LMFDB - Embedded newform 9025.2.a.cv.1.7

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:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 1805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.96724 q^{2} +3.10308 q^{3} +1.87002 q^{4} -6.10450 q^{6} -2.84392 q^{7} +0.255698 q^{8} +6.62912 q^{9} +O(q^{10})$	\(q-1.96724 q^{2} +3.10308 q^{3} +1.87002 q^{4} -6.10450 q^{6} -2.84392 q^{7} +0.255698 q^{8} +6.62912 q^{9} -0.295824 q^{11} +5.80283 q^{12} +2.61871 q^{13} +5.59466 q^{14} -4.24306 q^{16} -7.09714 q^{17} -13.0411 q^{18} -8.82491 q^{21} +0.581957 q^{22} -2.66459 q^{23} +0.793451 q^{24} -5.15162 q^{26} +11.2615 q^{27} -5.31819 q^{28} -1.25311 q^{29} -1.74251 q^{31} +7.83571 q^{32} -0.917968 q^{33} +13.9618 q^{34} +12.3966 q^{36} +0.722118 q^{37} +8.12606 q^{39} +10.1012 q^{41} +17.3607 q^{42} -4.02118 q^{43} -0.553198 q^{44} +5.24189 q^{46} -2.94767 q^{47} -13.1666 q^{48} +1.08787 q^{49} -22.0230 q^{51} +4.89704 q^{52} +6.98387 q^{53} -22.1540 q^{54} -0.727184 q^{56} +2.46517 q^{58} -8.84124 q^{59} +6.62954 q^{61} +3.42793 q^{62} -18.8527 q^{63} -6.92858 q^{64} +1.80586 q^{66} -1.93900 q^{67} -13.2718 q^{68} -8.26846 q^{69} +15.7012 q^{71} +1.69505 q^{72} +3.05470 q^{73} -1.42058 q^{74} +0.841300 q^{77} -15.9859 q^{78} +8.06734 q^{79} +15.0579 q^{81} -19.8714 q^{82} +13.8489 q^{83} -16.5028 q^{84} +7.91061 q^{86} -3.88851 q^{87} -0.0756416 q^{88} +0.551256 q^{89} -7.44739 q^{91} -4.98285 q^{92} -5.40716 q^{93} +5.79876 q^{94} +24.3149 q^{96} +6.60229 q^{97} -2.14010 q^{98} -1.96106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9}+O(q^{10}) $ 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9	$ 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9} + 20 q^{11} + 40 q^{16} + 92 q^{24} + 76 q^{26} + 156 q^{36} + 80 q^{39} + 48 q^{44} + 72 q^{49} + 32 q^{54} + 80 q^{61} + 72 q^{64} + 16 q^{66} + 100 q^{74} + 40 q^{81} + 380 q^{96} + 128 q^{99}+O(q^{100}) $ 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9 + 20 * q^11 + 40 * q^16 + 92 * q^24 + 76 * q^26 + 156 * q^36 + 80 * q^39 + 48 * q^44 + 72 * q^49 + 32 * q^54 + 80 * q^61 + 72 * q^64 + 16 * q^66 + 100 * q^74 + 40 * q^81 + 380 * q^96 + 128 * 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 $

$2$	−1.96724	−1.39105	−0.695523	−	0.718503i	$-0.744827\pi$
$2$	−1.96724	−1.39105	−0.695523	+	0.718503i	$0.744827\pi$
$3$	3.10308	1.79157	0.895783	−	0.444492i	$-0.146616\pi$
$3$	3.10308	1.79157	0.895783	+	0.444492i	$0.146616\pi$
$4$	1.87002	0.935011
$5$	0	0
$5$	0	0
$6$	−6.10450	−2.49215
$7$	−2.84392	−1.07490	−0.537450	−	0.843296i	$-0.680612\pi$
$7$	−2.84392	−1.07490	−0.537450	+	0.843296i	$0.680612\pi$
$8$	0.255698	0.0904028
$9$	6.62912	2.20971
$10$	0	0
$11$	−0.295824	−0.0891944	−0.0445972	−	0.999005i	$-0.514200\pi$
$11$	−0.295824	−0.0891944	−0.0445972	+	0.999005i	$0.514200\pi$
$12$	5.80283	1.67513
$13$	2.61871	0.726298	0.363149	−	0.931731i	$-0.381702\pi$
$13$	2.61871	0.726298	0.363149	+	0.931731i	$0.381702\pi$
$14$	5.59466	1.49524
$15$	0	0
$16$	−4.24306	−1.06077
$17$	−7.09714	−1.72131	−0.860655	−	0.509189i	$-0.829945\pi$
$17$	−7.09714	−1.72131	−0.860655	+	0.509189i	$0.829945\pi$
$18$	−13.0411	−3.07381
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−8.82491	−1.92575
$22$	0.581957	0.124074
$23$	−2.66459	−0.555606	−0.277803	−	0.960638i	$-0.589606\pi$
$23$	−2.66459	−0.555606	−0.277803	+	0.960638i	$0.589606\pi$
$24$	0.793451	0.161963
$25$	0	0
$26$	−5.15162	−1.01031
$27$	11.2615	2.16727
$28$	−5.31819	−1.00504
$29$	−1.25311	−0.232697	−0.116349	−	0.993208i	$-0.537119\pi$
$29$	−1.25311	−0.232697	−0.116349	+	0.993208i	$0.537119\pi$
$30$	0	0
$31$	−1.74251	−0.312964	−0.156482	−	0.987681i	$-0.550015\pi$
$31$	−1.74251	−0.312964	−0.156482	+	0.987681i	$0.550015\pi$
$32$	7.83571	1.38517
$33$	−0.917968	−0.159798
$34$	13.9618	2.39442
$35$	0	0
$36$	12.3966	2.06610
$37$	0.722118	0.118716	0.0593578	−	0.998237i	$-0.481095\pi$
$37$	0.722118	0.118716	0.0593578	+	0.998237i	$0.481095\pi$
$38$	0	0
$39$	8.12606	1.30121
$40$	0	0
$41$	10.1012	1.57754	0.788768	−	0.614691i	$-0.210719\pi$
$41$	10.1012	1.57754	0.788768	+	0.614691i	$0.210719\pi$
$42$	17.3607	2.67881
$43$	−4.02118	−0.613224	−0.306612	−	0.951835i	$-0.599195\pi$
$43$	−4.02118	−0.613224	−0.306612	+	0.951835i	$0.599195\pi$
$44$	−0.553198	−0.0833978
$45$	0	0
$46$	5.24189	0.772874
$47$	−2.94767	−0.429962	−0.214981	−	0.976618i	$-0.568969\pi$
$47$	−2.94767	−0.429962	−0.214981	+	0.976618i	$0.568969\pi$
$48$	−13.1666	−1.90043
$49$	1.08787	0.155410
$50$	0	0
$51$	−22.0230	−3.08384
$52$	4.89704	0.679097
$53$	6.98387	0.959308	0.479654	−	0.877458i	$-0.340762\pi$
$53$	6.98387	0.959308	0.479654	+	0.877458i	$0.340762\pi$
$54$	−22.1540	−3.01478
$55$	0	0
$56$	−0.727184	−0.0971740
$57$	0	0
$58$	2.46517	0.323692
$59$	−8.84124	−1.15103	−0.575516	−	0.817791i	$-0.695199\pi$
$59$	−8.84124	−1.15103	−0.575516	+	0.817791i	$0.695199\pi$
$60$	0	0
$61$	6.62954	0.848826	0.424413	−	0.905469i	$-0.360480\pi$
$61$	6.62954	0.848826	0.424413	+	0.905469i	$0.360480\pi$
$62$	3.42793	0.435348
$63$	−18.8527	−2.37522
$64$	−6.92858	−0.866073
$65$	0	0
$66$	1.80586	0.222286
$67$	−1.93900	−0.236886	−0.118443	−	0.992961i	$-0.537790\pi$
$67$	−1.93900	−0.236886	−0.118443	+	0.992961i	$0.537790\pi$
$68$	−13.2718	−1.60944
$69$	−8.26846	−0.995405
$70$	0	0
$71$	15.7012	1.86340	0.931698	−	0.363235i	$-0.118328\pi$
$71$	15.7012	1.86340	0.931698	+	0.363235i	$0.118328\pi$
$72$	1.69505	0.199764
$73$	3.05470	0.357526	0.178763	−	0.983892i	$-0.442791\pi$
$73$	3.05470	0.357526	0.178763	+	0.983892i	$0.442791\pi$
$74$	−1.42058	−0.165139
$75$	0	0
$76$	0	0
$77$	0.841300	0.0958751
$78$	−15.9859	−1.81005
$79$	8.06734	0.907647	0.453823	−	0.891092i	$-0.350060\pi$
$79$	8.06734	0.907647	0.453823	+	0.891092i	$0.350060\pi$
$80$	0	0
$81$	15.0579	1.67310
$82$	−19.8714	−2.19443
$83$	13.8489	1.52011	0.760057	−	0.649857i	$-0.225171\pi$
$83$	13.8489	1.52011	0.760057	+	0.649857i	$0.225171\pi$
$84$	−16.5028	−1.80060
$85$	0	0
$86$	7.91061	0.853023
$87$	−3.88851	−0.416892
$88$	−0.0756416	−0.00806343
$89$	0.551256	0.0584330	0.0292165	−	0.999573i	$-0.490699\pi$
$89$	0.551256	0.0584330	0.0292165	+	0.999573i	$0.490699\pi$
$90$	0	0
$91$	−7.44739	−0.780698
$92$	−4.98285	−0.519498
$93$	−5.40716	−0.560696
$94$	5.79876	0.598097
$95$	0	0
$96$	24.3149	2.48163
$97$	6.60229	0.670361	0.335180	−	0.942154i	$-0.391203\pi$
$97$	6.60229	0.670361	0.335180	+	0.942154i	$0.391203\pi$
$98$	−2.14010	−0.216183
$99$	−1.96106	−0.197094
$100$	0	0
$101$	−5.15989	−0.513428	−0.256714	−	0.966487i	$-0.582640\pi$
$101$	−5.15989	−0.513428	−0.256714	+	0.966487i	$0.582640\pi$
$102$	43.3245	4.28976
$103$	−5.91869	−0.583186	−0.291593	−	0.956542i	$-0.594185\pi$
$103$	−5.91869	−0.583186	−0.291593	+	0.956542i	$0.594185\pi$
$104$	0.669597	0.0656594
$105$	0	0
$106$	−13.7389	−1.33444
$107$	3.73476	0.361052	0.180526	−	0.983570i	$-0.442220\pi$
$107$	3.73476	0.361052	0.180526	+	0.983570i	$0.442220\pi$
$108$	21.0592	2.02642
$109$	8.67647	0.831055	0.415528	−	0.909581i	$-0.363597\pi$
$109$	8.67647	0.831055	0.415528	+	0.909581i	$0.363597\pi$
$110$	0	0
$111$	2.24079	0.212687
$112$	12.0669	1.14022
$113$	11.8569	1.11540	0.557701	−	0.830042i	$-0.311683\pi$
$113$	11.8569	1.11540	0.557701	+	0.830042i	$0.311683\pi$
$114$	0	0
$115$	0	0
$116$	−2.34335	−0.217574
$117$	17.3597	1.60491
$118$	17.3928	1.60114
$119$	20.1837	1.85024
$120$	0	0
$121$	−10.9125	−0.992044
$122$	−13.0419	−1.18076
$123$	31.3447	2.82626
$124$	−3.25854	−0.292625
$125$	0	0
$126$	37.0877	3.30404
$127$	11.3533	1.00745	0.503723	−	0.863865i	$-0.331963\pi$
$127$	11.3533	1.00745	0.503723	+	0.863865i	$0.331963\pi$
$128$	−2.04126	−0.180424
$129$	−12.4780	−1.09863
$130$	0	0
$131$	12.5054	1.09260	0.546299	−	0.837590i	$-0.316036\pi$
$131$	12.5054	1.09260	0.546299	+	0.837590i	$0.316036\pi$
$132$	−1.71662	−0.149413
$133$	0	0
$134$	3.81447	0.329520
$135$	0	0
$136$	−1.81472	−0.155611
$137$	14.5356	1.24186	0.620930	−	0.783866i	$-0.286755\pi$
$137$	14.5356	1.24186	0.620930	+	0.783866i	$0.286755\pi$
$138$	16.2660	1.38466
$139$	21.7752	1.84695	0.923473	−	0.383663i	$-0.125338\pi$
$139$	21.7752	1.84695	0.923473	+	0.383663i	$0.125338\pi$
$140$	0	0
$141$	−9.14686	−0.770305
$142$	−30.8881	−2.59207
$143$	−0.774677	−0.0647818
$144$	−28.1278	−2.34398
$145$	0	0
$146$	−6.00932	−0.497335
$147$	3.37575	0.278427
$148$	1.35038	0.111000
$149$	16.9257	1.38660	0.693302	−	0.720647i	$-0.256155\pi$
$149$	16.9257	1.38660	0.693302	+	0.720647i	$0.256155\pi$
$150$	0	0
$151$	16.4525	1.33889	0.669444	−	0.742863i	$-0.266533\pi$
$151$	16.4525	1.33889	0.669444	+	0.742863i	$0.266533\pi$
$152$	0	0
$153$	−47.0478	−3.80359
$154$	−1.65504	−0.133367
$155$	0	0
$156$	15.1959	1.21665
$157$	6.09304	0.486277	0.243139	−	0.969992i	$-0.421823\pi$
$157$	6.09304	0.486277	0.243139	+	0.969992i	$0.421823\pi$
$158$	−15.8704	−1.26258
$159$	21.6715	1.71866
$160$	0	0
$161$	7.57789	0.597221
$162$	−29.6225	−2.32736
$163$	4.98787	0.390680	0.195340	−	0.980736i	$-0.437419\pi$
$163$	4.98787	0.390680	0.195340	+	0.980736i	$0.437419\pi$
$164$	18.8894	1.47501
$165$	0	0
$166$	−27.2441	−2.11455
$167$	−15.9975	−1.23792	−0.618961	−	0.785422i	$-0.712446\pi$
$167$	−15.9975	−1.23792	−0.618961	+	0.785422i	$0.712446\pi$
$168$	−2.25651	−0.174094
$169$	−6.14238	−0.472491
$170$	0	0
$171$	0	0
$172$	−7.51969	−0.573371
$173$	−1.89170	−0.143823	−0.0719116	−	0.997411i	$-0.522910\pi$
$173$	−1.89170	−0.143823	−0.0719116	+	0.997411i	$0.522910\pi$
$174$	7.64962	0.579916
$175$	0	0
$176$	1.25520	0.0946144
$177$	−27.4351	−2.06215
$178$	−1.08445	−0.0812830
$179$	1.93323	0.144496	0.0722480	−	0.997387i	$-0.476983\pi$
$179$	1.93323	0.144496	0.0722480	+	0.997387i	$0.476983\pi$
$180$	0	0
$181$	−2.95409	−0.219576	−0.109788	−	0.993955i	$-0.535017\pi$
$181$	−2.95409	−0.219576	−0.109788	+	0.993955i	$0.535017\pi$
$182$	14.6508	1.08599
$183$	20.5720	1.52073
$184$	−0.681331	−0.0502284
$185$	0	0
$186$	10.6372	0.779955
$187$	2.09951	0.153531
$188$	−5.51221	−0.402019
$189$	−32.0267	−2.32960
$190$	0	0
$191$	−14.3187	−1.03607	−0.518033	−	0.855360i	$-0.673336\pi$
$191$	−14.3187	−1.03607	−0.518033	+	0.855360i	$0.673336\pi$
$192$	−21.5000	−1.55163
$193$	−18.2682	−1.31497	−0.657487	−	0.753466i	$-0.728381\pi$
$193$	−18.2682	−1.31497	−0.657487	+	0.753466i	$0.728381\pi$
$194$	−12.9883	−0.932503
$195$	0	0
$196$	2.03434	0.145310
$197$	−17.1912	−1.22482	−0.612410	−	0.790540i	$-0.709800\pi$
$197$	−17.1912	−1.22482	−0.612410	+	0.790540i	$0.709800\pi$
$198$	3.85786	0.274166
$199$	5.28601	0.374715	0.187358	−	0.982292i	$-0.440008\pi$
$199$	5.28601	0.374715	0.187358	+	0.982292i	$0.440008\pi$
$200$	0	0
$201$	−6.01687	−0.424397
$202$	10.1507	0.714203
$203$	3.56375	0.250126
$204$	−41.1835	−2.88342
$205$	0	0
$206$	11.6435	0.811239
$207$	−17.6639	−1.22773
$208$	−11.1113	−0.770432
$209$	0	0
$210$	0	0
$211$	22.3385	1.53784	0.768921	−	0.639344i	$-0.220794\pi$
$211$	22.3385	1.53784	0.768921	+	0.639344i	$0.220794\pi$
$212$	13.0600	0.896964
$213$	48.7223	3.33840
$214$	−7.34715	−0.502241
$215$	0	0
$216$	2.87953	0.195928
$217$	4.95556	0.336405
$218$	−17.0687	−1.15604
$219$	9.47899	0.640531
$220$	0	0
$221$	−18.5853	−1.25018
$222$	−4.40817	−0.295857
$223$	−8.49587	−0.568926	−0.284463	−	0.958687i	$-0.591815\pi$
$223$	−8.49587	−0.568926	−0.284463	+	0.958687i	$0.591815\pi$
$224$	−22.2841	−1.48892
$225$	0	0
$226$	−23.3253	−1.55158
$227$	−13.2798	−0.881411	−0.440706	−	0.897652i	$-0.645272\pi$
$227$	−13.2798	−0.881411	−0.440706	+	0.897652i	$0.645272\pi$
$228$	0	0
$229$	−15.7600	−1.04145	−0.520725	−	0.853724i	$-0.674338\pi$
$229$	−15.7600	−1.04145	−0.520725	+	0.853724i	$0.674338\pi$
$230$	0	0
$231$	2.61063	0.171767
$232$	−0.320418	−0.0210365
$233$	8.38097	0.549056	0.274528	−	0.961579i	$-0.411478\pi$
$233$	8.38097	0.549056	0.274528	+	0.961579i	$0.411478\pi$
$234$	−34.1507	−2.23250
$235$	0	0
$236$	−16.5333	−1.07623
$237$	25.0336	1.62611
$238$	−39.7061	−2.57376
$239$	3.99353	0.258320	0.129160	−	0.991624i	$-0.458772\pi$
$239$	3.99353	0.258320	0.129160	+	0.991624i	$0.458772\pi$
$240$	0	0
$241$	14.1034	0.908483	0.454241	−	0.890879i	$-0.349910\pi$
$241$	14.1034	0.908483	0.454241	+	0.890879i	$0.349910\pi$
$242$	21.4675	1.37998
$243$	12.9416	0.830201
$244$	12.3974	0.793662
$245$	0	0
$246$	−61.6625	−3.93146
$247$	0	0
$248$	−0.445556	−0.0282929
$249$	42.9743	2.72338
$250$	0	0
$251$	14.9564	0.944041	0.472021	−	0.881587i	$-0.343525\pi$
$251$	14.9564	0.944041	0.472021	+	0.881587i	$0.343525\pi$
$252$	−35.2549	−2.22085
$253$	0.788252	0.0495570
$254$	−22.3347	−1.40140
$255$	0	0
$256$	17.8728	1.11705
$257$	−8.64742	−0.539411	−0.269706	−	0.962943i	$-0.586926\pi$
$257$	−8.64742	−0.539411	−0.269706	+	0.962943i	$0.586926\pi$
$258$	24.5473	1.52825
$259$	−2.05365	−0.127607
$260$	0	0
$261$	−8.30704	−0.514193
$262$	−24.6010	−1.51986
$263$	15.3655	0.947476	0.473738	−	0.880666i	$-0.342904\pi$
$263$	15.3655	0.947476	0.473738	+	0.880666i	$0.342904\pi$
$264$	−0.234722	−0.0144462
$265$	0	0
$266$	0	0
$267$	1.71059	0.104687
$268$	−3.62597	−0.221491
$269$	16.5642	1.00993	0.504967	−	0.863139i	$-0.331505\pi$
$269$	16.5642	1.00993	0.504967	+	0.863139i	$0.331505\pi$
$270$	0	0
$271$	6.71990	0.408205	0.204103	−	0.978950i	$-0.434572\pi$
$271$	6.71990	0.408205	0.204103	+	0.978950i	$0.434572\pi$
$272$	30.1136	1.82591
$273$	−23.1099	−1.39867
$274$	−28.5949	−1.72748
$275$	0	0
$276$	−15.4622	−0.930715
$277$	−7.71506	−0.463553	−0.231777	−	0.972769i	$-0.574454\pi$
$277$	−7.71506	−0.463553	−0.231777	+	0.972769i	$0.574454\pi$
$278$	−42.8369	−2.56919
$279$	−11.5513	−0.691560
$280$	0	0
$281$	−13.7574	−0.820696	−0.410348	−	0.911929i	$-0.634593\pi$
$281$	−13.7574	−0.820696	−0.410348	+	0.911929i	$0.634593\pi$
$282$	17.9940	1.07153
$283$	−16.5978	−0.986639	−0.493320	−	0.869848i	$-0.664217\pi$
$283$	−16.5978	−0.986639	−0.493320	+	0.869848i	$0.664217\pi$
$284$	29.3617	1.74230
$285$	0	0
$286$	1.52397	0.0901144
$287$	−28.7269	−1.69569
$288$	51.9439	3.06083
$289$	33.3694	1.96291
$290$	0	0
$291$	20.4874	1.20100
$292$	5.71236	0.334290
$293$	−7.39839	−0.432219	−0.216109	−	0.976369i	$-0.569337\pi$
$293$	−7.39839	−0.432219	−0.216109	+	0.976369i	$0.569337\pi$
$294$	−6.64090	−0.387305
$295$	0	0
$296$	0.184644	0.0107322
$297$	−3.33142	−0.193309
$298$	−33.2968	−1.92883
$299$	−6.97779	−0.403536
$300$	0	0
$301$	11.4359	0.659154
$302$	−32.3660	−1.86245
$303$	−16.0116	−0.919841
$304$	0	0
$305$	0	0
$306$	92.5542	5.29097
$307$	−13.8884	−0.792656	−0.396328	−	0.918109i	$-0.629716\pi$
$307$	−13.8884	−0.792656	−0.396328	+	0.918109i	$0.629716\pi$
$308$	1.57325	0.0896442
$309$	−18.3662	−1.04482
$310$	0	0
$311$	26.4251	1.49843	0.749214	−	0.662328i	$-0.230431\pi$
$311$	26.4251	1.49843	0.749214	+	0.662328i	$0.230431\pi$
$312$	2.07782	0.117633
$313$	−6.91198	−0.390688	−0.195344	−	0.980735i	$-0.562582\pi$
$313$	−6.91198	−0.390688	−0.195344	+	0.980735i	$0.562582\pi$
$314$	−11.9864	−0.676434
$315$	0	0
$316$	15.0861	0.848660
$317$	28.7345	1.61389	0.806944	−	0.590628i	$-0.201120\pi$
$317$	28.7345	1.61389	0.806944	+	0.590628i	$0.201120\pi$
$318$	−42.6330	−2.39074
$319$	0.370701	0.0207553
$320$	0	0
$321$	11.5893	0.646849
$322$	−14.9075	−0.830763
$323$	0	0
$324$	28.1586	1.56437
$325$	0	0
$326$	−9.81232	−0.543454
$327$	26.9238	1.48889
$328$	2.58284	0.142614
$329$	8.38293	0.462166
$330$	0	0
$331$	−8.13446	−0.447110	−0.223555	−	0.974691i	$-0.571766\pi$
$331$	−8.13446	−0.447110	−0.223555	+	0.974691i	$0.571766\pi$
$332$	25.8977	1.42132
$333$	4.78701	0.262327
$334$	31.4708	1.72201
$335$	0	0
$336$	37.4447	2.04277
$337$	−6.76361	−0.368437	−0.184219	−	0.982885i	$-0.558975\pi$
$337$	−6.76361	−0.368437	−0.184219	+	0.982885i	$0.558975\pi$
$338$	12.0835	0.657257
$339$	36.7929	1.99832
$340$	0	0
$341$	0.515478	0.0279147
$342$	0	0
$343$	16.8136	0.907850
$344$	−1.02821	−0.0554371
$345$	0	0
$346$	3.72142	0.200065
$347$	15.5843	0.836609	0.418305	−	0.908307i	$-0.362624\pi$
$347$	15.5843	0.836609	0.418305	+	0.908307i	$0.362624\pi$
$348$	−7.27160	−0.389799
$349$	5.80011	0.310473	0.155237	−	0.987877i	$-0.450386\pi$
$349$	5.80011	0.310473	0.155237	+	0.987877i	$0.450386\pi$
$350$	0	0
$351$	29.4905	1.57409
$352$	−2.31800	−0.123550
$353$	−31.7700	−1.69095	−0.845474	−	0.534016i	$-0.820682\pi$
$353$	−31.7700	−1.69095	−0.845474	+	0.534016i	$0.820682\pi$
$354$	53.9714	2.86855
$355$	0	0
$356$	1.03086	0.0546355
$357$	62.6317	3.31482
$358$	−3.80311	−0.201001
$359$	13.0256	0.687464	0.343732	−	0.939068i	$-0.388309\pi$
$359$	13.0256	0.687464	0.343732	+	0.939068i	$0.388309\pi$
$360$	0	0
$361$	0	0
$362$	5.81140	0.305441
$363$	−33.8624	−1.77731
$364$	−13.9268	−0.729961
$365$	0	0
$366$	−40.4700	−2.11540
$367$	11.9948	0.626123	0.313062	−	0.949733i	$-0.398645\pi$
$367$	11.9948	0.626123	0.313062	+	0.949733i	$0.398645\pi$
$368$	11.3060	0.589368
$369$	66.9618	3.48589
$370$	0	0
$371$	−19.8616	−1.03116
$372$	−10.1115	−0.524257
$373$	−26.0276	−1.34766	−0.673829	−	0.738888i	$-0.735351\pi$
$373$	−26.0276	−1.34766	−0.673829	+	0.738888i	$0.735351\pi$
$374$	−4.13023	−0.213569
$375$	0	0
$376$	−0.753712	−0.0388697
$377$	−3.28153	−0.169007
$378$	63.0041	3.24058
$379$	6.45800	0.331725	0.165863	−	0.986149i	$-0.446959\pi$
$379$	6.45800	0.331725	0.165863	+	0.986149i	$0.446959\pi$
$380$	0	0
$381$	35.2304	1.80491
$382$	28.1683	1.44122
$383$	−0.663150	−0.0338854	−0.0169427	−	0.999856i	$-0.505393\pi$
$383$	−0.663150	−0.0338854	−0.0169427	+	0.999856i	$0.505393\pi$
$384$	−6.33421	−0.323241
$385$	0	0
$386$	35.9379	1.82919
$387$	−26.6569	−1.35505
$388$	12.3464	0.626795
$389$	31.6296	1.60368	0.801841	−	0.597537i	$-0.203854\pi$
$389$	31.6296	1.60368	0.801841	+	0.597537i	$0.203854\pi$
$390$	0	0
$391$	18.9110	0.956371
$392$	0.278166	0.0140495
$393$	38.8052	1.95746
$394$	33.8191	1.70378
$395$	0	0
$396$	−3.66722	−0.184285
$397$	29.1694	1.46397	0.731986	−	0.681319i	$-0.238593\pi$
$397$	29.1694	1.46397	0.731986	+	0.681319i	$0.238593\pi$
$398$	−10.3988	−0.521247
$399$	0	0
$400$	0	0
$401$	14.5778	0.727981	0.363990	−	0.931403i	$-0.381414\pi$
$401$	14.5778	0.727981	0.363990	+	0.931403i	$0.381414\pi$
$402$	11.8366	0.590357
$403$	−4.56313	−0.227306
$404$	−9.64911	−0.480061
$405$	0	0
$406$	−7.01074	−0.347937
$407$	−0.213620	−0.0105888
$408$	−5.63124	−0.278788
$409$	25.9273	1.28202	0.641011	−	0.767532i	$-0.278515\pi$
$409$	25.9273	1.28202	0.641011	+	0.767532i	$0.278515\pi$
$410$	0	0
$411$	45.1051	2.22487
$412$	−11.0681	−0.545285
$413$	25.1438	1.23724
$414$	34.7491	1.70783
$415$	0	0
$416$	20.5194	1.00605
$417$	67.5702	3.30893
$418$	0	0
$419$	−19.1795	−0.936981	−0.468491	−	0.883468i	$-0.655202\pi$
$419$	−19.1795	−0.936981	−0.468491	+	0.883468i	$0.655202\pi$
$420$	0	0
$421$	2.77299	0.135147	0.0675736	−	0.997714i	$-0.478474\pi$
$421$	2.77299	0.135147	0.0675736	+	0.997714i	$0.478474\pi$
$422$	−43.9450	−2.13921
$423$	−19.5405	−0.950090
$424$	1.78576	0.0867242
$425$	0	0
$426$	−95.8483	−4.64386
$427$	−18.8539	−0.912403
$428$	6.98407	0.337588
$429$	−2.40389	−0.116061
$430$	0	0
$431$	−7.17556	−0.345634	−0.172817	−	0.984954i	$-0.555287\pi$
$431$	−7.17556	−0.345634	−0.172817	+	0.984954i	$0.555287\pi$
$432$	−47.7831	−2.29897
$433$	−23.4728	−1.12803	−0.564017	−	0.825763i	$-0.690745\pi$
$433$	−23.4728	−1.12803	−0.564017	+	0.825763i	$0.690745\pi$
$434$	−9.74876	−0.467956
$435$	0	0
$436$	16.2252	0.777046
$437$	0	0
$438$	−18.6474	−0.891008
$439$	13.7755	0.657468	0.328734	−	0.944423i	$-0.393378\pi$
$439$	13.7755	0.657468	0.328734	+	0.944423i	$0.393378\pi$
$440$	0	0
$441$	7.21163	0.343411
$442$	36.5617	1.73906
$443$	−1.10536	−0.0525173	−0.0262587	−	0.999655i	$-0.508359\pi$
$443$	−1.10536	−0.0525173	−0.0262587	+	0.999655i	$0.508359\pi$
$444$	4.19033	0.198864
$445$	0	0
$446$	16.7134	0.791402
$447$	52.5217	2.48419
$448$	19.7043	0.930942
$449$	−36.2183	−1.70925	−0.854624	−	0.519248i	$-0.826212\pi$
$449$	−36.2183	−1.70925	−0.854624	+	0.519248i	$0.826212\pi$
$450$	0	0
$451$	−2.98817	−0.140707
$452$	22.1727	1.04291
$453$	51.0535	2.39870
$454$	26.1245	1.22608
$455$	0	0
$456$	0	0
$457$	−40.3095	−1.88560	−0.942800	−	0.333358i	$-0.891818\pi$
$457$	−40.3095	−1.88560	−0.942800	+	0.333358i	$0.891818\pi$
$458$	31.0037	1.44871
$459$	−79.9243	−3.73055
$460$	0	0
$461$	−17.1122	−0.796993	−0.398497	−	0.917170i	$-0.630468\pi$
$461$	−17.1122	−0.796993	−0.398497	+	0.917170i	$0.630468\pi$
$462$	−5.13572	−0.238935
$463$	−9.09776	−0.422809	−0.211404	−	0.977399i	$-0.567804\pi$
$463$	−9.09776	−0.422809	−0.211404	+	0.977399i	$0.567804\pi$
$464$	5.31703	0.246837
$465$	0	0
$466$	−16.4874	−0.763762
$467$	−34.4216	−1.59284	−0.796420	−	0.604744i	$-0.793275\pi$
$467$	−34.4216	−1.59284	−0.796420	+	0.604744i	$0.793275\pi$
$468$	32.4631	1.50061
$469$	5.51435	0.254629
$470$	0	0
$471$	18.9072	0.871198
$472$	−2.26069	−0.104056
$473$	1.18956	0.0546961
$474$	−49.2471	−2.26199
$475$	0	0
$476$	37.7439	1.72999
$477$	46.2970	2.11979
$478$	−7.85621	−0.359335
$479$	28.4249	1.29877	0.649383	−	0.760461i	$-0.275027\pi$
$479$	28.4249	1.29877	0.649383	+	0.760461i	$0.275027\pi$
$480$	0	0
$481$	1.89102	0.0862229
$482$	−27.7448	−1.26374
$483$	23.5148	1.06996
$484$	−20.4066	−0.927572
$485$	0	0
$486$	−25.4591	−1.15485
$487$	−31.5734	−1.43073	−0.715363	−	0.698753i	$-0.753739\pi$
$487$	−31.5734	−1.43073	−0.715363	+	0.698753i	$0.753739\pi$
$488$	1.69516	0.0767363
$489$	15.4778	0.699929
$490$	0	0
$491$	2.94848	0.133063	0.0665316	−	0.997784i	$-0.478807\pi$
$491$	2.94848	0.133063	0.0665316	+	0.997784i	$0.478807\pi$
$492$	58.6153	2.64258
$493$	8.89351	0.400544
$494$	0	0
$495$	0	0
$496$	7.39359	0.331982
$497$	−44.6531	−2.00296
$498$	−84.5406	−3.78835
$499$	−1.21530	−0.0544041	−0.0272020	−	0.999630i	$-0.508660\pi$
$499$	−1.21530	−0.0544041	−0.0272020	+	0.999630i	$0.508660\pi$
$500$	0	0
$501$	−49.6415	−2.21782
$502$	−29.4228	−1.31321
$503$	33.5439	1.49565	0.747824	−	0.663897i	$-0.231098\pi$
$503$	33.5439	1.49565	0.747824	+	0.663897i	$0.231098\pi$
$504$	−4.82059	−0.214726
$505$	0	0
$506$	−1.55068	−0.0689361
$507$	−19.0603	−0.846498
$508$	21.2310	0.941973
$509$	−31.8382	−1.41120	−0.705602	−	0.708608i	$-0.749323\pi$
$509$	−31.8382	−1.41120	−0.705602	+	0.708608i	$0.749323\pi$
$510$	0	0
$511$	−8.68732	−0.384304
$512$	−31.0775	−1.37345
$513$	0	0
$514$	17.0115	0.750346
$515$	0	0
$516$	−23.3342	−1.02723
$517$	0.871992	0.0383502
$518$	4.04001	0.177508
$519$	−5.87010	−0.257669
$520$	0	0
$521$	34.6420	1.51769	0.758846	−	0.651270i	$-0.225763\pi$
$521$	34.6420	1.51769	0.758846	+	0.651270i	$0.225763\pi$
$522$	16.3419	0.715266
$523$	31.4309	1.37438	0.687188	−	0.726480i	$-0.258845\pi$
$523$	31.4309	1.37438	0.687188	+	0.726480i	$0.258845\pi$
$524$	23.3853	1.02159
$525$	0	0
$526$	−30.2275	−1.31798
$527$	12.3669	0.538709
$528$	3.89499	0.169508
$529$	−15.8999	−0.691302
$530$	0	0
$531$	−58.6097	−2.54344
$532$	0	0
$533$	26.4520	1.14576
$534$	−3.36514	−0.145624
$535$	0	0
$536$	−0.495797	−0.0214152
$537$	5.99896	0.258874
$538$	−32.5856	−1.40487
$539$	−0.321819	−0.0138617
$540$	0	0
$541$	−39.3709	−1.69269	−0.846344	−	0.532636i	$-0.821202\pi$
$541$	−39.3709	−1.69269	−0.846344	+	0.532636i	$0.821202\pi$
$542$	−13.2196	−0.567832
$543$	−9.16680	−0.393385
$544$	−55.6112	−2.38431
$545$	0	0
$546$	45.4626	1.94562
$547$	−2.76298	−0.118136	−0.0590682	−	0.998254i	$-0.518813\pi$
$547$	−2.76298	−0.118136	−0.0590682	+	0.998254i	$0.518813\pi$
$548$	27.1819	1.16115
$549$	43.9481	1.87566
$550$	0	0
$551$	0	0
$552$	−2.11423	−0.0899875
$553$	−22.9429	−0.975630
$554$	15.1774	0.644824
$555$	0	0
$556$	40.7201	1.72692
$557$	−5.58153	−0.236497	−0.118249	−	0.992984i	$-0.537728\pi$
$557$	−5.58153	−0.236497	−0.118249	+	0.992984i	$0.537728\pi$
$558$	22.7242	0.961992
$559$	−10.5303	−0.445383
$560$	0	0
$561$	6.51495	0.275061
$562$	27.0640	1.14163
$563$	24.0365	1.01302	0.506509	−	0.862235i	$-0.330936\pi$
$563$	24.0365	1.01302	0.506509	+	0.862235i	$0.330936\pi$
$564$	−17.1048	−0.720243
$565$	0	0
$566$	32.6519	1.37246
$567$	−42.8235	−1.79842
$568$	4.01477	0.168456
$569$	4.92199	0.206340	0.103170	−	0.994664i	$-0.467101\pi$
$569$	4.92199	0.206340	0.103170	+	0.994664i	$0.467101\pi$
$570$	0	0
$571$	−31.4861	−1.31765	−0.658826	−	0.752295i	$-0.728947\pi$
$571$	−31.4861	−1.31765	−0.658826	+	0.752295i	$0.728947\pi$
$572$	−1.44866	−0.0605717
$573$	−44.4322	−1.85618
$574$	56.5125	2.35879
$575$	0	0
$576$	−45.9304	−1.91377
$577$	29.2520	1.21778	0.608888	−	0.793256i	$-0.291616\pi$
$577$	29.2520	1.21778	0.608888	+	0.793256i	$0.291616\pi$
$578$	−65.6455	−2.73049
$579$	−56.6878	−2.35586
$580$	0	0
$581$	−39.3851	−1.63397
$582$	−40.3037	−1.67064
$583$	−2.06600	−0.0855650
$584$	0.781080	0.0323213
$585$	0	0
$586$	14.5544	0.601236
$587$	−24.0082	−0.990924	−0.495462	−	0.868630i	$-0.665001\pi$
$587$	−24.0082	−0.990924	−0.495462	+	0.868630i	$0.665001\pi$
$588$	6.31273	0.260333
$589$	0	0
$590$	0	0
$591$	−53.3456	−2.19435
$592$	−3.06399	−0.125929
$593$	1.68162	0.0690558	0.0345279	−	0.999404i	$-0.489007\pi$
$593$	1.68162	0.0690558	0.0345279	+	0.999404i	$0.489007\pi$
$594$	6.55369	0.268901
$595$	0	0
$596$	31.6513	1.29649
$597$	16.4029	0.671327
$598$	13.7270	0.561337
$599$	−42.2900	−1.72792	−0.863960	−	0.503560i	$-0.832023\pi$
$599$	−42.2900	−1.72792	−0.863960	+	0.503560i	$0.832023\pi$
$600$	0	0
$601$	26.9576	1.09962	0.549811	−	0.835289i	$-0.314700\pi$
$601$	26.9576	1.09962	0.549811	+	0.835289i	$0.314700\pi$
$602$	−22.4971	−0.916914
$603$	−12.8539	−0.523450
$604$	30.7666	1.25187
$605$	0	0
$606$	31.4986	1.27954
$607$	−11.0115	−0.446944	−0.223472	−	0.974710i	$-0.571739\pi$
$607$	−11.0115	−0.446944	−0.223472	+	0.974710i	$0.571739\pi$
$608$	0	0
$609$	11.0586	0.448117
$610$	0	0
$611$	−7.71908	−0.312280
$612$	−87.9805	−3.55640
$613$	3.32175	0.134164	0.0670822	−	0.997747i	$-0.478631\pi$
$613$	3.32175	0.134164	0.0670822	+	0.997747i	$0.478631\pi$
$614$	27.3219	1.10262
$615$	0	0
$616$	0.215119	0.00866738
$617$	11.0613	0.445311	0.222655	−	0.974897i	$-0.428528\pi$
$617$	11.0613	0.445311	0.222655	+	0.974897i	$0.428528\pi$
$618$	36.1307	1.45339
$619$	36.2777	1.45812	0.729062	−	0.684448i	$-0.239957\pi$
$619$	36.2777	1.45812	0.729062	+	0.684448i	$0.239957\pi$
$620$	0	0
$621$	−30.0073	−1.20415
$622$	−51.9844	−2.08438
$623$	−1.56773	−0.0628096
$624$	−34.4794	−1.38028
$625$	0	0
$626$	13.5975	0.543465
$627$	0	0
$628$	11.3941	0.454674
$629$	−5.12498	−0.204346
$630$	0	0
$631$	−1.73816	−0.0691950	−0.0345975	−	0.999401i	$-0.511015\pi$
$631$	−1.73816	−0.0691950	−0.0345975	+	0.999401i	$0.511015\pi$
$632$	2.06280	0.0820538
$633$	69.3181	2.75515
$634$	−56.5275	−2.24499
$635$	0	0
$636$	40.5262	1.60697
$637$	2.84881	0.112874
$638$	−0.729257	−0.0288716
$639$	104.086	4.11756
$640$	0	0
$641$	36.2439	1.43155	0.715774	−	0.698332i	$-0.246074\pi$
$641$	36.2439	1.43155	0.715774	+	0.698332i	$0.246074\pi$
$642$	−22.7988	−0.899798
$643$	−31.8707	−1.25686	−0.628429	−	0.777867i	$-0.716302\pi$
$643$	−31.8707	−1.25686	−0.628429	+	0.777867i	$0.716302\pi$
$644$	14.1708	0.558408
$645$	0	0
$646$	0	0
$647$	21.1503	0.831504	0.415752	−	0.909478i	$-0.363518\pi$
$647$	21.1503	0.831504	0.415752	+	0.909478i	$0.363518\pi$
$648$	3.85028	0.151253
$649$	2.61545	0.102666
$650$	0	0
$651$	15.3775	0.602692
$652$	9.32743	0.365290
$653$	−18.0859	−0.707758	−0.353879	−	0.935291i	$-0.615137\pi$
$653$	−18.0859	−0.707758	−0.353879	+	0.935291i	$0.615137\pi$
$654$	−52.9655	−2.07112
$655$	0	0
$656$	−42.8598	−1.67340
$657$	20.2500	0.790027
$658$	−16.4912	−0.642894
$659$	11.0391	0.430024	0.215012	−	0.976611i	$-0.431021\pi$
$659$	11.0391	0.430024	0.215012	+	0.976611i	$0.431021\pi$
$660$	0	0
$661$	−14.9040	−0.579698	−0.289849	−	0.957072i	$-0.593605\pi$
$661$	−14.9040	−0.579698	−0.289849	+	0.957072i	$0.593605\pi$
$662$	16.0024	0.621951
$663$	−57.6718	−2.23979
$664$	3.54113	0.137423
$665$	0	0
$666$	−9.41719	−0.364909
$667$	3.33904	0.129288
$668$	−29.9156	−1.15747
$669$	−26.3634	−1.01927
$670$	0	0
$671$	−1.96118	−0.0757105
$672$	−69.1495	−2.66750
$673$	−1.42988	−0.0551178	−0.0275589	−	0.999620i	$-0.508773\pi$
$673$	−1.42988	−0.0551178	−0.0275589	+	0.999620i	$0.508773\pi$
$674$	13.3056	0.512513
$675$	0	0
$676$	−11.4864	−0.441784
$677$	4.76323	0.183066	0.0915330	−	0.995802i	$-0.470823\pi$
$677$	4.76323	0.183066	0.0915330	+	0.995802i	$0.470823\pi$
$678$	−72.3804	−2.77975
$679$	−18.7764	−0.720571
$680$	0	0
$681$	−41.2083	−1.57911
$682$	−1.01407	−0.0388306
$683$	44.7585	1.71264	0.856318	−	0.516450i	$-0.172747\pi$
$683$	44.7585	1.71264	0.856318	+	0.516450i	$0.172747\pi$
$684$	0	0
$685$	0	0
$686$	−33.0764	−1.26286
$687$	−48.9046	−1.86583
$688$	17.0621	0.650486
$689$	18.2887	0.696744
$690$	0	0
$691$	−19.5587	−0.744046	−0.372023	−	0.928223i	$-0.621336\pi$
$691$	−19.5587	−0.744046	−0.372023	+	0.928223i	$0.621336\pi$
$692$	−3.53752	−0.134476
$693$	5.57709	0.211856
$694$	−30.6580	−1.16376
$695$	0	0
$696$	−0.994283	−0.0376882
$697$	−71.6893	−2.71543
$698$	−11.4102	−0.431882
$699$	26.0069	0.983670
$700$	0	0
$701$	37.2131	1.40552	0.702760	−	0.711427i	$-0.251951\pi$
$701$	37.2131	1.40552	0.702760	+	0.711427i	$0.251951\pi$
$702$	−58.0148	−2.18963
$703$	0	0
$704$	2.04964	0.0772489
$705$	0	0
$706$	62.4992	2.35219
$707$	14.6743	0.551884
$708$	−51.3042	−1.92813
$709$	−42.2853	−1.58806	−0.794030	−	0.607879i	$-0.792021\pi$
$709$	−42.2853	−1.58806	−0.794030	+	0.607879i	$0.792021\pi$
$710$	0	0
$711$	53.4794	2.00563
$712$	0.140955	0.00528251
$713$	4.64309	0.173885
$714$	−123.211	−4.61107
$715$	0	0
$716$	3.61517	0.135105
$717$	12.3922	0.462797
$718$	−25.6244	−0.956295
$719$	28.1334	1.04920	0.524600	−	0.851349i	$-0.324215\pi$
$719$	28.1334	1.04920	0.524600	+	0.851349i	$0.324215\pi$
$720$	0	0
$721$	16.8323	0.626867
$722$	0	0
$723$	43.7642	1.62761
$724$	−5.52422	−0.205306
$725$	0	0
$726$	66.6153	2.47233
$727$	10.3337	0.383254	0.191627	−	0.981468i	$-0.438624\pi$
$727$	10.3337	0.383254	0.191627	+	0.981468i	$0.438624\pi$
$728$	−1.90428	−0.0705773
$729$	−5.01504	−0.185742
$730$	0	0
$731$	28.5389	1.05555
$732$	38.4701	1.42190
$733$	0.823810	0.0304281	0.0152141	−	0.999884i	$-0.495157\pi$
$733$	0.823810	0.0304281	0.0152141	+	0.999884i	$0.495157\pi$
$734$	−23.5966	−0.870967
$735$	0	0
$736$	−20.8790	−0.769610
$737$	0.573603	0.0211289
$738$	−131.730	−4.84904
$739$	34.6161	1.27337	0.636687	−	0.771122i	$-0.280304\pi$
$739$	34.6161	1.27337	0.636687	+	0.771122i	$0.280304\pi$
$740$	0	0
$741$	0	0
$742$	39.0724	1.43439
$743$	33.8604	1.24222	0.621109	−	0.783724i	$-0.286683\pi$
$743$	33.8604	1.24222	0.621109	+	0.783724i	$0.286683\pi$
$744$	−1.38260	−0.0506885
$745$	0	0
$746$	51.2024	1.87465
$747$	91.8060	3.35901
$748$	3.92613	0.143553
$749$	−10.6213	−0.388095
$750$	0	0
$751$	17.8196	0.650247	0.325124	−	0.945672i	$-0.394594\pi$
$751$	17.8196	0.650247	0.325124	+	0.945672i	$0.394594\pi$
$752$	12.5071	0.456089
$753$	46.4110	1.69131
$754$	6.45555	0.235097
$755$	0	0
$756$	−59.8907	−2.17820
$757$	−1.70824	−0.0620870	−0.0310435	−	0.999518i	$-0.509883\pi$
$757$	−1.70824	−0.0620870	−0.0310435	+	0.999518i	$0.509883\pi$
$758$	−12.7044	−0.461445
$759$	2.44601	0.0887846
$760$	0	0
$761$	2.70054	0.0978944	0.0489472	−	0.998801i	$-0.484413\pi$
$761$	2.70054	0.0978944	0.0489472	+	0.998801i	$0.484413\pi$
$762$	−69.3065	−2.51071
$763$	−24.6752	−0.893302
$764$	−26.7763	−0.968734
$765$	0	0
$766$	1.30457	0.0471362
$767$	−23.1526	−0.835992
$768$	55.4608	2.00127
$769$	25.2710	0.911296	0.455648	−	0.890160i	$-0.349408\pi$
$769$	25.2710	0.911296	0.455648	+	0.890160i	$0.349408\pi$
$770$	0	0
$771$	−26.8337	−0.966391
$772$	−34.1620	−1.22952
$773$	−44.9679	−1.61738	−0.808692	−	0.588233i	$-0.799824\pi$
$773$	−44.9679	−1.61738	−0.808692	+	0.588233i	$0.799824\pi$
$774$	52.4404	1.88493
$775$	0	0
$776$	1.68819	0.0606025
$777$	−6.37263	−0.228617
$778$	−62.2228	−2.23080
$779$	0	0
$780$	0	0
$781$	−4.64481	−0.166204
$782$	−37.2024	−1.33036
$783$	−14.1119	−0.504318
$784$	−4.61590	−0.164854
$785$	0	0
$786$	−76.3390	−2.72292
$787$	2.87342	0.102426	0.0512132	−	0.998688i	$-0.483691\pi$
$787$	2.87342	0.102426	0.0512132	+	0.998688i	$0.483691\pi$
$788$	−32.1479	−1.14522
$789$	47.6803	1.69747
$790$	0	0
$791$	−33.7200	−1.19895
$792$	−0.501438	−0.0178178
$793$	17.3608	0.616501
$794$	−57.3832	−2.03645
$795$	0	0
$796$	9.88496	0.350363
$797$	35.2445	1.24842	0.624212	−	0.781255i	$-0.285420\pi$
$797$	35.2445	1.24842	0.624212	+	0.781255i	$0.285420\pi$
$798$	0	0
$799$	20.9200	0.740097
$800$	0	0
$801$	3.65434	0.129120
$802$	−28.6780	−1.01266
$803$	−0.903655	−0.0318893
$804$	−11.2517	−0.396816
$805$	0	0
$806$	8.97675	0.316193
$807$	51.3999	1.80936
$808$	−1.31937	−0.0464154
$809$	−19.6395	−0.690487	−0.345243	−	0.938513i	$-0.612204\pi$
$809$	−19.6395	−0.690487	−0.345243	+	0.938513i	$0.612204\pi$
$810$	0	0
$811$	−28.6430	−1.00579	−0.502897	−	0.864347i	$-0.667732\pi$
$811$	−28.6430	−1.00579	−0.502897	+	0.864347i	$0.667732\pi$
$812$	6.66429	0.233871
$813$	20.8524	0.731326
$814$	0.420242	0.0147295
$815$	0	0
$816$	93.4450	3.27123
$817$	0	0
$818$	−51.0051	−1.78335
$819$	−49.3696	−1.72512
$820$	0	0
$821$	−23.4218	−0.817427	−0.408714	−	0.912663i	$-0.634022\pi$
$821$	−23.4218	−0.817427	−0.408714	+	0.912663i	$0.634022\pi$
$822$	−88.7325	−3.09490
$823$	8.33962	0.290701	0.145350	−	0.989380i	$-0.453569\pi$
$823$	8.33962	0.290701	0.145350	+	0.989380i	$0.453569\pi$
$824$	−1.51340	−0.0527217
$825$	0	0
$826$	−49.4637	−1.72106
$827$	−5.86827	−0.204060	−0.102030	−	0.994781i	$-0.532534\pi$
$827$	−5.86827	−0.204060	−0.102030	+	0.994781i	$0.532534\pi$
$828$	−33.0319	−1.14794
$829$	−12.1421	−0.421713	−0.210857	−	0.977517i	$-0.567625\pi$
$829$	−12.1421	−0.421713	−0.210857	+	0.977517i	$0.567625\pi$
$830$	0	0
$831$	−23.9405	−0.830486
$832$	−18.1439	−0.629027
$833$	−7.72077	−0.267509
$834$	−132.927	−4.60287
$835$	0	0
$836$	0	0
$837$	−19.6233	−0.678279
$838$	37.7307	1.30338
$839$	44.6011	1.53980	0.769900	−	0.638164i	$-0.220306\pi$
$839$	44.6011	1.53980	0.769900	+	0.638164i	$0.220306\pi$
$840$	0	0
$841$	−27.4297	−0.945852
$842$	−5.45512	−0.187996
$843$	−42.6903	−1.47033
$844$	41.7734	1.43790
$845$	0	0
$846$	38.4407	1.32162
$847$	31.0342	1.06635
$848$	−29.6330	−1.01760
$849$	−51.5045	−1.76763
$850$	0	0
$851$	−1.92415	−0.0659591
$852$	91.1117	3.12144
$853$	11.5477	0.395385	0.197693	−	0.980264i	$-0.436655\pi$
$853$	11.5477	0.395385	0.197693	+	0.980264i	$0.436655\pi$
$854$	37.0900	1.26920
$855$	0	0
$856$	0.954969	0.0326402
$857$	3.31493	0.113236	0.0566179	−	0.998396i	$-0.481968\pi$
$857$	3.31493	0.113236	0.0566179	+	0.998396i	$0.481968\pi$
$858$	4.72902	0.161446
$859$	−45.1590	−1.54080	−0.770402	−	0.637558i	$-0.779945\pi$
$859$	−45.1590	−1.54080	−0.770402	+	0.637558i	$0.779945\pi$
$860$	0	0
$861$	−89.1418	−3.03795
$862$	14.1160	0.480794
$863$	33.7618	1.14927	0.574633	−	0.818411i	$-0.305145\pi$
$863$	33.7618	1.14927	0.574633	+	0.818411i	$0.305145\pi$
$864$	88.2417	3.00204
$865$	0	0
$866$	46.1767	1.56915
$867$	103.548	3.51668
$868$	9.26701	0.314543
$869$	−2.38652	−0.0809570
$870$	0	0
$871$	−5.07766	−0.172050
$872$	2.21856	0.0751298
$873$	43.7674	1.48130
$874$	0	0
$875$	0	0
$876$	17.7259	0.598903
$877$	46.9447	1.58521	0.792604	−	0.609736i	$-0.208725\pi$
$877$	46.9447	1.58521	0.792604	+	0.609736i	$0.208725\pi$
$878$	−27.0996	−0.914568
$879$	−22.9578	−0.774348
$880$	0	0
$881$	−16.2541	−0.547613	−0.273807	−	0.961785i	$-0.588283\pi$
$881$	−16.2541	−0.547613	−0.273807	+	0.961785i	$0.588283\pi$
$882$	−14.1870	−0.477700
$883$	−34.0553	−1.14605	−0.573027	−	0.819537i	$-0.694231\pi$
$883$	−34.0553	−1.14605	−0.573027	+	0.819537i	$0.694231\pi$
$884$	−34.7550	−1.16894
$885$	0	0
$886$	2.17451	0.0730540
$887$	0.285914	0.00960005	0.00480002	−	0.999988i	$-0.498472\pi$
$887$	0.285914	0.00960005	0.00480002	+	0.999988i	$0.498472\pi$
$888$	0.572966	0.0192275
$889$	−32.2880	−1.08290
$890$	0	0
$891$	−4.45450	−0.149231
$892$	−15.8875	−0.531952
$893$	0	0
$894$	−103.323	−3.45563
$895$	0	0
$896$	5.80518	0.193938
$897$	−21.6527	−0.722961
$898$	71.2500	2.37764
$899$	2.18356	0.0728259
$900$	0	0
$901$	−49.5655	−1.65127
$902$	5.87844	0.195731
$903$	35.4865	1.18092
$904$	3.03178	0.100836
$905$	0	0
$906$	−100.434	−3.33671
$907$	−51.7442	−1.71814	−0.859068	−	0.511861i	$-0.828956\pi$
$907$	−51.7442	−1.71814	−0.859068	+	0.511861i	$0.828956\pi$
$908$	−24.8335	−0.824129
$909$	−34.2056	−1.13453
$910$	0	0
$911$	−21.7331	−0.720050	−0.360025	−	0.932943i	$-0.617232\pi$
$911$	−21.7331	−0.720050	−0.360025	+	0.932943i	$0.617232\pi$
$912$	0	0
$913$	−4.09684	−0.135586
$914$	79.2984	2.62296
$915$	0	0
$916$	−29.4716	−0.973768
$917$	−35.5642	−1.17443
$918$	157.230	5.18936
$919$	26.3182	0.868158	0.434079	−	0.900875i	$-0.357074\pi$
$919$	26.3182	0.868158	0.434079	+	0.900875i	$0.357074\pi$
$920$	0	0
$921$	−43.0970	−1.42009
$922$	33.6637	1.10865
$923$	41.1170	1.35338
$924$	4.88193	0.160604
$925$	0	0
$926$	17.8974	0.588147
$927$	−39.2357	−1.28867
$928$	−9.81903	−0.322325
$929$	−23.0700	−0.756901	−0.378451	−	0.925622i	$-0.623543\pi$
$929$	−23.0700	−0.756901	−0.378451	+	0.925622i	$0.623543\pi$
$930$	0	0
$931$	0	0
$932$	15.6726	0.513373
$933$	81.9992	2.68453
$934$	67.7154	2.21571
$935$	0	0
$936$	4.43884	0.145088
$937$	−40.8628	−1.33493	−0.667465	−	0.744641i	$-0.732621\pi$
$937$	−40.8628	−1.33493	−0.667465	+	0.744641i	$0.732621\pi$
$938$	−10.8480	−0.354201
$939$	−21.4484	−0.699943
$940$	0	0
$941$	49.2781	1.60642	0.803210	−	0.595695i	$-0.203123\pi$
$941$	49.2781	1.60642	0.803210	+	0.595695i	$0.203123\pi$
$942$	−37.1949	−1.21188
$943$	−26.9155	−0.876489
$944$	37.5139	1.22097
$945$	0	0
$946$	−2.34015	−0.0760849
$947$	14.4062	0.468140	0.234070	−	0.972220i	$-0.424796\pi$
$947$	14.4062	0.468140	0.234070	+	0.972220i	$0.424796\pi$
$948$	46.8134	1.52043
$949$	7.99936	0.259670
$950$	0	0
$951$	89.1654	2.89139
$952$	5.16092	0.167267
$953$	46.6902	1.51244	0.756222	−	0.654316i	$-0.227043\pi$
$953$	46.6902	1.51244	0.756222	+	0.654316i	$0.227043\pi$
$954$	−91.0771	−2.94873
$955$	0	0
$956$	7.46798	0.241532
$957$	1.15032	0.0371844
$958$	−55.9185	−1.80664
$959$	−41.3380	−1.33487
$960$	0	0
$961$	−27.9637	−0.902053
$962$	−3.72008	−0.119940
$963$	24.7582	0.797821
$964$	26.3738	0.849441
$965$	0	0
$966$	−46.2592	−1.48837
$967$	−15.6605	−0.503609	−0.251804	−	0.967778i	$-0.581024\pi$
$967$	−15.6605	−0.503609	−0.251804	+	0.967778i	$0.581024\pi$
$968$	−2.79030	−0.0896836
$969$	0	0
$970$	0	0
$971$	44.2514	1.42009	0.710047	−	0.704154i	$-0.248673\pi$
$971$	44.2514	1.42009	0.710047	+	0.704154i	$0.248673\pi$
$972$	24.2010	0.776247
$973$	−61.9268	−1.98528
$974$	62.1123	1.99021
$975$	0	0
$976$	−28.1296	−0.900405
$977$	−38.3791	−1.22786	−0.613928	−	0.789362i	$-0.710412\pi$
$977$	−38.3791	−1.22786	−0.613928	+	0.789362i	$0.710412\pi$
$978$	−30.4485	−0.973634
$979$	−0.163075	−0.00521190
$980$	0	0
$981$	57.5174	1.83639
$982$	−5.80036	−0.185097
$983$	28.0361	0.894213	0.447107	−	0.894481i	$-0.352454\pi$
$983$	28.0361	0.894213	0.447107	+	0.894481i	$0.352454\pi$
$984$	8.01478	0.255502
$985$	0	0
$986$	−17.4956	−0.557175
$987$	26.0129	0.828001
$988$	0	0
$989$	10.7148	0.340711
$990$	0	0
$991$	27.0434	0.859062	0.429531	−	0.903052i	$-0.358679\pi$
$991$	27.0434	0.859062	0.429531	+	0.903052i	$0.358679\pi$
$992$	−13.6538	−0.433509
$993$	−25.2419	−0.801027
$994$	87.8432	2.78622
$995$	0	0
$996$	80.3628	2.54639
$997$	−34.5872	−1.09539	−0.547694	−	0.836679i	$-0.684494\pi$
$997$	−34.5872	−1.09539	−0.547694	+	0.836679i	$0.684494\pi$
$998$	2.39077	0.0756786
$999$	8.13212	0.257289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cv.1.7		40
5.2	odd	4		1805.2.b.m.1084.8	yes	40
5.3	odd	4		1805.2.b.m.1084.33	yes	40
5.4	even	2	inner	9025.2.a.cv.1.34		40
19.18	odd	2	inner	9025.2.a.cv.1.33		40
95.18	even	4		1805.2.b.m.1084.7	✓	40
95.37	even	4		1805.2.b.m.1084.34	yes	40
95.94	odd	2	inner	9025.2.a.cv.1.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.7	✓	40	95.18	even	4
1805.2.b.m.1084.8	yes	40	5.2	odd	4
1805.2.b.m.1084.33	yes	40	5.3	odd	4
1805.2.b.m.1084.34	yes	40	95.37	even	4
9025.2.a.cv.1.7		40	1.1	even	1	trivial
9025.2.a.cv.1.8		40	95.94	odd	2	inner
9025.2.a.cv.1.33		40	19.18	odd	2	inner
9025.2.a.cv.1.34		40	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.96724 q^{2} +3.10308 q^{3} +1.87002 q^{4} -6.10450 q^{6} -2.84392 q^{7} +0.255698 q^{8} +6.62912 q^{9} +O(q^{10})\)	\(q-1.96724 q^{2} +3.10308 q^{3} +1.87002 q^{4} -6.10450 q^{6} -2.84392 q^{7} +0.255698 q^{8} +6.62912 q^{9} -0.295824 q^{11} +5.80283 q^{12} +2.61871 q^{13} +5.59466 q^{14} -4.24306 q^{16} -7.09714 q^{17} -13.0411 q^{18} -8.82491 q^{21} +0.581957 q^{22} -2.66459 q^{23} +0.793451 q^{24} -5.15162 q^{26} +11.2615 q^{27} -5.31819 q^{28} -1.25311 q^{29} -1.74251 q^{31} +7.83571 q^{32} -0.917968 q^{33} +13.9618 q^{34} +12.3966 q^{36} +0.722118 q^{37} +8.12606 q^{39} +10.1012 q^{41} +17.3607 q^{42} -4.02118 q^{43} -0.553198 q^{44} +5.24189 q^{46} -2.94767 q^{47} -13.1666 q^{48} +1.08787 q^{49} -22.0230 q^{51} +4.89704 q^{52} +6.98387 q^{53} -22.1540 q^{54} -0.727184 q^{56} +2.46517 q^{58} -8.84124 q^{59} +6.62954 q^{61} +3.42793 q^{62} -18.8527 q^{63} -6.92858 q^{64} +1.80586 q^{66} -1.93900 q^{67} -13.2718 q^{68} -8.26846 q^{69} +15.7012 q^{71} +1.69505 q^{72} +3.05470 q^{73} -1.42058 q^{74} +0.841300 q^{77} -15.9859 q^{78} +8.06734 q^{79} +15.0579 q^{81} -19.8714 q^{82} +13.8489 q^{83} -16.5028 q^{84} +7.91061 q^{86} -3.88851 q^{87} -0.0756416 q^{88} +0.551256 q^{89} -7.44739 q^{91} -4.98285 q^{92} -5.40716 q^{93} +5.79876 q^{94} +24.3149 q^{96} +6.60229 q^{97} -2.14010 q^{98} -1.96106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9}+O(q^{10}) \) 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9	\( 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9} + 20 q^{11} + 40 q^{16} + 92 q^{24} + 76 q^{26} + 156 q^{36} + 80 q^{39} + 48 q^{44} + 72 q^{49} + 32 q^{54} + 80 q^{61} + 72 q^{64} + 16 q^{66} + 100 q^{74} + 40 q^{81} + 380 q^{96} + 128 q^{99}+O(q^{100}) \) 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9 + 20 * q^11 + 40 * q^16 + 92 * q^24 + 76 * q^26 + 156 * q^36 + 80 * q^39 + 48 * q^44 + 72 * q^49 + 32 * q^54 + 80 * q^61 + 72 * q^64 + 16 * q^66 + 100 * q^74 + 40 * q^81 + 380 * q^96 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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