LMFDB - Embedded newform 8015.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.62540 q^{2} -0.161903 q^{3} +4.89272 q^{4} -1.00000 q^{5} +0.425059 q^{6} -1.00000 q^{7} -7.59456 q^{8} -2.97379 q^{9} +O(q^{10})$	\(q-2.62540 q^{2} -0.161903 q^{3} +4.89272 q^{4} -1.00000 q^{5} +0.425059 q^{6} -1.00000 q^{7} -7.59456 q^{8} -2.97379 q^{9} +2.62540 q^{10} +4.08537 q^{11} -0.792145 q^{12} -2.97820 q^{13} +2.62540 q^{14} +0.161903 q^{15} +10.1533 q^{16} -6.98878 q^{17} +7.80738 q^{18} -1.63666 q^{19} -4.89272 q^{20} +0.161903 q^{21} -10.7257 q^{22} -6.94131 q^{23} +1.22958 q^{24} +1.00000 q^{25} +7.81895 q^{26} +0.967172 q^{27} -4.89272 q^{28} +5.94000 q^{29} -0.425059 q^{30} -5.53057 q^{31} -11.4674 q^{32} -0.661433 q^{33} +18.3483 q^{34} +1.00000 q^{35} -14.5499 q^{36} +3.86057 q^{37} +4.29689 q^{38} +0.482178 q^{39} +7.59456 q^{40} +12.7837 q^{41} -0.425059 q^{42} +7.05184 q^{43} +19.9886 q^{44} +2.97379 q^{45} +18.2237 q^{46} +6.45339 q^{47} -1.64385 q^{48} +1.00000 q^{49} -2.62540 q^{50} +1.13150 q^{51} -14.5715 q^{52} -0.816549 q^{53} -2.53921 q^{54} -4.08537 q^{55} +7.59456 q^{56} +0.264980 q^{57} -15.5949 q^{58} +10.8678 q^{59} +0.792145 q^{60} -8.01077 q^{61} +14.5200 q^{62} +2.97379 q^{63} +9.79979 q^{64} +2.97820 q^{65} +1.73653 q^{66} +9.95593 q^{67} -34.1941 q^{68} +1.12382 q^{69} -2.62540 q^{70} +5.59513 q^{71} +22.5846 q^{72} -14.0728 q^{73} -10.1355 q^{74} -0.161903 q^{75} -8.00774 q^{76} -4.08537 q^{77} -1.26591 q^{78} +0.553831 q^{79} -10.1533 q^{80} +8.76477 q^{81} -33.5623 q^{82} +3.28055 q^{83} +0.792145 q^{84} +6.98878 q^{85} -18.5139 q^{86} -0.961701 q^{87} -31.0266 q^{88} -7.89324 q^{89} -7.80738 q^{90} +2.97820 q^{91} -33.9619 q^{92} +0.895414 q^{93} -16.9427 q^{94} +1.63666 q^{95} +1.85660 q^{96} +5.80235 q^{97} -2.62540 q^{98} -12.1490 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.62540	−1.85644	−0.928219	−	0.372034i	$-0.878660\pi$
$2$	−2.62540	−1.85644	−0.928219	+	0.372034i	$0.878660\pi$
$3$	−0.161903	−0.0934746	−0.0467373	−	0.998907i	$-0.514882\pi$
$3$	−0.161903	−0.0934746	−0.0467373	+	0.998907i	$0.514882\pi$
$4$	4.89272	2.44636
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.425059	0.173530
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.59456	−2.68508
$9$	−2.97379	−0.991263
$10$	2.62540	0.830224
$11$	4.08537	1.23179	0.615893	−	0.787830i	$-0.288795\pi$
$11$	4.08537	1.23179	0.615893	+	0.787830i	$0.288795\pi$
$12$	−0.792145	−0.228673
$13$	−2.97820	−0.826003	−0.413001	−	0.910730i	$-0.635520\pi$
$13$	−2.97820	−0.826003	−0.413001	+	0.910730i	$0.635520\pi$
$14$	2.62540	0.701668
$15$	0.161903	0.0418031
$16$	10.1533	2.53832
$17$	−6.98878	−1.69503	−0.847513	−	0.530774i	$-0.821901\pi$
$17$	−6.98878	−1.69503	−0.847513	+	0.530774i	$0.821901\pi$
$18$	7.80738	1.84022
$19$	−1.63666	−0.375476	−0.187738	−	0.982219i	$-0.560116\pi$
$19$	−1.63666	−0.375476	−0.187738	+	0.982219i	$0.560116\pi$
$20$	−4.89272	−1.09405
$21$	0.161903	0.0353301
$22$	−10.7257	−2.28674
$23$	−6.94131	−1.44736	−0.723682	−	0.690134i	$-0.757552\pi$
$23$	−6.94131	−1.44736	−0.723682	+	0.690134i	$0.757552\pi$
$24$	1.22958	0.250987
$25$	1.00000	0.200000
$26$	7.81895	1.53342
$27$	0.967172	0.186132
$28$	−4.89272	−0.924638
$29$	5.94000	1.10303	0.551515	−	0.834165i	$-0.314050\pi$
$29$	5.94000	1.10303	0.551515	+	0.834165i	$0.314050\pi$
$30$	−0.425059	−0.0776048
$31$	−5.53057	−0.993320	−0.496660	−	0.867945i	$-0.665440\pi$
$31$	−5.53057	−0.993320	−0.496660	+	0.867945i	$0.665440\pi$
$32$	−11.4674	−2.02716
$33$	−0.661433	−0.115141
$34$	18.3483	3.14671
$35$	1.00000	0.169031
$36$	−14.5499	−2.42499
$37$	3.86057	0.634673	0.317337	−	0.948313i	$-0.397212\pi$
$37$	3.86057	0.634673	0.317337	+	0.948313i	$0.397212\pi$
$38$	4.29689	0.697048
$39$	0.482178	0.0772102
$40$	7.59456	1.20080
$41$	12.7837	1.99648	0.998238	−	0.0593428i	$-0.0189005\pi$
$41$	12.7837	1.99648	0.998238	+	0.0593428i	$0.0189005\pi$
$42$	−0.425059	−0.0655881
$43$	7.05184	1.07540	0.537698	−	0.843138i	$-0.319294\pi$
$43$	7.05184	1.07540	0.537698	+	0.843138i	$0.319294\pi$
$44$	19.9886	3.01340
$45$	2.97379	0.443306
$46$	18.2237	2.68694
$47$	6.45339	0.941323	0.470662	−	0.882314i	$-0.344015\pi$
$47$	6.45339	0.941323	0.470662	+	0.882314i	$0.344015\pi$
$48$	−1.64385	−0.237269
$49$	1.00000	0.142857
$50$	−2.62540	−0.371288
$51$	1.13150	0.158442
$52$	−14.5715	−2.02070
$53$	−0.816549	−0.112162	−0.0560808	−	0.998426i	$-0.517860\pi$
$53$	−0.816549	−0.112162	−0.0560808	+	0.998426i	$0.517860\pi$
$54$	−2.53921	−0.345543
$55$	−4.08537	−0.550872
$56$	7.59456	1.01487
$57$	0.264980	0.0350975
$58$	−15.5949	−2.04771
$59$	10.8678	1.41486	0.707432	−	0.706782i	$-0.249854\pi$
$59$	10.8678	1.41486	0.707432	+	0.706782i	$0.249854\pi$
$60$	0.792145	0.102265
$61$	−8.01077	−1.02567	−0.512837	−	0.858486i	$-0.671405\pi$
$61$	−8.01077	−1.02567	−0.512837	+	0.858486i	$0.671405\pi$
$62$	14.5200	1.84404
$63$	2.97379	0.374662
$64$	9.79979	1.22497
$65$	2.97820	0.369400
$66$	1.73653	0.213752
$67$	9.95593	1.21631	0.608155	−	0.793818i	$-0.291910\pi$
$67$	9.95593	1.21631	0.608155	+	0.793818i	$0.291910\pi$
$68$	−34.1941	−4.14665
$69$	1.12382	0.135292
$70$	−2.62540	−0.313795
$71$	5.59513	0.664020	0.332010	−	0.943276i	$-0.392273\pi$
$71$	5.59513	0.664020	0.332010	+	0.943276i	$0.392273\pi$
$72$	22.5846	2.66162
$73$	−14.0728	−1.64710	−0.823548	−	0.567246i	$-0.808009\pi$
$73$	−14.0728	−1.64710	−0.823548	+	0.567246i	$0.808009\pi$
$74$	−10.1355	−1.17823
$75$	−0.161903	−0.0186949
$76$	−8.00774	−0.918551
$77$	−4.08537	−0.465572
$78$	−1.26591	−0.143336
$79$	0.553831	0.0623109	0.0311554	−	0.999515i	$-0.490081\pi$
$79$	0.553831	0.0623109	0.0311554	+	0.999515i	$0.490081\pi$
$80$	−10.1533	−1.13517
$81$	8.76477	0.973864
$82$	−33.5623	−3.70633
$83$	3.28055	0.360087	0.180044	−	0.983659i	$-0.442376\pi$
$83$	3.28055	0.360087	0.180044	+	0.983659i	$0.442376\pi$
$84$	0.792145	0.0864301
$85$	6.98878	0.758039
$86$	−18.5139	−1.99640
$87$	−0.961701	−0.103105
$88$	−31.0266	−3.30745
$89$	−7.89324	−0.836682	−0.418341	−	0.908290i	$-0.637388\pi$
$89$	−7.89324	−0.836682	−0.418341	+	0.908290i	$0.637388\pi$
$90$	−7.80738	−0.822970
$91$	2.97820	0.312200
$92$	−33.9619	−3.54077
$93$	0.895414	0.0928501
$94$	−16.9427	−1.74751
$95$	1.63666	0.167918
$96$	1.85660	0.189488
$97$	5.80235	0.589140	0.294570	−	0.955630i	$-0.404824\pi$
$97$	5.80235	0.589140	0.294570	+	0.955630i	$0.404824\pi$
$98$	−2.62540	−0.265205
$99$	−12.1490	−1.22102
$100$	4.89272	0.489272
$101$	10.2173	1.01666	0.508332	−	0.861161i	$-0.330262\pi$
$101$	10.2173	1.01666	0.508332	+	0.861161i	$0.330262\pi$
$102$	−2.97064	−0.294138
$103$	6.34349	0.625043	0.312521	−	0.949911i	$-0.398826\pi$
$103$	6.34349	0.625043	0.312521	+	0.949911i	$0.398826\pi$
$104$	22.6181	2.21788
$105$	−0.161903	−0.0158001
$106$	2.14377	0.208221
$107$	4.08427	0.394842	0.197421	−	0.980319i	$-0.436743\pi$
$107$	4.08427	0.394842	0.197421	+	0.980319i	$0.436743\pi$
$108$	4.73211	0.455347
$109$	14.7297	1.41085	0.705424	−	0.708786i	$-0.250757\pi$
$109$	14.7297	1.41085	0.705424	+	0.708786i	$0.250757\pi$
$110$	10.7257	1.02266
$111$	−0.625036	−0.0593258
$112$	−10.1533	−0.959396
$113$	5.99416	0.563883	0.281942	−	0.959432i	$-0.409022\pi$
$113$	5.99416	0.563883	0.281942	+	0.959432i	$0.409022\pi$
$114$	−0.695679	−0.0651563
$115$	6.94131	0.647280
$116$	29.0628	2.69841
$117$	8.85652	0.818786
$118$	−28.5322	−2.62661
$119$	6.98878	0.640660
$120$	−1.22958	−0.112245
$121$	5.69028	0.517299
$122$	21.0315	1.90410
$123$	−2.06971	−0.186620
$124$	−27.0596	−2.43002
$125$	−1.00000	−0.0894427
$126$	−7.80738	−0.695537
$127$	11.9541	1.06075	0.530376	−	0.847763i	$-0.322051\pi$
$127$	11.9541	1.06075	0.530376	+	0.847763i	$0.322051\pi$
$128$	−2.79366	−0.246927
$129$	−1.14171	−0.100522
$130$	−7.81895	−0.685768
$131$	−22.5564	−1.97076	−0.985379	−	0.170376i	$-0.945502\pi$
$131$	−22.5564	−1.97076	−0.985379	+	0.170376i	$0.945502\pi$
$132$	−3.23621	−0.281676
$133$	1.63666	0.141917
$134$	−26.1383	−2.25800
$135$	−0.967172	−0.0832409
$136$	53.0766	4.55128
$137$	11.6870	0.998489	0.499244	−	0.866461i	$-0.333611\pi$
$137$	11.6870	0.998489	0.499244	+	0.866461i	$0.333611\pi$
$138$	−2.95047	−0.251161
$139$	1.71363	0.145348	0.0726739	−	0.997356i	$-0.476847\pi$
$139$	1.71363	0.145348	0.0726739	+	0.997356i	$0.476847\pi$
$140$	4.89272	0.413511
$141$	−1.04482	−0.0879898
$142$	−14.6895	−1.23271
$143$	−12.1670	−1.01746
$144$	−30.1938	−2.51615
$145$	−5.94000	−0.493290
$146$	36.9467	3.05773
$147$	−0.161903	−0.0133535
$148$	18.8887	1.55264
$149$	−8.15812	−0.668339	−0.334170	−	0.942513i	$-0.608456\pi$
$149$	−8.15812	−0.668339	−0.334170	+	0.942513i	$0.608456\pi$
$150$	0.425059	0.0347059
$151$	−4.63272	−0.377006	−0.188503	−	0.982073i	$-0.560363\pi$
$151$	−4.63272	−0.377006	−0.188503	+	0.982073i	$0.560363\pi$
$152$	12.4297	1.00818
$153$	20.7831	1.68022
$154$	10.7257	0.864305
$155$	5.53057	0.444226
$156$	2.35916	0.188884
$157$	−12.7721	−1.01932	−0.509662	−	0.860374i	$-0.670230\pi$
$157$	−12.7721	−1.01932	−0.509662	+	0.860374i	$0.670230\pi$
$158$	−1.45403	−0.115676
$159$	0.132201	0.0104843
$160$	11.4674	0.906574
$161$	6.94131	0.547052
$162$	−23.0110	−1.80792
$163$	−22.7673	−1.78327	−0.891635	−	0.452756i	$-0.850441\pi$
$163$	−22.7673	−1.78327	−0.891635	+	0.452756i	$0.850441\pi$
$164$	62.5470	4.88410
$165$	0.661433	0.0514925
$166$	−8.61275	−0.668479
$167$	−5.06091	−0.391625	−0.195812	−	0.980641i	$-0.562734\pi$
$167$	−5.06091	−0.391625	−0.195812	+	0.980641i	$0.562734\pi$
$168$	−1.22958	−0.0948641
$169$	−4.13035	−0.317719
$170$	−18.3483	−1.40725
$171$	4.86709	0.372196
$172$	34.5027	2.63081
$173$	14.1225	1.07371	0.536857	−	0.843673i	$-0.319611\pi$
$173$	14.1225	1.07371	0.536857	+	0.843673i	$0.319611\pi$
$174$	2.52485	0.191408
$175$	−1.00000	−0.0755929
$176$	41.4800	3.12667
$177$	−1.75952	−0.132254
$178$	20.7229	1.55325
$179$	−1.90526	−0.142406	−0.0712029	−	0.997462i	$-0.522684\pi$
$179$	−1.90526	−0.142406	−0.0712029	+	0.997462i	$0.522684\pi$
$180$	14.5499	1.08449
$181$	−7.49095	−0.556798	−0.278399	−	0.960466i	$-0.589804\pi$
$181$	−7.49095	−0.556798	−0.278399	+	0.960466i	$0.589804\pi$
$182$	−7.81895	−0.579579
$183$	1.29696	0.0958744
$184$	52.7162	3.88629
$185$	−3.86057	−0.283834
$186$	−2.35082	−0.172371
$187$	−28.5518	−2.08791
$188$	31.5746	2.30282
$189$	−0.967172	−0.0703514
$190$	−4.29689	−0.311729
$191$	−14.8454	−1.07418	−0.537089	−	0.843526i	$-0.680476\pi$
$191$	−14.8454	−1.07418	−0.537089	+	0.843526i	$0.680476\pi$
$192$	−1.58661	−0.114504
$193$	−14.3781	−1.03496	−0.517479	−	0.855696i	$-0.673129\pi$
$193$	−14.3781	−1.03496	−0.517479	+	0.855696i	$0.673129\pi$
$194$	−15.2335	−1.09370
$195$	−0.482178	−0.0345295
$196$	4.89272	0.349480
$197$	−13.9332	−0.992699	−0.496349	−	0.868123i	$-0.665327\pi$
$197$	−13.9332	−0.992699	−0.496349	+	0.868123i	$0.665327\pi$
$198$	31.8961	2.26676
$199$	−19.9627	−1.41512	−0.707560	−	0.706653i	$-0.750204\pi$
$199$	−19.9627	−1.41512	−0.707560	+	0.706653i	$0.750204\pi$
$200$	−7.59456	−0.537016
$201$	−1.61189	−0.113694
$202$	−26.8246	−1.88737
$203$	−5.94000	−0.416906
$204$	5.53612	0.387606
$205$	−12.7837	−0.892851
$206$	−16.6542	−1.16035
$207$	20.6420	1.43472
$208$	−30.2385	−2.09666
$209$	−6.68638	−0.462507
$210$	0.425059	0.0293319
$211$	−20.2300	−1.39269	−0.696345	−	0.717707i	$-0.745192\pi$
$211$	−20.2300	−1.39269	−0.696345	+	0.717707i	$0.745192\pi$
$212$	−3.99515	−0.274388
$213$	−0.905867	−0.0620690
$214$	−10.7228	−0.732999
$215$	−7.05184	−0.480931
$216$	−7.34524	−0.499781
$217$	5.53057	0.375440
$218$	−38.6713	−2.61915
$219$	2.27842	0.153962
$220$	−19.9886	−1.34763
$221$	20.8139	1.40010
$222$	1.64097	0.110135
$223$	−7.71154	−0.516403	−0.258202	−	0.966091i	$-0.583130\pi$
$223$	−7.71154	−0.516403	−0.258202	+	0.966091i	$0.583130\pi$
$224$	11.4674	0.766195
$225$	−2.97379	−0.198253
$226$	−15.7371	−1.04681
$227$	10.7938	0.716410	0.358205	−	0.933643i	$-0.383389\pi$
$227$	10.7938	0.716410	0.358205	+	0.933643i	$0.383389\pi$
$228$	1.29647	0.0858611
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−18.2237	−1.20164
$231$	0.661433	0.0435191
$232$	−45.1116	−2.96172
$233$	−14.5640	−0.954119	−0.477060	−	0.878871i	$-0.658297\pi$
$233$	−14.5640	−0.954119	−0.477060	+	0.878871i	$0.658297\pi$
$234$	−23.2519	−1.52002
$235$	−6.45339	−0.420973
$236$	53.1730	3.46127
$237$	−0.0896668	−0.00582448
$238$	−18.3483	−1.18935
$239$	8.69670	0.562543	0.281271	−	0.959628i	$-0.409244\pi$
$239$	8.69670	0.562543	0.281271	+	0.959628i	$0.409244\pi$
$240$	1.64385	0.106110
$241$	25.5806	1.64779	0.823896	−	0.566741i	$-0.191796\pi$
$241$	25.5806	1.64779	0.823896	+	0.566741i	$0.191796\pi$
$242$	−14.9393	−0.960333
$243$	−4.32056	−0.277164
$244$	−39.1945	−2.50917
$245$	−1.00000	−0.0638877
$246$	5.43382	0.346448
$247$	4.87430	0.310144
$248$	42.0022	2.66714
$249$	−0.531130	−0.0336590
$250$	2.62540	0.166045
$251$	−2.74403	−0.173202	−0.0866009	−	0.996243i	$-0.527601\pi$
$251$	−2.74403	−0.173202	−0.0866009	+	0.996243i	$0.527601\pi$
$252$	14.5499	0.916559
$253$	−28.3578	−1.78284
$254$	−31.3842	−1.96922
$255$	−1.13150	−0.0708574
$256$	−12.2651	−0.766569
$257$	−17.1864	−1.07206	−0.536028	−	0.844200i	$-0.680076\pi$
$257$	−17.1864	−1.07206	−0.536028	+	0.844200i	$0.680076\pi$
$258$	2.99745	0.186613
$259$	−3.86057	−0.239884
$260$	14.5715	0.903685
$261$	−17.6643	−1.09339
$262$	59.2195	3.65859
$263$	28.4560	1.75467	0.877336	−	0.479877i	$-0.159319\pi$
$263$	28.4560	1.75467	0.877336	+	0.479877i	$0.159319\pi$
$264$	5.02329	0.309162
$265$	0.816549	0.0501602
$266$	−4.29689	−0.263460
$267$	1.27794	0.0782084
$268$	48.7116	2.97553
$269$	10.9099	0.665191	0.332596	−	0.943070i	$-0.392076\pi$
$269$	10.9099	0.665191	0.332596	+	0.943070i	$0.392076\pi$
$270$	2.53921	0.154532
$271$	5.74264	0.348841	0.174420	−	0.984671i	$-0.444195\pi$
$271$	5.74264	0.348841	0.174420	+	0.984671i	$0.444195\pi$
$272$	−70.9591	−4.30253
$273$	−0.482178	−0.0291827
$274$	−30.6831	−1.85363
$275$	4.08537	0.246357
$276$	5.49852	0.330972
$277$	−0.410586	−0.0246697	−0.0123349	−	0.999924i	$-0.503926\pi$
$277$	−0.410586	−0.0246697	−0.0123349	+	0.999924i	$0.503926\pi$
$278$	−4.49895	−0.269829
$279$	16.4467	0.984641
$280$	−7.59456	−0.453862
$281$	11.2979	0.673977	0.336988	−	0.941509i	$-0.390592\pi$
$281$	11.2979	0.673977	0.336988	+	0.941509i	$0.390592\pi$
$282$	2.74307	0.163348
$283$	−11.7172	−0.696515	−0.348257	−	0.937399i	$-0.613226\pi$
$283$	−11.7172	−0.696515	−0.348257	+	0.937399i	$0.613226\pi$
$284$	27.3754	1.62443
$285$	−0.264980	−0.0156961
$286$	31.9434	1.88885
$287$	−12.7837	−0.754597
$288$	34.1015	2.00945
$289$	31.8430	1.87312
$290$	15.5949	0.915762
$291$	−0.939416	−0.0550696
$292$	−68.8543	−4.02939
$293$	11.2764	0.658776	0.329388	−	0.944195i	$-0.393158\pi$
$293$	11.2764	0.658776	0.329388	+	0.944195i	$0.393158\pi$
$294$	0.425059	0.0247900
$295$	−10.8678	−0.632746
$296$	−29.3193	−1.70415
$297$	3.95126	0.229275
$298$	21.4183	1.24073
$299$	20.6726	1.19553
$300$	−0.792145	−0.0457345
$301$	−7.05184	−0.406461
$302$	12.1628	0.699888
$303$	−1.65422	−0.0950322
$304$	−16.6175	−0.953081
$305$	8.01077	0.458695
$306$	−54.5640	−3.11922
$307$	−5.30338	−0.302680	−0.151340	−	0.988482i	$-0.548359\pi$
$307$	−5.30338	−0.302680	−0.151340	+	0.988482i	$0.548359\pi$
$308$	−19.9886	−1.13896
$309$	−1.02703	−0.0584256
$310$	−14.5200	−0.824678
$311$	−21.4158	−1.21438	−0.607190	−	0.794556i	$-0.707703\pi$
$311$	−21.4158	−1.21438	−0.607190	+	0.794556i	$0.707703\pi$
$312$	−3.66193	−0.207316
$313$	−20.2249	−1.14318	−0.571591	−	0.820539i	$-0.693673\pi$
$313$	−20.2249	−1.14318	−0.571591	+	0.820539i	$0.693673\pi$
$314$	33.5319	1.89231
$315$	−2.97379	−0.167554
$316$	2.70974	0.152435
$317$	1.60919	0.0903813	0.0451906	−	0.998978i	$-0.485610\pi$
$317$	1.60919	0.0903813	0.0451906	+	0.998978i	$0.485610\pi$
$318$	−0.347082	−0.0194634
$319$	24.2671	1.35870
$320$	−9.79979	−0.547825
$321$	−0.661255	−0.0369076
$322$	−18.2237	−1.01557
$323$	11.4383	0.636442
$324$	42.8836	2.38242
$325$	−2.97820	−0.165201
$326$	59.7731	3.31053
$327$	−2.38478	−0.131878
$328$	−97.0864	−5.36070
$329$	−6.45339	−0.355787
$330$	−1.73653	−0.0955926
$331$	−18.8182	−1.03434	−0.517172	−	0.855881i	$-0.673015\pi$
$331$	−18.8182	−1.03434	−0.517172	+	0.855881i	$0.673015\pi$
$332$	16.0508	0.880903
$333$	−11.4805	−0.629128
$334$	13.2869	0.727027
$335$	−9.95593	−0.543950
$336$	1.64385	0.0896792
$337$	14.9553	0.814670	0.407335	−	0.913279i	$-0.366458\pi$
$337$	14.9553	0.814670	0.407335	+	0.913279i	$0.366458\pi$
$338$	10.8438	0.589827
$339$	−0.970471	−0.0527087
$340$	34.1941	1.85444
$341$	−22.5945	−1.22356
$342$	−12.7781	−0.690958
$343$	−1.00000	−0.0539949
$344$	−53.5556	−2.88752
$345$	−1.12382	−0.0605043
$346$	−37.0772	−1.99328
$347$	−2.92336	−0.156934	−0.0784670	−	0.996917i	$-0.525003\pi$
$347$	−2.92336	−0.156934	−0.0784670	+	0.996917i	$0.525003\pi$
$348$	−4.70534	−0.252233
$349$	15.6770	0.839173	0.419586	−	0.907715i	$-0.362175\pi$
$349$	15.6770	0.839173	0.419586	+	0.907715i	$0.362175\pi$
$350$	2.62540	0.140334
$351$	−2.88043	−0.153746
$352$	−46.8484	−2.49703
$353$	−8.00983	−0.426320	−0.213160	−	0.977017i	$-0.568376\pi$
$353$	−8.00983	−0.426320	−0.213160	+	0.977017i	$0.568376\pi$
$354$	4.61945	0.245521
$355$	−5.59513	−0.296959
$356$	−38.6194	−2.04683
$357$	−1.13150	−0.0598854
$358$	5.00207	0.264367
$359$	26.9925	1.42461	0.712304	−	0.701871i	$-0.247652\pi$
$359$	26.9925	1.42461	0.712304	+	0.701871i	$0.247652\pi$
$360$	−22.5846	−1.19031
$361$	−16.3213	−0.859018
$362$	19.6667	1.03366
$363$	−0.921272	−0.0483543
$364$	14.5715	0.763753
$365$	14.0728	0.736604
$366$	−3.40505	−0.177985
$367$	−24.4511	−1.27634	−0.638168	−	0.769897i	$-0.720307\pi$
$367$	−24.4511	−1.27634	−0.638168	+	0.769897i	$0.720307\pi$
$368$	−70.4772	−3.67388
$369$	−38.0159	−1.97903
$370$	10.1355	0.526921
$371$	0.816549	0.0423931
$372$	4.38101	0.227145
$373$	0.268115	0.0138824	0.00694122	−	0.999976i	$-0.497791\pi$
$373$	0.268115	0.0138824	0.00694122	+	0.999976i	$0.497791\pi$
$374$	74.9598	3.87608
$375$	0.161903	0.00836062
$376$	−49.0106	−2.52753
$377$	−17.6905	−0.911105
$378$	2.53921	0.130603
$379$	−17.3451	−0.890959	−0.445480	−	0.895292i	$-0.646967\pi$
$379$	−17.3451	−0.890959	−0.445480	+	0.895292i	$0.646967\pi$
$380$	8.00774	0.410788
$381$	−1.93539	−0.0991533
$382$	38.9752	1.99414
$383$	11.0968	0.567019	0.283509	−	0.958969i	$-0.408501\pi$
$383$	11.0968	0.567019	0.283509	+	0.958969i	$0.408501\pi$
$384$	0.452301	0.0230814
$385$	4.08537	0.208210
$386$	37.7482	1.92133
$387$	−20.9707	−1.06600
$388$	28.3893	1.44125
$389$	32.2968	1.63751	0.818757	−	0.574140i	$-0.194664\pi$
$389$	32.2968	1.63751	0.818757	+	0.574140i	$0.194664\pi$
$390$	1.26591	0.0641018
$391$	48.5113	2.45332
$392$	−7.59456	−0.383583
$393$	3.65193	0.184216
$394$	36.5802	1.84288
$395$	−0.553831	−0.0278663
$396$	−59.4419	−2.98707
$397$	30.2325	1.51733	0.758664	−	0.651482i	$-0.225853\pi$
$397$	30.2325	1.51733	0.758664	+	0.651482i	$0.225853\pi$
$398$	52.4101	2.62708
$399$	−0.264980	−0.0132656
$400$	10.1533	0.507665
$401$	15.4779	0.772929	0.386465	−	0.922304i	$-0.373696\pi$
$401$	15.4779	0.772929	0.386465	+	0.922304i	$0.373696\pi$
$402$	4.23186	0.211066
$403$	16.4711	0.820485
$404$	49.9907	2.48713
$405$	−8.76477	−0.435525
$406$	15.5949	0.773960
$407$	15.7719	0.781782
$408$	−8.59325	−0.425429
$409$	−22.6884	−1.12187	−0.560935	−	0.827860i	$-0.689558\pi$
$409$	−22.6884	−1.12187	−0.560935	+	0.827860i	$0.689558\pi$
$410$	33.5623	1.65752
$411$	−1.89216	−0.0933333
$412$	31.0370	1.52908
$413$	−10.8678	−0.534768
$414$	−54.1934	−2.66346
$415$	−3.28055	−0.161036
$416$	34.1520	1.67444
$417$	−0.277441	−0.0135863
$418$	17.5544	0.858615
$419$	−23.0795	−1.12751	−0.563753	−	0.825944i	$-0.690643\pi$
$419$	−23.0795	−1.12751	−0.563753	+	0.825944i	$0.690643\pi$
$420$	−0.792145	−0.0386527
$421$	6.40478	0.312150	0.156075	−	0.987745i	$-0.450116\pi$
$421$	6.40478	0.312150	0.156075	+	0.987745i	$0.450116\pi$
$422$	53.1118	2.58544
$423$	−19.1910	−0.933098
$424$	6.20133	0.301163
$425$	−6.98878	−0.339005
$426$	2.37826	0.115227
$427$	8.01077	0.387668
$428$	19.9832	0.965925
$429$	1.96988	0.0951065
$430$	18.5139	0.892819
$431$	−24.0505	−1.15847	−0.579235	−	0.815160i	$-0.696649\pi$
$431$	−24.0505	−1.15847	−0.579235	+	0.815160i	$0.696649\pi$
$432$	9.81999	0.472464
$433$	−22.8153	−1.09643	−0.548216	−	0.836337i	$-0.684693\pi$
$433$	−22.8153	−1.09643	−0.548216	+	0.836337i	$0.684693\pi$
$434$	−14.5200	−0.696980
$435$	0.961701	0.0461101
$436$	72.0683	3.45144
$437$	11.3606	0.543450
$438$	−5.98177	−0.285820
$439$	−9.98763	−0.476684	−0.238342	−	0.971181i	$-0.576604\pi$
$439$	−9.98763	−0.476684	−0.238342	+	0.971181i	$0.576604\pi$
$440$	31.0266	1.47914
$441$	−2.97379	−0.141609
$442$	−54.6449	−2.59919
$443$	6.85484	0.325683	0.162842	−	0.986652i	$-0.447934\pi$
$443$	6.85484	0.325683	0.162842	+	0.986652i	$0.447934\pi$
$444$	−3.05813	−0.145132
$445$	7.89324	0.374175
$446$	20.2459	0.958670
$447$	1.32082	0.0624727
$448$	−9.79979	−0.462997
$449$	−2.87815	−0.135828	−0.0679141	−	0.997691i	$-0.521634\pi$
$449$	−2.87815	−0.135828	−0.0679141	+	0.997691i	$0.521634\pi$
$450$	7.80738	0.368043
$451$	52.2261	2.45923
$452$	29.3278	1.37946
$453$	0.750050	0.0352404
$454$	−28.3380	−1.32997
$455$	−2.97820	−0.139620
$456$	−2.01241	−0.0942396
$457$	6.84770	0.320322	0.160161	−	0.987091i	$-0.448799\pi$
$457$	6.84770	0.320322	0.160161	+	0.987091i	$0.448799\pi$
$458$	2.62540	0.122677
$459$	−6.75935	−0.315499
$460$	33.9619	1.58348
$461$	13.1105	0.610615	0.305308	−	0.952254i	$-0.401241\pi$
$461$	13.1105	0.610615	0.305308	+	0.952254i	$0.401241\pi$
$462$	−1.73653	−0.0807905
$463$	4.65476	0.216325	0.108162	−	0.994133i	$-0.465503\pi$
$463$	4.65476	0.216325	0.108162	+	0.994133i	$0.465503\pi$
$464$	60.3106	2.79985
$465$	−0.895414	−0.0415238
$466$	38.2363	1.77126
$467$	13.4177	0.620895	0.310447	−	0.950591i	$-0.399521\pi$
$467$	13.4177	0.620895	0.310447	+	0.950591i	$0.399521\pi$
$468$	43.3325	2.00305
$469$	−9.95593	−0.459722
$470$	16.9427	0.781509
$471$	2.06784	0.0952810
$472$	−82.5359	−3.79902
$473$	28.8094	1.32466
$474$	0.235411	0.0108128
$475$	−1.63666	−0.0750952
$476$	34.1941	1.56729
$477$	2.42824	0.111182
$478$	−22.8323	−1.04433
$479$	20.3587	0.930213	0.465107	−	0.885255i	$-0.346016\pi$
$479$	20.3587	0.930213	0.465107	+	0.885255i	$0.346016\pi$
$480$	−1.85660	−0.0847416
$481$	−11.4975	−0.524242
$482$	−67.1593	−3.05902
$483$	−1.12382	−0.0511354
$484$	27.8410	1.26550
$485$	−5.80235	−0.263471
$486$	11.3432	0.514538
$487$	27.9513	1.26659	0.633297	−	0.773908i	$-0.281701\pi$
$487$	27.9513	1.26659	0.633297	+	0.773908i	$0.281701\pi$
$488$	60.8382	2.75402
$489$	3.68608	0.166690
$490$	2.62540	0.118603
$491$	−40.0748	−1.80855	−0.904276	−	0.426949i	$-0.859588\pi$
$491$	−40.0748	−1.80855	−0.904276	+	0.426949i	$0.859588\pi$
$492$	−10.1265	−0.456539
$493$	−41.5133	−1.86966
$494$	−12.7970	−0.575764
$495$	12.1490	0.546059
$496$	−56.1535	−2.52137
$497$	−5.59513	−0.250976
$498$	1.39443	0.0624858
$499$	4.20253	0.188131	0.0940655	−	0.995566i	$-0.470014\pi$
$499$	4.20253	0.188131	0.0940655	+	0.995566i	$0.470014\pi$
$500$	−4.89272	−0.218809
$501$	0.819374	0.0366069
$502$	7.20419	0.321539
$503$	−19.6735	−0.877198	−0.438599	−	0.898683i	$-0.644525\pi$
$503$	−19.6735	−0.877198	−0.438599	+	0.898683i	$0.644525\pi$
$504$	−22.5846	−1.00600
$505$	−10.2173	−0.454666
$506$	74.4507	3.30974
$507$	0.668715	0.0296987
$508$	58.4879	2.59498
$509$	−6.95734	−0.308379	−0.154189	−	0.988041i	$-0.549277\pi$
$509$	−6.95734	−0.308379	−0.154189	+	0.988041i	$0.549277\pi$
$510$	2.97064	0.131542
$511$	14.0728	0.622544
$512$	37.7881	1.67001
$513$	−1.58293	−0.0698883
$514$	45.1211	1.99021
$515$	−6.34349	−0.279528
$516$	−5.58608	−0.245913
$517$	26.3645	1.15951
$518$	10.1355	0.445329
$519$	−2.28647	−0.100365
$520$	−22.6181	−0.991868
$521$	2.12252	0.0929891	0.0464946	−	0.998919i	$-0.485195\pi$
$521$	2.12252	0.0929891	0.0464946	+	0.998919i	$0.485195\pi$
$522$	46.3758	2.02981
$523$	−24.0295	−1.05074	−0.525368	−	0.850875i	$-0.676072\pi$
$523$	−24.0295	−1.05074	−0.525368	+	0.850875i	$0.676072\pi$
$524$	−110.362	−4.82119
$525$	0.161903	0.00706601
$526$	−74.7083	−3.25744
$527$	38.6519	1.68370
$528$	−6.71573	−0.292265
$529$	25.1818	1.09486
$530$	−2.14377	−0.0931193
$531$	−32.3184	−1.40250
$532$	8.00774	0.347180
$533$	−38.0723	−1.64909
$534$	−3.35509	−0.145189
$535$	−4.08427	−0.176578
$536$	−75.6109	−3.26589
$537$	0.308466	0.0133113
$538$	−28.6430	−1.23489
$539$	4.08537	0.175970
$540$	−4.73211	−0.203637
$541$	−24.2183	−1.04122	−0.520612	−	0.853793i	$-0.674296\pi$
$541$	−24.2183	−1.04122	−0.520612	+	0.853793i	$0.674296\pi$
$542$	−15.0767	−0.647601
$543$	1.21280	0.0520464
$544$	80.1428	3.43609
$545$	−14.7297	−0.630950
$546$	1.26591	0.0541759
$547$	45.1317	1.92969	0.964847	−	0.262812i	$-0.0846498\pi$
$547$	45.1317	1.92969	0.964847	+	0.262812i	$0.0846498\pi$
$548$	57.1813	2.44266
$549$	23.8223	1.01671
$550$	−10.7257	−0.457347
$551$	−9.72177	−0.414161
$552$	−8.53489	−0.363269
$553$	−0.553831	−0.0235513
$554$	1.07795	0.0457978
$555$	0.625036	0.0265313
$556$	8.38430	0.355574
$557$	−33.4974	−1.41933	−0.709665	−	0.704539i	$-0.751154\pi$
$557$	−33.4974	−1.41933	−0.709665	+	0.704539i	$0.751154\pi$
$558$	−43.1793	−1.82792
$559$	−21.0017	−0.888279
$560$	10.1533	0.429055
$561$	4.62261	0.195167
$562$	−29.6615	−1.25120
$563$	−24.6078	−1.03710	−0.518548	−	0.855049i	$-0.673527\pi$
$563$	−24.6078	−1.03710	−0.518548	+	0.855049i	$0.673527\pi$
$564$	−5.11202	−0.215255
$565$	−5.99416	−0.252176
$566$	30.7623	1.29304
$567$	−8.76477	−0.368086
$568$	−42.4926	−1.78295
$569$	24.6504	1.03340	0.516700	−	0.856167i	$-0.327160\pi$
$569$	24.6504	1.03340	0.516700	+	0.856167i	$0.327160\pi$
$570$	0.695679	0.0291388
$571$	−24.0252	−1.00542	−0.502712	−	0.864454i	$-0.667665\pi$
$571$	−24.0252	−1.00542	−0.502712	+	0.864454i	$0.667665\pi$
$572$	−59.5300	−2.48907
$573$	2.40352	0.100408
$574$	33.5623	1.40086
$575$	−6.94131	−0.289473
$576$	−29.1425	−1.21427
$577$	−29.4200	−1.22477	−0.612386	−	0.790559i	$-0.709790\pi$
$577$	−29.4200	−1.22477	−0.612386	+	0.790559i	$0.709790\pi$
$578$	−83.6005	−3.47732
$579$	2.32785	0.0967422
$580$	−29.0628	−1.20677
$581$	−3.28055	−0.136100
$582$	2.46634	0.102233
$583$	−3.33591	−0.138159
$584$	106.877	4.42259
$585$	−8.85652	−0.366172
$586$	−29.6051	−1.22298
$587$	−0.358902	−0.0148135	−0.00740673	−	0.999973i	$-0.502358\pi$
$587$	−0.358902	−0.0148135	−0.00740673	+	0.999973i	$0.502358\pi$
$588$	−0.792145	−0.0326675
$589$	9.05168	0.372968
$590$	28.5322	1.17465
$591$	2.25582	0.0927921
$592$	39.1975	1.61101
$593$	−6.82507	−0.280272	−0.140136	−	0.990132i	$-0.544754\pi$
$593$	−6.82507	−0.280272	−0.140136	+	0.990132i	$0.544754\pi$
$594$	−10.3736	−0.425636
$595$	−6.98878	−0.286512
$596$	−39.9154	−1.63500
$597$	3.23202	0.132278
$598$	−54.2738	−2.21942
$599$	14.3718	0.587218	0.293609	−	0.955926i	$-0.405144\pi$
$599$	14.3718	0.587218	0.293609	+	0.955926i	$0.405144\pi$
$600$	1.22958	0.0501974
$601$	37.0704	1.51213	0.756066	−	0.654495i	$-0.227119\pi$
$601$	37.0704	1.51213	0.756066	+	0.654495i	$0.227119\pi$
$602$	18.5139	0.754570
$603$	−29.6068	−1.20568
$604$	−22.6666	−0.922292
$605$	−5.69028	−0.231343
$606$	4.34298	0.176421
$607$	12.0865	0.490575	0.245287	−	0.969450i	$-0.421118\pi$
$607$	12.0865	0.490575	0.245287	+	0.969450i	$0.421118\pi$
$608$	18.7682	0.761151
$609$	0.961701	0.0389701
$610$	−21.0315	−0.851539
$611$	−19.2194	−0.777536
$612$	101.686	4.11042
$613$	−22.9873	−0.928447	−0.464223	−	0.885718i	$-0.653667\pi$
$613$	−22.9873	−0.928447	−0.464223	+	0.885718i	$0.653667\pi$
$614$	13.9235	0.561906
$615$	2.06971	0.0834588
$616$	31.0266	1.25010
$617$	46.8202	1.88491	0.942454	−	0.334335i	$-0.108512\pi$
$617$	46.8202	1.88491	0.942454	+	0.334335i	$0.108512\pi$
$618$	2.69636	0.108464
$619$	−5.00800	−0.201289	−0.100644	−	0.994922i	$-0.532090\pi$
$619$	−5.00800	−0.201289	−0.100644	+	0.994922i	$0.532090\pi$
$620$	27.0596	1.08674
$621$	−6.71344	−0.269401
$622$	56.2251	2.25442
$623$	7.89324	0.316236
$624$	4.89569	0.195985
$625$	1.00000	0.0400000
$626$	53.0986	2.12225
$627$	1.08254	0.0432326
$628$	−62.4904	−2.49364
$629$	−26.9806	−1.07579
$630$	7.80738	0.311054
$631$	1.34647	0.0536023	0.0268011	−	0.999641i	$-0.491468\pi$
$631$	1.34647	0.0536023	0.0268011	+	0.999641i	$0.491468\pi$
$632$	−4.20610	−0.167310
$633$	3.27529	0.130181
$634$	−4.22477	−0.167787
$635$	−11.9541	−0.474382
$636$	0.646825	0.0256483
$637$	−2.97820	−0.118000
$638$	−63.7109	−2.52234
$639$	−16.6387	−0.658218
$640$	2.79366	0.110429
$641$	−14.4062	−0.569009	−0.284505	−	0.958675i	$-0.591829\pi$
$641$	−14.4062	−0.569009	−0.284505	+	0.958675i	$0.591829\pi$
$642$	1.73606	0.0685167
$643$	−11.5780	−0.456593	−0.228296	−	0.973592i	$-0.573316\pi$
$643$	−11.5780	−0.456593	−0.228296	+	0.973592i	$0.573316\pi$
$644$	33.9619	1.33829
$645$	1.14171	0.0449548
$646$	−30.0300	−1.18152
$647$	27.9712	1.09966	0.549831	−	0.835276i	$-0.314692\pi$
$647$	27.9712	1.09966	0.549831	+	0.835276i	$0.314692\pi$
$648$	−66.5646	−2.61490
$649$	44.3989	1.74281
$650$	7.81895	0.306685
$651$	−0.895414	−0.0350941
$652$	−111.394	−4.36252
$653$	−48.2468	−1.88804	−0.944021	−	0.329886i	$-0.892990\pi$
$653$	−48.2468	−1.88804	−0.944021	+	0.329886i	$0.892990\pi$
$654$	6.26099	0.244824
$655$	22.5564	0.881350
$656$	129.797	5.06770
$657$	41.8495	1.63271
$658$	16.9427	0.660496
$659$	3.87658	0.151010	0.0755051	−	0.997145i	$-0.475943\pi$
$659$	3.87658	0.151010	0.0755051	+	0.997145i	$0.475943\pi$
$660$	3.23621	0.125969
$661$	17.4896	0.680268	0.340134	−	0.940377i	$-0.389528\pi$
$661$	17.4896	0.680268	0.340134	+	0.940377i	$0.389528\pi$
$662$	49.4054	1.92020
$663$	−3.36983	−0.130873
$664$	−24.9143	−0.966863
$665$	−1.63666	−0.0634671
$666$	30.1409	1.16794
$667$	−41.2314	−1.59648
$668$	−24.7616	−0.958056
$669$	1.24852	0.0482705
$670$	26.1383	1.00981
$671$	−32.7270	−1.26341
$672$	−1.85660	−0.0716197
$673$	42.0603	1.62130	0.810652	−	0.585528i	$-0.199113\pi$
$673$	42.0603	1.62130	0.810652	+	0.585528i	$0.199113\pi$
$674$	−39.2638	−1.51238
$675$	0.967172	0.0372265
$676$	−20.2087	−0.777257
$677$	28.0351	1.07748	0.538738	−	0.842473i	$-0.318901\pi$
$677$	28.0351	1.07748	0.538738	+	0.842473i	$0.318901\pi$
$678$	2.54787	0.0978505
$679$	−5.80235	−0.222674
$680$	−53.0766	−2.03540
$681$	−1.74755	−0.0669661
$682$	59.3195	2.27146
$683$	−6.65835	−0.254775	−0.127387	−	0.991853i	$-0.540659\pi$
$683$	−6.65835	−0.254775	−0.127387	+	0.991853i	$0.540659\pi$
$684$	23.8133	0.910525
$685$	−11.6870	−0.446538
$686$	2.62540	0.100238
$687$	0.161903	0.00617697
$688$	71.5994	2.72970
$689$	2.43184	0.0926458
$690$	2.95047	0.112322
$691$	−0.312589	−0.0118914	−0.00594572	−	0.999982i	$-0.501893\pi$
$691$	−0.312589	−0.0118914	−0.00594572	+	0.999982i	$0.501893\pi$
$692$	69.0975	2.62669
$693$	12.1490	0.461504
$694$	7.67498	0.291338
$695$	−1.71363	−0.0650016
$696$	7.30369	0.276846
$697$	−89.3423	−3.38408
$698$	−41.1585	−1.55787
$699$	2.35795	0.0891859
$700$	−4.89272	−0.184928
$701$	−19.3086	−0.729274	−0.364637	−	0.931150i	$-0.618807\pi$
$701$	−19.3086	−0.729274	−0.364637	+	0.931150i	$0.618807\pi$
$702$	7.56227	0.285420
$703$	−6.31844	−0.238305
$704$	40.0358	1.50891
$705$	1.04482	0.0393502
$706$	21.0290	0.791437
$707$	−10.2173	−0.384263
$708$	−8.60885	−0.323540
$709$	19.5077	0.732627	0.366313	−	0.930492i	$-0.380620\pi$
$709$	19.5077	0.732627	0.366313	+	0.930492i	$0.380620\pi$
$710$	14.6895	0.551286
$711$	−1.64698	−0.0617665
$712$	59.9456	2.24656
$713$	38.3894	1.43769
$714$	2.97064	0.111174
$715$	12.1670	0.455022
$716$	−9.32190	−0.348376
$717$	−1.40802	−0.0525834
$718$	−70.8661	−2.64470
$719$	11.8382	0.441492	0.220746	−	0.975331i	$-0.429151\pi$
$719$	11.8382	0.441492	0.220746	+	0.975331i	$0.429151\pi$
$720$	30.1938	1.12525
$721$	−6.34349	−0.236244
$722$	42.8500	1.59471
$723$	−4.14157	−0.154027
$724$	−36.6511	−1.36213
$725$	5.94000	0.220606
$726$	2.41871	0.0897667
$727$	−32.1949	−1.19404	−0.597021	−	0.802226i	$-0.703649\pi$
$727$	−32.1949	−1.19404	−0.597021	+	0.802226i	$0.703649\pi$
$728$	−22.6181	−0.838281
$729$	−25.5948	−0.947956
$730$	−36.9467	−1.36746
$731$	−49.2837	−1.82282
$732$	6.34569	0.234543
$733$	−38.2161	−1.41155	−0.705773	−	0.708438i	$-0.749400\pi$
$733$	−38.2161	−1.41155	−0.705773	+	0.708438i	$0.749400\pi$
$734$	64.1938	2.36944
$735$	0.161903	0.00597187
$736$	79.5985	2.93404
$737$	40.6737	1.49823
$738$	99.8071	3.67395
$739$	−25.1658	−0.925741	−0.462870	−	0.886426i	$-0.653180\pi$
$739$	−25.1658	−0.925741	−0.462870	+	0.886426i	$0.653180\pi$
$740$	−18.8887	−0.694362
$741$	−0.789163	−0.0289906
$742$	−2.14377	−0.0787002
$743$	14.7462	0.540986	0.270493	−	0.962722i	$-0.412813\pi$
$743$	14.7462	0.540986	0.270493	+	0.962722i	$0.412813\pi$
$744$	−6.80027	−0.249310
$745$	8.15812	0.298890
$746$	−0.703908	−0.0257719
$747$	−9.75566	−0.356941
$748$	−139.696	−5.10779
$749$	−4.08427	−0.149236
$750$	−0.425059	−0.0155210
$751$	4.54107	0.165706	0.0828531	−	0.996562i	$-0.473597\pi$
$751$	4.54107	0.165706	0.0828531	+	0.996562i	$0.473597\pi$
$752$	65.5232	2.38938
$753$	0.444266	0.0161900
$754$	46.4446	1.69141
$755$	4.63272	0.168602
$756$	−4.73211	−0.172105
$757$	23.8760	0.867788	0.433894	−	0.900964i	$-0.357139\pi$
$757$	23.8760	0.867788	0.433894	+	0.900964i	$0.357139\pi$
$758$	45.5379	1.65401
$759$	4.59121	0.166650
$760$	−12.4297	−0.450874
$761$	−50.8022	−1.84158	−0.920788	−	0.390063i	$-0.872453\pi$
$761$	−50.8022	−1.84158	−0.920788	+	0.390063i	$0.872453\pi$
$762$	5.08118	0.184072
$763$	−14.7297	−0.533250
$764$	−72.6346	−2.62783
$765$	−20.7831	−0.751416
$766$	−29.1335	−1.05263
$767$	−32.3663	−1.16868
$768$	1.98575	0.0716547
$769$	38.5791	1.39120	0.695598	−	0.718431i	$-0.255139\pi$
$769$	38.5791	1.39120	0.695598	+	0.718431i	$0.255139\pi$
$770$	−10.7257	−0.386529
$771$	2.78252	0.100210
$772$	−70.3480	−2.53188
$773$	−33.3829	−1.20070	−0.600350	−	0.799737i	$-0.704972\pi$
$773$	−33.3829	−1.20070	−0.600350	+	0.799737i	$0.704972\pi$
$774$	55.0564	1.97896
$775$	−5.53057	−0.198664
$776$	−44.0663	−1.58189
$777$	0.625036	0.0224230
$778$	−84.7921	−3.03994
$779$	−20.9226	−0.749629
$780$	−2.35916	−0.0844716
$781$	22.8582	0.817931
$782$	−127.361	−4.55444
$783$	5.74500	0.205310
$784$	10.1533	0.362618
$785$	12.7721	0.455856
$786$	−9.58779	−0.341985
$787$	−10.0027	−0.356559	−0.178279	−	0.983980i	$-0.557053\pi$
$787$	−10.0027	−0.356559	−0.178279	+	0.983980i	$0.557053\pi$
$788$	−68.1713	−2.42850
$789$	−4.60710	−0.164017
$790$	1.45403	0.0517320
$791$	−5.99416	−0.213128
$792$	92.2665	3.27855
$793$	23.8576	0.847209
$794$	−79.3725	−2.81682
$795$	−0.132201	−0.00468870
$796$	−97.6721	−3.46190
$797$	−7.44104	−0.263575	−0.131788	−	0.991278i	$-0.542072\pi$
$797$	−7.44104	−0.263575	−0.131788	+	0.991278i	$0.542072\pi$
$798$	0.695679	0.0246268
$799$	−45.1013	−1.59557
$800$	−11.4674	−0.405432
$801$	23.4728	0.829371
$802$	−40.6357	−1.43490
$803$	−57.4927	−2.02887
$804$	−7.88654	−0.278137
$805$	−6.94131	−0.244649
$806$	−43.2433	−1.52318
$807$	−1.76635	−0.0621785
$808$	−77.5962	−2.72983
$809$	−12.7770	−0.449216	−0.224608	−	0.974449i	$-0.572110\pi$
$809$	−12.7770	−0.449216	−0.224608	+	0.974449i	$0.572110\pi$
$810$	23.0110	0.808525
$811$	16.8809	0.592768	0.296384	−	0.955069i	$-0.404219\pi$
$811$	16.8809	0.592768	0.296384	+	0.955069i	$0.404219\pi$
$812$	−29.0628	−1.01990
$813$	−0.929749	−0.0326077
$814$	−41.4074	−1.45133
$815$	22.7673	0.797502
$816$	11.4885	0.402177
$817$	−11.5415	−0.403785
$818$	59.5661	2.08268
$819$	−8.85652	−0.309472
$820$	−62.5470	−2.18424
$821$	12.6278	0.440713	0.220356	−	0.975419i	$-0.429278\pi$
$821$	12.6278	0.440713	0.220356	+	0.975419i	$0.429278\pi$
$822$	4.96767	0.173267
$823$	37.2083	1.29700	0.648500	−	0.761214i	$-0.275397\pi$
$823$	37.2083	1.29700	0.648500	+	0.761214i	$0.275397\pi$
$824$	−48.1760	−1.67829
$825$	−0.661433	−0.0230281
$826$	28.5322	0.992764
$827$	−12.1603	−0.422853	−0.211427	−	0.977394i	$-0.567811\pi$
$827$	−12.1603	−0.422853	−0.211427	+	0.977394i	$0.567811\pi$
$828$	100.996	3.50984
$829$	34.2655	1.19009	0.595045	−	0.803692i	$-0.297134\pi$
$829$	34.2655	1.19009	0.595045	+	0.803692i	$0.297134\pi$
$830$	8.61275	0.298953
$831$	0.0664750	0.00230599
$832$	−29.1857	−1.01183
$833$	−6.98878	−0.242147
$834$	0.728393	0.0252222
$835$	5.06091	0.175140
$836$	−32.7146	−1.13146
$837$	−5.34901	−0.184889
$838$	60.5928	2.09314
$839$	−19.6653	−0.678920	−0.339460	−	0.940620i	$-0.610244\pi$
$839$	−19.6653	−0.678920	−0.339460	+	0.940620i	$0.610244\pi$
$840$	1.22958	0.0424245
$841$	6.28356	0.216674
$842$	−16.8151	−0.579487
$843$	−1.82916	−0.0629997
$844$	−98.9798	−3.40703
$845$	4.13035	0.142088
$846$	50.3840	1.73224
$847$	−5.69028	−0.195520
$848$	−8.29067	−0.284703
$849$	1.89704	0.0651064
$850$	18.3483	0.629342
$851$	−26.7974	−0.918602
$852$	−4.43216	−0.151843
$853$	22.1934	0.759889	0.379944	−	0.925009i	$-0.375943\pi$
$853$	22.1934	0.759889	0.379944	+	0.925009i	$0.375943\pi$
$854$	−21.0315	−0.719682
$855$	−4.86709	−0.166451
$856$	−31.0182	−1.06018
$857$	0.980198	0.0334829	0.0167415	−	0.999860i	$-0.494671\pi$
$857$	0.980198	0.0334829	0.0167415	+	0.999860i	$0.494671\pi$
$858$	−5.17171	−0.176559
$859$	−22.4979	−0.767618	−0.383809	−	0.923413i	$-0.625388\pi$
$859$	−22.4979	−0.767618	−0.383809	+	0.923413i	$0.625388\pi$
$860$	−34.5027	−1.17653
$861$	2.06971	0.0705356
$862$	63.1421	2.15063
$863$	20.1536	0.686037	0.343018	−	0.939329i	$-0.388551\pi$
$863$	20.1536	0.686037	0.343018	+	0.939329i	$0.388551\pi$
$864$	−11.0909	−0.377320
$865$	−14.1225	−0.480180
$866$	59.8992	2.03546
$867$	−5.15546	−0.175089
$868$	27.0596	0.918461
$869$	2.26261	0.0767537
$870$	−2.52485	−0.0856004
$871$	−29.6507	−1.00468
$872$	−111.865	−3.78824
$873$	−17.2550	−0.583992
$874$	−29.8261	−1.00888
$875$	1.00000	0.0338062
$876$	11.1477	0.376646
$877$	−16.4433	−0.555250	−0.277625	−	0.960689i	$-0.589547\pi$
$877$	−16.4433	−0.555250	−0.277625	+	0.960689i	$0.589547\pi$
$878$	26.2215	0.884933
$879$	−1.82568	−0.0615788
$880$	−41.4800	−1.39829
$881$	52.0544	1.75376	0.876878	−	0.480712i	$-0.159622\pi$
$881$	52.0544	1.75376	0.876878	+	0.480712i	$0.159622\pi$
$882$	7.80738	0.262888
$883$	−30.8052	−1.03668	−0.518339	−	0.855175i	$-0.673450\pi$
$883$	−30.8052	−1.03668	−0.518339	+	0.855175i	$0.673450\pi$
$884$	101.837	3.42514
$885$	1.75952	0.0591457
$886$	−17.9967	−0.604611
$887$	−6.09932	−0.204795	−0.102398	−	0.994744i	$-0.532651\pi$
$887$	−6.09932	−0.204795	−0.102398	+	0.994744i	$0.532651\pi$
$888$	4.74687	0.159295
$889$	−11.9541	−0.400926
$890$	−20.7229	−0.694633
$891$	35.8074	1.19959
$892$	−37.7304	−1.26331
$893$	−10.5620	−0.353444
$894$	−3.46769	−0.115977
$895$	1.90526	0.0636858
$896$	2.79366	0.0933297
$897$	−3.34695	−0.111751
$898$	7.55629	0.252157
$899$	−32.8516	−1.09566
$900$	−14.5499	−0.484997
$901$	5.70668	0.190117
$902$	−137.114	−4.56541
$903$	1.14171	0.0379938
$904$	−45.5230	−1.51407
$905$	7.49095	0.249007
$906$	−1.96918	−0.0654217
$907$	7.16830	0.238020	0.119010	−	0.992893i	$-0.462028\pi$
$907$	7.16830	0.238020	0.119010	+	0.992893i	$0.462028\pi$
$908$	52.8111	1.75260
$909$	−30.3842	−1.00778
$910$	7.81895	0.259196
$911$	14.3040	0.473914	0.236957	−	0.971520i	$-0.423850\pi$
$911$	14.3040	0.473914	0.236957	+	0.971520i	$0.423850\pi$
$912$	2.69042	0.0890888
$913$	13.4023	0.443550
$914$	−17.9780	−0.594658
$915$	−1.29696	−0.0428763
$916$	−4.89272	−0.161660
$917$	22.5564	0.744877
$918$	17.7460	0.585705
$919$	0.107873	0.00355840	0.00177920	−	0.999998i	$-0.499434\pi$
$919$	0.107873	0.00355840	0.00177920	+	0.999998i	$0.499434\pi$
$920$	−52.7162	−1.73800
$921$	0.858631	0.0282928
$922$	−34.4202	−1.13357
$923$	−16.6634	−0.548482
$924$	3.23621	0.106463
$925$	3.86057	0.126935
$926$	−12.2206	−0.401594
$927$	−18.8642	−0.619582
$928$	−68.1160	−2.23602
$929$	31.7546	1.04183	0.520917	−	0.853607i	$-0.325590\pi$
$929$	31.7546	1.04183	0.520917	+	0.853607i	$0.325590\pi$
$930$	2.35082	0.0770864
$931$	−1.63666	−0.0536395
$932$	−71.2576	−2.33412
$933$	3.46728	0.113514
$934$	−35.2267	−1.15265
$935$	28.5518	0.933742
$936$	−67.2613	−2.19851
$937$	−23.0347	−0.752512	−0.376256	−	0.926516i	$-0.622789\pi$
$937$	−23.0347	−0.752512	−0.376256	+	0.926516i	$0.622789\pi$
$938$	26.1383	0.853445
$939$	3.27447	0.106858
$940$	−31.5746	−1.02985
$941$	−29.5612	−0.963668	−0.481834	−	0.876263i	$-0.660029\pi$
$941$	−29.5612	−0.963668	−0.481834	+	0.876263i	$0.660029\pi$
$942$	−5.42890	−0.176883
$943$	−88.7355	−2.88962
$944$	110.344	3.59138
$945$	0.967172	0.0314621
$946$	−75.6362	−2.45914
$947$	−43.5887	−1.41644	−0.708221	−	0.705991i	$-0.750502\pi$
$947$	−43.5887	−1.41644	−0.708221	+	0.705991i	$0.750502\pi$
$948$	−0.438715	−0.0142488
$949$	41.9116	1.36051
$950$	4.29689	0.139410
$951$	−0.260533	−0.00844835
$952$	−53.0766	−1.72022
$953$	−16.9908	−0.550385	−0.275193	−	0.961389i	$-0.588742\pi$
$953$	−16.9908	−0.550385	−0.275193	+	0.961389i	$0.588742\pi$
$954$	−6.37511	−0.206402
$955$	14.8454	0.480387
$956$	42.5505	1.37618
$957$	−3.92891	−0.127004
$958$	−53.4498	−1.72688
$959$	−11.6870	−0.377393
$960$	1.58661	0.0512077
$961$	−0.412784	−0.0133156
$962$	30.1856	0.973222
$963$	−12.1458	−0.391392
$964$	125.159	4.03110
$965$	14.3781	0.462847
$966$	2.95047	0.0949297
$967$	−5.85293	−0.188218	−0.0941088	−	0.995562i	$-0.530000\pi$
$967$	−5.85293	−0.188218	−0.0941088	+	0.995562i	$0.530000\pi$
$968$	−43.2152	−1.38899
$969$	−1.85189	−0.0594912
$970$	15.2335	0.489118
$971$	32.8653	1.05470	0.527349	−	0.849649i	$-0.323186\pi$
$971$	32.8653	1.05470	0.527349	+	0.849649i	$0.323186\pi$
$972$	−21.1393	−0.678043
$973$	−1.71363	−0.0549363
$974$	−73.3834	−2.35135
$975$	0.482178	0.0154420
$976$	−81.3357	−2.60349
$977$	−43.5284	−1.39260	−0.696299	−	0.717752i	$-0.745171\pi$
$977$	−43.5284	−1.39260	−0.696299	+	0.717752i	$0.745171\pi$
$978$	−9.67743	−0.309450
$979$	−32.2468	−1.03061
$980$	−4.89272	−0.156292
$981$	−43.8030	−1.39852
$982$	105.212	3.35746
$983$	−30.0765	−0.959292	−0.479646	−	0.877462i	$-0.659235\pi$
$983$	−30.0765	−0.959292	−0.479646	+	0.877462i	$0.659235\pi$
$984$	15.7185	0.501089
$985$	13.9332	0.443948
$986$	108.989	3.47092
$987$	1.04482	0.0332570
$988$	23.8486	0.758725
$989$	−48.9490	−1.55649
$990$	−31.8961	−1.01372
$991$	−31.1355	−0.989051	−0.494525	−	0.869163i	$-0.664658\pi$
$991$	−31.1355	−0.989051	−0.494525	+	0.869163i	$0.664658\pi$
$992$	63.4210	2.01362
$993$	3.04672	0.0966849
$994$	14.6895	0.465921
$995$	19.9627	0.632861
$996$	−2.59867	−0.0823420
$997$	25.1968	0.797991	0.398995	−	0.916953i	$-0.369359\pi$
$997$	25.1968	0.797991	0.398995	+	0.916953i	$0.369359\pi$
$998$	−11.0333	−0.349254
$999$	3.73383	0.118133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.3	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.3	✓	49	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62540 q^{2} -0.161903 q^{3} +4.89272 q^{4} -1.00000 q^{5} +0.425059 q^{6} -1.00000 q^{7} -7.59456 q^{8} -2.97379 q^{9} +O(q^{10})\)	\(q-2.62540 q^{2} -0.161903 q^{3} +4.89272 q^{4} -1.00000 q^{5} +0.425059 q^{6} -1.00000 q^{7} -7.59456 q^{8} -2.97379 q^{9} +2.62540 q^{10} +4.08537 q^{11} -0.792145 q^{12} -2.97820 q^{13} +2.62540 q^{14} +0.161903 q^{15} +10.1533 q^{16} -6.98878 q^{17} +7.80738 q^{18} -1.63666 q^{19} -4.89272 q^{20} +0.161903 q^{21} -10.7257 q^{22} -6.94131 q^{23} +1.22958 q^{24} +1.00000 q^{25} +7.81895 q^{26} +0.967172 q^{27} -4.89272 q^{28} +5.94000 q^{29} -0.425059 q^{30} -5.53057 q^{31} -11.4674 q^{32} -0.661433 q^{33} +18.3483 q^{34} +1.00000 q^{35} -14.5499 q^{36} +3.86057 q^{37} +4.29689 q^{38} +0.482178 q^{39} +7.59456 q^{40} +12.7837 q^{41} -0.425059 q^{42} +7.05184 q^{43} +19.9886 q^{44} +2.97379 q^{45} +18.2237 q^{46} +6.45339 q^{47} -1.64385 q^{48} +1.00000 q^{49} -2.62540 q^{50} +1.13150 q^{51} -14.5715 q^{52} -0.816549 q^{53} -2.53921 q^{54} -4.08537 q^{55} +7.59456 q^{56} +0.264980 q^{57} -15.5949 q^{58} +10.8678 q^{59} +0.792145 q^{60} -8.01077 q^{61} +14.5200 q^{62} +2.97379 q^{63} +9.79979 q^{64} +2.97820 q^{65} +1.73653 q^{66} +9.95593 q^{67} -34.1941 q^{68} +1.12382 q^{69} -2.62540 q^{70} +5.59513 q^{71} +22.5846 q^{72} -14.0728 q^{73} -10.1355 q^{74} -0.161903 q^{75} -8.00774 q^{76} -4.08537 q^{77} -1.26591 q^{78} +0.553831 q^{79} -10.1533 q^{80} +8.76477 q^{81} -33.5623 q^{82} +3.28055 q^{83} +0.792145 q^{84} +6.98878 q^{85} -18.5139 q^{86} -0.961701 q^{87} -31.0266 q^{88} -7.89324 q^{89} -7.80738 q^{90} +2.97820 q^{91} -33.9619 q^{92} +0.895414 q^{93} -16.9427 q^{94} +1.63666 q^{95} +1.85660 q^{96} +5.80235 q^{97} -2.62540 q^{98} -12.1490 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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