LMFDB - Embedded newform 1011.4.a.c.1.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1011,4,Mod(1,1011)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1011.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1011, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1011 = 3 \cdot 337 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1011.a (trivial)

Newform invariants

comment:select newform

sage:traces = [46] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$59.6509310158$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1011.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.67739 q^{2} -3.00000 q^{3} -5.18636 q^{4} -10.3096 q^{5} +5.03218 q^{6} -14.8478 q^{7} +22.1187 q^{8} +9.00000 q^{9} +17.2932 q^{10} -9.93668 q^{11} +15.5591 q^{12} +39.2709 q^{13} +24.9055 q^{14} +30.9287 q^{15} +4.38915 q^{16} +2.80710 q^{17} -15.0965 q^{18} -122.197 q^{19} +53.4692 q^{20} +44.5433 q^{21} +16.6677 q^{22} -99.2053 q^{23} -66.3561 q^{24} -18.7125 q^{25} -65.8726 q^{26} -27.0000 q^{27} +77.0059 q^{28} -250.263 q^{29} -51.8796 q^{30} +10.2296 q^{31} -184.312 q^{32} +29.8100 q^{33} -4.70861 q^{34} +153.074 q^{35} -46.6772 q^{36} -404.701 q^{37} +204.973 q^{38} -117.813 q^{39} -228.034 q^{40} -188.392 q^{41} -74.7166 q^{42} -58.2207 q^{43} +51.5351 q^{44} -92.7862 q^{45} +166.406 q^{46} -71.4635 q^{47} -13.1675 q^{48} -122.543 q^{49} +31.3883 q^{50} -8.42131 q^{51} -203.673 q^{52} -292.903 q^{53} +45.2896 q^{54} +102.443 q^{55} -328.413 q^{56} +366.592 q^{57} +419.789 q^{58} +189.031 q^{59} -160.408 q^{60} +566.690 q^{61} -17.1590 q^{62} -133.630 q^{63} +274.050 q^{64} -404.866 q^{65} -50.0031 q^{66} -798.385 q^{67} -14.5586 q^{68} +297.616 q^{69} -256.766 q^{70} +44.2663 q^{71} +199.068 q^{72} +1054.89 q^{73} +678.841 q^{74} +56.1376 q^{75} +633.760 q^{76} +147.538 q^{77} +197.618 q^{78} -1228.53 q^{79} -45.2503 q^{80} +81.0000 q^{81} +316.007 q^{82} +264.482 q^{83} -231.018 q^{84} -28.9401 q^{85} +97.6590 q^{86} +750.790 q^{87} -219.786 q^{88} -657.630 q^{89} +155.639 q^{90} -583.085 q^{91} +514.514 q^{92} -30.6887 q^{93} +119.872 q^{94} +1259.80 q^{95} +552.935 q^{96} +279.854 q^{97} +205.553 q^{98} -89.4301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) $ 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * 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 $

$2$	−1.67739	−0.593048	−0.296524	−	0.955025i	$-0.595827\pi$
$2$	−1.67739	−0.593048	−0.296524	+	0.955025i	$0.595827\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−5.18636	−0.648295
$5$	−10.3096	−0.922117	−0.461058	−	0.887370i	$-0.652530\pi$
$5$	−10.3096	−0.922117	−0.461058	+	0.887370i	$0.652530\pi$
$6$	5.03218	0.342396
$7$	−14.8478	−0.801705	−0.400852	−	0.916143i	$-0.631286\pi$
$7$	−14.8478	−0.801705	−0.400852	+	0.916143i	$0.631286\pi$
$8$	22.1187	0.977517
$9$	9.00000	0.333333
$10$	17.2932	0.546859
$11$	−9.93668	−0.272365	−0.136183	−	0.990684i	$-0.543483\pi$
$11$	−9.93668	−0.272365	−0.136183	+	0.990684i	$0.543483\pi$
$12$	15.5591	0.374293
$13$	39.2709	0.837829	0.418915	−	0.908026i	$-0.362411\pi$
$13$	39.2709	0.837829	0.418915	+	0.908026i	$0.362411\pi$
$14$	24.9055	0.475449
$15$	30.9287	0.532384
$16$	4.38915	0.0685805
$17$	2.80710	0.0400484	0.0200242	−	0.999799i	$-0.493626\pi$
$17$	2.80710	0.0400484	0.0200242	+	0.999799i	$0.493626\pi$
$18$	−15.0965	−0.197683
$19$	−122.197	−1.47547	−0.737737	−	0.675088i	$-0.764106\pi$
$19$	−122.197	−1.47547	−0.737737	+	0.675088i	$0.764106\pi$
$20$	53.4692	0.597803
$21$	44.5433	0.462865
$22$	16.6677	0.161526
$23$	−99.2053	−0.899379	−0.449690	−	0.893185i	$-0.648465\pi$
$23$	−99.2053	−0.899379	−0.449690	+	0.893185i	$0.648465\pi$
$24$	−66.3561	−0.564370
$25$	−18.7125	−0.149700
$26$	−65.8726	−0.496873
$27$	−27.0000	−0.192450
$28$	77.0059	0.519741
$29$	−250.263	−1.60251	−0.801254	−	0.598325i	$-0.795833\pi$
$29$	−250.263	−1.60251	−0.801254	+	0.598325i	$0.795833\pi$
$30$	−51.8796	−0.315729
$31$	10.2296	0.0592672	0.0296336	−	0.999561i	$-0.490566\pi$
$31$	10.2296	0.0592672	0.0296336	+	0.999561i	$0.490566\pi$
$32$	−184.312	−1.01819
$33$	29.8100	0.157250
$34$	−4.70861	−0.0237506
$35$	153.074	0.739266
$36$	−46.6772	−0.216098
$37$	−404.701	−1.79817	−0.899086	−	0.437772i	$-0.855768\pi$
$37$	−404.701	−1.79817	−0.899086	+	0.437772i	$0.855768\pi$
$38$	204.973	0.875027
$39$	−117.813	−0.483721
$40$	−228.034	−0.901385
$41$	−188.392	−0.717606	−0.358803	−	0.933413i	$-0.616815\pi$
$41$	−188.392	−0.717606	−0.358803	+	0.933413i	$0.616815\pi$
$42$	−74.7166	−0.274501
$43$	−58.2207	−0.206479	−0.103239	−	0.994657i	$-0.532921\pi$
$43$	−58.2207	−0.206479	−0.103239	+	0.994657i	$0.532921\pi$
$44$	51.5351	0.176573
$45$	−92.7862	−0.307372
$46$	166.406	0.533375
$47$	−71.4635	−0.221788	−0.110894	−	0.993832i	$-0.535371\pi$
$47$	−71.4635	−0.221788	−0.110894	+	0.993832i	$0.535371\pi$
$48$	−13.1675	−0.0395950
$49$	−122.543	−0.357269
$50$	31.3883	0.0887794
$51$	−8.42131	−0.0231219
$52$	−203.673	−0.543160
$53$	−292.903	−0.759119	−0.379560	−	0.925167i	$-0.623924\pi$
$53$	−292.903	−0.759119	−0.379560	+	0.925167i	$0.623924\pi$
$54$	45.2896	0.114132
$55$	102.443	0.251153
$56$	−328.413	−0.783680
$57$	366.592	0.851866
$58$	419.789	0.950363
$59$	189.031	0.417114	0.208557	−	0.978010i	$-0.433123\pi$
$59$	189.031	0.417114	0.208557	+	0.978010i	$0.433123\pi$
$60$	−160.408	−0.345142
$61$	566.690	1.18946	0.594731	−	0.803925i	$-0.297259\pi$
$61$	566.690	1.18946	0.594731	+	0.803925i	$0.297259\pi$
$62$	−17.1590	−0.0351483
$63$	−133.630	−0.267235
$64$	274.050	0.535254
$65$	−404.866	−0.772576
$66$	−50.0031	−0.0932569
$67$	−798.385	−1.45579	−0.727897	−	0.685686i	$-0.759502\pi$
$67$	−798.385	−1.45579	−0.727897	+	0.685686i	$0.759502\pi$
$68$	−14.5586	−0.0259631
$69$	297.616	0.519257
$70$	−256.766	−0.438420
$71$	44.2663	0.0739921	0.0369961	−	0.999315i	$-0.488221\pi$
$71$	44.2663	0.0739921	0.0369961	+	0.999315i	$0.488221\pi$
$72$	199.068	0.325839
$73$	1054.89	1.69131	0.845654	−	0.533732i	$-0.179211\pi$
$73$	1054.89	1.69131	0.845654	+	0.533732i	$0.179211\pi$
$74$	678.841	1.06640
$75$	56.1376	0.0864295
$76$	633.760	0.956542
$77$	147.538	0.218357
$78$	197.618	0.286869
$79$	−1228.53	−1.74962	−0.874811	−	0.484464i	$-0.839015\pi$
$79$	−1228.53	−1.74962	−0.874811	+	0.484464i	$0.839015\pi$
$80$	−45.2503	−0.0632393
$81$	81.0000	0.111111
$82$	316.007	0.425575
$83$	264.482	0.349767	0.174883	−	0.984589i	$-0.444045\pi$
$83$	264.482	0.349767	0.174883	+	0.984589i	$0.444045\pi$
$84$	−231.018	−0.300073
$85$	−28.9401	−0.0369293
$86$	97.6590	0.122452
$87$	750.790	0.925208
$88$	−219.786	−0.266242
$89$	−657.630	−0.783244	−0.391622	−	0.920126i	$-0.628086\pi$
$89$	−657.630	−0.783244	−0.391622	+	0.920126i	$0.628086\pi$
$90$	155.639	0.182286
$91$	−583.085	−0.671692
$92$	514.514	0.583063
$93$	−30.6887	−0.0342180
$94$	119.872	0.131531
$95$	1259.80	1.36056
$96$	552.935	0.587851
$97$	279.854	0.292937	0.146469	−	0.989215i	$-0.453209\pi$
$97$	279.854	0.292937	0.146469	+	0.989215i	$0.453209\pi$
$98$	205.553	0.211878
$99$	−89.4301	−0.0907885
$100$	97.0499	0.0970499
$101$	−903.486	−0.890102	−0.445051	−	0.895505i	$-0.646814\pi$
$101$	−903.486	−0.890102	−0.445051	+	0.895505i	$0.646814\pi$
$102$	14.1258	0.0137124
$103$	−370.383	−0.354320	−0.177160	−	0.984182i	$-0.556691\pi$
$103$	−370.383	−0.354320	−0.177160	+	0.984182i	$0.556691\pi$
$104$	868.620	0.818992
$105$	−459.223	−0.426815
$106$	491.313	0.450194
$107$	507.110	0.458170	0.229085	−	0.973406i	$-0.426427\pi$
$107$	507.110	0.458170	0.229085	+	0.973406i	$0.426427\pi$
$108$	140.032	0.124764
$109$	−574.293	−0.504654	−0.252327	−	0.967642i	$-0.581196\pi$
$109$	−574.293	−0.504654	−0.252327	+	0.967642i	$0.581196\pi$
$110$	−171.837	−0.148946
$111$	1214.10	1.03817
$112$	−65.1692	−0.0549814
$113$	732.656	0.609934	0.304967	−	0.952363i	$-0.401355\pi$
$113$	732.656	0.609934	0.304967	+	0.952363i	$0.401355\pi$
$114$	−614.919	−0.505197
$115$	1022.76	0.829333
$116$	1297.95	1.03890
$117$	353.438	0.279276
$118$	−317.079	−0.247369
$119$	−41.6792	−0.0321070
$120$	684.103	0.520415
$121$	−1232.26	−0.925817
$122$	−950.561	−0.705408
$123$	565.176	0.414310
$124$	−53.0542	−0.0384226
$125$	1481.62	1.06016
$126$	224.150	0.158483
$127$	−1753.99	−1.22552	−0.612762	−	0.790268i	$-0.709941\pi$
$127$	−1753.99	−1.22552	−0.612762	+	0.790268i	$0.709941\pi$
$128$	1014.81	0.700758
$129$	174.662	0.119210
$130$	679.119	0.458175
$131$	533.223	0.355633	0.177816	−	0.984064i	$-0.443097\pi$
$131$	533.223	0.355633	0.177816	+	0.984064i	$0.443097\pi$
$132$	−154.605	−0.101945
$133$	1814.36	1.18290
$134$	1339.20	0.863355
$135$	278.359	0.177461
$136$	62.0894	0.0391480
$137$	−2311.02	−1.44120	−0.720599	−	0.693352i	$-0.756133\pi$
$137$	−2311.02	−1.44120	−0.720599	+	0.693352i	$0.756133\pi$
$138$	−499.218	−0.307944
$139$	−898.490	−0.548265	−0.274133	−	0.961692i	$-0.588391\pi$
$139$	−898.490	−0.548265	−0.274133	+	0.961692i	$0.588391\pi$
$140$	−793.899	−0.479262
$141$	214.391	0.128049
$142$	−74.2519	−0.0438808
$143$	−390.222	−0.228196
$144$	39.5024	0.0228602
$145$	2580.11	1.47770
$146$	−1769.46	−1.00303
$147$	367.630	0.206270
$148$	2098.92	1.16575
$149$	422.041	0.232047	0.116023	−	0.993246i	$-0.462985\pi$
$149$	422.041	0.232047	0.116023	+	0.993246i	$0.462985\pi$
$150$	−94.1648	−0.0512568
$151$	1461.28	0.787532	0.393766	−	0.919211i	$-0.371172\pi$
$151$	1461.28	0.787532	0.393766	+	0.919211i	$0.371172\pi$
$152$	−2702.85	−1.44230
$153$	25.2639	0.0133495
$154$	−247.478	−0.129496
$155$	−105.463	−0.0546513
$156$	611.018	0.313594
$157$	2090.82	1.06284	0.531418	−	0.847110i	$-0.321659\pi$
$157$	2090.82	1.06284	0.531418	+	0.847110i	$0.321659\pi$
$158$	2060.72	1.03761
$159$	878.709	0.438278
$160$	1900.18	0.938889
$161$	1472.98	0.721037
$162$	−135.869	−0.0658942
$163$	−2844.26	−1.36675	−0.683373	−	0.730070i	$-0.739488\pi$
$163$	−2844.26	−1.36675	−0.683373	+	0.730070i	$0.739488\pi$
$164$	977.067	0.465220
$165$	−307.329	−0.145003
$166$	−443.640	−0.207428
$167$	−733.777	−0.340008	−0.170004	−	0.985443i	$-0.554378\pi$
$167$	−733.777	−0.340008	−0.170004	+	0.985443i	$0.554378\pi$
$168$	985.240	0.452458
$169$	−654.799	−0.298042
$170$	48.5438	0.0219008
$171$	−1099.78	−0.491825
$172$	301.953	0.133859
$173$	2538.76	1.11571	0.557856	−	0.829938i	$-0.311624\pi$
$173$	2538.76	1.11571	0.557856	+	0.829938i	$0.311624\pi$
$174$	−1259.37	−0.548692
$175$	277.840	0.120015
$176$	−43.6136	−0.0186790
$177$	−567.093	−0.240821
$178$	1103.10	0.464501
$179$	349.609	0.145983	0.0729915	−	0.997333i	$-0.476745\pi$
$179$	349.609	0.145983	0.0729915	+	0.997333i	$0.476745\pi$
$180$	481.223	0.199268
$181$	1200.84	0.493137	0.246569	−	0.969125i	$-0.420697\pi$
$181$	1200.84	0.493137	0.246569	+	0.969125i	$0.420697\pi$
$182$	978.062	0.398345
$183$	−1700.07	−0.686736
$184$	−2194.29	−0.879159
$185$	4172.29	1.65812
$186$	51.4770	0.0202929
$187$	−27.8933	−0.0109078
$188$	370.635	0.143784
$189$	400.890	0.154288
$190$	−2113.19	−0.806877
$191$	−3451.97	−1.30773	−0.653864	−	0.756613i	$-0.726853\pi$
$191$	−3451.97	−1.30773	−0.653864	+	0.756613i	$0.726853\pi$
$192$	−822.150	−0.309029
$193$	−3582.35	−1.33608	−0.668039	−	0.744127i	$-0.732866\pi$
$193$	−3582.35	−1.33608	−0.668039	+	0.744127i	$0.732866\pi$
$194$	−469.425	−0.173726
$195$	1214.60	0.446047
$196$	635.554	0.231616
$197$	3982.18	1.44019	0.720097	−	0.693873i	$-0.244097\pi$
$197$	3982.18	1.44019	0.720097	+	0.693873i	$0.244097\pi$
$198$	150.009	0.0538419
$199$	−3523.06	−1.25499	−0.627495	−	0.778620i	$-0.715920\pi$
$199$	−3523.06	−1.25499	−0.627495	+	0.778620i	$0.715920\pi$
$200$	−413.897	−0.146335
$201$	2395.15	0.840503
$202$	1515.50	0.527872
$203$	3715.85	1.28474
$204$	43.6759	0.0149898
$205$	1942.24	0.661717
$206$	621.278	0.210128
$207$	−892.847	−0.299793
$208$	172.366	0.0574588
$209$	1214.24	0.401868
$210$	770.297	0.253122
$211$	−2467.00	−0.804907	−0.402453	−	0.915441i	$-0.631842\pi$
$211$	−2467.00	−0.804907	−0.402453	+	0.915441i	$0.631842\pi$
$212$	1519.10	0.492133
$213$	−132.799	−0.0427194
$214$	−850.622	−0.271716
$215$	600.231	0.190397
$216$	−597.205	−0.188123
$217$	−151.886	−0.0475148
$218$	963.314	0.299284
$219$	−3164.67	−0.976477
$220$	−531.306	−0.162821
$221$	110.237	0.0335537
$222$	−2036.52	−0.615687
$223$	−1435.66	−0.431116	−0.215558	−	0.976491i	$-0.569157\pi$
$223$	−1435.66	−0.431116	−0.215558	+	0.976491i	$0.569157\pi$
$224$	2736.62	0.816287
$225$	−168.413	−0.0499001
$226$	−1228.95	−0.361720
$227$	925.185	0.270514	0.135257	−	0.990811i	$-0.456814\pi$
$227$	925.185	0.270514	0.135257	+	0.990811i	$0.456814\pi$
$228$	−1901.28	−0.552260
$229$	1467.31	0.423418	0.211709	−	0.977333i	$-0.432097\pi$
$229$	1467.31	0.423418	0.211709	+	0.977333i	$0.432097\pi$
$230$	−1715.58	−0.491834
$231$	−442.613	−0.126068
$232$	−5535.49	−1.56648
$233$	4658.93	1.30994	0.654972	−	0.755654i	$-0.272681\pi$
$233$	4658.93	1.30994	0.654972	+	0.755654i	$0.272681\pi$
$234$	−592.854	−0.165624
$235$	736.759	0.204514
$236$	−980.382	−0.270413
$237$	3685.58	1.01014
$238$	69.9124	0.0190410
$239$	3336.14	0.902915	0.451457	−	0.892293i	$-0.350904\pi$
$239$	3336.14	0.902915	0.451457	+	0.892293i	$0.350904\pi$
$240$	135.751	0.0365112
$241$	−750.819	−0.200682	−0.100341	−	0.994953i	$-0.531993\pi$
$241$	−750.819	−0.200682	−0.100341	+	0.994953i	$0.531993\pi$
$242$	2066.99	0.549054
$243$	−243.000	−0.0641500
$244$	−2939.06	−0.771122
$245$	1263.37	0.329444
$246$	−948.021	−0.245706
$247$	−4798.80	−1.23620
$248$	226.265	0.0579347
$249$	−793.446	−0.201938
$250$	−2485.25	−0.628724
$251$	−2760.11	−0.694089	−0.347045	−	0.937849i	$-0.612815\pi$
$251$	−2760.11	−0.694089	−0.347045	+	0.937849i	$0.612815\pi$
$252$	693.053	0.173247
$253$	985.770	0.244960
$254$	2942.13	0.726793
$255$	86.8202	0.0213211
$256$	−3894.63	−0.950836
$257$	3728.44	0.904957	0.452478	−	0.891775i	$-0.350540\pi$
$257$	3728.44	0.904957	0.452478	+	0.891775i	$0.350540\pi$
$258$	−292.977	−0.0706975
$259$	6008.90	1.44160
$260$	2099.78	0.500857
$261$	−2252.37	−0.534169
$262$	−894.423	−0.210907
$263$	7182.76	1.68406	0.842030	−	0.539431i	$-0.181360\pi$
$263$	7182.76	1.68406	0.842030	+	0.539431i	$0.181360\pi$
$264$	659.359	0.153715
$265$	3019.71	0.699997
$266$	−3043.39	−0.701513
$267$	1972.89	0.452206
$268$	4140.71	0.943784
$269$	4576.70	1.03735	0.518673	−	0.854973i	$-0.326426\pi$
$269$	4576.70	1.03735	0.518673	+	0.854973i	$0.326426\pi$
$270$	−466.917	−0.105243
$271$	8063.66	1.80750	0.903750	−	0.428062i	$-0.140803\pi$
$271$	8063.66	1.80750	0.903750	+	0.428062i	$0.140803\pi$
$272$	12.3208	0.00274654
$273$	1749.26	0.387801
$274$	3876.49	0.854699
$275$	185.940	0.0407732
$276$	−1543.54	−0.336631
$277$	4195.49	0.910045	0.455022	−	0.890480i	$-0.349631\pi$
$277$	4195.49	0.910045	0.455022	+	0.890480i	$0.349631\pi$
$278$	1507.12	0.325147
$279$	92.0661	0.0197557
$280$	3385.80	0.722645
$281$	−432.551	−0.0918286	−0.0459143	−	0.998945i	$-0.514620\pi$
$281$	−432.551	−0.0918286	−0.0459143	+	0.998945i	$0.514620\pi$
$282$	−359.617	−0.0759393
$283$	−3895.82	−0.818312	−0.409156	−	0.912464i	$-0.634177\pi$
$283$	−3895.82	−0.818312	−0.409156	+	0.912464i	$0.634177\pi$
$284$	−229.581	−0.0479687
$285$	−3779.41	−0.785520
$286$	654.555	0.135331
$287$	2797.20	0.575309
$288$	−1658.81	−0.339396
$289$	−4905.12	−0.998396
$290$	−4327.85	−0.876346
$291$	−839.563	−0.169127
$292$	−5471.03	−1.09647
$293$	1402.46	0.279633	0.139816	−	0.990177i	$-0.455349\pi$
$293$	1402.46	0.279633	0.139816	+	0.990177i	$0.455349\pi$
$294$	−616.660	−0.122328
$295$	−1948.83	−0.384628
$296$	−8951.44	−1.75774
$297$	268.290	0.0524168
$298$	−707.928	−0.137615
$299$	−3895.88	−0.753526
$300$	−291.150	−0.0560318
$301$	864.449	0.165535
$302$	−2451.14	−0.467044
$303$	2710.46	0.513900
$304$	−536.344	−0.101189
$305$	−5842.34	−1.09682
$306$	−42.3775	−0.00791686
$307$	8422.83	1.56585	0.782926	−	0.622115i	$-0.213726\pi$
$307$	8422.83	1.56585	0.782926	+	0.622115i	$0.213726\pi$
$308$	−765.183	−0.141559
$309$	1111.15	0.204567
$310$	176.902	0.0324108
$311$	435.936	0.0794844	0.0397422	−	0.999210i	$-0.487346\pi$
$311$	435.936	0.0794844	0.0397422	+	0.999210i	$0.487346\pi$
$312$	−2605.86	−0.472845
$313$	−5933.81	−1.07156	−0.535781	−	0.844357i	$-0.679983\pi$
$313$	−5933.81	−1.07156	−0.535781	+	0.844357i	$0.679983\pi$
$314$	−3507.12	−0.630312
$315$	1377.67	0.246422
$316$	6371.58	1.13427
$317$	1004.04	0.177894	0.0889471	−	0.996036i	$-0.471650\pi$
$317$	1004.04	0.177894	0.0889471	+	0.996036i	$0.471650\pi$
$318$	−1473.94	−0.259919
$319$	2486.78	0.436468
$320$	−2825.34	−0.493567
$321$	−1521.33	−0.264524
$322$	−2470.76	−0.427609
$323$	−343.021	−0.0590904
$324$	−420.095	−0.0720327
$325$	−734.858	−0.125423
$326$	4770.94	0.810545
$327$	1722.88	0.291362
$328$	−4166.98	−0.701473
$329$	1061.07	0.177808
$330$	515.511	0.0859938
$331$	−1332.75	−0.221313	−0.110656	−	0.993859i	$-0.535295\pi$
$331$	−1332.75	−0.221313	−0.110656	+	0.993859i	$0.535295\pi$
$332$	−1371.70	−0.226752
$333$	−3642.30	−0.599391
$334$	1230.83	0.201641
$335$	8231.01	1.34241
$336$	195.508	0.0317435
$337$	−337.000	−0.0544735
$337$	−337.000	−0.0544735
$338$	1098.35	0.176753
$339$	−2197.97	−0.352145
$340$	150.093	0.0239411
$341$	−101.648	−0.0161424
$342$	1844.76	0.291676
$343$	6912.29	1.08813
$344$	−1287.77	−0.201836
$345$	−3068.29	−0.478816
$346$	−4258.49	−0.661671
$347$	−2790.26	−0.431668	−0.215834	−	0.976430i	$-0.569247\pi$
$347$	−2790.26	−0.431668	−0.215834	+	0.976430i	$0.569247\pi$
$348$	−3893.86	−0.599807
$349$	−6308.64	−0.967604	−0.483802	−	0.875178i	$-0.660744\pi$
$349$	−6308.64	−0.967604	−0.483802	+	0.875178i	$0.660744\pi$
$350$	−466.046	−0.0711749
$351$	−1060.31	−0.161240
$352$	1831.45	0.277319
$353$	−2857.22	−0.430806	−0.215403	−	0.976525i	$-0.569106\pi$
$353$	−2857.22	−0.430806	−0.215403	+	0.976525i	$0.569106\pi$
$354$	951.237	0.142818
$355$	−456.367	−0.0682294
$356$	3410.71	0.507773
$357$	125.038	0.0185370
$358$	−586.431	−0.0865749
$359$	−1084.64	−0.159457	−0.0797286	−	0.996817i	$-0.525405\pi$
$359$	−1084.64	−0.159457	−0.0797286	+	0.996817i	$0.525405\pi$
$360$	−2052.31	−0.300462
$361$	8073.22	1.17703
$362$	−2014.28	−0.292454
$363$	3696.79	0.534521
$364$	3024.09	0.435454
$365$	−10875.5	−1.55958
$366$	2851.68	0.407267
$367$	−2979.41	−0.423771	−0.211886	−	0.977294i	$-0.567960\pi$
$367$	−2979.41	−0.423771	−0.211886	+	0.977294i	$0.567960\pi$
$368$	−435.427	−0.0616799
$369$	−1695.53	−0.239202
$370$	−6998.57	−0.983347
$371$	4348.96	0.608590
$372$	159.163	0.0221833
$373$	−5011.19	−0.695629	−0.347814	−	0.937563i	$-0.613076\pi$
$373$	−5011.19	−0.695629	−0.347814	+	0.937563i	$0.613076\pi$
$374$	46.7879	0.00646884
$375$	−4444.85	−0.612083
$376$	−1580.68	−0.216801
$377$	−9828.05	−1.34263
$378$	−672.450	−0.0915002
$379$	−2861.64	−0.387843	−0.193921	−	0.981017i	$-0.562121\pi$
$379$	−2861.64	−0.387843	−0.193921	+	0.981017i	$0.562121\pi$
$380$	−6533.80	−0.882044
$381$	5261.97	0.707556
$382$	5790.31	0.775544
$383$	−11653.6	−1.55476	−0.777378	−	0.629034i	$-0.783451\pi$
$383$	−11653.6	−1.55476	−0.777378	+	0.629034i	$0.783451\pi$
$384$	−3044.42	−0.404583
$385$	−1521.05	−0.201350
$386$	6009.00	0.792357
$387$	−523.987	−0.0688262
$388$	−1451.42	−0.189910
$389$	−1537.25	−0.200364	−0.100182	−	0.994969i	$-0.531943\pi$
$389$	−1537.25	−0.200364	−0.100182	+	0.994969i	$0.531943\pi$
$390$	−2037.36	−0.264527
$391$	−278.479	−0.0360187
$392$	−2710.50	−0.349237
$393$	−1599.67	−0.205325
$394$	−6679.67	−0.854104
$395$	12665.6	1.61336
$396$	463.816	0.0588577
$397$	−7284.28	−0.920875	−0.460438	−	0.887692i	$-0.652308\pi$
$397$	−7284.28	−0.920875	−0.460438	+	0.887692i	$0.652308\pi$
$398$	5909.55	0.744269
$399$	−5443.08	−0.682945
$400$	−82.1322	−0.0102665
$401$	11860.3	1.47699	0.738497	−	0.674256i	$-0.235536\pi$
$401$	11860.3	1.47699	0.738497	+	0.674256i	$0.235536\pi$
$402$	−4017.61	−0.498458
$403$	401.724	0.0496558
$404$	4685.80	0.577048
$405$	−835.076	−0.102457
$406$	−6232.94	−0.761911
$407$	4021.38	0.489760
$408$	−186.268	−0.0226021
$409$	−7975.44	−0.964206	−0.482103	−	0.876115i	$-0.660127\pi$
$409$	−7975.44	−0.964206	−0.482103	+	0.876115i	$0.660127\pi$
$410$	−3257.90	−0.392430
$411$	6933.07	0.832076
$412$	1920.94	0.229704
$413$	−2806.69	−0.334403
$414$	1497.65	0.177792
$415$	−2726.70	−0.322526
$416$	−7238.09	−0.853068
$417$	2695.47	0.316541
$418$	−2036.75	−0.238327
$419$	12976.6	1.51301	0.756504	−	0.653989i	$-0.226906\pi$
$419$	12976.6	1.51301	0.756504	+	0.653989i	$0.226906\pi$
$420$	2381.70	0.276702
$421$	7259.84	0.840435	0.420217	−	0.907423i	$-0.361954\pi$
$421$	7259.84	0.840435	0.420217	+	0.907423i	$0.361954\pi$
$422$	4138.13	0.477348
$423$	−643.172	−0.0739293
$424$	−6478.63	−0.742052
$425$	−52.5280	−0.00599525
$426$	222.756	0.0253346
$427$	−8414.09	−0.953598
$428$	−2630.05	−0.297029
$429$	1170.67	0.131749
$430$	−1006.82	−0.112915
$431$	16859.3	1.88419	0.942094	−	0.335349i	$-0.108854\pi$
$431$	16859.3	1.88419	0.942094	+	0.335349i	$0.108854\pi$
$432$	−118.507	−0.0131983
$433$	13152.3	1.45972	0.729860	−	0.683597i	$-0.239585\pi$
$433$	13152.3	1.45972	0.729860	+	0.683597i	$0.239585\pi$
$434$	254.773	0.0281786
$435$	−7740.33	−0.853150
$436$	2978.49	0.327164
$437$	12122.6	1.32701
$438$	5308.39	0.579097
$439$	−5870.42	−0.638222	−0.319111	−	0.947717i	$-0.603384\pi$
$439$	−5870.42	−0.638222	−0.319111	+	0.947717i	$0.603384\pi$
$440$	2265.90	0.245506
$441$	−1102.89	−0.119090
$442$	−184.911	−0.0198989
$443$	−13722.5	−1.47173	−0.735866	−	0.677127i	$-0.763225\pi$
$443$	−13722.5	−1.47173	−0.735866	+	0.677127i	$0.763225\pi$
$444$	−6296.76	−0.673043
$445$	6779.89	0.722242
$446$	2408.17	0.255672
$447$	−1266.12	−0.133972
$448$	−4069.03	−0.429115
$449$	294.858	0.0309915	0.0154958	−	0.999880i	$-0.495067\pi$
$449$	294.858	0.0309915	0.0154958	+	0.999880i	$0.495067\pi$
$450$	282.494	0.0295931
$451$	1871.99	0.195451
$452$	−3799.82	−0.395417
$453$	−4383.84	−0.454682
$454$	−1551.90	−0.160428
$455$	6011.36	0.619378
$456$	8108.54	0.832713
$457$	−16523.7	−1.69135	−0.845675	−	0.533698i	$-0.820802\pi$
$457$	−16523.7	−1.69135	−0.845675	+	0.533698i	$0.820802\pi$
$458$	−2461.26	−0.251107
$459$	−75.7918	−0.00770731
$460$	−5304.42	−0.537652
$461$	−8895.63	−0.898722	−0.449361	−	0.893350i	$-0.648348\pi$
$461$	−8895.63	−0.898722	−0.449361	+	0.893350i	$0.648348\pi$
$462$	742.435	0.0747645
$463$	−3172.94	−0.318486	−0.159243	−	0.987239i	$-0.550905\pi$
$463$	−3172.94	−0.318486	−0.159243	+	0.987239i	$0.550905\pi$
$464$	−1098.44	−0.109901
$465$	316.388	0.0315530
$466$	−7814.85	−0.776858
$467$	3365.57	0.333490	0.166745	−	0.986000i	$-0.446674\pi$
$467$	3365.57	0.333490	0.166745	+	0.986000i	$0.446674\pi$
$468$	−1833.05	−0.181053
$469$	11854.2	1.16712
$470$	−1235.83	−0.121287
$471$	−6272.45	−0.613629
$472$	4181.12	0.407736
$473$	578.521	0.0562376
$474$	−6182.17	−0.599064
$475$	2286.62	0.220879
$476$	216.163	0.0208148
$477$	−2636.13	−0.253040
$478$	−5596.01	−0.535471
$479$	−7678.15	−0.732409	−0.366204	−	0.930534i	$-0.619343\pi$
$479$	−7678.15	−0.732409	−0.366204	+	0.930534i	$0.619343\pi$
$480$	−5700.53	−0.542068
$481$	−15892.9	−1.50656
$482$	1259.42	0.119014
$483$	−4418.93	−0.416291
$484$	6390.95	0.600202
$485$	−2885.18	−0.270122
$486$	407.606	0.0380440
$487$	−11952.6	−1.11217	−0.556083	−	0.831127i	$-0.687696\pi$
$487$	−11952.6	−1.11217	−0.556083	+	0.831127i	$0.687696\pi$
$488$	12534.4	1.16272
$489$	8532.78	0.789091
$490$	−2119.17	−0.195376
$491$	3554.03	0.326662	0.163331	−	0.986571i	$-0.447776\pi$
$491$	3554.03	0.326662	0.163331	+	0.986571i	$0.447776\pi$
$492$	−2931.20	−0.268595
$493$	−702.514	−0.0641778
$494$	8049.47	0.733123
$495$	921.987	0.0837176
$496$	44.8992	0.00406458
$497$	−657.256	−0.0593198
$498$	1330.92	0.119759
$499$	6090.93	0.546428	0.273214	−	0.961953i	$-0.411913\pi$
$499$	6090.93	0.546428	0.273214	+	0.961953i	$0.411913\pi$
$500$	−7684.19	−0.687295
$501$	2201.33	0.196304
$502$	4629.78	0.411628
$503$	−6454.21	−0.572125	−0.286063	−	0.958211i	$-0.592347\pi$
$503$	−6454.21	−0.572125	−0.286063	+	0.958211i	$0.592347\pi$
$504$	−2955.72	−0.261227
$505$	9314.57	0.820778
$506$	−1653.52	−0.145273
$507$	1964.40	0.172075
$508$	9096.82	0.794500
$509$	−7226.90	−0.629325	−0.314663	−	0.949204i	$-0.601891\pi$
$509$	−7226.90	−0.629325	−0.314663	+	0.949204i	$0.601891\pi$
$510$	−145.631	−0.0126444
$511$	−15662.8	−1.35593
$512$	−1585.63	−0.136867
$513$	3299.33	0.283955
$514$	−6254.06	−0.536682
$515$	3818.50	0.326724
$516$	−905.860	−0.0772835
$517$	710.110	0.0604073
$518$	−10079.3	−0.854939
$519$	−7616.28	−0.644157
$520$	−8955.11	−0.755207
$521$	8422.91	0.708281	0.354140	−	0.935192i	$-0.384773\pi$
$521$	8422.91	0.708281	0.354140	+	0.935192i	$0.384773\pi$
$522$	3778.10	0.316788
$523$	−7304.01	−0.610673	−0.305336	−	0.952245i	$-0.598769\pi$
$523$	−7304.01	−0.610673	−0.305336	+	0.952245i	$0.598769\pi$
$524$	−2765.48	−0.230555
$525$	−833.519	−0.0692910
$526$	−12048.3	−0.998728
$527$	28.7154	0.00237356
$528$	130.841	0.0107843
$529$	−2325.32	−0.191117
$530$	−5065.23	−0.415131
$531$	1701.28	0.139038
$532$	−9409.92	−0.766865
$533$	−7398.31	−0.601232
$534$	−3309.31	−0.268180
$535$	−5228.09	−0.422486
$536$	−17659.2	−1.42306
$537$	−1048.83	−0.0842834
$538$	−7676.91	−0.615196
$539$	1217.67	0.0973078
$540$	−1443.67	−0.115047
$541$	−4023.94	−0.319783	−0.159892	−	0.987135i	$-0.551114\pi$
$541$	−4023.94	−0.319783	−0.159892	+	0.987135i	$0.551114\pi$
$542$	−13525.9	−1.07193
$543$	−3602.52	−0.284713
$544$	−517.382	−0.0407768
$545$	5920.72	0.465350
$546$	−2934.19	−0.229985
$547$	−3153.61	−0.246506	−0.123253	−	0.992375i	$-0.539333\pi$
$547$	−3153.61	−0.246506	−0.123253	+	0.992375i	$0.539333\pi$
$548$	11985.8	0.934321
$549$	5100.21	0.396487
$550$	−311.895	−0.0241804
$551$	30581.5	2.36446
$552$	6582.87	0.507583
$553$	18240.9	1.40268
$554$	−7037.47	−0.539700
$555$	−12516.9	−0.957319
$556$	4659.89	0.355438
$557$	5787.37	0.440249	0.220124	−	0.975472i	$-0.429354\pi$
$557$	5787.37	0.440249	0.220124	+	0.975472i	$0.429354\pi$
$558$	−154.431	−0.0117161
$559$	−2286.38	−0.172994
$560$	671.867	0.0506992
$561$	83.6798	0.00629762
$562$	725.557	0.0544587
$563$	3285.38	0.245936	0.122968	−	0.992411i	$-0.460759\pi$
$563$	3285.38	0.245936	0.122968	+	0.992411i	$0.460759\pi$
$564$	−1111.91	−0.0830136
$565$	−7553.38	−0.562430
$566$	6534.81	0.485298
$567$	−1202.67	−0.0890783
$568$	979.112	0.0723286
$569$	−24872.5	−1.83253	−0.916264	−	0.400576i	$-0.868810\pi$
$569$	−24872.5	−1.83253	−0.916264	+	0.400576i	$0.868810\pi$
$570$	6339.56	0.465851
$571$	11114.5	0.814586	0.407293	−	0.913298i	$-0.366473\pi$
$571$	11114.5	0.814586	0.407293	+	0.913298i	$0.366473\pi$
$572$	2023.83	0.147938
$573$	10355.9	0.755017
$574$	−4692.00	−0.341185
$575$	1856.38	0.134637
$576$	2466.45	0.178418
$577$	2805.82	0.202440	0.101220	−	0.994864i	$-0.467725\pi$
$577$	2805.82	0.202440	0.101220	+	0.994864i	$0.467725\pi$
$578$	8227.81	0.592096
$579$	10747.0	0.771384
$580$	−13381.4	−0.957984
$581$	−3926.97	−0.280410
$582$	1408.28	0.100301
$583$	2910.48	0.206758
$584$	23332.8	1.65328
$585$	−3643.80	−0.257525
$586$	−2352.47	−0.165836
$587$	−2943.89	−0.206997	−0.103498	−	0.994630i	$-0.533004\pi$
$587$	−2943.89	−0.206997	−0.103498	+	0.994630i	$0.533004\pi$
$588$	−1906.66	−0.133723
$589$	−1250.03	−0.0874473
$590$	3268.95	0.228103
$591$	−11946.5	−0.831497
$592$	−1776.29	−0.123320
$593$	−5627.31	−0.389690	−0.194845	−	0.980834i	$-0.562420\pi$
$593$	−5627.31	−0.389690	−0.194845	+	0.980834i	$0.562420\pi$
$594$	−450.028	−0.0310856
$595$	429.696	0.0296064
$596$	−2188.86	−0.150435
$597$	10569.2	0.724569
$598$	6534.91	0.446877
$599$	18078.1	1.23314	0.616571	−	0.787299i	$-0.288521\pi$
$599$	18078.1	1.23314	0.616571	+	0.787299i	$0.288521\pi$
$600$	1241.69	0.0844863
$601$	6504.91	0.441499	0.220750	−	0.975331i	$-0.429150\pi$
$601$	6504.91	0.441499	0.220750	+	0.975331i	$0.429150\pi$
$602$	−1450.02	−0.0981700
$603$	−7185.46	−0.485265
$604$	−7578.72	−0.510553
$605$	12704.1	0.853712
$606$	−4546.50	−0.304767
$607$	−4167.73	−0.278687	−0.139344	−	0.990244i	$-0.544499\pi$
$607$	−4167.73	−0.278687	−0.139344	+	0.990244i	$0.544499\pi$
$608$	22522.4	1.50231
$609$	−11147.6	−0.741744
$610$	9799.88	0.650468
$611$	−2806.43	−0.185820
$612$	−131.028	−0.00865438
$613$	−13736.7	−0.905087	−0.452544	−	0.891742i	$-0.649483\pi$
$613$	−13736.7	−0.905087	−0.452544	+	0.891742i	$0.649483\pi$
$614$	−14128.4	−0.928625
$615$	−5826.72	−0.382043
$616$	3263.34	0.213447
$617$	20375.6	1.32949	0.664743	−	0.747072i	$-0.268541\pi$
$617$	20375.6	1.32949	0.664743	+	0.747072i	$0.268541\pi$
$618$	−1863.83	−0.121318
$619$	−9457.67	−0.614113	−0.307056	−	0.951691i	$-0.599344\pi$
$619$	−9457.67	−0.614113	−0.307056	+	0.951691i	$0.599344\pi$
$620$	546.967	0.0354302
$621$	2678.54	0.173086
$622$	−731.235	−0.0471380
$623$	9764.35	0.627930
$624$	−517.098	−0.0331738
$625$	−12935.8	−0.827890
$626$	9953.32	0.635487
$627$	−3642.71	−0.232019
$628$	−10843.7	−0.689031
$629$	−1136.04	−0.0720139
$630$	−2310.89	−0.146140
$631$	26885.1	1.69616	0.848080	−	0.529868i	$-0.177758\pi$
$631$	26885.1	1.69616	0.848080	+	0.529868i	$0.177758\pi$
$632$	−27173.4	−1.71029
$633$	7401.00	0.464713
$634$	−1684.17	−0.105500
$635$	18082.9	1.13008
$636$	−4557.30	−0.284133
$637$	−4812.38	−0.299331
$638$	−4171.31	−0.258846
$639$	398.396	0.0246640
$640$	−10462.2	−0.646181
$641$	17436.6	1.07442	0.537209	−	0.843449i	$-0.319478\pi$
$641$	17436.6	1.07442	0.537209	+	0.843449i	$0.319478\pi$
$642$	2551.87	0.156876
$643$	−31629.0	−1.93985	−0.969927	−	0.243396i	$-0.921738\pi$
$643$	−31629.0	−1.93985	−0.969927	+	0.243396i	$0.921738\pi$
$644$	−7639.39	−0.467444
$645$	−1800.69	−0.109926
$646$	575.380	0.0350434
$647$	−23882.5	−1.45119	−0.725593	−	0.688124i	$-0.758435\pi$
$647$	−23882.5	−1.45119	−0.725593	+	0.688124i	$0.758435\pi$
$648$	1791.61	0.108613
$649$	−1878.34	−0.113608
$650$	1232.64	0.0743820
$651$	455.659	0.0274327
$652$	14751.3	0.886054
$653$	−3053.14	−0.182968	−0.0914842	−	0.995807i	$-0.529161\pi$
$653$	−3053.14	−0.182968	−0.0914842	+	0.995807i	$0.529161\pi$
$654$	−2889.94	−0.172792
$655$	−5497.30	−0.327935
$656$	−826.881	−0.0492138
$657$	9494.00	0.563769
$658$	−1779.84	−0.105449
$659$	11748.7	0.694484	0.347242	−	0.937776i	$-0.387118\pi$
$659$	11748.7	0.694484	0.347242	+	0.937776i	$0.387118\pi$
$660$	1593.92	0.0940048
$661$	31859.5	1.87472	0.937361	−	0.348361i	$-0.113262\pi$
$661$	31859.5	1.87472	0.937361	+	0.348361i	$0.113262\pi$
$662$	2235.54	0.131249
$663$	−330.712	−0.0193722
$664$	5849.99	0.341903
$665$	−18705.3	−1.09077
$666$	6109.57	0.355467
$667$	24827.4	1.44126
$668$	3805.63	0.220426
$669$	4306.98	0.248905
$670$	−13806.6	−0.796115
$671$	−5631.01	−0.323968
$672$	−8209.87	−0.471283
$673$	19659.2	1.12601	0.563005	−	0.826453i	$-0.309645\pi$
$673$	19659.2	1.12601	0.563005	+	0.826453i	$0.309645\pi$
$674$	565.281	0.0323054
$675$	505.238	0.0288098
$676$	3396.02	0.193219
$677$	−17594.9	−0.998857	−0.499428	−	0.866355i	$-0.666457\pi$
$677$	−17594.9	−0.998857	−0.499428	+	0.866355i	$0.666457\pi$
$678$	3686.85	0.208839
$679$	−4155.22	−0.234849
$680$	−640.116	−0.0360990
$681$	−2775.55	−0.156181
$682$	170.503	0.00957318
$683$	19842.2	1.11163	0.555814	−	0.831306i	$-0.312406\pi$
$683$	19842.2	1.11163	0.555814	+	0.831306i	$0.312406\pi$
$684$	5703.84	0.318847
$685$	23825.7	1.32895
$686$	−11594.6	−0.645312
$687$	−4401.94	−0.244461
$688$	−255.540	−0.0141604
$689$	−11502.6	−0.636012
$690$	5146.73	0.283960
$691$	−4356.96	−0.239865	−0.119932	−	0.992782i	$-0.538268\pi$
$691$	−4356.96	−0.239865	−0.119932	+	0.992782i	$0.538268\pi$
$692$	−13166.9	−0.723311
$693$	1327.84	0.0727856
$694$	4680.36	0.256000
$695$	9263.05	0.505565
$696$	16606.5	0.904407
$697$	−528.835	−0.0287390
$698$	10582.1	0.573835
$699$	−13976.8	−0.756296
$700$	−1440.98	−0.0778054
$701$	6115.70	0.329511	0.164755	−	0.986334i	$-0.447317\pi$
$701$	6115.70	0.329511	0.164755	+	0.986334i	$0.447317\pi$
$702$	1778.56	0.0956232
$703$	49453.4	2.65316
$704$	−2723.14	−0.145785
$705$	−2210.28	−0.118076
$706$	4792.68	0.255488
$707$	13414.8	0.713599
$708$	2941.15	0.156123
$709$	−19043.3	−1.00872	−0.504362	−	0.863492i	$-0.668272\pi$
$709$	−19043.3	−1.00872	−0.504362	+	0.863492i	$0.668272\pi$
$710$	765.506	0.0404633
$711$	−11056.7	−0.583207
$712$	−14545.9	−0.765634
$713$	−1014.83	−0.0533037
$714$	−209.737	−0.0109933
$715$	4023.02	0.210423
$716$	−1813.19	−0.0946401
$717$	−10008.4	−0.521298
$718$	1819.37	0.0945657
$719$	20187.5	1.04710	0.523551	−	0.851994i	$-0.324607\pi$
$719$	20187.5	1.04710	0.523551	+	0.851994i	$0.324607\pi$
$720$	−407.253	−0.0210798
$721$	5499.37	0.284060
$722$	−13542.0	−0.698032
$723$	2252.46	0.115864
$724$	−6227.99	−0.319698
$725$	4683.06	0.239896
$726$	−6200.96	−0.316996
$727$	−35027.4	−1.78693	−0.893464	−	0.449136i	$-0.851732\pi$
$727$	−35027.4	−1.78693	−0.893464	+	0.449136i	$0.851732\pi$
$728$	−12897.1	−0.656590
$729$	729.000	0.0370370
$730$	18242.4	0.924907
$731$	−163.432	−0.00826913
$732$	8817.17	0.445208
$733$	36071.6	1.81765	0.908823	−	0.417182i	$-0.136982\pi$
$733$	36071.6	1.81765	0.908823	+	0.417182i	$0.136982\pi$
$734$	4997.64	0.251317
$735$	−3790.11	−0.190205
$736$	18284.7	0.915738
$737$	7933.29	0.396508
$738$	2844.06	0.141858
$739$	21964.1	1.09332	0.546659	−	0.837355i	$-0.315899\pi$
$739$	21964.1	1.09332	0.546659	+	0.837355i	$0.315899\pi$
$740$	−21639.0	−1.07495
$741$	14396.4	0.713718
$742$	−7294.91	−0.360923
$743$	−30158.7	−1.48912	−0.744559	−	0.667557i	$-0.767340\pi$
$743$	−30158.7	−1.48912	−0.744559	+	0.667557i	$0.767340\pi$
$744$	−678.794	−0.0334486
$745$	−4351.07	−0.213974
$746$	8405.73	0.412541
$747$	2380.34	0.116589
$748$	144.664	0.00707146
$749$	−7529.46	−0.367317
$750$	7455.75	0.362994
$751$	−18943.4	−0.920444	−0.460222	−	0.887804i	$-0.652230\pi$
$751$	−18943.4	−0.920444	−0.460222	+	0.887804i	$0.652230\pi$
$752$	−313.664	−0.0152103
$753$	8280.32	0.400733
$754$	16485.5	0.796242
$755$	−15065.2	−0.726197
$756$	−2079.16	−0.100024
$757$	39599.3	1.90127	0.950636	−	0.310310i	$-0.100433\pi$
$757$	39599.3	1.90127	0.950636	+	0.310310i	$0.100433\pi$
$758$	4800.09	0.230009
$759$	−2957.31	−0.141428
$760$	27865.2	1.32997
$761$	38833.9	1.84984	0.924920	−	0.380163i	$-0.124132\pi$
$761$	38833.9	1.84984	0.924920	+	0.380163i	$0.124132\pi$
$762$	−8826.38	−0.419614
$763$	8526.98	0.404584
$764$	17903.2	0.847792
$765$	−260.460	−0.0123098
$766$	19547.7	0.922044
$767$	7423.41	0.349471
$768$	11683.9	0.548966
$769$	11997.8	0.562617	0.281309	−	0.959617i	$-0.409232\pi$
$769$	11997.8	0.562617	0.281309	+	0.959617i	$0.409232\pi$
$770$	2551.40	0.119410
$771$	−11185.3	−0.522477
$772$	18579.3	0.866172
$773$	15935.3	0.741467	0.370734	−	0.928739i	$-0.379106\pi$
$773$	15935.3	0.741467	0.370734	+	0.928739i	$0.379106\pi$
$774$	878.931	0.0408172
$775$	−191.421	−0.00887232
$776$	6190.01	0.286351
$777$	−18026.7	−0.832310
$778$	2578.57	0.118825
$779$	23021.0	1.05881
$780$	−6299.34	−0.289170
$781$	−439.860	−0.0201529
$782$	467.119	0.0213608
$783$	6757.11	0.308403
$784$	−537.862	−0.0245017
$785$	−21555.4	−0.980059
$786$	2683.27	0.121767
$787$	−25301.8	−1.14601	−0.573007	−	0.819550i	$-0.694223\pi$
$787$	−25301.8	−1.14601	−0.573007	+	0.819550i	$0.694223\pi$
$788$	−20653.0	−0.933670
$789$	−21548.3	−0.972293
$790$	−21245.2	−0.956797
$791$	−10878.3	−0.488987
$792$	−1978.08	−0.0887473
$793$	22254.4	0.996566
$794$	12218.6	0.546123
$795$	−9059.12	−0.404143
$796$	18271.8	0.813604
$797$	−11994.3	−0.533075	−0.266538	−	0.963825i	$-0.585880\pi$
$797$	−11994.3	−0.533075	−0.266538	+	0.963825i	$0.585880\pi$
$798$	9130.18	0.405019
$799$	−200.605	−0.00888224
$800$	3448.94	0.152423
$801$	−5918.67	−0.261081
$802$	−19894.4	−0.875928
$803$	−10482.1	−0.460654
$804$	−12422.1	−0.544894
$805$	−15185.8	−0.664880
$806$	−673.849	−0.0294483
$807$	−13730.1	−0.598912
$808$	−19983.9	−0.870089
$809$	31763.4	1.38040	0.690198	−	0.723621i	$-0.257523\pi$
$809$	31763.4	1.38040	0.690198	+	0.723621i	$0.257523\pi$
$810$	1400.75	0.0607621
$811$	−24325.7	−1.05326	−0.526628	−	0.850096i	$-0.676544\pi$
$811$	−24325.7	−1.05326	−0.526628	+	0.850096i	$0.676544\pi$
$812$	−19271.7	−0.832889
$813$	−24191.0	−1.04356
$814$	−6745.43	−0.290451
$815$	29323.1	1.26030
$816$	−36.9624	−0.00158572
$817$	7114.43	0.304654
$818$	13377.9	0.571820
$819$	−5247.77	−0.223897
$820$	−10073.2	−0.428988
$821$	−35696.0	−1.51741	−0.758707	−	0.651432i	$-0.774169\pi$
$821$	−35696.0	−1.51741	−0.758707	+	0.651432i	$0.774169\pi$
$822$	−11629.5	−0.493461
$823$	30980.4	1.31216	0.656080	−	0.754691i	$-0.272213\pi$
$823$	30980.4	1.31216	0.656080	+	0.754691i	$0.272213\pi$
$824$	−8192.39	−0.346354
$825$	−557.821	−0.0235404
$826$	4707.92	0.198317
$827$	18030.4	0.758134	0.379067	−	0.925369i	$-0.376245\pi$
$827$	18030.4	0.758134	0.379067	+	0.925369i	$0.376245\pi$
$828$	4630.62	0.194354
$829$	2536.56	0.106271	0.0531353	−	0.998587i	$-0.483079\pi$
$829$	2536.56	0.106271	0.0531353	+	0.998587i	$0.483079\pi$
$830$	4573.74	0.191273
$831$	−12586.5	−0.525414
$832$	10762.2	0.448451
$833$	−343.992	−0.0143081
$834$	−4521.36	−0.187724
$835$	7564.94	0.313528
$836$	−6297.46	−0.260529
$837$	−276.198	−0.0114060
$838$	−21766.9	−0.897286
$839$	−37150.0	−1.52868	−0.764338	−	0.644815i	$-0.776934\pi$
$839$	−37150.0	−1.52868	−0.764338	+	0.644815i	$0.776934\pi$
$840$	−10157.4	−0.417219
$841$	38242.7	1.56803
$842$	−12177.6	−0.498418
$843$	1297.65	0.0530173
$844$	12794.7	0.521817
$845$	6750.70	0.274830
$846$	1078.85	0.0438436
$847$	18296.4	0.742232
$848$	−1285.60	−0.0520608
$849$	11687.4	0.472453
$850$	88.1100	0.00355547
$851$	40148.4	1.61724
$852$	688.742	0.0276947
$853$	−26323.8	−1.05664	−0.528318	−	0.849047i	$-0.677177\pi$
$853$	−26323.8	−1.05664	−0.528318	+	0.849047i	$0.677177\pi$
$854$	14113.7	0.565529
$855$	11338.2	0.453520
$856$	11216.6	0.447869
$857$	29888.6	1.19134	0.595669	−	0.803230i	$-0.296887\pi$
$857$	29888.6	1.19134	0.595669	+	0.803230i	$0.296887\pi$
$858$	−1963.66	−0.0781333
$859$	15634.5	0.621003	0.310502	−	0.950573i	$-0.399503\pi$
$859$	15634.5	0.621003	0.310502	+	0.950573i	$0.399503\pi$
$860$	−3113.01	−0.123434
$861$	−8391.60	−0.332155
$862$	−28279.7	−1.11741
$863$	−22620.6	−0.892253	−0.446126	−	0.894970i	$-0.647197\pi$
$863$	−22620.6	−0.892253	−0.446126	+	0.894970i	$0.647197\pi$
$864$	4976.42	0.195950
$865$	−26173.5	−1.02882
$866$	−22061.5	−0.865683
$867$	14715.4	0.576424
$868$	787.737	0.0308036
$869$	12207.5	0.476537
$870$	12983.6	0.505959
$871$	−31353.3	−1.21971
$872$	−12702.6	−0.493308
$873$	2518.69	0.0976457
$874$	−20334.4	−0.786981
$875$	−21998.7	−0.849934
$876$	16413.1	0.633045
$877$	9427.94	0.363009	0.181505	−	0.983390i	$-0.441903\pi$
$877$	9427.94	0.363009	0.181505	+	0.983390i	$0.441903\pi$
$878$	9846.99	0.378496
$879$	−4207.37	−0.161446
$880$	449.638	0.0172242
$881$	6646.49	0.254172	0.127086	−	0.991892i	$-0.459438\pi$
$881$	6646.49	0.254172	0.127086	+	0.991892i	$0.459438\pi$
$882$	1849.98	0.0706259
$883$	−17018.2	−0.648592	−0.324296	−	0.945956i	$-0.605127\pi$
$883$	−17018.2	−0.648592	−0.324296	+	0.945956i	$0.605127\pi$
$884$	−571.730	−0.0217527
$885$	5846.49	0.222065
$886$	23018.1	0.872807
$887$	−40908.9	−1.54857	−0.774287	−	0.632834i	$-0.781891\pi$
$887$	−40908.9	−1.54857	−0.774287	+	0.632834i	$0.781891\pi$
$888$	26854.3	1.01483
$889$	26042.9	0.982508
$890$	−11372.5	−0.428324
$891$	−804.871	−0.0302628
$892$	7445.85	0.279490
$893$	8732.66	0.327242
$894$	2123.79	0.0794519
$895$	−3604.32	−0.134613
$896$	−15067.6	−0.561801
$897$	11687.6	0.435049
$898$	−494.592	−0.0183794
$899$	−2560.08	−0.0949762
$900$	873.449	0.0323500
$901$	−822.209	−0.0304015
$902$	−3140.06	−0.115912
$903$	−2593.35	−0.0955716
$904$	16205.4	0.596220
$905$	−12380.2	−0.454730
$906$	7353.42	0.269648
$907$	16417.0	0.601013	0.300507	−	0.953780i	$-0.402844\pi$
$907$	16417.0	0.601013	0.300507	+	0.953780i	$0.402844\pi$
$908$	−4798.34	−0.175373
$909$	−8131.38	−0.296701
$910$	−10083.4	−0.367321
$911$	−26559.1	−0.965906	−0.482953	−	0.875646i	$-0.660436\pi$
$911$	−26559.1	−0.965906	−0.482953	+	0.875646i	$0.660436\pi$
$912$	1609.03	0.0584214
$913$	−2628.07	−0.0952644
$914$	27716.7	1.00305
$915$	17527.0	0.633251
$916$	−7610.01	−0.274500
$917$	−7917.17	−0.285112
$918$	127.132	0.00457080
$919$	19843.6	0.712274	0.356137	−	0.934434i	$-0.384094\pi$
$919$	19843.6	0.712274	0.356137	+	0.934434i	$0.384094\pi$
$920$	22622.2	0.810687
$921$	−25268.5	−0.904045
$922$	14921.5	0.532985
$923$	1738.37	0.0619927
$924$	2295.55	0.0817294
$925$	7572.97	0.269187
$926$	5322.26	0.188877
$927$	−3333.45	−0.118107
$928$	46126.5	1.63165
$929$	26150.7	0.923548	0.461774	−	0.886998i	$-0.347213\pi$
$929$	26150.7	0.923548	0.461774	+	0.886998i	$0.347213\pi$
$930$	−530.706	−0.0187124
$931$	14974.5	0.527142
$932$	−24162.9	−0.849229
$933$	−1307.81	−0.0458904
$934$	−5645.38	−0.197776
$935$	287.568	0.0100583
$936$	7817.58	0.272997
$937$	−13406.0	−0.467400	−0.233700	−	0.972309i	$-0.575083\pi$
$937$	−13406.0	−0.467400	−0.233700	+	0.972309i	$0.575083\pi$
$938$	−19884.2	−0.692156
$939$	17801.4	0.618666
$940$	−3821.10	−0.132586
$941$	−19177.3	−0.664358	−0.332179	−	0.943216i	$-0.607784\pi$
$941$	−19177.3	−0.664358	−0.332179	+	0.943216i	$0.607784\pi$
$942$	10521.4	0.363911
$943$	18689.5	0.645400
$944$	829.686	0.0286059
$945$	−4133.01	−0.142272
$946$	−970.406	−0.0333516
$947$	−26672.0	−0.915231	−0.457616	−	0.889150i	$-0.651296\pi$
$947$	−26672.0	−0.915231	−0.457616	+	0.889150i	$0.651296\pi$
$948$	−19114.7	−0.654871
$949$	41426.4	1.41703
$950$	−3835.56	−0.130992
$951$	−3012.12	−0.102707
$952$	−921.890	−0.0313851
$953$	20204.2	0.686756	0.343378	−	0.939197i	$-0.388429\pi$
$953$	20204.2	0.686756	0.343378	+	0.939197i	$0.388429\pi$
$954$	4421.82	0.150065
$955$	35588.4	1.20588
$956$	−17302.4	−0.585355
$957$	−7460.35	−0.251995
$958$	12879.3	0.434353
$959$	34313.6	1.15542
$960$	8476.02	0.284961
$961$	−29686.4	−0.996487
$962$	26658.7	0.893462
$963$	4563.99	0.152723
$964$	3894.01	0.130101
$965$	36932.5	1.23202
$966$	7412.28	0.246880
$967$	23770.0	0.790477	0.395239	−	0.918578i	$-0.370662\pi$
$967$	23770.0	0.790477	0.395239	+	0.918578i	$0.370662\pi$
$968$	−27256.0	−0.905002
$969$	1029.06	0.0341158
$970$	4839.58	0.160195
$971$	−1622.51	−0.0536240	−0.0268120	−	0.999640i	$-0.508536\pi$
$971$	−1622.51	−0.0536240	−0.0268120	+	0.999640i	$0.508536\pi$
$972$	1260.28	0.0415881
$973$	13340.6	0.439547
$974$	20049.2	0.659567
$975$	2204.57	0.0724132
$976$	2487.29	0.0815740
$977$	−6449.51	−0.211196	−0.105598	−	0.994409i	$-0.533676\pi$
$977$	−6449.51	−0.211196	−0.105598	+	0.994409i	$0.533676\pi$
$978$	−14312.8	−0.467968
$979$	6534.66	0.213329
$980$	−6552.29	−0.213577
$981$	−5168.64	−0.168218
$982$	−5961.50	−0.193726
$983$	−13518.8	−0.438641	−0.219320	−	0.975653i	$-0.570384\pi$
$983$	−13518.8	−0.438641	−0.219320	+	0.975653i	$0.570384\pi$
$984$	12500.9	0.404995
$985$	−41054.6	−1.32803
$986$	1178.39	0.0380605
$987$	−3183.22	−0.102658
$988$	24888.3	0.801419
$989$	5775.80	0.185703
$990$	−1546.53	−0.0496485
$991$	16227.1	0.520152	0.260076	−	0.965588i	$-0.416252\pi$
$991$	16227.1	0.520152	0.260076	+	0.965588i	$0.416252\pi$
$992$	−1885.43	−0.0603452
$993$	3998.25	0.127775
$994$	1102.48	0.0351795
$995$	36321.3	1.15725
$996$	4115.09	0.130915
$997$	24179.1	0.768063	0.384032	−	0.923320i	$-0.374535\pi$
$997$	24179.1	0.768063	0.384032	+	0.923320i	$0.374535\pi$
$998$	−10216.9	−0.324058
$999$	10926.9	0.346058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1011.4.a.c.1.17	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1011.4.a.c.1.17	✓	46	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1011 = 3 \cdot 337 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67739 q^{2} -3.00000 q^{3} -5.18636 q^{4} -10.3096 q^{5} +5.03218 q^{6} -14.8478 q^{7} +22.1187 q^{8} +9.00000 q^{9} +17.2932 q^{10} -9.93668 q^{11} +15.5591 q^{12} +39.2709 q^{13} +24.9055 q^{14} +30.9287 q^{15} +4.38915 q^{16} +2.80710 q^{17} -15.0965 q^{18} -122.197 q^{19} +53.4692 q^{20} +44.5433 q^{21} +16.6677 q^{22} -99.2053 q^{23} -66.3561 q^{24} -18.7125 q^{25} -65.8726 q^{26} -27.0000 q^{27} +77.0059 q^{28} -250.263 q^{29} -51.8796 q^{30} +10.2296 q^{31} -184.312 q^{32} +29.8100 q^{33} -4.70861 q^{34} +153.074 q^{35} -46.6772 q^{36} -404.701 q^{37} +204.973 q^{38} -117.813 q^{39} -228.034 q^{40} -188.392 q^{41} -74.7166 q^{42} -58.2207 q^{43} +51.5351 q^{44} -92.7862 q^{45} +166.406 q^{46} -71.4635 q^{47} -13.1675 q^{48} -122.543 q^{49} +31.3883 q^{50} -8.42131 q^{51} -203.673 q^{52} -292.903 q^{53} +45.2896 q^{54} +102.443 q^{55} -328.413 q^{56} +366.592 q^{57} +419.789 q^{58} +189.031 q^{59} -160.408 q^{60} +566.690 q^{61} -17.1590 q^{62} -133.630 q^{63} +274.050 q^{64} -404.866 q^{65} -50.0031 q^{66} -798.385 q^{67} -14.5586 q^{68} +297.616 q^{69} -256.766 q^{70} +44.2663 q^{71} +199.068 q^{72} +1054.89 q^{73} +678.841 q^{74} +56.1376 q^{75} +633.760 q^{76} +147.538 q^{77} +197.618 q^{78} -1228.53 q^{79} -45.2503 q^{80} +81.0000 q^{81} +316.007 q^{82} +264.482 q^{83} -231.018 q^{84} -28.9401 q^{85} +97.6590 q^{86} +750.790 q^{87} -219.786 q^{88} -657.630 q^{89} +155.639 q^{90} -583.085 q^{91} +514.514 q^{92} -30.6887 q^{93} +119.872 q^{94} +1259.80 q^{95} +552.935 q^{96} +279.854 q^{97} +205.553 q^{98} -89.4301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) \) 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more