LMFDB - Embedded newform 9025.2.a.ct.1.19

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:	$24$
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+1.61907 q^{2} +1.18857 q^{3} +0.621387 q^{4} +1.92438 q^{6} +2.23190 q^{7} -2.23207 q^{8} -1.58730 q^{9} +O(q^{10})$	\(q+1.61907 q^{2} +1.18857 q^{3} +0.621387 q^{4} +1.92438 q^{6} +2.23190 q^{7} -2.23207 q^{8} -1.58730 q^{9} +5.64478 q^{11} +0.738562 q^{12} -4.70049 q^{13} +3.61361 q^{14} -4.85665 q^{16} -0.785842 q^{17} -2.56995 q^{18} +2.65277 q^{21} +9.13929 q^{22} -5.13041 q^{23} -2.65297 q^{24} -7.61043 q^{26} -5.45233 q^{27} +1.38688 q^{28} -3.03653 q^{29} -8.10416 q^{31} -3.39912 q^{32} +6.70922 q^{33} -1.27233 q^{34} -0.986329 q^{36} +0.985141 q^{37} -5.58687 q^{39} -1.41798 q^{41} +4.29502 q^{42} -1.52174 q^{43} +3.50759 q^{44} -8.30649 q^{46} +0.960695 q^{47} -5.77247 q^{48} -2.01861 q^{49} -0.934028 q^{51} -2.92083 q^{52} -4.41123 q^{53} -8.82770 q^{54} -4.98176 q^{56} -4.91635 q^{58} -9.87853 q^{59} +2.09604 q^{61} -13.1212 q^{62} -3.54270 q^{63} +4.20990 q^{64} +10.8627 q^{66} +3.24811 q^{67} -0.488312 q^{68} -6.09785 q^{69} -7.17702 q^{71} +3.54297 q^{72} +15.1625 q^{73} +1.59501 q^{74} +12.5986 q^{77} -9.04553 q^{78} -1.33973 q^{79} -1.71857 q^{81} -2.29581 q^{82} -7.52545 q^{83} +1.64840 q^{84} -2.46380 q^{86} -3.60912 q^{87} -12.5995 q^{88} -3.40299 q^{89} -10.4910 q^{91} -3.18797 q^{92} -9.63236 q^{93} +1.55543 q^{94} -4.04009 q^{96} +12.7601 q^{97} -3.26827 q^{98} -8.95997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

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 $

$2$	1.61907	1.14486	0.572428	−	0.819955i	$-0.306002\pi$
$2$	1.61907	1.14486	0.572428	+	0.819955i	$0.306002\pi$
$3$	1.18857	0.686221	0.343111	−	0.939295i	$-0.388519\pi$
$3$	1.18857	0.686221	0.343111	+	0.939295i	$0.388519\pi$
$4$	0.621387	0.310694
$5$	0	0
$5$	0	0
$6$	1.92438	0.785624
$7$	2.23190	0.843580	0.421790	−	0.906694i	$-0.361402\pi$
$7$	2.23190	0.843580	0.421790	+	0.906694i	$0.361402\pi$
$8$	−2.23207	−0.789156
$9$	−1.58730	−0.529100
$10$	0	0
$11$	5.64478	1.70197	0.850983	−	0.525194i	$-0.176007\pi$
$11$	5.64478	1.70197	0.850983	+	0.525194i	$0.176007\pi$
$12$	0.738562	0.213204
$13$	−4.70049	−1.30368	−0.651841	−	0.758355i	$-0.726003\pi$
$13$	−4.70049	−1.30368	−0.651841	+	0.758355i	$0.726003\pi$
$14$	3.61361	0.965777
$15$	0	0
$16$	−4.85665	−1.21416
$17$	−0.785842	−0.190595	−0.0952973	−	0.995449i	$-0.530380\pi$
$17$	−0.785842	−0.190595	−0.0952973	+	0.995449i	$0.530380\pi$
$18$	−2.56995	−0.605743
$19$	0	0
$19$	0	0
$20$	0	0
$21$	2.65277	0.578882
$22$	9.13929	1.94850
$23$	−5.13041	−1.06976	−0.534882	−	0.844927i	$-0.679644\pi$
$23$	−5.13041	−1.06976	−0.534882	+	0.844927i	$0.679644\pi$
$24$	−2.65297	−0.541536
$25$	0	0
$26$	−7.61043	−1.49253
$27$	−5.45233	−1.04930
$28$	1.38688	0.262095
$29$	−3.03653	−0.563869	−0.281934	−	0.959434i	$-0.590976\pi$
$29$	−3.03653	−0.563869	−0.281934	+	0.959434i	$0.590976\pi$
$30$	0	0
$31$	−8.10416	−1.45555	−0.727775	−	0.685816i	$-0.759445\pi$
$31$	−8.10416	−1.45555	−0.727775	+	0.685816i	$0.759445\pi$
$32$	−3.39912	−0.600885
$33$	6.70922	1.16792
$34$	−1.27233	−0.218203
$35$	0	0
$36$	−0.986329	−0.164388
$37$	0.985141	0.161956	0.0809781	−	0.996716i	$-0.474196\pi$
$37$	0.985141	0.161956	0.0809781	+	0.996716i	$0.474196\pi$
$38$	0	0
$39$	−5.58687	−0.894615
$40$	0	0
$41$	−1.41798	−0.221451	−0.110726	−	0.993851i	$-0.535318\pi$
$41$	−1.41798	−0.221451	−0.110726	+	0.993851i	$0.535318\pi$
$42$	4.29502	0.662737
$43$	−1.52174	−0.232063	−0.116031	−	0.993246i	$-0.537017\pi$
$43$	−1.52174	−0.232063	−0.116031	+	0.993246i	$0.537017\pi$
$44$	3.50759	0.528790
$45$	0	0
$46$	−8.30649	−1.22473
$47$	0.960695	0.140132	0.0700659	−	0.997542i	$-0.477679\pi$
$47$	0.960695	0.140132	0.0700659	+	0.997542i	$0.477679\pi$
$48$	−5.77247	−0.833184
$49$	−2.01861	−0.288373
$50$	0	0
$51$	−0.934028	−0.130790
$52$	−2.92083	−0.405046
$53$	−4.41123	−0.605929	−0.302964	−	0.953002i	$-0.597976\pi$
$53$	−4.41123	−0.605929	−0.302964	+	0.953002i	$0.597976\pi$
$54$	−8.82770	−1.20130
$55$	0	0
$56$	−4.98176	−0.665716
$57$	0	0
$58$	−4.91635	−0.645548
$59$	−9.87853	−1.28608	−0.643038	−	0.765835i	$-0.722326\pi$
$59$	−9.87853	−1.28608	−0.643038	+	0.765835i	$0.722326\pi$
$60$	0	0
$61$	2.09604	0.268370	0.134185	−	0.990956i	$-0.457158\pi$
$61$	2.09604	0.268370	0.134185	+	0.990956i	$0.457158\pi$
$62$	−13.1212	−1.66639
$63$	−3.54270	−0.446339
$64$	4.20990	0.526237
$65$	0	0
$66$	10.8627	1.33710
$67$	3.24811	0.396820	0.198410	−	0.980119i	$-0.436422\pi$
$67$	3.24811	0.396820	0.198410	+	0.980119i	$0.436422\pi$
$68$	−0.488312	−0.0592165
$69$	−6.09785	−0.734095
$70$	0	0
$71$	−7.17702	−0.851755	−0.425878	−	0.904781i	$-0.640035\pi$
$71$	−7.17702	−0.851755	−0.425878	+	0.904781i	$0.640035\pi$
$72$	3.54297	0.417543
$73$	15.1625	1.77463	0.887317	−	0.461160i	$-0.152567\pi$
$73$	15.1625	1.77463	0.887317	+	0.461160i	$0.152567\pi$
$74$	1.59501	0.185416
$75$	0	0
$76$	0	0
$77$	12.5986	1.43574
$78$	−9.04553	−1.02420
$79$	−1.33973	−0.150731	−0.0753655	−	0.997156i	$-0.524012\pi$
$79$	−1.33973	−0.150731	−0.0753655	+	0.997156i	$0.524012\pi$
$80$	0	0
$81$	−1.71857	−0.190952
$82$	−2.29581	−0.253530
$83$	−7.52545	−0.826026	−0.413013	−	0.910725i	$-0.635524\pi$
$83$	−7.52545	−0.826026	−0.413013	+	0.910725i	$0.635524\pi$
$84$	1.64840	0.179855
$85$	0	0
$86$	−2.46380	−0.265678
$87$	−3.60912	−0.386939
$88$	−12.5995	−1.34312
$89$	−3.40299	−0.360716	−0.180358	−	0.983601i	$-0.557726\pi$
$89$	−3.40299	−0.360716	−0.180358	+	0.983601i	$0.557726\pi$
$90$	0	0
$91$	−10.4910	−1.09976
$92$	−3.18797	−0.332369
$93$	−9.63236	−0.998829
$94$	1.55543	0.160431
$95$	0	0
$96$	−4.04009	−0.412340
$97$	12.7601	1.29559	0.647793	−	0.761816i	$-0.275692\pi$
$97$	12.7601	1.29559	0.647793	+	0.761816i	$0.275692\pi$
$98$	−3.26827	−0.330145
$99$	−8.95997	−0.900511
$100$	0	0
$101$	5.57300	0.554534	0.277267	−	0.960793i	$-0.410571\pi$
$101$	5.57300	0.554534	0.277267	+	0.960793i	$0.410571\pi$
$102$	−1.51226	−0.149736
$103$	3.30768	0.325915	0.162958	−	0.986633i	$-0.447897\pi$
$103$	3.30768	0.325915	0.162958	+	0.986633i	$0.447897\pi$
$104$	10.4918	1.02881
$105$	0	0
$106$	−7.14209	−0.693701
$107$	−6.67267	−0.645071	−0.322536	−	0.946557i	$-0.604535\pi$
$107$	−6.67267	−0.645071	−0.322536	+	0.946557i	$0.604535\pi$
$108$	−3.38801	−0.326011
$109$	−15.6813	−1.50199	−0.750996	−	0.660307i	$-0.770426\pi$
$109$	−15.6813	−1.50199	−0.750996	+	0.660307i	$0.770426\pi$
$110$	0	0
$111$	1.17091	0.111138
$112$	−10.8396	−1.02424
$113$	−6.58139	−0.619125	−0.309562	−	0.950879i	$-0.600183\pi$
$113$	−6.58139	−0.619125	−0.309562	+	0.950879i	$0.600183\pi$
$114$	0	0
$115$	0	0
$116$	−1.88686	−0.175190
$117$	7.46110	0.689779
$118$	−15.9940	−1.47237
$119$	−1.75392	−0.160782
$120$	0	0
$121$	20.8636	1.89669
$122$	3.39363	0.307245
$123$	−1.68537	−0.151965
$124$	−5.03582	−0.452230
$125$	0	0
$126$	−5.73588	−0.510993
$127$	−1.33460	−0.118427	−0.0592135	−	0.998245i	$-0.518859\pi$
$127$	−1.33460	−0.118427	−0.0592135	+	0.998245i	$0.518859\pi$
$128$	13.6144	1.20335
$129$	−1.80869	−0.159246
$130$	0	0
$131$	13.7788	1.20386	0.601930	−	0.798549i	$-0.294399\pi$
$131$	13.7788	1.20386	0.601930	+	0.798549i	$0.294399\pi$
$132$	4.16902	0.362867
$133$	0	0
$134$	5.25892	0.454302
$135$	0	0
$136$	1.75405	0.150409
$137$	−11.7423	−1.00321	−0.501605	−	0.865097i	$-0.667257\pi$
$137$	−11.7423	−1.00321	−0.501605	+	0.865097i	$0.667257\pi$
$138$	−9.87284	−0.840432
$139$	−9.34145	−0.792331	−0.396166	−	0.918179i	$-0.629659\pi$
$139$	−9.34145	−0.792331	−0.396166	+	0.918179i	$0.629659\pi$
$140$	0	0
$141$	1.14185	0.0961614
$142$	−11.6201	−0.975136
$143$	−26.5333	−2.21882
$144$	7.70897	0.642414
$145$	0	0
$146$	24.5491	2.03170
$147$	−2.39926	−0.197887
$148$	0.612154	0.0503187
$149$	18.0234	1.47653	0.738265	−	0.674510i	$-0.235645\pi$
$149$	18.0234	1.47653	0.738265	+	0.674510i	$0.235645\pi$
$150$	0	0
$151$	13.0159	1.05922	0.529611	−	0.848241i	$-0.322338\pi$
$151$	13.0159	1.05922	0.529611	+	0.848241i	$0.322338\pi$
$152$	0	0
$153$	1.24737	0.100844
$154$	20.3980	1.64372
$155$	0	0
$156$	−3.47161	−0.277951
$157$	−10.5071	−0.838560	−0.419280	−	0.907857i	$-0.637717\pi$
$157$	−10.5071	−0.838560	−0.419280	+	0.907857i	$0.637717\pi$
$158$	−2.16911	−0.172565
$159$	−5.24305	−0.415801
$160$	0	0
$161$	−11.4506	−0.902432
$162$	−2.78248	−0.218613
$163$	3.62389	0.283845	0.141923	−	0.989878i	$-0.454672\pi$
$163$	3.62389	0.283845	0.141923	+	0.989878i	$0.454672\pi$
$164$	−0.881115	−0.0688035
$165$	0	0
$166$	−12.1842	−0.945680
$167$	−10.6399	−0.823344	−0.411672	−	0.911332i	$-0.635055\pi$
$167$	−10.6399	−0.823344	−0.411672	+	0.911332i	$0.635055\pi$
$168$	−5.92118	−0.456829
$169$	9.09465	0.699588
$170$	0	0
$171$	0	0
$172$	−0.945588	−0.0721004
$173$	19.4108	1.47578	0.737888	−	0.674923i	$-0.235823\pi$
$173$	19.4108	1.47578	0.737888	+	0.674923i	$0.235823\pi$
$174$	−5.84342	−0.442989
$175$	0	0
$176$	−27.4147	−2.06646
$177$	−11.7413	−0.882532
$178$	−5.50967	−0.412967
$179$	−2.07052	−0.154758	−0.0773789	−	0.997002i	$-0.524655\pi$
$179$	−2.07052	−0.154758	−0.0773789	+	0.997002i	$0.524655\pi$
$180$	0	0
$181$	−21.6324	−1.60793	−0.803963	−	0.594679i	$-0.797279\pi$
$181$	−21.6324	−1.60793	−0.803963	+	0.594679i	$0.797279\pi$
$182$	−16.9857	−1.25907
$183$	2.49129	0.184161
$184$	11.4514	0.844211
$185$	0	0
$186$	−15.5955	−1.14351
$187$	−4.43590	−0.324385
$188$	0.596963	0.0435380
$189$	−12.1691	−0.885169
$190$	0	0
$191$	−22.4061	−1.62125	−0.810626	−	0.585565i	$-0.800873\pi$
$191$	−22.4061	−1.62125	−0.810626	+	0.585565i	$0.800873\pi$
$192$	5.00376	0.361115
$193$	19.5987	1.41075	0.705374	−	0.708835i	$-0.250779\pi$
$193$	19.5987	1.41075	0.705374	+	0.708835i	$0.250779\pi$
$194$	20.6594	1.48326
$195$	0	0
$196$	−1.25434	−0.0895955
$197$	−15.4597	−1.10146	−0.550729	−	0.834684i	$-0.685650\pi$
$197$	−15.4597	−1.10146	−0.550729	+	0.834684i	$0.685650\pi$
$198$	−14.5068	−1.03095
$199$	−1.37296	−0.0973268	−0.0486634	−	0.998815i	$-0.515496\pi$
$199$	−1.37296	−0.0973268	−0.0486634	+	0.998815i	$0.515496\pi$
$200$	0	0
$201$	3.86061	0.272306
$202$	9.02307	0.634861
$203$	−6.77723	−0.475668
$204$	−0.580393	−0.0406356
$205$	0	0
$206$	5.35536	0.373126
$207$	8.14350	0.566013
$208$	22.8287	1.58288
$209$	0	0
$210$	0	0
$211$	−9.57190	−0.658957	−0.329478	−	0.944163i	$-0.606873\pi$
$211$	−9.57190	−0.658957	−0.329478	+	0.944163i	$0.606873\pi$
$212$	−2.74108	−0.188258
$213$	−8.53039	−0.584492
$214$	−10.8035	−0.738513
$215$	0	0
$216$	12.1700	0.828062
$217$	−18.0877	−1.22787
$218$	−25.3890	−1.71956
$219$	18.0217	1.21779
$220$	0	0
$221$	3.69385	0.248475
$222$	1.89578	0.127237
$223$	6.53750	0.437783	0.218892	−	0.975749i	$-0.429756\pi$
$223$	6.53750	0.437783	0.218892	+	0.975749i	$0.429756\pi$
$224$	−7.58650	−0.506894
$225$	0	0
$226$	−10.6557	−0.708808
$227$	8.88867	0.589962	0.294981	−	0.955503i	$-0.404687\pi$
$227$	8.88867	0.589962	0.294981	+	0.955503i	$0.404687\pi$
$228$	0	0
$229$	−7.22494	−0.477438	−0.238719	−	0.971089i	$-0.576727\pi$
$229$	−7.22494	−0.477438	−0.238719	+	0.971089i	$0.576727\pi$
$230$	0	0
$231$	14.9743	0.985238
$232$	6.77774	0.444981
$233$	−24.9780	−1.63636	−0.818181	−	0.574961i	$-0.805017\pi$
$233$	−24.9780	−1.63636	−0.818181	+	0.574961i	$0.805017\pi$
$234$	12.0800	0.789697
$235$	0	0
$236$	−6.13839	−0.399575
$237$	−1.59236	−0.103435
$238$	−2.83972	−0.184072
$239$	16.8187	1.08791	0.543956	−	0.839114i	$-0.316926\pi$
$239$	16.8187	1.08791	0.543956	+	0.839114i	$0.316926\pi$
$240$	0	0
$241$	10.8463	0.698671	0.349335	−	0.936998i	$-0.386407\pi$
$241$	10.8463	0.698671	0.349335	+	0.936998i	$0.386407\pi$
$242$	33.7795	2.17143
$243$	14.3143	0.918266
$244$	1.30245	0.0833809
$245$	0	0
$246$	−2.72873	−0.173978
$247$	0	0
$248$	18.0891	1.14866
$249$	−8.94453	−0.566837
$250$	0	0
$251$	6.37067	0.402113	0.201056	−	0.979580i	$-0.435563\pi$
$251$	6.37067	0.402113	0.201056	+	0.979580i	$0.435563\pi$
$252$	−2.20139	−0.138675
$253$	−28.9600	−1.82070
$254$	−2.16082	−0.135582
$255$	0	0
$256$	13.6228	0.851425
$257$	−13.6465	−0.851245	−0.425623	−	0.904901i	$-0.639945\pi$
$257$	−13.6465	−0.851245	−0.425623	+	0.904901i	$0.639945\pi$
$258$	−2.92840	−0.182314
$259$	2.19874	0.136623
$260$	0	0
$261$	4.81988	0.298343
$262$	22.3088	1.37825
$263$	10.2215	0.630285	0.315143	−	0.949044i	$-0.397948\pi$
$263$	10.2215	0.630285	0.315143	+	0.949044i	$0.397948\pi$
$264$	−14.9754	−0.921675
$265$	0	0
$266$	0	0
$267$	−4.04469	−0.247531
$268$	2.01834	0.123289
$269$	14.4499	0.881028	0.440514	−	0.897746i	$-0.354796\pi$
$269$	14.4499	0.881028	0.440514	+	0.897746i	$0.354796\pi$
$270$	0	0
$271$	−16.2054	−0.984409	−0.492204	−	0.870480i	$-0.663809\pi$
$271$	−16.2054	−0.984409	−0.492204	+	0.870480i	$0.663809\pi$
$272$	3.81656	0.231413
$273$	−12.4693	−0.754679
$274$	−19.0116	−1.14853
$275$	0	0
$276$	−3.78912	−0.228079
$277$	28.5943	1.71806	0.859032	−	0.511922i	$-0.171066\pi$
$277$	28.5943	1.71806	0.859032	+	0.511922i	$0.171066\pi$
$278$	−15.1245	−0.907105
$279$	12.8637	0.770132
$280$	0	0
$281$	−7.17770	−0.428186	−0.214093	−	0.976813i	$-0.568680\pi$
$281$	−7.17770	−0.428186	−0.214093	+	0.976813i	$0.568680\pi$
$282$	1.84874	0.110091
$283$	−10.3656	−0.616173	−0.308086	−	0.951358i	$-0.599689\pi$
$283$	−10.3656	−0.616173	−0.308086	+	0.951358i	$0.599689\pi$
$284$	−4.45970	−0.264635
$285$	0	0
$286$	−42.9592	−2.54023
$287$	−3.16480	−0.186812
$288$	5.39542	0.317928
$289$	−16.3825	−0.963674
$290$	0	0
$291$	15.1662	0.889059
$292$	9.42177	0.551367
$293$	9.09056	0.531076	0.265538	−	0.964100i	$-0.414450\pi$
$293$	9.09056	0.531076	0.265538	+	0.964100i	$0.414450\pi$
$294$	−3.88457	−0.226553
$295$	0	0
$296$	−2.19890	−0.127809
$297$	−30.7772	−1.78587
$298$	29.1811	1.69041
$299$	24.1155	1.39463
$300$	0	0
$301$	−3.39637	−0.195764
$302$	21.0737	1.21266
$303$	6.62390	0.380533
$304$	0	0
$305$	0	0
$306$	2.01958	0.115451
$307$	−14.6641	−0.836923	−0.418461	−	0.908235i	$-0.637431\pi$
$307$	−14.6641	−0.836923	−0.418461	+	0.908235i	$0.637431\pi$
$308$	7.82861	0.446076
$309$	3.93141	0.223650
$310$	0	0
$311$	−31.5811	−1.79080	−0.895400	−	0.445263i	$-0.853110\pi$
$311$	−31.5811	−1.79080	−0.895400	+	0.445263i	$0.853110\pi$
$312$	12.4703	0.705991
$313$	8.99070	0.508184	0.254092	−	0.967180i	$-0.418223\pi$
$313$	8.99070	0.508184	0.254092	+	0.967180i	$0.418223\pi$
$314$	−17.0118	−0.960030
$315$	0	0
$316$	−0.832489	−0.0468312
$317$	−10.4204	−0.585269	−0.292635	−	0.956224i	$-0.594532\pi$
$317$	−10.4204	−0.585269	−0.292635	+	0.956224i	$0.594532\pi$
$318$	−8.48887	−0.476032
$319$	−17.1405	−0.959685
$320$	0	0
$321$	−7.93093	−0.442662
$322$	−18.5393	−1.03315
$323$	0	0
$324$	−1.06790	−0.0593276
$325$	0	0
$326$	5.86733	0.324962
$327$	−18.6383	−1.03070
$328$	3.16503	0.174760
$329$	2.14418	0.118212
$330$	0	0
$331$	4.03055	0.221539	0.110770	−	0.993846i	$-0.464668\pi$
$331$	4.03055	0.221539	0.110770	+	0.993846i	$0.464668\pi$
$332$	−4.67622	−0.256641
$333$	−1.56372	−0.0856911
$334$	−17.2268	−0.942609
$335$	0	0
$336$	−12.8836	−0.702858
$337$	−24.7816	−1.34994	−0.674969	−	0.737846i	$-0.735843\pi$
$337$	−24.7816	−1.34994	−0.674969	+	0.737846i	$0.735843\pi$
$338$	14.7249	0.800928
$339$	−7.82244	−0.424857
$340$	0	0
$341$	−45.7462	−2.47730
$342$	0	0
$343$	−20.1287	−1.08685
$344$	3.39663	0.183134
$345$	0	0
$346$	31.4275	1.68955
$347$	28.6239	1.53661	0.768306	−	0.640082i	$-0.221100\pi$
$347$	28.6239	1.53661	0.768306	+	0.640082i	$0.221100\pi$
$348$	−2.24266	−0.120219
$349$	10.2217	0.547154	0.273577	−	0.961850i	$-0.411793\pi$
$349$	10.2217	0.547154	0.273577	+	0.961850i	$0.411793\pi$
$350$	0	0
$351$	25.6286	1.36796
$352$	−19.1873	−1.02269
$353$	17.7919	0.946965	0.473483	−	0.880803i	$-0.342997\pi$
$353$	17.7919	0.946965	0.473483	+	0.880803i	$0.342997\pi$
$354$	−19.0100	−1.01037
$355$	0	0
$356$	−2.11457	−0.112072
$357$	−2.08466	−0.110332
$358$	−3.35231	−0.177175
$359$	−0.860591	−0.0454202	−0.0227101	−	0.999742i	$-0.507229\pi$
$359$	−0.860591	−0.0454202	−0.0227101	+	0.999742i	$0.507229\pi$
$360$	0	0
$361$	0	0
$362$	−35.0244	−1.84084
$363$	24.7978	1.30155
$364$	−6.51900	−0.341688
$365$	0	0
$366$	4.03357	0.210838
$367$	−21.3109	−1.11242	−0.556209	−	0.831043i	$-0.687744\pi$
$367$	−21.3109	−1.11242	−0.556209	+	0.831043i	$0.687744\pi$
$368$	24.9166	1.29887
$369$	2.25076	0.117170
$370$	0	0
$371$	−9.84543	−0.511150
$372$	−5.98542	−0.310330
$373$	−14.1725	−0.733822	−0.366911	−	0.930256i	$-0.619585\pi$
$373$	−14.1725	−0.733822	−0.366911	+	0.930256i	$0.619585\pi$
$374$	−7.18204	−0.371374
$375$	0	0
$376$	−2.14434	−0.110586
$377$	14.2732	0.735106
$378$	−19.7026	−1.01339
$379$	3.54496	0.182092	0.0910462	−	0.995847i	$-0.470979\pi$
$379$	3.54496	0.182092	0.0910462	+	0.995847i	$0.470979\pi$
$380$	0	0
$381$	−1.58627	−0.0812671
$382$	−36.2771	−1.85610
$383$	7.70846	0.393884	0.196942	−	0.980415i	$-0.436899\pi$
$383$	7.70846	0.393884	0.196942	+	0.980415i	$0.436899\pi$
$384$	16.1816	0.825764
$385$	0	0
$386$	31.7317	1.61510
$387$	2.41546	0.122785
$388$	7.92893	0.402530
$389$	1.79987	0.0912571	0.0456285	−	0.998958i	$-0.485471\pi$
$389$	1.79987	0.0912571	0.0456285	+	0.998958i	$0.485471\pi$
$390$	0	0
$391$	4.03169	0.203891
$392$	4.50568	0.227571
$393$	16.3771	0.826114
$394$	−25.0303	−1.26101
$395$	0	0
$396$	−5.56761	−0.279783
$397$	−17.6756	−0.887111	−0.443556	−	0.896247i	$-0.646283\pi$
$397$	−17.6756	−0.887111	−0.443556	+	0.896247i	$0.646283\pi$
$398$	−2.22292	−0.111425
$399$	0	0
$400$	0	0
$401$	27.1151	1.35406	0.677032	−	0.735954i	$-0.263266\pi$
$401$	27.1151	1.35406	0.677032	+	0.735954i	$0.263266\pi$
$402$	6.25060	0.311752
$403$	38.0936	1.89758
$404$	3.46299	0.172290
$405$	0	0
$406$	−10.9728	−0.544572
$407$	5.56090	0.275644
$408$	2.08482	0.103214
$409$	−33.8712	−1.67482	−0.837411	−	0.546574i	$-0.815932\pi$
$409$	−33.8712	−1.67482	−0.837411	+	0.546574i	$0.815932\pi$
$410$	0	0
$411$	−13.9565	−0.688424
$412$	2.05535	0.101260
$413$	−22.0479	−1.08491
$414$	13.1849	0.648003
$415$	0	0
$416$	15.9775	0.783363
$417$	−11.1030	−0.543714
$418$	0	0
$419$	−23.2338	−1.13505	−0.567524	−	0.823357i	$-0.692099\pi$
$419$	−23.2338	−1.13505	−0.567524	+	0.823357i	$0.692099\pi$
$420$	0	0
$421$	−19.3476	−0.942944	−0.471472	−	0.881881i	$-0.656277\pi$
$421$	−19.3476	−0.942944	−0.471472	+	0.881881i	$0.656277\pi$
$422$	−15.4976	−0.754410
$423$	−1.52491	−0.0741438
$424$	9.84617	0.478173
$425$	0	0
$426$	−13.8113	−0.669159
$427$	4.67815	0.226392
$428$	−4.14631	−0.200419
$429$	−31.5366	−1.52260
$430$	0	0
$431$	13.0559	0.628881	0.314440	−	0.949277i	$-0.398183\pi$
$431$	13.0559	0.628881	0.314440	+	0.949277i	$0.398183\pi$
$432$	26.4801	1.27402
$433$	5.82886	0.280117	0.140059	−	0.990143i	$-0.455271\pi$
$433$	5.82886	0.280117	0.140059	+	0.990143i	$0.455271\pi$
$434$	−29.2852	−1.40574
$435$	0	0
$436$	−9.74413	−0.466659
$437$	0	0
$438$	29.1783	1.39419
$439$	6.49004	0.309753	0.154876	−	0.987934i	$-0.450502\pi$
$439$	6.49004	0.309753	0.154876	+	0.987934i	$0.450502\pi$
$440$	0	0
$441$	3.20414	0.152578
$442$	5.98059	0.284468
$443$	9.20328	0.437261	0.218631	−	0.975808i	$-0.429841\pi$
$443$	9.20328	0.437261	0.218631	+	0.975808i	$0.429841\pi$
$444$	0.727588	0.0345298
$445$	0	0
$446$	10.5847	0.501198
$447$	21.4220	1.01323
$448$	9.39608	0.443923
$449$	17.4646	0.824206	0.412103	−	0.911137i	$-0.364794\pi$
$449$	17.4646	0.824206	0.412103	+	0.911137i	$0.364794\pi$
$450$	0	0
$451$	−8.00419	−0.376903
$452$	−4.08959	−0.192358
$453$	15.4703	0.726860
$454$	14.3914	0.675421
$455$	0	0
$456$	0	0
$457$	0.381827	0.0178611	0.00893055	−	0.999960i	$-0.497157\pi$
$457$	0.381827	0.0178611	0.00893055	+	0.999960i	$0.497157\pi$
$458$	−11.6977	−0.546597
$459$	4.28467	0.199991
$460$	0	0
$461$	8.51706	0.396679	0.198339	−	0.980133i	$-0.436445\pi$
$461$	8.51706	0.396679	0.198339	+	0.980133i	$0.436445\pi$
$462$	24.2445	1.12795
$463$	−37.0178	−1.72036	−0.860181	−	0.509988i	$-0.829650\pi$
$463$	−37.0178	−1.72036	−0.860181	+	0.509988i	$0.829650\pi$
$464$	14.7474	0.684629
$465$	0	0
$466$	−40.4411	−1.87340
$467$	25.9387	1.20030	0.600151	−	0.799887i	$-0.295107\pi$
$467$	25.9387	1.20030	0.600151	+	0.799887i	$0.295107\pi$
$468$	4.63623	0.214310
$469$	7.24948	0.334750
$470$	0	0
$471$	−12.4885	−0.575438
$472$	22.0496	1.01491
$473$	−8.58988	−0.394963
$474$	−2.57814	−0.118418
$475$	0	0
$476$	−1.08986	−0.0499539
$477$	7.00195	0.320597
$478$	27.2307	1.24550
$479$	11.8388	0.540929	0.270464	−	0.962730i	$-0.412823\pi$
$479$	11.8388	0.540929	0.270464	+	0.962730i	$0.412823\pi$
$480$	0	0
$481$	−4.63065	−0.211139
$482$	17.5609	0.799877
$483$	−13.6098	−0.619268
$484$	12.9643	0.589288
$485$	0	0
$486$	23.1759	1.05128
$487$	29.3813	1.33139	0.665696	−	0.746223i	$-0.268135\pi$
$487$	29.3813	1.33139	0.665696	+	0.746223i	$0.268135\pi$
$488$	−4.67851	−0.211786
$489$	4.30725	0.194781
$490$	0	0
$491$	−4.81838	−0.217451	−0.108725	−	0.994072i	$-0.534677\pi$
$491$	−4.81838	−0.217451	−0.108725	+	0.994072i	$0.534677\pi$
$492$	−1.04727	−0.0472145
$493$	2.38623	0.107470
$494$	0	0
$495$	0	0
$496$	39.3591	1.76727
$497$	−16.0184	−0.718524
$498$	−14.4818	−0.648946
$499$	0.188226	0.00842614	0.00421307	−	0.999991i	$-0.498659\pi$
$499$	0.188226	0.00842614	0.00421307	+	0.999991i	$0.498659\pi$
$500$	0	0
$501$	−12.6463	−0.564996
$502$	10.3146	0.460361
$503$	−2.27585	−0.101475	−0.0507375	−	0.998712i	$-0.516157\pi$
$503$	−2.27585	−0.101475	−0.0507375	+	0.998712i	$0.516157\pi$
$504$	7.90756	0.352231
$505$	0	0
$506$	−46.8883	−2.08444
$507$	10.8096	0.480072
$508$	−0.829306	−0.0367945
$509$	4.27456	0.189467	0.0947334	−	0.995503i	$-0.469800\pi$
$509$	4.27456	0.189467	0.0947334	+	0.995503i	$0.469800\pi$
$510$	0	0
$511$	33.8412	1.49705
$512$	−5.17245	−0.228592
$513$	0	0
$514$	−22.0946	−0.974552
$515$	0	0
$516$	−1.12390	−0.0494769
$517$	5.42291	0.238499
$518$	3.55991	0.156414
$519$	23.0711	1.01271
$520$	0	0
$521$	−32.3273	−1.41629	−0.708143	−	0.706069i	$-0.750467\pi$
$521$	−32.3273	−1.41629	−0.708143	+	0.706069i	$0.750467\pi$
$522$	7.80373	0.341560
$523$	29.5161	1.29065	0.645325	−	0.763908i	$-0.276722\pi$
$523$	29.5161	1.29065	0.645325	+	0.763908i	$0.276722\pi$
$524$	8.56197	0.374031
$525$	0	0
$526$	16.5493	0.721585
$527$	6.36859	0.277420
$528$	−32.5843	−1.41805
$529$	3.32109	0.144395
$530$	0	0
$531$	15.6802	0.680463
$532$	0	0
$533$	6.66521	0.288702
$534$	−6.54863	−0.283387
$535$	0	0
$536$	−7.25002	−0.313153
$537$	−2.46096	−0.106198
$538$	23.3954	1.00865
$539$	−11.3946	−0.490800
$540$	0	0
$541$	18.8753	0.811515	0.405757	−	0.913981i	$-0.367008\pi$
$541$	18.8753	0.811515	0.405757	+	0.913981i	$0.367008\pi$
$542$	−26.2377	−1.12701
$543$	−25.7117	−1.10339
$544$	2.67117	0.114525
$545$	0	0
$546$	−20.1887	−0.863998
$547$	−25.1190	−1.07401	−0.537006	−	0.843578i	$-0.680445\pi$
$547$	−25.1190	−1.07401	−0.537006	+	0.843578i	$0.680445\pi$
$548$	−7.29650	−0.311691
$549$	−3.32705	−0.141995
$550$	0	0
$551$	0	0
$552$	13.6108	0.579315
$553$	−2.99014	−0.127154
$554$	46.2961	1.96693
$555$	0	0
$556$	−5.80465	−0.246172
$557$	28.1731	1.19373	0.596867	−	0.802340i	$-0.296412\pi$
$557$	28.1731	1.19373	0.596867	+	0.802340i	$0.296412\pi$
$558$	20.8273	0.881690
$559$	7.15292	0.302536
$560$	0	0
$561$	−5.27238	−0.222600
$562$	−11.6212	−0.490211
$563$	20.4297	0.861010	0.430505	−	0.902588i	$-0.358336\pi$
$563$	20.4297	0.861010	0.430505	+	0.902588i	$0.358336\pi$
$564$	0.709533	0.0298767
$565$	0	0
$566$	−16.7827	−0.705428
$567$	−3.83568	−0.161083
$568$	16.0196	0.672168
$569$	35.8386	1.50243	0.751217	−	0.660056i	$-0.229467\pi$
$569$	35.8386	1.50243	0.751217	+	0.660056i	$0.229467\pi$
$570$	0	0
$571$	−2.82827	−0.118359	−0.0591797	−	0.998247i	$-0.518848\pi$
$571$	−2.82827	−0.118359	−0.0591797	+	0.998247i	$0.518848\pi$
$572$	−16.4874	−0.689374
$573$	−26.6313	−1.11254
$574$	−5.12403	−0.213873
$575$	0	0
$576$	−6.68237	−0.278432
$577$	−43.3132	−1.80315	−0.901575	−	0.432622i	$-0.857589\pi$
$577$	−43.3132	−1.80315	−0.901575	+	0.432622i	$0.857589\pi$
$578$	−26.5243	−1.10327
$579$	23.2945	0.968085
$580$	0	0
$581$	−16.7961	−0.696819
$582$	24.5552	1.01784
$583$	−24.9004	−1.03127
$584$	−33.8437	−1.40046
$585$	0	0
$586$	14.7183	0.608006
$587$	24.5741	1.01428	0.507141	−	0.861863i	$-0.330702\pi$
$587$	24.5741	1.01428	0.507141	+	0.861863i	$0.330702\pi$
$588$	−1.49087	−0.0614824
$589$	0	0
$590$	0	0
$591$	−18.3749	−0.755843
$592$	−4.78449	−0.196641
$593$	0.313720	0.0128829	0.00644147	−	0.999979i	$-0.497950\pi$
$593$	0.313720	0.0128829	0.00644147	+	0.999979i	$0.497950\pi$
$594$	−49.8304	−2.04457
$595$	0	0
$596$	11.1995	0.458748
$597$	−1.63186	−0.0667877
$598$	39.0446	1.59665
$599$	−24.4964	−1.00090	−0.500448	−	0.865767i	$-0.666831\pi$
$599$	−24.4964	−1.00090	−0.500448	+	0.865767i	$0.666831\pi$
$600$	0	0
$601$	7.83045	0.319411	0.159705	−	0.987165i	$-0.448946\pi$
$601$	7.83045	0.319411	0.159705	+	0.987165i	$0.448946\pi$
$602$	−5.49896	−0.224121
$603$	−5.15574	−0.209958
$604$	8.08793	0.329093
$605$	0	0
$606$	10.7246	0.435655
$607$	12.4142	0.503876	0.251938	−	0.967743i	$-0.418932\pi$
$607$	12.4142	0.503876	0.251938	+	0.967743i	$0.418932\pi$
$608$	0	0
$609$	−8.05522	−0.326414
$610$	0	0
$611$	−4.51574	−0.182687
$612$	0.775098	0.0313315
$613$	1.05853	0.0427534	0.0213767	−	0.999771i	$-0.493195\pi$
$613$	1.05853	0.0427534	0.0213767	+	0.999771i	$0.493195\pi$
$614$	−23.7422	−0.958156
$615$	0	0
$616$	−28.1210	−1.13303
$617$	28.5881	1.15091	0.575457	−	0.817832i	$-0.304824\pi$
$617$	28.5881	1.15091	0.575457	+	0.817832i	$0.304824\pi$
$618$	6.36522	0.256047
$619$	9.41956	0.378604	0.189302	−	0.981919i	$-0.439377\pi$
$619$	9.41956	0.378604	0.189302	+	0.981919i	$0.439377\pi$
$620$	0	0
$621$	27.9727	1.12250
$622$	−51.1320	−2.05021
$623$	−7.59514	−0.304293
$624$	27.1335	1.08621
$625$	0	0
$626$	14.5566	0.581797
$627$	0	0
$628$	−6.52899	−0.260535
$629$	−0.774165	−0.0308680
$630$	0	0
$631$	−39.6280	−1.57757	−0.788784	−	0.614671i	$-0.789289\pi$
$631$	−39.6280	−1.57757	−0.788784	+	0.614671i	$0.789289\pi$
$632$	2.99037	0.118950
$633$	−11.3769	−0.452190
$634$	−16.8714	−0.670049
$635$	0	0
$636$	−3.25797	−0.129187
$637$	9.48846	0.375947
$638$	−27.7517	−1.09870
$639$	11.3921	0.450664
$640$	0	0
$641$	−19.6559	−0.776360	−0.388180	−	0.921584i	$-0.626896\pi$
$641$	−19.6559	−0.776360	−0.388180	+	0.921584i	$0.626896\pi$
$642$	−12.8407	−0.506783
$643$	−28.7116	−1.13227	−0.566137	−	0.824311i	$-0.691563\pi$
$643$	−28.7116	−1.13227	−0.566137	+	0.824311i	$0.691563\pi$
$644$	−7.11524	−0.280380
$645$	0	0
$646$	0	0
$647$	17.4412	0.685686	0.342843	−	0.939393i	$-0.388610\pi$
$647$	17.4412	0.685686	0.342843	+	0.939393i	$0.388610\pi$
$648$	3.83597	0.150691
$649$	−55.7622	−2.18886
$650$	0	0
$651$	−21.4985	−0.842592
$652$	2.25184	0.0881889
$653$	30.3498	1.18768	0.593839	−	0.804584i	$-0.297612\pi$
$653$	30.3498	1.18768	0.593839	+	0.804584i	$0.297612\pi$
$654$	−30.1767	−1.18000
$655$	0	0
$656$	6.88664	0.268878
$657$	−24.0674	−0.938959
$658$	3.47157	0.135336
$659$	−6.53865	−0.254709	−0.127355	−	0.991857i	$-0.540649\pi$
$659$	−6.53865	−0.254709	−0.127355	+	0.991857i	$0.540649\pi$
$660$	0	0
$661$	−23.7996	−0.925699	−0.462849	−	0.886437i	$-0.653173\pi$
$661$	−23.7996	−0.925699	−0.462849	+	0.886437i	$0.653173\pi$
$662$	6.52575	0.253630
$663$	4.39039	0.170509
$664$	16.7973	0.651863
$665$	0	0
$666$	−2.53176	−0.0981039
$667$	15.5786	0.603207
$668$	−6.61152	−0.255808
$669$	7.77027	0.300416
$670$	0	0
$671$	11.8317	0.456757
$672$	−9.01709	−0.347842
$673$	49.9227	1.92438	0.962189	−	0.272381i	$-0.0878111\pi$
$673$	49.9227	1.92438	0.962189	+	0.272381i	$0.0878111\pi$
$674$	−40.1231	−1.54548
$675$	0	0
$676$	5.65130	0.217358
$677$	−34.5826	−1.32912	−0.664558	−	0.747237i	$-0.731380\pi$
$677$	−34.5826	−1.32912	−0.664558	+	0.747237i	$0.731380\pi$
$678$	−12.6651	−0.486399
$679$	28.4792	1.09293
$680$	0	0
$681$	10.5648	0.404844
$682$	−74.0663	−2.83614
$683$	−21.1277	−0.808429	−0.404214	−	0.914664i	$-0.632455\pi$
$683$	−21.1277	−0.808429	−0.404214	+	0.914664i	$0.632455\pi$
$684$	0	0
$685$	0	0
$686$	−32.5897	−1.24428
$687$	−8.58735	−0.327628
$688$	7.39055	0.281762
$689$	20.7350	0.789939
$690$	0	0
$691$	27.8861	1.06084	0.530418	−	0.847736i	$-0.322035\pi$
$691$	27.8861	1.06084	0.530418	+	0.847736i	$0.322035\pi$
$692$	12.0616	0.458514
$693$	−19.9978	−0.759653
$694$	46.3441	1.75920
$695$	0	0
$696$	8.05582	0.305355
$697$	1.11431	0.0422075
$698$	16.5496	0.626412
$699$	−29.6881	−1.12291
$700$	0	0
$701$	−39.3344	−1.48564	−0.742821	−	0.669490i	$-0.766513\pi$
$701$	−39.3344	−1.48564	−0.742821	+	0.669490i	$0.766513\pi$
$702$	41.4946	1.56611
$703$	0	0
$704$	23.7639	0.895637
$705$	0	0
$706$	28.8063	1.08414
$707$	12.4384	0.467794
$708$	−7.29591	−0.274197
$709$	4.28832	0.161051	0.0805256	−	0.996753i	$-0.474340\pi$
$709$	4.28832	0.161051	0.0805256	+	0.996753i	$0.474340\pi$
$710$	0	0
$711$	2.12655	0.0797519
$712$	7.59571	0.284661
$713$	41.5776	1.55710
$714$	−3.37521	−0.126314
$715$	0	0
$716$	−1.28659	−0.0480822
$717$	19.9902	0.746549
$718$	−1.39336	−0.0519996
$719$	−3.93252	−0.146658	−0.0733291	−	0.997308i	$-0.523362\pi$
$719$	−3.93252	−0.146658	−0.0733291	+	0.997308i	$0.523362\pi$
$720$	0	0
$721$	7.38242	0.274936
$722$	0	0
$723$	12.8916	0.479443
$724$	−13.4421	−0.499572
$725$	0	0
$726$	40.1494	1.49008
$727$	20.0574	0.743889	0.371944	−	0.928255i	$-0.378691\pi$
$727$	20.0574	0.743889	0.371944	+	0.928255i	$0.378691\pi$
$728$	23.4168	0.867883
$729$	22.1693	0.821086
$730$	0	0
$731$	1.19585	0.0442300
$732$	1.54805	0.0572177
$733$	0.205782	0.00760071	0.00380036	−	0.999993i	$-0.498790\pi$
$733$	0.205782	0.00760071	0.00380036	+	0.999993i	$0.498790\pi$
$734$	−34.5038	−1.27356
$735$	0	0
$736$	17.4389	0.642805
$737$	18.3349	0.675374
$738$	3.64414	0.134143
$739$	32.6116	1.19964	0.599819	−	0.800136i	$-0.295239\pi$
$739$	32.6116	1.19964	0.599819	+	0.800136i	$0.295239\pi$
$740$	0	0
$741$	0	0
$742$	−15.9404	−0.585192
$743$	−29.5603	−1.08446	−0.542231	−	0.840230i	$-0.682420\pi$
$743$	−29.5603	−1.08446	−0.542231	+	0.840230i	$0.682420\pi$
$744$	21.5001	0.788232
$745$	0	0
$746$	−22.9462	−0.840120
$747$	11.9452	0.437051
$748$	−2.75641	−0.100784
$749$	−14.8927	−0.544169
$750$	0	0
$751$	37.0458	1.35182	0.675909	−	0.736985i	$-0.263751\pi$
$751$	37.0458	1.35182	0.675909	+	0.736985i	$0.263751\pi$
$752$	−4.66576	−0.170143
$753$	7.57198	0.275938
$754$	23.1093	0.841590
$755$	0	0
$756$	−7.56170	−0.275016
$757$	−30.5480	−1.11029	−0.555143	−	0.831755i	$-0.687336\pi$
$757$	−30.5480	−1.11029	−0.555143	+	0.831755i	$0.687336\pi$
$758$	5.73954	0.208470
$759$	−34.4210	−1.24940
$760$	0	0
$761$	−46.0692	−1.67001	−0.835004	−	0.550244i	$-0.814535\pi$
$761$	−46.0692	−1.67001	−0.835004	+	0.550244i	$0.814535\pi$
$762$	−2.56828	−0.0930391
$763$	−34.9990	−1.26705
$764$	−13.9229	−0.503712
$765$	0	0
$766$	12.4805	0.450940
$767$	46.4340	1.67663
$768$	16.1916	0.584266
$769$	14.7199	0.530814	0.265407	−	0.964137i	$-0.414494\pi$
$769$	14.7199	0.530814	0.265407	+	0.964137i	$0.414494\pi$
$770$	0	0
$771$	−16.2198	−0.584142
$772$	12.1784	0.438310
$773$	8.86483	0.318846	0.159423	−	0.987210i	$-0.449037\pi$
$773$	8.86483	0.318846	0.159423	+	0.987210i	$0.449037\pi$
$774$	3.91079	0.140571
$775$	0	0
$776$	−28.4813	−1.02242
$777$	2.61336	0.0937536
$778$	2.91412	0.104476
$779$	0	0
$780$	0	0
$781$	−40.5127	−1.44966
$782$	6.52759	0.233426
$783$	16.5561	0.591668
$784$	9.80368	0.350132
$785$	0	0
$786$	26.5156	0.945781
$787$	13.1846	0.469979	0.234990	−	0.971998i	$-0.424494\pi$
$787$	13.1846	0.469979	0.234990	+	0.971998i	$0.424494\pi$
$788$	−9.60645	−0.342216
$789$	12.1490	0.432515
$790$	0	0
$791$	−14.6890	−0.522281
$792$	19.9993	0.710644
$793$	−9.85242	−0.349870
$794$	−28.6180	−1.01561
$795$	0	0
$796$	−0.853141	−0.0302388
$797$	−38.1858	−1.35261	−0.676306	−	0.736621i	$-0.736420\pi$
$797$	−38.1858	−1.35261	−0.676306	+	0.736621i	$0.736420\pi$
$798$	0	0
$799$	−0.754954	−0.0267084
$800$	0	0
$801$	5.40157	0.190855
$802$	43.9012	1.55021
$803$	85.5889	3.02037
$804$	2.39893	0.0846039
$805$	0	0
$806$	61.6761	2.17245
$807$	17.1747	0.604580
$808$	−12.4393	−0.437614
$809$	43.7667	1.53875	0.769377	−	0.638795i	$-0.220567\pi$
$809$	43.7667	1.53875	0.769377	+	0.638795i	$0.220567\pi$
$810$	0	0
$811$	5.95225	0.209012	0.104506	−	0.994524i	$-0.466674\pi$
$811$	5.95225	0.209012	0.104506	+	0.994524i	$0.466674\pi$
$812$	−4.21128	−0.147787
$813$	−19.2613	−0.675522
$814$	9.00349	0.315572
$815$	0	0
$816$	4.53625	0.158800
$817$	0	0
$818$	−54.8398	−1.91743
$819$	16.6525	0.581884
$820$	0	0
$821$	−7.97019	−0.278162	−0.139081	−	0.990281i	$-0.544415\pi$
$821$	−7.97019	−0.278162	−0.139081	+	0.990281i	$0.544415\pi$
$822$	−22.5966	−0.788146
$823$	28.1907	0.982666	0.491333	−	0.870972i	$-0.336510\pi$
$823$	28.1907	0.982666	0.491333	+	0.870972i	$0.336510\pi$
$824$	−7.38297	−0.257198
$825$	0	0
$826$	−35.6971	−1.24206
$827$	54.5094	1.89548	0.947738	−	0.319048i	$-0.103363\pi$
$827$	54.5094	1.89548	0.947738	+	0.319048i	$0.103363\pi$
$828$	5.06027	0.175856
$829$	−8.40522	−0.291925	−0.145963	−	0.989290i	$-0.546628\pi$
$829$	−8.40522	−0.291925	−0.145963	+	0.989290i	$0.546628\pi$
$830$	0	0
$831$	33.9863	1.17897
$832$	−19.7886	−0.686046
$833$	1.58631	0.0549623
$834$	−17.9765	−0.622474
$835$	0	0
$836$	0	0
$837$	44.1865	1.52731
$838$	−37.6172	−1.29947
$839$	−37.7155	−1.30208	−0.651041	−	0.759042i	$-0.725667\pi$
$839$	−37.7155	−1.30208	−0.651041	+	0.759042i	$0.725667\pi$
$840$	0	0
$841$	−19.7795	−0.682052
$842$	−31.3251	−1.07953
$843$	−8.53120	−0.293830
$844$	−5.94785	−0.204734
$845$	0	0
$846$	−2.46894	−0.0848839
$847$	46.5654	1.60001
$848$	21.4238	0.735696
$849$	−12.3203	−0.422831
$850$	0	0
$851$	−5.05418	−0.173255
$852$	−5.30067	−0.181598
$853$	41.2975	1.41400	0.707000	−	0.707214i	$-0.250048\pi$
$853$	41.2975	1.41400	0.707000	+	0.707214i	$0.250048\pi$
$854$	7.57426	0.259186
$855$	0	0
$856$	14.8939	0.509062
$857$	3.43473	0.117328	0.0586640	−	0.998278i	$-0.481316\pi$
$857$	3.43473	0.117328	0.0586640	+	0.998278i	$0.481316\pi$
$858$	−51.0600	−1.74316
$859$	−30.2921	−1.03355	−0.516777	−	0.856120i	$-0.672868\pi$
$859$	−30.2921	−1.03355	−0.516777	+	0.856120i	$0.672868\pi$
$860$	0	0
$861$	−3.76158	−0.128194
$862$	21.1384	0.719977
$863$	−23.8589	−0.812168	−0.406084	−	0.913836i	$-0.633106\pi$
$863$	−23.8589	−0.812168	−0.406084	+	0.913836i	$0.633106\pi$
$864$	18.5331	0.630509
$865$	0	0
$866$	9.43733	0.320694
$867$	−19.4717	−0.661293
$868$	−11.2395	−0.381492
$869$	−7.56246	−0.256539
$870$	0	0
$871$	−15.2677	−0.517328
$872$	35.0017	1.18531
$873$	−20.2540	−0.685496
$874$	0	0
$875$	0	0
$876$	11.1984	0.378360
$877$	−13.2757	−0.448288	−0.224144	−	0.974556i	$-0.571959\pi$
$877$	−13.2757	−0.448288	−0.224144	+	0.974556i	$0.571959\pi$
$878$	10.5078	0.354622
$879$	10.8048	0.364436
$880$	0	0
$881$	20.1998	0.680547	0.340274	−	0.940326i	$-0.389480\pi$
$881$	20.1998	0.680547	0.340274	+	0.940326i	$0.389480\pi$
$882$	5.18773	0.174680
$883$	58.2506	1.96029	0.980144	−	0.198289i	$-0.0635385\pi$
$883$	58.2506	1.96029	0.980144	+	0.198289i	$0.0635385\pi$
$884$	2.29531	0.0771995
$885$	0	0
$886$	14.9008	0.500601
$887$	46.0826	1.54730	0.773651	−	0.633612i	$-0.218429\pi$
$887$	46.0826	1.54730	0.773651	+	0.633612i	$0.218429\pi$
$888$	−2.61355	−0.0877050
$889$	−2.97871	−0.0999026
$890$	0	0
$891$	−9.70095	−0.324994
$892$	4.06232	0.136016
$893$	0	0
$894$	34.6837	1.16000
$895$	0	0
$896$	30.3859	1.01512
$897$	28.6629	0.957027
$898$	28.2764	0.943597
$899$	24.6085	0.820739
$900$	0	0
$901$	3.46653	0.115487
$902$	−12.9593	−0.431499
$903$	−4.03683	−0.134337
$904$	14.6901	0.488586
$905$	0	0
$906$	25.0476	0.832150
$907$	−43.6873	−1.45061	−0.725306	−	0.688426i	$-0.758302\pi$
$907$	−43.6873	−1.45061	−0.725306	+	0.688426i	$0.758302\pi$
$908$	5.52331	0.183297
$909$	−8.84603	−0.293404
$910$	0	0
$911$	30.7689	1.01942	0.509709	−	0.860347i	$-0.329753\pi$
$911$	30.7689	1.01942	0.509709	+	0.860347i	$0.329753\pi$
$912$	0	0
$913$	−42.4795	−1.40587
$914$	0.618204	0.0204484
$915$	0	0
$916$	−4.48949	−0.148337
$917$	30.7530	1.01555
$918$	6.93718	0.228961
$919$	12.0943	0.398953	0.199476	−	0.979903i	$-0.436076\pi$
$919$	12.0943	0.398953	0.199476	+	0.979903i	$0.436076\pi$
$920$	0	0
$921$	−17.4293	−0.574314
$922$	13.7897	0.454140
$923$	33.7355	1.11042
$924$	9.30485	0.306107
$925$	0	0
$926$	−59.9344	−1.96957
$927$	−5.25028	−0.172442
$928$	10.3215	0.338820
$929$	15.9647	0.523785	0.261892	−	0.965097i	$-0.415653\pi$
$929$	15.9647	0.523785	0.261892	+	0.965097i	$0.415653\pi$
$930$	0	0
$931$	0	0
$932$	−15.5210	−0.508407
$933$	−37.5363	−1.22888
$934$	41.9966	1.37417
$935$	0	0
$936$	−16.6537	−0.544343
$937$	−3.57961	−0.116941	−0.0584704	−	0.998289i	$-0.518622\pi$
$937$	−3.57961	−0.116941	−0.0584704	+	0.998289i	$0.518622\pi$
$938$	11.7374	0.383240
$939$	10.6861	0.348727
$940$	0	0
$941$	−34.7060	−1.13138	−0.565691	−	0.824617i	$-0.691391\pi$
$941$	−34.7060	−1.13138	−0.565691	+	0.824617i	$0.691391\pi$
$942$	−20.2197	−0.658793
$943$	7.27482	0.236901
$944$	47.9766	1.56151
$945$	0	0
$946$	−13.9076	−0.452176
$947$	44.9696	1.46132	0.730658	−	0.682743i	$-0.239213\pi$
$947$	44.9696	1.46132	0.730658	+	0.682743i	$0.239213\pi$
$948$	−0.989471	−0.0321365
$949$	−71.2711	−2.31356
$950$	0	0
$951$	−12.3854	−0.401624
$952$	3.91488	0.126882
$953$	−1.67348	−0.0542095	−0.0271047	−	0.999633i	$-0.508629\pi$
$953$	−1.67348	−0.0542095	−0.0271047	+	0.999633i	$0.508629\pi$
$954$	11.3366	0.367037
$955$	0	0
$956$	10.4509	0.338007
$957$	−20.3727	−0.658556
$958$	19.1679	0.619285
$959$	−26.2076	−0.846288
$960$	0	0
$961$	34.6774	1.11863
$962$	−7.49735	−0.241724
$963$	10.5915	0.341307
$964$	6.73974	0.217072
$965$	0	0
$966$	−22.0352	−0.708972
$967$	−18.1691	−0.584279	−0.292140	−	0.956376i	$-0.594367\pi$
$967$	−18.1691	−0.584279	−0.292140	+	0.956376i	$0.594367\pi$
$968$	−46.5689	−1.49678
$969$	0	0
$970$	0	0
$971$	−4.64954	−0.149211	−0.0746054	−	0.997213i	$-0.523770\pi$
$971$	−4.64954	−0.149211	−0.0746054	+	0.997213i	$0.523770\pi$
$972$	8.89475	0.285299
$973$	−20.8492	−0.668395
$974$	47.5703	1.52425
$975$	0	0
$976$	−10.1797	−0.325845
$977$	−13.7386	−0.439535	−0.219768	−	0.975552i	$-0.570530\pi$
$977$	−13.7386	−0.439535	−0.219768	+	0.975552i	$0.570530\pi$
$978$	6.97374	0.222996
$979$	−19.2091	−0.613926
$980$	0	0
$981$	24.8909	0.794704
$982$	−7.80130	−0.248949
$983$	−8.41202	−0.268302	−0.134151	−	0.990961i	$-0.542831\pi$
$983$	−8.41202	−0.268302	−0.134151	+	0.990961i	$0.542831\pi$
$984$	3.76187	0.119924
$985$	0	0
$986$	3.86347	0.123038
$987$	2.54850	0.0811198
$988$	0	0
$989$	7.80714	0.248253
$990$	0	0
$991$	−18.5779	−0.590145	−0.295072	−	0.955475i	$-0.595344\pi$
$991$	−18.5779	−0.590145	−0.295072	+	0.955475i	$0.595344\pi$
$992$	27.5470	0.874618
$993$	4.79059	0.152025
$994$	−25.9349	−0.822605
$995$	0	0
$996$	−5.55801	−0.176112
$997$	−38.4609	−1.21807	−0.609035	−	0.793143i	$-0.708443\pi$
$997$	−38.4609	−1.21807	−0.609035	+	0.793143i	$0.708443\pi$
$998$	0.304751	0.00964671
$999$	−5.37131	−0.169941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.ct.1.19		24
5.2	odd	4		1805.2.b.l.1084.19		24
5.3	odd	4		1805.2.b.l.1084.6		24
5.4	even	2	inner	9025.2.a.ct.1.6		24
19.14	odd	18		475.2.l.f.101.3		48
19.15	odd	18		475.2.l.f.301.3		48
19.18	odd	2		9025.2.a.cu.1.6		24
95.14	odd	18		475.2.l.f.101.6		48
95.18	even	4		1805.2.b.k.1084.19		24
95.33	even	36		95.2.p.a.44.6	yes	48
95.34	odd	18		475.2.l.f.301.6		48
95.37	even	4		1805.2.b.k.1084.6		24
95.52	even	36		95.2.p.a.44.3	✓	48
95.53	even	36		95.2.p.a.54.3	yes	48
95.72	even	36		95.2.p.a.54.6	yes	48
95.94	odd	2		9025.2.a.cu.1.19		24
285.53	odd	36		855.2.da.b.244.6		48
285.128	odd	36		855.2.da.b.424.3		48
285.167	odd	36		855.2.da.b.244.3		48
285.242	odd	36		855.2.da.b.424.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.3	✓	48	95.52	even	36
95.2.p.a.44.6	yes	48	95.33	even	36
95.2.p.a.54.3	yes	48	95.53	even	36
95.2.p.a.54.6	yes	48	95.72	even	36
475.2.l.f.101.3		48	19.14	odd	18
475.2.l.f.101.6		48	95.14	odd	18
475.2.l.f.301.3		48	19.15	odd	18
475.2.l.f.301.6		48	95.34	odd	18
855.2.da.b.244.3		48	285.167	odd	36
855.2.da.b.244.6		48	285.53	odd	36
855.2.da.b.424.3		48	285.128	odd	36
855.2.da.b.424.6		48	285.242	odd	36
1805.2.b.k.1084.6		24	95.37	even	4
1805.2.b.k.1084.19		24	95.18	even	4
1805.2.b.l.1084.6		24	5.3	odd	4
1805.2.b.l.1084.19		24	5.2	odd	4
9025.2.a.ct.1.6		24	5.4	even	2	inner
9025.2.a.ct.1.19		24	1.1	even	1	trivial
9025.2.a.cu.1.6		24	19.18	odd	2
9025.2.a.cu.1.19		24	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)

\(f(q)\)	\(=\)	\(q+1.61907 q^{2} +1.18857 q^{3} +0.621387 q^{4} +1.92438 q^{6} +2.23190 q^{7} -2.23207 q^{8} -1.58730 q^{9} +O(q^{10})\)	\(q+1.61907 q^{2} +1.18857 q^{3} +0.621387 q^{4} +1.92438 q^{6} +2.23190 q^{7} -2.23207 q^{8} -1.58730 q^{9} +5.64478 q^{11} +0.738562 q^{12} -4.70049 q^{13} +3.61361 q^{14} -4.85665 q^{16} -0.785842 q^{17} -2.56995 q^{18} +2.65277 q^{21} +9.13929 q^{22} -5.13041 q^{23} -2.65297 q^{24} -7.61043 q^{26} -5.45233 q^{27} +1.38688 q^{28} -3.03653 q^{29} -8.10416 q^{31} -3.39912 q^{32} +6.70922 q^{33} -1.27233 q^{34} -0.986329 q^{36} +0.985141 q^{37} -5.58687 q^{39} -1.41798 q^{41} +4.29502 q^{42} -1.52174 q^{43} +3.50759 q^{44} -8.30649 q^{46} +0.960695 q^{47} -5.77247 q^{48} -2.01861 q^{49} -0.934028 q^{51} -2.92083 q^{52} -4.41123 q^{53} -8.82770 q^{54} -4.98176 q^{56} -4.91635 q^{58} -9.87853 q^{59} +2.09604 q^{61} -13.1212 q^{62} -3.54270 q^{63} +4.20990 q^{64} +10.8627 q^{66} +3.24811 q^{67} -0.488312 q^{68} -6.09785 q^{69} -7.17702 q^{71} +3.54297 q^{72} +15.1625 q^{73} +1.59501 q^{74} +12.5986 q^{77} -9.04553 q^{78} -1.33973 q^{79} -1.71857 q^{81} -2.29581 q^{82} -7.52545 q^{83} +1.64840 q^{84} -2.46380 q^{86} -3.60912 q^{87} -12.5995 q^{88} -3.40299 q^{89} -10.4910 q^{91} -3.18797 q^{92} -9.63236 q^{93} +1.55543 q^{94} -4.04009 q^{96} +12.7601 q^{97} -3.26827 q^{98} -8.95997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

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