LMFDB - Embedded newform 4029.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.95682 q^{2} -1.00000 q^{3} +1.82914 q^{4} +0.334746 q^{5} -1.95682 q^{6} +4.67011 q^{7} -0.334351 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.95682 q^{2} -1.00000 q^{3} +1.82914 q^{4} +0.334746 q^{5} -1.95682 q^{6} +4.67011 q^{7} -0.334351 q^{8} +1.00000 q^{9} +0.655037 q^{10} -4.16183 q^{11} -1.82914 q^{12} -3.53757 q^{13} +9.13855 q^{14} -0.334746 q^{15} -4.31253 q^{16} +1.00000 q^{17} +1.95682 q^{18} -8.65413 q^{19} +0.612296 q^{20} -4.67011 q^{21} -8.14395 q^{22} +5.48597 q^{23} +0.334351 q^{24} -4.88794 q^{25} -6.92238 q^{26} -1.00000 q^{27} +8.54226 q^{28} -8.63893 q^{29} -0.655037 q^{30} -5.51539 q^{31} -7.77014 q^{32} +4.16183 q^{33} +1.95682 q^{34} +1.56330 q^{35} +1.82914 q^{36} -0.377305 q^{37} -16.9346 q^{38} +3.53757 q^{39} -0.111923 q^{40} +6.48579 q^{41} -9.13855 q^{42} +1.18575 q^{43} -7.61256 q^{44} +0.334746 q^{45} +10.7350 q^{46} -11.1486 q^{47} +4.31253 q^{48} +14.8099 q^{49} -9.56482 q^{50} -1.00000 q^{51} -6.47070 q^{52} +0.865790 q^{53} -1.95682 q^{54} -1.39316 q^{55} -1.56146 q^{56} +8.65413 q^{57} -16.9048 q^{58} -12.6158 q^{59} -0.612296 q^{60} +6.52067 q^{61} -10.7926 q^{62} +4.67011 q^{63} -6.57968 q^{64} -1.18419 q^{65} +8.14395 q^{66} +6.06500 q^{67} +1.82914 q^{68} -5.48597 q^{69} +3.05910 q^{70} +12.8915 q^{71} -0.334351 q^{72} -5.45950 q^{73} -0.738316 q^{74} +4.88794 q^{75} -15.8296 q^{76} -19.4362 q^{77} +6.92238 q^{78} +1.00000 q^{79} -1.44360 q^{80} +1.00000 q^{81} +12.6915 q^{82} +4.19877 q^{83} -8.54226 q^{84} +0.334746 q^{85} +2.32030 q^{86} +8.63893 q^{87} +1.39151 q^{88} -6.12600 q^{89} +0.655037 q^{90} -16.5208 q^{91} +10.0346 q^{92} +5.51539 q^{93} -21.8158 q^{94} -2.89694 q^{95} +7.77014 q^{96} +8.99445 q^{97} +28.9803 q^{98} -4.16183 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * 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 $

$2$	1.95682	1.38368	0.691840	−	0.722051i	$-0.256801\pi$
$2$	1.95682	1.38368	0.691840	+	0.722051i	$0.256801\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.82914	0.914568
$5$	0.334746	0.149703	0.0748515	−	0.997195i	$-0.476152\pi$
$5$	0.334746	0.149703	0.0748515	+	0.997195i	$0.476152\pi$
$6$	−1.95682	−0.798867
$7$	4.67011	1.76514	0.882568	−	0.470185i	$-0.155813\pi$
$7$	4.67011	1.76514	0.882568	+	0.470185i	$0.155813\pi$
$8$	−0.334351	−0.118211
$9$	1.00000	0.333333
$10$	0.655037	0.207141
$11$	−4.16183	−1.25484	−0.627420	−	0.778681i	$-0.715889\pi$
$11$	−4.16183	−1.25484	−0.627420	+	0.778681i	$0.715889\pi$
$12$	−1.82914	−0.528026
$13$	−3.53757	−0.981146	−0.490573	−	0.871400i	$-0.663212\pi$
$13$	−3.53757	−0.981146	−0.490573	+	0.871400i	$0.663212\pi$
$14$	9.13855	2.44238
$15$	−0.334746	−0.0864311
$16$	−4.31253	−1.07813
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.95682	0.461226
$19$	−8.65413	−1.98539	−0.992697	−	0.120638i	$-0.961506\pi$
$19$	−8.65413	−1.98539	−0.992697	+	0.120638i	$0.961506\pi$
$20$	0.612296	0.136914
$21$	−4.67011	−1.01910
$22$	−8.14395	−1.73630
$23$	5.48597	1.14390	0.571951	−	0.820287i	$-0.306187\pi$
$23$	5.48597	1.14390	0.571951	+	0.820287i	$0.306187\pi$
$24$	0.334351	0.0682491
$25$	−4.88794	−0.977589
$26$	−6.92238	−1.35759
$27$	−1.00000	−0.192450
$28$	8.54226	1.61434
$29$	−8.63893	−1.60421	−0.802104	−	0.597184i	$-0.796286\pi$
$29$	−8.63893	−1.60421	−0.802104	+	0.597184i	$0.796286\pi$
$30$	−0.655037	−0.119593
$31$	−5.51539	−0.990594	−0.495297	−	0.868724i	$-0.664941\pi$
$31$	−5.51539	−0.990594	−0.495297	+	0.868724i	$0.664941\pi$
$32$	−7.77014	−1.37358
$33$	4.16183	0.724482
$34$	1.95682	0.335591
$35$	1.56330	0.264246
$36$	1.82914	0.304856
$37$	−0.377305	−0.0620285	−0.0310142	−	0.999519i	$-0.509874\pi$
$37$	−0.377305	−0.0620285	−0.0310142	+	0.999519i	$0.509874\pi$
$38$	−16.9346	−2.74715
$39$	3.53757	0.566465
$40$	−0.111923	−0.0176965
$41$	6.48579	1.01291	0.506455	−	0.862266i	$-0.330956\pi$
$41$	6.48579	1.01291	0.506455	+	0.862266i	$0.330956\pi$
$42$	−9.13855	−1.41011
$43$	1.18575	0.180825	0.0904127	−	0.995904i	$-0.471181\pi$
$43$	1.18575	0.180825	0.0904127	+	0.995904i	$0.471181\pi$
$44$	−7.61256	−1.14764
$45$	0.334746	0.0499010
$46$	10.7350	1.58279
$47$	−11.1486	−1.62619	−0.813097	−	0.582128i	$-0.802220\pi$
$47$	−11.1486	−1.62619	−0.813097	+	0.582128i	$0.802220\pi$
$48$	4.31253	0.622461
$49$	14.8099	2.11570
$50$	−9.56482	−1.35267
$51$	−1.00000	−0.140028
$52$	−6.47070	−0.897324
$53$	0.865790	0.118925	0.0594627	−	0.998231i	$-0.481061\pi$
$53$	0.865790	0.118925	0.0594627	+	0.998231i	$0.481061\pi$
$54$	−1.95682	−0.266289
$55$	−1.39316	−0.187853
$56$	−1.56146	−0.208658
$57$	8.65413	1.14627
$58$	−16.9048	−2.21971
$59$	−12.6158	−1.64243	−0.821216	−	0.570617i	$-0.806704\pi$
$59$	−12.6158	−1.64243	−0.821216	+	0.570617i	$0.806704\pi$
$60$	−0.612296	−0.0790471
$61$	6.52067	0.834886	0.417443	−	0.908703i	$-0.362926\pi$
$61$	6.52067	0.834886	0.417443	+	0.908703i	$0.362926\pi$
$62$	−10.7926	−1.37066
$63$	4.67011	0.588378
$64$	−6.57968	−0.822460
$65$	−1.18419	−0.146881
$66$	8.14395	1.00245
$67$	6.06500	0.740957	0.370479	−	0.928841i	$-0.379194\pi$
$67$	6.06500	0.740957	0.370479	+	0.928841i	$0.379194\pi$
$68$	1.82914	0.221815
$69$	−5.48597	−0.660433
$70$	3.05910	0.365632
$71$	12.8915	1.52994	0.764971	−	0.644065i	$-0.222754\pi$
$71$	12.8915	1.52994	0.764971	+	0.644065i	$0.222754\pi$
$72$	−0.334351	−0.0394036
$73$	−5.45950	−0.638987	−0.319493	−	0.947589i	$-0.603513\pi$
$73$	−5.45950	−0.638987	−0.319493	+	0.947589i	$0.603513\pi$
$74$	−0.738316	−0.0858275
$75$	4.88794	0.564411
$76$	−15.8296	−1.81578
$77$	−19.4362	−2.21496
$78$	6.92238	0.783805
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−1.44360	−0.161400
$81$	1.00000	0.111111
$82$	12.6915	1.40154
$83$	4.19877	0.460875	0.230437	−	0.973087i	$-0.425984\pi$
$83$	4.19877	0.460875	0.230437	+	0.973087i	$0.425984\pi$
$84$	−8.54226	−0.932037
$85$	0.334746	0.0363083
$86$	2.32030	0.250204
$87$	8.63893	0.926190
$88$	1.39151	0.148336
$89$	−6.12600	−0.649354	−0.324677	−	0.945825i	$-0.605256\pi$
$89$	−6.12600	−0.649354	−0.324677	+	0.945825i	$0.605256\pi$
$90$	0.655037	0.0690470
$91$	−16.5208	−1.73186
$92$	10.0346	1.04618
$93$	5.51539	0.571920
$94$	−21.8158	−2.25013
$95$	−2.89694	−0.297219
$96$	7.77014	0.793037
$97$	8.99445	0.913248	0.456624	−	0.889660i	$-0.349059\pi$
$97$	8.99445	0.913248	0.456624	+	0.889660i	$0.349059\pi$
$98$	28.9803	2.92745
$99$	−4.16183	−0.418280
$100$	−8.94071	−0.894071
$101$	12.5126	1.24505	0.622525	−	0.782600i	$-0.286107\pi$
$101$	12.5126	1.24505	0.622525	+	0.782600i	$0.286107\pi$
$102$	−1.95682	−0.193754
$103$	3.54176	0.348980	0.174490	−	0.984659i	$-0.444172\pi$
$103$	3.54176	0.348980	0.174490	+	0.984659i	$0.444172\pi$
$104$	1.18279	0.115982
$105$	−1.56330	−0.152563
$106$	1.69419	0.164555
$107$	1.65645	0.160135	0.0800677	−	0.996789i	$-0.474486\pi$
$107$	1.65645	0.160135	0.0800677	+	0.996789i	$0.474486\pi$
$108$	−1.82914	−0.176009
$109$	−10.5440	−1.00994	−0.504968	−	0.863138i	$-0.668496\pi$
$109$	−10.5440	−1.00994	−0.504968	+	0.863138i	$0.668496\pi$
$110$	−2.72616	−0.259929
$111$	0.377305	0.0358122
$112$	−20.1400	−1.90305
$113$	6.31694	0.594248	0.297124	−	0.954839i	$-0.403972\pi$
$113$	6.31694	0.594248	0.297124	+	0.954839i	$0.403972\pi$
$114$	16.9346	1.58607
$115$	1.83641	0.171246
$116$	−15.8018	−1.46716
$117$	−3.53757	−0.327049
$118$	−24.6867	−2.27260
$119$	4.67011	0.428108
$120$	0.111923	0.0102171
$121$	6.32085	0.574623
$122$	12.7598	1.15521
$123$	−6.48579	−0.584804
$124$	−10.0884	−0.905965
$125$	−3.30995	−0.296051
$126$	9.13855	0.814127
$127$	2.58610	0.229479	0.114740	−	0.993396i	$-0.463397\pi$
$127$	2.58610	0.229479	0.114740	+	0.993396i	$0.463397\pi$
$128$	2.66505	0.235559
$129$	−1.18575	−0.104400
$130$	−2.31724	−0.203235
$131$	−0.929880	−0.0812440	−0.0406220	−	0.999175i	$-0.512934\pi$
$131$	−0.929880	−0.0812440	−0.0406220	+	0.999175i	$0.512934\pi$
$132$	7.61256	0.662588
$133$	−40.4157	−3.50449
$134$	11.8681	1.02525
$135$	−0.334746	−0.0288104
$136$	−0.334351	−0.0286704
$137$	−18.2146	−1.55618	−0.778091	−	0.628151i	$-0.783812\pi$
$137$	−18.2146	−1.55618	−0.778091	+	0.628151i	$0.783812\pi$
$138$	−10.7350	−0.913827
$139$	−2.36502	−0.200598	−0.100299	−	0.994957i	$-0.531980\pi$
$139$	−2.36502	−0.200598	−0.100299	+	0.994957i	$0.531980\pi$
$140$	2.85949	0.241671
$141$	11.1486	0.938884
$142$	25.2263	2.11695
$143$	14.7228	1.23118
$144$	−4.31253	−0.359378
$145$	−2.89185	−0.240155
$146$	−10.6833	−0.884152
$147$	−14.8099	−1.22150
$148$	−0.690141	−0.0567293
$149$	0.376963	0.0308820	0.0154410	−	0.999881i	$-0.495085\pi$
$149$	0.376963	0.0308820	0.0154410	+	0.999881i	$0.495085\pi$
$150$	9.56482	0.780964
$151$	2.06487	0.168037	0.0840185	−	0.996464i	$-0.473225\pi$
$151$	2.06487	0.168037	0.0840185	+	0.996464i	$0.473225\pi$
$152$	2.89352	0.234695
$153$	1.00000	0.0808452
$154$	−38.0331	−3.06480
$155$	−1.84626	−0.148295
$156$	6.47070	0.518070
$157$	−11.9957	−0.957360	−0.478680	−	0.877989i	$-0.658885\pi$
$157$	−11.9957	−0.957360	−0.478680	+	0.877989i	$0.658885\pi$
$158$	1.95682	0.155676
$159$	−0.865790	−0.0686616
$160$	−2.60103	−0.205629
$161$	25.6201	2.01914
$162$	1.95682	0.153742
$163$	−8.82920	−0.691556	−0.345778	−	0.938316i	$-0.612385\pi$
$163$	−8.82920	−0.691556	−0.345778	+	0.938316i	$0.612385\pi$
$164$	11.8634	0.926375
$165$	1.39316	0.108457
$166$	8.21622	0.637703
$167$	−17.4309	−1.34884	−0.674422	−	0.738346i	$-0.735607\pi$
$167$	−17.4309	−1.34884	−0.674422	+	0.738346i	$0.735607\pi$
$168$	1.56146	0.120469
$169$	−0.485589	−0.0373530
$170$	0.655037	0.0502391
$171$	−8.65413	−0.661798
$172$	2.16890	0.165377
$173$	11.2763	0.857321	0.428661	−	0.903466i	$-0.358986\pi$
$173$	11.2763	0.857321	0.428661	+	0.903466i	$0.358986\pi$
$174$	16.9048	1.28155
$175$	−22.8272	−1.72558
$176$	17.9480	1.35288
$177$	12.6158	0.948259
$178$	−11.9875	−0.898498
$179$	−1.64583	−0.123015	−0.0615076	−	0.998107i	$-0.519591\pi$
$179$	−1.64583	−0.123015	−0.0615076	+	0.998107i	$0.519591\pi$
$180$	0.612296	0.0456379
$181$	1.24868	0.0928134	0.0464067	−	0.998923i	$-0.485223\pi$
$181$	1.24868	0.0928134	0.0464067	+	0.998923i	$0.485223\pi$
$182$	−32.3283	−2.39633
$183$	−6.52067	−0.482022
$184$	−1.83424	−0.135222
$185$	−0.126301	−0.00928585
$186$	10.7926	0.791353
$187$	−4.16183	−0.304343
$188$	−20.3924	−1.48727
$189$	−4.67011	−0.339700
$190$	−5.66878	−0.411256
$191$	−17.6001	−1.27350	−0.636751	−	0.771070i	$-0.719722\pi$
$191$	−17.6001	−1.27350	−0.636751	+	0.771070i	$0.719722\pi$
$192$	6.57968	0.474848
$193$	−24.5534	−1.76739	−0.883697	−	0.468060i	$-0.844953\pi$
$193$	−24.5534	−1.76739	−0.883697	+	0.468060i	$0.844953\pi$
$194$	17.6005	1.26364
$195$	1.18419	0.0848015
$196$	27.0894	1.93495
$197$	26.4798	1.88661	0.943303	−	0.331932i	$-0.107701\pi$
$197$	26.4798	1.88661	0.943303	+	0.331932i	$0.107701\pi$
$198$	−8.14395	−0.578765
$199$	4.60738	0.326608	0.163304	−	0.986576i	$-0.447785\pi$
$199$	4.60738	0.326608	0.163304	+	0.986576i	$0.447785\pi$
$200$	1.63429	0.115562
$201$	−6.06500	−0.427792
$202$	24.4849	1.72275
$203$	−40.3447	−2.83165
$204$	−1.82914	−0.128065
$205$	2.17109	0.151636
$206$	6.93058	0.482877
$207$	5.48597	0.381301
$208$	15.2559	1.05781
$209$	36.0170	2.49135
$210$	−3.05910	−0.211098
$211$	−20.0129	−1.37774	−0.688872	−	0.724883i	$-0.741894\pi$
$211$	−20.0129	−1.37774	−0.688872	+	0.724883i	$0.741894\pi$
$212$	1.58365	0.108765
$213$	−12.8915	−0.883312
$214$	3.24138	0.221576
$215$	0.396926	0.0270701
$216$	0.334351	0.0227497
$217$	−25.7575	−1.74853
$218$	−20.6328	−1.39743
$219$	5.45950	0.368919
$220$	−2.54827	−0.171805
$221$	−3.53757	−0.237963
$222$	0.738316	0.0495525
$223$	19.7945	1.32553	0.662767	−	0.748825i	$-0.269382\pi$
$223$	19.7945	1.32553	0.662767	+	0.748825i	$0.269382\pi$
$224$	−36.2874	−2.42455
$225$	−4.88794	−0.325863
$226$	12.3611	0.822249
$227$	6.95790	0.461812	0.230906	−	0.972976i	$-0.425831\pi$
$227$	6.95790	0.461812	0.230906	+	0.972976i	$0.425831\pi$
$228$	15.8296	1.04834
$229$	−7.34974	−0.485684	−0.242842	−	0.970066i	$-0.578080\pi$
$229$	−7.34974	−0.485684	−0.242842	+	0.970066i	$0.578080\pi$
$230$	3.59351	0.236949
$231$	19.4362	1.27881
$232$	2.88843	0.189635
$233$	−12.0361	−0.788513	−0.394256	−	0.919001i	$-0.628998\pi$
$233$	−12.0361	−0.788513	−0.394256	+	0.919001i	$0.628998\pi$
$234$	−6.92238	−0.452530
$235$	−3.73196	−0.243446
$236$	−23.0759	−1.50212
$237$	−1.00000	−0.0649570
$238$	9.13855	0.592364
$239$	14.0769	0.910561	0.455280	−	0.890348i	$-0.349539\pi$
$239$	14.0769	0.910561	0.455280	+	0.890348i	$0.349539\pi$
$240$	1.44360	0.0931843
$241$	9.57866	0.617016	0.308508	−	0.951222i	$-0.400170\pi$
$241$	9.57866	0.617016	0.308508	+	0.951222i	$0.400170\pi$
$242$	12.3688	0.795094
$243$	−1.00000	−0.0641500
$244$	11.9272	0.763560
$245$	4.95757	0.316727
$246$	−12.6915	−0.809181
$247$	30.6146	1.94796
$248$	1.84408	0.117099
$249$	−4.19877	−0.266086
$250$	−6.47697	−0.409640
$251$	7.84453	0.495143	0.247571	−	0.968870i	$-0.420368\pi$
$251$	7.84453	0.495143	0.247571	+	0.968870i	$0.420368\pi$
$252$	8.54226	0.538112
$253$	−22.8317	−1.43541
$254$	5.06053	0.317526
$255$	−0.334746	−0.0209626
$256$	18.3744	1.14840
$257$	0.817171	0.0509737	0.0254869	−	0.999675i	$-0.491886\pi$
$257$	0.817171	0.0509737	0.0254869	+	0.999675i	$0.491886\pi$
$258$	−2.32030	−0.144456
$259$	−1.76205	−0.109489
$260$	−2.16604	−0.134332
$261$	−8.63893	−0.534736
$262$	−1.81961	−0.112416
$263$	24.3713	1.50280	0.751400	−	0.659847i	$-0.229379\pi$
$263$	24.3713	1.50280	0.751400	+	0.659847i	$0.229379\pi$
$264$	−1.39151	−0.0856417
$265$	0.289820	0.0178035
$266$	−79.0862	−4.84909
$267$	6.12600	0.374905
$268$	11.0937	0.677656
$269$	−28.4563	−1.73501	−0.867504	−	0.497430i	$-0.834277\pi$
$269$	−28.4563	−1.73501	−0.867504	+	0.497430i	$0.834277\pi$
$270$	−0.655037	−0.0398643
$271$	−26.6682	−1.61998	−0.809989	−	0.586445i	$-0.800527\pi$
$271$	−26.6682	−1.61998	−0.809989	+	0.586445i	$0.800527\pi$
$272$	−4.31253	−0.261486
$273$	16.5208	0.999887
$274$	−35.6427	−2.15326
$275$	20.3428	1.22672
$276$	−10.0346	−0.604010
$277$	27.3387	1.64262	0.821311	−	0.570481i	$-0.193243\pi$
$277$	27.3387	1.64262	0.821311	+	0.570481i	$0.193243\pi$
$278$	−4.62791	−0.277563
$279$	−5.51539	−0.330198
$280$	−0.522691	−0.0312368
$281$	4.64485	0.277089	0.138544	−	0.990356i	$-0.455758\pi$
$281$	4.64485	0.277089	0.138544	+	0.990356i	$0.455758\pi$
$282$	21.8158	1.29911
$283$	1.01640	0.0604188	0.0302094	−	0.999544i	$-0.490383\pi$
$283$	1.01640	0.0604188	0.0302094	+	0.999544i	$0.490383\pi$
$284$	23.5803	1.39923
$285$	2.89694	0.171600
$286$	28.8098	1.70356
$287$	30.2894	1.78792
$288$	−7.77014	−0.457860
$289$	1.00000	0.0588235
$290$	−5.65882	−0.332297
$291$	−8.99445	−0.527264
$292$	−9.98617	−0.584397
$293$	−4.73065	−0.276368	−0.138184	−	0.990407i	$-0.544126\pi$
$293$	−4.73065	−0.276368	−0.138184	+	0.990407i	$0.544126\pi$
$294$	−28.9803	−1.69017
$295$	−4.22308	−0.245877
$296$	0.126152	0.00733244
$297$	4.16183	0.241494
$298$	0.737647	0.0427308
$299$	−19.4070	−1.12234
$300$	8.94071	0.516192
$301$	5.53759	0.319181
$302$	4.04058	0.232509
$303$	−12.5126	−0.718830
$304$	37.3212	2.14052
$305$	2.18277	0.124985
$306$	1.95682	0.111864
$307$	1.10152	0.0628670	0.0314335	−	0.999506i	$-0.489993\pi$
$307$	1.10152	0.0628670	0.0314335	+	0.999506i	$0.489993\pi$
$308$	−35.5515	−2.02573
$309$	−3.54176	−0.201484
$310$	−3.61279	−0.205193
$311$	−1.54608	−0.0876704	−0.0438352	−	0.999039i	$-0.513958\pi$
$311$	−1.54608	−0.0876704	−0.0438352	+	0.999039i	$0.513958\pi$
$312$	−1.18279	−0.0669623
$313$	−30.9174	−1.74755	−0.873777	−	0.486326i	$-0.838337\pi$
$313$	−30.9174	−1.74755	−0.873777	+	0.486326i	$0.838337\pi$
$314$	−23.4734	−1.32468
$315$	1.56330	0.0880821
$316$	1.82914	0.102897
$317$	−9.80967	−0.550966	−0.275483	−	0.961306i	$-0.588838\pi$
$317$	−9.80967	−0.550966	−0.275483	+	0.961306i	$0.588838\pi$
$318$	−1.69419	−0.0950056
$319$	35.9538	2.01303
$320$	−2.20252	−0.123125
$321$	−1.65645	−0.0924543
$322$	50.1338	2.79385
$323$	−8.65413	−0.481529
$324$	1.82914	0.101619
$325$	17.2915	0.959157
$326$	−17.2771	−0.956891
$327$	10.5440	0.583087
$328$	−2.16853	−0.119737
$329$	−52.0653	−2.87045
$330$	2.72616	0.150070
$331$	0.262190	0.0144112	0.00720562	−	0.999974i	$-0.497706\pi$
$331$	0.262190	0.0144112	0.00720562	+	0.999974i	$0.497706\pi$
$332$	7.68012	0.421501
$333$	−0.377305	−0.0206762
$334$	−34.1091	−1.86637
$335$	2.03024	0.110924
$336$	20.1400	1.09873
$337$	−13.4905	−0.734875	−0.367437	−	0.930048i	$-0.619765\pi$
$337$	−13.4905	−0.734875	−0.367437	+	0.930048i	$0.619765\pi$
$338$	−0.950209	−0.0516846
$339$	−6.31694	−0.343089
$340$	0.612296	0.0332064
$341$	22.9541	1.24304
$342$	−16.9346	−0.915716
$343$	36.4732	1.96937
$344$	−0.396457	−0.0213755
$345$	−1.83641	−0.0988688
$346$	22.0657	1.18626
$347$	24.9739	1.34067	0.670334	−	0.742060i	$-0.266151\pi$
$347$	24.9739	1.34067	0.670334	+	0.742060i	$0.266151\pi$
$348$	15.8018	0.847064
$349$	28.7674	1.53988	0.769941	−	0.638115i	$-0.220286\pi$
$349$	28.7674	1.53988	0.769941	+	0.638115i	$0.220286\pi$
$350$	−44.6687	−2.38764
$351$	3.53757	0.188822
$352$	32.3380	1.72362
$353$	−4.06358	−0.216282	−0.108141	−	0.994136i	$-0.534490\pi$
$353$	−4.06358	−0.216282	−0.108141	+	0.994136i	$0.534490\pi$
$354$	24.6867	1.31209
$355$	4.31538	0.229037
$356$	−11.2053	−0.593879
$357$	−4.67011	−0.247168
$358$	−3.22059	−0.170214
$359$	4.97736	0.262695	0.131348	−	0.991336i	$-0.458070\pi$
$359$	4.97736	0.262695	0.131348	+	0.991336i	$0.458070\pi$
$360$	−0.111923	−0.00589884
$361$	55.8939	2.94179
$362$	2.44343	0.128424
$363$	−6.32085	−0.331759
$364$	−30.2189	−1.58390
$365$	−1.82755	−0.0956582
$366$	−12.7598	−0.666963
$367$	−23.9919	−1.25237	−0.626183	−	0.779676i	$-0.715384\pi$
$367$	−23.9919	−1.25237	−0.626183	+	0.779676i	$0.715384\pi$
$368$	−23.6584	−1.23328
$369$	6.48579	0.337637
$370$	−0.247149	−0.0128486
$371$	4.04333	0.209919
$372$	10.0884	0.523059
$373$	−27.4844	−1.42309	−0.711544	−	0.702642i	$-0.752004\pi$
$373$	−27.4844	−1.42309	−0.711544	+	0.702642i	$0.752004\pi$
$374$	−8.14395	−0.421114
$375$	3.30995	0.170925
$376$	3.72755	0.192234
$377$	30.5608	1.57396
$378$	−9.13855	−0.470036
$379$	−26.6426	−1.36854	−0.684268	−	0.729231i	$-0.739878\pi$
$379$	−26.6426	−1.36854	−0.684268	+	0.729231i	$0.739878\pi$
$380$	−5.29889	−0.271827
$381$	−2.58610	−0.132490
$382$	−34.4403	−1.76212
$383$	−34.4777	−1.76173	−0.880865	−	0.473368i	$-0.843038\pi$
$383$	−34.4777	−1.76173	−0.880865	+	0.473368i	$0.843038\pi$
$384$	−2.66505	−0.136000
$385$	−6.50620	−0.331587
$386$	−48.0465	−2.44550
$387$	1.18575	0.0602752
$388$	16.4521	0.835227
$389$	35.7699	1.81361	0.906803	−	0.421556i	$-0.138516\pi$
$389$	35.7699	1.81361	0.906803	+	0.421556i	$0.138516\pi$
$390$	2.31724	0.117338
$391$	5.48597	0.277437
$392$	−4.95171	−0.250099
$393$	0.929880	0.0469063
$394$	51.8161	2.61046
$395$	0.334746	0.0168429
$396$	−7.61256	−0.382545
$397$	−33.7144	−1.69207	−0.846037	−	0.533123i	$-0.821018\pi$
$397$	−33.7144	−1.69207	−0.846037	+	0.533123i	$0.821018\pi$
$398$	9.01579	0.451921
$399$	40.4157	2.02332
$400$	21.0794	1.05397
$401$	36.2947	1.81247	0.906236	−	0.422771i	$-0.138943\pi$
$401$	36.2947	1.81247	0.906236	+	0.422771i	$0.138943\pi$
$402$	−11.8681	−0.591927
$403$	19.5111	0.971917
$404$	22.8873	1.13868
$405$	0.334746	0.0166337
$406$	−78.9473	−3.91809
$407$	1.57028	0.0778358
$408$	0.334351	0.0165528
$409$	−1.61091	−0.0796542	−0.0398271	−	0.999207i	$-0.512681\pi$
$409$	−1.61091	−0.0796542	−0.0398271	+	0.999207i	$0.512681\pi$
$410$	4.24844	0.209815
$411$	18.2146	0.898462
$412$	6.47836	0.319166
$413$	−58.9170	−2.89912
$414$	10.7350	0.527598
$415$	1.40552	0.0689943
$416$	27.4874	1.34768
$417$	2.36502	0.115815
$418$	70.4788	3.44723
$419$	20.6509	1.00886	0.504430	−	0.863452i	$-0.331702\pi$
$419$	20.6509	1.00886	0.504430	+	0.863452i	$0.331702\pi$
$420$	−2.85949	−0.139529
$421$	−10.0657	−0.490571	−0.245285	−	0.969451i	$-0.578882\pi$
$421$	−10.0657	−0.490571	−0.245285	+	0.969451i	$0.578882\pi$
$422$	−39.1616	−1.90636
$423$	−11.1486	−0.542065
$424$	−0.289478	−0.0140583
$425$	−4.88794	−0.237100
$426$	−25.2263	−1.22222
$427$	30.4522	1.47369
$428$	3.02988	0.146455
$429$	−14.7228	−0.710823
$430$	0.776712	0.0374564
$431$	17.9275	0.863536	0.431768	−	0.901985i	$-0.357890\pi$
$431$	17.9275	0.863536	0.431768	+	0.901985i	$0.357890\pi$
$432$	4.31253	0.207487
$433$	−21.2968	−1.02346	−0.511730	−	0.859146i	$-0.670995\pi$
$433$	−21.2968	−1.02346	−0.511730	+	0.859146i	$0.670995\pi$
$434$	−50.4027	−2.41941
$435$	2.89185	0.138654
$436$	−19.2865	−0.923655
$437$	−47.4762	−2.27110
$438$	10.6833	0.510466
$439$	−20.6502	−0.985579	−0.492789	−	0.870149i	$-0.664023\pi$
$439$	−20.6502	−0.985579	−0.492789	+	0.870149i	$0.664023\pi$
$440$	0.465804	0.0222063
$441$	14.8099	0.705234
$442$	−6.92238	−0.329264
$443$	−32.4319	−1.54089	−0.770444	−	0.637508i	$-0.779965\pi$
$443$	−32.4319	−1.54089	−0.770444	+	0.637508i	$0.779965\pi$
$444$	0.690141	0.0327526
$445$	−2.05065	−0.0972103
$446$	38.7341	1.83411
$447$	−0.376963	−0.0178297
$448$	−30.7278	−1.45175
$449$	7.10112	0.335123	0.167561	−	0.985862i	$-0.446411\pi$
$449$	7.10112	0.335123	0.167561	+	0.985862i	$0.446411\pi$
$450$	−9.56482	−0.450890
$451$	−26.9928	−1.27104
$452$	11.5545	0.543480
$453$	−2.06487	−0.0970162
$454$	13.6153	0.638999
$455$	−5.53029	−0.259264
$456$	−2.89352	−0.135501
$457$	19.0986	0.893393	0.446697	−	0.894686i	$-0.352600\pi$
$457$	19.0986	0.893393	0.446697	+	0.894686i	$0.352600\pi$
$458$	−14.3821	−0.672031
$459$	−1.00000	−0.0466760
$460$	3.35904	0.156616
$461$	−13.2635	−0.617742	−0.308871	−	0.951104i	$-0.599951\pi$
$461$	−13.2635	−0.617742	−0.308871	+	0.951104i	$0.599951\pi$
$462$	38.0331	1.76946
$463$	−24.9610	−1.16003	−0.580017	−	0.814604i	$-0.696954\pi$
$463$	−24.9610	−1.16003	−0.580017	+	0.814604i	$0.696954\pi$
$464$	37.2557	1.72955
$465$	1.84626	0.0856181
$466$	−23.5525	−1.09105
$467$	2.19319	0.101489	0.0507444	−	0.998712i	$-0.483841\pi$
$467$	2.19319	0.101489	0.0507444	+	0.998712i	$0.483841\pi$
$468$	−6.47070	−0.299108
$469$	28.3242	1.30789
$470$	−7.30277	−0.336852
$471$	11.9957	0.552732
$472$	4.21809	0.194153
$473$	−4.93490	−0.226907
$474$	−1.95682	−0.0898796
$475$	42.3009	1.94090
$476$	8.54226	0.391534
$477$	0.865790	0.0396418
$478$	27.5460	1.25992
$479$	39.5299	1.80617	0.903084	−	0.429464i	$-0.141297\pi$
$479$	39.5299	1.80617	0.903084	+	0.429464i	$0.141297\pi$
$480$	2.60103	0.118720
$481$	1.33474	0.0608590
$482$	18.7437	0.853752
$483$	−25.6201	−1.16575
$484$	11.5617	0.525531
$485$	3.01086	0.136716
$486$	−1.95682	−0.0887631
$487$	−22.4254	−1.01619	−0.508095	−	0.861301i	$-0.669650\pi$
$487$	−22.4254	−1.01619	−0.508095	+	0.861301i	$0.669650\pi$
$488$	−2.18019	−0.0986926
$489$	8.82920	0.399270
$490$	9.70105	0.438249
$491$	20.7965	0.938535	0.469267	−	0.883056i	$-0.344518\pi$
$491$	20.7965	0.938535	0.469267	+	0.883056i	$0.344518\pi$
$492$	−11.8634	−0.534843
$493$	−8.63893	−0.389078
$494$	59.9072	2.69535
$495$	−1.39316	−0.0626178
$496$	23.7853	1.06799
$497$	60.2048	2.70055
$498$	−8.21622	−0.368178
$499$	−9.44736	−0.422922	−0.211461	−	0.977386i	$-0.567822\pi$
$499$	−9.44736	−0.422922	−0.211461	+	0.977386i	$0.567822\pi$
$500$	−6.05435	−0.270759
$501$	17.4309	0.778755
$502$	15.3503	0.685118
$503$	25.9968	1.15914	0.579570	−	0.814922i	$-0.303220\pi$
$503$	25.9968	1.15914	0.579570	+	0.814922i	$0.303220\pi$
$504$	−1.56146	−0.0695527
$505$	4.18855	0.186388
$506$	−44.6774	−1.98615
$507$	0.485589	0.0215658
$508$	4.73033	0.209874
$509$	14.8621	0.658750	0.329375	−	0.944199i	$-0.393162\pi$
$509$	14.8621	0.658750	0.329375	+	0.944199i	$0.393162\pi$
$510$	−0.655037	−0.0290055
$511$	−25.4965	−1.12790
$512$	30.6252	1.35346
$513$	8.65413	0.382089
$514$	1.59906	0.0705313
$515$	1.18559	0.0522434
$516$	−2.16890	−0.0954805
$517$	46.3987	2.04061
$518$	−3.44802	−0.151497
$519$	−11.2763	−0.494975
$520$	0.395935	0.0173629
$521$	35.3407	1.54830	0.774152	−	0.633000i	$-0.218177\pi$
$521$	35.3407	1.54830	0.774152	+	0.633000i	$0.218177\pi$
$522$	−16.9048	−0.739903
$523$	21.2400	0.928762	0.464381	−	0.885636i	$-0.346277\pi$
$523$	21.2400	0.928762	0.464381	+	0.885636i	$0.346277\pi$
$524$	−1.70088	−0.0743032
$525$	22.8272	0.996262
$526$	47.6902	2.07939
$527$	−5.51539	−0.240254
$528$	−17.9480	−0.781088
$529$	7.09582	0.308514
$530$	0.567125	0.0246343
$531$	−12.6158	−0.547478
$532$	−73.9258	−3.20509
$533$	−22.9440	−0.993813
$534$	11.9875	0.518748
$535$	0.554492	0.0239728
$536$	−2.02784	−0.0875892
$537$	1.64583	0.0710229
$538$	−55.6837	−2.40070
$539$	−61.6364	−2.65487
$540$	−0.612296	−0.0263490
$541$	38.1983	1.64227	0.821136	−	0.570733i	$-0.193341\pi$
$541$	38.1983	1.64227	0.821136	+	0.570733i	$0.193341\pi$
$542$	−52.1848	−2.24153
$543$	−1.24868	−0.0535858
$544$	−7.77014	−0.333142
$545$	−3.52958	−0.151191
$546$	32.3283	1.38352
$547$	−40.3443	−1.72500	−0.862499	−	0.506058i	$-0.831102\pi$
$547$	−40.3443	−1.72500	−0.862499	+	0.506058i	$0.831102\pi$
$548$	−33.3171	−1.42323
$549$	6.52067	0.278295
$550$	39.8072	1.69738
$551$	74.7624	3.18499
$552$	1.83424	0.0780703
$553$	4.67011	0.198593
$554$	53.4968	2.27286
$555$	0.126301	0.00536119
$556$	−4.32594	−0.183461
$557$	28.1156	1.19130	0.595649	−	0.803245i	$-0.296895\pi$
$557$	28.1156	1.19130	0.595649	+	0.803245i	$0.296895\pi$
$558$	−10.7926	−0.456888
$559$	−4.19468	−0.177416
$560$	−6.74179	−0.284893
$561$	4.16183	0.175713
$562$	9.08913	0.383402
$563$	22.0890	0.930939	0.465470	−	0.885064i	$-0.345885\pi$
$563$	22.0890	0.930939	0.465470	+	0.885064i	$0.345885\pi$
$564$	20.3924	0.858673
$565$	2.11457	0.0889608
$566$	1.98891	0.0836002
$567$	4.67011	0.196126
$568$	−4.31029	−0.180856
$569$	−8.66370	−0.363201	−0.181601	−	0.983372i	$-0.558128\pi$
$569$	−8.66370	−0.363201	−0.181601	+	0.983372i	$0.558128\pi$
$570$	5.66878	0.237439
$571$	−24.1896	−1.01230	−0.506152	−	0.862445i	$-0.668932\pi$
$571$	−24.1896	−1.01230	−0.506152	+	0.862445i	$0.668932\pi$
$572$	26.9300	1.12600
$573$	17.6001	0.735256
$574$	59.2708	2.47391
$575$	−26.8151	−1.11827
$576$	−6.57968	−0.274153
$577$	38.4970	1.60265	0.801326	−	0.598228i	$-0.204128\pi$
$577$	38.4970	1.60265	0.801326	+	0.598228i	$0.204128\pi$
$578$	1.95682	0.0813929
$579$	24.5534	1.02040
$580$	−5.28958	−0.219638
$581$	19.6087	0.813506
$582$	−17.6005	−0.729564
$583$	−3.60327	−0.149232
$584$	1.82539	0.0755352
$585$	−1.18419	−0.0489602
$586$	−9.25702	−0.382404
$587$	−9.44240	−0.389730	−0.194865	−	0.980830i	$-0.562427\pi$
$587$	−9.44240	−0.389730	−0.194865	+	0.980830i	$0.562427\pi$
$588$	−27.0894	−1.11715
$589$	47.7309	1.96672
$590$	−8.26380	−0.340215
$591$	−26.4798	−1.08923
$592$	1.62714	0.0668750
$593$	−28.5457	−1.17223	−0.586116	−	0.810227i	$-0.699344\pi$
$593$	−28.5457	−1.17223	−0.586116	+	0.810227i	$0.699344\pi$
$594$	8.14395	0.334150
$595$	1.56330	0.0640891
$596$	0.689516	0.0282437
$597$	−4.60738	−0.188567
$598$	−37.9759	−1.55295
$599$	−14.6355	−0.597988	−0.298994	−	0.954255i	$-0.596651\pi$
$599$	−14.6355	−0.597988	−0.298994	+	0.954255i	$0.596651\pi$
$600$	−1.63429	−0.0667196
$601$	9.62482	0.392605	0.196302	−	0.980543i	$-0.437107\pi$
$601$	9.62482	0.392605	0.196302	+	0.980543i	$0.437107\pi$
$602$	10.8361	0.441645
$603$	6.06500	0.246986
$604$	3.77693	0.153681
$605$	2.11588	0.0860228
$606$	−24.4849	−0.994631
$607$	−21.4502	−0.870639	−0.435319	−	0.900276i	$-0.643365\pi$
$607$	−21.4502	−0.870639	−0.435319	+	0.900276i	$0.643365\pi$
$608$	67.2438	2.72710
$609$	40.3447	1.63485
$610$	4.27128	0.172939
$611$	39.4391	1.59553
$612$	1.82914	0.0739384
$613$	1.49280	0.0602935	0.0301468	−	0.999545i	$-0.490403\pi$
$613$	1.49280	0.0602935	0.0301468	+	0.999545i	$0.490403\pi$
$614$	2.15547	0.0869877
$615$	−2.17109	−0.0875470
$616$	6.49852	0.261833
$617$	36.2278	1.45847	0.729237	−	0.684261i	$-0.239875\pi$
$617$	36.2278	1.45847	0.729237	+	0.684261i	$0.239875\pi$
$618$	−6.93058	−0.278789
$619$	−12.1391	−0.487911	−0.243956	−	0.969786i	$-0.578445\pi$
$619$	−12.1391	−0.487911	−0.243956	+	0.969786i	$0.578445\pi$
$620$	−3.37705	−0.135626
$621$	−5.48597	−0.220144
$622$	−3.02540	−0.121308
$623$	−28.6091	−1.14620
$624$	−15.2559	−0.610725
$625$	23.3317	0.933269
$626$	−60.4997	−2.41805
$627$	−36.0170	−1.43838
$628$	−21.9417	−0.875571
$629$	−0.377305	−0.0150441
$630$	3.05910	0.121877
$631$	−12.2457	−0.487492	−0.243746	−	0.969839i	$-0.578376\pi$
$631$	−12.2457	−0.487492	−0.243746	+	0.969839i	$0.578376\pi$
$632$	−0.334351	−0.0132998
$633$	20.0129	0.795441
$634$	−19.1957	−0.762360
$635$	0.865687	0.0343537
$636$	−1.58365	−0.0627957
$637$	−52.3912	−2.07581
$638$	70.3550	2.78538
$639$	12.8915	0.509980
$640$	0.892114	0.0352639
$641$	19.5689	0.772923	0.386462	−	0.922305i	$-0.373697\pi$
$641$	19.5689	0.772923	0.386462	+	0.922305i	$0.373697\pi$
$642$	−3.24138	−0.127927
$643$	4.80887	0.189643	0.0948217	−	0.995494i	$-0.469772\pi$
$643$	4.80887	0.189643	0.0948217	+	0.995494i	$0.469772\pi$
$644$	46.8626	1.84664
$645$	−0.396926	−0.0156289
$646$	−16.9346	−0.666281
$647$	31.5977	1.24223	0.621117	−	0.783717i	$-0.286679\pi$
$647$	31.5977	1.24223	0.621117	+	0.783717i	$0.286679\pi$
$648$	−0.334351	−0.0131345
$649$	52.5047	2.06099
$650$	33.8362	1.32717
$651$	25.7575	1.00952
$652$	−16.1498	−0.632475
$653$	−33.3110	−1.30356	−0.651781	−	0.758408i	$-0.725978\pi$
$653$	−33.3110	−1.30356	−0.651781	+	0.758408i	$0.725978\pi$
$654$	20.6328	0.806805
$655$	−0.311274	−0.0121625
$656$	−27.9702	−1.09205
$657$	−5.45950	−0.212996
$658$	−101.882	−3.97179
$659$	7.61639	0.296692	0.148346	−	0.988936i	$-0.452605\pi$
$659$	7.61639	0.296692	0.148346	+	0.988936i	$0.452605\pi$
$660$	2.54827	0.0991914
$661$	−8.49829	−0.330545	−0.165273	−	0.986248i	$-0.552850\pi$
$661$	−8.49829	−0.330545	−0.165273	+	0.986248i	$0.552850\pi$
$662$	0.513057	0.0199405
$663$	3.53757	0.137388
$664$	−1.40386	−0.0544804
$665$	−13.5290	−0.524633
$666$	−0.738316	−0.0286092
$667$	−47.3929	−1.83506
$668$	−31.8835	−1.23361
$669$	−19.7945	−0.765298
$670$	3.97280	0.153483
$671$	−27.1379	−1.04765
$672$	36.2874	1.39982
$673$	−36.8539	−1.42061	−0.710307	−	0.703892i	$-0.751444\pi$
$673$	−36.8539	−1.42061	−0.710307	+	0.703892i	$0.751444\pi$
$674$	−26.3985	−1.01683
$675$	4.88794	0.188137
$676$	−0.888208	−0.0341619
$677$	0.761305	0.0292593	0.0146297	−	0.999893i	$-0.495343\pi$
$677$	0.761305	0.0292593	0.0146297	+	0.999893i	$0.495343\pi$
$678$	−12.3611	−0.474726
$679$	42.0051	1.61201
$680$	−0.111923	−0.00429204
$681$	−6.95790	−0.266627
$682$	44.9171	1.71996
$683$	23.4517	0.897354	0.448677	−	0.893694i	$-0.351895\pi$
$683$	23.4517	0.897354	0.448677	+	0.893694i	$0.351895\pi$
$684$	−15.8296	−0.605259
$685$	−6.09728	−0.232965
$686$	71.3714	2.72497
$687$	7.34974	0.280410
$688$	−5.11360	−0.194954
$689$	−3.06279	−0.116683
$690$	−3.59351	−0.136803
$691$	19.4082	0.738322	0.369161	−	0.929365i	$-0.379645\pi$
$691$	19.4082	0.738322	0.369161	+	0.929365i	$0.379645\pi$
$692$	20.6259	0.784078
$693$	−19.4362	−0.738321
$694$	48.8693	1.85505
$695$	−0.791681	−0.0300302
$696$	−2.88843	−0.109486
$697$	6.48579	0.245667
$698$	56.2925	2.13070
$699$	12.0361	0.455248
$700$	−41.7541	−1.57816
$701$	−13.7247	−0.518376	−0.259188	−	0.965827i	$-0.583455\pi$
$701$	−13.7247	−0.518376	−0.259188	+	0.965827i	$0.583455\pi$
$702$	6.92238	0.261268
$703$	3.26524	0.123151
$704$	27.3835	1.03206
$705$	3.73196	0.140554
$706$	−7.95168	−0.299265
$707$	58.4352	2.19768
$708$	23.0759	0.867247
$709$	−9.21468	−0.346065	−0.173032	−	0.984916i	$-0.555356\pi$
$709$	−9.21468	−0.346065	−0.173032	+	0.984916i	$0.555356\pi$
$710$	8.44442	0.316913
$711$	1.00000	0.0375029
$712$	2.04823	0.0767608
$713$	−30.2573	−1.13314
$714$	−9.13855	−0.342002
$715$	4.92839	0.184312
$716$	−3.01045	−0.112506
$717$	−14.0769	−0.525712
$718$	9.73979	0.363486
$719$	−40.1283	−1.49653	−0.748267	−	0.663398i	$-0.769114\pi$
$719$	−40.1283	−1.49653	−0.748267	+	0.663398i	$0.769114\pi$
$720$	−1.44360	−0.0538000
$721$	16.5404	0.615997
$722$	109.374	4.07049
$723$	−9.57866	−0.356234
$724$	2.28400	0.0848841
$725$	42.2266	1.56826
$726$	−12.3688	−0.459047
$727$	−47.8402	−1.77430	−0.887148	−	0.461485i	$-0.847317\pi$
$727$	−47.8402	−1.77430	−0.887148	+	0.461485i	$0.847317\pi$
$728$	5.52376	0.204724
$729$	1.00000	0.0370370
$730$	−3.57618	−0.132360
$731$	1.18575	0.0438566
$732$	−11.9272	−0.440841
$733$	−1.75867	−0.0649578	−0.0324789	−	0.999472i	$-0.510340\pi$
$733$	−1.75867	−0.0649578	−0.0324789	+	0.999472i	$0.510340\pi$
$734$	−46.9477	−1.73287
$735$	−4.95757	−0.182863
$736$	−42.6267	−1.57124
$737$	−25.2415	−0.929783
$738$	12.6915	0.467181
$739$	−30.1098	−1.10761	−0.553803	−	0.832648i	$-0.686824\pi$
$739$	−30.1098	−1.10761	−0.553803	+	0.832648i	$0.686824\pi$
$740$	−0.231022	−0.00849254
$741$	−30.6146	−1.12466
$742$	7.91207	0.290461
$743$	0.823683	0.0302180	0.0151090	−	0.999886i	$-0.495190\pi$
$743$	0.823683	0.0302180	0.0151090	+	0.999886i	$0.495190\pi$
$744$	−1.84408	−0.0676071
$745$	0.126187	0.00462313
$746$	−53.7819	−1.96910
$747$	4.19877	0.153625
$748$	−7.61256	−0.278343
$749$	7.73582	0.282661
$750$	6.47697	0.236506
$751$	2.49383	0.0910011	0.0455005	−	0.998964i	$-0.485512\pi$
$751$	2.49383	0.0910011	0.0455005	+	0.998964i	$0.485512\pi$
$752$	48.0789	1.75326
$753$	−7.84453	−0.285871
$754$	59.8020	2.17786
$755$	0.691209	0.0251557
$756$	−8.54226	−0.310679
$757$	17.8051	0.647139	0.323569	−	0.946204i	$-0.395117\pi$
$757$	17.8051	0.647139	0.323569	+	0.946204i	$0.395117\pi$
$758$	−52.1346	−1.89361
$759$	22.8317	0.828737
$760$	0.968593	0.0351346
$761$	12.8780	0.466826	0.233413	−	0.972378i	$-0.425011\pi$
$761$	12.8780	0.466826	0.233413	+	0.972378i	$0.425011\pi$
$762$	−5.06053	−0.183323
$763$	−49.2418	−1.78267
$764$	−32.1930	−1.16470
$765$	0.334746	0.0121028
$766$	−67.4666	−2.43767
$767$	44.6292	1.61147
$768$	−18.3744	−0.663028
$769$	39.4468	1.42249	0.711243	−	0.702946i	$-0.248132\pi$
$769$	39.4468	1.42249	0.711243	+	0.702946i	$0.248132\pi$
$770$	−12.7314	−0.458809
$771$	−0.817171	−0.0294297
$772$	−44.9115	−1.61640
$773$	6.37915	0.229442	0.114721	−	0.993398i	$-0.463403\pi$
$773$	6.37915	0.229442	0.114721	+	0.993398i	$0.463403\pi$
$774$	2.32030	0.0834015
$775$	26.9589	0.968394
$776$	−3.00730	−0.107956
$777$	1.76205	0.0632133
$778$	69.9951	2.50945
$779$	−56.1289	−2.01103
$780$	2.16604	0.0775567
$781$	−53.6523	−1.91983
$782$	10.7350	0.383884
$783$	8.63893	0.308730
$784$	−63.8683	−2.28101
$785$	−4.01551	−0.143320
$786$	1.81961	0.0649032
$787$	−26.5727	−0.947213	−0.473607	−	0.880736i	$-0.657048\pi$
$787$	−26.5727	−0.947213	−0.473607	+	0.880736i	$0.657048\pi$
$788$	48.4351	1.72543
$789$	−24.3713	−0.867642
$790$	0.655037	0.0233052
$791$	29.5008	1.04893
$792$	1.39151	0.0494452
$793$	−23.0673	−0.819145
$794$	−65.9728	−2.34129
$795$	−0.289820	−0.0102789
$796$	8.42751	0.298705
$797$	6.84860	0.242590	0.121295	−	0.992617i	$-0.461295\pi$
$797$	6.84860	0.242590	0.121295	+	0.992617i	$0.461295\pi$
$798$	79.0862	2.79962
$799$	−11.1486	−0.394410
$800$	37.9800	1.34280
$801$	−6.12600	−0.216451
$802$	71.0222	2.50788
$803$	22.7215	0.801826
$804$	−11.0937	−0.391245
$805$	8.57622	0.302272
$806$	38.1797	1.34482
$807$	28.4563	1.00171
$808$	−4.18360	−0.147179
$809$	7.42957	0.261210	0.130605	−	0.991435i	$-0.458308\pi$
$809$	7.42957	0.261210	0.130605	+	0.991435i	$0.458308\pi$
$810$	0.655037	0.0230157
$811$	−40.1688	−1.41052	−0.705258	−	0.708951i	$-0.749169\pi$
$811$	−40.1688	−1.41052	−0.705258	+	0.708951i	$0.749169\pi$
$812$	−73.7960	−2.58973
$813$	26.6682	0.935295
$814$	3.07275	0.107700
$815$	−2.95554	−0.103528
$816$	4.31253	0.150969
$817$	−10.2616	−0.359010
$818$	−3.15225	−0.110216
$819$	−16.5208	−0.577285
$820$	3.97123	0.138681
$821$	−40.7390	−1.42180	−0.710900	−	0.703293i	$-0.751712\pi$
$821$	−40.7390	−1.42180	−0.710900	+	0.703293i	$0.751712\pi$
$822$	35.6427	1.24318
$823$	−7.41457	−0.258456	−0.129228	−	0.991615i	$-0.541250\pi$
$823$	−7.41457	−0.258456	−0.129228	+	0.991615i	$0.541250\pi$
$824$	−1.18419	−0.0412533
$825$	−20.3428	−0.708246
$826$	−115.290	−4.01145
$827$	−53.1006	−1.84649	−0.923245	−	0.384212i	$-0.874473\pi$
$827$	−53.1006	−1.84649	−0.923245	+	0.384212i	$0.874473\pi$
$828$	10.0346	0.348726
$829$	−33.8860	−1.17691	−0.588454	−	0.808530i	$-0.700263\pi$
$829$	−33.8860	−1.17691	−0.588454	+	0.808530i	$0.700263\pi$
$830$	2.75035	0.0954660
$831$	−27.3387	−0.948368
$832$	23.2761	0.806953
$833$	14.8099	0.513133
$834$	4.62791	0.160251
$835$	−5.83493	−0.201926
$836$	65.8800	2.27851
$837$	5.51539	0.190640
$838$	40.4100	1.39594
$839$	17.2912	0.596958	0.298479	−	0.954416i	$-0.403521\pi$
$839$	17.2912	0.596958	0.298479	+	0.954416i	$0.403521\pi$
$840$	0.522691	0.0180346
$841$	45.6311	1.57349
$842$	−19.6967	−0.678793
$843$	−4.64485	−0.159977
$844$	−36.6063	−1.26004
$845$	−0.162549	−0.00559186
$846$	−21.8158	−0.750044
$847$	29.5191	1.01429
$848$	−3.73375	−0.128217
$849$	−1.01640	−0.0348828
$850$	−9.56482	−0.328071
$851$	−2.06988	−0.0709546
$852$	−23.5803	−0.807848
$853$	−5.80711	−0.198832	−0.0994158	−	0.995046i	$-0.531697\pi$
$853$	−5.80711	−0.198832	−0.0994158	+	0.995046i	$0.531697\pi$
$854$	59.5895	2.03911
$855$	−2.89694	−0.0990731
$856$	−0.553837	−0.0189298
$857$	−38.8125	−1.32581	−0.662904	−	0.748704i	$-0.730676\pi$
$857$	−38.8125	−1.32581	−0.662904	+	0.748704i	$0.730676\pi$
$858$	−28.8098	−0.983550
$859$	8.67042	0.295831	0.147916	−	0.989000i	$-0.452744\pi$
$859$	8.67042	0.295831	0.147916	+	0.989000i	$0.452744\pi$
$860$	0.726031	0.0247575
$861$	−30.2894	−1.03226
$862$	35.0808	1.19486
$863$	−34.9626	−1.19014	−0.595070	−	0.803674i	$-0.702876\pi$
$863$	−34.9626	−1.19014	−0.595070	+	0.803674i	$0.702876\pi$
$864$	7.77014	0.264346
$865$	3.77470	0.128344
$866$	−41.6740	−1.41614
$867$	−1.00000	−0.0339618
$868$	−47.1139	−1.59915
$869$	−4.16183	−0.141181
$870$	5.65882	0.191852
$871$	−21.4554	−0.726987
$872$	3.52541	0.119385
$873$	8.99445	0.304416
$874$	−92.9024	−3.14247
$875$	−15.4578	−0.522570
$876$	9.98617	0.337401
$877$	34.0628	1.15022	0.575109	−	0.818077i	$-0.304960\pi$
$877$	34.0628	1.15022	0.575109	+	0.818077i	$0.304960\pi$
$878$	−40.4086	−1.36372
$879$	4.73065	0.159561
$880$	6.00804	0.202531
$881$	−19.7478	−0.665321	−0.332660	−	0.943047i	$-0.607946\pi$
$881$	−19.7478	−0.665321	−0.332660	+	0.943047i	$0.607946\pi$
$882$	28.9803	0.975818
$883$	54.7146	1.84129	0.920647	−	0.390396i	$-0.127662\pi$
$883$	54.7146	1.84129	0.920647	+	0.390396i	$0.127662\pi$
$884$	−6.47070	−0.217633
$885$	4.22308	0.141957
$886$	−63.4634	−2.13209
$887$	−44.2161	−1.48463	−0.742316	−	0.670050i	$-0.766273\pi$
$887$	−44.2161	−1.48463	−0.742316	+	0.670050i	$0.766273\pi$
$888$	−0.126152	−0.00423339
$889$	12.0774	0.405062
$890$	−4.01276	−0.134508
$891$	−4.16183	−0.139427
$892$	36.2067	1.21229
$893$	96.4817	3.22864
$894$	−0.737647	−0.0246706
$895$	−0.550936	−0.0184157
$896$	12.4461	0.415794
$897$	19.4070	0.647981
$898$	13.8956	0.463702
$899$	47.6471	1.58912
$900$	−8.94071	−0.298024
$901$	0.865790	0.0288436
$902$	−52.8200	−1.75871
$903$	−5.53759	−0.184279
$904$	−2.11208	−0.0702466
$905$	0.417990	0.0138944
$906$	−4.04058	−0.134239
$907$	24.5738	0.815959	0.407979	−	0.912991i	$-0.366234\pi$
$907$	24.5738	0.815959	0.407979	+	0.912991i	$0.366234\pi$
$908$	12.7269	0.422358
$909$	12.5126	0.415017
$910$	−10.8218	−0.358738
$911$	−33.8424	−1.12125	−0.560624	−	0.828070i	$-0.689439\pi$
$911$	−33.8424	−1.12125	−0.560624	+	0.828070i	$0.689439\pi$
$912$	−37.3212	−1.23583
$913$	−17.4746	−0.578324
$914$	37.3724	1.23617
$915$	−2.18277	−0.0721601
$916$	−13.4437	−0.444191
$917$	−4.34264	−0.143407
$918$	−1.95682	−0.0645846
$919$	26.5109	0.874513	0.437256	−	0.899337i	$-0.355950\pi$
$919$	26.5109	0.874513	0.437256	+	0.899337i	$0.355950\pi$
$920$	−0.614004	−0.0202431
$921$	−1.10152	−0.0362963
$922$	−25.9542	−0.854756
$923$	−45.6046	−1.50110
$924$	35.5515	1.16956
$925$	1.84424	0.0606384
$926$	−48.8441	−1.60512
$927$	3.54176	0.116327
$928$	67.1257	2.20351
$929$	11.0379	0.362141	0.181071	−	0.983470i	$-0.442044\pi$
$929$	11.0379	0.362141	0.181071	+	0.983470i	$0.442044\pi$
$930$	3.61279	0.118468
$931$	−128.167	−4.20050
$932$	−22.0157	−0.721148
$933$	1.54608	0.0506165
$934$	4.29168	0.140428
$935$	−1.39316	−0.0455611
$936$	1.18279	0.0386607
$937$	32.2687	1.05417	0.527086	−	0.849812i	$-0.323285\pi$
$937$	32.2687	1.05417	0.527086	+	0.849812i	$0.323285\pi$
$938$	55.4253	1.80970
$939$	30.9174	1.00895
$940$	−6.82626	−0.222648
$941$	38.8451	1.26632	0.633158	−	0.774023i	$-0.281758\pi$
$941$	38.8451	1.26632	0.633158	+	0.774023i	$0.281758\pi$
$942$	23.4734	0.764804
$943$	35.5808	1.15867
$944$	54.4059	1.77076
$945$	−1.56330	−0.0508542
$946$	−9.65670	−0.313966
$947$	−16.6669	−0.541600	−0.270800	−	0.962636i	$-0.587288\pi$
$947$	−16.6669	−0.541600	−0.270800	+	0.962636i	$0.587288\pi$
$948$	−1.82914	−0.0594076
$949$	19.3134	0.626939
$950$	82.7752	2.68558
$951$	9.80967	0.318100
$952$	−1.56146	−0.0506071
$953$	26.4629	0.857218	0.428609	−	0.903490i	$-0.359004\pi$
$953$	26.4629	0.857218	0.428609	+	0.903490i	$0.359004\pi$
$954$	1.69419	0.0548515
$955$	−5.89158	−0.190647
$956$	25.7486	0.832769
$957$	−35.9538	−1.16222
$958$	77.3528	2.49916
$959$	−85.0644	−2.74687
$960$	2.20252	0.0710861
$961$	−0.580433	−0.0187237
$962$	2.61185	0.0842093
$963$	1.65645	0.0533785
$964$	17.5207	0.564303
$965$	−8.21916	−0.264584
$966$	−50.1338	−1.61303
$967$	44.0870	1.41774	0.708872	−	0.705338i	$-0.249205\pi$
$967$	44.0870	1.41774	0.708872	+	0.705338i	$0.249205\pi$
$968$	−2.11338	−0.0679267
$969$	8.65413	0.278011
$970$	5.89170	0.189171
$971$	−9.02899	−0.289754	−0.144877	−	0.989450i	$-0.546279\pi$
$971$	−9.02899	−0.289754	−0.144877	+	0.989450i	$0.546279\pi$
$972$	−1.82914	−0.0586695
$973$	−11.0449	−0.354083
$974$	−43.8824	−1.40608
$975$	−17.2915	−0.553770
$976$	−28.1206	−0.900119
$977$	−2.72539	−0.0871929	−0.0435965	−	0.999049i	$-0.513882\pi$
$977$	−2.72539	−0.0871929	−0.0435965	+	0.999049i	$0.513882\pi$
$978$	17.2771	0.552462
$979$	25.4954	0.814836
$980$	9.06806	0.289668
$981$	−10.5440	−0.336645
$982$	40.6950	1.29863
$983$	−25.5188	−0.813924	−0.406962	−	0.913445i	$-0.633412\pi$
$983$	−25.5188	−0.813924	−0.406962	+	0.913445i	$0.633412\pi$
$984$	2.16853	0.0691302
$985$	8.86401	0.282431
$986$	−16.9048	−0.538359
$987$	52.0653	1.65726
$988$	55.9982	1.78154
$989$	6.50499	0.206847
$990$	−2.72616	−0.0866429
$991$	30.7599	0.977120	0.488560	−	0.872530i	$-0.337522\pi$
$991$	30.7599	0.977120	0.488560	+	0.872530i	$0.337522\pi$
$992$	42.8554	1.36066
$993$	−0.262190	−0.00832033
$994$	117.810	3.73670
$995$	1.54230	0.0488942
$996$	−7.68012	−0.243354
$997$	−52.0921	−1.64977	−0.824887	−	0.565297i	$-0.808762\pi$
$997$	−52.0921	−1.64977	−0.824887	+	0.565297i	$0.808762\pi$
$998$	−18.4868	−0.585188
$999$	0.377305	0.0119374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.f.1.18	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.f.1.18	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.95682 q^{2} -1.00000 q^{3} +1.82914 q^{4} +0.334746 q^{5} -1.95682 q^{6} +4.67011 q^{7} -0.334351 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.95682 q^{2} -1.00000 q^{3} +1.82914 q^{4} +0.334746 q^{5} -1.95682 q^{6} +4.67011 q^{7} -0.334351 q^{8} +1.00000 q^{9} +0.655037 q^{10} -4.16183 q^{11} -1.82914 q^{12} -3.53757 q^{13} +9.13855 q^{14} -0.334746 q^{15} -4.31253 q^{16} +1.00000 q^{17} +1.95682 q^{18} -8.65413 q^{19} +0.612296 q^{20} -4.67011 q^{21} -8.14395 q^{22} +5.48597 q^{23} +0.334351 q^{24} -4.88794 q^{25} -6.92238 q^{26} -1.00000 q^{27} +8.54226 q^{28} -8.63893 q^{29} -0.655037 q^{30} -5.51539 q^{31} -7.77014 q^{32} +4.16183 q^{33} +1.95682 q^{34} +1.56330 q^{35} +1.82914 q^{36} -0.377305 q^{37} -16.9346 q^{38} +3.53757 q^{39} -0.111923 q^{40} +6.48579 q^{41} -9.13855 q^{42} +1.18575 q^{43} -7.61256 q^{44} +0.334746 q^{45} +10.7350 q^{46} -11.1486 q^{47} +4.31253 q^{48} +14.8099 q^{49} -9.56482 q^{50} -1.00000 q^{51} -6.47070 q^{52} +0.865790 q^{53} -1.95682 q^{54} -1.39316 q^{55} -1.56146 q^{56} +8.65413 q^{57} -16.9048 q^{58} -12.6158 q^{59} -0.612296 q^{60} +6.52067 q^{61} -10.7926 q^{62} +4.67011 q^{63} -6.57968 q^{64} -1.18419 q^{65} +8.14395 q^{66} +6.06500 q^{67} +1.82914 q^{68} -5.48597 q^{69} +3.05910 q^{70} +12.8915 q^{71} -0.334351 q^{72} -5.45950 q^{73} -0.738316 q^{74} +4.88794 q^{75} -15.8296 q^{76} -19.4362 q^{77} +6.92238 q^{78} +1.00000 q^{79} -1.44360 q^{80} +1.00000 q^{81} +12.6915 q^{82} +4.19877 q^{83} -8.54226 q^{84} +0.334746 q^{85} +2.32030 q^{86} +8.63893 q^{87} +1.39151 q^{88} -6.12600 q^{89} +0.655037 q^{90} -16.5208 q^{91} +10.0346 q^{92} +5.51539 q^{93} -21.8158 q^{94} -2.89694 q^{95} +7.77014 q^{96} +8.99445 q^{97} +28.9803 q^{98} -4.16183 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

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