LMFDB - Embedded newform 2100.2.ce.e.1657.2

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			1657.2
Character	$\chi$	$=$	2100.1657
Dual form			2100.2.ce.e.493.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{3} +(1.70817 + 2.02043i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{3} +(1.70817 + 2.02043i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(1.21556 + 2.10542i) q^{11} +(0.728866 + 0.728866i) q^{13} +(7.33552 + 1.96555i) q^{17} +(1.84965 - 3.20369i) q^{19} +(-2.39370 + 1.12704i) q^{21} +(-0.759994 - 2.83634i) q^{23} +(0.707107 - 0.707107i) q^{27} -1.99120i q^{29} +(6.02262 - 3.47716i) q^{31} +(-2.34829 + 0.629222i) q^{33} +(-8.22068 + 2.20273i) q^{37} +(-0.892675 + 0.515386i) q^{39} +1.08701i q^{41} +(-5.91785 + 5.91785i) q^{43} +(1.28906 + 4.81085i) q^{47} +(-1.16431 + 6.90249i) q^{49} +(-3.79715 + 6.57685i) q^{51} +(6.56972 + 1.76035i) q^{53} +(2.61580 + 2.61580i) q^{57} +(-1.39403 - 2.41454i) q^{59} +(0.217574 + 0.125616i) q^{61} +(-0.469102 - 2.60383i) q^{63} +(2.08758 - 7.79096i) q^{67} +2.93639 q^{69} +14.5737 q^{71} +(-1.73216 + 6.46450i) q^{73} +(-2.17747 + 6.05238i) q^{77} +(9.54459 + 5.51057i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-9.90994 - 9.90994i) q^{83} +(1.92335 + 0.515361i) q^{87} +(-5.81468 + 10.0713i) q^{89} +(-0.227598 + 2.71765i) q^{91} +(1.79991 + 6.71736i) q^{93} +(-10.8833 + 10.8833i) q^{97} -2.43113i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$7$	1.70817	+	2.02043i	0.645628	+	0.763652i
$7$	1.70817	+	2.02043i	0.645628	+	0.763652i
$8$		0			0
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	1.21556	+	2.10542i	0.366506	+	0.634808i	0.989017	−	0.147804i	$-0.0472204\pi$
$11$	1.21556	+	2.10542i	0.366506	+	0.634808i	−0.622510	+	0.782612i	$0.713887\pi$
$12$		0			0
$13$	0.728866	+	0.728866i	0.202151	+	0.202151i	0.800921	−	0.598770i	$-0.204344\pi$
$13$	0.728866	+	0.728866i	0.202151	+	0.202151i	−0.598770	+	0.800921i	$0.704344\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.33552	+	1.96555i	1.77913	+	0.476715i	0.990424	−	0.138060i	$-0.0440867\pi$
$17$	7.33552	+	1.96555i	1.77913	+	0.476715i	0.788702	+	0.614776i	$0.210753\pi$
$18$		0			0
$19$	1.84965	−	3.20369i	0.424339	−	0.734977i	−0.572019	−	0.820240i	$-0.693840\pi$
$19$	1.84965	−	3.20369i	0.424339	−	0.734977i	0.996358	+	0.0852629i	$0.0271730\pi$
$20$		0			0
$21$	−2.39370	+	1.12704i	−0.522347	+	0.245940i
$22$		0			0
$23$	−0.759994	−	2.83634i	−0.158470	−	0.591417i	−0.998783	−	0.0493165i	$-0.984296\pi$
$23$	−0.759994	−	2.83634i	−0.158470	−	0.591417i	0.840313	−	0.542101i	$-0.182371\pi$
$24$		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	0.150342	−	0.988634i	$-0.451963\pi$
$31$	6.02262	−	3.47716i	1.08169	−	0.624517i	0.931353	+	0.364117i	$0.118629\pi$
$32$		0			0
$33$	−2.34829	+	0.629222i	−0.408785	+	0.109534i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−8.22068	+	2.20273i	−1.35147	+	0.362126i	−0.860678	−	0.509150i	$-0.829960\pi$
$37$	−8.22068	+	2.20273i	−1.35147	+	0.362126i	−0.490794	+	0.871276i	$0.663293\pi$
$38$		0			0
$39$	−0.892675	+	0.515386i	−0.142942	+	0.0825278i
$40$		0			0
$41$			1.08701i			0.169762i	0.996391	+	0.0848810i	$0.0270510\pi$
$41$			1.08701i			0.169762i	−0.996391	+	0.0848810i	$0.972949\pi$
$42$		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
$47$	1.28906	+	4.81085i	0.188029	+	0.701735i	0.993962	+	0.109727i	$0.0349978\pi$
$47$	1.28906	+	4.81085i	0.188029	+	0.701735i	−0.805932	+	0.592007i	$0.798336\pi$
$48$		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
$53$	6.56972	+	1.76035i	0.902420	+	0.241803i	0.680055	−	0.733161i	$-0.261956\pi$
$53$	6.56972	+	1.76035i	0.902420	+	0.241803i	0.222365	+	0.974964i	$0.428622\pi$
$54$		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	$-0.224758\pi$
$59$	−1.39403	−	2.41454i	−0.181488	−	0.314346i	−0.942387	+	0.334523i	$0.891425\pi$
$60$		0			0
$61$	0.217574	+	0.125616i	0.0278575	+	0.0160835i	0.513864	−	0.857872i	$-0.328214\pi$
$61$	0.217574	+	0.125616i	0.0278575	+	0.0160835i	−0.486007	+	0.873955i	$0.661547\pi$
$62$		0			0
$63$	−0.469102	−	2.60383i	−0.0591013	−	0.328052i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.08758	−	7.79096i	0.255039	−	0.951818i	−0.713030	−	0.701133i	$-0.752678\pi$
$67$	2.08758	−	7.79096i	0.255039	−	0.951818i	0.968069	−	0.250684i	$-0.0806556\pi$
$68$		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
$73$	−1.73216	+	6.46450i	−0.202734	+	0.756612i	0.787395	+	0.616449i	$0.211429\pi$
$73$	−1.73216	+	6.46450i	−0.202734	+	0.756612i	−0.990128	+	0.140163i	$0.955237\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.17747	+	6.05238i	−0.248146	+	0.689733i
$78$		0			0
$79$	9.54459	+	5.51057i	1.07385	+	0.619987i	0.929231	−	0.369500i	$-0.120471\pi$
$79$	9.54459	+	5.51057i	1.07385	+	0.619987i	0.144619	+	0.989487i	$0.453804\pi$
$80$		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	$-0.970675\pi$
$83$	−9.90994	−	9.90994i	−1.08776	−	1.08776i	−0.0919976	−	0.995759i	$-0.529325\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.92335	+	0.515361i	0.206205	+	0.0552525i
$88$		0			0
$89$	−5.81468	+	10.0713i	−0.616354	+	1.06756i	0.373791	+	0.927513i	$0.378058\pi$
$89$	−5.81468	+	10.0713i	−0.616354	+	1.06756i	−0.990145	+	0.140044i	$0.955276\pi$
$90$		0			0
$91$	−0.227598	+	2.71765i	−0.0238587	+	0.284887i
$92$		0			0
$93$	1.79991	+	6.71736i	0.186642	+	0.696558i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.8833	+	10.8833i	−1.10503	+	1.10503i	−0.111236	+	0.993794i	$0.535481\pi$
$97$	−10.8833	+	10.8833i	−1.10503	+	1.10503i	−0.993794	+	0.111236i	$0.964519\pi$
$98$		0			0
$99$		−	2.43113i		−	0.244338i
$100$		0			0
$101$	5.44655	−	3.14457i	0.541952	−	0.312896i	−0.203918	−	0.978988i	$-0.565367\pi$
$101$	5.44655	−	3.14457i	0.541952	−	0.312896i	0.745870	+	0.666092i	$0.232034\pi$
$102$		0			0
$103$	−14.5741	+	3.90512i	−1.43603	+	0.384782i	−0.891141	−	0.453727i	$-0.850094\pi$
$103$	−14.5741	+	3.90512i	−1.43603	+	0.384782i	−0.544887	+	0.838510i	$0.683427\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.1277	−	3.78551i	1.36578	−	0.365960i	0.499844	−	0.866115i	$-0.333391\pi$
$107$	14.1277	−	3.78551i	1.36578	−	0.365960i	0.865935	+	0.500156i	$0.166724\pi$
$108$		0			0
$109$	−10.3565	+	5.97935i	−0.991976	+	0.572718i	−0.905864	−	0.423568i	$-0.860778\pi$
$109$	−10.3565	+	5.97935i	−0.991976	+	0.572718i	−0.0861118	+	0.996285i	$0.527444\pi$
$110$		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
$117$	−0.266783	−	0.995650i	−0.0246641	−	0.0920478i
$118$		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
$123$	−1.04997	−	0.281338i	−0.0946724	−	0.0253674i
$124$		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	0.825716	−	0.564086i	$-0.190771\pi$
$131$	8.58485	+	4.95646i	0.750062	+	0.433048i	−0.0756546	+	0.997134i	$0.524105\pi$
$132$		0			0
$133$	9.63237	−	1.73535i	0.835232	−	0.150474i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.71987	+	13.8828i	−0.317810	+	1.18608i	0.603535	+	0.797337i	$0.293759\pi$
$137$	−3.71987	+	13.8828i	−0.317810	+	1.18608i	−0.921345	+	0.388747i	$0.872908\pi$
$138$		0			0
$139$	−11.0917			−0.940787			−0.470394	−	0.882457i	$-0.655888\pi$
$139$	−11.0917			−0.940787			−0.470394	+	0.882457i	$0.655888\pi$
$140$		0			0
$141$	−4.98056			−0.419439
$142$		0			0
$143$	−0.648585	+	2.42055i	−0.0542374	+	0.202417i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.36595	−	2.91113i	−0.525055	−	0.240106i
$148$		0			0
$149$	7.66332	+	4.42442i	0.627804	+	0.362463i	0.779901	−	0.625903i	$-0.215269\pi$
$149$	7.66332	+	4.42442i	0.627804	+	0.362463i	−0.152097	+	0.988366i	$0.548603\pi$
$150$		0			0
$151$	−0.901062	−	1.56068i	−0.0733274	−	0.127007i	0.827030	−	0.562157i	$-0.190028\pi$
$151$	−0.901062	−	1.56068i	−0.0733274	−	0.127007i	−0.900358	+	0.435151i	$0.856695\pi$
$152$		0			0
$153$	−5.36998	−	5.36998i	−0.434137	−	0.434137i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.0832	+	2.96972i	0.884532	+	0.237010i	0.672361	−	0.740223i	$-0.265280\pi$
$157$	11.0832	+	2.96972i	0.884532	+	0.237010i	0.212171	+	0.977233i	$0.431947\pi$
$158$		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
$163$	0.0813198	+	0.303489i	0.00636946	+	0.0237711i	0.969037	−	0.246914i	$-0.0794165\pi$
$163$	0.0813198	+	0.303489i	0.00636946	+	0.0237711i	−0.962668	+	0.270685i	$0.912750\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.10159	+	2.10159i	−0.162626	+	0.162626i	−0.783729	−	0.621103i	$-0.786685\pi$
$167$	−2.10159	+	2.10159i	−0.162626	+	0.162626i	0.621103	+	0.783729i	$0.286685\pi$
$168$		0			0
$169$		−	11.9375i		−	0.918270i
$170$		0			0
$171$	−3.20369	+	1.84965i	−0.244992	+	0.141446i
$172$		0			0
$173$	−9.48720	+	2.54209i	−0.721298	+	0.193271i	−0.600751	−	0.799436i	$-0.705132\pi$
$173$	−9.48720	+	2.54209i	−0.721298	+	0.193271i	−0.120547	+	0.992708i	$0.538465\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.69307	−	0.721606i	0.202423	−	0.0542392i
$178$		0			0
$179$	−15.8512	+	9.15169i	−1.18477	+	0.684030i	−0.957114	−	0.289711i	$-0.906441\pi$
$179$	−15.8512	+	9.15169i	−1.18477	+	0.684030i	−0.227660	+	0.973741i	$0.573107\pi$
$180$		0			0
$181$			20.1817i			1.50009i	0.661387	+	0.750045i	$0.269968\pi$
$181$			20.1817i			1.50009i	−0.661387	+	0.750045i	$0.730032\pi$
$182$		0			0
$183$	−0.177648	+	0.177648i	−0.0131321	+	0.0131321i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.77850	+	17.8336i	0.349439	+	1.30412i
$188$		0			0
$189$	2.63652	+	0.220803i	0.191779	+	0.0160611i
$190$		0			0
$191$	−1.24147	+	2.15029i	−0.0898297	+	0.155590i	−0.907439	−	0.420184i	$-0.861966\pi$
$191$	−1.24147	+	2.15029i	−0.0898297	+	0.155590i	0.817609	+	0.575773i	$0.195299\pi$
$192$		0			0
$193$	12.8390	+	3.44019i	0.924169	+	0.247630i	0.689366	−	0.724413i	$-0.257889\pi$
$193$	12.8390	+	3.44019i	0.924169	+	0.247630i	0.234802	+	0.972043i	$0.424556\pi$
$194$		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	$-0.314776\pi$
$199$	−6.32953	−	10.9631i	−0.448689	−	0.777152i	−0.998301	+	0.0582681i	$0.981442\pi$
$200$		0			0
$201$	6.98519	+	4.03290i	0.492697	+	0.284459i
$202$		0			0
$203$	4.02309	−	3.40131i	0.282366	−	0.238725i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.759994	+	2.83634i	−0.0528233	+	0.197139i
$208$		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
$213$	−3.77195	+	14.0771i	−0.258450	+	0.964548i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	17.3130	+	6.22872i	1.17529	+	0.422833i
$218$		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	$-0.944831\pi$
$223$	−17.2847	−	17.2847i	−1.15747	−	1.15747i	−0.172452	−	0.985018i	$-0.555169\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.81901	+	0.487401i	0.120732	+	0.0323499i	0.318679	−	0.947863i	$-0.396761\pi$
$227$	1.81901	+	0.487401i	0.120732	+	0.0323499i	−0.197947	+	0.980213i	$0.563427\pi$
$228$		0			0
$229$	12.5383	−	21.7171i	0.828557	−	1.43510i	−0.0706123	−	0.997504i	$-0.522495\pi$
$229$	12.5383	−	21.7171i	0.828557	−	1.43510i	0.899170	−	0.437600i	$-0.144171\pi$
$230$		0			0
$231$	−5.28258	−	3.66975i	−0.347568	−	0.241452i
$232$		0			0
$233$	5.80563	+	21.6669i	0.380340	+	1.41945i	0.845384	+	0.534159i	$0.179372\pi$
$233$	5.80563	+	21.6669i	0.380340	+	1.41945i	−0.465044	+	0.885287i	$0.653962\pi$
$234$		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	−0.919624	−	0.392799i	$-0.871507\pi$
$241$	−16.1337	+	9.31479i	−1.03926	+	0.600018i	−0.119638	+	0.992818i	$0.538173\pi$
$242$		0			0
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.68321	−	0.986914i	0.234357	−	0.0627958i
$248$		0			0
$249$	12.1371	−	7.00738i	0.769160	−	0.444075i
$250$		0			0
$251$		−	31.5776i		−	1.99316i	−0.0826181	−	0.996581i	$-0.526328\pi$
$251$		−	31.5776i		−	1.99316i	0.0826181	−	0.996581i	$-0.473672\pi$
$252$		0			0
$253$	5.04786	−	5.04786i	0.317356	−	0.317356i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.81126	−	17.9559i	−0.300118	−	1.12006i	−0.937067	−	0.349150i	$-0.886470\pi$
$257$	−4.81126	−	17.9559i	−0.300118	−	1.12006i	0.636949	−	0.770906i	$-0.280196\pi$
$258$		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
$263$	−5.52178	−	1.47956i	−0.340488	−	0.0912334i	0.0845235	−	0.996421i	$-0.473063\pi$
$263$	−5.52178	−	1.47956i	−0.340488	−	0.0912334i	−0.425011	+	0.905188i	$0.639730\pi$
$264$		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	$-0.142874\pi$
$269$	1.22482	+	2.12145i	0.0746785	+	0.129347i	−0.826268	+	0.563277i	$0.809540\pi$
$270$		0			0
$271$	−21.9156	−	12.6530i	−1.33128	−	0.768613i	−0.345782	−	0.938315i	$-0.612386\pi$
$271$	−21.9156	−	12.6530i	−1.33128	−	0.768613i	−0.985495	+	0.169702i	$0.945720\pi$
$272$		0			0
$273$	−2.56614	−	0.923223i	−0.155310	−	0.0558760i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	8.27697	−	30.8901i	0.497315	−	1.85600i	−0.0193451	−	0.999813i	$-0.506158\pi$
$277$	8.27697	−	30.8901i	0.497315	−	1.85600i	0.516660	−	0.856191i	$-0.327175\pi$
$278$		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
$283$	−0.584999	+	2.18325i	−0.0347746	+	0.129780i	−0.981131	−	0.193344i	$-0.938067\pi$
$283$	−0.584999	+	2.18325i	−0.0347746	+	0.129780i	0.946356	+	0.323125i	$0.104733\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.19623	+	1.85679i	−0.129639	+	0.109603i
$288$		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	0.794237	−	0.607608i	$-0.207871\pi$
$293$	3.19458	+	3.19458i	0.186629	+	0.186629i	−0.607608	+	0.794237i	$0.707871\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.34829	+	0.629222i	0.136262	+	0.0365112i
$298$		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
$303$	1.62775	+	6.07484i	0.0935117	+	0.348990i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	5.74597	−	5.74597i	0.327940	−	0.327940i	−0.523863	−	0.851803i	$-0.675510\pi$
$307$	5.74597	−	5.74597i	0.327940	−	0.327940i	0.851803	+	0.523863i	$0.175510\pi$
$308$		0			0
$309$		−	15.0882i		−	0.858338i
$310$		0			0
$311$	12.5238	−	7.23064i	0.710161	−	0.410012i	−0.100959	−	0.994891i	$-0.532191\pi$
$311$	12.5238	−	7.23064i	0.710161	−	0.410012i	0.811121	+	0.584879i	$0.198858\pi$
$312$		0			0
$313$	1.14185	−	0.305958i	0.0645412	−	0.0172938i	−0.226404	−	0.974033i	$-0.572697\pi$
$313$	1.14185	−	0.305958i	0.0645412	−	0.0172938i	0.290945	+	0.956740i	$0.406030\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.53996	+	2.28828i	−0.479652	+	0.128522i	−0.490541	−	0.871418i	$-0.663201\pi$
$317$	−8.53996	+	2.28828i	−0.479652	+	0.128522i	0.0108885	+	0.999941i	$0.496534\pi$
$318$		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
$327$	−3.09514	−	11.5512i	−0.171162	−	0.638784i
$328$		0			0
$329$	−7.51807	+	10.8222i	−0.414484	+	0.596649i
$330$		0			0
$331$	−10.9304	+	18.9320i	−0.600789	+	1.04060i	0.391913	+	0.920002i	$0.371814\pi$
$331$	−10.9304	+	18.9320i	−0.600789	+	1.04060i	−0.992702	+	0.120595i	$0.961520\pi$
$332$		0			0
$333$	8.22068	+	2.20273i	0.450491	+	0.120709i
$334$		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
$343$	−15.9349	+	9.43823i	−0.860402	+	0.509617i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.08442	−	4.04711i	0.0582148	−	0.217261i	−0.930691	−	0.365807i	$-0.880793\pi$
$347$	1.08442	−	4.04711i	0.0582148	−	0.217261i	0.988905	+	0.148547i	$0.0474596\pi$
$348$		0			0
$349$	−33.8258			−1.81065			−0.905327	−	0.424715i	$-0.860374\pi$
$349$	−33.8258			−1.81065			−0.905327	+	0.424715i	$0.860374\pi$
$350$		0			0
$351$	1.03077			0.0550186
$352$		0			0
$353$	8.70598	−	32.4911i	0.463372	−	1.72933i	−0.198857	−	0.980028i	$-0.563723\pi$
$353$	8.70598	−	32.4911i	0.463372	−	1.72933i	0.662230	−	0.749301i	$-0.269610\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−19.7743	+	3.56250i	−1.04657	+	0.188548i
$358$		0			0
$359$	14.0177	+	8.09313i	0.739826	+	0.427139i	0.822006	−	0.569479i	$-0.192855\pi$
$359$	14.0177	+	8.09313i	0.739826	+	0.427139i	−0.0821800	+	0.996618i	$0.526188\pi$
$360$		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
$367$	−15.6293	−	4.18786i	−0.815842	−	0.218604i	−0.173314	−	0.984867i	$-0.555448\pi$
$367$	−15.6293	−	4.18786i	−0.815842	−	0.218604i	−0.642528	+	0.766262i	$0.722114\pi$
$368$		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
$373$	0.962517	+	3.59216i	0.0498372	+	0.185995i	0.986357	−	0.164619i	$-0.0526395\pi$
$373$	0.962517	+	3.59216i	0.0498372	+	0.185995i	−0.936520	+	0.350614i	$0.885973\pi$
$374$		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
$383$	33.4767	−	8.97006i	1.71058	−	0.458349i	0.735014	−	0.678052i	$-0.237176\pi$
$383$	33.4767	−	8.97006i	1.71058	−	0.458349i	0.975567	+	0.219703i	$0.0705089\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.08394	−	2.16608i	0.410930	−	0.110108i
$388$		0			0
$389$	28.3146	−	16.3474i	1.43561	−	0.828847i	0.438065	−	0.898943i	$-0.355664\pi$
$389$	28.3146	−	16.3474i	1.43561	−	0.828847i	0.997540	+	0.0700961i	$0.0223306\pi$
$390$		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
$397$	−4.73087	−	17.6559i	−0.237436	−	0.886122i	−0.977036	−	0.213076i	$-0.931652\pi$
$397$	−4.73087	−	17.6559i	−0.237436	−	0.886122i	0.739600	−	0.673047i	$-0.235015\pi$
$398$		0			0
$399$	−0.816819	+	9.75330i	−0.0408921	+	0.488276i
$400$		0			0
$401$	−0.590882	+	1.02344i	−0.0295072	+	0.0511080i	−0.880402	−	0.474228i	$-0.842727\pi$
$401$	−0.590882	+	1.02344i	−0.0295072	+	0.0511080i	0.850895	+	0.525336i	$0.176060\pi$
$402$		0			0
$403$	6.92407	+	1.85530i	0.344913	+	0.0924190i
$404$		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	$-0.0352843\pi$
$409$	8.11235	+	14.0510i	0.401130	+	0.694777i	−0.592733	+	0.805399i	$0.701951\pi$
$410$		0			0
$411$	−12.4469	−	7.18624i	−0.613962	−	0.354471i
$412$		0			0
$413$	2.49717	−	6.94100i	0.122878	−	0.341544i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.87075	−	10.7138i	0.140581	−	0.524656i
$418$		0			0
$419$	−15.4289			−0.753750			−0.376875	−	0.926264i	$-0.623001\pi$
$419$	−15.4289			−0.753750			−0.376875	+	0.926264i	$0.623001\pi$
$420$		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
$423$	1.28906	−	4.81085i	0.0626764	−	0.233912i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.117854	+	0.654167i	0.00570335	+	0.0316574i
$428$		0			0
$429$	−2.17021	−	1.25297i	−0.104779	−	0.0604940i
$430$		0			0
$431$	−1.83304	−	3.17492i	−0.0882944	−	0.152930i	0.818496	−	0.574512i	$-0.194808\pi$
$431$	−1.83304	−	3.17492i	−0.0882944	−	0.152930i	−0.906790	+	0.421582i	$0.861475\pi$
$432$		0			0
$433$	9.74318	+	9.74318i	0.468227	+	0.468227i	0.901340	−	0.433112i	$-0.142585\pi$
$433$	9.74318	+	9.74318i	0.468227	+	0.468227i	−0.433112	+	0.901340i	$0.642585\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.4925	−	2.81145i	−0.501923	−	0.134490i
$438$		0			0
$439$	3.00918	−	5.21204i	0.143620	−	0.248757i	−0.785237	−	0.619195i	$-0.787459\pi$
$439$	3.00918	−	5.21204i	0.143620	−	0.248757i	0.928857	+	0.370438i	$0.120792\pi$
$440$		0			0
$441$	4.45956	−	5.39558i	0.212360	−	0.256932i
$442$		0			0
$443$	−5.25355	−	19.6065i	−0.249604	−	0.931534i	−0.971013	−	0.239025i	$-0.923172\pi$
$443$	−5.25355	−	19.6065i	−0.249604	−	0.931534i	0.721410	−	0.692509i	$-0.243495\pi$
$444$		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
$453$	1.74072	−	0.466424i	0.0817860	−	0.0219145i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−30.1623	+	8.08197i	−1.41093	+	0.378058i	−0.882258	−	0.470766i	$-0.843978\pi$
$457$	−30.1623	+	8.08197i	−1.41093	+	0.378058i	−0.528675	+	0.848824i	$0.677311\pi$
$458$		0			0
$459$	6.57685	−	3.79715i	0.306981	−	0.177236i
$460$		0			0
$461$		−	23.4059i		−	1.09012i	−0.838397	−	0.545060i	$-0.816507\pi$
$461$		−	23.4059i		−	1.09012i	0.838397	−	0.545060i	$-0.183493\pi$
$462$		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
$467$	−10.0990	−	37.6898i	−0.467324	−	1.74408i	−0.649068	−	0.760730i	$-0.724841\pi$
$467$	−10.0990	−	37.6898i	−0.467324	−	1.74408i	0.181744	−	0.983346i	$-0.441826\pi$
$468$		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
$473$	−19.6531	−	5.26603i	−0.903650	−	0.242132i
$474$		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	$-0.0528371\pi$
$479$	7.66084	+	13.2690i	0.350033	+	0.606275i	−0.636222	+	0.771506i	$0.719504\pi$
$480$		0			0
$481$	−7.59727	−	4.38628i	−0.346406	−	0.199997i
$482$		0			0
$483$	5.01586	+	5.93279i	0.228230	+	0.269951i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	4.32465	−	16.1398i	0.195968	−	0.731364i	−0.796046	−	0.605237i	$-0.793079\pi$
$487$	4.32465	−	16.1398i	0.195968	−	0.731364i	0.992014	−	0.126127i	$-0.0402548\pi$
$488$		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
$493$	3.91380	−	14.6065i	0.176269	−	0.657844i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.8944	+	29.4452i	1.11667	+	1.32080i
$498$		0			0
$499$	−12.1410	−	7.00959i	−0.543504	−	0.313792i	0.202994	−	0.979180i	$-0.434933\pi$
$499$	−12.1410	−	7.00959i	−0.543504	−	0.313792i	−0.746498	+	0.665388i	$0.768266\pi$
$500$		0			0
$501$	−1.48605	−	2.57391i	−0.0663917	−	0.114994i
$502$		0			0
$503$	20.0052	+	20.0052i	0.891989	+	0.891989i	0.994710	−	0.102721i	$-0.0327549\pi$
$503$	20.0052	+	20.0052i	0.891989	+	0.891989i	−0.102721	+	0.994710i	$0.532755\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	11.5307	+	3.08965i	0.512098	+	0.137216i
$508$		0			0
$509$	−6.58364	+	11.4032i	−0.291815	+	0.505438i	−0.974239	−	0.225518i	$-0.927592\pi$
$509$	−6.58364	+	11.4032i	−0.291815	+	0.505438i	0.682424	+	0.730956i	$0.260926\pi$
$510$		0			0
$511$	−16.0199	+	7.54276i	−0.708679	+	0.333672i
$512$		0			0
$513$	−0.957451	−	3.57325i	−0.0422725	−	0.157763i
$514$		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	−0.905645	−	0.424036i	$-0.860613\pi$
$521$	−22.6255	+	13.0628i	−0.991242	+	0.572294i	−0.0855965	+	0.996330i	$0.527280\pi$
$522$		0			0
$523$	5.53573	−	1.48330i	0.242061	−	0.0648600i	−0.135749	−	0.990743i	$-0.543344\pi$
$523$	5.53573	−	1.48330i	0.242061	−	0.0648600i	0.377810	+	0.925883i	$0.376677\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	51.0136	−	13.6691i	2.22219	−	0.595434i
$528$		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
$537$	−4.73727	−	17.6797i	−0.204428	−	0.762936i
$538$		0			0
$539$	−15.9479	+	5.93907i	−0.686926	+	0.255814i
$540$		0			0
$541$	−14.1293	+	24.4727i	−0.607468	+	1.05217i	0.384188	+	0.923255i	$0.374481\pi$
$541$	−14.1293	+	24.4727i	−0.607468	+	1.05217i	−0.991656	+	0.128910i	$0.958852\pi$
$542$		0			0
$543$	−19.4940	−	5.22340i	−0.836567	−	0.224157i
$544$		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
$553$	5.17004	+	28.6972i	0.219853	+	1.22033i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.73283	+	21.3952i	−0.242908	+	0.906544i	0.731516	+	0.681825i	$0.238813\pi$
$557$	−5.73283	+	21.3952i	−0.242908	+	0.906544i	−0.974423	+	0.224720i	$0.927853\pi$
$558$		0			0
$559$	−8.62664			−0.364868
$560$		0			0
$561$	−18.4627			−0.779496
$562$		0			0
$563$	0.337839	−	1.26083i	0.0142382	−	0.0531378i	−0.958441	−	0.285290i	$-0.907910\pi$
$563$	0.337839	−	1.26083i	0.0142382	−	0.0531378i	0.972679	+	0.232152i	$0.0745768\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.895662	+	2.48954i	−0.0376143	+	0.104551i
$568$		0			0
$569$	−0.426999	−	0.246528i	−0.0179007	−	0.0103350i	0.491023	−	0.871147i	$-0.336623\pi$
$569$	−0.426999	−	0.246528i	−0.0179007	−	0.0103350i	−0.508924	+	0.860812i	$0.669956\pi$
$570$		0			0
$571$	−1.79895	−	3.11588i	−0.0752839	−	0.130395i	0.825926	−	0.563779i	$-0.190653\pi$
$571$	−1.79895	−	3.11588i	−0.0752839	−	0.130395i	−0.901210	+	0.433383i	$0.857320\pi$
$572$		0			0
$573$	−1.75571	−	1.75571i	−0.0733456	−	0.0733456i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	12.2308	+	3.27724i	0.509177	+	0.136433i	0.504256	−	0.863554i	$-0.331767\pi$
$577$	12.2308	+	3.27724i	0.509177	+	0.136433i	0.00492102	+	0.999988i	$0.498434\pi$
$578$		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
$583$	4.27964	+	15.9718i	0.177245	+	0.661486i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.84683	+	2.84683i	−0.117501	+	0.117501i	−0.763413	−	0.645911i	$-0.776478\pi$
$587$	−2.84683	+	2.84683i	−0.117501	+	0.117501i	0.645911	+	0.763413i	$0.276478\pi$
$588$		0			0
$589$		−	25.7262i		−	1.06003i
$590$		0			0
$591$	−6.67736	+	3.85517i	−0.274670	+	0.158581i
$592$		0			0
$593$	30.7485	−	8.23903i	1.26269	−	0.338336i	0.435463	−	0.900206i	$-0.356585\pi$
$593$	30.7485	−	8.23903i	1.26269	−	0.338336i	0.827226	+	0.561870i	$0.189918\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	12.2277	−	3.27641i	0.500447	−	0.134094i
$598$		0			0
$599$	33.3274	−	19.2416i	1.36172	−	0.786191i	0.371869	−	0.928285i	$-0.378717\pi$
$599$	33.3274	−	19.2416i	1.36172	−	0.786191i	0.989853	+	0.142095i	$0.0453837\pi$
$600$		0			0
$601$		−	45.6842i		−	1.86350i	−0.363102	−	0.931750i	$-0.618282\pi$
$601$		−	45.6842i		−	1.86350i	0.363102	−	0.931750i	$-0.381718\pi$
$602$		0			0
$603$	−5.70338	+	5.70338i	−0.232260	+	0.232260i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.42220	+	23.9680i	0.260669	+	0.972831i	0.964848	+	0.262808i	$0.0846487\pi$
$607$	6.42220	+	23.9680i	0.260669	+	0.972831i	−0.704179	+	0.710023i	$0.748685\pi$
$608$		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
$613$	1.06899	+	0.286436i	0.0431762	+	0.0115690i	0.280343	−	0.959900i	$-0.409552\pi$
$613$	1.06899	+	0.286436i	0.0431762	+	0.0115690i	−0.237166	+	0.971469i	$0.576219\pi$
$614$		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	$-0.0121768\pi$
$619$	11.6067	+	20.1034i	0.466513	+	0.808024i	−0.532756	+	0.846269i	$0.678844\pi$
$620$		0			0
$621$	−2.54299	−	1.46820i	−0.102047	−	0.0589167i
$622$		0			0
$623$	−30.2809	+	5.45536i	−1.21318	+	0.218564i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.32769	+	8.68704i	−0.0929588	+	0.346927i
$628$		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
$633$	1.39150	−	5.19316i	0.0553073	−	0.206410i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−5.87961	+	4.18237i	−0.232959	+	0.165712i
$638$		0			0
$639$	−12.6212	−	7.28685i	−0.499287	−	0.288263i
$640$		0			0
$641$	18.7675	+	32.5062i	0.741271	+	1.28392i	0.951917	+	0.306356i	$0.0991099\pi$
$641$	18.7675	+	32.5062i	0.741271	+	1.28392i	−0.210646	+	0.977562i	$0.567557\pi$
$642$		0			0
$643$	−12.0570	−	12.0570i	−0.475483	−	0.475483i	0.428201	−	0.903684i	$-0.359148\pi$
$643$	−12.0570	−	12.0570i	−0.475483	−	0.475483i	−0.903684	+	0.428201i	$0.859148\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.0130	−	4.82656i	−0.708163	−	0.189752i	−0.113279	−	0.993563i	$-0.536135\pi$
$647$	−18.0130	−	4.82656i	−0.708163	−	0.189752i	−0.594884	+	0.803812i	$0.702802\pi$
$648$		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
$653$	4.34601	+	16.2195i	0.170073	+	0.634719i	0.997339	+	0.0729090i	$0.0232283\pi$
$653$	4.34601	+	16.2195i	0.170073	+	0.634719i	−0.827266	+	0.561810i	$0.810105\pi$
$654$		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	−0.280471	−	0.959862i	$-0.590491\pi$
$661$	10.5554	−	6.09418i	0.410558	−	0.237036i	0.691030	+	0.722826i	$0.257157\pi$
$662$		0			0
$663$	−7.56125	+	2.02603i	−0.293655	+	0.0786846i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.64772	+	1.51330i	−0.218681	+	0.0585953i
$668$		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
$677$	2.45115	+	9.14780i	0.0942052	+	0.351578i	0.996898	−	0.0787076i	$-0.0250794\pi$
$677$	2.45115	+	9.14780i	0.0942052	+	0.351578i	−0.902693	+	0.430286i	$0.858413\pi$
$678$		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
$683$	−20.7804	−	5.56809i	−0.795139	−	0.213057i	−0.161690	−	0.986842i	$-0.551695\pi$
$683$	−20.7804	−	5.56809i	−0.795139	−	0.213057i	−0.633449	+	0.773785i	$0.718361\pi$
$684$		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	0.599581	−	0.800314i	$-0.295334\pi$
$691$	5.42242	+	3.13064i	0.206279	+	0.119095i	−0.393302	+	0.919409i	$0.628667\pi$
$692$		0			0
$693$	4.91193	−	4.15278i	0.186589	−	0.157751i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.13656	+	7.97377i	−0.0809281	+	0.302028i
$698$		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
$703$	−8.14855	+	30.4108i	−0.307328	+	1.14697i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.6570	+	5.63294i	0.588843	+	0.211848i
$708$		0			0
$709$	0.279672	+	0.161469i	0.0105033	+	0.00606409i	0.505242	−	0.862977i	$-0.331403\pi$
$709$	0.279672	+	0.161469i	0.0105033	+	0.00606409i	−0.494739	+	0.869042i	$0.664736\pi$
$710$		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
$717$	6.17147	+	1.65364i	0.230478	+	0.0617563i
$718$		0			0
$719$	10.1034	−	17.4996i	0.376792	−	0.652623i	−0.613801	−	0.789460i	$-0.710360\pi$
$719$	10.1034	−	17.4996i	0.376792	−	0.652623i	0.990594	+	0.136837i	$0.0436938\pi$
$720$		0			0
$721$	−32.7851	−	22.7754i	−1.22098	−	0.848199i
$722$		0			0
$723$	−4.82169	−	17.9948i	−0.179321	−	0.669234i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	3.29844	−	3.29844i	0.122332	−	0.122332i	−0.643290	−	0.765622i	$-0.722431\pi$
$727$	3.29844	−	3.29844i	0.122332	−	0.122332i	0.765622	+	0.643290i	$0.222431\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−55.0424	+	31.7787i	−2.03582	+	1.17538i
$732$		0			0
$733$	−14.6701	+	3.93084i	−0.541852	+	0.145189i	−0.519356	−	0.854558i	$-0.673828\pi$
$733$	−14.6701	+	3.93084i	−0.541852	+	0.145189i	−0.0224964	+	0.999747i	$0.507161\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18.9408	−	5.07518i	0.697695	−	0.186947i
$738$		0			0
$739$	15.6624	−	9.04272i	0.576153	−	0.332642i	−0.183450	−	0.983029i	$-0.558727\pi$
$739$	15.6624	−	9.04272i	0.576153	−	0.332642i	0.759603	+	0.650387i	$0.225393\pi$
$740$		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
$747$	3.62729	+	13.5372i	0.132716	+	0.495301i
$748$		0			0
$749$	31.7810	+	22.0778i	1.16125	+	0.806707i
$750$		0			0
$751$	22.6070	−	39.1564i	0.824940	−	1.42884i	−0.0770253	−	0.997029i	$-0.524542\pi$
$751$	22.6070	−	39.1564i	0.824940	−	1.42884i	0.901965	−	0.431809i	$-0.142124\pi$
$752$		0			0
$753$	30.5017	+	8.17289i	1.11154	+	0.297837i
$754$		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	0.0356201	−	0.999365i	$-0.488659\pi$
$761$	−22.4013	−	12.9334i	−0.812046	−	0.468835i	−0.847666	+	0.530531i	$0.821993\pi$
$762$		0			0
$763$	−29.7716	−	10.7109i	−1.07780	−	0.387762i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.743811	−	2.77594i	0.0268575	−	0.100233i
$768$		0			0
$769$	−3.97934			−0.143499			−0.0717493	−	0.997423i	$-0.522858\pi$
$769$	−3.97934			−0.143499			−0.0717493	+	0.997423i	$0.522858\pi$
$770$		0			0
$771$	18.5893			0.669476
$772$		0			0
$773$	7.53332	−	28.1147i	0.270955	−	1.01122i	−0.687549	−	0.726138i	$-0.741314\pi$
$773$	7.53332	−	28.1147i	0.270955	−	1.01122i	0.958504	−	0.285079i	$-0.0920198\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	17.1953	−	14.5377i	0.616876	−	0.521537i
$778$		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
$787$	−29.3783	−	7.87190i	−1.04722	−	0.280603i	−0.306120	−	0.951993i	$-0.599031\pi$
$787$	−29.3783	−	7.87190i	−1.04722	−	0.280603i	−0.741104	+	0.671390i	$0.765698\pi$
$788$		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
$793$	0.0670247	+	0.250140i	0.00238012	+	0.00888272i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.04054	+	4.04054i	−0.143123	+	0.143123i	−0.775038	−	0.631915i	$-0.782269\pi$
$797$	−4.04054	+	4.04054i	−0.143123	+	0.143123i	0.631915	+	0.775038i	$0.282269\pi$
$798$		0			0
$799$			37.8238i			1.33811i
$800$		0			0
$801$	10.0713	−	5.81468i	0.355852	−	0.205451i
$802$		0			0
$803$	−15.7160	+	4.21110i	−0.554607	+	0.148606i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.36617	+	0.634013i	−0.0832931	+	0.0223183i
$808$		0			0
$809$	−37.9488	+	21.9098i	−1.33421	+	0.770306i	−0.985942	−	0.167089i	$-0.946563\pi$
$809$	−37.9488	+	21.9098i	−1.33421	+	0.770306i	−0.348268	+	0.937395i	$0.613230\pi$
$810$		0			0
$811$		−	1.74791i		−	0.0613774i	−0.999529	−	0.0306887i	$-0.990230\pi$
$811$		−	1.74791i		−	0.0613774i	0.999529	−	0.0306887i	$-0.00977005\pi$
$812$		0			0
$813$	17.8940	−	17.8940i	0.627570	−	0.627570i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	8.01301	+	29.9049i	0.280340	+	1.04624i
$818$		0			0
$819$	1.55593	−	2.23976i	0.0543687	−	0.0782635i
$820$		0			0
$821$	13.5210	−	23.4191i	0.471886	−	0.817331i	−0.527596	−	0.849495i	$-0.676907\pi$
$821$	13.5210	−	23.4191i	0.471886	−	0.817331i	0.999483	+	0.0321643i	$0.0102400\pi$
$822$		0			0
$823$	−2.50063	−	0.670043i	−0.0871667	−	0.0233562i	0.214972	−	0.976620i	$-0.431034\pi$
$823$	−2.50063	−	0.670043i	−0.0871667	−	0.0233562i	−0.302139	+	0.953264i	$0.597701\pi$
$824$		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	0.980132	+	0.198344i	$0.0635563\pi$
$829$	19.0559	+	33.0057i	0.661837	+	1.14634i	−0.318295	+	0.947992i	$0.603110\pi$
$830$		0			0
$831$	27.6953	+	15.9899i	0.960738	+	0.554682i
$832$		0			0
$833$	−22.1080	+	48.3449i	−0.765996	+	1.67505i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.79991	−	6.71736i	0.0622141	−	0.232186i
$838$		0			0
$839$	27.2101			0.939398			0.469699	−	0.882827i	$-0.344362\pi$
$839$	27.2101			0.939398			0.469699	+	0.882827i	$0.344362\pi$
$840$		0			0
$841$	25.0351			0.863280
$842$		0			0
$843$	−3.18462	+	11.8852i	−0.109684	+	0.409346i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	13.2525	−	2.38755i	0.455361	−	0.0820372i
$848$		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	0.884116	−	0.467268i	$-0.154762\pi$
$853$	12.1745	+	12.1745i	0.416848	+	0.416848i	−0.467268	+	0.884116i	$0.654762\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−33.5825	−	8.99840i	−1.14716	−	0.307379i	−0.365331	−	0.930878i	$-0.619044\pi$
$857$	−33.5825	−	8.99840i	−1.14716	−	0.307379i	−0.781825	+	0.623498i	$0.785711\pi$
$858$		0			0
$859$	−16.7607	+	29.0304i	−0.571869	+	0.990506i	0.424505	+	0.905426i	$0.360448\pi$
$859$	−16.7607	+	29.0304i	−0.571869	+	0.990506i	−0.996374	+	0.0850805i	$0.972885\pi$
$860$		0			0
$861$	−1.22510	−	2.60196i	−0.0417513	−	0.0886747i
$862$		0			0
$863$	8.79609	+	32.8275i	0.299422	+	1.11746i	0.937641	+	0.347605i	$0.113005\pi$
$863$	8.79609	+	32.8275i	0.299422	+	1.11746i	−0.638219	+	0.769855i	$0.720329\pi$
$864$		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
$873$	14.8668	−	3.98356i	0.503166	−	0.134823i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	17.6931	−	4.74085i	0.597454	−	0.160087i	0.0525963	−	0.998616i	$-0.483250\pi$
$877$	17.6931	−	4.74085i	0.597454	−	0.160087i	0.544858	+	0.838529i	$0.316584\pi$
$878$		0			0
$879$	−3.91255	+	2.25891i	−0.131967	+	0.0761911i
$880$		0			0
$881$			17.5109i			0.589956i	0.955504	+	0.294978i	$0.0953123\pi$
$881$			17.5109i			0.589956i	−0.955504	+	0.294978i	$0.904688\pi$
$882$		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
$887$	7.10104	+	26.5015i	0.238430	+	0.889832i	0.976573	+	0.215188i	$0.0690363\pi$
$887$	7.10104	+	26.5015i	0.238430	+	0.889832i	−0.738143	+	0.674644i	$0.764297\pi$
$888$		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
$893$	17.7968	+	4.76864i	0.595547	+	0.159576i
$894$		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
$903$	7.49589	−	20.8352i	0.249448	−	0.693352i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.829631	−	3.09623i	0.0275475	−	0.102809i	−0.950783	−	0.309857i	$-0.899719\pi$
$907$	0.829631	−	3.09623i	0.0275475	−	0.102809i	0.978331	+	0.207048i	$0.0663856\pi$
$908$		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
$913$	8.81841	−	32.9107i	0.291847	−	1.08919i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.65018	+	25.8116i	0.153562	+	0.852374i
$918$		0			0
$919$	41.7186	+	24.0862i	1.37617	+	0.794531i	0.991696	−	0.128605i	$-0.0410499\pi$
$919$	41.7186	+	24.0862i	1.37617	+	0.794531i	0.384473	+	0.923136i	$0.374383\pi$
$920$		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
$927$	14.5741	+	3.90512i	0.478676	+	0.128261i
$928$		0			0
$929$	−14.4707	+	25.0639i	−0.474767	+	0.822321i	−0.999582	−	0.0288955i	$-0.990801\pi$
$929$	−14.4707	+	25.0639i	−0.474767	+	0.822321i	0.524815	+	0.851216i	$0.324134\pi$
$930$		0			0
$931$	19.9599	+	16.4973i	0.654159	+	0.540677i
$932$		0			0
$933$	3.74285	+	13.9685i	0.122536	+	0.457309i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−9.57644	+	9.57644i	−0.312849	+	0.312849i	−0.846012	−	0.533164i	$-0.821003\pi$
$937$	−9.57644	+	9.57644i	−0.312849	+	0.312849i	0.533164	+	0.846012i	$0.321003\pi$
$938$		0			0
$939$			1.18213i			0.0385774i
$940$		0			0
$941$	13.8414	−	7.99136i	0.451218	−	0.260511i	−0.257127	−	0.966378i	$-0.582776\pi$
$941$	13.8414	−	7.99136i	0.451218	−	0.260511i	0.708344	+	0.705867i	$0.249442\pi$
$942$		0			0
$943$	3.08312	−	0.826119i	0.100400	−	0.0269021i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.97060	−	2.13572i	0.259010	−	0.0694015i	−0.126977	−	0.991906i	$-0.540528\pi$
$947$	7.97060	−	2.13572i	0.259010	−	0.0694015i	0.385987	+	0.922504i	$0.373861\pi$
$948$		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
$957$	1.25291	+	4.67592i	0.0405008	+	0.151151i
$958$		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
$963$	−14.1277	−	3.78551i	−0.455260	−	0.121987i
$964$		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	0.437661	−	0.899140i	$-0.355807\pi$
$971$	−3.80744	−	2.19823i	−0.122187	−	0.0705445i	−0.559848	+	0.828596i	$0.689140\pi$
$972$		0			0
$973$	−18.9466	−	22.4101i	−0.607399	−	0.718434i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.6307	+	39.6743i	−0.340106	+	1.26929i	0.558120	+	0.829760i	$0.311523\pi$
$977$	−10.6307	+	39.6743i	−0.340106	+	1.26929i	−0.898226	+	0.439534i	$0.855144\pi$
$978$		0			0
$979$	−28.2725			−0.903592
$980$		0			0
$981$	11.9587			0.381812
$982$		0			0
$983$	−0.682478	+	2.54704i	−0.0217677	+	0.0812380i	−0.975955	−	0.217971i	$-0.930056\pi$
$983$	−0.682478	+	2.54704i	−0.0217677	+	0.0812380i	0.954188	+	0.299209i	$0.0967228\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−8.50765	−	10.0629i	−0.270801	−	0.320305i
$988$		0			0
$989$	21.2826	+	12.2875i	0.676746	+	0.390720i
$990$		0			0
$991$	0.658365	+	1.14032i	0.0209136	+	0.0362235i	0.876293	−	0.481779i	$-0.160009\pi$
$991$	0.658365	+	1.14032i	0.0209136	+	0.0362235i	−0.855379	+	0.518002i	$0.826676\pi$
$992$		0			0
$993$	−15.4579	−	15.4579i	−0.490542	−	0.490542i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	49.5044	+	13.2647i	1.56782	+	0.420096i	0.935129	−	0.354307i	$-0.115283\pi$
$997$	49.5044	+	13.2647i	1.56782	+	0.420096i	0.632692	+	0.774404i	$0.281950\pi$
$998$		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.1657.2		32
5.2	odd	4		420.2.bo.a.313.5	yes	32
5.3	odd	4	inner	2100.2.ce.e.1993.4		32
5.4	even	2		420.2.bo.a.397.7	yes	32
7.3	odd	6	inner	2100.2.ce.e.157.4		32
15.2	even	4		1260.2.dq.c.1153.7		32
15.14	odd	2		1260.2.dq.c.397.4		32
35.2	odd	12		2940.2.x.c.1273.4		32
35.3	even	12	inner	2100.2.ce.e.493.2		32
35.9	even	6		2940.2.x.c.97.15		32
35.12	even	12		2940.2.x.c.1273.15		32
35.17	even	12		420.2.bo.a.73.7	✓	32
35.19	odd	6		2940.2.x.c.97.4		32
35.24	odd	6		420.2.bo.a.157.5	yes	32
105.17	odd	12		1260.2.dq.c.73.4		32
105.59	even	6		1260.2.dq.c.577.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.7	✓	32	35.17	even	12
420.2.bo.a.157.5	yes	32	35.24	odd	6
420.2.bo.a.313.5	yes	32	5.2	odd	4
420.2.bo.a.397.7	yes	32	5.4	even	2
1260.2.dq.c.73.4		32	105.17	odd	12
1260.2.dq.c.397.4		32	15.14	odd	2
1260.2.dq.c.577.7		32	105.59	even	6
1260.2.dq.c.1153.7		32	15.2	even	4
2100.2.ce.e.157.4		32	7.3	odd	6	inner
2100.2.ce.e.493.2		32	35.3	even	12	inner
2100.2.ce.e.1657.2		32	1.1	even	1	trivial
2100.2.ce.e.1993.4		32	5.3	odd	4	inner
2940.2.x.c.97.4		32	35.19	odd	6
2940.2.x.c.97.15		32	35.9	even	6
2940.2.x.c.1273.4		32	35.2	odd	12
2940.2.x.c.1273.15		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)

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

Varieties

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