LMFDB - Embedded newform 2001.4.a.h.1.12

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			1.12
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)

$f(q)$	$=$	$q-3.00964 q^{2} +3.00000 q^{3} +1.05794 q^{4} +17.7761 q^{5} -9.02892 q^{6} +14.5114 q^{7} +20.8931 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.00964 q^{2} +3.00000 q^{3} +1.05794 q^{4} +17.7761 q^{5} -9.02892 q^{6} +14.5114 q^{7} +20.8931 q^{8} +9.00000 q^{9} -53.4996 q^{10} -2.09165 q^{11} +3.17383 q^{12} -1.54642 q^{13} -43.6742 q^{14} +53.3283 q^{15} -71.3443 q^{16} +76.3653 q^{17} -27.0868 q^{18} +105.645 q^{19} +18.8061 q^{20} +43.5343 q^{21} +6.29511 q^{22} +23.0000 q^{23} +62.6793 q^{24} +190.989 q^{25} +4.65416 q^{26} +27.0000 q^{27} +15.3523 q^{28} -29.0000 q^{29} -160.499 q^{30} -201.679 q^{31} +47.5759 q^{32} -6.27495 q^{33} -229.832 q^{34} +257.957 q^{35} +9.52148 q^{36} +177.976 q^{37} -317.955 q^{38} -4.63925 q^{39} +371.398 q^{40} +171.144 q^{41} -131.023 q^{42} -372.314 q^{43} -2.21284 q^{44} +159.985 q^{45} -69.2218 q^{46} -121.968 q^{47} -214.033 q^{48} -132.418 q^{49} -574.809 q^{50} +229.096 q^{51} -1.63602 q^{52} +499.802 q^{53} -81.2603 q^{54} -37.1813 q^{55} +303.189 q^{56} +316.936 q^{57} +87.2796 q^{58} +684.081 q^{59} +56.4182 q^{60} -117.017 q^{61} +606.981 q^{62} +130.603 q^{63} +427.568 q^{64} -27.4892 q^{65} +18.8853 q^{66} -117.053 q^{67} +80.7900 q^{68} +69.0000 q^{69} -776.357 q^{70} +245.630 q^{71} +188.038 q^{72} +941.734 q^{73} -535.643 q^{74} +572.968 q^{75} +111.767 q^{76} -30.3528 q^{77} +13.9625 q^{78} +593.523 q^{79} -1268.22 q^{80} +81.0000 q^{81} -515.083 q^{82} +859.385 q^{83} +46.0568 q^{84} +1357.48 q^{85} +1120.53 q^{86} -87.0000 q^{87} -43.7010 q^{88} +546.183 q^{89} -481.497 q^{90} -22.4407 q^{91} +24.3327 q^{92} -605.037 q^{93} +367.081 q^{94} +1877.96 q^{95} +142.728 q^{96} -913.904 q^{97} +398.532 q^{98} -18.8248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.00964	−1.06407	−0.532034	−	0.846723i	$-0.678572\pi$
$2$	−3.00964	−1.06407	−0.532034	+	0.846723i	$0.678572\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	1.05794	0.132243
$5$	17.7761	1.58994	0.794971	−	0.606648i	$-0.207486\pi$
$5$	17.7761	1.58994	0.794971	+	0.606648i	$0.207486\pi$
$6$	−9.02892	−0.614340
$7$	14.5114	0.783544	0.391772	−	0.920062i	$-0.371862\pi$
$7$	14.5114	0.783544	0.391772	+	0.920062i	$0.371862\pi$
$8$	20.8931	0.923354
$9$	9.00000	0.333333
$10$	−53.4996	−1.69181
$11$	−2.09165	−0.0573324	−0.0286662	−	0.999589i	$-0.509126\pi$
$11$	−2.09165	−0.0573324	−0.0286662	+	0.999589i	$0.509126\pi$
$12$	3.17383	0.0763504
$13$	−1.54642	−0.0329922	−0.0164961	−	0.999864i	$-0.505251\pi$
$13$	−1.54642	−0.0329922	−0.0164961	+	0.999864i	$0.505251\pi$
$14$	−43.6742	−0.833745
$15$	53.3283	0.917953
$16$	−71.3443	−1.11475
$17$	76.3653	1.08949	0.544744	−	0.838602i	$-0.316627\pi$
$17$	76.3653	1.08949	0.544744	+	0.838602i	$0.316627\pi$
$18$	−27.0868	−0.354690
$19$	105.645	1.27562	0.637809	−	0.770195i	$-0.279841\pi$
$19$	105.645	1.27562	0.637809	+	0.770195i	$0.279841\pi$
$20$	18.8061	0.210258
$21$	43.5343	0.452379
$22$	6.29511	0.0610056
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	62.6793	0.533098
$25$	190.989	1.52791
$26$	4.65416	0.0351060
$27$	27.0000	0.192450
$28$	15.3523	0.103618
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−160.499	−0.976765
$31$	−201.679	−1.16847	−0.584235	−	0.811584i	$-0.698606\pi$
$31$	−201.679	−1.16847	−0.584235	+	0.811584i	$0.698606\pi$
$32$	47.5759	0.262822
$33$	−6.27495	−0.0331008
$34$	−229.832	−1.15929
$35$	257.957	1.24579
$36$	9.52148	0.0440809
$37$	177.976	0.790785	0.395392	−	0.918512i	$-0.370609\pi$
$37$	177.976	0.790785	0.395392	+	0.918512i	$0.370609\pi$
$38$	−317.955	−1.35734
$39$	−4.63925	−0.0190481
$40$	371.398	1.46808
$41$	171.144	0.651909	0.325954	−	0.945386i	$-0.394314\pi$
$41$	171.144	0.651909	0.325954	+	0.945386i	$0.394314\pi$
$42$	−131.023	−0.481363
$43$	−372.314	−1.32040	−0.660202	−	0.751088i	$-0.729530\pi$
$43$	−372.314	−1.32040	−0.660202	+	0.751088i	$0.729530\pi$
$44$	−2.21284	−0.00758179
$45$	159.985	0.529981
$46$	−69.2218	−0.221874
$47$	−121.968	−0.378530	−0.189265	−	0.981926i	$-0.560610\pi$
$47$	−121.968	−0.378530	−0.189265	+	0.981926i	$0.560610\pi$
$48$	−214.033	−0.643604
$49$	−132.418	−0.386059
$50$	−574.809	−1.62581
$51$	229.096	0.629016
$52$	−1.63602	−0.00436298
$53$	499.802	1.29534	0.647670	−	0.761921i	$-0.275743\pi$
$53$	499.802	1.29534	0.647670	+	0.761921i	$0.275743\pi$
$54$	−81.2603	−0.204780
$55$	−37.1813	−0.0911551
$56$	303.189	0.723488
$57$	316.936	0.736478
$58$	87.2796	0.197593
$59$	684.081	1.50949	0.754744	−	0.656020i	$-0.227761\pi$
$59$	684.081	1.50949	0.754744	+	0.656020i	$0.227761\pi$
$60$	56.4182	0.121393
$61$	−117.017	−0.245615	−0.122807	−	0.992431i	$-0.539190\pi$
$61$	−117.017	−0.245615	−0.122807	+	0.992431i	$0.539190\pi$
$62$	606.981	1.24333
$63$	130.603	0.261181
$64$	427.568	0.835094
$65$	−27.4892	−0.0524557
$66$	18.8853	0.0352216
$67$	−117.053	−0.213437	−0.106719	−	0.994289i	$-0.534034\pi$
$67$	−117.053	−0.213437	−0.106719	+	0.994289i	$0.534034\pi$
$68$	80.7900	0.144077
$69$	69.0000	0.120386
$70$	−776.357	−1.32561
$71$	245.630	0.410576	0.205288	−	0.978702i	$-0.434187\pi$
$71$	245.630	0.410576	0.205288	+	0.978702i	$0.434187\pi$
$72$	188.038	0.307785
$73$	941.734	1.50988	0.754942	−	0.655791i	$-0.227665\pi$
$73$	941.734	1.50988	0.754942	+	0.655791i	$0.227665\pi$
$74$	−535.643	−0.841450
$75$	572.968	0.882142
$76$	111.767	0.168691
$77$	−30.3528	−0.0449224
$78$	13.9625	0.0202685
$79$	593.523	0.845273	0.422637	−	0.906299i	$-0.361105\pi$
$79$	593.523	0.845273	0.422637	+	0.906299i	$0.361105\pi$
$80$	−1268.22	−1.77239
$81$	81.0000	0.111111
$82$	−515.083	−0.693676
$83$	859.385	1.13650	0.568252	−	0.822855i	$-0.307620\pi$
$83$	859.385	1.13650	0.568252	+	0.822855i	$0.307620\pi$
$84$	46.0568	0.0598239
$85$	1357.48	1.73222
$86$	1120.53	1.40500
$87$	−87.0000	−0.107211
$88$	−43.7010	−0.0529380
$89$	546.183	0.650509	0.325255	−	0.945626i	$-0.394550\pi$
$89$	546.183	0.650509	0.325255	+	0.945626i	$0.394550\pi$
$90$	−481.497	−0.563936
$91$	−22.4407	−0.0258509
$92$	24.3327	0.0275745
$93$	−605.037	−0.674617
$94$	367.081	0.402782
$95$	1877.96	2.02816
$96$	142.728	0.151740
$97$	−913.904	−0.956628	−0.478314	−	0.878189i	$-0.658752\pi$
$97$	−913.904	−0.956628	−0.478314	+	0.878189i	$0.658752\pi$
$98$	398.532	0.410794
$99$	−18.8248	−0.0191108
$100$	202.056	0.202056
$101$	−760.630	−0.749361	−0.374681	−	0.927154i	$-0.622248\pi$
$101$	−760.630	−0.749361	−0.374681	+	0.927154i	$0.622248\pi$
$102$	−689.496	−0.669317
$103$	−61.0578	−0.0584097	−0.0292049	−	0.999573i	$-0.509298\pi$
$103$	−61.0578	−0.0584097	−0.0292049	+	0.999573i	$0.509298\pi$
$104$	−32.3095	−0.0304635
$105$	773.870	0.719256
$106$	−1504.22	−1.37833
$107$	−61.3292	−0.0554104	−0.0277052	−	0.999616i	$-0.508820\pi$
$107$	−61.3292	−0.0554104	−0.0277052	+	0.999616i	$0.508820\pi$
$108$	28.5644	0.0254501
$109$	−1439.85	−1.26526	−0.632628	−	0.774456i	$-0.718024\pi$
$109$	−1439.85	−1.26526	−0.632628	+	0.774456i	$0.718024\pi$
$110$	111.902	0.0969953
$111$	533.927	0.456560
$112$	−1035.31	−0.873459
$113$	−1087.30	−0.905173	−0.452587	−	0.891720i	$-0.649499\pi$
$113$	−1087.30	−0.905173	−0.452587	+	0.891720i	$0.649499\pi$
$114$	−953.865	−0.783663
$115$	408.850	0.331526
$116$	−30.6803	−0.0245569
$117$	−13.9178	−0.0109974
$118$	−2058.84	−1.60620
$119$	1108.17	0.853662
$120$	1114.19	0.847595
$121$	−1326.63	−0.996713
$122$	352.179	0.261351
$123$	513.433	0.376380
$124$	−213.365	−0.154522
$125$	1173.03	0.839353
$126$	−393.068	−0.277915
$127$	1244.37	0.869445	0.434723	−	0.900564i	$-0.356846\pi$
$127$	1244.37	0.869445	0.434723	+	0.900564i	$0.356846\pi$
$128$	−1667.43	−1.15142
$129$	−1116.94	−0.762336
$130$	82.7328	0.0558165
$131$	115.289	0.0768920	0.0384460	−	0.999261i	$-0.487759\pi$
$131$	115.289	0.0768920	0.0384460	+	0.999261i	$0.487759\pi$
$132$	−6.63853	−0.00437735
$133$	1533.07	0.999502
$134$	352.288	0.227112
$135$	479.954	0.305984
$136$	1595.51	1.00598
$137$	386.225	0.240857	0.120429	−	0.992722i	$-0.461573\pi$
$137$	386.225	0.240857	0.120429	+	0.992722i	$0.461573\pi$
$138$	−207.665	−0.128099
$139$	−333.309	−0.203388	−0.101694	−	0.994816i	$-0.532426\pi$
$139$	−333.309	−0.203388	−0.101694	+	0.994816i	$0.532426\pi$
$140$	272.903	0.164747
$141$	−365.905	−0.218544
$142$	−739.258	−0.436881
$143$	3.23456	0.00189152
$144$	−642.099	−0.371585
$145$	−515.507	−0.295245
$146$	−2834.28	−1.60662
$147$	−397.255	−0.222891
$148$	188.288	0.104576
$149$	−2918.83	−1.60483	−0.802417	−	0.596764i	$-0.796453\pi$
$149$	−2918.83	−1.60483	−0.802417	+	0.596764i	$0.796453\pi$
$150$	−1724.43	−0.938660
$151$	−2900.26	−1.56304	−0.781522	−	0.623878i	$-0.785556\pi$
$151$	−2900.26	−1.56304	−0.781522	+	0.623878i	$0.785556\pi$
$152$	2207.26	1.17785
$153$	687.287	0.363163
$154$	91.3511	0.0478005
$155$	−3585.06	−1.85780
$156$	−4.90806	−0.00251897
$157$	−3037.75	−1.54420	−0.772098	−	0.635504i	$-0.780792\pi$
$157$	−3037.75	−1.54420	−0.772098	+	0.635504i	$0.780792\pi$
$158$	−1786.29	−0.899429
$159$	1499.41	0.747865
$160$	845.713	0.417872
$161$	333.763	0.163380
$162$	−243.781	−0.118230
$163$	2486.22	1.19470	0.597350	−	0.801981i	$-0.296220\pi$
$163$	2486.22	1.19470	0.597350	+	0.801981i	$0.296220\pi$
$164$	181.061	0.0862102
$165$	−111.544	−0.0526284
$166$	−2586.44	−1.20932
$167$	2022.25	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$167$	2022.25	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$168$	909.567	0.417706
$169$	−2194.61	−0.998912
$170$	−4085.51	−1.84320
$171$	950.809	0.425206
$172$	−393.887	−0.174614
$173$	−3902.53	−1.71505	−0.857527	−	0.514440i	$-0.828000\pi$
$173$	−3902.53	−1.71505	−0.857527	+	0.514440i	$0.828000\pi$
$174$	261.839	0.114080
$175$	2771.53	1.19719
$176$	149.227	0.0639115
$177$	2052.24	0.871503
$178$	−1643.82	−0.692187
$179$	468.268	0.195531	0.0977653	−	0.995210i	$-0.468831\pi$
$179$	468.268	0.195531	0.0977653	+	0.995210i	$0.468831\pi$
$180$	169.255	0.0700861
$181$	3411.95	1.40115	0.700576	−	0.713578i	$-0.252927\pi$
$181$	3411.95	1.40115	0.700576	+	0.713578i	$0.252927\pi$
$182$	67.5386	0.0275071
$183$	−351.051	−0.141806
$184$	480.541	0.192533
$185$	3163.71	1.25730
$186$	1820.94	0.717839
$187$	−159.729	−0.0624629
$188$	−129.035	−0.0500578
$189$	391.809	0.150793
$190$	−5652.00	−2.15810
$191$	−99.6711	−0.0377589	−0.0188795	−	0.999822i	$-0.506010\pi$
$191$	−99.6711	−0.0377589	−0.0188795	+	0.999822i	$0.506010\pi$
$192$	1282.70	0.482142
$193$	2910.64	1.08556	0.542778	−	0.839876i	$-0.317373\pi$
$193$	2910.64	1.08556	0.542778	+	0.839876i	$0.317373\pi$
$194$	2750.52	1.01792
$195$	−82.4677	−0.0302853
$196$	−140.091	−0.0510535
$197$	1048.02	0.379026	0.189513	−	0.981878i	$-0.439309\pi$
$197$	1048.02	0.379026	0.189513	+	0.981878i	$0.439309\pi$
$198$	56.6560	0.0203352
$199$	3887.40	1.38477	0.692387	−	0.721526i	$-0.256559\pi$
$199$	3887.40	1.38477	0.692387	+	0.721526i	$0.256559\pi$
$200$	3990.36	1.41080
$201$	−351.159	−0.123228
$202$	2289.22	0.797372
$203$	−420.832	−0.145500
$204$	242.370	0.0831828
$205$	3042.28	1.03650
$206$	183.762	0.0621520
$207$	207.000	0.0695048
$208$	110.328	0.0367782
$209$	−220.973	−0.0731342
$210$	−2329.07	−0.765339
$211$	−1525.90	−0.497856	−0.248928	−	0.968522i	$-0.580078\pi$
$211$	−1525.90	−0.497856	−0.248928	+	0.968522i	$0.580078\pi$
$212$	528.761	0.171299
$213$	736.890	0.237046
$214$	184.579	0.0589605
$215$	−6618.29	−2.09937
$216$	564.114	0.177699
$217$	−2926.65	−0.915548
$218$	4333.44	1.34632
$219$	2825.20	0.871732
$220$	−39.3357	−0.0120546
$221$	−118.093	−0.0359446
$222$	−1606.93	−0.485811
$223$	−6047.26	−1.81594	−0.907970	−	0.419035i	$-0.862368\pi$
$223$	−6047.26	−1.81594	−0.907970	+	0.419035i	$0.862368\pi$
$224$	690.395	0.205933
$225$	1718.90	0.509305
$226$	3272.38	0.963167
$227$	608.659	0.177965	0.0889826	−	0.996033i	$-0.471638\pi$
$227$	608.659	0.177965	0.0889826	+	0.996033i	$0.471638\pi$
$228$	335.300	0.0973939
$229$	4291.18	1.23829	0.619147	−	0.785275i	$-0.287478\pi$
$229$	4291.18	1.23829	0.619147	+	0.785275i	$0.287478\pi$
$230$	−1230.49	−0.352766
$231$	−91.0585	−0.0259360
$232$	−605.900	−0.171462
$233$	−5167.10	−1.45282	−0.726412	−	0.687259i	$-0.758814\pi$
$233$	−5167.10	−1.45282	−0.726412	+	0.687259i	$0.758814\pi$
$234$	41.8875	0.0117020
$235$	−2168.12	−0.601840
$236$	723.718	0.199619
$237$	1780.57	0.488019
$238$	−3335.19	−0.908355
$239$	5370.47	1.45350	0.726751	−	0.686902i	$-0.241030\pi$
$239$	5370.47	1.45350	0.726751	+	0.686902i	$0.241030\pi$
$240$	−3804.67	−1.02329
$241$	3396.86	0.907929	0.453964	−	0.891020i	$-0.350009\pi$
$241$	3396.86	0.907929	0.453964	+	0.891020i	$0.350009\pi$
$242$	3992.67	1.06057
$243$	243.000	0.0641500
$244$	−123.797	−0.0324807
$245$	−2353.88	−0.613811
$246$	−1545.25	−0.400494
$247$	−163.372	−0.0420855
$248$	−4213.70	−1.07891
$249$	2578.16	0.656161
$250$	−3530.40	−0.893129
$251$	−3100.86	−0.779779	−0.389890	−	0.920862i	$-0.627487\pi$
$251$	−3100.86	−0.779779	−0.389890	+	0.920862i	$0.627487\pi$
$252$	138.170	0.0345393
$253$	−48.1079	−0.0119546
$254$	−3745.09	−0.925150
$255$	4072.43	1.00010
$256$	1597.83	0.390096
$257$	−2279.54	−0.553283	−0.276642	−	0.960973i	$-0.589222\pi$
$257$	−2279.54	−0.553283	−0.276642	+	0.960973i	$0.589222\pi$
$258$	3361.60	0.811178
$259$	2582.68	0.619615
$260$	−29.0820	−0.00693689
$261$	−261.000	−0.0618984
$262$	−346.979	−0.0818184
$263$	590.570	0.138464	0.0692321	−	0.997601i	$-0.477945\pi$
$263$	590.570	0.138464	0.0692321	+	0.997601i	$0.477945\pi$
$264$	−131.103	−0.0305638
$265$	8884.52	2.05952
$266$	−4613.98	−1.06354
$267$	1638.55	0.375572
$268$	−123.835	−0.0282255
$269$	−4460.21	−1.01094	−0.505472	−	0.862843i	$-0.668682\pi$
$269$	−4460.21	−1.01094	−0.505472	+	0.862843i	$0.668682\pi$
$270$	−1444.49	−0.325588
$271$	−4163.61	−0.933289	−0.466644	−	0.884445i	$-0.654537\pi$
$271$	−4163.61	−0.933289	−0.466644	+	0.884445i	$0.654537\pi$
$272$	−5448.23	−1.21451
$273$	−67.3222	−0.0149250
$274$	−1162.40	−0.256289
$275$	−399.482	−0.0875989
$276$	72.9980	0.0159202
$277$	5778.63	1.25345	0.626723	−	0.779242i	$-0.284396\pi$
$277$	5778.63	1.25345	0.626723	+	0.779242i	$0.284396\pi$
$278$	1003.14	0.216419
$279$	−1815.11	−0.389490
$280$	5389.51	1.15030
$281$	−5843.25	−1.24049	−0.620247	−	0.784406i	$-0.712968\pi$
$281$	−5843.25	−1.24049	−0.620247	+	0.784406i	$0.712968\pi$
$282$	1101.24	0.232546
$283$	1171.13	0.245995	0.122998	−	0.992407i	$-0.460749\pi$
$283$	1171.13	0.245995	0.122998	+	0.992407i	$0.460749\pi$
$284$	259.862	0.0542957
$285$	5633.89	1.17096
$286$	−9.73487	−0.00201271
$287$	2483.55	0.510799
$288$	428.183	0.0876074
$289$	918.653	0.186984
$290$	1551.49	0.314161
$291$	−2741.71	−0.552310
$292$	996.299	0.199671
$293$	2968.92	0.591966	0.295983	−	0.955193i	$-0.404353\pi$
$293$	2968.92	0.591966	0.295983	+	0.955193i	$0.404353\pi$
$294$	1195.59	0.237172
$295$	12160.3	2.40000
$296$	3718.47	0.730174
$297$	−56.4745	−0.0110336
$298$	8784.65	1.70765
$299$	−35.5676	−0.00687935
$300$	606.167	0.116657
$301$	−5402.82	−1.03459
$302$	8728.73	1.66319
$303$	−2281.89	−0.432644
$304$	−7537.20	−1.42200
$305$	−2080.10	−0.390513
$306$	−2068.49	−0.386430
$307$	5762.71	1.07132	0.535660	−	0.844434i	$-0.320063\pi$
$307$	5762.71	1.07132	0.535660	+	0.844434i	$0.320063\pi$
$308$	−32.1115	−0.00594066
$309$	−183.173	−0.0337229
$310$	10789.7	1.97683
$311$	−9987.52	−1.82103	−0.910515	−	0.413476i	$-0.864314\pi$
$311$	−9987.52	−1.82103	−0.910515	+	0.413476i	$0.864314\pi$
$312$	−96.9284	−0.0175881
$313$	6359.31	1.14840	0.574200	−	0.818715i	$-0.305313\pi$
$313$	6359.31	1.14840	0.574200	+	0.818715i	$0.305313\pi$
$314$	9142.53	1.64313
$315$	2321.61	0.415263
$316$	627.913	0.111781
$317$	2914.95	0.516467	0.258234	−	0.966083i	$-0.416860\pi$
$317$	2914.95	0.516467	0.258234	+	0.966083i	$0.416860\pi$
$318$	−4512.67	−0.795780
$319$	60.6578	0.0106464
$320$	7600.49	1.32775
$321$	−183.988	−0.0319912
$322$	−1004.51	−0.173848
$323$	8067.64	1.38977
$324$	85.6933	0.0146936
$325$	−295.349	−0.0504093
$326$	−7482.64	−1.27124
$327$	−4319.56	−0.730496
$328$	3575.74	0.601942
$329$	−1769.93	−0.296595
$330$	335.707	0.0560003
$331$	−980.750	−0.162861	−0.0814304	−	0.996679i	$-0.525949\pi$
$331$	−980.750	−0.162861	−0.0814304	+	0.996679i	$0.525949\pi$
$332$	909.180	0.150294
$333$	1601.78	0.263595
$334$	−6086.24	−0.997078
$335$	−2080.74	−0.339353
$336$	−3105.92	−0.504292
$337$	4825.80	0.780054	0.390027	−	0.920803i	$-0.372466\pi$
$337$	4825.80	0.780054	0.390027	+	0.920803i	$0.372466\pi$
$338$	6604.99	1.06291
$339$	−3261.90	−0.522602
$340$	1436.13	0.229074
$341$	421.841	0.0669912
$342$	−2861.59	−0.452448
$343$	−6899.00	−1.08604
$344$	−7778.80	−1.21920
$345$	1226.55	0.191406
$346$	11745.2	1.82493
$347$	12813.9	1.98238	0.991189	−	0.132454i	$-0.0422858\pi$
$347$	12813.9	1.98238	0.991189	+	0.132454i	$0.0422858\pi$
$348$	−92.0409	−0.0141779
$349$	5360.51	0.822181	0.411091	−	0.911594i	$-0.365148\pi$
$349$	5360.51	0.822181	0.411091	+	0.911594i	$0.365148\pi$
$350$	−8341.31	−1.27389
$351$	−41.7533	−0.00634936
$352$	−99.5121	−0.0150682
$353$	−11750.6	−1.77173	−0.885864	−	0.463945i	$-0.846433\pi$
$353$	−11750.6	−1.77173	−0.885864	+	0.463945i	$0.846433\pi$
$354$	−6176.52	−0.927339
$355$	4366.34	0.652792
$356$	577.830	0.0860251
$357$	3324.51	0.492862
$358$	−1409.32	−0.208058
$359$	−1322.33	−0.194401	−0.0972006	−	0.995265i	$-0.530989\pi$
$359$	−1322.33	−0.194401	−0.0972006	+	0.995265i	$0.530989\pi$
$360$	3342.58	0.489359
$361$	4301.96	0.627200
$362$	−10268.8	−1.49092
$363$	−3979.88	−0.575453
$364$	−23.7410	−0.00341859
$365$	16740.3	2.40063
$366$	1056.54	0.150891
$367$	6544.50	0.930845	0.465422	−	0.885089i	$-0.345902\pi$
$367$	6544.50	0.930845	0.465422	+	0.885089i	$0.345902\pi$
$368$	−1640.92	−0.232442
$369$	1540.30	0.217303
$370$	−9521.64	−1.33786
$371$	7252.84	1.01496
$372$	−640.094	−0.0892132
$373$	−8596.59	−1.19334	−0.596669	−	0.802488i	$-0.703509\pi$
$373$	−8596.59	−1.19334	−0.596669	+	0.802488i	$0.703509\pi$
$374$	480.728	0.0664648
$375$	3519.09	0.484600
$376$	−2548.30	−0.349517
$377$	44.8461	0.00612650
$378$	−1179.20	−0.160454
$379$	−11532.4	−1.56301	−0.781506	−	0.623898i	$-0.785548\pi$
$379$	−11532.4	−1.56301	−0.781506	+	0.623898i	$0.785548\pi$
$380$	1986.78	0.268209
$381$	3733.10	0.501975
$382$	299.974	0.0401781
$383$	13565.8	1.80987	0.904936	−	0.425547i	$-0.139918\pi$
$383$	13565.8	1.80987	0.904936	+	0.425547i	$0.139918\pi$
$384$	−5002.30	−0.664772
$385$	−539.554	−0.0714240
$386$	−8759.97	−1.15511
$387$	−3350.83	−0.440135
$388$	−966.858	−0.126507
$389$	7531.04	0.981591	0.490796	−	0.871275i	$-0.336706\pi$
$389$	7531.04	0.981591	0.490796	+	0.871275i	$0.336706\pi$
$390$	248.198	0.0322257
$391$	1756.40	0.227174
$392$	−2766.63	−0.356469
$393$	345.867	0.0443936
$394$	−3154.16	−0.403310
$395$	10550.5	1.34394
$396$	−19.9156	−0.00252726
$397$	10806.0	1.36609	0.683047	−	0.730375i	$-0.260654\pi$
$397$	10806.0	1.36609	0.683047	+	0.730375i	$0.260654\pi$
$398$	−11699.7	−1.47350
$399$	4599.20	0.577063
$400$	−13626.0	−1.70325
$401$	−11294.4	−1.40652	−0.703261	−	0.710931i	$-0.748274\pi$
$401$	−11294.4	−1.40652	−0.703261	+	0.710931i	$0.748274\pi$
$402$	1056.86	0.131123
$403$	311.880	0.0385505
$404$	−804.702	−0.0990976
$405$	1439.86	0.176660
$406$	1266.55	0.154822
$407$	−372.263	−0.0453376
$408$	4786.52	0.580804
$409$	−1182.93	−0.143013	−0.0715064	−	0.997440i	$-0.522781\pi$
$409$	−1182.93	−0.143013	−0.0715064	+	0.997440i	$0.522781\pi$
$410$	−9156.16	−1.10290
$411$	1158.68	0.139059
$412$	−64.5956	−0.00772426
$413$	9927.00	1.18275
$414$	−622.996	−0.0739579
$415$	15276.5	1.80697
$416$	−73.5722	−0.00867109
$417$	−999.928	−0.117426
$418$	665.050	0.0778198
$419$	−12345.0	−1.43936	−0.719678	−	0.694308i	$-0.755711\pi$
$419$	−12345.0	−1.43936	−0.719678	+	0.694308i	$0.755711\pi$
$420$	818.709	0.0951165
$421$	−2812.70	−0.325611	−0.162806	−	0.986658i	$-0.552054\pi$
$421$	−2812.70	−0.325611	−0.162806	+	0.986658i	$0.552054\pi$
$422$	4592.43	0.529753
$423$	−1097.71	−0.126177
$424$	10442.4	1.19606
$425$	14584.9	1.66464
$426$	−2217.77	−0.252234
$427$	−1698.08	−0.192450
$428$	−64.8827	−0.00732763
$429$	9.70369	0.00109207
$430$	19918.7	2.23387
$431$	−765.071	−0.0855039	−0.0427519	−	0.999086i	$-0.513613\pi$
$431$	−765.071	−0.0855039	−0.0427519	+	0.999086i	$0.513613\pi$
$432$	−1926.30	−0.214535
$433$	2875.48	0.319138	0.159569	−	0.987187i	$-0.448990\pi$
$433$	2875.48	0.319138	0.159569	+	0.987187i	$0.448990\pi$
$434$	8808.17	0.974206
$435$	−1546.52	−0.170460
$436$	−1523.28	−0.167321
$437$	2429.85	0.265985
$438$	−8502.84	−0.927583
$439$	10174.5	1.10616	0.553080	−	0.833128i	$-0.313452\pi$
$439$	10174.5	1.10616	0.553080	+	0.833128i	$0.313452\pi$
$440$	−776.834	−0.0841684
$441$	−1191.76	−0.128686
$442$	355.416	0.0382476
$443$	−1677.66	−0.179927	−0.0899637	−	0.995945i	$-0.528675\pi$
$443$	−1677.66	−0.179927	−0.0899637	+	0.995945i	$0.528675\pi$
$444$	564.864	0.0603767
$445$	9709.00	1.03427
$446$	18200.1	1.93229
$447$	−8756.50	−0.926551
$448$	6204.62	0.654332
$449$	−7807.51	−0.820622	−0.410311	−	0.911946i	$-0.634580\pi$
$449$	−7807.51	−0.820622	−0.410311	+	0.911946i	$0.634580\pi$
$450$	−5173.28	−0.541935
$451$	−357.974	−0.0373755
$452$	−1150.30	−0.119703
$453$	−8700.77	−0.902424
$454$	−1831.84	−0.189367
$455$	−398.908	−0.0411013
$456$	6621.79	0.680030
$457$	7763.97	0.794711	0.397356	−	0.917665i	$-0.369928\pi$
$457$	7763.97	0.794711	0.397356	+	0.917665i	$0.369928\pi$
$458$	−12914.9	−1.31763
$459$	2061.86	0.209672
$460$	432.540	0.0438419
$461$	15720.5	1.58824	0.794119	−	0.607762i	$-0.207933\pi$
$461$	15720.5	1.58824	0.794119	+	0.607762i	$0.207933\pi$
$462$	274.053	0.0275977
$463$	386.981	0.0388435	0.0194217	−	0.999811i	$-0.493817\pi$
$463$	386.981	0.0388435	0.0194217	+	0.999811i	$0.493817\pi$
$464$	2068.98	0.207005
$465$	−10755.2	−1.07260
$466$	15551.1	1.54591
$467$	−12130.6	−1.20201	−0.601004	−	0.799246i	$-0.705232\pi$
$467$	−12130.6	−1.20201	−0.601004	+	0.799246i	$0.705232\pi$
$468$	−14.7242	−0.00145433
$469$	−1698.61	−0.167238
$470$	6525.26	0.640399
$471$	−9113.24	−0.891542
$472$	14292.6	1.39379
$473$	778.751	0.0757019
$474$	−5358.88	−0.519286
$475$	20177.1	1.94903
$476$	1172.38	0.112891
$477$	4498.22	0.431780
$478$	−16163.2	−1.54663
$479$	11384.0	1.08590	0.542951	−	0.839764i	$-0.317307\pi$
$479$	11384.0	1.08590	0.542951	+	0.839764i	$0.317307\pi$
$480$	2537.14	0.241258
$481$	−275.225	−0.0260898
$482$	−10223.3	−0.966099
$483$	1001.29	0.0943276
$484$	−1403.49	−0.131808
$485$	−16245.6	−1.52098
$486$	−731.343	−0.0682601
$487$	6591.05	0.613283	0.306642	−	0.951825i	$-0.400795\pi$
$487$	6591.05	0.613283	0.306642	+	0.951825i	$0.400795\pi$
$488$	−2444.85	−0.226789
$489$	7458.67	0.689760
$490$	7084.33	0.653138
$491$	−10936.6	−1.00522	−0.502610	−	0.864513i	$-0.667627\pi$
$491$	−10936.6	−1.00522	−0.502610	+	0.864513i	$0.667627\pi$
$492$	543.182	0.0497735
$493$	−2214.59	−0.202313
$494$	491.691	0.0447818
$495$	−334.632	−0.0303850
$496$	14388.6	1.30256
$497$	3564.44	0.321704
$498$	−7759.33	−0.698200
$499$	297.886	0.0267239	0.0133619	−	0.999911i	$-0.495747\pi$
$499$	297.886	0.0267239	0.0133619	+	0.999911i	$0.495747\pi$
$500$	1241.00	0.110998
$501$	6066.74	0.541002
$502$	9332.48	0.829739
$503$	17463.3	1.54801	0.774007	−	0.633176i	$-0.218249\pi$
$503$	17463.3	1.54801	0.774007	+	0.633176i	$0.218249\pi$
$504$	2728.70	0.241163
$505$	−13521.0	−1.19144
$506$	144.788	0.0127205
$507$	−6583.83	−0.576722
$508$	1316.47	0.114978
$509$	3068.67	0.267223	0.133611	−	0.991034i	$-0.457343\pi$
$509$	3068.67	0.267223	0.133611	+	0.991034i	$0.457343\pi$
$510$	−12256.5	−1.06417
$511$	13665.9	1.18306
$512$	8530.56	0.736330
$513$	2852.43	0.245493
$514$	6860.60	0.588732
$515$	−1085.37	−0.0928680
$516$	−1181.66	−0.100813
$517$	255.115	0.0217020
$518$	−7772.95	−0.659313
$519$	−11707.6	−0.990186
$520$	−574.336	−0.0484352
$521$	3431.56	0.288559	0.144280	−	0.989537i	$-0.453913\pi$
$521$	3431.56	0.288559	0.144280	+	0.989537i	$0.453913\pi$
$522$	785.516	0.0658642
$523$	20300.2	1.69726	0.848631	−	0.528986i	$-0.177427\pi$
$523$	20300.2	1.69726	0.848631	+	0.528986i	$0.177427\pi$
$524$	121.969	0.0101684
$525$	8314.58	0.691197
$526$	−1777.40	−0.147336
$527$	−15401.3	−1.27303
$528$	447.682	0.0368993
$529$	529.000	0.0434783
$530$	−26739.2	−2.19147
$531$	6156.73	0.503163
$532$	1621.90	0.132177
$533$	−264.661	−0.0215079
$534$	−4931.45	−0.399634
$535$	−1090.19	−0.0880994
$536$	−2445.60	−0.197078
$537$	1404.80	0.112890
$538$	13423.6	1.07571
$539$	276.973	0.0221337
$540$	507.764	0.0404642
$541$	22549.7	1.79203	0.896014	−	0.444026i	$-0.146450\pi$
$541$	22549.7	1.79203	0.896014	+	0.444026i	$0.146450\pi$
$542$	12531.0	0.993083
$543$	10235.9	0.808955
$544$	3633.15	0.286342
$545$	−25595.0	−2.01168
$546$	202.616	0.0158812
$547$	−10420.5	−0.814532	−0.407266	−	0.913310i	$-0.633518\pi$
$547$	−10420.5	−0.814532	−0.407266	+	0.913310i	$0.633518\pi$
$548$	408.604	0.0318516
$549$	−1053.15	−0.0818715
$550$	1202.30	0.0932113
$551$	−3063.72	−0.236876
$552$	1441.62	0.111159
$553$	8612.87	0.662309
$554$	−17391.6	−1.33375
$555$	9491.14	0.725903
$556$	−352.622	−0.0268966
$557$	22578.7	1.71757	0.858787	−	0.512332i	$-0.171218\pi$
$557$	22578.7	1.71757	0.858787	+	0.512332i	$0.171218\pi$
$558$	5462.83	0.414445
$559$	575.753	0.0435631
$560$	−18403.7	−1.38875
$561$	−479.188	−0.0360630
$562$	17586.1	1.31997
$563$	19272.0	1.44266	0.721332	−	0.692589i	$-0.243530\pi$
$563$	19272.0	1.44266	0.721332	+	0.692589i	$0.243530\pi$
$564$	−387.106	−0.0289009
$565$	−19327.9	−1.43917
$566$	−3524.69	−0.261756
$567$	1175.43	0.0870604
$568$	5131.97	0.379107
$569$	529.766	0.0390315	0.0195158	−	0.999810i	$-0.493788\pi$
$569$	529.766	0.0390315	0.0195158	+	0.999810i	$0.493788\pi$
$570$	−16956.0	−1.24598
$571$	−10107.6	−0.740789	−0.370395	−	0.928874i	$-0.620778\pi$
$571$	−10107.6	−0.740789	−0.370395	+	0.928874i	$0.620778\pi$
$572$	3.42198	0.000250140 0
$573$	−299.013	−0.0218001
$574$	−7474.60	−0.543525
$575$	4392.75	0.318592
$576$	3848.11	0.278365
$577$	−21716.7	−1.56686	−0.783430	−	0.621480i	$-0.786532\pi$
$577$	−21716.7	−1.56686	−0.783430	+	0.621480i	$0.786532\pi$
$578$	−2764.82	−0.198964
$579$	8731.91	0.626746
$580$	−545.376	−0.0390440
$581$	12470.9	0.890500
$582$	8251.57	0.587695
$583$	−1045.41	−0.0742649
$584$	19675.7	1.39416
$585$	−247.403	−0.0174852
$586$	−8935.38	−0.629892
$587$	−5763.89	−0.405283	−0.202642	−	0.979253i	$-0.564953\pi$
$587$	−5763.89	−0.405283	−0.202642	+	0.979253i	$0.564953\pi$
$588$	−420.273	−0.0294758
$589$	−21306.5	−1.49052
$590$	−36598.1	−2.55376
$591$	3144.05	0.218831
$592$	−12697.6	−0.881531
$593$	−6190.42	−0.428685	−0.214342	−	0.976759i	$-0.568761\pi$
$593$	−6190.42	−0.428685	−0.214342	+	0.976759i	$0.568761\pi$
$594$	169.968	0.0117405
$595$	19698.9	1.35727
$596$	−3087.96	−0.212228
$597$	11662.2	0.799500
$598$	107.046	0.00732011
$599$	−15380.1	−1.04910	−0.524552	−	0.851378i	$-0.675767\pi$
$599$	−15380.1	−1.04910	−0.524552	+	0.851378i	$0.675767\pi$
$600$	11971.1	0.814529
$601$	20069.9	1.36218	0.681090	−	0.732200i	$-0.261506\pi$
$601$	20069.9	1.36218	0.681090	+	0.732200i	$0.261506\pi$
$602$	16260.5	1.10088
$603$	−1053.48	−0.0711458
$604$	−3068.30	−0.206701
$605$	−23582.2	−1.58472
$606$	6867.67	0.460363
$607$	−16251.4	−1.08670	−0.543349	−	0.839507i	$-0.682844\pi$
$607$	−16251.4	−1.08670	−0.543349	+	0.839507i	$0.682844\pi$
$608$	5026.18	0.335261
$609$	−1262.49	−0.0840047
$610$	6260.37	0.415533
$611$	188.614	0.0124885
$612$	727.110	0.0480256
$613$	15513.4	1.02215	0.511076	−	0.859536i	$-0.329247\pi$
$613$	15513.4	1.02215	0.511076	+	0.859536i	$0.329247\pi$
$614$	−17343.7	−1.13996
$615$	9126.83	0.598422
$616$	−634.165	−0.0414793
$617$	16666.4	1.08746	0.543730	−	0.839260i	$-0.317012\pi$
$617$	16666.4	1.08746	0.543730	+	0.839260i	$0.317012\pi$
$618$	551.286	0.0358835
$619$	−7170.65	−0.465610	−0.232805	−	0.972523i	$-0.574790\pi$
$619$	−7170.65	−0.465610	−0.232805	+	0.972523i	$0.574790\pi$
$620$	−3792.79	−0.245681
$621$	621.000	0.0401286
$622$	30058.9	1.93770
$623$	7925.90	0.509703
$624$	330.984	0.0212339
$625$	−3021.76	−0.193393
$626$	−19139.2	−1.22198
$627$	−662.920	−0.0422240
$628$	−3213.76	−0.204209
$629$	13591.2	0.861551
$630$	−6987.21	−0.441868
$631$	20320.9	1.28203	0.641015	−	0.767528i	$-0.278514\pi$
$631$	20320.9	1.28203	0.641015	+	0.767528i	$0.278514\pi$
$632$	12400.5	0.780486
$633$	−4577.71	−0.287437
$634$	−8772.96	−0.549557
$635$	22119.9	1.38237
$636$	1586.28	0.0988997
$637$	204.774	0.0127370
$638$	−182.558	−0.0113285
$639$	2210.67	0.136859
$640$	−29640.4	−1.83069
$641$	−5767.58	−0.355391	−0.177695	−	0.984086i	$-0.556864\pi$
$641$	−5767.58	−0.355391	−0.177695	+	0.984086i	$0.556864\pi$
$642$	553.737	0.0340409
$643$	−13817.6	−0.847455	−0.423728	−	0.905790i	$-0.639279\pi$
$643$	−13817.6	−0.847455	−0.423728	+	0.905790i	$0.639279\pi$
$644$	353.102	0.0216058
$645$	−19854.9	−1.21207
$646$	−24280.7	−1.47881
$647$	−24399.9	−1.48263	−0.741313	−	0.671160i	$-0.765796\pi$
$647$	−24399.9	−1.48263	−0.741313	+	0.671160i	$0.765796\pi$
$648$	1692.34	0.102595
$649$	−1430.86	−0.0865425
$650$	888.895	0.0536390
$651$	−8779.95	−0.528592
$652$	2630.28	0.157990
$653$	−14692.4	−0.880487	−0.440244	−	0.897878i	$-0.645108\pi$
$653$	−14692.4	−0.880487	−0.440244	+	0.897878i	$0.645108\pi$
$654$	13000.3	0.777298
$655$	2049.39	0.122254
$656$	−12210.2	−0.726718
$657$	8475.60	0.503295
$658$	5326.87	0.315597
$659$	−5669.93	−0.335158	−0.167579	−	0.985859i	$-0.553595\pi$
$659$	−5669.93	−0.335158	−0.167579	+	0.985859i	$0.553595\pi$
$660$	−118.007	−0.00695973
$661$	−24804.4	−1.45958	−0.729789	−	0.683673i	$-0.760382\pi$
$661$	−24804.4	−1.45958	−0.729789	+	0.683673i	$0.760382\pi$
$662$	2951.71	0.173295
$663$	−354.278	−0.0207526
$664$	17955.2	1.04939
$665$	27251.9	1.58915
$666$	−4820.79	−0.280483
$667$	−667.000	−0.0387202
$668$	2139.42	0.123917
$669$	−18141.8	−1.04843
$670$	6262.30	0.361095
$671$	244.758	0.0140817
$672$	2071.18	0.118895
$673$	8858.63	0.507393	0.253696	−	0.967284i	$-0.418354\pi$
$673$	8858.63	0.507393	0.253696	+	0.967284i	$0.418354\pi$
$674$	−14523.9	−0.830031
$675$	5156.71	0.294047
$676$	−2321.77	−0.132099
$677$	−17105.0	−0.971046	−0.485523	−	0.874224i	$-0.661371\pi$
$677$	−17105.0	−0.971046	−0.485523	+	0.874224i	$0.661371\pi$
$678$	9817.15	0.556085
$679$	−13262.1	−0.749560
$680$	28361.9	1.59945
$681$	1825.98	0.102748
$682$	−1269.59	−0.0712832
$683$	−18933.3	−1.06071	−0.530354	−	0.847776i	$-0.677941\pi$
$683$	−18933.3	−1.06071	−0.530354	+	0.847776i	$0.677941\pi$
$684$	1005.90	0.0562304
$685$	6865.58	0.382949
$686$	20763.5	1.15562
$687$	12873.6	0.714930
$688$	26562.5	1.47193
$689$	−772.902	−0.0427362
$690$	−3691.48	−0.203670
$691$	20615.5	1.13495	0.567474	−	0.823391i	$-0.307921\pi$
$691$	20615.5	1.13495	0.567474	+	0.823391i	$0.307921\pi$
$692$	−4128.66	−0.226803
$693$	−273.175	−0.0149741
$694$	−38565.2	−2.10939
$695$	−5924.93	−0.323375
$696$	−1817.70	−0.0989939
$697$	13069.5	0.710247
$698$	−16133.2	−0.874858
$699$	−15501.3	−0.838789
$700$	2932.12	0.158319
$701$	−14998.1	−0.808088	−0.404044	−	0.914740i	$-0.632396\pi$
$701$	−14998.1	−0.808088	−0.404044	+	0.914740i	$0.632396\pi$
$702$	125.662	0.00675615
$703$	18802.3	1.00874
$704$	−894.322	−0.0478779
$705$	−6504.36	−0.347473
$706$	35365.0	1.88524
$707$	−11037.8	−0.587157
$708$	2171.15	0.115250
$709$	21046.4	1.11483	0.557416	−	0.830234i	$-0.311793\pi$
$709$	21046.4	1.11483	0.557416	+	0.830234i	$0.311793\pi$
$710$	−13141.1	−0.694616
$711$	5341.71	0.281758
$712$	11411.5	0.600650
$713$	−4638.61	−0.243643
$714$	−10005.6	−0.524439
$715$	57.4979	0.00300741
$716$	495.400	0.0258575
$717$	16111.4	0.839179
$718$	3979.75	0.206856
$719$	−3391.80	−0.175929	−0.0879645	−	0.996124i	$-0.528036\pi$
$719$	−3391.80	−0.175929	−0.0879645	+	0.996124i	$0.528036\pi$
$720$	−11414.0	−0.590798
$721$	−886.036	−0.0457666
$722$	−12947.4	−0.667384
$723$	10190.6	0.524193
$724$	3609.65	0.185292
$725$	−5538.69	−0.283727
$726$	11978.0	0.612321
$727$	26121.0	1.33257	0.666283	−	0.745699i	$-0.267884\pi$
$727$	26121.0	1.33257	0.666283	+	0.745699i	$0.267884\pi$
$728$	−468.857	−0.0238695
$729$	729.000	0.0370370
$730$	−50382.4	−2.55443
$731$	−28431.9	−1.43857
$732$	−371.392	−0.0187528
$733$	−38765.2	−1.95338	−0.976689	−	0.214657i	$-0.931137\pi$
$733$	−38765.2	−1.95338	−0.976689	+	0.214657i	$0.931137\pi$
$734$	−19696.6	−0.990483
$735$	−7061.64	−0.354384
$736$	1094.25	0.0548022
$737$	244.834	0.0122369
$738$	−4635.75	−0.231225
$739$	−37029.5	−1.84323	−0.921617	−	0.388100i	$-0.873132\pi$
$739$	−37029.5	−1.84323	−0.921617	+	0.388100i	$0.873132\pi$
$740$	3347.02	0.166269
$741$	−490.116	−0.0242981
$742$	−21828.4	−1.07998
$743$	11900.7	0.587612	0.293806	−	0.955865i	$-0.405078\pi$
$743$	11900.7	0.587612	0.293806	+	0.955865i	$0.405078\pi$
$744$	−12641.1	−0.622910
$745$	−51885.5	−2.55159
$746$	25872.7	1.26979
$747$	7734.47	0.378835
$748$	−168.984	−0.00826027
$749$	−889.975	−0.0434165
$750$	−10591.2	−0.515648
$751$	−8687.97	−0.422142	−0.211071	−	0.977471i	$-0.567695\pi$
$751$	−8687.97	−0.422142	−0.211071	+	0.977471i	$0.567695\pi$
$752$	8701.74	0.421968
$753$	−9302.58	−0.450206
$754$	−134.971	−0.00651902
$755$	−51555.2	−2.48515
$756$	414.511	0.0199413
$757$	−13922.2	−0.668444	−0.334222	−	0.942494i	$-0.608474\pi$
$757$	−13922.2	−0.668444	−0.334222	+	0.942494i	$0.608474\pi$
$758$	34708.5	1.66315
$759$	−144.324	−0.00690200
$760$	39236.5	1.87271
$761$	−22666.7	−1.07972	−0.539861	−	0.841754i	$-0.681523\pi$
$761$	−22666.7	−1.07972	−0.539861	+	0.841754i	$0.681523\pi$
$762$	−11235.3	−0.534136
$763$	−20894.3	−0.991384
$764$	−105.446	−0.00499334
$765$	12217.3	0.577407
$766$	−40828.3	−1.92583
$767$	−1057.87	−0.0498014
$768$	4793.50	0.225222
$769$	36894.0	1.73008	0.865039	−	0.501705i	$-0.167294\pi$
$769$	36894.0	1.73008	0.865039	+	0.501705i	$0.167294\pi$
$770$	1623.87	0.0760001
$771$	−6838.62	−0.319438
$772$	3079.28	0.143557
$773$	14605.5	0.679591	0.339796	−	0.940499i	$-0.389642\pi$
$773$	14605.5	0.679591	0.339796	+	0.940499i	$0.389642\pi$
$774$	10084.8	0.468334
$775$	−38518.5	−1.78532
$776$	−19094.3	−0.883306
$777$	7748.05	0.357735
$778$	−22665.7	−1.04448
$779$	18080.6	0.831586
$780$	−87.2461	−0.00400501
$781$	−513.772	−0.0235393
$782$	−5286.14	−0.241729
$783$	−783.000	−0.0357371
$784$	9447.29	0.430361
$785$	−53999.3	−2.45518
$786$	−1040.94	−0.0472379
$787$	−9561.06	−0.433056	−0.216528	−	0.976276i	$-0.569473\pi$
$787$	−9561.06	−0.433056	−0.216528	+	0.976276i	$0.569473\pi$
$788$	1108.74	0.0501235
$789$	1771.71	0.0799424
$790$	−31753.3	−1.43004
$791$	−15778.3	−0.709243
$792$	−393.309	−0.0176460
$793$	180.957	0.00810337
$794$	−32522.3	−1.45362
$795$	26653.6	1.18906
$796$	4112.64	0.183126
$797$	40822.8	1.81433	0.907164	−	0.420777i	$-0.138243\pi$
$797$	40822.8	1.81433	0.907164	+	0.420777i	$0.138243\pi$
$798$	−13841.9	−0.614035
$799$	−9314.14	−0.412404
$800$	9086.49	0.401570
$801$	4915.65	0.216836
$802$	33992.1	1.49664
$803$	−1969.78	−0.0865652
$804$	−371.506	−0.0162960
$805$	5933.00	0.259765
$806$	−938.646	−0.0410203
$807$	−13380.6	−0.583669
$808$	−15891.9	−0.691925
$809$	2865.49	0.124531	0.0622653	−	0.998060i	$-0.480168\pi$
$809$	2865.49	0.124531	0.0622653	+	0.998060i	$0.480168\pi$
$810$	−4333.47	−0.187979
$811$	39933.2	1.72903	0.864515	−	0.502607i	$-0.167626\pi$
$811$	39933.2	1.72903	0.864515	+	0.502607i	$0.167626\pi$
$812$	−445.215	−0.0192414
$813$	−12490.8	−0.538834
$814$	1120.38	0.0482423
$815$	44195.3	1.89950
$816$	−16344.7	−0.701199
$817$	−39333.3	−1.68433
$818$	3560.20	0.152176
$819$	−201.967	−0.00861695
$820$	3218.55	0.137069
$821$	−26095.6	−1.10931	−0.554655	−	0.832080i	$-0.687150\pi$
$821$	−26095.6	−1.10931	−0.554655	+	0.832080i	$0.687150\pi$
$822$	−3487.20	−0.147968
$823$	13962.9	0.591392	0.295696	−	0.955282i	$-0.404449\pi$
$823$	13962.9	0.591392	0.295696	+	0.955282i	$0.404449\pi$
$824$	−1275.69	−0.0539328
$825$	−1198.45	−0.0505753
$826$	−29876.7	−1.25853
$827$	−36873.1	−1.55043	−0.775214	−	0.631699i	$-0.782358\pi$
$827$	−36873.1	−1.55043	−0.775214	+	0.631699i	$0.782358\pi$
$828$	218.994	0.00919151
$829$	6055.38	0.253694	0.126847	−	0.991922i	$-0.459514\pi$
$829$	6055.38	0.253694	0.126847	+	0.991922i	$0.459514\pi$
$830$	−45976.8	−1.92275
$831$	17335.9	0.723677
$832$	−661.198	−0.0275516
$833$	−10112.2	−0.420607
$834$	3009.42	0.124949
$835$	35947.6	1.48984
$836$	−233.777	−0.00967146
$837$	−5445.33	−0.224872
$838$	37153.9	1.53157
$839$	25440.6	1.04685	0.523426	−	0.852071i	$-0.324654\pi$
$839$	25440.6	1.04685	0.523426	+	0.852071i	$0.324654\pi$
$840$	16168.5	0.664128
$841$	841.000	0.0344828
$842$	8465.21	0.346473
$843$	−17529.7	−0.716200
$844$	−1614.32	−0.0658378
$845$	−39011.6	−1.58821
$846$	3303.73	0.134261
$847$	−19251.2	−0.780968
$848$	−35658.0	−1.44399
$849$	3513.40	0.142025
$850$	−43895.5	−1.77130
$851$	4093.44	0.164890
$852$	779.587	0.0313477
$853$	21863.1	0.877582	0.438791	−	0.898589i	$-0.355407\pi$
$853$	21863.1	0.877582	0.438791	+	0.898589i	$0.355407\pi$
$854$	5110.62	0.204780
$855$	16901.7	0.676052
$856$	−1281.36	−0.0511634
$857$	−3880.49	−0.154673	−0.0773366	−	0.997005i	$-0.524642\pi$
$857$	−3880.49	−0.154673	−0.0773366	+	0.997005i	$0.524642\pi$
$858$	−29.2046	−0.00116204
$859$	−3760.81	−0.149380	−0.0746898	−	0.997207i	$-0.523797\pi$
$859$	−3760.81	−0.149380	−0.0746898	+	0.997207i	$0.523797\pi$
$860$	−7001.77	−0.277626
$861$	7450.65	0.294910
$862$	2302.59	0.0909820
$863$	13298.9	0.524565	0.262283	−	0.964991i	$-0.415525\pi$
$863$	13298.9	0.524565	0.262283	+	0.964991i	$0.415525\pi$
$864$	1284.55	0.0505802
$865$	−69371.8	−2.72683
$866$	−8654.17	−0.339585
$867$	2755.96	0.107955
$868$	−3096.23	−0.121075
$869$	−1241.44	−0.0484615
$870$	4654.47	0.181381
$871$	181.013	0.00704177
$872$	−30083.0	−1.16828
$873$	−8225.14	−0.318876
$874$	−7312.96	−0.283026
$875$	17022.4	0.657670
$876$	2988.90	0.115280
$877$	−12567.9	−0.483907	−0.241954	−	0.970288i	$-0.577788\pi$
$877$	−12567.9	−0.483907	−0.241954	+	0.970288i	$0.577788\pi$
$878$	−30621.7	−1.17703
$879$	8906.75	0.341772
$880$	2652.68	0.101616
$881$	−8683.72	−0.332079	−0.166040	−	0.986119i	$-0.553098\pi$
$881$	−8683.72	−0.332079	−0.166040	+	0.986119i	$0.553098\pi$
$882$	3586.78	0.136931
$883$	36288.5	1.38302	0.691509	−	0.722368i	$-0.256946\pi$
$883$	36288.5	1.38302	0.691509	+	0.722368i	$0.256946\pi$
$884$	−124.935	−0.00475342
$885$	36480.9	1.38564
$886$	5049.14	0.191455
$887$	2668.96	0.101032	0.0505158	−	0.998723i	$-0.483913\pi$
$887$	2668.96	0.101032	0.0505158	+	0.998723i	$0.483913\pi$
$888$	11155.4	0.421566
$889$	18057.5	0.681249
$890$	−29220.6	−1.10054
$891$	−169.424	−0.00637026
$892$	−6397.65	−0.240145
$893$	−12885.4	−0.482859
$894$	26353.9	0.985914
$895$	8323.97	0.310882
$896$	−24196.9	−0.902188
$897$	−106.703	−0.00397180
$898$	23497.8	0.873198
$899$	5848.69	0.216980
$900$	1818.50	0.0673519
$901$	38167.5	1.41126
$902$	1077.37	0.0397701
$903$	−16208.4	−0.597324
$904$	−22717.1	−0.835795
$905$	60651.2	2.22775
$906$	26186.2	0.960241
$907$	39262.4	1.43736	0.718680	−	0.695341i	$-0.244746\pi$
$907$	39262.4	1.43736	0.718680	+	0.695341i	$0.244746\pi$
$908$	643.926	0.0235346
$909$	−6845.67	−0.249787
$910$	1200.57	0.0437347
$911$	−16727.7	−0.608359	−0.304180	−	0.952615i	$-0.598382\pi$
$911$	−16727.7	−0.608359	−0.304180	+	0.952615i	$0.598382\pi$
$912$	−22611.6	−0.820992
$913$	−1797.53	−0.0651584
$914$	−23366.8	−0.845627
$915$	−6240.31	−0.225463
$916$	4539.82	0.163755
$917$	1673.01	0.0602483
$918$	−6205.47	−0.223106
$919$	46202.3	1.65840	0.829201	−	0.558950i	$-0.188796\pi$
$919$	46202.3	1.65840	0.829201	+	0.558950i	$0.188796\pi$
$920$	8542.15	0.306115
$921$	17288.1	0.618527
$922$	−47313.1	−1.69000
$923$	−379.846	−0.0135458
$924$	−96.3346	−0.00342984
$925$	33991.5	1.20825
$926$	−1164.67	−0.0413322
$927$	−549.520	−0.0194699
$928$	−1379.70	−0.0488049
$929$	−9045.89	−0.319468	−0.159734	−	0.987160i	$-0.551064\pi$
$929$	−9045.89	−0.319468	−0.159734	+	0.987160i	$0.551064\pi$
$930$	32369.2	1.14132
$931$	−13989.4	−0.492464
$932$	−5466.49	−0.192125
$933$	−29962.6	−1.05137
$934$	36508.8	1.27902
$935$	−2839.36	−0.0993124
$936$	−290.785	−0.0101545
$937$	−26101.2	−0.910019	−0.455010	−	0.890487i	$-0.650364\pi$
$937$	−26101.2	−0.910019	−0.455010	+	0.890487i	$0.650364\pi$
$938$	5112.20	0.177952
$939$	19077.9	0.663029
$940$	−2293.74	−0.0795890
$941$	−37515.4	−1.29965	−0.649824	−	0.760085i	$-0.725157\pi$
$941$	−37515.4	−1.29965	−0.649824	+	0.760085i	$0.725157\pi$
$942$	27427.6	0.948662
$943$	3936.32	0.135932
$944$	−48805.3	−1.68271
$945$	6964.83	0.239752
$946$	−2343.76	−0.0805521
$947$	21292.7	0.730645	0.365322	−	0.930881i	$-0.380959\pi$
$947$	21292.7	0.730645	0.365322	+	0.930881i	$0.380959\pi$
$948$	1883.74	0.0645369
$949$	−1456.31	−0.0498145
$950$	−60726.0	−2.07391
$951$	8744.86	0.298182
$952$	23153.1	0.788231
$953$	19777.9	0.672266	0.336133	−	0.941815i	$-0.390881\pi$
$953$	19777.9	0.672266	0.336133	+	0.941815i	$0.390881\pi$
$954$	−13538.0	−0.459444
$955$	−1771.76	−0.0600345
$956$	5681.64	0.192215
$957$	181.973	0.00614667
$958$	−34261.7	−1.15548
$959$	5604.68	0.188722
$960$	22801.5	0.766577
$961$	10883.4	0.365324
$962$	828.328	0.0277613
$963$	−551.963	−0.0184701
$964$	3593.68	0.120067
$965$	51739.7	1.72597
$966$	−3013.52	−0.100371
$967$	−25488.8	−0.847635	−0.423818	−	0.905748i	$-0.639310\pi$
$967$	−25488.8	−0.847635	−0.423818	+	0.905748i	$0.639310\pi$
$968$	−27717.3	−0.920318
$969$	24202.9	0.802384
$970$	48893.6	1.61843
$971$	9264.58	0.306194	0.153097	−	0.988211i	$-0.451075\pi$
$971$	9264.58	0.306194	0.153097	+	0.988211i	$0.451075\pi$
$972$	257.080	0.00848338
$973$	−4836.80	−0.159363
$974$	−19836.7	−0.652575
$975$	−886.047	−0.0291038
$976$	8348.49	0.273800
$977$	−2438.31	−0.0798448	−0.0399224	−	0.999203i	$-0.512711\pi$
$977$	−2438.31	−0.0798448	−0.0399224	+	0.999203i	$0.512711\pi$
$978$	−22447.9	−0.733952
$979$	−1142.42	−0.0372952
$980$	−2490.27	−0.0811721
$981$	−12958.7	−0.421752
$982$	32915.3	1.06962
$983$	297.109	0.00964019	0.00482010	−	0.999988i	$-0.498466\pi$
$983$	297.109	0.00964019	0.00482010	+	0.999988i	$0.498466\pi$
$984$	10727.2	0.347532
$985$	18629.7	0.602630
$986$	6665.13	0.215275
$987$	−5309.80	−0.171239
$988$	−172.838	−0.00556550
$989$	−8563.23	−0.275323
$990$	1007.12	0.0323318
$991$	−20776.6	−0.665984	−0.332992	−	0.942930i	$-0.608058\pi$
$991$	−20776.6	−0.665984	−0.332992	+	0.942930i	$0.608058\pi$
$992$	−9595.05	−0.307100
$993$	−2942.25	−0.0940277
$994$	−10727.7	−0.342316
$995$	69102.7	2.20171
$996$	2727.54	0.0867725
$997$	30689.4	0.974869	0.487434	−	0.873160i	$-0.337933\pi$
$997$	30689.4	0.974869	0.487434	+	0.873160i	$0.337933\pi$
$998$	−896.531	−0.0284361
$999$	4805.35	0.152187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.h.1.12	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.h.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-3.00964 q^{2} +3.00000 q^{3} +1.05794 q^{4} +17.7761 q^{5} -9.02892 q^{6} +14.5114 q^{7} +20.8931 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.00964 q^{2} +3.00000 q^{3} +1.05794 q^{4} +17.7761 q^{5} -9.02892 q^{6} +14.5114 q^{7} +20.8931 q^{8} +9.00000 q^{9} -53.4996 q^{10} -2.09165 q^{11} +3.17383 q^{12} -1.54642 q^{13} -43.6742 q^{14} +53.3283 q^{15} -71.3443 q^{16} +76.3653 q^{17} -27.0868 q^{18} +105.645 q^{19} +18.8061 q^{20} +43.5343 q^{21} +6.29511 q^{22} +23.0000 q^{23} +62.6793 q^{24} +190.989 q^{25} +4.65416 q^{26} +27.0000 q^{27} +15.3523 q^{28} -29.0000 q^{29} -160.499 q^{30} -201.679 q^{31} +47.5759 q^{32} -6.27495 q^{33} -229.832 q^{34} +257.957 q^{35} +9.52148 q^{36} +177.976 q^{37} -317.955 q^{38} -4.63925 q^{39} +371.398 q^{40} +171.144 q^{41} -131.023 q^{42} -372.314 q^{43} -2.21284 q^{44} +159.985 q^{45} -69.2218 q^{46} -121.968 q^{47} -214.033 q^{48} -132.418 q^{49} -574.809 q^{50} +229.096 q^{51} -1.63602 q^{52} +499.802 q^{53} -81.2603 q^{54} -37.1813 q^{55} +303.189 q^{56} +316.936 q^{57} +87.2796 q^{58} +684.081 q^{59} +56.4182 q^{60} -117.017 q^{61} +606.981 q^{62} +130.603 q^{63} +427.568 q^{64} -27.4892 q^{65} +18.8853 q^{66} -117.053 q^{67} +80.7900 q^{68} +69.0000 q^{69} -776.357 q^{70} +245.630 q^{71} +188.038 q^{72} +941.734 q^{73} -535.643 q^{74} +572.968 q^{75} +111.767 q^{76} -30.3528 q^{77} +13.9625 q^{78} +593.523 q^{79} -1268.22 q^{80} +81.0000 q^{81} -515.083 q^{82} +859.385 q^{83} +46.0568 q^{84} +1357.48 q^{85} +1120.53 q^{86} -87.0000 q^{87} -43.7010 q^{88} +546.183 q^{89} -481.497 q^{90} -22.4407 q^{91} +24.3327 q^{92} -605.037 q^{93} +367.081 q^{94} +1877.96 q^{95} +142.728 q^{96} -913.904 q^{97} +398.532 q^{98} -18.8248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) \) 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