LMFDB - Embedded newform 8015.2.a.j.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:	$45$
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)

$f(q)$	$=$	$q-2.78224 q^{2} -1.94372 q^{3} +5.74083 q^{4} -1.00000 q^{5} +5.40788 q^{6} +1.00000 q^{7} -10.4079 q^{8} +0.778035 q^{9} +O(q^{10})$	\(q-2.78224 q^{2} -1.94372 q^{3} +5.74083 q^{4} -1.00000 q^{5} +5.40788 q^{6} +1.00000 q^{7} -10.4079 q^{8} +0.778035 q^{9} +2.78224 q^{10} +5.57674 q^{11} -11.1586 q^{12} -3.13703 q^{13} -2.78224 q^{14} +1.94372 q^{15} +17.4755 q^{16} +0.487717 q^{17} -2.16468 q^{18} -0.117408 q^{19} -5.74083 q^{20} -1.94372 q^{21} -15.5158 q^{22} +1.43138 q^{23} +20.2300 q^{24} +1.00000 q^{25} +8.72796 q^{26} +4.31887 q^{27} +5.74083 q^{28} +0.546299 q^{29} -5.40788 q^{30} -2.50454 q^{31} -27.8052 q^{32} -10.8396 q^{33} -1.35694 q^{34} -1.00000 q^{35} +4.46657 q^{36} -3.10821 q^{37} +0.326658 q^{38} +6.09750 q^{39} +10.4079 q^{40} +3.54481 q^{41} +5.40788 q^{42} -7.12652 q^{43} +32.0151 q^{44} -0.778035 q^{45} -3.98244 q^{46} +8.51221 q^{47} -33.9674 q^{48} +1.00000 q^{49} -2.78224 q^{50} -0.947983 q^{51} -18.0092 q^{52} -1.37462 q^{53} -12.0161 q^{54} -5.57674 q^{55} -10.4079 q^{56} +0.228209 q^{57} -1.51993 q^{58} -7.96427 q^{59} +11.1586 q^{60} +3.06805 q^{61} +6.96822 q^{62} +0.778035 q^{63} +42.4096 q^{64} +3.13703 q^{65} +30.1583 q^{66} -9.83777 q^{67} +2.79990 q^{68} -2.78220 q^{69} +2.78224 q^{70} -4.46978 q^{71} -8.09770 q^{72} +6.23736 q^{73} +8.64776 q^{74} -1.94372 q^{75} -0.674022 q^{76} +5.57674 q^{77} -16.9647 q^{78} +3.79686 q^{79} -17.4755 q^{80} -10.7288 q^{81} -9.86251 q^{82} +7.41470 q^{83} -11.1586 q^{84} -0.487717 q^{85} +19.8277 q^{86} -1.06185 q^{87} -58.0420 q^{88} -7.49022 q^{89} +2.16468 q^{90} -3.13703 q^{91} +8.21733 q^{92} +4.86812 q^{93} -23.6830 q^{94} +0.117408 q^{95} +54.0454 q^{96} -4.95705 q^{97} -2.78224 q^{98} +4.33890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) $ 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * 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 $

$2$	−2.78224	−1.96734	−0.983669	−	0.179988i	$-0.942394\pi$
$2$	−2.78224	−1.96734	−0.983669	+	0.179988i	$0.942394\pi$
$3$	−1.94372	−1.12221	−0.561103	−	0.827746i	$-0.689623\pi$
$3$	−1.94372	−1.12221	−0.561103	+	0.827746i	$0.689623\pi$
$4$	5.74083	2.87042
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.40788	2.20776
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−10.4079	−3.67974
$9$	0.778035	0.259345
$10$	2.78224	0.879820
$11$	5.57674	1.68145	0.840725	−	0.541462i	$-0.182129\pi$
$11$	5.57674	1.68145	0.840725	+	0.541462i	$0.182129\pi$
$12$	−11.1586	−3.22120
$13$	−3.13703	−0.870056	−0.435028	−	0.900417i	$-0.643261\pi$
$13$	−3.13703	−0.870056	−0.435028	+	0.900417i	$0.643261\pi$
$14$	−2.78224	−0.743584
$15$	1.94372	0.501866
$16$	17.4755	4.36888
$17$	0.487717	0.118289	0.0591443	−	0.998249i	$-0.481163\pi$
$17$	0.487717	0.118289	0.0591443	+	0.998249i	$0.481163\pi$
$18$	−2.16468	−0.510219
$19$	−0.117408	−0.0269353	−0.0134677	−	0.999909i	$-0.504287\pi$
$19$	−0.117408	−0.0269353	−0.0134677	+	0.999909i	$0.504287\pi$
$20$	−5.74083	−1.28369
$21$	−1.94372	−0.424154
$22$	−15.5158	−3.30798
$23$	1.43138	0.298464	0.149232	−	0.988802i	$-0.452320\pi$
$23$	1.43138	0.298464	0.149232	+	0.988802i	$0.452320\pi$
$24$	20.2300	4.12943
$25$	1.00000	0.200000
$26$	8.72796	1.71169
$27$	4.31887	0.831167
$28$	5.74083	1.08492
$29$	0.546299	0.101445	0.0507226	−	0.998713i	$-0.483848\pi$
$29$	0.546299	0.101445	0.0507226	+	0.998713i	$0.483848\pi$
$30$	−5.40788	−0.987339
$31$	−2.50454	−0.449829	−0.224914	−	0.974379i	$-0.572210\pi$
$31$	−2.50454	−0.449829	−0.224914	+	0.974379i	$0.572210\pi$
$32$	−27.8052	−4.91531
$33$	−10.8396	−1.88693
$34$	−1.35694	−0.232714
$35$	−1.00000	−0.169031
$36$	4.46657	0.744429
$37$	−3.10821	−0.510986	−0.255493	−	0.966811i	$-0.582238\pi$
$37$	−3.10821	−0.510986	−0.255493	+	0.966811i	$0.582238\pi$
$38$	0.326658	0.0529909
$39$	6.09750	0.976381
$40$	10.4079	1.64563
$41$	3.54481	0.553607	0.276803	−	0.960927i	$-0.410725\pi$
$41$	3.54481	0.553607	0.276803	+	0.960927i	$0.410725\pi$
$42$	5.40788	0.834454
$43$	−7.12652	−1.08678	−0.543392	−	0.839479i	$-0.682860\pi$
$43$	−7.12652	−1.08678	−0.543392	+	0.839479i	$0.682860\pi$
$44$	32.0151	4.82646
$45$	−0.778035	−0.115983
$46$	−3.98244	−0.587179
$47$	8.51221	1.24163	0.620817	−	0.783956i	$-0.286801\pi$
$47$	8.51221	1.24163	0.620817	+	0.783956i	$0.286801\pi$
$48$	−33.9674	−4.90278
$49$	1.00000	0.142857
$50$	−2.78224	−0.393467
$51$	−0.947983	−0.132744
$52$	−18.0092	−2.49742
$53$	−1.37462	−0.188818	−0.0944092	−	0.995533i	$-0.530096\pi$
$53$	−1.37462	−0.188818	−0.0944092	+	0.995533i	$0.530096\pi$
$54$	−12.0161	−1.63519
$55$	−5.57674	−0.751967
$56$	−10.4079	−1.39081
$57$	0.228209	0.0302270
$58$	−1.51993	−0.199577
$59$	−7.96427	−1.03686	−0.518430	−	0.855120i	$-0.673483\pi$
$59$	−7.96427	−1.03686	−0.518430	+	0.855120i	$0.673483\pi$
$60$	11.1586	1.44056
$61$	3.06805	0.392823	0.196412	−	0.980522i	$-0.437071\pi$
$61$	3.06805	0.392823	0.196412	+	0.980522i	$0.437071\pi$
$62$	6.96822	0.884965
$63$	0.778035	0.0980232
$64$	42.4096	5.30120
$65$	3.13703	0.389101
$66$	30.1583	3.71223
$67$	−9.83777	−1.20188	−0.600938	−	0.799296i	$-0.705206\pi$
$67$	−9.83777	−1.20188	−0.600938	+	0.799296i	$0.705206\pi$
$68$	2.79990	0.339538
$69$	−2.78220	−0.334938
$70$	2.78224	0.332541
$71$	−4.46978	−0.530465	−0.265232	−	0.964184i	$-0.585449\pi$
$71$	−4.46978	−0.530465	−0.265232	+	0.964184i	$0.585449\pi$
$72$	−8.09770	−0.954323
$73$	6.23736	0.730028	0.365014	−	0.931002i	$-0.381064\pi$
$73$	6.23736	0.730028	0.365014	+	0.931002i	$0.381064\pi$
$74$	8.64776	1.00528
$75$	−1.94372	−0.224441
$76$	−0.674022	−0.0773156
$77$	5.57674	0.635528
$78$	−16.9647	−1.92087
$79$	3.79686	0.427181	0.213590	−	0.976923i	$-0.431484\pi$
$79$	3.79686	0.427181	0.213590	+	0.976923i	$0.431484\pi$
$80$	−17.4755	−1.95382
$81$	−10.7288	−1.19209
$82$	−9.86251	−1.08913
$83$	7.41470	0.813869	0.406935	−	0.913457i	$-0.366598\pi$
$83$	7.41470	0.813869	0.406935	+	0.913457i	$0.366598\pi$
$84$	−11.1586	−1.21750
$85$	−0.487717	−0.0529003
$86$	19.8277	2.13807
$87$	−1.06185	−0.113842
$88$	−58.0420	−6.18730
$89$	−7.49022	−0.793962	−0.396981	−	0.917827i	$-0.629942\pi$
$89$	−7.49022	−0.793962	−0.396981	+	0.917827i	$0.629942\pi$
$90$	2.16468	0.228177
$91$	−3.13703	−0.328850
$92$	8.21733	0.856716
$93$	4.86812	0.504800
$94$	−23.6830	−2.44271
$95$	0.117408	0.0120458
$96$	54.0454	5.51599
$97$	−4.95705	−0.503312	−0.251656	−	0.967817i	$-0.580975\pi$
$97$	−4.95705	−0.503312	−0.251656	+	0.967817i	$0.580975\pi$
$98$	−2.78224	−0.281048
$99$	4.33890	0.436076
$100$	5.74083	0.574083
$101$	13.8827	1.38138	0.690690	−	0.723151i	$-0.257307\pi$
$101$	13.8827	1.38138	0.690690	+	0.723151i	$0.257307\pi$
$102$	2.63751	0.261153
$103$	−5.32304	−0.524495	−0.262247	−	0.965001i	$-0.584464\pi$
$103$	−5.32304	−0.524495	−0.262247	+	0.965001i	$0.584464\pi$
$104$	32.6498	3.20158
$105$	1.94372	0.189687
$106$	3.82451	0.371470
$107$	8.13776	0.786707	0.393353	−	0.919387i	$-0.371315\pi$
$107$	8.13776	0.786707	0.393353	+	0.919387i	$0.371315\pi$
$108$	24.7939	2.38580
$109$	−18.6041	−1.78195	−0.890974	−	0.454054i	$-0.849977\pi$
$109$	−18.6041	−1.78195	−0.890974	+	0.454054i	$0.849977\pi$
$110$	15.5158	1.47937
$111$	6.04147	0.573431
$112$	17.4755	1.65128
$113$	4.41640	0.415460	0.207730	−	0.978186i	$-0.433393\pi$
$113$	4.41640	0.415460	0.207730	+	0.978186i	$0.433393\pi$
$114$	−0.634930	−0.0594666
$115$	−1.43138	−0.133477
$116$	3.13621	0.291190
$117$	−2.44072	−0.225645
$118$	22.1585	2.03985
$119$	0.487717	0.0447089
$120$	−20.2300	−1.84674
$121$	20.1000	1.82727
$122$	−8.53603	−0.772816
$123$	−6.89011	−0.621261
$124$	−14.3781	−1.29120
$125$	−1.00000	−0.0894427
$126$	−2.16468	−0.192845
$127$	−20.1008	−1.78366	−0.891830	−	0.452371i	$-0.850578\pi$
$127$	−20.1008	−1.78366	−0.891830	+	0.452371i	$0.850578\pi$
$128$	−62.3831	−5.51394
$129$	13.8519	1.21960
$130$	−8.72796	−0.765492
$131$	8.38295	0.732422	0.366211	−	0.930532i	$-0.380655\pi$
$131$	8.38295	0.732422	0.366211	+	0.930532i	$0.380655\pi$
$132$	−62.2284	−5.41628
$133$	−0.117408	−0.0101806
$134$	27.3710	2.36449
$135$	−4.31887	−0.371709
$136$	−5.07610	−0.435272
$137$	−8.38240	−0.716157	−0.358078	−	0.933692i	$-0.616568\pi$
$137$	−8.38240	−0.716157	−0.358078	+	0.933692i	$0.616568\pi$
$138$	7.74074	0.658936
$139$	−11.4827	−0.973946	−0.486973	−	0.873417i	$-0.661899\pi$
$139$	−11.4827	−0.973946	−0.486973	+	0.873417i	$0.661899\pi$
$140$	−5.74083	−0.485189
$141$	−16.5453	−1.39337
$142$	12.4360	1.04360
$143$	−17.4944	−1.46296
$144$	13.5966	1.13305
$145$	−0.546299	−0.0453676
$146$	−17.3538	−1.43621
$147$	−1.94372	−0.160315
$148$	−17.8437	−1.46674
$149$	−16.6710	−1.36574	−0.682871	−	0.730539i	$-0.739269\pi$
$149$	−16.6710	−1.36574	−0.682871	+	0.730539i	$0.739269\pi$
$150$	5.40788	0.441551
$151$	−3.18558	−0.259238	−0.129619	−	0.991564i	$-0.541375\pi$
$151$	−3.18558	−0.259238	−0.129619	+	0.991564i	$0.541375\pi$
$152$	1.22197	0.0991150
$153$	0.379461	0.0306776
$154$	−15.5158	−1.25030
$155$	2.50454	0.201169
$156$	35.0047	2.80262
$157$	20.8419	1.66336	0.831681	−	0.555254i	$-0.187379\pi$
$157$	20.8419	1.66336	0.831681	+	0.555254i	$0.187379\pi$
$158$	−10.5638	−0.840409
$159$	2.67187	0.211893
$160$	27.8052	2.19819
$161$	1.43138	0.112809
$162$	29.8500	2.34523
$163$	−0.802220	−0.0628348	−0.0314174	−	0.999506i	$-0.510002\pi$
$163$	−0.802220	−0.0628348	−0.0314174	+	0.999506i	$0.510002\pi$
$164$	20.3502	1.58908
$165$	10.8396	0.843862
$166$	−20.6295	−1.60116
$167$	−16.3124	−1.26229	−0.631146	−	0.775664i	$-0.717415\pi$
$167$	−16.3124	−1.26229	−0.631146	+	0.775664i	$0.717415\pi$
$168$	20.2300	1.56078
$169$	−3.15904	−0.243003
$170$	1.35694	0.104073
$171$	−0.0913478	−0.00698554
$172$	−40.9122	−3.11952
$173$	14.8444	1.12860	0.564300	−	0.825569i	$-0.309146\pi$
$173$	14.8444	1.12860	0.564300	+	0.825569i	$0.309146\pi$
$174$	2.95432	0.223966
$175$	1.00000	0.0755929
$176$	97.4563	7.34605
$177$	15.4803	1.16357
$178$	20.8396	1.56199
$179$	−5.69367	−0.425565	−0.212783	−	0.977100i	$-0.568253\pi$
$179$	−5.69367	−0.425565	−0.212783	+	0.977100i	$0.568253\pi$
$180$	−4.46657	−0.332919
$181$	14.8835	1.10628	0.553141	−	0.833088i	$-0.313429\pi$
$181$	14.8835	1.10628	0.553141	+	0.833088i	$0.313429\pi$
$182$	8.72796	0.646959
$183$	−5.96342	−0.440828
$184$	−14.8977	−1.09827
$185$	3.10821	0.228520
$186$	−13.5442	−0.993112
$187$	2.71987	0.198897
$188$	48.8672	3.56401
$189$	4.31887	0.314152
$190$	−0.326658	−0.0236982
$191$	13.0492	0.944205	0.472102	−	0.881544i	$-0.343495\pi$
$191$	13.0492	0.944205	0.472102	+	0.881544i	$0.343495\pi$
$192$	−82.4323	−5.94904
$193$	−16.3698	−1.17832	−0.589161	−	0.808016i	$-0.700542\pi$
$193$	−16.3698	−1.17832	−0.589161	+	0.808016i	$0.700542\pi$
$194$	13.7917	0.990185
$195$	−6.09750	−0.436651
$196$	5.74083	0.410060
$197$	12.7000	0.904838	0.452419	−	0.891805i	$-0.350561\pi$
$197$	12.7000	0.904838	0.452419	+	0.891805i	$0.350561\pi$
$198$	−12.0718	−0.857909
$199$	−21.3969	−1.51679	−0.758394	−	0.651796i	$-0.774016\pi$
$199$	−21.3969	−1.51679	−0.758394	+	0.651796i	$0.774016\pi$
$200$	−10.4079	−0.735948
$201$	19.1218	1.34875
$202$	−38.6249	−2.71764
$203$	0.546299	0.0383427
$204$	−5.44221	−0.381031
$205$	−3.54481	−0.247581
$206$	14.8100	1.03186
$207$	1.11367	0.0774052
$208$	−54.8212	−3.80116
$209$	−0.654756	−0.0452904
$210$	−5.40788	−0.373179
$211$	10.0242	0.690095	0.345048	−	0.938585i	$-0.387863\pi$
$211$	10.0242	0.690095	0.345048	+	0.938585i	$0.387863\pi$
$212$	−7.89146	−0.541988
$213$	8.68798	0.595291
$214$	−22.6412	−1.54772
$215$	7.12652	0.486025
$216$	−44.9503	−3.05848
$217$	−2.50454	−0.170019
$218$	51.7609	3.50569
$219$	−12.1237	−0.819241
$220$	−32.0151	−2.15846
$221$	−1.52998	−0.102918
$222$	−16.8088	−1.12813
$223$	10.2861	0.688805	0.344402	−	0.938822i	$-0.388082\pi$
$223$	10.2861	0.688805	0.344402	+	0.938822i	$0.388082\pi$
$224$	−27.8052	−1.85781
$225$	0.778035	0.0518690
$226$	−12.2875	−0.817349
$227$	−18.4465	−1.22434	−0.612170	−	0.790727i	$-0.709703\pi$
$227$	−18.4465	−1.22434	−0.612170	+	0.790727i	$0.709703\pi$
$228$	1.31011	0.0867640
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	3.98244	0.262595
$231$	−10.8396	−0.713194
$232$	−5.68581	−0.373292
$233$	−11.2342	−0.735974	−0.367987	−	0.929831i	$-0.619953\pi$
$233$	−11.2342	−0.735974	−0.367987	+	0.929831i	$0.619953\pi$
$234$	6.79066	0.443919
$235$	−8.51221	−0.555275
$236$	−45.7216	−2.97622
$237$	−7.38003	−0.479384
$238$	−1.35694	−0.0879575
$239$	−9.69653	−0.627216	−0.313608	−	0.949552i	$-0.601538\pi$
$239$	−9.69653	−0.627216	−0.313608	+	0.949552i	$0.601538\pi$
$240$	33.9674	2.19259
$241$	−7.24762	−0.466860	−0.233430	−	0.972374i	$-0.574995\pi$
$241$	−7.24762	−0.466860	−0.233430	+	0.972374i	$0.574995\pi$
$242$	−55.9230	−3.59487
$243$	7.89708	0.506598
$244$	17.6132	1.12757
$245$	−1.00000	−0.0638877
$246$	19.1699	1.22223
$247$	0.368313	0.0234352
$248$	26.0669	1.65525
$249$	−14.4121	−0.913329
$250$	2.78224	0.175964
$251$	−19.0738	−1.20393	−0.601965	−	0.798522i	$-0.705615\pi$
$251$	−19.0738	−1.20393	−0.601965	+	0.798522i	$0.705615\pi$
$252$	4.46657	0.281368
$253$	7.98245	0.501852
$254$	55.9252	3.50906
$255$	0.947983	0.0593650
$256$	88.7453	5.54658
$257$	1.50662	0.0939803	0.0469902	−	0.998895i	$-0.485037\pi$
$257$	1.50662	0.0939803	0.0469902	+	0.998895i	$0.485037\pi$
$258$	−38.5394	−2.39936
$259$	−3.10821	−0.193135
$260$	18.0092	1.11688
$261$	0.425040	0.0263093
$262$	−23.3233	−1.44092
$263$	−1.03922	−0.0640808	−0.0320404	−	0.999487i	$-0.510201\pi$
$263$	−1.03922	−0.0640808	−0.0320404	+	0.999487i	$0.510201\pi$
$264$	112.817	6.94342
$265$	1.37462	0.0844422
$266$	0.326658	0.0200287
$267$	14.5589	0.890988
$268$	−56.4770	−3.44988
$269$	14.3703	0.876170	0.438085	−	0.898933i	$-0.355657\pi$
$269$	14.3703	0.876170	0.438085	+	0.898933i	$0.355657\pi$
$270$	12.0161	0.731277
$271$	−13.3122	−0.808659	−0.404329	−	0.914613i	$-0.632495\pi$
$271$	−13.3122	−0.808659	−0.404329	+	0.914613i	$0.632495\pi$
$272$	8.52309	0.516789
$273$	6.09750	0.369037
$274$	23.3218	1.40892
$275$	5.57674	0.336290
$276$	−15.9722	−0.961411
$277$	−6.34886	−0.381466	−0.190733	−	0.981642i	$-0.561086\pi$
$277$	−6.34886	−0.381466	−0.190733	+	0.981642i	$0.561086\pi$
$278$	31.9474	1.91608
$279$	−1.94862	−0.116661
$280$	10.4079	0.621990
$281$	23.8115	1.42048	0.710238	−	0.703961i	$-0.248587\pi$
$281$	23.8115	1.42048	0.710238	+	0.703961i	$0.248587\pi$
$282$	46.0330	2.74123
$283$	14.1075	0.838602	0.419301	−	0.907847i	$-0.362275\pi$
$283$	14.1075	0.838602	0.419301	+	0.907847i	$0.362275\pi$
$284$	−25.6602	−1.52266
$285$	−0.228209	−0.0135179
$286$	48.6735	2.87813
$287$	3.54481	0.209244
$288$	−21.6334	−1.27476
$289$	−16.7621	−0.986008
$290$	1.51993	0.0892535
$291$	9.63511	0.564820
$292$	35.8077	2.09548
$293$	19.7831	1.15574	0.577872	−	0.816127i	$-0.303883\pi$
$293$	19.7831	1.15574	0.577872	+	0.816127i	$0.303883\pi$
$294$	5.40788	0.315394
$295$	7.96427	0.463698
$296$	32.3498	1.88030
$297$	24.0852	1.39757
$298$	46.3826	2.68687
$299$	−4.49029	−0.259680
$300$	−11.1586	−0.644239
$301$	−7.12652	−0.410766
$302$	8.86302	0.510009
$303$	−26.9840	−1.55019
$304$	−2.05177	−0.117677
$305$	−3.06805	−0.175676
$306$	−1.05575	−0.0603532
$307$	8.57154	0.489204	0.244602	−	0.969624i	$-0.421343\pi$
$307$	8.57154	0.489204	0.244602	+	0.969624i	$0.421343\pi$
$308$	32.0151	1.82423
$309$	10.3465	0.588591
$310$	−6.96822	−0.395768
$311$	21.7294	1.23216	0.616080	−	0.787684i	$-0.288720\pi$
$311$	21.7294	1.23216	0.616080	+	0.787684i	$0.288720\pi$
$312$	−63.4620	−3.59283
$313$	3.83577	0.216810	0.108405	−	0.994107i	$-0.465426\pi$
$313$	3.83577	0.216810	0.108405	+	0.994107i	$0.465426\pi$
$314$	−57.9870	−3.27239
$315$	−0.778035	−0.0438373
$316$	21.7972	1.22619
$317$	15.8116	0.888067	0.444033	−	0.896010i	$-0.353547\pi$
$317$	15.8116	0.888067	0.444033	+	0.896010i	$0.353547\pi$
$318$	−7.43377	−0.416865
$319$	3.04657	0.170575
$320$	−42.4096	−2.37077
$321$	−15.8175	−0.882846
$322$	−3.98244	−0.221933
$323$	−0.0572620	−0.00318614
$324$	−61.5921	−3.42178
$325$	−3.13703	−0.174011
$326$	2.23197	0.123617
$327$	36.1611	1.99971
$328$	−36.8940	−2.03713
$329$	8.51221	0.469293
$330$	−30.1583	−1.66016
$331$	30.1385	1.65656	0.828280	−	0.560315i	$-0.189320\pi$
$331$	30.1385	1.65656	0.828280	+	0.560315i	$0.189320\pi$
$332$	42.5666	2.33614
$333$	−2.41829	−0.132522
$334$	45.3850	2.48336
$335$	9.83777	0.537495
$336$	−33.9674	−1.85308
$337$	5.14483	0.280257	0.140128	−	0.990133i	$-0.455248\pi$
$337$	5.14483	0.280257	0.140128	+	0.990133i	$0.455248\pi$
$338$	8.78920	0.478069
$339$	−8.58422	−0.466231
$340$	−2.79990	−0.151846
$341$	−13.9672	−0.756364
$342$	0.254151	0.0137429
$343$	1.00000	0.0539949
$344$	74.1720	3.99908
$345$	2.78220	0.149789
$346$	−41.3007	−2.22034
$347$	21.2267	1.13951	0.569755	−	0.821814i	$-0.307038\pi$
$347$	21.2267	1.13951	0.569755	+	0.821814i	$0.307038\pi$
$348$	−6.09590	−0.326775
$349$	14.6602	0.784742	0.392371	−	0.919807i	$-0.371655\pi$
$349$	14.6602	0.784742	0.392371	+	0.919807i	$0.371655\pi$
$350$	−2.78224	−0.148717
$351$	−13.5484	−0.723161
$352$	−155.062	−8.26485
$353$	24.2423	1.29029	0.645144	−	0.764061i	$-0.276798\pi$
$353$	24.2423	1.29029	0.645144	+	0.764061i	$0.276798\pi$
$354$	−43.0698	−2.28913
$355$	4.46978	0.237231
$356$	−43.0001	−2.27900
$357$	−0.947983	−0.0501726
$358$	15.8411	0.837230
$359$	20.6922	1.09209	0.546046	−	0.837755i	$-0.316132\pi$
$359$	20.6922	1.09209	0.546046	+	0.837755i	$0.316132\pi$
$360$	8.09770	0.426786
$361$	−18.9862	−0.999274
$362$	−41.4094	−2.17643
$363$	−39.0688	−2.05058
$364$	−18.0092	−0.943937
$365$	−6.23736	−0.326478
$366$	16.5916	0.867258
$367$	12.7286	0.664427	0.332214	−	0.943204i	$-0.392204\pi$
$367$	12.7286	0.664427	0.332214	+	0.943204i	$0.392204\pi$
$368$	25.0141	1.30395
$369$	2.75799	0.143575
$370$	−8.64776	−0.449576
$371$	−1.37462	−0.0713667
$372$	27.9470	1.44899
$373$	−25.3609	−1.31314	−0.656568	−	0.754267i	$-0.727993\pi$
$373$	−25.3609	−1.31314	−0.656568	+	0.754267i	$0.727993\pi$
$374$	−7.56732	−0.391297
$375$	1.94372	0.100373
$376$	−88.5941	−4.56889
$377$	−1.71376	−0.0882629
$378$	−12.0161	−0.618042
$379$	−2.25655	−0.115911	−0.0579555	−	0.998319i	$-0.518458\pi$
$379$	−2.25655	−0.115911	−0.0579555	+	0.998319i	$0.518458\pi$
$380$	0.674022	0.0345766
$381$	39.0703	2.00163
$382$	−36.3059	−1.85757
$383$	8.09569	0.413671	0.206835	−	0.978376i	$-0.433684\pi$
$383$	8.09569	0.413671	0.206835	+	0.978376i	$0.433684\pi$
$384$	121.255	6.18778
$385$	−5.57674	−0.284217
$386$	45.5445	2.31816
$387$	−5.54469	−0.281852
$388$	−28.4576	−1.44472
$389$	0.109502	0.00555196	0.00277598	−	0.999996i	$-0.499116\pi$
$389$	0.109502	0.00555196	0.00277598	+	0.999996i	$0.499116\pi$
$390$	16.9647	0.859040
$391$	0.698109	0.0353049
$392$	−10.4079	−0.525677
$393$	−16.2941	−0.821928
$394$	−35.3344	−1.78012
$395$	−3.79686	−0.191041
$396$	24.9089	1.25172
$397$	−10.7037	−0.537203	−0.268602	−	0.963251i	$-0.586562\pi$
$397$	−10.7037	−0.537203	−0.268602	+	0.963251i	$0.586562\pi$
$398$	59.5313	2.98403
$399$	0.228209	0.0114247
$400$	17.4755	0.873775
$401$	−13.3479	−0.666562	−0.333281	−	0.942828i	$-0.608156\pi$
$401$	−13.3479	−0.666562	−0.333281	+	0.942828i	$0.608156\pi$
$402$	−53.2015	−2.65345
$403$	7.85682	0.391376
$404$	79.6983	3.96514
$405$	10.7288	0.533117
$406$	−1.51993	−0.0754329
$407$	−17.3337	−0.859197
$408$	9.86649	0.488464
$409$	4.18739	0.207053	0.103527	−	0.994627i	$-0.466987\pi$
$409$	4.18739	0.207053	0.103527	+	0.994627i	$0.466987\pi$
$410$	9.86251	0.487074
$411$	16.2930	0.803675
$412$	−30.5587	−1.50552
$413$	−7.96427	−0.391896
$414$	−3.09848	−0.152282
$415$	−7.41470	−0.363973
$416$	87.2258	4.27659
$417$	22.3190	1.09297
$418$	1.82168	0.0891015
$419$	22.7097	1.10944	0.554721	−	0.832036i	$-0.312825\pi$
$419$	22.7097	1.10944	0.554721	+	0.832036i	$0.312825\pi$
$420$	11.1586	0.544482
$421$	−22.2324	−1.08354	−0.541770	−	0.840527i	$-0.682246\pi$
$421$	−22.2324	−1.08354	−0.541770	+	0.840527i	$0.682246\pi$
$422$	−27.8897	−1.35765
$423$	6.62280	0.322012
$424$	14.3069	0.694803
$425$	0.487717	0.0236577
$426$	−24.1720	−1.17114
$427$	3.06805	0.148473
$428$	46.7175	2.25818
$429$	34.0042	1.64174
$430$	−19.8277	−0.956175
$431$	−29.0720	−1.40035	−0.700175	−	0.713971i	$-0.746895\pi$
$431$	−29.0720	−1.40035	−0.700175	+	0.713971i	$0.746895\pi$
$432$	75.4744	3.63127
$433$	22.4927	1.08093	0.540466	−	0.841366i	$-0.318248\pi$
$433$	22.4927	1.08093	0.540466	+	0.841366i	$0.318248\pi$
$434$	6.96822	0.334485
$435$	1.06185	0.0509118
$436$	−106.803	−5.11493
$437$	−0.168056	−0.00803922
$438$	33.7309	1.61172
$439$	18.5841	0.886969	0.443485	−	0.896282i	$-0.353742\pi$
$439$	18.5841	0.886969	0.443485	+	0.896282i	$0.353742\pi$
$440$	58.0420	2.76705
$441$	0.778035	0.0370493
$442$	4.25677	0.202474
$443$	−20.2461	−0.961920	−0.480960	−	0.876743i	$-0.659712\pi$
$443$	−20.2461	−0.961920	−0.480960	+	0.876743i	$0.659712\pi$
$444$	34.6831	1.64599
$445$	7.49022	0.355070
$446$	−28.6182	−1.35511
$447$	32.4037	1.53264
$448$	42.4096	2.00367
$449$	5.64732	0.266513	0.133257	−	0.991082i	$-0.457457\pi$
$449$	5.64732	0.266513	0.133257	+	0.991082i	$0.457457\pi$
$450$	−2.16468	−0.102044
$451$	19.7685	0.930862
$452$	25.3538	1.19254
$453$	6.19186	0.290919
$454$	51.3226	2.40869
$455$	3.13703	0.147066
$456$	−2.37517	−0.111227
$457$	7.54033	0.352722	0.176361	−	0.984326i	$-0.443567\pi$
$457$	7.54033	0.352722	0.176361	+	0.984326i	$0.443567\pi$
$458$	−2.78224	−0.130005
$459$	2.10639	0.0983176
$460$	−8.21733	−0.383135
$461$	20.1481	0.938390	0.469195	−	0.883095i	$-0.344544\pi$
$461$	20.1481	0.938390	0.469195	+	0.883095i	$0.344544\pi$
$462$	30.1583	1.40309
$463$	8.12497	0.377599	0.188800	−	0.982016i	$-0.439540\pi$
$463$	8.12497	0.377599	0.188800	+	0.982016i	$0.439540\pi$
$464$	9.54684	0.443201
$465$	−4.86812	−0.225753
$466$	31.2561	1.44791
$467$	−25.7141	−1.18991	−0.594953	−	0.803760i	$-0.702829\pi$
$467$	−25.7141	−1.18991	−0.594953	+	0.803760i	$0.702829\pi$
$468$	−14.0118	−0.647694
$469$	−9.83777	−0.454266
$470$	23.6830	1.09241
$471$	−40.5107	−1.86663
$472$	82.8912	3.81538
$473$	−39.7428	−1.82737
$474$	20.5330	0.943111
$475$	−0.117408	−0.00538706
$476$	2.79990	0.128333
$477$	−1.06950	−0.0489692
$478$	26.9780	1.23395
$479$	18.2091	0.831997	0.415998	−	0.909365i	$-0.363432\pi$
$479$	18.2091	0.831997	0.415998	+	0.909365i	$0.363432\pi$
$480$	−54.0454	−2.46683
$481$	9.75054	0.444586
$482$	20.1646	0.918472
$483$	−2.78220	−0.126595
$484$	115.391	5.24504
$485$	4.95705	0.225088
$486$	−21.9715	−0.996649
$487$	43.6298	1.97706	0.988528	−	0.151038i	$-0.0482617\pi$
$487$	43.6298	1.97706	0.988528	+	0.151038i	$0.0482617\pi$
$488$	−31.9319	−1.44549
$489$	1.55929	0.0705135
$490$	2.78224	0.125689
$491$	−27.0554	−1.22100	−0.610498	−	0.792018i	$-0.709030\pi$
$491$	−27.0554	−1.22100	−0.610498	+	0.792018i	$0.709030\pi$
$492$	−39.5550	−1.78328
$493$	0.266439	0.0119998
$494$	−1.02473	−0.0461050
$495$	−4.33890	−0.195019
$496$	−43.7681	−1.96525
$497$	−4.46978	−0.200497
$498$	40.0978	1.79683
$499$	−14.4371	−0.646295	−0.323148	−	0.946349i	$-0.604741\pi$
$499$	−14.4371	−0.646295	−0.323148	+	0.946349i	$0.604741\pi$
$500$	−5.74083	−0.256738
$501$	31.7067	1.41655
$502$	53.0679	2.36854
$503$	−43.0224	−1.91827	−0.959137	−	0.282943i	$-0.908689\pi$
$503$	−43.0224	−1.91827	−0.959137	+	0.282943i	$0.908689\pi$
$504$	−8.09770	−0.360700
$505$	−13.8827	−0.617772
$506$	−22.2091	−0.987313
$507$	6.14028	0.272700
$508$	−115.396	−5.11985
$509$	−3.76591	−0.166921	−0.0834606	−	0.996511i	$-0.526597\pi$
$509$	−3.76591	−0.166921	−0.0834606	+	0.996511i	$0.526597\pi$
$510$	−2.63751	−0.116791
$511$	6.23736	0.275925
$512$	−122.144	−5.39806
$513$	−0.507071	−0.0223877
$514$	−4.19177	−0.184891
$515$	5.32304	0.234561
$516$	79.5217	3.50075
$517$	47.4704	2.08775
$518$	8.64776	0.379961
$519$	−28.8534	−1.26652
$520$	−32.6498	−1.43179
$521$	−3.71447	−0.162734	−0.0813669	−	0.996684i	$-0.525929\pi$
$521$	−3.71447	−0.162734	−0.0813669	+	0.996684i	$0.525929\pi$
$522$	−1.18256	−0.0517593
$523$	31.5270	1.37858	0.689289	−	0.724486i	$-0.257923\pi$
$523$	31.5270	1.37858	0.689289	+	0.724486i	$0.257923\pi$
$524$	48.1251	2.10236
$525$	−1.94372	−0.0848308
$526$	2.89135	0.126069
$527$	−1.22151	−0.0532096
$528$	−189.428	−8.24377
$529$	−20.9511	−0.910919
$530$	−3.82451	−0.166126
$531$	−6.19649	−0.268905
$532$	−0.674022	−0.0292225
$533$	−11.1202	−0.481669
$534$	−40.5062	−1.75287
$535$	−8.13776	−0.351826
$536$	102.390	4.42259
$537$	11.0669	0.477572
$538$	−39.9815	−1.72372
$539$	5.57674	0.240207
$540$	−24.7939	−1.06696
$541$	6.74356	0.289928	0.144964	−	0.989437i	$-0.453693\pi$
$541$	6.74356	0.289928	0.144964	+	0.989437i	$0.453693\pi$
$542$	37.0377	1.59090
$543$	−28.9293	−1.24147
$544$	−13.5611	−0.581426
$545$	18.6041	0.796911
$546$	−16.9647	−0.726021
$547$	−14.2023	−0.607248	−0.303624	−	0.952792i	$-0.598197\pi$
$547$	−14.2023	−0.607248	−0.303624	+	0.952792i	$0.598197\pi$
$548$	−48.1220	−2.05567
$549$	2.38705	0.101877
$550$	−15.5158	−0.661596
$551$	−0.0641400	−0.00273246
$552$	28.9568	1.23248
$553$	3.79686	0.161459
$554$	17.6640	0.750473
$555$	−6.04147	−0.256446
$556$	−65.9200	−2.79563
$557$	−44.5238	−1.88653	−0.943266	−	0.332037i	$-0.892264\pi$
$557$	−44.5238	−1.88653	−0.943266	+	0.332037i	$0.892264\pi$
$558$	5.42152	0.229511
$559$	22.3561	0.945563
$560$	−17.4755	−0.738475
$561$	−5.28666	−0.223203
$562$	−66.2493	−2.79456
$563$	−8.79919	−0.370842	−0.185421	−	0.982659i	$-0.559365\pi$
$563$	−8.79919	−0.370842	−0.185421	+	0.982659i	$0.559365\pi$
$564$	−94.9840	−3.99955
$565$	−4.41640	−0.185799
$566$	−39.2503	−1.64981
$567$	−10.7288	−0.450566
$568$	46.5209	1.95197
$569$	−2.46464	−0.103323	−0.0516616	−	0.998665i	$-0.516452\pi$
$569$	−2.46464	−0.103323	−0.0516616	+	0.998665i	$0.516452\pi$
$570$	0.634930	0.0265943
$571$	1.14478	0.0479075	0.0239538	−	0.999713i	$-0.492375\pi$
$571$	1.14478	0.0479075	0.0239538	+	0.999713i	$0.492375\pi$
$572$	−100.432	−4.19929
$573$	−25.3639	−1.05959
$574$	−9.86251	−0.411653
$575$	1.43138	0.0596928
$576$	32.9962	1.37484
$577$	−36.9154	−1.53681	−0.768405	−	0.639964i	$-0.778949\pi$
$577$	−36.9154	−1.53681	−0.768405	+	0.639964i	$0.778949\pi$
$578$	46.6362	1.93981
$579$	31.8182	1.32232
$580$	−3.13621	−0.130224
$581$	7.41470	0.307614
$582$	−26.8071	−1.11119
$583$	−7.66589	−0.317489
$584$	−64.9177	−2.68631
$585$	2.44072	0.100911
$586$	−55.0414	−2.27374
$587$	23.6701	0.976970	0.488485	−	0.872572i	$-0.337550\pi$
$587$	23.6701	0.976970	0.488485	+	0.872572i	$0.337550\pi$
$588$	−11.1586	−0.460171
$589$	0.294054	0.0121163
$590$	−22.1585	−0.912250
$591$	−24.6852	−1.01541
$592$	−54.3175	−2.23243
$593$	33.1872	1.36284	0.681418	−	0.731894i	$-0.261364\pi$
$593$	33.1872	1.36284	0.681418	+	0.731894i	$0.261364\pi$
$594$	−67.0107	−2.74948
$595$	−0.487717	−0.0199944
$596$	−95.7054	−3.92025
$597$	41.5896	1.70215
$598$	12.4930	0.510879
$599$	1.00575	0.0410936	0.0205468	−	0.999789i	$-0.493459\pi$
$599$	1.00575	0.0410936	0.0205468	+	0.999789i	$0.493459\pi$
$600$	20.2300	0.825885
$601$	14.9329	0.609128	0.304564	−	0.952492i	$-0.401489\pi$
$601$	14.9329	0.609128	0.304564	+	0.952492i	$0.401489\pi$
$602$	19.8277	0.808115
$603$	−7.65414	−0.311701
$604$	−18.2879	−0.744122
$605$	−20.1000	−0.817182
$606$	75.0759	3.04975
$607$	5.99005	0.243129	0.121564	−	0.992584i	$-0.461209\pi$
$607$	5.99005	0.243129	0.121564	+	0.992584i	$0.461209\pi$
$608$	3.26456	0.132395
$609$	−1.06185	−0.0430283
$610$	8.53603	0.345614
$611$	−26.7031	−1.08029
$612$	2.17842	0.0880575
$613$	2.16253	0.0873439	0.0436719	−	0.999046i	$-0.486094\pi$
$613$	2.16253	0.0873439	0.0436719	+	0.999046i	$0.486094\pi$
$614$	−23.8480	−0.962428
$615$	6.89011	0.277836
$616$	−58.0420	−2.33858
$617$	35.8291	1.44243	0.721213	−	0.692713i	$-0.243585\pi$
$617$	35.8291	1.44243	0.721213	+	0.692713i	$0.243585\pi$
$618$	−28.7864	−1.15796
$619$	−31.3727	−1.26098	−0.630488	−	0.776199i	$-0.717145\pi$
$619$	−31.3727	−1.26098	−0.630488	+	0.776199i	$0.717145\pi$
$620$	14.3781	0.577440
$621$	6.18196	0.248073
$622$	−60.4562	−2.42407
$623$	−7.49022	−0.300089
$624$	106.557	4.26569
$625$	1.00000	0.0400000
$626$	−10.6720	−0.426539
$627$	1.27266	0.0508251
$628$	119.650	4.77454
$629$	−1.51592	−0.0604438
$630$	2.16468	0.0862428
$631$	−49.6328	−1.97585	−0.987925	−	0.154932i	$-0.950484\pi$
$631$	−49.6328	−1.97585	−0.987925	+	0.154932i	$0.950484\pi$
$632$	−39.5173	−1.57191
$633$	−19.4842	−0.774429
$634$	−43.9915	−1.74713
$635$	20.1008	0.797677
$636$	15.3388	0.608222
$637$	−3.13703	−0.124294
$638$	−8.47626	−0.335578
$639$	−3.47764	−0.137574
$640$	62.3831	2.46591
$641$	8.61495	0.340270	0.170135	−	0.985421i	$-0.445580\pi$
$641$	8.61495	0.340270	0.170135	+	0.985421i	$0.445580\pi$
$642$	44.0080	1.73686
$643$	3.66497	0.144532	0.0722661	−	0.997385i	$-0.476977\pi$
$643$	3.66497	0.144532	0.0722661	+	0.997385i	$0.476977\pi$
$644$	8.21733	0.323808
$645$	−13.8519	−0.545420
$646$	0.159316	0.00626822
$647$	−33.7974	−1.32871	−0.664356	−	0.747417i	$-0.731294\pi$
$647$	−33.7974	−1.32871	−0.664356	+	0.747417i	$0.731294\pi$
$648$	111.664	4.38657
$649$	−44.4147	−1.74343
$650$	8.72796	0.342339
$651$	4.86812	0.190797
$652$	−4.60541	−0.180362
$653$	−48.6804	−1.90501	−0.952505	−	0.304524i	$-0.901503\pi$
$653$	−48.6804	−1.90501	−0.952505	+	0.304524i	$0.901503\pi$
$654$	−100.609	−3.93411
$655$	−8.38295	−0.327549
$656$	61.9474	2.41864
$657$	4.85289	0.189329
$658$	−23.6830	−0.923258
$659$	32.9604	1.28396	0.641978	−	0.766723i	$-0.278114\pi$
$659$	32.9604	1.28396	0.641978	+	0.766723i	$0.278114\pi$
$660$	62.2284	2.42224
$661$	19.5993	0.762323	0.381161	−	0.924509i	$-0.375524\pi$
$661$	19.5993	0.762323	0.381161	+	0.924509i	$0.375524\pi$
$662$	−83.8523	−3.25901
$663$	2.97385	0.115495
$664$	−77.1713	−2.99483
$665$	0.117408	0.00455290
$666$	6.72826	0.260715
$667$	0.781963	0.0302777
$668$	−93.6469	−3.62331
$669$	−19.9932	−0.772981
$670$	−27.3710	−1.05743
$671$	17.1097	0.660513
$672$	54.0454	2.08485
$673$	4.38389	0.168987	0.0844934	−	0.996424i	$-0.473073\pi$
$673$	4.38389	0.168987	0.0844934	+	0.996424i	$0.473073\pi$
$674$	−14.3141	−0.551360
$675$	4.31887	0.166233
$676$	−18.1355	−0.697521
$677$	5.32785	0.204766	0.102383	−	0.994745i	$-0.467353\pi$
$677$	5.32785	0.204766	0.102383	+	0.994745i	$0.467353\pi$
$678$	23.8833	0.917234
$679$	−4.95705	−0.190234
$680$	5.07610	0.194659
$681$	35.8548	1.37396
$682$	38.8599	1.48802
$683$	−15.6930	−0.600475	−0.300237	−	0.953864i	$-0.597066\pi$
$683$	−15.6930	−0.600475	−0.300237	+	0.953864i	$0.597066\pi$
$684$	−0.524413	−0.0200514
$685$	8.38240	0.320275
$686$	−2.78224	−0.106226
$687$	−1.94372	−0.0741574
$688$	−124.540	−4.74803
$689$	4.31222	0.164283
$690$	−7.74074	−0.294685
$691$	33.9104	1.29001	0.645007	−	0.764177i	$-0.276855\pi$
$691$	33.9104	1.29001	0.645007	+	0.764177i	$0.276855\pi$
$692$	85.2194	3.23956
$693$	4.33890	0.164821
$694$	−59.0578	−2.24180
$695$	11.4827	0.435562
$696$	11.0516	0.418910
$697$	1.72886	0.0654854
$698$	−40.7881	−1.54385
$699$	21.8360	0.825914
$700$	5.74083	0.216983
$701$	52.3143	1.97588	0.987941	−	0.154830i	$-0.0494830\pi$
$701$	52.3143	1.97588	0.987941	+	0.154830i	$0.0494830\pi$
$702$	37.6949	1.42270
$703$	0.364929	0.0137636
$704$	236.507	8.91371
$705$	16.5453	0.623133
$706$	−67.4478	−2.53843
$707$	13.8827	0.522113
$708$	88.8698	3.33993
$709$	0.307046	0.0115313	0.00576567	−	0.999983i	$-0.498165\pi$
$709$	0.307046	0.0115313	0.00576567	+	0.999983i	$0.498165\pi$
$710$	−12.4360	−0.466714
$711$	2.95410	0.110787
$712$	77.9573	2.92157
$713$	−3.58495	−0.134258
$714$	2.63751	0.0987064
$715$	17.4944	0.654253
$716$	−32.6864	−1.22155
$717$	18.8473	0.703866
$718$	−57.5706	−2.14851
$719$	−25.9565	−0.968016	−0.484008	−	0.875064i	$-0.660819\pi$
$719$	−25.9565	−0.968016	−0.484008	+	0.875064i	$0.660819\pi$
$720$	−13.5966	−0.506714
$721$	−5.32304	−0.198240
$722$	52.8241	1.96591
$723$	14.0873	0.523913
$724$	85.4436	3.17549
$725$	0.546299	0.0202890
$726$	108.698	4.03418
$727$	−23.0447	−0.854680	−0.427340	−	0.904091i	$-0.640549\pi$
$727$	−23.0447	−0.854680	−0.427340	+	0.904091i	$0.640549\pi$
$728$	32.6498	1.21008
$729$	16.8366	0.623579
$730$	17.3538	0.642293
$731$	−3.47572	−0.128554
$732$	−34.2350	−1.26536
$733$	−43.3765	−1.60215	−0.801074	−	0.598566i	$-0.795738\pi$
$733$	−43.3765	−1.60215	−0.801074	+	0.598566i	$0.795738\pi$
$734$	−35.4140	−1.30715
$735$	1.94372	0.0716951
$736$	−39.7999	−1.46704
$737$	−54.8627	−2.02089
$738$	−7.67338	−0.282461
$739$	−36.8029	−1.35382	−0.676908	−	0.736067i	$-0.736681\pi$
$739$	−36.8029	−1.35382	−0.676908	+	0.736067i	$0.736681\pi$
$740$	17.8437	0.655947
$741$	−0.715897	−0.0262991
$742$	3.82451	0.140402
$743$	3.22736	0.118400	0.0592002	−	0.998246i	$-0.481145\pi$
$743$	3.22736	0.118400	0.0592002	+	0.998246i	$0.481145\pi$
$744$	−50.6668	−1.85753
$745$	16.6710	0.610778
$746$	70.5599	2.58338
$747$	5.76890	0.211073
$748$	15.6143	0.570916
$749$	8.13776	0.297347
$750$	−5.40788	−0.197468
$751$	−33.0318	−1.20535	−0.602674	−	0.797988i	$-0.705898\pi$
$751$	−33.0318	−1.20535	−0.602674	+	0.797988i	$0.705898\pi$
$752$	148.755	5.42454
$753$	37.0741	1.35106
$754$	4.76807	0.173643
$755$	3.18558	0.115935
$756$	24.7939	0.901746
$757$	−32.4642	−1.17993	−0.589966	−	0.807428i	$-0.700859\pi$
$757$	−32.4642	−1.17993	−0.589966	+	0.807428i	$0.700859\pi$
$758$	6.27824	0.228036
$759$	−15.5156	−0.563181
$760$	−1.22197	−0.0443256
$761$	−46.9899	−1.70338	−0.851692	−	0.524043i	$-0.824423\pi$
$761$	−46.9899	−1.70338	−0.851692	+	0.524043i	$0.824423\pi$
$762$	−108.703	−3.93789
$763$	−18.6041	−0.673513
$764$	74.9131	2.71026
$765$	−0.379461	−0.0137194
$766$	−22.5241	−0.813830
$767$	24.9842	0.902126
$768$	−172.496	−6.22440
$769$	−43.4885	−1.56824	−0.784118	−	0.620611i	$-0.786884\pi$
$769$	−43.4885	−1.56824	−0.784118	+	0.620611i	$0.786884\pi$
$770$	15.5158	0.559151
$771$	−2.92844	−0.105465
$772$	−93.9761	−3.38227
$773$	−31.4341	−1.13060	−0.565302	−	0.824884i	$-0.691241\pi$
$773$	−31.4341	−1.13060	−0.565302	+	0.824884i	$0.691241\pi$
$774$	15.4266	0.554498
$775$	−2.50454	−0.0899657
$776$	51.5924	1.85206
$777$	6.04147	0.216737
$778$	−0.304660	−0.0109226
$779$	−0.416191	−0.0149116
$780$	−35.0047	−1.25337
$781$	−24.9268	−0.891950
$782$	−1.94230	−0.0694567
$783$	2.35939	0.0843178
$784$	17.4755	0.624125
$785$	−20.8419	−0.743878
$786$	45.3340	1.61701
$787$	9.39616	0.334937	0.167468	−	0.985877i	$-0.446441\pi$
$787$	9.39616	0.334937	0.167468	+	0.985877i	$0.446441\pi$
$788$	72.9087	2.59726
$789$	2.01994	0.0719119
$790$	10.5638	0.375842
$791$	4.41640	0.157029
$792$	−45.1588	−1.60465
$793$	−9.62456	−0.341778
$794$	29.7802	1.05686
$795$	−2.67187	−0.0947615
$796$	−122.836	−4.35381
$797$	17.2829	0.612191	0.306096	−	0.952001i	$-0.400977\pi$
$797$	17.2829	0.612191	0.306096	+	0.952001i	$0.400977\pi$
$798$	−0.634930	−0.0224763
$799$	4.15155	0.146871
$800$	−27.8052	−0.983062
$801$	−5.82766	−0.205910
$802$	37.1370	1.31135
$803$	34.7841	1.22751
$804$	109.775	3.87148
$805$	−1.43138	−0.0504496
$806$	−21.8595	−0.769968
$807$	−27.9317	−0.983243
$808$	−144.489	−5.08312
$809$	31.7140	1.11501	0.557503	−	0.830175i	$-0.311759\pi$
$809$	31.7140	1.11501	0.557503	+	0.830175i	$0.311759\pi$
$810$	−29.8500	−1.04882
$811$	47.6221	1.67224	0.836120	−	0.548547i	$-0.184819\pi$
$811$	47.6221	1.67224	0.836120	+	0.548547i	$0.184819\pi$
$812$	3.13621	0.110059
$813$	25.8752	0.907481
$814$	48.2263	1.69033
$815$	0.802220	0.0281006
$816$	−16.5665	−0.579943
$817$	0.836713	0.0292729
$818$	−11.6503	−0.407344
$819$	−2.44072	−0.0852857
$820$	−20.3502	−0.710659
$821$	−12.8101	−0.447077	−0.223538	−	0.974695i	$-0.571761\pi$
$821$	−12.8101	−0.447077	−0.223538	+	0.974695i	$0.571761\pi$
$822$	−45.3310	−1.58110
$823$	−15.0843	−0.525807	−0.262904	−	0.964822i	$-0.584680\pi$
$823$	−15.0843	−0.525807	−0.262904	+	0.964822i	$0.584680\pi$
$824$	55.4016	1.93001
$825$	−10.8396	−0.377387
$826$	22.1585	0.770992
$827$	−18.9333	−0.658376	−0.329188	−	0.944264i	$-0.606775\pi$
$827$	−18.9333	−0.658376	−0.329188	+	0.944264i	$0.606775\pi$
$828$	6.39337	0.222185
$829$	−8.16070	−0.283433	−0.141716	−	0.989907i	$-0.545262\pi$
$829$	−8.16070	−0.283433	−0.141716	+	0.989907i	$0.545262\pi$
$830$	20.6295	0.716059
$831$	12.3404	0.428083
$832$	−133.040	−4.61234
$833$	0.487717	0.0168984
$834$	−62.0968	−2.15024
$835$	16.3124	0.564514
$836$	−3.75884	−0.130002
$837$	−10.8168	−0.373883
$838$	−63.1838	−2.18265
$839$	−52.6026	−1.81604	−0.908022	−	0.418922i	$-0.862408\pi$
$839$	−52.6026	−1.81604	−0.908022	+	0.418922i	$0.862408\pi$
$840$	−20.2300	−0.698000
$841$	−28.7016	−0.989709
$842$	61.8558	2.13169
$843$	−46.2829	−1.59407
$844$	57.5473	1.98086
$845$	3.15904	0.108674
$846$	−18.4262	−0.633506
$847$	20.1000	0.690645
$848$	−24.0222	−0.824925
$849$	−27.4209	−0.941084
$850$	−1.35694	−0.0465427
$851$	−4.44903	−0.152511
$852$	49.8763	1.70873
$853$	−16.0377	−0.549119	−0.274560	−	0.961570i	$-0.588532\pi$
$853$	−16.0377	−0.549119	−0.274560	+	0.961570i	$0.588532\pi$
$854$	−8.53603	−0.292097
$855$	0.0913478	0.00312403
$856$	−84.6968	−2.89488
$857$	0.744503	0.0254317	0.0127159	−	0.999919i	$-0.495952\pi$
$857$	0.744503	0.0254317	0.0127159	+	0.999919i	$0.495952\pi$
$858$	−94.6076	−3.22985
$859$	−46.5537	−1.58839	−0.794195	−	0.607662i	$-0.792107\pi$
$859$	−46.5537	−1.58839	−0.794195	+	0.607662i	$0.792107\pi$
$860$	40.9122	1.39509
$861$	−6.89011	−0.234814
$862$	80.8852	2.75496
$863$	−3.80777	−0.129618	−0.0648090	−	0.997898i	$-0.520644\pi$
$863$	−3.80777	−0.129618	−0.0648090	+	0.997898i	$0.520644\pi$
$864$	−120.087	−4.08544
$865$	−14.8444	−0.504726
$866$	−62.5801	−2.12656
$867$	32.5808	1.10650
$868$	−14.3781	−0.488026
$869$	21.1741	0.718283
$870$	−2.95432	−0.100161
$871$	30.8614	1.04570
$872$	193.629	6.55711
$873$	−3.85676	−0.130532
$874$	0.467572	0.0158159
$875$	−1.00000	−0.0338062
$876$	−69.6000	−2.35156
$877$	−3.45160	−0.116552	−0.0582761	−	0.998301i	$-0.518560\pi$
$877$	−3.45160	−0.116552	−0.0582761	+	0.998301i	$0.518560\pi$
$878$	−51.7052	−1.74497
$879$	−38.4528	−1.29698
$880$	−97.4563	−3.28525
$881$	−47.8380	−1.61170	−0.805851	−	0.592118i	$-0.798292\pi$
$881$	−47.8380	−1.61170	−0.805851	+	0.592118i	$0.798292\pi$
$882$	−2.16468	−0.0728885
$883$	12.7248	0.428223	0.214111	−	0.976809i	$-0.431314\pi$
$883$	12.7248	0.428223	0.214111	+	0.976809i	$0.431314\pi$
$884$	−8.78337	−0.295417
$885$	−15.4803	−0.520364
$886$	56.3293	1.89242
$887$	−53.0756	−1.78210	−0.891052	−	0.453900i	$-0.850032\pi$
$887$	−53.0756	−1.78210	−0.891052	+	0.453900i	$0.850032\pi$
$888$	−62.8789	−2.11008
$889$	−20.1008	−0.674160
$890$	−20.8396	−0.698543
$891$	−59.8315	−2.00443
$892$	59.0505	1.97716
$893$	−0.999404	−0.0334438
$894$	−90.1547	−3.01522
$895$	5.69367	0.190319
$896$	−62.3831	−2.08407
$897$	8.72785	0.291415
$898$	−15.7122	−0.524322
$899$	−1.36823	−0.0456329
$900$	4.46657	0.148886
$901$	−0.670425	−0.0223351
$902$	−55.0006	−1.83132
$903$	13.8519	0.460964
$904$	−45.9653	−1.52878
$905$	−14.8835	−0.494744
$906$	−17.2272	−0.572335
$907$	47.1236	1.56471	0.782357	−	0.622831i	$-0.214017\pi$
$907$	47.1236	1.56471	0.782357	+	0.622831i	$0.214017\pi$
$908$	−105.898	−3.51436
$909$	10.8012	0.358254
$910$	−8.72796	−0.289329
$911$	−42.4881	−1.40769	−0.703847	−	0.710351i	$-0.748536\pi$
$911$	−42.4881	−1.40769	−0.703847	+	0.710351i	$0.748536\pi$
$912$	3.98806	0.132058
$913$	41.3499	1.36848
$914$	−20.9790	−0.693923
$915$	5.96342	0.197144
$916$	5.74083	0.189682
$917$	8.38295	0.276829
$918$	−5.86046	−0.193424
$919$	48.6224	1.60391	0.801953	−	0.597387i	$-0.203794\pi$
$919$	48.6224	1.60391	0.801953	+	0.597387i	$0.203794\pi$
$920$	14.8977	0.491161
$921$	−16.6606	−0.548987
$922$	−56.0567	−1.84613
$923$	14.0218	0.461534
$924$	−62.2284	−2.04716
$925$	−3.10821	−0.102197
$926$	−22.6056	−0.742865
$927$	−4.14152	−0.136025
$928$	−15.1899	−0.498634
$929$	−0.601025	−0.0197190	−0.00985949	−	0.999951i	$-0.503138\pi$
$929$	−0.601025	−0.0197190	−0.00985949	+	0.999951i	$0.503138\pi$
$930$	13.5442	0.444133
$931$	−0.117408	−0.00384790
$932$	−64.4934	−2.11255
$933$	−42.2357	−1.38274
$934$	71.5426	2.34095
$935$	−2.71987	−0.0889492
$936$	25.4027	0.830314
$937$	−42.6345	−1.39281	−0.696404	−	0.717650i	$-0.745218\pi$
$937$	−42.6345	−1.39281	−0.696404	+	0.717650i	$0.745218\pi$
$938$	27.3710	0.893695
$939$	−7.45565	−0.243306
$940$	−48.8672	−1.59387
$941$	−19.7280	−0.643115	−0.321558	−	0.946890i	$-0.604206\pi$
$941$	−19.7280	−0.643115	−0.321558	+	0.946890i	$0.604206\pi$
$942$	112.710	3.67230
$943$	5.07399	0.165232
$944$	−139.180	−4.52991
$945$	−4.31887	−0.140493
$946$	110.574	3.59506
$947$	7.72331	0.250974	0.125487	−	0.992095i	$-0.459951\pi$
$947$	7.72331	0.250974	0.125487	+	0.992095i	$0.459951\pi$
$948$	−42.3675	−1.37603
$949$	−19.5668	−0.635165
$950$	0.326658	0.0105982
$951$	−30.7332	−0.996594
$952$	−5.07610	−0.164517
$953$	21.5006	0.696473	0.348237	−	0.937407i	$-0.386781\pi$
$953$	21.5006	0.696473	0.348237	+	0.937407i	$0.386781\pi$
$954$	2.97561	0.0963389
$955$	−13.0492	−0.422261
$956$	−55.6662	−1.80037
$957$	−5.92166	−0.191420
$958$	−50.6621	−1.63682
$959$	−8.38240	−0.270682
$960$	82.4323	2.66049
$961$	−24.7273	−0.797654
$962$	−27.1283	−0.874651
$963$	6.33146	0.204029
$964$	−41.6074	−1.34008
$965$	16.3698	0.526962
$966$	7.74074	0.249054
$967$	3.94146	0.126749	0.0633744	−	0.997990i	$-0.479814\pi$
$967$	3.94146	0.126749	0.0633744	+	0.997990i	$0.479814\pi$
$968$	−209.199	−6.72390
$969$	0.111301	0.00357551
$970$	−13.7917	−0.442824
$971$	−35.6820	−1.14509	−0.572545	−	0.819873i	$-0.694044\pi$
$971$	−35.6820	−1.14509	−0.572545	+	0.819873i	$0.694044\pi$
$972$	45.3358	1.45415
$973$	−11.4827	−0.368117
$974$	−121.388	−3.88954
$975$	6.09750	0.195276
$976$	53.6157	1.71620
$977$	−4.21695	−0.134912	−0.0674561	−	0.997722i	$-0.521488\pi$
$977$	−4.21695	−0.134912	−0.0674561	+	0.997722i	$0.521488\pi$
$978$	−4.33831	−0.138724
$979$	−41.7710	−1.33501
$980$	−5.74083	−0.183384
$981$	−14.4746	−0.462140
$982$	75.2746	2.40211
$983$	48.8294	1.55742	0.778708	−	0.627387i	$-0.215876\pi$
$983$	48.8294	1.55742	0.778708	+	0.627387i	$0.215876\pi$
$984$	71.7115	2.28608
$985$	−12.7000	−0.404656
$986$	−0.741296	−0.0236077
$987$	−16.5453	−0.526644
$988$	2.11443	0.0672689
$989$	−10.2008	−0.324366
$990$	12.0718	0.383668
$991$	−11.0045	−0.349570	−0.174785	−	0.984607i	$-0.555923\pi$
$991$	−11.0045	−0.349570	−0.174785	+	0.984607i	$0.555923\pi$
$992$	69.6392	2.21105
$993$	−58.5806	−1.85900
$994$	12.4360	0.394445
$995$	21.3969	0.678328
$996$	−82.7374	−2.62163
$997$	7.84526	0.248462	0.124231	−	0.992253i	$-0.460354\pi$
$997$	7.84526	0.248462	0.124231	+	0.992253i	$0.460354\pi$
$998$	40.1675	1.27148
$999$	−13.4239	−0.424715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.1	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.1	✓	45	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)

\(f(q)\)	\(=\)	\(q-2.78224 q^{2} -1.94372 q^{3} +5.74083 q^{4} -1.00000 q^{5} +5.40788 q^{6} +1.00000 q^{7} -10.4079 q^{8} +0.778035 q^{9} +O(q^{10})\)	\(q-2.78224 q^{2} -1.94372 q^{3} +5.74083 q^{4} -1.00000 q^{5} +5.40788 q^{6} +1.00000 q^{7} -10.4079 q^{8} +0.778035 q^{9} +2.78224 q^{10} +5.57674 q^{11} -11.1586 q^{12} -3.13703 q^{13} -2.78224 q^{14} +1.94372 q^{15} +17.4755 q^{16} +0.487717 q^{17} -2.16468 q^{18} -0.117408 q^{19} -5.74083 q^{20} -1.94372 q^{21} -15.5158 q^{22} +1.43138 q^{23} +20.2300 q^{24} +1.00000 q^{25} +8.72796 q^{26} +4.31887 q^{27} +5.74083 q^{28} +0.546299 q^{29} -5.40788 q^{30} -2.50454 q^{31} -27.8052 q^{32} -10.8396 q^{33} -1.35694 q^{34} -1.00000 q^{35} +4.46657 q^{36} -3.10821 q^{37} +0.326658 q^{38} +6.09750 q^{39} +10.4079 q^{40} +3.54481 q^{41} +5.40788 q^{42} -7.12652 q^{43} +32.0151 q^{44} -0.778035 q^{45} -3.98244 q^{46} +8.51221 q^{47} -33.9674 q^{48} +1.00000 q^{49} -2.78224 q^{50} -0.947983 q^{51} -18.0092 q^{52} -1.37462 q^{53} -12.0161 q^{54} -5.57674 q^{55} -10.4079 q^{56} +0.228209 q^{57} -1.51993 q^{58} -7.96427 q^{59} +11.1586 q^{60} +3.06805 q^{61} +6.96822 q^{62} +0.778035 q^{63} +42.4096 q^{64} +3.13703 q^{65} +30.1583 q^{66} -9.83777 q^{67} +2.79990 q^{68} -2.78220 q^{69} +2.78224 q^{70} -4.46978 q^{71} -8.09770 q^{72} +6.23736 q^{73} +8.64776 q^{74} -1.94372 q^{75} -0.674022 q^{76} +5.57674 q^{77} -16.9647 q^{78} +3.79686 q^{79} -17.4755 q^{80} -10.7288 q^{81} -9.86251 q^{82} +7.41470 q^{83} -11.1586 q^{84} -0.487717 q^{85} +19.8277 q^{86} -1.06185 q^{87} -58.0420 q^{88} -7.49022 q^{89} +2.16468 q^{90} -3.13703 q^{91} +8.21733 q^{92} +4.86812 q^{93} -23.6830 q^{94} +0.117408 q^{95} +54.0454 q^{96} -4.95705 q^{97} -2.78224 q^{98} +4.33890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

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