LMFDB - Embedded newform 99.17.c.b.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,17,Mod(10,99)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 17, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("99.10");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	99.c (of order $2$, degree $1$, 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:	$160.701298418$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 762654 x^{12} + 222057901680 x^{10} + \cdots + 52\!\cdots\!00 $ x^14 + 762654x^12 + 222057901680x^10 + 31126553561629440x^8 + 2178288986643965767680x^6 + 68943354209834930932285440x^4 + 663241956553385810373220761600x^2 + 526534944269351107365521326080000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{34}\cdot 3^{14}\cdot 5\cdot 11^{6} $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.1
Root			$-500.336i$ of defining polynomial
Character	$\chi$	$=$	99.10
Dual form			99.17.c.b.10.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-500.336i q^{2} -184800. q^{4} +411618. q^{5} +5.61072e6i q^{7} +5.96719e7i q^{8} +O(q^{10})$	\(q-500.336i q^{2} -184800. q^{4} +411618. q^{5} +5.61072e6i q^{7} +5.96719e7i q^{8} -2.05947e8i q^{10} +(-1.57603e8 - 1.45296e8i) q^{11} -9.84738e8i q^{13} +2.80724e9 q^{14} +1.77449e10 q^{16} +3.91109e9i q^{17} -6.54178e9i q^{19} -7.60669e10 q^{20} +(-7.26968e10 + 7.88545e10i) q^{22} +5.18551e9 q^{23} +1.68413e10 q^{25} -4.92700e11 q^{26} -1.03686e12i q^{28} -4.23938e11i q^{29} -9.55801e11 q^{31} -4.96777e12i q^{32} +1.95686e12 q^{34} +2.30947e12i q^{35} -6.48209e12 q^{37} -3.27308e12 q^{38} +2.45620e13i q^{40} +6.13562e12i q^{41} -2.61059e12i q^{43} +(2.91250e13 + 2.68507e13i) q^{44} -2.59449e12i q^{46} +4.60944e12 q^{47} +1.75278e12 q^{49} -8.42632e12i q^{50} +1.81979e14i q^{52} +5.01201e13 q^{53} +(-6.48723e13 - 5.98065e13i) q^{55} -3.34802e14 q^{56} -2.12111e14 q^{58} +1.49324e14 q^{59} -4.31237e13i q^{61} +4.78221e14i q^{62} -1.32262e15 q^{64} -4.05336e14i q^{65} +4.66203e14 q^{67} -7.22768e14i q^{68} +1.15551e15 q^{70} -3.68204e14 q^{71} +1.30177e15i q^{73} +3.24322e15i q^{74} +1.20892e15i q^{76} +(8.15215e14 - 8.84267e14i) q^{77} +1.29483e14i q^{79} +7.30413e15 q^{80} +3.06987e15 q^{82} +3.00771e14i q^{83} +1.60987e15i q^{85} -1.30617e15 q^{86} +(8.67010e15 - 9.40448e15i) q^{88} +4.02920e14 q^{89} +5.52509e15 q^{91} -9.58281e14 q^{92} -2.30627e15i q^{94} -2.69271e15i q^{95} -2.36411e15 q^{97} -8.76981e14i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 607804 q^{4} + 535618 q^{5}+O(q^{10}) $ 14 * q - 607804 * q^4 + 535618 * q^5	$ 14 q - 607804 q^{4} + 535618 q^{5} - 160637170 q^{11} + 3197599848 q^{14} + 35292427592 q^{16} + 99612496468 q^{20} + 127643346840 q^{22} + 305748171262 q^{23} + 289695273612 q^{25} - 1506094012008 q^{26} - 2810074524110 q^{31} - 4903464738408 q^{34} + 1225852399438 q^{37} - 19938057531240 q^{38} + 84053621084948 q^{44} - 54334138546628 q^{47} - 17095708773634 q^{49} + 314109617965972 q^{53} - 244204596500798 q^{55} - 506018447074416 q^{56} - 811982470463040 q^{58} - 487958802125282 q^{59} - 30\!\cdots\!12 q^{64}+ \cdots + 10\!\cdots\!98 q^{97}+O(q^{100}) $ 14 * q - 607804 * q^4 + 535618 * q^5 - 160637170 * q^11 + 3197599848 * q^14 + 35292427592 * q^16 + 99612496468 * q^20 + 127643346840 * q^22 + 305748171262 * q^23 + 289695273612 * q^25 - 1506094012008 * q^26 - 2810074524110 * q^31 - 4903464738408 * q^34 + 1225852399438 * q^37 - 19938057531240 * q^38 + 84053621084948 * q^44 - 54334138546628 * q^47 - 17095708773634 * q^49 + 314109617965972 * q^53 - 244204596500798 * q^55 - 506018447074416 * q^56 - 811982470463040 * q^58 - 487958802125282 * q^59 - 3058743051134512 * q^64 + 951784823334898 * q^67 + 2102378909371560 * q^70 - 2066090774899778 * q^71 + 2087904685537200 * q^77 + 5159446405219528 * q^80 + 10456916101015560 * q^82 - 11739026032493808 * q^86 + 2795712403748880 * q^88 - 8630276341635710 * q^89 + 7159890945002448 * q^91 + 13184625175008892 * q^92 + 10852702786337998 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	500.336i		−	1.95444i	−0.212238	−	0.977218i	$-0.568075\pi$
$2$		−	500.336i		−	1.95444i	0.212238	−	0.977218i	$-0.431925\pi$
$3$		0			0
$3$		0			0
$4$	−184800.			−2.81982
$5$	411618.			1.05374			0.526871	−	0.849945i	$-0.323365\pi$
$5$	411618.			1.05374			0.526871	+	0.849945i	$0.323365\pi$
$6$		0			0
$7$			5.61072e6i			0.973272i	0.873605	+	0.486636i	$0.161776\pi$
$7$			5.61072e6i			0.973272i	−0.873605	+	0.486636i	$0.838224\pi$
$8$			5.96719e7i			3.55672i
$9$		0			0
$10$		−	2.05947e8i		−	2.05947i
$11$	−1.57603e8	−	1.45296e8i	−0.735231	−	0.677817i
$11$	−1.57603e8	−	1.45296e8i	−0.735231	−	0.677817i
$12$		0			0
$13$		−	9.84738e8i		−	1.20719i	−0.797293	−	0.603593i	$-0.793735\pi$
$13$		−	9.84738e8i		−	1.20719i	0.797293	−	0.603593i	$-0.206265\pi$
$14$	2.80724e9			1.90220
$15$		0			0
$16$	1.77449e10			4.13157
$17$			3.91109e9i			0.560669i	0.959902	+	0.280334i	$0.0904453\pi$
$17$			3.91109e9i			0.560669i	−0.959902	+	0.280334i	$0.909555\pi$
$18$		0			0
$19$		−	6.54178e9i		−	0.385183i	−0.981279	−	0.192591i	$-0.938311\pi$
$19$		−	6.54178e9i		−	0.385183i	0.981279	−	0.192591i	$-0.0616892\pi$
$20$	−7.60669e10			−2.97136
$21$		0			0
$22$	−7.26968e10	+	7.88545e10i	−1.32475	+	1.43696i
$23$	5.18551e9			0.0662169			0.0331084	−	0.999452i	$-0.489459\pi$
$23$	5.18551e9			0.0662169			0.0331084	+	0.999452i	$0.489459\pi$
$24$		0			0
$25$	1.68413e10			0.110371
$26$	−4.92700e11			−2.35937
$27$		0			0
$28$		−	1.03686e12i		−	2.74445i
$29$		−	4.23938e11i		−	0.847459i	−0.905789	−	0.423730i	$-0.860721\pi$
$29$		−	4.23938e11i		−	0.847459i	0.905789	−	0.423730i	$-0.139279\pi$
$30$		0			0
$31$	−9.55801e11			−1.12066			−0.560330	−	0.828269i	$-0.689326\pi$
$31$	−9.55801e11			−1.12066			−0.560330	+	0.828269i	$0.689326\pi$
$32$		−	4.96777e12i		−	4.51816i
$33$		0			0
$34$	1.95686e12			1.09579
$35$			2.30947e12i			1.02558i
$36$		0			0
$37$	−6.48209e12			−1.84544			−0.922722	−	0.385465i	$-0.874041\pi$
$37$	−6.48209e12			−1.84544			−0.922722	+	0.385465i	$0.874041\pi$
$38$	−3.27308e12			−0.752815
$39$		0			0
$40$			2.45620e13i			3.74787i
$41$			6.13562e12i			0.768401i	0.923250	+	0.384200i	$0.125523\pi$
$41$			6.13562e12i			0.768401i	−0.923250	+	0.384200i	$0.874477\pi$
$42$		0			0
$43$		−	2.61059e12i		−	0.223353i	−0.993745	−	0.111676i	$-0.964378\pi$
$43$		−	2.61059e12i		−	0.223353i	0.993745	−	0.111676i	$-0.0356220\pi$
$44$	2.91250e13	+	2.68507e13i	2.07322	+	1.91132i
$45$		0			0
$46$		−	2.59449e12i		−	0.129417i
$47$	4.60944e12			0.193582			0.0967910	−	0.995305i	$-0.469142\pi$
$47$	4.60944e12			0.193582			0.0967910	+	0.995305i	$0.469142\pi$
$48$		0			0
$49$	1.75278e12			0.0527424
$50$		−	8.42632e12i		−	0.215714i
$51$		0			0
$52$			1.81979e14i			3.40405i
$53$	5.01201e13			0.805017			0.402509	−	0.915416i	$-0.368138\pi$
$53$	5.01201e13			0.805017			0.402509	+	0.915416i	$0.368138\pi$
$54$		0			0
$55$	−6.48723e13	−	5.98065e13i	−0.774743	−	0.714244i
$56$	−3.34802e14			−3.46166
$57$		0			0
$58$	−2.12111e14			−1.65630
$59$	1.49324e14			1.01698			0.508492	−	0.861067i	$-0.330203\pi$
$59$	1.49324e14			1.01698			0.508492	+	0.861067i	$0.330203\pi$
$60$		0			0
$61$		−	4.31237e13i		−	0.224946i	−0.993655	−	0.112473i	$-0.964123\pi$
$61$		−	4.31237e13i		−	0.224946i	0.993655	−	0.112473i	$-0.0358771\pi$
$62$			4.78221e14i			2.19026i
$63$		0			0
$64$	−1.32262e15			−4.69889
$65$		−	4.05336e14i		−	1.27206i
$66$		0			0
$67$	4.66203e14			1.14809			0.574046	−	0.818823i	$-0.305373\pi$
$67$	4.66203e14			1.14809			0.574046	+	0.818823i	$0.305373\pi$
$68$		−	7.22768e14i		−	1.58098i
$69$		0			0
$70$	1.15551e15			2.00442
$71$	−3.68204e14			−0.570193			−0.285096	−	0.958499i	$-0.592026\pi$
$71$	−3.68204e14			−0.570193			−0.285096	+	0.958499i	$0.592026\pi$
$72$		0			0
$73$			1.30177e15i			1.61418i	0.590428	+	0.807090i	$0.298959\pi$
$73$			1.30177e15i			1.61418i	−0.590428	+	0.807090i	$0.701041\pi$
$74$			3.24322e15i			3.60680i
$75$		0			0
$76$			1.20892e15i			1.08615i
$77$	8.15215e14	−	8.84267e14i	0.659700	−	0.715579i
$78$		0			0
$79$			1.29483e14i			0.0853486i	0.999089	+	0.0426743i	$0.0135878\pi$
$79$			1.29483e14i			0.0853486i	−0.999089	+	0.0426743i	$0.986412\pi$
$80$	7.30413e15			4.35360
$81$		0			0
$82$	3.06987e15			1.50179
$83$			3.00771e14i			0.133540i	0.997768	+	0.0667699i	$0.0212693\pi$
$83$			3.00771e14i			0.133540i	−0.997768	+	0.0667699i	$0.978731\pi$
$84$		0			0
$85$			1.60987e15i			0.590800i
$86$	−1.30617e15			−0.436529
$87$		0			0
$88$	8.67010e15	−	9.40448e15i	2.41081	−	2.61501i
$89$	4.02920e14			0.102353			0.0511763	−	0.998690i	$-0.483703\pi$
$89$	4.02920e14			0.102353			0.0511763	+	0.998690i	$0.483703\pi$
$90$		0			0
$91$	5.52509e15			1.17492
$92$	−9.58281e14			−0.186720
$93$		0			0
$94$		−	2.30627e15i		−	0.378344i
$95$		−	2.69271e15i		−	0.405883i
$96$		0			0
$97$	−2.36411e15			−0.301643			−0.150821	−	0.988561i	$-0.548192\pi$
$97$	−2.36411e15			−0.301643			−0.150821	+	0.988561i	$0.548192\pi$
$98$		−	8.76981e14i		−	0.103082i
$99$		0			0
$100$	−3.11227e15			−0.311227
$101$			3.30959e15i			0.305635i	0.988254	+	0.152817i	$0.0488346\pi$
$101$			3.30959e15i			0.305635i	−0.988254	+	0.152817i	$0.951165\pi$
$102$		0			0
$103$	−6.33861e15			−0.500376			−0.250188	−	0.968197i	$-0.580492\pi$
$103$	−6.33861e15			−0.500376			−0.250188	+	0.968197i	$0.580492\pi$
$104$	5.87612e16			4.29362
$105$		0			0
$106$		−	2.50769e16i		−	1.57335i
$107$			2.28964e16i			1.33259i	0.745688	+	0.666295i	$0.232121\pi$
$107$			2.28964e16i			1.33259i	−0.745688	+	0.666295i	$0.767879\pi$
$108$		0			0
$109$			3.31402e16i			1.66319i	0.555380	+	0.831597i	$0.312573\pi$
$109$			3.31402e16i			1.66319i	−0.555380	+	0.831597i	$0.687427\pi$
$110$	−2.99233e16	+	3.24579e16i	−1.39594	+	1.51419i
$111$		0			0
$112$			9.95619e16i			4.02114i
$113$	4.99360e16			1.87839			0.939197	−	0.343379i	$-0.111572\pi$
$113$	4.99360e16			1.87839			0.939197	+	0.343379i	$0.111572\pi$
$114$		0			0
$115$	2.13445e15			0.0697755
$116$			7.83437e16i			2.38968i
$117$		0			0
$118$		−	7.47122e16i		−	1.98763i
$119$	−2.19440e16			−0.545683
$120$		0			0
$121$	3.72781e15	+	4.57983e16i	0.0811281	+	0.996704i
$122$	−2.15763e16			−0.439642
$123$		0			0
$124$	1.76632e17			3.16006
$125$	−5.58757e16			−0.937439
$126$		0			0
$127$			6.13858e16i			0.907064i	0.891240	+	0.453532i	$0.149836\pi$
$127$			6.13858e16i			0.907064i	−0.891240	+	0.453532i	$0.850164\pi$
$128$			3.36186e17i			4.66552i
$129$		0			0
$130$	−2.02804e17			−2.48616
$131$		−	7.75100e16i		−	0.893691i	−0.894611	−	0.446846i	$-0.852547\pi$
$131$		−	7.75100e16i		−	0.893691i	0.894611	−	0.446846i	$-0.147453\pi$
$132$		0			0
$133$	3.67041e16			0.374888
$134$		−	2.33258e17i		−	2.24387i
$135$		0			0
$136$	−2.33382e17			−1.99414
$137$	−4.82056e16			−0.388448			−0.194224	−	0.980957i	$-0.562219\pi$
$137$	−4.82056e16			−0.388448			−0.194224	+	0.980957i	$0.562219\pi$
$138$		0			0
$139$		−	1.65872e17i		−	1.19029i	−0.803617	−	0.595146i	$-0.797094\pi$
$139$		−	1.65872e17i		−	1.19029i	0.803617	−	0.595146i	$-0.202906\pi$
$140$		−	4.26790e17i		−	2.89194i
$141$		0			0
$142$			1.84226e17i			1.11441i
$143$	−1.43079e17	+	1.55198e17i	−0.818251	+	0.887560i
$144$		0			0
$145$		−	1.74501e17i		−	0.893003i
$146$	6.51323e17			3.15481
$147$		0			0
$148$	1.19789e18			5.20382
$149$		−	2.96036e17i		−	1.21858i	−0.792947	−	0.609291i	$-0.791454\pi$
$149$		−	2.96036e17i		−	1.21858i	0.792947	−	0.609291i	$-0.208546\pi$
$150$		0			0
$151$			2.26939e17i			0.839641i	0.907607	+	0.419821i	$0.137907\pi$
$151$			2.26939e17i			0.839641i	−0.907607	+	0.419821i	$0.862093\pi$
$152$	3.90360e17			1.36999
$153$		0			0
$154$	−4.42430e17	−	4.07881e17i	−1.39855	−	1.28934i
$155$	−3.93425e17			−1.18089
$156$		0			0
$157$	1.66032e16			0.0449774			0.0224887	−	0.999747i	$-0.492841\pi$
$157$	1.66032e16			0.0449774			0.0224887	+	0.999747i	$0.492841\pi$
$158$	6.47850e16			0.166808
$159$		0			0
$160$		−	2.04482e18i		−	4.76097i
$161$			2.90944e16i			0.0644470i
$162$		0			0
$163$	1.94866e17			0.391052			0.195526	−	0.980699i	$-0.437359\pi$
$163$	1.94866e17			0.391052			0.195526	+	0.980699i	$0.437359\pi$
$164$		−	1.13386e18i		−	2.16675i
$165$		0			0
$166$	1.50486e17			0.260995
$167$			9.20482e17i			1.52154i	0.649021	+	0.760770i	$0.275179\pi$
$167$			9.20482e17i			1.52154i	−0.649021	+	0.760770i	$0.724821\pi$
$168$		0			0
$169$	−3.04293e17			−0.457296
$170$	8.05477e17			1.15468
$171$		0			0
$172$			4.82437e17i			0.629815i
$173$			4.34148e17i			0.541089i	0.962707	+	0.270545i	$0.0872037\pi$
$173$			4.34148e17i			0.541089i	−0.962707	+	0.270545i	$0.912796\pi$
$174$		0			0
$175$			9.44919e16i			0.107421i
$176$	−2.79666e18	−	2.57827e18i	−3.03765	−	2.80045i
$177$		0			0
$178$		−	2.01595e17i		−	0.200042i
$179$	4.45391e17			0.422588			0.211294	−	0.977423i	$-0.432232\pi$
$179$	4.45391e17			0.422588			0.211294	+	0.977423i	$0.432232\pi$
$180$		0			0
$181$	−3.68362e17			−0.319776			−0.159888	−	0.987135i	$-0.551113\pi$
$181$	−3.68362e17			−0.319776			−0.159888	+	0.987135i	$0.551113\pi$
$182$		−	2.76440e18i		−	2.29630i
$183$		0			0
$184$			3.09429e17i			0.235515i
$185$	−2.66814e18			−1.94462
$186$		0			0
$187$	5.68266e17	−	6.16400e17i	0.380031	−	0.412221i
$188$	−8.51823e17			−0.545867
$189$		0			0
$190$	−1.34726e18			−0.793273
$191$	3.38006e17			0.190835			0.0954174	−	0.995437i	$-0.469581\pi$
$191$	3.38006e17			0.190835			0.0954174	+	0.995437i	$0.469581\pi$
$192$		0			0
$193$			2.67800e18i			1.39108i	0.718488	+	0.695539i	$0.244835\pi$
$193$			2.67800e18i			1.39108i	−0.718488	+	0.695539i	$0.755165\pi$
$194$			1.18285e18i			0.589542i
$195$		0			0
$196$	−3.23914e17			−0.148724
$197$		−	2.41073e17i		−	0.106272i	−0.998587	−	0.0531361i	$-0.983078\pi$
$197$		−	2.41073e17i		−	0.106272i	0.998587	−	0.0531361i	$-0.0169217\pi$
$198$		0			0
$199$	−1.94330e18			−0.790160			−0.395080	−	0.918647i	$-0.629283\pi$
$199$	−1.94330e18			−0.790160			−0.395080	+	0.918647i	$0.629283\pi$
$200$			1.00495e18i			0.392560i
$201$		0			0
$202$	1.65590e18			0.597344
$203$	2.37860e18			0.824808
$204$		0			0
$205$			2.52553e18i			0.809696i
$206$			3.17143e18i			0.977953i
$207$		0			0
$208$		−	1.74741e19i		−	4.98757i
$209$	−9.50495e17	+	1.03101e18i	−0.261084	+	0.283198i
$210$		0			0
$211$			3.80400e18i			0.968236i	0.875003	+	0.484118i	$0.160860\pi$
$211$			3.80400e18i			0.968236i	−0.875003	+	0.484118i	$0.839140\pi$
$212$	−9.26219e18			−2.27000
$213$		0			0
$214$	1.14559e19			2.60446
$215$		−	1.07457e18i		−	0.235356i
$216$		0			0
$217$		−	5.36273e18i		−	1.09071i
$218$	1.65812e19			3.25061
$219$		0			0
$220$	1.19884e19	+	1.10522e19i	2.18464	+	2.01404i
$221$	3.85140e18			0.676831
$222$		0			0
$223$	−8.22763e18			−1.34535			−0.672676	−	0.739937i	$-0.734855\pi$
$223$	−8.22763e18			−1.34535			−0.672676	+	0.739937i	$0.734855\pi$
$224$	2.78727e19			4.39740
$225$		0			0
$226$		−	2.49848e19i		−	3.67120i
$227$		−	3.90486e18i		−	0.553858i	−0.960890	−	0.276929i	$-0.910683\pi$
$227$		−	3.90486e18i		−	0.553858i	0.960890	−	0.276929i	$-0.0893166\pi$
$228$		0			0
$229$	2.06368e18			0.272871			0.136436	−	0.990649i	$-0.456435\pi$
$229$	2.06368e18			0.272871			0.136436	+	0.990649i	$0.456435\pi$
$230$		−	1.06794e18i		−	0.136372i
$231$		0			0
$232$	2.52972e19			3.01418
$233$			4.77541e18i			0.549747i	0.961480	+	0.274874i	$0.0886360\pi$
$233$			4.77541e18i			0.549747i	−0.961480	+	0.274874i	$0.911364\pi$
$234$		0			0
$235$	1.89733e18			0.203985
$236$	−2.75951e19			−2.86771
$237$		0			0
$238$			1.09794e19i			1.06650i
$239$			1.32045e19i			1.24034i	0.784468	+	0.620169i	$0.212936\pi$
$239$			1.32045e19i			1.24034i	−0.784468	+	0.620169i	$0.787064\pi$
$240$		0			0
$241$		−	1.06699e19i		−	0.937616i	−0.883300	−	0.468808i	$-0.844684\pi$
$241$		−	1.06699e19i		−	0.937616i	0.883300	−	0.468808i	$-0.155316\pi$
$242$	2.29145e19	−	1.86516e18i	1.94799	−	0.158560i
$243$		0			0
$244$			7.96926e18i			0.634307i
$245$	7.21477e17			0.0555769
$246$		0			0
$247$	−6.44194e18			−0.464987
$248$		−	5.70345e19i		−	3.98588i
$249$		0			0
$250$			2.79566e19i			1.83216i
$251$	−1.37299e19			−0.871522			−0.435761	−	0.900062i	$-0.643521\pi$
$251$	−1.37299e19			−0.871522			−0.435761	+	0.900062i	$0.643521\pi$
$252$		0			0
$253$	−8.17253e17	−	7.53434e17i	−0.0486847	−	0.0448829i
$254$	3.07135e19			1.77280
$255$		0			0
$256$	8.15266e19			4.41957
$257$	1.52600e19			0.801841			0.400921	−	0.916113i	$-0.368690\pi$
$257$	1.52600e19			0.801841			0.400921	+	0.916113i	$0.368690\pi$
$258$		0			0
$259$		−	3.63692e19i		−	1.79612i
$260$			7.49059e19i			3.58698i
$261$		0			0
$262$	−3.87810e19			−1.74666
$263$			1.73585e19i			0.758344i	0.925326	+	0.379172i	$0.123791\pi$
$263$			1.73585e19i			0.758344i	−0.925326	+	0.379172i	$0.876209\pi$
$264$		0			0
$265$	2.06303e19			0.848280
$266$		−	1.83644e19i		−	0.732694i
$267$		0			0
$268$	−8.61542e19			−3.23741
$269$	9.43228e18			0.344032			0.172016	−	0.985094i	$-0.444972\pi$
$269$	9.43228e18			0.344032			0.172016	+	0.985094i	$0.444972\pi$
$270$		0			0
$271$			1.45307e18i			0.0499498i	0.999688	+	0.0249749i	$0.00795058\pi$
$271$			1.45307e18i			0.0499498i	−0.999688	+	0.0249749i	$0.992049\pi$
$272$			6.94020e19i			2.31644i
$273$		0			0
$274$			2.41190e19i			0.759197i
$275$	−2.65425e18	−	2.44698e18i	−0.0811484	−	0.0748116i
$276$		0			0
$277$			4.27073e19i			1.23215i	0.787687	+	0.616076i	$0.211279\pi$
$277$			4.27073e19i			1.23215i	−0.787687	+	0.616076i	$0.788721\pi$
$278$	−8.29915e19			−2.32635
$279$		0			0
$280$	−1.37811e20			−3.64769
$281$			1.91119e19i			0.491647i	0.969315	+	0.245824i	$0.0790584\pi$
$281$			1.91119e19i			0.491647i	−0.969315	+	0.245824i	$0.920942\pi$
$282$		0			0
$283$			7.03706e19i			1.71041i	0.518291	+	0.855204i	$0.326568\pi$
$283$			7.03706e19i			1.71041i	−0.518291	+	0.855204i	$0.673432\pi$
$284$	6.80440e19			1.60784
$285$		0			0
$286$	7.76510e19	+	7.15873e19i	1.73468	+	1.59922i
$287$	−3.44252e19			−0.747863
$288$		0			0
$289$	3.33646e19			0.685651
$290$	−8.73089e19			−1.74532
$291$		0			0
$292$		−	2.40567e20i		−	4.55170i
$293$		−	5.19146e18i		−	0.0955759i	−0.998858	−	0.0477880i	$-0.984783\pi$
$293$		−	5.19146e18i		−	0.0955759i	0.998858	−	0.0477880i	$-0.0152172\pi$
$294$		0			0
$295$	6.14645e19			1.07164
$296$		−	3.86798e20i		−	6.56373i
$297$		0			0
$298$	−1.48117e20			−2.38164
$299$		−	5.10637e18i		−	0.0799360i
$300$		0			0
$301$	1.46473e19			0.217383
$302$	1.13546e20			1.64103
$303$		0			0
$304$		−	1.16083e20i		−	1.59141i
$305$		−	1.77505e19i		−	0.237035i
$306$		0			0
$307$		−	9.82920e19i		−	1.24569i	−0.782344	−	0.622847i	$-0.785976\pi$
$307$		−	9.82920e19i		−	1.24569i	0.782344	−	0.622847i	$-0.214024\pi$
$308$	−1.50652e20	+	1.63412e20i	−1.86024	+	2.01780i
$309$		0			0
$310$			1.96844e20i			2.30797i
$311$	1.07883e20			1.23273			0.616366	−	0.787460i	$-0.288604\pi$
$311$	1.07883e20			1.23273			0.616366	+	0.787460i	$0.288604\pi$
$312$		0			0
$313$	1.51186e20			1.64119			0.820593	−	0.571513i	$-0.193643\pi$
$313$	1.51186e20			1.64119			0.820593	+	0.571513i	$0.193643\pi$
$314$		−	8.30717e18i		−	0.0879055i
$315$		0			0
$316$		−	2.39284e19i		−	0.240668i
$317$	2.91666e18			0.0286030			0.0143015	−	0.999898i	$-0.495448\pi$
$317$	2.91666e18			0.0286030			0.0143015	+	0.999898i	$0.495448\pi$
$318$		0			0
$319$	−6.15966e19	+	6.68140e19i	−0.574422	+	0.623078i
$320$	−5.44414e20			−4.95141
$321$		0			0
$322$	1.45570e19			0.125958
$323$	2.55855e19			0.215960
$324$		0			0
$325$		−	1.65843e19i		−	0.133239i
$326$		−	9.74982e19i		−	0.764286i
$327$		0			0
$328$	−3.66124e20			−2.73299
$329$			2.58623e19i			0.188408i
$330$		0			0
$331$	1.51698e19			0.105282			0.0526411	−	0.998613i	$-0.483236\pi$
$331$	1.51698e19			0.105282			0.0526411	+	0.998613i	$0.483236\pi$
$332$		−	5.55823e19i		−	0.376558i
$333$		0			0
$334$	4.60550e20			2.97375
$335$	1.91898e20			1.20979
$336$		0			0
$337$		−	9.06345e19i		−	0.544821i	−0.962181	−	0.272411i	$-0.912179\pi$
$337$		−	9.06345e19i		−	0.544821i	0.962181	−	0.272411i	$-0.0878209\pi$
$338$			1.52248e20i			0.893757i
$339$		0			0
$340$		−	2.97504e20i		−	1.66595i
$341$	1.50637e20	+	1.38874e20i	0.823944	+	0.759603i
$342$		0			0
$343$			1.96295e20i			1.02460i
$344$	1.55779e20			0.794404
$345$		0			0
$346$	2.17220e20			1.05752
$347$			6.22199e19i			0.296001i	0.988987	+	0.148001i	$0.0472838\pi$
$347$			6.22199e19i			0.296001i	−0.988987	+	0.148001i	$0.952716\pi$
$348$		0			0
$349$		−	1.54128e20i		−	0.700290i	−0.936695	−	0.350145i	$-0.886132\pi$
$349$		−	1.54128e20i		−	0.700290i	0.936695	−	0.350145i	$-0.113868\pi$
$350$	4.72777e19			0.209948
$351$		0			0
$352$	−7.21798e20	+	7.82936e20i	−3.06249	+	3.32189i
$353$	−2.82167e20			−1.17033			−0.585165	−	0.810915i	$-0.698970\pi$
$353$	−2.82167e20			−1.17033			−0.585165	+	0.810915i	$0.698970\pi$
$354$		0			0
$355$	−1.51559e20			−0.600836
$356$	−7.44595e19			−0.288616
$357$		0			0
$358$		−	2.22845e20i		−	0.825921i
$359$		−	3.47881e20i		−	1.26089i	−0.776236	−	0.630443i	$-0.782873\pi$
$359$		−	3.47881e20i		−	1.26089i	0.776236	−	0.630443i	$-0.217127\pi$
$360$		0			0
$361$	2.45647e20			0.851634
$362$			1.84305e20i			0.624982i
$363$		0			0
$364$	−1.02103e21			−3.31306
$365$			5.35833e20i			1.70093i
$366$		0			0
$367$	−6.23518e20			−1.89461			−0.947306	−	0.320330i	$-0.896206\pi$
$367$	−6.23518e20			−1.89461			−0.947306	+	0.320330i	$0.896206\pi$
$368$	9.20165e19			0.273579
$369$		0			0
$370$			1.33497e21i			3.80064i
$371$			2.81210e20i			0.783501i
$372$		0			0
$373$			5.08124e20i			1.35612i	0.735005	+	0.678062i	$0.237180\pi$
$373$			5.08124e20i			1.35612i	−0.735005	+	0.678062i	$0.762820\pi$
$374$	−3.08407e20	−	2.84324e20i	−0.805659	−	0.742746i
$375$		0			0
$376$			2.75054e20i			0.688518i
$377$	−4.17468e20			−1.02304
$378$		0			0
$379$	1.08912e20			0.255836			0.127918	−	0.991785i	$-0.459171\pi$
$379$	1.08912e20			0.255836			0.127918	+	0.991785i	$0.459171\pi$
$380$			4.97613e20i			1.14452i
$381$		0			0
$382$		−	1.69116e20i		−	0.372974i
$383$	3.22650e19			0.0696853			0.0348427	−	0.999393i	$-0.488907\pi$
$383$	3.22650e19			0.0696853			0.0348427	+	0.999393i	$0.488907\pi$
$384$		0			0
$385$	3.35557e20	−	3.63980e20i	0.695153	−	0.754035i
$386$	1.33990e21			2.71877
$387$		0			0
$388$	4.36886e20			0.850579
$389$	6.86982e19			0.131023			0.0655117	−	0.997852i	$-0.479132\pi$
$389$	6.86982e19			0.131023			0.0655117	+	0.997852i	$0.479132\pi$
$390$		0			0
$391$			2.02810e19i			0.0371257i
$392$			1.04592e20i			0.187590i
$393$		0			0
$394$	−1.20618e20			−0.207702
$395$			5.32976e19i			0.0899354i
$396$		0			0
$397$	8.83048e20			1.43107			0.715534	−	0.698578i	$-0.246184\pi$
$397$	8.83048e20			1.43107			0.715534	+	0.698578i	$0.246184\pi$
$398$			9.72301e20i			1.54432i
$399$		0			0
$400$	2.98848e20			0.456007
$401$	7.58837e20			1.13499			0.567497	−	0.823376i	$-0.307912\pi$
$401$	7.58837e20			1.13499			0.567497	+	0.823376i	$0.307912\pi$
$402$		0			0
$403$			9.41214e20i			1.35284i
$404$		−	6.11611e20i		−	0.861835i
$405$		0			0
$406$		−	1.19010e21i		−	1.61203i
$407$	1.02160e21	+	9.41822e20i	1.35683	+	1.25087i
$408$		0			0
$409$		−	1.18529e21i		−	1.51370i	−0.653590	−	0.756848i	$-0.726738\pi$
$409$		−	1.18529e21i		−	1.51370i	0.653590	−	0.756848i	$-0.273262\pi$
$410$	1.26361e21			1.58250
$411$		0			0
$412$	1.17137e21			1.41097
$413$			8.37816e20i			0.989801i
$414$		0			0
$415$			1.23803e20i			0.140716i
$416$	−4.89195e21			−5.45426
$417$		0			0
$418$	5.15849e20	+	4.75566e20i	0.553493	+	0.510271i
$419$	9.73230e20			1.02448			0.512240	−	0.858843i	$-0.328816\pi$
$419$	9.73230e20			1.02448			0.512240	+	0.858843i	$0.328816\pi$
$420$		0			0
$421$	−4.34103e20			−0.439882			−0.219941	−	0.975513i	$-0.570587\pi$
$421$	−4.34103e20			−0.439882			−0.219941	+	0.975513i	$0.570587\pi$
$422$	1.90328e21			1.89236
$423$		0			0
$424$			2.99076e21i			2.86322i
$425$			6.58679e19i			0.0618817i
$426$		0			0
$427$	2.41955e20			0.218933
$428$		−	4.23125e21i		−	3.75767i
$429$		0			0
$430$	−5.37644e20			−0.459988
$431$			4.83403e20i			0.405968i	0.979182	+	0.202984i	$0.0650639\pi$
$431$			4.83403e20i			0.405968i	−0.979182	+	0.202984i	$0.934936\pi$
$432$		0			0
$433$	6.58830e19			0.0533175			0.0266588	−	0.999645i	$-0.491513\pi$
$433$	6.58830e19			0.0533175			0.0266588	+	0.999645i	$0.491513\pi$
$434$	−2.68316e21			−2.13172
$435$		0			0
$436$		−	6.12430e21i		−	4.68991i
$437$		−	3.39224e19i		−	0.0255056i
$438$		0			0
$439$			2.38322e21i			1.72762i	0.503818	+	0.863810i	$0.331928\pi$
$439$			2.38322e21i			1.72762i	−0.503818	+	0.863810i	$0.668072\pi$
$440$	3.56877e21	−	3.87105e21i	2.54037	−	2.75555i
$441$		0			0
$442$		−	1.92699e21i		−	1.32282i
$443$	−1.06614e21			−0.718762			−0.359381	−	0.933191i	$-0.617012\pi$
$443$	−1.06614e21			−0.718762			−0.359381	+	0.933191i	$0.617012\pi$
$444$		0			0
$445$	1.65849e20			0.107853
$446$			4.11658e21i			2.62940i
$447$		0			0
$448$		−	7.42084e21i		−	4.57329i
$449$	2.31949e21			1.40418			0.702089	−	0.712089i	$-0.252251\pi$
$449$	2.31949e21			1.40418			0.702089	+	0.712089i	$0.252251\pi$
$450$		0			0
$451$	8.91482e20	−	9.66994e20i	0.520835	−	0.564952i
$452$	−9.22817e21			−5.29673
$453$		0			0
$454$	−1.95374e21			−1.08248
$455$	2.27422e21			1.23806
$456$		0			0
$457$			1.51542e20i			0.0796532i	0.999207	+	0.0398266i	$0.0126806\pi$
$457$			1.51542e20i			0.0796532i	−0.999207	+	0.0398266i	$0.987319\pi$
$458$		−	1.03253e21i		−	0.533309i
$459$		0			0
$460$	−3.94445e20			−0.196754
$461$			3.23095e21i			1.58388i	0.610599	+	0.791940i	$0.290929\pi$
$461$			3.23095e21i			1.58388i	−0.610599	+	0.791940i	$0.709071\pi$
$462$		0			0
$463$	−1.31527e21			−0.622827			−0.311414	−	0.950274i	$-0.600802\pi$
$463$	−1.31527e21			−0.622827			−0.311414	+	0.950274i	$0.600802\pi$
$464$		−	7.52276e21i		−	3.50133i
$465$		0			0
$466$	2.38931e21			1.07445
$467$	−3.55146e20			−0.156990			−0.0784950	−	0.996915i	$-0.525011\pi$
$467$	−3.55146e20			−0.156990			−0.0784950	+	0.996915i	$0.525011\pi$
$468$		0			0
$469$			2.61573e21i			1.11741i
$470$		−	9.49300e20i		−	0.398677i
$471$		0			0
$472$			8.91046e21i			3.61713i
$473$	−3.79309e20	+	4.11438e20i	−0.151392	+	0.164216i
$474$		0			0
$475$		−	1.10172e20i		−	0.0425131i
$476$	4.05525e21			1.53873
$477$		0			0
$478$	6.60670e21			2.42416
$479$			2.31150e21i			0.834082i	0.908888	+	0.417041i	$0.136933\pi$
$479$			2.31150e21i			0.834082i	−0.908888	+	0.417041i	$0.863067\pi$
$480$		0			0
$481$			6.38316e21i			2.22779i
$482$	−5.33854e21			−1.83251
$483$		0			0
$484$	−6.88899e20	−	8.46351e21i	−0.228767	−	2.81053i
$485$	−9.73108e20			−0.317854
$486$		0			0
$487$	−1.62509e21			−0.513626			−0.256813	−	0.966461i	$-0.582672\pi$
$487$	−1.62509e21			−0.513626			−0.256813	+	0.966461i	$0.582672\pi$
$488$	2.57328e21			0.800070
$489$		0			0
$490$		−	3.60981e20i		−	0.108621i
$491$		−	1.05092e21i		−	0.311113i	−0.987827	−	0.155556i	$-0.950283\pi$
$491$		−	1.05092e21i		−	0.311113i	0.987827	−	0.155556i	$-0.0497170\pi$
$492$		0			0
$493$	1.65806e21			0.475144
$494$			3.22313e21i			0.908788i
$495$		0			0
$496$	−1.69606e22			−4.63008
$497$		−	2.06589e21i		−	0.554952i
$498$		0			0
$499$	4.89587e21			1.27358			0.636789	−	0.771038i	$-0.280262\pi$
$499$	4.89587e21			1.27358			0.636789	+	0.771038i	$0.280262\pi$
$500$	1.03258e22			2.64341
$501$		0			0
$502$			6.86957e21i			1.70333i
$503$		−	4.66726e21i		−	1.13898i	−0.821997	−	0.569492i	$-0.807140\pi$
$503$		−	4.66726e21i		−	1.13898i	0.821997	−	0.569492i	$-0.192860\pi$
$504$		0			0
$505$			1.36229e21i			0.322060i
$506$	−3.76970e20	+	4.08901e20i	−0.0877208	+	0.0951511i
$507$		0			0
$508$		−	1.13441e22i		−	2.55776i
$509$	1.76096e21			0.390848			0.195424	−	0.980719i	$-0.437392\pi$
$509$	1.76096e21			0.390848			0.195424	+	0.980719i	$0.437392\pi$
$510$		0			0
$511$	−7.30388e21			−1.57104
$512$		−	1.87584e22i		−	3.97224i
$513$		0			0
$514$		−	7.63510e21i		−	1.56715i
$515$	−2.60909e21			−0.527267
$516$		0			0
$517$	−7.26462e20	−	6.69733e20i	−0.142327	−	0.131213i
$518$	−1.81968e22			−3.51040
$519$		0			0
$520$	2.41872e22			4.52437
$521$	5.65257e21			1.04122			0.520612	−	0.853794i	$-0.325704\pi$
$521$	5.65257e21			1.04122			0.520612	+	0.853794i	$0.325704\pi$
$522$		0			0
$523$		−	8.47715e21i		−	1.51438i	−0.653192	−	0.757192i	$-0.726571\pi$
$523$		−	8.47715e21i		−	1.51438i	0.653192	−	0.757192i	$-0.273429\pi$
$524$			1.43238e22i			2.52005i
$525$		0			0
$526$	8.68508e21			1.48214
$527$		−	3.73822e21i		−	0.628319i
$528$		0			0
$529$	−6.10572e21			−0.995615
$530$		−	1.03221e22i		−	1.65791i
$531$		0			0
$532$	−6.78290e21			−1.05712
$533$	6.04198e21			0.927602
$534$		0			0
$535$			9.42456e21i			1.40421i
$536$			2.78192e22i			4.08345i
$537$		0			0
$538$		−	4.71931e21i		−	0.672388i
$539$	−2.76244e20	−	2.54673e20i	−0.0387778	−	0.0357497i
$540$		0			0
$541$		−	4.10128e21i		−	0.558910i	−0.960159	−	0.279455i	$-0.909846\pi$
$541$		−	4.10128e21i		−	0.558910i	0.960159	−	0.279455i	$-0.0901538\pi$
$542$	7.27025e20			0.0976236
$543$		0			0
$544$	1.94294e22			2.53319
$545$			1.36411e22i			1.75258i
$546$		0			0
$547$		−	6.92437e21i		−	0.863936i	−0.901889	−	0.431968i	$-0.857819\pi$
$547$		−	6.92437e21i		−	0.863936i	0.901889	−	0.431968i	$-0.142181\pi$
$548$	8.90839e21			1.09535
$549$		0			0
$550$	−1.22431e21	+	1.32801e21i	−0.146214	+	0.158599i
$551$	−2.77331e21			−0.326427
$552$		0			0
$553$	−7.26493e20			−0.0830674
$554$	2.13680e22			2.40816
$555$		0			0
$556$			3.06530e22i			3.35641i
$557$		−	7.72797e21i		−	0.834111i	−0.908881	−	0.417055i	$-0.863062\pi$
$557$		−	7.72797e21i		−	0.834111i	0.908881	−	0.417055i	$-0.136938\pi$
$558$		0			0
$559$	−2.57075e21			−0.269628
$560$			4.09814e22i			4.23724i
$561$		0			0
$562$	9.56237e21			0.960893
$563$			1.89309e22i			1.87545i	0.347385	+	0.937723i	$0.387070\pi$
$563$			1.89309e22i			1.87545i	−0.347385	+	0.937723i	$0.612930\pi$
$564$		0			0
$565$	2.05546e22			1.97934
$566$	3.52089e22			3.34288
$567$		0			0
$568$		−	2.19714e22i		−	2.02802i
$569$		−	1.76500e22i		−	1.60637i	−0.595727	−	0.803187i	$-0.703136\pi$
$569$		−	1.76500e22i		−	1.60637i	0.595727	−	0.803187i	$-0.296864\pi$
$570$		0			0
$571$			4.60911e21i			0.407876i	0.978984	+	0.203938i	$0.0653741\pi$
$571$			4.60911e21i			0.407876i	−0.978984	+	0.203938i	$0.934626\pi$
$572$	2.64409e22	−	2.86805e22i	2.30732	−	2.50276i
$573$		0			0
$574$			1.72242e22i			1.46165i
$575$	8.73309e19			0.00730844
$576$		0			0
$577$	1.41021e22			1.14783			0.573915	−	0.818915i	$-0.305424\pi$
$577$	1.41021e22			1.14783			0.573915	+	0.818915i	$0.305424\pi$
$578$		−	1.66935e22i		−	1.34006i
$579$		0			0
$580$			3.22477e22i			2.51811i
$581$	−1.68754e21			−0.129971
$582$		0			0
$583$	−7.89909e21	−	7.28226e21i	−0.591873	−	0.545654i
$584$	−7.76792e22			−5.74119
$585$		0			0
$586$	−2.59747e21			−0.186797
$587$	−1.67561e22			−1.18869			−0.594344	−	0.804211i	$-0.702588\pi$
$587$	−1.67561e22			−1.18869			−0.594344	+	0.804211i	$0.702588\pi$
$588$		0			0
$589$			6.25264e21i			0.431659i
$590$		−	3.07529e22i		−	2.09445i
$591$		0			0
$592$	−1.15024e23			−7.62458
$593$			7.89724e21i			0.516461i	0.966083	+	0.258230i	$0.0831394\pi$
$593$			7.89724e21i			0.516461i	−0.966083	+	0.258230i	$0.916861\pi$
$594$		0			0
$595$	−9.03254e21			−0.575009
$596$			5.47074e22i			3.43618i
$597$		0			0
$598$	−2.55490e21			−0.156230
$599$	−2.28169e22			−1.37671			−0.688355	−	0.725374i	$-0.741667\pi$
$599$	−2.28169e22			−1.37671			−0.688355	+	0.725374i	$0.741667\pi$
$600$		0			0
$601$			6.22298e21i			0.365597i	0.983150	+	0.182799i	$0.0585156\pi$
$601$			6.22298e21i			0.365597i	−0.983150	+	0.182799i	$0.941484\pi$
$602$		−	7.32856e21i		−	0.424861i
$603$		0			0
$604$		−	4.19383e22i		−	2.36764i
$605$	1.53443e21	+	1.88514e22i	0.0854880	+	1.05027i
$606$		0			0
$607$		−	8.32099e21i		−	0.451508i	−0.974184	−	0.225754i	$-0.927515\pi$
$607$		−	8.32099e21i		−	0.451508i	0.974184	−	0.225754i	$-0.0724845\pi$
$608$	−3.24980e22			−1.74032
$609$		0			0
$610$	−8.88121e21			−0.463269
$611$		−	4.53909e21i		−	0.233689i
$612$		0			0
$613$			2.81744e22i			1.41309i	0.707666	+	0.706547i	$0.249748\pi$
$613$			2.81744e22i			1.41309i	−0.707666	+	0.706547i	$0.750252\pi$
$614$	−4.91790e22			−2.43463
$615$		0			0
$616$	5.27659e22	+	4.86455e22i	2.54512	+	2.34637i
$617$	1.34510e22			0.640433			0.320217	−	0.947344i	$-0.396244\pi$
$617$	1.34510e22			0.640433			0.320217	+	0.947344i	$0.396244\pi$
$618$		0			0
$619$	−1.10942e22			−0.514718			−0.257359	−	0.966316i	$-0.582852\pi$
$619$	−1.10942e22			−0.514718			−0.257359	+	0.966316i	$0.582852\pi$
$620$	7.27048e22			3.32989
$621$		0			0
$622$		−	5.39775e22i		−	2.40930i
$623$			2.26067e21i			0.0996169i
$624$		0			0
$625$	−2.55692e22			−1.09819
$626$		−	7.56439e22i		−	3.20759i
$627$		0			0
$628$	−3.06827e21			−0.126828
$629$		−	2.53520e22i		−	1.03468i
$630$		0			0
$631$	2.95288e22			1.17493			0.587464	−	0.809250i	$-0.300126\pi$
$631$	2.95288e22			1.17493			0.587464	+	0.809250i	$0.300126\pi$
$632$	−7.72650e21			−0.303561
$633$		0			0
$634$		−	1.45931e21i		−	0.0559027i
$635$			2.52675e22i			0.955811i
$636$		0			0
$637$		−	1.72603e21i		−	0.0636699i
$638$	3.34294e22	+	3.08190e22i	1.21777	+	1.12267i
$639$		0			0
$640$			1.38380e23i			4.91625i
$641$	−5.17884e22			−1.81706			−0.908528	−	0.417824i	$-0.862793\pi$
$641$	−5.17884e22			−1.81706			−0.908528	+	0.417824i	$0.862793\pi$
$642$		0			0
$643$	−2.68323e22			−0.918270			−0.459135	−	0.888366i	$-0.651841\pi$
$643$	−2.68323e22			−0.918270			−0.459135	+	0.888366i	$0.651841\pi$
$644$		−	5.37664e21i		−	0.181729i
$645$		0			0
$646$		−	1.28013e22i		−	0.422080i
$647$	−2.47781e22			−0.806927			−0.403464	−	0.914996i	$-0.632194\pi$
$647$	−2.47781e22			−0.806927			−0.403464	+	0.914996i	$0.632194\pi$
$648$		0			0
$649$	−2.35340e22	−	2.16962e22i	−0.747718	−	0.689329i
$650$	−8.29772e21			−0.260406
$651$		0			0
$652$	−3.60111e22			−1.10270
$653$	6.09047e22			1.84224			0.921118	−	0.389284i	$-0.127277\pi$
$653$	6.09047e22			1.84224			0.921118	+	0.389284i	$0.127277\pi$
$654$		0			0
$655$		−	3.19045e22i		−	0.941719i
$656$			1.08876e23i			3.17470i
$657$		0			0
$658$	1.29398e22			0.368231
$659$			2.61996e22i			0.736566i	0.929714	+	0.368283i	$0.120054\pi$
$659$			2.61996e22i			0.736566i	−0.929714	+	0.368283i	$0.879946\pi$
$660$		0			0
$661$	−2.98215e22			−0.818309			−0.409154	−	0.912465i	$-0.634176\pi$
$661$	−2.98215e22			−0.818309			−0.409154	+	0.912465i	$0.634176\pi$
$662$		−	7.58997e21i		−	0.205767i
$663$		0			0
$664$	−1.79476e22			−0.474964
$665$	1.51080e22			0.395035
$666$		0			0
$667$		−	2.19834e21i		−	0.0561161i
$668$		−	1.70105e23i		−	4.29047i
$669$		0			0
$670$		−	9.60132e22i		−	2.36446i
$671$	−6.26571e21	+	6.79644e21i	−0.152472	+	0.165387i
$672$		0			0
$673$		−	1.42205e22i		−	0.337905i	−0.985624	−	0.168953i	$-0.945962\pi$
$673$		−	1.42205e22i		−	0.337905i	0.985624	−	0.168953i	$-0.0540385\pi$
$674$	−4.53476e22			−1.06482
$675$		0			0
$676$	5.62332e22			1.28949
$677$		−	6.28102e22i		−	1.42338i	−0.702494	−	0.711690i	$-0.747930\pi$
$677$		−	6.28102e22i		−	1.42338i	0.702494	−	0.711690i	$-0.252070\pi$
$678$		0			0
$679$		−	1.32643e22i		−	0.293580i
$680$	−9.60642e22			−2.10131
$681$		0			0
$682$	6.94837e22	−	7.53692e22i	1.48459	−	1.61035i
$683$	−6.16408e22			−1.30168			−0.650838	−	0.759217i	$-0.725582\pi$
$683$	−6.16408e22			−1.30168			−0.650838	+	0.759217i	$0.725582\pi$
$684$		0			0
$685$	−1.98423e22			−0.409324
$686$	9.82134e22			2.00252
$687$		0			0
$688$		−	4.63248e22i		−	0.922797i
$689$		−	4.93552e22i		−	0.971805i
$690$		0			0
$691$	9.15053e22			1.76044			0.880221	−	0.474564i	$-0.157394\pi$
$691$	9.15053e22			1.76044			0.880221	+	0.474564i	$0.157394\pi$
$692$		−	8.02304e22i		−	1.52577i
$693$		0			0
$694$	3.11308e22			0.578515
$695$		−	6.82757e22i		−	1.25426i
$696$		0			0
$697$	−2.39970e22			−0.430818
$698$	−7.71157e22			−1.36867
$699$		0			0
$700$		−	1.74621e22i		−	0.302909i
$701$		−	6.81408e22i		−	1.16859i	−0.811540	−	0.584296i	$-0.801371\pi$
$701$		−	6.81408e22i		−	1.16859i	0.811540	−	0.584296i	$-0.198629\pi$
$702$		0			0
$703$			4.24044e22i			0.710834i
$704$	2.08449e23	+	1.92171e23i	3.45477	+	3.18499i
$705$		0			0
$706$			1.41178e23i			2.28733i
$707$	−1.85692e22			−0.297466
$708$		0			0
$709$	5.87952e21			0.0920814			0.0460407	−	0.998940i	$-0.485340\pi$
$709$	5.87952e21			0.0920814			0.0460407	+	0.998940i	$0.485340\pi$
$710$			7.58305e22i			1.17429i
$711$		0			0
$712$			2.40430e22i			0.364040i
$713$	−4.95631e21			−0.0742066
$714$		0			0
$715$	−5.88937e22	+	6.38822e22i	−0.862225	+	0.935258i
$716$	−8.23081e22			−1.19162
$717$		0			0
$718$	−1.74057e23			−2.46432
$719$	−7.67804e22			−1.07503			−0.537513	−	0.843255i	$-0.680636\pi$
$719$	−7.67804e22			−1.07503			−0.537513	+	0.843255i	$0.680636\pi$
$720$		0			0
$721$		−	3.55642e22i		−	0.487002i
$722$		−	1.22906e23i		−	1.66446i
$723$		0			0
$724$	6.80732e22			0.901711
$725$		−	7.13969e21i		−	0.0935352i
$726$		0			0
$727$	−1.23146e23			−1.57814			−0.789072	−	0.614301i	$-0.789438\pi$
$727$	−1.23146e23			−1.57814			−0.789072	+	0.614301i	$0.789438\pi$
$728$			3.29692e23i			4.17886i
$729$		0			0
$730$	2.68096e23			3.32436
$731$	1.02103e22			0.125227
$732$		0			0
$733$		−	3.13440e22i		−	0.376117i	−0.982158	−	0.188058i	$-0.939781\pi$
$733$		−	3.13440e22i		−	0.376117i	0.982158	−	0.188058i	$-0.0602194\pi$
$734$			3.11968e23i			3.70290i
$735$		0			0
$736$		−	2.57604e22i		−	0.299178i
$737$	−7.34751e22	−	6.77375e22i	−0.844113	−	0.778196i
$738$		0			0
$739$			1.70986e23i			1.92223i	0.276151	+	0.961114i	$0.410941\pi$
$739$			1.70986e23i			1.92223i	−0.276151	+	0.961114i	$0.589059\pi$
$740$	4.93072e23			5.48348
$741$		0			0
$742$	1.40699e23			1.53130
$743$			1.50978e23i			1.62556i	0.582569	+	0.812781i	$0.302048\pi$
$743$			1.50978e23i			1.62556i	−0.582569	+	0.812781i	$0.697952\pi$
$744$		0			0
$745$		−	1.21854e23i		−	1.28407i
$746$	2.54233e23			2.65046
$747$		0			0
$748$	−1.05015e23	+	1.13911e23i	−1.07162	+	1.16239i
$749$	−1.28465e23			−1.29697
$750$		0			0
$751$	4.15615e22			0.410745			0.205372	−	0.978684i	$-0.434159\pi$
$751$	4.15615e22			0.410745			0.205372	+	0.978684i	$0.434159\pi$
$752$	8.17942e22			0.799797
$753$		0			0
$754$			2.08874e23i			1.99947i
$755$			9.34122e22i			0.884765i
$756$		0			0
$757$	8.09591e20			0.00750756			0.00375378	−	0.999993i	$-0.498805\pi$
$757$	8.09591e20			0.00750756			0.00375378	+	0.999993i	$0.498805\pi$
$758$		−	5.44925e22i		−	0.500015i
$759$		0			0
$760$	1.60679e23			1.44361
$761$			1.27907e21i			0.0113715i	0.999984	+	0.00568576i	$0.00180984\pi$
$761$			1.27907e21i			0.0113715i	−0.999984	+	0.00568576i	$0.998190\pi$
$762$		0			0
$763$	−1.85940e23			−1.61874
$764$	−6.24634e22			−0.538120
$765$		0			0
$766$		−	1.61433e22i		−	0.136195i
$767$		−	1.47045e23i		−	1.22769i
$768$		0			0
$769$		−	1.03058e23i		−	0.842698i	−0.906899	−	0.421349i	$-0.861557\pi$
$769$		−	1.03058e23i		−	0.842698i	0.906899	−	0.421349i	$-0.138443\pi$
$770$	−1.82112e23	−	1.67891e23i	−1.47371	−	1.35863i
$771$		0			0
$772$		−	4.94893e23i		−	3.92259i
$773$	−1.89159e23			−1.48385			−0.741927	−	0.670481i	$-0.766088\pi$
$773$	−1.89159e23			−1.48385			−0.741927	+	0.670481i	$0.766088\pi$
$774$		0			0
$775$	−1.60970e22			−0.123689
$776$		−	1.41071e23i		−	1.07286i
$777$		0			0
$778$		−	3.43722e22i		−	0.256077i
$779$	4.01379e22			0.295975
$780$		0			0
$781$	5.80301e22	+	5.34986e22i	0.419223	+	0.386486i
$782$	1.01473e22			0.0725598
$783$		0			0
$784$	3.11031e22			0.217909
$785$	6.83417e21			0.0473946
$786$		0			0
$787$			2.49407e23i			1.69477i	0.530976	+	0.847387i	$0.321825\pi$
$787$			2.49407e23i			1.69477i	−0.530976	+	0.847387i	$0.678175\pi$
$788$			4.45503e22i			0.299668i
$789$		0			0
$790$	2.66667e22			0.175773
$791$			2.80177e23i			1.82819i
$792$		0			0
$793$	−4.24656e22			−0.271551
$794$		−	4.41820e23i		−	2.79693i
$795$		0			0
$796$	3.59121e23			2.22811
$797$	1.82879e23			1.12330			0.561651	−	0.827374i	$-0.310166\pi$
$797$	1.82879e23			1.12330			0.561651	+	0.827374i	$0.310166\pi$
$798$		0			0
$799$			1.80279e22i			0.108535i
$800$		−	8.36638e22i		−	0.498675i
$801$		0			0
$802$		−	3.79673e23i		−	2.21827i
$803$	1.89142e23	−	2.05164e23i	1.09412	−	1.18680i
$804$		0			0
$805$			1.19758e22i			0.0679105i
$806$	4.70923e23			2.64405
$807$		0			0
$808$	−1.97489e23			−1.08706
$809$		−	7.00865e22i		−	0.381985i	−0.981592	−	0.190992i	$-0.938829\pi$
$809$		−	7.00865e22i		−	0.381985i	0.981592	−	0.190992i	$-0.0611706\pi$
$810$		0			0
$811$		−	5.32593e22i		−	0.284596i	−0.989824	−	0.142298i	$-0.954551\pi$
$811$		−	5.32593e22i		−	0.284596i	0.989824	−	0.142298i	$-0.0454491\pi$
$812$	−4.39564e23			−2.32581
$813$		0			0
$814$	4.71227e23	−	5.11142e23i	2.44475	−	2.65183i
$815$	8.02102e22			0.412068
$816$		0			0
$817$	−1.70779e22			−0.0860317
$818$	−5.93044e23			−2.95842
$819$		0			0
$820$		−	4.66718e23i		−	2.28320i
$821$			3.42502e23i			1.65927i	0.558306	+	0.829635i	$0.311452\pi$
$821$			3.42502e23i			1.65927i	−0.558306	+	0.829635i	$0.688548\pi$
$822$		0			0
$823$	1.94150e23			0.922443			0.461222	−	0.887285i	$-0.347411\pi$
$823$	1.94150e23			0.922443			0.461222	+	0.887285i	$0.347411\pi$
$824$		−	3.78237e23i		−	1.77970i
$825$		0			0
$826$	4.19189e23			1.93450
$827$		−	2.77645e23i		−	1.26896i	−0.772941	−	0.634478i	$-0.781215\pi$
$827$		−	2.77645e23i		−	1.26896i	0.772941	−	0.634478i	$-0.218785\pi$
$828$		0			0
$829$	−2.92660e23			−1.31198			−0.655989	−	0.754770i	$-0.727748\pi$
$829$	−2.92660e23			−1.31198			−0.655989	+	0.754770i	$0.727748\pi$
$830$	6.19428e22			0.275021
$831$		0			0
$832$			1.30243e24i			5.67243i
$833$			6.85530e21i			0.0295710i
$834$		0			0
$835$			3.78887e23i			1.60331i
$836$	1.75651e23	−	1.90529e23i	0.736209	−	0.798568i
$837$		0			0
$838$		−	4.86941e23i		−	2.00228i
$839$	−5.74494e22			−0.233986			−0.116993	−	0.993133i	$-0.537326\pi$
$839$	−5.74494e22			−0.233986			−0.116993	+	0.993133i	$0.537326\pi$
$840$		0			0
$841$	7.05228e22			0.281813
$842$			2.17197e23i			0.859721i
$843$		0			0
$844$		−	7.02979e23i		−	2.73025i
$845$	−1.25252e23			−0.481872
$846$		0			0
$847$	−2.56961e23	+	2.09157e22i	−0.970063	+	0.0789596i
$848$	8.89379e23			3.32598
$849$		0			0
$850$	3.29561e22			0.120944
$851$	−3.36129e22			−0.122200
$852$		0			0
$853$			3.93963e23i			1.40561i	0.711385	+	0.702803i	$0.248068\pi$
$853$			3.93963e23i			1.40561i	−0.711385	+	0.702803i	$0.751932\pi$
$854$		−	1.21059e23i		−	0.427891i
$855$		0			0
$856$	−1.36627e24			−4.73965
$857$			2.20341e23i			0.757268i	0.925547	+	0.378634i	$0.123606\pi$
$857$			2.20341e23i			0.757268i	−0.925547	+	0.378634i	$0.876394\pi$
$858$		0			0
$859$	−1.61946e23			−0.546292			−0.273146	−	0.961973i	$-0.588064\pi$
$859$	−1.61946e23			−0.546292			−0.273146	+	0.961973i	$0.588064\pi$
$860$			1.98580e23i			0.663662i
$861$		0			0
$862$	2.41864e23			0.793438
$863$	−2.98151e23			−0.969058			−0.484529	−	0.874775i	$-0.661009\pi$
$863$	−2.98151e23			−0.969058			−0.484529	+	0.874775i	$0.661009\pi$
$864$		0			0
$865$			1.78703e23i			0.570168i
$866$		−	3.29636e22i		−	0.104206i
$867$		0			0
$868$			9.91031e23i			3.07560i
$869$	1.88134e22	−	2.04070e22i	0.0578507	−	0.0627509i
$870$		0			0
$871$		−	4.59088e23i		−	1.38596i
$872$	−1.97754e24			−5.91552
$873$		0			0
$874$	−1.69726e22			−0.0498491
$875$		−	3.13503e23i		−	0.912382i
$876$		0			0
$877$		−	2.56841e23i		−	0.733951i	−0.930231	−	0.366975i	$-0.880393\pi$
$877$		−	2.56841e23i		−	0.733951i	0.930231	−	0.366975i	$-0.119607\pi$
$878$	1.19241e24			3.37652
$879$		0			0
$880$	−1.15116e24	−	1.06126e24i	−3.20090	−	2.95095i
$881$	3.07105e23			0.846214			0.423107	−	0.906080i	$-0.360940\pi$
$881$	3.07105e23			0.846214			0.423107	+	0.906080i	$0.360940\pi$
$882$		0			0
$883$	−5.18355e23			−1.40262			−0.701312	−	0.712854i	$-0.747402\pi$
$883$	−5.18355e23			−1.40262			−0.701312	+	0.712854i	$0.747402\pi$
$884$	−7.11737e23			−1.90854
$885$		0			0
$886$			5.33429e23i			1.40477i
$887$			3.53002e23i			0.921273i	0.887589	+	0.460636i	$0.152379\pi$
$887$			3.53002e23i			0.921273i	−0.887589	+	0.460636i	$0.847621\pi$
$888$		0			0
$889$	−3.44418e23			−0.882820
$890$		−	8.29802e22i		−	0.210792i
$891$		0			0
$892$	1.52046e24			3.79365
$893$		−	3.01539e22i		−	0.0745645i
$894$		0			0
$895$	1.83331e23			0.445298
$896$	−1.88624e24			−4.54082
$897$		0			0
$898$		−	1.16052e24i		−	2.74438i
$899$			4.05201e23i			0.949714i
$900$		0			0
$901$			1.96024e23i			0.451348i
$902$	−4.83822e23	−	4.46040e23i	−1.10416	−	1.01794i
$903$		0			0
$904$			2.97978e24i			6.68092i
$905$	−1.51624e23			−0.336961
$906$		0			0
$907$	−1.59953e23			−0.349247			−0.174624	−	0.984635i	$-0.555871\pi$
$907$	−1.59953e23			−0.349247			−0.174624	+	0.984635i	$0.555871\pi$
$908$			7.21616e23i			1.56178i
$909$		0			0
$910$		−	1.13788e24i		−	2.41971i
$911$	2.32299e23			0.489666			0.244833	−	0.969565i	$-0.421267\pi$
$911$	2.32299e23			0.489666			0.244833	+	0.969565i	$0.421267\pi$
$912$		0			0
$913$	4.37008e22	−	4.74024e22i	0.0905156	−	0.0981826i
$914$	7.58218e22			0.155677
$915$		0			0
$916$	−3.81367e23			−0.769448
$917$	4.34887e23			0.869804
$918$		0			0
$919$			9.00965e23i			1.77086i	0.464773	+	0.885430i	$0.346136\pi$
$919$			9.00965e23i			1.77086i	−0.464773	+	0.885430i	$0.653864\pi$
$920$			1.27367e23i			0.248172i
$921$		0			0
$922$	1.61656e24			3.09559
$923$			3.62584e23i			0.688328i
$924$		0			0
$925$	−1.09167e23			−0.203684
$926$			6.58078e23i			1.21728i
$927$		0			0
$928$	−2.10603e24			−3.82896
$929$	−7.43974e23			−1.34101			−0.670505	−	0.741905i	$-0.733922\pi$
$929$	−7.43974e23			−1.34101			−0.670505	+	0.741905i	$0.733922\pi$
$930$		0			0
$931$		−	1.14663e22i		−	0.0203155i
$932$		−	8.82494e23i		−	1.55019i
$933$		0			0
$934$			1.77692e23i			0.306827i
$935$	2.33908e23	−	2.53721e23i	0.400454	−	0.434374i
$936$		0			0
$937$		−	2.83967e23i		−	0.477915i	−0.971030	−	0.238958i	$-0.923194\pi$
$937$		−	2.83967e23i		−	0.477915i	0.971030	−	0.238958i	$-0.0768057\pi$
$938$	1.30874e24			2.18390
$939$		0			0
$940$	−3.50626e23			−0.575202
$941$			1.09046e24i			1.77375i	0.462011	+	0.886874i	$0.347128\pi$
$941$			1.09046e24i			1.77375i	−0.462011	+	0.886874i	$0.652872\pi$
$942$		0			0
$943$			3.18163e22i			0.0508811i
$944$	2.64975e24			4.20174
$945$		0			0
$946$	2.05857e23	+	1.89782e23i	0.320949	+	0.295887i
$947$	1.28339e24			1.98407			0.992036	−	0.125957i	$-0.0402001\pi$
$947$	1.28339e24			1.98407			0.992036	+	0.125957i	$0.0402001\pi$
$948$		0			0
$949$	1.28191e24			1.94862
$950$	−5.51231e22			−0.0830892
$951$		0			0
$952$		−	1.30944e24i		−	1.94084i
$953$			8.44805e23i			1.24169i	0.783933	+	0.620845i	$0.213211\pi$
$953$			8.44805e23i			1.24169i	−0.783933	+	0.620845i	$0.786789\pi$
$954$		0			0
$955$	1.39129e23			0.201091
$956$		−	2.44020e24i		−	3.49753i
$957$		0			0
$958$	1.15652e24			1.63016
$959$		−	2.70468e23i		−	0.378066i
$960$		0			0
$961$	1.86133e23			0.255879
$962$	3.19372e24			4.35408
$963$		0			0
$964$			1.97180e24i			2.64391i
$965$			1.10231e24i			1.46584i
$966$		0			0
$967$			3.88234e23i			0.507787i	0.967232	+	0.253893i	$0.0817112\pi$
$967$			3.88234e23i			0.507787i	−0.967232	+	0.253893i	$0.918289\pi$
$968$	−2.73287e24	+	2.22446e23i	−3.54500	+	0.288550i
$969$		0			0
$970$			4.86881e23i			0.621225i
$971$	2.31749e22			0.0293267			0.0146633	−	0.999892i	$-0.495332\pi$
$971$	2.31749e22			0.0293267			0.0146633	+	0.999892i	$0.495332\pi$
$972$		0			0
$973$	9.30659e23			1.15848
$974$			8.13093e23i			1.00385i
$975$		0			0
$976$		−	7.65228e23i		−	0.929378i
$977$	−7.20804e23			−0.868282			−0.434141	−	0.900845i	$-0.642948\pi$
$977$	−7.20804e23			−0.868282			−0.434141	+	0.900845i	$0.642948\pi$
$978$		0			0
$979$	−6.35015e22	−	5.85427e22i	−0.0752528	−	0.0693763i
$980$	−1.33329e23			−0.156717
$981$		0			0
$982$	−5.25813e23			−0.608050
$983$	−1.09197e23			−0.125251			−0.0626257	−	0.998037i	$-0.519947\pi$
$983$	−1.09197e23			−0.125251			−0.0626257	+	0.998037i	$0.519947\pi$
$984$		0			0
$985$		−	9.92301e22i		−	0.111983i
$986$		−	8.29587e23i		−	0.928638i
$987$		0			0
$988$	1.19047e24			1.31118
$989$		−	1.35372e22i		−	0.0147897i
$990$		0			0
$991$	−4.53458e23			−0.487470			−0.243735	−	0.969842i	$-0.578373\pi$
$991$	−4.53458e23			−0.487470			−0.243735	+	0.969842i	$0.578373\pi$
$992$			4.74820e24i			5.06332i
$993$		0			0
$994$	−1.03364e24			−1.08462
$995$	−7.99896e23			−0.832624
$996$		0			0
$997$			1.09961e24i			1.12636i	0.826333	+	0.563182i	$0.190423\pi$
$997$			1.09961e24i			1.12636i	−0.826333	+	0.563182i	$0.809577\pi$
$998$		−	2.44958e24i		−	2.48913i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.17.c.b.10.1		14
3.2	odd	2		11.17.b.b.10.14	yes	14
11.10	odd	2	inner	99.17.c.b.10.14		14
33.32	even	2		11.17.b.b.10.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.17.b.b.10.1	✓	14	33.32	even	2
11.17.b.b.10.14	yes	14	3.2	odd	2
99.17.c.b.10.1		14	1.1	even	1	trivial
99.17.c.b.10.14		14	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	99.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-500.336i q^{2} -184800. q^{4} +411618. q^{5} +5.61072e6i q^{7} +5.96719e7i q^{8} +O(q^{10})\)	\(q-500.336i q^{2} -184800. q^{4} +411618. q^{5} +5.61072e6i q^{7} +5.96719e7i q^{8} -2.05947e8i q^{10} +(-1.57603e8 - 1.45296e8i) q^{11} -9.84738e8i q^{13} +2.80724e9 q^{14} +1.77449e10 q^{16} +3.91109e9i q^{17} -6.54178e9i q^{19} -7.60669e10 q^{20} +(-7.26968e10 + 7.88545e10i) q^{22} +5.18551e9 q^{23} +1.68413e10 q^{25} -4.92700e11 q^{26} -1.03686e12i q^{28} -4.23938e11i q^{29} -9.55801e11 q^{31} -4.96777e12i q^{32} +1.95686e12 q^{34} +2.30947e12i q^{35} -6.48209e12 q^{37} -3.27308e12 q^{38} +2.45620e13i q^{40} +6.13562e12i q^{41} -2.61059e12i q^{43} +(2.91250e13 + 2.68507e13i) q^{44} -2.59449e12i q^{46} +4.60944e12 q^{47} +1.75278e12 q^{49} -8.42632e12i q^{50} +1.81979e14i q^{52} +5.01201e13 q^{53} +(-6.48723e13 - 5.98065e13i) q^{55} -3.34802e14 q^{56} -2.12111e14 q^{58} +1.49324e14 q^{59} -4.31237e13i q^{61} +4.78221e14i q^{62} -1.32262e15 q^{64} -4.05336e14i q^{65} +4.66203e14 q^{67} -7.22768e14i q^{68} +1.15551e15 q^{70} -3.68204e14 q^{71} +1.30177e15i q^{73} +3.24322e15i q^{74} +1.20892e15i q^{76} +(8.15215e14 - 8.84267e14i) q^{77} +1.29483e14i q^{79} +7.30413e15 q^{80} +3.06987e15 q^{82} +3.00771e14i q^{83} +1.60987e15i q^{85} -1.30617e15 q^{86} +(8.67010e15 - 9.40448e15i) q^{88} +4.02920e14 q^{89} +5.52509e15 q^{91} -9.58281e14 q^{92} -2.30627e15i q^{94} -2.69271e15i q^{95} -2.36411e15 q^{97} -8.76981e14i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 607804 q^{4} + 535618 q^{5}+O(q^{10}) \) 14 * q - 607804 * q^4 + 535618 * q^5	\( 14 q - 607804 q^{4} + 535618 q^{5} - 160637170 q^{11} + 3197599848 q^{14} + 35292427592 q^{16} + 99612496468 q^{20} + 127643346840 q^{22} + 305748171262 q^{23} + 289695273612 q^{25} - 1506094012008 q^{26} - 2810074524110 q^{31} - 4903464738408 q^{34} + 1225852399438 q^{37} - 19938057531240 q^{38} + 84053621084948 q^{44} - 54334138546628 q^{47} - 17095708773634 q^{49} + 314109617965972 q^{53} - 244204596500798 q^{55} - 506018447074416 q^{56} - 811982470463040 q^{58} - 487958802125282 q^{59} - 30\!\cdots\!12 q^{64}+ \cdots + 10\!\cdots\!98 q^{97}+O(q^{100}) \) 14 * q - 607804 * q^4 + 535618 * q^5 - 160637170 * q^11 + 3197599848 * q^14 + 35292427592 * q^16 + 99612496468 * q^20 + 127643346840 * q^22 + 305748171262 * q^23 + 289695273612 * q^25 - 1506094012008 * q^26 - 2810074524110 * q^31 - 4903464738408 * q^34 + 1225852399438 * q^37 - 19938057531240 * q^38 + 84053621084948 * q^44 - 54334138546628 * q^47 - 17095708773634 * q^49 + 314109617965972 * q^53 - 244204596500798 * q^55 - 506018447074416 * q^56 - 811982470463040 * q^58 - 487958802125282 * q^59 - 3058743051134512 * q^64 + 951784823334898 * q^67 + 2102378909371560 * q^70 - 2066090774899778 * q^71 + 2087904685537200 * q^77 + 5159446405219528 * q^80 + 10456916101015560 * q^82 - 11739026032493808 * q^86 + 2795712403748880 * q^88 - 8630276341635710 * q^89 + 7159890945002448 * q^91 + 13184625175008892 * q^92 + 10852702786337998 * q^97

Introduction

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