LMFDB - Embedded newform 1075.6.a.l.1.26

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:	$52$
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
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)

$f(q)$	$=$	$q+0.791569 q^{2} -18.4548 q^{3} -31.3734 q^{4} -14.6082 q^{6} -121.091 q^{7} -50.1644 q^{8} +97.5785 q^{9} +O(q^{10})$	\(q+0.791569 q^{2} -18.4548 q^{3} -31.3734 q^{4} -14.6082 q^{6} -121.091 q^{7} -50.1644 q^{8} +97.5785 q^{9} +314.245 q^{11} +578.989 q^{12} -199.920 q^{13} -95.8521 q^{14} +964.241 q^{16} -412.522 q^{17} +77.2401 q^{18} -1718.50 q^{19} +2234.71 q^{21} +248.747 q^{22} +3160.06 q^{23} +925.773 q^{24} -158.251 q^{26} +2683.72 q^{27} +3799.04 q^{28} -5153.79 q^{29} -6197.27 q^{31} +2368.53 q^{32} -5799.33 q^{33} -326.540 q^{34} -3061.37 q^{36} -10496.9 q^{37} -1360.31 q^{38} +3689.49 q^{39} -12849.7 q^{41} +1768.93 q^{42} -1849.00 q^{43} -9858.95 q^{44} +2501.41 q^{46} +4315.97 q^{47} -17794.8 q^{48} -2143.92 q^{49} +7613.00 q^{51} +6272.19 q^{52} -21447.1 q^{53} +2124.35 q^{54} +6074.47 q^{56} +31714.5 q^{57} -4079.58 q^{58} +16225.6 q^{59} -4047.87 q^{61} -4905.57 q^{62} -11815.9 q^{63} -28980.9 q^{64} -4590.57 q^{66} -8297.28 q^{67} +12942.2 q^{68} -58318.2 q^{69} -57151.3 q^{71} -4894.97 q^{72} -73150.6 q^{73} -8309.02 q^{74} +53915.1 q^{76} -38052.3 q^{77} +2920.48 q^{78} -26058.4 q^{79} -73239.0 q^{81} -10171.5 q^{82} -52657.1 q^{83} -70110.5 q^{84} -1463.61 q^{86} +95112.0 q^{87} -15763.9 q^{88} +69764.6 q^{89} +24208.6 q^{91} -99141.9 q^{92} +114369. q^{93} +3416.39 q^{94} -43710.6 q^{96} -83813.3 q^{97} -1697.06 q^{98} +30663.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9}+O(q^{10}) $ 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9} - 664 q^{11} - 523 q^{12} + 2704 q^{13} + 150 q^{14} + 13474 q^{16} + 7266 q^{17} + 4860 q^{18} - 1970 q^{19} + 800 q^{21} + 14477 q^{22} + 9522 q^{23} + 314 q^{24} + 5514 q^{26} + 22926 q^{27} + 9408 q^{28} - 7188 q^{29} - 11556 q^{31} + 48390 q^{32} + 26136 q^{33} + 16774 q^{34} + 51872 q^{36} + 42558 q^{37} + 46208 q^{38} + 4682 q^{39} - 7746 q^{41} + 174265 q^{42} - 96148 q^{43} - 48600 q^{44} + 16182 q^{46} + 87136 q^{47} - 2912 q^{48} + 142286 q^{49} - 3710 q^{51} + 146868 q^{52} + 127034 q^{53} - 49563 q^{54} - 2849 q^{56} + 101594 q^{57} + 9480 q^{58} - 55924 q^{59} + 73702 q^{61} + 186016 q^{62} + 50120 q^{63} + 157750 q^{64} + 58211 q^{66} + 131996 q^{67} + 298560 q^{68} + 128436 q^{69} - 56284 q^{71} + 343775 q^{72} + 128620 q^{73} - 17721 q^{74} - 170410 q^{76} + 448438 q^{77} + 237616 q^{78} + 106204 q^{79} + 478568 q^{81} + 249596 q^{82} + 348616 q^{83} - 131855 q^{84} - 36980 q^{86} + 267478 q^{87} + 525216 q^{88} + 80410 q^{89} + 226376 q^{91} + 581456 q^{92} + 902902 q^{93} + 180980 q^{94} + 38543 q^{96} + 316148 q^{97} + 295095 q^{98} + 68428 q^{99}+O(q^{100}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9 - 664 * q^11 - 523 * q^12 + 2704 * q^13 + 150 * q^14 + 13474 * q^16 + 7266 * q^17 + 4860 * q^18 - 1970 * q^19 + 800 * q^21 + 14477 * q^22 + 9522 * q^23 + 314 * q^24 + 5514 * q^26 + 22926 * q^27 + 9408 * q^28 - 7188 * q^29 - 11556 * q^31 + 48390 * q^32 + 26136 * q^33 + 16774 * q^34 + 51872 * q^36 + 42558 * q^37 + 46208 * q^38 + 4682 * q^39 - 7746 * q^41 + 174265 * q^42 - 96148 * q^43 - 48600 * q^44 + 16182 * q^46 + 87136 * q^47 - 2912 * q^48 + 142286 * q^49 - 3710 * q^51 + 146868 * q^52 + 127034 * q^53 - 49563 * q^54 - 2849 * q^56 + 101594 * q^57 + 9480 * q^58 - 55924 * q^59 + 73702 * q^61 + 186016 * q^62 + 50120 * q^63 + 157750 * q^64 + 58211 * q^66 + 131996 * q^67 + 298560 * q^68 + 128436 * q^69 - 56284 * q^71 + 343775 * q^72 + 128620 * q^73 - 17721 * q^74 - 170410 * q^76 + 448438 * q^77 + 237616 * q^78 + 106204 * q^79 + 478568 * q^81 + 249596 * q^82 + 348616 * q^83 - 131855 * q^84 - 36980 * q^86 + 267478 * q^87 + 525216 * q^88 + 80410 * q^89 + 226376 * q^91 + 581456 * q^92 + 902902 * q^93 + 180980 * q^94 + 38543 * q^96 + 316148 * q^97 + 295095 * q^98 + 68428 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.791569	0.139931	0.0699655	−	0.997549i	$-0.477711\pi$
$2$	0.791569	0.139931	0.0699655	+	0.997549i	$0.477711\pi$
$3$	−18.4548	−1.18387	−0.591937	−	0.805984i	$-0.701637\pi$
$3$	−18.4548	−1.18387	−0.591937	+	0.805984i	$0.701637\pi$
$4$	−31.3734	−0.980419
$5$	0	0
$5$	0	0
$6$	−14.6082	−0.165661
$7$	−121.091	−0.934044	−0.467022	−	0.884246i	$-0.654673\pi$
$7$	−121.091	−0.934044	−0.467022	+	0.884246i	$0.654673\pi$
$8$	−50.1644	−0.277122
$9$	97.5785	0.401557
$10$	0	0
$11$	314.245	0.783046	0.391523	−	0.920168i	$-0.371948\pi$
$11$	314.245	0.783046	0.391523	+	0.920168i	$0.371948\pi$
$12$	578.989	1.16069
$13$	−199.920	−0.328094	−0.164047	−	0.986452i	$-0.552455\pi$
$13$	−199.920	−0.328094	−0.164047	+	0.986452i	$0.552455\pi$
$14$	−95.8521	−0.130702
$15$	0	0
$16$	964.241	0.941641
$17$	−412.522	−0.346198	−0.173099	−	0.984904i	$-0.555378\pi$
$17$	−412.522	−0.346198	−0.173099	+	0.984904i	$0.555378\pi$
$18$	77.2401	0.0561903
$19$	−1718.50	−1.09211	−0.546053	−	0.837751i	$-0.683870\pi$
$19$	−1718.50	−1.09211	−0.546053	+	0.837751i	$0.683870\pi$
$20$	0	0
$21$	2234.71	1.10579
$22$	248.747	0.109572
$23$	3160.06	1.24559	0.622796	−	0.782384i	$-0.285997\pi$
$23$	3160.06	1.24559	0.622796	+	0.782384i	$0.285997\pi$
$24$	925.773	0.328078
$25$	0	0
$26$	−158.251	−0.0459106
$27$	2683.72	0.708481
$28$	3799.04	0.915755
$29$	−5153.79	−1.13797	−0.568986	−	0.822347i	$-0.692664\pi$
$29$	−5153.79	−1.13797	−0.568986	+	0.822347i	$0.692664\pi$
$30$	0	0
$31$	−6197.27	−1.15823	−0.579117	−	0.815244i	$-0.696603\pi$
$31$	−6197.27	−1.15823	−0.579117	+	0.815244i	$0.696603\pi$
$32$	2368.53	0.408887
$33$	−5799.33	−0.927027
$34$	−326.540	−0.0484439
$35$	0	0
$36$	−3061.37	−0.393695
$37$	−10496.9	−1.26054	−0.630270	−	0.776376i	$-0.717056\pi$
$37$	−10496.9	−1.26054	−0.630270	+	0.776376i	$0.717056\pi$
$38$	−1360.31	−0.152819
$39$	3689.49	0.388422
$40$	0	0
$41$	−12849.7	−1.19381	−0.596904	−	0.802312i	$-0.703603\pi$
$41$	−12849.7	−1.19381	−0.596904	+	0.802312i	$0.703603\pi$
$42$	1768.93	0.154734
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−9858.95	−0.767713
$45$	0	0
$46$	2501.41	0.174297
$47$	4315.97	0.284993	0.142497	−	0.989795i	$-0.454487\pi$
$47$	4315.97	0.284993	0.142497	+	0.989795i	$0.454487\pi$
$48$	−17794.8	−1.11478
$49$	−2143.92	−0.127561
$50$	0	0
$51$	7613.00	0.409855
$52$	6272.19	0.321670
$53$	−21447.1	−1.04876	−0.524382	−	0.851483i	$-0.675704\pi$
$53$	−21447.1	−1.04876	−0.524382	+	0.851483i	$0.675704\pi$
$54$	2124.35	0.0991384
$55$	0	0
$56$	6074.47	0.258844
$57$	31714.5	1.29292
$58$	−4079.58	−0.159238
$59$	16225.6	0.606833	0.303417	−	0.952858i	$-0.401873\pi$
$59$	16225.6	0.606833	0.303417	+	0.952858i	$0.401873\pi$
$60$	0	0
$61$	−4047.87	−0.139284	−0.0696420	−	0.997572i	$-0.522186\pi$
$61$	−4047.87	−0.139284	−0.0696420	+	0.997572i	$0.522186\pi$
$62$	−4905.57	−0.162073
$63$	−11815.9	−0.375072
$64$	−28980.9	−0.884425
$65$	0	0
$66$	−4590.57	−0.129720
$67$	−8297.28	−0.225813	−0.112906	−	0.993606i	$-0.536016\pi$
$67$	−8297.28	−0.225813	−0.112906	+	0.993606i	$0.536016\pi$
$68$	12942.2	0.339419
$69$	−58318.2	−1.47462
$70$	0	0
$71$	−57151.3	−1.34549	−0.672745	−	0.739875i	$-0.734885\pi$
$71$	−57151.3	−1.34549	−0.672745	+	0.739875i	$0.734885\pi$
$72$	−4894.97	−0.111280
$73$	−73150.6	−1.60661	−0.803306	−	0.595567i	$-0.796927\pi$
$73$	−73150.6	−1.60661	−0.803306	+	0.595567i	$0.796927\pi$
$74$	−8309.02	−0.176389
$75$	0	0
$76$	53915.1	1.07072
$77$	−38052.3	−0.731399
$78$	2920.48	0.0543523
$79$	−26058.4	−0.469765	−0.234882	−	0.972024i	$-0.575471\pi$
$79$	−26058.4	−0.469765	−0.234882	+	0.972024i	$0.575471\pi$
$80$	0	0
$81$	−73239.0	−1.24031
$82$	−10171.5	−0.167051
$83$	−52657.1	−0.838999	−0.419500	−	0.907755i	$-0.637794\pi$
$83$	−52657.1	−0.838999	−0.419500	+	0.907755i	$0.637794\pi$
$84$	−70110.5	−1.08414
$85$	0	0
$86$	−1463.61	−0.0213393
$87$	95112.0	1.34722
$88$	−15763.9	−0.216999
$89$	69764.6	0.933599	0.466799	−	0.884363i	$-0.345407\pi$
$89$	69764.6	0.933599	0.466799	+	0.884363i	$0.345407\pi$
$90$	0	0
$91$	24208.6	0.306455
$92$	−99141.9	−1.22120
$93$	114369.	1.37120
$94$	3416.39	0.0398794
$95$	0	0
$96$	−43710.6	−0.484070
$97$	−83813.3	−0.904448	−0.452224	−	0.891904i	$-0.649369\pi$
$97$	−83813.3	−0.904448	−0.452224	+	0.891904i	$0.649369\pi$
$98$	−1697.06	−0.0178498
$99$	30663.6	0.314438
$100$	0	0
$101$	−161003.	−1.57048	−0.785238	−	0.619194i	$-0.787460\pi$
$101$	−161003.	−1.57048	−0.785238	+	0.619194i	$0.787460\pi$
$102$	6026.21	0.0573514
$103$	−25681.7	−0.238523	−0.119261	−	0.992863i	$-0.538053\pi$
$103$	−25681.7	−0.238523	−0.119261	+	0.992863i	$0.538053\pi$
$104$	10028.9	0.0909222
$105$	0	0
$106$	−16976.8	−0.146755
$107$	−12548.9	−0.105961	−0.0529804	−	0.998596i	$-0.516872\pi$
$107$	−12548.9	−0.105961	−0.0529804	+	0.998596i	$0.516872\pi$
$108$	−84197.5	−0.694608
$109$	−1576.85	−0.0127123	−0.00635615	−	0.999980i	$-0.502023\pi$
$109$	−1576.85	−0.0127123	−0.00635615	+	0.999980i	$0.502023\pi$
$110$	0	0
$111$	193718.	1.49232
$112$	−116761.	−0.879535
$113$	94496.2	0.696175	0.348088	−	0.937462i	$-0.386831\pi$
$113$	94496.2	0.696175	0.348088	+	0.937462i	$0.386831\pi$
$114$	25104.2	0.180919
$115$	0	0
$116$	161692.	1.11569
$117$	−19507.9	−0.131749
$118$	12843.7	0.0849148
$119$	49952.8	0.323364
$120$	0	0
$121$	−62300.9	−0.386839
$122$	−3204.17	−0.0194902
$123$	237139.	1.41332
$124$	194430.	1.13556
$125$	0	0
$126$	−9353.10	−0.0524843
$127$	76833.0	0.422706	0.211353	−	0.977410i	$-0.432213\pi$
$127$	76833.0	0.422706	0.211353	+	0.977410i	$0.432213\pi$
$128$	−98733.2	−0.532645
$129$	34122.9	0.180539
$130$	0	0
$131$	−222720.	−1.13392	−0.566958	−	0.823747i	$-0.691880\pi$
$131$	−222720.	−1.13392	−0.566958	+	0.823747i	$0.691880\pi$
$132$	181945.	0.908876
$133$	208095.	1.02008
$134$	−6567.87	−0.0315982
$135$	0	0
$136$	20693.9	0.0959391
$137$	240412.	1.09435	0.547173	−	0.837019i	$-0.315704\pi$
$137$	240412.	1.09435	0.547173	+	0.837019i	$0.315704\pi$
$138$	−46162.9	−0.206346
$139$	104734.	0.459780	0.229890	−	0.973217i	$-0.426163\pi$
$139$	104734.	0.459780	0.229890	+	0.973217i	$0.426163\pi$
$140$	0	0
$141$	−79650.3	−0.337396
$142$	−45239.2	−0.188276
$143$	−62824.1	−0.256913
$144$	94089.1	0.378123
$145$	0	0
$146$	−57903.8	−0.224815
$147$	39565.6	0.151017
$148$	329323.	1.23586
$149$	−492307.	−1.81665	−0.908323	−	0.418269i	$-0.862637\pi$
$149$	−492307.	−1.81665	−0.908323	+	0.418269i	$0.862637\pi$
$150$	0	0
$151$	−398501.	−1.42229	−0.711143	−	0.703047i	$-0.751822\pi$
$151$	−398501.	−1.42229	−0.711143	+	0.703047i	$0.751822\pi$
$152$	86207.5	0.302647
$153$	−40253.3	−0.139018
$154$	−30121.1	−0.102345
$155$	0	0
$156$	−115752.	−0.380817
$157$	−163328.	−0.528826	−0.264413	−	0.964410i	$-0.585178\pi$
$157$	−163328.	−0.528826	−0.264413	+	0.964410i	$0.585178\pi$
$158$	−20627.1	−0.0657347
$159$	395800.	1.24161
$160$	0	0
$161$	−382655.	−1.16344
$162$	−57973.7	−0.173558
$163$	520799.	1.53533	0.767665	−	0.640852i	$-0.221419\pi$
$163$	520799.	1.53533	0.767665	+	0.640852i	$0.221419\pi$
$164$	403140.	1.17043
$165$	0	0
$166$	−41681.7	−0.117402
$167$	−475407.	−1.31909	−0.659545	−	0.751665i	$-0.729251\pi$
$167$	−475407.	−1.31909	−0.659545	+	0.751665i	$0.729251\pi$
$168$	−112103.	−0.306439
$169$	−331325.	−0.892354
$170$	0	0
$171$	−167688.	−0.438543
$172$	58009.5	0.149513
$173$	454171.	1.15373	0.576864	−	0.816840i	$-0.304276\pi$
$173$	454171.	1.15373	0.576864	+	0.816840i	$0.304276\pi$
$174$	75287.7	0.188517
$175$	0	0
$176$	303008.	0.737348
$177$	−299439.	−0.718414
$178$	55223.5	0.130639
$179$	−500419.	−1.16735	−0.583675	−	0.811987i	$-0.698386\pi$
$179$	−500419.	−1.16735	−0.583675	+	0.811987i	$0.698386\pi$
$180$	0	0
$181$	98859.3	0.224296	0.112148	−	0.993692i	$-0.464227\pi$
$181$	98859.3	0.224296	0.112148	+	0.993692i	$0.464227\pi$
$182$	19162.8	0.0428825
$183$	74702.4	0.164895
$184$	−158523.	−0.345181
$185$	0	0
$186$	90531.2	0.191874
$187$	−129633.	−0.271089
$188$	−135407.	−0.279413
$189$	−324975.	−0.661752
$190$	0	0
$191$	687945.	1.36449	0.682245	−	0.731124i	$-0.261004\pi$
$191$	687945.	1.36449	0.682245	+	0.731124i	$0.261004\pi$
$192$	534835.	1.04705
$193$	320330.	0.619020	0.309510	−	0.950896i	$-0.399835\pi$
$193$	320330.	0.619020	0.309510	+	0.950896i	$0.399835\pi$
$194$	−66344.0	−0.126560
$195$	0	0
$196$	67262.2	0.125064
$197$	382454.	0.702124	0.351062	−	0.936352i	$-0.385821\pi$
$197$	382454.	0.702124	0.351062	+	0.936352i	$0.385821\pi$
$198$	24272.3	0.0439996
$199$	−60139.0	−0.107652	−0.0538262	−	0.998550i	$-0.517142\pi$
$199$	−60139.0	−0.107652	−0.0538262	+	0.998550i	$0.517142\pi$
$200$	0	0
$201$	153124.	0.267334
$202$	−127445.	−0.219758
$203$	624079.	1.06292
$204$	−238846.	−0.401830
$205$	0	0
$206$	−20328.8	−0.0333767
$207$	308354.	0.500177
$208$	−192771.	−0.308947
$209$	−540030.	−0.855169
$210$	0	0
$211$	−433380.	−0.670135	−0.335068	−	0.942194i	$-0.608759\pi$
$211$	−433380.	−0.670135	−0.335068	+	0.942194i	$0.608759\pi$
$212$	672867.	1.02823
$213$	1.05471e6	1.59289
$214$	−9933.30	−0.0148272
$215$	0	0
$216$	−134627.	−0.196336
$217$	750435.	1.08184
$218$	−1248.19	−0.00177885
$219$	1.34998e6	1.90203
$220$	0	0
$221$	82471.6	0.113586
$222$	153341.	0.208822
$223$	874627.	1.17777	0.588885	−	0.808217i	$-0.299567\pi$
$223$	874627.	1.17777	0.588885	+	0.808217i	$0.299567\pi$
$224$	−286808.	−0.381918
$225$	0	0
$226$	74800.3	0.0974165
$227$	−928077.	−1.19542	−0.597708	−	0.801714i	$-0.703922\pi$
$227$	−928077.	−1.19542	−0.597708	+	0.801714i	$0.703922\pi$
$228$	−994991.	−1.26760
$229$	343015.	0.432239	0.216120	−	0.976367i	$-0.430660\pi$
$229$	343015.	0.432239	0.216120	+	0.976367i	$0.430660\pi$
$230$	0	0
$231$	702247.	0.865885
$232$	258537.	0.315357
$233$	−961943.	−1.16081	−0.580403	−	0.814330i	$-0.697105\pi$
$233$	−961943.	−1.16081	−0.580403	+	0.814330i	$0.697105\pi$
$234$	−15441.9	−0.0184357
$235$	0	0
$236$	−509051.	−0.594951
$237$	480902.	0.556142
$238$	39541.1	0.0452487
$239$	−505566.	−0.572510	−0.286255	−	0.958153i	$-0.592411\pi$
$239$	−505566.	−0.572510	−0.286255	+	0.958153i	$0.592411\pi$
$240$	0	0
$241$	149779.	0.166114	0.0830571	−	0.996545i	$-0.473532\pi$
$241$	149779.	0.166114	0.0830571	+	0.996545i	$0.473532\pi$
$242$	−49315.4	−0.0541308
$243$	699465.	0.759889
$244$	126995.	0.136557
$245$	0	0
$246$	187712.	0.197767
$247$	343563.	0.358314
$248$	310883.	0.320972
$249$	971774.	0.993270
$250$	0	0
$251$	1.26875e6	1.27113	0.635566	−	0.772046i	$-0.280767\pi$
$251$	1.26875e6	1.27113	0.635566	+	0.772046i	$0.280767\pi$
$252$	370705.	0.367728
$253$	993034.	0.975355
$254$	60818.6	0.0591497
$255$	0	0
$256$	849233.	0.809892
$257$	1.37870e6	1.30208	0.651040	−	0.759044i	$-0.274333\pi$
$257$	1.37870e6	1.30208	0.651040	+	0.759044i	$0.274333\pi$
$258$	27010.6	0.0252630
$259$	1.27108e6	1.17740
$260$	0	0
$261$	−502899.	−0.456961
$262$	−176298.	−0.158670
$263$	−789360.	−0.703697	−0.351849	−	0.936057i	$-0.614447\pi$
$263$	−789360.	−0.703697	−0.351849	+	0.936057i	$0.614447\pi$
$264$	290920.	0.256900
$265$	0	0
$266$	164721.	0.142740
$267$	−1.28749e6	−1.10526
$268$	260314.	0.221391
$269$	729904.	0.615014	0.307507	−	0.951546i	$-0.400505\pi$
$269$	729904.	0.615014	0.307507	+	0.951546i	$0.400505\pi$
$270$	0	0
$271$	−116925.	−0.0967130	−0.0483565	−	0.998830i	$-0.515398\pi$
$271$	−116925.	−0.0967130	−0.0483565	+	0.998830i	$0.515398\pi$
$272$	−397770.	−0.325995
$273$	−446764.	−0.362804
$274$	190303.	0.153133
$275$	0	0
$276$	1.82964e6	1.44575
$277$	−65850.8	−0.0515658	−0.0257829	−	0.999668i	$-0.508208\pi$
$277$	−65850.8	−0.0515658	−0.0257829	+	0.999668i	$0.508208\pi$
$278$	82904.1	0.0643375
$279$	−604721.	−0.465098
$280$	0	0
$281$	−775389.	−0.585806	−0.292903	−	0.956142i	$-0.594621\pi$
$281$	−775389.	−0.585806	−0.292903	+	0.956142i	$0.594621\pi$
$282$	−63048.7	−0.0472121
$283$	−1.81328e6	−1.34586	−0.672928	−	0.739708i	$-0.734964\pi$
$283$	−1.81328e6	−1.34586	−0.672928	+	0.739708i	$0.734964\pi$
$284$	1.79303e6	1.31914
$285$	0	0
$286$	−49729.6	−0.0359501
$287$	1.55599e6	1.11507
$288$	231117.	0.164192
$289$	−1.24968e6	−0.880147
$290$	0	0
$291$	1.54676e6	1.07075
$292$	2.29498e6	1.57515
$293$	−224566.	−0.152818	−0.0764090	−	0.997077i	$-0.524345\pi$
$293$	−224566.	−0.152818	−0.0764090	+	0.997077i	$0.524345\pi$
$294$	31318.9	0.0211319
$295$	0	0
$296$	526571.	0.349323
$297$	843347.	0.554773
$298$	−389695.	−0.254205
$299$	−631761.	−0.408672
$300$	0	0
$301$	223898.	0.142440
$302$	−315441.	−0.199022
$303$	2.97128e6	1.85925
$304$	−1.65704e6	−1.02837
$305$	0	0
$306$	−31863.2	−0.0194530
$307$	−2.06611e6	−1.25114	−0.625572	−	0.780166i	$-0.715134\pi$
$307$	−2.06611e6	−1.25114	−0.625572	+	0.780166i	$0.715134\pi$
$308$	1.19383e6	0.717078
$309$	473949.	0.282381
$310$	0	0
$311$	−927980.	−0.544049	−0.272024	−	0.962290i	$-0.587693\pi$
$311$	−927980.	−0.544049	−0.272024	+	0.962290i	$0.587693\pi$
$312$	−185081.	−0.107640
$313$	2.92014e6	1.68478	0.842388	−	0.538871i	$-0.181149\pi$
$313$	2.92014e6	1.68478	0.842388	+	0.538871i	$0.181149\pi$
$314$	−129286.	−0.0739991
$315$	0	0
$316$	817542.	0.460567
$317$	3.00845e6	1.68149	0.840746	−	0.541430i	$-0.182117\pi$
$317$	3.00845e6	1.68149	0.840746	+	0.541430i	$0.182117\pi$
$318$	313303.	0.173739
$319$	−1.61955e6	−0.891085
$320$	0	0
$321$	231586.	0.125444
$322$	−302898.	−0.162801
$323$	708918.	0.378085
$324$	2.29776e6	1.21602
$325$	0	0
$326$	412249.	0.214840
$327$	29100.4	0.0150498
$328$	644600.	0.330831
$329$	−522626.	−0.266196
$330$	0	0
$331$	1.43004e6	0.717429	0.358714	−	0.933447i	$-0.383215\pi$
$331$	1.43004e6	0.717429	0.358714	+	0.933447i	$0.383215\pi$
$332$	1.65203e6	0.822571
$333$	−1.02427e6	−0.506179
$334$	−376318.	−0.184582
$335$	0	0
$336$	2.15480e6	1.04126
$337$	−938578.	−0.450190	−0.225095	−	0.974337i	$-0.572269\pi$
$337$	−938578.	−0.450190	−0.225095	+	0.974337i	$0.572269\pi$
$338$	−262267.	−0.124868
$339$	−1.74391e6	−0.824183
$340$	0	0
$341$	−1.94746e6	−0.906951
$342$	−132737.	−0.0613658
$343$	2.29479e6	1.05319
$344$	92754.1	0.0422607
$345$	0	0
$346$	359507.	0.161442
$347$	−2.47293e6	−1.10252	−0.551262	−	0.834332i	$-0.685853\pi$
$347$	−2.47293e6	−1.10252	−0.551262	+	0.834332i	$0.685853\pi$
$348$	−2.98399e6	−1.32084
$349$	4.46745e6	1.96334	0.981672	−	0.190579i	$-0.0610366\pi$
$349$	4.46745e6	1.96334	0.981672	+	0.190579i	$0.0610366\pi$
$350$	0	0
$351$	−536531.	−0.232448
$352$	744298.	0.320177
$353$	−139969.	−0.0597853	−0.0298926	−	0.999553i	$-0.509517\pi$
$353$	−139969.	−0.0597853	−0.0298926	+	0.999553i	$0.509517\pi$
$354$	−237027.	−0.100528
$355$	0	0
$356$	−2.18875e6	−0.915318
$357$	−921867.	−0.382823
$358$	−396116.	−0.163348
$359$	−2.57955e6	−1.05635	−0.528175	−	0.849135i	$-0.677124\pi$
$359$	−2.57955e6	−1.05635	−0.528175	+	0.849135i	$0.677124\pi$
$360$	0	0
$361$	477133.	0.192695
$362$	78254.0	0.0313859
$363$	1.14975e6	0.457969
$364$	−759507.	−0.300454
$365$	0	0
$366$	59132.1	0.0230739
$367$	−1.29375e6	−0.501399	−0.250700	−	0.968065i	$-0.580661\pi$
$367$	−1.29375e6	−0.501399	−0.250700	+	0.968065i	$0.580661\pi$
$368$	3.04706e6	1.17290
$369$	−1.25386e6	−0.479383
$370$	0	0
$371$	2.59705e6	0.979593
$372$	−3.58815e6	−1.34435
$373$	1.34681e6	0.501228	0.250614	−	0.968087i	$-0.419368\pi$
$373$	1.34681e6	0.501228	0.250614	+	0.968087i	$0.419368\pi$
$374$	−102614.	−0.0379338
$375$	0	0
$376$	−216508.	−0.0789778
$377$	1.03035e6	0.373362
$378$	−257240.	−0.0925996
$379$	−2.39306e6	−0.855767	−0.427884	−	0.903834i	$-0.640741\pi$
$379$	−2.39306e6	−0.855767	−0.427884	+	0.903834i	$0.640741\pi$
$380$	0	0
$381$	−1.41794e6	−0.500431
$382$	544556.	0.190934
$383$	−1.49710e6	−0.521500	−0.260750	−	0.965406i	$-0.583970\pi$
$383$	−1.49710e6	−0.521500	−0.260750	+	0.965406i	$0.583970\pi$
$384$	1.82210e6	0.630585
$385$	0	0
$386$	253563.	0.0866200
$387$	−180423.	−0.0612369
$388$	2.62951e6	0.886738
$389$	−2.98917e6	−1.00156	−0.500780	−	0.865575i	$-0.666953\pi$
$389$	−2.98917e6	−1.00156	−0.500780	+	0.865575i	$0.666953\pi$
$390$	0	0
$391$	−1.30359e6	−0.431222
$392$	107549.	0.0353501
$393$	4.11024e6	1.34241
$394$	302739.	0.0982488
$395$	0	0
$396$	−962021.	−0.308281
$397$	−18270.8	−0.00581809	−0.00290904	−	0.999996i	$-0.500926\pi$
$397$	−18270.8	−0.00581809	−0.00290904	+	0.999996i	$0.500926\pi$
$398$	−47604.2	−0.0150639
$399$	−3.84034e6	−1.20764
$400$	0	0
$401$	−6.07515e6	−1.88667	−0.943336	−	0.331840i	$-0.892331\pi$
$401$	−6.07515e6	−1.88667	−0.943336	+	0.331840i	$0.892331\pi$
$402$	121209.	0.0374083
$403$	1.23896e6	0.380010
$404$	5.05123e6	1.53973
$405$	0	0
$406$	494001.	0.148735
$407$	−3.29860e6	−0.987060
$408$	−381902.	−0.113580
$409$	5.42830e6	1.60456	0.802279	−	0.596949i	$-0.203621\pi$
$409$	5.42830e6	1.60456	0.802279	+	0.596949i	$0.203621\pi$
$410$	0	0
$411$	−4.43675e6	−1.29557
$412$	805721.	0.233852
$413$	−1.96477e6	−0.566809
$414$	244083.	0.0699902
$415$	0	0
$416$	−473517.	−0.134153
$417$	−1.93284e6	−0.544321
$418$	−427471.	−0.119665
$419$	850141.	0.236568	0.118284	−	0.992980i	$-0.462261\pi$
$419$	850141.	0.236568	0.118284	+	0.992980i	$0.462261\pi$
$420$	0	0
$421$	−946342.	−0.260221	−0.130111	−	0.991499i	$-0.541533\pi$
$421$	−946342.	−0.260221	−0.130111	+	0.991499i	$0.541533\pi$
$422$	−343050.	−0.0937727
$423$	421146.	0.114441
$424$	1.07588e6	0.290636
$425$	0	0
$426$	834879.	0.222895
$427$	490161.	0.130097
$428$	393701.	0.103886
$429$	1.15940e6	0.304153
$430$	0	0
$431$	−5.38768e6	−1.39704	−0.698520	−	0.715591i	$-0.746158\pi$
$431$	−5.38768e6	−1.39704	−0.698520	+	0.715591i	$0.746158\pi$
$432$	2.58775e6	0.667135
$433$	−6.61460e6	−1.69545	−0.847723	−	0.530439i	$-0.822027\pi$
$433$	−6.61460e6	−1.69545	−0.847723	+	0.530439i	$0.822027\pi$
$434$	594022.	0.151383
$435$	0	0
$436$	49471.2	0.0124634
$437$	−5.43055e6	−1.36032
$438$	1.06860e6	0.266152
$439$	−2.73329e6	−0.676900	−0.338450	−	0.940984i	$-0.609903\pi$
$439$	−2.73329e6	−0.676900	−0.338450	+	0.940984i	$0.609903\pi$
$440$	0	0
$441$	−209201.	−0.0512232
$442$	65282.0	0.0158942
$443$	923166.	0.223496	0.111748	−	0.993737i	$-0.464355\pi$
$443$	923166.	0.223496	0.111748	+	0.993737i	$0.464355\pi$
$444$	−6.07759e6	−1.46310
$445$	0	0
$446$	692328.	0.164807
$447$	9.08541e6	2.15068
$448$	3.50933e6	0.826092
$449$	4.49300e6	1.05177	0.525885	−	0.850556i	$-0.323734\pi$
$449$	4.49300e6	1.05177	0.525885	+	0.850556i	$0.323734\pi$
$450$	0	0
$451$	−4.03797e6	−0.934807
$452$	−2.96467e6	−0.682543
$453$	7.35425e6	1.68381
$454$	−734637.	−0.167276
$455$	0	0
$456$	−1.59094e6	−0.358295
$457$	4.94240e6	1.10700	0.553500	−	0.832849i	$-0.313292\pi$
$457$	4.94240e6	1.10700	0.553500	+	0.832849i	$0.313292\pi$
$458$	271520.	0.0604837
$459$	−1.10709e6	−0.245275
$460$	0	0
$461$	1.62206e6	0.355479	0.177740	−	0.984078i	$-0.443122\pi$
$461$	1.62206e6	0.355479	0.177740	+	0.984078i	$0.443122\pi$
$462$	555877.	0.121164
$463$	7.75455e6	1.68114	0.840571	−	0.541702i	$-0.182220\pi$
$463$	7.75455e6	1.68114	0.840571	+	0.541702i	$0.182220\pi$
$464$	−4.96949e6	−1.07156
$465$	0	0
$466$	−761444.	−0.162433
$467$	−4.58917e6	−0.973737	−0.486869	−	0.873475i	$-0.661861\pi$
$467$	−4.58917e6	−0.973737	−0.486869	+	0.873475i	$0.661861\pi$
$468$	612030.	0.129169
$469$	1.00473e6	0.210919
$470$	0	0
$471$	3.01419e6	0.626063
$472$	−813946.	−0.168167
$473$	−581040.	−0.119413
$474$	380667.	0.0778216
$475$	0	0
$476$	−1.56719e6	−0.317033
$477$	−2.09277e6	−0.421139
$478$	−400191.	−0.0801120
$479$	4.61888e6	0.919810	0.459905	−	0.887968i	$-0.347883\pi$
$479$	4.61888e6	0.919810	0.459905	+	0.887968i	$0.347883\pi$
$480$	0	0
$481$	2.09854e6	0.413576
$482$	118560.	0.0232445
$483$	7.06182e6	1.37736
$484$	1.95459e6	0.379265
$485$	0	0
$486$	553675.	0.106332
$487$	−33020.1	−0.00630894	−0.00315447	−	0.999995i	$-0.501004\pi$
$487$	−33020.1	−0.00630894	−0.00315447	+	0.999995i	$0.501004\pi$
$488$	203059.	0.0385987
$489$	−9.61123e6	−1.81764
$490$	0	0
$491$	−6.28653e6	−1.17681	−0.588407	−	0.808565i	$-0.700245\pi$
$491$	−6.28653e6	−1.17681	−0.588407	+	0.808565i	$0.700245\pi$
$492$	−7.43986e6	−1.38565
$493$	2.12605e6	0.393964
$494$	271954.	0.0501392
$495$	0	0
$496$	−5.97566e6	−1.09064
$497$	6.92052e6	1.25675
$498$	769227.	0.138989
$499$	−5.33264e6	−0.958718	−0.479359	−	0.877619i	$-0.659131\pi$
$499$	−5.33264e6	−0.958718	−0.479359	+	0.877619i	$0.659131\pi$
$500$	0	0
$501$	8.77353e6	1.56164
$502$	1.00430e6	0.177871
$503$	1.83489e6	0.323363	0.161682	−	0.986843i	$-0.448308\pi$
$503$	1.83489e6	0.323363	0.161682	+	0.986843i	$0.448308\pi$
$504$	592738.	0.103941
$505$	0	0
$506$	786055.	0.136482
$507$	6.11452e6	1.05643
$508$	−2.41051e6	−0.414429
$509$	84105.6	0.0143890	0.00719450	−	0.999974i	$-0.497710\pi$
$509$	84105.6	0.0143890	0.00719450	+	0.999974i	$0.497710\pi$
$510$	0	0
$511$	8.85789e6	1.50065
$512$	3.83169e6	0.645974
$513$	−4.61197e6	−0.773736
$514$	1.09134e6	0.182201
$515$	0	0
$516$	−1.07055e6	−0.177004
$517$	1.35627e6	0.223163
$518$	1.00615e6	0.164755
$519$	−8.38161e6	−1.36587
$520$	0	0
$521$	−2.19618e6	−0.354465	−0.177232	−	0.984169i	$-0.556714\pi$
$521$	−2.19618e6	−0.354465	−0.177232	+	0.984169i	$0.556714\pi$
$522$	−398079.	−0.0639431
$523$	1.14580e7	1.83170	0.915852	−	0.401516i	$-0.131517\pi$
$523$	1.14580e7	1.83170	0.915852	+	0.401516i	$0.131517\pi$
$524$	6.98748e6	1.11171
$525$	0	0
$526$	−624833.	−0.0984690
$527$	2.55651e6	0.400979
$528$	−5.59195e6	−0.872927
$529$	3.54964e6	0.551499
$530$	0	0
$531$	1.58326e6	0.243679
$532$	−6.52865e6	−1.00010
$533$	2.56893e6	0.391682
$534$	−1.01914e6	−0.154661
$535$	0	0
$536$	416229.	0.0625777
$537$	9.23512e6	1.38200
$538$	577770.	0.0860595
$539$	−673718.	−0.0998864
$540$	0	0
$541$	−8.45962e6	−1.24268	−0.621338	−	0.783543i	$-0.713410\pi$
$541$	−8.45962e6	−1.24268	−0.621338	+	0.783543i	$0.713410\pi$
$542$	−92554.3	−0.0135331
$543$	−1.82442e6	−0.265538
$544$	−977069.	−0.141556
$545$	0	0
$546$	−353645.	−0.0507675
$547$	−1.25382e6	−0.179170	−0.0895850	−	0.995979i	$-0.528554\pi$
$547$	−1.25382e6	−0.179170	−0.0895850	+	0.995979i	$0.528554\pi$
$548$	−7.54255e6	−1.07292
$549$	−394984.	−0.0559306
$550$	0	0
$551$	8.85677e6	1.24279
$552$	2.92550e6	0.408651
$553$	3.15545e6	0.438781
$554$	−52125.4	−0.00721565
$555$	0	0
$556$	−3.28586e6	−0.450777
$557$	−2.37387e6	−0.324204	−0.162102	−	0.986774i	$-0.551827\pi$
$557$	−2.37387e6	−0.324204	−0.162102	+	0.986774i	$0.551827\pi$
$558$	−478678.	−0.0650816
$559$	369653.	0.0500339
$560$	0	0
$561$	2.39235e6	0.320935
$562$	−613774.	−0.0819724
$563$	−1.00757e7	−1.33969	−0.669844	−	0.742502i	$-0.733639\pi$
$563$	−1.00757e7	−1.33969	−0.669844	+	0.742502i	$0.733639\pi$
$564$	2.49890e6	0.330789
$565$	0	0
$566$	−1.43534e6	−0.188327
$567$	8.86860e6	1.15850
$568$	2.86696e6	0.372865
$569$	−7.68830e6	−0.995519	−0.497760	−	0.867315i	$-0.665844\pi$
$569$	−7.68830e6	−0.995519	−0.497760	+	0.867315i	$0.665844\pi$
$570$	0	0
$571$	−7.84389e6	−1.00680	−0.503398	−	0.864055i	$-0.667917\pi$
$571$	−7.84389e6	−1.00680	−0.503398	+	0.864055i	$0.667917\pi$
$572$	1.97101e6	0.251882
$573$	−1.26959e7	−1.61538
$574$	1.23167e6	0.156033
$575$	0	0
$576$	−2.82791e6	−0.355148
$577$	6.26586e6	0.783504	0.391752	−	0.920071i	$-0.371869\pi$
$577$	6.26586e6	0.783504	0.391752	+	0.920071i	$0.371869\pi$
$578$	−989210.	−0.123160
$579$	−5.91162e6	−0.732841
$580$	0	0
$581$	6.37631e6	0.783663
$582$	1.22436e6	0.149831
$583$	−6.73964e6	−0.821231
$584$	3.66956e6	0.445227
$585$	0	0
$586$	−177759.	−0.0213840
$587$	8.23149e6	0.986015	0.493007	−	0.870025i	$-0.335898\pi$
$587$	8.23149e6	0.986015	0.493007	+	0.870025i	$0.335898\pi$
$588$	−1.24131e6	−0.148060
$589$	1.06500e7	1.26491
$590$	0	0
$591$	−7.05810e6	−0.831226
$592$	−1.01215e7	−1.18698
$593$	−1.50824e7	−1.76130	−0.880649	−	0.473770i	$-0.842893\pi$
$593$	−1.50824e7	−1.76130	−0.880649	+	0.473770i	$0.842893\pi$
$594$	667567.	0.0776299
$595$	0	0
$596$	1.54454e7	1.78107
$597$	1.10985e6	0.127447
$598$	−500082.	−0.0571858
$599$	−1.04520e7	−1.19023	−0.595115	−	0.803641i	$-0.702893\pi$
$599$	−1.04520e7	−1.19023	−0.595115	+	0.803641i	$0.702893\pi$
$600$	0	0
$601$	−4.36307e6	−0.492727	−0.246364	−	0.969177i	$-0.579236\pi$
$601$	−4.36307e6	−0.492727	−0.246364	+	0.969177i	$0.579236\pi$
$602$	177230.	0.0199318
$603$	−809636.	−0.0906769
$604$	1.25023e7	1.39444
$605$	0	0
$606$	2.35197e6	0.260166
$607$	−9.12224e6	−1.00492	−0.502458	−	0.864602i	$-0.667571\pi$
$607$	−9.12224e6	−1.00492	−0.502458	+	0.864602i	$0.667571\pi$
$608$	−4.07030e6	−0.446548
$609$	−1.15172e7	−1.25836
$610$	0	0
$611$	−862851.	−0.0935046
$612$	1.26288e6	0.136296
$613$	−1.20884e7	−1.29933	−0.649665	−	0.760221i	$-0.725091\pi$
$613$	−1.20884e7	−1.29933	−0.649665	+	0.760221i	$0.725091\pi$
$614$	−1.63547e6	−0.175074
$615$	0	0
$616$	1.90887e6	0.202687
$617$	7.84481e6	0.829602	0.414801	−	0.909912i	$-0.363851\pi$
$617$	7.84481e6	0.829602	0.414801	+	0.909912i	$0.363851\pi$
$618$	375164.	0.0395139
$619$	1.53189e7	1.60694	0.803471	−	0.595344i	$-0.202984\pi$
$619$	1.53189e7	1.60694	0.803471	+	0.595344i	$0.202984\pi$
$620$	0	0
$621$	8.48072e6	0.882477
$622$	−734560.	−0.0761293
$623$	−8.44788e6	−0.872023
$624$	3.55755e6	0.365755
$625$	0	0
$626$	2.31149e6	0.235752
$627$	9.96612e6	1.01241
$628$	5.12417e6	0.518471
$629$	4.33020e6	0.436396
$630$	0	0
$631$	1.56722e7	1.56695	0.783477	−	0.621421i	$-0.213444\pi$
$631$	1.56722e7	1.56695	0.783477	+	0.621421i	$0.213444\pi$
$632$	1.30721e6	0.130182
$633$	7.99793e6	0.793356
$634$	2.38140e6	0.235293
$635$	0	0
$636$	−1.24176e7	−1.21729
$637$	428614.	0.0418522
$638$	−1.28199e6	−0.124690
$639$	−5.57674e6	−0.540291
$640$	0	0
$641$	−5.56880e6	−0.535324	−0.267662	−	0.963513i	$-0.586251\pi$
$641$	−5.56880e6	−0.535324	−0.267662	+	0.963513i	$0.586251\pi$
$642$	183317.	0.0175535
$643$	1.19873e7	1.14339	0.571693	−	0.820468i	$-0.306287\pi$
$643$	1.19873e7	1.14339	0.571693	+	0.820468i	$0.306287\pi$
$644$	1.20052e7	1.14066
$645$	0	0
$646$	561157.	0.0529058
$647$	3.97123e6	0.372961	0.186481	−	0.982459i	$-0.440292\pi$
$647$	3.97123e6	0.372961	0.186481	+	0.982459i	$0.440292\pi$
$648$	3.67399e6	0.343717
$649$	5.09881e6	0.475178
$650$	0	0
$651$	−1.38491e7	−1.28076
$652$	−1.63393e7	−1.50527
$653$	−3.74038e6	−0.343267	−0.171634	−	0.985161i	$-0.554905\pi$
$653$	−3.74038e6	−0.343267	−0.171634	+	0.985161i	$0.554905\pi$
$654$	23035.0	0.00210593
$655$	0	0
$656$	−1.23902e7	−1.12414
$657$	−7.13792e6	−0.645147
$658$	−413695.	−0.0372491
$659$	982138.	0.0880966	0.0440483	−	0.999029i	$-0.485974\pi$
$659$	982138.	0.0880966	0.0440483	+	0.999029i	$0.485974\pi$
$660$	0	0
$661$	1.75001e7	1.55789	0.778947	−	0.627090i	$-0.215754\pi$
$661$	1.75001e7	1.55789	0.778947	+	0.627090i	$0.215754\pi$
$662$	1.13198e6	0.100391
$663$	−1.52199e6	−0.134471
$664$	2.64151e6	0.232505
$665$	0	0
$666$	−810781.	−0.0708301
$667$	−1.62863e7	−1.41745
$668$	1.49152e7	1.29326
$669$	−1.61410e7	−1.39433
$670$	0	0
$671$	−1.27202e6	−0.109066
$672$	5.29297e6	0.452143
$673$	−3.01062e6	−0.256223	−0.128111	−	0.991760i	$-0.540892\pi$
$673$	−3.01062e6	−0.256223	−0.128111	+	0.991760i	$0.540892\pi$
$674$	−742949.	−0.0629955
$675$	0	0
$676$	1.03948e7	0.874881
$677$	4.12619e6	0.346001	0.173001	−	0.984922i	$-0.444654\pi$
$677$	4.12619e6	0.346001	0.173001	+	0.984922i	$0.444654\pi$
$678$	−1.38042e6	−0.115329
$679$	1.01491e7	0.844795
$680$	0	0
$681$	1.71274e7	1.41522
$682$	−1.54155e6	−0.126911
$683$	−2.34961e7	−1.92728	−0.963640	−	0.267203i	$-0.913901\pi$
$683$	−2.34961e7	−1.92728	−0.963640	+	0.267203i	$0.913901\pi$
$684$	5.26096e6	0.429956
$685$	0	0
$686$	1.81649e6	0.147374
$687$	−6.33026e6	−0.511717
$688$	−1.78288e6	−0.143599
$689$	4.28770e6	0.344094
$690$	0	0
$691$	2.90430e6	0.231391	0.115695	−	0.993285i	$-0.463090\pi$
$691$	2.90430e6	0.231391	0.115695	+	0.993285i	$0.463090\pi$
$692$	−1.42489e7	−1.13114
$693$	−3.71309e6	−0.293699
$694$	−1.95749e6	−0.154277
$695$	0	0
$696$	−4.77124e6	−0.373343
$697$	5.30080e6	0.413294
$698$	3.53630e6	0.274733
$699$	1.77524e7	1.37425
$700$	0	0
$701$	2.97704e6	0.228818	0.114409	−	0.993434i	$-0.463503\pi$
$701$	2.97704e6	0.228818	0.114409	+	0.993434i	$0.463503\pi$
$702$	−424701.	−0.0325267
$703$	1.80389e7	1.37664
$704$	−9.10710e6	−0.692546
$705$	0	0
$706$	−110795.	−0.00836581
$707$	1.94961e7	1.46689
$708$	9.39442e6	0.704347
$709$	−7.07331e6	−0.528454	−0.264227	−	0.964461i	$-0.585117\pi$
$709$	−7.07331e6	−0.528454	−0.264227	+	0.964461i	$0.585117\pi$
$710$	0	0
$711$	−2.54274e6	−0.188638
$712$	−3.49970e6	−0.258721
$713$	−1.95838e7	−1.44269
$714$	−729721.	−0.0535688
$715$	0	0
$716$	1.56999e7	1.14449
$717$	9.33011e6	0.677780
$718$	−2.04189e6	−0.147816
$719$	−1.09162e7	−0.787494	−0.393747	−	0.919219i	$-0.628821\pi$
$719$	−1.09162e7	−0.787494	−0.393747	+	0.919219i	$0.628821\pi$
$720$	0	0
$721$	3.10982e6	0.222791
$722$	377684.	0.0269641
$723$	−2.76413e6	−0.196658
$724$	−3.10155e6	−0.219904
$725$	0	0
$726$	910105.	0.0640841
$727$	−2.08720e7	−1.46463	−0.732316	−	0.680965i	$-0.761560\pi$
$727$	−2.08720e7	−1.46463	−0.732316	+	0.680965i	$0.761560\pi$
$728$	−1.21441e6	−0.0849253
$729$	4.88862e6	0.340696
$730$	0	0
$731$	762753.	0.0527947
$732$	−2.34367e6	−0.161666
$733$	2.01734e7	1.38682	0.693409	−	0.720544i	$-0.256108\pi$
$733$	2.01734e7	1.38682	0.693409	+	0.720544i	$0.256108\pi$
$734$	−1.02409e6	−0.0701613
$735$	0	0
$736$	7.48468e6	0.509306
$737$	−2.60738e6	−0.176822
$738$	−992516.	−0.0670805
$739$	−2.05447e6	−0.138385	−0.0691924	−	0.997603i	$-0.522042\pi$
$739$	−2.05447e6	−0.138385	−0.0691924	+	0.997603i	$0.522042\pi$
$740$	0	0
$741$	−6.34037e6	−0.424198
$742$	2.05574e6	0.137075
$743$	2.78728e6	0.185229	0.0926144	−	0.995702i	$-0.470478\pi$
$743$	2.78728e6	0.185229	0.0926144	+	0.995702i	$0.470478\pi$
$744$	−5.73727e6	−0.379991
$745$	0	0
$746$	1.06610e6	0.0701373
$747$	−5.13820e6	−0.336906
$748$	4.06703e6	0.265781
$749$	1.51956e6	0.0989721
$750$	0	0
$751$	1.69430e6	0.109620	0.0548102	−	0.998497i	$-0.482545\pi$
$751$	1.69430e6	0.109620	0.0548102	+	0.998497i	$0.482545\pi$
$752$	4.16164e6	0.268361
$753$	−2.34144e7	−1.50486
$754$	815592.	0.0522450
$755$	0	0
$756$	1.01956e7	0.648795
$757$	−3.12959e7	−1.98494	−0.992471	−	0.122478i	$-0.960916\pi$
$757$	−3.12959e7	−1.98494	−0.992471	+	0.122478i	$0.960916\pi$
$758$	−1.89427e6	−0.119748
$759$	−1.83262e7	−1.15470
$760$	0	0
$761$	2.24278e7	1.40386	0.701931	−	0.712244i	$-0.252321\pi$
$761$	2.24278e7	1.40386	0.701931	+	0.712244i	$0.252321\pi$
$762$	−1.12239e6	−0.0700258
$763$	190943.	0.0118739
$764$	−2.15832e7	−1.33777
$765$	0	0
$766$	−1.18506e6	−0.0729741
$767$	−3.24382e6	−0.199099
$768$	−1.56724e7	−0.958810
$769$	−2.97269e7	−1.81273	−0.906365	−	0.422496i	$-0.861154\pi$
$769$	−2.97269e7	−1.81273	−0.906365	+	0.422496i	$0.861154\pi$
$770$	0	0
$771$	−2.54436e7	−1.54150
$772$	−1.00499e7	−0.606899
$773$	−2.30688e7	−1.38860	−0.694298	−	0.719688i	$-0.744285\pi$
$773$	−2.30688e7	−1.38860	−0.694298	+	0.719688i	$0.744285\pi$
$774$	−142817.	−0.00856895
$775$	0	0
$776$	4.20445e6	0.250643
$777$	−2.34575e7	−1.39389
$778$	−2.36613e6	−0.140149
$779$	2.20822e7	1.30377
$780$	0	0
$781$	−1.79595e7	−1.05358
$782$	−1.03189e6	−0.0603413
$783$	−1.38313e7	−0.806231
$784$	−2.06726e6	−0.120117
$785$	0	0
$786$	3.25354e6	0.187845
$787$	1.07165e7	0.616760	0.308380	−	0.951263i	$-0.400213\pi$
$787$	1.07165e7	0.616760	0.308380	+	0.951263i	$0.400213\pi$
$788$	−1.19989e7	−0.688375
$789$	1.45675e7	0.833089
$790$	0	0
$791$	−1.14427e7	−0.650258
$792$	−1.53822e6	−0.0871377
$793$	809251.	0.0456983
$794$	−14462.6	−0.000814131 0
$795$	0	0
$796$	1.88677e6	0.105544
$797$	−2.12135e7	−1.18295	−0.591476	−	0.806322i	$-0.701455\pi$
$797$	−2.12135e7	−1.18295	−0.591476	+	0.806322i	$0.701455\pi$
$798$	−3.03990e6	−0.168986
$799$	−1.78043e6	−0.0986641
$800$	0	0
$801$	6.80753e6	0.374894
$802$	−4.80890e6	−0.264004
$803$	−2.29872e7	−1.25805
$804$	−4.80404e6	−0.262099
$805$	0	0
$806$	980724.	0.0531752
$807$	−1.34702e7	−0.728099
$808$	8.07664e6	0.435214
$809$	7.18356e6	0.385894	0.192947	−	0.981209i	$-0.438195\pi$
$809$	7.18356e6	0.385894	0.192947	+	0.981209i	$0.438195\pi$
$810$	0	0
$811$	−2.32312e7	−1.24028	−0.620140	−	0.784491i	$-0.712924\pi$
$811$	−2.32312e7	−1.24028	−0.620140	+	0.784491i	$0.712924\pi$
$812$	−1.95795e7	−1.04210
$813$	2.15783e6	0.114496
$814$	−2.61107e6	−0.138120
$815$	0	0
$816$	7.34076e6	0.385936
$817$	3.17750e6	0.166545
$818$	4.29687e6	0.224527
$819$	2.36224e6	0.123059
$820$	0	0
$821$	3.39971e7	1.76029	0.880144	−	0.474707i	$-0.157446\pi$
$821$	3.39971e7	1.76029	0.880144	+	0.474707i	$0.157446\pi$
$822$	−3.51199e6	−0.181290
$823$	1.31524e7	0.676871	0.338435	−	0.940990i	$-0.390102\pi$
$823$	1.31524e7	0.676871	0.338435	+	0.940990i	$0.390102\pi$
$824$	1.28831e6	0.0660999
$825$	0	0
$826$	−1.55525e6	−0.0793142
$827$	−2.03257e7	−1.03343	−0.516716	−	0.856157i	$-0.672846\pi$
$827$	−2.03257e7	−1.03343	−0.516716	+	0.856157i	$0.672846\pi$
$828$	−9.67411e6	−0.490383
$829$	2.74173e7	1.38560	0.692800	−	0.721129i	$-0.256377\pi$
$829$	2.74173e7	1.38560	0.692800	+	0.721129i	$0.256377\pi$
$830$	0	0
$831$	1.21526e6	0.0610474
$832$	5.79386e6	0.290175
$833$	884416.	0.0441615
$834$	−1.52998e6	−0.0761674
$835$	0	0
$836$	1.69426e7	0.838424
$837$	−1.66318e7	−0.820587
$838$	672945.	0.0331032
$839$	1.17833e7	0.577912	0.288956	−	0.957342i	$-0.406692\pi$
$839$	1.17833e7	0.577912	0.288956	+	0.957342i	$0.406692\pi$
$840$	0	0
$841$	6.05041e6	0.294981
$842$	−749096.	−0.0364130
$843$	1.43096e7	0.693520
$844$	1.35966e7	0.657014
$845$	0	0
$846$	333366.	0.0160139
$847$	7.54409e6	0.361325
$848$	−2.06801e7	−0.987560
$849$	3.34636e7	1.59332
$850$	0	0
$851$	−3.31708e7	−1.57012
$852$	−3.30900e7	−1.56170
$853$	1.46706e7	0.690361	0.345181	−	0.938536i	$-0.387818\pi$
$853$	1.46706e7	0.690361	0.345181	+	0.938536i	$0.387818\pi$
$854$	387996.	0.0182047
$855$	0	0
$856$	629507.	0.0293641
$857$	3.14164e7	1.46118	0.730591	−	0.682815i	$-0.239244\pi$
$857$	3.14164e7	1.46118	0.730591	+	0.682815i	$0.239244\pi$
$858$	917748.	0.0425604
$859$	2.28019e7	1.05436	0.527178	−	0.849755i	$-0.323250\pi$
$859$	2.28019e7	1.05436	0.527178	+	0.849755i	$0.323250\pi$
$860$	0	0
$861$	−2.87154e7	−1.32010
$862$	−4.26472e6	−0.195489
$863$	2.19074e7	1.00130	0.500648	−	0.865651i	$-0.333095\pi$
$863$	2.19074e7	1.00130	0.500648	+	0.865651i	$0.333095\pi$
$864$	6.35646e6	0.289688
$865$	0	0
$866$	−5.23592e6	−0.237246
$867$	2.30626e7	1.04198
$868$	−2.35437e7	−1.06066
$869$	−8.18874e6	−0.367847
$870$	0	0
$871$	1.65880e6	0.0740880
$872$	79101.9	0.00352286
$873$	−8.17837e6	−0.363188
$874$	−4.29866e6	−0.190351
$875$	0	0
$876$	−4.23534e7	−1.86478
$877$	4.05326e7	1.77953	0.889766	−	0.456418i	$-0.150868\pi$
$877$	4.05326e7	1.77953	0.889766	+	0.456418i	$0.150868\pi$
$878$	−2.16359e6	−0.0947193
$879$	4.14431e6	0.180917
$880$	0	0
$881$	−2.80264e6	−0.121654	−0.0608271	−	0.998148i	$-0.519374\pi$
$881$	−2.80264e6	−0.121654	−0.0608271	+	0.998148i	$0.519374\pi$
$882$	−165597.	−0.00716771
$883$	−9.33316e6	−0.402835	−0.201417	−	0.979506i	$-0.564555\pi$
$883$	−9.33316e6	−0.402835	−0.201417	+	0.979506i	$0.564555\pi$
$884$	−2.58742e6	−0.111362
$885$	0	0
$886$	730750.	0.0312741
$887$	−2.27199e7	−0.969609	−0.484804	−	0.874623i	$-0.661109\pi$
$887$	−2.27199e7	−0.969609	−0.484804	+	0.874623i	$0.661109\pi$
$888$	−9.71774e6	−0.413555
$889$	−9.30380e6	−0.394826
$890$	0	0
$891$	−2.30150e7	−0.971219
$892$	−2.74400e7	−1.15471
$893$	−7.41699e6	−0.311243
$894$	7.19173e6	0.300947
$895$	0	0
$896$	1.19557e7	0.497514
$897$	1.16590e7	0.483816
$898$	3.55652e6	0.147175
$899$	3.19395e7	1.31804
$900$	0	0
$901$	8.84738e6	0.363080
$902$	−3.19633e6	−0.130808
$903$	−4.13198e6	−0.168631
$904$	−4.74035e6	−0.192925
$905$	0	0
$906$	5.82140e6	0.235617
$907$	2.87175e7	1.15912	0.579559	−	0.814930i	$-0.303225\pi$
$907$	2.87175e7	1.15912	0.579559	+	0.814930i	$0.303225\pi$
$908$	2.91169e7	1.17201
$909$	−1.57105e7	−0.630637
$910$	0	0
$911$	1.77779e7	0.709715	0.354857	−	0.934920i	$-0.384529\pi$
$911$	1.77779e7	0.709715	0.354857	+	0.934920i	$0.384529\pi$
$912$	3.05804e7	1.21746
$913$	−1.65472e7	−0.656975
$914$	3.91225e6	0.154904
$915$	0	0
$916$	−1.07615e7	−0.423776
$917$	2.69694e7	1.05913
$918$	−876341.	−0.0343215
$919$	−3.34005e7	−1.30456	−0.652281	−	0.757977i	$-0.726188\pi$
$919$	−3.34005e7	−1.30456	−0.652281	+	0.757977i	$0.726188\pi$
$920$	0	0
$921$	3.81296e7	1.48120
$922$	1.28397e6	0.0497426
$923$	1.14257e7	0.441448
$924$	−2.20319e7	−0.848930
$925$	0	0
$926$	6.13826e6	0.235244
$927$	−2.50598e6	−0.0957806
$928$	−1.22069e7	−0.465302
$929$	3.55086e7	1.34988	0.674938	−	0.737875i	$-0.264170\pi$
$929$	3.55086e7	1.34988	0.674938	+	0.737875i	$0.264170\pi$
$930$	0	0
$931$	3.68433e6	0.139311
$932$	3.01794e7	1.13808
$933$	1.71257e7	0.644085
$934$	−3.63264e6	−0.136256
$935$	0	0
$936$	978605.	0.0365105
$937$	4.81654e6	0.179220	0.0896100	−	0.995977i	$-0.471438\pi$
$937$	4.81654e6	0.179220	0.0896100	+	0.995977i	$0.471438\pi$
$938$	795312.	0.0295141
$939$	−5.38904e7	−1.99456
$940$	0	0
$941$	−2.82054e7	−1.03838	−0.519192	−	0.854658i	$-0.673767\pi$
$941$	−2.82054e7	−1.03838	−0.519192	+	0.854658i	$0.673767\pi$
$942$	2.38594e6	0.0876056
$943$	−4.06060e7	−1.48700
$944$	1.56453e7	0.571420
$945$	0	0
$946$	−459933.	−0.0167096
$947$	−4.49485e7	−1.62870	−0.814349	−	0.580376i	$-0.802906\pi$
$947$	−4.49485e7	−1.62870	−0.814349	+	0.580376i	$0.802906\pi$
$948$	−1.50875e7	−0.545253
$949$	1.46243e7	0.527120
$950$	0	0
$951$	−5.55203e7	−1.99067
$952$	−2.50585e6	−0.0896114
$953$	4.84818e7	1.72920	0.864602	−	0.502457i	$-0.167571\pi$
$953$	4.84818e7	1.72920	0.864602	+	0.502457i	$0.167571\pi$
$954$	−1.65657e6	−0.0589304
$955$	0	0
$956$	1.58613e7	0.561300
$957$	2.98885e7	1.05493
$958$	3.65617e6	0.128710
$959$	−2.91118e7	−1.02217
$960$	0	0
$961$	9.77706e6	0.341507
$962$	1.66114e6	0.0578721
$963$	−1.22450e6	−0.0425493
$964$	−4.69906e6	−0.162862
$965$	0	0
$966$	5.58992e6	0.192736
$967$	−1.11669e6	−0.0384032	−0.0192016	−	0.999816i	$-0.506112\pi$
$967$	−1.11669e6	−0.0384032	−0.0192016	+	0.999816i	$0.506112\pi$
$968$	3.12529e6	0.107202
$969$	−1.30829e7	−0.447605
$970$	0	0
$971$	1.27453e7	0.433811	0.216905	−	0.976193i	$-0.430404\pi$
$971$	1.27453e7	0.433811	0.216905	+	0.976193i	$0.430404\pi$
$972$	−2.19446e7	−0.745010
$973$	−1.26823e7	−0.429455
$974$	−26137.7	−0.000882816 0
$975$	0	0
$976$	−3.90312e6	−0.131156
$977$	3.85306e7	1.29142	0.645712	−	0.763581i	$-0.276560\pi$
$977$	3.85306e7	1.29142	0.645712	+	0.763581i	$0.276560\pi$
$978$	−7.60796e6	−0.254344
$979$	2.19232e7	0.731051
$980$	0	0
$981$	−153867.	−0.00510472
$982$	−4.97623e6	−0.164673
$983$	−3.81590e7	−1.25955	−0.629773	−	0.776780i	$-0.716852\pi$
$983$	−3.81590e7	−1.25955	−0.629773	+	0.776780i	$0.716852\pi$
$984$	−1.18959e7	−0.391662
$985$	0	0
$986$	1.68292e6	0.0551278
$987$	9.64495e6	0.315143
$988$	−1.07787e7	−0.351298
$989$	−5.84295e6	−0.189951
$990$	0	0
$991$	3.73229e7	1.20723	0.603617	−	0.797274i	$-0.293725\pi$
$991$	3.73229e7	1.20723	0.603617	+	0.797274i	$0.293725\pi$
$992$	−1.46784e7	−0.473587
$993$	−2.63911e7	−0.849345
$994$	5.47807e6	0.175858
$995$	0	0
$996$	−3.04879e7	−0.973821
$997$	683063.	0.0217632	0.0108816	−	0.999941i	$-0.496536\pi$
$997$	683063.	0.0217632	0.0108816	+	0.999941i	$0.496536\pi$
$998$	−4.22115e6	−0.134154
$999$	−2.81707e7	−0.893068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.l.1.26		52
5.2	odd	4		215.6.b.a.44.54	yes	104
5.3	odd	4		215.6.b.a.44.51	✓	104
5.4	even	2		1075.6.a.k.1.27		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.6.b.a.44.51	✓	104	5.3	odd	4
215.6.b.a.44.54	yes	104	5.2	odd	4
1075.6.a.k.1.27		52	5.4	even	2
1075.6.a.l.1.26		52	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)

\(f(q)\)	\(=\)	\(q+0.791569 q^{2} -18.4548 q^{3} -31.3734 q^{4} -14.6082 q^{6} -121.091 q^{7} -50.1644 q^{8} +97.5785 q^{9} +O(q^{10})\)	\(q+0.791569 q^{2} -18.4548 q^{3} -31.3734 q^{4} -14.6082 q^{6} -121.091 q^{7} -50.1644 q^{8} +97.5785 q^{9} +314.245 q^{11} +578.989 q^{12} -199.920 q^{13} -95.8521 q^{14} +964.241 q^{16} -412.522 q^{17} +77.2401 q^{18} -1718.50 q^{19} +2234.71 q^{21} +248.747 q^{22} +3160.06 q^{23} +925.773 q^{24} -158.251 q^{26} +2683.72 q^{27} +3799.04 q^{28} -5153.79 q^{29} -6197.27 q^{31} +2368.53 q^{32} -5799.33 q^{33} -326.540 q^{34} -3061.37 q^{36} -10496.9 q^{37} -1360.31 q^{38} +3689.49 q^{39} -12849.7 q^{41} +1768.93 q^{42} -1849.00 q^{43} -9858.95 q^{44} +2501.41 q^{46} +4315.97 q^{47} -17794.8 q^{48} -2143.92 q^{49} +7613.00 q^{51} +6272.19 q^{52} -21447.1 q^{53} +2124.35 q^{54} +6074.47 q^{56} +31714.5 q^{57} -4079.58 q^{58} +16225.6 q^{59} -4047.87 q^{61} -4905.57 q^{62} -11815.9 q^{63} -28980.9 q^{64} -4590.57 q^{66} -8297.28 q^{67} +12942.2 q^{68} -58318.2 q^{69} -57151.3 q^{71} -4894.97 q^{72} -73150.6 q^{73} -8309.02 q^{74} +53915.1 q^{76} -38052.3 q^{77} +2920.48 q^{78} -26058.4 q^{79} -73239.0 q^{81} -10171.5 q^{82} -52657.1 q^{83} -70110.5 q^{84} -1463.61 q^{86} +95112.0 q^{87} -15763.9 q^{88} +69764.6 q^{89} +24208.6 q^{91} -99141.9 q^{92} +114369. q^{93} +3416.39 q^{94} -43710.6 q^{96} -83813.3 q^{97} -1697.06 q^{98} +30663.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9}+O(q^{10}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9} - 664 q^{11} - 523 q^{12} + 2704 q^{13} + 150 q^{14} + 13474 q^{16} + 7266 q^{17} + 4860 q^{18} - 1970 q^{19} + 800 q^{21} + 14477 q^{22} + 9522 q^{23} + 314 q^{24} + 5514 q^{26} + 22926 q^{27} + 9408 q^{28} - 7188 q^{29} - 11556 q^{31} + 48390 q^{32} + 26136 q^{33} + 16774 q^{34} + 51872 q^{36} + 42558 q^{37} + 46208 q^{38} + 4682 q^{39} - 7746 q^{41} + 174265 q^{42} - 96148 q^{43} - 48600 q^{44} + 16182 q^{46} + 87136 q^{47} - 2912 q^{48} + 142286 q^{49} - 3710 q^{51} + 146868 q^{52} + 127034 q^{53} - 49563 q^{54} - 2849 q^{56} + 101594 q^{57} + 9480 q^{58} - 55924 q^{59} + 73702 q^{61} + 186016 q^{62} + 50120 q^{63} + 157750 q^{64} + 58211 q^{66} + 131996 q^{67} + 298560 q^{68} + 128436 q^{69} - 56284 q^{71} + 343775 q^{72} + 128620 q^{73} - 17721 q^{74} - 170410 q^{76} + 448438 q^{77} + 237616 q^{78} + 106204 q^{79} + 478568 q^{81} + 249596 q^{82} + 348616 q^{83} - 131855 q^{84} - 36980 q^{86} + 267478 q^{87} + 525216 q^{88} + 80410 q^{89} + 226376 q^{91} + 581456 q^{92} + 902902 q^{93} + 180980 q^{94} + 38543 q^{96} + 316148 q^{97} + 295095 q^{98} + 68428 q^{99}+O(q^{100}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9 - 664 * q^11 - 523 * q^12 + 2704 * q^13 + 150 * q^14 + 13474 * q^16 + 7266 * q^17 + 4860 * q^18 - 1970 * q^19 + 800 * q^21 + 14477 * q^22 + 9522 * q^23 + 314 * q^24 + 5514 * q^26 + 22926 * q^27 + 9408 * q^28 - 7188 * q^29 - 11556 * q^31 + 48390 * q^32 + 26136 * q^33 + 16774 * q^34 + 51872 * q^36 + 42558 * q^37 + 46208 * q^38 + 4682 * q^39 - 7746 * q^41 + 174265 * q^42 - 96148 * q^43 - 48600 * q^44 + 16182 * q^46 + 87136 * q^47 - 2912 * q^48 + 142286 * q^49 - 3710 * q^51 + 146868 * q^52 + 127034 * q^53 - 49563 * q^54 - 2849 * q^56 + 101594 * q^57 + 9480 * q^58 - 55924 * q^59 + 73702 * q^61 + 186016 * q^62 + 50120 * q^63 + 157750 * q^64 + 58211 * q^66 + 131996 * q^67 + 298560 * q^68 + 128436 * q^69 - 56284 * q^71 + 343775 * q^72 + 128620 * q^73 - 17721 * q^74 - 170410 * q^76 + 448438 * q^77 + 237616 * q^78 + 106204 * q^79 + 478568 * q^81 + 249596 * q^82 + 348616 * q^83 - 131855 * q^84 - 36980 * q^86 + 267478 * q^87 + 525216 * q^88 + 80410 * q^89 + 226376 * q^91 + 581456 * q^92 + 902902 * q^93 + 180980 * q^94 + 38543 * q^96 + 316148 * q^97 + 295095 * q^98 + 68428 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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