LMFDB - Embedded newform 1734.4.a.bd.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,4,Mod(1,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, 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("1734.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1734.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:	$102.309311950$
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} - 2x^{5} - 441x^{4} + 280x^{3} + 48672x^{2} + 38656x - 45712 $ x^6 - 2x^5 - 441x^4 + 280x^3 + 48672x^2 + 38656*x - 45712
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 102)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.47294$ of defining polynomial
Character	$\chi$	$=$	1734.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +0.887153 q^{5} -6.00000 q^{6} +18.8933 q^{7} +8.00000 q^{8} +9.00000 q^{9} +1.77431 q^{10} -59.7478 q^{11} -12.0000 q^{12} -36.6745 q^{13} +37.7867 q^{14} -2.66146 q^{15} +16.0000 q^{16} +18.0000 q^{18} +117.094 q^{19} +3.54861 q^{20} -56.6800 q^{21} -119.496 q^{22} +186.637 q^{23} -24.0000 q^{24} -124.213 q^{25} -73.3490 q^{26} -27.0000 q^{27} +75.5734 q^{28} -130.917 q^{29} -5.32292 q^{30} -238.953 q^{31} +32.0000 q^{32} +179.243 q^{33} +16.7613 q^{35} +36.0000 q^{36} -14.1221 q^{37} +234.189 q^{38} +110.024 q^{39} +7.09723 q^{40} -480.524 q^{41} -113.360 q^{42} +194.715 q^{43} -238.991 q^{44} +7.98438 q^{45} +373.274 q^{46} -40.2448 q^{47} -48.0000 q^{48} +13.9584 q^{49} -248.426 q^{50} -146.698 q^{52} -40.8393 q^{53} -54.0000 q^{54} -53.0055 q^{55} +151.147 q^{56} -351.283 q^{57} -261.834 q^{58} +447.653 q^{59} -10.6458 q^{60} +154.466 q^{61} -477.906 q^{62} +170.040 q^{63} +64.0000 q^{64} -32.5359 q^{65} +358.487 q^{66} -438.990 q^{67} -559.910 q^{69} +33.5226 q^{70} +608.063 q^{71} +72.0000 q^{72} -365.386 q^{73} -28.2441 q^{74} +372.639 q^{75} +468.378 q^{76} -1128.84 q^{77} +220.047 q^{78} -1333.90 q^{79} +14.1945 q^{80} +81.0000 q^{81} -961.048 q^{82} -516.632 q^{83} -226.720 q^{84} +389.430 q^{86} +392.752 q^{87} -477.983 q^{88} +821.409 q^{89} +15.9688 q^{90} -692.904 q^{91} +746.547 q^{92} +716.860 q^{93} -80.4897 q^{94} +103.881 q^{95} -96.0000 q^{96} -1328.77 q^{97} +27.9168 q^{98} -537.730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 18 q^{3} + 24 q^{4} - 14 q^{5} - 36 q^{6} - 28 q^{7} + 48 q^{8} + 54 q^{9} - 28 q^{10} - 34 q^{11} - 72 q^{12} + 34 q^{13} - 56 q^{14} + 42 q^{15} + 96 q^{16} + 108 q^{18} + 70 q^{19} - 56 q^{20}+ \cdots - 306 q^{99}+O(q^{100}) $ 6 * q + 12 * q^2 - 18 * q^3 + 24 * q^4 - 14 * q^5 - 36 * q^6 - 28 * q^7 + 48 * q^8 + 54 * q^9 - 28 * q^10 - 34 * q^11 - 72 * q^12 + 34 * q^13 - 56 * q^14 + 42 * q^15 + 96 * q^16 + 108 * q^18 + 70 * q^19 - 56 * q^20 + 84 * q^21 - 68 * q^22 - 78 * q^23 - 144 * q^24 + 188 * q^25 + 68 * q^26 - 162 * q^27 - 112 * q^28 - 280 * q^29 + 84 * q^30 - 508 * q^31 + 192 * q^32 + 102 * q^33 + 196 * q^35 + 216 * q^36 - 308 * q^37 + 140 * q^38 - 102 * q^39 - 112 * q^40 - 442 * q^41 + 168 * q^42 - 46 * q^43 - 136 * q^44 - 126 * q^45 - 156 * q^46 + 1460 * q^47 - 288 * q^48 + 1042 * q^49 + 376 * q^50 + 136 * q^52 + 476 * q^53 - 324 * q^54 - 578 * q^55 - 224 * q^56 - 210 * q^57 - 560 * q^58 + 688 * q^59 + 168 * q^60 + 84 * q^61 - 1016 * q^62 - 252 * q^63 + 384 * q^64 - 1526 * q^65 + 204 * q^66 - 1004 * q^67 + 234 * q^69 + 392 * q^70 - 332 * q^71 + 432 * q^72 - 1132 * q^73 - 616 * q^74 - 564 * q^75 + 280 * q^76 - 1548 * q^77 - 204 * q^78 - 4512 * q^79 - 224 * q^80 + 486 * q^81 - 884 * q^82 + 68 * q^83 + 336 * q^84 - 92 * q^86 + 840 * q^87 - 272 * q^88 - 2652 * q^89 - 252 * q^90 - 3052 * q^91 - 312 * q^92 + 1524 * q^93 + 2920 * q^94 + 622 * q^95 - 576 * q^96 + 1152 * q^97 + 2084 * q^98 - 306 * q^99

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	0.887153	0.0793494	0.0396747	−	0.999213i	$-0.487368\pi$
$5$	0.887153	0.0793494	0.0396747	+	0.999213i	$0.487368\pi$
$6$	−6.00000	−0.408248
$7$	18.8933	1.02014	0.510072	−	0.860132i	$-0.329619\pi$
$7$	18.8933	1.02014	0.510072	+	0.860132i	$0.329619\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	1.77431	0.0561085
$11$	−59.7478	−1.63770	−0.818848	−	0.574011i	$-0.805387\pi$
$11$	−59.7478	−1.63770	−0.818848	+	0.574011i	$0.805387\pi$
$12$	−12.0000	−0.288675
$13$	−36.6745	−0.782437	−0.391219	−	0.920298i	$-0.627946\pi$
$13$	−36.6745	−0.782437	−0.391219	+	0.920298i	$0.627946\pi$
$14$	37.7867	0.721351
$15$	−2.66146	−0.0458124
$16$	16.0000	0.250000
$17$	0	0
$17$	0	0
$18$	18.0000	0.235702
$19$	117.094	1.41386	0.706929	−	0.707284i	$-0.250080\pi$
$19$	117.094	1.41386	0.706929	+	0.707284i	$0.250080\pi$
$20$	3.54861	0.0396747
$21$	−56.6800	−0.588981
$22$	−119.496	−1.15803
$23$	186.637	1.69202	0.846010	−	0.533167i	$-0.178998\pi$
$23$	186.637	1.69202	0.846010	+	0.533167i	$0.178998\pi$
$24$	−24.0000	−0.204124
$25$	−124.213	−0.993704
$26$	−73.3490	−0.553267
$27$	−27.0000	−0.192450
$28$	75.5734	0.510072
$29$	−130.917	−0.838301	−0.419150	−	0.907917i	$-0.637672\pi$
$29$	−130.917	−0.838301	−0.419150	+	0.907917i	$0.637672\pi$
$30$	−5.32292	−0.0323943
$31$	−238.953	−1.38443	−0.692214	−	0.721692i	$-0.743364\pi$
$31$	−238.953	−1.38443	−0.692214	+	0.721692i	$0.743364\pi$
$32$	32.0000	0.176777
$33$	179.243	0.945524
$34$	0	0
$35$	16.7613	0.0809479
$36$	36.0000	0.166667
$37$	−14.1221	−0.0627474	−0.0313737	−	0.999508i	$-0.509988\pi$
$37$	−14.1221	−0.0627474	−0.0313737	+	0.999508i	$0.509988\pi$
$38$	234.189	0.999749
$39$	110.024	0.451740
$40$	7.09723	0.0280543
$41$	−480.524	−1.83037	−0.915186	−	0.403032i	$-0.867956\pi$
$41$	−480.524	−1.83037	−0.915186	+	0.403032i	$0.867956\pi$
$42$	−113.360	−0.416472
$43$	194.715	0.690553	0.345277	−	0.938501i	$-0.387785\pi$
$43$	194.715	0.690553	0.345277	+	0.938501i	$0.387785\pi$
$44$	−238.991	−0.818848
$45$	7.98438	0.0264498
$46$	373.274	1.19644
$47$	−40.2448	−0.124900	−0.0624501	−	0.998048i	$-0.519891\pi$
$47$	−40.2448	−0.124900	−0.0624501	+	0.998048i	$0.519891\pi$
$48$	−48.0000	−0.144338
$49$	13.9584	0.0406950
$50$	−248.426	−0.702655
$51$	0	0
$52$	−146.698	−0.391219
$53$	−40.8393	−0.105844	−0.0529218	−	0.998599i	$-0.516853\pi$
$53$	−40.8393	−0.105844	−0.0529218	+	0.998599i	$0.516853\pi$
$54$	−54.0000	−0.136083
$55$	−53.0055	−0.129950
$56$	151.147	0.360676
$57$	−351.283	−0.816292
$58$	−261.834	−0.592768
$59$	447.653	0.987788	0.493894	−	0.869522i	$-0.335573\pi$
$59$	447.653	0.987788	0.493894	+	0.869522i	$0.335573\pi$
$60$	−10.6458	−0.0229062
$61$	154.466	0.324219	0.162109	−	0.986773i	$-0.448170\pi$
$61$	154.466	0.324219	0.162109	+	0.986773i	$0.448170\pi$
$62$	−477.906	−0.978938
$63$	170.040	0.340048
$64$	64.0000	0.125000
$65$	−32.5359	−0.0620859
$66$	358.487	0.668586
$67$	−438.990	−0.800464	−0.400232	−	0.916414i	$-0.631071\pi$
$67$	−438.990	−0.800464	−0.400232	+	0.916414i	$0.631071\pi$
$68$	0	0
$69$	−559.910	−0.976888
$70$	33.5226	0.0572388
$71$	608.063	1.01639	0.508196	−	0.861242i	$-0.330313\pi$
$71$	608.063	1.01639	0.508196	+	0.861242i	$0.330313\pi$
$72$	72.0000	0.117851
$73$	−365.386	−0.585824	−0.292912	−	0.956139i	$-0.594624\pi$
$73$	−365.386	−0.585824	−0.292912	+	0.956139i	$0.594624\pi$
$74$	−28.2441	−0.0443691
$75$	372.639	0.573715
$76$	468.378	0.706929
$77$	−1128.84	−1.67069
$78$	220.047	0.319429
$79$	−1333.90	−1.89969	−0.949847	−	0.312716i	$-0.898761\pi$
$79$	−1333.90	−1.89969	−0.949847	+	0.312716i	$0.898761\pi$
$80$	14.1945	0.0198374
$81$	81.0000	0.111111
$82$	−961.048	−1.29427
$83$	−516.632	−0.683226	−0.341613	−	0.939841i	$-0.610973\pi$
$83$	−516.632	−0.683226	−0.341613	+	0.939841i	$0.610973\pi$
$84$	−226.720	−0.294490
$85$	0	0
$86$	389.430	0.488295
$87$	392.752	0.483993
$88$	−477.983	−0.579013
$89$	821.409	0.978305	0.489153	−	0.872198i	$-0.337306\pi$
$89$	821.409	0.978305	0.489153	+	0.872198i	$0.337306\pi$
$90$	15.9688	0.0187028
$91$	−692.904	−0.798199
$92$	746.547	0.846010
$93$	716.860	0.799300
$94$	−80.4897	−0.0883178
$95$	103.881	0.112189
$96$	−96.0000	−0.102062
$97$	−1328.77	−1.39089	−0.695444	−	0.718580i	$-0.744792\pi$
$97$	−1328.77	−1.39089	−0.695444	+	0.718580i	$0.744792\pi$
$98$	27.9168	0.0287757
$99$	−537.730	−0.545898
$100$	−496.852	−0.496852
$101$	798.976	0.787140	0.393570	−	0.919295i	$-0.371240\pi$
$101$	798.976	0.787140	0.393570	+	0.919295i	$0.371240\pi$
$102$	0	0
$103$	−59.1043	−0.0565410	−0.0282705	−	0.999600i	$-0.509000\pi$
$103$	−59.1043	−0.0565410	−0.0282705	+	0.999600i	$0.509000\pi$
$104$	−293.396	−0.276633
$105$	−50.2839	−0.0467353
$106$	−81.6787	−0.0748428
$107$	809.404	0.731290	0.365645	−	0.930754i	$-0.380848\pi$
$107$	809.404	0.731290	0.365645	+	0.930754i	$0.380848\pi$
$108$	−108.000	−0.0962250
$109$	−1654.16	−1.45358	−0.726789	−	0.686861i	$-0.758988\pi$
$109$	−1654.16	−1.45358	−0.726789	+	0.686861i	$0.758988\pi$
$110$	−106.011	−0.0918886
$111$	42.3662	0.0362272
$112$	302.293	0.255036
$113$	−480.786	−0.400252	−0.200126	−	0.979770i	$-0.564135\pi$
$113$	−480.786	−0.400252	−0.200126	+	0.979770i	$0.564135\pi$
$114$	−702.567	−0.577205
$115$	165.575	0.134261
$116$	−523.669	−0.419150
$117$	−330.071	−0.260812
$118$	895.307	0.698472
$119$	0	0
$120$	−21.2917	−0.0161971
$121$	2238.80	1.68205
$122$	308.932	0.229257
$123$	1441.57	1.05677
$124$	−955.813	−0.692214
$125$	−221.090	−0.158199
$126$	340.080	0.240450
$127$	1505.29	1.05176	0.525878	−	0.850560i	$-0.323737\pi$
$127$	1505.29	1.05176	0.525878	+	0.850560i	$0.323737\pi$
$128$	128.000	0.0883883
$129$	−584.146	−0.398691
$130$	−65.0719	−0.0439014
$131$	1130.66	0.754096	0.377048	−	0.926194i	$-0.376939\pi$
$131$	1130.66	0.754096	0.377048	+	0.926194i	$0.376939\pi$
$132$	716.974	0.472762
$133$	2212.31	1.44234
$134$	−877.979	−0.566014
$135$	−23.9531	−0.0152708
$136$	0	0
$137$	−1079.13	−0.672966	−0.336483	−	0.941690i	$-0.609237\pi$
$137$	−1079.13	−0.672966	−0.336483	+	0.941690i	$0.609237\pi$
$138$	−1119.82	−0.690764
$139$	−699.837	−0.427046	−0.213523	−	0.976938i	$-0.568494\pi$
$139$	−699.837	−0.427046	−0.213523	+	0.976938i	$0.568494\pi$
$140$	67.0452	0.0404739
$141$	120.735	0.0721112
$142$	1216.13	0.718697
$143$	2191.22	1.28139
$144$	144.000	0.0833333
$145$	−116.144	−0.0665187
$146$	−730.771	−0.414240
$147$	−41.8752	−0.0234953
$148$	−56.4883	−0.0313737
$149$	1357.34	0.746293	0.373147	−	0.927772i	$-0.378279\pi$
$149$	1357.34	0.746293	0.373147	+	0.927772i	$0.378279\pi$
$150$	745.278	0.405678
$151$	−1762.54	−0.949889	−0.474945	−	0.880016i	$-0.657532\pi$
$151$	−1762.54	−0.949889	−0.474945	+	0.880016i	$0.657532\pi$
$152$	936.756	0.499874
$153$	0	0
$154$	−2257.67	−1.18135
$155$	−211.988	−0.109854
$156$	440.094	0.225870
$157$	−64.0852	−0.0325768	−0.0162884	−	0.999867i	$-0.505185\pi$
$157$	−64.0852	−0.0325768	−0.0162884	+	0.999867i	$0.505185\pi$
$158$	−2667.81	−1.34329
$159$	122.518	0.0611089
$160$	28.3889	0.0140271
$161$	3526.19	1.72610
$162$	162.000	0.0785674
$163$	−2362.97	−1.13547	−0.567737	−	0.823210i	$-0.692181\pi$
$163$	−2362.97	−1.13547	−0.567737	+	0.823210i	$0.692181\pi$
$164$	−1922.10	−0.915186
$165$	159.016	0.0750268
$166$	−1033.26	−0.483114
$167$	−2169.65	−1.00534	−0.502671	−	0.864478i	$-0.667649\pi$
$167$	−2169.65	−1.00534	−0.502671	+	0.864478i	$0.667649\pi$
$168$	−453.440	−0.208236
$169$	−851.979	−0.387792
$170$	0	0
$171$	1053.85	0.471286
$172$	778.861	0.345277
$173$	−3330.57	−1.46369	−0.731846	−	0.681470i	$-0.761341\pi$
$173$	−3330.57	−1.46369	−0.731846	+	0.681470i	$0.761341\pi$
$174$	785.503	0.342235
$175$	−2346.80	−1.01372
$176$	−955.965	−0.409424
$177$	−1342.96	−0.570300
$178$	1642.82	0.691766
$179$	−3541.26	−1.47870	−0.739348	−	0.673324i	$-0.764866\pi$
$179$	−3541.26	−1.47870	−0.739348	+	0.673324i	$0.764866\pi$
$180$	31.9375	0.0132249
$181$	−1717.66	−0.705375	−0.352687	−	0.935741i	$-0.614732\pi$
$181$	−1717.66	−0.705375	−0.352687	+	0.935741i	$0.614732\pi$
$182$	−1385.81	−0.564412
$183$	−463.398	−0.187188
$184$	1493.09	0.598219
$185$	−12.5284	−0.00497897
$186$	1433.72	0.565190
$187$	0	0
$188$	−160.979	−0.0624501
$189$	−510.120	−0.196327
$190$	207.762	0.0793295
$191$	−1714.57	−0.649538	−0.324769	−	0.945793i	$-0.605287\pi$
$191$	−1714.57	−0.649538	−0.324769	+	0.945793i	$0.605287\pi$
$192$	−192.000	−0.0721688
$193$	−3494.59	−1.30335	−0.651673	−	0.758500i	$-0.725933\pi$
$193$	−3494.59	−1.30335	−0.651673	+	0.758500i	$0.725933\pi$
$194$	−2657.54	−0.983506
$195$	97.6078	0.0358453
$196$	55.8336	0.0203475
$197$	2770.20	1.00187	0.500936	−	0.865485i	$-0.332989\pi$
$197$	2770.20	1.00187	0.500936	+	0.865485i	$0.332989\pi$
$198$	−1075.46	−0.386008
$199$	3328.98	1.18585	0.592927	−	0.805256i	$-0.297972\pi$
$199$	3328.98	1.18585	0.592927	+	0.805256i	$0.297972\pi$
$200$	−993.704	−0.351327
$201$	1316.97	0.462148
$202$	1597.95	0.556592
$203$	−2473.46	−0.855188
$204$	0	0
$205$	−426.298	−0.145239
$206$	−118.209	−0.0399805
$207$	1679.73	0.564007
$208$	−586.792	−0.195609
$209$	−6996.14	−2.31547
$210$	−100.568	−0.0330468
$211$	−3871.11	−1.26302	−0.631512	−	0.775366i	$-0.717565\pi$
$211$	−3871.11	−1.26302	−0.631512	+	0.775366i	$0.717565\pi$
$212$	−163.357	−0.0529218
$213$	−1824.19	−0.586814
$214$	1618.81	0.517100
$215$	172.742	0.0547950
$216$	−216.000	−0.0680414
$217$	−4514.62	−1.41232
$218$	−3308.32	−1.02783
$219$	1096.16	0.338226
$220$	−212.022	−0.0649751
$221$	0	0
$222$	84.7324	0.0256165
$223$	−5294.36	−1.58985	−0.794925	−	0.606708i	$-0.792490\pi$
$223$	−5294.36	−1.58985	−0.794925	+	0.606708i	$0.792490\pi$
$224$	604.587	0.180338
$225$	−1117.92	−0.331235
$226$	−961.571	−0.283021
$227$	−5224.55	−1.52760	−0.763801	−	0.645452i	$-0.776669\pi$
$227$	−5224.55	−1.52760	−0.763801	+	0.645452i	$0.776669\pi$
$228$	−1405.13	−0.408146
$229$	−1878.50	−0.542074	−0.271037	−	0.962569i	$-0.587367\pi$
$229$	−1878.50	−0.542074	−0.271037	+	0.962569i	$0.587367\pi$
$230$	331.151	0.0949367
$231$	3386.51	0.964571
$232$	−1047.34	−0.296384
$233$	1660.50	0.466879	0.233439	−	0.972371i	$-0.425002\pi$
$233$	1660.50	0.466879	0.233439	+	0.972371i	$0.425002\pi$
$234$	−660.141	−0.184422
$235$	−35.7034	−0.00991077
$236$	1790.61	0.493894
$237$	4001.71	1.09679
$238$	0	0
$239$	−5017.17	−1.35788	−0.678941	−	0.734192i	$-0.737561\pi$
$239$	−5017.17	−1.35788	−0.678941	+	0.734192i	$0.737561\pi$
$240$	−42.5834	−0.0114531
$241$	5872.04	1.56951	0.784754	−	0.619807i	$-0.212789\pi$
$241$	5872.04	1.56951	0.784754	+	0.619807i	$0.212789\pi$
$242$	4477.61	1.18939
$243$	−243.000	−0.0641500
$244$	617.864	0.162109
$245$	12.3832	0.00322913
$246$	2883.14	0.747246
$247$	−4294.38	−1.10626
$248$	−1911.63	−0.489469
$249$	1549.90	0.394461
$250$	−442.180	−0.111864
$251$	6899.16	1.73495	0.867473	−	0.497485i	$-0.165743\pi$
$251$	6899.16	1.73495	0.867473	+	0.497485i	$0.165743\pi$
$252$	680.160	0.170024
$253$	−11151.1	−2.77101
$254$	3010.58	0.743704
$255$	0	0
$256$	256.000	0.0625000
$257$	−1910.33	−0.463669	−0.231835	−	0.972755i	$-0.574473\pi$
$257$	−1910.33	−0.463669	−0.231835	+	0.972755i	$0.574473\pi$
$258$	−1168.29	−0.281917
$259$	−266.813	−0.0640114
$260$	−130.144	−0.0310430
$261$	−1178.26	−0.279434
$262$	2261.33	0.533227
$263$	−2690.00	−0.630693	−0.315346	−	0.948977i	$-0.602121\pi$
$263$	−2690.00	−0.630693	−0.315346	+	0.948977i	$0.602121\pi$
$264$	1433.95	0.334293
$265$	−36.2308	−0.00839863
$266$	4424.61	1.01989
$267$	−2464.23	−0.564825
$268$	−1755.96	−0.400232
$269$	1888.66	0.428080	0.214040	−	0.976825i	$-0.431338\pi$
$269$	1888.66	0.428080	0.214040	+	0.976825i	$0.431338\pi$
$270$	−47.9063	−0.0107981
$271$	4172.66	0.935317	0.467659	−	0.883909i	$-0.345098\pi$
$271$	4172.66	0.935317	0.467659	+	0.883909i	$0.345098\pi$
$272$	0	0
$273$	2078.71	0.460840
$274$	−2158.26	−0.475859
$275$	7421.45	1.62738
$276$	−2239.64	−0.488444
$277$	−740.569	−0.160637	−0.0803186	−	0.996769i	$-0.525594\pi$
$277$	−740.569	−0.160637	−0.0803186	+	0.996769i	$0.525594\pi$
$278$	−1399.67	−0.301967
$279$	−2150.58	−0.461476
$280$	134.090	0.0286194
$281$	325.056	0.0690078	0.0345039	−	0.999405i	$-0.489015\pi$
$281$	325.056	0.0690078	0.0345039	+	0.999405i	$0.489015\pi$
$282$	241.469	0.0509903
$283$	−4827.08	−1.01392	−0.506962	−	0.861969i	$-0.669231\pi$
$283$	−4827.08	−1.01392	−0.506962	+	0.861969i	$0.669231\pi$
$284$	2432.25	0.508196
$285$	−311.642	−0.0647723
$286$	4382.45	0.906082
$287$	−9078.70	−1.86724
$288$	288.000	0.0589256
$289$	0	0
$290$	−232.287	−0.0470358
$291$	3986.31	0.803029
$292$	−1461.54	−0.292912
$293$	1038.13	0.206991	0.103496	−	0.994630i	$-0.466997\pi$
$293$	1038.13	0.206991	0.103496	+	0.994630i	$0.466997\pi$
$294$	−83.7504	−0.0166137
$295$	397.137	0.0783804
$296$	−112.977	−0.0221845
$297$	1613.19	0.315175
$298$	2714.68	0.527709
$299$	−6844.81	−1.32390
$300$	1490.56	0.286858
$301$	3678.82	0.704464
$302$	−3525.07	−0.671673
$303$	−2396.93	−0.454455
$304$	1873.51	0.353465
$305$	137.035	0.0257266
$306$	0	0
$307$	−6737.14	−1.25247	−0.626236	−	0.779634i	$-0.715405\pi$
$307$	−6737.14	−1.25247	−0.626236	+	0.779634i	$0.715405\pi$
$308$	−4515.34	−0.835343
$309$	177.313	0.0326439
$310$	−423.976	−0.0776782
$311$	−4747.62	−0.865637	−0.432818	−	0.901481i	$-0.642481\pi$
$311$	−4747.62	−0.865637	−0.432818	+	0.901481i	$0.642481\pi$
$312$	880.189	0.159714
$313$	6028.93	1.08874	0.544369	−	0.838846i	$-0.316769\pi$
$313$	6028.93	1.08874	0.544369	+	0.838846i	$0.316769\pi$
$314$	−128.170	−0.0230353
$315$	150.852	0.0269826
$316$	−5335.61	−0.949847
$317$	7008.56	1.24177	0.620884	−	0.783903i	$-0.286774\pi$
$317$	7008.56	1.24177	0.620884	+	0.783903i	$0.286774\pi$
$318$	245.036	0.0432105
$319$	7822.02	1.37288
$320$	56.7778	0.00991868
$321$	−2428.21	−0.422211
$322$	7052.38	1.22054
$323$	0	0
$324$	324.000	0.0555556
$325$	4555.45	0.777511
$326$	−4725.95	−0.802902
$327$	4962.49	0.839224
$328$	−3844.19	−0.647134
$329$	−760.360	−0.127416
$330$	318.033	0.0530519
$331$	5517.53	0.916227	0.458113	−	0.888894i	$-0.348525\pi$
$331$	5517.53	0.916227	0.458113	+	0.888894i	$0.348525\pi$
$332$	−2066.53	−0.341613
$333$	−127.099	−0.0209158
$334$	−4339.29	−0.710885
$335$	−389.451	−0.0635164
$336$	−906.880	−0.147245
$337$	6916.68	1.11803	0.559014	−	0.829158i	$-0.311180\pi$
$337$	6916.68	1.11803	0.559014	+	0.829158i	$0.311180\pi$
$338$	−1703.96	−0.274211
$339$	1442.36	0.231086
$340$	0	0
$341$	14276.9	2.26727
$342$	2107.70	0.333250
$343$	−6216.70	−0.978630
$344$	1557.72	0.244147
$345$	−496.726	−0.0775155
$346$	−6661.15	−1.03499
$347$	−3774.33	−0.583910	−0.291955	−	0.956432i	$-0.594306\pi$
$347$	−3774.33	−0.583910	−0.291955	+	0.956432i	$0.594306\pi$
$348$	1571.01	0.241997
$349$	529.191	0.0811660	0.0405830	−	0.999176i	$-0.487078\pi$
$349$	529.191	0.0811660	0.0405830	+	0.999176i	$0.487078\pi$
$350$	−4693.60	−0.716809
$351$	990.212	0.150580
$352$	−1911.93	−0.289506
$353$	3779.39	0.569849	0.284924	−	0.958550i	$-0.408032\pi$
$353$	3779.39	0.569849	0.284924	+	0.958550i	$0.408032\pi$
$354$	−2685.92	−0.403263
$355$	539.445	0.0806501
$356$	3285.64	0.489153
$357$	0	0
$358$	−7082.53	−1.04560
$359$	3764.01	0.553362	0.276681	−	0.960962i	$-0.410765\pi$
$359$	3764.01	0.553362	0.276681	+	0.960962i	$0.410765\pi$
$360$	63.8750	0.00935142
$361$	6852.11	0.998996
$362$	−3435.32	−0.498775
$363$	−6716.41	−0.971130
$364$	−2771.62	−0.399099
$365$	−324.153	−0.0464848
$366$	−926.795	−0.132362
$367$	7404.30	1.05314	0.526568	−	0.850133i	$-0.323478\pi$
$367$	7404.30	1.05314	0.526568	+	0.850133i	$0.323478\pi$
$368$	2986.19	0.423005
$369$	−4324.72	−0.610124
$370$	−25.0569	−0.00352066
$371$	−771.592	−0.107976
$372$	2867.44	0.399650
$373$	11940.8	1.65756	0.828779	−	0.559576i	$-0.189036\pi$
$373$	11940.8	1.65756	0.828779	+	0.559576i	$0.189036\pi$
$374$	0	0
$375$	663.270	0.0913364
$376$	−321.959	−0.0441589
$377$	4801.33	0.655918
$378$	−1020.24	−0.138824
$379$	9126.85	1.23698	0.618489	−	0.785793i	$-0.287745\pi$
$379$	9126.85	1.23698	0.618489	+	0.785793i	$0.287745\pi$
$380$	415.523	0.0560944
$381$	−4515.88	−0.607232
$382$	−3429.14	−0.459293
$383$	−9261.13	−1.23557	−0.617783	−	0.786349i	$-0.711969\pi$
$383$	−9261.13	−1.23557	−0.617783	+	0.786349i	$0.711969\pi$
$384$	−384.000	−0.0510310
$385$	−1001.45	−0.132568
$386$	−6989.17	−0.921605
$387$	1752.44	0.230184
$388$	−5315.08	−0.695444
$389$	−1854.73	−0.241745	−0.120872	−	0.992668i	$-0.538569\pi$
$389$	−1854.73	−0.241745	−0.120872	+	0.992668i	$0.538569\pi$
$390$	195.216	0.0253465
$391$	0	0
$392$	111.667	0.0143879
$393$	−3391.99	−0.435378
$394$	5540.40	0.708430
$395$	−1183.38	−0.150740
$396$	−2150.92	−0.272949
$397$	−9421.24	−1.19103	−0.595514	−	0.803345i	$-0.703052\pi$
$397$	−9421.24	−1.19103	−0.595514	+	0.803345i	$0.703052\pi$
$398$	6657.95	0.838525
$399$	−6636.92	−0.832736
$400$	−1987.41	−0.248426
$401$	3386.15	0.421687	0.210843	−	0.977520i	$-0.432379\pi$
$401$	3386.15	0.421687	0.210843	+	0.977520i	$0.432379\pi$
$402$	2633.94	0.326788
$403$	8763.49	1.08323
$404$	3195.91	0.393570
$405$	71.8594	0.00881660
$406$	−4946.93	−0.604709
$407$	843.763	0.102761
$408$	0	0
$409$	−9820.58	−1.18728	−0.593638	−	0.804732i	$-0.702309\pi$
$409$	−9820.58	−1.18728	−0.593638	+	0.804732i	$0.702309\pi$
$410$	−852.597	−0.102699
$411$	3237.39	0.388537
$412$	−236.417	−0.0282705
$413$	8457.67	1.00769
$414$	3359.46	0.398813
$415$	−458.332	−0.0542136
$416$	−1173.58	−0.138317
$417$	2099.51	0.246555
$418$	−13992.3	−1.63728
$419$	−9904.03	−1.15476	−0.577379	−	0.816477i	$-0.695924\pi$
$419$	−9904.03	−1.15476	−0.577379	+	0.816477i	$0.695924\pi$
$420$	−201.136	−0.0233676
$421$	−4639.35	−0.537074	−0.268537	−	0.963269i	$-0.586540\pi$
$421$	−4639.35	−0.537074	−0.268537	+	0.963269i	$0.586540\pi$
$422$	−7742.21	−0.893092
$423$	−362.204	−0.0416334
$424$	−326.715	−0.0374214
$425$	0	0
$426$	−3648.38	−0.414940
$427$	2918.38	0.330750
$428$	3237.62	0.365645
$429$	−6573.67	−0.739813
$430$	345.485	0.0387459
$431$	−2531.31	−0.282898	−0.141449	−	0.989946i	$-0.545176\pi$
$431$	−2531.31	−0.282898	−0.141449	+	0.989946i	$0.545176\pi$
$432$	−432.000	−0.0481125
$433$	−7126.68	−0.790962	−0.395481	−	0.918474i	$-0.629422\pi$
$433$	−7126.68	−0.790962	−0.395481	+	0.918474i	$0.629422\pi$
$434$	−9029.25	−0.998658
$435$	348.431	0.0384046
$436$	−6616.65	−0.726789
$437$	21854.1	2.39228
$438$	2192.31	0.239162
$439$	16253.1	1.76701	0.883506	−	0.468421i	$-0.155177\pi$
$439$	16253.1	1.76701	0.883506	+	0.468421i	$0.155177\pi$
$440$	−424.044	−0.0459443
$441$	125.626	0.0135650
$442$	0	0
$443$	9083.04	0.974149	0.487075	−	0.873360i	$-0.338064\pi$
$443$	9083.04	0.974149	0.487075	+	0.873360i	$0.338064\pi$
$444$	169.465	0.0181136
$445$	728.716	0.0776279
$446$	−10588.7	−1.12419
$447$	−4072.02	−0.430873
$448$	1209.17	0.127518
$449$	−1820.75	−0.191373	−0.0956864	−	0.995412i	$-0.530505\pi$
$449$	−1820.75	−0.191373	−0.0956864	+	0.995412i	$0.530505\pi$
$450$	−2235.83	−0.234218
$451$	28710.3	2.99759
$452$	−1923.14	−0.200126
$453$	5287.61	0.548419
$454$	−10449.1	−1.08018
$455$	−614.712	−0.0633366
$456$	−2810.27	−0.288603
$457$	−16585.9	−1.69772	−0.848858	−	0.528621i	$-0.822709\pi$
$457$	−16585.9	−1.69772	−0.848858	+	0.528621i	$0.822709\pi$
$458$	−3757.01	−0.383304
$459$	0	0
$460$	662.302	0.0671304
$461$	−7357.94	−0.743370	−0.371685	−	0.928359i	$-0.621220\pi$
$461$	−7357.94	−0.743370	−0.371685	+	0.928359i	$0.621220\pi$
$462$	6773.02	0.682055
$463$	−14132.1	−1.41852	−0.709258	−	0.704949i	$-0.750970\pi$
$463$	−14132.1	−1.41852	−0.709258	+	0.704949i	$0.750970\pi$
$464$	−2094.68	−0.209575
$465$	635.964	0.0634240
$466$	3320.99	0.330133
$467$	3807.01	0.377232	0.188616	−	0.982051i	$-0.439600\pi$
$467$	3807.01	0.377232	0.188616	+	0.982051i	$0.439600\pi$
$468$	−1320.28	−0.130406
$469$	−8293.98	−0.816589
$470$	−71.4067	−0.00700797
$471$	192.256	0.0188082
$472$	3581.23	0.349236
$473$	−11633.8	−1.13092
$474$	8003.42	0.775547
$475$	−14544.7	−1.40496
$476$	0	0
$477$	−367.554	−0.0352812
$478$	−10034.3	−0.960168
$479$	14048.6	1.34008	0.670041	−	0.742324i	$-0.266277\pi$
$479$	14048.6	1.34008	0.670041	+	0.742324i	$0.266277\pi$
$480$	−85.1667	−0.00809857
$481$	517.920	0.0490959
$482$	11744.1	1.10981
$483$	−10578.6	−0.996567
$484$	8955.21	0.841023
$485$	−1178.82	−0.110366
$486$	−486.000	−0.0453609
$487$	5097.02	0.474267	0.237134	−	0.971477i	$-0.423792\pi$
$487$	5097.02	0.474267	0.237134	+	0.971477i	$0.423792\pi$
$488$	1235.73	0.114629
$489$	7088.92	0.655567
$490$	24.7665	0.00228334
$491$	6390.91	0.587409	0.293704	−	0.955896i	$-0.405112\pi$
$491$	6390.91	0.587409	0.293704	+	0.955896i	$0.405112\pi$
$492$	5766.29	0.528383
$493$	0	0
$494$	−8588.77	−0.782241
$495$	−477.049	−0.0433167
$496$	−3823.25	−0.346107
$497$	11488.3	1.03687
$498$	3099.79	0.278926
$499$	−5209.56	−0.467358	−0.233679	−	0.972314i	$-0.575077\pi$
$499$	−5209.56	−0.467358	−0.233679	+	0.972314i	$0.575077\pi$
$500$	−884.361	−0.0790996
$501$	6508.94	0.580435
$502$	13798.3	1.22679
$503$	11096.4	0.983626	0.491813	−	0.870701i	$-0.336334\pi$
$503$	11096.4	0.983626	0.491813	+	0.870701i	$0.336334\pi$
$504$	1360.32	0.120225
$505$	708.815	0.0624591
$506$	−22302.3	−1.95940
$507$	2555.94	0.223892
$508$	6021.17	0.525878
$509$	−2967.70	−0.258430	−0.129215	−	0.991617i	$-0.541246\pi$
$509$	−2967.70	−0.258430	−0.129215	+	0.991617i	$0.541246\pi$
$510$	0	0
$511$	−6903.36	−0.597625
$512$	512.000	0.0441942
$513$	−3161.55	−0.272097
$514$	−3820.66	−0.327864
$515$	−52.4346	−0.00448649
$516$	−2336.58	−0.199346
$517$	2404.54	0.204549
$518$	−533.626	−0.0452629
$519$	9991.72	0.845063
$520$	−260.287	−0.0219507
$521$	−300.725	−0.0252880	−0.0126440	−	0.999920i	$-0.504025\pi$
$521$	−300.725	−0.0252880	−0.0126440	+	0.999920i	$0.504025\pi$
$522$	−2356.51	−0.197589
$523$	6172.53	0.516073	0.258036	−	0.966135i	$-0.416925\pi$
$523$	6172.53	0.516073	0.258036	+	0.966135i	$0.416925\pi$
$524$	4522.66	0.377048
$525$	7040.39	0.585272
$526$	−5379.99	−0.445967
$527$	0	0
$528$	2867.90	0.236381
$529$	22666.3	1.86293
$530$	−72.4615	−0.00593873
$531$	4028.88	0.329263
$532$	8849.22	0.721170
$533$	17623.0	1.43215
$534$	−4928.45	−0.399391
$535$	718.066	0.0580274
$536$	−3511.92	−0.283007
$537$	10623.8	0.853725
$538$	3777.32	0.302698
$539$	−833.984	−0.0666461
$540$	−95.8126	−0.00763540
$541$	8456.76	0.672060	0.336030	−	0.941851i	$-0.390916\pi$
$541$	8456.76	0.672060	0.336030	+	0.941851i	$0.390916\pi$
$542$	8345.32	0.661369
$543$	5152.99	0.407248
$544$	0	0
$545$	−1467.50	−0.115341
$546$	4157.43	0.325863
$547$	3781.66	0.295598	0.147799	−	0.989017i	$-0.452781\pi$
$547$	3781.66	0.295598	0.147799	+	0.989017i	$0.452781\pi$
$548$	−4316.52	−0.336483
$549$	1390.19	0.108073
$550$	14842.9	1.15073
$551$	−15329.7	−1.18524
$552$	−4479.28	−0.345382
$553$	−25201.9	−1.93796
$554$	−1481.14	−0.113588
$555$	37.5853	0.00287461
$556$	−2799.35	−0.213523
$557$	24045.8	1.82918	0.914589	−	0.404385i	$-0.132515\pi$
$557$	24045.8	1.82918	0.914589	+	0.404385i	$0.132515\pi$
$558$	−4301.16	−0.326313
$559$	−7141.09	−0.540315
$560$	268.181	0.0202370
$561$	0	0
$562$	650.111	0.0487959
$563$	13789.7	1.03227	0.516135	−	0.856507i	$-0.327370\pi$
$563$	13789.7	1.03227	0.516135	+	0.856507i	$0.327370\pi$
$564$	482.938	0.0360556
$565$	−426.531	−0.0317598
$566$	−9654.17	−0.716952
$567$	1530.36	0.113349
$568$	4864.50	0.359349
$569$	−19638.1	−1.44687	−0.723437	−	0.690390i	$-0.757439\pi$
$569$	−19638.1	−1.44687	−0.723437	+	0.690390i	$0.757439\pi$
$570$	−623.285	−0.0458009
$571$	15274.5	1.11947	0.559735	−	0.828672i	$-0.310903\pi$
$571$	15274.5	1.11947	0.559735	+	0.828672i	$0.310903\pi$
$572$	8764.89	0.640697
$573$	5143.70	0.375011
$574$	−18157.4	−1.32034
$575$	−23182.7	−1.68137
$576$	576.000	0.0416667
$577$	−11093.2	−0.800371	−0.400186	−	0.916434i	$-0.631054\pi$
$577$	−11093.2	−0.800371	−0.400186	+	0.916434i	$0.631054\pi$
$578$	0	0
$579$	10483.8	0.752487
$580$	−464.575	−0.0332593
$581$	−9760.91	−0.696990
$582$	7972.62	0.567828
$583$	2440.06	0.173340
$584$	−2923.09	−0.207120
$585$	−292.823	−0.0206953
$586$	2076.27	0.146365
$587$	9450.73	0.664520	0.332260	−	0.943188i	$-0.392189\pi$
$587$	9450.73	0.664520	0.332260	+	0.943188i	$0.392189\pi$
$588$	−167.501	−0.0117476
$589$	−27980.1	−1.95738
$590$	794.275	0.0554233
$591$	−8310.60	−0.578431
$592$	−225.953	−0.0156868
$593$	15181.4	1.05131	0.525655	−	0.850698i	$-0.323820\pi$
$593$	15181.4	1.05131	0.525655	+	0.850698i	$0.323820\pi$
$594$	3226.38	0.222862
$595$	0	0
$596$	5429.36	0.373147
$597$	−9986.93	−0.684653
$598$	−13689.6	−0.936138
$599$	3015.99	0.205726	0.102863	−	0.994696i	$-0.467200\pi$
$599$	3015.99	0.205726	0.102863	+	0.994696i	$0.467200\pi$
$600$	2981.11	0.202839
$601$	12422.7	0.843149	0.421575	−	0.906794i	$-0.361478\pi$
$601$	12422.7	0.843149	0.421575	+	0.906794i	$0.361478\pi$
$602$	7357.64	0.498131
$603$	−3950.91	−0.266821
$604$	−7050.15	−0.474945
$605$	1986.16	0.133469
$606$	−4793.86	−0.321348
$607$	2438.93	0.163086	0.0815430	−	0.996670i	$-0.474015\pi$
$607$	2438.93	0.163086	0.0815430	+	0.996670i	$0.474015\pi$
$608$	3747.02	0.249937
$609$	7420.39	0.493743
$610$	274.070	0.0181914
$611$	1475.96	0.0977266
$612$	0	0
$613$	14288.9	0.941477	0.470738	−	0.882273i	$-0.343988\pi$
$613$	14288.9	0.941477	0.470738	+	0.882273i	$0.343988\pi$
$614$	−13474.3	−0.885631
$615$	1278.90	0.0838537
$616$	−9030.69	−0.590677
$617$	10058.5	0.656306	0.328153	−	0.944625i	$-0.393574\pi$
$617$	10058.5	0.656306	0.328153	+	0.944625i	$0.393574\pi$
$618$	354.626	0.0230828
$619$	26199.0	1.70117	0.850586	−	0.525835i	$-0.176247\pi$
$619$	26199.0	1.70117	0.850586	+	0.525835i	$0.176247\pi$
$620$	−847.952	−0.0549268
$621$	−5039.19	−0.325629
$622$	−9495.25	−0.612098
$623$	15519.2	0.998013
$624$	1760.38	0.112935
$625$	15330.5	0.981151
$626$	12057.9	0.769854
$627$	20988.4	1.33684
$628$	−256.341	−0.0162884
$629$	0	0
$630$	301.703	0.0190796
$631$	2855.15	0.180129	0.0900647	−	0.995936i	$-0.471293\pi$
$631$	2855.15	0.180129	0.0900647	+	0.995936i	$0.471293\pi$
$632$	−10671.2	−0.671643
$633$	11613.3	0.729207
$634$	14017.1	0.878062
$635$	1335.43	0.0834563
$636$	490.072	0.0305544
$637$	−511.918	−0.0318413
$638$	15644.0	0.970773
$639$	5472.57	0.338797
$640$	113.556	0.00701356
$641$	−12620.8	−0.777679	−0.388840	−	0.921305i	$-0.627124\pi$
$641$	−12620.8	−0.777679	−0.388840	+	0.921305i	$0.627124\pi$
$642$	−4856.42	−0.298548
$643$	17780.1	1.09048	0.545239	−	0.838281i	$-0.316439\pi$
$643$	17780.1	1.09048	0.545239	+	0.838281i	$0.316439\pi$
$644$	14104.8	0.863052
$645$	−518.227	−0.0316359
$646$	0	0
$647$	−2887.24	−0.175439	−0.0877197	−	0.996145i	$-0.527958\pi$
$647$	−2887.24	−0.175439	−0.0877197	+	0.996145i	$0.527958\pi$
$648$	648.000	0.0392837
$649$	−26746.3	−1.61770
$650$	9110.90	0.549783
$651$	13543.9	0.815401
$652$	−9451.90	−0.567737
$653$	25653.1	1.53734	0.768670	−	0.639645i	$-0.220919\pi$
$653$	25653.1	1.53734	0.768670	+	0.639645i	$0.220919\pi$
$654$	9924.97	0.593421
$655$	1003.07	0.0598371
$656$	−7688.38	−0.457593
$657$	−3288.47	−0.195275
$658$	−1520.72	−0.0900970
$659$	22255.0	1.31552	0.657762	−	0.753226i	$-0.271503\pi$
$659$	22255.0	1.31552	0.657762	+	0.753226i	$0.271503\pi$
$660$	636.066	0.0375134
$661$	−5678.09	−0.334118	−0.167059	−	0.985947i	$-0.553427\pi$
$661$	−5678.09	−0.334118	−0.167059	+	0.985947i	$0.553427\pi$
$662$	11035.1	0.647870
$663$	0	0
$664$	−4133.06	−0.241557
$665$	1962.65	0.114449
$666$	−254.197	−0.0147897
$667$	−24434.0	−1.41842
$668$	−8678.58	−0.502671
$669$	15883.1	0.917900
$670$	−778.902	−0.0449129
$671$	−9229.00	−0.530971
$672$	−1813.76	−0.104118
$673$	−6871.08	−0.393552	−0.196776	−	0.980448i	$-0.563047\pi$
$673$	−6871.08	−0.393552	−0.196776	+	0.980448i	$0.563047\pi$
$674$	13833.4	0.790566
$675$	3353.75	0.191238
$676$	−3407.92	−0.193896
$677$	9929.79	0.563711	0.281856	−	0.959457i	$-0.409050\pi$
$677$	9929.79	0.563711	0.281856	+	0.959457i	$0.409050\pi$
$678$	2884.71	0.163402
$679$	−25104.9	−1.41891
$680$	0	0
$681$	15673.7	0.881962
$682$	28553.9	1.60320
$683$	4903.53	0.274712	0.137356	−	0.990522i	$-0.456140\pi$
$683$	4903.53	0.274712	0.137356	+	0.990522i	$0.456140\pi$
$684$	4215.40	0.235643
$685$	−957.354	−0.0533995
$686$	−12433.4	−0.691996
$687$	5635.51	0.312967
$688$	3115.44	0.172638
$689$	1497.76	0.0828160
$690$	−993.453	−0.0548117
$691$	2336.83	0.128650	0.0643249	−	0.997929i	$-0.479511\pi$
$691$	2336.83	0.128650	0.0643249	+	0.997929i	$0.479511\pi$
$692$	−13322.3	−0.731846
$693$	−10159.5	−0.556895
$694$	−7548.67	−0.412887
$695$	−620.863	−0.0338858
$696$	3142.01	0.171117
$697$	0	0
$698$	1058.38	0.0573930
$699$	−4981.49	−0.269552
$700$	−9387.19	−0.506861
$701$	−11924.7	−0.642498	−0.321249	−	0.946995i	$-0.604103\pi$
$701$	−11924.7	−0.642498	−0.321249	+	0.946995i	$0.604103\pi$
$702$	1980.42	0.106476
$703$	−1653.62	−0.0887159
$704$	−3823.86	−0.204712
$705$	107.110	0.00572198
$706$	7558.78	0.402944
$707$	15095.3	0.802996
$708$	−5371.84	−0.285150
$709$	−8039.30	−0.425842	−0.212921	−	0.977069i	$-0.568298\pi$
$709$	−8039.30	−0.425842	−0.212921	+	0.977069i	$0.568298\pi$
$710$	1078.89	0.0570282
$711$	−12005.1	−0.633231
$712$	6571.27	0.345883
$713$	−44597.4	−2.34248
$714$	0	0
$715$	1943.95	0.101678
$716$	−14165.1	−0.739348
$717$	15051.5	0.783974
$718$	7528.03	0.391286
$719$	16258.2	0.843294	0.421647	−	0.906760i	$-0.361452\pi$
$719$	16258.2	0.843294	0.421647	+	0.906760i	$0.361452\pi$
$720$	127.750	0.00661245
$721$	−1116.68	−0.0576800
$722$	13704.2	0.706397
$723$	−17616.1	−0.906156
$724$	−6870.65	−0.352687
$725$	16261.6	0.833022
$726$	−13432.8	−0.686692
$727$	−32634.5	−1.66485	−0.832426	−	0.554136i	$-0.813049\pi$
$727$	−32634.5	−1.66485	−0.832426	+	0.554136i	$0.813049\pi$
$728$	−5543.23	−0.282206
$729$	729.000	0.0370370
$730$	−648.306	−0.0328697
$731$	0	0
$732$	−1853.59	−0.0935938
$733$	−30175.2	−1.52053	−0.760264	−	0.649614i	$-0.774930\pi$
$733$	−30175.2	−1.52053	−0.760264	+	0.649614i	$0.774930\pi$
$734$	14808.6	0.744680
$735$	−37.1497	−0.00186434
$736$	5972.38	0.299110
$737$	26228.7	1.31092
$738$	−8649.43	−0.431423
$739$	25108.8	1.24985	0.624926	−	0.780684i	$-0.285129\pi$
$739$	25108.8	1.24985	0.624926	+	0.780684i	$0.285129\pi$
$740$	−50.1138	−0.00248948
$741$	12883.2	0.638697
$742$	−1543.18	−0.0763505
$743$	−3787.46	−0.187010	−0.0935051	−	0.995619i	$-0.529807\pi$
$743$	−3787.46	−0.187010	−0.0935051	+	0.995619i	$0.529807\pi$
$744$	5734.88	0.282595
$745$	1204.17	0.0592179
$746$	23881.5	1.17207
$747$	−4649.69	−0.227742
$748$	0	0
$749$	15292.3	0.746022
$750$	1326.54	0.0645846
$751$	−36264.4	−1.76206	−0.881030	−	0.473061i	$-0.843149\pi$
$751$	−36264.4	−1.76206	−0.881030	+	0.473061i	$0.843149\pi$
$752$	−643.918	−0.0312251
$753$	−20697.5	−1.00167
$754$	9602.65	0.463804
$755$	−1563.64	−0.0753731
$756$	−2040.48	−0.0981635
$757$	19664.2	0.944132	0.472066	−	0.881563i	$-0.343508\pi$
$757$	19664.2	0.944132	0.472066	+	0.881563i	$0.343508\pi$
$758$	18253.7	0.874676
$759$	33453.4	1.59984
$760$	831.046	0.0396647
$761$	−9962.11	−0.474542	−0.237271	−	0.971444i	$-0.576253\pi$
$761$	−9962.11	−0.474542	−0.237271	+	0.971444i	$0.576253\pi$
$762$	−9031.75	−0.429378
$763$	−31252.7	−1.48286
$764$	−6858.27	−0.324769
$765$	0	0
$766$	−18522.3	−0.873677
$767$	−16417.5	−0.772882
$768$	−768.000	−0.0360844
$769$	5619.91	0.263536	0.131768	−	0.991281i	$-0.457935\pi$
$769$	5619.91	0.263536	0.131768	+	0.991281i	$0.457935\pi$
$770$	−2002.90	−0.0937397
$771$	5730.99	0.267700
$772$	−13978.3	−0.651673
$773$	−10503.4	−0.488722	−0.244361	−	0.969684i	$-0.578578\pi$
$773$	−10503.4	−0.488722	−0.244361	+	0.969684i	$0.578578\pi$
$774$	3504.87	0.162765
$775$	29681.1	1.37571
$776$	−10630.2	−0.491753
$777$	800.439	0.0369570
$778$	−3709.47	−0.170939
$779$	−56266.7	−2.58789
$780$	390.431	0.0179227
$781$	−36330.4	−1.66454
$782$	0	0
$783$	3534.77	0.161331
$784$	223.334	0.0101738
$785$	−56.8534	−0.00258495
$786$	−6783.99	−0.307859
$787$	15340.8	0.694841	0.347421	−	0.937709i	$-0.387058\pi$
$787$	15340.8	0.694841	0.347421	+	0.937709i	$0.387058\pi$
$788$	11080.8	0.500936
$789$	8069.99	0.364131
$790$	−2366.75	−0.106589
$791$	−9083.65	−0.408315
$792$	−4301.84	−0.193004
$793$	−5664.96	−0.253681
$794$	−18842.5	−0.842185
$795$	108.692	0.00484895
$796$	13315.9	0.592927
$797$	14361.1	0.638266	0.319133	−	0.947710i	$-0.396608\pi$
$797$	14361.1	0.638266	0.319133	+	0.947710i	$0.396608\pi$
$798$	−13273.8	−0.588833
$799$	0	0
$800$	−3974.81	−0.175664
$801$	7392.68	0.326102
$802$	6772.30	0.298178
$803$	21831.0	0.959401
$804$	5267.87	0.231074
$805$	3128.27	0.136965
$806$	17527.0	0.765958
$807$	−5665.98	−0.247152
$808$	6391.81	0.278296
$809$	2315.88	0.100645	0.0503227	−	0.998733i	$-0.483975\pi$
$809$	2315.88	0.100645	0.0503227	+	0.998733i	$0.483975\pi$
$810$	143.719	0.00623428
$811$	−13135.6	−0.568747	−0.284373	−	0.958714i	$-0.591786\pi$
$811$	−13135.6	−0.568747	−0.284373	+	0.958714i	$0.591786\pi$
$812$	−9893.86	−0.427594
$813$	−12518.0	−0.540006
$814$	1687.53	0.0726631
$815$	−2096.32	−0.0900993
$816$	0	0
$817$	22800.1	0.976345
$818$	−19641.2	−0.839531
$819$	−6236.14	−0.266066
$820$	−1705.19	−0.0726195
$821$	39346.2	1.67258	0.836292	−	0.548285i	$-0.184719\pi$
$821$	39346.2	1.67258	0.836292	+	0.548285i	$0.184719\pi$
$822$	6474.78	0.274737
$823$	25509.2	1.08043	0.540216	−	0.841526i	$-0.318343\pi$
$823$	25509.2	1.08043	0.540216	+	0.841526i	$0.318343\pi$
$824$	−472.834	−0.0199903
$825$	−22264.4	−0.939570
$826$	16915.3	0.712542
$827$	−37544.1	−1.57864	−0.789321	−	0.613981i	$-0.789567\pi$
$827$	−37544.1	−1.57864	−0.789321	+	0.613981i	$0.789567\pi$
$828$	6718.92	0.282003
$829$	−14101.2	−0.590778	−0.295389	−	0.955377i	$-0.595449\pi$
$829$	−14101.2	−0.590778	−0.295389	+	0.955377i	$0.595449\pi$
$830$	−916.664	−0.0383348
$831$	2221.71	0.0927439
$832$	−2347.17	−0.0978046
$833$	0	0
$834$	4199.02	0.174341
$835$	−1924.81	−0.0797734
$836$	−27984.6	−1.15773
$837$	6451.74	0.266433
$838$	−19808.1	−0.816537
$839$	−35774.9	−1.47209	−0.736046	−	0.676931i	$-0.763309\pi$
$839$	−35774.9	−1.47209	−0.736046	+	0.676931i	$0.763309\pi$
$840$	−402.271	−0.0165234
$841$	−7249.68	−0.297252
$842$	−9278.70	−0.379769
$843$	−975.167	−0.0398417
$844$	−15484.4	−0.631512
$845$	−755.837	−0.0307711
$846$	−724.407	−0.0294393
$847$	42298.5	1.71593
$848$	−653.429	−0.0264609
$849$	14481.2	0.585389
$850$	0	0
$851$	−2635.70	−0.106170
$852$	−7296.75	−0.293407
$853$	−3151.61	−0.126505	−0.0632526	−	0.997998i	$-0.520147\pi$
$853$	−3151.61	−0.126505	−0.0632526	+	0.997998i	$0.520147\pi$
$854$	5836.75	0.233875
$855$	934.927	0.0373963
$856$	6475.23	0.258550
$857$	−23583.7	−0.940029	−0.470014	−	0.882659i	$-0.655751\pi$
$857$	−23583.7	−0.940029	−0.470014	+	0.882659i	$0.655751\pi$
$858$	−13147.3	−0.523127
$859$	36967.7	1.46836	0.734181	−	0.678954i	$-0.237567\pi$
$859$	36967.7	1.46836	0.734181	+	0.678954i	$0.237567\pi$
$860$	690.969	0.0273975
$861$	27236.1	1.07805
$862$	−5062.62	−0.200039
$863$	−46451.4	−1.83224	−0.916120	−	0.400905i	$-0.868696\pi$
$863$	−46451.4	−1.83224	−0.916120	+	0.400905i	$0.868696\pi$
$864$	−864.000	−0.0340207
$865$	−2954.73	−0.116143
$866$	−14253.4	−0.559295
$867$	0	0
$868$	−18058.5	−0.706158
$869$	79697.8	3.11112
$870$	696.862	0.0271561
$871$	16099.7	0.626313
$872$	−13233.3	−0.513917
$873$	−11958.9	−0.463629
$874$	43708.3	1.69160
$875$	−4177.13	−0.161386
$876$	4384.63	0.169113
$877$	−28731.1	−1.10625	−0.553125	−	0.833098i	$-0.686565\pi$
$877$	−28731.1	−1.10625	−0.553125	+	0.833098i	$0.686565\pi$
$878$	32506.2	1.24947
$879$	−3114.40	−0.119506
$880$	−848.088	−0.0324875
$881$	26394.9	1.00938	0.504692	−	0.863299i	$-0.331606\pi$
$881$	26394.9	1.00938	0.504692	+	0.863299i	$0.331606\pi$
$882$	251.251	0.00959191
$883$	−29247.0	−1.11466	−0.557328	−	0.830293i	$-0.688173\pi$
$883$	−29247.0	−1.11466	−0.557328	+	0.830293i	$0.688173\pi$
$884$	0	0
$885$	−1191.41	−0.0452530
$886$	18166.1	0.688828
$887$	−36513.4	−1.38219	−0.691093	−	0.722766i	$-0.742871\pi$
$887$	−36513.4	−1.38219	−0.691093	+	0.722766i	$0.742871\pi$
$888$	338.930	0.0128083
$889$	28440.0	1.07294
$890$	1457.43	0.0548912
$891$	−4839.57	−0.181966
$892$	−21177.4	−0.794925
$893$	−4712.45	−0.176591
$894$	−8144.04	−0.304673
$895$	−3141.64	−0.117334
$896$	2418.35	0.0901689
$897$	20534.4	0.764353
$898$	−3641.49	−0.135321
$899$	31283.1	1.16057
$900$	−4471.67	−0.165617
$901$	0	0
$902$	57420.5	2.11962
$903$	−11036.5	−0.406723
$904$	−3846.28	−0.141511
$905$	−1523.83	−0.0559711
$906$	10575.2	0.387791
$907$	−5074.72	−0.185781	−0.0928905	−	0.995676i	$-0.529611\pi$
$907$	−5074.72	−0.185781	−0.0928905	+	0.995676i	$0.529611\pi$
$908$	−20898.2	−0.763801
$909$	7190.79	0.262380
$910$	−1229.42	−0.0447858
$911$	−1307.08	−0.0475361	−0.0237681	−	0.999717i	$-0.507566\pi$
$911$	−1307.08	−0.0475361	−0.0237681	+	0.999717i	$0.507566\pi$
$912$	−5620.53	−0.204073
$913$	30867.7	1.11892
$914$	−33171.8	−1.20047
$915$	−411.105	−0.0148532
$916$	−7514.02	−0.271037
$917$	21362.0	0.769287
$918$	0	0
$919$	−34616.0	−1.24252	−0.621260	−	0.783605i	$-0.713379\pi$
$919$	−34616.0	−1.24252	−0.621260	+	0.783605i	$0.713379\pi$
$920$	1324.60	0.0474684
$921$	20211.4	0.723115
$922$	−14715.9	−0.525642
$923$	−22300.4	−0.795262
$924$	13546.0	0.482286
$925$	1754.14	0.0623523
$926$	−28264.1	−1.00304
$927$	−531.939	−0.0188470
$928$	−4189.35	−0.148192
$929$	−12183.1	−0.430264	−0.215132	−	0.976585i	$-0.569018\pi$
$929$	−12183.1	−0.430264	−0.215132	+	0.976585i	$0.569018\pi$
$930$	1271.93	0.0448475
$931$	1634.45	0.0575370
$932$	6641.98	0.233439
$933$	14242.9	0.499776
$934$	7614.02	0.266743
$935$	0	0
$936$	−2640.57	−0.0922111
$937$	37258.1	1.29901	0.649503	−	0.760359i	$-0.274977\pi$
$937$	37258.1	1.29901	0.649503	+	0.760359i	$0.274977\pi$
$938$	−16588.0	−0.577416
$939$	−18086.8	−0.628583
$940$	−142.813	−0.00495538
$941$	32270.4	1.11794	0.558972	−	0.829187i	$-0.311196\pi$
$941$	32270.4	1.11794	0.558972	+	0.829187i	$0.311196\pi$
$942$	384.511	0.0132994
$943$	−89683.4	−3.09702
$944$	7162.46	0.246947
$945$	−452.555	−0.0155784
$946$	−23267.6	−0.799678
$947$	27626.2	0.947973	0.473987	−	0.880532i	$-0.342814\pi$
$947$	27626.2	0.947973	0.473987	+	0.880532i	$0.342814\pi$
$948$	16006.8	0.548394
$949$	13400.3	0.458370
$950$	−29089.3	−0.993454
$951$	−21025.7	−0.716935
$952$	0	0
$953$	34202.3	1.16256	0.581281	−	0.813703i	$-0.302552\pi$
$953$	34202.3	1.16256	0.581281	+	0.813703i	$0.302552\pi$
$954$	−735.108	−0.0249476
$955$	−1521.08	−0.0515405
$956$	−20068.7	−0.678941
$957$	−23466.1	−0.792633
$958$	28097.3	0.947581
$959$	−20388.4	−0.686523
$960$	−170.333	−0.00572655
$961$	27307.6	0.916640
$962$	1035.84	0.0347160
$963$	7284.64	0.243763
$964$	23488.2	0.784754
$965$	−3100.23	−0.103420
$966$	−21157.2	−0.704679
$967$	12249.7	0.407367	0.203684	−	0.979037i	$-0.434709\pi$
$967$	12249.7	0.407367	0.203684	+	0.979037i	$0.434709\pi$
$968$	17910.4	0.594693
$969$	0	0
$970$	−2357.64	−0.0780406
$971$	−10482.5	−0.346445	−0.173222	−	0.984883i	$-0.555418\pi$
$971$	−10482.5	−0.346445	−0.173222	+	0.984883i	$0.555418\pi$
$972$	−972.000	−0.0320750
$973$	−13222.3	−0.435649
$974$	10194.0	0.335358
$975$	−13666.4	−0.448896
$976$	2471.45	0.0810546
$977$	47676.1	1.56120	0.780600	−	0.625031i	$-0.214914\pi$
$977$	47676.1	1.56120	0.780600	+	0.625031i	$0.214914\pi$
$978$	14177.8	0.463556
$979$	−49077.4	−1.60217
$980$	49.5330	0.00161456
$981$	−14887.5	−0.484526
$982$	12781.8	0.415361
$983$	38056.7	1.23481	0.617407	−	0.786644i	$-0.288183\pi$
$983$	38056.7	1.23481	0.617407	+	0.786644i	$0.288183\pi$
$984$	11532.6	0.373623
$985$	2457.59	0.0794979
$986$	0	0
$987$	2281.08	0.0735639
$988$	−17177.5	−0.553128
$989$	36341.0	1.16843
$990$	−954.099	−0.0306295
$991$	−25197.0	−0.807679	−0.403840	−	0.914830i	$-0.632325\pi$
$991$	−25197.0	−0.807679	−0.403840	+	0.914830i	$0.632325\pi$
$992$	−7646.50	−0.244735
$993$	−16552.6	−0.528984
$994$	22976.7	0.733175
$995$	2953.31	0.0940968
$996$	6199.59	0.197230
$997$	−13983.6	−0.444197	−0.222099	−	0.975024i	$-0.571291\pi$
$997$	−13983.6	−0.444197	−0.222099	+	0.975024i	$0.571291\pi$
$998$	−10419.1	−0.330472
$999$	381.296	0.0120757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.4.a.bd.1.4		6
17.8	even	8		102.4.f.c.13.5	✓	12
17.15	even	8		102.4.f.c.55.5	yes	12
17.16	even	2		1734.4.a.be.1.3		6
51.8	odd	8		306.4.g.g.217.4		12
51.32	odd	8		306.4.g.g.55.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.4.f.c.13.5	✓	12	17.8	even	8
102.4.f.c.55.5	yes	12	17.15	even	8
306.4.g.g.55.4		12	51.32	odd	8
306.4.g.g.217.4		12	51.8	odd	8
1734.4.a.bd.1.4		6	1.1	even	1	trivial
1734.4.a.be.1.3		6	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1734.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +0.887153 q^{5} -6.00000 q^{6} +18.8933 q^{7} +8.00000 q^{8} +9.00000 q^{9} +1.77431 q^{10} -59.7478 q^{11} -12.0000 q^{12} -36.6745 q^{13} +37.7867 q^{14} -2.66146 q^{15} +16.0000 q^{16} +18.0000 q^{18} +117.094 q^{19} +3.54861 q^{20} -56.6800 q^{21} -119.496 q^{22} +186.637 q^{23} -24.0000 q^{24} -124.213 q^{25} -73.3490 q^{26} -27.0000 q^{27} +75.5734 q^{28} -130.917 q^{29} -5.32292 q^{30} -238.953 q^{31} +32.0000 q^{32} +179.243 q^{33} +16.7613 q^{35} +36.0000 q^{36} -14.1221 q^{37} +234.189 q^{38} +110.024 q^{39} +7.09723 q^{40} -480.524 q^{41} -113.360 q^{42} +194.715 q^{43} -238.991 q^{44} +7.98438 q^{45} +373.274 q^{46} -40.2448 q^{47} -48.0000 q^{48} +13.9584 q^{49} -248.426 q^{50} -146.698 q^{52} -40.8393 q^{53} -54.0000 q^{54} -53.0055 q^{55} +151.147 q^{56} -351.283 q^{57} -261.834 q^{58} +447.653 q^{59} -10.6458 q^{60} +154.466 q^{61} -477.906 q^{62} +170.040 q^{63} +64.0000 q^{64} -32.5359 q^{65} +358.487 q^{66} -438.990 q^{67} -559.910 q^{69} +33.5226 q^{70} +608.063 q^{71} +72.0000 q^{72} -365.386 q^{73} -28.2441 q^{74} +372.639 q^{75} +468.378 q^{76} -1128.84 q^{77} +220.047 q^{78} -1333.90 q^{79} +14.1945 q^{80} +81.0000 q^{81} -961.048 q^{82} -516.632 q^{83} -226.720 q^{84} +389.430 q^{86} +392.752 q^{87} -477.983 q^{88} +821.409 q^{89} +15.9688 q^{90} -692.904 q^{91} +746.547 q^{92} +716.860 q^{93} -80.4897 q^{94} +103.881 q^{95} -96.0000 q^{96} -1328.77 q^{97} +27.9168 q^{98} -537.730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 18 q^{3} + 24 q^{4} - 14 q^{5} - 36 q^{6} - 28 q^{7} + 48 q^{8} + 54 q^{9} - 28 q^{10} - 34 q^{11} - 72 q^{12} + 34 q^{13} - 56 q^{14} + 42 q^{15} + 96 q^{16} + 108 q^{18} + 70 q^{19} - 56 q^{20}+ \cdots - 306 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 18 * q^3 + 24 * q^4 - 14 * q^5 - 36 * q^6 - 28 * q^7 + 48 * q^8 + 54 * q^9 - 28 * q^10 - 34 * q^11 - 72 * q^12 + 34 * q^13 - 56 * q^14 + 42 * q^15 + 96 * q^16 + 108 * q^18 + 70 * q^19 - 56 * q^20 + 84 * q^21 - 68 * q^22 - 78 * q^23 - 144 * q^24 + 188 * q^25 + 68 * q^26 - 162 * q^27 - 112 * q^28 - 280 * q^29 + 84 * q^30 - 508 * q^31 + 192 * q^32 + 102 * q^33 + 196 * q^35 + 216 * q^36 - 308 * q^37 + 140 * q^38 - 102 * q^39 - 112 * q^40 - 442 * q^41 + 168 * q^42 - 46 * q^43 - 136 * q^44 - 126 * q^45 - 156 * q^46 + 1460 * q^47 - 288 * q^48 + 1042 * q^49 + 376 * q^50 + 136 * q^52 + 476 * q^53 - 324 * q^54 - 578 * q^55 - 224 * q^56 - 210 * q^57 - 560 * q^58 + 688 * q^59 + 168 * q^60 + 84 * q^61 - 1016 * q^62 - 252 * q^63 + 384 * q^64 - 1526 * q^65 + 204 * q^66 - 1004 * q^67 + 234 * q^69 + 392 * q^70 - 332 * q^71 + 432 * q^72 - 1132 * q^73 - 616 * q^74 - 564 * q^75 + 280 * q^76 - 1548 * q^77 - 204 * q^78 - 4512 * q^79 - 224 * q^80 + 486 * q^81 - 884 * q^82 + 68 * q^83 + 336 * q^84 - 92 * q^86 + 840 * q^87 - 272 * q^88 - 2652 * q^89 - 252 * q^90 - 3052 * q^91 - 312 * q^92 + 1524 * q^93 + 2920 * q^94 + 622 * q^95 - 576 * q^96 + 1152 * q^97 + 2084 * q^98 - 306 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more