LMFDB - Embedded newform 1700.2.m.a.1449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1700,2,Mod(149,1700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1700, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1700.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1700 = 2^{2} \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1700.m (of order $4$, degree $2$, not 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:	$13.5745683436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1449.1
Root			$-2.30278i$ of defining polynomial
Character	$\chi$	$=$	1700.1449
Dual form			1700.2.m.a.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30278 - 2.30278i) q^{3} +(2.30278 - 2.30278i) q^{7} +7.60555i q^{9} +(-0.302776 - 0.302776i) q^{11} +2.60555i q^{13} +(2.00000 - 3.60555i) q^{17} -0.605551i q^{19} -10.6056 q^{21} +(4.30278 - 4.30278i) q^{23} +(10.6056 - 10.6056i) q^{27} +(1.60555 - 1.60555i) q^{29} +(4.30278 - 4.30278i) q^{31} +1.39445i q^{33} +(-3.00000 - 3.00000i) q^{37} +(6.00000 - 6.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} +3.39445 q^{43} +4.00000i q^{47} -3.60555i q^{49} +(-12.9083 + 3.69722i) q^{51} +5.21110 q^{53} +(-1.39445 + 1.39445i) q^{57} +8.60555i q^{59} +(-6.21110 - 6.21110i) q^{61} +(17.5139 + 17.5139i) q^{63} -9.21110i q^{67} -19.8167 q^{69} +(2.90833 - 2.90833i) q^{71} +(-7.00000 - 7.00000i) q^{73} -1.39445 q^{77} +(0.302776 + 0.302776i) q^{79} -26.0278 q^{81} -17.8167 q^{83} -7.39445 q^{87} -7.81665 q^{89} +(6.00000 + 6.00000i) q^{91} -19.8167 q^{93} +(7.60555 + 7.60555i) q^{97} +(2.30278 - 2.30278i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{7} + 6 q^{11} + 8 q^{17} - 28 q^{21} + 10 q^{23} + 28 q^{27} - 8 q^{29} + 10 q^{31} - 12 q^{37} + 24 q^{39} + 4 q^{41} + 28 q^{43} - 30 q^{51} - 8 q^{53} - 20 q^{57} + 4 q^{61} + 34 q^{63}+ \cdots + 2 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^7 + 6 * q^11 + 8 * q^17 - 28 * q^21 + 10 * q^23 + 28 * q^27 - 8 * q^29 + 10 * q^31 - 12 * q^37 + 24 * q^39 + 4 * q^41 + 28 * q^43 - 30 * q^51 - 8 * q^53 - 20 * q^57 + 4 * q^61 + 34 * q^63 - 36 * q^69 - 10 * q^71 - 28 * q^73 - 20 * q^77 - 6 * q^79 - 32 * q^81 - 28 * q^83 - 44 * q^87 + 12 * q^89 + 24 * q^91 - 36 * q^93 + 16 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1700\mathbb{Z}\right)^\times$.

$n$	$477$	$851$	$1601$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−2.30278	−	2.30278i	−1.32951	−	1.32951i	−0.905798	−	0.423710i	$-0.860727\pi$
$3$	−2.30278	−	2.30278i	−1.32951	−	1.32951i	−0.423710	−	0.905798i	$-0.639273\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.30278	−	2.30278i	0.870367	−	0.870367i	−0.122145	−	0.992512i	$-0.538977\pi$
$7$	2.30278	−	2.30278i	0.870367	−	0.870367i	0.992512	+	0.122145i	$0.0389773\pi$
$8$		0			0
$9$			7.60555i			2.53518i
$10$		0			0
$11$	−0.302776	−	0.302776i	−0.0912903	−	0.0912903i	0.659987	−	0.751277i	$-0.270562\pi$
$11$	−0.302776	−	0.302776i	−0.0912903	−	0.0912903i	−0.751277	+	0.659987i	$0.770562\pi$
$12$		0			0
$13$			2.60555i			0.722650i	0.932440	+	0.361325i	$0.117675\pi$
$13$			2.60555i			0.722650i	−0.932440	+	0.361325i	$0.882325\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.00000	−	3.60555i	0.485071	−	0.874475i
$17$	2.00000	−	3.60555i	0.485071	−	0.874475i
$18$		0			0
$19$		−	0.605551i		−	0.138923i	−0.997585	−	0.0694615i	$-0.977872\pi$
$19$		−	0.605551i		−	0.138923i	0.997585	−	0.0694615i	$-0.0221281\pi$
$20$		0			0
$21$	−10.6056			−2.31432
$22$		0			0
$23$	4.30278	−	4.30278i	0.897191	−	0.897191i	−0.0979961	−	0.995187i	$-0.531243\pi$
$23$	4.30278	−	4.30278i	0.897191	−	0.897191i	0.995187	+	0.0979961i	$0.0312433\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	10.6056	−	10.6056i	2.04104	−	2.04104i
$28$		0			0
$29$	1.60555	−	1.60555i	0.298143	−	0.298143i	−0.542143	−	0.840286i	$-0.682387\pi$
$29$	1.60555	−	1.60555i	0.298143	−	0.298143i	0.840286	+	0.542143i	$0.182387\pi$
$30$		0			0
$31$	4.30278	−	4.30278i	0.772801	−	0.772801i	−0.205794	−	0.978595i	$-0.565978\pi$
$31$	4.30278	−	4.30278i	0.772801	−	0.772801i	0.978595	+	0.205794i	$0.0659777\pi$
$32$		0			0
$33$			1.39445i			0.242742i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$		0			0
$39$	6.00000	−	6.00000i	0.960769	−	0.960769i
$40$		0			0
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	1.00000	+	1.00000i	0.156174	+	0.156174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$	3.39445			0.517649			0.258824	−	0.965924i	$-0.416665\pi$
$43$	3.39445			0.517649			0.258824	+	0.965924i	$0.416665\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$		0			0
$49$		−	3.60555i		−	0.515079i
$50$		0			0
$51$	−12.9083	+	3.69722i	−1.80753	+	0.517715i
$52$		0			0
$53$	5.21110			0.715800			0.357900	−	0.933760i	$-0.383493\pi$
$53$	5.21110			0.715800			0.357900	+	0.933760i	$0.383493\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.39445	+	1.39445i	−0.184699	+	0.184699i
$58$		0			0
$59$			8.60555i			1.12035i	0.828375	+	0.560174i	$0.189266\pi$
$59$			8.60555i			1.12035i	−0.828375	+	0.560174i	$0.810734\pi$
$60$		0			0
$61$	−6.21110	−	6.21110i	−0.795250	−	0.795250i	0.187092	−	0.982342i	$-0.440094\pi$
$61$	−6.21110	−	6.21110i	−0.795250	−	0.795250i	−0.982342	+	0.187092i	$0.940094\pi$
$62$		0			0
$63$	17.5139	+	17.5139i	2.20654	+	2.20654i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	9.21110i		−	1.12532i	−0.826690	−	0.562658i	$-0.809779\pi$
$67$		−	9.21110i		−	1.12532i	0.826690	−	0.562658i	$-0.190221\pi$
$68$		0			0
$69$	−19.8167			−2.38564
$70$		0			0
$71$	2.90833	−	2.90833i	0.345155	−	0.345155i	−0.513146	−	0.858301i	$-0.671520\pi$
$71$	2.90833	−	2.90833i	0.345155	−	0.345155i	0.858301	+	0.513146i	$0.171520\pi$
$72$		0			0
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	0.166717	−	0.986005i	$-0.446683\pi$
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	−0.986005	+	0.166717i	$0.946683\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.39445			−0.158912
$78$		0			0
$79$	0.302776	+	0.302776i	0.0340649	+	0.0340649i	0.723934	−	0.689869i	$-0.242332\pi$
$79$	0.302776	+	0.302776i	0.0340649	+	0.0340649i	−0.689869	+	0.723934i	$0.742332\pi$
$80$		0			0
$81$	−26.0278			−2.89197
$82$		0			0
$83$	−17.8167			−1.95563			−0.977816	−	0.209466i	$-0.932827\pi$
$83$	−17.8167			−1.95563			−0.977816	+	0.209466i	$0.932827\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−7.39445			−0.792768
$88$		0			0
$89$	−7.81665			−0.828564			−0.414282	−	0.910149i	$-0.635967\pi$
$89$	−7.81665			−0.828564			−0.414282	+	0.910149i	$0.635967\pi$
$90$		0			0
$91$	6.00000	+	6.00000i	0.628971	+	0.628971i
$92$		0			0
$93$	−19.8167			−2.05489
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.60555	+	7.60555i	0.772227	+	0.772227i	0.978495	−	0.206269i	$-0.0661321\pi$
$97$	7.60555	+	7.60555i	0.772227	+	0.772227i	−0.206269	+	0.978495i	$0.566132\pi$
$98$		0			0
$99$	2.30278	−	2.30278i	0.231438	−	0.231438i
$100$		0			0
$101$	10.6056			1.05529			0.527646	−	0.849464i	$-0.323075\pi$
$101$	10.6056			1.05529			0.527646	+	0.849464i	$0.323075\pi$
$102$		0			0
$103$		−	13.2111i		−	1.30173i	−0.759194	−	0.650864i	$-0.774407\pi$
$103$		−	13.2111i		−	1.30173i	0.759194	−	0.650864i	$-0.225593\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.69722	−	5.69722i	−0.550771	−	0.550771i	0.375892	−	0.926663i	$-0.377336\pi$
$107$	−5.69722	−	5.69722i	−0.550771	−	0.550771i	−0.926663	+	0.375892i	$0.877336\pi$
$108$		0			0
$109$	6.21110	+	6.21110i	0.594916	+	0.594916i	0.938955	−	0.344039i	$-0.111795\pi$
$109$	6.21110	+	6.21110i	0.594916	+	0.594916i	−0.344039	+	0.938955i	$0.611795\pi$
$110$		0			0
$111$			13.8167i			1.31142i
$112$		0			0
$113$	−9.60555	+	9.60555i	−0.903614	+	0.903614i	−0.995747	−	0.0921325i	$-0.970632\pi$
$113$	−9.60555	+	9.60555i	−0.903614	+	0.903614i	0.0921325	+	0.995747i	$0.470632\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−19.8167			−1.83205
$118$		0			0
$119$	−3.69722	−	12.9083i	−0.338924	−	1.18330i
$120$		0			0
$121$		−	10.8167i		−	0.983332i
$122$		0			0
$123$		−	4.60555i		−	0.415269i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−0.605551			−0.0537340			−0.0268670	−	0.999639i	$-0.508553\pi$
$127$	−0.605551			−0.0537340			−0.0268670	+	0.999639i	$0.508553\pi$
$128$		0			0
$129$	−7.81665	−	7.81665i	−0.688218	−	0.688218i
$130$		0			0
$131$	−6.30278	+	6.30278i	−0.550676	+	0.550676i	−0.926636	−	0.375960i	$-0.877313\pi$
$131$	−6.30278	+	6.30278i	−0.550676	+	0.550676i	0.375960	+	0.926636i	$0.377313\pi$
$132$		0			0
$133$	−1.39445	−	1.39445i	−0.120914	−	0.120914i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			2.60555i			0.222607i	0.993786	+	0.111304i	$0.0355026\pi$
$137$			2.60555i			0.222607i	−0.993786	+	0.111304i	$0.964497\pi$
$138$		0			0
$139$	−0.302776	+	0.302776i	−0.0256811	+	0.0256811i	−0.719831	−	0.694150i	$-0.755781\pi$
$139$	−0.302776	+	0.302776i	−0.0256811	+	0.0256811i	0.694150	+	0.719831i	$0.255781\pi$
$140$		0			0
$141$	9.21110	−	9.21110i	0.775715	−	0.775715i
$142$		0			0
$143$	0.788897	−	0.788897i	0.0659709	−	0.0659709i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−8.30278	+	8.30278i	−0.684801	+	0.684801i
$148$		0			0
$149$	−8.42221			−0.689974			−0.344987	−	0.938607i	$-0.612117\pi$
$149$	−8.42221			−0.689974			−0.344987	+	0.938607i	$0.612117\pi$
$150$		0			0
$151$			4.60555i			0.374794i	0.982284	+	0.187397i	$0.0600052\pi$
$151$			4.60555i			0.374794i	−0.982284	+	0.187397i	$0.939995\pi$
$152$		0			0
$153$	27.4222	+	15.2111i	2.21695	+	1.22974i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			8.42221i			0.672165i	0.941833	+	0.336083i	$0.109102\pi$
$157$			8.42221i			0.672165i	−0.941833	+	0.336083i	$0.890898\pi$
$158$		0			0
$159$	−12.0000	−	12.0000i	−0.951662	−	0.951662i
$160$		0			0
$161$		−	19.8167i		−	1.56177i
$162$		0			0
$163$	4.30278	−	4.30278i	0.337019	−	0.337019i	−0.518225	−	0.855244i	$-0.673407\pi$
$163$	4.30278	−	4.30278i	0.337019	−	0.337019i	0.855244	+	0.518225i	$0.173407\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.9083	−	14.9083i	−1.15364	−	1.15364i	−0.985817	−	0.167824i	$-0.946326\pi$
$167$	−14.9083	−	14.9083i	−1.15364	−	1.15364i	−0.167824	−	0.985817i	$-0.553674\pi$
$168$		0			0
$169$	6.21110			0.477777
$170$		0			0
$171$	4.60555			0.352195
$172$		0			0
$173$	−14.8167	−	14.8167i	−1.12649	−	1.12649i	−0.990744	−	0.135746i	$-0.956657\pi$
$173$	−14.8167	−	14.8167i	−1.12649	−	1.12649i	−0.135746	−	0.990744i	$-0.543343\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	19.8167	−	19.8167i	1.48951	−	1.48951i
$178$		0			0
$179$			15.0278i			1.12323i	0.827400	+	0.561614i	$0.189819\pi$
$179$			15.0278i			1.12323i	−0.827400	+	0.561614i	$0.810181\pi$
$180$		0			0
$181$	−13.0000	−	13.0000i	−0.966282	−	0.966282i	0.0331674	−	0.999450i	$-0.489441\pi$
$181$	−13.0000	−	13.0000i	−0.966282	−	0.966282i	−0.999450	+	0.0331674i	$0.989441\pi$
$182$		0			0
$183$			28.6056i			2.11458i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.69722	+	0.486122i	−0.124113	+	0.0355487i
$188$		0			0
$189$		−	48.8444i		−	3.55291i
$190$		0			0
$191$	6.78890			0.491227			0.245614	−	0.969368i	$-0.421011\pi$
$191$	6.78890			0.491227			0.245614	+	0.969368i	$0.421011\pi$
$192$		0			0
$193$	8.21110	−	8.21110i	0.591048	−	0.591048i	−0.346866	−	0.937915i	$-0.612754\pi$
$193$	8.21110	−	8.21110i	0.591048	−	0.591048i	0.937915	+	0.346866i	$0.112754\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−17.6056	+	17.6056i	−1.25434	+	1.25434i	−0.300590	+	0.953753i	$0.597184\pi$
$197$	−17.6056	+	17.6056i	−1.25434	+	1.25434i	−0.953753	+	0.300590i	$0.902816\pi$
$198$		0			0
$199$	10.1194	−	10.1194i	0.717347	−	0.717347i	−0.250714	−	0.968061i	$-0.580665\pi$
$199$	10.1194	−	10.1194i	0.717347	−	0.717347i	0.968061	+	0.250714i	$0.0806653\pi$
$200$		0			0
$201$	−21.2111	+	21.2111i	−1.49612	+	1.49612i
$202$		0			0
$203$		−	7.39445i		−	0.518989i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	32.7250	+	32.7250i	2.27454	+	2.27454i
$208$		0			0
$209$	−0.183346	+	0.183346i	−0.0126823	+	0.0126823i
$210$		0			0
$211$	15.5139	+	15.5139i	1.06802	+	1.06802i	0.997511	+	0.0705082i	$0.0224621\pi$
$211$	15.5139	+	15.5139i	1.06802	+	1.06802i	0.0705082	+	0.997511i	$0.477538\pi$
$212$		0			0
$213$	−13.3944			−0.917773
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	19.8167i		−	1.34524i
$218$		0			0
$219$			32.2389i			2.17850i
$220$		0			0
$221$	9.39445	+	5.21110i	0.631939	+	0.350537i
$222$		0			0
$223$	17.8167			1.19309			0.596546	−	0.802579i	$-0.296539\pi$
$223$	17.8167			1.19309			0.596546	+	0.802579i	$0.296539\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.302776	+	0.302776i	−0.0200959	+	0.0200959i	−0.717083	−	0.696987i	$-0.754523\pi$
$227$	−0.302776	+	0.302776i	−0.0200959	+	0.0200959i	0.696987	+	0.717083i	$0.254523\pi$
$228$		0			0
$229$		−	4.60555i		−	0.304343i	−0.988354	−	0.152172i	$-0.951373\pi$
$229$		−	4.60555i		−	0.304343i	0.988354	−	0.152172i	$-0.0486267\pi$
$230$		0			0
$231$	3.21110	+	3.21110i	0.211275	+	0.211275i
$232$		0			0
$233$	5.60555	+	5.60555i	0.367232	+	0.367232i	0.866467	−	0.499235i	$-0.166386\pi$
$233$	5.60555	+	5.60555i	0.367232	+	0.367232i	−0.499235	+	0.866467i	$0.666386\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	1.39445i		−	0.0905792i
$238$		0			0
$239$	14.7889			0.956614			0.478307	−	0.878193i	$-0.341251\pi$
$239$	14.7889			0.956614			0.478307	+	0.878193i	$0.341251\pi$
$240$		0			0
$241$	9.00000	−	9.00000i	0.579741	−	0.579741i	−0.355091	−	0.934832i	$-0.615550\pi$
$241$	9.00000	−	9.00000i	0.579741	−	0.579741i	0.934832	+	0.355091i	$0.115550\pi$
$242$		0			0
$243$	28.1194	+	28.1194i	1.80386	+	1.80386i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.57779			0.100393
$248$		0			0
$249$	41.0278	+	41.0278i	2.60003	+	2.60003i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−2.60555			−0.163810
$254$		0			0
$255$		0			0
$256$		0			0
$257$	19.3944			1.20979			0.604896	−	0.796304i	$-0.293215\pi$
$257$	19.3944			1.20979			0.604896	+	0.796304i	$0.293215\pi$
$258$		0			0
$259$	−13.8167			−0.858525
$260$		0			0
$261$	12.2111	+	12.2111i	0.755848	+	0.755848i
$262$		0			0
$263$	−23.0278			−1.41995			−0.709976	−	0.704226i	$-0.751294\pi$
$263$	−23.0278			−1.41995			−0.709976	+	0.704226i	$0.751294\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.0000	+	18.0000i	1.10158	+	1.10158i
$268$		0			0
$269$	−17.4222	+	17.4222i	−1.06225	+	1.06225i	−0.0643214	+	0.997929i	$0.520488\pi$
$269$	−17.4222	+	17.4222i	−1.06225	+	1.06225i	−0.997929	+	0.0643214i	$0.979512\pi$
$270$		0			0
$271$	1.21110			0.0735692			0.0367846	−	0.999323i	$-0.488288\pi$
$271$	1.21110			0.0735692			0.0367846	+	0.999323i	$0.488288\pi$
$272$		0			0
$273$		−	27.6333i		−	1.67244i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.60555	−	3.60555i	−0.216637	−	0.216637i	0.590443	−	0.807079i	$-0.298953\pi$
$277$	−3.60555	−	3.60555i	−0.216637	−	0.216637i	−0.807079	+	0.590443i	$0.798953\pi$
$278$		0			0
$279$	32.7250	+	32.7250i	1.95919	+	1.95919i
$280$		0			0
$281$			18.4222i			1.09898i	0.835501	+	0.549488i	$0.185177\pi$
$281$			18.4222i			1.09898i	−0.835501	+	0.549488i	$0.814823\pi$
$282$		0			0
$283$	−2.11943	+	2.11943i	−0.125987	+	0.125987i	−0.767289	−	0.641302i	$-0.778395\pi$
$283$	−2.11943	+	2.11943i	−0.125987	+	0.125987i	0.641302	+	0.767289i	$0.278395\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.60555			0.271857
$288$		0			0
$289$	−9.00000	−	14.4222i	−0.529412	−	0.848365i
$290$		0			0
$291$		−	35.0278i		−	2.05336i
$292$		0			0
$293$		−	21.6333i		−	1.26383i	−0.775037	−	0.631916i	$-0.782269\pi$
$293$		−	21.6333i		−	1.26383i	0.775037	−	0.631916i	$-0.217731\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−6.42221			−0.372654
$298$		0			0
$299$	11.2111	+	11.2111i	0.648355	+	0.648355i
$300$		0			0
$301$	7.81665	−	7.81665i	0.450544	−	0.450544i
$302$		0			0
$303$	−24.4222	−	24.4222i	−1.40302	−	1.40302i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	21.2111i		−	1.21058i	−0.796004	−	0.605291i	$-0.793057\pi$
$307$		−	21.2111i		−	1.21058i	0.796004	−	0.605291i	$-0.206943\pi$
$308$		0			0
$309$	−30.4222	+	30.4222i	−1.73066	+	1.73066i
$310$		0			0
$311$	18.9083	−	18.9083i	1.07219	−	1.07219i	0.0750101	−	0.997183i	$-0.476101\pi$
$311$	18.9083	−	18.9083i	1.07219	−	1.07219i	0.997183	−	0.0750101i	$-0.0238989\pi$
$312$		0			0
$313$	−6.21110	+	6.21110i	−0.351072	+	0.351072i	−0.860508	−	0.509436i	$-0.829854\pi$
$313$	−6.21110	+	6.21110i	−0.351072	+	0.351072i	0.509436	+	0.860508i	$0.329854\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	19.6056	−	19.6056i	1.10116	−	1.10116i	0.106886	−	0.994271i	$-0.465912\pi$
$317$	19.6056	−	19.6056i	1.10116	−	1.10116i	0.994271	−	0.106886i	$-0.0340881\pi$
$318$		0			0
$319$	−0.972244			−0.0544352
$320$		0			0
$321$			26.2389i			1.46451i
$322$		0			0
$323$	−2.18335	−	1.21110i	−0.121485	−	0.0673875i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	28.6056i		−	1.58189i
$328$		0			0
$329$	9.21110	+	9.21110i	0.507825	+	0.507825i
$330$		0			0
$331$		−	3.39445i		−	0.186576i	−0.995639	−	0.0932879i	$-0.970262\pi$
$331$		−	3.39445i		−	0.186576i	0.995639	−	0.0932879i	$-0.0297377\pi$
$332$		0			0
$333$	22.8167	−	22.8167i	1.25034	−	1.25034i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	16.2111	+	16.2111i	0.883075	+	0.883075i	0.993846	−	0.110771i	$-0.0353320\pi$
$337$	16.2111	+	16.2111i	0.883075	+	0.883075i	−0.110771	+	0.993846i	$0.535332\pi$
$338$		0			0
$339$	44.2389			2.40273
$340$		0			0
$341$	−2.60555			−0.141099
$342$		0			0
$343$	7.81665	+	7.81665i	0.422060	+	0.422060i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.51388	+	5.51388i	−0.296000	+	0.296000i	−0.839445	−	0.543445i	$-0.817120\pi$
$347$	−5.51388	+	5.51388i	−0.296000	+	0.296000i	0.543445	+	0.839445i	$0.317120\pi$
$348$		0			0
$349$		−	23.6333i		−	1.26506i	−0.774535	−	0.632531i	$-0.782016\pi$
$349$		−	23.6333i		−	1.26506i	0.774535	−	0.632531i	$-0.217984\pi$
$350$		0			0
$351$	27.6333	+	27.6333i	1.47496	+	1.47496i
$352$		0			0
$353$		−	31.2111i		−	1.66120i	−0.556870	−	0.830600i	$-0.687998\pi$
$353$		−	31.2111i		−	1.66120i	0.556870	−	0.830600i	$-0.312002\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−21.2111	+	38.2389i	−1.12261	+	2.02382i
$358$		0			0
$359$		−	16.6056i		−	0.876407i	−0.898876	−	0.438204i	$-0.855615\pi$
$359$		−	16.6056i		−	0.876407i	0.898876	−	0.438204i	$-0.144385\pi$
$360$		0			0
$361$	18.6333			0.980700
$362$		0			0
$363$	−24.9083	+	24.9083i	−1.30735	+	1.30735i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−6.90833	+	6.90833i	−0.360612	+	0.360612i	−0.864038	−	0.503426i	$-0.832073\pi$
$367$	−6.90833	+	6.90833i	−0.360612	+	0.360612i	0.503426	+	0.864038i	$0.332073\pi$
$368$		0			0
$369$	−7.60555	+	7.60555i	−0.395929	+	0.395929i
$370$		0			0
$371$	12.0000	−	12.0000i	0.623009	−	0.623009i
$372$		0			0
$373$			21.0278i			1.08878i	0.838834	+	0.544388i	$0.183238\pi$
$373$			21.0278i			1.08878i	−0.838834	+	0.544388i	$0.816762\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.18335	+	4.18335i	0.215453	+	0.215453i
$378$		0			0
$379$	20.7250	−	20.7250i	1.06457	−	1.06457i	0.0668047	−	0.997766i	$-0.478720\pi$
$379$	20.7250	−	20.7250i	1.06457	−	1.06457i	0.997766	−	0.0668047i	$-0.0212804\pi$
$380$		0			0
$381$	1.39445	+	1.39445i	0.0714398	+	0.0714398i
$382$		0			0
$383$	19.3944			0.991010			0.495505	−	0.868605i	$-0.334983\pi$
$383$	19.3944			0.991010			0.495505	+	0.868605i	$0.334983\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			25.8167i			1.31233i
$388$		0			0
$389$		−	10.1833i		−	0.516316i	−0.966103	−	0.258158i	$-0.916884\pi$
$389$		−	10.1833i		−	0.516316i	0.966103	−	0.258158i	$-0.0831155\pi$
$390$		0			0
$391$	−6.90833	−	24.1194i	−0.349369	−	1.21977i
$392$		0			0
$393$	29.0278			1.46426
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−9.00000	+	9.00000i	−0.451697	+	0.451697i	−0.895918	−	0.444220i	$-0.853481\pi$
$397$	−9.00000	+	9.00000i	−0.451697	+	0.451697i	0.444220	+	0.895918i	$0.353481\pi$
$398$		0			0
$399$			6.42221i			0.321512i
$400$		0			0
$401$	−7.00000	−	7.00000i	−0.349563	−	0.349563i	0.510384	−	0.859947i	$-0.329503\pi$
$401$	−7.00000	−	7.00000i	−0.349563	−	0.349563i	−0.859947	+	0.510384i	$0.829503\pi$
$402$		0			0
$403$	11.2111	+	11.2111i	0.558465	+	0.558465i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			1.81665i			0.0900482i
$408$		0			0
$409$	−23.2111			−1.14772			−0.573858	−	0.818955i	$-0.694554\pi$
$409$	−23.2111			−1.14772			−0.573858	+	0.818955i	$0.694554\pi$
$410$		0			0
$411$	6.00000	−	6.00000i	0.295958	−	0.295958i
$412$		0			0
$413$	19.8167	+	19.8167i	0.975114	+	0.975114i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.39445			0.0682864
$418$		0			0
$419$	−2.30278	−	2.30278i	−0.112498	−	0.112498i	0.648617	−	0.761115i	$-0.275348\pi$
$419$	−2.30278	−	2.30278i	−0.112498	−	0.112498i	−0.761115	+	0.648617i	$0.775348\pi$
$420$		0			0
$421$	18.6056			0.906779			0.453390	−	0.891312i	$-0.350215\pi$
$421$	18.6056			0.906779			0.453390	+	0.891312i	$0.350215\pi$
$422$		0			0
$423$	−30.4222			−1.47918
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−28.6056			−1.38432
$428$		0			0
$429$	−3.63331			−0.175418
$430$		0			0
$431$	−1.88057	−	1.88057i	−0.0905839	−	0.0905839i	0.660363	−	0.750947i	$-0.270403\pi$
$431$	−1.88057	−	1.88057i	−0.0905839	−	0.0905839i	−0.750947	+	0.660363i	$0.770403\pi$
$432$		0			0
$433$	15.0278			0.722188			0.361094	−	0.932529i	$-0.382403\pi$
$433$	15.0278			0.722188			0.361094	+	0.932529i	$0.382403\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.60555	−	2.60555i	−0.124640	−	0.124640i
$438$		0			0
$439$	26.3028	−	26.3028i	1.25536	−	1.25536i	0.302081	−	0.953282i	$-0.402319\pi$
$439$	26.3028	−	26.3028i	1.25536	−	1.25536i	0.953282	−	0.302081i	$-0.0976812\pi$
$440$		0			0
$441$	27.4222			1.30582
$442$		0			0
$443$		−	17.2111i		−	0.817724i	−0.912596	−	0.408862i	$-0.865926\pi$
$443$		−	17.2111i		−	0.817724i	0.912596	−	0.408862i	$-0.134074\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	19.3944	+	19.3944i	0.917326	+	0.917326i
$448$		0			0
$449$	16.8167	+	16.8167i	0.793627	+	0.793627i	0.982082	−	0.188455i	$-0.0603479\pi$
$449$	16.8167	+	16.8167i	0.793627	+	0.793627i	−0.188455	+	0.982082i	$0.560348\pi$
$450$		0			0
$451$		−	0.605551i		−	0.0285143i
$452$		0			0
$453$	10.6056	−	10.6056i	0.498292	−	0.498292i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−36.6056			−1.71234			−0.856168	−	0.516698i	$-0.827161\pi$
$457$	−36.6056			−1.71234			−0.856168	+	0.516698i	$0.827161\pi$
$458$		0			0
$459$	−17.0278	−	59.4500i	−0.794788	−	2.77489i
$460$		0			0
$461$			29.2111i			1.36050i	0.732982	+	0.680248i	$0.238128\pi$
$461$			29.2111i			1.36050i	−0.732982	+	0.680248i	$0.761872\pi$
$462$		0			0
$463$		−	39.6333i		−	1.84192i	−0.389662	−	0.920958i	$-0.627408\pi$
$463$		−	39.6333i		−	1.84192i	0.389662	−	0.920958i	$-0.372592\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.2389			0.751445			0.375722	−	0.926732i	$-0.377395\pi$
$467$	16.2389			0.751445			0.375722	+	0.926732i	$0.377395\pi$
$468$		0			0
$469$	−21.2111	−	21.2111i	−0.979438	−	0.979438i
$470$		0			0
$471$	19.3944	−	19.3944i	0.893649	−	0.893649i
$472$		0			0
$473$	−1.02776	−	1.02776i	−0.0472563	−	0.0472563i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			39.6333i			1.81468i
$478$		0			0
$479$	−12.3028	+	12.3028i	−0.562128	+	0.562128i	−0.929912	−	0.367783i	$-0.880117\pi$
$479$	−12.3028	+	12.3028i	−0.562128	+	0.562128i	0.367783	+	0.929912i	$0.380117\pi$
$480$		0			0
$481$	7.81665	−	7.81665i	0.356409	−	0.356409i
$482$		0			0
$483$	−45.6333	+	45.6333i	−2.07639	+	2.07639i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−17.3305	+	17.3305i	−0.785321	+	0.785321i	−0.980723	−	0.195402i	$-0.937399\pi$
$487$	−17.3305	+	17.3305i	−0.785321	+	0.785321i	0.195402	+	0.980723i	$0.437399\pi$
$488$		0			0
$489$	−19.8167			−0.896140
$490$		0			0
$491$		−	9.81665i		−	0.443019i	−0.975158	−	0.221510i	$-0.928902\pi$
$491$		−	9.81665i		−	0.443019i	0.975158	−	0.221510i	$-0.0710984\pi$
$492$		0			0
$493$	−2.57779	−	9.00000i	−0.116098	−	0.405340i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	13.3944i		−	0.600823i
$498$		0			0
$499$	−10.3028	−	10.3028i	−0.461216	−	0.461216i	0.437838	−	0.899054i	$-0.355744\pi$
$499$	−10.3028	−	10.3028i	−0.461216	−	0.461216i	−0.899054	+	0.437838i	$0.855744\pi$
$500$		0			0
$501$			68.6611i			3.06755i
$502$		0			0
$503$	−27.5139	+	27.5139i	−1.22678	+	1.22678i	−0.261609	+	0.965174i	$0.584253\pi$
$503$	−27.5139	+	27.5139i	−1.22678	+	1.22678i	−0.965174	+	0.261609i	$0.915747\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−14.3028	−	14.3028i	−0.635209	−	0.635209i
$508$		0			0
$509$	3.21110			0.142330			0.0711648	−	0.997465i	$-0.477328\pi$
$509$	3.21110			0.142330			0.0711648	+	0.997465i	$0.477328\pi$
$510$		0			0
$511$	−32.2389			−1.42616
$512$		0			0
$513$	−6.42221	−	6.42221i	−0.283547	−	0.283547i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	1.21110	−	1.21110i	0.0532642	−	0.0532642i
$518$		0			0
$519$			68.2389i			2.99535i
$520$		0			0
$521$	13.0000	+	13.0000i	0.569540	+	0.569540i	0.932000	−	0.362459i	$-0.118063\pi$
$521$	13.0000	+	13.0000i	0.569540	+	0.569540i	−0.362459	+	0.932000i	$0.618063\pi$
$522$		0			0
$523$		−	12.0000i		−	0.524723i	−0.964970	−	0.262362i	$-0.915499\pi$
$523$		−	12.0000i		−	0.524723i	0.964970	−	0.262362i	$-0.0845013\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.90833	−	24.1194i	−0.300931	−	1.05066i
$528$		0			0
$529$		−	14.0278i		−	0.609902i
$530$		0			0
$531$	−65.4500			−2.84029
$532$		0			0
$533$	−2.60555	+	2.60555i	−0.112859	+	0.112859i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	34.6056	−	34.6056i	1.49334	−	1.49334i
$538$		0			0
$539$	−1.09167	+	1.09167i	−0.0470217	+	0.0470217i
$540$		0			0
$541$	3.00000	−	3.00000i	0.128980	−	0.128980i	−0.639670	−	0.768650i	$-0.720929\pi$
$541$	3.00000	−	3.00000i	0.128980	−	0.128980i	0.768650	+	0.639670i	$0.220929\pi$
$542$		0			0
$543$			59.8722i			2.56936i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	11.5139	+	11.5139i	0.492298	+	0.492298i	0.909030	−	0.416732i	$-0.136825\pi$
$547$	11.5139	+	11.5139i	0.492298	+	0.492298i	−0.416732	+	0.909030i	$0.636825\pi$
$548$		0			0
$549$	47.2389	−	47.2389i	2.01611	−	2.01611i
$550$		0			0
$551$	−0.972244	−	0.972244i	−0.0414190	−	0.0414190i
$552$		0			0
$553$	1.39445			0.0592980
$554$		0			0
$555$		0			0
$556$		0			0
$557$			21.3944i			0.906512i	0.891380	+	0.453256i	$0.149738\pi$
$557$			21.3944i			0.906512i	−0.891380	+	0.453256i	$0.850262\pi$
$558$		0			0
$559$			8.84441i			0.374079i
$560$		0			0
$561$	5.02776	+	2.78890i	0.212272	+	0.117747i
$562$		0			0
$563$	−20.6056			−0.868420			−0.434210	−	0.900812i	$-0.642972\pi$
$563$	−20.6056			−0.868420			−0.434210	+	0.900812i	$0.642972\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−59.9361	+	59.9361i	−2.51708	+	2.51708i
$568$		0			0
$569$			30.4222i			1.27537i	0.770299	+	0.637683i	$0.220107\pi$
$569$			30.4222i			1.27537i	−0.770299	+	0.637683i	$0.779893\pi$
$570$		0			0
$571$	2.30278	+	2.30278i	0.0963682	+	0.0963682i	0.753647	−	0.657279i	$-0.228293\pi$
$571$	2.30278	+	2.30278i	0.0963682	+	0.0963682i	−0.657279	+	0.753647i	$0.728293\pi$
$572$		0			0
$573$	−15.6333	−	15.6333i	−0.653091	−	0.653091i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			31.4500i			1.30928i	0.755941	+	0.654640i	$0.227180\pi$
$577$			31.4500i			1.30928i	−0.755941	+	0.654640i	$0.772820\pi$
$578$		0			0
$579$	−37.8167			−1.57161
$580$		0			0
$581$	−41.0278	+	41.0278i	−1.70212	+	1.70212i
$582$		0			0
$583$	−1.57779	−	1.57779i	−0.0653456	−	0.0653456i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.60555			−0.190091			−0.0950457	−	0.995473i	$-0.530300\pi$
$587$	−4.60555			−0.190091			−0.0950457	+	0.995473i	$0.530300\pi$
$588$		0			0
$589$	−2.60555	−	2.60555i	−0.107360	−	0.107360i
$590$		0			0
$591$	81.0833			3.33532
$592$		0			0
$593$	−1.57779			−0.0647923			−0.0323961	−	0.999475i	$-0.510314\pi$
$593$	−1.57779			−0.0647923			−0.0323961	+	0.999475i	$0.510314\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−46.6056			−1.90744
$598$		0			0
$599$	−26.0555			−1.06460			−0.532300	−	0.846556i	$-0.678672\pi$
$599$	−26.0555			−1.06460			−0.532300	+	0.846556i	$0.678672\pi$
$600$		0			0
$601$	−4.21110	−	4.21110i	−0.171774	−	0.171774i	0.615984	−	0.787759i	$-0.288759\pi$
$601$	−4.21110	−	4.21110i	−0.171774	−	0.171774i	−0.787759	+	0.615984i	$0.788759\pi$
$602$		0			0
$603$	70.0555			2.85288
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−9.51388	−	9.51388i	−0.386156	−	0.386156i	0.487158	−	0.873314i	$-0.338034\pi$
$607$	−9.51388	−	9.51388i	−0.386156	−	0.386156i	−0.873314	+	0.487158i	$0.838034\pi$
$608$		0			0
$609$	−17.0278	+	17.0278i	−0.690000	+	0.690000i
$610$		0			0
$611$	−10.4222			−0.421637
$612$		0			0
$613$			40.4222i			1.63264i	0.577602	+	0.816319i	$0.303989\pi$
$613$			40.4222i			1.63264i	−0.577602	+	0.816319i	$0.696011\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.60555	−	1.60555i	−0.0646371	−	0.0646371i	0.674049	−	0.738686i	$-0.264554\pi$
$617$	−1.60555	−	1.60555i	−0.0646371	−	0.0646371i	−0.738686	+	0.674049i	$0.764554\pi$
$618$		0			0
$619$	−14.4861	−	14.4861i	−0.582246	−	0.582246i	0.353274	−	0.935520i	$-0.385068\pi$
$619$	−14.4861	−	14.4861i	−0.582246	−	0.582246i	−0.935520	+	0.353274i	$0.885068\pi$
$620$		0			0
$621$		−	91.2666i		−	3.66240i
$622$		0			0
$623$	−18.0000	+	18.0000i	−0.721155	+	0.721155i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.844410			0.0337225
$628$		0			0
$629$	−16.8167	+	4.81665i	−0.670524	+	0.192053i
$630$		0			0
$631$			24.2389i			0.964934i	0.875914	+	0.482467i	$0.160259\pi$
$631$			24.2389i			0.964934i	−0.875914	+	0.482467i	$0.839741\pi$
$632$		0			0
$633$		−	71.4500i		−	2.83988i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.39445			0.372222
$638$		0			0
$639$	22.1194	+	22.1194i	0.875031	+	0.875031i
$640$		0			0
$641$	30.8167	−	30.8167i	1.21718	−	1.21718i	0.248571	−	0.968614i	$-0.420039\pi$
$641$	30.8167	−	30.8167i	1.21718	−	1.21718i	0.968614	−	0.248571i	$-0.0799609\pi$
$642$		0			0
$643$	4.11943	+	4.11943i	0.162454	+	0.162454i	0.783653	−	0.621199i	$-0.213354\pi$
$643$	4.11943	+	4.11943i	0.162454	+	0.162454i	−0.621199	+	0.783653i	$0.713354\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			17.2111i			0.676638i	0.941031	+	0.338319i	$0.109858\pi$
$647$			17.2111i			0.676638i	−0.941031	+	0.338319i	$0.890142\pi$
$648$		0			0
$649$	2.60555	−	2.60555i	0.102277	−	0.102277i
$650$		0			0
$651$	−45.6333	+	45.6333i	−1.78851	+	1.78851i
$652$		0			0
$653$	−24.8167	+	24.8167i	−0.971151	+	0.971151i	−0.999595	−	0.0284447i	$-0.990945\pi$
$653$	−24.8167	+	24.8167i	−0.971151	+	0.971151i	0.0284447	+	0.999595i	$0.490945\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	53.2389	−	53.2389i	2.07705	−	2.07705i
$658$		0			0
$659$	32.0000			1.24654			0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000			1.24654			0.623272	+	0.782006i	$0.285803\pi$
$660$		0			0
$661$		−	1.21110i		−	0.0471064i	−0.999723	−	0.0235532i	$-0.992502\pi$
$661$		−	1.21110i		−	0.0471064i	0.999723	−	0.0235532i	$-0.00749791\pi$
$662$		0			0
$663$	−9.63331	−	33.6333i	−0.374127	−	1.30621i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	13.8167i		−	0.534983i
$668$		0			0
$669$	−41.0278	−	41.0278i	−1.58622	−	1.58622i
$670$		0			0
$671$			3.76114i			0.145197i
$672$		0			0
$673$	−5.60555	+	5.60555i	−0.216078	+	0.216078i	−0.806843	−	0.590765i	$-0.798826\pi$
$673$	−5.60555	+	5.60555i	−0.216078	+	0.216078i	0.590765	+	0.806843i	$0.298826\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.0278	+	16.0278i	0.615997	+	0.615997i	0.944502	−	0.328505i	$-0.106545\pi$
$677$	16.0278	+	16.0278i	0.615997	+	0.615997i	−0.328505	+	0.944502i	$0.606545\pi$
$678$		0			0
$679$	35.0278			1.34424
$680$		0			0
$681$	1.39445			0.0534354
$682$		0			0
$683$	−0.724981	−	0.724981i	−0.0277406	−	0.0277406i	0.693100	−	0.720841i	$-0.256244\pi$
$683$	−0.724981	−	0.724981i	−0.0277406	−	0.0277406i	−0.720841	+	0.693100i	$0.756244\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−10.6056	+	10.6056i	−0.404627	+	0.404627i
$688$		0			0
$689$			13.5778i			0.517273i
$690$		0			0
$691$	−5.51388	−	5.51388i	−0.209758	−	0.209758i	0.594407	−	0.804165i	$-0.297387\pi$
$691$	−5.51388	−	5.51388i	−0.209758	−	0.209758i	−0.804165	+	0.594407i	$0.797387\pi$
$692$		0			0
$693$		−	10.6056i		−	0.402872i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	5.60555	−	1.60555i	0.212325	−	0.0608146i
$698$		0			0
$699$		−	25.8167i		−	0.976476i
$700$		0			0
$701$	−7.81665			−0.295231			−0.147615	−	0.989045i	$-0.547160\pi$
$701$	−7.81665			−0.295231			−0.147615	+	0.989045i	$0.547160\pi$
$702$		0			0
$703$	−1.81665	+	1.81665i	−0.0685164	+	0.0685164i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	24.4222	−	24.4222i	0.918492	−	0.918492i
$708$		0			0
$709$	−14.3944	+	14.3944i	−0.540595	+	0.540595i	−0.923703	−	0.383108i	$-0.874854\pi$
$709$	−14.3944	+	14.3944i	−0.540595	+	0.540595i	0.383108	+	0.923703i	$0.374854\pi$
$710$		0			0
$711$	−2.30278	+	2.30278i	−0.0863608	+	0.0863608i
$712$		0			0
$713$		−	37.0278i		−	1.38670i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−34.0555	−	34.0555i	−1.27183	−	1.27183i
$718$		0			0
$719$	4.72498	−	4.72498i	0.176212	−	0.176212i	−0.613490	−	0.789702i	$-0.710235\pi$
$719$	4.72498	−	4.72498i	0.176212	−	0.176212i	0.789702	+	0.613490i	$0.210235\pi$
$720$		0			0
$721$	−30.4222	−	30.4222i	−1.13298	−	1.13298i
$722$		0			0
$723$	−41.4500			−1.54154
$724$		0			0
$725$		0			0
$726$		0			0
$727$			6.42221i			0.238186i	0.992883	+	0.119093i	$0.0379987\pi$
$727$			6.42221i			0.238186i	−0.992883	+	0.119093i	$0.962001\pi$
$728$		0			0
$729$		−	51.4222i		−	1.90453i
$730$		0			0
$731$	6.78890	−	12.2389i	0.251096	−	0.452671i
$732$		0			0
$733$	46.0555			1.70110			0.850550	−	0.525895i	$-0.176269\pi$
$733$	46.0555			1.70110			0.850550	+	0.525895i	$0.176269\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.78890	+	2.78890i	−0.102730	+	0.102730i
$738$		0			0
$739$		−	34.6611i		−	1.27503i	−0.770439	−	0.637514i	$-0.779963\pi$
$739$		−	34.6611i		−	1.27503i	0.770439	−	0.637514i	$-0.220037\pi$
$740$		0			0
$741$	−3.63331	−	3.63331i	−0.133473	−	0.133473i
$742$		0			0
$743$	14.7250	+	14.7250i	0.540207	+	0.540207i	0.923590	−	0.383383i	$-0.125241\pi$
$743$	14.7250	+	14.7250i	0.540207	+	0.540207i	−0.383383	+	0.923590i	$0.625241\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	135.505i		−	4.95789i
$748$		0			0
$749$	−26.2389			−0.958747
$750$		0			0
$751$	1.69722	−	1.69722i	0.0619326	−	0.0619326i	−0.675462	−	0.737395i	$-0.736056\pi$
$751$	1.69722	−	1.69722i	0.0619326	−	0.0619326i	0.737395	+	0.675462i	$0.236056\pi$
$752$		0			0
$753$	27.6333	+	27.6333i	1.00701	+	1.00701i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	39.0278			1.41849			0.709244	−	0.704963i	$-0.249036\pi$
$757$	39.0278			1.41849			0.709244	+	0.704963i	$0.249036\pi$
$758$		0			0
$759$	6.00000	+	6.00000i	0.217786	+	0.217786i
$760$		0			0
$761$	−31.4500			−1.14006			−0.570030	−	0.821624i	$-0.693068\pi$
$761$	−31.4500			−1.14006			−0.570030	+	0.821624i	$0.693068\pi$
$762$		0			0
$763$	28.6056			1.03559
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−22.4222			−0.809619
$768$		0			0
$769$	18.6056			0.670933			0.335467	−	0.942052i	$-0.391106\pi$
$769$	18.6056			0.670933			0.335467	+	0.942052i	$0.391106\pi$
$770$		0			0
$771$	−44.6611	−	44.6611i	−1.60843	−	1.60843i
$772$		0			0
$773$	28.6056			1.02887			0.514435	−	0.857529i	$-0.328002\pi$
$773$	28.6056			1.02887			0.514435	+	0.857529i	$0.328002\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	31.8167	+	31.8167i	1.14142	+	1.14142i
$778$		0			0
$779$	0.605551	−	0.605551i	0.0216961	−	0.0216961i
$780$		0			0
$781$	−1.76114			−0.0630186
$782$		0			0
$783$		−	34.0555i		−	1.21704i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−14.7250	−	14.7250i	−0.524889	−	0.524889i	0.394155	−	0.919044i	$-0.371037\pi$
$787$	−14.7250	−	14.7250i	−0.524889	−	0.524889i	−0.919044	+	0.394155i	$0.871037\pi$
$788$		0			0
$789$	53.0278	+	53.0278i	1.88784	+	1.88784i
$790$		0			0
$791$			44.2389i			1.57295i
$792$		0			0
$793$	16.1833	−	16.1833i	0.574687	−	0.574687i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.63331			0.128698			0.0643492	−	0.997927i	$-0.479503\pi$
$797$	3.63331			0.128698			0.0643492	+	0.997927i	$0.479503\pi$
$798$		0			0
$799$	14.4222	+	8.00000i	0.510221	+	0.283020i
$800$		0			0
$801$		−	59.4500i		−	2.10056i
$802$		0			0
$803$			4.23886i			0.149586i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	80.2389			2.82454
$808$		0			0
$809$	20.8167	+	20.8167i	0.731875	+	0.731875i	0.970991	−	0.239116i	$-0.0768577\pi$
$809$	20.8167	+	20.8167i	0.731875	+	0.731875i	−0.239116	+	0.970991i	$0.576858\pi$
$810$		0			0
$811$	10.7250	−	10.7250i	0.376605	−	0.376605i	−0.493271	−	0.869876i	$-0.664199\pi$
$811$	10.7250	−	10.7250i	0.376605	−	0.376605i	0.869876	+	0.493271i	$0.164199\pi$
$812$		0			0
$813$	−2.78890	−	2.78890i	−0.0978109	−	0.0978109i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	2.05551i		−	0.0719133i
$818$		0			0
$819$	−45.6333	+	45.6333i	−1.59456	+	1.59456i
$820$		0			0
$821$	12.8167	−	12.8167i	0.447304	−	0.447304i	−0.447153	−	0.894457i	$-0.647562\pi$
$821$	12.8167	−	12.8167i	0.447304	−	0.447304i	0.894457	+	0.447153i	$0.147562\pi$
$822$		0			0
$823$	−12.9083	+	12.9083i	−0.449956	+	0.449956i	−0.895340	−	0.445384i	$-0.853067\pi$
$823$	−12.9083	+	12.9083i	−0.449956	+	0.449956i	0.445384	+	0.895340i	$0.353067\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.30278	−	6.30278i	0.219169	−	0.219169i	−0.588979	−	0.808148i	$-0.700470\pi$
$827$	6.30278	−	6.30278i	0.219169	−	0.219169i	0.808148	+	0.588979i	$0.200470\pi$
$828$		0			0
$829$	18.8444			0.654493			0.327247	−	0.944939i	$-0.393879\pi$
$829$	18.8444			0.654493			0.327247	+	0.944939i	$0.393879\pi$
$830$		0			0
$831$			16.6056i			0.576040i
$832$		0			0
$833$	−13.0000	−	7.21110i	−0.450423	−	0.249850i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	91.2666i		−	3.15464i
$838$		0			0
$839$	14.9083	+	14.9083i	0.514693	+	0.514693i	0.915961	−	0.401268i	$-0.131430\pi$
$839$	14.9083	+	14.9083i	0.514693	+	0.514693i	−0.401268	+	0.915961i	$0.631430\pi$
$840$		0			0
$841$			23.8444i			0.822221i
$842$		0			0
$843$	42.4222	−	42.4222i	1.46110	−	1.46110i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−24.9083	−	24.9083i	−0.855860	−	0.855860i
$848$		0			0
$849$	9.76114			0.335001
$850$		0			0
$851$	−25.8167			−0.884983
$852$		0			0
$853$	29.4222	+	29.4222i	1.00740	+	1.00740i	0.999972	+	0.00742468i	$0.00236337\pi$
$853$	29.4222	+	29.4222i	1.00740	+	1.00740i	0.00742468	+	0.999972i	$0.497637\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.6333	+	18.6333i	−0.636502	+	0.636502i	−0.949691	−	0.313189i	$-0.898603\pi$
$857$	−18.6333	+	18.6333i	−0.636502	+	0.636502i	0.313189	+	0.949691i	$0.398603\pi$
$858$		0			0
$859$		−	1.81665i		−	0.0619834i	−0.999520	−	0.0309917i	$-0.990133\pi$
$859$		−	1.81665i		−	0.0619834i	0.999520	−	0.0309917i	$-0.00986655\pi$
$860$		0			0
$861$	−10.6056	−	10.6056i	−0.361436	−	0.361436i
$862$		0			0
$863$		−	52.4777i		−	1.78636i	−0.449697	−	0.893181i	$-0.648468\pi$
$863$		−	52.4777i		−	1.78636i	0.449697	−	0.893181i	$-0.351532\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−12.4861	+	53.9361i	−0.424051	+	1.83177i
$868$		0			0
$869$		−	0.183346i		−	0.00621959i
$870$		0			0
$871$	24.0000			0.813209
$872$		0			0
$873$	−57.8444	+	57.8444i	−1.95774	+	1.95774i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.78890	−	1.78890i	0.0604068	−	0.0604068i	−0.676258	−	0.736665i	$-0.736400\pi$
$877$	1.78890	−	1.78890i	0.0604068	−	0.0604068i	0.736665	+	0.676258i	$0.236400\pi$
$878$		0			0
$879$	−49.8167	+	49.8167i	−1.68027	+	1.68027i
$880$		0			0
$881$	−24.2111	+	24.2111i	−0.815693	+	0.815693i	−0.985481	−	0.169788i	$-0.945692\pi$
$881$	−24.2111	+	24.2111i	−0.815693	+	0.815693i	0.169788	+	0.985481i	$0.445692\pi$
$882$		0			0
$883$			25.5778i			0.860761i	0.902647	+	0.430381i	$0.141621\pi$
$883$			25.5778i			0.860761i	−0.902647	+	0.430381i	$0.858379\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.6972	+	11.6972i	0.392754	+	0.392754i	0.875668	−	0.482914i	$-0.160421\pi$
$887$	11.6972	+	11.6972i	0.392754	+	0.392754i	−0.482914	+	0.875668i	$0.660421\pi$
$888$		0			0
$889$	−1.39445	+	1.39445i	−0.0467683	+	0.0467683i
$890$		0			0
$891$	7.88057	+	7.88057i	0.264009	+	0.264009i
$892$		0			0
$893$	2.42221			0.0810560
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	51.6333i		−	1.72399i
$898$		0			0
$899$		−	13.8167i		−	0.460811i
$900$		0			0
$901$	10.4222	−	18.7889i	0.347214	−	0.625949i
$902$		0			0
$903$	−36.0000			−1.19800
$904$		0			0
$905$		0			0
$906$		0			0
$907$	24.5416	−	24.5416i	0.814892	−	0.814892i	−0.170471	−	0.985363i	$-0.554529\pi$
$907$	24.5416	−	24.5416i	0.814892	−	0.814892i	0.985363	+	0.170471i	$0.0545289\pi$
$908$		0			0
$909$			80.6611i			2.67536i
$910$		0			0
$911$	4.72498	+	4.72498i	0.156546	+	0.156546i	0.781034	−	0.624488i	$-0.214693\pi$
$911$	4.72498	+	4.72498i	0.156546	+	0.156546i	−0.624488	+	0.781034i	$0.714693\pi$
$912$		0			0
$913$	5.39445	+	5.39445i	0.178530	+	0.178530i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			29.0278i			0.958581i
$918$		0			0
$919$	−40.8444			−1.34733			−0.673666	−	0.739036i	$-0.735282\pi$
$919$	−40.8444			−1.34733			−0.673666	+	0.739036i	$0.735282\pi$
$920$		0			0
$921$	−48.8444	+	48.8444i	−1.60948	+	1.60948i
$922$		0			0
$923$	7.57779	+	7.57779i	0.249426	+	0.249426i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	100.478			3.30012
$928$		0			0
$929$	−1.00000	−	1.00000i	−0.0328089	−	0.0328089i	0.690512	−	0.723321i	$-0.257385\pi$
$929$	−1.00000	−	1.00000i	−0.0328089	−	0.0328089i	−0.723321	+	0.690512i	$0.757385\pi$
$930$		0			0
$931$	−2.18335			−0.0715563
$932$		0			0
$933$	−87.0833			−2.85098
$934$		0			0
$935$		0			0
$936$		0			0
$937$	6.42221			0.209804			0.104902	−	0.994483i	$-0.466547\pi$
$937$	6.42221			0.209804			0.104902	+	0.994483i	$0.466547\pi$
$938$		0			0
$939$	28.6056			0.933507
$940$		0			0
$941$	−16.0278	−	16.0278i	−0.522490	−	0.522490i	0.395833	−	0.918323i	$-0.370456\pi$
$941$	−16.0278	−	16.0278i	−0.522490	−	0.522490i	−0.918323	+	0.395833i	$0.870456\pi$
$942$		0			0
$943$	8.60555			0.280235
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.27502	+	9.27502i	0.301398	+	0.301398i	0.841560	−	0.540163i	$-0.181637\pi$
$947$	9.27502	+	9.27502i	0.301398	+	0.301398i	−0.540163	+	0.841560i	$0.681637\pi$
$948$		0			0
$949$	18.2389	−	18.2389i	0.592058	−	0.592058i
$950$		0			0
$951$	−90.2944			−2.92800
$952$		0			0
$953$			50.2389i			1.62740i	0.581288	+	0.813698i	$0.302549\pi$
$953$			50.2389i			1.62740i	−0.581288	+	0.813698i	$0.697451\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.23886	+	2.23886i	0.0723720	+	0.0723720i
$958$		0			0
$959$	6.00000	+	6.00000i	0.193750	+	0.193750i
$960$		0			0
$961$		−	6.02776i		−	0.194444i
$962$		0			0
$963$	43.3305	−	43.3305i	1.39631	−	1.39631i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	21.8167			0.701576			0.350788	−	0.936455i	$-0.385914\pi$
$967$	21.8167			0.701576			0.350788	+	0.936455i	$0.385914\pi$
$968$		0			0
$969$	2.23886	+	7.81665i	0.0719225	+	0.251107i
$970$		0			0
$971$			55.0278i			1.76592i	0.469444	+	0.882962i	$0.344454\pi$
$971$			55.0278i			1.76592i	−0.469444	+	0.882962i	$0.655546\pi$
$972$		0			0
$973$			1.39445i			0.0447040i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.8444			0.538900			0.269450	−	0.963014i	$-0.413158\pi$
$977$	16.8444			0.538900			0.269450	+	0.963014i	$0.413158\pi$
$978$		0			0
$979$	2.36669	+	2.36669i	0.0756398	+	0.0756398i
$980$		0			0
$981$	−47.2389	+	47.2389i	−1.50822	+	1.50822i
$982$		0			0
$983$	8.11943	+	8.11943i	0.258970	+	0.258970i	0.824635	−	0.565665i	$-0.191381\pi$
$983$	8.11943	+	8.11943i	0.258970	+	0.258970i	−0.565665	+	0.824635i	$0.691381\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	42.4222i		−	1.35031i
$988$		0			0
$989$	14.6056	−	14.6056i	0.464430	−	0.464430i
$990$		0			0
$991$	−23.5139	+	23.5139i	−0.746943	+	0.746943i	−0.973904	−	0.226961i	$-0.927121\pi$
$991$	−23.5139	+	23.5139i	−0.746943	+	0.746943i	0.226961	+	0.973904i	$0.427121\pi$
$992$		0			0
$993$	−7.81665	+	7.81665i	−0.248054	+	0.248054i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	39.2389	−	39.2389i	1.24271	−	1.24271i	0.283834	−	0.958874i	$-0.408394\pi$
$997$	39.2389	−	39.2389i	1.24271	−	1.24271i	0.958874	−	0.283834i	$-0.0916063\pi$
$998$		0			0
$999$	−63.6333			−2.01327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1700.2.m.a.1449.1		4
5.2	odd	4		68.2.e.a.21.1	yes	4
5.3	odd	4		1700.2.o.c.701.2		4
5.4	even	2		1700.2.m.b.1449.2		4
15.2	even	4		612.2.k.e.361.2		4
17.13	even	4		1700.2.m.b.149.2		4
20.7	even	4		272.2.o.g.225.2		4
40.27	even	4		1088.2.o.s.769.1		4
40.37	odd	4		1088.2.o.t.769.2		4
60.47	odd	4		2448.2.be.u.1585.1		4
85.2	odd	8		1156.2.b.a.577.4		4
85.7	even	16		1156.2.h.e.757.4		16
85.12	even	16		1156.2.h.e.1001.4		16
85.13	odd	4		1700.2.o.c.1101.2		4
85.22	even	16		1156.2.h.e.1001.1		16
85.27	even	16		1156.2.h.e.757.1		16
85.32	odd	8		1156.2.b.a.577.1		4
85.37	even	16		1156.2.h.e.733.1		16
85.42	odd	8		1156.2.a.h.1.4		4
85.47	odd	4		68.2.e.a.13.1	✓	4
85.57	even	16		1156.2.h.e.977.1		16
85.62	even	16		1156.2.h.e.977.4		16
85.64	even	4	inner	1700.2.m.a.149.1		4
85.67	odd	4		1156.2.e.c.905.2		4
85.72	odd	4		1156.2.e.c.829.2		4
85.77	odd	8		1156.2.a.h.1.1		4
85.82	even	16		1156.2.h.e.733.4		16
255.47	even	4		612.2.k.e.217.2		4
340.47	even	4		272.2.o.g.81.2		4
340.127	even	8		4624.2.a.bq.1.1		4
340.247	even	8		4624.2.a.bq.1.4		4
680.387	even	4		1088.2.o.s.897.1		4
680.557	odd	4		1088.2.o.t.897.2		4
1020.47	odd	4		2448.2.be.u.1441.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.e.a.13.1	✓	4	85.47	odd	4
68.2.e.a.21.1	yes	4	5.2	odd	4
272.2.o.g.81.2		4	340.47	even	4
272.2.o.g.225.2		4	20.7	even	4
612.2.k.e.217.2		4	255.47	even	4
612.2.k.e.361.2		4	15.2	even	4
1088.2.o.s.769.1		4	40.27	even	4
1088.2.o.s.897.1		4	680.387	even	4
1088.2.o.t.769.2		4	40.37	odd	4
1088.2.o.t.897.2		4	680.557	odd	4
1156.2.a.h.1.1		4	85.77	odd	8
1156.2.a.h.1.4		4	85.42	odd	8
1156.2.b.a.577.1		4	85.32	odd	8
1156.2.b.a.577.4		4	85.2	odd	8
1156.2.e.c.829.2		4	85.72	odd	4
1156.2.e.c.905.2		4	85.67	odd	4
1156.2.h.e.733.1		16	85.37	even	16
1156.2.h.e.733.4		16	85.82	even	16
1156.2.h.e.757.1		16	85.27	even	16
1156.2.h.e.757.4		16	85.7	even	16
1156.2.h.e.977.1		16	85.57	even	16
1156.2.h.e.977.4		16	85.62	even	16
1156.2.h.e.1001.1		16	85.22	even	16
1156.2.h.e.1001.4		16	85.12	even	16
1700.2.m.a.149.1		4	85.64	even	4	inner
1700.2.m.a.1449.1		4	1.1	even	1	trivial
1700.2.m.b.149.2		4	17.13	even	4
1700.2.m.b.1449.2		4	5.4	even	2
1700.2.o.c.701.2		4	5.3	odd	4
1700.2.o.c.1101.2		4	85.13	odd	4
2448.2.be.u.1441.1		4	1020.47	odd	4
2448.2.be.u.1585.1		4	60.47	odd	4
4624.2.a.bq.1.1		4	340.127	even	8
4624.2.a.bq.1.4		4	340.247	even	8

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:	\( N \)	\(=\)	\( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1700.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.30278 - 2.30278i) q^{3} +(2.30278 - 2.30278i) q^{7} +7.60555i q^{9} +(-0.302776 - 0.302776i) q^{11} +2.60555i q^{13} +(2.00000 - 3.60555i) q^{17} -0.605551i q^{19} -10.6056 q^{21} +(4.30278 - 4.30278i) q^{23} +(10.6056 - 10.6056i) q^{27} +(1.60555 - 1.60555i) q^{29} +(4.30278 - 4.30278i) q^{31} +1.39445i q^{33} +(-3.00000 - 3.00000i) q^{37} +(6.00000 - 6.00000i) q^{39} +(1.00000 + 1.00000i) q^{41} +3.39445 q^{43} +4.00000i q^{47} -3.60555i q^{49} +(-12.9083 + 3.69722i) q^{51} +5.21110 q^{53} +(-1.39445 + 1.39445i) q^{57} +8.60555i q^{59} +(-6.21110 - 6.21110i) q^{61} +(17.5139 + 17.5139i) q^{63} -9.21110i q^{67} -19.8167 q^{69} +(2.90833 - 2.90833i) q^{71} +(-7.00000 - 7.00000i) q^{73} -1.39445 q^{77} +(0.302776 + 0.302776i) q^{79} -26.0278 q^{81} -17.8167 q^{83} -7.39445 q^{87} -7.81665 q^{89} +(6.00000 + 6.00000i) q^{91} -19.8167 q^{93} +(7.60555 + 7.60555i) q^{97} +(2.30278 - 2.30278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{7} + 6 q^{11} + 8 q^{17} - 28 q^{21} + 10 q^{23} + 28 q^{27} - 8 q^{29} + 10 q^{31} - 12 q^{37} + 24 q^{39} + 4 q^{41} + 28 q^{43} - 30 q^{51} - 8 q^{53} - 20 q^{57} + 4 q^{61} + 34 q^{63}+ \cdots + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^7 + 6 * q^11 + 8 * q^17 - 28 * q^21 + 10 * q^23 + 28 * q^27 - 8 * q^29 + 10 * q^31 - 12 * q^37 + 24 * q^39 + 4 * q^41 + 28 * q^43 - 30 * q^51 - 8 * q^53 - 20 * q^57 + 4 * q^61 + 34 * q^63 - 36 * q^69 - 10 * q^71 - 28 * q^73 - 20 * q^77 - 6 * q^79 - 32 * q^81 - 28 * q^83 - 44 * q^87 + 12 * q^89 + 24 * q^91 - 36 * q^93 + 16 * q^97 + 2 * q^99

Introduction

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