LMFDB - Embedded newform 2107.4.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2107,4,Mod(1,2107)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2107, 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("2107.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2107 = 7^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2107.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:	$124.317024382$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 $ x^6 - 32x^4 - 16x^3 + 251x^2 + 276x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.15653$ of defining polynomial
Character	$\chi$	$=$	2107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.15653 q^{2} -7.20925 q^{3} +1.96369 q^{4} -1.36370 q^{5} +22.7562 q^{6} +19.0538 q^{8} +24.9733 q^{9} +O(q^{10})$	\(q-3.15653 q^{2} -7.20925 q^{3} +1.96369 q^{4} -1.36370 q^{5} +22.7562 q^{6} +19.0538 q^{8} +24.9733 q^{9} +4.30455 q^{10} +64.7677 q^{11} -14.1567 q^{12} +19.2944 q^{13} +9.83123 q^{15} -75.8534 q^{16} +54.1213 q^{17} -78.8289 q^{18} +69.0659 q^{19} -2.67787 q^{20} -204.441 q^{22} +29.6031 q^{23} -137.364 q^{24} -123.140 q^{25} -60.9032 q^{26} +14.6112 q^{27} +13.1279 q^{29} -31.0326 q^{30} -185.439 q^{31} +87.0032 q^{32} -466.927 q^{33} -170.836 q^{34} +49.0397 q^{36} -369.949 q^{37} -218.009 q^{38} -139.098 q^{39} -25.9836 q^{40} +294.860 q^{41} -43.0000 q^{43} +127.183 q^{44} -34.0560 q^{45} -93.4431 q^{46} -367.319 q^{47} +546.846 q^{48} +388.696 q^{50} -390.174 q^{51} +37.8881 q^{52} +708.046 q^{53} -46.1207 q^{54} -88.3236 q^{55} -497.914 q^{57} -41.4385 q^{58} -116.159 q^{59} +19.3054 q^{60} -218.910 q^{61} +585.344 q^{62} +332.199 q^{64} -26.3116 q^{65} +1473.87 q^{66} -133.114 q^{67} +106.277 q^{68} -213.416 q^{69} -926.738 q^{71} +475.836 q^{72} -455.867 q^{73} +1167.75 q^{74} +887.749 q^{75} +135.624 q^{76} +439.067 q^{78} -620.178 q^{79} +103.441 q^{80} -779.614 q^{81} -930.734 q^{82} +1317.85 q^{83} -73.8050 q^{85} +135.731 q^{86} -94.6419 q^{87} +1234.07 q^{88} -509.295 q^{89} +107.499 q^{90} +58.1312 q^{92} +1336.88 q^{93} +1159.45 q^{94} -94.1850 q^{95} -627.228 q^{96} -965.870 q^{97} +1617.46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 + 3 * q^6 + 54 * q^8 + 81 * q^9	\( 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9} - 57 q^{10} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 124 q^{15} - 54 q^{16} - 19 q^{17} - 81 q^{18} + 75 q^{19} - 135 q^{20} - 504 q^{22} + 131 q^{23} + 567 q^{24} + 105 q^{25} - 44 q^{26} - 238 q^{27} + 515 q^{29} - 396 q^{30} - 237 q^{31} + 558 q^{32} - 540 q^{33} + 107 q^{34} + 73 q^{36} + 269 q^{37} - 527 q^{38} + 290 q^{39} - 613 q^{40} - 471 q^{41} - 258 q^{43} - 428 q^{44} - 334 q^{45} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 1335 q^{50} - 1241 q^{51} + 8 q^{52} + 450 q^{53} - 402 q^{54} + 1732 q^{55} - 1000 q^{57} - 1055 q^{58} - 356 q^{59} - 2732 q^{60} + 1328 q^{61} - 1603 q^{62} + 466 q^{64} - 62 q^{65} - 156 q^{66} - 632 q^{67} - 571 q^{68} + 1130 q^{69} - 144 q^{71} + 567 q^{72} - 864 q^{73} + 1207 q^{74} + 2494 q^{75} - 1005 q^{76} + 2222 q^{78} - 1613 q^{79} - 2399 q^{80} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 84 q^{85} - 258 q^{86} - 449 q^{87} - 608 q^{88} - 3378 q^{89} - 930 q^{90} + 3491 q^{92} + 1879 q^{93} - 3197 q^{94} - 79 q^{95} + 591 q^{96} + 55 q^{97} - 1612 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 + 3 * q^6 + 54 * q^8 + 81 * q^9 - 57 * q^10 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 124 * q^15 - 54 * q^16 - 19 * q^17 - 81 * q^18 + 75 * q^19 - 135 * q^20 - 504 * q^22 + 131 * q^23 + 567 * q^24 + 105 * q^25 - 44 * q^26 - 238 * q^27 + 515 * q^29 - 396 * q^30 - 237 * q^31 + 558 * q^32 - 540 * q^33 + 107 * q^34 + 73 * q^36 + 269 * q^37 - 527 * q^38 + 290 * q^39 - 613 * q^40 - 471 * q^41 - 258 * q^43 - 428 * q^44 - 334 * q^45 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 1335 * q^50 - 1241 * q^51 + 8 * q^52 + 450 * q^53 - 402 * q^54 + 1732 * q^55 - 1000 * q^57 - 1055 * q^58 - 356 * q^59 - 2732 * q^60 + 1328 * q^61 - 1603 * q^62 + 466 * q^64 - 62 * q^65 - 156 * q^66 - 632 * q^67 - 571 * q^68 + 1130 * q^69 - 144 * q^71 + 567 * q^72 - 864 * q^73 + 1207 * q^74 + 2494 * q^75 - 1005 * q^76 + 2222 * q^78 - 1613 * q^79 - 2399 * q^80 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 84 * q^85 - 258 * q^86 - 449 * q^87 - 608 * q^88 - 3378 * q^89 - 930 * q^90 + 3491 * q^92 + 1879 * q^93 - 3197 * q^94 - 79 * q^95 + 591 * q^96 + 55 * q^97 - 1612 * 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 $

$2$	−3.15653	−1.11600	−0.558001	−	0.829840i	$-0.688431\pi$
$2$	−3.15653	−1.11600	−0.558001	+	0.829840i	$0.688431\pi$
$3$	−7.20925	−1.38742	−0.693710	−	0.720254i	$-0.744025\pi$
$3$	−7.20925	−1.38742	−0.693710	+	0.720254i	$0.744025\pi$
$4$	1.96369	0.245461
$5$	−1.36370	−0.121973	−0.0609864	−	0.998139i	$-0.519425\pi$
$5$	−1.36370	−0.121973	−0.0609864	+	0.998139i	$0.519425\pi$
$6$	22.7562	1.54836
$7$	0	0
$7$	0	0
$8$	19.0538	0.842067
$9$	24.9733	0.924936
$10$	4.30455	0.136122
$11$	64.7677	1.77529	0.887646	−	0.460527i	$-0.152339\pi$
$11$	64.7677	1.77529	0.887646	+	0.460527i	$0.152339\pi$
$12$	−14.1567	−0.340557
$13$	19.2944	0.411638	0.205819	−	0.978590i	$-0.434014\pi$
$13$	19.2944	0.411638	0.205819	+	0.978590i	$0.434014\pi$
$14$	0	0
$15$	9.83123	0.169227
$16$	−75.8534	−1.18521
$17$	54.1213	0.772138	0.386069	−	0.922470i	$-0.373833\pi$
$17$	54.1213	0.772138	0.386069	+	0.922470i	$0.373833\pi$
$18$	−78.8289	−1.03223
$19$	69.0659	0.833938	0.416969	−	0.908921i	$-0.363092\pi$
$19$	69.0659	0.833938	0.416969	+	0.908921i	$0.363092\pi$
$20$	−2.67787	−0.0299395
$21$	0	0
$22$	−204.441	−1.98123
$23$	29.6031	0.268377	0.134189	−	0.990956i	$-0.457157\pi$
$23$	29.6031	0.268377	0.134189	+	0.990956i	$0.457157\pi$
$24$	−137.364	−1.16830
$25$	−123.140	−0.985123
$26$	−60.9032	−0.459389
$27$	14.6112	0.104145
$28$	0	0
$29$	13.1279	0.0840614	0.0420307	−	0.999116i	$-0.486617\pi$
$29$	13.1279	0.0840614	0.0420307	+	0.999116i	$0.486617\pi$
$30$	−31.0326	−0.188858
$31$	−185.439	−1.07438	−0.537191	−	0.843461i	$-0.680514\pi$
$31$	−185.439	−1.07438	−0.537191	+	0.843461i	$0.680514\pi$
$32$	87.0032	0.480629
$33$	−466.927	−2.46308
$34$	−170.836	−0.861707
$35$	0	0
$36$	49.0397	0.227035
$37$	−369.949	−1.64376	−0.821881	−	0.569659i	$-0.807075\pi$
$37$	−369.949	−1.64376	−0.821881	+	0.569659i	$0.807075\pi$
$38$	−218.009	−0.930676
$39$	−139.098	−0.571115
$40$	−25.9836	−0.102709
$41$	294.860	1.12315	0.561577	−	0.827424i	$-0.310195\pi$
$41$	294.860	1.12315	0.561577	+	0.827424i	$0.310195\pi$
$42$	0	0
$43$	−43.0000	−0.152499
$43$	−43.0000	−0.152499
$44$	127.183	0.435764
$45$	−34.0560	−0.112817
$46$	−93.4431	−0.299509
$47$	−367.319	−1.13998	−0.569989	−	0.821652i	$-0.693053\pi$
$47$	−367.319	−1.13998	−0.569989	+	0.821652i	$0.693053\pi$
$48$	546.846	1.64438
$49$	0	0
$50$	388.696	1.09940
$51$	−390.174	−1.07128
$52$	37.8881	0.101041
$53$	708.046	1.83505	0.917524	−	0.397680i	$-0.130185\pi$
$53$	708.046	1.83505	0.917524	+	0.397680i	$0.130185\pi$
$54$	−46.1207	−0.116226
$55$	−88.3236	−0.216537
$56$	0	0
$57$	−497.914	−1.15702
$58$	−41.4385	−0.0938127
$59$	−116.159	−0.256316	−0.128158	−	0.991754i	$-0.540906\pi$
$59$	−116.159	−0.256316	−0.128158	+	0.991754i	$0.540906\pi$
$60$	19.3054	0.0415387
$61$	−218.910	−0.459484	−0.229742	−	0.973252i	$-0.573788\pi$
$61$	−218.910	−0.459484	−0.229742	+	0.973252i	$0.573788\pi$
$62$	585.344	1.19901
$63$	0	0
$64$	332.199	0.648827
$65$	−26.3116	−0.0502086
$66$	1473.87	2.74880
$67$	−133.114	−0.242723	−0.121361	−	0.992608i	$-0.538726\pi$
$67$	−133.114	−0.242723	−0.121361	+	0.992608i	$0.538726\pi$
$68$	106.277	0.189529
$69$	−213.416	−0.372352
$70$	0	0
$71$	−926.738	−1.54906	−0.774532	−	0.632535i	$-0.782015\pi$
$71$	−926.738	−1.54906	−0.774532	+	0.632535i	$0.782015\pi$
$72$	475.836	0.778858
$73$	−455.867	−0.730893	−0.365446	−	0.930832i	$-0.619084\pi$
$73$	−455.867	−0.730893	−0.365446	+	0.930832i	$0.619084\pi$
$74$	1167.75	1.83444
$75$	887.749	1.36678
$76$	135.624	0.204699
$77$	0	0
$78$	439.067	0.637365
$79$	−620.178	−0.883234	−0.441617	−	0.897204i	$-0.645595\pi$
$79$	−620.178	−0.883234	−0.441617	+	0.897204i	$0.645595\pi$
$80$	103.441	0.144563
$81$	−779.614	−1.06943
$82$	−930.734	−1.25344
$83$	1317.85	1.74281	0.871405	−	0.490564i	$-0.163209\pi$
$83$	1317.85	1.74281	0.871405	+	0.490564i	$0.163209\pi$
$84$	0	0
$85$	−73.8050	−0.0941797
$86$	135.731	0.170189
$87$	−94.6419	−0.116629
$88$	1234.07	1.49492
$89$	−509.295	−0.606575	−0.303287	−	0.952899i	$-0.598084\pi$
$89$	−509.295	−0.606575	−0.303287	+	0.952899i	$0.598084\pi$
$90$	107.499	0.125904
$91$	0	0
$92$	58.1312	0.0658760
$93$	1336.88	1.49062
$94$	1159.45	1.27222
$95$	−94.1850	−0.101718
$96$	−627.228	−0.666835
$97$	−965.870	−1.01102	−0.505511	−	0.862820i	$-0.668696\pi$
$97$	−965.870	−1.01102	−0.505511	+	0.862820i	$0.668696\pi$
$98$	0	0
$99$	1617.46	1.64203
$100$	−241.809	−0.241809
$101$	1501.80	1.47955	0.739776	−	0.672853i	$-0.234932\pi$
$101$	1501.80	1.47955	0.739776	+	0.672853i	$0.234932\pi$
$102$	1231.60	1.19555
$103$	−1312.60	−1.25567	−0.627837	−	0.778345i	$-0.716060\pi$
$103$	−1312.60	−1.25567	−0.627837	+	0.778345i	$0.716060\pi$
$104$	367.631	0.346627
$105$	0	0
$106$	−2234.97	−2.04792
$107$	−611.656	−0.552627	−0.276313	−	0.961068i	$-0.589113\pi$
$107$	−611.656	−0.552627	−0.276313	+	0.961068i	$0.589113\pi$
$108$	28.6918	0.0255636
$109$	−946.664	−0.831871	−0.415935	−	0.909394i	$-0.636546\pi$
$109$	−946.664	−0.831871	−0.415935	+	0.909394i	$0.636546\pi$
$110$	278.796	0.241656
$111$	2667.05	2.28059
$112$	0	0
$113$	2109.50	1.75615	0.878076	−	0.478521i	$-0.158827\pi$
$113$	2109.50	1.75615	0.878076	+	0.478521i	$0.158827\pi$
$114$	1571.68	1.29124
$115$	−40.3696	−0.0327347
$116$	25.7790	0.0206338
$117$	481.843	0.380739
$118$	366.660	0.286049
$119$	0	0
$120$	187.322	0.142501
$121$	2863.86	2.15166
$122$	690.996	0.512785
$123$	−2125.72	−1.55829
$124$	−364.144	−0.263718
$125$	338.388	0.242131
$126$	0	0
$127$	788.583	0.550988	0.275494	−	0.961303i	$-0.411159\pi$
$127$	788.583	0.550988	0.275494	+	0.961303i	$0.411159\pi$
$128$	−1744.62	−1.20472
$129$	309.998	0.211580
$130$	83.0535	0.0560329
$131$	−1873.57	−1.24957	−0.624787	−	0.780795i	$-0.714814\pi$
$131$	−1873.57	−1.24957	−0.624787	+	0.780795i	$0.714814\pi$
$132$	−916.897	−0.604588
$133$	0	0
$134$	420.177	0.270879
$135$	−19.9252	−0.0127029
$136$	1031.22	0.650192
$137$	−1860.27	−1.16010	−0.580050	−	0.814581i	$-0.696967\pi$
$137$	−1860.27	−1.16010	−0.580050	+	0.814581i	$0.696967\pi$
$138$	673.654	0.415545
$139$	2822.52	1.72232	0.861161	−	0.508333i	$-0.169738\pi$
$139$	2822.52	1.72232	0.861161	+	0.508333i	$0.169738\pi$
$140$	0	0
$141$	2648.09	1.58163
$142$	2925.28	1.72876
$143$	1249.65	0.730777
$144$	−1894.31	−1.09624
$145$	−17.9024	−0.0102532
$146$	1438.96	0.815678
$147$	0	0
$148$	−726.463	−0.403479
$149$	1615.30	0.888126	0.444063	−	0.895996i	$-0.353537\pi$
$149$	1615.30	0.888126	0.444063	+	0.895996i	$0.353537\pi$
$150$	−2802.21	−1.52533
$151$	1399.96	0.754483	0.377241	−	0.926115i	$-0.376873\pi$
$151$	1399.96	0.754483	0.377241	+	0.926115i	$0.376873\pi$
$152$	1315.97	0.702232
$153$	1351.59	0.714178
$154$	0	0
$155$	252.882	0.131045
$156$	−273.144	−0.140186
$157$	−2933.25	−1.49108	−0.745539	−	0.666462i	$-0.767808\pi$
$157$	−2933.25	−1.49108	−0.745539	+	0.666462i	$0.767808\pi$
$158$	1957.61	0.985691
$159$	−5104.48	−2.54598
$160$	−118.646	−0.0586237
$161$	0	0
$162$	2460.88	1.19349
$163$	−166.212	−0.0798695	−0.0399347	−	0.999202i	$-0.512715\pi$
$163$	−166.212	−0.0798695	−0.0399347	+	0.999202i	$0.512715\pi$
$164$	579.012	0.275690
$165$	636.746	0.300428
$166$	−4159.85	−1.94498
$167$	−2143.42	−0.993191	−0.496595	−	0.867982i	$-0.665417\pi$
$167$	−2143.42	−0.993191	−0.496595	+	0.867982i	$0.665417\pi$
$168$	0	0
$169$	−1824.73	−0.830554
$170$	232.968	0.105105
$171$	1724.80	0.771339
$172$	−84.4385	−0.0374324
$173$	119.018	0.0523050	0.0261525	−	0.999658i	$-0.491674\pi$
$173$	119.018	0.0523050	0.0261525	+	0.999658i	$0.491674\pi$
$174$	298.740	0.130158
$175$	0	0
$176$	−4912.85	−2.10409
$177$	837.420	0.355618
$178$	1607.61	0.676939
$179$	2572.05	1.07399	0.536995	−	0.843585i	$-0.319559\pi$
$179$	2572.05	1.07399	0.536995	+	0.843585i	$0.319559\pi$
$180$	−66.8752	−0.0276921
$181$	−1429.30	−0.586956	−0.293478	−	0.955966i	$-0.594813\pi$
$181$	−1429.30	−0.586956	−0.293478	+	0.955966i	$0.594813\pi$
$182$	0	0
$183$	1578.18	0.637498
$184$	564.052	0.225992
$185$	504.498	0.200494
$186$	−4219.89	−1.66353
$187$	3505.31	1.37077
$188$	−721.299	−0.279820
$189$	0	0
$190$	297.298	0.113517
$191$	411.149	0.155758	0.0778788	−	0.996963i	$-0.475185\pi$
$191$	411.149	0.155758	0.0778788	+	0.996963i	$0.475185\pi$
$192$	−2394.91	−0.900195
$193$	−3108.57	−1.15938	−0.579689	−	0.814838i	$-0.696826\pi$
$193$	−3108.57	−1.15938	−0.579689	+	0.814838i	$0.696826\pi$
$194$	3048.80	1.12830
$195$	189.687	0.0696604
$196$	0	0
$197$	1960.75	0.709125	0.354563	−	0.935032i	$-0.384630\pi$
$197$	1960.75	0.709125	0.354563	+	0.935032i	$0.384630\pi$
$198$	−5105.57	−1.83251
$199$	−456.187	−0.162504	−0.0812519	−	0.996694i	$-0.525892\pi$
$199$	−456.187	−0.162504	−0.0812519	+	0.996694i	$0.525892\pi$
$200$	−2346.29	−0.829540
$201$	959.650	0.336759
$202$	−4740.48	−1.65118
$203$	0	0
$204$	−766.179	−0.262957
$205$	−402.099	−0.136994
$206$	4143.27	1.40133
$207$	739.286	0.248232
$208$	−1463.54	−0.487877
$209$	4473.24	1.48048
$210$	0	0
$211$	−1742.50	−0.568524	−0.284262	−	0.958747i	$-0.591749\pi$
$211$	−1742.50	−0.568524	−0.284262	+	0.958747i	$0.591749\pi$
$212$	1390.38	0.450432
$213$	6681.08	2.14920
$214$	1930.71	0.616732
$215$	58.6390	0.0186007
$216$	278.399	0.0876974
$217$	0	0
$218$	2988.17	0.928370
$219$	3286.46	1.01406
$220$	−173.440	−0.0531514
$221$	1044.24	0.317841
$222$	−8418.63	−2.54514
$223$	−3149.26	−0.945697	−0.472848	−	0.881144i	$-0.656774\pi$
$223$	−3149.26	−0.945697	−0.472848	+	0.881144i	$0.656774\pi$
$224$	0	0
$225$	−3075.22	−0.911175
$226$	−6658.71	−1.95987
$227$	−2108.03	−0.616365	−0.308182	−	0.951327i	$-0.599721\pi$
$227$	−2108.03	−0.616365	−0.308182	+	0.951327i	$0.599721\pi$
$228$	−977.746	−0.284003
$229$	−1529.66	−0.441409	−0.220704	−	0.975341i	$-0.570836\pi$
$229$	−1529.66	−0.441409	−0.220704	+	0.975341i	$0.570836\pi$
$230$	127.428	0.0365320
$231$	0	0
$232$	250.136	0.0707854
$233$	2999.86	0.843466	0.421733	−	0.906720i	$-0.361422\pi$
$233$	2999.86	0.843466	0.421733	+	0.906720i	$0.361422\pi$
$234$	−1520.95	−0.424905
$235$	500.912	0.139046
$236$	−228.100	−0.0629154
$237$	4471.02	1.22542
$238$	0	0
$239$	3421.34	0.925976	0.462988	−	0.886364i	$-0.346777\pi$
$239$	3421.34	0.925976	0.462988	+	0.886364i	$0.346777\pi$
$240$	−745.732	−0.200570
$241$	4496.86	1.20194	0.600971	−	0.799271i	$-0.294781\pi$
$241$	4496.86	1.20194	0.600971	+	0.799271i	$0.294781\pi$
$242$	−9039.86	−2.40126
$243$	5225.93	1.37960
$244$	−429.870	−0.112785
$245$	0	0
$246$	6709.89	1.73905
$247$	1332.58	0.343280
$248$	−3533.32	−0.904701
$249$	−9500.74	−2.41801
$250$	−1068.13	−0.270219
$251$	−1478.05	−0.371688	−0.185844	−	0.982579i	$-0.559502\pi$
$251$	−1478.05	−0.371688	−0.185844	+	0.982579i	$0.559502\pi$
$252$	0	0
$253$	1917.33	0.476448
$254$	−2489.19	−0.614904
$255$	532.079	0.130667
$256$	2849.36	0.695645
$257$	−677.467	−0.164433	−0.0822164	−	0.996614i	$-0.526200\pi$
$257$	−677.467	−0.164433	−0.0822164	+	0.996614i	$0.526200\pi$
$258$	−978.517	−0.236123
$259$	0	0
$260$	−51.6678	−0.0123242
$261$	327.845	0.0777514
$262$	5913.97	1.39453
$263$	−7753.56	−1.81789	−0.908944	−	0.416917i	$-0.863110\pi$
$263$	−7753.56	−1.81789	−0.908944	+	0.416917i	$0.863110\pi$
$264$	−8896.73	−2.07408
$265$	−965.560	−0.223826
$266$	0	0
$267$	3671.63	0.841574
$268$	−261.393	−0.0595789
$269$	300.965	0.0682161	0.0341081	−	0.999418i	$-0.489141\pi$
$269$	300.965	0.0682161	0.0341081	+	0.999418i	$0.489141\pi$
$270$	62.8946	0.0141765
$271$	2176.33	0.487833	0.243917	−	0.969796i	$-0.421568\pi$
$271$	2176.33	0.487833	0.243917	+	0.969796i	$0.421568\pi$
$272$	−4105.28	−0.915145
$273$	0	0
$274$	5872.00	1.29467
$275$	−7975.52	−1.74888
$276$	−419.082	−0.0913978
$277$	2947.64	0.639373	0.319687	−	0.947523i	$-0.396422\pi$
$277$	2947.64	0.639373	0.319687	+	0.947523i	$0.396422\pi$
$278$	−8909.36	−1.92211
$279$	−4631.02	−0.993734
$280$	0	0
$281$	459.209	0.0974879	0.0487440	−	0.998811i	$-0.484478\pi$
$281$	459.209	0.0974879	0.0487440	+	0.998811i	$0.484478\pi$
$282$	−8358.79	−1.76510
$283$	−6190.86	−1.30038	−0.650192	−	0.759770i	$-0.725312\pi$
$283$	−6190.86	−1.30038	−0.650192	+	0.759770i	$0.725312\pi$
$284$	−1819.82	−0.380234
$285$	679.003	0.141125
$286$	−3944.56	−0.815549
$287$	0	0
$288$	2172.75	0.444551
$289$	−1983.89	−0.403803
$290$	56.5095	0.0114426
$291$	6963.20	1.40271
$292$	−895.179	−0.179405
$293$	−5693.95	−1.13530	−0.567652	−	0.823269i	$-0.692148\pi$
$293$	−5693.95	−1.13530	−0.567652	+	0.823269i	$0.692148\pi$
$294$	0	0
$295$	158.406	0.0312635
$296$	−7048.93	−1.38416
$297$	946.333	0.184888
$298$	−5098.75	−0.991150
$299$	571.173	0.110474
$300$	1743.26	0.335491
$301$	0	0
$302$	−4419.01	−0.842005
$303$	−10826.9	−2.05276
$304$	−5238.89	−0.988391
$305$	298.527	0.0560446
$306$	−4266.32	−0.797024
$307$	5108.18	0.949639	0.474819	−	0.880083i	$-0.342513\pi$
$307$	5108.18	0.949639	0.474819	+	0.880083i	$0.342513\pi$
$308$	0	0
$309$	9462.87	1.74215
$310$	−798.231	−0.146247
$311$	1048.11	0.191102	0.0955511	−	0.995425i	$-0.469539\pi$
$311$	1048.11	0.191102	0.0955511	+	0.995425i	$0.469539\pi$
$312$	−2650.34	−0.480917
$313$	−4279.92	−0.772893	−0.386446	−	0.922312i	$-0.626298\pi$
$313$	−4279.92	−0.772893	−0.386446	+	0.922312i	$0.626298\pi$
$314$	9258.91	1.66405
$315$	0	0
$316$	−1217.83	−0.216799
$317$	5929.95	1.05066	0.525330	−	0.850899i	$-0.323942\pi$
$317$	5929.95	1.05066	0.525330	+	0.850899i	$0.323942\pi$
$318$	16112.4	2.84132
$319$	850.261	0.149234
$320$	−453.019	−0.0791392
$321$	4409.58	0.766725
$322$	0	0
$323$	3737.94	0.643915
$324$	−1530.92	−0.262503
$325$	−2375.91	−0.405514
$326$	524.653	0.0891345
$327$	6824.73	1.15415
$328$	5618.20	0.945772
$329$	0	0
$330$	−2009.91	−0.335278
$331$	509.174	0.0845521	0.0422761	−	0.999106i	$-0.486539\pi$
$331$	509.174	0.0845521	0.0422761	+	0.999106i	$0.486539\pi$
$332$	2587.85	0.427792
$333$	−9238.83	−1.52037
$334$	6765.77	1.10840
$335$	181.527	0.0296056
$336$	0	0
$337$	−10856.3	−1.75484	−0.877419	−	0.479724i	$-0.840737\pi$
$337$	−10856.3	−1.75484	−0.877419	+	0.479724i	$0.840737\pi$
$338$	5759.81	0.926900
$339$	−15207.9	−2.43652
$340$	−144.930	−0.0231174
$341$	−12010.5	−1.90734
$342$	−5444.39	−0.860816
$343$	0	0
$344$	−819.314	−0.128414
$345$	291.035	0.0454168
$346$	−375.684	−0.0583725
$347$	8973.74	1.38829	0.694143	−	0.719837i	$-0.255783\pi$
$347$	8973.74	1.38829	0.694143	+	0.719837i	$0.255783\pi$
$348$	−185.847	−0.0286277
$349$	5.70408	0.000874877 0	0.000437439	−	1.00000i	$-0.499861\pi$
$349$	5.70408	0.000874877 0	0.000437439		1.00000i	$0.499861\pi$
$350$	0	0
$351$	281.913	0.0428702
$352$	5635.00	0.853257
$353$	1504.40	0.226830	0.113415	−	0.993548i	$-0.463821\pi$
$353$	1504.40	0.226830	0.113415	+	0.993548i	$0.463821\pi$
$354$	−2643.34	−0.396870
$355$	1263.79	0.188944
$356$	−1000.10	−0.148890
$357$	0	0
$358$	−8118.76	−1.19857
$359$	−1296.86	−0.190657	−0.0953285	−	0.995446i	$-0.530390\pi$
$359$	−1296.86	−0.190657	−0.0953285	+	0.995446i	$0.530390\pi$
$360$	−648.896	−0.0949995
$361$	−2088.90	−0.304548
$362$	4511.63	0.655044
$363$	−20646.3	−2.98526
$364$	0	0
$365$	621.664	0.0891490
$366$	−4981.56	−0.711449
$367$	−12908.3	−1.83599	−0.917995	−	0.396592i	$-0.870193\pi$
$367$	−12908.3	−1.83599	−0.917995	+	0.396592i	$0.870193\pi$
$368$	−2245.50	−0.318083
$369$	7363.61	1.03885
$370$	−1592.46	−0.223752
$371$	0	0
$372$	2625.20	0.365888
$373$	−1371.48	−0.190382	−0.0951908	−	0.995459i	$-0.530346\pi$
$373$	−1371.48	−0.190382	−0.0951908	+	0.995459i	$0.530346\pi$
$374$	−11064.6	−1.52978
$375$	−2439.52	−0.335937
$376$	−6998.83	−0.959939
$377$	253.293	0.0346029
$378$	0	0
$379$	−458.768	−0.0621776	−0.0310888	−	0.999517i	$-0.509897\pi$
$379$	−458.768	−0.0621776	−0.0310888	+	0.999517i	$0.509897\pi$
$380$	−184.950	−0.0249677
$381$	−5685.09	−0.764452
$382$	−1297.80	−0.173826
$383$	−9513.45	−1.26923	−0.634614	−	0.772829i	$-0.718841\pi$
$383$	−9513.45	−1.26923	−0.634614	+	0.772829i	$0.718841\pi$
$384$	12577.4	1.67145
$385$	0	0
$386$	9812.31	1.29387
$387$	−1073.85	−0.141051
$388$	−1896.66	−0.248166
$389$	5643.25	0.735538	0.367769	−	0.929917i	$-0.380122\pi$
$389$	5643.25	0.735538	0.367769	+	0.929917i	$0.380122\pi$
$390$	−598.754	−0.0777412
$391$	1602.16	0.207224
$392$	0	0
$393$	13507.0	1.73369
$394$	−6189.17	−0.791385
$395$	845.735	0.107730
$396$	3176.19	0.403054
$397$	13816.5	1.74668	0.873340	−	0.487110i	$-0.161949\pi$
$397$	13816.5	1.74668	0.873340	+	0.487110i	$0.161949\pi$
$398$	1439.97	0.181355
$399$	0	0
$400$	9340.62	1.16758
$401$	3544.45	0.441400	0.220700	−	0.975342i	$-0.429166\pi$
$401$	3544.45	0.441400	0.220700	+	0.975342i	$0.429166\pi$
$402$	−3029.16	−0.375823
$403$	−3577.93	−0.442256
$404$	2949.06	0.363172
$405$	1063.16	0.130441
$406$	0	0
$407$	−23960.7	−2.91816
$408$	−7434.30	−0.902090
$409$	2736.88	0.330880	0.165440	−	0.986220i	$-0.447096\pi$
$409$	2736.88	0.330880	0.165440	+	0.986220i	$0.447096\pi$
$410$	1269.24	0.152886
$411$	13411.2	1.60955
$412$	−2577.54	−0.308219
$413$	0	0
$414$	−2333.58	−0.277027
$415$	−1797.15	−0.212575
$416$	1678.67	0.197845
$417$	−20348.2	−2.38958
$418$	−14119.9	−1.65222
$419$	−9280.65	−1.08208	−0.541038	−	0.840998i	$-0.681968\pi$
$419$	−9280.65	−1.08208	−0.541038	+	0.840998i	$0.681968\pi$
$420$	0	0
$421$	−7308.00	−0.846010	−0.423005	−	0.906127i	$-0.639025\pi$
$421$	−7308.00	−0.846010	−0.423005	+	0.906127i	$0.639025\pi$
$422$	5500.26	0.634475
$423$	−9173.16	−1.05441
$424$	13491.0	1.54523
$425$	−6664.51	−0.760650
$426$	−21089.0	−2.39852
$427$	0	0
$428$	−1201.10	−0.135648
$429$	−9009.05	−1.01390
$430$	−185.096	−0.0207584
$431$	−953.510	−0.106564	−0.0532818	−	0.998580i	$-0.516968\pi$
$431$	−953.510	−0.106564	−0.0532818	+	0.998580i	$0.516968\pi$
$432$	−1108.31	−0.123434
$433$	−3447.00	−0.382569	−0.191284	−	0.981535i	$-0.561265\pi$
$433$	−3447.00	−0.382569	−0.191284	+	0.981535i	$0.561265\pi$
$434$	0	0
$435$	129.063	0.0142255
$436$	−1858.95	−0.204192
$437$	2044.57	0.223810
$438$	−10373.8	−1.13169
$439$	9245.65	1.00517	0.502586	−	0.864527i	$-0.332382\pi$
$439$	9245.65	1.00517	0.502586	+	0.864527i	$0.332382\pi$
$440$	−1682.90	−0.182339
$441$	0	0
$442$	−3296.16	−0.354711
$443$	−3885.76	−0.416745	−0.208372	−	0.978050i	$-0.566817\pi$
$443$	−3885.76	−0.416745	−0.208372	+	0.978050i	$0.566817\pi$
$444$	5237.25	0.559795
$445$	694.524	0.0739856
$446$	9940.75	1.05540
$447$	−11645.1	−1.23220
$448$	0	0
$449$	−14413.1	−1.51491	−0.757455	−	0.652887i	$-0.773557\pi$
$449$	−14413.1	−1.51491	−0.757455	+	0.652887i	$0.773557\pi$
$450$	9707.02	1.01687
$451$	19097.4	1.99393
$452$	4142.40	0.431066
$453$	−10092.6	−1.04679
$454$	6654.06	0.687864
$455$	0	0
$456$	−9487.15	−0.974291
$457$	−1765.21	−0.180685	−0.0903424	−	0.995911i	$-0.528796\pi$
$457$	−1765.21	−0.180685	−0.0903424	+	0.995911i	$0.528796\pi$
$458$	4828.41	0.492613
$459$	790.776	0.0804145
$460$	−79.2733	−0.00803508
$461$	−7626.64	−0.770517	−0.385258	−	0.922809i	$-0.625888\pi$
$461$	−7626.64	−0.770517	−0.385258	+	0.922809i	$0.625888\pi$
$462$	0	0
$463$	−5954.18	−0.597655	−0.298827	−	0.954307i	$-0.596595\pi$
$463$	−5954.18	−0.597655	−0.298827	+	0.954307i	$0.596595\pi$
$464$	−995.792	−0.0996304
$465$	−1823.09	−0.181815
$466$	−9469.16	−0.941310
$467$	−153.388	−0.0151991	−0.00759954	−	0.999971i	$-0.502419\pi$
$467$	−153.388	−0.0151991	−0.00759954	+	0.999971i	$0.502419\pi$
$468$	946.189	0.0934564
$469$	0	0
$470$	−1581.14	−0.155176
$471$	21146.6	2.06875
$472$	−2213.27	−0.215835
$473$	−2785.01	−0.270729
$474$	−14112.9	−1.36757
$475$	−8504.80	−0.821531
$476$	0	0
$477$	17682.2	1.69730
$478$	−10799.6	−1.03339
$479$	11334.3	1.08117	0.540584	−	0.841290i	$-0.318203\pi$
$479$	11334.3	1.08117	0.540584	+	0.841290i	$0.318203\pi$
$480$	855.348	0.0813357
$481$	−7137.92	−0.676635
$482$	−14194.5	−1.34137
$483$	0	0
$484$	5623.72	0.528148
$485$	1317.15	0.123317
$486$	−16495.8	−1.53964
$487$	−2845.89	−0.264804	−0.132402	−	0.991196i	$-0.542269\pi$
$487$	−2845.89	−0.264804	−0.132402	+	0.991196i	$0.542269\pi$
$488$	−4171.07	−0.386917
$489$	1198.26	0.110813
$490$	0	0
$491$	−8345.94	−0.767102	−0.383551	−	0.923520i	$-0.625299\pi$
$491$	−8345.94	−0.767102	−0.383551	+	0.923520i	$0.625299\pi$
$492$	−4174.24	−0.382499
$493$	710.496	0.0649070
$494$	−4206.34	−0.383101
$495$	−2205.73	−0.200283
$496$	14066.2	1.27337
$497$	0	0
$498$	29989.4	2.69851
$499$	17591.1	1.57813	0.789064	−	0.614311i	$-0.210566\pi$
$499$	17591.1	1.57813	0.789064	+	0.614311i	$0.210566\pi$
$500$	664.488	0.0594336
$501$	15452.5	1.37797
$502$	4665.51	0.414805
$503$	7975.83	0.707008	0.353504	−	0.935433i	$-0.384990\pi$
$503$	7975.83	0.707008	0.353504	+	0.935433i	$0.384990\pi$
$504$	0	0
$505$	−2048.00	−0.180465
$506$	−6052.10	−0.531717
$507$	13154.9	1.15233
$508$	1548.53	0.135246
$509$	9016.94	0.785204	0.392602	−	0.919708i	$-0.371575\pi$
$509$	9016.94	0.785204	0.392602	+	0.919708i	$0.371575\pi$
$510$	−1679.52	−0.145825
$511$	0	0
$512$	4962.89	0.428380
$513$	1009.14	0.0868507
$514$	2138.45	0.183507
$515$	1789.99	0.153158
$516$	608.738	0.0519345
$517$	−23790.4	−2.02379
$518$	0	0
$519$	−858.030	−0.0725691
$520$	−501.337	−0.0422790
$521$	3086.13	0.259512	0.129756	−	0.991546i	$-0.458581\pi$
$521$	3086.13	0.259512	0.129756	+	0.991546i	$0.458581\pi$
$522$	−1034.85	−0.0867707
$523$	−8338.32	−0.697149	−0.348575	−	0.937281i	$-0.613334\pi$
$523$	−8338.32	−0.697149	−0.348575	+	0.937281i	$0.613334\pi$
$524$	−3679.10	−0.306722
$525$	0	0
$526$	24474.3	2.02877
$527$	−10036.2	−0.829570
$528$	35418.0	2.91926
$529$	−11290.7	−0.927974
$530$	3047.82	0.249790
$531$	−2900.87	−0.237076
$532$	0	0
$533$	5689.13	0.462333
$534$	−11589.6	−0.939199
$535$	834.114	0.0674054
$536$	−2536.32	−0.204389
$537$	−18542.6	−1.49008
$538$	−950.004	−0.0761293
$539$	0	0
$540$	−39.1269	−0.00311806
$541$	−14924.6	−1.18606	−0.593029	−	0.805181i	$-0.702068\pi$
$541$	−14924.6	−1.18606	−0.593029	+	0.805181i	$0.702068\pi$
$542$	−6869.66	−0.544423
$543$	10304.2	0.814355
$544$	4708.72	0.371112
$545$	1290.96	0.101466
$546$	0	0
$547$	10658.3	0.833120	0.416560	−	0.909108i	$-0.363236\pi$
$547$	10658.3	0.833120	0.416560	+	0.909108i	$0.363236\pi$
$548$	−3652.99	−0.284759
$549$	−5466.90	−0.424994
$550$	25175.0	1.95175
$551$	906.687	0.0701020
$552$	−4066.39	−0.313545
$553$	0	0
$554$	−9304.31	−0.713542
$555$	−3637.05	−0.278170
$556$	5542.53	0.422762
$557$	4303.28	0.327354	0.163677	−	0.986514i	$-0.447665\pi$
$557$	4303.28	0.327354	0.163677	+	0.986514i	$0.447665\pi$
$558$	14617.9	1.10901
$559$	−829.657	−0.0627742
$560$	0	0
$561$	−25270.7	−1.90183
$562$	−1449.51	−0.108797
$563$	13280.8	0.994173	0.497086	−	0.867701i	$-0.334403\pi$
$563$	13280.8	0.994173	0.497086	+	0.867701i	$0.334403\pi$
$564$	5200.02	0.388228
$565$	−2876.72	−0.214203
$566$	19541.7	1.45123
$567$	0	0
$568$	−17657.9	−1.30442
$569$	11641.6	0.857720	0.428860	−	0.903371i	$-0.358915\pi$
$569$	11641.6	0.857720	0.428860	+	0.903371i	$0.358915\pi$
$570$	−2143.29	−0.157496
$571$	21799.0	1.59765	0.798825	−	0.601563i	$-0.205455\pi$
$571$	21799.0	1.59765	0.798825	+	0.601563i	$0.205455\pi$
$572$	2453.92	0.179377
$573$	−2964.07	−0.216101
$574$	0	0
$575$	−3645.34	−0.264384
$576$	8296.10	0.600123
$577$	−6854.44	−0.494548	−0.247274	−	0.968946i	$-0.579535\pi$
$577$	−6854.44	−0.494548	−0.247274	+	0.968946i	$0.579535\pi$
$578$	6262.20	0.450645
$579$	22410.5	1.60855
$580$	−35.1547	−0.00251676
$581$	0	0
$582$	−21979.5	−1.56543
$583$	45858.5	3.25775
$584$	−8686.00	−0.615461
$585$	−657.088	−0.0464397
$586$	17973.1	1.26700
$587$	16741.7	1.17718	0.588589	−	0.808433i	$-0.299684\pi$
$587$	16741.7	1.17718	0.588589	+	0.808433i	$0.299684\pi$
$588$	0	0
$589$	−12807.5	−0.895967
$590$	−500.012	−0.0348902
$591$	−14135.5	−0.983855
$592$	28061.9	1.94820
$593$	−21885.0	−1.51553	−0.757764	−	0.652529i	$-0.773708\pi$
$593$	−21885.0	−1.51553	−0.757764	+	0.652529i	$0.773708\pi$
$594$	−2987.13	−0.206336
$595$	0	0
$596$	3171.95	0.218000
$597$	3288.77	0.225461
$598$	−1802.92	−0.123289
$599$	−14440.9	−0.985039	−0.492519	−	0.870301i	$-0.663924\pi$
$599$	−14440.9	−0.985039	−0.492519	+	0.870301i	$0.663924\pi$
$600$	16915.0	1.15092
$601$	−2570.21	−0.174444	−0.0872221	−	0.996189i	$-0.527799\pi$
$601$	−2570.21	−0.174444	−0.0872221	+	0.996189i	$0.527799\pi$
$602$	0	0
$603$	−3324.28	−0.224503
$604$	2749.08	0.185196
$605$	−3905.44	−0.262444
$606$	34175.3	2.29089
$607$	11683.5	0.781249	0.390624	−	0.920550i	$-0.372259\pi$
$607$	11683.5	0.781249	0.390624	+	0.920550i	$0.372259\pi$
$608$	6008.96	0.400815
$609$	0	0
$610$	−942.309	−0.0625458
$611$	−7087.18	−0.469258
$612$	2654.09	0.175303
$613$	12739.0	0.839356	0.419678	−	0.907673i	$-0.362143\pi$
$613$	12739.0	0.839356	0.419678	+	0.907673i	$0.362143\pi$
$614$	−16124.1	−1.05980
$615$	2898.83	0.190069
$616$	0	0
$617$	4380.70	0.285835	0.142918	−	0.989735i	$-0.454352\pi$
$617$	4380.70	0.285835	0.142918	+	0.989735i	$0.454352\pi$
$618$	−29869.8	−1.94424
$619$	5157.68	0.334902	0.167451	−	0.985880i	$-0.446446\pi$
$619$	5157.68	0.334902	0.167451	+	0.985880i	$0.446446\pi$
$620$	496.582	0.0321665
$621$	432.536	0.0279502
$622$	−3308.39	−0.213270
$623$	0	0
$624$	10551.0	0.676891
$625$	14931.1	0.955589
$626$	13509.7	0.862550
$627$	−32248.7	−2.05405
$628$	−5759.99	−0.366001
$629$	−20022.1	−1.26921
$630$	0	0
$631$	−27679.9	−1.74631	−0.873154	−	0.487444i	$-0.837929\pi$
$631$	−27679.9	−1.74631	−0.873154	+	0.487444i	$0.837929\pi$
$632$	−11816.8	−0.743743
$633$	12562.1	0.788783
$634$	−18718.1	−1.17254
$635$	−1075.39	−0.0672055
$636$	−10023.6	−0.624939
$637$	0	0
$638$	−2683.88	−0.166545
$639$	−23143.7	−1.43278
$640$	2379.14	0.146943
$641$	−16453.5	−1.01384	−0.506921	−	0.861992i	$-0.669217\pi$
$641$	−16453.5	−1.01384	−0.506921	+	0.861992i	$0.669217\pi$
$642$	−13919.0	−0.855667
$643$	29203.6	1.79110	0.895551	−	0.444958i	$-0.146781\pi$
$643$	29203.6	1.79110	0.895551	+	0.444958i	$0.146781\pi$
$644$	0	0
$645$	−422.743	−0.0258070
$646$	−11798.9	−0.718610
$647$	16835.6	1.02299	0.511495	−	0.859286i	$-0.329092\pi$
$647$	16835.6	1.02299	0.511495	+	0.859286i	$0.329092\pi$
$648$	−14854.6	−0.900532
$649$	−7523.36	−0.455035
$650$	7499.64	0.452554
$651$	0	0
$652$	−326.388	−0.0196048
$653$	−13735.1	−0.823117	−0.411558	−	0.911383i	$-0.635015\pi$
$653$	−13735.1	−0.823117	−0.411558	+	0.911383i	$0.635015\pi$
$654$	−21542.5	−1.28804
$655$	2554.98	0.152414
$656$	−22366.1	−1.33117
$657$	−11384.5	−0.676029
$658$	0	0
$659$	−5708.76	−0.337453	−0.168727	−	0.985663i	$-0.553966\pi$
$659$	−5708.76	−0.337453	−0.168727	+	0.985663i	$0.553966\pi$
$660$	1250.37	0.0737433
$661$	−18339.5	−1.07916	−0.539578	−	0.841936i	$-0.681416\pi$
$661$	−18339.5	−1.07916	−0.539578	+	0.841936i	$0.681416\pi$
$662$	−1607.22	−0.0943604
$663$	−7528.15	−0.440979
$664$	25110.1	1.46756
$665$	0	0
$666$	29162.7	1.69674
$667$	388.625	0.0225602
$668$	−4209.00	−0.243789
$669$	22703.8	1.31208
$670$	−572.995	−0.0330399
$671$	−14178.3	−0.815719
$672$	0	0
$673$	−482.234	−0.0276207	−0.0138104	−	0.999905i	$-0.504396\pi$
$673$	−482.234	−0.0276207	−0.0138104	+	0.999905i	$0.504396\pi$
$674$	34268.3	1.95840
$675$	−1799.23	−0.102596
$676$	−3583.19	−0.203868
$677$	−31086.0	−1.76474	−0.882372	−	0.470553i	$-0.844055\pi$
$677$	−31086.0	−1.76474	−0.882372	+	0.470553i	$0.844055\pi$
$678$	48004.3	2.71916
$679$	0	0
$680$	−1406.27	−0.0793057
$681$	15197.3	0.855157
$682$	37911.4	2.12860
$683$	31381.0	1.75807	0.879034	−	0.476758i	$-0.158188\pi$
$683$	31381.0	1.75807	0.879034	+	0.476758i	$0.158188\pi$
$684$	3386.97	0.189333
$685$	2536.85	0.141501
$686$	0	0
$687$	11027.7	0.612420
$688$	3261.70	0.180743
$689$	13661.3	0.755375
$690$	−918.660	−0.0506852
$691$	−19856.9	−1.09319	−0.546593	−	0.837398i	$-0.684076\pi$
$691$	−19856.9	−1.09319	−0.546593	+	0.837398i	$0.684076\pi$
$692$	233.714	0.0128388
$693$	0	0
$694$	−28325.9	−1.54933
$695$	−3849.06	−0.210076
$696$	−1803.29	−0.0982091
$697$	15958.2	0.867230
$698$	−18.0051	−0.000976365 0
$699$	−21626.8	−1.17024
$700$	0	0
$701$	2722.80	0.146703	0.0733514	−	0.997306i	$-0.476631\pi$
$701$	2722.80	0.146703	0.0733514	+	0.997306i	$0.476631\pi$
$702$	−889.868	−0.0478432
$703$	−25550.9	−1.37079
$704$	21515.8	1.15186
$705$	−3611.20	−0.192916
$706$	−4748.67	−0.253143
$707$	0	0
$708$	1644.43	0.0872901
$709$	−1225.30	−0.0649043	−0.0324521	−	0.999473i	$-0.510332\pi$
$709$	−1225.30	−0.0649043	−0.0324521	+	0.999473i	$0.510332\pi$
$710$	−3989.19	−0.210861
$711$	−15487.9	−0.816935
$712$	−9704.01	−0.510777
$713$	−5489.57	−0.288339
$714$	0	0
$715$	−1704.15	−0.0891349
$716$	5050.70	0.263622
$717$	−24665.3	−1.28472
$718$	4093.59	0.212774
$719$	28875.1	1.49772	0.748858	−	0.662730i	$-0.230602\pi$
$719$	28875.1	1.49772	0.748858	+	0.662730i	$0.230602\pi$
$720$	2583.26	0.133712
$721$	0	0
$722$	6593.67	0.339876
$723$	−32419.0	−1.66760
$724$	−2806.70	−0.144075
$725$	−1616.57	−0.0828108
$726$	65170.6	3.33155
$727$	25072.0	1.27905	0.639525	−	0.768770i	$-0.279131\pi$
$727$	25072.0	1.27905	0.639525	+	0.768770i	$0.279131\pi$
$728$	0	0
$729$	−16625.5	−0.844660
$730$	−1962.30	−0.0994905
$731$	−2327.22	−0.117750
$732$	3099.04	0.156481
$733$	−1017.07	−0.0512503	−0.0256251	−	0.999672i	$-0.508158\pi$
$733$	−1017.07	−0.0512503	−0.0256251	+	0.999672i	$0.508158\pi$
$734$	40745.5	2.04897
$735$	0	0
$736$	2575.56	0.128990
$737$	−8621.47	−0.430904
$738$	−23243.5	−1.15935
$739$	−1001.77	−0.0498658	−0.0249329	−	0.999689i	$-0.507937\pi$
$739$	−1001.77	−0.0498658	−0.0249329	+	0.999689i	$0.507937\pi$
$740$	990.675	0.0492134
$741$	−9606.92	−0.476274
$742$	0	0
$743$	−2115.35	−0.104448	−0.0522238	−	0.998635i	$-0.516631\pi$
$743$	−2115.35	−0.104448	−0.0522238	+	0.998635i	$0.516631\pi$
$744$	25472.6	1.25520
$745$	−2202.78	−0.108327
$746$	4329.11	0.212466
$747$	32911.1	1.61199
$748$	6883.33	0.336470
$749$	0	0
$750$	7700.43	0.374907
$751$	39172.1	1.90334	0.951671	−	0.307119i	$-0.0993649\pi$
$751$	39172.1	1.90334	0.951671	+	0.307119i	$0.0993649\pi$
$752$	27862.4	1.35111
$753$	10655.6	0.515688
$754$	−799.528	−0.0386169
$755$	−1909.12	−0.0920263
$756$	0	0
$757$	5944.10	0.285392	0.142696	−	0.989767i	$-0.454423\pi$
$757$	5944.10	0.285392	0.142696	+	0.989767i	$0.454423\pi$
$758$	1448.12	0.0693904
$759$	−13822.5	−0.661033
$760$	−1794.58	−0.0856531
$761$	1954.89	0.0931205	0.0465603	−	0.998915i	$-0.485174\pi$
$761$	1954.89	0.0931205	0.0465603	+	0.998915i	$0.485174\pi$
$762$	17945.2	0.853130
$763$	0	0
$764$	807.367	0.0382324
$765$	−1843.15	−0.0871102
$766$	30029.5	1.41646
$767$	−2241.21	−0.105509
$768$	−20541.7	−0.965152
$769$	39312.9	1.84351	0.921756	−	0.387770i	$-0.126755\pi$
$769$	39312.9	1.84351	0.921756	+	0.387770i	$0.126755\pi$
$770$	0	0
$771$	4884.03	0.228138
$772$	−6104.26	−0.284582
$773$	5102.38	0.237413	0.118706	−	0.992929i	$-0.462125\pi$
$773$	5102.38	0.237413	0.118706	+	0.992929i	$0.462125\pi$
$774$	3389.64	0.157414
$775$	22835.0	1.05840
$776$	−18403.5	−0.851349
$777$	0	0
$778$	−17813.1	−0.820862
$779$	20364.8	0.936641
$780$	372.486	0.0170989
$781$	−60022.7	−2.75004
$782$	−5057.26	−0.231262
$783$	191.813	0.00875460
$784$	0	0
$785$	4000.07	0.181871
$786$	−42635.3	−1.93480
$787$	−21898.3	−0.991855	−0.495928	−	0.868364i	$-0.665172\pi$
$787$	−21898.3	−0.991855	−0.495928	+	0.868364i	$0.665172\pi$
$788$	3850.30	0.174062
$789$	55897.3	2.52218
$790$	−2669.59	−0.120227
$791$	0	0
$792$	30818.8	1.38270
$793$	−4223.73	−0.189141
$794$	−43612.3	−1.94930
$795$	6960.96	0.310541
$796$	−895.809	−0.0398883
$797$	−18262.4	−0.811652	−0.405826	−	0.913950i	$-0.633016\pi$
$797$	−18262.4	−0.811652	−0.405826	+	0.913950i	$0.633016\pi$
$798$	0	0
$799$	−19879.8	−0.880220
$800$	−10713.6	−0.473479
$801$	−12718.8	−0.561043
$802$	−11188.2	−0.492604
$803$	−29525.5	−1.29755
$804$	1884.45	0.0826610
$805$	0	0
$806$	11293.8	0.493559
$807$	−2169.73	−0.0946444
$808$	28615.0	1.24588
$809$	26097.8	1.13418	0.567089	−	0.823656i	$-0.308069\pi$
$809$	26097.8	1.13418	0.567089	+	0.823656i	$0.308069\pi$
$810$	−3355.89	−0.145573
$811$	−1067.58	−0.0462243	−0.0231122	−	0.999733i	$-0.507357\pi$
$811$	−1067.58	−0.0462243	−0.0231122	+	0.999733i	$0.507357\pi$
$812$	0	0
$813$	−15689.7	−0.676830
$814$	75632.8	3.25667
$815$	226.663	0.00974190
$816$	29596.0	1.26969
$817$	−2969.84	−0.127174
$818$	−8639.05	−0.369263
$819$	0	0
$820$	−789.596	−0.0336267
$821$	−20127.0	−0.855585	−0.427793	−	0.903877i	$-0.640709\pi$
$821$	−20127.0	−0.855585	−0.427793	+	0.903877i	$0.640709\pi$
$822$	−42332.7	−1.79626
$823$	−3011.70	−0.127559	−0.0637797	−	0.997964i	$-0.520315\pi$
$823$	−3011.70	−0.127559	−0.0637797	+	0.997964i	$0.520315\pi$
$824$	−25010.1	−1.05736
$825$	57497.5	2.42643
$826$	0	0
$827$	−13138.4	−0.552437	−0.276219	−	0.961095i	$-0.589081\pi$
$827$	−13138.4	−0.552437	−0.276219	+	0.961095i	$0.589081\pi$
$828$	1451.73	0.0609311
$829$	−19550.4	−0.819075	−0.409538	−	0.912293i	$-0.634310\pi$
$829$	−19550.4	−0.819075	−0.409538	+	0.912293i	$0.634310\pi$
$830$	5672.77	0.237235
$831$	−21250.2	−0.887079
$832$	6409.57	0.267082
$833$	0	0
$834$	64229.8	2.66678
$835$	2922.98	0.121142
$836$	8784.05	0.363400
$837$	−2709.48	−0.111892
$838$	29294.7	1.20760
$839$	−3227.69	−0.132816	−0.0664078	−	0.997793i	$-0.521154\pi$
$839$	−3227.69	−0.132816	−0.0664078	+	0.997793i	$0.521154\pi$
$840$	0	0
$841$	−24216.7	−0.992934
$842$	23067.9	0.944149
$843$	−3310.55	−0.135257
$844$	−3421.72	−0.139550
$845$	2488.38	0.101305
$846$	28955.4	1.17672
$847$	0	0
$848$	−53707.7	−2.17492
$849$	44631.5	1.80418
$850$	21036.7	0.848887
$851$	−10951.6	−0.441148
$852$	13119.5	0.527545
$853$	−12419.8	−0.498530	−0.249265	−	0.968435i	$-0.580189\pi$
$853$	−12419.8	−0.498530	−0.249265	+	0.968435i	$0.580189\pi$
$854$	0	0
$855$	−2352.11	−0.0940823
$856$	−11654.4	−0.465349
$857$	−18592.3	−0.741075	−0.370537	−	0.928818i	$-0.620826\pi$
$857$	−18592.3	−0.741075	−0.370537	+	0.928818i	$0.620826\pi$
$858$	28437.3	1.13151
$859$	−6443.09	−0.255920	−0.127960	−	0.991779i	$-0.540843\pi$
$859$	−6443.09	−0.255920	−0.127960	+	0.991779i	$0.540843\pi$
$860$	115.148	0.00456573
$861$	0	0
$862$	3009.78	0.118925
$863$	−22085.1	−0.871132	−0.435566	−	0.900157i	$-0.643452\pi$
$863$	−22085.1	−0.871132	−0.435566	+	0.900157i	$0.643452\pi$
$864$	1271.22	0.0500553
$865$	−162.304	−0.00637979
$866$	10880.6	0.426948
$867$	14302.3	0.560245
$868$	0	0
$869$	−40167.5	−1.56800
$870$	−407.391	−0.0158757
$871$	−2568.34	−0.0999139
$872$	−18037.5	−0.700491
$873$	−24120.9	−0.935131
$874$	−6453.73	−0.249772
$875$	0	0
$876$	6453.57	0.248911
$877$	39786.3	1.53191	0.765956	−	0.642893i	$-0.222266\pi$
$877$	39786.3	1.53191	0.765956	+	0.642893i	$0.222266\pi$
$878$	−29184.2	−1.12177
$879$	41049.1	1.57514
$880$	6699.64	0.256642
$881$	−38834.0	−1.48508	−0.742538	−	0.669804i	$-0.766378\pi$
$881$	−38834.0	−1.48508	−0.742538	+	0.669804i	$0.766378\pi$
$882$	0	0
$883$	−5483.65	−0.208992	−0.104496	−	0.994525i	$-0.533323\pi$
$883$	−5483.65	−0.208992	−0.104496	+	0.994525i	$0.533323\pi$
$884$	2050.55	0.0780175
$885$	−1141.99	−0.0433756
$886$	12265.5	0.465088
$887$	−21289.7	−0.805905	−0.402953	−	0.915221i	$-0.632016\pi$
$887$	−21289.7	−0.805905	−0.402953	+	0.915221i	$0.632016\pi$
$888$	50817.5	1.92041
$889$	0	0
$890$	−2192.29	−0.0825681
$891$	−50493.8	−1.89855
$892$	−6184.17	−0.232131
$893$	−25369.2	−0.950671
$894$	36758.2	1.37514
$895$	−3507.50	−0.130997
$896$	0	0
$897$	−4117.73	−0.153274
$898$	45495.3	1.69064
$899$	−2434.41	−0.0903140
$900$	−6038.76	−0.223658
$901$	38320.4	1.41691
$902$	−60281.5	−2.22523
$903$	0	0
$904$	40194.0	1.47880
$905$	1949.13	0.0715927
$906$	31857.7	1.16821
$907$	16875.4	0.617794	0.308897	−	0.951095i	$-0.400040\pi$
$907$	16875.4	0.617794	0.308897	+	0.951095i	$0.400040\pi$
$908$	−4139.51	−0.151293
$909$	37504.9	1.36849
$910$	0	0
$911$	17586.7	0.639597	0.319799	−	0.947486i	$-0.396385\pi$
$911$	17586.7	0.639597	0.319799	+	0.947486i	$0.396385\pi$
$912$	37768.4	1.37131
$913$	85354.4	3.09400
$914$	5571.94	0.201645
$915$	−2152.15	−0.0777574
$916$	−3003.77	−0.108349
$917$	0	0
$918$	−2496.11	−0.0897428
$919$	−43891.7	−1.57547	−0.787733	−	0.616017i	$-0.788745\pi$
$919$	−43891.7	−1.57547	−0.787733	+	0.616017i	$0.788745\pi$
$920$	−769.196	−0.0275648
$921$	−36826.1	−1.31755
$922$	24073.7	0.859898
$923$	−17880.8	−0.637653
$924$	0	0
$925$	45555.6	1.61931
$926$	18794.5	0.666984
$927$	−32779.9	−1.16142
$928$	1142.16	0.0404024
$929$	41161.8	1.45369	0.726844	−	0.686803i	$-0.240987\pi$
$929$	41161.8	1.45369	0.726844	+	0.686803i	$0.240987\pi$
$930$	5754.65	0.202906
$931$	0	0
$932$	5890.79	0.207038
$933$	−7556.08	−0.265139
$934$	484.175	0.0169622
$935$	−4780.18	−0.167197
$936$	9180.95	0.320608
$937$	−41754.1	−1.45576	−0.727880	−	0.685705i	$-0.759494\pi$
$937$	−41754.1	−1.45576	−0.727880	+	0.685705i	$0.759494\pi$
$938$	0	0
$939$	30855.0	1.07233
$940$	983.633	0.0341304
$941$	37587.5	1.30214	0.651071	−	0.759016i	$-0.274320\pi$
$941$	37587.5	1.30214	0.651071	+	0.759016i	$0.274320\pi$
$942$	−66749.8	−2.30873
$943$	8728.76	0.301429
$944$	8811.06	0.303788
$945$	0	0
$946$	8790.98	0.302135
$947$	−25689.0	−0.881500	−0.440750	−	0.897630i	$-0.645287\pi$
$947$	−25689.0	−0.881500	−0.440750	+	0.897630i	$0.645287\pi$
$948$	8779.67	0.300792
$949$	−8795.66	−0.300863
$950$	26845.7	0.916830
$951$	−42750.5	−1.45771
$952$	0	0
$953$	−10527.3	−0.357831	−0.178916	−	0.983864i	$-0.557259\pi$
$953$	−10527.3	−0.357831	−0.178916	+	0.983864i	$0.557259\pi$
$954$	−55814.5	−1.89419
$955$	−560.682	−0.0189982
$956$	6718.44	0.227291
$957$	−6129.75	−0.207050
$958$	−35777.2	−1.20659
$959$	0	0
$960$	3265.93	0.109799
$961$	4596.60	0.154295
$962$	22531.1	0.755126
$963$	−15275.1	−0.511144
$964$	8830.41	0.295029
$965$	4239.15	0.141413
$966$	0	0
$967$	4292.71	0.142755	0.0713776	−	0.997449i	$-0.477260\pi$
$967$	4292.71	0.142755	0.0713776	+	0.997449i	$0.477260\pi$
$968$	54567.5	1.81184
$969$	−26947.7	−0.893380
$970$	−4157.63	−0.137622
$971$	41459.8	1.37025	0.685123	−	0.728427i	$-0.259748\pi$
$971$	41459.8	1.37025	0.685123	+	0.728427i	$0.259748\pi$
$972$	10262.1	0.338638
$973$	0	0
$974$	8983.13	0.295522
$975$	17128.6	0.562618
$976$	16605.1	0.544585
$977$	3577.72	0.117156	0.0585779	−	0.998283i	$-0.481343\pi$
$977$	3577.72	0.117156	0.0585779	+	0.998283i	$0.481343\pi$
$978$	−3782.36	−0.123667
$979$	−32985.9	−1.07685
$980$	0	0
$981$	−23641.3	−0.769427
$982$	26344.2	0.856088
$983$	−50532.3	−1.63960	−0.819802	−	0.572647i	$-0.805917\pi$
$983$	−50532.3	−1.63960	−0.819802	+	0.572647i	$0.805917\pi$
$984$	−40503.0	−1.31218
$985$	−2673.87	−0.0864939
$986$	−2242.70	−0.0724363
$987$	0	0
$988$	2616.77	0.0842618
$989$	−1272.93	−0.0409271
$990$	6962.45	0.223516
$991$	46280.6	1.48350	0.741752	−	0.670674i	$-0.233995\pi$
$991$	46280.6	1.48350	0.741752	+	0.670674i	$0.233995\pi$
$992$	−16133.8	−0.516379
$993$	−3670.76	−0.117309
$994$	0	0
$995$	622.101	0.0198210
$996$	−18656.5	−0.593527
$997$	−53334.8	−1.69421	−0.847107	−	0.531423i	$-0.821658\pi$
$997$	−53334.8	−1.69421	−0.847107	+	0.531423i	$0.821658\pi$
$998$	−55526.9	−1.76119
$999$	−5405.39	−0.171190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2107.4.a.c.1.2		6
7.6	odd	2		43.4.a.b.1.2	✓	6
21.20	even	2		387.4.a.h.1.5		6
28.27	even	2		688.4.a.i.1.2		6
35.34	odd	2		1075.4.a.b.1.5		6
301.300	even	2		1849.4.a.c.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.2	✓	6	7.6	odd	2
387.4.a.h.1.5		6	21.20	even	2
688.4.a.i.1.2		6	28.27	even	2
1075.4.a.b.1.5		6	35.34	odd	2
1849.4.a.c.1.5		6	301.300	even	2
2107.4.a.c.1.2		6	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:	\( N \)	\(=\)	\( 2107 = 7^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2107.a (trivial)

\(f(q)\)	\(=\)	\(q-3.15653 q^{2} -7.20925 q^{3} +1.96369 q^{4} -1.36370 q^{5} +22.7562 q^{6} +19.0538 q^{8} +24.9733 q^{9} +O(q^{10})\)	\(q-3.15653 q^{2} -7.20925 q^{3} +1.96369 q^{4} -1.36370 q^{5} +22.7562 q^{6} +19.0538 q^{8} +24.9733 q^{9} +4.30455 q^{10} +64.7677 q^{11} -14.1567 q^{12} +19.2944 q^{13} +9.83123 q^{15} -75.8534 q^{16} +54.1213 q^{17} -78.8289 q^{18} +69.0659 q^{19} -2.67787 q^{20} -204.441 q^{22} +29.6031 q^{23} -137.364 q^{24} -123.140 q^{25} -60.9032 q^{26} +14.6112 q^{27} +13.1279 q^{29} -31.0326 q^{30} -185.439 q^{31} +87.0032 q^{32} -466.927 q^{33} -170.836 q^{34} +49.0397 q^{36} -369.949 q^{37} -218.009 q^{38} -139.098 q^{39} -25.9836 q^{40} +294.860 q^{41} -43.0000 q^{43} +127.183 q^{44} -34.0560 q^{45} -93.4431 q^{46} -367.319 q^{47} +546.846 q^{48} +388.696 q^{50} -390.174 q^{51} +37.8881 q^{52} +708.046 q^{53} -46.1207 q^{54} -88.3236 q^{55} -497.914 q^{57} -41.4385 q^{58} -116.159 q^{59} +19.3054 q^{60} -218.910 q^{61} +585.344 q^{62} +332.199 q^{64} -26.3116 q^{65} +1473.87 q^{66} -133.114 q^{67} +106.277 q^{68} -213.416 q^{69} -926.738 q^{71} +475.836 q^{72} -455.867 q^{73} +1167.75 q^{74} +887.749 q^{75} +135.624 q^{76} +439.067 q^{78} -620.178 q^{79} +103.441 q^{80} -779.614 q^{81} -930.734 q^{82} +1317.85 q^{83} -73.8050 q^{85} +135.731 q^{86} -94.6419 q^{87} +1234.07 q^{88} -509.295 q^{89} +107.499 q^{90} +58.1312 q^{92} +1336.88 q^{93} +1159.45 q^{94} -94.1850 q^{95} -627.228 q^{96} -965.870 q^{97} +1617.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 + 3 * q^6 + 54 * q^8 + 81 * q^9	\( 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9} - 57 q^{10} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 124 q^{15} - 54 q^{16} - 19 q^{17} - 81 q^{18} + 75 q^{19} - 135 q^{20} - 504 q^{22} + 131 q^{23} + 567 q^{24} + 105 q^{25} - 44 q^{26} - 238 q^{27} + 515 q^{29} - 396 q^{30} - 237 q^{31} + 558 q^{32} - 540 q^{33} + 107 q^{34} + 73 q^{36} + 269 q^{37} - 527 q^{38} + 290 q^{39} - 613 q^{40} - 471 q^{41} - 258 q^{43} - 428 q^{44} - 334 q^{45} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 1335 q^{50} - 1241 q^{51} + 8 q^{52} + 450 q^{53} - 402 q^{54} + 1732 q^{55} - 1000 q^{57} - 1055 q^{58} - 356 q^{59} - 2732 q^{60} + 1328 q^{61} - 1603 q^{62} + 466 q^{64} - 62 q^{65} - 156 q^{66} - 632 q^{67} - 571 q^{68} + 1130 q^{69} - 144 q^{71} + 567 q^{72} - 864 q^{73} + 1207 q^{74} + 2494 q^{75} - 1005 q^{76} + 2222 q^{78} - 1613 q^{79} - 2399 q^{80} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 84 q^{85} - 258 q^{86} - 449 q^{87} - 608 q^{88} - 3378 q^{89} - 930 q^{90} + 3491 q^{92} + 1879 q^{93} - 3197 q^{94} - 79 q^{95} + 591 q^{96} + 55 q^{97} - 1612 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 + 3 * q^6 + 54 * q^8 + 81 * q^9 - 57 * q^10 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 124 * q^15 - 54 * q^16 - 19 * q^17 - 81 * q^18 + 75 * q^19 - 135 * q^20 - 504 * q^22 + 131 * q^23 + 567 * q^24 + 105 * q^25 - 44 * q^26 - 238 * q^27 + 515 * q^29 - 396 * q^30 - 237 * q^31 + 558 * q^32 - 540 * q^33 + 107 * q^34 + 73 * q^36 + 269 * q^37 - 527 * q^38 + 290 * q^39 - 613 * q^40 - 471 * q^41 - 258 * q^43 - 428 * q^44 - 334 * q^45 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 1335 * q^50 - 1241 * q^51 + 8 * q^52 + 450 * q^53 - 402 * q^54 + 1732 * q^55 - 1000 * q^57 - 1055 * q^58 - 356 * q^59 - 2732 * q^60 + 1328 * q^61 - 1603 * q^62 + 466 * q^64 - 62 * q^65 - 156 * q^66 - 632 * q^67 - 571 * q^68 + 1130 * q^69 - 144 * q^71 + 567 * q^72 - 864 * q^73 + 1207 * q^74 + 2494 * q^75 - 1005 * q^76 + 2222 * q^78 - 1613 * q^79 - 2399 * q^80 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 84 * q^85 - 258 * q^86 - 449 * q^87 - 608 * q^88 - 3378 * q^89 - 930 * q^90 + 3491 * q^92 + 1879 * q^93 - 3197 * q^94 - 79 * q^95 + 591 * q^96 + 55 * q^97 - 1612 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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