LMFDB - Embedded newform 6001.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13704 q^{2} -0.352862 q^{3} +2.56694 q^{4} +0.777890 q^{5} +0.754080 q^{6} +0.156355 q^{7} -1.21157 q^{8} -2.87549 q^{9} +O(q^{10})$	\(q-2.13704 q^{2} -0.352862 q^{3} +2.56694 q^{4} +0.777890 q^{5} +0.754080 q^{6} +0.156355 q^{7} -1.21157 q^{8} -2.87549 q^{9} -1.66238 q^{10} +0.375905 q^{11} -0.905774 q^{12} +0.578743 q^{13} -0.334137 q^{14} -0.274488 q^{15} -2.54471 q^{16} -1.00000 q^{17} +6.14503 q^{18} -1.57959 q^{19} +1.99679 q^{20} -0.0551718 q^{21} -0.803323 q^{22} -7.66615 q^{23} +0.427516 q^{24} -4.39489 q^{25} -1.23680 q^{26} +2.07324 q^{27} +0.401354 q^{28} +1.24255 q^{29} +0.586591 q^{30} +2.87128 q^{31} +7.86128 q^{32} -0.132643 q^{33} +2.13704 q^{34} +0.121627 q^{35} -7.38120 q^{36} -1.69051 q^{37} +3.37564 q^{38} -0.204216 q^{39} -0.942465 q^{40} -3.75910 q^{41} +0.117904 q^{42} -3.70174 q^{43} +0.964924 q^{44} -2.23681 q^{45} +16.3829 q^{46} -3.60782 q^{47} +0.897931 q^{48} -6.97555 q^{49} +9.39205 q^{50} +0.352862 q^{51} +1.48560 q^{52} -0.578301 q^{53} -4.43059 q^{54} +0.292413 q^{55} -0.189435 q^{56} +0.557375 q^{57} -2.65538 q^{58} +0.819339 q^{59} -0.704593 q^{60} +11.8297 q^{61} -6.13604 q^{62} -0.449597 q^{63} -11.7104 q^{64} +0.450199 q^{65} +0.283462 q^{66} -10.0333 q^{67} -2.56694 q^{68} +2.70509 q^{69} -0.259922 q^{70} +6.74799 q^{71} +3.48384 q^{72} +9.80368 q^{73} +3.61269 q^{74} +1.55079 q^{75} -4.05470 q^{76} +0.0587747 q^{77} +0.436419 q^{78} -3.64420 q^{79} -1.97950 q^{80} +7.89490 q^{81} +8.03335 q^{82} +14.6150 q^{83} -0.141622 q^{84} -0.777890 q^{85} +7.91077 q^{86} -0.438449 q^{87} -0.455434 q^{88} -16.7631 q^{89} +4.78016 q^{90} +0.0904895 q^{91} -19.6785 q^{92} -1.01317 q^{93} +7.71006 q^{94} -1.22874 q^{95} -2.77395 q^{96} +9.68554 q^{97} +14.9070 q^{98} -1.08091 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.13704	−1.51111	−0.755557	−	0.655082i	$-0.772634\pi$
$2$	−2.13704	−1.51111	−0.755557	+	0.655082i	$0.772634\pi$
$3$	−0.352862	−0.203725	−0.101862	−	0.994798i	$-0.532480\pi$
$3$	−0.352862	−0.203725	−0.101862	+	0.994798i	$0.532480\pi$
$4$	2.56694	1.28347
$5$	0.777890	0.347883	0.173942	−	0.984756i	$-0.444350\pi$
$5$	0.777890	0.347883	0.173942	+	0.984756i	$0.444350\pi$
$6$	0.754080	0.307852
$7$	0.156355	0.0590967	0.0295483	−	0.999563i	$-0.490593\pi$
$7$	0.156355	0.0590967	0.0295483	+	0.999563i	$0.490593\pi$
$8$	−1.21157	−0.428353
$9$	−2.87549	−0.958496
$10$	−1.66238	−0.525691
$11$	0.375905	0.113340	0.0566698	−	0.998393i	$-0.481952\pi$
$11$	0.375905	0.113340	0.0566698	+	0.998393i	$0.481952\pi$
$12$	−0.905774	−0.261475
$13$	0.578743	0.160515	0.0802573	−	0.996774i	$-0.474426\pi$
$13$	0.578743	0.160515	0.0802573	+	0.996774i	$0.474426\pi$
$14$	−0.334137	−0.0893019
$15$	−0.274488	−0.0708725
$16$	−2.54471	−0.636177
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	6.14503	1.44840
$19$	−1.57959	−0.362382	−0.181191	−	0.983448i	$-0.557995\pi$
$19$	−1.57959	−0.362382	−0.181191	+	0.983448i	$0.557995\pi$
$20$	1.99679	0.446497
$21$	−0.0551718	−0.0120395
$22$	−0.803323	−0.171269
$23$	−7.66615	−1.59850	−0.799251	−	0.600997i	$-0.794770\pi$
$23$	−7.66615	−1.59850	−0.799251	+	0.600997i	$0.794770\pi$
$24$	0.427516	0.0872663
$25$	−4.39489	−0.878977
$26$	−1.23680	−0.242556
$27$	2.07324	0.398995
$28$	0.401354	0.0758487
$29$	1.24255	0.230736	0.115368	−	0.993323i	$-0.463195\pi$
$29$	1.24255	0.230736	0.115368	+	0.993323i	$0.463195\pi$
$30$	0.586591	0.107096
$31$	2.87128	0.515697	0.257849	−	0.966185i	$-0.416986\pi$
$31$	2.87128	0.515697	0.257849	+	0.966185i	$0.416986\pi$
$32$	7.86128	1.38969
$33$	−0.132643	−0.0230901
$34$	2.13704	0.366499
$35$	0.121627	0.0205587
$36$	−7.38120	−1.23020
$37$	−1.69051	−0.277919	−0.138959	−	0.990298i	$-0.544376\pi$
$37$	−1.69051	−0.277919	−0.138959	+	0.990298i	$0.544376\pi$
$38$	3.37564	0.547600
$39$	−0.204216	−0.0327008
$40$	−0.942465	−0.149017
$41$	−3.75910	−0.587073	−0.293536	−	0.955948i	$-0.594832\pi$
$41$	−3.75910	−0.587073	−0.293536	+	0.955948i	$0.594832\pi$
$42$	0.117904	0.0181930
$43$	−3.70174	−0.564510	−0.282255	−	0.959339i	$-0.591083\pi$
$43$	−3.70174	−0.564510	−0.282255	+	0.959339i	$0.591083\pi$
$44$	0.964924	0.145468
$45$	−2.23681	−0.333445
$46$	16.3829	2.41552
$47$	−3.60782	−0.526255	−0.263128	−	0.964761i	$-0.584754\pi$
$47$	−3.60782	−0.526255	−0.263128	+	0.964761i	$0.584754\pi$
$48$	0.897931	0.129605
$49$	−6.97555	−0.996508
$50$	9.39205	1.32824
$51$	0.352862	0.0494106
$52$	1.48560	0.206015
$53$	−0.578301	−0.0794357	−0.0397179	−	0.999211i	$-0.512646\pi$
$53$	−0.578301	−0.0794357	−0.0397179	+	0.999211i	$0.512646\pi$
$54$	−4.43059	−0.602927
$55$	0.292413	0.0394289
$56$	−0.189435	−0.0253143
$57$	0.557375	0.0738262
$58$	−2.65538	−0.348668
$59$	0.819339	0.106669	0.0533344	−	0.998577i	$-0.483015\pi$
$59$	0.819339	0.106669	0.0533344	+	0.998577i	$0.483015\pi$
$60$	−0.704593	−0.0909626
$61$	11.8297	1.51464	0.757320	−	0.653044i	$-0.226508\pi$
$61$	11.8297	1.51464	0.757320	+	0.653044i	$0.226508\pi$
$62$	−6.13604	−0.779278
$63$	−0.449597	−0.0566439
$64$	−11.7104	−1.46380
$65$	0.450199	0.0558403
$66$	0.283462	0.0348918
$67$	−10.0333	−1.22576	−0.612879	−	0.790177i	$-0.709989\pi$
$67$	−10.0333	−1.22576	−0.612879	+	0.790177i	$0.709989\pi$
$68$	−2.56694	−0.311287
$69$	2.70509	0.325655
$70$	−0.259922	−0.0310666
$71$	6.74799	0.800839	0.400419	−	0.916332i	$-0.368864\pi$
$71$	6.74799	0.800839	0.400419	+	0.916332i	$0.368864\pi$
$72$	3.48384	0.410575
$73$	9.80368	1.14743	0.573717	−	0.819053i	$-0.305501\pi$
$73$	9.80368	1.14743	0.573717	+	0.819053i	$0.305501\pi$
$74$	3.61269	0.419967
$75$	1.55079	0.179070
$76$	−4.05470	−0.465105
$77$	0.0587747	0.00669799
$78$	0.436419	0.0494147
$79$	−3.64420	−0.410005	−0.205002	−	0.978761i	$-0.565720\pi$
$79$	−3.64420	−0.410005	−0.205002	+	0.978761i	$0.565720\pi$
$80$	−1.97950	−0.221315
$81$	7.89490	0.877211
$82$	8.03335	0.887135
$83$	14.6150	1.60420	0.802102	−	0.597186i	$-0.203715\pi$
$83$	14.6150	1.60420	0.802102	+	0.597186i	$0.203715\pi$
$84$	−0.141622	−0.0154523
$85$	−0.777890	−0.0843740
$86$	7.91077	0.853040
$87$	−0.438449	−0.0470067
$88$	−0.455434	−0.0485494
$89$	−16.7631	−1.77689	−0.888443	−	0.458988i	$-0.848212\pi$
$89$	−16.7631	−1.77689	−0.888443	+	0.458988i	$0.848212\pi$
$90$	4.78016	0.503873
$91$	0.0904895	0.00948588
$92$	−19.6785	−2.05163
$93$	−1.01317	−0.105060
$94$	7.71006	0.795232
$95$	−1.22874	−0.126066
$96$	−2.77395	−0.283115
$97$	9.68554	0.983417	0.491709	−	0.870760i	$-0.336373\pi$
$97$	9.68554	0.983417	0.491709	+	0.870760i	$0.336373\pi$
$98$	14.9070	1.50584
$99$	−1.08091	−0.108636
$100$	−11.2814	−1.12814
$101$	−3.26809	−0.325188	−0.162594	−	0.986693i	$-0.551986\pi$
$101$	−3.26809	−0.325188	−0.162594	+	0.986693i	$0.551986\pi$
$102$	−0.754080	−0.0746650
$103$	1.82334	0.179659	0.0898293	−	0.995957i	$-0.471368\pi$
$103$	1.82334	0.179659	0.0898293	+	0.995957i	$0.471368\pi$
$104$	−0.701186	−0.0687569
$105$	−0.0429176	−0.00418833
$106$	1.23585	0.120036
$107$	8.97797	0.867933	0.433967	−	0.900929i	$-0.357114\pi$
$107$	8.97797	0.867933	0.433967	+	0.900929i	$0.357114\pi$
$108$	5.32187	0.512097
$109$	9.21468	0.882606	0.441303	−	0.897358i	$-0.354516\pi$
$109$	9.21468	0.882606	0.441303	+	0.897358i	$0.354516\pi$
$110$	−0.624897	−0.0595816
$111$	0.596518	0.0566190
$112$	−0.397878	−0.0375960
$113$	12.2382	1.15127	0.575637	−	0.817705i	$-0.304754\pi$
$113$	12.2382	1.15127	0.575637	+	0.817705i	$0.304754\pi$
$114$	−1.19113	−0.111560
$115$	−5.96342	−0.556092
$116$	3.18955	0.296142
$117$	−1.66417	−0.153853
$118$	−1.75096	−0.161189
$119$	−0.156355	−0.0143331
$120$	0.332560	0.0303585
$121$	−10.8587	−0.987154
$122$	−25.2806	−2.28880
$123$	1.32644	0.119601
$124$	7.37040	0.661881
$125$	−7.30819	−0.653664
$126$	0.960807	0.0855955
$127$	−9.78197	−0.868009	−0.434005	−	0.900911i	$-0.642900\pi$
$127$	−9.78197	−0.868009	−0.434005	+	0.900911i	$0.642900\pi$
$128$	9.30311	0.822287
$129$	1.30620	0.115005
$130$	−0.962092	−0.0843811
$131$	14.7882	1.29205	0.646024	−	0.763317i	$-0.276430\pi$
$131$	14.7882	1.29205	0.646024	+	0.763317i	$0.276430\pi$
$132$	−0.340485	−0.0296354
$133$	−0.246976	−0.0214156
$134$	21.4415	1.85226
$135$	1.61275	0.138803
$136$	1.21157	0.103891
$137$	−1.39955	−0.119571	−0.0597857	−	0.998211i	$-0.519042\pi$
$137$	−1.39955	−0.119571	−0.0597857	+	0.998211i	$0.519042\pi$
$138$	−5.78089	−0.492102
$139$	5.40477	0.458426	0.229213	−	0.973376i	$-0.426385\pi$
$139$	5.40477	0.458426	0.229213	+	0.973376i	$0.426385\pi$
$140$	0.312209	0.0263865
$141$	1.27306	0.107211
$142$	−14.4207	−1.21016
$143$	0.217552	0.0181926
$144$	7.31728	0.609773
$145$	0.966568	0.0802691
$146$	−20.9509	−1.73391
$147$	2.46141	0.203013
$148$	−4.33944	−0.356700
$149$	2.11968	0.173651	0.0868254	−	0.996224i	$-0.472328\pi$
$149$	2.11968	0.173651	0.0868254	+	0.996224i	$0.472328\pi$
$150$	−3.31410	−0.270595
$151$	−1.56538	−0.127389	−0.0636944	−	0.997969i	$-0.520288\pi$
$151$	−1.56538	−0.127389	−0.0636944	+	0.997969i	$0.520288\pi$
$152$	1.91377	0.155227
$153$	2.87549	0.232469
$154$	−0.125604	−0.0101214
$155$	2.23354	0.179402
$156$	−0.524211	−0.0419705
$157$	4.32365	0.345065	0.172532	−	0.985004i	$-0.444805\pi$
$157$	4.32365	0.345065	0.172532	+	0.985004i	$0.444805\pi$
$158$	7.78781	0.619565
$159$	0.204060	0.0161830
$160$	6.11521	0.483450
$161$	−1.19864	−0.0944662
$162$	−16.8717	−1.32557
$163$	1.47889	0.115836	0.0579179	−	0.998321i	$-0.481554\pi$
$163$	1.47889	0.115836	0.0579179	+	0.998321i	$0.481554\pi$
$164$	−9.64937	−0.753489
$165$	−0.103181	−0.00803265
$166$	−31.2328	−2.42414
$167$	15.4286	1.19390	0.596952	−	0.802277i	$-0.296378\pi$
$167$	15.4286	1.19390	0.596952	+	0.802277i	$0.296378\pi$
$168$	0.0668443	0.00515715
$169$	−12.6651	−0.974235
$170$	1.66238	0.127499
$171$	4.54208	0.347341
$172$	−9.50214	−0.724531
$173$	1.77125	0.134666	0.0673329	−	0.997731i	$-0.478551\pi$
$173$	1.77125	0.134666	0.0673329	+	0.997731i	$0.478551\pi$
$174$	0.936983	0.0710325
$175$	−0.687163	−0.0519447
$176$	−0.956568	−0.0721041
$177$	−0.289114	−0.0217311
$178$	35.8234	2.68508
$179$	8.94177	0.668339	0.334170	−	0.942513i	$-0.391544\pi$
$179$	8.94177	0.668339	0.334170	+	0.942513i	$0.391544\pi$
$180$	−5.74176	−0.427966
$181$	−3.01627	−0.224198	−0.112099	−	0.993697i	$-0.535757\pi$
$181$	−3.01627	−0.224198	−0.112099	+	0.993697i	$0.535757\pi$
$182$	−0.193380	−0.0143342
$183$	−4.17426	−0.308570
$184$	9.28805	0.684724
$185$	−1.31503	−0.0966832
$186$	2.16517	0.158758
$187$	−0.375905	−0.0274889
$188$	−9.26106	−0.675432
$189$	0.324161	0.0235793
$190$	2.62587	0.190501
$191$	15.6820	1.13471	0.567355	−	0.823473i	$-0.307967\pi$
$191$	15.6820	1.13471	0.567355	+	0.823473i	$0.307967\pi$
$192$	4.13217	0.298214
$193$	7.52899	0.541948	0.270974	−	0.962587i	$-0.412654\pi$
$193$	7.52899	0.541948	0.270974	+	0.962587i	$0.412654\pi$
$194$	−20.6984	−1.48606
$195$	−0.158858	−0.0113761
$196$	−17.9058	−1.27899
$197$	−4.16720	−0.296901	−0.148450	−	0.988920i	$-0.547428\pi$
$197$	−4.16720	−0.296901	−0.148450	+	0.988920i	$0.547428\pi$
$198$	2.30995	0.164161
$199$	−2.75350	−0.195191	−0.0975953	−	0.995226i	$-0.531115\pi$
$199$	−2.75350	−0.195191	−0.0975953	+	0.995226i	$0.531115\pi$
$200$	5.32470	0.376513
$201$	3.54035	0.249717
$202$	6.98405	0.491396
$203$	0.194279	0.0136357
$204$	0.905774	0.0634169
$205$	−2.92417	−0.204233
$206$	−3.89654	−0.271485
$207$	22.0439	1.53216
$208$	−1.47273	−0.102116
$209$	−0.593774	−0.0410722
$210$	0.0917166	0.00632904
$211$	15.9370	1.09715	0.548576	−	0.836101i	$-0.315170\pi$
$211$	15.9370	1.09715	0.548576	+	0.836101i	$0.315170\pi$
$212$	−1.48446	−0.101953
$213$	−2.38111	−0.163151
$214$	−19.1863	−1.31155
$215$	−2.87955	−0.196384
$216$	−2.51186	−0.170911
$217$	0.448939	0.0304760
$218$	−19.6921	−1.33372
$219$	−3.45935	−0.233761
$220$	0.750605	0.0506058
$221$	−0.578743	−0.0389305
$222$	−1.27478	−0.0855578
$223$	−6.04051	−0.404502	−0.202251	−	0.979334i	$-0.564826\pi$
$223$	−6.04051	−0.404502	−0.202251	+	0.979334i	$0.564826\pi$
$224$	1.22915	0.0821261
$225$	12.6374	0.842496
$226$	−26.1535	−1.73971
$227$	−17.8924	−1.18756	−0.593780	−	0.804627i	$-0.702365\pi$
$227$	−17.8924	−1.18756	−0.593780	+	0.804627i	$0.702365\pi$
$228$	1.43075	0.0947536
$229$	6.64052	0.438818	0.219409	−	0.975633i	$-0.429587\pi$
$229$	6.64052	0.438818	0.219409	+	0.975633i	$0.429587\pi$
$230$	12.7441	0.840319
$231$	−0.0207393	−0.00136455
$232$	−1.50543	−0.0988365
$233$	−9.83896	−0.644572	−0.322286	−	0.946642i	$-0.604451\pi$
$233$	−9.83896	−0.644572	−0.322286	+	0.946642i	$0.604451\pi$
$234$	3.55640	0.232489
$235$	−2.80649	−0.183075
$236$	2.10319	0.136906
$237$	1.28590	0.0835282
$238$	0.334137	0.0216589
$239$	15.2829	0.988568	0.494284	−	0.869300i	$-0.335430\pi$
$239$	15.2829	0.988568	0.494284	+	0.869300i	$0.335430\pi$
$240$	0.698492	0.0450874
$241$	29.6415	1.90937	0.954687	−	0.297611i	$-0.0961899\pi$
$241$	29.6415	1.90937	0.954687	+	0.297611i	$0.0961899\pi$
$242$	23.2055	1.49170
$243$	−9.00552	−0.577704
$244$	30.3661	1.94399
$245$	−5.42621	−0.346668
$246$	−2.83466	−0.180731
$247$	−0.914174	−0.0581675
$248$	−3.47875	−0.220901
$249$	−5.15708	−0.326817
$250$	15.6179	0.987762
$251$	−3.79635	−0.239623	−0.119812	−	0.992797i	$-0.538229\pi$
$251$	−3.79635	−0.239623	−0.119812	+	0.992797i	$0.538229\pi$
$252$	−1.15409	−0.0727007
$253$	−2.88174	−0.181174
$254$	20.9045	1.31166
$255$	0.274488	0.0171891
$256$	3.53976	0.221235
$257$	−7.31500	−0.456297	−0.228149	−	0.973626i	$-0.573267\pi$
$257$	−7.31500	−0.456297	−0.228149	+	0.973626i	$0.573267\pi$
$258$	−2.79141	−0.173786
$259$	−0.264321	−0.0164241
$260$	1.15563	0.0716692
$261$	−3.57294	−0.221159
$262$	−31.6029	−1.95243
$263$	−16.8387	−1.03832	−0.519161	−	0.854677i	$-0.673755\pi$
$263$	−16.8387	−1.03832	−0.519161	+	0.854677i	$0.673755\pi$
$264$	0.160705	0.00989072
$265$	−0.449854	−0.0276343
$266$	0.527798	0.0323614
$267$	5.91506	0.361996
$268$	−25.7547	−1.57322
$269$	0.666161	0.0406166	0.0203083	−	0.999794i	$-0.493535\pi$
$269$	0.666161	0.0406166	0.0203083	+	0.999794i	$0.493535\pi$
$270$	−3.44651	−0.209748
$271$	−30.3251	−1.84212	−0.921058	−	0.389425i	$-0.872674\pi$
$271$	−30.3251	−1.84212	−0.921058	+	0.389425i	$0.872674\pi$
$272$	2.54471	0.154296
$273$	−0.0319303	−0.00193251
$274$	2.99089	0.180686
$275$	−1.65206	−0.0996229
$276$	6.94380	0.417968
$277$	13.9213	0.836448	0.418224	−	0.908344i	$-0.362653\pi$
$277$	13.9213	0.836448	0.418224	+	0.908344i	$0.362653\pi$
$278$	−11.5502	−0.692735
$279$	−8.25633	−0.494294
$280$	−0.147359	−0.00880640
$281$	12.1787	0.726520	0.363260	−	0.931688i	$-0.381664\pi$
$281$	12.1787	0.726520	0.363260	+	0.931688i	$0.381664\pi$
$282$	−2.72059	−0.162009
$283$	−23.6345	−1.40493	−0.702463	−	0.711720i	$-0.747916\pi$
$283$	−23.6345	−1.40493	−0.702463	+	0.711720i	$0.747916\pi$
$284$	17.3217	1.02785
$285$	0.433577	0.0256829
$286$	−0.464918	−0.0274912
$287$	−0.587755	−0.0346941
$288$	−22.6050	−1.33201
$289$	1.00000	0.0588235
$290$	−2.06559	−0.121296
$291$	−3.41766	−0.200347
$292$	25.1654	1.47270
$293$	−4.38262	−0.256036	−0.128018	−	0.991772i	$-0.540861\pi$
$293$	−4.38262	−0.256036	−0.128018	+	0.991772i	$0.540861\pi$
$294$	−5.26012	−0.306777
$295$	0.637356	0.0371083
$296$	2.04817	0.119047
$297$	0.779340	0.0452219
$298$	−4.52983	−0.262406
$299$	−4.43673	−0.256583
$300$	3.98078	0.229830
$301$	−0.578787	−0.0333607
$302$	3.34528	0.192499
$303$	1.15319	0.0662488
$304$	4.01958	0.230539
$305$	9.20222	0.526918
$306$	−6.14503	−0.351288
$307$	−3.60397	−0.205690	−0.102845	−	0.994697i	$-0.532794\pi$
$307$	−3.60397	−0.205690	−0.102845	+	0.994697i	$0.532794\pi$
$308$	0.150871	0.00859666
$309$	−0.643386	−0.0366009
$310$	−4.77316	−0.271098
$311$	0.672032	0.0381074	0.0190537	−	0.999818i	$-0.493935\pi$
$311$	0.672032	0.0381074	0.0190537	+	0.999818i	$0.493935\pi$
$312$	0.247422	0.0140075
$313$	−14.9602	−0.845599	−0.422799	−	0.906223i	$-0.638953\pi$
$313$	−14.9602	−0.845599	−0.422799	+	0.906223i	$0.638953\pi$
$314$	−9.23981	−0.521433
$315$	−0.349737	−0.0197055
$316$	−9.35444	−0.526228
$317$	4.93686	0.277282	0.138641	−	0.990343i	$-0.455727\pi$
$317$	4.93686	0.277282	0.138641	+	0.990343i	$0.455727\pi$
$318$	−0.436085	−0.0244544
$319$	0.467081	0.0261515
$320$	−9.10943	−0.509233
$321$	−3.16798	−0.176820
$322$	2.56154	0.142749
$323$	1.57959	0.0878905
$324$	20.2657	1.12587
$325$	−2.54351	−0.141089
$326$	−3.16045	−0.175041
$327$	−3.25151	−0.179809
$328$	4.55440	0.251475
$329$	−0.564102	−0.0310999
$330$	0.220502	0.0121383
$331$	−11.8065	−0.648947	−0.324473	−	0.945895i	$-0.605187\pi$
$331$	−11.8065	−0.648947	−0.324473	+	0.945895i	$0.605187\pi$
$332$	37.5158	2.05895
$333$	4.86105	0.266384
$334$	−32.9716	−1.80413
$335$	−7.80477	−0.426420
$336$	0.140396	0.00765924
$337$	−13.9723	−0.761120	−0.380560	−	0.924756i	$-0.624269\pi$
$337$	−13.9723	−0.761120	−0.380560	+	0.924756i	$0.624269\pi$
$338$	27.0657	1.47218
$339$	−4.31840	−0.234543
$340$	−1.99679	−0.108291
$341$	1.07933	0.0584489
$342$	−9.70660	−0.524873
$343$	−2.18515	−0.117987
$344$	4.48491	0.241810
$345$	2.10426	0.113290
$346$	−3.78523	−0.203495
$347$	35.4870	1.90504	0.952520	−	0.304477i	$-0.0984815\pi$
$347$	35.4870	1.90504	0.952520	+	0.304477i	$0.0984815\pi$
$348$	−1.12547	−0.0603316
$349$	35.3413	1.89178	0.945888	−	0.324494i	$-0.105194\pi$
$349$	35.3413	1.89178	0.945888	+	0.324494i	$0.105194\pi$
$350$	1.46849	0.0784943
$351$	1.19987	0.0640444
$352$	2.95509	0.157507
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	0.617847	0.0328382
$355$	5.24919	0.278598
$356$	−43.0298	−2.28058
$357$	0.0551718	0.00292000
$358$	−19.1089	−1.00994
$359$	18.1503	0.957937	0.478969	−	0.877832i	$-0.341011\pi$
$359$	18.1503	0.957937	0.478969	+	0.877832i	$0.341011\pi$
$360$	2.71005	0.142832
$361$	−16.5049	−0.868680
$362$	6.44590	0.338789
$363$	3.83162	0.201108
$364$	0.232281	0.0121748
$365$	7.62619	0.399173
$366$	8.92055	0.466285
$367$	−25.8804	−1.35094	−0.675472	−	0.737385i	$-0.736060\pi$
$367$	−25.8804	−1.35094	−0.675472	+	0.737385i	$0.736060\pi$
$368$	19.5081	1.01693
$369$	10.8093	0.562707
$370$	2.81028	0.146099
$371$	−0.0904203	−0.00469439
$372$	−2.60073	−0.134842
$373$	−0.460624	−0.0238502	−0.0119251	−	0.999929i	$-0.503796\pi$
$373$	−0.460624	−0.0238502	−0.0119251	+	0.999929i	$0.503796\pi$
$374$	0.803323	0.0415389
$375$	2.57878	0.133168
$376$	4.37112	0.225423
$377$	0.719118	0.0370365
$378$	−0.692745	−0.0356310
$379$	−18.8186	−0.966647	−0.483324	−	0.875442i	$-0.660571\pi$
$379$	−18.8186	−0.966647	−0.483324	+	0.875442i	$0.660571\pi$
$380$	−3.15411	−0.161802
$381$	3.45168	0.176835
$382$	−33.5131	−1.71468
$383$	−24.5072	−1.25226	−0.626130	−	0.779719i	$-0.715362\pi$
$383$	−24.5072	−1.25226	−0.626130	+	0.779719i	$0.715362\pi$
$384$	−3.28271	−0.167520
$385$	0.0457202	0.00233012
$386$	−16.0897	−0.818946
$387$	10.6443	0.541081
$388$	24.8622	1.26219
$389$	16.8718	0.855435	0.427717	−	0.903913i	$-0.359318\pi$
$389$	16.8718	0.855435	0.427717	+	0.903913i	$0.359318\pi$
$390$	0.339486	0.0171905
$391$	7.66615	0.387694
$392$	8.45134	0.426857
$393$	−5.21818	−0.263223
$394$	8.90546	0.448651
$395$	−2.83479	−0.142634
$396$	−2.77463	−0.139430
$397$	8.15241	0.409158	0.204579	−	0.978850i	$-0.434418\pi$
$397$	8.15241	0.409158	0.204579	+	0.978850i	$0.434418\pi$
$398$	5.88434	0.294956
$399$	0.0871485	0.00436288
$400$	11.1837	0.559185
$401$	−33.1855	−1.65720	−0.828602	−	0.559838i	$-0.810863\pi$
$401$	−33.1855	−1.65720	−0.828602	+	0.559838i	$0.810863\pi$
$402$	−7.56588	−0.377352
$403$	1.66173	0.0827769
$404$	−8.38899	−0.417368
$405$	6.14136	0.305167
$406$	−0.415182	−0.0206052
$407$	−0.635472	−0.0314992
$408$	−0.427516	−0.0211652
$409$	−22.2796	−1.10165	−0.550827	−	0.834619i	$-0.685688\pi$
$409$	−22.2796	−1.10165	−0.550827	+	0.834619i	$0.685688\pi$
$410$	6.24906	0.308619
$411$	0.493847	0.0243597
$412$	4.68039	0.230586
$413$	0.128108	0.00630378
$414$	−47.1087	−2.31527
$415$	11.3689	0.558076
$416$	4.54966	0.223065
$417$	−1.90714	−0.0933929
$418$	1.26892	0.0620648
$419$	32.6676	1.59592	0.797958	−	0.602713i	$-0.205914\pi$
$419$	32.6676	1.59592	0.797958	+	0.602713i	$0.205914\pi$
$420$	−0.110167	−0.00537559
$421$	−5.89623	−0.287365	−0.143682	−	0.989624i	$-0.545894\pi$
$421$	−5.89623	−0.287365	−0.143682	+	0.989624i	$0.545894\pi$
$422$	−34.0581	−1.65792
$423$	10.3743	0.504414
$424$	0.700650	0.0340266
$425$	4.39489	0.213183
$426$	5.08852	0.246540
$427$	1.84964	0.0895102
$428$	23.0459	1.11396
$429$	−0.0767660	−0.00370630
$430$	6.15371	0.296758
$431$	18.7529	0.903297	0.451648	−	0.892196i	$-0.350836\pi$
$431$	18.7529	0.903297	0.451648	+	0.892196i	$0.350836\pi$
$432$	−5.27578	−0.253831
$433$	−6.42838	−0.308928	−0.154464	−	0.987998i	$-0.549365\pi$
$433$	−6.42838	−0.308928	−0.154464	+	0.987998i	$0.549365\pi$
$434$	−0.959401	−0.0460527
$435$	−0.341065	−0.0163528
$436$	23.6535	1.13280
$437$	12.1093	0.579268
$438$	7.39276	0.353240
$439$	−17.8998	−0.854312	−0.427156	−	0.904178i	$-0.640485\pi$
$439$	−17.8998	−0.854312	−0.427156	+	0.904178i	$0.640485\pi$
$440$	−0.354277	−0.0168895
$441$	20.0581	0.955149
$442$	1.23680	0.0588284
$443$	25.6961	1.22086	0.610430	−	0.792070i	$-0.290997\pi$
$443$	25.6961	1.22086	0.610430	+	0.792070i	$0.290997\pi$
$444$	1.53122	0.0726687
$445$	−13.0399	−0.618148
$446$	12.9088	0.611249
$447$	−0.747954	−0.0353770
$448$	−1.83099	−0.0865060
$449$	9.00202	0.424831	0.212416	−	0.977179i	$-0.431867\pi$
$449$	9.00202	0.424831	0.212416	+	0.977179i	$0.431867\pi$
$450$	−27.0067	−1.27311
$451$	−1.41306	−0.0665386
$452$	31.4147	1.47762
$453$	0.552363	0.0259523
$454$	38.2368	1.79454
$455$	0.0703909	0.00329998
$456$	−0.675297	−0.0316237
$457$	−11.2944	−0.528328	−0.264164	−	0.964478i	$-0.585096\pi$
$457$	−11.2944	−0.528328	−0.264164	+	0.964478i	$0.585096\pi$
$458$	−14.1911	−0.663105
$459$	−2.07324	−0.0967704
$460$	−15.3077	−0.713726
$461$	22.1441	1.03135	0.515676	−	0.856784i	$-0.327541\pi$
$461$	22.1441	1.03135	0.515676	+	0.856784i	$0.327541\pi$
$462$	0.0443208	0.00206199
$463$	−12.4873	−0.580335	−0.290167	−	0.956976i	$-0.593711\pi$
$463$	−12.4873	−0.580335	−0.290167	+	0.956976i	$0.593711\pi$
$464$	−3.16193	−0.146789
$465$	−0.788132	−0.0365487
$466$	21.0263	0.974022
$467$	19.3004	0.893117	0.446558	−	0.894754i	$-0.352649\pi$
$467$	19.3004	0.893117	0.446558	+	0.894754i	$0.352649\pi$
$468$	−4.27182	−0.197465
$469$	−1.56875	−0.0724382
$470$	5.99758	0.276648
$471$	−1.52565	−0.0702983
$472$	−0.992684	−0.0456920
$473$	−1.39150	−0.0639814
$474$	−2.74802	−0.126221
$475$	6.94210	0.318525
$476$	−0.401354	−0.0183960
$477$	1.66290	0.0761388
$478$	−32.6602	−1.49384
$479$	−15.6577	−0.715417	−0.357709	−	0.933833i	$-0.616442\pi$
$479$	−15.6577	−0.715417	−0.357709	+	0.933833i	$0.616442\pi$
$480$	−2.15782	−0.0984908
$481$	−0.978374	−0.0446100
$482$	−63.3450	−2.88528
$483$	0.422955	0.0192451
$484$	−27.8736	−1.26698
$485$	7.53428	0.342114
$486$	19.2451	0.872978
$487$	11.4982	0.521033	0.260516	−	0.965469i	$-0.416107\pi$
$487$	11.4982	0.521033	0.260516	+	0.965469i	$0.416107\pi$
$488$	−14.3325	−0.648801
$489$	−0.521845	−0.0235986
$490$	11.5960	0.523855
$491$	38.6283	1.74327	0.871635	−	0.490156i	$-0.163060\pi$
$491$	38.6283	1.74327	0.871635	+	0.490156i	$0.163060\pi$
$492$	3.40490	0.153505
$493$	−1.24255	−0.0559617
$494$	1.95363	0.0878978
$495$	−0.840829	−0.0377925
$496$	−7.30657	−0.328075
$497$	1.05508	0.0473269
$498$	11.0209	0.493857
$499$	−8.51296	−0.381093	−0.190546	−	0.981678i	$-0.561026\pi$
$499$	−8.51296	−0.381093	−0.190546	+	0.981678i	$0.561026\pi$
$500$	−18.7597	−0.838958
$501$	−5.44418	−0.243228
$502$	8.11294	0.362098
$503$	19.4605	0.867699	0.433849	−	0.900985i	$-0.357155\pi$
$503$	19.4605	0.867699	0.433849	+	0.900985i	$0.357155\pi$
$504$	0.544717	0.0242636
$505$	−2.54222	−0.113127
$506$	6.15840	0.273774
$507$	4.46902	0.198476
$508$	−25.1097	−1.11406
$509$	−28.5630	−1.26603	−0.633016	−	0.774139i	$-0.718183\pi$
$509$	−28.5630	−1.26603	−0.633016	+	0.774139i	$0.718183\pi$
$510$	−0.586591	−0.0259747
$511$	1.53286	0.0678096
$512$	−26.1708	−1.15660
$513$	−3.27485	−0.144588
$514$	15.6325	0.689518
$515$	1.41835	0.0625002
$516$	3.35294	0.147605
$517$	−1.35620	−0.0596455
$518$	0.564863	0.0248187
$519$	−0.625007	−0.0274348
$520$	−0.545446	−0.0239194
$521$	17.9747	0.787486	0.393743	−	0.919221i	$-0.371180\pi$
$521$	17.9747	0.787486	0.393743	+	0.919221i	$0.371180\pi$
$522$	7.63551	0.334197
$523$	37.4523	1.63768	0.818838	−	0.574024i	$-0.194619\pi$
$523$	37.4523	1.63768	0.818838	+	0.574024i	$0.194619\pi$
$524$	37.9603	1.65830
$525$	0.242474	0.0105824
$526$	35.9851	1.56902
$527$	−2.87128	−0.125075
$528$	0.337537	0.0146894
$529$	35.7698	1.55521
$530$	0.961356	0.0417587
$531$	−2.35600	−0.102242
$532$	−0.633972	−0.0274862
$533$	−2.17555	−0.0942337
$534$	−12.6407	−0.547017
$535$	6.98388	0.301939
$536$	12.1560	0.525057
$537$	−3.15521	−0.136157
$538$	−1.42361	−0.0613763
$539$	−2.62214	−0.112944
$540$	4.13983	0.178150
$541$	22.8702	0.983268	0.491634	−	0.870802i	$-0.336400\pi$
$541$	22.8702	0.983268	0.491634	+	0.870802i	$0.336400\pi$
$542$	64.8058	2.78365
$543$	1.06433	0.0456747
$544$	−7.86128	−0.337049
$545$	7.16801	0.307044
$546$	0.0682363	0.00292024
$547$	41.5809	1.77787	0.888936	−	0.458032i	$-0.151446\pi$
$547$	41.5809	1.77787	0.888936	+	0.458032i	$0.151446\pi$
$548$	−3.59255	−0.153466
$549$	−34.0162	−1.45178
$550$	3.53052	0.150542
$551$	−1.96271	−0.0836145
$552$	−3.27740	−0.139495
$553$	−0.569790	−0.0242299
$554$	−29.7503	−1.26397
$555$	0.464026	0.0196968
$556$	13.8737	0.588376
$557$	45.3031	1.91956	0.959778	−	0.280760i	$-0.0905866\pi$
$557$	45.3031	1.91956	0.959778	+	0.280760i	$0.0905866\pi$
$558$	17.6441	0.746935
$559$	−2.14236	−0.0906121
$560$	−0.309506	−0.0130790
$561$	0.132643	0.00560017
$562$	−26.0264	−1.09786
$563$	30.9989	1.30645	0.653223	−	0.757165i	$-0.273416\pi$
$563$	30.9989	1.30645	0.653223	+	0.757165i	$0.273416\pi$
$564$	3.26787	0.137602
$565$	9.51998	0.400509
$566$	50.5079	2.12300
$567$	1.23441	0.0518403
$568$	−8.17563	−0.343042
$569$	26.5840	1.11446	0.557229	−	0.830359i	$-0.311864\pi$
$569$	26.5840	1.11446	0.557229	+	0.830359i	$0.311864\pi$
$570$	−0.926571	−0.0388098
$571$	26.8346	1.12299	0.561496	−	0.827479i	$-0.310226\pi$
$571$	26.8346	1.12299	0.561496	+	0.827479i	$0.310226\pi$
$572$	0.558443	0.0233497
$573$	−5.53358	−0.231169
$574$	1.25605	0.0524267
$575$	33.6919	1.40505
$576$	33.6732	1.40305
$577$	25.9272	1.07936	0.539682	−	0.841869i	$-0.318544\pi$
$577$	25.9272	1.07936	0.539682	+	0.841869i	$0.318544\pi$
$578$	−2.13704	−0.0888891
$579$	−2.65669	−0.110408
$580$	2.48112	0.103023
$581$	2.28513	0.0948032
$582$	7.30367	0.302747
$583$	−0.217386	−0.00900321
$584$	−11.8778	−0.491507
$585$	−1.29454	−0.0535227
$586$	9.36584	0.386899
$587$	15.8733	0.655163	0.327581	−	0.944823i	$-0.393766\pi$
$587$	15.8733	0.655163	0.327581	+	0.944823i	$0.393766\pi$
$588$	6.31828	0.260561
$589$	−4.53543	−0.186879
$590$	−1.36205	−0.0560749
$591$	1.47045	0.0604860
$592$	4.30187	0.176806
$593$	12.2484	0.502980	0.251490	−	0.967860i	$-0.419079\pi$
$593$	12.2484	0.502980	0.251490	+	0.967860i	$0.419079\pi$
$594$	−1.66548	−0.0683354
$595$	−0.121627	−0.00498623
$596$	5.44108	0.222875
$597$	0.971606	0.0397652
$598$	9.48147	0.387726
$599$	5.15524	0.210638	0.105319	−	0.994439i	$-0.466414\pi$
$599$	5.15524	0.210638	0.105319	+	0.994439i	$0.466414\pi$
$600$	−1.87888	−0.0767051
$601$	−3.00856	−0.122722	−0.0613608	−	0.998116i	$-0.519544\pi$
$601$	−3.00856	−0.122722	−0.0613608	+	0.998116i	$0.519544\pi$
$602$	1.23689	0.0504119
$603$	28.8505	1.17488
$604$	−4.01823	−0.163499
$605$	−8.44687	−0.343414
$606$	−2.46440	−0.100110
$607$	41.5888	1.68804	0.844019	−	0.536314i	$-0.180184\pi$
$607$	41.5888	1.68804	0.844019	+	0.536314i	$0.180184\pi$
$608$	−12.4176	−0.503598
$609$	−0.0685537	−0.00277794
$610$	−19.6655	−0.796233
$611$	−2.08800	−0.0844716
$612$	7.38120	0.298367
$613$	8.05399	0.325298	0.162649	−	0.986684i	$-0.447996\pi$
$613$	8.05399	0.325298	0.162649	+	0.986684i	$0.447996\pi$
$614$	7.70183	0.310821
$615$	1.03183	0.0416073
$616$	−0.0712094	−0.00286911
$617$	13.3935	0.539200	0.269600	−	0.962972i	$-0.413108\pi$
$617$	13.3935	0.539200	0.269600	+	0.962972i	$0.413108\pi$
$618$	1.37494	0.0553082
$619$	9.28306	0.373118	0.186559	−	0.982444i	$-0.440267\pi$
$619$	9.28306	0.373118	0.186559	+	0.982444i	$0.440267\pi$
$620$	5.73336	0.230257
$621$	−15.8937	−0.637794
$622$	−1.43616	−0.0575847
$623$	−2.62100	−0.105008
$624$	0.519672	0.0208035
$625$	16.2895	0.651579
$626$	31.9705	1.27780
$627$	0.209520	0.00836743
$628$	11.0985	0.442880
$629$	1.69051	0.0674052
$630$	0.747403	0.0297772
$631$	−30.1133	−1.19879	−0.599395	−	0.800453i	$-0.704592\pi$
$631$	−30.1133	−1.19879	−0.599395	+	0.800453i	$0.704592\pi$
$632$	4.41519	0.175627
$633$	−5.62358	−0.223517
$634$	−10.5503	−0.419004
$635$	−7.60930	−0.301966
$636$	0.523810	0.0207704
$637$	−4.03705	−0.159954
$638$	−0.998170	−0.0395179
$639$	−19.4038	−0.767601
$640$	7.23680	0.286060
$641$	4.68563	0.185071	0.0925356	−	0.995709i	$-0.470503\pi$
$641$	4.68563	0.185071	0.0925356	+	0.995709i	$0.470503\pi$
$642$	6.77011	0.267195
$643$	14.8949	0.587397	0.293698	−	0.955898i	$-0.405114\pi$
$643$	14.8949	0.587397	0.293698	+	0.955898i	$0.405114\pi$
$644$	−3.07684	−0.121244
$645$	1.01608	0.0400082
$646$	−3.37564	−0.132813
$647$	−24.0243	−0.944491	−0.472246	−	0.881467i	$-0.656556\pi$
$647$	−24.0243	−0.944491	−0.472246	+	0.881467i	$0.656556\pi$
$648$	−9.56519	−0.375756
$649$	0.307994	0.0120898
$650$	5.43558	0.213201
$651$	−0.158414	−0.00620872
$652$	3.79622	0.148672
$653$	−10.2064	−0.399407	−0.199704	−	0.979856i	$-0.563998\pi$
$653$	−10.2064	−0.399407	−0.199704	+	0.979856i	$0.563998\pi$
$654$	6.94861	0.271712
$655$	11.5036	0.449482
$656$	9.56582	0.373482
$657$	−28.1904	−1.09981
$658$	1.20551	0.0469956
$659$	−27.2079	−1.05987	−0.529934	−	0.848039i	$-0.677783\pi$
$659$	−27.2079	−1.05987	−0.529934	+	0.848039i	$0.677783\pi$
$660$	−0.264860	−0.0103097
$661$	10.7350	0.417542	0.208771	−	0.977965i	$-0.433054\pi$
$661$	10.7350	0.417542	0.208771	+	0.977965i	$0.433054\pi$
$662$	25.2311	0.980633
$663$	0.204216	0.00793111
$664$	−17.7070	−0.687167
$665$	−0.192120	−0.00745011
$666$	−10.3883	−0.402537
$667$	−9.52558	−0.368832
$668$	39.6044	1.53234
$669$	2.13146	0.0824072
$670$	16.6791	0.644370
$671$	4.44685	0.171669
$672$	−0.433721	−0.0167311
$673$	−13.5584	−0.522638	−0.261319	−	0.965252i	$-0.584157\pi$
$673$	−13.5584	−0.522638	−0.261319	+	0.965252i	$0.584157\pi$
$674$	29.8594	1.15014
$675$	−9.11164	−0.350707
$676$	−32.5104	−1.25040
$677$	4.35426	0.167348	0.0836740	−	0.996493i	$-0.473335\pi$
$677$	4.35426	0.167348	0.0836740	+	0.996493i	$0.473335\pi$
$678$	9.22859	0.354422
$679$	1.51438	0.0581167
$680$	0.942465	0.0361419
$681$	6.31355	0.241936
$682$	−2.30657	−0.0883230
$683$	35.6845	1.36543	0.682714	−	0.730686i	$-0.260800\pi$
$683$	35.6845	1.36543	0.682714	+	0.730686i	$0.260800\pi$
$684$	11.6592	0.445802
$685$	−1.08869	−0.0415968
$686$	4.66975	0.178292
$687$	−2.34319	−0.0893982
$688$	9.41986	0.359129
$689$	−0.334688	−0.0127506
$690$	−4.49690	−0.171194
$691$	8.55478	0.325439	0.162720	−	0.986672i	$-0.447973\pi$
$691$	8.55478	0.325439	0.162720	+	0.986672i	$0.447973\pi$
$692$	4.54669	0.172839
$693$	−0.169006	−0.00642000
$694$	−75.8370	−2.87873
$695$	4.20431	0.159479
$696$	0.531210	0.0201355
$697$	3.75910	0.142386
$698$	−75.5257	−2.85869
$699$	3.47180	0.131315
$700$	−1.76390	−0.0666693
$701$	37.4793	1.41557	0.707786	−	0.706427i	$-0.249694\pi$
$701$	37.4793	1.41557	0.707786	+	0.706427i	$0.249694\pi$
$702$	−2.56417	−0.0967785
$703$	2.67031	0.100713
$704$	−4.40201	−0.165907
$705$	0.990304	0.0372970
$706$	−2.13704	−0.0804285
$707$	−0.510983	−0.0192175
$708$	−0.742136	−0.0278912
$709$	−1.99809	−0.0750399	−0.0375200	−	0.999296i	$-0.511946\pi$
$709$	−1.99809	−0.0750399	−0.0375200	+	0.999296i	$0.511946\pi$
$710$	−11.2177	−0.420994
$711$	10.4789	0.392988
$712$	20.3096	0.761135
$713$	−22.0117	−0.824343
$714$	−0.117904	−0.00441246
$715$	0.169232	0.00632891
$716$	22.9530	0.857792
$717$	−5.39275	−0.201396
$718$	−38.7879	−1.44755
$719$	−13.3681	−0.498545	−0.249273	−	0.968433i	$-0.580192\pi$
$719$	−13.3681	−0.498545	−0.249273	+	0.968433i	$0.580192\pi$
$720$	5.69204	0.212130
$721$	0.285088	0.0106172
$722$	35.2716	1.31267
$723$	−10.4593	−0.388987
$724$	−7.74259	−0.287751
$725$	−5.46087	−0.202812
$726$	−8.18832	−0.303897
$727$	−49.3235	−1.82931	−0.914654	−	0.404239i	$-0.867536\pi$
$727$	−49.3235	−1.82931	−0.914654	+	0.404239i	$0.867536\pi$
$728$	−0.109634	−0.00406331
$729$	−20.5070	−0.759518
$730$	−16.2975	−0.603196
$731$	3.70174	0.136914
$732$	−10.7151	−0.396040
$733$	−46.8040	−1.72874	−0.864372	−	0.502853i	$-0.832284\pi$
$733$	−46.8040	−1.72874	−0.864372	+	0.502853i	$0.832284\pi$
$734$	55.3074	2.04143
$735$	1.91470	0.0706249
$736$	−60.2657	−2.22142
$737$	−3.77155	−0.138927
$738$	−23.0998	−0.850315
$739$	5.21204	0.191728	0.0958640	−	0.995394i	$-0.469439\pi$
$739$	5.21204	0.191728	0.0958640	+	0.995394i	$0.469439\pi$
$740$	−3.37561	−0.124090
$741$	0.322577	0.0118502
$742$	0.193232	0.00709376
$743$	42.9155	1.57442	0.787208	−	0.616687i	$-0.211526\pi$
$743$	42.9155	1.57442	0.787208	+	0.616687i	$0.211526\pi$
$744$	1.22752	0.0450030
$745$	1.64888	0.0604102
$746$	0.984371	0.0360404
$747$	−42.0253	−1.53762
$748$	−0.964924	−0.0352811
$749$	1.40375	0.0512920
$750$	−5.51096	−0.201232
$751$	7.51894	0.274370	0.137185	−	0.990545i	$-0.456195\pi$
$751$	7.51894	0.274370	0.137185	+	0.990545i	$0.456195\pi$
$752$	9.18086	0.334792
$753$	1.33959	0.0488172
$754$	−1.53678	−0.0559663
$755$	−1.21769	−0.0443164
$756$	0.832101	0.0302632
$757$	−20.3152	−0.738367	−0.369184	−	0.929356i	$-0.620363\pi$
$757$	−20.3152	−0.738367	−0.369184	+	0.929356i	$0.620363\pi$
$758$	40.2161	1.46071
$759$	1.01686	0.0369096
$760$	1.48870	0.0540010
$761$	16.5980	0.601676	0.300838	−	0.953675i	$-0.402734\pi$
$761$	16.5980	0.601676	0.300838	+	0.953675i	$0.402734\pi$
$762$	−7.37639	−0.267218
$763$	1.44076	0.0521591
$764$	40.2547	1.45636
$765$	2.23681	0.0808722
$766$	52.3728	1.89231
$767$	0.474187	0.0171219
$768$	−1.24905	−0.0450711
$769$	44.1706	1.59283	0.796416	−	0.604749i	$-0.206727\pi$
$769$	44.1706	1.59283	0.796416	+	0.604749i	$0.206727\pi$
$770$	−0.0977059	−0.00352108
$771$	2.58119	0.0929592
$772$	19.3264	0.695574
$773$	−15.8349	−0.569540	−0.284770	−	0.958596i	$-0.591917\pi$
$773$	−15.8349	−0.569540	−0.284770	+	0.958596i	$0.591917\pi$
$774$	−22.7473	−0.817636
$775$	−12.6190	−0.453286
$776$	−11.7347	−0.421250
$777$	0.0932687	0.00334600
$778$	−36.0557	−1.29266
$779$	5.93782	0.212744
$780$	−0.407778	−0.0146008
$781$	2.53660	0.0907667
$782$	−16.3829	−0.585850
$783$	2.57610	0.0920624
$784$	17.7508	0.633955
$785$	3.36333	0.120042
$786$	11.1515	0.397760
$787$	−5.13264	−0.182959	−0.0914794	−	0.995807i	$-0.529160\pi$
$787$	−5.13264	−0.182959	−0.0914794	+	0.995807i	$0.529160\pi$
$788$	−10.6969	−0.381062
$789$	5.94175	0.211532
$790$	6.05806	0.215536
$791$	1.91351	0.0680365
$792$	1.30959	0.0465344
$793$	6.84637	0.243122
$794$	−17.4220	−0.618284
$795$	0.158737	0.00562980
$796$	−7.06807	−0.250521
$797$	−18.5973	−0.658749	−0.329374	−	0.944199i	$-0.606838\pi$
$797$	−18.5973	−0.658749	−0.329374	+	0.944199i	$0.606838\pi$
$798$	−0.186240	−0.00659282
$799$	3.60782	0.127636
$800$	−34.5494	−1.22151
$801$	48.2021	1.70314
$802$	70.9187	2.50423
$803$	3.68525	0.130050
$804$	9.08787	0.320504
$805$	−0.932412	−0.0328632
$806$	−3.55119	−0.125085
$807$	−0.235063	−0.00827461
$808$	3.95951	0.139295
$809$	40.8320	1.43558	0.717788	−	0.696261i	$-0.245154\pi$
$809$	40.8320	1.43558	0.717788	+	0.696261i	$0.245154\pi$
$810$	−13.1243	−0.461142
$811$	8.82025	0.309721	0.154860	−	0.987936i	$-0.450507\pi$
$811$	8.82025	0.309721	0.154860	+	0.987936i	$0.450507\pi$
$812$	0.498702	0.0175010
$813$	10.7006	0.375285
$814$	1.35803	0.0475989
$815$	1.15042	0.0402973
$816$	−0.897931	−0.0314339
$817$	5.84722	0.204568
$818$	47.6123	1.66473
$819$	−0.260201	−0.00909218
$820$	−7.50615	−0.262126
$821$	−19.1072	−0.666847	−0.333423	−	0.942777i	$-0.608204\pi$
$821$	−19.1072	−0.666847	−0.333423	+	0.942777i	$0.608204\pi$
$822$	−1.05537	−0.0368103
$823$	31.2395	1.08894	0.544470	−	0.838780i	$-0.316731\pi$
$823$	31.2395	1.08894	0.544470	+	0.838780i	$0.316731\pi$
$824$	−2.20909	−0.0769573
$825$	0.582949	0.0202957
$826$	−0.273772	−0.00952573
$827$	−43.7273	−1.52055	−0.760273	−	0.649603i	$-0.774935\pi$
$827$	−43.7273	−1.52055	−0.760273	+	0.649603i	$0.774935\pi$
$828$	56.5854	1.96648
$829$	22.9070	0.795595	0.397797	−	0.917473i	$-0.369775\pi$
$829$	22.9070	0.795595	0.397797	+	0.917473i	$0.369775\pi$
$830$	−24.2957	−0.843316
$831$	−4.91229	−0.170405
$832$	−6.77734	−0.234962
$833$	6.97555	0.241689
$834$	4.07562	0.141127
$835$	12.0018	0.415339
$836$	−1.52418	−0.0527148
$837$	5.95284	0.205760
$838$	−69.8119	−2.41161
$839$	−20.8269	−0.719026	−0.359513	−	0.933140i	$-0.617057\pi$
$839$	−20.8269	−0.719026	−0.359513	+	0.933140i	$0.617057\pi$
$840$	0.0519975	0.00179408
$841$	−27.4561	−0.946761
$842$	12.6005	0.434241
$843$	−4.29740	−0.148010
$844$	40.9094	1.40816
$845$	−9.85202	−0.338920
$846$	−22.1702	−0.762227
$847$	−1.69781	−0.0583375
$848$	1.47161	0.0505352
$849$	8.33972	0.286218
$850$	−9.39205	−0.322145
$851$	12.9597	0.444254
$852$	−6.11215	−0.209399
$853$	−18.4147	−0.630507	−0.315253	−	0.949008i	$-0.602090\pi$
$853$	−18.4147	−0.630507	−0.315253	+	0.949008i	$0.602090\pi$
$854$	−3.95275	−0.135260
$855$	3.53324	0.120834
$856$	−10.8774	−0.371782
$857$	−34.3025	−1.17175	−0.585876	−	0.810400i	$-0.699250\pi$
$857$	−34.3025	−1.17175	−0.585876	+	0.810400i	$0.699250\pi$
$858$	0.164052	0.00560064
$859$	−17.0905	−0.583120	−0.291560	−	0.956553i	$-0.594174\pi$
$859$	−17.0905	−0.583120	−0.291560	+	0.956553i	$0.594174\pi$
$860$	−7.39162	−0.252052
$861$	0.207396	0.00706805
$862$	−40.0758	−1.36499
$863$	−2.09664	−0.0713705	−0.0356852	−	0.999363i	$-0.511361\pi$
$863$	−2.09664	−0.0713705	−0.0356852	+	0.999363i	$0.511361\pi$
$864$	16.2983	0.554479
$865$	1.37784	0.0468479
$866$	13.7377	0.466826
$867$	−0.352862	−0.0119838
$868$	1.15240	0.0391150
$869$	−1.36987	−0.0464698
$870$	0.728869	0.0247110
$871$	−5.80668	−0.196752
$872$	−11.1642	−0.378067
$873$	−27.8507	−0.942602
$874$	−25.8781	−0.875341
$875$	−1.14267	−0.0386294
$876$	−8.87993	−0.300025
$877$	−11.6715	−0.394120	−0.197060	−	0.980391i	$-0.563139\pi$
$877$	−11.6715	−0.394120	−0.197060	+	0.980391i	$0.563139\pi$
$878$	38.2526	1.29096
$879$	1.54646	0.0521608
$880$	−0.744105	−0.0250838
$881$	42.9501	1.44703	0.723513	−	0.690310i	$-0.242526\pi$
$881$	42.9501	1.44703	0.723513	+	0.690310i	$0.242526\pi$
$882$	−42.8650	−1.44334
$883$	−12.3565	−0.415828	−0.207914	−	0.978147i	$-0.566667\pi$
$883$	−12.3565	−0.415828	−0.207914	+	0.978147i	$0.566667\pi$
$884$	−1.48560	−0.0499661
$885$	−0.224899	−0.00755989
$886$	−54.9136	−1.84486
$887$	21.7092	0.728924	0.364462	−	0.931218i	$-0.381253\pi$
$887$	21.7092	0.728924	0.364462	+	0.931218i	$0.381253\pi$
$888$	−0.722721	−0.0242529
$889$	−1.52946	−0.0512965
$890$	27.8667	0.934093
$891$	2.96773	0.0994227
$892$	−15.5056	−0.519166
$893$	5.69886	0.190705
$894$	1.59841	0.0534587
$895$	6.95571	0.232504
$896$	1.45459	0.0485944
$897$	1.56555	0.0522723
$898$	−19.2377	−0.641969
$899$	3.56771	0.118990
$900$	32.4395	1.08132
$901$	0.578301	0.0192660
$902$	3.01977	0.100547
$903$	0.204232	0.00679641
$904$	−14.8274	−0.493152
$905$	−2.34633	−0.0779946
$906$	−1.18042	−0.0392169
$907$	−3.14018	−0.104268	−0.0521340	−	0.998640i	$-0.516602\pi$
$907$	−3.14018	−0.104268	−0.0521340	+	0.998640i	$0.516602\pi$
$908$	−45.9287	−1.52420
$909$	9.39737	0.311691
$910$	−0.150428	−0.00498664
$911$	17.1589	0.568501	0.284250	−	0.958750i	$-0.408255\pi$
$911$	17.1589	0.568501	0.284250	+	0.958750i	$0.408255\pi$
$912$	−1.41836	−0.0469665
$913$	5.49385	0.181820
$914$	24.1365	0.798365
$915$	−3.24711	−0.107346
$916$	17.0458	0.563209
$917$	2.31221	0.0763558
$918$	4.43059	0.146231
$919$	49.6398	1.63747	0.818734	−	0.574174i	$-0.194677\pi$
$919$	49.6398	1.63747	0.818734	+	0.574174i	$0.194677\pi$
$920$	7.22508	0.238204
$921$	1.27170	0.0419041
$922$	−47.3228	−1.55849
$923$	3.90535	0.128546
$924$	−0.0532366	−0.00175135
$925$	7.42962	0.244284
$926$	26.6859	0.876953
$927$	−5.24298	−0.172202
$928$	9.76803	0.320651
$929$	11.8854	0.389947	0.194974	−	0.980809i	$-0.437538\pi$
$929$	11.8854	0.389947	0.194974	+	0.980809i	$0.437538\pi$
$930$	1.68427	0.0552293
$931$	11.0185	0.361116
$932$	−25.2560	−0.827288
$933$	−0.237135	−0.00776344
$934$	−41.2458	−1.34960
$935$	−0.292413	−0.00956292
$936$	2.01625	0.0659033
$937$	−45.5740	−1.48884	−0.744419	−	0.667713i	$-0.767273\pi$
$937$	−45.5740	−1.48884	−0.744419	+	0.667713i	$0.767273\pi$
$938$	3.35248	0.109462
$939$	5.27887	0.172270
$940$	−7.20408	−0.234971
$941$	6.68001	0.217762	0.108881	−	0.994055i	$-0.465273\pi$
$941$	6.68001	0.217762	0.108881	+	0.994055i	$0.465273\pi$
$942$	3.26038	0.106229
$943$	28.8178	0.938438
$944$	−2.08498	−0.0678603
$945$	0.252162	0.00820282
$946$	2.97370	0.0966832
$947$	41.8083	1.35859	0.679294	−	0.733867i	$-0.262286\pi$
$947$	41.8083	1.35859	0.679294	+	0.733867i	$0.262286\pi$
$948$	3.30083	0.107206
$949$	5.67382	0.184180
$950$	−14.8355	−0.481328
$951$	−1.74203	−0.0564892
$952$	0.189435	0.00613961
$953$	8.44022	0.273406	0.136703	−	0.990612i	$-0.456349\pi$
$953$	8.44022	0.273406	0.136703	+	0.990612i	$0.456349\pi$
$954$	−3.55368	−0.115055
$955$	12.1989	0.394746
$956$	39.2302	1.26880
$957$	−0.164815	−0.00532771
$958$	33.4611	1.08108
$959$	−0.218826	−0.00706627
$960$	3.21437	0.103743
$961$	−22.7557	−0.734056
$962$	2.09082	0.0674108
$963$	−25.8161	−0.831911
$964$	76.0878	2.45062
$965$	5.85673	0.188535
$966$	−0.903872	−0.0290816
$967$	20.0177	0.643724	0.321862	−	0.946787i	$-0.395691\pi$
$967$	20.0177	0.643724	0.321862	+	0.946787i	$0.395691\pi$
$968$	13.1560	0.422851
$969$	−0.557375	−0.0179055
$970$	−16.1011	−0.516974
$971$	26.3170	0.844552	0.422276	−	0.906467i	$-0.361231\pi$
$971$	26.3170	0.844552	0.422276	+	0.906467i	$0.361231\pi$
$972$	−23.1166	−0.741465
$973$	0.845063	0.0270915
$974$	−24.5721	−0.787340
$975$	0.897508	0.0287433
$976$	−30.1032	−0.963580
$977$	−0.841853	−0.0269333	−0.0134666	−	0.999909i	$-0.504287\pi$
$977$	−0.841853	−0.0269333	−0.0134666	+	0.999909i	$0.504287\pi$
$978$	1.11520	0.0356602
$979$	−6.30133	−0.201391
$980$	−13.9287	−0.444938
$981$	−26.4967	−0.845975
$982$	−82.5501	−2.63428
$983$	−9.15921	−0.292133	−0.146067	−	0.989275i	$-0.546661\pi$
$983$	−9.15921	−0.292133	−0.146067	+	0.989275i	$0.546661\pi$
$984$	−1.60707	−0.0512317
$985$	−3.24162	−0.103287
$986$	2.65538	0.0845645
$987$	0.199050	0.00633583
$988$	−2.34663	−0.0746562
$989$	28.3781	0.902372
$990$	1.79688	0.0571088
$991$	39.7559	1.26289	0.631444	−	0.775422i	$-0.282463\pi$
$991$	39.7559	1.26289	0.631444	+	0.775422i	$0.282463\pi$
$992$	22.5719	0.716659
$993$	4.16608	0.132207
$994$	−2.25475	−0.0715164
$995$	−2.14192	−0.0679035
$996$	−13.2379	−0.419459
$997$	7.12142	0.225538	0.112769	−	0.993621i	$-0.464028\pi$
$997$	7.12142	0.225538	0.112769	+	0.993621i	$0.464028\pi$
$998$	18.1925	0.575875
$999$	−3.50484	−0.110888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.17	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.17	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13704 q^{2} -0.352862 q^{3} +2.56694 q^{4} +0.777890 q^{5} +0.754080 q^{6} +0.156355 q^{7} -1.21157 q^{8} -2.87549 q^{9} +O(q^{10})\)	\(q-2.13704 q^{2} -0.352862 q^{3} +2.56694 q^{4} +0.777890 q^{5} +0.754080 q^{6} +0.156355 q^{7} -1.21157 q^{8} -2.87549 q^{9} -1.66238 q^{10} +0.375905 q^{11} -0.905774 q^{12} +0.578743 q^{13} -0.334137 q^{14} -0.274488 q^{15} -2.54471 q^{16} -1.00000 q^{17} +6.14503 q^{18} -1.57959 q^{19} +1.99679 q^{20} -0.0551718 q^{21} -0.803323 q^{22} -7.66615 q^{23} +0.427516 q^{24} -4.39489 q^{25} -1.23680 q^{26} +2.07324 q^{27} +0.401354 q^{28} +1.24255 q^{29} +0.586591 q^{30} +2.87128 q^{31} +7.86128 q^{32} -0.132643 q^{33} +2.13704 q^{34} +0.121627 q^{35} -7.38120 q^{36} -1.69051 q^{37} +3.37564 q^{38} -0.204216 q^{39} -0.942465 q^{40} -3.75910 q^{41} +0.117904 q^{42} -3.70174 q^{43} +0.964924 q^{44} -2.23681 q^{45} +16.3829 q^{46} -3.60782 q^{47} +0.897931 q^{48} -6.97555 q^{49} +9.39205 q^{50} +0.352862 q^{51} +1.48560 q^{52} -0.578301 q^{53} -4.43059 q^{54} +0.292413 q^{55} -0.189435 q^{56} +0.557375 q^{57} -2.65538 q^{58} +0.819339 q^{59} -0.704593 q^{60} +11.8297 q^{61} -6.13604 q^{62} -0.449597 q^{63} -11.7104 q^{64} +0.450199 q^{65} +0.283462 q^{66} -10.0333 q^{67} -2.56694 q^{68} +2.70509 q^{69} -0.259922 q^{70} +6.74799 q^{71} +3.48384 q^{72} +9.80368 q^{73} +3.61269 q^{74} +1.55079 q^{75} -4.05470 q^{76} +0.0587747 q^{77} +0.436419 q^{78} -3.64420 q^{79} -1.97950 q^{80} +7.89490 q^{81} +8.03335 q^{82} +14.6150 q^{83} -0.141622 q^{84} -0.777890 q^{85} +7.91077 q^{86} -0.438449 q^{87} -0.455434 q^{88} -16.7631 q^{89} +4.78016 q^{90} +0.0904895 q^{91} -19.6785 q^{92} -1.01317 q^{93} +7.71006 q^{94} -1.22874 q^{95} -2.77395 q^{96} +9.68554 q^{97} +14.9070 q^{98} -1.08091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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