LMFDB - Embedded newform 6002.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.40047 q^{3} +1.00000 q^{4} -0.810151 q^{5} +3.40047 q^{6} +1.45096 q^{7} -1.00000 q^{8} +8.56323 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.40047 q^{3} +1.00000 q^{4} -0.810151 q^{5} +3.40047 q^{6} +1.45096 q^{7} -1.00000 q^{8} +8.56323 q^{9} +0.810151 q^{10} -4.98807 q^{11} -3.40047 q^{12} -1.28399 q^{13} -1.45096 q^{14} +2.75490 q^{15} +1.00000 q^{16} -6.08866 q^{17} -8.56323 q^{18} -5.59957 q^{19} -0.810151 q^{20} -4.93394 q^{21} +4.98807 q^{22} +2.15747 q^{23} +3.40047 q^{24} -4.34365 q^{25} +1.28399 q^{26} -18.9176 q^{27} +1.45096 q^{28} -5.17132 q^{29} -2.75490 q^{30} +3.15551 q^{31} -1.00000 q^{32} +16.9618 q^{33} +6.08866 q^{34} -1.17549 q^{35} +8.56323 q^{36} -3.56769 q^{37} +5.59957 q^{38} +4.36619 q^{39} +0.810151 q^{40} -6.98547 q^{41} +4.93394 q^{42} -3.48458 q^{43} -4.98807 q^{44} -6.93751 q^{45} -2.15747 q^{46} +1.00059 q^{47} -3.40047 q^{48} -4.89473 q^{49} +4.34365 q^{50} +20.7043 q^{51} -1.28399 q^{52} +4.99268 q^{53} +18.9176 q^{54} +4.04109 q^{55} -1.45096 q^{56} +19.0412 q^{57} +5.17132 q^{58} +3.81684 q^{59} +2.75490 q^{60} -5.14319 q^{61} -3.15551 q^{62} +12.4249 q^{63} +1.00000 q^{64} +1.04023 q^{65} -16.9618 q^{66} +8.11348 q^{67} -6.08866 q^{68} -7.33643 q^{69} +1.17549 q^{70} -13.3559 q^{71} -8.56323 q^{72} -6.33435 q^{73} +3.56769 q^{74} +14.7705 q^{75} -5.59957 q^{76} -7.23747 q^{77} -4.36619 q^{78} +8.17624 q^{79} -0.810151 q^{80} +38.6392 q^{81} +6.98547 q^{82} -2.75590 q^{83} -4.93394 q^{84} +4.93273 q^{85} +3.48458 q^{86} +17.5849 q^{87} +4.98807 q^{88} -7.74484 q^{89} +6.93751 q^{90} -1.86302 q^{91} +2.15747 q^{92} -10.7302 q^{93} -1.00059 q^{94} +4.53650 q^{95} +3.40047 q^{96} -2.22550 q^{97} +4.89473 q^{98} -42.7140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.40047	−1.96327	−0.981633	−	0.190782i	$-0.938898\pi$
$3$	−3.40047	−1.96327	−0.981633	+	0.190782i	$0.938898\pi$
$4$	1.00000	0.500000
$5$	−0.810151	−0.362311	−0.181155	−	0.983454i	$-0.557984\pi$
$5$	−0.810151	−0.362311	−0.181155	+	0.983454i	$0.557984\pi$
$6$	3.40047	1.38824
$7$	1.45096	0.548410	0.274205	−	0.961671i	$-0.411585\pi$
$7$	1.45096	0.548410	0.274205	+	0.961671i	$0.411585\pi$
$8$	−1.00000	−0.353553
$9$	8.56323	2.85441
$10$	0.810151	0.256192
$11$	−4.98807	−1.50396	−0.751980	−	0.659186i	$-0.770901\pi$
$11$	−4.98807	−1.50396	−0.751980	+	0.659186i	$0.770901\pi$
$12$	−3.40047	−0.981633
$13$	−1.28399	−0.356116	−0.178058	−	0.984020i	$-0.556981\pi$
$13$	−1.28399	−0.356116	−0.178058	+	0.984020i	$0.556981\pi$
$14$	−1.45096	−0.387784
$15$	2.75490	0.711312
$16$	1.00000	0.250000
$17$	−6.08866	−1.47672	−0.738358	−	0.674409i	$-0.764399\pi$
$17$	−6.08866	−1.47672	−0.738358	+	0.674409i	$0.764399\pi$
$18$	−8.56323	−2.01837
$19$	−5.59957	−1.28463	−0.642315	−	0.766441i	$-0.722026\pi$
$19$	−5.59957	−1.28463	−0.642315	+	0.766441i	$0.722026\pi$
$20$	−0.810151	−0.181155
$21$	−4.93394	−1.07667
$22$	4.98807	1.06346
$23$	2.15747	0.449864	0.224932	−	0.974374i	$-0.427784\pi$
$23$	2.15747	0.449864	0.224932	+	0.974374i	$0.427784\pi$
$24$	3.40047	0.694119
$25$	−4.34365	−0.868731
$26$	1.28399	0.251812
$27$	−18.9176	−3.64070
$28$	1.45096	0.274205
$29$	−5.17132	−0.960290	−0.480145	−	0.877189i	$-0.659416\pi$
$29$	−5.17132	−0.960290	−0.480145	+	0.877189i	$0.659416\pi$
$30$	−2.75490	−0.502973
$31$	3.15551	0.566746	0.283373	−	0.959010i	$-0.408547\pi$
$31$	3.15551	0.566746	0.283373	+	0.959010i	$0.408547\pi$
$32$	−1.00000	−0.176777
$33$	16.9618	2.95267
$34$	6.08866	1.04420
$35$	−1.17549	−0.198695
$36$	8.56323	1.42720
$37$	−3.56769	−0.586524	−0.293262	−	0.956032i	$-0.594741\pi$
$37$	−3.56769	−0.586524	−0.293262	+	0.956032i	$0.594741\pi$
$38$	5.59957	0.908371
$39$	4.36619	0.699149
$40$	0.810151	0.128096
$41$	−6.98547	−1.09095	−0.545474	−	0.838128i	$-0.683650\pi$
$41$	−6.98547	−1.09095	−0.545474	+	0.838128i	$0.683650\pi$
$42$	4.93394	0.761323
$43$	−3.48458	−0.531394	−0.265697	−	0.964057i	$-0.585602\pi$
$43$	−3.48458	−0.531394	−0.265697	+	0.964057i	$0.585602\pi$
$44$	−4.98807	−0.751980
$45$	−6.93751	−1.03418
$46$	−2.15747	−0.318102
$47$	1.00059	0.145951	0.0729756	−	0.997334i	$-0.476750\pi$
$47$	1.00059	0.145951	0.0729756	+	0.997334i	$0.476750\pi$
$48$	−3.40047	−0.490816
$49$	−4.89473	−0.699247
$50$	4.34365	0.614286
$51$	20.7043	2.89919
$52$	−1.28399	−0.178058
$53$	4.99268	0.685797	0.342899	−	0.939372i	$-0.388591\pi$
$53$	4.99268	0.685797	0.342899	+	0.939372i	$0.388591\pi$
$54$	18.9176	2.57436
$55$	4.04109	0.544900
$56$	−1.45096	−0.193892
$57$	19.0412	2.52207
$58$	5.17132	0.679027
$59$	3.81684	0.496910	0.248455	−	0.968643i	$-0.420077\pi$
$59$	3.81684	0.496910	0.248455	+	0.968643i	$0.420077\pi$
$60$	2.75490	0.355656
$61$	−5.14319	−0.658518	−0.329259	−	0.944240i	$-0.606799\pi$
$61$	−5.14319	−0.658518	−0.329259	+	0.944240i	$0.606799\pi$
$62$	−3.15551	−0.400750
$63$	12.4249	1.56539
$64$	1.00000	0.125000
$65$	1.04023	0.129025
$66$	−16.9618	−2.08785
$67$	8.11348	0.991219	0.495610	−	0.868545i	$-0.334945\pi$
$67$	8.11348	0.991219	0.495610	+	0.868545i	$0.334945\pi$
$68$	−6.08866	−0.738358
$69$	−7.33643	−0.883202
$70$	1.17549	0.140498
$71$	−13.3559	−1.58506	−0.792529	−	0.609834i	$-0.791236\pi$
$71$	−13.3559	−1.58506	−0.792529	+	0.609834i	$0.791236\pi$
$72$	−8.56323	−1.00919
$73$	−6.33435	−0.741380	−0.370690	−	0.928757i	$-0.620879\pi$
$73$	−6.33435	−0.741380	−0.370690	+	0.928757i	$0.620879\pi$
$74$	3.56769	0.414735
$75$	14.7705	1.70555
$76$	−5.59957	−0.642315
$77$	−7.23747	−0.824786
$78$	−4.36619	−0.494373
$79$	8.17624	0.919898	0.459949	−	0.887945i	$-0.347868\pi$
$79$	8.17624	0.919898	0.459949	+	0.887945i	$0.347868\pi$
$80$	−0.810151	−0.0905777
$81$	38.6392	4.29324
$82$	6.98547	0.771417
$83$	−2.75590	−0.302500	−0.151250	−	0.988496i	$-0.548330\pi$
$83$	−2.75590	−0.302500	−0.151250	+	0.988496i	$0.548330\pi$
$84$	−4.93394	−0.538337
$85$	4.93273	0.535030
$86$	3.48458	0.375752
$87$	17.5849	1.88530
$88$	4.98807	0.531730
$89$	−7.74484	−0.820952	−0.410476	−	0.911871i	$-0.634637\pi$
$89$	−7.74484	−0.820952	−0.410476	+	0.911871i	$0.634637\pi$
$90$	6.93751	0.731278
$91$	−1.86302	−0.195297
$92$	2.15747	0.224932
$93$	−10.7302	−1.11267
$94$	−1.00059	−0.103203
$95$	4.53650	0.465435
$96$	3.40047	0.347060
$97$	−2.22550	−0.225965	−0.112983	−	0.993597i	$-0.536040\pi$
$97$	−2.22550	−0.225965	−0.112983	+	0.993597i	$0.536040\pi$
$98$	4.89473	0.494442
$99$	−42.7140	−4.29292
$100$	−4.34365	−0.434365
$101$	−13.8496	−1.37809	−0.689044	−	0.724720i	$-0.741969\pi$
$101$	−13.8496	−1.37809	−0.689044	+	0.724720i	$0.741969\pi$
$102$	−20.7043	−2.05003
$103$	−0.449493	−0.0442899	−0.0221449	−	0.999755i	$-0.507050\pi$
$103$	−0.449493	−0.0442899	−0.0221449	+	0.999755i	$0.507050\pi$
$104$	1.28399	0.125906
$105$	3.99724	0.390090
$106$	−4.99268	−0.484932
$107$	5.89979	0.570355	0.285177	−	0.958475i	$-0.407948\pi$
$107$	5.89979	0.570355	0.285177	+	0.958475i	$0.407948\pi$
$108$	−18.9176	−1.82035
$109$	−13.2323	−1.26743	−0.633714	−	0.773567i	$-0.718471\pi$
$109$	−13.2323	−1.26743	−0.633714	+	0.773567i	$0.718471\pi$
$110$	−4.04109	−0.385303
$111$	12.1318	1.15150
$112$	1.45096	0.137102
$113$	−8.86457	−0.833908	−0.416954	−	0.908928i	$-0.636902\pi$
$113$	−8.86457	−0.833908	−0.416954	+	0.908928i	$0.636902\pi$
$114$	−19.0412	−1.78337
$115$	−1.74788	−0.162991
$116$	−5.17132	−0.480145
$117$	−10.9951	−1.01650
$118$	−3.81684	−0.351368
$119$	−8.83437	−0.809846
$120$	−2.75490	−0.251487
$121$	13.8808	1.26189
$122$	5.14319	0.465642
$123$	23.7539	2.14182
$124$	3.15551	0.283373
$125$	7.56977	0.677061
$126$	−12.4249	−1.10690
$127$	12.5644	1.11491	0.557454	−	0.830208i	$-0.311778\pi$
$127$	12.5644	1.11491	0.557454	+	0.830208i	$0.311778\pi$
$128$	−1.00000	−0.0883883
$129$	11.8492	1.04327
$130$	−1.04023	−0.0912341
$131$	−22.1394	−1.93433	−0.967166	−	0.254147i	$-0.918205\pi$
$131$	−22.1394	−1.93433	−0.967166	+	0.254147i	$0.918205\pi$
$132$	16.9618	1.47634
$133$	−8.12473	−0.704504
$134$	−8.11348	−0.700898
$135$	15.3261	1.31906
$136$	6.08866	0.522098
$137$	−2.87514	−0.245640	−0.122820	−	0.992429i	$-0.539194\pi$
$137$	−2.87514	−0.245640	−0.122820	+	0.992429i	$0.539194\pi$
$138$	7.33643	0.624518
$139$	−9.18888	−0.779391	−0.389695	−	0.920944i	$-0.627420\pi$
$139$	−9.18888	−0.779391	−0.389695	+	0.920944i	$0.627420\pi$
$140$	−1.17549	−0.0993474
$141$	−3.40249	−0.286541
$142$	13.3559	1.12081
$143$	6.40465	0.535583
$144$	8.56323	0.713602
$145$	4.18955	0.347923
$146$	6.33435	0.524235
$147$	16.6444	1.37281
$148$	−3.56769	−0.293262
$149$	11.9355	0.977791	0.488895	−	0.872342i	$-0.337400\pi$
$149$	11.9355	0.977791	0.488895	+	0.872342i	$0.337400\pi$
$150$	−14.7705	−1.20601
$151$	1.41943	0.115512	0.0577558	−	0.998331i	$-0.481606\pi$
$151$	1.41943	0.115512	0.0577558	+	0.998331i	$0.481606\pi$
$152$	5.59957	0.454185
$153$	−52.1386	−4.21515
$154$	7.23747	0.583212
$155$	−2.55644	−0.205338
$156$	4.36619	0.349575
$157$	−4.44925	−0.355089	−0.177544	−	0.984113i	$-0.556815\pi$
$157$	−4.44925	−0.355089	−0.177544	+	0.984113i	$0.556815\pi$
$158$	−8.17624	−0.650466
$159$	−16.9775	−1.34640
$160$	0.810151	0.0640481
$161$	3.13040	0.246710
$162$	−38.6392	−3.03578
$163$	−1.50824	−0.118135	−0.0590674	−	0.998254i	$-0.518813\pi$
$163$	−1.50824	−0.118135	−0.0590674	+	0.998254i	$0.518813\pi$
$164$	−6.98547	−0.545474
$165$	−13.7416	−1.06978
$166$	2.75590	0.213900
$167$	−7.31735	−0.566233	−0.283117	−	0.959085i	$-0.591368\pi$
$167$	−7.31735	−0.566233	−0.283117	+	0.959085i	$0.591368\pi$
$168$	4.93394	0.380662
$169$	−11.3514	−0.873182
$170$	−4.93273	−0.378323
$171$	−47.9504	−3.66686
$172$	−3.48458	−0.265697
$173$	−14.4182	−1.09619	−0.548096	−	0.836415i	$-0.684647\pi$
$173$	−14.4182	−1.09619	−0.548096	+	0.836415i	$0.684647\pi$
$174$	−17.5849	−1.33311
$175$	−6.30245	−0.476421
$176$	−4.98807	−0.375990
$177$	−12.9791	−0.975566
$178$	7.74484	0.580500
$179$	−16.7271	−1.25025	−0.625123	−	0.780526i	$-0.714951\pi$
$179$	−16.7271	−1.25025	−0.625123	+	0.780526i	$0.714951\pi$
$180$	−6.93751	−0.517092
$181$	−16.0158	−1.19044	−0.595222	−	0.803561i	$-0.702936\pi$
$181$	−16.0158	−1.19044	−0.595222	+	0.803561i	$0.702936\pi$
$182$	1.86302	0.138096
$183$	17.4893	1.29285
$184$	−2.15747	−0.159051
$185$	2.89037	0.212504
$186$	10.7302	0.786779
$187$	30.3706	2.22092
$188$	1.00059	0.0729756
$189$	−27.4486	−1.99659
$190$	−4.53650	−0.329112
$191$	−10.7819	−0.780149	−0.390075	−	0.920783i	$-0.627551\pi$
$191$	−10.7819	−0.780149	−0.390075	+	0.920783i	$0.627551\pi$
$192$	−3.40047	−0.245408
$193$	−25.0009	−1.79961	−0.899803	−	0.436297i	$-0.856290\pi$
$193$	−25.0009	−1.79961	−0.899803	+	0.436297i	$0.856290\pi$
$194$	2.22550	0.159782
$195$	−3.53727	−0.253309
$196$	−4.89473	−0.349623
$197$	0.669338	0.0476884	0.0238442	−	0.999716i	$-0.492409\pi$
$197$	0.669338	0.0476884	0.0238442	+	0.999716i	$0.492409\pi$
$198$	42.7140	3.03555
$199$	25.5145	1.80868	0.904339	−	0.426815i	$-0.140365\pi$
$199$	25.5145	1.80868	0.904339	+	0.426815i	$0.140365\pi$
$200$	4.34365	0.307143
$201$	−27.5897	−1.94603
$202$	13.8496	0.974455
$203$	−7.50336	−0.526632
$204$	20.7043	1.44959
$205$	5.65929	0.395262
$206$	0.449493	0.0313177
$207$	18.4749	1.28410
$208$	−1.28399	−0.0890289
$209$	27.9310	1.93203
$210$	−3.99724	−0.275836
$211$	20.0227	1.37842	0.689209	−	0.724563i	$-0.257958\pi$
$211$	20.0227	1.37842	0.689209	+	0.724563i	$0.257958\pi$
$212$	4.99268	0.342899
$213$	45.4165	3.11189
$214$	−5.89979	−0.403302
$215$	2.82304	0.192530
$216$	18.9176	1.28718
$217$	4.57851	0.310809
$218$	13.2323	0.896207
$219$	21.5398	1.45553
$220$	4.04109	0.272450
$221$	7.81779	0.525882
$222$	−12.1318	−0.814235
$223$	−3.76337	−0.252014	−0.126007	−	0.992029i	$-0.540216\pi$
$223$	−3.76337	−0.252014	−0.126007	+	0.992029i	$0.540216\pi$
$224$	−1.45096	−0.0969461
$225$	−37.1957	−2.47971
$226$	8.86457	0.589662
$227$	−8.69772	−0.577288	−0.288644	−	0.957436i	$-0.593204\pi$
$227$	−8.69772	−0.577288	−0.288644	+	0.957436i	$0.593204\pi$
$228$	19.0412	1.26103
$229$	8.31287	0.549330	0.274665	−	0.961540i	$-0.411433\pi$
$229$	8.31287	0.549330	0.274665	+	0.961540i	$0.411433\pi$
$230$	1.74788	0.115252
$231$	24.6108	1.61927
$232$	5.17132	0.339514
$233$	−13.0521	−0.855068	−0.427534	−	0.903999i	$-0.640618\pi$
$233$	−13.0521	−0.855068	−0.427534	+	0.903999i	$0.640618\pi$
$234$	10.9951	0.718774
$235$	−0.810631	−0.0528797
$236$	3.81684	0.248455
$237$	−27.8031	−1.80600
$238$	8.83437	0.572647
$239$	10.6977	0.691977	0.345988	−	0.938239i	$-0.387544\pi$
$239$	10.6977	0.691977	0.345988	+	0.938239i	$0.387544\pi$
$240$	2.75490	0.177828
$241$	−0.436411	−0.0281117	−0.0140558	−	0.999901i	$-0.504474\pi$
$241$	−0.436411	−0.0281117	−0.0140558	+	0.999901i	$0.504474\pi$
$242$	−13.8808	−0.892293
$243$	−74.6388	−4.78808
$244$	−5.14319	−0.329259
$245$	3.96547	0.253345
$246$	−23.7539	−1.51450
$247$	7.18981	0.457477
$248$	−3.15551	−0.200375
$249$	9.37138	0.593887
$250$	−7.56977	−0.478755
$251$	−25.7916	−1.62795	−0.813975	−	0.580900i	$-0.802701\pi$
$251$	−25.7916	−1.62795	−0.813975	+	0.580900i	$0.802701\pi$
$252$	12.4249	0.782693
$253$	−10.7616	−0.676577
$254$	−12.5644	−0.788359
$255$	−16.7736	−1.05041
$256$	1.00000	0.0625000
$257$	21.0821	1.31506	0.657532	−	0.753427i	$-0.271601\pi$
$257$	21.0821	1.31506	0.657532	+	0.753427i	$0.271601\pi$
$258$	−11.8492	−0.737701
$259$	−5.17656	−0.321656
$260$	1.04023	0.0645123
$261$	−44.2832	−2.74106
$262$	22.1394	1.36778
$263$	−5.95923	−0.367462	−0.183731	−	0.982977i	$-0.558818\pi$
$263$	−5.95923	−0.367462	−0.183731	+	0.982977i	$0.558818\pi$
$264$	−16.9618	−1.04393
$265$	−4.04483	−0.248472
$266$	8.12473	0.498159
$267$	26.3361	1.61175
$268$	8.11348	0.495610
$269$	−20.3987	−1.24373	−0.621866	−	0.783124i	$-0.713625\pi$
$269$	−20.3987	−1.24373	−0.621866	+	0.783124i	$0.713625\pi$
$270$	−15.3261	−0.932719
$271$	9.64879	0.586122	0.293061	−	0.956094i	$-0.405326\pi$
$271$	9.64879	0.586122	0.293061	+	0.956094i	$0.405326\pi$
$272$	−6.08866	−0.369179
$273$	6.33514	0.383420
$274$	2.87514	0.173694
$275$	21.6664	1.30654
$276$	−7.33643	−0.441601
$277$	21.1361	1.26995	0.634974	−	0.772534i	$-0.281011\pi$
$277$	21.1361	1.26995	0.634974	+	0.772534i	$0.281011\pi$
$278$	9.18888	0.551113
$279$	27.0214	1.61773
$280$	1.17549	0.0702492
$281$	−4.46372	−0.266283	−0.133142	−	0.991097i	$-0.542506\pi$
$281$	−4.46372	−0.266283	−0.133142	+	0.991097i	$0.542506\pi$
$282$	3.40249	0.202615
$283$	16.1959	0.962746	0.481373	−	0.876516i	$-0.340138\pi$
$283$	16.1959	0.962746	0.481373	+	0.876516i	$0.340138\pi$
$284$	−13.3559	−0.792529
$285$	−15.4263	−0.913773
$286$	−6.40465	−0.378715
$287$	−10.1356	−0.598287
$288$	−8.56323	−0.504593
$289$	20.0717	1.18069
$290$	−4.18955	−0.246019
$291$	7.56776	0.443630
$292$	−6.33435	−0.370690
$293$	−5.31577	−0.310551	−0.155275	−	0.987871i	$-0.549627\pi$
$293$	−5.31577	−0.310551	−0.155275	+	0.987871i	$0.549627\pi$
$294$	−16.6444	−0.970721
$295$	−3.09222	−0.180036
$296$	3.56769	0.207368
$297$	94.3624	5.47546
$298$	−11.9355	−0.691403
$299$	−2.77018	−0.160204
$300$	14.7705	0.852775
$301$	−5.05597	−0.291421
$302$	−1.41943	−0.0816790
$303$	47.0953	2.70555
$304$	−5.59957	−0.321158
$305$	4.16676	0.238588
$306$	52.1386	2.98056
$307$	11.4485	0.653401	0.326701	−	0.945128i	$-0.394063\pi$
$307$	11.4485	0.653401	0.326701	+	0.945128i	$0.394063\pi$
$308$	−7.23747	−0.412393
$309$	1.52849	0.0869527
$310$	2.55644	0.145196
$311$	1.74090	0.0987172	0.0493586	−	0.998781i	$-0.484282\pi$
$311$	1.74090	0.0987172	0.0493586	+	0.998781i	$0.484282\pi$
$312$	−4.36619	−0.247187
$313$	24.1279	1.36379	0.681895	−	0.731450i	$-0.261156\pi$
$313$	24.1279	1.36379	0.681895	+	0.731450i	$0.261156\pi$
$314$	4.44925	0.251086
$315$	−10.0660	−0.567156
$316$	8.17624	0.459949
$317$	−27.9791	−1.57146	−0.785731	−	0.618568i	$-0.787713\pi$
$317$	−27.9791	−1.57146	−0.785731	+	0.618568i	$0.787713\pi$
$318$	16.9775	0.952050
$319$	25.7949	1.44424
$320$	−0.810151	−0.0452888
$321$	−20.0621	−1.11976
$322$	−3.13040	−0.174450
$323$	34.0939	1.89703
$324$	38.6392	2.14662
$325$	5.57722	0.309369
$326$	1.50824	0.0835339
$327$	44.9963	2.48830
$328$	6.98547	0.385708
$329$	1.45181	0.0800411
$330$	13.7416	0.756452
$331$	−20.1391	−1.10694	−0.553471	−	0.832868i	$-0.686697\pi$
$331$	−20.1391	−1.10694	−0.553471	+	0.832868i	$0.686697\pi$
$332$	−2.75590	−0.151250
$333$	−30.5509	−1.67418
$334$	7.31735	0.400387
$335$	−6.57315	−0.359129
$336$	−4.93394	−0.269168
$337$	7.39962	0.403083	0.201542	−	0.979480i	$-0.435405\pi$
$337$	7.39962	0.403083	0.201542	+	0.979480i	$0.435405\pi$
$338$	11.3514	0.617433
$339$	30.1437	1.63718
$340$	4.93273	0.267515
$341$	−15.7399	−0.852363
$342$	47.9504	2.59286
$343$	−17.2587	−0.931884
$344$	3.48458	0.187876
$345$	5.94362	0.319994
$346$	14.4182	0.775125
$347$	14.5547	0.781336	0.390668	−	0.920532i	$-0.372244\pi$
$347$	14.5547	0.781336	0.390668	+	0.920532i	$0.372244\pi$
$348$	17.5849	0.942652
$349$	−19.2320	−1.02947	−0.514734	−	0.857350i	$-0.672109\pi$
$349$	−19.2320	−1.02947	−0.514734	+	0.857350i	$0.672109\pi$
$350$	6.30245	0.336880
$351$	24.2901	1.29651
$352$	4.98807	0.265865
$353$	−3.39084	−0.180476	−0.0902381	−	0.995920i	$-0.528763\pi$
$353$	−3.39084	−0.180476	−0.0902381	+	0.995920i	$0.528763\pi$
$354$	12.9791	0.689829
$355$	10.8203	0.574284
$356$	−7.74484	−0.410476
$357$	30.0411	1.58994
$358$	16.7271	0.884057
$359$	−3.99546	−0.210872	−0.105436	−	0.994426i	$-0.533624\pi$
$359$	−3.99546	−0.210872	−0.105436	+	0.994426i	$0.533624\pi$
$360$	6.93751	0.365639
$361$	12.3552	0.650274
$362$	16.0158	0.841771
$363$	−47.2014	−2.47743
$364$	−1.86302	−0.0976487
$365$	5.13179	0.268610
$366$	−17.4893	−0.914180
$367$	7.79697	0.406999	0.203499	−	0.979075i	$-0.434769\pi$
$367$	7.79697	0.406999	0.203499	+	0.979075i	$0.434769\pi$
$368$	2.15747	0.112466
$369$	−59.8182	−3.11401
$370$	−2.89037	−0.150263
$371$	7.24416	0.376098
$372$	−10.7302	−0.556337
$373$	16.6933	0.864346	0.432173	−	0.901791i	$-0.357747\pi$
$373$	16.6933	0.864346	0.432173	+	0.901791i	$0.357747\pi$
$374$	−30.3706	−1.57043
$375$	−25.7408	−1.32925
$376$	−1.00059	−0.0516016
$377$	6.63994	0.341974
$378$	27.4486	1.41181
$379$	−11.0268	−0.566408	−0.283204	−	0.959060i	$-0.591397\pi$
$379$	−11.0268	−0.566408	−0.283204	+	0.959060i	$0.591397\pi$
$380$	4.53650	0.232718
$381$	−42.7248	−2.18886
$382$	10.7819	0.551649
$383$	16.3206	0.833945	0.416973	−	0.908919i	$-0.363091\pi$
$383$	16.3206	0.833945	0.416973	+	0.908919i	$0.363091\pi$
$384$	3.40047	0.173530
$385$	5.86344	0.298829
$386$	25.0009	1.27251
$387$	−29.8393	−1.51681
$388$	−2.22550	−0.112983
$389$	17.4965	0.887106	0.443553	−	0.896248i	$-0.353718\pi$
$389$	17.4965	0.887106	0.443553	+	0.896248i	$0.353718\pi$
$390$	3.53727	0.179117
$391$	−13.1361	−0.664321
$392$	4.89473	0.247221
$393$	75.2846	3.79760
$394$	−0.669338	−0.0337208
$395$	−6.62399	−0.333289
$396$	−42.7140	−2.14646
$397$	21.8105	1.09464	0.547319	−	0.836924i	$-0.315648\pi$
$397$	21.8105	1.09464	0.547319	+	0.836924i	$0.315648\pi$
$398$	−25.5145	−1.27893
$399$	27.6280	1.38313
$400$	−4.34365	−0.217183
$401$	0.0835301	0.00417129	0.00208565	−	0.999998i	$-0.499336\pi$
$401$	0.0835301	0.00417129	0.00208565	+	0.999998i	$0.499336\pi$
$402$	27.5897	1.37605
$403$	−4.05165	−0.201827
$404$	−13.8496	−0.689044
$405$	−31.3036	−1.55549
$406$	7.50336	0.372385
$407$	17.7959	0.882108
$408$	−20.7043	−1.02502
$409$	23.0910	1.14178	0.570889	−	0.821027i	$-0.306599\pi$
$409$	23.0910	1.14178	0.570889	+	0.821027i	$0.306599\pi$
$410$	−5.65929	−0.279492
$411$	9.77685	0.482256
$412$	−0.449493	−0.0221449
$413$	5.53806	0.272510
$414$	−18.4749	−0.907993
$415$	2.23270	0.109599
$416$	1.28399	0.0629529
$417$	31.2466	1.53015
$418$	−27.9310	−1.36615
$419$	−3.99547	−0.195192	−0.0975958	−	0.995226i	$-0.531115\pi$
$419$	−3.99547	−0.195192	−0.0975958	+	0.995226i	$0.531115\pi$
$420$	3.99724	0.195045
$421$	15.5068	0.755755	0.377878	−	0.925856i	$-0.376654\pi$
$421$	15.5068	0.755755	0.377878	+	0.925856i	$0.376654\pi$
$422$	−20.0227	−0.974688
$423$	8.56829	0.416605
$424$	−4.99268	−0.242466
$425$	26.4470	1.28287
$426$	−45.4165	−2.20044
$427$	−7.46254	−0.361138
$428$	5.89979	0.285177
$429$	−21.7788	−1.05149
$430$	−2.82304	−0.136139
$431$	15.5966	0.751263	0.375632	−	0.926769i	$-0.377426\pi$
$431$	15.5966	0.751263	0.375632	+	0.926769i	$0.377426\pi$
$432$	−18.9176	−0.910174
$433$	20.7791	0.998581	0.499291	−	0.866435i	$-0.333594\pi$
$433$	20.7791	0.998581	0.499291	+	0.866435i	$0.333594\pi$
$434$	−4.57851	−0.219775
$435$	−14.2465	−0.683066
$436$	−13.2323	−0.633714
$437$	−12.0809	−0.577909
$438$	−21.5398	−1.02921
$439$	−33.9253	−1.61917	−0.809583	−	0.587005i	$-0.800307\pi$
$439$	−33.9253	−1.61917	−0.809583	+	0.587005i	$0.800307\pi$
$440$	−4.04109	−0.192651
$441$	−41.9147	−1.99594
$442$	−7.81779	−0.371855
$443$	−30.6284	−1.45520	−0.727600	−	0.686001i	$-0.759364\pi$
$443$	−30.6284	−1.45520	−0.727600	+	0.686001i	$0.759364\pi$
$444$	12.1318	0.575751
$445$	6.27449	0.297440
$446$	3.76337	0.178201
$447$	−40.5862	−1.91966
$448$	1.45096	0.0685512
$449$	−20.3370	−0.959764	−0.479882	−	0.877333i	$-0.659320\pi$
$449$	−20.3370	−0.959764	−0.479882	+	0.877333i	$0.659320\pi$
$450$	37.1957	1.75342
$451$	34.8440	1.64074
$452$	−8.86457	−0.416954
$453$	−4.82673	−0.226780
$454$	8.69772	0.408204
$455$	1.50933	0.0707583
$456$	−19.0412	−0.891686
$457$	17.2680	0.807762	0.403881	−	0.914811i	$-0.367661\pi$
$457$	17.2680	0.807762	0.403881	+	0.914811i	$0.367661\pi$
$458$	−8.31287	−0.388435
$459$	115.183	5.37628
$460$	−1.74788	−0.0814953
$461$	−6.47990	−0.301799	−0.150900	−	0.988549i	$-0.548217\pi$
$461$	−6.47990	−0.301799	−0.150900	+	0.988549i	$0.548217\pi$
$462$	−24.6108	−1.14500
$463$	−8.82312	−0.410045	−0.205023	−	0.978757i	$-0.565727\pi$
$463$	−8.82312	−0.410045	−0.205023	+	0.978757i	$0.565727\pi$
$464$	−5.17132	−0.240072
$465$	8.69311	0.403133
$466$	13.0521	0.604625
$467$	36.6236	1.69474	0.847369	−	0.531005i	$-0.178185\pi$
$467$	36.6236	1.69474	0.847369	+	0.531005i	$0.178185\pi$
$468$	−10.9951	−0.508250
$469$	11.7723	0.543595
$470$	0.810631	0.0373916
$471$	15.1296	0.697133
$472$	−3.81684	−0.175684
$473$	17.3813	0.799194
$474$	27.8031	1.27704
$475$	24.3226	1.11600
$476$	−8.83437	−0.404923
$477$	42.7535	1.95755
$478$	−10.6977	−0.489301
$479$	11.1860	0.511100	0.255550	−	0.966796i	$-0.417743\pi$
$479$	11.1860	0.511100	0.255550	+	0.966796i	$0.417743\pi$
$480$	−2.75490	−0.125743
$481$	4.58089	0.208870
$482$	0.436411	0.0198780
$483$	−10.6448	−0.484357
$484$	13.8808	0.630946
$485$	1.80299	0.0818696
$486$	74.6388	3.38568
$487$	−41.2222	−1.86796	−0.933979	−	0.357328i	$-0.883688\pi$
$487$	−41.2222	−1.86796	−0.933979	+	0.357328i	$0.883688\pi$
$488$	5.14319	0.232821
$489$	5.12875	0.231930
$490$	−3.96547	−0.179142
$491$	15.3792	0.694052	0.347026	−	0.937855i	$-0.387191\pi$
$491$	15.3792	0.694052	0.347026	+	0.937855i	$0.387191\pi$
$492$	23.7539	1.07091
$493$	31.4864	1.41808
$494$	−7.18981	−0.323485
$495$	34.6048	1.55537
$496$	3.15551	0.141687
$497$	−19.3789	−0.869262
$498$	−9.37138	−0.419942
$499$	−8.81623	−0.394669	−0.197334	−	0.980336i	$-0.563228\pi$
$499$	−8.81623	−0.394669	−0.197334	+	0.980336i	$0.563228\pi$
$500$	7.56977	0.338531
$501$	24.8825	1.11167
$502$	25.7916	1.15113
$503$	−1.92743	−0.0859399	−0.0429699	−	0.999076i	$-0.513682\pi$
$503$	−1.92743	−0.0859399	−0.0429699	+	0.999076i	$0.513682\pi$
$504$	−12.4249	−0.553448
$505$	11.2203	0.499296
$506$	10.7616	0.478412
$507$	38.6000	1.71429
$508$	12.5644	0.557454
$509$	−29.3973	−1.30301	−0.651506	−	0.758644i	$-0.725862\pi$
$509$	−29.3973	−1.30301	−0.651506	+	0.758644i	$0.725862\pi$
$510$	16.7736	0.742749
$511$	−9.19087	−0.406580
$512$	−1.00000	−0.0441942
$513$	105.931	4.67695
$514$	−21.0821	−0.929890
$515$	0.364157	0.0160467
$516$	11.8492	0.521633
$517$	−4.99102	−0.219505
$518$	5.17656	0.227445
$519$	49.0286	2.15212
$520$	−1.04023	−0.0456171
$521$	−14.5483	−0.637373	−0.318686	−	0.947860i	$-0.603242\pi$
$521$	−14.5483	−0.637373	−0.318686	+	0.947860i	$0.603242\pi$
$522$	44.2832	1.93822
$523$	−16.7561	−0.732693	−0.366346	−	0.930479i	$-0.619391\pi$
$523$	−16.7561	−0.732693	−0.366346	+	0.930479i	$0.619391\pi$
$524$	−22.1394	−0.967166
$525$	21.4313	0.935340
$526$	5.95923	0.259835
$527$	−19.2128	−0.836923
$528$	16.9618	0.738168
$529$	−18.3453	−0.797622
$530$	4.04483	0.175696
$531$	32.6845	1.41838
$532$	−8.12473	−0.352252
$533$	8.96930	0.388504
$534$	−26.3361	−1.13968
$535$	−4.77973	−0.206646
$536$	−8.11348	−0.350449
$537$	56.8802	2.45456
$538$	20.3987	0.879451
$539$	24.4152	1.05164
$540$	15.3261	0.659532
$541$	−32.9089	−1.41487	−0.707433	−	0.706780i	$-0.750147\pi$
$541$	−32.9089	−1.41487	−0.707433	+	0.706780i	$0.750147\pi$
$542$	−9.64879	−0.414451
$543$	54.4613	2.33716
$544$	6.08866	0.261049
$545$	10.7202	0.459203
$546$	−6.33514	−0.271119
$547$	21.2959	0.910548	0.455274	−	0.890351i	$-0.349541\pi$
$547$	21.2959	0.910548	0.455274	+	0.890351i	$0.349541\pi$
$548$	−2.87514	−0.122820
$549$	−44.0423	−1.87968
$550$	−21.6664	−0.923860
$551$	28.9572	1.23362
$552$	7.33643	0.312259
$553$	11.8634	0.504481
$554$	−21.1361	−0.897988
$555$	−9.82862	−0.417202
$556$	−9.18888	−0.389695
$557$	21.5902	0.914806	0.457403	−	0.889259i	$-0.348780\pi$
$557$	21.5902	0.914806	0.457403	+	0.889259i	$0.348780\pi$
$558$	−27.0214	−1.14391
$559$	4.47418	0.189238
$560$	−1.17549	−0.0496737
$561$	−103.275	−4.36026
$562$	4.46372	0.188291
$563$	31.1213	1.31160	0.655802	−	0.754933i	$-0.272330\pi$
$563$	31.1213	1.31160	0.655802	+	0.754933i	$0.272330\pi$
$564$	−3.40249	−0.143271
$565$	7.18164	0.302134
$566$	−16.1959	−0.680764
$567$	56.0638	2.35446
$568$	13.3559	0.560403
$569$	16.5941	0.695660	0.347830	−	0.937558i	$-0.386919\pi$
$569$	16.5941	0.695660	0.347830	+	0.937558i	$0.386919\pi$
$570$	15.4263	0.646135
$571$	−0.530633	−0.0222063	−0.0111032	−	0.999938i	$-0.503534\pi$
$571$	−0.530633	−0.0222063	−0.0111032	+	0.999938i	$0.503534\pi$
$572$	6.40465	0.267792
$573$	36.6635	1.53164
$574$	10.1356	0.423052
$575$	−9.37131	−0.390811
$576$	8.56323	0.356801
$577$	31.2738	1.30195	0.650973	−	0.759101i	$-0.274361\pi$
$577$	31.2738	1.30195	0.650973	+	0.759101i	$0.274361\pi$
$578$	−20.0717	−0.834874
$579$	85.0150	3.53310
$580$	4.18955	0.173962
$581$	−3.99869	−0.165894
$582$	−7.56776	−0.313694
$583$	−24.9038	−1.03141
$584$	6.33435	0.262117
$585$	8.90772	0.368289
$586$	5.31577	0.219593
$587$	−44.6739	−1.84389	−0.921944	−	0.387323i	$-0.873400\pi$
$587$	−44.6739	−1.84389	−0.921944	+	0.387323i	$0.873400\pi$
$588$	16.6444	0.686403
$589$	−17.6695	−0.728059
$590$	3.09222	0.127305
$591$	−2.27607	−0.0936249
$592$	−3.56769	−0.146631
$593$	−20.4515	−0.839844	−0.419922	−	0.907560i	$-0.637943\pi$
$593$	−20.4515	−0.839844	−0.419922	+	0.907560i	$0.637943\pi$
$594$	−94.3624	−3.87173
$595$	7.15718	0.293416
$596$	11.9355	0.488895
$597$	−86.7615	−3.55091
$598$	2.77018	0.113281
$599$	−0.412077	−0.0168370	−0.00841851	−	0.999965i	$-0.502680\pi$
$599$	−0.412077	−0.0168370	−0.00841851	+	0.999965i	$0.502680\pi$
$600$	−14.7705	−0.603003
$601$	−27.9193	−1.13885	−0.569426	−	0.822043i	$-0.692834\pi$
$601$	−27.9193	−1.13885	−0.569426	+	0.822043i	$0.692834\pi$
$602$	5.05597	0.206066
$603$	69.4776	2.82935
$604$	1.41943	0.0577558
$605$	−11.2456	−0.457197
$606$	−47.0953	−1.91311
$607$	−26.5820	−1.07893	−0.539464	−	0.842009i	$-0.681373\pi$
$607$	−26.5820	−1.07893	−0.539464	+	0.842009i	$0.681373\pi$
$608$	5.59957	0.227093
$609$	25.5150	1.03392
$610$	−4.16676	−0.168707
$611$	−1.28475	−0.0519755
$612$	−52.1386	−2.10758
$613$	33.3708	1.34783	0.673917	−	0.738807i	$-0.264610\pi$
$613$	33.3708	1.34783	0.673917	+	0.738807i	$0.264610\pi$
$614$	−11.4485	−0.462024
$615$	−19.2443	−0.776004
$616$	7.23747	0.291606
$617$	5.56295	0.223956	0.111978	−	0.993711i	$-0.464281\pi$
$617$	5.56295	0.223956	0.111978	+	0.993711i	$0.464281\pi$
$618$	−1.52849	−0.0614849
$619$	8.81618	0.354352	0.177176	−	0.984179i	$-0.443304\pi$
$619$	8.81618	0.354352	0.177176	+	0.984179i	$0.443304\pi$
$620$	−2.55644	−0.102669
$621$	−40.8142	−1.63782
$622$	−1.74090	−0.0698036
$623$	−11.2374	−0.450218
$624$	4.36619	0.174787
$625$	15.5856	0.623424
$626$	−24.1279	−0.964345
$627$	−94.9788	−3.79309
$628$	−4.44925	−0.177544
$629$	21.7224	0.866130
$630$	10.0660	0.401040
$631$	38.7739	1.54357	0.771783	−	0.635886i	$-0.219365\pi$
$631$	38.7739	1.54357	0.771783	+	0.635886i	$0.219365\pi$
$632$	−8.17624	−0.325233
$633$	−68.0866	−2.70620
$634$	27.9791	1.11119
$635$	−10.1790	−0.403943
$636$	−16.9775	−0.673201
$637$	6.28480	0.249013
$638$	−25.7949	−1.02123
$639$	−114.370	−4.52441
$640$	0.810151	0.0320240
$641$	37.2524	1.47138	0.735690	−	0.677318i	$-0.236858\pi$
$641$	37.2524	1.47138	0.735690	+	0.677318i	$0.236858\pi$
$642$	20.0621	0.791788
$643$	−16.8855	−0.665901	−0.332951	−	0.942944i	$-0.608044\pi$
$643$	−16.8855	−0.665901	−0.332951	+	0.942944i	$0.608044\pi$
$644$	3.13040	0.123355
$645$	−9.59967	−0.377987
$646$	−34.0939	−1.34141
$647$	−29.1569	−1.14627	−0.573137	−	0.819459i	$-0.694274\pi$
$647$	−29.1569	−1.14627	−0.573137	+	0.819459i	$0.694274\pi$
$648$	−38.6392	−1.51789
$649$	−19.0386	−0.747332
$650$	−5.57722	−0.218757
$651$	−15.5691	−0.610201
$652$	−1.50824	−0.0590674
$653$	4.36526	0.170826	0.0854130	−	0.996346i	$-0.472779\pi$
$653$	4.36526	0.170826	0.0854130	+	0.996346i	$0.472779\pi$
$654$	−44.9963	−1.75949
$655$	17.9363	0.700829
$656$	−6.98547	−0.272737
$657$	−54.2425	−2.11620
$658$	−1.45181	−0.0565976
$659$	20.0459	0.780879	0.390439	−	0.920629i	$-0.372323\pi$
$659$	20.0459	0.780879	0.390439	+	0.920629i	$0.372323\pi$
$660$	−13.7416	−0.534892
$661$	−30.3707	−1.18128	−0.590642	−	0.806933i	$-0.701126\pi$
$661$	−30.3707	−1.18128	−0.590642	+	0.806933i	$0.701126\pi$
$662$	20.1391	0.782727
$663$	−26.5842	−1.03245
$664$	2.75590	0.106950
$665$	6.58226	0.255249
$666$	30.5509	1.18382
$667$	−11.1570	−0.432000
$668$	−7.31735	−0.283117
$669$	12.7972	0.494770
$670$	6.57315	0.253943
$671$	25.6546	0.990384
$672$	4.93394	0.190331
$673$	20.2390	0.780155	0.390078	−	0.920782i	$-0.372448\pi$
$673$	20.2390	0.780155	0.390078	+	0.920782i	$0.372448\pi$
$674$	−7.39962	−0.285023
$675$	82.1716	3.16279
$676$	−11.3514	−0.436591
$677$	−24.4180	−0.938460	−0.469230	−	0.883076i	$-0.655469\pi$
$677$	−24.4180	−0.938460	−0.469230	+	0.883076i	$0.655469\pi$
$678$	−30.1437	−1.15766
$679$	−3.22910	−0.123922
$680$	−4.93273	−0.189162
$681$	29.5764	1.13337
$682$	15.7399	0.602712
$683$	23.7508	0.908798	0.454399	−	0.890798i	$-0.349854\pi$
$683$	23.7508	0.908798	0.454399	+	0.890798i	$0.349854\pi$
$684$	−47.9504	−1.83343
$685$	2.32930	0.0889980
$686$	17.2587	0.658941
$687$	−28.2677	−1.07848
$688$	−3.48458	−0.132848
$689$	−6.41057	−0.244223
$690$	−5.94362	−0.226270
$691$	−40.0625	−1.52405	−0.762025	−	0.647548i	$-0.775795\pi$
$691$	−40.0625	−1.52405	−0.762025	+	0.647548i	$0.775795\pi$
$692$	−14.4182	−0.548096
$693$	−61.9761	−2.35428
$694$	−14.5547	−0.552488
$695$	7.44439	0.282382
$696$	−17.5849	−0.666555
$697$	42.5322	1.61102
$698$	19.2320	0.727943
$699$	44.3832	1.67873
$700$	−6.30245	−0.238210
$701$	−38.9968	−1.47289	−0.736445	−	0.676497i	$-0.763497\pi$
$701$	−38.9968	−1.47289	−0.736445	+	0.676497i	$0.763497\pi$
$702$	−24.2901	−0.916771
$703$	19.9775	0.753467
$704$	−4.98807	−0.187995
$705$	2.75653	0.103817
$706$	3.39084	0.127616
$707$	−20.0952	−0.755757
$708$	−12.9791	−0.487783
$709$	−48.2397	−1.81168	−0.905839	−	0.423622i	$-0.860758\pi$
$709$	−48.2397	−1.81168	−0.905839	+	0.423622i	$0.860758\pi$
$710$	−10.8203	−0.406080
$711$	70.0150	2.62577
$712$	7.74484	0.290250
$713$	6.80792	0.254959
$714$	−30.0411	−1.12426
$715$	−5.18873	−0.194048
$716$	−16.7271	−0.625123
$717$	−36.3772	−1.35853
$718$	3.99546	0.149109
$719$	−4.05455	−0.151209	−0.0756046	−	0.997138i	$-0.524089\pi$
$719$	−4.05455	−0.151209	−0.0756046	+	0.997138i	$0.524089\pi$
$720$	−6.93751	−0.258546
$721$	−0.652194	−0.0242890
$722$	−12.3552	−0.459813
$723$	1.48400	0.0551907
$724$	−16.0158	−0.595222
$725$	22.4624	0.834233
$726$	47.2014	1.75181
$727$	−0.702729	−0.0260628	−0.0130314	−	0.999915i	$-0.504148\pi$
$727$	−0.702729	−0.0260628	−0.0130314	+	0.999915i	$0.504148\pi$
$728$	1.86302	0.0690480
$729$	137.890	5.10702
$730$	−5.13179	−0.189936
$731$	21.2164	0.784717
$732$	17.4893	0.646423
$733$	−23.4933	−0.867747	−0.433873	−	0.900974i	$-0.642853\pi$
$733$	−23.4933	−0.867747	−0.433873	+	0.900974i	$0.642853\pi$
$734$	−7.79697	−0.287791
$735$	−13.4845	−0.497382
$736$	−2.15747	−0.0795255
$737$	−40.4706	−1.49075
$738$	59.8182	2.20194
$739$	−28.5188	−1.04908	−0.524540	−	0.851386i	$-0.675763\pi$
$739$	−28.5188	−1.04908	−0.524540	+	0.851386i	$0.675763\pi$
$740$	2.89037	0.106252
$741$	−24.4488	−0.898148
$742$	−7.24416	−0.265941
$743$	24.7079	0.906446	0.453223	−	0.891397i	$-0.350274\pi$
$743$	24.7079	0.906446	0.453223	+	0.891397i	$0.350274\pi$
$744$	10.7302	0.393389
$745$	−9.66953	−0.354264
$746$	−16.6933	−0.611185
$747$	−23.5994	−0.863458
$748$	30.3706	1.11046
$749$	8.56034	0.312788
$750$	25.7408	0.939922
$751$	23.7910	0.868144	0.434072	−	0.900878i	$-0.357076\pi$
$751$	23.7910	0.868144	0.434072	+	0.900878i	$0.357076\pi$
$752$	1.00059	0.0364878
$753$	87.7036	3.19610
$754$	−6.63994	−0.241812
$755$	−1.14995	−0.0418511
$756$	−27.4486	−0.998297
$757$	−23.5087	−0.854438	−0.427219	−	0.904148i	$-0.640507\pi$
$757$	−23.5087	−0.854438	−0.427219	+	0.904148i	$0.640507\pi$
$758$	11.0268	0.400511
$759$	36.5946	1.32830
$760$	−4.53650	−0.164556
$761$	39.8894	1.44599	0.722994	−	0.690854i	$-0.242765\pi$
$761$	39.8894	1.44599	0.722994	+	0.690854i	$0.242765\pi$
$762$	42.7248	1.54776
$763$	−19.1996	−0.695070
$764$	−10.7819	−0.390075
$765$	42.2401	1.52719
$766$	−16.3206	−0.589688
$767$	−4.90079	−0.176957
$768$	−3.40047	−0.122704
$769$	−8.61971	−0.310835	−0.155417	−	0.987849i	$-0.549672\pi$
$769$	−8.61971	−0.310835	−0.155417	+	0.987849i	$0.549672\pi$
$770$	−5.86344	−0.211304
$771$	−71.6891	−2.58182
$772$	−25.0009	−0.899803
$773$	29.9928	1.07877	0.539383	−	0.842061i	$-0.318658\pi$
$773$	29.9928	1.07877	0.539383	+	0.842061i	$0.318658\pi$
$774$	29.8393	1.07255
$775$	−13.7064	−0.492350
$776$	2.22550	0.0798908
$777$	17.6028	0.631495
$778$	−17.4965	−0.627278
$779$	39.1157	1.40146
$780$	−3.53727	−0.126655
$781$	66.6203	2.38386
$782$	13.1361	0.469746
$783$	97.8290	3.49612
$784$	−4.89473	−0.174812
$785$	3.60457	0.128652
$786$	−75.2846	−2.68531
$787$	20.8437	0.742997	0.371498	−	0.928434i	$-0.378844\pi$
$787$	20.8437	0.742997	0.371498	+	0.928434i	$0.378844\pi$
$788$	0.669338	0.0238442
$789$	20.2642	0.721425
$790$	6.62399	0.235671
$791$	−12.8621	−0.457323
$792$	42.7140	1.51777
$793$	6.60382	0.234509
$794$	−21.8105	−0.774026
$795$	13.7543	0.487816
$796$	25.5145	0.904339
$797$	−40.3611	−1.42966	−0.714832	−	0.699296i	$-0.753497\pi$
$797$	−40.3611	−1.42966	−0.714832	+	0.699296i	$0.753497\pi$
$798$	−27.6280	−0.978019
$799$	−6.09226	−0.215529
$800$	4.34365	0.153571
$801$	−66.3209	−2.34333
$802$	−0.0835301	−0.00294955
$803$	31.5962	1.11501
$804$	−27.5897	−0.973013
$805$	−2.53610	−0.0893856
$806$	4.05165	0.142713
$807$	69.3653	2.44177
$808$	13.8496	0.487228
$809$	−13.0241	−0.457904	−0.228952	−	0.973438i	$-0.573530\pi$
$809$	−13.0241	−0.457904	−0.228952	+	0.973438i	$0.573530\pi$
$810$	31.3036	1.09990
$811$	0.901317	0.0316495	0.0158248	−	0.999875i	$-0.494963\pi$
$811$	0.901317	0.0316495	0.0158248	+	0.999875i	$0.494963\pi$
$812$	−7.50336	−0.263316
$813$	−32.8105	−1.15071
$814$	−17.7959	−0.623745
$815$	1.22191	0.0428015
$816$	20.7043	0.724796
$817$	19.5122	0.682644
$818$	−23.0910	−0.807359
$819$	−15.9534	−0.557459
$820$	5.65929	0.197631
$821$	−20.3709	−0.710950	−0.355475	−	0.934686i	$-0.615681\pi$
$821$	−20.3709	−0.710950	−0.355475	+	0.934686i	$0.615681\pi$
$822$	−9.77685	−0.341007
$823$	19.1598	0.667867	0.333933	−	0.942597i	$-0.391624\pi$
$823$	19.1598	0.667867	0.333933	+	0.942597i	$0.391624\pi$
$824$	0.449493	0.0156588
$825$	−73.6762	−2.56508
$826$	−5.53806	−0.192694
$827$	−7.86930	−0.273642	−0.136821	−	0.990596i	$-0.543689\pi$
$827$	−7.86930	−0.273642	−0.136821	+	0.990596i	$0.543689\pi$
$828$	18.4749	0.642048
$829$	−6.00558	−0.208582	−0.104291	−	0.994547i	$-0.533257\pi$
$829$	−6.00558	−0.208582	−0.104291	+	0.994547i	$0.533257\pi$
$830$	−2.23270	−0.0774981
$831$	−71.8729	−2.49324
$832$	−1.28399	−0.0445145
$833$	29.8023	1.03259
$834$	−31.2466	−1.08198
$835$	5.92816	0.205152
$836$	27.9310	0.966016
$837$	−59.6947	−2.06335
$838$	3.99547	0.138021
$839$	3.13883	0.108365	0.0541823	−	0.998531i	$-0.482745\pi$
$839$	3.13883	0.108365	0.0541823	+	0.998531i	$0.482745\pi$
$840$	−3.99724	−0.137918
$841$	−2.25746	−0.0778435
$842$	−15.5068	−0.534400
$843$	15.1788	0.522784
$844$	20.0227	0.689209
$845$	9.19632	0.316363
$846$	−8.56829	−0.294584
$847$	20.1405	0.692035
$848$	4.99268	0.171449
$849$	−55.0737	−1.89012
$850$	−26.4470	−0.907125
$851$	−7.69719	−0.263856
$852$	45.4165	1.55594
$853$	−20.3392	−0.696399	−0.348200	−	0.937420i	$-0.613207\pi$
$853$	−20.3392	−0.696399	−0.348200	+	0.937420i	$0.613207\pi$
$854$	7.46254	0.255363
$855$	38.8471	1.32854
$856$	−5.89979	−0.201651
$857$	−42.1575	−1.44007	−0.720036	−	0.693937i	$-0.755875\pi$
$857$	−42.1575	−1.44007	−0.720036	+	0.693937i	$0.755875\pi$
$858$	21.7788	0.743517
$859$	54.0907	1.84555	0.922775	−	0.385339i	$-0.125915\pi$
$859$	54.0907	1.84555	0.922775	+	0.385339i	$0.125915\pi$
$860$	2.82304	0.0962648
$861$	34.4659	1.17460
$862$	−15.5966	−0.531223
$863$	12.8092	0.436031	0.218015	−	0.975945i	$-0.430042\pi$
$863$	12.8092	0.436031	0.218015	+	0.975945i	$0.430042\pi$
$864$	18.9176	0.643590
$865$	11.6809	0.397162
$866$	−20.7791	−0.706104
$867$	−68.2534	−2.31801
$868$	4.57851	0.155405
$869$	−40.7836	−1.38349
$870$	14.2465	0.483000
$871$	−10.4177	−0.352989
$872$	13.2323	0.448104
$873$	−19.0575	−0.644997
$874$	12.0809	0.408643
$875$	10.9834	0.371307
$876$	21.5398	0.727763
$877$	55.1022	1.86067	0.930335	−	0.366711i	$-0.119516\pi$
$877$	55.1022	1.86067	0.930335	+	0.366711i	$0.119516\pi$
$878$	33.9253	1.14492
$879$	18.0762	0.609694
$880$	4.04109	0.136225
$881$	46.0816	1.55253	0.776265	−	0.630407i	$-0.217112\pi$
$881$	46.0816	1.55253	0.776265	+	0.630407i	$0.217112\pi$
$882$	41.9147	1.41134
$883$	−5.68399	−0.191282	−0.0956408	−	0.995416i	$-0.530490\pi$
$883$	−5.68399	−0.191282	−0.0956408	+	0.995416i	$0.530490\pi$
$884$	7.81779	0.262941
$885$	10.5150	0.353458
$886$	30.6284	1.02898
$887$	36.2577	1.21742	0.608708	−	0.793395i	$-0.291688\pi$
$887$	36.2577	1.21742	0.608708	+	0.793395i	$0.291688\pi$
$888$	−12.1318	−0.407118
$889$	18.2303	0.611426
$890$	−6.27449	−0.210322
$891$	−192.735	−6.45686
$892$	−3.76337	−0.126007
$893$	−5.60288	−0.187493
$894$	40.5862	1.35741
$895$	13.5515	0.452977
$896$	−1.45096	−0.0484730
$897$	9.41993	0.314522
$898$	20.3370	0.678655
$899$	−16.3181	−0.544241
$900$	−37.1957	−1.23986
$901$	−30.3987	−1.01273
$902$	−34.8440	−1.16018
$903$	17.1927	0.572138
$904$	8.86457	0.294831
$905$	12.9752	0.431311
$906$	4.82673	0.160357
$907$	23.4761	0.779512	0.389756	−	0.920918i	$-0.372559\pi$
$907$	23.4761	0.779512	0.389756	+	0.920918i	$0.372559\pi$
$908$	−8.69772	−0.288644
$909$	−118.597	−3.93363
$910$	−1.50933	−0.0500337
$911$	21.8788	0.724876	0.362438	−	0.932008i	$-0.381945\pi$
$911$	21.8788	0.724876	0.362438	+	0.932008i	$0.381945\pi$
$912$	19.0412	0.630517
$913$	13.7466	0.454947
$914$	−17.2680	−0.571174
$915$	−14.1690	−0.468412
$916$	8.31287	0.274665
$917$	−32.1233	−1.06081
$918$	−115.183	−3.80160
$919$	46.5404	1.53523	0.767613	−	0.640914i	$-0.221444\pi$
$919$	46.5404	1.53523	0.767613	+	0.640914i	$0.221444\pi$
$920$	1.74788	0.0576259
$921$	−38.9304	−1.28280
$922$	6.47990	0.213404
$923$	17.1489	0.564464
$924$	24.6108	0.809637
$925$	15.4968	0.509532
$926$	8.82312	0.289946
$927$	−3.84911	−0.126421
$928$	5.17132	0.169757
$929$	35.8196	1.17520	0.587602	−	0.809150i	$-0.300072\pi$
$929$	35.8196	1.17520	0.587602	+	0.809150i	$0.300072\pi$
$930$	−8.69311	−0.285058
$931$	27.4084	0.898273
$932$	−13.0521	−0.427534
$933$	−5.91987	−0.193808
$934$	−36.6236	−1.19836
$935$	−24.6048	−0.804663
$936$	10.9951	0.359387
$937$	−41.0516	−1.34110	−0.670549	−	0.741865i	$-0.733941\pi$
$937$	−41.0516	−1.34110	−0.670549	+	0.741865i	$0.733941\pi$
$938$	−11.7723	−0.384379
$939$	−82.0464	−2.67748
$940$	−0.810631	−0.0264399
$941$	37.1000	1.20943	0.604713	−	0.796444i	$-0.293288\pi$
$941$	37.1000	1.20943	0.604713	+	0.796444i	$0.293288\pi$
$942$	−15.1296	−0.492948
$943$	−15.0710	−0.490778
$944$	3.81684	0.124228
$945$	22.2375	0.723387
$946$	−17.3813	−0.565116
$947$	1.79552	0.0583467	0.0291734	−	0.999574i	$-0.490713\pi$
$947$	1.79552	0.0583467	0.0291734	+	0.999574i	$0.490713\pi$
$948$	−27.8031	−0.903002
$949$	8.13327	0.264017
$950$	−24.3226	−0.789130
$951$	95.1422	3.08520
$952$	8.83437	0.286324
$953$	−8.96860	−0.290522	−0.145261	−	0.989393i	$-0.546402\pi$
$953$	−8.96860	−0.290522	−0.145261	+	0.989393i	$0.546402\pi$
$954$	−42.7535	−1.38419
$955$	8.73495	0.282656
$956$	10.6977	0.345988
$957$	−87.7149	−2.83542
$958$	−11.1860	−0.361403
$959$	−4.17170	−0.134711
$960$	2.75490	0.0889140
$961$	−21.0428	−0.678799
$962$	−4.58089	−0.147694
$963$	50.5213	1.62803
$964$	−0.436411	−0.0140558
$965$	20.2545	0.652016
$966$	10.6448	0.342492
$967$	−4.88064	−0.156951	−0.0784755	−	0.996916i	$-0.525005\pi$
$967$	−4.88064	−0.156951	−0.0784755	+	0.996916i	$0.525005\pi$
$968$	−13.8808	−0.446147
$969$	−115.935	−3.72438
$970$	−1.80299	−0.0578906
$971$	−44.6718	−1.43359	−0.716794	−	0.697285i	$-0.754391\pi$
$971$	−44.6718	−1.43359	−0.716794	+	0.697285i	$0.754391\pi$
$972$	−74.6388	−2.39404
$973$	−13.3327	−0.427426
$974$	41.2222	1.32085
$975$	−18.9652	−0.607373
$976$	−5.14319	−0.164629
$977$	25.8785	0.827926	0.413963	−	0.910294i	$-0.364144\pi$
$977$	25.8785	0.827926	0.413963	+	0.910294i	$0.364144\pi$
$978$	−5.12875	−0.163999
$979$	38.6318	1.23468
$980$	3.96547	0.126672
$981$	−113.312	−3.61776
$982$	−15.3792	−0.490769
$983$	20.0450	0.639336	0.319668	−	0.947530i	$-0.396429\pi$
$983$	20.0450	0.639336	0.319668	+	0.947530i	$0.396429\pi$
$984$	−23.7539	−0.757248
$985$	−0.542265	−0.0172780
$986$	−31.4864	−1.00273
$987$	−4.93686	−0.157142
$988$	7.18981	0.228738
$989$	−7.51789	−0.239055
$990$	−34.6048	−1.09981
$991$	−28.3770	−0.901425	−0.450713	−	0.892669i	$-0.648830\pi$
$991$	−28.3770	−0.901425	−0.450713	+	0.892669i	$0.648830\pi$
$992$	−3.15551	−0.100188
$993$	68.4824	2.17322
$994$	19.3789	0.614661
$995$	−20.6706	−0.655303
$996$	9.37138	0.296944
$997$	49.4657	1.56659	0.783297	−	0.621648i	$-0.213537\pi$
$997$	49.4657	1.56659	0.783297	+	0.621648i	$0.213537\pi$
$998$	8.81623	0.279073
$999$	67.4921	2.13536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.c.1.1	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.c.1.1	✓	69	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.40047 q^{3} +1.00000 q^{4} -0.810151 q^{5} +3.40047 q^{6} +1.45096 q^{7} -1.00000 q^{8} +8.56323 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.40047 q^{3} +1.00000 q^{4} -0.810151 q^{5} +3.40047 q^{6} +1.45096 q^{7} -1.00000 q^{8} +8.56323 q^{9} +0.810151 q^{10} -4.98807 q^{11} -3.40047 q^{12} -1.28399 q^{13} -1.45096 q^{14} +2.75490 q^{15} +1.00000 q^{16} -6.08866 q^{17} -8.56323 q^{18} -5.59957 q^{19} -0.810151 q^{20} -4.93394 q^{21} +4.98807 q^{22} +2.15747 q^{23} +3.40047 q^{24} -4.34365 q^{25} +1.28399 q^{26} -18.9176 q^{27} +1.45096 q^{28} -5.17132 q^{29} -2.75490 q^{30} +3.15551 q^{31} -1.00000 q^{32} +16.9618 q^{33} +6.08866 q^{34} -1.17549 q^{35} +8.56323 q^{36} -3.56769 q^{37} +5.59957 q^{38} +4.36619 q^{39} +0.810151 q^{40} -6.98547 q^{41} +4.93394 q^{42} -3.48458 q^{43} -4.98807 q^{44} -6.93751 q^{45} -2.15747 q^{46} +1.00059 q^{47} -3.40047 q^{48} -4.89473 q^{49} +4.34365 q^{50} +20.7043 q^{51} -1.28399 q^{52} +4.99268 q^{53} +18.9176 q^{54} +4.04109 q^{55} -1.45096 q^{56} +19.0412 q^{57} +5.17132 q^{58} +3.81684 q^{59} +2.75490 q^{60} -5.14319 q^{61} -3.15551 q^{62} +12.4249 q^{63} +1.00000 q^{64} +1.04023 q^{65} -16.9618 q^{66} +8.11348 q^{67} -6.08866 q^{68} -7.33643 q^{69} +1.17549 q^{70} -13.3559 q^{71} -8.56323 q^{72} -6.33435 q^{73} +3.56769 q^{74} +14.7705 q^{75} -5.59957 q^{76} -7.23747 q^{77} -4.36619 q^{78} +8.17624 q^{79} -0.810151 q^{80} +38.6392 q^{81} +6.98547 q^{82} -2.75590 q^{83} -4.93394 q^{84} +4.93273 q^{85} +3.48458 q^{86} +17.5849 q^{87} +4.98807 q^{88} -7.74484 q^{89} +6.93751 q^{90} -1.86302 q^{91} +2.15747 q^{92} -10.7302 q^{93} -1.00059 q^{94} +4.53650 q^{95} +3.40047 q^{96} -2.22550 q^{97} +4.89473 q^{98} -42.7140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * q^99

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