LMFDB - Embedded newform 4015.2.a.h.1.6

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			1.6
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)

$f(q)$	$=$	$q-1.99859 q^{2} +2.62046 q^{3} +1.99434 q^{4} +1.00000 q^{5} -5.23721 q^{6} +2.62346 q^{7} +0.0113035 q^{8} +3.86680 q^{9} +O(q^{10})$	\(q-1.99859 q^{2} +2.62046 q^{3} +1.99434 q^{4} +1.00000 q^{5} -5.23721 q^{6} +2.62346 q^{7} +0.0113035 q^{8} +3.86680 q^{9} -1.99859 q^{10} +1.00000 q^{11} +5.22609 q^{12} -1.22641 q^{13} -5.24320 q^{14} +2.62046 q^{15} -4.01128 q^{16} -6.75860 q^{17} -7.72812 q^{18} +5.20995 q^{19} +1.99434 q^{20} +6.87466 q^{21} -1.99859 q^{22} -0.411436 q^{23} +0.0296204 q^{24} +1.00000 q^{25} +2.45109 q^{26} +2.27140 q^{27} +5.23208 q^{28} +2.08179 q^{29} -5.23721 q^{30} -5.35960 q^{31} +7.99428 q^{32} +2.62046 q^{33} +13.5076 q^{34} +2.62346 q^{35} +7.71172 q^{36} -8.62271 q^{37} -10.4125 q^{38} -3.21376 q^{39} +0.0113035 q^{40} +4.78486 q^{41} -13.7396 q^{42} +7.01675 q^{43} +1.99434 q^{44} +3.86680 q^{45} +0.822290 q^{46} +9.82038 q^{47} -10.5114 q^{48} -0.117475 q^{49} -1.99859 q^{50} -17.7106 q^{51} -2.44589 q^{52} +10.9519 q^{53} -4.53959 q^{54} +1.00000 q^{55} +0.0296543 q^{56} +13.6525 q^{57} -4.16064 q^{58} +5.13101 q^{59} +5.22609 q^{60} +13.4387 q^{61} +10.7116 q^{62} +10.1444 q^{63} -7.95469 q^{64} -1.22641 q^{65} -5.23721 q^{66} -0.917153 q^{67} -13.4790 q^{68} -1.07815 q^{69} -5.24320 q^{70} +2.96839 q^{71} +0.0437084 q^{72} +1.00000 q^{73} +17.2332 q^{74} +2.62046 q^{75} +10.3904 q^{76} +2.62346 q^{77} +6.42297 q^{78} +7.46040 q^{79} -4.01128 q^{80} -5.64828 q^{81} -9.56296 q^{82} +11.6845 q^{83} +13.7104 q^{84} -6.75860 q^{85} -14.0236 q^{86} +5.45524 q^{87} +0.0113035 q^{88} +11.3988 q^{89} -7.72812 q^{90} -3.21744 q^{91} -0.820545 q^{92} -14.0446 q^{93} -19.6269 q^{94} +5.20995 q^{95} +20.9487 q^{96} -4.28912 q^{97} +0.234784 q^{98} +3.86680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.99859	−1.41321	−0.706607	−	0.707607i	$-0.749775\pi$
$2$	−1.99859	−1.41321	−0.706607	+	0.707607i	$0.749775\pi$
$3$	2.62046	1.51292	0.756461	−	0.654039i	$-0.226927\pi$
$3$	2.62046	1.51292	0.756461	+	0.654039i	$0.226927\pi$
$4$	1.99434	0.997172
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.23721	−2.13808
$7$	2.62346	0.991573	0.495787	−	0.868444i	$-0.334880\pi$
$7$	2.62346	0.991573	0.495787	+	0.868444i	$0.334880\pi$
$8$	0.0113035	0.00399639
$9$	3.86680	1.28893
$10$	−1.99859	−0.632008
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.22609	1.50864
$13$	−1.22641	−0.340145	−0.170073	−	0.985432i	$-0.554400\pi$
$13$	−1.22641	−0.340145	−0.170073	+	0.985432i	$0.554400\pi$
$14$	−5.24320	−1.40130
$15$	2.62046	0.676599
$16$	−4.01128	−1.00282
$17$	−6.75860	−1.63920	−0.819600	−	0.572936i	$-0.805804\pi$
$17$	−6.75860	−1.63920	−0.819600	+	0.572936i	$0.805804\pi$
$18$	−7.72812	−1.82154
$19$	5.20995	1.19525	0.597623	−	0.801777i	$-0.296112\pi$
$19$	5.20995	1.19525	0.597623	+	0.801777i	$0.296112\pi$
$20$	1.99434	0.445949
$21$	6.87466	1.50017
$22$	−1.99859	−0.426100
$23$	−0.411436	−0.0857904	−0.0428952	−	0.999080i	$-0.513658\pi$
$23$	−0.411436	−0.0857904	−0.0428952	+	0.999080i	$0.513658\pi$
$24$	0.0296204	0.00604623
$25$	1.00000	0.200000
$26$	2.45109	0.480698
$27$	2.27140	0.437131
$28$	5.23208	0.988769
$29$	2.08179	0.386579	0.193289	−	0.981142i	$-0.438084\pi$
$29$	2.08179	0.386579	0.193289	+	0.981142i	$0.438084\pi$
$30$	−5.23721	−0.956179
$31$	−5.35960	−0.962613	−0.481307	−	0.876552i	$-0.659838\pi$
$31$	−5.35960	−0.962613	−0.481307	+	0.876552i	$0.659838\pi$
$32$	7.99428	1.41320
$33$	2.62046	0.456163
$34$	13.5076	2.31654
$35$	2.62346	0.443445
$36$	7.71172	1.28529
$37$	−8.62271	−1.41757	−0.708783	−	0.705427i	$-0.750755\pi$
$37$	−8.62271	−1.41757	−0.708783	+	0.705427i	$0.750755\pi$
$38$	−10.4125	−1.68914
$39$	−3.21376	−0.514613
$40$	0.0113035	0.00178724
$41$	4.78486	0.747270	0.373635	−	0.927576i	$-0.378111\pi$
$41$	4.78486	0.747270	0.373635	+	0.927576i	$0.378111\pi$
$42$	−13.7396	−2.12006
$43$	7.01675	1.07004	0.535022	−	0.844838i	$-0.320303\pi$
$43$	7.01675	1.07004	0.535022	+	0.844838i	$0.320303\pi$
$44$	1.99434	0.300659
$45$	3.86680	0.576428
$46$	0.822290	0.121240
$47$	9.82038	1.43245	0.716225	−	0.697870i	$-0.245869\pi$
$47$	9.82038	1.43245	0.716225	+	0.697870i	$0.245869\pi$
$48$	−10.5114	−1.51719
$49$	−0.117475	−0.0167821
$50$	−1.99859	−0.282643
$51$	−17.7106	−2.47998
$52$	−2.44589	−0.339184
$53$	10.9519	1.50435	0.752177	−	0.658961i	$-0.229004\pi$
$53$	10.9519	1.50435	0.752177	+	0.658961i	$0.229004\pi$
$54$	−4.53959	−0.617760
$55$	1.00000	0.134840
$56$	0.0296543	0.00396272
$57$	13.6525	1.80831
$58$	−4.16064	−0.546319
$59$	5.13101	0.668001	0.334000	−	0.942573i	$-0.391601\pi$
$59$	5.13101	0.668001	0.334000	+	0.942573i	$0.391601\pi$
$60$	5.22609	0.674686
$61$	13.4387	1.72065	0.860324	−	0.509748i	$-0.170261\pi$
$61$	13.4387	1.72065	0.860324	+	0.509748i	$0.170261\pi$
$62$	10.7116	1.36038
$63$	10.1444	1.27807
$64$	−7.95469	−0.994336
$65$	−1.22641	−0.152118
$66$	−5.23721	−0.644656
$67$	−0.917153	−0.112048	−0.0560240	−	0.998429i	$-0.517842\pi$
$67$	−0.917153	−0.112048	−0.0560240	+	0.998429i	$0.517842\pi$
$68$	−13.4790	−1.63457
$69$	−1.07815	−0.129794
$70$	−5.24320	−0.626683
$71$	2.96839	0.352284	0.176142	−	0.984365i	$-0.443638\pi$
$71$	2.96839	0.352284	0.176142	+	0.984365i	$0.443638\pi$
$72$	0.0437084	0.00515108
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	17.2332	2.00332
$75$	2.62046	0.302584
$76$	10.3904	1.19187
$77$	2.62346	0.298971
$78$	6.42297	0.727259
$79$	7.46040	0.839360	0.419680	−	0.907672i	$-0.362142\pi$
$79$	7.46040	0.839360	0.419680	+	0.907672i	$0.362142\pi$
$80$	−4.01128	−0.448475
$81$	−5.64828	−0.627587
$82$	−9.56296	−1.05605
$83$	11.6845	1.28254	0.641269	−	0.767316i	$-0.278408\pi$
$83$	11.6845	1.28254	0.641269	+	0.767316i	$0.278408\pi$
$84$	13.7104	1.49593
$85$	−6.75860	−0.733073
$86$	−14.0236	−1.51220
$87$	5.45524	0.584864
$88$	0.0113035	0.00120496
$89$	11.3988	1.20827	0.604135	−	0.796882i	$-0.293519\pi$
$89$	11.3988	1.20827	0.604135	+	0.796882i	$0.293519\pi$
$90$	−7.72812	−0.814616
$91$	−3.21744	−0.337279
$92$	−0.820545	−0.0855478
$93$	−14.0446	−1.45636
$94$	−19.6269	−2.02436
$95$	5.20995	0.534530
$96$	20.9487	2.13806
$97$	−4.28912	−0.435494	−0.217747	−	0.976005i	$-0.569871\pi$
$97$	−4.28912	−0.435494	−0.217747	+	0.976005i	$0.569871\pi$
$98$	0.234784	0.0237167
$99$	3.86680	0.388628
$100$	1.99434	0.199434
$101$	1.36798	0.136120	0.0680598	−	0.997681i	$-0.478319\pi$
$101$	1.36798	0.136120	0.0680598	+	0.997681i	$0.478319\pi$
$102$	35.3962	3.50474
$103$	−5.68073	−0.559739	−0.279870	−	0.960038i	$-0.590291\pi$
$103$	−5.68073	−0.559739	−0.279870	+	0.960038i	$0.590291\pi$
$104$	−0.0138628	−0.00135936
$105$	6.87466	0.670898
$106$	−21.8882	−2.12597
$107$	6.96733	0.673557	0.336778	−	0.941584i	$-0.390663\pi$
$107$	6.96733	0.673557	0.336778	+	0.941584i	$0.390663\pi$
$108$	4.52995	0.435895
$109$	0.552609	0.0529303	0.0264652	−	0.999650i	$-0.491575\pi$
$109$	0.552609	0.0529303	0.0264652	+	0.999650i	$0.491575\pi$
$110$	−1.99859	−0.190558
$111$	−22.5955	−2.14467
$112$	−10.5234	−0.994370
$113$	2.91171	0.273911	0.136955	−	0.990577i	$-0.456268\pi$
$113$	2.91171	0.273911	0.136955	+	0.990577i	$0.456268\pi$
$114$	−27.2856	−2.55553
$115$	−0.411436	−0.0383666
$116$	4.15181	0.385486
$117$	−4.74228	−0.438424
$118$	−10.2548	−0.944027
$119$	−17.7309	−1.62539
$120$	0.0296204	0.00270396
$121$	1.00000	0.0909091
$122$	−26.8584	−2.43164
$123$	12.5385	1.13056
$124$	−10.6889	−0.959891
$125$	1.00000	0.0894427
$126$	−20.2744	−1.80619
$127$	19.7891	1.75599	0.877997	−	0.478666i	$-0.158879\pi$
$127$	19.7891	1.75599	0.877997	+	0.478666i	$0.158879\pi$
$128$	−0.0904277	−0.00799276
$129$	18.3871	1.61889
$130$	2.45109	0.214975
$131$	−10.6278	−0.928558	−0.464279	−	0.885689i	$-0.653686\pi$
$131$	−10.6278	−0.928558	−0.464279	+	0.885689i	$0.653686\pi$
$132$	5.22609	0.454873
$133$	13.6681	1.18517
$134$	1.83301	0.158348
$135$	2.27140	0.195491
$136$	−0.0763959	−0.00655089
$137$	2.11478	0.180678	0.0903388	−	0.995911i	$-0.471205\pi$
$137$	2.11478	0.180678	0.0903388	+	0.995911i	$0.471205\pi$
$138$	2.15478	0.183427
$139$	21.2705	1.80414	0.902071	−	0.431588i	$-0.142046\pi$
$139$	21.2705	1.80414	0.902071	+	0.431588i	$0.142046\pi$
$140$	5.23208	0.442191
$141$	25.7339	2.16718
$142$	−5.93259	−0.497852
$143$	−1.22641	−0.102558
$144$	−15.5108	−1.29257
$145$	2.08179	0.172883
$146$	−1.99859	−0.165404
$147$	−0.307838	−0.0253901
$148$	−17.1967	−1.41356
$149$	−14.5755	−1.19407	−0.597035	−	0.802215i	$-0.703655\pi$
$149$	−14.5755	−1.19407	−0.597035	+	0.802215i	$0.703655\pi$
$150$	−5.23721	−0.427616
$151$	−19.3490	−1.57460	−0.787298	−	0.616572i	$-0.788521\pi$
$151$	−19.3490	−1.57460	−0.787298	+	0.616572i	$0.788521\pi$
$152$	0.0588908	0.00477667
$153$	−26.1341	−2.11282
$154$	−5.24320	−0.422509
$155$	−5.35960	−0.430494
$156$	−6.40934	−0.513158
$157$	−4.96387	−0.396160	−0.198080	−	0.980186i	$-0.563471\pi$
$157$	−4.96387	−0.396160	−0.198080	+	0.980186i	$0.563471\pi$
$158$	−14.9102	−1.18620
$159$	28.6989	2.27597
$160$	7.99428	0.632003
$161$	−1.07938	−0.0850675
$162$	11.2886	0.886914
$163$	−10.2786	−0.805079	−0.402539	−	0.915403i	$-0.631872\pi$
$163$	−10.2786	−0.805079	−0.402539	+	0.915403i	$0.631872\pi$
$164$	9.54267	0.745157
$165$	2.62046	0.204002
$166$	−23.3524	−1.81250
$167$	11.3997	0.882132	0.441066	−	0.897475i	$-0.354600\pi$
$167$	11.3997	0.882132	0.441066	+	0.897475i	$0.354600\pi$
$168$	0.0777077	0.00599528
$169$	−11.4959	−0.884301
$170$	13.5076	1.03599
$171$	20.1458	1.54059
$172$	13.9938	1.06702
$173$	7.45096	0.566486	0.283243	−	0.959048i	$-0.408590\pi$
$173$	7.45096	0.566486	0.283243	+	0.959048i	$0.408590\pi$
$174$	−10.9028	−0.826537
$175$	2.62346	0.198315
$176$	−4.01128	−0.302362
$177$	13.4456	1.01063
$178$	−22.7815	−1.70754
$179$	18.6247	1.39207	0.696037	−	0.718006i	$-0.254945\pi$
$179$	18.6247	1.39207	0.696037	+	0.718006i	$0.254945\pi$
$180$	7.71172	0.574798
$181$	5.28582	0.392892	0.196446	−	0.980515i	$-0.437060\pi$
$181$	5.28582	0.392892	0.196446	+	0.980515i	$0.437060\pi$
$182$	6.43033	0.476647
$183$	35.2155	2.60320
$184$	−0.00465067	−0.000342852 0
$185$	−8.62271	−0.633955
$186$	28.0694	2.05814
$187$	−6.75860	−0.494238
$188$	19.5852	1.42840
$189$	5.95892	0.433448
$190$	−10.4125	−0.755405
$191$	−7.42434	−0.537207	−0.268603	−	0.963251i	$-0.586562\pi$
$191$	−7.42434	−0.537207	−0.268603	+	0.963251i	$0.586562\pi$
$192$	−20.8449	−1.50435
$193$	−9.18309	−0.661013	−0.330507	−	0.943804i	$-0.607220\pi$
$193$	−9.18309	−0.661013	−0.330507	+	0.943804i	$0.607220\pi$
$194$	8.57216	0.615446
$195$	−3.21376	−0.230142
$196$	−0.234286	−0.0167347
$197$	−4.63996	−0.330584	−0.165292	−	0.986245i	$-0.552857\pi$
$197$	−4.63996	−0.330584	−0.165292	+	0.986245i	$0.552857\pi$
$198$	−7.72812	−0.549214
$199$	9.71917	0.688974	0.344487	−	0.938791i	$-0.388053\pi$
$199$	9.71917	0.688974	0.344487	+	0.938791i	$0.388053\pi$
$200$	0.0113035	0.000799279 0
$201$	−2.40336	−0.169520
$202$	−2.73403	−0.192366
$203$	5.46149	0.383321
$204$	−35.3211	−2.47297
$205$	4.78486	0.334189
$206$	11.3534	0.791031
$207$	−1.59094	−0.110578
$208$	4.91948	0.341105
$209$	5.20995	0.360380
$210$	−13.7396	−0.948122
$211$	5.83305	0.401563	0.200782	−	0.979636i	$-0.435652\pi$
$211$	5.83305	0.401563	0.200782	+	0.979636i	$0.435652\pi$
$212$	21.8418	1.50010
$213$	7.77855	0.532977
$214$	−13.9248	−0.951880
$215$	7.01675	0.478538
$216$	0.0256748	0.00174695
$217$	−14.0607	−0.954502
$218$	−1.10444	−0.0748018
$219$	2.62046	0.177074
$220$	1.99434	0.134459
$221$	8.28882	0.557567
$222$	45.1589	3.03087
$223$	−8.56703	−0.573691	−0.286845	−	0.957977i	$-0.592607\pi$
$223$	−8.56703	−0.573691	−0.286845	+	0.957977i	$0.592607\pi$
$224$	20.9726	1.40129
$225$	3.86680	0.257786
$226$	−5.81931	−0.387095
$227$	25.2766	1.67767	0.838834	−	0.544387i	$-0.183238\pi$
$227$	25.2766	1.67767	0.838834	+	0.544387i	$0.183238\pi$
$228$	27.2277	1.80320
$229$	−19.6282	−1.29707	−0.648533	−	0.761187i	$-0.724617\pi$
$229$	−19.6282	−1.29707	−0.648533	+	0.761187i	$0.724617\pi$
$230$	0.822290	0.0542202
$231$	6.87466	0.452319
$232$	0.0235316	0.00154492
$233$	−20.7670	−1.36049	−0.680245	−	0.732985i	$-0.738127\pi$
$233$	−20.7670	−1.36049	−0.680245	+	0.732985i	$0.738127\pi$
$234$	9.47786	0.619587
$235$	9.82038	0.640611
$236$	10.2330	0.666112
$237$	19.5497	1.26989
$238$	35.4367	2.29702
$239$	3.04598	0.197028	0.0985140	−	0.995136i	$-0.468591\pi$
$239$	3.04598	0.197028	0.0985140	+	0.995136i	$0.468591\pi$
$240$	−10.5114	−0.678507
$241$	−17.7298	−1.14207	−0.571037	−	0.820924i	$-0.693459\pi$
$241$	−17.7298	−1.14207	−0.571037	+	0.820924i	$0.693459\pi$
$242$	−1.99859	−0.128474
$243$	−21.6153	−1.38662
$244$	26.8014	1.71578
$245$	−0.117475	−0.00750520
$246$	−25.0593	−1.59772
$247$	−6.38955	−0.406557
$248$	−0.0605823	−0.00384698
$249$	30.6187	1.94038
$250$	−1.99859	−0.126402
$251$	−18.1516	−1.14572	−0.572859	−	0.819654i	$-0.694166\pi$
$251$	−18.1516	−1.14572	−0.572859	+	0.819654i	$0.694166\pi$
$252$	20.2314	1.27446
$253$	−0.411436	−0.0258668
$254$	−39.5501	−2.48160
$255$	−17.7106	−1.10908
$256$	16.0901	1.00563
$257$	−27.1482	−1.69346	−0.846731	−	0.532022i	$-0.821432\pi$
$257$	−27.1482	−1.69346	−0.846731	+	0.532022i	$0.821432\pi$
$258$	−36.7482	−2.28784
$259$	−22.6213	−1.40562
$260$	−2.44589	−0.151688
$261$	8.04986	0.498274
$262$	21.2406	1.31225
$263$	−23.6698	−1.45954	−0.729770	−	0.683692i	$-0.760373\pi$
$263$	−23.6698	−1.45954	−0.729770	+	0.683692i	$0.760373\pi$
$264$	0.0296204	0.00182301
$265$	10.9519	0.672768
$266$	−27.3168	−1.67490
$267$	29.8701	1.82802
$268$	−1.82912	−0.111731
$269$	−30.7845	−1.87696	−0.938481	−	0.345331i	$-0.887767\pi$
$269$	−30.7845	−1.87696	−0.938481	+	0.345331i	$0.887767\pi$
$270$	−4.53959	−0.276270
$271$	28.0750	1.70543	0.852716	−	0.522374i	$-0.174954\pi$
$271$	28.0750	1.70543	0.852716	+	0.522374i	$0.174954\pi$
$272$	27.1106	1.64382
$273$	−8.43116	−0.510277
$274$	−4.22656	−0.255336
$275$	1.00000	0.0603023
$276$	−2.15020	−0.129427
$277$	−32.0371	−1.92492	−0.962461	−	0.271419i	$-0.912507\pi$
$277$	−32.0371	−1.92492	−0.962461	+	0.271419i	$0.912507\pi$
$278$	−42.5110	−2.54964
$279$	−20.7245	−1.24074
$280$	0.0296543	0.00177218
$281$	−2.84913	−0.169965	−0.0849824	−	0.996382i	$-0.527083\pi$
$281$	−2.84913	−0.169965	−0.0849824	+	0.996382i	$0.527083\pi$
$282$	−51.4314	−3.06269
$283$	−2.64800	−0.157407	−0.0787037	−	0.996898i	$-0.525078\pi$
$283$	−2.64800	−0.157407	−0.0787037	+	0.996898i	$0.525078\pi$
$284$	5.92000	0.351287
$285$	13.6525	0.808702
$286$	2.45109	0.144936
$287$	12.5529	0.740973
$288$	30.9122	1.82152
$289$	28.6786	1.68698
$290$	−4.16064	−0.244321
$291$	−11.2394	−0.658868
$292$	1.99434	0.116710
$293$	−33.4740	−1.95557	−0.977786	−	0.209607i	$-0.932781\pi$
$293$	−33.4740	−1.95557	−0.977786	+	0.209607i	$0.932781\pi$
$294$	0.615241	0.0358816
$295$	5.13101	0.298739
$296$	−0.0974669	−0.00566515
$297$	2.27140	0.131800
$298$	29.1304	1.68748
$299$	0.504590	0.0291812
$300$	5.22609	0.301729
$301$	18.4081	1.06103
$302$	38.6706	2.22524
$303$	3.58474	0.205938
$304$	−20.8986	−1.19862
$305$	13.4387	0.769497
$306$	52.2313	2.98586
$307$	−12.1957	−0.696045	−0.348023	−	0.937486i	$-0.613147\pi$
$307$	−12.1957	−0.696045	−0.348023	+	0.937486i	$0.613147\pi$
$308$	5.23208	0.298125
$309$	−14.8861	−0.846841
$310$	10.7116	0.608379
$311$	2.77001	0.157073	0.0785365	−	0.996911i	$-0.474975\pi$
$311$	2.77001	0.157073	0.0785365	+	0.996911i	$0.474975\pi$
$312$	−0.0363268	−0.00205660
$313$	17.1827	0.971226	0.485613	−	0.874174i	$-0.338596\pi$
$313$	17.1827	0.971226	0.485613	+	0.874174i	$0.338596\pi$
$314$	9.92071	0.559858
$315$	10.1444	0.571571
$316$	14.8786	0.836987
$317$	21.4701	1.20588	0.602940	−	0.797787i	$-0.293996\pi$
$317$	21.4701	1.20588	0.602940	+	0.797787i	$0.293996\pi$
$318$	−57.3572	−3.21643
$319$	2.08179	0.116558
$320$	−7.95469	−0.444681
$321$	18.2576	1.01904
$322$	2.15724	0.120218
$323$	−35.2120	−1.95925
$324$	−11.2646	−0.625812
$325$	−1.22641	−0.0680291
$326$	20.5426	1.13775
$327$	1.44809	0.0800794
$328$	0.0540858	0.00298639
$329$	25.7633	1.42038
$330$	−5.23721	−0.288299
$331$	−7.23522	−0.397684	−0.198842	−	0.980032i	$-0.563718\pi$
$331$	−7.23522	−0.397684	−0.198842	+	0.980032i	$0.563718\pi$
$332$	23.3029	1.27891
$333$	−33.3423	−1.82715
$334$	−22.7832	−1.24664
$335$	−0.917153	−0.0501094
$336$	−27.5762	−1.50440
$337$	−26.9370	−1.46735	−0.733675	−	0.679501i	$-0.762196\pi$
$337$	−26.9370	−1.46735	−0.733675	+	0.679501i	$0.762196\pi$
$338$	22.9756	1.24971
$339$	7.63002	0.414406
$340$	−13.4790	−0.731000
$341$	−5.35960	−0.290239
$342$	−40.2632	−2.17718
$343$	−18.6724	−1.00821
$344$	0.0793139	0.00427632
$345$	−1.07815	−0.0580457
$346$	−14.8914	−0.800566
$347$	22.5590	1.21103	0.605515	−	0.795834i	$-0.292967\pi$
$347$	22.5590	1.21103	0.605515	+	0.795834i	$0.292967\pi$
$348$	10.8796	0.583210
$349$	0.498528	0.0266856	0.0133428	−	0.999911i	$-0.495753\pi$
$349$	0.498528	0.0266856	0.0133428	+	0.999911i	$0.495753\pi$
$350$	−5.24320	−0.280261
$351$	−2.78567	−0.148688
$352$	7.99428	0.426096
$353$	−5.77983	−0.307629	−0.153815	−	0.988100i	$-0.549156\pi$
$353$	−5.77983	−0.307629	−0.153815	+	0.988100i	$0.549156\pi$
$354$	−26.8722	−1.42824
$355$	2.96839	0.157546
$356$	22.7331	1.20485
$357$	−46.4630	−2.45908
$358$	−37.2230	−1.96730
$359$	24.6654	1.30179	0.650895	−	0.759167i	$-0.274394\pi$
$359$	24.6654	1.30179	0.650895	+	0.759167i	$0.274394\pi$
$360$	0.0437084	0.00230363
$361$	8.14362	0.428612
$362$	−10.5642	−0.555241
$363$	2.62046	0.137538
$364$	−6.41668	−0.336325
$365$	1.00000	0.0523424
$366$	−70.3812	−3.67888
$367$	−19.6725	−1.02690	−0.513449	−	0.858120i	$-0.671632\pi$
$367$	−19.6725	−1.02690	−0.513449	+	0.858120i	$0.671632\pi$
$368$	1.65039	0.0860323
$369$	18.5021	0.963180
$370$	17.2332	0.895913
$371$	28.7317	1.49168
$372$	−28.0098	−1.45224
$373$	−10.6054	−0.549127	−0.274564	−	0.961569i	$-0.588533\pi$
$373$	−10.6054	−0.549127	−0.274564	+	0.961569i	$0.588533\pi$
$374$	13.5076	0.698463
$375$	2.62046	0.135320
$376$	0.111005	0.00572463
$377$	−2.55313	−0.131493
$378$	−11.9094	−0.612554
$379$	−24.4129	−1.25401	−0.627004	−	0.779016i	$-0.715719\pi$
$379$	−24.4129	−1.25401	−0.627004	+	0.779016i	$0.715719\pi$
$380$	10.3904	0.533018
$381$	51.8564	2.65668
$382$	14.8382	0.759188
$383$	−34.1520	−1.74509	−0.872543	−	0.488538i	$-0.837530\pi$
$383$	−34.1520	−1.74509	−0.872543	+	0.488538i	$0.837530\pi$
$384$	−0.236962	−0.0120924
$385$	2.62346	0.133704
$386$	18.3532	0.934153
$387$	27.1323	1.37921
$388$	−8.55397	−0.434262
$389$	23.6171	1.19744	0.598718	−	0.800960i	$-0.295677\pi$
$389$	23.6171	1.19744	0.598718	+	0.800960i	$0.295677\pi$
$390$	6.42297	0.325240
$391$	2.78073	0.140628
$392$	−0.00132788	−6.70681e−5 0
$393$	−27.8498	−1.40484
$394$	9.27336	0.467185
$395$	7.46040	0.375373
$396$	7.71172	0.387529
$397$	−11.2353	−0.563884	−0.281942	−	0.959431i	$-0.590979\pi$
$397$	−11.2353	−0.563884	−0.281942	+	0.959431i	$0.590979\pi$
$398$	−19.4246	−0.973667
$399$	35.8166	1.79307
$400$	−4.01128	−0.200564
$401$	−1.42302	−0.0710621	−0.0355311	−	0.999369i	$-0.511312\pi$
$401$	−1.42302	−0.0710621	−0.0355311	+	0.999369i	$0.511312\pi$
$402$	4.80332	0.239568
$403$	6.57308	0.327428
$404$	2.72823	0.135735
$405$	−5.64828	−0.280665
$406$	−10.9153	−0.541715
$407$	−8.62271	−0.427412
$408$	−0.200192	−0.00991099
$409$	6.81810	0.337133	0.168567	−	0.985690i	$-0.446086\pi$
$409$	6.81810	0.337133	0.168567	+	0.985690i	$0.446086\pi$
$410$	−9.56296	−0.472281
$411$	5.54168	0.273351
$412$	−11.3293	−0.558156
$413$	13.4610	0.662372
$414$	3.17963	0.156270
$415$	11.6845	0.573569
$416$	−9.80428	−0.480694
$417$	55.7385	2.72953
$418$	−10.4125	−0.509294
$419$	6.57583	0.321250	0.160625	−	0.987015i	$-0.448649\pi$
$419$	6.57583	0.321250	0.160625	+	0.987015i	$0.448649\pi$
$420$	13.7104	0.669000
$421$	20.3330	0.990969	0.495484	−	0.868617i	$-0.334991\pi$
$421$	20.3330	0.990969	0.495484	+	0.868617i	$0.334991\pi$
$422$	−11.6578	−0.567495
$423$	37.9734	1.84633
$424$	0.123795	0.00601199
$425$	−6.75860	−0.327840
$426$	−15.5461	−0.753211
$427$	35.2558	1.70615
$428$	13.8952	0.671652
$429$	−3.21376	−0.155162
$430$	−14.0236	−0.676277
$431$	30.1939	1.45439	0.727194	−	0.686432i	$-0.240824\pi$
$431$	30.1939	1.45439	0.727194	+	0.686432i	$0.240824\pi$
$432$	−9.11122	−0.438364
$433$	−37.5707	−1.80553	−0.902767	−	0.430131i	$-0.858467\pi$
$433$	−37.5707	−1.80553	−0.902767	+	0.430131i	$0.858467\pi$
$434$	28.1015	1.34891
$435$	5.45524	0.261559
$436$	1.10209	0.0527806
$437$	−2.14356	−0.102541
$438$	−5.23721	−0.250243
$439$	−23.8925	−1.14033	−0.570163	−	0.821532i	$-0.693120\pi$
$439$	−23.8925	−1.14033	−0.570163	+	0.821532i	$0.693120\pi$
$440$	0.0113035	0.000538874 0
$441$	−0.454252	−0.0216310
$442$	−16.5659	−0.787961
$443$	38.1447	1.81231	0.906154	−	0.422948i	$-0.139005\pi$
$443$	38.1447	1.81231	0.906154	+	0.422948i	$0.139005\pi$
$444$	−45.0631	−2.13860
$445$	11.3988	0.540355
$446$	17.1219	0.810748
$447$	−38.1944	−1.80654
$448$	−20.8688	−0.985957
$449$	−19.8517	−0.936862	−0.468431	−	0.883500i	$-0.655180\pi$
$449$	−19.8517	−0.936862	−0.468431	+	0.883500i	$0.655180\pi$
$450$	−7.72812	−0.364307
$451$	4.78486	0.225310
$452$	5.80696	0.273136
$453$	−50.7031	−2.38224
$454$	−50.5175	−2.37090
$455$	−3.21744	−0.150836
$456$	0.154321	0.00722673
$457$	−20.8215	−0.973986	−0.486993	−	0.873406i	$-0.661906\pi$
$457$	−20.8215	−0.973986	−0.486993	+	0.873406i	$0.661906\pi$
$458$	39.2286	1.83303
$459$	−15.3515	−0.716546
$460$	−0.820545	−0.0382581
$461$	13.4533	0.626582	0.313291	−	0.949657i	$-0.398569\pi$
$461$	13.4533	0.626582	0.313291	+	0.949657i	$0.398569\pi$
$462$	−13.7396	−0.639223
$463$	−8.56951	−0.398259	−0.199129	−	0.979973i	$-0.563811\pi$
$463$	−8.56951	−0.398259	−0.199129	+	0.979973i	$0.563811\pi$
$464$	−8.35065	−0.387669
$465$	−14.0446	−0.651303
$466$	41.5046	1.92266
$467$	12.8520	0.594719	0.297359	−	0.954766i	$-0.403894\pi$
$467$	12.8520	0.594719	0.297359	+	0.954766i	$0.403894\pi$
$468$	−9.45775	−0.437184
$469$	−2.40611	−0.111104
$470$	−19.6269	−0.905320
$471$	−13.0076	−0.599359
$472$	0.0579984	0.00266959
$473$	7.01675	0.322630
$474$	−39.0717	−1.79462
$475$	5.20995	0.239049
$476$	−35.3615	−1.62079
$477$	42.3486	1.93901
$478$	−6.08765	−0.278443
$479$	10.3567	0.473210	0.236605	−	0.971606i	$-0.423965\pi$
$479$	10.3567	0.473210	0.236605	+	0.971606i	$0.423965\pi$
$480$	20.9487	0.956171
$481$	10.5750	0.482178
$482$	35.4344	1.61399
$483$	−2.82848	−0.128700
$484$	1.99434	0.0906520
$485$	−4.28912	−0.194759
$486$	43.2000	1.95959
$487$	−2.71602	−0.123075	−0.0615373	−	0.998105i	$-0.519600\pi$
$487$	−2.71602	−0.123075	−0.0615373	+	0.998105i	$0.519600\pi$
$488$	0.151904	0.00687639
$489$	−26.9345	−1.21802
$490$	0.234784	0.0106065
$491$	2.15605	0.0973012	0.0486506	−	0.998816i	$-0.484508\pi$
$491$	2.15605	0.0973012	0.0486506	+	0.998816i	$0.484508\pi$
$492$	25.0061	1.12736
$493$	−14.0700	−0.633680
$494$	12.7701	0.574552
$495$	3.86680	0.173800
$496$	21.4989	0.965328
$497$	7.78745	0.349315
$498$	−61.1941	−2.74217
$499$	22.5530	1.00961	0.504805	−	0.863233i	$-0.331564\pi$
$499$	22.5530	1.00961	0.504805	+	0.863233i	$0.331564\pi$
$500$	1.99434	0.0891898
$501$	29.8723	1.33460
$502$	36.2775	1.61914
$503$	24.6173	1.09763	0.548816	−	0.835943i	$-0.315079\pi$
$503$	24.6173	1.09763	0.548816	+	0.835943i	$0.315079\pi$
$504$	0.114667	0.00510767
$505$	1.36798	0.0608745
$506$	0.822290	0.0365553
$507$	−30.1245	−1.33788
$508$	39.4662	1.75103
$509$	−18.2615	−0.809429	−0.404714	−	0.914443i	$-0.632629\pi$
$509$	−18.2615	−0.809429	−0.404714	+	0.914443i	$0.632629\pi$
$510$	35.3962	1.56737
$511$	2.62346	0.116055
$512$	−31.9766	−1.41318
$513$	11.8339	0.522479
$514$	54.2581	2.39322
$515$	−5.68073	−0.250323
$516$	36.6702	1.61431
$517$	9.82038	0.431900
$518$	45.2106	1.98644
$519$	19.5249	0.857049
$520$	−0.0138628	−0.000607922 0
$521$	23.9877	1.05092	0.525461	−	0.850818i	$-0.323893\pi$
$521$	23.9877	1.05092	0.525461	+	0.850818i	$0.323893\pi$
$522$	−16.0883	−0.704167
$523$	27.2475	1.19145	0.595726	−	0.803188i	$-0.296865\pi$
$523$	27.2475	1.19145	0.595726	+	0.803188i	$0.296865\pi$
$524$	−21.1955	−0.925932
$525$	6.87466	0.300035
$526$	47.3061	2.06264
$527$	36.2234	1.57792
$528$	−10.5114	−0.457449
$529$	−22.8307	−0.992640
$530$	−21.8882	−0.950764
$531$	19.8406	0.861007
$532$	27.2589	1.18182
$533$	−5.86821	−0.254181
$534$	−59.6979	−2.58338
$535$	6.96733	0.301224
$536$	−0.0103670	−0.000447788 0
$537$	48.8052	2.10610
$538$	61.5254	2.65255
$539$	−0.117475	−0.00506001
$540$	4.52995	0.194938
$541$	2.72379	0.117105	0.0585525	−	0.998284i	$-0.481351\pi$
$541$	2.72379	0.117105	0.0585525	+	0.998284i	$0.481351\pi$
$542$	−56.1102	−2.41014
$543$	13.8513	0.594415
$544$	−54.0301	−2.31652
$545$	0.552609	0.0236712
$546$	16.8504	0.721130
$547$	8.33868	0.356536	0.178268	−	0.983982i	$-0.442951\pi$
$547$	8.33868	0.356536	0.178268	+	0.983982i	$0.442951\pi$
$548$	4.21759	0.180167
$549$	51.9646	2.21780
$550$	−1.99859	−0.0852200
$551$	10.8460	0.462057
$552$	−0.0121869	−0.000518708 0
$553$	19.5720	0.832287
$554$	64.0289	2.72033
$555$	−22.5955	−0.959124
$556$	42.4207	1.79904
$557$	−18.5301	−0.785146	−0.392573	−	0.919721i	$-0.628415\pi$
$557$	−18.5301	−0.785146	−0.392573	+	0.919721i	$0.628415\pi$
$558$	41.4197	1.75343
$559$	−8.60542	−0.363971
$560$	−10.5234	−0.444696
$561$	−17.7106	−0.747743
$562$	5.69423	0.240197
$563$	−7.77217	−0.327558	−0.163779	−	0.986497i	$-0.552368\pi$
$563$	−7.77217	−0.327558	−0.163779	+	0.986497i	$0.552368\pi$
$564$	51.3222	2.16106
$565$	2.91171	0.122497
$566$	5.29226	0.222450
$567$	−14.8180	−0.622298
$568$	0.0335533	0.00140786
$569$	34.6487	1.45255	0.726275	−	0.687404i	$-0.241250\pi$
$569$	34.6487	1.45255	0.726275	+	0.687404i	$0.241250\pi$
$570$	−27.2856	−1.14287
$571$	18.8747	0.789880	0.394940	−	0.918707i	$-0.370765\pi$
$571$	18.8747	0.789880	0.394940	+	0.918707i	$0.370765\pi$
$572$	−2.44589	−0.102268
$573$	−19.4552	−0.812751
$574$	−25.0880	−1.04715
$575$	−0.411436	−0.0171581
$576$	−30.7592	−1.28163
$577$	9.64512	0.401532	0.200766	−	0.979639i	$-0.435657\pi$
$577$	9.64512	0.401532	0.200766	+	0.979639i	$0.435657\pi$
$578$	−57.3167	−2.38406
$579$	−24.0639	−1.00006
$580$	4.15181	0.172394
$581$	30.6537	1.27173
$582$	22.4630	0.931121
$583$	10.9519	0.453580
$584$	0.0113035	0.000467743 0
$585$	−4.74228	−0.196069
$586$	66.9006	2.76364
$587$	−5.43089	−0.224157	−0.112078	−	0.993699i	$-0.535751\pi$
$587$	−5.43089	−0.224157	−0.112078	+	0.993699i	$0.535751\pi$
$588$	−0.613935	−0.0253183
$589$	−27.9233	−1.15056
$590$	−10.2548	−0.422182
$591$	−12.1588	−0.500147
$592$	34.5881	1.42156
$593$	0.679684	0.0279113	0.0139556	−	0.999903i	$-0.495558\pi$
$593$	0.679684	0.0279113	0.0139556	+	0.999903i	$0.495558\pi$
$594$	−4.53959	−0.186262
$595$	−17.7309	−0.726896
$596$	−29.0685	−1.19069
$597$	25.4687	1.04236
$598$	−1.00847	−0.0412393
$599$	24.7597	1.01165	0.505826	−	0.862635i	$-0.331188\pi$
$599$	24.7597	1.01165	0.505826	+	0.862635i	$0.331188\pi$
$600$	0.0296204	0.00120925
$601$	−28.5268	−1.16363	−0.581817	−	0.813320i	$-0.697658\pi$
$601$	−28.5268	−1.16363	−0.581817	+	0.813320i	$0.697658\pi$
$602$	−36.7902	−1.49946
$603$	−3.54644	−0.144422
$604$	−38.5885	−1.57014
$605$	1.00000	0.0406558
$606$	−7.16442	−0.291035
$607$	−22.1726	−0.899959	−0.449979	−	0.893039i	$-0.648569\pi$
$607$	−22.1726	−0.899959	−0.449979	+	0.893039i	$0.648569\pi$
$608$	41.6498	1.68912
$609$	14.3116	0.579935
$610$	−26.8584	−1.08746
$611$	−12.0438	−0.487241
$612$	−52.1204	−2.10684
$613$	−9.78775	−0.395323	−0.197662	−	0.980270i	$-0.563335\pi$
$613$	−9.78775	−0.395323	−0.197662	+	0.980270i	$0.563335\pi$
$614$	24.3741	0.983660
$615$	12.5385	0.505602
$616$	0.0296543	0.00119480
$617$	−23.7038	−0.954280	−0.477140	−	0.878827i	$-0.658327\pi$
$617$	−23.7038	−0.954280	−0.477140	+	0.878827i	$0.658327\pi$
$618$	29.7512	1.19677
$619$	−18.9929	−0.763388	−0.381694	−	0.924289i	$-0.624659\pi$
$619$	−18.9929	−0.763388	−0.381694	+	0.924289i	$0.624659\pi$
$620$	−10.6889	−0.429276
$621$	−0.934536	−0.0375016
$622$	−5.53611	−0.221978
$623$	29.9043	1.19809
$624$	12.8913	0.516065
$625$	1.00000	0.0400000
$626$	−34.3412	−1.37255
$627$	13.6525	0.545227
$628$	−9.89966	−0.395039
$629$	58.2775	2.32367
$630$	−20.2744	−0.807751
$631$	4.92498	0.196060	0.0980301	−	0.995183i	$-0.468746\pi$
$631$	4.92498	0.196060	0.0980301	+	0.995183i	$0.468746\pi$
$632$	0.0843287	0.00335442
$633$	15.2852	0.607534
$634$	−42.9098	−1.70417
$635$	19.7891	0.785305
$636$	57.2355	2.26953
$637$	0.144073	0.00570837
$638$	−4.16064	−0.164721
$639$	11.4782	0.454069
$640$	−0.0904277	−0.00357447
$641$	−34.4888	−1.36222	−0.681112	−	0.732179i	$-0.738503\pi$
$641$	−34.4888	−1.36222	−0.681112	+	0.732179i	$0.738503\pi$
$642$	−36.4893	−1.44012
$643$	−20.4666	−0.807126	−0.403563	−	0.914952i	$-0.632228\pi$
$643$	−20.4666	−0.807126	−0.403563	+	0.914952i	$0.632228\pi$
$644$	−2.15267	−0.0848269
$645$	18.3871	0.723991
$646$	70.3742	2.76883
$647$	−24.6827	−0.970376	−0.485188	−	0.874410i	$-0.661249\pi$
$647$	−24.6827	−0.970376	−0.485188	+	0.874410i	$0.661249\pi$
$648$	−0.0638454	−0.00250808
$649$	5.13101	0.201410
$650$	2.45109	0.0961396
$651$	−36.8454	−1.44409
$652$	−20.4990	−0.802802
$653$	0.216924	0.00848890	0.00424445	−	0.999991i	$-0.498649\pi$
$653$	0.216924	0.00848890	0.00424445	+	0.999991i	$0.498649\pi$
$654$	−2.89413	−0.113169
$655$	−10.6278	−0.415264
$656$	−19.1934	−0.749377
$657$	3.86680	0.150858
$658$	−51.4902	−2.00730
$659$	10.5633	0.411489	0.205745	−	0.978606i	$-0.434038\pi$
$659$	10.5633	0.411489	0.205745	+	0.978606i	$0.434038\pi$
$660$	5.22609	0.203425
$661$	14.6463	0.569674	0.284837	−	0.958576i	$-0.408061\pi$
$661$	14.6463	0.569674	0.284837	+	0.958576i	$0.408061\pi$
$662$	14.4602	0.562012
$663$	21.7205	0.843555
$664$	0.132076	0.00512553
$665$	13.6681	0.530026
$666$	66.6374	2.58215
$667$	−0.856524	−0.0331648
$668$	22.7348	0.879637
$669$	−22.4495	−0.867949
$670$	1.83301	0.0708153
$671$	13.4387	0.518795
$672$	54.9579	2.12005
$673$	−0.298628	−0.0115113	−0.00575563	−	0.999983i	$-0.501832\pi$
$673$	−0.298628	−0.0115113	−0.00575563	+	0.999983i	$0.501832\pi$
$674$	53.8358	2.07368
$675$	2.27140	0.0874262
$676$	−22.9268	−0.881800
$677$	−14.4113	−0.553872	−0.276936	−	0.960888i	$-0.589319\pi$
$677$	−14.4113	−0.553872	−0.276936	+	0.960888i	$0.589319\pi$
$678$	−15.2492	−0.585644
$679$	−11.2523	−0.431824
$680$	−0.0763959	−0.00292965
$681$	66.2363	2.53818
$682$	10.7116	0.410169
$683$	15.9312	0.609591	0.304795	−	0.952418i	$-0.401412\pi$
$683$	15.9312	0.609591	0.304795	+	0.952418i	$0.401412\pi$
$684$	40.1777	1.53623
$685$	2.11478	0.0808015
$686$	37.3184	1.42482
$687$	−51.4348	−1.96236
$688$	−28.1461	−1.07306
$689$	−13.4315	−0.511699
$690$	2.15478	0.0820309
$691$	23.0094	0.875317	0.437659	−	0.899141i	$-0.355808\pi$
$691$	23.0094	0.875317	0.437659	+	0.899141i	$0.355808\pi$
$692$	14.8598	0.564884
$693$	10.1444	0.385353
$694$	−45.0861	−1.71144
$695$	21.2705	0.806837
$696$	0.0616634	0.00233735
$697$	−32.3390	−1.22493
$698$	−0.996350	−0.0377124
$699$	−54.4190	−2.05831
$700$	5.23208	0.197754
$701$	50.3427	1.90142	0.950708	−	0.310087i	$-0.100358\pi$
$701$	50.3427	1.90142	0.950708	+	0.310087i	$0.100358\pi$
$702$	5.56740	0.210128
$703$	−44.9239	−1.69434
$704$	−7.95469	−0.299804
$705$	25.7339	0.969194
$706$	11.5515	0.434746
$707$	3.58885	0.134972
$708$	26.8151	1.00777
$709$	22.0214	0.827031	0.413515	−	0.910497i	$-0.364301\pi$
$709$	22.0214	0.827031	0.413515	+	0.910497i	$0.364301\pi$
$710$	−5.93259	−0.222646
$711$	28.8478	1.08188
$712$	0.128846	0.00482872
$713$	2.20513	0.0825829
$714$	92.8603	3.47521
$715$	−1.22641	−0.0458652
$716$	37.1440	1.38814
$717$	7.98186	0.298088
$718$	−49.2959	−1.83971
$719$	−34.7955	−1.29765	−0.648827	−	0.760936i	$-0.724740\pi$
$719$	−34.7955	−1.29765	−0.648827	+	0.760936i	$0.724740\pi$
$720$	−15.5108	−0.578053
$721$	−14.9032	−0.555022
$722$	−16.2757	−0.605720
$723$	−46.4601	−1.72787
$724$	10.5418	0.391781
$725$	2.08179	0.0773158
$726$	−5.23721	−0.194371
$727$	−6.87342	−0.254921	−0.127461	−	0.991844i	$-0.540683\pi$
$727$	−6.87342	−0.254921	−0.127461	+	0.991844i	$0.540683\pi$
$728$	−0.0363684	−0.00134790
$729$	−39.6971	−1.47026
$730$	−1.99859	−0.0739710
$731$	−47.4234	−1.75402
$732$	70.2318	2.59584
$733$	−38.2079	−1.41124	−0.705621	−	0.708590i	$-0.749332\pi$
$733$	−38.2079	−1.41124	−0.705621	+	0.708590i	$0.749332\pi$
$734$	39.3172	1.45122
$735$	−0.307838	−0.0113548
$736$	−3.28914	−0.121239
$737$	−0.917153	−0.0337838
$738$	−36.9780	−1.36118
$739$	−27.3184	−1.00493	−0.502463	−	0.864599i	$-0.667573\pi$
$739$	−27.3184	−1.00493	−0.502463	+	0.864599i	$0.667573\pi$
$740$	−17.1967	−0.632162
$741$	−16.7435	−0.615089
$742$	−57.4228	−2.10806
$743$	−35.6716	−1.30867	−0.654333	−	0.756207i	$-0.727050\pi$
$743$	−35.6716	−1.30867	−0.654333	+	0.756207i	$0.727050\pi$
$744$	−0.158753	−0.00582018
$745$	−14.5755	−0.534005
$746$	21.1958	0.776034
$747$	45.1815	1.65311
$748$	−13.4790	−0.492840
$749$	18.2785	0.667881
$750$	−5.23721	−0.191236
$751$	−3.93690	−0.143659	−0.0718297	−	0.997417i	$-0.522884\pi$
$751$	−3.93690	−0.143659	−0.0718297	+	0.997417i	$0.522884\pi$
$752$	−39.3923	−1.43649
$753$	−47.5654	−1.73338
$754$	5.10266	0.185828
$755$	−19.3490	−0.704181
$756$	11.8841	0.432222
$757$	37.3787	1.35855	0.679275	−	0.733884i	$-0.262294\pi$
$757$	37.3787	1.35855	0.679275	+	0.733884i	$0.262294\pi$
$758$	48.7914	1.77218
$759$	−1.07815	−0.0391344
$760$	0.0588908	0.00213619
$761$	−9.97039	−0.361427	−0.180713	−	0.983536i	$-0.557841\pi$
$761$	−9.97039	−0.361427	−0.180713	+	0.983536i	$0.557841\pi$
$762$	−103.639	−3.75446
$763$	1.44975	0.0524843
$764$	−14.8067	−0.535687
$765$	−26.1341	−0.944881
$766$	68.2557	2.46618
$767$	−6.29273	−0.227217
$768$	42.1634	1.52144
$769$	−16.7703	−0.604753	−0.302377	−	0.953189i	$-0.597780\pi$
$769$	−16.7703	−0.604753	−0.302377	+	0.953189i	$0.597780\pi$
$770$	−5.24320	−0.188952
$771$	−71.1408	−2.56207
$772$	−18.3142	−0.659144
$773$	−42.7338	−1.53703	−0.768515	−	0.639832i	$-0.779004\pi$
$773$	−42.7338	−1.53703	−0.768515	+	0.639832i	$0.779004\pi$
$774$	−54.2263	−1.94912
$775$	−5.35960	−0.192523
$776$	−0.0484821	−0.00174040
$777$	−59.2782	−2.12659
$778$	−47.2008	−1.69223
$779$	24.9289	0.893171
$780$	−6.40934	−0.229491
$781$	2.96839	0.106217
$782$	−5.55753	−0.198737
$783$	4.72858	0.168986
$784$	0.471225	0.0168295
$785$	−4.96387	−0.177168
$786$	55.6601	1.98533
$787$	24.0922	0.858793	0.429396	−	0.903116i	$-0.358726\pi$
$787$	24.0922	0.858793	0.429396	+	0.903116i	$0.358726\pi$
$788$	−9.25368	−0.329649
$789$	−62.0256	−2.20817
$790$	−14.9102	−0.530483
$791$	7.63875	0.271603
$792$	0.0437084	0.00155311
$793$	−16.4814	−0.585270
$794$	22.4547	0.796888
$795$	28.6989	1.01784
$796$	19.3834	0.687025
$797$	50.3800	1.78455	0.892276	−	0.451491i	$-0.149108\pi$
$797$	50.3800	1.78455	0.892276	+	0.451491i	$0.149108\pi$
$798$	−71.5826	−2.53400
$799$	−66.3720	−2.34807
$800$	7.99428	0.282640
$801$	44.0768	1.55738
$802$	2.84402	0.100426
$803$	1.00000	0.0352892
$804$	−4.79313	−0.169041
$805$	−1.07938	−0.0380433
$806$	−13.1369	−0.462726
$807$	−80.6694	−2.83970
$808$	0.0154630	0.000543987 0
$809$	−21.7283	−0.763927	−0.381964	−	0.924177i	$-0.624752\pi$
$809$	−21.7283	−0.763927	−0.381964	+	0.924177i	$0.624752\pi$
$810$	11.2886	0.396640
$811$	−9.27741	−0.325774	−0.162887	−	0.986645i	$-0.552081\pi$
$811$	−9.27741	−0.325774	−0.162887	+	0.986645i	$0.552081\pi$
$812$	10.8921	0.382237
$813$	73.5692	2.58019
$814$	17.2332	0.604024
$815$	−10.2786	−0.360042
$816$	71.0422	2.48698
$817$	36.5569	1.27897
$818$	−13.6265	−0.476441
$819$	−12.4412	−0.434730
$820$	9.54267	0.333244
$821$	−5.01148	−0.174902	−0.0874509	−	0.996169i	$-0.527872\pi$
$821$	−5.01148	−0.174902	−0.0874509	+	0.996169i	$0.527872\pi$
$822$	−11.0755	−0.386303
$823$	−17.6243	−0.614345	−0.307172	−	0.951654i	$-0.599383\pi$
$823$	−17.6243	−0.614345	−0.307172	+	0.951654i	$0.599383\pi$
$824$	−0.0642122	−0.00223694
$825$	2.62046	0.0912326
$826$	−26.9029	−0.936073
$827$	−25.0585	−0.871370	−0.435685	−	0.900099i	$-0.643494\pi$
$827$	−25.0585	−0.871370	−0.435685	+	0.900099i	$0.643494\pi$
$828$	−3.17288	−0.110265
$829$	−1.96838	−0.0683647	−0.0341824	−	0.999416i	$-0.510883\pi$
$829$	−1.96838	−0.0683647	−0.0341824	+	0.999416i	$0.510883\pi$
$830$	−23.3524	−0.810575
$831$	−83.9518	−2.91226
$832$	9.75573	0.338219
$833$	0.793966	0.0275093
$834$	−111.398	−3.85740
$835$	11.3997	0.394501
$836$	10.3904	0.359361
$837$	−12.1738	−0.420788
$838$	−13.1424	−0.453995
$839$	49.9876	1.72576	0.862882	−	0.505405i	$-0.168657\pi$
$839$	49.9876	1.72576	0.862882	+	0.505405i	$0.168657\pi$
$840$	0.0777077	0.00268117
$841$	−24.6661	−0.850557
$842$	−40.6372	−1.40045
$843$	−7.46602	−0.257143
$844$	11.6331	0.400428
$845$	−11.4959	−0.395471
$846$	−75.8931	−2.60926
$847$	2.62346	0.0901430
$848$	−43.9310	−1.50860
$849$	−6.93897	−0.238145
$850$	13.5076	0.463308
$851$	3.54770	0.121613
$852$	15.5131	0.531470
$853$	8.48391	0.290484	0.145242	−	0.989396i	$-0.453604\pi$
$853$	8.48391	0.290484	0.145242	+	0.989396i	$0.453604\pi$
$854$	−70.4618	−2.41115
$855$	20.1458	0.688973
$856$	0.0787552	0.00269180
$857$	15.8496	0.541412	0.270706	−	0.962662i	$-0.412743\pi$
$857$	15.8496	0.541412	0.270706	+	0.962662i	$0.412743\pi$
$858$	6.42297	0.219277
$859$	51.2662	1.74918	0.874590	−	0.484864i	$-0.161131\pi$
$859$	51.2662	1.74918	0.874590	+	0.484864i	$0.161131\pi$
$860$	13.9938	0.477185
$861$	32.8943	1.12103
$862$	−60.3451	−2.05536
$863$	−9.53741	−0.324657	−0.162329	−	0.986737i	$-0.551900\pi$
$863$	−9.53741	−0.324657	−0.162329	+	0.986737i	$0.551900\pi$
$864$	18.1582	0.617755
$865$	7.45096	0.253340
$866$	75.0883	2.55160
$867$	75.1512	2.55227
$868$	−28.0418	−0.951802
$869$	7.46040	0.253077
$870$	−10.9028	−0.369639
$871$	1.12481	0.0381126
$872$	0.00624642	0.000211530 0
$873$	−16.5851	−0.561322
$874$	4.28410	0.144912
$875$	2.62346	0.0886890
$876$	5.22609	0.176573
$877$	42.5714	1.43753	0.718767	−	0.695251i	$-0.244707\pi$
$877$	42.5714	1.43753	0.718767	+	0.695251i	$0.244707\pi$
$878$	47.7511	1.61152
$879$	−87.7171	−2.95863
$880$	−4.01128	−0.135220
$881$	−17.6254	−0.593813	−0.296907	−	0.954906i	$-0.595955\pi$
$881$	−17.6254	−0.593813	−0.296907	+	0.954906i	$0.595955\pi$
$882$	0.907861	0.0305693
$883$	38.3531	1.29069	0.645343	−	0.763893i	$-0.276714\pi$
$883$	38.3531	1.29069	0.645343	+	0.763893i	$0.276714\pi$
$884$	16.5308	0.555990
$885$	13.4456	0.451969
$886$	−76.2354	−2.56118
$887$	−15.4545	−0.518911	−0.259456	−	0.965755i	$-0.583543\pi$
$887$	−15.4545	−0.518911	−0.259456	+	0.965755i	$0.583543\pi$
$888$	−0.255408	−0.00857093
$889$	51.9157	1.74120
$890$	−22.7815	−0.763637
$891$	−5.64828	−0.189224
$892$	−17.0856	−0.572069
$893$	51.1637	1.71213
$894$	76.3349	2.55302
$895$	18.6247	0.622554
$896$	−0.237233	−0.00792541
$897$	1.32226	0.0441489
$898$	39.6754	1.32399
$899$	−11.1576	−0.372126
$900$	7.71172	0.257057
$901$	−74.0192	−2.46594
$902$	−9.56296	−0.318412
$903$	48.2377	1.60525
$904$	0.0329126	0.00109466
$905$	5.28582	0.175707
$906$	101.335	3.36662
$907$	−49.1781	−1.63293	−0.816467	−	0.577393i	$-0.804070\pi$
$907$	−49.1781	−1.63293	−0.816467	+	0.577393i	$0.804070\pi$
$908$	50.4103	1.67292
$909$	5.28971	0.175449
$910$	6.43033	0.213163
$911$	−10.4727	−0.346976	−0.173488	−	0.984836i	$-0.555504\pi$
$911$	−10.4727	−0.346976	−0.173488	+	0.984836i	$0.555504\pi$
$912$	−54.7638	−1.81341
$913$	11.6845	0.386700
$914$	41.6135	1.37645
$915$	35.2155	1.16419
$916$	−39.1453	−1.29340
$917$	−27.8816	−0.920733
$918$	30.6812	1.01263
$919$	−45.9107	−1.51445	−0.757227	−	0.653152i	$-0.773446\pi$
$919$	−45.9107	−1.51445	−0.757227	+	0.653152i	$0.773446\pi$
$920$	−0.00465067	−0.000153328 0
$921$	−31.9583	−1.05306
$922$	−26.8875	−0.885493
$923$	−3.64047	−0.119828
$924$	13.7104	0.451040
$925$	−8.62271	−0.283513
$926$	17.1269	0.562825
$927$	−21.9662	−0.721465
$928$	16.6424	0.546314
$929$	42.5041	1.39451	0.697257	−	0.716821i	$-0.254404\pi$
$929$	42.5041	1.39451	0.697257	+	0.716821i	$0.254404\pi$
$930$	28.0694	0.920430
$931$	−0.612039	−0.0200588
$932$	−41.4165	−1.35664
$933$	7.25870	0.237639
$934$	−25.6858	−0.840464
$935$	−6.75860	−0.221030
$936$	−0.0536045	−0.00175212
$937$	−30.8978	−1.00939	−0.504693	−	0.863299i	$-0.668394\pi$
$937$	−30.8978	−1.00939	−0.504693	+	0.863299i	$0.668394\pi$
$938$	4.80882	0.157013
$939$	45.0266	1.46939
$940$	19.5852	0.638799
$941$	−21.2158	−0.691615	−0.345808	−	0.938305i	$-0.612395\pi$
$941$	−21.2158	−0.691615	−0.345808	+	0.938305i	$0.612395\pi$
$942$	25.9968	0.847022
$943$	−1.96867	−0.0641086
$944$	−20.5819	−0.669884
$945$	5.95892	0.193844
$946$	−14.0236	−0.455946
$947$	−9.88968	−0.321372	−0.160686	−	0.987006i	$-0.551371\pi$
$947$	−9.88968	−0.321372	−0.160686	+	0.987006i	$0.551371\pi$
$948$	38.9887	1.26630
$949$	−1.22641	−0.0398110
$950$	−10.4125	−0.337827
$951$	56.2614	1.82440
$952$	−0.200421	−0.00649569
$953$	44.8956	1.45431	0.727155	−	0.686473i	$-0.240842\pi$
$953$	44.8956	1.45431	0.727155	+	0.686473i	$0.240842\pi$
$954$	−84.6373	−2.74024
$955$	−7.42434	−0.240246
$956$	6.07473	0.196471
$957$	5.45524	0.176343
$958$	−20.6988	−0.668747
$959$	5.54803	0.179155
$960$	−20.8449	−0.672767
$961$	−2.27465	−0.0733760
$962$	−21.1350	−0.681421
$963$	26.9412	0.868169
$964$	−35.3593	−1.13884
$965$	−9.18309	−0.295614
$966$	5.65296	0.181881
$967$	−7.79733	−0.250745	−0.125373	−	0.992110i	$-0.540013\pi$
$967$	−7.79733	−0.250745	−0.125373	+	0.992110i	$0.540013\pi$
$968$	0.0113035	0.000363309 0
$969$	−92.2715	−2.96419
$970$	8.57216	0.275236
$971$	42.2902	1.35716	0.678579	−	0.734527i	$-0.262596\pi$
$971$	42.2902	1.35716	0.678579	+	0.734527i	$0.262596\pi$
$972$	−43.1083	−1.38270
$973$	55.8023	1.78894
$974$	5.42820	0.173931
$975$	−3.21376	−0.102923
$976$	−53.9063	−1.72550
$977$	31.1327	0.996022	0.498011	−	0.867171i	$-0.334064\pi$
$977$	31.1327	0.996022	0.498011	+	0.867171i	$0.334064\pi$
$978$	53.8309	1.72132
$979$	11.3988	0.364307
$980$	−0.234286	−0.00748398
$981$	2.13682	0.0682236
$982$	−4.30905	−0.137507
$983$	17.8492	0.569300	0.284650	−	0.958632i	$-0.408123\pi$
$983$	17.8492	0.569300	0.284650	+	0.958632i	$0.408123\pi$
$984$	0.141729	0.00451817
$985$	−4.63996	−0.147842
$986$	28.1201	0.895526
$987$	67.5117	2.14892
$988$	−12.7430	−0.405408
$989$	−2.88694	−0.0917995
$990$	−7.72812	−0.245616
$991$	35.6820	1.13348	0.566738	−	0.823898i	$-0.308205\pi$
$991$	35.6820	1.13348	0.566738	+	0.823898i	$0.308205\pi$
$992$	−42.8462	−1.36037
$993$	−18.9596	−0.601664
$994$	−15.5639	−0.493657
$995$	9.71917	0.308118
$996$	61.0642	1.93489
$997$	6.34846	0.201058	0.100529	−	0.994934i	$-0.467947\pi$
$997$	6.34846	0.201058	0.100529	+	0.994934i	$0.467947\pi$
$998$	−45.0741	−1.42679
$999$	−19.5856	−0.619662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.6	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.99859 q^{2} +2.62046 q^{3} +1.99434 q^{4} +1.00000 q^{5} -5.23721 q^{6} +2.62346 q^{7} +0.0113035 q^{8} +3.86680 q^{9} +O(q^{10})\)	\(q-1.99859 q^{2} +2.62046 q^{3} +1.99434 q^{4} +1.00000 q^{5} -5.23721 q^{6} +2.62346 q^{7} +0.0113035 q^{8} +3.86680 q^{9} -1.99859 q^{10} +1.00000 q^{11} +5.22609 q^{12} -1.22641 q^{13} -5.24320 q^{14} +2.62046 q^{15} -4.01128 q^{16} -6.75860 q^{17} -7.72812 q^{18} +5.20995 q^{19} +1.99434 q^{20} +6.87466 q^{21} -1.99859 q^{22} -0.411436 q^{23} +0.0296204 q^{24} +1.00000 q^{25} +2.45109 q^{26} +2.27140 q^{27} +5.23208 q^{28} +2.08179 q^{29} -5.23721 q^{30} -5.35960 q^{31} +7.99428 q^{32} +2.62046 q^{33} +13.5076 q^{34} +2.62346 q^{35} +7.71172 q^{36} -8.62271 q^{37} -10.4125 q^{38} -3.21376 q^{39} +0.0113035 q^{40} +4.78486 q^{41} -13.7396 q^{42} +7.01675 q^{43} +1.99434 q^{44} +3.86680 q^{45} +0.822290 q^{46} +9.82038 q^{47} -10.5114 q^{48} -0.117475 q^{49} -1.99859 q^{50} -17.7106 q^{51} -2.44589 q^{52} +10.9519 q^{53} -4.53959 q^{54} +1.00000 q^{55} +0.0296543 q^{56} +13.6525 q^{57} -4.16064 q^{58} +5.13101 q^{59} +5.22609 q^{60} +13.4387 q^{61} +10.7116 q^{62} +10.1444 q^{63} -7.95469 q^{64} -1.22641 q^{65} -5.23721 q^{66} -0.917153 q^{67} -13.4790 q^{68} -1.07815 q^{69} -5.24320 q^{70} +2.96839 q^{71} +0.0437084 q^{72} +1.00000 q^{73} +17.2332 q^{74} +2.62046 q^{75} +10.3904 q^{76} +2.62346 q^{77} +6.42297 q^{78} +7.46040 q^{79} -4.01128 q^{80} -5.64828 q^{81} -9.56296 q^{82} +11.6845 q^{83} +13.7104 q^{84} -6.75860 q^{85} -14.0236 q^{86} +5.45524 q^{87} +0.0113035 q^{88} +11.3988 q^{89} -7.72812 q^{90} -3.21744 q^{91} -0.820545 q^{92} -14.0446 q^{93} -19.6269 q^{94} +5.20995 q^{95} +20.9487 q^{96} -4.28912 q^{97} +0.234784 q^{98} +3.86680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 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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