LMFDB - Embedded newform 4015.2.a.h.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.16251 q^{2} -1.28072 q^{3} -0.648575 q^{4} +1.00000 q^{5} +1.48884 q^{6} -0.641997 q^{7} +3.07899 q^{8} -1.35976 q^{9} +O(q^{10})$	\(q-1.16251 q^{2} -1.28072 q^{3} -0.648575 q^{4} +1.00000 q^{5} +1.48884 q^{6} -0.641997 q^{7} +3.07899 q^{8} -1.35976 q^{9} -1.16251 q^{10} +1.00000 q^{11} +0.830642 q^{12} -2.10809 q^{13} +0.746327 q^{14} -1.28072 q^{15} -2.28220 q^{16} +0.343722 q^{17} +1.58073 q^{18} -5.83884 q^{19} -0.648575 q^{20} +0.822217 q^{21} -1.16251 q^{22} -6.18504 q^{23} -3.94332 q^{24} +1.00000 q^{25} +2.45067 q^{26} +5.58362 q^{27} +0.416383 q^{28} +7.74570 q^{29} +1.48884 q^{30} +2.91101 q^{31} -3.50490 q^{32} -1.28072 q^{33} -0.399579 q^{34} -0.641997 q^{35} +0.881908 q^{36} +0.493087 q^{37} +6.78770 q^{38} +2.69986 q^{39} +3.07899 q^{40} -8.13803 q^{41} -0.955834 q^{42} +3.22980 q^{43} -0.648575 q^{44} -1.35976 q^{45} +7.19015 q^{46} -8.99741 q^{47} +2.92285 q^{48} -6.58784 q^{49} -1.16251 q^{50} -0.440211 q^{51} +1.36725 q^{52} +11.9039 q^{53} -6.49101 q^{54} +1.00000 q^{55} -1.97670 q^{56} +7.47791 q^{57} -9.00444 q^{58} -10.3591 q^{59} +0.830642 q^{60} +7.45034 q^{61} -3.38407 q^{62} +0.872963 q^{63} +8.63888 q^{64} -2.10809 q^{65} +1.48884 q^{66} -2.50494 q^{67} -0.222929 q^{68} +7.92129 q^{69} +0.746327 q^{70} +12.8491 q^{71} -4.18669 q^{72} +1.00000 q^{73} -0.573217 q^{74} -1.28072 q^{75} +3.78693 q^{76} -0.641997 q^{77} -3.13861 q^{78} +0.783251 q^{79} -2.28220 q^{80} -3.07176 q^{81} +9.46053 q^{82} -10.4618 q^{83} -0.533270 q^{84} +0.343722 q^{85} -3.75467 q^{86} -9.92006 q^{87} +3.07899 q^{88} -2.69997 q^{89} +1.58073 q^{90} +1.35339 q^{91} +4.01146 q^{92} -3.72818 q^{93} +10.4596 q^{94} -5.83884 q^{95} +4.48879 q^{96} +9.65525 q^{97} +7.65842 q^{98} -1.35976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.16251	−0.822017	−0.411009	−	0.911631i	$-0.634823\pi$
$2$	−1.16251	−0.822017	−0.411009	+	0.911631i	$0.634823\pi$
$3$	−1.28072	−0.739423	−0.369711	−	0.929147i	$-0.620543\pi$
$3$	−1.28072	−0.739423	−0.369711	+	0.929147i	$0.620543\pi$
$4$	−0.648575	−0.324288
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.48884	0.607818
$7$	−0.641997	−0.242652	−0.121326	−	0.992613i	$-0.538715\pi$
$7$	−0.641997	−0.242652	−0.121326	+	0.992613i	$0.538715\pi$
$8$	3.07899	1.08859
$9$	−1.35976	−0.453254
$10$	−1.16251	−0.367617
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.830642	0.239786
$13$	−2.10809	−0.584678	−0.292339	−	0.956315i	$-0.594434\pi$
$13$	−2.10809	−0.584678	−0.292339	+	0.956315i	$0.594434\pi$
$14$	0.746327	0.199464
$15$	−1.28072	−0.330680
$16$	−2.28220	−0.570550
$17$	0.343722	0.0833648	0.0416824	−	0.999131i	$-0.486728\pi$
$17$	0.343722	0.0833648	0.0416824	+	0.999131i	$0.486728\pi$
$18$	1.58073	0.372583
$19$	−5.83884	−1.33952	−0.669761	−	0.742576i	$-0.733604\pi$
$19$	−5.83884	−1.33952	−0.669761	+	0.742576i	$0.733604\pi$
$20$	−0.648575	−0.145026
$21$	0.822217	0.179422
$22$	−1.16251	−0.247848
$23$	−6.18504	−1.28967	−0.644835	−	0.764322i	$-0.723074\pi$
$23$	−6.18504	−1.28967	−0.644835	+	0.764322i	$0.723074\pi$
$24$	−3.94332	−0.804926
$25$	1.00000	0.200000
$26$	2.45067	0.480616
$27$	5.58362	1.07457
$28$	0.416383	0.0786891
$29$	7.74570	1.43834	0.719170	−	0.694834i	$-0.244522\pi$
$29$	7.74570	1.43834	0.719170	+	0.694834i	$0.244522\pi$
$30$	1.48884	0.271825
$31$	2.91101	0.522832	0.261416	−	0.965226i	$-0.415811\pi$
$31$	2.91101	0.522832	0.261416	+	0.965226i	$0.415811\pi$
$32$	−3.50490	−0.619585
$33$	−1.28072	−0.222944
$34$	−0.399579	−0.0685273
$35$	−0.641997	−0.108517
$36$	0.881908	0.146985
$37$	0.493087	0.0810630	0.0405315	−	0.999178i	$-0.487095\pi$
$37$	0.493087	0.0810630	0.0405315	+	0.999178i	$0.487095\pi$
$38$	6.78770	1.10111
$39$	2.69986	0.432324
$40$	3.07899	0.486831
$41$	−8.13803	−1.27095	−0.635474	−	0.772122i	$-0.719195\pi$
$41$	−8.13803	−1.27095	−0.635474	+	0.772122i	$0.719195\pi$
$42$	−0.955834	−0.147488
$43$	3.22980	0.492540	0.246270	−	0.969201i	$-0.420795\pi$
$43$	3.22980	0.492540	0.246270	+	0.969201i	$0.420795\pi$
$44$	−0.648575	−0.0977764
$45$	−1.35976	−0.202701
$46$	7.19015	1.06013
$47$	−8.99741	−1.31241	−0.656204	−	0.754584i	$-0.727839\pi$
$47$	−8.99741	−1.31241	−0.656204	+	0.754584i	$0.727839\pi$
$48$	2.92285	0.421878
$49$	−6.58784	−0.941120
$50$	−1.16251	−0.164403
$51$	−0.440211	−0.0616418
$52$	1.36725	0.189604
$53$	11.9039	1.63513	0.817563	−	0.575840i	$-0.195325\pi$
$53$	11.9039	1.63513	0.817563	+	0.575840i	$0.195325\pi$
$54$	−6.49101	−0.883314
$55$	1.00000	0.134840
$56$	−1.97670	−0.264148
$57$	7.47791	0.990474
$58$	−9.00444	−1.18234
$59$	−10.3591	−1.34863	−0.674317	−	0.738442i	$-0.735562\pi$
$59$	−10.3591	−1.34863	−0.674317	+	0.738442i	$0.735562\pi$
$60$	0.830642	0.107235
$61$	7.45034	0.953918	0.476959	−	0.878926i	$-0.341739\pi$
$61$	7.45034	0.953918	0.476959	+	0.878926i	$0.341739\pi$
$62$	−3.38407	−0.429777
$63$	0.872963	0.109983
$64$	8.63888	1.07986
$65$	−2.10809	−0.261476
$66$	1.48884	0.183264
$67$	−2.50494	−0.306027	−0.153014	−	0.988224i	$-0.548898\pi$
$67$	−2.50494	−0.306027	−0.153014	+	0.988224i	$0.548898\pi$
$68$	−0.222929	−0.0270342
$69$	7.92129	0.953611
$70$	0.746327	0.0892031
$71$	12.8491	1.52491	0.762456	−	0.647040i	$-0.223993\pi$
$71$	12.8491	1.52491	0.762456	+	0.647040i	$0.223993\pi$
$72$	−4.18669	−0.493407
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−0.573217	−0.0666352
$75$	−1.28072	−0.147885
$76$	3.78693	0.434391
$77$	−0.641997	−0.0731623
$78$	−3.13861	−0.355378
$79$	0.783251	0.0881227	0.0440613	−	0.999029i	$-0.485970\pi$
$79$	0.783251	0.0881227	0.0440613	+	0.999029i	$0.485970\pi$
$80$	−2.28220	−0.255158
$81$	−3.07176	−0.341307
$82$	9.46053	1.04474
$83$	−10.4618	−1.14834	−0.574168	−	0.818738i	$-0.694674\pi$
$83$	−10.4618	−1.14834	−0.574168	+	0.818738i	$0.694674\pi$
$84$	−0.533270	−0.0581845
$85$	0.343722	0.0372819
$86$	−3.75467	−0.404876
$87$	−9.92006	−1.06354
$88$	3.07899	0.328221
$89$	−2.69997	−0.286197	−0.143098	−	0.989708i	$-0.545707\pi$
$89$	−2.69997	−0.286197	−0.143098	+	0.989708i	$0.545707\pi$
$90$	1.58073	0.166624
$91$	1.35339	0.141873
$92$	4.01146	0.418224
$93$	−3.72818	−0.386594
$94$	10.4596	1.07882
$95$	−5.83884	−0.599053
$96$	4.48879	0.458136
$97$	9.65525	0.980342	0.490171	−	0.871626i	$-0.336934\pi$
$97$	9.65525	0.980342	0.490171	+	0.871626i	$0.336934\pi$
$98$	7.65842	0.773617
$99$	−1.35976	−0.136661
$100$	−0.648575	−0.0648575
$101$	−10.1399	−1.00896	−0.504480	−	0.863423i	$-0.668316\pi$
$101$	−10.1399	−1.00896	−0.504480	+	0.863423i	$0.668316\pi$
$102$	0.511748	0.0506706
$103$	−10.8550	−1.06957	−0.534787	−	0.844987i	$-0.679608\pi$
$103$	−10.8550	−1.06957	−0.534787	+	0.844987i	$0.679608\pi$
$104$	−6.49078	−0.636473
$105$	0.822217	0.0802402
$106$	−13.8384	−1.34410
$107$	−14.2220	−1.37489	−0.687444	−	0.726237i	$-0.741267\pi$
$107$	−14.2220	−1.37489	−0.687444	+	0.726237i	$0.741267\pi$
$108$	−3.62140	−0.348469
$109$	−1.17084	−0.112146	−0.0560729	−	0.998427i	$-0.517858\pi$
$109$	−1.17084	−0.112146	−0.0560729	+	0.998427i	$0.517858\pi$
$110$	−1.16251	−0.110841
$111$	−0.631505	−0.0599398
$112$	1.46517	0.138445
$113$	−7.96633	−0.749409	−0.374704	−	0.927144i	$-0.622256\pi$
$113$	−7.96633	−0.749409	−0.374704	+	0.927144i	$0.622256\pi$
$114$	−8.69313	−0.814186
$115$	−6.18504	−0.576758
$116$	−5.02367	−0.466436
$117$	2.86650	0.265008
$118$	12.0425	1.10860
$119$	−0.220668	−0.0202286
$120$	−3.94332	−0.359974
$121$	1.00000	0.0909091
$122$	−8.66107	−0.784137
$123$	10.4225	0.939767
$124$	−1.88801	−0.169548
$125$	1.00000	0.0894427
$126$	−1.01483	−0.0904079
$127$	−14.7034	−1.30471	−0.652357	−	0.757912i	$-0.726220\pi$
$127$	−14.7034	−1.30471	−0.652357	+	0.757912i	$0.726220\pi$
$128$	−3.03296	−0.268078
$129$	−4.13646	−0.364195
$130$	2.45067	0.214938
$131$	9.68402	0.846097	0.423048	−	0.906107i	$-0.360960\pi$
$131$	9.68402	0.846097	0.423048	+	0.906107i	$0.360960\pi$
$132$	0.830642	0.0722981
$133$	3.74852	0.325038
$134$	2.91202	0.251560
$135$	5.58362	0.480562
$136$	1.05832	0.0907498
$137$	−9.21897	−0.787630	−0.393815	−	0.919190i	$-0.628845\pi$
$137$	−9.21897	−0.787630	−0.393815	+	0.919190i	$0.628845\pi$
$138$	−9.20856	−0.783884
$139$	20.7333	1.75857	0.879287	−	0.476291i	$-0.158019\pi$
$139$	20.7333	1.75857	0.879287	+	0.476291i	$0.158019\pi$
$140$	0.416383	0.0351908
$141$	11.5231	0.970424
$142$	−14.9372	−1.25350
$143$	−2.10809	−0.176287
$144$	3.10325	0.258604
$145$	7.74570	0.643246
$146$	−1.16251	−0.0962098
$147$	8.43716	0.695885
$148$	−0.319804	−0.0262877
$149$	−16.8512	−1.38051	−0.690254	−	0.723567i	$-0.742501\pi$
$149$	−16.8512	−1.38051	−0.690254	+	0.723567i	$0.742501\pi$
$150$	1.48884	0.121564
$151$	14.4040	1.17218	0.586091	−	0.810245i	$-0.300666\pi$
$151$	14.4040	1.17218	0.586091	+	0.810245i	$0.300666\pi$
$152$	−17.9777	−1.45819
$153$	−0.467380	−0.0377854
$154$	0.746327	0.0601407
$155$	2.91101	0.233818
$156$	−1.75107	−0.140197
$157$	10.5072	0.838566	0.419283	−	0.907856i	$-0.362282\pi$
$157$	10.5072	0.838566	0.419283	+	0.907856i	$0.362282\pi$
$158$	−0.910536	−0.0724384
$159$	−15.2455	−1.20905
$160$	−3.50490	−0.277087
$161$	3.97077	0.312941
$162$	3.57095	0.280560
$163$	−8.50054	−0.665814	−0.332907	−	0.942960i	$-0.608030\pi$
$163$	−8.50054	−0.665814	−0.332907	+	0.942960i	$0.608030\pi$
$164$	5.27813	0.412153
$165$	−1.28072	−0.0997037
$166$	12.1620	0.943952
$167$	16.5246	1.27871	0.639357	−	0.768910i	$-0.279200\pi$
$167$	16.5246	1.27871	0.639357	+	0.768910i	$0.279200\pi$
$168$	2.53160	0.195317
$169$	−8.55597	−0.658151
$170$	−0.399579	−0.0306463
$171$	7.93944	0.607144
$172$	−2.09477	−0.159725
$173$	24.6751	1.87601	0.938005	−	0.346622i	$-0.112671\pi$
$173$	24.6751	1.87601	0.938005	+	0.346622i	$0.112671\pi$
$174$	11.5321	0.874250
$175$	−0.641997	−0.0485304
$176$	−2.28220	−0.172027
$177$	13.2670	0.997211
$178$	3.13874	0.235259
$179$	8.44486	0.631199	0.315599	−	0.948893i	$-0.397794\pi$
$179$	8.44486	0.631199	0.315599	+	0.948893i	$0.397794\pi$
$180$	0.881908	0.0657336
$181$	3.37821	0.251100	0.125550	−	0.992087i	$-0.459930\pi$
$181$	3.37821	0.251100	0.125550	+	0.992087i	$0.459930\pi$
$182$	−1.57332	−0.116622
$183$	−9.54178	−0.705348
$184$	−19.0437	−1.40392
$185$	0.493087	0.0362525
$186$	4.33403	0.317787
$187$	0.343722	0.0251354
$188$	5.83550	0.425598
$189$	−3.58467	−0.260746
$190$	6.78770	0.492432
$191$	21.2462	1.53732	0.768660	−	0.639657i	$-0.220924\pi$
$191$	21.2462	1.53732	0.768660	+	0.639657i	$0.220924\pi$
$192$	−11.0640	−0.798473
$193$	−20.8242	−1.49896	−0.749481	−	0.662026i	$-0.769697\pi$
$193$	−20.8242	−1.49896	−0.749481	+	0.662026i	$0.769697\pi$
$194$	−11.2243	−0.805858
$195$	2.69986	0.193341
$196$	4.27271	0.305194
$197$	19.9368	1.42044	0.710220	−	0.703980i	$-0.248596\pi$
$197$	19.9368	1.42044	0.710220	+	0.703980i	$0.248596\pi$
$198$	1.58073	0.112338
$199$	4.40291	0.312114	0.156057	−	0.987748i	$-0.450122\pi$
$199$	4.40291	0.312114	0.156057	+	0.987748i	$0.450122\pi$
$200$	3.07899	0.217717
$201$	3.20812	0.226284
$202$	11.7877	0.829383
$203$	−4.97272	−0.349016
$204$	0.285510	0.0199897
$205$	−8.13803	−0.568385
$206$	12.6190	0.879209
$207$	8.41018	0.584548
$208$	4.81108	0.333588
$209$	−5.83884	−0.403881
$210$	−0.955834	−0.0659588
$211$	3.29263	0.226674	0.113337	−	0.993557i	$-0.463846\pi$
$211$	3.29263	0.226674	0.113337	+	0.993557i	$0.463846\pi$
$212$	−7.72057	−0.530251
$213$	−16.4561	−1.12755
$214$	16.5331	1.13018
$215$	3.22980	0.220271
$216$	17.1919	1.16976
$217$	−1.86886	−0.126866
$218$	1.36111	0.0921858
$219$	−1.28072	−0.0865429
$220$	−0.648575	−0.0437269
$221$	−0.724596	−0.0487416
$222$	0.734130	0.0492716
$223$	8.17772	0.547620	0.273810	−	0.961784i	$-0.411716\pi$
$223$	8.17772	0.547620	0.273810	+	0.961784i	$0.411716\pi$
$224$	2.25014	0.150344
$225$	−1.35976	−0.0906508
$226$	9.26092	0.616027
$227$	0.158982	0.0105520	0.00527600	−	0.999986i	$-0.498321\pi$
$227$	0.158982	0.0105520	0.00527600	+	0.999986i	$0.498321\pi$
$228$	−4.84999	−0.321198
$229$	18.7188	1.23698	0.618488	−	0.785794i	$-0.287746\pi$
$229$	18.7188	1.23698	0.618488	+	0.785794i	$0.287746\pi$
$230$	7.19015	0.474105
$231$	0.822217	0.0540979
$232$	23.8489	1.56576
$233$	9.43469	0.618087	0.309044	−	0.951048i	$-0.399991\pi$
$233$	9.43469	0.618087	0.309044	+	0.951048i	$0.399991\pi$
$234$	−3.33233	−0.217841
$235$	−8.99741	−0.586927
$236$	6.71863	0.437345
$237$	−1.00312	−0.0651599
$238$	0.256529	0.0166283
$239$	−20.0848	−1.29918	−0.649589	−	0.760286i	$-0.725059\pi$
$239$	−20.0848	−1.29918	−0.649589	+	0.760286i	$0.725059\pi$
$240$	2.92285	0.188669
$241$	−7.05229	−0.454278	−0.227139	−	0.973862i	$-0.572937\pi$
$241$	−7.05229	−0.454278	−0.227139	+	0.973862i	$0.572937\pi$
$242$	−1.16251	−0.0747288
$243$	−12.8168	−0.822199
$244$	−4.83210	−0.309344
$245$	−6.58784	−0.420882
$246$	−12.1163	−0.772505
$247$	12.3088	0.783190
$248$	8.96296	0.569148
$249$	13.3987	0.849105
$250$	−1.16251	−0.0735235
$251$	20.0992	1.26865	0.634326	−	0.773065i	$-0.281278\pi$
$251$	20.0992	1.26865	0.634326	+	0.773065i	$0.281278\pi$
$252$	−0.566182	−0.0356661
$253$	−6.18504	−0.388850
$254$	17.0928	1.07250
$255$	−0.440211	−0.0275671
$256$	−13.7519	−0.859495
$257$	−5.22396	−0.325862	−0.162931	−	0.986637i	$-0.552095\pi$
$257$	−5.22396	−0.325862	−0.162931	+	0.986637i	$0.552095\pi$
$258$	4.80867	0.299375
$259$	−0.316560	−0.0196701
$260$	1.36725	0.0847935
$261$	−10.5323	−0.651934
$262$	−11.2577	−0.695506
$263$	−17.9094	−1.10434	−0.552170	−	0.833732i	$-0.686200\pi$
$263$	−17.9094	−1.10434	−0.552170	+	0.833732i	$0.686200\pi$
$264$	−3.94332	−0.242694
$265$	11.9039	0.731250
$266$	−4.35768	−0.267187
$267$	3.45790	0.211620
$268$	1.62464	0.0992409
$269$	23.2089	1.41507	0.707537	−	0.706677i	$-0.249806\pi$
$269$	23.2089	1.41507	0.707537	+	0.706677i	$0.249806\pi$
$270$	−6.49101	−0.395030
$271$	17.8723	1.08566	0.542832	−	0.839841i	$-0.317352\pi$
$271$	17.8723	1.08566	0.542832	+	0.839841i	$0.317352\pi$
$272$	−0.784442	−0.0475638
$273$	−1.73331	−0.104904
$274$	10.7171	0.647445
$275$	1.00000	0.0603023
$276$	−5.13755	−0.309244
$277$	31.9780	1.92137	0.960687	−	0.277633i	$-0.0895500\pi$
$277$	31.9780	1.92137	0.960687	+	0.277633i	$0.0895500\pi$
$278$	−24.1026	−1.44558
$279$	−3.95828	−0.236976
$280$	−1.97670	−0.118131
$281$	16.4603	0.981941	0.490970	−	0.871176i	$-0.336642\pi$
$281$	16.4603	0.981941	0.490970	+	0.871176i	$0.336642\pi$
$282$	−13.3957	−0.797705
$283$	−17.7881	−1.05740	−0.528698	−	0.848810i	$-0.677320\pi$
$283$	−17.7881	−1.05740	−0.528698	+	0.848810i	$0.677320\pi$
$284$	−8.33363	−0.494510
$285$	7.47791	0.442953
$286$	2.45067	0.144911
$287$	5.22459	0.308398
$288$	4.76584	0.280830
$289$	−16.8819	−0.993050
$290$	−9.00444	−0.528759
$291$	−12.3657	−0.724887
$292$	−0.648575	−0.0379550
$293$	−0.740470	−0.0432587	−0.0216294	−	0.999766i	$-0.506885\pi$
$293$	−0.740470	−0.0432587	−0.0216294	+	0.999766i	$0.506885\pi$
$294$	−9.80827	−0.572030
$295$	−10.3591	−0.603127
$296$	1.51821	0.0882441
$297$	5.58362	0.323995
$298$	19.5897	1.13480
$299$	13.0386	0.754042
$300$	0.830642	0.0479571
$301$	−2.07352	−0.119516
$302$	−16.7448	−0.963553
$303$	12.9864	0.746048
$304$	13.3254	0.764265
$305$	7.45034	0.426605
$306$	0.543333	0.0310603
$307$	22.9235	1.30831	0.654155	−	0.756360i	$-0.273024\pi$
$307$	22.9235	1.30831	0.654155	+	0.756360i	$0.273024\pi$
$308$	0.416383	0.0237256
$309$	13.9022	0.790868
$310$	−3.38407	−0.192202
$311$	15.5490	0.881704	0.440852	−	0.897580i	$-0.354676\pi$
$311$	15.5490	0.881704	0.440852	+	0.897580i	$0.354676\pi$
$312$	8.31286	0.470623
$313$	29.1446	1.64735	0.823676	−	0.567061i	$-0.191920\pi$
$313$	29.1446	1.64735	0.823676	+	0.567061i	$0.191920\pi$
$314$	−12.2147	−0.689316
$315$	0.872963	0.0491859
$316$	−0.507997	−0.0285771
$317$	−20.5857	−1.15621	−0.578103	−	0.815964i	$-0.696207\pi$
$317$	−20.5857	−1.15621	−0.578103	+	0.815964i	$0.696207\pi$
$318$	17.7230	0.993859
$319$	7.74570	0.433676
$320$	8.63888	0.482928
$321$	18.2143	1.01662
$322$	−4.61606	−0.257243
$323$	−2.00694	−0.111669
$324$	1.99227	0.110682
$325$	−2.10809	−0.116936
$326$	9.88195	0.547311
$327$	1.49951	0.0829231
$328$	−25.0569	−1.38354
$329$	5.77631	0.318458
$330$	1.48884	0.0819582
$331$	12.4856	0.686270	0.343135	−	0.939286i	$-0.388511\pi$
$331$	12.4856	0.686270	0.343135	+	0.939286i	$0.388511\pi$
$332$	6.78529	0.372391
$333$	−0.670481	−0.0367421
$334$	−19.2100	−1.05113
$335$	−2.50494	−0.136860
$336$	−1.87646	−0.102369
$337$	−21.3598	−1.16354	−0.581771	−	0.813353i	$-0.697640\pi$
$337$	−21.3598	−1.16354	−0.581771	+	0.813353i	$0.697640\pi$
$338$	9.94638	0.541012
$339$	10.2026	0.554130
$340$	−0.222929	−0.0120900
$341$	2.91101	0.157640
$342$	−9.22966	−0.499083
$343$	8.72335	0.471017
$344$	9.94452	0.536173
$345$	7.92129	0.426468
$346$	−28.6850	−1.54211
$347$	−15.9975	−0.858789	−0.429395	−	0.903117i	$-0.641273\pi$
$347$	−15.9975	−0.858789	−0.429395	+	0.903117i	$0.641273\pi$
$348$	6.43390	0.344893
$349$	34.9206	1.86926	0.934630	−	0.355623i	$-0.115731\pi$
$349$	34.9206	1.86926	0.934630	+	0.355623i	$0.115731\pi$
$350$	0.746327	0.0398928
$351$	−11.7708	−0.628277
$352$	−3.50490	−0.186812
$353$	−0.409740	−0.0218083	−0.0109041	−	0.999941i	$-0.503471\pi$
$353$	−0.409740	−0.0218083	−0.0109041	+	0.999941i	$0.503471\pi$
$354$	−15.4230	−0.819724
$355$	12.8491	0.681961
$356$	1.75114	0.0928100
$357$	0.282614	0.0149575
$358$	−9.81722	−0.518856
$359$	23.9073	1.26178	0.630888	−	0.775874i	$-0.282691\pi$
$359$	23.9073	1.26178	0.630888	+	0.775874i	$0.282691\pi$
$360$	−4.18669	−0.220658
$361$	15.0921	0.794321
$362$	−3.92719	−0.206409
$363$	−1.28072	−0.0672202
$364$	−0.877773	−0.0460078
$365$	1.00000	0.0523424
$366$	11.0924	0.579809
$367$	−20.4451	−1.06722	−0.533612	−	0.845729i	$-0.679166\pi$
$367$	−20.4451	−1.06722	−0.533612	+	0.845729i	$0.679166\pi$
$368$	14.1155	0.735821
$369$	11.0658	0.576062
$370$	−0.573217	−0.0298002
$371$	−7.64226	−0.396766
$372$	2.41800	0.125368
$373$	−12.2237	−0.632919	−0.316459	−	0.948606i	$-0.602494\pi$
$373$	−12.2237	−0.632919	−0.316459	+	0.948606i	$0.602494\pi$
$374$	−0.399579	−0.0206618
$375$	−1.28072	−0.0661360
$376$	−27.7029	−1.42867
$377$	−16.3286	−0.840967
$378$	4.16721	0.214338
$379$	−12.2749	−0.630518	−0.315259	−	0.949006i	$-0.602091\pi$
$379$	−12.2749	−0.630518	−0.315259	+	0.949006i	$0.602091\pi$
$380$	3.78693	0.194265
$381$	18.8309	0.964736
$382$	−24.6989	−1.26370
$383$	6.57504	0.335969	0.167985	−	0.985790i	$-0.446274\pi$
$383$	6.57504	0.335969	0.167985	+	0.985790i	$0.446274\pi$
$384$	3.88436	0.198223
$385$	−0.641997	−0.0327192
$386$	24.2083	1.23217
$387$	−4.39176	−0.223246
$388$	−6.26216	−0.317913
$389$	34.0102	1.72439	0.862193	−	0.506580i	$-0.169091\pi$
$389$	34.0102	1.72439	0.862193	+	0.506580i	$0.169091\pi$
$390$	−3.13861	−0.158930
$391$	−2.12593	−0.107513
$392$	−20.2839	−1.02449
$393$	−12.4025	−0.625623
$394$	−23.1767	−1.16763
$395$	0.783251	0.0394097
$396$	0.881908	0.0443176
$397$	37.8535	1.89981	0.949907	−	0.312532i	$-0.101177\pi$
$397$	37.8535	1.89981	0.949907	+	0.312532i	$0.101177\pi$
$398$	−5.11842	−0.256563
$399$	−4.80080	−0.240340
$400$	−2.28220	−0.114110
$401$	19.2150	0.959550	0.479775	−	0.877391i	$-0.340718\pi$
$401$	19.2150	0.959550	0.479775	+	0.877391i	$0.340718\pi$
$402$	−3.72947	−0.186009
$403$	−6.13665	−0.305689
$404$	6.57651	0.327193
$405$	−3.07176	−0.152637
$406$	5.78082	0.286897
$407$	0.493087	0.0244414
$408$	−1.35540	−0.0671025
$409$	38.3034	1.89398	0.946992	−	0.321258i	$-0.104106\pi$
$409$	38.3034	1.89398	0.946992	+	0.321258i	$0.104106\pi$
$410$	9.46053	0.467222
$411$	11.8069	0.582392
$412$	7.04028	0.346850
$413$	6.65048	0.327249
$414$	−9.77690	−0.480508
$415$	−10.4618	−0.513551
$416$	7.38864	0.362258
$417$	−26.5535	−1.30033
$418$	6.78770	0.331997
$419$	31.2650	1.52739	0.763697	−	0.645575i	$-0.223382\pi$
$419$	31.2650	1.52739	0.763697	+	0.645575i	$0.223382\pi$
$420$	−0.533270	−0.0260209
$421$	36.3796	1.77303	0.886516	−	0.462698i	$-0.153119\pi$
$421$	36.3796	1.77303	0.886516	+	0.462698i	$0.153119\pi$
$422$	−3.82770	−0.186330
$423$	12.2343	0.594854
$424$	36.6520	1.77998
$425$	0.343722	0.0166730
$426$	19.1304	0.926869
$427$	−4.78309	−0.231470
$428$	9.22401	0.445859
$429$	2.69986	0.130351
$430$	−3.75467	−0.181066
$431$	25.4862	1.22763	0.613814	−	0.789451i	$-0.289635\pi$
$431$	25.4862	1.22763	0.613814	+	0.789451i	$0.289635\pi$
$432$	−12.7429	−0.613095
$433$	−22.0419	−1.05927	−0.529633	−	0.848227i	$-0.677670\pi$
$433$	−22.0419	−1.05927	−0.529633	+	0.848227i	$0.677670\pi$
$434$	2.17256	0.104286
$435$	−9.92006	−0.475630
$436$	0.759376	0.0363675
$437$	36.1135	1.72754
$438$	1.48884	0.0711397
$439$	−19.8566	−0.947703	−0.473851	−	0.880605i	$-0.657137\pi$
$439$	−19.8566	−0.947703	−0.473851	+	0.880605i	$0.657137\pi$
$440$	3.07899	0.146785
$441$	8.95790	0.426566
$442$	0.842348	0.0400664
$443$	10.3372	0.491137	0.245569	−	0.969379i	$-0.421025\pi$
$443$	10.3372	0.491137	0.245569	+	0.969379i	$0.421025\pi$
$444$	0.409579	0.0194377
$445$	−2.69997	−0.127991
$446$	−9.50666	−0.450153
$447$	21.5817	1.02078
$448$	−5.54613	−0.262030
$449$	−26.5637	−1.25362	−0.626809	−	0.779173i	$-0.715639\pi$
$449$	−26.5637	−1.25362	−0.626809	+	0.779173i	$0.715639\pi$
$450$	1.58073	0.0745165
$451$	−8.13803	−0.383205
$452$	5.16676	0.243024
$453$	−18.4475	−0.866738
$454$	−0.184818	−0.00867392
$455$	1.35339	0.0634477
$456$	23.0244	1.07822
$457$	−15.1963	−0.710855	−0.355427	−	0.934704i	$-0.615665\pi$
$457$	−15.1963	−0.710855	−0.355427	+	0.934704i	$0.615665\pi$
$458$	−21.7608	−1.01682
$459$	1.91921	0.0895812
$460$	4.01146	0.187035
$461$	1.16768	0.0543844	0.0271922	−	0.999630i	$-0.491343\pi$
$461$	1.16768	0.0543844	0.0271922	+	0.999630i	$0.491343\pi$
$462$	−0.955834	−0.0444694
$463$	16.7162	0.776867	0.388434	−	0.921477i	$-0.373016\pi$
$463$	16.7162	0.776867	0.388434	+	0.921477i	$0.373016\pi$
$464$	−17.6772	−0.820645
$465$	−3.72818	−0.172890
$466$	−10.9679	−0.508078
$467$	−29.8868	−1.38300	−0.691498	−	0.722378i	$-0.743049\pi$
$467$	−29.8868	−1.38300	−0.691498	+	0.722378i	$0.743049\pi$
$468$	−1.85914	−0.0859388
$469$	1.60817	0.0742582
$470$	10.4596	0.482464
$471$	−13.4568	−0.620055
$472$	−31.8954	−1.46811
$473$	3.22980	0.148506
$474$	1.16614	0.0535626
$475$	−5.83884	−0.267905
$476$	0.143120	0.00655990
$477$	−16.1865	−0.741127
$478$	23.3487	1.06795
$479$	11.4894	0.524963	0.262482	−	0.964937i	$-0.415459\pi$
$479$	11.4894	0.524963	0.262482	+	0.964937i	$0.415459\pi$
$480$	4.48879	0.204884
$481$	−1.03947	−0.0473958
$482$	8.19834	0.373424
$483$	−5.08544	−0.231396
$484$	−0.648575	−0.0294807
$485$	9.65525	0.438422
$486$	14.8997	0.675862
$487$	−12.7468	−0.577611	−0.288805	−	0.957388i	$-0.593258\pi$
$487$	−12.7468	−0.577611	−0.288805	+	0.957388i	$0.593258\pi$
$488$	22.9395	1.03842
$489$	10.8868	0.492318
$490$	7.65842	0.345972
$491$	15.7570	0.711104	0.355552	−	0.934657i	$-0.384293\pi$
$491$	15.7570	0.711104	0.355552	+	0.934657i	$0.384293\pi$
$492$	−6.75979	−0.304755
$493$	2.66237	0.119907
$494$	−14.3091	−0.643796
$495$	−1.35976	−0.0611168
$496$	−6.64350	−0.298302
$497$	−8.24911	−0.370023
$498$	−15.5760	−0.697979
$499$	−32.0281	−1.43377	−0.716887	−	0.697189i	$-0.754434\pi$
$499$	−32.0281	−1.43377	−0.716887	+	0.697189i	$0.754434\pi$
$500$	−0.648575	−0.0290052
$501$	−21.1634	−0.945511
$502$	−23.3655	−1.04285
$503$	6.01405	0.268153	0.134077	−	0.990971i	$-0.457193\pi$
$503$	6.01405	0.268153	0.134077	+	0.990971i	$0.457193\pi$
$504$	2.68784	0.119726
$505$	−10.1399	−0.451221
$506$	7.19015	0.319641
$507$	10.9578	0.486652
$508$	9.53625	0.423103
$509$	−21.9128	−0.971269	−0.485635	−	0.874162i	$-0.661411\pi$
$509$	−21.9128	−0.971269	−0.485635	+	0.874162i	$0.661411\pi$
$510$	0.511748	0.0226606
$511$	−0.641997	−0.0284003
$512$	22.0526	0.974598
$513$	−32.6019	−1.43941
$514$	6.07290	0.267864
$515$	−10.8550	−0.478328
$516$	2.68281	0.118104
$517$	−8.99741	−0.395706
$518$	0.368004	0.0161692
$519$	−31.6018	−1.38716
$520$	−6.49078	−0.284640
$521$	0.338487	0.0148294	0.00741468	−	0.999973i	$-0.497640\pi$
$521$	0.338487	0.0148294	0.00741468	+	0.999973i	$0.497640\pi$
$522$	12.2439	0.535901
$523$	10.0100	0.437707	0.218853	−	0.975758i	$-0.429768\pi$
$523$	10.0100	0.437707	0.218853	+	0.975758i	$0.429768\pi$
$524$	−6.28081	−0.274379
$525$	0.822217	0.0358845
$526$	20.8198	0.907786
$527$	1.00058	0.0435858
$528$	2.92285	0.127201
$529$	15.2547	0.663247
$530$	−13.8384	−0.601100
$531$	14.0859	0.611274
$532$	−2.43120	−0.105406
$533$	17.1557	0.743095
$534$	−4.01984	−0.173956
$535$	−14.2220	−0.614869
$536$	−7.71269	−0.333138
$537$	−10.8155	−0.466723
$538$	−26.9806	−1.16321
$539$	−6.58784	−0.283758
$540$	−3.62140	−0.155840
$541$	2.06743	0.0888858	0.0444429	−	0.999012i	$-0.485849\pi$
$541$	2.06743	0.0888858	0.0444429	+	0.999012i	$0.485849\pi$
$542$	−20.7767	−0.892435
$543$	−4.32653	−0.185669
$544$	−1.20471	−0.0516516
$545$	−1.17084	−0.0501531
$546$	2.01498	0.0862332
$547$	−42.6737	−1.82460	−0.912298	−	0.409526i	$-0.865694\pi$
$547$	−42.6737	−1.82460	−0.912298	+	0.409526i	$0.865694\pi$
$548$	5.97920	0.255419
$549$	−10.1307	−0.432367
$550$	−1.16251	−0.0495695
$551$	−45.2259	−1.92669
$552$	24.3896	1.03809
$553$	−0.502845	−0.0213831
$554$	−37.1747	−1.57940
$555$	−0.631505	−0.0268059
$556$	−13.4471	−0.570284
$557$	2.53121	0.107251	0.0536255	−	0.998561i	$-0.482922\pi$
$557$	2.53121	0.107251	0.0536255	+	0.998561i	$0.482922\pi$
$558$	4.60153	0.194798
$559$	−6.80870	−0.287977
$560$	1.46517	0.0619145
$561$	−0.440211	−0.0185857
$562$	−19.1353	−0.807172
$563$	0.616117	0.0259662	0.0129831	−	0.999916i	$-0.495867\pi$
$563$	0.616117	0.0259662	0.0129831	+	0.999916i	$0.495867\pi$
$564$	−7.47363	−0.314696
$565$	−7.96633	−0.335146
$566$	20.6789	0.869198
$567$	1.97206	0.0828188
$568$	39.5624	1.66000
$569$	43.1724	1.80988	0.904941	−	0.425537i	$-0.139915\pi$
$569$	43.1724	1.80988	0.904941	+	0.425537i	$0.139915\pi$
$570$	−8.69313	−0.364115
$571$	−2.74532	−0.114888	−0.0574440	−	0.998349i	$-0.518295\pi$
$571$	−2.74532	−0.114888	−0.0574440	+	0.998349i	$0.518295\pi$
$572$	1.36725	0.0571677
$573$	−27.2104	−1.13673
$574$	−6.07363	−0.253508
$575$	−6.18504	−0.257934
$576$	−11.7468	−0.489451
$577$	44.2576	1.84247	0.921235	−	0.389007i	$-0.127182\pi$
$577$	44.2576	1.84247	0.921235	+	0.389007i	$0.127182\pi$
$578$	19.6253	0.816304
$579$	26.6700	1.10837
$580$	−5.02367	−0.208597
$581$	6.71647	0.278646
$582$	14.3752	0.595870
$583$	11.9039	0.493009
$584$	3.07899	0.127410
$585$	2.86650	0.118515
$586$	0.860803	0.0355594
$587$	−15.7514	−0.650128	−0.325064	−	0.945692i	$-0.605386\pi$
$587$	−15.7514	−0.650128	−0.325064	+	0.945692i	$0.605386\pi$
$588$	−5.47214	−0.225667
$589$	−16.9969	−0.700345
$590$	12.0425	0.495781
$591$	−25.5334	−1.05031
$592$	−1.12532	−0.0462505
$593$	39.7770	1.63345	0.816724	−	0.577029i	$-0.195788\pi$
$593$	39.7770	1.63345	0.816724	+	0.577029i	$0.195788\pi$
$594$	−6.49101	−0.266329
$595$	−0.220668	−0.00904652
$596$	10.9293	0.447681
$597$	−5.63889	−0.230784
$598$	−15.1575	−0.619835
$599$	−21.0557	−0.860314	−0.430157	−	0.902754i	$-0.641542\pi$
$599$	−21.0557	−0.860314	−0.430157	+	0.902754i	$0.641542\pi$
$600$	−3.94332	−0.160985
$601$	−48.0495	−1.95998	−0.979991	−	0.199042i	$-0.936217\pi$
$601$	−48.0495	−1.95998	−0.979991	+	0.199042i	$0.936217\pi$
$602$	2.41049	0.0982441
$603$	3.40613	0.138708
$604$	−9.34208	−0.380124
$605$	1.00000	0.0406558
$606$	−15.0968	−0.613265
$607$	27.7153	1.12493	0.562464	−	0.826822i	$-0.309853\pi$
$607$	27.7153	1.12493	0.562464	+	0.826822i	$0.309853\pi$
$608$	20.4646	0.829949
$609$	6.36865	0.258071
$610$	−8.66107	−0.350677
$611$	18.9673	0.767336
$612$	0.303131	0.0122533
$613$	−33.4178	−1.34973	−0.674866	−	0.737941i	$-0.735798\pi$
$613$	−33.4178	−1.34973	−0.674866	+	0.737941i	$0.735798\pi$
$614$	−26.6487	−1.07545
$615$	10.4225	0.420277
$616$	−1.97670	−0.0796436
$617$	23.1616	0.932452	0.466226	−	0.884666i	$-0.345613\pi$
$617$	23.1616	0.932452	0.466226	+	0.884666i	$0.345613\pi$
$618$	−16.1614	−0.650107
$619$	−5.26923	−0.211788	−0.105894	−	0.994377i	$-0.533770\pi$
$619$	−5.26923	−0.211788	−0.105894	+	0.994377i	$0.533770\pi$
$620$	−1.88801	−0.0758242
$621$	−34.5349	−1.38584
$622$	−18.0759	−0.724776
$623$	1.73337	0.0694462
$624$	−6.16163	−0.246663
$625$	1.00000	0.0400000
$626$	−33.8809	−1.35415
$627$	7.47791	0.298639
$628$	−6.81471	−0.271937
$629$	0.169485	0.00675780
$630$	−1.01483	−0.0404317
$631$	17.2592	0.687080	0.343540	−	0.939138i	$-0.388374\pi$
$631$	17.2592	0.687080	0.343540	+	0.939138i	$0.388374\pi$
$632$	2.41162	0.0959292
$633$	−4.21692	−0.167608
$634$	23.9310	0.950421
$635$	−14.7034	−0.583486
$636$	9.88787	0.392080
$637$	13.8877	0.550252
$638$	−9.00444	−0.356489
$639$	−17.4718	−0.691173
$640$	−3.03296	−0.119888
$641$	21.7023	0.857191	0.428595	−	0.903497i	$-0.359009\pi$
$641$	21.7023	0.857191	0.428595	+	0.903497i	$0.359009\pi$
$642$	−21.1743	−0.835682
$643$	18.3770	0.724717	0.362359	−	0.932039i	$-0.381972\pi$
$643$	18.3770	0.724717	0.362359	+	0.932039i	$0.381972\pi$
$644$	−2.57535	−0.101483
$645$	−4.13646	−0.162873
$646$	2.33308	0.0917939
$647$	25.1345	0.988139	0.494070	−	0.869422i	$-0.335509\pi$
$647$	25.1345	0.988139	0.494070	+	0.869422i	$0.335509\pi$
$648$	−9.45792	−0.371542
$649$	−10.3591	−0.406628
$650$	2.45067	0.0961231
$651$	2.39348	0.0938078
$652$	5.51324	0.215915
$653$	−37.8993	−1.48311	−0.741557	−	0.670889i	$-0.765913\pi$
$653$	−37.8993	−1.48311	−0.741557	+	0.670889i	$0.765913\pi$
$654$	−1.74319	−0.0681643
$655$	9.68402	0.378386
$656$	18.5726	0.725139
$657$	−1.35976	−0.0530494
$658$	−6.71501	−0.261778
$659$	24.0360	0.936311	0.468155	−	0.883646i	$-0.344919\pi$
$659$	24.0360	0.936311	0.468155	+	0.883646i	$0.344919\pi$
$660$	0.830642	0.0323327
$661$	18.3613	0.714173	0.357087	−	0.934071i	$-0.383770\pi$
$661$	18.3613	0.714173	0.357087	+	0.934071i	$0.383770\pi$
$662$	−14.5146	−0.564126
$663$	0.928002	0.0360406
$664$	−32.2119	−1.25006
$665$	3.74852	0.145361
$666$	0.779439	0.0302027
$667$	−47.9074	−1.85498
$668$	−10.7175	−0.414671
$669$	−10.4733	−0.404923
$670$	2.91202	0.112501
$671$	7.45034	0.287617
$672$	−2.88179	−0.111168
$673$	23.3996	0.901990	0.450995	−	0.892527i	$-0.351069\pi$
$673$	23.3996	0.901990	0.450995	+	0.892527i	$0.351069\pi$
$674$	24.8309	0.956451
$675$	5.58362	0.214914
$676$	5.54919	0.213430
$677$	−19.3597	−0.744054	−0.372027	−	0.928222i	$-0.621337\pi$
$677$	−19.3597	−0.744054	−0.372027	+	0.928222i	$0.621337\pi$
$678$	−11.8606	−0.455504
$679$	−6.19864	−0.237882
$680$	1.05832	0.0405846
$681$	−0.203611	−0.00780238
$682$	−3.38407	−0.129583
$683$	24.8583	0.951176	0.475588	−	0.879668i	$-0.342235\pi$
$683$	24.8583	0.951176	0.475588	+	0.879668i	$0.342235\pi$
$684$	−5.14932	−0.196889
$685$	−9.21897	−0.352239
$686$	−10.1410	−0.387184
$687$	−23.9735	−0.914648
$688$	−7.37105	−0.281019
$689$	−25.0944	−0.956022
$690$	−9.20856	−0.350564
$691$	−13.0023	−0.494629	−0.247315	−	0.968935i	$-0.579548\pi$
$691$	−13.0023	−0.494629	−0.247315	+	0.968935i	$0.579548\pi$
$692$	−16.0036	−0.608367
$693$	0.872963	0.0331611
$694$	18.5972	0.705940
$695$	20.7333	0.786459
$696$	−30.5438	−1.15776
$697$	−2.79722	−0.105952
$698$	−40.5955	−1.53656
$699$	−12.0832	−0.457028
$700$	0.416383	0.0157378
$701$	43.9312	1.65926	0.829630	−	0.558314i	$-0.188551\pi$
$701$	43.9312	1.65926	0.829630	+	0.558314i	$0.188551\pi$
$702$	13.6836	0.516455
$703$	−2.87906	−0.108586
$704$	8.63888	0.325590
$705$	11.5231	0.433987
$706$	0.476327	0.0179268
$707$	6.50980	0.244826
$708$	−8.60466	−0.323383
$709$	−37.5591	−1.41056	−0.705282	−	0.708927i	$-0.749179\pi$
$709$	−37.5591	−1.41056	−0.705282	+	0.708927i	$0.749179\pi$
$710$	−14.9372	−0.560584
$711$	−1.06504	−0.0399420
$712$	−8.31319	−0.311550
$713$	−18.0047	−0.674280
$714$	−0.328541	−0.0122953
$715$	−2.10809	−0.0788380
$716$	−5.47713	−0.204690
$717$	25.7230	0.960642
$718$	−27.7924	−1.03720
$719$	18.2787	0.681682	0.340841	−	0.940121i	$-0.389288\pi$
$719$	18.2787	0.681682	0.340841	+	0.940121i	$0.389288\pi$
$720$	3.10325	0.115651
$721$	6.96887	0.259534
$722$	−17.5447	−0.652946
$723$	9.03199	0.335903
$724$	−2.19102	−0.0814287
$725$	7.74570	0.287668
$726$	1.48884	0.0552562
$727$	−22.7314	−0.843062	−0.421531	−	0.906814i	$-0.638507\pi$
$727$	−22.7314	−0.843062	−0.421531	+	0.906814i	$0.638507\pi$
$728$	4.16706	0.154442
$729$	25.6300	0.949259
$730$	−1.16251	−0.0430263
$731$	1.11015	0.0410605
$732$	6.18856	0.228736
$733$	22.9236	0.846702	0.423351	−	0.905966i	$-0.360854\pi$
$733$	22.9236	0.846702	0.423351	+	0.905966i	$0.360854\pi$
$734$	23.7676	0.877277
$735$	8.43716	0.311209
$736$	21.6780	0.799060
$737$	−2.50494	−0.0922707
$738$	−12.8641	−0.473533
$739$	11.4772	0.422196	0.211098	−	0.977465i	$-0.432296\pi$
$739$	11.4772	0.422196	0.211098	+	0.977465i	$0.432296\pi$
$740$	−0.319804	−0.0117562
$741$	−15.7641	−0.579108
$742$	8.88419	0.326149
$743$	−36.9618	−1.35600	−0.677998	−	0.735064i	$-0.737152\pi$
$743$	−36.9618	−1.35600	−0.677998	+	0.735064i	$0.737152\pi$
$744$	−11.4790	−0.420841
$745$	−16.8512	−0.617382
$746$	14.2101	0.520270
$747$	14.2256	0.520488
$748$	−0.222929	−0.00815111
$749$	9.13045	0.333620
$750$	1.48884	0.0543649
$751$	−40.1220	−1.46407	−0.732036	−	0.681266i	$-0.761430\pi$
$751$	−40.1220	−1.46407	−0.732036	+	0.681266i	$0.761430\pi$
$752$	20.5339	0.748794
$753$	−25.7415	−0.938071
$754$	18.9821	0.691289
$755$	14.4040	0.524215
$756$	2.32493	0.0845568
$757$	22.2082	0.807172	0.403586	−	0.914942i	$-0.367764\pi$
$757$	22.2082	0.807172	0.403586	+	0.914942i	$0.367764\pi$
$758$	14.2696	0.518297
$759$	7.92129	0.287524
$760$	−17.9777	−0.652121
$761$	7.05678	0.255808	0.127904	−	0.991787i	$-0.459175\pi$
$761$	7.05678	0.255808	0.127904	+	0.991787i	$0.459175\pi$
$762$	−21.8911	−0.793029
$763$	0.751673	0.0272124
$764$	−13.7798	−0.498534
$765$	−0.467380	−0.0168982
$766$	−7.64354	−0.276172
$767$	21.8378	0.788517
$768$	17.6123	0.635530
$769$	−6.98753	−0.251977	−0.125988	−	0.992032i	$-0.540210\pi$
$769$	−6.98753	−0.251977	−0.125988	+	0.992032i	$0.540210\pi$
$770$	0.746327	0.0268957
$771$	6.69042	0.240950
$772$	13.5061	0.486095
$773$	12.1432	0.436760	0.218380	−	0.975864i	$-0.429923\pi$
$773$	12.1432	0.436760	0.218380	+	0.975864i	$0.429923\pi$
$774$	5.10546	0.183512
$775$	2.91101	0.104566
$776$	29.7284	1.06719
$777$	0.405424	0.0145445
$778$	−39.5371	−1.41747
$779$	47.5167	1.70246
$780$	−1.75107	−0.0626982
$781$	12.8491	0.459778
$782$	2.47141	0.0883775
$783$	43.2491	1.54560
$784$	15.0348	0.536956
$785$	10.5072	0.375018
$786$	14.4180	0.514273
$787$	23.6451	0.842857	0.421428	−	0.906862i	$-0.361529\pi$
$787$	23.6451	0.842857	0.421428	+	0.906862i	$0.361529\pi$
$788$	−12.9305	−0.460631
$789$	22.9369	0.816574
$790$	−0.910536	−0.0323954
$791$	5.11436	0.181846
$792$	−4.18669	−0.148768
$793$	−15.7060	−0.557735
$794$	−44.0050	−1.56168
$795$	−15.2455	−0.540703
$796$	−2.85562	−0.101215
$797$	10.2348	0.362536	0.181268	−	0.983434i	$-0.441980\pi$
$797$	10.2348	0.362536	0.181268	+	0.983434i	$0.441980\pi$
$798$	5.58096	0.197564
$799$	−3.09261	−0.109409
$800$	−3.50490	−0.123917
$801$	3.67132	0.129720
$802$	−22.3376	−0.788767
$803$	1.00000	0.0352892
$804$	−2.08071	−0.0733810
$805$	3.97077	0.139951
$806$	7.13391	0.251281
$807$	−29.7241	−1.04634
$808$	−31.2207	−1.09834
$809$	38.6785	1.35986	0.679931	−	0.733276i	$-0.262010\pi$
$809$	38.6785	1.35986	0.679931	+	0.733276i	$0.262010\pi$
$810$	3.57095	0.125470
$811$	−19.1862	−0.673720	−0.336860	−	0.941555i	$-0.609365\pi$
$811$	−19.1862	−0.673720	−0.336860	+	0.941555i	$0.609365\pi$
$812$	3.22518	0.113182
$813$	−22.8894	−0.802765
$814$	−0.573217	−0.0200913
$815$	−8.50054	−0.297761
$816$	1.00465	0.0351697
$817$	−18.8583	−0.659768
$818$	−44.5281	−1.55689
$819$	−1.84028	−0.0643047
$820$	5.27813	0.184320
$821$	−9.70172	−0.338592	−0.169296	−	0.985565i	$-0.554149\pi$
$821$	−9.70172	−0.338592	−0.169296	+	0.985565i	$0.554149\pi$
$822$	−13.7256	−0.478736
$823$	−14.3591	−0.500526	−0.250263	−	0.968178i	$-0.580517\pi$
$823$	−14.3591	−0.500526	−0.250263	+	0.968178i	$0.580517\pi$
$824$	−33.4224	−1.16433
$825$	−1.28072	−0.0445889
$826$	−7.73124	−0.269004
$827$	−13.1106	−0.455901	−0.227951	−	0.973673i	$-0.573202\pi$
$827$	−13.1106	−0.455901	−0.227951	+	0.973673i	$0.573202\pi$
$828$	−5.45463	−0.189562
$829$	−38.9606	−1.35316	−0.676578	−	0.736371i	$-0.736538\pi$
$829$	−38.9606	−1.35316	−0.676578	+	0.736371i	$0.736538\pi$
$830$	12.1620	0.422148
$831$	−40.9548	−1.42071
$832$	−18.2115	−0.631371
$833$	−2.26438	−0.0784563
$834$	30.8686	1.06889
$835$	16.5246	0.571859
$836$	3.78693	0.130974
$837$	16.2540	0.561819
$838$	−36.3458	−1.25554
$839$	−21.7647	−0.751400	−0.375700	−	0.926741i	$-0.622598\pi$
$839$	−21.7647	−0.751400	−0.375700	+	0.926741i	$0.622598\pi$
$840$	2.53160	0.0873484
$841$	30.9959	1.06882
$842$	−42.2915	−1.45746
$843$	−21.0810	−0.726069
$844$	−2.13552	−0.0735075
$845$	−8.55597	−0.294334
$846$	−14.2225	−0.488980
$847$	−0.641997	−0.0220593
$848$	−27.1671	−0.932921
$849$	22.7816	0.781862
$850$	−0.399579	−0.0137055
$851$	−3.04976	−0.104544
$852$	10.6730	0.365652
$853$	38.6878	1.32465	0.662323	−	0.749219i	$-0.269571\pi$
$853$	38.6878	1.32465	0.662323	+	0.749219i	$0.269571\pi$
$854$	5.56038	0.190272
$855$	7.93944	0.271523
$856$	−43.7893	−1.49669
$857$	−38.2257	−1.30577	−0.652883	−	0.757459i	$-0.726440\pi$
$857$	−38.2257	−1.30577	−0.652883	+	0.757459i	$0.726440\pi$
$858$	−3.13861	−0.107151
$859$	−41.9322	−1.43071	−0.715355	−	0.698762i	$-0.753735\pi$
$859$	−41.9322	−1.43071	−0.715355	+	0.698762i	$0.753735\pi$
$860$	−2.09477	−0.0714310
$861$	−6.69123	−0.228036
$862$	−29.6279	−1.00913
$863$	−35.3178	−1.20223	−0.601116	−	0.799162i	$-0.705277\pi$
$863$	−35.3178	−1.20223	−0.601116	+	0.799162i	$0.705277\pi$
$864$	−19.5701	−0.665787
$865$	24.6751	0.838977
$866$	25.6239	0.870735
$867$	21.6209	0.734284
$868$	1.21209	0.0411412
$869$	0.783251	0.0265700
$870$	11.5321	0.390976
$871$	5.28064	0.178928
$872$	−3.60499	−0.122080
$873$	−13.1288	−0.444344
$874$	−41.9822	−1.42007
$875$	−0.641997	−0.0217035
$876$	0.830642	0.0280648
$877$	41.4778	1.40061	0.700303	−	0.713846i	$-0.253048\pi$
$877$	41.4778	1.40061	0.700303	+	0.713846i	$0.253048\pi$
$878$	23.0834	0.779028
$879$	0.948334	0.0319865
$880$	−2.28220	−0.0769329
$881$	−59.2808	−1.99722	−0.998611	−	0.0526882i	$-0.983221\pi$
$881$	−59.2808	−1.99722	−0.998611	+	0.0526882i	$0.983221\pi$
$882$	−10.4136	−0.350645
$883$	−27.8672	−0.937807	−0.468904	−	0.883249i	$-0.655351\pi$
$883$	−27.8672	−0.937807	−0.468904	+	0.883249i	$0.655351\pi$
$884$	0.469955	0.0158063
$885$	13.2670	0.445966
$886$	−12.0171	−0.403723
$887$	48.6053	1.63201	0.816003	−	0.578047i	$-0.196185\pi$
$887$	48.6053	1.63201	0.816003	+	0.578047i	$0.196185\pi$
$888$	−1.94440	−0.0652497
$889$	9.43953	0.316592
$890$	3.13874	0.105211
$891$	−3.07176	−0.102908
$892$	−5.30386	−0.177586
$893$	52.5345	1.75800
$894$	−25.0889	−0.839098
$895$	8.44486	0.282281
$896$	1.94715	0.0650497
$897$	−16.6988	−0.557555
$898$	30.8805	1.03050
$899$	22.5478	0.752011
$900$	0.881908	0.0293969
$901$	4.09163	0.136312
$902$	9.46053	0.315001
$903$	2.65560	0.0883727
$904$	−24.5282	−0.815797
$905$	3.37821	0.112295
$906$	21.4453	0.712473
$907$	−30.0342	−0.997270	−0.498635	−	0.866812i	$-0.666165\pi$
$907$	−30.0342	−0.997270	−0.498635	+	0.866812i	$0.666165\pi$
$908$	−0.103112	−0.00342188
$909$	13.7879	0.457316
$910$	−1.57332	−0.0521551
$911$	−12.7657	−0.422947	−0.211474	−	0.977384i	$-0.567826\pi$
$911$	−12.7657	−0.422947	−0.211474	+	0.977384i	$0.567826\pi$
$912$	−17.0661	−0.565115
$913$	−10.4618	−0.346236
$914$	17.6659	0.584335
$915$	−9.54178	−0.315441
$916$	−12.1406	−0.401136
$917$	−6.21711	−0.205307
$918$	−2.23110	−0.0736373
$919$	−25.0385	−0.825943	−0.412971	−	0.910744i	$-0.635509\pi$
$919$	−25.0385	−0.825943	−0.412971	+	0.910744i	$0.635509\pi$
$920$	−19.0437	−0.627851
$921$	−29.3585	−0.967395
$922$	−1.35744	−0.0447049
$923$	−27.0871	−0.891583
$924$	−0.533270	−0.0175433
$925$	0.493087	0.0162126
$926$	−19.4327	−0.638598
$927$	14.7602	0.484789
$928$	−27.1479	−0.891175
$929$	−23.7027	−0.777662	−0.388831	−	0.921309i	$-0.627121\pi$
$929$	−23.7027	−0.777662	−0.388831	+	0.921309i	$0.627121\pi$
$930$	4.33403	0.142119
$931$	38.4654	1.26065
$932$	−6.11911	−0.200438
$933$	−19.9139	−0.651952
$934$	34.7437	1.13685
$935$	0.343722	0.0112409
$936$	8.82592	0.288484
$937$	−25.9282	−0.847037	−0.423518	−	0.905887i	$-0.639205\pi$
$937$	−25.9282	−0.847037	−0.423518	+	0.905887i	$0.639205\pi$
$938$	−1.86951	−0.0610415
$939$	−37.3260	−1.21809
$940$	5.83550	0.190333
$941$	5.08695	0.165830	0.0829149	−	0.996557i	$-0.473577\pi$
$941$	5.08695	0.165830	0.0829149	+	0.996557i	$0.473577\pi$
$942$	15.6436	0.509696
$943$	50.3340	1.63910
$944$	23.6414	0.769463
$945$	−3.58467	−0.116609
$946$	−3.75467	−0.122075
$947$	−14.8039	−0.481063	−0.240532	−	0.970641i	$-0.577322\pi$
$947$	−14.8039	−0.481063	−0.240532	+	0.970641i	$0.577322\pi$
$948$	0.650601	0.0211305
$949$	−2.10809	−0.0684314
$950$	6.78770	0.220222
$951$	26.3644	0.854925
$952$	−0.679436	−0.0220206
$953$	−0.375995	−0.0121797	−0.00608983	−	0.999981i	$-0.501938\pi$
$953$	−0.375995	−0.0121797	−0.00608983	+	0.999981i	$0.501938\pi$
$954$	18.8169	0.609219
$955$	21.2462	0.687511
$956$	13.0265	0.421307
$957$	−9.92006	−0.320670
$958$	−13.3565	−0.431529
$959$	5.91855	0.191120
$960$	−11.0640	−0.357088
$961$	−22.5260	−0.726647
$962$	1.20839	0.0389601
$963$	19.3385	0.623174
$964$	4.57394	0.147317
$965$	−20.8242	−0.670356
$966$	5.91187	0.190211
$967$	23.3201	0.749923	0.374961	−	0.927040i	$-0.377656\pi$
$967$	23.3201	0.749923	0.374961	+	0.927040i	$0.377656\pi$
$968$	3.07899	0.0989625
$969$	2.57032	0.0825706
$970$	−11.2243	−0.360391
$971$	42.7422	1.37166	0.685832	−	0.727760i	$-0.259439\pi$
$971$	42.7422	1.37166	0.685832	+	0.727760i	$0.259439\pi$
$972$	8.31267	0.266629
$973$	−13.3107	−0.426722
$974$	14.8182	0.474806
$975$	2.69986	0.0864649
$976$	−17.0032	−0.544258
$977$	3.09301	0.0989543	0.0494771	−	0.998775i	$-0.484245\pi$
$977$	3.09301	0.0989543	0.0494771	+	0.998775i	$0.484245\pi$
$978$	−12.6560	−0.404694
$979$	−2.69997	−0.0862915
$980$	4.27271	0.136487
$981$	1.59206	0.0508305
$982$	−18.3176	−0.584540
$983$	−25.8146	−0.823359	−0.411680	−	0.911329i	$-0.635058\pi$
$983$	−25.8146	−0.823359	−0.411680	+	0.911329i	$0.635058\pi$
$984$	32.0908	1.02302
$985$	19.9368	0.635240
$986$	−3.09502	−0.0985656
$987$	−7.39783	−0.235475
$988$	−7.98318	−0.253979
$989$	−19.9764	−0.635214
$990$	1.58073	0.0502390
$991$	−32.2806	−1.02543	−0.512714	−	0.858559i	$-0.671360\pi$
$991$	−32.2806	−1.02543	−0.512714	+	0.858559i	$0.671360\pi$
$992$	−10.2028	−0.323939
$993$	−15.9905	−0.507444
$994$	9.58965	0.304165
$995$	4.40291	0.139582
$996$	−8.69004	−0.275354
$997$	−38.9896	−1.23481	−0.617406	−	0.786644i	$-0.711817\pi$
$997$	−38.9896	−1.23481	−0.617406	+	0.786644i	$0.711817\pi$
$998$	37.2329	1.17859
$999$	2.75321	0.0871078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.11	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.11	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.16251 q^{2} -1.28072 q^{3} -0.648575 q^{4} +1.00000 q^{5} +1.48884 q^{6} -0.641997 q^{7} +3.07899 q^{8} -1.35976 q^{9} +O(q^{10})\)	\(q-1.16251 q^{2} -1.28072 q^{3} -0.648575 q^{4} +1.00000 q^{5} +1.48884 q^{6} -0.641997 q^{7} +3.07899 q^{8} -1.35976 q^{9} -1.16251 q^{10} +1.00000 q^{11} +0.830642 q^{12} -2.10809 q^{13} +0.746327 q^{14} -1.28072 q^{15} -2.28220 q^{16} +0.343722 q^{17} +1.58073 q^{18} -5.83884 q^{19} -0.648575 q^{20} +0.822217 q^{21} -1.16251 q^{22} -6.18504 q^{23} -3.94332 q^{24} +1.00000 q^{25} +2.45067 q^{26} +5.58362 q^{27} +0.416383 q^{28} +7.74570 q^{29} +1.48884 q^{30} +2.91101 q^{31} -3.50490 q^{32} -1.28072 q^{33} -0.399579 q^{34} -0.641997 q^{35} +0.881908 q^{36} +0.493087 q^{37} +6.78770 q^{38} +2.69986 q^{39} +3.07899 q^{40} -8.13803 q^{41} -0.955834 q^{42} +3.22980 q^{43} -0.648575 q^{44} -1.35976 q^{45} +7.19015 q^{46} -8.99741 q^{47} +2.92285 q^{48} -6.58784 q^{49} -1.16251 q^{50} -0.440211 q^{51} +1.36725 q^{52} +11.9039 q^{53} -6.49101 q^{54} +1.00000 q^{55} -1.97670 q^{56} +7.47791 q^{57} -9.00444 q^{58} -10.3591 q^{59} +0.830642 q^{60} +7.45034 q^{61} -3.38407 q^{62} +0.872963 q^{63} +8.63888 q^{64} -2.10809 q^{65} +1.48884 q^{66} -2.50494 q^{67} -0.222929 q^{68} +7.92129 q^{69} +0.746327 q^{70} +12.8491 q^{71} -4.18669 q^{72} +1.00000 q^{73} -0.573217 q^{74} -1.28072 q^{75} +3.78693 q^{76} -0.641997 q^{77} -3.13861 q^{78} +0.783251 q^{79} -2.28220 q^{80} -3.07176 q^{81} +9.46053 q^{82} -10.4618 q^{83} -0.533270 q^{84} +0.343722 q^{85} -3.75467 q^{86} -9.92006 q^{87} +3.07899 q^{88} -2.69997 q^{89} +1.58073 q^{90} +1.35339 q^{91} +4.01146 q^{92} -3.72818 q^{93} +10.4596 q^{94} -5.83884 q^{95} +4.48879 q^{96} +9.65525 q^{97} +7.65842 q^{98} -1.35976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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