LMFDB - Embedded newform 2001.4.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,4,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2001.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2001.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:	$118.062821921$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.24407 q^{2} +3.00000 q^{3} +2.52397 q^{4} -19.5917 q^{5} -9.73220 q^{6} +36.4327 q^{7} +17.7646 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.24407 q^{2} +3.00000 q^{3} +2.52397 q^{4} -19.5917 q^{5} -9.73220 q^{6} +36.4327 q^{7} +17.7646 q^{8} +9.00000 q^{9} +63.5566 q^{10} -30.4047 q^{11} +7.57190 q^{12} -16.3433 q^{13} -118.190 q^{14} -58.7750 q^{15} -77.8213 q^{16} +57.0435 q^{17} -29.1966 q^{18} +127.772 q^{19} -49.4487 q^{20} +109.298 q^{21} +98.6350 q^{22} +23.0000 q^{23} +53.2939 q^{24} +258.833 q^{25} +53.0189 q^{26} +27.0000 q^{27} +91.9549 q^{28} -29.0000 q^{29} +190.670 q^{30} -17.5428 q^{31} +110.341 q^{32} -91.2142 q^{33} -185.053 q^{34} -713.777 q^{35} +22.7157 q^{36} -50.8943 q^{37} -414.502 q^{38} -49.0300 q^{39} -348.038 q^{40} +436.201 q^{41} -354.570 q^{42} +156.872 q^{43} -76.7405 q^{44} -176.325 q^{45} -74.6135 q^{46} -98.9994 q^{47} -233.464 q^{48} +984.343 q^{49} -839.672 q^{50} +171.130 q^{51} -41.2500 q^{52} -603.808 q^{53} -87.5898 q^{54} +595.679 q^{55} +647.213 q^{56} +383.317 q^{57} +94.0779 q^{58} +664.386 q^{59} -148.346 q^{60} -295.305 q^{61} +56.9099 q^{62} +327.894 q^{63} +264.618 q^{64} +320.193 q^{65} +295.905 q^{66} -168.332 q^{67} +143.976 q^{68} +69.0000 q^{69} +2315.54 q^{70} -225.932 q^{71} +159.882 q^{72} -475.959 q^{73} +165.104 q^{74} +776.499 q^{75} +322.493 q^{76} -1107.73 q^{77} +159.057 q^{78} +1042.07 q^{79} +1524.65 q^{80} +81.0000 q^{81} -1415.06 q^{82} -739.213 q^{83} +275.865 q^{84} -1117.58 q^{85} -508.902 q^{86} -87.0000 q^{87} -540.129 q^{88} -616.883 q^{89} +572.010 q^{90} -595.432 q^{91} +58.0512 q^{92} -52.6283 q^{93} +321.161 q^{94} -2503.27 q^{95} +331.022 q^{96} +269.902 q^{97} -3193.27 q^{98} -273.643 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) $ 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.24407	−1.14695	−0.573475	−	0.819223i	$-0.694405\pi$
$2$	−3.24407	−1.14695	−0.573475	+	0.819223i	$0.694405\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	2.52397	0.315496
$5$	−19.5917	−1.75233	−0.876166	−	0.482010i	$-0.839907\pi$
$5$	−19.5917	−1.75233	−0.876166	+	0.482010i	$0.839907\pi$
$6$	−9.73220	−0.662192
$7$	36.4327	1.96718	0.983591	−	0.180413i	$-0.0577434\pi$
$7$	36.4327	1.96718	0.983591	+	0.180413i	$0.0577434\pi$
$8$	17.7646	0.785093
$9$	9.00000	0.333333
$10$	63.5566	2.00984
$11$	−30.4047	−0.833398	−0.416699	−	0.909045i	$-0.636813\pi$
$11$	−30.4047	−0.833398	−0.416699	+	0.909045i	$0.636813\pi$
$12$	7.57190	0.182151
$13$	−16.3433	−0.348679	−0.174340	−	0.984686i	$-0.555779\pi$
$13$	−16.3433	−0.348679	−0.174340	+	0.984686i	$0.555779\pi$
$14$	−118.190	−2.25626
$15$	−58.7750	−1.01171
$16$	−77.8213	−1.21596
$17$	57.0435	0.813828	0.406914	−	0.913467i	$-0.366605\pi$
$17$	57.0435	0.813828	0.406914	+	0.913467i	$0.366605\pi$
$18$	−29.1966	−0.382317
$19$	127.772	1.54279	0.771394	−	0.636358i	$-0.219560\pi$
$19$	127.772	1.54279	0.771394	+	0.636358i	$0.219560\pi$
$20$	−49.4487	−0.552853
$21$	109.298	1.13575
$22$	98.6350	0.955866
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	53.2939	0.453273
$25$	258.833	2.07066
$26$	53.0189	0.399918
$27$	27.0000	0.192450
$28$	91.9549	0.620637
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	190.670	1.16038
$31$	−17.5428	−0.101638	−0.0508189	−	0.998708i	$-0.516183\pi$
$31$	−17.5428	−0.101638	−0.0508189	+	0.998708i	$0.516183\pi$
$32$	110.341	0.609551
$33$	−91.2142	−0.481162
$34$	−185.053	−0.933420
$35$	−713.777	−3.44715
$36$	22.7157	0.105165
$37$	−50.8943	−0.226134	−0.113067	−	0.993587i	$-0.536068\pi$
$37$	−50.8943	−0.226134	−0.113067	+	0.993587i	$0.536068\pi$
$38$	−414.502	−1.76950
$39$	−49.0300	−0.201310
$40$	−348.038	−1.37574
$41$	436.201	1.66154	0.830770	−	0.556617i	$-0.187901\pi$
$41$	436.201	1.66154	0.830770	+	0.556617i	$0.187901\pi$
$42$	−354.570	−1.30265
$43$	156.872	0.556342	0.278171	−	0.960532i	$-0.410272\pi$
$43$	156.872	0.556342	0.278171	+	0.960532i	$0.410272\pi$
$44$	−76.7405	−0.262933
$45$	−176.325	−0.584110
$46$	−74.6135	−0.239156
$47$	−98.9994	−0.307246	−0.153623	−	0.988130i	$-0.549094\pi$
$47$	−98.9994	−0.307246	−0.153623	+	0.988130i	$0.549094\pi$
$48$	−233.464	−0.702034
$49$	984.343	2.86980
$50$	−839.672	−2.37495
$51$	171.130	0.469864
$52$	−41.2500	−0.110007
$53$	−603.808	−1.56489	−0.782447	−	0.622718i	$-0.786029\pi$
$53$	−603.808	−1.56489	−0.782447	+	0.622718i	$0.786029\pi$
$54$	−87.5898	−0.220731
$55$	595.679	1.46039
$56$	647.213	1.54442
$57$	383.317	0.890729
$58$	94.0779	0.212983
$59$	664.386	1.46603	0.733015	−	0.680213i	$-0.238113\pi$
$59$	664.386	1.46603	0.733015	+	0.680213i	$0.238113\pi$
$60$	−148.346	−0.319190
$61$	−295.305	−0.619836	−0.309918	−	0.950763i	$-0.600302\pi$
$61$	−295.305	−0.619836	−0.309918	+	0.950763i	$0.600302\pi$
$62$	56.9099	0.116574
$63$	327.894	0.655727
$64$	264.618	0.516833
$65$	320.193	0.611001
$66$	295.905	0.551869
$67$	−168.332	−0.306940	−0.153470	−	0.988153i	$-0.549045\pi$
$67$	−168.332	−0.306940	−0.153470	+	0.988153i	$0.549045\pi$
$68$	143.976	0.256759
$69$	69.0000	0.120386
$70$	2315.54	3.95372
$71$	−225.932	−0.377651	−0.188826	−	0.982011i	$-0.560468\pi$
$71$	−225.932	−0.377651	−0.188826	+	0.982011i	$0.560468\pi$
$72$	159.882	0.261698
$73$	−475.959	−0.763107	−0.381553	−	0.924347i	$-0.624611\pi$
$73$	−475.959	−0.763107	−0.381553	+	0.924347i	$0.624611\pi$
$74$	165.104	0.259365
$75$	776.499	1.19550
$76$	322.493	0.486743
$77$	−1107.73	−1.63944
$78$	159.057	0.230893
$79$	1042.07	1.48408	0.742040	−	0.670356i	$-0.233859\pi$
$79$	1042.07	1.48408	0.742040	+	0.670356i	$0.233859\pi$
$80$	1524.65	2.13076
$81$	81.0000	0.111111
$82$	−1415.06	−1.90570
$83$	−739.213	−0.977581	−0.488790	−	0.872401i	$-0.662562\pi$
$83$	−739.213	−0.977581	−0.488790	+	0.872401i	$0.662562\pi$
$84$	275.865	0.358325
$85$	−1117.58	−1.42610
$86$	−508.902	−0.638097
$87$	−87.0000	−0.107211
$88$	−540.129	−0.654294
$89$	−616.883	−0.734713	−0.367357	−	0.930080i	$-0.619737\pi$
$89$	−616.883	−0.734713	−0.367357	+	0.930080i	$0.619737\pi$
$90$	572.010	0.669946
$91$	−595.432	−0.685915
$92$	58.0512	0.0657854
$93$	−52.6283	−0.0586806
$94$	321.161	0.352396
$95$	−2503.27	−2.70347
$96$	331.022	0.351925
$97$	269.902	0.282520	0.141260	−	0.989973i	$-0.454885\pi$
$97$	269.902	0.282520	0.141260	+	0.989973i	$0.454885\pi$
$98$	−3193.27	−3.29152
$99$	−273.643	−0.277799
$100$	653.286	0.653286
$101$	1124.70	1.10804	0.554021	−	0.832502i	$-0.313093\pi$
$101$	1124.70	1.10804	0.554021	+	0.832502i	$0.313093\pi$
$102$	−555.158	−0.538910
$103$	1523.40	1.45733	0.728663	−	0.684872i	$-0.240142\pi$
$103$	1523.40	1.45733	0.728663	+	0.684872i	$0.240142\pi$
$104$	−290.333	−0.273745
$105$	−2141.33	−1.99022
$106$	1958.79	1.79486
$107$	−692.905	−0.626035	−0.313017	−	0.949747i	$-0.601340\pi$
$107$	−692.905	−0.626035	−0.313017	+	0.949747i	$0.601340\pi$
$108$	68.1471	0.0607172
$109$	−148.142	−0.130178	−0.0650892	−	0.997879i	$-0.520733\pi$
$109$	−148.142	−0.130178	−0.0650892	+	0.997879i	$0.520733\pi$
$110$	−1932.42	−1.67499
$111$	−152.683	−0.130559
$112$	−2835.24	−2.39201
$113$	−1321.73	−1.10033	−0.550167	−	0.835055i	$-0.685436\pi$
$113$	−1321.73	−1.10033	−0.550167	+	0.835055i	$0.685436\pi$
$114$	−1243.50	−1.02162
$115$	−450.608	−0.365386
$116$	−73.1950	−0.0585861
$117$	−147.090	−0.116226
$118$	−2155.31	−1.68146
$119$	2078.25	1.60095
$120$	−1044.12	−0.794285
$121$	−406.552	−0.305449
$122$	957.990	0.710921
$123$	1308.60	0.959290
$124$	−44.2773	−0.0320663
$125$	−2622.01	−1.87616
$126$	−1063.71	−0.752087
$127$	−1240.60	−0.866815	−0.433407	−	0.901198i	$-0.642689\pi$
$127$	−1240.60	−0.866815	−0.433407	+	0.901198i	$0.642689\pi$
$128$	−1741.16	−1.20233
$129$	470.615	0.321204
$130$	−1038.73	−0.700788
$131$	−917.805	−0.612130	−0.306065	−	0.952011i	$-0.599012\pi$
$131$	−917.805	−0.612130	−0.306065	+	0.952011i	$0.599012\pi$
$132$	−230.221	−0.151805
$133$	4655.09	3.03494
$134$	546.079	0.352045
$135$	−528.975	−0.337236
$136$	1013.36	0.638930
$137$	−3116.04	−1.94322	−0.971611	−	0.236584i	$-0.923972\pi$
$137$	−3116.04	−1.94322	−0.971611	+	0.236584i	$0.923972\pi$
$138$	−223.841	−0.138077
$139$	460.672	0.281106	0.140553	−	0.990073i	$-0.455112\pi$
$139$	460.672	0.281106	0.140553	+	0.990073i	$0.455112\pi$
$140$	−1801.55	−1.08756
$141$	−296.998	−0.177388
$142$	732.940	0.433147
$143$	496.915	0.290588
$144$	−700.392	−0.405319
$145$	568.158	0.325400
$146$	1544.04	0.875246
$147$	2953.03	1.65688
$148$	−128.455	−0.0713444
$149$	215.908	0.118711	0.0593553	−	0.998237i	$-0.481096\pi$
$149$	215.908	0.118711	0.0593553	+	0.998237i	$0.481096\pi$
$150$	−2519.01	−1.37118
$151$	−1122.29	−0.604838	−0.302419	−	0.953175i	$-0.597794\pi$
$151$	−1122.29	−0.604838	−0.302419	+	0.953175i	$0.597794\pi$
$152$	2269.82	1.21123
$153$	513.391	0.271276
$154$	3593.54	1.88036
$155$	343.692	0.178103
$156$	−123.750	−0.0635124
$157$	3161.13	1.60691	0.803457	−	0.595363i	$-0.202992\pi$
$157$	3161.13	1.60691	0.803457	+	0.595363i	$0.202992\pi$
$158$	−3380.55	−1.70217
$159$	−1811.42	−0.903492
$160$	−2161.75	−1.06814
$161$	837.953	0.410186
$162$	−262.769	−0.127439
$163$	497.497	0.239061	0.119531	−	0.992831i	$-0.461861\pi$
$163$	497.497	0.239061	0.119531	+	0.992831i	$0.461861\pi$
$164$	1100.96	0.524208
$165$	1787.04	0.843156
$166$	2398.06	1.12124
$167$	3133.55	1.45198	0.725992	−	0.687704i	$-0.241381\pi$
$167$	3133.55	1.45198	0.725992	+	0.687704i	$0.241381\pi$
$168$	1941.64	0.891671
$169$	−1929.90	−0.878423
$170$	3625.49	1.63566
$171$	1149.95	0.514262
$172$	395.939	0.175523
$173$	1124.91	0.494368	0.247184	−	0.968969i	$-0.420495\pi$
$173$	1124.91	0.494368	0.247184	+	0.968969i	$0.420495\pi$
$174$	282.234	0.122966
$175$	9429.99	4.07337
$176$	2366.14	1.01338
$177$	1993.16	0.846412
$178$	2001.21	0.842680
$179$	488.722	0.204071	0.102036	−	0.994781i	$-0.467464\pi$
$179$	488.722	0.204071	0.102036	+	0.994781i	$0.467464\pi$
$180$	−445.038	−0.184284
$181$	−4201.11	−1.72523	−0.862613	−	0.505865i	$-0.831173\pi$
$181$	−4201.11	−1.72523	−0.862613	+	0.505865i	$0.831173\pi$
$182$	1931.62	0.786711
$183$	−885.916	−0.357862
$184$	408.586	0.163703
$185$	997.103	0.396262
$186$	170.730	0.0673038
$187$	−1734.39	−0.678242
$188$	−249.871	−0.0969347
$189$	983.683	0.378584
$190$	8120.77	3.10075
$191$	−2937.28	−1.11274	−0.556372	−	0.830933i	$-0.687807\pi$
$191$	−2937.28	−1.11274	−0.556372	+	0.830933i	$0.687807\pi$
$192$	793.855	0.298394
$193$	−3954.47	−1.47487	−0.737433	−	0.675421i	$-0.763962\pi$
$193$	−3954.47	−1.47487	−0.737433	+	0.675421i	$0.763962\pi$
$194$	−875.581	−0.324037
$195$	960.580	0.352762
$196$	2484.45	0.905411
$197$	1119.36	0.404826	0.202413	−	0.979300i	$-0.435122\pi$
$197$	1119.36	0.404826	0.202413	+	0.979300i	$0.435122\pi$
$198$	887.715	0.318622
$199$	5417.73	1.92991	0.964956	−	0.262412i	$-0.0845180\pi$
$199$	5417.73	1.92991	0.964956	+	0.262412i	$0.0845180\pi$
$200$	4598.07	1.62566
$201$	−504.995	−0.177212
$202$	−3648.62	−1.27087
$203$	−1056.55	−0.365297
$204$	431.927	0.148240
$205$	−8545.89	−2.91157
$206$	−4942.00	−1.67148
$207$	207.000	0.0695048
$208$	1271.86	0.423979
$209$	−3884.88	−1.28576
$210$	6946.62	2.28268
$211$	2509.92	0.818911	0.409456	−	0.912330i	$-0.365719\pi$
$211$	2509.92	0.818911	0.409456	+	0.912330i	$0.365719\pi$
$212$	−1523.99	−0.493717
$213$	−677.797	−0.218037
$214$	2247.83	0.718031
$215$	−3073.38	−0.974895
$216$	479.645	0.151091
$217$	−639.131	−0.199940
$218$	480.583	0.149308
$219$	−1427.88	−0.440580
$220$	1503.47	0.460746
$221$	−932.281	−0.283765
$222$	495.313	0.149744
$223$	4143.67	1.24431	0.622154	−	0.782895i	$-0.286258\pi$
$223$	4143.67	1.24431	0.622154	+	0.782895i	$0.286258\pi$
$224$	4020.01	1.19910
$225$	2329.50	0.690221
$226$	4287.77	1.26203
$227$	1330.15	0.388920	0.194460	−	0.980910i	$-0.437704\pi$
$227$	1330.15	0.388920	0.194460	+	0.980910i	$0.437704\pi$
$228$	967.478	0.281021
$229$	4390.78	1.26704	0.633518	−	0.773728i	$-0.281610\pi$
$229$	4390.78	1.26704	0.633518	+	0.773728i	$0.281610\pi$
$230$	1461.80	0.419080
$231$	−3323.18	−0.946534
$232$	−515.174	−0.145788
$233$	2182.86	0.613749	0.306875	−	0.951750i	$-0.400717\pi$
$233$	2182.86	0.613749	0.306875	+	0.951750i	$0.400717\pi$
$234$	477.170	0.133306
$235$	1939.56	0.538396
$236$	1676.89	0.462526
$237$	3126.22	0.856834
$238$	−6741.98	−1.83621
$239$	2329.47	0.630465	0.315232	−	0.949014i	$-0.397918\pi$
$239$	2329.47	0.630465	0.315232	+	0.949014i	$0.397918\pi$
$240$	4573.95	1.23020
$241$	−4254.92	−1.13728	−0.568638	−	0.822588i	$-0.692529\pi$
$241$	−4254.92	−1.13728	−0.568638	+	0.822588i	$0.692529\pi$
$242$	1318.88	0.350334
$243$	243.000	0.0641500
$244$	−745.340	−0.195555
$245$	−19284.9	−5.02885
$246$	−4245.19	−1.10026
$247$	−2088.23	−0.537938
$248$	−311.641	−0.0797951
$249$	−2217.64	−0.564406
$250$	8505.98	2.15186
$251$	−1645.75	−0.413860	−0.206930	−	0.978356i	$-0.566347\pi$
$251$	−1645.75	−0.413860	−0.206930	+	0.978356i	$0.566347\pi$
$252$	827.594	0.206879
$253$	−699.309	−0.173775
$254$	4024.59	0.994193
$255$	−3352.73	−0.823357
$256$	3531.50	0.862184
$257$	7468.91	1.81283	0.906417	−	0.422385i	$-0.138807\pi$
$257$	7468.91	1.81283	0.906417	+	0.422385i	$0.138807\pi$
$258$	−1526.71	−0.368405
$259$	−1854.22	−0.444847
$260$	808.157	0.192768
$261$	−261.000	−0.0618984
$262$	2977.42	0.702082
$263$	530.760	0.124441	0.0622207	−	0.998062i	$-0.480182\pi$
$263$	530.760	0.124441	0.0622207	+	0.998062i	$0.480182\pi$
$264$	−1620.39	−0.377757
$265$	11829.6	2.74221
$266$	−15101.4	−3.48093
$267$	−1850.65	−0.424187
$268$	−424.863	−0.0968382
$269$	4696.37	1.06447	0.532236	−	0.846596i	$-0.321352\pi$
$269$	4696.37	1.06447	0.532236	+	0.846596i	$0.321352\pi$
$270$	1716.03	0.386793
$271$	1950.13	0.437130	0.218565	−	0.975822i	$-0.429862\pi$
$271$	1950.13	0.437130	0.218565	+	0.975822i	$0.429862\pi$
$272$	−4439.20	−0.989580
$273$	−1786.30	−0.396013
$274$	10108.6	2.22878
$275$	−7869.75	−1.72569
$276$	174.154	0.0379812
$277$	−2217.59	−0.481019	−0.240510	−	0.970647i	$-0.577315\pi$
$277$	−2217.59	−0.481019	−0.240510	+	0.970647i	$0.577315\pi$
$278$	−1494.45	−0.322414
$279$	−157.885	−0.0338793
$280$	−12680.0	−2.70634
$281$	460.925	0.0978523	0.0489261	−	0.998802i	$-0.484420\pi$
$281$	460.925	0.0978523	0.0489261	+	0.998802i	$0.484420\pi$
$282$	963.482	0.203456
$283$	1308.08	0.274760	0.137380	−	0.990518i	$-0.456132\pi$
$283$	1308.08	0.274760	0.137380	+	0.990518i	$0.456132\pi$
$284$	−570.246	−0.119147
$285$	−7509.81	−1.56085
$286$	−1612.03	−0.333290
$287$	15892.0	3.26855
$288$	993.065	0.203184
$289$	−1659.04	−0.337684
$290$	−1843.14	−0.373217
$291$	809.707	0.163113
$292$	−1201.30	−0.240757
$293$	6118.69	1.21999	0.609996	−	0.792405i	$-0.291171\pi$
$293$	6118.69	1.21999	0.609996	+	0.792405i	$0.291171\pi$
$294$	−9579.82	−1.90036
$295$	−13016.4	−2.56897
$296$	−904.118	−0.177536
$297$	−820.928	−0.160387
$298$	−700.420	−0.136155
$299$	−375.897	−0.0727046
$300$	1959.86	0.377175
$301$	5715.26	1.09443
$302$	3640.78	0.693720
$303$	3374.11	0.639729
$304$	−9943.40	−1.87596
$305$	5785.52	1.08616
$306$	−1665.47	−0.311140
$307$	−3050.96	−0.567191	−0.283595	−	0.958944i	$-0.591527\pi$
$307$	−3050.96	−0.567191	−0.283595	+	0.958944i	$0.591527\pi$
$308$	−2795.87	−0.517238
$309$	4570.19	0.841388
$310$	−1114.96	−0.204276
$311$	2117.98	0.386172	0.193086	−	0.981182i	$-0.438150\pi$
$311$	2117.98	0.386172	0.193086	+	0.981182i	$0.438150\pi$
$312$	−871.000	−0.158047
$313$	5975.96	1.07917	0.539586	−	0.841930i	$-0.318581\pi$
$313$	5975.96	1.07917	0.539586	+	0.841930i	$0.318581\pi$
$314$	−10254.9	−1.84305
$315$	−6424.00	−1.14905
$316$	2630.15	0.468221
$317$	8409.45	1.48997	0.744987	−	0.667079i	$-0.232456\pi$
$317$	8409.45	1.48997	0.744987	+	0.667079i	$0.232456\pi$
$318$	5876.38	1.03626
$319$	881.737	0.154758
$320$	−5184.31	−0.905663
$321$	−2078.72	−0.361441
$322$	−2718.37	−0.470463
$323$	7288.57	1.25556
$324$	204.441	0.0350551
$325$	−4230.20	−0.721997
$326$	−1613.91	−0.274191
$327$	−444.427	−0.0751586
$328$	7748.94	1.30446
$329$	−3606.82	−0.604408
$330$	−5797.27	−0.967058
$331$	−9414.63	−1.56337	−0.781684	−	0.623675i	$-0.785639\pi$
$331$	−9414.63	−1.56337	−0.781684	+	0.623675i	$0.785639\pi$
$332$	−1865.75	−0.308422
$333$	−458.049	−0.0753781
$334$	−10165.4	−1.66535
$335$	3297.90	0.537861
$336$	−8505.73	−1.38103
$337$	−3207.00	−0.518387	−0.259193	−	0.965825i	$-0.583457\pi$
$337$	−3207.00	−0.518387	−0.259193	+	0.965825i	$0.583457\pi$
$338$	6260.71	1.00751
$339$	−3965.18	−0.635278
$340$	−2820.72	−0.449927
$341$	533.383	0.0847047
$342$	−3730.51	−0.589834
$343$	23365.9	3.67825
$344$	2786.76	0.436780
$345$	−1351.82	−0.210956
$346$	−3649.30	−0.567016
$347$	−9835.06	−1.52154	−0.760769	−	0.649023i	$-0.775178\pi$
$347$	−9835.06	−1.52154	−0.760769	+	0.649023i	$0.775178\pi$
$348$	−219.585	−0.0338247
$349$	−1310.23	−0.200960	−0.100480	−	0.994939i	$-0.532038\pi$
$349$	−1310.23	−0.200960	−0.100480	+	0.994939i	$0.532038\pi$
$350$	−30591.5	−4.67196
$351$	−441.270	−0.0671033
$352$	−3354.88	−0.507999
$353$	5428.63	0.818518	0.409259	−	0.912418i	$-0.365787\pi$
$353$	5428.63	0.818518	0.409259	+	0.912418i	$0.365787\pi$
$354$	−6465.94	−0.970793
$355$	4426.39	0.661770
$356$	−1556.99	−0.231799
$357$	6234.75	0.924307
$358$	−1585.45	−0.234060
$359$	7157.65	1.05227	0.526137	−	0.850400i	$-0.323640\pi$
$359$	7157.65	1.05227	0.526137	+	0.850400i	$0.323640\pi$
$360$	−3132.35	−0.458581
$361$	9466.74	1.38019
$362$	13628.7	1.97875
$363$	−1219.66	−0.176351
$364$	−1502.85	−0.216403
$365$	9324.83	1.33722
$366$	2873.97	0.410450
$367$	2355.64	0.335050	0.167525	−	0.985868i	$-0.446423\pi$
$367$	2355.64	0.335050	0.167525	+	0.985868i	$0.446423\pi$
$368$	−1789.89	−0.253545
$369$	3925.81	0.553846
$370$	−3234.67	−0.454493
$371$	−21998.4	−3.07843
$372$	−132.832	−0.0185135
$373$	−5718.24	−0.793778	−0.396889	−	0.917867i	$-0.629910\pi$
$373$	−5718.24	−0.793778	−0.396889	+	0.917867i	$0.629910\pi$
$374$	5626.48	0.777910
$375$	−7866.03	−1.08320
$376$	−1758.69	−0.241216
$377$	473.957	0.0647481
$378$	−3191.13	−0.434218
$379$	12548.8	1.70076	0.850382	−	0.526166i	$-0.176371\pi$
$379$	12548.8	1.70076	0.850382	+	0.526166i	$0.176371\pi$
$380$	−6318.17	−0.852934
$381$	−3721.80	−0.500456
$382$	9528.74	1.27626
$383$	1592.88	0.212513	0.106257	−	0.994339i	$-0.466114\pi$
$383$	1592.88	0.212513	0.106257	+	0.994339i	$0.466114\pi$
$384$	−5223.49	−0.694167
$385$	21702.2	2.87285
$386$	12828.6	1.69160
$387$	1411.84	0.185447
$388$	681.224	0.0891338
$389$	10342.9	1.34808	0.674041	−	0.738694i	$-0.264557\pi$
$389$	10342.9	1.34808	0.674041	+	0.738694i	$0.264557\pi$
$390$	−3116.18	−0.404600
$391$	1312.00	0.169695
$392$	17486.5	2.25306
$393$	−2753.41	−0.353413
$394$	−3631.26	−0.464316
$395$	−20415.9	−2.60060
$396$	−690.664	−0.0876444
$397$	614.947	0.0777413	0.0388706	−	0.999244i	$-0.487624\pi$
$397$	614.947	0.0777413	0.0388706	+	0.999244i	$0.487624\pi$
$398$	−17575.5	−2.21351
$399$	13965.3	1.75223
$400$	−20142.7	−2.51784
$401$	12336.8	1.53633	0.768166	−	0.640250i	$-0.221169\pi$
$401$	12336.8	1.53633	0.768166	+	0.640250i	$0.221169\pi$
$402$	1638.24	0.203253
$403$	286.707	0.0354390
$404$	2838.72	0.349583
$405$	−1586.92	−0.194703
$406$	3427.51	0.418977
$407$	1547.43	0.188460
$408$	3040.07	0.368887
$409$	12910.3	1.56082	0.780408	−	0.625271i	$-0.215011\pi$
$409$	12910.3	1.56082	0.780408	+	0.625271i	$0.215011\pi$
$410$	27723.4	3.33942
$411$	−9348.13	−1.12192
$412$	3845.00	0.459780
$413$	24205.4	2.88395
$414$	−671.522	−0.0797186
$415$	14482.4	1.71305
$416$	−1803.33	−0.212538
$417$	1382.02	0.162296
$418$	12602.8	1.47470
$419$	4615.84	0.538183	0.269091	−	0.963115i	$-0.413277\pi$
$419$	4615.84	0.538183	0.269091	+	0.963115i	$0.413277\pi$
$420$	−5404.65	−0.627904
$421$	7759.09	0.898230	0.449115	−	0.893474i	$-0.351739\pi$
$421$	7759.09	0.898230	0.449115	+	0.893474i	$0.351739\pi$
$422$	−8142.36	−0.939250
$423$	−890.995	−0.102415
$424$	−10726.4	−1.22859
$425$	14764.7	1.68516
$426$	2198.82	0.250078
$427$	−10758.8	−1.21933
$428$	−1748.87	−0.197511
$429$	1490.75	0.167771
$430$	9970.23	1.11816
$431$	10316.2	1.15294	0.576469	−	0.817119i	$-0.304430\pi$
$431$	10316.2	1.15294	0.576469	+	0.817119i	$0.304430\pi$
$432$	−2101.18	−0.234011
$433$	−11157.5	−1.23832	−0.619162	−	0.785263i	$-0.712528\pi$
$433$	−11157.5	−1.23832	−0.619162	+	0.785263i	$0.712528\pi$
$434$	2073.38	0.229321
$435$	1704.47	0.187870
$436$	−373.906	−0.0410707
$437$	2938.76	0.321693
$438$	4632.13	0.505323
$439$	14271.9	1.55162	0.775809	−	0.630967i	$-0.217342\pi$
$439$	14271.9	1.55162	0.775809	+	0.630967i	$0.217342\pi$
$440$	10582.0	1.14654
$441$	8859.09	0.956602
$442$	3024.38	0.325464
$443$	−13164.2	−1.41185	−0.705924	−	0.708287i	$-0.749468\pi$
$443$	−13164.2	−1.41185	−0.705924	+	0.708287i	$0.749468\pi$
$444$	−385.366	−0.0411907
$445$	12085.8	1.28746
$446$	−13442.4	−1.42716
$447$	647.724	0.0685376
$448$	9640.77	1.01670
$449$	−12293.1	−1.29209	−0.646045	−	0.763299i	$-0.723578\pi$
$449$	−12293.1	−1.29209	−0.646045	+	0.763299i	$0.723578\pi$
$450$	−7557.04	−0.791650
$451$	−13262.6	−1.38472
$452$	−3335.99	−0.347150
$453$	−3366.87	−0.349204
$454$	−4315.08	−0.446072
$455$	11665.5	1.20195
$456$	6809.47	0.699305
$457$	3326.34	0.340480	0.170240	−	0.985403i	$-0.445546\pi$
$457$	3326.34	0.340480	0.170240	+	0.985403i	$0.445546\pi$
$458$	−14244.0	−1.45323
$459$	1540.17	0.156621
$460$	−1137.32	−0.115278
$461$	−4788.85	−0.483815	−0.241908	−	0.970299i	$-0.577773\pi$
$461$	−4788.85	−0.483815	−0.241908	+	0.970299i	$0.577773\pi$
$462$	10780.6	1.08563
$463$	−12284.5	−1.23307	−0.616533	−	0.787329i	$-0.711463\pi$
$463$	−12284.5	−1.23307	−0.616533	+	0.787329i	$0.711463\pi$
$464$	2256.82	0.225798
$465$	1031.08	0.102828
$466$	−7081.33	−0.703940
$467$	−4240.83	−0.420218	−0.210109	−	0.977678i	$-0.567382\pi$
$467$	−4240.83	−0.420218	−0.210109	+	0.977678i	$0.567382\pi$
$468$	−371.250	−0.0366689
$469$	−6132.78	−0.603807
$470$	−6292.07	−0.617514
$471$	9483.38	0.927752
$472$	11802.6	1.15097
$473$	−4769.64	−0.463654
$474$	−10141.7	−0.982746
$475$	33071.7	3.19459
$476$	5245.43	0.505092
$477$	−5434.27	−0.521631
$478$	−7556.97	−0.723112
$479$	542.520	0.0517502	0.0258751	−	0.999665i	$-0.491763\pi$
$479$	542.520	0.0517502	0.0258751	+	0.999665i	$0.491763\pi$
$480$	−6485.26	−0.616688
$481$	831.783	0.0788483
$482$	13803.2	1.30440
$483$	2513.86	0.236821
$484$	−1026.12	−0.0963677
$485$	−5287.84	−0.495069
$486$	−788.308	−0.0735769
$487$	−293.695	−0.0273277	−0.0136639	−	0.999907i	$-0.504349\pi$
$487$	−293.695	−0.0273277	−0.0136639	+	0.999907i	$0.504349\pi$
$488$	−5245.99	−0.486628
$489$	1492.49	0.138022
$490$	62561.5	5.76784
$491$	−5674.06	−0.521520	−0.260760	−	0.965404i	$-0.583973\pi$
$491$	−5674.06	−0.521520	−0.260760	+	0.965404i	$0.583973\pi$
$492$	3302.87	0.302652
$493$	−1654.26	−0.151124
$494$	6774.34	0.616988
$495$	5361.11	0.486796
$496$	1365.20	0.123587
$497$	−8231.33	−0.742909
$498$	7194.17	0.647346
$499$	−8602.29	−0.771726	−0.385863	−	0.922556i	$-0.626096\pi$
$499$	−8602.29	−0.771726	−0.385863	+	0.922556i	$0.626096\pi$
$500$	−6617.87	−0.591920
$501$	9400.64	0.838303
$502$	5338.93	0.474677
$503$	291.275	0.0258197	0.0129099	−	0.999917i	$-0.495891\pi$
$503$	291.275	0.0258197	0.0129099	+	0.999917i	$0.495891\pi$
$504$	5824.92	0.514807
$505$	−22034.8	−1.94166
$506$	2268.60	0.199312
$507$	−5789.69	−0.507158
$508$	−3131.23	−0.273476
$509$	−4315.47	−0.375796	−0.187898	−	0.982189i	$-0.560167\pi$
$509$	−4315.47	−0.375796	−0.187898	+	0.982189i	$0.560167\pi$
$510$	10876.5	0.944350
$511$	−17340.5	−1.50117
$512$	2472.88	0.213451
$513$	3449.85	0.296910
$514$	−24229.7	−2.07923
$515$	−29845.8	−2.55372
$516$	1187.82	0.101339
$517$	3010.05	0.256058
$518$	6015.20	0.510218
$519$	3374.74	0.285423
$520$	5688.11	0.479693
$521$	−6517.09	−0.548021	−0.274010	−	0.961727i	$-0.588350\pi$
$521$	−6517.09	−0.548021	−0.274010	+	0.961727i	$0.588350\pi$
$522$	846.701	0.0709945
$523$	5054.76	0.422618	0.211309	−	0.977419i	$-0.432227\pi$
$523$	5054.76	0.422618	0.211309	+	0.977419i	$0.432227\pi$
$524$	−2316.51	−0.193124
$525$	28290.0	2.35176
$526$	−1721.82	−0.142728
$527$	−1000.70	−0.0827157
$528$	7098.41	0.585073
$529$	529.000	0.0434783
$530$	−38376.0	−3.14518
$531$	5979.48	0.488676
$532$	11749.3	0.957511
$533$	−7128.98	−0.579344
$534$	6003.63	0.486521
$535$	13575.2	1.09702
$536$	−2990.35	−0.240976
$537$	1466.16	0.117821
$538$	−15235.3	−1.22090
$539$	−29928.7	−2.39169
$540$	−1335.11	−0.106397
$541$	7415.86	0.589339	0.294670	−	0.955599i	$-0.404790\pi$
$541$	7415.86	0.589339	0.294670	+	0.955599i	$0.404790\pi$
$542$	−6326.37	−0.501367
$543$	−12603.3	−0.996059
$544$	6294.21	0.496070
$545$	2902.35	0.228116
$546$	5794.87	0.454208
$547$	8542.01	0.667696	0.333848	−	0.942627i	$-0.391653\pi$
$547$	8542.01	0.667696	0.333848	+	0.942627i	$0.391653\pi$
$548$	−7864.78	−0.613078
$549$	−2657.75	−0.206612
$550$	25530.0	1.97928
$551$	−3705.39	−0.286488
$552$	1225.76	0.0945141
$553$	37965.5	2.91945
$554$	7194.02	0.551705
$555$	2991.31	0.228782
$556$	1162.72	0.0886876
$557$	19707.8	1.49919	0.749593	−	0.661899i	$-0.230249\pi$
$557$	19707.8	1.49919	0.749593	+	0.661899i	$0.230249\pi$
$558$	512.189	0.0388579
$559$	−2563.81	−0.193985
$560$	55547.1	4.19160
$561$	−5203.17	−0.391583
$562$	−1495.27	−0.112232
$563$	9325.91	0.698118	0.349059	−	0.937101i	$-0.386501\pi$
$563$	9325.91	0.698118	0.349059	+	0.937101i	$0.386501\pi$
$564$	−749.613	−0.0559653
$565$	25894.8	1.92815
$566$	−4243.49	−0.315136
$567$	2951.05	0.218576
$568$	−4013.60	−0.296491
$569$	16753.3	1.23433	0.617166	−	0.786833i	$-0.288281\pi$
$569$	16753.3	1.23433	0.617166	+	0.786833i	$0.288281\pi$
$570$	24362.3	1.79022
$571$	13299.2	0.974699	0.487349	−	0.873207i	$-0.337964\pi$
$571$	13299.2	0.974699	0.487349	+	0.873207i	$0.337964\pi$
$572$	1254.20	0.0916793
$573$	−8811.85	−0.642444
$574$	−51554.6	−3.74886
$575$	5953.16	0.431763
$576$	2381.57	0.172278
$577$	15468.6	1.11606	0.558030	−	0.829821i	$-0.311557\pi$
$577$	15468.6	1.11606	0.558030	+	0.829821i	$0.311557\pi$
$578$	5382.05	0.387307
$579$	−11863.4	−0.851514
$580$	1434.01	0.102662
$581$	−26931.6	−1.92308
$582$	−2626.74	−0.187083
$583$	18358.6	1.30418
$584$	−8455.23	−0.599109
$585$	2881.74	0.203667
$586$	−19849.4	−1.39927
$587$	−21294.1	−1.49728	−0.748639	−	0.662978i	$-0.769292\pi$
$587$	−21294.1	−1.49728	−0.748639	+	0.662978i	$0.769292\pi$
$588$	7453.34	0.522739
$589$	−2241.48	−0.156806
$590$	42226.2	2.94648
$591$	3358.07	0.233727
$592$	3960.66	0.274970
$593$	21433.4	1.48425	0.742127	−	0.670259i	$-0.233817\pi$
$593$	21433.4	1.48425	0.742127	+	0.670259i	$0.233817\pi$
$594$	2663.14	0.183956
$595$	−40716.3	−2.80539
$596$	544.945	0.0374527
$597$	16253.2	1.11424
$598$	1219.43	0.0833886
$599$	24294.8	1.65719	0.828596	−	0.559846i	$-0.189140\pi$
$599$	24294.8	1.65719	0.828596	+	0.559846i	$0.189140\pi$
$600$	13794.2	0.938577
$601$	−10419.6	−0.707195	−0.353597	−	0.935398i	$-0.615042\pi$
$601$	−10419.6	−0.707195	−0.353597	+	0.935398i	$0.615042\pi$
$602$	−18540.7	−1.25525
$603$	−1514.98	−0.102313
$604$	−2832.62	−0.190824
$605$	7965.03	0.535247
$606$	−10945.9	−0.733737
$607$	−19191.9	−1.28332	−0.641659	−	0.766990i	$-0.721754\pi$
$607$	−19191.9	−1.28332	−0.641659	+	0.766990i	$0.721754\pi$
$608$	14098.5	0.940408
$609$	−3169.65	−0.210904
$610$	−18768.6	−1.24577
$611$	1617.98	0.107130
$612$	1295.78	0.0855864
$613$	−1782.00	−0.117413	−0.0587065	−	0.998275i	$-0.518698\pi$
$613$	−1782.00	−0.117413	−0.0587065	+	0.998275i	$0.518698\pi$
$614$	9897.52	0.650540
$615$	−25637.7	−1.68099
$616$	−19678.4	−1.28712
$617$	18903.3	1.23342	0.616709	−	0.787191i	$-0.288466\pi$
$617$	18903.3	1.23342	0.616709	+	0.787191i	$0.288466\pi$
$618$	−14826.0	−0.965030
$619$	10906.1	0.708161	0.354080	−	0.935215i	$-0.384794\pi$
$619$	10906.1	0.708161	0.354080	+	0.935215i	$0.384794\pi$
$620$	867.466	0.0561908
$621$	621.000	0.0401286
$622$	−6870.85	−0.442920
$623$	−22474.7	−1.44531
$624$	3815.58	0.244784
$625$	19015.4	1.21699
$626$	−19386.4	−1.23776
$627$	−11654.6	−0.742331
$628$	7978.57	0.506974
$629$	−2903.19	−0.184034
$630$	20839.9	1.31791
$631$	19987.9	1.26102	0.630511	−	0.776180i	$-0.282845\pi$
$631$	19987.9	1.26102	0.630511	+	0.776180i	$0.282845\pi$
$632$	18512.0	1.16514
$633$	7529.77	0.472798
$634$	−27280.8	−1.70893
$635$	24305.4	1.51895
$636$	−4571.97	−0.285048
$637$	−16087.5	−1.00064
$638$	−2860.41	−0.177500
$639$	−2033.39	−0.125884
$640$	34112.3	2.10689
$641$	9785.59	0.602976	0.301488	−	0.953470i	$-0.402517\pi$
$641$	9785.59	0.602976	0.301488	+	0.953470i	$0.402517\pi$
$642$	6743.49	0.414555
$643$	−6996.65	−0.429115	−0.214557	−	0.976711i	$-0.568831\pi$
$643$	−6996.65	−0.429115	−0.214557	+	0.976711i	$0.568831\pi$
$644$	2114.96	0.129412
$645$	−9220.13	−0.562856
$646$	−23644.6	−1.44007
$647$	15946.8	0.968985	0.484493	−	0.874795i	$-0.339004\pi$
$647$	15946.8	0.968985	0.484493	+	0.874795i	$0.339004\pi$
$648$	1438.93	0.0872325
$649$	−20200.5	−1.22179
$650$	13723.0	0.828095
$651$	−1917.39	−0.115436
$652$	1255.67	0.0754228
$653$	6129.10	0.367305	0.183653	−	0.982991i	$-0.441208\pi$
$653$	6129.10	0.367305	0.183653	+	0.982991i	$0.441208\pi$
$654$	1441.75	0.0862032
$655$	17981.3	1.07265
$656$	−33945.7	−2.02036
$657$	−4283.63	−0.254369
$658$	11700.8	0.693226
$659$	−18830.7	−1.11311	−0.556556	−	0.830810i	$-0.687878\pi$
$659$	−18830.7	−1.11311	−0.556556	+	0.830810i	$0.687878\pi$
$660$	4510.42	0.266012
$661$	13429.4	0.790232	0.395116	−	0.918631i	$-0.370704\pi$
$661$	13429.4	0.790232	0.395116	+	0.918631i	$0.370704\pi$
$662$	30541.7	1.79311
$663$	−2796.84	−0.163832
$664$	−13131.8	−0.767491
$665$	−91200.9	−5.31823
$666$	1485.94	0.0864550
$667$	−667.000	−0.0387202
$668$	7908.96	0.458094
$669$	12431.0	0.718402
$670$	−10698.6	−0.616899
$671$	8978.68	0.516569
$672$	12060.0	0.692300
$673$	−18744.2	−1.07361	−0.536803	−	0.843708i	$-0.680368\pi$
$673$	−18744.2	−1.07361	−0.536803	+	0.843708i	$0.680368\pi$
$674$	10403.7	0.594564
$675$	6988.49	0.398500
$676$	−4870.99	−0.277139
$677$	−17655.1	−1.00228	−0.501139	−	0.865367i	$-0.667086\pi$
$677$	−17655.1	−1.00228	−0.501139	+	0.865367i	$0.667086\pi$
$678$	12863.3	0.728632
$679$	9833.28	0.555768
$680$	−19853.3	−1.11962
$681$	3990.44	0.224543
$682$	−1730.33	−0.0971522
$683$	−20873.7	−1.16942	−0.584708	−	0.811244i	$-0.698791\pi$
$683$	−20873.7	−1.16942	−0.584708	+	0.811244i	$0.698791\pi$
$684$	2902.43	0.162248
$685$	61048.4	3.40517
$686$	−75800.4	−4.21877
$687$	13172.3	0.731523
$688$	−12208.0	−0.676488
$689$	9868.24	0.545646
$690$	4385.41	0.241956
$691$	21973.9	1.20974	0.604868	−	0.796326i	$-0.293226\pi$
$691$	21973.9	1.20974	0.604868	+	0.796326i	$0.293226\pi$
$692$	2839.24	0.155971
$693$	−9969.55	−0.546482
$694$	31905.6	1.74513
$695$	−9025.33	−0.492590
$696$	−1545.52	−0.0841708
$697$	24882.4	1.35221
$698$	4250.47	0.230491
$699$	6548.57	0.354348
$700$	23801.0	1.28513
$701$	−27118.8	−1.46114	−0.730572	−	0.682836i	$-0.760746\pi$
$701$	−27118.8	−1.46114	−0.730572	+	0.682836i	$0.760746\pi$
$702$	1431.51	0.0769642
$703$	−6502.88	−0.348877
$704$	−8045.66	−0.430727
$705$	5818.69	0.310843
$706$	−17610.8	−0.938799
$707$	40976.1	2.17972
$708$	5030.66	0.267039
$709$	−18759.1	−0.993671	−0.496836	−	0.867845i	$-0.665505\pi$
$709$	−18759.1	−0.993671	−0.496836	+	0.867845i	$0.665505\pi$
$710$	−14359.5	−0.759018
$711$	9378.65	0.494693
$712$	−10958.7	−0.576818
$713$	−403.484	−0.0211930
$714$	−20225.9	−1.06013
$715$	−9735.39	−0.509207
$716$	1233.52	0.0643836
$717$	6988.42	0.363999
$718$	−23219.9	−1.20691
$719$	−32808.4	−1.70174	−0.850868	−	0.525379i	$-0.823923\pi$
$719$	−32808.4	−1.70174	−0.850868	+	0.525379i	$0.823923\pi$
$720$	13721.8	0.710254
$721$	55501.5	2.86683
$722$	−30710.7	−1.58301
$723$	−12764.8	−0.656606
$724$	−10603.4	−0.544301
$725$	−7506.16	−0.384513
$726$	3956.64	0.202266
$727$	13418.4	0.684542	0.342271	−	0.939601i	$-0.388804\pi$
$727$	13418.4	0.684542	0.342271	+	0.939601i	$0.388804\pi$
$728$	−10577.6	−0.538507
$729$	729.000	0.0370370
$730$	−30250.4	−1.53372
$731$	8948.50	0.452766
$732$	−2236.02	−0.112904
$733$	−2325.59	−0.117186	−0.0585931	−	0.998282i	$-0.518661\pi$
$733$	−2325.59	−0.117186	−0.0585931	+	0.998282i	$0.518661\pi$
$734$	−7641.84	−0.384285
$735$	−57854.7	−2.90341
$736$	2537.83	0.127100
$737$	5118.08	0.255803
$738$	−12735.6	−0.635234
$739$	6074.10	0.302354	0.151177	−	0.988507i	$-0.451694\pi$
$739$	6074.10	0.302354	0.151177	+	0.988507i	$0.451694\pi$
$740$	2516.65	0.125019
$741$	−6264.68	−0.310578
$742$	71364.1	3.53081
$743$	15630.3	0.771765	0.385882	−	0.922548i	$-0.373897\pi$
$743$	15630.3	0.771765	0.385882	+	0.922548i	$0.373897\pi$
$744$	−934.922	−0.0460697
$745$	−4230.00	−0.208020
$746$	18550.3	0.910424
$747$	−6652.92	−0.325860
$748$	−4377.54	−0.213982
$749$	−25244.4	−1.23152
$750$	25517.9	1.24238
$751$	−3139.71	−0.152556	−0.0762780	−	0.997087i	$-0.524304\pi$
$751$	−3139.71	−0.152556	−0.0762780	+	0.997087i	$0.524304\pi$
$752$	7704.26	0.373598
$753$	−4937.26	−0.238942
$754$	−1537.55	−0.0742629
$755$	21987.5	1.05988
$756$	2482.78	0.119442
$757$	−22244.6	−1.06803	−0.534013	−	0.845476i	$-0.679317\pi$
$757$	−22244.6	−1.06803	−0.534013	+	0.845476i	$0.679317\pi$
$758$	−40709.2	−1.95069
$759$	−2097.93	−0.100329
$760$	−44469.6	−2.12248
$761$	18135.4	0.863871	0.431936	−	0.901904i	$-0.357831\pi$
$761$	18135.4	0.863871	0.431936	+	0.901904i	$0.357831\pi$
$762$	12073.8	0.573998
$763$	−5397.23	−0.256085
$764$	−7413.60	−0.351066
$765$	−10058.2	−0.475365
$766$	−5167.42	−0.243742
$767$	−10858.3	−0.511174
$768$	10594.5	0.497782
$769$	−13698.6	−0.642372	−0.321186	−	0.947016i	$-0.604082\pi$
$769$	−13698.6	−0.642372	−0.321186	+	0.947016i	$0.604082\pi$
$770$	−70403.4	−3.29502
$771$	22406.7	1.04664
$772$	−9980.95	−0.465314
$773$	−18656.4	−0.868080	−0.434040	−	0.900894i	$-0.642912\pi$
$773$	−18656.4	−0.868080	−0.434040	+	0.900894i	$0.642912\pi$
$774$	−4580.12	−0.212699
$775$	−4540.65	−0.210458
$776$	4794.71	0.221804
$777$	−5562.65	−0.256833
$778$	−33552.9	−1.54618
$779$	55734.3	2.56340
$780$	2424.47	0.111295
$781$	6869.42	0.314734
$782$	−4256.21	−0.194632
$783$	−783.000	−0.0357371
$784$	−76602.9	−3.48956
$785$	−61931.7	−2.81584
$786$	8932.26	0.405347
$787$	−29504.1	−1.33635	−0.668176	−	0.744003i	$-0.732925\pi$
$787$	−29504.1	−1.33635	−0.668176	+	0.744003i	$0.732925\pi$
$788$	2825.22	0.127721
$789$	1592.28	0.0718463
$790$	66230.6	2.98276
$791$	−48154.1	−2.16456
$792$	−4861.16	−0.218098
$793$	4826.28	0.216124
$794$	−1994.93	−0.0891654
$795$	35488.8	1.58322
$796$	13674.2	0.608879
$797$	1655.79	0.0735898	0.0367949	−	0.999323i	$-0.488285\pi$
$797$	1655.79	0.0735898	0.0367949	+	0.999323i	$0.488285\pi$
$798$	−45304.3	−2.00972
$799$	−5647.27	−0.250045
$800$	28559.8	1.26218
$801$	−5551.95	−0.244904
$802$	−40021.3	−1.76210
$803$	14471.4	0.635971
$804$	−1274.59	−0.0559096
$805$	−16416.9	−0.718781
$806$	−930.098	−0.0406468
$807$	14089.1	0.614573
$808$	19980.0	0.869916
$809$	18010.6	0.782717	0.391358	−	0.920238i	$-0.372005\pi$
$809$	18010.6	0.782717	0.391358	+	0.920238i	$0.372005\pi$
$810$	5148.09	0.223315
$811$	−27421.5	−1.18730	−0.593648	−	0.804725i	$-0.702313\pi$
$811$	−27421.5	−1.18730	−0.593648	+	0.804725i	$0.702313\pi$
$812$	−2666.69	−0.115249
$813$	5850.40	0.252377
$814$	−5019.96	−0.216154
$815$	−9746.79	−0.418914
$816$	−13317.6	−0.571335
$817$	20043.8	0.858317
$818$	−41881.9	−1.79018
$819$	−5358.89	−0.228638
$820$	−21569.5	−0.918587
$821$	31769.7	1.35051	0.675255	−	0.737584i	$-0.264034\pi$
$821$	31769.7	1.35051	0.675255	+	0.737584i	$0.264034\pi$
$822$	30325.9	1.28679
$823$	21793.0	0.923033	0.461517	−	0.887131i	$-0.347305\pi$
$823$	21793.0	0.923033	0.461517	+	0.887131i	$0.347305\pi$
$824$	27062.5	1.14414
$825$	−23609.3	−0.996326
$826$	−78523.9	−3.30774
$827$	−6655.30	−0.279840	−0.139920	−	0.990163i	$-0.544685\pi$
$827$	−6655.30	−0.279840	−0.139920	+	0.990163i	$0.544685\pi$
$828$	522.461	0.0219285
$829$	18992.4	0.795696	0.397848	−	0.917451i	$-0.369757\pi$
$829$	18992.4	0.795696	0.397848	+	0.917451i	$0.369757\pi$
$830$	−46981.9	−1.96478
$831$	−6652.78	−0.277717
$832$	−4324.75	−0.180209
$833$	56150.3	2.33553
$834$	−4483.35	−0.186146
$835$	−61391.4	−2.54436
$836$	−9805.30	−0.405650
$837$	−473.655	−0.0195602
$838$	−14974.1	−0.617269
$839$	−30597.6	−1.25906	−0.629528	−	0.776978i	$-0.716752\pi$
$839$	−30597.6	−1.25906	−0.629528	+	0.776978i	$0.716752\pi$
$840$	−38039.9	−1.56250
$841$	841.000	0.0344828
$842$	−25171.0	−1.03023
$843$	1382.78	0.0564950
$844$	6334.96	0.258363
$845$	37809.8	1.53929
$846$	2890.45	0.117465
$847$	−14811.8	−0.600873
$848$	46989.1	1.90284
$849$	3924.23	0.158633
$850$	−47897.8	−1.93280
$851$	−1170.57	−0.0471523
$852$	−1710.74	−0.0687898
$853$	−16666.1	−0.668977	−0.334489	−	0.942400i	$-0.608564\pi$
$853$	−16666.1	−0.668977	−0.334489	+	0.942400i	$0.608564\pi$
$854$	34902.2	1.39851
$855$	−22529.4	−0.901158
$856$	−12309.2	−0.491495
$857$	46890.4	1.86902	0.934508	−	0.355943i	$-0.115840\pi$
$857$	46890.4	1.86902	0.934508	+	0.355943i	$0.115840\pi$
$858$	−4836.08	−0.192425
$859$	−3184.33	−0.126482	−0.0632409	−	0.997998i	$-0.520144\pi$
$859$	−3184.33	−0.126482	−0.0632409	+	0.997998i	$0.520144\pi$
$860$	−7757.09	−0.307575
$861$	47675.9	1.88710
$862$	−33466.6	−1.32236
$863$	−32732.9	−1.29112	−0.645562	−	0.763708i	$-0.723377\pi$
$863$	−32732.9	−1.29112	−0.645562	+	0.763708i	$0.723377\pi$
$864$	2979.20	0.117308
$865$	−22038.9	−0.866296
$866$	36195.6	1.42030
$867$	−4977.13	−0.194962
$868$	−1613.14	−0.0630803
$869$	−31683.9	−1.23683
$870$	−5529.43	−0.215477
$871$	2751.10	0.107024
$872$	−2631.69	−0.102202
$873$	2429.12	0.0941733
$874$	−9533.54	−0.368966
$875$	−95527.0	−3.69075
$876$	−3603.91	−0.139001
$877$	8311.81	0.320034	0.160017	−	0.987114i	$-0.448845\pi$
$877$	8311.81	0.320034	0.160017	+	0.987114i	$0.448845\pi$
$878$	−46299.0	−1.77963
$879$	18356.1	0.704362
$880$	−46356.5	−1.77577
$881$	−21562.5	−0.824585	−0.412292	−	0.911052i	$-0.635272\pi$
$881$	−21562.5	−0.824585	−0.412292	+	0.911052i	$0.635272\pi$
$882$	−28739.5	−1.09717
$883$	−7903.59	−0.301220	−0.150610	−	0.988593i	$-0.548124\pi$
$883$	−7903.59	−0.301220	−0.150610	+	0.988593i	$0.548124\pi$
$884$	−2353.04	−0.0895265
$885$	−39049.3	−1.48319
$886$	42705.4	1.61932
$887$	29610.2	1.12087	0.560436	−	0.828198i	$-0.310634\pi$
$887$	29610.2	1.12087	0.560436	+	0.828198i	$0.310634\pi$
$888$	−2712.35	−0.102501
$889$	−45198.4	−1.70518
$890$	−39207.0	−1.47665
$891$	−2462.78	−0.0925997
$892$	10458.5	0.392574
$893$	−12649.4	−0.474015
$894$	−2101.26	−0.0786093
$895$	−9574.87	−0.357601
$896$	−63435.4	−2.36521
$897$	−1127.69	−0.0419760
$898$	39879.7	1.48196
$899$	508.740	0.0188737
$900$	5879.57	0.217762
$901$	−34443.3	−1.27355
$902$	43024.6	1.58821
$903$	17145.8	0.631867
$904$	−23480.0	−0.863864
$905$	82306.6	3.02317
$906$	10922.3	0.400519
$907$	−2167.48	−0.0793495	−0.0396747	−	0.999213i	$-0.512632\pi$
$907$	−2167.48	−0.0793495	−0.0396747	+	0.999213i	$0.512632\pi$
$908$	3357.24	0.122703
$909$	10122.3	0.369348
$910$	−37843.7	−1.37858
$911$	−47945.3	−1.74369	−0.871843	−	0.489786i	$-0.837075\pi$
$911$	−47945.3	−1.74369	−0.871843	+	0.489786i	$0.837075\pi$
$912$	−29830.2	−1.08309
$913$	22475.6	0.814713
$914$	−10790.9	−0.390514
$915$	17356.6	0.627093
$916$	11082.2	0.399744
$917$	−33438.1	−1.20417
$918$	−4996.42	−0.179637
$919$	15104.2	0.542157	0.271078	−	0.962557i	$-0.412620\pi$
$919$	15104.2	0.542157	0.271078	+	0.962557i	$0.412620\pi$
$920$	−8004.88	−0.286862
$921$	−9152.88	−0.327468
$922$	15535.3	0.554912
$923$	3692.49	0.131679
$924$	−8387.60	−0.298627
$925$	−13173.1	−0.468248
$926$	39851.8	1.41427
$927$	13710.6	0.485776
$928$	−3199.88	−0.113191
$929$	−42443.0	−1.49893	−0.749467	−	0.662041i	$-0.769690\pi$
$929$	−42443.0	−1.49893	−0.749467	+	0.662041i	$0.769690\pi$
$930$	−3344.88	−0.117939
$931$	125772.	4.42750
$932$	5509.45	0.193635
$933$	6353.93	0.222956
$934$	13757.5	0.481970
$935$	33979.6	1.18850
$936$	−2613.00	−0.0912485
$937$	−24659.3	−0.859748	−0.429874	−	0.902889i	$-0.641442\pi$
$937$	−24659.3	−0.859748	−0.429874	+	0.902889i	$0.641442\pi$
$938$	19895.1	0.692537
$939$	17927.9	0.623061
$940$	4895.39	0.169862
$941$	33869.2	1.17333	0.586666	−	0.809829i	$-0.300440\pi$
$941$	33869.2	1.17333	0.586666	+	0.809829i	$0.300440\pi$
$942$	−30764.7	−1.06409
$943$	10032.6	0.346455
$944$	−51703.4	−1.78263
$945$	−19272.0	−0.663405
$946$	15473.0	0.531788
$947$	5879.90	0.201765	0.100882	−	0.994898i	$-0.467833\pi$
$947$	5879.90	0.201765	0.100882	+	0.994898i	$0.467833\pi$
$948$	7890.46	0.270327
$949$	7778.76	0.266079
$950$	−107287.	−3.66404
$951$	25228.4	0.860237
$952$	36919.3	1.25689
$953$	15036.8	0.511111	0.255556	−	0.966794i	$-0.417742\pi$
$953$	15036.8	0.511111	0.255556	+	0.966794i	$0.417742\pi$
$954$	17629.1	0.598285
$955$	57546.2	1.94990
$956$	5879.51	0.198909
$957$	2645.21	0.0893496
$958$	−1759.97	−0.0593549
$959$	−113526.	−3.82267
$960$	−15552.9	−0.522885
$961$	−29483.3	−0.989670
$962$	−2698.36	−0.0904351
$963$	−6236.15	−0.208678
$964$	−10739.3	−0.358806
$965$	77474.6	2.58445
$966$	−8155.12	−0.271622
$967$	−36445.2	−1.21199	−0.605997	−	0.795467i	$-0.707226\pi$
$967$	−36445.2	−1.21199	−0.605997	+	0.795467i	$0.707226\pi$
$968$	−7222.24	−0.239805
$969$	21865.7	0.724900
$970$	17154.1	0.567819
$971$	−49219.4	−1.62670	−0.813350	−	0.581774i	$-0.802359\pi$
$971$	−49219.4	−1.62670	−0.813350	+	0.581774i	$0.802359\pi$
$972$	613.324	0.0202391
$973$	16783.5	0.552986
$974$	952.766	0.0313435
$975$	−12690.6	−0.416845
$976$	22981.0	0.753694
$977$	−20970.8	−0.686710	−0.343355	−	0.939206i	$-0.611563\pi$
$977$	−20970.8	−0.686710	−0.343355	+	0.939206i	$0.611563\pi$
$978$	−4841.74	−0.158304
$979$	18756.2	0.612308
$980$	−48674.4	−1.58658
$981$	−1333.28	−0.0433928
$982$	18407.0	0.598158
$983$	−25136.2	−0.815586	−0.407793	−	0.913074i	$-0.633701\pi$
$983$	−25136.2	−0.815586	−0.407793	+	0.913074i	$0.633701\pi$
$984$	23246.8	0.753132
$985$	−21930.0	−0.709390
$986$	5366.53	0.173332
$987$	−10820.5	−0.348955
$988$	−5270.61	−0.169717
$989$	3608.05	0.116005
$990$	−17391.8	−0.558331
$991$	−9053.21	−0.290196	−0.145098	−	0.989417i	$-0.546350\pi$
$991$	−9053.21	−0.290196	−0.145098	+	0.989417i	$0.546350\pi$
$992$	−1935.68	−0.0619535
$993$	−28243.9	−0.902611
$994$	26703.0	0.852080
$995$	−106142.	−3.38184
$996$	−5597.25	−0.178068
$997$	14842.5	0.471482	0.235741	−	0.971816i	$-0.424248\pi$
$997$	14842.5	0.471482	0.235741	+	0.971816i	$0.424248\pi$
$998$	27906.4	0.885132
$999$	−1374.15	−0.0435196

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.h.1.10	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.h.1.10	✓	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-3.24407 q^{2} +3.00000 q^{3} +2.52397 q^{4} -19.5917 q^{5} -9.73220 q^{6} +36.4327 q^{7} +17.7646 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.24407 q^{2} +3.00000 q^{3} +2.52397 q^{4} -19.5917 q^{5} -9.73220 q^{6} +36.4327 q^{7} +17.7646 q^{8} +9.00000 q^{9} +63.5566 q^{10} -30.4047 q^{11} +7.57190 q^{12} -16.3433 q^{13} -118.190 q^{14} -58.7750 q^{15} -77.8213 q^{16} +57.0435 q^{17} -29.1966 q^{18} +127.772 q^{19} -49.4487 q^{20} +109.298 q^{21} +98.6350 q^{22} +23.0000 q^{23} +53.2939 q^{24} +258.833 q^{25} +53.0189 q^{26} +27.0000 q^{27} +91.9549 q^{28} -29.0000 q^{29} +190.670 q^{30} -17.5428 q^{31} +110.341 q^{32} -91.2142 q^{33} -185.053 q^{34} -713.777 q^{35} +22.7157 q^{36} -50.8943 q^{37} -414.502 q^{38} -49.0300 q^{39} -348.038 q^{40} +436.201 q^{41} -354.570 q^{42} +156.872 q^{43} -76.7405 q^{44} -176.325 q^{45} -74.6135 q^{46} -98.9994 q^{47} -233.464 q^{48} +984.343 q^{49} -839.672 q^{50} +171.130 q^{51} -41.2500 q^{52} -603.808 q^{53} -87.5898 q^{54} +595.679 q^{55} +647.213 q^{56} +383.317 q^{57} +94.0779 q^{58} +664.386 q^{59} -148.346 q^{60} -295.305 q^{61} +56.9099 q^{62} +327.894 q^{63} +264.618 q^{64} +320.193 q^{65} +295.905 q^{66} -168.332 q^{67} +143.976 q^{68} +69.0000 q^{69} +2315.54 q^{70} -225.932 q^{71} +159.882 q^{72} -475.959 q^{73} +165.104 q^{74} +776.499 q^{75} +322.493 q^{76} -1107.73 q^{77} +159.057 q^{78} +1042.07 q^{79} +1524.65 q^{80} +81.0000 q^{81} -1415.06 q^{82} -739.213 q^{83} +275.865 q^{84} -1117.58 q^{85} -508.902 q^{86} -87.0000 q^{87} -540.129 q^{88} -616.883 q^{89} +572.010 q^{90} -595.432 q^{91} +58.0512 q^{92} -52.6283 q^{93} +321.161 q^{94} -2503.27 q^{95} +331.022 q^{96} +269.902 q^{97} -3193.27 q^{98} -273.643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more