LMFDB - Embedded newform 4017.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54007 q^{2} -1.00000 q^{3} +0.371810 q^{4} -0.217078 q^{5} +1.54007 q^{6} +2.62202 q^{7} +2.50752 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.54007 q^{2} -1.00000 q^{3} +0.371810 q^{4} -0.217078 q^{5} +1.54007 q^{6} +2.62202 q^{7} +2.50752 q^{8} +1.00000 q^{9} +0.334314 q^{10} +5.07293 q^{11} -0.371810 q^{12} -1.00000 q^{13} -4.03809 q^{14} +0.217078 q^{15} -4.60538 q^{16} +5.14634 q^{17} -1.54007 q^{18} +1.44102 q^{19} -0.0807116 q^{20} -2.62202 q^{21} -7.81266 q^{22} -7.34041 q^{23} -2.50752 q^{24} -4.95288 q^{25} +1.54007 q^{26} -1.00000 q^{27} +0.974892 q^{28} -3.87353 q^{29} -0.334314 q^{30} -0.681553 q^{31} +2.07755 q^{32} -5.07293 q^{33} -7.92572 q^{34} -0.569182 q^{35} +0.371810 q^{36} -9.20012 q^{37} -2.21926 q^{38} +1.00000 q^{39} -0.544328 q^{40} -1.77982 q^{41} +4.03809 q^{42} +7.81726 q^{43} +1.88616 q^{44} -0.217078 q^{45} +11.3047 q^{46} -11.5761 q^{47} +4.60538 q^{48} -0.125007 q^{49} +7.62777 q^{50} -5.14634 q^{51} -0.371810 q^{52} -8.69775 q^{53} +1.54007 q^{54} -1.10122 q^{55} +6.57478 q^{56} -1.44102 q^{57} +5.96550 q^{58} -3.74377 q^{59} +0.0807116 q^{60} -3.80722 q^{61} +1.04964 q^{62} +2.62202 q^{63} +6.01119 q^{64} +0.217078 q^{65} +7.81266 q^{66} -10.3207 q^{67} +1.91346 q^{68} +7.34041 q^{69} +0.876579 q^{70} +0.735348 q^{71} +2.50752 q^{72} +7.10147 q^{73} +14.1688 q^{74} +4.95288 q^{75} +0.535784 q^{76} +13.3013 q^{77} -1.54007 q^{78} +7.45464 q^{79} +0.999725 q^{80} +1.00000 q^{81} +2.74104 q^{82} -2.26215 q^{83} -0.974892 q^{84} -1.11716 q^{85} -12.0391 q^{86} +3.87353 q^{87} +12.7205 q^{88} -4.83089 q^{89} +0.334314 q^{90} -2.62202 q^{91} -2.72924 q^{92} +0.681553 q^{93} +17.8280 q^{94} -0.312813 q^{95} -2.07755 q^{96} -14.6428 q^{97} +0.192520 q^{98} +5.07293 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	−1.54007	−1.08899	−0.544496	−	0.838763i	$-0.683279\pi$
$2$	−1.54007	−1.08899	−0.544496	+	0.838763i	$0.683279\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.371810	0.185905
$5$	−0.217078	−0.0970801	−0.0485401	−	0.998821i	$-0.515457\pi$
$5$	−0.217078	−0.0970801	−0.0485401	+	0.998821i	$0.515457\pi$
$6$	1.54007	0.628730
$7$	2.62202	0.991031	0.495515	−	0.868599i	$-0.334979\pi$
$7$	2.62202	0.991031	0.495515	+	0.868599i	$0.334979\pi$
$8$	2.50752	0.886544
$9$	1.00000	0.333333
$10$	0.334314	0.105720
$11$	5.07293	1.52955	0.764773	−	0.644300i	$-0.222851\pi$
$11$	5.07293	1.52955	0.764773	+	0.644300i	$0.222851\pi$
$12$	−0.371810	−0.107332
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.03809	−1.07923
$15$	0.217078	0.0560492
$16$	−4.60538	−1.15134
$17$	5.14634	1.24817	0.624086	−	0.781356i	$-0.285472\pi$
$17$	5.14634	1.24817	0.624086	+	0.781356i	$0.285472\pi$
$18$	−1.54007	−0.362998
$19$	1.44102	0.330592	0.165296	−	0.986244i	$-0.447142\pi$
$19$	1.44102	0.330592	0.165296	+	0.986244i	$0.447142\pi$
$20$	−0.0807116	−0.0180477
$21$	−2.62202	−0.572172
$22$	−7.81266	−1.66566
$23$	−7.34041	−1.53058	−0.765291	−	0.643684i	$-0.777405\pi$
$23$	−7.34041	−1.53058	−0.765291	+	0.643684i	$0.777405\pi$
$24$	−2.50752	−0.511846
$25$	−4.95288	−0.990575
$26$	1.54007	0.302032
$27$	−1.00000	−0.192450
$28$	0.974892	0.184237
$29$	−3.87353	−0.719296	−0.359648	−	0.933088i	$-0.617103\pi$
$29$	−3.87353	−0.719296	−0.359648	+	0.933088i	$0.617103\pi$
$30$	−0.334314	−0.0610372
$31$	−0.681553	−0.122411	−0.0612053	−	0.998125i	$-0.519494\pi$
$31$	−0.681553	−0.122411	−0.0612053	+	0.998125i	$0.519494\pi$
$32$	2.07755	0.367262
$33$	−5.07293	−0.883084
$34$	−7.92572	−1.35925
$35$	−0.569182	−0.0962094
$36$	0.371810	0.0619683
$37$	−9.20012	−1.51249	−0.756246	−	0.654288i	$-0.772968\pi$
$37$	−9.20012	−1.51249	−0.756246	+	0.654288i	$0.772968\pi$
$38$	−2.21926	−0.360012
$39$	1.00000	0.160128
$40$	−0.544328	−0.0860657
$41$	−1.77982	−0.277961	−0.138981	−	0.990295i	$-0.544383\pi$
$41$	−1.77982	−0.277961	−0.138981	+	0.990295i	$0.544383\pi$
$42$	4.03809	0.623091
$43$	7.81726	1.19212	0.596060	−	0.802940i	$-0.296732\pi$
$43$	7.81726	1.19212	0.596060	+	0.802940i	$0.296732\pi$
$44$	1.88616	0.284350
$45$	−0.217078	−0.0323600
$46$	11.3047	1.66679
$47$	−11.5761	−1.68855	−0.844275	−	0.535910i	$-0.819969\pi$
$47$	−11.5761	−1.68855	−0.844275	+	0.535910i	$0.819969\pi$
$48$	4.60538	0.664729
$49$	−0.125007	−0.0178582
$50$	7.62777	1.07873
$51$	−5.14634	−0.720632
$52$	−0.371810	−0.0515607
$53$	−8.69775	−1.19473	−0.597364	−	0.801970i	$-0.703785\pi$
$53$	−8.69775	−1.19473	−0.597364	+	0.801970i	$0.703785\pi$
$54$	1.54007	0.209577
$55$	−1.10122	−0.148489
$56$	6.57478	0.878592
$57$	−1.44102	−0.190867
$58$	5.96550	0.783308
$59$	−3.74377	−0.487398	−0.243699	−	0.969851i	$-0.578361\pi$
$59$	−3.74377	−0.487398	−0.243699	+	0.969851i	$0.578361\pi$
$60$	0.0807116	0.0104198
$61$	−3.80722	−0.487465	−0.243732	−	0.969843i	$-0.578372\pi$
$61$	−3.80722	−0.487465	−0.243732	+	0.969843i	$0.578372\pi$
$62$	1.04964	0.133304
$63$	2.62202	0.330344
$64$	6.01119	0.751399
$65$	0.217078	0.0269252
$66$	7.81266	0.961672
$67$	−10.3207	−1.26087	−0.630435	−	0.776242i	$-0.717124\pi$
$67$	−10.3207	−1.26087	−0.630435	+	0.776242i	$0.717124\pi$
$68$	1.91346	0.232041
$69$	7.34041	0.883682
$70$	0.876579	0.104771
$71$	0.735348	0.0872697	0.0436348	−	0.999048i	$-0.486106\pi$
$71$	0.735348	0.0872697	0.0436348	+	0.999048i	$0.486106\pi$
$72$	2.50752	0.295515
$73$	7.10147	0.831164	0.415582	−	0.909556i	$-0.363578\pi$
$73$	7.10147	0.831164	0.415582	+	0.909556i	$0.363578\pi$
$74$	14.1688	1.64709
$75$	4.95288	0.571909
$76$	0.535784	0.0614586
$77$	13.3013	1.51583
$78$	−1.54007	−0.174378
$79$	7.45464	0.838713	0.419356	−	0.907822i	$-0.362256\pi$
$79$	7.45464	0.838713	0.419356	+	0.907822i	$0.362256\pi$
$80$	0.999725	0.111773
$81$	1.00000	0.111111
$82$	2.74104	0.302698
$83$	−2.26215	−0.248304	−0.124152	−	0.992263i	$-0.539621\pi$
$83$	−2.26215	−0.248304	−0.124152	+	0.992263i	$0.539621\pi$
$84$	−0.974892	−0.106369
$85$	−1.11716	−0.121173
$86$	−12.0391	−1.29821
$87$	3.87353	0.415286
$88$	12.7205	1.35601
$89$	−4.83089	−0.512073	−0.256037	−	0.966667i	$-0.582417\pi$
$89$	−4.83089	−0.512073	−0.256037	+	0.966667i	$0.582417\pi$
$90$	0.334314	0.0352398
$91$	−2.62202	−0.274862
$92$	−2.72924	−0.284543
$93$	0.681553	0.0706738
$94$	17.8280	1.83882
$95$	−0.312813	−0.0320939
$96$	−2.07755	−0.212039
$97$	−14.6428	−1.48675	−0.743377	−	0.668872i	$-0.766777\pi$
$97$	−14.6428	−1.48675	−0.743377	+	0.668872i	$0.766777\pi$
$98$	0.192520	0.0194474
$99$	5.07293	0.509849
$100$	−1.84153	−0.184153
$101$	−16.3505	−1.62694	−0.813470	−	0.581607i	$-0.802424\pi$
$101$	−16.3505	−1.62694	−0.813470	+	0.581607i	$0.802424\pi$
$102$	7.92572	0.784763
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.50752	−0.245883
$105$	0.569182	0.0555465
$106$	13.3951	1.30105
$107$	−3.61867	−0.349830	−0.174915	−	0.984584i	$-0.555965\pi$
$107$	−3.61867	−0.349830	−0.174915	+	0.984584i	$0.555965\pi$
$108$	−0.371810	−0.0357774
$109$	10.9512	1.04894	0.524468	−	0.851430i	$-0.324264\pi$
$109$	10.9512	1.04894	0.524468	+	0.851430i	$0.324264\pi$
$110$	1.69595	0.161703
$111$	9.20012	0.873237
$112$	−12.0754	−1.14102
$113$	4.68639	0.440859	0.220429	−	0.975403i	$-0.429254\pi$
$113$	4.68639	0.440859	0.220429	+	0.975403i	$0.429254\pi$
$114$	2.21926	0.207853
$115$	1.59344	0.148589
$116$	−1.44022	−0.133721
$117$	−1.00000	−0.0924500
$118$	5.76567	0.530773
$119$	13.4938	1.23698
$120$	0.544328	0.0496901
$121$	14.7346	1.33951
$122$	5.86338	0.530845
$123$	1.77982	0.160481
$124$	−0.253408	−0.0227567
$125$	2.16055	0.193245
$126$	−4.03809	−0.359742
$127$	9.07025	0.804854	0.402427	−	0.915452i	$-0.368167\pi$
$127$	9.07025	0.804854	0.402427	+	0.915452i	$0.368167\pi$
$128$	−13.4127	−1.18553
$129$	−7.81726	−0.688271
$130$	−0.334314	−0.0293213
$131$	−16.1517	−1.41118	−0.705592	−	0.708618i	$-0.749319\pi$
$131$	−16.1517	−1.41118	−0.705592	+	0.708618i	$0.749319\pi$
$132$	−1.88616	−0.164170
$133$	3.77838	0.327627
$134$	15.8945	1.37308
$135$	0.217078	0.0186831
$136$	12.9046	1.10656
$137$	−7.76682	−0.663564	−0.331782	−	0.943356i	$-0.607650\pi$
$137$	−7.76682	−0.663564	−0.331782	+	0.943356i	$0.607650\pi$
$138$	−11.3047	−0.962323
$139$	9.07355	0.769609	0.384804	−	0.922998i	$-0.374269\pi$
$139$	9.07355	0.769609	0.384804	+	0.922998i	$0.374269\pi$
$140$	−0.211627	−0.0178858
$141$	11.5761	0.974885
$142$	−1.13249	−0.0950361
$143$	−5.07293	−0.424220
$144$	−4.60538	−0.383781
$145$	0.840857	0.0698294
$146$	−10.9367	−0.905131
$147$	0.125007	0.0103104
$148$	−3.42069	−0.281179
$149$	−14.6073	−1.19667	−0.598336	−	0.801245i	$-0.704171\pi$
$149$	−14.6073	−1.19667	−0.598336	+	0.801245i	$0.704171\pi$
$150$	−7.62777	−0.622805
$151$	−11.4247	−0.929731	−0.464866	−	0.885381i	$-0.653897\pi$
$151$	−11.4247	−0.929731	−0.464866	+	0.885381i	$0.653897\pi$
$152$	3.61338	0.293084
$153$	5.14634	0.416057
$154$	−20.4850	−1.65072
$155$	0.147950	0.0118836
$156$	0.371810	0.0297686
$157$	3.61398	0.288427	0.144213	−	0.989547i	$-0.453935\pi$
$157$	3.61398	0.288427	0.144213	+	0.989547i	$0.453935\pi$
$158$	−11.4807	−0.913352
$159$	8.69775	0.689776
$160$	−0.450989	−0.0356538
$161$	−19.2467	−1.51685
$162$	−1.54007	−0.120999
$163$	7.80263	0.611149	0.305575	−	0.952168i	$-0.401151\pi$
$163$	7.80263	0.611149	0.305575	+	0.952168i	$0.401151\pi$
$164$	−0.661754	−0.0516743
$165$	1.10122	0.0857299
$166$	3.48387	0.270401
$167$	0.924672	0.0715533	0.0357766	−	0.999360i	$-0.488610\pi$
$167$	0.924672	0.0715533	0.0357766	+	0.999360i	$0.488610\pi$
$168$	−6.57478	−0.507255
$169$	1.00000	0.0769231
$170$	1.72050	0.131956
$171$	1.44102	0.110197
$172$	2.90653	0.221621
$173$	−9.80238	−0.745261	−0.372630	−	0.927980i	$-0.621544\pi$
$173$	−9.80238	−0.745261	−0.372630	+	0.927980i	$0.621544\pi$
$174$	−5.96550	−0.452243
$175$	−12.9865	−0.981691
$176$	−23.3628	−1.76103
$177$	3.74377	0.281399
$178$	7.43990	0.557644
$179$	7.69699	0.575300	0.287650	−	0.957736i	$-0.407126\pi$
$179$	7.69699	0.575300	0.287650	+	0.957736i	$0.407126\pi$
$180$	−0.0807116	−0.00601589
$181$	11.3224	0.841587	0.420793	−	0.907157i	$-0.361752\pi$
$181$	11.3224	0.841587	0.420793	+	0.907157i	$0.361752\pi$
$182$	4.03809	0.299323
$183$	3.80722	0.281438
$184$	−18.4063	−1.35693
$185$	1.99714	0.146833
$186$	−1.04964	−0.0769632
$187$	26.1070	1.90914
$188$	−4.30411	−0.313910
$189$	−2.62202	−0.190724
$190$	0.481753	0.0349500
$191$	−26.6219	−1.92629	−0.963147	−	0.268976i	$-0.913315\pi$
$191$	−26.6219	−1.92629	−0.963147	+	0.268976i	$0.913315\pi$
$192$	−6.01119	−0.433820
$193$	−17.2988	−1.24519	−0.622596	−	0.782543i	$-0.713922\pi$
$193$	−17.2988	−1.24519	−0.622596	+	0.782543i	$0.713922\pi$
$194$	22.5510	1.61906
$195$	−0.217078	−0.0155453
$196$	−0.0464789	−0.00331992
$197$	12.2421	0.872214	0.436107	−	0.899895i	$-0.356357\pi$
$197$	12.2421	0.872214	0.436107	+	0.899895i	$0.356357\pi$
$198$	−7.81266	−0.555222
$199$	10.0886	0.715161	0.357580	−	0.933882i	$-0.383602\pi$
$199$	10.0886	0.715161	0.357580	+	0.933882i	$0.383602\pi$
$200$	−12.4195	−0.878188
$201$	10.3207	0.727964
$202$	25.1809	1.77173
$203$	−10.1565	−0.712845
$204$	−1.91346	−0.133969
$205$	0.386359	0.0269845
$206$	1.54007	0.107302
$207$	−7.34041	−0.510194
$208$	4.60538	0.319325
$209$	7.31018	0.505656
$210$	−0.876579	−0.0604897
$211$	13.5691	0.934133	0.467067	−	0.884222i	$-0.345311\pi$
$211$	13.5691	0.934133	0.467067	+	0.884222i	$0.345311\pi$
$212$	−3.23391	−0.222106
$213$	−0.735348	−0.0503852
$214$	5.57300	0.380962
$215$	−1.69695	−0.115731
$216$	−2.50752	−0.170615
$217$	−1.78705	−0.121313
$218$	−16.8656	−1.14228
$219$	−7.10147	−0.479873
$220$	−0.409444	−0.0276047
$221$	−5.14634	−0.346180
$222$	−14.1688	−0.950949
$223$	14.7375	0.986894	0.493447	−	0.869776i	$-0.335737\pi$
$223$	14.7375	0.986894	0.493447	+	0.869776i	$0.335737\pi$
$224$	5.44737	0.363968
$225$	−4.95288	−0.330192
$226$	−7.21736	−0.480092
$227$	17.5182	1.16272	0.581362	−	0.813645i	$-0.302520\pi$
$227$	17.5182	1.16272	0.581362	+	0.813645i	$0.302520\pi$
$228$	−0.535784	−0.0354831
$229$	−13.4870	−0.891249	−0.445624	−	0.895220i	$-0.647018\pi$
$229$	−13.4870	−0.891249	−0.445624	+	0.895220i	$0.647018\pi$
$230$	−2.45401	−0.161812
$231$	−13.3013	−0.875163
$232$	−9.71297	−0.637688
$233$	15.8142	1.03602	0.518012	−	0.855374i	$-0.326672\pi$
$233$	15.8142	1.03602	0.518012	+	0.855374i	$0.326672\pi$
$234$	1.54007	0.100677
$235$	2.51292	0.163925
$236$	−1.39197	−0.0906096
$237$	−7.45464	−0.484231
$238$	−20.7814	−1.34706
$239$	−6.81316	−0.440707	−0.220353	−	0.975420i	$-0.570721\pi$
$239$	−6.81316	−0.440707	−0.220353	+	0.975420i	$0.570721\pi$
$240$	−0.999725	−0.0645320
$241$	−14.5029	−0.934211	−0.467105	−	0.884202i	$-0.654703\pi$
$241$	−14.5029	−0.934211	−0.467105	+	0.884202i	$0.654703\pi$
$242$	−22.6923	−1.45872
$243$	−1.00000	−0.0641500
$244$	−1.41556	−0.0906220
$245$	0.0271363	0.00173367
$246$	−2.74104	−0.174763
$247$	−1.44102	−0.0916897
$248$	−1.70901	−0.108522
$249$	2.26215	0.143358
$250$	−3.32739	−0.210443
$251$	6.48307	0.409208	0.204604	−	0.978845i	$-0.434409\pi$
$251$	6.48307	0.409208	0.204604	+	0.978845i	$0.434409\pi$
$252$	0.974892	0.0614125
$253$	−37.2374	−2.34110
$254$	−13.9688	−0.876480
$255$	1.11716	0.0699590
$256$	8.63414	0.539634
$257$	14.8831	0.928383	0.464192	−	0.885735i	$-0.346345\pi$
$257$	14.8831	0.928383	0.464192	+	0.885735i	$0.346345\pi$
$258$	12.0391	0.749522
$259$	−24.1229	−1.49893
$260$	0.0807116	0.00500552
$261$	−3.87353	−0.239765
$262$	24.8748	1.53677
$263$	−11.2675	−0.694787	−0.347393	−	0.937720i	$-0.612933\pi$
$263$	−11.2675	−0.694787	−0.347393	+	0.937720i	$0.612933\pi$
$264$	−12.7205	−0.782893
$265$	1.88809	0.115984
$266$	−5.81896	−0.356783
$267$	4.83089	0.295646
$268$	−3.83732	−0.234402
$269$	31.1362	1.89841	0.949204	−	0.314663i	$-0.101891\pi$
$269$	31.1362	1.89841	0.949204	+	0.314663i	$0.101891\pi$
$270$	−0.334314	−0.0203457
$271$	−12.0903	−0.734435	−0.367217	−	0.930135i	$-0.619689\pi$
$271$	−12.0903	−0.734435	−0.367217	+	0.930135i	$0.619689\pi$
$272$	−23.7008	−1.43707
$273$	2.62202	0.158692
$274$	11.9614	0.722616
$275$	−25.1256	−1.51513
$276$	2.72924	0.164281
$277$	−28.5812	−1.71728	−0.858638	−	0.512583i	$-0.828689\pi$
$277$	−28.5812	−1.71728	−0.858638	+	0.512583i	$0.828689\pi$
$278$	−13.9739	−0.838098
$279$	−0.681553	−0.0408035
$280$	−1.42724	−0.0852938
$281$	−23.9200	−1.42695	−0.713474	−	0.700682i	$-0.752879\pi$
$281$	−23.9200	−1.42695	−0.713474	+	0.700682i	$0.752879\pi$
$282$	−17.8280	−1.06164
$283$	−27.0530	−1.60813	−0.804067	−	0.594539i	$-0.797334\pi$
$283$	−27.0530	−1.60813	−0.804067	+	0.594539i	$0.797334\pi$
$284$	0.273409	0.0162239
$285$	0.312813	0.0185294
$286$	7.81266	0.461972
$287$	−4.66672	−0.275468
$288$	2.07755	0.122421
$289$	9.48482	0.557931
$290$	−1.29498	−0.0760436
$291$	14.6428	0.858378
$292$	2.64039	0.154517
$293$	−18.4073	−1.07537	−0.537683	−	0.843147i	$-0.680700\pi$
$293$	−18.4073	−1.07537	−0.537683	+	0.843147i	$0.680700\pi$
$294$	−0.192520	−0.0112280
$295$	0.812690	0.0473166
$296$	−23.0695	−1.34089
$297$	−5.07293	−0.294361
$298$	22.4962	1.30317
$299$	7.34041	0.424507
$300$	1.84153	0.106321
$301$	20.4970	1.18143
$302$	17.5949	1.01247
$303$	16.3505	0.939314
$304$	−6.63642	−0.380625
$305$	0.826463	0.0473231
$306$	−7.92572	−0.453083
$307$	15.9105	0.908061	0.454031	−	0.890986i	$-0.349986\pi$
$307$	15.9105	0.908061	0.454031	+	0.890986i	$0.349986\pi$
$308$	4.94556	0.281800
$309$	1.00000	0.0568880
$310$	−0.227853	−0.0129412
$311$	−9.18987	−0.521110	−0.260555	−	0.965459i	$-0.583906\pi$
$311$	−9.18987	−0.521110	−0.260555	+	0.965459i	$0.583906\pi$
$312$	2.50752	0.141961
$313$	−10.0811	−0.569816	−0.284908	−	0.958555i	$-0.591963\pi$
$313$	−10.0811	−0.569816	−0.284908	+	0.958555i	$0.591963\pi$
$314$	−5.56577	−0.314095
$315$	−0.569182	−0.0320698
$316$	2.77171	0.155921
$317$	21.4784	1.20635	0.603173	−	0.797611i	$-0.293903\pi$
$317$	21.4784	1.20635	0.603173	+	0.797611i	$0.293903\pi$
$318$	−13.3951	−0.751161
$319$	−19.6501	−1.10020
$320$	−1.30490	−0.0729459
$321$	3.61867	0.201974
$322$	29.6413	1.65184
$323$	7.41596	0.412635
$324$	0.371810	0.0206561
$325$	4.95288	0.274736
$326$	−12.0166	−0.665537
$327$	−10.9512	−0.605603
$328$	−4.46294	−0.246425
$329$	−30.3528	−1.67341
$330$	−1.69595	−0.0933592
$331$	20.8236	1.14457	0.572285	−	0.820055i	$-0.306057\pi$
$331$	20.8236	1.14457	0.572285	+	0.820055i	$0.306057\pi$
$332$	−0.841090	−0.0461608
$333$	−9.20012	−0.504164
$334$	−1.42406	−0.0779210
$335$	2.24039	0.122405
$336$	12.0754	0.658767
$337$	8.47027	0.461405	0.230703	−	0.973024i	$-0.425898\pi$
$337$	8.47027	0.461405	0.230703	+	0.973024i	$0.425898\pi$
$338$	−1.54007	−0.0837687
$339$	−4.68639	−0.254530
$340$	−0.415369	−0.0225266
$341$	−3.45747	−0.187233
$342$	−2.21926	−0.120004
$343$	−18.6819	−1.00873
$344$	19.6020	1.05687
$345$	−1.59344	−0.0857879
$346$	15.0963	0.811583
$347$	−8.64259	−0.463959	−0.231979	−	0.972721i	$-0.574520\pi$
$347$	−8.64259	−0.463959	−0.231979	+	0.972721i	$0.574520\pi$
$348$	1.44022	0.0772036
$349$	−14.8786	−0.796436	−0.398218	−	0.917291i	$-0.630371\pi$
$349$	−14.8786	−0.796436	−0.398218	+	0.917291i	$0.630371\pi$
$350$	20.0002	1.06905
$351$	1.00000	0.0533761
$352$	10.5392	0.561744
$353$	−8.09030	−0.430603	−0.215302	−	0.976548i	$-0.569074\pi$
$353$	−8.09030	−0.430603	−0.215302	+	0.976548i	$0.569074\pi$
$354$	−5.76567	−0.306442
$355$	−0.159628	−0.00847215
$356$	−1.79617	−0.0951968
$357$	−13.4938	−0.714168
$358$	−11.8539	−0.626497
$359$	−0.820720	−0.0433160	−0.0216580	−	0.999765i	$-0.506894\pi$
$359$	−0.820720	−0.0433160	−0.0216580	+	0.999765i	$0.506894\pi$
$360$	−0.544328	−0.0286886
$361$	−16.9235	−0.890709
$362$	−17.4373	−0.916482
$363$	−14.7346	−0.773368
$364$	−0.974892	−0.0510982
$365$	−1.54157	−0.0806895
$366$	−5.86338	−0.306484
$367$	27.3724	1.42883	0.714413	−	0.699724i	$-0.246694\pi$
$367$	27.3724	1.42883	0.714413	+	0.699724i	$0.246694\pi$
$368$	33.8054	1.76223
$369$	−1.77982	−0.0926537
$370$	−3.07573	−0.159900
$371$	−22.8057	−1.18401
$372$	0.253408	0.0131386
$373$	14.4938	0.750461	0.375230	−	0.926932i	$-0.377564\pi$
$373$	14.4938	0.750461	0.375230	+	0.926932i	$0.377564\pi$
$374$	−40.2066	−2.07903
$375$	−2.16055	−0.111570
$376$	−29.0274	−1.49697
$377$	3.87353	0.199497
$378$	4.03809	0.207697
$379$	36.4111	1.87031	0.935156	−	0.354236i	$-0.115259\pi$
$379$	36.4111	1.87031	0.935156	+	0.354236i	$0.115259\pi$
$380$	−0.116307	−0.00596641
$381$	−9.07025	−0.464683
$382$	40.9996	2.09772
$383$	−7.25723	−0.370827	−0.185414	−	0.982661i	$-0.559362\pi$
$383$	−7.25723	−0.370827	−0.185414	+	0.982661i	$0.559362\pi$
$384$	13.4127	0.684466
$385$	−2.88742	−0.147157
$386$	26.6413	1.35601
$387$	7.81726	0.397374
$388$	−5.44435	−0.276395
$389$	4.46273	0.226269	0.113135	−	0.993580i	$-0.463911\pi$
$389$	4.46273	0.226269	0.113135	+	0.993580i	$0.463911\pi$
$390$	0.334314	0.0169287
$391$	−37.7763	−1.91043
$392$	−0.313459	−0.0158321
$393$	16.1517	0.814747
$394$	−18.8537	−0.949834
$395$	−1.61824	−0.0814223
$396$	1.88616	0.0947833
$397$	−10.1109	−0.507453	−0.253727	−	0.967276i	$-0.581656\pi$
$397$	−10.1109	−0.507453	−0.253727	+	0.967276i	$0.581656\pi$
$398$	−15.5371	−0.778805
$399$	−3.77838	−0.189155
$400$	22.8099	1.14049
$401$	12.9926	0.648819	0.324409	−	0.945917i	$-0.394834\pi$
$401$	12.9926	0.648819	0.324409	+	0.945917i	$0.394834\pi$
$402$	−15.8945	−0.792747
$403$	0.681553	0.0339506
$404$	−6.07929	−0.302456
$405$	−0.217078	−0.0107867
$406$	15.6417	0.776283
$407$	−46.6716	−2.31343
$408$	−12.9046	−0.638872
$409$	13.2229	0.653832	0.326916	−	0.945053i	$-0.393991\pi$
$409$	13.2229	0.653832	0.326916	+	0.945053i	$0.393991\pi$
$410$	−0.595019	−0.0293859
$411$	7.76682	0.383109
$412$	−0.371810	−0.0183177
$413$	−9.81625	−0.483026
$414$	11.3047	0.555598
$415$	0.491063	0.0241053
$416$	−2.07755	−0.101860
$417$	−9.07355	−0.444334
$418$	−11.2582	−0.550655
$419$	−2.97445	−0.145311	−0.0726557	−	0.997357i	$-0.523147\pi$
$419$	−2.97445	−0.145311	−0.0726557	+	0.997357i	$0.523147\pi$
$420$	0.211627	0.0103264
$421$	23.5951	1.14995	0.574977	−	0.818169i	$-0.305011\pi$
$421$	23.5951	1.14995	0.574977	+	0.818169i	$0.305011\pi$
$422$	−20.8973	−1.01726
$423$	−11.5761	−0.562850
$424$	−21.8098	−1.05918
$425$	−25.4892	−1.23641
$426$	1.13249	0.0548691
$427$	−9.98261	−0.483093
$428$	−1.34546	−0.0650351
$429$	5.07293	0.244923
$430$	2.61342	0.126030
$431$	13.3640	0.643722	0.321861	−	0.946787i	$-0.395692\pi$
$431$	13.3640	0.643722	0.321861	+	0.946787i	$0.395692\pi$
$432$	4.60538	0.221576
$433$	−1.85801	−0.0892904	−0.0446452	−	0.999003i	$-0.514216\pi$
$433$	−1.85801	−0.0892904	−0.0446452	+	0.999003i	$0.514216\pi$
$434$	2.75217	0.132109
$435$	−0.840857	−0.0403160
$436$	4.07176	0.195002
$437$	−10.5777	−0.505998
$438$	10.9367	0.522578
$439$	16.5859	0.791603	0.395801	−	0.918336i	$-0.370467\pi$
$439$	16.5859	0.791603	0.395801	+	0.918336i	$0.370467\pi$
$440$	−2.76134	−0.131642
$441$	−0.125007	−0.00595273
$442$	7.92572	0.376988
$443$	−39.5802	−1.88051	−0.940256	−	0.340469i	$-0.889414\pi$
$443$	−39.5802	−1.88051	−0.940256	+	0.340469i	$0.889414\pi$
$444$	3.42069	0.162339
$445$	1.04868	0.0497121
$446$	−22.6967	−1.07472
$447$	14.6073	0.690899
$448$	15.7615	0.744659
$449$	38.6409	1.82358	0.911788	−	0.410661i	$-0.134702\pi$
$449$	38.6409	1.82358	0.911788	+	0.410661i	$0.134702\pi$
$450$	7.62777	0.359576
$451$	−9.02890	−0.425154
$452$	1.74245	0.0819577
$453$	11.4247	0.536780
$454$	−26.9792	−1.26620
$455$	0.569182	0.0266837
$456$	−3.61338	−0.169212
$457$	39.8796	1.86549	0.932744	−	0.360540i	$-0.117408\pi$
$457$	39.8796	1.86549	0.932744	+	0.360540i	$0.117408\pi$
$458$	20.7710	0.970563
$459$	−5.14634	−0.240211
$460$	0.592456	0.0276234
$461$	13.5106	0.629250	0.314625	−	0.949216i	$-0.398121\pi$
$461$	13.5106	0.629250	0.314625	+	0.949216i	$0.398121\pi$
$462$	20.4850	0.953046
$463$	−30.3343	−1.40976	−0.704878	−	0.709329i	$-0.748998\pi$
$463$	−30.3343	−1.40976	−0.704878	+	0.709329i	$0.748998\pi$
$464$	17.8391	0.828158
$465$	−0.147950	−0.00686102
$466$	−24.3550	−1.12822
$467$	−15.9951	−0.740163	−0.370081	−	0.928999i	$-0.620670\pi$
$467$	−15.9951	−0.740163	−0.370081	+	0.928999i	$0.620670\pi$
$468$	−0.371810	−0.0171869
$469$	−27.0610	−1.24956
$470$	−3.87006	−0.178513
$471$	−3.61398	−0.166523
$472$	−9.38760	−0.432099
$473$	39.6564	1.82340
$474$	11.4807	0.527324
$475$	−7.13718	−0.327476
$476$	5.01713	0.229960
$477$	−8.69775	−0.398243
$478$	10.4927	0.479926
$479$	6.48342	0.296235	0.148117	−	0.988970i	$-0.452679\pi$
$479$	6.48342	0.296235	0.148117	+	0.988970i	$0.452679\pi$
$480$	0.450989	0.0205847
$481$	9.20012	0.419490
$482$	22.3354	1.01735
$483$	19.2467	0.875756
$484$	5.47848	0.249022
$485$	3.17863	0.144334
$486$	1.54007	0.0698589
$487$	23.7729	1.07725	0.538626	−	0.842545i	$-0.318944\pi$
$487$	23.7729	1.07725	0.538626	+	0.842545i	$0.318944\pi$
$488$	−9.54670	−0.432159
$489$	−7.80263	−0.352847
$490$	−0.0417917	−0.00188796
$491$	−1.82672	−0.0824388	−0.0412194	−	0.999150i	$-0.513124\pi$
$491$	−1.82672	−0.0824388	−0.0412194	+	0.999150i	$0.513124\pi$
$492$	0.661754	0.0298342
$493$	−19.9345	−0.897805
$494$	2.21926	0.0998494
$495$	−1.10122	−0.0494962
$496$	3.13881	0.140937
$497$	1.92810	0.0864869
$498$	−3.48387	−0.156116
$499$	7.05581	0.315861	0.157931	−	0.987450i	$-0.449518\pi$
$499$	7.05581	0.315861	0.157931	+	0.987450i	$0.449518\pi$
$500$	0.803312	0.0359252
$501$	−0.924672	−0.0413113
$502$	−9.98437	−0.445624
$503$	−19.5877	−0.873374	−0.436687	−	0.899614i	$-0.643848\pi$
$503$	−19.5877	−0.873374	−0.436687	+	0.899614i	$0.643848\pi$
$504$	6.57478	0.292864
$505$	3.54934	0.157943
$506$	57.3482	2.54944
$507$	−1.00000	−0.0444116
$508$	3.37241	0.149626
$509$	−8.59828	−0.381112	−0.190556	−	0.981676i	$-0.561029\pi$
$509$	−8.59828	−0.381112	−0.190556	+	0.981676i	$0.561029\pi$
$510$	−1.72050	−0.0761849
$511$	18.6202	0.823709
$512$	13.5283	0.597872
$513$	−1.44102	−0.0636224
$514$	−22.9210	−1.01100
$515$	0.217078	0.00956559
$516$	−2.90653	−0.127953
$517$	−58.7249	−2.58272
$518$	37.1509	1.63232
$519$	9.80238	0.430277
$520$	0.544328	0.0238703
$521$	−8.31808	−0.364422	−0.182211	−	0.983259i	$-0.558325\pi$
$521$	−8.31808	−0.364422	−0.182211	+	0.983259i	$0.558325\pi$
$522$	5.96550	0.261103
$523$	33.8561	1.48042	0.740212	−	0.672374i	$-0.234725\pi$
$523$	33.8561	1.48042	0.740212	+	0.672374i	$0.234725\pi$
$524$	−6.00537	−0.262346
$525$	12.9865	0.566779
$526$	17.3528	0.756618
$527$	−3.50751	−0.152789
$528$	23.3628	1.01673
$529$	30.8817	1.34268
$530$	−2.90778	−0.126306
$531$	−3.74377	−0.162466
$532$	1.40484	0.0609074
$533$	1.77982	0.0770926
$534$	−7.43990	−0.321956
$535$	0.785533	0.0339615
$536$	−25.8793	−1.11782
$537$	−7.69699	−0.332150
$538$	−47.9519	−2.06735
$539$	−0.634153	−0.0273149
$540$	0.0807116	0.00347327
$541$	−9.33507	−0.401346	−0.200673	−	0.979658i	$-0.564313\pi$
$541$	−9.33507	−0.401346	−0.200673	+	0.979658i	$0.564313\pi$
$542$	18.6199	0.799794
$543$	−11.3224	−0.485890
$544$	10.6918	0.458405
$545$	−2.37726	−0.101831
$546$	−4.03809	−0.172814
$547$	−42.2525	−1.80659	−0.903293	−	0.429025i	$-0.858857\pi$
$547$	−42.2525	−1.80659	−0.903293	+	0.429025i	$0.858857\pi$
$548$	−2.88778	−0.123360
$549$	−3.80722	−0.162488
$550$	38.6951	1.64997
$551$	−5.58182	−0.237793
$552$	18.4063	0.783423
$553$	19.5462	0.831190
$554$	44.0169	1.87010
$555$	−1.99714	−0.0847740
$556$	3.37363	0.143074
$557$	6.49237	0.275090	0.137545	−	0.990495i	$-0.456079\pi$
$557$	6.49237	0.275090	0.137545	+	0.990495i	$0.456079\pi$
$558$	1.04964	0.0444347
$559$	−7.81726	−0.330635
$560$	2.62130	0.110770
$561$	−26.1070	−1.10224
$562$	36.8384	1.55394
$563$	35.3015	1.48778	0.743890	−	0.668302i	$-0.232979\pi$
$563$	35.3015	1.48778	0.743890	+	0.668302i	$0.232979\pi$
$564$	4.30411	0.181236
$565$	−1.01731	−0.0427986
$566$	41.6634	1.75125
$567$	2.62202	0.110115
$568$	1.84390	0.0773684
$569$	16.8154	0.704938	0.352469	−	0.935823i	$-0.385342\pi$
$569$	16.8154	0.704938	0.352469	+	0.935823i	$0.385342\pi$
$570$	−0.481753	−0.0201784
$571$	11.1503	0.466624	0.233312	−	0.972402i	$-0.425044\pi$
$571$	11.1503	0.466624	0.233312	+	0.972402i	$0.425044\pi$
$572$	−1.88616	−0.0788645
$573$	26.6219	1.11215
$574$	7.18707	0.299983
$575$	36.3562	1.51616
$576$	6.01119	0.250466
$577$	−42.1649	−1.75535	−0.877673	−	0.479260i	$-0.840905\pi$
$577$	−42.1649	−1.75535	−0.877673	+	0.479260i	$0.840905\pi$
$578$	−14.6073	−0.607583
$579$	17.2988	0.718912
$580$	0.312639	0.0129816
$581$	−5.93141	−0.246076
$582$	−22.5510	−0.934768
$583$	−44.1231	−1.82739
$584$	17.8071	0.736863
$585$	0.217078	0.00897506
$586$	28.3485	1.17107
$587$	−41.8373	−1.72681	−0.863406	−	0.504510i	$-0.831673\pi$
$587$	−41.8373	−1.72681	−0.863406	+	0.504510i	$0.831673\pi$
$588$	0.0464789	0.00191676
$589$	−0.982130	−0.0404680
$590$	−1.25160	−0.0515275
$591$	−12.2421	−0.503573
$592$	42.3700	1.74140
$593$	−23.2489	−0.954720	−0.477360	−	0.878708i	$-0.658406\pi$
$593$	−23.2489	−0.954720	−0.477360	+	0.878708i	$0.658406\pi$
$594$	7.81266	0.320557
$595$	−2.92921	−0.120086
$596$	−5.43112	−0.222467
$597$	−10.0886	−0.412898
$598$	−11.3047	−0.462285
$599$	−45.0611	−1.84115	−0.920573	−	0.390570i	$-0.872278\pi$
$599$	−45.0611	−1.84115	−0.920573	+	0.390570i	$0.872278\pi$
$600$	12.4195	0.507022
$601$	37.1743	1.51637	0.758186	−	0.652039i	$-0.226086\pi$
$601$	37.1743	1.51637	0.758186	+	0.652039i	$0.226086\pi$
$602$	−31.5668	−1.28657
$603$	−10.3207	−0.420290
$604$	−4.24782	−0.172841
$605$	−3.19856	−0.130040
$606$	−25.1809	−1.02291
$607$	−21.2874	−0.864028	−0.432014	−	0.901867i	$-0.642197\pi$
$607$	−21.2874	−0.864028	−0.432014	+	0.901867i	$0.642197\pi$
$608$	2.99378	0.121414
$609$	10.1565	0.411561
$610$	−1.27281	−0.0515345
$611$	11.5761	0.468320
$612$	1.91346	0.0773470
$613$	−37.3042	−1.50670	−0.753350	−	0.657619i	$-0.771564\pi$
$613$	−37.3042	−1.50670	−0.753350	+	0.657619i	$0.771564\pi$
$614$	−24.5033	−0.988872
$615$	−0.386359	−0.0155795
$616$	33.3534	1.34385
$617$	20.1484	0.811143	0.405571	−	0.914063i	$-0.367073\pi$
$617$	20.1484	0.811143	0.405571	+	0.914063i	$0.367073\pi$
$618$	−1.54007	−0.0619506
$619$	36.9437	1.48489	0.742446	−	0.669906i	$-0.233665\pi$
$619$	36.9437	1.48489	0.742446	+	0.669906i	$0.233665\pi$
$620$	0.0550093	0.00220922
$621$	7.34041	0.294561
$622$	14.1530	0.567485
$623$	−12.6667	−0.507480
$624$	−4.60538	−0.184363
$625$	24.2954	0.971815
$626$	15.5255	0.620525
$627$	−7.31018	−0.291940
$628$	1.34371	0.0536199
$629$	−47.3470	−1.88785
$630$	0.876579	0.0349238
$631$	−32.1293	−1.27905	−0.639525	−	0.768771i	$-0.720869\pi$
$631$	−32.1293	−1.27905	−0.639525	+	0.768771i	$0.720869\pi$
$632$	18.6927	0.743556
$633$	−13.5691	−0.539322
$634$	−33.0782	−1.31370
$635$	−1.96895	−0.0781354
$636$	3.23391	0.128233
$637$	0.125007	0.00495297
$638$	30.2626	1.19811
$639$	0.735348	0.0290899
$640$	2.91161	0.115091
$641$	6.71445	0.265205	0.132602	−	0.991169i	$-0.457667\pi$
$641$	6.71445	0.265205	0.132602	+	0.991169i	$0.457667\pi$
$642$	−5.57300	−0.219949
$643$	10.6234	0.418945	0.209472	−	0.977815i	$-0.432825\pi$
$643$	10.6234	0.418945	0.209472	+	0.977815i	$0.432825\pi$
$644$	−7.15611	−0.281990
$645$	1.69695	0.0668174
$646$	−11.4211	−0.449357
$647$	−31.7547	−1.24840	−0.624202	−	0.781263i	$-0.714576\pi$
$647$	−31.7547	−1.24840	−0.624202	+	0.781263i	$0.714576\pi$
$648$	2.50752	0.0985048
$649$	−18.9919	−0.745498
$650$	−7.62777	−0.299186
$651$	1.78705	0.0700399
$652$	2.90109	0.113616
$653$	−7.80789	−0.305546	−0.152773	−	0.988261i	$-0.548820\pi$
$653$	−7.80789	−0.305546	−0.152773	+	0.988261i	$0.548820\pi$
$654$	16.8656	0.659497
$655$	3.50618	0.136998
$656$	8.19674	0.320029
$657$	7.10147	0.277055
$658$	46.7454	1.82233
$659$	14.9777	0.583447	0.291723	−	0.956503i	$-0.405771\pi$
$659$	14.9777	0.583447	0.291723	+	0.956503i	$0.405771\pi$
$660$	0.409444	0.0159376
$661$	−5.05027	−0.196433	−0.0982164	−	0.995165i	$-0.531314\pi$
$661$	−5.05027	−0.196433	−0.0982164	+	0.995165i	$0.531314\pi$
$662$	−32.0698	−1.24643
$663$	5.14634	0.199867
$664$	−5.67240	−0.220132
$665$	−0.820201	−0.0318060
$666$	14.1688	0.549031
$667$	28.4333	1.10094
$668$	0.343802	0.0133021
$669$	−14.7375	−0.569784
$670$	−3.45035	−0.133299
$671$	−19.3138	−0.745600
$672$	−5.44737	−0.210137
$673$	32.5562	1.25495	0.627474	−	0.778637i	$-0.284089\pi$
$673$	32.5562	1.25495	0.627474	+	0.778637i	$0.284089\pi$
$674$	−13.0448	−0.502467
$675$	4.95288	0.190636
$676$	0.371810	0.0143004
$677$	−51.0029	−1.96020	−0.980100	−	0.198503i	$-0.936392\pi$
$677$	−51.0029	−1.96020	−0.980100	+	0.198503i	$0.936392\pi$
$678$	7.21736	0.277181
$679$	−38.3938	−1.47342
$680$	−2.80130	−0.107425
$681$	−17.5182	−0.671299
$682$	5.32475	0.203895
$683$	−38.1128	−1.45835	−0.729173	−	0.684330i	$-0.760095\pi$
$683$	−38.1128	−1.45835	−0.729173	+	0.684330i	$0.760095\pi$
$684$	0.535784	0.0204862
$685$	1.68600	0.0644189
$686$	28.7714	1.09850
$687$	13.4870	0.514563
$688$	−36.0014	−1.37254
$689$	8.69775	0.331358
$690$	2.45401	0.0934224
$691$	−46.9291	−1.78527	−0.892634	−	0.450782i	$-0.851145\pi$
$691$	−46.9291	−1.78527	−0.892634	+	0.450782i	$0.851145\pi$
$692$	−3.64462	−0.138548
$693$	13.3013	0.505276
$694$	13.3102	0.505247
$695$	−1.96967	−0.0747137
$696$	9.71297	0.368169
$697$	−9.15956	−0.346943
$698$	22.9141	0.867313
$699$	−15.8142	−0.598148
$700$	−4.82852	−0.182501
$701$	−42.3112	−1.59807	−0.799037	−	0.601282i	$-0.794657\pi$
$701$	−42.3112	−1.59807	−0.799037	+	0.601282i	$0.794657\pi$
$702$	−1.54007	−0.0581261
$703$	−13.2575	−0.500017
$704$	30.4944	1.14930
$705$	−2.51292	−0.0946419
$706$	12.4596	0.468924
$707$	−42.8715	−1.61235
$708$	1.39197	0.0523135
$709$	−7.85314	−0.294931	−0.147465	−	0.989067i	$-0.547112\pi$
$709$	−7.85314	−0.294931	−0.147465	+	0.989067i	$0.547112\pi$
$710$	0.245837	0.00922611
$711$	7.45464	0.279571
$712$	−12.1136	−0.453975
$713$	5.00288	0.187359
$714$	20.7814	0.777724
$715$	1.10122	0.0411833
$716$	2.86181	0.106951
$717$	6.81316	0.254442
$718$	1.26396	0.0471707
$719$	14.2326	0.530786	0.265393	−	0.964140i	$-0.414498\pi$
$719$	14.2326	0.530786	0.265393	+	0.964140i	$0.414498\pi$
$720$	0.999725	0.0372575
$721$	−2.62202	−0.0976492
$722$	26.0633	0.969975
$723$	14.5029	0.539367
$724$	4.20977	0.156455
$725$	19.1851	0.712517
$726$	22.6923	0.842192
$727$	−31.2360	−1.15848	−0.579239	−	0.815158i	$-0.696650\pi$
$727$	−31.2360	−1.15848	−0.579239	+	0.815158i	$0.696650\pi$
$728$	−6.57478	−0.243678
$729$	1.00000	0.0370370
$730$	2.37412	0.0878703
$731$	40.2303	1.48797
$732$	1.41556	0.0523207
$733$	50.5539	1.86725	0.933626	−	0.358250i	$-0.116626\pi$
$733$	50.5539	1.86725	0.933626	+	0.358250i	$0.116626\pi$
$734$	−42.1553	−1.55598
$735$	−0.0271363	−0.00100094
$736$	−15.2500	−0.562124
$737$	−52.3561	−1.92856
$738$	2.74104	0.100899
$739$	9.35975	0.344304	0.172152	−	0.985070i	$-0.444928\pi$
$739$	9.35975	0.344304	0.172152	+	0.985070i	$0.444928\pi$
$740$	0.742557	0.0272969
$741$	1.44102	0.0529371
$742$	35.1223	1.28938
$743$	−18.3122	−0.671809	−0.335904	−	0.941896i	$-0.609042\pi$
$743$	−18.3122	−0.671809	−0.335904	+	0.941896i	$0.609042\pi$
$744$	1.70901	0.0626554
$745$	3.17091	0.116173
$746$	−22.3214	−0.817246
$747$	−2.26215	−0.0827678
$748$	9.70685	0.354917
$749$	−9.48823	−0.346692
$750$	3.32739	0.121499
$751$	5.30915	0.193734	0.0968669	−	0.995297i	$-0.469118\pi$
$751$	5.30915	0.193734	0.0968669	+	0.995297i	$0.469118\pi$
$752$	53.3124	1.94410
$753$	−6.48307	−0.236256
$754$	−5.96550	−0.217251
$755$	2.48005	0.0902584
$756$	−0.974892	−0.0354565
$757$	26.2557	0.954281	0.477141	−	0.878827i	$-0.341673\pi$
$757$	26.2557	0.954281	0.477141	+	0.878827i	$0.341673\pi$
$758$	−56.0756	−2.03676
$759$	37.2374	1.35163
$760$	−0.784385	−0.0284526
$761$	7.04107	0.255238	0.127619	−	0.991823i	$-0.459266\pi$
$761$	7.04107	0.255238	0.127619	+	0.991823i	$0.459266\pi$
$762$	13.9688	0.506036
$763$	28.7143	1.03953
$764$	−9.89828	−0.358107
$765$	−1.11716	−0.0403909
$766$	11.1766	0.403828
$767$	3.74377	0.135180
$768$	−8.63414	−0.311558
$769$	14.6338	0.527709	0.263855	−	0.964562i	$-0.415006\pi$
$769$	14.6338	0.527709	0.263855	+	0.964562i	$0.415006\pi$
$770$	4.44683	0.160253
$771$	−14.8831	−0.536002
$772$	−6.43185	−0.231487
$773$	1.26403	0.0454639	0.0227320	−	0.999742i	$-0.492764\pi$
$773$	1.26403	0.0454639	0.0227320	+	0.999742i	$0.492764\pi$
$774$	−12.0391	−0.432737
$775$	3.37565	0.121257
$776$	−36.7173	−1.31807
$777$	24.1229	0.865405
$778$	−6.87291	−0.246406
$779$	−2.56475	−0.0918917
$780$	−0.0807116	−0.00288994
$781$	3.73037	0.133483
$782$	58.1780	2.08044
$783$	3.87353	0.138429
$784$	0.575706	0.0205609
$785$	−0.784514	−0.0280005
$786$	−24.8748	−0.887254
$787$	9.95457	0.354842	0.177421	−	0.984135i	$-0.443225\pi$
$787$	9.95457	0.354842	0.177421	+	0.984135i	$0.443225\pi$
$788$	4.55173	0.162149
$789$	11.2675	0.401135
$790$	2.49220	0.0886683
$791$	12.2878	0.436905
$792$	12.7205	0.452003
$793$	3.80722	0.135198
$794$	15.5715	0.552613
$795$	−1.88809	−0.0669636
$796$	3.75103	0.132952
$797$	18.5672	0.657684	0.328842	−	0.944385i	$-0.393342\pi$
$797$	18.5672	0.657684	0.328842	+	0.944385i	$0.393342\pi$
$798$	5.81896	0.205989
$799$	−59.5746	−2.10760
$800$	−10.2898	−0.363800
$801$	−4.83089	−0.170691
$802$	−20.0095	−0.706559
$803$	36.0253	1.27130
$804$	3.83732	0.135332
$805$	4.17803	0.147256
$806$	−1.04964	−0.0369719
$807$	−31.1362	−1.09605
$808$	−40.9994	−1.44235
$809$	27.5404	0.968270	0.484135	−	0.874993i	$-0.339134\pi$
$809$	27.5404	0.968270	0.484135	+	0.874993i	$0.339134\pi$
$810$	0.334314	0.0117466
$811$	−2.73253	−0.0959522	−0.0479761	−	0.998848i	$-0.515277\pi$
$811$	−2.73253	−0.0959522	−0.0479761	+	0.998848i	$0.515277\pi$
$812$	−3.77627	−0.132521
$813$	12.0903	0.424026
$814$	71.8774	2.51930
$815$	−1.69378	−0.0593304
$816$	23.7008	0.829695
$817$	11.2648	0.394105
$818$	−20.3642	−0.712018
$819$	−2.62202	−0.0916208
$820$	0.143652	0.00501655
$821$	−6.12735	−0.213846	−0.106923	−	0.994267i	$-0.534100\pi$
$821$	−6.12735	−0.213846	−0.106923	+	0.994267i	$0.534100\pi$
$822$	−11.9614	−0.417203
$823$	40.8784	1.42493	0.712467	−	0.701706i	$-0.247578\pi$
$823$	40.8784	1.42493	0.712467	+	0.701706i	$0.247578\pi$
$824$	−2.50752	−0.0873537
$825$	25.1256	0.874761
$826$	15.1177	0.526012
$827$	43.5054	1.51283	0.756416	−	0.654091i	$-0.226949\pi$
$827$	43.5054	1.51283	0.756416	+	0.654091i	$0.226949\pi$
$828$	−2.72924	−0.0948475
$829$	24.1679	0.839387	0.419693	−	0.907666i	$-0.362138\pi$
$829$	24.1679	0.839387	0.419693	+	0.907666i	$0.362138\pi$
$830$	−0.756270	−0.0262505
$831$	28.5812	0.991470
$832$	−6.01119	−0.208401
$833$	−0.643330	−0.0222901
$834$	13.9739	0.483876
$835$	−0.200726	−0.00694640
$836$	2.71799	0.0940038
$837$	0.681553	0.0235579
$838$	4.58086	0.158243
$839$	40.2077	1.38812	0.694061	−	0.719916i	$-0.255820\pi$
$839$	40.2077	1.38812	0.694061	+	0.719916i	$0.255820\pi$
$840$	1.42724	0.0492444
$841$	−13.9958	−0.482613
$842$	−36.3381	−1.25229
$843$	23.9200	0.823849
$844$	5.04511	0.173660
$845$	−0.217078	−0.00746770
$846$	17.8280	0.612940
$847$	38.6345	1.32750
$848$	40.0564	1.37554
$849$	27.0530	0.928456
$850$	39.2551	1.34644
$851$	67.5327	2.31499
$852$	−0.273409	−0.00936685
$853$	42.5145	1.45567	0.727835	−	0.685752i	$-0.240527\pi$
$853$	42.5145	1.45567	0.727835	+	0.685752i	$0.240527\pi$
$854$	15.3739	0.526084
$855$	−0.312813	−0.0106980
$856$	−9.07390	−0.310140
$857$	20.3587	0.695442	0.347721	−	0.937598i	$-0.386956\pi$
$857$	20.3587	0.695442	0.347721	+	0.937598i	$0.386956\pi$
$858$	−7.81266	−0.266720
$859$	−5.74479	−0.196010	−0.0980049	−	0.995186i	$-0.531246\pi$
$859$	−5.74479	−0.196010	−0.0980049	+	0.995186i	$0.531246\pi$
$860$	−0.630943	−0.0215150
$861$	4.66672	0.159042
$862$	−20.5815	−0.701008
$863$	18.3527	0.624734	0.312367	−	0.949961i	$-0.398878\pi$
$863$	18.3527	0.624734	0.312367	+	0.949961i	$0.398878\pi$
$864$	−2.07755	−0.0706795
$865$	2.12788	0.0723500
$866$	2.86147	0.0972366
$867$	−9.48482	−0.322122
$868$	−0.664441	−0.0225526
$869$	37.8169	1.28285
$870$	1.29498	0.0439038
$871$	10.3207	0.349703
$872$	27.4604	0.929927
$873$	−14.6428	−0.495585
$874$	16.2903	0.551028
$875$	5.66500	0.191512
$876$	−2.64039	−0.0892106
$877$	−13.8873	−0.468941	−0.234470	−	0.972123i	$-0.575336\pi$
$877$	−13.8873	−0.468941	−0.234470	+	0.972123i	$0.575336\pi$
$878$	−25.5434	−0.862049
$879$	18.4073	0.620863
$880$	5.07154	0.170961
$881$	24.8378	0.836805	0.418403	−	0.908262i	$-0.362590\pi$
$881$	24.8378	0.836805	0.418403	+	0.908262i	$0.362590\pi$
$882$	0.192520	0.00648248
$883$	−31.9282	−1.07447	−0.537235	−	0.843433i	$-0.680531\pi$
$883$	−31.9282	−1.07447	−0.537235	+	0.843433i	$0.680531\pi$
$884$	−1.91346	−0.0643566
$885$	−0.812690	−0.0273183
$886$	60.9562	2.04786
$887$	43.0231	1.44458	0.722288	−	0.691593i	$-0.243091\pi$
$887$	43.0231	1.44458	0.722288	+	0.691593i	$0.243091\pi$
$888$	23.0695	0.774163
$889$	23.7824	0.797635
$890$	−1.61504	−0.0541361
$891$	5.07293	0.169950
$892$	5.47953	0.183468
$893$	−16.6814	−0.558221
$894$	−22.4962	−0.752384
$895$	−1.67084	−0.0558502
$896$	−35.1685	−1.17490
$897$	−7.34041	−0.245089
$898$	−59.5096	−1.98586
$899$	2.64002	0.0880495
$900$	−1.84153	−0.0613842
$901$	−44.7616	−1.49122
$902$	13.9051	0.462990
$903$	−20.4970	−0.682098
$904$	11.7512	0.390840
$905$	−2.45784	−0.0817013
$906$	−17.5949	−0.584550
$907$	20.8033	0.690761	0.345380	−	0.938463i	$-0.387750\pi$
$907$	20.8033	0.690761	0.345380	+	0.938463i	$0.387750\pi$
$908$	6.51343	0.216156
$909$	−16.3505	−0.542313
$910$	−0.876579	−0.0290583
$911$	6.91900	0.229237	0.114618	−	0.993410i	$-0.463435\pi$
$911$	6.91900	0.229237	0.114618	+	0.993410i	$0.463435\pi$
$912$	6.63642	0.219754
$913$	−11.4757	−0.379792
$914$	−61.4172	−2.03150
$915$	−0.826463	−0.0273220
$916$	−5.01461	−0.165687
$917$	−42.3502	−1.39853
$918$	7.92572	0.261588
$919$	41.3766	1.36489	0.682444	−	0.730938i	$-0.260917\pi$
$919$	41.3766	1.36489	0.682444	+	0.730938i	$0.260917\pi$
$920$	3.99559	0.131731
$921$	−15.9105	−0.524270
$922$	−20.8072	−0.685249
$923$	−0.735348	−0.0242043
$924$	−4.94556	−0.162697
$925$	45.5671	1.49824
$926$	46.7169	1.53521
$927$	−1.00000	−0.0328443
$928$	−8.04743	−0.264170
$929$	−39.0924	−1.28258	−0.641291	−	0.767298i	$-0.721601\pi$
$929$	−39.0924	−1.28258	−0.641291	+	0.767298i	$0.721601\pi$
$930$	0.227853	0.00747160
$931$	−0.180138	−0.00590377
$932$	5.87987	0.192602
$933$	9.18987	0.300863
$934$	24.6335	0.806032
$935$	−5.66726	−0.185339
$936$	−2.50752	−0.0819610
$937$	10.4598	0.341708	0.170854	−	0.985296i	$-0.445347\pi$
$937$	10.4598	0.341708	0.170854	+	0.985296i	$0.445347\pi$
$938$	41.6758	1.36076
$939$	10.0811	0.328983
$940$	0.934327	0.0304744
$941$	19.6486	0.640525	0.320263	−	0.947329i	$-0.396229\pi$
$941$	19.6486	0.640525	0.320263	+	0.947329i	$0.396229\pi$
$942$	5.56577	0.181343
$943$	13.0646	0.425442
$944$	17.2415	0.561163
$945$	0.569182	0.0185155
$946$	−61.0736	−1.98567
$947$	−2.96943	−0.0964934	−0.0482467	−	0.998835i	$-0.515363\pi$
$947$	−2.96943	−0.0964934	−0.0482467	+	0.998835i	$0.515363\pi$
$948$	−2.77171	−0.0900209
$949$	−7.10147	−0.230523
$950$	10.9917	0.356619
$951$	−21.4784	−0.696484
$952$	33.8361	1.09663
$953$	−46.8317	−1.51703	−0.758514	−	0.651657i	$-0.774074\pi$
$953$	−46.8317	−1.51703	−0.758514	+	0.651657i	$0.774074\pi$
$954$	13.3951	0.433683
$955$	5.77902	0.187005
$956$	−2.53320	−0.0819295
$957$	19.6501	0.635199
$958$	−9.98490	−0.322598
$959$	−20.3648	−0.657612
$960$	1.30490	0.0421153
$961$	−30.5355	−0.985016
$962$	−14.1688	−0.456821
$963$	−3.61867	−0.116610
$964$	−5.39230	−0.173674
$965$	3.75518	0.120883
$966$	−29.6413	−0.953692
$967$	−16.5250	−0.531410	−0.265705	−	0.964054i	$-0.585605\pi$
$967$	−16.5250	−0.531410	−0.265705	+	0.964054i	$0.585605\pi$
$968$	36.9475	1.18754
$969$	−7.41596	−0.238235
$970$	−4.89531	−0.157179
$971$	−38.8635	−1.24719	−0.623595	−	0.781747i	$-0.714329\pi$
$971$	−38.8635	−1.24719	−0.623595	+	0.781747i	$0.714329\pi$
$972$	−0.371810	−0.0119258
$973$	23.7910	0.762706
$974$	−36.6118	−1.17312
$975$	−4.95288	−0.158619
$976$	17.5337	0.561240
$977$	−17.6507	−0.564696	−0.282348	−	0.959312i	$-0.591113\pi$
$977$	−17.6507	−0.564696	−0.282348	+	0.959312i	$0.591113\pi$
$978$	12.0166	0.384248
$979$	−24.5068	−0.783240
$980$	0.0100895	0.000322298 0
$981$	10.9512	0.349645
$982$	2.81328	0.0897752
$983$	40.6084	1.29521	0.647603	−	0.761978i	$-0.275772\pi$
$983$	40.6084	1.29521	0.647603	+	0.761978i	$0.275772\pi$
$984$	4.46294	0.142273
$985$	−2.65749	−0.0846746
$986$	30.7005	0.977703
$987$	30.3528	0.966141
$988$	−0.535784	−0.0170456
$989$	−57.3819	−1.82464
$990$	1.69595	0.0539010
$991$	−39.7162	−1.26163	−0.630813	−	0.775935i	$-0.717278\pi$
$991$	−39.7162	−1.26163	−0.630813	+	0.775935i	$0.717278\pi$
$992$	−1.41596	−0.0449567
$993$	−20.8236	−0.660818
$994$	−2.96940	−0.0941836
$995$	−2.19001	−0.0694279
$996$	0.841090	0.0266510
$997$	−35.7109	−1.13097	−0.565487	−	0.824757i	$-0.691312\pi$
$997$	−35.7109	−1.13097	−0.565487	+	0.824757i	$0.691312\pi$
$998$	−10.8664	−0.343971
$999$	9.20012	0.291079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.7	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.7	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.54007 q^{2} -1.00000 q^{3} +0.371810 q^{4} -0.217078 q^{5} +1.54007 q^{6} +2.62202 q^{7} +2.50752 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.54007 q^{2} -1.00000 q^{3} +0.371810 q^{4} -0.217078 q^{5} +1.54007 q^{6} +2.62202 q^{7} +2.50752 q^{8} +1.00000 q^{9} +0.334314 q^{10} +5.07293 q^{11} -0.371810 q^{12} -1.00000 q^{13} -4.03809 q^{14} +0.217078 q^{15} -4.60538 q^{16} +5.14634 q^{17} -1.54007 q^{18} +1.44102 q^{19} -0.0807116 q^{20} -2.62202 q^{21} -7.81266 q^{22} -7.34041 q^{23} -2.50752 q^{24} -4.95288 q^{25} +1.54007 q^{26} -1.00000 q^{27} +0.974892 q^{28} -3.87353 q^{29} -0.334314 q^{30} -0.681553 q^{31} +2.07755 q^{32} -5.07293 q^{33} -7.92572 q^{34} -0.569182 q^{35} +0.371810 q^{36} -9.20012 q^{37} -2.21926 q^{38} +1.00000 q^{39} -0.544328 q^{40} -1.77982 q^{41} +4.03809 q^{42} +7.81726 q^{43} +1.88616 q^{44} -0.217078 q^{45} +11.3047 q^{46} -11.5761 q^{47} +4.60538 q^{48} -0.125007 q^{49} +7.62777 q^{50} -5.14634 q^{51} -0.371810 q^{52} -8.69775 q^{53} +1.54007 q^{54} -1.10122 q^{55} +6.57478 q^{56} -1.44102 q^{57} +5.96550 q^{58} -3.74377 q^{59} +0.0807116 q^{60} -3.80722 q^{61} +1.04964 q^{62} +2.62202 q^{63} +6.01119 q^{64} +0.217078 q^{65} +7.81266 q^{66} -10.3207 q^{67} +1.91346 q^{68} +7.34041 q^{69} +0.876579 q^{70} +0.735348 q^{71} +2.50752 q^{72} +7.10147 q^{73} +14.1688 q^{74} +4.95288 q^{75} +0.535784 q^{76} +13.3013 q^{77} -1.54007 q^{78} +7.45464 q^{79} +0.999725 q^{80} +1.00000 q^{81} +2.74104 q^{82} -2.26215 q^{83} -0.974892 q^{84} -1.11716 q^{85} -12.0391 q^{86} +3.87353 q^{87} +12.7205 q^{88} -4.83089 q^{89} +0.334314 q^{90} -2.62202 q^{91} -2.72924 q^{92} +0.681553 q^{93} +17.8280 q^{94} -0.312813 q^{95} -2.07755 q^{96} -14.6428 q^{97} +0.192520 q^{98} +5.07293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

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