LMFDB - Embedded newform 6009.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, 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("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48563 q^{2} +1.00000 q^{3} +4.17837 q^{4} +2.55956 q^{5} -2.48563 q^{6} +1.79588 q^{7} -5.41463 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.48563 q^{2} +1.00000 q^{3} +4.17837 q^{4} +2.55956 q^{5} -2.48563 q^{6} +1.79588 q^{7} -5.41463 q^{8} +1.00000 q^{9} -6.36212 q^{10} +0.0841132 q^{11} +4.17837 q^{12} +4.62871 q^{13} -4.46389 q^{14} +2.55956 q^{15} +5.10204 q^{16} +0.301444 q^{17} -2.48563 q^{18} -6.15254 q^{19} +10.6948 q^{20} +1.79588 q^{21} -0.209075 q^{22} +7.12685 q^{23} -5.41463 q^{24} +1.55133 q^{25} -11.5053 q^{26} +1.00000 q^{27} +7.50384 q^{28} +0.722924 q^{29} -6.36212 q^{30} -4.20575 q^{31} -1.85254 q^{32} +0.0841132 q^{33} -0.749280 q^{34} +4.59665 q^{35} +4.17837 q^{36} -0.341855 q^{37} +15.2929 q^{38} +4.62871 q^{39} -13.8590 q^{40} -6.75121 q^{41} -4.46389 q^{42} +4.18177 q^{43} +0.351456 q^{44} +2.55956 q^{45} -17.7147 q^{46} +6.30652 q^{47} +5.10204 q^{48} -3.77482 q^{49} -3.85603 q^{50} +0.301444 q^{51} +19.3405 q^{52} +11.5844 q^{53} -2.48563 q^{54} +0.215293 q^{55} -9.72401 q^{56} -6.15254 q^{57} -1.79692 q^{58} -1.61013 q^{59} +10.6948 q^{60} +7.39830 q^{61} +10.4539 q^{62} +1.79588 q^{63} -5.59935 q^{64} +11.8474 q^{65} -0.209075 q^{66} -7.98191 q^{67} +1.25955 q^{68} +7.12685 q^{69} -11.4256 q^{70} -3.54694 q^{71} -5.41463 q^{72} +1.81848 q^{73} +0.849726 q^{74} +1.55133 q^{75} -25.7076 q^{76} +0.151057 q^{77} -11.5053 q^{78} -8.12862 q^{79} +13.0590 q^{80} +1.00000 q^{81} +16.7810 q^{82} +12.8259 q^{83} +7.50384 q^{84} +0.771564 q^{85} -10.3943 q^{86} +0.722924 q^{87} -0.455442 q^{88} -5.47104 q^{89} -6.36212 q^{90} +8.31259 q^{91} +29.7786 q^{92} -4.20575 q^{93} -15.6757 q^{94} -15.7478 q^{95} -1.85254 q^{96} -14.2848 q^{97} +9.38282 q^{98} +0.0841132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * 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 $

$2$	−2.48563	−1.75761	−0.878804	−	0.477183i	$-0.841658\pi$
$2$	−2.48563	−1.75761	−0.878804	+	0.477183i	$0.841658\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.17837	2.08919
$5$	2.55956	1.14467	0.572334	−	0.820020i	$-0.306038\pi$
$5$	2.55956	1.14467	0.572334	+	0.820020i	$0.306038\pi$
$6$	−2.48563	−1.01476
$7$	1.79588	0.678778	0.339389	−	0.940646i	$-0.389780\pi$
$7$	1.79588	0.678778	0.339389	+	0.940646i	$0.389780\pi$
$8$	−5.41463	−1.91436
$9$	1.00000	0.333333
$10$	−6.36212	−2.01188
$11$	0.0841132	0.0253611	0.0126805	−	0.999920i	$-0.495964\pi$
$11$	0.0841132	0.0253611	0.0126805	+	0.999920i	$0.495964\pi$
$12$	4.17837	1.20619
$13$	4.62871	1.28377	0.641886	−	0.766800i	$-0.278152\pi$
$13$	4.62871	1.28377	0.641886	+	0.766800i	$0.278152\pi$
$14$	−4.46389	−1.19303
$15$	2.55956	0.660875
$16$	5.10204	1.27551
$17$	0.301444	0.0731110	0.0365555	−	0.999332i	$-0.488361\pi$
$17$	0.301444	0.0731110	0.0365555	+	0.999332i	$0.488361\pi$
$18$	−2.48563	−0.585869
$19$	−6.15254	−1.41149	−0.705744	−	0.708467i	$-0.749387\pi$
$19$	−6.15254	−1.41149	−0.705744	+	0.708467i	$0.749387\pi$
$20$	10.6948	2.39142
$21$	1.79588	0.391893
$22$	−0.209075	−0.0445749
$23$	7.12685	1.48605	0.743025	−	0.669263i	$-0.233390\pi$
$23$	7.12685	1.48605	0.743025	+	0.669263i	$0.233390\pi$
$24$	−5.41463	−1.10526
$25$	1.55133	0.310266
$26$	−11.5053	−2.25637
$27$	1.00000	0.192450
$28$	7.50384	1.41809
$29$	0.722924	0.134244	0.0671218	−	0.997745i	$-0.478618\pi$
$29$	0.722924	0.134244	0.0671218	+	0.997745i	$0.478618\pi$
$30$	−6.36212	−1.16156
$31$	−4.20575	−0.755374	−0.377687	−	0.925933i	$-0.623281\pi$
$31$	−4.20575	−0.755374	−0.377687	+	0.925933i	$0.623281\pi$
$32$	−1.85254	−0.327486
$33$	0.0841132	0.0146422
$34$	−0.749280	−0.128500
$35$	4.59665	0.776976
$36$	4.17837	0.696395
$37$	−0.341855	−0.0562006	−0.0281003	−	0.999605i	$-0.508946\pi$
$37$	−0.341855	−0.0562006	−0.0281003	+	0.999605i	$0.508946\pi$
$38$	15.2929	2.48084
$39$	4.62871	0.741186
$40$	−13.8590	−2.19131
$41$	−6.75121	−1.05436	−0.527181	−	0.849753i	$-0.676751\pi$
$41$	−6.75121	−1.05436	−0.527181	+	0.849753i	$0.676751\pi$
$42$	−4.46389	−0.688794
$43$	4.18177	0.637714	0.318857	−	0.947803i	$-0.396701\pi$
$43$	4.18177	0.637714	0.318857	+	0.947803i	$0.396701\pi$
$44$	0.351456	0.0529840
$45$	2.55956	0.381556
$46$	−17.7147	−2.61189
$47$	6.30652	0.919901	0.459951	−	0.887945i	$-0.347867\pi$
$47$	6.30652	0.919901	0.459951	+	0.887945i	$0.347867\pi$
$48$	5.10204	0.736416
$49$	−3.77482	−0.539260
$50$	−3.85603	−0.545325
$51$	0.301444	0.0422106
$52$	19.3405	2.68204
$53$	11.5844	1.59124	0.795621	−	0.605795i	$-0.207145\pi$
$53$	11.5844	1.59124	0.795621	+	0.605795i	$0.207145\pi$
$54$	−2.48563	−0.338252
$55$	0.215293	0.0290300
$56$	−9.72401	−1.29943
$57$	−6.15254	−0.814923
$58$	−1.79692	−0.235948
$59$	−1.61013	−0.209620	−0.104810	−	0.994492i	$-0.533424\pi$
$59$	−1.61013	−0.209620	−0.104810	+	0.994492i	$0.533424\pi$
$60$	10.6948	1.38069
$61$	7.39830	0.947255	0.473628	−	0.880725i	$-0.342944\pi$
$61$	7.39830	0.947255	0.473628	+	0.880725i	$0.342944\pi$
$62$	10.4539	1.32765
$63$	1.79588	0.226259
$64$	−5.59935	−0.699919
$65$	11.8474	1.46949
$66$	−0.209075	−0.0257353
$67$	−7.98191	−0.975146	−0.487573	−	0.873082i	$-0.662118\pi$
$67$	−7.98191	−0.975146	−0.487573	+	0.873082i	$0.662118\pi$
$68$	1.25955	0.152742
$69$	7.12685	0.857972
$70$	−11.4256	−1.36562
$71$	−3.54694	−0.420944	−0.210472	−	0.977600i	$-0.567500\pi$
$71$	−3.54694	−0.420944	−0.210472	+	0.977600i	$0.567500\pi$
$72$	−5.41463	−0.638120
$73$	1.81848	0.212837	0.106419	−	0.994321i	$-0.466062\pi$
$73$	1.81848	0.212837	0.106419	+	0.994321i	$0.466062\pi$
$74$	0.849726	0.0987786
$75$	1.55133	0.179132
$76$	−25.7076	−2.94886
$77$	0.151057	0.0172146
$78$	−11.5053	−1.30271
$79$	−8.12862	−0.914541	−0.457271	−	0.889328i	$-0.651173\pi$
$79$	−8.12862	−0.914541	−0.457271	+	0.889328i	$0.651173\pi$
$80$	13.0590	1.46004
$81$	1.00000	0.111111
$82$	16.7810	1.85316
$83$	12.8259	1.40783	0.703915	−	0.710285i	$-0.251434\pi$
$83$	12.8259	1.40783	0.703915	+	0.710285i	$0.251434\pi$
$84$	7.50384	0.818737
$85$	0.771564	0.0836878
$86$	−10.3943	−1.12085
$87$	0.722924	0.0775056
$88$	−0.455442	−0.0485503
$89$	−5.47104	−0.579930	−0.289965	−	0.957037i	$-0.593644\pi$
$89$	−5.47104	−0.579930	−0.289965	+	0.957037i	$0.593644\pi$
$90$	−6.36212	−0.670626
$91$	8.31259	0.871396
$92$	29.7786	3.10464
$93$	−4.20575	−0.436116
$94$	−15.6757	−1.61683
$95$	−15.7478	−1.61569
$96$	−1.85254	−0.189074
$97$	−14.2848	−1.45040	−0.725202	−	0.688537i	$-0.758253\pi$
$97$	−14.2848	−1.45040	−0.725202	+	0.688537i	$0.758253\pi$
$98$	9.38282	0.947808
$99$	0.0841132	0.00845370
$100$	6.48202	0.648202
$101$	3.66070	0.364253	0.182127	−	0.983275i	$-0.441702\pi$
$101$	3.66070	0.364253	0.182127	+	0.983275i	$0.441702\pi$
$102$	−0.749280	−0.0741897
$103$	15.7509	1.55198	0.775989	−	0.630747i	$-0.217251\pi$
$103$	15.7509	1.55198	0.775989	+	0.630747i	$0.217251\pi$
$104$	−25.0627	−2.45760
$105$	4.59665	0.448587
$106$	−28.7946	−2.79678
$107$	10.8850	1.05230	0.526148	−	0.850393i	$-0.323636\pi$
$107$	10.8850	1.05230	0.526148	+	0.850393i	$0.323636\pi$
$108$	4.17837	0.402064
$109$	20.4390	1.95770	0.978852	−	0.204569i	$-0.0655793\pi$
$109$	20.4390	1.95770	0.978852	+	0.204569i	$0.0655793\pi$
$110$	−0.535138	−0.0510234
$111$	−0.341855	−0.0324474
$112$	9.16264	0.865788
$113$	12.4852	1.17451	0.587256	−	0.809401i	$-0.300208\pi$
$113$	12.4852	1.17451	0.587256	+	0.809401i	$0.300208\pi$
$114$	15.2929	1.43232
$115$	18.2416	1.70104
$116$	3.02065	0.280460
$117$	4.62871	0.427924
$118$	4.00218	0.368431
$119$	0.541357	0.0496261
$120$	−13.8590	−1.26515
$121$	−10.9929	−0.999357
$122$	−18.3895	−1.66490
$123$	−6.75121	−0.608736
$124$	−17.5732	−1.57812
$125$	−8.82707	−0.789517
$126$	−4.46389	−0.397675
$127$	1.83940	0.163220	0.0816100	−	0.996664i	$-0.473994\pi$
$127$	1.83940	0.163220	0.0816100	+	0.996664i	$0.473994\pi$
$128$	17.6230	1.55767
$129$	4.18177	0.368184
$130$	−29.4484	−2.58279
$131$	18.9954	1.65963	0.829816	−	0.558037i	$-0.188445\pi$
$131$	18.9954	1.65963	0.829816	+	0.558037i	$0.188445\pi$
$132$	0.351456	0.0305903
$133$	−11.0492	−0.958087
$134$	19.8401	1.71392
$135$	2.55956	0.220292
$136$	−1.63221	−0.139961
$137$	−3.84793	−0.328751	−0.164375	−	0.986398i	$-0.552561\pi$
$137$	−3.84793	−0.328751	−0.164375	+	0.986398i	$0.552561\pi$
$138$	−17.7147	−1.50798
$139$	6.38717	0.541753	0.270876	−	0.962614i	$-0.412687\pi$
$139$	6.38717	0.541753	0.270876	+	0.962614i	$0.412687\pi$
$140$	19.2065	1.62325
$141$	6.30652	0.531105
$142$	8.81639	0.739855
$143$	0.389335	0.0325579
$144$	5.10204	0.425170
$145$	1.85037	0.153664
$146$	−4.52008	−0.374084
$147$	−3.77482	−0.311342
$148$	−1.42840	−0.117413
$149$	−7.23972	−0.593101	−0.296551	−	0.955017i	$-0.595836\pi$
$149$	−7.23972	−0.593101	−0.296551	+	0.955017i	$0.595836\pi$
$150$	−3.85603	−0.314844
$151$	11.3163	0.920907	0.460454	−	0.887684i	$-0.347687\pi$
$151$	11.3163	0.920907	0.460454	+	0.887684i	$0.347687\pi$
$152$	33.3137	2.70210
$153$	0.301444	0.0243703
$154$	−0.375472	−0.0302564
$155$	−10.7648	−0.864653
$156$	19.3405	1.54848
$157$	2.18009	0.173990	0.0869952	−	0.996209i	$-0.472274\pi$
$157$	2.18009	0.173990	0.0869952	+	0.996209i	$0.472274\pi$
$158$	20.2048	1.60740
$159$	11.5844	0.918704
$160$	−4.74168	−0.374862
$161$	12.7990	1.00870
$162$	−2.48563	−0.195290
$163$	4.43989	0.347759	0.173879	−	0.984767i	$-0.444370\pi$
$163$	4.43989	0.347759	0.173879	+	0.984767i	$0.444370\pi$
$164$	−28.2091	−2.20276
$165$	0.215293	0.0167605
$166$	−31.8806	−2.47441
$167$	−2.71632	−0.210195	−0.105098	−	0.994462i	$-0.533515\pi$
$167$	−2.71632	−0.210195	−0.105098	+	0.994462i	$0.533515\pi$
$168$	−9.72401	−0.750224
$169$	8.42492	0.648071
$170$	−1.91782	−0.147090
$171$	−6.15254	−0.470496
$172$	17.4730	1.33230
$173$	2.03446	0.154677	0.0773386	−	0.997005i	$-0.475358\pi$
$173$	2.03446	0.154677	0.0773386	+	0.997005i	$0.475358\pi$
$174$	−1.79692	−0.136225
$175$	2.78600	0.210602
$176$	0.429149	0.0323483
$177$	−1.61013	−0.121024
$178$	13.5990	1.01929
$179$	24.0919	1.80071	0.900356	−	0.435154i	$-0.143306\pi$
$179$	24.0919	1.80071	0.900356	+	0.435154i	$0.143306\pi$
$180$	10.6948	0.797141
$181$	22.8817	1.70079	0.850393	−	0.526148i	$-0.176364\pi$
$181$	22.8817	1.70079	0.850393	+	0.526148i	$0.176364\pi$
$182$	−20.6621	−1.53157
$183$	7.39830	0.546898
$184$	−38.5892	−2.84484
$185$	−0.874997	−0.0643310
$186$	10.4539	0.766520
$187$	0.0253554	0.00185417
$188$	26.3510	1.92184
$189$	1.79588	0.130631
$190$	39.1432	2.83974
$191$	−9.34525	−0.676199	−0.338099	−	0.941110i	$-0.609784\pi$
$191$	−9.34525	−0.676199	−0.338099	+	0.941110i	$0.609784\pi$
$192$	−5.59935	−0.404098
$193$	−12.7545	−0.918089	−0.459045	−	0.888413i	$-0.651808\pi$
$193$	−12.7545	−0.918089	−0.459045	+	0.888413i	$0.651808\pi$
$194$	35.5068	2.54924
$195$	11.8474	0.848412
$196$	−15.7726	−1.12661
$197$	−3.53679	−0.251986	−0.125993	−	0.992031i	$-0.540212\pi$
$197$	−3.53679	−0.251986	−0.125993	+	0.992031i	$0.540212\pi$
$198$	−0.209075	−0.0148583
$199$	−11.4237	−0.809803	−0.404901	−	0.914360i	$-0.632694\pi$
$199$	−11.4237	−0.809803	−0.404901	+	0.914360i	$0.632694\pi$
$200$	−8.39987	−0.593960
$201$	−7.98191	−0.563001
$202$	−9.09915	−0.640214
$203$	1.29828	0.0911217
$204$	1.25955	0.0881858
$205$	−17.2801	−1.20690
$206$	−39.1508	−2.72777
$207$	7.12685	0.495350
$208$	23.6158	1.63746
$209$	−0.517510	−0.0357969
$210$	−11.4256	−0.788440
$211$	21.7805	1.49943	0.749717	−	0.661759i	$-0.230190\pi$
$211$	21.7805	1.49943	0.749717	+	0.661759i	$0.230190\pi$
$212$	48.4040	3.32440
$213$	−3.54694	−0.243032
$214$	−27.0562	−1.84952
$215$	10.7035	0.729971
$216$	−5.41463	−0.368419
$217$	−7.55301	−0.512732
$218$	−50.8039	−3.44088
$219$	1.81848	0.122882
$220$	0.899572	0.0606491
$221$	1.39530	0.0938578
$222$	0.849726	0.0570299
$223$	4.17214	0.279387	0.139694	−	0.990195i	$-0.455388\pi$
$223$	4.17214	0.279387	0.139694	+	0.990195i	$0.455388\pi$
$224$	−3.32693	−0.222290
$225$	1.55133	0.103422
$226$	−31.0337	−2.06433
$227$	21.6560	1.43736	0.718681	−	0.695340i	$-0.244746\pi$
$227$	21.6560	1.43736	0.718681	+	0.695340i	$0.244746\pi$
$228$	−25.7076	−1.70253
$229$	−11.1099	−0.734165	−0.367082	−	0.930188i	$-0.619643\pi$
$229$	−11.1099	−0.734165	−0.367082	+	0.930188i	$0.619643\pi$
$230$	−45.3419	−2.98975
$231$	0.151057	0.00993883
$232$	−3.91437	−0.256991
$233$	27.5940	1.80774	0.903871	−	0.427806i	$-0.140713\pi$
$233$	27.5940	1.80774	0.903871	+	0.427806i	$0.140713\pi$
$234$	−11.5053	−0.752123
$235$	16.1419	1.05298
$236$	−6.72770	−0.437936
$237$	−8.12862	−0.528011
$238$	−1.34562	−0.0872233
$239$	−9.44941	−0.611231	−0.305616	−	0.952155i	$-0.598862\pi$
$239$	−9.44941	−0.611231	−0.305616	+	0.952155i	$0.598862\pi$
$240$	13.0590	0.842952
$241$	−8.63796	−0.556420	−0.278210	−	0.960520i	$-0.589741\pi$
$241$	−8.63796	−0.556420	−0.278210	+	0.960520i	$0.589741\pi$
$242$	27.3244	1.75648
$243$	1.00000	0.0641500
$244$	30.9128	1.97899
$245$	−9.66187	−0.617274
$246$	16.7810	1.06992
$247$	−28.4783	−1.81203
$248$	22.7726	1.44606
$249$	12.8259	0.812811
$250$	21.9409	1.38766
$251$	−17.7578	−1.12086	−0.560431	−	0.828201i	$-0.689365\pi$
$251$	−17.7578	−1.12086	−0.560431	+	0.828201i	$0.689365\pi$
$252$	7.50384	0.472698
$253$	0.599462	0.0376879
$254$	−4.57206	−0.286877
$255$	0.771564	0.0483172
$256$	−32.6056	−2.03785
$257$	6.45464	0.402629	0.201315	−	0.979527i	$-0.435479\pi$
$257$	6.45464	0.402629	0.201315	+	0.979527i	$0.435479\pi$
$258$	−10.3943	−0.647124
$259$	−0.613930	−0.0381477
$260$	49.5030	3.07004
$261$	0.722924	0.0447479
$262$	−47.2155	−2.91698
$263$	−26.3564	−1.62520	−0.812602	−	0.582819i	$-0.801950\pi$
$263$	−26.3564	−1.62520	−0.812602	+	0.582819i	$0.801950\pi$
$264$	−0.455442	−0.0280305
$265$	29.6510	1.82144
$266$	27.4643	1.68394
$267$	−5.47104	−0.334823
$268$	−33.3514	−2.03726
$269$	3.65565	0.222889	0.111444	−	0.993771i	$-0.464452\pi$
$269$	3.65565	0.222889	0.111444	+	0.993771i	$0.464452\pi$
$270$	−6.36212	−0.387186
$271$	−17.5684	−1.06721	−0.533603	−	0.845735i	$-0.679162\pi$
$271$	−17.5684	−1.06721	−0.533603	+	0.845735i	$0.679162\pi$
$272$	1.53798	0.0932538
$273$	8.31259	0.503101
$274$	9.56454	0.577815
$275$	0.130487	0.00786867
$276$	29.7786	1.79246
$277$	−2.85488	−0.171533	−0.0857665	−	0.996315i	$-0.527334\pi$
$277$	−2.85488	−0.171533	−0.0857665	+	0.996315i	$0.527334\pi$
$278$	−15.8762	−0.952189
$279$	−4.20575	−0.251791
$280$	−24.8892	−1.48741
$281$	−8.79703	−0.524787	−0.262393	−	0.964961i	$-0.584512\pi$
$281$	−8.79703	−0.524787	−0.262393	+	0.964961i	$0.584512\pi$
$282$	−15.6757	−0.933475
$283$	−10.4847	−0.623253	−0.311627	−	0.950205i	$-0.600874\pi$
$283$	−10.4847	−0.623253	−0.311627	+	0.950205i	$0.600874\pi$
$284$	−14.8204	−0.879430
$285$	−15.7478	−0.932817
$286$	−0.967745	−0.0572240
$287$	−12.1244	−0.715678
$288$	−1.85254	−0.109162
$289$	−16.9091	−0.994655
$290$	−4.59933	−0.270082
$291$	−14.2848	−0.837391
$292$	7.59829	0.444656
$293$	19.3092	1.12806	0.564029	−	0.825755i	$-0.309251\pi$
$293$	19.3092	1.12806	0.564029	+	0.825755i	$0.309251\pi$
$294$	9.38282	0.547217
$295$	−4.12121	−0.239946
$296$	1.85102	0.107588
$297$	0.0841132	0.00488074
$298$	17.9953	1.04244
$299$	32.9881	1.90775
$300$	6.48202	0.374240
$301$	7.50995	0.432866
$302$	−28.1282	−1.61859
$303$	3.66070	0.210302
$304$	−31.3905	−1.80037
$305$	18.9364	1.08429
$306$	−0.749280	−0.0428335
$307$	18.5268	1.05738	0.528690	−	0.848815i	$-0.322683\pi$
$307$	18.5268	1.05738	0.528690	+	0.848815i	$0.322683\pi$
$308$	0.631173	0.0359644
$309$	15.7509	0.896035
$310$	26.7574	1.51972
$311$	−13.9298	−0.789887	−0.394943	−	0.918705i	$-0.629236\pi$
$311$	−13.9298	−0.789887	−0.394943	+	0.918705i	$0.629236\pi$
$312$	−25.0627	−1.41890
$313$	−13.2863	−0.750986	−0.375493	−	0.926825i	$-0.622527\pi$
$313$	−13.2863	−0.750986	−0.375493	+	0.926825i	$0.622527\pi$
$314$	−5.41891	−0.305807
$315$	4.59665	0.258992
$316$	−33.9644	−1.91065
$317$	−10.1989	−0.572826	−0.286413	−	0.958106i	$-0.592463\pi$
$317$	−10.1989	−0.572826	−0.286413	+	0.958106i	$0.592463\pi$
$318$	−28.7946	−1.61472
$319$	0.0608075	0.00340457
$320$	−14.3319	−0.801175
$321$	10.8850	0.607543
$322$	−31.8135	−1.77290
$323$	−1.85465	−0.103195
$324$	4.17837	0.232132
$325$	7.18064	0.398310
$326$	−11.0359	−0.611224
$327$	20.4390	1.13028
$328$	36.5553	2.01843
$329$	11.3257	0.624409
$330$	−0.535138	−0.0294584
$331$	22.3858	1.23043	0.615217	−	0.788358i	$-0.289068\pi$
$331$	22.3858	1.23043	0.615217	+	0.788358i	$0.289068\pi$
$332$	53.5915	2.94122
$333$	−0.341855	−0.0187335
$334$	6.75177	0.369441
$335$	−20.4302	−1.11622
$336$	9.16264	0.499863
$337$	−14.0917	−0.767626	−0.383813	−	0.923411i	$-0.625389\pi$
$337$	−14.0917	−0.767626	−0.383813	+	0.923411i	$0.625389\pi$
$338$	−20.9413	−1.13905
$339$	12.4852	0.678105
$340$	3.22388	0.174839
$341$	−0.353759	−0.0191571
$342$	15.2929	0.826948
$343$	−19.3503	−1.04482
$344$	−22.6427	−1.22081
$345$	18.2416	0.982093
$346$	−5.05692	−0.271862
$347$	−21.1972	−1.13793	−0.568963	−	0.822363i	$-0.692655\pi$
$347$	−21.1972	−1.13793	−0.568963	+	0.822363i	$0.692655\pi$
$348$	3.02065	0.161924
$349$	−20.2858	−1.08587	−0.542937	−	0.839773i	$-0.682688\pi$
$349$	−20.2858	−1.08587	−0.542937	+	0.839773i	$0.682688\pi$
$350$	−6.92496	−0.370155
$351$	4.62871	0.247062
$352$	−0.155823	−0.00830539
$353$	12.8134	0.681990	0.340995	−	0.940065i	$-0.389236\pi$
$353$	12.8134	0.681990	0.340995	+	0.940065i	$0.389236\pi$
$354$	4.00218	0.212713
$355$	−9.07859	−0.481841
$356$	−22.8601	−1.21158
$357$	0.541357	0.0286517
$358$	−59.8836	−3.16495
$359$	−17.3742	−0.916977	−0.458488	−	0.888700i	$-0.651609\pi$
$359$	−17.3742	−0.916977	−0.458488	+	0.888700i	$0.651609\pi$
$360$	−13.8590	−0.730436
$361$	18.8537	0.992300
$362$	−56.8756	−2.98932
$363$	−10.9929	−0.576979
$364$	34.7331	1.82051
$365$	4.65451	0.243628
$366$	−18.3895	−0.961232
$367$	−11.0631	−0.577488	−0.288744	−	0.957406i	$-0.593238\pi$
$367$	−11.0631	−0.577488	−0.288744	+	0.957406i	$0.593238\pi$
$368$	36.3615	1.89547
$369$	−6.75121	−0.351454
$370$	2.17492	0.113069
$371$	20.8042	1.08010
$372$	−17.5732	−0.911126
$373$	−3.64864	−0.188920	−0.0944598	−	0.995529i	$-0.530112\pi$
$373$	−3.64864	−0.188920	−0.0944598	+	0.995529i	$0.530112\pi$
$374$	−0.0630243	−0.00325891
$375$	−8.82707	−0.455828
$376$	−34.1475	−1.76102
$377$	3.34620	0.172338
$378$	−4.46389	−0.229598
$379$	8.92190	0.458287	0.229143	−	0.973393i	$-0.426407\pi$
$379$	8.92190	0.458287	0.229143	+	0.973393i	$0.426407\pi$
$380$	−65.8000	−3.37547
$381$	1.83940	0.0942351
$382$	23.2289	1.18849
$383$	−17.2018	−0.878970	−0.439485	−	0.898250i	$-0.644839\pi$
$383$	−17.2018	−0.878970	−0.439485	+	0.898250i	$0.644839\pi$
$384$	17.6230	0.899320
$385$	0.386639	0.0197050
$386$	31.7030	1.61364
$387$	4.18177	0.212571
$388$	−59.6873	−3.03016
$389$	−13.0643	−0.662387	−0.331193	−	0.943563i	$-0.607451\pi$
$389$	−13.0643	−0.662387	−0.331193	+	0.943563i	$0.607451\pi$
$390$	−29.4484	−1.49118
$391$	2.14835	0.108647
$392$	20.4393	1.03234
$393$	18.9954	0.958189
$394$	8.79116	0.442892
$395$	−20.8057	−1.04685
$396$	0.351456	0.0176613
$397$	−29.8464	−1.49795	−0.748975	−	0.662598i	$-0.769454\pi$
$397$	−29.8464	−1.49795	−0.748975	+	0.662598i	$0.769454\pi$
$398$	28.3951	1.42332
$399$	−11.0492	−0.553152
$400$	7.91494	0.395747
$401$	−2.13631	−0.106682	−0.0533410	−	0.998576i	$-0.516987\pi$
$401$	−2.13631	−0.106682	−0.0533410	+	0.998576i	$0.516987\pi$
$402$	19.8401	0.989535
$403$	−19.4672	−0.969728
$404$	15.2958	0.760992
$405$	2.55956	0.127185
$406$	−3.22706	−0.160156
$407$	−0.0287545	−0.00142531
$408$	−1.63221	−0.0808064
$409$	−23.2003	−1.14718	−0.573591	−	0.819142i	$-0.694450\pi$
$409$	−23.2003	−1.14718	−0.573591	+	0.819142i	$0.694450\pi$
$410$	42.9520	2.12125
$411$	−3.84793	−0.189804
$412$	65.8129	3.24237
$413$	−2.89159	−0.142286
$414$	−17.7147	−0.870632
$415$	32.8287	1.61150
$416$	−8.57485	−0.420417
$417$	6.38717	0.312781
$418$	1.28634	0.0629169
$419$	12.5967	0.615390	0.307695	−	0.951485i	$-0.400442\pi$
$419$	12.5967	0.615390	0.307695	+	0.951485i	$0.400442\pi$
$420$	19.2065	0.937182
$421$	−19.1214	−0.931920	−0.465960	−	0.884806i	$-0.654291\pi$
$421$	−19.1214	−0.931920	−0.465960	+	0.884806i	$0.654291\pi$
$422$	−54.1384	−2.63542
$423$	6.30652	0.306634
$424$	−62.7253	−3.04621
$425$	0.467639	0.0226838
$426$	8.81639	0.427155
$427$	13.2864	0.642976
$428$	45.4817	2.19844
$429$	0.389335	0.0187973
$430$	−26.6049	−1.28300
$431$	17.2026	0.828622	0.414311	−	0.910135i	$-0.364023\pi$
$431$	17.2026	0.828622	0.414311	+	0.910135i	$0.364023\pi$
$432$	5.10204	0.245472
$433$	−1.46333	−0.0703233	−0.0351616	−	0.999382i	$-0.511195\pi$
$433$	−1.46333	−0.0703233	−0.0351616	+	0.999382i	$0.511195\pi$
$434$	18.7740	0.901181
$435$	1.85037	0.0887182
$436$	85.4019	4.09001
$437$	−43.8482	−2.09754
$438$	−4.52008	−0.215978
$439$	20.5467	0.980640	0.490320	−	0.871542i	$-0.336880\pi$
$439$	20.5467	0.980640	0.490320	+	0.871542i	$0.336880\pi$
$440$	−1.16573	−0.0555740
$441$	−3.77482	−0.179753
$442$	−3.46820	−0.164965
$443$	−8.67793	−0.412301	−0.206150	−	0.978520i	$-0.566094\pi$
$443$	−8.67793	−0.412301	−0.206150	+	0.978520i	$0.566094\pi$
$444$	−1.42840	−0.0677887
$445$	−14.0034	−0.663827
$446$	−10.3704	−0.491053
$447$	−7.23972	−0.342427
$448$	−10.0557	−0.475090
$449$	−33.2507	−1.56920	−0.784599	−	0.620003i	$-0.787131\pi$
$449$	−33.2507	−1.56920	−0.784599	+	0.620003i	$0.787131\pi$
$450$	−3.85603	−0.181775
$451$	−0.567866	−0.0267398
$452$	52.1680	2.45377
$453$	11.3163	0.531686
$454$	−53.8290	−2.52632
$455$	21.2765	0.997460
$456$	33.3137	1.56006
$457$	−23.1675	−1.08373	−0.541865	−	0.840466i	$-0.682282\pi$
$457$	−23.1675	−1.08373	−0.541865	+	0.840466i	$0.682282\pi$
$458$	27.6152	1.29037
$459$	0.301444	0.0140702
$460$	76.2200	3.55378
$461$	20.9317	0.974888	0.487444	−	0.873154i	$-0.337929\pi$
$461$	20.9317	0.974888	0.487444	+	0.873154i	$0.337929\pi$
$462$	−0.375472	−0.0174686
$463$	−23.5495	−1.09444	−0.547218	−	0.836990i	$-0.684313\pi$
$463$	−23.5495	−1.09444	−0.547218	+	0.836990i	$0.684313\pi$
$464$	3.68839	0.171229
$465$	−10.7648	−0.499208
$466$	−68.5885	−3.17730
$467$	−5.32443	−0.246385	−0.123193	−	0.992383i	$-0.539313\pi$
$467$	−5.32443	−0.246385	−0.123193	+	0.992383i	$0.539313\pi$
$468$	19.3405	0.894013
$469$	−14.3345	−0.661908
$470$	−40.1228	−1.85073
$471$	2.18009	0.100453
$472$	8.71823	0.401289
$473$	0.351742	0.0161731
$474$	20.2048	0.928036
$475$	−9.54460	−0.437936
$476$	2.26199	0.103678
$477$	11.5844	0.530414
$478$	23.4878	1.07430
$479$	25.0883	1.14632	0.573158	−	0.819445i	$-0.305718\pi$
$479$	25.0883	1.14632	0.573158	+	0.819445i	$0.305718\pi$
$480$	−4.74168	−0.216427
$481$	−1.58235	−0.0721488
$482$	21.4708	0.977968
$483$	12.7990	0.582373
$484$	−45.9325	−2.08784
$485$	−36.5628	−1.66023
$486$	−2.48563	−0.112751
$487$	17.5454	0.795058	0.397529	−	0.917590i	$-0.369868\pi$
$487$	17.5454	0.795058	0.397529	+	0.917590i	$0.369868\pi$
$488$	−40.0591	−1.81339
$489$	4.43989	0.200779
$490$	24.0159	1.08493
$491$	11.7714	0.531235	0.265618	−	0.964078i	$-0.414424\pi$
$491$	11.7714	0.531235	0.265618	+	0.964078i	$0.414424\pi$
$492$	−28.2091	−1.27176
$493$	0.217921	0.00981469
$494$	70.7865	3.18484
$495$	0.215293	0.00967668
$496$	−21.4579	−0.963487
$497$	−6.36987	−0.285728
$498$	−31.8806	−1.42860
$499$	30.9880	1.38721	0.693607	−	0.720353i	$-0.256020\pi$
$499$	30.9880	1.38721	0.693607	+	0.720353i	$0.256020\pi$
$500$	−36.8828	−1.64945
$501$	−2.71632	−0.121356
$502$	44.1394	1.97004
$503$	28.3632	1.26465	0.632326	−	0.774703i	$-0.282100\pi$
$503$	28.3632	1.26465	0.632326	+	0.774703i	$0.282100\pi$
$504$	−9.72401	−0.433142
$505$	9.36977	0.416949
$506$	−1.49004	−0.0662405
$507$	8.42492	0.374164
$508$	7.68567	0.340997
$509$	−17.3228	−0.767822	−0.383911	−	0.923370i	$-0.625423\pi$
$509$	−17.3228	−0.767822	−0.383911	+	0.923370i	$0.625423\pi$
$510$	−1.91782	−0.0849227
$511$	3.26577	0.144469
$512$	45.7996	2.02407
$513$	−6.15254	−0.271641
$514$	−16.0439	−0.707664
$515$	40.3152	1.77650
$516$	17.4730	0.769205
$517$	0.530462	0.0233297
$518$	1.52600	0.0670488
$519$	2.03446	0.0893030
$520$	−64.1495	−2.81314
$521$	37.3691	1.63717	0.818586	−	0.574384i	$-0.194758\pi$
$521$	37.3691	1.63717	0.818586	+	0.574384i	$0.194758\pi$
$522$	−1.79692	−0.0786493
$523$	−0.266544	−0.0116552	−0.00582759	−	0.999983i	$-0.501855\pi$
$523$	−0.266544	−0.0116552	−0.00582759	+	0.999983i	$0.501855\pi$
$524$	79.3697	3.46728
$525$	2.78600	0.121591
$526$	65.5123	2.85647
$527$	−1.26780	−0.0552261
$528$	0.429149	0.0186763
$529$	27.7920	1.20835
$530$	−73.7014	−3.20138
$531$	−1.61013	−0.0698735
$532$	−46.1677	−2.00162
$533$	−31.2494	−1.35356
$534$	13.5990	0.588487
$535$	27.8608	1.20453
$536$	43.2191	1.86678
$537$	24.0919	1.03964
$538$	−9.08660	−0.391751
$539$	−0.317512	−0.0136762
$540$	10.6948	0.460230
$541$	−16.0981	−0.692110	−0.346055	−	0.938214i	$-0.612479\pi$
$541$	−16.0981	−0.692110	−0.346055	+	0.938214i	$0.612479\pi$
$542$	43.6686	1.87573
$543$	22.8817	0.981950
$544$	−0.558437	−0.0239428
$545$	52.3149	2.24092
$546$	−20.6621	−0.884254
$547$	−15.6710	−0.670042	−0.335021	−	0.942211i	$-0.608743\pi$
$547$	−15.6710	−0.670042	−0.335021	+	0.942211i	$0.608743\pi$
$548$	−16.0781	−0.686821
$549$	7.39830	0.315752
$550$	−0.324343	−0.0138300
$551$	−4.44782	−0.189483
$552$	−38.5892	−1.64247
$553$	−14.5980	−0.620771
$554$	7.09618	0.301488
$555$	−0.874997	−0.0371415
$556$	26.6880	1.13182
$557$	26.4202	1.11946	0.559731	−	0.828674i	$-0.310905\pi$
$557$	26.4202	1.11946	0.559731	+	0.828674i	$0.310905\pi$
$558$	10.4539	0.442551
$559$	19.3562	0.818679
$560$	23.4523	0.991040
$561$	0.0253554	0.00107051
$562$	21.8662	0.922369
$563$	10.4971	0.442401	0.221201	−	0.975228i	$-0.429002\pi$
$563$	10.4971	0.442401	0.221201	+	0.975228i	$0.429002\pi$
$564$	26.3510	1.10958
$565$	31.9567	1.34443
$566$	26.0612	1.09543
$567$	1.79588	0.0754198
$568$	19.2054	0.805839
$569$	−42.4796	−1.78084	−0.890418	−	0.455144i	$-0.849588\pi$
$569$	−42.4796	−1.78084	−0.890418	+	0.455144i	$0.849588\pi$
$570$	39.1432	1.63953
$571$	25.7034	1.07565	0.537826	−	0.843056i	$-0.319246\pi$
$571$	25.7034	1.07565	0.537826	+	0.843056i	$0.319246\pi$
$572$	1.62679	0.0680194
$573$	−9.34525	−0.390403
$574$	30.1367	1.25788
$575$	11.0561	0.461071
$576$	−5.59935	−0.233306
$577$	−10.6609	−0.443818	−0.221909	−	0.975067i	$-0.571229\pi$
$577$	−10.6609	−0.443818	−0.221909	+	0.975067i	$0.571229\pi$
$578$	42.0299	1.74821
$579$	−12.7545	−0.530059
$580$	7.73151	0.321034
$581$	23.0338	0.955604
$582$	35.5068	1.47180
$583$	0.974403	0.0403556
$584$	−9.84640	−0.407447
$585$	11.8474	0.489831
$586$	−47.9957	−1.98268
$587$	−20.5684	−0.848947	−0.424473	−	0.905440i	$-0.639541\pi$
$587$	−20.5684	−0.848947	−0.424473	+	0.905440i	$0.639541\pi$
$588$	−15.7726	−0.650451
$589$	25.8760	1.06620
$590$	10.2438	0.421731
$591$	−3.53679	−0.145484
$592$	−1.74416	−0.0716844
$593$	37.4240	1.53682	0.768409	−	0.639959i	$-0.221049\pi$
$593$	37.4240	1.53682	0.768409	+	0.639959i	$0.221049\pi$
$594$	−0.209075	−0.00857843
$595$	1.38563	0.0568055
$596$	−30.2502	−1.23910
$597$	−11.4237	−0.467540
$598$	−81.9963	−3.35308
$599$	−32.2842	−1.31910	−0.659548	−	0.751662i	$-0.729252\pi$
$599$	−32.2842	−1.31910	−0.659548	+	0.751662i	$0.729252\pi$
$600$	−8.39987	−0.342923
$601$	12.1048	0.493766	0.246883	−	0.969045i	$-0.420594\pi$
$601$	12.1048	0.493766	0.246883	+	0.969045i	$0.420594\pi$
$602$	−18.6670	−0.760809
$603$	−7.98191	−0.325049
$604$	47.2837	1.92395
$605$	−28.1370	−1.14393
$606$	−9.09915	−0.369628
$607$	1.31745	0.0534735	0.0267368	−	0.999643i	$-0.491488\pi$
$607$	1.31745	0.0534735	0.0267368	+	0.999643i	$0.491488\pi$
$608$	11.3978	0.462242
$609$	1.29828	0.0526091
$610$	−47.0688	−1.90576
$611$	29.1910	1.18094
$612$	1.25955	0.0509141
$613$	−2.57302	−0.103923	−0.0519616	−	0.998649i	$-0.516547\pi$
$613$	−2.57302	−0.103923	−0.0519616	+	0.998649i	$0.516547\pi$
$614$	−46.0508	−1.85846
$615$	−17.2801	−0.696801
$616$	−0.817918	−0.0329549
$617$	10.0637	0.405149	0.202575	−	0.979267i	$-0.435069\pi$
$617$	10.0637	0.405149	0.202575	+	0.979267i	$0.435069\pi$
$618$	−39.1508	−1.57488
$619$	5.27443	0.211997	0.105999	−	0.994366i	$-0.466196\pi$
$619$	5.27443	0.211997	0.105999	+	0.994366i	$0.466196\pi$
$620$	−44.9795	−1.80642
$621$	7.12685	0.285991
$622$	34.6244	1.38831
$623$	−9.82533	−0.393644
$624$	23.6158	0.945390
$625$	−30.3500	−1.21400
$626$	33.0248	1.31994
$627$	−0.517510	−0.0206673
$628$	9.10924	0.363498
$629$	−0.103050	−0.00410888
$630$	−11.4256	−0.455206
$631$	−6.40003	−0.254781	−0.127391	−	0.991853i	$-0.540660\pi$
$631$	−6.40003	−0.254781	−0.127391	+	0.991853i	$0.540660\pi$
$632$	44.0135	1.75076
$633$	21.7805	0.865698
$634$	25.3507	1.00680
$635$	4.70804	0.186833
$636$	48.4040	1.91934
$637$	−17.4725	−0.692287
$638$	−0.151145	−0.00598389
$639$	−3.54694	−0.140315
$640$	45.1071	1.78301
$641$	−39.9636	−1.57847	−0.789234	−	0.614092i	$-0.789522\pi$
$641$	−39.9636	−1.57847	−0.789234	+	0.614092i	$0.789522\pi$
$642$	−27.0562	−1.06782
$643$	−10.0451	−0.396139	−0.198070	−	0.980188i	$-0.563467\pi$
$643$	−10.0451	−0.396139	−0.198070	+	0.980188i	$0.563467\pi$
$644$	53.4788	2.10736
$645$	10.7035	0.421449
$646$	4.60997	0.181377
$647$	−47.3265	−1.86060	−0.930299	−	0.366802i	$-0.880453\pi$
$647$	−47.3265	−1.86060	−0.930299	+	0.366802i	$0.880453\pi$
$648$	−5.41463	−0.212707
$649$	−0.135433	−0.00531620
$650$	−17.8484	−0.700073
$651$	−7.55301	−0.296026
$652$	18.5515	0.726533
$653$	19.1726	0.750283	0.375141	−	0.926968i	$-0.377594\pi$
$653$	19.1726	0.750283	0.375141	+	0.926968i	$0.377594\pi$
$654$	−50.8039	−1.98659
$655$	48.6197	1.89973
$656$	−34.4450	−1.34485
$657$	1.81848	0.0709457
$658$	−28.1517	−1.09747
$659$	−26.5250	−1.03327	−0.516633	−	0.856207i	$-0.672815\pi$
$659$	−26.5250	−1.03327	−0.516633	+	0.856207i	$0.672815\pi$
$660$	0.899572	0.0350158
$661$	45.2999	1.76196	0.880981	−	0.473151i	$-0.156883\pi$
$661$	45.2999	1.76196	0.880981	+	0.473151i	$0.156883\pi$
$662$	−55.6428	−2.16262
$663$	1.39530	0.0541888
$664$	−69.4477	−2.69509
$665$	−28.2811	−1.09669
$666$	0.849726	0.0329262
$667$	5.15217	0.199493
$668$	−11.3498	−0.439137
$669$	4.17214	0.161304
$670$	50.7819	1.96187
$671$	0.622295	0.0240234
$672$	−3.32693	−0.128339
$673$	31.9333	1.23094	0.615469	−	0.788161i	$-0.288967\pi$
$673$	31.9333	1.23094	0.615469	+	0.788161i	$0.288967\pi$
$674$	35.0269	1.34919
$675$	1.55133	0.0597106
$676$	35.2024	1.35394
$677$	8.32676	0.320023	0.160012	−	0.987115i	$-0.448847\pi$
$677$	8.32676	0.320023	0.160012	+	0.987115i	$0.448847\pi$
$678$	−31.0337	−1.19184
$679$	−25.6538	−0.984502
$680$	−4.17773	−0.160209
$681$	21.6560	0.829861
$682$	0.879315	0.0336707
$683$	−8.20876	−0.314099	−0.157050	−	0.987591i	$-0.550198\pi$
$683$	−8.20876	−0.314099	−0.157050	+	0.987591i	$0.550198\pi$
$684$	−25.7076	−0.982954
$685$	−9.84899	−0.376310
$686$	48.0977	1.83638
$687$	−11.1099	−0.423870
$688$	21.3356	0.813410
$689$	53.6209	2.04279
$690$	−45.3419	−1.72613
$691$	37.3734	1.42175	0.710876	−	0.703317i	$-0.248299\pi$
$691$	37.3734	1.42175	0.710876	+	0.703317i	$0.248299\pi$
$692$	8.50073	0.323149
$693$	0.151057	0.00573818
$694$	52.6884	2.00003
$695$	16.3483	0.620127
$696$	−3.91437	−0.148374
$697$	−2.03511	−0.0770854
$698$	50.4231	1.90854
$699$	27.5940	1.04370
$700$	11.6409	0.439986
$701$	−0.799577	−0.0301996	−0.0150998	−	0.999886i	$-0.504807\pi$
$701$	−0.799577	−0.0301996	−0.0150998	+	0.999886i	$0.504807\pi$
$702$	−11.5053	−0.434238
$703$	2.10327	0.0793265
$704$	−0.470979	−0.0177507
$705$	16.1419	0.607939
$706$	−31.8495	−1.19867
$707$	6.57417	0.247247
$708$	−6.72770	−0.252842
$709$	−13.5313	−0.508179	−0.254089	−	0.967181i	$-0.581776\pi$
$709$	−13.5313	−0.508179	−0.254089	+	0.967181i	$0.581776\pi$
$710$	22.5660	0.846888
$711$	−8.12862	−0.304847
$712$	29.6237	1.11019
$713$	−29.9737	−1.12252
$714$	−1.34562	−0.0503584
$715$	0.996526	0.0372680
$716$	100.665	3.76202
$717$	−9.44941	−0.352895
$718$	43.1860	1.61169
$719$	9.32037	0.347591	0.173796	−	0.984782i	$-0.444397\pi$
$719$	9.32037	0.347591	0.173796	+	0.984782i	$0.444397\pi$
$720$	13.0590	0.486679
$721$	28.2866	1.05345
$722$	−46.8634	−1.74407
$723$	−8.63796	−0.321249
$724$	95.6084	3.55326
$725$	1.12149	0.0416512
$726$	27.3244	1.01410
$727$	19.6837	0.730028	0.365014	−	0.931002i	$-0.381064\pi$
$727$	19.6837	0.730028	0.365014	+	0.931002i	$0.381064\pi$
$728$	−45.0096	−1.66817
$729$	1.00000	0.0370370
$730$	−11.5694	−0.428202
$731$	1.26057	0.0466239
$732$	30.9128	1.14257
$733$	−47.9029	−1.76933	−0.884667	−	0.466223i	$-0.845614\pi$
$733$	−47.9029	−1.76933	−0.884667	+	0.466223i	$0.845614\pi$
$734$	27.4988	1.01500
$735$	−9.66187	−0.356383
$736$	−13.2028	−0.486660
$737$	−0.671385	−0.0247308
$738$	16.7810	0.617718
$739$	45.8147	1.68532	0.842661	−	0.538445i	$-0.180988\pi$
$739$	45.8147	1.68532	0.842661	+	0.538445i	$0.180988\pi$
$740$	−3.65606	−0.134399
$741$	−28.4783	−1.04618
$742$	−51.7116	−1.89839
$743$	42.0534	1.54279	0.771395	−	0.636356i	$-0.219559\pi$
$743$	42.0534	1.54279	0.771395	+	0.636356i	$0.219559\pi$
$744$	22.7726	0.834882
$745$	−18.5305	−0.678904
$746$	9.06919	0.332046
$747$	12.8259	0.469276
$748$	0.105944	0.00387371
$749$	19.5482	0.714275
$750$	21.9409	0.801167
$751$	49.4584	1.80476	0.902382	−	0.430937i	$-0.141817\pi$
$751$	49.4584	1.80476	0.902382	+	0.430937i	$0.141817\pi$
$752$	32.1761	1.17334
$753$	−17.7578	−0.647131
$754$	−8.31744	−0.302903
$755$	28.9647	1.05413
$756$	7.50384	0.272912
$757$	−2.35421	−0.0855653	−0.0427827	−	0.999084i	$-0.513622\pi$
$757$	−2.35421	−0.0855653	−0.0427827	+	0.999084i	$0.513622\pi$
$758$	−22.1766	−0.805489
$759$	0.599462	0.0217591
$760$	85.2683	3.09301
$761$	−38.1952	−1.38458	−0.692288	−	0.721621i	$-0.743397\pi$
$761$	−38.1952	−1.38458	−0.692288	+	0.721621i	$0.743397\pi$
$762$	−4.57206	−0.165628
$763$	36.7060	1.32885
$764$	−39.0479	−1.41270
$765$	0.771564	0.0278959
$766$	42.7573	1.54489
$767$	−7.45280	−0.269105
$768$	−32.6056	−1.17655
$769$	−50.8837	−1.83491	−0.917456	−	0.397837i	$-0.869761\pi$
$769$	−50.8837	−1.83491	−0.917456	+	0.397837i	$0.869761\pi$
$770$	−0.961043	−0.0346336
$771$	6.45464	0.232458
$772$	−53.2930	−1.91806
$773$	22.8231	0.820890	0.410445	−	0.911885i	$-0.365373\pi$
$773$	22.8231	0.820890	0.410445	+	0.911885i	$0.365373\pi$
$774$	−10.3943	−0.373617
$775$	−6.52449	−0.234367
$776$	77.3470	2.77659
$777$	−0.613930	−0.0220246
$778$	32.4731	1.16422
$779$	41.5371	1.48822
$780$	49.5030	1.77249
$781$	−0.298344	−0.0106756
$782$	−5.34000	−0.190958
$783$	0.722924	0.0258352
$784$	−19.2593	−0.687832
$785$	5.58007	0.199161
$786$	−47.2155	−1.68412
$787$	−30.0640	−1.07167	−0.535833	−	0.844324i	$-0.680002\pi$
$787$	−30.0640	−1.07167	−0.535833	+	0.844324i	$0.680002\pi$
$788$	−14.7780	−0.526445
$789$	−26.3564	−0.938312
$790$	51.7152	1.83995
$791$	22.4220	0.797233
$792$	−0.455442	−0.0161834
$793$	34.2446	1.21606
$794$	74.1873	2.63281
$795$	29.6510	1.05161
$796$	−47.7323	−1.69183
$797$	53.8973	1.90914	0.954571	−	0.297984i	$-0.0963144\pi$
$797$	53.8973	1.90914	0.954571	+	0.297984i	$0.0963144\pi$
$798$	27.4643	0.972224
$799$	1.90107	0.0672549
$800$	−2.87389	−0.101608
$801$	−5.47104	−0.193310
$802$	5.31007	0.187505
$803$	0.152958	0.00539778
$804$	−33.3514	−1.17621
$805$	32.7596	1.15463
$806$	48.3882	1.70440
$807$	3.65565	0.128685
$808$	−19.8213	−0.697312
$809$	−1.71412	−0.0602654	−0.0301327	−	0.999546i	$-0.509593\pi$
$809$	−1.71412	−0.0602654	−0.0301327	+	0.999546i	$0.509593\pi$
$810$	−6.36212	−0.223542
$811$	−12.7018	−0.446020	−0.223010	−	0.974816i	$-0.571588\pi$
$811$	−12.7018	−0.446020	−0.223010	+	0.974816i	$0.571588\pi$
$812$	5.42471	0.190370
$813$	−17.5684	−0.616151
$814$	0.0714732	0.00250513
$815$	11.3641	0.398069
$816$	1.53798	0.0538401
$817$	−25.7285	−0.900126
$818$	57.6675	2.01630
$819$	8.31259	0.290465
$820$	−72.2027	−2.52143
$821$	40.4292	1.41099	0.705494	−	0.708716i	$-0.250725\pi$
$821$	40.4292	1.41099	0.705494	+	0.708716i	$0.250725\pi$
$822$	9.56454	0.333602
$823$	6.70586	0.233751	0.116876	−	0.993147i	$-0.462712\pi$
$823$	6.70586	0.233751	0.116876	+	0.993147i	$0.462712\pi$
$824$	−85.2850	−2.97105
$825$	0.130487	0.00454298
$826$	7.18743	0.250083
$827$	−4.52959	−0.157509	−0.0787546	−	0.996894i	$-0.525094\pi$
$827$	−4.52959	−0.157509	−0.0787546	+	0.996894i	$0.525094\pi$
$828$	29.7786	1.03488
$829$	−29.8552	−1.03691	−0.518457	−	0.855103i	$-0.673494\pi$
$829$	−29.8552	−1.03691	−0.518457	+	0.855103i	$0.673494\pi$
$830$	−81.6001	−2.83238
$831$	−2.85488	−0.0990346
$832$	−25.9177	−0.898536
$833$	−1.13790	−0.0394258
$834$	−15.8762	−0.549746
$835$	−6.95257	−0.240604
$836$	−2.16235	−0.0747863
$837$	−4.20575	−0.145372
$838$	−31.3108	−1.08162
$839$	−15.1794	−0.524049	−0.262025	−	0.965061i	$-0.584390\pi$
$839$	−15.1794	−0.524049	−0.262025	+	0.965061i	$0.584390\pi$
$840$	−24.8892	−0.858758
$841$	−28.4774	−0.981979
$842$	47.5288	1.63795
$843$	−8.79703	−0.302986
$844$	91.0071	3.13259
$845$	21.5641	0.741826
$846$	−15.6757	−0.538942
$847$	−19.7420	−0.678342
$848$	59.1042	2.02964
$849$	−10.4847	−0.359835
$850$	−1.16238	−0.0398693
$851$	−2.43635	−0.0835169
$852$	−14.8204	−0.507739
$853$	9.07746	0.310806	0.155403	−	0.987851i	$-0.450332\pi$
$853$	9.07746	0.310806	0.155403	+	0.987851i	$0.450332\pi$
$854$	−33.0252	−1.13010
$855$	−15.7478	−0.538562
$856$	−58.9384	−2.01447
$857$	23.1081	0.789358	0.394679	−	0.918819i	$-0.370856\pi$
$857$	23.1081	0.789358	0.394679	+	0.918819i	$0.370856\pi$
$858$	−0.967745	−0.0330383
$859$	−37.8247	−1.29056	−0.645282	−	0.763945i	$-0.723260\pi$
$859$	−37.8247	−1.29056	−0.645282	+	0.763945i	$0.723260\pi$
$860$	44.7231	1.52504
$861$	−12.1244	−0.413197
$862$	−42.7595	−1.45639
$863$	6.15724	0.209595	0.104797	−	0.994494i	$-0.466581\pi$
$863$	6.15724	0.209595	0.104797	+	0.994494i	$0.466581\pi$
$864$	−1.85254	−0.0630246
$865$	5.20732	0.177054
$866$	3.63731	0.123601
$867$	−16.9091	−0.574264
$868$	−31.5593	−1.07119
$869$	−0.683724	−0.0231938
$870$	−4.59933	−0.155932
$871$	−36.9459	−1.25187
$872$	−110.670	−3.74775
$873$	−14.2848	−0.483468
$874$	108.991	3.68666
$875$	−15.8523	−0.535907
$876$	7.59829	0.256722
$877$	−52.7799	−1.78225	−0.891124	−	0.453759i	$-0.850083\pi$
$877$	−52.7799	−1.78225	−0.891124	+	0.453759i	$0.850083\pi$
$878$	−51.0716	−1.72358
$879$	19.3092	0.651284
$880$	1.09843	0.0370281
$881$	−9.79521	−0.330009	−0.165004	−	0.986293i	$-0.552764\pi$
$881$	−9.79521	−0.330009	−0.165004	+	0.986293i	$0.552764\pi$
$882$	9.38282	0.315936
$883$	47.9232	1.61275	0.806373	−	0.591407i	$-0.201428\pi$
$883$	47.9232	1.61275	0.806373	+	0.591407i	$0.201428\pi$
$884$	5.83007	0.196086
$885$	−4.12121	−0.138533
$886$	21.5702	0.724663
$887$	9.92939	0.333396	0.166698	−	0.986008i	$-0.446689\pi$
$887$	9.92939	0.333396	0.166698	+	0.986008i	$0.446689\pi$
$888$	1.85102	0.0621161
$889$	3.30333	0.110790
$890$	34.8074	1.16675
$891$	0.0841132	0.00281790
$892$	17.4328	0.583692
$893$	−38.8011	−1.29843
$894$	17.9953	0.601853
$895$	61.6645	2.06122
$896$	31.6488	1.05731
$897$	32.9881	1.10144
$898$	82.6491	2.75804
$899$	−3.04044	−0.101404
$900$	6.48202	0.216067
$901$	3.49206	0.116337
$902$	1.41151	0.0469980
$903$	7.50995	0.249915
$904$	−67.6029	−2.24844
$905$	58.5671	1.94684
$906$	−28.1282	−0.934496
$907$	−9.13519	−0.303329	−0.151664	−	0.988432i	$-0.548463\pi$
$907$	−9.13519	−0.303329	−0.151664	+	0.988432i	$0.548463\pi$
$908$	90.4870	3.00292
$909$	3.66070	0.121418
$910$	−52.8857	−1.75314
$911$	−5.85660	−0.194038	−0.0970189	−	0.995283i	$-0.530931\pi$
$911$	−5.85660	−0.194038	−0.0970189	+	0.995283i	$0.530931\pi$
$912$	−31.3905	−1.03944
$913$	1.07883	0.0357041
$914$	57.5859	1.90477
$915$	18.9364	0.626017
$916$	−46.4214	−1.53381
$917$	34.1134	1.12652
$918$	−0.749280	−0.0247299
$919$	−8.45601	−0.278938	−0.139469	−	0.990226i	$-0.544540\pi$
$919$	−8.45601	−0.278938	−0.139469	+	0.990226i	$0.544540\pi$
$920$	−98.7714	−3.25640
$921$	18.5268	0.610478
$922$	−52.0286	−1.71347
$923$	−16.4177	−0.540396
$924$	0.631173	0.0207641
$925$	−0.530329	−0.0174371
$926$	58.5353	1.92359
$927$	15.7509	0.517326
$928$	−1.33924	−0.0439629
$929$	−37.5552	−1.23215	−0.616074	−	0.787688i	$-0.711278\pi$
$929$	−37.5552	−1.23215	−0.616074	+	0.787688i	$0.711278\pi$
$930$	26.7574	0.877411
$931$	23.2247	0.761160
$932$	115.298	3.77671
$933$	−13.9298	−0.456041
$934$	13.2346	0.433049
$935$	0.0648987	0.00212241
$936$	−25.0627	−0.819201
$937$	−15.4042	−0.503232	−0.251616	−	0.967827i	$-0.580962\pi$
$937$	−15.4042	−0.503232	−0.251616	+	0.967827i	$0.580962\pi$
$938$	35.6304	1.16337
$939$	−13.2863	−0.433582
$940$	67.4469	2.19987
$941$	−26.4349	−0.861754	−0.430877	−	0.902411i	$-0.641796\pi$
$941$	−26.4349	−0.861754	−0.430877	+	0.902411i	$0.641796\pi$
$942$	−5.41891	−0.176558
$943$	−48.1149	−1.56684
$944$	−8.21492	−0.267373
$945$	4.59665	0.149529
$946$	−0.874302	−0.0284260
$947$	−13.7695	−0.447448	−0.223724	−	0.974653i	$-0.571821\pi$
$947$	−13.7695	−0.447448	−0.223724	+	0.974653i	$0.571821\pi$
$948$	−33.9644	−1.10311
$949$	8.41722	0.273234
$950$	23.7244	0.769720
$951$	−10.1989	−0.330721
$952$	−2.93125	−0.0950023
$953$	11.6061	0.375959	0.187979	−	0.982173i	$-0.439806\pi$
$953$	11.6061	0.375959	0.187979	+	0.982173i	$0.439806\pi$
$954$	−28.7946	−0.932260
$955$	−23.9197	−0.774023
$956$	−39.4831	−1.27698
$957$	0.0608075	0.00196563
$958$	−62.3604	−2.01477
$959$	−6.91041	−0.223149
$960$	−14.3319	−0.462558
$961$	−13.3117	−0.429410
$962$	3.93313	0.126809
$963$	10.8850	0.350765
$964$	−36.0926	−1.16246
$965$	−32.6459	−1.05091
$966$	−31.8135	−1.02358
$967$	28.0732	0.902774	0.451387	−	0.892328i	$-0.350929\pi$
$967$	28.0732	0.902774	0.451387	+	0.892328i	$0.350929\pi$
$968$	59.5226	1.91313
$969$	−1.85465	−0.0595798
$970$	90.8817	2.91803
$971$	9.33825	0.299679	0.149839	−	0.988710i	$-0.452124\pi$
$971$	9.33825	0.299679	0.149839	+	0.988710i	$0.452124\pi$
$972$	4.17837	0.134021
$973$	11.4706	0.367730
$974$	−43.6114	−1.39740
$975$	7.18064	0.229965
$976$	37.7464	1.20823
$977$	−11.6089	−0.371401	−0.185700	−	0.982606i	$-0.559455\pi$
$977$	−11.6089	−0.371401	−0.185700	+	0.982606i	$0.559455\pi$
$978$	−11.0359	−0.352890
$979$	−0.460187	−0.0147076
$980$	−40.3709	−1.28960
$981$	20.4390	0.652568
$982$	−29.2593	−0.933703
$983$	25.7516	0.821348	0.410674	−	0.911782i	$-0.365293\pi$
$983$	25.7516	0.821348	0.410674	+	0.911782i	$0.365293\pi$
$984$	36.5553	1.16534
$985$	−9.05261	−0.288440
$986$	−0.541673	−0.0172504
$987$	11.3257	0.360503
$988$	−118.993	−3.78567
$989$	29.8028	0.947675
$990$	−0.535138	−0.0170078
$991$	47.3377	1.50373	0.751866	−	0.659316i	$-0.229154\pi$
$991$	47.3377	1.50373	0.751866	+	0.659316i	$0.229154\pi$
$992$	7.79130	0.247374
$993$	22.3858	0.710391
$994$	15.8332	0.502197
$995$	−29.2395	−0.926956
$996$	53.5915	1.69811
$997$	33.9444	1.07503	0.537515	−	0.843254i	$-0.319363\pi$
$997$	33.9444	1.07503	0.537515	+	0.843254i	$0.319363\pi$
$998$	−77.0249	−2.43818
$999$	−0.341855	−0.0108158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.c.1.6	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.c.1.6	✓	92	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48563 q^{2} +1.00000 q^{3} +4.17837 q^{4} +2.55956 q^{5} -2.48563 q^{6} +1.79588 q^{7} -5.41463 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.48563 q^{2} +1.00000 q^{3} +4.17837 q^{4} +2.55956 q^{5} -2.48563 q^{6} +1.79588 q^{7} -5.41463 q^{8} +1.00000 q^{9} -6.36212 q^{10} +0.0841132 q^{11} +4.17837 q^{12} +4.62871 q^{13} -4.46389 q^{14} +2.55956 q^{15} +5.10204 q^{16} +0.301444 q^{17} -2.48563 q^{18} -6.15254 q^{19} +10.6948 q^{20} +1.79588 q^{21} -0.209075 q^{22} +7.12685 q^{23} -5.41463 q^{24} +1.55133 q^{25} -11.5053 q^{26} +1.00000 q^{27} +7.50384 q^{28} +0.722924 q^{29} -6.36212 q^{30} -4.20575 q^{31} -1.85254 q^{32} +0.0841132 q^{33} -0.749280 q^{34} +4.59665 q^{35} +4.17837 q^{36} -0.341855 q^{37} +15.2929 q^{38} +4.62871 q^{39} -13.8590 q^{40} -6.75121 q^{41} -4.46389 q^{42} +4.18177 q^{43} +0.351456 q^{44} +2.55956 q^{45} -17.7147 q^{46} +6.30652 q^{47} +5.10204 q^{48} -3.77482 q^{49} -3.85603 q^{50} +0.301444 q^{51} +19.3405 q^{52} +11.5844 q^{53} -2.48563 q^{54} +0.215293 q^{55} -9.72401 q^{56} -6.15254 q^{57} -1.79692 q^{58} -1.61013 q^{59} +10.6948 q^{60} +7.39830 q^{61} +10.4539 q^{62} +1.79588 q^{63} -5.59935 q^{64} +11.8474 q^{65} -0.209075 q^{66} -7.98191 q^{67} +1.25955 q^{68} +7.12685 q^{69} -11.4256 q^{70} -3.54694 q^{71} -5.41463 q^{72} +1.81848 q^{73} +0.849726 q^{74} +1.55133 q^{75} -25.7076 q^{76} +0.151057 q^{77} -11.5053 q^{78} -8.12862 q^{79} +13.0590 q^{80} +1.00000 q^{81} +16.7810 q^{82} +12.8259 q^{83} +7.50384 q^{84} +0.771564 q^{85} -10.3943 q^{86} +0.722924 q^{87} -0.455442 q^{88} -5.47104 q^{89} -6.36212 q^{90} +8.31259 q^{91} +29.7786 q^{92} -4.20575 q^{93} -15.6757 q^{94} -15.7478 q^{95} -1.85254 q^{96} -14.2848 q^{97} +9.38282 q^{98} +0.0841132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * q^99

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