LMFDB - Embedded newform 1075.6.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.9530 q^{2} -11.8111 q^{3} +87.9689 q^{4} +129.367 q^{6} +32.4628 q^{7} -613.029 q^{8} -103.499 q^{9} +O(q^{10})$	\(q-10.9530 q^{2} -11.8111 q^{3} +87.9689 q^{4} +129.367 q^{6} +32.4628 q^{7} -613.029 q^{8} -103.499 q^{9} +452.701 q^{11} -1039.01 q^{12} +141.862 q^{13} -355.567 q^{14} +3899.52 q^{16} -675.128 q^{17} +1133.63 q^{18} +2391.10 q^{19} -383.420 q^{21} -4958.45 q^{22} +555.813 q^{23} +7240.52 q^{24} -1553.82 q^{26} +4092.52 q^{27} +2855.72 q^{28} +3189.92 q^{29} -5900.16 q^{31} -23094.7 q^{32} -5346.88 q^{33} +7394.70 q^{34} -9104.70 q^{36} -6790.60 q^{37} -26189.7 q^{38} -1675.54 q^{39} +14747.7 q^{41} +4199.61 q^{42} +1849.00 q^{43} +39823.6 q^{44} -6087.84 q^{46} +17582.7 q^{47} -46057.5 q^{48} -15753.2 q^{49} +7973.98 q^{51} +12479.5 q^{52} +6273.29 q^{53} -44825.5 q^{54} -19900.7 q^{56} -28241.4 q^{57} -34939.3 q^{58} +15164.1 q^{59} +12045.2 q^{61} +64624.7 q^{62} -3359.87 q^{63} +128172. q^{64} +58564.6 q^{66} +18311.0 q^{67} -59390.3 q^{68} -6564.74 q^{69} +47273.6 q^{71} +63447.9 q^{72} +10557.7 q^{73} +74377.6 q^{74} +210342. q^{76} +14696.0 q^{77} +18352.3 q^{78} +43451.9 q^{79} -23186.7 q^{81} -161532. q^{82} +89160.0 q^{83} -33729.1 q^{84} -20252.2 q^{86} -37676.3 q^{87} -277519. q^{88} -9801.95 q^{89} +4605.25 q^{91} +48894.3 q^{92} +69687.1 q^{93} -192584. q^{94} +272772. q^{96} -152599. q^{97} +172545. q^{98} -46854.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9}+O(q^{10}) $ 37 * q + 630 * q^4 + 291 * q^6 + 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9} + 675 q^{11} - 4446 q^{12} + 1241 q^{13} + 2375 q^{14} + 10518 q^{16} + 1153 q^{17} - 6680 q^{18} + 4065 q^{19} + 9953 q^{21} + 9283 q^{22} - 360 q^{23} + 2265 q^{24} + 23695 q^{26} + 1323 q^{27} - 30375 q^{28} + 19290 q^{29} + 23291 q^{31} + 8166 q^{32} - 10388 q^{33} - 13153 q^{34} + 148705 q^{36} + 13501 q^{37} - 8127 q^{38} - 1327 q^{39} + 38345 q^{41} - 21835 q^{42} + 68413 q^{43} + 47768 q^{44} + 48755 q^{46} + 84859 q^{47} - 208720 q^{48} + 107255 q^{49} + 62027 q^{51} + 128320 q^{52} - 53559 q^{53} + 44158 q^{54} + 107538 q^{56} + 104239 q^{57} - 85186 q^{58} + 48186 q^{59} + 82364 q^{61} + 206506 q^{62} - 75269 q^{63} + 161467 q^{64} + 91969 q^{66} + 38168 q^{67} + 95991 q^{68} + 287103 q^{69} + 155302 q^{71} + 9979 q^{72} + 31927 q^{73} + 59946 q^{74} + 225407 q^{76} - 80007 q^{77} - 67815 q^{78} + 150174 q^{79} + 417489 q^{81} + 60603 q^{82} + 266568 q^{83} + 586273 q^{84} - 57554 q^{87} + 323054 q^{88} + 334356 q^{89} + 51747 q^{91} - 258529 q^{92} - 285287 q^{93} + 302744 q^{94} + 287282 q^{96} - 78640 q^{97} - 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 + 213 * q^8 + 3535 * q^9 + 675 * q^11 - 4446 * q^12 + 1241 * q^13 + 2375 * q^14 + 10518 * q^16 + 1153 * q^17 - 6680 * q^18 + 4065 * q^19 + 9953 * q^21 + 9283 * q^22 - 360 * q^23 + 2265 * q^24 + 23695 * q^26 + 1323 * q^27 - 30375 * q^28 + 19290 * q^29 + 23291 * q^31 + 8166 * q^32 - 10388 * q^33 - 13153 * q^34 + 148705 * q^36 + 13501 * q^37 - 8127 * q^38 - 1327 * q^39 + 38345 * q^41 - 21835 * q^42 + 68413 * q^43 + 47768 * q^44 + 48755 * q^46 + 84859 * q^47 - 208720 * q^48 + 107255 * q^49 + 62027 * q^51 + 128320 * q^52 - 53559 * q^53 + 44158 * q^54 + 107538 * q^56 + 104239 * q^57 - 85186 * q^58 + 48186 * q^59 + 82364 * q^61 + 206506 * q^62 - 75269 * q^63 + 161467 * q^64 + 91969 * q^66 + 38168 * q^67 + 95991 * q^68 + 287103 * q^69 + 155302 * q^71 + 9979 * q^72 + 31927 * q^73 + 59946 * q^74 + 225407 * q^76 - 80007 * q^77 - 67815 * q^78 + 150174 * q^79 + 417489 * q^81 + 60603 * q^82 + 266568 * q^83 + 586273 * q^84 - 57554 * q^87 + 323054 * q^88 + 334356 * q^89 + 51747 * q^91 - 258529 * q^92 - 285287 * q^93 + 302744 * q^94 + 287282 * q^96 - 78640 * q^97 - 397117 * q^98 + 362152 * 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 $

$2$	−10.9530	−1.93624	−0.968120	−	0.250486i	$-0.919410\pi$
$2$	−10.9530	−1.93624	−0.968120	+	0.250486i	$0.919410\pi$
$3$	−11.8111	−0.757679	−0.378840	−	0.925462i	$-0.623677\pi$
$3$	−11.8111	−0.757679	−0.378840	+	0.925462i	$0.623677\pi$
$4$	87.9689	2.74903
$5$	0	0
$5$	0	0
$6$	129.367	1.46705
$7$	32.4628	0.250404	0.125202	−	0.992131i	$-0.460042\pi$
$7$	32.4628	0.250404	0.125202	+	0.992131i	$0.460042\pi$
$8$	−613.029	−3.38654
$9$	−103.499	−0.425922
$10$	0	0
$11$	452.701	1.12805	0.564027	−	0.825756i	$-0.309251\pi$
$11$	452.701	1.12805	0.564027	+	0.825756i	$0.309251\pi$
$12$	−1039.01	−2.08288
$13$	141.862	0.232814	0.116407	−	0.993202i	$-0.462862\pi$
$13$	141.862	0.232814	0.116407	+	0.993202i	$0.462862\pi$
$14$	−355.567	−0.484843
$15$	0	0
$16$	3899.52	3.80813
$17$	−675.128	−0.566584	−0.283292	−	0.959034i	$-0.591427\pi$
$17$	−675.128	−0.566584	−0.283292	+	0.959034i	$0.591427\pi$
$18$	1133.63	0.824687
$19$	2391.10	1.51954	0.759771	−	0.650190i	$-0.225311\pi$
$19$	2391.10	1.51954	0.759771	+	0.650190i	$0.225311\pi$
$20$	0	0
$21$	−383.420	−0.189726
$22$	−4958.45	−2.18419
$23$	555.813	0.219083	0.109542	−	0.993982i	$-0.465062\pi$
$23$	555.813	0.219083	0.109542	+	0.993982i	$0.465062\pi$
$24$	7240.52	2.56591
$25$	0	0
$26$	−1553.82	−0.450783
$27$	4092.52	1.08039
$28$	2855.72	0.688368
$29$	3189.92	0.704344	0.352172	−	0.935935i	$-0.385443\pi$
$29$	3189.92	0.704344	0.352172	+	0.935935i	$0.385443\pi$
$30$	0	0
$31$	−5900.16	−1.10271	−0.551353	−	0.834272i	$-0.685888\pi$
$31$	−5900.16	−1.10271	−0.551353	+	0.834272i	$0.685888\pi$
$32$	−23094.7	−3.98691
$33$	−5346.88	−0.854704
$34$	7394.70	1.09704
$35$	0	0
$36$	−9104.70	−1.17087
$37$	−6790.60	−0.815462	−0.407731	−	0.913102i	$-0.633680\pi$
$37$	−6790.60	−0.815462	−0.407731	+	0.913102i	$0.633680\pi$
$38$	−26189.7	−2.94220
$39$	−1675.54	−0.176398
$40$	0	0
$41$	14747.7	1.37014	0.685069	−	0.728478i	$-0.259772\pi$
$41$	14747.7	1.37014	0.685069	+	0.728478i	$0.259772\pi$
$42$	4199.61	0.367355
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	39823.6	3.10105
$45$	0	0
$46$	−6087.84	−0.424198
$47$	17582.7	1.16103	0.580513	−	0.814251i	$-0.302852\pi$
$47$	17582.7	1.16103	0.580513	+	0.814251i	$0.302852\pi$
$48$	−46057.5	−2.88534
$49$	−15753.2	−0.937298
$50$	0	0
$51$	7973.98	0.429289
$52$	12479.5	0.640011
$53$	6273.29	0.306765	0.153382	−	0.988167i	$-0.450983\pi$
$53$	6273.29	0.306765	0.153382	+	0.988167i	$0.450983\pi$
$54$	−44825.5	−2.09190
$55$	0	0
$56$	−19900.7	−0.848003
$57$	−28241.4	−1.15133
$58$	−34939.3	−1.36378
$59$	15164.1	0.567134	0.283567	−	0.958952i	$-0.408482\pi$
$59$	15164.1	0.567134	0.283567	+	0.958952i	$0.408482\pi$
$60$	0	0
$61$	12045.2	0.414467	0.207233	−	0.978292i	$-0.433554\pi$
$61$	12045.2	0.414467	0.207233	+	0.978292i	$0.433554\pi$
$62$	64624.7	2.13510
$63$	−3359.87	−0.106653
$64$	128172.	3.91149
$65$	0	0
$66$	58564.6	1.65491
$67$	18311.0	0.498340	0.249170	−	0.968460i	$-0.419842\pi$
$67$	18311.0	0.498340	0.249170	+	0.968460i	$0.419842\pi$
$68$	−59390.3	−1.55755
$69$	−6564.74	−0.165995
$70$	0	0
$71$	47273.6	1.11294	0.556471	−	0.830867i	$-0.312155\pi$
$71$	47273.6	1.11294	0.556471	+	0.830867i	$0.312155\pi$
$72$	63447.9	1.44240
$73$	10557.7	0.231880	0.115940	−	0.993256i	$-0.463012\pi$
$73$	10557.7	0.231880	0.115940	+	0.993256i	$0.463012\pi$
$74$	74377.6	1.57893
$75$	0	0
$76$	210342.	4.17727
$77$	14696.0	0.282470
$78$	18352.3	0.341549
$79$	43451.9	0.783324	0.391662	−	0.920109i	$-0.371900\pi$
$79$	43451.9	0.783324	0.391662	+	0.920109i	$0.371900\pi$
$80$	0	0
$81$	−23186.7	−0.392669
$82$	−161532.	−2.65292
$83$	89160.0	1.42061	0.710305	−	0.703894i	$-0.248557\pi$
$83$	89160.0	1.42061	0.710305	+	0.703894i	$0.248557\pi$
$84$	−33729.1	−0.521562
$85$	0	0
$86$	−20252.2	−0.295274
$87$	−37676.3	−0.533667
$88$	−277519.	−3.82020
$89$	−9801.95	−0.131171	−0.0655855	−	0.997847i	$-0.520891\pi$
$89$	−9801.95	−0.131171	−0.0655855	+	0.997847i	$0.520891\pi$
$90$	0	0
$91$	4605.25	0.0582975
$92$	48894.3	0.602266
$93$	69687.1	0.835498
$94$	−192584.	−2.24802
$95$	0	0
$96$	272772.	3.02080
$97$	−152599.	−1.64673	−0.823366	−	0.567510i	$-0.807907\pi$
$97$	−152599.	−1.64673	−0.823366	+	0.567510i	$0.807907\pi$
$98$	172545.	1.81483
$99$	−46854.2	−0.480463
$100$	0	0
$101$	144477.	1.40928	0.704639	−	0.709566i	$-0.251109\pi$
$101$	144477.	1.40928	0.704639	+	0.709566i	$0.251109\pi$
$102$	−87339.2	−0.831206
$103$	−50524.7	−0.469257	−0.234629	−	0.972085i	$-0.575387\pi$
$103$	−50524.7	−0.469257	−0.234629	+	0.972085i	$0.575387\pi$
$104$	−86965.6	−0.788432
$105$	0	0
$106$	−68711.5	−0.593971
$107$	152991.	1.29183	0.645915	−	0.763410i	$-0.276476\pi$
$107$	152991.	1.29183	0.645915	+	0.763410i	$0.276476\pi$
$108$	360014.	2.97003
$109$	64230.0	0.517811	0.258906	−	0.965903i	$-0.416638\pi$
$109$	64230.0	0.517811	0.258906	+	0.965903i	$0.416638\pi$
$110$	0	0
$111$	80204.1	0.617859
$112$	126590.	0.953570
$113$	−201987.	−1.48809	−0.744043	−	0.668131i	$-0.767094\pi$
$113$	−201987.	−1.48809	−0.744043	+	0.668131i	$0.767094\pi$
$114$	309328.	2.22924
$115$	0	0
$116$	280614.	1.93626
$117$	−14682.6	−0.0991604
$118$	−166092.	−1.09811
$119$	−21916.6	−0.141875
$120$	0	0
$121$	43887.6	0.272508
$122$	−131932.	−0.802507
$123$	−174186.	−1.03813
$124$	−519031.	−3.03137
$125$	0	0
$126$	36800.8	0.206505
$127$	200022.	1.10045	0.550223	−	0.835018i	$-0.314543\pi$
$127$	200022.	1.10045	0.550223	+	0.835018i	$0.314543\pi$
$128$	−664840.	−3.58668
$129$	−21838.6	−0.115545
$130$	0	0
$131$	−56371.2	−0.286998	−0.143499	−	0.989650i	$-0.545835\pi$
$131$	−56371.2	−0.286998	−0.143499	+	0.989650i	$0.545835\pi$
$132$	−470359.	−2.34960
$133$	77621.7	0.380500
$134$	−200561.	−0.964906
$135$	0	0
$136$	413873.	1.91876
$137$	124783.	0.568007	0.284003	−	0.958823i	$-0.408337\pi$
$137$	124783.	0.568007	0.284003	+	0.958823i	$0.408337\pi$
$138$	71903.8	0.321406
$139$	−86274.1	−0.378742	−0.189371	−	0.981906i	$-0.560645\pi$
$139$	−86274.1	−0.378742	−0.189371	+	0.981906i	$0.560645\pi$
$140$	0	0
$141$	−207671.	−0.879685
$142$	−517789.	−2.15492
$143$	64221.2	0.262626
$144$	−403597.	−1.62196
$145$	0	0
$146$	−115639.	−0.448976
$147$	186061.	0.710171
$148$	−597361.	−2.24173
$149$	−284788.	−1.05089	−0.525443	−	0.850829i	$-0.676100\pi$
$149$	−284788.	−1.05089	−0.525443	+	0.850829i	$0.676100\pi$
$150$	0	0
$151$	−253148.	−0.903510	−0.451755	−	0.892142i	$-0.649202\pi$
$151$	−253148.	−0.903510	−0.451755	+	0.892142i	$0.649202\pi$
$152$	−1.46581e6	−5.14599
$153$	69875.1	0.241320
$154$	−160965.	−0.546929
$155$	0	0
$156$	−147396.	−0.484923
$157$	−516943.	−1.67376	−0.836881	−	0.547384i	$-0.815624\pi$
$157$	−516943.	−1.67376	−0.836881	+	0.547384i	$0.815624\pi$
$158$	−475930.	−1.51670
$159$	−74094.1	−0.232429
$160$	0	0
$161$	18043.3	0.0548593
$162$	253964.	0.760301
$163$	63152.7	0.186176	0.0930878	−	0.995658i	$-0.470326\pi$
$163$	63152.7	0.186176	0.0930878	+	0.995658i	$0.470326\pi$
$164$	1.29734e6	3.76655
$165$	0	0
$166$	−976572.	−2.75064
$167$	338435.	0.939039	0.469520	−	0.882922i	$-0.344427\pi$
$167$	338435.	0.939039	0.469520	+	0.882922i	$0.344427\pi$
$168$	235048.	0.642515
$169$	−351168.	−0.945798
$170$	0	0
$171$	−247476.	−0.647207
$172$	162654.	0.419223
$173$	−566092.	−1.43804	−0.719021	−	0.694988i	$-0.755410\pi$
$173$	−566092.	−1.43804	−0.719021	+	0.694988i	$0.755410\pi$
$174$	412670.	1.03331
$175$	0	0
$176$	1.76532e6	4.29578
$177$	−179103.	−0.429705
$178$	107361.	0.253978
$179$	−634.527	−0.00148019	−0.000740095	−	1.00000i	$-0.500236\pi$
$179$	−634.527	−0.00148019	−0.000740095		1.00000i	$0.500236\pi$
$180$	0	0
$181$	−133359.	−0.302571	−0.151285	−	0.988490i	$-0.548341\pi$
$181$	−133359.	−0.302571	−0.151285	+	0.988490i	$0.548341\pi$
$182$	−50441.4	−0.112878
$183$	−142267.	−0.314033
$184$	−340730.	−0.741934
$185$	0	0
$186$	−763285.	−1.61772
$187$	−305632.	−0.639137
$188$	1.54673e6	3.19169
$189$	132855.	0.270534
$190$	0	0
$191$	−529068.	−1.04937	−0.524684	−	0.851297i	$-0.675817\pi$
$191$	−529068.	−1.04937	−0.524684	+	0.851297i	$0.675817\pi$
$192$	−1.51384e6	−2.96366
$193$	719259.	1.38993	0.694964	−	0.719045i	$-0.255420\pi$
$193$	719259.	1.38993	0.694964	+	0.719045i	$0.255420\pi$
$194$	1.67142e6	3.18847
$195$	0	0
$196$	−1.38579e6	−2.57666
$197$	−293875.	−0.539506	−0.269753	−	0.962929i	$-0.586942\pi$
$197$	−293875.	−0.539506	−0.269753	+	0.962929i	$0.586942\pi$
$198$	513195.	0.930293
$199$	−431142.	−0.771770	−0.385885	−	0.922547i	$-0.626104\pi$
$199$	−431142.	−0.771770	−0.385885	+	0.922547i	$0.626104\pi$
$200$	0	0
$201$	−216273.	−0.377582
$202$	−1.58247e6	−2.72870
$203$	103554.	0.176371
$204$	701462.	1.18013
$205$	0	0
$206$	553399.	0.908595
$207$	−57526.1	−0.0933124
$208$	553195.	0.886583
$209$	1.08245e6	1.71413
$210$	0	0
$211$	361014.	0.558236	0.279118	−	0.960257i	$-0.409958\pi$
$211$	361014.	0.558236	0.279118	+	0.960257i	$0.409958\pi$
$212$	551854.	0.843305
$213$	−558351.	−0.843253
$214$	−1.67571e6	−2.50129
$215$	0	0
$216$	−2.50883e6	−3.65879
$217$	−191536.	−0.276122
$218$	−703513.	−1.00261
$219$	−124698.	−0.175691
$220$	0	0
$221$	−95775.2	−0.131908
$222$	−878478.	−1.19632
$223$	1.29281e6	1.74089	0.870446	−	0.492264i	$-0.163831\pi$
$223$	1.29281e6	1.74089	0.870446	+	0.492264i	$0.163831\pi$
$224$	−749718.	−0.998339
$225$	0	0
$226$	2.21237e6	2.88129
$227$	−671509.	−0.864942	−0.432471	−	0.901648i	$-0.642358\pi$
$227$	−671509.	−0.864942	−0.432471	+	0.901648i	$0.642358\pi$
$228$	−2.48436e6	−3.16503
$229$	−1.28271e6	−1.61636	−0.808181	−	0.588934i	$-0.799548\pi$
$229$	−1.28271e6	−1.61636	−0.808181	+	0.588934i	$0.799548\pi$
$230$	0	0
$231$	−173575.	−0.214021
$232$	−1.95551e6	−2.38529
$233$	1.22192e6	1.47452	0.737262	−	0.675606i	$-0.236118\pi$
$233$	1.22192e6	1.47452	0.737262	+	0.675606i	$0.236118\pi$
$234$	160819.	0.191998
$235$	0	0
$236$	1.33397e6	1.55907
$237$	−513213.	−0.593508
$238$	240053.	0.274704
$239$	−1.14477e6	−1.29635	−0.648177	−	0.761490i	$-0.724468\pi$
$239$	−1.14477e6	−1.29635	−0.648177	+	0.761490i	$0.724468\pi$
$240$	0	0
$241$	1.39991e6	1.55259	0.776295	−	0.630369i	$-0.217097\pi$
$241$	1.39991e6	1.55259	0.776295	+	0.630369i	$0.217097\pi$
$242$	−480703.	−0.527640
$243$	−720623.	−0.782875
$244$	1.05960e6	1.13938
$245$	0	0
$246$	1.90786e6	2.01006
$247$	339206.	0.353770
$248$	3.61697e6	3.73436
$249$	−1.05307e6	−1.07637
$250$	0	0
$251$	194616.	0.194981	0.0974907	−	0.995236i	$-0.468918\pi$
$251$	194616.	0.194981	0.0974907	+	0.995236i	$0.468918\pi$
$252$	−295564.	−0.293191
$253$	251617.	0.247138
$254$	−2.19085e6	−2.13073
$255$	0	0
$256$	3.18052e6	3.03318
$257$	1.10302e6	1.04172	0.520858	−	0.853643i	$-0.325612\pi$
$257$	1.10302e6	1.04172	0.520858	+	0.853643i	$0.325612\pi$
$258$	239199.	0.223723
$259$	−220442.	−0.204195
$260$	0	0
$261$	−330154.	−0.299996
$262$	617436.	0.555698
$263$	1.66413e6	1.48354	0.741768	−	0.670657i	$-0.233988\pi$
$263$	1.66413e6	1.48354	0.741768	+	0.670657i	$0.233988\pi$
$264$	3.27779e6	2.89449
$265$	0	0
$266$	−850193.	−0.736739
$267$	115771.	0.0993855
$268$	1.61080e6	1.36995
$269$	−1.96434e6	−1.65515	−0.827573	−	0.561358i	$-0.810279\pi$
$269$	−1.96434e6	−1.65515	−0.827573	+	0.561358i	$0.810279\pi$
$270$	0	0
$271$	336220.	0.278099	0.139050	−	0.990285i	$-0.455595\pi$
$271$	336220.	0.278099	0.139050	+	0.990285i	$0.455595\pi$
$272$	−2.63268e6	−2.15762
$273$	−54392.8	−0.0441708
$274$	−1.36675e6	−1.09980
$275$	0	0
$276$	−577493.	−0.456324
$277$	−690656.	−0.540832	−0.270416	−	0.962744i	$-0.587161\pi$
$277$	−690656.	−0.540832	−0.270416	+	0.962744i	$0.587161\pi$
$278$	944963.	0.733336
$279$	610661.	0.469667
$280$	0	0
$281$	−2.29589e6	−1.73455	−0.867273	−	0.497833i	$-0.834129\pi$
$281$	−2.29589e6	−1.73455	−0.867273	+	0.497833i	$0.834129\pi$
$282$	2.27462e6	1.70328
$283$	1.31466e6	0.975767	0.487883	−	0.872909i	$-0.337769\pi$
$283$	1.31466e6	0.975767	0.487883	+	0.872909i	$0.337769\pi$
$284$	4.15860e6	3.05951
$285$	0	0
$286$	−703417.	−0.508508
$287$	478752.	0.343088
$288$	2.39027e6	1.69811
$289$	−964059.	−0.678983
$290$	0	0
$291$	1.80236e6	1.24770
$292$	928753.	0.637446
$293$	−640327.	−0.435745	−0.217873	−	0.975977i	$-0.569912\pi$
$293$	−640327.	−0.435745	−0.217873	+	0.975977i	$0.569912\pi$
$294$	−2.03794e6	−1.37506
$295$	0	0
$296$	4.16283e6	2.76159
$297$	1.85269e6	1.21874
$298$	3.11929e6	2.03477
$299$	78848.8	0.0510055
$300$	0	0
$301$	60023.8	0.0381863
$302$	2.77274e6	1.74941
$303$	−1.70643e6	−1.06778
$304$	9.32413e6	5.78661
$305$	0	0
$306$	−765345.	−0.467254
$307$	−418147.	−0.253211	−0.126606	−	0.991953i	$-0.540408\pi$
$307$	−418147.	−0.253211	−0.126606	+	0.991953i	$0.540408\pi$
$308$	1.29279e6	0.776517
$309$	596750.	0.355546
$310$	0	0
$311$	1.88375e6	1.10439	0.552195	−	0.833715i	$-0.313790\pi$
$311$	1.88375e6	1.10439	0.552195	+	0.833715i	$0.313790\pi$
$312$	1.02716e6	0.597379
$313$	492899.	0.284379	0.142189	−	0.989839i	$-0.454586\pi$
$313$	492899.	0.284379	0.142189	+	0.989839i	$0.454586\pi$
$314$	5.66210e6	3.24081
$315$	0	0
$316$	3.82242e6	2.15338
$317$	−1.01308e6	−0.566232	−0.283116	−	0.959086i	$-0.591368\pi$
$317$	−1.01308e6	−0.566232	−0.283116	+	0.959086i	$0.591368\pi$
$318$	811555.	0.450039
$319$	1.44408e6	0.794539
$320$	0	0
$321$	−1.80698e6	−0.978792
$322$	−197628.	−0.106221
$323$	−1.61430e6	−0.860948
$324$	−2.03971e6	−1.07946
$325$	0	0
$326$	−691713.	−0.360481
$327$	−758624.	−0.392335
$328$	−9.04076e6	−4.64003
$329$	570785.	0.290725
$330$	0	0
$331$	−368396.	−0.184818	−0.0924090	−	0.995721i	$-0.529457\pi$
$331$	−368396.	−0.184818	−0.0924090	+	0.995721i	$0.529457\pi$
$332$	7.84330e6	3.90529
$333$	702820.	0.347323
$334$	−3.70689e6	−1.81821
$335$	0	0
$336$	−1.49516e6	−0.722501
$337$	−2.13234e6	−1.02278	−0.511390	−	0.859349i	$-0.670869\pi$
$337$	−2.13234e6	−1.02278	−0.511390	+	0.859349i	$0.670869\pi$
$338$	3.84636e6	1.83129
$339$	2.38568e6	1.12749
$340$	0	0
$341$	−2.67101e6	−1.24391
$342$	2.71061e6	1.25315
$343$	−1.05700e6	−0.485107
$344$	−1.13349e6	−0.516442
$345$	0	0
$346$	6.20042e6	2.78440
$347$	−907976.	−0.404810	−0.202405	−	0.979302i	$-0.564876\pi$
$347$	−907976.	−0.404810	−0.202405	+	0.979302i	$0.564876\pi$
$348$	−3.31434e6	−1.46707
$349$	−813004.	−0.357297	−0.178648	−	0.983913i	$-0.557172\pi$
$349$	−813004.	−0.357297	−0.178648	+	0.983913i	$0.557172\pi$
$350$	0	0
$351$	580574.	0.251530
$352$	−1.04550e7	−4.49745
$353$	648459.	0.276978	0.138489	−	0.990364i	$-0.455775\pi$
$353$	648459.	0.276978	0.138489	+	0.990364i	$0.455775\pi$
$354$	1.96173e6	0.832013
$355$	0	0
$356$	−862267.	−0.360593
$357$	258858.	0.107496
$358$	6949.99	0.00286600
$359$	3.93838e6	1.61281	0.806403	−	0.591367i	$-0.201411\pi$
$359$	3.93838e6	1.61281	0.806403	+	0.591367i	$0.201411\pi$
$360$	0	0
$361$	3.24124e6	1.30901
$362$	1.46069e6	0.585850
$363$	−518359.	−0.206473
$364$	405119.	0.160261
$365$	0	0
$366$	1.55825e6	0.608043
$367$	125166.	0.0485090	0.0242545	−	0.999706i	$-0.492279\pi$
$367$	125166.	0.0485090	0.0242545	+	0.999706i	$0.492279\pi$
$368$	2.16740e6	0.834297
$369$	−1.52637e6	−0.583572
$370$	0	0
$371$	203649.	0.0768152
$372$	6.13030e6	2.29681
$373$	−2.56923e6	−0.956160	−0.478080	−	0.878316i	$-0.658667\pi$
$373$	−2.56923e6	−0.956160	−0.478080	+	0.878316i	$0.658667\pi$
$374$	3.34759e6	1.23752
$375$	0	0
$376$	−1.07787e7	−3.93186
$377$	452529.	0.163981
$378$	−1.45516e6	−0.523820
$379$	71988.3	0.0257433	0.0128716	−	0.999917i	$-0.495903\pi$
$379$	71988.3	0.0257433	0.0128716	+	0.999917i	$0.495903\pi$
$380$	0	0
$381$	−2.36247e6	−0.833785
$382$	5.79490e6	2.03183
$383$	1.87160e6	0.651952	0.325976	−	0.945378i	$-0.394307\pi$
$383$	1.87160e6	0.651952	0.325976	+	0.945378i	$0.394307\pi$
$384$	7.85247e6	2.71755
$385$	0	0
$386$	−7.87807e6	−2.69123
$387$	−191370.	−0.0649525
$388$	−1.34240e7	−4.52691
$389$	−4.55451e6	−1.52605	−0.763023	−	0.646371i	$-0.776286\pi$
$389$	−4.55451e6	−1.52605	−0.763023	+	0.646371i	$0.776286\pi$
$390$	0	0
$391$	−375245.	−0.124129
$392$	9.65715e6	3.17420
$393$	665803.	0.217453
$394$	3.21882e6	1.04461
$395$	0	0
$396$	−4.12171e6	−1.32081
$397$	4.30687e6	1.37147	0.685734	−	0.727852i	$-0.259481\pi$
$397$	4.30687e6	1.37147	0.685734	+	0.727852i	$0.259481\pi$
$398$	4.72232e6	1.49433
$399$	−916795.	−0.288297
$400$	0	0
$401$	−103280.	−0.0320742	−0.0160371	−	0.999871i	$-0.505105\pi$
$401$	−103280.	−0.0320742	−0.0160371	+	0.999871i	$0.505105\pi$
$402$	2.36884e6	0.731089
$403$	−837010.	−0.256725
$404$	1.27095e7	3.87414
$405$	0	0
$406$	−1.13423e6	−0.341496
$407$	−3.07411e6	−0.919886
$408$	−4.88828e6	−1.45380
$409$	−5.67006e6	−1.67602	−0.838011	−	0.545653i	$-0.816282\pi$
$409$	−5.67006e6	−1.67602	−0.838011	+	0.545653i	$0.816282\pi$
$410$	0	0
$411$	−1.47382e6	−0.430367
$412$	−4.44460e6	−1.29000
$413$	492268.	0.142013
$414$	630085.	0.180675
$415$	0	0
$416$	−3.27626e6	−0.928207
$417$	1.01899e6	0.286965
$418$	−1.18561e7	−3.31896
$419$	−2.91429e6	−0.810958	−0.405479	−	0.914104i	$-0.632895\pi$
$419$	−2.91429e6	−0.810958	−0.405479	+	0.914104i	$0.632895\pi$
$420$	0	0
$421$	6.46477e6	1.77766	0.888829	−	0.458240i	$-0.151520\pi$
$421$	6.46477e6	1.77766	0.888829	+	0.458240i	$0.151520\pi$
$422$	−3.95420e6	−1.08088
$423$	−1.81980e6	−0.494506
$424$	−3.84571e6	−1.03887
$425$	0	0
$426$	6.11563e6	1.63274
$427$	391022.	0.103784
$428$	1.34584e7	3.55127
$429$	−758520.	−0.198987
$430$	0	0
$431$	4.97112e6	1.28903	0.644513	−	0.764594i	$-0.277060\pi$
$431$	4.97112e6	1.28903	0.644513	+	0.764594i	$0.277060\pi$
$432$	1.59589e7	4.11427
$433$	435836.	0.111713	0.0558564	−	0.998439i	$-0.482211\pi$
$433$	435836.	0.111713	0.0558564	+	0.998439i	$0.482211\pi$
$434$	2.09790e6	0.534639
$435$	0	0
$436$	5.65024e6	1.42348
$437$	1.32900e6	0.332906
$438$	1.36582e6	0.340180
$439$	1.90833e6	0.472599	0.236299	−	0.971680i	$-0.424065\pi$
$439$	1.90833e6	0.472599	0.236299	+	0.971680i	$0.424065\pi$
$440$	0	0
$441$	1.63044e6	0.399216
$442$	1.04903e6	0.255406
$443$	3.50670e6	0.848965	0.424483	−	0.905436i	$-0.360456\pi$
$443$	3.50670e6	0.848965	0.424483	+	0.905436i	$0.360456\pi$
$444$	7.05547e6	1.69851
$445$	0	0
$446$	−1.41602e7	−3.37079
$447$	3.36364e6	0.796234
$448$	4.16082e6	0.979454
$449$	−1.75532e6	−0.410903	−0.205452	−	0.978667i	$-0.565866\pi$
$449$	−1.75532e6	−0.410903	−0.205452	+	0.978667i	$0.565866\pi$
$450$	0	0
$451$	6.67630e6	1.54559
$452$	−1.77686e7	−4.09079
$453$	2.98995e6	0.684571
$454$	7.35506e6	1.67474
$455$	0	0
$456$	1.73128e7	3.89901
$457$	−5.98014e6	−1.33943	−0.669716	−	0.742617i	$-0.733584\pi$
$457$	−5.98014e6	−1.33943	−0.669716	+	0.742617i	$0.733584\pi$
$458$	1.40495e7	3.12967
$459$	−2.76298e6	−0.612132
$460$	0	0
$461$	4.63238e6	1.01520	0.507601	−	0.861592i	$-0.330532\pi$
$461$	4.63238e6	1.01520	0.507601	+	0.861592i	$0.330532\pi$
$462$	1.90117e6	0.414397
$463$	−816087.	−0.176923	−0.0884614	−	0.996080i	$-0.528195\pi$
$463$	−816087.	−0.176923	−0.0884614	+	0.996080i	$0.528195\pi$
$464$	1.24392e7	2.68223
$465$	0	0
$466$	−1.33837e7	−2.85504
$467$	5.63092e6	1.19478	0.597389	−	0.801952i	$-0.296205\pi$
$467$	5.63092e6	1.19478	0.597389	+	0.801952i	$0.296205\pi$
$468$	−1.29161e6	−0.272595
$469$	594428.	0.124786
$470$	0	0
$471$	6.10565e6	1.26818
$472$	−9.29601e6	−1.92062
$473$	837045.	0.172027
$474$	5.62124e6	1.14918
$475$	0	0
$476$	−1.92798e6	−0.390018
$477$	−649279.	−0.130658
$478$	1.25387e7	2.51005
$479$	2.22103e6	0.442298	0.221149	−	0.975240i	$-0.429019\pi$
$479$	2.22103e6	0.442298	0.221149	+	0.975240i	$0.429019\pi$
$480$	0	0
$481$	−963329.	−0.189851
$482$	−1.53332e7	−3.00619
$483$	−213110.	−0.0415658
$484$	3.86075e6	0.749131
$485$	0	0
$486$	7.89300e6	1.51583
$487$	4.71811e6	0.901459	0.450729	−	0.892661i	$-0.351164\pi$
$487$	4.71811e6	0.901459	0.450729	+	0.892661i	$0.351164\pi$
$488$	−7.38406e6	−1.40361
$489$	−745900.	−0.141061
$490$	0	0
$491$	−5.46177e6	−1.02242	−0.511211	−	0.859455i	$-0.670803\pi$
$491$	−5.46177e6	−1.02242	−0.511211	+	0.859455i	$0.670803\pi$
$492$	−1.53229e7	−2.85384
$493$	−2.15361e6	−0.399070
$494$	−3.71533e6	−0.684984
$495$	0	0
$496$	−2.30078e7	−4.19924
$497$	1.53463e6	0.278685
$498$	1.15343e7	2.08410
$499$	809679.	0.145567	0.0727833	−	0.997348i	$-0.476812\pi$
$499$	809679.	0.145567	0.0727833	+	0.997348i	$0.476812\pi$
$500$	0	0
$501$	−3.99727e6	−0.711491
$502$	−2.13163e6	−0.377531
$503$	−481660.	−0.0848829	−0.0424415	−	0.999099i	$-0.513514\pi$
$503$	−481660.	−0.0848829	−0.0424415	+	0.999099i	$0.513514\pi$
$504$	2.05970e6	0.361183
$505$	0	0
$506$	−2.75597e6	−0.478518
$507$	4.14767e6	0.716612
$508$	1.75957e7	3.02516
$509$	1.09462e6	0.187271	0.0936354	−	0.995607i	$-0.470151\pi$
$509$	1.09462e6	0.187271	0.0936354	+	0.995607i	$0.470151\pi$
$510$	0	0
$511$	342734.	0.0580638
$512$	−1.35615e7	−2.28629
$513$	9.78560e6	1.64170
$514$	−1.20814e7	−2.01701
$515$	0	0
$516$	−1.92112e6	−0.317636
$517$	7.95973e6	1.30970
$518$	2.41451e6	0.395371
$519$	6.68614e6	1.08958
$520$	0	0
$521$	2.03292e6	0.328114	0.164057	−	0.986451i	$-0.447542\pi$
$521$	2.03292e6	0.328114	0.164057	+	0.986451i	$0.447542\pi$
$522$	3.61618e6	0.580864
$523$	8.18716e6	1.30882	0.654408	−	0.756141i	$-0.272918\pi$
$523$	8.18716e6	1.30882	0.654408	+	0.756141i	$0.272918\pi$
$524$	−4.95891e6	−0.788966
$525$	0	0
$526$	−1.82273e7	−2.87248
$527$	3.98337e6	0.624775
$528$	−2.08503e7	−3.25482
$529$	−6.12741e6	−0.952003
$530$	0	0
$531$	−1.56947e6	−0.241555
$532$	6.82830e6	1.04600
$533$	2.09214e6	0.318987
$534$	−1.26805e6	−0.192434
$535$	0	0
$536$	−1.12252e7	−1.68765
$537$	7494.43	0.00112151
$538$	2.15155e7	3.20476
$539$	−7.13148e6	−1.05732
$540$	0	0
$541$	1.31163e7	1.92671	0.963356	−	0.268226i	$-0.0864375\pi$
$541$	1.31163e7	1.92671	0.963356	+	0.268226i	$0.0864375\pi$
$542$	−3.68263e6	−0.538467
$543$	1.57512e6	0.229252
$544$	1.55919e7	2.25892
$545$	0	0
$546$	595766.	0.0855253
$547$	−500718.	−0.0715525	−0.0357763	−	0.999360i	$-0.511390\pi$
$547$	−500718.	−0.0715525	−0.0357763	+	0.999360i	$0.511390\pi$
$548$	1.09770e7	1.56147
$549$	−1.24667e6	−0.176530
$550$	0	0
$551$	7.62740e6	1.07028
$552$	4.02437e6	0.562148
$553$	1.41057e6	0.196148
$554$	7.56477e6	1.04718
$555$	0	0
$556$	−7.58944e6	−1.04117
$557$	1.12017e7	1.52984	0.764919	−	0.644126i	$-0.222779\pi$
$557$	1.12017e7	1.52984	0.764919	+	0.644126i	$0.222779\pi$
$558$	−6.68859e6	−0.909388
$559$	262303.	0.0355037
$560$	0	0
$561$	3.60983e6	0.484261
$562$	2.51470e7	3.35850
$563$	−3.77110e6	−0.501415	−0.250707	−	0.968063i	$-0.580663\pi$
$563$	−3.77110e6	−0.501415	−0.250707	+	0.968063i	$0.580663\pi$
$564$	−1.82685e7	−2.41828
$565$	0	0
$566$	−1.43995e7	−1.88932
$567$	−752706.	−0.0983258
$568$	−2.89801e7	−3.76902
$569$	1.24551e7	1.61275	0.806373	−	0.591408i	$-0.201428\pi$
$569$	1.24551e7	1.61275	0.806373	+	0.591408i	$0.201428\pi$
$570$	0	0
$571$	3.61102e6	0.463489	0.231745	−	0.972777i	$-0.425557\pi$
$571$	3.61102e6	0.463489	0.231745	+	0.972777i	$0.425557\pi$
$572$	5.64947e6	0.721967
$573$	6.24885e6	0.795085
$574$	−5.24379e6	−0.664301
$575$	0	0
$576$	−1.32657e7	−1.66599
$577$	−9.92131e6	−1.24059	−0.620297	−	0.784367i	$-0.712988\pi$
$577$	−9.92131e6	−1.24059	−0.620297	+	0.784367i	$0.712988\pi$
$578$	1.05594e7	1.31467
$579$	−8.49521e6	−1.05312
$580$	0	0
$581$	2.89439e6	0.355726
$582$	−1.97413e7	−2.41584
$583$	2.83993e6	0.346048
$584$	−6.47221e6	−0.785272
$585$	0	0
$586$	7.01352e6	0.843707
$587$	−287186.	−0.0344008	−0.0172004	−	0.999852i	$-0.505475\pi$
$587$	−287186.	−0.0344008	−0.0172004	+	0.999852i	$0.505475\pi$
$588$	1.63676e7	1.95228
$589$	−1.41079e7	−1.67561
$590$	0	0
$591$	3.47097e6	0.408773
$592$	−2.64801e7	−3.10538
$593$	−7.88056e6	−0.920281	−0.460140	−	0.887846i	$-0.652201\pi$
$593$	−7.88056e6	−0.920281	−0.460140	+	0.887846i	$0.652201\pi$
$594$	−2.02926e7	−2.35978
$595$	0	0
$596$	−2.50524e7	−2.88891
$597$	5.09225e6	0.584755
$598$	−863634.	−0.0987590
$599$	−5.21976e6	−0.594407	−0.297203	−	0.954814i	$-0.596054\pi$
$599$	−5.21976e6	−0.594407	−0.297203	+	0.954814i	$0.596054\pi$
$600$	0	0
$601$	−1.35782e7	−1.53340	−0.766700	−	0.642006i	$-0.778103\pi$
$601$	−1.35782e7	−1.53340	−0.766700	+	0.642006i	$0.778103\pi$
$602$	−657442.	−0.0739378
$603$	−1.89517e6	−0.212254
$604$	−2.22692e7	−2.48377
$605$	0	0
$606$	1.86906e7	2.06748
$607$	−1.31721e7	−1.45106	−0.725528	−	0.688193i	$-0.758404\pi$
$607$	−1.31721e7	−1.45106	−0.725528	+	0.688193i	$0.758404\pi$
$608$	−5.52215e7	−6.05828
$609$	−1.22308e6	−0.133632
$610$	0	0
$611$	2.49432e6	0.270302
$612$	6.14684e6	0.663397
$613$	−1.23652e7	−1.32908	−0.664540	−	0.747253i	$-0.731372\pi$
$613$	−1.23652e7	−1.32908	−0.664540	+	0.747253i	$0.731372\pi$
$614$	4.57998e6	0.490278
$615$	0	0
$616$	−9.00906e6	−0.956594
$617$	1.65349e7	1.74859	0.874294	−	0.485396i	$-0.161325\pi$
$617$	1.65349e7	1.74859	0.874294	+	0.485396i	$0.161325\pi$
$618$	−6.53622e6	−0.688424
$619$	4.47426e6	0.469347	0.234674	−	0.972074i	$-0.424598\pi$
$619$	4.47426e6	0.469347	0.234674	+	0.972074i	$0.424598\pi$
$620$	0	0
$621$	2.27467e6	0.236696
$622$	−2.06328e7	−2.13837
$623$	−318199.	−0.0328457
$624$	−6.53381e6	−0.671746
$625$	0	0
$626$	−5.39874e6	−0.550626
$627$	−1.27849e7	−1.29876
$628$	−4.54749e7	−4.60122
$629$	4.58452e6	0.462027
$630$	0	0
$631$	7.83088e6	0.782956	0.391478	−	0.920188i	$-0.371964\pi$
$631$	7.83088e6	0.782956	0.391478	+	0.920188i	$0.371964\pi$
$632$	−2.66373e7	−2.65276
$633$	−4.26396e6	−0.422964
$634$	1.10963e7	1.09636
$635$	0	0
$636$	−6.51798e6	−0.638955
$637$	−2.23478e6	−0.218216
$638$	−1.58171e7	−1.53842
$639$	−4.89277e6	−0.474026
$640$	0	0
$641$	−259101.	−0.0249071	−0.0124536	−	0.999922i	$-0.503964\pi$
$641$	−259101.	−0.0249071	−0.0124536	+	0.999922i	$0.503964\pi$
$642$	1.97919e7	1.89518
$643$	6.35184e6	0.605860	0.302930	−	0.953013i	$-0.402035\pi$
$643$	6.35184e6	0.605860	0.302930	+	0.953013i	$0.402035\pi$
$644$	1.58725e6	0.150810
$645$	0	0
$646$	1.76814e7	1.66700
$647$	−1.02893e7	−0.966329	−0.483165	−	0.875530i	$-0.660513\pi$
$647$	−1.02893e7	−0.966329	−0.483165	+	0.875530i	$0.660513\pi$
$648$	1.42141e7	1.32979
$649$	6.86479e6	0.639758
$650$	0	0
$651$	2.26224e6	0.209212
$652$	5.55547e6	0.511802
$653$	−1.99863e6	−0.183421	−0.0917107	−	0.995786i	$-0.529233\pi$
$653$	−1.99863e6	−0.183421	−0.0917107	+	0.995786i	$0.529233\pi$
$654$	8.30923e6	0.759655
$655$	0	0
$656$	5.75089e7	5.21766
$657$	−1.09272e6	−0.0987630
$658$	−6.25183e6	−0.562914
$659$	2.03074e6	0.182154	0.0910772	−	0.995844i	$-0.470969\pi$
$659$	2.03074e6	0.182154	0.0910772	+	0.995844i	$0.470969\pi$
$660$	0	0
$661$	1.56979e7	1.39745	0.698727	−	0.715388i	$-0.253750\pi$
$661$	1.56979e7	1.39745	0.698727	+	0.715388i	$0.253750\pi$
$662$	4.03505e6	0.357852
$663$	1.13121e6	0.0999442
$664$	−5.46576e7	−4.81095
$665$	0	0
$666$	−7.69801e6	−0.672501
$667$	1.77300e6	0.154310
$668$	2.97717e7	2.58145
$669$	−1.52694e7	−1.31904
$670$	0	0
$671$	5.45288e6	0.467541
$672$	8.85496e6	0.756421
$673$	1.50938e7	1.28458	0.642288	−	0.766464i	$-0.277985\pi$
$673$	1.50938e7	1.28458	0.642288	+	0.766464i	$0.277985\pi$
$674$	2.33556e7	1.98035
$675$	0	0
$676$	−3.08919e7	−2.60002
$677$	−1.77133e7	−1.48535	−0.742674	−	0.669653i	$-0.766443\pi$
$677$	−1.77133e7	−1.48535	−0.742674	+	0.669653i	$0.766443\pi$
$678$	−2.61305e7	−2.18310
$679$	−4.95381e6	−0.412349
$680$	0	0
$681$	7.93123e6	0.655349
$682$	2.92557e7	2.40852
$683$	1.65440e7	1.35703	0.678515	−	0.734587i	$-0.262624\pi$
$683$	1.65440e7	1.35703	0.678515	+	0.734587i	$0.262624\pi$
$684$	−2.17702e7	−1.77919
$685$	0	0
$686$	1.15773e7	0.939284
$687$	1.51501e7	1.22468
$688$	7.21022e6	0.580734
$689$	889942.	0.0714190
$690$	0	0
$691$	−1.27729e7	−1.01764	−0.508818	−	0.860874i	$-0.669918\pi$
$691$	−1.27729e7	−1.01764	−0.508818	+	0.860874i	$0.669918\pi$
$692$	−4.97985e7	−3.95322
$693$	−1.52102e6	−0.120310
$694$	9.94509e6	0.783809
$695$	0	0
$696$	2.30967e7	1.80728
$697$	−9.95659e6	−0.776298
$698$	8.90486e6	0.691812
$699$	−1.44321e7	−1.11722
$700$	0	0
$701$	1.87678e7	1.44251	0.721255	−	0.692669i	$-0.243565\pi$
$701$	1.87678e7	1.44251	0.721255	+	0.692669i	$0.243565\pi$
$702$	−6.35904e6	−0.487022
$703$	−1.62370e7	−1.23913
$704$	5.80235e7	4.41238
$705$	0	0
$706$	−7.10259e6	−0.536297
$707$	4.69015e6	0.352889
$708$	−1.57555e7	−1.18127
$709$	−3.89479e6	−0.290984	−0.145492	−	0.989359i	$-0.546476\pi$
$709$	−3.89479e6	−0.290984	−0.145492	+	0.989359i	$0.546476\pi$
$710$	0	0
$711$	−4.49723e6	−0.333635
$712$	6.00888e6	0.444215
$713$	−3.27939e6	−0.241584
$714$	−2.83528e6	−0.208137
$715$	0	0
$716$	−55818.6	−0.00406908
$717$	1.35209e7	0.982220
$718$	−4.31372e7	−3.12278
$719$	2.02327e7	1.45960	0.729798	−	0.683663i	$-0.239614\pi$
$719$	2.02327e7	1.45960	0.729798	+	0.683663i	$0.239614\pi$
$720$	0	0
$721$	−1.64018e6	−0.117504
$722$	−3.55014e7	−2.53456
$723$	−1.65344e7	−1.17637
$724$	−1.17315e7	−0.831776
$725$	0	0
$726$	5.67760e6	0.399782
$727$	−1.10081e7	−0.772460	−0.386230	−	0.922403i	$-0.626223\pi$
$727$	−1.10081e7	−0.772460	−0.386230	+	0.922403i	$0.626223\pi$
$728$	−2.82315e6	−0.197427
$729$	1.41457e7	0.985837
$730$	0	0
$731$	−1.24831e6	−0.0864032
$732$	−1.25150e7	−0.863285
$733$	1.32245e7	0.909116	0.454558	−	0.890717i	$-0.349797\pi$
$733$	1.32245e7	0.909116	0.454558	+	0.890717i	$0.349797\pi$
$734$	−1.37095e6	−0.0939251
$735$	0	0
$736$	−1.28363e7	−0.873465
$737$	8.28943e6	0.562155
$738$	1.67184e7	1.12994
$739$	−1.66514e7	−1.12160	−0.560801	−	0.827951i	$-0.689507\pi$
$739$	−1.66514e7	−1.12160	−0.560801	+	0.827951i	$0.689507\pi$
$740$	0	0
$741$	−4.00638e6	−0.268044
$742$	−2.23057e6	−0.148733
$743$	2.28153e7	1.51619	0.758095	−	0.652144i	$-0.226130\pi$
$743$	2.28153e7	1.51619	0.758095	+	0.652144i	$0.226130\pi$
$744$	−4.27202e7	−2.82945
$745$	0	0
$746$	2.81408e7	1.85136
$747$	−9.22797e6	−0.605069
$748$	−2.68861e7	−1.75701
$749$	4.96651e6	0.323479
$750$	0	0
$751$	3.05593e7	1.97717	0.988584	−	0.150672i	$-0.0481438\pi$
$751$	3.05593e7	1.97717	0.988584	+	0.150672i	$0.0481438\pi$
$752$	6.85642e7	4.42133
$753$	−2.29862e6	−0.147733
$754$	−4.95657e6	−0.317506
$755$	0	0
$756$	1.16871e7	0.743707
$757$	−3.45228e6	−0.218961	−0.109480	−	0.993989i	$-0.534919\pi$
$757$	−3.45228e6	−0.218961	−0.109480	+	0.993989i	$0.534919\pi$
$758$	−788490.	−0.0498452
$759$	−2.97187e6	−0.187251
$760$	0	0
$761$	1.13988e7	0.713506	0.356753	−	0.934199i	$-0.383884\pi$
$761$	1.13988e7	0.713506	0.356753	+	0.934199i	$0.383884\pi$
$762$	2.58762e7	1.61441
$763$	2.08509e6	0.129662
$764$	−4.65415e7	−2.88474
$765$	0	0
$766$	−2.04997e7	−1.26234
$767$	2.15121e6	0.132036
$768$	−3.75653e7	−2.29818
$769$	3.18347e7	1.94126	0.970632	−	0.240569i	$-0.0773341\pi$
$769$	3.18347e7	1.94126	0.970632	+	0.240569i	$0.0773341\pi$
$770$	0	0
$771$	−1.30278e7	−0.789286
$772$	6.32724e7	3.82095
$773$	−4.82434e6	−0.290395	−0.145197	−	0.989403i	$-0.546382\pi$
$773$	−4.82434e6	−0.290395	−0.145197	+	0.989403i	$0.546382\pi$
$774$	2.09608e6	0.125764
$775$	0	0
$776$	9.35478e7	5.57672
$777$	2.60365e6	0.154714
$778$	4.98857e7	2.95479
$779$	3.52631e7	2.08198
$780$	0	0
$781$	2.14008e7	1.25546
$782$	4.11007e6	0.240344
$783$	1.30548e7	0.760967
$784$	−6.14298e7	−3.56935
$785$	0	0
$786$	−7.29257e6	−0.421041
$787$	2.06052e7	1.18588	0.592940	−	0.805246i	$-0.297967\pi$
$787$	2.06052e7	1.18588	0.592940	+	0.805246i	$0.297967\pi$
$788$	−2.58518e7	−1.48312
$789$	−1.96551e7	−1.12404
$790$	0	0
$791$	−6.55709e6	−0.372623
$792$	2.87230e7	1.62711
$793$	1.70876e6	0.0964935
$794$	−4.71733e7	−2.65549
$795$	0	0
$796$	−3.79271e7	−2.12162
$797$	5.20114e6	0.290036	0.145018	−	0.989429i	$-0.453676\pi$
$797$	5.20114e6	0.290036	0.145018	+	0.989429i	$0.453676\pi$
$798$	1.00417e7	0.558212
$799$	−1.18706e7	−0.657818
$800$	0	0
$801$	1.01449e6	0.0558686
$802$	1.13123e6	0.0621034
$803$	4.77951e6	0.261574
$804$	−1.90253e7	−1.03798
$805$	0	0
$806$	9.16780e6	0.497081
$807$	2.32009e7	1.25407
$808$	−8.85689e7	−4.77257
$809$	−3.19510e7	−1.71638	−0.858188	−	0.513335i	$-0.828410\pi$
$809$	−3.19510e7	−1.71638	−0.858188	+	0.513335i	$0.828410\pi$
$810$	0	0
$811$	−2.17153e7	−1.15935	−0.579675	−	0.814848i	$-0.696820\pi$
$811$	−2.17153e7	−1.15935	−0.579675	+	0.814848i	$0.696820\pi$
$812$	9.10952e6	0.484848
$813$	−3.97111e6	−0.210710
$814$	3.36709e7	1.78112
$815$	0	0
$816$	3.10947e7	1.63479
$817$	4.42114e6	0.231728
$818$	6.21044e7	3.24518
$819$	−476639.	−0.0248302
$820$	0	0
$821$	1.61249e7	0.834911	0.417456	−	0.908697i	$-0.362922\pi$
$821$	1.61249e7	0.834911	0.417456	+	0.908697i	$0.362922\pi$
$822$	1.61428e7	0.833294
$823$	−2.41687e6	−0.124381	−0.0621904	−	0.998064i	$-0.519809\pi$
$823$	−2.41687e6	−0.124381	−0.0621904	+	0.998064i	$0.519809\pi$
$824$	3.09731e7	1.58916
$825$	0	0
$826$	−5.39183e6	−0.274971
$827$	3.47693e7	1.76780	0.883898	−	0.467680i	$-0.154910\pi$
$827$	3.47693e7	1.76780	0.883898	+	0.467680i	$0.154910\pi$
$828$	−5.06051e6	−0.256518
$829$	1.08558e7	0.548627	0.274314	−	0.961640i	$-0.411549\pi$
$829$	1.08558e7	0.548627	0.274314	+	0.961640i	$0.411549\pi$
$830$	0	0
$831$	8.15737e6	0.409777
$832$	1.81827e7	0.910648
$833$	1.06354e7	0.531058
$834$	−1.11610e7	−0.555633
$835$	0	0
$836$	9.52221e7	4.71218
$837$	−2.41465e7	−1.19135
$838$	3.19203e7	1.57021
$839$	−1.44613e6	−0.0709255	−0.0354627	−	0.999371i	$-0.511291\pi$
$839$	−1.44613e6	−0.0709255	−0.0354627	+	0.999371i	$0.511291\pi$
$840$	0	0
$841$	−1.03356e7	−0.503899
$842$	−7.08089e7	−3.44197
$843$	2.71169e7	1.31423
$844$	3.17580e7	1.53461
$845$	0	0
$846$	1.99323e7	0.957483
$847$	1.42472e6	0.0682370
$848$	2.44628e7	1.16820
$849$	−1.55275e7	−0.739318
$850$	0	0
$851$	−3.77430e6	−0.178654
$852$	−4.91175e7	−2.31813
$853$	−1.13382e7	−0.533547	−0.266773	−	0.963759i	$-0.585958\pi$
$853$	−1.13382e7	−0.533547	−0.266773	+	0.963759i	$0.585958\pi$
$854$	−4.28287e6	−0.200951
$855$	0	0
$856$	−9.37876e7	−4.37483
$857$	3.49802e7	1.62694	0.813469	−	0.581609i	$-0.197577\pi$
$857$	3.49802e7	1.62694	0.813469	+	0.581609i	$0.197577\pi$
$858$	8.30810e6	0.385286
$859$	−905073.	−0.0418505	−0.0209253	−	0.999781i	$-0.506661\pi$
$859$	−905073.	−0.0418505	−0.0209253	+	0.999781i	$0.506661\pi$
$860$	0	0
$861$	−5.65456e6	−0.259951
$862$	−5.44489e7	−2.49586
$863$	2.54525e7	1.16333	0.581666	−	0.813427i	$-0.302401\pi$
$863$	2.54525e7	1.16333	0.581666	+	0.813427i	$0.302401\pi$
$864$	−9.45153e7	−4.30742
$865$	0	0
$866$	−4.77372e6	−0.216303
$867$	1.13865e7	0.514451
$868$	−1.68492e7	−0.759067
$869$	1.96708e7	0.883632
$870$	0	0
$871$	2.59764e6	0.116020
$872$	−3.93749e7	−1.75359
$873$	1.57939e7	0.701380
$874$	−1.45566e7	−0.644587
$875$	0	0
$876$	−1.09696e7	−0.482980
$877$	9.71240e6	0.426410	0.213205	−	0.977007i	$-0.431610\pi$
$877$	9.71240e6	0.426410	0.213205	+	0.977007i	$0.431610\pi$
$878$	−2.09020e7	−0.915065
$879$	7.56293e6	0.330155
$880$	0	0
$881$	1.95220e7	0.847394	0.423697	−	0.905804i	$-0.360732\pi$
$881$	1.95220e7	0.847394	0.423697	+	0.905804i	$0.360732\pi$
$882$	−1.78582e7	−0.772978
$883$	−3.12357e7	−1.34819	−0.674093	−	0.738647i	$-0.735465\pi$
$883$	−3.12357e7	−1.34819	−0.674093	+	0.738647i	$0.735465\pi$
$884$	−8.42524e6	−0.362620
$885$	0	0
$886$	−3.84090e7	−1.64380
$887$	−3.05965e7	−1.30576	−0.652879	−	0.757462i	$-0.726439\pi$
$887$	−3.05965e7	−1.30576	−0.652879	+	0.757462i	$0.726439\pi$
$888$	−4.91674e7	−2.09240
$889$	6.49328e6	0.275556
$890$	0	0
$891$	−1.04966e7	−0.442952
$892$	1.13727e8	4.78576
$893$	4.20420e7	1.76423
$894$	−3.68421e7	−1.54170
$895$	0	0
$896$	−2.15826e7	−0.898119
$897$	−931288.	−0.0386458
$898$	1.92260e7	0.795607
$899$	−1.88211e7	−0.776685
$900$	0	0
$901$	−4.23527e6	−0.173808
$902$	−7.31257e7	−2.99264
$903$	−708944.	−0.0289329
$904$	1.23824e8	5.03946
$905$	0	0
$906$	−3.27490e7	−1.32549
$907$	−4.02015e7	−1.62265	−0.811324	−	0.584597i	$-0.801253\pi$
$907$	−4.02015e7	−1.62265	−0.811324	+	0.584597i	$0.801253\pi$
$908$	−5.90719e7	−2.37775
$909$	−1.49533e7	−0.600242
$910$	0	0
$911$	4.43330e7	1.76983	0.884914	−	0.465755i	$-0.154217\pi$
$911$	4.43330e7	1.76983	0.884914	+	0.465755i	$0.154217\pi$
$912$	−1.10128e8	−4.38440
$913$	4.03628e7	1.60253
$914$	6.55006e7	2.59346
$915$	0	0
$916$	−1.12838e8	−4.44343
$917$	−1.82997e6	−0.0718655
$918$	3.02630e7	1.18524
$919$	1.25394e7	0.489764	0.244882	−	0.969553i	$-0.421251\pi$
$919$	1.25394e7	0.489764	0.244882	+	0.969553i	$0.421251\pi$
$920$	0	0
$921$	4.93876e6	0.191853
$922$	−5.07387e7	−1.96567
$923$	6.70633e6	0.259108
$924$	−1.52692e7	−0.588351
$925$	0	0
$926$	8.93862e6	0.342565
$927$	5.22926e6	0.199867
$928$	−7.36701e7	−2.80816
$929$	−3.89251e7	−1.47976	−0.739880	−	0.672739i	$-0.765118\pi$
$929$	−3.89251e7	−1.47976	−0.739880	+	0.672739i	$0.765118\pi$
$930$	0	0
$931$	−3.76673e7	−1.42426
$932$	1.07491e8	4.05351
$933$	−2.22491e7	−0.836774
$934$	−6.16756e7	−2.31338
$935$	0	0
$936$	9.00086e6	0.335811
$937$	−3.75575e6	−0.139749	−0.0698744	−	0.997556i	$-0.522260\pi$
$937$	−3.75575e6	−0.139749	−0.0698744	+	0.997556i	$0.522260\pi$
$938$	−6.51079e6	−0.241616
$939$	−5.82166e6	−0.215468
$940$	0	0
$941$	−3.11325e6	−0.114614	−0.0573072	−	0.998357i	$-0.518251\pi$
$941$	−3.11325e6	−0.114614	−0.0573072	+	0.998357i	$0.518251\pi$
$942$	−6.68753e7	−2.45549
$943$	8.19696e6	0.300174
$944$	5.91326e7	2.15972
$945$	0	0
$946$	−9.16818e6	−0.333085
$947$	−5.76062e6	−0.208735	−0.104367	−	0.994539i	$-0.533282\pi$
$947$	−5.76062e6	−0.208735	−0.104367	+	0.994539i	$0.533282\pi$
$948$	−4.51468e7	−1.63157
$949$	1.49775e6	0.0539849
$950$	0	0
$951$	1.19655e7	0.429022
$952$	1.34355e7	0.480465
$953$	4.92617e7	1.75702	0.878510	−	0.477724i	$-0.158538\pi$
$953$	4.92617e7	1.75702	0.878510	+	0.477724i	$0.158538\pi$
$954$	7.11158e6	0.252985
$955$	0	0
$956$	−1.00704e8	−3.56371
$957$	−1.70561e7	−0.602006
$958$	−2.43270e7	−0.856396
$959$	4.05081e6	0.142231
$960$	0	0
$961$	6.18278e6	0.215961
$962$	1.05514e7	0.367596
$963$	−1.58344e7	−0.550218
$964$	1.23148e8	4.26812
$965$	0	0
$966$	2.33420e6	0.0804814
$967$	2.87331e7	0.988135	0.494068	−	0.869423i	$-0.335509\pi$
$967$	2.87331e7	0.988135	0.494068	+	0.869423i	$0.335509\pi$
$968$	−2.69044e7	−0.922858
$969$	1.90665e7	0.652323
$970$	0	0
$971$	1.73763e7	0.591438	0.295719	−	0.955275i	$-0.404441\pi$
$971$	1.73763e7	0.591438	0.295719	+	0.955275i	$0.404441\pi$
$972$	−6.33924e7	−2.15214
$973$	−2.80070e6	−0.0948385
$974$	−5.16776e7	−1.74544
$975$	0	0
$976$	4.69705e7	1.57834
$977$	−1.97702e7	−0.662634	−0.331317	−	0.943519i	$-0.607493\pi$
$977$	−1.97702e7	−0.662634	−0.331317	+	0.943519i	$0.607493\pi$
$978$	8.16986e6	0.273129
$979$	−4.43736e6	−0.147968
$980$	0	0
$981$	−6.64774e6	−0.220547
$982$	5.98230e7	1.97965
$983$	−3.78996e7	−1.25098	−0.625490	−	0.780232i	$-0.715101\pi$
$983$	−3.78996e7	−1.25098	−0.625490	+	0.780232i	$0.715101\pi$
$984$	1.06781e8	3.51565
$985$	0	0
$986$	2.35885e7	0.772695
$987$	−6.74158e6	−0.220277
$988$	2.98396e7	0.972524
$989$	1.02770e6	0.0334099
$990$	0	0
$991$	−4.03466e7	−1.30504	−0.652519	−	0.757773i	$-0.726288\pi$
$991$	−4.03466e7	−1.30504	−0.652519	+	0.757773i	$0.726288\pi$
$992$	1.36262e8	4.39639
$993$	4.35114e6	0.140033
$994$	−1.68089e7	−0.539602
$995$	0	0
$996$	−9.26377e7	−2.95896
$997$	4.01839e7	1.28031	0.640153	−	0.768247i	$-0.278871\pi$
$997$	4.01839e7	1.28031	0.640153	+	0.768247i	$0.278871\pi$
$998$	−8.86844e6	−0.281852
$999$	−2.77906e7	−0.881018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.j.1.1	yes	37
5.4	even	2		1075.6.a.i.1.37	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.6.a.i.1.37	✓	37	5.4	even	2
1075.6.a.j.1.1	yes	37	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-10.9530 q^{2} -11.8111 q^{3} +87.9689 q^{4} +129.367 q^{6} +32.4628 q^{7} -613.029 q^{8} -103.499 q^{9} +O(q^{10})\)	\(q-10.9530 q^{2} -11.8111 q^{3} +87.9689 q^{4} +129.367 q^{6} +32.4628 q^{7} -613.029 q^{8} -103.499 q^{9} +452.701 q^{11} -1039.01 q^{12} +141.862 q^{13} -355.567 q^{14} +3899.52 q^{16} -675.128 q^{17} +1133.63 q^{18} +2391.10 q^{19} -383.420 q^{21} -4958.45 q^{22} +555.813 q^{23} +7240.52 q^{24} -1553.82 q^{26} +4092.52 q^{27} +2855.72 q^{28} +3189.92 q^{29} -5900.16 q^{31} -23094.7 q^{32} -5346.88 q^{33} +7394.70 q^{34} -9104.70 q^{36} -6790.60 q^{37} -26189.7 q^{38} -1675.54 q^{39} +14747.7 q^{41} +4199.61 q^{42} +1849.00 q^{43} +39823.6 q^{44} -6087.84 q^{46} +17582.7 q^{47} -46057.5 q^{48} -15753.2 q^{49} +7973.98 q^{51} +12479.5 q^{52} +6273.29 q^{53} -44825.5 q^{54} -19900.7 q^{56} -28241.4 q^{57} -34939.3 q^{58} +15164.1 q^{59} +12045.2 q^{61} +64624.7 q^{62} -3359.87 q^{63} +128172. q^{64} +58564.6 q^{66} +18311.0 q^{67} -59390.3 q^{68} -6564.74 q^{69} +47273.6 q^{71} +63447.9 q^{72} +10557.7 q^{73} +74377.6 q^{74} +210342. q^{76} +14696.0 q^{77} +18352.3 q^{78} +43451.9 q^{79} -23186.7 q^{81} -161532. q^{82} +89160.0 q^{83} -33729.1 q^{84} -20252.2 q^{86} -37676.3 q^{87} -277519. q^{88} -9801.95 q^{89} +4605.25 q^{91} +48894.3 q^{92} +69687.1 q^{93} -192584. q^{94} +272772. q^{96} -152599. q^{97} +172545. q^{98} -46854.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 37 * q + 630 * q^4 + 291 * q^6 + 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} + 213 q^{8} + 3535 q^{9} + 675 q^{11} - 4446 q^{12} + 1241 q^{13} + 2375 q^{14} + 10518 q^{16} + 1153 q^{17} - 6680 q^{18} + 4065 q^{19} + 9953 q^{21} + 9283 q^{22} - 360 q^{23} + 2265 q^{24} + 23695 q^{26} + 1323 q^{27} - 30375 q^{28} + 19290 q^{29} + 23291 q^{31} + 8166 q^{32} - 10388 q^{33} - 13153 q^{34} + 148705 q^{36} + 13501 q^{37} - 8127 q^{38} - 1327 q^{39} + 38345 q^{41} - 21835 q^{42} + 68413 q^{43} + 47768 q^{44} + 48755 q^{46} + 84859 q^{47} - 208720 q^{48} + 107255 q^{49} + 62027 q^{51} + 128320 q^{52} - 53559 q^{53} + 44158 q^{54} + 107538 q^{56} + 104239 q^{57} - 85186 q^{58} + 48186 q^{59} + 82364 q^{61} + 206506 q^{62} - 75269 q^{63} + 161467 q^{64} + 91969 q^{66} + 38168 q^{67} + 95991 q^{68} + 287103 q^{69} + 155302 q^{71} + 9979 q^{72} + 31927 q^{73} + 59946 q^{74} + 225407 q^{76} - 80007 q^{77} - 67815 q^{78} + 150174 q^{79} + 417489 q^{81} + 60603 q^{82} + 266568 q^{83} + 586273 q^{84} - 57554 q^{87} + 323054 q^{88} + 334356 q^{89} + 51747 q^{91} - 258529 q^{92} - 285287 q^{93} + 302744 q^{94} + 287282 q^{96} - 78640 q^{97} - 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 + 213 * q^8 + 3535 * q^9 + 675 * q^11 - 4446 * q^12 + 1241 * q^13 + 2375 * q^14 + 10518 * q^16 + 1153 * q^17 - 6680 * q^18 + 4065 * q^19 + 9953 * q^21 + 9283 * q^22 - 360 * q^23 + 2265 * q^24 + 23695 * q^26 + 1323 * q^27 - 30375 * q^28 + 19290 * q^29 + 23291 * q^31 + 8166 * q^32 - 10388 * q^33 - 13153 * q^34 + 148705 * q^36 + 13501 * q^37 - 8127 * q^38 - 1327 * q^39 + 38345 * q^41 - 21835 * q^42 + 68413 * q^43 + 47768 * q^44 + 48755 * q^46 + 84859 * q^47 - 208720 * q^48 + 107255 * q^49 + 62027 * q^51 + 128320 * q^52 - 53559 * q^53 + 44158 * q^54 + 107538 * q^56 + 104239 * q^57 - 85186 * q^58 + 48186 * q^59 + 82364 * q^61 + 206506 * q^62 - 75269 * q^63 + 161467 * q^64 + 91969 * q^66 + 38168 * q^67 + 95991 * q^68 + 287103 * q^69 + 155302 * q^71 + 9979 * q^72 + 31927 * q^73 + 59946 * q^74 + 225407 * q^76 - 80007 * q^77 - 67815 * q^78 + 150174 * q^79 + 417489 * q^81 + 60603 * q^82 + 266568 * q^83 + 586273 * q^84 - 57554 * q^87 + 323054 * q^88 + 334356 * q^89 + 51747 * q^91 - 258529 * q^92 - 285287 * q^93 + 302744 * q^94 + 287282 * q^96 - 78640 * q^97 - 397117 * q^98 + 362152 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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