12	even	12
420.2.bo.a.397.7	yes	32	35.19	odd	6
1260.2.dq.c.73.4		32	15.2	even	4
1260.2.dq.c.397.4		32	105.89	even	6
1260.2.dq.c.577.7		32	15.14	odd	2
1260.2.dq.c.1153.7		32	105.47	odd	12
2100.2.ce.e.157.4		32	1.1	even	1	trivial
2100.2.ce.e.493.2		32	5.3	odd	4	inner
2100.2.ce.e.1657.2		32	7.5	odd	6	inner
2100.2.ce.e.1993.4		32	35.33	even	12	inner
2940.2.x.c.97.4		32	35.4	even	6
2940.2.x.c.97.15		32	35.24	odd	6
2940.2.x.c.1273.4		32	35.17	even	12
2940.2.x.c.1273.15		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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{3} +(2.02043 + 1.70817i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{3} +(2.02043 + 1.70817i) q^{7} +(0.866025 - 0.500000i) q^{9} +(1.21556 - 2.10542i) q^{11} +(-0.728866 - 0.728866i) q^{13} +(1.96555 + 7.33552i) q^{17} +(-1.84965 - 3.20369i) q^{19} +(-2.39370 - 1.12704i) q^{21} +(2.83634 + 0.759994i) q^{23} +(-0.707107 + 0.707107i) q^{27} -1.99120i q^{29} +(6.02262 + 3.47716i) q^{31} +(-0.629222 + 2.34829i) q^{33} +(2.20273 - 8.22068i) q^{37} +(0.892675 + 0.515386i) q^{39} -1.08701i q^{41} +(-5.91785 + 5.91785i) q^{43} +(4.81085 + 1.28906i) q^{47} +(1.16431 + 6.90249i) q^{49} +(-3.79715 - 6.57685i) q^{51} +(-1.76035 - 6.56972i) q^{53} +(2.61580 + 2.61580i) q^{57} +(1.39403 - 2.41454i) q^{59} +(0.217574 - 0.125616i) q^{61} +(2.60383 + 0.469102i) q^{63} +(-7.79096 + 2.08758i) q^{67} -2.93639 q^{69} +14.5737 q^{71} +(-6.46450 + 1.73216i) q^{73} +(6.05238 - 2.17747i) q^{77} +(-9.54459 + 5.51057i) q^{79} +(0.500000 - 0.866025i) q^{81} +(9.90994 + 9.90994i) q^{83} +(0.515361 + 1.92335i) q^{87} +(5.81468 + 10.0713i) q^{89} +(-0.227598 - 2.71765i) q^{91} +(-6.71736 - 1.79991i) q^{93} +(10.8833 - 10.8833i) q^{97} -2.43113i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) \) 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Introduction

L-functions

Modular forms

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