LMFDB - Embedded newform 2107.4.a.c.1.1

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			1.1
Root			$4.31455$ 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)

$f(q)$	$=$	$q-3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} -8.51910 q^{5} -23.5469 q^{6} +16.6183 q^{8} +23.4681 q^{9} +O(q^{10})$	\(q-3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} -8.51910 q^{5} -23.5469 q^{6} +16.6183 q^{8} +23.4681 q^{9} +28.2370 q^{10} +0.597776 q^{11} +21.2147 q^{12} -34.9021 q^{13} -60.5204 q^{15} -78.9723 q^{16} -91.3552 q^{17} -77.7863 q^{18} +24.0324 q^{19} -25.4403 q^{20} -1.98136 q^{22} +127.719 q^{23} +118.058 q^{24} -52.4250 q^{25} +115.685 q^{26} -25.0908 q^{27} +285.724 q^{29} +200.598 q^{30} +192.699 q^{31} +128.812 q^{32} +4.24666 q^{33} +302.802 q^{34} +70.0821 q^{36} +363.399 q^{37} -79.6565 q^{38} -247.948 q^{39} -141.573 q^{40} -191.586 q^{41} -43.0000 q^{43} +1.78512 q^{44} -199.927 q^{45} -423.330 q^{46} +458.267 q^{47} -561.027 q^{48} +173.765 q^{50} -648.995 q^{51} -104.227 q^{52} -583.068 q^{53} +83.1648 q^{54} -5.09252 q^{55} +170.728 q^{57} -947.047 q^{58} -416.589 q^{59} -180.730 q^{60} +30.9376 q^{61} -638.710 q^{62} +204.825 q^{64} +297.334 q^{65} -14.0758 q^{66} +16.1466 q^{67} -272.811 q^{68} +907.324 q^{69} -219.461 q^{71} +390.000 q^{72} -1031.07 q^{73} -1204.50 q^{74} -372.432 q^{75} +71.7670 q^{76} +821.836 q^{78} +445.438 q^{79} +672.773 q^{80} -811.887 q^{81} +635.022 q^{82} -298.511 q^{83} +778.264 q^{85} +142.526 q^{86} +2029.81 q^{87} +9.93402 q^{88} -846.185 q^{89} +662.669 q^{90} +381.402 q^{92} +1368.95 q^{93} -1518.95 q^{94} -204.734 q^{95} +915.091 q^{96} +259.068 q^{97} +14.0287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.31455	−1.17187	−0.585936	−	0.810357i	$-0.699273\pi$
$2$	−3.31455	−1.17187	−0.585936	+	0.810357i	$0.699273\pi$
$3$	7.10409	1.36718	0.683592	−	0.729865i	$-0.260417\pi$
$3$	7.10409	1.36718	0.683592	+	0.729865i	$0.260417\pi$
$4$	2.98627	0.373283
$5$	−8.51910	−0.761971	−0.380986	−	0.924581i	$-0.624415\pi$
$5$	−8.51910	−0.761971	−0.380986	+	0.924581i	$0.624415\pi$
$6$	−23.5469	−1.60216
$7$	0	0
$7$	0	0
$8$	16.6183	0.734432
$9$	23.4681	0.869190
$10$	28.2370	0.892933
$11$	0.597776	0.0163851	0.00819256	−	0.999966i	$-0.497392\pi$
$11$	0.597776	0.0163851	0.00819256	+	0.999966i	$0.497392\pi$
$12$	21.2147	0.510347
$13$	−34.9021	−0.744623	−0.372311	−	0.928108i	$-0.621435\pi$
$13$	−34.9021	−0.744623	−0.372311	+	0.928108i	$0.621435\pi$
$14$	0	0
$15$	−60.5204	−1.04175
$16$	−78.9723	−1.23394
$17$	−91.3552	−1.30335	−0.651673	−	0.758500i	$-0.725933\pi$
$17$	−91.3552	−1.30335	−0.651673	+	0.758500i	$0.725933\pi$
$18$	−77.7863	−1.01858
$19$	24.0324	0.290179	0.145089	−	0.989419i	$-0.453653\pi$
$19$	24.0324	0.290179	0.145089	+	0.989419i	$0.453653\pi$
$20$	−25.4403	−0.284431
$21$	0	0
$22$	−1.98136	−0.0192013
$23$	127.719	1.15788	0.578938	−	0.815371i	$-0.303467\pi$
$23$	127.719	1.15788	0.578938	+	0.815371i	$0.303467\pi$
$24$	118.058	1.00410
$25$	−52.4250	−0.419400
$26$	115.685	0.872602
$27$	−25.0908	−0.178842
$28$	0	0
$29$	285.724	1.82957	0.914786	−	0.403939i	$-0.132359\pi$
$29$	285.724	1.82957	0.914786	+	0.403939i	$0.132359\pi$
$30$	200.598	1.22080
$31$	192.699	1.11644	0.558221	−	0.829692i	$-0.311484\pi$
$31$	192.699	1.11644	0.558221	+	0.829692i	$0.311484\pi$
$32$	128.812	0.711591
$33$	4.24666	0.0224015
$34$	302.802	1.52735
$35$	0	0
$36$	70.0821	0.324454
$37$	363.399	1.61466	0.807329	−	0.590101i	$-0.200912\pi$
$37$	363.399	1.61466	0.807329	+	0.590101i	$0.200912\pi$
$38$	−79.6565	−0.340053
$39$	−247.948	−1.01804
$40$	−141.573	−0.559616
$41$	−191.586	−0.729774	−0.364887	−	0.931052i	$-0.618892\pi$
$41$	−191.586	−0.729774	−0.364887	+	0.931052i	$0.618892\pi$
$42$	0	0
$43$	−43.0000	−0.152499
$43$	−43.0000	−0.152499
$44$	1.78512	0.00611629
$45$	−199.927	−0.662297
$46$	−423.330	−1.35688
$47$	458.267	1.42223	0.711117	−	0.703073i	$-0.248189\pi$
$47$	458.267	1.42223	0.711117	+	0.703073i	$0.248189\pi$
$48$	−561.027	−1.68703
$49$	0	0
$50$	173.765	0.491483
$51$	−648.995	−1.78191
$52$	−104.227	−0.277955
$53$	−583.068	−1.51114	−0.755572	−	0.655066i	$-0.772641\pi$
$53$	−583.068	−1.51114	−0.755572	+	0.655066i	$0.772641\pi$
$54$	83.1648	0.209580
$55$	−5.09252	−0.0124850
$56$	0	0
$57$	170.728	0.396728
$58$	−947.047	−2.14402
$59$	−416.589	−0.919243	−0.459621	−	0.888115i	$-0.652015\pi$
$59$	−416.589	−0.919243	−0.459621	+	0.888115i	$0.652015\pi$
$60$	−180.730	−0.388869
$61$	30.9376	0.0649369	0.0324685	−	0.999473i	$-0.489663\pi$
$61$	30.9376	0.0649369	0.0324685	+	0.999473i	$0.489663\pi$
$62$	−638.710	−1.30833
$63$	0	0
$64$	204.825	0.400049
$65$	297.334	0.567381
$66$	−14.0758	−0.0262516
$67$	16.1466	0.0294421	0.0147210	−	0.999892i	$-0.495314\pi$
$67$	16.1466	0.0294421	0.0147210	+	0.999892i	$0.495314\pi$
$68$	−272.811	−0.486517
$69$	907.324	1.58303
$70$	0	0
$71$	−219.461	−0.366835	−0.183418	−	0.983035i	$-0.558716\pi$
$71$	−219.461	−0.366835	−0.183418	+	0.983035i	$0.558716\pi$
$72$	390.000	0.638360
$73$	−1031.07	−1.65311	−0.826557	−	0.562853i	$-0.809704\pi$
$73$	−1031.07	−1.65311	−0.826557	+	0.562853i	$0.809704\pi$
$74$	−1204.50	−1.89217
$75$	−372.432	−0.573396
$76$	71.7670	0.108319
$77$	0	0
$78$	821.836	1.19301
$79$	445.438	0.634375	0.317188	−	0.948363i	$-0.397262\pi$
$79$	445.438	0.634375	0.317188	+	0.948363i	$0.397262\pi$
$80$	672.773	0.940229
$81$	−811.887	−1.11370
$82$	635.022	0.855201
$83$	−298.511	−0.394769	−0.197384	−	0.980326i	$-0.563245\pi$
$83$	−298.511	−0.394769	−0.197384	+	0.980326i	$0.563245\pi$
$84$	0	0
$85$	778.264	0.993112
$86$	142.526	0.178709
$87$	2029.81	2.50136
$88$	9.93402	0.0120338
$89$	−846.185	−1.00781	−0.503907	−	0.863758i	$-0.668105\pi$
$89$	−846.185	−1.00781	−0.503907	+	0.863758i	$0.668105\pi$
$90$	662.669	0.776128
$91$	0	0
$92$	381.402	0.432216
$93$	1368.95	1.52638
$94$	−1518.95	−1.66668
$95$	−204.734	−0.221108
$96$	915.091	0.972876
$97$	259.068	0.271179	0.135590	−	0.990765i	$-0.456707\pi$
$97$	259.068	0.271179	0.135590	+	0.990765i	$0.456707\pi$
$98$	0	0
$99$	14.0287	0.0142418
$100$	−156.555	−0.156555
$101$	1182.01	1.16450	0.582252	−	0.813009i	$-0.302172\pi$
$101$	1182.01	1.16450	0.582252	+	0.813009i	$0.302172\pi$
$102$	2151.13	2.08817
$103$	−319.565	−0.305706	−0.152853	−	0.988249i	$-0.548846\pi$
$103$	−319.565	−0.305706	−0.152853	+	0.988249i	$0.548846\pi$
$104$	−580.013	−0.546874
$105$	0	0
$106$	1932.61	1.77087
$107$	1647.14	1.48818	0.744089	−	0.668081i	$-0.232884\pi$
$107$	1647.14	1.48818	0.744089	+	0.668081i	$0.232884\pi$
$108$	−74.9279	−0.0667587
$109$	−560.538	−0.492567	−0.246283	−	0.969198i	$-0.579209\pi$
$109$	−560.538	−0.492567	−0.246283	+	0.969198i	$0.579209\pi$
$110$	16.8794	0.0146308
$111$	2581.62	2.20753
$112$	0	0
$113$	−65.6852	−0.0546827	−0.0273414	−	0.999626i	$-0.508704\pi$
$113$	−65.6852	−0.0546827	−0.0273414	+	0.999626i	$0.508704\pi$
$114$	−565.887	−0.464914
$115$	−1088.05	−0.882269
$116$	853.248	0.682949
$117$	−819.086	−0.647218
$118$	1380.81	1.07723
$119$	0	0
$120$	−1005.75	−0.765097
$121$	−1330.64	−0.999732
$122$	−102.544	−0.0760977
$123$	−1361.05	−0.997734
$124$	575.450	0.416749
$125$	1511.50	1.08154
$126$	0	0
$127$	−1906.92	−1.33238	−0.666189	−	0.745783i	$-0.732076\pi$
$127$	−1906.92	−1.33238	−0.666189	+	0.745783i	$0.732076\pi$
$128$	−1709.40	−1.18040
$129$	−305.476	−0.208493
$130$	−985.530	−0.664898
$131$	1536.09	1.02449	0.512246	−	0.858839i	$-0.328814\pi$
$131$	1536.09	1.02449	0.512246	+	0.858839i	$0.328814\pi$
$132$	12.6817	0.00836209
$133$	0	0
$134$	−53.5187	−0.0345023
$135$	213.751	0.136272
$136$	−1518.17	−0.957218
$137$	−1695.38	−1.05727	−0.528634	−	0.848850i	$-0.677296\pi$
$137$	−1695.38	−1.05727	−0.528634	+	0.848850i	$0.677296\pi$
$138$	−3007.38	−1.85511
$139$	−947.580	−0.578221	−0.289110	−	0.957296i	$-0.593359\pi$
$139$	−947.580	−0.578221	−0.289110	+	0.957296i	$0.593359\pi$
$140$	0	0
$141$	3255.57	1.94446
$142$	727.417	0.429884
$143$	−20.8636	−0.0122007
$144$	−1853.33	−1.07253
$145$	−2434.11	−1.39408
$146$	3417.53	1.93724
$147$	0	0
$148$	1085.21	0.602725
$149$	3084.10	1.69570	0.847850	−	0.530236i	$-0.177897\pi$
$149$	3084.10	1.69570	0.847850	+	0.530236i	$0.177897\pi$
$150$	1234.45	0.671947
$151$	−2346.83	−1.26478	−0.632391	−	0.774649i	$-0.717926\pi$
$151$	−2346.83	−1.26478	−0.632391	+	0.774649i	$0.717926\pi$
$152$	399.377	0.213117
$153$	−2143.93	−1.13285
$154$	0	0
$155$	−1641.62	−0.850697
$156$	−740.438	−0.380016
$157$	−1582.73	−0.804556	−0.402278	−	0.915517i	$-0.631782\pi$
$157$	−1582.73	−0.804556	−0.402278	+	0.915517i	$0.631782\pi$
$158$	−1476.43	−0.743406
$159$	−4142.17	−2.06601
$160$	−1097.36	−0.542212
$161$	0	0
$162$	2691.04	1.30511
$163$	−820.887	−0.394459	−0.197229	−	0.980357i	$-0.563194\pi$
$163$	−820.887	−0.394459	−0.197229	+	0.980357i	$0.563194\pi$
$164$	−572.127	−0.272412
$165$	−36.1777	−0.0170693
$166$	989.430	0.462618
$167$	−1690.58	−0.783358	−0.391679	−	0.920102i	$-0.628106\pi$
$167$	−1690.58	−0.783358	−0.391679	+	0.920102i	$0.628106\pi$
$168$	0	0
$169$	−978.845	−0.445537
$170$	−2579.60	−1.16380
$171$	563.994	0.252221
$172$	−128.409	−0.0569252
$173$	−1390.24	−0.610973	−0.305486	−	0.952196i	$-0.598819\pi$
$173$	−1390.24	−0.610973	−0.305486	+	0.952196i	$0.598819\pi$
$174$	−6727.91	−2.93127
$175$	0	0
$176$	−47.2078	−0.0202183
$177$	−2959.49	−1.25677
$178$	2804.73	1.18103
$179$	693.895	0.289744	0.144872	−	0.989450i	$-0.453723\pi$
$179$	693.895	0.289744	0.144872	+	0.989450i	$0.453723\pi$
$180$	−597.036	−0.247225
$181$	2355.50	0.967309	0.483655	−	0.875259i	$-0.339309\pi$
$181$	2355.50	0.967309	0.483655	+	0.875259i	$0.339309\pi$
$182$	0	0
$183$	219.783	0.0887807
$184$	2122.46	0.850381
$185$	−3095.83	−1.23032
$186$	−4537.46	−1.78872
$187$	−54.6100	−0.0213555
$188$	1368.51	0.530897
$189$	0	0
$190$	678.602	0.259110
$191$	−2168.09	−0.821349	−0.410674	−	0.911782i	$-0.634707\pi$
$191$	−2168.09	−0.821349	−0.410674	+	0.911782i	$0.634707\pi$
$192$	1455.10	0.546940
$193$	1305.00	0.486717	0.243358	−	0.969936i	$-0.421751\pi$
$193$	1305.00	0.486717	0.243358	+	0.969936i	$0.421751\pi$
$194$	−858.695	−0.317787
$195$	2112.29	0.775714
$196$	0	0
$197$	−4800.27	−1.73607	−0.868033	−	0.496507i	$-0.834616\pi$
$197$	−4800.27	−1.73607	−0.868033	+	0.496507i	$0.834616\pi$
$198$	−46.4988	−0.0166895
$199$	2113.34	0.752816	0.376408	−	0.926454i	$-0.377159\pi$
$199$	2113.34	0.752816	0.376408	+	0.926454i	$0.377159\pi$
$200$	−871.213	−0.308020
$201$	114.707	0.0402527
$202$	−3917.85	−1.36465
$203$	0	0
$204$	−1938.07	−0.665158
$205$	1632.14	0.556067
$206$	1059.22	0.358248
$207$	2997.31	1.00641
$208$	2756.30	0.918822
$209$	14.3660	0.00475462
$210$	0	0
$211$	5564.31	1.81546	0.907732	−	0.419551i	$-0.137812\pi$
$211$	5564.31	1.81546	0.907732	+	0.419551i	$0.137812\pi$
$212$	−1741.20	−0.564085
$213$	−1559.07	−0.501531
$214$	−5459.53	−1.74395
$215$	366.321	0.116200
$216$	−416.966	−0.131347
$217$	0	0
$218$	1857.93	0.577225
$219$	−7324.80	−2.26011
$220$	−15.2076	−0.00466044
$221$	3188.49	0.970501
$222$	−8556.91	−2.58695
$223$	1709.75	0.513422	0.256711	−	0.966488i	$-0.417361\pi$
$223$	1709.75	0.513422	0.256711	+	0.966488i	$0.417361\pi$
$224$	0	0
$225$	−1230.32	−0.364538
$226$	217.717	0.0640811
$227$	−347.506	−0.101607	−0.0508035	−	0.998709i	$-0.516178\pi$
$227$	−347.506	−0.101607	−0.0508035	+	0.998709i	$0.516178\pi$
$228$	509.840	0.148092
$229$	−713.508	−0.205895	−0.102947	−	0.994687i	$-0.532827\pi$
$229$	−713.508	−0.205895	−0.102947	+	0.994687i	$0.532827\pi$
$230$	3606.39	1.03391
$231$	0	0
$232$	4748.24	1.34370
$233$	−6539.93	−1.83882	−0.919410	−	0.393300i	$-0.871333\pi$
$233$	−6539.93	−1.83882	−0.919410	+	0.393300i	$0.871333\pi$
$234$	2714.91	0.758457
$235$	−3904.02	−1.08370
$236$	−1244.05	−0.343138
$237$	3164.43	0.867307
$238$	0	0
$239$	−2561.41	−0.693238	−0.346619	−	0.938006i	$-0.612670\pi$
$239$	−2561.41	−0.693238	−0.346619	+	0.938006i	$0.612670\pi$
$240$	4779.44	1.28547
$241$	4656.80	1.24469	0.622346	−	0.782742i	$-0.286180\pi$
$241$	4656.80	1.24469	0.622346	+	0.782742i	$0.286180\pi$
$242$	4410.49	1.17156
$243$	−5090.27	−1.34379
$244$	92.3879	0.0242399
$245$	0	0
$246$	4511.26	1.16922
$247$	−838.779	−0.216074
$248$	3202.32	0.819950
$249$	−2120.65	−0.539721
$250$	−5009.95	−1.26743
$251$	−6104.04	−1.53499	−0.767497	−	0.641053i	$-0.778498\pi$
$251$	−6104.04	−1.53499	−0.767497	+	0.641053i	$0.778498\pi$
$252$	0	0
$253$	76.3471	0.0189720
$254$	6320.60	1.56138
$255$	5528.86	1.35777
$256$	4027.29	0.983225
$257$	−682.439	−0.165640	−0.0828199	−	0.996565i	$-0.526393\pi$
$257$	−682.439	−0.165640	−0.0828199	+	0.996565i	$0.526393\pi$
$258$	1012.52	0.244328
$259$	0	0
$260$	887.919	0.211794
$261$	6705.40	1.59024
$262$	−5091.44	−1.20057
$263$	1671.87	0.391984	0.195992	−	0.980605i	$-0.437207\pi$
$263$	1671.87	0.391984	0.195992	+	0.980605i	$0.437207\pi$
$264$	70.5722	0.0164523
$265$	4967.22	1.15145
$266$	0	0
$267$	−6011.38	−1.37787
$268$	48.2180	0.0109902
$269$	261.999	0.0593843	0.0296921	−	0.999559i	$-0.490547\pi$
$269$	261.999	0.0593843	0.0296921	+	0.999559i	$0.490547\pi$
$270$	−708.489	−0.159694
$271$	−4620.04	−1.03560	−0.517800	−	0.855502i	$-0.673249\pi$
$271$	−4620.04	−1.03560	−0.517800	+	0.855502i	$0.673249\pi$
$272$	7214.53	1.60825
$273$	0	0
$274$	5619.41	1.23898
$275$	−31.3384	−0.00687192
$276$	2709.51	0.590918
$277$	5163.93	1.12011	0.560055	−	0.828456i	$-0.310780\pi$
$277$	5163.93	1.12011	0.560055	+	0.828456i	$0.310780\pi$
$278$	3140.81	0.677601
$279$	4522.28	0.970400
$280$	0	0
$281$	−5275.67	−1.12000	−0.560000	−	0.828493i	$-0.689199\pi$
$281$	−5275.67	−1.12000	−0.560000	+	0.828493i	$0.689199\pi$
$282$	−10790.8	−2.27865
$283$	5028.34	1.05620	0.528098	−	0.849183i	$-0.322905\pi$
$283$	5028.34	1.05620	0.528098	+	0.849183i	$0.322905\pi$
$284$	−655.371	−0.136933
$285$	−1454.45	−0.302295
$286$	69.1537	0.0142977
$287$	0	0
$288$	3022.97	0.618508
$289$	3432.77	0.698711
$290$	8067.99	1.63368
$291$	1840.44	0.370751
$292$	−3079.04	−0.617080
$293$	−8840.69	−1.76273	−0.881363	−	0.472439i	$-0.843374\pi$
$293$	−8840.69	−1.76273	−0.881363	+	0.472439i	$0.843374\pi$
$294$	0	0
$295$	3548.96	0.700436
$296$	6039.06	1.18586
$297$	−14.9987	−0.00293035
$298$	−10222.4	−1.98714
$299$	−4457.64	−0.862181
$300$	−1112.18	−0.214039
$301$	0	0
$302$	7778.68	1.48216
$303$	8397.14	1.59209
$304$	−1897.89	−0.358064
$305$	−263.560	−0.0494801
$306$	7106.18	1.32756
$307$	−6565.15	−1.22050	−0.610249	−	0.792209i	$-0.708931\pi$
$307$	−6565.15	−1.22050	−0.610249	+	0.792209i	$0.708931\pi$
$308$	0	0
$309$	−2270.22	−0.417956
$310$	5441.23	0.996908
$311$	−1250.31	−0.227969	−0.113985	−	0.993483i	$-0.536361\pi$
$311$	−1250.31	−0.227969	−0.113985	+	0.993483i	$0.536361\pi$
$312$	−4120.46	−0.747677
$313$	2968.85	0.536132	0.268066	−	0.963401i	$-0.413615\pi$
$313$	2968.85	0.536132	0.268066	+	0.963401i	$0.413615\pi$
$314$	5246.03	0.942837
$315$	0	0
$316$	1330.20	0.236802
$317$	1054.32	0.186803	0.0934013	−	0.995629i	$-0.470226\pi$
$317$	1054.32	0.186803	0.0934013	+	0.995629i	$0.470226\pi$
$318$	13729.4	2.42110
$319$	170.799	0.0299778
$320$	−1744.93	−0.304826
$321$	11701.4	2.03461
$322$	0	0
$323$	−2195.48	−0.378204
$324$	−2424.51	−0.415725
$325$	1829.74	0.312295
$326$	2720.87	0.462255
$327$	−3982.11	−0.673429
$328$	−3183.83	−0.535969
$329$	0	0
$330$	119.913	0.0200030
$331$	−2881.73	−0.478532	−0.239266	−	0.970954i	$-0.576907\pi$
$331$	−2881.73	−0.478532	−0.239266	+	0.970954i	$0.576907\pi$
$332$	−891.432	−0.147361
$333$	8528.28	1.40344
$334$	5603.51	0.917995
$335$	−137.554	−0.0224340
$336$	0	0
$337$	−6147.77	−0.993740	−0.496870	−	0.867825i	$-0.665517\pi$
$337$	−6147.77	−0.993740	−0.496870	+	0.867825i	$0.665517\pi$
$338$	3244.43	0.522112
$339$	−466.634	−0.0747613
$340$	2324.10	0.370712
$341$	115.191	0.0182930
$342$	−1869.39	−0.295570
$343$	0	0
$344$	−714.586	−0.112000
$345$	−7729.58	−1.20622
$346$	4608.04	0.715982
$347$	1404.42	0.217271	0.108636	−	0.994082i	$-0.465352\pi$
$347$	1404.42	0.217271	0.108636	+	0.994082i	$0.465352\pi$
$348$	6061.55	0.933716
$349$	4472.14	0.685926	0.342963	−	0.939349i	$-0.388570\pi$
$349$	4472.14	0.685926	0.342963	+	0.939349i	$0.388570\pi$
$350$	0	0
$351$	875.721	0.133170
$352$	77.0007	0.0116595
$353$	−2146.48	−0.323642	−0.161821	−	0.986820i	$-0.551737\pi$
$353$	−2146.48	−0.323642	−0.161821	+	0.986820i	$0.551737\pi$
$354$	9809.38	1.47278
$355$	1869.61	0.279518
$356$	−2526.93	−0.376200
$357$	0	0
$358$	−2299.95	−0.339543
$359$	1960.49	0.288219	0.144109	−	0.989562i	$-0.453968\pi$
$359$	1960.49	0.288219	0.144109	+	0.989562i	$0.453968\pi$
$360$	−3322.45	−0.486412
$361$	−6281.45	−0.915796
$362$	−7807.43	−1.13356
$363$	−9453.01	−1.36682
$364$	0	0
$365$	8783.77	1.25963
$366$	−728.484	−0.104040
$367$	−13485.2	−1.91804	−0.959021	−	0.283337i	$-0.908559\pi$
$367$	−13485.2	−1.91804	−0.959021	+	0.283337i	$0.908559\pi$
$368$	−10086.2	−1.42875
$369$	−4496.16	−0.634312
$370$	10261.3	1.44178
$371$	0	0
$372$	4088.05	0.569773
$373$	−12034.5	−1.67057	−0.835285	−	0.549817i	$-0.814697\pi$
$373$	−12034.5	−1.67057	−0.835285	+	0.549817i	$0.814697\pi$
$374$	181.008	0.0250259
$375$	10737.8	1.47867
$376$	7615.60	1.04453
$377$	−9972.36	−1.36234
$378$	0	0
$379$	−10185.1	−1.38041	−0.690204	−	0.723615i	$-0.742479\pi$
$379$	−10185.1	−1.38041	−0.690204	+	0.723615i	$0.742479\pi$
$380$	−611.390	−0.0825359
$381$	−13546.9	−1.82160
$382$	7186.26	0.962515
$383$	−13508.3	−1.80219	−0.901097	−	0.433618i	$-0.857237\pi$
$383$	−13508.3	−1.80219	−0.901097	+	0.433618i	$0.857237\pi$
$384$	−12143.7	−1.61382
$385$	0	0
$386$	−4325.51	−0.570369
$387$	−1009.13	−0.132550
$388$	773.646	0.101227
$389$	−6651.52	−0.866954	−0.433477	−	0.901165i	$-0.642714\pi$
$389$	−6651.52	−0.866954	−0.433477	+	0.901165i	$0.642714\pi$
$390$	−7001.30	−0.909037
$391$	−11667.7	−1.50911
$392$	0	0
$393$	10912.5	1.40067
$394$	15910.7	2.03445
$395$	−3794.73	−0.483376
$396$	41.8934	0.00531622
$397$	8308.29	1.05033	0.525165	−	0.851000i	$-0.324004\pi$
$397$	8308.29	1.05033	0.525165	+	0.851000i	$0.324004\pi$
$398$	−7004.77	−0.882204
$399$	0	0
$400$	4140.12	0.517515
$401$	2963.57	0.369061	0.184530	−	0.982827i	$-0.440924\pi$
$401$	2963.57	0.369061	0.184530	+	0.982827i	$0.440924\pi$
$402$	−380.202	−0.0471710
$403$	−6725.59	−0.831328
$404$	3529.81	0.434690
$405$	6916.54	0.848607
$406$	0	0
$407$	217.231	0.0264564
$408$	−10785.2	−1.30869
$409$	9951.28	1.20308	0.601540	−	0.798843i	$-0.294554\pi$
$409$	9951.28	1.20308	0.601540	+	0.798843i	$0.294554\pi$
$410$	−5409.82	−0.651639
$411$	−12044.1	−1.44548
$412$	−954.308	−0.114115
$413$	0	0
$414$	−9934.76	−1.17939
$415$	2543.04	0.300802
$416$	−4495.80	−0.529867
$417$	−6731.70	−0.790534
$418$	−47.6168	−0.00557180
$419$	−5281.70	−0.615818	−0.307909	−	0.951416i	$-0.599629\pi$
$419$	−5281.70	−0.615818	−0.307909	+	0.951416i	$0.599629\pi$
$420$	0	0
$421$	−1668.54	−0.193159	−0.0965795	−	0.995325i	$-0.530790\pi$
$421$	−1668.54	−0.193159	−0.0965795	+	0.995325i	$0.530790\pi$
$422$	−18443.2	−2.12749
$423$	10754.7	1.23619
$424$	−9689.60	−1.10983
$425$	4789.29	0.546623
$426$	5167.64	0.587730
$427$	0	0
$428$	4918.80	0.555512
$429$	−148.217	−0.0166806
$430$	−1214.19	−0.136171
$431$	−10348.7	−1.15657	−0.578284	−	0.815835i	$-0.696278\pi$
$431$	−10348.7	−1.15657	−0.578284	+	0.815835i	$0.696278\pi$
$432$	1981.48	0.220681
$433$	−2968.27	−0.329436	−0.164718	−	0.986341i	$-0.552671\pi$
$433$	−2968.27	−0.329436	−0.164718	+	0.986341i	$0.552671\pi$
$434$	0	0
$435$	−17292.1	−1.90596
$436$	−1673.91	−0.183867
$437$	3069.38	0.335991
$438$	24278.4	2.64856
$439$	9224.53	1.00288	0.501438	−	0.865194i	$-0.332804\pi$
$439$	9224.53	1.00288	0.501438	+	0.865194i	$0.332804\pi$
$440$	−84.6289	−0.00916937
$441$	0	0
$442$	−10568.4	−1.13730
$443$	−10115.5	−1.08488	−0.542438	−	0.840096i	$-0.682499\pi$
$443$	−10115.5	−1.08488	−0.542438	+	0.840096i	$0.682499\pi$
$444$	7709.40	0.824036
$445$	7208.73	0.767925
$446$	−5667.05	−0.601665
$447$	21909.7	2.31833
$448$	0	0
$449$	14386.0	1.51207	0.756034	−	0.654532i	$-0.227134\pi$
$449$	14386.0	1.51207	0.756034	+	0.654532i	$0.227134\pi$
$450$	4077.95	0.427192
$451$	−114.526	−0.0119574
$452$	−196.154	−0.0204121
$453$	−16672.1	−1.72919
$454$	1151.83	0.119070
$455$	0	0
$456$	2837.21	0.291369
$457$	−10031.8	−1.02684	−0.513421	−	0.858137i	$-0.671622\pi$
$457$	−10031.8	−1.02684	−0.513421	+	0.858137i	$0.671622\pi$
$458$	2364.96	0.241282
$459$	2292.18	0.233093
$460$	−3249.20	−0.329336
$461$	124.788	0.0126072	0.00630362	−	0.999980i	$-0.497993\pi$
$461$	124.788	0.0126072	0.00630362	+	0.999980i	$0.497993\pi$
$462$	0	0
$463$	15438.9	1.54969	0.774847	−	0.632148i	$-0.217827\pi$
$463$	15438.9	1.54969	0.774847	+	0.632148i	$0.217827\pi$
$464$	−22564.3	−2.25759
$465$	−11662.2	−1.16306
$466$	21677.0	2.15486
$467$	12014.7	1.19052	0.595259	−	0.803534i	$-0.297049\pi$
$467$	12014.7	1.19052	0.595259	+	0.803534i	$0.297049\pi$
$468$	−2446.01	−0.241596
$469$	0	0
$470$	12940.1	1.26996
$471$	−11243.8	−1.09998
$472$	−6923.00	−0.675121
$473$	−25.7044	−0.00249871
$474$	−10488.7	−1.01637
$475$	−1259.90	−0.121701
$476$	0	0
$477$	−13683.5	−1.31347
$478$	8489.93	0.812386
$479$	−6241.39	−0.595358	−0.297679	−	0.954666i	$-0.596212\pi$
$479$	−6241.39	−0.595358	−0.297679	+	0.954666i	$0.596212\pi$
$480$	−7795.75	−0.741303
$481$	−12683.4	−1.20231
$482$	−15435.2	−1.45862
$483$	0	0
$484$	−3973.65	−0.373183
$485$	−2207.03	−0.206631
$486$	16872.0	1.57475
$487$	924.180	0.0859930	0.0429965	−	0.999075i	$-0.486310\pi$
$487$	924.180	0.0859930	0.0429965	+	0.999075i	$0.486310\pi$
$488$	514.130	0.0476917
$489$	−5831.65	−0.539297
$490$	0	0
$491$	−7044.15	−0.647451	−0.323725	−	0.946151i	$-0.604935\pi$
$491$	−7044.15	−0.647451	−0.323725	+	0.946151i	$0.604935\pi$
$492$	−4064.44	−0.372438
$493$	−26102.3	−2.38457
$494$	2780.18	0.253211
$495$	−119.512	−0.0108518
$496$	−15217.9	−1.37763
$497$	0	0
$498$	7029.00	0.632484
$499$	−3981.76	−0.357210	−0.178605	−	0.983921i	$-0.557158\pi$
$499$	−3981.76	−0.357210	−0.178605	+	0.983921i	$0.557158\pi$
$500$	4513.74	0.403722
$501$	−12010.0	−1.07099
$502$	20232.2	1.79882
$503$	11650.2	1.03272	0.516358	−	0.856373i	$-0.327288\pi$
$503$	11650.2	1.03272	0.516358	+	0.856373i	$0.327288\pi$
$504$	0	0
$505$	−10069.7	−0.887318
$506$	−253.057	−0.0222327
$507$	−6953.80	−0.609131
$508$	−5694.58	−0.497354
$509$	−11408.7	−0.993481	−0.496740	−	0.867899i	$-0.665470\pi$
$509$	−11408.7	−0.993481	−0.496740	+	0.867899i	$0.665470\pi$
$510$	−18325.7	−1.59113
$511$	0	0
$512$	326.513	0.0281836
$513$	−602.991	−0.0518961
$514$	2261.98	0.194108
$515$	2722.41	0.232939
$516$	−912.233	−0.0778271
$517$	273.941	0.0233035
$518$	0	0
$519$	−9876.42	−0.835312
$520$	4941.19	0.416703
$521$	−15272.4	−1.28425	−0.642127	−	0.766598i	$-0.721948\pi$
$521$	−15272.4	−1.28425	−0.642127	+	0.766598i	$0.721948\pi$
$522$	−22225.4	−1.86356
$523$	20831.4	1.74167	0.870835	−	0.491575i	$-0.163579\pi$
$523$	20831.4	1.74167	0.870835	+	0.491575i	$0.163579\pi$
$524$	4587.16	0.382426
$525$	0	0
$526$	−5541.50	−0.459355
$527$	−17604.0	−1.45511
$528$	−335.369	−0.0276421
$529$	4145.03	0.340678
$530$	−16464.1	−1.34935
$531$	−9776.57	−0.798996
$532$	0	0
$533$	6686.75	0.543406
$534$	19925.0	1.61468
$535$	−14032.1	−1.13395
$536$	268.328	0.0216232
$537$	4929.50	0.396133
$538$	−868.410	−0.0695907
$539$	0	0
$540$	638.318	0.0508682
$541$	−1411.76	−0.112192	−0.0560962	−	0.998425i	$-0.517865\pi$
$541$	−1411.76	−0.112192	−0.0560962	+	0.998425i	$0.517865\pi$
$542$	15313.4	1.21359
$543$	16733.7	1.32249
$544$	−11767.6	−0.927450
$545$	4775.27	0.375322
$546$	0	0
$547$	−328.281	−0.0256605	−0.0128302	−	0.999918i	$-0.504084\pi$
$547$	−328.281	−0.0256605	−0.0128302	+	0.999918i	$0.504084\pi$
$548$	−5062.84	−0.394661
$549$	726.047	0.0564425
$550$	103.873	0.00805301
$551$	6866.62	0.530903
$552$	15078.2	1.16263
$553$	0	0
$554$	−17116.1	−1.31262
$555$	−21993.1	−1.68208
$556$	−2829.73	−0.215840
$557$	−1908.49	−0.145180	−0.0725901	−	0.997362i	$-0.523126\pi$
$557$	−1908.49	−0.145180	−0.0725901	+	0.997362i	$0.523126\pi$
$558$	−14989.3	−1.13718
$559$	1500.79	0.113554
$560$	0	0
$561$	−387.954	−0.0291969
$562$	17486.5	1.31250
$563$	−3413.23	−0.255507	−0.127753	−	0.991806i	$-0.540777\pi$
$563$	−3413.23	−0.255507	−0.127753	+	0.991806i	$0.540777\pi$
$564$	9721.99	0.725833
$565$	559.579	0.0416667
$566$	−16666.7	−1.23773
$567$	0	0
$568$	−3647.07	−0.269415
$569$	−15405.8	−1.13505	−0.567527	−	0.823355i	$-0.692100\pi$
$569$	−15405.8	−1.13505	−0.567527	+	0.823355i	$0.692100\pi$
$570$	4820.85	0.354251
$571$	18819.2	1.37926	0.689632	−	0.724160i	$-0.257772\pi$
$571$	18819.2	1.37926	0.689632	+	0.724160i	$0.257772\pi$
$572$	−62.3044	−0.00455433
$573$	−15402.3	−1.12293
$574$	0	0
$575$	−6695.64	−0.485613
$576$	4806.86	0.347719
$577$	−8098.53	−0.584309	−0.292154	−	0.956371i	$-0.594372\pi$
$577$	−8098.53	−0.584309	−0.292154	+	0.956371i	$0.594372\pi$
$578$	−11378.1	−0.818799
$579$	9270.87	0.665431
$580$	−7268.90	−0.520387
$581$	0	0
$582$	−6100.25	−0.434473
$583$	−348.545	−0.0247603
$584$	−17134.6	−1.21410
$585$	6977.87	0.493162
$586$	29303.0	2.06569
$587$	3631.44	0.255342	0.127671	−	0.991817i	$-0.459250\pi$
$587$	3631.44	0.255342	0.127671	+	0.991817i	$0.459250\pi$
$588$	0	0
$589$	4631.00	0.323968
$590$	−11763.2	−0.820822
$591$	−34101.5	−2.37352
$592$	−28698.4	−1.99240
$593$	14298.2	0.990147	0.495073	−	0.868851i	$-0.335141\pi$
$593$	14298.2	0.990147	0.495073	+	0.868851i	$0.335141\pi$
$594$	49.7140	0.00343399
$595$	0	0
$596$	9209.95	0.632977
$597$	15013.3	1.02924
$598$	14775.1	1.01037
$599$	−27823.6	−1.89790	−0.948949	−	0.315430i	$-0.897851\pi$
$599$	−27823.6	−1.89790	−0.948949	+	0.315430i	$0.897851\pi$
$600$	−6189.18	−0.421120
$601$	−3557.15	−0.241430	−0.120715	−	0.992687i	$-0.538519\pi$
$601$	−3557.15	−0.241430	−0.120715	+	0.992687i	$0.538519\pi$
$602$	0	0
$603$	378.930	0.0255907
$604$	−7008.25	−0.472122
$605$	11335.9	0.761767
$606$	−27832.8	−1.86572
$607$	−19170.9	−1.28192	−0.640958	−	0.767576i	$-0.721463\pi$
$607$	−19170.9	−1.28192	−0.640958	+	0.767576i	$0.721463\pi$
$608$	3095.65	0.206489
$609$	0	0
$610$	873.585	0.0579843
$611$	−15994.5	−1.05903
$612$	−6402.36	−0.422876
$613$	4287.83	0.282518	0.141259	−	0.989973i	$-0.454885\pi$
$613$	4287.83	0.282518	0.141259	+	0.989973i	$0.454885\pi$
$614$	21760.6	1.43027
$615$	11594.9	0.760245
$616$	0	0
$617$	−10569.5	−0.689649	−0.344824	−	0.938667i	$-0.612062\pi$
$617$	−10569.5	−0.689649	−0.344824	+	0.938667i	$0.612062\pi$
$618$	7524.77	0.489791
$619$	−19947.5	−1.29525	−0.647624	−	0.761960i	$-0.724237\pi$
$619$	−19947.5	−1.29525	−0.647624	+	0.761960i	$0.724237\pi$
$620$	−4902.31	−0.317551
$621$	−3204.56	−0.207077
$622$	4144.21	0.267150
$623$	0	0
$624$	19581.0	1.25620
$625$	−6323.50	−0.404704
$626$	−9840.42	−0.628278
$627$	102.057	0.00650043
$628$	−4726.44	−0.300328
$629$	−33198.3	−2.10446
$630$	0	0
$631$	8854.29	0.558611	0.279306	−	0.960202i	$-0.409896\pi$
$631$	8854.29	0.558611	0.279306	+	0.960202i	$0.409896\pi$
$632$	7402.41	0.465905
$633$	39529.4	2.48207
$634$	−3494.60	−0.218909
$635$	16245.3	1.01523
$636$	−12369.6	−0.771207
$637$	0	0
$638$	−566.122	−0.0351301
$639$	−5150.35	−0.318849
$640$	14562.5	0.899429
$641$	10022.5	0.617571	0.308786	−	0.951132i	$-0.400077\pi$
$641$	10022.5	0.617571	0.308786	+	0.951132i	$0.400077\pi$
$642$	−38785.0	−2.38430
$643$	5806.52	0.356123	0.178061	−	0.984019i	$-0.443017\pi$
$643$	5806.52	0.356123	0.178061	+	0.984019i	$0.443017\pi$
$644$	0	0
$645$	2602.38	0.158866
$646$	7277.04	0.443206
$647$	−8583.93	−0.521591	−0.260795	−	0.965394i	$-0.583985\pi$
$647$	−8583.93	−0.521591	−0.260795	+	0.965394i	$0.583985\pi$
$648$	−13492.2	−0.817936
$649$	−249.027	−0.0150619
$650$	−6064.77	−0.365969
$651$	0	0
$652$	−2451.39	−0.147245
$653$	17048.8	1.02170	0.510849	−	0.859670i	$-0.329331\pi$
$653$	17048.8	1.02170	0.510849	+	0.859670i	$0.329331\pi$
$654$	13198.9	0.789172
$655$	−13086.1	−0.780633
$656$	15130.0	0.900499
$657$	−24197.2	−1.43687
$658$	0	0
$659$	−2694.69	−0.159287	−0.0796437	−	0.996823i	$-0.525378\pi$
$659$	−2694.69	−0.159287	−0.0796437	+	0.996823i	$0.525378\pi$
$660$	−108.036	−0.00637168
$661$	29666.8	1.74570	0.872848	−	0.487992i	$-0.162270\pi$
$661$	29666.8	1.74570	0.872848	+	0.487992i	$0.162270\pi$
$662$	9551.64	0.560778
$663$	22651.3	1.32685
$664$	−4960.74	−0.289931
$665$	0	0
$666$	−28267.5	−1.64466
$667$	36492.2	2.11842
$668$	−5048.52	−0.292415
$669$	12146.2	0.701942
$670$	455.931	0.0262898
$671$	18.4938	0.00106400
$672$	0	0
$673$	17932.8	1.02713	0.513564	−	0.858051i	$-0.328325\pi$
$673$	17932.8	1.02713	0.513564	+	0.858051i	$0.328325\pi$
$674$	20377.1	1.16454
$675$	1315.39	0.0750062
$676$	−2923.09	−0.166312
$677$	−2440.74	−0.138560	−0.0692801	−	0.997597i	$-0.522070\pi$
$677$	−2440.74	−0.138560	−0.0692801	+	0.997597i	$0.522070\pi$
$678$	1546.68	0.0876106
$679$	0	0
$680$	12933.4	0.729373
$681$	−2468.72	−0.138915
$682$	−381.806	−0.0214371
$683$	−12722.2	−0.712737	−0.356369	−	0.934345i	$-0.615985\pi$
$683$	−12722.2	−0.712737	−0.356369	+	0.934345i	$0.615985\pi$
$684$	1684.24	0.0941497
$685$	14443.1	0.805608
$686$	0	0
$687$	−5068.83	−0.281496
$688$	3395.81	0.188175
$689$	20350.3	1.12523
$690$	25620.1	1.41354
$691$	5584.80	0.307461	0.153731	−	0.988113i	$-0.450871\pi$
$691$	5584.80	0.307461	0.153731	+	0.988113i	$0.450871\pi$
$692$	−4151.64	−0.228066
$693$	0	0
$694$	−4655.02	−0.254614
$695$	8072.53	0.440588
$696$	33731.9	1.83708
$697$	17502.4	0.951148
$698$	−14823.1	−0.803817
$699$	−46460.3	−2.51400
$700$	0	0
$701$	19891.2	1.07173	0.535864	−	0.844304i	$-0.319986\pi$
$701$	19891.2	1.07173	0.535864	+	0.844304i	$0.319986\pi$
$702$	−2902.63	−0.156058
$703$	8733.33	0.468540
$704$	122.440	0.00655486
$705$	−27734.5	−1.48162
$706$	7114.62	0.379266
$707$	0	0
$708$	−8837.82	−0.469132
$709$	−14613.5	−0.774078	−0.387039	−	0.922063i	$-0.626502\pi$
$709$	−14613.5	−0.774078	−0.387039	+	0.922063i	$0.626502\pi$
$710$	−6196.94	−0.327559
$711$	10453.6	0.551392
$712$	−14062.1	−0.740170
$713$	24611.2	1.29270
$714$	0	0
$715$	177.739	0.00929661
$716$	2072.16	0.108157
$717$	−18196.5	−0.947783
$718$	−6498.14	−0.337755
$719$	11027.7	0.571995	0.285998	−	0.958230i	$-0.407675\pi$
$719$	11027.7	0.571995	0.285998	+	0.958230i	$0.407675\pi$
$720$	15788.7	0.817237
$721$	0	0
$722$	20820.2	1.07320
$723$	33082.3	1.70172
$724$	7034.15	0.361080
$725$	−14979.1	−0.767322
$726$	31332.5	1.60173
$727$	−1650.84	−0.0842178	−0.0421089	−	0.999113i	$-0.513408\pi$
$727$	−1650.84	−0.0842178	−0.0421089	+	0.999113i	$0.513408\pi$
$728$	0	0
$729$	−14240.8	−0.723506
$730$	−29114.3	−1.47612
$731$	3928.27	0.198758
$732$	656.332	0.0331403
$733$	28314.8	1.42678	0.713391	−	0.700767i	$-0.247159\pi$
$733$	28314.8	1.42678	0.713391	+	0.700767i	$0.247159\pi$
$734$	44697.4	2.24770
$735$	0	0
$736$	16451.7	0.823935
$737$	9.65204	0.000482412 0
$738$	14902.8	0.743332
$739$	−28963.4	−1.44172	−0.720862	−	0.693078i	$-0.756254\pi$
$739$	−28963.4	−1.44172	−0.720862	+	0.693078i	$0.756254\pi$
$740$	−9244.97	−0.459259
$741$	−5958.76	−0.295413
$742$	0	0
$743$	−15510.4	−0.765844	−0.382922	−	0.923781i	$-0.625082\pi$
$743$	−15510.4	−0.765844	−0.382922	+	0.923781i	$0.625082\pi$
$744$	22749.6	1.12102
$745$	−26273.8	−1.29208
$746$	39889.0	1.95769
$747$	−7005.48	−0.343129
$748$	−163.080	−0.00797165
$749$	0	0
$750$	−35591.1	−1.73281
$751$	−2901.63	−0.140988	−0.0704941	−	0.997512i	$-0.522458\pi$
$751$	−2901.63	−0.140988	−0.0704941	+	0.997512i	$0.522458\pi$
$752$	−36190.4	−1.75496
$753$	−43363.6	−2.09862
$754$	33053.9	1.59649
$755$	19992.8	0.963727
$756$	0	0
$757$	9260.00	0.444598	0.222299	−	0.974979i	$-0.428644\pi$
$757$	9260.00	0.444598	0.222299	+	0.974979i	$0.428644\pi$
$758$	33759.2	1.61766
$759$	542.377	0.0259381
$760$	−3402.33	−0.162389
$761$	6418.29	0.305733	0.152866	−	0.988247i	$-0.451150\pi$
$761$	6418.29	0.305733	0.152866	+	0.988247i	$0.451150\pi$
$762$	44902.1	2.13469
$763$	0	0
$764$	−6474.50	−0.306596
$765$	18264.4	0.863203
$766$	44773.9	2.11194
$767$	14539.8	0.684489
$768$	28610.2	1.34425
$769$	−5335.88	−0.250217	−0.125108	−	0.992143i	$-0.539928\pi$
$769$	−5335.88	−0.250217	−0.125108	+	0.992143i	$0.539928\pi$
$770$	0	0
$771$	−4848.11	−0.226460
$772$	3897.09	0.181683
$773$	−20062.9	−0.933520	−0.466760	−	0.884384i	$-0.654579\pi$
$773$	−20062.9	−0.933520	−0.466760	+	0.884384i	$0.654579\pi$
$774$	3344.81	0.155332
$775$	−10102.2	−0.468236
$776$	4305.27	0.199162
$777$	0	0
$778$	22046.8	1.01596
$779$	−4604.26	−0.211765
$780$	6307.86	0.289561
$781$	−131.189	−0.00601064
$782$	38673.4	1.76849
$783$	−7169.04	−0.327204
$784$	0	0
$785$	13483.4	0.613049
$786$	−36170.1	−1.64140
$787$	−17182.2	−0.778248	−0.389124	−	0.921185i	$-0.627222\pi$
$787$	−17182.2	−0.778248	−0.389124	+	0.921185i	$0.627222\pi$
$788$	−14334.9	−0.648045
$789$	11877.1	0.535914
$790$	12577.8	0.566454
$791$	0	0
$792$	233.133	0.0104596
$793$	−1079.79	−0.0483535
$794$	−27538.3	−1.23085
$795$	35287.6	1.57424
$796$	6310.99	0.281014
$797$	3342.90	0.148572	0.0742859	−	0.997237i	$-0.476332\pi$
$797$	3342.90	0.148572	0.0742859	+	0.997237i	$0.476332\pi$
$798$	0	0
$799$	−41865.0	−1.85366
$800$	−6752.95	−0.298441
$801$	−19858.4	−0.875981
$802$	−9822.90	−0.432492
$803$	−616.348	−0.0270865
$804$	342.545	0.0150257
$805$	0	0
$806$	22292.3	0.974210
$807$	1861.27	0.0811892
$808$	19643.1	0.855248
$809$	−10782.5	−0.468596	−0.234298	−	0.972165i	$-0.575279\pi$
$809$	−10782.5	−0.468596	−0.234298	+	0.972165i	$0.575279\pi$
$810$	−22925.2	−0.994458
$811$	22440.1	0.971612	0.485806	−	0.874067i	$-0.338526\pi$
$811$	22440.1	0.971612	0.485806	+	0.874067i	$0.338526\pi$
$812$	0	0
$813$	−32821.2	−1.41586
$814$	−720.024	−0.0310035
$815$	6993.21	0.300566
$816$	51252.7	2.19878
$817$	−1033.39	−0.0442519
$818$	−32984.1	−1.40985
$819$	0	0
$820$	4874.01	0.207570
$821$	−10938.7	−0.464996	−0.232498	−	0.972597i	$-0.574690\pi$
$821$	−10938.7	−0.464996	−0.232498	+	0.972597i	$0.574690\pi$
$822$	39920.8	1.69392
$823$	−37928.5	−1.60645	−0.803223	−	0.595678i	$-0.796883\pi$
$823$	−37928.5	−1.60645	−0.803223	+	0.595678i	$0.796883\pi$
$824$	−5310.63	−0.224520
$825$	−222.631	−0.00939517
$826$	0	0
$827$	36038.1	1.51532	0.757660	−	0.652650i	$-0.226343\pi$
$827$	36038.1	1.51532	0.757660	+	0.652650i	$0.226343\pi$
$828$	8950.78	0.375678
$829$	−29221.5	−1.22425	−0.612127	−	0.790760i	$-0.709686\pi$
$829$	−29221.5	−1.22425	−0.612127	+	0.790760i	$0.709686\pi$
$830$	−8429.05	−0.352502
$831$	36685.0	1.53139
$832$	−7148.82	−0.297886
$833$	0	0
$834$	22312.6	0.926404
$835$	14402.2	0.596896
$836$	42.9006	0.00177482
$837$	−4834.97	−0.199667
$838$	17506.5	0.721660
$839$	6285.44	0.258638	0.129319	−	0.991603i	$-0.458721\pi$
$839$	6285.44	0.258638	0.129319	+	0.991603i	$0.458721\pi$
$840$	0	0
$841$	57249.1	2.34733
$842$	5530.48	0.226357
$843$	−37478.8	−1.53125
$844$	16616.5	0.677682
$845$	8338.87	0.339486
$846$	−35646.9	−1.44866
$847$	0	0
$848$	46046.3	1.86466
$849$	35721.8	1.44401
$850$	−15874.4	−0.640572
$851$	46412.8	1.86958
$852$	−4655.81	−0.187213
$853$	35129.3	1.41009	0.705044	−	0.709164i	$-0.250927\pi$
$853$	35129.3	1.41009	0.705044	+	0.709164i	$0.250927\pi$
$854$	0	0
$855$	−4804.72	−0.192185
$856$	27372.6	1.09296
$857$	−32983.7	−1.31470	−0.657352	−	0.753584i	$-0.728324\pi$
$857$	−32983.7	−1.31470	−0.657352	+	0.753584i	$0.728324\pi$
$858$	491.274	0.0195476
$859$	35152.9	1.39628	0.698139	−	0.715962i	$-0.254012\pi$
$859$	35152.9	1.39628	0.698139	+	0.715962i	$0.254012\pi$
$860$	1093.93	0.0433753
$861$	0	0
$862$	34301.4	1.35535
$863$	24925.6	0.983173	0.491587	−	0.870829i	$-0.336417\pi$
$863$	24925.6	0.983173	0.491587	+	0.870829i	$0.336417\pi$
$864$	−3231.99	−0.127262
$865$	11843.6	0.465544
$866$	9838.48	0.386057
$867$	24386.7	0.955266
$868$	0	0
$869$	266.272	0.0103943
$870$	57315.7	2.23355
$871$	−563.549	−0.0219232
$872$	−9315.17	−0.361756
$873$	6079.84	0.235706
$874$	−10173.6	−0.393739
$875$	0	0
$876$	−21873.8	−0.843661
$877$	2057.63	0.0792261	0.0396131	−	0.999215i	$-0.487387\pi$
$877$	2057.63	0.0792261	0.0396131	+	0.999215i	$0.487387\pi$
$878$	−30575.2	−1.17524
$879$	−62805.1	−2.40997
$880$	402.168	0.0154058
$881$	−17912.5	−0.685004	−0.342502	−	0.939517i	$-0.611274\pi$
$881$	−17912.5	−0.685004	−0.342502	+	0.939517i	$0.611274\pi$
$882$	0	0
$883$	−27215.2	−1.03722	−0.518610	−	0.855011i	$-0.673550\pi$
$883$	−27215.2	−1.03722	−0.518610	+	0.855011i	$0.673550\pi$
$884$	9521.67	0.362272
$885$	25212.2	0.957625
$886$	33528.2	1.27133
$887$	−25313.0	−0.958206	−0.479103	−	0.877759i	$-0.659038\pi$
$887$	−25313.0	−0.958206	−0.479103	+	0.877759i	$0.659038\pi$
$888$	42902.1	1.62128
$889$	0	0
$890$	−23893.7	−0.899910
$891$	−485.327	−0.0182481
$892$	5105.76	0.191652
$893$	11013.2	0.412703
$894$	−72621.0	−2.71679
$895$	−5911.36	−0.220777
$896$	0	0
$897$	−31667.5	−1.17876
$898$	−47683.3	−1.77195
$899$	55058.6	2.04261
$900$	−3674.05	−0.136076
$901$	53266.3	1.96954
$902$	379.601	0.0140126
$903$	0	0
$904$	−1091.58	−0.0401607
$905$	−20066.7	−0.737062
$906$	55260.5	2.02639
$907$	45998.9	1.68398	0.841989	−	0.539495i	$-0.181385\pi$
$907$	45998.9	1.68398	0.841989	+	0.539495i	$0.181385\pi$
$908$	−1037.75	−0.0379282
$909$	27739.7	1.01217
$910$	0	0
$911$	−46592.7	−1.69449	−0.847247	−	0.531199i	$-0.821742\pi$
$911$	−46592.7	−1.69449	−0.847247	+	0.531199i	$0.821742\pi$
$912$	−13482.8	−0.489539
$913$	−178.443	−0.00646833
$914$	33250.9	1.20333
$915$	−1872.36	−0.0676483
$916$	−2130.72	−0.0768571
$917$	0	0
$918$	−7597.54	−0.273155
$919$	33168.1	1.19055	0.595274	−	0.803523i	$-0.297043\pi$
$919$	33168.1	1.19055	0.595274	+	0.803523i	$0.297043\pi$
$920$	−18081.5	−0.647966
$921$	−46639.5	−1.66865
$922$	−413.615	−0.0147741
$923$	7659.66	0.273154
$924$	0	0
$925$	−19051.2	−0.677188
$926$	−51173.2	−1.81604
$927$	−7499.60	−0.265716
$928$	36804.6	1.30191
$929$	−19909.9	−0.703148	−0.351574	−	0.936160i	$-0.614353\pi$
$929$	−19909.9	−0.703148	−0.351574	+	0.936160i	$0.614353\pi$
$930$	38655.0	1.36296
$931$	0	0
$932$	−19530.0	−0.686401
$933$	−8882.29	−0.311675
$934$	−39823.2	−1.39514
$935$	465.228	0.0162723
$936$	−13611.8	−0.475338
$937$	−26262.2	−0.915634	−0.457817	−	0.889046i	$-0.651369\pi$
$937$	−26262.2	−0.915634	−0.457817	+	0.889046i	$0.651369\pi$
$938$	0	0
$939$	21091.0	0.732991
$940$	−11658.4	−0.404528
$941$	−42227.8	−1.46290	−0.731449	−	0.681896i	$-0.761155\pi$
$941$	−42227.8	−1.46290	−0.731449	+	0.681896i	$0.761155\pi$
$942$	37268.3	1.28903
$943$	−24469.1	−0.844988
$944$	32899.0	1.13429
$945$	0	0
$946$	85.1986	0.00292817
$947$	−35227.0	−1.20879	−0.604394	−	0.796685i	$-0.706585\pi$
$947$	−35227.0	−1.20879	−0.604394	+	0.796685i	$0.706585\pi$
$948$	9449.83	0.323751
$949$	35986.4	1.23095
$950$	4175.99	0.142618
$951$	7489.98	0.255393
$952$	0	0
$953$	49209.9	1.67268	0.836340	−	0.548211i	$-0.184691\pi$
$953$	49209.9	1.67268	0.836340	+	0.548211i	$0.184691\pi$
$954$	45354.8	1.53922
$955$	18470.2	0.625844
$956$	−7649.06	−0.258774
$957$	1213.37	0.0409851
$958$	20687.4	0.697683
$959$	0	0
$960$	−12396.1	−0.416753
$961$	7341.79	0.246443
$962$	42039.7	1.40895
$963$	38655.3	1.29351
$964$	13906.4	0.464623
$965$	−11117.5	−0.370864
$966$	0	0
$967$	13452.5	0.447366	0.223683	−	0.974662i	$-0.428192\pi$
$967$	13452.5	0.447366	0.223683	+	0.974662i	$0.428192\pi$
$968$	−22113.0	−0.734234
$969$	−15596.9	−0.517074
$970$	7315.30	0.242145
$971$	−37322.8	−1.23352	−0.616758	−	0.787152i	$-0.711554\pi$
$971$	−37322.8	−1.23352	−0.616758	+	0.787152i	$0.711554\pi$
$972$	−15200.9	−0.501614
$973$	0	0
$974$	−3063.24	−0.100773
$975$	12998.6	0.426964
$976$	−2443.21	−0.0801285
$977$	−45153.4	−1.47859	−0.739297	−	0.673380i	$-0.764842\pi$
$977$	−45153.4	−1.47859	−0.739297	+	0.673380i	$0.764842\pi$
$978$	19329.3	0.631987
$979$	−505.829	−0.0165132
$980$	0	0
$981$	−13154.8	−0.428134
$982$	23348.2	0.758729
$983$	15802.7	0.512745	0.256372	−	0.966578i	$-0.417473\pi$
$983$	15802.7	0.512745	0.256372	+	0.966578i	$0.417473\pi$
$984$	−22618.2	−0.732767
$985$	40894.0	1.32283
$986$	86517.6	2.79440
$987$	0	0
$988$	−2504.82	−0.0806568
$989$	−5491.90	−0.176575
$990$	396.128	0.0127169
$991$	27570.0	0.883744	0.441872	−	0.897078i	$-0.354315\pi$
$991$	27570.0	0.883744	0.441872	+	0.897078i	$0.354315\pi$
$992$	24821.9	0.794451
$993$	−20472.1	−0.654241
$994$	0	0
$995$	−18003.7	−0.573624
$996$	−6332.82	−0.201469
$997$	14969.8	0.475526	0.237763	−	0.971323i	$-0.423586\pi$
$997$	14969.8	0.475526	0.237763	+	0.971323i	$0.423586\pi$
$998$	13197.7	0.418605
$999$	−9117.97	−0.288768

Twists

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

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

\(f(q)\)	\(=\)	\(q-3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} -8.51910 q^{5} -23.5469 q^{6} +16.6183 q^{8} +23.4681 q^{9} +O(q^{10})\)	\(q-3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} -8.51910 q^{5} -23.5469 q^{6} +16.6183 q^{8} +23.4681 q^{9} +28.2370 q^{10} +0.597776 q^{11} +21.2147 q^{12} -34.9021 q^{13} -60.5204 q^{15} -78.9723 q^{16} -91.3552 q^{17} -77.7863 q^{18} +24.0324 q^{19} -25.4403 q^{20} -1.98136 q^{22} +127.719 q^{23} +118.058 q^{24} -52.4250 q^{25} +115.685 q^{26} -25.0908 q^{27} +285.724 q^{29} +200.598 q^{30} +192.699 q^{31} +128.812 q^{32} +4.24666 q^{33} +302.802 q^{34} +70.0821 q^{36} +363.399 q^{37} -79.6565 q^{38} -247.948 q^{39} -141.573 q^{40} -191.586 q^{41} -43.0000 q^{43} +1.78512 q^{44} -199.927 q^{45} -423.330 q^{46} +458.267 q^{47} -561.027 q^{48} +173.765 q^{50} -648.995 q^{51} -104.227 q^{52} -583.068 q^{53} +83.1648 q^{54} -5.09252 q^{55} +170.728 q^{57} -947.047 q^{58} -416.589 q^{59} -180.730 q^{60} +30.9376 q^{61} -638.710 q^{62} +204.825 q^{64} +297.334 q^{65} -14.0758 q^{66} +16.1466 q^{67} -272.811 q^{68} +907.324 q^{69} -219.461 q^{71} +390.000 q^{72} -1031.07 q^{73} -1204.50 q^{74} -372.432 q^{75} +71.7670 q^{76} +821.836 q^{78} +445.438 q^{79} +672.773 q^{80} -811.887 q^{81} +635.022 q^{82} -298.511 q^{83} +778.264 q^{85} +142.526 q^{86} +2029.81 q^{87} +9.93402 q^{88} -846.185 q^{89} +662.669 q^{90} +381.402 q^{92} +1368.95 q^{93} -1518.95 q^{94} -204.734 q^{95} +915.091 q^{96} +259.068 q^{97} +14.0287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more