LMFDB - Embedded newform 9025.2.a.bu.1.2

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:	$6$
Coefficient field:	6.6.4227136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} + 7x^{2} - 1 $ x^6 - 6x^4 + 7x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.15904$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.862781 q^{2} -3.07914 q^{3} -1.25561 q^{4} +2.65662 q^{6} -0.566520 q^{7} +2.80888 q^{8} +6.48108 q^{9} +O(q^{10})$	\(q-0.862781 q^{2} -3.07914 q^{3} -1.25561 q^{4} +2.65662 q^{6} -0.566520 q^{7} +2.80888 q^{8} +6.48108 q^{9} -1.91223 q^{11} +3.86619 q^{12} -0.194531 q^{13} +0.488783 q^{14} +0.0877708 q^{16} -5.29549 q^{17} -5.59175 q^{18} +1.74439 q^{21} +1.64984 q^{22} -3.37540 q^{23} -8.64892 q^{24} +0.167838 q^{26} -10.7187 q^{27} +0.711327 q^{28} -8.73669 q^{29} +5.65662 q^{31} -5.69348 q^{32} +5.88801 q^{33} +4.56885 q^{34} -8.13770 q^{36} -0.955582 q^{37} +0.598988 q^{39} +10.0499 q^{41} -1.50503 q^{42} +4.93243 q^{43} +2.40101 q^{44} +2.91223 q^{46} -8.83942 q^{47} -0.270258 q^{48} -6.67906 q^{49} +16.3055 q^{51} +0.244255 q^{52} +8.20610 q^{53} +9.24791 q^{54} -1.59128 q^{56} +7.53785 q^{58} +3.71425 q^{59} -3.51122 q^{61} -4.88043 q^{62} -3.67166 q^{63} +4.73669 q^{64} -5.08007 q^{66} -4.04365 q^{67} +6.64906 q^{68} +10.3933 q^{69} +5.19533 q^{71} +18.2046 q^{72} -8.60409 q^{73} +0.824458 q^{74} +1.08332 q^{77} -0.516796 q^{78} +6.62648 q^{79} +13.5611 q^{81} -8.67089 q^{82} +4.51737 q^{83} -2.19027 q^{84} -4.25561 q^{86} +26.9014 q^{87} -5.37122 q^{88} +3.37352 q^{89} +0.110206 q^{91} +4.23818 q^{92} -17.4175 q^{93} +7.62648 q^{94} +17.5310 q^{96} -15.1922 q^{97} +5.76256 q^{98} -12.3933 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{4} + 12 q^{6} + 8 q^{9}+O(q^{10}) $ 6 * q + 2 * q^4 + 12 * q^6 + 8 * q^9	$ 6 q + 2 q^{4} + 12 q^{6} + 8 q^{9} + 2 q^{11} + 22 q^{14} + 14 q^{16} + 20 q^{21} + 2 q^{24} - 22 q^{26} - 12 q^{29} + 30 q^{31} + 10 q^{34} - 14 q^{36} - 2 q^{39} + 12 q^{41} + 20 q^{44} + 4 q^{46} + 2 q^{49} + 40 q^{51} - 4 q^{54} + 46 q^{56} + 20 q^{59} - 2 q^{61} - 12 q^{64} + 6 q^{66} + 18 q^{69} - 2 q^{71} - 22 q^{74} + 24 q^{79} + 14 q^{81} + 48 q^{84} - 16 q^{86} + 36 q^{89} - 24 q^{91} + 30 q^{94} + 26 q^{96} - 30 q^{99}+O(q^{100}) $ 6 * q + 2 * q^4 + 12 * q^6 + 8 * q^9 + 2 * q^11 + 22 * q^14 + 14 * q^16 + 20 * q^21 + 2 * q^24 - 22 * q^26 - 12 * q^29 + 30 * q^31 + 10 * q^34 - 14 * q^36 - 2 * q^39 + 12 * q^41 + 20 * q^44 + 4 * q^46 + 2 * q^49 + 40 * q^51 - 4 * q^54 + 46 * q^56 + 20 * q^59 - 2 * q^61 - 12 * q^64 + 6 * q^66 + 18 * q^69 - 2 * q^71 - 22 * q^74 + 24 * q^79 + 14 * q^81 + 48 * q^84 - 16 * q^86 + 36 * q^89 - 24 * q^91 + 30 * q^94 + 26 * q^96 - 30 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.862781	−0.610078	−0.305039	−	0.952340i	$-0.598670\pi$
$2$	−0.862781	−0.610078	−0.305039	+	0.952340i	$0.598670\pi$
$3$	−3.07914	−1.77774	−0.888870	−	0.458159i	$-0.848509\pi$
$3$	−3.07914	−1.77774	−0.888870	+	0.458159i	$0.848509\pi$
$4$	−1.25561	−0.627804
$5$	0	0
$5$	0	0
$6$	2.65662	1.08456
$7$	−0.566520	−0.214124	−0.107062	−	0.994252i	$-0.534144\pi$
$7$	−0.566520	−0.214124	−0.107062	+	0.994252i	$0.534144\pi$
$8$	2.80888	0.993088
$9$	6.48108	2.16036
$10$	0	0
$11$	−1.91223	−0.576559	−0.288279	−	0.957546i	$-0.593083\pi$
$11$	−1.91223	−0.576559	−0.288279	+	0.957546i	$0.593083\pi$
$12$	3.86619	1.11607
$13$	−0.194531	−0.0539533	−0.0269766	−	0.999636i	$-0.508588\pi$
$13$	−0.194531	−0.0539533	−0.0269766	+	0.999636i	$0.508588\pi$
$14$	0.488783	0.130633
$15$	0	0
$16$	0.0877708	0.0219427
$17$	−5.29549	−1.28435	−0.642173	−	0.766560i	$-0.721967\pi$
$17$	−5.29549	−1.28435	−0.642173	+	0.766560i	$0.721967\pi$
$18$	−5.59175	−1.31799
$19$	0	0
$19$	0	0
$20$	0	0
$21$	1.74439	0.380657
$22$	1.64984	0.351746
$23$	−3.37540	−0.703819	−0.351910	−	0.936034i	$-0.614468\pi$
$23$	−3.37540	−0.703819	−0.351910	+	0.936034i	$0.614468\pi$
$24$	−8.64892	−1.76545
$25$	0	0
$26$	0.167838	0.0329157
$27$	−10.7187	−2.06282
$28$	0.711327	0.134428
$29$	−8.73669	−1.62236	−0.811181	−	0.584795i	$-0.801175\pi$
$29$	−8.73669	−1.62236	−0.811181	+	0.584795i	$0.801175\pi$
$30$	0	0
$31$	5.65662	1.01596	0.507980	−	0.861369i	$-0.330393\pi$
$31$	5.65662	1.01596	0.507980	+	0.861369i	$0.330393\pi$
$32$	−5.69348	−1.00648
$33$	5.88801	1.02497
$34$	4.56885	0.783551
$35$	0	0
$36$	−8.13770	−1.35628
$37$	−0.955582	−0.157097	−0.0785484	−	0.996910i	$-0.525029\pi$
$37$	−0.955582	−0.157097	−0.0785484	+	0.996910i	$0.525029\pi$
$38$	0	0
$39$	0.598988	0.0959149
$40$	0	0
$41$	10.0499	1.56954	0.784768	−	0.619790i	$-0.212782\pi$
$41$	10.0499	1.56954	0.784768	+	0.619790i	$0.212782\pi$
$42$	−1.50503	−0.232231
$43$	4.93243	0.752189	0.376094	−	0.926581i	$-0.377267\pi$
$43$	4.93243	0.752189	0.376094	+	0.926581i	$0.377267\pi$
$44$	2.40101	0.361966
$45$	0	0
$46$	2.91223	0.429385
$47$	−8.83942	−1.28936	−0.644681	−	0.764452i	$-0.723010\pi$
$47$	−8.83942	−1.28936	−0.644681	+	0.764452i	$0.723010\pi$
$48$	−0.270258	−0.0390084
$49$	−6.67906	−0.954151
$50$	0	0
$51$	16.3055	2.28323
$52$	0.244255	0.0338721
$53$	8.20610	1.12719	0.563597	−	0.826050i	$-0.309417\pi$
$53$	8.20610	1.12719	0.563597	+	0.826050i	$0.309417\pi$
$54$	9.24791	1.25848
$55$	0	0
$56$	−1.59128	−0.212644
$57$	0	0
$58$	7.53785	0.989768
$59$	3.71425	0.483554	0.241777	−	0.970332i	$-0.422270\pi$
$59$	3.71425	0.483554	0.241777	+	0.970332i	$0.422270\pi$
$60$	0	0
$61$	−3.51122	−0.449565	−0.224783	−	0.974409i	$-0.572167\pi$
$61$	−3.51122	−0.449565	−0.224783	+	0.974409i	$0.572167\pi$
$62$	−4.88043	−0.619815
$63$	−3.67166	−0.462586
$64$	4.73669	0.592086
$65$	0	0
$66$	−5.08007	−0.625313
$67$	−4.04365	−0.494010	−0.247005	−	0.969014i	$-0.579446\pi$
$67$	−4.04365	−0.494010	−0.247005	+	0.969014i	$0.579446\pi$
$68$	6.64906	0.806318
$69$	10.3933	1.25121
$70$	0	0
$71$	5.19533	0.616572	0.308286	−	0.951294i	$-0.400245\pi$
$71$	5.19533	0.616572	0.308286	+	0.951294i	$0.400245\pi$
$72$	18.2046	2.14543
$73$	−8.60409	−1.00703	−0.503516	−	0.863986i	$-0.667961\pi$
$73$	−8.60409	−1.00703	−0.503516	+	0.863986i	$0.667961\pi$
$74$	0.824458	0.0958413
$75$	0	0
$76$	0	0
$77$	1.08332	0.123455
$78$	−0.516796	−0.0585156
$79$	6.62648	0.745537	0.372769	−	0.927924i	$-0.378408\pi$
$79$	6.62648	0.745537	0.372769	+	0.927924i	$0.378408\pi$
$80$	0	0
$81$	13.5611	1.50679
$82$	−8.67089	−0.957539
$83$	4.51737	0.495845	0.247923	−	0.968780i	$-0.420252\pi$
$83$	4.51737	0.495845	0.247923	+	0.968780i	$0.420252\pi$
$84$	−2.19027	−0.238978
$85$	0	0
$86$	−4.25561	−0.458894
$87$	26.9014	2.88414
$88$	−5.37122	−0.572574
$89$	3.37352	0.357592	0.178796	−	0.983886i	$-0.442780\pi$
$89$	3.37352	0.357592	0.178796	+	0.983886i	$0.442780\pi$
$90$	0	0
$91$	0.110206	0.0115527
$92$	4.23818	0.441861
$93$	−17.4175	−1.80611
$94$	7.62648	0.786612
$95$	0	0
$96$	17.5310	1.78925
$97$	−15.1922	−1.54254	−0.771268	−	0.636510i	$-0.780377\pi$
$97$	−15.1922	−1.54254	−0.771268	+	0.636510i	$0.780377\pi$
$98$	5.76256	0.582107
$99$	−12.3933	−1.24557
$100$	0	0
$101$	3.54136	0.352378	0.176189	−	0.984356i	$-0.443623\pi$
$101$	3.54136	0.352378	0.176189	+	0.984356i	$0.443623\pi$
$102$	−14.0681	−1.39295
$103$	−15.6919	−1.54617	−0.773086	−	0.634301i	$-0.781288\pi$
$103$	−15.6919	−1.54617	−0.773086	+	0.634301i	$0.781288\pi$
$104$	−0.546415	−0.0535804
$105$	0	0
$106$	−7.08007	−0.687677
$107$	−1.05731	−0.102214	−0.0511071	−	0.998693i	$-0.516275\pi$
$107$	−1.05731	−0.102214	−0.0511071	+	0.998693i	$0.516275\pi$
$108$	13.4585	1.29505
$109$	−6.74439	−0.645996	−0.322998	−	0.946400i	$-0.604691\pi$
$109$	−6.74439	−0.645996	−0.322998	+	0.946400i	$0.604691\pi$
$110$	0	0
$111$	2.94237	0.279277
$112$	−0.0497239	−0.00469847
$113$	7.90091	0.743255	0.371627	−	0.928382i	$-0.378800\pi$
$113$	7.90091	0.743255	0.371627	+	0.928382i	$0.378800\pi$
$114$	0	0
$115$	0	0
$116$	10.9699	1.01853
$117$	−1.26077	−0.116558
$118$	−3.20459	−0.295006
$119$	3.00000	0.275010
$120$	0	0
$121$	−7.34338	−0.667580
$122$	3.02941	0.274270
$123$	−30.9451	−2.79023
$124$	−7.10250	−0.637824
$125$	0	0
$126$	3.16784	0.282213
$127$	8.47636	0.752155	0.376078	−	0.926588i	$-0.377273\pi$
$127$	8.47636	0.752155	0.376078	+	0.926588i	$0.377273\pi$
$128$	7.30024	0.645256
$129$	−15.1876	−1.33720
$130$	0	0
$131$	1.87439	0.163766	0.0818830	−	0.996642i	$-0.473907\pi$
$131$	1.87439	0.163766	0.0818830	+	0.996642i	$0.473907\pi$
$132$	−7.39304	−0.643482
$133$	0	0
$134$	3.48878	0.301385
$135$	0	0
$136$	−14.8744	−1.27547
$137$	−12.4614	−1.06465	−0.532323	−	0.846542i	$-0.678681\pi$
$137$	−12.4614	−1.06465	−0.532323	+	0.846542i	$0.678681\pi$
$138$	−8.96715	−0.763334
$139$	−0.313241	−0.0265687	−0.0132844	−	0.999912i	$-0.504229\pi$
$139$	−0.313241	−0.0265687	−0.0132844	+	0.999912i	$0.504229\pi$
$140$	0	0
$141$	27.2178	2.29215
$142$	−4.48243	−0.376157
$143$	0.371988	0.0311072
$144$	0.568850	0.0474041
$145$	0	0
$146$	7.42345	0.614369
$147$	20.5657	1.69623
$148$	1.19984	0.0986260
$149$	4.36581	0.357661	0.178831	−	0.983880i	$-0.442769\pi$
$149$	4.36581	0.357661	0.178831	+	0.983880i	$0.442769\pi$
$150$	0	0
$151$	0.197977	0.0161111	0.00805555	−	0.999968i	$-0.497436\pi$
$151$	0.197977	0.0161111	0.00805555	+	0.999968i	$0.497436\pi$
$152$	0	0
$153$	−34.3205	−2.77465
$154$	−0.934664	−0.0753174
$155$	0	0
$156$	−0.752095	−0.0602158
$157$	−15.7700	−1.25858	−0.629290	−	0.777171i	$-0.716654\pi$
$157$	−15.7700	−1.25858	−0.629290	+	0.777171i	$0.716654\pi$
$158$	−5.71720	−0.454836
$159$	−25.2677	−2.00386
$160$	0	0
$161$	1.91223	0.150705
$162$	−11.7003	−0.919262
$163$	−9.18768	−0.719635	−0.359817	−	0.933023i	$-0.617161\pi$
$163$	−9.18768	−0.719635	−0.359817	+	0.933023i	$0.617161\pi$
$164$	−12.6188	−0.985361
$165$	0	0
$166$	−3.89750	−0.302505
$167$	3.07021	0.237580	0.118790	−	0.992919i	$-0.462099\pi$
$167$	3.07021	0.237580	0.118790	+	0.992919i	$0.462099\pi$
$168$	4.89978	0.378026
$169$	−12.9622	−0.997089
$170$	0	0
$171$	0	0
$172$	−6.19320	−0.472227
$173$	−10.4135	−0.791726	−0.395863	−	0.918310i	$-0.629554\pi$
$173$	−10.4135	−0.791726	−0.395863	+	0.918310i	$0.629554\pi$
$174$	−23.2101	−1.75955
$175$	0	0
$176$	−0.167838	−0.0126513
$177$	−11.4367	−0.859634
$178$	−2.91061	−0.218159
$179$	−13.4432	−1.00479	−0.502397	−	0.864637i	$-0.667549\pi$
$179$	−13.4432	−1.00479	−0.502397	+	0.864637i	$0.667549\pi$
$180$	0	0
$181$	7.96216	0.591823	0.295911	−	0.955215i	$-0.404377\pi$
$181$	7.96216	0.591823	0.295911	+	0.955215i	$0.404377\pi$
$182$	−0.0950835	−0.00704806
$183$	10.8115	0.799210
$184$	−9.48108	−0.698954
$185$	0	0
$186$	15.0275	1.10187
$187$	10.1262	0.740501
$188$	11.0988	0.809467
$189$	6.07236	0.441699
$190$	0	0
$191$	−14.0999	−1.02023	−0.510115	−	0.860106i	$-0.670397\pi$
$191$	−14.0999	−1.02023	−0.510115	+	0.860106i	$0.670397\pi$
$192$	−14.5849	−1.05257
$193$	−3.97685	−0.286260	−0.143130	−	0.989704i	$-0.545717\pi$
$193$	−3.97685	−0.286260	−0.143130	+	0.989704i	$0.545717\pi$
$194$	13.1076	0.941068
$195$	0	0
$196$	8.38628	0.599020
$197$	−18.3494	−1.30734	−0.653669	−	0.756781i	$-0.726771\pi$
$197$	−18.3494	−1.30734	−0.653669	+	0.756781i	$0.726771\pi$
$198$	10.6927	0.759898
$199$	−1.60669	−0.113895	−0.0569477	−	0.998377i	$-0.518137\pi$
$199$	−1.60669	−0.113895	−0.0569477	+	0.998377i	$0.518137\pi$
$200$	0	0
$201$	12.4509	0.878222
$202$	−3.05542	−0.214978
$203$	4.94951	0.347387
$204$	−20.4734	−1.43342
$205$	0	0
$206$	13.5387	0.943287
$207$	−21.8762	−1.52050
$208$	−0.0170742	−0.00118388
$209$	0	0
$210$	0	0
$211$	−6.09986	−0.419931	−0.209966	−	0.977709i	$-0.567335\pi$
$211$	−6.09986	−0.419931	−0.209966	+	0.977709i	$0.567335\pi$
$212$	−10.3036	−0.707658
$213$	−15.9971	−1.09611
$214$	0.912229	0.0623587
$215$	0	0
$216$	−30.1076	−2.04856
$217$	−3.20459	−0.217542
$218$	5.81893	0.394108
$219$	26.4932	1.79024
$220$	0	0
$221$	1.03014	0.0692946
$222$	−2.53862	−0.170381
$223$	−17.2253	−1.15349	−0.576744	−	0.816925i	$-0.695677\pi$
$223$	−17.2253	−1.15349	−0.576744	+	0.816925i	$0.695677\pi$
$224$	3.22547	0.215511
$225$	0	0
$226$	−6.81675	−0.453444
$227$	−1.18505	−0.0786542	−0.0393271	−	0.999226i	$-0.512521\pi$
$227$	−1.18505	−0.0786542	−0.0393271	+	0.999226i	$0.512521\pi$
$228$	0	0
$229$	6.24791	0.412873	0.206437	−	0.978460i	$-0.433813\pi$
$229$	6.24791	0.412873	0.206437	+	0.978460i	$0.433813\pi$
$230$	0	0
$231$	−3.33568	−0.219471
$232$	−24.5403	−1.61115
$233$	2.75687	0.180609	0.0903043	−	0.995914i	$-0.471216\pi$
$233$	2.75687	0.180609	0.0903043	+	0.995914i	$0.471216\pi$
$234$	1.08777	0.0711098
$235$	0	0
$236$	−4.66365	−0.303578
$237$	−20.4038	−1.32537
$238$	−2.58834	−0.167777
$239$	17.3055	1.11940	0.559701	−	0.828695i	$-0.310916\pi$
$239$	17.3055	1.11940	0.559701	+	0.828695i	$0.310916\pi$
$240$	0	0
$241$	−4.78662	−0.308333	−0.154167	−	0.988045i	$-0.549269\pi$
$241$	−4.78662	−0.308333	−0.154167	+	0.988045i	$0.549269\pi$
$242$	6.33573	0.407276
$243$	−9.60047	−0.615870
$244$	4.40872	0.282239
$245$	0	0
$246$	26.6988	1.70226
$247$	0	0
$248$	15.8888	1.00894
$249$	−13.9096	−0.881484
$250$	0	0
$251$	−26.2479	−1.65675	−0.828377	−	0.560172i	$-0.810735\pi$
$251$	−26.2479	−1.65675	−0.828377	+	0.560172i	$0.810735\pi$
$252$	4.61017	0.290413
$253$	6.45453	0.405793
$254$	−7.31324	−0.458874
$255$	0	0
$256$	−15.7719	−0.985743
$257$	22.2505	1.38795	0.693974	−	0.720000i	$-0.255858\pi$
$257$	22.2505	1.38795	0.693974	+	0.720000i	$0.255858\pi$
$258$	13.1036	0.815794
$259$	0.541356	0.0336382
$260$	0	0
$261$	−56.6232	−3.50489
$262$	−1.61719	−0.0999101
$263$	−8.81341	−0.543458	−0.271729	−	0.962374i	$-0.587595\pi$
$263$	−8.81341	−0.543458	−0.271729	+	0.962374i	$0.587595\pi$
$264$	16.5387	1.01789
$265$	0	0
$266$	0	0
$267$	−10.3875	−0.635706
$268$	5.07724	0.310142
$269$	−4.76418	−0.290477	−0.145239	−	0.989397i	$-0.546395\pi$
$269$	−4.76418	−0.290477	−0.145239	+	0.989397i	$0.546395\pi$
$270$	0	0
$271$	3.51892	0.213759	0.106880	−	0.994272i	$-0.465914\pi$
$271$	3.51892	0.213759	0.106880	+	0.994272i	$0.465914\pi$
$272$	−0.464790	−0.0281820
$273$	−0.339339	−0.0205377
$274$	10.7514	0.649517
$275$	0	0
$276$	−13.0499	−0.785513
$277$	−32.7724	−1.96910	−0.984551	−	0.175098i	$-0.943976\pi$
$277$	−32.7724	−1.96910	−0.984551	+	0.175098i	$0.943976\pi$
$278$	0.270258	0.0162090
$279$	36.6610	2.19484
$280$	0	0
$281$	9.91993	0.591774	0.295887	−	0.955223i	$-0.404385\pi$
$281$	9.91993	0.591774	0.295887	+	0.955223i	$0.404385\pi$
$282$	−23.4830	−1.39839
$283$	2.47182	0.146935	0.0734673	−	0.997298i	$-0.476594\pi$
$283$	2.47182	0.146935	0.0734673	+	0.997298i	$0.476594\pi$
$284$	−6.52330	−0.387087
$285$	0	0
$286$	−0.320945	−0.0189779
$287$	−5.69348	−0.336076
$288$	−36.8999	−2.17435
$289$	11.0422	0.649543
$290$	0	0
$291$	46.7789	2.74223
$292$	10.8034	0.632219
$293$	−17.0284	−0.994812	−0.497406	−	0.867518i	$-0.665714\pi$
$293$	−17.0284	−0.994812	−0.497406	+	0.867518i	$0.665714\pi$
$294$	−17.7437	−1.03483
$295$	0	0
$296$	−2.68411	−0.156011
$297$	20.4966	1.18934
$298$	−3.76674	−0.218202
$299$	0.656620	0.0379733
$300$	0	0
$301$	−2.79432	−0.161062
$302$	−0.170810	−0.00982904
$303$	−10.9043	−0.626437
$304$	0	0
$305$	0	0
$306$	29.6111	1.69275
$307$	20.9793	1.19735	0.598676	−	0.800992i	$-0.295694\pi$
$307$	20.9793	1.19735	0.598676	+	0.800992i	$0.295694\pi$
$308$	−1.36022	−0.0775058
$309$	48.3176	2.74869
$310$	0	0
$311$	−3.14805	−0.178509	−0.0892547	−	0.996009i	$-0.528449\pi$
$311$	−3.14805	−0.178509	−0.0892547	+	0.996009i	$0.528449\pi$
$312$	1.68248	0.0952520
$313$	12.2928	0.694831	0.347416	−	0.937711i	$-0.387059\pi$
$313$	12.2928	0.694831	0.347416	+	0.937711i	$0.387059\pi$
$314$	13.6060	0.767832
$315$	0	0
$316$	−8.32027	−0.468052
$317$	−11.4619	−0.643765	−0.321882	−	0.946780i	$-0.604316\pi$
$317$	−11.4619	−0.643765	−0.321882	+	0.946780i	$0.604316\pi$
$318$	21.8005	1.22251
$319$	16.7065	0.935387
$320$	0	0
$321$	3.25561	0.181710
$322$	−1.64984	−0.0919417
$323$	0	0
$324$	−17.0275	−0.945972
$325$	0	0
$326$	7.92696	0.439034
$327$	20.7669	1.14841
$328$	28.2290	1.55869
$329$	5.00770	0.276084
$330$	0	0
$331$	5.85724	0.321943	0.160972	−	0.986959i	$-0.448537\pi$
$331$	5.85724	0.321943	0.160972	+	0.986959i	$0.448537\pi$
$332$	−5.67204	−0.311294
$333$	−6.19320	−0.339385
$334$	−2.64892	−0.144942
$335$	0	0
$336$	0.153107	0.00835265
$337$	−8.60995	−0.469014	−0.234507	−	0.972114i	$-0.575348\pi$
$337$	−8.60995	−0.469014	−0.234507	+	0.972114i	$0.575348\pi$
$338$	11.1835	0.608302
$339$	−24.3280	−1.32131
$340$	0	0
$341$	−10.8168	−0.585760
$342$	0	0
$343$	7.74945	0.418431
$344$	13.8546	0.746990
$345$	0	0
$346$	8.98459	0.483015
$347$	12.0901	0.649033	0.324517	−	0.945880i	$-0.394798\pi$
$347$	12.0901	0.649033	0.324517	+	0.945880i	$0.394798\pi$
$348$	−33.7777	−1.81067
$349$	18.9819	1.01608	0.508040	−	0.861333i	$-0.330370\pi$
$349$	18.9819	1.01608	0.508040	+	0.861333i	$0.330370\pi$
$350$	0	0
$351$	2.08513	0.111296
$352$	10.8872	0.580292
$353$	7.71759	0.410766	0.205383	−	0.978682i	$-0.434156\pi$
$353$	7.71759	0.410766	0.205383	+	0.978682i	$0.434156\pi$
$354$	9.86736	0.524444
$355$	0	0
$356$	−4.23582	−0.224498
$357$	−9.23741	−0.488895
$358$	11.5986	0.613003
$359$	−7.03014	−0.371037	−0.185518	−	0.982641i	$-0.559396\pi$
$359$	−7.03014	−0.371037	−0.185518	+	0.982641i	$0.559396\pi$
$360$	0	0
$361$	0	0
$362$	−6.86960	−0.361058
$363$	22.6113	1.18678
$364$	−0.138375	−0.00725284
$365$	0	0
$366$	−9.32797	−0.487581
$367$	33.7109	1.75969	0.879847	−	0.475257i	$-0.157645\pi$
$367$	33.7109	1.75969	0.879847	+	0.475257i	$0.157645\pi$
$368$	−0.296261	−0.0154437
$369$	65.1344	3.39076
$370$	0	0
$371$	−4.64892	−0.241360
$372$	21.8696	1.13388
$373$	−10.0097	−0.518281	−0.259141	−	0.965840i	$-0.583439\pi$
$373$	−10.0097	−0.518281	−0.259141	+	0.965840i	$0.583439\pi$
$374$	−8.73669	−0.451763
$375$	0	0
$376$	−24.8288	−1.28045
$377$	1.69956	0.0875317
$378$	−5.23912	−0.269471
$379$	−35.8064	−1.83925	−0.919626	−	0.392796i	$-0.871508\pi$
$379$	−35.8064	−1.83925	−0.919626	+	0.392796i	$0.871508\pi$
$380$	0	0
$381$	−26.0999	−1.33714
$382$	12.1651	0.622420
$383$	16.2495	0.830312	0.415156	−	0.909750i	$-0.363727\pi$
$383$	16.2495	0.830312	0.415156	+	0.909750i	$0.363727\pi$
$384$	−22.4784	−1.14710
$385$	0	0
$386$	3.43115	0.174641
$387$	31.9675	1.62500
$388$	19.0755	0.968411
$389$	−19.3856	−0.982889	−0.491445	−	0.870909i	$-0.663531\pi$
$389$	−19.3856	−0.982889	−0.491445	+	0.870909i	$0.663531\pi$
$390$	0	0
$391$	17.8744	0.903947
$392$	−18.7607	−0.947556
$393$	−5.77149	−0.291133
$394$	15.8315	0.797579
$395$	0	0
$396$	15.5611	0.781977
$397$	−5.35414	−0.268717	−0.134358	−	0.990933i	$-0.542897\pi$
$397$	−5.35414	−0.268717	−0.134358	+	0.990933i	$0.542897\pi$
$398$	1.38622	0.0694851
$399$	0	0
$400$	0	0
$401$	8.33832	0.416396	0.208198	−	0.978087i	$-0.433240\pi$
$401$	8.33832	0.416396	0.208198	+	0.978087i	$0.433240\pi$
$402$	−10.7424	−0.535784
$403$	−1.10039	−0.0548143
$404$	−4.44656	−0.221225
$405$	0	0
$406$	−4.27034	−0.211933
$407$	1.82729	0.0905755
$408$	45.8003	2.26745
$409$	−35.3227	−1.74659	−0.873297	−	0.487188i	$-0.838023\pi$
$409$	−35.3227	−1.74659	−0.873297	+	0.487188i	$0.838023\pi$
$410$	0	0
$411$	38.3702	1.89266
$412$	19.7029	0.970694
$413$	−2.10420	−0.103541
$414$	18.8744	0.927626
$415$	0	0
$416$	1.10756	0.0543026
$417$	0.964511	0.0472323
$418$	0	0
$419$	21.2453	1.03790	0.518949	−	0.854805i	$-0.326323\pi$
$419$	21.2453	1.03790	0.518949	+	0.854805i	$0.326323\pi$
$420$	0	0
$421$	−14.8744	−0.724933	−0.362467	−	0.931997i	$-0.618065\pi$
$421$	−14.8744	−0.724933	−0.362467	+	0.931997i	$0.618065\pi$
$422$	5.26284	0.256191
$423$	−57.2890	−2.78548
$424$	23.0499	1.11940
$425$	0	0
$426$	13.8020	0.668710
$427$	1.98917	0.0962629
$428$	1.32757	0.0641706
$429$	−1.14540	−0.0553006
$430$	0	0
$431$	−16.9518	−0.816540	−0.408270	−	0.912861i	$-0.633868\pi$
$431$	−16.9518	−0.816540	−0.408270	+	0.912861i	$0.633868\pi$
$432$	−0.940790	−0.0452638
$433$	−23.1459	−1.11232	−0.556161	−	0.831075i	$-0.687726\pi$
$433$	−23.1459	−1.11232	−0.556161	+	0.831075i	$0.687726\pi$
$434$	2.76486	0.132717
$435$	0	0
$436$	8.46832	0.405559
$437$	0	0
$438$	−22.8578	−1.09219
$439$	33.5457	1.60105	0.800525	−	0.599299i	$-0.204554\pi$
$439$	33.5457	1.60105	0.800525	+	0.599299i	$0.204554\pi$
$440$	0	0
$441$	−43.2875	−2.06131
$442$	−0.888784	−0.0422752
$443$	31.3579	1.48986	0.744929	−	0.667144i	$-0.232483\pi$
$443$	31.3579	1.48986	0.744929	+	0.667144i	$0.232483\pi$
$444$	−3.69446	−0.175331
$445$	0	0
$446$	14.8616	0.703718
$447$	−13.4429	−0.635829
$448$	−2.68343	−0.126780
$449$	−16.0301	−0.756509	−0.378255	−	0.925702i	$-0.623476\pi$
$449$	−16.0301	−0.756509	−0.378255	+	0.925702i	$0.623476\pi$
$450$	0	0
$451$	−19.2178	−0.904929
$452$	−9.92045	−0.466619
$453$	−0.609597	−0.0286414
$454$	1.02243	0.0479853
$455$	0	0
$456$	0	0
$457$	15.3980	0.720286	0.360143	−	0.932897i	$-0.382728\pi$
$457$	15.3980	0.720286	0.360143	+	0.932897i	$0.382728\pi$
$458$	−5.39057	−0.251885
$459$	56.7609	2.64937
$460$	0	0
$461$	−5.81411	−0.270790	−0.135395	−	0.990792i	$-0.543230\pi$
$461$	−5.81411	−0.270790	−0.135395	+	0.990792i	$0.543230\pi$
$462$	2.87796	0.133895
$463$	32.6788	1.51871	0.759356	−	0.650675i	$-0.225514\pi$
$463$	32.6788	1.51871	0.759356	+	0.650675i	$0.225514\pi$
$464$	−0.766826	−0.0355990
$465$	0	0
$466$	−2.37858	−0.110185
$467$	−6.59041	−0.304968	−0.152484	−	0.988306i	$-0.548727\pi$
$467$	−6.59041	−0.304968	−0.152484	+	0.988306i	$0.548727\pi$
$468$	1.58304	0.0731759
$469$	2.29081	0.105780
$470$	0	0
$471$	48.5578	2.23743
$472$	10.4329	0.480212
$473$	−9.43194	−0.433681
$474$	17.6040	0.808581
$475$	0	0
$476$	−3.76683	−0.172652
$477$	53.1844	2.43515
$478$	−14.9309	−0.682923
$479$	−36.8064	−1.68173	−0.840864	−	0.541247i	$-0.817952\pi$
$479$	−36.8064	−1.68173	−0.840864	+	0.541247i	$0.817952\pi$
$480$	0	0
$481$	0.185891	0.00847588
$482$	4.12980	0.188107
$483$	−5.88801	−0.267914
$484$	9.22041	0.419110
$485$	0	0
$486$	8.28310	0.375729
$487$	2.45475	0.111235	0.0556176	−	0.998452i	$-0.482287\pi$
$487$	2.45475	0.111235	0.0556176	+	0.998452i	$0.482287\pi$
$488$	−9.86258	−0.446458
$489$	28.2901	1.27932
$490$	0	0
$491$	17.7943	0.803046	0.401523	−	0.915849i	$-0.368481\pi$
$491$	17.7943	0.803046	0.401523	+	0.915849i	$0.368481\pi$
$492$	38.8549	1.75172
$493$	46.2651	2.08367
$494$	0	0
$495$	0	0
$496$	0.496486	0.0222929
$497$	−2.94326	−0.132023
$498$	12.0009	0.537774
$499$	−29.2798	−1.31074	−0.655371	−	0.755307i	$-0.727488\pi$
$499$	−29.2798	−1.31074	−0.655371	+	0.755307i	$0.727488\pi$
$500$	0	0
$501$	−9.45359	−0.422355
$502$	22.6462	1.01075
$503$	−29.4378	−1.31257	−0.656283	−	0.754515i	$-0.727872\pi$
$503$	−29.4378	−1.31257	−0.656283	+	0.754515i	$0.727872\pi$
$504$	−10.3132	−0.459388
$505$	0	0
$506$	−5.56885	−0.247566
$507$	39.9122	1.77257
$508$	−10.6430	−0.472206
$509$	6.69446	0.296727	0.148363	−	0.988933i	$-0.452599\pi$
$509$	6.69446	0.296727	0.148363	+	0.988933i	$0.452599\pi$
$510$	0	0
$511$	4.87439	0.215630
$512$	−0.992797	−0.0438758
$513$	0	0
$514$	−19.1973	−0.846757
$515$	0	0
$516$	19.0697	0.839498
$517$	16.9030	0.743393
$518$	−0.467072	−0.0205220
$519$	32.0647	1.40748
$520$	0	0
$521$	20.0801	0.879724	0.439862	−	0.898065i	$-0.355027\pi$
$521$	20.0801	0.879724	0.439862	+	0.898065i	$0.355027\pi$
$522$	48.8534	2.13825
$523$	36.4440	1.59359	0.796793	−	0.604252i	$-0.206528\pi$
$523$	36.4440	1.59359	0.796793	+	0.604252i	$0.206528\pi$
$524$	−2.35350	−0.102813
$525$	0	0
$526$	7.60405	0.331552
$527$	−29.9546	−1.30484
$528$	0.516796	0.0224907
$529$	−11.6067	−0.504639
$530$	0	0
$531$	24.0724	1.04465
$532$	0	0
$533$	−1.95503	−0.0846816
$534$	8.96216	0.387830
$535$	0	0
$536$	−11.3581	−0.490596
$537$	41.3936	1.78626
$538$	4.11045	0.177214
$539$	12.7719	0.550124
$540$	0	0
$541$	−14.6291	−0.628955	−0.314478	−	0.949265i	$-0.601829\pi$
$541$	−14.6291	−0.628955	−0.314478	+	0.949265i	$0.601829\pi$
$542$	−3.03606	−0.130410
$543$	−24.5166	−1.05211
$544$	30.1498	1.29266
$545$	0	0
$546$	0.292775	0.0125296
$547$	−20.4186	−0.873038	−0.436519	−	0.899695i	$-0.643789\pi$
$547$	−20.4186	−0.873038	−0.436519	+	0.899695i	$0.643789\pi$
$548$	15.6466	0.668389
$549$	−22.7565	−0.971223
$550$	0	0
$551$	0	0
$552$	29.1935	1.24256
$553$	−3.75403	−0.159638
$554$	28.2754	1.20131
$555$	0	0
$556$	0.393308	0.0166800
$557$	−35.8798	−1.52028	−0.760138	−	0.649761i	$-0.774869\pi$
$557$	−35.8798	−1.52028	−0.760138	+	0.649761i	$0.774869\pi$
$558$	−31.6304	−1.33902
$559$	−0.959512	−0.0405830
$560$	0	0
$561$	−31.1799	−1.31642
$562$	−8.55873	−0.361028
$563$	−37.7708	−1.59185	−0.795925	−	0.605395i	$-0.793015\pi$
$563$	−37.7708	−1.59185	−0.795925	+	0.605395i	$0.793015\pi$
$564$	−34.1749	−1.43902
$565$	0	0
$566$	−2.13264	−0.0896416
$567$	−7.68266	−0.322641
$568$	14.5931	0.612311
$569$	28.0844	1.17736	0.588681	−	0.808366i	$-0.299648\pi$
$569$	28.0844	1.17736	0.588681	+	0.808366i	$0.299648\pi$
$570$	0	0
$571$	20.6040	0.862253	0.431126	−	0.902292i	$-0.358116\pi$
$571$	20.6040	0.862253	0.431126	+	0.902292i	$0.358116\pi$
$572$	−0.467072	−0.0195293
$573$	43.4154	1.81370
$574$	4.91223	0.205032
$575$	0	0
$576$	30.6988	1.27912
$577$	43.8371	1.82496	0.912481	−	0.409119i	$-0.134164\pi$
$577$	43.8371	1.82496	0.912481	+	0.409119i	$0.134164\pi$
$578$	−9.52702	−0.396272
$579$	12.2453	0.508896
$580$	0	0
$581$	−2.55918	−0.106173
$582$	−40.3600	−1.67297
$583$	−15.6919	−0.649894
$584$	−24.1678	−1.00007
$585$	0	0
$586$	14.6918	0.606913
$587$	37.9809	1.56764	0.783821	−	0.620987i	$-0.213268\pi$
$587$	37.9809	1.56764	0.783821	+	0.620987i	$0.213268\pi$
$588$	−25.8225	−1.06490
$589$	0	0
$590$	0	0
$591$	56.5002	2.32411
$592$	−0.0838722	−0.00344713
$593$	−5.38015	−0.220936	−0.110468	−	0.993880i	$-0.535235\pi$
$593$	−5.38015	−0.220936	−0.110468	+	0.993880i	$0.535235\pi$
$594$	−17.6841	−0.725588
$595$	0	0
$596$	−5.48175	−0.224541
$597$	4.94722	0.202476
$598$	−0.566520	−0.0231667
$599$	22.4285	0.916404	0.458202	−	0.888848i	$-0.348494\pi$
$599$	22.4285	0.916404	0.458202	+	0.888848i	$0.348494\pi$
$600$	0	0
$601$	−29.5732	−1.20632	−0.603159	−	0.797621i	$-0.706091\pi$
$601$	−29.5732	−1.20632	−0.603159	+	0.797621i	$0.706091\pi$
$602$	2.41089	0.0982604
$603$	−26.2072	−1.06724
$604$	−0.248581	−0.0101146
$605$	0	0
$606$	9.40804	0.382175
$607$	24.5915	0.998139	0.499069	−	0.866562i	$-0.333675\pi$
$607$	24.5915	0.998139	0.499069	+	0.866562i	$0.333675\pi$
$608$	0	0
$609$	−15.2402	−0.617564
$610$	0	0
$611$	1.71954	0.0695653
$612$	43.0931	1.74194
$613$	29.8901	1.20725	0.603624	−	0.797269i	$-0.293723\pi$
$613$	29.8901	1.20725	0.603624	+	0.797269i	$0.293723\pi$
$614$	−18.1005	−0.730478
$615$	0	0
$616$	3.04290	0.122602
$617$	40.7141	1.63909	0.819544	−	0.573017i	$-0.194227\pi$
$617$	40.7141	1.63909	0.819544	+	0.573017i	$0.194227\pi$
$618$	−41.6875	−1.67692
$619$	−28.4784	−1.14464	−0.572322	−	0.820029i	$-0.693957\pi$
$619$	−28.4784	−1.14464	−0.572322	+	0.820029i	$0.693957\pi$
$620$	0	0
$621$	36.1799	1.45185
$622$	2.71608	0.108905
$623$	−1.91116	−0.0765692
$624$	0.0525737	0.00210463
$625$	0	0
$626$	−10.6060	−0.423902
$627$	0	0
$628$	19.8009	0.790141
$629$	5.06028	0.201766
$630$	0	0
$631$	42.4201	1.68872	0.844359	−	0.535777i	$-0.179981\pi$
$631$	42.4201	1.68872	0.844359	+	0.535777i	$0.179981\pi$
$632$	18.6130	0.740384
$633$	18.7823	0.746529
$634$	9.88912	0.392747
$635$	0	0
$636$	31.7263	1.25803
$637$	1.29929	0.0514796
$638$	−14.4141	−0.570659
$639$	33.6714	1.33202
$640$	0	0
$641$	−29.5259	−1.16620	−0.583102	−	0.812399i	$-0.698161\pi$
$641$	−29.5259	−1.16620	−0.583102	+	0.812399i	$0.698161\pi$
$642$	−2.80888	−0.110858
$643$	−21.5970	−0.851704	−0.425852	−	0.904793i	$-0.640026\pi$
$643$	−21.5970	−0.851704	−0.425852	+	0.904793i	$0.640026\pi$
$644$	−2.40101	−0.0946131
$645$	0	0
$646$	0	0
$647$	12.6128	0.495861	0.247930	−	0.968778i	$-0.420250\pi$
$647$	12.6128	0.495861	0.247930	+	0.968778i	$0.420250\pi$
$648$	38.0916	1.49638
$649$	−7.10250	−0.278798
$650$	0	0
$651$	9.86736	0.386732
$652$	11.5361	0.451790
$653$	26.6312	1.04216	0.521080	−	0.853508i	$-0.325529\pi$
$653$	26.6312	1.04216	0.521080	+	0.853508i	$0.325529\pi$
$654$	−17.9173	−0.700621
$655$	0	0
$656$	0.882090	0.0344398
$657$	−55.7638	−2.17555
$658$	−4.32055	−0.168433
$659$	39.9545	1.55640	0.778202	−	0.628014i	$-0.216132\pi$
$659$	39.9545	1.55640	0.778202	+	0.628014i	$0.216132\pi$
$660$	0	0
$661$	−13.5233	−0.525996	−0.262998	−	0.964796i	$-0.584711\pi$
$661$	−13.5233	−0.525996	−0.262998	+	0.964796i	$0.584711\pi$
$662$	−5.05352	−0.196411
$663$	−3.17194	−0.123188
$664$	12.6887	0.492418
$665$	0	0
$666$	5.34338	0.207052
$667$	29.4898	1.14185
$668$	−3.85498	−0.149154
$669$	53.0389	2.05060
$670$	0	0
$671$	6.71425	0.259201
$672$	−9.93166	−0.383122
$673$	−34.4110	−1.32645	−0.663224	−	0.748421i	$-0.730812\pi$
$673$	−34.4110	−1.32645	−0.663224	+	0.748421i	$0.730812\pi$
$674$	7.42851	0.286135
$675$	0	0
$676$	16.2754	0.625977
$677$	29.6650	1.14012	0.570059	−	0.821604i	$-0.306920\pi$
$677$	29.6650	1.14012	0.570059	+	0.821604i	$0.306920\pi$
$678$	20.9897	0.806105
$679$	8.60669	0.330295
$680$	0	0
$681$	3.64892	0.139827
$682$	9.33249	0.357360
$683$	27.8978	1.06748	0.533740	−	0.845648i	$-0.320786\pi$
$683$	27.8978	1.06748	0.533740	+	0.845648i	$0.320786\pi$
$684$	0	0
$685$	0	0
$686$	−6.68608	−0.255276
$687$	−19.2381	−0.733981
$688$	0.432924	0.0165051
$689$	−1.59634	−0.0608158
$690$	0	0
$691$	−49.6386	−1.88834	−0.944170	−	0.329459i	$-0.893134\pi$
$691$	−49.6386	−1.88834	−0.944170	+	0.329459i	$0.893134\pi$
$692$	13.0753	0.497049
$693$	7.02105	0.266708
$694$	−10.4312	−0.395961
$695$	0	0
$696$	75.5629	2.86420
$697$	−53.2193	−2.01582
$698$	−16.3773	−0.619889
$699$	−8.48878	−0.321075
$700$	0	0
$701$	−49.9813	−1.88777	−0.943883	−	0.330279i	$-0.892857\pi$
$701$	−49.9813	−1.88777	−0.943883	+	0.330279i	$0.892857\pi$
$702$	−1.79901	−0.0678991
$703$	0	0
$704$	−9.05763	−0.341372
$705$	0	0
$706$	−6.65859	−0.250599
$707$	−2.00625	−0.0754527
$708$	14.3600	0.539682
$709$	25.1876	0.945941	0.472971	−	0.881078i	$-0.343182\pi$
$709$	25.1876	0.945941	0.472971	+	0.881078i	$0.343182\pi$
$710$	0	0
$711$	42.9468	1.61063
$712$	9.47580	0.355121
$713$	−19.0933	−0.715051
$714$	7.96986	0.298265
$715$	0	0
$716$	16.8794	0.630814
$717$	−53.2861	−1.99001
$718$	6.06547	0.226361
$719$	17.1755	0.640540	0.320270	−	0.947326i	$-0.396226\pi$
$719$	17.1755	0.640540	0.320270	+	0.947326i	$0.396226\pi$
$720$	0	0
$721$	8.88979	0.331073
$722$	0	0
$723$	14.7386	0.548136
$724$	−9.99735	−0.371549
$725$	0	0
$726$	−19.5086	−0.724031
$727$	1.05653	0.0391845	0.0195922	−	0.999808i	$-0.493763\pi$
$727$	1.05653	0.0391845	0.0195922	+	0.999808i	$0.493763\pi$
$728$	0.309555	0.0114729
$729$	−11.1223	−0.411937
$730$	0	0
$731$	−26.1196	−0.966070
$732$	−13.5750	−0.501748
$733$	−20.5025	−0.757277	−0.378639	−	0.925545i	$-0.623608\pi$
$733$	−20.5025	−0.757277	−0.378639	+	0.925545i	$0.623608\pi$
$734$	−29.0851	−1.07355
$735$	0	0
$736$	19.2178	0.708376
$737$	7.73238	0.284826
$738$	−56.1967	−2.06863
$739$	24.9096	0.916314	0.458157	−	0.888871i	$-0.348510\pi$
$739$	24.9096	0.916314	0.458157	+	0.888871i	$0.348510\pi$
$740$	0	0
$741$	0	0
$742$	4.01100	0.147248
$743$	−13.2573	−0.486364	−0.243182	−	0.969981i	$-0.578191\pi$
$743$	−13.2573	−0.486364	−0.243182	+	0.969981i	$0.578191\pi$
$744$	−48.9236	−1.79363
$745$	0	0
$746$	8.63615	0.316192
$747$	29.2774	1.07120
$748$	−12.7145	−0.464889
$749$	0.598988	0.0218866
$750$	0	0
$751$	24.8365	0.906298	0.453149	−	0.891435i	$-0.350300\pi$
$751$	24.8365	0.906298	0.453149	+	0.891435i	$0.350300\pi$
$752$	−0.775843	−0.0282921
$753$	80.8209	2.94528
$754$	−1.46635	−0.0534012
$755$	0	0
$756$	−7.62451	−0.277301
$757$	−48.4658	−1.76152	−0.880760	−	0.473562i	$-0.842968\pi$
$757$	−48.4658	−1.76152	−0.880760	+	0.473562i	$0.842968\pi$
$758$	30.8931	1.12209
$759$	−19.8744	−0.721395
$760$	0	0
$761$	40.3726	1.46351	0.731753	−	0.681570i	$-0.238702\pi$
$761$	40.3726	1.46351	0.731753	+	0.681570i	$0.238702\pi$
$762$	22.5185	0.815758
$763$	3.82083	0.138323
$764$	17.7039	0.640505
$765$	0	0
$766$	−14.0198	−0.506556
$767$	−0.722538	−0.0260893
$768$	48.5638	1.75239
$769$	−44.9545	−1.62110	−0.810550	−	0.585670i	$-0.800831\pi$
$769$	−44.9545	−1.62110	−0.810550	+	0.585670i	$0.800831\pi$
$770$	0	0
$771$	−68.5123	−2.46741
$772$	4.99337	0.179715
$773$	−3.68645	−0.132592	−0.0662962	−	0.997800i	$-0.521118\pi$
$773$	−3.68645	−0.132592	−0.0662962	+	0.997800i	$0.521118\pi$
$774$	−27.5809	−0.991376
$775$	0	0
$776$	−42.6731	−1.53187
$777$	−1.66691	−0.0598000
$778$	16.7255	0.599639
$779$	0	0
$780$	0	0
$781$	−9.93466	−0.355490
$782$	−15.4217	−0.551478
$783$	93.6461	3.34664
$784$	−0.586226	−0.0209366
$785$	0	0
$786$	4.97953	0.177614
$787$	−45.7141	−1.62953	−0.814766	−	0.579790i	$-0.803135\pi$
$787$	−45.7141	−1.62953	−0.814766	+	0.579790i	$0.803135\pi$
$788$	23.0396	0.820753
$789$	27.1377	0.966128
$790$	0	0
$791$	−4.47602	−0.159149
$792$	−34.8113	−1.23697
$793$	0.683042	0.0242555
$794$	4.61945	0.163938
$795$	0	0
$796$	2.01738	0.0715040
$797$	30.3378	1.07462	0.537310	−	0.843385i	$-0.319441\pi$
$797$	30.3378	1.07462	0.537310	+	0.843385i	$0.319441\pi$
$798$	0	0
$799$	46.8091	1.65599
$800$	0	0
$801$	21.8640	0.772528
$802$	−7.19415	−0.254034
$803$	16.4530	0.580614
$804$	−15.6335	−0.551351
$805$	0	0
$806$	0.949395	0.0334410
$807$	14.6696	0.516393
$808$	9.94724	0.349943
$809$	34.5585	1.21501	0.607506	−	0.794315i	$-0.292170\pi$
$809$	34.5585	1.21501	0.607506	+	0.794315i	$0.292170\pi$
$810$	0	0
$811$	33.2754	1.16846	0.584229	−	0.811589i	$-0.301397\pi$
$811$	33.2754	1.16846	0.584229	+	0.811589i	$0.301397\pi$
$812$	−6.21464	−0.218091
$813$	−10.8352	−0.380008
$814$	−1.57655	−0.0552582
$815$	0	0
$816$	1.43115	0.0501003
$817$	0	0
$818$	30.4757	1.06556
$819$	0.714253	0.0249580
$820$	0	0
$821$	12.7013	0.443277	0.221638	−	0.975129i	$-0.428860\pi$
$821$	12.7013	0.443277	0.221638	+	0.975129i	$0.428860\pi$
$822$	−33.1051	−1.15467
$823$	12.0091	0.418610	0.209305	−	0.977850i	$-0.432880\pi$
$823$	12.0091	0.418610	0.209305	+	0.977850i	$0.432880\pi$
$824$	−44.0767	−1.53549
$825$	0	0
$826$	1.81546	0.0631680
$827$	−8.54544	−0.297154	−0.148577	−	0.988901i	$-0.547469\pi$
$827$	−8.54544	−0.297154	−0.148577	+	0.988901i	$0.547469\pi$
$828$	27.4680	0.954578
$829$	−27.1042	−0.941369	−0.470685	−	0.882302i	$-0.655993\pi$
$829$	−27.1042	−0.941369	−0.470685	+	0.882302i	$0.655993\pi$
$830$	0	0
$831$	100.911	3.50055
$832$	−0.921434	−0.0319450
$833$	35.3689	1.22546
$834$	−0.832162	−0.0288154
$835$	0	0
$836$	0	0
$837$	−60.6317	−2.09574
$838$	−18.3300	−0.633200
$839$	−36.4379	−1.25798	−0.628989	−	0.777414i	$-0.716531\pi$
$839$	−36.4379	−1.25798	−0.628989	+	0.777414i	$0.716531\pi$
$840$	0	0
$841$	47.3297	1.63206
$842$	12.8333	0.442266
$843$	−30.5448	−1.05202
$844$	7.65903	0.263635
$845$	0	0
$846$	49.4278	1.69936
$847$	4.16017	0.142945
$848$	0.720256	0.0247337
$849$	−7.61107	−0.261211
$850$	0	0
$851$	3.22547	0.110568
$852$	20.0861	0.688140
$853$	18.3471	0.628192	0.314096	−	0.949391i	$-0.398299\pi$
$853$	18.3471	0.628192	0.314096	+	0.949391i	$0.398299\pi$
$854$	−1.71622	−0.0587279
$855$	0	0
$856$	−2.96986	−0.101508
$857$	7.85783	0.268418	0.134209	−	0.990953i	$-0.457151\pi$
$857$	7.85783	0.268418	0.134209	+	0.990953i	$0.457151\pi$
$858$	0.988232	0.0337377
$859$	−34.3022	−1.17038	−0.585188	−	0.810897i	$-0.698979\pi$
$859$	−34.3022	−1.17038	−0.585188	+	0.810897i	$0.698979\pi$
$860$	0	0
$861$	17.5310	0.597455
$862$	14.6257	0.498153
$863$	35.9451	1.22359	0.611793	−	0.791018i	$-0.290449\pi$
$863$	35.9451	1.22359	0.611793	+	0.791018i	$0.290449\pi$
$864$	61.0268	2.07617
$865$	0	0
$866$	19.9699	0.678604
$867$	−34.0005	−1.15472
$868$	4.02371	0.136574
$869$	−12.6714	−0.429846
$870$	0	0
$871$	0.786616	0.0266535
$872$	−18.9442	−0.641531
$873$	−98.4620	−3.33243
$874$	0	0
$875$	0	0
$876$	−33.2650	−1.12392
$877$	25.2516	0.852686	0.426343	−	0.904561i	$-0.359802\pi$
$877$	25.2516	0.852686	0.426343	+	0.904561i	$0.359802\pi$
$878$	−28.9426	−0.976766
$879$	52.4329	1.76852
$880$	0	0
$881$	17.7796	0.599010	0.299505	−	0.954095i	$-0.403179\pi$
$881$	17.7796	0.599010	0.299505	+	0.954095i	$0.403179\pi$
$882$	37.3476	1.25756
$883$	−7.55342	−0.254193	−0.127096	−	0.991890i	$-0.540566\pi$
$883$	−7.55342	−0.254193	−0.127096	+	0.991890i	$0.540566\pi$
$884$	−1.29345	−0.0435035
$885$	0	0
$886$	−27.0550	−0.908930
$887$	16.2406	0.545306	0.272653	−	0.962112i	$-0.412099\pi$
$887$	16.2406	0.545306	0.272653	+	0.962112i	$0.412099\pi$
$888$	8.26475	0.277347
$889$	−4.80202	−0.161055
$890$	0	0
$891$	−25.9320	−0.868755
$892$	21.6282	0.724165
$893$	0	0
$894$	11.5983	0.387906
$895$	0	0
$896$	−4.13573	−0.138165
$897$	−2.02182	−0.0675067
$898$	13.8305	0.461530
$899$	−49.4201	−1.64825
$900$	0	0
$901$	−43.4553	−1.44771
$902$	16.5807	0.552078
$903$	8.60409	0.286326
$904$	22.1927	0.738118
$905$	0	0
$906$	0.525949	0.0174735
$907$	18.2535	0.606097	0.303049	−	0.952975i	$-0.401996\pi$
$907$	18.2535	0.606097	0.303049	+	0.952975i	$0.401996\pi$
$908$	1.48795	0.0493795
$909$	22.9518	0.761263
$910$	0	0
$911$	15.9019	0.526853	0.263426	−	0.964679i	$-0.415147\pi$
$911$	15.9019	0.526853	0.263426	+	0.964679i	$0.415147\pi$
$912$	0	0
$913$	−8.63824	−0.285884
$914$	−13.2851	−0.439431
$915$	0	0
$916$	−7.84492	−0.259204
$917$	−1.06188	−0.0350663
$918$	−48.9722	−1.61632
$919$	−30.0748	−0.992075	−0.496038	−	0.868301i	$-0.665212\pi$
$919$	−30.0748	−0.992075	−0.496038	+	0.868301i	$0.665212\pi$
$920$	0	0
$921$	−64.5981	−2.12858
$922$	5.01630	0.165203
$923$	−1.01065	−0.0332661
$924$	4.18830	0.137785
$925$	0	0
$926$	−28.1947	−0.926534
$927$	−101.701	−3.34029
$928$	49.7422	1.63287
$929$	−36.8442	−1.20882	−0.604410	−	0.796673i	$-0.706591\pi$
$929$	−36.8442	−1.20882	−0.604410	+	0.796673i	$0.706591\pi$
$930$	0	0
$931$	0	0
$932$	−3.46155	−0.113387
$933$	9.69327	0.317343
$934$	5.68608	0.186054
$935$	0	0
$936$	−3.54136	−0.115753
$937$	43.2321	1.41233	0.706165	−	0.708047i	$-0.250424\pi$
$937$	43.2321	1.41233	0.706165	+	0.708047i	$0.250424\pi$
$938$	−1.97646	−0.0645338
$939$	−37.8513	−1.23523
$940$	0	0
$941$	−20.3203	−0.662422	−0.331211	−	0.943557i	$-0.607457\pi$
$941$	−20.3203	−0.662422	−0.331211	+	0.943557i	$0.607457\pi$
$942$	−41.8948	−1.36501
$943$	−33.9225	−1.10467
$944$	0.326003	0.0106105
$945$	0	0
$946$	8.13770	0.264579
$947$	21.5050	0.698819	0.349409	−	0.936970i	$-0.386382\pi$
$947$	21.5050	0.698819	0.349409	+	0.936970i	$0.386382\pi$
$948$	25.6192	0.832074
$949$	1.67376	0.0543327
$950$	0	0
$951$	35.2928	1.14445
$952$	8.42663	0.273109
$953$	−17.7301	−0.574333	−0.287166	−	0.957881i	$-0.592713\pi$
$953$	−17.7301	−0.574333	−0.287166	+	0.957881i	$0.592713\pi$
$954$	−45.8865	−1.48563
$955$	0	0
$956$	−21.7290	−0.702766
$957$	−51.4417	−1.66288
$958$	31.7559	1.02599
$959$	7.05960	0.227966
$960$	0	0
$961$	0.997355	0.0321727
$962$	−0.160383	−0.00517095
$963$	−6.85253	−0.220820
$964$	6.01012	0.193573
$965$	0	0
$966$	5.08007	0.163448
$967$	13.6530	0.439052	0.219526	−	0.975607i	$-0.429549\pi$
$967$	13.6530	0.439052	0.219526	+	0.975607i	$0.429549\pi$
$968$	−20.6267	−0.662966
$969$	0	0
$970$	0	0
$971$	27.9595	0.897263	0.448632	−	0.893717i	$-0.351911\pi$
$971$	27.9595	0.897263	0.448632	+	0.893717i	$0.351911\pi$
$972$	12.0544	0.386646
$973$	0.177457	0.00568901
$974$	−2.11791	−0.0678622
$975$	0	0
$976$	−0.308182	−0.00986468
$977$	−17.8540	−0.571200	−0.285600	−	0.958349i	$-0.592193\pi$
$977$	−17.8540	−0.571200	−0.285600	+	0.958349i	$0.592193\pi$
$978$	−24.4082	−0.780488
$979$	−6.45094	−0.206173
$980$	0	0
$981$	−43.7109	−1.39558
$982$	−15.3526	−0.489921
$983$	49.0443	1.56427	0.782136	−	0.623108i	$-0.214130\pi$
$983$	49.0443	1.56427	0.782136	+	0.623108i	$0.214130\pi$
$984$	−86.9210	−2.77094
$985$	0	0
$986$	−39.9166	−1.27120
$987$	−15.4194	−0.490805
$988$	0	0
$989$	−16.6489	−0.529405
$990$	0	0
$991$	−25.0673	−0.796289	−0.398145	−	0.917323i	$-0.630346\pi$
$991$	−25.0673	−0.796289	−0.398145	+	0.917323i	$0.630346\pi$
$992$	−32.2059	−1.02254
$993$	−18.0352	−0.572331
$994$	2.53939	0.0805445
$995$	0	0
$996$	17.4650	0.553400
$997$	−30.0222	−0.950811	−0.475406	−	0.879767i	$-0.657699\pi$
$997$	−30.0222	−0.950811	−0.475406	+	0.879767i	$0.657699\pi$
$998$	25.2620	0.799656
$999$	10.2426	0.324062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.bu.1.2		6
5.2	odd	4		1805.2.b.f.1084.2		6
5.3	odd	4		1805.2.b.f.1084.5		6
5.4	even	2	inner	9025.2.a.bu.1.5		6
19.7	even	3		475.2.e.g.201.5		12
19.11	even	3		475.2.e.g.26.5		12
19.18	odd	2		9025.2.a.bt.1.5		6
95.7	odd	12		95.2.i.b.49.5	yes	12
95.18	even	4		1805.2.b.g.1084.2		6
95.37	even	4		1805.2.b.g.1084.5		6
95.49	even	6		475.2.e.g.26.2		12
95.64	even	6		475.2.e.g.201.2		12
95.68	odd	12		95.2.i.b.64.5	yes	12
95.83	odd	12		95.2.i.b.49.2	✓	12
95.87	odd	12		95.2.i.b.64.2	yes	12
95.94	odd	2		9025.2.a.bt.1.2		6
285.68	even	12		855.2.be.d.64.2		12
285.83	even	12		855.2.be.d.334.5		12
285.182	even	12		855.2.be.d.64.5		12
285.197	even	12		855.2.be.d.334.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.2	✓	12	95.83	odd	12
95.2.i.b.49.5	yes	12	95.7	odd	12
95.2.i.b.64.2	yes	12	95.87	odd	12
95.2.i.b.64.5	yes	12	95.68	odd	12
475.2.e.g.26.2		12	95.49	even	6
475.2.e.g.26.5		12	19.11	even	3
475.2.e.g.201.2		12	95.64	even	6
475.2.e.g.201.5		12	19.7	even	3
855.2.be.d.64.2		12	285.68	even	12
855.2.be.d.64.5		12	285.182	even	12
855.2.be.d.334.2		12	285.197	even	12
855.2.be.d.334.5		12	285.83	even	12
1805.2.b.f.1084.2		6	5.2	odd	4
1805.2.b.f.1084.5		6	5.3	odd	4
1805.2.b.g.1084.2		6	95.18	even	4
1805.2.b.g.1084.5		6	95.37	even	4
9025.2.a.bt.1.2		6	95.94	odd	2
9025.2.a.bt.1.5		6	19.18	odd	2
9025.2.a.bu.1.2		6	1.1	even	1	trivial
9025.2.a.bu.1.5		6	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)

\(f(q)\)	\(=\)	\(q-0.862781 q^{2} -3.07914 q^{3} -1.25561 q^{4} +2.65662 q^{6} -0.566520 q^{7} +2.80888 q^{8} +6.48108 q^{9} +O(q^{10})\)	\(q-0.862781 q^{2} -3.07914 q^{3} -1.25561 q^{4} +2.65662 q^{6} -0.566520 q^{7} +2.80888 q^{8} +6.48108 q^{9} -1.91223 q^{11} +3.86619 q^{12} -0.194531 q^{13} +0.488783 q^{14} +0.0877708 q^{16} -5.29549 q^{17} -5.59175 q^{18} +1.74439 q^{21} +1.64984 q^{22} -3.37540 q^{23} -8.64892 q^{24} +0.167838 q^{26} -10.7187 q^{27} +0.711327 q^{28} -8.73669 q^{29} +5.65662 q^{31} -5.69348 q^{32} +5.88801 q^{33} +4.56885 q^{34} -8.13770 q^{36} -0.955582 q^{37} +0.598988 q^{39} +10.0499 q^{41} -1.50503 q^{42} +4.93243 q^{43} +2.40101 q^{44} +2.91223 q^{46} -8.83942 q^{47} -0.270258 q^{48} -6.67906 q^{49} +16.3055 q^{51} +0.244255 q^{52} +8.20610 q^{53} +9.24791 q^{54} -1.59128 q^{56} +7.53785 q^{58} +3.71425 q^{59} -3.51122 q^{61} -4.88043 q^{62} -3.67166 q^{63} +4.73669 q^{64} -5.08007 q^{66} -4.04365 q^{67} +6.64906 q^{68} +10.3933 q^{69} +5.19533 q^{71} +18.2046 q^{72} -8.60409 q^{73} +0.824458 q^{74} +1.08332 q^{77} -0.516796 q^{78} +6.62648 q^{79} +13.5611 q^{81} -8.67089 q^{82} +4.51737 q^{83} -2.19027 q^{84} -4.25561 q^{86} +26.9014 q^{87} -5.37122 q^{88} +3.37352 q^{89} +0.110206 q^{91} +4.23818 q^{92} -17.4175 q^{93} +7.62648 q^{94} +17.5310 q^{96} -15.1922 q^{97} +5.76256 q^{98} -12.3933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{4} + 12 q^{6} + 8 q^{9}+O(q^{10}) \) 6 * q + 2 * q^4 + 12 * q^6 + 8 * q^9	\( 6 q + 2 q^{4} + 12 q^{6} + 8 q^{9} + 2 q^{11} + 22 q^{14} + 14 q^{16} + 20 q^{21} + 2 q^{24} - 22 q^{26} - 12 q^{29} + 30 q^{31} + 10 q^{34} - 14 q^{36} - 2 q^{39} + 12 q^{41} + 20 q^{44} + 4 q^{46} + 2 q^{49} + 40 q^{51} - 4 q^{54} + 46 q^{56} + 20 q^{59} - 2 q^{61} - 12 q^{64} + 6 q^{66} + 18 q^{69} - 2 q^{71} - 22 q^{74} + 24 q^{79} + 14 q^{81} + 48 q^{84} - 16 q^{86} + 36 q^{89} - 24 q^{91} + 30 q^{94} + 26 q^{96} - 30 q^{99}+O(q^{100}) \) 6 * q + 2 * q^4 + 12 * q^6 + 8 * q^9 + 2 * q^11 + 22 * q^14 + 14 * q^16 + 20 * q^21 + 2 * q^24 - 22 * q^26 - 12 * q^29 + 30 * q^31 + 10 * q^34 - 14 * q^36 - 2 * q^39 + 12 * q^41 + 20 * q^44 + 4 * q^46 + 2 * q^49 + 40 * q^51 - 4 * q^54 + 46 * q^56 + 20 * q^59 - 2 * q^61 - 12 * q^64 + 6 * q^66 + 18 * q^69 - 2 * q^71 - 22 * q^74 + 24 * q^79 + 14 * q^81 + 48 * q^84 - 16 * q^86 + 36 * q^89 - 24 * q^91 + 30 * q^94 + 26 * q^96 - 30 * q^99

Introduction

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