LMFDB - Embedded newform 9025.2.a.cr.1.1

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			1.1
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31644 q^{2} +2.09061 q^{3} +3.36590 q^{4} -4.84277 q^{6} +2.98971 q^{7} -3.16403 q^{8} +1.37064 q^{9} +O(q^{10})$	\(q-2.31644 q^{2} +2.09061 q^{3} +3.36590 q^{4} -4.84277 q^{6} +2.98971 q^{7} -3.16403 q^{8} +1.37064 q^{9} -2.06439 q^{11} +7.03677 q^{12} -2.80770 q^{13} -6.92548 q^{14} +0.597485 q^{16} -8.15512 q^{17} -3.17500 q^{18} +6.25030 q^{21} +4.78204 q^{22} +4.41871 q^{23} -6.61474 q^{24} +6.50388 q^{26} -3.40636 q^{27} +10.0631 q^{28} +8.16287 q^{29} -5.00967 q^{31} +4.94402 q^{32} -4.31583 q^{33} +18.8909 q^{34} +4.61342 q^{36} +1.47168 q^{37} -5.86980 q^{39} +6.77607 q^{41} -14.4785 q^{42} +6.86237 q^{43} -6.94854 q^{44} -10.2357 q^{46} -0.799446 q^{47} +1.24911 q^{48} +1.93835 q^{49} -17.0491 q^{51} -9.45044 q^{52} +9.74696 q^{53} +7.89063 q^{54} -9.45952 q^{56} -18.9088 q^{58} +9.05866 q^{59} -2.05016 q^{61} +11.6046 q^{62} +4.09780 q^{63} -12.6475 q^{64} +9.99737 q^{66} +1.61846 q^{67} -27.4493 q^{68} +9.23778 q^{69} -5.41382 q^{71} -4.33673 q^{72} -14.6746 q^{73} -3.40906 q^{74} -6.17193 q^{77} +13.5970 q^{78} -12.4575 q^{79} -11.2333 q^{81} -15.6964 q^{82} +7.70860 q^{83} +21.0379 q^{84} -15.8963 q^{86} +17.0653 q^{87} +6.53179 q^{88} +0.560005 q^{89} -8.39421 q^{91} +14.8729 q^{92} -10.4732 q^{93} +1.85187 q^{94} +10.3360 q^{96} +15.0046 q^{97} -4.49007 q^{98} -2.82953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.31644	−1.63797	−0.818986	−	0.573814i	$-0.805463\pi$
$2$	−2.31644	−1.63797	−0.818986	+	0.573814i	$0.805463\pi$
$3$	2.09061	1.20701	0.603506	−	0.797358i	$-0.293770\pi$
$3$	2.09061	1.20701	0.603506	+	0.797358i	$0.293770\pi$
$4$	3.36590	1.68295
$5$	0	0
$5$	0	0
$6$	−4.84277	−1.97705
$7$	2.98971	1.13000	0.565002	−	0.825090i	$-0.308876\pi$
$7$	2.98971	1.13000	0.565002	+	0.825090i	$0.308876\pi$
$8$	−3.16403	−1.11865
$9$	1.37064	0.456879
$10$	0	0
$11$	−2.06439	−0.622437	−0.311219	−	0.950338i	$-0.600737\pi$
$11$	−2.06439	−0.622437	−0.311219	+	0.950338i	$0.600737\pi$
$12$	7.03677	2.03134
$13$	−2.80770	−0.778716	−0.389358	−	0.921086i	$-0.627303\pi$
$13$	−2.80770	−0.778716	−0.389358	+	0.921086i	$0.627303\pi$
$14$	−6.92548	−1.85091
$15$	0	0
$16$	0.597485	0.149371
$17$	−8.15512	−1.97791	−0.988953	−	0.148228i	$-0.952643\pi$
$17$	−8.15512	−1.97791	−0.988953	+	0.148228i	$0.952643\pi$
$18$	−3.17500	−0.748354
$19$	0	0
$19$	0	0
$20$	0	0
$21$	6.25030	1.36393
$22$	4.78204	1.01953
$23$	4.41871	0.921364	0.460682	−	0.887565i	$-0.347605\pi$
$23$	4.41871	0.921364	0.460682	+	0.887565i	$0.347605\pi$
$24$	−6.61474	−1.35023
$25$	0	0
$26$	6.50388	1.27552
$27$	−3.40636	−0.655554
$28$	10.0631	1.90174
$29$	8.16287	1.51581	0.757903	−	0.652367i	$-0.226224\pi$
$29$	8.16287	1.51581	0.757903	+	0.652367i	$0.226224\pi$
$30$	0	0
$31$	−5.00967	−0.899763	−0.449881	−	0.893088i	$-0.648534\pi$
$31$	−5.00967	−0.899763	−0.449881	+	0.893088i	$0.648534\pi$
$32$	4.94402	0.873987
$33$	−4.31583	−0.751290
$34$	18.8909	3.23975
$35$	0	0
$36$	4.61342	0.768904
$37$	1.47168	0.241943	0.120971	−	0.992656i	$-0.461399\pi$
$37$	1.47168	0.241943	0.120971	+	0.992656i	$0.461399\pi$
$38$	0	0
$39$	−5.86980	−0.939920
$40$	0	0
$41$	6.77607	1.05824	0.529122	−	0.848546i	$-0.322521\pi$
$41$	6.77607	1.05824	0.529122	+	0.848546i	$0.322521\pi$
$42$	−14.4785	−2.23407
$43$	6.86237	1.04650	0.523251	−	0.852179i	$-0.324719\pi$
$43$	6.86237	1.04650	0.523251	+	0.852179i	$0.324719\pi$
$44$	−6.94854	−1.04753
$45$	0	0
$46$	−10.2357	−1.50917
$47$	−0.799446	−0.116611	−0.0583056	−	0.998299i	$-0.518570\pi$
$47$	−0.799446	−0.116611	−0.0583056	+	0.998299i	$0.518570\pi$
$48$	1.24911	0.180293
$49$	1.93835	0.276907
$50$	0	0
$51$	−17.0491	−2.38736
$52$	−9.45044	−1.31054
$53$	9.74696	1.33885	0.669424	−	0.742880i	$-0.266541\pi$
$53$	9.74696	1.33885	0.669424	+	0.742880i	$0.266541\pi$
$54$	7.89063	1.07378
$55$	0	0
$56$	−9.45952	−1.26408
$57$	0	0
$58$	−18.9088	−2.48285
$59$	9.05866	1.17934	0.589669	−	0.807645i	$-0.299258\pi$
$59$	9.05866	1.17934	0.589669	+	0.807645i	$0.299258\pi$
$60$	0	0
$61$	−2.05016	−0.262496	−0.131248	−	0.991350i	$-0.541898\pi$
$61$	−2.05016	−0.262496	−0.131248	+	0.991350i	$0.541898\pi$
$62$	11.6046	1.47379
$63$	4.09780	0.516274
$64$	−12.6475	−1.58094
$65$	0	0
$66$	9.99737	1.23059
$67$	1.61846	0.197726	0.0988631	−	0.995101i	$-0.468479\pi$
$67$	1.61846	0.197726	0.0988631	+	0.995101i	$0.468479\pi$
$68$	−27.4493	−3.32872
$69$	9.23778	1.11210
$70$	0	0
$71$	−5.41382	−0.642502	−0.321251	−	0.946994i	$-0.604103\pi$
$71$	−5.41382	−0.642502	−0.321251	+	0.946994i	$0.604103\pi$
$72$	−4.33673	−0.511089
$73$	−14.6746	−1.71753	−0.858765	−	0.512370i	$-0.828767\pi$
$73$	−14.6746	−1.71753	−0.858765	+	0.512370i	$0.828767\pi$
$74$	−3.40906	−0.396296
$75$	0	0
$76$	0	0
$77$	−6.17193	−0.703356
$78$	13.5970	1.53956
$79$	−12.4575	−1.40158	−0.700788	−	0.713370i	$-0.747168\pi$
$79$	−12.4575	−1.40158	−0.700788	+	0.713370i	$0.747168\pi$
$80$	0	0
$81$	−11.2333	−1.24814
$82$	−15.6964	−1.73337
$83$	7.70860	0.846129	0.423065	−	0.906100i	$-0.360954\pi$
$83$	7.70860	0.846129	0.423065	+	0.906100i	$0.360954\pi$
$84$	21.0379	2.29542
$85$	0	0
$86$	−15.8963	−1.71414
$87$	17.0653	1.82960
$88$	6.53179	0.696291
$89$	0.560005	0.0593604	0.0296802	−	0.999559i	$-0.490551\pi$
$89$	0.560005	0.0593604	0.0296802	+	0.999559i	$0.490551\pi$
$90$	0	0
$91$	−8.39421	−0.879952
$92$	14.8729	1.55061
$93$	−10.4732	−1.08602
$94$	1.85187	0.191006
$95$	0	0
$96$	10.3360	1.05491
$97$	15.0046	1.52349	0.761745	−	0.647877i	$-0.224343\pi$
$97$	15.0046	1.52349	0.761745	+	0.647877i	$0.224343\pi$
$98$	−4.49007	−0.453566
$99$	−2.82953	−0.284378
$100$	0	0
$101$	6.46781	0.643571	0.321785	−	0.946813i	$-0.395717\pi$
$101$	6.46781	0.643571	0.321785	+	0.946813i	$0.395717\pi$
$102$	39.4933	3.91042
$103$	5.06991	0.499553	0.249776	−	0.968304i	$-0.419643\pi$
$103$	5.06991	0.499553	0.249776	+	0.968304i	$0.419643\pi$
$104$	8.88365	0.871113
$105$	0	0
$106$	−22.5783	−2.19299
$107$	8.27328	0.799808	0.399904	−	0.916557i	$-0.369043\pi$
$107$	8.27328	0.799808	0.399904	+	0.916557i	$0.369043\pi$
$108$	−11.4655	−1.10327
$109$	4.85267	0.464801	0.232401	−	0.972620i	$-0.425342\pi$
$109$	4.85267	0.464801	0.232401	+	0.972620i	$0.425342\pi$
$110$	0	0
$111$	3.07671	0.292028
$112$	1.78630	0.168790
$113$	−10.4314	−0.981300	−0.490650	−	0.871357i	$-0.663241\pi$
$113$	−10.4314	−0.981300	−0.490650	+	0.871357i	$0.663241\pi$
$114$	0	0
$115$	0	0
$116$	27.4754	2.55103
$117$	−3.84834	−0.355779
$118$	−20.9839	−1.93172
$119$	−24.3814	−2.23504
$120$	0	0
$121$	−6.73829	−0.612572
$122$	4.74907	0.429961
$123$	14.1661	1.27731
$124$	−16.8620	−1.51426
$125$	0	0
$126$	−9.49231	−0.845642
$127$	10.4897	0.930812	0.465406	−	0.885097i	$-0.345908\pi$
$127$	10.4897	0.930812	0.465406	+	0.885097i	$0.345908\pi$
$128$	19.4091	1.71554
$129$	14.3465	1.26314
$130$	0	0
$131$	0.698557	0.0610332	0.0305166	−	0.999534i	$-0.490285\pi$
$131$	0.698557	0.0610332	0.0305166	+	0.999534i	$0.490285\pi$
$132$	−14.5267	−1.26438
$133$	0	0
$134$	−3.74906	−0.323870
$135$	0	0
$136$	25.8030	2.21259
$137$	12.4853	1.06669	0.533345	−	0.845898i	$-0.320935\pi$
$137$	12.4853	1.06669	0.533345	+	0.845898i	$0.320935\pi$
$138$	−21.3988	−1.82158
$139$	10.7089	0.908319	0.454159	−	0.890920i	$-0.349940\pi$
$139$	10.7089	0.908319	0.454159	+	0.890920i	$0.349940\pi$
$140$	0	0
$141$	−1.67133	−0.140751
$142$	12.5408	1.05240
$143$	5.79619	0.484702
$144$	0.818934	0.0682445
$145$	0	0
$146$	33.9928	2.81326
$147$	4.05232	0.334230
$148$	4.95353	0.407178
$149$	−2.90975	−0.238376	−0.119188	−	0.992872i	$-0.538029\pi$
$149$	−2.90975	−0.238376	−0.119188	+	0.992872i	$0.538029\pi$
$150$	0	0
$151$	4.19725	0.341568	0.170784	−	0.985309i	$-0.445370\pi$
$151$	4.19725	0.341568	0.170784	+	0.985309i	$0.445370\pi$
$152$	0	0
$153$	−11.1777	−0.903663
$154$	14.2969	1.15208
$155$	0	0
$156$	−19.7572	−1.58184
$157$	20.1878	1.61116	0.805581	−	0.592485i	$-0.201853\pi$
$157$	20.1878	1.61116	0.805581	+	0.592485i	$0.201853\pi$
$158$	28.8570	2.29574
$159$	20.3771	1.61601
$160$	0	0
$161$	13.2106	1.04114
$162$	26.0212	2.04442
$163$	5.58453	0.437414	0.218707	−	0.975791i	$-0.429816\pi$
$163$	5.58453	0.437414	0.218707	+	0.975791i	$0.429816\pi$
$164$	22.8076	1.78097
$165$	0	0
$166$	−17.8565	−1.38594
$167$	20.7079	1.60242	0.801212	−	0.598381i	$-0.204189\pi$
$167$	20.7079	1.60242	0.801212	+	0.598381i	$0.204189\pi$
$168$	−19.7761	−1.52576
$169$	−5.11681	−0.393601
$170$	0	0
$171$	0	0
$172$	23.0980	1.76121
$173$	21.1844	1.61062	0.805308	−	0.592856i	$-0.202000\pi$
$173$	21.1844	1.61062	0.805308	+	0.592856i	$0.202000\pi$
$174$	−39.5309	−2.99683
$175$	0	0
$176$	−1.23344	−0.0929742
$177$	18.9381	1.42347
$178$	−1.29722	−0.0972307
$179$	8.43282	0.630299	0.315149	−	0.949042i	$-0.397945\pi$
$179$	8.43282	0.630299	0.315149	+	0.949042i	$0.397945\pi$
$180$	0	0
$181$	−13.2997	−0.988557	−0.494278	−	0.869304i	$-0.664568\pi$
$181$	−13.2997	−0.988557	−0.494278	+	0.869304i	$0.664568\pi$
$182$	19.4447	1.44134
$183$	−4.28608	−0.316836
$184$	−13.9809	−1.03069
$185$	0	0
$186$	24.2607	1.77888
$187$	16.8354	1.23112
$188$	−2.69085	−0.196251
$189$	−10.1840	−0.740778
$190$	0	0
$191$	17.8925	1.29465	0.647327	−	0.762213i	$-0.275887\pi$
$191$	17.8925	1.29465	0.647327	+	0.762213i	$0.275887\pi$
$192$	−26.4409	−1.90821
$193$	−2.85677	−0.205635	−0.102817	−	0.994700i	$-0.532786\pi$
$193$	−2.85677	−0.205635	−0.102817	+	0.994700i	$0.532786\pi$
$194$	−34.7574	−2.49543
$195$	0	0
$196$	6.52429	0.466021
$197$	−5.99757	−0.427309	−0.213654	−	0.976909i	$-0.568537\pi$
$197$	−5.99757	−0.427309	−0.213654	+	0.976909i	$0.568537\pi$
$198$	6.55444	0.465804
$199$	−8.18020	−0.579879	−0.289939	−	0.957045i	$-0.593635\pi$
$199$	−8.18020	−0.579879	−0.289939	+	0.957045i	$0.593635\pi$
$200$	0	0
$201$	3.38356	0.238658
$202$	−14.9823	−1.05415
$203$	24.4046	1.71287
$204$	−57.3857	−4.01780
$205$	0	0
$206$	−11.7441	−0.818253
$207$	6.05644	0.420951
$208$	−1.67756	−0.116318
$209$	0	0
$210$	0	0
$211$	−9.36220	−0.644520	−0.322260	−	0.946651i	$-0.604443\pi$
$211$	−9.36220	−0.644520	−0.322260	+	0.946651i	$0.604443\pi$
$212$	32.8073	2.25321
$213$	−11.3182	−0.775508
$214$	−19.1646	−1.31006
$215$	0	0
$216$	10.7778	0.733338
$217$	−14.9774	−1.01673
$218$	−11.2409	−0.761331
$219$	−30.6788	−2.07308
$220$	0	0
$221$	22.8971	1.54023
$222$	−7.12701	−0.478334
$223$	−4.47051	−0.299367	−0.149684	−	0.988734i	$-0.547826\pi$
$223$	−4.47051	−0.299367	−0.149684	+	0.988734i	$0.547826\pi$
$224$	14.7812	0.987608
$225$	0	0
$226$	24.1636	1.60734
$227$	14.9692	0.993542	0.496771	−	0.867882i	$-0.334519\pi$
$227$	14.9692	0.993542	0.496771	+	0.867882i	$0.334519\pi$
$228$	0	0
$229$	−24.7467	−1.63531	−0.817653	−	0.575711i	$-0.804725\pi$
$229$	−24.7467	−1.63531	−0.817653	+	0.575711i	$0.804725\pi$
$230$	0	0
$231$	−12.9031	−0.848960
$232$	−25.8275	−1.69566
$233$	−22.3437	−1.46378	−0.731891	−	0.681422i	$-0.761362\pi$
$233$	−22.3437	−1.46378	−0.731891	+	0.681422i	$0.761362\pi$
$234$	8.91445	0.582756
$235$	0	0
$236$	30.4906	1.98477
$237$	−26.0437	−1.69172
$238$	56.4781	3.66093
$239$	−11.1798	−0.723163	−0.361581	−	0.932341i	$-0.617763\pi$
$239$	−11.1798	−0.723163	−0.361581	+	0.932341i	$0.617763\pi$
$240$	0	0
$241$	−0.456807	−0.0294255	−0.0147128	−	0.999892i	$-0.504683\pi$
$241$	−0.456807	−0.0294255	−0.0147128	+	0.999892i	$0.504683\pi$
$242$	15.6088	1.00337
$243$	−13.2653	−0.850967
$244$	−6.90063	−0.441768
$245$	0	0
$246$	−32.8149	−2.09220
$247$	0	0
$248$	15.8507	1.00652
$249$	16.1157	1.02129
$250$	0	0
$251$	19.1138	1.20645	0.603226	−	0.797571i	$-0.293882\pi$
$251$	19.1138	1.20645	0.603226	+	0.797571i	$0.293882\pi$
$252$	13.7928	0.868864
$253$	−9.12194	−0.573491
$254$	−24.2988	−1.52464
$255$	0	0
$256$	−19.6652	−1.22907
$257$	−5.20487	−0.324671	−0.162335	−	0.986736i	$-0.551903\pi$
$257$	−5.20487	−0.324671	−0.162335	+	0.986736i	$0.551903\pi$
$258$	−33.2328	−2.06899
$259$	4.39990	0.273396
$260$	0	0
$261$	11.1883	0.692539
$262$	−1.61817	−0.0999707
$263$	−2.72929	−0.168295	−0.0841477	−	0.996453i	$-0.526817\pi$
$263$	−2.72929	−0.168295	−0.0841477	+	0.996453i	$0.526817\pi$
$264$	13.6554	0.840432
$265$	0	0
$266$	0	0
$267$	1.17075	0.0716488
$268$	5.44757	0.332763
$269$	5.99137	0.365300	0.182650	−	0.983178i	$-0.441532\pi$
$269$	5.99137	0.365300	0.182650	+	0.983178i	$0.441532\pi$
$270$	0	0
$271$	−21.9876	−1.33565	−0.667826	−	0.744317i	$-0.732775\pi$
$271$	−21.9876	−1.33565	−0.667826	+	0.744317i	$0.732775\pi$
$272$	−4.87256	−0.295442
$273$	−17.5490	−1.06211
$274$	−28.9214	−1.74721
$275$	0	0
$276$	31.0934	1.87160
$277$	2.25035	0.135211	0.0676053	−	0.997712i	$-0.478464\pi$
$277$	2.25035	0.135211	0.0676053	+	0.997712i	$0.478464\pi$
$278$	−24.8066	−1.48780
$279$	−6.86643	−0.411082
$280$	0	0
$281$	2.58551	0.154239	0.0771193	−	0.997022i	$-0.475428\pi$
$281$	2.58551	0.154239	0.0771193	+	0.997022i	$0.475428\pi$
$282$	3.87153	0.230546
$283$	24.0610	1.43028	0.715139	−	0.698983i	$-0.246364\pi$
$283$	24.0610	1.43028	0.715139	+	0.698983i	$0.246364\pi$
$284$	−18.2224	−1.08130
$285$	0	0
$286$	−13.4265	−0.793928
$287$	20.2585	1.19582
$288$	6.77645	0.399306
$289$	49.5059	2.91211
$290$	0	0
$291$	31.3688	1.83887
$292$	−49.3932	−2.89052
$293$	15.0223	0.877611	0.438805	−	0.898582i	$-0.355402\pi$
$293$	15.0223	0.877611	0.438805	+	0.898582i	$0.355402\pi$
$294$	−9.38697	−0.547459
$295$	0	0
$296$	−4.65644	−0.270650
$297$	7.03206	0.408041
$298$	6.74027	0.390453
$299$	−12.4064	−0.717481
$300$	0	0
$301$	20.5165	1.18255
$302$	−9.72269	−0.559478
$303$	13.5216	0.776798
$304$	0	0
$305$	0	0
$306$	25.8925	1.48017
$307$	30.4411	1.73737	0.868683	−	0.495369i	$-0.164967\pi$
$307$	30.4411	1.73737	0.868683	+	0.495369i	$0.164967\pi$
$308$	−20.7741	−1.18371
$309$	10.5992	0.602966
$310$	0	0
$311$	21.9935	1.24714	0.623570	−	0.781768i	$-0.285682\pi$
$311$	21.9935	1.24714	0.623570	+	0.781768i	$0.285682\pi$
$312$	18.5722	1.05144
$313$	5.30053	0.299603	0.149802	−	0.988716i	$-0.452136\pi$
$313$	5.30053	0.299603	0.149802	+	0.988716i	$0.452136\pi$
$314$	−46.7639	−2.63904
$315$	0	0
$316$	−41.9306	−2.35878
$317$	27.6630	1.55371	0.776855	−	0.629680i	$-0.216814\pi$
$317$	27.6630	1.55371	0.776855	+	0.629680i	$0.216814\pi$
$318$	−47.2023	−2.64697
$319$	−16.8514	−0.943495
$320$	0	0
$321$	17.2962	0.965378
$322$	−30.6017	−1.70536
$323$	0	0
$324$	−37.8101	−2.10056
$325$	0	0
$326$	−12.9362	−0.716471
$327$	10.1450	0.561021
$328$	−21.4397	−1.18381
$329$	−2.39011	−0.131771
$330$	0	0
$331$	9.58294	0.526726	0.263363	−	0.964697i	$-0.415168\pi$
$331$	9.58294	0.526726	0.263363	+	0.964697i	$0.415168\pi$
$332$	25.9464	1.42399
$333$	2.01714	0.110539
$334$	−47.9686	−2.62472
$335$	0	0
$336$	3.73446	0.203731
$337$	25.7337	1.40180	0.700902	−	0.713257i	$-0.252781\pi$
$337$	25.7337	1.40180	0.700902	+	0.713257i	$0.252781\pi$
$338$	11.8528	0.644707
$339$	−21.8079	−1.18444
$340$	0	0
$341$	10.3419	0.560046
$342$	0	0
$343$	−15.1329	−0.817097
$344$	−21.7127	−1.17067
$345$	0	0
$346$	−49.0723	−2.63814
$347$	−23.6724	−1.27080	−0.635400	−	0.772183i	$-0.719165\pi$
$347$	−23.6724	−1.27080	−0.635400	+	0.772183i	$0.719165\pi$
$348$	57.4402	3.07912
$349$	−3.04285	−0.162880	−0.0814401	−	0.996678i	$-0.525952\pi$
$349$	−3.04285	−0.162880	−0.0814401	+	0.996678i	$0.525952\pi$
$350$	0	0
$351$	9.56404	0.510491
$352$	−10.2064	−0.544002
$353$	7.25801	0.386305	0.193152	−	0.981169i	$-0.438129\pi$
$353$	7.25801	0.386305	0.193152	+	0.981169i	$0.438129\pi$
$354$	−43.8690	−2.33161
$355$	0	0
$356$	1.88492	0.0999006
$357$	−50.9719	−2.69772
$358$	−19.5341	−1.03241
$359$	12.6505	0.667667	0.333834	−	0.942632i	$-0.391658\pi$
$359$	12.6505	0.667667	0.333834	+	0.942632i	$0.391658\pi$
$360$	0	0
$361$	0	0
$362$	30.8079	1.61923
$363$	−14.0871	−0.739382
$364$	−28.2541	−1.48092
$365$	0	0
$366$	9.92844	0.518968
$367$	−17.5243	−0.914762	−0.457381	−	0.889271i	$-0.651212\pi$
$367$	−17.5243	−0.914762	−0.457381	+	0.889271i	$0.651212\pi$
$368$	2.64011	0.137625
$369$	9.28752	0.483489
$370$	0	0
$371$	29.1406	1.51290
$372$	−35.2519	−1.82773
$373$	−7.39846	−0.383078	−0.191539	−	0.981485i	$-0.561348\pi$
$373$	−7.39846	−0.383078	−0.191539	+	0.981485i	$0.561348\pi$
$374$	−38.9981	−2.01654
$375$	0	0
$376$	2.52947	0.130447
$377$	−22.9189	−1.18038
$378$	23.5907	1.21337
$379$	15.6602	0.804409	0.402204	−	0.915550i	$-0.368244\pi$
$379$	15.6602	0.804409	0.402204	+	0.915550i	$0.368244\pi$
$380$	0	0
$381$	21.9299	1.12350
$382$	−41.4468	−2.12060
$383$	3.28724	0.167970	0.0839851	−	0.996467i	$-0.473235\pi$
$383$	3.28724	0.167970	0.0839851	+	0.996467i	$0.473235\pi$
$384$	40.5769	2.07068
$385$	0	0
$386$	6.61754	0.336824
$387$	9.40580	0.478124
$388$	50.5041	2.56396
$389$	26.3825	1.33764	0.668822	−	0.743422i	$-0.266799\pi$
$389$	26.3825	1.33764	0.668822	+	0.743422i	$0.266799\pi$
$390$	0	0
$391$	−36.0351	−1.82237
$392$	−6.13299	−0.309763
$393$	1.46041	0.0736678
$394$	13.8930	0.699920
$395$	0	0
$396$	−9.52391	−0.478595
$397$	13.9301	0.699132	0.349566	−	0.936912i	$-0.386329\pi$
$397$	13.9301	0.699132	0.349566	+	0.936912i	$0.386329\pi$
$398$	18.9489	0.949825
$399$	0	0
$400$	0	0
$401$	−17.2682	−0.862331	−0.431166	−	0.902273i	$-0.641898\pi$
$401$	−17.2682	−0.862331	−0.431166	+	0.902273i	$0.641898\pi$
$402$	−7.83782	−0.390915
$403$	14.0656	0.700660
$404$	21.7700	1.08310
$405$	0	0
$406$	−56.5318	−2.80563
$407$	−3.03813	−0.150594
$408$	53.9440	2.67062
$409$	23.9164	1.18259	0.591296	−	0.806455i	$-0.298617\pi$
$409$	23.9164	1.18259	0.591296	+	0.806455i	$0.298617\pi$
$410$	0	0
$411$	26.1018	1.28751
$412$	17.0648	0.840723
$413$	27.0827	1.33265
$414$	−14.0294	−0.689506
$415$	0	0
$416$	−13.8813	−0.680588
$417$	22.3881	1.09635
$418$	0	0
$419$	10.2371	0.500113	0.250056	−	0.968231i	$-0.419551\pi$
$419$	10.2371	0.500113	0.250056	+	0.968231i	$0.419551\pi$
$420$	0	0
$421$	−22.7071	−1.10668	−0.553339	−	0.832956i	$-0.686647\pi$
$421$	−22.7071	−1.10668	−0.553339	+	0.832956i	$0.686647\pi$
$422$	21.6870	1.05571
$423$	−1.09575	−0.0532771
$424$	−30.8397	−1.49771
$425$	0	0
$426$	26.2179	1.27026
$427$	−6.12938	−0.296621
$428$	27.8470	1.34604
$429$	12.1176	0.585041
$430$	0	0
$431$	−8.45973	−0.407491	−0.203745	−	0.979024i	$-0.565311\pi$
$431$	−8.45973	−0.407491	−0.203745	+	0.979024i	$0.565311\pi$
$432$	−2.03525	−0.0979209
$433$	6.39945	0.307538	0.153769	−	0.988107i	$-0.450859\pi$
$433$	6.39945	0.307538	0.153769	+	0.988107i	$0.450859\pi$
$434$	34.6944	1.66538
$435$	0	0
$436$	16.3336	0.782237
$437$	0	0
$438$	71.0656	3.39564
$439$	−8.74857	−0.417546	−0.208773	−	0.977964i	$-0.566947\pi$
$439$	−8.74857	−0.417546	−0.208773	+	0.977964i	$0.566947\pi$
$440$	0	0
$441$	2.65677	0.126513
$442$	−53.0399	−2.52285
$443$	−7.54575	−0.358509	−0.179255	−	0.983803i	$-0.557369\pi$
$443$	−7.54575	−0.358509	−0.179255	+	0.983803i	$0.557369\pi$
$444$	10.3559	0.491469
$445$	0	0
$446$	10.3557	0.490355
$447$	−6.08314	−0.287723
$448$	−37.8123	−1.78646
$449$	28.4010	1.34033	0.670163	−	0.742214i	$-0.266224\pi$
$449$	28.4010	1.34033	0.670163	+	0.742214i	$0.266224\pi$
$450$	0	0
$451$	−13.9885	−0.658691
$452$	−35.1109	−1.65148
$453$	8.77480	0.412276
$454$	−34.6753	−1.62739
$455$	0	0
$456$	0	0
$457$	39.0146	1.82503	0.912514	−	0.409046i	$-0.134138\pi$
$457$	39.0146	1.82503	0.912514	+	0.409046i	$0.134138\pi$
$458$	57.3242	2.67858
$459$	27.7793	1.29662
$460$	0	0
$461$	−10.4326	−0.485894	−0.242947	−	0.970040i	$-0.578114\pi$
$461$	−10.4326	−0.485894	−0.242947	+	0.970040i	$0.578114\pi$
$462$	29.8892	1.39057
$463$	−9.01417	−0.418924	−0.209462	−	0.977817i	$-0.567171\pi$
$463$	−9.01417	−0.418924	−0.209462	+	0.977817i	$0.567171\pi$
$464$	4.87719	0.226418
$465$	0	0
$466$	51.7578	2.39763
$467$	−26.3077	−1.21737	−0.608687	−	0.793411i	$-0.708303\pi$
$467$	−26.3077	−1.21737	−0.608687	+	0.793411i	$0.708303\pi$
$468$	−12.9531	−0.598758
$469$	4.83872	0.223431
$470$	0	0
$471$	42.2048	1.94469
$472$	−28.6619	−1.31927
$473$	−14.1666	−0.651381
$474$	60.3287	2.77099
$475$	0	0
$476$	−82.0654	−3.76146
$477$	13.3595	0.611691
$478$	25.8974	1.18452
$479$	19.1783	0.876278	0.438139	−	0.898907i	$-0.355638\pi$
$479$	19.1783	0.876278	0.438139	+	0.898907i	$0.355638\pi$
$480$	0	0
$481$	−4.13204	−0.188405
$482$	1.05817	0.0481981
$483$	27.6182	1.25667
$484$	−22.6804	−1.03093
$485$	0	0
$486$	30.7282	1.39386
$487$	−32.7301	−1.48314	−0.741571	−	0.670874i	$-0.765919\pi$
$487$	−32.7301	−1.48314	−0.741571	+	0.670874i	$0.765919\pi$
$488$	6.48676	0.293642
$489$	11.6750	0.527964
$490$	0	0
$491$	−30.2271	−1.36413	−0.682064	−	0.731292i	$-0.738918\pi$
$491$	−30.2271	−1.36413	−0.682064	+	0.731292i	$0.738918\pi$
$492$	47.6817	2.14966
$493$	−66.5691	−2.99812
$494$	0	0
$495$	0	0
$496$	−2.99320	−0.134399
$497$	−16.1857	−0.726029
$498$	−37.3310	−1.67284
$499$	11.3112	0.506357	0.253179	−	0.967420i	$-0.418524\pi$
$499$	11.3112	0.506357	0.253179	+	0.967420i	$0.418524\pi$
$500$	0	0
$501$	43.2920	1.93415
$502$	−44.2760	−1.97613
$503$	−34.0142	−1.51662	−0.758309	−	0.651896i	$-0.773974\pi$
$503$	−34.0142	−1.51662	−0.758309	+	0.651896i	$0.773974\pi$
$504$	−12.9656	−0.577532
$505$	0	0
$506$	21.1304	0.939363
$507$	−10.6972	−0.475081
$508$	35.3073	1.56651
$509$	−0.317387	−0.0140679	−0.00703396	−	0.999975i	$-0.502239\pi$
$509$	−0.317387	−0.0140679	−0.00703396	+	0.999975i	$0.502239\pi$
$510$	0	0
$511$	−43.8727	−1.94081
$512$	6.73489	0.297643
$513$	0	0
$514$	12.0568	0.531801
$515$	0	0
$516$	48.2889	2.12580
$517$	1.65037	0.0725831
$518$	−10.1921	−0.447815
$519$	44.2881	1.94403
$520$	0	0
$521$	−38.0598	−1.66743	−0.833716	−	0.552194i	$-0.813791\pi$
$521$	−38.0598	−1.66743	−0.833716	+	0.552194i	$0.813791\pi$
$522$	−25.9171	−1.13436
$523$	−11.3389	−0.495815	−0.247907	−	0.968784i	$-0.579743\pi$
$523$	−11.3389	−0.495815	−0.247907	+	0.968784i	$0.579743\pi$
$524$	2.35127	0.102716
$525$	0	0
$526$	6.32225	0.275663
$527$	40.8544	1.77965
$528$	−2.57864	−0.112221
$529$	−3.47503	−0.151088
$530$	0	0
$531$	12.4161	0.538814
$532$	0	0
$533$	−19.0252	−0.824072
$534$	−2.71197	−0.117359
$535$	0	0
$536$	−5.12085	−0.221187
$537$	17.6297	0.760778
$538$	−13.8787	−0.598351
$539$	−4.00151	−0.172357
$540$	0	0
$541$	13.5373	0.582013	0.291006	−	0.956721i	$-0.406010\pi$
$541$	13.5373	0.582013	0.291006	+	0.956721i	$0.406010\pi$
$542$	50.9330	2.18776
$543$	−27.8044	−1.19320
$544$	−40.3190	−1.72866
$545$	0	0
$546$	40.6512	1.73971
$547$	37.0981	1.58620	0.793100	−	0.609092i	$-0.208466\pi$
$547$	37.0981	1.58620	0.793100	+	0.609092i	$0.208466\pi$
$548$	42.0242	1.79519
$549$	−2.81002	−0.119929
$550$	0	0
$551$	0	0
$552$	−29.2286	−1.24405
$553$	−37.2442	−1.58379
$554$	−5.21281	−0.221471
$555$	0	0
$556$	36.0452	1.52866
$557$	−1.78178	−0.0754964	−0.0377482	−	0.999287i	$-0.512018\pi$
$557$	−1.78178	−0.0754964	−0.0377482	+	0.999287i	$0.512018\pi$
$558$	15.9057	0.673341
$559$	−19.2675	−0.814927
$560$	0	0
$561$	35.1961	1.48598
$562$	−5.98918	−0.252638
$563$	−20.8434	−0.878445	−0.439222	−	0.898378i	$-0.644746\pi$
$563$	−20.8434	−0.878445	−0.439222	+	0.898378i	$0.644746\pi$
$564$	−5.62552	−0.236877
$565$	0	0
$566$	−55.7359	−2.34275
$567$	−33.5842	−1.41040
$568$	17.1295	0.718737
$569$	−4.50848	−0.189005	−0.0945026	−	0.995525i	$-0.530126\pi$
$569$	−4.50848	−0.189005	−0.0945026	+	0.995525i	$0.530126\pi$
$570$	0	0
$571$	18.1758	0.760633	0.380316	−	0.924856i	$-0.375815\pi$
$571$	18.1758	0.760633	0.380316	+	0.924856i	$0.375815\pi$
$572$	19.5094	0.815730
$573$	37.4061	1.56266
$574$	−46.9275	−1.95872
$575$	0	0
$576$	−17.3351	−0.722296
$577$	−13.2472	−0.551490	−0.275745	−	0.961231i	$-0.588924\pi$
$577$	−13.2472	−0.551490	−0.275745	+	0.961231i	$0.588924\pi$
$578$	−114.678	−4.76996
$579$	−5.97238	−0.248204
$580$	0	0
$581$	23.0465	0.956128
$582$	−72.6640	−3.01202
$583$	−20.1215	−0.833349
$584$	46.4308	1.92132
$585$	0	0
$586$	−34.7982	−1.43750
$587$	−4.58988	−0.189444	−0.0947222	−	0.995504i	$-0.530196\pi$
$587$	−4.58988	−0.189444	−0.0947222	+	0.995504i	$0.530196\pi$
$588$	13.6397	0.562493
$589$	0	0
$590$	0	0
$591$	−12.5386	−0.515767
$592$	0.879307	0.0361393
$593$	−1.67684	−0.0688596	−0.0344298	−	0.999407i	$-0.510962\pi$
$593$	−1.67684	−0.0688596	−0.0344298	+	0.999407i	$0.510962\pi$
$594$	−16.2894	−0.668360
$595$	0	0
$596$	−9.79393	−0.401175
$597$	−17.1016	−0.699921
$598$	28.7387	1.17521
$599$	−24.1953	−0.988592	−0.494296	−	0.869294i	$-0.664574\pi$
$599$	−24.1953	−0.988592	−0.494296	+	0.869294i	$0.664574\pi$
$600$	0	0
$601$	21.2626	0.867320	0.433660	−	0.901077i	$-0.357222\pi$
$601$	21.2626	0.867320	0.433660	+	0.901077i	$0.357222\pi$
$602$	−47.5252	−1.93698
$603$	2.21832	0.0903369
$604$	14.1275	0.574841
$605$	0	0
$606$	−31.3221	−1.27237
$607$	36.9992	1.50175	0.750876	−	0.660443i	$-0.229631\pi$
$607$	36.9992	1.50175	0.750876	+	0.660443i	$0.229631\pi$
$608$	0	0
$609$	51.0204	2.06745
$610$	0	0
$611$	2.24460	0.0908070
$612$	−37.6230	−1.52082
$613$	35.4733	1.43275	0.716377	−	0.697714i	$-0.245799\pi$
$613$	35.4733	1.43275	0.716377	+	0.697714i	$0.245799\pi$
$614$	−70.5150	−2.84575
$615$	0	0
$616$	19.5281	0.786811
$617$	20.9419	0.843088	0.421544	−	0.906808i	$-0.361488\pi$
$617$	20.9419	0.843088	0.421544	+	0.906808i	$0.361488\pi$
$618$	−24.5524	−0.987642
$619$	11.3013	0.454237	0.227119	−	0.973867i	$-0.427069\pi$
$619$	11.3013	0.454237	0.227119	+	0.973867i	$0.427069\pi$
$620$	0	0
$621$	−15.0517	−0.604004
$622$	−50.9468	−2.04278
$623$	1.67425	0.0670775
$624$	−3.50711	−0.140397
$625$	0	0
$626$	−12.2784	−0.490742
$627$	0	0
$628$	67.9501	2.71151
$629$	−12.0017	−0.478541
$630$	0	0
$631$	−10.8325	−0.431234	−0.215617	−	0.976478i	$-0.569176\pi$
$631$	−10.8325	−0.431234	−0.215617	+	0.976478i	$0.569176\pi$
$632$	39.4158	1.56788
$633$	−19.5727	−0.777944
$634$	−64.0798	−2.54493
$635$	0	0
$636$	68.5872	2.71966
$637$	−5.44230	−0.215632
$638$	39.0352	1.54542
$639$	−7.42037	−0.293545
$640$	0	0
$641$	13.5849	0.536570	0.268285	−	0.963340i	$-0.413543\pi$
$641$	13.5849	0.536570	0.268285	+	0.963340i	$0.413543\pi$
$642$	−40.0656	−1.58126
$643$	−14.4214	−0.568723	−0.284362	−	0.958717i	$-0.591782\pi$
$643$	−14.4214	−0.568723	−0.284362	+	0.958717i	$0.591782\pi$
$644$	44.4657	1.75219
$645$	0	0
$646$	0	0
$647$	−17.6253	−0.692923	−0.346462	−	0.938064i	$-0.612617\pi$
$647$	−17.6253	−0.692923	−0.346462	+	0.938064i	$0.612617\pi$
$648$	35.5424	1.39624
$649$	−18.7006	−0.734064
$650$	0	0
$651$	−31.3119	−1.22721
$652$	18.7970	0.736146
$653$	34.3332	1.34356	0.671782	−	0.740749i	$-0.265529\pi$
$653$	34.3332	1.34356	0.671782	+	0.740749i	$0.265529\pi$
$654$	−23.5003	−0.918936
$655$	0	0
$656$	4.04860	0.158071
$657$	−20.1135	−0.784702
$658$	5.53654	0.215837
$659$	−6.44014	−0.250872	−0.125436	−	0.992102i	$-0.540033\pi$
$659$	−6.44014	−0.250872	−0.125436	+	0.992102i	$0.540033\pi$
$660$	0	0
$661$	−19.6639	−0.764838	−0.382419	−	0.923989i	$-0.624909\pi$
$661$	−19.6639	−0.764838	−0.382419	+	0.923989i	$0.624909\pi$
$662$	−22.1983	−0.862762
$663$	47.8689	1.85907
$664$	−24.3902	−0.946525
$665$	0	0
$666$	−4.67259	−0.181059
$667$	36.0693	1.39661
$668$	69.7007	2.69680
$669$	−9.34607	−0.361340
$670$	0	0
$671$	4.23233	0.163387
$672$	30.9016	1.19206
$673$	−4.45318	−0.171657	−0.0858287	−	0.996310i	$-0.527354\pi$
$673$	−4.45318	−0.171657	−0.0858287	+	0.996310i	$0.527354\pi$
$674$	−59.6106	−2.29612
$675$	0	0
$676$	−17.2227	−0.662411
$677$	5.24805	0.201699	0.100849	−	0.994902i	$-0.467844\pi$
$677$	5.24805	0.201699	0.100849	+	0.994902i	$0.467844\pi$
$678$	50.5166	1.94008
$679$	44.8595	1.72155
$680$	0	0
$681$	31.2947	1.19922
$682$	−23.9564	−0.917339
$683$	−18.6438	−0.713386	−0.356693	−	0.934222i	$-0.616096\pi$
$683$	−18.6438	−0.713386	−0.356693	+	0.934222i	$0.616096\pi$
$684$	0	0
$685$	0	0
$686$	35.0544	1.33838
$687$	−51.7356	−1.97383
$688$	4.10016	0.156317
$689$	−27.3666	−1.04258
$690$	0	0
$691$	12.7926	0.486654	0.243327	−	0.969944i	$-0.421761\pi$
$691$	12.7926	0.486654	0.243327	+	0.969944i	$0.421761\pi$
$692$	71.3044	2.71059
$693$	−8.45946	−0.321348
$694$	54.8357	2.08153
$695$	0	0
$696$	−53.9952	−2.04668
$697$	−55.2596	−2.09311
$698$	7.04859	0.266793
$699$	−46.7118	−1.76680
$700$	0	0
$701$	−31.9007	−1.20487	−0.602436	−	0.798167i	$-0.705803\pi$
$701$	−31.9007	−1.20487	−0.602436	+	0.798167i	$0.705803\pi$
$702$	−22.1545	−0.836169
$703$	0	0
$704$	26.1094	0.984034
$705$	0	0
$706$	−16.8127	−0.632756
$707$	19.3368	0.727237
$708$	63.7438	2.39564
$709$	−13.5200	−0.507755	−0.253878	−	0.967236i	$-0.581706\pi$
$709$	−13.5200	−0.507755	−0.253878	+	0.967236i	$0.581706\pi$
$710$	0	0
$711$	−17.0747	−0.640350
$712$	−1.77187	−0.0664037
$713$	−22.1362	−0.829009
$714$	118.074	4.41879
$715$	0	0
$716$	28.3840	1.06076
$717$	−23.3726	−0.872867
$718$	−29.3041	−1.09362
$719$	−29.2834	−1.09209	−0.546043	−	0.837757i	$-0.683866\pi$
$719$	−29.2834	−1.09209	−0.546043	+	0.837757i	$0.683866\pi$
$720$	0	0
$721$	15.1575	0.564496
$722$	0	0
$723$	−0.955003	−0.0355170
$724$	−44.7654	−1.66369
$725$	0	0
$726$	32.6320	1.21109
$727$	16.8259	0.624037	0.312018	−	0.950076i	$-0.398995\pi$
$727$	16.8259	0.624037	0.312018	+	0.950076i	$0.398995\pi$
$728$	26.5595	0.984361
$729$	5.96736	0.221013
$730$	0	0
$731$	−55.9634	−2.06988
$732$	−14.4265	−0.533219
$733$	−7.42524	−0.274258	−0.137129	−	0.990553i	$-0.543787\pi$
$733$	−7.42524	−0.274258	−0.137129	+	0.990553i	$0.543787\pi$
$734$	40.5941	1.49835
$735$	0	0
$736$	21.8462	0.805260
$737$	−3.34113	−0.123072
$738$	−21.5140	−0.791941
$739$	12.4942	0.459607	0.229803	−	0.973237i	$-0.426192\pi$
$739$	12.4942	0.459607	0.229803	+	0.973237i	$0.426192\pi$
$740$	0	0
$741$	0	0
$742$	−67.5024	−2.47809
$743$	11.3042	0.414711	0.207355	−	0.978266i	$-0.433514\pi$
$743$	11.3042	0.414711	0.207355	+	0.978266i	$0.433514\pi$
$744$	33.1376	1.21488
$745$	0	0
$746$	17.1381	0.627471
$747$	10.5657	0.386578
$748$	56.6661	2.07192
$749$	24.7347	0.903785
$750$	0	0
$751$	−48.1086	−1.75551	−0.877754	−	0.479111i	$-0.840959\pi$
$751$	−48.1086	−1.75551	−0.877754	+	0.479111i	$0.840959\pi$
$752$	−0.477656	−0.0174183
$753$	39.9594	1.45620
$754$	53.0903	1.93343
$755$	0	0
$756$	−34.2784	−1.24669
$757$	9.87125	0.358777	0.179388	−	0.983778i	$-0.442588\pi$
$757$	9.87125	0.358777	0.179388	+	0.983778i	$0.442588\pi$
$758$	−36.2759	−1.31760
$759$	−19.0704	−0.692211
$760$	0	0
$761$	−24.4437	−0.886083	−0.443042	−	0.896501i	$-0.646101\pi$
$761$	−24.4437	−0.886083	−0.443042	+	0.896501i	$0.646101\pi$
$762$	−50.7993	−1.84026
$763$	14.5080	0.525227
$764$	60.2242	2.17884
$765$	0	0
$766$	−7.61470	−0.275130
$767$	−25.4340	−0.918369
$768$	−41.1121	−1.48351
$769$	20.8504	0.751883	0.375942	−	0.926643i	$-0.377319\pi$
$769$	20.8504	0.751883	0.375942	+	0.926643i	$0.377319\pi$
$770$	0	0
$771$	−10.8813	−0.391882
$772$	−9.61560	−0.346073
$773$	25.8885	0.931144	0.465572	−	0.885010i	$-0.345849\pi$
$773$	25.8885	0.931144	0.465572	+	0.885010i	$0.345849\pi$
$774$	−21.7880	−0.783153
$775$	0	0
$776$	−47.4751	−1.70426
$777$	9.19845	0.329993
$778$	−61.1134	−2.19102
$779$	0	0
$780$	0	0
$781$	11.1762	0.399917
$782$	83.4731	2.98499
$783$	−27.8057	−0.993693
$784$	1.15813	0.0413619
$785$	0	0
$786$	−3.38295	−0.120666
$787$	11.9308	0.425288	0.212644	−	0.977130i	$-0.431793\pi$
$787$	11.9308	0.425288	0.212644	+	0.977130i	$0.431793\pi$
$788$	−20.1872	−0.719140
$789$	−5.70588	−0.203135
$790$	0	0
$791$	−31.1867	−1.10887
$792$	8.95271	0.318121
$793$	5.75624	0.204410
$794$	−32.2683	−1.14516
$795$	0	0
$796$	−27.5337	−0.975907
$797$	−0.806993	−0.0285852	−0.0142926	−	0.999898i	$-0.504550\pi$
$797$	−0.806993	−0.0285852	−0.0142926	+	0.999898i	$0.504550\pi$
$798$	0	0
$799$	6.51957	0.230646
$800$	0	0
$801$	0.767563	0.0271205
$802$	40.0007	1.41247
$803$	30.2941	1.06905
$804$	11.3887	0.401649
$805$	0	0
$806$	−32.5823	−1.14766
$807$	12.5256	0.440922
$808$	−20.4643	−0.719932
$809$	28.2619	0.993637	0.496818	−	0.867855i	$-0.334501\pi$
$809$	28.2619	0.993637	0.496818	+	0.867855i	$0.334501\pi$
$810$	0	0
$811$	−14.1673	−0.497481	−0.248740	−	0.968570i	$-0.580017\pi$
$811$	−14.1673	−0.497481	−0.248740	+	0.968570i	$0.580017\pi$
$812$	82.1434	2.88267
$813$	−45.9675	−1.61215
$814$	7.03764	0.246669
$815$	0	0
$816$	−10.1866	−0.356602
$817$	0	0
$818$	−55.4010	−1.93705
$819$	−11.5054	−0.402031
$820$	0	0
$821$	40.2124	1.40342	0.701710	−	0.712462i	$-0.252420\pi$
$821$	40.2124	1.40342	0.701710	+	0.712462i	$0.252420\pi$
$822$	−60.4634	−2.10890
$823$	−2.40897	−0.0839715	−0.0419858	−	0.999118i	$-0.513368\pi$
$823$	−2.40897	−0.0839715	−0.0419858	+	0.999118i	$0.513368\pi$
$824$	−16.0413	−0.558826
$825$	0	0
$826$	−62.7356	−2.18285
$827$	−35.3549	−1.22941	−0.614706	−	0.788756i	$-0.710725\pi$
$827$	−35.3549	−1.22941	−0.614706	+	0.788756i	$0.710725\pi$
$828$	20.3854	0.708440
$829$	31.1560	1.08209	0.541046	−	0.840993i	$-0.318028\pi$
$829$	31.1560	1.08209	0.541046	+	0.840993i	$0.318028\pi$
$830$	0	0
$831$	4.70460	0.163201
$832$	35.5104	1.23110
$833$	−15.8075	−0.547696
$834$	−51.8608	−1.79579
$835$	0	0
$836$	0	0
$837$	17.0647	0.589843
$838$	−23.7135	−0.819171
$839$	−12.0818	−0.417110	−0.208555	−	0.978011i	$-0.566876\pi$
$839$	−12.0818	−0.417110	−0.208555	+	0.978011i	$0.566876\pi$
$840$	0	0
$841$	37.6324	1.29767
$842$	52.5998	1.81271
$843$	5.40528	0.186168
$844$	−31.5122	−1.08470
$845$	0	0
$846$	2.53824	0.0872664
$847$	−20.1455	−0.692208
$848$	5.82366	0.199985
$849$	50.3021	1.72636
$850$	0	0
$851$	6.50293	0.222918
$852$	−38.0958	−1.30514
$853$	−1.06434	−0.0364423	−0.0182212	−	0.999834i	$-0.505800\pi$
$853$	−1.06434	−0.0364423	−0.0182212	+	0.999834i	$0.505800\pi$
$854$	14.1983	0.485857
$855$	0	0
$856$	−26.1769	−0.894707
$857$	24.0728	0.822313	0.411156	−	0.911565i	$-0.365125\pi$
$857$	24.0728	0.822313	0.411156	+	0.911565i	$0.365125\pi$
$858$	−28.0696	−0.958281
$859$	24.4265	0.833420	0.416710	−	0.909039i	$-0.363183\pi$
$859$	24.4265	0.833420	0.416710	+	0.909039i	$0.363183\pi$
$860$	0	0
$861$	42.3525	1.44337
$862$	19.5965	0.667458
$863$	−10.2157	−0.347745	−0.173873	−	0.984768i	$-0.555628\pi$
$863$	−10.2157	−0.347745	−0.173873	+	0.984768i	$0.555628\pi$
$864$	−16.8411	−0.572946
$865$	0	0
$866$	−14.8239	−0.503738
$867$	103.497	3.51496
$868$	−50.4126	−1.71111
$869$	25.7171	0.872393
$870$	0	0
$871$	−4.54415	−0.153973
$872$	−15.3540	−0.519951
$873$	20.5659	0.696050
$874$	0	0
$875$	0	0
$876$	−103.262	−3.48889
$877$	−42.3861	−1.43128	−0.715638	−	0.698472i	$-0.753864\pi$
$877$	−42.3861	−1.43128	−0.715638	+	0.698472i	$0.753864\pi$
$878$	20.2655	0.683929
$879$	31.4057	1.05929
$880$	0	0
$881$	13.1500	0.443034	0.221517	−	0.975156i	$-0.428899\pi$
$881$	13.1500	0.443034	0.221517	+	0.975156i	$0.428899\pi$
$882$	−6.15425	−0.207224
$883$	50.5620	1.70155	0.850774	−	0.525532i	$-0.176134\pi$
$883$	50.5620	1.70155	0.850774	+	0.525532i	$0.176134\pi$
$884$	77.0695	2.59213
$885$	0	0
$886$	17.4793	0.587228
$887$	−18.4132	−0.618255	−0.309128	−	0.951021i	$-0.600037\pi$
$887$	−18.4132	−0.618255	−0.309128	+	0.951021i	$0.600037\pi$
$888$	−9.73479	−0.326678
$889$	31.3612	1.05182
$890$	0	0
$891$	23.1899	0.776889
$892$	−15.0473	−0.503820
$893$	0	0
$894$	14.0912	0.471282
$895$	0	0
$896$	58.0277	1.93857
$897$	−25.9369	−0.866009
$898$	−65.7893	−2.19542
$899$	−40.8932	−1.36387
$900$	0	0
$901$	−79.4876	−2.64812
$902$	32.4034	1.07892
$903$	42.8919	1.42735
$904$	33.0051	1.09773
$905$	0	0
$906$	−20.3263	−0.675297
$907$	−44.2582	−1.46957	−0.734785	−	0.678300i	$-0.762717\pi$
$907$	−44.2582	−1.46957	−0.734785	+	0.678300i	$0.762717\pi$
$908$	50.3849	1.67208
$909$	8.86501	0.294034
$910$	0	0
$911$	−38.3563	−1.27080	−0.635401	−	0.772182i	$-0.719165\pi$
$911$	−38.3563	−1.27080	−0.635401	+	0.772182i	$0.719165\pi$
$912$	0	0
$913$	−15.9136	−0.526662
$914$	−90.3751	−2.98934
$915$	0	0
$916$	−83.2948	−2.75214
$917$	2.08848	0.0689677
$918$	−64.3490	−2.12383
$919$	9.41893	0.310702	0.155351	−	0.987859i	$-0.450349\pi$
$919$	9.41893	0.310702	0.155351	+	0.987859i	$0.450349\pi$
$920$	0	0
$921$	63.6404	2.09702
$922$	24.1665	0.795881
$923$	15.2004	0.500327
$924$	−43.4304	−1.42876
$925$	0	0
$926$	20.8808	0.686186
$927$	6.94900	0.228235
$928$	40.3574	1.32480
$929$	−18.9520	−0.621794	−0.310897	−	0.950444i	$-0.600629\pi$
$929$	−18.9520	−0.621794	−0.310897	+	0.950444i	$0.600629\pi$
$930$	0	0
$931$	0	0
$932$	−75.2065	−2.46347
$933$	45.9799	1.50531
$934$	60.9402	1.99402
$935$	0	0
$936$	12.1762	0.397993
$937$	−8.83113	−0.288500	−0.144250	−	0.989541i	$-0.546077\pi$
$937$	−8.83113	−0.288500	−0.144250	+	0.989541i	$0.546077\pi$
$938$	−11.2086	−0.365974
$939$	11.0813	0.361625
$940$	0	0
$941$	18.0100	0.587111	0.293555	−	0.955942i	$-0.405161\pi$
$941$	18.0100	0.587111	0.293555	+	0.955942i	$0.405161\pi$
$942$	−97.7649	−3.18535
$943$	29.9415	0.975028
$944$	5.41241	0.176159
$945$	0	0
$946$	32.8161	1.06694
$947$	−8.09531	−0.263062	−0.131531	−	0.991312i	$-0.541989\pi$
$947$	−8.09531	−0.263062	−0.131531	+	0.991312i	$0.541989\pi$
$948$	−87.6605	−2.84708
$949$	41.2018	1.33747
$950$	0	0
$951$	57.8325	1.87535
$952$	77.1435	2.50023
$953$	24.6260	0.797713	0.398856	−	0.917013i	$-0.369407\pi$
$953$	24.6260	0.797713	0.398856	+	0.917013i	$0.369407\pi$
$954$	−30.9466	−1.00193
$955$	0	0
$956$	−37.6302	−1.21705
$957$	−35.2295	−1.13881
$958$	−44.4253	−1.43532
$959$	37.3274	1.20536
$960$	0	0
$961$	−5.90324	−0.190427
$962$	9.57163	0.308602
$963$	11.3397	0.365415
$964$	−1.53757	−0.0495217
$965$	0	0
$966$	−63.9760	−2.05840
$967$	−49.0312	−1.57674	−0.788368	−	0.615204i	$-0.789074\pi$
$967$	−49.0312	−1.57674	−0.788368	+	0.615204i	$0.789074\pi$
$968$	21.3201	0.685255
$969$	0	0
$970$	0	0
$971$	6.31163	0.202550	0.101275	−	0.994858i	$-0.467708\pi$
$971$	6.31163	0.202550	0.101275	+	0.994858i	$0.467708\pi$
$972$	−44.6495	−1.43213
$973$	32.0165	1.02640
$974$	75.8173	2.42934
$975$	0	0
$976$	−1.22494	−0.0392093
$977$	−25.3776	−0.811900	−0.405950	−	0.913895i	$-0.633059\pi$
$977$	−25.3776	−0.811900	−0.405950	+	0.913895i	$0.633059\pi$
$978$	−27.0446	−0.864790
$979$	−1.15607	−0.0369482
$980$	0	0
$981$	6.65124	0.212358
$982$	70.0192	2.23440
$983$	0.305696	0.00975020	0.00487510	−	0.999988i	$-0.498448\pi$
$983$	0.305696	0.00975020	0.00487510	+	0.999988i	$0.498448\pi$
$984$	−44.8219	−1.42887
$985$	0	0
$986$	154.203	4.91084
$987$	−4.99678	−0.159049
$988$	0	0
$989$	30.3228	0.964208
$990$	0	0
$991$	−55.4518	−1.76148	−0.880742	−	0.473596i	$-0.842956\pi$
$991$	−55.4518	−1.76148	−0.880742	+	0.473596i	$0.842956\pi$
$992$	−24.7679	−0.786381
$993$	20.0342	0.635765
$994$	37.4933	1.18922
$995$	0	0
$996$	54.2437	1.71878
$997$	55.6450	1.76229	0.881147	−	0.472842i	$-0.156772\pi$
$997$	55.6450	1.76229	0.881147	+	0.472842i	$0.156772\pi$
$998$	−26.2017	−0.829399
$999$	−5.01308	−0.158607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cr.1.1		21
5.4	even	2		9025.2.a.cp.1.21		21
19.2	odd	18		475.2.l.d.251.1	yes	42
19.10	odd	18		475.2.l.d.176.1	✓	42
19.18	odd	2		9025.2.a.cq.1.21		21
95.2	even	36		475.2.u.d.99.13		84
95.29	odd	18		475.2.l.e.176.7	yes	42
95.48	even	36		475.2.u.d.24.13		84
95.59	odd	18		475.2.l.e.251.7	yes	42
95.67	even	36		475.2.u.d.24.2		84
95.78	even	36		475.2.u.d.99.2		84
95.94	odd	2		9025.2.a.cs.1.1		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.l.d.176.1	✓	42	19.10	odd	18
475.2.l.d.251.1	yes	42	19.2	odd	18
475.2.l.e.176.7	yes	42	95.29	odd	18
475.2.l.e.251.7	yes	42	95.59	odd	18
475.2.u.d.24.2		84	95.67	even	36
475.2.u.d.24.13		84	95.48	even	36
475.2.u.d.99.2		84	95.78	even	36
475.2.u.d.99.13		84	95.2	even	36
9025.2.a.cp.1.21		21	5.4	even	2
9025.2.a.cq.1.21		21	19.18	odd	2
9025.2.a.cr.1.1		21	1.1	even	1	trivial
9025.2.a.cs.1.1		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)

\(f(q)\)	\(=\)	\(q-2.31644 q^{2} +2.09061 q^{3} +3.36590 q^{4} -4.84277 q^{6} +2.98971 q^{7} -3.16403 q^{8} +1.37064 q^{9} +O(q^{10})\)	\(q-2.31644 q^{2} +2.09061 q^{3} +3.36590 q^{4} -4.84277 q^{6} +2.98971 q^{7} -3.16403 q^{8} +1.37064 q^{9} -2.06439 q^{11} +7.03677 q^{12} -2.80770 q^{13} -6.92548 q^{14} +0.597485 q^{16} -8.15512 q^{17} -3.17500 q^{18} +6.25030 q^{21} +4.78204 q^{22} +4.41871 q^{23} -6.61474 q^{24} +6.50388 q^{26} -3.40636 q^{27} +10.0631 q^{28} +8.16287 q^{29} -5.00967 q^{31} +4.94402 q^{32} -4.31583 q^{33} +18.8909 q^{34} +4.61342 q^{36} +1.47168 q^{37} -5.86980 q^{39} +6.77607 q^{41} -14.4785 q^{42} +6.86237 q^{43} -6.94854 q^{44} -10.2357 q^{46} -0.799446 q^{47} +1.24911 q^{48} +1.93835 q^{49} -17.0491 q^{51} -9.45044 q^{52} +9.74696 q^{53} +7.89063 q^{54} -9.45952 q^{56} -18.9088 q^{58} +9.05866 q^{59} -2.05016 q^{61} +11.6046 q^{62} +4.09780 q^{63} -12.6475 q^{64} +9.99737 q^{66} +1.61846 q^{67} -27.4493 q^{68} +9.23778 q^{69} -5.41382 q^{71} -4.33673 q^{72} -14.6746 q^{73} -3.40906 q^{74} -6.17193 q^{77} +13.5970 q^{78} -12.4575 q^{79} -11.2333 q^{81} -15.6964 q^{82} +7.70860 q^{83} +21.0379 q^{84} -15.8963 q^{86} +17.0653 q^{87} +6.53179 q^{88} +0.560005 q^{89} -8.39421 q^{91} +14.8729 q^{92} -10.4732 q^{93} +1.85187 q^{94} +10.3360 q^{96} +15.0046 q^{97} -4.49007 q^{98} -2.82953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{2} + 9 q^{3} + 24 q^{4} + 18 q^{8} + 24 q^{9}+O(q^{10}) \) 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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