LMFDB - Embedded newform 1075.6.a.f.1.4

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			1.4
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)

$f(q)$	$=$	$q-8.90907 q^{2} -30.7734 q^{3} +47.3715 q^{4} +274.162 q^{6} +85.8137 q^{7} -136.946 q^{8} +704.001 q^{9} +O(q^{10})$	\(q-8.90907 q^{2} -30.7734 q^{3} +47.3715 q^{4} +274.162 q^{6} +85.8137 q^{7} -136.946 q^{8} +704.001 q^{9} -38.5228 q^{11} -1457.78 q^{12} +176.278 q^{13} -764.520 q^{14} -295.830 q^{16} -548.015 q^{17} -6271.99 q^{18} -47.1547 q^{19} -2640.78 q^{21} +343.202 q^{22} +3007.28 q^{23} +4214.28 q^{24} -1570.47 q^{26} -14186.5 q^{27} +4065.12 q^{28} +1082.69 q^{29} +3690.62 q^{31} +7017.83 q^{32} +1185.48 q^{33} +4882.31 q^{34} +33349.6 q^{36} +11826.9 q^{37} +420.105 q^{38} -5424.67 q^{39} +8997.36 q^{41} +23526.9 q^{42} +1849.00 q^{43} -1824.88 q^{44} -26792.1 q^{46} +9718.61 q^{47} +9103.69 q^{48} -9443.02 q^{49} +16864.3 q^{51} +8350.55 q^{52} +31862.8 q^{53} +126389. q^{54} -11751.8 q^{56} +1451.11 q^{57} -9645.79 q^{58} +8139.01 q^{59} +50243.4 q^{61} -32880.0 q^{62} +60412.9 q^{63} -53055.7 q^{64} -10561.5 q^{66} +2213.02 q^{67} -25960.3 q^{68} -92544.3 q^{69} -23190.0 q^{71} -96409.8 q^{72} +86030.4 q^{73} -105366. q^{74} -2233.79 q^{76} -3305.78 q^{77} +48328.7 q^{78} -19647.4 q^{79} +265496. q^{81} -80158.1 q^{82} -34938.0 q^{83} -125097. q^{84} -16472.9 q^{86} -33318.1 q^{87} +5275.52 q^{88} +99773.2 q^{89} +15127.1 q^{91} +142460. q^{92} -113573. q^{93} -86583.7 q^{94} -215962. q^{96} -63506.0 q^{97} +84128.5 q^{98} -27120.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.90907	−1.57492	−0.787458	−	0.616369i	$-0.788603\pi$
$2$	−8.90907	−1.57492	−0.787458	+	0.616369i	$0.788603\pi$
$3$	−30.7734	−1.97411	−0.987057	−	0.160373i	$-0.948730\pi$
$3$	−30.7734	−1.97411	−0.987057	+	0.160373i	$0.948730\pi$
$4$	47.3715	1.48036
$5$	0	0
$5$	0	0
$6$	274.162	3.10906
$7$	85.8137	0.661929	0.330964	−	0.943643i	$-0.392626\pi$
$7$	85.8137	0.661929	0.330964	+	0.943643i	$0.392626\pi$
$8$	−136.946	−0.756525
$9$	704.001	2.89712
$10$	0	0
$11$	−38.5228	−0.0959921	−0.0479961	−	0.998848i	$-0.515283\pi$
$11$	−38.5228	−0.0959921	−0.0479961	+	0.998848i	$0.515283\pi$
$12$	−1457.78	−2.92240
$13$	176.278	0.289294	0.144647	−	0.989483i	$-0.453795\pi$
$13$	176.278	0.289294	0.144647	+	0.989483i	$0.453795\pi$
$14$	−764.520	−1.04248
$15$	0	0
$16$	−295.830	−0.288897
$17$	−548.015	−0.459907	−0.229954	−	0.973202i	$-0.573857\pi$
$17$	−548.015	−0.459907	−0.229954	+	0.973202i	$0.573857\pi$
$18$	−6271.99	−4.56272
$19$	−47.1547	−0.0299669	−0.0149834	−	0.999888i	$-0.504770\pi$
$19$	−47.1547	−0.0299669	−0.0149834	+	0.999888i	$0.504770\pi$
$20$	0	0
$21$	−2640.78	−1.30672
$22$	343.202	0.151180
$23$	3007.28	1.18537	0.592686	−	0.805433i	$-0.298067\pi$
$23$	3007.28	1.18537	0.592686	+	0.805433i	$0.298067\pi$
$24$	4214.28	1.49347
$25$	0	0
$26$	−1570.47	−0.455614
$27$	−14186.5	−3.74513
$28$	4065.12	0.979892
$29$	1082.69	0.239062	0.119531	−	0.992830i	$-0.461861\pi$
$29$	1082.69	0.239062	0.119531	+	0.992830i	$0.461861\pi$
$30$	0	0
$31$	3690.62	0.689756	0.344878	−	0.938648i	$-0.387920\pi$
$31$	3690.62	0.689756	0.344878	+	0.938648i	$0.387920\pi$
$32$	7017.83	1.21151
$33$	1185.48	0.189499
$34$	4882.31	0.724315
$35$	0	0
$36$	33349.6	4.28878
$37$	11826.9	1.42025	0.710125	−	0.704075i	$-0.248638\pi$
$37$	11826.9	1.42025	0.710125	+	0.704075i	$0.248638\pi$
$38$	420.105	0.0471953
$39$	−5424.67	−0.571099
$40$	0	0
$41$	8997.36	0.835902	0.417951	−	0.908470i	$-0.362748\pi$
$41$	8997.36	0.835902	0.417951	+	0.908470i	$0.362748\pi$
$42$	23526.9	2.05798
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	−1824.88	−0.142103
$45$	0	0
$46$	−26792.1	−1.86686
$47$	9718.61	0.641740	0.320870	−	0.947123i	$-0.396025\pi$
$47$	9718.61	0.641740	0.320870	+	0.947123i	$0.396025\pi$
$48$	9103.69	0.570314
$49$	−9443.02	−0.561850
$50$	0	0
$51$	16864.3	0.907909
$52$	8350.55	0.428259
$53$	31862.8	1.55810	0.779049	−	0.626964i	$-0.215703\pi$
$53$	31862.8	1.55810	0.779049	+	0.626964i	$0.215703\pi$
$54$	126389.	5.89827
$55$	0	0
$56$	−11751.8	−0.500765
$57$	1451.11	0.0591580
$58$	−9645.79	−0.376502
$59$	8139.01	0.304398	0.152199	−	0.988350i	$-0.451365\pi$
$59$	8139.01	0.304398	0.152199	+	0.988350i	$0.451365\pi$
$60$	0	0
$61$	50243.4	1.72884	0.864419	−	0.502771i	$-0.167686\pi$
$61$	50243.4	1.72884	0.864419	+	0.502771i	$0.167686\pi$
$62$	−32880.0	−1.08631
$63$	60412.9	1.91769
$64$	−53055.7	−1.61913
$65$	0	0
$66$	−10561.5	−0.298445
$67$	2213.02	0.0602280	0.0301140	−	0.999546i	$-0.490413\pi$
$67$	2213.02	0.0602280	0.0301140	+	0.999546i	$0.490413\pi$
$68$	−25960.3	−0.680828
$69$	−92544.3	−2.34006
$70$	0	0
$71$	−23190.0	−0.545953	−0.272976	−	0.962021i	$-0.588008\pi$
$71$	−23190.0	−0.545953	−0.272976	+	0.962021i	$0.588008\pi$
$72$	−96409.8	−2.19174
$73$	86030.4	1.88949	0.944746	−	0.327805i	$-0.106309\pi$
$73$	86030.4	1.88949	0.944746	+	0.327805i	$0.106309\pi$
$74$	−105366.	−2.23677
$75$	0	0
$76$	−2233.79	−0.0443617
$77$	−3305.78	−0.0635400
$78$	48328.7	0.899433
$79$	−19647.4	−0.354191	−0.177095	−	0.984194i	$-0.556670\pi$
$79$	−19647.4	−0.354191	−0.177095	+	0.984194i	$0.556670\pi$
$80$	0	0
$81$	265496.	4.49620
$82$	−80158.1	−1.31648
$83$	−34938.0	−0.556677	−0.278339	−	0.960483i	$-0.589784\pi$
$83$	−34938.0	−0.556677	−0.278339	+	0.960483i	$0.589784\pi$
$84$	−125097.	−1.93442
$85$	0	0
$86$	−16472.9	−0.240172
$87$	−33318.1	−0.471935
$88$	5275.52	0.0726204
$89$	99773.2	1.33518	0.667588	−	0.744531i	$-0.267327\pi$
$89$	99773.2	1.33518	0.667588	+	0.744531i	$0.267327\pi$
$90$	0	0
$91$	15127.1	0.191492
$92$	142460.	1.75478
$93$	−113573.	−1.36166
$94$	−86583.7	−1.01069
$95$	0	0
$96$	−215962.	−2.39166
$97$	−63506.0	−0.685307	−0.342654	−	0.939462i	$-0.611326\pi$
$97$	−63506.0	−0.685307	−0.342654	+	0.939462i	$0.611326\pi$
$98$	84128.5	0.884867
$99$	−27120.1	−0.278101
$100$	0	0
$101$	56620.5	0.552294	0.276147	−	0.961115i	$-0.410942\pi$
$101$	56620.5	0.552294	0.276147	+	0.961115i	$0.410942\pi$
$102$	−150245.	−1.42988
$103$	−12950.3	−0.120278	−0.0601391	−	0.998190i	$-0.519154\pi$
$103$	−12950.3	−0.120278	−0.0601391	+	0.998190i	$0.519154\pi$
$104$	−24140.5	−0.218858
$105$	0	0
$106$	−283868.	−2.45387
$107$	167648.	1.41560	0.707798	−	0.706414i	$-0.249688\pi$
$107$	167648.	1.41560	0.707798	+	0.706414i	$0.249688\pi$
$108$	−672038.	−5.54414
$109$	197155.	1.58943	0.794714	−	0.606984i	$-0.207621\pi$
$109$	197155.	1.58943	0.794714	+	0.606984i	$0.207621\pi$
$110$	0	0
$111$	−363952.	−2.80374
$112$	−25386.3	−0.191229
$113$	−234982.	−1.73116	−0.865581	−	0.500769i	$-0.833051\pi$
$113$	−234982.	−1.73116	−0.865581	+	0.500769i	$0.833051\pi$
$114$	−12928.0	−0.0931688
$115$	0	0
$116$	51288.8	0.353897
$117$	124100.	0.838120
$118$	−72511.0	−0.479401
$119$	−47027.2	−0.304426
$120$	0	0
$121$	−159567.	−0.990786
$122$	−447622.	−2.72278
$123$	−276879.	−1.65017
$124$	174830.	1.02109
$125$	0	0
$126$	−538222.	−3.02020
$127$	238025.	1.30952	0.654761	−	0.755836i	$-0.272769\pi$
$127$	238025.	1.30952	0.654761	+	0.755836i	$0.272769\pi$
$128$	248107.	1.33849
$129$	−56900.0	−0.301049
$130$	0	0
$131$	254657.	1.29651	0.648257	−	0.761422i	$-0.275498\pi$
$131$	254657.	1.29651	0.648257	+	0.761422i	$0.275498\pi$
$132$	56157.7	0.280527
$133$	−4046.52	−0.0198359
$134$	−19715.9	−0.0948539
$135$	0	0
$136$	75048.3	0.347931
$137$	−23426.8	−0.106638	−0.0533190	−	0.998578i	$-0.516980\pi$
$137$	−23426.8	−0.106638	−0.0533190	+	0.998578i	$0.516980\pi$
$138$	824483.	3.68540
$139$	153547.	0.674070	0.337035	−	0.941492i	$-0.390576\pi$
$139$	153547.	0.674070	0.337035	+	0.941492i	$0.390576\pi$
$140$	0	0
$141$	−299074.	−1.26687
$142$	206601.	0.859829
$143$	−6790.71	−0.0277700
$144$	−208265.	−0.836969
$145$	0	0
$146$	−766451.	−2.97579
$147$	290593.	1.10916
$148$	560256.	2.10248
$149$	271522.	1.00193	0.500967	−	0.865467i	$-0.332978\pi$
$149$	271522.	1.00193	0.500967	+	0.865467i	$0.332978\pi$
$150$	0	0
$151$	47095.6	0.168089	0.0840443	−	0.996462i	$-0.473216\pi$
$151$	47095.6	0.168089	0.0840443	+	0.996462i	$0.473216\pi$
$152$	6457.63	0.0226707
$153$	−385803.	−1.33241
$154$	29451.4	0.100070
$155$	0	0
$156$	−256975.	−0.845432
$157$	−448633.	−1.45259	−0.726293	−	0.687385i	$-0.758758\pi$
$157$	−448633.	−1.45259	−0.726293	+	0.687385i	$0.758758\pi$
$158$	175040.	0.557821
$159$	−980527.	−3.07586
$160$	0	0
$161$	258066.	0.784632
$162$	−2.36532e6	−7.08113
$163$	−426923.	−1.25858	−0.629290	−	0.777170i	$-0.716654\pi$
$163$	−426923.	−1.25858	−0.629290	+	0.777170i	$0.716654\pi$
$164$	426218.	1.23743
$165$	0	0
$166$	311265.	0.876719
$167$	513700.	1.42534	0.712669	−	0.701500i	$-0.247486\pi$
$167$	513700.	1.42534	0.712669	+	0.701500i	$0.247486\pi$
$168$	361643.	0.988568
$169$	−340219.	−0.916309
$170$	0	0
$171$	−33197.0	−0.0868177
$172$	87589.9	0.225753
$173$	642845.	1.63302	0.816509	−	0.577333i	$-0.195907\pi$
$173$	642845.	1.63302	0.816509	+	0.577333i	$0.195907\pi$
$174$	296833.	0.743258
$175$	0	0
$176$	11396.2	0.0277318
$177$	−250465.	−0.600916
$178$	−888886.	−2.10279
$179$	−550408.	−1.28396	−0.641981	−	0.766721i	$-0.721887\pi$
$179$	−550408.	−1.28396	−0.641981	+	0.766721i	$0.721887\pi$
$180$	0	0
$181$	−478703.	−1.08610	−0.543050	−	0.839701i	$-0.682731\pi$
$181$	−478703.	−1.08610	−0.543050	+	0.839701i	$0.682731\pi$
$182$	−134768.	−0.301584
$183$	−1.54616e6	−3.41292
$184$	−411834.	−0.896764
$185$	0	0
$186$	1.01183e6	2.14449
$187$	21111.1	0.0441475
$188$	460385.	0.950006
$189$	−1.21740e6	−2.47901
$190$	0	0
$191$	264269.	0.524158	0.262079	−	0.965046i	$-0.415592\pi$
$191$	264269.	0.524158	0.262079	+	0.965046i	$0.415592\pi$
$192$	1.63270e6	3.19635
$193$	−11397.1	−0.0220242	−0.0110121	−	0.999939i	$-0.503505\pi$
$193$	−11397.1	−0.0220242	−0.0110121	+	0.999939i	$0.503505\pi$
$194$	565779.	1.07930
$195$	0	0
$196$	−447330.	−0.831740
$197$	575663.	1.05682	0.528412	−	0.848988i	$-0.322788\pi$
$197$	575663.	1.05682	0.528412	+	0.848988i	$0.322788\pi$
$198$	241614.	0.437986
$199$	304769.	0.545555	0.272777	−	0.962077i	$-0.412058\pi$
$199$	304769.	0.545555	0.272777	+	0.962077i	$0.412058\pi$
$200$	0	0
$201$	−68102.1	−0.118897
$202$	−504436.	−0.869816
$203$	92909.9	0.158242
$204$	798886.	1.34403
$205$	0	0
$206$	115375.	0.189428
$207$	2.11713e6	3.43417
$208$	−52148.3	−0.0835761
$209$	1816.53	0.00287658
$210$	0	0
$211$	−654230.	−1.01164	−0.505818	−	0.862640i	$-0.668809\pi$
$211$	−654230.	−1.01164	−0.505818	+	0.862640i	$0.668809\pi$
$212$	1.50939e6	2.30654
$213$	713635.	1.07777
$214$	−1.49359e6	−2.22945
$215$	0	0
$216$	1.94279e6	2.83329
$217$	316706.	0.456569
$218$	−1.75646e6	−2.50322
$219$	−2.64745e6	−3.73007
$220$	0	0
$221$	−96603.0	−0.133048
$222$	3.24248e6	4.41565
$223$	7090.22	0.00954768	0.00477384	−	0.999989i	$-0.498480\pi$
$223$	7090.22	0.00954768	0.00477384	+	0.999989i	$0.498480\pi$
$224$	602226.	0.801935
$225$	0	0
$226$	2.09347e6	2.72643
$227$	−278089.	−0.358194	−0.179097	−	0.983831i	$-0.557318\pi$
$227$	−278089.	−0.358194	−0.179097	+	0.983831i	$0.557318\pi$
$228$	68741.2	0.0875750
$229$	22162.2	0.0279269	0.0139635	−	0.999903i	$-0.495555\pi$
$229$	22162.2	0.0279269	0.0139635	+	0.999903i	$0.495555\pi$
$230$	0	0
$231$	101730.	0.125435
$232$	−148270.	−0.180856
$233$	−1.11652e6	−1.34733	−0.673667	−	0.739035i	$-0.735282\pi$
$233$	−1.11652e6	−1.34733	−0.673667	+	0.739035i	$0.735282\pi$
$234$	−1.10561e6	−1.31997
$235$	0	0
$236$	385557.	0.450618
$237$	604617.	0.699213
$238$	418968.	0.479445
$239$	214188.	0.242550	0.121275	−	0.992619i	$-0.461302\pi$
$239$	214188.	0.242550	0.121275	+	0.992619i	$0.461302\pi$
$240$	0	0
$241$	−137272.	−0.152244	−0.0761219	−	0.997099i	$-0.524254\pi$
$241$	−137272.	−0.152244	−0.0761219	+	0.997099i	$0.524254\pi$
$242$	1.42159e6	1.56040
$243$	−4.72287e6	−5.13086
$244$	2.38010e6	2.55930
$245$	0	0
$246$	2.46673e6	2.59887
$247$	−8312.34	−0.00866924
$248$	−505414.	−0.521817
$249$	1.07516e6	1.09894
$250$	0	0
$251$	1.21275e6	1.21503	0.607513	−	0.794310i	$-0.292167\pi$
$251$	1.21275e6	1.21503	0.607513	+	0.794310i	$0.292167\pi$
$252$	2.86185e6	2.83887
$253$	−115849.	−0.113786
$254$	−2.12058e6	−2.06239
$255$	0	0
$256$	−512616.	−0.488868
$257$	−1.53764e6	−1.45219	−0.726094	−	0.687596i	$-0.758666\pi$
$257$	−1.53764e6	−1.45219	−0.726094	+	0.687596i	$0.758666\pi$
$258$	506926.	0.474127
$259$	1.01491e6	0.940105
$260$	0	0
$261$	762217.	0.692592
$262$	−2.26875e6	−2.04190
$263$	−886077.	−0.789918	−0.394959	−	0.918699i	$-0.629241\pi$
$263$	−886077.	−0.789918	−0.394959	+	0.918699i	$0.629241\pi$
$264$	−162346.	−0.143361
$265$	0	0
$266$	36050.7	0.0312399
$267$	−3.07036e6	−2.63579
$268$	104834.	0.0891590
$269$	−163572.	−0.137825	−0.0689125	−	0.997623i	$-0.521953\pi$
$269$	−163572.	−0.137825	−0.0689125	+	0.997623i	$0.521953\pi$
$270$	0	0
$271$	−14768.8	−0.0122158	−0.00610790	−	0.999981i	$-0.501944\pi$
$271$	−14768.8	−0.0122158	−0.00610790	+	0.999981i	$0.501944\pi$
$272$	162119.	0.132866
$273$	−465511.	−0.378027
$274$	208711.	0.167946
$275$	0	0
$276$	−4.38396e6	−3.46413
$277$	2.38288e6	1.86597	0.932983	−	0.359922i	$-0.117197\pi$
$277$	2.38288e6	1.86597	0.932983	+	0.359922i	$0.117197\pi$
$278$	−1.36796e6	−1.06160
$279$	2.59820e6	1.99831
$280$	0	0
$281$	2.31928e6	1.75221	0.876106	−	0.482119i	$-0.160133\pi$
$281$	2.31928e6	1.75221	0.876106	+	0.482119i	$0.160133\pi$
$282$	2.66447e6	1.99521
$283$	523430.	0.388501	0.194251	−	0.980952i	$-0.437772\pi$
$283$	523430.	0.388501	0.194251	+	0.980952i	$0.437772\pi$
$284$	−1.09855e6	−0.808206
$285$	0	0
$286$	60498.9	0.0437353
$287$	772096.	0.553308
$288$	4.94056e6	3.50990
$289$	−1.11954e6	−0.788485
$290$	0	0
$291$	1.95429e6	1.35287
$292$	4.07539e6	2.79712
$293$	−1.47145e6	−1.00133	−0.500663	−	0.865642i	$-0.666911\pi$
$293$	−1.47145e6	−1.00133	−0.500663	+	0.865642i	$0.666911\pi$
$294$	−2.58892e6	−1.74683
$295$	0	0
$296$	−1.61964e6	−1.07445
$297$	546505.	0.359503
$298$	−2.41900e6	−1.57796
$299$	530118.	0.342921
$300$	0	0
$301$	158669.	0.100943
$302$	−419578.	−0.264725
$303$	−1.74240e6	−1.09029
$304$	13949.8	0.00865732
$305$	0	0
$306$	3.43715e6	2.09843
$307$	154772.	0.0937233	0.0468617	−	0.998901i	$-0.485078\pi$
$307$	154772.	0.0937233	0.0468617	+	0.998901i	$0.485078\pi$
$308$	−156600.	−0.0940620
$309$	398524.	0.237443
$310$	0	0
$311$	2.80983e6	1.64733	0.823664	−	0.567079i	$-0.191927\pi$
$311$	2.80983e6	1.64733	0.823664	+	0.567079i	$0.191927\pi$
$312$	742884.	0.432051
$313$	−696058.	−0.401591	−0.200796	−	0.979633i	$-0.564353\pi$
$313$	−696058.	−0.401591	−0.200796	+	0.979633i	$0.564353\pi$
$314$	3.99690e6	2.28770
$315$	0	0
$316$	−930726.	−0.524330
$317$	−2.39232e6	−1.33712	−0.668561	−	0.743658i	$-0.733089\pi$
$317$	−2.39232e6	−1.33712	−0.668561	+	0.743658i	$0.733089\pi$
$318$	8.73558e6	4.84422
$319$	−41708.3	−0.0229481
$320$	0	0
$321$	−5.15910e6	−2.79455
$322$	−2.29913e6	−1.23573
$323$	25841.5	0.0137820
$324$	1.25769e7	6.65598
$325$	0	0
$326$	3.80349e6	1.98216
$327$	−6.06712e6	−3.13771
$328$	−1.23215e6	−0.632380
$329$	833989.	0.424787
$330$	0	0
$331$	2.20895e6	1.10819	0.554096	−	0.832453i	$-0.313064\pi$
$331$	2.20895e6	1.10819	0.554096	+	0.832453i	$0.313064\pi$
$332$	−1.65507e6	−0.824082
$333$	8.32612e6	4.11464
$334$	−4.57658e6	−2.24479
$335$	0	0
$336$	781221.	0.377508
$337$	3.08005e6	1.47735	0.738675	−	0.674061i	$-0.235452\pi$
$337$	3.08005e6	1.47735	0.738675	+	0.674061i	$0.235452\pi$
$338$	3.03103e6	1.44311
$339$	7.23118e6	3.41751
$340$	0	0
$341$	−142173.	−0.0662111
$342$	295754.	0.136730
$343$	−2.25261e6	−1.03383
$344$	−253212.	−0.115369
$345$	0	0
$346$	−5.72715e6	−2.57186
$347$	2.30215e6	1.02638	0.513191	−	0.858274i	$-0.328463\pi$
$347$	2.30215e6	1.02638	0.513191	+	0.858274i	$0.328463\pi$
$348$	−1.57833e6	−0.698633
$349$	1.85840e6	0.816725	0.408362	−	0.912820i	$-0.366100\pi$
$349$	1.85840e6	0.816725	0.408362	+	0.912820i	$0.366100\pi$
$350$	0	0
$351$	−2.50078e6	−1.08345
$352$	−270346.	−0.116296
$353$	94125.0	0.0402039	0.0201019	−	0.999798i	$-0.493601\pi$
$353$	94125.0	0.0402039	0.0201019	+	0.999798i	$0.493601\pi$
$354$	2.23141e6	0.946392
$355$	0	0
$356$	4.72640e6	1.97654
$357$	1.44719e6	0.600971
$358$	4.90362e6	2.02213
$359$	−477225.	−0.195428	−0.0977141	−	0.995215i	$-0.531153\pi$
$359$	−477225.	−0.195428	−0.0977141	+	0.995215i	$0.531153\pi$
$360$	0	0
$361$	−2.47388e6	−0.999102
$362$	4.26480e6	1.71051
$363$	4.91042e6	1.95592
$364$	716591.	0.283477
$365$	0	0
$366$	1.37748e7	5.37507
$367$	−3.71729e6	−1.44066	−0.720329	−	0.693633i	$-0.756009\pi$
$367$	−3.71729e6	−1.44066	−0.720329	+	0.693633i	$0.756009\pi$
$368$	−889645.	−0.342450
$369$	6.33415e6	2.42171
$370$	0	0
$371$	2.73427e6	1.03135
$372$	−5.38012e6	−2.01574
$373$	−2.50954e6	−0.933948	−0.466974	−	0.884271i	$-0.654656\pi$
$373$	−2.50954e6	−0.933948	−0.466974	+	0.884271i	$0.654656\pi$
$374$	−188080.	−0.0695286
$375$	0	0
$376$	−1.33092e6	−0.485492
$377$	190855.	0.0691592
$378$	1.08459e7	3.90423
$379$	−454386.	−0.162490	−0.0812451	−	0.996694i	$-0.525890\pi$
$379$	−454386.	−0.162490	−0.0812451	+	0.996694i	$0.525890\pi$
$380$	0	0
$381$	−7.32483e6	−2.58515
$382$	−2.35439e6	−0.825505
$383$	−2.94231e6	−1.02492	−0.512461	−	0.858710i	$-0.671266\pi$
$383$	−2.94231e6	−1.02492	−0.512461	+	0.858710i	$0.671266\pi$
$384$	−7.63508e6	−2.64232
$385$	0	0
$386$	101537.	0.0346863
$387$	1.30170e6	0.441807
$388$	−3.00837e6	−1.01450
$389$	−3.27976e6	−1.09893	−0.549463	−	0.835518i	$-0.685168\pi$
$389$	−3.27976e6	−1.09893	−0.549463	+	0.835518i	$0.685168\pi$
$390$	0	0
$391$	−1.64804e6	−0.545162
$392$	1.29318e6	0.425053
$393$	−7.83665e6	−2.55946
$394$	−5.12862e6	−1.66441
$395$	0	0
$396$	−1.28472e6	−0.411689
$397$	−944985.	−0.300918	−0.150459	−	0.988616i	$-0.548075\pi$
$397$	−944985.	−0.300918	−0.150459	+	0.988616i	$0.548075\pi$
$398$	−2.71521e6	−0.859202
$399$	124525.	0.0391584
$400$	0	0
$401$	−378935.	−0.117680	−0.0588402	−	0.998267i	$-0.518740\pi$
$401$	−378935.	−0.117680	−0.0588402	+	0.998267i	$0.518740\pi$
$402$	606726.	0.187252
$403$	650575.	0.199542
$404$	2.68220e6	0.817593
$405$	0	0
$406$	−827740.	−0.249218
$407$	−455603.	−0.136333
$408$	−2.30949e6	−0.686856
$409$	−2.18011e6	−0.644421	−0.322210	−	0.946668i	$-0.604426\pi$
$409$	−2.18011e6	−0.644421	−0.322210	+	0.946668i	$0.604426\pi$
$410$	0	0
$411$	720922.	0.210515
$412$	−613475.	−0.178055
$413$	698439.	0.201490
$414$	−1.88617e7	−5.40853
$415$	0	0
$416$	1.23709e6	0.350483
$417$	−4.72517e6	−1.33069
$418$	−16183.6	−0.00453038
$419$	−2.80943e6	−0.781778	−0.390889	−	0.920438i	$-0.627832\pi$
$419$	−2.80943e6	−0.781778	−0.390889	+	0.920438i	$0.627832\pi$
$420$	0	0
$421$	−2.38086e6	−0.654680	−0.327340	−	0.944907i	$-0.606152\pi$
$421$	−2.38086e6	−0.654680	−0.327340	+	0.944907i	$0.606152\pi$
$422$	5.82858e6	1.59324
$423$	6.84191e6	1.85920
$424$	−4.36347e6	−1.17874
$425$	0	0
$426$	−6.35782e6	−1.69740
$427$	4.31157e6	1.14437
$428$	7.94175e6	2.09559
$429$	208973.	0.0548210
$430$	0	0
$431$	−5.03729e6	−1.30618	−0.653092	−	0.757279i	$-0.726528\pi$
$431$	−5.03729e6	−1.30618	−0.653092	+	0.757279i	$0.726528\pi$
$432$	4.19681e6	1.08196
$433$	321671.	0.0824504	0.0412252	−	0.999150i	$-0.486874\pi$
$433$	321671.	0.0824504	0.0412252	+	0.999150i	$0.486874\pi$
$434$	−2.82155e6	−0.719058
$435$	0	0
$436$	9.33951e6	2.35292
$437$	−141808.	−0.0355219
$438$	2.35863e7	5.87454
$439$	−5.47432e6	−1.35572	−0.677858	−	0.735193i	$-0.737092\pi$
$439$	−5.47432e6	−1.35572	−0.677858	+	0.735193i	$0.737092\pi$
$440$	0	0
$441$	−6.64789e6	−1.62775
$442$	860643.	0.209540
$443$	6.13040e6	1.48415	0.742077	−	0.670314i	$-0.233841\pi$
$443$	6.13040e6	1.48415	0.742077	+	0.670314i	$0.233841\pi$
$444$	−1.72410e7	−4.15053
$445$	0	0
$446$	−63167.3	−0.0150368
$447$	−8.35564e6	−1.97793
$448$	−4.55291e6	−1.07175
$449$	5.14596e6	1.20462	0.602311	−	0.798262i	$-0.294247\pi$
$449$	5.14596e6	1.20462	0.602311	+	0.798262i	$0.294247\pi$
$450$	0	0
$451$	−346603.	−0.0802400
$452$	−1.11314e7	−2.56274
$453$	−1.44929e6	−0.331826
$454$	2.47751e6	0.564126
$455$	0	0
$456$	−198723.	−0.0447545
$457$	2.52197e6	0.564871	0.282436	−	0.959286i	$-0.408858\pi$
$457$	2.52197e6	0.564871	0.282436	+	0.959286i	$0.408858\pi$
$458$	−197444.	−0.0439826
$459$	7.77445e6	1.72241
$460$	0	0
$461$	7.03491e6	1.54172	0.770861	−	0.637003i	$-0.219826\pi$
$461$	7.03491e6	1.54172	0.770861	+	0.637003i	$0.219826\pi$
$462$	−906319.	−0.197550
$463$	−7.29689e6	−1.58192	−0.790962	−	0.611866i	$-0.790419\pi$
$463$	−7.29689e6	−1.58192	−0.790962	+	0.611866i	$0.790419\pi$
$464$	−320293.	−0.0690642
$465$	0	0
$466$	9.94712e6	2.12194
$467$	1.34110e6	0.284558	0.142279	−	0.989827i	$-0.454557\pi$
$467$	1.34110e6	0.284558	0.142279	+	0.989827i	$0.454557\pi$
$468$	5.87879e6	1.24072
$469$	189907.	0.0398666
$470$	0	0
$471$	1.38059e7	2.86757
$472$	−1.11460e6	−0.230285
$473$	−71228.6	−0.0146387
$474$	−5.38657e6	−1.10120
$475$	0	0
$476$	−2.22775e6	−0.450660
$477$	2.24314e7	4.51400
$478$	−1.90822e6	−0.381995
$479$	−3.35910e6	−0.668934	−0.334467	−	0.942407i	$-0.608556\pi$
$479$	−3.35910e6	−0.668934	−0.334467	+	0.942407i	$0.608556\pi$
$480$	0	0
$481$	2.08481e6	0.410870
$482$	1.22297e6	0.239771
$483$	−7.94157e6	−1.54895
$484$	−7.55893e6	−1.46672
$485$	0	0
$486$	4.20764e7	8.08068
$487$	−1.98498e6	−0.379257	−0.189628	−	0.981856i	$-0.560728\pi$
$487$	−1.98498e6	−0.379257	−0.189628	+	0.981856i	$0.560728\pi$
$488$	−6.88061e6	−1.30791
$489$	1.31379e7	2.48458
$490$	0	0
$491$	−6.76726e6	−1.26680	−0.633401	−	0.773823i	$-0.718342\pi$
$491$	−6.76726e6	−1.26680	−0.633401	+	0.773823i	$0.718342\pi$
$492$	−1.31162e7	−2.44284
$493$	−593332.	−0.109946
$494$	74055.2	0.0136533
$495$	0	0
$496$	−1.09180e6	−0.199268
$497$	−1.99002e6	−0.361382
$498$	−9.57869e6	−1.73074
$499$	−5.11265e6	−0.919168	−0.459584	−	0.888134i	$-0.652002\pi$
$499$	−5.11265e6	−0.919168	−0.459584	+	0.888134i	$0.652002\pi$
$500$	0	0
$501$	−1.58083e7	−2.81378
$502$	−1.08044e7	−1.91356
$503$	2.22401e6	0.391938	0.195969	−	0.980610i	$-0.437215\pi$
$503$	2.22401e6	0.391938	0.195969	+	0.980610i	$0.437215\pi$
$504$	−8.27328e6	−1.45078
$505$	0	0
$506$	1.03211e6	0.179204
$507$	1.04697e7	1.80890
$508$	1.12756e7	1.93856
$509$	−5.14193e6	−0.879695	−0.439847	−	0.898073i	$-0.644967\pi$
$509$	−5.14193e6	−0.879695	−0.439847	+	0.898073i	$0.644967\pi$
$510$	0	0
$511$	7.38258e6	1.25071
$512$	−3.37249e6	−0.568559
$513$	668963.	0.112230
$514$	1.36990e7	2.28707
$515$	0	0
$516$	−2.69544e6	−0.445661
$517$	−374388.	−0.0616020
$518$	−9.04186e6	−1.48059
$519$	−1.97825e7	−3.22376
$520$	0	0
$521$	1.10069e7	1.77652	0.888259	−	0.459344i	$-0.151915\pi$
$521$	1.10069e7	1.77652	0.888259	+	0.459344i	$0.151915\pi$
$522$	−6.79064e6	−1.09077
$523$	−3.46843e6	−0.554470	−0.277235	−	0.960802i	$-0.589418\pi$
$523$	−3.46843e6	−0.554470	−0.277235	+	0.960802i	$0.589418\pi$
$524$	1.20635e7	1.91930
$525$	0	0
$526$	7.89412e6	1.24405
$527$	−2.02252e6	−0.317224
$528$	−350699.	−0.0547457
$529$	2.60742e6	0.405109
$530$	0	0
$531$	5.72987e6	0.881878
$532$	−191690.	−0.0293643
$533$	1.58604e6	0.241821
$534$	2.73540e7	4.15115
$535$	0	0
$536$	−303063.	−0.0455639
$537$	1.69379e7	2.53469
$538$	1.45727e6	0.217063
$539$	363771.	0.0539332
$540$	0	0
$541$	2.47049e6	0.362903	0.181451	−	0.983400i	$-0.441920\pi$
$541$	2.47049e6	0.362903	0.181451	+	0.983400i	$0.441920\pi$
$542$	131576.	0.0192388
$543$	1.47313e7	2.14408
$544$	−3.84588e6	−0.557183
$545$	0	0
$546$	4.14726e6	0.595361
$547$	−9.59369e6	−1.37094	−0.685469	−	0.728102i	$-0.740403\pi$
$547$	−9.59369e6	−1.37094	−0.685469	+	0.728102i	$0.740403\pi$
$548$	−1.10976e6	−0.157862
$549$	3.53714e7	5.00866
$550$	0	0
$551$	−51054.1	−0.00716393
$552$	1.26735e7	1.77031
$553$	−1.68602e6	−0.234449
$554$	−2.12293e7	−2.93874
$555$	0	0
$556$	7.27376e6	0.997866
$557$	1.36914e7	1.86986	0.934928	−	0.354837i	$-0.115463\pi$
$557$	1.36914e7	1.86986	0.934928	+	0.354837i	$0.115463\pi$
$558$	−2.31475e7	−3.14716
$559$	325938.	0.0441169
$560$	0	0
$561$	−649659.	−0.0871522
$562$	−2.06626e7	−2.75959
$563$	−1.05280e7	−1.39983	−0.699917	−	0.714224i	$-0.746780\pi$
$563$	−1.05280e7	−1.39983	−0.699917	+	0.714224i	$0.746780\pi$
$564$	−1.41676e7	−1.87542
$565$	0	0
$566$	−4.66327e6	−0.611857
$567$	2.27832e7	2.97616
$568$	3.17577e6	0.413027
$569$	−1.41040e6	−0.182625	−0.0913125	−	0.995822i	$-0.529106\pi$
$569$	−1.41040e6	−0.182625	−0.0913125	+	0.995822i	$0.529106\pi$
$570$	0	0
$571$	−9.36724e6	−1.20232	−0.601162	−	0.799128i	$-0.705295\pi$
$571$	−9.36724e6	−1.20232	−0.601162	+	0.799128i	$0.705295\pi$
$572$	−321686.	−0.0411095
$573$	−8.13244e6	−1.03475
$574$	−6.87866e6	−0.871413
$575$	0	0
$576$	−3.73513e7	−4.69083
$577$	−1.20789e7	−1.51039	−0.755193	−	0.655503i	$-0.772457\pi$
$577$	−1.20789e7	−1.51039	−0.755193	+	0.655503i	$0.772457\pi$
$578$	9.97402e6	1.24180
$579$	350727.	0.0434783
$580$	0	0
$581$	−2.99816e6	−0.368481
$582$	−1.74109e7	−2.13066
$583$	−1.22744e6	−0.149565
$584$	−1.17815e7	−1.42945
$585$	0	0
$586$	1.31092e7	1.57700
$587$	449022.	0.0537864	0.0268932	−	0.999638i	$-0.491439\pi$
$587$	449022.	0.0537864	0.0268932	+	0.999638i	$0.491439\pi$
$588$	1.37658e7	1.64195
$589$	−174030.	−0.0206698
$590$	0	0
$591$	−1.77151e7	−2.08629
$592$	−3.49874e6	−0.410305
$593$	5.17722e6	0.604589	0.302294	−	0.953215i	$-0.402247\pi$
$593$	5.17722e6	0.604589	0.302294	+	0.953215i	$0.402247\pi$
$594$	−4.86885e6	−0.566188
$595$	0	0
$596$	1.28624e7	1.48322
$597$	−9.37877e6	−1.07699
$598$	−4.72286e6	−0.540072
$599$	−1.01772e7	−1.15895	−0.579473	−	0.814991i	$-0.696742\pi$
$599$	−1.01772e7	−1.15895	−0.579473	+	0.814991i	$0.696742\pi$
$600$	0	0
$601$	3.46234e6	0.391006	0.195503	−	0.980703i	$-0.437366\pi$
$601$	3.46234e6	0.391006	0.195503	+	0.980703i	$0.437366\pi$
$602$	−1.41360e6	−0.158977
$603$	1.55797e6	0.174488
$604$	2.23099e6	0.248831
$605$	0	0
$606$	1.55232e7	1.71711
$607$	1.17286e6	0.129203	0.0646015	−	0.997911i	$-0.479422\pi$
$607$	1.17286e6	0.129203	0.0646015	+	0.997911i	$0.479422\pi$
$608$	−330924.	−0.0363052
$609$	−2.85915e6	−0.312388
$610$	0	0
$611$	1.71318e6	0.185652
$612$	−1.82761e7	−1.97244
$613$	2.88741e6	0.310354	0.155177	−	0.987887i	$-0.450405\pi$
$613$	2.88741e6	0.310354	0.155177	+	0.987887i	$0.450405\pi$
$614$	−1.37888e6	−0.147606
$615$	0	0
$616$	452712.	0.0480696
$617$	6.41287e6	0.678171	0.339086	−	0.940756i	$-0.389882\pi$
$617$	6.41287e6	0.678171	0.339086	+	0.940756i	$0.389882\pi$
$618$	−3.55048e6	−0.373952
$619$	1.57679e7	1.65404	0.827021	−	0.562171i	$-0.190034\pi$
$619$	1.57679e7	1.65404	0.827021	+	0.562171i	$0.190034\pi$
$620$	0	0
$621$	−4.26630e7	−4.43938
$622$	−2.50330e7	−2.59440
$623$	8.56190e6	0.883792
$624$	1.60478e6	0.164989
$625$	0	0
$626$	6.20122e6	0.632472
$627$	−55900.8	−0.00567870
$628$	−2.12524e7	−2.15035
$629$	−6.48130e6	−0.653184
$630$	0	0
$631$	−1.46351e7	−1.46327	−0.731633	−	0.681698i	$-0.761242\pi$
$631$	−1.46351e7	−1.46327	−0.731633	+	0.681698i	$0.761242\pi$
$632$	2.69062e6	0.267954
$633$	2.01329e7	1.99708
$634$	2.13133e7	2.10585
$635$	0	0
$636$	−4.64490e7	−4.55338
$637$	−1.66460e6	−0.162540
$638$	371582.	0.0361413
$639$	−1.63258e7	−1.58169
$640$	0	0
$641$	6.29017e6	0.604669	0.302334	−	0.953202i	$-0.402234\pi$
$641$	6.29017e6	0.604669	0.302334	+	0.953202i	$0.402234\pi$
$642$	4.59628e7	4.40118
$643$	2.68730e6	0.256324	0.128162	−	0.991753i	$-0.459092\pi$
$643$	2.68730e6	0.256324	0.128162	+	0.991753i	$0.459092\pi$
$644$	1.22250e7	1.16154
$645$	0	0
$646$	−230224.	−0.0217055
$647$	−5.08681e6	−0.477733	−0.238866	−	0.971052i	$-0.576776\pi$
$647$	−5.08681e6	−0.477733	−0.238866	+	0.971052i	$0.576776\pi$
$648$	−3.63585e7	−3.40148
$649$	−313537.	−0.0292198
$650$	0	0
$651$	−9.74610e6	−0.901319
$652$	−2.02240e7	−1.86315
$653$	−3.15825e6	−0.289844	−0.144922	−	0.989443i	$-0.546293\pi$
$653$	−3.15825e6	−0.289844	−0.144922	+	0.989443i	$0.546293\pi$
$654$	5.40524e7	4.94163
$655$	0	0
$656$	−2.66169e6	−0.241489
$657$	6.05655e7	5.47409
$658$	−7.43007e6	−0.669003
$659$	−2.54692e6	−0.228456	−0.114228	−	0.993455i	$-0.536439\pi$
$659$	−2.54692e6	−0.228456	−0.114228	+	0.993455i	$0.536439\pi$
$660$	0	0
$661$	2.12344e7	1.89032	0.945160	−	0.326607i	$-0.105905\pi$
$661$	2.12344e7	1.89032	0.945160	+	0.326607i	$0.105905\pi$
$662$	−1.96797e7	−1.74531
$663$	2.97280e6	0.262653
$664$	4.78461e6	0.421140
$665$	0	0
$666$	−7.41779e7	−6.48021
$667$	3.25597e6	0.283377
$668$	2.43347e7	2.11001
$669$	−218190.	−0.0188482
$670$	0	0
$671$	−1.93551e6	−0.165955
$672$	−1.85325e7	−1.58311
$673$	2.60860e6	0.222008	0.111004	−	0.993820i	$-0.464593\pi$
$673$	2.60860e6	0.222008	0.111004	+	0.993820i	$0.464593\pi$
$674$	−2.74404e7	−2.32670
$675$	0	0
$676$	−1.61167e7	−1.35647
$677$	1.24426e7	1.04337	0.521684	−	0.853139i	$-0.325304\pi$
$677$	1.24426e7	1.04337	0.521684	+	0.853139i	$0.325304\pi$
$678$	−6.44230e7	−5.38229
$679$	−5.44968e6	−0.453625
$680$	0	0
$681$	8.55773e6	0.707116
$682$	1.26663e6	0.104277
$683$	−2.28434e7	−1.87374	−0.936870	−	0.349679i	$-0.886291\pi$
$683$	−2.28434e7	−1.87374	−0.936870	+	0.349679i	$0.886291\pi$
$684$	−1.57259e6	−0.128521
$685$	0	0
$686$	2.00687e7	1.62820
$687$	−682005.	−0.0551309
$688$	−546990.	−0.0440563
$689$	5.61671e6	0.450748
$690$	0	0
$691$	−1.16698e7	−0.929757	−0.464878	−	0.885374i	$-0.653902\pi$
$691$	−1.16698e7	−0.929757	−0.464878	+	0.885374i	$0.653902\pi$
$692$	3.04525e7	2.41745
$693$	−2.32727e6	−0.184083
$694$	−2.05100e7	−1.61647
$695$	0	0
$696$	4.56277e6	0.357031
$697$	−4.93069e6	−0.384438
$698$	−1.65566e7	−1.28627
$699$	3.43590e7	2.65979
$700$	0	0
$701$	1.25384e7	0.963713	0.481857	−	0.876250i	$-0.339963\pi$
$701$	1.25384e7	0.963713	0.481857	+	0.876250i	$0.339963\pi$
$702$	2.22796e7	1.70633
$703$	−557692.	−0.0425605
$704$	2.04385e6	0.155424
$705$	0	0
$706$	−838566.	−0.0633177
$707$	4.85881e6	0.365579
$708$	−1.18649e7	−0.889571
$709$	5.41345e6	0.404444	0.202222	−	0.979340i	$-0.435184\pi$
$709$	5.41345e6	0.404444	0.202222	+	0.979340i	$0.435184\pi$
$710$	0	0
$711$	−1.38318e7	−1.02613
$712$	−1.36635e7	−1.01009
$713$	1.10987e7	0.817618
$714$	−1.28931e7	−0.946479
$715$	0	0
$716$	−2.60736e7	−1.90072
$717$	−6.59130e6	−0.478821
$718$	4.25163e6	0.307783
$719$	−2.42388e7	−1.74860	−0.874298	−	0.485390i	$-0.838678\pi$
$719$	−2.42388e7	−1.74860	−0.874298	+	0.485390i	$0.838678\pi$
$720$	0	0
$721$	−1.11131e6	−0.0796156
$722$	2.20399e7	1.57350
$723$	4.22433e6	0.300547
$724$	−2.26769e7	−1.60782
$725$	0	0
$726$	−4.37472e7	−3.08041
$727$	1.29408e7	0.908083	0.454042	−	0.890980i	$-0.349982\pi$
$727$	1.29408e7	0.908083	0.454042	+	0.890980i	$0.349982\pi$
$728$	−2.07158e6	−0.144868
$729$	8.08232e7	5.63271
$730$	0	0
$731$	−1.01328e6	−0.0701352
$732$	−7.32439e7	−5.05235
$733$	7.29743e6	0.501661	0.250830	−	0.968031i	$-0.419296\pi$
$733$	7.29743e6	0.501661	0.250830	+	0.968031i	$0.419296\pi$
$734$	3.31175e7	2.26891
$735$	0	0
$736$	2.11046e7	1.43609
$737$	−85251.6	−0.00578141
$738$	−5.64313e7	−3.81399
$739$	−1.32365e6	−0.0891582	−0.0445791	−	0.999006i	$-0.514195\pi$
$739$	−1.32365e6	−0.0891582	−0.0445791	+	0.999006i	$0.514195\pi$
$740$	0	0
$741$	255799.	0.0171141
$742$	−2.43598e7	−1.62429
$743$	6.37614e6	0.423727	0.211863	−	0.977299i	$-0.432047\pi$
$743$	6.37614e6	0.423727	0.211863	+	0.977299i	$0.432047\pi$
$744$	1.55533e7	1.03013
$745$	0	0
$746$	2.23577e7	1.47089
$747$	−2.45964e7	−1.61276
$748$	1.00006e6	0.0653541
$749$	1.43865e7	0.937024
$750$	0	0
$751$	1.92999e6	0.124869	0.0624345	−	0.998049i	$-0.480114\pi$
$751$	1.92999e6	0.124869	0.0624345	+	0.998049i	$0.480114\pi$
$752$	−2.87506e6	−0.185397
$753$	−3.73203e7	−2.39860
$754$	−1.70034e6	−0.108920
$755$	0	0
$756$	−5.76700e7	−3.66983
$757$	−3.10102e7	−1.96682	−0.983411	−	0.181389i	$-0.941941\pi$
$757$	−3.10102e7	−1.96682	−0.983411	+	0.181389i	$0.941941\pi$
$758$	4.04816e6	0.255908
$759$	3.56506e6	0.224627
$760$	0	0
$761$	−2.51685e7	−1.57542	−0.787708	−	0.616049i	$-0.788732\pi$
$761$	−2.51685e7	−1.57542	−0.787708	+	0.616049i	$0.788732\pi$
$762$	6.52574e7	4.07139
$763$	1.69186e7	1.05209
$764$	1.25188e7	0.775942
$765$	0	0
$766$	2.62132e7	1.61417
$767$	1.43473e6	0.0880605
$768$	1.57749e7	0.965081
$769$	996876.	0.0607890	0.0303945	−	0.999538i	$-0.490324\pi$
$769$	996876.	0.0607890	0.0303945	+	0.999538i	$0.490324\pi$
$770$	0	0
$771$	4.73185e7	2.86678
$772$	−539897.	−0.0326037
$773$	2.33419e7	1.40504	0.702518	−	0.711666i	$-0.252059\pi$
$773$	2.33419e7	1.40504	0.702518	+	0.711666i	$0.252059\pi$
$774$	−1.15969e7	−0.695809
$775$	0	0
$776$	8.69686e6	0.518452
$777$	−3.12321e7	−1.85587
$778$	2.92196e7	1.73072
$779$	−424268.	−0.0250494
$780$	0	0
$781$	893343.	0.0524072
$782$	1.46825e7	0.858584
$783$	−1.53597e7	−0.895319
$784$	2.79353e6	0.162317
$785$	0	0
$786$	6.98172e7	4.03094
$787$	2.17248e7	1.25032	0.625158	−	0.780498i	$-0.285035\pi$
$787$	2.17248e7	1.25032	0.625158	+	0.780498i	$0.285035\pi$
$788$	2.72700e7	1.56448
$789$	2.72676e7	1.55939
$790$	0	0
$791$	−2.01646e7	−1.14591
$792$	3.71397e6	0.210390
$793$	8.85680e6	0.500143
$794$	8.41893e6	0.473921
$795$	0	0
$796$	1.44374e7	0.807617
$797$	2.34792e7	1.30930	0.654649	−	0.755933i	$-0.272817\pi$
$797$	2.34792e7	1.30930	0.654649	+	0.755933i	$0.272817\pi$
$798$	−1.10940e6	−0.0616711
$799$	−5.32595e6	−0.295141
$800$	0	0
$801$	7.02404e7	3.86817
$802$	3.37596e6	0.185337
$803$	−3.31413e6	−0.181376
$804$	−3.22610e6	−0.176010
$805$	0	0
$806$	−5.79602e6	−0.314262
$807$	5.03366e6	0.272082
$808$	−7.75392e6	−0.417824
$809$	−2.90695e7	−1.56159	−0.780793	−	0.624789i	$-0.785185\pi$
$809$	−2.90695e7	−1.56159	−0.780793	+	0.624789i	$0.785185\pi$
$810$	0	0
$811$	3.49123e7	1.86392	0.931959	−	0.362563i	$-0.118098\pi$
$811$	3.49123e7	1.86392	0.931959	+	0.362563i	$0.118098\pi$
$812$	4.40128e6	0.234255
$813$	454485.	0.0241154
$814$	4.05900e6	0.214713
$815$	0	0
$816$	−4.98896e6	−0.262292
$817$	−87189.1	−0.00456990
$818$	1.94227e7	1.01491
$819$	1.06495e7	0.554776
$820$	0	0
$821$	8.88435e6	0.460011	0.230005	−	0.973189i	$-0.426126\pi$
$821$	8.88435e6	0.460011	0.230005	+	0.973189i	$0.426126\pi$
$822$	−6.42274e6	−0.331544
$823$	−1.36781e7	−0.703923	−0.351961	−	0.936015i	$-0.614485\pi$
$823$	−1.36781e7	−0.703923	−0.351961	+	0.936015i	$0.614485\pi$
$824$	1.77349e6	0.0909934
$825$	0	0
$826$	−6.22244e6	−0.317329
$827$	3.15912e7	1.60621	0.803105	−	0.595838i	$-0.203180\pi$
$827$	3.15912e7	1.60621	0.803105	+	0.595838i	$0.203180\pi$
$828$	1.00292e8	5.08380
$829$	−3.23893e6	−0.163687	−0.0818436	−	0.996645i	$-0.526081\pi$
$829$	−3.23893e6	−0.163687	−0.0818436	+	0.996645i	$0.526081\pi$
$830$	0	0
$831$	−7.33294e7	−3.68363
$832$	−9.35256e6	−0.468406
$833$	5.17492e6	0.258399
$834$	4.20969e7	2.09573
$835$	0	0
$836$	86051.7	0.00425838
$837$	−5.23572e7	−2.58323
$838$	2.50294e7	1.23123
$839$	−3.30853e7	−1.62267	−0.811335	−	0.584581i	$-0.801259\pi$
$839$	−3.30853e7	−1.62267	−0.811335	+	0.584581i	$0.801259\pi$
$840$	0	0
$841$	−1.93389e7	−0.942849
$842$	2.12113e7	1.03107
$843$	−7.13719e7	−3.45906
$844$	−3.09919e7	−1.49759
$845$	0	0
$846$	−6.09550e7	−2.92808
$847$	−1.36930e7	−0.655830
$848$	−9.42598e6	−0.450129
$849$	−1.61077e7	−0.766946
$850$	0	0
$851$	3.55667e7	1.68353
$852$	3.38059e7	1.59549
$853$	1.28462e7	0.604507	0.302253	−	0.953228i	$-0.402261\pi$
$853$	1.28462e7	0.604507	0.302253	+	0.953228i	$0.402261\pi$
$854$	−3.84121e7	−1.80228
$855$	0	0
$856$	−2.29587e7	−1.07093
$857$	2.71502e7	1.26276	0.631381	−	0.775473i	$-0.282489\pi$
$857$	2.71502e7	1.26276	0.631381	+	0.775473i	$0.282489\pi$
$858$	−1.86176e6	−0.0863385
$859$	−9.76899e6	−0.451718	−0.225859	−	0.974160i	$-0.572519\pi$
$859$	−9.76899e6	−0.451718	−0.225859	+	0.974160i	$0.572519\pi$
$860$	0	0
$861$	−2.37600e7	−1.09229
$862$	4.48776e7	2.05713
$863$	4.01335e7	1.83434	0.917171	−	0.398493i	$-0.130467\pi$
$863$	4.01335e7	1.83434	0.917171	+	0.398493i	$0.130467\pi$
$864$	−9.95588e7	−4.53728
$865$	0	0
$866$	−2.86579e6	−0.129852
$867$	3.44519e7	1.55656
$868$	1.50028e7	0.675886
$869$	756872.	0.0339995
$870$	0	0
$871$	390106.	0.0174236
$872$	−2.69995e7	−1.20244
$873$	−4.47083e7	−1.98542
$874$	1.26337e6	0.0559440
$875$	0	0
$876$	−1.25413e8	−5.52184
$877$	620112.	0.0272252	0.0136126	−	0.999907i	$-0.495667\pi$
$877$	620112.	0.0272252	0.0136126	+	0.999907i	$0.495667\pi$
$878$	4.87711e7	2.13514
$879$	4.52814e7	1.97673
$880$	0	0
$881$	−2.66687e6	−0.115761	−0.0578806	−	0.998324i	$-0.518434\pi$
$881$	−2.66687e6	−0.115761	−0.0578806	+	0.998324i	$0.518434\pi$
$882$	5.92265e7	2.56357
$883$	−3.52924e7	−1.52328	−0.761640	−	0.648001i	$-0.775605\pi$
$883$	−3.52924e7	−1.52328	−0.761640	+	0.648001i	$0.775605\pi$
$884$	−4.57623e6	−0.196960
$885$	0	0
$886$	−5.46161e7	−2.33742
$887$	1.61157e7	0.687764	0.343882	−	0.939013i	$-0.388258\pi$
$887$	1.61157e7	0.687764	0.343882	+	0.939013i	$0.388258\pi$
$888$	4.98417e7	2.12109
$889$	2.04258e7	0.866811
$890$	0	0
$891$	−1.02276e7	−0.431599
$892$	335874.	0.0141340
$893$	−458278.	−0.0192309
$894$	7.44409e7	3.11507
$895$	0	0
$896$	2.12909e7	0.885982
$897$	−1.63135e7	−0.676965
$898$	−4.58457e7	−1.89718
$899$	3.99581e6	0.164894
$900$	0	0
$901$	−1.74613e7	−0.716580
$902$	3.08791e6	0.126371
$903$	−4.88279e6	−0.199273
$904$	3.21797e7	1.30967
$905$	0	0
$906$	1.29118e7	0.522598
$907$	−1.06365e7	−0.429318	−0.214659	−	0.976689i	$-0.568864\pi$
$907$	−1.06365e7	−0.429318	−0.214659	+	0.976689i	$0.568864\pi$
$908$	−1.31735e7	−0.530256
$909$	3.98608e7	1.60006
$910$	0	0
$911$	−1.24400e7	−0.496622	−0.248311	−	0.968680i	$-0.579875\pi$
$911$	−1.24400e7	−0.496622	−0.248311	+	0.968680i	$0.579875\pi$
$912$	−429282.	−0.0170905
$913$	1.34591e6	0.0534366
$914$	−2.24684e7	−0.889624
$915$	0	0
$916$	1.04985e6	0.0413419
$917$	2.18530e7	0.858199
$918$	−6.92631e7	−2.71266
$919$	−2.71496e7	−1.06041	−0.530206	−	0.847869i	$-0.677885\pi$
$919$	−2.71496e7	−1.06041	−0.530206	+	0.847869i	$0.677885\pi$
$920$	0	0
$921$	−4.76287e6	−0.185020
$922$	−6.26745e7	−2.42808
$923$	−4.08789e6	−0.157941
$924$	4.81910e6	0.185689
$925$	0	0
$926$	6.50085e7	2.49140
$927$	−9.11702e6	−0.348461
$928$	7.59815e6	0.289626
$929$	4.48394e7	1.70459	0.852296	−	0.523060i	$-0.175209\pi$
$929$	4.48394e7	1.70459	0.852296	+	0.523060i	$0.175209\pi$
$930$	0	0
$931$	445283.	0.0168369
$932$	−5.28910e7	−1.99454
$933$	−8.64681e7	−3.25201
$934$	−1.19480e7	−0.448154
$935$	0	0
$936$	−1.69949e7	−0.634059
$937$	1.25288e7	0.466189	0.233095	−	0.972454i	$-0.425115\pi$
$937$	1.25288e7	0.466189	0.233095	+	0.972454i	$0.425115\pi$
$938$	−1.69190e6	−0.0627866
$939$	2.14200e7	0.792787
$940$	0	0
$941$	6.82930e6	0.251421	0.125711	−	0.992067i	$-0.459879\pi$
$941$	6.82930e6	0.251421	0.125711	+	0.992067i	$0.459879\pi$
$942$	−1.22998e8	−4.51618
$943$	2.70576e7	0.990856
$944$	−2.40776e6	−0.0879395
$945$	0	0
$946$	634580.	0.0230547
$947$	4.43251e7	1.60611	0.803054	−	0.595906i	$-0.203207\pi$
$947$	4.43251e7	1.60611	0.803054	+	0.595906i	$0.203207\pi$
$948$	2.86416e7	1.03509
$949$	1.51653e7	0.546619
$950$	0	0
$951$	7.36197e7	2.63963
$952$	6.44017e6	0.230306
$953$	−5.19397e6	−0.185254	−0.0926269	−	0.995701i	$-0.529526\pi$
$953$	−5.19397e6	−0.185254	−0.0926269	+	0.995701i	$0.529526\pi$
$954$	−1.99843e8	−7.10917
$955$	0	0
$956$	1.01464e7	0.359061
$957$	1.28351e6	0.0453021
$958$	2.99264e7	1.05352
$959$	−2.01034e6	−0.0705867
$960$	0	0
$961$	−1.50085e7	−0.524237
$962$	−1.85737e7	−0.647086
$963$	1.18024e8	4.10116
$964$	−6.50279e6	−0.225376
$965$	0	0
$966$	7.07519e7	2.43947
$967$	−2.40529e7	−0.827182	−0.413591	−	0.910463i	$-0.635726\pi$
$967$	−2.40529e7	−0.827182	−0.413591	+	0.910463i	$0.635726\pi$
$968$	2.18520e7	0.749554
$969$	−795231.	−0.0272072
$970$	0	0
$971$	−2.97435e6	−0.101238	−0.0506191	−	0.998718i	$-0.516119\pi$
$971$	−2.97435e6	−0.101238	−0.0506191	+	0.998718i	$0.516119\pi$
$972$	−2.23729e8	−7.59552
$973$	1.31765e7	0.446187
$974$	1.76843e7	0.597297
$975$	0	0
$976$	−1.48635e7	−0.499456
$977$	2.46291e7	0.825492	0.412746	−	0.910846i	$-0.364570\pi$
$977$	2.46291e7	0.825492	0.412746	+	0.910846i	$0.364570\pi$
$978$	−1.17046e8	−3.91300
$979$	−3.84354e6	−0.128166
$980$	0	0
$981$	1.38797e8	4.60477
$982$	6.02900e7	1.99511
$983$	−2.21814e7	−0.732157	−0.366079	−	0.930584i	$-0.619300\pi$
$983$	−2.21814e7	−0.732157	−0.366079	+	0.930584i	$0.619300\pi$
$984$	3.79174e7	1.24839
$985$	0	0
$986$	5.28604e6	0.173156
$987$	−2.56647e7	−0.838577
$988$	−393768.	−0.0128336
$989$	5.56047e6	0.180768
$990$	0	0
$991$	3.59571e6	0.116306	0.0581528	−	0.998308i	$-0.481479\pi$
$991$	3.59571e6	0.116306	0.0581528	+	0.998308i	$0.481479\pi$
$992$	2.59001e7	0.835647
$993$	−6.79767e7	−2.18770
$994$	1.77292e7	0.569146
$995$	0	0
$996$	5.09320e7	1.62683
$997$	−6.12307e6	−0.195088	−0.0975442	−	0.995231i	$-0.531099\pi$
$997$	−6.12307e6	−0.195088	−0.0975442	+	0.995231i	$0.531099\pi$
$998$	4.55490e7	1.44761
$999$	−1.67782e8	−5.31903

Twists

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

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

\(f(q)\)	\(=\)	\(q-8.90907 q^{2} -30.7734 q^{3} +47.3715 q^{4} +274.162 q^{6} +85.8137 q^{7} -136.946 q^{8} +704.001 q^{9} +O(q^{10})\)	\(q-8.90907 q^{2} -30.7734 q^{3} +47.3715 q^{4} +274.162 q^{6} +85.8137 q^{7} -136.946 q^{8} +704.001 q^{9} -38.5228 q^{11} -1457.78 q^{12} +176.278 q^{13} -764.520 q^{14} -295.830 q^{16} -548.015 q^{17} -6271.99 q^{18} -47.1547 q^{19} -2640.78 q^{21} +343.202 q^{22} +3007.28 q^{23} +4214.28 q^{24} -1570.47 q^{26} -14186.5 q^{27} +4065.12 q^{28} +1082.69 q^{29} +3690.62 q^{31} +7017.83 q^{32} +1185.48 q^{33} +4882.31 q^{34} +33349.6 q^{36} +11826.9 q^{37} +420.105 q^{38} -5424.67 q^{39} +8997.36 q^{41} +23526.9 q^{42} +1849.00 q^{43} -1824.88 q^{44} -26792.1 q^{46} +9718.61 q^{47} +9103.69 q^{48} -9443.02 q^{49} +16864.3 q^{51} +8350.55 q^{52} +31862.8 q^{53} +126389. q^{54} -11751.8 q^{56} +1451.11 q^{57} -9645.79 q^{58} +8139.01 q^{59} +50243.4 q^{61} -32880.0 q^{62} +60412.9 q^{63} -53055.7 q^{64} -10561.5 q^{66} +2213.02 q^{67} -25960.3 q^{68} -92544.3 q^{69} -23190.0 q^{71} -96409.8 q^{72} +86030.4 q^{73} -105366. q^{74} -2233.79 q^{76} -3305.78 q^{77} +48328.7 q^{78} -19647.4 q^{79} +265496. q^{81} -80158.1 q^{82} -34938.0 q^{83} -125097. q^{84} -16472.9 q^{86} -33318.1 q^{87} +5275.52 q^{88} +99773.2 q^{89} +15127.1 q^{91} +142460. q^{92} -113573. q^{93} -86583.7 q^{94} -215962. q^{96} -63506.0 q^{97} +84128.5 q^{98} -27120.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 5 q^{2} - 20 q^{3} + 427 q^{4} + 248 q^{6} - 118 q^{7} - 561 q^{8} + 2618 q^{9}+O(q^{10}) \) 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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Groups

Database

Properties

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