LMFDB - Embedded newform 8006.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, 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("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.23032 q^{3} +1.00000 q^{4} +0.193126 q^{5} +3.23032 q^{6} +0.0724171 q^{7} -1.00000 q^{8} +7.43498 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.23032 q^{3} +1.00000 q^{4} +0.193126 q^{5} +3.23032 q^{6} +0.0724171 q^{7} -1.00000 q^{8} +7.43498 q^{9} -0.193126 q^{10} -0.360323 q^{11} -3.23032 q^{12} -5.34812 q^{13} -0.0724171 q^{14} -0.623859 q^{15} +1.00000 q^{16} +2.69708 q^{17} -7.43498 q^{18} -3.65562 q^{19} +0.193126 q^{20} -0.233930 q^{21} +0.360323 q^{22} -8.97245 q^{23} +3.23032 q^{24} -4.96270 q^{25} +5.34812 q^{26} -14.3264 q^{27} +0.0724171 q^{28} -0.516141 q^{29} +0.623859 q^{30} -6.96486 q^{31} -1.00000 q^{32} +1.16396 q^{33} -2.69708 q^{34} +0.0139856 q^{35} +7.43498 q^{36} -1.78186 q^{37} +3.65562 q^{38} +17.2762 q^{39} -0.193126 q^{40} +2.03696 q^{41} +0.233930 q^{42} -8.18436 q^{43} -0.360323 q^{44} +1.43589 q^{45} +8.97245 q^{46} -11.0641 q^{47} -3.23032 q^{48} -6.99476 q^{49} +4.96270 q^{50} -8.71243 q^{51} -5.34812 q^{52} -1.31678 q^{53} +14.3264 q^{54} -0.0695878 q^{55} -0.0724171 q^{56} +11.8088 q^{57} +0.516141 q^{58} +12.8908 q^{59} -0.623859 q^{60} +14.8749 q^{61} +6.96486 q^{62} +0.538419 q^{63} +1.00000 q^{64} -1.03286 q^{65} -1.16396 q^{66} +7.25530 q^{67} +2.69708 q^{68} +28.9839 q^{69} -0.0139856 q^{70} +1.22036 q^{71} -7.43498 q^{72} -0.185753 q^{73} +1.78186 q^{74} +16.0311 q^{75} -3.65562 q^{76} -0.0260936 q^{77} -17.2762 q^{78} -6.47435 q^{79} +0.193126 q^{80} +23.9740 q^{81} -2.03696 q^{82} -13.1729 q^{83} -0.233930 q^{84} +0.520876 q^{85} +8.18436 q^{86} +1.66730 q^{87} +0.360323 q^{88} -16.0750 q^{89} -1.43589 q^{90} -0.387295 q^{91} -8.97245 q^{92} +22.4987 q^{93} +11.0641 q^{94} -0.705996 q^{95} +3.23032 q^{96} +1.45016 q^{97} +6.99476 q^{98} -2.67900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) $ 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * 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
$3$	−3.23032	−1.86503	−0.932514	−	0.361135i	$-0.882389\pi$
$3$	−3.23032	−1.86503	−0.932514	+	0.361135i	$0.882389\pi$
$4$	1.00000	0.500000
$5$	0.193126	0.0863686	0.0431843	−	0.999067i	$-0.486250\pi$
$5$	0.193126	0.0863686	0.0431843	+	0.999067i	$0.486250\pi$
$6$	3.23032	1.31877
$7$	0.0724171	0.0273711	0.0136855	−	0.999906i	$-0.495644\pi$
$7$	0.0724171	0.0273711	0.0136855	+	0.999906i	$0.495644\pi$
$8$	−1.00000	−0.353553
$9$	7.43498	2.47833
$10$	−0.193126	−0.0610718
$11$	−0.360323	−0.108642	−0.0543208	−	0.998524i	$-0.517299\pi$
$11$	−0.360323	−0.108642	−0.0543208	+	0.998524i	$0.517299\pi$
$12$	−3.23032	−0.932514
$13$	−5.34812	−1.48330	−0.741651	−	0.670786i	$-0.765957\pi$
$13$	−5.34812	−1.48330	−0.741651	+	0.670786i	$0.765957\pi$
$14$	−0.0724171	−0.0193543
$15$	−0.623859	−0.161080
$16$	1.00000	0.250000
$17$	2.69708	0.654137	0.327069	−	0.945001i	$-0.393939\pi$
$17$	2.69708	0.654137	0.327069	+	0.945001i	$0.393939\pi$
$18$	−7.43498	−1.75244
$19$	−3.65562	−0.838657	−0.419329	−	0.907835i	$-0.637734\pi$
$19$	−3.65562	−0.838657	−0.419329	+	0.907835i	$0.637734\pi$
$20$	0.193126	0.0431843
$21$	−0.233930	−0.0510478
$22$	0.360323	0.0768212
$23$	−8.97245	−1.87089	−0.935443	−	0.353477i	$-0.884999\pi$
$23$	−8.97245	−1.87089	−0.935443	+	0.353477i	$0.884999\pi$
$24$	3.23032	0.659387
$25$	−4.96270	−0.992540
$26$	5.34812	1.04885
$27$	−14.3264	−2.75712
$28$	0.0724171	0.0136855
$29$	−0.516141	−0.0958450	−0.0479225	−	0.998851i	$-0.515260\pi$
$29$	−0.516141	−0.0958450	−0.0479225	+	0.998851i	$0.515260\pi$
$30$	0.623859	0.113901
$31$	−6.96486	−1.25093	−0.625463	−	0.780254i	$-0.715090\pi$
$31$	−6.96486	−1.25093	−0.625463	+	0.780254i	$0.715090\pi$
$32$	−1.00000	−0.176777
$33$	1.16396	0.202619
$34$	−2.69708	−0.462545
$35$	0.0139856	0.00236400
$36$	7.43498	1.23916
$37$	−1.78186	−0.292936	−0.146468	−	0.989215i	$-0.546791\pi$
$37$	−1.78186	−0.292936	−0.146468	+	0.989215i	$0.546791\pi$
$38$	3.65562	0.593020
$39$	17.2762	2.76640
$40$	−0.193126	−0.0305359
$41$	2.03696	0.318120	0.159060	−	0.987269i	$-0.449154\pi$
$41$	2.03696	0.318120	0.159060	+	0.987269i	$0.449154\pi$
$42$	0.233930	0.0360963
$43$	−8.18436	−1.24810	−0.624052	−	0.781383i	$-0.714514\pi$
$43$	−8.18436	−1.24810	−0.624052	+	0.781383i	$0.714514\pi$
$44$	−0.360323	−0.0543208
$45$	1.43589	0.214050
$46$	8.97245	1.32292
$47$	−11.0641	−1.61387	−0.806933	−	0.590643i	$-0.798874\pi$
$47$	−11.0641	−1.61387	−0.806933	+	0.590643i	$0.798874\pi$
$48$	−3.23032	−0.466257
$49$	−6.99476	−0.999251
$50$	4.96270	0.701832
$51$	−8.71243	−1.21998
$52$	−5.34812	−0.741651
$53$	−1.31678	−0.180873	−0.0904367	−	0.995902i	$-0.528826\pi$
$53$	−1.31678	−0.180873	−0.0904367	+	0.995902i	$0.528826\pi$
$54$	14.3264	1.94958
$55$	−0.0695878	−0.00938322
$56$	−0.0724171	−0.00967714
$57$	11.8088	1.56412
$58$	0.516141	0.0677727
$59$	12.8908	1.67824	0.839120	−	0.543946i	$-0.183070\pi$
$59$	12.8908	1.67824	0.839120	+	0.543946i	$0.183070\pi$
$60$	−0.623859	−0.0805399
$61$	14.8749	1.90453	0.952267	−	0.305267i	$-0.0987457\pi$
$61$	14.8749	1.90453	0.952267	+	0.305267i	$0.0987457\pi$
$62$	6.96486	0.884539
$63$	0.538419	0.0678345
$64$	1.00000	0.125000
$65$	−1.03286	−0.128111
$66$	−1.16396	−0.143274
$67$	7.25530	0.886376	0.443188	−	0.896429i	$-0.353847\pi$
$67$	7.25530	0.886376	0.443188	+	0.896429i	$0.353847\pi$
$68$	2.69708	0.327069
$69$	28.9839	3.48925
$70$	−0.0139856	−0.00167160
$71$	1.22036	0.144830	0.0724150	−	0.997375i	$-0.476929\pi$
$71$	1.22036	0.144830	0.0724150	+	0.997375i	$0.476929\pi$
$72$	−7.43498	−0.876221
$73$	−0.185753	−0.0217408	−0.0108704	−	0.999941i	$-0.503460\pi$
$73$	−0.185753	−0.0217408	−0.0108704	+	0.999941i	$0.503460\pi$
$74$	1.78186	0.207137
$75$	16.0311	1.85111
$76$	−3.65562	−0.419329
$77$	−0.0260936	−0.00297364
$78$	−17.2762	−1.95614
$79$	−6.47435	−0.728422	−0.364211	−	0.931317i	$-0.618661\pi$
$79$	−6.47435	−0.728422	−0.364211	+	0.931317i	$0.618661\pi$
$80$	0.193126	0.0215922
$81$	23.9740	2.66377
$82$	−2.03696	−0.224945
$83$	−13.1729	−1.44592	−0.722958	−	0.690892i	$-0.757218\pi$
$83$	−13.1729	−1.44592	−0.722958	+	0.690892i	$0.757218\pi$
$84$	−0.233930	−0.0255239
$85$	0.520876	0.0564969
$86$	8.18436	0.882542
$87$	1.66730	0.178754
$88$	0.360323	0.0384106
$89$	−16.0750	−1.70394	−0.851971	−	0.523589i	$-0.824593\pi$
$89$	−16.0750	−1.70394	−0.851971	+	0.523589i	$0.824593\pi$
$90$	−1.43589	−0.151356
$91$	−0.387295	−0.0405996
$92$	−8.97245	−0.935443
$93$	22.4987	2.33301
$94$	11.0641	1.14118
$95$	−0.705996	−0.0724337
$96$	3.23032	0.329693
$97$	1.45016	0.147242	0.0736209	−	0.997286i	$-0.476545\pi$
$97$	1.45016	0.147242	0.0736209	+	0.997286i	$0.476545\pi$
$98$	6.99476	0.706577
$99$	−2.67900	−0.269249
$100$	−4.96270	−0.496270
$101$	6.79061	0.675691	0.337845	−	0.941202i	$-0.390302\pi$
$101$	6.79061	0.675691	0.337845	+	0.941202i	$0.390302\pi$
$102$	8.71243	0.862659
$103$	−12.1500	−1.19718	−0.598590	−	0.801056i	$-0.704272\pi$
$103$	−12.1500	−1.19718	−0.598590	+	0.801056i	$0.704272\pi$
$104$	5.34812	0.524427
$105$	−0.0451781	−0.00440893
$106$	1.31678	0.127897
$107$	−5.86276	−0.566774	−0.283387	−	0.959006i	$-0.591458\pi$
$107$	−5.86276	−0.566774	−0.283387	+	0.959006i	$0.591458\pi$
$108$	−14.3264	−1.37856
$109$	−15.8148	−1.51478	−0.757391	−	0.652961i	$-0.773526\pi$
$109$	−15.8148	−1.51478	−0.757391	+	0.652961i	$0.773526\pi$
$110$	0.0695878	0.00663494
$111$	5.75598	0.546334
$112$	0.0724171	0.00684277
$113$	9.59791	0.902895	0.451448	−	0.892298i	$-0.350908\pi$
$113$	9.59791	0.902895	0.451448	+	0.892298i	$0.350908\pi$
$114$	−11.8088	−1.10600
$115$	−1.73282	−0.161586
$116$	−0.516141	−0.0479225
$117$	−39.7632	−3.67611
$118$	−12.8908	−1.18669
$119$	0.195314	0.0179044
$120$	0.623859	0.0569503
$121$	−10.8702	−0.988197
$122$	−14.8749	−1.34671
$123$	−6.58004	−0.593302
$124$	−6.96486	−0.625463
$125$	−1.92406	−0.172093
$126$	−0.538419	−0.0479662
$127$	13.5913	1.20604	0.603018	−	0.797728i	$-0.293965\pi$
$127$	13.5913	1.20604	0.603018	+	0.797728i	$0.293965\pi$
$128$	−1.00000	−0.0883883
$129$	26.4381	2.32775
$130$	1.03286	0.0905880
$131$	−0.968775	−0.0846423	−0.0423212	−	0.999104i	$-0.513475\pi$
$131$	−0.968775	−0.0846423	−0.0423212	+	0.999104i	$0.513475\pi$
$132$	1.16396	0.101310
$133$	−0.264729	−0.0229550
$134$	−7.25530	−0.626762
$135$	−2.76680	−0.238129
$136$	−2.69708	−0.231272
$137$	−4.77812	−0.408223	−0.204111	−	0.978948i	$-0.565430\pi$
$137$	−4.77812	−0.408223	−0.204111	+	0.978948i	$0.565430\pi$
$138$	−28.9839	−2.46727
$139$	−19.0029	−1.61180	−0.805900	−	0.592051i	$-0.798318\pi$
$139$	−19.0029	−1.61180	−0.805900	+	0.592051i	$0.798318\pi$
$140$	0.0139856	0.00118200
$141$	35.7406	3.00990
$142$	−1.22036	−0.102410
$143$	1.92705	0.161148
$144$	7.43498	0.619582
$145$	−0.0996803	−0.00827800
$146$	0.185753	0.0153731
$147$	22.5953	1.86363
$148$	−1.78186	−0.146468
$149$	12.9376	1.05989	0.529946	−	0.848031i	$-0.322212\pi$
$149$	12.9376	1.05989	0.529946	+	0.848031i	$0.322212\pi$
$150$	−16.0311	−1.30894
$151$	2.61632	0.212913	0.106457	−	0.994317i	$-0.466050\pi$
$151$	2.61632	0.212913	0.106457	+	0.994317i	$0.466050\pi$
$152$	3.65562	0.296510
$153$	20.0527	1.62117
$154$	0.0260936	0.00210268
$155$	−1.34510	−0.108041
$156$	17.2762	1.38320
$157$	−5.09684	−0.406772	−0.203386	−	0.979099i	$-0.565195\pi$
$157$	−5.09684	−0.406772	−0.203386	+	0.979099i	$0.565195\pi$
$158$	6.47435	0.515072
$159$	4.25362	0.337334
$160$	−0.193126	−0.0152680
$161$	−0.649759	−0.0512082
$162$	−23.9740	−1.88357
$163$	20.8450	1.63271	0.816355	−	0.577551i	$-0.195992\pi$
$163$	20.8450	1.63271	0.816355	+	0.577551i	$0.195992\pi$
$164$	2.03696	0.159060
$165$	0.224791	0.0175000
$166$	13.1729	1.02242
$167$	1.38142	0.106897	0.0534486	−	0.998571i	$-0.482979\pi$
$167$	1.38142	0.106897	0.0534486	+	0.998571i	$0.482979\pi$
$168$	0.233930	0.0180481
$169$	15.6024	1.20019
$170$	−0.520876	−0.0399494
$171$	−27.1795	−2.07847
$172$	−8.18436	−0.624052
$173$	−11.6138	−0.882979	−0.441489	−	0.897266i	$-0.645550\pi$
$173$	−11.6138	−0.882979	−0.441489	+	0.897266i	$0.645550\pi$
$174$	−1.66730	−0.126398
$175$	−0.359384	−0.0271669
$176$	−0.360323	−0.0271604
$177$	−41.6415	−3.12996
$178$	16.0750	1.20487
$179$	23.2672	1.73907	0.869537	−	0.493869i	$-0.164418\pi$
$179$	23.2672	1.73907	0.869537	+	0.493869i	$0.164418\pi$
$180$	1.43589	0.107025
$181$	9.97058	0.741108	0.370554	−	0.928811i	$-0.379168\pi$
$181$	9.97058	0.741108	0.370554	+	0.928811i	$0.379168\pi$
$182$	0.387295	0.0287082
$183$	−48.0507	−3.55201
$184$	8.97245	0.661458
$185$	−0.344124	−0.0253005
$186$	−22.4987	−1.64969
$187$	−0.971820	−0.0710665
$188$	−11.0641	−0.806933
$189$	−1.03748	−0.0754653
$190$	0.705996	0.0512183
$191$	−5.28625	−0.382500	−0.191250	−	0.981541i	$-0.561254\pi$
$191$	−5.28625	−0.382500	−0.191250	+	0.981541i	$0.561254\pi$
$192$	−3.23032	−0.233128
$193$	−1.62277	−0.116809	−0.0584047	−	0.998293i	$-0.518601\pi$
$193$	−1.62277	−0.116809	−0.0584047	+	0.998293i	$0.518601\pi$
$194$	−1.45016	−0.104116
$195$	3.33648	0.238930
$196$	−6.99476	−0.499625
$197$	−8.48068	−0.604224	−0.302112	−	0.953272i	$-0.597692\pi$
$197$	−8.48068	−0.604224	−0.302112	+	0.953272i	$0.597692\pi$
$198$	2.67900	0.190388
$199$	15.0152	1.06440	0.532201	−	0.846618i	$-0.321365\pi$
$199$	15.0152	1.06440	0.532201	+	0.846618i	$0.321365\pi$
$200$	4.96270	0.350916
$201$	−23.4369	−1.65311
$202$	−6.79061	−0.477785
$203$	−0.0373774	−0.00262338
$204$	−8.71243	−0.609992
$205$	0.393391	0.0274756
$206$	12.1500	0.846534
$207$	−66.7100	−4.63667
$208$	−5.34812	−0.370826
$209$	1.31721	0.0911130
$210$	0.0451781	0.00311758
$211$	−7.18685	−0.494763	−0.247382	−	0.968918i	$-0.579570\pi$
$211$	−7.18685	−0.494763	−0.247382	+	0.968918i	$0.579570\pi$
$212$	−1.31678	−0.0904367
$213$	−3.94215	−0.270112
$214$	5.86276	0.400770
$215$	−1.58061	−0.107797
$216$	14.3264	0.974789
$217$	−0.504375	−0.0342392
$218$	15.8148	1.07111
$219$	0.600044	0.0405472
$220$	−0.0695878	−0.00469161
$221$	−14.4243	−0.970283
$222$	−5.75598	−0.386316
$223$	−18.0020	−1.20550	−0.602751	−	0.797930i	$-0.705929\pi$
$223$	−18.0020	−1.20550	−0.602751	+	0.797930i	$0.705929\pi$
$224$	−0.0724171	−0.00483857
$225$	−36.8976	−2.45984
$226$	−9.59791	−0.638443
$227$	2.22149	0.147446	0.0737228	−	0.997279i	$-0.476512\pi$
$227$	2.22149	0.147446	0.0737228	+	0.997279i	$0.476512\pi$
$228$	11.8088	0.782059
$229$	−15.3023	−1.01120	−0.505601	−	0.862767i	$-0.668729\pi$
$229$	−15.3023	−1.01120	−0.505601	+	0.862767i	$0.668729\pi$
$230$	1.73282	0.114258
$231$	0.0842906	0.00554591
$232$	0.516141	0.0338863
$233$	6.08073	0.398362	0.199181	−	0.979963i	$-0.436172\pi$
$233$	6.08073	0.398362	0.199181	+	0.979963i	$0.436172\pi$
$234$	39.7632	2.59940
$235$	−2.13677	−0.139387
$236$	12.8908	0.839120
$237$	20.9142	1.35853
$238$	−0.195314	−0.0126604
$239$	−10.8361	−0.700929	−0.350465	−	0.936576i	$-0.613976\pi$
$239$	−10.8361	−0.700929	−0.350465	+	0.936576i	$0.613976\pi$
$240$	−0.623859	−0.0402700
$241$	−6.65705	−0.428818	−0.214409	−	0.976744i	$-0.568783\pi$
$241$	−6.65705	−0.428818	−0.214409	+	0.976744i	$0.568783\pi$
$242$	10.8702	0.698761
$243$	−34.4644	−2.21089
$244$	14.8749	0.952267
$245$	−1.35087	−0.0863039
$246$	6.58004	0.419528
$247$	19.5507	1.24398
$248$	6.96486	0.442269
$249$	42.5528	2.69667
$250$	1.92406	0.121688
$251$	−21.6330	−1.36546	−0.682732	−	0.730669i	$-0.739208\pi$
$251$	−21.6330	−1.36546	−0.682732	+	0.730669i	$0.739208\pi$
$252$	0.538419	0.0339172
$253$	3.23298	0.203256
$254$	−13.5913	−0.852796
$255$	−1.68260	−0.105368
$256$	1.00000	0.0625000
$257$	0.0626729	0.00390943	0.00195471	−	0.999998i	$-0.499378\pi$
$257$	0.0626729	0.00390943	0.00195471	+	0.999998i	$0.499378\pi$
$258$	−26.4381	−1.64597
$259$	−0.129037	−0.00801797
$260$	−1.03286	−0.0640554
$261$	−3.83750	−0.237535
$262$	0.968775	0.0598511
$263$	−12.1645	−0.750093	−0.375047	−	0.927006i	$-0.622373\pi$
$263$	−12.1645	−0.750093	−0.375047	+	0.927006i	$0.622373\pi$
$264$	−1.16396	−0.0716368
$265$	−0.254304	−0.0156218
$266$	0.264729	0.0162316
$267$	51.9273	3.17790
$268$	7.25530	0.443188
$269$	−3.56161	−0.217155	−0.108578	−	0.994088i	$-0.534630\pi$
$269$	−3.56161	−0.217155	−0.108578	+	0.994088i	$0.534630\pi$
$270$	2.76680	0.168382
$271$	17.7347	1.07730	0.538652	−	0.842528i	$-0.318934\pi$
$271$	17.7347	1.07730	0.538652	+	0.842528i	$0.318934\pi$
$272$	2.69708	0.163534
$273$	1.25109	0.0757193
$274$	4.77812	0.288657
$275$	1.78818	0.107831
$276$	28.9839	1.74463
$277$	8.58142	0.515608	0.257804	−	0.966197i	$-0.417001\pi$
$277$	8.58142	0.515608	0.257804	+	0.966197i	$0.417001\pi$
$278$	19.0029	1.13972
$279$	−51.7836	−3.10020
$280$	−0.0139856	−0.000835801 0
$281$	−15.4347	−0.920757	−0.460378	−	0.887723i	$-0.652286\pi$
$281$	−15.4347	−0.920757	−0.460378	+	0.887723i	$0.652286\pi$
$282$	−35.7406	−2.12832
$283$	−25.4869	−1.51504	−0.757520	−	0.652813i	$-0.773589\pi$
$283$	−25.4869	−1.51504	−0.757520	+	0.652813i	$0.773589\pi$
$284$	1.22036	0.0724150
$285$	2.28059	0.135091
$286$	−1.92705	−0.113949
$287$	0.147511	0.00870729
$288$	−7.43498	−0.438110
$289$	−9.72577	−0.572104
$290$	0.0996803	0.00585343
$291$	−4.68449	−0.274610
$292$	−0.185753	−0.0108704
$293$	−28.0237	−1.63716	−0.818581	−	0.574391i	$-0.805239\pi$
$293$	−28.0237	−1.63716	−0.818581	+	0.574391i	$0.805239\pi$
$294$	−22.5953	−1.31779
$295$	2.48955	0.144947
$296$	1.78186	0.103569
$297$	5.16214	0.299538
$298$	−12.9376	−0.749457
$299$	47.9858	2.77509
$300$	16.0311	0.925557
$301$	−0.592687	−0.0341619
$302$	−2.61632	−0.150552
$303$	−21.9358	−1.26018
$304$	−3.65562	−0.209664
$305$	2.87273	0.164492
$306$	−20.0527	−1.14634
$307$	7.21560	0.411816	0.205908	−	0.978571i	$-0.433985\pi$
$307$	7.21560	0.411816	0.205908	+	0.978571i	$0.433985\pi$
$308$	−0.0260936	−0.00148682
$309$	39.2486	2.23277
$310$	1.34510	0.0763964
$311$	−13.5478	−0.768227	−0.384113	−	0.923286i	$-0.625493\pi$
$311$	−13.5478	−0.768227	−0.384113	+	0.923286i	$0.625493\pi$
$312$	−17.2762	−0.978070
$313$	−11.4097	−0.644913	−0.322456	−	0.946584i	$-0.604509\pi$
$313$	−11.4097	−0.644913	−0.322456	+	0.946584i	$0.604509\pi$
$314$	5.09684	0.287631
$315$	0.103983	0.00585877
$316$	−6.47435	−0.364211
$317$	3.24475	0.182243	0.0911216	−	0.995840i	$-0.470955\pi$
$317$	3.24475	0.182243	0.0911216	+	0.995840i	$0.470955\pi$
$318$	−4.25362	−0.238531
$319$	0.185978	0.0104128
$320$	0.193126	0.0107961
$321$	18.9386	1.05705
$322$	0.649759	0.0362096
$323$	−9.85949	−0.548597
$324$	23.9740	1.33189
$325$	26.5411	1.47224
$326$	−20.8450	−1.15450
$327$	51.0869	2.82511
$328$	−2.03696	−0.112472
$329$	−0.801230	−0.0441733
$330$	−0.224791	−0.0123743
$331$	−21.5263	−1.18319	−0.591596	−	0.806234i	$-0.701502\pi$
$331$	−21.5263	−1.18319	−0.591596	+	0.806234i	$0.701502\pi$
$332$	−13.1729	−0.722958
$333$	−13.2481	−0.725991
$334$	−1.38142	−0.0755877
$335$	1.40119	0.0765550
$336$	−0.233930	−0.0127620
$337$	−9.38739	−0.511364	−0.255682	−	0.966761i	$-0.582300\pi$
$337$	−9.38739	−0.511364	−0.255682	+	0.966761i	$0.582300\pi$
$338$	−15.6024	−0.848659
$339$	−31.0043	−1.68392
$340$	0.520876	0.0282485
$341$	2.50960	0.135903
$342$	27.1795	1.46970
$343$	−1.01346	−0.0547217
$344$	8.18436	0.441271
$345$	5.59755	0.301362
$346$	11.6138	0.624360
$347$	24.7252	1.32732	0.663658	−	0.748036i	$-0.269003\pi$
$347$	24.7252	1.32732	0.663658	+	0.748036i	$0.269003\pi$
$348$	1.66730	0.0893768
$349$	2.33609	0.125048	0.0625240	−	0.998043i	$-0.480085\pi$
$349$	2.33609	0.125048	0.0625240	+	0.998043i	$0.480085\pi$
$350$	0.359384	0.0192099
$351$	76.6194	4.08964
$352$	0.360323	0.0192053
$353$	−5.22316	−0.278000	−0.139000	−	0.990292i	$-0.544389\pi$
$353$	−5.22316	−0.278000	−0.139000	+	0.990292i	$0.544389\pi$
$354$	41.6415	2.21322
$355$	0.235683	0.0125088
$356$	−16.0750	−0.851971
$357$	−0.630929	−0.0333923
$358$	−23.2672	−1.22971
$359$	−19.8651	−1.04844	−0.524220	−	0.851583i	$-0.675643\pi$
$359$	−19.8651	−1.04844	−0.524220	+	0.851583i	$0.675643\pi$
$360$	−1.43589	−0.0756780
$361$	−5.63643	−0.296654
$362$	−9.97058	−0.524042
$363$	35.1141	1.84301
$364$	−0.387295	−0.0202998
$365$	−0.0358738	−0.00187772
$366$	48.0507	2.51165
$367$	−5.54321	−0.289353	−0.144677	−	0.989479i	$-0.546214\pi$
$367$	−5.54321	−0.289353	−0.144677	+	0.989479i	$0.546214\pi$
$368$	−8.97245	−0.467722
$369$	15.1448	0.788405
$370$	0.344124	0.0178901
$371$	−0.0953573	−0.00495070
$372$	22.4987	1.16651
$373$	32.1800	1.66622	0.833108	−	0.553110i	$-0.186559\pi$
$373$	32.1800	1.66622	0.833108	+	0.553110i	$0.186559\pi$
$374$	0.971820	0.0502516
$375$	6.21533	0.320958
$376$	11.0641	0.570588
$377$	2.76039	0.142167
$378$	1.03748	0.0533620
$379$	−14.0853	−0.723513	−0.361757	−	0.932273i	$-0.617823\pi$
$379$	−14.0853	−0.723513	−0.361757	+	0.932273i	$0.617823\pi$
$380$	−0.705996	−0.0362168
$381$	−43.9044	−2.24929
$382$	5.28625	0.270468
$383$	−4.99944	−0.255459	−0.127730	−	0.991809i	$-0.540769\pi$
$383$	−4.99944	−0.255459	−0.127730	+	0.991809i	$0.540769\pi$
$384$	3.23032	0.164847
$385$	−0.00503935	−0.000256829 0
$386$	1.62277	0.0825967
$387$	−60.8505	−3.09321
$388$	1.45016	0.0736209
$389$	17.5809	0.891386	0.445693	−	0.895186i	$-0.352957\pi$
$389$	17.5809	0.891386	0.445693	+	0.895186i	$0.352957\pi$
$390$	−3.33648	−0.168949
$391$	−24.1994	−1.22382
$392$	6.99476	0.353289
$393$	3.12946	0.157860
$394$	8.48068	0.427251
$395$	−1.25037	−0.0629128
$396$	−2.67900	−0.134625
$397$	31.7715	1.59457	0.797283	−	0.603606i	$-0.206270\pi$
$397$	31.7715	1.59457	0.797283	+	0.603606i	$0.206270\pi$
$398$	−15.0152	−0.752646
$399$	0.855161	0.0428116
$400$	−4.96270	−0.248135
$401$	−3.75991	−0.187761	−0.0938804	−	0.995583i	$-0.529927\pi$
$401$	−3.75991	−0.187761	−0.0938804	+	0.995583i	$0.529927\pi$
$402$	23.4369	1.16893
$403$	37.2489	1.85550
$404$	6.79061	0.337845
$405$	4.63000	0.230067
$406$	0.0373774	0.00185501
$407$	0.642046	0.0318250
$408$	8.71243	0.431329
$409$	24.1786	1.19555	0.597777	−	0.801663i	$-0.296051\pi$
$409$	24.1786	1.19555	0.597777	+	0.801663i	$0.296051\pi$
$410$	−0.393391	−0.0194282
$411$	15.4349	0.761347
$412$	−12.1500	−0.598590
$413$	0.933515	0.0459352
$414$	66.7100	3.27862
$415$	−2.54403	−0.124882
$416$	5.34812	0.262213
$417$	61.3853	3.00605
$418$	−1.31721	−0.0644266
$419$	24.9855	1.22062	0.610310	−	0.792162i	$-0.291045\pi$
$419$	24.9855	1.22062	0.610310	+	0.792162i	$0.291045\pi$
$420$	−0.0451781	−0.00220446
$421$	28.8411	1.40563	0.702815	−	0.711373i	$-0.251926\pi$
$421$	28.8411	1.40563	0.702815	+	0.711373i	$0.251926\pi$
$422$	7.18685	0.349850
$423$	−82.2614	−3.99969
$424$	1.31678	0.0639484
$425$	−13.3848	−0.649258
$426$	3.94215	0.190998
$427$	1.07720	0.0521291
$428$	−5.86276	−0.283387
$429$	−6.22500	−0.300546
$430$	1.58061	0.0762240
$431$	18.4972	0.890977	0.445488	−	0.895288i	$-0.353030\pi$
$431$	18.4972	0.890977	0.445488	+	0.895288i	$0.353030\pi$
$432$	−14.3264	−0.689280
$433$	26.1002	1.25429	0.627147	−	0.778901i	$-0.284222\pi$
$433$	26.1002	1.25429	0.627147	+	0.778901i	$0.284222\pi$
$434$	0.504375	0.0242108
$435$	0.322000	0.0154387
$436$	−15.8148	−0.757391
$437$	32.7999	1.56903
$438$	−0.600044	−0.0286712
$439$	−7.56512	−0.361063	−0.180532	−	0.983569i	$-0.557782\pi$
$439$	−7.56512	−0.361063	−0.180532	+	0.983569i	$0.557782\pi$
$440$	0.0695878	0.00331747
$441$	−52.0059	−2.47647
$442$	14.4243	0.686094
$443$	−19.4770	−0.925379	−0.462690	−	0.886520i	$-0.653116\pi$
$443$	−19.4770	−0.925379	−0.462690	+	0.886520i	$0.653116\pi$
$444$	5.75598	0.273167
$445$	−3.10449	−0.147167
$446$	18.0020	0.852418
$447$	−41.7927	−1.97673
$448$	0.0724171	0.00342139
$449$	−14.0208	−0.661680	−0.330840	−	0.943687i	$-0.607332\pi$
$449$	−14.0208	−0.661680	−0.330840	+	0.943687i	$0.607332\pi$
$450$	36.8976	1.73937
$451$	−0.733965	−0.0345611
$452$	9.59791	0.451448
$453$	−8.45155	−0.397089
$454$	−2.22149	−0.104260
$455$	−0.0747969	−0.00350653
$456$	−11.8088	−0.552999
$457$	2.69680	0.126151	0.0630755	−	0.998009i	$-0.479909\pi$
$457$	2.69680	0.126151	0.0630755	+	0.998009i	$0.479909\pi$
$458$	15.3023	0.715028
$459$	−38.6394	−1.80353
$460$	−1.73282	−0.0807929
$461$	0.0628009	0.00292493	0.00146247	−	0.999999i	$-0.499534\pi$
$461$	0.0628009	0.00292493	0.00146247	+	0.999999i	$0.499534\pi$
$462$	−0.0842906	−0.00392155
$463$	−3.09474	−0.143825	−0.0719123	−	0.997411i	$-0.522910\pi$
$463$	−3.09474	−0.143825	−0.0719123	+	0.997411i	$0.522910\pi$
$464$	−0.516141	−0.0239613
$465$	4.34510	0.201499
$466$	−6.08073	−0.281685
$467$	−10.9831	−0.508239	−0.254119	−	0.967173i	$-0.581786\pi$
$467$	−10.9831	−0.508239	−0.254119	+	0.967173i	$0.581786\pi$
$468$	−39.7632	−1.83805
$469$	0.525407	0.0242611
$470$	2.13677	0.0985618
$471$	16.4644	0.758641
$472$	−12.8908	−0.593347
$473$	2.94902	0.135596
$474$	−20.9142	−0.960623
$475$	18.1418	0.832401
$476$	0.195314	0.00895222
$477$	−9.79022	−0.448264
$478$	10.8361	0.495632
$479$	−9.24527	−0.422427	−0.211214	−	0.977440i	$-0.567742\pi$
$479$	−9.24527	−0.422427	−0.211214	+	0.977440i	$0.567742\pi$
$480$	0.623859	0.0284752
$481$	9.52960	0.434513
$482$	6.65705	0.303220
$483$	2.09893	0.0955046
$484$	−10.8702	−0.494099
$485$	0.280064	0.0127171
$486$	34.4644	1.56334
$487$	20.6573	0.936069	0.468035	−	0.883710i	$-0.344962\pi$
$487$	20.6573	0.936069	0.468035	+	0.883710i	$0.344962\pi$
$488$	−14.8749	−0.673354
$489$	−67.3362	−3.04505
$490$	1.35087	0.0610261
$491$	4.16075	0.187772	0.0938860	−	0.995583i	$-0.470071\pi$
$491$	4.16075	0.187772	0.0938860	+	0.995583i	$0.470071\pi$
$492$	−6.58004	−0.296651
$493$	−1.39207	−0.0626958
$494$	−19.5507	−0.879628
$495$	−0.517384	−0.0232547
$496$	−6.96486	−0.312732
$497$	0.0883748	0.00396415
$498$	−42.5528	−1.90683
$499$	−18.4960	−0.827996	−0.413998	−	0.910278i	$-0.635868\pi$
$499$	−18.4960	−0.827996	−0.413998	+	0.910278i	$0.635868\pi$
$500$	−1.92406	−0.0860465
$501$	−4.46242	−0.199366
$502$	21.6330	0.965529
$503$	−30.8622	−1.37608	−0.688039	−	0.725674i	$-0.741528\pi$
$503$	−30.8622	−1.37608	−0.688039	+	0.725674i	$0.741528\pi$
$504$	−0.538419	−0.0239831
$505$	1.31144	0.0583585
$506$	−3.23298	−0.143724
$507$	−50.4008	−2.23838
$508$	13.5913	0.603018
$509$	35.7483	1.58452	0.792258	−	0.610186i	$-0.208905\pi$
$509$	35.7483	1.58452	0.792258	+	0.610186i	$0.208905\pi$
$510$	1.68260	0.0745067
$511$	−0.0134517	−0.000595069 0
$512$	−1.00000	−0.0441942
$513$	52.3719	2.31228
$514$	−0.0626729	−0.00276438
$515$	−2.34649	−0.103399
$516$	26.4381	1.16387
$517$	3.98666	0.175333
$518$	0.129037	0.00566956
$519$	37.5162	1.64678
$520$	1.03286	0.0452940
$521$	−13.4455	−0.589058	−0.294529	−	0.955643i	$-0.595163\pi$
$521$	−13.4455	−0.589058	−0.294529	+	0.955643i	$0.595163\pi$
$522$	3.83750	0.167963
$523$	40.5863	1.77471	0.887356	−	0.461084i	$-0.152539\pi$
$523$	40.5863	1.77471	0.887356	+	0.461084i	$0.152539\pi$
$524$	−0.968775	−0.0423212
$525$	1.16093	0.0506670
$526$	12.1645	0.530396
$527$	−18.7848	−0.818278
$528$	1.16396	0.0506549
$529$	57.5049	2.50021
$530$	0.254304	0.0110463
$531$	95.8429	4.15923
$532$	−0.264729	−0.0114775
$533$	−10.8939	−0.471868
$534$	−51.9273	−2.24711
$535$	−1.13225	−0.0489515
$536$	−7.25530	−0.313381
$537$	−75.1606	−3.24342
$538$	3.56161	0.153552
$539$	2.52037	0.108560
$540$	−2.76680	−0.119064
$541$	25.8099	1.10965	0.554827	−	0.831966i	$-0.312785\pi$
$541$	25.8099	1.10965	0.554827	+	0.831966i	$0.312785\pi$
$542$	−17.7347	−0.761769
$543$	−32.2082	−1.38219
$544$	−2.69708	−0.115636
$545$	−3.05425	−0.130830
$546$	−1.25109	−0.0535417
$547$	−1.02985	−0.0440332	−0.0220166	−	0.999758i	$-0.507009\pi$
$547$	−1.02985	−0.0440332	−0.0220166	+	0.999758i	$0.507009\pi$
$548$	−4.77812	−0.204111
$549$	110.594	4.72006
$550$	−1.78818	−0.0762481
$551$	1.88682	0.0803811
$552$	−28.9839	−1.23364
$553$	−0.468854	−0.0199377
$554$	−8.58142	−0.364590
$555$	1.11163	0.0471861
$556$	−19.0029	−0.805900
$557$	−30.1201	−1.27623	−0.638115	−	0.769941i	$-0.720286\pi$
$557$	−30.1201	−1.27623	−0.638115	+	0.769941i	$0.720286\pi$
$558$	51.7836	2.19217
$559$	43.7710	1.85131
$560$	0.0139856	0.000591001 0
$561$	3.13929	0.132541
$562$	15.4347	0.651073
$563$	−14.2061	−0.598715	−0.299358	−	0.954141i	$-0.596772\pi$
$563$	−14.2061	−0.598715	−0.299358	+	0.954141i	$0.596772\pi$
$564$	35.7406	1.50495
$565$	1.85361	0.0779818
$566$	25.4869	1.07129
$567$	1.73612	0.0729104
$568$	−1.22036	−0.0512051
$569$	31.0374	1.30116	0.650578	−	0.759439i	$-0.274527\pi$
$569$	31.0374	1.30116	0.650578	+	0.759439i	$0.274527\pi$
$570$	−2.28059	−0.0955236
$571$	−0.886426	−0.0370958	−0.0185479	−	0.999828i	$-0.505904\pi$
$571$	−0.886426	−0.0370958	−0.0185479	+	0.999828i	$0.505904\pi$
$572$	1.92705	0.0805741
$573$	17.0763	0.713372
$574$	−0.147511	−0.00615698
$575$	44.5276	1.85693
$576$	7.43498	0.309791
$577$	−25.2349	−1.05054	−0.525272	−	0.850934i	$-0.676036\pi$
$577$	−25.2349	−1.05054	−0.525272	+	0.850934i	$0.676036\pi$
$578$	9.72577	0.404539
$579$	5.24206	0.217853
$580$	−0.0996803	−0.00413900
$581$	−0.953944	−0.0395763
$582$	4.68449	0.194178
$583$	0.474466	0.0196504
$584$	0.185753	0.00768653
$585$	−7.67931	−0.317500
$586$	28.0237	1.15765
$587$	34.7700	1.43511	0.717556	−	0.696501i	$-0.245261\pi$
$587$	34.7700	1.43511	0.717556	+	0.696501i	$0.245261\pi$
$588$	22.5953	0.931815
$589$	25.4609	1.04910
$590$	−2.48955	−0.102493
$591$	27.3953	1.12689
$592$	−1.78186	−0.0732340
$593$	20.5153	0.842462	0.421231	−	0.906953i	$-0.361598\pi$
$593$	20.5153	0.842462	0.421231	+	0.906953i	$0.361598\pi$
$594$	−5.16214	−0.211805
$595$	0.0377203	0.00154638
$596$	12.9376	0.529946
$597$	−48.5040	−1.98514
$598$	−47.9858	−1.96228
$599$	0.303913	0.0124176	0.00620878	−	0.999981i	$-0.498024\pi$
$599$	0.303913	0.0124176	0.00620878	+	0.999981i	$0.498024\pi$
$600$	−16.0311	−0.654468
$601$	4.63633	0.189120	0.0945600	−	0.995519i	$-0.469856\pi$
$601$	4.63633	0.189120	0.0945600	+	0.995519i	$0.469856\pi$
$602$	0.592687	0.0241561
$603$	53.9430	2.19673
$604$	2.61632	0.106457
$605$	−2.09931	−0.0853492
$606$	21.9358	0.891083
$607$	24.9678	1.01341	0.506706	−	0.862119i	$-0.330863\pi$
$607$	24.9678	1.01341	0.506706	+	0.862119i	$0.330863\pi$
$608$	3.65562	0.148255
$609$	0.120741	0.00489268
$610$	−2.87273	−0.116313
$611$	59.1722	2.39385
$612$	20.0527	0.810583
$613$	11.9780	0.483787	0.241893	−	0.970303i	$-0.422232\pi$
$613$	11.9780	0.483787	0.241893	+	0.970303i	$0.422232\pi$
$614$	−7.21560	−0.291198
$615$	−1.27078	−0.0512427
$616$	0.0260936	0.00105134
$617$	46.9705	1.89096	0.945481	−	0.325677i	$-0.105592\pi$
$617$	46.9705	1.89096	0.945481	+	0.325677i	$0.105592\pi$
$618$	−39.2486	−1.57881
$619$	12.7339	0.511819	0.255910	−	0.966701i	$-0.417625\pi$
$619$	12.7339	0.511819	0.255910	+	0.966701i	$0.417625\pi$
$620$	−1.34510	−0.0540204
$621$	128.543	5.15825
$622$	13.5478	0.543219
$623$	−1.16410	−0.0466387
$624$	17.2762	0.691600
$625$	24.4419	0.977677
$626$	11.4097	0.456022
$627$	−4.25500	−0.169928
$628$	−5.09684	−0.203386
$629$	−4.80581	−0.191620
$630$	−0.103983	−0.00414278
$631$	37.6995	1.50079	0.750397	−	0.660987i	$-0.229862\pi$
$631$	37.6995	1.50079	0.750397	+	0.660987i	$0.229862\pi$
$632$	6.47435	0.257536
$633$	23.2158	0.922747
$634$	−3.24475	−0.128865
$635$	2.62484	0.104164
$636$	4.25362	0.168667
$637$	37.4088	1.48219
$638$	−0.185978	−0.00736293
$639$	9.07334	0.358936
$640$	−0.193126	−0.00763398
$641$	−48.4805	−1.91487	−0.957433	−	0.288657i	$-0.906791\pi$
$641$	−48.4805	−1.91487	−0.957433	+	0.288657i	$0.906791\pi$
$642$	−18.9386	−0.747447
$643$	3.24424	0.127940	0.0639702	−	0.997952i	$-0.479624\pi$
$643$	3.24424	0.127940	0.0639702	+	0.997952i	$0.479624\pi$
$644$	−0.649759	−0.0256041
$645$	5.10589	0.201044
$646$	9.85949	0.387917
$647$	−30.6128	−1.20352	−0.601758	−	0.798679i	$-0.705533\pi$
$647$	−30.6128	−1.20352	−0.601758	+	0.798679i	$0.705533\pi$
$648$	−23.9740	−0.941786
$649$	−4.64486	−0.182327
$650$	−26.5411	−1.04103
$651$	1.62929	0.0638571
$652$	20.8450	0.816355
$653$	−40.0374	−1.56679	−0.783393	−	0.621527i	$-0.786513\pi$
$653$	−40.0374	−1.56679	−0.783393	+	0.621527i	$0.786513\pi$
$654$	−51.0869	−1.99766
$655$	−0.187096	−0.00731044
$656$	2.03696	0.0795300
$657$	−1.38107	−0.0538808
$658$	0.801230	0.0312352
$659$	−27.1507	−1.05764	−0.528821	−	0.848733i	$-0.677366\pi$
$659$	−27.1507	−1.05764	−0.528821	+	0.848733i	$0.677366\pi$
$660$	0.224791	0.00874998
$661$	0.526274	0.0204697	0.0102348	−	0.999948i	$-0.496742\pi$
$661$	0.526274	0.0204697	0.0102348	+	0.999948i	$0.496742\pi$
$662$	21.5263	0.836643
$663$	46.5951	1.80960
$664$	13.1729	0.511208
$665$	−0.0511262	−0.00198259
$666$	13.2481	0.513353
$667$	4.63105	0.179315
$668$	1.38142	0.0534486
$669$	58.1522	2.24829
$670$	−1.40119	−0.0541326
$671$	−5.35977	−0.206911
$672$	0.233930	0.00902406
$673$	19.8427	0.764880	0.382440	−	0.923980i	$-0.375084\pi$
$673$	19.8427	0.764880	0.382440	+	0.923980i	$0.375084\pi$
$674$	9.38739	0.361589
$675$	71.0977	2.73655
$676$	15.6024	0.600093
$677$	28.9509	1.11267	0.556337	−	0.830956i	$-0.312206\pi$
$677$	28.9509	1.11267	0.556337	+	0.830956i	$0.312206\pi$
$678$	31.0043	1.19071
$679$	0.105017	0.00403016
$680$	−0.520876	−0.0199747
$681$	−7.17613	−0.274990
$682$	−2.50960	−0.0960976
$683$	−40.5436	−1.55136	−0.775680	−	0.631127i	$-0.782593\pi$
$683$	−40.5436	−1.55136	−0.775680	+	0.631127i	$0.782593\pi$
$684$	−27.1795	−1.03923
$685$	−0.922781	−0.0352576
$686$	1.01346	0.0386941
$687$	49.4313	1.88592
$688$	−8.18436	−0.312026
$689$	7.04229	0.268290
$690$	−5.59755	−0.213095
$691$	−32.7084	−1.24429	−0.622143	−	0.782904i	$-0.713738\pi$
$691$	−32.7084	−1.24429	−0.622143	+	0.782904i	$0.713738\pi$
$692$	−11.6138	−0.441489
$693$	−0.194005	−0.00736964
$694$	−24.7252	−0.938554
$695$	−3.66995	−0.139209
$696$	−1.66730	−0.0631989
$697$	5.49384	0.208094
$698$	−2.33609	−0.0884223
$699$	−19.6427	−0.742956
$700$	−0.359384	−0.0135835
$701$	−8.87938	−0.335370	−0.167685	−	0.985841i	$-0.553629\pi$
$701$	−8.87938	−0.335370	−0.167685	+	0.985841i	$0.553629\pi$
$702$	−76.6194	−2.89181
$703$	6.51381	0.245673
$704$	−0.360323	−0.0135802
$705$	6.90245	0.259961
$706$	5.22316	0.196576
$707$	0.491756	0.0184944
$708$	−41.6415	−1.56498
$709$	36.5953	1.37437	0.687183	−	0.726484i	$-0.258847\pi$
$709$	36.5953	1.37437	0.687183	+	0.726484i	$0.258847\pi$
$710$	−0.235683	−0.00884503
$711$	−48.1367	−1.80527
$712$	16.0750	0.602435
$713$	62.4919	2.34034
$714$	0.630929	0.0236119
$715$	0.372164	0.0139182
$716$	23.2672	0.869537
$717$	35.0041	1.30725
$718$	19.8651	0.741359
$719$	27.3761	1.02095	0.510477	−	0.859891i	$-0.329469\pi$
$719$	27.3761	1.02095	0.510477	+	0.859891i	$0.329469\pi$
$720$	1.43589	0.0535124
$721$	−0.879871	−0.0327681
$722$	5.63643	0.209766
$723$	21.5044	0.799758
$724$	9.97058	0.370554
$725$	2.56145	0.0951300
$726$	−35.1141	−1.30321
$727$	28.3507	1.05147	0.525734	−	0.850649i	$-0.323791\pi$
$727$	28.3507	1.05147	0.525734	+	0.850649i	$0.323791\pi$
$728$	0.387295	0.0143541
$729$	39.4092	1.45960
$730$	0.0358738	0.00132775
$731$	−22.0739	−0.816431
$732$	−48.0507	−1.77600
$733$	−28.2939	−1.04506	−0.522530	−	0.852621i	$-0.675012\pi$
$733$	−28.2939	−1.04506	−0.522530	+	0.852621i	$0.675012\pi$
$734$	5.54321	0.204604
$735$	4.36374	0.160959
$736$	8.97245	0.330729
$737$	−2.61425	−0.0962972
$738$	−15.1448	−0.557487
$739$	−0.308586	−0.0113515	−0.00567576	−	0.999984i	$-0.501807\pi$
$739$	−0.308586	−0.0113515	−0.00567576	+	0.999984i	$0.501807\pi$
$740$	−0.344124	−0.0126502
$741$	−63.1551	−2.32006
$742$	0.0953573	0.00350068
$743$	2.55507	0.0937364	0.0468682	−	0.998901i	$-0.485076\pi$
$743$	2.55507	0.0937364	0.0468682	+	0.998901i	$0.485076\pi$
$744$	−22.4987	−0.824844
$745$	2.49860	0.0915415
$746$	−32.1800	−1.17819
$747$	−97.9403	−3.58345
$748$	−0.971820	−0.0355333
$749$	−0.424564	−0.0155132
$750$	−6.21533	−0.226952
$751$	−0.915818	−0.0334187	−0.0167093	−	0.999860i	$-0.505319\pi$
$751$	−0.915818	−0.0334187	−0.0167093	+	0.999860i	$0.505319\pi$
$752$	−11.0641	−0.403466
$753$	69.8816	2.54663
$754$	−2.76039	−0.100527
$755$	0.505280	0.0183890
$756$	−1.03748	−0.0377327
$757$	3.87376	0.140794	0.0703971	−	0.997519i	$-0.477573\pi$
$757$	3.87376	0.140794	0.0703971	+	0.997519i	$0.477573\pi$
$758$	14.0853	0.511601
$759$	−10.4436	−0.379078
$760$	0.705996	0.0256092
$761$	−27.8525	−1.00965	−0.504827	−	0.863221i	$-0.668444\pi$
$761$	−27.8525	−1.00965	−0.504827	+	0.863221i	$0.668444\pi$
$762$	43.9044	1.59049
$763$	−1.14526	−0.0414612
$764$	−5.28625	−0.191250
$765$	3.87270	0.140018
$766$	4.99944	0.180637
$767$	−68.9416	−2.48934
$768$	−3.23032	−0.116564
$769$	−24.6071	−0.887353	−0.443677	−	0.896187i	$-0.646326\pi$
$769$	−24.6071	−0.887353	−0.443677	+	0.896187i	$0.646326\pi$
$770$	0.00503935	0.000181605 0
$771$	−0.202454	−0.00729119
$772$	−1.62277	−0.0584047
$773$	18.1808	0.653918	0.326959	−	0.945038i	$-0.393976\pi$
$773$	18.1808	0.653918	0.326959	+	0.945038i	$0.393976\pi$
$774$	60.8505	2.18723
$775$	34.5645	1.24160
$776$	−1.45016	−0.0520578
$777$	0.416831	0.0149537
$778$	−17.5809	−0.630305
$779$	−7.44636	−0.266794
$780$	3.33648	0.119465
$781$	−0.439724	−0.0157346
$782$	24.1994	0.865369
$783$	7.39445	0.264256
$784$	−6.99476	−0.249813
$785$	−0.984333	−0.0351323
$786$	−3.12946	−0.111624
$787$	13.8102	0.492281	0.246141	−	0.969234i	$-0.420837\pi$
$787$	13.8102	0.492281	0.246141	+	0.969234i	$0.420837\pi$
$788$	−8.48068	−0.302112
$789$	39.2952	1.39894
$790$	1.25037	0.0444860
$791$	0.695053	0.0247132
$792$	2.67900	0.0951940
$793$	−79.5527	−2.82500
$794$	−31.7715	−1.12753
$795$	0.821485	0.0291351
$796$	15.0152	0.532201
$797$	1.79764	0.0636756	0.0318378	−	0.999493i	$-0.489864\pi$
$797$	1.79764	0.0636756	0.0318378	+	0.999493i	$0.489864\pi$
$798$	−0.855161	−0.0302724
$799$	−29.8408	−1.05569
$800$	4.96270	0.175458
$801$	−119.517	−4.22292
$802$	3.75991	0.132767
$803$	0.0669313	0.00236195
$804$	−23.4369	−0.826557
$805$	−0.125485	−0.00442278
$806$	−37.2489	−1.31204
$807$	11.5051	0.405000
$808$	−6.79061	−0.238893
$809$	−5.34208	−0.187818	−0.0939088	−	0.995581i	$-0.529936\pi$
$809$	−5.34208	−0.187818	−0.0939088	+	0.995581i	$0.529936\pi$
$810$	−4.63000	−0.162682
$811$	28.9837	1.01775	0.508877	−	0.860839i	$-0.330061\pi$
$811$	28.9837	1.01775	0.508877	+	0.860839i	$0.330061\pi$
$812$	−0.0373774	−0.00131169
$813$	−57.2887	−2.00920
$814$	−0.642046	−0.0225037
$815$	4.02572	0.141015
$816$	−8.71243	−0.304996
$817$	29.9189	1.04673
$818$	−24.1786	−0.845384
$819$	−2.87953	−0.100619
$820$	0.393391	0.0137378
$821$	7.07999	0.247093	0.123547	−	0.992339i	$-0.460573\pi$
$821$	7.07999	0.247093	0.123547	+	0.992339i	$0.460573\pi$
$822$	−15.4349	−0.538353
$823$	−1.96955	−0.0686541	−0.0343271	−	0.999411i	$-0.510929\pi$
$823$	−1.96955	−0.0686541	−0.0343271	+	0.999411i	$0.510929\pi$
$824$	12.1500	0.423267
$825$	−5.77639	−0.201108
$826$	−0.933515	−0.0324811
$827$	52.0453	1.80979	0.904896	−	0.425632i	$-0.139948\pi$
$827$	52.0453	1.80979	0.904896	+	0.425632i	$0.139948\pi$
$828$	−66.7100	−2.31833
$829$	16.3752	0.568734	0.284367	−	0.958716i	$-0.408217\pi$
$829$	16.3752	0.568734	0.284367	+	0.958716i	$0.408217\pi$
$830$	2.54403	0.0883047
$831$	−27.7207	−0.961622
$832$	−5.34812	−0.185413
$833$	−18.8654	−0.653647
$834$	−61.3853	−2.12560
$835$	0.266788	0.00923256
$836$	1.31721	0.0455565
$837$	99.7815	3.44895
$838$	−24.9855	−0.863109
$839$	9.57196	0.330461	0.165230	−	0.986255i	$-0.447163\pi$
$839$	9.57196	0.330461	0.165230	+	0.986255i	$0.447163\pi$
$840$	0.0451781	0.00155879
$841$	−28.7336	−0.990814
$842$	−28.8411	−0.993930
$843$	49.8590	1.71724
$844$	−7.18685	−0.247382
$845$	3.01323	0.103658
$846$	82.2614	2.82821
$847$	−0.787186	−0.0270480
$848$	−1.31678	−0.0452184
$849$	82.3309	2.82559
$850$	13.3848	0.459095
$851$	15.9877	0.548050
$852$	−3.94215	−0.135056
$853$	−50.6967	−1.73582	−0.867911	−	0.496720i	$-0.834537\pi$
$853$	−50.6967	−1.73582	−0.867911	+	0.496720i	$0.834537\pi$
$854$	−1.07720	−0.0368609
$855$	−5.24907	−0.179514
$856$	5.86276	0.200385
$857$	−50.1006	−1.71140	−0.855701	−	0.517470i	$-0.826874\pi$
$857$	−50.1006	−1.71140	−0.855701	+	0.517470i	$0.826874\pi$
$858$	6.22500	0.212518
$859$	−56.2598	−1.91956	−0.959780	−	0.280752i	$-0.909416\pi$
$859$	−56.2598	−1.91956	−0.959780	+	0.280752i	$0.909416\pi$
$860$	−1.58061	−0.0538985
$861$	−0.476507	−0.0162393
$862$	−18.4972	−0.630016
$863$	−3.48269	−0.118552	−0.0592761	−	0.998242i	$-0.518879\pi$
$863$	−3.48269	−0.118552	−0.0592761	+	0.998242i	$0.518879\pi$
$864$	14.3264	0.487394
$865$	−2.24292	−0.0762617
$866$	−26.1002	−0.886920
$867$	31.4174	1.06699
$868$	−0.504375	−0.0171196
$869$	2.33286	0.0791369
$870$	−0.322000	−0.0109168
$871$	−38.8022	−1.31476
$872$	15.8148	0.535557
$873$	10.7819	0.364913
$874$	−32.7999	−1.10947
$875$	−0.139335	−0.00471037
$876$	0.600044	0.0202736
$877$	23.6870	0.799852	0.399926	−	0.916547i	$-0.369036\pi$
$877$	23.6870	0.799852	0.399926	+	0.916547i	$0.369036\pi$
$878$	7.56512	0.255310
$879$	90.5256	3.05335
$880$	−0.0695878	−0.00234581
$881$	23.0599	0.776908	0.388454	−	0.921468i	$-0.373009\pi$
$881$	23.0599	0.776908	0.388454	+	0.921468i	$0.373009\pi$
$882$	52.0059	1.75113
$883$	39.5077	1.32954	0.664770	−	0.747048i	$-0.268529\pi$
$883$	39.5077	1.32954	0.664770	+	0.747048i	$0.268529\pi$
$884$	−14.4243	−0.485142
$885$	−8.04205	−0.270331
$886$	19.4770	0.654342
$887$	−7.85909	−0.263882	−0.131941	−	0.991258i	$-0.542121\pi$
$887$	−7.85909	−0.263882	−0.131941	+	0.991258i	$0.542121\pi$
$888$	−5.75598	−0.193158
$889$	0.984244	0.0330105
$890$	3.10449	0.104063
$891$	−8.63838	−0.289397
$892$	−18.0020	−0.602751
$893$	40.4462	1.35348
$894$	41.7927	1.39776
$895$	4.49351	0.150201
$896$	−0.0724171	−0.00241928
$897$	−155.010	−5.17562
$898$	14.0208	0.467879
$899$	3.59485	0.119895
$900$	−36.8976	−1.22992
$901$	−3.55145	−0.118316
$902$	0.733965	0.0244384
$903$	1.91457	0.0637129
$904$	−9.59791	−0.319222
$905$	1.92558	0.0640085
$906$	8.45155	0.280784
$907$	−51.2285	−1.70102	−0.850508	−	0.525962i	$-0.823705\pi$
$907$	−51.2285	−1.70102	−0.850508	+	0.525962i	$0.823705\pi$
$908$	2.22149	0.0737228
$909$	50.4880	1.67458
$910$	0.0747969	0.00247949
$911$	−2.01140	−0.0666407	−0.0333203	−	0.999445i	$-0.510608\pi$
$911$	−2.01140	−0.0666407	−0.0333203	+	0.999445i	$0.510608\pi$
$912$	11.8088	0.391030
$913$	4.74651	0.157086
$914$	−2.69680	−0.0892022
$915$	−9.27984	−0.306782
$916$	−15.3023	−0.505601
$917$	−0.0701559	−0.00231675
$918$	38.6394	1.27529
$919$	−15.1834	−0.500855	−0.250428	−	0.968135i	$-0.580571\pi$
$919$	−15.1834	−0.500855	−0.250428	+	0.968135i	$0.580571\pi$
$920$	1.73282	0.0571292
$921$	−23.3087	−0.768048
$922$	−0.0628009	−0.00206824
$923$	−6.52663	−0.214827
$924$	0.0842906	0.00277296
$925$	8.84284	0.290751
$926$	3.09474	0.101699
$927$	−90.3353	−2.96700
$928$	0.516141	0.0169432
$929$	33.1451	1.08746	0.543728	−	0.839262i	$-0.317012\pi$
$929$	33.1451	1.08746	0.543728	+	0.839262i	$0.317012\pi$
$930$	−4.34510	−0.142481
$931$	25.5702	0.838029
$932$	6.08073	0.199181
$933$	43.7639	1.43276
$934$	10.9831	0.359379
$935$	−0.187684	−0.00613792
$936$	39.7632	1.29970
$937$	−15.9838	−0.522168	−0.261084	−	0.965316i	$-0.584080\pi$
$937$	−15.9838	−0.522168	−0.261084	+	0.965316i	$0.584080\pi$
$938$	−0.525407	−0.0171552
$939$	36.8569	1.20278
$940$	−2.13677	−0.0696937
$941$	−21.2825	−0.693790	−0.346895	−	0.937904i	$-0.612764\pi$
$941$	−21.2825	−0.693790	−0.346895	+	0.937904i	$0.612764\pi$
$942$	−16.4644	−0.536440
$943$	−18.2765	−0.595166
$944$	12.8908	0.419560
$945$	−0.200364	−0.00651784
$946$	−2.94902	−0.0958808
$947$	−47.4389	−1.54156	−0.770778	−	0.637104i	$-0.780132\pi$
$947$	−47.4389	−1.54156	−0.770778	+	0.637104i	$0.780132\pi$
$948$	20.9142	0.679263
$949$	0.993432	0.0322482
$950$	−18.1418	−0.588596
$951$	−10.4816	−0.339888
$952$	−0.195314	−0.00633018
$953$	−28.9890	−0.939046	−0.469523	−	0.882920i	$-0.655574\pi$
$953$	−28.9890	−0.939046	−0.469523	+	0.882920i	$0.655574\pi$
$954$	9.79022	0.316970
$955$	−1.02091	−0.0330360
$956$	−10.8361	−0.350465
$957$	−0.600768	−0.0194201
$958$	9.24527	0.298701
$959$	−0.346018	−0.0111735
$960$	−0.623859	−0.0201350
$961$	17.5093	0.564817
$962$	−9.52960	−0.307247
$963$	−43.5895	−1.40465
$964$	−6.65705	−0.214409
$965$	−0.313399	−0.0100887
$966$	−2.09893	−0.0675320
$967$	4.92608	0.158412	0.0792060	−	0.996858i	$-0.474762\pi$
$967$	4.92608	0.158412	0.0792060	+	0.996858i	$0.474762\pi$
$968$	10.8702	0.349380
$969$	31.8493	1.02315
$970$	−0.280064	−0.00899232
$971$	−40.4388	−1.29774	−0.648872	−	0.760898i	$-0.724759\pi$
$971$	−40.4388	−1.29774	−0.648872	+	0.760898i	$0.724759\pi$
$972$	−34.4644	−1.10545
$973$	−1.37613	−0.0441167
$974$	−20.6573	−0.661901
$975$	−85.7364	−2.74576
$976$	14.8749	0.476133
$977$	−43.2385	−1.38332	−0.691662	−	0.722222i	$-0.743121\pi$
$977$	−43.2385	−1.38332	−0.691662	+	0.722222i	$0.743121\pi$
$978$	67.3362	2.15317
$979$	5.79218	0.185119
$980$	−1.35087	−0.0431520
$981$	−117.583	−3.75413
$982$	−4.16075	−0.132775
$983$	−14.8646	−0.474106	−0.237053	−	0.971497i	$-0.576181\pi$
$983$	−14.8646	−0.474106	−0.237053	+	0.971497i	$0.576181\pi$
$984$	6.58004	0.209764
$985$	−1.63784	−0.0521860
$986$	1.39207	0.0443326
$987$	2.58823	0.0823843
$988$	19.5507	0.621991
$989$	73.4338	2.33506
$990$	0.517384	0.0164435
$991$	−7.33103	−0.232878	−0.116439	−	0.993198i	$-0.537148\pi$
$991$	−7.33103	−0.232878	−0.116439	+	0.993198i	$0.537148\pi$
$992$	6.96486	0.221135
$993$	69.5369	2.20669
$994$	−0.0883748	−0.00280308
$995$	2.89983	0.0919309
$996$	42.5528	1.34834
$997$	11.2063	0.354906	0.177453	−	0.984129i	$-0.443214\pi$
$997$	11.2063	0.354906	0.177453	+	0.984129i	$0.443214\pi$
$998$	18.4960	0.585482
$999$	25.5277	0.807659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.c.1.5	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.c.1.5	✓	92	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.23032 q^{3} +1.00000 q^{4} +0.193126 q^{5} +3.23032 q^{6} +0.0724171 q^{7} -1.00000 q^{8} +7.43498 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.23032 q^{3} +1.00000 q^{4} +0.193126 q^{5} +3.23032 q^{6} +0.0724171 q^{7} -1.00000 q^{8} +7.43498 q^{9} -0.193126 q^{10} -0.360323 q^{11} -3.23032 q^{12} -5.34812 q^{13} -0.0724171 q^{14} -0.623859 q^{15} +1.00000 q^{16} +2.69708 q^{17} -7.43498 q^{18} -3.65562 q^{19} +0.193126 q^{20} -0.233930 q^{21} +0.360323 q^{22} -8.97245 q^{23} +3.23032 q^{24} -4.96270 q^{25} +5.34812 q^{26} -14.3264 q^{27} +0.0724171 q^{28} -0.516141 q^{29} +0.623859 q^{30} -6.96486 q^{31} -1.00000 q^{32} +1.16396 q^{33} -2.69708 q^{34} +0.0139856 q^{35} +7.43498 q^{36} -1.78186 q^{37} +3.65562 q^{38} +17.2762 q^{39} -0.193126 q^{40} +2.03696 q^{41} +0.233930 q^{42} -8.18436 q^{43} -0.360323 q^{44} +1.43589 q^{45} +8.97245 q^{46} -11.0641 q^{47} -3.23032 q^{48} -6.99476 q^{49} +4.96270 q^{50} -8.71243 q^{51} -5.34812 q^{52} -1.31678 q^{53} +14.3264 q^{54} -0.0695878 q^{55} -0.0724171 q^{56} +11.8088 q^{57} +0.516141 q^{58} +12.8908 q^{59} -0.623859 q^{60} +14.8749 q^{61} +6.96486 q^{62} +0.538419 q^{63} +1.00000 q^{64} -1.03286 q^{65} -1.16396 q^{66} +7.25530 q^{67} +2.69708 q^{68} +28.9839 q^{69} -0.0139856 q^{70} +1.22036 q^{71} -7.43498 q^{72} -0.185753 q^{73} +1.78186 q^{74} +16.0311 q^{75} -3.65562 q^{76} -0.0260936 q^{77} -17.2762 q^{78} -6.47435 q^{79} +0.193126 q^{80} +23.9740 q^{81} -2.03696 q^{82} -13.1729 q^{83} -0.233930 q^{84} +0.520876 q^{85} +8.18436 q^{86} +1.66730 q^{87} +0.360323 q^{88} -16.0750 q^{89} -1.43589 q^{90} -0.387295 q^{91} -8.97245 q^{92} +22.4987 q^{93} +11.0641 q^{94} -0.705996 q^{95} +3.23032 q^{96} +1.45016 q^{97} +6.99476 q^{98} -2.67900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * q^99

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