LMFDB - Embedded newform 4011.2.a.j.1.13

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			1.13
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)

$f(q)$	$=$	$q-0.163923 q^{2} -1.00000 q^{3} -1.97313 q^{4} +0.716872 q^{5} +0.163923 q^{6} -1.00000 q^{7} +0.651287 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.163923 q^{2} -1.00000 q^{3} -1.97313 q^{4} +0.716872 q^{5} +0.163923 q^{6} -1.00000 q^{7} +0.651287 q^{8} +1.00000 q^{9} -0.117512 q^{10} -0.769923 q^{11} +1.97313 q^{12} -0.567788 q^{13} +0.163923 q^{14} -0.716872 q^{15} +3.83950 q^{16} +6.99026 q^{17} -0.163923 q^{18} -5.99415 q^{19} -1.41448 q^{20} +1.00000 q^{21} +0.126208 q^{22} +5.47895 q^{23} -0.651287 q^{24} -4.48609 q^{25} +0.0930735 q^{26} -1.00000 q^{27} +1.97313 q^{28} +2.95347 q^{29} +0.117512 q^{30} -7.76575 q^{31} -1.93195 q^{32} +0.769923 q^{33} -1.14586 q^{34} -0.716872 q^{35} -1.97313 q^{36} -4.22615 q^{37} +0.982578 q^{38} +0.567788 q^{39} +0.466889 q^{40} +3.27377 q^{41} -0.163923 q^{42} +6.03174 q^{43} +1.51916 q^{44} +0.716872 q^{45} -0.898125 q^{46} -5.82813 q^{47} -3.83950 q^{48} +1.00000 q^{49} +0.735373 q^{50} -6.99026 q^{51} +1.12032 q^{52} -4.99787 q^{53} +0.163923 q^{54} -0.551936 q^{55} -0.651287 q^{56} +5.99415 q^{57} -0.484141 q^{58} -1.13244 q^{59} +1.41448 q^{60} -6.81149 q^{61} +1.27298 q^{62} -1.00000 q^{63} -7.36230 q^{64} -0.407032 q^{65} -0.126208 q^{66} -1.23546 q^{67} -13.7927 q^{68} -5.47895 q^{69} +0.117512 q^{70} +9.20036 q^{71} +0.651287 q^{72} +15.7859 q^{73} +0.692763 q^{74} +4.48609 q^{75} +11.8272 q^{76} +0.769923 q^{77} -0.0930735 q^{78} -12.4901 q^{79} +2.75243 q^{80} +1.00000 q^{81} -0.536646 q^{82} +11.7874 q^{83} -1.97313 q^{84} +5.01113 q^{85} -0.988740 q^{86} -2.95347 q^{87} -0.501440 q^{88} -4.82663 q^{89} -0.117512 q^{90} +0.567788 q^{91} -10.8107 q^{92} +7.76575 q^{93} +0.955364 q^{94} -4.29704 q^{95} +1.93195 q^{96} -9.07205 q^{97} -0.163923 q^{98} -0.769923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.163923	−0.115911	−0.0579555	−	0.998319i	$-0.518458\pi$
$2$	−0.163923	−0.115911	−0.0579555	+	0.998319i	$0.518458\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97313	−0.986565
$5$	0.716872	0.320595	0.160297	−	0.987069i	$-0.448755\pi$
$5$	0.716872	0.320595	0.160297	+	0.987069i	$0.448755\pi$
$6$	0.163923	0.0669212
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.651287	0.230265
$9$	1.00000	0.333333
$10$	−0.117512	−0.0371605
$11$	−0.769923	−0.232140	−0.116070	−	0.993241i	$-0.537030\pi$
$11$	−0.769923	−0.232140	−0.116070	+	0.993241i	$0.537030\pi$
$12$	1.97313	0.569593
$13$	−0.567788	−0.157476	−0.0787381	−	0.996895i	$-0.525089\pi$
$13$	−0.567788	−0.157476	−0.0787381	+	0.996895i	$0.525089\pi$
$14$	0.163923	0.0438102
$15$	−0.716872	−0.185096
$16$	3.83950	0.959874
$17$	6.99026	1.69539	0.847694	−	0.530485i	$-0.177990\pi$
$17$	6.99026	1.69539	0.847694	+	0.530485i	$0.177990\pi$
$18$	−0.163923	−0.0386370
$19$	−5.99415	−1.37515	−0.687576	−	0.726112i	$-0.741325\pi$
$19$	−5.99415	−1.37515	−0.687576	+	0.726112i	$0.741325\pi$
$20$	−1.41448	−0.316288
$21$	1.00000	0.218218
$22$	0.126208	0.0269076
$23$	5.47895	1.14244	0.571220	−	0.820797i	$-0.306470\pi$
$23$	5.47895	1.14244	0.571220	+	0.820797i	$0.306470\pi$
$24$	−0.651287	−0.132943
$25$	−4.48609	−0.897219
$26$	0.0930735	0.0182532
$27$	−1.00000	−0.192450
$28$	1.97313	0.372886
$29$	2.95347	0.548445	0.274222	−	0.961666i	$-0.411580\pi$
$29$	2.95347	0.548445	0.274222	+	0.961666i	$0.411580\pi$
$30$	0.117512	0.0214546
$31$	−7.76575	−1.39477	−0.697385	−	0.716697i	$-0.745653\pi$
$31$	−7.76575	−1.39477	−0.697385	+	0.716697i	$0.745653\pi$
$32$	−1.93195	−0.341525
$33$	0.769923	0.134026
$34$	−1.14586	−0.196514
$35$	−0.716872	−0.121174
$36$	−1.97313	−0.328855
$37$	−4.22615	−0.694775	−0.347388	−	0.937722i	$-0.612931\pi$
$37$	−4.22615	−0.694775	−0.347388	+	0.937722i	$0.612931\pi$
$38$	0.982578	0.159395
$39$	0.567788	0.0909189
$40$	0.466889	0.0738217
$41$	3.27377	0.511277	0.255639	−	0.966772i	$-0.417714\pi$
$41$	3.27377	0.511277	0.255639	+	0.966772i	$0.417714\pi$
$42$	−0.163923	−0.0252938
$43$	6.03174	0.919832	0.459916	−	0.887962i	$-0.347879\pi$
$43$	6.03174	0.919832	0.459916	+	0.887962i	$0.347879\pi$
$44$	1.51916	0.229022
$45$	0.716872	0.106865
$46$	−0.898125	−0.132421
$47$	−5.82813	−0.850120	−0.425060	−	0.905165i	$-0.639747\pi$
$47$	−5.82813	−0.850120	−0.425060	+	0.905165i	$0.639747\pi$
$48$	−3.83950	−0.554184
$49$	1.00000	0.142857
$50$	0.735373	0.103997
$51$	−6.99026	−0.978833
$52$	1.12032	0.155360
$53$	−4.99787	−0.686511	−0.343255	−	0.939242i	$-0.611530\pi$
$53$	−4.99787	−0.686511	−0.343255	+	0.939242i	$0.611530\pi$
$54$	0.163923	0.0223071
$55$	−0.551936	−0.0744231
$56$	−0.651287	−0.0870318
$57$	5.99415	0.793945
$58$	−0.484141	−0.0635708
$59$	−1.13244	−0.147431	−0.0737154	−	0.997279i	$-0.523486\pi$
$59$	−1.13244	−0.147431	−0.0737154	+	0.997279i	$0.523486\pi$
$60$	1.41448	0.182609
$61$	−6.81149	−0.872122	−0.436061	−	0.899917i	$-0.643627\pi$
$61$	−6.81149	−0.872122	−0.436061	+	0.899917i	$0.643627\pi$
$62$	1.27298	0.161669
$63$	−1.00000	−0.125988
$64$	−7.36230	−0.920288
$65$	−0.407032	−0.0504861
$66$	−0.126208	−0.0155351
$67$	−1.23546	−0.150935	−0.0754676	−	0.997148i	$-0.524045\pi$
$67$	−1.23546	−0.150935	−0.0754676	+	0.997148i	$0.524045\pi$
$68$	−13.7927	−1.67261
$69$	−5.47895	−0.659588
$70$	0.117512	0.0140453
$71$	9.20036	1.09188	0.545941	−	0.837823i	$-0.316172\pi$
$71$	9.20036	1.09188	0.545941	+	0.837823i	$0.316172\pi$
$72$	0.651287	0.0767549
$73$	15.7859	1.84760	0.923800	−	0.382876i	$-0.125067\pi$
$73$	15.7859	1.84760	0.923800	+	0.382876i	$0.125067\pi$
$74$	0.692763	0.0805321
$75$	4.48609	0.518010
$76$	11.8272	1.35668
$77$	0.769923	0.0877408
$78$	−0.0930735	−0.0105385
$79$	−12.4901	−1.40525	−0.702625	−	0.711560i	$-0.747989\pi$
$79$	−12.4901	−1.40525	−0.702625	+	0.711560i	$0.747989\pi$
$80$	2.75243	0.307731
$81$	1.00000	0.111111
$82$	−0.536646	−0.0592626
$83$	11.7874	1.29383	0.646916	−	0.762562i	$-0.276059\pi$
$83$	11.7874	1.29383	0.646916	+	0.762562i	$0.276059\pi$
$84$	−1.97313	−0.215286
$85$	5.01113	0.543533
$86$	−0.988740	−0.106619
$87$	−2.95347	−0.316645
$88$	−0.501440	−0.0534537
$89$	−4.82663	−0.511622	−0.255811	−	0.966727i	$-0.582342\pi$
$89$	−4.82663	−0.511622	−0.255811	+	0.966727i	$0.582342\pi$
$90$	−0.117512	−0.0123868
$91$	0.567788	0.0595204
$92$	−10.8107	−1.12709
$93$	7.76575	0.805271
$94$	0.955364	0.0985382
$95$	−4.29704	−0.440867
$96$	1.93195	0.197179
$97$	−9.07205	−0.921127	−0.460564	−	0.887627i	$-0.652353\pi$
$97$	−9.07205	−0.921127	−0.460564	+	0.887627i	$0.652353\pi$
$98$	−0.163923	−0.0165587
$99$	−0.769923	−0.0773802
$100$	8.85164	0.885164
$101$	1.74125	0.173261	0.0866304	−	0.996241i	$-0.472390\pi$
$101$	1.74125	0.173261	0.0866304	+	0.996241i	$0.472390\pi$
$102$	1.14586	0.113457
$103$	−12.1742	−1.19956	−0.599780	−	0.800165i	$-0.704745\pi$
$103$	−12.1742	−1.19956	−0.599780	+	0.800165i	$0.704745\pi$
$104$	−0.369793	−0.0362612
$105$	0.716872	0.0699596
$106$	0.819265	0.0795741
$107$	−3.65162	−0.353015	−0.176508	−	0.984299i	$-0.556480\pi$
$107$	−3.65162	−0.353015	−0.176508	+	0.984299i	$0.556480\pi$
$108$	1.97313	0.189864
$109$	18.4979	1.77178	0.885890	−	0.463896i	$-0.153549\pi$
$109$	18.4979	1.77178	0.885890	+	0.463896i	$0.153549\pi$
$110$	0.0904750	0.00862645
$111$	4.22615	0.401129
$112$	−3.83950	−0.362798
$113$	14.3203	1.34714	0.673571	−	0.739122i	$-0.264760\pi$
$113$	14.3203	1.34714	0.673571	+	0.739122i	$0.264760\pi$
$114$	−0.982578	−0.0920269
$115$	3.92771	0.366260
$116$	−5.82757	−0.541076
$117$	−0.567788	−0.0524920
$118$	0.185632	0.0170889
$119$	−6.99026	−0.640796
$120$	−0.466889	−0.0426210
$121$	−10.4072	−0.946111
$122$	1.11656	0.101089
$123$	−3.27377	−0.295186
$124$	15.3228	1.37603
$125$	−6.80032	−0.608239
$126$	0.163923	0.0146034
$127$	6.77096	0.600825	0.300413	−	0.953809i	$-0.402876\pi$
$127$	6.77096	0.600825	0.300413	+	0.953809i	$0.402876\pi$
$128$	5.07076	0.448196
$129$	−6.03174	−0.531065
$130$	0.0667218	0.00585189
$131$	−0.441646	−0.0385868	−0.0192934	−	0.999814i	$-0.506142\pi$
$131$	−0.441646	−0.0385868	−0.0192934	+	0.999814i	$0.506142\pi$
$132$	−1.51916	−0.132226
$133$	5.99415	0.519759
$134$	0.202520	0.0174950
$135$	−0.716872	−0.0616985
$136$	4.55267	0.390388
$137$	13.5761	1.15989	0.579943	−	0.814657i	$-0.303075\pi$
$137$	13.5761	1.15989	0.579943	+	0.814657i	$0.303075\pi$
$138$	0.898125	0.0764535
$139$	14.2047	1.20482	0.602412	−	0.798185i	$-0.294207\pi$
$139$	14.2047	1.20482	0.602412	+	0.798185i	$0.294207\pi$
$140$	1.41448	0.119546
$141$	5.82813	0.490817
$142$	−1.50815	−0.126561
$143$	0.437153	0.0365566
$144$	3.83950	0.319958
$145$	2.11726	0.175829
$146$	−2.58767	−0.214157
$147$	−1.00000	−0.0824786
$148$	8.33875	0.685441
$149$	18.6433	1.52732	0.763658	−	0.645621i	$-0.223401\pi$
$149$	18.6433	1.52732	0.763658	+	0.645621i	$0.223401\pi$
$150$	−0.735373	−0.0600430
$151$	2.90997	0.236810	0.118405	−	0.992965i	$-0.462222\pi$
$151$	2.90997	0.236810	0.118405	+	0.992965i	$0.462222\pi$
$152$	−3.90391	−0.316649
$153$	6.99026	0.565129
$154$	−0.126208	−0.0101701
$155$	−5.56705	−0.447156
$156$	−1.12032	−0.0896974
$157$	22.3084	1.78041	0.890203	−	0.455563i	$-0.150562\pi$
$157$	22.3084	1.78041	0.890203	+	0.455563i	$0.150562\pi$
$158$	2.04742	0.162884
$159$	4.99787	0.396357
$160$	−1.38496	−0.109491
$161$	−5.47895	−0.431802
$162$	−0.163923	−0.0128790
$163$	4.03766	0.316254	0.158127	−	0.987419i	$-0.449455\pi$
$163$	4.03766	0.316254	0.158127	+	0.987419i	$0.449455\pi$
$164$	−6.45957	−0.504408
$165$	0.551936	0.0429682
$166$	−1.93222	−0.149969
$167$	6.49321	0.502460	0.251230	−	0.967927i	$-0.419165\pi$
$167$	6.49321	0.502460	0.251230	+	0.967927i	$0.419165\pi$
$168$	0.651287	0.0502479
$169$	−12.6776	−0.975201
$170$	−0.821438	−0.0630014
$171$	−5.99415	−0.458384
$172$	−11.9014	−0.907474
$173$	13.9307	1.05913	0.529566	−	0.848269i	$-0.322355\pi$
$173$	13.9307	1.05913	0.529566	+	0.848269i	$0.322355\pi$
$174$	0.484141	0.0367026
$175$	4.48609	0.339117
$176$	−2.95612	−0.222826
$177$	1.13244	0.0851192
$178$	0.791195	0.0593026
$179$	−3.53011	−0.263853	−0.131926	−	0.991260i	$-0.542116\pi$
$179$	−3.53011	−0.263853	−0.131926	+	0.991260i	$0.542116\pi$
$180$	−1.41448	−0.105429
$181$	−4.30521	−0.320004	−0.160002	−	0.987117i	$-0.551150\pi$
$181$	−4.30521	−0.320004	−0.160002	+	0.987117i	$0.551150\pi$
$182$	−0.0930735	−0.00689906
$183$	6.81149	0.503520
$184$	3.56837	0.263063
$185$	−3.02961	−0.222741
$186$	−1.27298	−0.0933397
$187$	−5.38196	−0.393568
$188$	11.4997	0.838699
$189$	1.00000	0.0727393
$190$	0.704383	0.0511013
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	7.36230	0.531329
$193$	−20.4429	−1.47151	−0.735757	−	0.677246i	$-0.763173\pi$
$193$	−20.4429	−1.47151	−0.735757	+	0.677246i	$0.763173\pi$
$194$	1.48712	0.106769
$195$	0.407032	0.0291481
$196$	−1.97313	−0.140938
$197$	3.33814	0.237833	0.118916	−	0.992904i	$-0.462058\pi$
$197$	3.33814	0.237833	0.118916	+	0.992904i	$0.462058\pi$
$198$	0.126208	0.00896921
$199$	10.3879	0.736377	0.368189	−	0.929751i	$-0.379978\pi$
$199$	10.3879	0.736377	0.368189	+	0.929751i	$0.379978\pi$
$200$	−2.92173	−0.206598
$201$	1.23546	0.0871425
$202$	−0.285430	−0.0200828
$203$	−2.95347	−0.207293
$204$	13.7927	0.965682
$205$	2.34688	0.163913
$206$	1.99563	0.139042
$207$	5.47895	0.380813
$208$	−2.18002	−0.151157
$209$	4.61503	0.319228
$210$	−0.117512	−0.00810908
$211$	−14.5120	−0.999049	−0.499525	−	0.866300i	$-0.666492\pi$
$211$	−14.5120	−0.999049	−0.499525	+	0.866300i	$0.666492\pi$
$212$	9.86145	0.677287
$213$	−9.20036	−0.630399
$214$	0.598583	0.0409183
$215$	4.32399	0.294894
$216$	−0.651287	−0.0443144
$217$	7.76575	0.527174
$218$	−3.03223	−0.205369
$219$	−15.7859	−1.06671
$220$	1.08904	0.0734232
$221$	−3.96899	−0.266983
$222$	−0.692763	−0.0464952
$223$	14.6598	0.981696	0.490848	−	0.871245i	$-0.336687\pi$
$223$	14.6598	0.981696	0.490848	+	0.871245i	$0.336687\pi$
$224$	1.93195	0.129084
$225$	−4.48609	−0.299073
$226$	−2.34743	−0.156149
$227$	−12.6415	−0.839045	−0.419522	−	0.907745i	$-0.637802\pi$
$227$	−12.6415	−0.839045	−0.419522	+	0.907745i	$0.637802\pi$
$228$	−11.8272	−0.783278
$229$	7.37125	0.487106	0.243553	−	0.969888i	$-0.421687\pi$
$229$	7.37125	0.487106	0.243553	+	0.969888i	$0.421687\pi$
$230$	−0.643841	−0.0424536
$231$	−0.769923	−0.0506572
$232$	1.92355	0.126287
$233$	5.74320	0.376250	0.188125	−	0.982145i	$-0.439759\pi$
$233$	5.74320	0.376250	0.188125	+	0.982145i	$0.439759\pi$
$234$	0.0930735	0.00608440
$235$	−4.17802	−0.272544
$236$	2.23445	0.145450
$237$	12.4901	0.811322
$238$	1.14586	0.0742753
$239$	18.1759	1.17570	0.587850	−	0.808970i	$-0.299975\pi$
$239$	18.1759	1.17570	0.587850	+	0.808970i	$0.299975\pi$
$240$	−2.75243	−0.177669
$241$	1.42413	0.0917361	0.0458681	−	0.998948i	$-0.485395\pi$
$241$	1.42413	0.0917361	0.0458681	+	0.998948i	$0.485395\pi$
$242$	1.70598	0.109665
$243$	−1.00000	−0.0641500
$244$	13.4400	0.860405
$245$	0.716872	0.0457993
$246$	0.536646	0.0342153
$247$	3.40341	0.216554
$248$	−5.05773	−0.321166
$249$	−11.7874	−0.746994
$250$	1.11473	0.0705015
$251$	−8.42452	−0.531751	−0.265875	−	0.964007i	$-0.585661\pi$
$251$	−8.42452	−0.531751	−0.265875	+	0.964007i	$0.585661\pi$
$252$	1.97313	0.124295
$253$	−4.21837	−0.265207
$254$	−1.10991	−0.0696422
$255$	−5.01113	−0.313809
$256$	13.8934	0.868337
$257$	20.0973	1.25364	0.626819	−	0.779165i	$-0.284357\pi$
$257$	20.0973	1.25364	0.626819	+	0.779165i	$0.284357\pi$
$258$	0.988740	0.0615563
$259$	4.22615	0.262600
$260$	0.803126	0.0498078
$261$	2.95347	0.182815
$262$	0.0723959	0.00447263
$263$	15.9354	0.982621	0.491311	−	0.870984i	$-0.336518\pi$
$263$	15.9354	0.982621	0.491311	+	0.870984i	$0.336518\pi$
$264$	0.501440	0.0308615
$265$	−3.58284	−0.220092
$266$	−0.982578	−0.0602457
$267$	4.82663	0.295385
$268$	2.43772	0.148907
$269$	−4.12018	−0.251212	−0.125606	−	0.992080i	$-0.540087\pi$
$269$	−4.12018	−0.251212	−0.125606	+	0.992080i	$0.540087\pi$
$270$	0.117512	0.00715154
$271$	−2.08870	−0.126880	−0.0634398	−	0.997986i	$-0.520207\pi$
$271$	−2.08870	−0.126880	−0.0634398	+	0.997986i	$0.520207\pi$
$272$	26.8391	1.62736
$273$	−0.567788	−0.0343641
$274$	−2.22544	−0.134444
$275$	3.45395	0.208281
$276$	10.8107	0.650726
$277$	28.7652	1.72834	0.864168	−	0.503204i	$-0.167845\pi$
$277$	28.7652	1.72834	0.864168	+	0.503204i	$0.167845\pi$
$278$	−2.32847	−0.139652
$279$	−7.76575	−0.464923
$280$	−0.466889	−0.0279020
$281$	0.968270	0.0577622	0.0288811	−	0.999583i	$-0.490806\pi$
$281$	0.968270	0.0577622	0.0288811	+	0.999583i	$0.490806\pi$
$282$	−0.955364	−0.0568911
$283$	10.9177	0.648990	0.324495	−	0.945887i	$-0.394806\pi$
$283$	10.9177	0.648990	0.324495	+	0.945887i	$0.394806\pi$
$284$	−18.1535	−1.07721
$285$	4.29704	0.254535
$286$	−0.0716594	−0.00423731
$287$	−3.27377	−0.193245
$288$	−1.93195	−0.113842
$289$	31.8638	1.87434
$290$	−0.347067	−0.0203805
$291$	9.07205	0.531813
$292$	−31.1476	−1.82278
$293$	29.1730	1.70430	0.852152	−	0.523294i	$-0.175297\pi$
$293$	29.1730	1.70430	0.852152	+	0.523294i	$0.175297\pi$
$294$	0.163923	0.00956017
$295$	−0.811813	−0.0472656
$296$	−2.75244	−0.159982
$297$	0.769923	0.0446755
$298$	−3.05606	−0.177033
$299$	−3.11088	−0.179907
$300$	−8.85164	−0.511050
$301$	−6.03174	−0.347664
$302$	−0.477010	−0.0274488
$303$	−1.74125	−0.100032
$304$	−23.0145	−1.31997
$305$	−4.88297	−0.279598
$306$	−1.14586	−0.0655047
$307$	14.8033	0.844868	0.422434	−	0.906394i	$-0.361176\pi$
$307$	14.8033	0.844868	0.422434	+	0.906394i	$0.361176\pi$
$308$	−1.51916	−0.0865620
$309$	12.1742	0.692566
$310$	0.912567	0.0518303
$311$	−10.7431	−0.609183	−0.304591	−	0.952483i	$-0.598520\pi$
$311$	−10.7431	−0.609183	−0.304591	+	0.952483i	$0.598520\pi$
$312$	0.369793	0.0209354
$313$	8.18187	0.462466	0.231233	−	0.972898i	$-0.425724\pi$
$313$	8.18187	0.462466	0.231233	+	0.972898i	$0.425724\pi$
$314$	−3.65686	−0.206369
$315$	−0.716872	−0.0403912
$316$	24.6447	1.38637
$317$	31.6276	1.77638	0.888191	−	0.459475i	$-0.151962\pi$
$317$	31.6276	1.77638	0.888191	+	0.459475i	$0.151962\pi$
$318$	−0.819265	−0.0459421
$319$	−2.27394	−0.127316
$320$	−5.27783	−0.295040
$321$	3.65162	0.203813
$322$	0.898125	0.0500505
$323$	−41.9007	−2.33142
$324$	−1.97313	−0.109618
$325$	2.54715	0.141291
$326$	−0.661864	−0.0366573
$327$	−18.4979	−1.02294
$328$	2.13216	0.117729
$329$	5.82813	0.321315
$330$	−0.0904750	−0.00498048
$331$	−26.9863	−1.48330	−0.741651	−	0.670786i	$-0.765957\pi$
$331$	−26.9863	−1.48330	−0.741651	+	0.670786i	$0.765957\pi$
$332$	−23.2580	−1.27645
$333$	−4.22615	−0.231592
$334$	−1.06439	−0.0582406
$335$	−0.885665	−0.0483891
$336$	3.83950	0.209462
$337$	−9.77622	−0.532545	−0.266272	−	0.963898i	$-0.585792\pi$
$337$	−9.77622	−0.532545	−0.266272	+	0.963898i	$0.585792\pi$
$338$	2.07815	0.113037
$339$	−14.3203	−0.777773
$340$	−9.88760	−0.536230
$341$	5.97903	0.323783
$342$	0.982578	0.0531317
$343$	−1.00000	−0.0539949
$344$	3.92839	0.211805
$345$	−3.92771	−0.211461
$346$	−2.28356	−0.122765
$347$	14.2037	0.762492	0.381246	−	0.924474i	$-0.375495\pi$
$347$	14.2037	0.762492	0.381246	+	0.924474i	$0.375495\pi$
$348$	5.82757	0.312391
$349$	35.4912	1.89980	0.949899	−	0.312556i	$-0.101185\pi$
$349$	35.4912	1.89980	0.949899	+	0.312556i	$0.101185\pi$
$350$	−0.735373	−0.0393074
$351$	0.567788	0.0303063
$352$	1.48746	0.0792817
$353$	−22.8044	−1.21376	−0.606878	−	0.794795i	$-0.707578\pi$
$353$	−22.8044	−1.21376	−0.606878	+	0.794795i	$0.707578\pi$
$354$	−0.185632	−0.00986625
$355$	6.59549	0.350052
$356$	9.52357	0.504748
$357$	6.99026	0.369964
$358$	0.578665	0.0305834
$359$	−8.44315	−0.445613	−0.222806	−	0.974863i	$-0.571522\pi$
$359$	−8.44315	−0.445613	−0.222806	+	0.974863i	$0.571522\pi$
$360$	0.466889	0.0246072
$361$	16.9298	0.891044
$362$	0.705722	0.0370919
$363$	10.4072	0.546237
$364$	−1.12032	−0.0587207
$365$	11.3165	0.592331
$366$	−1.11656	−0.0583635
$367$	−21.8477	−1.14044	−0.570219	−	0.821493i	$-0.693142\pi$
$367$	−21.8477	−1.14044	−0.570219	+	0.821493i	$0.693142\pi$
$368$	21.0364	1.09660
$369$	3.27377	0.170426
$370$	0.496623	0.0258182
$371$	4.99787	0.259477
$372$	−15.3228	−0.794452
$373$	20.8204	1.07804	0.539019	−	0.842293i	$-0.318795\pi$
$373$	20.8204	1.07804	0.539019	+	0.842293i	$0.318795\pi$
$374$	0.882227	0.0456189
$375$	6.80032	0.351167
$376$	−3.79578	−0.195753
$377$	−1.67694	−0.0863670
$378$	−0.163923	−0.00843128
$379$	21.0579	1.08167	0.540835	−	0.841129i	$-0.318108\pi$
$379$	21.0579	1.08167	0.540835	+	0.841129i	$0.318108\pi$
$380$	8.47861	0.434944
$381$	−6.77096	−0.346887
$382$	−0.163923	−0.00838702
$383$	−7.12161	−0.363897	−0.181949	−	0.983308i	$-0.558240\pi$
$383$	−7.12161	−0.363897	−0.181949	+	0.983308i	$0.558240\pi$
$384$	−5.07076	−0.258766
$385$	0.551936	0.0281293
$386$	3.35106	0.170565
$387$	6.03174	0.306611
$388$	17.9003	0.908752
$389$	−33.5545	−1.70128	−0.850641	−	0.525747i	$-0.823786\pi$
$389$	−33.5545	−1.70128	−0.850641	+	0.525747i	$0.823786\pi$
$390$	−0.0667218	−0.00337859
$391$	38.2993	1.93688
$392$	0.651287	0.0328949
$393$	0.441646	0.0222781
$394$	−0.547197	−0.0275674
$395$	−8.95383	−0.450516
$396$	1.51916	0.0763405
$397$	−2.78514	−0.139782	−0.0698910	−	0.997555i	$-0.522265\pi$
$397$	−2.78514	−0.139782	−0.0698910	+	0.997555i	$0.522265\pi$
$398$	−1.70281	−0.0853542
$399$	−5.99415	−0.300083
$400$	−17.2243	−0.861217
$401$	−28.8584	−1.44112	−0.720561	−	0.693392i	$-0.756116\pi$
$401$	−28.8584	−1.44112	−0.720561	+	0.693392i	$0.756116\pi$
$402$	−0.202520	−0.0101008
$403$	4.40930	0.219643
$404$	−3.43571	−0.170933
$405$	0.716872	0.0356217
$406$	0.484141	0.0240275
$407$	3.25381	0.161285
$408$	−4.55267	−0.225391
$409$	16.6447	0.823027	0.411514	−	0.911404i	$-0.365000\pi$
$409$	16.6447	0.823027	0.411514	+	0.911404i	$0.365000\pi$
$410$	−0.384706	−0.0189993
$411$	−13.5761	−0.669661
$412$	24.0213	1.18344
$413$	1.13244	0.0557236
$414$	−0.898125	−0.0441404
$415$	8.45003	0.414796
$416$	1.09694	0.0537820
$417$	−14.2047	−0.695605
$418$	−0.756509	−0.0370021
$419$	11.5804	0.565742	0.282871	−	0.959158i	$-0.408713\pi$
$419$	11.5804	0.565742	0.282871	+	0.959158i	$0.408713\pi$
$420$	−1.41448	−0.0690196
$421$	20.8023	1.01384	0.506921	−	0.861992i	$-0.330783\pi$
$421$	20.8023	1.01384	0.506921	+	0.861992i	$0.330783\pi$
$422$	2.37885	0.115801
$423$	−5.82813	−0.283373
$424$	−3.25505	−0.158079
$425$	−31.3590	−1.52113
$426$	1.50815	0.0730701
$427$	6.81149	0.329631
$428$	7.20511	0.348272
$429$	−0.437153	−0.0211060
$430$	−0.708800	−0.0341814
$431$	29.2940	1.41104	0.705522	−	0.708688i	$-0.250713\pi$
$431$	29.2940	1.41104	0.705522	+	0.708688i	$0.250713\pi$
$432$	−3.83950	−0.184728
$433$	−5.42794	−0.260850	−0.130425	−	0.991458i	$-0.541634\pi$
$433$	−5.42794	−0.260850	−0.130425	+	0.991458i	$0.541634\pi$
$434$	−1.27298	−0.0611052
$435$	−2.11726	−0.101515
$436$	−36.4988	−1.74798
$437$	−32.8416	−1.57103
$438$	2.58767	0.123644
$439$	21.8561	1.04314	0.521568	−	0.853210i	$-0.325347\pi$
$439$	21.8561	1.04314	0.521568	+	0.853210i	$0.325347\pi$
$440$	−0.359469	−0.0171370
$441$	1.00000	0.0476190
$442$	0.650608	0.0309463
$443$	12.6248	0.599822	0.299911	−	0.953967i	$-0.403043\pi$
$443$	12.6248	0.599822	0.299911	+	0.953967i	$0.403043\pi$
$444$	−8.33875	−0.395739
$445$	−3.46008	−0.164023
$446$	−2.40308	−0.113789
$447$	−18.6433	−0.881796
$448$	7.36230	0.347836
$449$	19.7427	0.931717	0.465858	−	0.884859i	$-0.345746\pi$
$449$	19.7427	0.931717	0.465858	+	0.884859i	$0.345746\pi$
$450$	0.735373	0.0346658
$451$	−2.52055	−0.118688
$452$	−28.2558	−1.32904
$453$	−2.90997	−0.136722
$454$	2.07223	0.0972545
$455$	0.407032	0.0190819
$456$	3.90391	0.182817
$457$	1.08673	0.0508353	0.0254176	−	0.999677i	$-0.491908\pi$
$457$	1.08673	0.0508353	0.0254176	+	0.999677i	$0.491908\pi$
$458$	−1.20832	−0.0564609
$459$	−6.99026	−0.326278
$460$	−7.74987	−0.361340
$461$	−32.5185	−1.51454	−0.757268	−	0.653104i	$-0.773466\pi$
$461$	−32.5185	−1.51454	−0.757268	+	0.653104i	$0.773466\pi$
$462$	0.126208	0.00587172
$463$	−18.0040	−0.836715	−0.418357	−	0.908282i	$-0.637394\pi$
$463$	−18.0040	−0.836715	−0.418357	+	0.908282i	$0.637394\pi$
$464$	11.3398	0.526438
$465$	5.56705	0.258166
$466$	−0.941442	−0.0436115
$467$	2.01551	0.0932668	0.0466334	−	0.998912i	$-0.485151\pi$
$467$	2.01551	0.0932668	0.0466334	+	0.998912i	$0.485151\pi$
$468$	1.12032	0.0517868
$469$	1.23546	0.0570481
$470$	0.684874	0.0315909
$471$	−22.3084	−1.02792
$472$	−0.737542	−0.0339481
$473$	−4.64398	−0.213530
$474$	−2.04742	−0.0940411
$475$	26.8903	1.23381
$476$	13.7927	0.632187
$477$	−4.99787	−0.228837
$478$	−2.97944	−0.136276
$479$	−22.2043	−1.01454	−0.507271	−	0.861786i	$-0.669346\pi$
$479$	−22.2043	−1.01454	−0.507271	+	0.861786i	$0.669346\pi$
$480$	1.38496	0.0632147
$481$	2.39956	0.109411
$482$	−0.233447	−0.0106332
$483$	5.47895	0.249301
$484$	20.5348	0.933399
$485$	−6.50350	−0.295309
$486$	0.163923	0.00743569
$487$	−5.94158	−0.269239	−0.134619	−	0.990897i	$-0.542981\pi$
$487$	−5.94158	−0.269239	−0.134619	+	0.990897i	$0.542981\pi$
$488$	−4.43623	−0.200819
$489$	−4.03766	−0.182589
$490$	−0.117512	−0.00530864
$491$	27.6877	1.24953	0.624764	−	0.780813i	$-0.285195\pi$
$491$	27.6877	1.24953	0.624764	+	0.780813i	$0.285195\pi$
$492$	6.45957	0.291220
$493$	20.6455	0.929827
$494$	−0.557896	−0.0251009
$495$	−0.551936	−0.0248077
$496$	−29.8166	−1.33880
$497$	−9.20036	−0.412693
$498$	1.93222	0.0865847
$499$	36.6118	1.63897	0.819484	−	0.573102i	$-0.194260\pi$
$499$	36.6118	1.63897	0.819484	+	0.573102i	$0.194260\pi$
$500$	13.4179	0.600067
$501$	−6.49321	−0.290095
$502$	1.38097	0.0616357
$503$	17.6637	0.787587	0.393793	−	0.919199i	$-0.371163\pi$
$503$	17.6637	0.787587	0.393793	+	0.919199i	$0.371163\pi$
$504$	−0.651287	−0.0290106
$505$	1.24825	0.0555465
$506$	0.691487	0.0307403
$507$	12.6776	0.563033
$508$	−13.3600	−0.592753
$509$	−7.32331	−0.324600	−0.162300	−	0.986741i	$-0.551891\pi$
$509$	−7.32331	−0.324600	−0.162300	+	0.986741i	$0.551891\pi$
$510$	0.821438	0.0363739
$511$	−15.7859	−0.698327
$512$	−12.4190	−0.548846
$513$	5.99415	0.264648
$514$	−3.29441	−0.145310
$515$	−8.72735	−0.384573
$516$	11.9014	0.523930
$517$	4.48721	0.197347
$518$	−0.692763	−0.0304383
$519$	−13.9307	−0.611491
$520$	−0.265094	−0.0116252
$521$	−9.70670	−0.425258	−0.212629	−	0.977133i	$-0.568203\pi$
$521$	−9.70670	−0.425258	−0.212629	+	0.977133i	$0.568203\pi$
$522$	−0.484141	−0.0211903
$523$	10.9021	0.476718	0.238359	−	0.971177i	$-0.423391\pi$
$523$	10.9021	0.476718	0.238359	+	0.971177i	$0.423391\pi$
$524$	0.871425	0.0380684
$525$	−4.48609	−0.195789
$526$	−2.61218	−0.113897
$527$	−54.2847	−2.36468
$528$	2.95612	0.128648
$529$	7.01888	0.305169
$530$	0.587309	0.0255111
$531$	−1.13244	−0.0491436
$532$	−11.8272	−0.512776
$533$	−1.85881	−0.0805140
$534$	−0.791195	−0.0342384
$535$	−2.61774	−0.113175
$536$	−0.804637	−0.0347550
$537$	3.53011	0.152335
$538$	0.675391	0.0291182
$539$	−0.769923	−0.0331629
$540$	1.41448	0.0608696
$541$	44.5156	1.91388	0.956938	−	0.290293i	$-0.0937528\pi$
$541$	44.5156	1.91388	0.956938	+	0.290293i	$0.0937528\pi$
$542$	0.342386	0.0147067
$543$	4.30521	0.184754
$544$	−13.5049	−0.579017
$545$	13.2606	0.568024
$546$	0.0930735	0.00398318
$547$	−0.364826	−0.0155988	−0.00779942	−	0.999970i	$-0.502483\pi$
$547$	−0.364826	−0.0155988	−0.00779942	+	0.999970i	$0.502483\pi$
$548$	−26.7875	−1.14430
$549$	−6.81149	−0.290707
$550$	−0.566181	−0.0241420
$551$	−17.7035	−0.754195
$552$	−3.56837	−0.151880
$553$	12.4901	0.531135
$554$	−4.71528	−0.200333
$555$	3.02961	0.128600
$556$	−28.0276	−1.18864
$557$	33.8252	1.43322	0.716610	−	0.697474i	$-0.245693\pi$
$557$	33.8252	1.43322	0.716610	+	0.697474i	$0.245693\pi$
$558$	1.27298	0.0538897
$559$	−3.42475	−0.144852
$560$	−2.75243	−0.116311
$561$	5.38196	0.227227
$562$	−0.158722	−0.00669527
$563$	−18.1484	−0.764865	−0.382433	−	0.923983i	$-0.624914\pi$
$563$	−18.1484	−0.764865	−0.382433	+	0.923983i	$0.624914\pi$
$564$	−11.4997	−0.484223
$565$	10.2658	0.431887
$566$	−1.78966	−0.0752250
$567$	−1.00000	−0.0419961
$568$	5.99207	0.251422
$569$	−10.9165	−0.457643	−0.228821	−	0.973468i	$-0.573487\pi$
$569$	−10.9165	−0.457643	−0.228821	+	0.973468i	$0.573487\pi$
$570$	−0.704383	−0.0295034
$571$	−12.6312	−0.528598	−0.264299	−	0.964441i	$-0.585141\pi$
$571$	−12.6312	−0.528598	−0.264299	+	0.964441i	$0.585141\pi$
$572$	−0.862560	−0.0360654
$573$	−1.00000	−0.0417756
$574$	0.536646	0.0223992
$575$	−24.5791	−1.02502
$576$	−7.36230	−0.306763
$577$	−31.5130	−1.31190	−0.655952	−	0.754803i	$-0.727732\pi$
$577$	−31.5130	−1.31190	−0.655952	+	0.754803i	$0.727732\pi$
$578$	−5.22320	−0.217257
$579$	20.4429	0.849579
$580$	−4.17762	−0.173466
$581$	−11.7874	−0.489022
$582$	−1.48712	−0.0616430
$583$	3.84798	0.159367
$584$	10.2811	0.425437
$585$	−0.407032	−0.0168287
$586$	−4.78212	−0.197548
$587$	−12.2533	−0.505748	−0.252874	−	0.967499i	$-0.581376\pi$
$587$	−12.2533	−0.505748	−0.252874	+	0.967499i	$0.581376\pi$
$588$	1.97313	0.0813705
$589$	46.5491	1.91802
$590$	0.133075	0.00547860
$591$	−3.33814	−0.137313
$592$	−16.2263	−0.666897
$593$	−11.7973	−0.484457	−0.242228	−	0.970219i	$-0.577878\pi$
$593$	−11.7973	−0.484457	−0.242228	+	0.970219i	$0.577878\pi$
$594$	−0.126208	−0.00517837
$595$	−5.01113	−0.205436
$596$	−36.7856	−1.50680
$597$	−10.3879	−0.425148
$598$	0.509945	0.0208532
$599$	−42.4639	−1.73503	−0.867514	−	0.497414i	$-0.834283\pi$
$599$	−42.4639	−1.73503	−0.867514	+	0.497414i	$0.834283\pi$
$600$	2.92173	0.119279
$601$	−30.6042	−1.24837	−0.624186	−	0.781276i	$-0.714569\pi$
$601$	−30.6042	−1.24837	−0.624186	+	0.781276i	$0.714569\pi$
$602$	0.988740	0.0402981
$603$	−1.23546	−0.0503117
$604$	−5.74174	−0.233628
$605$	−7.46065	−0.303318
$606$	0.285430	0.0115948
$607$	−30.4845	−1.23733	−0.618664	−	0.785656i	$-0.712326\pi$
$607$	−30.4845	−1.23733	−0.618664	+	0.785656i	$0.712326\pi$
$608$	11.5804	0.469648
$609$	2.95347	0.119680
$610$	0.800430	0.0324085
$611$	3.30914	0.133874
$612$	−13.7927	−0.557537
$613$	−9.93896	−0.401431	−0.200715	−	0.979650i	$-0.564327\pi$
$613$	−9.93896	−0.401431	−0.200715	+	0.979650i	$0.564327\pi$
$614$	−2.42660	−0.0979294
$615$	−2.34688	−0.0946352
$616$	0.501440	0.0202036
$617$	11.6225	0.467905	0.233952	−	0.972248i	$-0.424834\pi$
$617$	11.6225	0.467905	0.233952	+	0.972248i	$0.424834\pi$
$618$	−1.99563	−0.0802760
$619$	6.94737	0.279238	0.139619	−	0.990205i	$-0.455412\pi$
$619$	6.94737	0.279238	0.139619	+	0.990205i	$0.455412\pi$
$620$	10.9845	0.441149
$621$	−5.47895	−0.219863
$622$	1.76103	0.0706110
$623$	4.82663	0.193375
$624$	2.18002	0.0872707
$625$	17.5555	0.702221
$626$	−1.34119	−0.0536049
$627$	−4.61503	−0.184307
$628$	−44.0174	−1.75649
$629$	−29.5419	−1.17791
$630$	0.117512	0.00468178
$631$	−26.0178	−1.03575	−0.517875	−	0.855456i	$-0.673277\pi$
$631$	−26.0178	−1.03575	−0.517875	+	0.855456i	$0.673277\pi$
$632$	−8.13466	−0.323579
$633$	14.5120	0.576801
$634$	−5.18448	−0.205902
$635$	4.85391	0.192622
$636$	−9.86145	−0.391032
$637$	−0.567788	−0.0224966
$638$	0.372751	0.0147573
$639$	9.20036	0.363961
$640$	3.63509	0.143689
$641$	−32.1853	−1.27124	−0.635622	−	0.772000i	$-0.719256\pi$
$641$	−32.1853	−1.27124	−0.635622	+	0.772000i	$0.719256\pi$
$642$	−0.598583	−0.0236242
$643$	24.9488	0.983887	0.491943	−	0.870627i	$-0.336287\pi$
$643$	24.9488	0.983887	0.491943	+	0.870627i	$0.336287\pi$
$644$	10.8107	0.426000
$645$	−4.32399	−0.170257
$646$	6.86848	0.270237
$647$	−22.2789	−0.875873	−0.437936	−	0.899006i	$-0.644291\pi$
$647$	−22.2789	−0.875873	−0.437936	+	0.899006i	$0.644291\pi$
$648$	0.651287	0.0255850
$649$	0.871890	0.0342247
$650$	−0.417536	−0.0163771
$651$	−7.76575	−0.304364
$652$	−7.96682	−0.312005
$653$	21.4125	0.837937	0.418969	−	0.908001i	$-0.362392\pi$
$653$	21.4125	0.837937	0.418969	+	0.908001i	$0.362392\pi$
$654$	3.03223	0.118570
$655$	−0.316604	−0.0123707
$656$	12.5696	0.490762
$657$	15.7859	0.615866
$658$	−0.955364	−0.0372440
$659$	18.3474	0.714712	0.357356	−	0.933968i	$-0.383678\pi$
$659$	18.3474	0.714712	0.357356	+	0.933968i	$0.383678\pi$
$660$	−1.08904	−0.0423909
$661$	−18.8803	−0.734357	−0.367179	−	0.930150i	$-0.619676\pi$
$661$	−18.8803	−0.734357	−0.367179	+	0.930150i	$0.619676\pi$
$662$	4.42368	0.171931
$663$	3.96899	0.154143
$664$	7.67695	0.297923
$665$	4.29704	0.166632
$666$	0.692763	0.0268440
$667$	16.1819	0.626565
$668$	−12.8119	−0.495709
$669$	−14.6598	−0.566782
$670$	0.145181	0.00560882
$671$	5.24432	0.202455
$672$	−1.93195	−0.0745268
$673$	4.16981	0.160734	0.0803672	−	0.996765i	$-0.474391\pi$
$673$	4.16981	0.160734	0.0803672	+	0.996765i	$0.474391\pi$
$674$	1.60255	0.0617277
$675$	4.48609	0.172670
$676$	25.0146	0.962099
$677$	−37.4751	−1.44028	−0.720142	−	0.693827i	$-0.755923\pi$
$677$	−37.4751	−1.44028	−0.720142	+	0.693827i	$0.755923\pi$
$678$	2.34743	0.0901524
$679$	9.07205	0.348153
$680$	3.26368	0.125156
$681$	12.6415	0.484423
$682$	−0.980099	−0.0375299
$683$	−30.9438	−1.18403	−0.592016	−	0.805926i	$-0.701668\pi$
$683$	−30.9438	−1.18403	−0.592016	+	0.805926i	$0.701668\pi$
$684$	11.8272	0.452226
$685$	9.73235	0.371854
$686$	0.163923	0.00625860
$687$	−7.37125	−0.281231
$688$	23.1589	0.882923
$689$	2.83773	0.108109
$690$	0.643841	0.0245106
$691$	−30.9814	−1.17859	−0.589294	−	0.807919i	$-0.700594\pi$
$691$	−30.9814	−1.17859	−0.589294	+	0.807919i	$0.700594\pi$
$692$	−27.4871	−1.04490
$693$	0.769923	0.0292469
$694$	−2.32830	−0.0883812
$695$	10.1829	0.386260
$696$	−1.92355	−0.0729121
$697$	22.8845	0.866813
$698$	−5.81781	−0.220207
$699$	−5.74320	−0.217228
$700$	−8.85164	−0.334561
$701$	28.9864	1.09480	0.547401	−	0.836870i	$-0.315617\pi$
$701$	28.9864	1.09480	0.547401	+	0.836870i	$0.315617\pi$
$702$	−0.0930735	−0.00351283
$703$	25.3322	0.955422
$704$	5.66841	0.213636
$705$	4.17802	0.157354
$706$	3.73816	0.140688
$707$	−1.74125	−0.0654864
$708$	−2.23445	−0.0839756
$709$	28.4902	1.06997	0.534985	−	0.844861i	$-0.320317\pi$
$709$	28.4902	1.06997	0.534985	+	0.844861i	$0.320317\pi$
$710$	−1.08115	−0.0405749
$711$	−12.4901	−0.468417
$712$	−3.14352	−0.117808
$713$	−42.5482	−1.59344
$714$	−1.14586	−0.0428829
$715$	0.313383	0.0117199
$716$	6.96536	0.260308
$717$	−18.1759	−0.678790
$718$	1.38403	0.0516514
$719$	42.6932	1.59219	0.796094	−	0.605173i	$-0.206896\pi$
$719$	42.6932	1.59219	0.796094	+	0.605173i	$0.206896\pi$
$720$	2.75243	0.102577
$721$	12.1742	0.453391
$722$	−2.77519	−0.103282
$723$	−1.42413	−0.0529639
$724$	8.49473	0.315704
$725$	−13.2495	−0.492075
$726$	−1.70598	−0.0633149
$727$	−49.4422	−1.83371	−0.916854	−	0.399222i	$-0.869280\pi$
$727$	−49.4422	−1.83371	−0.916854	+	0.399222i	$0.869280\pi$
$728$	0.369793	0.0137054
$729$	1.00000	0.0370370
$730$	−1.85503	−0.0686576
$731$	42.1635	1.55947
$732$	−13.4400	−0.496755
$733$	−23.5660	−0.870432	−0.435216	−	0.900326i	$-0.643328\pi$
$733$	−23.5660	−0.870432	−0.435216	+	0.900326i	$0.643328\pi$
$734$	3.58133	0.132189
$735$	−0.716872	−0.0264422
$736$	−10.5851	−0.390171
$737$	0.951207	0.0350382
$738$	−0.536646	−0.0197542
$739$	12.7129	0.467650	0.233825	−	0.972279i	$-0.424876\pi$
$739$	12.7129	0.467650	0.233825	+	0.972279i	$0.424876\pi$
$740$	5.97782	0.219749
$741$	−3.40341	−0.125027
$742$	−0.819265	−0.0300762
$743$	21.2376	0.779131	0.389566	−	0.920999i	$-0.372625\pi$
$743$	21.2376	0.779131	0.389566	+	0.920999i	$0.372625\pi$
$744$	5.05773	0.185425
$745$	13.3648	0.489650
$746$	−3.41294	−0.124956
$747$	11.7874	0.431277
$748$	10.6193	0.388280
$749$	3.65162	0.133427
$750$	−1.11473	−0.0407041
$751$	21.8807	0.798436	0.399218	−	0.916856i	$-0.369282\pi$
$751$	21.8807	0.798436	0.399218	+	0.916856i	$0.369282\pi$
$752$	−22.3771	−0.816009
$753$	8.42452	0.307006
$754$	0.274889	0.0100109
$755$	2.08607	0.0759200
$756$	−1.97313	−0.0717620
$757$	35.8221	1.30198	0.650988	−	0.759088i	$-0.274355\pi$
$757$	35.8221	1.30198	0.650988	+	0.759088i	$0.274355\pi$
$758$	−3.45186	−0.125377
$759$	4.21837	0.153117
$760$	−2.79860	−0.101516
$761$	10.1611	0.368339	0.184170	−	0.982894i	$-0.441040\pi$
$761$	10.1611	0.368339	0.184170	+	0.982894i	$0.441040\pi$
$762$	1.10991	0.0402080
$763$	−18.4979	−0.669670
$764$	−1.97313	−0.0713853
$765$	5.01113	0.181178
$766$	1.16739	0.0421797
$767$	0.642985	0.0232168
$768$	−13.8934	−0.501335
$769$	−3.54254	−0.127747	−0.0638737	−	0.997958i	$-0.520345\pi$
$769$	−3.54254	−0.127747	−0.0638737	+	0.997958i	$0.520345\pi$
$770$	−0.0904750	−0.00326049
$771$	−20.0973	−0.723788
$772$	40.3365	1.45174
$773$	33.0537	1.18886	0.594430	−	0.804148i	$-0.297378\pi$
$773$	33.0537	1.18886	0.594430	+	0.804148i	$0.297378\pi$
$774$	−0.988740	−0.0355395
$775$	34.8379	1.25141
$776$	−5.90851	−0.212103
$777$	−4.22615	−0.151612
$778$	5.50035	0.197197
$779$	−19.6235	−0.703084
$780$	−0.803126	−0.0287565
$781$	−7.08357	−0.253470
$782$	−6.27813	−0.224505
$783$	−2.95347	−0.105548
$784$	3.83950	0.137125
$785$	15.9923	0.570790
$786$	−0.0723959	−0.00258227
$787$	15.6588	0.558174	0.279087	−	0.960266i	$-0.409968\pi$
$787$	15.6588	0.558174	0.279087	+	0.960266i	$0.409968\pi$
$788$	−6.58658	−0.234637
$789$	−15.9354	−0.567317
$790$	1.46774	0.0522198
$791$	−14.3203	−0.509172
$792$	−0.501440	−0.0178179
$793$	3.86749	0.137338
$794$	0.456547	0.0162023
$795$	3.58284	0.127070
$796$	−20.4966	−0.726484
$797$	−45.8246	−1.62319	−0.811595	−	0.584221i	$-0.801400\pi$
$797$	−45.8246	−1.62319	−0.811595	+	0.584221i	$0.801400\pi$
$798$	0.982578	0.0347829
$799$	−40.7402	−1.44128
$800$	8.66693	0.306422
$801$	−4.82663	−0.170541
$802$	4.73056	0.167042
$803$	−12.1539	−0.428903
$804$	−2.43772	−0.0859717
$805$	−3.92771	−0.138433
$806$	−0.722785	−0.0254590
$807$	4.12018	0.145037
$808$	1.13405	0.0398958
$809$	1.76537	0.0620673	0.0310336	−	0.999518i	$-0.490120\pi$
$809$	1.76537	0.0620673	0.0310336	+	0.999518i	$0.490120\pi$
$810$	−0.117512	−0.00412894
$811$	26.8218	0.941840	0.470920	−	0.882176i	$-0.343922\pi$
$811$	26.8218	0.941840	0.470920	+	0.882176i	$0.343922\pi$
$812$	5.82757	0.204508
$813$	2.08870	0.0732540
$814$	−0.533374	−0.0186948
$815$	2.89448	0.101389
$816$	−26.8391	−0.939557
$817$	−36.1552	−1.26491
$818$	−2.72845	−0.0953979
$819$	0.567788	0.0198401
$820$	−4.63069	−0.161711
$821$	−7.90227	−0.275791	−0.137896	−	0.990447i	$-0.544034\pi$
$821$	−7.90227	−0.275791	−0.137896	+	0.990447i	$0.544034\pi$
$822$	2.22544	0.0776210
$823$	3.04660	0.106198	0.0530989	−	0.998589i	$-0.483090\pi$
$823$	3.04660	0.106198	0.0530989	+	0.998589i	$0.483090\pi$
$824$	−7.92890	−0.276216
$825$	−3.45395	−0.120251
$826$	−0.185632	−0.00645898
$827$	9.41173	0.327278	0.163639	−	0.986520i	$-0.447677\pi$
$827$	9.41173	0.327278	0.163639	+	0.986520i	$0.447677\pi$
$828$	−10.8107	−0.375697
$829$	−34.5491	−1.19994	−0.599970	−	0.800023i	$-0.704821\pi$
$829$	−34.5491	−1.19994	−0.599970	+	0.800023i	$0.704821\pi$
$830$	−1.38515	−0.0480794
$831$	−28.7652	−0.997855
$832$	4.18023	0.144923
$833$	6.99026	0.242198
$834$	2.32847	0.0806283
$835$	4.65480	0.161086
$836$	−9.10606	−0.314940
$837$	7.76575	0.268424
$838$	−1.89830	−0.0655757
$839$	−4.90373	−0.169295	−0.0846477	−	0.996411i	$-0.526976\pi$
$839$	−4.90373	−0.169295	−0.0846477	+	0.996411i	$0.526976\pi$
$840$	0.466889	0.0161092
$841$	−20.2770	−0.699208
$842$	−3.40997	−0.117515
$843$	−0.968270	−0.0333490
$844$	28.6341	0.985627
$845$	−9.08823	−0.312645
$846$	0.955364	0.0328461
$847$	10.4072	0.357596
$848$	−19.1893	−0.658964
$849$	−10.9177	−0.374694
$850$	5.14045	0.176316
$851$	−23.1549	−0.793739
$852$	18.1535	0.621929
$853$	−31.5239	−1.07936	−0.539679	−	0.841871i	$-0.681454\pi$
$853$	−31.5239	−1.07936	−0.539679	+	0.841871i	$0.681454\pi$
$854$	−1.11656	−0.0382079
$855$	−4.29704	−0.146956
$856$	−2.37825	−0.0812869
$857$	2.46526	0.0842117	0.0421058	−	0.999113i	$-0.486593\pi$
$857$	2.46526	0.0842117	0.0421058	+	0.999113i	$0.486593\pi$
$858$	0.0716594	0.00244641
$859$	38.0137	1.29701	0.648505	−	0.761210i	$-0.275394\pi$
$859$	38.0137	1.29701	0.648505	+	0.761210i	$0.275394\pi$
$860$	−8.53179	−0.290932
$861$	3.27377	0.111570
$862$	−4.80196	−0.163555
$863$	9.76139	0.332282	0.166141	−	0.986102i	$-0.446869\pi$
$863$	9.76139	0.332282	0.166141	+	0.986102i	$0.446869\pi$
$864$	1.93195	0.0657264
$865$	9.98654	0.339553
$866$	0.889763	0.0302354
$867$	−31.8638	−1.08215
$868$	−15.3228	−0.520091
$869$	9.61644	0.326215
$870$	0.347067	0.0117667
$871$	0.701478	0.0237687
$872$	12.0474	0.407978
$873$	−9.07205	−0.307042
$874$	5.38350	0.182099
$875$	6.80032	0.229893
$876$	31.1476	1.05238
$877$	−27.3070	−0.922093	−0.461046	−	0.887376i	$-0.652526\pi$
$877$	−27.3070	−0.922093	−0.461046	+	0.887376i	$0.652526\pi$
$878$	−3.58272	−0.120911
$879$	−29.1730	−0.983981
$880$	−2.11916	−0.0714368
$881$	21.0065	0.707727	0.353863	−	0.935297i	$-0.384868\pi$
$881$	21.0065	0.707727	0.353863	+	0.935297i	$0.384868\pi$
$882$	−0.163923	−0.00551957
$883$	−29.1043	−0.979437	−0.489719	−	0.871881i	$-0.662901\pi$
$883$	−29.1043	−0.979437	−0.489719	+	0.871881i	$0.662901\pi$
$884$	7.83133	0.263396
$885$	0.811813	0.0272888
$886$	−2.06949	−0.0695260
$887$	−44.7519	−1.50262	−0.751311	−	0.659948i	$-0.770578\pi$
$887$	−44.7519	−1.50262	−0.751311	+	0.659948i	$0.770578\pi$
$888$	2.75244	0.0923657
$889$	−6.77096	−0.227091
$890$	0.567186	0.0190121
$891$	−0.769923	−0.0257934
$892$	−28.9258	−0.968506
$893$	34.9347	1.16904
$894$	3.05606	0.102210
$895$	−2.53064	−0.0845898
$896$	−5.07076	−0.169402
$897$	3.11088	0.103869
$898$	−3.23628	−0.107996
$899$	−22.9359	−0.764955
$900$	8.85164	0.295055
$901$	−34.9365	−1.16390
$902$	0.413176	0.0137573
$903$	6.03174	0.200724
$904$	9.32663	0.310199
$905$	−3.08628	−0.102592
$906$	0.477010	0.0158476
$907$	−14.7904	−0.491108	−0.245554	−	0.969383i	$-0.578970\pi$
$907$	−14.7904	−0.491108	−0.245554	+	0.969383i	$0.578970\pi$
$908$	24.9433	0.827772
$909$	1.74125	0.0577536
$910$	−0.0667218	−0.00221181
$911$	−56.5813	−1.87462	−0.937311	−	0.348493i	$-0.886694\pi$
$911$	−56.5813	−1.87462	−0.937311	+	0.348493i	$0.886694\pi$
$912$	23.0145	0.762087
$913$	−9.07536	−0.300351
$914$	−0.178140	−0.00589236
$915$	4.88297	0.161426
$916$	−14.5444	−0.480561
$917$	0.441646	0.0145844
$918$	1.14586	0.0378191
$919$	−32.1410	−1.06023	−0.530117	−	0.847925i	$-0.677852\pi$
$919$	−32.1410	−1.06023	−0.530117	+	0.847925i	$0.677852\pi$
$920$	2.55806	0.0843368
$921$	−14.8033	−0.487785
$922$	5.33052	0.175551
$923$	−5.22386	−0.171945
$924$	1.51916	0.0499766
$925$	18.9589	0.623366
$926$	2.95126	0.0969844
$927$	−12.1742	−0.399853
$928$	−5.70596	−0.187307
$929$	43.9086	1.44060	0.720298	−	0.693665i	$-0.244005\pi$
$929$	43.9086	1.44060	0.720298	+	0.693665i	$0.244005\pi$
$930$	−0.912567	−0.0299242
$931$	−5.99415	−0.196450
$932$	−11.3321	−0.371195
$933$	10.7431	0.351712
$934$	−0.330388	−0.0108106
$935$	−3.85818	−0.126176
$936$	−0.369793	−0.0120871
$937$	9.17484	0.299729	0.149864	−	0.988707i	$-0.452116\pi$
$937$	9.17484	0.299729	0.149864	+	0.988707i	$0.452116\pi$
$938$	−0.202520	−0.00661250
$939$	−8.18187	−0.267005
$940$	8.24378	0.268883
$941$	35.9228	1.17105	0.585524	−	0.810655i	$-0.300889\pi$
$941$	35.9228	1.17105	0.585524	+	0.810655i	$0.300889\pi$
$942$	3.65686	0.119147
$943$	17.9368	0.584103
$944$	−4.34799	−0.141515
$945$	0.716872	0.0233199
$946$	0.761254	0.0247505
$947$	0.465899	0.0151397	0.00756984	−	0.999971i	$-0.497590\pi$
$947$	0.465899	0.0151397	0.00756984	+	0.999971i	$0.497590\pi$
$948$	−24.6447	−0.800421
$949$	−8.96305	−0.290953
$950$	−4.40794	−0.143012
$951$	−31.6276	−1.02559
$952$	−4.55267	−0.147553
$953$	19.9315	0.645643	0.322822	−	0.946460i	$-0.395369\pi$
$953$	19.9315	0.645643	0.322822	+	0.946460i	$0.395369\pi$
$954$	0.819265	0.0265247
$955$	0.716872	0.0231974
$956$	−35.8634	−1.15990
$957$	2.27394	0.0735061
$958$	3.63980	0.117597
$959$	−13.5761	−0.438396
$960$	5.27783	0.170341
$961$	29.3069	0.945384
$962$	−0.393343	−0.0126819
$963$	−3.65162	−0.117672
$964$	−2.80999	−0.0905036
$965$	−14.6550	−0.471760
$966$	−0.898125	−0.0288967
$967$	45.0487	1.44867	0.724335	−	0.689448i	$-0.242147\pi$
$967$	45.0487	1.44867	0.724335	+	0.689448i	$0.242147\pi$
$968$	−6.77808	−0.217856
$969$	41.9007	1.34604
$970$	1.06607	0.0342295
$971$	57.9992	1.86128	0.930642	−	0.365930i	$-0.119249\pi$
$971$	57.9992	1.86128	0.930642	+	0.365930i	$0.119249\pi$
$972$	1.97313	0.0632882
$973$	−14.2047	−0.455381
$974$	0.973961	0.0312077
$975$	−2.54715	−0.0815741
$976$	−26.1527	−0.837128
$977$	−22.9895	−0.735500	−0.367750	−	0.929925i	$-0.619872\pi$
$977$	−22.9895	−0.735500	−0.367750	+	0.929925i	$0.619872\pi$
$978$	0.661864	0.0211641
$979$	3.71613	0.118768
$980$	−1.41448	−0.0451840
$981$	18.4979	0.590593
$982$	−4.53865	−0.144834
$983$	41.3680	1.31943	0.659717	−	0.751514i	$-0.270676\pi$
$983$	41.3680	1.31943	0.659717	+	0.751514i	$0.270676\pi$
$984$	−2.13216	−0.0679709
$985$	2.39302	0.0762479
$986$	−3.38427	−0.107777
$987$	−5.82813	−0.185511
$988$	−6.71536	−0.213644
$989$	33.0476	1.05085
$990$	0.0904750	0.00287548
$991$	6.75720	0.214650	0.107325	−	0.994224i	$-0.465772\pi$
$991$	6.75720	0.214650	0.107325	+	0.994224i	$0.465772\pi$
$992$	15.0031	0.476348
$993$	26.9863	0.856385
$994$	1.50815	0.0478356
$995$	7.44678	0.236079
$996$	23.2580	0.736958
$997$	11.1263	0.352374	0.176187	−	0.984357i	$-0.443624\pi$
$997$	11.1263	0.352374	0.176187	+	0.984357i	$0.443624\pi$
$998$	−6.00150	−0.189974
$999$	4.22615	0.133710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.13	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-0.163923 q^{2} -1.00000 q^{3} -1.97313 q^{4} +0.716872 q^{5} +0.163923 q^{6} -1.00000 q^{7} +0.651287 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.163923 q^{2} -1.00000 q^{3} -1.97313 q^{4} +0.716872 q^{5} +0.163923 q^{6} -1.00000 q^{7} +0.651287 q^{8} +1.00000 q^{9} -0.117512 q^{10} -0.769923 q^{11} +1.97313 q^{12} -0.567788 q^{13} +0.163923 q^{14} -0.716872 q^{15} +3.83950 q^{16} +6.99026 q^{17} -0.163923 q^{18} -5.99415 q^{19} -1.41448 q^{20} +1.00000 q^{21} +0.126208 q^{22} +5.47895 q^{23} -0.651287 q^{24} -4.48609 q^{25} +0.0930735 q^{26} -1.00000 q^{27} +1.97313 q^{28} +2.95347 q^{29} +0.117512 q^{30} -7.76575 q^{31} -1.93195 q^{32} +0.769923 q^{33} -1.14586 q^{34} -0.716872 q^{35} -1.97313 q^{36} -4.22615 q^{37} +0.982578 q^{38} +0.567788 q^{39} +0.466889 q^{40} +3.27377 q^{41} -0.163923 q^{42} +6.03174 q^{43} +1.51916 q^{44} +0.716872 q^{45} -0.898125 q^{46} -5.82813 q^{47} -3.83950 q^{48} +1.00000 q^{49} +0.735373 q^{50} -6.99026 q^{51} +1.12032 q^{52} -4.99787 q^{53} +0.163923 q^{54} -0.551936 q^{55} -0.651287 q^{56} +5.99415 q^{57} -0.484141 q^{58} -1.13244 q^{59} +1.41448 q^{60} -6.81149 q^{61} +1.27298 q^{62} -1.00000 q^{63} -7.36230 q^{64} -0.407032 q^{65} -0.126208 q^{66} -1.23546 q^{67} -13.7927 q^{68} -5.47895 q^{69} +0.117512 q^{70} +9.20036 q^{71} +0.651287 q^{72} +15.7859 q^{73} +0.692763 q^{74} +4.48609 q^{75} +11.8272 q^{76} +0.769923 q^{77} -0.0930735 q^{78} -12.4901 q^{79} +2.75243 q^{80} +1.00000 q^{81} -0.536646 q^{82} +11.7874 q^{83} -1.97313 q^{84} +5.01113 q^{85} -0.988740 q^{86} -2.95347 q^{87} -0.501440 q^{88} -4.82663 q^{89} -0.117512 q^{90} +0.567788 q^{91} -10.8107 q^{92} +7.76575 q^{93} +0.955364 q^{94} -4.29704 q^{95} +1.93195 q^{96} -9.07205 q^{97} -0.163923 q^{98} -0.769923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 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

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