LMFDB - Embedded newform 1075.6.a.f.1.19

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:	$22$
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+8.10364 q^{2} -9.59374 q^{3} +33.6690 q^{4} -77.7442 q^{6} +225.147 q^{7} +13.5249 q^{8} -150.960 q^{9} +O(q^{10})$	\(q+8.10364 q^{2} -9.59374 q^{3} +33.6690 q^{4} -77.7442 q^{6} +225.147 q^{7} +13.5249 q^{8} -150.960 q^{9} -739.708 q^{11} -323.011 q^{12} -220.650 q^{13} +1824.51 q^{14} -967.807 q^{16} -899.627 q^{17} -1223.33 q^{18} +407.555 q^{19} -2160.00 q^{21} -5994.33 q^{22} +402.273 q^{23} -129.755 q^{24} -1788.07 q^{26} +3779.55 q^{27} +7580.46 q^{28} +5511.99 q^{29} -649.172 q^{31} -8275.56 q^{32} +7096.57 q^{33} -7290.25 q^{34} -5082.68 q^{36} +10765.2 q^{37} +3302.68 q^{38} +2116.86 q^{39} +13595.6 q^{41} -17503.8 q^{42} +1849.00 q^{43} -24905.2 q^{44} +3259.87 q^{46} +13448.7 q^{47} +9284.88 q^{48} +33884.0 q^{49} +8630.78 q^{51} -7429.07 q^{52} +2101.35 q^{53} +30628.1 q^{54} +3045.09 q^{56} -3909.97 q^{57} +44667.2 q^{58} +3828.83 q^{59} -3097.64 q^{61} -5260.66 q^{62} -33988.2 q^{63} -36092.3 q^{64} +57508.0 q^{66} -63977.1 q^{67} -30289.5 q^{68} -3859.30 q^{69} +60342.2 q^{71} -2041.73 q^{72} -52747.0 q^{73} +87237.7 q^{74} +13722.0 q^{76} -166543. q^{77} +17154.3 q^{78} -4013.14 q^{79} +423.318 q^{81} +110174. q^{82} +102136. q^{83} -72724.9 q^{84} +14983.6 q^{86} -52880.6 q^{87} -10004.5 q^{88} +110079. q^{89} -49678.7 q^{91} +13544.1 q^{92} +6227.99 q^{93} +108983. q^{94} +79393.5 q^{96} -9280.39 q^{97} +274584. q^{98} +111667. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9}+O(q^{10}) $ 22 * q - 5 * q^2 - 20 * q^3 + 427 * q^4 + 248 * q^6 - 118 * q^7 - 561 * q^8 + 2618 * q^9	\( 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9} + 1206 q^{11} - 2175 q^{12} - 1942 q^{13} + 2531 q^{14} + 8851 q^{16} - 2470 q^{17} - 1279 q^{18} + 3020 q^{19} + 5632 q^{21} + 3227 q^{22} + 1326 q^{23} + 11040 q^{24} - 3415 q^{26} - 5156 q^{27} + 11489 q^{28} + 17906 q^{29} + 7982 q^{31} - 2427 q^{32} - 10100 q^{33} + 25248 q^{34} - 14813 q^{36} - 22640 q^{37} + 13695 q^{38} + 29048 q^{39} + 29112 q^{41} - 9163 q^{42} + 40678 q^{43} + 63924 q^{44} - 14944 q^{46} - 57080 q^{47} - 54894 q^{48} + 165560 q^{49} - 1576 q^{51} - 97639 q^{52} + 8054 q^{53} + 167379 q^{54} + 269326 q^{56} - 125424 q^{57} - 49485 q^{58} + 193484 q^{59} + 107466 q^{61} - 162441 q^{62} - 183778 q^{63} + 412603 q^{64} + 240489 q^{66} - 109764 q^{67} - 144300 q^{68} + 202444 q^{69} + 182964 q^{71} - 341504 q^{72} - 134468 q^{73} + 198067 q^{74} + 247729 q^{76} + 28416 q^{77} + 7286 q^{78} + 11148 q^{79} + 385246 q^{81} - 23657 q^{82} - 33850 q^{83} + 176749 q^{84} - 9245 q^{86} + 298280 q^{87} + 111354 q^{88} + 244912 q^{89} + 158092 q^{91} + 124762 q^{92} - 239860 q^{93} - 192166 q^{94} - 147719 q^{96} - 232826 q^{97} + 482463 q^{98} - 346894 q^{99}+O(q^{100}) \) 22 * q - 5 * q^2 - 20 * q^3 + 427 * q^4 + 248 * q^6 - 118 * q^7 - 561 * q^8 + 2618 * q^9 + 1206 * q^11 - 2175 * q^12 - 1942 * q^13 + 2531 * q^14 + 8851 * q^16 - 2470 * q^17 - 1279 * q^18 + 3020 * q^19 + 5632 * q^21 + 3227 * q^22 + 1326 * q^23 + 11040 * q^24 - 3415 * q^26 - 5156 * q^27 + 11489 * q^28 + 17906 * q^29 + 7982 * q^31 - 2427 * q^32 - 10100 * q^33 + 25248 * q^34 - 14813 * q^36 - 22640 * q^37 + 13695 * q^38 + 29048 * q^39 + 29112 * q^41 - 9163 * q^42 + 40678 * q^43 + 63924 * q^44 - 14944 * q^46 - 57080 * q^47 - 54894 * q^48 + 165560 * q^49 - 1576 * q^51 - 97639 * q^52 + 8054 * q^53 + 167379 * q^54 + 269326 * q^56 - 125424 * q^57 - 49485 * q^58 + 193484 * q^59 + 107466 * q^61 - 162441 * q^62 - 183778 * q^63 + 412603 * q^64 + 240489 * q^66 - 109764 * q^67 - 144300 * q^68 + 202444 * q^69 + 182964 * q^71 - 341504 * q^72 - 134468 * q^73 + 198067 * q^74 + 247729 * q^76 + 28416 * q^77 + 7286 * q^78 + 11148 * q^79 + 385246 * q^81 - 23657 * q^82 - 33850 * q^83 + 176749 * q^84 - 9245 * q^86 + 298280 * q^87 + 111354 * q^88 + 244912 * q^89 + 158092 * q^91 + 124762 * q^92 - 239860 * q^93 - 192166 * q^94 - 147719 * q^96 - 232826 * q^97 + 482463 * q^98 - 346894 * 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 $

$2$	8.10364	1.43253	0.716267	−	0.697826i	$-0.245849\pi$
$2$	8.10364	1.43253	0.716267	+	0.697826i	$0.245849\pi$
$3$	−9.59374	−0.615439	−0.307719	−	0.951477i	$-0.599566\pi$
$3$	−9.59374	−0.615439	−0.307719	+	0.951477i	$0.599566\pi$
$4$	33.6690	1.05216
$5$	0	0
$5$	0	0
$6$	−77.7442	−0.881637
$7$	225.147	1.73668	0.868341	−	0.495968i	$-0.165187\pi$
$7$	225.147	1.73668	0.868341	+	0.495968i	$0.165187\pi$
$8$	13.5249	0.0747154
$9$	−150.960	−0.621235
$10$	0	0
$11$	−739.708	−1.84323	−0.921613	−	0.388109i	$-0.873128\pi$
$11$	−739.708	−1.84323	−0.921613	+	0.388109i	$0.873128\pi$
$12$	−323.011	−0.647537
$13$	−220.650	−0.362115	−0.181057	−	0.983473i	$-0.557952\pi$
$13$	−220.650	−0.362115	−0.181057	+	0.983473i	$0.557952\pi$
$14$	1824.51	2.48786
$15$	0	0
$16$	−967.807	−0.945124
$17$	−899.627	−0.754988	−0.377494	−	0.926012i	$-0.623214\pi$
$17$	−899.627	−0.754988	−0.377494	+	0.926012i	$0.623214\pi$
$18$	−1223.33	−0.889941
$19$	407.555	0.259001	0.129501	−	0.991579i	$-0.458663\pi$
$19$	407.555	0.259001	0.129501	+	0.991579i	$0.458663\pi$
$20$	0	0
$21$	−2160.00	−1.06882
$22$	−5994.33	−2.64049
$23$	402.273	0.158563	0.0792813	−	0.996852i	$-0.474737\pi$
$23$	402.273	0.158563	0.0792813	+	0.996852i	$0.474737\pi$
$24$	−129.755	−0.0459828
$25$	0	0
$26$	−1788.07	−0.518742
$27$	3779.55	0.997771
$28$	7580.46	1.82726
$29$	5511.99	1.21706	0.608532	−	0.793529i	$-0.291759\pi$
$29$	5511.99	1.21706	0.608532	+	0.793529i	$0.291759\pi$
$30$	0	0
$31$	−649.172	−0.121326	−0.0606632	−	0.998158i	$-0.519322\pi$
$31$	−649.172	−0.121326	−0.0606632	+	0.998158i	$0.519322\pi$
$32$	−8275.56	−1.42864
$33$	7096.57	1.13439
$34$	−7290.25	−1.08155
$35$	0	0
$36$	−5082.68	−0.653637
$37$	10765.2	1.29276	0.646382	−	0.763014i	$-0.276281\pi$
$37$	10765.2	1.29276	0.646382	+	0.763014i	$0.276281\pi$
$38$	3302.68	0.371028
$39$	2116.86	0.222859
$40$	0	0
$41$	13595.6	1.26311	0.631554	−	0.775332i	$-0.282418\pi$
$41$	13595.6	1.26311	0.631554	+	0.775332i	$0.282418\pi$
$42$	−17503.8	−1.53112
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	−24905.2	−1.93936
$45$	0	0
$46$	3259.87	0.227147
$47$	13448.7	0.888046	0.444023	−	0.896015i	$-0.353551\pi$
$47$	13448.7	0.888046	0.444023	+	0.896015i	$0.353551\pi$
$48$	9284.88	0.581665
$49$	33884.0	2.01606
$50$	0	0
$51$	8630.78	0.464649
$52$	−7429.07	−0.381001
$53$	2101.35	0.102756	0.0513781	−	0.998679i	$-0.483639\pi$
$53$	2101.35	0.102756	0.0513781	+	0.998679i	$0.483639\pi$
$54$	30628.1	1.42934
$55$	0	0
$56$	3045.09	0.129757
$57$	−3909.97	−0.159399
$58$	44667.2	1.74349
$59$	3828.83	0.143198	0.0715989	−	0.997434i	$-0.477190\pi$
$59$	3828.83	0.143198	0.0715989	+	0.997434i	$0.477190\pi$
$60$	0	0
$61$	−3097.64	−0.106587	−0.0532937	−	0.998579i	$-0.516972\pi$
$61$	−3097.64	−0.106587	−0.0532937	+	0.998579i	$0.516972\pi$
$62$	−5260.66	−0.173804
$63$	−33988.2	−1.07889
$64$	−36092.3	−1.10145
$65$	0	0
$66$	57508.0	1.62506
$67$	−63977.1	−1.74116	−0.870578	−	0.492030i	$-0.836255\pi$
$67$	−63977.1	−1.74116	−0.870578	+	0.492030i	$0.836255\pi$
$68$	−30289.5	−0.794365
$69$	−3859.30	−0.0975856
$70$	0	0
$71$	60342.2	1.42061	0.710306	−	0.703893i	$-0.248557\pi$
$71$	60342.2	1.42061	0.710306	+	0.703893i	$0.248557\pi$
$72$	−2041.73	−0.0464159
$73$	−52747.0	−1.15849	−0.579243	−	0.815155i	$-0.696652\pi$
$73$	−52747.0	−1.15849	−0.579243	+	0.815155i	$0.696652\pi$
$74$	87237.7	1.85193
$75$	0	0
$76$	13722.0	0.272510
$77$	−166543.	−3.20110
$78$	17154.3	0.319254
$79$	−4013.14	−0.0723463	−0.0361732	−	0.999346i	$-0.511517\pi$
$79$	−4013.14	−0.0723463	−0.0361732	+	0.999346i	$0.511517\pi$
$80$	0	0
$81$	423.318	0.00716892
$82$	110174.	1.80945
$83$	102136.	1.62735	0.813676	−	0.581319i	$-0.197463\pi$
$83$	102136.	1.62735	0.813676	+	0.581319i	$0.197463\pi$
$84$	−72724.9	−1.12457
$85$	0	0
$86$	14983.6	0.218460
$87$	−52880.6	−0.749028
$88$	−10004.5	−0.137718
$89$	110079.	1.47309	0.736543	−	0.676391i	$-0.236457\pi$
$89$	110079.	1.47309	0.736543	+	0.676391i	$0.236457\pi$
$90$	0	0
$91$	−49678.7	−0.628878
$92$	13544.1	0.166833
$93$	6227.99	0.0746690
$94$	108983.	1.27216
$95$	0	0
$96$	79393.5	0.879239
$97$	−9280.39	−0.100147	−0.0500734	−	0.998746i	$-0.515946\pi$
$97$	−9280.39	−0.100147	−0.0500734	+	0.998746i	$0.515946\pi$
$98$	274584.	2.88808
$99$	111667.	1.14508
$100$	0	0
$101$	−137916.	−1.34527	−0.672637	−	0.739973i	$-0.734838\pi$
$101$	−137916.	−1.34527	−0.672637	+	0.739973i	$0.734838\pi$
$102$	69940.8	0.665626
$103$	29651.5	0.275393	0.137697	−	0.990474i	$-0.456030\pi$
$103$	29651.5	0.275393	0.137697	+	0.990474i	$0.456030\pi$
$104$	−2984.28	−0.0270556
$105$	0	0
$106$	17028.5	0.147202
$107$	129584.	1.09419	0.547094	−	0.837071i	$-0.315734\pi$
$107$	129584.	1.09419	0.547094	+	0.837071i	$0.315734\pi$
$108$	127254.	1.04981
$109$	140814.	1.13522	0.567610	−	0.823298i	$-0.307868\pi$
$109$	140814.	1.13522	0.567610	+	0.823298i	$0.307868\pi$
$110$	0	0
$111$	−103279.	−0.795617
$112$	−217898.	−1.64138
$113$	−95818.8	−0.705919	−0.352959	−	0.935639i	$-0.614825\pi$
$113$	−95818.8	−0.705919	−0.352959	+	0.935639i	$0.614825\pi$
$114$	−31685.0	−0.228345
$115$	0	0
$116$	185583.	1.28054
$117$	33309.4	0.224959
$118$	31027.5	0.205136
$119$	−202548.	−1.31117
$120$	0	0
$121$	386117.	2.39749
$122$	−25102.1	−0.152690
$123$	−130433.	−0.777365
$124$	−21857.0	−0.127654
$125$	0	0
$126$	−275428.	−1.54555
$127$	−104338.	−0.574027	−0.287014	−	0.957927i	$-0.592662\pi$
$127$	−104338.	−0.574027	−0.287014	+	0.957927i	$0.592662\pi$
$128$	−27661.4	−0.149228
$129$	−17738.8	−0.0938535
$130$	0	0
$131$	−115583.	−0.588458	−0.294229	−	0.955735i	$-0.595063\pi$
$131$	−115583.	−0.588458	−0.294229	+	0.955735i	$0.595063\pi$
$132$	238934.	1.19356
$133$	91759.6	0.449803
$134$	−518448.	−2.49427
$135$	0	0
$136$	−12167.4	−0.0564093
$137$	−87922.2	−0.400219	−0.200109	−	0.979774i	$-0.564130\pi$
$137$	−87922.2	−0.400219	−0.200109	+	0.979774i	$0.564130\pi$
$138$	−31274.4	−0.139795
$139$	−177184.	−0.777837	−0.388918	−	0.921272i	$-0.627151\pi$
$139$	−177184.	−0.777837	−0.388918	+	0.921272i	$0.627151\pi$
$140$	0	0
$141$	−129023.	−0.546538
$142$	488992.	2.03508
$143$	163217.	0.667460
$144$	146100.	0.587144
$145$	0	0
$146$	−427443.	−1.65957
$147$	−325074.	−1.24076
$148$	362455.	1.36019
$149$	335302.	1.23729	0.618643	−	0.785672i	$-0.287683\pi$
$149$	335302.	1.23729	0.618643	+	0.785672i	$0.287683\pi$
$150$	0	0
$151$	470908.	1.68071	0.840356	−	0.542035i	$-0.182346\pi$
$151$	470908.	1.68071	0.840356	+	0.542035i	$0.182346\pi$
$152$	5512.15	0.0193514
$153$	135808.	0.469025
$154$	−1.34960e6	−4.58569
$155$	0	0
$156$	71272.6	0.234483
$157$	260014.	0.841876	0.420938	−	0.907090i	$-0.361701\pi$
$157$	260014.	0.841876	0.420938	+	0.907090i	$0.361701\pi$
$158$	−32521.0	−0.103639
$159$	−20159.8	−0.0632401
$160$	0	0
$161$	90570.3	0.275373
$162$	3430.42	0.0102697
$163$	−101460.	−0.299108	−0.149554	−	0.988754i	$-0.547784\pi$
$163$	−101460.	−0.299108	−0.149554	+	0.988754i	$0.547784\pi$
$164$	457752.	1.32899
$165$	0	0
$166$	827670.	2.33124
$167$	−162916.	−0.452035	−0.226018	−	0.974123i	$-0.572571\pi$
$167$	−162916.	−0.452035	−0.226018	+	0.974123i	$0.572571\pi$
$168$	−29213.8	−0.0798574
$169$	−322606.	−0.868873
$170$	0	0
$171$	−61524.5	−0.160901
$172$	62254.0	0.160452
$173$	109499.	0.278159	0.139080	−	0.990281i	$-0.455586\pi$
$173$	109499.	0.278159	0.139080	+	0.990281i	$0.455586\pi$
$174$	−428525.	−1.07301
$175$	0	0
$176$	715895.	1.74208
$177$	−36732.8	−0.0881294
$178$	892037.	2.11025
$179$	−509015.	−1.18740	−0.593702	−	0.804685i	$-0.702334\pi$
$179$	−509015.	−1.18740	−0.593702	+	0.804685i	$0.702334\pi$
$180$	0	0
$181$	777702.	1.76448	0.882240	−	0.470800i	$-0.156035\pi$
$181$	777702.	1.76448	0.882240	+	0.470800i	$0.156035\pi$
$182$	−402578.	−0.900890
$183$	29717.9	0.0655980
$184$	5440.71	0.0118471
$185$	0	0
$186$	50469.4	0.106966
$187$	665462.	1.39161
$188$	452804.	0.934363
$189$	850953.	1.73281
$190$	0	0
$191$	−257732.	−0.511193	−0.255596	−	0.966784i	$-0.582272\pi$
$191$	−257732.	−0.511193	−0.255596	+	0.966784i	$0.582272\pi$
$192$	346260.	0.677875
$193$	−495424.	−0.957378	−0.478689	−	0.877985i	$-0.658888\pi$
$193$	−495424.	−0.957378	−0.478689	+	0.877985i	$0.658888\pi$
$194$	−75204.9	−0.143464
$195$	0	0
$196$	1.14084e6	2.12121
$197$	587017.	1.07767	0.538834	−	0.842412i	$-0.318865\pi$
$197$	587017.	1.07767	0.538834	+	0.842412i	$0.318865\pi$
$198$	904905.	1.64036
$199$	593074.	1.06164	0.530819	−	0.847485i	$-0.321884\pi$
$199$	593074.	1.06164	0.530819	+	0.847485i	$0.321884\pi$
$200$	0	0
$201$	613780.	1.07157
$202$	−1.11762e6	−1.92715
$203$	1.24101e6	2.11365
$204$	290590.	0.488883
$205$	0	0
$206$	240285.	0.394510
$207$	−60727.2	−0.0985048
$208$	213547.	0.342243
$209$	−301472.	−0.477398
$210$	0	0
$211$	777729.	1.20260	0.601301	−	0.799023i	$-0.294649\pi$
$211$	777729.	1.20260	0.601301	+	0.799023i	$0.294649\pi$
$212$	70750.2	0.108115
$213$	−578907.	−0.874299
$214$	1.05010e6	1.56746
$215$	0	0
$216$	51118.2	0.0745489
$217$	−146159.	−0.210706
$218$	1.14111e6	1.62624
$219$	506041.	0.712976
$220$	0	0
$221$	198503.	0.273392
$222$	−836935.	−1.13975
$223$	−904905.	−1.21854	−0.609272	−	0.792962i	$-0.708538\pi$
$223$	−904905.	−1.21854	−0.609272	+	0.792962i	$0.708538\pi$
$224$	−1.86321e6	−2.48109
$225$	0	0
$226$	−776481.	−1.01125
$227$	−414418.	−0.533794	−0.266897	−	0.963725i	$-0.585998\pi$
$227$	−414418.	−0.533794	−0.266897	+	0.963725i	$0.585998\pi$
$228$	−131645.	−0.167713
$229$	251989.	0.317535	0.158768	−	0.987316i	$-0.449248\pi$
$229$	251989.	0.317535	0.158768	+	0.987316i	$0.449248\pi$
$230$	0	0
$231$	1.59777e6	1.97008
$232$	74549.3	0.0909335
$233$	319397.	0.385426	0.192713	−	0.981255i	$-0.438271\pi$
$233$	319397.	0.385426	0.192713	+	0.981255i	$0.438271\pi$
$234$	269928.	0.322261
$235$	0	0
$236$	128913.	0.150666
$237$	38501.0	0.0445247
$238$	−1.64138e6	−1.87830
$239$	875455.	0.991378	0.495689	−	0.868500i	$-0.334916\pi$
$239$	875455.	0.991378	0.495689	+	0.868500i	$0.334916\pi$
$240$	0	0
$241$	−667969.	−0.740821	−0.370411	−	0.928868i	$-0.620783\pi$
$241$	−667969.	−0.740821	−0.370411	+	0.928868i	$0.620783\pi$
$242$	3.12896e6	3.43448
$243$	−922492.	−1.00218
$244$	−104294.	−0.112147
$245$	0	0
$246$	−1.05698e6	−1.11360
$247$	−89927.1	−0.0937882
$248$	−8780.01	−0.00906496
$249$	−979861.	−1.00154
$250$	0	0
$251$	−818650.	−0.820189	−0.410095	−	0.912043i	$-0.634504\pi$
$251$	−818650.	−0.820189	−0.410095	+	0.912043i	$0.634504\pi$
$252$	−1.14435e6	−1.13516
$253$	−297564.	−0.292267
$254$	−845516.	−0.822314
$255$	0	0
$256$	930796.	0.887676
$257$	505304.	0.477222	0.238611	−	0.971115i	$-0.423308\pi$
$257$	505304.	0.477222	0.238611	+	0.971115i	$0.423308\pi$
$258$	−143749.	−0.134448
$259$	2.42376e6	2.24512
$260$	0	0
$261$	−832091.	−0.756083
$262$	−936642.	−0.842986
$263$	577463.	0.514796	0.257398	−	0.966306i	$-0.417135\pi$
$263$	577463.	0.514796	0.257398	+	0.966306i	$0.417135\pi$
$264$	95980.6	0.0847567
$265$	0	0
$266$	743587.	0.644358
$267$	−1.05607e6	−0.906593
$268$	−2.15405e6	−1.83197
$269$	−372682.	−0.314020	−0.157010	−	0.987597i	$-0.550186\pi$
$269$	−372682.	−0.314020	−0.157010	+	0.987597i	$0.550186\pi$
$270$	0	0
$271$	1.95969e6	1.62093	0.810466	−	0.585786i	$-0.199214\pi$
$271$	1.95969e6	1.62093	0.810466	+	0.585786i	$0.199214\pi$
$272$	870665.	0.713557
$273$	476604.	0.387036
$274$	−712490.	−0.573327
$275$	0	0
$276$	−129939.	−0.102675
$277$	1.84287e6	1.44310	0.721548	−	0.692364i	$-0.243431\pi$
$277$	1.84287e6	1.44310	0.721548	+	0.692364i	$0.243431\pi$
$278$	−1.43584e6	−1.11428
$279$	97999.2	0.0753723
$280$	0	0
$281$	−1.35549e6	−1.02407	−0.512035	−	0.858965i	$-0.671108\pi$
$281$	−1.35549e6	−1.02407	−0.512035	+	0.858965i	$0.671108\pi$
$282$	−1.04556e6	−0.782935
$283$	1.58467e6	1.17618	0.588090	−	0.808796i	$-0.299880\pi$
$283$	1.58467e6	1.17618	0.588090	+	0.808796i	$0.299880\pi$
$284$	2.03166e6	1.49471
$285$	0	0
$286$	1.32265e6	0.956159
$287$	3.06101e6	2.19362
$288$	1.24928e6	0.887521
$289$	−610528.	−0.429993
$290$	0	0
$291$	89033.6	0.0616342
$292$	−1.77594e6	−1.21891
$293$	568582.	0.386923	0.193461	−	0.981108i	$-0.438029\pi$
$293$	568582.	0.386923	0.193461	+	0.981108i	$0.438029\pi$
$294$	−2.63428e6	−1.77744
$295$	0	0
$296$	145599.	0.0965895
$297$	−2.79577e6	−1.83912
$298$	2.71716e6	1.77245
$299$	−88761.6	−0.0574179
$300$	0	0
$301$	416296.	0.264842
$302$	3.81607e6	2.40768
$303$	1.32313e6	0.827933
$304$	−394434.	−0.244788
$305$	0	0
$306$	1.10054e6	0.671895
$307$	1.05105e6	0.636468	0.318234	−	0.948012i	$-0.396910\pi$
$307$	1.05105e6	0.636468	0.318234	+	0.948012i	$0.396910\pi$
$308$	−5.60733e6	−3.36806
$309$	−284468.	−0.169487
$310$	0	0
$311$	−630646.	−0.369730	−0.184865	−	0.982764i	$-0.559185\pi$
$311$	−630646.	−0.369730	−0.184865	+	0.982764i	$0.559185\pi$
$312$	28630.4	0.0166510
$313$	−2.06009e6	−1.18857	−0.594286	−	0.804254i	$-0.702565\pi$
$313$	−2.06009e6	−1.18857	−0.594286	+	0.804254i	$0.702565\pi$
$314$	2.10706e6	1.20602
$315$	0	0
$316$	−135118.	−0.0761196
$317$	793958.	0.443761	0.221881	−	0.975074i	$-0.428780\pi$
$317$	793958.	0.443761	0.221881	+	0.975074i	$0.428780\pi$
$318$	−163367.	−0.0905936
$319$	−4.07726e6	−2.24332
$320$	0	0
$321$	−1.24320e6	−0.673406
$322$	733949.	0.394481
$323$	−366647.	−0.195543
$324$	14252.7	0.00754283
$325$	0	0
$326$	−822198.	−0.428482
$327$	−1.35093e6	−0.698658
$328$	183880.	0.0943736
$329$	3.02793e6	1.54225
$330$	0	0
$331$	−1.65785e6	−0.831715	−0.415857	−	0.909430i	$-0.636518\pi$
$331$	−1.65785e6	−0.831715	−0.415857	+	0.909430i	$0.636518\pi$
$332$	3.43880e6	1.71223
$333$	−1.62512e6	−0.803111
$334$	−1.32021e6	−0.647556
$335$	0	0
$336$	2.09046e6	1.01017
$337$	−338048.	−0.162145	−0.0810725	−	0.996708i	$-0.525835\pi$
$337$	−338048.	−0.162145	−0.0810725	+	0.996708i	$0.525835\pi$
$338$	−2.61429e6	−1.24469
$339$	919260.	0.434449
$340$	0	0
$341$	480198.	0.223632
$342$	−498573.	−0.230496
$343$	3.84483e6	1.76458
$344$	25007.6	0.0113940
$345$	0	0
$346$	887337.	0.398473
$347$	3.21094e6	1.43155	0.715777	−	0.698328i	$-0.246073\pi$
$347$	3.21094e6	1.43155	0.715777	+	0.698328i	$0.246073\pi$
$348$	−1.78044e6	−0.788094
$349$	−4.06391e6	−1.78599	−0.892997	−	0.450063i	$-0.851402\pi$
$349$	−4.06391e6	−1.78599	−0.892997	+	0.450063i	$0.851402\pi$
$350$	0	0
$351$	−833959.	−0.361307
$352$	6.12150e6	2.63330
$353$	−1.44841e6	−0.618664	−0.309332	−	0.950954i	$-0.600105\pi$
$353$	−1.44841e6	−0.618664	−0.309332	+	0.950954i	$0.600105\pi$
$354$	−297670.	−0.126248
$355$	0	0
$356$	3.70624e6	1.54992
$357$	1.94319e6	0.806947
$358$	−4.12488e6	−1.70100
$359$	2.41633e6	0.989512	0.494756	−	0.869032i	$-0.335257\pi$
$359$	2.41633e6	0.989512	0.494756	+	0.869032i	$0.335257\pi$
$360$	0	0
$361$	−2.31000e6	−0.932918
$362$	6.30222e6	2.52768
$363$	−3.70431e6	−1.47550
$364$	−1.67263e6	−0.661678
$365$	0	0
$366$	240823.	0.0939715
$367$	−3.36339e6	−1.30350	−0.651751	−	0.758433i	$-0.725965\pi$
$367$	−3.36339e6	−1.30350	−0.651751	+	0.758433i	$0.725965\pi$
$368$	−389322.	−0.149861
$369$	−2.05240e6	−0.784687
$370$	0	0
$371$	473111.	0.178455
$372$	209690.	0.0785634
$373$	3.28187e6	1.22138	0.610688	−	0.791871i	$-0.290893\pi$
$373$	3.28187e6	1.22138	0.610688	+	0.791871i	$0.290893\pi$
$374$	5.39266e6	1.99354
$375$	0	0
$376$	181893.	0.0663508
$377$	−1.21622e6	−0.440717
$378$	6.89582e6	2.48231
$379$	5.55463e6	1.98636	0.993179	−	0.116601i	$-0.0371998\pi$
$379$	5.55463e6	1.98636	0.993179	+	0.116601i	$0.0371998\pi$
$380$	0	0
$381$	1.00099e6	0.353278
$382$	−2.08857e6	−0.732301
$383$	4.79764e6	1.67121	0.835605	−	0.549331i	$-0.185117\pi$
$383$	4.79764e6	1.67121	0.835605	+	0.549331i	$0.185117\pi$
$384$	265376.	0.0918404
$385$	0	0
$386$	−4.01473e6	−1.37148
$387$	−279125.	−0.0947375
$388$	−312461.	−0.105370
$389$	5.21934e6	1.74881	0.874403	−	0.485200i	$-0.161253\pi$
$389$	5.21934e6	1.74881	0.874403	+	0.485200i	$0.161253\pi$
$390$	0	0
$391$	−361895.	−0.119713
$392$	458279.	0.150631
$393$	1.10887e6	0.362159
$394$	4.75698e6	1.54380
$395$	0	0
$396$	3.75970e6	1.20480
$397$	−1.42762e6	−0.454608	−0.227304	−	0.973824i	$-0.572991\pi$
$397$	−1.42762e6	−0.454608	−0.227304	+	0.973824i	$0.572991\pi$
$398$	4.80606e6	1.52083
$399$	−880317.	−0.276826
$400$	0	0
$401$	3.22923e6	1.00285	0.501427	−	0.865200i	$-0.332809\pi$
$401$	3.22923e6	1.00285	0.501427	+	0.865200i	$0.332809\pi$
$402$	4.97385e6	1.53507
$403$	143240.	0.0439341
$404$	−4.64349e6	−1.41544
$405$	0	0
$406$	1.00567e7	3.02788
$407$	−7.96314e6	−2.38286
$408$	116731.	0.0347164
$409$	−4.89619e6	−1.44727	−0.723635	−	0.690182i	$-0.757530\pi$
$409$	−4.89619e6	−1.44727	−0.723635	+	0.690182i	$0.757530\pi$
$410$	0	0
$411$	843503.	0.246310
$412$	998335.	0.289756
$413$	862049.	0.248689
$414$	−492111.	−0.141111
$415$	0	0
$416$	1.82600e6	0.517331
$417$	1.69986e6	0.478711
$418$	−2.44302e6	−0.683889
$419$	−5.54792e6	−1.54382	−0.771908	−	0.635734i	$-0.780697\pi$
$419$	−5.54792e6	−1.54382	−0.771908	+	0.635734i	$0.780697\pi$
$420$	0	0
$421$	−1.52060e6	−0.418128	−0.209064	−	0.977902i	$-0.567042\pi$
$421$	−1.52060e6	−0.418128	−0.209064	+	0.977902i	$0.567042\pi$
$422$	6.30243e6	1.72277
$423$	−2.03022e6	−0.551686
$424$	28420.6	0.00767747
$425$	0	0
$426$	−4.69126e6	−1.25246
$427$	−697423.	−0.185109
$428$	4.36296e6	1.15126
$429$	−1.56586e6	−0.410780
$430$	0	0
$431$	1.20050e6	0.311293	0.155646	−	0.987813i	$-0.450254\pi$
$431$	1.20050e6	0.311293	0.155646	+	0.987813i	$0.450254\pi$
$432$	−3.65787e6	−0.943017
$433$	−5.14058e6	−1.31763	−0.658813	−	0.752307i	$-0.728941\pi$
$433$	−5.14058e6	−1.31763	−0.658813	+	0.752307i	$0.728941\pi$
$434$	−1.18442e6	−0.301843
$435$	0	0
$436$	4.74107e6	1.19443
$437$	163948.	0.0410679
$438$	4.10077e6	1.02136
$439$	−1.56317e6	−0.387119	−0.193560	−	0.981089i	$-0.562003\pi$
$439$	−1.56317e6	−0.387119	−0.193560	+	0.981089i	$0.562003\pi$
$440$	0	0
$441$	−5.11514e6	−1.25245
$442$	1.60860e6	0.391644
$443$	−2.79199e6	−0.675935	−0.337967	−	0.941158i	$-0.609739\pi$
$443$	−2.79199e6	−0.675935	−0.337967	+	0.941158i	$0.609739\pi$
$444$	−3.47730e6	−0.837114
$445$	0	0
$446$	−7.33303e6	−1.74561
$447$	−3.21680e6	−0.761473
$448$	−8.12606e6	−1.91287
$449$	−3.58314e6	−0.838780	−0.419390	−	0.907806i	$-0.637756\pi$
$449$	−3.58314e6	−0.838780	−0.419390	+	0.907806i	$0.637756\pi$
$450$	0	0
$451$	−1.00568e7	−2.32819
$452$	−3.22612e6	−0.742736
$453$	−4.51776e6	−1.03437
$454$	−3.35829e6	−0.764678
$455$	0	0
$456$	−52882.1	−0.0119096
$457$	−311099.	−0.0696801	−0.0348401	−	0.999393i	$-0.511092\pi$
$457$	−311099.	−0.0696801	−0.0348401	+	0.999393i	$0.511092\pi$
$458$	2.04203e6	0.454881
$459$	−3.40019e6	−0.753305
$460$	0	0
$461$	1.98094e6	0.434130	0.217065	−	0.976157i	$-0.430352\pi$
$461$	1.98094e6	0.434130	0.217065	+	0.976157i	$0.430352\pi$
$462$	1.29477e7	2.82221
$463$	−5.80999e6	−1.25957	−0.629786	−	0.776769i	$-0.716857\pi$
$463$	−5.80999e6	−1.25957	−0.629786	+	0.776769i	$0.716857\pi$
$464$	−5.33454e6	−1.15028
$465$	0	0
$466$	2.58828e6	0.552136
$467$	−6.08182e6	−1.29045	−0.645225	−	0.763993i	$-0.723236\pi$
$467$	−6.08182e6	−1.29045	−0.645225	+	0.763993i	$0.723236\pi$
$468$	1.12149e6	0.236691
$469$	−1.44042e7	−3.02384
$470$	0	0
$471$	−2.49451e6	−0.518123
$472$	51784.7	0.0106991
$473$	−1.36772e6	−0.281089
$474$	311998.	0.0637832
$475$	0	0
$476$	−6.81959e6	−1.37956
$477$	−317220.	−0.0638357
$478$	7.09437e6	1.42018
$479$	6.91550e6	1.37716	0.688581	−	0.725160i	$-0.258234\pi$
$479$	6.91550e6	1.37716	0.688581	+	0.725160i	$0.258234\pi$
$480$	0	0
$481$	−2.37535e6	−0.468129
$482$	−5.41298e6	−1.06125
$483$	−868908.	−0.169475
$484$	1.30002e7	2.52253
$485$	0	0
$486$	−7.47554e6	−1.43566
$487$	−1.82097e6	−0.347920	−0.173960	−	0.984753i	$-0.555656\pi$
$487$	−1.82097e6	−0.347920	−0.173960	+	0.984753i	$0.555656\pi$
$488$	−41895.4	−0.00796373
$489$	973384.	0.184082
$490$	0	0
$491$	6.51232e6	1.21908	0.609539	−	0.792756i	$-0.291354\pi$
$491$	6.51232e6	1.21908	0.609539	+	0.792756i	$0.291354\pi$
$492$	−4.39155e6	−0.817909
$493$	−4.95873e6	−0.918869
$494$	−728737.	−0.134355
$495$	0	0
$496$	628273.	0.114669
$497$	1.35858e7	2.46715
$498$	−7.94044e6	−1.43473
$499$	9.85118e6	1.77108	0.885538	−	0.464568i	$-0.153790\pi$
$499$	9.85118e6	1.77108	0.885538	+	0.464568i	$0.153790\pi$
$500$	0	0
$501$	1.56297e6	0.278200
$502$	−6.63405e6	−1.17495
$503$	3.02169e6	0.532512	0.266256	−	0.963902i	$-0.414213\pi$
$503$	3.02169e6	0.532512	0.266256	+	0.963902i	$0.414213\pi$
$504$	−459688.	−0.0806096
$505$	0	0
$506$	−2.41136e6	−0.418683
$507$	3.09500e6	0.534738
$508$	−3.51295e6	−0.603966
$509$	2.60970e6	0.446474	0.223237	−	0.974764i	$-0.428338\pi$
$509$	2.60970e6	0.446474	0.223237	+	0.974764i	$0.428338\pi$
$510$	0	0
$511$	−1.18758e7	−2.01192
$512$	8.42800e6	1.42085
$513$	1.54037e6	0.258424
$514$	4.09480e6	0.683637
$515$	0	0
$516$	−597248.	−0.0987485
$517$	−9.94811e6	−1.63687
$518$	1.96413e7	3.21621
$519$	−1.05050e6	−0.171190
$520$	0	0
$521$	7.28994e6	1.17660	0.588301	−	0.808642i	$-0.299797\pi$
$521$	7.28994e6	1.17660	0.588301	+	0.808642i	$0.299797\pi$
$522$	−6.74297e6	−1.08312
$523$	5.13124e6	0.820292	0.410146	−	0.912020i	$-0.365478\pi$
$523$	5.13124e6	0.820292	0.410146	+	0.912020i	$0.365478\pi$
$524$	−3.89156e6	−0.619149
$525$	0	0
$526$	4.67955e6	0.737463
$527$	584013.	0.0916001
$528$	−6.86810e6	−1.07214
$529$	−6.27452e6	−0.974858
$530$	0	0
$531$	−578001.	−0.0889595
$532$	3.08945e6	0.473263
$533$	−2.99988e6	−0.457390
$534$	−8.55797e6	−1.29873
$535$	0	0
$536$	−865287.	−0.130091
$537$	4.88336e6	0.730774
$538$	−3.02008e6	−0.449845
$539$	−2.50643e7	−3.71607
$540$	0	0
$541$	−9.79553e6	−1.43891	−0.719457	−	0.694537i	$-0.755609\pi$
$541$	−9.79553e6	−1.43891	−0.719457	+	0.694537i	$0.755609\pi$
$542$	1.58806e7	2.32204
$543$	−7.46107e6	−1.08593
$544$	7.44491e6	1.07860
$545$	0	0
$546$	3.86223e6	0.554442
$547$	−7.19126e6	−1.02763	−0.513815	−	0.857901i	$-0.671768\pi$
$547$	−7.19126e6	−1.02763	−0.513815	+	0.857901i	$0.671768\pi$
$548$	−2.96025e6	−0.421092
$549$	467620.	0.0662159
$550$	0	0
$551$	2.24644e6	0.315221
$552$	−52196.8	−0.00729115
$553$	−903545.	−0.125643
$554$	1.49340e7	2.06729
$555$	0	0
$556$	−5.96562e6	−0.818406
$557$	−1.28091e7	−1.74937	−0.874683	−	0.484696i	$-0.838930\pi$
$557$	−1.28091e7	−1.74937	−0.874683	+	0.484696i	$0.838930\pi$
$558$	794150.	0.107973
$559$	−407982.	−0.0552220
$560$	0	0
$561$	−6.38426e6	−0.856453
$562$	−1.09844e7	−1.46702
$563$	861034.	0.114485	0.0572426	−	0.998360i	$-0.481769\pi$
$563$	861034.	0.114485	0.0572426	+	0.998360i	$0.481769\pi$
$564$	−4.34408e6	−0.575043
$565$	0	0
$566$	1.28416e7	1.68492
$567$	95308.6	0.0124501
$568$	816125.	0.106142
$569$	−664038.	−0.0859830	−0.0429915	−	0.999075i	$-0.513689\pi$
$569$	−664038.	−0.0859830	−0.0429915	+	0.999075i	$0.513689\pi$
$570$	0	0
$571$	1.04082e7	1.33594	0.667969	−	0.744189i	$-0.267164\pi$
$571$	1.04082e7	1.33594	0.667969	+	0.744189i	$0.267164\pi$
$572$	5.49535e6	0.702272
$573$	2.47261e6	0.314608
$574$	2.48054e7	3.14243
$575$	0	0
$576$	5.44850e6	0.684260
$577$	4.08946e6	0.511360	0.255680	−	0.966762i	$-0.417701\pi$
$577$	4.08946e6	0.511360	0.255680	+	0.966762i	$0.417701\pi$
$578$	−4.94750e6	−0.615980
$579$	4.75296e6	0.589207
$580$	0	0
$581$	2.29955e7	2.82619
$582$	721496.	0.0882931
$583$	−1.55438e6	−0.189403
$584$	−713400.	−0.0865567
$585$	0	0
$586$	4.60759e6	0.554280
$587$	−5.62033e6	−0.673235	−0.336617	−	0.941641i	$-0.609283\pi$
$587$	−5.62033e6	−0.673235	−0.336617	+	0.941641i	$0.609283\pi$
$588$	−1.09449e7	−1.30548
$589$	−264573.	−0.0314237
$590$	0	0
$591$	−5.63169e6	−0.663239
$592$	−1.04187e7	−1.22182
$593$	−2.62237e6	−0.306237	−0.153118	−	0.988208i	$-0.548932\pi$
$593$	−2.62237e6	−0.306237	−0.153118	+	0.988208i	$0.548932\pi$
$594$	−2.26559e7	−2.63460
$595$	0	0
$596$	1.12893e7	1.30182
$597$	−5.68980e6	−0.653373
$598$	−719292.	−0.0822531
$599$	−8.18381e6	−0.931941	−0.465970	−	0.884800i	$-0.654295\pi$
$599$	−8.18381e6	−0.931941	−0.465970	+	0.884800i	$0.654295\pi$
$600$	0	0
$601$	3.41470e6	0.385626	0.192813	−	0.981236i	$-0.438239\pi$
$601$	3.41470e6	0.385626	0.192813	+	0.981236i	$0.438239\pi$
$602$	3.37351e6	0.379395
$603$	9.65800e6	1.08167
$604$	1.58550e7	1.76837
$605$	0	0
$606$	1.07222e7	1.18604
$607$	1.31756e7	1.45143	0.725717	−	0.687994i	$-0.241508\pi$
$607$	1.31756e7	1.45143	0.725717	+	0.687994i	$0.241508\pi$
$608$	−3.37274e6	−0.370019
$609$	−1.19059e7	−1.30082
$610$	0	0
$611$	−2.96746e6	−0.321575
$612$	4.57251e6	0.493488
$613$	−362975.	−0.0390144	−0.0195072	−	0.999810i	$-0.506210\pi$
$613$	−362975.	−0.0390144	−0.0195072	+	0.999810i	$0.506210\pi$
$614$	8.51732e6	0.911763
$615$	0	0
$616$	−2.25248e6	−0.239172
$617$	1.06911e7	1.13060	0.565300	−	0.824886i	$-0.308760\pi$
$617$	1.06911e7	1.13060	0.565300	+	0.824886i	$0.308760\pi$
$618$	−2.30523e6	−0.242797
$619$	1.51044e7	1.58444	0.792221	−	0.610234i	$-0.208925\pi$
$619$	1.51044e7	1.58444	0.792221	+	0.610234i	$0.208925\pi$
$620$	0	0
$621$	1.52041e6	0.158209
$622$	−5.11053e6	−0.529651
$623$	2.47838e7	2.55828
$624$	−2.04871e6	−0.210630
$625$	0	0
$626$	−1.66942e7	−1.70267
$627$	2.89224e6	0.293809
$628$	8.75442e6	0.885785
$629$	−9.68470e6	−0.976022
$630$	0	0
$631$	−1.36596e7	−1.36573	−0.682864	−	0.730545i	$-0.739266\pi$
$631$	−1.36596e7	−1.36573	−0.682864	+	0.730545i	$0.739266\pi$
$632$	−54277.5	−0.00540539
$633$	−7.46132e6	−0.740128
$634$	6.43395e6	0.635703
$635$	0	0
$636$	−678759.	−0.0665384
$637$	−7.47652e6	−0.730047
$638$	−3.30407e7	−3.21364
$639$	−9.10927e6	−0.882534
$640$	0	0
$641$	1.08848e7	1.04635	0.523174	−	0.852226i	$-0.324748\pi$
$641$	1.08848e7	1.04635	0.523174	+	0.852226i	$0.324748\pi$
$642$	−1.00744e7	−0.964677
$643$	−4.76098e6	−0.454118	−0.227059	−	0.973881i	$-0.572911\pi$
$643$	−4.76098e6	−0.454118	−0.227059	+	0.973881i	$0.572911\pi$
$644$	3.04941e6	0.289735
$645$	0	0
$646$	−2.97118e6	−0.280122
$647$	−2.05783e7	−1.93263	−0.966314	−	0.257365i	$-0.917146\pi$
$647$	−2.05783e7	−1.93263	−0.966314	+	0.257365i	$0.917146\pi$
$648$	5725.35	0.000535629 0
$649$	−2.83222e6	−0.263946
$650$	0	0
$651$	1.40221e6	0.129676
$652$	−3.41607e6	−0.314708
$653$	5.05976e6	0.464352	0.232176	−	0.972674i	$-0.425416\pi$
$653$	5.05976e6	0.464352	0.232176	+	0.972674i	$0.425416\pi$
$654$	−1.09475e7	−1.00085
$655$	0	0
$656$	−1.31580e7	−1.19379
$657$	7.96270e6	0.719692
$658$	2.45372e7	2.20933
$659$	6.13149e6	0.549987	0.274994	−	0.961446i	$-0.411324\pi$
$659$	6.13149e6	0.549987	0.274994	+	0.961446i	$0.411324\pi$
$660$	0	0
$661$	2.05262e7	1.82728	0.913638	−	0.406528i	$-0.133261\pi$
$661$	2.05262e7	1.82728	0.913638	+	0.406528i	$0.133261\pi$
$662$	−1.34346e7	−1.19146
$663$	−1.90439e6	−0.168256
$664$	1.38138e6	0.121588
$665$	0	0
$666$	−1.31694e7	−1.15048
$667$	2.21732e6	0.192981
$668$	−5.48521e6	−0.475612
$669$	8.68142e6	0.749939
$670$	0	0
$671$	2.29135e6	0.196465
$672$	1.78752e7	1.52696
$673$	−2.08851e7	−1.77745	−0.888727	−	0.458437i	$-0.848409\pi$
$673$	−2.08851e7	−1.77745	−0.888727	+	0.458437i	$0.848409\pi$
$674$	−2.73942e6	−0.232278
$675$	0	0
$676$	−1.08618e7	−0.914190
$677$	7.44884e6	0.624622	0.312311	−	0.949980i	$-0.398897\pi$
$677$	7.44884e6	0.624622	0.312311	+	0.949980i	$0.398897\pi$
$678$	7.44936e6	0.622364
$679$	−2.08945e6	−0.173923
$680$	0	0
$681$	3.97581e6	0.328517
$682$	3.89135e6	0.320361
$683$	1.56778e7	1.28597	0.642987	−	0.765877i	$-0.277695\pi$
$683$	1.56778e7	1.28597	0.642987	+	0.765877i	$0.277695\pi$
$684$	−2.07147e6	−0.169293
$685$	0	0
$686$	3.11571e7	2.52782
$687$	−2.41751e6	−0.195424
$688$	−1.78947e6	−0.144130
$689$	−463662.	−0.0372095
$690$	0	0
$691$	2.37021e6	0.188839	0.0944195	−	0.995533i	$-0.469901\pi$
$691$	2.37021e6	0.188839	0.0944195	+	0.995533i	$0.469901\pi$
$692$	3.68671e6	0.292667
$693$	2.51413e7	1.98864
$694$	2.60203e7	2.05075
$695$	0	0
$696$	−715207.	−0.0559639
$697$	−1.22310e7	−0.953631
$698$	−3.29324e7	−2.55850
$699$	−3.06421e6	−0.237206
$700$	0	0
$701$	−4.97479e6	−0.382366	−0.191183	−	0.981554i	$-0.561232\pi$
$701$	−4.97479e6	−0.382366	−0.191183	+	0.981554i	$0.561232\pi$
$702$	−6.75810e6	−0.517586
$703$	4.38743e6	0.334828
$704$	2.66978e7	2.03022
$705$	0	0
$706$	−1.17374e7	−0.886258
$707$	−3.10513e7	−2.33631
$708$	−1.23676e6	−0.0927259
$709$	8.57238e6	0.640451	0.320225	−	0.947341i	$-0.396241\pi$
$709$	8.57238e6	0.640451	0.320225	+	0.947341i	$0.396241\pi$
$710$	0	0
$711$	605824.	0.0449441
$712$	1.48881e6	0.110062
$713$	−261144.	−0.0192379
$714$	1.57469e7	1.15598
$715$	0	0
$716$	−1.71380e7	−1.24933
$717$	−8.39888e6	−0.610132
$718$	1.95811e7	1.41751
$719$	−4.73861e6	−0.341844	−0.170922	−	0.985285i	$-0.554675\pi$
$719$	−4.73861e6	−0.341844	−0.170922	+	0.985285i	$0.554675\pi$
$720$	0	0
$721$	6.67593e6	0.478270
$722$	−1.87194e7	−1.33644
$723$	6.40831e6	0.455930
$724$	2.61844e7	1.85651
$725$	0	0
$726$	−3.00184e7	−2.11371
$727$	1.59278e7	1.11769	0.558844	−	0.829273i	$-0.311245\pi$
$727$	1.59278e7	1.11769	0.558844	+	0.829273i	$0.311245\pi$
$728$	−671901.	−0.0469869
$729$	8.74728e6	0.609613
$730$	0	0
$731$	−1.66341e6	−0.115135
$732$	1.00057e6	0.0690194
$733$	1.08726e7	0.747435	0.373717	−	0.927543i	$-0.378083\pi$
$733$	1.08726e7	0.747435	0.373717	+	0.927543i	$0.378083\pi$
$734$	−2.72557e7	−1.86731
$735$	0	0
$736$	−3.32903e6	−0.226529
$737$	4.73244e7	3.20935
$738$	−1.66319e7	−1.12409
$739$	1.84184e7	1.24062	0.620312	−	0.784356i	$-0.287006\pi$
$739$	1.84184e7	1.24062	0.620312	+	0.784356i	$0.287006\pi$
$740$	0	0
$741$	862737.	0.0577209
$742$	3.83392e6	0.255643
$743$	1.66812e7	1.10855	0.554276	−	0.832333i	$-0.312995\pi$
$743$	1.66812e7	1.10855	0.554276	+	0.832333i	$0.312995\pi$
$744$	84233.1	0.00557893
$745$	0	0
$746$	2.65951e7	1.74966
$747$	−1.54184e7	−1.01097
$748$	2.24054e7	1.46420
$749$	2.91754e7	1.90026
$750$	0	0
$751$	−1.24065e7	−0.802692	−0.401346	−	0.915927i	$-0.631458\pi$
$751$	−1.24065e7	−0.802692	−0.401346	+	0.915927i	$0.631458\pi$
$752$	−1.30157e7	−0.839313
$753$	7.85391e6	0.504776
$754$	−9.85583e6	−0.631342
$755$	0	0
$756$	2.86507e7	1.82319
$757$	−2.36729e7	−1.50146	−0.750728	−	0.660612i	$-0.770297\pi$
$757$	−2.36729e7	−1.50146	−0.750728	+	0.660612i	$0.770297\pi$
$758$	4.50128e7	2.84553
$759$	2.85476e6	0.179872
$760$	0	0
$761$	3.94561e6	0.246975	0.123487	−	0.992346i	$-0.460592\pi$
$761$	3.94561e6	0.246975	0.123487	+	0.992346i	$0.460592\pi$
$762$	8.11166e6	0.506084
$763$	3.17038e7	1.97152
$764$	−8.67757e6	−0.537855
$765$	0	0
$766$	3.88784e7	2.39407
$767$	−844833.	−0.0518540
$768$	−8.92981e6	−0.546310
$769$	2.87402e7	1.75256	0.876282	−	0.481799i	$-0.160017\pi$
$769$	2.87402e7	1.75256	0.876282	+	0.481799i	$0.160017\pi$
$770$	0	0
$771$	−4.84776e6	−0.293701
$772$	−1.66804e7	−1.00731
$773$	1.97047e7	1.18610	0.593048	−	0.805167i	$-0.297924\pi$
$773$	1.97047e7	1.18610	0.593048	+	0.805167i	$0.297924\pi$
$774$	−2.26193e6	−0.135715
$775$	0	0
$776$	−125517.	−0.00748251
$777$	−2.32529e7	−1.38173
$778$	4.22957e7	2.50523
$779$	5.54097e6	0.327146
$780$	0	0
$781$	−4.46356e7	−2.61851
$782$	−2.93267e6	−0.171493
$783$	2.08328e7	1.21435
$784$	−3.27932e7	−1.90543
$785$	0	0
$786$	8.98590e6	0.518806
$787$	−1.94263e7	−1.11803	−0.559016	−	0.829157i	$-0.688821\pi$
$787$	−1.94263e7	−1.11803	−0.559016	+	0.829157i	$0.688821\pi$
$788$	1.97643e7	1.13388
$789$	−5.54003e6	−0.316825
$790$	0	0
$791$	−2.15733e7	−1.22596
$792$	1.51028e6	0.0855550
$793$	683495.	0.0385969
$794$	−1.15689e7	−0.651242
$795$	0	0
$796$	1.99682e7	1.11701
$797$	−2.01523e7	−1.12377	−0.561887	−	0.827214i	$-0.689924\pi$
$797$	−2.01523e7	−1.12377	−0.561887	+	0.827214i	$0.689924\pi$
$798$	−7.13377e6	−0.396563
$799$	−1.20988e7	−0.670464
$800$	0	0
$801$	−1.66175e7	−0.915133
$802$	2.61685e7	1.43662
$803$	3.90174e7	2.13535
$804$	2.06653e7	1.12746
$805$	0	0
$806$	1.16077e6	0.0629371
$807$	3.57541e6	0.193260
$808$	−1.86530e6	−0.100513
$809$	1.57769e7	0.847521	0.423761	−	0.905774i	$-0.360710\pi$
$809$	1.57769e7	0.847521	0.423761	+	0.905774i	$0.360710\pi$
$810$	0	0
$811$	−1.75504e7	−0.936987	−0.468494	−	0.883467i	$-0.655203\pi$
$811$	−1.75504e7	−0.936987	−0.468494	+	0.883467i	$0.655203\pi$
$812$	4.17834e7	2.22389
$813$	−1.88008e7	−0.997584
$814$	−6.45304e7	−3.41353
$815$	0	0
$816$	−8.35293e6	−0.439151
$817$	753569.	0.0394973
$818$	−3.96770e7	−2.07327
$819$	7.49950e6	0.390681
$820$	0	0
$821$	−3.47218e7	−1.79781	−0.898906	−	0.438142i	$-0.855637\pi$
$821$	−3.47218e7	−1.79781	−0.898906	+	0.438142i	$0.855637\pi$
$822$	6.83544e6	0.352848
$823$	1.66368e7	0.856191	0.428095	−	0.903734i	$-0.359185\pi$
$823$	1.66368e7	0.856191	0.428095	+	0.903734i	$0.359185\pi$
$824$	401034.	0.0205761
$825$	0	0
$826$	6.98573e6	0.356256
$827$	7.00103e6	0.355957	0.177979	−	0.984034i	$-0.443044\pi$
$827$	7.00103e6	0.355957	0.177979	+	0.984034i	$0.443044\pi$
$828$	−2.04462e6	−0.103642
$829$	3.80168e7	1.92127	0.960636	−	0.277809i	$-0.0896083\pi$
$829$	3.80168e7	1.92127	0.960636	+	0.277809i	$0.0896083\pi$
$830$	0	0
$831$	−1.76800e7	−0.888137
$832$	7.96378e6	0.398851
$833$	−3.04830e7	−1.52211
$834$	1.37751e7	0.685770
$835$	0	0
$836$	−1.01502e7	−0.502297
$837$	−2.45358e6	−0.121056
$838$	−4.49584e7	−2.21157
$839$	−9.13042e6	−0.447802	−0.223901	−	0.974612i	$-0.571879\pi$
$839$	−9.13042e6	−0.447802	−0.223901	+	0.974612i	$0.571879\pi$
$840$	0	0
$841$	9.87087e6	0.481244
$842$	−1.23224e7	−0.598983
$843$	1.30042e7	0.630252
$844$	2.61853e7	1.26533
$845$	0	0
$846$	−1.64522e7	−0.790309
$847$	8.69330e7	4.16367
$848$	−2.03370e6	−0.0971172
$849$	−1.52029e7	−0.723866
$850$	0	0
$851$	4.33056e6	0.204984
$852$	−1.94912e7	−0.919899
$853$	2.43914e7	1.14779	0.573896	−	0.818928i	$-0.305431\pi$
$853$	2.43914e7	1.14779	0.573896	+	0.818928i	$0.305431\pi$
$854$	−5.65166e6	−0.265174
$855$	0	0
$856$	1.75262e6	0.0817528
$857$	6.71666e6	0.312393	0.156196	−	0.987726i	$-0.450077\pi$
$857$	6.71666e6	0.312393	0.156196	+	0.987726i	$0.450077\pi$
$858$	−1.26892e7	−0.588457
$859$	−3.62770e7	−1.67745	−0.838723	−	0.544559i	$-0.816697\pi$
$859$	−3.62770e7	−1.67745	−0.838723	+	0.544559i	$0.816697\pi$
$860$	0	0
$861$	−2.93666e7	−1.35004
$862$	9.72843e6	0.445938
$863$	1.47176e7	0.672681	0.336340	−	0.941740i	$-0.390811\pi$
$863$	1.47176e7	0.672681	0.336340	+	0.941740i	$0.390811\pi$
$864$	−3.12779e7	−1.42545
$865$	0	0
$866$	−4.16574e7	−1.88755
$867$	5.85725e6	0.264634
$868$	−4.92102e6	−0.221695
$869$	2.96855e6	0.133351
$870$	0	0
$871$	1.41166e7	0.630498
$872$	1.90450e6	0.0848184
$873$	1.40097e6	0.0622147
$874$	1.32858e6	0.0588313
$875$	0	0
$876$	1.70379e7	0.750163
$877$	1.36460e7	0.599109	0.299555	−	0.954079i	$-0.403162\pi$
$877$	1.36460e7	0.599109	0.299555	+	0.954079i	$0.403162\pi$
$878$	−1.26674e7	−0.554562
$879$	−5.45483e6	−0.238127
$880$	0	0
$881$	1.44762e7	0.628367	0.314184	−	0.949362i	$-0.398269\pi$
$881$	1.44762e7	0.628367	0.314184	+	0.949362i	$0.398269\pi$
$882$	−4.14512e7	−1.79418
$883$	−4.41394e7	−1.90513	−0.952565	−	0.304334i	$-0.901566\pi$
$883$	−4.41394e7	−1.90513	−0.952565	+	0.304334i	$0.901566\pi$
$884$	6.68340e6	0.287651
$885$	0	0
$886$	−2.26253e7	−0.968300
$887$	1.43793e7	0.613662	0.306831	−	0.951764i	$-0.400731\pi$
$887$	1.43793e7	0.613662	0.306831	+	0.951764i	$0.400731\pi$
$888$	−1.39684e6	−0.0594449
$889$	−2.34913e7	−0.996903
$890$	0	0
$891$	−313132.	−0.0132140
$892$	−3.04673e7	−1.28210
$893$	5.48108e6	0.230005
$894$	−2.60678e7	−1.09084
$895$	0	0
$896$	−6.22787e6	−0.259161
$897$	851555.	0.0353372
$898$	−2.90365e7	−1.20158
$899$	−3.57823e6	−0.147662
$900$	0	0
$901$	−1.89043e6	−0.0775797
$902$	−8.14968e7	−3.33522
$903$	−3.99384e6	−0.162994
$904$	−1.29594e6	−0.0527430
$905$	0	0
$906$	−3.66103e7	−1.48178
$907$	−4.89533e7	−1.97589	−0.987947	−	0.154792i	$-0.950529\pi$
$907$	−4.89533e7	−1.97589	−0.987947	+	0.154792i	$0.950529\pi$
$908$	−1.39530e7	−0.561635
$909$	2.08198e7	0.835732
$910$	0	0
$911$	1.59138e7	0.635297	0.317648	−	0.948209i	$-0.397107\pi$
$911$	1.59138e7	0.635297	0.317648	+	0.948209i	$0.397107\pi$
$912$	3.78410e6	0.150652
$913$	−7.55505e7	−2.99958
$914$	−2.52104e6	−0.0998192
$915$	0	0
$916$	8.48420e6	0.334097
$917$	−2.60231e7	−1.02196
$918$	−2.75539e7	−1.07914
$919$	2.01700e7	0.787803	0.393901	−	0.919153i	$-0.371125\pi$
$919$	2.01700e7	0.787803	0.393901	+	0.919153i	$0.371125\pi$
$920$	0	0
$921$	−1.00835e7	−0.391707
$922$	1.60529e7	0.621906
$923$	−1.33145e7	−0.514424
$924$	5.37952e7	2.07283
$925$	0	0
$926$	−4.70821e7	−1.80438
$927$	−4.47619e6	−0.171084
$928$	−4.56148e7	−1.73874
$929$	2.28202e7	0.867523	0.433762	−	0.901028i	$-0.357186\pi$
$929$	2.28202e7	0.867523	0.433762	+	0.901028i	$0.357186\pi$
$930$	0	0
$931$	1.38096e7	0.522163
$932$	1.07538e7	0.405528
$933$	6.05025e6	0.227546
$934$	−4.92849e7	−1.84861
$935$	0	0
$936$	450508.	0.0168079
$937$	−4.70480e7	−1.75062	−0.875310	−	0.483561i	$-0.839343\pi$
$937$	−4.70480e7	−1.75062	−0.875310	+	0.483561i	$0.839343\pi$
$938$	−1.16727e8	−4.33175
$939$	1.97640e7	0.731493
$940$	0	0
$941$	4.14115e7	1.52457	0.762284	−	0.647243i	$-0.224078\pi$
$941$	4.14115e7	1.52457	0.762284	+	0.647243i	$0.224078\pi$
$942$	−2.02146e7	−0.742229
$943$	5.46916e6	0.200282
$944$	−3.70557e6	−0.135340
$945$	0	0
$946$	−1.10835e7	−0.402670
$947$	−1.23104e6	−0.0446064	−0.0223032	−	0.999751i	$-0.507100\pi$
$947$	−1.23104e6	−0.0446064	−0.0223032	+	0.999751i	$0.507100\pi$
$948$	1.29629e6	0.0468470
$949$	1.16386e7	0.419505
$950$	0	0
$951$	−7.61702e6	−0.273108
$952$	−2.73945e6	−0.0979650
$953$	−1.03123e7	−0.367810	−0.183905	−	0.982944i	$-0.558874\pi$
$953$	−1.03123e7	−0.367810	−0.183905	+	0.982944i	$0.558874\pi$
$954$	−2.57063e6	−0.0914469
$955$	0	0
$956$	2.94757e7	1.04308
$957$	3.91162e7	1.38063
$958$	5.60407e7	1.97283
$959$	−1.97954e7	−0.695052
$960$	0	0
$961$	−2.82077e7	−0.985280
$962$	−1.92490e7	−0.670611
$963$	−1.95620e7	−0.679749
$964$	−2.24898e7	−0.779460
$965$	0	0
$966$	−7.04132e6	−0.242779
$967$	−1.51462e7	−0.520879	−0.260440	−	0.965490i	$-0.583868\pi$
$967$	−1.51462e7	−0.520879	−0.260440	+	0.965490i	$0.583868\pi$
$968$	5.22222e6	0.179129
$969$	3.51752e6	0.120345
$970$	0	0
$971$	3.23338e7	1.10055	0.550274	−	0.834984i	$-0.314523\pi$
$971$	3.23338e7	1.10055	0.550274	+	0.834984i	$0.314523\pi$
$972$	−3.10594e7	−1.05445
$973$	−3.98925e7	−1.35086
$974$	−1.47565e7	−0.498407
$975$	0	0
$976$	2.99791e6	0.100738
$977$	−1.90256e7	−0.637680	−0.318840	−	0.947809i	$-0.603293\pi$
$977$	−1.90256e7	−0.637680	−0.318840	+	0.947809i	$0.603293\pi$
$978$	7.88796e6	0.263704
$979$	−8.14261e7	−2.71523
$980$	0	0
$981$	−2.12573e7	−0.705239
$982$	5.27735e7	1.74637
$983$	3.05511e7	1.00842	0.504212	−	0.863580i	$-0.331783\pi$
$983$	3.05511e7	1.00842	0.504212	+	0.863580i	$0.331783\pi$
$984$	−1.76410e6	−0.0580812
$985$	0	0
$986$	−4.01838e7	−1.31631
$987$	−2.90492e7	−0.949163
$988$	−3.02775e6	−0.0986798
$989$	743802.	0.0241806
$990$	0	0
$991$	−2.43945e7	−0.789056	−0.394528	−	0.918884i	$-0.629092\pi$
$991$	−2.43945e7	−0.789056	−0.394528	+	0.918884i	$0.629092\pi$
$992$	5.37226e6	0.173332
$993$	1.59049e7	0.511869
$994$	1.10095e8	3.53428
$995$	0	0
$996$	−3.29909e7	−1.05377
$997$	1.04454e7	0.332802	0.166401	−	0.986058i	$-0.446785\pi$
$997$	1.04454e7	0.332802	0.166401	+	0.986058i	$0.446785\pi$
$998$	7.98304e7	2.53713
$999$	4.06878e7	1.28988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.f.1.19		22
5.4	even	2		215.6.a.d.1.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.6.a.d.1.4	✓	22	5.4	even	2
1075.6.a.f.1.19		22	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)

\(f(q)\)	\(=\)	\(q+8.10364 q^{2} -9.59374 q^{3} +33.6690 q^{4} -77.7442 q^{6} +225.147 q^{7} +13.5249 q^{8} -150.960 q^{9} +O(q^{10})\)	\(q+8.10364 q^{2} -9.59374 q^{3} +33.6690 q^{4} -77.7442 q^{6} +225.147 q^{7} +13.5249 q^{8} -150.960 q^{9} -739.708 q^{11} -323.011 q^{12} -220.650 q^{13} +1824.51 q^{14} -967.807 q^{16} -899.627 q^{17} -1223.33 q^{18} +407.555 q^{19} -2160.00 q^{21} -5994.33 q^{22} +402.273 q^{23} -129.755 q^{24} -1788.07 q^{26} +3779.55 q^{27} +7580.46 q^{28} +5511.99 q^{29} -649.172 q^{31} -8275.56 q^{32} +7096.57 q^{33} -7290.25 q^{34} -5082.68 q^{36} +10765.2 q^{37} +3302.68 q^{38} +2116.86 q^{39} +13595.6 q^{41} -17503.8 q^{42} +1849.00 q^{43} -24905.2 q^{44} +3259.87 q^{46} +13448.7 q^{47} +9284.88 q^{48} +33884.0 q^{49} +8630.78 q^{51} -7429.07 q^{52} +2101.35 q^{53} +30628.1 q^{54} +3045.09 q^{56} -3909.97 q^{57} +44667.2 q^{58} +3828.83 q^{59} -3097.64 q^{61} -5260.66 q^{62} -33988.2 q^{63} -36092.3 q^{64} +57508.0 q^{66} -63977.1 q^{67} -30289.5 q^{68} -3859.30 q^{69} +60342.2 q^{71} -2041.73 q^{72} -52747.0 q^{73} +87237.7 q^{74} +13722.0 q^{76} -166543. q^{77} +17154.3 q^{78} -4013.14 q^{79} +423.318 q^{81} +110174. q^{82} +102136. q^{83} -72724.9 q^{84} +14983.6 q^{86} -52880.6 q^{87} -10004.5 q^{88} +110079. q^{89} -49678.7 q^{91} +13544.1 q^{92} +6227.99 q^{93} +108983. q^{94} +79393.5 q^{96} -9280.39 q^{97} +274584. q^{98} +111667. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9}+O(q^{10}) \) 22 * q - 5 * q^2 - 20 * q^3 + 427 * q^4 + 248 * q^6 - 118 * q^7 - 561 * q^8 + 2618 * q^9	\( 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9} + 1206 q^{11} - 2175 q^{12} - 1942 q^{13} + 2531 q^{14} + 8851 q^{16} - 2470 q^{17} - 1279 q^{18} + 3020 q^{19} + 5632 q^{21} + 3227 q^{22} + 1326 q^{23} + 11040 q^{24} - 3415 q^{26} - 5156 q^{27} + 11489 q^{28} + 17906 q^{29} + 7982 q^{31} - 2427 q^{32} - 10100 q^{33} + 25248 q^{34} - 14813 q^{36} - 22640 q^{37} + 13695 q^{38} + 29048 q^{39} + 29112 q^{41} - 9163 q^{42} + 40678 q^{43} + 63924 q^{44} - 14944 q^{46} - 57080 q^{47} - 54894 q^{48} + 165560 q^{49} - 1576 q^{51} - 97639 q^{52} + 8054 q^{53} + 167379 q^{54} + 269326 q^{56} - 125424 q^{57} - 49485 q^{58} + 193484 q^{59} + 107466 q^{61} - 162441 q^{62} - 183778 q^{63} + 412603 q^{64} + 240489 q^{66} - 109764 q^{67} - 144300 q^{68} + 202444 q^{69} + 182964 q^{71} - 341504 q^{72} - 134468 q^{73} + 198067 q^{74} + 247729 q^{76} + 28416 q^{77} + 7286 q^{78} + 11148 q^{79} + 385246 q^{81} - 23657 q^{82} - 33850 q^{83} + 176749 q^{84} - 9245 q^{86} + 298280 q^{87} + 111354 q^{88} + 244912 q^{89} + 158092 q^{91} + 124762 q^{92} - 239860 q^{93} - 192166 q^{94} - 147719 q^{96} - 232826 q^{97} + 482463 q^{98} - 346894 q^{99}+O(q^{100}) \) 22 * q - 5 * q^2 - 20 * q^3 + 427 * q^4 + 248 * q^6 - 118 * q^7 - 561 * q^8 + 2618 * q^9 + 1206 * q^11 - 2175 * q^12 - 1942 * q^13 + 2531 * q^14 + 8851 * q^16 - 2470 * q^17 - 1279 * q^18 + 3020 * q^19 + 5632 * q^21 + 3227 * q^22 + 1326 * q^23 + 11040 * q^24 - 3415 * q^26 - 5156 * q^27 + 11489 * q^28 + 17906 * q^29 + 7982 * q^31 - 2427 * q^32 - 10100 * q^33 + 25248 * q^34 - 14813 * q^36 - 22640 * q^37 + 13695 * q^38 + 29048 * q^39 + 29112 * q^41 - 9163 * q^42 + 40678 * q^43 + 63924 * q^44 - 14944 * q^46 - 57080 * q^47 - 54894 * q^48 + 165560 * q^49 - 1576 * q^51 - 97639 * q^52 + 8054 * q^53 + 167379 * q^54 + 269326 * q^56 - 125424 * q^57 - 49485 * q^58 + 193484 * q^59 + 107466 * q^61 - 162441 * q^62 - 183778 * q^63 + 412603 * q^64 + 240489 * q^66 - 109764 * q^67 - 144300 * q^68 + 202444 * q^69 + 182964 * q^71 - 341504 * q^72 - 134468 * q^73 + 198067 * q^74 + 247729 * q^76 + 28416 * q^77 + 7286 * q^78 + 11148 * q^79 + 385246 * q^81 - 23657 * q^82 - 33850 * q^83 + 176749 * q^84 - 9245 * q^86 + 298280 * q^87 + 111354 * q^88 + 244912 * q^89 + 158092 * q^91 + 124762 * q^92 - 239860 * q^93 - 192166 * q^94 - 147719 * q^96 - 232826 * q^97 + 482463 * q^98 - 346894 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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