LMFDB - Embedded newform 4011.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79513 q^{2} -1.00000 q^{3} +5.81272 q^{4} +0.438876 q^{5} +2.79513 q^{6} -1.00000 q^{7} -10.6570 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.79513 q^{2} -1.00000 q^{3} +5.81272 q^{4} +0.438876 q^{5} +2.79513 q^{6} -1.00000 q^{7} -10.6570 q^{8} +1.00000 q^{9} -1.22671 q^{10} -5.11393 q^{11} -5.81272 q^{12} +3.57639 q^{13} +2.79513 q^{14} -0.438876 q^{15} +18.1623 q^{16} -3.22421 q^{17} -2.79513 q^{18} +4.20197 q^{19} +2.55107 q^{20} +1.00000 q^{21} +14.2941 q^{22} +5.74699 q^{23} +10.6570 q^{24} -4.80739 q^{25} -9.99647 q^{26} -1.00000 q^{27} -5.81272 q^{28} +4.80783 q^{29} +1.22671 q^{30} +4.33839 q^{31} -29.4518 q^{32} +5.11393 q^{33} +9.01206 q^{34} -0.438876 q^{35} +5.81272 q^{36} -1.07132 q^{37} -11.7450 q^{38} -3.57639 q^{39} -4.67712 q^{40} -4.91241 q^{41} -2.79513 q^{42} -9.33741 q^{43} -29.7259 q^{44} +0.438876 q^{45} -16.0635 q^{46} -4.27628 q^{47} -18.1623 q^{48} +1.00000 q^{49} +13.4372 q^{50} +3.22421 q^{51} +20.7886 q^{52} +2.74214 q^{53} +2.79513 q^{54} -2.24438 q^{55} +10.6570 q^{56} -4.20197 q^{57} -13.4385 q^{58} +10.0082 q^{59} -2.55107 q^{60} -2.23200 q^{61} -12.1263 q^{62} -1.00000 q^{63} +45.9970 q^{64} +1.56959 q^{65} -14.2941 q^{66} -2.87342 q^{67} -18.7414 q^{68} -5.74699 q^{69} +1.22671 q^{70} -8.53382 q^{71} -10.6570 q^{72} -1.54704 q^{73} +2.99446 q^{74} +4.80739 q^{75} +24.4249 q^{76} +5.11393 q^{77} +9.99647 q^{78} -7.00338 q^{79} +7.97101 q^{80} +1.00000 q^{81} +13.7308 q^{82} +6.26712 q^{83} +5.81272 q^{84} -1.41503 q^{85} +26.0992 q^{86} -4.80783 q^{87} +54.4994 q^{88} +14.6086 q^{89} -1.22671 q^{90} -3.57639 q^{91} +33.4056 q^{92} -4.33839 q^{93} +11.9527 q^{94} +1.84414 q^{95} +29.4518 q^{96} +9.32022 q^{97} -2.79513 q^{98} -5.11393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * 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 $

$2$	−2.79513	−1.97645	−0.988226	−	0.153002i	$-0.951106\pi$
$2$	−2.79513	−1.97645	−0.988226	+	0.153002i	$0.951106\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.81272	2.90636
$5$	0.438876	0.196271	0.0981357	−	0.995173i	$-0.468712\pi$
$5$	0.438876	0.196271	0.0981357	+	0.995173i	$0.468712\pi$
$6$	2.79513	1.14111
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.6570	−3.76783
$9$	1.00000	0.333333
$10$	−1.22671	−0.387921
$11$	−5.11393	−1.54191	−0.770954	−	0.636891i	$-0.780220\pi$
$11$	−5.11393	−1.54191	−0.770954	+	0.636891i	$0.780220\pi$
$12$	−5.81272	−1.67799
$13$	3.57639	0.991913	0.495957	−	0.868347i	$-0.334817\pi$
$13$	3.57639	0.991913	0.495957	+	0.868347i	$0.334817\pi$
$14$	2.79513	0.747029
$15$	−0.438876	−0.113317
$16$	18.1623	4.54058
$17$	−3.22421	−0.781985	−0.390992	−	0.920394i	$-0.627868\pi$
$17$	−3.22421	−0.781985	−0.390992	+	0.920394i	$0.627868\pi$
$18$	−2.79513	−0.658817
$19$	4.20197	0.963997	0.481999	−	0.876172i	$-0.339911\pi$
$19$	4.20197	0.963997	0.481999	+	0.876172i	$0.339911\pi$
$20$	2.55107	0.570436
$21$	1.00000	0.218218
$22$	14.2941	3.04751
$23$	5.74699	1.19833	0.599165	−	0.800626i	$-0.295499\pi$
$23$	5.74699	1.19833	0.599165	+	0.800626i	$0.295499\pi$
$24$	10.6570	2.17536
$25$	−4.80739	−0.961478
$26$	−9.99647	−1.96047
$27$	−1.00000	−0.192450
$28$	−5.81272	−1.09850
$29$	4.80783	0.892791	0.446396	−	0.894836i	$-0.352707\pi$
$29$	4.80783	0.892791	0.446396	+	0.894836i	$0.352707\pi$
$30$	1.22671	0.223966
$31$	4.33839	0.779198	0.389599	−	0.920985i	$-0.372614\pi$
$31$	4.33839	0.779198	0.389599	+	0.920985i	$0.372614\pi$
$32$	−29.4518	−5.20640
$33$	5.11393	0.890221
$34$	9.01206	1.54556
$35$	−0.438876	−0.0741836
$36$	5.81272	0.968787
$37$	−1.07132	−0.176123	−0.0880617	−	0.996115i	$-0.528067\pi$
$37$	−1.07132	−0.176123	−0.0880617	+	0.996115i	$0.528067\pi$
$38$	−11.7450	−1.90529
$39$	−3.57639	−0.572681
$40$	−4.67712	−0.739518
$41$	−4.91241	−0.767190	−0.383595	−	0.923501i	$-0.625314\pi$
$41$	−4.91241	−0.767190	−0.383595	+	0.923501i	$0.625314\pi$
$42$	−2.79513	−0.431297
$43$	−9.33741	−1.42394	−0.711971	−	0.702209i	$-0.752197\pi$
$43$	−9.33741	−1.42394	−0.711971	+	0.702209i	$0.752197\pi$
$44$	−29.7259	−4.48134
$45$	0.438876	0.0654238
$46$	−16.0635	−2.36844
$47$	−4.27628	−0.623759	−0.311880	−	0.950122i	$-0.600959\pi$
$47$	−4.27628	−0.623759	−0.311880	+	0.950122i	$0.600959\pi$
$48$	−18.1623	−2.62150
$49$	1.00000	0.142857
$50$	13.4372	1.90031
$51$	3.22421	0.451479
$52$	20.7886	2.88286
$53$	2.74214	0.376663	0.188331	−	0.982106i	$-0.439692\pi$
$53$	2.74214	0.376663	0.188331	+	0.982106i	$0.439692\pi$
$54$	2.79513	0.380368
$55$	−2.24438	−0.302632
$56$	10.6570	1.42411
$57$	−4.20197	−0.556564
$58$	−13.4385	−1.76456
$59$	10.0082	1.30296	0.651478	−	0.758667i	$-0.274149\pi$
$59$	10.0082	1.30296	0.651478	+	0.758667i	$0.274149\pi$
$60$	−2.55107	−0.329341
$61$	−2.23200	−0.285779	−0.142889	−	0.989739i	$-0.545639\pi$
$61$	−2.23200	−0.285779	−0.142889	+	0.989739i	$0.545639\pi$
$62$	−12.1263	−1.54005
$63$	−1.00000	−0.125988
$64$	45.9970	5.74962
$65$	1.56959	0.194684
$66$	−14.2941	−1.75948
$67$	−2.87342	−0.351044	−0.175522	−	0.984476i	$-0.556161\pi$
$67$	−2.87342	−0.351044	−0.175522	+	0.984476i	$0.556161\pi$
$68$	−18.7414	−2.27273
$69$	−5.74699	−0.691856
$70$	1.22671	0.146620
$71$	−8.53382	−1.01278	−0.506389	−	0.862305i	$-0.669020\pi$
$71$	−8.53382	−1.01278	−0.506389	+	0.862305i	$0.669020\pi$
$72$	−10.6570	−1.25594
$73$	−1.54704	−0.181067	−0.0905337	−	0.995893i	$-0.528857\pi$
$73$	−1.54704	−0.181067	−0.0905337	+	0.995893i	$0.528857\pi$
$74$	2.99446	0.348099
$75$	4.80739	0.555109
$76$	24.4249	2.80172
$77$	5.11393	0.582786
$78$	9.99647	1.13188
$79$	−7.00338	−0.787942	−0.393971	−	0.919123i	$-0.628899\pi$
$79$	−7.00338	−0.787942	−0.393971	+	0.919123i	$0.628899\pi$
$80$	7.97101	0.891186
$81$	1.00000	0.111111
$82$	13.7308	1.51631
$83$	6.26712	0.687906	0.343953	−	0.938987i	$-0.388234\pi$
$83$	6.26712	0.687906	0.343953	+	0.938987i	$0.388234\pi$
$84$	5.81272	0.634220
$85$	−1.41503	−0.153481
$86$	26.0992	2.81435
$87$	−4.80783	−0.515453
$88$	54.4994	5.80965
$89$	14.6086	1.54851	0.774254	−	0.632875i	$-0.218125\pi$
$89$	14.6086	1.54851	0.774254	+	0.632875i	$0.218125\pi$
$90$	−1.22671	−0.129307
$91$	−3.57639	−0.374908
$92$	33.4056	3.48278
$93$	−4.33839	−0.449870
$94$	11.9527	1.23283
$95$	1.84414	0.189205
$96$	29.4518	3.00592
$97$	9.32022	0.946325	0.473163	−	0.880975i	$-0.343112\pi$
$97$	9.32022	0.946325	0.473163	+	0.880975i	$0.343112\pi$
$98$	−2.79513	−0.282350
$99$	−5.11393	−0.513969
$100$	−27.9440	−2.79440
$101$	−7.51014	−0.747287	−0.373643	−	0.927572i	$-0.621892\pi$
$101$	−7.51014	−0.747287	−0.373643	+	0.927572i	$0.621892\pi$
$102$	−9.01206	−0.892327
$103$	8.52683	0.840174	0.420087	−	0.907484i	$-0.362000\pi$
$103$	8.52683	0.840174	0.420087	+	0.907484i	$0.362000\pi$
$104$	−38.1138	−3.73736
$105$	0.438876	0.0428299
$106$	−7.66464	−0.744455
$107$	−5.66320	−0.547482	−0.273741	−	0.961803i	$-0.588261\pi$
$107$	−5.66320	−0.547482	−0.273741	+	0.961803i	$0.588261\pi$
$108$	−5.81272	−0.559330
$109$	−5.12266	−0.490662	−0.245331	−	0.969439i	$-0.578897\pi$
$109$	−5.12266	−0.490662	−0.245331	+	0.969439i	$0.578897\pi$
$110$	6.27333	0.598139
$111$	1.07132	0.101685
$112$	−18.1623	−1.71618
$113$	−16.4236	−1.54500	−0.772501	−	0.635014i	$-0.780994\pi$
$113$	−16.4236	−1.54500	−0.772501	+	0.635014i	$0.780994\pi$
$114$	11.7450	1.10002
$115$	2.52222	0.235198
$116$	27.9466	2.59477
$117$	3.57639	0.330638
$118$	−27.9742	−2.57523
$119$	3.22421	0.295563
$120$	4.67712	0.426961
$121$	15.1523	1.37748
$122$	6.23873	0.564828
$123$	4.91241	0.442937
$124$	25.2179	2.26463
$125$	−4.30423	−0.384982
$126$	2.79513	0.249010
$127$	−1.64221	−0.145722	−0.0728612	−	0.997342i	$-0.523213\pi$
$127$	−1.64221	−0.145722	−0.0728612	+	0.997342i	$0.523213\pi$
$128$	−69.6636	−6.15745
$129$	9.33741	0.822113
$130$	−4.38721	−0.384784
$131$	9.47030	0.827424	0.413712	−	0.910408i	$-0.364232\pi$
$131$	9.47030	0.827424	0.413712	+	0.910408i	$0.364232\pi$
$132$	29.7259	2.58730
$133$	−4.20197	−0.364357
$134$	8.03156	0.693821
$135$	−0.438876	−0.0377725
$136$	34.3605	2.94639
$137$	13.2603	1.13291	0.566453	−	0.824094i	$-0.308315\pi$
$137$	13.2603	1.13291	0.566453	+	0.824094i	$0.308315\pi$
$138$	16.0635	1.36742
$139$	−11.9000	−1.00935	−0.504674	−	0.863310i	$-0.668387\pi$
$139$	−11.9000	−1.00935	−0.504674	+	0.863310i	$0.668387\pi$
$140$	−2.55107	−0.215604
$141$	4.27628	0.360128
$142$	23.8531	2.00171
$143$	−18.2894	−1.52944
$144$	18.1623	1.51353
$145$	2.11004	0.175229
$146$	4.32417	0.357871
$147$	−1.00000	−0.0824786
$148$	−6.22727	−0.511878
$149$	15.4284	1.26394	0.631970	−	0.774993i	$-0.282247\pi$
$149$	15.4284	1.26394	0.631970	+	0.774993i	$0.282247\pi$
$150$	−13.4372	−1.09715
$151$	22.9567	1.86819	0.934096	−	0.357021i	$-0.116208\pi$
$151$	22.9567	1.86819	0.934096	+	0.357021i	$0.116208\pi$
$152$	−44.7805	−3.63218
$153$	−3.22421	−0.260662
$154$	−14.2941	−1.15185
$155$	1.90402	0.152934
$156$	−20.7886	−1.66442
$157$	−3.11364	−0.248496	−0.124248	−	0.992251i	$-0.539652\pi$
$157$	−3.11364	−0.248496	−0.124248	+	0.992251i	$0.539652\pi$
$158$	19.5753	1.55733
$159$	−2.74214	−0.217466
$160$	−12.9257	−1.02187
$161$	−5.74699	−0.452926
$162$	−2.79513	−0.219606
$163$	−17.4205	−1.36448	−0.682240	−	0.731128i	$-0.738994\pi$
$163$	−17.4205	−1.36448	−0.682240	+	0.731128i	$0.738994\pi$
$164$	−28.5545	−2.22973
$165$	2.24438	0.174725
$166$	−17.5174	−1.35961
$167$	−15.2151	−1.17738	−0.588690	−	0.808359i	$-0.700356\pi$
$167$	−15.2151	−1.17738	−0.588690	+	0.808359i	$0.700356\pi$
$168$	−10.6570	−0.822208
$169$	−0.209405	−0.0161081
$170$	3.95518	0.303348
$171$	4.20197	0.321332
$172$	−54.2758	−4.13849
$173$	3.49995	0.266096	0.133048	−	0.991110i	$-0.457524\pi$
$173$	3.49995	0.266096	0.133048	+	0.991110i	$0.457524\pi$
$174$	13.4385	1.01877
$175$	4.80739	0.363404
$176$	−92.8808	−7.00115
$177$	−10.0082	−0.752262
$178$	−40.8329	−3.06055
$179$	15.8138	1.18198	0.590988	−	0.806680i	$-0.298738\pi$
$179$	15.8138	1.18198	0.590988	+	0.806680i	$0.298738\pi$
$180$	2.55107	0.190145
$181$	−11.7949	−0.876705	−0.438352	−	0.898803i	$-0.644438\pi$
$181$	−11.7949	−0.876705	−0.438352	+	0.898803i	$0.644438\pi$
$182$	9.99647	0.740988
$183$	2.23200	0.164994
$184$	−61.2459	−4.51510
$185$	−0.470175	−0.0345680
$186$	12.1263	0.889147
$187$	16.4884	1.20575
$188$	−24.8568	−1.81287
$189$	1.00000	0.0727393
$190$	−5.15461	−0.373955
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−45.9970	−3.31955
$193$	13.9096	1.00123	0.500616	−	0.865669i	$-0.333107\pi$
$193$	13.9096	1.00123	0.500616	+	0.865669i	$0.333107\pi$
$194$	−26.0512	−1.87037
$195$	−1.56959	−0.112401
$196$	5.81272	0.415195
$197$	15.3562	1.09409	0.547043	−	0.837104i	$-0.315753\pi$
$197$	15.3562	1.09409	0.547043	+	0.837104i	$0.315753\pi$
$198$	14.2941	1.01584
$199$	4.34907	0.308297	0.154149	−	0.988048i	$-0.450737\pi$
$199$	4.34907	0.308297	0.154149	+	0.988048i	$0.450737\pi$
$200$	51.2325	3.62269
$201$	2.87342	0.202675
$202$	20.9918	1.47698
$203$	−4.80783	−0.337443
$204$	18.7414	1.31216
$205$	−2.15594	−0.150577
$206$	−23.8336	−1.66056
$207$	5.74699	0.399443
$208$	64.9556	4.50386
$209$	−21.4886	−1.48639
$210$	−1.22671	−0.0846513
$211$	−17.4608	−1.20205	−0.601026	−	0.799230i	$-0.705241\pi$
$211$	−17.4608	−1.20205	−0.601026	+	0.799230i	$0.705241\pi$
$212$	15.9393	1.09472
$213$	8.53382	0.584728
$214$	15.8293	1.08207
$215$	−4.09797	−0.279479
$216$	10.6570	0.725120
$217$	−4.33839	−0.294509
$218$	14.3185	0.969769
$219$	1.54704	0.104539
$220$	−13.0460	−0.879560
$221$	−11.5310	−0.775661
$222$	−2.99446	−0.200975
$223$	−1.32547	−0.0887600	−0.0443800	−	0.999015i	$-0.514131\pi$
$223$	−1.32547	−0.0887600	−0.0443800	+	0.999015i	$0.514131\pi$
$224$	29.4518	1.96783
$225$	−4.80739	−0.320493
$226$	45.9060	3.05362
$227$	−25.1595	−1.66990	−0.834948	−	0.550329i	$-0.814502\pi$
$227$	−25.1595	−1.66990	−0.834948	+	0.550329i	$0.814502\pi$
$228$	−24.4249	−1.61758
$229$	18.6387	1.23168	0.615841	−	0.787870i	$-0.288816\pi$
$229$	18.6387	1.23168	0.615841	+	0.787870i	$0.288816\pi$
$230$	−7.04991	−0.464857
$231$	−5.11393	−0.336472
$232$	−51.2372	−3.36389
$233$	−16.1829	−1.06018	−0.530089	−	0.847942i	$-0.677842\pi$
$233$	−16.1829	−1.06018	−0.530089	+	0.847942i	$0.677842\pi$
$234$	−9.99647	−0.653490
$235$	−1.87676	−0.122426
$236$	58.1749	3.78686
$237$	7.00338	0.454919
$238$	−9.01206	−0.584165
$239$	23.6342	1.52877	0.764386	−	0.644759i	$-0.223042\pi$
$239$	23.6342	1.52877	0.764386	+	0.644759i	$0.223042\pi$
$240$	−7.97101	−0.514526
$241$	27.7039	1.78457	0.892283	−	0.451477i	$-0.149103\pi$
$241$	27.7039	1.78457	0.892283	+	0.451477i	$0.149103\pi$
$242$	−42.3525	−2.72252
$243$	−1.00000	−0.0641500
$244$	−12.9740	−0.830577
$245$	0.438876	0.0280388
$246$	−13.7308	−0.875444
$247$	15.0279	0.956201
$248$	−46.2344	−2.93589
$249$	−6.26712	−0.397163
$250$	12.0309	0.760898
$251$	−30.2060	−1.90658	−0.953292	−	0.302051i	$-0.902329\pi$
$251$	−30.2060	−1.90658	−0.953292	+	0.302051i	$0.902329\pi$
$252$	−5.81272	−0.366167
$253$	−29.3897	−1.84771
$254$	4.59018	0.288013
$255$	1.41503	0.0886125
$256$	102.725	6.42028
$257$	7.54089	0.470388	0.235194	−	0.971948i	$-0.424428\pi$
$257$	7.54089	0.470388	0.235194	+	0.971948i	$0.424428\pi$
$258$	−26.0992	−1.62487
$259$	1.07132	0.0665684
$260$	9.12362	0.565823
$261$	4.80783	0.297597
$262$	−26.4707	−1.63536
$263$	−26.8503	−1.65566	−0.827829	−	0.560981i	$-0.810424\pi$
$263$	−26.8503	−1.65566	−0.827829	+	0.560981i	$0.810424\pi$
$264$	−54.4994	−3.35420
$265$	1.20346	0.0739281
$266$	11.7450	0.720133
$267$	−14.6086	−0.894032
$268$	−16.7024	−1.02026
$269$	23.8803	1.45601	0.728003	−	0.685574i	$-0.240449\pi$
$269$	23.8803	1.45601	0.728003	+	0.685574i	$0.240449\pi$
$270$	1.22671	0.0746554
$271$	15.7654	0.957682	0.478841	−	0.877902i	$-0.341057\pi$
$271$	15.7654	0.957682	0.478841	+	0.877902i	$0.341057\pi$
$272$	−58.5590	−3.55066
$273$	3.57639	0.216453
$274$	−37.0643	−2.23913
$275$	24.5846	1.48251
$276$	−33.4056	−2.01078
$277$	9.60378	0.577035	0.288518	−	0.957475i	$-0.406838\pi$
$277$	9.60378	0.577035	0.288518	+	0.957475i	$0.406838\pi$
$278$	33.2621	1.99493
$279$	4.33839	0.259733
$280$	4.67712	0.279511
$281$	0.905900	0.0540415	0.0270207	−	0.999635i	$-0.491398\pi$
$281$	0.905900	0.0540415	0.0270207	+	0.999635i	$0.491398\pi$
$282$	−11.9527	−0.711775
$283$	−16.6169	−0.987774	−0.493887	−	0.869526i	$-0.664424\pi$
$283$	−16.6169	−0.987774	−0.493887	+	0.869526i	$0.664424\pi$
$284$	−49.6047	−2.94350
$285$	−1.84414	−0.109238
$286$	51.1212	3.02286
$287$	4.91241	0.289971
$288$	−29.4518	−1.73547
$289$	−6.60449	−0.388500
$290$	−5.89783	−0.346333
$291$	−9.32022	−0.546361
$292$	−8.99252	−0.526248
$293$	23.1218	1.35079	0.675394	−	0.737457i	$-0.263973\pi$
$293$	23.1218	1.35079	0.675394	+	0.737457i	$0.263973\pi$
$294$	2.79513	0.163015
$295$	4.39236	0.255733
$296$	11.4171	0.663603
$297$	5.11393	0.296740
$298$	−43.1242	−2.49812
$299$	20.5535	1.18864
$300$	27.9440	1.61335
$301$	9.33741	0.538199
$302$	−64.1669	−3.69239
$303$	7.51014	0.431446
$304$	76.3174	4.37710
$305$	−0.979573	−0.0560902
$306$	9.01206	0.515185
$307$	−16.7370	−0.955231	−0.477616	−	0.878569i	$-0.658499\pi$
$307$	−16.7370	−0.955231	−0.477616	+	0.878569i	$0.658499\pi$
$308$	29.7259	1.69379
$309$	−8.52683	−0.485075
$310$	−5.32196	−0.302267
$311$	−11.2635	−0.638697	−0.319349	−	0.947637i	$-0.603464\pi$
$311$	−11.2635	−0.638697	−0.319349	+	0.947637i	$0.603464\pi$
$312$	38.1138	2.15777
$313$	14.7439	0.833372	0.416686	−	0.909050i	$-0.363191\pi$
$313$	14.7439	0.833372	0.416686	+	0.909050i	$0.363191\pi$
$314$	8.70302	0.491140
$315$	−0.438876	−0.0247279
$316$	−40.7087	−2.29004
$317$	16.4851	0.925897	0.462949	−	0.886385i	$-0.346791\pi$
$317$	16.4851	0.925897	0.462949	+	0.886385i	$0.346791\pi$
$318$	7.66464	0.429812
$319$	−24.5869	−1.37660
$320$	20.1870	1.12849
$321$	5.66320	0.316089
$322$	16.0635	0.895186
$323$	−13.5480	−0.753831
$324$	5.81272	0.322929
$325$	−17.1931	−0.953702
$326$	48.6925	2.69683
$327$	5.12266	0.283284
$328$	52.3518	2.89064
$329$	4.27628	0.235759
$330$	−6.27333	−0.345335
$331$	21.8658	1.20185	0.600926	−	0.799304i	$-0.294798\pi$
$331$	21.8658	1.20185	0.600926	+	0.799304i	$0.294798\pi$
$332$	36.4291	1.99930
$333$	−1.07132	−0.0587078
$334$	42.5281	2.32704
$335$	−1.26107	−0.0688999
$336$	18.1623	0.990835
$337$	15.0985	0.822468	0.411234	−	0.911530i	$-0.365098\pi$
$337$	15.0985	0.822468	0.411234	+	0.911530i	$0.365098\pi$
$338$	0.585313	0.0318368
$339$	16.4236	0.892007
$340$	−8.22517	−0.446072
$341$	−22.1862	−1.20145
$342$	−11.7450	−0.635098
$343$	−1.00000	−0.0539949
$344$	99.5092	5.36517
$345$	−2.52222	−0.135792
$346$	−9.78280	−0.525926
$347$	29.6008	1.58906	0.794528	−	0.607228i	$-0.207718\pi$
$347$	29.6008	1.58906	0.794528	+	0.607228i	$0.207718\pi$
$348$	−27.9466	−1.49809
$349$	15.4311	0.826007	0.413003	−	0.910729i	$-0.364480\pi$
$349$	15.4311	0.826007	0.413003	+	0.910729i	$0.364480\pi$
$350$	−13.4372	−0.718251
$351$	−3.57639	−0.190894
$352$	150.615	8.02779
$353$	26.4653	1.40861	0.704303	−	0.709899i	$-0.251260\pi$
$353$	26.4653	1.40861	0.704303	+	0.709899i	$0.251260\pi$
$354$	27.9742	1.48681
$355$	−3.74529	−0.198779
$356$	84.9157	4.50053
$357$	−3.22421	−0.170643
$358$	−44.2015	−2.33612
$359$	−3.45254	−0.182218	−0.0911090	−	0.995841i	$-0.529041\pi$
$359$	−3.45254	−0.182218	−0.0911090	+	0.995841i	$0.529041\pi$
$360$	−4.67712	−0.246506
$361$	−1.34348	−0.0707097
$362$	32.9681	1.73276
$363$	−15.1523	−0.795289
$364$	−20.7886	−1.08962
$365$	−0.678960	−0.0355384
$366$	−6.23873	−0.326104
$367$	−8.10264	−0.422954	−0.211477	−	0.977383i	$-0.567827\pi$
$367$	−8.10264	−0.422954	−0.211477	+	0.977383i	$0.567827\pi$
$368$	104.379	5.44111
$369$	−4.91241	−0.255730
$370$	1.31420	0.0683219
$371$	−2.74214	−0.142365
$372$	−25.2179	−1.30749
$373$	−25.1694	−1.30322	−0.651612	−	0.758553i	$-0.725907\pi$
$373$	−25.1694	−1.30322	−0.651612	+	0.758553i	$0.725907\pi$
$374$	−46.0871	−2.38310
$375$	4.30423	0.222269
$376$	45.5725	2.35022
$377$	17.1947	0.885572
$378$	−2.79513	−0.143766
$379$	19.5024	1.00177	0.500884	−	0.865514i	$-0.333008\pi$
$379$	19.5024	1.00177	0.500884	+	0.865514i	$0.333008\pi$
$380$	10.7195	0.549898
$381$	1.64221	0.0841329
$382$	−2.79513	−0.143011
$383$	−1.30425	−0.0666442	−0.0333221	−	0.999445i	$-0.510609\pi$
$383$	−1.30425	−0.0666442	−0.0333221	+	0.999445i	$0.510609\pi$
$384$	69.6636	3.55501
$385$	2.24438	0.114384
$386$	−38.8790	−1.97889
$387$	−9.33741	−0.474647
$388$	54.1759	2.75036
$389$	15.4885	0.785298	0.392649	−	0.919688i	$-0.371559\pi$
$389$	15.4885	0.785298	0.392649	+	0.919688i	$0.371559\pi$
$390$	4.38721	0.222155
$391$	−18.5295	−0.937076
$392$	−10.6570	−0.538262
$393$	−9.47030	−0.477713
$394$	−42.9226	−2.16241
$395$	−3.07362	−0.154651
$396$	−29.7259	−1.49378
$397$	31.4407	1.57796	0.788982	−	0.614416i	$-0.210608\pi$
$397$	31.4407	1.57796	0.788982	+	0.614416i	$0.210608\pi$
$398$	−12.1562	−0.609335
$399$	4.20197	0.210361
$400$	−87.3133	−4.36566
$401$	−13.9712	−0.697691	−0.348845	−	0.937180i	$-0.613426\pi$
$401$	−13.9712	−0.697691	−0.348845	+	0.937180i	$0.613426\pi$
$402$	−8.03156	−0.400578
$403$	15.5158	0.772897
$404$	−43.6544	−2.17189
$405$	0.438876	0.0218079
$406$	13.4385	0.666941
$407$	5.47864	0.271566
$408$	−34.3605	−1.70110
$409$	37.8302	1.87058	0.935291	−	0.353881i	$-0.115138\pi$
$409$	37.8302	1.87058	0.935291	+	0.353881i	$0.115138\pi$
$410$	6.02613	0.297609
$411$	−13.2603	−0.654083
$412$	49.5641	2.44185
$413$	−10.0082	−0.492471
$414$	−16.0635	−0.789480
$415$	2.75049	0.135016
$416$	−105.331	−5.16430
$417$	11.9000	0.582747
$418$	60.0632	2.93779
$419$	25.8137	1.26108	0.630541	−	0.776156i	$-0.282833\pi$
$419$	25.8137	1.26108	0.630541	+	0.776156i	$0.282833\pi$
$420$	2.55107	0.124479
$421$	−1.96823	−0.0959257	−0.0479629	−	0.998849i	$-0.515273\pi$
$421$	−1.96823	−0.0959257	−0.0479629	+	0.998849i	$0.515273\pi$
$422$	48.8051	2.37580
$423$	−4.27628	−0.207920
$424$	−29.2231	−1.41920
$425$	15.5000	0.751861
$426$	−23.8531	−1.15569
$427$	2.23200	0.108014
$428$	−32.9186	−1.59118
$429$	18.2894	0.883022
$430$	11.4543	0.552377
$431$	−2.67916	−0.129050	−0.0645252	−	0.997916i	$-0.520553\pi$
$431$	−2.67916	−0.129050	−0.0645252	+	0.997916i	$0.520553\pi$
$432$	−18.1623	−0.873835
$433$	41.3542	1.98736	0.993678	−	0.112267i	$-0.0358113\pi$
$433$	41.3542	1.98736	0.993678	+	0.112267i	$0.0358113\pi$
$434$	12.1263	0.582083
$435$	−2.11004	−0.101169
$436$	−29.7766	−1.42604
$437$	24.1486	1.15519
$438$	−4.32417	−0.206617
$439$	−13.0448	−0.622592	−0.311296	−	0.950313i	$-0.600763\pi$
$439$	−13.0448	−0.622592	−0.311296	+	0.950313i	$0.600763\pi$
$440$	23.9185	1.14027
$441$	1.00000	0.0476190
$442$	32.2307	1.53306
$443$	19.3856	0.921039	0.460520	−	0.887650i	$-0.347663\pi$
$443$	19.3856	0.921039	0.460520	+	0.887650i	$0.347663\pi$
$444$	6.22727	0.295533
$445$	6.41137	0.303928
$446$	3.70485	0.175430
$447$	−15.4284	−0.729736
$448$	−45.9970	−2.17315
$449$	3.45777	0.163182	0.0815912	−	0.996666i	$-0.474000\pi$
$449$	3.45777	0.163182	0.0815912	+	0.996666i	$0.474000\pi$
$450$	13.4372	0.633438
$451$	25.1217	1.18294
$452$	−95.4658	−4.49033
$453$	−22.9567	−1.07860
$454$	70.3240	3.30047
$455$	−1.56959	−0.0735837
$456$	44.7805	2.09704
$457$	7.35649	0.344122	0.172061	−	0.985086i	$-0.444957\pi$
$457$	7.35649	0.344122	0.172061	+	0.985086i	$0.444957\pi$
$458$	−52.0976	−2.43436
$459$	3.22421	0.150493
$460$	14.6609	0.683570
$461$	−29.9546	−1.39512	−0.697562	−	0.716524i	$-0.745732\pi$
$461$	−29.9546	−1.39512	−0.697562	+	0.716524i	$0.745732\pi$
$462$	14.2941	0.665021
$463$	7.60887	0.353614	0.176807	−	0.984246i	$-0.443423\pi$
$463$	7.60887	0.353614	0.176807	+	0.984246i	$0.443423\pi$
$464$	87.3213	4.05379
$465$	−1.90402	−0.0882967
$466$	45.2333	2.09539
$467$	6.61993	0.306334	0.153167	−	0.988200i	$-0.451053\pi$
$467$	6.61993	0.306334	0.153167	+	0.988200i	$0.451053\pi$
$468$	20.7886	0.960953
$469$	2.87342	0.132682
$470$	5.24577	0.241969
$471$	3.11364	0.143469
$472$	−106.658	−4.90932
$473$	47.7509	2.19559
$474$	−19.5753	−0.899125
$475$	−20.2005	−0.926861
$476$	18.7414	0.859012
$477$	2.74214	0.125554
$478$	−66.0606	−3.02154
$479$	26.5899	1.21492	0.607462	−	0.794349i	$-0.292188\pi$
$479$	26.5899	1.21492	0.607462	+	0.794349i	$0.292188\pi$
$480$	12.9257	0.589976
$481$	−3.83145	−0.174699
$482$	−77.4359	−3.52711
$483$	5.74699	0.261497
$484$	88.0760	4.00346
$485$	4.09043	0.185737
$486$	2.79513	0.126789
$487$	16.4158	0.743872	0.371936	−	0.928258i	$-0.378694\pi$
$487$	16.4158	0.743872	0.371936	+	0.928258i	$0.378694\pi$
$488$	23.7866	1.07677
$489$	17.4205	0.787783
$490$	−1.22671	−0.0554173
$491$	23.8212	1.07503	0.537517	−	0.843253i	$-0.319362\pi$
$491$	23.8212	1.07503	0.537517	+	0.843253i	$0.319362\pi$
$492$	28.5545	1.28734
$493$	−15.5014	−0.698149
$494$	−42.0048	−1.88989
$495$	−2.24438	−0.100877
$496$	78.7952	3.53801
$497$	8.53382	0.382794
$498$	17.5174	0.784973
$499$	−35.0320	−1.56825	−0.784123	−	0.620605i	$-0.786887\pi$
$499$	−35.0320	−1.56825	−0.784123	+	0.620605i	$0.786887\pi$
$500$	−25.0193	−1.11890
$501$	15.2151	0.679761
$502$	84.4294	3.76827
$503$	−39.5216	−1.76218	−0.881090	−	0.472949i	$-0.843190\pi$
$503$	−39.5216	−1.76218	−0.881090	+	0.472949i	$0.843190\pi$
$504$	10.6570	0.474702
$505$	−3.29602	−0.146671
$506$	82.1479	3.65192
$507$	0.209405	0.00929999
$508$	−9.54571	−0.423522
$509$	−18.6767	−0.827832	−0.413916	−	0.910315i	$-0.635839\pi$
$509$	−18.6767	−0.827832	−0.413916	+	0.910315i	$0.635839\pi$
$510$	−3.95518	−0.175138
$511$	1.54704	0.0684371
$512$	−147.801	−6.53193
$513$	−4.20197	−0.185521
$514$	−21.0777	−0.929698
$515$	3.74222	0.164902
$516$	54.2758	2.38936
$517$	21.8686	0.961779
$518$	−2.99446	−0.131569
$519$	−3.49995	−0.153631
$520$	−16.7272	−0.733538
$521$	4.03970	0.176983	0.0884913	−	0.996077i	$-0.471795\pi$
$521$	4.03970	0.176983	0.0884913	+	0.996077i	$0.471795\pi$
$522$	−13.4385	−0.588186
$523$	1.66124	0.0726411	0.0363205	−	0.999340i	$-0.488436\pi$
$523$	1.66124	0.0726411	0.0363205	+	0.999340i	$0.488436\pi$
$524$	55.0482	2.40479
$525$	−4.80739	−0.209812
$526$	75.0498	3.27233
$527$	−13.9879	−0.609321
$528$	92.8808	4.04212
$529$	10.0279	0.435994
$530$	−3.36383	−0.146115
$531$	10.0082	0.434319
$532$	−24.4249	−1.05895
$533$	−17.5687	−0.760986
$534$	40.8329	1.76701
$535$	−2.48544	−0.107455
$536$	30.6221	1.32267
$537$	−15.8138	−0.682414
$538$	−66.7484	−2.87773
$539$	−5.11393	−0.220273
$540$	−2.55107	−0.109780
$541$	−11.7976	−0.507218	−0.253609	−	0.967307i	$-0.581618\pi$
$541$	−11.7976	−0.507218	−0.253609	+	0.967307i	$0.581618\pi$
$542$	−44.0664	−1.89281
$543$	11.7949	0.506166
$544$	94.9588	4.07133
$545$	−2.24821	−0.0963029
$546$	−9.99647	−0.427809
$547$	−0.354746	−0.0151678	−0.00758392	−	0.999971i	$-0.502414\pi$
$547$	−0.354746	−0.0151678	−0.00758392	+	0.999971i	$0.502414\pi$
$548$	77.0786	3.29263
$549$	−2.23200	−0.0952596
$550$	−68.7172	−2.93011
$551$	20.2023	0.860648
$552$	61.2459	2.60680
$553$	7.00338	0.297814
$554$	−26.8438	−1.14048
$555$	0.470175	0.0199578
$556$	−69.1716	−2.93353
$557$	−35.3669	−1.49854	−0.749272	−	0.662262i	$-0.769597\pi$
$557$	−35.3669	−1.49854	−0.749272	+	0.662262i	$0.769597\pi$
$558$	−12.1263	−0.513349
$559$	−33.3943	−1.41243
$560$	−7.97101	−0.336837
$561$	−16.4884	−0.696139
$562$	−2.53210	−0.106810
$563$	17.7533	0.748213	0.374107	−	0.927386i	$-0.377949\pi$
$563$	17.7533	0.748213	0.374107	+	0.927386i	$0.377949\pi$
$564$	24.8568	1.04666
$565$	−7.20792	−0.303240
$566$	46.4464	1.95229
$567$	−1.00000	−0.0419961
$568$	90.9453	3.81598
$569$	33.1380	1.38922	0.694609	−	0.719387i	$-0.255577\pi$
$569$	33.1380	1.38922	0.694609	+	0.719387i	$0.255577\pi$
$570$	5.15461	0.215903
$571$	9.18992	0.384586	0.192293	−	0.981338i	$-0.438408\pi$
$571$	9.18992	0.384586	0.192293	+	0.981338i	$0.438408\pi$
$572$	−106.311	−4.44510
$573$	−1.00000	−0.0417756
$574$	−13.7308	−0.573113
$575$	−27.6280	−1.15217
$576$	45.9970	1.91654
$577$	−16.5673	−0.689707	−0.344853	−	0.938657i	$-0.612071\pi$
$577$	−16.5673	−0.689707	−0.344853	+	0.938657i	$0.612071\pi$
$578$	18.4604	0.767851
$579$	−13.9096	−0.578062
$580$	12.2651	0.509280
$581$	−6.26712	−0.260004
$582$	26.0512	1.07986
$583$	−14.0231	−0.580779
$584$	16.4869	0.682232
$585$	1.56959	0.0648947
$586$	−64.6283	−2.66977
$587$	−7.92173	−0.326965	−0.163482	−	0.986546i	$-0.552273\pi$
$587$	−7.92173	−0.326965	−0.163482	+	0.986546i	$0.552273\pi$
$588$	−5.81272	−0.239713
$589$	18.2298	0.751145
$590$	−12.2772	−0.505444
$591$	−15.3562	−0.631671
$592$	−19.4576	−0.799702
$593$	42.4401	1.74280	0.871402	−	0.490570i	$-0.163211\pi$
$593$	42.4401	1.74280	0.871402	+	0.490570i	$0.163211\pi$
$594$	−14.2941	−0.586493
$595$	1.41503	0.0580105
$596$	89.6808	3.67347
$597$	−4.34907	−0.177995
$598$	−57.4496	−2.34929
$599$	5.29945	0.216530	0.108265	−	0.994122i	$-0.465471\pi$
$599$	5.29945	0.216530	0.108265	+	0.994122i	$0.465471\pi$
$600$	−51.2325	−2.09156
$601$	45.4937	1.85573	0.927864	−	0.372918i	$-0.121643\pi$
$601$	45.4937	1.85573	0.927864	+	0.372918i	$0.121643\pi$
$602$	−26.0992	−1.06373
$603$	−2.87342	−0.117015
$604$	133.441	5.42964
$605$	6.64998	0.270360
$606$	−20.9918	−0.852732
$607$	−27.4040	−1.11229	−0.556147	−	0.831084i	$-0.687721\pi$
$607$	−27.4040	−1.11229	−0.556147	+	0.831084i	$0.687721\pi$
$608$	−123.756	−5.01895
$609$	4.80783	0.194823
$610$	2.73803	0.110860
$611$	−15.2937	−0.618715
$612$	−18.7414	−0.757577
$613$	3.40430	0.137498	0.0687492	−	0.997634i	$-0.478099\pi$
$613$	3.40430	0.137498	0.0687492	+	0.997634i	$0.478099\pi$
$614$	46.7820	1.88797
$615$	2.15594	0.0869360
$616$	−54.4994	−2.19584
$617$	40.4112	1.62689	0.813447	−	0.581639i	$-0.197588\pi$
$617$	40.4112	1.62689	0.813447	+	0.581639i	$0.197588\pi$
$618$	23.8336	0.958726
$619$	32.6621	1.31280	0.656400	−	0.754413i	$-0.272078\pi$
$619$	32.6621	1.31280	0.656400	+	0.754413i	$0.272078\pi$
$620$	11.0675	0.444482
$621$	−5.74699	−0.230619
$622$	31.4830	1.26235
$623$	−14.6086	−0.585281
$624$	−64.9556	−2.60030
$625$	22.1479	0.885917
$626$	−41.2109	−1.64712
$627$	21.4886	0.858170
$628$	−18.0987	−0.722218
$629$	3.45415	0.137726
$630$	1.22671	0.0488735
$631$	−5.47414	−0.217922	−0.108961	−	0.994046i	$-0.534752\pi$
$631$	−5.47414	−0.217922	−0.108961	+	0.994046i	$0.534752\pi$
$632$	74.6353	2.96883
$633$	17.4608	0.694005
$634$	−46.0780	−1.82999
$635$	−0.720726	−0.0286012
$636$	−15.9393	−0.632036
$637$	3.57639	0.141702
$638$	68.7235	2.72079
$639$	−8.53382	−0.337593
$640$	−30.5737	−1.20853
$641$	−12.9623	−0.511982	−0.255991	−	0.966679i	$-0.582402\pi$
$641$	−12.9623	−0.511982	−0.255991	+	0.966679i	$0.582402\pi$
$642$	−15.8293	−0.624734
$643$	36.6812	1.44656	0.723282	−	0.690553i	$-0.242633\pi$
$643$	36.6812	1.44656	0.723282	+	0.690553i	$0.242633\pi$
$644$	−33.4056	−1.31637
$645$	4.09797	0.161357
$646$	37.8684	1.48991
$647$	−10.3424	−0.406600	−0.203300	−	0.979116i	$-0.565167\pi$
$647$	−10.3424	−0.406600	−0.203300	+	0.979116i	$0.565167\pi$
$648$	−10.6570	−0.418648
$649$	−51.1812	−2.00904
$650$	48.0569	1.88495
$651$	4.33839	0.170035
$652$	−101.261	−3.96567
$653$	14.7202	0.576046	0.288023	−	0.957623i	$-0.407002\pi$
$653$	14.7202	0.576046	0.288023	+	0.957623i	$0.407002\pi$
$654$	−14.3185	−0.559897
$655$	4.15629	0.162400
$656$	−89.2208	−3.48349
$657$	−1.54704	−0.0603558
$658$	−11.9527	−0.465966
$659$	−20.1513	−0.784985	−0.392493	−	0.919755i	$-0.628387\pi$
$659$	−20.1513	−0.784985	−0.392493	+	0.919755i	$0.628387\pi$
$660$	13.0460	0.507814
$661$	−32.8745	−1.27867	−0.639334	−	0.768929i	$-0.720790\pi$
$661$	−32.8745	−1.27867	−0.639334	+	0.768929i	$0.720790\pi$
$662$	−61.1176	−2.37540
$663$	11.5310	0.447828
$664$	−66.7890	−2.59192
$665$	−1.84414	−0.0715128
$666$	2.99446	0.116033
$667$	27.6305	1.06986
$668$	−88.4412	−3.42189
$669$	1.32547	0.0512456
$670$	3.52486	0.136177
$671$	11.4143	0.440645
$672$	−29.4518	−1.13613
$673$	−22.5830	−0.870511	−0.435256	−	0.900307i	$-0.643342\pi$
$673$	−22.5830	−0.870511	−0.435256	+	0.900307i	$0.643342\pi$
$674$	−42.2022	−1.62557
$675$	4.80739	0.185036
$676$	−1.21721	−0.0468159
$677$	24.5641	0.944074	0.472037	−	0.881579i	$-0.343519\pi$
$677$	24.5641	0.944074	0.472037	+	0.881579i	$0.343519\pi$
$678$	−45.9060	−1.76301
$679$	−9.32022	−0.357677
$680$	15.0800	0.578292
$681$	25.1595	0.964115
$682$	62.0133	2.37461
$683$	−17.5757	−0.672516	−0.336258	−	0.941770i	$-0.609161\pi$
$683$	−17.5757	−0.672516	−0.336258	+	0.941770i	$0.609161\pi$
$684$	24.4249	0.933908
$685$	5.81964	0.222357
$686$	2.79513	0.106718
$687$	−18.6387	−0.711112
$688$	−169.589	−6.46552
$689$	9.80699	0.373617
$690$	7.04991	0.268385
$691$	−10.6386	−0.404713	−0.202357	−	0.979312i	$-0.564860\pi$
$691$	−10.6386	−0.404713	−0.202357	+	0.979312i	$0.564860\pi$
$692$	20.3442	0.773372
$693$	5.11393	0.194262
$694$	−82.7380	−3.14069
$695$	−5.22264	−0.198106
$696$	51.2372	1.94214
$697$	15.8386	0.599931
$698$	−43.1318	−1.63256
$699$	16.1829	0.612094
$700$	27.9440	1.05618
$701$	36.6179	1.38304	0.691520	−	0.722357i	$-0.256941\pi$
$701$	36.6179	1.38304	0.691520	+	0.722357i	$0.256941\pi$
$702$	9.99647	0.377292
$703$	−4.50163	−0.169782
$704$	−235.225	−8.86539
$705$	1.87676	0.0706827
$706$	−73.9739	−2.78404
$707$	7.51014	0.282448
$708$	−58.1749	−2.18635
$709$	39.8295	1.49583	0.747914	−	0.663796i	$-0.231056\pi$
$709$	39.8295	1.49583	0.747914	+	0.663796i	$0.231056\pi$
$710$	10.4686	0.392878
$711$	−7.00338	−0.262647
$712$	−155.684	−5.83452
$713$	24.9327	0.933736
$714$	9.01206	0.337268
$715$	−8.02680	−0.300185
$716$	91.9211	3.43525
$717$	−23.6342	−0.882636
$718$	9.65027	0.360145
$719$	42.6300	1.58983	0.794915	−	0.606721i	$-0.207516\pi$
$719$	42.6300	1.58983	0.794915	+	0.606721i	$0.207516\pi$
$720$	7.97101	0.297062
$721$	−8.52683	−0.317556
$722$	3.75521	0.139754
$723$	−27.7039	−1.03032
$724$	−68.5602	−2.54802
$725$	−23.1131	−0.858399
$726$	42.3525	1.57185
$727$	−41.1125	−1.52478	−0.762388	−	0.647120i	$-0.775973\pi$
$727$	−41.1125	−1.52478	−0.762388	+	0.647120i	$0.775973\pi$
$728$	38.1138	1.41259
$729$	1.00000	0.0370370
$730$	1.89778	0.0702399
$731$	30.1057	1.11350
$732$	12.9740	0.479534
$733$	−18.4931	−0.683058	−0.341529	−	0.939871i	$-0.610945\pi$
$733$	−18.4931	−0.683058	−0.341529	+	0.939871i	$0.610945\pi$
$734$	22.6479	0.835949
$735$	−0.438876	−0.0161882
$736$	−169.259	−6.23898
$737$	14.6945	0.541277
$738$	13.7308	0.505438
$739$	10.0368	0.369209	0.184605	−	0.982813i	$-0.440900\pi$
$739$	10.0368	0.369209	0.184605	+	0.982813i	$0.440900\pi$
$740$	−2.73300	−0.100467
$741$	−15.0279	−0.552063
$742$	7.66464	0.281378
$743$	19.6515	0.720943	0.360471	−	0.932770i	$-0.382616\pi$
$743$	19.6515	0.720943	0.360471	+	0.932770i	$0.382616\pi$
$744$	46.2344	1.69504
$745$	6.77114	0.248075
$746$	70.3517	2.57576
$747$	6.26712	0.229302
$748$	95.8423	3.50434
$749$	5.66320	0.206929
$750$	−12.0309	−0.439305
$751$	−48.9085	−1.78470	−0.892348	−	0.451347i	$-0.850944\pi$
$751$	−48.9085	−1.78470	−0.892348	+	0.451347i	$0.850944\pi$
$752$	−77.6671	−2.83223
$753$	30.2060	1.10077
$754$	−48.0613	−1.75029
$755$	10.0752	0.366673
$756$	5.81272	0.211407
$757$	32.5184	1.18190	0.590950	−	0.806708i	$-0.298753\pi$
$757$	32.5184	1.18190	0.590950	+	0.806708i	$0.298753\pi$
$758$	−54.5115	−1.97995
$759$	29.3897	1.06678
$760$	−19.6531	−0.712893
$761$	29.9107	1.08426	0.542131	−	0.840294i	$-0.317618\pi$
$761$	29.9107	1.08426	0.542131	+	0.840294i	$0.317618\pi$
$762$	−4.59018	−0.166285
$763$	5.12266	0.185453
$764$	5.81272	0.210297
$765$	−1.41503	−0.0511604
$766$	3.64555	0.131719
$767$	35.7933	1.29242
$768$	−102.725	−3.70675
$769$	35.5130	1.28063	0.640316	−	0.768112i	$-0.278803\pi$
$769$	35.5130	1.28063	0.640316	+	0.768112i	$0.278803\pi$
$770$	−6.27333	−0.226075
$771$	−7.54089	−0.271578
$772$	80.8525	2.90994
$773$	23.6448	0.850445	0.425222	−	0.905089i	$-0.360196\pi$
$773$	23.6448	0.850445	0.425222	+	0.905089i	$0.360196\pi$
$774$	26.0992	0.938118
$775$	−20.8563	−0.749181
$776$	−99.3260	−3.56560
$777$	−1.07132	−0.0384333
$778$	−43.2923	−1.55210
$779$	−20.6418	−0.739569
$780$	−9.12362	−0.326678
$781$	43.6414	1.56161
$782$	51.7922	1.85208
$783$	−4.80783	−0.171818
$784$	18.1623	0.648654
$785$	−1.36650	−0.0487726
$786$	26.4707	0.944177
$787$	18.0330	0.642807	0.321403	−	0.946942i	$-0.395845\pi$
$787$	18.0330	0.642807	0.321403	+	0.946942i	$0.395845\pi$
$788$	89.2616	3.17981
$789$	26.8503	0.955894
$790$	8.59115	0.305659
$791$	16.4236	0.583956
$792$	54.4994	1.93655
$793$	−7.98252	−0.283468
$794$	−87.8807	−3.11877
$795$	−1.20346	−0.0426824
$796$	25.2799	0.896023
$797$	35.9599	1.27377	0.636883	−	0.770960i	$-0.280223\pi$
$797$	35.9599	1.27377	0.636883	+	0.770960i	$0.280223\pi$
$798$	−11.7450	−0.415769
$799$	13.7876	0.487770
$800$	141.586	5.00584
$801$	14.6086	0.516169
$802$	39.0514	1.37895
$803$	7.91146	0.279189
$804$	16.7024	0.589048
$805$	−2.52222	−0.0888964
$806$	−43.3686	−1.52759
$807$	−23.8803	−0.840626
$808$	80.0358	2.81565
$809$	7.15677	0.251619	0.125809	−	0.992054i	$-0.459847\pi$
$809$	7.15677	0.251619	0.125809	+	0.992054i	$0.459847\pi$
$810$	−1.22671	−0.0431023
$811$	−52.8781	−1.85680	−0.928400	−	0.371583i	$-0.878815\pi$
$811$	−52.8781	−1.85680	−0.928400	+	0.371583i	$0.878815\pi$
$812$	−27.9466	−0.980733
$813$	−15.7654	−0.552918
$814$	−15.3135	−0.536737
$815$	−7.64545	−0.267809
$816$	58.5590	2.04998
$817$	−39.2355	−1.37268
$818$	−105.740	−3.69711
$819$	−3.57639	−0.124969
$820$	−12.5319	−0.437633
$821$	15.2852	0.533457	0.266728	−	0.963772i	$-0.414057\pi$
$821$	15.2852	0.533457	0.266728	+	0.963772i	$0.414057\pi$
$822$	37.0643	1.29276
$823$	5.78334	0.201595	0.100797	−	0.994907i	$-0.467861\pi$
$823$	5.78334	0.201595	0.100797	+	0.994907i	$0.467861\pi$
$824$	−90.8708	−3.16563
$825$	−24.5846	−0.855928
$826$	27.9742	0.973346
$827$	44.9937	1.56459	0.782293	−	0.622911i	$-0.214050\pi$
$827$	44.9937	1.56459	0.782293	+	0.622911i	$0.214050\pi$
$828$	33.4056	1.16093
$829$	−43.7872	−1.52079	−0.760396	−	0.649459i	$-0.774995\pi$
$829$	−43.7872	−1.52079	−0.760396	+	0.649459i	$0.774995\pi$
$830$	−7.68797	−0.266853
$831$	−9.60378	−0.333152
$832$	164.503	5.70313
$833$	−3.22421	−0.111712
$834$	−33.2621	−1.15177
$835$	−6.67755	−0.231086
$836$	−124.907	−4.32000
$837$	−4.33839	−0.149957
$838$	−72.1525	−2.49247
$839$	−12.7852	−0.441396	−0.220698	−	0.975342i	$-0.570833\pi$
$839$	−12.7852	−0.441396	−0.220698	+	0.975342i	$0.570833\pi$
$840$	−4.67712	−0.161376
$841$	−5.88478	−0.202924
$842$	5.50145	0.189593
$843$	−0.905900	−0.0312009
$844$	−101.495	−3.49360
$845$	−0.0919028	−0.00316155
$846$	11.9527	0.410943
$847$	−15.1523	−0.520639
$848$	49.8037	1.71027
$849$	16.6169	0.570292
$850$	−43.3245	−1.48602
$851$	−6.15684	−0.211054
$852$	49.6047	1.69943
$853$	−23.1114	−0.791320	−0.395660	−	0.918397i	$-0.629484\pi$
$853$	−23.1114	−0.791320	−0.395660	+	0.918397i	$0.629484\pi$
$854$	−6.23873	−0.213485
$855$	1.84414	0.0630684
$856$	60.3529	2.06282
$857$	−16.9975	−0.580624	−0.290312	−	0.956932i	$-0.593759\pi$
$857$	−16.9975	−0.580624	−0.290312	+	0.956932i	$0.593759\pi$
$858$	−51.1212	−1.74525
$859$	−13.9685	−0.476598	−0.238299	−	0.971192i	$-0.576590\pi$
$859$	−13.9685	−0.476598	−0.238299	+	0.971192i	$0.576590\pi$
$860$	−23.8204	−0.812267
$861$	−4.91241	−0.167415
$862$	7.48858	0.255062
$863$	44.5075	1.51505	0.757526	−	0.652805i	$-0.226408\pi$
$863$	44.5075	1.51505	0.757526	+	0.652805i	$0.226408\pi$
$864$	29.4518	1.00197
$865$	1.53604	0.0522271
$866$	−115.590	−3.92791
$867$	6.60449	0.224300
$868$	−25.2179	−0.855950
$869$	35.8148	1.21493
$870$	5.89783	0.199955
$871$	−10.2765	−0.348205
$872$	54.5924	1.84873
$873$	9.32022	0.315442
$874$	−67.4985	−2.28317
$875$	4.30423	0.145510
$876$	8.99252	0.303829
$877$	7.27246	0.245573	0.122787	−	0.992433i	$-0.460817\pi$
$877$	7.27246	0.245573	0.122787	+	0.992433i	$0.460817\pi$
$878$	36.4617	1.23052
$879$	−23.1218	−0.779878
$880$	−40.7632	−1.37413
$881$	−3.49977	−0.117910	−0.0589551	−	0.998261i	$-0.518777\pi$
$881$	−3.49977	−0.117910	−0.0589551	+	0.998261i	$0.518777\pi$
$882$	−2.79513	−0.0941168
$883$	39.2050	1.31935	0.659677	−	0.751549i	$-0.270693\pi$
$883$	39.2050	1.31935	0.659677	+	0.751549i	$0.270693\pi$
$884$	−67.0267	−2.25435
$885$	−4.39236	−0.147648
$886$	−54.1853	−1.82039
$887$	2.50017	0.0839476	0.0419738	−	0.999119i	$-0.486635\pi$
$887$	2.50017	0.0839476	0.0419738	+	0.999119i	$0.486635\pi$
$888$	−11.4171	−0.383131
$889$	1.64221	0.0550779
$890$	−17.9206	−0.600699
$891$	−5.11393	−0.171323
$892$	−7.70459	−0.257969
$893$	−17.9688	−0.601302
$894$	43.1242	1.44229
$895$	6.94029	0.231988
$896$	69.6636	2.32730
$897$	−20.5535	−0.686261
$898$	−9.66491	−0.322522
$899$	20.8582	0.695661
$900$	−27.9440	−0.931467
$901$	−8.84124	−0.294544
$902$	−70.2184	−2.33802
$903$	−9.33741	−0.310730
$904$	175.027	5.82131
$905$	−5.17648	−0.172072
$906$	64.1669	2.13180
$907$	59.1752	1.96488	0.982441	−	0.186575i	$-0.0597389\pi$
$907$	59.1752	1.96488	0.982441	+	0.186575i	$0.0597389\pi$
$908$	−146.245	−4.85332
$909$	−7.51014	−0.249096
$910$	4.38721	0.145435
$911$	−43.1779	−1.43055	−0.715274	−	0.698844i	$-0.753698\pi$
$911$	−43.1779	−1.43055	−0.715274	+	0.698844i	$0.753698\pi$
$912$	−76.3174	−2.52712
$913$	−32.0496	−1.06069
$914$	−20.5623	−0.680140
$915$	0.979573	0.0323837
$916$	108.342	3.57972
$917$	−9.47030	−0.312737
$918$	−9.01206	−0.297442
$919$	8.46844	0.279348	0.139674	−	0.990198i	$-0.455395\pi$
$919$	8.46844	0.279348	0.139674	+	0.990198i	$0.455395\pi$
$920$	−26.8794	−0.886186
$921$	16.7370	0.551503
$922$	83.7268	2.75740
$923$	−30.5203	−1.00459
$924$	−29.7259	−0.977909
$925$	5.15023	0.169339
$926$	−21.2678	−0.698902
$927$	8.52683	0.280058
$928$	−141.599	−4.64823
$929$	7.16519	0.235082	0.117541	−	0.993068i	$-0.462499\pi$
$929$	7.16519	0.235082	0.117541	+	0.993068i	$0.462499\pi$
$930$	5.32196	0.174514
$931$	4.20197	0.137714
$932$	−94.0668	−3.08126
$933$	11.2635	0.368752
$934$	−18.5035	−0.605454
$935$	7.23635	0.236654
$936$	−38.1138	−1.24579
$937$	24.8796	0.812780	0.406390	−	0.913700i	$-0.366787\pi$
$937$	24.8796	0.812780	0.406390	+	0.913700i	$0.366787\pi$
$938$	−8.03156	−0.262240
$939$	−14.7439	−0.481148
$940$	−10.9091	−0.355815
$941$	13.9563	0.454962	0.227481	−	0.973782i	$-0.426951\pi$
$941$	13.9563	0.454962	0.227481	+	0.973782i	$0.426951\pi$
$942$	−8.70302	−0.283560
$943$	−28.2316	−0.919347
$944$	181.772	5.91617
$945$	0.438876	0.0142766
$946$	−133.470	−4.33947
$947$	−11.6927	−0.379963	−0.189981	−	0.981788i	$-0.560843\pi$
$947$	−11.6927	−0.379963	−0.189981	+	0.981788i	$0.560843\pi$
$948$	40.7087	1.32216
$949$	−5.53283	−0.179603
$950$	56.4629	1.83190
$951$	−16.4851	−0.534567
$952$	−34.3605	−1.11363
$953$	0.621506	0.0201325	0.0100663	−	0.999949i	$-0.496796\pi$
$953$	0.621506	0.0201325	0.0100663	+	0.999949i	$0.496796\pi$
$954$	−7.66464	−0.248152
$955$	0.438876	0.0142017
$956$	137.379	4.44316
$957$	24.5869	0.794782
$958$	−74.3221	−2.40124
$959$	−13.2603	−0.428198
$960$	−20.1870	−0.651532
$961$	−12.1784	−0.392851
$962$	10.7094	0.345284
$963$	−5.66320	−0.182494
$964$	161.035	5.18659
$965$	6.10458	0.196513
$966$	−16.0635	−0.516836
$967$	23.1558	0.744641	0.372320	−	0.928104i	$-0.378562\pi$
$967$	23.1558	0.744641	0.372320	+	0.928104i	$0.378562\pi$
$968$	−161.479	−5.19012
$969$	13.5480	0.435225
$970$	−11.4333	−0.367100
$971$	57.5786	1.84779	0.923893	−	0.382650i	$-0.124989\pi$
$971$	57.5786	1.84779	0.923893	+	0.382650i	$0.124989\pi$
$972$	−5.81272	−0.186443
$973$	11.9000	0.381498
$974$	−45.8843	−1.47023
$975$	17.1931	0.550620
$976$	−40.5383	−1.29760
$977$	−32.8905	−1.05226	−0.526130	−	0.850404i	$-0.676358\pi$
$977$	−32.8905	−1.05226	−0.526130	+	0.850404i	$0.676358\pi$
$978$	−48.6925	−1.55702
$979$	−74.7074	−2.38766
$980$	2.55107	0.0814908
$981$	−5.12266	−0.163554
$982$	−66.5832	−2.12475
$983$	−10.1993	−0.325307	−0.162653	−	0.986683i	$-0.552005\pi$
$983$	−10.1993	−0.325307	−0.162653	+	0.986683i	$0.552005\pi$
$984$	−52.3518	−1.66891
$985$	6.73949	0.214738
$986$	43.3284	1.37986
$987$	−4.27628	−0.136115
$988$	87.3529	2.77907
$989$	−53.6620	−1.70635
$990$	6.27333	0.199380
$991$	−13.5660	−0.430939	−0.215469	−	0.976511i	$-0.569128\pi$
$991$	−13.5660	−0.430939	−0.215469	+	0.976511i	$0.569128\pi$
$992$	−127.774	−4.05682
$993$	−21.8658	−0.693890
$994$	−23.8531	−0.756574
$995$	1.90870	0.0605099
$996$	−36.4291	−1.15430
$997$	−32.0886	−1.01626	−0.508128	−	0.861282i	$-0.669662\pi$
$997$	−32.0886	−1.01626	−0.508128	+	0.861282i	$0.669662\pi$
$998$	97.9188	3.09956
$999$	1.07132	0.0338949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.1	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.1	✓	26	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79513 q^{2} -1.00000 q^{3} +5.81272 q^{4} +0.438876 q^{5} +2.79513 q^{6} -1.00000 q^{7} -10.6570 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.79513 q^{2} -1.00000 q^{3} +5.81272 q^{4} +0.438876 q^{5} +2.79513 q^{6} -1.00000 q^{7} -10.6570 q^{8} +1.00000 q^{9} -1.22671 q^{10} -5.11393 q^{11} -5.81272 q^{12} +3.57639 q^{13} +2.79513 q^{14} -0.438876 q^{15} +18.1623 q^{16} -3.22421 q^{17} -2.79513 q^{18} +4.20197 q^{19} +2.55107 q^{20} +1.00000 q^{21} +14.2941 q^{22} +5.74699 q^{23} +10.6570 q^{24} -4.80739 q^{25} -9.99647 q^{26} -1.00000 q^{27} -5.81272 q^{28} +4.80783 q^{29} +1.22671 q^{30} +4.33839 q^{31} -29.4518 q^{32} +5.11393 q^{33} +9.01206 q^{34} -0.438876 q^{35} +5.81272 q^{36} -1.07132 q^{37} -11.7450 q^{38} -3.57639 q^{39} -4.67712 q^{40} -4.91241 q^{41} -2.79513 q^{42} -9.33741 q^{43} -29.7259 q^{44} +0.438876 q^{45} -16.0635 q^{46} -4.27628 q^{47} -18.1623 q^{48} +1.00000 q^{49} +13.4372 q^{50} +3.22421 q^{51} +20.7886 q^{52} +2.74214 q^{53} +2.79513 q^{54} -2.24438 q^{55} +10.6570 q^{56} -4.20197 q^{57} -13.4385 q^{58} +10.0082 q^{59} -2.55107 q^{60} -2.23200 q^{61} -12.1263 q^{62} -1.00000 q^{63} +45.9970 q^{64} +1.56959 q^{65} -14.2941 q^{66} -2.87342 q^{67} -18.7414 q^{68} -5.74699 q^{69} +1.22671 q^{70} -8.53382 q^{71} -10.6570 q^{72} -1.54704 q^{73} +2.99446 q^{74} +4.80739 q^{75} +24.4249 q^{76} +5.11393 q^{77} +9.99647 q^{78} -7.00338 q^{79} +7.97101 q^{80} +1.00000 q^{81} +13.7308 q^{82} +6.26712 q^{83} +5.81272 q^{84} -1.41503 q^{85} +26.0992 q^{86} -4.80783 q^{87} +54.4994 q^{88} +14.6086 q^{89} -1.22671 q^{90} -3.57639 q^{91} +33.4056 q^{92} -4.33839 q^{93} +11.9527 q^{94} +1.84414 q^{95} +29.4518 q^{96} +9.32022 q^{97} -2.79513 q^{98} -5.11393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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