LMFDB - Embedded newform 9025.2.a.bx.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.a (trivial)

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:	yes
Analytic conductor:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.66064384.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} + 13x^{2} - 1 $ x^6 - 9x^4 + 13x^2 - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.30397$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41987 q^{2} -0.537080 q^{3} +3.85577 q^{4} -1.29966 q^{6} -3.18676 q^{7} +4.49073 q^{8} -2.71155 q^{9} +O(q^{10})$	\(q+2.41987 q^{2} -0.537080 q^{3} +3.85577 q^{4} -1.29966 q^{6} -3.18676 q^{7} +4.49073 q^{8} -2.71155 q^{9} +4.15544 q^{11} -2.07086 q^{12} -2.07086 q^{13} -7.71155 q^{14} +3.15544 q^{16} +5.79470 q^{17} -6.56159 q^{18} +1.71155 q^{21} +10.0556 q^{22} -2.60794 q^{23} -2.41188 q^{24} -5.01121 q^{26} +3.06756 q^{27} -12.2874 q^{28} -6.00000 q^{29} -2.59933 q^{31} -1.34571 q^{32} -2.23180 q^{33} +14.0224 q^{34} -10.4551 q^{36} -4.30266 q^{37} +1.11222 q^{39} +0.599328 q^{41} +4.14172 q^{42} +3.18676 q^{43} +16.0224 q^{44} -6.31087 q^{46} +11.7086 q^{47} -1.69472 q^{48} +3.15544 q^{49} -3.11222 q^{51} -7.98476 q^{52} -11.7503 q^{53} +7.42309 q^{54} -14.3109 q^{56} -14.5192 q^{58} +1.71155 q^{59} -8.75476 q^{61} -6.29004 q^{62} +8.64104 q^{63} -9.56732 q^{64} -5.40067 q^{66} -4.76228 q^{67} +22.3430 q^{68} +1.40067 q^{69} -13.7115 q^{71} -12.1768 q^{72} -2.72714 q^{73} -10.4119 q^{74} -13.2424 q^{77} +2.69142 q^{78} +1.40067 q^{79} +6.48711 q^{81} +1.45030 q^{82} -7.07154 q^{83} +6.59933 q^{84} +7.71155 q^{86} +3.22248 q^{87} +18.6609 q^{88} -16.5353 q^{89} +6.59933 q^{91} -10.0556 q^{92} +1.39605 q^{93} +28.3333 q^{94} +0.722754 q^{96} -2.07086 q^{97} +7.63575 q^{98} -11.2677 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{4} + 14 q^{9}+O(q^{10}) $ 6 * q + 8 * q^4 + 14 * q^9	$ 6 q + 8 q^{4} + 14 q^{9} + 2 q^{11} - 16 q^{14} - 4 q^{16} - 20 q^{21} + 8 q^{24} + 8 q^{26} - 36 q^{29} + 8 q^{34} - 32 q^{36} - 8 q^{39} - 12 q^{41} + 20 q^{44} + 8 q^{46} - 4 q^{49} - 4 q^{51} - 16 q^{54} - 40 q^{56} - 20 q^{59} - 14 q^{61} - 12 q^{64} - 48 q^{66} + 24 q^{69} - 52 q^{71} - 40 q^{74} + 24 q^{79} + 38 q^{81} + 24 q^{84} + 16 q^{86} - 24 q^{89} + 24 q^{91} + 48 q^{94} - 64 q^{96} - 30 q^{99}+O(q^{100}) $ 6 * q + 8 * q^4 + 14 * q^9 + 2 * q^11 - 16 * q^14 - 4 * q^16 - 20 * q^21 + 8 * q^24 + 8 * q^26 - 36 * q^29 + 8 * q^34 - 32 * q^36 - 8 * q^39 - 12 * q^41 + 20 * q^44 + 8 * q^46 - 4 * q^49 - 4 * q^51 - 16 * q^54 - 40 * q^56 - 20 * q^59 - 14 * q^61 - 12 * q^64 - 48 * q^66 + 24 * q^69 - 52 * q^71 - 40 * q^74 + 24 * q^79 + 38 * q^81 + 24 * q^84 + 16 * q^86 - 24 * q^89 + 24 * q^91 + 48 * q^94 - 64 * q^96 - 30 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	2.41987	1.71111	0.855553	−	0.517715i	$-0.173217\pi$
$2$	2.41987	1.71111	0.855553	+	0.517715i	$0.173217\pi$
$3$	−0.537080	−0.310083	−0.155042	−	0.987908i	$-0.549551\pi$
$3$	−0.537080	−0.310083	−0.155042	+	0.987908i	$0.549551\pi$
$4$	3.85577	1.92789
$5$	0	0
$5$	0	0
$6$	−1.29966	−0.530586
$7$	−3.18676	−1.20448	−0.602241	−	0.798314i	$-0.705725\pi$
$7$	−3.18676	−1.20448	−0.602241	+	0.798314i	$0.705725\pi$
$8$	4.49073	1.58771
$9$	−2.71155	−0.903848
$10$	0	0
$11$	4.15544	1.25291	0.626456	−	0.779457i	$-0.284505\pi$
$11$	4.15544	1.25291	0.626456	+	0.779457i	$0.284505\pi$
$12$	−2.07086	−0.597805
$13$	−2.07086	−0.574353	−0.287176	−	0.957878i	$-0.592717\pi$
$13$	−2.07086	−0.574353	−0.287176	+	0.957878i	$0.592717\pi$
$14$	−7.71155	−2.06100
$15$	0	0
$16$	3.15544	0.788859
$17$	5.79470	1.40542	0.702710	−	0.711476i	$-0.251973\pi$
$17$	5.79470	1.40542	0.702710	+	0.711476i	$0.251973\pi$
$18$	−6.56159	−1.54658
$19$	0	0
$19$	0	0
$20$	0	0
$21$	1.71155	0.373490
$22$	10.0556	2.14386
$23$	−2.60794	−0.543793	−0.271896	−	0.962327i	$-0.587651\pi$
$23$	−2.60794	−0.543793	−0.271896	+	0.962327i	$0.587651\pi$
$24$	−2.41188	−0.492323
$25$	0	0
$26$	−5.01121	−0.982779
$27$	3.06756	0.590352
$28$	−12.2874	−2.32210
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−2.59933	−0.466853	−0.233427	−	0.972374i	$-0.574994\pi$
$31$	−2.59933	−0.466853	−0.233427	+	0.972374i	$0.574994\pi$
$32$	−1.34571	−0.237890
$33$	−2.23180	−0.388507
$34$	14.0224	2.40482
$35$	0	0
$36$	−10.4551	−1.74252
$37$	−4.30266	−0.707353	−0.353677	−	0.935368i	$-0.615069\pi$
$37$	−4.30266	−0.707353	−0.353677	+	0.935368i	$0.615069\pi$
$38$	0	0
$39$	1.11222	0.178097
$40$	0	0
$41$	0.599328	0.0935993	0.0467997	−	0.998904i	$-0.485098\pi$
$41$	0.599328	0.0935993	0.0467997	+	0.998904i	$0.485098\pi$
$42$	4.14172	0.639081
$43$	3.18676	0.485976	0.242988	−	0.970029i	$-0.421872\pi$
$43$	3.18676	0.485976	0.242988	+	0.970029i	$0.421872\pi$
$44$	16.0224	2.41547
$45$	0	0
$46$	−6.31087	−0.930487
$47$	11.7086	1.70787	0.853937	−	0.520376i	$-0.174208\pi$
$47$	11.7086	1.70787	0.853937	+	0.520376i	$0.174208\pi$
$48$	−1.69472	−0.244612
$49$	3.15544	0.450777
$50$	0	0
$51$	−3.11222	−0.435798
$52$	−7.98476	−1.10729
$53$	−11.7503	−1.61403	−0.807017	−	0.590529i	$-0.798919\pi$
$53$	−11.7503	−1.61403	−0.807017	+	0.590529i	$0.798919\pi$
$54$	7.42309	1.01015
$55$	0	0
$56$	−14.3109	−1.91237
$57$	0	0
$58$	−14.5192	−1.90647
$59$	1.71155	0.222824	0.111412	−	0.993774i	$-0.464463\pi$
$59$	1.71155	0.222824	0.111412	+	0.993774i	$0.464463\pi$
$60$	0	0
$61$	−8.75476	−1.12093	−0.560466	−	0.828177i	$-0.689378\pi$
$61$	−8.75476	−1.12093	−0.560466	+	0.828177i	$0.689378\pi$
$62$	−6.29004	−0.798836
$63$	8.64104	1.08867
$64$	−9.56732	−1.19591
$65$	0	0
$66$	−5.40067	−0.664777
$67$	−4.76228	−0.581805	−0.290902	−	0.956753i	$-0.593956\pi$
$67$	−4.76228	−0.581805	−0.290902	+	0.956753i	$0.593956\pi$
$68$	22.3430	2.70949
$69$	1.40067	0.168621
$70$	0	0
$71$	−13.7115	−1.62726	−0.813631	−	0.581382i	$-0.802512\pi$
$71$	−13.7115	−1.62726	−0.813631	+	0.581382i	$0.802512\pi$
$72$	−12.1768	−1.43505
$73$	−2.72714	−0.319188	−0.159594	−	0.987183i	$-0.551018\pi$
$73$	−2.72714	−0.319188	−0.159594	+	0.987183i	$0.551018\pi$
$74$	−10.4119	−1.21036
$75$	0	0
$76$	0	0
$77$	−13.2424	−1.50911
$78$	2.69142	0.304743
$79$	1.40067	0.157588	0.0787939	−	0.996891i	$-0.474893\pi$
$79$	1.40067	0.157588	0.0787939	+	0.996891i	$0.474893\pi$
$80$	0	0
$81$	6.48711	0.720790
$82$	1.45030	0.160158
$83$	−7.07154	−0.776203	−0.388101	−	0.921617i	$-0.626869\pi$
$83$	−7.07154	−0.776203	−0.388101	+	0.921617i	$0.626869\pi$
$84$	6.59933	0.720046
$85$	0	0
$86$	7.71155	0.831557
$87$	3.22248	0.345486
$88$	18.6609	1.98926
$89$	−16.5353	−1.75274	−0.876370	−	0.481639i	$-0.840042\pi$
$89$	−16.5353	−1.75274	−0.876370	+	0.481639i	$0.840042\pi$
$90$	0	0
$91$	6.59933	0.691798
$92$	−10.0556	−1.04837
$93$	1.39605	0.144763
$94$	28.3333	2.92236
$95$	0	0
$96$	0.722754	0.0737658
$97$	−2.07086	−0.210264	−0.105132	−	0.994458i	$-0.533526\pi$
$97$	−2.07086	−0.210264	−0.105132	+	0.994458i	$0.533526\pi$
$98$	7.63575	0.771327
$99$	−11.2677	−1.13244
$100$	0	0
$101$	−1.71155	−0.170305	−0.0851525	−	0.996368i	$-0.527138\pi$
$101$	−1.71155	−0.170305	−0.0851525	+	0.996368i	$0.527138\pi$
$102$	−7.53116	−0.745696
$103$	−5.75296	−0.566856	−0.283428	−	0.958994i	$-0.591472\pi$
$103$	−5.75296	−0.566856	−0.283428	+	0.958994i	$0.591472\pi$
$104$	−9.29966	−0.911907
$105$	0	0
$106$	−28.4343	−2.76178
$107$	15.4324	1.49191	0.745955	−	0.665996i	$-0.231993\pi$
$107$	15.4324	1.49191	0.745955	+	0.665996i	$0.231993\pi$
$108$	11.8278	1.13813
$109$	−11.7115	−1.12176	−0.560881	−	0.827896i	$-0.689538\pi$
$109$	−11.7115	−1.12176	−0.560881	+	0.827896i	$0.689538\pi$
$110$	0	0
$111$	2.31087	0.219338
$112$	−10.0556	−0.950167
$113$	10.5927	0.996477	0.498239	−	0.867040i	$-0.333980\pi$
$113$	10.5927	0.996477	0.498239	+	0.867040i	$0.333980\pi$
$114$	0	0
$115$	0	0
$116$	−23.1346	−2.14800
$117$	5.61523	0.519128
$118$	4.14172	0.381276
$119$	−18.4663	−1.69280
$120$	0	0
$121$	6.26765	0.569787
$122$	−21.1854	−1.91804
$123$	−0.321887	−0.0290236
$124$	−10.0224	−0.900040
$125$	0	0
$126$	20.9102	1.86283
$127$	6.07484	0.539055	0.269528	−	0.962993i	$-0.413132\pi$
$127$	6.07484	0.539055	0.269528	+	0.962993i	$0.413132\pi$
$128$	−20.4602	−1.80845
$129$	−1.71155	−0.150693
$130$	0	0
$131$	−13.5785	−1.18636	−0.593181	−	0.805069i	$-0.702128\pi$
$131$	−13.5785	−1.18636	−0.593181	+	0.805069i	$0.702128\pi$
$132$	−8.60532	−0.748997
$133$	0	0
$134$	−11.5241	−0.995530
$135$	0	0
$136$	26.0224	2.23140
$137$	−7.94302	−0.678618	−0.339309	−	0.940675i	$-0.610193\pi$
$137$	−7.94302	−0.678618	−0.339309	+	0.940675i	$0.610193\pi$
$138$	3.38944	0.288529
$139$	3.26765	0.277159	0.138579	−	0.990351i	$-0.455746\pi$
$139$	3.26765	0.277159	0.138579	+	0.990351i	$0.455746\pi$
$140$	0	0
$141$	−6.28845	−0.529583
$142$	−33.1802	−2.78442
$143$	−8.60532	−0.719613
$144$	−8.55611	−0.713009
$145$	0	0
$146$	−6.59933	−0.546164
$147$	−1.69472	−0.139778
$148$	−16.5901	−1.36370
$149$	8.44389	0.691751	0.345875	−	0.938280i	$-0.387582\pi$
$149$	8.44389	0.691751	0.345875	+	0.938280i	$0.387582\pi$
$150$	0	0
$151$	−0.887783	−0.0722468	−0.0361234	−	0.999347i	$-0.511501\pi$
$151$	−0.887783	−0.0722468	−0.0361234	+	0.999347i	$0.511501\pi$
$152$	0	0
$153$	−15.7126	−1.27029
$154$	−32.0448	−2.58225
$155$	0	0
$156$	4.28845	0.343351
$157$	4.14172	0.330545	0.165273	−	0.986248i	$-0.447150\pi$
$157$	4.14172	0.330545	0.165273	+	0.986248i	$0.447150\pi$
$158$	3.38944	0.269650
$159$	6.31087	0.500485
$160$	0	0
$161$	8.31087	0.654989
$162$	15.6980	1.23335
$163$	−24.7126	−1.93564	−0.967819	−	0.251647i	$-0.919028\pi$
$163$	−24.7126	−1.93564	−0.967819	+	0.251647i	$0.919028\pi$
$164$	2.31087	0.180449
$165$	0	0
$166$	−17.1122	−1.32817
$167$	3.60464	0.278935	0.139468	−	0.990227i	$-0.455461\pi$
$167$	3.60464	0.278935	0.139468	+	0.990227i	$0.455461\pi$
$168$	7.68608	0.592994
$169$	−8.71155	−0.670119
$170$	0	0
$171$	0	0
$172$	12.2874	0.936907
$173$	22.4205	1.70460	0.852300	−	0.523054i	$-0.175207\pi$
$173$	22.4205	1.70460	0.852300	+	0.523054i	$0.175207\pi$
$174$	7.79798	0.591164
$175$	0	0
$176$	13.1122	0.988371
$177$	−0.919237	−0.0690941
$178$	−40.0133	−2.99912
$179$	5.13464	0.383781	0.191890	−	0.981416i	$-0.438538\pi$
$179$	5.13464	0.383781	0.191890	+	0.981416i	$0.438538\pi$
$180$	0	0
$181$	−20.8462	−1.54948	−0.774742	−	0.632277i	$-0.782120\pi$
$181$	−20.8462	−1.54948	−0.774742	+	0.632277i	$0.782120\pi$
$182$	15.9695	1.18374
$183$	4.70201	0.347583
$184$	−11.7115	−0.863387
$185$	0	0
$186$	3.37825	0.247706
$187$	24.0795	1.76087
$188$	45.1457	3.29259
$189$	−9.77557	−0.711068
$190$	0	0
$191$	−5.26765	−0.381154	−0.190577	−	0.981672i	$-0.561036\pi$
$191$	−5.26765	−0.381154	−0.190577	+	0.981672i	$0.561036\pi$
$192$	5.13842	0.370833
$193$	−2.07086	−0.149064	−0.0745318	−	0.997219i	$-0.523746\pi$
$193$	−2.07086	−0.149064	−0.0745318	+	0.997219i	$0.523746\pi$
$194$	−5.01121	−0.359784
$195$	0	0
$196$	12.1666	0.869046
$197$	10.4318	0.743232	0.371616	−	0.928387i	$-0.378804\pi$
$197$	10.4318	0.743232	0.371616	+	0.928387i	$0.378804\pi$
$198$	−27.2663	−1.93773
$199$	−2.73235	−0.193691	−0.0968455	−	0.995299i	$-0.530875\pi$
$199$	−2.73235	−0.193691	−0.0968455	+	0.995299i	$0.530875\pi$
$200$	0	0
$201$	2.55773	0.180408
$202$	−4.14172	−0.291410
$203$	19.1206	1.34200
$204$	−12.0000	−0.840168
$205$	0	0
$206$	−13.9214	−0.969951
$207$	7.07154	0.491506
$208$	−6.53446	−0.453083
$209$	0	0
$210$	0	0
$211$	15.7340	1.08317	0.541585	−	0.840646i	$-0.317824\pi$
$211$	15.7340	1.08317	0.541585	+	0.840646i	$0.317824\pi$
$212$	−45.3066	−3.11167
$213$	7.36420	0.504586
$214$	37.3445	2.55282
$215$	0	0
$216$	13.7756	0.937309
$217$	8.28343	0.562316
$218$	−28.3404	−1.91946
$219$	1.46469	0.0989748
$220$	0	0
$221$	−12.0000	−0.807207
$222$	5.59201	0.375311
$223$	−18.8219	−1.26041	−0.630203	−	0.776430i	$-0.717028\pi$
$223$	−18.8219	−1.26041	−0.630203	+	0.776430i	$0.717028\pi$
$224$	4.28845	0.286534
$225$	0	0
$226$	25.6330	1.70508
$227$	14.4418	0.958533	0.479267	−	0.877669i	$-0.340903\pi$
$227$	14.4418	0.958533	0.479267	+	0.877669i	$0.340903\pi$
$228$	0	0
$229$	−4.17785	−0.276080	−0.138040	−	0.990427i	$-0.544080\pi$
$229$	−4.17785	−0.276080	−0.138040	+	0.990427i	$0.544080\pi$
$230$	0	0
$231$	7.11222	0.467950
$232$	−26.9444	−1.76898
$233$	12.0847	0.791697	0.395849	−	0.918316i	$-0.370450\pi$
$233$	12.0847	0.791697	0.395849	+	0.918316i	$0.370450\pi$
$234$	13.5881	0.888283
$235$	0	0
$236$	6.59933	0.429580
$237$	−0.752273	−0.0488654
$238$	−44.6861	−2.89657
$239$	−11.3541	−0.734435	−0.367218	−	0.930135i	$-0.619690\pi$
$239$	−11.3541	−0.734435	−0.367218	+	0.930135i	$0.619690\pi$
$240$	0	0
$241$	3.40067	0.219057	0.109528	−	0.993984i	$-0.465066\pi$
$241$	3.40067	0.219057	0.109528	+	0.993984i	$0.465066\pi$
$242$	15.1669	0.974966
$243$	−12.6868	−0.813857
$244$	−33.7564	−2.16103
$245$	0	0
$246$	−0.778925	−0.0496625
$247$	0	0
$248$	−11.6729	−0.741229
$249$	3.79798	0.240687
$250$	0	0
$251$	3.04322	0.192086	0.0960432	−	0.995377i	$-0.469381\pi$
$251$	3.04322	0.192086	0.0960432	+	0.995377i	$0.469381\pi$
$252$	33.3179	2.09883
$253$	−10.8371	−0.681324
$254$	14.7003	0.922381
$255$	0	0
$256$	−30.3765	−1.89853
$257$	−17.2881	−1.07840	−0.539201	−	0.842177i	$-0.681274\pi$
$257$	−17.2881	−1.07840	−0.539201	+	0.842177i	$0.681274\pi$
$258$	−4.14172	−0.257852
$259$	13.7115	0.851994
$260$	0	0
$261$	16.2693	1.00704
$262$	−32.8583	−2.02999
$263$	−1.19336	−0.0735859	−0.0367930	−	0.999323i	$-0.511714\pi$
$263$	−1.19336	−0.0735859	−0.0367930	+	0.999323i	$0.511714\pi$
$264$	−10.0224	−0.616837
$265$	0	0
$266$	0	0
$267$	8.88078	0.543495
$268$	−18.3623	−1.12165
$269$	−22.1089	−1.34800	−0.674000	−	0.738731i	$-0.735425\pi$
$269$	−22.1089	−1.34800	−0.674000	+	0.738731i	$0.735425\pi$
$270$	0	0
$271$	−4.08644	−0.248234	−0.124117	−	0.992268i	$-0.539610\pi$
$271$	−4.08644	−0.248234	−0.124117	+	0.992268i	$0.539610\pi$
$272$	18.2848	1.10868
$273$	−3.54437	−0.214515
$274$	−19.2211	−1.16119
$275$	0	0
$276$	5.40067	0.325082
$277$	−10.0199	−0.602037	−0.301019	−	0.953618i	$-0.597327\pi$
$277$	−10.0199	−0.602037	−0.301019	+	0.953618i	$0.597327\pi$
$278$	7.90730	0.474248
$279$	7.04820	0.421964
$280$	0	0
$281$	−0.599328	−0.0357529	−0.0178765	−	0.999840i	$-0.505691\pi$
$281$	−0.599328	−0.0357529	−0.0178765	+	0.999840i	$0.505691\pi$
$282$	−15.2172	−0.906174
$283$	5.41856	0.322100	0.161050	−	0.986946i	$-0.448512\pi$
$283$	5.41856	0.322100	0.161050	+	0.986946i	$0.448512\pi$
$284$	−52.8686	−3.13717
$285$	0	0
$286$	−20.8238	−1.23133
$287$	−1.90991	−0.112739
$288$	3.64895	0.215017
$289$	16.5785	0.975207
$290$	0	0
$291$	1.11222	0.0651993
$292$	−10.5152	−0.615358
$293$	−3.46691	−0.202539	−0.101269	−	0.994859i	$-0.532290\pi$
$293$	−3.46691	−0.202539	−0.101269	+	0.994859i	$0.532290\pi$
$294$	−4.10101	−0.239176
$295$	0	0
$296$	−19.3221	−1.12307
$297$	12.7470	0.739658
$298$	20.4331	1.18366
$299$	5.40067	0.312329
$300$	0	0
$301$	−10.1554	−0.585350
$302$	−2.14832	−0.123622
$303$	0.919237	0.0528088
$304$	0	0
$305$	0	0
$306$	−38.0224	−2.17360
$307$	16.5901	0.946846	0.473423	−	0.880835i	$-0.343018\pi$
$307$	16.5901	0.946846	0.473423	+	0.880835i	$0.343018\pi$
$308$	−51.0596	−2.90939
$309$	3.08980	0.175772
$310$	0	0
$311$	−4.15544	−0.235633	−0.117817	−	0.993035i	$-0.537589\pi$
$311$	−4.15544	−0.235633	−0.117817	+	0.993035i	$0.537589\pi$
$312$	4.99466	0.282767
$313$	−0.919237	−0.0519583	−0.0259792	−	0.999662i	$-0.508270\pi$
$313$	−0.919237	−0.0519583	−0.0259792	+	0.999662i	$0.508270\pi$
$314$	10.0224	0.565598
$315$	0	0
$316$	5.40067	0.303812
$317$	26.7292	1.50126	0.750630	−	0.660723i	$-0.229750\pi$
$317$	26.7292	1.50126	0.750630	+	0.660723i	$0.229750\pi$
$318$	15.2715	0.856383
$319$	−24.9326	−1.39596
$320$	0	0
$321$	−8.28845	−0.462616
$322$	20.1112	1.12076
$323$	0	0
$324$	25.0128	1.38960
$325$	0	0
$326$	−59.8012	−3.31208
$327$	6.29004	0.347840
$328$	2.69142	0.148609
$329$	−37.3125	−2.05710
$330$	0	0
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	−27.2663	−1.49643
$333$	11.6669	0.639340
$334$	8.72275	0.477288
$335$	0	0
$336$	5.40067	0.294631
$337$	−22.5040	−1.22587	−0.612935	−	0.790133i	$-0.710011\pi$
$337$	−22.5040	−1.22587	−0.612935	+	0.790133i	$0.710011\pi$
$338$	−21.0808	−1.14664
$339$	−5.68913	−0.308991
$340$	0	0
$341$	−10.8013	−0.584926
$342$	0	0
$343$	12.2517	0.661530
$344$	14.3109	0.771591
$345$	0	0
$346$	54.2547	2.91675
$347$	−14.4543	−0.775946	−0.387973	−	0.921671i	$-0.626825\pi$
$347$	−14.4543	−0.775946	−0.387973	+	0.921671i	$0.626825\pi$
$348$	12.4252	0.666058
$349$	−13.3541	−0.714828	−0.357414	−	0.933946i	$-0.616342\pi$
$349$	−13.3541	−0.714828	−0.357414	+	0.933946i	$0.616342\pi$
$350$	0	0
$351$	−6.35248	−0.339070
$352$	−5.59201	−0.298055
$353$	17.6410	0.938937	0.469469	−	0.882949i	$-0.344446\pi$
$353$	17.6410	0.938937	0.469469	+	0.882949i	$0.344446\pi$
$354$	−2.22443	−0.118227
$355$	0	0
$356$	−63.7564	−3.37908
$357$	9.91789	0.524910
$358$	12.4252	0.656690
$359$	12.4663	0.657947	0.328973	−	0.944339i	$-0.393297\pi$
$359$	12.4663	0.657947	0.328973	+	0.944339i	$0.393297\pi$
$360$	0	0
$361$	0	0
$362$	−50.4451	−2.65133
$363$	−3.36623	−0.176681
$364$	25.4455	1.33371
$365$	0	0
$366$	11.3783	0.594751
$367$	−16.4291	−0.857594	−0.428797	−	0.903401i	$-0.641062\pi$
$367$	−16.4291	−0.857594	−0.428797	+	0.903401i	$0.641062\pi$
$368$	−8.22918	−0.428976
$369$	−1.62511	−0.0845996
$370$	0	0
$371$	37.4455	1.94407
$372$	5.38284	0.279087
$373$	5.29334	0.274079	0.137039	−	0.990566i	$-0.456241\pi$
$373$	5.29334	0.274079	0.137039	+	0.990566i	$0.456241\pi$
$374$	58.2693	3.01303
$375$	0	0
$376$	52.5801	2.71161
$377$	12.4252	0.639928
$378$	−23.6556	−1.21671
$379$	−14.5353	−0.746629	−0.373314	−	0.927705i	$-0.621779\pi$
$379$	−14.5353	−0.746629	−0.373314	+	0.927705i	$0.621779\pi$
$380$	0	0
$381$	−3.26268	−0.167152
$382$	−12.7470	−0.652195
$383$	−0.453598	−0.0231778	−0.0115889	−	0.999933i	$-0.503689\pi$
$383$	−0.453598	−0.0231778	−0.0115889	+	0.999933i	$0.503689\pi$
$384$	10.9888	0.560769
$385$	0	0
$386$	−5.01121	−0.255064
$387$	−8.64104	−0.439249
$388$	−7.98476	−0.405365
$389$	16.1554	0.819113	0.409557	−	0.912285i	$-0.365683\pi$
$389$	16.1554	0.819113	0.409557	+	0.912285i	$0.365683\pi$
$390$	0	0
$391$	−15.1122	−0.764258
$392$	14.1702	0.715704
$393$	7.29276	0.367871
$394$	25.2435	1.27175
$395$	0	0
$396$	−43.4455	−2.18322
$397$	32.7563	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$397$	32.7563	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$398$	−6.61192	−0.331426
$399$	0	0
$400$	0	0
$401$	−12.0864	−0.603568	−0.301784	−	0.953376i	$-0.597582\pi$
$401$	−12.0864	−0.603568	−0.301784	+	0.953376i	$0.597582\pi$
$402$	6.18936	0.308697
$403$	5.38284	0.268138
$404$	−6.59933	−0.328329
$405$	0	0
$406$	46.2693	2.29631
$407$	−17.8794	−0.886251
$408$	−13.9761	−0.691921
$409$	19.1346	0.946147	0.473073	−	0.881023i	$-0.343145\pi$
$409$	19.1346	0.946147	0.473073	+	0.881023i	$0.343145\pi$
$410$	0	0
$411$	4.26604	0.210428
$412$	−22.1821	−1.09283
$413$	−5.45428	−0.268388
$414$	17.1122	0.841020
$415$	0	0
$416$	2.78678	0.136633
$417$	−1.75499	−0.0859423
$418$	0	0
$419$	8.04484	0.393016	0.196508	−	0.980502i	$-0.437040\pi$
$419$	8.04484	0.393016	0.196508	+	0.980502i	$0.437040\pi$
$420$	0	0
$421$	29.3591	1.43087	0.715437	−	0.698678i	$-0.246228\pi$
$421$	29.3591	1.43087	0.715437	+	0.698678i	$0.246228\pi$
$422$	38.0742	1.85342
$423$	−31.7484	−1.54366
$424$	−52.7676	−2.56262
$425$	0	0
$426$	17.8204	0.863401
$427$	27.8993	1.35014
$428$	59.5040	2.87623
$429$	4.62175	0.223140
$430$	0	0
$431$	32.0448	1.54355	0.771773	−	0.635898i	$-0.219370\pi$
$431$	32.0448	1.54355	0.771773	+	0.635898i	$0.219370\pi$
$432$	9.67948	0.465704
$433$	−0.482831	−0.0232034	−0.0116017	−	0.999933i	$-0.503693\pi$
$433$	−0.482831	−0.0232034	−0.0116017	+	0.999933i	$0.503693\pi$
$434$	20.0448	0.962183
$435$	0	0
$436$	−45.1571	−2.16263
$437$	0	0
$438$	3.54437	0.169356
$439$	27.3591	1.30578	0.652889	−	0.757454i	$-0.273557\pi$
$439$	27.3591	1.30578	0.652889	+	0.757454i	$0.273557\pi$
$440$	0	0
$441$	−8.55611	−0.407434
$442$	−29.0384	−1.38122
$443$	23.3815	1.11089	0.555444	−	0.831554i	$-0.312548\pi$
$443$	23.3815	1.11089	0.555444	+	0.831554i	$0.312548\pi$
$444$	8.91020	0.422859
$445$	0	0
$446$	−45.5465	−2.15669
$447$	−4.53505	−0.214500
$448$	30.4887	1.44046
$449$	−23.1346	−1.09179	−0.545895	−	0.837853i	$-0.683810\pi$
$449$	−23.1346	−1.09179	−0.545895	+	0.837853i	$0.683810\pi$
$450$	0	0
$451$	2.49047	0.117272
$452$	40.8430	1.92109
$453$	0.476811	0.0224025
$454$	34.9472	1.64015
$455$	0	0
$456$	0	0
$457$	21.2503	0.994049	0.497025	−	0.867736i	$-0.334426\pi$
$457$	21.2503	0.994049	0.497025	+	0.867736i	$0.334426\pi$
$458$	−10.1099	−0.472403
$459$	17.7756	0.829692
$460$	0	0
$461$	31.5785	1.47076	0.735379	−	0.677656i	$-0.237004\pi$
$461$	31.5785	1.47076	0.735379	+	0.677656i	$0.237004\pi$
$462$	17.2106	0.800712
$463$	−15.6119	−0.725547	−0.362774	−	0.931877i	$-0.618170\pi$
$463$	−15.6119	−0.725547	−0.362774	+	0.931877i	$0.618170\pi$
$464$	−18.9326	−0.878925
$465$	0	0
$466$	29.2435	1.35468
$467$	−29.8264	−1.38020	−0.690101	−	0.723713i	$-0.742434\pi$
$467$	−29.8264	−1.38020	−0.690101	+	0.723713i	$0.742434\pi$
$468$	21.6510	1.00082
$469$	15.1762	0.700774
$470$	0	0
$471$	−2.22443	−0.102496
$472$	7.68608	0.353781
$473$	13.2424	0.608885
$474$	−1.82040	−0.0836139
$475$	0	0
$476$	−71.2019	−3.26353
$477$	31.8616	1.45884
$478$	−27.4754	−1.25670
$479$	4.53531	0.207223	0.103612	−	0.994618i	$-0.466960\pi$
$479$	4.53531	0.207223	0.103612	+	0.994618i	$0.466960\pi$
$480$	0	0
$481$	8.91020	0.406270
$482$	8.22918	0.374829
$483$	−4.46360	−0.203101
$484$	24.1666	1.09848
$485$	0	0
$486$	−30.7003	−1.39260
$487$	−39.2550	−1.77881	−0.889407	−	0.457116i	$-0.848882\pi$
$487$	−39.2550	−1.77881	−0.889407	+	0.457116i	$0.848882\pi$
$488$	−39.3153	−1.77972
$489$	13.2726	0.600209
$490$	0	0
$491$	38.8910	1.75513	0.877564	−	0.479460i	$-0.159168\pi$
$491$	38.8910	1.75513	0.877564	+	0.479460i	$0.159168\pi$
$492$	−1.24112	−0.0559542
$493$	−34.7682	−1.56588
$494$	0	0
$495$	0	0
$496$	−8.20202	−0.368281
$497$	43.6954	1.96001
$498$	9.19063	0.411842
$499$	4.73235	0.211849	0.105924	−	0.994374i	$-0.466220\pi$
$499$	4.73235	0.211849	0.105924	+	0.994374i	$0.466220\pi$
$500$	0	0
$501$	−1.93598	−0.0864931
$502$	7.36420	0.328680
$503$	1.85567	0.0827400	0.0413700	−	0.999144i	$-0.486828\pi$
$503$	1.85567	0.0827400	0.0413700	+	0.999144i	$0.486828\pi$
$504$	38.8046	1.72849
$505$	0	0
$506$	−26.2244	−1.16582
$507$	4.67880	0.207793
$508$	23.4232	1.03924
$509$	−22.8878	−1.01448	−0.507242	−	0.861804i	$-0.669335\pi$
$509$	−22.8878	−1.01448	−0.507242	+	0.861804i	$0.669335\pi$
$510$	0	0
$511$	8.69074	0.384456
$512$	−32.5867	−1.44014
$513$	0	0
$514$	−41.8350	−1.84526
$515$	0	0
$516$	−6.59933	−0.290519
$517$	48.6543	2.13982
$518$	33.1802	1.45785
$519$	−12.0416	−0.528568
$520$	0	0
$521$	29.7340	1.30267	0.651334	−	0.758791i	$-0.274210\pi$
$521$	29.7340	1.30267	0.651334	+	0.758791i	$0.274210\pi$
$522$	39.3695	1.72316
$523$	−30.6497	−1.34022	−0.670109	−	0.742263i	$-0.733752\pi$
$523$	−30.6497	−1.34022	−0.670109	+	0.742263i	$0.733752\pi$
$524$	−52.3557	−2.28717
$525$	0	0
$526$	−2.88778	−0.125913
$527$	−15.0623	−0.656125
$528$	−7.04231	−0.306477
$529$	−16.1987	−0.704289
$530$	0	0
$531$	−4.64093	−0.201399
$532$	0	0
$533$	−1.24112	−0.0537590
$534$	21.4903	0.929978
$535$	0	0
$536$	−21.3861	−0.923739
$537$	−2.75771	−0.119004
$538$	−53.5006	−2.30657
$539$	13.1122	0.564783
$540$	0	0
$541$	2.21946	0.0954220	0.0477110	−	0.998861i	$-0.484807\pi$
$541$	2.21946	0.0954220	0.0477110	+	0.998861i	$0.484807\pi$
$542$	−9.88865	−0.424754
$543$	11.1961	0.480469
$544$	−7.79798	−0.334336
$545$	0	0
$546$	−8.57691	−0.367058
$547$	14.4297	0.616970	0.308485	−	0.951229i	$-0.400178\pi$
$547$	14.4297	0.616970	0.308485	+	0.951229i	$0.400178\pi$
$548$	−30.6265	−1.30830
$549$	23.7389	1.01315
$550$	0	0
$551$	0	0
$552$	6.29004	0.267722
$553$	−4.46360	−0.189812
$554$	−24.2469	−1.03015
$555$	0	0
$556$	12.5993	0.534331
$557$	19.4610	0.824588	0.412294	−	0.911051i	$-0.364728\pi$
$557$	19.4610	0.824588	0.412294	+	0.911051i	$0.364728\pi$
$558$	17.0557	0.722026
$559$	−6.59933	−0.279122
$560$	0	0
$561$	−12.9326	−0.546016
$562$	−1.45030	−0.0611771
$563$	12.3649	0.521118	0.260559	−	0.965458i	$-0.416093\pi$
$563$	12.3649	0.521118	0.260559	+	0.965458i	$0.416093\pi$
$564$	−24.2469	−1.02098
$565$	0	0
$566$	13.1122	0.551148
$567$	−20.6729	−0.868179
$568$	−61.5748	−2.58362
$569$	−15.0898	−0.632597	−0.316299	−	0.948660i	$-0.602440\pi$
$569$	−15.0898	−0.632597	−0.316299	+	0.948660i	$0.602440\pi$
$570$	0	0
$571$	17.1571	0.718000	0.359000	−	0.933337i	$-0.383118\pi$
$571$	17.1571	0.718000	0.359000	+	0.933337i	$0.383118\pi$
$572$	−33.1802	−1.38733
$573$	2.82915	0.118190
$574$	−4.62175	−0.192908
$575$	0	0
$576$	25.9422	1.08093
$577$	−22.5165	−0.937374	−0.468687	−	0.883364i	$-0.655273\pi$
$577$	−22.5165	−0.937374	−0.468687	+	0.883364i	$0.655273\pi$
$578$	40.1179	1.66868
$579$	1.11222	0.0462222
$580$	0	0
$581$	22.5353	0.934922
$582$	2.69142	0.111563
$583$	−48.8278	−2.02224
$584$	−12.2469	−0.506778
$585$	0	0
$586$	−8.38946	−0.346566
$587$	7.49544	0.309370	0.154685	−	0.987964i	$-0.450564\pi$
$587$	7.49544	0.309370	0.154685	+	0.987964i	$0.450564\pi$
$588$	−6.53446	−0.269477
$589$	0	0
$590$	0	0
$591$	−5.60269	−0.230464
$592$	−13.5768	−0.558002
$593$	27.8094	1.14199	0.570997	−	0.820952i	$-0.306557\pi$
$593$	27.8094	1.14199	0.570997	+	0.820952i	$0.306557\pi$
$594$	30.8462	1.26563
$595$	0	0
$596$	32.5577	1.33362
$597$	1.46749	0.0600603
$598$	13.0689	0.534428
$599$	45.4903	1.85869	0.929343	−	0.369219i	$-0.120375\pi$
$599$	45.4903	1.85869	0.929343	+	0.369219i	$0.120375\pi$
$600$	0	0
$601$	16.5993	0.677101	0.338550	−	0.940948i	$-0.390063\pi$
$601$	16.5993	0.677101	0.338550	+	0.940948i	$0.390063\pi$
$602$	−24.5748	−1.00160
$603$	12.9131	0.525863
$604$	−3.42309	−0.139284
$605$	0	0
$606$	2.22443	0.0903614
$607$	5.08417	0.206360	0.103180	−	0.994663i	$-0.467098\pi$
$607$	5.08417	0.206360	0.103180	+	0.994663i	$0.467098\pi$
$608$	0	0
$609$	−10.2693	−0.416132
$610$	0	0
$611$	−24.2469	−0.980923
$612$	−60.5842	−2.44897
$613$	4.63706	0.187289	0.0936445	−	0.995606i	$-0.470148\pi$
$613$	4.63706	0.187289	0.0936445	+	0.995606i	$0.470148\pi$
$614$	40.1458	1.62015
$615$	0	0
$616$	−59.4679	−2.39603
$617$	40.2874	1.62191	0.810955	−	0.585108i	$-0.198948\pi$
$617$	40.2874	1.62191	0.810955	+	0.585108i	$0.198948\pi$
$618$	7.47691	0.300766
$619$	−43.3815	−1.74365	−0.871825	−	0.489818i	$-0.837063\pi$
$619$	−43.3815	−1.74365	−0.871825	+	0.489818i	$0.837063\pi$
$620$	0	0
$621$	−8.00000	−0.321029
$622$	−10.0556	−0.403194
$623$	52.6940	2.11114
$624$	3.50953	0.140494
$625$	0	0
$626$	−2.22443	−0.0889062
$627$	0	0
$628$	15.9695	0.637253
$629$	−24.9326	−0.994129
$630$	0	0
$631$	7.53369	0.299911	0.149956	−	0.988693i	$-0.452087\pi$
$631$	7.53369	0.299911	0.149956	+	0.988693i	$0.452087\pi$
$632$	6.29004	0.250204
$633$	−8.45040	−0.335873
$634$	64.6812	2.56882
$635$	0	0
$636$	24.3333	0.964878
$637$	−6.53446	−0.258905
$638$	−60.3337	−2.38863
$639$	37.1795	1.47080
$640$	0	0
$641$	23.3075	0.920591	0.460296	−	0.887766i	$-0.347743\pi$
$641$	23.3075	0.920591	0.460296	+	0.887766i	$0.347743\pi$
$642$	−20.0570	−0.791586
$643$	1.87419	0.0739110	0.0369555	−	0.999317i	$-0.488234\pi$
$643$	1.87419	0.0739110	0.0369555	+	0.999317i	$0.488234\pi$
$644$	32.0448	1.26274
$645$	0	0
$646$	0	0
$647$	−47.0371	−1.84922	−0.924609	−	0.380917i	$-0.875608\pi$
$647$	−47.0371	−1.84922	−0.924609	+	0.380917i	$0.875608\pi$
$648$	29.1319	1.14441
$649$	7.11222	0.279179
$650$	0	0
$651$	−4.44887	−0.174365
$652$	−95.2861	−3.73169
$653$	24.1630	0.945571	0.472785	−	0.881178i	$-0.343249\pi$
$653$	24.1630	0.945571	0.472785	+	0.881178i	$0.343249\pi$
$654$	15.2211	0.595191
$655$	0	0
$656$	1.89114	0.0738367
$657$	7.39477	0.288497
$658$	−90.2914	−3.51992
$659$	−10.2885	−0.400781	−0.200391	−	0.979716i	$-0.564221\pi$
$659$	−10.2885	−0.400781	−0.200391	+	0.979716i	$0.564221\pi$
$660$	0	0
$661$	−5.93598	−0.230883	−0.115441	−	0.993314i	$-0.536828\pi$
$661$	−5.93598	−0.230883	−0.115441	+	0.993314i	$0.536828\pi$
$662$	−19.3590	−0.752407
$663$	6.44496	0.250302
$664$	−31.7564	−1.23239
$665$	0	0
$666$	28.2323	1.09398
$667$	15.6476	0.605879
$668$	13.8987	0.537755
$669$	10.1089	0.390831
$670$	0	0
$671$	−36.3799	−1.40443
$672$	−2.30324	−0.0888496
$673$	40.7053	1.56907	0.784537	−	0.620082i	$-0.212901\pi$
$673$	40.7053	1.56907	0.784537	+	0.620082i	$0.212901\pi$
$674$	−54.4567	−2.09759
$675$	0	0
$676$	−33.5897	−1.29191
$677$	−18.8761	−0.725469	−0.362734	−	0.931893i	$-0.618157\pi$
$677$	−18.8761	−0.725469	−0.362734	+	0.931893i	$0.618157\pi$
$678$	−13.7669	−0.528716
$679$	6.59933	0.253259
$680$	0	0
$681$	−7.75638	−0.297225
$682$	−26.1379	−1.00087
$683$	19.6576	0.752179	0.376089	−	0.926583i	$-0.377269\pi$
$683$	19.6576	0.752179	0.376089	+	0.926583i	$0.377269\pi$
$684$	0	0
$685$	0	0
$686$	29.6475	1.13195
$687$	2.24384	0.0856079
$688$	10.0556	0.383367
$689$	24.3333	0.927025
$690$	0	0
$691$	−48.2451	−1.83533	−0.917665	−	0.397354i	$-0.869928\pi$
$691$	−48.2451	−1.83533	−0.917665	+	0.397354i	$0.869928\pi$
$692$	86.4483	3.28627
$693$	35.9073	1.36401
$694$	−34.9775	−1.32773
$695$	0	0
$696$	14.4713	0.548533
$697$	3.47293	0.131546
$698$	−32.3152	−1.22315
$699$	−6.49047	−0.245492
$700$	0	0
$701$	0.512889	0.0193715	0.00968577	−	0.999953i	$-0.496917\pi$
$701$	0.512889	0.0193715	0.00968577	+	0.999953i	$0.496917\pi$
$702$	−15.3722	−0.580185
$703$	0	0
$704$	−39.7564	−1.49838
$705$	0	0
$706$	42.6890	1.60662
$707$	5.45428	0.205129
$708$	−3.54437	−0.133205
$709$	−8.84618	−0.332225	−0.166113	−	0.986107i	$-0.553122\pi$
$709$	−8.84618	−0.332225	−0.166113	+	0.986107i	$0.553122\pi$
$710$	0	0
$711$	−3.79798	−0.142436
$712$	−74.2556	−2.78285
$713$	6.77889	0.253871
$714$	24.0000	0.898177
$715$	0	0
$716$	19.7980	0.739885
$717$	6.09806	0.227736
$718$	30.1669	1.12582
$719$	7.84456	0.292553	0.146276	−	0.989244i	$-0.453271\pi$
$719$	7.84456	0.292553	0.146276	+	0.989244i	$0.453271\pi$
$720$	0	0
$721$	18.3333	0.682767
$722$	0	0
$723$	−1.82643	−0.0679258
$724$	−80.3781	−2.98723
$725$	0	0
$726$	−8.14584	−0.302321
$727$	−2.91130	−0.107974	−0.0539870	−	0.998542i	$-0.517193\pi$
$727$	−2.91130	−0.107974	−0.0539870	+	0.998542i	$0.517193\pi$
$728$	29.6358	1.09838
$729$	−12.6475	−0.468427
$730$	0	0
$731$	18.4663	0.683001
$732$	18.1299	0.670100
$733$	−33.7775	−1.24760	−0.623800	−	0.781584i	$-0.714412\pi$
$733$	−33.7775	−1.24760	−0.623800	+	0.781584i	$0.714412\pi$
$734$	−39.7564	−1.46743
$735$	0	0
$736$	3.50953	0.129363
$737$	−19.7893	−0.728950
$738$	−3.93254	−0.144759
$739$	−35.8030	−1.31703	−0.658517	−	0.752566i	$-0.728816\pi$
$739$	−35.8030	−1.31703	−0.658517	+	0.752566i	$0.728816\pi$
$740$	0	0
$741$	0	0
$742$	90.6133	3.32652
$743$	5.66948	0.207993	0.103996	−	0.994578i	$-0.466837\pi$
$743$	5.66948	0.207993	0.103996	+	0.994578i	$0.466837\pi$
$744$	6.26927	0.229843
$745$	0	0
$746$	12.8092	0.468978
$747$	19.1748	0.701569
$748$	92.8451	3.39475
$749$	−49.1795	−1.79698
$750$	0	0
$751$	27.4679	1.00232	0.501159	−	0.865355i	$-0.332907\pi$
$751$	27.4679	1.00232	0.501159	+	0.865355i	$0.332907\pi$
$752$	36.9457	1.34727
$753$	−1.63445	−0.0595628
$754$	30.0673	1.09498
$755$	0	0
$756$	−37.6924	−1.37086
$757$	−41.6370	−1.51332	−0.756662	−	0.653806i	$-0.773171\pi$
$757$	−41.6370	−1.51332	−0.756662	+	0.653806i	$0.773171\pi$
$758$	−35.1736	−1.27756
$759$	5.82040	0.211267
$760$	0	0
$761$	−9.46967	−0.343275	−0.171638	−	0.985160i	$-0.554906\pi$
$761$	−9.46967	−0.343275	−0.171638	+	0.985160i	$0.554906\pi$
$762$	−7.89526	−0.286015
$763$	37.3219	1.35114
$764$	−20.3109	−0.734822
$765$	0	0
$766$	−1.09765	−0.0396597
$767$	−3.54437	−0.127980
$768$	16.3146	0.588703
$769$	1.90858	0.0688253	0.0344127	−	0.999408i	$-0.489044\pi$
$769$	1.90858	0.0688253	0.0344127	+	0.999408i	$0.489044\pi$
$770$	0	0
$771$	9.28510	0.334395
$772$	−7.98476	−0.287378
$773$	28.4007	1.02150	0.510751	−	0.859729i	$-0.329367\pi$
$773$	28.4007	1.02150	0.510751	+	0.859729i	$0.329367\pi$
$774$	−20.9102	−0.751602
$775$	0	0
$776$	−9.29966	−0.333838
$777$	−7.36420	−0.264189
$778$	39.0941	1.40159
$779$	0	0
$780$	0	0
$781$	−56.9775	−2.03881
$782$	−36.5696	−1.30773
$783$	−18.4053	−0.657753
$784$	9.95678	0.355599
$785$	0	0
$786$	17.6475	0.629466
$787$	−15.6708	−0.558605	−0.279303	−	0.960203i	$-0.590103\pi$
$787$	−15.6708	−0.558605	−0.279303	+	0.960203i	$0.590103\pi$
$788$	40.2225	1.43287
$789$	0.640931	0.0228178
$790$	0	0
$791$	−33.7564	−1.20024
$792$	−50.6000	−1.79799
$793$	18.1299	0.643811
$794$	79.2659	2.81304
$795$	0	0
$796$	−10.5353	−0.373414
$797$	36.9225	1.30786	0.653932	−	0.756554i	$-0.273118\pi$
$797$	36.9225	1.30786	0.653932	+	0.756554i	$0.273118\pi$
$798$	0	0
$799$	67.8478	2.40028
$800$	0	0
$801$	44.8362	1.58421
$802$	−29.2476	−1.03277
$803$	−11.3325	−0.399914
$804$	9.86201	0.347806
$805$	0	0
$806$	13.0258	0.458813
$807$	11.8742	0.417993
$808$	−7.68608	−0.270396
$809$	43.0465	1.51343	0.756716	−	0.653743i	$-0.226802\pi$
$809$	43.0465	1.51343	0.756716	+	0.653743i	$0.226802\pi$
$810$	0	0
$811$	−32.2469	−1.13234	−0.566170	−	0.824288i	$-0.691575\pi$
$811$	−32.2469	−1.13234	−0.566170	+	0.824288i	$0.691575\pi$
$812$	73.7245	2.58722
$813$	2.19475	0.0769731
$814$	−43.2659	−1.51647
$815$	0	0
$816$	−9.82040	−0.343783
$817$	0	0
$818$	46.3033	1.61896
$819$	−17.8944	−0.625280
$820$	0	0
$821$	5.18121	0.180826	0.0904128	−	0.995904i	$-0.471181\pi$
$821$	5.18121	0.180826	0.0904128	+	0.995904i	$0.471181\pi$
$822$	10.3233	0.360065
$823$	−25.8517	−0.901133	−0.450567	−	0.892743i	$-0.648778\pi$
$823$	−25.8517	−0.901133	−0.450567	+	0.892743i	$0.648778\pi$
$824$	−25.8350	−0.900004
$825$	0	0
$826$	−13.1987	−0.459240
$827$	9.97816	0.346974	0.173487	−	0.984836i	$-0.444496\pi$
$827$	9.97816	0.346974	0.173487	+	0.984836i	$0.444496\pi$
$828$	27.2663	0.947568
$829$	−21.9808	−0.763425	−0.381713	−	0.924281i	$-0.624666\pi$
$829$	−21.9808	−0.763425	−0.381713	+	0.924281i	$0.624666\pi$
$830$	0	0
$831$	5.38149	0.186682
$832$	19.8126	0.686877
$833$	18.2848	0.633531
$834$	−4.24685	−0.147056
$835$	0	0
$836$	0	0
$837$	−7.97359	−0.275607
$838$	19.4675	0.672492
$839$	16.1089	0.556140	0.278070	−	0.960561i	$-0.410305\pi$
$839$	16.1089	0.556140	0.278070	+	0.960561i	$0.410305\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	71.0451	2.44838
$843$	0.321887	0.0110864
$844$	60.6666	2.08823
$845$	0	0
$846$	−76.8270	−2.64137
$847$	−19.9735	−0.686298
$848$	−37.0775	−1.27324
$849$	−2.91020	−0.0998779
$850$	0	0
$851$	11.2211	0.384653
$852$	28.3947	0.972785
$853$	44.9615	1.53945	0.769727	−	0.638373i	$-0.220392\pi$
$853$	44.9615	1.53945	0.769727	+	0.638373i	$0.220392\pi$
$854$	67.5128	2.31024
$855$	0	0
$856$	69.3029	2.36872
$857$	46.2431	1.57963	0.789817	−	0.613343i	$-0.210176\pi$
$857$	46.2431	1.57963	0.789817	+	0.613343i	$0.210176\pi$
$858$	11.1840	0.381816
$859$	−10.7772	−0.367713	−0.183856	−	0.982953i	$-0.558858\pi$
$859$	−10.7772	−0.367713	−0.183856	+	0.982953i	$0.558858\pi$
$860$	0	0
$861$	1.02578	0.0349584
$862$	77.5443	2.64117
$863$	−22.7966	−0.776007	−0.388003	−	0.921658i	$-0.626835\pi$
$863$	−22.7966	−0.776007	−0.388003	+	0.921658i	$0.626835\pi$
$864$	−4.12804	−0.140439
$865$	0	0
$866$	−1.16839	−0.0397034
$867$	−8.90400	−0.302396
$868$	31.9390	1.08408
$869$	5.82040	0.197444
$870$	0	0
$871$	9.86201	0.334161
$872$	−52.5934	−1.78104
$873$	5.61523	0.190047
$874$	0	0
$875$	0	0
$876$	5.64752	0.190812
$877$	4.94644	0.167029	0.0835146	−	0.996507i	$-0.473385\pi$
$877$	4.94644	0.167029	0.0835146	+	0.996507i	$0.473385\pi$
$878$	66.2054	2.23432
$879$	1.86201	0.0628039
$880$	0	0
$881$	2.53033	0.0852490	0.0426245	−	0.999091i	$-0.486428\pi$
$881$	2.53033	0.0852490	0.0426245	+	0.999091i	$0.486428\pi$
$882$	−20.7047	−0.697163
$883$	29.7430	1.00093	0.500465	−	0.865757i	$-0.333162\pi$
$883$	29.7430	1.00093	0.500465	+	0.865757i	$0.333162\pi$
$884$	−46.2693	−1.55620
$885$	0	0
$886$	56.5801	1.90085
$887$	−45.5450	−1.52925	−0.764626	−	0.644474i	$-0.777076\pi$
$887$	−45.5450	−1.52925	−0.764626	+	0.644474i	$0.777076\pi$
$888$	10.3775	0.348246
$889$	−19.3591	−0.649282
$890$	0	0
$891$	26.9568	0.903086
$892$	−72.5729	−2.42992
$893$	0	0
$894$	−10.9742	−0.367033
$895$	0	0
$896$	65.2019	2.17824
$897$	−2.90059	−0.0968480
$898$	−55.9828	−1.86817
$899$	15.5960	0.520155
$900$	0	0
$901$	−68.0897	−2.26840
$902$	6.02662	0.200664
$903$	5.45428	0.181507
$904$	47.5689	1.58212
$905$	0	0
$906$	1.15382	0.0383331
$907$	−33.2034	−1.10250	−0.551250	−	0.834340i	$-0.685849\pi$
$907$	−33.2034	−1.10250	−0.551250	+	0.834340i	$0.685849\pi$
$908$	55.6841	1.84794
$909$	4.64093	0.153930
$910$	0	0
$911$	−55.7788	−1.84803	−0.924017	−	0.382351i	$-0.875114\pi$
$911$	−55.7788	−1.84803	−0.924017	+	0.382351i	$0.875114\pi$
$912$	0	0
$913$	−29.3853	−0.972513
$914$	51.4231	1.70092
$915$	0	0
$916$	−16.1089	−0.532252
$917$	43.2715	1.42895
$918$	43.0146	1.41969
$919$	−28.5769	−0.942665	−0.471333	−	0.881956i	$-0.656227\pi$
$919$	−28.5769	−0.942665	−0.471333	+	0.881956i	$0.656227\pi$
$920$	0	0
$921$	−8.91020	−0.293601
$922$	76.4159	2.51662
$923$	28.3947	0.934622
$924$	27.4231	0.902153
$925$	0	0
$926$	−37.7788	−1.24149
$927$	15.5994	0.512352
$928$	8.07426	0.265051
$929$	−54.4937	−1.78788	−0.893940	−	0.448186i	$-0.852070\pi$
$929$	−54.4937	−1.78788	−0.893940	+	0.448186i	$0.852070\pi$
$930$	0	0
$931$	0	0
$932$	46.5960	1.52630
$933$	2.23180	0.0730659
$934$	−72.1761	−2.36167
$935$	0	0
$936$	25.2165	0.824226
$937$	−37.1484	−1.21359	−0.606793	−	0.794860i	$-0.707544\pi$
$937$	−37.1484	−1.21359	−0.606793	+	0.794860i	$0.707544\pi$
$938$	36.7245	1.19910
$939$	0.493704	0.0161114
$940$	0	0
$941$	−32.3973	−1.05612	−0.528061	−	0.849206i	$-0.677081\pi$
$941$	−32.3973	−1.05612	−0.528061	+	0.849206i	$0.677081\pi$
$942$	−5.38284	−0.175382
$943$	−1.56301	−0.0508986
$944$	5.40067	0.175777
$945$	0	0
$946$	32.0448	1.04187
$947$	35.4662	1.15250	0.576249	−	0.817275i	$-0.304516\pi$
$947$	35.4662	1.15250	0.576249	+	0.817275i	$0.304516\pi$
$948$	−2.90059	−0.0942069
$949$	5.64752	0.183326
$950$	0	0
$951$	−14.3557	−0.465516
$952$	−82.9272	−2.68769
$953$	14.3411	0.464553	0.232277	−	0.972650i	$-0.425383\pi$
$953$	14.3411	0.464553	0.232277	+	0.972650i	$0.425383\pi$
$954$	77.1009	2.49623
$955$	0	0
$956$	−43.7788	−1.41591
$957$	13.3908	0.432864
$958$	10.9749	0.354581
$959$	25.3125	0.817383
$960$	0	0
$961$	−24.2435	−0.782048
$962$	21.5615	0.695172
$963$	−41.8458	−1.34846
$964$	13.1122	0.422316
$965$	0	0
$966$	−10.8013	−0.347528
$967$	−27.9351	−0.898331	−0.449165	−	0.893449i	$-0.648279\pi$
$967$	−27.9351	−0.898331	−0.449165	+	0.893449i	$0.648279\pi$
$968$	28.1463	0.904657
$969$	0	0
$970$	0	0
$971$	42.5993	1.36708	0.683539	−	0.729914i	$-0.260440\pi$
$971$	42.5993	1.36708	0.683539	+	0.729914i	$0.260440\pi$
$972$	−48.9173	−1.56902
$973$	−10.4132	−0.333833
$974$	−94.9920	−3.04374
$975$	0	0
$976$	−27.6251	−0.884258
$977$	−39.5597	−1.26563	−0.632813	−	0.774304i	$-0.718100\pi$
$977$	−39.5597	−1.26563	−0.632813	+	0.774304i	$0.718100\pi$
$978$	32.1180	1.02702
$979$	−68.7114	−2.19603
$980$	0	0
$981$	31.7564	1.01390
$982$	94.1112	3.00321
$983$	39.7689	1.26843	0.634215	−	0.773157i	$-0.281323\pi$
$983$	39.7689	1.26843	0.634215	+	0.773157i	$0.281323\pi$
$984$	−1.44551	−0.0460811
$985$	0	0
$986$	−84.1345	−2.67939
$987$	20.0398	0.637874
$988$	0	0
$989$	−8.31087	−0.264270
$990$	0	0
$991$	−55.2019	−1.75355	−0.876773	−	0.480905i	$-0.840308\pi$
$991$	−55.2019	−1.75355	−0.876773	+	0.480905i	$0.840308\pi$
$992$	3.49794	0.111060
$993$	4.29664	0.136350
$994$	105.737	3.35378
$995$	0	0
$996$	14.6442	0.464018
$997$	−11.6543	−0.369097	−0.184548	−	0.982823i	$-0.559082\pi$
$997$	−11.6543	−0.369097	−0.184548	+	0.982823i	$0.559082\pi$
$998$	11.4517	0.362496
$999$	−13.1987	−0.417587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.bx.1.6		6
5.2	odd	4		1805.2.b.e.1084.6		6
5.3	odd	4		1805.2.b.e.1084.1		6
5.4	even	2	inner	9025.2.a.bx.1.1		6
19.18	odd	2		475.2.a.j.1.1		6
57.56	even	2		4275.2.a.br.1.6		6
76.75	even	2		7600.2.a.ck.1.3		6
95.18	even	4		95.2.b.b.39.6	yes	6
95.37	even	4		95.2.b.b.39.1	✓	6
95.94	odd	2		475.2.a.j.1.6		6
285.113	odd	4		855.2.c.d.514.1		6
285.227	odd	4		855.2.c.d.514.6		6
285.284	even	2		4275.2.a.br.1.1		6
380.227	odd	4		1520.2.d.h.609.4		6
380.303	odd	4		1520.2.d.h.609.3		6
380.379	even	2		7600.2.a.ck.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.b.b.39.1	✓	6	95.37	even	4
95.2.b.b.39.6	yes	6	95.18	even	4
475.2.a.j.1.1		6	19.18	odd	2
475.2.a.j.1.6		6	95.94	odd	2
855.2.c.d.514.1		6	285.113	odd	4
855.2.c.d.514.6		6	285.227	odd	4
1520.2.d.h.609.3		6	380.303	odd	4
1520.2.d.h.609.4		6	380.227	odd	4
1805.2.b.e.1084.1		6	5.3	odd	4
1805.2.b.e.1084.6		6	5.2	odd	4
4275.2.a.br.1.1		6	285.284	even	2
4275.2.a.br.1.6		6	57.56	even	2
7600.2.a.ck.1.3		6	76.75	even	2
7600.2.a.ck.1.4		6	380.379	even	2
9025.2.a.bx.1.1		6	5.4	even	2	inner
9025.2.a.bx.1.6		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41987 q^{2} -0.537080 q^{3} +3.85577 q^{4} -1.29966 q^{6} -3.18676 q^{7} +4.49073 q^{8} -2.71155 q^{9} +O(q^{10})\)	\(q+2.41987 q^{2} -0.537080 q^{3} +3.85577 q^{4} -1.29966 q^{6} -3.18676 q^{7} +4.49073 q^{8} -2.71155 q^{9} +4.15544 q^{11} -2.07086 q^{12} -2.07086 q^{13} -7.71155 q^{14} +3.15544 q^{16} +5.79470 q^{17} -6.56159 q^{18} +1.71155 q^{21} +10.0556 q^{22} -2.60794 q^{23} -2.41188 q^{24} -5.01121 q^{26} +3.06756 q^{27} -12.2874 q^{28} -6.00000 q^{29} -2.59933 q^{31} -1.34571 q^{32} -2.23180 q^{33} +14.0224 q^{34} -10.4551 q^{36} -4.30266 q^{37} +1.11222 q^{39} +0.599328 q^{41} +4.14172 q^{42} +3.18676 q^{43} +16.0224 q^{44} -6.31087 q^{46} +11.7086 q^{47} -1.69472 q^{48} +3.15544 q^{49} -3.11222 q^{51} -7.98476 q^{52} -11.7503 q^{53} +7.42309 q^{54} -14.3109 q^{56} -14.5192 q^{58} +1.71155 q^{59} -8.75476 q^{61} -6.29004 q^{62} +8.64104 q^{63} -9.56732 q^{64} -5.40067 q^{66} -4.76228 q^{67} +22.3430 q^{68} +1.40067 q^{69} -13.7115 q^{71} -12.1768 q^{72} -2.72714 q^{73} -10.4119 q^{74} -13.2424 q^{77} +2.69142 q^{78} +1.40067 q^{79} +6.48711 q^{81} +1.45030 q^{82} -7.07154 q^{83} +6.59933 q^{84} +7.71155 q^{86} +3.22248 q^{87} +18.6609 q^{88} -16.5353 q^{89} +6.59933 q^{91} -10.0556 q^{92} +1.39605 q^{93} +28.3333 q^{94} +0.722754 q^{96} -2.07086 q^{97} +7.63575 q^{98} -11.2677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{4} + 14 q^{9}+O(q^{10}) \) 6 * q + 8 * q^4 + 14 * q^9	\( 6 q + 8 q^{4} + 14 q^{9} + 2 q^{11} - 16 q^{14} - 4 q^{16} - 20 q^{21} + 8 q^{24} + 8 q^{26} - 36 q^{29} + 8 q^{34} - 32 q^{36} - 8 q^{39} - 12 q^{41} + 20 q^{44} + 8 q^{46} - 4 q^{49} - 4 q^{51} - 16 q^{54} - 40 q^{56} - 20 q^{59} - 14 q^{61} - 12 q^{64} - 48 q^{66} + 24 q^{69} - 52 q^{71} - 40 q^{74} + 24 q^{79} + 38 q^{81} + 24 q^{84} + 16 q^{86} - 24 q^{89} + 24 q^{91} + 48 q^{94} - 64 q^{96} - 30 q^{99}+O(q^{100}) \) 6 * q + 8 * q^4 + 14 * q^9 + 2 * q^11 - 16 * q^14 - 4 * q^16 - 20 * q^21 + 8 * q^24 + 8 * q^26 - 36 * q^29 + 8 * q^34 - 32 * q^36 - 8 * q^39 - 12 * q^41 + 20 * q^44 + 8 * q^46 - 4 * q^49 - 4 * q^51 - 16 * q^54 - 40 * q^56 - 20 * q^59 - 14 * q^61 - 12 * q^64 - 48 * q^66 + 24 * q^69 - 52 * q^71 - 40 * q^74 + 24 * q^79 + 38 * q^81 + 24 * q^84 + 16 * q^86 - 24 * q^89 + 24 * q^91 + 48 * q^94 - 64 * q^96 - 30 * q^99

Introduction

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