LMFDB - Embedded newform 6002.2.a.a.1.12

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:	$1$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.68417 q^{3} +1.00000 q^{4} -2.87245 q^{5} -1.68417 q^{6} -3.82153 q^{7} +1.00000 q^{8} -0.163575 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.68417 q^{3} +1.00000 q^{4} -2.87245 q^{5} -1.68417 q^{6} -3.82153 q^{7} +1.00000 q^{8} -0.163575 q^{9} -2.87245 q^{10} -1.07042 q^{11} -1.68417 q^{12} +3.46531 q^{13} -3.82153 q^{14} +4.83769 q^{15} +1.00000 q^{16} -0.673955 q^{17} -0.163575 q^{18} +4.31032 q^{19} -2.87245 q^{20} +6.43610 q^{21} -1.07042 q^{22} +4.95465 q^{23} -1.68417 q^{24} +3.25096 q^{25} +3.46531 q^{26} +5.32799 q^{27} -3.82153 q^{28} +7.29015 q^{29} +4.83769 q^{30} -8.80047 q^{31} +1.00000 q^{32} +1.80276 q^{33} -0.673955 q^{34} +10.9771 q^{35} -0.163575 q^{36} +0.558056 q^{37} +4.31032 q^{38} -5.83617 q^{39} -2.87245 q^{40} -3.02674 q^{41} +6.43610 q^{42} +1.33431 q^{43} -1.07042 q^{44} +0.469860 q^{45} +4.95465 q^{46} -6.99057 q^{47} -1.68417 q^{48} +7.60407 q^{49} +3.25096 q^{50} +1.13505 q^{51} +3.46531 q^{52} -6.99376 q^{53} +5.32799 q^{54} +3.07472 q^{55} -3.82153 q^{56} -7.25932 q^{57} +7.29015 q^{58} +15.0702 q^{59} +4.83769 q^{60} +6.17987 q^{61} -8.80047 q^{62} +0.625105 q^{63} +1.00000 q^{64} -9.95393 q^{65} +1.80276 q^{66} -13.3164 q^{67} -0.673955 q^{68} -8.34446 q^{69} +10.9771 q^{70} +14.1119 q^{71} -0.163575 q^{72} +3.74139 q^{73} +0.558056 q^{74} -5.47516 q^{75} +4.31032 q^{76} +4.09063 q^{77} -5.83617 q^{78} +9.83671 q^{79} -2.87245 q^{80} -8.48252 q^{81} -3.02674 q^{82} +5.75597 q^{83} +6.43610 q^{84} +1.93590 q^{85} +1.33431 q^{86} -12.2778 q^{87} -1.07042 q^{88} -10.3528 q^{89} +0.469860 q^{90} -13.2428 q^{91} +4.95465 q^{92} +14.8215 q^{93} -6.99057 q^{94} -12.3812 q^{95} -1.68417 q^{96} +11.9491 q^{97} +7.60407 q^{98} +0.175093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * 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
$3$	−1.68417	−0.972355	−0.486178	−	0.873860i	$-0.661609\pi$
$3$	−1.68417	−0.972355	−0.486178	+	0.873860i	$0.661609\pi$
$4$	1.00000	0.500000
$5$	−2.87245	−1.28460	−0.642299	−	0.766454i	$-0.722019\pi$
$5$	−2.87245	−1.28460	−0.642299	+	0.766454i	$0.722019\pi$
$6$	−1.68417	−0.687559
$7$	−3.82153	−1.44440	−0.722201	−	0.691684i	$-0.756869\pi$
$7$	−3.82153	−1.44440	−0.722201	+	0.691684i	$0.756869\pi$
$8$	1.00000	0.353553
$9$	−0.163575	−0.0545249
$10$	−2.87245	−0.908348
$11$	−1.07042	−0.322743	−0.161371	−	0.986894i	$-0.551592\pi$
$11$	−1.07042	−0.322743	−0.161371	+	0.986894i	$0.551592\pi$
$12$	−1.68417	−0.486178
$13$	3.46531	0.961105	0.480552	−	0.876966i	$-0.340436\pi$
$13$	3.46531	0.961105	0.480552	+	0.876966i	$0.340436\pi$
$14$	−3.82153	−1.02135
$15$	4.83769	1.24909
$16$	1.00000	0.250000
$17$	−0.673955	−0.163458	−0.0817291	−	0.996655i	$-0.526044\pi$
$17$	−0.673955	−0.163458	−0.0817291	+	0.996655i	$0.526044\pi$
$18$	−0.163575	−0.0385549
$19$	4.31032	0.988856	0.494428	−	0.869218i	$-0.335378\pi$
$19$	4.31032	0.988856	0.494428	+	0.869218i	$0.335378\pi$
$20$	−2.87245	−0.642299
$21$	6.43610	1.40447
$22$	−1.07042	−0.228214
$23$	4.95465	1.03311	0.516557	−	0.856253i	$-0.327213\pi$
$23$	4.95465	1.03311	0.516557	+	0.856253i	$0.327213\pi$
$24$	−1.68417	−0.343780
$25$	3.25096	0.650191
$26$	3.46531	0.679604
$27$	5.32799	1.02537
$28$	−3.82153	−0.722201
$29$	7.29015	1.35375	0.676873	−	0.736100i	$-0.263334\pi$
$29$	7.29015	1.35375	0.676873	+	0.736100i	$0.263334\pi$
$30$	4.83769	0.883237
$31$	−8.80047	−1.58061	−0.790305	−	0.612713i	$-0.790078\pi$
$31$	−8.80047	−1.58061	−0.790305	+	0.612713i	$0.790078\pi$
$32$	1.00000	0.176777
$33$	1.80276	0.313821
$34$	−0.673955	−0.115582
$35$	10.9771	1.85547
$36$	−0.163575	−0.0272624
$37$	0.558056	0.0917439	0.0458720	−	0.998947i	$-0.485393\pi$
$37$	0.558056	0.0917439	0.0458720	+	0.998947i	$0.485393\pi$
$38$	4.31032	0.699227
$39$	−5.83617	−0.934536
$40$	−2.87245	−0.454174
$41$	−3.02674	−0.472698	−0.236349	−	0.971668i	$-0.575951\pi$
$41$	−3.02674	−0.472698	−0.236349	+	0.971668i	$0.575951\pi$
$42$	6.43610	0.993111
$43$	1.33431	0.203481	0.101740	−	0.994811i	$-0.467559\pi$
$43$	1.33431	0.203481	0.101740	+	0.994811i	$0.467559\pi$
$44$	−1.07042	−0.161371
$45$	0.469860	0.0700425
$46$	4.95465	0.730523
$47$	−6.99057	−1.01968	−0.509840	−	0.860269i	$-0.670295\pi$
$47$	−6.99057	−1.01968	−0.509840	+	0.860269i	$0.670295\pi$
$48$	−1.68417	−0.243089
$49$	7.60407	1.08630
$50$	3.25096	0.459755
$51$	1.13505	0.158939
$52$	3.46531	0.480552
$53$	−6.99376	−0.960667	−0.480333	−	0.877086i	$-0.659484\pi$
$53$	−6.99376	−0.960667	−0.480333	+	0.877086i	$0.659484\pi$
$54$	5.32799	0.725048
$55$	3.07472	0.414595
$56$	−3.82153	−0.510673
$57$	−7.25932	−0.961520
$58$	7.29015	0.957243
$59$	15.0702	1.96198	0.980988	−	0.194068i	$-0.0621681\pi$
$59$	15.0702	1.96198	0.980988	+	0.194068i	$0.0621681\pi$
$60$	4.83769	0.624543
$61$	6.17987	0.791252	0.395626	−	0.918412i	$-0.370528\pi$
$61$	6.17987	0.791252	0.395626	+	0.918412i	$0.370528\pi$
$62$	−8.80047	−1.11766
$63$	0.625105	0.0787558
$64$	1.00000	0.125000
$65$	−9.95393	−1.23463
$66$	1.80276	0.221905
$67$	−13.3164	−1.62686	−0.813431	−	0.581662i	$-0.802403\pi$
$67$	−13.3164	−1.62686	−0.813431	+	0.581662i	$0.802403\pi$
$68$	−0.673955	−0.0817291
$69$	−8.34446	−1.00455
$70$	10.9771	1.31202
$71$	14.1119	1.67477	0.837386	−	0.546613i	$-0.184083\pi$
$71$	14.1119	1.67477	0.837386	+	0.546613i	$0.184083\pi$
$72$	−0.163575	−0.0192775
$73$	3.74139	0.437897	0.218948	−	0.975736i	$-0.429737\pi$
$73$	3.74139	0.437897	0.218948	+	0.975736i	$0.429737\pi$
$74$	0.558056	0.0648727
$75$	−5.47516	−0.632217
$76$	4.31032	0.494428
$77$	4.09063	0.466170
$78$	−5.83617	−0.660816
$79$	9.83671	1.10672	0.553358	−	0.832943i	$-0.313346\pi$
$79$	9.83671	1.10672	0.553358	+	0.832943i	$0.313346\pi$
$80$	−2.87245	−0.321149
$81$	−8.48252	−0.942502
$82$	−3.02674	−0.334248
$83$	5.75597	0.631800	0.315900	−	0.948792i	$-0.397694\pi$
$83$	5.75597	0.631800	0.315900	+	0.948792i	$0.397694\pi$
$84$	6.43610	0.702236
$85$	1.93590	0.209978
$86$	1.33431	0.143883
$87$	−12.2778	−1.31632
$88$	−1.07042	−0.114107
$89$	−10.3528	−1.09739	−0.548695	−	0.836023i	$-0.684875\pi$
$89$	−10.3528	−1.09739	−0.548695	+	0.836023i	$0.684875\pi$
$90$	0.469860	0.0495276
$91$	−13.2428	−1.38822
$92$	4.95465	0.516557
$93$	14.8215	1.53692
$94$	−6.99057	−0.721023
$95$	−12.3812	−1.27028
$96$	−1.68417	−0.171890
$97$	11.9491	1.21325	0.606623	−	0.794990i	$-0.292524\pi$
$97$	11.9491	1.21325	0.606623	+	0.794990i	$0.292524\pi$
$98$	7.60407	0.768127
$99$	0.175093	0.0175975
$100$	3.25096	0.325096
$101$	−15.8224	−1.57439	−0.787196	−	0.616703i	$-0.788468\pi$
$101$	−15.8224	−1.57439	−0.787196	+	0.616703i	$0.788468\pi$
$102$	1.13505	0.112387
$103$	9.93578	0.979002	0.489501	−	0.872003i	$-0.337179\pi$
$103$	9.93578	0.979002	0.489501	+	0.872003i	$0.337179\pi$
$104$	3.46531	0.339802
$105$	−18.4874	−1.80418
$106$	−6.99376	−0.679294
$107$	−3.33331	−0.322243	−0.161121	−	0.986935i	$-0.551511\pi$
$107$	−3.33331	−0.322243	−0.161121	+	0.986935i	$0.551511\pi$
$108$	5.32799	0.512687
$109$	−14.1698	−1.35722	−0.678612	−	0.734497i	$-0.737418\pi$
$109$	−14.1698	−1.35722	−0.678612	+	0.734497i	$0.737418\pi$
$110$	3.07472	0.293163
$111$	−0.939861	−0.0892077
$112$	−3.82153	−0.361100
$113$	−9.14173	−0.859982	−0.429991	−	0.902833i	$-0.641483\pi$
$113$	−9.14173	−0.859982	−0.429991	+	0.902833i	$0.641483\pi$
$114$	−7.25932	−0.679897
$115$	−14.2320	−1.32714
$116$	7.29015	0.676873
$117$	−0.566837	−0.0524041
$118$	15.0702	1.38733
$119$	2.57554	0.236099
$120$	4.83769	0.441618
$121$	−9.85421	−0.895837
$122$	6.17987	0.559500
$123$	5.09755	0.459631
$124$	−8.80047	−0.790305
$125$	5.02404	0.449364
$126$	0.625105	0.0556888
$127$	−21.2015	−1.88133	−0.940666	−	0.339334i	$-0.889798\pi$
$127$	−21.2015	−1.88133	−0.940666	+	0.339334i	$0.889798\pi$
$128$	1.00000	0.0883883
$129$	−2.24721	−0.197856
$130$	−9.95393	−0.873017
$131$	−4.08463	−0.356876	−0.178438	−	0.983951i	$-0.557104\pi$
$131$	−4.08463	−0.356876	−0.178438	+	0.983951i	$0.557104\pi$
$132$	1.80276	0.156910
$133$	−16.4720	−1.42831
$134$	−13.3164	−1.15036
$135$	−15.3044	−1.31719
$136$	−0.673955	−0.0577912
$137$	−20.8752	−1.78349	−0.891743	−	0.452541i	$-0.850517\pi$
$137$	−20.8752	−1.78349	−0.891743	+	0.452541i	$0.850517\pi$
$138$	−8.34446	−0.710328
$139$	11.6143	0.985116	0.492558	−	0.870280i	$-0.336062\pi$
$139$	11.6143	0.985116	0.492558	+	0.870280i	$0.336062\pi$
$140$	10.9771	0.927737
$141$	11.7733	0.991491
$142$	14.1119	1.18424
$143$	−3.70933	−0.310190
$144$	−0.163575	−0.0136312
$145$	−20.9406	−1.73902
$146$	3.74139	0.309640
$147$	−12.8065	−1.05626
$148$	0.558056	0.0458720
$149$	1.76361	0.144481	0.0722404	−	0.997387i	$-0.476985\pi$
$149$	1.76361	0.144481	0.0722404	+	0.997387i	$0.476985\pi$
$150$	−5.47516	−0.447045
$151$	−23.1338	−1.88261	−0.941303	−	0.337564i	$-0.890397\pi$
$151$	−23.1338	−1.88261	−0.941303	+	0.337564i	$0.890397\pi$
$152$	4.31032	0.349614
$153$	0.110242	0.00891254
$154$	4.09063	0.329632
$155$	25.2789	2.03045
$156$	−5.83617	−0.467268
$157$	11.2301	0.896259	0.448130	−	0.893969i	$-0.352090\pi$
$157$	11.2301	0.896259	0.448130	+	0.893969i	$0.352090\pi$
$158$	9.83671	0.782567
$159$	11.7787	0.934110
$160$	−2.87245	−0.227087
$161$	−18.9343	−1.49223
$162$	−8.48252	−0.666450
$163$	9.03004	0.707287	0.353643	−	0.935380i	$-0.384943\pi$
$163$	9.03004	0.707287	0.353643	+	0.935380i	$0.384943\pi$
$164$	−3.02674	−0.236349
$165$	−5.17834	−0.403133
$166$	5.75597	0.446750
$167$	−15.4023	−1.19186	−0.595932	−	0.803035i	$-0.703217\pi$
$167$	−15.4023	−1.19186	−0.595932	+	0.803035i	$0.703217\pi$
$168$	6.43610	0.496556
$169$	−0.991605	−0.0762773
$170$	1.93590	0.148477
$171$	−0.705060	−0.0539173
$172$	1.33431	0.101740
$173$	−5.81255	−0.441920	−0.220960	−	0.975283i	$-0.570919\pi$
$173$	−5.81255	−0.441920	−0.220960	+	0.975283i	$0.570919\pi$
$174$	−12.2778	−0.930781
$175$	−12.4236	−0.939137
$176$	−1.07042	−0.0806857
$177$	−25.3808	−1.90774
$178$	−10.3528	−0.775972
$179$	−6.18849	−0.462549	−0.231275	−	0.972889i	$-0.574290\pi$
$179$	−6.18849	−0.462549	−0.231275	+	0.972889i	$0.574290\pi$
$180$	0.469860	0.0350213
$181$	11.5073	0.855331	0.427665	−	0.903937i	$-0.359336\pi$
$181$	11.5073	0.855331	0.427665	+	0.903937i	$0.359336\pi$
$182$	−13.2428	−0.981621
$183$	−10.4080	−0.769378
$184$	4.95465	0.365261
$185$	−1.60299	−0.117854
$186$	14.8215	1.08676
$187$	0.721413	0.0527550
$188$	−6.99057	−0.509840
$189$	−20.3611	−1.48105
$190$	−12.3812	−0.898225
$191$	−0.526412	−0.0380898	−0.0190449	−	0.999819i	$-0.506063\pi$
$191$	−0.526412	−0.0380898	−0.0190449	+	0.999819i	$0.506063\pi$
$192$	−1.68417	−0.121544
$193$	−3.58357	−0.257951	−0.128975	−	0.991648i	$-0.541169\pi$
$193$	−3.58357	−0.257951	−0.128975	+	0.991648i	$0.541169\pi$
$194$	11.9491	0.857894
$195$	16.7641	1.20050
$196$	7.60407	0.543148
$197$	−1.92440	−0.137108	−0.0685541	−	0.997647i	$-0.521839\pi$
$197$	−1.92440	−0.137108	−0.0685541	+	0.997647i	$0.521839\pi$
$198$	0.175093	0.0124433
$199$	−0.345163	−0.0244680	−0.0122340	−	0.999925i	$-0.503894\pi$
$199$	−0.345163	−0.0244680	−0.0122340	+	0.999925i	$0.503894\pi$
$200$	3.25096	0.229877
$201$	22.4271	1.58189
$202$	−15.8224	−1.11326
$203$	−27.8595	−1.95535
$204$	1.13505	0.0794697
$205$	8.69416	0.607227
$206$	9.93578	0.692259
$207$	−0.810454	−0.0563305
$208$	3.46531	0.240276
$209$	−4.61384	−0.319146
$210$	−18.4874	−1.27575
$211$	2.03910	0.140377	0.0701887	−	0.997534i	$-0.477640\pi$
$211$	2.03910	0.140377	0.0701887	+	0.997534i	$0.477640\pi$
$212$	−6.99376	−0.480333
$213$	−23.7668	−1.62847
$214$	−3.33331	−0.227860
$215$	−3.83275	−0.261391
$216$	5.32799	0.362524
$217$	33.6312	2.28304
$218$	−14.1698	−0.959703
$219$	−6.30114	−0.425791
$220$	3.07472	0.207297
$221$	−2.33547	−0.157100
$222$	−0.939861	−0.0630794
$223$	8.82565	0.591009	0.295504	−	0.955341i	$-0.404512\pi$
$223$	8.82565	0.591009	0.295504	+	0.955341i	$0.404512\pi$
$224$	−3.82153	−0.255336
$225$	−0.531774	−0.0354516
$226$	−9.14173	−0.608099
$227$	18.9479	1.25761	0.628807	−	0.777561i	$-0.283543\pi$
$227$	18.9479	1.25761	0.628807	+	0.777561i	$0.283543\pi$
$228$	−7.25932	−0.480760
$229$	−1.50686	−0.0995759	−0.0497880	−	0.998760i	$-0.515855\pi$
$229$	−1.50686	−0.0995759	−0.0497880	+	0.998760i	$0.515855\pi$
$230$	−14.2320	−0.938428
$231$	−6.88931	−0.453283
$232$	7.29015	0.478622
$233$	2.17398	0.142422	0.0712111	−	0.997461i	$-0.477314\pi$
$233$	2.17398	0.142422	0.0712111	+	0.997461i	$0.477314\pi$
$234$	−0.566837	−0.0370553
$235$	20.0801	1.30988
$236$	15.0702	0.980988
$237$	−16.5667	−1.07612
$238$	2.57554	0.166947
$239$	18.4839	1.19563	0.597813	−	0.801636i	$-0.296037\pi$
$239$	18.4839	1.19563	0.597813	+	0.801636i	$0.296037\pi$
$240$	4.83769	0.312271
$241$	14.3543	0.924641	0.462320	−	0.886713i	$-0.347017\pi$
$241$	14.3543	0.924641	0.462320	+	0.886713i	$0.347017\pi$
$242$	−9.85421	−0.633452
$243$	−1.69799	−0.108926
$244$	6.17987	0.395626
$245$	−21.8423	−1.39545
$246$	5.09755	0.325008
$247$	14.9366	0.950395
$248$	−8.80047	−0.558830
$249$	−9.69403	−0.614334
$250$	5.02404	0.317748
$251$	−24.2506	−1.53068	−0.765342	−	0.643623i	$-0.777430\pi$
$251$	−24.2506	−1.53068	−0.765342	+	0.643623i	$0.777430\pi$
$252$	0.625105	0.0393779
$253$	−5.30354	−0.333430
$254$	−21.2015	−1.33030
$255$	−3.26039	−0.204173
$256$	1.00000	0.0625000
$257$	−10.9569	−0.683475	−0.341737	−	0.939795i	$-0.611015\pi$
$257$	−10.9569	−0.683475	−0.341737	+	0.939795i	$0.611015\pi$
$258$	−2.24721	−0.139905
$259$	−2.13263	−0.132515
$260$	−9.95393	−0.617317
$261$	−1.19248	−0.0738129
$262$	−4.08463	−0.252350
$263$	23.4685	1.44713	0.723566	−	0.690255i	$-0.242502\pi$
$263$	23.4685	1.44713	0.723566	+	0.690255i	$0.242502\pi$
$264$	1.80276	0.110952
$265$	20.0892	1.23407
$266$	−16.4720	−1.00996
$267$	17.4358	1.06705
$268$	−13.3164	−0.813431
$269$	27.8252	1.69653	0.848267	−	0.529568i	$-0.177646\pi$
$269$	27.8252	1.69653	0.848267	+	0.529568i	$0.177646\pi$
$270$	−15.3044	−0.931395
$271$	−10.6338	−0.645956	−0.322978	−	0.946406i	$-0.604684\pi$
$271$	−10.6338	−0.645956	−0.322978	+	0.946406i	$0.604684\pi$
$272$	−0.673955	−0.0408645
$273$	22.3031	1.34984
$274$	−20.8752	−1.26112
$275$	−3.47988	−0.209845
$276$	−8.34446	−0.502277
$277$	−17.7173	−1.06453	−0.532265	−	0.846578i	$-0.678659\pi$
$277$	−17.7173	−1.06453	−0.532265	+	0.846578i	$0.678659\pi$
$278$	11.6143	0.696582
$279$	1.43953	0.0861826
$280$	10.9771	0.656009
$281$	7.52845	0.449109	0.224555	−	0.974461i	$-0.427907\pi$
$281$	7.52845	0.449109	0.224555	+	0.974461i	$0.427907\pi$
$282$	11.7733	0.701090
$283$	−11.5501	−0.686580	−0.343290	−	0.939230i	$-0.611541\pi$
$283$	−11.5501	−0.686580	−0.343290	+	0.939230i	$0.611541\pi$
$284$	14.1119	0.837386
$285$	20.8520	1.23517
$286$	−3.70933	−0.219337
$287$	11.5668	0.682766
$288$	−0.163575	−0.00963873
$289$	−16.5458	−0.973281
$290$	−20.9406	−1.22967
$291$	−20.1243	−1.17971
$292$	3.74139	0.218948
$293$	−7.43820	−0.434544	−0.217272	−	0.976111i	$-0.569716\pi$
$293$	−7.43820	−0.434544	−0.217272	+	0.976111i	$0.569716\pi$
$294$	−12.8065	−0.746892
$295$	−43.2884	−2.52035
$296$	0.558056	0.0324364
$297$	−5.70318	−0.330932
$298$	1.76361	0.102163
$299$	17.1694	0.992932
$300$	−5.47516	−0.316108
$301$	−5.09912	−0.293908
$302$	−23.1338	−1.33120
$303$	26.6477	1.53087
$304$	4.31032	0.247214
$305$	−17.7514	−1.01644
$306$	0.110242	0.00630212
$307$	5.17101	0.295125	0.147562	−	0.989053i	$-0.452857\pi$
$307$	5.17101	0.295125	0.147562	+	0.989053i	$0.452857\pi$
$308$	4.09063	0.233085
$309$	−16.7335	−0.951937
$310$	25.2789	1.43574
$311$	−13.0485	−0.739910	−0.369955	−	0.929050i	$-0.620627\pi$
$311$	−13.0485	−0.739910	−0.369955	+	0.929050i	$0.620627\pi$
$312$	−5.83617	−0.330408
$313$	−33.6332	−1.90106	−0.950531	−	0.310628i	$-0.899461\pi$
$313$	−33.6332	−1.90106	−0.950531	+	0.310628i	$0.899461\pi$
$314$	11.2301	0.633751
$315$	−1.79558	−0.101170
$316$	9.83671	0.553358
$317$	30.7873	1.72919	0.864593	−	0.502473i	$-0.167576\pi$
$317$	30.7873	1.72919	0.864593	+	0.502473i	$0.167576\pi$
$318$	11.7787	0.660515
$319$	−7.80350	−0.436912
$320$	−2.87245	−0.160575
$321$	5.61385	0.313335
$322$	−18.9343	−1.05517
$323$	−2.90497	−0.161637
$324$	−8.48252	−0.471251
$325$	11.2656	0.624902
$326$	9.03004	0.500127
$327$	23.8644	1.31970
$328$	−3.02674	−0.167124
$329$	26.7147	1.47283
$330$	−5.17834	−0.285058
$331$	−23.0346	−1.26610	−0.633048	−	0.774113i	$-0.718196\pi$
$331$	−23.0346	−1.26610	−0.633048	+	0.774113i	$0.718196\pi$
$332$	5.75597	0.315900
$333$	−0.0912839	−0.00500233
$334$	−15.4023	−0.842775
$335$	38.2508	2.08986
$336$	6.43610	0.351118
$337$	−16.7351	−0.911620	−0.455810	−	0.890077i	$-0.650650\pi$
$337$	−16.7351	−0.911620	−0.455810	+	0.890077i	$0.650650\pi$
$338$	−0.991605	−0.0539362
$339$	15.3962	0.836208
$340$	1.93590	0.104989
$341$	9.42017	0.510131
$342$	−0.705060	−0.0381253
$343$	−2.30845	−0.124645
$344$	1.33431	0.0719414
$345$	23.9690	1.29045
$346$	−5.81255	−0.312485
$347$	−11.4029	−0.612138	−0.306069	−	0.952009i	$-0.599014\pi$
$347$	−11.4029	−0.612138	−0.306069	+	0.952009i	$0.599014\pi$
$348$	−12.2778	−0.658161
$349$	−3.00186	−0.160686	−0.0803430	−	0.996767i	$-0.525602\pi$
$349$	−3.00186	−0.160686	−0.0803430	+	0.996767i	$0.525602\pi$
$350$	−12.4236	−0.664070
$351$	18.4632	0.985491
$352$	−1.07042	−0.0570534
$353$	−12.2188	−0.650343	−0.325172	−	0.945655i	$-0.605422\pi$
$353$	−12.2188	−0.650343	−0.325172	+	0.945655i	$0.605422\pi$
$354$	−25.3808	−1.34897
$355$	−40.5356	−2.15141
$356$	−10.3528	−0.548695
$357$	−4.33764	−0.229572
$358$	−6.18849	−0.327072
$359$	26.4193	1.39436	0.697180	−	0.716897i	$-0.254438\pi$
$359$	26.4193	1.39436	0.697180	+	0.716897i	$0.254438\pi$
$360$	0.469860	0.0247638
$361$	−0.421101	−0.0221632
$362$	11.5073	0.604810
$363$	16.5962	0.871072
$364$	−13.2428	−0.694111
$365$	−10.7470	−0.562521
$366$	−10.4080	−0.544032
$367$	−24.7863	−1.29383	−0.646917	−	0.762560i	$-0.723942\pi$
$367$	−24.7863	−1.29383	−0.646917	+	0.762560i	$0.723942\pi$
$368$	4.95465	0.258279
$369$	0.495099	0.0257738
$370$	−1.60299	−0.0833354
$371$	26.7268	1.38759
$372$	14.8215	0.768458
$373$	−1.51751	−0.0785736	−0.0392868	−	0.999228i	$-0.512509\pi$
$373$	−1.51751	−0.0785736	−0.0392868	+	0.999228i	$0.512509\pi$
$374$	0.721413	0.0373034
$375$	−8.46133	−0.436941
$376$	−6.99057	−0.360511
$377$	25.2626	1.30109
$378$	−20.3611	−1.04726
$379$	2.06923	0.106289	0.0531446	−	0.998587i	$-0.483076\pi$
$379$	2.06923	0.106289	0.0531446	+	0.998587i	$0.483076\pi$
$380$	−12.3812	−0.635141
$381$	35.7070	1.82932
$382$	−0.526412	−0.0269336
$383$	7.83280	0.400237	0.200119	−	0.979772i	$-0.435867\pi$
$383$	7.83280	0.400237	0.200119	+	0.979772i	$0.435867\pi$
$384$	−1.68417	−0.0859449
$385$	−11.7501	−0.598841
$386$	−3.58357	−0.182399
$387$	−0.218260	−0.0110948
$388$	11.9491	0.606623
$389$	7.71466	0.391149	0.195574	−	0.980689i	$-0.437343\pi$
$389$	7.71466	0.391149	0.195574	+	0.980689i	$0.437343\pi$
$390$	16.7641	0.848883
$391$	−3.33921	−0.168871
$392$	7.60407	0.384063
$393$	6.87922	0.347011
$394$	−1.92440	−0.0969501
$395$	−28.2554	−1.42169
$396$	0.175093	0.00879876
$397$	−16.2728	−0.816706	−0.408353	−	0.912824i	$-0.633897\pi$
$397$	−16.2728	−0.816706	−0.408353	+	0.912824i	$0.633897\pi$
$398$	−0.345163	−0.0173015
$399$	27.7417	1.38882
$400$	3.25096	0.162548
$401$	−6.77307	−0.338231	−0.169115	−	0.985596i	$-0.554091\pi$
$401$	−6.77307	−0.338231	−0.169115	+	0.985596i	$0.554091\pi$
$402$	22.4271	1.11856
$403$	−30.4964	−1.51913
$404$	−15.8224	−0.787196
$405$	24.3656	1.21074
$406$	−27.8595	−1.38264
$407$	−0.597353	−0.0296097
$408$	1.13505	0.0561936
$409$	−2.73800	−0.135385	−0.0676927	−	0.997706i	$-0.521564\pi$
$409$	−2.73800	−0.135385	−0.0676927	+	0.997706i	$0.521564\pi$
$410$	8.69416	0.429374
$411$	35.1573	1.73418
$412$	9.93578	0.489501
$413$	−57.5913	−2.83388
$414$	−0.810454	−0.0398317
$415$	−16.5337	−0.811609
$416$	3.46531	0.169901
$417$	−19.5605	−0.957883
$418$	−4.61384	−0.225671
$419$	19.7905	0.966827	0.483413	−	0.875392i	$-0.339397\pi$
$419$	19.7905	0.966827	0.483413	+	0.875392i	$0.339397\pi$
$420$	−18.4874	−0.902090
$421$	−2.02683	−0.0987817	−0.0493909	−	0.998780i	$-0.515728\pi$
$421$	−2.02683	−0.0987817	−0.0493909	+	0.998780i	$0.515728\pi$
$422$	2.03910	0.0992618
$423$	1.14348	0.0555979
$424$	−6.99376	−0.339647
$425$	−2.19100	−0.106279
$426$	−23.7668	−1.15150
$427$	−23.6166	−1.14289
$428$	−3.33331	−0.161121
$429$	6.24714	0.301615
$430$	−3.83275	−0.184831
$431$	−13.9727	−0.673040	−0.336520	−	0.941676i	$-0.609250\pi$
$431$	−13.9727	−0.673040	−0.336520	+	0.941676i	$0.609250\pi$
$432$	5.32799	0.256343
$433$	−14.6483	−0.703952	−0.351976	−	0.936009i	$-0.614490\pi$
$433$	−14.6483	−0.703952	−0.351976	+	0.936009i	$0.614490\pi$
$434$	33.6312	1.61435
$435$	35.2675	1.69095
$436$	−14.1698	−0.678612
$437$	21.3561	1.02160
$438$	−6.30114	−0.301080
$439$	26.0779	1.24463	0.622315	−	0.782767i	$-0.286192\pi$
$439$	26.0779	1.24463	0.622315	+	0.782767i	$0.286192\pi$
$440$	3.07472	0.146581
$441$	−1.24383	−0.0592301
$442$	−2.33547	−0.111087
$443$	6.61406	0.314243	0.157122	−	0.987579i	$-0.449778\pi$
$443$	6.61406	0.314243	0.157122	+	0.987579i	$0.449778\pi$
$444$	−0.939861	−0.0446038
$445$	29.7377	1.40970
$446$	8.82565	0.417906
$447$	−2.97022	−0.140487
$448$	−3.82153	−0.180550
$449$	−4.22222	−0.199259	−0.0996294	−	0.995025i	$-0.531766\pi$
$449$	−4.22222	−0.199259	−0.0996294	+	0.995025i	$0.531766\pi$
$450$	−0.531774	−0.0250681
$451$	3.23988	0.152560
$452$	−9.14173	−0.429991
$453$	38.9613	1.83056
$454$	18.9479	0.889268
$455$	38.0392	1.78331
$456$	−7.25932	−0.339949
$457$	34.8010	1.62792	0.813962	−	0.580919i	$-0.197307\pi$
$457$	34.8010	1.62792	0.813962	+	0.580919i	$0.197307\pi$
$458$	−1.50686	−0.0704108
$459$	−3.59083	−0.167606
$460$	−14.2320	−0.663569
$461$	19.6132	0.913476	0.456738	−	0.889601i	$-0.349018\pi$
$461$	19.6132	0.913476	0.456738	+	0.889601i	$0.349018\pi$
$462$	−6.88931	−0.320520
$463$	0.833700	0.0387453	0.0193727	−	0.999812i	$-0.493833\pi$
$463$	0.833700	0.0387453	0.0193727	+	0.999812i	$0.493833\pi$
$464$	7.29015	0.338437
$465$	−42.5739	−1.97432
$466$	2.17398	0.100708
$467$	−24.1467	−1.11738	−0.558688	−	0.829378i	$-0.688695\pi$
$467$	−24.1467	−1.11738	−0.558688	+	0.829378i	$0.688695\pi$
$468$	−0.566837	−0.0262021
$469$	50.8891	2.34984
$470$	20.0801	0.926224
$471$	−18.9134	−0.871483
$472$	15.0702	0.693663
$473$	−1.42827	−0.0656720
$474$	−16.5667	−0.760933
$475$	14.0127	0.642946
$476$	2.57554	0.118050
$477$	1.14400	0.0523802
$478$	18.4839	0.845435
$479$	−0.305619	−0.0139641	−0.00698203	−	0.999976i	$-0.502222\pi$
$479$	−0.305619	−0.0139641	−0.00698203	+	0.999976i	$0.502222\pi$
$480$	4.83769	0.220809
$481$	1.93384	0.0881755
$482$	14.3543	0.653820
$483$	31.8886	1.45098
$484$	−9.85421	−0.447919
$485$	−34.3231	−1.55853
$486$	−1.69799	−0.0770223
$487$	10.7668	0.487888	0.243944	−	0.969789i	$-0.421559\pi$
$487$	10.7668	0.487888	0.243944	+	0.969789i	$0.421559\pi$
$488$	6.17987	0.279750
$489$	−15.2081	−0.687734
$490$	−21.8423	−0.986734
$491$	−0.247433	−0.0111665	−0.00558325	−	0.999984i	$-0.501777\pi$
$491$	−0.247433	−0.0111665	−0.00558325	+	0.999984i	$0.501777\pi$
$492$	5.09755	0.229815
$493$	−4.91324	−0.221281
$494$	14.9366	0.672031
$495$	−0.502946	−0.0226057
$496$	−8.80047	−0.395153
$497$	−53.9289	−2.41904
$498$	−9.69403	−0.434400
$499$	−10.6384	−0.476241	−0.238121	−	0.971236i	$-0.576531\pi$
$499$	−10.6384	−0.476241	−0.238121	+	0.971236i	$0.576531\pi$
$500$	5.02404	0.224682
$501$	25.9400	1.15892
$502$	−24.2506	−1.08236
$503$	20.3200	0.906025	0.453013	−	0.891504i	$-0.350349\pi$
$503$	20.3200	0.906025	0.453013	+	0.891504i	$0.350349\pi$
$504$	0.625105	0.0278444
$505$	45.4492	2.02246
$506$	−5.30354	−0.235771
$507$	1.67003	0.0741687
$508$	−21.2015	−0.940666
$509$	−35.9753	−1.59458	−0.797288	−	0.603600i	$-0.793733\pi$
$509$	−35.9753	−1.59458	−0.797288	+	0.603600i	$0.793733\pi$
$510$	−3.26039	−0.144372
$511$	−14.2978	−0.632499
$512$	1.00000	0.0441942
$513$	22.9654	1.01395
$514$	−10.9569	−0.483290
$515$	−28.5400	−1.25762
$516$	−2.24721	−0.0989279
$517$	7.48283	0.329094
$518$	−2.13263	−0.0937023
$519$	9.78931	0.429703
$520$	−9.95393	−0.436509
$521$	−0.268341	−0.0117563	−0.00587813	−	0.999983i	$-0.501871\pi$
$521$	−0.268341	−0.0117563	−0.00587813	+	0.999983i	$0.501871\pi$
$522$	−1.19248	−0.0521936
$523$	−18.6484	−0.815437	−0.407718	−	0.913108i	$-0.633675\pi$
$523$	−18.6484	−0.815437	−0.407718	+	0.913108i	$0.633675\pi$
$524$	−4.08463	−0.178438
$525$	20.9235	0.913175
$526$	23.4685	1.02328
$527$	5.93112	0.258364
$528$	1.80276	0.0784552
$529$	1.54851	0.0673266
$530$	20.0892	0.872619
$531$	−2.46511	−0.106977
$532$	−16.4720	−0.714153
$533$	−10.4886	−0.454312
$534$	17.4358	0.754520
$535$	9.57475	0.413953
$536$	−13.3164	−0.575182
$537$	10.4225	0.449762
$538$	27.8252	1.19963
$539$	−8.13952	−0.350594
$540$	−15.3044	−0.658596
$541$	−26.6408	−1.14538	−0.572690	−	0.819772i	$-0.694100\pi$
$541$	−26.6408	−1.14538	−0.572690	+	0.819772i	$0.694100\pi$
$542$	−10.6338	−0.456760
$543$	−19.3802	−0.831686
$544$	−0.673955	−0.0288956
$545$	40.7021	1.74349
$546$	22.3031	0.954484
$547$	−35.3258	−1.51042	−0.755211	−	0.655481i	$-0.772466\pi$
$547$	−35.3258	−1.51042	−0.755211	+	0.655481i	$0.772466\pi$
$548$	−20.8752	−0.891743
$549$	−1.01087	−0.0431429
$550$	−3.47988	−0.148382
$551$	31.4229	1.33866
$552$	−8.34446	−0.355164
$553$	−37.5913	−1.59854
$554$	−17.7173	−0.752736
$555$	2.69970	0.114596
$556$	11.6143	0.492558
$557$	−13.2358	−0.560819	−0.280410	−	0.959880i	$-0.590470\pi$
$557$	−13.2358	−0.560819	−0.280410	+	0.959880i	$0.590470\pi$
$558$	1.43953	0.0609403
$559$	4.62382	0.195567
$560$	10.9771	0.463869
$561$	−1.21498	−0.0512966
$562$	7.52845	0.317568
$563$	29.6320	1.24884	0.624421	−	0.781088i	$-0.285335\pi$
$563$	29.6320	1.24884	0.624421	+	0.781088i	$0.285335\pi$
$564$	11.7733	0.495746
$565$	26.2592	1.10473
$566$	−11.5501	−0.485485
$567$	32.4162	1.36135
$568$	14.1119	0.592121
$569$	−44.7228	−1.87488	−0.937439	−	0.348150i	$-0.886810\pi$
$569$	−44.7228	−1.87488	−0.937439	+	0.348150i	$0.886810\pi$
$570$	20.8520	0.873394
$571$	40.2738	1.68541	0.842704	−	0.538378i	$-0.180963\pi$
$571$	40.2738	1.68541	0.842704	+	0.538378i	$0.180963\pi$
$572$	−3.70933	−0.155095
$573$	0.886566	0.0370368
$574$	11.5668	0.482788
$575$	16.1073	0.671722
$576$	−0.163575	−0.00681561
$577$	−17.1132	−0.712431	−0.356216	−	0.934404i	$-0.615933\pi$
$577$	−17.1132	−0.712431	−0.356216	+	0.934404i	$0.615933\pi$
$578$	−16.5458	−0.688214
$579$	6.03534	0.250820
$580$	−20.9406	−0.869510
$581$	−21.9966	−0.912573
$582$	−20.1243	−0.834178
$583$	7.48624	0.310048
$584$	3.74139	0.154820
$585$	1.62821	0.0673182
$586$	−7.43820	−0.307269
$587$	25.7385	1.06234	0.531171	−	0.847264i	$-0.321752\pi$
$587$	25.7385	1.06234	0.531171	+	0.847264i	$0.321752\pi$
$588$	−12.8065	−0.528132
$589$	−37.9329	−1.56300
$590$	−43.2884	−1.78216
$591$	3.24102	0.133318
$592$	0.558056	0.0229360
$593$	20.6287	0.847118	0.423559	−	0.905868i	$-0.360781\pi$
$593$	20.6287	0.847118	0.423559	+	0.905868i	$0.360781\pi$
$594$	−5.70318	−0.234004
$595$	−7.39810	−0.303293
$596$	1.76361	0.0722404
$597$	0.581313	0.0237916
$598$	17.1694	0.702109
$599$	−26.5668	−1.08549	−0.542744	−	0.839898i	$-0.682615\pi$
$599$	−26.5668	−1.08549	−0.542744	+	0.839898i	$0.682615\pi$
$600$	−5.47516	−0.223522
$601$	−32.1744	−1.31242	−0.656210	−	0.754578i	$-0.727841\pi$
$601$	−32.1744	−1.31242	−0.656210	+	0.754578i	$0.727841\pi$
$602$	−5.09912	−0.207824
$603$	2.17823	0.0887044
$604$	−23.1338	−0.941303
$605$	28.3057	1.15079
$606$	26.6477	1.08249
$607$	−26.9265	−1.09291	−0.546456	−	0.837488i	$-0.684024\pi$
$607$	−26.9265	−1.09291	−0.546456	+	0.837488i	$0.684024\pi$
$608$	4.31032	0.174807
$609$	46.9201	1.90130
$610$	−17.7514	−0.718732
$611$	−24.2245	−0.980020
$612$	0.110242	0.00445627
$613$	40.0029	1.61570	0.807850	−	0.589388i	$-0.200631\pi$
$613$	40.0029	1.61570	0.807850	+	0.589388i	$0.200631\pi$
$614$	5.17101	0.208685
$615$	−14.6424	−0.590440
$616$	4.09063	0.164816
$617$	38.1246	1.53484	0.767420	−	0.641145i	$-0.221540\pi$
$617$	38.1246	1.53484	0.767420	+	0.641145i	$0.221540\pi$
$618$	−16.7335	−0.673121
$619$	29.3903	1.18130	0.590648	−	0.806929i	$-0.298872\pi$
$619$	29.3903	1.18130	0.590648	+	0.806929i	$0.298872\pi$
$620$	25.2789	1.01522
$621$	26.3983	1.05933
$622$	−13.0485	−0.523195
$623$	39.5633	1.58507
$624$	−5.83617	−0.233634
$625$	−30.6861	−1.22744
$626$	−33.6332	−1.34425
$627$	7.77049	0.310324
$628$	11.2301	0.448130
$629$	−0.376105	−0.0149963
$630$	−1.79558	−0.0715377
$631$	−24.3460	−0.969201	−0.484600	−	0.874736i	$-0.661035\pi$
$631$	−24.3460	−0.969201	−0.484600	+	0.874736i	$0.661035\pi$
$632$	9.83671	0.391283
$633$	−3.43419	−0.136497
$634$	30.7873	1.22272
$635$	60.9003	2.41675
$636$	11.7787	0.467055
$637$	26.3505	1.04404
$638$	−7.80350	−0.308943
$639$	−2.30834	−0.0913167
$640$	−2.87245	−0.113543
$641$	9.78664	0.386549	0.193274	−	0.981145i	$-0.438089\pi$
$641$	9.78664	0.386549	0.193274	+	0.981145i	$0.438089\pi$
$642$	5.61385	0.221561
$643$	43.1661	1.70230	0.851152	−	0.524920i	$-0.175905\pi$
$643$	43.1661	1.70230	0.851152	+	0.524920i	$0.175905\pi$
$644$	−18.9343	−0.746116
$645$	6.45499	0.254165
$646$	−2.90497	−0.114294
$647$	9.38430	0.368935	0.184467	−	0.982839i	$-0.440944\pi$
$647$	9.38430	0.368935	0.184467	+	0.982839i	$0.440944\pi$
$648$	−8.48252	−0.333225
$649$	−16.1314	−0.633214
$650$	11.2656	0.441872
$651$	−56.6407	−2.21992
$652$	9.03004	0.353643
$653$	−9.47730	−0.370875	−0.185438	−	0.982656i	$-0.559370\pi$
$653$	−9.47730	−0.370875	−0.185438	+	0.982656i	$0.559370\pi$
$654$	23.8644	0.933172
$655$	11.7329	0.458442
$656$	−3.02674	−0.118175
$657$	−0.611997	−0.0238763
$658$	26.7147	1.04145
$659$	−8.31711	−0.323989	−0.161994	−	0.986792i	$-0.551793\pi$
$659$	−8.31711	−0.323989	−0.161994	+	0.986792i	$0.551793\pi$
$660$	−5.17834	−0.201567
$661$	−29.9815	−1.16615	−0.583073	−	0.812420i	$-0.698150\pi$
$661$	−29.9815	−1.16615	−0.583073	+	0.812420i	$0.698150\pi$
$662$	−23.0346	−0.895265
$663$	3.93332	0.152757
$664$	5.75597	0.223375
$665$	47.3150	1.83480
$666$	−0.0912839	−0.00353718
$667$	36.1201	1.39858
$668$	−15.4023	−0.595932
$669$	−14.8639	−0.574671
$670$	38.2508	1.47776
$671$	−6.61504	−0.255371
$672$	6.43610	0.248278
$673$	−14.9852	−0.577637	−0.288818	−	0.957384i	$-0.593262\pi$
$673$	−14.9852	−0.577637	−0.288818	+	0.957384i	$0.593262\pi$
$674$	−16.7351	−0.644613
$675$	17.3211	0.666688
$676$	−0.991605	−0.0381387
$677$	−47.4610	−1.82407	−0.912037	−	0.410108i	$-0.865491\pi$
$677$	−47.4610	−1.82407	−0.912037	+	0.410108i	$0.865491\pi$
$678$	15.3962	0.591289
$679$	−45.6638	−1.75241
$680$	1.93590	0.0742384
$681$	−31.9114	−1.22285
$682$	9.42017	0.360717
$683$	−23.4688	−0.898007	−0.449004	−	0.893530i	$-0.648221\pi$
$683$	−23.4688	−0.898007	−0.449004	+	0.893530i	$0.648221\pi$
$684$	−0.705060	−0.0269586
$685$	59.9629	2.29106
$686$	−2.30845	−0.0881371
$687$	2.53780	0.0968232
$688$	1.33431	0.0508702
$689$	−24.2356	−0.923302
$690$	23.9690	0.912485
$691$	30.5289	1.16137	0.580687	−	0.814127i	$-0.302784\pi$
$691$	30.5289	1.16137	0.580687	+	0.814127i	$0.302784\pi$
$692$	−5.81255	−0.220960
$693$	−0.669123	−0.0254179
$694$	−11.4029	−0.432847
$695$	−33.3616	−1.26548
$696$	−12.2778	−0.465390
$697$	2.03989	0.0772664
$698$	−3.00186	−0.113622
$699$	−3.66135	−0.138485
$700$	−12.4236	−0.469568
$701$	20.5469	0.776046	0.388023	−	0.921650i	$-0.373158\pi$
$701$	20.5469	0.776046	0.388023	+	0.921650i	$0.373158\pi$
$702$	18.4632	0.696847
$703$	2.40540	0.0907215
$704$	−1.07042	−0.0403429
$705$	−33.8182	−1.27367
$706$	−12.2188	−0.459862
$707$	60.4659	2.27405
$708$	−25.3808	−0.953869
$709$	9.05115	0.339923	0.169962	−	0.985451i	$-0.445636\pi$
$709$	9.05115	0.339923	0.169962	+	0.985451i	$0.445636\pi$
$710$	−40.5356	−1.52127
$711$	−1.60904	−0.0603436
$712$	−10.3528	−0.387986
$713$	−43.6032	−1.63295
$714$	−4.33764	−0.162332
$715$	10.6549	0.398469
$716$	−6.18849	−0.231275
$717$	−31.1301	−1.16257
$718$	26.4193	0.985961
$719$	−9.89327	−0.368957	−0.184478	−	0.982837i	$-0.559060\pi$
$719$	−9.89327	−0.368957	−0.184478	+	0.982837i	$0.559060\pi$
$720$	0.469860	0.0175106
$721$	−37.9698	−1.41407
$722$	−0.421101	−0.0156717
$723$	−24.1750	−0.899079
$724$	11.5073	0.427665
$725$	23.6999	0.880194
$726$	16.5962	0.615941
$727$	−18.9334	−0.702201	−0.351101	−	0.936338i	$-0.614192\pi$
$727$	−18.9334	−0.702201	−0.351101	+	0.936338i	$0.614192\pi$
$728$	−13.2428	−0.490810
$729$	28.3073	1.04842
$730$	−10.7470	−0.397762
$731$	−0.899268	−0.0332606
$732$	−10.4080	−0.384689
$733$	26.2883	0.970979	0.485490	−	0.874242i	$-0.338641\pi$
$733$	26.2883	0.970979	0.485490	+	0.874242i	$0.338641\pi$
$734$	−24.7863	−0.914879
$735$	36.7861	1.35688
$736$	4.95465	0.182631
$737$	14.2541	0.525058
$738$	0.495099	0.0182248
$739$	15.2110	0.559546	0.279773	−	0.960066i	$-0.409741\pi$
$739$	15.2110	0.559546	0.279773	+	0.960066i	$0.409741\pi$
$740$	−1.60299	−0.0589270
$741$	−25.1558	−0.924121
$742$	26.7268	0.981173
$743$	25.2499	0.926329	0.463164	−	0.886272i	$-0.346714\pi$
$743$	25.2499	0.926329	0.463164	+	0.886272i	$0.346714\pi$
$744$	14.8215	0.543382
$745$	−5.06589	−0.185600
$746$	−1.51751	−0.0555599
$747$	−0.941531	−0.0344488
$748$	0.721413	0.0263775
$749$	12.7383	0.465448
$750$	−8.46133	−0.308964
$751$	22.9788	0.838509	0.419255	−	0.907869i	$-0.362291\pi$
$751$	22.9788	0.838509	0.419255	+	0.907869i	$0.362291\pi$
$752$	−6.99057	−0.254920
$753$	40.8421	1.48837
$754$	25.2626	0.920011
$755$	66.4507	2.41839
$756$	−20.3611	−0.740525
$757$	−45.1904	−1.64247	−0.821236	−	0.570589i	$-0.806715\pi$
$757$	−45.1904	−1.64247	−0.821236	+	0.570589i	$0.806715\pi$
$758$	2.06923	0.0751578
$759$	8.93205	0.324213
$760$	−12.3812	−0.449113
$761$	25.0304	0.907350	0.453675	−	0.891167i	$-0.350113\pi$
$761$	25.0304	0.907350	0.453675	+	0.891167i	$0.350113\pi$
$762$	35.7070	1.29353
$763$	54.1504	1.96038
$764$	−0.526412	−0.0190449
$765$	−0.316664	−0.0114490
$766$	7.83280	0.283010
$767$	52.2231	1.88567
$768$	−1.68417	−0.0607722
$769$	−25.5354	−0.920829	−0.460415	−	0.887704i	$-0.652299\pi$
$769$	−25.5354	−0.920829	−0.460415	+	0.887704i	$0.652299\pi$
$770$	−11.7501	−0.423445
$771$	18.4533	0.664581
$772$	−3.58357	−0.128975
$773$	12.5114	0.450003	0.225001	−	0.974358i	$-0.427761\pi$
$773$	12.5114	0.450003	0.225001	+	0.974358i	$0.427761\pi$
$774$	−0.218260	−0.00784519
$775$	−28.6099	−1.02770
$776$	11.9491	0.428947
$777$	3.59171	0.128852
$778$	7.71466	0.276584
$779$	−13.0463	−0.467430
$780$	16.7641	0.600251
$781$	−15.1056	−0.540520
$782$	−3.33921	−0.119410
$783$	38.8419	1.38810
$784$	7.60407	0.271574
$785$	−32.2579	−1.15133
$786$	6.87922	0.245373
$787$	24.1613	0.861258	0.430629	−	0.902529i	$-0.358292\pi$
$787$	24.1613	0.861258	0.430629	+	0.902529i	$0.358292\pi$
$788$	−1.92440	−0.0685541
$789$	−39.5250	−1.40713
$790$	−28.2554	−1.00528
$791$	34.9354	1.24216
$792$	0.175093	0.00622166
$793$	21.4152	0.760476
$794$	−16.2728	−0.577498
$795$	−33.8336	−1.19995
$796$	−0.345163	−0.0122340
$797$	−35.5381	−1.25883	−0.629413	−	0.777071i	$-0.716704\pi$
$797$	−35.5381	−1.25883	−0.629413	+	0.777071i	$0.716704\pi$
$798$	27.7417	0.982044
$799$	4.71134	0.166675
$800$	3.25096	0.114939
$801$	1.69345	0.0598350
$802$	−6.77307	−0.239165
$803$	−4.00485	−0.141328
$804$	22.4271	0.790944
$805$	54.3878	1.91692
$806$	−30.4964	−1.07419
$807$	−46.8624	−1.64963
$808$	−15.8224	−0.556632
$809$	23.8141	0.837259	0.418629	−	0.908157i	$-0.362511\pi$
$809$	23.8141	0.837259	0.418629	+	0.908157i	$0.362511\pi$
$810$	24.3656	0.856120
$811$	−34.4298	−1.20900	−0.604498	−	0.796607i	$-0.706626\pi$
$811$	−34.4298	−1.20900	−0.604498	+	0.796607i	$0.706626\pi$
$812$	−27.8595	−0.977677
$813$	17.9091	0.628099
$814$	−0.597353	−0.0209372
$815$	−25.9383	−0.908579
$816$	1.13505	0.0397349
$817$	5.75133	0.201213
$818$	−2.73800	−0.0957319
$819$	2.16618	0.0756926
$820$	8.69416	0.303613
$821$	−18.1532	−0.633552	−0.316776	−	0.948500i	$-0.602600\pi$
$821$	−18.1532	−0.633552	−0.316776	+	0.948500i	$0.602600\pi$
$822$	35.1573	1.22625
$823$	−39.4461	−1.37501	−0.687503	−	0.726182i	$-0.741293\pi$
$823$	−39.4461	−1.37501	−0.687503	+	0.726182i	$0.741293\pi$
$824$	9.93578	0.346129
$825$	5.86070	0.204043
$826$	−57.5913	−2.00386
$827$	−46.2175	−1.60714	−0.803570	−	0.595211i	$-0.797069\pi$
$827$	−46.2175	−1.60714	−0.803570	+	0.595211i	$0.797069\pi$
$828$	−0.810454	−0.0281652
$829$	−51.0962	−1.77464	−0.887322	−	0.461150i	$-0.847437\pi$
$829$	−51.0962	−1.77464	−0.887322	+	0.461150i	$0.847437\pi$
$830$	−16.5337	−0.573894
$831$	29.8389	1.03510
$832$	3.46531	0.120138
$833$	−5.12480	−0.177564
$834$	−19.5605	−0.677325
$835$	44.2422	1.53107
$836$	−4.61384	−0.159573
$837$	−46.8888	−1.62072
$838$	19.7905	0.683650
$839$	−18.4046	−0.635397	−0.317699	−	0.948192i	$-0.602910\pi$
$839$	−18.4046	−0.635397	−0.317699	+	0.948192i	$0.602910\pi$
$840$	−18.4874	−0.637874
$841$	24.1463	0.832630
$842$	−2.02683	−0.0698492
$843$	−12.6792	−0.436694
$844$	2.03910	0.0701887
$845$	2.84833	0.0979857
$846$	1.14348	0.0393137
$847$	37.6581	1.29395
$848$	−6.99376	−0.240167
$849$	19.4523	0.667599
$850$	−2.19100	−0.0751506
$851$	2.76497	0.0947820
$852$	−23.7668	−0.814236
$853$	−22.1024	−0.756773	−0.378386	−	0.925648i	$-0.623521\pi$
$853$	−22.1024	−0.756773	−0.378386	+	0.925648i	$0.623521\pi$
$854$	−23.6166	−0.808142
$855$	2.02525	0.0692620
$856$	−3.33331	−0.113930
$857$	−4.28243	−0.146285	−0.0731425	−	0.997321i	$-0.523303\pi$
$857$	−4.28243	−0.146285	−0.0731425	+	0.997321i	$0.523303\pi$
$858$	6.24714	0.213274
$859$	11.5410	0.393773	0.196886	−	0.980426i	$-0.436917\pi$
$859$	11.5410	0.393773	0.196886	+	0.980426i	$0.436917\pi$
$860$	−3.83275	−0.130696
$861$	−19.4804	−0.663891
$862$	−13.9727	−0.475911
$863$	−8.21809	−0.279747	−0.139874	−	0.990169i	$-0.544670\pi$
$863$	−8.21809	−0.279747	−0.139874	+	0.990169i	$0.544670\pi$
$864$	5.32799	0.181262
$865$	16.6962	0.567689
$866$	−14.6483	−0.497769
$867$	27.8659	0.946375
$868$	33.6312	1.14152
$869$	−10.5294	−0.357185
$870$	35.2675	1.19568
$871$	−46.1456	−1.56358
$872$	−14.1698	−0.479851
$873$	−1.95457	−0.0661521
$874$	21.3561	0.722382
$875$	−19.1995	−0.649061
$876$	−6.30114	−0.212896
$877$	−22.6626	−0.765263	−0.382632	−	0.923901i	$-0.624982\pi$
$877$	−22.6626	−0.765263	−0.382632	+	0.923901i	$0.624982\pi$
$878$	26.0779	0.880086
$879$	12.5272	0.422532
$880$	3.07472	0.103649
$881$	−31.4845	−1.06074	−0.530370	−	0.847766i	$-0.677947\pi$
$881$	−31.4845	−1.06074	−0.530370	+	0.847766i	$0.677947\pi$
$882$	−1.24383	−0.0418820
$883$	−43.2244	−1.45462	−0.727308	−	0.686312i	$-0.759229\pi$
$883$	−43.2244	−1.45462	−0.727308	+	0.686312i	$0.759229\pi$
$884$	−2.33547	−0.0785502
$885$	72.9050	2.45068
$886$	6.61406	0.222204
$887$	51.7788	1.73856	0.869281	−	0.494318i	$-0.164582\pi$
$887$	51.7788	1.73856	0.869281	+	0.494318i	$0.164582\pi$
$888$	−0.939861	−0.0315397
$889$	81.0222	2.71740
$890$	29.7377	0.996811
$891$	9.07983	0.304186
$892$	8.82565	0.295504
$893$	−30.1316	−1.00832
$894$	−2.97022	−0.0993391
$895$	17.7761	0.594190
$896$	−3.82153	−0.127668
$897$	−28.9162	−0.965483
$898$	−4.22222	−0.140897
$899$	−64.1567	−2.13975
$900$	−0.531774	−0.0177258
$901$	4.71348	0.157029
$902$	3.23988	0.107876
$903$	8.58777	0.285783
$904$	−9.14173	−0.304050
$905$	−33.0541	−1.09876
$906$	38.9613	1.29440
$907$	−15.3058	−0.508219	−0.254110	−	0.967175i	$-0.581782\pi$
$907$	−15.3058	−0.508219	−0.254110	+	0.967175i	$0.581782\pi$
$908$	18.9479	0.628807
$909$	2.58815	0.0858436
$910$	38.0392	1.26099
$911$	−33.5071	−1.11014	−0.555069	−	0.831804i	$-0.687308\pi$
$911$	−33.5071	−1.11014	−0.555069	+	0.831804i	$0.687308\pi$
$912$	−7.25932	−0.240380
$913$	−6.16129	−0.203909
$914$	34.8010	1.15112
$915$	29.8963	0.988341
$916$	−1.50686	−0.0497880
$917$	15.6095	0.515472
$918$	−3.59083	−0.118515
$919$	−28.1927	−0.929992	−0.464996	−	0.885313i	$-0.653944\pi$
$919$	−28.1927	−0.929992	−0.464996	+	0.885313i	$0.653944\pi$
$920$	−14.2320	−0.469214
$921$	−8.70885	−0.286966
$922$	19.6132	0.645925
$923$	48.9021	1.60963
$924$	−6.88931	−0.226642
$925$	1.81422	0.0596511
$926$	0.833700	0.0273971
$927$	−1.62524	−0.0533799
$928$	7.29015	0.239311
$929$	−11.9143	−0.390897	−0.195449	−	0.980714i	$-0.562616\pi$
$929$	−11.9143	−0.390897	−0.195449	+	0.980714i	$0.562616\pi$
$930$	−42.5739	−1.39605
$931$	32.7760	1.07419
$932$	2.17398	0.0712111
$933$	21.9758	0.719456
$934$	−24.1467	−0.790105
$935$	−2.07222	−0.0677689
$936$	−0.566837	−0.0185277
$937$	−18.7708	−0.613215	−0.306607	−	0.951836i	$-0.599194\pi$
$937$	−18.7708	−0.613215	−0.306607	+	0.951836i	$0.599194\pi$
$938$	50.8891	1.66159
$939$	56.6441	1.84851
$940$	20.0801	0.654939
$941$	−0.938200	−0.0305844	−0.0152922	−	0.999883i	$-0.504868\pi$
$941$	−0.938200	−0.0305844	−0.0152922	+	0.999883i	$0.504868\pi$
$942$	−18.9134	−0.616231
$943$	−14.9964	−0.488351
$944$	15.0702	0.490494
$945$	58.4861	1.90255
$946$	−1.42827	−0.0464371
$947$	−59.2388	−1.92500	−0.962501	−	0.271280i	$-0.912553\pi$
$947$	−59.2388	−1.92500	−0.962501	+	0.271280i	$0.912553\pi$
$948$	−16.5667	−0.538061
$949$	12.9651	0.420865
$950$	14.0127	0.454631
$951$	−51.8510	−1.68138
$952$	2.57554	0.0834737
$953$	7.99251	0.258903	0.129451	−	0.991586i	$-0.458678\pi$
$953$	7.99251	0.258903	0.129451	+	0.991586i	$0.458678\pi$
$954$	1.14400	0.0370384
$955$	1.51209	0.0489301
$956$	18.4839	0.597813
$957$	13.1424	0.424834
$958$	−0.305619	−0.00987409
$959$	79.7750	2.57607
$960$	4.83769	0.156136
$961$	46.4482	1.49833
$962$	1.93384	0.0623495
$963$	0.545245	0.0175703
$964$	14.3543	0.462320
$965$	10.2936	0.331363
$966$	31.8886	1.02600
$967$	51.7754	1.66499	0.832493	−	0.554036i	$-0.186913\pi$
$967$	51.7754	1.66499	0.832493	+	0.554036i	$0.186913\pi$
$968$	−9.85421	−0.316726
$969$	4.89245	0.157168
$970$	−34.3231	−1.10205
$971$	31.1789	1.00058	0.500289	−	0.865859i	$-0.333227\pi$
$971$	31.1789	1.00058	0.500289	+	0.865859i	$0.333227\pi$
$972$	−1.69799	−0.0544630
$973$	−44.3845	−1.42290
$974$	10.7668	0.344989
$975$	−18.9731	−0.607627
$976$	6.17987	0.197813
$977$	−24.1691	−0.773238	−0.386619	−	0.922239i	$-0.626357\pi$
$977$	−24.1691	−0.773238	−0.386619	+	0.922239i	$0.626357\pi$
$978$	−15.2081	−0.486302
$979$	11.0818	0.354175
$980$	−21.8423	−0.697726
$981$	2.31783	0.0740025
$982$	−0.247433	−0.00789591
$983$	1.41538	0.0451437	0.0225719	−	0.999745i	$-0.492815\pi$
$983$	1.41538	0.0451437	0.0225719	+	0.999745i	$0.492815\pi$
$984$	5.09755	0.162504
$985$	5.52775	0.176129
$986$	−4.91324	−0.156469
$987$	−44.9920	−1.43211
$988$	14.9366	0.475197
$989$	6.61105	0.210219
$990$	−0.502946	−0.0159847
$991$	23.2608	0.738904	0.369452	−	0.929250i	$-0.379545\pi$
$991$	23.2608	0.738904	0.369452	+	0.929250i	$0.379545\pi$
$992$	−8.80047	−0.279415
$993$	38.7941	1.23109
$994$	−53.9289	−1.71052
$995$	0.991464	0.0314315
$996$	−9.69403	−0.307167
$997$	−16.4655	−0.521467	−0.260734	−	0.965411i	$-0.583964\pi$
$997$	−16.4655	−0.521467	−0.260734	+	0.965411i	$0.583964\pi$
$998$	−10.6384	−0.336754
$999$	2.97332	0.0940717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.a.1.12	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.a.1.12	✓	47	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.68417 q^{3} +1.00000 q^{4} -2.87245 q^{5} -1.68417 q^{6} -3.82153 q^{7} +1.00000 q^{8} -0.163575 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.68417 q^{3} +1.00000 q^{4} -2.87245 q^{5} -1.68417 q^{6} -3.82153 q^{7} +1.00000 q^{8} -0.163575 q^{9} -2.87245 q^{10} -1.07042 q^{11} -1.68417 q^{12} +3.46531 q^{13} -3.82153 q^{14} +4.83769 q^{15} +1.00000 q^{16} -0.673955 q^{17} -0.163575 q^{18} +4.31032 q^{19} -2.87245 q^{20} +6.43610 q^{21} -1.07042 q^{22} +4.95465 q^{23} -1.68417 q^{24} +3.25096 q^{25} +3.46531 q^{26} +5.32799 q^{27} -3.82153 q^{28} +7.29015 q^{29} +4.83769 q^{30} -8.80047 q^{31} +1.00000 q^{32} +1.80276 q^{33} -0.673955 q^{34} +10.9771 q^{35} -0.163575 q^{36} +0.558056 q^{37} +4.31032 q^{38} -5.83617 q^{39} -2.87245 q^{40} -3.02674 q^{41} +6.43610 q^{42} +1.33431 q^{43} -1.07042 q^{44} +0.469860 q^{45} +4.95465 q^{46} -6.99057 q^{47} -1.68417 q^{48} +7.60407 q^{49} +3.25096 q^{50} +1.13505 q^{51} +3.46531 q^{52} -6.99376 q^{53} +5.32799 q^{54} +3.07472 q^{55} -3.82153 q^{56} -7.25932 q^{57} +7.29015 q^{58} +15.0702 q^{59} +4.83769 q^{60} +6.17987 q^{61} -8.80047 q^{62} +0.625105 q^{63} +1.00000 q^{64} -9.95393 q^{65} +1.80276 q^{66} -13.3164 q^{67} -0.673955 q^{68} -8.34446 q^{69} +10.9771 q^{70} +14.1119 q^{71} -0.163575 q^{72} +3.74139 q^{73} +0.558056 q^{74} -5.47516 q^{75} +4.31032 q^{76} +4.09063 q^{77} -5.83617 q^{78} +9.83671 q^{79} -2.87245 q^{80} -8.48252 q^{81} -3.02674 q^{82} +5.75597 q^{83} +6.43610 q^{84} +1.93590 q^{85} +1.33431 q^{86} -12.2778 q^{87} -1.07042 q^{88} -10.3528 q^{89} +0.469860 q^{90} -13.2428 q^{91} +4.95465 q^{92} +14.8215 q^{93} -6.99057 q^{94} -12.3812 q^{95} -1.68417 q^{96} +11.9491 q^{97} +7.60407 q^{98} +0.175093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

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