LMFDB - Embedded newform 4015.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58511 q^{2} -0.179292 q^{3} +4.68277 q^{4} +1.00000 q^{5} +0.463488 q^{6} +2.09214 q^{7} -6.93525 q^{8} -2.96785 q^{9} +O(q^{10})$	\(q-2.58511 q^{2} -0.179292 q^{3} +4.68277 q^{4} +1.00000 q^{5} +0.463488 q^{6} +2.09214 q^{7} -6.93525 q^{8} -2.96785 q^{9} -2.58511 q^{10} +1.00000 q^{11} -0.839582 q^{12} -4.99735 q^{13} -5.40839 q^{14} -0.179292 q^{15} +8.56281 q^{16} +6.36330 q^{17} +7.67222 q^{18} -4.13266 q^{19} +4.68277 q^{20} -0.375103 q^{21} -2.58511 q^{22} -6.06585 q^{23} +1.24343 q^{24} +1.00000 q^{25} +12.9187 q^{26} +1.06999 q^{27} +9.79700 q^{28} -8.53637 q^{29} +0.463488 q^{30} +0.350326 q^{31} -8.26527 q^{32} -0.179292 q^{33} -16.4498 q^{34} +2.09214 q^{35} -13.8978 q^{36} +0.503875 q^{37} +10.6834 q^{38} +0.895983 q^{39} -6.93525 q^{40} +11.4873 q^{41} +0.969681 q^{42} -3.35980 q^{43} +4.68277 q^{44} -2.96785 q^{45} +15.6809 q^{46} -10.9259 q^{47} -1.53524 q^{48} -2.62296 q^{49} -2.58511 q^{50} -1.14089 q^{51} -23.4014 q^{52} -6.15103 q^{53} -2.76603 q^{54} +1.00000 q^{55} -14.5095 q^{56} +0.740953 q^{57} +22.0674 q^{58} +10.9021 q^{59} -0.839582 q^{60} +12.5067 q^{61} -0.905630 q^{62} -6.20916 q^{63} +4.24098 q^{64} -4.99735 q^{65} +0.463488 q^{66} +0.730531 q^{67} +29.7979 q^{68} +1.08756 q^{69} -5.40839 q^{70} +9.27558 q^{71} +20.5828 q^{72} +1.00000 q^{73} -1.30257 q^{74} -0.179292 q^{75} -19.3523 q^{76} +2.09214 q^{77} -2.31621 q^{78} +13.0212 q^{79} +8.56281 q^{80} +8.71172 q^{81} -29.6958 q^{82} -2.88990 q^{83} -1.75652 q^{84} +6.36330 q^{85} +8.68544 q^{86} +1.53050 q^{87} -6.93525 q^{88} +12.2092 q^{89} +7.67222 q^{90} -10.4551 q^{91} -28.4050 q^{92} -0.0628105 q^{93} +28.2447 q^{94} -4.13266 q^{95} +1.48189 q^{96} +2.56372 q^{97} +6.78064 q^{98} -2.96785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.58511	−1.82795	−0.913973	−	0.405775i	$-0.867002\pi$
$2$	−2.58511	−1.82795	−0.913973	+	0.405775i	$0.867002\pi$
$3$	−0.179292	−0.103514	−0.0517571	−	0.998660i	$-0.516482\pi$
$3$	−0.179292	−0.103514	−0.0517571	+	0.998660i	$0.516482\pi$
$4$	4.68277	2.34139
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.463488	0.189218
$7$	2.09214	0.790753	0.395377	−	0.918519i	$-0.370614\pi$
$7$	2.09214	0.790753	0.395377	+	0.918519i	$0.370614\pi$
$8$	−6.93525	−2.45198
$9$	−2.96785	−0.989285
$10$	−2.58511	−0.817482
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.839582	−0.242367
$13$	−4.99735	−1.38602	−0.693008	−	0.720930i	$-0.743715\pi$
$13$	−4.99735	−1.38602	−0.693008	+	0.720930i	$0.743715\pi$
$14$	−5.40839	−1.44545
$15$	−0.179292	−0.0462929
$16$	8.56281	2.14070
$17$	6.36330	1.54333	0.771663	−	0.636032i	$-0.219425\pi$
$17$	6.36330	1.54333	0.771663	+	0.636032i	$0.219425\pi$
$18$	7.67222	1.80836
$19$	−4.13266	−0.948098	−0.474049	−	0.880498i	$-0.657208\pi$
$19$	−4.13266	−0.948098	−0.474049	+	0.880498i	$0.657208\pi$
$20$	4.68277	1.04710
$21$	−0.375103	−0.0818542
$22$	−2.58511	−0.551146
$23$	−6.06585	−1.26482	−0.632408	−	0.774635i	$-0.717933\pi$
$23$	−6.06585	−1.26482	−0.632408	+	0.774635i	$0.717933\pi$
$24$	1.24343	0.253815
$25$	1.00000	0.200000
$26$	12.9187	2.53356
$27$	1.06999	0.205919
$28$	9.79700	1.85146
$29$	−8.53637	−1.58516	−0.792582	−	0.609765i	$-0.791264\pi$
$29$	−8.53637	−1.58516	−0.792582	+	0.609765i	$0.791264\pi$
$30$	0.463488	0.0846210
$31$	0.350326	0.0629204	0.0314602	−	0.999505i	$-0.489984\pi$
$31$	0.350326	0.0629204	0.0314602	+	0.999505i	$0.489984\pi$
$32$	−8.26527	−1.46111
$33$	−0.179292	−0.0312107
$34$	−16.4498	−2.82112
$35$	2.09214	0.353636
$36$	−13.8978	−2.31630
$37$	0.503875	0.0828365	0.0414182	−	0.999142i	$-0.486812\pi$
$37$	0.503875	0.0828365	0.0414182	+	0.999142i	$0.486812\pi$
$38$	10.6834	1.73307
$39$	0.895983	0.143472
$40$	−6.93525	−1.09656
$41$	11.4873	1.79401	0.897006	−	0.442019i	$-0.145737\pi$
$41$	11.4873	1.79401	0.897006	+	0.442019i	$0.145737\pi$
$42$	0.969681	0.149625
$43$	−3.35980	−0.512365	−0.256182	−	0.966628i	$-0.582465\pi$
$43$	−3.35980	−0.512365	−0.256182	+	0.966628i	$0.582465\pi$
$44$	4.68277	0.705954
$45$	−2.96785	−0.442422
$46$	15.6809	2.31202
$47$	−10.9259	−1.59371	−0.796854	−	0.604171i	$-0.793504\pi$
$47$	−10.9259	−1.59371	−0.796854	+	0.604171i	$0.793504\pi$
$48$	−1.53524	−0.221593
$49$	−2.62296	−0.374709
$50$	−2.58511	−0.365589
$51$	−1.14089	−0.159756
$52$	−23.4014	−3.24520
$53$	−6.15103	−0.844909	−0.422454	−	0.906384i	$-0.638831\pi$
$53$	−6.15103	−0.844909	−0.422454	+	0.906384i	$0.638831\pi$
$54$	−2.76603	−0.376409
$55$	1.00000	0.134840
$56$	−14.5095	−1.93891
$57$	0.740953	0.0981416
$58$	22.0674	2.89759
$59$	10.9021	1.41933	0.709666	−	0.704538i	$-0.248846\pi$
$59$	10.9021	1.41933	0.709666	+	0.704538i	$0.248846\pi$
$60$	−0.839582	−0.108390
$61$	12.5067	1.60132	0.800658	−	0.599122i	$-0.204483\pi$
$61$	12.5067	1.60132	0.800658	+	0.599122i	$0.204483\pi$
$62$	−0.905630	−0.115015
$63$	−6.20916	−0.782280
$64$	4.24098	0.530122
$65$	−4.99735	−0.619845
$66$	0.463488	0.0570514
$67$	0.730531	0.0892486	0.0446243	−	0.999004i	$-0.485791\pi$
$67$	0.730531	0.0892486	0.0446243	+	0.999004i	$0.485791\pi$
$68$	29.7979	3.61352
$69$	1.08756	0.130926
$70$	−5.40839	−0.646427
$71$	9.27558	1.10081	0.550404	−	0.834898i	$-0.314474\pi$
$71$	9.27558	1.10081	0.550404	+	0.834898i	$0.314474\pi$
$72$	20.5828	2.42571
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−1.30257	−0.151421
$75$	−0.179292	−0.0207028
$76$	−19.3523	−2.21986
$77$	2.09214	0.238421
$78$	−2.31621	−0.262259
$79$	13.0212	1.46499	0.732497	−	0.680770i	$-0.238355\pi$
$79$	13.0212	1.46499	0.732497	+	0.680770i	$0.238355\pi$
$80$	8.56281	0.957351
$81$	8.71172	0.967969
$82$	−29.6958	−3.27936
$83$	−2.88990	−0.317208	−0.158604	−	0.987342i	$-0.550699\pi$
$83$	−2.88990	−0.317208	−0.158604	+	0.987342i	$0.550699\pi$
$84$	−1.75652	−0.191652
$85$	6.36330	0.690196
$86$	8.68544	0.936575
$87$	1.53050	0.164087
$88$	−6.93525	−0.739300
$89$	12.2092	1.29418	0.647088	−	0.762416i	$-0.275987\pi$
$89$	12.2092	1.29418	0.647088	+	0.762416i	$0.275987\pi$
$90$	7.67222	0.808723
$91$	−10.4551	−1.09600
$92$	−28.4050	−2.96142
$93$	−0.0628105	−0.00651315
$94$	28.2447	2.91321
$95$	−4.13266	−0.424002
$96$	1.48189	0.151245
$97$	2.56372	0.260306	0.130153	−	0.991494i	$-0.458453\pi$
$97$	2.56372	0.260306	0.130153	+	0.991494i	$0.458453\pi$
$98$	6.78064	0.684948
$99$	−2.96785	−0.298281
$100$	4.68277	0.468277
$101$	18.8240	1.87306	0.936529	−	0.350589i	$-0.114019\pi$
$101$	18.8240	1.87306	0.936529	+	0.350589i	$0.114019\pi$
$102$	2.94931	0.292025
$103$	−5.37508	−0.529622	−0.264811	−	0.964300i	$-0.585310\pi$
$103$	−5.37508	−0.529622	−0.264811	+	0.964300i	$0.585310\pi$
$104$	34.6579	3.39848
$105$	−0.375103	−0.0366063
$106$	15.9011	1.54445
$107$	11.0181	1.06516	0.532582	−	0.846378i	$-0.321222\pi$
$107$	11.0181	1.06516	0.532582	+	0.846378i	$0.321222\pi$
$108$	5.01051	0.482136
$109$	−6.05401	−0.579869	−0.289934	−	0.957047i	$-0.593633\pi$
$109$	−6.05401	−0.579869	−0.289934	+	0.957047i	$0.593633\pi$
$110$	−2.58511	−0.246480
$111$	−0.0903406	−0.00857475
$112$	17.9146	1.69277
$113$	13.4676	1.26692	0.633461	−	0.773774i	$-0.281634\pi$
$113$	13.4676	1.26692	0.633461	+	0.773774i	$0.281634\pi$
$114$	−1.91544	−0.179397
$115$	−6.06585	−0.565643
$116$	−39.9739	−3.71148
$117$	14.8314	1.37116
$118$	−28.1831	−2.59446
$119$	13.3129	1.22039
$120$	1.24343	0.113509
$121$	1.00000	0.0909091
$122$	−32.3311	−2.92712
$123$	−2.05957	−0.185706
$124$	1.64050	0.147321
$125$	1.00000	0.0894427
$126$	16.0513	1.42997
$127$	−0.00610286	−0.000541541 0	−0.000270771	−	1.00000i	$-0.500086\pi$
$127$	−0.00610286	−0.000541541 0	−0.000270771		1.00000i	$0.500086\pi$
$128$	5.56716	0.492072
$129$	0.602384	0.0530370
$130$	12.9187	1.13304
$131$	17.0010	1.48538	0.742691	−	0.669634i	$-0.233549\pi$
$131$	17.0010	1.48538	0.742691	+	0.669634i	$0.233549\pi$
$132$	−0.839582	−0.0730763
$133$	−8.64610	−0.749712
$134$	−1.88850	−0.163142
$135$	1.06999	0.0920898
$136$	−44.1310	−3.78421
$137$	−3.05839	−0.261296	−0.130648	−	0.991429i	$-0.541706\pi$
$137$	−3.05839	−0.261296	−0.130648	+	0.991429i	$0.541706\pi$
$138$	−2.81145	−0.239326
$139$	12.9025	1.09438	0.547190	−	0.837008i	$-0.315698\pi$
$139$	12.9025	1.09438	0.547190	+	0.837008i	$0.315698\pi$
$140$	9.79700	0.827998
$141$	1.95893	0.164971
$142$	−23.9784	−2.01222
$143$	−4.99735	−0.417899
$144$	−25.4132	−2.11776
$145$	−8.53637	−0.708907
$146$	−2.58511	−0.213945
$147$	0.470276	0.0387877
$148$	2.35953	0.193952
$149$	−17.9085	−1.46712	−0.733562	−	0.679623i	$-0.762143\pi$
$149$	−17.9085	−1.46712	−0.733562	+	0.679623i	$0.762143\pi$
$150$	0.463488	0.0378436
$151$	−0.140306	−0.0114179	−0.00570897	−	0.999984i	$-0.501817\pi$
$151$	−0.140306	−0.0114179	−0.00570897	+	0.999984i	$0.501817\pi$
$152$	28.6611	2.32472
$153$	−18.8853	−1.52679
$154$	−5.40839	−0.435821
$155$	0.350326	0.0281389
$156$	4.19569	0.335924
$157$	−11.6156	−0.927030	−0.463515	−	0.886089i	$-0.653412\pi$
$157$	−11.6156	−0.927030	−0.463515	+	0.886089i	$0.653412\pi$
$158$	−33.6611	−2.67793
$159$	1.10283	0.0874600
$160$	−8.26527	−0.653427
$161$	−12.6906	−1.00016
$162$	−22.5207	−1.76940
$163$	9.50264	0.744304	0.372152	−	0.928172i	$-0.378620\pi$
$163$	9.50264	0.744304	0.372152	+	0.928172i	$0.378620\pi$
$164$	53.7923	4.20047
$165$	−0.179292	−0.0139578
$166$	7.47071	0.579840
$167$	−7.27332	−0.562826	−0.281413	−	0.959587i	$-0.590803\pi$
$167$	−7.27332	−0.562826	−0.281413	+	0.959587i	$0.590803\pi$
$168$	2.60143	0.200705
$169$	11.9735	0.921038
$170$	−16.4498	−1.26164
$171$	12.2651	0.937939
$172$	−15.7332	−1.19964
$173$	14.1344	1.07462	0.537309	−	0.843386i	$-0.319441\pi$
$173$	14.1344	1.07462	0.537309	+	0.843386i	$0.319441\pi$
$174$	−3.95651	−0.299942
$175$	2.09214	0.158151
$176$	8.56281	0.645446
$177$	−1.95466	−0.146921
$178$	−31.5621	−2.36568
$179$	18.6613	1.39481	0.697404	−	0.716678i	$-0.254338\pi$
$179$	18.6613	1.39481	0.697404	+	0.716678i	$0.254338\pi$
$180$	−13.8978	−1.03588
$181$	−20.3374	−1.51166	−0.755832	−	0.654765i	$-0.772767\pi$
$181$	−20.3374	−1.51166	−0.755832	+	0.654765i	$0.772767\pi$
$182$	27.0276	2.00342
$183$	−2.24234	−0.165759
$184$	42.0682	3.10131
$185$	0.503875	0.0370456
$186$	0.162372	0.0119057
$187$	6.36330	0.465330
$188$	−51.1636	−3.73149
$189$	2.23856	0.162831
$190$	10.6834	0.775053
$191$	6.61643	0.478748	0.239374	−	0.970927i	$-0.423058\pi$
$191$	6.61643	0.478748	0.239374	+	0.970927i	$0.423058\pi$
$192$	−0.760372	−0.0548751
$193$	5.22653	0.376214	0.188107	−	0.982149i	$-0.439765\pi$
$193$	5.22653	0.376214	0.188107	+	0.982149i	$0.439765\pi$
$194$	−6.62749	−0.475826
$195$	0.895983	0.0641627
$196$	−12.2827	−0.877339
$197$	−1.70479	−0.121462	−0.0607308	−	0.998154i	$-0.519343\pi$
$197$	−1.70479	−0.121462	−0.0607308	+	0.998154i	$0.519343\pi$
$198$	7.67222	0.545241
$199$	−22.5770	−1.60044	−0.800220	−	0.599706i	$-0.795284\pi$
$199$	−22.5770	−1.60044	−0.800220	+	0.599706i	$0.795284\pi$
$200$	−6.93525	−0.490396
$201$	−0.130978	−0.00923849
$202$	−48.6621	−3.42385
$203$	−17.8593	−1.25347
$204$	−5.34251	−0.374051
$205$	11.4873	0.802306
$206$	13.8952	0.968121
$207$	18.0026	1.25126
$208$	−42.7913	−2.96705
$209$	−4.13266	−0.285862
$210$	0.969681	0.0669143
$211$	7.96175	0.548110	0.274055	−	0.961714i	$-0.411635\pi$
$211$	7.96175	0.548110	0.274055	+	0.961714i	$0.411635\pi$
$212$	−28.8039	−1.97826
$213$	−1.66303	−0.113949
$214$	−28.4831	−1.94706
$215$	−3.35980	−0.229136
$216$	−7.42063	−0.504910
$217$	0.732930	0.0497545
$218$	15.6502	1.05997
$219$	−0.179292	−0.0121154
$220$	4.68277	0.315712
$221$	−31.7996	−2.13907
$222$	0.233540	0.0156742
$223$	−9.86209	−0.660414	−0.330207	−	0.943908i	$-0.607119\pi$
$223$	−9.86209	−0.660414	−0.330207	+	0.943908i	$0.607119\pi$
$224$	−17.2921	−1.15538
$225$	−2.96785	−0.197857
$226$	−34.8151	−2.31587
$227$	11.1074	0.737227	0.368613	−	0.929583i	$-0.379833\pi$
$227$	11.1074	0.737227	0.368613	+	0.929583i	$0.379833\pi$
$228$	3.46971	0.229787
$229$	−11.4937	−0.759524	−0.379762	−	0.925084i	$-0.623994\pi$
$229$	−11.4937	−0.759524	−0.379762	+	0.925084i	$0.623994\pi$
$230$	15.6809	1.03397
$231$	−0.375103	−0.0246800
$232$	59.2019	3.88679
$233$	5.63328	0.369048	0.184524	−	0.982828i	$-0.440926\pi$
$233$	5.63328	0.369048	0.184524	+	0.982828i	$0.440926\pi$
$234$	−38.3407	−2.50641
$235$	−10.9259	−0.712728
$236$	51.0520	3.32320
$237$	−2.33459	−0.151648
$238$	−34.4152	−2.23081
$239$	−2.26256	−0.146353	−0.0731766	−	0.997319i	$-0.523314\pi$
$239$	−2.26256	−0.146353	−0.0731766	+	0.997319i	$0.523314\pi$
$240$	−1.53524	−0.0990994
$241$	−1.52060	−0.0979504	−0.0489752	−	0.998800i	$-0.515596\pi$
$241$	−1.52060	−0.0979504	−0.0489752	+	0.998800i	$0.515596\pi$
$242$	−2.58511	−0.166177
$243$	−4.77190	−0.306118
$244$	58.5659	3.74930
$245$	−2.62296	−0.167575
$246$	5.32422	0.339460
$247$	20.6524	1.31408
$248$	−2.42960	−0.154280
$249$	0.518136	0.0328355
$250$	−2.58511	−0.163496
$251$	−17.7964	−1.12330	−0.561648	−	0.827376i	$-0.689833\pi$
$251$	−17.7964	−1.12330	−0.561648	+	0.827376i	$0.689833\pi$
$252$	−29.0761	−1.83162
$253$	−6.06585	−0.381357
$254$	0.0157765	0.000989908 0
$255$	−1.14089	−0.0714451
$256$	−22.8737	−1.42960
$257$	12.0147	0.749459	0.374729	−	0.927134i	$-0.377736\pi$
$257$	12.0147	0.749459	0.374729	+	0.927134i	$0.377736\pi$
$258$	−1.55723	−0.0969487
$259$	1.05417	0.0655032
$260$	−23.4014	−1.45130
$261$	25.3347	1.56818
$262$	−43.9493	−2.71520
$263$	10.4883	0.646735	0.323367	−	0.946274i	$-0.395185\pi$
$263$	10.4883	0.646735	0.323367	+	0.946274i	$0.395185\pi$
$264$	1.24343	0.0765280
$265$	−6.15103	−0.377855
$266$	22.3511	1.37043
$267$	−2.18901	−0.133965
$268$	3.42091	0.208965
$269$	5.80278	0.353802	0.176901	−	0.984229i	$-0.443393\pi$
$269$	5.80278	0.353802	0.176901	+	0.984229i	$0.443393\pi$
$270$	−2.76603	−0.168335
$271$	−13.2023	−0.801980	−0.400990	−	0.916082i	$-0.631334\pi$
$271$	−13.2023	−0.801980	−0.400990	+	0.916082i	$0.631334\pi$
$272$	54.4877	3.30380
$273$	1.87452	0.113451
$274$	7.90626	0.477634
$275$	1.00000	0.0603023
$276$	5.09278	0.306549
$277$	−27.7143	−1.66519	−0.832595	−	0.553882i	$-0.813146\pi$
$277$	−27.7143	−1.66519	−0.832595	+	0.553882i	$0.813146\pi$
$278$	−33.3545	−2.00047
$279$	−1.03972	−0.0622462
$280$	−14.5095	−0.867108
$281$	26.3737	1.57333	0.786663	−	0.617383i	$-0.211807\pi$
$281$	26.3737	1.57333	0.786663	+	0.617383i	$0.211807\pi$
$282$	−5.06403	−0.301559
$283$	−3.57311	−0.212399	−0.106200	−	0.994345i	$-0.533868\pi$
$283$	−3.57311	−0.212399	−0.106200	+	0.994345i	$0.533868\pi$
$284$	43.4354	2.57742
$285$	0.740953	0.0438902
$286$	12.9187	0.763897
$287$	24.0330	1.41862
$288$	24.5301	1.44545
$289$	23.4915	1.38185
$290$	22.0674	1.29584
$291$	−0.459654	−0.0269454
$292$	4.68277	0.274039
$293$	5.34700	0.312375	0.156187	−	0.987727i	$-0.450080\pi$
$293$	5.34700	0.312375	0.156187	+	0.987727i	$0.450080\pi$
$294$	−1.21571	−0.0709018
$295$	10.9021	0.634745
$296$	−3.49450	−0.203114
$297$	1.06999	0.0620869
$298$	46.2954	2.68182
$299$	30.3132	1.75305
$300$	−0.839582	−0.0484733
$301$	−7.02916	−0.405154
$302$	0.362706	0.0208714
$303$	−3.37499	−0.193888
$304$	−35.3872	−2.02960
$305$	12.5067	0.716130
$306$	48.8206	2.79089
$307$	3.47864	0.198537	0.0992683	−	0.995061i	$-0.468350\pi$
$307$	3.47864	0.198537	0.0992683	+	0.995061i	$0.468350\pi$
$308$	9.79700	0.558236
$309$	0.963708	0.0548234
$310$	−0.905630	−0.0514363
$311$	15.9762	0.905928	0.452964	−	0.891529i	$-0.350367\pi$
$311$	15.9762	0.905928	0.452964	+	0.891529i	$0.350367\pi$
$312$	−6.21387	−0.351791
$313$	26.1388	1.47746	0.738728	−	0.674004i	$-0.235427\pi$
$313$	26.1388	1.47746	0.738728	+	0.674004i	$0.235427\pi$
$314$	30.0277	1.69456
$315$	−6.20916	−0.349846
$316$	60.9751	3.43012
$317$	8.07302	0.453426	0.226713	−	0.973962i	$-0.427202\pi$
$317$	8.07302	0.453426	0.226713	+	0.973962i	$0.427202\pi$
$318$	−2.85093	−0.159872
$319$	−8.53637	−0.477945
$320$	4.24098	0.237078
$321$	−1.97546	−0.110260
$322$	32.8065	1.82823
$323$	−26.2974	−1.46322
$324$	40.7950	2.26639
$325$	−4.99735	−0.277203
$326$	−24.5653	−1.36055
$327$	1.08543	0.0600246
$328$	−79.6672	−4.39888
$329$	−22.8585	−1.26023
$330$	0.463488	0.0255142
$331$	−27.5545	−1.51453	−0.757266	−	0.653106i	$-0.773466\pi$
$331$	−27.5545	−1.51453	−0.757266	+	0.653106i	$0.773466\pi$
$332$	−13.5328	−0.742707
$333$	−1.49543	−0.0819489
$334$	18.8023	1.02882
$335$	0.730531	0.0399132
$336$	−3.21193	−0.175225
$337$	16.4754	0.897473	0.448736	−	0.893664i	$-0.351874\pi$
$337$	16.4754	0.897473	0.448736	+	0.893664i	$0.351874\pi$
$338$	−30.9527	−1.68361
$339$	−2.41462	−0.131144
$340$	29.7979	1.61602
$341$	0.350326	0.0189712
$342$	−31.7067	−1.71450
$343$	−20.1326	−1.08706
$344$	23.3010	1.25631
$345$	1.08756	0.0585521
$346$	−36.5389	−1.96434
$347$	12.5370	0.673022	0.336511	−	0.941680i	$-0.390753\pi$
$347$	12.5370	0.673022	0.336511	+	0.941680i	$0.390753\pi$
$348$	7.16699	0.384191
$349$	−8.88010	−0.475341	−0.237670	−	0.971346i	$-0.576384\pi$
$349$	−8.88010	−0.475341	−0.237670	+	0.971346i	$0.576384\pi$
$350$	−5.40839	−0.289091
$351$	−5.34710	−0.285407
$352$	−8.26527	−0.440540
$353$	−7.50649	−0.399530	−0.199765	−	0.979844i	$-0.564018\pi$
$353$	−7.50649	−0.399530	−0.199765	+	0.979844i	$0.564018\pi$
$354$	5.05299	0.268564
$355$	9.27558	0.492297
$356$	57.1730	3.03016
$357$	−2.38689	−0.126328
$358$	−48.2414	−2.54964
$359$	31.9973	1.68875	0.844377	−	0.535749i	$-0.179971\pi$
$359$	31.9973	1.68875	0.844377	+	0.535749i	$0.179971\pi$
$360$	20.5828	1.08481
$361$	−1.92109	−0.101110
$362$	52.5742	2.76324
$363$	−0.179292	−0.00941038
$364$	−48.9590	−2.56615
$365$	1.00000	0.0523424
$366$	5.79670	0.302998
$367$	28.8148	1.50412	0.752059	−	0.659095i	$-0.229061\pi$
$367$	28.8148	1.50412	0.752059	+	0.659095i	$0.229061\pi$
$368$	−51.9407	−2.70760
$369$	−34.0926	−1.77479
$370$	−1.30257	−0.0677174
$371$	−12.8688	−0.668115
$372$	−0.294127	−0.0152498
$373$	20.6301	1.06818	0.534092	−	0.845426i	$-0.320653\pi$
$373$	20.6301	1.06818	0.534092	+	0.845426i	$0.320653\pi$
$374$	−16.4498	−0.850599
$375$	−0.179292	−0.00925859
$376$	75.7740	3.90774
$377$	42.6592	2.19706
$378$	−5.78691	−0.297647
$379$	−1.14856	−0.0589978	−0.0294989	−	0.999565i	$-0.509391\pi$
$379$	−1.14856	−0.0589978	−0.0294989	+	0.999565i	$0.509391\pi$
$380$	−19.3523	−0.992753
$381$	0.00109419	5.60572e−5 0
$382$	−17.1042	−0.875126
$383$	−5.38815	−0.275322	−0.137661	−	0.990479i	$-0.543958\pi$
$383$	−5.38815	−0.275322	−0.137661	+	0.990479i	$0.543958\pi$
$384$	−0.998147	−0.0509365
$385$	2.09214	0.106625
$386$	−13.5111	−0.687699
$387$	9.97139	0.506874
$388$	12.0053	0.609477
$389$	−0.261601	−0.0132637	−0.00663185	−	0.999978i	$-0.502111\pi$
$389$	−0.261601	−0.0132637	−0.00663185	+	0.999978i	$0.502111\pi$
$390$	−2.31621	−0.117286
$391$	−38.5988	−1.95202
$392$	18.1909	0.918780
$393$	−3.04813	−0.153758
$394$	4.40707	0.222025
$395$	13.0212	0.655165
$396$	−13.8978	−0.698390
$397$	−9.96780	−0.500270	−0.250135	−	0.968211i	$-0.580475\pi$
$397$	−9.96780	−0.500270	−0.250135	+	0.968211i	$0.580475\pi$
$398$	58.3639	2.92552
$399$	1.55017	0.0776058
$400$	8.56281	0.428140
$401$	21.5435	1.07583	0.537917	−	0.842998i	$-0.319211\pi$
$401$	21.5435	1.07583	0.537917	+	0.842998i	$0.319211\pi$
$402$	0.338593	0.0168875
$403$	−1.75070	−0.0872086
$404$	88.1485	4.38555
$405$	8.71172	0.432889
$406$	46.1681	2.29128
$407$	0.503875	0.0249761
$408$	7.91233	0.391719
$409$	−4.12783	−0.204108	−0.102054	−	0.994779i	$-0.532541\pi$
$409$	−4.12783	−0.204108	−0.102054	+	0.994779i	$0.532541\pi$
$410$	−29.6958	−1.46657
$411$	0.548344	0.0270478
$412$	−25.1703	−1.24005
$413$	22.8087	1.12234
$414$	−46.5385	−2.28724
$415$	−2.88990	−0.141860
$416$	41.3044	2.02512
$417$	−2.31332	−0.113284
$418$	10.6834	0.522541
$419$	−27.0062	−1.31934	−0.659669	−	0.751556i	$-0.729303\pi$
$419$	−27.0062	−1.31934	−0.659669	+	0.751556i	$0.729303\pi$
$420$	−1.75652	−0.0857095
$421$	0.901224	0.0439230	0.0219615	−	0.999759i	$-0.493009\pi$
$421$	0.901224	0.0439230	0.0219615	+	0.999759i	$0.493009\pi$
$422$	−20.5820	−1.00191
$423$	32.4265	1.57663
$424$	42.6589	2.07170
$425$	6.36330	0.308665
$426$	4.29912	0.208293
$427$	26.1657	1.26625
$428$	51.5955	2.49396
$429$	0.895983	0.0432585
$430$	8.68544	0.418849
$431$	−13.1919	−0.635432	−0.317716	−	0.948186i	$-0.602916\pi$
$431$	−13.1919	−0.635432	−0.317716	+	0.948186i	$0.602916\pi$
$432$	9.16210	0.440812
$433$	−0.366034	−0.0175905	−0.00879524	−	0.999961i	$-0.502800\pi$
$433$	−0.366034	−0.0175905	−0.00879524	+	0.999961i	$0.502800\pi$
$434$	−1.89470	−0.0909485
$435$	1.53050	0.0733819
$436$	−28.3495	−1.35770
$437$	25.0681	1.19917
$438$	0.463488	0.0221463
$439$	4.48337	0.213980	0.106990	−	0.994260i	$-0.465879\pi$
$439$	4.48337	0.213980	0.106990	+	0.994260i	$0.465879\pi$
$440$	−6.93525	−0.330625
$441$	7.78458	0.370694
$442$	82.2053	3.91011
$443$	−23.2967	−1.10686	−0.553429	−	0.832896i	$-0.686681\pi$
$443$	−23.2967	−1.10686	−0.553429	+	0.832896i	$0.686681\pi$
$444$	−0.423044	−0.0200768
$445$	12.2092	0.578773
$446$	25.4945	1.20720
$447$	3.21085	0.151868
$448$	8.87270	0.419196
$449$	21.9408	1.03545	0.517724	−	0.855547i	$-0.326779\pi$
$449$	21.9408	1.03545	0.517724	+	0.855547i	$0.326779\pi$
$450$	7.67222	0.361672
$451$	11.4873	0.540915
$452$	63.0656	2.96635
$453$	0.0251557	0.00118192
$454$	−28.7139	−1.34761
$455$	−10.4551	−0.490144
$456$	−5.13869	−0.240641
$457$	−4.68888	−0.219337	−0.109668	−	0.993968i	$-0.534979\pi$
$457$	−4.68888	−0.219337	−0.109668	+	0.993968i	$0.534979\pi$
$458$	29.7124	1.38837
$459$	6.80864	0.317800
$460$	−28.4050	−1.32439
$461$	4.56239	0.212492	0.106246	−	0.994340i	$-0.466117\pi$
$461$	4.56239	0.212492	0.106246	+	0.994340i	$0.466117\pi$
$462$	0.969681	0.0451136
$463$	−8.20782	−0.381450	−0.190725	−	0.981644i	$-0.561084\pi$
$463$	−8.20782	−0.381450	−0.190725	+	0.981644i	$0.561084\pi$
$464$	−73.0953	−3.39336
$465$	−0.0628105	−0.00291277
$466$	−14.5626	−0.674600
$467$	13.6034	0.629492	0.314746	−	0.949176i	$-0.398081\pi$
$467$	13.6034	0.629492	0.314746	+	0.949176i	$0.398081\pi$
$468$	69.4521	3.21042
$469$	1.52837	0.0705736
$470$	28.2447	1.30283
$471$	2.08259	0.0959607
$472$	−75.6088	−3.48018
$473$	−3.35980	−0.154484
$474$	6.03515	0.277204
$475$	−4.13266	−0.189620
$476$	62.3412	2.85740
$477$	18.2554	0.835856
$478$	5.84897	0.267526
$479$	−1.29325	−0.0590901	−0.0295450	−	0.999563i	$-0.509406\pi$
$479$	−1.29325	−0.0590901	−0.0295450	+	0.999563i	$0.509406\pi$
$480$	1.48189	0.0676389
$481$	−2.51804	−0.114813
$482$	3.93091	0.179048
$483$	2.27532	0.103530
$484$	4.68277	0.212853
$485$	2.56372	0.116412
$486$	12.3359	0.559566
$487$	28.5653	1.29442	0.647209	−	0.762312i	$-0.275936\pi$
$487$	28.5653	1.29442	0.647209	+	0.762312i	$0.275936\pi$
$488$	−86.7369	−3.92640
$489$	−1.70374	−0.0770460
$490$	6.78064	0.306318
$491$	24.6944	1.11444	0.557221	−	0.830364i	$-0.311867\pi$
$491$	24.6944	1.11444	0.557221	+	0.830364i	$0.311867\pi$
$492$	−9.64452	−0.434808
$493$	−54.3195	−2.44643
$494$	−53.3885	−2.40206
$495$	−2.96785	−0.133395
$496$	2.99977	0.134694
$497$	19.4058	0.870468
$498$	−1.33944	−0.0600216
$499$	14.0234	0.627772	0.313886	−	0.949461i	$-0.398369\pi$
$499$	14.0234	0.627772	0.313886	+	0.949461i	$0.398369\pi$
$500$	4.68277	0.209420
$501$	1.30405	0.0582605
$502$	46.0055	2.05333
$503$	−11.2115	−0.499896	−0.249948	−	0.968259i	$-0.580414\pi$
$503$	−11.2115	−0.499896	−0.249948	+	0.968259i	$0.580414\pi$
$504$	43.0621	1.91814
$505$	18.8240	0.837657
$506$	15.6809	0.697099
$507$	−2.14675	−0.0953404
$508$	−0.0285783	−0.00126796
$509$	−27.9960	−1.24090	−0.620451	−	0.784245i	$-0.713051\pi$
$509$	−27.9960	−1.24090	−0.620451	+	0.784245i	$0.713051\pi$
$510$	2.94931	0.130598
$511$	2.09214	0.0925507
$512$	47.9965	2.12117
$513$	−4.42190	−0.195232
$514$	−31.0594	−1.36997
$515$	−5.37508	−0.236854
$516$	2.82083	0.124180
$517$	−10.9259	−0.480521
$518$	−2.72515	−0.119736
$519$	−2.53418	−0.111238
$520$	34.6579	1.51985
$521$	−33.4094	−1.46369	−0.731846	−	0.681471i	$-0.761341\pi$
$521$	−33.4094	−1.46369	−0.731846	+	0.681471i	$0.761341\pi$
$522$	−65.4929	−2.86655
$523$	7.85907	0.343653	0.171826	−	0.985127i	$-0.445033\pi$
$523$	7.85907	0.343653	0.171826	+	0.985127i	$0.445033\pi$
$524$	79.6117	3.47785
$525$	−0.375103	−0.0163708
$526$	−27.1133	−1.18220
$527$	2.22923	0.0971067
$528$	−1.53524	−0.0668128
$529$	13.7945	0.599761
$530$	15.9011	0.690698
$531$	−32.3558	−1.40412
$532$	−40.4877	−1.75536
$533$	−57.4059	−2.48653
$534$	5.65883	0.244882
$535$	11.0181	0.476356
$536$	−5.06642	−0.218836
$537$	−3.34581	−0.144382
$538$	−15.0008	−0.646730
$539$	−2.62296	−0.112979
$540$	5.01051	0.215618
$541$	22.9379	0.986179	0.493090	−	0.869978i	$-0.335867\pi$
$541$	22.9379	0.986179	0.493090	+	0.869978i	$0.335867\pi$
$542$	34.1292	1.46598
$543$	3.64632	0.156479
$544$	−52.5944	−2.25496
$545$	−6.05401	−0.259325
$546$	−4.84583	−0.207382
$547$	−21.6771	−0.926848	−0.463424	−	0.886137i	$-0.653379\pi$
$547$	−21.6771	−0.926848	−0.463424	+	0.886137i	$0.653379\pi$
$548$	−14.3217	−0.611794
$549$	−37.1180	−1.58416
$550$	−2.58511	−0.110229
$551$	35.2780	1.50289
$552$	−7.54247	−0.321029
$553$	27.2420	1.15845
$554$	71.6444	3.04388
$555$	−0.0903406	−0.00383474
$556$	60.4197	2.56237
$557$	−34.3352	−1.45483	−0.727414	−	0.686199i	$-0.759278\pi$
$557$	−34.3352	−1.45483	−0.727414	+	0.686199i	$0.759278\pi$
$558$	2.68778	0.113783
$559$	16.7901	0.710145
$560$	17.9146	0.757029
$561$	−1.14089	−0.0481683
$562$	−68.1789	−2.87595
$563$	−6.73012	−0.283641	−0.141820	−	0.989892i	$-0.545296\pi$
$563$	−6.73012	−0.283641	−0.141820	+	0.989892i	$0.545296\pi$
$564$	9.17321	0.386262
$565$	13.4676	0.566585
$566$	9.23687	0.388255
$567$	18.2261	0.765425
$568$	−64.3284	−2.69916
$569$	12.9829	0.544270	0.272135	−	0.962259i	$-0.412270\pi$
$569$	12.9829	0.544270	0.272135	+	0.962259i	$0.412270\pi$
$570$	−1.91544	−0.0802290
$571$	25.7028	1.07563	0.537815	−	0.843063i	$-0.319250\pi$
$571$	25.7028	1.07563	0.537815	+	0.843063i	$0.319250\pi$
$572$	−23.4014	−0.978463
$573$	−1.18627	−0.0495572
$574$	−62.1277	−2.59316
$575$	−6.06585	−0.252963
$576$	−12.5866	−0.524442
$577$	−10.6899	−0.445026	−0.222513	−	0.974930i	$-0.571426\pi$
$577$	−10.6899	−0.445026	−0.222513	+	0.974930i	$0.571426\pi$
$578$	−60.7281	−2.52596
$579$	−0.937074	−0.0389435
$580$	−39.9739	−1.65982
$581$	−6.04608	−0.250834
$582$	1.18825	0.0492547
$583$	−6.15103	−0.254750
$584$	−6.93525	−0.286983
$585$	14.8314	0.613203
$586$	−13.8225	−0.571004
$587$	−9.65922	−0.398679	−0.199339	−	0.979931i	$-0.563880\pi$
$587$	−9.65922	−0.398679	−0.199339	+	0.979931i	$0.563880\pi$
$588$	2.20219	0.0908170
$589$	−1.44778	−0.0596547
$590$	−28.1831	−1.16028
$591$	0.305655	0.0125730
$592$	4.31458	0.177328
$593$	−11.0147	−0.452320	−0.226160	−	0.974090i	$-0.572617\pi$
$593$	−11.0147	−0.452320	−0.226160	+	0.974090i	$0.572617\pi$
$594$	−2.76603	−0.113492
$595$	13.3129	0.545775
$596$	−83.8615	−3.43510
$597$	4.04787	0.165668
$598$	−78.3627	−3.20449
$599$	28.2804	1.15550	0.577752	−	0.816212i	$-0.303930\pi$
$599$	28.2804	1.15550	0.577752	+	0.816212i	$0.303930\pi$
$600$	1.24343	0.0507629
$601$	37.9620	1.54850	0.774251	−	0.632878i	$-0.218127\pi$
$601$	37.9620	1.54850	0.774251	+	0.632878i	$0.218127\pi$
$602$	18.1711	0.740599
$603$	−2.16811	−0.0882923
$604$	−0.657021	−0.0267338
$605$	1.00000	0.0406558
$606$	8.72471	0.354417
$607$	10.8604	0.440810	0.220405	−	0.975408i	$-0.429262\pi$
$607$	10.8604	0.440810	0.220405	+	0.975408i	$0.429262\pi$
$608$	34.1576	1.38527
$609$	3.20202	0.129752
$610$	−32.3311	−1.30905
$611$	54.6006	2.20890
$612$	−88.4357	−3.57480
$613$	31.8532	1.28654	0.643269	−	0.765640i	$-0.277578\pi$
$613$	31.8532	1.28654	0.643269	+	0.765640i	$0.277578\pi$
$614$	−8.99266	−0.362914
$615$	−2.05957	−0.0830501
$616$	−14.5095	−0.584604
$617$	36.5701	1.47226	0.736128	−	0.676842i	$-0.236652\pi$
$617$	36.5701	1.47226	0.736128	+	0.676842i	$0.236652\pi$
$618$	−2.49129	−0.100214
$619$	18.9817	0.762938	0.381469	−	0.924382i	$-0.375418\pi$
$619$	18.9817	0.762938	0.381469	+	0.924382i	$0.375418\pi$
$620$	1.64050	0.0658839
$621$	−6.49038	−0.260450
$622$	−41.3002	−1.65599
$623$	25.5434	1.02337
$624$	7.67213	0.307131
$625$	1.00000	0.0400000
$626$	−67.5717	−2.70071
$627$	0.740953	0.0295908
$628$	−54.3934	−2.17053
$629$	3.20630	0.127844
$630$	16.0513	0.639500
$631$	−7.09028	−0.282260	−0.141130	−	0.989991i	$-0.545074\pi$
$631$	−7.09028	−0.282260	−0.141130	+	0.989991i	$0.545074\pi$
$632$	−90.3050	−3.59214
$633$	−1.42748	−0.0567371
$634$	−20.8696	−0.828838
$635$	−0.00610286	−0.000242185 0
$636$	5.16430	0.204778
$637$	13.1079	0.519353
$638$	22.0674	0.873658
$639$	−27.5286	−1.08901
$640$	5.56716	0.220061
$641$	8.41090	0.332211	0.166105	−	0.986108i	$-0.446881\pi$
$641$	8.41090	0.332211	0.166105	+	0.986108i	$0.446881\pi$
$642$	5.10678	0.201549
$643$	43.0220	1.69662	0.848311	−	0.529499i	$-0.177620\pi$
$643$	43.0220	1.69662	0.848311	+	0.529499i	$0.177620\pi$
$644$	−59.4271	−2.34176
$645$	0.602384	0.0237189
$646$	67.9815	2.67470
$647$	−30.4454	−1.19693	−0.598466	−	0.801148i	$-0.704223\pi$
$647$	−30.4454	−1.19693	−0.598466	+	0.801148i	$0.704223\pi$
$648$	−60.4180	−2.37344
$649$	10.9021	0.427945
$650$	12.9187	0.506712
$651$	−0.131408	−0.00515030
$652$	44.4987	1.74270
$653$	−38.8776	−1.52140	−0.760700	−	0.649104i	$-0.775144\pi$
$653$	−38.8776	−1.52140	−0.760700	+	0.649104i	$0.775144\pi$
$654$	−2.80596	−0.109722
$655$	17.0010	0.664283
$656$	98.3634	3.84045
$657$	−2.96785	−0.115787
$658$	59.0917	2.30363
$659$	11.3235	0.441100	0.220550	−	0.975376i	$-0.429215\pi$
$659$	11.3235	0.441100	0.220550	+	0.975376i	$0.429215\pi$
$660$	−0.839582	−0.0326807
$661$	−0.189124	−0.00735607	−0.00367803	−	0.999993i	$-0.501171\pi$
$661$	−0.189124	−0.00735607	−0.00367803	+	0.999993i	$0.501171\pi$
$662$	71.2313	2.76848
$663$	5.70141	0.221424
$664$	20.0422	0.777789
$665$	−8.64610	−0.335281
$666$	3.86584	0.149798
$667$	51.7803	2.00494
$668$	−34.0593	−1.31779
$669$	1.76819	0.0683622
$670$	−1.88850	−0.0729591
$671$	12.5067	0.482815
$672$	3.10033	0.119598
$673$	38.9986	1.50328	0.751642	−	0.659571i	$-0.229262\pi$
$673$	38.9986	1.50328	0.751642	+	0.659571i	$0.229262\pi$
$674$	−42.5907	−1.64053
$675$	1.06999	0.0411838
$676$	56.0691	2.15650
$677$	−44.1618	−1.69728	−0.848638	−	0.528975i	$-0.822577\pi$
$677$	−44.1618	−1.69728	−0.848638	+	0.528975i	$0.822577\pi$
$678$	6.24206	0.239725
$679$	5.36365	0.205838
$680$	−44.1310	−1.69235
$681$	−1.99147	−0.0763134
$682$	−0.905630	−0.0346783
$683$	6.81871	0.260911	0.130455	−	0.991454i	$-0.458356\pi$
$683$	6.81871	0.260911	0.130455	+	0.991454i	$0.458356\pi$
$684$	57.4349	2.19608
$685$	−3.05839	−0.116855
$686$	52.0448	1.98708
$687$	2.06072	0.0786215
$688$	−28.7693	−1.09682
$689$	30.7388	1.17106
$690$	−2.81145	−0.107030
$691$	26.8674	1.02208	0.511042	−	0.859556i	$-0.329260\pi$
$691$	26.8674	1.02208	0.511042	+	0.859556i	$0.329260\pi$
$692$	66.1881	2.51609
$693$	−6.20916	−0.235866
$694$	−32.4095	−1.23025
$695$	12.9025	0.489422
$696$	−10.6144	−0.402338
$697$	73.0970	2.76874
$698$	22.9560	0.868897
$699$	−1.01000	−0.0382017
$700$	9.79700	0.370292
$701$	−6.55924	−0.247739	−0.123870	−	0.992299i	$-0.539530\pi$
$701$	−6.55924	−0.247739	−0.123870	+	0.992299i	$0.539530\pi$
$702$	13.8228	0.521709
$703$	−2.08235	−0.0785371
$704$	4.24098	0.159838
$705$	1.95893	0.0737775
$706$	19.4051	0.730320
$707$	39.3824	1.48113
$708$	−9.15321	−0.343999
$709$	19.8773	0.746509	0.373254	−	0.927729i	$-0.378242\pi$
$709$	19.8773	0.746509	0.373254	+	0.927729i	$0.378242\pi$
$710$	−23.9784	−0.899891
$711$	−38.6449	−1.44930
$712$	−84.6740	−3.17329
$713$	−2.12502	−0.0795828
$714$	6.17036	0.230920
$715$	−4.99735	−0.186890
$716$	87.3865	3.26579
$717$	0.405659	0.0151496
$718$	−82.7165	−3.08695
$719$	1.86277	0.0694694	0.0347347	−	0.999397i	$-0.488941\pi$
$719$	1.86277	0.0694694	0.0347347	+	0.999397i	$0.488941\pi$
$720$	−25.4132	−0.947093
$721$	−11.2454	−0.418801
$722$	4.96621	0.184823
$723$	0.272631	0.0101392
$724$	−95.2352	−3.53939
$725$	−8.53637	−0.317033
$726$	0.463488	0.0172017
$727$	−15.5780	−0.577755	−0.288877	−	0.957366i	$-0.593282\pi$
$727$	−15.5780	−0.577755	−0.288877	+	0.957366i	$0.593282\pi$
$728$	72.5090	2.68736
$729$	−25.2796	−0.936282
$730$	−2.58511	−0.0956791
$731$	−21.3794	−0.790745
$732$	−10.5004	−0.388105
$733$	40.3439	1.49014	0.745068	−	0.666989i	$-0.232417\pi$
$733$	40.3439	1.49014	0.745068	+	0.666989i	$0.232417\pi$
$734$	−74.4892	−2.74945
$735$	0.470276	0.0173464
$736$	50.1359	1.84803
$737$	0.730531	0.0269095
$738$	88.1329	3.24422
$739$	44.3015	1.62966	0.814829	−	0.579701i	$-0.196831\pi$
$739$	44.3015	1.62966	0.814829	+	0.579701i	$0.196831\pi$
$740$	2.35953	0.0867381
$741$	−3.70280	−0.136026
$742$	33.2672	1.22128
$743$	−17.4037	−0.638480	−0.319240	−	0.947674i	$-0.603428\pi$
$743$	−17.4037	−0.638480	−0.319240	+	0.947674i	$0.603428\pi$
$744$	0.435607	0.0159701
$745$	−17.9085	−0.656117
$746$	−53.3309	−1.95258
$747$	8.57682	0.313809
$748$	29.7979	1.08952
$749$	23.0515	0.842282
$750$	0.463488	0.0169242
$751$	30.7370	1.12161	0.560804	−	0.827949i	$-0.310492\pi$
$751$	30.7370	1.12161	0.560804	+	0.827949i	$0.310492\pi$
$752$	−93.5566	−3.41166
$753$	3.19074	0.116277
$754$	−110.279	−4.01611
$755$	−0.140306	−0.00510626
$756$	10.4827	0.381251
$757$	−18.3644	−0.667466	−0.333733	−	0.942668i	$-0.608308\pi$
$757$	−18.3644	−0.667466	−0.333733	+	0.942668i	$0.608308\pi$
$758$	2.96916	0.107845
$759$	1.08756	0.0394758
$760$	28.6611	1.03965
$761$	0.638564	0.0231479	0.0115740	−	0.999933i	$-0.496316\pi$
$761$	0.638564	0.0231479	0.0115740	+	0.999933i	$0.496316\pi$
$762$	−0.00282860	−0.000102470 0
$763$	−12.6658	−0.458533
$764$	30.9833	1.12093
$765$	−18.8853	−0.682801
$766$	13.9289	0.503273
$767$	−54.4816	−1.96722
$768$	4.10106	0.147984
$769$	22.1001	0.796949	0.398474	−	0.917179i	$-0.369540\pi$
$769$	22.1001	0.796949	0.398474	+	0.917179i	$0.369540\pi$
$770$	−5.40839	−0.194905
$771$	−2.15414	−0.0775796
$772$	24.4746	0.880862
$773$	50.3966	1.81264	0.906320	−	0.422591i	$-0.138879\pi$
$773$	50.3966	1.81264	0.906320	+	0.422591i	$0.138879\pi$
$774$	−25.7771	−0.926539
$775$	0.350326	0.0125841
$776$	−17.7800	−0.638266
$777$	−0.189005	−0.00678051
$778$	0.676266	0.0242453
$779$	−47.4731	−1.70090
$780$	4.19569	0.150230
$781$	9.27558	0.331906
$782$	99.7819	3.56819
$783$	−9.13381	−0.326416
$784$	−22.4599	−0.802141
$785$	−11.6156	−0.414580
$786$	7.87975	0.281061
$787$	−37.6568	−1.34232	−0.671161	−	0.741312i	$-0.734204\pi$
$787$	−37.6568	−1.34232	−0.671161	+	0.741312i	$0.734204\pi$
$788$	−7.98316	−0.284388
$789$	−1.88046	−0.0669462
$790$	−33.6611	−1.19761
$791$	28.1760	1.00182
$792$	20.5828	0.731378
$793$	−62.5002	−2.21945
$794$	25.7678	0.914466
$795$	1.10283	0.0391133
$796$	−105.723	−3.74725
$797$	−40.5494	−1.43633	−0.718167	−	0.695871i	$-0.755019\pi$
$797$	−40.5494	−1.43633	−0.718167	+	0.695871i	$0.755019\pi$
$798$	−4.00736	−0.141859
$799$	−69.5248	−2.45961
$800$	−8.26527	−0.292221
$801$	−36.2352	−1.28031
$802$	−55.6924	−1.96657
$803$	1.00000	0.0352892
$804$	−0.613341	−0.0216309
$805$	−12.6906	−0.447284
$806$	4.52575	0.159413
$807$	−1.04039	−0.0366235
$808$	−130.549	−4.59270
$809$	−4.91724	−0.172881	−0.0864405	−	0.996257i	$-0.527549\pi$
$809$	−4.91724	−0.172881	−0.0864405	+	0.996257i	$0.527549\pi$
$810$	−22.5207	−0.791298
$811$	−47.5932	−1.67122	−0.835612	−	0.549320i	$-0.814887\pi$
$811$	−47.5932	−1.67122	−0.835612	+	0.549320i	$0.814887\pi$
$812$	−83.6308	−2.93487
$813$	2.36706	0.0830163
$814$	−1.30257	−0.0456550
$815$	9.50264	0.332863
$816$	−9.76919	−0.341990
$817$	13.8849	0.485772
$818$	10.6709	0.373099
$819$	31.0293	1.08425
$820$	53.7923	1.87851
$821$	17.7401	0.619132	0.309566	−	0.950878i	$-0.399816\pi$
$821$	17.7401	0.619132	0.309566	+	0.950878i	$0.399816\pi$
$822$	−1.41753	−0.0494419
$823$	1.08036	0.0376591	0.0188296	−	0.999823i	$-0.494006\pi$
$823$	1.08036	0.0376591	0.0188296	+	0.999823i	$0.494006\pi$
$824$	37.2775	1.29862
$825$	−0.179292	−0.00624214
$826$	−58.9628	−2.05158
$827$	−41.4352	−1.44084	−0.720422	−	0.693536i	$-0.756052\pi$
$827$	−41.4352	−1.44084	−0.720422	+	0.693536i	$0.756052\pi$
$828$	84.3018	2.92969
$829$	49.9878	1.73615	0.868074	−	0.496435i	$-0.165358\pi$
$829$	49.9878	1.73615	0.868074	+	0.496435i	$0.165358\pi$
$830$	7.47071	0.259312
$831$	4.96894	0.172371
$832$	−21.1936	−0.734757
$833$	−16.6907	−0.578298
$834$	5.98018	0.207077
$835$	−7.27332	−0.251704
$836$	−19.3523	−0.669314
$837$	0.374844	0.0129565
$838$	69.8138	2.41168
$839$	−51.9410	−1.79320	−0.896602	−	0.442837i	$-0.853972\pi$
$839$	−51.9410	−1.79320	−0.896602	+	0.442837i	$0.853972\pi$
$840$	2.60143	0.0897579
$841$	43.8696	1.51275
$842$	−2.32976	−0.0802888
$843$	−4.72859	−0.162861
$844$	37.2831	1.28334
$845$	11.9735	0.411901
$846$	−83.8260	−2.88200
$847$	2.09214	0.0718867
$848$	−52.6701	−1.80870
$849$	0.640630	0.0219863
$850$	−16.4498	−0.564223
$851$	−3.05643	−0.104773
$852$	−7.78761	−0.266799
$853$	−35.1271	−1.20273	−0.601365	−	0.798974i	$-0.705376\pi$
$853$	−35.1271	−1.20273	−0.601365	+	0.798974i	$0.705376\pi$
$854$	−67.6410	−2.31463
$855$	12.2651	0.419459
$856$	−76.4136	−2.61176
$857$	−7.27774	−0.248603	−0.124301	−	0.992244i	$-0.539669\pi$
$857$	−7.27774	−0.248603	−0.124301	+	0.992244i	$0.539669\pi$
$858$	−2.31621	−0.0790742
$859$	−43.2845	−1.47685	−0.738425	−	0.674336i	$-0.764430\pi$
$859$	−43.2845	−1.47685	−0.738425	+	0.674336i	$0.764430\pi$
$860$	−15.7332	−0.536497
$861$	−4.30891	−0.146847
$862$	34.1025	1.16154
$863$	47.4135	1.61397	0.806987	−	0.590570i	$-0.201097\pi$
$863$	47.4135	1.61397	0.806987	+	0.590570i	$0.201097\pi$
$864$	−8.84373	−0.300870
$865$	14.1344	0.480583
$866$	0.946237	0.0321544
$867$	−4.21184	−0.143042
$868$	3.43214	0.116495
$869$	13.0212	0.441712
$870$	−3.95651	−0.134138
$871$	−3.65072	−0.123700
$872$	41.9860	1.42183
$873$	−7.60875	−0.257517
$874$	−64.8037	−2.19202
$875$	2.09214	0.0707271
$876$	−0.839582	−0.0283669
$877$	36.3976	1.22906	0.614529	−	0.788894i	$-0.289346\pi$
$877$	36.3976	1.22906	0.614529	+	0.788894i	$0.289346\pi$
$878$	−11.5900	−0.391143
$879$	−0.958672	−0.0323352
$880$	8.56281	0.288652
$881$	−34.3913	−1.15867	−0.579336	−	0.815089i	$-0.696688\pi$
$881$	−34.3913	−1.15867	−0.579336	+	0.815089i	$0.696688\pi$
$882$	−20.1240	−0.677609
$883$	−16.5031	−0.555373	−0.277686	−	0.960672i	$-0.589568\pi$
$883$	−16.5031	−0.555373	−0.277686	+	0.960672i	$0.589568\pi$
$884$	−148.910	−5.00840
$885$	−1.95466	−0.0657050
$886$	60.2244	2.02328
$887$	−10.5975	−0.355830	−0.177915	−	0.984046i	$-0.556935\pi$
$887$	−10.5975	−0.355830	−0.177915	+	0.984046i	$0.556935\pi$
$888$	0.626534	0.0210251
$889$	−0.0127680	−0.000428226 0
$890$	−31.5621	−1.05797
$891$	8.71172	0.291854
$892$	−46.1819	−1.54629
$893$	45.1532	1.51099
$894$	−8.30039	−0.277606
$895$	18.6613	0.623777
$896$	11.6473	0.389108
$897$	−5.43490	−0.181466
$898$	−56.7192	−1.89274
$899$	−2.99051	−0.0997392
$900$	−13.8978	−0.463260
$901$	−39.1408	−1.30397
$902$	−29.6958	−0.988763
$903$	1.26027	0.0419392
$904$	−93.4010	−3.10647
$905$	−20.3374	−0.676037
$906$	−0.0650302	−0.00216048
$907$	−39.3670	−1.30716	−0.653581	−	0.756857i	$-0.726734\pi$
$907$	−39.3670	−1.30716	−0.653581	+	0.756857i	$0.726734\pi$
$908$	52.0136	1.72613
$909$	−55.8669	−1.85299
$910$	27.0276	0.895957
$911$	−21.8867	−0.725140	−0.362570	−	0.931957i	$-0.618101\pi$
$911$	−21.8867	−0.725140	−0.362570	+	0.931957i	$0.618101\pi$
$912$	6.34464	0.210092
$913$	−2.88990	−0.0956419
$914$	12.1213	0.400936
$915$	−2.24234	−0.0741296
$916$	−53.8223	−1.77834
$917$	35.5684	1.17457
$918$	−17.6011	−0.580922
$919$	−41.2236	−1.35984	−0.679920	−	0.733287i	$-0.737985\pi$
$919$	−41.2236	−1.35984	−0.679920	+	0.733287i	$0.737985\pi$
$920$	42.0682	1.38695
$921$	−0.623692	−0.0205513
$922$	−11.7943	−0.388423
$923$	−46.3533	−1.52574
$924$	−1.75652	−0.0577853
$925$	0.503875	0.0165673
$926$	21.2181	0.697269
$927$	15.9525	0.523947
$928$	70.5554	2.31609
$929$	−24.9756	−0.819424	−0.409712	−	0.912215i	$-0.634371\pi$
$929$	−24.9756	−0.819424	−0.409712	+	0.912215i	$0.634371\pi$
$930$	0.162372	0.00532438
$931$	10.8398	0.355261
$932$	26.3793	0.864084
$933$	−2.86440	−0.0937764
$934$	−35.1663	−1.15068
$935$	6.36330	0.208102
$936$	−102.859	−3.36207
$937$	−25.7485	−0.841166	−0.420583	−	0.907254i	$-0.638174\pi$
$937$	−25.7485	−0.841166	−0.420583	+	0.907254i	$0.638174\pi$
$938$	−3.95100	−0.129005
$939$	−4.68648	−0.152938
$940$	−51.1636	−1.66877
$941$	−43.8309	−1.42885	−0.714423	−	0.699714i	$-0.753311\pi$
$941$	−43.8309	−1.42885	−0.714423	+	0.699714i	$0.753311\pi$
$942$	−5.38372	−0.175411
$943$	−69.6801	−2.26910
$944$	93.3526	3.03837
$945$	2.23856	0.0728203
$946$	8.68544	0.282388
$947$	−33.9831	−1.10430	−0.552151	−	0.833744i	$-0.686193\pi$
$947$	−33.9831	−1.10430	−0.552151	+	0.833744i	$0.686193\pi$
$948$	−10.9323	−0.355066
$949$	−4.99735	−0.162221
$950$	10.6834	0.346614
$951$	−1.44743	−0.0469360
$952$	−92.3282	−2.99237
$953$	40.3866	1.30825	0.654125	−	0.756386i	$-0.273037\pi$
$953$	40.3866	1.30825	0.654125	+	0.756386i	$0.273037\pi$
$954$	−47.1920	−1.52790
$955$	6.61643	0.214103
$956$	−10.5951	−0.342669
$957$	1.53050	0.0494741
$958$	3.34319	0.108013
$959$	−6.39857	−0.206620
$960$	−0.760372	−0.0245409
$961$	−30.8773	−0.996041
$962$	6.50939	0.209871
$963$	−32.7003	−1.05375
$964$	−7.12062	−0.229340
$965$	5.22653	0.168248
$966$	−5.88193	−0.189248
$967$	48.5341	1.56075	0.780375	−	0.625312i	$-0.215028\pi$
$967$	48.5341	1.56075	0.780375	+	0.625312i	$0.215028\pi$
$968$	−6.93525	−0.222907
$969$	4.71490	0.151464
$970$	−6.62749	−0.212796
$971$	22.5799	0.724622	0.362311	−	0.932057i	$-0.381988\pi$
$971$	22.5799	0.724622	0.362311	+	0.932057i	$0.381988\pi$
$972$	−22.3457	−0.716740
$973$	26.9939	0.865385
$974$	−73.8444	−2.36613
$975$	0.895983	0.0286944
$976$	107.092	3.42794
$977$	15.5469	0.497391	0.248695	−	0.968582i	$-0.419998\pi$
$977$	15.5469	0.497391	0.248695	+	0.968582i	$0.419998\pi$
$978$	4.40436	0.140836
$979$	12.2092	0.390209
$980$	−12.2827	−0.392358
$981$	17.9674	0.573655
$982$	−63.8376	−2.03714
$983$	49.0249	1.56365	0.781826	−	0.623497i	$-0.214289\pi$
$983$	49.0249	1.56365	0.781826	+	0.623497i	$0.214289\pi$
$984$	14.2837	0.455347
$985$	−1.70479	−0.0543192
$986$	140.422	4.47193
$987$	4.09834	0.130452
$988$	96.7103	3.07676
$989$	20.3800	0.648047
$990$	7.67222	0.243839
$991$	−22.3033	−0.708487	−0.354243	−	0.935153i	$-0.615262\pi$
$991$	−22.3033	−0.708487	−0.354243	+	0.935153i	$0.615262\pi$
$992$	−2.89554	−0.0919334
$993$	4.94030	0.156776
$994$	−50.1660	−1.59117
$995$	−22.5770	−0.715739
$996$	2.42631	0.0768807
$997$	60.7675	1.92452	0.962262	−	0.272124i	$-0.0877259\pi$
$997$	60.7675	1.92452	0.962262	+	0.272124i	$0.0877259\pi$
$998$	−36.2519	−1.14753
$999$	0.539139	0.0170576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.2	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.2	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58511 q^{2} -0.179292 q^{3} +4.68277 q^{4} +1.00000 q^{5} +0.463488 q^{6} +2.09214 q^{7} -6.93525 q^{8} -2.96785 q^{9} +O(q^{10})\)	\(q-2.58511 q^{2} -0.179292 q^{3} +4.68277 q^{4} +1.00000 q^{5} +0.463488 q^{6} +2.09214 q^{7} -6.93525 q^{8} -2.96785 q^{9} -2.58511 q^{10} +1.00000 q^{11} -0.839582 q^{12} -4.99735 q^{13} -5.40839 q^{14} -0.179292 q^{15} +8.56281 q^{16} +6.36330 q^{17} +7.67222 q^{18} -4.13266 q^{19} +4.68277 q^{20} -0.375103 q^{21} -2.58511 q^{22} -6.06585 q^{23} +1.24343 q^{24} +1.00000 q^{25} +12.9187 q^{26} +1.06999 q^{27} +9.79700 q^{28} -8.53637 q^{29} +0.463488 q^{30} +0.350326 q^{31} -8.26527 q^{32} -0.179292 q^{33} -16.4498 q^{34} +2.09214 q^{35} -13.8978 q^{36} +0.503875 q^{37} +10.6834 q^{38} +0.895983 q^{39} -6.93525 q^{40} +11.4873 q^{41} +0.969681 q^{42} -3.35980 q^{43} +4.68277 q^{44} -2.96785 q^{45} +15.6809 q^{46} -10.9259 q^{47} -1.53524 q^{48} -2.62296 q^{49} -2.58511 q^{50} -1.14089 q^{51} -23.4014 q^{52} -6.15103 q^{53} -2.76603 q^{54} +1.00000 q^{55} -14.5095 q^{56} +0.740953 q^{57} +22.0674 q^{58} +10.9021 q^{59} -0.839582 q^{60} +12.5067 q^{61} -0.905630 q^{62} -6.20916 q^{63} +4.24098 q^{64} -4.99735 q^{65} +0.463488 q^{66} +0.730531 q^{67} +29.7979 q^{68} +1.08756 q^{69} -5.40839 q^{70} +9.27558 q^{71} +20.5828 q^{72} +1.00000 q^{73} -1.30257 q^{74} -0.179292 q^{75} -19.3523 q^{76} +2.09214 q^{77} -2.31621 q^{78} +13.0212 q^{79} +8.56281 q^{80} +8.71172 q^{81} -29.6958 q^{82} -2.88990 q^{83} -1.75652 q^{84} +6.36330 q^{85} +8.68544 q^{86} +1.53050 q^{87} -6.93525 q^{88} +12.2092 q^{89} +7.67222 q^{90} -10.4551 q^{91} -28.4050 q^{92} -0.0628105 q^{93} +28.2447 q^{94} -4.13266 q^{95} +1.48189 q^{96} +2.56372 q^{97} +6.78064 q^{98} -2.96785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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