LMFDB - Embedded newform 490.4.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("490.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{113})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 59x^{2} + 60x + 674 $ x^4 - 2x^3 - 59x^2 + 60*x + 674
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-6.22929$ of defining polynomial
Character	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +1.40086 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.80172 q^{6} +8.00000 q^{8} -25.0376 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +1.40086 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.80172 q^{6} +8.00000 q^{8} -25.0376 q^{9} -10.0000 q^{10} +0.0289997 q^{11} +5.60344 q^{12} -11.5691 q^{13} -7.00430 q^{15} +16.0000 q^{16} -42.8087 q^{17} -50.0752 q^{18} -158.906 q^{19} -20.0000 q^{20} +0.0579993 q^{22} +120.474 q^{23} +11.2069 q^{24} +25.0000 q^{25} -23.1382 q^{26} -72.8973 q^{27} -101.091 q^{29} -14.0086 q^{30} -74.1934 q^{31} +32.0000 q^{32} +0.0406244 q^{33} -85.6175 q^{34} -100.150 q^{36} -91.7860 q^{37} -317.813 q^{38} -16.2067 q^{39} -40.0000 q^{40} -92.8086 q^{41} -294.437 q^{43} +0.115999 q^{44} +125.188 q^{45} +240.948 q^{46} -298.697 q^{47} +22.4137 q^{48} +50.0000 q^{50} -59.9690 q^{51} -46.2763 q^{52} +670.372 q^{53} -145.795 q^{54} -0.144998 q^{55} -222.605 q^{57} -202.181 q^{58} +95.8035 q^{59} -28.0172 q^{60} -387.264 q^{61} -148.387 q^{62} +64.0000 q^{64} +57.8454 q^{65} +0.0812489 q^{66} +479.788 q^{67} -171.235 q^{68} +168.767 q^{69} -617.958 q^{71} -200.301 q^{72} -562.682 q^{73} -183.572 q^{74} +35.0215 q^{75} -635.625 q^{76} -32.4133 q^{78} +8.95079 q^{79} -80.0000 q^{80} +573.896 q^{81} -185.617 q^{82} -196.990 q^{83} +214.044 q^{85} -588.874 q^{86} -141.614 q^{87} +0.231997 q^{88} -1154.44 q^{89} +250.376 q^{90} +481.895 q^{92} -103.935 q^{93} -597.395 q^{94} +794.532 q^{95} +44.8275 q^{96} +1219.70 q^{97} -0.726082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 10 q^{3} + 16 q^{4} - 20 q^{5} - 20 q^{6} + 32 q^{8} + 38 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 - 10 * q^3 + 16 * q^4 - 20 * q^5 - 20 * q^6 + 32 * q^8 + 38 * q^9	\( 4 q + 8 q^{2} - 10 q^{3} + 16 q^{4} - 20 q^{5} - 20 q^{6} + 32 q^{8} + 38 q^{9} - 40 q^{10} + 18 q^{11} - 40 q^{12} - 130 q^{13} + 50 q^{15} + 64 q^{16} - 110 q^{17} + 76 q^{18} - 40 q^{19} - 80 q^{20} + 36 q^{22} - 164 q^{23} - 80 q^{24} + 100 q^{25} - 260 q^{26} - 430 q^{27} + 94 q^{29} + 100 q^{30} - 180 q^{31} + 128 q^{32} - 650 q^{33} - 220 q^{34} + 152 q^{36} + 16 q^{37} - 80 q^{38} - 10 q^{39} - 160 q^{40} - 540 q^{41} - 560 q^{43} + 72 q^{44} - 190 q^{45} - 328 q^{46} - 1150 q^{47} - 160 q^{48} + 200 q^{50} - 926 q^{51} - 520 q^{52} - 244 q^{53} - 860 q^{54} - 90 q^{55} - 840 q^{57} + 188 q^{58} - 400 q^{59} + 200 q^{60} - 1540 q^{61} - 360 q^{62} + 256 q^{64} + 650 q^{65} - 1300 q^{66} - 760 q^{67} - 440 q^{68} + 1480 q^{69} + 52 q^{71} + 304 q^{72} - 800 q^{73} + 32 q^{74} - 250 q^{75} - 160 q^{76} - 20 q^{78} + 398 q^{79} - 320 q^{80} + 348 q^{81} - 1080 q^{82} + 1220 q^{83} + 550 q^{85} - 1120 q^{86} + 930 q^{87} + 144 q^{88} - 200 q^{89} - 380 q^{90} - 656 q^{92} + 1408 q^{93} - 2300 q^{94} + 200 q^{95} - 320 q^{96} + 670 q^{97} + 2292 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 10 * q^3 + 16 * q^4 - 20 * q^5 - 20 * q^6 + 32 * q^8 + 38 * q^9 - 40 * q^10 + 18 * q^11 - 40 * q^12 - 130 * q^13 + 50 * q^15 + 64 * q^16 - 110 * q^17 + 76 * q^18 - 40 * q^19 - 80 * q^20 + 36 * q^22 - 164 * q^23 - 80 * q^24 + 100 * q^25 - 260 * q^26 - 430 * q^27 + 94 * q^29 + 100 * q^30 - 180 * q^31 + 128 * q^32 - 650 * q^33 - 220 * q^34 + 152 * q^36 + 16 * q^37 - 80 * q^38 - 10 * q^39 - 160 * q^40 - 540 * q^41 - 560 * q^43 + 72 * q^44 - 190 * q^45 - 328 * q^46 - 1150 * q^47 - 160 * q^48 + 200 * q^50 - 926 * q^51 - 520 * q^52 - 244 * q^53 - 860 * q^54 - 90 * q^55 - 840 * q^57 + 188 * q^58 - 400 * q^59 + 200 * q^60 - 1540 * q^61 - 360 * q^62 + 256 * q^64 + 650 * q^65 - 1300 * q^66 - 760 * q^67 - 440 * q^68 + 1480 * q^69 + 52 * q^71 + 304 * q^72 - 800 * q^73 + 32 * q^74 - 250 * q^75 - 160 * q^76 - 20 * q^78 + 398 * q^79 - 320 * q^80 + 348 * q^81 - 1080 * q^82 + 1220 * q^83 + 550 * q^85 - 1120 * q^86 + 930 * q^87 + 144 * q^88 - 200 * q^89 - 380 * q^90 - 656 * q^92 + 1408 * q^93 - 2300 * q^94 + 200 * q^95 - 320 * q^96 + 670 * q^97 + 2292 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	1.40086	0.269596	0.134798	−	0.990873i	$-0.456962\pi$
$3$	1.40086	0.269596	0.134798	+	0.990873i	$0.456962\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	2.80172	0.190633
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−25.0376	−0.927318
$10$	−10.0000	−0.316228
$11$	0.0289997	0.000794884 0	0.000397442	−	1.00000i	$-0.499873\pi$
$11$	0.0289997	0.000794884 0	0.000397442		1.00000i	$0.499873\pi$
$12$	5.60344	0.134798
$13$	−11.5691	−0.246822	−0.123411	−	0.992356i	$-0.539383\pi$
$13$	−11.5691	−0.246822	−0.123411	+	0.992356i	$0.539383\pi$
$14$	0	0
$15$	−7.00430	−0.120567
$16$	16.0000	0.250000
$17$	−42.8087	−0.610744	−0.305372	−	0.952233i	$-0.598781\pi$
$17$	−42.8087	−0.610744	−0.305372	+	0.952233i	$0.598781\pi$
$18$	−50.0752	−0.655713
$19$	−158.906	−1.91872	−0.959358	−	0.282191i	$-0.908939\pi$
$19$	−158.906	−1.91872	−0.959358	+	0.282191i	$0.908939\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	0.0579993	0.000562068 0
$23$	120.474	1.09220	0.546098	−	0.837721i	$-0.316113\pi$
$23$	120.474	1.09220	0.546098	+	0.837721i	$0.316113\pi$
$24$	11.2069	0.0953164
$25$	25.0000	0.200000
$26$	−23.1382	−0.174530
$27$	−72.8973	−0.519596
$28$	0	0
$29$	−101.091	−0.647312	−0.323656	−	0.946175i	$-0.604912\pi$
$29$	−101.091	−0.647312	−0.323656	+	0.946175i	$0.604912\pi$
$30$	−14.0086	−0.0852536
$31$	−74.1934	−0.429856	−0.214928	−	0.976630i	$-0.568952\pi$
$31$	−74.1934	−0.429856	−0.214928	+	0.976630i	$0.568952\pi$
$32$	32.0000	0.176777
$33$	0.0406244	0.000214297 0
$34$	−85.6175	−0.431861
$35$	0	0
$36$	−100.150	−0.463659
$37$	−91.7860	−0.407825	−0.203912	−	0.978989i	$-0.565366\pi$
$37$	−91.7860	−0.407825	−0.203912	+	0.978989i	$0.565366\pi$
$38$	−317.813	−1.35674
$39$	−16.2067	−0.0665421
$40$	−40.0000	−0.158114
$41$	−92.8086	−0.353519	−0.176759	−	0.984254i	$-0.556561\pi$
$41$	−92.8086	−0.353519	−0.176759	+	0.984254i	$0.556561\pi$
$42$	0	0
$43$	−294.437	−1.04421	−0.522107	−	0.852880i	$-0.674854\pi$
$43$	−294.437	−1.04421	−0.522107	+	0.852880i	$0.674854\pi$
$44$	0.115999	0.000397442 0
$45$	125.188	0.414709
$46$	240.948	0.772299
$47$	−298.697	−0.927011	−0.463505	−	0.886094i	$-0.653409\pi$
$47$	−298.697	−0.927011	−0.463505	+	0.886094i	$0.653409\pi$
$48$	22.4137	0.0673989
$49$	0	0
$50$	50.0000	0.141421
$51$	−59.9690	−0.164654
$52$	−46.2763	−0.123411
$53$	670.372	1.73741	0.868704	−	0.495331i	$-0.164953\pi$
$53$	670.372	1.73741	0.868704	+	0.495331i	$0.164953\pi$
$54$	−145.795	−0.367410
$55$	−0.144998	−0.000355483 0
$56$	0	0
$57$	−222.605	−0.517277
$58$	−202.181	−0.457719
$59$	95.8035	0.211399	0.105700	−	0.994398i	$-0.466292\pi$
$59$	95.8035	0.211399	0.105700	+	0.994398i	$0.466292\pi$
$60$	−28.0172	−0.0602834
$61$	−387.264	−0.812853	−0.406427	−	0.913683i	$-0.633225\pi$
$61$	−387.264	−0.812853	−0.406427	+	0.913683i	$0.633225\pi$
$62$	−148.387	−0.303954
$63$	0	0
$64$	64.0000	0.125000
$65$	57.8454	0.110382
$66$	0.0812489	0.000151531 0
$67$	479.788	0.874857	0.437429	−	0.899253i	$-0.355889\pi$
$67$	479.788	0.874857	0.437429	+	0.899253i	$0.355889\pi$
$68$	−171.235	−0.305372
$69$	168.767	0.294451
$70$	0	0
$71$	−617.958	−1.03293	−0.516466	−	0.856308i	$-0.672753\pi$
$71$	−617.958	−1.03293	−0.516466	+	0.856308i	$0.672753\pi$
$72$	−200.301	−0.327857
$73$	−562.682	−0.902150	−0.451075	−	0.892486i	$-0.648959\pi$
$73$	−562.682	−0.902150	−0.451075	+	0.892486i	$0.648959\pi$
$74$	−183.572	−0.288376
$75$	35.0215	0.0539191
$76$	−635.625	−0.959358
$77$	0	0
$78$	−32.4133	−0.0470524
$79$	8.95079	0.0127474	0.00637369	−	0.999980i	$-0.497971\pi$
$79$	8.95079	0.0127474	0.00637369	+	0.999980i	$0.497971\pi$
$80$	−80.0000	−0.111803
$81$	573.896	0.787237
$82$	−185.617	−0.249975
$83$	−196.990	−0.260512	−0.130256	−	0.991480i	$-0.541580\pi$
$83$	−196.990	−0.260512	−0.130256	+	0.991480i	$0.541580\pi$
$84$	0	0
$85$	214.044	0.273133
$86$	−588.874	−0.738371
$87$	−141.614	−0.174512
$88$	0.231997	0.000281034 0
$89$	−1154.44	−1.37495	−0.687474	−	0.726209i	$-0.741280\pi$
$89$	−1154.44	−1.37495	−0.687474	+	0.726209i	$0.741280\pi$
$90$	250.376	0.293244
$91$	0	0
$92$	481.895	0.546098
$93$	−103.935	−0.115887
$94$	−597.395	−0.655496
$95$	794.532	0.858076
$96$	44.8275	0.0476582
$97$	1219.70	1.27672	0.638361	−	0.769737i	$-0.279613\pi$
$97$	1219.70	1.27672	0.638361	+	0.769737i	$0.279613\pi$
$98$	0	0
$99$	−0.726082	−0.000737111 0
$100$	100.000	0.100000
$101$	1251.07	1.23254	0.616268	−	0.787537i	$-0.288644\pi$
$101$	1251.07	1.23254	0.616268	+	0.787537i	$0.288644\pi$
$102$	−119.938	−0.116428
$103$	562.210	0.537827	0.268913	−	0.963164i	$-0.413335\pi$
$103$	562.210	0.537827	0.268913	+	0.963164i	$0.413335\pi$
$104$	−92.5527	−0.0872648
$105$	0	0
$106$	1340.74	1.22853
$107$	−1284.24	−1.16030	−0.580148	−	0.814511i	$-0.697005\pi$
$107$	−1284.24	−1.16030	−0.580148	+	0.814511i	$0.697005\pi$
$108$	−291.589	−0.259798
$109$	1819.90	1.59922	0.799610	−	0.600520i	$-0.205040\pi$
$109$	1819.90	1.59922	0.799610	+	0.600520i	$0.205040\pi$
$110$	−0.289997	−0.000251364 0
$111$	−128.579	−0.109948
$112$	0	0
$113$	−20.1951	−0.0168124	−0.00840619	−	0.999965i	$-0.502676\pi$
$113$	−20.1951	−0.0168124	−0.00840619	+	0.999965i	$0.502676\pi$
$114$	−445.211	−0.365770
$115$	−602.369	−0.488445
$116$	−404.362	−0.323656
$117$	289.662	0.228883
$118$	191.607	0.149482
$119$	0	0
$120$	−56.0344	−0.0426268
$121$	−1331.00	−0.999999
$122$	−774.528	−0.574774
$123$	−130.012	−0.0953070
$124$	−296.774	−0.214928
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−1884.98	−1.31704	−0.658522	−	0.752561i	$-0.728818\pi$
$127$	−1884.98	−1.31704	−0.658522	+	0.752561i	$0.728818\pi$
$128$	128.000	0.0883883
$129$	−412.465	−0.281515
$130$	115.691	0.0780520
$131$	663.852	0.442756	0.221378	−	0.975188i	$-0.428945\pi$
$131$	663.852	0.442756	0.221378	+	0.975188i	$0.428945\pi$
$132$	0.162498	0.000107149 0
$133$	0	0
$134$	959.576	0.618618
$135$	364.487	0.232371
$136$	−342.470	−0.215931
$137$	−1832.93	−1.14305	−0.571524	−	0.820585i	$-0.693648\pi$
$137$	−1832.93	−1.14305	−0.571524	+	0.820585i	$0.693648\pi$
$138$	337.534	0.208208
$139$	1354.55	0.826558	0.413279	−	0.910604i	$-0.364383\pi$
$139$	1354.55	0.826558	0.413279	+	0.910604i	$0.364383\pi$
$140$	0	0
$141$	−418.433	−0.249918
$142$	−1235.92	−0.730393
$143$	−0.335500	−0.000196195 0
$144$	−400.601	−0.231830
$145$	505.453	0.289487
$146$	−1125.36	−0.637916
$147$	0	0
$148$	−367.144	−0.203912
$149$	1759.63	0.967478	0.483739	−	0.875212i	$-0.339278\pi$
$149$	1759.63	0.967478	0.483739	+	0.875212i	$0.339278\pi$
$150$	70.0430	0.0381266
$151$	816.905	0.440257	0.220128	−	0.975471i	$-0.429352\pi$
$151$	816.905	0.440257	0.220128	+	0.975471i	$0.429352\pi$
$152$	−1271.25	−0.678369
$153$	1071.83	0.566354
$154$	0	0
$155$	370.967	0.192237
$156$	−64.8266	−0.0332711
$157$	1803.62	0.916846	0.458423	−	0.888734i	$-0.348414\pi$
$157$	1803.62	0.916846	0.458423	+	0.888734i	$0.348414\pi$
$158$	17.9016	0.00901375
$159$	939.097	0.468398
$160$	−160.000	−0.0790569
$161$	0	0
$162$	1147.79	0.556661
$163$	2534.78	1.21803	0.609016	−	0.793158i	$-0.291565\pi$
$163$	2534.78	1.21803	0.609016	+	0.793158i	$0.291565\pi$
$164$	−371.234	−0.176759
$165$	−0.203122	−9.58366e−5 0
$166$	−393.981	−0.184210
$167$	1851.96	0.858139	0.429070	−	0.903271i	$-0.358841\pi$
$167$	1851.96	0.858139	0.429070	+	0.903271i	$0.358841\pi$
$168$	0	0
$169$	−2063.16	−0.939079
$170$	428.087	0.193134
$171$	3978.63	1.77926
$172$	−1177.75	−0.522107
$173$	1229.15	0.540178	0.270089	−	0.962835i	$-0.412947\pi$
$173$	1229.15	0.540178	0.270089	+	0.962835i	$0.412947\pi$
$174$	−283.227	−0.123399
$175$	0	0
$176$	0.463995	0.000198721 0
$177$	134.207	0.0569923
$178$	−2308.88	−0.972235
$179$	−4644.34	−1.93930	−0.969649	−	0.244502i	$-0.921376\pi$
$179$	−4644.34	−1.93930	−0.969649	+	0.244502i	$0.921376\pi$
$180$	500.752	0.207355
$181$	−4119.04	−1.69152	−0.845761	−	0.533562i	$-0.820853\pi$
$181$	−4119.04	−1.69152	−0.845761	+	0.533562i	$0.820853\pi$
$182$	0	0
$183$	−542.502	−0.219142
$184$	963.790	0.386150
$185$	458.930	0.182385
$186$	−207.869	−0.0819446
$187$	−1.24144	−0.000485471 0
$188$	−1194.79	−0.463505
$189$	0	0
$190$	1589.06	0.606751
$191$	1594.46	0.604037	0.302018	−	0.953302i	$-0.402340\pi$
$191$	1594.46	0.604037	0.302018	+	0.953302i	$0.402340\pi$
$192$	89.6550	0.0336994
$193$	1641.29	0.612138	0.306069	−	0.952009i	$-0.400986\pi$
$193$	1641.29	0.612138	0.306069	+	0.952009i	$0.400986\pi$
$194$	2439.41	0.902779
$195$	81.0333	0.0297585
$196$	0	0
$197$	−1379.91	−0.499058	−0.249529	−	0.968367i	$-0.580276\pi$
$197$	−1379.91	−0.499058	−0.249529	+	0.968367i	$0.580276\pi$
$198$	−1.45216	−0.000521216 0
$199$	3701.18	1.31844	0.659220	−	0.751950i	$-0.270887\pi$
$199$	3701.18	1.31844	0.659220	+	0.751950i	$0.270887\pi$
$200$	200.000	0.0707107
$201$	672.116	0.235858
$202$	2502.14	0.871535
$203$	0	0
$204$	−239.876	−0.0823269
$205$	464.043	0.158098
$206$	1124.42	0.380301
$207$	−3016.37	−1.01281
$208$	−185.105	−0.0617055
$209$	−4.60823	−0.00152516
$210$	0	0
$211$	4038.16	1.31753	0.658765	−	0.752349i	$-0.271079\pi$
$211$	4038.16	1.31753	0.658765	+	0.752349i	$0.271079\pi$
$212$	2681.49	0.868704
$213$	−865.672	−0.278474
$214$	−2568.47	−0.820454
$215$	1472.18	0.466987
$216$	−583.179	−0.183705
$217$	0	0
$218$	3639.80	1.13082
$219$	−788.238	−0.243216
$220$	−0.579993	−0.000177742 0
$221$	495.258	0.150745
$222$	−257.159	−0.0777448
$223$	4497.23	1.35048	0.675239	−	0.737599i	$-0.264041\pi$
$223$	4497.23	1.35048	0.675239	+	0.737599i	$0.264041\pi$
$224$	0	0
$225$	−625.940	−0.185464
$226$	−40.3903	−0.0118881
$227$	−2704.28	−0.790702	−0.395351	−	0.918530i	$-0.629377\pi$
$227$	−2704.28	−0.790702	−0.395351	+	0.918530i	$0.629377\pi$
$228$	−890.422	−0.258639
$229$	−2501.56	−0.721868	−0.360934	−	0.932591i	$-0.617542\pi$
$229$	−2501.56	−0.721868	−0.360934	+	0.932591i	$0.617542\pi$
$230$	−1204.74	−0.345383
$231$	0	0
$232$	−808.724	−0.228859
$233$	5714.37	1.60670	0.803349	−	0.595508i	$-0.203049\pi$
$233$	5714.37	1.60670	0.803349	+	0.595508i	$0.203049\pi$
$234$	579.324	0.161844
$235$	1493.49	0.414572
$236$	383.214	0.105700
$237$	12.5388	0.00343663
$238$	0	0
$239$	−48.0045	−0.0129923	−0.00649613	−	0.999979i	$-0.502068\pi$
$239$	−48.0045	−0.0129923	−0.00649613	+	0.999979i	$0.502068\pi$
$240$	−112.069	−0.0301417
$241$	3433.11	0.917619	0.458809	−	0.888535i	$-0.348276\pi$
$241$	3433.11	0.917619	0.458809	+	0.888535i	$0.348276\pi$
$242$	−2662.00	−0.707106
$243$	2772.18	0.731832
$244$	−1549.06	−0.406427
$245$	0	0
$246$	−260.023	−0.0673922
$247$	1838.40	0.473582
$248$	−593.547	−0.151977
$249$	−275.956	−0.0702329
$250$	−250.000	−0.0632456
$251$	−6388.81	−1.60661	−0.803303	−	0.595571i	$-0.796926\pi$
$251$	−6388.81	−1.60661	−0.803303	+	0.595571i	$0.796926\pi$
$252$	0	0
$253$	3.49370	0.000868170 0
$254$	−3769.95	−0.931291
$255$	299.845	0.0736354
$256$	256.000	0.0625000
$257$	433.385	0.105190	0.0525950	−	0.998616i	$-0.483251\pi$
$257$	433.385	0.105190	0.0525950	+	0.998616i	$0.483251\pi$
$258$	−824.929	−0.199061
$259$	0	0
$260$	231.382	0.0551911
$261$	2531.06	0.600264
$262$	1327.70	0.313076
$263$	−5900.70	−1.38347	−0.691735	−	0.722152i	$-0.743153\pi$
$263$	−5900.70	−1.38347	−0.691735	+	0.722152i	$0.743153\pi$
$264$	0.324996	7.57655e−5 0
$265$	−3351.86	−0.776993
$266$	0	0
$267$	−1617.21	−0.370680
$268$	1919.15	0.437429
$269$	−4548.19	−1.03089	−0.515443	−	0.856924i	$-0.672372\pi$
$269$	−4548.19	−1.03089	−0.515443	+	0.856924i	$0.672372\pi$
$270$	728.973	0.164311
$271$	5062.46	1.13477	0.567384	−	0.823453i	$-0.307955\pi$
$271$	5062.46	1.13477	0.567384	+	0.823453i	$0.307955\pi$
$272$	−684.940	−0.152686
$273$	0	0
$274$	−3665.86	−0.808257
$275$	0.724991	0.000158977 0
$276$	675.067	0.147226
$277$	−4239.41	−0.919571	−0.459786	−	0.888030i	$-0.652074\pi$
$277$	−4239.41	−0.919571	−0.459786	+	0.888030i	$0.652074\pi$
$278$	2709.10	0.584465
$279$	1857.62	0.398613
$280$	0	0
$281$	6869.64	1.45839	0.729196	−	0.684305i	$-0.239894\pi$
$281$	6869.64	1.45839	0.729196	+	0.684305i	$0.239894\pi$
$282$	−836.866	−0.176719
$283$	−682.026	−0.143259	−0.0716294	−	0.997431i	$-0.522820\pi$
$283$	−682.026	−0.143259	−0.0716294	+	0.997431i	$0.522820\pi$
$284$	−2471.83	−0.516466
$285$	1113.03	0.231333
$286$	−0.670999	−0.000138731 0
$287$	0	0
$288$	−801.203	−0.163928
$289$	−3080.41	−0.626992
$290$	1010.91	0.204698
$291$	1708.63	0.344199
$292$	−2250.73	−0.451075
$293$	4207.79	0.838981	0.419491	−	0.907760i	$-0.362209\pi$
$293$	4207.79	0.838981	0.419491	+	0.907760i	$0.362209\pi$
$294$	0	0
$295$	−479.017	−0.0945406
$296$	−734.288	−0.144188
$297$	−2.11400	−0.000413019 0
$298$	3519.25	0.684110
$299$	−1393.77	−0.269578
$300$	140.086	0.0269596
$301$	0	0
$302$	1633.81	0.311309
$303$	1752.57	0.332286
$304$	−2542.50	−0.479679
$305$	1936.32	0.363519
$306$	2143.66	0.400473
$307$	5064.75	0.941566	0.470783	−	0.882249i	$-0.343971\pi$
$307$	5064.75	0.941566	0.470783	+	0.882249i	$0.343971\pi$
$308$	0	0
$309$	787.577	0.144996
$310$	741.934	0.135932
$311$	6765.29	1.23352	0.616760	−	0.787151i	$-0.288445\pi$
$311$	6765.29	1.23352	0.616760	+	0.787151i	$0.288445\pi$
$312$	−129.653	−0.0235262
$313$	−5404.30	−0.975940	−0.487970	−	0.872860i	$-0.662262\pi$
$313$	−5404.30	−0.975940	−0.487970	+	0.872860i	$0.662262\pi$
$314$	3607.25	0.648308
$315$	0	0
$316$	35.8032	0.00637369
$317$	−9704.56	−1.71944	−0.859720	−	0.510766i	$-0.829362\pi$
$317$	−9704.56	−1.71944	−0.859720	+	0.510766i	$0.829362\pi$
$318$	1878.19	0.331207
$319$	−2.93159	−0.000514538 0
$320$	−320.000	−0.0559017
$321$	−1799.03	−0.312811
$322$	0	0
$323$	6802.58	1.17184
$324$	2295.58	0.393619
$325$	−289.227	−0.0493644
$326$	5069.56	0.861279
$327$	2549.43	0.431142
$328$	−742.468	−0.124988
$329$	0	0
$330$	−0.406244	−6.77667e−5 0
$331$	−1007.24	−0.167260	−0.0836300	−	0.996497i	$-0.526651\pi$
$331$	−1007.24	−0.167260	−0.0836300	+	0.996497i	$0.526651\pi$
$332$	−787.961	−0.130256
$333$	2298.10	0.378184
$334$	3703.93	0.606796
$335$	−2398.94	−0.391248
$336$	0	0
$337$	−8848.07	−1.43022	−0.715112	−	0.699010i	$-0.753624\pi$
$337$	−8848.07	−1.43022	−0.715112	+	0.699010i	$0.753624\pi$
$338$	−4126.31	−0.664029
$339$	−28.2905	−0.00453254
$340$	856.175	0.136566
$341$	−2.15158	−0.000341686 0
$342$	7957.26	1.25813
$343$	0	0
$344$	−2355.50	−0.369185
$345$	−843.834	−0.131683
$346$	2458.31	0.381964
$347$	−8042.12	−1.24416	−0.622080	−	0.782953i	$-0.713712\pi$
$347$	−8042.12	−1.24416	−0.622080	+	0.782953i	$0.713712\pi$
$348$	−566.455	−0.0872562
$349$	8737.71	1.34017	0.670085	−	0.742285i	$-0.266258\pi$
$349$	8737.71	1.34017	0.670085	+	0.742285i	$0.266258\pi$
$350$	0	0
$351$	843.356	0.128248
$352$	0.927989	0.000140517 0
$353$	−4509.56	−0.679942	−0.339971	−	0.940436i	$-0.610417\pi$
$353$	−4509.56	−0.679942	−0.339971	+	0.940436i	$0.610417\pi$
$354$	268.414	0.0402996
$355$	3089.79	0.461941
$356$	−4617.76	−0.687474
$357$	0	0
$358$	−9288.68	−1.37129
$359$	−378.504	−0.0556454	−0.0278227	−	0.999613i	$-0.508857\pi$
$359$	−378.504	−0.0556454	−0.0278227	+	0.999613i	$0.508857\pi$
$360$	1001.50	0.146622
$361$	18392.2	2.68147
$362$	−8238.07	−1.19609
$363$	−1864.54	−0.269595
$364$	0	0
$365$	2813.41	0.403454
$366$	−1085.00	−0.154957
$367$	−9770.54	−1.38969	−0.694847	−	0.719157i	$-0.744528\pi$
$367$	−9770.54	−1.38969	−0.694847	+	0.719157i	$0.744528\pi$
$368$	1927.58	0.273049
$369$	2323.70	0.327824
$370$	917.860	0.128966
$371$	0	0
$372$	−415.738	−0.0579436
$373$	−13676.4	−1.89850	−0.949248	−	0.314530i	$-0.898153\pi$
$373$	−13676.4	−1.89850	−0.949248	+	0.314530i	$0.898153\pi$
$374$	−2.48288	−0.000343280 0
$375$	−175.107	−0.0241134
$376$	−2389.58	−0.327748
$377$	1169.53	0.159771
$378$	0	0
$379$	3101.97	0.420416	0.210208	−	0.977657i	$-0.432586\pi$
$379$	3101.97	0.420416	0.210208	+	0.977657i	$0.432586\pi$
$380$	3178.13	0.429038
$381$	−2640.59	−0.355069
$382$	3188.92	0.427118
$383$	−9600.40	−1.28083	−0.640415	−	0.768029i	$-0.721237\pi$
$383$	−9600.40	−1.28083	−0.640415	+	0.768029i	$0.721237\pi$
$384$	179.310	0.0238291
$385$	0	0
$386$	3282.58	0.432847
$387$	7371.99	0.968319
$388$	4878.81	0.638361
$389$	−37.6412	−0.00490613	−0.00245307	−	0.999997i	$-0.500781\pi$
$389$	−37.6412	−0.00490613	−0.00245307	+	0.999997i	$0.500781\pi$
$390$	162.067	0.0210425
$391$	−5157.33	−0.667052
$392$	0	0
$393$	929.963	0.119365
$394$	−2759.82	−0.352887
$395$	−44.7539	−0.00570080
$396$	−2.90433	−0.000368555 0
$397$	−13759.3	−1.73945	−0.869723	−	0.493540i	$-0.835703\pi$
$397$	−13759.3	−1.73945	−0.869723	+	0.493540i	$0.835703\pi$
$398$	7402.36	0.932278
$399$	0	0
$400$	400.000	0.0500000
$401$	−3674.43	−0.457586	−0.228793	−	0.973475i	$-0.573478\pi$
$401$	−3674.43	−0.457586	−0.228793	+	0.973475i	$0.573478\pi$
$402$	1344.23	0.166777
$403$	858.350	0.106098
$404$	5004.28	0.616268
$405$	−2869.48	−0.352063
$406$	0	0
$407$	−2.66176	−0.000324174 0
$408$	−479.752	−0.0582139
$409$	−5930.97	−0.717035	−0.358518	−	0.933523i	$-0.616718\pi$
$409$	−5930.97	−0.717035	−0.358518	+	0.933523i	$0.616718\pi$
$410$	928.086	0.111792
$411$	−2567.68	−0.308161
$412$	2248.84	0.268913
$413$	0	0
$414$	−6032.75	−0.716167
$415$	984.952	0.116505
$416$	−370.211	−0.0436324
$417$	1897.54	0.222836
$418$	−9.21646	−0.00107845
$419$	1186.39	0.138327	0.0691635	−	0.997605i	$-0.477967\pi$
$419$	1186.39	0.138327	0.0691635	+	0.997605i	$0.477967\pi$
$420$	0	0
$421$	−3344.52	−0.387178	−0.193589	−	0.981083i	$-0.562013\pi$
$421$	−3344.52	−0.387178	−0.193589	+	0.981083i	$0.562013\pi$
$422$	8076.33	0.931634
$423$	7478.67	0.859634
$424$	5362.98	0.614267
$425$	−1070.22	−0.122149
$426$	−1731.34	−0.196911
$427$	0	0
$428$	−5136.94	−0.580148
$429$	−0.469988	−5.28933e−5 0
$430$	2944.37	0.330209
$431$	3713.55	0.415024	0.207512	−	0.978232i	$-0.433463\pi$
$431$	3713.55	0.415024	0.207512	+	0.978232i	$0.433463\pi$
$432$	−1166.36	−0.129899
$433$	−11407.8	−1.26610	−0.633052	−	0.774109i	$-0.718198\pi$
$433$	−11407.8	−1.26610	−0.633052	+	0.774109i	$0.718198\pi$
$434$	0	0
$435$	708.068	0.0780443
$436$	7279.61	0.799610
$437$	−19144.0	−2.09562
$438$	−1576.48	−0.171979
$439$	−15362.3	−1.67017	−0.835085	−	0.550122i	$-0.814581\pi$
$439$	−15362.3	−1.67017	−0.835085	+	0.550122i	$0.814581\pi$
$440$	−1.15999	−0.000125682 0
$441$	0	0
$442$	990.516	0.106593
$443$	−9406.58	−1.00885	−0.504424	−	0.863456i	$-0.668295\pi$
$443$	−9406.58	−1.00885	−0.504424	+	0.863456i	$0.668295\pi$
$444$	−514.317	−0.0549739
$445$	5772.20	0.614895
$446$	8994.45	0.954932
$447$	2464.99	0.260828
$448$	0	0
$449$	5904.84	0.620639	0.310319	−	0.950632i	$-0.399564\pi$
$449$	5904.84	0.620639	0.310319	+	0.950632i	$0.399564\pi$
$450$	−1251.88	−0.131143
$451$	−2.69142	−0.000281006 0
$452$	−80.7805	−0.00840619
$453$	1144.37	0.118691
$454$	−5408.56	−0.559111
$455$	0	0
$456$	−1780.84	−0.182885
$457$	−17910.6	−1.83331	−0.916655	−	0.399678i	$-0.869122\pi$
$457$	−17910.6	−1.83331	−0.916655	+	0.399678i	$0.869122\pi$
$458$	−5003.12	−0.510438
$459$	3120.64	0.317340
$460$	−2409.48	−0.244223
$461$	−17050.6	−1.72262	−0.861309	−	0.508081i	$-0.830355\pi$
$461$	−17050.6	−1.72262	−0.861309	+	0.508081i	$0.830355\pi$
$462$	0	0
$463$	−376.884	−0.0378300	−0.0189150	−	0.999821i	$-0.506021\pi$
$463$	−376.884	−0.0378300	−0.0189150	+	0.999821i	$0.506021\pi$
$464$	−1617.45	−0.161828
$465$	519.673	0.0518263
$466$	11428.7	1.13611
$467$	14558.4	1.44258	0.721288	−	0.692635i	$-0.243550\pi$
$467$	14558.4	1.44258	0.721288	+	0.692635i	$0.243550\pi$
$468$	1158.65	0.114441
$469$	0	0
$470$	2986.97	0.293147
$471$	2526.62	0.247178
$472$	766.428	0.0747409
$473$	−8.53857	−0.000830029 0
$474$	25.0776	0.00243007
$475$	−3972.66	−0.383743
$476$	0	0
$477$	−16784.5	−1.61113
$478$	−96.0090	−0.00918692
$479$	−10401.5	−0.992190	−0.496095	−	0.868268i	$-0.665233\pi$
$479$	−10401.5	−0.992190	−0.496095	+	0.868268i	$0.665233\pi$
$480$	−224.137	−0.0213134
$481$	1061.88	0.100660
$482$	6866.22	0.648855
$483$	0	0
$484$	−5324.00	−0.500000
$485$	−6098.52	−0.570968
$486$	5544.35	0.517483
$487$	−15904.7	−1.47990	−0.739951	−	0.672660i	$-0.765152\pi$
$487$	−15904.7	−1.47990	−0.739951	+	0.672660i	$0.765152\pi$
$488$	−3098.11	−0.287387
$489$	3550.87	0.328376
$490$	0	0
$491$	21125.9	1.94175	0.970873	−	0.239595i	$-0.0770146\pi$
$491$	21125.9	1.94175	0.970873	+	0.239595i	$0.0770146\pi$
$492$	−520.047	−0.0476535
$493$	4327.56	0.395342
$494$	3676.80	0.334873
$495$	3.63041	0.000329646 0
$496$	−1187.09	−0.107464
$497$	0	0
$498$	−551.911	−0.0496621
$499$	4552.52	0.408414	0.204207	−	0.978928i	$-0.434538\pi$
$499$	4552.52	0.408414	0.204207	+	0.978928i	$0.434538\pi$
$500$	−500.000	−0.0447214
$501$	2594.34	0.231351
$502$	−12777.6	−1.13604
$503$	−5023.53	−0.445305	−0.222652	−	0.974898i	$-0.571471\pi$
$503$	−5023.53	−0.445305	−0.222652	+	0.974898i	$0.571471\pi$
$504$	0	0
$505$	−6255.35	−0.551207
$506$	6.98740	0.000613889 0
$507$	−2890.19	−0.253171
$508$	−7539.91	−0.658522
$509$	−20979.0	−1.82687	−0.913436	−	0.406981i	$-0.866581\pi$
$509$	−20979.0	−1.82687	−0.913436	+	0.406981i	$0.866581\pi$
$510$	599.690	0.0520681
$511$	0	0
$512$	512.000	0.0441942
$513$	11583.9	0.996958
$514$	866.770	0.0743805
$515$	−2811.05	−0.240524
$516$	−1649.86	−0.140758
$517$	−8.66213	−0.000736866 0
$518$	0	0
$519$	1721.87	0.145630
$520$	462.763	0.0390260
$521$	−19303.2	−1.62321	−0.811603	−	0.584209i	$-0.801405\pi$
$521$	−19303.2	−1.62321	−0.811603	+	0.584209i	$0.801405\pi$
$522$	5062.13	0.424451
$523$	5818.71	0.486491	0.243245	−	0.969965i	$-0.421788\pi$
$523$	5818.71	0.486491	0.243245	+	0.969965i	$0.421788\pi$
$524$	2655.41	0.221378
$525$	0	0
$526$	−11801.4	−0.978261
$527$	3176.13	0.262532
$528$	0.649991	5.35743e−5 0
$529$	2346.93	0.192893
$530$	−6703.72	−0.549417
$531$	−2398.69	−0.196034
$532$	0	0
$533$	1073.71	0.0872562
$534$	−3234.42	−0.262110
$535$	6421.18	0.518900
$536$	3838.30	0.309309
$537$	−6506.07	−0.522826
$538$	−9096.38	−0.728946
$539$	0	0
$540$	1457.95	0.116185
$541$	14584.7	1.15905	0.579524	−	0.814955i	$-0.303239\pi$
$541$	14584.7	1.15905	0.579524	+	0.814955i	$0.303239\pi$
$542$	10124.9	0.802403
$543$	−5770.19	−0.456027
$544$	−1369.88	−0.107965
$545$	−9099.51	−0.715193
$546$	0	0
$547$	−7361.14	−0.575392	−0.287696	−	0.957722i	$-0.592889\pi$
$547$	−7361.14	−0.575392	−0.287696	+	0.957722i	$0.592889\pi$
$548$	−7331.71	−0.571524
$549$	9696.15	0.753774
$550$	1.44998	0.000112414 0
$551$	16063.9	1.24201
$552$	1350.13	0.104104
$553$	0	0
$554$	−8478.81	−0.650235
$555$	642.896	0.0491701
$556$	5418.21	0.413279
$557$	2935.97	0.223341	0.111670	−	0.993745i	$-0.464380\pi$
$557$	2935.97	0.223341	0.111670	+	0.993745i	$0.464380\pi$
$558$	3715.25	0.281862
$559$	3406.37	0.257735
$560$	0	0
$561$	−1.73908	−0.000130881 0
$562$	13739.3	1.03124
$563$	−924.214	−0.0691847	−0.0345923	−	0.999402i	$-0.511013\pi$
$563$	−924.214	−0.0691847	−0.0345923	+	0.999402i	$0.511013\pi$
$564$	−1673.73	−0.124959
$565$	100.976	0.00751872
$566$	−1364.05	−0.101299
$567$	0	0
$568$	−4943.66	−0.365196
$569$	2227.77	0.164136	0.0820678	−	0.996627i	$-0.473848\pi$
$569$	2227.77	0.164136	0.0820678	+	0.996627i	$0.473848\pi$
$570$	2226.05	0.163577
$571$	7459.52	0.546710	0.273355	−	0.961913i	$-0.411867\pi$
$571$	7459.52	0.546710	0.273355	+	0.961913i	$0.411867\pi$
$572$	−1.34200	−9.80975e−5 0
$573$	2233.61	0.162846
$574$	0	0
$575$	3011.84	0.218439
$576$	−1602.41	−0.115915
$577$	−10855.4	−0.783218	−0.391609	−	0.920132i	$-0.628081\pi$
$577$	−10855.4	−0.783218	−0.391609	+	0.920132i	$0.628081\pi$
$578$	−6160.82	−0.443350
$579$	2299.22	0.165030
$580$	2021.81	0.144743
$581$	0	0
$582$	3417.27	0.243385
$583$	19.4406	0.00138104
$584$	−4501.46	−0.318958
$585$	−1448.31	−0.102359
$586$	8415.57	0.593249
$587$	−5276.59	−0.371019	−0.185509	−	0.982642i	$-0.559394\pi$
$587$	−5276.59	−0.371019	−0.185509	+	0.982642i	$0.559394\pi$
$588$	0	0
$589$	11789.8	0.824771
$590$	−958.035	−0.0668503
$591$	−1933.06	−0.134544
$592$	−1468.58	−0.101956
$593$	−21791.3	−1.50904	−0.754522	−	0.656274i	$-0.772131\pi$
$593$	−21791.3	−1.50904	−0.754522	+	0.656274i	$0.772131\pi$
$594$	−4.22800	−0.000292048 0
$595$	0	0
$596$	7038.50	0.483739
$597$	5184.83	0.355445
$598$	−2787.54	−0.190621
$599$	−26484.1	−1.80653	−0.903265	−	0.429082i	$-0.858837\pi$
$599$	−26484.1	−1.80653	−0.903265	+	0.429082i	$0.858837\pi$
$600$	280.172	0.0190633
$601$	13898.1	0.943287	0.471644	−	0.881789i	$-0.343661\pi$
$601$	13898.1	0.943287	0.471644	+	0.881789i	$0.343661\pi$
$602$	0	0
$603$	−12012.7	−0.811271
$604$	3267.62	0.220128
$605$	6655.00	0.447213
$606$	3505.15	0.234962
$607$	24029.1	1.60678	0.803388	−	0.595456i	$-0.203029\pi$
$607$	24029.1	1.60678	0.803388	+	0.595456i	$0.203029\pi$
$608$	−5085.00	−0.339184
$609$	0	0
$610$	3872.64	0.257047
$611$	3455.66	0.228807
$612$	4287.31	0.283177
$613$	9145.88	0.602608	0.301304	−	0.953528i	$-0.402578\pi$
$613$	9145.88	0.602608	0.301304	+	0.953528i	$0.402578\pi$
$614$	10129.5	0.665788
$615$	650.059	0.0426226
$616$	0	0
$617$	5066.01	0.330551	0.165276	−	0.986247i	$-0.447149\pi$
$617$	5066.01	0.330551	0.165276	+	0.986247i	$0.447149\pi$
$618$	1575.15	0.102527
$619$	27423.0	1.78065	0.890327	−	0.455322i	$-0.150476\pi$
$619$	27423.0	1.78065	0.890327	+	0.455322i	$0.150476\pi$
$620$	1483.87	0.0961187
$621$	−8782.22	−0.567501
$622$	13530.6	0.872230
$623$	0	0
$624$	−259.307	−0.0166355
$625$	625.000	0.0400000
$626$	−10808.6	−0.690094
$627$	−6.45548	−0.000411176 0
$628$	7214.49	0.458423
$629$	3929.24	0.249077
$630$	0	0
$631$	2759.88	0.174119	0.0870594	−	0.996203i	$-0.472253\pi$
$631$	2759.88	0.174119	0.0870594	+	0.996203i	$0.472253\pi$
$632$	71.6063	0.00450688
$633$	5656.90	0.355200
$634$	−19409.1	−1.21583
$635$	9424.88	0.589000
$636$	3756.39	0.234199
$637$	0	0
$638$	−5.86318	−0.000363833 0
$639$	15472.2	0.957856
$640$	−640.000	−0.0395285
$641$	−10194.0	−0.628145	−0.314072	−	0.949399i	$-0.601693\pi$
$641$	−10194.0	−0.628145	−0.314072	+	0.949399i	$0.601693\pi$
$642$	−3598.07	−0.221191
$643$	18165.8	1.11413	0.557066	−	0.830468i	$-0.311927\pi$
$643$	18165.8	1.11413	0.557066	+	0.830468i	$0.311927\pi$
$644$	0	0
$645$	2062.32	0.125898
$646$	13605.2	0.828619
$647$	3816.39	0.231898	0.115949	−	0.993255i	$-0.463009\pi$
$647$	3816.39	0.231898	0.115949	+	0.993255i	$0.463009\pi$
$648$	4591.17	0.278330
$649$	2.77827	0.000168038 0
$650$	−578.454	−0.0349059
$651$	0	0
$652$	10139.1	0.609016
$653$	−17063.2	−1.02257	−0.511283	−	0.859413i	$-0.670829\pi$
$653$	−17063.2	−1.02257	−0.511283	+	0.859413i	$0.670829\pi$
$654$	5098.85	0.304864
$655$	−3319.26	−0.198006
$656$	−1484.94	−0.0883796
$657$	14088.2	0.836580
$658$	0	0
$659$	16157.3	0.955083	0.477542	−	0.878609i	$-0.341528\pi$
$659$	16157.3	0.955083	0.477542	+	0.878609i	$0.341528\pi$
$660$	−0.812489	−4.79183e−5 0
$661$	5148.39	0.302949	0.151474	−	0.988461i	$-0.451598\pi$
$661$	5148.39	0.302949	0.151474	+	0.988461i	$0.451598\pi$
$662$	−2014.48	−0.118271
$663$	693.787	0.0406402
$664$	−1575.92	−0.0921049
$665$	0	0
$666$	4596.20	0.267416
$667$	−12178.8	−0.706992
$668$	7407.86	0.429070
$669$	6299.98	0.364083
$670$	−4797.88	−0.276654
$671$	−11.2305	−0.000646124 0
$672$	0	0
$673$	1446.37	0.0828433	0.0414216	−	0.999142i	$-0.486811\pi$
$673$	1446.37	0.0828433	0.0414216	+	0.999142i	$0.486811\pi$
$674$	−17696.1	−1.01132
$675$	−1822.43	−0.103919
$676$	−8252.63	−0.469539
$677$	21125.2	1.19927	0.599636	−	0.800273i	$-0.295312\pi$
$677$	21125.2	1.19927	0.599636	+	0.800273i	$0.295312\pi$
$678$	−56.5811	−0.00320499
$679$	0	0
$680$	1712.35	0.0965671
$681$	−3788.32	−0.213170
$682$	−4.30317	−0.000241608 0
$683$	−24657.9	−1.38142	−0.690708	−	0.723134i	$-0.742701\pi$
$683$	−24657.9	−1.38142	−0.690708	+	0.723134i	$0.742701\pi$
$684$	15914.5	0.889630
$685$	9164.64	0.511187
$686$	0	0
$687$	−3504.33	−0.194612
$688$	−4710.99	−0.261054
$689$	−7755.59	−0.428831
$690$	−1687.67	−0.0931136
$691$	28743.7	1.58243	0.791216	−	0.611537i	$-0.209448\pi$
$691$	28743.7	1.58243	0.791216	+	0.611537i	$0.209448\pi$
$692$	4916.61	0.270089
$693$	0	0
$694$	−16084.2	−0.879755
$695$	−6772.76	−0.369648
$696$	−1132.91	−0.0616994
$697$	3973.02	0.215909
$698$	17475.4	0.947643
$699$	8005.03	0.433159
$700$	0	0
$701$	−5830.39	−0.314138	−0.157069	−	0.987588i	$-0.550204\pi$
$701$	−5830.39	−0.314138	−0.157069	+	0.987588i	$0.550204\pi$
$702$	1686.71	0.0906849
$703$	14585.4	0.782501
$704$	1.85598	9.93605e−5 0
$705$	2092.17	0.111767
$706$	−9019.12	−0.480792
$707$	0	0
$708$	536.829	0.0284961
$709$	9696.20	0.513609	0.256804	−	0.966463i	$-0.417330\pi$
$709$	9696.20	0.513609	0.256804	+	0.966463i	$0.417330\pi$
$710$	6179.58	0.326642
$711$	−224.106	−0.0118209
$712$	−9235.52	−0.486118
$713$	−8938.36	−0.469487
$714$	0	0
$715$	1.67750	8.77410e−5 0
$716$	−18577.4	−0.969649
$717$	−67.2475	−0.00350266
$718$	−757.009	−0.0393472
$719$	9077.75	0.470853	0.235426	−	0.971892i	$-0.424351\pi$
$719$	9077.75	0.470853	0.235426	+	0.971892i	$0.424351\pi$
$720$	2003.01	0.103677
$721$	0	0
$722$	36784.5	1.89609
$723$	4809.31	0.247386
$724$	−16476.1	−0.845761
$725$	−2527.26	−0.129462
$726$	−3729.09	−0.190633
$727$	−11809.9	−0.602483	−0.301241	−	0.953548i	$-0.597401\pi$
$727$	−11809.9	−0.602483	−0.301241	+	0.953548i	$0.597401\pi$
$728$	0	0
$729$	−11611.8	−0.589939
$730$	5626.82	0.285285
$731$	12604.5	0.637747
$732$	−2170.01	−0.109571
$733$	7680.93	0.387042	0.193521	−	0.981096i	$-0.438009\pi$
$733$	7680.93	0.387042	0.193521	+	0.981096i	$0.438009\pi$
$734$	−19541.1	−0.982662
$735$	0	0
$736$	3855.16	0.193075
$737$	13.9137	0.000695410 0
$738$	4647.41	0.231807
$739$	3588.45	0.178624	0.0893122	−	0.996004i	$-0.471533\pi$
$739$	3588.45	0.178624	0.0893122	+	0.996004i	$0.471533\pi$
$740$	1835.72	0.0911924
$741$	2575.34	0.127675
$742$	0	0
$743$	31383.3	1.54958	0.774791	−	0.632217i	$-0.217855\pi$
$743$	31383.3	1.54958	0.774791	+	0.632217i	$0.217855\pi$
$744$	−831.476	−0.0409723
$745$	−8798.13	−0.432669
$746$	−27352.9	−1.34244
$747$	4932.16	0.241578
$748$	−4.96576	−0.000242735 0
$749$	0	0
$750$	−350.215	−0.0170507
$751$	16655.7	0.809287	0.404643	−	0.914475i	$-0.367396\pi$
$751$	16655.7	0.809287	0.404643	+	0.914475i	$0.367396\pi$
$752$	−4779.16	−0.231753
$753$	−8949.82	−0.433134
$754$	2339.05	0.112975
$755$	−4084.53	−0.196889
$756$	0	0
$757$	−9873.08	−0.474033	−0.237017	−	0.971506i	$-0.576170\pi$
$757$	−9873.08	−0.474033	−0.237017	+	0.971506i	$0.576170\pi$
$758$	6203.94	0.297279
$759$	4.89418	0.000234055 0
$760$	6356.25	0.303376
$761$	−19410.0	−0.924589	−0.462295	−	0.886726i	$-0.652974\pi$
$761$	−19410.0	−0.924589	−0.462295	+	0.886726i	$0.652974\pi$
$762$	−5281.17	−0.251072
$763$	0	0
$764$	6377.84	0.302018
$765$	−5359.14	−0.253281
$766$	−19200.8	−0.905683
$767$	−1108.36	−0.0521780
$768$	358.620	0.0168497
$769$	16257.0	0.762344	0.381172	−	0.924504i	$-0.375521\pi$
$769$	16257.0	0.762344	0.381172	+	0.924504i	$0.375521\pi$
$770$	0	0
$771$	607.111	0.0283587
$772$	6565.17	0.306069
$773$	5804.01	0.270059	0.135030	−	0.990842i	$-0.456887\pi$
$773$	5804.01	0.270059	0.135030	+	0.990842i	$0.456887\pi$
$774$	14744.0	0.684705
$775$	−1854.84	−0.0859712
$776$	9757.63	0.451390
$777$	0	0
$778$	−75.2824	−0.00346916
$779$	14747.9	0.678302
$780$	324.133	0.0148793
$781$	−17.9206	−0.000821061 0
$782$	−10314.7	−0.471677
$783$	7369.23	0.336341
$784$	0	0
$785$	−9018.12	−0.410026
$786$	1859.93	0.0844038
$787$	39700.3	1.79817	0.899086	−	0.437771i	$-0.144232\pi$
$787$	39700.3	1.79817	0.899086	+	0.437771i	$0.144232\pi$
$788$	−5519.64	−0.249529
$789$	−8266.04	−0.372977
$790$	−89.5079	−0.00403107
$791$	0	0
$792$	−5.80865	−0.000260608 0
$793$	4480.29	0.200630
$794$	−27518.6	−1.22997
$795$	−4695.48	−0.209474
$796$	14804.7	0.659220
$797$	−27287.4	−1.21276	−0.606381	−	0.795174i	$-0.707379\pi$
$797$	−27287.4	−1.21276	−0.606381	+	0.795174i	$0.707379\pi$
$798$	0	0
$799$	12786.9	0.566166
$800$	800.000	0.0353553
$801$	28904.4	1.27501
$802$	−7348.85	−0.323562
$803$	−16.3176	−0.000717105 0
$804$	2688.46	0.117929
$805$	0	0
$806$	1716.70	0.0750225
$807$	−6371.38	−0.277922
$808$	10008.6	0.435767
$809$	14829.4	0.644465	0.322233	−	0.946660i	$-0.395567\pi$
$809$	14829.4	0.644465	0.322233	+	0.946660i	$0.395567\pi$
$810$	−5738.96	−0.248946
$811$	26813.2	1.16096	0.580480	−	0.814274i	$-0.302865\pi$
$811$	26813.2	1.16096	0.580480	+	0.814274i	$0.302865\pi$
$812$	0	0
$813$	7091.79	0.305929
$814$	−5.32352	−0.000229225 0
$815$	−12673.9	−0.544720
$816$	−959.504	−0.0411634
$817$	46787.9	2.00355
$818$	−11861.9	−0.507020
$819$	0	0
$820$	1856.17	0.0790492
$821$	−7114.91	−0.302451	−0.151225	−	0.988499i	$-0.548322\pi$
$821$	−7114.91	−0.302451	−0.151225	+	0.988499i	$0.548322\pi$
$822$	−5135.35	−0.217903
$823$	−11167.2	−0.472984	−0.236492	−	0.971633i	$-0.575998\pi$
$823$	−11167.2	−0.472984	−0.236492	+	0.971633i	$0.575998\pi$
$824$	4497.68	0.190151
$825$	1.01561	4.28594e−5 0
$826$	0	0
$827$	−2977.35	−0.125191	−0.0625954	−	0.998039i	$-0.519938\pi$
$827$	−2977.35	−0.125191	−0.0625954	+	0.998039i	$0.519938\pi$
$828$	−12065.5	−0.506407
$829$	14391.7	0.602947	0.301474	−	0.953474i	$-0.402521\pi$
$829$	14391.7	0.602947	0.301474	+	0.953474i	$0.402521\pi$
$830$	1969.90	0.0823811
$831$	−5938.81	−0.247912
$832$	−740.421	−0.0308528
$833$	0	0
$834$	3795.07	0.157569
$835$	−9259.82	−0.383772
$836$	−18.4329	−0.000762579 0
$837$	5408.50	0.223351
$838$	2372.78	0.0978119
$839$	−5208.40	−0.214320	−0.107160	−	0.994242i	$-0.534176\pi$
$839$	−5208.40	−0.214320	−0.107160	+	0.994242i	$0.534176\pi$
$840$	0	0
$841$	−14169.7	−0.580987
$842$	−6689.04	−0.273776
$843$	9623.39	0.393176
$844$	16152.7	0.658765
$845$	10315.8	0.419969
$846$	14957.3	0.607853
$847$	0	0
$848$	10726.0	0.434352
$849$	−955.423	−0.0386219
$850$	−2140.44	−0.0863722
$851$	−11057.8	−0.445425
$852$	−3462.69	−0.139237
$853$	4674.58	0.187637	0.0938185	−	0.995589i	$-0.470093\pi$
$853$	4674.58	0.187637	0.0938185	+	0.995589i	$0.470093\pi$
$854$	0	0
$855$	−19893.2	−0.795710
$856$	−10273.9	−0.410227
$857$	−10127.2	−0.403660	−0.201830	−	0.979421i	$-0.564689\pi$
$857$	−10127.2	−0.403660	−0.201830	+	0.979421i	$0.564689\pi$
$858$	−0.939975	−3.74012e−5 0
$859$	19883.2	0.789763	0.394881	−	0.918732i	$-0.370786\pi$
$859$	19883.2	0.789763	0.394881	+	0.918732i	$0.370786\pi$
$860$	5888.74	0.233493
$861$	0	0
$862$	7427.09	0.293466
$863$	38593.6	1.52230	0.761148	−	0.648578i	$-0.224636\pi$
$863$	38593.6	1.52230	0.761148	+	0.648578i	$0.224636\pi$
$864$	−2332.72	−0.0918525
$865$	−6145.77	−0.241575
$866$	−22815.6	−0.895271
$867$	−4315.22	−0.169034
$868$	0	0
$869$	0.259570	1.01327e−5 0
$870$	1416.14	0.0551857
$871$	−5550.71	−0.215934
$872$	14559.2	0.565410
$873$	−30538.4	−1.18393
$874$	−38288.1	−1.48182
$875$	0	0
$876$	−3152.95	−0.121608
$877$	−5665.06	−0.218125	−0.109062	−	0.994035i	$-0.534785\pi$
$877$	−5665.06	−0.218125	−0.109062	+	0.994035i	$0.534785\pi$
$878$	−30724.7	−1.18099
$879$	5894.52	0.226186
$880$	−2.31997	−8.88708e−5 0
$881$	18059.2	0.690614	0.345307	−	0.938490i	$-0.387775\pi$
$881$	18059.2	0.690614	0.345307	+	0.938490i	$0.387775\pi$
$882$	0	0
$883$	−28281.2	−1.07785	−0.538924	−	0.842355i	$-0.681169\pi$
$883$	−28281.2	−1.07785	−0.538924	+	0.842355i	$0.681169\pi$
$884$	1981.03	0.0753725
$885$	−671.036	−0.0254877
$886$	−18813.2	−0.713364
$887$	−14276.5	−0.540425	−0.270212	−	0.962801i	$-0.587094\pi$
$887$	−14276.5	−0.540425	−0.270212	+	0.962801i	$0.587094\pi$
$888$	−1028.63	−0.0388724
$889$	0	0
$890$	11544.4	0.434797
$891$	16.6428	0.000625763 0
$892$	17988.9	0.675239
$893$	47464.9	1.77867
$894$	4929.98	0.184433
$895$	23221.7	0.867280
$896$	0	0
$897$	−1952.48	−0.0726771
$898$	11809.7	0.438858
$899$	7500.25	0.278251
$900$	−2503.76	−0.0927318
$901$	−28697.8	−1.06111
$902$	−5.38283	−0.000198701 0
$903$	0	0
$904$	−161.561	−0.00594407
$905$	20595.2	0.756472
$906$	2288.74	0.0839274
$907$	22055.3	0.807424	0.403712	−	0.914886i	$-0.367720\pi$
$907$	22055.3	0.807424	0.403712	+	0.914886i	$0.367720\pi$
$908$	−10817.1	−0.395351
$909$	−31323.8	−1.14295
$910$	0	0
$911$	−25893.1	−0.941686	−0.470843	−	0.882217i	$-0.656050\pi$
$911$	−25893.1	−0.941686	−0.470843	+	0.882217i	$0.656050\pi$
$912$	−3561.69	−0.129319
$913$	−5.71265	−0.000207077 0
$914$	−35821.2	−1.29635
$915$	2712.51	0.0980031
$916$	−10006.2	−0.360934
$917$	0	0
$918$	6241.29	0.224393
$919$	25106.1	0.901168	0.450584	−	0.892734i	$-0.351216\pi$
$919$	25106.1	0.901168	0.450584	+	0.892734i	$0.351216\pi$
$920$	−4818.95	−0.172691
$921$	7095.01	0.253842
$922$	−34101.3	−1.21807
$923$	7149.21	0.254950
$924$	0	0
$925$	−2294.65	−0.0815650
$926$	−753.768	−0.0267498
$927$	−14076.4	−0.498737
$928$	−3234.90	−0.114430
$929$	−20618.2	−0.728160	−0.364080	−	0.931368i	$-0.618617\pi$
$929$	−20618.2	−0.728160	−0.364080	+	0.931368i	$0.618617\pi$
$930$	1039.35	0.0366467
$931$	0	0
$932$	22857.5	0.803349
$933$	9477.23	0.332551
$934$	29116.8	1.02006
$935$	6.20719	0.000217109 0
$936$	2317.30	0.0809222
$937$	9765.55	0.340477	0.170238	−	0.985403i	$-0.445546\pi$
$937$	9765.55	0.340477	0.170238	+	0.985403i	$0.445546\pi$
$938$	0	0
$939$	−7570.67	−0.263109
$940$	5973.95	0.207286
$941$	−34672.1	−1.20115	−0.600573	−	0.799570i	$-0.705061\pi$
$941$	−34672.1	−1.20115	−0.600573	+	0.799570i	$0.705061\pi$
$942$	5053.25	0.174781
$943$	−11181.0	−0.386112
$944$	1532.86	0.0528498
$945$	0	0
$946$	−17.0771	−0.000586919 0
$947$	3199.05	0.109773	0.0548866	−	0.998493i	$-0.482520\pi$
$947$	3199.05	0.109773	0.0548866	+	0.998493i	$0.482520\pi$
$948$	50.1552	0.00171832
$949$	6509.72	0.222671
$950$	−7945.32	−0.271348
$951$	−13594.7	−0.463553
$952$	0	0
$953$	−19440.5	−0.660797	−0.330399	−	0.943842i	$-0.607183\pi$
$953$	−19440.5	−0.660797	−0.330399	+	0.943842i	$0.607183\pi$
$954$	−33569.0	−1.13924
$955$	−7972.30	−0.270133
$956$	−192.018	−0.00649613
$957$	−4.10675	−0.000138717 0
$958$	−20803.1	−0.701584
$959$	0	0
$960$	−448.275	−0.0150708
$961$	−24286.3	−0.815224
$962$	2123.76	0.0711775
$963$	32154.2	1.07596
$964$	13732.4	0.458809
$965$	−8206.46	−0.273757
$966$	0	0
$967$	−36714.1	−1.22094	−0.610468	−	0.792041i	$-0.709019\pi$
$967$	−36714.1	−1.22094	−0.610468	+	0.792041i	$0.709019\pi$
$968$	−10648.0	−0.353553
$969$	9529.46	0.315924
$970$	−12197.0	−0.403735
$971$	−45812.2	−1.51409	−0.757046	−	0.653362i	$-0.773358\pi$
$971$	−45812.2	−1.51409	−0.757046	+	0.653362i	$0.773358\pi$
$972$	11088.7	0.365916
$973$	0	0
$974$	−31809.5	−1.04645
$975$	−405.167	−0.0133084
$976$	−6196.22	−0.203213
$977$	29886.0	0.978647	0.489323	−	0.872102i	$-0.337244\pi$
$977$	29886.0	0.978647	0.489323	+	0.872102i	$0.337244\pi$
$978$	7101.74	0.232197
$979$	−33.4784	−0.00109292
$980$	0	0
$981$	−45566.0	−1.48299
$982$	42251.7	1.37302
$983$	−41794.7	−1.35610	−0.678049	−	0.735017i	$-0.737174\pi$
$983$	−41794.7	−1.35610	−0.678049	+	0.735017i	$0.737174\pi$
$984$	−1040.09	−0.0336961
$985$	6899.55	0.223186
$986$	8655.12	0.279549
$987$	0	0
$988$	7353.60	0.236791
$989$	−35471.9	−1.14049
$990$	7.26082	0.000233095 0
$991$	−37285.3	−1.19516	−0.597582	−	0.801808i	$-0.703872\pi$
$991$	−37285.3	−1.19516	−0.597582	+	0.801808i	$0.703872\pi$
$992$	−2374.19	−0.0759885
$993$	−1411.00	−0.0450925
$994$	0	0
$995$	−18505.9	−0.589624
$996$	−1103.82	−0.0351164
$997$	20848.3	0.662259	0.331130	−	0.943585i	$-0.392570\pi$
$997$	20848.3	0.662259	0.331130	+	0.943585i	$0.392570\pi$
$998$	9105.04	0.288793
$999$	6690.96	0.211904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.x.1.3	✓	4
5.4	even	2		2450.4.a.cp.1.2		4
7.2	even	3		490.4.e.ba.361.2		8
7.3	odd	6		490.4.e.z.471.3		8
7.4	even	3		490.4.e.ba.471.2		8
7.5	odd	6		490.4.e.z.361.3		8
7.6	odd	2		490.4.a.y.1.2	yes	4
35.34	odd	2		2450.4.a.cj.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.a.x.1.3	✓	4	1.1	even	1	trivial
490.4.a.y.1.2	yes	4	7.6	odd	2
490.4.e.z.361.3		8	7.5	odd	6
490.4.e.z.471.3		8	7.3	odd	6
490.4.e.ba.361.2		8	7.2	even	3
490.4.e.ba.471.2		8	7.4	even	3
2450.4.a.cj.1.3		4	35.34	odd	2
2450.4.a.cp.1.2		4	5.4	even	2

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +1.40086 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.80172 q^{6} +8.00000 q^{8} -25.0376 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +1.40086 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.80172 q^{6} +8.00000 q^{8} -25.0376 q^{9} -10.0000 q^{10} +0.0289997 q^{11} +5.60344 q^{12} -11.5691 q^{13} -7.00430 q^{15} +16.0000 q^{16} -42.8087 q^{17} -50.0752 q^{18} -158.906 q^{19} -20.0000 q^{20} +0.0579993 q^{22} +120.474 q^{23} +11.2069 q^{24} +25.0000 q^{25} -23.1382 q^{26} -72.8973 q^{27} -101.091 q^{29} -14.0086 q^{30} -74.1934 q^{31} +32.0000 q^{32} +0.0406244 q^{33} -85.6175 q^{34} -100.150 q^{36} -91.7860 q^{37} -317.813 q^{38} -16.2067 q^{39} -40.0000 q^{40} -92.8086 q^{41} -294.437 q^{43} +0.115999 q^{44} +125.188 q^{45} +240.948 q^{46} -298.697 q^{47} +22.4137 q^{48} +50.0000 q^{50} -59.9690 q^{51} -46.2763 q^{52} +670.372 q^{53} -145.795 q^{54} -0.144998 q^{55} -222.605 q^{57} -202.181 q^{58} +95.8035 q^{59} -28.0172 q^{60} -387.264 q^{61} -148.387 q^{62} +64.0000 q^{64} +57.8454 q^{65} +0.0812489 q^{66} +479.788 q^{67} -171.235 q^{68} +168.767 q^{69} -617.958 q^{71} -200.301 q^{72} -562.682 q^{73} -183.572 q^{74} +35.0215 q^{75} -635.625 q^{76} -32.4133 q^{78} +8.95079 q^{79} -80.0000 q^{80} +573.896 q^{81} -185.617 q^{82} -196.990 q^{83} +214.044 q^{85} -588.874 q^{86} -141.614 q^{87} +0.231997 q^{88} -1154.44 q^{89} +250.376 q^{90} +481.895 q^{92} -103.935 q^{93} -597.395 q^{94} +794.532 q^{95} +44.8275 q^{96} +1219.70 q^{97} -0.726082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 10 q^{3} + 16 q^{4} - 20 q^{5} - 20 q^{6} + 32 q^{8} + 38 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 - 10 * q^3 + 16 * q^4 - 20 * q^5 - 20 * q^6 + 32 * q^8 + 38 * q^9	\( 4 q + 8 q^{2} - 10 q^{3} + 16 q^{4} - 20 q^{5} - 20 q^{6} + 32 q^{8} + 38 q^{9} - 40 q^{10} + 18 q^{11} - 40 q^{12} - 130 q^{13} + 50 q^{15} + 64 q^{16} - 110 q^{17} + 76 q^{18} - 40 q^{19} - 80 q^{20} + 36 q^{22} - 164 q^{23} - 80 q^{24} + 100 q^{25} - 260 q^{26} - 430 q^{27} + 94 q^{29} + 100 q^{30} - 180 q^{31} + 128 q^{32} - 650 q^{33} - 220 q^{34} + 152 q^{36} + 16 q^{37} - 80 q^{38} - 10 q^{39} - 160 q^{40} - 540 q^{41} - 560 q^{43} + 72 q^{44} - 190 q^{45} - 328 q^{46} - 1150 q^{47} - 160 q^{48} + 200 q^{50} - 926 q^{51} - 520 q^{52} - 244 q^{53} - 860 q^{54} - 90 q^{55} - 840 q^{57} + 188 q^{58} - 400 q^{59} + 200 q^{60} - 1540 q^{61} - 360 q^{62} + 256 q^{64} + 650 q^{65} - 1300 q^{66} - 760 q^{67} - 440 q^{68} + 1480 q^{69} + 52 q^{71} + 304 q^{72} - 800 q^{73} + 32 q^{74} - 250 q^{75} - 160 q^{76} - 20 q^{78} + 398 q^{79} - 320 q^{80} + 348 q^{81} - 1080 q^{82} + 1220 q^{83} + 550 q^{85} - 1120 q^{86} + 930 q^{87} + 144 q^{88} - 200 q^{89} - 380 q^{90} - 656 q^{92} + 1408 q^{93} - 2300 q^{94} + 200 q^{95} - 320 q^{96} + 670 q^{97} + 2292 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 10 * q^3 + 16 * q^4 - 20 * q^5 - 20 * q^6 + 32 * q^8 + 38 * q^9 - 40 * q^10 + 18 * q^11 - 40 * q^12 - 130 * q^13 + 50 * q^15 + 64 * q^16 - 110 * q^17 + 76 * q^18 - 40 * q^19 - 80 * q^20 + 36 * q^22 - 164 * q^23 - 80 * q^24 + 100 * q^25 - 260 * q^26 - 430 * q^27 + 94 * q^29 + 100 * q^30 - 180 * q^31 + 128 * q^32 - 650 * q^33 - 220 * q^34 + 152 * q^36 + 16 * q^37 - 80 * q^38 - 10 * q^39 - 160 * q^40 - 540 * q^41 - 560 * q^43 + 72 * q^44 - 190 * q^45 - 328 * q^46 - 1150 * q^47 - 160 * q^48 + 200 * q^50 - 926 * q^51 - 520 * q^52 - 244 * q^53 - 860 * q^54 - 90 * q^55 - 840 * q^57 + 188 * q^58 - 400 * q^59 + 200 * q^60 - 1540 * q^61 - 360 * q^62 + 256 * q^64 + 650 * q^65 - 1300 * q^66 - 760 * q^67 - 440 * q^68 + 1480 * q^69 + 52 * q^71 + 304 * q^72 - 800 * q^73 + 32 * q^74 - 250 * q^75 - 160 * q^76 - 20 * q^78 + 398 * q^79 - 320 * q^80 + 348 * q^81 - 1080 * q^82 + 1220 * q^83 + 550 * q^85 - 1120 * q^86 + 930 * q^87 + 144 * q^88 - 200 * q^89 - 380 * q^90 - 656 * q^92 + 1408 * q^93 - 2300 * q^94 + 200 * q^95 - 320 * q^96 + 670 * q^97 + 2292 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more