LMFDB - Embedded newform 2107.4.a.c.1.6

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			1.6
Root			$-4.15251$ 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)

$f(q)$	$=$	$q+5.15251 q^{2} +6.49933 q^{3} +18.5484 q^{4} -17.2665 q^{5} +33.4879 q^{6} +54.3507 q^{8} +15.2413 q^{9} +O(q^{10})$	\(q+5.15251 q^{2} +6.49933 q^{3} +18.5484 q^{4} -17.2665 q^{5} +33.4879 q^{6} +54.3507 q^{8} +15.2413 q^{9} -88.9661 q^{10} -60.5580 q^{11} +120.552 q^{12} -10.9419 q^{13} -112.221 q^{15} +131.656 q^{16} +3.57473 q^{17} +78.5308 q^{18} -33.2403 q^{19} -320.267 q^{20} -312.026 q^{22} +63.7158 q^{23} +353.243 q^{24} +173.134 q^{25} -56.3783 q^{26} -76.4239 q^{27} -89.3510 q^{29} -578.220 q^{30} -222.839 q^{31} +243.552 q^{32} -393.586 q^{33} +18.4188 q^{34} +282.701 q^{36} -59.6535 q^{37} -171.271 q^{38} -71.1150 q^{39} -938.449 q^{40} +143.837 q^{41} -43.0000 q^{43} -1123.25 q^{44} -263.164 q^{45} +328.296 q^{46} -379.013 q^{47} +855.674 q^{48} +892.073 q^{50} +23.2334 q^{51} -202.955 q^{52} -150.129 q^{53} -393.775 q^{54} +1045.63 q^{55} -216.040 q^{57} -460.382 q^{58} -207.310 q^{59} -2081.52 q^{60} +486.557 q^{61} -1148.18 q^{62} +201.659 q^{64} +188.929 q^{65} -2027.96 q^{66} +1019.41 q^{67} +66.3055 q^{68} +414.110 q^{69} +13.8437 q^{71} +828.374 q^{72} -411.158 q^{73} -307.365 q^{74} +1125.25 q^{75} -616.555 q^{76} -366.421 q^{78} -1315.13 q^{79} -2273.24 q^{80} -908.218 q^{81} +741.120 q^{82} -813.425 q^{83} -61.7233 q^{85} -221.558 q^{86} -580.721 q^{87} -3291.37 q^{88} +350.573 q^{89} -1355.96 q^{90} +1181.83 q^{92} -1448.30 q^{93} -1952.87 q^{94} +573.946 q^{95} +1582.92 q^{96} +1187.03 q^{97} -922.981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.15251	1.82169	0.910844	−	0.412750i	$-0.135432\pi$
$2$	5.15251	1.82169	0.910844	+	0.412750i	$0.135432\pi$
$3$	6.49933	1.25080	0.625398	−	0.780306i	$-0.284937\pi$
$3$	6.49933	1.25080	0.625398	+	0.780306i	$0.284937\pi$
$4$	18.5484	2.31855
$5$	−17.2665	−1.54437	−0.772183	−	0.635400i	$-0.780835\pi$
$5$	−17.2665	−1.54437	−0.772183	+	0.635400i	$0.780835\pi$
$6$	33.4879	2.27856
$7$	0	0
$7$	0	0
$8$	54.3507	2.40199
$9$	15.2413	0.564491
$10$	−88.9661	−2.81336
$11$	−60.5580	−1.65990	−0.829951	−	0.557836i	$-0.811632\pi$
$11$	−60.5580	−1.65990	−0.829951	+	0.557836i	$0.811632\pi$
$12$	120.552	2.90003
$13$	−10.9419	−0.233441	−0.116721	−	0.993165i	$-0.537238\pi$
$13$	−10.9419	−0.233441	−0.116721	+	0.993165i	$0.537238\pi$
$14$	0	0
$15$	−112.221	−1.93169
$16$	131.656	2.05712
$17$	3.57473	0.0510000	0.0255000	−	0.999675i	$-0.491882\pi$
$17$	3.57473	0.0510000	0.0255000	+	0.999675i	$0.491882\pi$
$18$	78.5308	1.02833
$19$	−33.2403	−0.401361	−0.200680	−	0.979657i	$-0.564315\pi$
$19$	−33.2403	−0.401361	−0.200680	+	0.979657i	$0.564315\pi$
$20$	−320.267	−3.58069
$21$	0	0
$22$	−312.026	−3.02383
$23$	63.7158	0.577637	0.288819	−	0.957384i	$-0.406738\pi$
$23$	63.7158	0.577637	0.288819	+	0.957384i	$0.406738\pi$
$24$	353.243	3.00440
$25$	173.134	1.38507
$26$	−56.3783	−0.425257
$27$	−76.4239	−0.544733
$28$	0	0
$29$	−89.3510	−0.572140	−0.286070	−	0.958209i	$-0.592349\pi$
$29$	−89.3510	−0.572140	−0.286070	+	0.958209i	$0.592349\pi$
$30$	−578.220	−3.51893
$31$	−222.839	−1.29106	−0.645532	−	0.763733i	$-0.723364\pi$
$31$	−222.839	−1.29106	−0.645532	+	0.763733i	$0.723364\pi$
$32$	243.552	1.34545
$33$	−393.586	−2.07620
$34$	18.4188	0.0929061
$35$	0	0
$36$	282.701	1.30880
$37$	−59.6535	−0.265053	−0.132527	−	0.991179i	$-0.542309\pi$
$37$	−59.6535	−0.265053	−0.132527	+	0.991179i	$0.542309\pi$
$38$	−171.271	−0.731154
$39$	−71.1150	−0.291987
$40$	−938.449	−3.70955
$41$	143.837	0.547890	0.273945	−	0.961745i	$-0.411671\pi$
$41$	143.837	0.547890	0.273945	+	0.961745i	$0.411671\pi$
$42$	0	0
$43$	−43.0000	−0.152499
$43$	−43.0000	−0.152499
$44$	−1123.25	−3.84857
$45$	−263.164	−0.871782
$46$	328.296	1.05228
$47$	−379.013	−1.17627	−0.588135	−	0.808763i	$-0.700138\pi$
$47$	−379.013	−1.17627	−0.588135	+	0.808763i	$0.700138\pi$
$48$	855.674	2.57304
$49$	0	0
$50$	892.073	2.52316
$51$	23.2334	0.0637906
$52$	−202.955	−0.541245
$53$	−150.129	−0.389090	−0.194545	−	0.980894i	$-0.562323\pi$
$53$	−150.129	−0.389090	−0.194545	+	0.980894i	$0.562323\pi$
$54$	−393.775	−0.992333
$55$	1045.63	2.56350
$56$	0	0
$57$	−216.040	−0.502021
$58$	−460.382	−1.04226
$59$	−207.310	−0.457448	−0.228724	−	0.973491i	$-0.573455\pi$
$59$	−207.310	−0.457448	−0.228724	+	0.973491i	$0.573455\pi$
$60$	−2081.52	−4.47871
$61$	486.557	1.02127	0.510633	−	0.859799i	$-0.329411\pi$
$61$	486.557	1.02127	0.510633	+	0.859799i	$0.329411\pi$
$62$	−1148.18	−2.35192
$63$	0	0
$64$	201.659	0.393866
$65$	188.929	0.360519
$66$	−2027.96	−3.78219
$67$	1019.41	1.85882	0.929408	−	0.369054i	$-0.120318\pi$
$67$	1019.41	1.85882	0.929408	+	0.369054i	$0.120318\pi$
$68$	66.3055	0.118246
$69$	414.110	0.722507
$70$	0	0
$71$	13.8437	0.0231400	0.0115700	−	0.999933i	$-0.496317\pi$
$71$	13.8437	0.0231400	0.0115700	+	0.999933i	$0.496317\pi$
$72$	828.374	1.35590
$73$	−411.158	−0.659211	−0.329605	−	0.944119i	$-0.606916\pi$
$73$	−411.158	−0.659211	−0.329605	+	0.944119i	$0.606916\pi$
$74$	−307.365	−0.482844
$75$	1125.25	1.73244
$76$	−616.555	−0.930575
$77$	0	0
$78$	−366.421	−0.531910
$79$	−1315.13	−1.87296	−0.936481	−	0.350718i	$-0.885938\pi$
$79$	−1315.13	−1.87296	−0.936481	+	0.350718i	$0.885938\pi$
$80$	−2273.24	−3.17695
$81$	−908.218	−1.24584
$82$	741.120	0.998085
$83$	−813.425	−1.07572	−0.537861	−	0.843033i	$-0.680768\pi$
$83$	−813.425	−1.07572	−0.537861	+	0.843033i	$0.680768\pi$
$84$	0	0
$85$	−61.7233	−0.0787627
$86$	−221.558	−0.277805
$87$	−580.721	−0.715630
$88$	−3291.37	−3.98706
$89$	350.573	0.417535	0.208768	−	0.977965i	$-0.433055\pi$
$89$	350.573	0.417535	0.208768	+	0.977965i	$0.433055\pi$
$90$	−1355.96	−1.58811
$91$	0	0
$92$	1181.83	1.33928
$93$	−1448.30	−1.61486
$94$	−1952.87	−2.14280
$95$	573.946	0.619848
$96$	1582.92	1.68288
$97$	1187.03	1.24252	0.621262	−	0.783603i	$-0.286620\pi$
$97$	1187.03	1.24252	0.621262	+	0.783603i	$0.286620\pi$
$98$	0	0
$99$	−922.981	−0.937001
$100$	3211.35	3.21135
$101$	−469.014	−0.462066	−0.231033	−	0.972946i	$-0.574210\pi$
$101$	−469.014	−0.462066	−0.231033	+	0.972946i	$0.574210\pi$
$102$	119.710	0.116207
$103$	1299.82	1.24345	0.621725	−	0.783235i	$-0.286432\pi$
$103$	1299.82	1.24345	0.621725	+	0.783235i	$0.286432\pi$
$104$	−594.700	−0.560722
$105$	0	0
$106$	−773.541	−0.708801
$107$	−1480.92	−1.33800	−0.669000	−	0.743263i	$-0.733277\pi$
$107$	−1480.92	−1.33800	−0.669000	+	0.743263i	$0.733277\pi$
$108$	−1417.54	−1.26299
$109$	350.586	0.308073	0.154037	−	0.988065i	$-0.450773\pi$
$109$	350.586	0.308073	0.154037	+	0.988065i	$0.450773\pi$
$110$	5387.61	4.66990
$111$	−387.707	−0.331528
$112$	0	0
$113$	785.106	0.653598	0.326799	−	0.945094i	$-0.394030\pi$
$113$	785.106	0.653598	0.326799	+	0.945094i	$0.394030\pi$
$114$	−1113.15	−0.914525
$115$	−1100.15	−0.892084
$116$	−1657.32	−1.32653
$117$	−166.768	−0.131776
$118$	−1068.17	−0.833329
$119$	0	0
$120$	−6099.29	−4.63989
$121$	2336.27	1.75528
$122$	2506.99	1.86043
$123$	934.841	0.685299
$124$	−4133.30	−2.99340
$125$	−831.100	−0.594687
$126$	0	0
$127$	−731.562	−0.511147	−0.255573	−	0.966790i	$-0.582264\pi$
$127$	−731.562	−0.511147	−0.255573	+	0.966790i	$0.582264\pi$
$128$	−909.364	−0.627947
$129$	−279.471	−0.190745
$130$	973.458	0.656753
$131$	−2462.56	−1.64240	−0.821202	−	0.570638i	$-0.806696\pi$
$131$	−2462.56	−1.64240	−0.821202	+	0.570638i	$0.806696\pi$
$132$	−7300.40	−4.81377
$133$	0	0
$134$	5252.52	3.38618
$135$	1319.58	0.841267
$136$	194.289	0.122501
$137$	2384.64	1.48710	0.743552	−	0.668678i	$-0.233139\pi$
$137$	2384.64	1.48710	0.743552	+	0.668678i	$0.233139\pi$
$138$	2133.71	1.31618
$139$	3086.87	1.88363	0.941816	−	0.336129i	$-0.109118\pi$
$139$	3086.87	1.88363	0.941816	+	0.336129i	$0.109118\pi$
$140$	0	0
$141$	−2463.33	−1.47127
$142$	71.3297	0.0421539
$143$	662.619	0.387490
$144$	2006.60	1.16123
$145$	1542.78	0.883594
$146$	−2118.50	−1.20088
$147$	0	0
$148$	−1106.48	−0.614539
$149$	−1445.58	−0.794808	−0.397404	−	0.917644i	$-0.630089\pi$
$149$	−1445.58	−0.794808	−0.397404	+	0.917644i	$0.630089\pi$
$150$	5797.88	3.15596
$151$	−825.878	−0.445093	−0.222546	−	0.974922i	$-0.571437\pi$
$151$	−825.878	−0.445093	−0.222546	+	0.974922i	$0.571437\pi$
$152$	−1806.64	−0.964063
$153$	54.4834	0.0287891
$154$	0	0
$155$	3847.65	1.99388
$156$	−1319.07	−0.676987
$157$	−1187.82	−0.603809	−0.301904	−	0.953338i	$-0.597622\pi$
$157$	−1187.82	−0.603809	−0.301904	+	0.953338i	$0.597622\pi$
$158$	−6776.24	−3.41195
$159$	−975.737	−0.486673
$160$	−4205.30	−2.07786
$161$	0	0
$162$	−4679.61	−2.26953
$163$	1514.60	0.727809	0.363904	−	0.931436i	$-0.381443\pi$
$163$	1514.60	0.727809	0.363904	+	0.931436i	$0.381443\pi$
$164$	2667.94	1.27031
$165$	6795.88	3.20641
$166$	−4191.18	−1.95963
$167$	3354.48	1.55435	0.777177	−	0.629282i	$-0.216651\pi$
$167$	3354.48	1.55435	0.777177	+	0.629282i	$0.216651\pi$
$168$	0	0
$169$	−2077.27	−0.945505
$170$	−318.030	−0.143481
$171$	−506.625	−0.226565
$172$	−797.581	−0.353575
$173$	−1654.64	−0.727166	−0.363583	−	0.931562i	$-0.618447\pi$
$173$	−1654.64	−0.727166	−0.363583	+	0.931562i	$0.618447\pi$
$174$	−2992.17	−1.30366
$175$	0	0
$176$	−7972.81	−3.41462
$177$	−1347.38	−0.572175
$178$	1806.33	0.760619
$179$	−1334.05	−0.557049	−0.278524	−	0.960429i	$-0.589845\pi$
$179$	−1334.05	−0.557049	−0.278524	+	0.960429i	$0.589845\pi$
$180$	−4881.27	−2.02127
$181$	−2771.58	−1.13817	−0.569087	−	0.822277i	$-0.692703\pi$
$181$	−2771.58	−1.13817	−0.569087	+	0.822277i	$0.692703\pi$
$182$	0	0
$183$	3162.29	1.27740
$184$	3463.00	1.38748
$185$	1030.01	0.409339
$186$	−7462.39	−2.94177
$187$	−216.479	−0.0846550
$188$	−7030.08	−2.72724
$189$	0	0
$190$	2957.26	1.12917
$191$	81.5135	0.0308802	0.0154401	−	0.999881i	$-0.495085\pi$
$191$	81.5135	0.0308802	0.0154401	+	0.999881i	$0.495085\pi$
$192$	1310.65	0.492646
$193$	3305.29	1.23275	0.616373	−	0.787454i	$-0.288601\pi$
$193$	3305.29	1.23275	0.616373	+	0.787454i	$0.288601\pi$
$194$	6116.20	2.26349
$195$	1227.91	0.450936
$196$	0	0
$197$	2241.99	0.810840	0.405420	−	0.914131i	$-0.367125\pi$
$197$	2241.99	0.810840	0.405420	+	0.914131i	$0.367125\pi$
$198$	−4755.67	−1.70692
$199$	4074.29	1.45135	0.725675	−	0.688037i	$-0.241528\pi$
$199$	4074.29	1.45135	0.725675	+	0.688037i	$0.241528\pi$
$200$	9409.94	3.32691
$201$	6625.48	2.32500
$202$	−2416.60	−0.841740
$203$	0	0
$204$	430.941	0.147902
$205$	−2483.56	−0.846143
$206$	6697.36	2.26518
$207$	971.109	0.326071
$208$	−1440.56	−0.480217
$209$	2012.97	0.666220
$210$	0	0
$211$	4267.62	1.39239	0.696196	−	0.717851i	$-0.254874\pi$
$211$	4267.62	1.39239	0.696196	+	0.717851i	$0.254874\pi$
$212$	−2784.65	−0.902125
$213$	89.9746	0.0289435
$214$	−7630.46	−2.43742
$215$	742.461	0.235514
$216$	−4153.69	−1.30844
$217$	0	0
$218$	1806.40	0.561214
$219$	−2672.25	−0.824538
$220$	19394.7	5.94360
$221$	−39.1143	−0.0119055
$222$	−1997.67	−0.603940
$223$	889.370	0.267070	0.133535	−	0.991044i	$-0.457367\pi$
$223$	889.370	0.267070	0.133535	+	0.991044i	$0.457367\pi$
$224$	0	0
$225$	2638.78	0.781859
$226$	4045.27	1.19065
$227$	−232.389	−0.0679479	−0.0339739	−	0.999423i	$-0.510816\pi$
$227$	−232.389	−0.0679479	−0.0339739	+	0.999423i	$0.510816\pi$
$228$	−4007.19	−1.16396
$229$	−851.806	−0.245803	−0.122902	−	0.992419i	$-0.539220\pi$
$229$	−851.806	−0.245803	−0.122902	+	0.992419i	$0.539220\pi$
$230$	−5668.54	−1.62510
$231$	0	0
$232$	−4856.29	−1.37427
$233$	−2083.62	−0.585848	−0.292924	−	0.956136i	$-0.594628\pi$
$233$	−2083.62	−0.585848	−0.292924	+	0.956136i	$0.594628\pi$
$234$	−859.276	−0.240054
$235$	6544.24	1.81659
$236$	−3845.27	−1.06062
$237$	−8547.48	−2.34269
$238$	0	0
$239$	986.983	0.267124	0.133562	−	0.991040i	$-0.457358\pi$
$239$	986.983	0.267124	0.133562	+	0.991040i	$0.457358\pi$
$240$	−14774.5	−3.97372
$241$	−14.8772	−0.00397644	−0.00198822	−	0.999998i	$-0.500633\pi$
$241$	−14.8772	−0.00397644	−0.00198822	+	0.999998i	$0.500633\pi$
$242$	12037.7	3.19757
$243$	−3839.36	−1.01356
$244$	9024.85	2.36786
$245$	0	0
$246$	4816.78	1.24840
$247$	363.712	0.0936942
$248$	−12111.4	−3.10112
$249$	−5286.72	−1.34551
$250$	−4282.26	−1.08333
$251$	3027.27	0.761274	0.380637	−	0.924725i	$-0.375705\pi$
$251$	3027.27	0.761274	0.380637	+	0.924725i	$0.375705\pi$
$252$	0	0
$253$	−3858.50	−0.958822
$254$	−3769.38	−0.931150
$255$	−401.160	−0.0985161
$256$	−6298.79	−1.53779
$257$	−5759.92	−1.39803	−0.699016	−	0.715106i	$-0.746378\pi$
$257$	−5759.92	−1.39803	−0.699016	+	0.715106i	$0.746378\pi$
$258$	−1439.98	−0.347477
$259$	0	0
$260$	3504.32	0.835881
$261$	−1361.82	−0.322968
$262$	−12688.4	−2.99195
$263$	2545.09	0.596719	0.298359	−	0.954454i	$-0.403561\pi$
$263$	2545.09	0.596719	0.298359	+	0.954454i	$0.403561\pi$
$264$	−21391.7	−4.98700
$265$	2592.21	0.600898
$266$	0	0
$267$	2278.49	0.522252
$268$	18908.4	4.30976
$269$	−6757.89	−1.53173	−0.765866	−	0.643001i	$-0.777689\pi$
$269$	−6757.89	−1.53173	−0.765866	+	0.643001i	$0.777689\pi$
$270$	6799.13	1.53253
$271$	−2485.54	−0.557143	−0.278571	−	0.960415i	$-0.589861\pi$
$271$	−2485.54	−0.557143	−0.278571	+	0.960415i	$0.589861\pi$
$272$	470.634	0.104913
$273$	0	0
$274$	12286.9	2.70904
$275$	−10484.6	−2.29908
$276$	7681.07	1.67517
$277$	−2090.19	−0.453385	−0.226692	−	0.973966i	$-0.572791\pi$
$277$	−2090.19	−0.453385	−0.226692	+	0.973966i	$0.572791\pi$
$278$	15905.1	3.43139
$279$	−3396.34	−0.728795
$280$	0	0
$281$	−6049.22	−1.28422	−0.642111	−	0.766612i	$-0.721941\pi$
$281$	−6049.22	−1.28422	−0.642111	+	0.766612i	$0.721941\pi$
$282$	−12692.3	−2.68020
$283$	650.183	0.136570	0.0682851	−	0.997666i	$-0.478247\pi$
$283$	650.183	0.136570	0.0682851	+	0.997666i	$0.478247\pi$
$284$	256.778	0.0536513
$285$	3730.26	0.775304
$286$	3414.16	0.705885
$287$	0	0
$288$	3712.04	0.759494
$289$	−4900.22	−0.997399
$290$	7949.21	1.60963
$291$	7714.92	1.55415
$292$	−7626.31	−1.52841
$293$	2172.20	0.433110	0.216555	−	0.976270i	$-0.430518\pi$
$293$	2172.20	0.433110	0.216555	+	0.976270i	$0.430518\pi$
$294$	0	0
$295$	3579.53	0.706468
$296$	−3242.21	−0.636654
$297$	4628.08	0.904203
$298$	−7448.36	−1.44789
$299$	−697.171	−0.134844
$300$	20871.6	4.01674
$301$	0	0
$302$	−4255.35	−0.810820
$303$	−3048.28	−0.577950
$304$	−4376.28	−0.825648
$305$	−8401.16	−1.57721
$306$	280.727	0.0524447
$307$	−1257.47	−0.233771	−0.116885	−	0.993145i	$-0.537291\pi$
$307$	−1257.47	−0.233771	−0.116885	+	0.993145i	$0.537291\pi$
$308$	0	0
$309$	8447.98	1.55530
$310$	19825.1	3.63222
$311$	1316.02	0.239950	0.119975	−	0.992777i	$-0.461719\pi$
$311$	1316.02	0.239950	0.119975	+	0.992777i	$0.461719\pi$
$312$	−3865.15	−0.701350
$313$	−3137.09	−0.566514	−0.283257	−	0.959044i	$-0.591415\pi$
$313$	−3137.09	−0.566514	−0.283257	+	0.959044i	$0.591415\pi$
$314$	−6120.24	−1.09995
$315$	0	0
$316$	−24393.6	−4.34256
$317$	571.518	0.101261	0.0506303	−	0.998717i	$-0.483877\pi$
$317$	571.518	0.101261	0.0506303	+	0.998717i	$0.483877\pi$
$318$	−5027.50	−0.886566
$319$	5410.92	0.949696
$320$	−3481.96	−0.608273
$321$	−9624.99	−1.67356
$322$	0	0
$323$	−118.825	−0.0204694
$324$	−16846.0	−2.88854
$325$	−1894.41	−0.323332
$326$	7804.01	1.32584
$327$	2278.57	0.385337
$328$	7817.62	1.31602
$329$	0	0
$330$	35015.8	5.84109
$331$	−2257.30	−0.374841	−0.187420	−	0.982280i	$-0.560013\pi$
$331$	−2257.30	−0.374841	−0.187420	+	0.982280i	$0.560013\pi$
$332$	−15087.7	−2.49412
$333$	−909.194	−0.149620
$334$	17284.0	2.83155
$335$	−17601.7	−2.87069
$336$	0	0
$337$	−9222.66	−1.49077	−0.745386	−	0.666633i	$-0.767735\pi$
$337$	−9222.66	−1.49077	−0.745386	+	0.666633i	$0.767735\pi$
$338$	−10703.2	−1.72242
$339$	5102.66	0.817517
$340$	−1144.87	−0.182615
$341$	13494.7	2.14304
$342$	−2610.39	−0.412730
$343$	0	0
$344$	−2337.08	−0.366299
$345$	−7150.24	−1.11582
$346$	−8525.54	−1.32467
$347$	8840.48	1.36767	0.683835	−	0.729636i	$-0.260311\pi$
$347$	8840.48	1.36767	0.683835	+	0.729636i	$0.260311\pi$
$348$	−10771.4	−1.65922
$349$	−1431.64	−0.219581	−0.109791	−	0.993955i	$-0.535018\pi$
$349$	−1431.64	−0.219581	−0.109791	+	0.993955i	$0.535018\pi$
$350$	0	0
$351$	836.222	0.127163
$352$	−14749.0	−2.23331
$353$	8308.06	1.25267	0.626336	−	0.779553i	$-0.284554\pi$
$353$	8308.06	1.25267	0.626336	+	0.779553i	$0.284554\pi$
$354$	−6942.37	−1.04232
$355$	−239.032	−0.0357367
$356$	6502.56	0.968076
$357$	0	0
$358$	−6873.72	−1.01477
$359$	11642.2	1.71157	0.855786	−	0.517330i	$-0.173074\pi$
$359$	11642.2	1.71157	0.855786	+	0.517330i	$0.173074\pi$
$360$	−14303.2	−2.09401
$361$	−5754.08	−0.838909
$362$	−14280.6	−2.07340
$363$	15184.2	2.19549
$364$	0	0
$365$	7099.27	1.01806
$366$	16293.8	2.32702
$367$	−4373.93	−0.622119	−0.311059	−	0.950391i	$-0.600684\pi$
$367$	−4373.93	−0.622119	−0.311059	+	0.950391i	$0.600684\pi$
$368$	8388.55	1.18827
$369$	2192.25	0.309279
$370$	5307.14	0.745689
$371$	0	0
$372$	−26863.7	−3.74413
$373$	7970.63	1.10644	0.553222	−	0.833034i	$-0.313398\pi$
$373$	7970.63	1.10644	0.553222	+	0.833034i	$0.313398\pi$
$374$	−1115.41	−0.154215
$375$	−5401.59	−0.743832
$376$	−20599.6	−2.82538
$377$	977.669	0.133561
$378$	0	0
$379$	−2020.56	−0.273850	−0.136925	−	0.990581i	$-0.543722\pi$
$379$	−2020.56	−0.273850	−0.136925	+	0.990581i	$0.543722\pi$
$380$	10645.8	1.43715
$381$	−4754.66	−0.639340
$382$	420.000	0.0562540
$383$	−11625.0	−1.55094	−0.775468	−	0.631386i	$-0.782486\pi$
$383$	−11625.0	−1.55094	−0.775468	+	0.631386i	$0.782486\pi$
$384$	−5910.26	−0.785434
$385$	0	0
$386$	17030.5	2.24568
$387$	−655.375	−0.0860841
$388$	22017.6	2.88086
$389$	6212.26	0.809702	0.404851	−	0.914383i	$-0.367323\pi$
$389$	6212.26	0.809702	0.404851	+	0.914383i	$0.367323\pi$
$390$	6326.82	0.821464
$391$	227.767	0.0294595
$392$	0	0
$393$	−16005.0	−2.05431
$394$	11551.9	1.47710
$395$	22707.8	2.89254
$396$	−17119.8	−2.17248
$397$	1647.75	0.208307	0.104154	−	0.994561i	$-0.466787\pi$
$397$	1647.75	0.208307	0.104154	+	0.994561i	$0.466787\pi$
$398$	20992.8	2.64391
$399$	0	0
$400$	22794.0	2.84925
$401$	6893.37	0.858450	0.429225	−	0.903198i	$-0.358787\pi$
$401$	6893.37	0.858450	0.429225	+	0.903198i	$0.358787\pi$
$402$	34137.8	4.23543
$403$	2438.28	0.301388
$404$	−8699.46	−1.07132
$405$	15681.8	1.92404
$406$	0	0
$407$	3612.49	0.439962
$408$	1262.75	0.153224
$409$	2962.23	0.358125	0.179062	−	0.983838i	$-0.442694\pi$
$409$	2962.23	0.358125	0.179062	+	0.983838i	$0.442694\pi$
$410$	−12796.6	−1.54141
$411$	15498.5	1.86006
$412$	24109.6	2.88300
$413$	0	0
$414$	5003.65	0.594000
$415$	14045.0	1.66131
$416$	−2664.92	−0.314083
$417$	20062.6	2.35604
$418$	10371.8	1.21365
$419$	5520.25	0.643633	0.321816	−	0.946802i	$-0.395707\pi$
$419$	5520.25	0.643633	0.321816	+	0.946802i	$0.395707\pi$
$420$	0	0
$421$	11017.9	1.27548	0.637742	−	0.770250i	$-0.279868\pi$
$421$	11017.9	1.27548	0.637742	+	0.770250i	$0.279868\pi$
$422$	21989.0	2.53651
$423$	−5776.63	−0.663994
$424$	−8159.61	−0.934589
$425$	618.906	0.0706385
$426$	463.595	0.0527260
$427$	0	0
$428$	−27468.7	−3.10222
$429$	4306.58	0.484671
$430$	3825.54	0.429033
$431$	8825.55	0.986338	0.493169	−	0.869934i	$-0.335838\pi$
$431$	8825.55	0.986338	0.493169	+	0.869934i	$0.335838\pi$
$432$	−10061.6	−1.12058
$433$	−4570.88	−0.507303	−0.253652	−	0.967296i	$-0.581632\pi$
$433$	−4570.88	−0.507303	−0.253652	+	0.967296i	$0.581632\pi$
$434$	0	0
$435$	10027.0	1.10520
$436$	6502.80	0.714283
$437$	−2117.93	−0.231841
$438$	−13768.8	−1.50205
$439$	3059.73	0.332649	0.166325	−	0.986071i	$-0.446810\pi$
$439$	3059.73	0.332649	0.166325	+	0.986071i	$0.446810\pi$
$440$	56830.6	6.15749
$441$	0	0
$442$	−201.537	−0.0216881
$443$	−2764.55	−0.296496	−0.148248	−	0.988950i	$-0.547363\pi$
$443$	−2764.55	−0.296496	−0.148248	+	0.988950i	$0.547363\pi$
$444$	−7191.35	−0.768663
$445$	−6053.18	−0.644828
$446$	4582.49	0.486518
$447$	−9395.29	−0.994143
$448$	0	0
$449$	7567.33	0.795377	0.397688	−	0.917521i	$-0.369812\pi$
$449$	7567.33	0.795377	0.397688	+	0.917521i	$0.369812\pi$
$450$	13596.3	1.42430
$451$	−8710.46	−0.909444
$452$	14562.4	1.51540
$453$	−5367.65	−0.556720
$454$	−1197.38	−0.123780
$455$	0	0
$456$	−11741.9	−1.20585
$457$	−8079.05	−0.826963	−0.413482	−	0.910512i	$-0.635687\pi$
$457$	−8079.05	−0.826963	−0.413482	+	0.910512i	$0.635687\pi$
$458$	−4388.94	−0.447777
$459$	−273.195	−0.0277813
$460$	−20406.0	−2.06834
$461$	−14466.4	−1.46154	−0.730770	−	0.682624i	$-0.760839\pi$
$461$	−14466.4	−1.46154	−0.730770	+	0.682624i	$0.760839\pi$
$462$	0	0
$463$	−7966.79	−0.799672	−0.399836	−	0.916587i	$-0.630933\pi$
$463$	−7966.79	−0.799672	−0.399836	+	0.916587i	$0.630933\pi$
$464$	−11763.6	−1.17696
$465$	25007.2	2.49393
$466$	−10735.9	−1.06723
$467$	−6737.29	−0.667590	−0.333795	−	0.942646i	$-0.608329\pi$
$467$	−6737.29	−0.667590	−0.333795	+	0.942646i	$0.608329\pi$
$468$	−3093.29	−0.305528
$469$	0	0
$470$	33719.3	3.30927
$471$	−7720.00	−0.755242
$472$	−11267.4	−1.09878
$473$	2603.99	0.253133
$474$	−44041.0	−4.26766
$475$	−5755.02	−0.555912
$476$	0	0
$477$	−2288.15	−0.219638
$478$	5085.44	0.486616
$479$	18115.7	1.72803	0.864014	−	0.503468i	$-0.167943\pi$
$479$	18115.7	1.72803	0.864014	+	0.503468i	$0.167943\pi$
$480$	−27331.6	−2.59899
$481$	652.722	0.0618743
$482$	−76.6548	−0.00724384
$483$	0	0
$484$	43334.1	4.06969
$485$	−20496.0	−1.91891
$486$	−19782.4	−1.84639
$487$	−14966.4	−1.39260	−0.696298	−	0.717753i	$-0.745171\pi$
$487$	−14966.4	−1.39260	−0.696298	+	0.717753i	$0.745171\pi$
$488$	26444.7	2.45307
$489$	9843.90	0.910341
$490$	0	0
$491$	−15713.8	−1.44430	−0.722151	−	0.691736i	$-0.756846\pi$
$491$	−15713.8	−1.44430	−0.722151	+	0.691736i	$0.756846\pi$
$492$	17339.8	1.58890
$493$	−319.406	−0.0291791
$494$	1874.03	0.170682
$495$	15936.7	1.44707
$496$	−29338.0	−2.65588
$497$	0	0
$498$	−27239.9	−2.45110
$499$	−15391.5	−1.38080	−0.690398	−	0.723430i	$-0.742565\pi$
$499$	−15391.5	−1.38080	−0.690398	+	0.723430i	$0.742565\pi$
$500$	−15415.6	−1.37881
$501$	21801.8	1.94418
$502$	15598.1	1.38680
$503$	12150.9	1.07710	0.538548	−	0.842595i	$-0.318973\pi$
$503$	12150.9	1.07710	0.538548	+	0.842595i	$0.318973\pi$
$504$	0	0
$505$	8098.25	0.713599
$506$	−19881.0	−1.74667
$507$	−13500.9	−1.18263
$508$	−13569.3	−1.18512
$509$	−16646.6	−1.44960	−0.724799	−	0.688960i	$-0.758067\pi$
$509$	−16646.6	−1.44960	−0.724799	+	0.688960i	$0.758067\pi$
$510$	−2066.98	−0.179466
$511$	0	0
$512$	−25179.7	−2.17343
$513$	2540.35	0.218634
$514$	−29678.1	−2.54678
$515$	−22443.5	−1.92034
$516$	−5183.74	−0.442251
$517$	22952.3	1.95249
$518$	0	0
$519$	−10754.0	−0.909536
$520$	10268.4	0.865961
$521$	−16675.9	−1.40227	−0.701135	−	0.713028i	$-0.747323\pi$
$521$	−16675.9	−1.40227	−0.701135	+	0.713028i	$0.747323\pi$
$522$	−7016.81	−0.588347
$523$	−14326.5	−1.19781	−0.598903	−	0.800821i	$-0.704397\pi$
$523$	−14326.5	−1.19781	−0.598903	+	0.800821i	$0.704397\pi$
$524$	−45676.5	−3.80799
$525$	0	0
$526$	13113.6	1.08704
$527$	−796.588	−0.0658443
$528$	−51817.9	−4.27099
$529$	−8107.30	−0.666335
$530$	13356.4	1.09465
$531$	−3159.67	−0.258226
$532$	0	0
$533$	−1573.84	−0.127900
$534$	11739.9	0.951380
$535$	25570.4	2.06636
$536$	55405.6	4.46485
$537$	−8670.44	−0.696754
$538$	−34820.1	−2.79034
$539$	0	0
$540$	24476.0	1.95052
$541$	−8159.73	−0.648455	−0.324228	−	0.945979i	$-0.605104\pi$
$541$	−8159.73	−0.648455	−0.324228	+	0.945979i	$0.605104\pi$
$542$	−12806.8	−1.01494
$543$	−18013.4	−1.42362
$544$	870.633	0.0686178
$545$	−6053.40	−0.475778
$546$	0	0
$547$	−6089.67	−0.476006	−0.238003	−	0.971264i	$-0.576493\pi$
$547$	−6089.67	−0.476006	−0.238003	+	0.971264i	$0.576493\pi$
$548$	44231.2	3.44793
$549$	7415.74	0.576496
$550$	−54022.2	−4.18821
$551$	2970.06	0.229635
$552$	22507.2	1.73545
$553$	0	0
$554$	−10769.8	−0.825926
$555$	6694.37	0.512000
$556$	57256.5	4.36729
$557$	4160.66	0.316504	0.158252	−	0.987399i	$-0.449414\pi$
$557$	4160.66	0.316504	0.158252	+	0.987399i	$0.449414\pi$
$558$	−17499.7	−1.32764
$559$	470.501	0.0355995
$560$	0	0
$561$	−1406.97	−0.105886
$562$	−31168.7	−2.33945
$563$	−7731.24	−0.578744	−0.289372	−	0.957217i	$-0.593446\pi$
$563$	−7731.24	−0.578744	−0.289372	+	0.957217i	$0.593446\pi$
$564$	−45690.8	−3.41122
$565$	−13556.1	−1.00939
$566$	3350.08	0.248788
$567$	0	0
$568$	752.414	0.0555820
$569$	9134.32	0.672989	0.336494	−	0.941685i	$-0.390759\pi$
$569$	9134.32	0.672989	0.336494	+	0.941685i	$0.390759\pi$
$570$	19220.2	1.41236
$571$	10421.5	0.763797	0.381898	−	0.924204i	$-0.375270\pi$
$571$	10421.5	0.763797	0.381898	+	0.924204i	$0.375270\pi$
$572$	12290.5	0.898414
$573$	529.783	0.0386248
$574$	0	0
$575$	11031.3	0.800067
$576$	3073.54	0.222334
$577$	−806.571	−0.0581941	−0.0290971	−	0.999577i	$-0.509263\pi$
$577$	−806.571	−0.0581941	−0.0290971	+	0.999577i	$0.509263\pi$
$578$	−25248.5	−1.81695
$579$	21482.2	1.54191
$580$	28616.1	2.04866
$581$	0	0
$582$	39751.2	2.83117
$583$	9091.50	0.645852
$584$	−22346.7	−1.58341
$585$	2879.51	0.203510
$586$	11192.3	0.788992
$587$	−11514.2	−0.809614	−0.404807	−	0.914402i	$-0.632661\pi$
$587$	−11514.2	−0.809614	−0.404807	+	0.914402i	$0.632661\pi$
$588$	0	0
$589$	7407.23	0.518183
$590$	18443.6	1.28696
$591$	14571.5	1.01420
$592$	−7853.72	−0.545246
$593$	−2702.41	−0.187141	−0.0935706	−	0.995613i	$-0.529828\pi$
$593$	−2702.41	−0.187141	−0.0935706	+	0.995613i	$0.529828\pi$
$594$	23846.2	1.64718
$595$	0	0
$596$	−26813.1	−1.84280
$597$	26480.1	1.81534
$598$	−3592.18	−0.245644
$599$	−27360.1	−1.86628	−0.933142	−	0.359507i	$-0.882945\pi$
$599$	−27360.1	−1.86628	−0.933142	+	0.359507i	$0.882945\pi$
$600$	61158.3	4.16129
$601$	11506.8	0.780985	0.390492	−	0.920606i	$-0.372305\pi$
$601$	11506.8	0.780985	0.390492	+	0.920606i	$0.372305\pi$
$602$	0	0
$603$	15537.1	1.04929
$604$	−15318.7	−1.03197
$605$	−40339.4	−2.71079
$606$	−15706.3	−1.05285
$607$	−8189.12	−0.547588	−0.273794	−	0.961788i	$-0.588279\pi$
$607$	−8189.12	−0.547588	−0.273794	+	0.961788i	$0.588279\pi$
$608$	−8095.75	−0.540010
$609$	0	0
$610$	−43287.1	−2.87318
$611$	4147.12	0.274590
$612$	1010.58	0.0667488
$613$	−24210.1	−1.59517	−0.797583	−	0.603209i	$-0.793889\pi$
$613$	−24210.1	−1.59517	−0.797583	+	0.603209i	$0.793889\pi$
$614$	−6479.14	−0.425858
$615$	−16141.5	−1.05835
$616$	0	0
$617$	−8779.45	−0.572848	−0.286424	−	0.958103i	$-0.592467\pi$
$617$	−8779.45	−0.572848	−0.286424	+	0.958103i	$0.592467\pi$
$618$	43528.3	2.83328
$619$	6089.56	0.395412	0.197706	−	0.980261i	$-0.436651\pi$
$619$	6089.56	0.395412	0.197706	+	0.980261i	$0.436651\pi$
$620$	71367.8	4.62290
$621$	−4869.40	−0.314658
$622$	6780.79	0.437114
$623$	0	0
$624$	−9362.69	−0.600653
$625$	−7291.47	−0.466654
$626$	−16163.9	−1.03201
$627$	13082.9	0.833305
$628$	−22032.1	−1.39996
$629$	−213.245	−0.0135177
$630$	0	0
$631$	13768.3	0.868634	0.434317	−	0.900760i	$-0.356990\pi$
$631$	13768.3	0.868634	0.434317	+	0.900760i	$0.356990\pi$
$632$	−71478.5	−4.49883
$633$	27736.6	1.74160
$634$	2944.75	0.184465
$635$	12631.5	0.789398
$636$	−18098.3	−1.12837
$637$	0	0
$638$	27879.8	1.73005
$639$	210.995	0.0130623
$640$	15701.6	0.969780
$641$	393.612	0.0242539	0.0121269	−	0.999926i	$-0.496140\pi$
$641$	393.612	0.0242539	0.0121269	+	0.999926i	$0.496140\pi$
$642$	−49592.9	−3.04871
$643$	29944.9	1.83656	0.918281	−	0.395929i	$-0.129577\pi$
$643$	29944.9	1.83656	0.918281	+	0.395929i	$0.129577\pi$
$644$	0	0
$645$	4825.50	0.294580
$646$	−612.249	−0.0372889
$647$	8372.05	0.508716	0.254358	−	0.967110i	$-0.418136\pi$
$647$	8372.05	0.508716	0.254358	+	0.967110i	$0.418136\pi$
$648$	−49362.3	−2.99249
$649$	12554.3	0.759320
$650$	−9760.97	−0.589010
$651$	0	0
$652$	28093.4	1.68746
$653$	7203.34	0.431682	0.215841	−	0.976429i	$-0.430751\pi$
$653$	7203.34	0.431682	0.215841	+	0.976429i	$0.430751\pi$
$654$	11740.4	0.701964
$655$	42519.9	2.53647
$656$	18936.9	1.12708
$657$	−6266.56	−0.372119
$658$	0	0
$659$	−28054.8	−1.65836	−0.829182	−	0.558979i	$-0.811193\pi$
$659$	−28054.8	−1.65836	−0.829182	+	0.558979i	$0.811193\pi$
$660$	126053.	7.43423
$661$	11582.1	0.681531	0.340766	−	0.940148i	$-0.389314\pi$
$661$	11582.1	0.681531	0.340766	+	0.940148i	$0.389314\pi$
$662$	−11630.8	−0.682843
$663$	−254.217	−0.0148914
$664$	−44210.2	−2.58387
$665$	0	0
$666$	−4684.64	−0.272561
$667$	−5693.07	−0.330489
$668$	62220.1	3.60385
$669$	5780.31	0.334050
$670$	−90692.9	−5.22951
$671$	−29464.9	−1.69520
$672$	0	0
$673$	9582.65	0.548862	0.274431	−	0.961607i	$-0.411511\pi$
$673$	9582.65	0.548862	0.274431	+	0.961607i	$0.411511\pi$
$674$	−47519.9	−2.71572
$675$	−13231.5	−0.754492
$676$	−38530.1	−2.19220
$677$	−8247.63	−0.468216	−0.234108	−	0.972211i	$-0.575217\pi$
$677$	−8247.63	−0.468216	−0.234108	+	0.972211i	$0.575217\pi$
$678$	26291.5	1.48926
$679$	0	0
$680$	−3354.70	−0.189187
$681$	−1510.37	−0.0849890
$682$	69531.5	3.90395
$683$	23171.1	1.29812	0.649061	−	0.760736i	$-0.275162\pi$
$683$	23171.1	1.29812	0.649061	+	0.760736i	$0.275162\pi$
$684$	−9397.08	−0.525301
$685$	−41174.4	−2.29663
$686$	0	0
$687$	−5536.16	−0.307450
$688$	−5661.20	−0.313708
$689$	1642.69	0.0908297
$690$	−36841.7	−2.03267
$691$	−24019.8	−1.32237	−0.661185	−	0.750223i	$-0.729946\pi$
$691$	−24019.8	−1.32237	−0.661185	+	0.750223i	$0.729946\pi$
$692$	−30690.8	−1.68597
$693$	0	0
$694$	45550.7	2.49147
$695$	−53299.6	−2.90902
$696$	−31562.6	−1.71893
$697$	514.177	0.0279424
$698$	−7376.54	−0.400009
$699$	−13542.1	−0.732776
$700$	0	0
$701$	−756.339	−0.0407511	−0.0203755	−	0.999792i	$-0.506486\pi$
$701$	−756.339	−0.0407511	−0.0203755	+	0.999792i	$0.506486\pi$
$702$	4308.64	0.231651
$703$	1982.90	0.106382
$704$	−12212.1	−0.653779
$705$	42533.2	2.27219
$706$	42807.4	2.28198
$707$	0	0
$708$	−24991.7	−1.32662
$709$	−26580.1	−1.40795	−0.703975	−	0.710224i	$-0.748594\pi$
$709$	−26580.1	−1.40795	−0.703975	+	0.710224i	$0.748594\pi$
$710$	−1231.62	−0.0651011
$711$	−20044.3	−1.05727
$712$	19053.9	1.00291
$713$	−14198.3	−0.745767
$714$	0	0
$715$	−11441.1	−0.598426
$716$	−24744.5	−1.29154
$717$	6414.72	0.334118
$718$	59986.8	3.11795
$719$	−14125.2	−0.732656	−0.366328	−	0.930486i	$-0.619385\pi$
$719$	−14125.2	−0.732656	−0.366328	+	0.930486i	$0.619385\pi$
$720$	−34647.1	−1.79336
$721$	0	0
$722$	−29648.0	−1.52823
$723$	−96.6916	−0.00497372
$724$	−51408.3	−2.63891
$725$	−15469.6	−0.792453
$726$	78236.8	3.99951
$727$	19206.2	0.979805	0.489903	−	0.871777i	$-0.337032\pi$
$727$	19206.2	0.979805	0.489903	+	0.871777i	$0.337032\pi$
$728$	0	0
$729$	−431.393	−0.0219170
$730$	36579.1	1.85459
$731$	−153.713	−0.00777742
$732$	58655.5	2.96170
$733$	29831.4	1.50320	0.751602	−	0.659617i	$-0.229282\pi$
$733$	29831.4	1.50320	0.751602	+	0.659617i	$0.229282\pi$
$734$	−22536.8	−1.13331
$735$	0	0
$736$	15518.1	0.777181
$737$	−61733.4	−3.08545
$738$	11295.6	0.563411
$739$	11720.8	0.583431	0.291715	−	0.956505i	$-0.405774\pi$
$739$	11720.8	0.583431	0.291715	+	0.956505i	$0.405774\pi$
$740$	19105.0	0.949073
$741$	2363.89	0.117192
$742$	0	0
$743$	4257.57	0.210222	0.105111	−	0.994460i	$-0.466480\pi$
$743$	4257.57	0.210222	0.105111	+	0.994460i	$0.466480\pi$
$744$	−78716.3	−3.87887
$745$	24960.1	1.22747
$746$	41068.8	2.01560
$747$	−12397.6	−0.607236
$748$	−4015.33	−0.196277
$749$	0	0
$750$	−27831.8	−1.35503
$751$	−16414.4	−0.797564	−0.398782	−	0.917046i	$-0.630567\pi$
$751$	−16414.4	−0.797564	−0.398782	+	0.917046i	$0.630567\pi$
$752$	−49899.2	−2.41973
$753$	19675.2	0.952199
$754$	5037.45	0.243307
$755$	14260.1	0.687386
$756$	0	0
$757$	−22813.5	−1.09534	−0.547668	−	0.836696i	$-0.684484\pi$
$757$	−22813.5	−1.09534	−0.547668	+	0.836696i	$0.684484\pi$
$758$	−10410.9	−0.498869
$759$	−25077.7	−1.19929
$760$	31194.4	1.48887
$761$	−1695.44	−0.0807617	−0.0403808	−	0.999184i	$-0.512857\pi$
$761$	−1695.44	−0.0807617	−0.0403808	+	0.999184i	$0.512857\pi$
$762$	−24498.5	−1.16468
$763$	0	0
$764$	1511.95	0.0715972
$765$	−940.741	−0.0444609
$766$	−59897.9	−2.82532
$767$	2268.36	0.106787
$768$	−40937.9	−1.92346
$769$	−21604.9	−1.01313	−0.506563	−	0.862203i	$-0.669084\pi$
$769$	−21604.9	−1.01313	−0.506563	+	0.862203i	$0.669084\pi$
$770$	0	0
$771$	−37435.6	−1.74865
$772$	61307.8	2.85818
$773$	−34435.4	−1.60227	−0.801136	−	0.598482i	$-0.795771\pi$
$773$	−34435.4	−1.60227	−0.801136	+	0.598482i	$0.795771\pi$
$774$	−3376.83	−0.156818
$775$	−38580.9	−1.78821
$776$	64516.1	2.98453
$777$	0	0
$778$	32008.8	1.47503
$779$	−4781.18	−0.219902
$780$	22775.8	1.04552
$781$	−838.345	−0.0384102
$782$	1173.57	0.0536660
$783$	6828.54	0.311663
$784$	0	0
$785$	20509.5	0.932502
$786$	−82465.9	−3.74232
$787$	12352.5	0.559490	0.279745	−	0.960074i	$-0.409750\pi$
$787$	12352.5	0.559490	0.279745	+	0.960074i	$0.409750\pi$
$788$	41585.4	1.87997
$789$	16541.4	0.746374
$790$	117002.	5.26931
$791$	0	0
$792$	−50164.7	−2.25066
$793$	−5323.85	−0.238406
$794$	8490.03	0.379471
$795$	16847.6	0.751601
$796$	75571.5	3.36503
$797$	−29811.8	−1.32495	−0.662477	−	0.749083i	$-0.730495\pi$
$797$	−29811.8	−1.32495	−0.662477	+	0.749083i	$0.730495\pi$
$798$	0	0
$799$	−1354.87	−0.0599897
$800$	42167.0	1.86354
$801$	5343.17	0.235695
$802$	35518.2	1.56383
$803$	24898.9	1.09423
$804$	122892.	5.39063
$805$	0	0
$806$	12563.3	0.549035
$807$	−43921.7	−1.91588
$808$	−25491.3	−1.10988
$809$	−1273.45	−0.0553424	−0.0276712	−	0.999617i	$-0.508809\pi$
$809$	−1273.45	−0.0553424	−0.0276712	+	0.999617i	$0.508809\pi$
$810$	80800.6	3.50499
$811$	−37825.5	−1.63777	−0.818886	−	0.573956i	$-0.805408\pi$
$811$	−37825.5	−1.63777	−0.818886	+	0.573956i	$0.805408\pi$
$812$	0	0
$813$	−16154.3	−0.696872
$814$	18613.4	0.801475
$815$	−26152.0	−1.12400
$816$	3058.80	0.131225
$817$	1429.33	0.0612070
$818$	15262.9	0.652391
$819$	0	0
$820$	−46066.1	−1.96182
$821$	189.193	0.00804247	0.00402124	−	0.999992i	$-0.498720\pi$
$821$	189.193	0.00804247	0.00402124	+	0.999992i	$0.498720\pi$
$822$	79856.4	3.38846
$823$	26388.5	1.11767	0.558837	−	0.829278i	$-0.311248\pi$
$823$	26388.5	1.11767	0.558837	+	0.829278i	$0.311248\pi$
$824$	70646.4	2.98675
$825$	−68143.0	−2.87568
$826$	0	0
$827$	−37247.2	−1.56616	−0.783079	−	0.621923i	$-0.786352\pi$
$827$	−37247.2	−1.56616	−0.783079	+	0.621923i	$0.786352\pi$
$828$	18012.5	0.756012
$829$	18429.8	0.772128	0.386064	−	0.922472i	$-0.373834\pi$
$829$	18429.8	0.772128	0.386064	+	0.922472i	$0.373834\pi$
$830$	72367.2	3.02639
$831$	−13584.9	−0.567092
$832$	−2206.54	−0.0919445
$833$	0	0
$834$	103373.	4.29197
$835$	−57920.2	−2.40049
$836$	37337.3	1.54466
$837$	17030.2	0.703285
$838$	28443.2	1.17250
$839$	−24344.3	−1.00174	−0.500870	−	0.865523i	$-0.666986\pi$
$839$	−24344.3	−1.00174	−0.500870	+	0.865523i	$0.666986\pi$
$840$	0	0
$841$	−16405.4	−0.672656
$842$	56769.8	2.32354
$843$	−39315.9	−1.60630
$844$	79157.5	3.22833
$845$	35867.4	1.46021
$846$	−29764.2	−1.20959
$847$	0	0
$848$	−19765.3	−0.800406
$849$	4225.75	0.170822
$850$	3188.92	0.128681
$851$	−3800.87	−0.153105
$852$	1668.88	0.0671068
$853$	−14146.8	−0.567852	−0.283926	−	0.958846i	$-0.591637\pi$
$853$	−14146.8	−0.567852	−0.283926	+	0.958846i	$0.591637\pi$
$854$	0	0
$855$	8747.66	0.349899
$856$	−80489.1	−3.21386
$857$	−8682.05	−0.346060	−0.173030	−	0.984917i	$-0.555356\pi$
$857$	−8682.05	−0.346060	−0.173030	+	0.984917i	$0.555356\pi$
$858$	22189.7	0.882919
$859$	25428.8	1.01003	0.505017	−	0.863110i	$-0.331486\pi$
$859$	25428.8	1.01003	0.505017	+	0.863110i	$0.331486\pi$
$860$	13771.5	0.546050
$861$	0	0
$862$	45473.7	1.79680
$863$	−39552.6	−1.56012	−0.780062	−	0.625703i	$-0.784812\pi$
$863$	−39552.6	−1.56012	−0.780062	+	0.625703i	$0.784812\pi$
$864$	−18613.2	−0.732909
$865$	28569.9	1.12301
$866$	−23551.5	−0.924148
$867$	−31848.1	−1.24754
$868$	0	0
$869$	79641.9	3.10894
$870$	51664.5	2.01332
$871$	−11154.3	−0.433924
$872$	19054.6	0.739988
$873$	18091.9	0.701395
$874$	−10912.7	−0.422342
$875$	0	0
$876$	−49565.9	−1.91173
$877$	1955.60	0.0752975	0.0376487	−	0.999291i	$-0.488013\pi$
$877$	1955.60	0.0752975	0.0376487	+	0.999291i	$0.488013\pi$
$878$	15765.3	0.605983
$879$	14117.8	0.541733
$880$	137663.	5.27343
$881$	−3037.09	−0.116143	−0.0580716	−	0.998312i	$-0.518495\pi$
$881$	−3037.09	−0.116143	−0.0580716	+	0.998312i	$0.518495\pi$
$882$	0	0
$883$	15702.3	0.598443	0.299222	−	0.954184i	$-0.403273\pi$
$883$	15702.3	0.598443	0.299222	+	0.954184i	$0.403273\pi$
$884$	−725.508	−0.0276035
$885$	23264.5	0.883648
$886$	−14244.4	−0.540123
$887$	−2964.83	−0.112231	−0.0561157	−	0.998424i	$-0.517872\pi$
$887$	−2964.83	−0.112231	−0.0561157	+	0.998424i	$0.517872\pi$
$888$	−21072.2	−0.796324
$889$	0	0
$890$	−31189.1	−1.17467
$891$	54999.9	2.06797
$892$	16496.4	0.619215
$893$	12598.5	0.472109
$894$	−48409.3	−1.81102
$895$	23034.5	0.860287
$896$	0	0
$897$	−4531.14	−0.168663
$898$	38990.8	1.44893
$899$	19910.9	0.738670
$900$	48945.0	1.81278
$901$	−536.670	−0.0198436
$902$	−44880.7	−1.65672
$903$	0	0
$904$	42671.1	1.56993
$905$	47855.5	1.75776
$906$	−27656.9	−1.01417
$907$	47065.4	1.72302	0.861511	−	0.507738i	$-0.169518\pi$
$907$	47065.4	1.72302	0.861511	+	0.507738i	$0.169518\pi$
$908$	−4310.43	−0.157540
$909$	−7148.37	−0.260832
$910$	0	0
$911$	−40218.3	−1.46267	−0.731335	−	0.682018i	$-0.761102\pi$
$911$	−40218.3	−1.46267	−0.731335	+	0.682018i	$0.761102\pi$
$912$	−28442.9	−1.03272
$913$	49259.4	1.78559
$914$	−41627.4	−1.50647
$915$	−54601.9	−1.97277
$916$	−15799.6	−0.569906
$917$	0	0
$918$	−1407.64	−0.0506090
$919$	−13015.3	−0.467175	−0.233587	−	0.972336i	$-0.575047\pi$
$919$	−13015.3	−0.467175	−0.233587	+	0.972336i	$0.575047\pi$
$920$	−59794.0	−2.14277
$921$	−8172.72	−0.292400
$922$	−74538.6	−2.66247
$923$	−151.476	−0.00540184
$924$	0	0
$925$	−10328.0	−0.367117
$926$	−41049.0	−1.45675
$927$	19811.0	0.701917
$928$	−21761.6	−0.769784
$929$	17365.8	0.613298	0.306649	−	0.951823i	$-0.400792\pi$
$929$	17365.8	0.613298	0.306649	+	0.951823i	$0.400792\pi$
$930$	128850.	4.54317
$931$	0	0
$932$	−38647.8	−1.35832
$933$	8553.22	0.300128
$934$	−34714.0	−1.21614
$935$	3737.84	0.130738
$936$	−9063.98	−0.316523
$937$	41655.6	1.45232	0.726162	−	0.687523i	$-0.241302\pi$
$937$	41655.6	1.45232	0.726162	+	0.687523i	$0.241302\pi$
$938$	0	0
$939$	−20389.0	−0.708593
$940$	121385.	4.21186
$941$	11377.5	0.394149	0.197075	−	0.980388i	$-0.436856\pi$
$941$	11377.5	0.394149	0.197075	+	0.980388i	$0.436856\pi$
$942$	−39777.4	−1.37582
$943$	9164.66	0.316482
$944$	−27293.5	−0.941027
$945$	0	0
$946$	13417.1	0.461129
$947$	39835.0	1.36691	0.683455	−	0.729992i	$-0.260476\pi$
$947$	39835.0	1.36691	0.683455	+	0.729992i	$0.260476\pi$
$948$	−158542.	−5.43165
$949$	4498.84	0.153887
$950$	−29652.8	−1.01270
$951$	3714.48	0.126656
$952$	0	0
$953$	16468.3	0.559769	0.279885	−	0.960034i	$-0.409704\pi$
$953$	16468.3	0.559769	0.279885	+	0.960034i	$0.409704\pi$
$954$	−11789.7	−0.400112
$955$	−1407.46	−0.0476903
$956$	18306.9	0.619340
$957$	35167.3	1.18788
$958$	93341.2	3.14793
$959$	0	0
$960$	−22630.4	−0.760826
$961$	19866.1	0.666848
$962$	3363.16	0.112716
$963$	−22571.1	−0.755289
$964$	−275.948	−0.00921958
$965$	−57070.9	−1.90381
$966$	0	0
$967$	55135.3	1.83354	0.916770	−	0.399416i	$-0.130787\pi$
$967$	55135.3	1.83354	0.916770	+	0.399416i	$0.130787\pi$
$968$	126978.	4.21615
$969$	−772.284	−0.0256030
$970$	−105606.	−3.49566
$971$	13040.1	0.430975	0.215488	−	0.976507i	$-0.430866\pi$
$971$	13040.1	0.430975	0.215488	+	0.976507i	$0.430866\pi$
$972$	−71214.0	−2.34999
$973$	0	0
$974$	−77114.7	−2.53687
$975$	−12312.4	−0.404423
$976$	64058.0	2.10087
$977$	−45144.9	−1.47831	−0.739157	−	0.673534i	$-0.764776\pi$
$977$	−45144.9	−1.47831	−0.739157	+	0.673534i	$0.764776\pi$
$978$	50720.8	1.65836
$979$	−21230.0	−0.693068
$980$	0	0
$981$	5343.37	0.173905
$982$	−80965.4	−2.63107
$983$	26573.6	0.862225	0.431113	−	0.902298i	$-0.358121\pi$
$983$	26573.6	0.862225	0.431113	+	0.902298i	$0.358121\pi$
$984$	50809.3	1.64608
$985$	−38711.5	−1.25223
$986$	−1645.74	−0.0531553
$987$	0	0
$988$	6746.28	0.217235
$989$	−2739.78	−0.0880889
$990$	82114.0	2.63612
$991$	20658.0	0.662183	0.331092	−	0.943599i	$-0.392583\pi$
$991$	20658.0	0.662183	0.331092	+	0.943599i	$0.392583\pi$
$992$	−54272.8	−1.73706
$993$	−14670.9	−0.468850
$994$	0	0
$995$	−70348.9	−2.24142
$996$	−98060.1	−3.11963
$997$	27284.2	0.866701	0.433350	−	0.901226i	$-0.357331\pi$
$997$	27284.2	0.866701	0.433350	+	0.901226i	$0.357331\pi$
$998$	−79304.8	−2.51538
$999$	4558.95	0.144383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2107.4.a.c.1.6		6
7.6	odd	2		43.4.a.b.1.6	✓	6
21.20	even	2		387.4.a.h.1.1		6
28.27	even	2		688.4.a.i.1.5		6
35.34	odd	2		1075.4.a.b.1.1		6
301.300	even	2		1849.4.a.c.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.6	✓	6	7.6	odd	2
387.4.a.h.1.1		6	21.20	even	2
688.4.a.i.1.5		6	28.27	even	2
1075.4.a.b.1.1		6	35.34	odd	2
1849.4.a.c.1.1		6	301.300	even	2
2107.4.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q+5.15251 q^{2} +6.49933 q^{3} +18.5484 q^{4} -17.2665 q^{5} +33.4879 q^{6} +54.3507 q^{8} +15.2413 q^{9} +O(q^{10})\)	\(q+5.15251 q^{2} +6.49933 q^{3} +18.5484 q^{4} -17.2665 q^{5} +33.4879 q^{6} +54.3507 q^{8} +15.2413 q^{9} -88.9661 q^{10} -60.5580 q^{11} +120.552 q^{12} -10.9419 q^{13} -112.221 q^{15} +131.656 q^{16} +3.57473 q^{17} +78.5308 q^{18} -33.2403 q^{19} -320.267 q^{20} -312.026 q^{22} +63.7158 q^{23} +353.243 q^{24} +173.134 q^{25} -56.3783 q^{26} -76.4239 q^{27} -89.3510 q^{29} -578.220 q^{30} -222.839 q^{31} +243.552 q^{32} -393.586 q^{33} +18.4188 q^{34} +282.701 q^{36} -59.6535 q^{37} -171.271 q^{38} -71.1150 q^{39} -938.449 q^{40} +143.837 q^{41} -43.0000 q^{43} -1123.25 q^{44} -263.164 q^{45} +328.296 q^{46} -379.013 q^{47} +855.674 q^{48} +892.073 q^{50} +23.2334 q^{51} -202.955 q^{52} -150.129 q^{53} -393.775 q^{54} +1045.63 q^{55} -216.040 q^{57} -460.382 q^{58} -207.310 q^{59} -2081.52 q^{60} +486.557 q^{61} -1148.18 q^{62} +201.659 q^{64} +188.929 q^{65} -2027.96 q^{66} +1019.41 q^{67} +66.3055 q^{68} +414.110 q^{69} +13.8437 q^{71} +828.374 q^{72} -411.158 q^{73} -307.365 q^{74} +1125.25 q^{75} -616.555 q^{76} -366.421 q^{78} -1315.13 q^{79} -2273.24 q^{80} -908.218 q^{81} +741.120 q^{82} -813.425 q^{83} -61.7233 q^{85} -221.558 q^{86} -580.721 q^{87} -3291.37 q^{88} +350.573 q^{89} -1355.96 q^{90} +1181.83 q^{92} -1448.30 q^{93} -1952.87 q^{94} +573.946 q^{95} +1582.92 q^{96} +1187.03 q^{97} -922.981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9}+O(q^{10}) \) 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

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Database

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