LMFDB - Embedded newform 88.2.k.a.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(19,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("88.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.k (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			35.1
Root			$-1.34500 - 0.437016i$ of defining polynomial
Character	$\chi$	$=$	88.35
Dual form			88.2.k.a.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34500 - 0.437016i) q^{2} +(1.67625 - 1.21787i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-2.78678 + 0.905480i) q^{6} +(-1.66251 - 2.28825i) q^{8} +(0.399565 - 1.22973i) q^{9} +O(q^{10})$	\(q+(-1.34500 - 0.437016i) q^{2} +(1.67625 - 1.21787i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-2.78678 + 0.905480i) q^{6} +(-1.66251 - 2.28825i) q^{8} +(0.399565 - 1.22973i) q^{9} +(1.59580 - 2.90748i) q^{11} +4.14392 q^{12} +(1.23607 + 3.80423i) q^{16} +(-7.70660 + 2.50403i) q^{17} +(-1.07483 + 1.47937i) q^{18} +(3.34401 + 4.60263i) q^{19} +(-3.41696 + 3.21316i) q^{22} +(-5.57356 - 1.81096i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(1.09293 + 3.36369i) q^{27} -5.65685i q^{32} +(-0.865968 - 6.81713i) q^{33} +11.4597 q^{34} +(2.09215 - 1.52003i) q^{36} +(-2.48626 - 7.65191i) q^{38} +(5.40907 + 7.44495i) q^{41} -12.1327i q^{43} +(6.00000 - 2.82843i) q^{44} +(6.70500 + 4.87147i) q^{48} +(-2.16312 - 6.65740i) q^{49} +(6.72499 - 2.18508i) q^{50} +(-9.86863 + 13.5830i) q^{51} -5.00179i q^{54} +(11.2108 + 3.64261i) q^{57} +(-10.6520 - 7.73916i) q^{59} +(-2.47214 + 7.60845i) q^{64} +(-1.81447 + 9.54747i) q^{66} -6.33871 q^{67} +(-15.4132 - 5.00805i) q^{68} +(-3.47821 + 1.13014i) q^{72} +(1.96442 - 2.70380i) q^{73} +(-3.20135 + 9.85276i) q^{75} +11.3783i q^{76} +(9.06678 + 6.58740i) q^{81} +(-4.02163 - 12.3773i) q^{82} +(17.1124 - 5.56016i) q^{83} +(-5.30217 + 16.3184i) q^{86} +(-9.30605 + 1.18213i) q^{88} +10.9423 q^{89} +(-6.88930 - 9.48231i) q^{96} +(5.94244 - 18.2889i) q^{97} +9.89949i q^{98} +(-2.93780 - 3.12413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 20 q^{6} - 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 20 * q^6 - 2 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 20 q^{6} - 2 q^{9} + 6 q^{11} + 8 q^{12} - 8 q^{16} + 40 q^{18} - 10 q^{19} - 4 q^{22} - 40 q^{24} - 10 q^{25} + 38 q^{27} - 38 q^{33} + 16 q^{34} + 24 q^{36} - 24 q^{38} + 48 q^{44} - 16 q^{48} + 14 q^{49} - 70 q^{51} + 70 q^{57} - 18 q^{59} + 16 q^{64} - 8 q^{66} - 28 q^{67} + 30 q^{75} - 8 q^{81} - 48 q^{82} + 90 q^{83} - 36 q^{86} + 8 q^{88} - 36 q^{89} + 30 q^{97} + 6 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 20 * q^6 - 2 * q^9 + 6 * q^11 + 8 * q^12 - 8 * q^16 + 40 * q^18 - 10 * q^19 - 4 * q^22 - 40 * q^24 - 10 * q^25 + 38 * q^27 - 38 * q^33 + 16 * q^34 + 24 * q^36 - 24 * q^38 + 48 * q^44 - 16 * q^48 + 14 * q^49 - 70 * q^51 + 70 * q^57 - 18 * q^59 + 16 * q^64 - 8 * q^66 - 28 * q^67 + 30 * q^75 - 8 * q^81 - 48 * q^82 + 90 * q^83 - 36 * q^86 + 8 * q^88 - 36 * q^89 + 30 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.34500	−	0.437016i	−0.951057	−	0.309017i
$2$	−1.34500	−	0.437016i	−0.951057	−	0.309017i
$3$	1.67625	−	1.21787i	0.967784	−	0.703136i	0.0128385	−	0.999918i	$-0.495913\pi$
$3$	1.67625	−	1.21787i	0.967784	−	0.703136i	0.954945	+	0.296781i	$0.0959133\pi$
$4$	1.61803	+	1.17557i	0.809017	+	0.587785i
$5$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$5$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$6$	−2.78678	+	0.905480i	−1.13770	+	0.369661i
$7$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$7$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$8$	−1.66251	−	2.28825i	−0.587785	−	0.809017i
$9$	0.399565	−	1.22973i	0.133188	−	0.409911i
$10$		0			0
$11$	1.59580	−	2.90748i	0.481151	−	0.876638i
$11$	1.59580	−	2.90748i	0.481151	−	0.876638i
$12$	4.14392			1.19625
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$		0			0
$15$		0			0
$16$	1.23607	+	3.80423i	0.309017	+	0.951057i
$17$	−7.70660	+	2.50403i	−1.86913	+	0.607316i	−0.877262	+	0.480011i	$0.840633\pi$
$17$	−7.70660	+	2.50403i	−1.86913	+	0.607316i	−0.991864	+	0.127304i	$0.959367\pi$
$18$	−1.07483	+	1.47937i	−0.253339	+	0.348691i
$19$	3.34401	+	4.60263i	0.767168	+	1.05592i	0.996584	+	0.0825877i	$0.0263185\pi$
$19$	3.34401	+	4.60263i	0.767168	+	1.05592i	−0.229416	+	0.973329i	$0.573682\pi$
$20$		0			0
$21$		0			0
$22$	−3.41696	+	3.21316i	−0.728498	+	0.685048i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−5.57356	−	1.81096i	−1.13770	−	0.369661i
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$		0			0
$27$	1.09293	+	3.36369i	0.210335	+	0.647343i
$28$		0			0
$29$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$29$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$30$		0			0
$31$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$31$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$32$		−	5.65685i		−	1.00000i
$33$	−0.865968	−	6.81713i	−0.150746	−	1.18671i
$34$	11.4597			1.96532
$35$		0			0
$36$	2.09215	−	1.52003i	0.348691	−	0.253339i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$	−2.48626	−	7.65191i	−0.403324	−	1.24130i
$39$		0			0
$40$		0			0
$41$	5.40907	+	7.44495i	0.844756	+	1.16271i	0.984994	+	0.172588i	$0.0552131\pi$
$41$	5.40907	+	7.44495i	0.844756	+	1.16271i	−0.140238	+	0.990118i	$0.544787\pi$
$42$		0			0
$43$		−	12.1327i		−	1.85021i	−0.379707	−	0.925107i	$-0.623975\pi$
$43$		−	12.1327i		−	1.85021i	0.379707	−	0.925107i	$-0.376025\pi$
$44$	6.00000	−	2.82843i	0.904534	−	0.426401i
$45$		0			0
$46$		0			0
$47$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$47$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$48$	6.70500	+	4.87147i	0.967784	+	0.703136i
$49$	−2.16312	−	6.65740i	−0.309017	−	0.951057i
$50$	6.72499	−	2.18508i	0.951057	−	0.309017i
$51$	−9.86863	+	13.5830i	−1.38188	+	1.90200i
$52$		0			0
$53$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$53$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$54$		−	5.00179i		−	0.680657i
$55$		0			0
$56$		0			0
$57$	11.2108	+	3.64261i	1.48491	+	0.482475i
$58$		0			0
$59$	−10.6520	−	7.73916i	−1.38678	−	1.00755i	−0.996210	−	0.0869778i	$-0.972279\pi$
$59$	−10.6520	−	7.73916i	−1.38678	−	1.00755i	−0.390567	−	0.920575i	$-0.627721\pi$
$60$		0			0
$61$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$61$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$62$		0			0
$63$		0			0
$64$	−2.47214	+	7.60845i	−0.309017	+	0.951057i
$65$		0			0
$66$	−1.81447	+	9.54747i	−0.223346	+	1.17521i
$67$	−6.33871			−0.774397			−0.387199	−	0.921996i	$-0.626557\pi$
$67$	−6.33871			−0.774397			−0.387199	+	0.921996i	$0.626557\pi$
$68$	−15.4132	−	5.00805i	−1.86913	−	0.607316i
$69$		0			0
$70$		0			0
$71$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$71$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$72$	−3.47821	+	1.13014i	−0.409911	+	0.133188i
$73$	1.96442	−	2.70380i	0.229919	−	0.316456i	−0.678434	−	0.734662i	$-0.737341\pi$
$73$	1.96442	−	2.70380i	0.229919	−	0.316456i	0.908352	+	0.418206i	$0.137341\pi$
$74$		0			0
$75$	−3.20135	+	9.85276i	−0.369661	+	1.13770i
$76$			11.3783i			1.30518i
$77$		0			0
$78$		0			0
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$		0			0
$81$	9.06678	+	6.58740i	1.00742	+	0.731934i
$82$	−4.02163	−	12.3773i	−0.444114	−	1.36684i
$83$	17.1124	−	5.56016i	1.87833	−	0.610307i	0.890452	−	0.455077i	$-0.150388\pi$
$83$	17.1124	−	5.56016i	1.87833	−	0.610307i	0.987878	−	0.155230i	$-0.0496119\pi$
$84$		0			0
$85$		0			0
$86$	−5.30217	+	16.3184i	−0.571747	+	1.75966i
$87$		0			0
$88$	−9.30605	+	1.18213i	−0.992028	+	0.126015i
$89$	10.9423			1.15988			0.579940	−	0.814659i	$-0.303076\pi$
$89$	10.9423			1.15988			0.579940	+	0.814659i	$0.303076\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−6.88930	−	9.48231i	−0.703136	−	0.967784i
$97$	5.94244	−	18.2889i	0.603363	−	1.85696i	0.0956901	−	0.995411i	$-0.469494\pi$
$97$	5.94244	−	18.2889i	0.603363	−	1.85696i	0.507673	−	0.861550i	$-0.330506\pi$
$98$			9.89949i			1.00000i
$99$	−2.93780	−	3.12413i	−0.295260	−	0.313987i
$100$	−10.0000			−1.00000
$101$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$101$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$102$	19.2093	−	13.9563i	1.90200	−	1.38188i
$103$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$103$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.242100	−	0.333222i	−0.0234047	−	0.0322138i	0.797154	−	0.603776i	$-0.206338\pi$
$107$	−0.242100	−	0.333222i	−0.0234047	−	0.0322138i	−0.820559	+	0.571562i	$0.806338\pi$
$108$	−2.18586	+	6.72739i	−0.210335	+	0.647343i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−17.1611	+	12.4683i	−1.61438	+	1.17292i	−0.767736	+	0.640767i	$0.778617\pi$
$113$	−17.1611	+	12.4683i	−1.61438	+	1.17292i	−0.846649	+	0.532152i	$0.821383\pi$
$114$	−13.4866	−	9.79859i	−1.26314	−	0.917722i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	10.9448	+	15.0643i	1.00755	+	1.38678i
$119$		0			0
$120$		0			0
$121$	−5.90686	−	9.27949i	−0.536988	−	0.843590i
$122$		0			0
$123$	18.1339	+	5.89207i	1.63508	+	0.531270i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$127$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$128$	6.65003	−	9.15298i	0.587785	−	0.809017i
$129$	−14.7760	−	20.3374i	−1.30095	−	1.79061i
$130$		0			0
$131$		−	0.861094i		−	0.0752341i	−0.999292	−	0.0376170i	$-0.988023\pi$
$131$		−	0.861094i		−	0.0752341i	0.999292	−	0.0376170i	$-0.0119767\pi$
$132$	6.61286	−	12.0484i	0.575575	−	1.04868i
$133$		0			0
$134$	8.52555	+	2.77012i	0.736496	+	0.239302i
$135$		0			0
$136$	18.5421	+	13.4716i	1.58997	+	1.15518i
$137$	7.22298	+	22.2300i	0.617101	+	1.89924i	0.360794	+	0.932646i	$0.382506\pi$
$137$	7.22298	+	22.2300i	0.617101	+	1.89924i	0.256307	+	0.966595i	$0.417494\pi$
$138$		0			0
$139$	−4.98752	+	6.86474i	−0.423036	+	0.582259i	−0.966337	−	0.257279i	$-0.917174\pi$
$139$	−4.98752	+	6.86474i	−0.423036	+	0.582259i	0.543301	+	0.839538i	$0.317174\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	5.17207			0.431006
$145$		0			0
$146$	−3.82375	+	2.77812i	−0.316456	+	0.229919i
$147$	−11.7338	−	8.52507i	−0.967784	−	0.703136i
$148$		0			0
$149$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$149$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$150$	8.61162	−	11.8529i	0.703136	−	0.967784i
$151$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$151$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$152$	4.97251	−	15.3038i	0.403324	−	1.24130i
$153$			10.4776i			0.847063i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$157$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−9.31599	−	12.8224i	−0.731934	−	1.00742i
$163$	5.12369	−	15.7691i	0.401318	−	1.23513i	−0.522612	−	0.852570i	$-0.675042\pi$
$163$	5.12369	−	15.7691i	0.401318	−	1.23513i	0.923931	−	0.382560i	$-0.124958\pi$
$164$			18.4049i			1.43718i
$165$		0			0
$166$	−25.4460			−1.97499
$167$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$167$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$168$		0			0
$169$	10.5172	+	7.64121i	0.809017	+	0.587785i
$170$		0			0
$171$	6.99616	−	2.27319i	0.535010	−	0.173835i
$172$	14.2628	−	19.6311i	1.08753	−	1.49685i
$173$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$173$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$174$		0			0
$175$		0			0
$176$	13.0332	+	2.47693i	0.982416	+	0.186706i
$177$	−27.2808			−2.05055
$178$	−14.7174	−	4.78196i	−1.10311	−	0.358423i
$179$	−2.36617	+	1.71913i	−0.176856	+	0.128494i	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−2.36617	+	1.71913i	−0.176856	+	0.128494i	0.495835	+	0.868416i	$0.334862\pi$
$180$		0			0
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−5.01777	+	26.4027i	−0.366936	+	1.93076i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$	5.12217	+	15.7644i	0.369661	+	1.13770i
$193$	−16.1400	+	5.24419i	−1.16178	+	0.377485i	−0.825569	−	0.564301i	$-0.809146\pi$
$193$	−16.1400	+	5.24419i	−1.16178	+	0.377485i	−0.336211	+	0.941787i	$0.609146\pi$
$194$	−15.9851	+	22.0016i	−1.14766	+	1.57963i
$195$		0			0
$196$	4.32624	−	13.3148i	0.309017	−	0.951057i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	2.58604	+	5.48581i	0.183782	+	0.389860i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	13.4500	+	4.37016i	0.951057	+	0.309017i
$201$	−10.6253	+	7.71972i	−0.749449	+	0.544507i
$202$		0			0
$203$		0			0
$204$	−31.9356	+	10.3765i	−2.23594	+	0.726500i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	18.7184	−	2.37776i	1.29478	−	0.164473i
$210$		0			0
$211$	5.18183	+	1.68368i	0.356732	+	0.115909i	0.481900	−	0.876226i	$-0.339947\pi$
$211$	5.18183	+	1.68368i	0.356732	+	0.115909i	−0.125168	+	0.992136i	$0.539947\pi$
$212$		0			0
$213$		0			0
$214$	0.180000	+	0.553984i	0.0123046	+	0.0378696i
$215$		0			0
$216$	5.87995	−	8.09306i	0.400080	−	0.550663i
$217$		0			0
$218$		0			0
$219$		−	6.92465i		−	0.467925i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$223$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$224$		0			0
$225$	1.99782	+	6.14867i	0.133188	+	0.409911i
$226$	28.5305	−	9.27013i	1.89782	−	0.616640i
$227$	9.01975	−	12.4146i	0.598662	−	0.823987i	−0.396923	−	0.917852i	$-0.629922\pi$
$227$	9.01975	−	12.4146i	0.598662	−	0.823987i	0.995585	+	0.0938647i	$0.0299221\pi$
$228$	13.8573	+	19.0729i	0.917722	+	1.26314i
$229$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$229$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−25.4727	−	8.27660i	−1.66878	−	0.542218i	−0.686092	−	0.727514i	$-0.740675\pi$
$233$	−25.4727	−	8.27660i	−1.66878	−	0.542218i	−0.982683	+	0.185296i	$0.940675\pi$
$234$		0			0
$235$		0			0
$236$	−8.13743	−	25.0444i	−0.529702	−	1.63025i
$237$		0			0
$238$		0			0
$239$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$239$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$240$		0			0
$241$		−	1.55294i		−	0.100034i	−0.998748	−	0.0500169i	$-0.984072\pi$
$241$		−	1.55294i		−	0.100034i	0.998748	−	0.0500169i	$-0.0159275\pi$
$242$	3.88943	+	15.0623i	0.250022	+	0.968240i
$243$	12.6104			0.808957
$244$		0			0
$245$		0			0
$246$	−21.8152	−	15.8496i	−1.39088	−	1.01054i
$247$		0			0
$248$		0			0
$249$	21.9132	−	30.1609i	1.38869	−	1.91137i
$250$		0			0
$251$	1.85410	−	5.70634i	0.117030	−	0.360181i	−0.875335	−	0.483517i	$-0.839359\pi$
$251$	1.85410	−	5.70634i	0.117030	−	0.360181i	0.992365	+	0.123336i	$0.0393592\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	1.20500	+	0.875486i	0.0751661	+	0.0546113i	0.624734	−	0.780838i	$-0.285208\pi$
$257$	1.20500	+	0.875486i	0.0751661	+	0.0546113i	−0.549568	+	0.835449i	$0.685208\pi$
$258$	10.9859	+	33.8111i	0.683951	+	2.10498i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.376312	+	1.15817i	−0.0232486	+	0.0715519i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−14.1596	+	13.3151i	−0.871463	+	0.819487i
$265$		0			0
$266$		0			0
$267$	18.3420	−	13.3263i	1.12251	−	0.815554i
$268$	−10.2563	−	7.45161i	−0.626501	−	0.455179i
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$		0			0
$271$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$271$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$272$	−19.0518	−	26.2225i	−1.15518	−	1.58997i
$273$		0			0
$274$		−	33.0559i		−	1.99698i
$275$	2.08973	+	16.4509i	0.126015	+	0.992028i
$276$		0			0
$277$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$277$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$278$	9.70820	−	7.05342i	0.582259	−	0.423036i
$279$		0			0
$280$		0			0
$281$	7.96861	−	2.58916i	0.475368	−	0.154456i	−0.0615273	−	0.998105i	$-0.519597\pi$
$281$	7.96861	−	2.58916i	0.475368	−	0.154456i	0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	14.9626	+	20.5942i	0.889432	+	1.22420i	0.973718	+	0.227757i	$0.0731392\pi$
$283$	14.9626	+	20.5942i	0.889432	+	1.22420i	−0.0842855	+	0.996442i	$0.526861\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−6.95642	−	2.26028i	−0.409911	−	0.133188i
$289$	39.3683	−	28.6027i	2.31578	−	1.68251i
$290$		0			0
$291$	−12.3125	−	37.8940i	−0.721771	−	2.22138i
$292$	6.35701	−	2.06552i	0.372016	−	0.120875i
$293$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$293$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$294$	12.0563	+	16.5940i	0.703136	+	0.967784i
$295$		0			0
$296$		0			0
$297$	11.5240	+	2.19010i	0.668688	+	0.127083i
$298$		0			0
$299$		0			0
$300$	−16.7625	+	12.1787i	−0.967784	+	0.703136i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−13.3760	+	18.4105i	−0.767168	+	1.05592i
$305$		0			0
$306$	4.57888	−	14.0923i	0.261757	−	0.805605i
$307$			29.7138i			1.69586i	0.530110	+	0.847929i	$0.322151\pi$
$307$			29.7138i			1.69586i	−0.530110	+	0.847929i	$0.677849\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$	8.66492	+	26.6679i	0.489770	+	1.50736i	0.824951	+	0.565204i	$0.191202\pi$
$313$	8.66492	+	26.6679i	0.489770	+	1.50736i	−0.335181	+	0.942154i	$0.608798\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$317$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.811641	−	0.263718i	−0.0453014	−	0.0147193i
$322$		0			0
$323$	−37.2961	−	27.0972i	−2.07521	−	1.50773i
$324$	6.92640	+	21.3173i	0.384800	+	1.18429i
$325$		0			0
$326$	−13.7827	+	18.9702i	−0.763353	+	1.05066i
$327$		0			0
$328$	8.04325	−	24.7546i	0.444114	−	1.36684i
$329$		0			0
$330$		0			0
$331$	−32.2444			−1.77231			−0.886156	−	0.463387i	$-0.846634\pi$
$331$	−32.2444			−1.77231			−0.886156	+	0.463387i	$0.846634\pi$
$332$	34.2248	+	11.1203i	1.87833	+	0.610307i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−20.9768	+	28.8722i	−1.14268	+	1.57277i	−0.381314	+	0.924445i	$0.624528\pi$
$337$	−20.9768	+	28.8722i	−1.14268	+	1.57277i	−0.761367	+	0.648321i	$0.775472\pi$
$338$	−10.8063	−	14.8736i	−0.587785	−	0.809017i
$339$	−13.5816	+	41.8000i	−0.737654	+	2.27026i
$340$		0			0
$341$		0			0
$342$	−10.4032			−0.562542
$343$		0			0
$344$	−27.7625	+	20.1706i	−1.49685	+	1.08753i
$345$		0			0
$346$		0			0
$347$	−31.6454	+	10.2822i	−1.69881	+	0.551978i	−0.988409	−	0.151817i	$-0.951488\pi$
$347$	−31.6454	+	10.2822i	−1.69881	+	0.551978i	−0.710404	+	0.703795i	$0.751488\pi$
$348$		0			0
$349$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$349$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$350$		0			0
$351$		0			0
$352$	−16.4472	−	9.02719i	−0.876638	−	0.481151i
$353$	10.9704			0.583898			0.291949	−	0.956434i	$-0.405696\pi$
$353$	10.9704			0.583898			0.291949	+	0.956434i	$0.405696\pi$
$354$	36.6925	+	11.9221i	1.95019	+	0.633654i
$355$		0			0
$356$	17.7050	+	12.8634i	0.938363	+	0.681761i
$357$		0			0
$358$	3.93378	−	1.27816i	0.207907	−	0.0675530i
$359$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$359$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$360$		0			0
$361$	−4.13051	+	12.7124i	−0.217395	+	0.669074i
$362$		0			0
$363$	−21.2026	−	8.36098i	−1.11285	−	0.438838i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$367$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$368$		0			0
$369$	11.3166	−	3.67698i	0.589118	−	0.191416i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$	18.2873	−	33.3187i	0.945613	−	1.72287i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−6.12244	−	18.8429i	−0.314489	−	0.967896i	−0.975964	−	0.217930i	$-0.930070\pi$
$379$	−6.12244	−	18.8429i	−0.314489	−	0.967896i	0.661476	−	0.749966i	$-0.269930\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$383$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$384$		−	23.4416i		−	1.19625i
$385$		0			0
$386$	24.0000			1.22157
$387$	−14.9199	−	4.84778i	−0.758423	−	0.246427i
$388$	31.1150	−	22.6064i	1.57963	−	1.14766i
$389$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$389$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$390$		0			0
$391$		0			0
$392$	−11.6376	+	16.0177i	−0.587785	+	0.809017i
$393$	−1.04870	−	1.44341i	−0.0528998	−	0.0728103i
$394$		0			0
$395$		0			0
$396$	−1.08082	−	8.50854i	−0.0543134	−	0.427570i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	−16.1803	−	11.7557i	−0.809017	−	0.587785i
$401$	−11.0646	−	34.0534i	−0.552540	−	1.70054i	−0.702353	−	0.711829i	$-0.747867\pi$
$401$	−11.0646	−	34.0534i	−0.552540	−	1.70054i	0.149813	−	0.988714i	$-0.452133\pi$
$402$	17.6646	−	5.73958i	0.881030	−	0.286264i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	47.4879			2.35100
$409$	−32.2799	−	10.4884i	−1.59614	−	0.518617i	−0.629991	−	0.776603i	$-0.716941\pi$
$409$	−32.2799	−	10.4884i	−1.59614	−	0.518617i	−0.966149	+	0.257985i	$0.916941\pi$
$410$		0			0
$411$	39.1808	+	28.4665i	1.93265	+	1.40415i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$			17.5812i			0.860953i
$418$	−26.2153	−	4.98216i	−1.28223	−	0.243685i
$419$	40.5322			1.98013			0.990064	−	0.140614i	$-0.0449077\pi$
$419$	40.5322			1.98013			0.990064	+	0.140614i	$0.0449077\pi$
$420$		0			0
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$	−6.23376	−	4.52909i	−0.303455	−	0.220473i
$423$		0			0
$424$		0			0
$425$	23.8147	−	32.7781i	1.15518	−	1.58997i
$426$		0			0
$427$		0			0
$428$		−	0.823770i		−	0.0398184i
$429$		0			0
$430$		0			0
$431$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$431$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$432$	−11.4453	+	8.31551i	−0.550663	+	0.400080i
$433$	32.9413	+	23.9333i	1.58306	+	1.15016i	0.913082	+	0.407777i	$0.133696\pi$
$433$	32.9413	+	23.9333i	1.58306	+	1.15016i	0.669976	+	0.742382i	$0.266304\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−3.02619	+	9.31364i	−0.144597	+	0.445023i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	−9.05113			−0.431006
$442$		0			0
$443$	12.6763	−	9.20984i	0.602267	−	0.437572i	−0.244416	−	0.969670i	$-0.578596\pi$
$443$	12.6763	−	9.20984i	0.602267	−	0.437572i	0.846683	+	0.532098i	$0.178596\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.5275	+	35.4780i	−0.544016	+	1.67431i	0.179303	+	0.983794i	$0.442616\pi$
$449$	−11.5275	+	35.4780i	−0.544016	+	1.67431i	−0.723319	+	0.690514i	$0.757384\pi$
$450$		−	9.14302i		−	0.431006i
$451$	30.2778	−	3.84613i	1.42573	−	0.181107i
$452$	−42.4247			−1.99549
$453$		0			0
$454$	−17.5569	+	12.7559i	−0.823987	+	0.598662i
$455$		0			0
$456$	−10.3028	−	31.7089i	−0.482475	−	1.48491i
$457$	−13.5422	+	4.40012i	−0.633476	+	0.205829i	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−13.5422	+	4.40012i	−0.633476	+	0.205829i	−0.0253618	+	0.999678i	$0.508074\pi$
$458$		0			0
$459$	−16.8456	−	23.1859i	−0.786284	−	1.08223i
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$	30.6438	+	22.2640i	1.41954	+	1.03136i
$467$	9.27051	+	28.5317i	0.428988	+	1.32029i	0.899123	+	0.437695i	$0.144205\pi$
$467$	9.27051	+	28.5317i	0.428988	+	1.32029i	−0.470135	+	0.882594i	$0.655795\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$			37.2409i			1.71415i
$473$	−35.2755	−	19.3613i	−1.62197	−	0.890232i
$474$		0			0
$475$	−27.0536	−	8.79025i	−1.24130	−	0.403324i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$479$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$480$		0			0
$481$		0			0
$482$	−0.678661	+	2.08870i	−0.0309122	+	0.0951378i
$483$		0			0
$484$	1.35119	−	21.9585i	0.0614178	−	0.998112i
$485$		0			0
$486$	−16.9609	−	5.51094i	−0.769364	−	0.249981i
$487$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$487$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$488$		0			0
$489$	−10.6161	−	32.6729i	−0.480076	−	1.47752i
$490$		0			0
$491$	20.9100	−	28.7801i	0.943655	−	1.29883i	−0.0106338	−	0.999943i	$-0.503385\pi$
$491$	20.9100	−	28.7801i	0.943655	−	1.29883i	0.954289	−	0.298886i	$-0.0966151\pi$
$492$	22.4148	+	30.8513i	1.01054	+	1.39088i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−42.6539	+	30.9899i	−1.91137	+	1.38869i
$499$	36.1438	+	26.2600i	1.61802	+	1.17556i	0.811697	+	0.584079i	$0.198544\pi$
$499$	36.1438	+	26.2600i	1.61802	+	1.17556i	0.806321	+	0.591479i	$0.201456\pi$
$500$		0			0
$501$		0			0
$502$	−4.98752	+	6.86474i	−0.222604	+	0.306388i
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	26.9355			1.19625
$508$		0			0
$509$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$509$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	21.5200	−	6.99226i	0.951057	−	0.309017i
$513$	−11.8271	+	16.2786i	−0.522178	+	0.718717i
$514$	−1.23812	−	1.70413i	−0.0546113	−	0.0751661i
$515$		0			0
$516$		−	50.2768i		−	2.21331i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−25.4470	−	18.4883i	−1.11485	−	0.809988i	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−25.4470	−	18.4883i	−1.11485	−	0.809988i	−0.983421	+	0.181337i	$0.941958\pi$
$522$		0			0
$523$	40.8289	−	13.2661i	1.78532	−	0.580087i	0.786049	−	0.618165i	$-0.212124\pi$
$523$	40.8289	−	13.2661i	1.78532	−	0.580087i	0.999275	+	0.0380781i	$0.0121236\pi$
$524$	1.01228	−	1.39328i	0.0442215	−	0.0608657i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	24.8635	−	11.7208i	1.08205	−	0.510081i
$529$	23.0000			1.00000
$530$		0			0
$531$	−13.7733	+	10.0069i	−0.597709	+	0.434261i
$532$		0			0
$533$		0			0
$534$	−30.4938	+	9.90803i	−1.31959	+	0.428762i
$535$		0			0
$536$	10.5382	+	14.5045i	0.455179	+	0.626501i
$537$	−1.87263	+	5.76337i	−0.0808101	+	0.248708i
$538$		0			0
$539$	−22.8081	−	4.33463i	−0.982416	−	0.186706i
$540$		0			0
$541$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$541$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$542$		0			0
$543$		0			0
$544$	14.1649	+	43.5951i	0.607316	+	1.86913i
$545$		0			0
$546$		0			0
$547$	−11.8576	−	16.3206i	−0.506995	−	0.697819i	0.476414	−	0.879221i	$-0.341936\pi$
$547$	−11.8576	−	16.3206i	−0.506995	−	0.697819i	−0.983409	+	0.181402i	$0.941936\pi$
$548$	−14.4460	+	44.4601i	−0.617101	+	1.89924i
$549$		0			0
$550$	4.37864	−	23.0397i	0.186706	−	0.982416i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−16.1400	+	5.24419i	−0.684487	+	0.222403i
$557$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$557$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	23.7440	+	50.3685i	1.00247	+	2.12656i
$562$	−11.8493			−0.499831
$563$	−16.3290	−	5.30560i	−0.688183	−	0.223604i	−0.0560088	−	0.998430i	$-0.517837\pi$
$563$	−16.3290	−	5.30560i	−0.688183	−	0.223604i	−0.632175	+	0.774826i	$0.717837\pi$
$564$		0			0
$565$		0			0
$566$	−11.1246	−	34.2380i	−0.467602	−	1.43913i
$567$		0			0
$568$		0			0
$569$	3.75067	+	5.16235i	0.157236	+	0.216417i	0.880366	−	0.474295i	$-0.157297\pi$
$569$	3.75067	+	5.16235i	0.157236	+	0.216417i	−0.723130	+	0.690712i	$0.757297\pi$
$570$		0			0
$571$		−	42.4264i		−	1.77549i	−0.460336	−	0.887745i	$-0.652271\pi$
$571$		−	42.4264i		−	1.77549i	0.460336	−	0.887745i	$-0.347729\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	8.36859	+	6.08014i	0.348691	+	0.253339i
$577$	−2.33508	−	7.18664i	−0.0972107	−	0.299184i	0.890613	−	0.454762i	$-0.150276\pi$
$577$	−2.33508	−	7.18664i	−0.0972107	−	0.299184i	−0.987824	+	0.155579i	$0.950276\pi$
$578$	−65.4501	+	21.2660i	−2.72237	+	0.884550i
$579$	−20.6679	+	28.4469i	−0.858929	+	1.18221i
$580$		0			0
$581$		0			0
$582$			56.3480i			2.33570i
$583$		0			0
$584$	−9.45283			−0.391161
$585$		0			0
$586$		0			0
$587$	18.9379	+	13.7592i	0.781651	+	0.567902i	0.905474	−	0.424402i	$-0.139516\pi$
$587$	18.9379	+	13.7592i	0.781651	+	0.567902i	−0.123823	+	0.992304i	$0.539516\pi$
$588$	−8.96379	−	27.5877i	−0.369661	−	1.13770i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	26.0318i		−	1.06900i	−0.845169	−	0.534499i	$-0.820500\pi$
$593$		−	26.0318i		−	1.06900i	0.845169	−	0.534499i	$-0.179500\pi$
$594$	−14.5426	−	7.98184i	−0.596690	−	0.327499i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$599$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$600$	27.8678	−	9.05480i	1.13770	−	0.369661i
$601$	−22.6323	+	31.1507i	−0.923192	+	1.27066i	0.0392649	+	0.999229i	$0.487498\pi$
$601$	−22.6323	+	31.1507i	−0.923192	+	1.27066i	−0.962457	+	0.271436i	$0.912502\pi$
$602$		0			0
$603$	−2.53273	+	7.79493i	−0.103141	+	0.317434i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$607$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$608$	26.0364	−	18.9166i	1.05592	−	0.767168i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−12.3171	+	16.9531i	−0.497891	+	0.685288i
$613$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$613$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$614$	12.9854	−	39.9650i	0.524049	−	1.61286i
$615$		0			0
$616$		0			0
$617$	47.5456			1.91411			0.957057	−	0.289899i	$-0.0936217\pi$
$617$	47.5456			1.91411			0.957057	+	0.289899i	$0.0936217\pi$
$618$		0			0
$619$	−3.15773	+	2.29423i	−0.126920	+	0.0922128i	−0.649434	−	0.760418i	$-0.724994\pi$
$619$	−3.15773	+	2.29423i	−0.126920	+	0.0922128i	0.522514	+	0.852631i	$0.324994\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$		−	39.6549i		−	1.58493i
$627$	28.4810	−	26.7823i	1.13742	−	1.06958i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$631$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$632$		0			0
$633$	10.7366	−	3.48852i	0.426740	−	0.138656i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.2625	+	8.18269i	−0.444842	+	0.323197i	−0.787556	−	0.616243i	$-0.788654\pi$
$641$	−11.2625	+	8.18269i	−0.444842	+	0.323197i	0.342714	+	0.939440i	$0.388654\pi$
$642$	0.976406	+	0.709400i	0.0385357	+	0.0279978i
$643$	2.28081	+	7.01962i	0.0899465	+	0.276827i	0.985904	−	0.167313i	$-0.0535092\pi$
$643$	2.28081	+	7.01962i	0.0899465	+	0.276827i	−0.895957	+	0.444140i	$0.853509\pi$
$644$		0			0
$645$		0			0
$646$	38.3212	+	52.7446i	1.50773	+	2.07521i
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$		−	31.6986i		−	1.24524i
$649$	−39.4999	+	18.6204i	−1.55051	+	0.730916i
$650$		0			0
$651$		0			0
$652$	26.8280	−	19.4917i	1.05066	−	0.763353i
$653$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$653$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$654$		0			0
$655$		0			0
$656$	−21.6363	+	29.7798i	−0.844756	+	1.16271i
$657$	−2.54004	−	3.49606i	−0.0990963	−	0.136394i
$658$		0			0
$659$			49.4803i			1.92748i	0.266844	+	0.963740i	$0.414019\pi$
$659$			49.4803i			1.92748i	−0.266844	+	0.963740i	$0.585981\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	43.3686	+	14.0913i	1.68557	+	0.547674i
$663$		0			0
$664$	−41.1725	−	29.9136i	−1.59780	−	1.16087i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	44.7627	+	14.5443i	1.72547	+	0.560641i	0.992784	−	0.119920i	$-0.0382640\pi$
$673$	44.7627	+	14.5443i	1.72547	+	0.560641i	0.732691	+	0.680561i	$0.238264\pi$
$674$	40.8314	−	29.6657i	1.57277	−	1.14268i
$675$	−14.3066	−	10.3944i	−0.550663	−	0.400080i
$676$	8.03444	+	24.7275i	0.309017	+	0.951057i
$677$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$677$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$678$	36.5345	−	50.2855i	1.40310	−	1.93120i
$679$		0			0
$680$		0			0
$681$		−	31.7949i		−	1.21838i
$682$		0			0
$683$	−42.0000			−1.60709			−0.803543	−	0.595247i	$-0.797054\pi$
$683$	−42.0000			−1.60709			−0.803543	+	0.595247i	$0.797054\pi$
$684$	13.9923	+	4.54638i	0.535010	+	0.173835i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	46.1554	−	14.9968i	1.75966	−	0.571747i
$689$		0			0
$690$		0			0
$691$	16.1237	−	49.6236i	0.613374	−	1.88777i	0.190117	−	0.981761i	$-0.439113\pi$
$691$	16.1237	−	49.6236i	0.613374	−	1.88777i	0.423257	−	0.906010i	$-0.360887\pi$
$692$		0			0
$693$		0			0
$694$	47.0564			1.78624
$695$		0			0
$696$		0			0
$697$	−60.3280	−	43.8308i	−2.28508	−	1.66021i
$698$		0			0
$699$	−52.7785	+	17.1488i	−1.99627	+	0.648626i
$700$		0			0
$701$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$701$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$702$		0			0
$703$		0			0
$704$	18.1764	+	19.3292i	0.685048	+	0.728498i
$705$		0			0
$706$	−14.7552	−	4.79426i	−0.555320	−	0.180434i
$707$		0			0
$708$	−44.1412	−	32.0704i	−1.65893	−	1.20528i
$709$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$709$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$710$		0			0
$711$		0			0
$712$	−18.1916	−	25.0387i	−0.681761	−	0.938363i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−5.84950			−0.218606
$717$		0			0
$718$		0			0
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$		0			0
$721$		0			0
$722$	11.1110	−	15.2930i	0.413510	−	0.569148i
$723$	−1.89128	−	2.60312i	−0.0703374	−	0.0968111i
$724$		0			0
$725$		0			0
$726$	24.8635	+	20.5114i	0.922772	+	0.761248i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−6.06216	+	4.40442i	−0.224525	+	0.163127i
$730$		0			0
$731$	30.3805	+	93.5016i	1.12366	+	3.45828i
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.1153	+	18.4297i	−0.372602	+	0.678866i
$738$	−16.8277			−0.619435
$739$	−51.6503	−	16.7822i	−1.89999	−	0.617344i	−0.964595	−	0.263734i	$-0.915046\pi$
$739$	−51.6503	−	16.7822i	−1.89999	−	0.617344i	−0.935393	−	0.353610i	$-0.884954\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$743$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	23.2653i		−	0.851234i
$748$	−39.1572	+	36.8217i	−1.43173	+	1.34634i
$749$		0			0
$750$		0			0
$751$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$751$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$752$		0			0
$753$	−3.84163	−	11.8233i	−0.139997	−	0.430865i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$757$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$758$			28.0193i			1.01771i
$759$		0			0
$760$		0			0
$761$	21.4819	+	6.97990i	0.778719	+	0.253021i	0.671293	−	0.741192i	$-0.265739\pi$
$761$	21.4819	+	6.97990i	0.778719	+	0.253021i	0.107426	+	0.994213i	$0.465739\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−10.2443	+	31.5288i	−0.369661	+	1.13770i
$769$			50.9117i			1.83592i	0.396670	+	0.917961i	$0.370166\pi$
$769$			50.9117i			1.83592i	−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$	3.08611			0.111144
$772$	−32.2799	−	10.4884i	−1.16178	−	0.377485i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	17.9487	+	13.0405i	0.645153	+	0.468731i
$775$		0			0
$776$	−51.7289	+	16.8078i	−1.85696	+	0.603363i
$777$		0			0
$778$		0			0
$779$	−16.1784	+	49.7920i	−0.579651	+	1.78398i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	22.6525	−	16.4580i	0.809017	−	0.587785i
$785$		0			0
$786$	0.779703	+	2.39968i	0.0278111	+	0.0855937i
$787$	−8.36459	+	2.71782i	−0.298165	+	0.0968798i	−0.454280	−	0.890859i	$-0.650103\pi$
$787$	−8.36459	+	2.71782i	−0.298165	+	0.0968798i	0.156114	+	0.987739i	$0.450103\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−2.26466	+	11.9163i	−0.0804713	+	0.423427i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$797$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$798$		0			0
$799$		0			0
$800$	16.6251	+	22.8825i	0.587785	+	0.809017i
$801$	4.37215	−	13.4561i	0.154482	−	0.475448i
$802$			50.6371i			1.78806i
$803$	−4.72641	−	10.0262i	−0.166792	−	0.353818i
$804$	−26.2671			−0.926370
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	40.1709	−	13.0523i	1.41233	−	0.458895i	0.499176	−	0.866501i	$-0.333636\pi$
$809$	40.1709	−	13.0523i	1.41233	−	0.458895i	0.913158	+	0.407605i	$0.133636\pi$
$810$		0			0
$811$	−13.5365	−	18.6314i	−0.475331	−	0.654237i	0.502268	−	0.864712i	$-0.332499\pi$
$811$	−13.5365	−	18.6314i	−0.475331	−	0.654237i	−0.977599	+	0.210475i	$0.932499\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−63.8711	−	20.7530i	−2.23594	−	0.726500i
$817$	55.8422	−	40.5717i	1.95367	−	1.41942i
$818$	38.8328	+	28.2137i	1.35776	+	0.986469i
$819$		0			0
$820$		0			0
$821$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$821$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$822$	−40.2577	−	55.4100i	−1.40415	−	1.93265i
$823$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$823$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$824$		0			0
$825$	23.5380	+	25.0309i	0.819487	+	0.871463i
$826$		0			0
$827$	45.4207	+	14.7581i	1.57943	+	0.513188i	0.961910	−	0.273366i	$-0.0881369\pi$
$827$	45.4207	+	14.7581i	1.57943	+	0.513188i	0.617521	+	0.786554i	$0.288137\pi$
$828$		0			0
$829$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$829$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	33.3406	+	45.8894i	1.15518	+	1.58997i
$834$	7.68325	−	23.6466i	0.266049	−	0.818815i
$835$		0			0
$836$	33.0823	+	18.1575i	1.14417	+	0.627991i
$837$		0			0
$838$	−54.5157	−	17.7132i	−1.88321	−	0.611893i
$839$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$839$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$840$		0			0
$841$	−8.96149	−	27.5806i	−0.309017	−	0.951057i
$842$		0			0
$843$	10.2041	−	14.0448i	0.351449	−	0.483729i
$844$	6.40510	+	8.81586i	0.220473	+	0.303455i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	50.1620	+	16.2986i	1.72156	+	0.559368i
$850$	−46.3553	+	33.6791i	−1.58997	+	1.15518i
$851$		0			0
$852$		0			0
$853$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$853$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$854$		0			0
$855$		0			0
$856$	−0.360001	+	1.10797i	−0.0123046	+	0.0378696i
$857$		−	44.3648i		−	1.51547i	−0.652561	−	0.757736i	$-0.726305\pi$
$857$		−	44.3648i		−	1.51547i	0.652561	−	0.757736i	$-0.273695\pi$
$858$		0			0
$859$	−41.9355			−1.43082			−0.715410	−	0.698705i	$-0.753760\pi$
$859$	−41.9355			−1.43082			−0.715410	+	0.698705i	$0.753760\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$863$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$864$	19.0279	−	6.18255i	0.647343	−	0.210335i
$865$		0			0
$866$	−33.8467	−	46.5860i	−1.15016	−	1.58306i
$867$	31.1568	−	95.8908i	1.05814	−	3.25662i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−20.1161	−	14.6152i	−0.680828	−	0.494651i
$874$		0			0
$875$		0			0
$876$	8.14042	−	11.2043i	0.275039	−	0.378559i
$877$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$877$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−48.2376			−1.62517			−0.812583	−	0.582846i	$-0.801939\pi$
$881$	−48.2376			−1.62517			−0.812583	+	0.582846i	$0.801939\pi$
$882$	12.1737	+	3.95549i	0.409911	+	0.133188i
$883$	−46.2013	+	33.5672i	−1.55480	+	1.12963i	−0.614678	+	0.788778i	$0.710714\pi$
$883$	−46.2013	+	33.5672i	−1.55480	+	1.12963i	−0.940119	+	0.340848i	$0.889286\pi$
$884$		0			0
$885$		0			0
$886$	−21.0744	+	6.84748i	−0.708007	+	0.230045i
$887$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$887$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	33.6215	−	15.8493i	1.12636	−	0.530972i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	31.0089	−	42.6800i	1.03478	−	1.42425i
$899$		0			0
$900$	−3.99565	+	12.2973i	−0.133188	+	0.409911i
$901$		0			0
$902$	−42.4044	−	8.05885i	−1.41191	−	0.268331i
$903$		0			0
$904$	57.0611	+	18.5403i	1.89782	+	0.616640i
$905$		0			0
$906$		0			0
$907$	−8.28861	−	25.5097i	−0.275219	−	0.847036i	−0.989161	−	0.146832i	$-0.953092\pi$
$907$	−8.28861	−	25.5097i	−0.275219	−	0.847036i	0.713943	−	0.700204i	$-0.246908\pi$
$908$	29.1885	−	9.48392i	0.968655	−	0.314735i
$909$		0			0
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$			47.1509i			1.56132i
$913$	11.1419	−	58.6268i	0.368743	−	1.94027i
$914$	20.1371			0.666076
$915$		0			0
$916$		0			0
$917$		0			0
$918$	12.5246	+	38.5468i	0.413374	+	1.27223i
$919$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$919$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$920$		0			0
$921$	36.1875	+	49.8078i	1.19242	+	1.64122i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.36257	+	25.7373i	0.274367	+	0.844415i	0.989386	+	0.145310i	$0.0464179\pi$
$929$	8.36257	+	25.7373i	0.274367	+	0.844415i	−0.715019	+	0.699105i	$0.753582\pi$
$930$		0			0
$931$	23.4081	−	32.2184i	0.767168	−	1.05592i
$932$	−31.4860	−	43.3368i	−1.03136	−	1.41954i
$933$		0			0
$934$		−	42.4264i		−	1.38823i
$935$		0			0
$936$		0			0
$937$	20.1659	+	6.55231i	0.658792	+	0.214055i	0.619287	−	0.785165i	$-0.287422\pi$
$937$	20.1659	+	6.55231i	0.658792	+	0.214055i	0.0395055	+	0.999219i	$0.487422\pi$
$938$		0			0
$939$	47.0025	+	34.1493i	1.53387	+	1.11442i
$940$		0			0
$941$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$941$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$942$		0			0
$943$		0			0
$944$	16.2749	−	50.0889i	0.529702	−	1.63025i
$945$		0			0
$946$	38.9842	+	41.4568i	1.26749	+	1.34788i
$947$	−7.31714			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$947$	−7.31714			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$948$		0			0
$949$		0			0
$950$	32.5455	+	23.6457i	1.05592	+	0.767168i
$951$		0			0
$952$		0			0
$953$	15.2588	−	21.0020i	0.494282	−	0.680320i	−0.486889	−	0.873464i	$-0.661868\pi$
$953$	15.2588	−	21.0020i	0.494282	−	0.680320i	0.981171	+	0.193143i	$0.0618683\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−25.0795	−	18.2213i	−0.809017	−	0.587785i
$962$		0			0
$963$	−0.506509	+	0.164575i	−0.0163220	+	0.00530335i
$964$	1.82559	−	2.51271i	0.0587984	−	0.0809291i
$965$		0			0
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	−11.4136	+	28.9436i	−0.366845	+	0.930282i
$969$	−95.5183			−3.06849
$970$		0			0
$971$	−43.6869	+	31.7404i	−1.40198	+	1.01860i	−0.407552	+	0.913182i	$0.633617\pi$
$971$	−43.6869	+	31.7404i	−1.40198	+	1.01860i	−0.994428	+	0.105416i	$0.966383\pi$
$972$	20.4040	+	14.8244i	0.654460	+	0.475493i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.85410	−	5.70634i	0.0593180	−	0.182562i	−0.917007	−	0.398871i	$-0.869402\pi$
$977$	1.85410	−	5.70634i	0.0593180	−	0.182562i	0.976325	+	0.216309i	$0.0694020\pi$
$978$			48.5844i			1.55356i
$979$	17.4617	−	31.8145i	0.558078	−	1.01680i
$980$		0			0
$981$		0			0
$982$	−40.7013	+	29.5712i	−1.29883	+	0.943655i
$983$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$983$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$984$	−16.6653	−	51.2905i	−0.531270	−	1.63508i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$	−54.0497	+	39.2694i	−1.71521	+	1.24618i
$994$		0			0
$995$		0			0
$996$	70.9124	−	23.0409i	2.24695	−	0.730077i
$997$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$997$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$998$	−37.1372	−	51.1150i	−1.17556	−	1.61802i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.k.a.35.1	✓	8
3.2	odd	2		792.2.bp.a.739.2		8
4.3	odd	2		352.2.s.a.79.1		8
8.3	odd	2	CM	88.2.k.a.35.1	✓	8
8.5	even	2		352.2.s.a.79.1		8
11.2	odd	10		968.2.k.c.723.1		8
11.3	even	5		968.2.k.c.403.1		8
11.4	even	5		968.2.g.a.483.2		8
11.5	even	5		968.2.k.b.699.2		8
11.6	odd	10	inner	88.2.k.a.83.1	yes	8
11.7	odd	10		968.2.g.a.483.6		8
11.8	odd	10		968.2.k.d.403.2		8
11.9	even	5		968.2.k.d.723.2		8
11.10	odd	2		968.2.k.b.475.2		8
24.11	even	2		792.2.bp.a.739.2		8
33.17	even	10		792.2.bp.a.523.2		8
44.7	even	10		3872.2.g.b.1935.5		8
44.15	odd	10		3872.2.g.b.1935.6		8
44.39	even	10		352.2.s.a.303.1		8
88.3	odd	10		968.2.k.c.403.1		8
88.19	even	10		968.2.k.d.403.2		8
88.27	odd	10		968.2.k.b.699.2		8
88.29	odd	10		3872.2.g.b.1935.5		8
88.35	even	10		968.2.k.c.723.1		8
88.37	even	10		3872.2.g.b.1935.6		8
88.43	even	2		968.2.k.b.475.2		8
88.51	even	10		968.2.g.a.483.6		8
88.59	odd	10		968.2.g.a.483.2		8
88.61	odd	10		352.2.s.a.303.1		8
88.75	odd	10		968.2.k.d.723.2		8
88.83	even	10	inner	88.2.k.a.83.1	yes	8
264.83	odd	10		792.2.bp.a.523.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.k.a.35.1	✓	8	1.1	even	1	trivial
88.2.k.a.35.1	✓	8	8.3	odd	2	CM
88.2.k.a.83.1	yes	8	11.6	odd	10	inner
88.2.k.a.83.1	yes	8	88.83	even	10	inner
352.2.s.a.79.1		8	4.3	odd	2
352.2.s.a.79.1		8	8.5	even	2
352.2.s.a.303.1		8	44.39	even	10
352.2.s.a.303.1		8	88.61	odd	10
792.2.bp.a.523.2		8	33.17	even	10
792.2.bp.a.523.2		8	264.83	odd	10
792.2.bp.a.739.2		8	3.2	odd	2
792.2.bp.a.739.2		8	24.11	even	2
968.2.g.a.483.2		8	11.4	even	5
968.2.g.a.483.2		8	88.59	odd	10
968.2.g.a.483.6		8	11.7	odd	10
968.2.g.a.483.6		8	88.51	even	10
968.2.k.b.475.2		8	11.10	odd	2
968.2.k.b.475.2		8	88.43	even	2
968.2.k.b.699.2		8	11.5	even	5
968.2.k.b.699.2		8	88.27	odd	10
968.2.k.c.403.1		8	11.3	even	5
968.2.k.c.403.1		8	88.3	odd	10
968.2.k.c.723.1		8	11.2	odd	10
968.2.k.c.723.1		8	88.35	even	10
968.2.k.d.403.2		8	11.8	odd	10
968.2.k.d.403.2		8	88.19	even	10
968.2.k.d.723.2		8	11.9	even	5
968.2.k.d.723.2		8	88.75	odd	10
3872.2.g.b.1935.5		8	44.7	even	10
3872.2.g.b.1935.5		8	88.29	odd	10
3872.2.g.b.1935.6		8	44.15	odd	10
3872.2.g.b.1935.6		8	88.37	even	10

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 - 0.437016i) q^{2} +(1.67625 - 1.21787i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-2.78678 + 0.905480i) q^{6} +(-1.66251 - 2.28825i) q^{8} +(0.399565 - 1.22973i) q^{9} +O(q^{10})\)	\(q+(-1.34500 - 0.437016i) q^{2} +(1.67625 - 1.21787i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-2.78678 + 0.905480i) q^{6} +(-1.66251 - 2.28825i) q^{8} +(0.399565 - 1.22973i) q^{9} +(1.59580 - 2.90748i) q^{11} +4.14392 q^{12} +(1.23607 + 3.80423i) q^{16} +(-7.70660 + 2.50403i) q^{17} +(-1.07483 + 1.47937i) q^{18} +(3.34401 + 4.60263i) q^{19} +(-3.41696 + 3.21316i) q^{22} +(-5.57356 - 1.81096i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(1.09293 + 3.36369i) q^{27} -5.65685i q^{32} +(-0.865968 - 6.81713i) q^{33} +11.4597 q^{34} +(2.09215 - 1.52003i) q^{36} +(-2.48626 - 7.65191i) q^{38} +(5.40907 + 7.44495i) q^{41} -12.1327i q^{43} +(6.00000 - 2.82843i) q^{44} +(6.70500 + 4.87147i) q^{48} +(-2.16312 - 6.65740i) q^{49} +(6.72499 - 2.18508i) q^{50} +(-9.86863 + 13.5830i) q^{51} -5.00179i q^{54} +(11.2108 + 3.64261i) q^{57} +(-10.6520 - 7.73916i) q^{59} +(-2.47214 + 7.60845i) q^{64} +(-1.81447 + 9.54747i) q^{66} -6.33871 q^{67} +(-15.4132 - 5.00805i) q^{68} +(-3.47821 + 1.13014i) q^{72} +(1.96442 - 2.70380i) q^{73} +(-3.20135 + 9.85276i) q^{75} +11.3783i q^{76} +(9.06678 + 6.58740i) q^{81} +(-4.02163 - 12.3773i) q^{82} +(17.1124 - 5.56016i) q^{83} +(-5.30217 + 16.3184i) q^{86} +(-9.30605 + 1.18213i) q^{88} +10.9423 q^{89} +(-6.88930 - 9.48231i) q^{96} +(5.94244 - 18.2889i) q^{97} +9.89949i q^{98} +(-2.93780 - 3.12413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 20 q^{6} - 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 20 * q^6 - 2 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 20 q^{6} - 2 q^{9} + 6 q^{11} + 8 q^{12} - 8 q^{16} + 40 q^{18} - 10 q^{19} - 4 q^{22} - 40 q^{24} - 10 q^{25} + 38 q^{27} - 38 q^{33} + 16 q^{34} + 24 q^{36} - 24 q^{38} + 48 q^{44} - 16 q^{48} + 14 q^{49} - 70 q^{51} + 70 q^{57} - 18 q^{59} + 16 q^{64} - 8 q^{66} - 28 q^{67} + 30 q^{75} - 8 q^{81} - 48 q^{82} + 90 q^{83} - 36 q^{86} + 8 q^{88} - 36 q^{89} + 30 q^{97} + 6 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 20 * q^6 - 2 * q^9 + 6 * q^11 + 8 * q^12 - 8 * q^16 + 40 * q^18 - 10 * q^19 - 4 * q^22 - 40 * q^24 - 10 * q^25 + 38 * q^27 - 38 * q^33 + 16 * q^34 + 24 * q^36 - 24 * q^38 + 48 * q^44 - 16 * q^48 + 14 * q^49 - 70 * q^51 + 70 * q^57 - 18 * q^59 + 16 * q^64 - 8 * q^66 - 28 * q^67 + 30 * q^75 - 8 * q^81 - 48 * q^82 + 90 * q^83 - 36 * q^86 + 8 * q^88 - 36 * q^89 + 30 * q^97 + 6 * q^99

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