LMFDB - Embedded newform 8015.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67776 q^{2} -3.22300 q^{3} +5.17039 q^{4} -1.00000 q^{5} +8.63041 q^{6} -1.00000 q^{7} -8.48955 q^{8} +7.38771 q^{9} +O(q^{10})$	\(q-2.67776 q^{2} -3.22300 q^{3} +5.17039 q^{4} -1.00000 q^{5} +8.63041 q^{6} -1.00000 q^{7} -8.48955 q^{8} +7.38771 q^{9} +2.67776 q^{10} +0.611343 q^{11} -16.6642 q^{12} +1.44388 q^{13} +2.67776 q^{14} +3.22300 q^{15} +12.3922 q^{16} +0.0160768 q^{17} -19.7825 q^{18} -4.79068 q^{19} -5.17039 q^{20} +3.22300 q^{21} -1.63703 q^{22} +5.47353 q^{23} +27.3618 q^{24} +1.00000 q^{25} -3.86636 q^{26} -14.1416 q^{27} -5.17039 q^{28} +6.57782 q^{29} -8.63041 q^{30} +4.34436 q^{31} -16.2042 q^{32} -1.97036 q^{33} -0.0430499 q^{34} +1.00000 q^{35} +38.1974 q^{36} -6.17199 q^{37} +12.8283 q^{38} -4.65362 q^{39} +8.48955 q^{40} -6.51377 q^{41} -8.63041 q^{42} -4.62756 q^{43} +3.16088 q^{44} -7.38771 q^{45} -14.6568 q^{46} +6.14224 q^{47} -39.9400 q^{48} +1.00000 q^{49} -2.67776 q^{50} -0.0518156 q^{51} +7.46543 q^{52} +2.69487 q^{53} +37.8678 q^{54} -0.611343 q^{55} +8.48955 q^{56} +15.4403 q^{57} -17.6138 q^{58} +9.26225 q^{59} +16.6642 q^{60} +3.15102 q^{61} -11.6332 q^{62} -7.38771 q^{63} +18.6065 q^{64} -1.44388 q^{65} +5.27614 q^{66} +2.84953 q^{67} +0.0831235 q^{68} -17.6412 q^{69} -2.67776 q^{70} -4.09415 q^{71} -62.7184 q^{72} -16.6129 q^{73} +16.5271 q^{74} -3.22300 q^{75} -24.7697 q^{76} -0.611343 q^{77} +12.4613 q^{78} +5.83519 q^{79} -12.3922 q^{80} +23.4152 q^{81} +17.4423 q^{82} -0.264587 q^{83} +16.6642 q^{84} -0.0160768 q^{85} +12.3915 q^{86} -21.2003 q^{87} -5.19003 q^{88} -14.0286 q^{89} +19.7825 q^{90} -1.44388 q^{91} +28.3003 q^{92} -14.0019 q^{93} -16.4475 q^{94} +4.79068 q^{95} +52.2261 q^{96} -4.03010 q^{97} -2.67776 q^{98} +4.51643 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * 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 $

$2$	−2.67776	−1.89346	−0.946731	−	0.322026i	$-0.895636\pi$
$2$	−2.67776	−1.89346	−0.946731	+	0.322026i	$0.895636\pi$
$3$	−3.22300	−1.86080	−0.930399	−	0.366548i	$-0.880540\pi$
$3$	−3.22300	−1.86080	−0.930399	+	0.366548i	$0.880540\pi$
$4$	5.17039	2.58520
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	8.63041	3.52335
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−8.48955	−3.00151
$9$	7.38771	2.46257
$10$	2.67776	0.846782
$11$	0.611343	0.184327	0.0921634	−	0.995744i	$-0.470622\pi$
$11$	0.611343	0.184327	0.0921634	+	0.995744i	$0.470622\pi$
$12$	−16.6642	−4.81053
$13$	1.44388	0.400460	0.200230	−	0.979749i	$-0.435831\pi$
$13$	1.44388	0.400460	0.200230	+	0.979749i	$0.435831\pi$
$14$	2.67776	0.715661
$15$	3.22300	0.832174
$16$	12.3922	3.09805
$17$	0.0160768	0.00389920	0.00194960	−	0.999998i	$-0.499379\pi$
$17$	0.0160768	0.00389920	0.00194960	+	0.999998i	$0.499379\pi$
$18$	−19.7825	−4.66278
$19$	−4.79068	−1.09906	−0.549529	−	0.835475i	$-0.685193\pi$
$19$	−4.79068	−1.09906	−0.549529	+	0.835475i	$0.685193\pi$
$20$	−5.17039	−1.15614
$21$	3.22300	0.703316
$22$	−1.63703	−0.349016
$23$	5.47353	1.14131	0.570655	−	0.821190i	$-0.306689\pi$
$23$	5.47353	1.14131	0.570655	+	0.821190i	$0.306689\pi$
$24$	27.3618	5.58521
$25$	1.00000	0.200000
$26$	−3.86636	−0.758256
$27$	−14.1416	−2.72155
$28$	−5.17039	−0.977113
$29$	6.57782	1.22147	0.610735	−	0.791835i	$-0.290874\pi$
$29$	6.57782	1.22147	0.610735	+	0.791835i	$0.290874\pi$
$30$	−8.63041	−1.57569
$31$	4.34436	0.780270	0.390135	−	0.920758i	$-0.372428\pi$
$31$	4.34436	0.780270	0.390135	+	0.920758i	$0.372428\pi$
$32$	−16.2042	−2.86452
$33$	−1.97036	−0.342995
$34$	−0.0430499	−0.00738299
$35$	1.00000	0.169031
$36$	38.1974	6.36623
$37$	−6.17199	−1.01467	−0.507334	−	0.861749i	$-0.669369\pi$
$37$	−6.17199	−1.01467	−0.507334	+	0.861749i	$0.669369\pi$
$38$	12.8283	2.08102
$39$	−4.65362	−0.745175
$40$	8.48955	1.34232
$41$	−6.51377	−1.01728	−0.508640	−	0.860979i	$-0.669852\pi$
$41$	−6.51377	−1.01728	−0.508640	+	0.860979i	$0.669852\pi$
$42$	−8.63041	−1.33170
$43$	−4.62756	−0.705696	−0.352848	−	0.935681i	$-0.614787\pi$
$43$	−4.62756	−0.705696	−0.352848	+	0.935681i	$0.614787\pi$
$44$	3.16088	0.476521
$45$	−7.38771	−1.10130
$46$	−14.6568	−2.16103
$47$	6.14224	0.895938	0.447969	−	0.894049i	$-0.352147\pi$
$47$	6.14224	0.895938	0.447969	+	0.894049i	$0.352147\pi$
$48$	−39.9400	−5.76484
$49$	1.00000	0.142857
$50$	−2.67776	−0.378692
$51$	−0.0518156	−0.00725563
$52$	7.46543	1.03527
$53$	2.69487	0.370168	0.185084	−	0.982723i	$-0.440744\pi$
$53$	2.69487	0.370168	0.185084	+	0.982723i	$0.440744\pi$
$54$	37.8678	5.15315
$55$	−0.611343	−0.0824335
$56$	8.48955	1.13446
$57$	15.4403	2.04512
$58$	−17.6138	−2.31281
$59$	9.26225	1.20584	0.602921	−	0.797801i	$-0.294003\pi$
$59$	9.26225	1.20584	0.602921	+	0.797801i	$0.294003\pi$
$60$	16.6642	2.15133
$61$	3.15102	0.403447	0.201723	−	0.979443i	$-0.435346\pi$
$61$	3.15102	0.403447	0.201723	+	0.979443i	$0.435346\pi$
$62$	−11.6332	−1.47741
$63$	−7.38771	−0.930764
$64$	18.6065	2.32582
$65$	−1.44388	−0.179091
$66$	5.27614	0.649448
$67$	2.84953	0.348125	0.174063	−	0.984735i	$-0.444310\pi$
$67$	2.84953	0.348125	0.174063	+	0.984735i	$0.444310\pi$
$68$	0.0831235	0.0100802
$69$	−17.6412	−2.12375
$70$	−2.67776	−0.320053
$71$	−4.09415	−0.485887	−0.242943	−	0.970040i	$-0.578113\pi$
$71$	−4.09415	−0.485887	−0.242943	+	0.970040i	$0.578113\pi$
$72$	−62.7184	−7.39143
$73$	−16.6129	−1.94439	−0.972197	−	0.234166i	$-0.924764\pi$
$73$	−16.6129	−1.94439	−0.972197	+	0.234166i	$0.924764\pi$
$74$	16.5271	1.92124
$75$	−3.22300	−0.372160
$76$	−24.7697	−2.84128
$77$	−0.611343	−0.0696690
$78$	12.4613	1.41096
$79$	5.83519	0.656510	0.328255	−	0.944589i	$-0.393539\pi$
$79$	5.83519	0.656510	0.328255	+	0.944589i	$0.393539\pi$
$80$	−12.3922	−1.38549
$81$	23.4152	2.60168
$82$	17.4423	1.92618
$83$	−0.264587	−0.0290422	−0.0145211	−	0.999895i	$-0.504622\pi$
$83$	−0.264587	−0.0290422	−0.0145211	+	0.999895i	$0.504622\pi$
$84$	16.6642	1.81821
$85$	−0.0160768	−0.00174378
$86$	12.3915	1.33621
$87$	−21.2003	−2.27291
$88$	−5.19003	−0.553259
$89$	−14.0286	−1.48703	−0.743513	−	0.668722i	$-0.766842\pi$
$89$	−14.0286	−1.48703	−0.743513	+	0.668722i	$0.766842\pi$
$90$	19.7825	2.08526
$91$	−1.44388	−0.151360
$92$	28.3003	2.95051
$93$	−14.0019	−1.45193
$94$	−16.4475	−1.69643
$95$	4.79068	0.491513
$96$	52.2261	5.33030
$97$	−4.03010	−0.409195	−0.204597	−	0.978846i	$-0.565588\pi$
$97$	−4.03010	−0.409195	−0.204597	+	0.978846i	$0.565588\pi$
$98$	−2.67776	−0.270495
$99$	4.51643	0.453918
$100$	5.17039	0.517039
$101$	−0.625252	−0.0622149	−0.0311074	−	0.999516i	$-0.509903\pi$
$101$	−0.625252	−0.0622149	−0.0311074	+	0.999516i	$0.509903\pi$
$102$	0.138750	0.0137383
$103$	−7.54437	−0.743369	−0.371684	−	0.928359i	$-0.621220\pi$
$103$	−7.54437	−0.743369	−0.371684	+	0.928359i	$0.621220\pi$
$104$	−12.2579	−1.20198
$105$	−3.22300	−0.314532
$106$	−7.21620	−0.700900
$107$	−0.615814	−0.0595330	−0.0297665	−	0.999557i	$-0.509476\pi$
$107$	−0.615814	−0.0595330	−0.0297665	+	0.999557i	$0.509476\pi$
$108$	−73.1176	−7.03574
$109$	−1.16169	−0.111270	−0.0556350	−	0.998451i	$-0.517718\pi$
$109$	−1.16169	−0.111270	−0.0556350	+	0.998451i	$0.517718\pi$
$110$	1.63703	0.156085
$111$	19.8923	1.88809
$112$	−12.3922	−1.17095
$113$	−11.7424	−1.10463	−0.552316	−	0.833635i	$-0.686256\pi$
$113$	−11.7424	−1.10463	−0.552316	+	0.833635i	$0.686256\pi$
$114$	−41.3455	−3.87236
$115$	−5.47353	−0.510409
$116$	34.0099	3.15774
$117$	10.6670	0.986161
$118$	−24.8021	−2.28322
$119$	−0.0160768	−0.00147376
$120$	−27.3618	−2.49778
$121$	−10.6263	−0.966024
$122$	−8.43768	−0.763911
$123$	20.9939	1.89295
$124$	22.4621	2.01715
$125$	−1.00000	−0.0894427
$126$	19.7825	1.76237
$127$	19.7170	1.74960	0.874802	−	0.484480i	$-0.160991\pi$
$127$	19.7170	1.74960	0.874802	+	0.484480i	$0.160991\pi$
$128$	−17.4155	−1.53932
$129$	14.9146	1.31316
$130$	3.86636	0.339102
$131$	6.79560	0.593734	0.296867	−	0.954919i	$-0.404058\pi$
$131$	6.79560	0.593734	0.296867	+	0.954919i	$0.404058\pi$
$132$	−10.1875	−0.886710
$133$	4.79068	0.415405
$134$	−7.63035	−0.659162
$135$	14.1416	1.21711
$136$	−0.136485	−0.0117035
$137$	2.94586	0.251682	0.125841	−	0.992050i	$-0.459837\pi$
$137$	2.94586	0.251682	0.125841	+	0.992050i	$0.459837\pi$
$138$	47.2388	4.02124
$139$	1.56933	0.133109	0.0665545	−	0.997783i	$-0.478799\pi$
$139$	1.56933	0.133109	0.0665545	+	0.997783i	$0.478799\pi$
$140$	5.17039	0.436978
$141$	−19.7964	−1.66716
$142$	10.9632	0.920008
$143$	0.882705	0.0738155
$144$	91.5499	7.62916
$145$	−6.57782	−0.546258
$146$	44.4854	3.68163
$147$	−3.22300	−0.265828
$148$	−31.9116	−2.62312
$149$	−0.785975	−0.0643896	−0.0321948	−	0.999482i	$-0.510250\pi$
$149$	−0.785975	−0.0643896	−0.0321948	+	0.999482i	$0.510250\pi$
$150$	8.63041	0.704670
$151$	−20.6311	−1.67894	−0.839469	−	0.543408i	$-0.817134\pi$
$151$	−20.6311	−1.67894	−0.839469	+	0.543408i	$0.817134\pi$
$152$	40.6707	3.29883
$153$	0.118771	0.00960206
$154$	1.63703	0.131916
$155$	−4.34436	−0.348947
$156$	−24.0610	−1.92643
$157$	−16.0583	−1.28159	−0.640797	−	0.767710i	$-0.721396\pi$
$157$	−16.0583	−1.28159	−0.640797	+	0.767710i	$0.721396\pi$
$158$	−15.6252	−1.24308
$159$	−8.68555	−0.688809
$160$	16.2042	1.28105
$161$	−5.47353	−0.431375
$162$	−62.7001	−4.92619
$163$	20.7088	1.62204	0.811019	−	0.585020i	$-0.198913\pi$
$163$	20.7088	1.62204	0.811019	+	0.585020i	$0.198913\pi$
$164$	−33.6788	−2.62987
$165$	1.97036	0.153392
$166$	0.708501	0.0549903
$167$	−16.3477	−1.26502	−0.632511	−	0.774551i	$-0.717976\pi$
$167$	−16.3477	−1.26502	−0.632511	+	0.774551i	$0.717976\pi$
$168$	−27.3618	−2.11101
$169$	−10.9152	−0.839632
$170$	0.0430499	0.00330177
$171$	−35.3922	−2.70651
$172$	−23.9263	−1.82436
$173$	12.2208	0.929130	0.464565	−	0.885539i	$-0.346211\pi$
$173$	12.2208	0.929130	0.464565	+	0.885539i	$0.346211\pi$
$174$	56.7693	4.30367
$175$	−1.00000	−0.0755929
$176$	7.57588	0.571053
$177$	−29.8522	−2.24383
$178$	37.5651	2.81563
$179$	5.10169	0.381318	0.190659	−	0.981656i	$-0.438938\pi$
$179$	5.10169	0.381318	0.190659	+	0.981656i	$0.438938\pi$
$180$	−38.1974	−2.84706
$181$	−17.6893	−1.31484	−0.657418	−	0.753526i	$-0.728352\pi$
$181$	−17.6893	−1.31484	−0.657418	+	0.753526i	$0.728352\pi$
$182$	3.86636	0.286594
$183$	−10.1557	−0.750733
$184$	−46.4678	−3.42565
$185$	6.17199	0.453774
$186$	37.4936	2.74917
$187$	0.00982845	0.000718728 0
$188$	31.7578	2.31618
$189$	14.1416	1.02865
$190$	−12.8283	−0.930662
$191$	−2.10498	−0.152311	−0.0761554	−	0.997096i	$-0.524264\pi$
$191$	−2.10498	−0.152311	−0.0761554	+	0.997096i	$0.524264\pi$
$192$	−59.9689	−4.32788
$193$	2.30049	0.165593	0.0827964	−	0.996566i	$-0.473615\pi$
$193$	2.30049	0.165593	0.0827964	+	0.996566i	$0.473615\pi$
$194$	10.7916	0.774795
$195$	4.65362	0.333253
$196$	5.17039	0.369314
$197$	0.266572	0.0189925	0.00949624	−	0.999955i	$-0.496977\pi$
$197$	0.266572	0.0189925	0.00949624	+	0.999955i	$0.496977\pi$
$198$	−12.0939	−0.859476
$199$	10.6476	0.754791	0.377395	−	0.926052i	$-0.376820\pi$
$199$	10.6476	0.754791	0.377395	+	0.926052i	$0.376820\pi$
$200$	−8.48955	−0.600302
$201$	−9.18402	−0.647791
$202$	1.67427	0.117801
$203$	−6.57782	−0.461673
$204$	−0.267907	−0.0187572
$205$	6.51377	0.454941
$206$	20.2020	1.40754
$207$	40.4369	2.81056
$208$	17.8928	1.24064
$209$	−2.92875	−0.202586
$210$	8.63041	0.595555
$211$	−3.11278	−0.214293	−0.107146	−	0.994243i	$-0.534171\pi$
$211$	−3.11278	−0.214293	−0.107146	+	0.994243i	$0.534171\pi$
$212$	13.9335	0.956958
$213$	13.1954	0.904137
$214$	1.64900	0.112723
$215$	4.62756	0.315597
$216$	120.056	8.16876
$217$	−4.34436	−0.294914
$218$	3.11073	0.210685
$219$	53.5433	3.61812
$220$	−3.16088	−0.213107
$221$	0.0232130	0.00156148
$222$	−53.2668	−3.57503
$223$	−19.9970	−1.33910	−0.669550	−	0.742767i	$-0.733513\pi$
$223$	−19.9970	−1.33910	−0.669550	+	0.742767i	$0.733513\pi$
$224$	16.2042	1.08269
$225$	7.38771	0.492514
$226$	31.4433	2.09158
$227$	14.4809	0.961128	0.480564	−	0.876960i	$-0.340432\pi$
$227$	14.4809	0.961128	0.480564	+	0.876960i	$0.340432\pi$
$228$	79.8327	5.28705
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	14.6568	0.966441
$231$	1.97036	0.129640
$232$	−55.8428	−3.66626
$233$	16.1336	1.05695	0.528473	−	0.848950i	$-0.322765\pi$
$233$	16.1336	1.05695	0.528473	+	0.848950i	$0.322765\pi$
$234$	−28.5636	−1.86726
$235$	−6.14224	−0.400676
$236$	47.8895	3.11734
$237$	−18.8068	−1.22163
$238$	0.0430499	0.00279051
$239$	−6.47538	−0.418857	−0.209429	−	0.977824i	$-0.567160\pi$
$239$	−6.47538	−0.418857	−0.209429	+	0.977824i	$0.567160\pi$
$240$	39.9400	2.57812
$241$	−11.7817	−0.758926	−0.379463	−	0.925207i	$-0.623891\pi$
$241$	−11.7817	−0.758926	−0.379463	+	0.925207i	$0.623891\pi$
$242$	28.4546	1.82913
$243$	−33.0422	−2.11966
$244$	16.2920	1.04299
$245$	−1.00000	−0.0638877
$246$	−56.2165	−3.58423
$247$	−6.91716	−0.440129
$248$	−36.8817	−2.34199
$249$	0.852764	0.0540417
$250$	2.67776	0.169356
$251$	26.6757	1.68375	0.841877	−	0.539670i	$-0.181451\pi$
$251$	26.6757	1.68375	0.841877	+	0.539670i	$0.181451\pi$
$252$	−38.1974	−2.40621
$253$	3.34620	0.210374
$254$	−52.7975	−3.31281
$255$	0.0518156	0.00324482
$256$	9.42134	0.588834
$257$	−5.95509	−0.371468	−0.185734	−	0.982600i	$-0.559466\pi$
$257$	−5.95509	−0.371468	−0.185734	+	0.982600i	$0.559466\pi$
$258$	−39.9377	−2.48641
$259$	6.17199	0.383509
$260$	−7.46543	−0.462986
$261$	48.5950	3.00796
$262$	−18.1970	−1.12421
$263$	24.9320	1.53737	0.768686	−	0.639626i	$-0.220911\pi$
$263$	24.9320	1.53737	0.768686	+	0.639626i	$0.220911\pi$
$264$	16.7274	1.02950
$265$	−2.69487	−0.165544
$266$	−12.8283	−0.786553
$267$	45.2140	2.76705
$268$	14.7332	0.899973
$269$	13.8063	0.841786	0.420893	−	0.907110i	$-0.361717\pi$
$269$	13.8063	0.841786	0.420893	+	0.907110i	$0.361717\pi$
$270$	−37.8678	−2.30456
$271$	17.2219	1.04616	0.523079	−	0.852284i	$-0.324783\pi$
$271$	17.2219	1.04616	0.523079	+	0.852284i	$0.324783\pi$
$272$	0.199227	0.0120799
$273$	4.65362	0.281650
$274$	−7.88830	−0.476550
$275$	0.611343	0.0368654
$276$	−91.2118	−5.49031
$277$	−0.0670290	−0.00402738	−0.00201369	−	0.999998i	$-0.500641\pi$
$277$	−0.0670290	−0.00402738	−0.00201369	+	0.999998i	$0.500641\pi$
$278$	−4.20229	−0.252037
$279$	32.0949	1.92147
$280$	−8.48955	−0.507348
$281$	24.3845	1.45466	0.727330	−	0.686288i	$-0.240761\pi$
$281$	24.3845	1.45466	0.727330	+	0.686288i	$0.240761\pi$
$282$	53.0101	3.15671
$283$	14.1659	0.842073	0.421037	−	0.907044i	$-0.361666\pi$
$283$	14.1659	0.842073	0.421037	+	0.907044i	$0.361666\pi$
$284$	−21.1684	−1.25611
$285$	−15.4403	−0.914607
$286$	−2.36367	−0.139767
$287$	6.51377	0.384496
$288$	−119.712	−7.05409
$289$	−16.9997	−0.999985
$290$	17.6138	1.03432
$291$	12.9890	0.761429
$292$	−85.8953	−5.02664
$293$	−8.97858	−0.524534	−0.262267	−	0.964995i	$-0.584470\pi$
$293$	−8.97858	−0.524534	−0.262267	+	0.964995i	$0.584470\pi$
$294$	8.63041	0.503336
$295$	−9.26225	−0.539269
$296$	52.3974	3.04554
$297$	−8.64536	−0.501654
$298$	2.10465	0.121919
$299$	7.90312	0.457049
$300$	−16.6642	−0.962106
$301$	4.62756	0.266728
$302$	55.2452	3.17900
$303$	2.01518	0.115769
$304$	−59.3670	−3.40493
$305$	−3.15102	−0.180427
$306$	−0.318040	−0.0181811
$307$	6.67025	0.380691	0.190346	−	0.981717i	$-0.439039\pi$
$307$	6.67025	0.380691	0.190346	+	0.981717i	$0.439039\pi$
$308$	−3.16088	−0.180108
$309$	24.3155	1.38326
$310$	11.6332	0.660719
$311$	3.81284	0.216206	0.108103	−	0.994140i	$-0.465522\pi$
$311$	3.81284	0.216206	0.108103	+	0.994140i	$0.465522\pi$
$312$	39.5071	2.23665
$313$	14.4272	0.815474	0.407737	−	0.913099i	$-0.366318\pi$
$313$	14.4272	0.815474	0.407737	+	0.913099i	$0.366318\pi$
$314$	43.0003	2.42665
$315$	7.38771	0.416250
$316$	30.1702	1.69721
$317$	14.0875	0.791231	0.395616	−	0.918416i	$-0.370531\pi$
$317$	14.0875	0.791231	0.395616	+	0.918416i	$0.370531\pi$
$318$	23.2578	1.30423
$319$	4.02130	0.225150
$320$	−18.6065	−1.04014
$321$	1.98477	0.110779
$322$	14.6568	0.816791
$323$	−0.0770189	−0.00428545
$324$	121.066	6.72586
$325$	1.44388	0.0800920
$326$	−55.4531	−3.07127
$327$	3.74413	0.207051
$328$	55.2990	3.05338
$329$	−6.14224	−0.338633
$330$	−5.27614	−0.290442
$331$	10.7690	0.591920	0.295960	−	0.955200i	$-0.404360\pi$
$331$	10.7690	0.591920	0.295960	+	0.955200i	$0.404360\pi$
$332$	−1.36802	−0.0750798
$333$	−45.5969	−2.49869
$334$	43.7752	2.39527
$335$	−2.84953	−0.155686
$336$	39.9400	2.17891
$337$	−31.0633	−1.69213	−0.846063	−	0.533083i	$-0.821033\pi$
$337$	−31.0633	−1.69213	−0.846063	+	0.533083i	$0.821033\pi$
$338$	29.2283	1.58981
$339$	37.8457	2.05550
$340$	−0.0831235	−0.00450801
$341$	2.65589	0.143825
$342$	94.7717	5.12467
$343$	−1.00000	−0.0539949
$344$	39.2859	2.11815
$345$	17.6412	0.949769
$346$	−32.7243	−1.75927
$347$	32.6419	1.75231	0.876155	−	0.482030i	$-0.160100\pi$
$347$	32.6419	1.75231	0.876155	+	0.482030i	$0.160100\pi$
$348$	−109.614	−5.87592
$349$	−2.90572	−0.155540	−0.0777698	−	0.996971i	$-0.524780\pi$
$349$	−2.90572	−0.155540	−0.0777698	+	0.996971i	$0.524780\pi$
$350$	2.67776	0.143132
$351$	−20.4187	−1.08987
$352$	−9.90632	−0.528009
$353$	6.22962	0.331569	0.165785	−	0.986162i	$-0.446984\pi$
$353$	6.22962	0.331569	0.165785	+	0.986162i	$0.446984\pi$
$354$	79.9370	4.24861
$355$	4.09415	0.217295
$356$	−72.5332	−3.84425
$357$	0.0518156	0.00274237
$358$	−13.6611	−0.722011
$359$	−26.6491	−1.40649	−0.703244	−	0.710948i	$-0.748266\pi$
$359$	−26.6491	−1.40649	−0.703244	+	0.710948i	$0.748266\pi$
$360$	62.7184	3.30555
$361$	3.95062	0.207927
$362$	47.3677	2.48959
$363$	34.2484	1.79758
$364$	−7.46543	−0.391295
$365$	16.6129	0.869559
$366$	27.1946	1.42148
$367$	−27.0158	−1.41021	−0.705107	−	0.709101i	$-0.749101\pi$
$367$	−27.0158	−1.41021	−0.705107	+	0.709101i	$0.749101\pi$
$368$	67.8290	3.53583
$369$	−48.1219	−2.50512
$370$	−16.5271	−0.859203
$371$	−2.69487	−0.139911
$372$	−72.3952	−3.75351
$373$	35.2149	1.82336	0.911680	−	0.410902i	$-0.134786\pi$
$373$	35.2149	1.82336	0.911680	+	0.410902i	$0.134786\pi$
$374$	−0.0263182	−0.00136088
$375$	3.22300	0.166435
$376$	−52.1449	−2.68917
$377$	9.49758	0.489150
$378$	−37.8678	−1.94771
$379$	−22.5523	−1.15843	−0.579216	−	0.815174i	$-0.696641\pi$
$379$	−22.5523	−1.15843	−0.579216	+	0.815174i	$0.696641\pi$
$380$	24.7697	1.27066
$381$	−63.5480	−3.25566
$382$	5.63662	0.288394
$383$	8.88203	0.453851	0.226925	−	0.973912i	$-0.427133\pi$
$383$	8.88203	0.453851	0.226925	+	0.973912i	$0.427133\pi$
$384$	56.1300	2.86437
$385$	0.611343	0.0311569
$386$	−6.16015	−0.313543
$387$	−34.1870	−1.73783
$388$	−20.8372	−1.05785
$389$	19.7466	1.00119	0.500595	−	0.865681i	$-0.333115\pi$
$389$	19.7466	1.00119	0.500595	+	0.865681i	$0.333115\pi$
$390$	−12.4613	−0.631001
$391$	0.0879970	0.00445020
$392$	−8.48955	−0.428787
$393$	−21.9022	−1.10482
$394$	−0.713816	−0.0359615
$395$	−5.83519	−0.293600
$396$	23.3517	1.17347
$397$	24.8690	1.24814	0.624070	−	0.781369i	$-0.285478\pi$
$397$	24.8690	1.24814	0.624070	+	0.781369i	$0.285478\pi$
$398$	−28.5118	−1.42917
$399$	−15.4403	−0.772984
$400$	12.3922	0.619609
$401$	−11.8249	−0.590508	−0.295254	−	0.955419i	$-0.595404\pi$
$401$	−11.8249	−0.590508	−0.295254	+	0.955419i	$0.595404\pi$
$402$	24.5926	1.22657
$403$	6.27273	0.312467
$404$	−3.23280	−0.160838
$405$	−23.4152	−1.16351
$406$	17.6138	0.874159
$407$	−3.77320	−0.187031
$408$	0.439891	0.0217778
$409$	32.9426	1.62891	0.814453	−	0.580230i	$-0.197037\pi$
$409$	32.9426	1.62891	0.814453	+	0.580230i	$0.197037\pi$
$410$	−17.4423	−0.861414
$411$	−9.49450	−0.468329
$412$	−39.0074	−1.92176
$413$	−9.26225	−0.455766
$414$	−108.280	−5.32168
$415$	0.264587	0.0129881
$416$	−23.3969	−1.14713
$417$	−5.05795	−0.247689
$418$	7.84248	0.383588
$419$	−14.0028	−0.684082	−0.342041	−	0.939685i	$-0.611118\pi$
$419$	−14.0028	−0.684082	−0.342041	+	0.939685i	$0.611118\pi$
$420$	−16.6642	−0.813128
$421$	−14.2128	−0.692692	−0.346346	−	0.938107i	$-0.612578\pi$
$421$	−14.2128	−0.692692	−0.346346	+	0.938107i	$0.612578\pi$
$422$	8.33527	0.405755
$423$	45.3771	2.20631
$424$	−22.8782	−1.11106
$425$	0.0160768	0.000779841 0
$426$	−35.3342	−1.71195
$427$	−3.15102	−0.152489
$428$	−3.18400	−0.153904
$429$	−2.84496	−0.137356
$430$	−12.3915	−0.597570
$431$	30.3889	1.46378	0.731890	−	0.681423i	$-0.238638\pi$
$431$	30.3889	1.46378	0.731890	+	0.681423i	$0.238638\pi$
$432$	−175.245	−8.43149
$433$	4.18581	0.201157	0.100579	−	0.994929i	$-0.467931\pi$
$433$	4.18581	0.201157	0.100579	+	0.994929i	$0.467931\pi$
$434$	11.6332	0.558409
$435$	21.2003	1.01648
$436$	−6.00641	−0.287655
$437$	−26.2219	−1.25437
$438$	−143.376	−6.85078
$439$	−8.21222	−0.391948	−0.195974	−	0.980609i	$-0.562787\pi$
$439$	−8.21222	−0.391948	−0.195974	+	0.980609i	$0.562787\pi$
$440$	5.19003	0.247425
$441$	7.38771	0.351796
$442$	−0.0621588	−0.00295659
$443$	−5.44397	−0.258651	−0.129325	−	0.991602i	$-0.541281\pi$
$443$	−5.44397	−0.258651	−0.129325	+	0.991602i	$0.541281\pi$
$444$	102.851	4.88110
$445$	14.0286	0.665018
$446$	53.5472	2.53553
$447$	2.53319	0.119816
$448$	−18.6065	−0.879077
$449$	−20.1448	−0.950691	−0.475345	−	0.879799i	$-0.657677\pi$
$449$	−20.1448	−0.950691	−0.475345	+	0.879799i	$0.657677\pi$
$450$	−19.7825	−0.932557
$451$	−3.98215	−0.187512
$452$	−60.7128	−2.85569
$453$	66.4941	3.12416
$454$	−38.7763	−1.81986
$455$	1.44388	0.0676901
$456$	−131.082	−6.13846
$457$	26.9097	1.25878	0.629391	−	0.777089i	$-0.283304\pi$
$457$	26.9097	1.25878	0.629391	+	0.777089i	$0.283304\pi$
$458$	2.67776	0.125123
$459$	−0.227352	−0.0106119
$460$	−28.3003	−1.31951
$461$	−28.4509	−1.32509	−0.662545	−	0.749022i	$-0.730524\pi$
$461$	−28.4509	−1.32509	−0.662545	+	0.749022i	$0.730524\pi$
$462$	−5.27614	−0.245468
$463$	−11.4399	−0.531657	−0.265828	−	0.964020i	$-0.585645\pi$
$463$	−11.4399	−0.531657	−0.265828	+	0.964020i	$0.585645\pi$
$464$	81.5136	3.78417
$465$	14.0019	0.649321
$466$	−43.2018	−2.00129
$467$	−2.66704	−0.123416	−0.0617080	−	0.998094i	$-0.519655\pi$
$467$	−2.66704	−0.123416	−0.0617080	+	0.998094i	$0.519655\pi$
$468$	55.1524	2.54942
$469$	−2.84953	−0.131579
$470$	16.4475	0.758664
$471$	51.7559	2.38479
$472$	−78.6324	−3.61935
$473$	−2.82902	−0.130079
$474$	50.3601	2.31311
$475$	−4.79068	−0.219811
$476$	−0.0831235	−0.00380996
$477$	19.9089	0.911566
$478$	17.3395	0.793090
$479$	23.8235	1.08853	0.544263	−	0.838915i	$-0.316809\pi$
$479$	23.8235	1.08853	0.544263	+	0.838915i	$0.316809\pi$
$480$	−52.2261	−2.38378
$481$	−8.91161	−0.406334
$482$	31.5486	1.43700
$483$	17.6412	0.802701
$484$	−54.9420	−2.49736
$485$	4.03010	0.182997
$486$	88.4791	4.01349
$487$	43.1042	1.95324	0.976619	−	0.214976i	$-0.0689674\pi$
$487$	43.1042	1.95324	0.976619	+	0.214976i	$0.0689674\pi$
$488$	−26.7508	−1.21095
$489$	−66.7444	−3.01828
$490$	2.67776	0.120969
$491$	42.1433	1.90190	0.950950	−	0.309344i	$-0.100109\pi$
$491$	42.1433	1.90190	0.950950	+	0.309344i	$0.100109\pi$
$492$	108.547	4.89366
$493$	0.105750	0.00476276
$494$	18.5225	0.833367
$495$	−4.51643	−0.202998
$496$	53.8361	2.41731
$497$	4.09415	0.183648
$498$	−2.28350	−0.102326
$499$	−23.9002	−1.06992	−0.534961	−	0.844877i	$-0.679674\pi$
$499$	−23.9002	−1.06992	−0.534961	+	0.844877i	$0.679674\pi$
$500$	−5.17039	−0.231227
$501$	52.6886	2.35395
$502$	−71.4310	−3.18812
$503$	−18.2120	−0.812032	−0.406016	−	0.913866i	$-0.633082\pi$
$503$	−18.2120	−0.812032	−0.406016	+	0.913866i	$0.633082\pi$
$504$	62.7184	2.79370
$505$	0.625252	0.0278233
$506$	−8.96033	−0.398335
$507$	35.1797	1.56239
$508$	101.945	4.52307
$509$	−28.9731	−1.28421	−0.642104	−	0.766618i	$-0.721938\pi$
$509$	−28.9731	−1.28421	−0.642104	+	0.766618i	$0.721938\pi$
$510$	−0.138750	−0.00614394
$511$	16.6129	0.734912
$512$	9.60286	0.424390
$513$	67.7478	2.99114
$514$	15.9463	0.703360
$515$	7.54437	0.332445
$516$	77.1144	3.39477
$517$	3.75502	0.165145
$518$	−16.5271	−0.726159
$519$	−39.3876	−1.72892
$520$	12.2579	0.537544
$521$	7.97651	0.349457	0.174729	−	0.984617i	$-0.444095\pi$
$521$	7.97651	0.349457	0.174729	+	0.984617i	$0.444095\pi$
$522$	−130.126	−5.69545
$523$	17.2365	0.753698	0.376849	−	0.926275i	$-0.377008\pi$
$523$	17.2365	0.753698	0.376849	+	0.926275i	$0.377008\pi$
$524$	35.1359	1.53492
$525$	3.22300	0.140663
$526$	−66.7618	−2.91095
$527$	0.0698435	0.00304243
$528$	−24.4170	−1.06261
$529$	6.95955	0.302589
$530$	7.21620	0.313452
$531$	68.4268	2.96947
$532$	24.7697	1.07390
$533$	−9.40510	−0.407380
$534$	−121.072	−5.23931
$535$	0.615814	0.0266240
$536$	−24.1912	−1.04490
$537$	−16.4427	−0.709556
$538$	−36.9700	−1.59389
$539$	0.611343	0.0263324
$540$	73.1176	3.14648
$541$	16.3777	0.704134	0.352067	−	0.935975i	$-0.385479\pi$
$541$	16.3777	0.704134	0.352067	+	0.935975i	$0.385479\pi$
$542$	−46.1162	−1.98086
$543$	57.0126	2.44665
$544$	−0.260512	−0.0111694
$545$	1.16169	0.0497614
$546$	−12.4613	−0.533293
$547$	34.2227	1.46326	0.731629	−	0.681703i	$-0.238760\pi$
$547$	34.2227	1.46326	0.731629	+	0.681703i	$0.238760\pi$
$548$	15.2313	0.650647
$549$	23.2788	0.993516
$550$	−1.63703	−0.0698032
$551$	−31.5122	−1.34247
$552$	149.766	6.37445
$553$	−5.83519	−0.248137
$554$	0.179487	0.00762569
$555$	−19.8923	−0.844381
$556$	8.11406	0.344113
$557$	6.67179	0.282693	0.141346	−	0.989960i	$-0.454857\pi$
$557$	6.67179	0.282693	0.141346	+	0.989960i	$0.454857\pi$
$558$	−85.9424	−3.63823
$559$	−6.68163	−0.282603
$560$	12.3922	0.523666
$561$	−0.0316771	−0.00133741
$562$	−65.2959	−2.75434
$563$	−28.9585	−1.22046	−0.610228	−	0.792226i	$-0.708922\pi$
$563$	−28.9585	−1.22046	−0.610228	+	0.792226i	$0.708922\pi$
$564$	−102.355	−4.30994
$565$	11.7424	0.494006
$566$	−37.9328	−1.59443
$567$	−23.4152	−0.983344
$568$	34.7575	1.45839
$569$	−2.53257	−0.106171	−0.0530855	−	0.998590i	$-0.516906\pi$
$569$	−2.53257	−0.106171	−0.0530855	+	0.998590i	$0.516906\pi$
$570$	41.3455	1.73177
$571$	43.0549	1.80179	0.900895	−	0.434037i	$-0.142911\pi$
$571$	43.0549	1.80179	0.900895	+	0.434037i	$0.142911\pi$
$572$	4.56394	0.190828
$573$	6.78433	0.283420
$574$	−17.4423	−0.728028
$575$	5.47353	0.228262
$576$	137.460	5.72749
$577$	−6.20845	−0.258461	−0.129231	−	0.991615i	$-0.541251\pi$
$577$	−6.20845	−0.258461	−0.129231	+	0.991615i	$0.541251\pi$
$578$	45.5212	1.89343
$579$	−7.41446	−0.308135
$580$	−34.0099	−1.41219
$581$	0.264587	0.0109769
$582$	−34.7814	−1.44174
$583$	1.64749	0.0682320
$584$	141.036	5.83612
$585$	−10.6670	−0.441025
$586$	24.0425	0.993185
$587$	4.21883	0.174130	0.0870649	−	0.996203i	$-0.472251\pi$
$587$	4.21883	0.174130	0.0870649	+	0.996203i	$0.472251\pi$
$588$	−16.6642	−0.687219
$589$	−20.8124	−0.857562
$590$	24.8021	1.02109
$591$	−0.859162	−0.0353412
$592$	−76.4845	−3.14349
$593$	8.57155	0.351991	0.175996	−	0.984391i	$-0.443686\pi$
$593$	8.57155	0.351991	0.175996	+	0.984391i	$0.443686\pi$
$594$	23.1502	0.949864
$595$	0.0160768	0.000659086 0
$596$	−4.06380	−0.166460
$597$	−34.3173	−1.40451
$598$	−21.1626	−0.865405
$599$	−44.1595	−1.80431	−0.902155	−	0.431413i	$-0.858015\pi$
$599$	−44.1595	−1.80431	−0.902155	+	0.431413i	$0.858015\pi$
$600$	27.3618	1.11704
$601$	−41.0754	−1.67550	−0.837751	−	0.546052i	$-0.816130\pi$
$601$	−41.0754	−1.67550	−0.837751	+	0.546052i	$0.816130\pi$
$602$	−12.3915	−0.505039
$603$	21.0515	0.857283
$604$	−106.671	−4.34038
$605$	10.6263	0.432019
$606$	−5.39618	−0.219205
$607$	−37.4884	−1.52161	−0.760803	−	0.648983i	$-0.775195\pi$
$607$	−37.4884	−1.52161	−0.760803	+	0.648983i	$0.775195\pi$
$608$	77.6291	3.14828
$609$	21.2003	0.859079
$610$	8.43768	0.341632
$611$	8.86866	0.358788
$612$	0.614093	0.0248232
$613$	−2.63811	−0.106552	−0.0532762	−	0.998580i	$-0.516966\pi$
$613$	−2.63811	−0.106552	−0.0532762	+	0.998580i	$0.516966\pi$
$614$	−17.8613	−0.720824
$615$	−20.9939	−0.846554
$616$	5.19003	0.209112
$617$	−30.4497	−1.22586	−0.612930	−	0.790138i	$-0.710009\pi$
$617$	−30.4497	−1.22586	−0.612930	+	0.790138i	$0.710009\pi$
$618$	−65.1110	−2.61915
$619$	4.24389	0.170576	0.0852881	−	0.996356i	$-0.472819\pi$
$619$	4.24389	0.170576	0.0852881	+	0.996356i	$0.472819\pi$
$620$	−22.4621	−0.902098
$621$	−77.4044	−3.10613
$622$	−10.2099	−0.409378
$623$	14.0286	0.562043
$624$	−57.6685	−2.30859
$625$	1.00000	0.0400000
$626$	−38.6326	−1.54407
$627$	9.43935	0.376971
$628$	−83.0279	−3.31317
$629$	−0.0992260	−0.00395640
$630$	−19.7825	−0.788154
$631$	−28.2026	−1.12273	−0.561363	−	0.827569i	$-0.689723\pi$
$631$	−28.2026	−1.12273	−0.561363	+	0.827569i	$0.689723\pi$
$632$	−49.5381	−1.97052
$633$	10.0325	0.398755
$634$	−37.7229	−1.49817
$635$	−19.7170	−0.782447
$636$	−44.9077	−1.78071
$637$	1.44388	0.0572086
$638$	−10.7681	−0.426313
$639$	−30.2464	−1.19653
$640$	17.4155	0.688407
$641$	3.20514	0.126595	0.0632977	−	0.997995i	$-0.479838\pi$
$641$	3.20514	0.126595	0.0632977	+	0.997995i	$0.479838\pi$
$642$	−5.31473	−0.209756
$643$	17.9759	0.708899	0.354449	−	0.935075i	$-0.384668\pi$
$643$	17.9759	0.708899	0.354449	+	0.935075i	$0.384668\pi$
$644$	−28.3003	−1.11519
$645$	−14.9146	−0.587262
$646$	0.206238	0.00811433
$647$	−19.8434	−0.780123	−0.390062	−	0.920789i	$-0.627546\pi$
$647$	−19.8434	−0.780123	−0.390062	+	0.920789i	$0.627546\pi$
$648$	−198.784	−7.80898
$649$	5.66241	0.222269
$650$	−3.86636	−0.151651
$651$	14.0019	0.548776
$652$	107.073	4.19329
$653$	10.9954	0.430285	0.215142	−	0.976583i	$-0.430978\pi$
$653$	10.9954	0.430285	0.215142	+	0.976583i	$0.430978\pi$
$654$	−10.0259	−0.392043
$655$	−6.79560	−0.265526
$656$	−80.7199	−3.15158
$657$	−122.731	−4.78821
$658$	16.4475	0.641188
$659$	−31.8024	−1.23884	−0.619422	−	0.785058i	$-0.712633\pi$
$659$	−31.8024	−1.23884	−0.619422	+	0.785058i	$0.712633\pi$
$660$	10.1875	0.396549
$661$	−1.40649	−0.0547060	−0.0273530	−	0.999626i	$-0.508708\pi$
$661$	−1.40649	−0.0547060	−0.0273530	+	0.999626i	$0.508708\pi$
$662$	−28.8369	−1.12078
$663$	−0.0748154	−0.00290559
$664$	2.24623	0.0871705
$665$	−4.79068	−0.185775
$666$	122.097	4.73118
$667$	36.0039	1.39408
$668$	−84.5240	−3.27033
$669$	64.4503	2.49179
$670$	7.63035	0.294786
$671$	1.92635	0.0743661
$672$	−52.2261	−2.01466
$673$	11.6688	0.449797	0.224899	−	0.974382i	$-0.427795\pi$
$673$	11.6688	0.449797	0.224899	+	0.974382i	$0.427795\pi$
$674$	83.1800	3.20398
$675$	−14.1416	−0.544310
$676$	−56.4360	−2.17061
$677$	24.8847	0.956396	0.478198	−	0.878252i	$-0.341290\pi$
$677$	24.8847	0.956396	0.478198	+	0.878252i	$0.341290\pi$
$678$	−101.342	−3.89200
$679$	4.03010	0.154661
$680$	0.136485	0.00523396
$681$	−46.6718	−1.78847
$682$	−7.11185	−0.272327
$683$	−20.8712	−0.798614	−0.399307	−	0.916817i	$-0.630749\pi$
$683$	−20.8712	−0.798614	−0.399307	+	0.916817i	$0.630749\pi$
$684$	−182.991	−6.99685
$685$	−2.94586	−0.112556
$686$	2.67776	0.102237
$687$	3.22300	0.122965
$688$	−57.3455	−2.18628
$689$	3.89106	0.148238
$690$	−47.2388	−1.79835
$691$	−31.3923	−1.19422	−0.597110	−	0.802159i	$-0.703685\pi$
$691$	−31.3923	−1.19422	−0.597110	+	0.802159i	$0.703685\pi$
$692$	63.1863	2.40198
$693$	−4.51643	−0.171565
$694$	−87.4072	−3.31793
$695$	−1.56933	−0.0595281
$696$	179.981	6.82216
$697$	−0.104721	−0.00396658
$698$	7.78081	0.294508
$699$	−51.9985	−1.96676
$700$	−5.17039	−0.195423
$701$	20.3032	0.766839	0.383420	−	0.923574i	$-0.374746\pi$
$701$	20.3032	0.766839	0.383420	+	0.923574i	$0.374746\pi$
$702$	54.6765	2.06363
$703$	29.5680	1.11518
$704$	11.3750	0.428711
$705$	19.7964	0.745577
$706$	−16.6814	−0.627814
$707$	0.625252	0.0235150
$708$	−154.348	−5.80074
$709$	22.5059	0.845226	0.422613	−	0.906310i	$-0.361113\pi$
$709$	22.5059	0.845226	0.422613	+	0.906310i	$0.361113\pi$
$710$	−10.9632	−0.411440
$711$	43.1087	1.61670
$712$	119.096	4.46332
$713$	23.7790	0.890530
$714$	−0.138750	−0.00519257
$715$	−0.882705	−0.0330113
$716$	26.3777	0.985782
$717$	20.8701	0.779409
$718$	71.3600	2.66313
$719$	−38.1383	−1.42232	−0.711160	−	0.703030i	$-0.751830\pi$
$719$	−38.1383	−1.42232	−0.711160	+	0.703030i	$0.751830\pi$
$720$	−91.5499	−3.41186
$721$	7.54437	0.280967
$722$	−10.5788	−0.393702
$723$	37.9724	1.41221
$724$	−91.4608	−3.39911
$725$	6.57782	0.244294
$726$	−91.7090	−3.40364
$727$	−36.8172	−1.36547	−0.682737	−	0.730664i	$-0.739211\pi$
$727$	−36.8172	−1.36547	−0.682737	+	0.730664i	$0.739211\pi$
$728$	12.2579	0.454308
$729$	36.2495	1.34258
$730$	−44.4854	−1.64648
$731$	−0.0743964	−0.00275165
$732$	−52.5091	−1.94079
$733$	−41.8150	−1.54447	−0.772235	−	0.635337i	$-0.780861\pi$
$733$	−41.8150	−1.54447	−0.772235	+	0.635337i	$0.780861\pi$
$734$	72.3419	2.67019
$735$	3.22300	0.118882
$736$	−88.6942	−3.26931
$737$	1.74204	0.0641688
$738$	128.859	4.74336
$739$	0.188630	0.00693887	0.00346944	−	0.999994i	$-0.498896\pi$
$739$	0.188630	0.00693887	0.00346944	+	0.999994i	$0.498896\pi$
$740$	31.9116	1.17309
$741$	22.2940	0.818991
$742$	7.21620	0.264915
$743$	−29.0085	−1.06422	−0.532109	−	0.846676i	$-0.678600\pi$
$743$	−29.0085	−1.06422	−0.532109	+	0.846676i	$0.678600\pi$
$744$	118.870	4.35797
$745$	0.785975	0.0287959
$746$	−94.2971	−3.45246
$747$	−1.95469	−0.0715185
$748$	0.0508170	0.00185805
$749$	0.615814	0.0225013
$750$	−8.63041	−0.315138
$751$	−7.73354	−0.282201	−0.141100	−	0.989995i	$-0.545064\pi$
$751$	−7.73354	−0.282201	−0.141100	+	0.989995i	$0.545064\pi$
$752$	76.1159	2.77566
$753$	−85.9756	−3.13313
$754$	−25.4322	−0.926187
$755$	20.6311	0.750844
$756$	73.1176	2.65926
$757$	16.5966	0.603215	0.301607	−	0.953432i	$-0.402477\pi$
$757$	16.5966	0.603215	0.301607	+	0.953432i	$0.402477\pi$
$758$	60.3896	2.19345
$759$	−10.7848	−0.391464
$760$	−40.6707	−1.47528
$761$	22.7372	0.824221	0.412111	−	0.911134i	$-0.364792\pi$
$761$	22.7372	0.824221	0.412111	+	0.911134i	$0.364792\pi$
$762$	170.166	6.16447
$763$	1.16169	0.0420561
$764$	−10.8836	−0.393753
$765$	−0.118771	−0.00429417
$766$	−23.7839	−0.859349
$767$	13.3736	0.482892
$768$	−30.3650	−1.09570
$769$	29.1717	1.05196	0.525978	−	0.850498i	$-0.323699\pi$
$769$	29.1717	1.05196	0.525978	+	0.850498i	$0.323699\pi$
$770$	−1.63703	−0.0589944
$771$	19.1932	0.691227
$772$	11.8944	0.428090
$773$	−14.5311	−0.522647	−0.261323	−	0.965251i	$-0.584159\pi$
$773$	−14.5311	−0.522647	−0.261323	+	0.965251i	$0.584159\pi$
$774$	91.5447	3.29051
$775$	4.34436	0.156054
$776$	34.2138	1.22820
$777$	−19.8923	−0.713632
$778$	−52.8765	−1.89572
$779$	31.2054	1.11805
$780$	24.0610	0.861524
$781$	−2.50293	−0.0895620
$782$	−0.235635	−0.00842628
$783$	−93.0208	−3.32429
$784$	12.3922	0.442578
$785$	16.0583	0.573146
$786$	58.6488	2.09193
$787$	−22.3625	−0.797139	−0.398569	−	0.917138i	$-0.630493\pi$
$787$	−22.3625	−0.797139	−0.398569	+	0.917138i	$0.630493\pi$
$788$	1.37828	0.0490993
$789$	−80.3557	−2.86074
$790$	15.6252	0.555921
$791$	11.7424	0.417511
$792$	−38.3424	−1.36244
$793$	4.54969	0.161564
$794$	−66.5932	−2.36330
$795$	8.68555	0.308045
$796$	55.0525	1.95128
$797$	−33.5537	−1.18853	−0.594267	−	0.804268i	$-0.702558\pi$
$797$	−33.5537	−1.18853	−0.594267	+	0.804268i	$0.702558\pi$
$798$	41.3455	1.46362
$799$	0.0987478	0.00349345
$800$	−16.2042	−0.572905
$801$	−103.639	−3.66190
$802$	31.6643	1.11810
$803$	−10.1562	−0.358404
$804$	−47.4850	−1.67467
$805$	5.47353	0.192917
$806$	−16.7969	−0.591644
$807$	−44.4977	−1.56639
$808$	5.30811	0.186739
$809$	−36.5516	−1.28509	−0.642543	−	0.766250i	$-0.722120\pi$
$809$	−36.5516	−1.28509	−0.642543	+	0.766250i	$0.722120\pi$
$810$	62.7001	2.20306
$811$	−43.2419	−1.51843	−0.759215	−	0.650840i	$-0.774417\pi$
$811$	−43.2419	−1.51843	−0.759215	+	0.650840i	$0.774417\pi$
$812$	−34.0099	−1.19351
$813$	−55.5062	−1.94669
$814$	10.1037	0.354135
$815$	−20.7088	−0.725397
$816$	−0.642108	−0.0224783
$817$	22.1691	0.775600
$818$	−88.2123	−3.08427
$819$	−10.6670	−0.372734
$820$	33.6788	1.17611
$821$	−45.3291	−1.58200	−0.790998	−	0.611819i	$-0.790438\pi$
$821$	−45.3291	−1.58200	−0.790998	+	0.611819i	$0.790438\pi$
$822$	25.4240	0.886763
$823$	−16.5510	−0.576930	−0.288465	−	0.957490i	$-0.593145\pi$
$823$	−16.5510	−0.576930	−0.288465	+	0.957490i	$0.593145\pi$
$824$	64.0483	2.23123
$825$	−1.97036	−0.0685990
$826$	24.8021	0.862975
$827$	28.3108	0.984462	0.492231	−	0.870465i	$-0.336182\pi$
$827$	28.3108	0.984462	0.492231	+	0.870465i	$0.336182\pi$
$828$	209.075	7.26584
$829$	−38.6417	−1.34208	−0.671041	−	0.741421i	$-0.734152\pi$
$829$	−38.6417	−1.34208	−0.671041	+	0.741421i	$0.734152\pi$
$830$	−0.708501	−0.0245924
$831$	0.216034	0.00749414
$832$	26.8656	0.931398
$833$	0.0160768	0.000557029 0
$834$	13.5440	0.468989
$835$	16.3477	0.565735
$836$	−15.1428	−0.523724
$837$	−61.4361	−2.12354
$838$	37.4962	1.29528
$839$	23.5304	0.812359	0.406179	−	0.913793i	$-0.366861\pi$
$839$	23.5304	0.812359	0.406179	+	0.913793i	$0.366861\pi$
$840$	27.3618	0.944072
$841$	14.2677	0.491991
$842$	38.0586	1.31159
$843$	−78.5913	−2.70683
$844$	−16.0943	−0.553989
$845$	10.9152	0.375495
$846$	−121.509	−4.17757
$847$	10.6263	0.365123
$848$	33.3953	1.14680
$849$	−45.6565	−1.56693
$850$	−0.0430499	−0.00147660
$851$	−33.7826	−1.15805
$852$	68.2257	2.33737
$853$	−3.86299	−0.132266	−0.0661331	−	0.997811i	$-0.521066\pi$
$853$	−3.86299	−0.132266	−0.0661331	+	0.997811i	$0.521066\pi$
$854$	8.43768	0.288731
$855$	35.3922	1.21039
$856$	5.22798	0.178689
$857$	40.4638	1.38222	0.691109	−	0.722751i	$-0.257123\pi$
$857$	40.4638	1.38222	0.691109	+	0.722751i	$0.257123\pi$
$858$	7.61811	0.260078
$859$	50.5618	1.72515	0.862573	−	0.505933i	$-0.168852\pi$
$859$	50.5618	1.72515	0.862573	+	0.505933i	$0.168852\pi$
$860$	23.9263	0.815880
$861$	−20.9939	−0.715469
$862$	−81.3741	−2.77161
$863$	−44.4598	−1.51343	−0.756714	−	0.653746i	$-0.773197\pi$
$863$	−44.4598	−1.51343	−0.756714	+	0.653746i	$0.773197\pi$
$864$	229.153	7.79594
$865$	−12.2208	−0.415519
$866$	−11.2086	−0.380883
$867$	54.7901	1.86077
$868$	−22.4621	−0.762412
$869$	3.56730	0.121012
$870$	−56.7693	−1.92466
$871$	4.11438	0.139410
$872$	9.86225	0.333978
$873$	−29.7732	−1.00767
$874$	70.2160	2.37509
$875$	1.00000	0.0338062
$876$	276.840	9.35356
$877$	−17.2636	−0.582949	−0.291475	−	0.956579i	$-0.594146\pi$
$877$	−17.2636	−0.582949	−0.291475	+	0.956579i	$0.594146\pi$
$878$	21.9904	0.742139
$879$	28.9379	0.976052
$880$	−7.57588	−0.255383
$881$	−18.0006	−0.606456	−0.303228	−	0.952918i	$-0.598064\pi$
$881$	−18.0006	−0.606456	−0.303228	+	0.952918i	$0.598064\pi$
$882$	−19.7825	−0.666112
$883$	−39.2921	−1.32229	−0.661143	−	0.750260i	$-0.729928\pi$
$883$	−39.2921	−1.32229	−0.661143	+	0.750260i	$0.729928\pi$
$884$	0.120020	0.00403672
$885$	29.8522	1.00347
$886$	14.5776	0.489746
$887$	39.0945	1.31267	0.656333	−	0.754471i	$-0.272107\pi$
$887$	39.0945	1.31267	0.656333	+	0.754471i	$0.272107\pi$
$888$	−168.877	−5.66713
$889$	−19.7170	−0.661288
$890$	−37.5651	−1.25919
$891$	14.3147	0.479560
$892$	−103.392	−3.46184
$893$	−29.4255	−0.984688
$894$	−6.78328	−0.226867
$895$	−5.10169	−0.170531
$896$	17.4155	0.581810
$897$	−25.4717	−0.850476
$898$	53.9429	1.80010
$899$	28.5764	0.953077
$900$	38.1974	1.27325
$901$	0.0433249	0.00144336
$902$	10.6632	0.355047
$903$	−14.9146	−0.496327
$904$	99.6877	3.31556
$905$	17.6893	0.588013
$906$	−178.055	−5.91549
$907$	7.30322	0.242499	0.121250	−	0.992622i	$-0.461310\pi$
$907$	7.30322	0.242499	0.121250	+	0.992622i	$0.461310\pi$
$908$	74.8718	2.48471
$909$	−4.61918	−0.153209
$910$	−3.86636	−0.128169
$911$	−16.4797	−0.545998	−0.272999	−	0.962014i	$-0.588016\pi$
$911$	−16.4797	−0.545998	−0.272999	+	0.962014i	$0.588016\pi$
$912$	191.340	6.33589
$913$	−0.161753	−0.00535326
$914$	−72.0576	−2.38345
$915$	10.1557	0.335738
$916$	−5.17039	−0.170835
$917$	−6.79560	−0.224411
$918$	0.608793	0.0200932
$919$	11.3664	0.374944	0.187472	−	0.982270i	$-0.439971\pi$
$919$	11.3664	0.374944	0.187472	+	0.982270i	$0.439971\pi$
$920$	46.4678	1.53200
$921$	−21.4982	−0.708390
$922$	76.1847	2.50901
$923$	−5.91147	−0.194578
$924$	10.1875	0.335145
$925$	−6.17199	−0.202934
$926$	30.6333	1.00667
$927$	−55.7356	−1.83060
$928$	−106.588	−3.49893
$929$	28.0353	0.919809	0.459904	−	0.887968i	$-0.347884\pi$
$929$	28.0353	0.919809	0.459904	+	0.887968i	$0.347884\pi$
$930$	−37.4936	−1.22946
$931$	−4.79068	−0.157008
$932$	83.4169	2.73241
$933$	−12.2888	−0.402316
$934$	7.14170	0.233683
$935$	−0.00982845	−0.000321425 0
$936$	−90.5578	−2.95997
$937$	38.1767	1.24718	0.623590	−	0.781752i	$-0.285674\pi$
$937$	38.1767	1.24718	0.623590	+	0.781752i	$0.285674\pi$
$938$	7.63035	0.249140
$939$	−46.4989	−1.51743
$940$	−31.7578	−1.03583
$941$	48.0458	1.56625	0.783123	−	0.621866i	$-0.213625\pi$
$941$	48.0458	1.56625	0.783123	+	0.621866i	$0.213625\pi$
$942$	−138.590	−4.51551
$943$	−35.6533	−1.16103
$944$	114.780	3.73576
$945$	−14.1416	−0.460026
$946$	7.57544	0.246299
$947$	−20.0483	−0.651483	−0.325742	−	0.945459i	$-0.605614\pi$
$947$	−20.0483	−0.651483	−0.325742	+	0.945459i	$0.605614\pi$
$948$	−97.2385	−3.15816
$949$	−23.9870	−0.778652
$950$	12.8283	0.416205
$951$	−45.4039	−1.47232
$952$	0.136485	0.00442351
$953$	−40.9320	−1.32592	−0.662959	−	0.748656i	$-0.730700\pi$
$953$	−40.9320	−1.32592	−0.662959	+	0.748656i	$0.730700\pi$
$954$	−53.3112	−1.72602
$955$	2.10498	0.0681154
$956$	−33.4803	−1.08283
$957$	−12.9607	−0.418958
$958$	−63.7937	−2.06108
$959$	−2.94586	−0.0951268
$960$	59.9689	1.93549
$961$	−12.1265	−0.391178
$962$	23.8631	0.769378
$963$	−4.54946	−0.146604
$964$	−60.9160	−1.96197
$965$	−2.30049	−0.0740553
$966$	−47.2388	−1.51988
$967$	−27.0396	−0.869535	−0.434768	−	0.900543i	$-0.643170\pi$
$967$	−27.0396	−0.869535	−0.434768	+	0.900543i	$0.643170\pi$
$968$	90.2122	2.89953
$969$	0.248232	0.00797435
$970$	−10.7916	−0.346499
$971$	−26.5279	−0.851321	−0.425661	−	0.904883i	$-0.639958\pi$
$971$	−26.5279	−0.851321	−0.425661	+	0.904883i	$0.639958\pi$
$972$	−170.841	−5.47974
$973$	−1.56933	−0.0503104
$974$	−115.423	−3.69838
$975$	−4.65362	−0.149035
$976$	39.0480	1.24990
$977$	−25.9943	−0.831632	−0.415816	−	0.909449i	$-0.636504\pi$
$977$	−25.9943	−0.831632	−0.415816	+	0.909449i	$0.636504\pi$
$978$	178.725	5.71501
$979$	−8.57627	−0.274099
$980$	−5.17039	−0.165162
$981$	−8.58225	−0.274010
$982$	−112.850	−3.60118
$983$	−36.6745	−1.16973	−0.584867	−	0.811129i	$-0.698853\pi$
$983$	−36.6745	−1.16973	−0.584867	+	0.811129i	$0.698853\pi$
$984$	−178.229	−5.68172
$985$	−0.266572	−0.00849370
$986$	−0.283174	−0.00901811
$987$	19.7964	0.630128
$988$	−35.7645	−1.13782
$989$	−25.3291	−0.805418
$990$	12.0939	0.384369
$991$	34.2097	1.08671	0.543353	−	0.839504i	$-0.317154\pi$
$991$	34.2097	1.08671	0.543353	+	0.839504i	$0.317154\pi$
$992$	−70.3969	−2.23510
$993$	−34.7086	−1.10144
$994$	−10.9632	−0.347730
$995$	−10.6476	−0.337553
$996$	4.40912	0.139708
$997$	−48.6633	−1.54118	−0.770591	−	0.637331i	$-0.780039\pi$
$997$	−48.6633	−1.54118	−0.770591	+	0.637331i	$0.780039\pi$
$998$	63.9991	2.02586
$999$	87.2817	2.76147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.1	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.1	✓	49	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67776 q^{2} -3.22300 q^{3} +5.17039 q^{4} -1.00000 q^{5} +8.63041 q^{6} -1.00000 q^{7} -8.48955 q^{8} +7.38771 q^{9} +O(q^{10})\)	\(q-2.67776 q^{2} -3.22300 q^{3} +5.17039 q^{4} -1.00000 q^{5} +8.63041 q^{6} -1.00000 q^{7} -8.48955 q^{8} +7.38771 q^{9} +2.67776 q^{10} +0.611343 q^{11} -16.6642 q^{12} +1.44388 q^{13} +2.67776 q^{14} +3.22300 q^{15} +12.3922 q^{16} +0.0160768 q^{17} -19.7825 q^{18} -4.79068 q^{19} -5.17039 q^{20} +3.22300 q^{21} -1.63703 q^{22} +5.47353 q^{23} +27.3618 q^{24} +1.00000 q^{25} -3.86636 q^{26} -14.1416 q^{27} -5.17039 q^{28} +6.57782 q^{29} -8.63041 q^{30} +4.34436 q^{31} -16.2042 q^{32} -1.97036 q^{33} -0.0430499 q^{34} +1.00000 q^{35} +38.1974 q^{36} -6.17199 q^{37} +12.8283 q^{38} -4.65362 q^{39} +8.48955 q^{40} -6.51377 q^{41} -8.63041 q^{42} -4.62756 q^{43} +3.16088 q^{44} -7.38771 q^{45} -14.6568 q^{46} +6.14224 q^{47} -39.9400 q^{48} +1.00000 q^{49} -2.67776 q^{50} -0.0518156 q^{51} +7.46543 q^{52} +2.69487 q^{53} +37.8678 q^{54} -0.611343 q^{55} +8.48955 q^{56} +15.4403 q^{57} -17.6138 q^{58} +9.26225 q^{59} +16.6642 q^{60} +3.15102 q^{61} -11.6332 q^{62} -7.38771 q^{63} +18.6065 q^{64} -1.44388 q^{65} +5.27614 q^{66} +2.84953 q^{67} +0.0831235 q^{68} -17.6412 q^{69} -2.67776 q^{70} -4.09415 q^{71} -62.7184 q^{72} -16.6129 q^{73} +16.5271 q^{74} -3.22300 q^{75} -24.7697 q^{76} -0.611343 q^{77} +12.4613 q^{78} +5.83519 q^{79} -12.3922 q^{80} +23.4152 q^{81} +17.4423 q^{82} -0.264587 q^{83} +16.6642 q^{84} -0.0160768 q^{85} +12.3915 q^{86} -21.2003 q^{87} -5.19003 q^{88} -14.0286 q^{89} +19.7825 q^{90} -1.44388 q^{91} +28.3003 q^{92} -14.0019 q^{93} -16.4475 q^{94} +4.79068 q^{95} +52.2261 q^{96} -4.03010 q^{97} -2.67776 q^{98} +4.51643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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