LMFDB - Embedded newform 6025.2.a.j.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.11717 q^{2} -3.26371 q^{3} -0.751931 q^{4} -3.64612 q^{6} +3.89846 q^{7} -3.07438 q^{8} +7.65181 q^{9} +O(q^{10})$	\(q+1.11717 q^{2} -3.26371 q^{3} -0.751931 q^{4} -3.64612 q^{6} +3.89846 q^{7} -3.07438 q^{8} +7.65181 q^{9} +2.23037 q^{11} +2.45408 q^{12} -0.399996 q^{13} +4.35525 q^{14} -1.93074 q^{16} -1.78100 q^{17} +8.54837 q^{18} +0.862005 q^{19} -12.7235 q^{21} +2.49170 q^{22} -7.16231 q^{23} +10.0339 q^{24} -0.446864 q^{26} -15.1821 q^{27} -2.93138 q^{28} -2.17762 q^{29} -10.0812 q^{31} +3.99179 q^{32} -7.27928 q^{33} -1.98968 q^{34} -5.75363 q^{36} +8.09337 q^{37} +0.963006 q^{38} +1.30547 q^{39} +11.3966 q^{41} -14.2143 q^{42} -2.23153 q^{43} -1.67708 q^{44} -8.00152 q^{46} -9.14440 q^{47} +6.30137 q^{48} +8.19803 q^{49} +5.81267 q^{51} +0.300769 q^{52} -11.0046 q^{53} -16.9610 q^{54} -11.9853 q^{56} -2.81334 q^{57} -2.43277 q^{58} +4.84356 q^{59} +9.70876 q^{61} -11.2624 q^{62} +29.8303 q^{63} +8.32098 q^{64} -8.13220 q^{66} -0.167311 q^{67} +1.33919 q^{68} +23.3757 q^{69} +2.29573 q^{71} -23.5245 q^{72} +15.2859 q^{73} +9.04167 q^{74} -0.648168 q^{76} +8.69502 q^{77} +1.45843 q^{78} +4.52045 q^{79} +26.5947 q^{81} +12.7320 q^{82} +9.83480 q^{83} +9.56716 q^{84} -2.49300 q^{86} +7.10713 q^{87} -6.85699 q^{88} -9.64864 q^{89} -1.55937 q^{91} +5.38556 q^{92} +32.9021 q^{93} -10.2159 q^{94} -13.0280 q^{96} -4.60063 q^{97} +9.15859 q^{98} +17.0664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.11717	0.789959	0.394979	−	0.918690i	$-0.370752\pi$
$2$	1.11717	0.789959	0.394979	+	0.918690i	$0.370752\pi$
$3$	−3.26371	−1.88430	−0.942152	−	0.335186i	$-0.891201\pi$
$3$	−3.26371	−1.88430	−0.942152	+	0.335186i	$0.891201\pi$
$4$	−0.751931	−0.375965
$5$	0	0
$5$	0	0
$6$	−3.64612	−1.48852
$7$	3.89846	1.47348	0.736741	−	0.676176i	$-0.236364\pi$
$7$	3.89846	1.47348	0.736741	+	0.676176i	$0.236364\pi$
$8$	−3.07438	−1.08696
$9$	7.65181	2.55060
$10$	0	0
$11$	2.23037	0.672482	0.336241	−	0.941776i	$-0.390844\pi$
$11$	2.23037	0.672482	0.336241	+	0.941776i	$0.390844\pi$
$12$	2.45408	0.708433
$13$	−0.399996	−0.110939	−0.0554695	−	0.998460i	$-0.517666\pi$
$13$	−0.399996	−0.110939	−0.0554695	+	0.998460i	$0.517666\pi$
$14$	4.35525	1.16399
$15$	0	0
$16$	−1.93074	−0.482685
$17$	−1.78100	−0.431956	−0.215978	−	0.976398i	$-0.569294\pi$
$17$	−1.78100	−0.431956	−0.215978	+	0.976398i	$0.569294\pi$
$18$	8.54837	2.01487
$19$	0.862005	0.197758	0.0988788	−	0.995099i	$-0.468474\pi$
$19$	0.862005	0.197758	0.0988788	+	0.995099i	$0.468474\pi$
$20$	0	0
$21$	−12.7235	−2.77649
$22$	2.49170	0.531233
$23$	−7.16231	−1.49345	−0.746723	−	0.665135i	$-0.768374\pi$
$23$	−7.16231	−1.49345	−0.746723	+	0.665135i	$0.768374\pi$
$24$	10.0339	2.04816
$25$	0	0
$26$	−0.446864	−0.0876372
$27$	−15.1821	−2.92181
$28$	−2.93138	−0.553978
$29$	−2.17762	−0.404374	−0.202187	−	0.979347i	$-0.564805\pi$
$29$	−2.17762	−0.404374	−0.202187	+	0.979347i	$0.564805\pi$
$30$	0	0
$31$	−10.0812	−1.81064	−0.905319	−	0.424732i	$-0.860368\pi$
$31$	−10.0812	−1.81064	−0.905319	+	0.424732i	$0.860368\pi$
$32$	3.99179	0.705655
$33$	−7.27928	−1.26716
$34$	−1.98968	−0.341228
$35$	0	0
$36$	−5.75363	−0.958938
$37$	8.09337	1.33054	0.665271	−	0.746602i	$-0.268316\pi$
$37$	8.09337	1.33054	0.665271	+	0.746602i	$0.268316\pi$
$38$	0.963006	0.156220
$39$	1.30547	0.209043
$40$	0	0
$41$	11.3966	1.77985	0.889927	−	0.456102i	$-0.150755\pi$
$41$	11.3966	1.77985	0.889927	+	0.456102i	$0.150755\pi$
$42$	−14.2143	−2.19331
$43$	−2.23153	−0.340305	−0.170153	−	0.985418i	$-0.554426\pi$
$43$	−2.23153	−0.340305	−0.170153	+	0.985418i	$0.554426\pi$
$44$	−1.67708	−0.252830
$45$	0	0
$46$	−8.00152	−1.17976
$47$	−9.14440	−1.33385	−0.666924	−	0.745126i	$-0.732389\pi$
$47$	−9.14440	−1.33385	−0.666924	+	0.745126i	$0.732389\pi$
$48$	6.30137	0.909525
$49$	8.19803	1.17115
$50$	0	0
$51$	5.81267	0.813937
$52$	0.300769	0.0417092
$53$	−11.0046	−1.51160	−0.755801	−	0.654802i	$-0.772752\pi$
$53$	−11.0046	−1.51160	−0.755801	+	0.654802i	$0.772752\pi$
$54$	−16.9610	−2.30811
$55$	0	0
$56$	−11.9853	−1.60161
$57$	−2.81334	−0.372635
$58$	−2.43277	−0.319439
$59$	4.84356	0.630578	0.315289	−	0.948996i	$-0.397899\pi$
$59$	4.84356	0.630578	0.315289	+	0.948996i	$0.397899\pi$
$60$	0	0
$61$	9.70876	1.24308	0.621539	−	0.783383i	$-0.286508\pi$
$61$	9.70876	1.24308	0.621539	+	0.783383i	$0.286508\pi$
$62$	−11.2624	−1.43033
$63$	29.8303	3.75826
$64$	8.32098	1.04012
$65$	0	0
$66$	−8.13220	−1.00100
$67$	−0.167311	−0.0204403	−0.0102202	−	0.999948i	$-0.503253\pi$
$67$	−0.167311	−0.0204403	−0.0102202	+	0.999948i	$0.503253\pi$
$68$	1.33919	0.162401
$69$	23.3757	2.81411
$70$	0	0
$71$	2.29573	0.272454	0.136227	−	0.990678i	$-0.456502\pi$
$71$	2.29573	0.272454	0.136227	+	0.990678i	$0.456502\pi$
$72$	−23.5245	−2.77239
$73$	15.2859	1.78908	0.894539	−	0.446990i	$-0.147504\pi$
$73$	15.2859	1.78908	0.894539	+	0.446990i	$0.147504\pi$
$74$	9.04167	1.05107
$75$	0	0
$76$	−0.648168	−0.0743500
$77$	8.69502	0.990889
$78$	1.45843	0.165135
$79$	4.52045	0.508590	0.254295	−	0.967127i	$-0.418157\pi$
$79$	4.52045	0.508590	0.254295	+	0.967127i	$0.418157\pi$
$80$	0	0
$81$	26.5947	2.95497
$82$	12.7320	1.40601
$83$	9.83480	1.07951	0.539755	−	0.841822i	$-0.318517\pi$
$83$	9.83480	1.07951	0.539755	+	0.841822i	$0.318517\pi$
$84$	9.56716	1.04386
$85$	0	0
$86$	−2.49300	−0.268827
$87$	7.10713	0.761964
$88$	−6.85699	−0.730958
$89$	−9.64864	−1.02275	−0.511377	−	0.859357i	$-0.670864\pi$
$89$	−9.64864	−1.02275	−0.511377	+	0.859357i	$0.670864\pi$
$90$	0	0
$91$	−1.55937	−0.163467
$92$	5.38556	0.561484
$93$	32.9021	3.41179
$94$	−10.2159	−1.05368
$95$	0	0
$96$	−13.0280	−1.32967
$97$	−4.60063	−0.467123	−0.233562	−	0.972342i	$-0.575038\pi$
$97$	−4.60063	−0.467123	−0.233562	+	0.972342i	$0.575038\pi$
$98$	9.15859	0.925157
$99$	17.0664	1.71523
$100$	0	0
$101$	−10.3319	−1.02807	−0.514033	−	0.857770i	$-0.671849\pi$
$101$	−10.3319	−1.02807	−0.514033	+	0.857770i	$0.671849\pi$
$102$	6.49374	0.642976
$103$	−3.61893	−0.356584	−0.178292	−	0.983978i	$-0.557057\pi$
$103$	−3.61893	−0.356584	−0.178292	+	0.983978i	$0.557057\pi$
$104$	1.22974	0.120586
$105$	0	0
$106$	−12.2940	−1.19410
$107$	−2.05623	−0.198783	−0.0993914	−	0.995048i	$-0.531690\pi$
$107$	−2.05623	−0.198783	−0.0993914	+	0.995048i	$0.531690\pi$
$108$	11.4159	1.09850
$109$	−18.1815	−1.74147	−0.870737	−	0.491748i	$-0.836358\pi$
$109$	−18.1815	−1.74147	−0.870737	+	0.491748i	$0.836358\pi$
$110$	0	0
$111$	−26.4144	−2.50715
$112$	−7.52692	−0.711227
$113$	−5.57025	−0.524005	−0.262002	−	0.965067i	$-0.584383\pi$
$113$	−5.57025	−0.524005	−0.262002	+	0.965067i	$0.584383\pi$
$114$	−3.14297	−0.294366
$115$	0	0
$116$	1.63742	0.152031
$117$	−3.06069	−0.282961
$118$	5.41108	0.498130
$119$	−6.94317	−0.636479
$120$	0	0
$121$	−6.02545	−0.547768
$122$	10.8463	0.981981
$123$	−37.1953	−3.35379
$124$	7.58037	0.680737
$125$	0	0
$126$	33.3255	2.96887
$127$	1.29637	0.115034	0.0575172	−	0.998345i	$-0.481682\pi$
$127$	1.29637	0.115034	0.0575172	+	0.998345i	$0.481682\pi$
$128$	1.31238	0.115999
$129$	7.28307	0.641238
$130$	0	0
$131$	5.81758	0.508285	0.254142	−	0.967167i	$-0.418207\pi$
$131$	5.81758	0.508285	0.254142	+	0.967167i	$0.418207\pi$
$132$	5.47351	0.476408
$133$	3.36050	0.291392
$134$	−0.186915	−0.0161470
$135$	0	0
$136$	5.47547	0.469517
$137$	−16.1509	−1.37986	−0.689932	−	0.723874i	$-0.742360\pi$
$137$	−16.1509	−1.37986	−0.689932	+	0.723874i	$0.742360\pi$
$138$	26.1147	2.22303
$139$	−5.88978	−0.499565	−0.249783	−	0.968302i	$-0.580359\pi$
$139$	−5.88978	−0.499565	−0.249783	+	0.968302i	$0.580359\pi$
$140$	0	0
$141$	29.8447	2.51338
$142$	2.56473	0.215227
$143$	−0.892140	−0.0746045
$144$	−14.7736	−1.23114
$145$	0	0
$146$	17.0769	1.41330
$147$	−26.7560	−2.20680
$148$	−6.08566	−0.500238
$149$	−11.5836	−0.948962	−0.474481	−	0.880266i	$-0.657364\pi$
$149$	−11.5836	−0.948962	−0.474481	+	0.880266i	$0.657364\pi$
$150$	0	0
$151$	7.45540	0.606712	0.303356	−	0.952877i	$-0.401893\pi$
$151$	7.45540	0.606712	0.303356	+	0.952877i	$0.401893\pi$
$152$	−2.65013	−0.214954
$153$	−13.6279	−1.10175
$154$	9.71382	0.782762
$155$	0	0
$156$	−0.981624	−0.0785929
$157$	4.42589	0.353225	0.176612	−	0.984281i	$-0.443486\pi$
$157$	4.42589	0.353225	0.176612	+	0.984281i	$0.443486\pi$
$158$	5.05011	0.401765
$159$	35.9159	2.84832
$160$	0	0
$161$	−27.9220	−2.20056
$162$	29.7108	2.33430
$163$	−18.0676	−1.41517	−0.707583	−	0.706630i	$-0.750214\pi$
$163$	−18.0676	−1.41517	−0.707583	+	0.706630i	$0.750214\pi$
$164$	−8.56948	−0.669164
$165$	0	0
$166$	10.9871	0.852768
$167$	14.4638	1.11924	0.559620	−	0.828749i	$-0.310947\pi$
$167$	14.4638	1.11924	0.559620	+	0.828749i	$0.310947\pi$
$168$	39.1167	3.01792
$169$	−12.8400	−0.987693
$170$	0	0
$171$	6.59590	0.504401
$172$	1.67796	0.127943
$173$	−2.34787	−0.178506	−0.0892528	−	0.996009i	$-0.528448\pi$
$173$	−2.34787	−0.178506	−0.0892528	+	0.996009i	$0.528448\pi$
$174$	7.93987	0.601920
$175$	0	0
$176$	−4.30626	−0.324597
$177$	−15.8080	−1.18820
$178$	−10.7792	−0.807933
$179$	4.06885	0.304120	0.152060	−	0.988371i	$-0.451409\pi$
$179$	4.06885	0.304120	0.152060	+	0.988371i	$0.451409\pi$
$180$	0	0
$181$	−14.6581	−1.08953	−0.544766	−	0.838588i	$-0.683381\pi$
$181$	−14.6581	−1.08953	−0.544766	+	0.838588i	$0.683381\pi$
$182$	−1.74208	−0.129132
$183$	−31.6866	−2.34234
$184$	22.0196	1.62331
$185$	0	0
$186$	36.7573	2.69518
$187$	−3.97229	−0.290483
$188$	6.87596	0.501481
$189$	−59.1871	−4.30522
$190$	0	0
$191$	−25.1515	−1.81990	−0.909950	−	0.414718i	$-0.863880\pi$
$191$	−25.1515	−1.81990	−0.909950	+	0.414718i	$0.863880\pi$
$192$	−27.1573	−1.95991
$193$	18.9918	1.36706	0.683531	−	0.729922i	$-0.260444\pi$
$193$	18.9918	1.36706	0.683531	+	0.729922i	$0.260444\pi$
$194$	−5.13968	−0.369008
$195$	0	0
$196$	−6.16435	−0.440311
$197$	12.4235	0.885138	0.442569	−	0.896734i	$-0.354067\pi$
$197$	12.4235	0.885138	0.442569	+	0.896734i	$0.354067\pi$
$198$	19.0660	1.35496
$199$	−14.3427	−1.01673	−0.508364	−	0.861142i	$-0.669750\pi$
$199$	−14.3427	−1.01673	−0.508364	+	0.861142i	$0.669750\pi$
$200$	0	0
$201$	0.546055	0.0385157
$202$	−11.5425	−0.812130
$203$	−8.48938	−0.595838
$204$	−4.37073	−0.306012
$205$	0	0
$206$	−4.04296	−0.281687
$207$	−54.8046	−3.80919
$208$	0.772288	0.0535486
$209$	1.92259	0.132988
$210$	0	0
$211$	21.1320	1.45479	0.727394	−	0.686220i	$-0.240731\pi$
$211$	21.1320	1.45479	0.727394	+	0.686220i	$0.240731\pi$
$212$	8.27471	0.568310
$213$	−7.49261	−0.513385
$214$	−2.29715	−0.157030
$215$	0	0
$216$	46.6756	3.17587
$217$	−39.3012	−2.66794
$218$	−20.3119	−1.37569
$219$	−49.8887	−3.37117
$220$	0	0
$221$	0.712394	0.0479208
$222$	−29.5094	−1.98054
$223$	−0.351813	−0.0235591	−0.0117796	−	0.999931i	$-0.503750\pi$
$223$	−0.351813	−0.0235591	−0.0117796	+	0.999931i	$0.503750\pi$
$224$	15.5618	1.03977
$225$	0	0
$226$	−6.22292	−0.413942
$227$	−14.2775	−0.947630	−0.473815	−	0.880624i	$-0.657123\pi$
$227$	−14.2775	−0.947630	−0.473815	+	0.880624i	$0.657123\pi$
$228$	2.11543	0.140098
$229$	12.5016	0.826126	0.413063	−	0.910702i	$-0.364459\pi$
$229$	12.5016	0.826126	0.413063	+	0.910702i	$0.364459\pi$
$230$	0	0
$231$	−28.3780	−1.86714
$232$	6.69482	0.439537
$233$	23.9237	1.56729	0.783645	−	0.621208i	$-0.213358\pi$
$233$	23.9237	1.56729	0.783645	+	0.621208i	$0.213358\pi$
$234$	−3.41932	−0.223528
$235$	0	0
$236$	−3.64202	−0.237075
$237$	−14.7534	−0.958339
$238$	−7.75670	−0.502792
$239$	−19.7973	−1.28058	−0.640291	−	0.768133i	$-0.721186\pi$
$239$	−19.7973	−1.28058	−0.640291	+	0.768133i	$0.721186\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−6.73145	−0.432714
$243$	−41.2510	−2.64625
$244$	−7.30031	−0.467355
$245$	0	0
$246$	−41.5535	−2.64935
$247$	−0.344799	−0.0219390
$248$	30.9934	1.96808
$249$	−32.0979	−2.03412
$250$	0	0
$251$	−7.96623	−0.502824	−0.251412	−	0.967880i	$-0.580895\pi$
$251$	−7.96623	−0.502824	−0.251412	+	0.967880i	$0.580895\pi$
$252$	−22.4303	−1.41298
$253$	−15.9746	−1.00432
$254$	1.44827	0.0908725
$255$	0	0
$256$	−15.1758	−0.948488
$257$	24.1844	1.50858	0.754290	−	0.656541i	$-0.227981\pi$
$257$	24.1844	1.50858	0.754290	+	0.656541i	$0.227981\pi$
$258$	8.13643	0.506552
$259$	31.5517	1.96053
$260$	0	0
$261$	−16.6627	−1.03140
$262$	6.49923	0.401524
$263$	−13.4413	−0.828824	−0.414412	−	0.910089i	$-0.636013\pi$
$263$	−13.4413	−0.828824	−0.414412	+	0.910089i	$0.636013\pi$
$264$	22.3792	1.37735
$265$	0	0
$266$	3.75425	0.230188
$267$	31.4904	1.92718
$268$	0.125806	0.00768485
$269$	15.9153	0.970375	0.485187	−	0.874410i	$-0.338751\pi$
$269$	15.9153	0.970375	0.485187	+	0.874410i	$0.338751\pi$
$270$	0	0
$271$	10.8339	0.658111	0.329056	−	0.944311i	$-0.393270\pi$
$271$	10.8339	0.658111	0.329056	+	0.944311i	$0.393270\pi$
$272$	3.43865	0.208499
$273$	5.08934	0.308021
$274$	−18.0433	−1.09004
$275$	0	0
$276$	−17.5769	−1.05801
$277$	16.5665	0.995386	0.497693	−	0.867353i	$-0.334181\pi$
$277$	16.5665	0.995386	0.497693	+	0.867353i	$0.334181\pi$
$278$	−6.57989	−0.394636
$279$	−77.1394	−4.61822
$280$	0	0
$281$	−3.64795	−0.217618	−0.108809	−	0.994063i	$-0.534704\pi$
$281$	−3.64795	−0.217618	−0.108809	+	0.994063i	$0.534704\pi$
$282$	33.3416	1.98546
$283$	17.5445	1.04291	0.521456	−	0.853278i	$-0.325389\pi$
$283$	17.5445	1.04291	0.521456	+	0.853278i	$0.325389\pi$
$284$	−1.72623	−0.102433
$285$	0	0
$286$	−0.996672	−0.0589344
$287$	44.4294	2.62258
$288$	30.5444	1.79984
$289$	−13.8280	−0.813414
$290$	0	0
$291$	15.0151	0.880202
$292$	−11.4939	−0.672631
$293$	−3.86524	−0.225810	−0.112905	−	0.993606i	$-0.536016\pi$
$293$	−3.86524	−0.225810	−0.112905	+	0.993606i	$0.536016\pi$
$294$	−29.8910	−1.74328
$295$	0	0
$296$	−24.8821	−1.44624
$297$	−33.8618	−1.96486
$298$	−12.9408	−0.749640
$299$	2.86490	0.165681
$300$	0	0
$301$	−8.69954	−0.501433
$302$	8.32895	0.479277
$303$	33.7204	1.93719
$304$	−1.66431	−0.0954545
$305$	0	0
$306$	−15.2247	−0.870336
$307$	−7.41551	−0.423226	−0.211613	−	0.977354i	$-0.567872\pi$
$307$	−7.41551	−0.423226	−0.211613	+	0.977354i	$0.567872\pi$
$308$	−6.53805	−0.372540
$309$	11.8111	0.671913
$310$	0	0
$311$	−26.7568	−1.51724	−0.758620	−	0.651533i	$-0.774126\pi$
$311$	−26.7568	−1.51724	−0.758620	+	0.651533i	$0.774126\pi$
$312$	−4.01351	−0.227220
$313$	−6.44449	−0.364264	−0.182132	−	0.983274i	$-0.558300\pi$
$313$	−6.44449	−0.364264	−0.182132	+	0.983274i	$0.558300\pi$
$314$	4.94447	0.279033
$315$	0	0
$316$	−3.39907	−0.191212
$317$	−13.7728	−0.773558	−0.386779	−	0.922172i	$-0.626412\pi$
$317$	−13.7728	−0.773558	−0.386779	+	0.922172i	$0.626412\pi$
$318$	40.1242	2.25005
$319$	−4.85690	−0.271934
$320$	0	0
$321$	6.71093	0.374567
$322$	−31.1937	−1.73835
$323$	−1.53523	−0.0854226
$324$	−19.9974	−1.11097
$325$	0	0
$326$	−20.1846	−1.11792
$327$	59.3393	3.28147
$328$	−35.0375	−1.93462
$329$	−35.6491	−1.96540
$330$	0	0
$331$	15.5223	0.853184	0.426592	−	0.904444i	$-0.359714\pi$
$331$	15.5223	0.853184	0.426592	+	0.904444i	$0.359714\pi$
$332$	−7.39509	−0.405858
$333$	61.9289	3.39368
$334$	16.1585	0.884154
$335$	0	0
$336$	24.5657	1.34017
$337$	−29.0429	−1.58207	−0.791034	−	0.611772i	$-0.790457\pi$
$337$	−29.0429	−1.58207	−0.791034	+	0.611772i	$0.790457\pi$
$338$	−14.3445	−0.780236
$339$	18.1797	0.987385
$340$	0	0
$341$	−22.4848	−1.21762
$342$	7.36874	0.398456
$343$	4.67047	0.252181
$344$	6.86056	0.369897
$345$	0	0
$346$	−2.62297	−0.141012
$347$	16.0380	0.860962	0.430481	−	0.902600i	$-0.358344\pi$
$347$	16.0380	0.860962	0.430481	+	0.902600i	$0.358344\pi$
$348$	−5.34407	−0.286472
$349$	−8.76026	−0.468926	−0.234463	−	0.972125i	$-0.575333\pi$
$349$	−8.76026	−0.468926	−0.234463	+	0.972125i	$0.575333\pi$
$350$	0	0
$351$	6.07280	0.324142
$352$	8.90316	0.474540
$353$	−27.9385	−1.48702	−0.743509	−	0.668726i	$-0.766840\pi$
$353$	−27.9385	−1.48702	−0.743509	+	0.668726i	$0.766840\pi$
$354$	−17.6602	−0.938629
$355$	0	0
$356$	7.25511	0.384520
$357$	22.6605	1.19932
$358$	4.54560	0.240242
$359$	−13.6826	−0.722142	−0.361071	−	0.932538i	$-0.617589\pi$
$359$	−13.6826	−0.722142	−0.361071	+	0.932538i	$0.617589\pi$
$360$	0	0
$361$	−18.2569	−0.960892
$362$	−16.3756	−0.860685
$363$	19.6653	1.03216
$364$	1.17254	0.0614578
$365$	0	0
$366$	−35.3993	−1.85035
$367$	−6.31501	−0.329641	−0.164820	−	0.986324i	$-0.552704\pi$
$367$	−6.31501	−0.329641	−0.164820	+	0.986324i	$0.552704\pi$
$368$	13.8286	0.720863
$369$	87.2048	4.53970
$370$	0	0
$371$	−42.9011	−2.22732
$372$	−24.7401	−1.28272
$373$	14.1144	0.730815	0.365407	−	0.930848i	$-0.380930\pi$
$373$	14.1144	0.730815	0.365407	+	0.930848i	$0.380930\pi$
$374$	−4.43773	−0.229469
$375$	0	0
$376$	28.1133	1.44983
$377$	0.871040	0.0448609
$378$	−66.1220	−3.40095
$379$	−34.4351	−1.76881	−0.884405	−	0.466720i	$-0.845436\pi$
$379$	−34.4351	−1.76881	−0.884405	+	0.466720i	$0.845436\pi$
$380$	0	0
$381$	−4.23099	−0.216760
$382$	−28.0985	−1.43765
$383$	−18.1894	−0.929433	−0.464716	−	0.885460i	$-0.653844\pi$
$383$	−18.1894	−0.929433	−0.464716	+	0.885460i	$0.653844\pi$
$384$	−4.28323	−0.218578
$385$	0	0
$386$	21.2171	1.07992
$387$	−17.0752	−0.867983
$388$	3.45935	0.175622
$389$	34.0998	1.72893	0.864464	−	0.502695i	$-0.167658\pi$
$389$	34.0998	1.72893	0.864464	+	0.502695i	$0.167658\pi$
$390$	0	0
$391$	12.7561	0.645103
$392$	−25.2038	−1.27298
$393$	−18.9869	−0.957763
$394$	13.8792	0.699222
$395$	0	0
$396$	−12.8327	−0.644868
$397$	28.3223	1.42145	0.710727	−	0.703468i	$-0.248366\pi$
$397$	28.3223	1.42145	0.710727	+	0.703468i	$0.248366\pi$
$398$	−16.0233	−0.803174
$399$	−10.9677	−0.549071
$400$	0	0
$401$	8.42110	0.420530	0.210265	−	0.977644i	$-0.432567\pi$
$401$	8.42110	0.420530	0.210265	+	0.977644i	$0.432567\pi$
$402$	0.610036	0.0304258
$403$	4.03245	0.200870
$404$	7.76890	0.386517
$405$	0	0
$406$	−9.48408	−0.470687
$407$	18.0512	0.894765
$408$	−17.8703	−0.884713
$409$	10.6471	0.526466	0.263233	−	0.964732i	$-0.415211\pi$
$409$	10.6471	0.526466	0.263233	+	0.964732i	$0.415211\pi$
$410$	0	0
$411$	52.7118	2.60008
$412$	2.72119	0.134063
$413$	18.8824	0.929144
$414$	−61.2261	−3.00910
$415$	0	0
$416$	−1.59670	−0.0782846
$417$	19.2226	0.941332
$418$	2.14786	0.105055
$419$	−19.1339	−0.934752	−0.467376	−	0.884059i	$-0.654801\pi$
$419$	−19.1339	−0.934752	−0.467376	+	0.884059i	$0.654801\pi$
$420$	0	0
$421$	−29.0709	−1.41683	−0.708414	−	0.705797i	$-0.750589\pi$
$421$	−29.0709	−1.41683	−0.708414	+	0.705797i	$0.750589\pi$
$422$	23.6081	1.14922
$423$	−69.9712	−3.40212
$424$	33.8323	1.64304
$425$	0	0
$426$	−8.37052	−0.405553
$427$	37.8492	1.83165
$428$	1.54614	0.0747355
$429$	2.91169	0.140577
$430$	0	0
$431$	−8.07999	−0.389200	−0.194600	−	0.980883i	$-0.562341\pi$
$431$	−8.07999	−0.389200	−0.194600	+	0.980883i	$0.562341\pi$
$432$	29.3128	1.41031
$433$	4.46824	0.214730	0.107365	−	0.994220i	$-0.465759\pi$
$433$	4.46824	0.214730	0.107365	+	0.994220i	$0.465759\pi$
$434$	−43.9062	−2.10756
$435$	0	0
$436$	13.6713	0.654734
$437$	−6.17395	−0.295340
$438$	−55.7342	−2.66308
$439$	−17.0425	−0.813394	−0.406697	−	0.913563i	$-0.633320\pi$
$439$	−17.0425	−0.813394	−0.406697	+	0.913563i	$0.633320\pi$
$440$	0	0
$441$	62.7297	2.98713
$442$	0.795865	0.0378554
$443$	−29.6892	−1.41058	−0.705288	−	0.708921i	$-0.749182\pi$
$443$	−29.6892	−1.41058	−0.705288	+	0.708921i	$0.749182\pi$
$444$	19.8618	0.942600
$445$	0	0
$446$	−0.393035	−0.0186107
$447$	37.8054	1.78813
$448$	32.4391	1.53260
$449$	−35.7184	−1.68565	−0.842827	−	0.538184i	$-0.819111\pi$
$449$	−35.7184	−1.68565	−0.842827	+	0.538184i	$0.819111\pi$
$450$	0	0
$451$	25.4187	1.19692
$452$	4.18844	0.197008
$453$	−24.3323	−1.14323
$454$	−15.9504	−0.748588
$455$	0	0
$456$	8.64925	0.405038
$457$	2.31971	0.108511	0.0542557	−	0.998527i	$-0.482721\pi$
$457$	2.31971	0.108511	0.0542557	+	0.998527i	$0.482721\pi$
$458$	13.9664	0.652606
$459$	27.0394	1.26209
$460$	0	0
$461$	−15.3196	−0.713505	−0.356752	−	0.934199i	$-0.616116\pi$
$461$	−15.3196	−0.713505	−0.356752	+	0.934199i	$0.616116\pi$
$462$	−31.7031	−1.47496
$463$	−24.9757	−1.16072	−0.580359	−	0.814360i	$-0.697088\pi$
$463$	−24.9757	−1.16072	−0.580359	+	0.814360i	$0.697088\pi$
$464$	4.20442	0.195185
$465$	0	0
$466$	26.7268	1.23809
$467$	−10.3681	−0.479778	−0.239889	−	0.970800i	$-0.577111\pi$
$467$	−10.3681	−0.479778	−0.239889	+	0.970800i	$0.577111\pi$
$468$	2.30143	0.106384
$469$	−0.652256	−0.0301184
$470$	0	0
$471$	−14.4448	−0.665582
$472$	−14.8909	−0.685410
$473$	−4.97714	−0.228849
$474$	−16.4821	−0.757048
$475$	0	0
$476$	5.22078	0.239294
$477$	−84.2052	−3.85549
$478$	−22.1170	−1.01161
$479$	−13.4109	−0.612759	−0.306379	−	0.951910i	$-0.599118\pi$
$479$	−13.4109	−0.612759	−0.306379	+	0.951910i	$0.599118\pi$
$480$	0	0
$481$	−3.23732	−0.147609
$482$	−1.11717	−0.0508857
$483$	91.1294	4.14653
$484$	4.53072	0.205942
$485$	0	0
$486$	−46.0844	−2.09043
$487$	−26.2990	−1.19172	−0.595862	−	0.803087i	$-0.703189\pi$
$487$	−26.2990	−1.19172	−0.595862	+	0.803087i	$0.703189\pi$
$488$	−29.8484	−1.35117
$489$	58.9675	2.66660
$490$	0	0
$491$	−29.1118	−1.31380	−0.656898	−	0.753979i	$-0.728132\pi$
$491$	−29.1118	−1.31380	−0.656898	+	0.753979i	$0.728132\pi$
$492$	27.9683	1.26091
$493$	3.87835	0.174672
$494$	−0.385199	−0.0173309
$495$	0	0
$496$	19.4642	0.873967
$497$	8.94984	0.401455
$498$	−35.8589	−1.60687
$499$	−29.0098	−1.29866	−0.649329	−	0.760508i	$-0.724950\pi$
$499$	−29.0098	−1.29866	−0.649329	+	0.760508i	$0.724950\pi$
$500$	0	0
$501$	−47.2056	−2.10899
$502$	−8.89964	−0.397210
$503$	−38.4306	−1.71354	−0.856768	−	0.515701i	$-0.827531\pi$
$503$	−38.4306	−1.71354	−0.856768	+	0.515701i	$0.827531\pi$
$504$	−91.7095	−4.08507
$505$	0	0
$506$	−17.8464	−0.793367
$507$	41.9061	1.86111
$508$	−0.974783	−0.0432490
$509$	31.7558	1.40755	0.703774	−	0.710423i	$-0.251497\pi$
$509$	31.7558	1.40755	0.703774	+	0.710423i	$0.251497\pi$
$510$	0	0
$511$	59.5915	2.63617
$512$	−19.5787	−0.865266
$513$	−13.0871	−0.577809
$514$	27.0181	1.19172
$515$	0	0
$516$	−5.47636	−0.241083
$517$	−20.3954	−0.896989
$518$	35.2487	1.54874
$519$	7.66278	0.336359
$520$	0	0
$521$	19.2843	0.844860	0.422430	−	0.906396i	$-0.361177\pi$
$521$	19.2843	0.844860	0.422430	+	0.906396i	$0.361177\pi$
$522$	−18.6151	−0.814761
$523$	25.4005	1.11069	0.555343	−	0.831621i	$-0.312587\pi$
$523$	25.4005	1.11069	0.555343	+	0.831621i	$0.312587\pi$
$524$	−4.37442	−0.191097
$525$	0	0
$526$	−15.0162	−0.654736
$527$	17.9546	0.782116
$528$	14.0544	0.611639
$529$	28.2988	1.23038
$530$	0	0
$531$	37.0620	1.60835
$532$	−2.52686	−0.109553
$533$	−4.55861	−0.197455
$534$	35.1801	1.52239
$535$	0	0
$536$	0.514377	0.0222177
$537$	−13.2795	−0.573054
$538$	17.7801	0.766556
$539$	18.2846	0.787575
$540$	0	0
$541$	−12.8241	−0.551352	−0.275676	−	0.961251i	$-0.588902\pi$
$541$	−12.8241	−0.551352	−0.275676	+	0.961251i	$0.588902\pi$
$542$	12.1033	0.519881
$543$	47.8399	2.05301
$544$	−7.10938	−0.304812
$545$	0	0
$546$	5.68566	0.243324
$547$	32.7899	1.40199	0.700997	−	0.713164i	$-0.252738\pi$
$547$	32.7899	1.40199	0.700997	+	0.713164i	$0.252738\pi$
$548$	12.1444	0.518781
$549$	74.2895	3.17060
$550$	0	0
$551$	−1.87712	−0.0799680
$552$	−71.8657	−3.05881
$553$	17.6228	0.749398
$554$	18.5076	0.786314
$555$	0	0
$556$	4.42871	0.187819
$557$	−23.2579	−0.985471	−0.492735	−	0.870179i	$-0.664003\pi$
$557$	−23.2579	−0.985471	−0.492735	+	0.870179i	$0.664003\pi$
$558$	−86.1779	−3.64820
$559$	0.892604	0.0377531
$560$	0	0
$561$	12.9644	0.547358
$562$	−4.07538	−0.171910
$563$	22.4854	0.947647	0.473823	−	0.880620i	$-0.342873\pi$
$563$	22.4854	0.947647	0.473823	+	0.880620i	$0.342873\pi$
$564$	−22.4411	−0.944942
$565$	0	0
$566$	19.6002	0.823858
$567$	103.679	4.35409
$568$	−7.05795	−0.296145
$569$	−2.11507	−0.0886682	−0.0443341	−	0.999017i	$-0.514117\pi$
$569$	−2.11507	−0.0886682	−0.0443341	+	0.999017i	$0.514117\pi$
$570$	0	0
$571$	27.6202	1.15587	0.577935	−	0.816083i	$-0.303859\pi$
$571$	27.6202	1.15587	0.577935	+	0.816083i	$0.303859\pi$
$572$	0.670827	0.0280487
$573$	82.0873	3.42925
$574$	49.6352	2.07173
$575$	0	0
$576$	63.6705	2.65294
$577$	−9.72735	−0.404955	−0.202478	−	0.979287i	$-0.564899\pi$
$577$	−9.72735	−0.404955	−0.202478	+	0.979287i	$0.564899\pi$
$578$	−15.4483	−0.642563
$579$	−61.9838	−2.57596
$580$	0	0
$581$	38.3406	1.59064
$582$	16.7744	0.695323
$583$	−24.5444	−1.01652
$584$	−46.9945	−1.94465
$585$	0	0
$586$	−4.31813	−0.178380
$587$	−12.6223	−0.520977	−0.260489	−	0.965477i	$-0.583884\pi$
$587$	−12.6223	−0.520977	−0.260489	+	0.965477i	$0.583884\pi$
$588$	20.1186	0.829679
$589$	−8.69005	−0.358067
$590$	0	0
$591$	−40.5467	−1.66787
$592$	−15.6262	−0.642232
$593$	31.9354	1.31143	0.655716	−	0.755008i	$-0.272367\pi$
$593$	31.9354	1.31143	0.655716	+	0.755008i	$0.272367\pi$
$594$	−37.8294	−1.55216
$595$	0	0
$596$	8.71003	0.356777
$597$	46.8105	1.91583
$598$	3.20058	0.130881
$599$	−23.4985	−0.960122	−0.480061	−	0.877235i	$-0.659385\pi$
$599$	−23.4985	−0.960122	−0.480061	+	0.877235i	$0.659385\pi$
$600$	0	0
$601$	14.4004	0.587405	0.293703	−	0.955897i	$-0.405112\pi$
$601$	14.4004	0.587405	0.293703	+	0.955897i	$0.405112\pi$
$602$	−9.71887	−0.396111
$603$	−1.28023	−0.0521351
$604$	−5.60594	−0.228103
$605$	0	0
$606$	37.6715	1.53030
$607$	−9.82042	−0.398598	−0.199299	−	0.979939i	$-0.563867\pi$
$607$	−9.82042	−0.398598	−0.199299	+	0.979939i	$0.563867\pi$
$608$	3.44094	0.139549
$609$	27.7069	1.12274
$610$	0	0
$611$	3.65773	0.147976
$612$	10.2472	0.414219
$613$	−11.5045	−0.464661	−0.232331	−	0.972637i	$-0.574635\pi$
$613$	−11.5045	−0.464661	−0.232331	+	0.972637i	$0.574635\pi$
$614$	−8.28439	−0.334331
$615$	0	0
$616$	−26.7317	−1.07705
$617$	−19.3104	−0.777408	−0.388704	−	0.921363i	$-0.627077\pi$
$617$	−19.3104	−0.777408	−0.388704	+	0.921363i	$0.627077\pi$
$618$	13.1951	0.530783
$619$	39.6321	1.59295	0.796474	−	0.604672i	$-0.206696\pi$
$619$	39.6321	1.59295	0.796474	+	0.604672i	$0.206696\pi$
$620$	0	0
$621$	108.739	4.36356
$622$	−29.8919	−1.19856
$623$	−37.6149	−1.50701
$624$	−2.52053	−0.100902
$625$	0	0
$626$	−7.19959	−0.287754
$627$	−6.27478	−0.250590
$628$	−3.32796	−0.132800
$629$	−14.4143	−0.574736
$630$	0	0
$631$	−21.2723	−0.846838	−0.423419	−	0.905934i	$-0.639170\pi$
$631$	−21.2723	−0.846838	−0.423419	+	0.905934i	$0.639170\pi$
$632$	−13.8976	−0.552815
$633$	−68.9688	−2.74126
$634$	−15.3866	−0.611079
$635$	0	0
$636$	−27.0063	−1.07087
$637$	−3.27918	−0.129926
$638$	−5.42599	−0.214817
$639$	17.5665	0.694920
$640$	0	0
$641$	12.8329	0.506868	0.253434	−	0.967353i	$-0.418440\pi$
$641$	12.8329	0.506868	0.253434	+	0.967353i	$0.418440\pi$
$642$	7.49725	0.295893
$643$	−38.7097	−1.52656	−0.763280	−	0.646068i	$-0.776412\pi$
$643$	−38.7097	−1.52656	−0.763280	+	0.646068i	$0.776412\pi$
$644$	20.9954	0.827336
$645$	0	0
$646$	−1.71512	−0.0674803
$647$	−25.4725	−1.00143	−0.500713	−	0.865614i	$-0.666929\pi$
$647$	−25.4725	−1.00143	−0.500713	+	0.865614i	$0.666929\pi$
$648$	−81.7621	−3.21192
$649$	10.8029	0.424052
$650$	0	0
$651$	128.268	5.02721
$652$	13.5856	0.532053
$653$	−16.6030	−0.649724	−0.324862	−	0.945761i	$-0.605318\pi$
$653$	−16.6030	−0.649724	−0.324862	+	0.945761i	$0.605318\pi$
$654$	66.2920	2.59222
$655$	0	0
$656$	−22.0039	−0.859109
$657$	116.965	4.56322
$658$	−39.8261	−1.55258
$659$	17.5080	0.682015	0.341008	−	0.940061i	$-0.389232\pi$
$659$	17.5080	0.682015	0.341008	+	0.940061i	$0.389232\pi$
$660$	0	0
$661$	−7.28228	−0.283248	−0.141624	−	0.989921i	$-0.545232\pi$
$661$	−7.28228	−0.283248	−0.141624	+	0.989921i	$0.545232\pi$
$662$	17.3411	0.673980
$663$	−2.32505	−0.0902973
$664$	−30.2359	−1.17338
$665$	0	0
$666$	69.1851	2.68087
$667$	15.5968	0.603911
$668$	−10.8758	−0.420796
$669$	1.14822	0.0443926
$670$	0	0
$671$	21.6541	0.835948
$672$	−50.7893	−1.95924
$673$	−4.57250	−0.176257	−0.0881284	−	0.996109i	$-0.528089\pi$
$673$	−4.57250	−0.176257	−0.0881284	+	0.996109i	$0.528089\pi$
$674$	−32.4459	−1.24977
$675$	0	0
$676$	9.65479	0.371338
$677$	−39.9218	−1.53432	−0.767159	−	0.641457i	$-0.778330\pi$
$677$	−39.9218	−1.53432	−0.767159	+	0.641457i	$0.778330\pi$
$678$	20.3098	0.779993
$679$	−17.9354	−0.688297
$680$	0	0
$681$	46.5976	1.78562
$682$	−25.1194	−0.961871
$683$	−5.71832	−0.218805	−0.109403	−	0.993998i	$-0.534894\pi$
$683$	−5.71832	−0.218805	−0.109403	+	0.993998i	$0.534894\pi$
$684$	−4.95966	−0.189637
$685$	0	0
$686$	5.21771	0.199213
$687$	−40.8015	−1.55667
$688$	4.30850	0.164260
$689$	4.40181	0.167696
$690$	0	0
$691$	−17.4707	−0.664617	−0.332308	−	0.943171i	$-0.607827\pi$
$691$	−17.4707	−0.664617	−0.332308	+	0.943171i	$0.607827\pi$
$692$	1.76544	0.0671119
$693$	66.5326	2.52736
$694$	17.9171	0.680125
$695$	0	0
$696$	−21.8500	−0.828221
$697$	−20.2974	−0.768819
$698$	−9.78670	−0.370432
$699$	−78.0799	−2.95325
$700$	0	0
$701$	−29.6516	−1.11993	−0.559963	−	0.828517i	$-0.689185\pi$
$701$	−29.6516	−1.11993	−0.559963	+	0.828517i	$0.689185\pi$
$702$	6.78435	0.256059
$703$	6.97653	0.263125
$704$	18.5589	0.699464
$705$	0	0
$706$	−31.2121	−1.17468
$707$	−40.2787	−1.51484
$708$	11.8865	0.446722
$709$	−28.2889	−1.06241	−0.531207	−	0.847242i	$-0.678261\pi$
$709$	−28.2889	−1.06241	−0.531207	+	0.847242i	$0.678261\pi$
$710$	0	0
$711$	34.5896	1.29721
$712$	29.6635	1.11169
$713$	72.2048	2.70409
$714$	25.3156	0.947414
$715$	0	0
$716$	−3.05949	−0.114339
$717$	64.6127	2.41300
$718$	−15.2858	−0.570462
$719$	44.6164	1.66391	0.831955	−	0.554843i	$-0.187222\pi$
$719$	44.6164	1.66391	0.831955	+	0.554843i	$0.187222\pi$
$720$	0	0
$721$	−14.1083	−0.525420
$722$	−20.3961	−0.759065
$723$	3.26371	0.121379
$724$	11.0219	0.409626
$725$	0	0
$726$	21.9695	0.815365
$727$	1.11466	0.0413404	0.0206702	−	0.999786i	$-0.493420\pi$
$727$	1.11466	0.0413404	0.0206702	+	0.999786i	$0.493420\pi$
$728$	4.79409	0.177681
$729$	54.8471	2.03138
$730$	0	0
$731$	3.97436	0.146997
$732$	23.8261	0.880638
$733$	1.28394	0.0474234	0.0237117	−	0.999719i	$-0.492452\pi$
$733$	1.28394	0.0474234	0.0237117	+	0.999719i	$0.492452\pi$
$734$	−7.05494	−0.260403
$735$	0	0
$736$	−28.5904	−1.05386
$737$	−0.373166	−0.0137457
$738$	97.4226	3.58618
$739$	−18.2571	−0.671597	−0.335799	−	0.941934i	$-0.609006\pi$
$739$	−18.2571	−0.671597	−0.335799	+	0.941934i	$0.609006\pi$
$740$	0	0
$741$	1.12532	0.0413398
$742$	−47.9279	−1.75949
$743$	−34.5017	−1.26574	−0.632872	−	0.774256i	$-0.718124\pi$
$743$	−34.5017	−1.26574	−0.632872	+	0.774256i	$0.718124\pi$
$744$	−101.154	−3.70847
$745$	0	0
$746$	15.7682	0.577314
$747$	75.2540	2.75340
$748$	2.98689	0.109211
$749$	−8.01613	−0.292903
$750$	0	0
$751$	31.2492	1.14030	0.570150	−	0.821540i	$-0.306885\pi$
$751$	31.2492	1.14030	0.570150	+	0.821540i	$0.306885\pi$
$752$	17.6555	0.643828
$753$	25.9995	0.947474
$754$	0.973100	0.0354382
$755$	0	0
$756$	44.5046	1.61862
$757$	0.354864	0.0128977	0.00644887	−	0.999979i	$-0.497947\pi$
$757$	0.354864	0.0128977	0.00644887	+	0.999979i	$0.497947\pi$
$758$	−38.4698	−1.39729
$759$	52.1365	1.89244
$760$	0	0
$761$	17.6609	0.640208	0.320104	−	0.947382i	$-0.396282\pi$
$761$	17.6609	0.640208	0.320104	+	0.947382i	$0.396282\pi$
$762$	−4.72673	−0.171231
$763$	−70.8801	−2.56603
$764$	18.9122	0.684219
$765$	0	0
$766$	−20.3206	−0.734213
$767$	−1.93741	−0.0699556
$768$	49.5295	1.78724
$769$	−55.1578	−1.98904	−0.994520	−	0.104546i	$-0.966661\pi$
$769$	−55.1578	−1.98904	−0.994520	+	0.104546i	$0.966661\pi$
$770$	0	0
$771$	−78.9308	−2.84262
$772$	−14.2805	−0.513968
$773$	0.552632	0.0198768	0.00993840	−	0.999951i	$-0.496836\pi$
$773$	0.552632	0.0198768	0.00993840	+	0.999951i	$0.496836\pi$
$774$	−19.0759	−0.685670
$775$	0	0
$776$	14.1441	0.507742
$777$	−102.976	−3.69423
$778$	38.0953	1.36578
$779$	9.82395	0.351980
$780$	0	0
$781$	5.12034	0.183220
$782$	14.2507	0.509605
$783$	33.0610	1.18150
$784$	−15.8282	−0.565295
$785$	0	0
$786$	−21.2116	−0.756593
$787$	5.37517	0.191604	0.0958021	−	0.995400i	$-0.469458\pi$
$787$	5.37517	0.191604	0.0958021	+	0.995400i	$0.469458\pi$
$788$	−9.34161	−0.332781
$789$	43.8684	1.56176
$790$	0	0
$791$	−21.7154	−0.772111
$792$	−52.4684	−1.86438
$793$	−3.88347	−0.137906
$794$	31.6408	1.12289
$795$	0	0
$796$	10.7847	0.382255
$797$	7.58698	0.268745	0.134372	−	0.990931i	$-0.457098\pi$
$797$	7.58698	0.268745	0.134372	+	0.990931i	$0.457098\pi$
$798$	−12.2528	−0.433743
$799$	16.2862	0.576164
$800$	0	0
$801$	−73.8295	−2.60864
$802$	9.40781	0.332201
$803$	34.0932	1.20312
$804$	−0.410596	−0.0144806
$805$	0	0
$806$	4.50493	0.158679
$807$	−51.9430	−1.82848
$808$	31.7642	1.11746
$809$	35.8174	1.25927	0.629637	−	0.776890i	$-0.283204\pi$
$809$	35.8174	1.25927	0.629637	+	0.776890i	$0.283204\pi$
$810$	0	0
$811$	30.6969	1.07792	0.538958	−	0.842333i	$-0.318818\pi$
$811$	30.6969	1.07792	0.538958	+	0.842333i	$0.318818\pi$
$812$	6.38343	0.224014
$813$	−35.3586	−1.24008
$814$	20.1663	0.706828
$815$	0	0
$816$	−11.2228	−0.392875
$817$	−1.92359	−0.0672979
$818$	11.8946	0.415886
$819$	−11.9320	−0.416938
$820$	0	0
$821$	15.3434	0.535487	0.267743	−	0.963490i	$-0.413722\pi$
$821$	15.3434	0.535487	0.267743	+	0.963490i	$0.413722\pi$
$822$	58.8881	2.05396
$823$	13.2338	0.461300	0.230650	−	0.973037i	$-0.425915\pi$
$823$	13.2338	0.461300	0.230650	+	0.973037i	$0.425915\pi$
$824$	11.1260	0.387591
$825$	0	0
$826$	21.0949	0.733985
$827$	−3.02123	−0.105058	−0.0525292	−	0.998619i	$-0.516728\pi$
$827$	−3.02123	−0.105058	−0.0525292	+	0.998619i	$0.516728\pi$
$828$	41.2093	1.43212
$829$	−9.77604	−0.339536	−0.169768	−	0.985484i	$-0.554302\pi$
$829$	−9.77604	−0.339536	−0.169768	+	0.985484i	$0.554302\pi$
$830$	0	0
$831$	−54.0683	−1.87561
$832$	−3.32836	−0.115390
$833$	−14.6007	−0.505884
$834$	21.4749	0.743614
$835$	0	0
$836$	−1.44565	−0.0499990
$837$	153.054	5.29033
$838$	−21.3758	−0.738416
$839$	22.2155	0.766964	0.383482	−	0.923548i	$-0.374725\pi$
$839$	22.2155	0.766964	0.383482	+	0.923548i	$0.374725\pi$
$840$	0	0
$841$	−24.2580	−0.836482
$842$	−32.4771	−1.11924
$843$	11.9058	0.410059
$844$	−15.8898	−0.546950
$845$	0	0
$846$	−78.1697	−2.68753
$847$	−23.4900	−0.807126
$848$	21.2471	0.729627
$849$	−57.2602	−1.96516
$850$	0	0
$851$	−57.9673	−1.98709
$852$	5.63392	0.193015
$853$	11.8934	0.407221	0.203611	−	0.979052i	$-0.434732\pi$
$853$	11.8934	0.407221	0.203611	+	0.979052i	$0.434732\pi$
$854$	42.2841	1.44693
$855$	0	0
$856$	6.32161	0.216068
$857$	7.07707	0.241748	0.120874	−	0.992668i	$-0.461430\pi$
$857$	7.07707	0.241748	0.120874	+	0.992668i	$0.461430\pi$
$858$	3.25285	0.111050
$859$	43.7342	1.49219	0.746097	−	0.665838i	$-0.231926\pi$
$859$	43.7342	1.49219	0.746097	+	0.665838i	$0.231926\pi$
$860$	0	0
$861$	−145.005	−4.94174
$862$	−9.02673	−0.307452
$863$	−0.996591	−0.0339243	−0.0169622	−	0.999856i	$-0.505399\pi$
$863$	−0.996591	−0.0339243	−0.0169622	+	0.999856i	$0.505399\pi$
$864$	−60.6039	−2.06179
$865$	0	0
$866$	4.99179	0.169628
$867$	45.1307	1.53272
$868$	29.5518	1.00305
$869$	10.0823	0.342018
$870$	0	0
$871$	0.0669238	0.00226763
$872$	55.8968	1.89291
$873$	−35.2031	−1.19144
$874$	−6.89736	−0.233307
$875$	0	0
$876$	37.5128	1.26744
$877$	8.43931	0.284975	0.142488	−	0.989797i	$-0.454490\pi$
$877$	8.43931	0.284975	0.142488	+	0.989797i	$0.454490\pi$
$878$	−19.0394	−0.642548
$879$	12.6150	0.425494
$880$	0	0
$881$	−16.1434	−0.543885	−0.271942	−	0.962314i	$-0.587666\pi$
$881$	−16.1434	−0.543885	−0.271942	+	0.962314i	$0.587666\pi$
$882$	70.0798	2.35971
$883$	−14.4511	−0.486317	−0.243159	−	0.969987i	$-0.578184\pi$
$883$	−14.4511	−0.486317	−0.243159	+	0.969987i	$0.578184\pi$
$884$	−0.535671	−0.0180166
$885$	0	0
$886$	−33.1679	−1.11430
$887$	−22.7129	−0.762625	−0.381313	−	0.924446i	$-0.624528\pi$
$887$	−22.7129	−0.762625	−0.381313	+	0.924446i	$0.624528\pi$
$888$	81.2078	2.72516
$889$	5.05386	0.169501
$890$	0	0
$891$	59.3160	1.98716
$892$	0.264539	0.00885742
$893$	−7.88252	−0.263779
$894$	42.2350	1.41255
$895$	0	0
$896$	5.11627	0.170923
$897$	−9.35020	−0.312194
$898$	−39.9035	−1.33160
$899$	21.9531	0.732175
$900$	0	0
$901$	19.5992	0.652945
$902$	28.3970	0.945517
$903$	28.3928	0.944853
$904$	17.1250	0.569570
$905$	0	0
$906$	−27.1833	−0.903104
$907$	16.2063	0.538120	0.269060	−	0.963123i	$-0.413287\pi$
$907$	16.2063	0.538120	0.269060	+	0.963123i	$0.413287\pi$
$908$	10.7357	0.356276
$909$	−79.0580	−2.62219
$910$	0	0
$911$	30.2421	1.00197	0.500983	−	0.865457i	$-0.332972\pi$
$911$	30.2421	1.00197	0.500983	+	0.865457i	$0.332972\pi$
$912$	5.43182	0.179865
$913$	21.9352	0.725950
$914$	2.59151	0.0857195
$915$	0	0
$916$	−9.40031	−0.310595
$917$	22.6796	0.748948
$918$	30.2076	0.997000
$919$	49.0433	1.61779	0.808895	−	0.587953i	$-0.200066\pi$
$919$	49.0433	1.61779	0.808895	+	0.587953i	$0.200066\pi$
$920$	0	0
$921$	24.2021	0.797486
$922$	−17.1146	−0.563639
$923$	−0.918285	−0.0302257
$924$	21.3383	0.701979
$925$	0	0
$926$	−27.9021	−0.916920
$927$	−27.6914	−0.909504
$928$	−8.69260	−0.285349
$929$	−6.09092	−0.199837	−0.0999184	−	0.994996i	$-0.531858\pi$
$929$	−6.09092	−0.199837	−0.0999184	+	0.994996i	$0.531858\pi$
$930$	0	0
$931$	7.06674	0.231603
$932$	−17.9889	−0.589247
$933$	87.3265	2.85894
$934$	−11.5829	−0.379005
$935$	0	0
$936$	9.40972	0.307566
$937$	19.6222	0.641030	0.320515	−	0.947243i	$-0.396144\pi$
$937$	19.6222	0.641030	0.320515	+	0.947243i	$0.396144\pi$
$938$	−0.728681	−0.0237923
$939$	21.0329	0.686384
$940$	0	0
$941$	−13.7273	−0.447499	−0.223749	−	0.974647i	$-0.571830\pi$
$941$	−13.7273	−0.447499	−0.223749	+	0.974647i	$0.571830\pi$
$942$	−16.1373	−0.525783
$943$	−81.6262	−2.65812
$944$	−9.35165	−0.304370
$945$	0	0
$946$	−5.56031	−0.180781
$947$	32.9584	1.07100	0.535502	−	0.844534i	$-0.320122\pi$
$947$	32.9584	1.07100	0.535502	+	0.844534i	$0.320122\pi$
$948$	11.0936	0.360302
$949$	−6.11430	−0.198478
$950$	0	0
$951$	44.9504	1.45762
$952$	21.3459	0.691825
$953$	−7.66342	−0.248243	−0.124121	−	0.992267i	$-0.539611\pi$
$953$	−7.66342	−0.248243	−0.124121	+	0.992267i	$0.539611\pi$
$954$	−94.0716	−3.04568
$955$	0	0
$956$	14.8862	0.481454
$957$	15.8515	0.512407
$958$	−14.9822	−0.484054
$959$	−62.9637	−2.03320
$960$	0	0
$961$	70.6308	2.27841
$962$	−3.61664	−0.116605
$963$	−15.7338	−0.507016
$964$	0.751931	0.0242181
$965$	0	0
$966$	101.807	3.27559
$967$	23.4175	0.753057	0.376529	−	0.926405i	$-0.377118\pi$
$967$	23.4175	0.753057	0.376529	+	0.926405i	$0.377118\pi$
$968$	18.5245	0.595400
$969$	5.01055	0.160962
$970$	0	0
$971$	2.75350	0.0883640	0.0441820	−	0.999023i	$-0.485932\pi$
$971$	2.75350	0.0883640	0.0441820	+	0.999023i	$0.485932\pi$
$972$	31.0179	0.994899
$973$	−22.9611	−0.736100
$974$	−29.3805	−0.941412
$975$	0	0
$976$	−18.7451	−0.600015
$977$	27.8674	0.891558	0.445779	−	0.895143i	$-0.352927\pi$
$977$	27.8674	0.891558	0.445779	+	0.895143i	$0.352927\pi$
$978$	65.8767	2.10651
$979$	−21.5200	−0.687783
$980$	0	0
$981$	−139.122	−4.44181
$982$	−32.5228	−1.03785
$983$	3.25633	0.103861	0.0519304	−	0.998651i	$-0.483463\pi$
$983$	3.25633	0.103861	0.0519304	+	0.998651i	$0.483463\pi$
$984$	114.352	3.64542
$985$	0	0
$986$	4.33277	0.137984
$987$	116.348	3.70341
$988$	0.259265	0.00824831
$989$	15.9829	0.508227
$990$	0	0
$991$	−37.8144	−1.20121	−0.600606	−	0.799545i	$-0.705074\pi$
$991$	−37.8144	−1.20121	−0.600606	+	0.799545i	$0.705074\pi$
$992$	−40.2420	−1.27769
$993$	−50.6604	−1.60766
$994$	9.99849	0.317133
$995$	0	0
$996$	24.1354	0.764760
$997$	−46.9409	−1.48663	−0.743317	−	0.668939i	$-0.766749\pi$
$997$	−46.9409	−1.48663	−0.743317	+	0.668939i	$0.766749\pi$
$998$	−32.4089	−1.02589
$999$	−122.875	−3.88759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.j.1.17		25
5.4	even	2		1205.2.a.e.1.9	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.9	✓	25	5.4	even	2
6025.2.a.j.1.17		25	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.11717 q^{2} -3.26371 q^{3} -0.751931 q^{4} -3.64612 q^{6} +3.89846 q^{7} -3.07438 q^{8} +7.65181 q^{9} +O(q^{10})\)	\(q+1.11717 q^{2} -3.26371 q^{3} -0.751931 q^{4} -3.64612 q^{6} +3.89846 q^{7} -3.07438 q^{8} +7.65181 q^{9} +2.23037 q^{11} +2.45408 q^{12} -0.399996 q^{13} +4.35525 q^{14} -1.93074 q^{16} -1.78100 q^{17} +8.54837 q^{18} +0.862005 q^{19} -12.7235 q^{21} +2.49170 q^{22} -7.16231 q^{23} +10.0339 q^{24} -0.446864 q^{26} -15.1821 q^{27} -2.93138 q^{28} -2.17762 q^{29} -10.0812 q^{31} +3.99179 q^{32} -7.27928 q^{33} -1.98968 q^{34} -5.75363 q^{36} +8.09337 q^{37} +0.963006 q^{38} +1.30547 q^{39} +11.3966 q^{41} -14.2143 q^{42} -2.23153 q^{43} -1.67708 q^{44} -8.00152 q^{46} -9.14440 q^{47} +6.30137 q^{48} +8.19803 q^{49} +5.81267 q^{51} +0.300769 q^{52} -11.0046 q^{53} -16.9610 q^{54} -11.9853 q^{56} -2.81334 q^{57} -2.43277 q^{58} +4.84356 q^{59} +9.70876 q^{61} -11.2624 q^{62} +29.8303 q^{63} +8.32098 q^{64} -8.13220 q^{66} -0.167311 q^{67} +1.33919 q^{68} +23.3757 q^{69} +2.29573 q^{71} -23.5245 q^{72} +15.2859 q^{73} +9.04167 q^{74} -0.648168 q^{76} +8.69502 q^{77} +1.45843 q^{78} +4.52045 q^{79} +26.5947 q^{81} +12.7320 q^{82} +9.83480 q^{83} +9.56716 q^{84} -2.49300 q^{86} +7.10713 q^{87} -6.85699 q^{88} -9.64864 q^{89} -1.55937 q^{91} +5.38556 q^{92} +32.9021 q^{93} -10.2159 q^{94} -13.0280 q^{96} -4.60063 q^{97} +9.15859 q^{98} +17.0664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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Database

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