LMFDB - Embedded newform 4011.2.a.m.1.22

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:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
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)

$f(q)$	$=$	$q+2.08228 q^{2} +1.00000 q^{3} +2.33590 q^{4} +3.00885 q^{5} +2.08228 q^{6} -1.00000 q^{7} +0.699442 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.08228 q^{2} +1.00000 q^{3} +2.33590 q^{4} +3.00885 q^{5} +2.08228 q^{6} -1.00000 q^{7} +0.699442 q^{8} +1.00000 q^{9} +6.26527 q^{10} -1.53256 q^{11} +2.33590 q^{12} +1.44622 q^{13} -2.08228 q^{14} +3.00885 q^{15} -3.21537 q^{16} -1.92048 q^{17} +2.08228 q^{18} +6.21371 q^{19} +7.02837 q^{20} -1.00000 q^{21} -3.19123 q^{22} +7.68070 q^{23} +0.699442 q^{24} +4.05316 q^{25} +3.01143 q^{26} +1.00000 q^{27} -2.33590 q^{28} -1.92190 q^{29} +6.26527 q^{30} +9.93301 q^{31} -8.09419 q^{32} -1.53256 q^{33} -3.99897 q^{34} -3.00885 q^{35} +2.33590 q^{36} -2.50185 q^{37} +12.9387 q^{38} +1.44622 q^{39} +2.10451 q^{40} -2.39448 q^{41} -2.08228 q^{42} -6.24531 q^{43} -3.57992 q^{44} +3.00885 q^{45} +15.9934 q^{46} +10.3340 q^{47} -3.21537 q^{48} +1.00000 q^{49} +8.43983 q^{50} -1.92048 q^{51} +3.37822 q^{52} +11.3305 q^{53} +2.08228 q^{54} -4.61125 q^{55} -0.699442 q^{56} +6.21371 q^{57} -4.00194 q^{58} +4.98460 q^{59} +7.02837 q^{60} +0.290436 q^{61} +20.6833 q^{62} -1.00000 q^{63} -10.4237 q^{64} +4.35145 q^{65} -3.19123 q^{66} -13.3393 q^{67} -4.48604 q^{68} +7.68070 q^{69} -6.26527 q^{70} -8.64230 q^{71} +0.699442 q^{72} +5.65772 q^{73} -5.20955 q^{74} +4.05316 q^{75} +14.5146 q^{76} +1.53256 q^{77} +3.01143 q^{78} -1.47449 q^{79} -9.67455 q^{80} +1.00000 q^{81} -4.98599 q^{82} -12.4680 q^{83} -2.33590 q^{84} -5.77842 q^{85} -13.0045 q^{86} -1.92190 q^{87} -1.07194 q^{88} -5.84054 q^{89} +6.26527 q^{90} -1.44622 q^{91} +17.9414 q^{92} +9.93301 q^{93} +21.5182 q^{94} +18.6961 q^{95} -8.09419 q^{96} +16.1562 q^{97} +2.08228 q^{98} -1.53256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * 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 $

$2$	2.08228	1.47240	0.736198	−	0.676766i	$-0.236619\pi$
$2$	2.08228	1.47240	0.736198	+	0.676766i	$0.236619\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.33590	1.16795
$5$	3.00885	1.34560	0.672799	−	0.739826i	$-0.265092\pi$
$5$	3.00885	1.34560	0.672799	+	0.739826i	$0.265092\pi$
$6$	2.08228	0.850088
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.699442	0.247290
$9$	1.00000	0.333333
$10$	6.26527	1.98125
$11$	−1.53256	−0.462085	−0.231042	−	0.972944i	$-0.574214\pi$
$11$	−1.53256	−0.462085	−0.231042	+	0.972944i	$0.574214\pi$
$12$	2.33590	0.674317
$13$	1.44622	0.401108	0.200554	−	0.979683i	$-0.435726\pi$
$13$	1.44622	0.401108	0.200554	+	0.979683i	$0.435726\pi$
$14$	−2.08228	−0.556513
$15$	3.00885	0.776881
$16$	−3.21537	−0.803842
$17$	−1.92048	−0.465784	−0.232892	−	0.972503i	$-0.574819\pi$
$17$	−1.92048	−0.465784	−0.232892	+	0.972503i	$0.574819\pi$
$18$	2.08228	0.490799
$19$	6.21371	1.42552	0.712761	−	0.701407i	$-0.247444\pi$
$19$	6.21371	1.42552	0.712761	+	0.701407i	$0.247444\pi$
$20$	7.02837	1.57159
$21$	−1.00000	−0.218218
$22$	−3.19123	−0.680372
$23$	7.68070	1.60154	0.800769	−	0.598974i	$-0.204425\pi$
$23$	7.68070	1.60154	0.800769	+	0.598974i	$0.204425\pi$
$24$	0.699442	0.142773
$25$	4.05316	0.810632
$26$	3.01143	0.590590
$27$	1.00000	0.192450
$28$	−2.33590	−0.441444
$29$	−1.92190	−0.356888	−0.178444	−	0.983950i	$-0.557106\pi$
$29$	−1.92190	−0.356888	−0.178444	+	0.983950i	$0.557106\pi$
$30$	6.26527	1.14388
$31$	9.93301	1.78402	0.892011	−	0.452014i	$-0.149294\pi$
$31$	9.93301	1.78402	0.892011	+	0.452014i	$0.149294\pi$
$32$	−8.09419	−1.43086
$33$	−1.53256	−0.266785
$34$	−3.99897	−0.685819
$35$	−3.00885	−0.508588
$36$	2.33590	0.389317
$37$	−2.50185	−0.411301	−0.205650	−	0.978626i	$-0.565931\pi$
$37$	−2.50185	−0.411301	−0.205650	+	0.978626i	$0.565931\pi$
$38$	12.9387	2.09893
$39$	1.44622	0.231580
$40$	2.10451	0.332753
$41$	−2.39448	−0.373956	−0.186978	−	0.982364i	$-0.559869\pi$
$41$	−2.39448	−0.373956	−0.186978	+	0.982364i	$0.559869\pi$
$42$	−2.08228	−0.321303
$43$	−6.24531	−0.952400	−0.476200	−	0.879337i	$-0.657986\pi$
$43$	−6.24531	−0.952400	−0.476200	+	0.879337i	$0.657986\pi$
$44$	−3.57992	−0.539692
$45$	3.00885	0.448532
$46$	15.9934	2.35810
$47$	10.3340	1.50736	0.753681	−	0.657241i	$-0.228276\pi$
$47$	10.3340	1.50736	0.753681	+	0.657241i	$0.228276\pi$
$48$	−3.21537	−0.464098
$49$	1.00000	0.142857
$50$	8.43983	1.19357
$51$	−1.92048	−0.268920
$52$	3.37822	0.468475
$53$	11.3305	1.55636	0.778181	−	0.628041i	$-0.216143\pi$
$53$	11.3305	1.55636	0.778181	+	0.628041i	$0.216143\pi$
$54$	2.08228	0.283363
$55$	−4.61125	−0.621780
$56$	−0.699442	−0.0934669
$57$	6.21371	0.823026
$58$	−4.00194	−0.525481
$59$	4.98460	0.648939	0.324470	−	0.945896i	$-0.394814\pi$
$59$	4.98460	0.648939	0.324470	+	0.945896i	$0.394814\pi$
$60$	7.02837	0.907359
$61$	0.290436	0.0371865	0.0185933	−	0.999827i	$-0.494081\pi$
$61$	0.290436	0.0371865	0.0185933	+	0.999827i	$0.494081\pi$
$62$	20.6833	2.62679
$63$	−1.00000	−0.125988
$64$	−10.4237	−1.30296
$65$	4.35145	0.539730
$66$	−3.19123	−0.392813
$67$	−13.3393	−1.62966	−0.814828	−	0.579703i	$-0.803169\pi$
$67$	−13.3393	−1.62966	−0.814828	+	0.579703i	$0.803169\pi$
$68$	−4.48604	−0.544013
$69$	7.68070	0.924648
$70$	−6.26527	−0.748843
$71$	−8.64230	−1.02565	−0.512826	−	0.858492i	$-0.671402\pi$
$71$	−8.64230	−1.02565	−0.512826	+	0.858492i	$0.671402\pi$
$72$	0.699442	0.0824300
$73$	5.65772	0.662186	0.331093	−	0.943598i	$-0.392583\pi$
$73$	5.65772	0.662186	0.331093	+	0.943598i	$0.392583\pi$
$74$	−5.20955	−0.605598
$75$	4.05316	0.468019
$76$	14.5146	1.66494
$77$	1.53256	0.174652
$78$	3.01143	0.340978
$79$	−1.47449	−0.165893	−0.0829463	−	0.996554i	$-0.526433\pi$
$79$	−1.47449	−0.165893	−0.0829463	+	0.996554i	$0.526433\pi$
$80$	−9.67455	−1.08165
$81$	1.00000	0.111111
$82$	−4.98599	−0.550611
$83$	−12.4680	−1.36854	−0.684271	−	0.729228i	$-0.739879\pi$
$83$	−12.4680	−1.36854	−0.684271	+	0.729228i	$0.739879\pi$
$84$	−2.33590	−0.254868
$85$	−5.77842	−0.626758
$86$	−13.0045	−1.40231
$87$	−1.92190	−0.206050
$88$	−1.07194	−0.114269
$89$	−5.84054	−0.619096	−0.309548	−	0.950884i	$-0.600178\pi$
$89$	−5.84054	−0.619096	−0.309548	+	0.950884i	$0.600178\pi$
$90$	6.26527	0.660418
$91$	−1.44622	−0.151605
$92$	17.9414	1.87052
$93$	9.93301	1.03001
$94$	21.5182	2.21943
$95$	18.6961	1.91818
$96$	−8.09419	−0.826110
$97$	16.1562	1.64042	0.820208	−	0.572066i	$-0.193858\pi$
$97$	16.1562	1.64042	0.820208	+	0.572066i	$0.193858\pi$
$98$	2.08228	0.210342
$99$	−1.53256	−0.154028
$100$	9.46779	0.946779
$101$	−13.0353	−1.29706	−0.648532	−	0.761187i	$-0.724617\pi$
$101$	−13.0353	−1.29706	−0.648532	+	0.761187i	$0.724617\pi$
$102$	−3.99897	−0.395958
$103$	−18.2880	−1.80197	−0.900986	−	0.433848i	$-0.857156\pi$
$103$	−18.2880	−1.80197	−0.900986	+	0.433848i	$0.857156\pi$
$104$	1.01154	0.0991901
$105$	−3.00885	−0.293633
$106$	23.5933	2.29158
$107$	8.20798	0.793495	0.396748	−	0.917928i	$-0.370139\pi$
$107$	8.20798	0.793495	0.396748	+	0.917928i	$0.370139\pi$
$108$	2.33590	0.224772
$109$	2.95016	0.282574	0.141287	−	0.989969i	$-0.454876\pi$
$109$	2.95016	0.282574	0.141287	+	0.989969i	$0.454876\pi$
$110$	−9.60192	−0.915507
$111$	−2.50185	−0.237465
$112$	3.21537	0.303824
$113$	11.9406	1.12328	0.561641	−	0.827381i	$-0.310170\pi$
$113$	11.9406	1.12328	0.561641	+	0.827381i	$0.310170\pi$
$114$	12.9387	1.21182
$115$	23.1101	2.15502
$116$	−4.48937	−0.416828
$117$	1.44622	0.133703
$118$	10.3793	0.955496
$119$	1.92048	0.176050
$120$	2.10451	0.192115
$121$	−8.65125	−0.786477
$122$	0.604770	0.0547533
$123$	−2.39448	−0.215903
$124$	23.2025	2.08365
$125$	−2.84889	−0.254812
$126$	−2.08228	−0.185504
$127$	−13.2097	−1.17217	−0.586084	−	0.810250i	$-0.699331\pi$
$127$	−13.2097	−1.17217	−0.586084	+	0.810250i	$0.699331\pi$
$128$	−5.51662	−0.487605
$129$	−6.24531	−0.549869
$130$	9.06094	0.794697
$131$	10.4268	0.910992	0.455496	−	0.890238i	$-0.349462\pi$
$131$	10.4268	0.910992	0.455496	+	0.890238i	$0.349462\pi$
$132$	−3.57992	−0.311592
$133$	−6.21371	−0.538797
$134$	−27.7762	−2.39950
$135$	3.00885	0.258960
$136$	−1.34326	−0.115184
$137$	−20.8572	−1.78195	−0.890976	−	0.454050i	$-0.849979\pi$
$137$	−20.8572	−1.78195	−0.890976	+	0.454050i	$0.849979\pi$
$138$	15.9934	1.36145
$139$	−10.4127	−0.883195	−0.441597	−	0.897213i	$-0.645588\pi$
$139$	−10.4127	−0.883195	−0.441597	+	0.897213i	$0.645588\pi$
$140$	−7.02837	−0.594006
$141$	10.3340	0.870276
$142$	−17.9957	−1.51017
$143$	−2.21642	−0.185346
$144$	−3.21537	−0.267947
$145$	−5.78271	−0.480228
$146$	11.7810	0.975001
$147$	1.00000	0.0824786
$148$	−5.84407	−0.480379
$149$	−16.9829	−1.39129	−0.695647	−	0.718384i	$-0.744882\pi$
$149$	−16.9829	−1.39129	−0.695647	+	0.718384i	$0.744882\pi$
$150$	8.43983	0.689109
$151$	−10.2027	−0.830286	−0.415143	−	0.909756i	$-0.636268\pi$
$151$	−10.2027	−0.830286	−0.415143	+	0.909756i	$0.636268\pi$
$152$	4.34613	0.352518
$153$	−1.92048	−0.155261
$154$	3.19123	0.257157
$155$	29.8869	2.40058
$156$	3.37822	0.270474
$157$	−13.3287	−1.06375	−0.531873	−	0.846824i	$-0.678512\pi$
$157$	−13.3287	−1.06375	−0.531873	+	0.846824i	$0.678512\pi$
$158$	−3.07030	−0.244260
$159$	11.3305	0.898566
$160$	−24.3542	−1.92537
$161$	−7.68070	−0.605324
$162$	2.08228	0.163600
$163$	16.0762	1.25919	0.629593	−	0.776926i	$-0.283222\pi$
$163$	16.0762	1.25919	0.629593	+	0.776926i	$0.283222\pi$
$164$	−5.59328	−0.436762
$165$	−4.61125	−0.358985
$166$	−25.9619	−2.01504
$167$	−1.39078	−0.107622	−0.0538108	−	0.998551i	$-0.517137\pi$
$167$	−1.39078	−0.107622	−0.0538108	+	0.998551i	$0.517137\pi$
$168$	−0.699442	−0.0539631
$169$	−10.9085	−0.839112
$170$	−12.0323	−0.922836
$171$	6.21371	0.475174
$172$	−14.5884	−1.11236
$173$	5.83851	0.443894	0.221947	−	0.975059i	$-0.428759\pi$
$173$	5.83851	0.443894	0.221947	+	0.975059i	$0.428759\pi$
$174$	−4.00194	−0.303387
$175$	−4.05316	−0.306390
$176$	4.92775	0.371443
$177$	4.98460	0.374665
$178$	−12.1616	−0.911554
$179$	−16.1187	−1.20477	−0.602385	−	0.798206i	$-0.705783\pi$
$179$	−16.1187	−1.20477	−0.602385	+	0.798206i	$0.705783\pi$
$180$	7.02837	0.523864
$181$	−0.0223664	−0.00166248	−0.000831241	−	1.00000i	$-0.500265\pi$
$181$	−0.0223664	−0.00166248	−0.000831241		1.00000i	$0.500265\pi$
$182$	−3.01143	−0.223222
$183$	0.290436	0.0214697
$184$	5.37221	0.396044
$185$	−7.52767	−0.553445
$186$	20.6833	1.51658
$187$	2.94325	0.215232
$188$	24.1391	1.76052
$189$	−1.00000	−0.0727393
$190$	38.9306	2.82432
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−10.4237	−0.752262
$193$	6.13544	0.441639	0.220819	−	0.975315i	$-0.429127\pi$
$193$	6.13544	0.441639	0.220819	+	0.975315i	$0.429127\pi$
$194$	33.6418	2.41534
$195$	4.35145	0.311613
$196$	2.33590	0.166850
$197$	−17.4735	−1.24494	−0.622469	−	0.782645i	$-0.713870\pi$
$197$	−17.4735	−1.24494	−0.622469	+	0.782645i	$0.713870\pi$
$198$	−3.19123	−0.226791
$199$	8.53633	0.605124	0.302562	−	0.953130i	$-0.402158\pi$
$199$	8.53633	0.605124	0.302562	+	0.953130i	$0.402158\pi$
$200$	2.83495	0.200461
$201$	−13.3393	−0.940882
$202$	−27.1432	−1.90979
$203$	1.92190	0.134891
$204$	−4.48604	−0.314086
$205$	−7.20464	−0.503194
$206$	−38.0808	−2.65322
$207$	7.68070	0.533846
$208$	−4.65012	−0.322428
$209$	−9.52289	−0.658712
$210$	−6.26527	−0.432345
$211$	14.4696	0.996127	0.498063	−	0.867141i	$-0.334045\pi$
$211$	14.4696	0.996127	0.498063	+	0.867141i	$0.334045\pi$
$212$	26.4669	1.81775
$213$	−8.64230	−0.592161
$214$	17.0913	1.16834
$215$	−18.7912	−1.28155
$216$	0.699442	0.0475910
$217$	−9.93301	−0.674297
$218$	6.14306	0.416061
$219$	5.65772	0.382313
$220$	−10.7714	−0.726209
$221$	−2.77743	−0.186830
$222$	−5.20955	−0.349642
$223$	−13.6289	−0.912658	−0.456329	−	0.889811i	$-0.650836\pi$
$223$	−13.6289	−0.912658	−0.456329	+	0.889811i	$0.650836\pi$
$224$	8.09419	0.540816
$225$	4.05316	0.270211
$226$	24.8638	1.65392
$227$	−12.8040	−0.849831	−0.424916	−	0.905233i	$-0.639696\pi$
$227$	−12.8040	−0.849831	−0.424916	+	0.905233i	$0.639696\pi$
$228$	14.5146	0.961253
$229$	−4.53785	−0.299870	−0.149935	−	0.988696i	$-0.547906\pi$
$229$	−4.53785	−0.299870	−0.149935	+	0.988696i	$0.547906\pi$
$230$	48.1217	3.17305
$231$	1.53256	0.100835
$232$	−1.34426	−0.0882549
$233$	−3.35082	−0.219520	−0.109760	−	0.993958i	$-0.535008\pi$
$233$	−3.35082	−0.219520	−0.109760	+	0.993958i	$0.535008\pi$
$234$	3.01143	0.196863
$235$	31.0933	2.02830
$236$	11.6435	0.757929
$237$	−1.47449	−0.0957782
$238$	3.99897	0.259215
$239$	−17.8823	−1.15671	−0.578355	−	0.815785i	$-0.696305\pi$
$239$	−17.8823	−1.15671	−0.578355	+	0.815785i	$0.696305\pi$
$240$	−9.67455	−0.624489
$241$	29.6263	1.90840	0.954200	−	0.299170i	$-0.0967098\pi$
$241$	29.6263	1.90840	0.954200	+	0.299170i	$0.0967098\pi$
$242$	−18.0144	−1.15801
$243$	1.00000	0.0641500
$244$	0.678430	0.0434320
$245$	3.00885	0.192228
$246$	−4.98599	−0.317895
$247$	8.98637	0.571789
$248$	6.94757	0.441171
$249$	−12.4680	−0.790128
$250$	−5.93219	−0.375185
$251$	−9.74107	−0.614851	−0.307425	−	0.951572i	$-0.599467\pi$
$251$	−9.74107	−0.614851	−0.307425	+	0.951572i	$0.599467\pi$
$252$	−2.33590	−0.147148
$253$	−11.7712	−0.740046
$254$	−27.5063	−1.72590
$255$	−5.77842	−0.361859
$256$	9.36015	0.585009
$257$	−5.80860	−0.362330	−0.181165	−	0.983453i	$-0.557987\pi$
$257$	−5.80860	−0.362330	−0.181165	+	0.983453i	$0.557987\pi$
$258$	−13.0045	−0.809625
$259$	2.50185	0.155457
$260$	10.1645	0.630379
$261$	−1.92190	−0.118963
$262$	21.7115	1.34134
$263$	6.74619	0.415988	0.207994	−	0.978130i	$-0.433307\pi$
$263$	6.74619	0.415988	0.207994	+	0.978130i	$0.433307\pi$
$264$	−1.07194	−0.0659733
$265$	34.0917	2.09424
$266$	−12.9387	−0.793322
$267$	−5.84054	−0.357435
$268$	−31.1593	−1.90336
$269$	15.6189	0.952301	0.476151	−	0.879364i	$-0.342032\pi$
$269$	15.6189	0.952301	0.476151	+	0.879364i	$0.342032\pi$
$270$	6.26527	0.381292
$271$	−13.3592	−0.811511	−0.405756	−	0.913982i	$-0.632992\pi$
$271$	−13.3592	−0.811511	−0.405756	+	0.913982i	$0.632992\pi$
$272$	6.17504	0.374417
$273$	−1.44622	−0.0875290
$274$	−43.4306	−2.62374
$275$	−6.21172	−0.374581
$276$	17.9414	1.07994
$277$	4.90068	0.294453	0.147227	−	0.989103i	$-0.452965\pi$
$277$	4.90068	0.294453	0.147227	+	0.989103i	$0.452965\pi$
$278$	−21.6822	−1.30041
$279$	9.93301	0.594674
$280$	−2.10451	−0.125769
$281$	15.7324	0.938517	0.469258	−	0.883061i	$-0.344521\pi$
$281$	15.7324	0.938517	0.469258	+	0.883061i	$0.344521\pi$
$282$	21.5182	1.28139
$283$	24.8973	1.47999	0.739995	−	0.672613i	$-0.234828\pi$
$283$	24.8973	1.47999	0.739995	+	0.672613i	$0.234828\pi$
$284$	−20.1876	−1.19791
$285$	18.6961	1.10746
$286$	−4.61521	−0.272903
$287$	2.39448	0.141342
$288$	−8.09419	−0.476955
$289$	−13.3118	−0.783045
$290$	−12.0412	−0.707086
$291$	16.1562	0.947094
$292$	13.2159	0.773401
$293$	24.7373	1.44517	0.722584	−	0.691283i	$-0.242954\pi$
$293$	24.7373	1.44517	0.722584	+	0.691283i	$0.242954\pi$
$294$	2.08228	0.121441
$295$	14.9979	0.873211
$296$	−1.74990	−0.101711
$297$	−1.53256	−0.0889283
$298$	−35.3632	−2.04854
$299$	11.1080	0.642390
$300$	9.46779	0.546623
$301$	6.24531	0.359974
$302$	−21.2449	−1.22251
$303$	−13.0353	−0.748860
$304$	−19.9793	−1.14589
$305$	0.873878	0.0500381
$306$	−3.99897	−0.228606
$307$	−30.6935	−1.75177	−0.875884	−	0.482521i	$-0.839721\pi$
$307$	−30.6935	−1.75177	−0.875884	+	0.482521i	$0.839721\pi$
$308$	3.57992	0.203985
$309$	−18.2880	−1.04037
$310$	62.2330	3.53460
$311$	−6.53146	−0.370365	−0.185183	−	0.982704i	$-0.559288\pi$
$311$	−6.53146	−0.370365	−0.185183	+	0.982704i	$0.559288\pi$
$312$	1.01154	0.0572675
$313$	21.1113	1.19328	0.596641	−	0.802508i	$-0.296502\pi$
$313$	21.1113	1.19328	0.596641	+	0.802508i	$0.296502\pi$
$314$	−27.7541	−1.56625
$315$	−3.00885	−0.169529
$316$	−3.44426	−0.193754
$317$	4.00166	0.224755	0.112378	−	0.993666i	$-0.464153\pi$
$317$	4.00166	0.224755	0.112378	+	0.993666i	$0.464153\pi$
$318$	23.5933	1.32304
$319$	2.94543	0.164913
$320$	−31.3632	−1.75326
$321$	8.20798	0.458125
$322$	−15.9934	−0.891277
$323$	−11.9333	−0.663985
$324$	2.33590	0.129772
$325$	5.86175	0.325151
$326$	33.4752	1.85402
$327$	2.95016	0.163144
$328$	−1.67480	−0.0924755
$329$	−10.3340	−0.569729
$330$	−9.60192	−0.528568
$331$	15.3247	0.842322	0.421161	−	0.906986i	$-0.361623\pi$
$331$	15.3247	0.842322	0.421161	+	0.906986i	$0.361623\pi$
$332$	−29.1240	−1.59839
$333$	−2.50185	−0.137100
$334$	−2.89599	−0.158462
$335$	−40.1359	−2.19286
$336$	3.21537	0.175413
$337$	−24.9362	−1.35836	−0.679181	−	0.733971i	$-0.737665\pi$
$337$	−24.9362	−1.35836	−0.679181	+	0.733971i	$0.737665\pi$
$338$	−22.7145	−1.23551
$339$	11.9406	0.648527
$340$	−13.4978	−0.732022
$341$	−15.2230	−0.824370
$342$	12.9387	0.699644
$343$	−1.00000	−0.0539949
$344$	−4.36823	−0.235519
$345$	23.1101	1.24420
$346$	12.1574	0.653588
$347$	16.7744	0.900495	0.450248	−	0.892904i	$-0.351336\pi$
$347$	16.7744	0.900495	0.450248	+	0.892904i	$0.351336\pi$
$348$	−4.48937	−0.240656
$349$	−5.78488	−0.309658	−0.154829	−	0.987941i	$-0.549483\pi$
$349$	−5.78488	−0.309658	−0.154829	+	0.987941i	$0.549483\pi$
$350$	−8.43983	−0.451128
$351$	1.44622	0.0771933
$352$	12.4048	0.661181
$353$	17.8611	0.950648	0.475324	−	0.879811i	$-0.342331\pi$
$353$	17.8611	0.950648	0.475324	+	0.879811i	$0.342331\pi$
$354$	10.3793	0.551656
$355$	−26.0034	−1.38012
$356$	−13.6429	−0.723073
$357$	1.92048	0.101642
$358$	−33.5637	−1.77390
$359$	4.33171	0.228619	0.114309	−	0.993445i	$-0.463534\pi$
$359$	4.33171	0.228619	0.114309	+	0.993445i	$0.463534\pi$
$360$	2.10451	0.110918
$361$	19.6102	1.03211
$362$	−0.0465732	−0.00244783
$363$	−8.65125	−0.454073
$364$	−3.37822	−0.177067
$365$	17.0232	0.891036
$366$	0.604770	0.0316118
$367$	−15.1176	−0.789132	−0.394566	−	0.918868i	$-0.629105\pi$
$367$	−15.1176	−0.789132	−0.394566	+	0.918868i	$0.629105\pi$
$368$	−24.6963	−1.28738
$369$	−2.39448	−0.124652
$370$	−15.6747	−0.814891
$371$	−11.3305	−0.588249
$372$	23.2025	1.20300
$373$	−4.94468	−0.256026	−0.128013	−	0.991772i	$-0.540860\pi$
$373$	−4.94468	−0.256026	−0.128013	+	0.991772i	$0.540860\pi$
$374$	6.12868	0.316906
$375$	−2.84889	−0.147116
$376$	7.22800	0.372756
$377$	−2.77949	−0.143151
$378$	−2.08228	−0.107101
$379$	27.2030	1.39733	0.698663	−	0.715451i	$-0.253779\pi$
$379$	27.2030	1.39733	0.698663	+	0.715451i	$0.253779\pi$
$380$	43.6722	2.24034
$381$	−13.2097	−0.676752
$382$	−2.08228	−0.106539
$383$	−26.2478	−1.34120	−0.670601	−	0.741819i	$-0.733964\pi$
$383$	−26.2478	−1.34120	−0.670601	+	0.741819i	$0.733964\pi$
$384$	−5.51662	−0.281519
$385$	4.61125	0.235011
$386$	12.7757	0.650267
$387$	−6.24531	−0.317467
$388$	37.7393	1.91592
$389$	33.4237	1.69465	0.847325	−	0.531075i	$-0.178212\pi$
$389$	33.4237	1.69465	0.847325	+	0.531075i	$0.178212\pi$
$390$	9.06094	0.458819
$391$	−14.7506	−0.745970
$392$	0.699442	0.0353272
$393$	10.4268	0.525962
$394$	−36.3848	−1.83304
$395$	−4.43650	−0.223225
$396$	−3.57992	−0.179897
$397$	21.7893	1.09358	0.546788	−	0.837271i	$-0.315850\pi$
$397$	21.7893	1.09358	0.546788	+	0.837271i	$0.315850\pi$
$398$	17.7751	0.890983
$399$	−6.21371	−0.311074
$400$	−13.0324	−0.651620
$401$	22.7470	1.13593	0.567967	−	0.823052i	$-0.307730\pi$
$401$	22.7470	1.13593	0.567967	+	0.823052i	$0.307730\pi$
$402$	−27.7762	−1.38535
$403$	14.3653	0.715586
$404$	−30.4493	−1.51491
$405$	3.00885	0.149511
$406$	4.00194	0.198613
$407$	3.83423	0.190056
$408$	−1.34326	−0.0665014
$409$	−12.4892	−0.617554	−0.308777	−	0.951135i	$-0.599920\pi$
$409$	−12.4892	−0.617554	−0.308777	+	0.951135i	$0.599920\pi$
$410$	−15.0021	−0.740901
$411$	−20.8572	−1.02881
$412$	−42.7190	−2.10462
$413$	−4.98460	−0.245276
$414$	15.9934	0.786033
$415$	−37.5143	−1.84151
$416$	−11.7059	−0.573931
$417$	−10.4127	−0.509913
$418$	−19.8294	−0.969886
$419$	−36.9689	−1.80605	−0.903025	−	0.429589i	$-0.858658\pi$
$419$	−36.9689	−1.80605	−0.903025	+	0.429589i	$0.858658\pi$
$420$	−7.02837	−0.342949
$421$	32.8307	1.60007	0.800035	−	0.599953i	$-0.204814\pi$
$421$	32.8307	1.60007	0.800035	+	0.599953i	$0.204814\pi$
$422$	30.1297	1.46669
$423$	10.3340	0.502454
$424$	7.92501	0.384873
$425$	−7.78400	−0.377580
$426$	−17.9957	−0.871895
$427$	−0.290436	−0.0140552
$428$	19.1730	0.926764
$429$	−2.21642	−0.107010
$430$	−39.1285	−1.88695
$431$	8.72165	0.420107	0.210054	−	0.977690i	$-0.432636\pi$
$431$	8.72165	0.420107	0.210054	+	0.977690i	$0.432636\pi$
$432$	−3.21537	−0.154699
$433$	17.3459	0.833592	0.416796	−	0.909000i	$-0.363153\pi$
$433$	17.3459	0.833592	0.416796	+	0.909000i	$0.363153\pi$
$434$	−20.6833	−0.992832
$435$	−5.78271	−0.277260
$436$	6.89128	0.330032
$437$	47.7256	2.28303
$438$	11.7810	0.562917
$439$	−22.1628	−1.05777	−0.528886	−	0.848693i	$-0.677390\pi$
$439$	−22.1628	−1.05777	−0.528886	+	0.848693i	$0.677390\pi$
$440$	−3.22530	−0.153760
$441$	1.00000	0.0476190
$442$	−5.78338	−0.275088
$443$	21.0276	0.999051	0.499526	−	0.866299i	$-0.333508\pi$
$443$	21.0276	0.999051	0.499526	+	0.866299i	$0.333508\pi$
$444$	−5.84407	−0.277347
$445$	−17.5733	−0.833053
$446$	−28.3792	−1.34379
$447$	−16.9829	−0.803264
$448$	10.4237	0.492471
$449$	21.5866	1.01873	0.509367	−	0.860549i	$-0.329880\pi$
$449$	21.5866	1.01873	0.509367	+	0.860549i	$0.329880\pi$
$450$	8.43983	0.397857
$451$	3.66970	0.172799
$452$	27.8922	1.31194
$453$	−10.2027	−0.479366
$454$	−26.6615	−1.25129
$455$	−4.35145	−0.203999
$456$	4.34613	0.203526
$457$	3.35752	0.157058	0.0785291	−	0.996912i	$-0.474978\pi$
$457$	3.35752	0.157058	0.0785291	+	0.996912i	$0.474978\pi$
$458$	−9.44910	−0.441527
$459$	−1.92048	−0.0896402
$460$	53.9828	2.51696
$461$	−11.6818	−0.544075	−0.272038	−	0.962287i	$-0.587698\pi$
$461$	−11.6818	−0.544075	−0.272038	+	0.962287i	$0.587698\pi$
$462$	3.19123	0.148469
$463$	−2.46186	−0.114412	−0.0572061	−	0.998362i	$-0.518219\pi$
$463$	−2.46186	−0.114412	−0.0572061	+	0.998362i	$0.518219\pi$
$464$	6.17962	0.286882
$465$	29.8869	1.38597
$466$	−6.97736	−0.323220
$467$	1.07631	0.0498057	0.0249028	−	0.999690i	$-0.492072\pi$
$467$	1.07631	0.0498057	0.0249028	+	0.999690i	$0.492072\pi$
$468$	3.37822	0.156158
$469$	13.3393	0.615952
$470$	64.7450	2.98646
$471$	−13.3287	−0.614154
$472$	3.48644	0.160476
$473$	9.57132	0.440090
$474$	−3.07030	−0.141023
$475$	25.1852	1.15557
$476$	4.48604	0.205617
$477$	11.3305	0.518787
$478$	−37.2360	−1.70314
$479$	19.3123	0.882402	0.441201	−	0.897408i	$-0.354553\pi$
$479$	19.3123	0.882402	0.441201	+	0.897408i	$0.354553\pi$
$480$	−24.3542	−1.11161
$481$	−3.61821	−0.164976
$482$	61.6904	2.80992
$483$	−7.68070	−0.349484
$484$	−20.2085	−0.918567
$485$	48.6116	2.20734
$486$	2.08228	0.0944543
$487$	−20.3050	−0.920109	−0.460054	−	0.887891i	$-0.652170\pi$
$487$	−20.3050	−0.920109	−0.460054	+	0.887891i	$0.652170\pi$
$488$	0.203143	0.00919586
$489$	16.0762	0.726991
$490$	6.26527	0.283036
$491$	14.7964	0.667754	0.333877	−	0.942617i	$-0.391643\pi$
$491$	14.7964	0.667754	0.333877	+	0.942617i	$0.391643\pi$
$492$	−5.59328	−0.252165
$493$	3.69097	0.166233
$494$	18.7122	0.841900
$495$	−4.61125	−0.207260
$496$	−31.9383	−1.43407
$497$	8.64230	0.387660
$498$	−25.9619	−1.16338
$499$	36.7410	1.64475	0.822377	−	0.568943i	$-0.192647\pi$
$499$	36.7410	1.64475	0.822377	+	0.568943i	$0.192647\pi$
$500$	−6.65473	−0.297608
$501$	−1.39078	−0.0621354
$502$	−20.2837	−0.905304
$503$	−39.0327	−1.74038	−0.870190	−	0.492716i	$-0.836004\pi$
$503$	−39.0327	−1.74038	−0.870190	+	0.492716i	$0.836004\pi$
$504$	−0.699442	−0.0311556
$505$	−39.2213	−1.74533
$506$	−24.5109	−1.08964
$507$	−10.9085	−0.484462
$508$	−30.8565	−1.36904
$509$	−10.5685	−0.468441	−0.234220	−	0.972184i	$-0.575254\pi$
$509$	−10.5685	−0.468441	−0.234220	+	0.972184i	$0.575254\pi$
$510$	−12.0323	−0.532799
$511$	−5.65772	−0.250283
$512$	30.5237	1.34897
$513$	6.21371	0.274342
$514$	−12.0951	−0.533494
$515$	−55.0259	−2.42473
$516$	−14.5884	−0.642220
$517$	−15.8374	−0.696529
$518$	5.20955	0.228894
$519$	5.83851	0.256282
$520$	3.04358	0.133470
$521$	−2.74729	−0.120361	−0.0601804	−	0.998188i	$-0.519168\pi$
$521$	−2.74729	−0.120361	−0.0601804	+	0.998188i	$0.519168\pi$
$522$	−4.00194	−0.175160
$523$	−40.7789	−1.78314	−0.891568	−	0.452887i	$-0.850394\pi$
$523$	−40.7789	−1.78314	−0.891568	+	0.452887i	$0.850394\pi$
$524$	24.3559	1.06399
$525$	−4.05316	−0.176895
$526$	14.0475	0.612499
$527$	−19.0761	−0.830969
$528$	4.92775	0.214453
$529$	35.9932	1.56492
$530$	70.9885	3.08354
$531$	4.98460	0.216313
$532$	−14.5146	−0.629288
$533$	−3.46294	−0.149997
$534$	−12.1616	−0.526286
$535$	24.6966	1.06773
$536$	−9.33007	−0.402998
$537$	−16.1187	−0.695574
$538$	32.5230	1.40217
$539$	−1.53256	−0.0660121
$540$	7.02837	0.302453
$541$	−32.2023	−1.38449	−0.692244	−	0.721664i	$-0.743378\pi$
$541$	−32.2023	−1.38449	−0.692244	+	0.721664i	$0.743378\pi$
$542$	−27.8176	−1.19487
$543$	−0.0223664	−0.000959834 0
$544$	15.5447	0.666473
$545$	8.87657	0.380231
$546$	−3.01143	−0.128877
$547$	5.96919	0.255224	0.127612	−	0.991824i	$-0.459269\pi$
$547$	5.96919	0.255224	0.127612	+	0.991824i	$0.459269\pi$
$548$	−48.7204	−2.08123
$549$	0.290436	0.0123955
$550$	−12.9346	−0.551532
$551$	−11.9421	−0.508752
$552$	5.37221	0.228656
$553$	1.47449	0.0627015
$554$	10.2046	0.433552
$555$	−7.52767	−0.319532
$556$	−24.3231	−1.03153
$557$	−8.48071	−0.359339	−0.179670	−	0.983727i	$-0.557503\pi$
$557$	−8.48071	−0.359339	−0.179670	+	0.983727i	$0.557503\pi$
$558$	20.6833	0.875596
$559$	−9.03207	−0.382016
$560$	9.67455	0.408824
$561$	2.94325	0.124264
$562$	32.7593	1.38187
$563$	18.3762	0.774465	0.387233	−	0.921982i	$-0.373431\pi$
$563$	18.3762	0.774465	0.387233	+	0.921982i	$0.373431\pi$
$564$	24.1391	1.01644
$565$	35.9276	1.51149
$566$	51.8432	2.17913
$567$	−1.00000	−0.0419961
$568$	−6.04479	−0.253634
$569$	−17.4765	−0.732651	−0.366326	−	0.930487i	$-0.619384\pi$
$569$	−17.4765	−0.732651	−0.366326	+	0.930487i	$0.619384\pi$
$570$	38.9306	1.63062
$571$	0.784692	0.0328383	0.0164192	−	0.999865i	$-0.494773\pi$
$571$	0.784692	0.0328383	0.0164192	+	0.999865i	$0.494773\pi$
$572$	−5.17733	−0.216475
$573$	−1.00000	−0.0417756
$574$	4.98599	0.208111
$575$	31.1311	1.29826
$576$	−10.4237	−0.434319
$577$	32.1673	1.33914	0.669571	−	0.742748i	$-0.266478\pi$
$577$	32.1673	1.33914	0.669571	+	0.742748i	$0.266478\pi$
$578$	−27.7189	−1.15295
$579$	6.13544	0.254980
$580$	−13.5078	−0.560883
$581$	12.4680	0.517260
$582$	33.6418	1.39450
$583$	−17.3647	−0.719171
$584$	3.95725	0.163752
$585$	4.35145	0.179910
$586$	51.5100	2.12786
$587$	25.6930	1.06046	0.530231	−	0.847853i	$-0.322105\pi$
$587$	25.6930	1.06046	0.530231	+	0.847853i	$0.322105\pi$
$588$	2.33590	0.0963310
$589$	61.7208	2.54316
$590$	31.2299	1.28571
$591$	−17.4735	−0.718765
$592$	8.04435	0.330621
$593$	−20.7249	−0.851071	−0.425536	−	0.904942i	$-0.639914\pi$
$593$	−20.7249	−0.851071	−0.425536	+	0.904942i	$0.639914\pi$
$594$	−3.19123	−0.130938
$595$	5.77842	0.236892
$596$	−39.6704	−1.62496
$597$	8.53633	0.349369
$598$	23.1299	0.945853
$599$	30.1281	1.23100	0.615500	−	0.788137i	$-0.288954\pi$
$599$	30.1281	1.23100	0.615500	+	0.788137i	$0.288954\pi$
$600$	2.83495	0.115736
$601$	−25.5169	−1.04086	−0.520429	−	0.853905i	$-0.674228\pi$
$601$	−25.5169	−1.04086	−0.520429	+	0.853905i	$0.674228\pi$
$602$	13.0045	0.530024
$603$	−13.3393	−0.543219
$604$	−23.8326	−0.969733
$605$	−26.0303	−1.05828
$606$	−27.1432	−1.10262
$607$	33.9460	1.37783	0.688913	−	0.724844i	$-0.258088\pi$
$607$	33.9460	1.37783	0.688913	+	0.724844i	$0.258088\pi$
$608$	−50.2949	−2.03973
$609$	1.92190	0.0778794
$610$	1.81966	0.0736759
$611$	14.9451	0.604615
$612$	−4.48604	−0.181338
$613$	23.6727	0.956130	0.478065	−	0.878324i	$-0.341338\pi$
$613$	23.6727	0.956130	0.478065	+	0.878324i	$0.341338\pi$
$614$	−63.9125	−2.57930
$615$	−7.20464	−0.290519
$616$	1.07194	0.0431896
$617$	10.1434	0.408359	0.204179	−	0.978933i	$-0.434547\pi$
$617$	10.1434	0.408359	0.204179	+	0.978933i	$0.434547\pi$
$618$	−38.0808	−1.53184
$619$	−34.3597	−1.38103	−0.690517	−	0.723317i	$-0.742617\pi$
$619$	−34.3597	−1.38103	−0.690517	+	0.723317i	$0.742617\pi$
$620$	69.8129	2.80375
$621$	7.68070	0.308216
$622$	−13.6004	−0.545325
$623$	5.84054	0.233996
$624$	−4.65012	−0.186154
$625$	−28.8377	−1.15351
$626$	43.9597	1.75698
$627$	−9.52289	−0.380308
$628$	−31.1345	−1.24240
$629$	4.80474	0.191577
$630$	−6.26527	−0.249614
$631$	−21.8951	−0.871628	−0.435814	−	0.900037i	$-0.643540\pi$
$631$	−21.8951	−0.871628	−0.435814	+	0.900037i	$0.643540\pi$
$632$	−1.03132	−0.0410236
$633$	14.4696	0.575114
$634$	8.33258	0.330929
$635$	−39.7459	−1.57727
$636$	26.4669	1.04948
$637$	1.44622	0.0573012
$638$	6.13323	0.242817
$639$	−8.64230	−0.341884
$640$	−16.5987	−0.656120
$641$	−15.9527	−0.630095	−0.315047	−	0.949076i	$-0.602020\pi$
$641$	−15.9527	−0.630095	−0.315047	+	0.949076i	$0.602020\pi$
$642$	17.0913	0.674541
$643$	−14.0872	−0.555546	−0.277773	−	0.960647i	$-0.589596\pi$
$643$	−14.0872	−0.555546	−0.277773	+	0.960647i	$0.589596\pi$
$644$	−17.9414	−0.706989
$645$	−18.7912	−0.739902
$646$	−24.8485	−0.977649
$647$	−35.1504	−1.38191	−0.690953	−	0.722900i	$-0.742809\pi$
$647$	−35.1504	−1.38191	−0.690953	+	0.722900i	$0.742809\pi$
$648$	0.699442	0.0274767
$649$	−7.63921	−0.299865
$650$	12.2058	0.478752
$651$	−9.93301	−0.389306
$652$	37.5524	1.47067
$653$	−18.7061	−0.732026	−0.366013	−	0.930610i	$-0.619277\pi$
$653$	−18.7061	−0.732026	−0.366013	+	0.930610i	$0.619277\pi$
$654$	6.14306	0.240213
$655$	31.3726	1.22583
$656$	7.69915	0.300601
$657$	5.65772	0.220729
$658$	−21.5182	−0.838867
$659$	32.4195	1.26289	0.631443	−	0.775422i	$-0.282463\pi$
$659$	32.4195	1.26289	0.631443	+	0.775422i	$0.282463\pi$
$660$	−10.7714	−0.419277
$661$	−31.7911	−1.23653	−0.618265	−	0.785970i	$-0.712164\pi$
$661$	−31.7911	−1.23653	−0.618265	+	0.785970i	$0.712164\pi$
$662$	31.9104	1.24023
$663$	−2.77743	−0.107866
$664$	−8.72065	−0.338427
$665$	−18.6961	−0.725003
$666$	−5.20955	−0.201866
$667$	−14.7616	−0.571570
$668$	−3.24872	−0.125697
$669$	−13.6289	−0.526923
$670$	−83.5744	−3.22876
$671$	−0.445111	−0.0171833
$672$	8.09419	0.312240
$673$	29.3623	1.13183	0.565917	−	0.824462i	$-0.308522\pi$
$673$	29.3623	1.13183	0.565917	+	0.824462i	$0.308522\pi$
$674$	−51.9242	−2.00005
$675$	4.05316	0.156006
$676$	−25.4811	−0.980042
$677$	40.8181	1.56877	0.784383	−	0.620277i	$-0.212980\pi$
$677$	40.8181	1.56877	0.784383	+	0.620277i	$0.212980\pi$
$678$	24.8638	0.954889
$679$	−16.1562	−0.620019
$680$	−4.04167	−0.154991
$681$	−12.8040	−0.490650
$682$	−31.6985	−1.21380
$683$	−16.7496	−0.640906	−0.320453	−	0.947264i	$-0.603835\pi$
$683$	−16.7496	−0.640906	−0.320453	+	0.947264i	$0.603835\pi$
$684$	14.5146	0.554980
$685$	−62.7562	−2.39779
$686$	−2.08228	−0.0795019
$687$	−4.53785	−0.173130
$688$	20.0810	0.765579
$689$	16.3863	0.624269
$690$	48.1217	1.83196
$691$	−19.3103	−0.734597	−0.367299	−	0.930103i	$-0.619717\pi$
$691$	−19.3103	−0.734597	−0.367299	+	0.930103i	$0.619717\pi$
$692$	13.6382	0.518446
$693$	1.53256	0.0582172
$694$	34.9290	1.32589
$695$	−31.3303	−1.18842
$696$	−1.34426	−0.0509540
$697$	4.59855	0.174183
$698$	−12.0458	−0.455939
$699$	−3.35082	−0.126740
$700$	−9.46779	−0.357849
$701$	4.52856	0.171042	0.0855208	−	0.996336i	$-0.472745\pi$
$701$	4.52856	0.171042	0.0855208	+	0.996336i	$0.472745\pi$
$702$	3.01143	0.113659
$703$	−15.5457	−0.586319
$704$	15.9749	0.602077
$705$	31.0933	1.17104
$706$	37.1918	1.39973
$707$	13.0353	0.490244
$708$	11.6435	0.437591
$709$	27.3610	1.02756	0.513782	−	0.857921i	$-0.328244\pi$
$709$	27.3610	1.02756	0.513782	+	0.857921i	$0.328244\pi$
$710$	−54.1464	−2.03208
$711$	−1.47449	−0.0552976
$712$	−4.08512	−0.153096
$713$	76.2925	2.85718
$714$	3.99897	0.149658
$715$	−6.66886	−0.249401
$716$	−37.6517	−1.40711
$717$	−17.8823	−0.667827
$718$	9.01985	0.336618
$719$	9.55952	0.356510	0.178255	−	0.983984i	$-0.442955\pi$
$719$	9.55952	0.356510	0.178255	+	0.983984i	$0.442955\pi$
$720$	−9.67455	−0.360549
$721$	18.2880	0.681082
$722$	40.8339	1.51968
$723$	29.6263	1.10182
$724$	−0.0522457	−0.00194170
$725$	−7.78978	−0.289305
$726$	−18.0144	−0.668575
$727$	20.6096	0.764367	0.382183	−	0.924086i	$-0.375172\pi$
$727$	20.6096	0.764367	0.382183	+	0.924086i	$0.375172\pi$
$728$	−1.01154	−0.0374903
$729$	1.00000	0.0370370
$730$	35.4472	1.31196
$731$	11.9940	0.443613
$732$	0.678430	0.0250755
$733$	−18.0383	−0.666259	−0.333130	−	0.942881i	$-0.608105\pi$
$733$	−18.0383	−0.666259	−0.333130	+	0.942881i	$0.608105\pi$
$734$	−31.4791	−1.16191
$735$	3.00885	0.110983
$736$	−62.1691	−2.29158
$737$	20.4433	0.753039
$738$	−4.98599	−0.183537
$739$	−39.1133	−1.43880	−0.719402	−	0.694594i	$-0.755584\pi$
$739$	−39.1133	−1.43880	−0.719402	+	0.694594i	$0.755584\pi$
$740$	−17.5839	−0.646397
$741$	8.98637	0.330122
$742$	−23.5933	−0.866136
$743$	−24.4744	−0.897880	−0.448940	−	0.893562i	$-0.648198\pi$
$743$	−24.4744	−0.897880	−0.448940	+	0.893562i	$0.648198\pi$
$744$	6.94757	0.254710
$745$	−51.0990	−1.87212
$746$	−10.2962	−0.376972
$747$	−12.4680	−0.456181
$748$	6.87514	0.251380
$749$	−8.20798	−0.299913
$750$	−5.93219	−0.216613
$751$	−10.0635	−0.367221	−0.183611	−	0.982999i	$-0.558779\pi$
$751$	−10.0635	−0.367221	−0.183611	+	0.982999i	$0.558779\pi$
$752$	−33.2274	−1.21168
$753$	−9.74107	−0.354984
$754$	−5.78768	−0.210775
$755$	−30.6984	−1.11723
$756$	−2.33590	−0.0849559
$757$	38.1520	1.38666	0.693329	−	0.720621i	$-0.256143\pi$
$757$	38.1520	1.38666	0.693329	+	0.720621i	$0.256143\pi$
$758$	56.6444	2.05742
$759$	−11.7712	−0.427266
$760$	13.0768	0.474347
$761$	46.3402	1.67983	0.839916	−	0.542717i	$-0.182604\pi$
$761$	46.3402	1.67983	0.839916	+	0.542717i	$0.182604\pi$
$762$	−27.5063	−0.996447
$763$	−2.95016	−0.106803
$764$	−2.33590	−0.0845100
$765$	−5.77842	−0.208919
$766$	−54.6554	−1.97478
$767$	7.20881	0.260295
$768$	9.36015	0.337755
$769$	18.3555	0.661916	0.330958	−	0.943645i	$-0.392628\pi$
$769$	18.3555	0.661916	0.330958	+	0.943645i	$0.392628\pi$
$770$	9.60192	0.346029
$771$	−5.80860	−0.209192
$772$	14.3318	0.515812
$773$	−4.91864	−0.176911	−0.0884555	−	0.996080i	$-0.528193\pi$
$773$	−4.91864	−0.176911	−0.0884555	+	0.996080i	$0.528193\pi$
$774$	−13.0045	−0.467437
$775$	40.2601	1.44619
$776$	11.3003	0.405659
$777$	2.50185	0.0897532
$778$	69.5976	2.49520
$779$	−14.8786	−0.533082
$780$	10.1645	0.363949
$781$	13.2449	0.473939
$782$	−30.7149	−1.09836
$783$	−1.92190	−0.0686832
$784$	−3.21537	−0.114835
$785$	−40.1040	−1.43137
$786$	21.7115	0.774424
$787$	11.6922	0.416782	0.208391	−	0.978046i	$-0.433177\pi$
$787$	11.6922	0.416782	0.208391	+	0.978046i	$0.433177\pi$
$788$	−40.8164	−1.45403
$789$	6.74619	0.240171
$790$	−9.23806	−0.328675
$791$	−11.9406	−0.424561
$792$	−1.07194	−0.0380897
$793$	0.420034	0.0149158
$794$	45.3716	1.61018
$795$	34.0917	1.20911
$796$	19.9400	0.706756
$797$	−22.0288	−0.780299	−0.390149	−	0.920752i	$-0.627577\pi$
$797$	−22.0288	−0.780299	−0.390149	+	0.920752i	$0.627577\pi$
$798$	−12.9387	−0.458025
$799$	−19.8461	−0.702105
$800$	−32.8071	−1.15990
$801$	−5.84054	−0.206365
$802$	47.3658	1.67254
$803$	−8.67081	−0.305986
$804$	−31.1593	−1.09890
$805$	−23.1101	−0.814523
$806$	29.9126	1.05363
$807$	15.6189	0.549811
$808$	−9.11746	−0.320751
$809$	−24.8115	−0.872327	−0.436163	−	0.899868i	$-0.643663\pi$
$809$	−24.8115	−0.872327	−0.436163	+	0.899868i	$0.643663\pi$
$810$	6.26527	0.220139
$811$	−30.2843	−1.06343	−0.531713	−	0.846924i	$-0.678452\pi$
$811$	−30.2843	−1.06343	−0.531713	+	0.846924i	$0.678452\pi$
$812$	4.48937	0.157546
$813$	−13.3592	−0.468526
$814$	7.98396	0.279838
$815$	48.3708	1.69436
$816$	6.17504	0.216170
$817$	−38.8065	−1.35767
$818$	−26.0061	−0.909284
$819$	−1.44622	−0.0505349
$820$	−16.8293	−0.587706
$821$	20.5307	0.716525	0.358262	−	0.933621i	$-0.383369\pi$
$821$	20.5307	0.716525	0.358262	+	0.933621i	$0.383369\pi$
$822$	−43.4306	−1.51482
$823$	−50.2290	−1.75087	−0.875437	−	0.483332i	$-0.839426\pi$
$823$	−50.2290	−1.75087	−0.875437	+	0.483332i	$0.839426\pi$
$824$	−12.7914	−0.445610
$825$	−6.21172	−0.216264
$826$	−10.3793	−0.361144
$827$	14.7194	0.511845	0.255923	−	0.966697i	$-0.417621\pi$
$827$	14.7194	0.511845	0.255923	+	0.966697i	$0.417621\pi$
$828$	17.9414	0.623506
$829$	−18.6528	−0.647840	−0.323920	−	0.946084i	$-0.605001\pi$
$829$	−18.6528	−0.647840	−0.323920	+	0.946084i	$0.605001\pi$
$830$	−78.1154	−2.71143
$831$	4.90068	0.170003
$832$	−15.0749	−0.522627
$833$	−1.92048	−0.0665406
$834$	−21.6822	−0.750793
$835$	−4.18464	−0.144815
$836$	−22.2445	−0.769344
$837$	9.93301	0.343335
$838$	−76.9797	−2.65922
$839$	31.7526	1.09622	0.548111	−	0.836405i	$-0.315347\pi$
$839$	31.7526	1.09622	0.548111	+	0.836405i	$0.315347\pi$
$840$	−2.10451	−0.0726126
$841$	−25.3063	−0.872631
$842$	68.3628	2.35594
$843$	15.7324	0.541853
$844$	33.7995	1.16343
$845$	−32.8219	−1.12911
$846$	21.5182	0.739811
$847$	8.65125	0.297261
$848$	−36.4317	−1.25107
$849$	24.8973	0.854472
$850$	−16.2085	−0.555947
$851$	−19.2159	−0.658714
$852$	−20.1876	−0.691615
$853$	−36.9931	−1.26662	−0.633310	−	0.773898i	$-0.718304\pi$
$853$	−36.9931	−1.26662	−0.633310	+	0.773898i	$0.718304\pi$
$854$	−0.604770	−0.0206948
$855$	18.6961	0.639393
$856$	5.74101	0.196224
$857$	−47.1426	−1.61036	−0.805181	−	0.593030i	$-0.797932\pi$
$857$	−47.1426	−1.61036	−0.805181	+	0.593030i	$0.797932\pi$
$858$	−4.61521	−0.157561
$859$	7.43742	0.253762	0.126881	−	0.991918i	$-0.459503\pi$
$859$	7.43742	0.253762	0.126881	+	0.991918i	$0.459503\pi$
$860$	−43.8943	−1.49678
$861$	2.39448	0.0816038
$862$	18.1609	0.618564
$863$	−16.4881	−0.561263	−0.280631	−	0.959816i	$-0.590544\pi$
$863$	−16.4881	−0.561263	−0.280631	+	0.959816i	$0.590544\pi$
$864$	−8.09419	−0.275370
$865$	17.5672	0.597302
$866$	36.1191	1.22738
$867$	−13.3118	−0.452091
$868$	−23.2025	−0.787546
$869$	2.25974	0.0766565
$870$	−12.0412	−0.408236
$871$	−19.2915	−0.653669
$872$	2.06346	0.0698777
$873$	16.1562	0.546805
$874$	99.3783	3.36152
$875$	2.84889	0.0963101
$876$	13.2159	0.446523
$877$	4.21728	0.142407	0.0712037	−	0.997462i	$-0.477316\pi$
$877$	4.21728	0.142407	0.0712037	+	0.997462i	$0.477316\pi$
$878$	−46.1491	−1.55746
$879$	24.7373	0.834368
$880$	14.8268	0.499813
$881$	−56.6166	−1.90746	−0.953732	−	0.300659i	$-0.902793\pi$
$881$	−56.6166	−1.90746	−0.953732	+	0.300659i	$0.902793\pi$
$882$	2.08228	0.0701141
$883$	−29.1943	−0.982465	−0.491233	−	0.871028i	$-0.663453\pi$
$883$	−29.1943	−0.982465	−0.491233	+	0.871028i	$0.663453\pi$
$884$	−6.48779	−0.218208
$885$	14.9979	0.504149
$886$	43.7854	1.47100
$887$	−9.48691	−0.318539	−0.159270	−	0.987235i	$-0.550914\pi$
$887$	−9.48691	−0.318539	−0.159270	+	0.987235i	$0.550914\pi$
$888$	−1.74990	−0.0587227
$889$	13.2097	0.443038
$890$	−36.5925	−1.22658
$891$	−1.53256	−0.0513428
$892$	−31.8357	−1.06594
$893$	64.2121	2.14878
$894$	−35.3632	−1.18272
$895$	−48.4988	−1.62114
$896$	5.51662	0.184297
$897$	11.1080	0.370884
$898$	44.9494	1.49998
$899$	−19.0903	−0.636696
$900$	9.46779	0.315593
$901$	−21.7599	−0.724928
$902$	7.64135	0.254429
$903$	6.24531	0.207831
$904$	8.35179	0.277776
$905$	−0.0672971	−0.00223703
$906$	−21.2449	−0.705816
$907$	−38.1694	−1.26739	−0.633697	−	0.773582i	$-0.718463\pi$
$907$	−38.1694	−1.26739	−0.633697	+	0.773582i	$0.718463\pi$
$908$	−29.9089	−0.992561
$909$	−13.0353	−0.432355
$910$	−9.06094	−0.300367
$911$	45.2166	1.49809	0.749046	−	0.662518i	$-0.230512\pi$
$911$	45.2166	1.49809	0.749046	+	0.662518i	$0.230512\pi$
$912$	−19.9793	−0.661582
$913$	19.1080	0.632382
$914$	6.99130	0.231252
$915$	0.873878	0.0288895
$916$	−10.6000	−0.350233
$917$	−10.4268	−0.344323
$918$	−3.99897	−0.131986
$919$	51.5730	1.70124	0.850618	−	0.525784i	$-0.176228\pi$
$919$	51.5730	1.70124	0.850618	+	0.525784i	$0.176228\pi$
$920$	16.1642	0.532916
$921$	−30.6935	−1.01138
$922$	−24.3248	−0.801094
$923$	−12.4986	−0.411398
$924$	3.57992	0.117771
$925$	−10.1404	−0.333414
$926$	−5.12628	−0.168460
$927$	−18.2880	−0.600657
$928$	15.5562	0.510658
$929$	12.7299	0.417656	0.208828	−	0.977952i	$-0.433035\pi$
$929$	12.7299	0.417656	0.208828	+	0.977952i	$0.433035\pi$
$930$	62.2330	2.04070
$931$	6.21371	0.203646
$932$	−7.82719	−0.256388
$933$	−6.53146	−0.213831
$934$	2.24118	0.0733337
$935$	8.85579	0.289615
$936$	1.01154	0.0330634
$937$	25.7289	0.840525	0.420263	−	0.907402i	$-0.361938\pi$
$937$	25.7289	0.840525	0.420263	+	0.907402i	$0.361938\pi$
$938$	27.7762	0.906925
$939$	21.1113	0.688942
$940$	72.6309	2.36896
$941$	25.8418	0.842418	0.421209	−	0.906964i	$-0.361606\pi$
$941$	25.8418	0.842418	0.421209	+	0.906964i	$0.361606\pi$
$942$	−27.7541	−0.904278
$943$	−18.3913	−0.598904
$944$	−16.0273	−0.521645
$945$	−3.00885	−0.0978778
$946$	19.9302	0.647987
$947$	−14.0974	−0.458104	−0.229052	−	0.973414i	$-0.573563\pi$
$947$	−14.0974	−0.458104	−0.229052	+	0.973414i	$0.573563\pi$
$948$	−3.44426	−0.111864
$949$	8.18229	0.265608
$950$	52.4426	1.70146
$951$	4.00166	0.129763
$952$	1.34326	0.0435354
$953$	14.7860	0.478964	0.239482	−	0.970901i	$-0.423022\pi$
$953$	14.7860	0.478964	0.239482	+	0.970901i	$0.423022\pi$
$954$	23.5933	0.763860
$955$	−3.00885	−0.0973640
$956$	−41.7713	−1.35098
$957$	2.94543	0.0952124
$958$	40.2137	1.29924
$959$	20.8572	0.673515
$960$	−31.3632	−1.01224
$961$	67.6648	2.18273
$962$	−7.53414	−0.242910
$963$	8.20798	0.264498
$964$	69.2042	2.22892
$965$	18.4606	0.594268
$966$	−15.9934	−0.514579
$967$	6.26794	0.201564	0.100782	−	0.994909i	$-0.467866\pi$
$967$	6.26794	0.201564	0.100782	+	0.994909i	$0.467866\pi$
$968$	−6.05105	−0.194488
$969$	−11.9333	−0.383352
$970$	101.223	3.25008
$971$	−27.7447	−0.890371	−0.445185	−	0.895438i	$-0.646862\pi$
$971$	−27.7447	−0.890371	−0.445185	+	0.895438i	$0.646862\pi$
$972$	2.33590	0.0749241
$973$	10.4127	0.333816
$974$	−42.2808	−1.35476
$975$	5.86175	0.187726
$976$	−0.933859	−0.0298921
$977$	−4.69883	−0.150329	−0.0751644	−	0.997171i	$-0.523948\pi$
$977$	−4.69883	−0.150329	−0.0751644	+	0.997171i	$0.523948\pi$
$978$	33.4752	1.07042
$979$	8.95099	0.286075
$980$	7.02837	0.224513
$981$	2.95016	0.0941913
$982$	30.8104	0.983199
$983$	22.2342	0.709162	0.354581	−	0.935025i	$-0.384623\pi$
$983$	22.2342	0.709162	0.354581	+	0.935025i	$0.384623\pi$
$984$	−1.67480	−0.0533908
$985$	−52.5752	−1.67518
$986$	7.68564	0.244761
$987$	−10.3340	−0.328933
$988$	20.9913	0.667821
$989$	−47.9684	−1.52531
$990$	−9.60192	−0.305169
$991$	−8.52217	−0.270716	−0.135358	−	0.990797i	$-0.543218\pi$
$991$	−8.52217	−0.270716	−0.135358	+	0.990797i	$0.543218\pi$
$992$	−80.3997	−2.55269
$993$	15.3247	0.486315
$994$	17.9957	0.570790
$995$	25.6845	0.814254
$996$	−29.1240	−0.922830
$997$	61.3507	1.94300	0.971498	−	0.237050i	$-0.0761804\pi$
$997$	61.3507	1.94300	0.971498	+	0.237050i	$0.0761804\pi$
$998$	76.5052	2.42173
$999$	−2.50185	−0.0791549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.22	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.22	✓	29	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)

\(f(q)\)	\(=\)	\(q+2.08228 q^{2} +1.00000 q^{3} +2.33590 q^{4} +3.00885 q^{5} +2.08228 q^{6} -1.00000 q^{7} +0.699442 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.08228 q^{2} +1.00000 q^{3} +2.33590 q^{4} +3.00885 q^{5} +2.08228 q^{6} -1.00000 q^{7} +0.699442 q^{8} +1.00000 q^{9} +6.26527 q^{10} -1.53256 q^{11} +2.33590 q^{12} +1.44622 q^{13} -2.08228 q^{14} +3.00885 q^{15} -3.21537 q^{16} -1.92048 q^{17} +2.08228 q^{18} +6.21371 q^{19} +7.02837 q^{20} -1.00000 q^{21} -3.19123 q^{22} +7.68070 q^{23} +0.699442 q^{24} +4.05316 q^{25} +3.01143 q^{26} +1.00000 q^{27} -2.33590 q^{28} -1.92190 q^{29} +6.26527 q^{30} +9.93301 q^{31} -8.09419 q^{32} -1.53256 q^{33} -3.99897 q^{34} -3.00885 q^{35} +2.33590 q^{36} -2.50185 q^{37} +12.9387 q^{38} +1.44622 q^{39} +2.10451 q^{40} -2.39448 q^{41} -2.08228 q^{42} -6.24531 q^{43} -3.57992 q^{44} +3.00885 q^{45} +15.9934 q^{46} +10.3340 q^{47} -3.21537 q^{48} +1.00000 q^{49} +8.43983 q^{50} -1.92048 q^{51} +3.37822 q^{52} +11.3305 q^{53} +2.08228 q^{54} -4.61125 q^{55} -0.699442 q^{56} +6.21371 q^{57} -4.00194 q^{58} +4.98460 q^{59} +7.02837 q^{60} +0.290436 q^{61} +20.6833 q^{62} -1.00000 q^{63} -10.4237 q^{64} +4.35145 q^{65} -3.19123 q^{66} -13.3393 q^{67} -4.48604 q^{68} +7.68070 q^{69} -6.26527 q^{70} -8.64230 q^{71} +0.699442 q^{72} +5.65772 q^{73} -5.20955 q^{74} +4.05316 q^{75} +14.5146 q^{76} +1.53256 q^{77} +3.01143 q^{78} -1.47449 q^{79} -9.67455 q^{80} +1.00000 q^{81} -4.98599 q^{82} -12.4680 q^{83} -2.33590 q^{84} -5.77842 q^{85} -13.0045 q^{86} -1.92190 q^{87} -1.07194 q^{88} -5.84054 q^{89} +6.26527 q^{90} -1.44622 q^{91} +17.9414 q^{92} +9.93301 q^{93} +21.5182 q^{94} +18.6961 q^{95} -8.09419 q^{96} +16.1562 q^{97} +2.08228 q^{98} -1.53256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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