LMFDB - Embedded newform 6002.2.a.c.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.19747 q^{3} +1.00000 q^{4} -2.90019 q^{5} +2.19747 q^{6} -0.534047 q^{7} -1.00000 q^{8} +1.82886 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.19747 q^{3} +1.00000 q^{4} -2.90019 q^{5} +2.19747 q^{6} -0.534047 q^{7} -1.00000 q^{8} +1.82886 q^{9} +2.90019 q^{10} -0.0358323 q^{11} -2.19747 q^{12} -5.77309 q^{13} +0.534047 q^{14} +6.37308 q^{15} +1.00000 q^{16} +8.04287 q^{17} -1.82886 q^{18} -0.636483 q^{19} -2.90019 q^{20} +1.17355 q^{21} +0.0358323 q^{22} +1.51728 q^{23} +2.19747 q^{24} +3.41111 q^{25} +5.77309 q^{26} +2.57353 q^{27} -0.534047 q^{28} +9.98302 q^{29} -6.37308 q^{30} -2.19910 q^{31} -1.00000 q^{32} +0.0787404 q^{33} -8.04287 q^{34} +1.54884 q^{35} +1.82886 q^{36} -5.83431 q^{37} +0.636483 q^{38} +12.6862 q^{39} +2.90019 q^{40} -12.1318 q^{41} -1.17355 q^{42} +1.09099 q^{43} -0.0358323 q^{44} -5.30405 q^{45} -1.51728 q^{46} -8.86684 q^{47} -2.19747 q^{48} -6.71479 q^{49} -3.41111 q^{50} -17.6739 q^{51} -5.77309 q^{52} -0.514905 q^{53} -2.57353 q^{54} +0.103921 q^{55} +0.534047 q^{56} +1.39865 q^{57} -9.98302 q^{58} -8.44835 q^{59} +6.37308 q^{60} +0.784207 q^{61} +2.19910 q^{62} -0.976700 q^{63} +1.00000 q^{64} +16.7430 q^{65} -0.0787404 q^{66} -3.14146 q^{67} +8.04287 q^{68} -3.33417 q^{69} -1.54884 q^{70} -1.05356 q^{71} -1.82886 q^{72} +6.67791 q^{73} +5.83431 q^{74} -7.49580 q^{75} -0.636483 q^{76} +0.0191361 q^{77} -12.6862 q^{78} +8.36495 q^{79} -2.90019 q^{80} -11.1418 q^{81} +12.1318 q^{82} -15.6226 q^{83} +1.17355 q^{84} -23.3259 q^{85} -1.09099 q^{86} -21.9374 q^{87} +0.0358323 q^{88} -13.9960 q^{89} +5.30405 q^{90} +3.08310 q^{91} +1.51728 q^{92} +4.83246 q^{93} +8.86684 q^{94} +1.84592 q^{95} +2.19747 q^{96} +11.8852 q^{97} +6.71479 q^{98} -0.0655324 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.19747	−1.26871	−0.634354	−	0.773042i	$-0.718734\pi$
$3$	−2.19747	−1.26871	−0.634354	+	0.773042i	$0.718734\pi$
$4$	1.00000	0.500000
$5$	−2.90019	−1.29700	−0.648502	−	0.761213i	$-0.724604\pi$
$5$	−2.90019	−1.29700	−0.648502	+	0.761213i	$0.724604\pi$
$6$	2.19747	0.897112
$7$	−0.534047	−0.201851	−0.100925	−	0.994894i	$-0.532180\pi$
$7$	−0.534047	−0.201851	−0.100925	+	0.994894i	$0.532180\pi$
$8$	−1.00000	−0.353553
$9$	1.82886	0.609621
$10$	2.90019	0.917121
$11$	−0.0358323	−0.0108039	−0.00540193	−	0.999985i	$-0.501719\pi$
$11$	−0.0358323	−0.0108039	−0.00540193	+	0.999985i	$0.501719\pi$
$12$	−2.19747	−0.634354
$13$	−5.77309	−1.60117	−0.800583	−	0.599222i	$-0.795477\pi$
$13$	−5.77309	−1.60117	−0.800583	+	0.599222i	$0.795477\pi$
$14$	0.534047	0.142730
$15$	6.37308	1.64552
$16$	1.00000	0.250000
$17$	8.04287	1.95068	0.975341	−	0.220701i	$-0.0708346\pi$
$17$	8.04287	1.95068	0.975341	+	0.220701i	$0.0708346\pi$
$18$	−1.82886	−0.431067
$19$	−0.636483	−0.146019	−0.0730096	−	0.997331i	$-0.523260\pi$
$19$	−0.636483	−0.146019	−0.0730096	+	0.997331i	$0.523260\pi$
$20$	−2.90019	−0.648502
$21$	1.17355	0.256090
$22$	0.0358323	0.00763948
$23$	1.51728	0.316374	0.158187	−	0.987409i	$-0.449435\pi$
$23$	1.51728	0.316374	0.158187	+	0.987409i	$0.449435\pi$
$24$	2.19747	0.448556
$25$	3.41111	0.682221
$26$	5.77309	1.13220
$27$	2.57353	0.495277
$28$	−0.534047	−0.100925
$29$	9.98302	1.85380	0.926900	−	0.375308i	$-0.122463\pi$
$29$	9.98302	1.85380	0.926900	+	0.375308i	$0.122463\pi$
$30$	−6.37308	−1.16356
$31$	−2.19910	−0.394970	−0.197485	−	0.980306i	$-0.563277\pi$
$31$	−2.19910	−0.394970	−0.197485	+	0.980306i	$0.563277\pi$
$32$	−1.00000	−0.176777
$33$	0.0787404	0.0137069
$34$	−8.04287	−1.37934
$35$	1.54884	0.261802
$36$	1.82886	0.304811
$37$	−5.83431	−0.959155	−0.479578	−	0.877499i	$-0.659210\pi$
$37$	−5.83431	−0.959155	−0.479578	+	0.877499i	$0.659210\pi$
$38$	0.636483	0.103251
$39$	12.6862	2.03141
$40$	2.90019	0.458560
$41$	−12.1318	−1.89467	−0.947334	−	0.320248i	$-0.896234\pi$
$41$	−12.1318	−1.89467	−0.947334	+	0.320248i	$0.896234\pi$
$42$	−1.17355	−0.181083
$43$	1.09099	0.166374	0.0831870	−	0.996534i	$-0.473490\pi$
$43$	1.09099	0.166374	0.0831870	+	0.996534i	$0.473490\pi$
$44$	−0.0358323	−0.00540193
$45$	−5.30405	−0.790682
$46$	−1.51728	−0.223710
$47$	−8.86684	−1.29336	−0.646681	−	0.762760i	$-0.723844\pi$
$47$	−8.86684	−1.29336	−0.646681	+	0.762760i	$0.723844\pi$
$48$	−2.19747	−0.317177
$49$	−6.71479	−0.959256
$50$	−3.41111	−0.482403
$51$	−17.6739	−2.47485
$52$	−5.77309	−0.800583
$53$	−0.514905	−0.0707276	−0.0353638	−	0.999375i	$-0.511259\pi$
$53$	−0.514905	−0.0707276	−0.0353638	+	0.999375i	$0.511259\pi$
$54$	−2.57353	−0.350214
$55$	0.103921	0.0140126
$56$	0.534047	0.0713651
$57$	1.39865	0.185256
$58$	−9.98302	−1.31083
$59$	−8.44835	−1.09988	−0.549940	−	0.835204i	$-0.685350\pi$
$59$	−8.44835	−1.09988	−0.549940	+	0.835204i	$0.685350\pi$
$60$	6.37308	0.822760
$61$	0.784207	0.100407	0.0502037	−	0.998739i	$-0.484013\pi$
$61$	0.784207	0.100407	0.0502037	+	0.998739i	$0.484013\pi$
$62$	2.19910	0.279286
$63$	−0.976700	−0.123053
$64$	1.00000	0.125000
$65$	16.7430	2.07672
$66$	−0.0787404	−0.00969227
$67$	−3.14146	−0.383790	−0.191895	−	0.981415i	$-0.561463\pi$
$67$	−3.14146	−0.383790	−0.191895	+	0.981415i	$0.561463\pi$
$68$	8.04287	0.975341
$69$	−3.33417	−0.401387
$70$	−1.54884	−0.185122
$71$	−1.05356	−0.125034	−0.0625170	−	0.998044i	$-0.519913\pi$
$71$	−1.05356	−0.125034	−0.0625170	+	0.998044i	$0.519913\pi$
$72$	−1.82886	−0.215534
$73$	6.67791	0.781591	0.390795	−	0.920478i	$-0.372200\pi$
$73$	6.67791	0.781591	0.390795	+	0.920478i	$0.372200\pi$
$74$	5.83431	0.678225
$75$	−7.49580	−0.865540
$76$	−0.636483	−0.0730096
$77$	0.0191361	0.00218077
$78$	−12.6862	−1.43643
$79$	8.36495	0.941130	0.470565	−	0.882365i	$-0.344050\pi$
$79$	8.36495	0.941130	0.470565	+	0.882365i	$0.344050\pi$
$80$	−2.90019	−0.324251
$81$	−11.1418	−1.23798
$82$	12.1318	1.33973
$83$	−15.6226	−1.71480	−0.857399	−	0.514651i	$-0.827921\pi$
$83$	−15.6226	−1.71480	−0.857399	+	0.514651i	$0.827921\pi$
$84$	1.17355	0.128045
$85$	−23.3259	−2.53004
$86$	−1.09099	−0.117644
$87$	−21.9374	−2.35193
$88$	0.0358323	0.00381974
$89$	−13.9960	−1.48357	−0.741785	−	0.670638i	$-0.766021\pi$
$89$	−13.9960	−1.48357	−0.741785	+	0.670638i	$0.766021\pi$
$90$	5.30405	0.559096
$91$	3.08310	0.323197
$92$	1.51728	0.158187
$93$	4.83246	0.501102
$94$	8.86684	0.914545
$95$	1.84592	0.189388
$96$	2.19747	0.224278
$97$	11.8852	1.20676	0.603380	−	0.797454i	$-0.293820\pi$
$97$	11.8852	1.20676	0.603380	+	0.797454i	$0.293820\pi$
$98$	6.71479	0.678297
$99$	−0.0655324	−0.00658626
$100$	3.41111	0.341111
$101$	−8.71155	−0.866831	−0.433416	−	0.901194i	$-0.642692\pi$
$101$	−8.71155	−0.866831	−0.433416	+	0.901194i	$0.642692\pi$
$102$	17.6739	1.74998
$103$	7.30941	0.720217	0.360109	−	0.932910i	$-0.382740\pi$
$103$	7.30941	0.720217	0.360109	+	0.932910i	$0.382740\pi$
$104$	5.77309	0.566098
$105$	−3.40352	−0.332150
$106$	0.514905	0.0500120
$107$	15.0706	1.45693	0.728463	−	0.685085i	$-0.240235\pi$
$107$	15.0706	1.45693	0.728463	+	0.685085i	$0.240235\pi$
$108$	2.57353	0.247638
$109$	−9.99727	−0.957564	−0.478782	−	0.877934i	$-0.658922\pi$
$109$	−9.99727	−0.957564	−0.478782	+	0.877934i	$0.658922\pi$
$110$	−0.103921	−0.00990844
$111$	12.8207	1.21689
$112$	−0.534047	−0.0504627
$113$	11.2209	1.05557	0.527786	−	0.849378i	$-0.323022\pi$
$113$	11.2209	1.05557	0.527786	+	0.849378i	$0.323022\pi$
$114$	−1.39865	−0.130996
$115$	−4.40039	−0.410339
$116$	9.98302	0.926900
$117$	−10.5582	−0.976105
$118$	8.44835	0.777733
$119$	−4.29527	−0.393747
$120$	−6.37308	−0.581780
$121$	−10.9987	−0.999883
$122$	−0.784207	−0.0709987
$123$	26.6592	2.40378
$124$	−2.19910	−0.197485
$125$	4.60809	0.412160
$126$	0.976700	0.0870113
$127$	8.66596	0.768979	0.384490	−	0.923129i	$-0.374377\pi$
$127$	8.66596	0.768979	0.384490	+	0.923129i	$0.374377\pi$
$128$	−1.00000	−0.0883883
$129$	−2.39741	−0.211080
$130$	−16.7430	−1.46846
$131$	−13.5746	−1.18602	−0.593009	−	0.805196i	$-0.702060\pi$
$131$	−13.5746	−1.18602	−0.593009	+	0.805196i	$0.702060\pi$
$132$	0.0787404	0.00685347
$133$	0.339912	0.0294741
$134$	3.14146	0.271380
$135$	−7.46374	−0.642376
$136$	−8.04287	−0.689671
$137$	−11.9731	−1.02293	−0.511464	−	0.859305i	$-0.670897\pi$
$137$	−11.9731	−1.02293	−0.511464	+	0.859305i	$0.670897\pi$
$138$	3.33417	0.283823
$139$	2.72840	0.231420	0.115710	−	0.993283i	$-0.463086\pi$
$139$	2.72840	0.231420	0.115710	+	0.993283i	$0.463086\pi$
$140$	1.54884	0.130901
$141$	19.4846	1.64090
$142$	1.05356	0.0884125
$143$	0.206863	0.0172988
$144$	1.82886	0.152405
$145$	−28.9527	−2.40439
$146$	−6.67791	−0.552668
$147$	14.7555	1.21702
$148$	−5.83431	−0.479578
$149$	7.17958	0.588174	0.294087	−	0.955779i	$-0.404984\pi$
$149$	7.17958	0.588174	0.294087	+	0.955779i	$0.404984\pi$
$150$	7.49580	0.612029
$151$	10.6981	0.870601	0.435300	−	0.900285i	$-0.356642\pi$
$151$	10.6981	0.870601	0.435300	+	0.900285i	$0.356642\pi$
$152$	0.636483	0.0516256
$153$	14.7093	1.18918
$154$	−0.0191361	−0.00154203
$155$	6.37782	0.512279
$156$	12.6862	1.01571
$157$	−17.8791	−1.42691	−0.713455	−	0.700701i	$-0.752871\pi$
$157$	−17.8791	−1.42691	−0.713455	+	0.700701i	$0.752871\pi$
$158$	−8.36495	−0.665480
$159$	1.13149	0.0897327
$160$	2.90019	0.229280
$161$	−0.810298	−0.0638604
$162$	11.1418	0.875386
$163$	−3.87411	−0.303444	−0.151722	−	0.988423i	$-0.548482\pi$
$163$	−3.87411	−0.303444	−0.151722	+	0.988423i	$0.548482\pi$
$164$	−12.1318	−0.947334
$165$	−0.228362	−0.0177780
$166$	15.6226	1.21255
$167$	−11.5535	−0.894039	−0.447019	−	0.894524i	$-0.647514\pi$
$167$	−11.5535	−0.894039	−0.447019	+	0.894524i	$0.647514\pi$
$168$	−1.17355	−0.0905415
$169$	20.3285	1.56373
$170$	23.3259	1.78901
$171$	−1.16404	−0.0890165
$172$	1.09099	0.0831870
$173$	−8.40086	−0.638705	−0.319353	−	0.947636i	$-0.603465\pi$
$173$	−8.40086	−0.638705	−0.319353	+	0.947636i	$0.603465\pi$
$174$	21.9374	1.66307
$175$	−1.82169	−0.137707
$176$	−0.0358323	−0.00270096
$177$	18.5650	1.39543
$178$	13.9960	1.04904
$179$	−19.3003	−1.44257	−0.721285	−	0.692638i	$-0.756448\pi$
$179$	−19.3003	−1.44257	−0.721285	+	0.692638i	$0.756448\pi$
$180$	−5.30405	−0.395341
$181$	0.0193743	0.00144008	0.000720041	−	1.00000i	$-0.499771\pi$
$181$	0.0193743	0.00144008	0.000720041		1.00000i	$0.499771\pi$
$182$	−3.08310	−0.228535
$183$	−1.72327	−0.127388
$184$	−1.51728	−0.111855
$185$	16.9206	1.24403
$186$	−4.83246	−0.354333
$187$	−0.288195	−0.0210749
$188$	−8.86684	−0.646681
$189$	−1.37439	−0.0999720
$190$	−1.84592	−0.133917
$191$	−20.3228	−1.47050	−0.735252	−	0.677794i	$-0.762936\pi$
$191$	−20.3228	−1.47050	−0.735252	+	0.677794i	$0.762936\pi$
$192$	−2.19747	−0.158589
$193$	−13.0219	−0.937340	−0.468670	−	0.883373i	$-0.655267\pi$
$193$	−13.0219	−0.937340	−0.468670	+	0.883373i	$0.655267\pi$
$194$	−11.8852	−0.853308
$195$	−36.7923	−2.63475
$196$	−6.71479	−0.479628
$197$	21.7669	1.55082	0.775412	−	0.631456i	$-0.217542\pi$
$197$	21.7669	1.55082	0.775412	+	0.631456i	$0.217542\pi$
$198$	0.0655324	0.00465719
$199$	−8.22098	−0.582770	−0.291385	−	0.956606i	$-0.594116\pi$
$199$	−8.22098	−0.582770	−0.291385	+	0.956606i	$0.594116\pi$
$200$	−3.41111	−0.241202
$201$	6.90325	0.486918
$202$	8.71155	0.612942
$203$	−5.33140	−0.374191
$204$	−17.6739	−1.23742
$205$	35.1845	2.45739
$206$	−7.30941	−0.509271
$207$	2.77489	0.192868
$208$	−5.77309	−0.400291
$209$	0.0228067	0.00157757
$210$	3.40352	0.234865
$211$	−24.0080	−1.65278	−0.826390	−	0.563099i	$-0.809609\pi$
$211$	−24.0080	−1.65278	−0.826390	+	0.563099i	$0.809609\pi$
$212$	−0.514905	−0.0353638
$213$	2.31516	0.158632
$214$	−15.0706	−1.03020
$215$	−3.16407	−0.215788
$216$	−2.57353	−0.175107
$217$	1.17442	0.0797251
$218$	9.99727	0.677100
$219$	−14.6745	−0.991611
$220$	0.103921	0.00700632
$221$	−46.4322	−3.12337
$222$	−12.8207	−0.860470
$223$	4.99962	0.334799	0.167400	−	0.985889i	$-0.446463\pi$
$223$	4.99962	0.334799	0.167400	+	0.985889i	$0.446463\pi$
$224$	0.534047	0.0356825
$225$	6.23845	0.415897
$226$	−11.2209	−0.746402
$227$	−20.8767	−1.38564	−0.692819	−	0.721111i	$-0.743632\pi$
$227$	−20.8767	−1.38564	−0.692819	+	0.721111i	$0.743632\pi$
$228$	1.39865	0.0926279
$229$	−8.57407	−0.566591	−0.283295	−	0.959033i	$-0.591428\pi$
$229$	−8.57407	−0.566591	−0.283295	+	0.959033i	$0.591428\pi$
$230$	4.40039	0.290153
$231$	−0.0420511	−0.00276676
$232$	−9.98302	−0.655417
$233$	19.0219	1.24616	0.623081	−	0.782157i	$-0.285881\pi$
$233$	19.0219	1.24616	0.623081	+	0.782157i	$0.285881\pi$
$234$	10.5582	0.690210
$235$	25.7155	1.67750
$236$	−8.44835	−0.549940
$237$	−18.3817	−1.19402
$238$	4.29527	0.278421
$239$	20.9744	1.35672	0.678359	−	0.734731i	$-0.262691\pi$
$239$	20.9744	1.35672	0.678359	+	0.734731i	$0.262691\pi$
$240$	6.37308	0.411380
$241$	4.57021	0.294393	0.147197	−	0.989107i	$-0.452975\pi$
$241$	4.57021	0.294393	0.147197	+	0.989107i	$0.452975\pi$
$242$	10.9987	0.707024
$243$	16.7633	1.07536
$244$	0.784207	0.0502037
$245$	19.4742	1.24416
$246$	−26.6592	−1.69973
$247$	3.67447	0.233801
$248$	2.19910	0.139643
$249$	34.3301	2.17558
$250$	−4.60809	−0.291441
$251$	13.3942	0.845432	0.422716	−	0.906262i	$-0.361077\pi$
$251$	13.3942	0.845432	0.422716	+	0.906262i	$0.361077\pi$
$252$	−0.976700	−0.0615263
$253$	−0.0543676	−0.00341806
$254$	−8.66596	−0.543751
$255$	51.2578	3.20989
$256$	1.00000	0.0625000
$257$	−14.7272	−0.918658	−0.459329	−	0.888266i	$-0.651910\pi$
$257$	−14.7272	−0.918658	−0.459329	+	0.888266i	$0.651910\pi$
$258$	2.39741	0.149256
$259$	3.11580	0.193606
$260$	16.7430	1.03836
$261$	18.2576	1.13012
$262$	13.5746	0.838642
$263$	−15.0142	−0.925813	−0.462906	−	0.886407i	$-0.653193\pi$
$263$	−15.0142	−0.925813	−0.462906	+	0.886407i	$0.653193\pi$
$264$	−0.0787404	−0.00484613
$265$	1.49332	0.0917340
$266$	−0.339912	−0.0208413
$267$	30.7557	1.88222
$268$	−3.14146	−0.191895
$269$	2.92602	0.178403	0.0892013	−	0.996014i	$-0.471569\pi$
$269$	2.92602	0.178403	0.0892013	+	0.996014i	$0.471569\pi$
$270$	7.46374	0.454229
$271$	11.0788	0.672991	0.336495	−	0.941685i	$-0.390758\pi$
$271$	11.0788	0.672991	0.336495	+	0.941685i	$0.390758\pi$
$272$	8.04287	0.487671
$273$	−6.77501	−0.410042
$274$	11.9731	0.723319
$275$	−0.122228	−0.00737062
$276$	−3.33417	−0.200693
$277$	8.18281	0.491658	0.245829	−	0.969313i	$-0.420940\pi$
$277$	8.18281	0.491658	0.245829	+	0.969313i	$0.420940\pi$
$278$	−2.72840	−0.163638
$279$	−4.02186	−0.240782
$280$	−1.54884	−0.0925608
$281$	3.19110	0.190365	0.0951826	−	0.995460i	$-0.469657\pi$
$281$	3.19110	0.190365	0.0951826	+	0.995460i	$0.469657\pi$
$282$	−19.4846	−1.16029
$283$	22.0333	1.30974	0.654872	−	0.755740i	$-0.272723\pi$
$283$	22.0333	1.30974	0.654872	+	0.755740i	$0.272723\pi$
$284$	−1.05356	−0.0625170
$285$	−4.05636	−0.240278
$286$	−0.206863	−0.0122321
$287$	6.47895	0.382440
$288$	−1.82886	−0.107767
$289$	47.6878	2.80516
$290$	28.9527	1.70016
$291$	−26.1174	−1.53103
$292$	6.67791	0.390795
$293$	3.10844	0.181597	0.0907984	−	0.995869i	$-0.471058\pi$
$293$	3.10844	0.181597	0.0907984	+	0.995869i	$0.471058\pi$
$294$	−14.7555	−0.860561
$295$	24.5018	1.42655
$296$	5.83431	0.339113
$297$	−0.0922157	−0.00535090
$298$	−7.17958	−0.415902
$299$	−8.75937	−0.506568
$300$	−7.49580	−0.432770
$301$	−0.582638	−0.0335827
$302$	−10.6981	−0.615608
$303$	19.1433	1.09976
$304$	−0.636483	−0.0365048
$305$	−2.27435	−0.130229
$306$	−14.7093	−0.840876
$307$	10.3935	0.593189	0.296594	−	0.955004i	$-0.404149\pi$
$307$	10.3935	0.593189	0.296594	+	0.955004i	$0.404149\pi$
$308$	0.0191361	0.00109038
$309$	−16.0622	−0.913746
$310$	−6.37782	−0.362236
$311$	−2.34485	−0.132964	−0.0664821	−	0.997788i	$-0.521178\pi$
$311$	−2.34485	−0.132964	−0.0664821	+	0.997788i	$0.521178\pi$
$312$	−12.6862	−0.718213
$313$	14.8452	0.839102	0.419551	−	0.907732i	$-0.362188\pi$
$313$	14.8452	0.839102	0.419551	+	0.907732i	$0.362188\pi$
$314$	17.8791	1.00898
$315$	2.83262	0.159600
$316$	8.36495	0.470565
$317$	11.4118	0.640952	0.320476	−	0.947257i	$-0.396157\pi$
$317$	11.4118	0.640952	0.320476	+	0.947257i	$0.396157\pi$
$318$	−1.13149	−0.0634506
$319$	−0.357715	−0.0200282
$320$	−2.90019	−0.162126
$321$	−33.1171	−1.84841
$322$	0.810298	0.0451561
$323$	−5.11915	−0.284837
$324$	−11.1418	−0.618992
$325$	−19.6926	−1.09235
$326$	3.87411	0.214567
$327$	21.9687	1.21487
$328$	12.1318	0.669866
$329$	4.73531	0.261066
$330$	0.228362	0.0125709
$331$	10.2369	0.562672	0.281336	−	0.959609i	$-0.409222\pi$
$331$	10.2369	0.562672	0.281336	+	0.959609i	$0.409222\pi$
$332$	−15.6226	−0.857399
$333$	−10.6702	−0.584722
$334$	11.5535	0.632181
$335$	9.11082	0.497777
$336$	1.17355	0.0640225
$337$	5.36124	0.292045	0.146023	−	0.989281i	$-0.453353\pi$
$337$	5.36124	0.292045	0.146023	+	0.989281i	$0.453353\pi$
$338$	−20.3285	−1.10573
$339$	−24.6575	−1.33921
$340$	−23.3259	−1.26502
$341$	0.0787989	0.00426720
$342$	1.16404	0.0629441
$343$	7.32435	0.395478
$344$	−1.09099	−0.0588221
$345$	9.66973	0.520600
$346$	8.40086	0.451633
$347$	−12.7875	−0.686467	−0.343234	−	0.939250i	$-0.611522\pi$
$347$	−12.7875	−0.686467	−0.343234	+	0.939250i	$0.611522\pi$
$348$	−21.9374	−1.17597
$349$	−11.2482	−0.602100	−0.301050	−	0.953608i	$-0.597337\pi$
$349$	−11.2482	−0.602100	−0.301050	+	0.953608i	$0.597337\pi$
$350$	1.82169	0.0973735
$351$	−14.8572	−0.793020
$352$	0.0358323	0.00190987
$353$	15.7207	0.836728	0.418364	−	0.908280i	$-0.362604\pi$
$353$	15.7207	0.836728	0.418364	+	0.908280i	$0.362604\pi$
$354$	−18.5650	−0.986717
$355$	3.05551	0.162170
$356$	−13.9960	−0.741785
$357$	9.43872	0.499550
$358$	19.3003	1.02005
$359$	9.67944	0.510861	0.255431	−	0.966827i	$-0.417783\pi$
$359$	9.67944	0.510861	0.255431	+	0.966827i	$0.417783\pi$
$360$	5.30405	0.279548
$361$	−18.5949	−0.978678
$362$	−0.0193743	−0.00101829
$363$	24.1693	1.26856
$364$	3.08310	0.161598
$365$	−19.3672	−1.01373
$366$	1.72327	0.0900767
$367$	14.2691	0.744841	0.372421	−	0.928064i	$-0.378528\pi$
$367$	14.2691	0.744841	0.372421	+	0.928064i	$0.378528\pi$
$368$	1.51728	0.0790936
$369$	−22.1874	−1.15503
$370$	−16.9206	−0.879661
$371$	0.274983	0.0142764
$372$	4.83246	0.250551
$373$	−0.205136	−0.0106215	−0.00531077	−	0.999986i	$-0.501690\pi$
$373$	−0.205136	−0.0106215	−0.00531077	+	0.999986i	$0.501690\pi$
$374$	0.288195	0.0149022
$375$	−10.1261	−0.522911
$376$	8.86684	0.457273
$377$	−57.6328	−2.96824
$378$	1.37439	0.0706909
$379$	26.7629	1.37472	0.687360	−	0.726317i	$-0.258769\pi$
$379$	26.7629	1.37472	0.687360	+	0.726317i	$0.258769\pi$
$380$	1.84592	0.0946938
$381$	−19.0432	−0.975611
$382$	20.3228	1.03980
$383$	21.7865	1.11324	0.556618	−	0.830768i	$-0.312099\pi$
$383$	21.7865	1.11324	0.556618	+	0.830768i	$0.312099\pi$
$384$	2.19747	0.112139
$385$	−0.0554985	−0.00282846
$386$	13.0219	0.662800
$387$	1.99527	0.101425
$388$	11.8852	0.603380
$389$	−32.7036	−1.65814	−0.829068	−	0.559147i	$-0.811129\pi$
$389$	−32.7036	−1.65814	−0.829068	+	0.559147i	$0.811129\pi$
$390$	36.7923	1.86305
$391$	12.2033	0.617146
$392$	6.71479	0.339148
$393$	29.8297	1.50471
$394$	−21.7669	−1.09660
$395$	−24.2599	−1.22065
$396$	−0.0655324	−0.00329313
$397$	2.16998	0.108908	0.0544541	−	0.998516i	$-0.482658\pi$
$397$	2.16998	0.108908	0.0544541	+	0.998516i	$0.482658\pi$
$398$	8.22098	0.412080
$399$	−0.746946	−0.0373941
$400$	3.41111	0.170555
$401$	9.36089	0.467461	0.233730	−	0.972301i	$-0.424907\pi$
$401$	9.36089	0.467461	0.233730	+	0.972301i	$0.424907\pi$
$402$	−6.90325	−0.344303
$403$	12.6956	0.632413
$404$	−8.71155	−0.433416
$405$	32.3135	1.60567
$406$	5.33140	0.264593
$407$	0.209057	0.0103626
$408$	17.6739	0.874991
$409$	16.0110	0.791691	0.395845	−	0.918317i	$-0.370452\pi$
$409$	16.0110	0.791691	0.395845	+	0.918317i	$0.370452\pi$
$410$	−35.1845	−1.73764
$411$	26.3104	1.29780
$412$	7.30941	0.360109
$413$	4.51182	0.222012
$414$	−2.77489	−0.136379
$415$	45.3084	2.22410
$416$	5.77309	0.283049
$417$	−5.99556	−0.293604
$418$	−0.0228067	−0.00111551
$419$	−3.93556	−0.192265	−0.0961324	−	0.995369i	$-0.530647\pi$
$419$	−3.93556	−0.192265	−0.0961324	+	0.995369i	$0.530647\pi$
$420$	−3.40352	−0.166075
$421$	−25.7510	−1.25503	−0.627513	−	0.778606i	$-0.715927\pi$
$421$	−25.7510	−1.25503	−0.627513	+	0.778606i	$0.715927\pi$
$422$	24.0080	1.16869
$423$	−16.2163	−0.788461
$424$	0.514905	0.0250060
$425$	27.4351	1.33080
$426$	−2.31516	−0.112170
$427$	−0.418803	−0.0202673
$428$	15.0706	0.728463
$429$	−0.454575	−0.0219471
$430$	3.16407	0.152585
$431$	19.1385	0.921868	0.460934	−	0.887434i	$-0.347514\pi$
$431$	19.1385	0.921868	0.460934	+	0.887434i	$0.347514\pi$
$432$	2.57353	0.123819
$433$	2.67515	0.128559	0.0642797	−	0.997932i	$-0.479525\pi$
$433$	2.67515	0.128559	0.0642797	+	0.997932i	$0.479525\pi$
$434$	−1.17442	−0.0563742
$435$	63.6225	3.05047
$436$	−9.99727	−0.478782
$437$	−0.965722	−0.0461967
$438$	14.6745	0.701175
$439$	18.5386	0.884799	0.442399	−	0.896818i	$-0.354127\pi$
$439$	18.5386	0.884799	0.442399	+	0.896818i	$0.354127\pi$
$440$	−0.103921	−0.00495422
$441$	−12.2804	−0.584783
$442$	46.4322	2.20855
$443$	−6.50337	−0.308985	−0.154492	−	0.987994i	$-0.549374\pi$
$443$	−6.50337	−0.308985	−0.154492	+	0.987994i	$0.549374\pi$
$444$	12.8207	0.608444
$445$	40.5910	1.92420
$446$	−4.99962	−0.236739
$447$	−15.7769	−0.746221
$448$	−0.534047	−0.0252314
$449$	−18.2078	−0.859279	−0.429640	−	0.903000i	$-0.641359\pi$
$449$	−18.2078	−0.859279	−0.429640	+	0.903000i	$0.641359\pi$
$450$	−6.23845	−0.294083
$451$	0.434710	0.0204697
$452$	11.2209	0.527786
$453$	−23.5088	−1.10454
$454$	20.8767	0.979794
$455$	−8.94158	−0.419188
$456$	−1.39865	−0.0654978
$457$	6.37047	0.297998	0.148999	−	0.988837i	$-0.452395\pi$
$457$	6.37047	0.297998	0.148999	+	0.988837i	$0.452395\pi$
$458$	8.57407	0.400640
$459$	20.6986	0.966128
$460$	−4.40039	−0.205169
$461$	−6.12265	−0.285160	−0.142580	−	0.989783i	$-0.545540\pi$
$461$	−6.12265	−0.285160	−0.142580	+	0.989783i	$0.545540\pi$
$462$	0.0420511	0.00195639
$463$	22.6965	1.05480	0.527398	−	0.849619i	$-0.323168\pi$
$463$	22.6965	1.05480	0.527398	+	0.849619i	$0.323168\pi$
$464$	9.98302	0.463450
$465$	−14.0150	−0.649932
$466$	−19.0219	−0.881170
$467$	3.16566	0.146489	0.0732446	−	0.997314i	$-0.476665\pi$
$467$	3.16566	0.146489	0.0732446	+	0.997314i	$0.476665\pi$
$468$	−10.5582	−0.488052
$469$	1.67769	0.0774683
$470$	−25.7155	−1.18617
$471$	39.2888	1.81033
$472$	8.44835	0.388867
$473$	−0.0390926	−0.00179748
$474$	18.3817	0.844300
$475$	−2.17111	−0.0996175
$476$	−4.29527	−0.196873
$477$	−0.941691	−0.0431171
$478$	−20.9744	−0.959345
$479$	16.1182	0.736461	0.368230	−	0.929735i	$-0.379964\pi$
$479$	16.1182	0.736461	0.368230	+	0.929735i	$0.379964\pi$
$480$	−6.37308	−0.290890
$481$	33.6820	1.53577
$482$	−4.57021	−0.208167
$483$	1.78060	0.0810203
$484$	−10.9987	−0.499942
$485$	−34.4694	−1.56517
$486$	−16.7633	−0.760396
$487$	6.25784	0.283570	0.141785	−	0.989897i	$-0.454716\pi$
$487$	6.25784	0.283570	0.141785	+	0.989897i	$0.454716\pi$
$488$	−0.784207	−0.0354994
$489$	8.51324	0.384982
$490$	−19.4742	−0.879754
$491$	−3.16227	−0.142711	−0.0713556	−	0.997451i	$-0.522733\pi$
$491$	−3.16227	−0.142711	−0.0713556	+	0.997451i	$0.522733\pi$
$492$	26.6592	1.20189
$493$	80.2921	3.61618
$494$	−3.67447	−0.165322
$495$	0.190057	0.00854241
$496$	−2.19910	−0.0987426
$497$	0.562649	0.0252382
$498$	−34.3301	−1.53837
$499$	−39.9097	−1.78660	−0.893302	−	0.449457i	$-0.851617\pi$
$499$	−39.9097	−1.78660	−0.893302	+	0.449457i	$0.851617\pi$
$500$	4.60809	0.206080
$501$	25.3885	1.13427
$502$	−13.3942	−0.597810
$503$	32.1931	1.43542	0.717711	−	0.696341i	$-0.245190\pi$
$503$	32.1931	1.43542	0.717711	+	0.696341i	$0.245190\pi$
$504$	0.976700	0.0435057
$505$	25.2652	1.12428
$506$	0.0543676	0.00241693
$507$	−44.6713	−1.98392
$508$	8.66596	0.384490
$509$	−35.2623	−1.56297	−0.781486	−	0.623922i	$-0.785538\pi$
$509$	−35.2623	−1.56297	−0.781486	+	0.623922i	$0.785538\pi$
$510$	−51.2578	−2.26973
$511$	−3.56632	−0.157765
$512$	−1.00000	−0.0441942
$513$	−1.63801	−0.0723199
$514$	14.7272	0.649589
$515$	−21.1987	−0.934125
$516$	−2.39741	−0.105540
$517$	0.317720	0.0139733
$518$	−3.11580	−0.136900
$519$	18.4606	0.810331
$520$	−16.7430	−0.734231
$521$	34.8481	1.52672	0.763361	−	0.645972i	$-0.223548\pi$
$521$	34.8481	1.52672	0.763361	+	0.645972i	$0.223548\pi$
$522$	−18.2576	−0.799113
$523$	20.2284	0.884525	0.442262	−	0.896886i	$-0.354176\pi$
$523$	20.2284	0.884525	0.442262	+	0.896886i	$0.354176\pi$
$524$	−13.5746	−0.593009
$525$	4.00311	0.174710
$526$	15.0142	0.654649
$527$	−17.6871	−0.770462
$528$	0.0787404	0.00342673
$529$	−20.6979	−0.899907
$530$	−1.49332	−0.0648658
$531$	−15.4509	−0.670511
$532$	0.339912	0.0147371
$533$	70.0379	3.03368
$534$	−30.7557	−1.33093
$535$	−43.7075	−1.88964
$536$	3.14146	0.135690
$537$	42.4117	1.83020
$538$	−2.92602	−0.126150
$539$	0.240607	0.0103637
$540$	−7.46374	−0.321188
$541$	−2.00353	−0.0861385	−0.0430692	−	0.999072i	$-0.513714\pi$
$541$	−2.00353	−0.0861385	−0.0430692	+	0.999072i	$0.513714\pi$
$542$	−11.0788	−0.475876
$543$	−0.0425745	−0.00182704
$544$	−8.04287	−0.344835
$545$	28.9940	1.24197
$546$	6.77501	0.289944
$547$	28.8152	1.23205	0.616025	−	0.787726i	$-0.288742\pi$
$547$	28.8152	1.23205	0.616025	+	0.787726i	$0.288742\pi$
$548$	−11.9731	−0.511464
$549$	1.43421	0.0612105
$550$	0.122228	0.00521181
$551$	−6.35402	−0.270691
$552$	3.33417	0.141912
$553$	−4.46728	−0.189968
$554$	−8.18281	−0.347654
$555$	−37.1825	−1.57831
$556$	2.72840	0.115710
$557$	−46.1822	−1.95680	−0.978400	−	0.206718i	$-0.933722\pi$
$557$	−46.1822	−1.95680	−0.978400	+	0.206718i	$0.933722\pi$
$558$	4.02186	0.170259
$559$	−6.29836	−0.266392
$560$	1.54884	0.0654504
$561$	0.633299	0.0267379
$562$	−3.19110	−0.134609
$563$	−4.37792	−0.184507	−0.0922536	−	0.995736i	$-0.529407\pi$
$563$	−4.37792	−0.184507	−0.0922536	+	0.995736i	$0.529407\pi$
$564$	19.4846	0.820450
$565$	−32.5427	−1.36908
$566$	−22.0333	−0.926129
$567$	5.95027	0.249888
$568$	1.05356	0.0442062
$569$	14.1426	0.592889	0.296444	−	0.955050i	$-0.404199\pi$
$569$	14.1426	0.592889	0.296444	+	0.955050i	$0.404199\pi$
$570$	4.05636	0.169902
$571$	−21.6920	−0.907780	−0.453890	−	0.891058i	$-0.649964\pi$
$571$	−21.6920	−0.907780	−0.453890	+	0.891058i	$0.649964\pi$
$572$	0.206863	0.00864938
$573$	44.6586	1.86564
$574$	−6.47895	−0.270426
$575$	5.17560	0.215837
$576$	1.82886	0.0762027
$577$	−39.2914	−1.63572	−0.817861	−	0.575416i	$-0.804840\pi$
$577$	−39.2914	−1.63572	−0.817861	+	0.575416i	$0.804840\pi$
$578$	−47.6878	−1.98355
$579$	28.6153	1.18921
$580$	−28.9527	−1.20219
$581$	8.34318	0.346134
$582$	26.1174	1.08260
$583$	0.0184502	0.000764131 0
$584$	−6.67791	−0.276334
$585$	30.6208	1.26601
$586$	−3.10844	−0.128408
$587$	−34.2846	−1.41508	−0.707539	−	0.706674i	$-0.750195\pi$
$587$	−34.2846	−1.41508	−0.707539	+	0.706674i	$0.750195\pi$
$588$	14.7555	0.608508
$589$	1.39969	0.0576733
$590$	−24.5018	−1.00872
$591$	−47.8319	−1.96754
$592$	−5.83431	−0.239789
$593$	−18.2759	−0.750501	−0.375251	−	0.926923i	$-0.622443\pi$
$593$	−18.2759	−0.750501	−0.375251	+	0.926923i	$0.622443\pi$
$594$	0.0922157	0.00378366
$595$	12.4571	0.510692
$596$	7.17958	0.294087
$597$	18.0653	0.739365
$598$	8.75937	0.358197
$599$	17.2035	0.702915	0.351457	−	0.936204i	$-0.385686\pi$
$599$	17.2035	0.702915	0.351457	+	0.936204i	$0.385686\pi$
$600$	7.49580	0.306015
$601$	42.8574	1.74819	0.874096	−	0.485754i	$-0.161455\pi$
$601$	42.8574	1.74819	0.874096	+	0.485754i	$0.161455\pi$
$602$	0.582638	0.0237466
$603$	−5.74530	−0.233967
$604$	10.6981	0.435300
$605$	31.8984	1.29685
$606$	−19.1433	−0.777645
$607$	37.4368	1.51951	0.759756	−	0.650208i	$-0.225318\pi$
$607$	37.4368	1.51951	0.759756	+	0.650208i	$0.225318\pi$
$608$	0.636483	0.0258128
$609$	11.7156	0.474740
$610$	2.27435	0.0920857
$611$	51.1891	2.07089
$612$	14.7093	0.594589
$613$	26.2793	1.06141	0.530705	−	0.847557i	$-0.321927\pi$
$613$	26.2793	1.06141	0.530705	+	0.847557i	$0.321927\pi$
$614$	−10.3935	−0.419448
$615$	−77.3168	−3.11771
$616$	−0.0191361	−0.000771017 0
$617$	−22.6053	−0.910055	−0.455027	−	0.890477i	$-0.650371\pi$
$617$	−22.6053	−0.910055	−0.455027	+	0.890477i	$0.650371\pi$
$618$	16.0622	0.646116
$619$	−22.7073	−0.912683	−0.456342	−	0.889805i	$-0.650841\pi$
$619$	−22.7073	−0.912683	−0.456342	+	0.889805i	$0.650841\pi$
$620$	6.37782	0.256139
$621$	3.90477	0.156693
$622$	2.34485	0.0940199
$623$	7.47451	0.299460
$624$	12.6862	0.507853
$625$	−30.4199	−1.21680
$626$	−14.8452	−0.593335
$627$	−0.0501169	−0.00200148
$628$	−17.8791	−0.713455
$629$	−46.9246	−1.87101
$630$	−2.83262	−0.112854
$631$	10.0409	0.399721	0.199861	−	0.979824i	$-0.435951\pi$
$631$	10.0409	0.399721	0.199861	+	0.979824i	$0.435951\pi$
$632$	−8.36495	−0.332740
$633$	52.7568	2.09690
$634$	−11.4118	−0.453221
$635$	−25.1329	−0.997370
$636$	1.13149	0.0448664
$637$	38.7651	1.53593
$638$	0.357715	0.0141621
$639$	−1.92681	−0.0762234
$640$	2.90019	0.114640
$641$	21.8892	0.864570	0.432285	−	0.901737i	$-0.357707\pi$
$641$	21.8892	0.864570	0.432285	+	0.901737i	$0.357707\pi$
$642$	33.1171	1.30703
$643$	25.3028	0.997843	0.498922	−	0.866647i	$-0.333730\pi$
$643$	25.3028	0.997843	0.498922	+	0.866647i	$0.333730\pi$
$644$	−0.810298	−0.0319302
$645$	6.95294	0.273772
$646$	5.11915	0.201410
$647$	9.84831	0.387177	0.193589	−	0.981083i	$-0.437987\pi$
$647$	9.84831	0.387177	0.193589	+	0.981083i	$0.437987\pi$
$648$	11.1418	0.437693
$649$	0.302724	0.0118829
$650$	19.6926	0.772408
$651$	−2.58076	−0.101148
$652$	−3.87411	−0.151722
$653$	−40.2346	−1.57450	−0.787251	−	0.616632i	$-0.788496\pi$
$653$	−40.2346	−1.57450	−0.787251	+	0.616632i	$0.788496\pi$
$654$	−21.9687	−0.859043
$655$	39.3689	1.53827
$656$	−12.1318	−0.473667
$657$	12.2130	0.476474
$658$	−4.73531	−0.184602
$659$	−11.0579	−0.430755	−0.215377	−	0.976531i	$-0.569098\pi$
$659$	−11.0579	−0.430755	−0.215377	+	0.976531i	$0.569098\pi$
$660$	−0.228362	−0.00888898
$661$	−8.20447	−0.319117	−0.159558	−	0.987188i	$-0.551007\pi$
$661$	−8.20447	−0.319117	−0.159558	+	0.987188i	$0.551007\pi$
$662$	−10.2369	−0.397869
$663$	102.033	3.96264
$664$	15.6226	0.606273
$665$	−0.985810	−0.0382281
$666$	10.6702	0.413461
$667$	15.1470	0.586495
$668$	−11.5535	−0.447019
$669$	−10.9865	−0.424762
$670$	−9.11082	−0.351982
$671$	−0.0280999	−0.00108479
$672$	−1.17355	−0.0452707
$673$	−43.8893	−1.69181	−0.845905	−	0.533334i	$-0.820939\pi$
$673$	−43.8893	−1.69181	−0.845905	+	0.533334i	$0.820939\pi$
$674$	−5.36124	−0.206507
$675$	8.77860	0.337888
$676$	20.3285	0.781866
$677$	−11.9842	−0.460589	−0.230294	−	0.973121i	$-0.573969\pi$
$677$	−11.9842	−0.460589	−0.230294	+	0.973121i	$0.573969\pi$
$678$	24.6575	0.946966
$679$	−6.34726	−0.243586
$680$	23.3259	0.894506
$681$	45.8760	1.75797
$682$	−0.0787989	−0.00301737
$683$	−42.5920	−1.62974	−0.814868	−	0.579647i	$-0.803191\pi$
$683$	−42.5920	−1.62974	−0.814868	+	0.579647i	$0.803191\pi$
$684$	−1.16404	−0.0445082
$685$	34.7242	1.32674
$686$	−7.32435	−0.279645
$687$	18.8412	0.718838
$688$	1.09099	0.0415935
$689$	2.97259	0.113247
$690$	−9.66973	−0.368120
$691$	10.8510	0.412790	0.206395	−	0.978469i	$-0.433827\pi$
$691$	10.8510	0.412790	0.206395	+	0.978469i	$0.433827\pi$
$692$	−8.40086	−0.319353
$693$	0.0349974	0.00132944
$694$	12.7875	0.485405
$695$	−7.91287	−0.300152
$696$	21.9374	0.831534
$697$	−97.5744	−3.69589
$698$	11.2482	0.425749
$699$	−41.7999	−1.58102
$700$	−1.82169	−0.0688535
$701$	43.1256	1.62883	0.814416	−	0.580282i	$-0.197058\pi$
$701$	43.1256	1.62883	0.814416	+	0.580282i	$0.197058\pi$
$702$	14.8572	0.560750
$703$	3.71344	0.140055
$704$	−0.0358323	−0.00135048
$705$	−56.5091	−2.12825
$706$	−15.7207	−0.591656
$707$	4.65238	0.174971
$708$	18.5650	0.697714
$709$	−14.4386	−0.542254	−0.271127	−	0.962544i	$-0.587396\pi$
$709$	−14.4386	−0.542254	−0.271127	+	0.962544i	$0.587396\pi$
$710$	−3.05551	−0.114671
$711$	15.2984	0.573733
$712$	13.9960	0.524521
$713$	−3.33665	−0.124959
$714$	−9.43872	−0.353235
$715$	−0.599942	−0.0224366
$716$	−19.3003	−0.721285
$717$	−46.0905	−1.72128
$718$	−9.67944	−0.361234
$719$	7.93622	0.295971	0.147985	−	0.988990i	$-0.452721\pi$
$719$	7.93622	0.295971	0.147985	+	0.988990i	$0.452721\pi$
$720$	−5.30405	−0.197670
$721$	−3.90357	−0.145377
$722$	18.5949	0.692030
$723$	−10.0429	−0.373499
$724$	0.0193743	0.000720041 0
$725$	34.0531	1.26470
$726$	−24.1693	−0.897008
$727$	−41.5537	−1.54114	−0.770571	−	0.637354i	$-0.780029\pi$
$727$	−41.5537	−1.54114	−0.770571	+	0.637354i	$0.780029\pi$
$728$	−3.08310	−0.114267
$729$	−3.41115	−0.126339
$730$	19.3672	0.716813
$731$	8.77467	0.324543
$732$	−1.72327	−0.0636938
$733$	18.5616	0.685587	0.342794	−	0.939411i	$-0.388627\pi$
$733$	18.5616	0.685587	0.342794	+	0.939411i	$0.388627\pi$
$734$	−14.2691	−0.526682
$735$	−42.7939	−1.57848
$736$	−1.51728	−0.0559276
$737$	0.112566	0.00414641
$738$	22.1874	0.816729
$739$	36.6406	1.34785	0.673923	−	0.738801i	$-0.264608\pi$
$739$	36.6406	1.34785	0.673923	+	0.738801i	$0.264608\pi$
$740$	16.9206	0.622015
$741$	−8.07453	−0.296625
$742$	−0.274983	−0.0100950
$743$	36.3097	1.33208	0.666038	−	0.745918i	$-0.267989\pi$
$743$	36.3097	1.33208	0.666038	+	0.745918i	$0.267989\pi$
$744$	−4.83246	−0.177166
$745$	−20.8222	−0.762865
$746$	0.205136	0.00751056
$747$	−28.5715	−1.04538
$748$	−0.288195	−0.0105374
$749$	−8.04839	−0.294082
$750$	10.1261	0.369754
$751$	−37.0334	−1.35137	−0.675683	−	0.737192i	$-0.736151\pi$
$751$	−37.0334	−1.35137	−0.675683	+	0.737192i	$0.736151\pi$
$752$	−8.86684	−0.323341
$753$	−29.4332	−1.07261
$754$	57.6328	2.09886
$755$	−31.0266	−1.12917
$756$	−1.37439	−0.0499860
$757$	32.6570	1.18694	0.593469	−	0.804857i	$-0.297758\pi$
$757$	32.6570	1.18694	0.593469	+	0.804857i	$0.297758\pi$
$758$	−26.7629	−0.972074
$759$	0.119471	0.00433652
$760$	−1.84592	−0.0669587
$761$	−28.9139	−1.04813	−0.524064	−	0.851679i	$-0.675585\pi$
$761$	−28.9139	−1.04813	−0.524064	+	0.851679i	$0.675585\pi$
$762$	19.0432	0.689861
$763$	5.33901	0.193285
$764$	−20.3228	−0.735252
$765$	−42.6598	−1.54237
$766$	−21.7865	−0.787177
$767$	48.7730	1.76109
$768$	−2.19747	−0.0792943
$769$	3.32086	0.119753	0.0598767	−	0.998206i	$-0.480929\pi$
$769$	3.32086	0.119753	0.0598767	+	0.998206i	$0.480929\pi$
$770$	0.0554985	0.00200003
$771$	32.3626	1.16551
$772$	−13.0219	−0.468670
$773$	−24.8968	−0.895476	−0.447738	−	0.894165i	$-0.647770\pi$
$773$	−24.8968	−0.895476	−0.447738	+	0.894165i	$0.647770\pi$
$774$	−1.99527	−0.0717184
$775$	−7.50137	−0.269457
$776$	−11.8852	−0.426654
$777$	−6.84687	−0.245630
$778$	32.7036	1.17248
$779$	7.72168	0.276658
$780$	−36.7923	−1.31738
$781$	0.0377514	0.00135085
$782$	−12.2033	−0.436388
$783$	25.6916	0.918144
$784$	−6.71479	−0.239814
$785$	51.8529	1.85071
$786$	−29.8297	−1.06399
$787$	49.9784	1.78154	0.890769	−	0.454456i	$-0.150166\pi$
$787$	49.9784	1.78154	0.890769	+	0.454456i	$0.150166\pi$
$788$	21.7669	0.775412
$789$	32.9931	1.17459
$790$	24.2599	0.863130
$791$	−5.99248	−0.213068
$792$	0.0655324	0.00232859
$793$	−4.52729	−0.160769
$794$	−2.16998	−0.0770097
$795$	−3.28153	−0.116384
$796$	−8.22098	−0.291385
$797$	9.63871	0.341421	0.170710	−	0.985321i	$-0.445394\pi$
$797$	9.63871	0.341421	0.170710	+	0.985321i	$0.445394\pi$
$798$	0.746946	0.0264416
$799$	−71.3149	−2.52294
$800$	−3.41111	−0.120601
$801$	−25.5967	−0.904416
$802$	−9.36089	−0.330545
$803$	−0.239285	−0.00844419
$804$	6.90325	0.243459
$805$	2.35002	0.0828273
$806$	−12.6956	−0.447184
$807$	−6.42983	−0.226341
$808$	8.71155	0.306471
$809$	−25.8067	−0.907315	−0.453657	−	0.891176i	$-0.649881\pi$
$809$	−25.8067	−0.907315	−0.453657	+	0.891176i	$0.649881\pi$
$810$	−32.3135	−1.13538
$811$	−41.0345	−1.44092	−0.720458	−	0.693499i	$-0.756068\pi$
$811$	−41.0345	−1.44092	−0.720458	+	0.693499i	$0.756068\pi$
$812$	−5.33140	−0.187096
$813$	−24.3454	−0.853829
$814$	−0.209057	−0.00732744
$815$	11.2357	0.393568
$816$	−17.6739	−0.618712
$817$	−0.694395	−0.0242938
$818$	−16.0110	−0.559810
$819$	5.63857	0.197028
$820$	35.1845	1.22870
$821$	−4.07622	−0.142261	−0.0711305	−	0.997467i	$-0.522661\pi$
$821$	−4.07622	−0.142261	−0.0711305	+	0.997467i	$0.522661\pi$
$822$	−26.3104	−0.917681
$823$	53.8514	1.87714	0.938570	−	0.345089i	$-0.112151\pi$
$823$	53.8514	1.87714	0.938570	+	0.345089i	$0.112151\pi$
$824$	−7.30941	−0.254635
$825$	0.268592	0.00935117
$826$	−4.51182	−0.156986
$827$	40.6489	1.41350	0.706750	−	0.707463i	$-0.250160\pi$
$827$	40.6489	1.41350	0.706750	+	0.707463i	$0.250160\pi$
$828$	2.77489	0.0964342
$829$	27.1778	0.943923	0.471962	−	0.881619i	$-0.343546\pi$
$829$	27.1778	0.943923	0.471962	+	0.881619i	$0.343546\pi$
$830$	−45.3084	−1.57268
$831$	−17.9815	−0.623770
$832$	−5.77309	−0.200146
$833$	−54.0062	−1.87120
$834$	5.99556	0.207609
$835$	33.5074	1.15957
$836$	0.0228067	0.000788785 0
$837$	−5.65946	−0.195620
$838$	3.93556	0.135952
$839$	50.8330	1.75495	0.877475	−	0.479622i	$-0.159226\pi$
$839$	50.8330	1.75495	0.877475	+	0.479622i	$0.159226\pi$
$840$	3.40352	0.117433
$841$	70.6607	2.43658
$842$	25.7510	0.887437
$843$	−7.01234	−0.241518
$844$	−24.0080	−0.826390
$845$	−58.9566	−2.02817
$846$	16.2163	0.557526
$847$	5.87383	0.201827
$848$	−0.514905	−0.0176819
$849$	−48.4175	−1.66168
$850$	−27.4351	−0.941016
$851$	−8.85227	−0.303452
$852$	2.31516	0.0793159
$853$	5.29235	0.181207	0.0906034	−	0.995887i	$-0.471120\pi$
$853$	5.29235	0.181207	0.0906034	+	0.995887i	$0.471120\pi$
$854$	0.418803	0.0143312
$855$	3.37594	0.115455
$856$	−15.0706	−0.515101
$857$	−7.19077	−0.245632	−0.122816	−	0.992429i	$-0.539193\pi$
$857$	−7.19077	−0.245632	−0.122816	+	0.992429i	$0.539193\pi$
$858$	0.454575	0.0155189
$859$	35.7136	1.21853	0.609266	−	0.792966i	$-0.291464\pi$
$859$	35.7136	1.21853	0.609266	+	0.792966i	$0.291464\pi$
$860$	−3.16407	−0.107894
$861$	−14.2373	−0.485205
$862$	−19.1385	−0.651859
$863$	11.8798	0.404394	0.202197	−	0.979345i	$-0.435192\pi$
$863$	11.8798	0.404394	0.202197	+	0.979345i	$0.435192\pi$
$864$	−2.57353	−0.0875534
$865$	24.3641	0.828404
$866$	−2.67515	−0.0909052
$867$	−104.792	−3.55893
$868$	1.17442	0.0398626
$869$	−0.299736	−0.0101678
$870$	−63.6225	−2.15701
$871$	18.1359	0.614511
$872$	9.99727	0.338550
$873$	21.7364	0.735667
$874$	0.965722	0.0326660
$875$	−2.46094	−0.0831949
$876$	−14.6745	−0.495805
$877$	9.94948	0.335970	0.167985	−	0.985790i	$-0.446274\pi$
$877$	9.94948	0.335970	0.167985	+	0.985790i	$0.446274\pi$
$878$	−18.5386	−0.625647
$879$	−6.83069	−0.230393
$880$	0.103921	0.00350316
$881$	−15.7263	−0.529832	−0.264916	−	0.964271i	$-0.585344\pi$
$881$	−15.7263	−0.529832	−0.264916	+	0.964271i	$0.585344\pi$
$882$	12.2804	0.413504
$883$	−21.8801	−0.736324	−0.368162	−	0.929762i	$-0.620013\pi$
$883$	−21.8801	−0.736324	−0.368162	+	0.929762i	$0.620013\pi$
$884$	−46.4322	−1.56168
$885$	−53.8419	−1.80988
$886$	6.50337	0.218485
$887$	−47.2794	−1.58749	−0.793743	−	0.608253i	$-0.791870\pi$
$887$	−47.2794	−1.58749	−0.793743	+	0.608253i	$0.791870\pi$
$888$	−12.8207	−0.430235
$889$	−4.62803	−0.155219
$890$	−40.5910	−1.36061
$891$	0.399238	0.0133750
$892$	4.99962	0.167400
$893$	5.64360	0.188856
$894$	15.7769	0.527658
$895$	55.9745	1.87102
$896$	0.534047	0.0178413
$897$	19.2484	0.642687
$898$	18.2078	0.607602
$899$	−21.9537	−0.732196
$900$	6.23845	0.207948
$901$	−4.14131	−0.137967
$902$	−0.434710	−0.0144743
$903$	1.28033	0.0426067
$904$	−11.2209	−0.373201
$905$	−0.0561892	−0.00186779
$906$	23.5088	0.781027
$907$	19.4639	0.646288	0.323144	−	0.946350i	$-0.395260\pi$
$907$	19.4639	0.646288	0.323144	+	0.946350i	$0.395260\pi$
$908$	−20.8767	−0.692819
$909$	−15.9322	−0.528439
$910$	8.94158	0.296410
$911$	8.61420	0.285401	0.142701	−	0.989766i	$-0.454421\pi$
$911$	8.61420	0.285401	0.142701	+	0.989766i	$0.454421\pi$
$912$	1.39865	0.0463140
$913$	0.559793	0.0185264
$914$	−6.37047	−0.210717
$915$	4.99781	0.165222
$916$	−8.57407	−0.283295
$917$	7.24948	0.239399
$918$	−20.6986	−0.683156
$919$	38.5408	1.27134	0.635672	−	0.771960i	$-0.280723\pi$
$919$	38.5408	1.27134	0.635672	+	0.771960i	$0.280723\pi$
$920$	4.40039	0.145077
$921$	−22.8394	−0.752584
$922$	6.12265	0.201639
$923$	6.08227	0.200200
$924$	−0.0420511	−0.00138338
$925$	−19.9015	−0.654356
$926$	−22.6965	−0.745853
$927$	13.3679	0.439060
$928$	−9.98302	−0.327709
$929$	−13.8420	−0.454142	−0.227071	−	0.973878i	$-0.572915\pi$
$929$	−13.8420	−0.454142	−0.227071	+	0.973878i	$0.572915\pi$
$930$	14.0150	0.459571
$931$	4.27385	0.140070
$932$	19.0219	0.623081
$933$	5.15273	0.168693
$934$	−3.16566	−0.103583
$935$	0.835820	0.0273342
$936$	10.5582	0.345105
$937$	40.2391	1.31455	0.657277	−	0.753649i	$-0.271708\pi$
$937$	40.2391	1.31455	0.657277	+	0.753649i	$0.271708\pi$
$938$	−1.67769	−0.0547784
$939$	−32.6219	−1.06458
$940$	25.7155	0.838748
$941$	4.82799	0.157388	0.0786939	−	0.996899i	$-0.474925\pi$
$941$	4.82799	0.157388	0.0786939	+	0.996899i	$0.474925\pi$
$942$	−39.2888	−1.28010
$943$	−18.4073	−0.599424
$944$	−8.44835	−0.274970
$945$	3.98599	0.129664
$946$	0.0390926	0.00127101
$947$	−18.2854	−0.594195	−0.297097	−	0.954847i	$-0.596019\pi$
$947$	−18.2854	−0.594195	−0.297097	+	0.954847i	$0.596019\pi$
$948$	−18.3817	−0.597010
$949$	−38.5522	−1.25146
$950$	2.17111	0.0704402
$951$	−25.0771	−0.813181
$952$	4.29527	0.139211
$953$	47.4045	1.53558	0.767791	−	0.640701i	$-0.221356\pi$
$953$	47.4045	1.53558	0.767791	+	0.640701i	$0.221356\pi$
$954$	0.941691	0.0304884
$955$	58.9399	1.90725
$956$	20.9744	0.678359
$957$	0.786067	0.0254099
$958$	−16.1182	−0.520757
$959$	6.39418	0.206479
$960$	6.37308	0.205690
$961$	−26.1639	−0.843998
$962$	−33.6820	−1.08595
$963$	27.5620	0.888173
$964$	4.57021	0.147197
$965$	37.7661	1.21573
$966$	−1.78060	−0.0572900
$967$	−26.1471	−0.840836	−0.420418	−	0.907331i	$-0.638116\pi$
$967$	−26.1471	−0.840836	−0.420418	+	0.907331i	$0.638116\pi$
$968$	10.9987	0.353512
$969$	11.2492	0.361375
$970$	34.4694	1.10675
$971$	−31.0676	−0.997006	−0.498503	−	0.866888i	$-0.666117\pi$
$971$	−31.0676	−0.997006	−0.498503	+	0.866888i	$0.666117\pi$
$972$	16.7633	0.537682
$973$	−1.45709	−0.0467122
$974$	−6.25784	−0.200514
$975$	43.2739	1.38587
$976$	0.784207	0.0251018
$977$	−20.8182	−0.666033	−0.333017	−	0.942921i	$-0.608067\pi$
$977$	−20.8182	−0.666033	−0.333017	+	0.942921i	$0.608067\pi$
$978$	−8.51324	−0.272223
$979$	0.501508	0.0160283
$980$	19.4742	0.622080
$981$	−18.2836	−0.583752
$982$	3.16227	0.100912
$983$	25.6693	0.818723	0.409362	−	0.912372i	$-0.365751\pi$
$983$	25.6693	0.818723	0.409362	+	0.912372i	$0.365751\pi$
$984$	−26.6592	−0.849865
$985$	−63.1280	−2.01143
$986$	−80.2921	−2.55702
$987$	−10.4057	−0.331217
$988$	3.67447	0.116901
$989$	1.65533	0.0526364
$990$	−0.190057	−0.00604039
$991$	18.4834	0.587144	0.293572	−	0.955937i	$-0.405156\pi$
$991$	18.4834	0.587144	0.293572	+	0.955937i	$0.405156\pi$
$992$	2.19910	0.0698216
$993$	−22.4953	−0.713867
$994$	−0.562649	−0.0178461
$995$	23.8424	0.755855
$996$	34.3301	1.08779
$997$	−16.2159	−0.513562	−0.256781	−	0.966470i	$-0.582662\pi$
$997$	−16.2159	−0.513562	−0.256781	+	0.966470i	$0.582662\pi$
$998$	39.9097	1.26332
$999$	−15.0148	−0.475047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.c.1.14	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.c.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.19747 q^{3} +1.00000 q^{4} -2.90019 q^{5} +2.19747 q^{6} -0.534047 q^{7} -1.00000 q^{8} +1.82886 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.19747 q^{3} +1.00000 q^{4} -2.90019 q^{5} +2.19747 q^{6} -0.534047 q^{7} -1.00000 q^{8} +1.82886 q^{9} +2.90019 q^{10} -0.0358323 q^{11} -2.19747 q^{12} -5.77309 q^{13} +0.534047 q^{14} +6.37308 q^{15} +1.00000 q^{16} +8.04287 q^{17} -1.82886 q^{18} -0.636483 q^{19} -2.90019 q^{20} +1.17355 q^{21} +0.0358323 q^{22} +1.51728 q^{23} +2.19747 q^{24} +3.41111 q^{25} +5.77309 q^{26} +2.57353 q^{27} -0.534047 q^{28} +9.98302 q^{29} -6.37308 q^{30} -2.19910 q^{31} -1.00000 q^{32} +0.0787404 q^{33} -8.04287 q^{34} +1.54884 q^{35} +1.82886 q^{36} -5.83431 q^{37} +0.636483 q^{38} +12.6862 q^{39} +2.90019 q^{40} -12.1318 q^{41} -1.17355 q^{42} +1.09099 q^{43} -0.0358323 q^{44} -5.30405 q^{45} -1.51728 q^{46} -8.86684 q^{47} -2.19747 q^{48} -6.71479 q^{49} -3.41111 q^{50} -17.6739 q^{51} -5.77309 q^{52} -0.514905 q^{53} -2.57353 q^{54} +0.103921 q^{55} +0.534047 q^{56} +1.39865 q^{57} -9.98302 q^{58} -8.44835 q^{59} +6.37308 q^{60} +0.784207 q^{61} +2.19910 q^{62} -0.976700 q^{63} +1.00000 q^{64} +16.7430 q^{65} -0.0787404 q^{66} -3.14146 q^{67} +8.04287 q^{68} -3.33417 q^{69} -1.54884 q^{70} -1.05356 q^{71} -1.82886 q^{72} +6.67791 q^{73} +5.83431 q^{74} -7.49580 q^{75} -0.636483 q^{76} +0.0191361 q^{77} -12.6862 q^{78} +8.36495 q^{79} -2.90019 q^{80} -11.1418 q^{81} +12.1318 q^{82} -15.6226 q^{83} +1.17355 q^{84} -23.3259 q^{85} -1.09099 q^{86} -21.9374 q^{87} +0.0358323 q^{88} -13.9960 q^{89} +5.30405 q^{90} +3.08310 q^{91} +1.51728 q^{92} +4.83246 q^{93} +8.86684 q^{94} +1.84592 q^{95} +2.19747 q^{96} +11.8852 q^{97} +6.71479 q^{98} -0.0655324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) \) 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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