LMFDB - Embedded newform 6025.2.a.m.1.6

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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.30867 q^{2} -1.94403 q^{3} +3.32995 q^{4} +4.48812 q^{6} -0.292911 q^{7} -3.07041 q^{8} +0.779258 q^{9} +O(q^{10})$	\(q-2.30867 q^{2} -1.94403 q^{3} +3.32995 q^{4} +4.48812 q^{6} -0.292911 q^{7} -3.07041 q^{8} +0.779258 q^{9} +5.73922 q^{11} -6.47352 q^{12} -6.40571 q^{13} +0.676233 q^{14} +0.428662 q^{16} +1.19943 q^{17} -1.79905 q^{18} -6.61334 q^{19} +0.569427 q^{21} -13.2499 q^{22} -4.21193 q^{23} +5.96897 q^{24} +14.7887 q^{26} +4.31719 q^{27} -0.975377 q^{28} +7.24434 q^{29} +5.26186 q^{31} +5.15118 q^{32} -11.1572 q^{33} -2.76908 q^{34} +2.59489 q^{36} +5.15921 q^{37} +15.2680 q^{38} +12.4529 q^{39} -4.48901 q^{41} -1.31462 q^{42} +1.68248 q^{43} +19.1113 q^{44} +9.72394 q^{46} +6.59272 q^{47} -0.833332 q^{48} -6.91420 q^{49} -2.33173 q^{51} -21.3307 q^{52} +0.965274 q^{53} -9.96697 q^{54} +0.899356 q^{56} +12.8565 q^{57} -16.7248 q^{58} +3.89748 q^{59} -6.97659 q^{61} -12.1479 q^{62} -0.228253 q^{63} -12.7497 q^{64} +25.7583 q^{66} -12.8365 q^{67} +3.99404 q^{68} +8.18812 q^{69} -14.7940 q^{71} -2.39264 q^{72} -6.70963 q^{73} -11.9109 q^{74} -22.0221 q^{76} -1.68108 q^{77} -28.7496 q^{78} +11.4509 q^{79} -10.7305 q^{81} +10.3636 q^{82} +5.98135 q^{83} +1.89616 q^{84} -3.88428 q^{86} -14.0832 q^{87} -17.6218 q^{88} +6.24872 q^{89} +1.87630 q^{91} -14.0255 q^{92} -10.2292 q^{93} -15.2204 q^{94} -10.0141 q^{96} +4.42495 q^{97} +15.9626 q^{98} +4.47233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * 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 $

$2$	−2.30867	−1.63247	−0.816237	−	0.577717i	$-0.803944\pi$
$2$	−2.30867	−1.63247	−0.816237	+	0.577717i	$0.803944\pi$
$3$	−1.94403	−1.12239	−0.561193	−	0.827685i	$-0.689658\pi$
$3$	−1.94403	−1.12239	−0.561193	+	0.827685i	$0.689658\pi$
$4$	3.32995	1.66497
$5$	0	0
$5$	0	0
$6$	4.48812	1.83227
$7$	−0.292911	−0.110710	−0.0553549	−	0.998467i	$-0.517629\pi$
$7$	−0.292911	−0.110710	−0.0553549	+	0.998467i	$0.517629\pi$
$8$	−3.07041	−1.08555
$9$	0.779258	0.259753
$10$	0	0
$11$	5.73922	1.73044	0.865220	−	0.501393i	$-0.167179\pi$
$11$	5.73922	1.73044	0.865220	+	0.501393i	$0.167179\pi$
$12$	−6.47352	−1.86875
$13$	−6.40571	−1.77662	−0.888312	−	0.459240i	$-0.848122\pi$
$13$	−6.40571	−1.77662	−0.888312	+	0.459240i	$0.848122\pi$
$14$	0.676233	0.180731
$15$	0	0
$16$	0.428662	0.107165
$17$	1.19943	0.290904	0.145452	−	0.989365i	$-0.453536\pi$
$17$	1.19943	0.290904	0.145452	+	0.989365i	$0.453536\pi$
$18$	−1.79905	−0.424040
$19$	−6.61334	−1.51720	−0.758602	−	0.651554i	$-0.774117\pi$
$19$	−6.61334	−1.51720	−0.758602	+	0.651554i	$0.774117\pi$
$20$	0	0
$21$	0.569427	0.124259
$22$	−13.2499	−2.82490
$23$	−4.21193	−0.878248	−0.439124	−	0.898427i	$-0.644711\pi$
$23$	−4.21193	−0.878248	−0.439124	+	0.898427i	$0.644711\pi$
$24$	5.96897	1.21841
$25$	0	0
$26$	14.7887	2.90029
$27$	4.31719	0.830844
$28$	−0.975377	−0.184329
$29$	7.24434	1.34524	0.672620	−	0.739988i	$-0.265169\pi$
$29$	7.24434	1.34524	0.672620	+	0.739988i	$0.265169\pi$
$30$	0	0
$31$	5.26186	0.945058	0.472529	−	0.881315i	$-0.343341\pi$
$31$	5.26186	0.945058	0.472529	+	0.881315i	$0.343341\pi$
$32$	5.15118	0.910609
$33$	−11.1572	−1.94222
$34$	−2.76908	−0.474894
$35$	0	0
$36$	2.59489	0.432481
$37$	5.15921	0.848169	0.424084	−	0.905623i	$-0.360596\pi$
$37$	5.15921	0.848169	0.424084	+	0.905623i	$0.360596\pi$
$38$	15.2680	2.47680
$39$	12.4529	1.99406
$40$	0	0
$41$	−4.48901	−0.701065	−0.350533	−	0.936551i	$-0.613999\pi$
$41$	−4.48901	−0.701065	−0.350533	+	0.936551i	$0.613999\pi$
$42$	−1.31462	−0.202850
$43$	1.68248	0.256575	0.128288	−	0.991737i	$-0.459052\pi$
$43$	1.68248	0.256575	0.128288	+	0.991737i	$0.459052\pi$
$44$	19.1113	2.88114
$45$	0	0
$46$	9.72394	1.43372
$47$	6.59272	0.961647	0.480824	−	0.876817i	$-0.340338\pi$
$47$	6.59272	0.961647	0.480824	+	0.876817i	$0.340338\pi$
$48$	−0.833332	−0.120281
$49$	−6.91420	−0.987743
$50$	0	0
$51$	−2.33173	−0.326507
$52$	−21.3307	−2.95803
$53$	0.965274	0.132591	0.0662953	−	0.997800i	$-0.478882\pi$
$53$	0.965274	0.132591	0.0662953	+	0.997800i	$0.478882\pi$
$54$	−9.96697	−1.35633
$55$	0	0
$56$	0.899356	0.120181
$57$	12.8565	1.70289
$58$	−16.7248	−2.19607
$59$	3.89748	0.507409	0.253704	−	0.967282i	$-0.418351\pi$
$59$	3.89748	0.507409	0.253704	+	0.967282i	$0.418351\pi$
$60$	0	0
$61$	−6.97659	−0.893261	−0.446630	−	0.894719i	$-0.647376\pi$
$61$	−6.97659	−0.893261	−0.446630	+	0.894719i	$0.647376\pi$
$62$	−12.1479	−1.54278
$63$	−0.228253	−0.0287572
$64$	−12.7497	−1.59371
$65$	0	0
$66$	25.7583	3.17063
$67$	−12.8365	−1.56823	−0.784116	−	0.620614i	$-0.786883\pi$
$67$	−12.8365	−1.56823	−0.784116	+	0.620614i	$0.786883\pi$
$68$	3.99404	0.484348
$69$	8.18812	0.985734
$70$	0	0
$71$	−14.7940	−1.75572	−0.877861	−	0.478916i	$-0.841030\pi$
$71$	−14.7940	−1.75572	−0.877861	+	0.478916i	$0.841030\pi$
$72$	−2.39264	−0.281975
$73$	−6.70963	−0.785303	−0.392651	−	0.919687i	$-0.628442\pi$
$73$	−6.70963	−0.785303	−0.392651	+	0.919687i	$0.628442\pi$
$74$	−11.9109	−1.38461
$75$	0	0
$76$	−22.0221	−2.52611
$77$	−1.68108	−0.191577
$78$	−28.7496	−3.25525
$79$	11.4509	1.28833	0.644165	−	0.764886i	$-0.277205\pi$
$79$	11.4509	1.28833	0.644165	+	0.764886i	$0.277205\pi$
$80$	0	0
$81$	−10.7305	−1.19228
$82$	10.3636	1.14447
$83$	5.98135	0.656539	0.328269	−	0.944584i	$-0.393535\pi$
$83$	5.98135	0.656539	0.328269	+	0.944584i	$0.393535\pi$
$84$	1.89616	0.206888
$85$	0	0
$86$	−3.88428	−0.418852
$87$	−14.0832	−1.50988
$88$	−17.6218	−1.87849
$89$	6.24872	0.662363	0.331182	−	0.943567i	$-0.392553\pi$
$89$	6.24872	0.662363	0.331182	+	0.943567i	$0.392553\pi$
$90$	0	0
$91$	1.87630	0.196690
$92$	−14.0255	−1.46226
$93$	−10.2292	−1.06072
$94$	−15.2204	−1.56987
$95$	0	0
$96$	−10.0141	−1.02206
$97$	4.42495	0.449285	0.224643	−	0.974441i	$-0.427879\pi$
$97$	4.42495	0.449285	0.224643	+	0.974441i	$0.427879\pi$
$98$	15.9626	1.61247
$99$	4.47233	0.449486
$100$	0	0
$101$	8.37015	0.832861	0.416431	−	0.909168i	$-0.363281\pi$
$101$	8.37015	0.832861	0.416431	+	0.909168i	$0.363281\pi$
$102$	5.38318	0.533015
$103$	16.3557	1.61157	0.805787	−	0.592206i	$-0.201743\pi$
$103$	16.3557	1.61157	0.805787	+	0.592206i	$0.201743\pi$
$104$	19.6682	1.92862
$105$	0	0
$106$	−2.22850	−0.216451
$107$	−16.3423	−1.57987	−0.789933	−	0.613193i	$-0.789885\pi$
$107$	−16.3423	−1.57987	−0.789933	+	0.613193i	$0.789885\pi$
$108$	14.3760	1.38333
$109$	10.9278	1.04669	0.523345	−	0.852121i	$-0.324684\pi$
$109$	10.9278	1.04669	0.523345	+	0.852121i	$0.324684\pi$
$110$	0	0
$111$	−10.0297	−0.951973
$112$	−0.125560	−0.0118643
$113$	−18.4087	−1.73175	−0.865873	−	0.500265i	$-0.833236\pi$
$113$	−18.4087	−1.73175	−0.865873	+	0.500265i	$0.833236\pi$
$114$	−29.6815	−2.77993
$115$	0	0
$116$	24.1233	2.23979
$117$	−4.99170	−0.461483
$118$	−8.99799	−0.828332
$119$	−0.351325	−0.0322059
$120$	0	0
$121$	21.9386	1.99442
$122$	16.1066	1.45823
$123$	8.72677	0.786866
$124$	17.5217	1.57350
$125$	0	0
$126$	0.526960	0.0469453
$127$	6.47523	0.574583	0.287292	−	0.957843i	$-0.407245\pi$
$127$	6.47523	0.574583	0.287292	+	0.957843i	$0.407245\pi$
$128$	19.1325	1.69109
$129$	−3.27078	−0.287977
$130$	0	0
$131$	11.4855	1.00349	0.501747	−	0.865014i	$-0.332691\pi$
$131$	11.4855	1.00349	0.501747	+	0.865014i	$0.332691\pi$
$132$	−37.1530	−3.23375
$133$	1.93712	0.167969
$134$	29.6353	2.56010
$135$	0	0
$136$	−3.68274	−0.315792
$137$	9.67900	0.826933	0.413466	−	0.910519i	$-0.364318\pi$
$137$	9.67900	0.826933	0.413466	+	0.910519i	$0.364318\pi$
$138$	−18.9037	−1.60919
$139$	1.44600	0.122648	0.0613240	−	0.998118i	$-0.480468\pi$
$139$	1.44600	0.122648	0.0613240	+	0.998118i	$0.480468\pi$
$140$	0	0
$141$	−12.8165	−1.07934
$142$	34.1544	2.86617
$143$	−36.7638	−3.07434
$144$	0.334038	0.0278365
$145$	0	0
$146$	15.4903	1.28199
$147$	13.4414	1.10863
$148$	17.1799	1.41218
$149$	−22.1763	−1.81675	−0.908377	−	0.418151i	$-0.862678\pi$
$149$	−22.1763	−1.81675	−0.908377	+	0.418151i	$0.862678\pi$
$150$	0	0
$151$	−1.72016	−0.139984	−0.0699922	−	0.997548i	$-0.522297\pi$
$151$	−1.72016	−0.139984	−0.0699922	+	0.997548i	$0.522297\pi$
$152$	20.3057	1.64701
$153$	0.934664	0.0755631
$154$	3.88105	0.312744
$155$	0	0
$156$	41.4675	3.32006
$157$	−9.00291	−0.718511	−0.359255	−	0.933239i	$-0.616969\pi$
$157$	−9.00291	−0.718511	−0.359255	+	0.933239i	$0.616969\pi$
$158$	−26.4364	−2.10317
$159$	−1.87652	−0.148818
$160$	0	0
$161$	1.23372	0.0972306
$162$	24.7732	1.94637
$163$	5.63396	0.441286	0.220643	−	0.975355i	$-0.429184\pi$
$163$	5.63396	0.441286	0.220643	+	0.975355i	$0.429184\pi$
$164$	−14.9482	−1.16726
$165$	0	0
$166$	−13.8090	−1.07178
$167$	10.7115	0.828879	0.414440	−	0.910077i	$-0.363978\pi$
$167$	10.7115	0.828879	0.414440	+	0.910077i	$0.363978\pi$
$168$	−1.74838	−0.134890
$169$	28.0331	2.15639
$170$	0	0
$171$	−5.15350	−0.394098
$172$	5.60256	0.427191
$173$	16.6343	1.26468	0.632340	−	0.774691i	$-0.282095\pi$
$173$	16.6343	1.26468	0.632340	+	0.774691i	$0.282095\pi$
$174$	32.5135	2.46484
$175$	0	0
$176$	2.46018	0.185443
$177$	−7.57683	−0.569509
$178$	−14.4262	−1.08129
$179$	−14.2937	−1.06836	−0.534182	−	0.845370i	$-0.679380\pi$
$179$	−14.2937	−1.06836	−0.534182	+	0.845370i	$0.679380\pi$
$180$	0	0
$181$	−15.3718	−1.14258	−0.571288	−	0.820750i	$-0.693556\pi$
$181$	−15.3718	−1.14258	−0.571288	+	0.820750i	$0.693556\pi$
$182$	−4.33175	−0.321091
$183$	13.5627	1.00258
$184$	12.9323	0.953385
$185$	0	0
$186$	23.6159	1.73160
$187$	6.88378	0.503392
$188$	21.9534	1.60112
$189$	−1.26455	−0.0919826
$190$	0	0
$191$	−3.35561	−0.242804	−0.121402	−	0.992603i	$-0.538739\pi$
$191$	−3.35561	−0.242804	−0.121402	+	0.992603i	$0.538739\pi$
$192$	24.7858	1.78876
$193$	−23.2755	−1.67541	−0.837703	−	0.546126i	$-0.816102\pi$
$193$	−23.2755	−1.67541	−0.837703	+	0.546126i	$0.816102\pi$
$194$	−10.2157	−0.733447
$195$	0	0
$196$	−23.0239	−1.64457
$197$	3.10381	0.221137	0.110569	−	0.993868i	$-0.464733\pi$
$197$	3.10381	0.221137	0.110569	+	0.993868i	$0.464733\pi$
$198$	−10.3251	−0.733775
$199$	8.39878	0.595374	0.297687	−	0.954664i	$-0.403785\pi$
$199$	8.39878	0.595374	0.297687	+	0.954664i	$0.403785\pi$
$200$	0	0
$201$	24.9546	1.76016
$202$	−19.3239	−1.35962
$203$	−2.12194	−0.148931
$204$	−7.76453	−0.543626
$205$	0	0
$206$	−37.7599	−2.63085
$207$	−3.28218	−0.228127
$208$	−2.74588	−0.190393
$209$	−37.9554	−2.62543
$210$	0	0
$211$	0.0373418	0.00257072	0.00128536	−	0.999999i	$-0.499591\pi$
$211$	0.0373418	0.00257072	0.00128536	+	0.999999i	$0.499591\pi$
$212$	3.21431	0.220760
$213$	28.7599	1.97060
$214$	37.7289	2.57909
$215$	0	0
$216$	−13.2556	−0.901926
$217$	−1.54126	−0.104627
$218$	−25.2286	−1.70870
$219$	13.0437	0.881414
$220$	0	0
$221$	−7.68319	−0.516827
$222$	23.1552	1.55407
$223$	18.4555	1.23587	0.617935	−	0.786229i	$-0.287970\pi$
$223$	18.4555	1.23587	0.617935	+	0.786229i	$0.287970\pi$
$224$	−1.50884	−0.100813
$225$	0	0
$226$	42.4996	2.82703
$227$	26.5110	1.75960	0.879800	−	0.475344i	$-0.157677\pi$
$227$	26.5110	1.75960	0.879800	+	0.475344i	$0.157677\pi$
$228$	42.8116	2.83527
$229$	14.7836	0.976928	0.488464	−	0.872584i	$-0.337557\pi$
$229$	14.7836	0.976928	0.488464	+	0.872584i	$0.337557\pi$
$230$	0	0
$231$	3.26807	0.215023
$232$	−22.2431	−1.46033
$233$	8.14413	0.533540	0.266770	−	0.963760i	$-0.414044\pi$
$233$	8.14413	0.533540	0.266770	+	0.963760i	$0.414044\pi$
$234$	11.5242	0.753359
$235$	0	0
$236$	12.9784	0.844823
$237$	−22.2610	−1.44601
$238$	0.811094	0.0525754
$239$	8.74909	0.565932	0.282966	−	0.959130i	$-0.408682\pi$
$239$	8.74909	0.565932	0.282966	+	0.959130i	$0.408682\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−50.6490	−3.25584
$243$	7.90891	0.507357
$244$	−23.2317	−1.48726
$245$	0	0
$246$	−20.1472	−1.28454
$247$	42.3631	2.69550
$248$	−16.1561	−1.02591
$249$	−11.6279	−0.736891
$250$	0	0
$251$	1.60434	0.101265	0.0506326	−	0.998717i	$-0.483876\pi$
$251$	1.60434	0.101265	0.0506326	+	0.998717i	$0.483876\pi$
$252$	−0.760070	−0.0478799
$253$	−24.1732	−1.51975
$254$	−14.9492	−0.937993
$255$	0	0
$256$	−18.6711	−1.16694
$257$	24.8136	1.54783	0.773915	−	0.633290i	$-0.218296\pi$
$257$	24.8136	1.54783	0.773915	+	0.633290i	$0.218296\pi$
$258$	7.55116	0.470114
$259$	−1.51119	−0.0939006
$260$	0	0
$261$	5.64521	0.349430
$262$	−26.5162	−1.63818
$263$	−28.4078	−1.75170	−0.875850	−	0.482584i	$-0.839698\pi$
$263$	−28.4078	−1.75170	−0.875850	+	0.482584i	$0.839698\pi$
$264$	34.2572	2.10839
$265$	0	0
$266$	−4.47216	−0.274206
$267$	−12.1477	−0.743428
$268$	−42.7450	−2.61107
$269$	−15.4960	−0.944809	−0.472405	−	0.881382i	$-0.656614\pi$
$269$	−15.4960	−0.944809	−0.472405	+	0.881382i	$0.656614\pi$
$270$	0	0
$271$	−23.8870	−1.45103	−0.725515	−	0.688207i	$-0.758398\pi$
$271$	−23.8870	−1.45103	−0.725515	+	0.688207i	$0.758398\pi$
$272$	0.514149	0.0311749
$273$	−3.64759	−0.220762
$274$	−22.3456	−1.34995
$275$	0	0
$276$	27.2660	1.64122
$277$	28.7438	1.72705	0.863525	−	0.504306i	$-0.168251\pi$
$277$	28.7438	1.72705	0.863525	+	0.504306i	$0.168251\pi$
$278$	−3.33833	−0.200220
$279$	4.10035	0.245481
$280$	0	0
$281$	−5.03120	−0.300136	−0.150068	−	0.988676i	$-0.547949\pi$
$281$	−5.03120	−0.300136	−0.150068	+	0.988676i	$0.547949\pi$
$282$	29.5890	1.76200
$283$	−16.4147	−0.975750	−0.487875	−	0.872913i	$-0.662228\pi$
$283$	−16.4147	−0.975750	−0.487875	+	0.872913i	$0.662228\pi$
$284$	−49.2632	−2.92323
$285$	0	0
$286$	84.8753	5.01878
$287$	1.31488	0.0776148
$288$	4.01410	0.236533
$289$	−15.5614	−0.915375
$290$	0	0
$291$	−8.60223	−0.504272
$292$	−22.3427	−1.30751
$293$	−12.9185	−0.754708	−0.377354	−	0.926069i	$-0.623166\pi$
$293$	−12.9185	−0.754708	−0.377354	+	0.926069i	$0.623166\pi$
$294$	−31.0318	−1.80981
$295$	0	0
$296$	−15.8409	−0.920733
$297$	24.7773	1.43773
$298$	51.1978	2.96581
$299$	26.9804	1.56032
$300$	0	0
$301$	−0.492815	−0.0284054
$302$	3.97127	0.228521
$303$	−16.2718	−0.934792
$304$	−2.83489	−0.162592
$305$	0	0
$306$	−2.15783	−0.123355
$307$	−26.1062	−1.48996	−0.744981	−	0.667086i	$-0.767541\pi$
$307$	−26.1062	−1.48996	−0.744981	+	0.667086i	$0.767541\pi$
$308$	−5.59790	−0.318970
$309$	−31.7960	−1.80881
$310$	0	0
$311$	19.4595	1.10345	0.551724	−	0.834027i	$-0.313970\pi$
$311$	19.4595	1.10345	0.551724	+	0.834027i	$0.313970\pi$
$312$	−38.2355	−2.16466
$313$	30.0951	1.70107	0.850537	−	0.525916i	$-0.176277\pi$
$313$	30.0951	1.70107	0.850537	+	0.525916i	$0.176277\pi$
$314$	20.7847	1.17295
$315$	0	0
$316$	38.1310	2.14504
$317$	8.58103	0.481959	0.240979	−	0.970530i	$-0.422531\pi$
$317$	8.58103	0.481959	0.240979	+	0.970530i	$0.422531\pi$
$318$	4.33227	0.242942
$319$	41.5769	2.32786
$320$	0	0
$321$	31.7699	1.77322
$322$	−2.84825	−0.158727
$323$	−7.93223	−0.441361
$324$	−35.7321	−1.98512
$325$	0	0
$326$	−13.0070	−0.720388
$327$	−21.2439	−1.17479
$328$	13.7831	0.761044
$329$	−1.93108	−0.106464
$330$	0	0
$331$	14.7127	0.808682	0.404341	−	0.914608i	$-0.367501\pi$
$331$	14.7127	0.808682	0.404341	+	0.914608i	$0.367501\pi$
$332$	19.9176	1.09312
$333$	4.02035	0.220314
$334$	−24.7293	−1.35312
$335$	0	0
$336$	0.244092	0.0133163
$337$	4.00924	0.218397	0.109199	−	0.994020i	$-0.465172\pi$
$337$	4.00924	0.218397	0.109199	+	0.994020i	$0.465172\pi$
$338$	−64.7191	−3.52026
$339$	35.7871	1.94369
$340$	0	0
$341$	30.1990	1.63537
$342$	11.8977	0.643355
$343$	4.07562	0.220063
$344$	−5.16589	−0.278526
$345$	0	0
$346$	−38.4030	−2.06456
$347$	−4.59816	−0.246842	−0.123421	−	0.992354i	$-0.539387\pi$
$347$	−4.59816	−0.246842	−0.123421	+	0.992354i	$0.539387\pi$
$348$	−46.8964	−2.51391
$349$	11.9897	0.641795	0.320897	−	0.947114i	$-0.396016\pi$
$349$	11.9897	0.641795	0.320897	+	0.947114i	$0.396016\pi$
$350$	0	0
$351$	−27.6547	−1.47610
$352$	29.5638	1.57575
$353$	−19.7293	−1.05008	−0.525042	−	0.851077i	$-0.675950\pi$
$353$	−19.7293	−1.05008	−0.525042	+	0.851077i	$0.675950\pi$
$354$	17.4924	0.929709
$355$	0	0
$356$	20.8079	1.10282
$357$	0.682987	0.0361475
$358$	32.9995	1.74408
$359$	−0.989574	−0.0522277	−0.0261139	−	0.999659i	$-0.508313\pi$
$359$	−0.989574	−0.0522277	−0.0261139	+	0.999659i	$0.508313\pi$
$360$	0	0
$361$	24.7362	1.30191
$362$	35.4884	1.86523
$363$	−42.6494	−2.23851
$364$	6.24798	0.327483
$365$	0	0
$366$	−31.3118	−1.63669
$367$	−21.2188	−1.10761	−0.553807	−	0.832645i	$-0.686825\pi$
$367$	−21.2188	−1.10761	−0.553807	+	0.832645i	$0.686825\pi$
$368$	−1.80549	−0.0941178
$369$	−3.49809	−0.182103
$370$	0	0
$371$	−0.282739	−0.0146791
$372$	−34.0628	−1.76607
$373$	11.8023	0.611097	0.305549	−	0.952176i	$-0.401160\pi$
$373$	11.8023	0.611097	0.305549	+	0.952176i	$0.401160\pi$
$374$	−15.8924	−0.821775
$375$	0	0
$376$	−20.2424	−1.04392
$377$	−46.4052	−2.38999
$378$	2.91943	0.150159
$379$	−20.6708	−1.06179	−0.530893	−	0.847439i	$-0.678143\pi$
$379$	−20.6708	−1.06179	−0.530893	+	0.847439i	$0.678143\pi$
$380$	0	0
$381$	−12.5880	−0.644905
$382$	7.74699	0.396371
$383$	29.9357	1.52964	0.764820	−	0.644244i	$-0.222828\pi$
$383$	29.9357	1.52964	0.764820	+	0.644244i	$0.222828\pi$
$384$	−37.1941	−1.89805
$385$	0	0
$386$	53.7354	2.73506
$387$	1.31108	0.0666460
$388$	14.7348	0.748048
$389$	−22.4984	−1.14071	−0.570357	−	0.821397i	$-0.693195\pi$
$389$	−22.4984	−1.14071	−0.570357	+	0.821397i	$0.693195\pi$
$390$	0	0
$391$	−5.05191	−0.255486
$392$	21.2294	1.07225
$393$	−22.3282	−1.12631
$394$	−7.16567	−0.361001
$395$	0	0
$396$	14.8926	0.748383
$397$	2.11971	0.106385	0.0531925	−	0.998584i	$-0.483060\pi$
$397$	2.11971	0.106385	0.0531925	+	0.998584i	$0.483060\pi$
$398$	−19.3900	−0.971933
$399$	−3.76582	−0.188527
$400$	0	0
$401$	−24.2787	−1.21242	−0.606210	−	0.795304i	$-0.707311\pi$
$401$	−24.2787	−1.21242	−0.606210	+	0.795304i	$0.707311\pi$
$402$	−57.6120	−2.87342
$403$	−33.7060	−1.67901
$404$	27.8722	1.38669
$405$	0	0
$406$	4.89887	0.243127
$407$	29.6098	1.46770
$408$	7.15936	0.354441
$409$	4.21431	0.208384	0.104192	−	0.994557i	$-0.466774\pi$
$409$	4.21431	0.208384	0.104192	+	0.994557i	$0.466774\pi$
$410$	0	0
$411$	−18.8163	−0.928138
$412$	54.4636	2.68323
$413$	−1.14161	−0.0561751
$414$	7.57746	0.372412
$415$	0	0
$416$	−32.9970	−1.61781
$417$	−2.81107	−0.137659
$418$	87.6264	4.28595
$419$	−39.4953	−1.92947	−0.964735	−	0.263223i	$-0.915214\pi$
$419$	−39.4953	−1.92947	−0.964735	+	0.263223i	$0.915214\pi$
$420$	0	0
$421$	30.0058	1.46239	0.731196	−	0.682168i	$-0.238963\pi$
$421$	30.0058	1.46239	0.731196	+	0.682168i	$0.238963\pi$
$422$	−0.0862099	−0.00419663
$423$	5.13743	0.249790
$424$	−2.96379	−0.143934
$425$	0	0
$426$	−66.3972	−3.21695
$427$	2.04352	0.0988927
$428$	−54.4189	−2.63044
$429$	71.4699	3.45060
$430$	0	0
$431$	40.1362	1.93329	0.966647	−	0.256112i	$-0.0824416\pi$
$431$	40.1362	1.93329	0.966647	+	0.256112i	$0.0824416\pi$
$432$	1.85062	0.0890378
$433$	−5.10052	−0.245115	−0.122558	−	0.992461i	$-0.539110\pi$
$433$	−5.10052	−0.245115	−0.122558	+	0.992461i	$0.539110\pi$
$434$	3.55825	0.170801
$435$	0	0
$436$	36.3889	1.74271
$437$	27.8549	1.33248
$438$	−30.1136	−1.43889
$439$	−30.0613	−1.43475	−0.717375	−	0.696687i	$-0.754656\pi$
$439$	−30.0613	−1.43475	−0.717375	+	0.696687i	$0.754656\pi$
$440$	0	0
$441$	−5.38795	−0.256569
$442$	17.7379	0.843708
$443$	−2.89103	−0.137357	−0.0686785	−	0.997639i	$-0.521878\pi$
$443$	−2.89103	−0.137357	−0.0686785	+	0.997639i	$0.521878\pi$
$444$	−33.3983	−1.58501
$445$	0	0
$446$	−42.6075	−2.01753
$447$	43.1115	2.03910
$448$	3.73452	0.176440
$449$	−34.7026	−1.63772	−0.818859	−	0.573995i	$-0.805393\pi$
$449$	−34.7026	−1.63772	−0.818859	+	0.573995i	$0.805393\pi$
$450$	0	0
$451$	−25.7634	−1.21315
$452$	−61.3000	−2.88331
$453$	3.34404	0.157117
$454$	−61.2052	−2.87250
$455$	0	0
$456$	−39.4749	−1.84858
$457$	21.6357	1.01207	0.506037	−	0.862512i	$-0.331110\pi$
$457$	21.6357	1.01207	0.506037	+	0.862512i	$0.331110\pi$
$458$	−34.1304	−1.59481
$459$	5.17816	0.241696
$460$	0	0
$461$	−21.7357	−1.01233	−0.506165	−	0.862437i	$-0.668937\pi$
$461$	−21.7357	−1.01233	−0.506165	+	0.862437i	$0.668937\pi$
$462$	−7.54488	−0.351020
$463$	−2.83805	−0.131895	−0.0659476	−	0.997823i	$-0.521007\pi$
$463$	−2.83805	−0.131895	−0.0659476	+	0.997823i	$0.521007\pi$
$464$	3.10537	0.144163
$465$	0	0
$466$	−18.8021	−0.870991
$467$	−1.54010	−0.0712672	−0.0356336	−	0.999365i	$-0.511345\pi$
$467$	−1.54010	−0.0712672	−0.0356336	+	0.999365i	$0.511345\pi$
$468$	−16.6221	−0.768357
$469$	3.75996	0.173619
$470$	0	0
$471$	17.5019	0.806447
$472$	−11.9669	−0.550820
$473$	9.65609	0.443988
$474$	51.3932	2.36057
$475$	0	0
$476$	−1.16990	−0.0536221
$477$	0.752197	0.0344407
$478$	−20.1988	−0.923870
$479$	−30.9218	−1.41285	−0.706426	−	0.707787i	$-0.749694\pi$
$479$	−30.9218	−1.41285	−0.706426	+	0.707787i	$0.749694\pi$
$480$	0	0
$481$	−33.0484	−1.50688
$482$	−2.30867	−0.105157
$483$	−2.39839	−0.109130
$484$	73.0545	3.32066
$485$	0	0
$486$	−18.2590	−0.828247
$487$	−19.7324	−0.894162	−0.447081	−	0.894493i	$-0.647536\pi$
$487$	−19.7324	−0.894162	−0.447081	+	0.894493i	$0.647536\pi$
$488$	21.4210	0.969683
$489$	−10.9526	−0.495294
$490$	0	0
$491$	20.1445	0.909111	0.454555	−	0.890719i	$-0.349798\pi$
$491$	20.1445	0.909111	0.454555	+	0.890719i	$0.349798\pi$
$492$	29.0597	1.31011
$493$	8.68907	0.391336
$494$	−97.8024	−4.40034
$495$	0	0
$496$	2.25556	0.101278
$497$	4.33331	0.194376
$498$	26.8451	1.20296
$499$	−38.2372	−1.71173	−0.855867	−	0.517196i	$-0.826976\pi$
$499$	−38.2372	−1.71173	−0.855867	+	0.517196i	$0.826976\pi$
$500$	0	0
$501$	−20.8235	−0.930323
$502$	−3.70390	−0.165313
$503$	26.2255	1.16934	0.584668	−	0.811273i	$-0.301225\pi$
$503$	26.2255	1.16934	0.584668	+	0.811273i	$0.301225\pi$
$504$	0.700830	0.0312174
$505$	0	0
$506$	55.8078	2.48096
$507$	−54.4972	−2.42031
$508$	21.5622	0.956667
$509$	28.7622	1.27486	0.637431	−	0.770507i	$-0.279997\pi$
$509$	28.7622	1.27486	0.637431	+	0.770507i	$0.279997\pi$
$510$	0	0
$511$	1.96532	0.0869407
$512$	4.84045	0.213920
$513$	−28.5511	−1.26056
$514$	−57.2863	−2.52679
$515$	0	0
$516$	−10.8915	−0.479474
$517$	37.8371	1.66407
$518$	3.48883	0.153290
$519$	−32.3375	−1.41946
$520$	0	0
$521$	−4.24646	−0.186041	−0.0930205	−	0.995664i	$-0.529652\pi$
$521$	−4.24646	−0.186041	−0.0930205	+	0.995664i	$0.529652\pi$
$522$	−13.0329	−0.570435
$523$	29.2669	1.27975	0.639877	−	0.768478i	$-0.278985\pi$
$523$	29.2669	1.27975	0.639877	+	0.768478i	$0.278985\pi$
$524$	38.2462	1.67079
$525$	0	0
$526$	65.5842	2.85961
$527$	6.31123	0.274921
$528$	−4.78267	−0.208139
$529$	−5.25967	−0.228681
$530$	0	0
$531$	3.03714	0.131801
$532$	6.45050	0.279665
$533$	28.7553	1.24553
$534$	28.0450	1.21363
$535$	0	0
$536$	39.4134	1.70240
$537$	27.7875	1.19912
$538$	35.7752	1.54238
$539$	−39.6821	−1.70923
$540$	0	0
$541$	0.238109	0.0102371	0.00511856	−	0.999987i	$-0.498371\pi$
$541$	0.238109	0.0102371	0.00511856	+	0.999987i	$0.498371\pi$
$542$	55.1471	2.36877
$543$	29.8832	1.28241
$544$	6.17848	0.264900
$545$	0	0
$546$	8.42107	0.360388
$547$	−17.0425	−0.728685	−0.364343	−	0.931265i	$-0.618706\pi$
$547$	−17.0425	−0.728685	−0.364343	+	0.931265i	$0.618706\pi$
$548$	32.2306	1.37682
$549$	−5.43656	−0.232027
$550$	0	0
$551$	−47.9093	−2.04100
$552$	−25.1409	−1.07007
$553$	−3.35410	−0.142631
$554$	−66.3600	−2.81937
$555$	0	0
$556$	4.81510	0.204206
$557$	−24.3065	−1.02990	−0.514950	−	0.857220i	$-0.672190\pi$
$557$	−24.3065	−1.02990	−0.514950	+	0.857220i	$0.672190\pi$
$558$	−9.46634	−0.400742
$559$	−10.7774	−0.455837
$560$	0	0
$561$	−13.3823	−0.565001
$562$	11.6154	0.489965
$563$	−13.2612	−0.558892	−0.279446	−	0.960161i	$-0.590151\pi$
$563$	−13.2612	−0.558892	−0.279446	+	0.960161i	$0.590151\pi$
$564$	−42.6782	−1.79707
$565$	0	0
$566$	37.8960	1.59289
$567$	3.14309	0.131997
$568$	45.4236	1.90593
$569$	−23.7530	−0.995779	−0.497889	−	0.867241i	$-0.665891\pi$
$569$	−23.7530	−0.995779	−0.497889	+	0.867241i	$0.665891\pi$
$570$	0	0
$571$	−23.0823	−0.965963	−0.482981	−	0.875631i	$-0.660446\pi$
$571$	−23.0823	−0.965963	−0.482981	+	0.875631i	$0.660446\pi$
$572$	−122.421	−5.11870
$573$	6.52341	0.272520
$574$	−3.03562	−0.126704
$575$	0	0
$576$	−9.93530	−0.413971
$577$	0.285078	0.0118679	0.00593397	−	0.999982i	$-0.498111\pi$
$577$	0.285078	0.0118679	0.00593397	+	0.999982i	$0.498111\pi$
$578$	35.9260	1.49433
$579$	45.2483	1.88045
$580$	0	0
$581$	−1.75200	−0.0726853
$582$	19.8597	0.823211
$583$	5.53992	0.229440
$584$	20.6013	0.852489
$585$	0	0
$586$	29.8246	1.23204
$587$	−14.9471	−0.616934	−0.308467	−	0.951235i	$-0.599816\pi$
$587$	−14.9471	−0.616934	−0.308467	+	0.951235i	$0.599816\pi$
$588$	44.7593	1.84584
$589$	−34.7985	−1.43385
$590$	0	0
$591$	−6.03390	−0.248202
$592$	2.21156	0.0908944
$593$	−11.3172	−0.464742	−0.232371	−	0.972627i	$-0.574648\pi$
$593$	−11.3172	−0.464742	−0.232371	+	0.972627i	$0.574648\pi$
$594$	−57.2026	−2.34705
$595$	0	0
$596$	−73.8460	−3.02485
$597$	−16.3275	−0.668240
$598$	−62.2888	−2.54718
$599$	7.37136	0.301186	0.150593	−	0.988596i	$-0.451882\pi$
$599$	7.37136	0.301186	0.150593	+	0.988596i	$0.451882\pi$
$600$	0	0
$601$	20.9847	0.855985	0.427993	−	0.903782i	$-0.359221\pi$
$601$	20.9847	0.855985	0.427993	+	0.903782i	$0.359221\pi$
$602$	1.13775	0.0463711
$603$	−10.0030	−0.407352
$604$	−5.72803	−0.233070
$605$	0	0
$606$	37.5663	1.52603
$607$	−18.6656	−0.757612	−0.378806	−	0.925476i	$-0.623665\pi$
$607$	−18.6656	−0.757612	−0.378806	+	0.925476i	$0.623665\pi$
$608$	−34.0665	−1.38158
$609$	4.12513	0.167159
$610$	0	0
$611$	−42.2311	−1.70849
$612$	3.11238	0.125811
$613$	−18.0247	−0.728010	−0.364005	−	0.931397i	$-0.618591\pi$
$613$	−18.0247	−0.728010	−0.364005	+	0.931397i	$0.618591\pi$
$614$	60.2707	2.43233
$615$	0	0
$616$	5.16160	0.207967
$617$	−24.5988	−0.990312	−0.495156	−	0.868804i	$-0.664889\pi$
$617$	−24.5988	−0.990312	−0.495156	+	0.868804i	$0.664889\pi$
$618$	73.4063	2.95284
$619$	19.3155	0.776354	0.388177	−	0.921585i	$-0.373105\pi$
$619$	19.3155	0.776354	0.388177	+	0.921585i	$0.373105\pi$
$620$	0	0
$621$	−18.1837	−0.729687
$622$	−44.9255	−1.80135
$623$	−1.83032	−0.0733301
$624$	5.33808	0.213694
$625$	0	0
$626$	−69.4795	−2.77696
$627$	73.7865	2.94675
$628$	−29.9792	−1.19630
$629$	6.18810	0.246736
$630$	0	0
$631$	−33.3641	−1.32820	−0.664102	−	0.747642i	$-0.731186\pi$
$631$	−33.3641	−1.32820	−0.664102	+	0.747642i	$0.731186\pi$
$632$	−35.1591	−1.39855
$633$	−0.0725937	−0.00288534
$634$	−19.8108	−0.786785
$635$	0	0
$636$	−6.24873	−0.247778
$637$	44.2904	1.75485
$638$	−95.9872	−3.80017
$639$	−11.5283	−0.456053
$640$	0	0
$641$	−11.0477	−0.436359	−0.218179	−	0.975909i	$-0.570012\pi$
$641$	−11.0477	−0.436359	−0.218179	+	0.975909i	$0.570012\pi$
$642$	−73.3461	−2.89474
$643$	−29.4072	−1.15971	−0.579853	−	0.814721i	$-0.696890\pi$
$643$	−29.4072	−1.15971	−0.579853	+	0.814721i	$0.696890\pi$
$644$	4.10822	0.161886
$645$	0	0
$646$	18.3129	0.720511
$647$	−14.8752	−0.584803	−0.292401	−	0.956296i	$-0.594454\pi$
$647$	−14.8752	−0.584803	−0.292401	+	0.956296i	$0.594454\pi$
$648$	32.9471	1.29429
$649$	22.3685	0.878040
$650$	0	0
$651$	2.99625	0.117432
$652$	18.7608	0.734730
$653$	−26.9060	−1.05291	−0.526456	−	0.850202i	$-0.676480\pi$
$653$	−26.9060	−1.05291	−0.526456	+	0.850202i	$0.676480\pi$
$654$	49.0452	1.91782
$655$	0	0
$656$	−1.92427	−0.0751300
$657$	−5.22853	−0.203984
$658$	4.45822	0.173799
$659$	15.9122	0.619852	0.309926	−	0.950761i	$-0.399696\pi$
$659$	15.9122	0.619852	0.309926	+	0.950761i	$0.399696\pi$
$660$	0	0
$661$	−7.26109	−0.282424	−0.141212	−	0.989979i	$-0.545100\pi$
$661$	−7.26109	−0.282424	−0.141212	+	0.989979i	$0.545100\pi$
$662$	−33.9667	−1.32015
$663$	14.9364	0.580080
$664$	−18.3652	−0.712708
$665$	0	0
$666$	−9.28166	−0.359657
$667$	−30.5127	−1.18145
$668$	35.6687	1.38006
$669$	−35.8780	−1.38712
$670$	0	0
$671$	−40.0402	−1.54573
$672$	2.93322	0.113152
$673$	2.38014	0.0917476	0.0458738	−	0.998947i	$-0.485393\pi$
$673$	2.38014	0.0917476	0.0458738	+	0.998947i	$0.485393\pi$
$674$	−9.25600	−0.356528
$675$	0	0
$676$	93.3488	3.59034
$677$	−1.47980	−0.0568734	−0.0284367	−	0.999596i	$-0.509053\pi$
$677$	−1.47980	−0.0568734	−0.0284367	+	0.999596i	$0.509053\pi$
$678$	−82.6205	−3.17302
$679$	−1.29611	−0.0497403
$680$	0	0
$681$	−51.5383	−1.97495
$682$	−69.7194	−2.66969
$683$	−33.7413	−1.29108	−0.645538	−	0.763728i	$-0.723367\pi$
$683$	−33.7413	−1.29108	−0.645538	+	0.763728i	$0.723367\pi$
$684$	−17.1609	−0.656162
$685$	0	0
$686$	−9.40925	−0.359247
$687$	−28.7398	−1.09649
$688$	0.721213	0.0274960
$689$	−6.18326	−0.235564
$690$	0	0
$691$	28.5117	1.08464	0.542318	−	0.840173i	$-0.317547\pi$
$691$	28.5117	1.08464	0.542318	+	0.840173i	$0.317547\pi$
$692$	55.3913	2.10566
$693$	−1.30999	−0.0497625
$694$	10.6156	0.402963
$695$	0	0
$696$	43.2413	1.63906
$697$	−5.38424	−0.203943
$698$	−27.6803	−1.04771
$699$	−15.8325	−0.598838
$700$	0	0
$701$	17.2053	0.649834	0.324917	−	0.945743i	$-0.394664\pi$
$701$	17.2053	0.649834	0.324917	+	0.945743i	$0.394664\pi$
$702$	63.8455	2.40969
$703$	−34.1196	−1.28684
$704$	−73.1733	−2.75782
$705$	0	0
$706$	45.5483	1.71423
$707$	−2.45171	−0.0922059
$708$	−25.2304	−0.948218
$709$	12.0299	0.451791	0.225895	−	0.974152i	$-0.427469\pi$
$709$	12.0299	0.451791	0.225895	+	0.974152i	$0.427469\pi$
$710$	0	0
$711$	8.92323	0.334647
$712$	−19.1861	−0.719031
$713$	−22.1626	−0.829995
$714$	−1.57679	−0.0590099
$715$	0	0
$716$	−47.5974	−1.77880
$717$	−17.0085	−0.635195
$718$	2.28460	0.0852604
$719$	7.72118	0.287951	0.143976	−	0.989581i	$-0.454011\pi$
$719$	7.72118	0.287951	0.143976	+	0.989581i	$0.454011\pi$
$720$	0	0
$721$	−4.79075	−0.178417
$722$	−57.1078	−2.12533
$723$	−1.94403	−0.0722993
$724$	−51.1873	−1.90236
$725$	0	0
$726$	98.4632	3.65431
$727$	−28.2210	−1.04666	−0.523329	−	0.852131i	$-0.675310\pi$
$727$	−28.2210	−1.04666	−0.523329	+	0.852131i	$0.675310\pi$
$728$	−5.76101	−0.213517
$729$	16.8164	0.622831
$730$	0	0
$731$	2.01801	0.0746388
$732$	45.1631	1.66928
$733$	−10.2638	−0.379104	−0.189552	−	0.981871i	$-0.560704\pi$
$733$	−10.2638	−0.379104	−0.189552	+	0.981871i	$0.560704\pi$
$734$	48.9872	1.80815
$735$	0	0
$736$	−21.6964	−0.799740
$737$	−73.6717	−2.71373
$738$	8.07594	0.297279
$739$	−3.90040	−0.143478	−0.0717392	−	0.997423i	$-0.522855\pi$
$739$	−3.90040	−0.143478	−0.0717392	+	0.997423i	$0.522855\pi$
$740$	0	0
$741$	−82.3552	−3.02540
$742$	0.652750	0.0239632
$743$	−23.5902	−0.865442	−0.432721	−	0.901528i	$-0.642446\pi$
$743$	−23.5902	−0.865442	−0.432721	+	0.901528i	$0.642446\pi$
$744$	31.4079	1.15147
$745$	0	0
$746$	−27.2475	−0.997601
$747$	4.66102	0.170538
$748$	22.9226	0.838135
$749$	4.78682	0.174907
$750$	0	0
$751$	−50.6501	−1.84825	−0.924124	−	0.382092i	$-0.875204\pi$
$751$	−50.6501	−1.84825	−0.924124	+	0.382092i	$0.875204\pi$
$752$	2.82605	0.103055
$753$	−3.11889	−0.113659
$754$	107.134	3.90159
$755$	0	0
$756$	−4.21089	−0.153149
$757$	−51.4870	−1.87133	−0.935664	−	0.352892i	$-0.885198\pi$
$757$	−51.4870	−1.87133	−0.935664	+	0.352892i	$0.885198\pi$
$758$	47.7219	1.73334
$759$	46.9934	1.70575
$760$	0	0
$761$	35.9275	1.30237	0.651186	−	0.758918i	$-0.274272\pi$
$761$	35.9275	1.30237	0.651186	+	0.758918i	$0.274272\pi$
$762$	29.0616	1.05279
$763$	−3.20086	−0.115879
$764$	−11.1740	−0.404262
$765$	0	0
$766$	−69.1115	−2.49710
$767$	−24.9661	−0.901475
$768$	36.2972	1.30976
$769$	14.5414	0.524376	0.262188	−	0.965017i	$-0.415556\pi$
$769$	14.5414	0.524376	0.262188	+	0.965017i	$0.415556\pi$
$770$	0	0
$771$	−48.2384	−1.73726
$772$	−77.5062	−2.78951
$773$	23.5772	0.848013	0.424006	−	0.905659i	$-0.360623\pi$
$773$	23.5772	0.848013	0.424006	+	0.905659i	$0.360623\pi$
$774$	−3.02685	−0.108798
$775$	0	0
$776$	−13.5864	−0.487723
$777$	2.93779	0.105393
$778$	51.9413	1.86219
$779$	29.6873	1.06366
$780$	0	0
$781$	−84.9058	−3.03817
$782$	11.6632	0.417074
$783$	31.2752	1.11769
$784$	−2.96386	−0.105852
$785$	0	0
$786$	51.5484	1.83867
$787$	35.2557	1.25673	0.628365	−	0.777919i	$-0.283725\pi$
$787$	35.2557	1.25673	0.628365	+	0.777919i	$0.283725\pi$
$788$	10.3355	0.368188
$789$	55.2256	1.96608
$790$	0	0
$791$	5.39210	0.191721
$792$	−13.7319	−0.487941
$793$	44.6900	1.58699
$794$	−4.89370	−0.173671
$795$	0	0
$796$	27.9675	0.991282
$797$	17.4507	0.618137	0.309068	−	0.951040i	$-0.399983\pi$
$797$	17.4507	0.618137	0.309068	+	0.951040i	$0.399983\pi$
$798$	8.69402	0.307765
$799$	7.90750	0.279747
$800$	0	0
$801$	4.86937	0.172051
$802$	56.0515	1.97925
$803$	−38.5080	−1.35892
$804$	83.0976	2.93063
$805$	0	0
$806$	77.8159	2.74095
$807$	30.1248	1.06044
$808$	−25.6998	−0.904116
$809$	41.2844	1.45148	0.725742	−	0.687967i	$-0.241497\pi$
$809$	41.2844	1.45148	0.725742	+	0.687967i	$0.241497\pi$
$810$	0	0
$811$	26.9583	0.946633	0.473317	−	0.880892i	$-0.343057\pi$
$811$	26.9583	0.946633	0.473317	+	0.880892i	$0.343057\pi$
$812$	−7.06597	−0.247967
$813$	46.4370	1.62862
$814$	−68.3592	−2.39599
$815$	0	0
$816$	−0.999522	−0.0349903
$817$	−11.1268	−0.389277
$818$	−9.72944	−0.340182
$819$	1.46212	0.0510906
$820$	0	0
$821$	−0.235283	−0.00821142	−0.00410571	−	0.999992i	$-0.501307\pi$
$821$	−0.235283	−0.00821142	−0.00410571	+	0.999992i	$0.501307\pi$
$822$	43.4405	1.51516
$823$	10.6061	0.369705	0.184853	−	0.982766i	$-0.440819\pi$
$823$	10.6061	0.369705	0.184853	+	0.982766i	$0.440819\pi$
$824$	−50.2187	−1.74945
$825$	0	0
$826$	2.63561	0.0917045
$827$	11.5662	0.402195	0.201098	−	0.979571i	$-0.435549\pi$
$827$	11.5662	0.402195	0.201098	+	0.979571i	$0.435549\pi$
$828$	−10.9295	−0.379826
$829$	40.0901	1.39239	0.696193	−	0.717854i	$-0.254876\pi$
$829$	40.0901	1.39239	0.696193	+	0.717854i	$0.254876\pi$
$830$	0	0
$831$	−55.8789	−1.93842
$832$	81.6709	2.83143
$833$	−8.29309	−0.287339
$834$	6.48982	0.224724
$835$	0	0
$836$	−126.390	−4.37127
$837$	22.7165	0.785196
$838$	91.1815	3.14981
$839$	−50.2055	−1.73329	−0.866643	−	0.498929i	$-0.833727\pi$
$839$	−50.2055	−1.73329	−0.866643	+	0.498929i	$0.833727\pi$
$840$	0	0
$841$	23.4805	0.809673
$842$	−69.2733	−2.38732
$843$	9.78082	0.336869
$844$	0.124346	0.00428018
$845$	0	0
$846$	−11.8606	−0.407777
$847$	−6.42605	−0.220802
$848$	0.413776	0.0142091
$849$	31.9106	1.09517
$850$	0	0
$851$	−21.7302	−0.744902
$852$	95.7692	3.28100
$853$	17.5888	0.602229	0.301115	−	0.953588i	$-0.402641\pi$
$853$	17.5888	0.602229	0.301115	+	0.953588i	$0.402641\pi$
$854$	−4.71780	−0.161440
$855$	0	0
$856$	50.1775	1.71503
$857$	13.2328	0.452024	0.226012	−	0.974125i	$-0.427431\pi$
$857$	13.2328	0.452024	0.226012	+	0.974125i	$0.427431\pi$
$858$	−165.000	−5.63302
$859$	−24.5546	−0.837793	−0.418897	−	0.908034i	$-0.637583\pi$
$859$	−24.5546	−0.837793	−0.418897	+	0.908034i	$0.637583\pi$
$860$	0	0
$861$	−2.55616	−0.0871138
$862$	−92.6612	−3.15605
$863$	−52.6570	−1.79247	−0.896233	−	0.443584i	$-0.853707\pi$
$863$	−52.6570	−1.79247	−0.896233	+	0.443584i	$0.853707\pi$
$864$	22.2387	0.756574
$865$	0	0
$866$	11.7754	0.400145
$867$	30.2518	1.02740
$868$	−5.13230	−0.174202
$869$	65.7194	2.22938
$870$	0	0
$871$	82.2271	2.78616
$872$	−33.5527	−1.13624
$873$	3.44817	0.116703
$874$	−64.3077	−2.17524
$875$	0	0
$876$	43.4350	1.46753
$877$	−27.6387	−0.933293	−0.466646	−	0.884444i	$-0.654538\pi$
$877$	−27.6387	−0.933293	−0.466646	+	0.884444i	$0.654538\pi$
$878$	69.4017	2.34219
$879$	25.1140	0.847074
$880$	0	0
$881$	13.1068	0.441581	0.220790	−	0.975321i	$-0.429136\pi$
$881$	13.1068	0.441581	0.220790	+	0.975321i	$0.429136\pi$
$882$	12.4390	0.418842
$883$	−3.56424	−0.119946	−0.0599731	−	0.998200i	$-0.519101\pi$
$883$	−3.56424	−0.119946	−0.0599731	+	0.998200i	$0.519101\pi$
$884$	−25.5846	−0.860504
$885$	0	0
$886$	6.67443	0.224232
$887$	−14.2749	−0.479303	−0.239652	−	0.970859i	$-0.577033\pi$
$887$	−14.2749	−0.479303	−0.239652	+	0.970859i	$0.577033\pi$
$888$	30.7952	1.03342
$889$	−1.89666	−0.0636120
$890$	0	0
$891$	−61.5848	−2.06317
$892$	61.4558	2.05769
$893$	−43.5999	−1.45902
$894$	−99.5300	−3.32878
$895$	0	0
$896$	−5.60410	−0.187220
$897$	−52.4507	−1.75128
$898$	80.1168	2.67353
$899$	38.1187	1.27133
$900$	0	0
$901$	1.15778	0.0385712
$902$	59.4791	1.98044
$903$	0.958047	0.0318818
$904$	56.5223	1.87990
$905$	0	0
$906$	−7.72027	−0.256489
$907$	54.5912	1.81267	0.906335	−	0.422561i	$-0.138869\pi$
$907$	54.5912	1.81267	0.906335	+	0.422561i	$0.138869\pi$
$908$	88.2804	2.92969
$909$	6.52250	0.216338
$910$	0	0
$911$	−18.5285	−0.613876	−0.306938	−	0.951729i	$-0.599304\pi$
$911$	−18.5285	−0.613876	−0.306938	+	0.951729i	$0.599304\pi$
$912$	5.51111	0.182491
$913$	34.3283	1.13610
$914$	−49.9496	−1.65218
$915$	0	0
$916$	49.2287	1.62656
$917$	−3.36423	−0.111097
$918$	−11.9547	−0.394563
$919$	−19.1843	−0.632833	−0.316416	−	0.948620i	$-0.602480\pi$
$919$	−19.1843	−0.632833	−0.316416	+	0.948620i	$0.602480\pi$
$920$	0	0
$921$	50.7514	1.67231
$922$	50.1804	1.65260
$923$	94.7659	3.11926
$924$	10.8825	0.358008
$925$	0	0
$926$	6.55211	0.215316
$927$	12.7453	0.418610
$928$	37.3169	1.22499
$929$	9.55480	0.313483	0.156741	−	0.987640i	$-0.449901\pi$
$929$	9.55480	0.313483	0.156741	+	0.987640i	$0.449901\pi$
$930$	0	0
$931$	45.7260	1.49861
$932$	27.1196	0.888330
$933$	−37.8299	−1.23849
$934$	3.55558	0.116342
$935$	0	0
$936$	15.3266	0.500964
$937$	−1.85505	−0.0606019	−0.0303010	−	0.999541i	$-0.509647\pi$
$937$	−1.85505	−0.0606019	−0.0303010	+	0.999541i	$0.509647\pi$
$938$	−8.68049	−0.283428
$939$	−58.5057	−1.90926
$940$	0	0
$941$	59.5454	1.94112	0.970562	−	0.240850i	$-0.0774263\pi$
$941$	59.5454	1.94112	0.970562	+	0.240850i	$0.0774263\pi$
$942$	−40.4062	−1.31650
$943$	18.9074	0.615709
$944$	1.67070	0.0543767
$945$	0	0
$946$	−22.2927	−0.724798
$947$	−38.5235	−1.25185	−0.625923	−	0.779885i	$-0.715278\pi$
$947$	−38.5235	−1.25185	−0.625923	+	0.779885i	$0.715278\pi$
$948$	−74.1279	−2.40756
$949$	42.9799	1.39519
$950$	0	0
$951$	−16.6818	−0.540944
$952$	1.07871	0.0349613
$953$	−8.32416	−0.269646	−0.134823	−	0.990870i	$-0.543047\pi$
$953$	−8.32416	−0.269646	−0.134823	+	0.990870i	$0.543047\pi$
$954$	−1.73657	−0.0562237
$955$	0	0
$956$	29.1340	0.942262
$957$	−80.8267	−2.61276
$958$	71.3881	2.30645
$959$	−2.83508	−0.0915495
$960$	0	0
$961$	−3.31280	−0.106864
$962$	76.2978	2.45994
$963$	−12.7348	−0.410374
$964$	3.32995	0.107250
$965$	0	0
$966$	5.53708	0.178153
$967$	−13.5748	−0.436536	−0.218268	−	0.975889i	$-0.570041\pi$
$967$	−13.5748	−0.436536	−0.218268	+	0.975889i	$0.570041\pi$
$968$	−67.3606	−2.16505
$969$	15.4205	0.495378
$970$	0	0
$971$	−42.9847	−1.37944	−0.689722	−	0.724075i	$-0.742267\pi$
$971$	−42.9847	−1.37944	−0.689722	+	0.724075i	$0.742267\pi$
$972$	26.3363	0.844736
$973$	−0.423548	−0.0135783
$974$	45.5556	1.45970
$975$	0	0
$976$	−2.99060	−0.0957267
$977$	−25.2634	−0.808249	−0.404124	−	0.914704i	$-0.632424\pi$
$977$	−25.2634	−0.808249	−0.404124	+	0.914704i	$0.632424\pi$
$978$	25.2859	0.808555
$979$	35.8628	1.14618
$980$	0	0
$981$	8.51555	0.271881
$982$	−46.5071	−1.48410
$983$	−38.3646	−1.22364	−0.611820	−	0.790997i	$-0.709562\pi$
$983$	−38.3646	−1.22364	−0.611820	+	0.790997i	$0.709562\pi$
$984$	−26.7948	−0.854186
$985$	0	0
$986$	−20.0602	−0.638846
$987$	3.75408	0.119494
$988$	141.067	4.48794
$989$	−7.08646	−0.225336
$990$	0	0
$991$	−26.9316	−0.855512	−0.427756	−	0.903894i	$-0.640696\pi$
$991$	−26.9316	−0.855512	−0.427756	+	0.903894i	$0.640696\pi$
$992$	27.1048	0.860579
$993$	−28.6019	−0.907654
$994$	−10.0042	−0.317313
$995$	0	0
$996$	−38.7204	−1.22690
$997$	−50.6621	−1.60448	−0.802242	−	0.596999i	$-0.796360\pi$
$997$	−50.6621	−1.60448	−0.802242	+	0.596999i	$0.796360\pi$
$998$	88.2771	2.79436
$999$	22.2733	0.704696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.m.1.6	✓	40
5.4	even	2		6025.2.a.n.1.35	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.6	✓	40	1.1	even	1	trivial
6025.2.a.n.1.35	yes	40	5.4	even	2

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-2.30867 q^{2} -1.94403 q^{3} +3.32995 q^{4} +4.48812 q^{6} -0.292911 q^{7} -3.07041 q^{8} +0.779258 q^{9} +O(q^{10})\)	\(q-2.30867 q^{2} -1.94403 q^{3} +3.32995 q^{4} +4.48812 q^{6} -0.292911 q^{7} -3.07041 q^{8} +0.779258 q^{9} +5.73922 q^{11} -6.47352 q^{12} -6.40571 q^{13} +0.676233 q^{14} +0.428662 q^{16} +1.19943 q^{17} -1.79905 q^{18} -6.61334 q^{19} +0.569427 q^{21} -13.2499 q^{22} -4.21193 q^{23} +5.96897 q^{24} +14.7887 q^{26} +4.31719 q^{27} -0.975377 q^{28} +7.24434 q^{29} +5.26186 q^{31} +5.15118 q^{32} -11.1572 q^{33} -2.76908 q^{34} +2.59489 q^{36} +5.15921 q^{37} +15.2680 q^{38} +12.4529 q^{39} -4.48901 q^{41} -1.31462 q^{42} +1.68248 q^{43} +19.1113 q^{44} +9.72394 q^{46} +6.59272 q^{47} -0.833332 q^{48} -6.91420 q^{49} -2.33173 q^{51} -21.3307 q^{52} +0.965274 q^{53} -9.96697 q^{54} +0.899356 q^{56} +12.8565 q^{57} -16.7248 q^{58} +3.89748 q^{59} -6.97659 q^{61} -12.1479 q^{62} -0.228253 q^{63} -12.7497 q^{64} +25.7583 q^{66} -12.8365 q^{67} +3.99404 q^{68} +8.18812 q^{69} -14.7940 q^{71} -2.39264 q^{72} -6.70963 q^{73} -11.9109 q^{74} -22.0221 q^{76} -1.68108 q^{77} -28.7496 q^{78} +11.4509 q^{79} -10.7305 q^{81} +10.3636 q^{82} +5.98135 q^{83} +1.89616 q^{84} -3.88428 q^{86} -14.0832 q^{87} -17.6218 q^{88} +6.24872 q^{89} +1.87630 q^{91} -14.0255 q^{92} -10.2292 q^{93} -15.2204 q^{94} -10.0141 q^{96} +4.42495 q^{97} +15.9626 q^{98} +4.47233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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