LMFDB - Embedded newform 9025.2.a.cr.1.14

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:	$21$
Twist minimal:	no (minimal twist has level 475)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q+1.27496 q^{2} +0.195863 q^{3} -0.374490 q^{4} +0.249717 q^{6} -1.39855 q^{7} -3.02737 q^{8} -2.96164 q^{9} +O(q^{10})$	\(q+1.27496 q^{2} +0.195863 q^{3} -0.374490 q^{4} +0.249717 q^{6} -1.39855 q^{7} -3.02737 q^{8} -2.96164 q^{9} -5.82492 q^{11} -0.0733487 q^{12} -6.90017 q^{13} -1.78309 q^{14} -3.11078 q^{16} -5.19508 q^{17} -3.77595 q^{18} -0.273924 q^{21} -7.42651 q^{22} +3.60392 q^{23} -0.592949 q^{24} -8.79741 q^{26} -1.16766 q^{27} +0.523743 q^{28} +5.27624 q^{29} -2.26297 q^{31} +2.08863 q^{32} -1.14089 q^{33} -6.62350 q^{34} +1.10910 q^{36} -0.979100 q^{37} -1.35149 q^{39} -10.0415 q^{41} -0.349241 q^{42} +7.90021 q^{43} +2.18137 q^{44} +4.59483 q^{46} -8.02867 q^{47} -0.609286 q^{48} -5.04406 q^{49} -1.01752 q^{51} +2.58404 q^{52} +6.54927 q^{53} -1.48872 q^{54} +4.23393 q^{56} +6.72697 q^{58} -7.91530 q^{59} +5.35586 q^{61} -2.88519 q^{62} +4.14200 q^{63} +8.88447 q^{64} -1.45458 q^{66} -9.53168 q^{67} +1.94551 q^{68} +0.705874 q^{69} +4.72405 q^{71} +8.96597 q^{72} -3.60944 q^{73} -1.24831 q^{74} +8.14645 q^{77} -1.72309 q^{78} -9.34009 q^{79} +8.65621 q^{81} -12.8024 q^{82} +0.621535 q^{83} +0.102582 q^{84} +10.0724 q^{86} +1.03342 q^{87} +17.6342 q^{88} +8.89254 q^{89} +9.65024 q^{91} -1.34963 q^{92} -0.443233 q^{93} -10.2362 q^{94} +0.409086 q^{96} -4.82792 q^{97} -6.43094 q^{98} +17.2513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{2} + 9 q^{3} + 24 q^{4} + 18 q^{8} + 24 q^{9}+O(q^{10}) $ 21 * q + 6 * q^2 + 9 * q^3 + 24 * q^4 + 18 * q^8 + 24 * q^9	$ 21 q + 6 q^{2} + 9 q^{3} + 24 q^{4} + 18 q^{8} + 24 q^{9} + 24 q^{12} + 12 q^{13} - 6 q^{14} + 30 q^{16} - 9 q^{17} + 18 q^{18} + 12 q^{22} - 6 q^{23} + 18 q^{24} + 18 q^{26} + 30 q^{27} - 15 q^{28} - 3 q^{29} - 6 q^{31} + 57 q^{32} + 45 q^{33} - 3 q^{34} + 60 q^{36} + 24 q^{37} - 30 q^{39} + 12 q^{41} + 18 q^{42} + 18 q^{43} + 24 q^{44} - 15 q^{46} + 18 q^{47} + 84 q^{48} + 33 q^{49} - 12 q^{51} + 36 q^{52} + 42 q^{53} - 18 q^{56} + 12 q^{58} + 6 q^{59} - 36 q^{61} - 3 q^{62} - 6 q^{63} - 21 q^{66} + 24 q^{67} - 78 q^{68} + 15 q^{69} + 12 q^{71} + 87 q^{72} + 18 q^{73} - 45 q^{74} - 9 q^{77} - 60 q^{78} + 3 q^{79} + 21 q^{81} + 42 q^{82} + 36 q^{84} + 30 q^{86} - 6 q^{87} + 60 q^{88} + 3 q^{89} - 3 q^{91} + 60 q^{92} + 12 q^{93} + 18 q^{94} + 111 q^{96} + 12 q^{97} + 105 q^{98} + 84 q^{99}+O(q^{100}) $ 21 * q + 6 * q^2 + 9 * q^3 + 24 * q^4 + 18 * q^8 + 24 * q^9 + 24 * q^12 + 12 * q^13 - 6 * q^14 + 30 * q^16 - 9 * q^17 + 18 * q^18 + 12 * q^22 - 6 * q^23 + 18 * q^24 + 18 * q^26 + 30 * q^27 - 15 * q^28 - 3 * q^29 - 6 * q^31 + 57 * q^32 + 45 * q^33 - 3 * q^34 + 60 * q^36 + 24 * q^37 - 30 * q^39 + 12 * q^41 + 18 * q^42 + 18 * q^43 + 24 * q^44 - 15 * q^46 + 18 * q^47 + 84 * q^48 + 33 * q^49 - 12 * q^51 + 36 * q^52 + 42 * q^53 - 18 * q^56 + 12 * q^58 + 6 * q^59 - 36 * q^61 - 3 * q^62 - 6 * q^63 - 21 * q^66 + 24 * q^67 - 78 * q^68 + 15 * q^69 + 12 * q^71 + 87 * q^72 + 18 * q^73 - 45 * q^74 - 9 * q^77 - 60 * q^78 + 3 * q^79 + 21 * q^81 + 42 * q^82 + 36 * q^84 + 30 * q^86 - 6 * q^87 + 60 * q^88 + 3 * q^89 - 3 * q^91 + 60 * q^92 + 12 * q^93 + 18 * q^94 + 111 * q^96 + 12 * q^97 + 105 * q^98 + 84 * 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 $

$2$	1.27496	0.901529	0.450765	−	0.892643i	$-0.351151\pi$
$2$	1.27496	0.901529	0.450765	+	0.892643i	$0.351151\pi$
$3$	0.195863	0.113082	0.0565408	−	0.998400i	$-0.481993\pi$
$3$	0.195863	0.113082	0.0565408	+	0.998400i	$0.481993\pi$
$4$	−0.374490	−0.187245
$5$	0	0
$5$	0	0
$6$	0.249717	0.101946
$7$	−1.39855	−0.528602	−0.264301	−	0.964440i	$-0.585141\pi$
$7$	−1.39855	−0.528602	−0.264301	+	0.964440i	$0.585141\pi$
$8$	−3.02737	−1.07034
$9$	−2.96164	−0.987213
$10$	0	0
$11$	−5.82492	−1.75628	−0.878140	−	0.478404i	$-0.841215\pi$
$11$	−5.82492	−1.75628	−0.878140	+	0.478404i	$0.841215\pi$
$12$	−0.0733487	−0.0211739
$13$	−6.90017	−1.91376	−0.956881	−	0.290479i	$-0.906185\pi$
$13$	−6.90017	−1.91376	−0.956881	+	0.290479i	$0.906185\pi$
$14$	−1.78309	−0.476551
$15$	0	0
$16$	−3.11078	−0.777695
$17$	−5.19508	−1.25999	−0.629997	−	0.776598i	$-0.716944\pi$
$17$	−5.19508	−1.25999	−0.629997	+	0.776598i	$0.716944\pi$
$18$	−3.77595	−0.890001
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−0.273924	−0.0597752
$22$	−7.42651	−1.58334
$23$	3.60392	0.751469	0.375734	−	0.926727i	$-0.377391\pi$
$23$	3.60392	0.751469	0.375734	+	0.926727i	$0.377391\pi$
$24$	−0.592949	−0.121035
$25$	0	0
$26$	−8.79741	−1.72531
$27$	−1.16766	−0.224717
$28$	0.523743	0.0989781
$29$	5.27624	0.979773	0.489887	−	0.871786i	$-0.337038\pi$
$29$	5.27624	0.979773	0.489887	+	0.871786i	$0.337038\pi$
$30$	0	0
$31$	−2.26297	−0.406442	−0.203221	−	0.979133i	$-0.565141\pi$
$31$	−2.26297	−0.406442	−0.203221	+	0.979133i	$0.565141\pi$
$32$	2.08863	0.369222
$33$	−1.14089	−0.198603
$34$	−6.62350	−1.13592
$35$	0	0
$36$	1.10910	0.184850
$37$	−0.979100	−0.160963	−0.0804815	−	0.996756i	$-0.525646\pi$
$37$	−0.979100	−0.160963	−0.0804815	+	0.996756i	$0.525646\pi$
$38$	0	0
$39$	−1.35149	−0.216411
$40$	0	0
$41$	−10.0415	−1.56822	−0.784108	−	0.620624i	$-0.786879\pi$
$41$	−10.0415	−1.56822	−0.784108	+	0.620624i	$0.786879\pi$
$42$	−0.349241	−0.0538891
$43$	7.90021	1.20477	0.602386	−	0.798205i	$-0.294217\pi$
$43$	7.90021	1.20477	0.602386	+	0.798205i	$0.294217\pi$
$44$	2.18137	0.328854
$45$	0	0
$46$	4.59483	0.677471
$47$	−8.02867	−1.17110	−0.585551	−	0.810636i	$-0.699122\pi$
$47$	−8.02867	−1.17110	−0.585551	+	0.810636i	$0.699122\pi$
$48$	−0.609286	−0.0879429
$49$	−5.04406	−0.720579
$50$	0	0
$51$	−1.01752	−0.142482
$52$	2.58404	0.358342
$53$	6.54927	0.899611	0.449805	−	0.893127i	$-0.351493\pi$
$53$	6.54927	0.899611	0.449805	+	0.893127i	$0.351493\pi$
$54$	−1.48872	−0.202589
$55$	0	0
$56$	4.23393	0.565782
$57$	0	0
$58$	6.72697	0.883294
$59$	−7.91530	−1.03048	−0.515242	−	0.857045i	$-0.672298\pi$
$59$	−7.91530	−1.03048	−0.515242	+	0.857045i	$0.672298\pi$
$60$	0	0
$61$	5.35586	0.685747	0.342874	−	0.939382i	$-0.388600\pi$
$61$	5.35586	0.685747	0.342874	+	0.939382i	$0.388600\pi$
$62$	−2.88519	−0.366420
$63$	4.14200	0.521843
$64$	8.88447	1.11056
$65$	0	0
$66$	−1.45458	−0.179046
$67$	−9.53168	−1.16448	−0.582240	−	0.813017i	$-0.697824\pi$
$67$	−9.53168	−1.16448	−0.582240	+	0.813017i	$0.697824\pi$
$68$	1.94551	0.235927
$69$	0.705874	0.0849773
$70$	0	0
$71$	4.72405	0.560642	0.280321	−	0.959906i	$-0.409559\pi$
$71$	4.72405	0.560642	0.280321	+	0.959906i	$0.409559\pi$
$72$	8.96597	1.05665
$73$	−3.60944	−0.422453	−0.211226	−	0.977437i	$-0.567746\pi$
$73$	−3.60944	−0.422453	−0.211226	+	0.977437i	$0.567746\pi$
$74$	−1.24831	−0.145113
$75$	0	0
$76$	0	0
$77$	8.14645	0.928374
$78$	−1.72309	−0.195101
$79$	−9.34009	−1.05084	−0.525421	−	0.850842i	$-0.676092\pi$
$79$	−9.34009	−1.05084	−0.525421	+	0.850842i	$0.676092\pi$
$80$	0	0
$81$	8.65621	0.961801
$82$	−12.8024	−1.41379
$83$	0.621535	0.0682223	0.0341112	−	0.999418i	$-0.489140\pi$
$83$	0.621535	0.0682223	0.0341112	+	0.999418i	$0.489140\pi$
$84$	0.102582	0.0111926
$85$	0	0
$86$	10.0724	1.08614
$87$	1.03342	0.110794
$88$	17.6342	1.87981
$89$	8.89254	0.942608	0.471304	−	0.881971i	$-0.343784\pi$
$89$	8.89254	0.942608	0.471304	+	0.881971i	$0.343784\pi$
$90$	0	0
$91$	9.65024	1.01162
$92$	−1.34963	−0.140709
$93$	−0.443233	−0.0459611
$94$	−10.2362	−1.05578
$95$	0	0
$96$	0.409086	0.0417521
$97$	−4.82792	−0.490201	−0.245100	−	0.969498i	$-0.578821\pi$
$97$	−4.82792	−0.490201	−0.245100	+	0.969498i	$0.578821\pi$
$98$	−6.43094	−0.649624
$99$	17.2513	1.73382
$100$	0	0
$101$	−4.46914	−0.444696	−0.222348	−	0.974967i	$-0.571372\pi$
$101$	−4.46914	−0.444696	−0.222348	+	0.974967i	$0.571372\pi$
$102$	−1.29730	−0.128452
$103$	11.7098	1.15380	0.576902	−	0.816813i	$-0.304262\pi$
$103$	11.7098	1.15380	0.576902	+	0.816813i	$0.304262\pi$
$104$	20.8893	2.04837
$105$	0	0
$106$	8.35002	0.811026
$107$	−5.11740	−0.494717	−0.247359	−	0.968924i	$-0.579563\pi$
$107$	−5.11740	−0.494717	−0.247359	+	0.968924i	$0.579563\pi$
$108$	0.437278	0.0420771
$109$	−12.7298	−1.21930	−0.609648	−	0.792672i	$-0.708689\pi$
$109$	−12.7298	−1.21930	−0.609648	+	0.792672i	$0.708689\pi$
$110$	0	0
$111$	−0.191769	−0.0182019
$112$	4.35058	0.411091
$113$	1.27695	0.120126	0.0600628	−	0.998195i	$-0.480870\pi$
$113$	1.27695	0.120126	0.0600628	+	0.998195i	$0.480870\pi$
$114$	0	0
$115$	0	0
$116$	−1.97590	−0.183457
$117$	20.4358	1.88929
$118$	−10.0917	−0.929012
$119$	7.26559	0.666035
$120$	0	0
$121$	22.9297	2.08452
$122$	6.82848	0.618221
$123$	−1.96676	−0.177336
$124$	0.847461	0.0761042
$125$	0	0
$126$	5.28086	0.470457
$127$	−7.30667	−0.648362	−0.324181	−	0.945995i	$-0.605089\pi$
$127$	−7.30667	−0.648362	−0.324181	+	0.945995i	$0.605089\pi$
$128$	7.15003	0.631980
$129$	1.54736	0.136237
$130$	0	0
$131$	−0.499969	−0.0436825	−0.0218413	−	0.999761i	$-0.506953\pi$
$131$	−0.499969	−0.0436825	−0.0218413	+	0.999761i	$0.506953\pi$
$132$	0.427250	0.0371874
$133$	0	0
$134$	−12.1525	−1.04981
$135$	0	0
$136$	15.7274	1.34862
$137$	−2.64571	−0.226038	−0.113019	−	0.993593i	$-0.536052\pi$
$137$	−2.64571	−0.226038	−0.113019	+	0.993593i	$0.536052\pi$
$138$	0.899958	0.0766095
$139$	10.0820	0.855140	0.427570	−	0.903982i	$-0.359370\pi$
$139$	10.0820	0.855140	0.427570	+	0.903982i	$0.359370\pi$
$140$	0	0
$141$	−1.57252	−0.132430
$142$	6.02295	0.505435
$143$	40.1929	3.36110
$144$	9.21300	0.767750
$145$	0	0
$146$	−4.60187	−0.380854
$147$	−0.987944	−0.0814842
$148$	0.366663	0.0301395
$149$	−19.3691	−1.58678	−0.793388	−	0.608717i	$-0.791685\pi$
$149$	−19.3691	−1.58678	−0.793388	+	0.608717i	$0.791685\pi$
$150$	0	0
$151$	−5.54302	−0.451084	−0.225542	−	0.974233i	$-0.572415\pi$
$151$	−5.54302	−0.451084	−0.225542	+	0.974233i	$0.572415\pi$
$152$	0	0
$153$	15.3860	1.24388
$154$	10.3864	0.836956
$155$	0	0
$156$	0.506118	0.0405219
$157$	2.92691	0.233593	0.116796	−	0.993156i	$-0.462737\pi$
$157$	2.92691	0.233593	0.116796	+	0.993156i	$0.462737\pi$
$158$	−11.9082	−0.947365
$159$	1.28276	0.101729
$160$	0	0
$161$	−5.04026	−0.397228
$162$	11.0363	0.867092
$163$	−18.5287	−1.45128	−0.725640	−	0.688075i	$-0.758456\pi$
$163$	−18.5287	−1.45128	−0.725640	+	0.688075i	$0.758456\pi$
$164$	3.76043	0.293640
$165$	0	0
$166$	0.792429	0.0615044
$167$	−0.638301	−0.0493932	−0.0246966	−	0.999695i	$-0.507862\pi$
$167$	−0.638301	−0.0493932	−0.0246966	+	0.999695i	$0.507862\pi$
$168$	0.829270	0.0639795
$169$	34.6123	2.66249
$170$	0	0
$171$	0	0
$172$	−2.95855	−0.225587
$173$	−10.1214	−0.769518	−0.384759	−	0.923017i	$-0.625715\pi$
$173$	−10.1214	−0.769518	−0.384759	+	0.923017i	$0.625715\pi$
$174$	1.31756	0.0998843
$175$	0	0
$176$	18.1200	1.36585
$177$	−1.55031	−0.116529
$178$	11.3376	0.849788
$179$	−10.5706	−0.790085	−0.395043	−	0.918663i	$-0.629270\pi$
$179$	−10.5706	−0.790085	−0.395043	+	0.918663i	$0.629270\pi$
$180$	0	0
$181$	15.6694	1.16470	0.582348	−	0.812939i	$-0.302134\pi$
$181$	15.6694	1.16470	0.582348	+	0.812939i	$0.302134\pi$
$182$	12.3036	0.912005
$183$	1.04901	0.0775454
$184$	−10.9104	−0.804324
$185$	0	0
$186$	−0.565102	−0.0414353
$187$	30.2610	2.21290
$188$	3.00665	0.219283
$189$	1.63304	0.118786
$190$	0	0
$191$	0.0220554	0.00159587	0.000797935	−	1.00000i	$-0.499746\pi$
$191$	0.0220554	0.00159587	0.000797935		1.00000i	$0.499746\pi$
$192$	1.74014	0.125584
$193$	−6.30370	−0.453750	−0.226875	−	0.973924i	$-0.572851\pi$
$193$	−6.30370	−0.453750	−0.226875	+	0.973924i	$0.572851\pi$
$194$	−6.15538	−0.441930
$195$	0	0
$196$	1.88895	0.134925
$197$	−0.455699	−0.0324672	−0.0162336	−	0.999868i	$-0.505168\pi$
$197$	−0.455699	−0.0324672	−0.0162336	+	0.999868i	$0.505168\pi$
$198$	21.9946	1.56309
$199$	−2.79939	−0.198443	−0.0992217	−	0.995065i	$-0.531635\pi$
$199$	−2.79939	−0.198443	−0.0992217	+	0.995065i	$0.531635\pi$
$200$	0	0
$201$	−1.86690	−0.131681
$202$	−5.69796	−0.400907
$203$	−7.37909	−0.517911
$204$	0.381052	0.0266790
$205$	0	0
$206$	14.9295	1.04019
$207$	−10.6735	−0.741859
$208$	21.4649	1.48832
$209$	0	0
$210$	0	0
$211$	−11.7226	−0.807016	−0.403508	−	0.914976i	$-0.632209\pi$
$211$	−11.7226	−0.807016	−0.403508	+	0.914976i	$0.632209\pi$
$212$	−2.45263	−0.168447
$213$	0.925267	0.0633982
$214$	−6.52445	−0.446002
$215$	0	0
$216$	3.53495	0.240523
$217$	3.16489	0.214846
$218$	−16.2300	−1.09923
$219$	−0.706956	−0.0477716
$220$	0	0
$221$	35.8470	2.41133
$222$	−0.244497	−0.0164096
$223$	3.26328	0.218526	0.109263	−	0.994013i	$-0.465151\pi$
$223$	3.26328	0.218526	0.109263	+	0.994013i	$0.465151\pi$
$224$	−2.92106	−0.195171
$225$	0	0
$226$	1.62806	0.108297
$227$	18.1760	1.20638	0.603192	−	0.797596i	$-0.293895\pi$
$227$	18.1760	1.20638	0.603192	+	0.797596i	$0.293895\pi$
$228$	0	0
$229$	−14.4487	−0.954794	−0.477397	−	0.878688i	$-0.658420\pi$
$229$	−14.4487	−0.954794	−0.477397	+	0.878688i	$0.658420\pi$
$230$	0	0
$231$	1.59559	0.104982
$232$	−15.9731	−1.04869
$233$	23.2071	1.52035	0.760175	−	0.649718i	$-0.225113\pi$
$233$	23.2071	1.52035	0.760175	+	0.649718i	$0.225113\pi$
$234$	26.0547	1.70325
$235$	0	0
$236$	2.96420	0.192953
$237$	−1.82938	−0.118831
$238$	9.26330	0.600451
$239$	−2.05228	−0.132751	−0.0663756	−	0.997795i	$-0.521144\pi$
$239$	−2.05228	−0.132751	−0.0663756	+	0.997795i	$0.521144\pi$
$240$	0	0
$241$	−8.39495	−0.540767	−0.270383	−	0.962753i	$-0.587150\pi$
$241$	−8.39495	−0.540767	−0.270383	+	0.962753i	$0.587150\pi$
$242$	29.2343	1.87925
$243$	5.19842	0.333479
$244$	−2.00571	−0.128403
$245$	0	0
$246$	−2.50753	−0.159874
$247$	0	0
$248$	6.85086	0.435030
$249$	0.121736	0.00771469
$250$	0	0
$251$	−18.0852	−1.14153	−0.570764	−	0.821114i	$-0.693353\pi$
$251$	−18.0852	−1.14153	−0.570764	+	0.821114i	$0.693353\pi$
$252$	−1.55114	−0.0977124
$253$	−20.9925	−1.31979
$254$	−9.31568	−0.584518
$255$	0	0
$256$	−8.65297	−0.540810
$257$	5.22960	0.326213	0.163107	−	0.986608i	$-0.447849\pi$
$257$	5.22960	0.326213	0.163107	+	0.986608i	$0.447849\pi$
$258$	1.97281	0.122822
$259$	1.36932	0.0850854
$260$	0	0
$261$	−15.6263	−0.967245
$262$	−0.637439	−0.0393811
$263$	0.613918	0.0378558	0.0189279	−	0.999821i	$-0.493975\pi$
$263$	0.613918	0.0378558	0.0189279	+	0.999821i	$0.493975\pi$
$264$	3.45388	0.212572
$265$	0	0
$266$	0	0
$267$	1.74172	0.106592
$268$	3.56952	0.218043
$269$	1.78880	0.109065	0.0545325	−	0.998512i	$-0.482633\pi$
$269$	1.78880	0.109065	0.0545325	+	0.998512i	$0.482633\pi$
$270$	0	0
$271$	−2.06081	−0.125185	−0.0625926	−	0.998039i	$-0.519937\pi$
$271$	−2.06081	−0.125185	−0.0625926	+	0.998039i	$0.519937\pi$
$272$	16.1608	0.979890
$273$	1.89012	0.114396
$274$	−3.37316	−0.203780
$275$	0	0
$276$	−0.264343	−0.0159115
$277$	−20.1100	−1.20830	−0.604148	−	0.796872i	$-0.706486\pi$
$277$	−20.1100	−1.20830	−0.604148	+	0.796872i	$0.706486\pi$
$278$	12.8540	0.770934
$279$	6.70211	0.401245
$280$	0	0
$281$	−4.05207	−0.241726	−0.120863	−	0.992669i	$-0.538566\pi$
$281$	−4.05207	−0.241726	−0.120863	+	0.992669i	$0.538566\pi$
$282$	−2.00489	−0.119390
$283$	19.5772	1.16374	0.581872	−	0.813280i	$-0.302320\pi$
$283$	19.5772	1.16374	0.581872	+	0.813280i	$0.302320\pi$
$284$	−1.76911	−0.104977
$285$	0	0
$286$	51.2442	3.03013
$287$	14.0435	0.828963
$288$	−6.18577	−0.364500
$289$	9.98890	0.587582
$290$	0	0
$291$	−0.945610	−0.0554326
$292$	1.35170	0.0791021
$293$	−7.62842	−0.445657	−0.222828	−	0.974858i	$-0.571529\pi$
$293$	−7.62842	−0.445657	−0.222828	+	0.974858i	$0.571529\pi$
$294$	−1.25958	−0.0734604
$295$	0	0
$296$	2.96409	0.172284
$297$	6.80155	0.394666
$298$	−24.6947	−1.43052
$299$	−24.8676	−1.43813
$300$	0	0
$301$	−11.0489	−0.636845
$302$	−7.06710	−0.406666
$303$	−0.875340	−0.0502870
$304$	0	0
$305$	0	0
$306$	19.6164	1.12140
$307$	−3.73079	−0.212928	−0.106464	−	0.994317i	$-0.533953\pi$
$307$	−3.73079	−0.212928	−0.106464	+	0.994317i	$0.533953\pi$
$308$	−3.05076	−0.173833
$309$	2.29352	0.130474
$310$	0	0
$311$	−20.6036	−1.16832	−0.584160	−	0.811638i	$-0.698576\pi$
$311$	−20.6036	−1.16832	−0.584160	+	0.811638i	$0.698576\pi$
$312$	4.09145	0.231633
$313$	−25.7091	−1.45316	−0.726582	−	0.687080i	$-0.758892\pi$
$313$	−25.7091	−1.45316	−0.726582	+	0.687080i	$0.758892\pi$
$314$	3.73168	0.210591
$315$	0	0
$316$	3.49777	0.196765
$317$	−15.0537	−0.845499	−0.422749	−	0.906247i	$-0.638935\pi$
$317$	−15.0537	−0.845499	−0.422749	+	0.906247i	$0.638935\pi$
$318$	1.63546	0.0917120
$319$	−30.7337	−1.72076
$320$	0	0
$321$	−1.00231	−0.0559434
$322$	−6.42611	−0.358113
$323$	0	0
$324$	−3.24166	−0.180092
$325$	0	0
$326$	−23.6232	−1.30837
$327$	−2.49330	−0.137880
$328$	30.3993	1.67852
$329$	11.2285	0.619047
$330$	0	0
$331$	21.7816	1.19722	0.598612	−	0.801039i	$-0.295719\pi$
$331$	21.7816	1.19722	0.598612	+	0.801039i	$0.295719\pi$
$332$	−0.232758	−0.0127743
$333$	2.89974	0.158905
$334$	−0.813805	−0.0445294
$335$	0	0
$336$	0.852118	0.0464868
$337$	−12.0123	−0.654351	−0.327176	−	0.944964i	$-0.606097\pi$
$337$	−12.0123	−0.654351	−0.327176	+	0.944964i	$0.606097\pi$
$338$	44.1292	2.40031
$339$	0.250108	0.0135840
$340$	0	0
$341$	13.1816	0.713826
$342$	0	0
$343$	16.8442	0.909503
$344$	−23.9169	−1.28951
$345$	0	0
$346$	−12.9044	−0.693743
$347$	−21.1956	−1.13784	−0.568920	−	0.822393i	$-0.692639\pi$
$347$	−21.1956	−1.13784	−0.568920	+	0.822393i	$0.692639\pi$
$348$	−0.387005	−0.0207457
$349$	15.6557	0.838029	0.419015	−	0.907979i	$-0.362376\pi$
$349$	15.6557	0.838029	0.419015	+	0.907979i	$0.362376\pi$
$350$	0	0
$351$	8.05708	0.430055
$352$	−12.1661	−0.648456
$353$	18.9918	1.01083	0.505417	−	0.862875i	$-0.331339\pi$
$353$	18.9918	1.01083	0.505417	+	0.862875i	$0.331339\pi$
$354$	−1.97658	−0.105054
$355$	0	0
$356$	−3.33016	−0.176498
$357$	1.42306	0.0753163
$358$	−13.4771	−0.712285
$359$	−17.3197	−0.914097	−0.457048	−	0.889442i	$-0.651093\pi$
$359$	−17.3197	−0.914097	−0.457048	+	0.889442i	$0.651093\pi$
$360$	0	0
$361$	0	0
$362$	19.9778	1.05001
$363$	4.49108	0.235721
$364$	−3.61391	−0.189421
$365$	0	0
$366$	1.33745	0.0699094
$367$	−34.7088	−1.81178	−0.905892	−	0.423509i	$-0.860798\pi$
$367$	−34.7088	−1.81178	−0.905892	+	0.423509i	$0.860798\pi$
$368$	−11.2110	−0.584413
$369$	29.7392	1.54816
$370$	0	0
$371$	−9.15948	−0.475537
$372$	0.165986	0.00860598
$373$	18.3183	0.948488	0.474244	−	0.880394i	$-0.342722\pi$
$373$	18.3183	0.948488	0.474244	+	0.880394i	$0.342722\pi$
$374$	38.5814	1.99499
$375$	0	0
$376$	24.3057	1.25347
$377$	−36.4070	−1.87505
$378$	2.08205	0.107089
$379$	0.229891	0.0118087	0.00590434	−	0.999983i	$-0.498121\pi$
$379$	0.229891	0.0118087	0.00590434	+	0.999983i	$0.498121\pi$
$380$	0	0
$381$	−1.43111	−0.0733178
$382$	0.0281196	0.00143872
$383$	−5.54954	−0.283568	−0.141784	−	0.989898i	$-0.545284\pi$
$383$	−5.54954	−0.283568	−0.141784	+	0.989898i	$0.545284\pi$
$384$	1.40043	0.0714653
$385$	0	0
$386$	−8.03694	−0.409069
$387$	−23.3976	−1.18937
$388$	1.80800	0.0917875
$389$	28.5077	1.44540	0.722698	−	0.691164i	$-0.242902\pi$
$389$	28.5077	1.44540	0.722698	+	0.691164i	$0.242902\pi$
$390$	0	0
$391$	−18.7227	−0.946845
$392$	15.2702	0.771262
$393$	−0.0979255	−0.00493969
$394$	−0.580995	−0.0292701
$395$	0	0
$396$	−6.46043	−0.324649
$397$	−14.3904	−0.722234	−0.361117	−	0.932521i	$-0.617605\pi$
$397$	−14.3904	−0.722234	−0.361117	+	0.932521i	$0.617605\pi$
$398$	−3.56909	−0.178902
$399$	0	0
$400$	0	0
$401$	−23.2498	−1.16104	−0.580521	−	0.814245i	$-0.697151\pi$
$401$	−23.2498	−1.16104	−0.580521	+	0.814245i	$0.697151\pi$
$402$	−2.38022	−0.118715
$403$	15.6149	0.777834
$404$	1.67365	0.0832671
$405$	0	0
$406$	−9.40801	−0.466912
$407$	5.70318	0.282696
$408$	3.08042	0.152504
$409$	−8.47856	−0.419238	−0.209619	−	0.977783i	$-0.567222\pi$
$409$	−8.47856	−0.419238	−0.209619	+	0.977783i	$0.567222\pi$
$410$	0	0
$411$	−0.518196	−0.0255607
$412$	−4.38521	−0.216044
$413$	11.0700	0.544717
$414$	−13.6082	−0.668808
$415$	0	0
$416$	−14.4119	−0.706602
$417$	1.97468	0.0967006
$418$	0	0
$419$	−20.9841	−1.02514	−0.512571	−	0.858645i	$-0.671307\pi$
$419$	−20.9841	−1.02514	−0.512571	+	0.858645i	$0.671307\pi$
$420$	0	0
$421$	−30.3972	−1.48147	−0.740734	−	0.671799i	$-0.765522\pi$
$421$	−30.3972	−1.48147	−0.740734	+	0.671799i	$0.765522\pi$
$422$	−14.9458	−0.727549
$423$	23.7780	1.15613
$424$	−19.8270	−0.962886
$425$	0	0
$426$	1.17967	0.0571554
$427$	−7.49044	−0.362488
$428$	1.91641	0.0926333
$429$	7.87231	0.380079
$430$	0	0
$431$	−34.7595	−1.67431	−0.837153	−	0.546968i	$-0.815782\pi$
$431$	−34.7595	−1.67431	−0.837153	+	0.546968i	$0.815782\pi$
$432$	3.63234	0.174761
$433$	22.0765	1.06093	0.530464	−	0.847708i	$-0.322018\pi$
$433$	22.0765	1.06093	0.530464	+	0.847708i	$0.322018\pi$
$434$	4.03509	0.193690
$435$	0	0
$436$	4.76719	0.228307
$437$	0	0
$438$	−0.901337	−0.0430675
$439$	27.7782	1.32578	0.662890	−	0.748717i	$-0.269330\pi$
$439$	27.7782	1.32578	0.662890	+	0.748717i	$0.269330\pi$
$440$	0	0
$441$	14.9387	0.711365
$442$	45.7033	2.17388
$443$	8.18618	0.388937	0.194469	−	0.980909i	$-0.437702\pi$
$443$	8.18618	0.388937	0.194469	+	0.980909i	$0.437702\pi$
$444$	0.0718156	0.00340822
$445$	0	0
$446$	4.16054	0.197007
$447$	−3.79368	−0.179435
$448$	−12.4254	−0.587044
$449$	8.14815	0.384535	0.192268	−	0.981343i	$-0.438416\pi$
$449$	8.14815	0.384535	0.192268	+	0.981343i	$0.438416\pi$
$450$	0	0
$451$	58.4909	2.75423
$452$	−0.478206	−0.0224929
$453$	−1.08567	−0.0510093
$454$	23.1736	1.08759
$455$	0	0
$456$	0	0
$457$	30.7619	1.43898	0.719490	−	0.694502i	$-0.244375\pi$
$457$	30.7619	1.43898	0.719490	+	0.694502i	$0.244375\pi$
$458$	−18.4214	−0.860775
$459$	6.06611	0.283142
$460$	0	0
$461$	18.5528	0.864089	0.432045	−	0.901852i	$-0.357792\pi$
$461$	18.5528	0.864089	0.432045	+	0.901852i	$0.357792\pi$
$462$	2.03430	0.0946443
$463$	−19.2982	−0.896863	−0.448432	−	0.893817i	$-0.648017\pi$
$463$	−19.2982	−0.896863	−0.448432	+	0.893817i	$0.648017\pi$
$464$	−16.4132	−0.761964
$465$	0	0
$466$	29.5881	1.37064
$467$	−0.373385	−0.0172782	−0.00863911	−	0.999963i	$-0.502750\pi$
$467$	−0.373385	−0.0172782	−0.00863911	+	0.999963i	$0.502750\pi$
$468$	−7.65299	−0.353760
$469$	13.3305	0.615547
$470$	0	0
$471$	0.573273	0.0264150
$472$	23.9625	1.10296
$473$	−46.0181	−2.11592
$474$	−2.33238	−0.107130
$475$	0	0
$476$	−2.72089	−0.124712
$477$	−19.3966	−0.888107
$478$	−2.61657	−0.119679
$479$	−7.94282	−0.362917	−0.181458	−	0.983399i	$-0.558082\pi$
$479$	−7.94282	−0.362917	−0.181458	+	0.983399i	$0.558082\pi$
$480$	0	0
$481$	6.75595	0.308045
$482$	−10.7032	−0.487517
$483$	−0.987201	−0.0449192
$484$	−8.58694	−0.390315
$485$	0	0
$486$	6.62776	0.300641
$487$	−5.46097	−0.247460	−0.123730	−	0.992316i	$-0.539486\pi$
$487$	−5.46097	−0.247460	−0.123730	+	0.992316i	$0.539486\pi$
$488$	−16.2141	−0.733980
$489$	−3.62909	−0.164113
$490$	0	0
$491$	−4.23665	−0.191197	−0.0955986	−	0.995420i	$-0.530477\pi$
$491$	−4.23665	−0.191197	−0.0955986	+	0.995420i	$0.530477\pi$
$492$	0.736530	0.0332053
$493$	−27.4105	−1.23451
$494$	0	0
$495$	0	0
$496$	7.03961	0.316088
$497$	−6.60683	−0.296357
$498$	0.155208	0.00695502
$499$	−31.5561	−1.41264	−0.706322	−	0.707891i	$-0.749647\pi$
$499$	−31.5561	−1.41264	−0.706322	+	0.707891i	$0.749647\pi$
$500$	0	0
$501$	−0.125019	−0.00558546
$502$	−23.0578	−1.02912
$503$	31.8595	1.42055	0.710273	−	0.703926i	$-0.248571\pi$
$503$	31.8595	1.42055	0.710273	+	0.703926i	$0.248571\pi$
$504$	−12.5394	−0.558547
$505$	0	0
$506$	−26.7645	−1.18983
$507$	6.77928	0.301078
$508$	2.73627	0.121402
$509$	9.43761	0.418315	0.209157	−	0.977882i	$-0.432928\pi$
$509$	9.43761	0.418315	0.209157	+	0.977882i	$0.432928\pi$
$510$	0	0
$511$	5.04798	0.223310
$512$	−25.3322	−1.11954
$513$	0	0
$514$	6.66750	0.294091
$515$	0	0
$516$	−0.579470	−0.0255098
$517$	46.7664	2.05678
$518$	1.74582	0.0767070
$519$	−1.98241	−0.0870183
$520$	0	0
$521$	3.25713	0.142697	0.0713487	−	0.997451i	$-0.477270\pi$
$521$	3.25713	0.142697	0.0713487	+	0.997451i	$0.477270\pi$
$522$	−19.9228	−0.871999
$523$	20.2354	0.884832	0.442416	−	0.896810i	$-0.354121\pi$
$523$	20.2354	0.884832	0.442416	+	0.896810i	$0.354121\pi$
$524$	0.187233	0.00817933
$525$	0	0
$526$	0.782718	0.0341281
$527$	11.7563	0.512114
$528$	3.54905	0.154452
$529$	−10.0118	−0.435295
$530$	0	0
$531$	23.4423	1.01731
$532$	0	0
$533$	69.2880	3.00119
$534$	2.22061	0.0960954
$535$	0	0
$536$	28.8559	1.24639
$537$	−2.07039	−0.0893441
$538$	2.28064	0.0983252
$539$	29.3812	1.26554
$540$	0	0
$541$	−27.6833	−1.19020	−0.595100	−	0.803652i	$-0.702888\pi$
$541$	−27.6833	−1.19020	−0.595100	+	0.803652i	$0.702888\pi$
$542$	−2.62744	−0.112858
$543$	3.06905	0.131706
$544$	−10.8506	−0.465217
$545$	0	0
$546$	2.40982	0.103131
$547$	32.6697	1.39686	0.698428	−	0.715680i	$-0.253883\pi$
$547$	32.6697	1.39686	0.698428	+	0.715680i	$0.253883\pi$
$548$	0.990789	0.0423244
$549$	−15.8621	−0.676978
$550$	0	0
$551$	0	0
$552$	−2.13694	−0.0909542
$553$	13.0626	0.555478
$554$	−25.6394	−1.08931
$555$	0	0
$556$	−3.77559	−0.160121
$557$	8.11331	0.343772	0.171886	−	0.985117i	$-0.445014\pi$
$557$	8.11331	0.343772	0.171886	+	0.985117i	$0.445014\pi$
$558$	8.54489	0.361734
$559$	−54.5128	−2.30565
$560$	0	0
$561$	5.92700	0.250238
$562$	−5.16621	−0.217923
$563$	29.0575	1.22463	0.612314	−	0.790615i	$-0.290239\pi$
$563$	29.0575	1.22463	0.612314	+	0.790615i	$0.290239\pi$
$564$	0.588892	0.0247968
$565$	0	0
$566$	24.9601	1.04915
$567$	−12.1061	−0.508411
$568$	−14.3014	−0.600075
$569$	−7.74794	−0.324811	−0.162405	−	0.986724i	$-0.551925\pi$
$569$	−7.74794	−0.324811	−0.162405	+	0.986724i	$0.551925\pi$
$570$	0	0
$571$	−14.2711	−0.597227	−0.298614	−	0.954374i	$-0.596524\pi$
$571$	−14.2711	−0.597227	−0.298614	+	0.954374i	$0.596524\pi$
$572$	−15.0518	−0.629349
$573$	0.00431983	0.000180463 0
$574$	17.9049	0.747335
$575$	0	0
$576$	−26.3126	−1.09636
$577$	32.7500	1.36340	0.681700	−	0.731632i	$-0.261241\pi$
$577$	32.7500	1.36340	0.681700	+	0.731632i	$0.261241\pi$
$578$	12.7354	0.529723
$579$	−1.23466	−0.0513108
$580$	0	0
$581$	−0.869248	−0.0360625
$582$	−1.20561	−0.0499742
$583$	−38.1490	−1.57997
$584$	10.9271	0.452167
$585$	0	0
$586$	−9.72589	−0.401773
$587$	7.98484	0.329570	0.164785	−	0.986330i	$-0.447307\pi$
$587$	7.98484	0.329570	0.164785	+	0.986330i	$0.447307\pi$
$588$	0.369975	0.0152575
$589$	0	0
$590$	0	0
$591$	−0.0892545	−0.00367144
$592$	3.04576	0.125180
$593$	−36.9344	−1.51672	−0.758358	−	0.651838i	$-0.773998\pi$
$593$	−36.9344	−1.51672	−0.758358	+	0.651838i	$0.773998\pi$
$594$	8.67167	0.355803
$595$	0	0
$596$	7.25351	0.297115
$597$	−0.548296	−0.0224403
$598$	−31.7051	−1.29652
$599$	−8.60871	−0.351742	−0.175871	−	0.984413i	$-0.556274\pi$
$599$	−8.60871	−0.351742	−0.175871	+	0.984413i	$0.556274\pi$
$600$	0	0
$601$	−3.21509	−0.131146	−0.0655731	−	0.997848i	$-0.520888\pi$
$601$	−3.21509	−0.131146	−0.0655731	+	0.997848i	$0.520888\pi$
$602$	−14.0868	−0.574135
$603$	28.2294	1.14959
$604$	2.07580	0.0844632
$605$	0	0
$606$	−1.11602	−0.0453352
$607$	26.0312	1.05657	0.528286	−	0.849066i	$-0.322835\pi$
$607$	26.0312	1.05657	0.528286	+	0.849066i	$0.322835\pi$
$608$	0	0
$609$	−1.44529	−0.0585661
$610$	0	0
$611$	55.3992	2.24121
$612$	−5.76188	−0.232910
$613$	−39.7116	−1.60393	−0.801967	−	0.597368i	$-0.796213\pi$
$613$	−39.7116	−1.60393	−0.801967	+	0.597368i	$0.796213\pi$
$614$	−4.75660	−0.191961
$615$	0	0
$616$	−24.6623	−0.993672
$617$	−7.10777	−0.286148	−0.143074	−	0.989712i	$-0.545699\pi$
$617$	−7.10777	−0.286148	−0.143074	+	0.989712i	$0.545699\pi$
$618$	2.92414	0.117626
$619$	−26.4709	−1.06396	−0.531978	−	0.846758i	$-0.678551\pi$
$619$	−26.4709	−1.06396	−0.531978	+	0.846758i	$0.678551\pi$
$620$	0	0
$621$	−4.20817	−0.168868
$622$	−26.2686	−1.05328
$623$	−12.4367	−0.498265
$624$	4.20418	0.168302
$625$	0	0
$626$	−32.7779	−1.31007
$627$	0	0
$628$	−1.09610	−0.0437390
$629$	5.08650	0.202812
$630$	0	0
$631$	−22.0260	−0.876840	−0.438420	−	0.898770i	$-0.644462\pi$
$631$	−22.0260	−0.876840	−0.438420	+	0.898770i	$0.644462\pi$
$632$	28.2759	1.12475
$633$	−2.29602	−0.0912586
$634$	−19.1928	−0.762242
$635$	0	0
$636$	−0.480380	−0.0190483
$637$	34.8048	1.37902
$638$	−39.1841	−1.55131
$639$	−13.9909	−0.553473
$640$	0	0
$641$	−19.3476	−0.764184	−0.382092	−	0.924124i	$-0.624796\pi$
$641$	−19.3476	−0.764184	−0.382092	+	0.924124i	$0.624796\pi$
$642$	−1.27790	−0.0504346
$643$	16.9655	0.669052	0.334526	−	0.942386i	$-0.391424\pi$
$643$	16.9655	0.669052	0.334526	+	0.942386i	$0.391424\pi$
$644$	1.88753	0.0743789
$645$	0	0
$646$	0	0
$647$	−35.4458	−1.39352	−0.696759	−	0.717306i	$-0.745375\pi$
$647$	−35.4458	−1.39352	−0.696759	+	0.717306i	$0.745375\pi$
$648$	−26.2055	−1.02945
$649$	46.1060	1.80982
$650$	0	0
$651$	0.619884	0.0242952
$652$	6.93880	0.271744
$653$	15.8833	0.621563	0.310781	−	0.950481i	$-0.399409\pi$
$653$	15.8833	0.621563	0.310781	+	0.950481i	$0.399409\pi$
$654$	−3.17885	−0.124303
$655$	0	0
$656$	31.2368	1.21959
$657$	10.6899	0.417051
$658$	14.3158	0.558089
$659$	−14.5206	−0.565644	−0.282822	−	0.959172i	$-0.591271\pi$
$659$	−14.5206	−0.565644	−0.282822	+	0.959172i	$0.591271\pi$
$660$	0	0
$661$	18.7986	0.731179	0.365589	−	0.930776i	$-0.380867\pi$
$661$	18.7986	0.731179	0.365589	+	0.930776i	$0.380867\pi$
$662$	27.7705	1.07933
$663$	7.02109	0.272677
$664$	−1.88161	−0.0730208
$665$	0	0
$666$	3.69704	0.143257
$667$	19.0151	0.736269
$668$	0.239037	0.00924862
$669$	0.639156	0.0247112
$670$	0	0
$671$	−31.1974	−1.20436
$672$	−0.572127	−0.0220703
$673$	17.7919	0.685828	0.342914	−	0.939367i	$-0.388586\pi$
$673$	17.7919	0.685828	0.342914	+	0.939367i	$0.388586\pi$
$674$	−15.3151	−0.589917
$675$	0	0
$676$	−12.9620	−0.498537
$677$	25.3804	0.975449	0.487724	−	0.872998i	$-0.337827\pi$
$677$	25.3804	0.975449	0.487724	+	0.872998i	$0.337827\pi$
$678$	0.318876	0.0122464
$679$	6.75209	0.259121
$680$	0	0
$681$	3.56001	0.136420
$682$	16.8060	0.643535
$683$	49.7930	1.90528	0.952638	−	0.304107i	$-0.0983581\pi$
$683$	49.7930	1.90528	0.952638	+	0.304107i	$0.0983581\pi$
$684$	0	0
$685$	0	0
$686$	21.4756	0.819943
$687$	−2.82996	−0.107970
$688$	−24.5758	−0.936944
$689$	−45.1910	−1.72164
$690$	0	0
$691$	14.6555	0.557520	0.278760	−	0.960361i	$-0.410077\pi$
$691$	14.6555	0.557520	0.278760	+	0.960361i	$0.410077\pi$
$692$	3.79037	0.144088
$693$	−24.1268	−0.916502
$694$	−27.0235	−1.02580
$695$	0	0
$696$	−3.12854	−0.118587
$697$	52.1664	1.97594
$698$	19.9603	0.755508
$699$	4.54542	0.171924
$700$	0	0
$701$	36.8876	1.39323	0.696613	−	0.717447i	$-0.254689\pi$
$701$	36.8876	1.39323	0.696613	+	0.717447i	$0.254689\pi$
$702$	10.2724	0.387707
$703$	0	0
$704$	−51.7513	−1.95045
$705$	0	0
$706$	24.2137	0.911296
$707$	6.25032	0.235068
$708$	0.580577	0.0218194
$709$	28.0210	1.05235	0.526175	−	0.850377i	$-0.323626\pi$
$709$	28.0210	1.05235	0.526175	+	0.850377i	$0.323626\pi$
$710$	0	0
$711$	27.6620	1.03740
$712$	−26.9210	−1.00891
$713$	−8.15557	−0.305429
$714$	1.81434	0.0678999
$715$	0	0
$716$	3.95859	0.147939
$717$	−0.401966	−0.0150117
$718$	−22.0818	−0.824085
$719$	20.9872	0.782691	0.391346	−	0.920244i	$-0.372010\pi$
$719$	20.9872	0.782691	0.391346	+	0.920244i	$0.372010\pi$
$720$	0	0
$721$	−16.3768	−0.609903
$722$	0	0
$723$	−1.64426	−0.0611507
$724$	−5.86802	−0.218083
$725$	0	0
$726$	5.72593	0.212509
$727$	−19.3072	−0.716063	−0.358031	−	0.933710i	$-0.616552\pi$
$727$	−19.3072	−0.716063	−0.358031	+	0.933710i	$0.616552\pi$
$728$	−29.2148	−1.08277
$729$	−24.9505	−0.924091
$730$	0	0
$731$	−41.0423	−1.51800
$732$	−0.392845	−0.0145200
$733$	38.9371	1.43817	0.719087	−	0.694920i	$-0.244560\pi$
$733$	38.9371	1.43817	0.719087	+	0.694920i	$0.244560\pi$
$734$	−44.2521	−1.63338
$735$	0	0
$736$	7.52726	0.277458
$737$	55.5213	2.04515
$738$	37.9162	1.39571
$739$	−37.8845	−1.39360	−0.696802	−	0.717264i	$-0.745394\pi$
$739$	−37.8845	−1.39360	−0.696802	+	0.717264i	$0.745394\pi$
$740$	0	0
$741$	0	0
$742$	−11.6779	−0.428710
$743$	44.1058	1.61808	0.809042	−	0.587751i	$-0.199987\pi$
$743$	44.1058	1.61808	0.809042	+	0.587751i	$0.199987\pi$
$744$	1.34183	0.0491939
$745$	0	0
$746$	23.3551	0.855089
$747$	−1.84076	−0.0673499
$748$	−11.3324	−0.414354
$749$	7.15694	0.261509
$750$	0	0
$751$	−41.9339	−1.53019	−0.765095	−	0.643917i	$-0.777308\pi$
$751$	−41.9339	−1.53019	−0.765095	+	0.643917i	$0.777308\pi$
$752$	24.9754	0.910760
$753$	−3.54222	−0.129086
$754$	−46.4172	−1.69042
$755$	0	0
$756$	−0.611556	−0.0222421
$757$	−27.0591	−0.983480	−0.491740	−	0.870742i	$-0.663639\pi$
$757$	−27.0591	−0.983480	−0.491740	+	0.870742i	$0.663639\pi$
$758$	0.293100	0.0106459
$759$	−4.11166	−0.149244
$760$	0	0
$761$	3.95472	0.143359	0.0716793	−	0.997428i	$-0.477164\pi$
$761$	3.95472	0.143359	0.0716793	+	0.997428i	$0.477164\pi$
$762$	−1.82460	−0.0660982
$763$	17.8033	0.644523
$764$	−0.00825950	−0.000298818 0
$765$	0	0
$766$	−7.07542	−0.255645
$767$	54.6169	1.97210
$768$	−1.69480	−0.0611557
$769$	7.86416	0.283589	0.141794	−	0.989896i	$-0.454713\pi$
$769$	7.86416	0.283589	0.141794	+	0.989896i	$0.454713\pi$
$770$	0	0
$771$	1.02429	0.0368887
$772$	2.36067	0.0849624
$773$	43.4380	1.56236	0.781178	−	0.624309i	$-0.214619\pi$
$773$	43.4380	1.56236	0.781178	+	0.624309i	$0.214619\pi$
$774$	−29.8309	−1.07225
$775$	0	0
$776$	14.6159	0.524679
$777$	0.268199	0.00962159
$778$	36.3460	1.30307
$779$	0	0
$780$	0	0
$781$	−27.5172	−0.984644
$782$	−23.8705	−0.853609
$783$	−6.16088	−0.220172
$784$	15.6909	0.560391
$785$	0	0
$786$	−0.124851	−0.00445327
$787$	12.2949	0.438267	0.219133	−	0.975695i	$-0.429677\pi$
$787$	12.2949	0.438267	0.219133	+	0.975695i	$0.429677\pi$
$788$	0.170654	0.00607931
$789$	0.120244	0.00428079
$790$	0	0
$791$	−1.78588	−0.0634987
$792$	−52.2260	−1.85577
$793$	−36.9563	−1.31236
$794$	−18.3471	−0.651115
$795$	0	0
$796$	1.04834	0.0371575
$797$	−7.58688	−0.268741	−0.134370	−	0.990931i	$-0.542901\pi$
$797$	−7.58688	−0.268741	−0.134370	+	0.990931i	$0.542901\pi$
$798$	0	0
$799$	41.7096	1.47558
$800$	0	0
$801$	−26.3365	−0.930554
$802$	−29.6425	−1.04671
$803$	21.0247	0.741945
$804$	0.699136	0.0246566
$805$	0	0
$806$	19.9083	0.701240
$807$	0.350359	0.0123332
$808$	13.5297	0.475975
$809$	30.4530	1.07067	0.535335	−	0.844640i	$-0.320185\pi$
$809$	30.4530	1.07067	0.535335	+	0.844640i	$0.320185\pi$
$810$	0	0
$811$	35.4975	1.24649	0.623243	−	0.782028i	$-0.285815\pi$
$811$	35.4975	1.24649	0.623243	+	0.782028i	$0.285815\pi$
$812$	2.76339	0.0969761
$813$	−0.403636	−0.0141561
$814$	7.27130	0.254859
$815$	0	0
$816$	3.16529	0.110807
$817$	0	0
$818$	−10.8098	−0.377955
$819$	−28.5805	−0.998684
$820$	0	0
$821$	−42.9044	−1.49737	−0.748687	−	0.662924i	$-0.769315\pi$
$821$	−42.9044	−1.49737	−0.748687	+	0.662924i	$0.769315\pi$
$822$	−0.660676	−0.0230437
$823$	−47.7532	−1.66457	−0.832286	−	0.554346i	$-0.812969\pi$
$823$	−47.7532	−1.66457	−0.832286	+	0.554346i	$0.812969\pi$
$824$	−35.4500	−1.23496
$825$	0	0
$826$	14.1137	0.491078
$827$	37.6844	1.31041	0.655207	−	0.755449i	$-0.272581\pi$
$827$	37.6844	1.31041	0.655207	+	0.755449i	$0.272581\pi$
$828$	3.99711	0.138909
$829$	−38.2682	−1.32911	−0.664554	−	0.747240i	$-0.731379\pi$
$829$	−38.2682	−1.32911	−0.664554	+	0.747240i	$0.731379\pi$
$830$	0	0
$831$	−3.93881	−0.136636
$832$	−61.3043	−2.12535
$833$	26.2043	0.907925
$834$	2.51763	0.0871784
$835$	0	0
$836$	0	0
$837$	2.64239	0.0913345
$838$	−26.7538	−0.924195
$839$	16.9819	0.586280	0.293140	−	0.956070i	$-0.405300\pi$
$839$	16.9819	0.586280	0.293140	+	0.956070i	$0.405300\pi$
$840$	0	0
$841$	−1.16128	−0.0400442
$842$	−38.7550	−1.33559
$843$	−0.793650	−0.0273348
$844$	4.38999	0.151110
$845$	0	0
$846$	30.3159	1.04228
$847$	−32.0684	−1.10188
$848$	−20.3733	−0.699622
$849$	3.83445	0.131598
$850$	0	0
$851$	−3.52859	−0.120959
$852$	−0.346503	−0.0118710
$853$	−22.0339	−0.754425	−0.377212	−	0.926127i	$-0.623117\pi$
$853$	−22.0339	−0.754425	−0.377212	+	0.926127i	$0.623117\pi$
$854$	−9.54997	−0.326793
$855$	0	0
$856$	15.4922	0.529514
$857$	31.0358	1.06016	0.530081	−	0.847947i	$-0.322161\pi$
$857$	31.0358	1.06016	0.530081	+	0.847947i	$0.322161\pi$
$858$	10.0368	0.342652
$859$	−2.57137	−0.0877341	−0.0438671	−	0.999037i	$-0.513968\pi$
$859$	−2.57137	−0.0877341	−0.0438671	+	0.999037i	$0.513968\pi$
$860$	0	0
$861$	2.75061	0.0937405
$862$	−44.3168	−1.50944
$863$	39.2227	1.33516	0.667579	−	0.744539i	$-0.267331\pi$
$863$	39.2227	1.33516	0.667579	+	0.744539i	$0.267331\pi$
$864$	−2.43882	−0.0829704
$865$	0	0
$866$	28.1465	0.956457
$867$	1.95646	0.0664447
$868$	−1.18522	−0.0402289
$869$	54.4053	1.84557
$870$	0	0
$871$	65.7702	2.22854
$872$	38.5379	1.30506
$873$	14.2985	0.483932
$874$	0	0
$875$	0	0
$876$	0.264748	0.00894499
$877$	7.65106	0.258358	0.129179	−	0.991621i	$-0.458766\pi$
$877$	7.65106	0.258358	0.129179	+	0.991621i	$0.458766\pi$
$878$	35.4159	1.19523
$879$	−1.49412	−0.0503956
$880$	0	0
$881$	15.1855	0.511612	0.255806	−	0.966728i	$-0.417659\pi$
$881$	15.1855	0.511612	0.255806	+	0.966728i	$0.417659\pi$
$882$	19.0461	0.641316
$883$	12.9129	0.434553	0.217276	−	0.976110i	$-0.430283\pi$
$883$	12.9129	0.434553	0.217276	+	0.976110i	$0.430283\pi$
$884$	−13.4243	−0.451509
$885$	0	0
$886$	10.4370	0.350638
$887$	8.97125	0.301225	0.150613	−	0.988593i	$-0.451875\pi$
$887$	8.97125	0.301225	0.150613	+	0.988593i	$0.451875\pi$
$888$	0.580556	0.0194822
$889$	10.2188	0.342726
$890$	0	0
$891$	−50.4217	−1.68919
$892$	−1.22207	−0.0409178
$893$	0	0
$894$	−4.83678	−0.161766
$895$	0	0
$896$	−9.99969	−0.334066
$897$	−4.87065	−0.162626
$898$	10.3885	0.346670
$899$	−11.9400	−0.398221
$900$	0	0
$901$	−34.0240	−1.13350
$902$	74.5732	2.48302
$903$	−2.16406	−0.0720154
$904$	−3.86581	−0.128575
$905$	0	0
$906$	−1.38418	−0.0459864
$907$	11.3302	0.376214	0.188107	−	0.982149i	$-0.439765\pi$
$907$	11.3302	0.376214	0.188107	+	0.982149i	$0.439765\pi$
$908$	−6.80672	−0.225889
$909$	13.2360	0.439010
$910$	0	0
$911$	16.4588	0.545306	0.272653	−	0.962112i	$-0.412099\pi$
$911$	16.4588	0.545306	0.272653	+	0.962112i	$0.412099\pi$
$912$	0	0
$913$	−3.62039	−0.119817
$914$	39.2200	1.29728
$915$	0	0
$916$	5.41087	0.178780
$917$	0.699233	0.0230907
$918$	7.73402	0.255261
$919$	−24.4835	−0.807635	−0.403818	−	0.914839i	$-0.632317\pi$
$919$	−24.4835	−0.807635	−0.403818	+	0.914839i	$0.632317\pi$
$920$	0	0
$921$	−0.730725	−0.0240782
$922$	23.6540	0.779002
$923$	−32.5968	−1.07294
$924$	−0.597531	−0.0196573
$925$	0	0
$926$	−24.6043	−0.808549
$927$	−34.6803	−1.13905
$928$	11.0201	0.361753
$929$	−18.0997	−0.593833	−0.296916	−	0.954903i	$-0.595958\pi$
$929$	−18.0997	−0.593833	−0.296916	+	0.954903i	$0.595958\pi$
$930$	0	0
$931$	0	0
$932$	−8.69083	−0.284678
$933$	−4.03548	−0.132116
$934$	−0.476050	−0.0155768
$935$	0	0
$936$	−61.8667	−2.02218
$937$	60.0096	1.96043	0.980214	−	0.197941i	$-0.0634256\pi$
$937$	60.0096	1.96043	0.980214	+	0.197941i	$0.0634256\pi$
$938$	16.9958	0.554934
$939$	−5.03546	−0.164326
$940$	0	0
$941$	−52.1915	−1.70139	−0.850697	−	0.525657i	$-0.823820\pi$
$941$	−52.1915	−1.70139	−0.850697	+	0.525657i	$0.823820\pi$
$942$	0.730898	0.0238139
$943$	−36.1887	−1.17847
$944$	24.6227	0.801402
$945$	0	0
$946$	−58.6710	−1.90756
$947$	−36.0842	−1.17258	−0.586289	−	0.810102i	$-0.699412\pi$
$947$	−36.0842	−1.17258	−0.586289	+	0.810102i	$0.699412\pi$
$948$	0.685083	0.0222505
$949$	24.9057	0.808475
$950$	0	0
$951$	−2.94846	−0.0956103
$952$	−21.9956	−0.712882
$953$	12.1709	0.394256	0.197128	−	0.980378i	$-0.436839\pi$
$953$	12.1709	0.394256	0.197128	+	0.980378i	$0.436839\pi$
$954$	−24.7297	−0.800655
$955$	0	0
$956$	0.768558	0.0248570
$957$	−6.01959	−0.194586
$958$	−10.1267	−0.327180
$959$	3.70015	0.119484
$960$	0	0
$961$	−25.8789	−0.834805
$962$	8.61354	0.277712
$963$	15.1559	0.488391
$964$	3.14382	0.101256
$965$	0	0
$966$	−1.25864	−0.0404960
$967$	8.42625	0.270970	0.135485	−	0.990779i	$-0.456741\pi$
$967$	8.42625	0.270970	0.135485	+	0.990779i	$0.456741\pi$
$968$	−69.4166	−2.23114
$969$	0	0
$970$	0	0
$971$	−34.7309	−1.11457	−0.557284	−	0.830322i	$-0.688157\pi$
$971$	−34.7309	−1.11457	−0.557284	+	0.830322i	$0.688157\pi$
$972$	−1.94676	−0.0624422
$973$	−14.1001	−0.452029
$974$	−6.96249	−0.223093
$975$	0	0
$976$	−16.6609	−0.533302
$977$	−0.363165	−0.0116187	−0.00580934	−	0.999983i	$-0.501849\pi$
$977$	−0.363165	−0.0116187	−0.00580934	+	0.999983i	$0.501849\pi$
$978$	−4.62692	−0.147953
$979$	−51.7984	−1.65548
$980$	0	0
$981$	37.7011	1.20370
$982$	−5.40153	−0.172370
$983$	11.4056	0.363782	0.181891	−	0.983319i	$-0.441778\pi$
$983$	11.4056	0.363782	0.181891	+	0.983319i	$0.441778\pi$
$984$	5.95409	0.189810
$985$	0	0
$986$	−34.9472	−1.11294
$987$	2.19925	0.0700029
$988$	0	0
$989$	28.4717	0.905348
$990$	0	0
$991$	−17.7006	−0.562277	−0.281138	−	0.959667i	$-0.590712\pi$
$991$	−17.7006	−0.562277	−0.281138	+	0.959667i	$0.590712\pi$
$992$	−4.72652	−0.150067
$993$	4.26620	0.135384
$994$	−8.42341	−0.267174
$995$	0	0
$996$	−0.0455887	−0.00144453
$997$	7.93228	0.251218	0.125609	−	0.992080i	$-0.459912\pi$
$997$	7.93228	0.251218	0.125609	+	0.992080i	$0.459912\pi$
$998$	−40.2326	−1.27354
$999$	1.14326	0.0361711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cr.1.14		21
5.4	even	2		9025.2.a.cp.1.8		21
19.14	odd	18		475.2.l.d.101.3	✓	42
19.15	odd	18		475.2.l.d.301.3	yes	42
19.18	odd	2		9025.2.a.cq.1.8		21
95.14	odd	18		475.2.l.e.101.5	yes	42
95.33	even	36		475.2.u.d.424.11		84
95.34	odd	18		475.2.l.e.301.5	yes	42
95.52	even	36		475.2.u.d.424.4		84
95.53	even	36		475.2.u.d.149.4		84
95.72	even	36		475.2.u.d.149.11		84
95.94	odd	2		9025.2.a.cs.1.14		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.l.d.101.3	✓	42	19.14	odd	18
475.2.l.d.301.3	yes	42	19.15	odd	18
475.2.l.e.101.5	yes	42	95.14	odd	18
475.2.l.e.301.5	yes	42	95.34	odd	18
475.2.u.d.149.4		84	95.53	even	36
475.2.u.d.149.11		84	95.72	even	36
475.2.u.d.424.4		84	95.52	even	36
475.2.u.d.424.11		84	95.33	even	36
9025.2.a.cp.1.8		21	5.4	even	2
9025.2.a.cq.1.8		21	19.18	odd	2
9025.2.a.cr.1.14		21	1.1	even	1	trivial
9025.2.a.cs.1.14		21	95.94	odd	2

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)

\(f(q)\)	\(=\)	\(q+1.27496 q^{2} +0.195863 q^{3} -0.374490 q^{4} +0.249717 q^{6} -1.39855 q^{7} -3.02737 q^{8} -2.96164 q^{9} +O(q^{10})\)	\(q+1.27496 q^{2} +0.195863 q^{3} -0.374490 q^{4} +0.249717 q^{6} -1.39855 q^{7} -3.02737 q^{8} -2.96164 q^{9} -5.82492 q^{11} -0.0733487 q^{12} -6.90017 q^{13} -1.78309 q^{14} -3.11078 q^{16} -5.19508 q^{17} -3.77595 q^{18} -0.273924 q^{21} -7.42651 q^{22} +3.60392 q^{23} -0.592949 q^{24} -8.79741 q^{26} -1.16766 q^{27} +0.523743 q^{28} +5.27624 q^{29} -2.26297 q^{31} +2.08863 q^{32} -1.14089 q^{33} -6.62350 q^{34} +1.10910 q^{36} -0.979100 q^{37} -1.35149 q^{39} -10.0415 q^{41} -0.349241 q^{42} +7.90021 q^{43} +2.18137 q^{44} +4.59483 q^{46} -8.02867 q^{47} -0.609286 q^{48} -5.04406 q^{49} -1.01752 q^{51} +2.58404 q^{52} +6.54927 q^{53} -1.48872 q^{54} +4.23393 q^{56} +6.72697 q^{58} -7.91530 q^{59} +5.35586 q^{61} -2.88519 q^{62} +4.14200 q^{63} +8.88447 q^{64} -1.45458 q^{66} -9.53168 q^{67} +1.94551 q^{68} +0.705874 q^{69} +4.72405 q^{71} +8.96597 q^{72} -3.60944 q^{73} -1.24831 q^{74} +8.14645 q^{77} -1.72309 q^{78} -9.34009 q^{79} +8.65621 q^{81} -12.8024 q^{82} +0.621535 q^{83} +0.102582 q^{84} +10.0724 q^{86} +1.03342 q^{87} +17.6342 q^{88} +8.89254 q^{89} +9.65024 q^{91} -1.34963 q^{92} -0.443233 q^{93} -10.2362 q^{94} +0.409086 q^{96} -4.82792 q^{97} -6.43094 q^{98} +17.2513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{2} + 9 q^{3} + 24 q^{4} + 18 q^{8} + 24 q^{9}+O(q^{10}) \) 21 * q + 6 * q^2 + 9 * q^3 + 24 * q^4 + 18 * q^8 + 24 * q^9	\( 21 q + 6 q^{2} + 9 q^{3} + 24 q^{4} + 18 q^{8} + 24 q^{9} + 24 q^{12} + 12 q^{13} - 6 q^{14} + 30 q^{16} - 9 q^{17} + 18 q^{18} + 12 q^{22} - 6 q^{23} + 18 q^{24} + 18 q^{26} + 30 q^{27} - 15 q^{28} - 3 q^{29} - 6 q^{31} + 57 q^{32} + 45 q^{33} - 3 q^{34} + 60 q^{36} + 24 q^{37} - 30 q^{39} + 12 q^{41} + 18 q^{42} + 18 q^{43} + 24 q^{44} - 15 q^{46} + 18 q^{47} + 84 q^{48} + 33 q^{49} - 12 q^{51} + 36 q^{52} + 42 q^{53} - 18 q^{56} + 12 q^{58} + 6 q^{59} - 36 q^{61} - 3 q^{62} - 6 q^{63} - 21 q^{66} + 24 q^{67} - 78 q^{68} + 15 q^{69} + 12 q^{71} + 87 q^{72} + 18 q^{73} - 45 q^{74} - 9 q^{77} - 60 q^{78} + 3 q^{79} + 21 q^{81} + 42 q^{82} + 36 q^{84} + 30 q^{86} - 6 q^{87} + 60 q^{88} + 3 q^{89} - 3 q^{91} + 60 q^{92} + 12 q^{93} + 18 q^{94} + 111 q^{96} + 12 q^{97} + 105 q^{98} + 84 q^{99}+O(q^{100}) \) 21 * q + 6 * q^2 + 9 * q^3 + 24 * q^4 + 18 * q^8 + 24 * q^9 + 24 * q^12 + 12 * q^13 - 6 * q^14 + 30 * q^16 - 9 * q^17 + 18 * q^18 + 12 * q^22 - 6 * q^23 + 18 * q^24 + 18 * q^26 + 30 * q^27 - 15 * q^28 - 3 * q^29 - 6 * q^31 + 57 * q^32 + 45 * q^33 - 3 * q^34 + 60 * q^36 + 24 * q^37 - 30 * q^39 + 12 * q^41 + 18 * q^42 + 18 * q^43 + 24 * q^44 - 15 * q^46 + 18 * q^47 + 84 * q^48 + 33 * q^49 - 12 * q^51 + 36 * q^52 + 42 * q^53 - 18 * q^56 + 12 * q^58 + 6 * q^59 - 36 * q^61 - 3 * q^62 - 6 * q^63 - 21 * q^66 + 24 * q^67 - 78 * q^68 + 15 * q^69 + 12 * q^71 + 87 * q^72 + 18 * q^73 - 45 * q^74 - 9 * q^77 - 60 * q^78 + 3 * q^79 + 21 * q^81 + 42 * q^82 + 36 * q^84 + 30 * q^86 - 6 * q^87 + 60 * q^88 + 3 * q^89 - 3 * q^91 + 60 * q^92 + 12 * q^93 + 18 * q^94 + 111 * q^96 + 12 * q^97 + 105 * q^98 + 84 * q^99

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