LMFDB - Embedded newform 8014.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$91$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.06251 q^{3} +1.00000 q^{4} +1.40510 q^{5} +3.06251 q^{6} +4.44564 q^{7} -1.00000 q^{8} +6.37896 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.06251 q^{3} +1.00000 q^{4} +1.40510 q^{5} +3.06251 q^{6} +4.44564 q^{7} -1.00000 q^{8} +6.37896 q^{9} -1.40510 q^{10} +6.29563 q^{11} -3.06251 q^{12} -1.70453 q^{13} -4.44564 q^{14} -4.30312 q^{15} +1.00000 q^{16} -2.76477 q^{17} -6.37896 q^{18} +4.62385 q^{19} +1.40510 q^{20} -13.6148 q^{21} -6.29563 q^{22} -0.661500 q^{23} +3.06251 q^{24} -3.02570 q^{25} +1.70453 q^{26} -10.3481 q^{27} +4.44564 q^{28} +3.12091 q^{29} +4.30312 q^{30} +1.06486 q^{31} -1.00000 q^{32} -19.2804 q^{33} +2.76477 q^{34} +6.24656 q^{35} +6.37896 q^{36} -8.84817 q^{37} -4.62385 q^{38} +5.22014 q^{39} -1.40510 q^{40} -11.8647 q^{41} +13.6148 q^{42} +1.66327 q^{43} +6.29563 q^{44} +8.96306 q^{45} +0.661500 q^{46} +8.04992 q^{47} -3.06251 q^{48} +12.7637 q^{49} +3.02570 q^{50} +8.46712 q^{51} -1.70453 q^{52} +0.669690 q^{53} +10.3481 q^{54} +8.84597 q^{55} -4.44564 q^{56} -14.1606 q^{57} -3.12091 q^{58} +9.19448 q^{59} -4.30312 q^{60} -1.43078 q^{61} -1.06486 q^{62} +28.3586 q^{63} +1.00000 q^{64} -2.39503 q^{65} +19.2804 q^{66} +11.7814 q^{67} -2.76477 q^{68} +2.02585 q^{69} -6.24656 q^{70} -14.1229 q^{71} -6.37896 q^{72} +12.1127 q^{73} +8.84817 q^{74} +9.26624 q^{75} +4.62385 q^{76} +27.9881 q^{77} -5.22014 q^{78} +4.21790 q^{79} +1.40510 q^{80} +12.5543 q^{81} +11.8647 q^{82} -3.05791 q^{83} -13.6148 q^{84} -3.88477 q^{85} -1.66327 q^{86} -9.55780 q^{87} -6.29563 q^{88} +14.8286 q^{89} -8.96306 q^{90} -7.57773 q^{91} -0.661500 q^{92} -3.26114 q^{93} -8.04992 q^{94} +6.49696 q^{95} +3.06251 q^{96} -17.3954 q^{97} -12.7637 q^{98} +40.1596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) $ 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.06251	−1.76814	−0.884070	−	0.467354i	$-0.845207\pi$
$3$	−3.06251	−1.76814	−0.884070	+	0.467354i	$0.845207\pi$
$4$	1.00000	0.500000
$5$	1.40510	0.628379	0.314189	−	0.949360i	$-0.398267\pi$
$5$	1.40510	0.628379	0.314189	+	0.949360i	$0.398267\pi$
$6$	3.06251	1.25026
$7$	4.44564	1.68029	0.840147	−	0.542359i	$-0.182469\pi$
$7$	4.44564	1.68029	0.840147	+	0.542359i	$0.182469\pi$
$8$	−1.00000	−0.353553
$9$	6.37896	2.12632
$10$	−1.40510	−0.444331
$11$	6.29563	1.89820	0.949102	−	0.314968i	$-0.101994\pi$
$11$	6.29563	1.89820	0.949102	+	0.314968i	$0.101994\pi$
$12$	−3.06251	−0.884070
$13$	−1.70453	−0.472752	−0.236376	−	0.971662i	$-0.575960\pi$
$13$	−1.70453	−0.472752	−0.236376	+	0.971662i	$0.575960\pi$
$14$	−4.44564	−1.18815
$15$	−4.30312	−1.11106
$16$	1.00000	0.250000
$17$	−2.76477	−0.670554	−0.335277	−	0.942120i	$-0.608830\pi$
$17$	−2.76477	−0.670554	−0.335277	+	0.942120i	$0.608830\pi$
$18$	−6.37896	−1.50354
$19$	4.62385	1.06078	0.530392	−	0.847753i	$-0.322045\pi$
$19$	4.62385	1.06078	0.530392	+	0.847753i	$0.322045\pi$
$20$	1.40510	0.314189
$21$	−13.6148	−2.97100
$22$	−6.29563	−1.34223
$23$	−0.661500	−0.137932	−0.0689662	−	0.997619i	$-0.521970\pi$
$23$	−0.661500	−0.137932	−0.0689662	+	0.997619i	$0.521970\pi$
$24$	3.06251	0.625132
$25$	−3.02570	−0.605140
$26$	1.70453	0.334286
$27$	−10.3481	−1.99149
$28$	4.44564	0.840147
$29$	3.12091	0.579538	0.289769	−	0.957097i	$-0.406422\pi$
$29$	3.12091	0.579538	0.289769	+	0.957097i	$0.406422\pi$
$30$	4.30312	0.785639
$31$	1.06486	0.191254	0.0956272	−	0.995417i	$-0.469514\pi$
$31$	1.06486	0.191254	0.0956272	+	0.995417i	$0.469514\pi$
$32$	−1.00000	−0.176777
$33$	−19.2804	−3.35629
$34$	2.76477	0.474154
$35$	6.24656	1.05586
$36$	6.37896	1.06316
$37$	−8.84817	−1.45463	−0.727315	−	0.686303i	$-0.759232\pi$
$37$	−8.84817	−1.45463	−0.727315	+	0.686303i	$0.759232\pi$
$38$	−4.62385	−0.750087
$39$	5.22014	0.835892
$40$	−1.40510	−0.222165
$41$	−11.8647	−1.85296	−0.926481	−	0.376342i	$-0.877182\pi$
$41$	−11.8647	−1.85296	−0.926481	+	0.376342i	$0.877182\pi$
$42$	13.6148	2.10081
$43$	1.66327	0.253647	0.126823	−	0.991925i	$-0.459522\pi$
$43$	1.66327	0.253647	0.126823	+	0.991925i	$0.459522\pi$
$44$	6.29563	0.949102
$45$	8.96306	1.33613
$46$	0.661500	0.0975329
$47$	8.04992	1.17420	0.587100	−	0.809514i	$-0.300269\pi$
$47$	8.04992	1.17420	0.587100	+	0.809514i	$0.300269\pi$
$48$	−3.06251	−0.442035
$49$	12.7637	1.82339
$50$	3.02570	0.427899
$51$	8.46712	1.18563
$52$	−1.70453	−0.236376
$53$	0.669690	0.0919890	0.0459945	−	0.998942i	$-0.485354\pi$
$53$	0.669690	0.0919890	0.0459945	+	0.998942i	$0.485354\pi$
$54$	10.3481	1.40820
$55$	8.84597	1.19279
$56$	−4.44564	−0.594074
$57$	−14.1606	−1.87561
$58$	−3.12091	−0.409795
$59$	9.19448	1.19702	0.598509	−	0.801116i	$-0.295760\pi$
$59$	9.19448	1.19702	0.598509	+	0.801116i	$0.295760\pi$
$60$	−4.30312	−0.555531
$61$	−1.43078	−0.183192	−0.0915961	−	0.995796i	$-0.529197\pi$
$61$	−1.43078	−0.183192	−0.0915961	+	0.995796i	$0.529197\pi$
$62$	−1.06486	−0.135237
$63$	28.3586	3.57284
$64$	1.00000	0.125000
$65$	−2.39503	−0.297067
$66$	19.2804	2.37326
$67$	11.7814	1.43933	0.719666	−	0.694321i	$-0.244295\pi$
$67$	11.7814	1.43933	0.719666	+	0.694321i	$0.244295\pi$
$68$	−2.76477	−0.335277
$69$	2.02585	0.243884
$70$	−6.24656	−0.746606
$71$	−14.1229	−1.67608	−0.838042	−	0.545605i	$-0.816300\pi$
$71$	−14.1229	−1.67608	−0.838042	+	0.545605i	$0.816300\pi$
$72$	−6.37896	−0.751768
$73$	12.1127	1.41768	0.708842	−	0.705367i	$-0.249218\pi$
$73$	12.1127	1.41768	0.708842	+	0.705367i	$0.249218\pi$
$74$	8.84817	1.02858
$75$	9.26624	1.06997
$76$	4.62385	0.530392
$77$	27.9881	3.18954
$78$	−5.22014	−0.591065
$79$	4.21790	0.474551	0.237275	−	0.971442i	$-0.423746\pi$
$79$	4.21790	0.474551	0.237275	+	0.971442i	$0.423746\pi$
$80$	1.40510	0.157095
$81$	12.5543	1.39492
$82$	11.8647	1.31024
$83$	−3.05791	−0.335649	−0.167824	−	0.985817i	$-0.553674\pi$
$83$	−3.05791	−0.335649	−0.167824	+	0.985817i	$0.553674\pi$
$84$	−13.6148	−1.48550
$85$	−3.88477	−0.421362
$86$	−1.66327	−0.179356
$87$	−9.55780	−1.02470
$88$	−6.29563	−0.671117
$89$	14.8286	1.57183	0.785913	−	0.618337i	$-0.212193\pi$
$89$	14.8286	1.57183	0.785913	+	0.618337i	$0.212193\pi$
$90$	−8.96306	−0.944790
$91$	−7.57773	−0.794362
$92$	−0.661500	−0.0689662
$93$	−3.26114	−0.338165
$94$	−8.04992	−0.830285
$95$	6.49696	0.666574
$96$	3.06251	0.312566
$97$	−17.3954	−1.76624	−0.883118	−	0.469151i	$-0.844560\pi$
$97$	−17.3954	−1.76624	−0.883118	+	0.469151i	$0.844560\pi$
$98$	−12.7637	−1.28933
$99$	40.1596	4.03619
$100$	−3.02570	−0.302570
$101$	18.1411	1.80511	0.902555	−	0.430574i	$-0.141689\pi$
$101$	18.1411	1.80511	0.902555	+	0.430574i	$0.141689\pi$
$102$	−8.46712	−0.838370
$103$	−10.6283	−1.04724	−0.523621	−	0.851951i	$-0.675419\pi$
$103$	−10.6283	−1.04724	−0.523621	+	0.851951i	$0.675419\pi$
$104$	1.70453	0.167143
$105$	−19.1301	−1.86691
$106$	−0.669690	−0.0650461
$107$	2.83150	0.273732	0.136866	−	0.990590i	$-0.456297\pi$
$107$	2.83150	0.273732	0.136866	+	0.990590i	$0.456297\pi$
$108$	−10.3481	−0.995747
$109$	0.424140	0.0406252	0.0203126	−	0.999794i	$-0.493534\pi$
$109$	0.424140	0.0406252	0.0203126	+	0.999794i	$0.493534\pi$
$110$	−8.84597	−0.843431
$111$	27.0976	2.57199
$112$	4.44564	0.420073
$113$	15.4146	1.45009	0.725043	−	0.688704i	$-0.241820\pi$
$113$	15.4146	1.45009	0.725043	+	0.688704i	$0.241820\pi$
$114$	14.1606	1.32626
$115$	−0.929472	−0.0866737
$116$	3.12091	0.289769
$117$	−10.8731	−1.00522
$118$	−9.19448	−0.846420
$119$	−12.2912	−1.12673
$120$	4.30312	0.392820
$121$	28.6350	2.60318
$122$	1.43078	0.129536
$123$	36.3359	3.27630
$124$	1.06486	0.0956272
$125$	−11.2769	−1.00864
$126$	−28.3586	−2.52638
$127$	−11.2519	−0.998446	−0.499223	−	0.866474i	$-0.666381\pi$
$127$	−11.2519	−0.998446	−0.499223	+	0.866474i	$0.666381\pi$
$128$	−1.00000	−0.0883883
$129$	−5.09379	−0.448484
$130$	2.39503	0.210058
$131$	−13.9662	−1.22023	−0.610117	−	0.792311i	$-0.708878\pi$
$131$	−13.9662	−1.22023	−0.610117	+	0.792311i	$0.708878\pi$
$132$	−19.2804	−1.67815
$133$	20.5560	1.78243
$134$	−11.7814	−1.01776
$135$	−14.5401	−1.25141
$136$	2.76477	0.237077
$137$	18.0329	1.54065	0.770327	−	0.637649i	$-0.220093\pi$
$137$	18.0329	1.54065	0.770327	+	0.637649i	$0.220093\pi$
$138$	−2.02585	−0.172452
$139$	−4.34704	−0.368711	−0.184356	−	0.982860i	$-0.559020\pi$
$139$	−4.34704	−0.368711	−0.184356	+	0.982860i	$0.559020\pi$
$140$	6.24656	0.527930
$141$	−24.6529	−2.07615
$142$	14.1229	1.18517
$143$	−10.7311	−0.897380
$144$	6.37896	0.531580
$145$	4.38518	0.364169
$146$	−12.1127	−1.00245
$147$	−39.0890	−3.22401
$148$	−8.84817	−0.727315
$149$	−1.62994	−0.133530	−0.0667651	−	0.997769i	$-0.521268\pi$
$149$	−1.62994	−0.133530	−0.0667651	+	0.997769i	$0.521268\pi$
$150$	−9.26624	−0.756585
$151$	19.0098	1.54699	0.773496	−	0.633801i	$-0.218506\pi$
$151$	19.0098	1.54699	0.773496	+	0.633801i	$0.218506\pi$
$152$	−4.62385	−0.375044
$153$	−17.6363	−1.42581
$154$	−27.9881	−2.25535
$155$	1.49623	0.120180
$156$	5.22014	0.417946
$157$	−13.0967	−1.04523	−0.522617	−	0.852568i	$-0.675044\pi$
$157$	−13.0967	−1.04523	−0.522617	+	0.852568i	$0.675044\pi$
$158$	−4.21790	−0.335558
$159$	−2.05093	−0.162650
$160$	−1.40510	−0.111083
$161$	−2.94079	−0.231767
$162$	−12.5543	−0.986358
$163$	10.7262	0.840140	0.420070	−	0.907492i	$-0.362006\pi$
$163$	10.7262	0.840140	0.420070	+	0.907492i	$0.362006\pi$
$164$	−11.8647	−0.926481
$165$	−27.0909	−2.10902
$166$	3.05791	0.237340
$167$	−15.0949	−1.16808	−0.584040	−	0.811725i	$-0.698529\pi$
$167$	−15.0949	−1.16808	−0.584040	+	0.811725i	$0.698529\pi$
$168$	13.6148	1.05041
$169$	−10.0946	−0.776506
$170$	3.88477	0.297948
$171$	29.4954	2.25557
$172$	1.66327	0.126823
$173$	20.6630	1.57098	0.785490	−	0.618874i	$-0.212411\pi$
$173$	20.6630	1.57098	0.785490	+	0.618874i	$0.212411\pi$
$174$	9.55780	0.724575
$175$	−13.4512	−1.01681
$176$	6.29563	0.474551
$177$	−28.1582	−2.11650
$178$	−14.8286	−1.11145
$179$	−12.6836	−0.948020	−0.474010	−	0.880519i	$-0.657194\pi$
$179$	−12.6836	−0.948020	−0.474010	+	0.880519i	$0.657194\pi$
$180$	8.96306	0.668067
$181$	9.52582	0.708048	0.354024	−	0.935236i	$-0.384813\pi$
$181$	9.52582	0.708048	0.354024	+	0.935236i	$0.384813\pi$
$182$	7.57773	0.561699
$183$	4.38177	0.323910
$184$	0.661500	0.0487664
$185$	−12.4325	−0.914059
$186$	3.26114	0.239118
$187$	−17.4060	−1.27285
$188$	8.04992	0.587100
$189$	−46.0040	−3.34630
$190$	−6.49696	−0.471339
$191$	23.7405	1.71780	0.858901	−	0.512141i	$-0.171148\pi$
$191$	23.7405	1.71780	0.858901	+	0.512141i	$0.171148\pi$
$192$	−3.06251	−0.221018
$193$	−4.63854	−0.333889	−0.166945	−	0.985966i	$-0.553390\pi$
$193$	−4.63854	−0.333889	−0.166945	+	0.985966i	$0.553390\pi$
$194$	17.3954	1.24892
$195$	7.33481	0.525256
$196$	12.7637	0.911694
$197$	15.5492	1.10783	0.553917	−	0.832572i	$-0.313132\pi$
$197$	15.5492	1.10783	0.553917	+	0.832572i	$0.313132\pi$
$198$	−40.1596	−2.85402
$199$	27.0388	1.91673	0.958364	−	0.285549i	$-0.0921761\pi$
$199$	27.0388	1.91673	0.958364	+	0.285549i	$0.0921761\pi$
$200$	3.02570	0.213949
$201$	−36.0808	−2.54494
$202$	−18.1411	−1.27641
$203$	13.8744	0.973794
$204$	8.46712	0.592817
$205$	−16.6711	−1.16436
$206$	10.6283	0.740512
$207$	−4.21969	−0.293288
$208$	−1.70453	−0.118188
$209$	29.1100	2.01358
$210$	19.1301	1.32010
$211$	22.3672	1.53982	0.769912	−	0.638150i	$-0.220300\pi$
$211$	22.3672	1.53982	0.769912	+	0.638150i	$0.220300\pi$
$212$	0.669690	0.0459945
$213$	43.2516	2.96355
$214$	−2.83150	−0.193557
$215$	2.33706	0.159386
$216$	10.3481	0.704100
$217$	4.73398	0.321364
$218$	−0.424140	−0.0287264
$219$	−37.0953	−2.50667
$220$	8.84597	0.596395
$221$	4.71263	0.317006
$222$	−27.0976	−1.81867
$223$	−6.30296	−0.422078	−0.211039	−	0.977478i	$-0.567685\pi$
$223$	−6.30296	−0.422078	−0.211039	+	0.977478i	$0.567685\pi$
$224$	−4.44564	−0.297037
$225$	−19.3008	−1.28672
$226$	−15.4146	−1.02537
$227$	−21.6526	−1.43713	−0.718565	−	0.695460i	$-0.755201\pi$
$227$	−21.6526	−1.43713	−0.718565	+	0.695460i	$0.755201\pi$
$228$	−14.1606	−0.937807
$229$	−6.93507	−0.458282	−0.229141	−	0.973393i	$-0.573592\pi$
$229$	−6.93507	−0.458282	−0.229141	+	0.973393i	$0.573592\pi$
$230$	0.929472	0.0612876
$231$	−85.7139	−5.63956
$232$	−3.12091	−0.204897
$233$	1.45320	0.0952024	0.0476012	−	0.998866i	$-0.484842\pi$
$233$	1.45320	0.0952024	0.0476012	+	0.998866i	$0.484842\pi$
$234$	10.8731	0.710800
$235$	11.3109	0.737843
$236$	9.19448	0.598509
$237$	−12.9174	−0.839073
$238$	12.2912	0.796717
$239$	−4.49323	−0.290643	−0.145322	−	0.989384i	$-0.546422\pi$
$239$	−4.49323	−0.290643	−0.145322	+	0.989384i	$0.546422\pi$
$240$	−4.30312	−0.277765
$241$	10.3047	0.663784	0.331892	−	0.943317i	$-0.392313\pi$
$241$	10.3047	0.663784	0.331892	+	0.943317i	$0.392313\pi$
$242$	−28.6350	−1.84073
$243$	−7.40330	−0.474922
$244$	−1.43078	−0.0915961
$245$	17.9343	1.14578
$246$	−36.3359	−2.31669
$247$	−7.88149	−0.501487
$248$	−1.06486	−0.0676186
$249$	9.36486	0.593474
$250$	11.2769	0.713213
$251$	−7.83350	−0.494446	−0.247223	−	0.968959i	$-0.579518\pi$
$251$	−7.83350	−0.494446	−0.247223	+	0.968959i	$0.579518\pi$
$252$	28.3586	1.78642
$253$	−4.16456	−0.261824
$254$	11.2519	0.706008
$255$	11.8971	0.745027
$256$	1.00000	0.0625000
$257$	−18.7127	−1.16726	−0.583632	−	0.812019i	$-0.698369\pi$
$257$	−18.7127	−1.16726	−0.583632	+	0.812019i	$0.698369\pi$
$258$	5.09379	0.317126
$259$	−39.3358	−2.44421
$260$	−2.39503	−0.148534
$261$	19.9081	1.23228
$262$	13.9662	0.862836
$263$	−27.2447	−1.67998	−0.839990	−	0.542602i	$-0.817439\pi$
$263$	−27.2447	−1.67998	−0.839990	+	0.542602i	$0.817439\pi$
$264$	19.2804	1.18663
$265$	0.940980	0.0578039
$266$	−20.5560	−1.26037
$267$	−45.4127	−2.77921
$268$	11.7814	0.719666
$269$	−3.03481	−0.185036	−0.0925179	−	0.995711i	$-0.529492\pi$
$269$	−3.03481	−0.185036	−0.0925179	+	0.995711i	$0.529492\pi$
$270$	14.5401	0.884882
$271$	−1.88422	−0.114458	−0.0572291	−	0.998361i	$-0.518227\pi$
$271$	−1.88422	−0.114458	−0.0572291	+	0.998361i	$0.518227\pi$
$272$	−2.76477	−0.167639
$273$	23.2069	1.40454
$274$	−18.0329	−1.08941
$275$	−19.0487	−1.14868
$276$	2.02585	0.121942
$277$	−26.8124	−1.61100	−0.805501	−	0.592594i	$-0.798104\pi$
$277$	−26.8124	−1.61100	−0.805501	+	0.592594i	$0.798104\pi$
$278$	4.34704	0.260718
$279$	6.79270	0.406668
$280$	−6.24656	−0.373303
$281$	30.6904	1.83083	0.915417	−	0.402508i	$-0.131861\pi$
$281$	30.6904	1.83083	0.915417	+	0.402508i	$0.131861\pi$
$282$	24.6529	1.46806
$283$	−19.2190	−1.14245	−0.571225	−	0.820793i	$-0.693532\pi$
$283$	−19.2190	−1.14245	−0.571225	+	0.820793i	$0.693532\pi$
$284$	−14.1229	−0.838042
$285$	−19.8970	−1.17860
$286$	10.7311	0.634543
$287$	−52.7464	−3.11352
$288$	−6.37896	−0.375884
$289$	−9.35606	−0.550357
$290$	−4.38518	−0.257506
$291$	53.2736	3.12295
$292$	12.1127	0.708842
$293$	−8.89057	−0.519393	−0.259696	−	0.965690i	$-0.583622\pi$
$293$	−8.89057	−0.519393	−0.259696	+	0.965690i	$0.583622\pi$
$294$	39.0890	2.27972
$295$	12.9191	0.752181
$296$	8.84817	0.514290
$297$	−65.1479	−3.78026
$298$	1.62994	0.0944201
$299$	1.12755	0.0652078
$300$	9.26624	0.534987
$301$	7.39432	0.426201
$302$	−19.0098	−1.09389
$303$	−55.5574	−3.19169
$304$	4.62385	0.265196
$305$	−2.01038	−0.115114
$306$	17.6363	1.00820
$307$	9.03253	0.515514	0.257757	−	0.966210i	$-0.417017\pi$
$307$	9.03253	0.515514	0.257757	+	0.966210i	$0.417017\pi$
$308$	27.9881	1.59477
$309$	32.5494	1.85167
$310$	−1.49623	−0.0849802
$311$	10.3280	0.585646	0.292823	−	0.956167i	$-0.405405\pi$
$311$	10.3280	0.585646	0.292823	+	0.956167i	$0.405405\pi$
$312$	−5.22014	−0.295532
$313$	26.8450	1.51737	0.758686	−	0.651457i	$-0.225842\pi$
$313$	26.8450	1.51737	0.758686	+	0.651457i	$0.225842\pi$
$314$	13.0967	0.739091
$315$	39.8466	2.24510
$316$	4.21790	0.237275
$317$	12.2756	0.689468	0.344734	−	0.938700i	$-0.387969\pi$
$317$	12.2756	0.689468	0.344734	+	0.938700i	$0.387969\pi$
$318$	2.05093	0.115011
$319$	19.6481	1.10008
$320$	1.40510	0.0785473
$321$	−8.67150	−0.483996
$322$	2.94079	0.163884
$323$	−12.7839	−0.711313
$324$	12.5543	0.697460
$325$	5.15740	0.286081
$326$	−10.7262	−0.594068
$327$	−1.29893	−0.0718311
$328$	11.8647	0.655121
$329$	35.7870	1.97300
$330$	27.0909	1.49130
$331$	−36.0221	−1.97995	−0.989976	−	0.141239i	$-0.954891\pi$
$331$	−36.0221	−1.97995	−0.989976	+	0.141239i	$0.954891\pi$
$332$	−3.05791	−0.167824
$333$	−56.4422	−3.09301
$334$	15.0949	0.825958
$335$	16.5541	0.904445
$336$	−13.6148	−0.742749
$337$	3.27115	0.178191	0.0890953	−	0.996023i	$-0.471602\pi$
$337$	3.27115	0.178191	0.0890953	+	0.996023i	$0.471602\pi$
$338$	10.0946	0.549072
$339$	−47.2074	−2.56396
$340$	−3.88477	−0.210681
$341$	6.70396	0.363040
$342$	−29.4954	−1.59493
$343$	25.6234	1.38353
$344$	−1.66327	−0.0896778
$345$	2.84652	0.153251
$346$	−20.6630	−1.11085
$347$	28.3994	1.52456	0.762279	−	0.647249i	$-0.224081\pi$
$347$	28.3994	1.52456	0.762279	+	0.647249i	$0.224081\pi$
$348$	−9.55780	−0.512352
$349$	−4.34438	−0.232549	−0.116275	−	0.993217i	$-0.537095\pi$
$349$	−4.34438	−0.232549	−0.116275	+	0.993217i	$0.537095\pi$
$350$	13.4512	0.718996
$351$	17.6387	0.941483
$352$	−6.29563	−0.335558
$353$	−3.16056	−0.168220	−0.0841099	−	0.996456i	$-0.526805\pi$
$353$	−3.16056	−0.168220	−0.0841099	+	0.996456i	$0.526805\pi$
$354$	28.1582	1.49659
$355$	−19.8441	−1.05322
$356$	14.8286	0.785913
$357$	37.6418	1.99221
$358$	12.6836	0.670351
$359$	25.8756	1.36566	0.682831	−	0.730576i	$-0.260749\pi$
$359$	25.8756	1.36566	0.682831	+	0.730576i	$0.260749\pi$
$360$	−8.96306	−0.472395
$361$	2.37997	0.125262
$362$	−9.52582	−0.500666
$363$	−87.6949	−4.60279
$364$	−7.57773	−0.397181
$365$	17.0195	0.890842
$366$	−4.38177	−0.229039
$367$	12.3970	0.647120	0.323560	−	0.946208i	$-0.395120\pi$
$367$	12.3970	0.647120	0.323560	+	0.946208i	$0.395120\pi$
$368$	−0.661500	−0.0344831
$369$	−75.6848	−3.93999
$370$	12.4325	0.646337
$371$	2.97720	0.154569
$372$	−3.26114	−0.169082
$373$	2.61658	0.135481	0.0677406	−	0.997703i	$-0.478421\pi$
$373$	2.61658	0.135481	0.0677406	+	0.997703i	$0.478421\pi$
$374$	17.4060	0.900040
$375$	34.5356	1.78341
$376$	−8.04992	−0.415143
$377$	−5.31968	−0.273978
$378$	46.0040	2.36619
$379$	−9.51295	−0.488648	−0.244324	−	0.969694i	$-0.578566\pi$
$379$	−9.51295	−0.488648	−0.244324	+	0.969694i	$0.578566\pi$
$380$	6.49696	0.333287
$381$	34.4591	1.76539
$382$	−23.7405	−1.21467
$383$	32.7306	1.67245	0.836227	−	0.548384i	$-0.184757\pi$
$383$	32.7306	1.67245	0.836227	+	0.548384i	$0.184757\pi$
$384$	3.06251	0.156283
$385$	39.3260	2.00424
$386$	4.63854	0.236095
$387$	10.6100	0.539335
$388$	−17.3954	−0.883118
$389$	−8.39804	−0.425798	−0.212899	−	0.977074i	$-0.568290\pi$
$389$	−8.39804	−0.425798	−0.212899	+	0.977074i	$0.568290\pi$
$390$	−7.33481	−0.371412
$391$	1.82889	0.0924911
$392$	−12.7637	−0.644665
$393$	42.7717	2.15754
$394$	−15.5492	−0.783357
$395$	5.92656	0.298198
$396$	40.1596	2.01810
$397$	2.03234	0.102000	0.0510000	−	0.998699i	$-0.483759\pi$
$397$	2.03234	0.102000	0.0510000	+	0.998699i	$0.483759\pi$
$398$	−27.0388	−1.35533
$399$	−62.9528	−3.15158
$400$	−3.02570	−0.151285
$401$	14.6729	0.732731	0.366365	−	0.930471i	$-0.380602\pi$
$401$	14.6729	0.732731	0.366365	+	0.930471i	$0.380602\pi$
$402$	36.0808	1.79954
$403$	−1.81509	−0.0904159
$404$	18.1411	0.902555
$405$	17.6400	0.876538
$406$	−13.8744	−0.688576
$407$	−55.7049	−2.76119
$408$	−8.46712	−0.419185
$409$	33.0156	1.63251	0.816257	−	0.577689i	$-0.196045\pi$
$409$	33.0156	1.63251	0.816257	+	0.577689i	$0.196045\pi$
$410$	16.6711	0.823328
$411$	−55.2259	−2.72409
$412$	−10.6283	−0.523621
$413$	40.8753	2.01134
$414$	4.21969	0.207386
$415$	−4.29665	−0.210914
$416$	1.70453	0.0835715
$417$	13.3129	0.651933
$418$	−29.1100	−1.42382
$419$	−17.3714	−0.848649	−0.424324	−	0.905510i	$-0.639488\pi$
$419$	−17.3714	−0.848649	−0.424324	+	0.905510i	$0.639488\pi$
$420$	−19.1301	−0.933455
$421$	−22.3290	−1.08825	−0.544124	−	0.839005i	$-0.683138\pi$
$421$	−22.3290	−1.08825	−0.544124	+	0.839005i	$0.683138\pi$
$422$	−22.3672	−1.08882
$423$	51.3501	2.49673
$424$	−0.669690	−0.0325230
$425$	8.36536	0.405780
$426$	−43.2516	−2.09555
$427$	−6.36072	−0.307817
$428$	2.83150	0.136866
$429$	32.8641	1.58669
$430$	−2.33706	−0.112703
$431$	−24.5415	−1.18212	−0.591062	−	0.806626i	$-0.701291\pi$
$431$	−24.5415	−1.18212	−0.591062	+	0.806626i	$0.701291\pi$
$432$	−10.3481	−0.497874
$433$	−1.92551	−0.0925342	−0.0462671	−	0.998929i	$-0.514733\pi$
$433$	−1.92551	−0.0925342	−0.0462671	+	0.998929i	$0.514733\pi$
$434$	−4.73398	−0.227238
$435$	−13.4296	−0.643902
$436$	0.424140	0.0203126
$437$	−3.05868	−0.146316
$438$	37.0953	1.77248
$439$	−9.83494	−0.469396	−0.234698	−	0.972068i	$-0.575410\pi$
$439$	−9.83494	−0.469396	−0.234698	+	0.972068i	$0.575410\pi$
$440$	−8.84597	−0.421715
$441$	81.4193	3.87711
$442$	−4.71263	−0.224157
$443$	28.4880	1.35350	0.676752	−	0.736211i	$-0.263387\pi$
$443$	28.4880	1.35350	0.676752	+	0.736211i	$0.263387\pi$
$444$	27.0976	1.28600
$445$	20.8356	0.987702
$446$	6.30296	0.298454
$447$	4.99172	0.236100
$448$	4.44564	0.210037
$449$	12.4132	0.585815	0.292907	−	0.956141i	$-0.405377\pi$
$449$	12.4132	0.585815	0.292907	+	0.956141i	$0.405377\pi$
$450$	19.3008	0.909851
$451$	−74.6960	−3.51730
$452$	15.4146	0.725043
$453$	−58.2176	−2.73530
$454$	21.6526	1.01620
$455$	−10.6474	−0.499160
$456$	14.1606	0.663130
$457$	16.7490	0.783484	0.391742	−	0.920075i	$-0.371873\pi$
$457$	16.7490	0.783484	0.391742	+	0.920075i	$0.371873\pi$
$458$	6.93507	0.324055
$459$	28.6101	1.33541
$460$	−0.929472	−0.0433369
$461$	18.7921	0.875235	0.437618	−	0.899161i	$-0.355822\pi$
$461$	18.7921	0.875235	0.437618	+	0.899161i	$0.355822\pi$
$462$	85.7139	3.98777
$463$	−21.3711	−0.993199	−0.496600	−	0.867980i	$-0.665418\pi$
$463$	−21.3711	−0.993199	−0.496600	+	0.867980i	$0.665418\pi$
$464$	3.12091	0.144884
$465$	−4.58222	−0.212495
$466$	−1.45320	−0.0673182
$467$	25.0291	1.15821	0.579105	−	0.815253i	$-0.303402\pi$
$467$	25.0291	1.15821	0.579105	+	0.815253i	$0.303402\pi$
$468$	−10.8731	−0.502611
$469$	52.3760	2.41850
$470$	−11.3109	−0.521734
$471$	40.1089	1.84812
$472$	−9.19448	−0.423210
$473$	10.4714	0.481474
$474$	12.9174	0.593314
$475$	−13.9904	−0.641923
$476$	−12.2912	−0.563364
$477$	4.27193	0.195598
$478$	4.49323	0.205516
$479$	11.0741	0.505989	0.252995	−	0.967468i	$-0.418585\pi$
$479$	11.0741	0.505989	0.252995	+	0.967468i	$0.418585\pi$
$480$	4.30312	0.196410
$481$	15.0820	0.687680
$482$	−10.3047	−0.469366
$483$	9.00620	0.409796
$484$	28.6350	1.30159
$485$	−24.4422	−1.10986
$486$	7.40330	0.335820
$487$	34.1222	1.54623	0.773113	−	0.634268i	$-0.218698\pi$
$487$	34.1222	1.54623	0.773113	+	0.634268i	$0.218698\pi$
$488$	1.43078	0.0647682
$489$	−32.8490	−1.48548
$490$	−17.9343	−0.810187
$491$	3.26553	0.147371	0.0736856	−	0.997282i	$-0.476524\pi$
$491$	3.26553	0.147371	0.0736856	+	0.997282i	$0.476524\pi$
$492$	36.3359	1.63815
$493$	−8.62858	−0.388612
$494$	7.88149	0.354605
$495$	56.4281	2.53626
$496$	1.06486	0.0478136
$497$	−62.7855	−2.81632
$498$	−9.36486	−0.419650
$499$	43.1551	1.93189	0.965943	−	0.258756i	$-0.0833125\pi$
$499$	43.1551	1.93189	0.965943	+	0.258756i	$0.0833125\pi$
$500$	−11.2769	−0.504318
$501$	46.2284	2.06533
$502$	7.83350	0.349626
$503$	−33.7267	−1.50380	−0.751899	−	0.659278i	$-0.770862\pi$
$503$	−33.7267	−1.50380	−0.751899	+	0.659278i	$0.770862\pi$
$504$	−28.3586	−1.26319
$505$	25.4901	1.13429
$506$	4.16456	0.185137
$507$	30.9147	1.37297
$508$	−11.2519	−0.499223
$509$	−12.7656	−0.565826	−0.282913	−	0.959146i	$-0.591301\pi$
$509$	−12.7656	−0.565826	−0.282913	+	0.959146i	$0.591301\pi$
$510$	−11.8971	−0.526814
$511$	53.8487	2.38213
$512$	−1.00000	−0.0441942
$513$	−47.8481	−2.11254
$514$	18.7127	0.825380
$515$	−14.9339	−0.658065
$516$	−5.09379	−0.224242
$517$	50.6793	2.22887
$518$	39.3358	1.72832
$519$	−63.2807	−2.77772
$520$	2.39503	0.105029
$521$	20.0659	0.879102	0.439551	−	0.898218i	$-0.355138\pi$
$521$	20.0659	0.879102	0.439551	+	0.898218i	$0.355138\pi$
$522$	−19.9081	−0.871356
$523$	−36.6506	−1.60262	−0.801309	−	0.598251i	$-0.795863\pi$
$523$	−36.6506	−1.60262	−0.801309	+	0.598251i	$0.795863\pi$
$524$	−13.9662	−0.610117
$525$	41.1944	1.79787
$526$	27.2447	1.18792
$527$	−2.94409	−0.128246
$528$	−19.2804	−0.839073
$529$	−22.5624	−0.980975
$530$	−0.940980	−0.0408735
$531$	58.6512	2.54525
$532$	20.5560	0.891214
$533$	20.2238	0.875991
$534$	45.4127	1.96520
$535$	3.97853	0.172007
$536$	−11.7814	−0.508881
$537$	38.8438	1.67623
$538$	3.03481	0.130840
$539$	80.3556	3.46116
$540$	−14.5401	−0.625706
$541$	−11.8235	−0.508331	−0.254166	−	0.967161i	$-0.581801\pi$
$541$	−11.8235	−0.508331	−0.254166	+	0.967161i	$0.581801\pi$
$542$	1.88422	0.0809341
$543$	−29.1729	−1.25193
$544$	2.76477	0.118538
$545$	0.595957	0.0255280
$546$	−23.2069	−0.993163
$547$	16.0459	0.686075	0.343037	−	0.939322i	$-0.388544\pi$
$547$	16.0459	0.686075	0.343037	+	0.939322i	$0.388544\pi$
$548$	18.0329	0.770327
$549$	−9.12688	−0.389526
$550$	19.0487	0.812240
$551$	14.4306	0.614764
$552$	−2.02585	−0.0862259
$553$	18.7513	0.797385
$554$	26.8124	1.13915
$555$	38.0748	1.61618
$556$	−4.34704	−0.184356
$557$	2.04014	0.0864435	0.0432217	−	0.999066i	$-0.486238\pi$
$557$	2.04014	0.0864435	0.0432217	+	0.999066i	$0.486238\pi$
$558$	−6.79270	−0.287558
$559$	−2.83510	−0.119912
$560$	6.24656	0.263965
$561$	53.3059	2.25058
$562$	−30.6904	−1.29459
$563$	34.6544	1.46051	0.730254	−	0.683176i	$-0.239402\pi$
$563$	34.6544	1.46051	0.730254	+	0.683176i	$0.239402\pi$
$564$	−24.6529	−1.03808
$565$	21.6590	0.911203
$566$	19.2190	0.807835
$567$	55.8118	2.34388
$568$	14.1229	0.592586
$569$	3.77826	0.158393	0.0791964	−	0.996859i	$-0.474765\pi$
$569$	3.77826	0.158393	0.0791964	+	0.996859i	$0.474765\pi$
$570$	19.8970	0.833393
$571$	1.20880	0.0505869	0.0252934	−	0.999680i	$-0.491948\pi$
$571$	1.20880	0.0505869	0.0252934	+	0.999680i	$0.491948\pi$
$572$	−10.7311	−0.448690
$573$	−72.7055	−3.03732
$574$	52.7464	2.20159
$575$	2.00150	0.0834684
$576$	6.37896	0.265790
$577$	−6.28183	−0.261516	−0.130758	−	0.991414i	$-0.541741\pi$
$577$	−6.28183	−0.261516	−0.130758	+	0.991414i	$0.541741\pi$
$578$	9.35606	0.389161
$579$	14.2056	0.590363
$580$	4.38518	0.182084
$581$	−13.5943	−0.563989
$582$	−53.2736	−2.20826
$583$	4.21612	0.174614
$584$	−12.1127	−0.501227
$585$	−15.2778	−0.631660
$586$	8.89057	0.367266
$587$	−21.9046	−0.904101	−0.452051	−	0.891992i	$-0.649307\pi$
$587$	−21.9046	−0.904101	−0.452051	+	0.891992i	$0.649307\pi$
$588$	−39.0890	−1.61200
$589$	4.92375	0.202879
$590$	−12.9191	−0.531872
$591$	−47.6195	−1.95881
$592$	−8.84817	−0.363658
$593$	11.5677	0.475026	0.237513	−	0.971384i	$-0.423668\pi$
$593$	11.5677	0.475026	0.237513	+	0.971384i	$0.423668\pi$
$594$	65.1479	2.67305
$595$	−17.2703	−0.708012
$596$	−1.62994	−0.0667651
$597$	−82.8065	−3.38904
$598$	−1.12755	−0.0461089
$599$	24.4968	1.00091	0.500456	−	0.865762i	$-0.333166\pi$
$599$	24.4968	1.00091	0.500456	+	0.865762i	$0.333166\pi$
$600$	−9.26624	−0.378293
$601$	−25.4400	−1.03772	−0.518860	−	0.854859i	$-0.673644\pi$
$601$	−25.4400	−1.03772	−0.518860	+	0.854859i	$0.673644\pi$
$602$	−7.39432	−0.301370
$603$	75.1533	3.06048
$604$	19.0098	0.773496
$605$	40.2349	1.63578
$606$	55.5574	2.25687
$607$	16.1746	0.656505	0.328253	−	0.944590i	$-0.393540\pi$
$607$	16.1746	0.656505	0.328253	+	0.944590i	$0.393540\pi$
$608$	−4.62385	−0.187522
$609$	−42.4905	−1.72180
$610$	2.01038	0.0813979
$611$	−13.7213	−0.555106
$612$	−17.6363	−0.712907
$613$	−38.3765	−1.55001	−0.775005	−	0.631955i	$-0.782253\pi$
$613$	−38.3765	−1.55001	−0.775005	+	0.631955i	$0.782253\pi$
$614$	−9.03253	−0.364523
$615$	51.0554	2.05875
$616$	−27.9881	−1.12767
$617$	−6.52446	−0.262665	−0.131332	−	0.991338i	$-0.541926\pi$
$617$	−6.52446	−0.262665	−0.131332	+	0.991338i	$0.541926\pi$
$618$	−32.5494	−1.30933
$619$	−2.86512	−0.115159	−0.0575795	−	0.998341i	$-0.518338\pi$
$619$	−2.86512	−0.115159	−0.0575795	+	0.998341i	$0.518338\pi$
$620$	1.49623	0.0600901
$621$	6.84527	0.274691
$622$	−10.3280	−0.414114
$623$	65.9225	2.64113
$624$	5.22014	0.208973
$625$	−0.716616	−0.0286646
$626$	−26.8450	−1.07294
$627$	−89.1498	−3.56030
$628$	−13.0967	−0.522617
$629$	24.4631	0.975409
$630$	−39.8466	−1.58752
$631$	43.4661	1.73036	0.865180	−	0.501462i	$-0.167204\pi$
$631$	43.4661	1.73036	0.865180	+	0.501462i	$0.167204\pi$
$632$	−4.21790	−0.167779
$633$	−68.4999	−2.72263
$634$	−12.2756	−0.487527
$635$	−15.8100	−0.627402
$636$	−2.05093	−0.0813248
$637$	−21.7561	−0.862010
$638$	−19.6481	−0.777875
$639$	−90.0897	−3.56389
$640$	−1.40510	−0.0555413
$641$	18.2933	0.722543	0.361272	−	0.932461i	$-0.382343\pi$
$641$	18.2933	0.722543	0.361272	+	0.932461i	$0.382343\pi$
$642$	8.67150	0.342237
$643$	−14.5755	−0.574800	−0.287400	−	0.957811i	$-0.592791\pi$
$643$	−14.5755	−0.574800	−0.287400	+	0.957811i	$0.592791\pi$
$644$	−2.94079	−0.115883
$645$	−7.15728	−0.281817
$646$	12.7839	0.502974
$647$	48.7687	1.91729	0.958647	−	0.284597i	$-0.0918599\pi$
$647$	48.7687	1.91729	0.958647	+	0.284597i	$0.0918599\pi$
$648$	−12.5543	−0.493179
$649$	57.8850	2.27219
$650$	−5.15740	−0.202290
$651$	−14.4979	−0.568216
$652$	10.7262	0.420070
$653$	−47.7714	−1.86944	−0.934720	−	0.355386i	$-0.884349\pi$
$653$	−47.7714	−1.86944	−0.934720	+	0.355386i	$0.884349\pi$
$654$	1.29893	0.0507923
$655$	−19.6239	−0.766769
$656$	−11.8647	−0.463240
$657$	77.2665	3.01445
$658$	−35.7870	−1.39512
$659$	−19.6202	−0.764293	−0.382147	−	0.924102i	$-0.624815\pi$
$659$	−19.6202	−0.764293	−0.382147	+	0.924102i	$0.624815\pi$
$660$	−27.0909	−1.05451
$661$	−5.84427	−0.227316	−0.113658	−	0.993520i	$-0.536257\pi$
$661$	−5.84427	−0.227316	−0.113658	+	0.993520i	$0.536257\pi$
$662$	36.0221	1.40004
$663$	−14.4325	−0.560511
$664$	3.05791	0.118670
$665$	28.8831	1.12004
$666$	56.4422	2.18709
$667$	−2.06448	−0.0799370
$668$	−15.0949	−0.584040
$669$	19.3029	0.746293
$670$	−16.5541	−0.639539
$671$	−9.00765	−0.347736
$672$	13.6148	0.525203
$673$	47.2308	1.82061	0.910306	−	0.413935i	$-0.135846\pi$
$673$	47.2308	1.82061	0.910306	+	0.413935i	$0.135846\pi$
$674$	−3.27115	−0.126000
$675$	31.3103	1.20513
$676$	−10.0946	−0.388253
$677$	−17.9194	−0.688699	−0.344349	−	0.938842i	$-0.611900\pi$
$677$	−17.9194	−0.688699	−0.344349	+	0.938842i	$0.611900\pi$
$678$	47.2074	1.81299
$679$	−77.3337	−2.96779
$680$	3.88477	0.148974
$681$	66.3111	2.54105
$682$	−6.70396	−0.256708
$683$	10.9142	0.417619	0.208810	−	0.977956i	$-0.433041\pi$
$683$	10.9142	0.417619	0.208810	+	0.977956i	$0.433041\pi$
$684$	29.4954	1.12778
$685$	25.3380	0.968114
$686$	−25.6234	−0.978306
$687$	21.2387	0.810308
$688$	1.66327	0.0634117
$689$	−1.14151	−0.0434880
$690$	−2.84652	−0.108365
$691$	−19.1886	−0.729970	−0.364985	−	0.931013i	$-0.618926\pi$
$691$	−19.1886	−0.729970	−0.364985	+	0.931013i	$0.618926\pi$
$692$	20.6630	0.785490
$693$	178.535	6.78199
$694$	−28.3994	−1.07802
$695$	−6.10802	−0.231690
$696$	9.55780	0.362288
$697$	32.8032	1.24251
$698$	4.34438	0.164437
$699$	−4.45044	−0.168331
$700$	−13.4512	−0.508407
$701$	−4.64375	−0.175392	−0.0876960	−	0.996147i	$-0.527950\pi$
$701$	−4.64375	−0.175392	−0.0876960	+	0.996147i	$0.527950\pi$
$702$	−17.6387	−0.665729
$703$	−40.9126	−1.54305
$704$	6.29563	0.237276
$705$	−34.6398	−1.30461
$706$	3.16056	0.118949
$707$	80.6490	3.03312
$708$	−28.1582	−1.05825
$709$	5.19506	0.195104	0.0975522	−	0.995230i	$-0.468899\pi$
$709$	5.19506	0.195104	0.0975522	+	0.995230i	$0.468899\pi$
$710$	19.8441	0.744736
$711$	26.9058	1.00905
$712$	−14.8286	−0.555724
$713$	−0.704405	−0.0263802
$714$	−37.6418	−1.40871
$715$	−15.0782	−0.563894
$716$	−12.6836	−0.474010
$717$	13.7606	0.513898
$718$	−25.8756	−0.965669
$719$	−32.1322	−1.19833	−0.599165	−	0.800625i	$-0.704501\pi$
$719$	−32.1322	−1.19833	−0.599165	+	0.800625i	$0.704501\pi$
$720$	8.96306	0.334034
$721$	−47.2498	−1.75968
$722$	−2.37997	−0.0885734
$723$	−31.5582	−1.17366
$724$	9.52582	0.354024
$725$	−9.44293	−0.350702
$726$	87.6949	3.25466
$727$	−39.9749	−1.48259	−0.741294	−	0.671181i	$-0.765787\pi$
$727$	−39.9749	−1.48259	−0.741294	+	0.671181i	$0.765787\pi$
$728$	7.57773	0.280849
$729$	−14.9902	−0.555192
$730$	−17.0195	−0.629921
$731$	−4.59857	−0.170084
$732$	4.38177	0.161955
$733$	−21.6966	−0.801383	−0.400692	−	0.916213i	$-0.631230\pi$
$733$	−21.6966	−0.801383	−0.400692	+	0.916213i	$0.631230\pi$
$734$	−12.3970	−0.457583
$735$	−54.9238	−2.02590
$736$	0.661500	0.0243832
$737$	74.1716	2.73215
$738$	75.6848	2.78599
$739$	−17.9453	−0.660128	−0.330064	−	0.943958i	$-0.607070\pi$
$739$	−17.9453	−0.660128	−0.330064	+	0.943958i	$0.607070\pi$
$740$	−12.4325	−0.457029
$741$	24.1371	0.886700
$742$	−2.97720	−0.109297
$743$	33.6361	1.23399	0.616995	−	0.786967i	$-0.288350\pi$
$743$	33.6361	1.23399	0.616995	+	0.786967i	$0.288350\pi$
$744$	3.26114	0.119559
$745$	−2.29023	−0.0839075
$746$	−2.61658	−0.0957996
$747$	−19.5063	−0.713697
$748$	−17.4060	−0.636425
$749$	12.5878	0.459949
$750$	−34.5356	−1.26106
$751$	−19.1376	−0.698341	−0.349171	−	0.937059i	$-0.613537\pi$
$751$	−19.1376	−0.698341	−0.349171	+	0.937059i	$0.613537\pi$
$752$	8.04992	0.293550
$753$	23.9902	0.874251
$754$	5.31968	0.193731
$755$	26.7106	0.972097
$756$	−46.0040	−1.67315
$757$	−35.8850	−1.30426	−0.652131	−	0.758107i	$-0.726125\pi$
$757$	−35.8850	−1.30426	−0.652131	+	0.758107i	$0.726125\pi$
$758$	9.51295	0.345526
$759$	12.7540	0.462941
$760$	−6.49696	−0.235669
$761$	−18.2591	−0.661893	−0.330947	−	0.943649i	$-0.607368\pi$
$761$	−18.2591	−0.661893	−0.330947	+	0.943649i	$0.607368\pi$
$762$	−34.4591	−1.24832
$763$	1.88557	0.0682623
$764$	23.7405	0.858901
$765$	−24.7808	−0.895951
$766$	−32.7306	−1.18260
$767$	−15.6723	−0.565893
$768$	−3.06251	−0.110509
$769$	1.69653	0.0611786	0.0305893	−	0.999532i	$-0.490262\pi$
$769$	1.69653	0.0611786	0.0305893	+	0.999532i	$0.490262\pi$
$770$	−39.3260	−1.41721
$771$	57.3077	2.06389
$772$	−4.63854	−0.166945
$773$	4.97489	0.178934	0.0894672	−	0.995990i	$-0.471484\pi$
$773$	4.97489	0.178934	0.0894672	+	0.995990i	$0.471484\pi$
$774$	−10.6100	−0.381367
$775$	−3.22195	−0.115736
$776$	17.3954	0.624459
$777$	120.466	4.32170
$778$	8.39804	0.301084
$779$	−54.8608	−1.96559
$780$	7.33481	0.262628
$781$	−88.9129	−3.18155
$782$	−1.82889	−0.0654011
$783$	−32.2955	−1.15415
$784$	12.7637	0.455847
$785$	−18.4022	−0.656802
$786$	−42.7717	−1.52561
$787$	30.2046	1.07668	0.538338	−	0.842729i	$-0.319052\pi$
$787$	30.2046	1.07668	0.538338	+	0.842729i	$0.319052\pi$
$788$	15.5492	0.553917
$789$	83.4371	2.97044
$790$	−5.92656	−0.210858
$791$	68.5279	2.43657
$792$	−40.1596	−1.42701
$793$	2.43880	0.0866045
$794$	−2.03234	−0.0721249
$795$	−2.88176	−0.102205
$796$	27.0388	0.958364
$797$	27.3351	0.968260	0.484130	−	0.874996i	$-0.339136\pi$
$797$	27.3351	0.968260	0.484130	+	0.874996i	$0.339136\pi$
$798$	62.9528	2.22851
$799$	−22.2561	−0.787366
$800$	3.02570	0.106975
$801$	94.5910	3.34221
$802$	−14.6729	−0.518119
$803$	76.2571	2.69105
$804$	−36.0808	−1.27247
$805$	−4.13210	−0.145637
$806$	1.81509	0.0639337
$807$	9.29415	0.327169
$808$	−18.1411	−0.638203
$809$	−12.8040	−0.450165	−0.225083	−	0.974340i	$-0.572265\pi$
$809$	−12.8040	−0.450165	−0.225083	+	0.974340i	$0.572265\pi$
$810$	−17.6400	−0.619806
$811$	−12.4736	−0.438006	−0.219003	−	0.975724i	$-0.570280\pi$
$811$	−12.4736	−0.438006	−0.219003	+	0.975724i	$0.570280\pi$
$812$	13.8744	0.486897
$813$	5.77044	0.202378
$814$	55.7049	1.95245
$815$	15.0713	0.527926
$816$	8.46712	0.296409
$817$	7.69073	0.269065
$818$	−33.0156	−1.15436
$819$	−48.3381	−1.68907
$820$	−16.6711	−0.582181
$821$	−21.3328	−0.744518	−0.372259	−	0.928129i	$-0.621417\pi$
$821$	−21.3328	−0.744518	−0.372259	+	0.928129i	$0.621417\pi$
$822$	55.2259	1.92623
$823$	−47.7300	−1.66376	−0.831881	−	0.554954i	$-0.812736\pi$
$823$	−47.7300	−1.66376	−0.831881	+	0.554954i	$0.812736\pi$
$824$	10.6283	0.370256
$825$	58.3368	2.03103
$826$	−40.8753	−1.42223
$827$	−16.7732	−0.583263	−0.291631	−	0.956531i	$-0.594198\pi$
$827$	−16.7732	−0.583263	−0.291631	+	0.956531i	$0.594198\pi$
$828$	−4.21969	−0.146644
$829$	−56.4130	−1.95930	−0.979651	−	0.200706i	$-0.935676\pi$
$829$	−56.4130	−1.95930	−0.979651	+	0.200706i	$0.935676\pi$
$830$	4.29665	0.149139
$831$	82.1133	2.84848
$832$	−1.70453	−0.0590940
$833$	−35.2887	−1.22268
$834$	−13.3129	−0.460987
$835$	−21.2098	−0.733997
$836$	29.1100	1.00679
$837$	−11.0193	−0.380882
$838$	17.3714	0.600085
$839$	2.03370	0.0702112	0.0351056	−	0.999384i	$-0.488823\pi$
$839$	2.03370	0.0702112	0.0351056	+	0.999384i	$0.488823\pi$
$840$	19.1301	0.660052
$841$	−19.2599	−0.664136
$842$	22.3290	0.769507
$843$	−93.9895	−3.23717
$844$	22.3672	0.769912
$845$	−14.1839	−0.487939
$846$	−51.3501	−1.76545
$847$	127.301	4.37411
$848$	0.669690	0.0229973
$849$	58.8584	2.02001
$850$	−8.36536	−0.286930
$851$	5.85307	0.200641
$852$	43.2516	1.48178
$853$	−2.01542	−0.0690066	−0.0345033	−	0.999405i	$-0.510985\pi$
$853$	−2.01542	−0.0690066	−0.0345033	+	0.999405i	$0.510985\pi$
$854$	6.36072	0.217659
$855$	41.4438	1.41735
$856$	−2.83150	−0.0967787
$857$	29.5852	1.01061	0.505305	−	0.862941i	$-0.331380\pi$
$857$	29.5852	1.01061	0.505305	+	0.862941i	$0.331380\pi$
$858$	−32.8641	−1.12196
$859$	−5.87225	−0.200359	−0.100179	−	0.994969i	$-0.531942\pi$
$859$	−5.87225	−0.200359	−0.100179	+	0.994969i	$0.531942\pi$
$860$	2.33706	0.0796932
$861$	161.536	5.50514
$862$	24.5415	0.835888
$863$	−23.6641	−0.805536	−0.402768	−	0.915302i	$-0.631952\pi$
$863$	−23.6641	−0.805536	−0.402768	+	0.915302i	$0.631952\pi$
$864$	10.3481	0.352050
$865$	29.0336	0.987171
$866$	1.92551	0.0654316
$867$	28.6530	0.973108
$868$	4.73398	0.160682
$869$	26.5544	0.900795
$870$	13.4296	0.455307
$871$	−20.0818	−0.680447
$872$	−0.424140	−0.0143632
$873$	−110.965	−3.75558
$874$	3.05868	0.103461
$875$	−50.1330	−1.69480
$876$	−37.0953	−1.25333
$877$	−16.4477	−0.555400	−0.277700	−	0.960668i	$-0.589572\pi$
$877$	−16.4477	−0.555400	−0.277700	+	0.960668i	$0.589572\pi$
$878$	9.83494	0.331913
$879$	27.2275	0.918359
$880$	8.84597	0.298198
$881$	−9.24904	−0.311608	−0.155804	−	0.987788i	$-0.549797\pi$
$881$	−9.24904	−0.311608	−0.155804	+	0.987788i	$0.549797\pi$
$882$	−81.4193	−2.74153
$883$	34.2858	1.15381	0.576905	−	0.816811i	$-0.304260\pi$
$883$	34.2858	1.15381	0.576905	+	0.816811i	$0.304260\pi$
$884$	4.71263	0.158503
$885$	−39.5650	−1.32996
$886$	−28.4880	−0.957072
$887$	−22.1018	−0.742106	−0.371053	−	0.928612i	$-0.621003\pi$
$887$	−22.1018	−0.742106	−0.371053	+	0.928612i	$0.621003\pi$
$888$	−27.0976	−0.909337
$889$	−50.0220	−1.67768
$890$	−20.8356	−0.698411
$891$	79.0372	2.64784
$892$	−6.30296	−0.211039
$893$	37.2216	1.24557
$894$	−4.99172	−0.166948
$895$	−17.8218	−0.595715
$896$	−4.44564	−0.148518
$897$	−3.45313	−0.115296
$898$	−12.4132	−0.414234
$899$	3.32333	0.110839
$900$	−19.3008	−0.643361
$901$	−1.85154	−0.0616837
$902$	74.6960	2.48711
$903$	−22.6452	−0.753584
$904$	−15.4146	−0.512683
$905$	13.3847	0.444922
$906$	58.2176	1.93415
$907$	41.7557	1.38648	0.693238	−	0.720709i	$-0.256183\pi$
$907$	41.7557	1.38648	0.693238	+	0.720709i	$0.256183\pi$
$908$	−21.6526	−0.718565
$909$	115.722	3.83825
$910$	10.6474	0.352960
$911$	9.00609	0.298385	0.149192	−	0.988808i	$-0.452333\pi$
$911$	9.00609	0.298385	0.149192	+	0.988808i	$0.452333\pi$
$912$	−14.1606	−0.468904
$913$	−19.2514	−0.637130
$914$	−16.7490	−0.554007
$915$	6.15681	0.203538
$916$	−6.93507	−0.229141
$917$	−62.0888	−2.05035
$918$	−28.6101	−0.944274
$919$	15.0110	0.495166	0.247583	−	0.968867i	$-0.420364\pi$
$919$	15.0110	0.495166	0.247583	+	0.968867i	$0.420364\pi$
$920$	0.929472	0.0306438
$921$	−27.6622	−0.911501
$922$	−18.7921	−0.618885
$923$	24.0730	0.792372
$924$	−85.7139	−2.81978
$925$	26.7719	0.880256
$926$	21.3711	0.702298
$927$	−67.7979	−2.22677
$928$	−3.12091	−0.102449
$929$	19.0145	0.623845	0.311923	−	0.950108i	$-0.399027\pi$
$929$	19.0145	0.623845	0.311923	+	0.950108i	$0.399027\pi$
$930$	4.58222	0.150257
$931$	59.0175	1.93422
$932$	1.45320	0.0476012
$933$	−31.6296	−1.03551
$934$	−25.0291	−0.818978
$935$	−24.4571	−0.799831
$936$	10.8731	0.355400
$937$	−15.6407	−0.510961	−0.255480	−	0.966814i	$-0.582234\pi$
$937$	−15.6407	−0.510961	−0.255480	+	0.966814i	$0.582234\pi$
$938$	−52.3760	−1.71014
$939$	−82.2132	−2.68293
$940$	11.3109	0.368921
$941$	9.44711	0.307967	0.153983	−	0.988073i	$-0.450790\pi$
$941$	9.44711	0.307967	0.153983	+	0.988073i	$0.450790\pi$
$942$	−40.1089	−1.30682
$943$	7.84853	0.255583
$944$	9.19448	0.299255
$945$	−64.6400	−2.10274
$946$	−10.4714	−0.340453
$947$	−29.8241	−0.969153	−0.484576	−	0.874749i	$-0.661026\pi$
$947$	−29.8241	−0.969153	−0.484576	+	0.874749i	$0.661026\pi$
$948$	−12.9174	−0.419536
$949$	−20.6465	−0.670213
$950$	13.9904	0.453908
$951$	−37.5942	−1.21908
$952$	12.2912	0.398359
$953$	8.12107	0.263067	0.131534	−	0.991312i	$-0.458010\pi$
$953$	8.12107	0.263067	0.131534	+	0.991312i	$0.458010\pi$
$954$	−4.27193	−0.138309
$955$	33.3577	1.07943
$956$	−4.49323	−0.145322
$957$	−60.1724	−1.94510
$958$	−11.0741	−0.357788
$959$	80.1678	2.58875
$960$	−4.30312	−0.138883
$961$	−29.8661	−0.963422
$962$	−15.0820	−0.486263
$963$	18.0620	0.582041
$964$	10.3047	0.331892
$965$	−6.51759	−0.209809
$966$	−9.00620	−0.289770
$967$	27.9975	0.900337	0.450169	−	0.892944i	$-0.351364\pi$
$967$	27.9975	0.900337	0.450169	+	0.892944i	$0.351364\pi$
$968$	−28.6350	−0.920363
$969$	39.1507	1.25770
$970$	24.4422	0.784793
$971$	−13.6675	−0.438612	−0.219306	−	0.975656i	$-0.570379\pi$
$971$	−13.6675	−0.438612	−0.219306	+	0.975656i	$0.570379\pi$
$972$	−7.40330	−0.237461
$973$	−19.3254	−0.619543
$974$	−34.1222	−1.09335
$975$	−15.7946	−0.505832
$976$	−1.43078	−0.0457981
$977$	−47.4663	−1.51858	−0.759291	−	0.650751i	$-0.774454\pi$
$977$	−47.4663	−1.51858	−0.759291	+	0.650751i	$0.774454\pi$
$978$	32.8490	1.05040
$979$	93.3553	2.98365
$980$	17.9343	0.572889
$981$	2.70557	0.0863823
$982$	−3.26553	−0.104207
$983$	10.8276	0.345346	0.172673	−	0.984979i	$-0.444760\pi$
$983$	10.8276	0.345346	0.172673	+	0.984979i	$0.444760\pi$
$984$	−36.3359	−1.15835
$985$	21.8481	0.696139
$986$	8.62858	0.274790
$987$	−109.598	−3.48855
$988$	−7.88149	−0.250744
$989$	−1.10026	−0.0349861
$990$	−56.4281	−1.79340
$991$	−13.5675	−0.430984	−0.215492	−	0.976506i	$-0.569136\pi$
$991$	−13.5675	−0.430984	−0.215492	+	0.976506i	$0.569136\pi$
$992$	−1.06486	−0.0338093
$993$	110.318	3.50083
$994$	62.7855	1.99144
$995$	37.9921	1.20443
$996$	9.36486	0.296737
$997$	−46.8220	−1.48287	−0.741434	−	0.671025i	$-0.765854\pi$
$997$	−46.8220	−1.48287	−0.741434	+	0.671025i	$0.765854\pi$
$998$	−43.1551	−1.36605
$999$	91.5619	2.89689

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.e.1.8	✓	91

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.8	✓	91	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.06251 q^{3} +1.00000 q^{4} +1.40510 q^{5} +3.06251 q^{6} +4.44564 q^{7} -1.00000 q^{8} +6.37896 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.06251 q^{3} +1.00000 q^{4} +1.40510 q^{5} +3.06251 q^{6} +4.44564 q^{7} -1.00000 q^{8} +6.37896 q^{9} -1.40510 q^{10} +6.29563 q^{11} -3.06251 q^{12} -1.70453 q^{13} -4.44564 q^{14} -4.30312 q^{15} +1.00000 q^{16} -2.76477 q^{17} -6.37896 q^{18} +4.62385 q^{19} +1.40510 q^{20} -13.6148 q^{21} -6.29563 q^{22} -0.661500 q^{23} +3.06251 q^{24} -3.02570 q^{25} +1.70453 q^{26} -10.3481 q^{27} +4.44564 q^{28} +3.12091 q^{29} +4.30312 q^{30} +1.06486 q^{31} -1.00000 q^{32} -19.2804 q^{33} +2.76477 q^{34} +6.24656 q^{35} +6.37896 q^{36} -8.84817 q^{37} -4.62385 q^{38} +5.22014 q^{39} -1.40510 q^{40} -11.8647 q^{41} +13.6148 q^{42} +1.66327 q^{43} +6.29563 q^{44} +8.96306 q^{45} +0.661500 q^{46} +8.04992 q^{47} -3.06251 q^{48} +12.7637 q^{49} +3.02570 q^{50} +8.46712 q^{51} -1.70453 q^{52} +0.669690 q^{53} +10.3481 q^{54} +8.84597 q^{55} -4.44564 q^{56} -14.1606 q^{57} -3.12091 q^{58} +9.19448 q^{59} -4.30312 q^{60} -1.43078 q^{61} -1.06486 q^{62} +28.3586 q^{63} +1.00000 q^{64} -2.39503 q^{65} +19.2804 q^{66} +11.7814 q^{67} -2.76477 q^{68} +2.02585 q^{69} -6.24656 q^{70} -14.1229 q^{71} -6.37896 q^{72} +12.1127 q^{73} +8.84817 q^{74} +9.26624 q^{75} +4.62385 q^{76} +27.9881 q^{77} -5.22014 q^{78} +4.21790 q^{79} +1.40510 q^{80} +12.5543 q^{81} +11.8647 q^{82} -3.05791 q^{83} -13.6148 q^{84} -3.88477 q^{85} -1.66327 q^{86} -9.55780 q^{87} -6.29563 q^{88} +14.8286 q^{89} -8.96306 q^{90} -7.57773 q^{91} -0.661500 q^{92} -3.26114 q^{93} -8.04992 q^{94} +6.49696 q^{95} +3.06251 q^{96} -17.3954 q^{97} -12.7637 q^{98} +40.1596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

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