LMFDB - Embedded newform 4017.2.a.j.1.6

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:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-1.55573 q^{2} -1.00000 q^{3} +0.420296 q^{4} -1.90089 q^{5} +1.55573 q^{6} +0.0358686 q^{7} +2.45759 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.55573 q^{2} -1.00000 q^{3} +0.420296 q^{4} -1.90089 q^{5} +1.55573 q^{6} +0.0358686 q^{7} +2.45759 q^{8} +1.00000 q^{9} +2.95727 q^{10} -4.89487 q^{11} -0.420296 q^{12} +1.00000 q^{13} -0.0558019 q^{14} +1.90089 q^{15} -4.66394 q^{16} +0.534376 q^{17} -1.55573 q^{18} +0.251892 q^{19} -0.798937 q^{20} -0.0358686 q^{21} +7.61509 q^{22} +9.05681 q^{23} -2.45759 q^{24} -1.38661 q^{25} -1.55573 q^{26} -1.00000 q^{27} +0.0150754 q^{28} +1.09475 q^{29} -2.95727 q^{30} -0.0390860 q^{31} +2.34065 q^{32} +4.89487 q^{33} -0.831345 q^{34} -0.0681824 q^{35} +0.420296 q^{36} -7.85613 q^{37} -0.391876 q^{38} -1.00000 q^{39} -4.67162 q^{40} +4.76621 q^{41} +0.0558019 q^{42} -12.1897 q^{43} -2.05729 q^{44} -1.90089 q^{45} -14.0900 q^{46} +0.236387 q^{47} +4.66394 q^{48} -6.99871 q^{49} +2.15720 q^{50} -0.534376 q^{51} +0.420296 q^{52} -4.29403 q^{53} +1.55573 q^{54} +9.30461 q^{55} +0.0881505 q^{56} -0.251892 q^{57} -1.70314 q^{58} +13.8587 q^{59} +0.798937 q^{60} -4.97793 q^{61} +0.0608072 q^{62} +0.0358686 q^{63} +5.68646 q^{64} -1.90089 q^{65} -7.61509 q^{66} -8.32506 q^{67} +0.224596 q^{68} -9.05681 q^{69} +0.106073 q^{70} -1.08614 q^{71} +2.45759 q^{72} +7.48444 q^{73} +12.2220 q^{74} +1.38661 q^{75} +0.105869 q^{76} -0.175572 q^{77} +1.55573 q^{78} +1.11032 q^{79} +8.86565 q^{80} +1.00000 q^{81} -7.41494 q^{82} -12.3101 q^{83} -0.0150754 q^{84} -1.01579 q^{85} +18.9638 q^{86} -1.09475 q^{87} -12.0296 q^{88} +12.9144 q^{89} +2.95727 q^{90} +0.0358686 q^{91} +3.80654 q^{92} +0.0390860 q^{93} -0.367754 q^{94} -0.478820 q^{95} -2.34065 q^{96} +19.5036 q^{97} +10.8881 q^{98} -4.89487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	−1.55573	−1.10007	−0.550034	−	0.835142i	$-0.685385\pi$
$2$	−1.55573	−1.10007	−0.550034	+	0.835142i	$0.685385\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.420296	0.210148
$5$	−1.90089	−0.850104	−0.425052	−	0.905169i	$-0.639744\pi$
$5$	−1.90089	−0.850104	−0.425052	+	0.905169i	$0.639744\pi$
$6$	1.55573	0.635124
$7$	0.0358686	0.0135571	0.00677853	−	0.999977i	$-0.497842\pi$
$7$	0.0358686	0.0135571	0.00677853	+	0.999977i	$0.497842\pi$
$8$	2.45759	0.868890
$9$	1.00000	0.333333
$10$	2.95727	0.935172
$11$	−4.89487	−1.47586	−0.737929	−	0.674879i	$-0.764196\pi$
$11$	−4.89487	−1.47586	−0.737929	+	0.674879i	$0.764196\pi$
$12$	−0.420296	−0.121329
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.0558019	−0.0149137
$15$	1.90089	0.490808
$16$	−4.66394	−1.16599
$17$	0.534376	0.129605	0.0648026	−	0.997898i	$-0.479358\pi$
$17$	0.534376	0.129605	0.0648026	+	0.997898i	$0.479358\pi$
$18$	−1.55573	−0.366689
$19$	0.251892	0.0577880	0.0288940	−	0.999582i	$-0.490801\pi$
$19$	0.251892	0.0577880	0.0288940	+	0.999582i	$0.490801\pi$
$20$	−0.798937	−0.178648
$21$	−0.0358686	−0.00782718
$22$	7.61509	1.62354
$23$	9.05681	1.88848	0.944238	−	0.329265i	$-0.106801\pi$
$23$	9.05681	1.88848	0.944238	+	0.329265i	$0.106801\pi$
$24$	−2.45759	−0.501654
$25$	−1.38661	−0.277323
$26$	−1.55573	−0.305104
$27$	−1.00000	−0.192450
$28$	0.0150754	0.00284899
$29$	1.09475	0.203290	0.101645	−	0.994821i	$-0.467589\pi$
$29$	1.09475	0.203290	0.101645	+	0.994821i	$0.467589\pi$
$30$	−2.95727	−0.539922
$31$	−0.0390860	−0.00702004	−0.00351002	−	0.999994i	$-0.501117\pi$
$31$	−0.0390860	−0.00702004	−0.00351002	+	0.999994i	$0.501117\pi$
$32$	2.34065	0.413773
$33$	4.89487	0.852087
$34$	−0.831345	−0.142574
$35$	−0.0681824	−0.0115249
$36$	0.420296	0.0700494
$37$	−7.85613	−1.29154	−0.645770	−	0.763532i	$-0.723463\pi$
$37$	−7.85613	−1.29154	−0.645770	+	0.763532i	$0.723463\pi$
$38$	−0.391876	−0.0635707
$39$	−1.00000	−0.160128
$40$	−4.67162	−0.738647
$41$	4.76621	0.744357	0.372179	−	0.928161i	$-0.378611\pi$
$41$	4.76621	0.744357	0.372179	+	0.928161i	$0.378611\pi$
$42$	0.0558019	0.00861042
$43$	−12.1897	−1.85891	−0.929454	−	0.368938i	$-0.879721\pi$
$43$	−12.1897	−1.85891	−0.929454	+	0.368938i	$0.879721\pi$
$44$	−2.05729	−0.310149
$45$	−1.90089	−0.283368
$46$	−14.0900	−2.07745
$47$	0.236387	0.0344805	0.0172403	−	0.999851i	$-0.494512\pi$
$47$	0.236387	0.0344805	0.0172403	+	0.999851i	$0.494512\pi$
$48$	4.66394	0.673182
$49$	−6.99871	−0.999816
$50$	2.15720	0.305073
$51$	−0.534376	−0.0748276
$52$	0.420296	0.0582846
$53$	−4.29403	−0.589831	−0.294915	−	0.955523i	$-0.595292\pi$
$53$	−4.29403	−0.589831	−0.294915	+	0.955523i	$0.595292\pi$
$54$	1.55573	0.211708
$55$	9.30461	1.25463
$56$	0.0881505	0.0117796
$57$	−0.251892	−0.0333639
$58$	−1.70314	−0.223633
$59$	13.8587	1.80424	0.902122	−	0.431481i	$-0.142009\pi$
$59$	13.8587	1.80424	0.902122	+	0.431481i	$0.142009\pi$
$60$	0.798937	0.103142
$61$	−4.97793	−0.637358	−0.318679	−	0.947863i	$-0.603239\pi$
$61$	−4.97793	−0.637358	−0.318679	+	0.947863i	$0.603239\pi$
$62$	0.0608072	0.00772252
$63$	0.0358686	0.00451902
$64$	5.68646	0.710808
$65$	−1.90089	−0.235777
$66$	−7.61509	−0.937353
$67$	−8.32506	−1.01707	−0.508534	−	0.861042i	$-0.669812\pi$
$67$	−8.32506	−1.01707	−0.508534	+	0.861042i	$0.669812\pi$
$68$	0.224596	0.0272363
$69$	−9.05681	−1.09031
$70$	0.106073	0.0126782
$71$	−1.08614	−0.128901	−0.0644503	−	0.997921i	$-0.520529\pi$
$71$	−1.08614	−0.128901	−0.0644503	+	0.997921i	$0.520529\pi$
$72$	2.45759	0.289630
$73$	7.48444	0.875987	0.437994	−	0.898978i	$-0.355689\pi$
$73$	7.48444	0.875987	0.437994	+	0.898978i	$0.355689\pi$
$74$	12.2220	1.42078
$75$	1.38661	0.160112
$76$	0.105869	0.0121440
$77$	−0.175572	−0.0200083
$78$	1.55573	0.176152
$79$	1.11032	0.124921	0.0624604	−	0.998047i	$-0.480105\pi$
$79$	1.11032	0.124921	0.0624604	+	0.998047i	$0.480105\pi$
$80$	8.86565	0.991210
$81$	1.00000	0.111111
$82$	−7.41494	−0.818843
$83$	−12.3101	−1.35121	−0.675605	−	0.737264i	$-0.736118\pi$
$83$	−12.3101	−1.35121	−0.675605	+	0.737264i	$0.736118\pi$
$84$	−0.0150754	−0.00164487
$85$	−1.01579	−0.110178
$86$	18.9638	2.04492
$87$	−1.09475	−0.117370
$88$	−12.0296	−1.28236
$89$	12.9144	1.36893	0.684463	−	0.729048i	$-0.260037\pi$
$89$	12.9144	1.36893	0.684463	+	0.729048i	$0.260037\pi$
$90$	2.95727	0.311724
$91$	0.0358686	0.00376005
$92$	3.80654	0.396859
$93$	0.0390860	0.00405302
$94$	−0.367754	−0.0379309
$95$	−0.478820	−0.0491259
$96$	−2.34065	−0.238892
$97$	19.5036	1.98029	0.990146	−	0.140041i	$-0.0447233\pi$
$97$	19.5036	1.98029	0.990146	+	0.140041i	$0.0447233\pi$
$98$	10.8881	1.09987
$99$	−4.89487	−0.491952
$100$	−0.582788	−0.0582788
$101$	−11.1103	−1.10551	−0.552756	−	0.833343i	$-0.686424\pi$
$101$	−11.1103	−1.10551	−0.552756	+	0.833343i	$0.686424\pi$
$102$	0.831345	0.0823154
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.45759	0.240987
$105$	0.0681824	0.00665392
$106$	6.68036	0.648854
$107$	−5.69522	−0.550578	−0.275289	−	0.961362i	$-0.588774\pi$
$107$	−5.69522	−0.550578	−0.275289	+	0.961362i	$0.588774\pi$
$108$	−0.420296	−0.0404430
$109$	−14.8709	−1.42437	−0.712187	−	0.701990i	$-0.752295\pi$
$109$	−14.8709	−1.42437	−0.712187	+	0.701990i	$0.752295\pi$
$110$	−14.4755	−1.38018
$111$	7.85613	0.745671
$112$	−0.167289	−0.0158074
$113$	−18.8154	−1.77000	−0.885001	−	0.465588i	$-0.845843\pi$
$113$	−18.8154	−1.77000	−0.885001	+	0.465588i	$0.845843\pi$
$114$	0.391876	0.0367026
$115$	−17.2160	−1.60540
$116$	0.460119	0.0427210
$117$	1.00000	0.0924500
$118$	−21.5603	−1.98479
$119$	0.0191673	0.00175707
$120$	4.67162	0.426458
$121$	12.9597	1.17816
$122$	7.74431	0.701137
$123$	−4.76621	−0.429755
$124$	−0.0164277	−0.00147525
$125$	12.1403	1.08586
$126$	−0.0558019	−0.00497123
$127$	2.47435	0.219563	0.109781	−	0.993956i	$-0.464985\pi$
$127$	2.47435	0.219563	0.109781	+	0.993956i	$0.464985\pi$
$128$	−13.5279	−1.19571
$129$	12.1897	1.07324
$130$	2.95727	0.259370
$131$	−15.4870	−1.35310	−0.676551	−	0.736395i	$-0.736526\pi$
$131$	−15.4870	−1.35310	−0.676551	+	0.736395i	$0.736526\pi$
$132$	2.05729	0.179064
$133$	0.00903503	0.000783436 0
$134$	12.9515	1.11884
$135$	1.90089	0.163603
$136$	1.31328	0.112613
$137$	−0.396590	−0.0338830	−0.0169415	−	0.999856i	$-0.505393\pi$
$137$	−0.396590	−0.0338830	−0.0169415	+	0.999856i	$0.505393\pi$
$138$	14.0900	1.19942
$139$	−5.42392	−0.460051	−0.230025	−	0.973185i	$-0.573881\pi$
$139$	−5.42392	−0.460051	−0.230025	+	0.973185i	$0.573881\pi$
$140$	−0.0286568	−0.00242194
$141$	−0.236387	−0.0199073
$142$	1.68974	0.141799
$143$	−4.89487	−0.409329
$144$	−4.66394	−0.388662
$145$	−2.08100	−0.172818
$146$	−11.6438	−0.963645
$147$	6.99871	0.577244
$148$	−3.30190	−0.271414
$149$	13.5439	1.10956	0.554781	−	0.831996i	$-0.312802\pi$
$149$	13.5439	1.10956	0.554781	+	0.831996i	$0.312802\pi$
$150$	−2.15720	−0.176134
$151$	−12.0602	−0.981442	−0.490721	−	0.871317i	$-0.663267\pi$
$151$	−12.0602	−0.981442	−0.490721	+	0.871317i	$0.663267\pi$
$152$	0.619048	0.0502115
$153$	0.534376	0.0432017
$154$	0.273143	0.0220105
$155$	0.0742981	0.00596777
$156$	−0.420296	−0.0336506
$157$	−22.4909	−1.79497	−0.897484	−	0.441047i	$-0.854607\pi$
$157$	−22.4909	−1.79497	−0.897484	+	0.441047i	$0.854607\pi$
$158$	−1.72736	−0.137421
$159$	4.29403	0.340539
$160$	−4.44932	−0.351750
$161$	0.324855	0.0256022
$162$	−1.55573	−0.122230
$163$	−0.477456	−0.0373973	−0.0186986	−	0.999825i	$-0.505952\pi$
$163$	−0.477456	−0.0373973	−0.0186986	+	0.999825i	$0.505952\pi$
$164$	2.00322	0.156425
$165$	−9.30461	−0.724363
$166$	19.1512	1.48642
$167$	−11.8831	−0.919541	−0.459770	−	0.888038i	$-0.652068\pi$
$167$	−11.8831	−0.919541	−0.459770	+	0.888038i	$0.652068\pi$
$168$	−0.0881505	−0.00680096
$169$	1.00000	0.0769231
$170$	1.58030	0.121203
$171$	0.251892	0.0192627
$172$	−5.12327	−0.390646
$173$	−5.75389	−0.437460	−0.218730	−	0.975785i	$-0.570191\pi$
$173$	−5.75389	−0.437460	−0.218730	+	0.975785i	$0.570191\pi$
$174$	1.70314	0.129114
$175$	−0.0497359	−0.00375968
$176$	22.8294	1.72083
$177$	−13.8587	−1.04168
$178$	−20.0914	−1.50591
$179$	6.33310	0.473358	0.236679	−	0.971588i	$-0.423941\pi$
$179$	6.33310	0.473358	0.236679	+	0.971588i	$0.423941\pi$
$180$	−0.798937	−0.0595493
$181$	1.06556	0.0792022	0.0396011	−	0.999216i	$-0.487391\pi$
$181$	1.06556	0.0792022	0.0396011	+	0.999216i	$0.487391\pi$
$182$	−0.0558019	−0.00413631
$183$	4.97793	0.367979
$184$	22.2579	1.64088
$185$	14.9336	1.09794
$186$	−0.0608072	−0.00445860
$187$	−2.61570	−0.191279
$188$	0.0993524	0.00724602
$189$	−0.0358686	−0.00260906
$190$	0.744914	0.0540417
$191$	6.58878	0.476747	0.238374	−	0.971174i	$-0.423386\pi$
$191$	6.58878	0.476747	0.238374	+	0.971174i	$0.423386\pi$
$192$	−5.68646	−0.410385
$193$	−4.43314	−0.319104	−0.159552	−	0.987190i	$-0.551005\pi$
$193$	−4.43314	−0.319104	−0.159552	+	0.987190i	$0.551005\pi$
$194$	−30.3424	−2.17845
$195$	1.90089	0.136126
$196$	−2.94153	−0.210109
$197$	14.1993	1.01165	0.505827	−	0.862635i	$-0.331187\pi$
$197$	14.1993	1.01165	0.505827	+	0.862635i	$0.331187\pi$
$198$	7.61509	0.541181
$199$	18.5251	1.31321	0.656606	−	0.754234i	$-0.271992\pi$
$199$	18.5251	1.31321	0.656606	+	0.754234i	$0.271992\pi$
$200$	−3.40773	−0.240963
$201$	8.32506	0.587204
$202$	17.2846	1.21614
$203$	0.0392672	0.00275602
$204$	−0.224596	−0.0157249
$205$	−9.06005	−0.632782
$206$	1.55573	0.108393
$207$	9.05681	0.629492
$208$	−4.66394	−0.323386
$209$	−1.23298	−0.0852869
$210$	−0.106073	−0.00731976
$211$	19.0545	1.31177	0.655884	−	0.754861i	$-0.272296\pi$
$211$	19.0545	1.31177	0.655884	+	0.754861i	$0.272296\pi$
$212$	−1.80477	−0.123952
$213$	1.08614	0.0744209
$214$	8.86023	0.605673
$215$	23.1712	1.58027
$216$	−2.45759	−0.167218
$217$	−0.00140196	−9.51712e−5 0
$218$	23.1351	1.56691
$219$	−7.48444	−0.505751
$220$	3.91069	0.263659
$221$	0.534376	0.0359460
$222$	−12.2220	−0.820288
$223$	25.1849	1.68651	0.843253	−	0.537516i	$-0.180637\pi$
$223$	25.1849	1.68651	0.843253	+	0.537516i	$0.180637\pi$
$224$	0.0839560	0.00560954
$225$	−1.38661	−0.0924408
$226$	29.2717	1.94712
$227$	29.0343	1.92707	0.963536	−	0.267580i	$-0.0862238\pi$
$227$	29.0343	1.92707	0.963536	+	0.267580i	$0.0862238\pi$
$228$	−0.105869	−0.00701137
$229$	1.96397	0.129783	0.0648913	−	0.997892i	$-0.479330\pi$
$229$	1.96397	0.129783	0.0648913	+	0.997892i	$0.479330\pi$
$230$	26.7835	1.76605
$231$	0.175572	0.0115518
$232$	2.69045	0.176637
$233$	7.21438	0.472630	0.236315	−	0.971677i	$-0.424060\pi$
$233$	7.21438	0.472630	0.236315	+	0.971677i	$0.424060\pi$
$234$	−1.55573	−0.101701
$235$	−0.449345	−0.0293121
$236$	5.82474	0.379158
$237$	−1.11032	−0.0721230
$238$	−0.0298192	−0.00193289
$239$	−13.4023	−0.866920	−0.433460	−	0.901173i	$-0.642707\pi$
$239$	−13.4023	−0.866920	−0.433460	+	0.901173i	$0.642707\pi$
$240$	−8.86565	−0.572275
$241$	−11.8626	−0.764137	−0.382069	−	0.924134i	$-0.624788\pi$
$241$	−11.8626	−0.764137	−0.382069	+	0.924134i	$0.624788\pi$
$242$	−20.1618	−1.29605
$243$	−1.00000	−0.0641500
$244$	−2.09220	−0.133940
$245$	13.3038	0.849948
$246$	7.41494	0.472759
$247$	0.251892	0.0160275
$248$	−0.0960574	−0.00609965
$249$	12.3101	0.780122
$250$	−18.8870	−1.19452
$251$	1.30407	0.0823120	0.0411560	−	0.999153i	$-0.486896\pi$
$251$	1.30407	0.0823120	0.0411560	+	0.999153i	$0.486896\pi$
$252$	0.0150754	0.000949664 0
$253$	−44.3319	−2.78712
$254$	−3.84942	−0.241534
$255$	1.01579	0.0636113
$256$	9.67284	0.604553
$257$	19.9765	1.24610	0.623049	−	0.782183i	$-0.285894\pi$
$257$	19.9765	1.24610	0.623049	+	0.782183i	$0.285894\pi$
$258$	−18.9638	−1.18064
$259$	−0.281789	−0.0175095
$260$	−0.798937	−0.0495480
$261$	1.09475	0.0677633
$262$	24.0935	1.48850
$263$	26.2345	1.61769	0.808845	−	0.588022i	$-0.200093\pi$
$263$	26.2345	1.61769	0.808845	+	0.588022i	$0.200093\pi$
$264$	12.0296	0.740370
$265$	8.16249	0.501418
$266$	−0.0140561	−0.000861833 0
$267$	−12.9144	−0.790350
$268$	−3.49899	−0.213735
$269$	−1.20388	−0.0734021	−0.0367011	−	0.999326i	$-0.511685\pi$
$269$	−1.20388	−0.0734021	−0.0367011	+	0.999326i	$0.511685\pi$
$270$	−2.95727	−0.179974
$271$	26.2188	1.59268	0.796340	−	0.604849i	$-0.206767\pi$
$271$	26.2188	1.59268	0.796340	+	0.604849i	$0.206767\pi$
$272$	−2.49230	−0.151118
$273$	−0.0358686	−0.00217087
$274$	0.616987	0.0372736
$275$	6.78728	0.409289
$276$	−3.80654	−0.229127
$277$	−5.26115	−0.316112	−0.158056	−	0.987430i	$-0.550523\pi$
$277$	−5.26115	−0.316112	−0.158056	+	0.987430i	$0.550523\pi$
$278$	8.43816	0.506087
$279$	−0.0390860	−0.00234001
$280$	−0.167565	−0.0100139
$281$	−7.49919	−0.447364	−0.223682	−	0.974662i	$-0.571808\pi$
$281$	−7.49919	−0.447364	−0.223682	+	0.974662i	$0.571808\pi$
$282$	0.367754	0.0218994
$283$	−9.16187	−0.544617	−0.272308	−	0.962210i	$-0.587787\pi$
$283$	−9.16187	−0.544617	−0.272308	+	0.962210i	$0.587787\pi$
$284$	−0.456499	−0.0270882
$285$	0.478820	0.0283628
$286$	7.61509	0.450290
$287$	0.170958	0.0100913
$288$	2.34065	0.137924
$289$	−16.7144	−0.983202
$290$	3.23748	0.190111
$291$	−19.5036	−1.14332
$292$	3.14568	0.184087
$293$	9.32109	0.544544	0.272272	−	0.962220i	$-0.412225\pi$
$293$	9.32109	0.544544	0.272272	+	0.962220i	$0.412225\pi$
$294$	−10.8881	−0.635007
$295$	−26.3438	−1.53380
$296$	−19.3072	−1.12221
$297$	4.89487	0.284029
$298$	−21.0707	−1.22059
$299$	9.05681	0.523769
$300$	0.582788	0.0336473
$301$	−0.437227	−0.0252013
$302$	18.7624	1.07965
$303$	11.1103	0.638267
$304$	−1.17481	−0.0673800
$305$	9.46250	0.541821
$306$	−0.831345	−0.0475248
$307$	21.8385	1.24639	0.623194	−	0.782067i	$-0.285835\pi$
$307$	21.8385	1.24639	0.623194	+	0.782067i	$0.285835\pi$
$308$	−0.0737923	−0.00420471
$309$	1.00000	0.0568880
$310$	−0.115588	−0.00656495
$311$	31.0320	1.75966	0.879831	−	0.475287i	$-0.157656\pi$
$311$	31.0320	1.75966	0.879831	+	0.475287i	$0.157656\pi$
$312$	−2.45759	−0.139134
$313$	18.5465	1.04831	0.524155	−	0.851623i	$-0.324381\pi$
$313$	18.5465	1.04831	0.524155	+	0.851623i	$0.324381\pi$
$314$	34.9898	1.97459
$315$	−0.0681824	−0.00384164
$316$	0.466663	0.0262519
$317$	31.9655	1.79536	0.897682	−	0.440644i	$-0.145250\pi$
$317$	31.9655	1.79536	0.897682	+	0.440644i	$0.145250\pi$
$318$	−6.68036	−0.374616
$319$	−5.35865	−0.300027
$320$	−10.8094	−0.604261
$321$	5.69522	0.317876
$322$	−0.505387	−0.0281641
$323$	0.134605	0.00748963
$324$	0.420296	0.0233498
$325$	−1.38661	−0.0769154
$326$	0.742793	0.0411395
$327$	14.8709	0.822363
$328$	11.7134	0.646765
$329$	0.00847887	0.000467455 0
$330$	14.4755	0.796848
$331$	7.25012	0.398502	0.199251	−	0.979948i	$-0.436149\pi$
$331$	7.25012	0.398502	0.199251	+	0.979948i	$0.436149\pi$
$332$	−5.17389	−0.283954
$333$	−7.85613	−0.430513
$334$	18.4869	1.01156
$335$	15.8250	0.864614
$336$	0.167289	0.00912638
$337$	−18.0727	−0.984484	−0.492242	−	0.870458i	$-0.663823\pi$
$337$	−18.0727	−0.984484	−0.492242	+	0.870458i	$0.663823\pi$
$338$	−1.55573	−0.0846206
$339$	18.8154	1.02191
$340$	−0.426933	−0.0231537
$341$	0.191320	0.0103606
$342$	−0.391876	−0.0211902
$343$	−0.502115	−0.0271116
$344$	−29.9573	−1.61519
$345$	17.2160	0.926879
$346$	8.95150	0.481235
$347$	35.4091	1.90086	0.950431	−	0.310936i	$-0.100643\pi$
$347$	35.4091	1.90086	0.950431	+	0.310936i	$0.100643\pi$
$348$	−0.460119	−0.0246650
$349$	−5.28216	−0.282748	−0.141374	−	0.989956i	$-0.545152\pi$
$349$	−5.28216	−0.282748	−0.141374	+	0.989956i	$0.545152\pi$
$350$	0.0773756	0.00413590
$351$	−1.00000	−0.0533761
$352$	−11.4572	−0.610669
$353$	−26.5517	−1.41321	−0.706603	−	0.707610i	$-0.749773\pi$
$353$	−26.5517	−1.41321	−0.706603	+	0.707610i	$0.749773\pi$
$354$	21.5603	1.14592
$355$	2.06463	0.109579
$356$	5.42788	0.287677
$357$	−0.0191673	−0.00101444
$358$	−9.85260	−0.520726
$359$	0.438112	0.0231227	0.0115613	−	0.999933i	$-0.496320\pi$
$359$	0.438112	0.0231227	0.0115613	+	0.999933i	$0.496320\pi$
$360$	−4.67162	−0.246216
$361$	−18.9366	−0.996661
$362$	−1.65772	−0.0871277
$363$	−12.9597	−0.680208
$364$	0.0150754	0.000790168 0
$365$	−14.2271	−0.744681
$366$	−7.74431	−0.404802
$367$	−3.56264	−0.185968	−0.0929842	−	0.995668i	$-0.529641\pi$
$367$	−3.56264	−0.185968	−0.0929842	+	0.995668i	$0.529641\pi$
$368$	−42.2404	−2.20194
$369$	4.76621	0.248119
$370$	−23.2327	−1.20781
$371$	−0.154021	−0.00799638
$372$	0.0164277	0.000851735 0
$373$	34.4069	1.78152	0.890761	−	0.454472i	$-0.150172\pi$
$373$	34.4069	1.78152	0.890761	+	0.454472i	$0.150172\pi$
$374$	4.06932	0.210420
$375$	−12.1403	−0.626920
$376$	0.580942	0.0299598
$377$	1.09475	0.0563825
$378$	0.0558019	0.00287014
$379$	23.6696	1.21583	0.607913	−	0.794004i	$-0.292007\pi$
$379$	23.6696	1.21583	0.607913	+	0.794004i	$0.292007\pi$
$380$	−0.201246	−0.0103237
$381$	−2.47435	−0.126765
$382$	−10.2504	−0.524454
$383$	32.0837	1.63940	0.819700	−	0.572793i	$-0.194140\pi$
$383$	32.0837	1.63940	0.819700	+	0.572793i	$0.194140\pi$
$384$	13.5279	0.690343
$385$	0.333744	0.0170091
$386$	6.89676	0.351036
$387$	−12.1897	−0.619636
$388$	8.19729	0.416154
$389$	−27.2417	−1.38121	−0.690604	−	0.723233i	$-0.742655\pi$
$389$	−27.2417	−1.38121	−0.690604	+	0.723233i	$0.742655\pi$
$390$	−2.95727	−0.149747
$391$	4.83974	0.244756
$392$	−17.2000	−0.868731
$393$	15.4870	0.781214
$394$	−22.0902	−1.11289
$395$	−2.11060	−0.106196
$396$	−2.05729	−0.103383
$397$	−3.20402	−0.160805	−0.0804026	−	0.996762i	$-0.525621\pi$
$397$	−3.20402	−0.160805	−0.0804026	+	0.996762i	$0.525621\pi$
$398$	−28.8201	−1.44462
$399$	−0.00903503	−0.000452317 0
$400$	6.46708	0.323354
$401$	5.76770	0.288025	0.144013	−	0.989576i	$-0.453999\pi$
$401$	5.76770	0.288025	0.144013	+	0.989576i	$0.453999\pi$
$402$	−12.9515	−0.645964
$403$	−0.0390860	−0.00194701
$404$	−4.66960	−0.232321
$405$	−1.90089	−0.0944560
$406$	−0.0610891	−0.00303180
$407$	38.4547	1.90613
$408$	−1.31328	−0.0650170
$409$	32.2722	1.59576	0.797879	−	0.602818i	$-0.205956\pi$
$409$	32.2722	1.59576	0.797879	+	0.602818i	$0.205956\pi$
$410$	14.0950	0.696102
$411$	0.396590	0.0195624
$412$	−0.420296	−0.0207065
$413$	0.497091	0.0244603
$414$	−14.0900	−0.692483
$415$	23.4002	1.14867
$416$	2.34065	0.114760
$417$	5.42392	0.265611
$418$	1.91818	0.0938213
$419$	30.3398	1.48220	0.741098	−	0.671397i	$-0.234306\pi$
$419$	30.3398	1.48220	0.741098	+	0.671397i	$0.234306\pi$
$420$	0.0286568	0.00139831
$421$	8.42042	0.410386	0.205193	−	0.978721i	$-0.434218\pi$
$421$	8.42042	0.410386	0.205193	+	0.978721i	$0.434218\pi$
$422$	−29.6437	−1.44303
$423$	0.236387	0.0114935
$424$	−10.5530	−0.512498
$425$	−0.740973	−0.0359424
$426$	−1.68974	−0.0818679
$427$	−0.178551	−0.00864071
$428$	−2.39368	−0.115703
$429$	4.89487	0.236326
$430$	−36.0482	−1.73840
$431$	−33.7404	−1.62522	−0.812610	−	0.582808i	$-0.801954\pi$
$431$	−33.7404	−1.62522	−0.812610	+	0.582808i	$0.801954\pi$
$432$	4.66394	0.224394
$433$	30.1503	1.44893	0.724466	−	0.689311i	$-0.242087\pi$
$433$	30.1503	1.44893	0.724466	+	0.689311i	$0.242087\pi$
$434$	0.00218107	0.000104695 0
$435$	2.08100	0.0997763
$436$	−6.25018	−0.299329
$437$	2.28134	0.109131
$438$	11.6438	0.556361
$439$	−26.8258	−1.28033	−0.640163	−	0.768239i	$-0.721133\pi$
$439$	−26.8258	−1.28033	−0.640163	+	0.768239i	$0.721133\pi$
$440$	22.8669	1.09014
$441$	−6.99871	−0.333272
$442$	−0.831345	−0.0395430
$443$	2.45757	0.116763	0.0583813	−	0.998294i	$-0.481406\pi$
$443$	2.45757	0.116763	0.0583813	+	0.998294i	$0.481406\pi$
$444$	3.30190	0.156701
$445$	−24.5489	−1.16373
$446$	−39.1809	−1.85527
$447$	−13.5439	−0.640606
$448$	0.203966	0.00963647
$449$	−17.3572	−0.819138	−0.409569	−	0.912279i	$-0.634321\pi$
$449$	−17.3572	−0.819138	−0.409569	+	0.912279i	$0.634321\pi$
$450$	2.15720	0.101691
$451$	−23.3300	−1.09857
$452$	−7.90803	−0.371963
$453$	12.0602	0.566636
$454$	−45.1695	−2.11991
$455$	−0.0681824	−0.00319644
$456$	−0.619048	−0.0289896
$457$	−10.0498	−0.470108	−0.235054	−	0.971982i	$-0.575527\pi$
$457$	−10.0498	−0.470108	−0.235054	+	0.971982i	$0.575527\pi$
$458$	−3.05540	−0.142770
$459$	−0.534376	−0.0249425
$460$	−7.23582	−0.337372
$461$	−8.90788	−0.414881	−0.207441	−	0.978248i	$-0.566513\pi$
$461$	−8.90788	−0.414881	−0.207441	+	0.978248i	$0.566513\pi$
$462$	−0.273143	−0.0127078
$463$	12.1778	0.565949	0.282975	−	0.959127i	$-0.408679\pi$
$463$	12.1778	0.565949	0.282975	+	0.959127i	$0.408679\pi$
$464$	−5.10585	−0.237033
$465$	−0.0742981	−0.00344549
$466$	−11.2236	−0.519925
$467$	−30.3265	−1.40334	−0.701671	−	0.712501i	$-0.747562\pi$
$467$	−30.3265	−1.40334	−0.701671	+	0.712501i	$0.747562\pi$
$468$	0.420296	0.0194282
$469$	−0.298608	−0.0137885
$470$	0.699060	0.0322452
$471$	22.4909	1.03633
$472$	34.0589	1.56769
$473$	59.6668	2.74348
$474$	1.72736	0.0793402
$475$	−0.349277	−0.0160259
$476$	0.00805596	0.000369244 0
$477$	−4.29403	−0.196610
$478$	20.8503	0.953670
$479$	−28.8604	−1.31867	−0.659333	−	0.751851i	$-0.729161\pi$
$479$	−28.8604	−1.31867	−0.659333	+	0.751851i	$0.729161\pi$
$480$	4.44932	0.203083
$481$	−7.85613	−0.358209
$482$	18.4550	0.840602
$483$	−0.324855	−0.0147814
$484$	5.44691	0.247587
$485$	−37.0742	−1.68345
$486$	1.55573	0.0705694
$487$	−29.7213	−1.34680	−0.673400	−	0.739278i	$-0.735167\pi$
$487$	−29.7213	−1.34680	−0.673400	+	0.739278i	$0.735167\pi$
$488$	−12.2337	−0.553794
$489$	0.477456	0.0215913
$490$	−20.6971	−0.935000
$491$	27.1608	1.22575	0.612875	−	0.790180i	$-0.290013\pi$
$491$	27.1608	1.22575	0.612875	+	0.790180i	$0.290013\pi$
$492$	−2.00322	−0.0903122
$493$	0.585008	0.0263474
$494$	−0.391876	−0.0176313
$495$	9.30461	0.418211
$496$	0.182295	0.00818527
$497$	−0.0389582	−0.00174752
$498$	−19.1512	−0.858186
$499$	−0.717096	−0.0321016	−0.0160508	−	0.999871i	$-0.505109\pi$
$499$	−0.717096	−0.0321016	−0.0160508	+	0.999871i	$0.505109\pi$
$500$	5.10250	0.228191
$501$	11.8831	0.530897
$502$	−2.02878	−0.0905488
$503$	−32.0236	−1.42786	−0.713931	−	0.700216i	$-0.753087\pi$
$503$	−32.0236	−1.42786	−0.713931	+	0.700216i	$0.753087\pi$
$504$	0.0881505	0.00392654
$505$	21.1194	0.939800
$506$	68.9684	3.06602
$507$	−1.00000	−0.0444116
$508$	1.03996	0.0461407
$509$	28.3129	1.25495	0.627473	−	0.778638i	$-0.284089\pi$
$509$	28.3129	1.25495	0.627473	+	0.778638i	$0.284089\pi$
$510$	−1.58030	−0.0699767
$511$	0.268457	0.0118758
$512$	12.0075	0.530661
$513$	−0.251892	−0.0111213
$514$	−31.0780	−1.37079
$515$	1.90089	0.0837633
$516$	5.12327	0.225539
$517$	−1.15708	−0.0508884
$518$	0.438387	0.0192616
$519$	5.75389	0.252568
$520$	−4.67162	−0.204864
$521$	−20.5538	−0.900480	−0.450240	−	0.892908i	$-0.648662\pi$
$521$	−20.5538	−0.900480	−0.450240	+	0.892908i	$0.648662\pi$
$522$	−1.70314	−0.0745442
$523$	14.8844	0.650851	0.325425	−	0.945568i	$-0.394492\pi$
$523$	14.8844	0.650851	0.325425	+	0.945568i	$0.394492\pi$
$524$	−6.50911	−0.284352
$525$	0.0497359	0.00217065
$526$	−40.8139	−1.77957
$527$	−0.0208866	−0.000909834 0
$528$	−22.8294	−0.993521
$529$	59.0258	2.56634
$530$	−12.6986	−0.551593
$531$	13.8587	0.601415
$532$	0.00379739	0.000164638 0
$533$	4.76621	0.206448
$534$	20.0914	0.869438
$535$	10.8260	0.468049
$536$	−20.4596	−0.883720
$537$	−6.33310	−0.273294
$538$	1.87292	0.0807473
$539$	34.2578	1.47559
$540$	0.798937	0.0343808
$541$	−1.01832	−0.0437808	−0.0218904	−	0.999760i	$-0.506968\pi$
$541$	−1.01832	−0.0437808	−0.0218904	+	0.999760i	$0.506968\pi$
$542$	−40.7894	−1.75206
$543$	−1.06556	−0.0457274
$544$	1.25079	0.0536271
$545$	28.2680	1.21087
$546$	0.0558019	0.00238810
$547$	−4.97328	−0.212642	−0.106321	−	0.994332i	$-0.533907\pi$
$547$	−4.97328	−0.212642	−0.106321	+	0.994332i	$0.533907\pi$
$548$	−0.166685	−0.00712045
$549$	−4.97793	−0.212453
$550$	−10.5592	−0.450245
$551$	0.275759	0.0117477
$552$	−22.2579	−0.947361
$553$	0.0398257	0.00169356
$554$	8.18493	0.347744
$555$	−14.9336	−0.633898
$556$	−2.27965	−0.0966788
$557$	38.8606	1.64658	0.823288	−	0.567624i	$-0.192137\pi$
$557$	38.8606	1.64658	0.823288	+	0.567624i	$0.192137\pi$
$558$	0.0608072	0.00257417
$559$	−12.1897	−0.515568
$560$	0.317999	0.0134379
$561$	2.61570	0.110435
$562$	11.6667	0.492131
$563$	18.8758	0.795520	0.397760	−	0.917489i	$-0.369788\pi$
$563$	18.8758	0.795520	0.397760	+	0.917489i	$0.369788\pi$
$564$	−0.0993524	−0.00418349
$565$	35.7660	1.50469
$566$	14.2534	0.599115
$567$	0.0358686	0.00150634
$568$	−2.66928	−0.112001
$569$	45.2348	1.89634	0.948170	−	0.317764i	$-0.102932\pi$
$569$	45.2348	1.89634	0.948170	+	0.317764i	$0.102932\pi$
$570$	−0.744914	−0.0312010
$571$	−43.7121	−1.82930	−0.914648	−	0.404251i	$-0.867532\pi$
$571$	−43.7121	−1.82930	−0.914648	+	0.404251i	$0.867532\pi$
$572$	−2.05729	−0.0860197
$573$	−6.58878	−0.275250
$574$	−0.265964	−0.0111011
$575$	−12.5583	−0.523717
$576$	5.68646	0.236936
$577$	21.8607	0.910074	0.455037	−	0.890473i	$-0.349626\pi$
$577$	21.8607	0.910074	0.455037	+	0.890473i	$0.349626\pi$
$578$	26.0032	1.08159
$579$	4.43314	0.184235
$580$	−0.874636	−0.0363173
$581$	−0.441547	−0.0183185
$582$	30.3424	1.25773
$583$	21.0187	0.870506
$584$	18.3937	0.761137
$585$	−1.90089	−0.0785922
$586$	−14.5011	−0.599035
$587$	40.3603	1.66585	0.832924	−	0.553388i	$-0.186665\pi$
$587$	40.3603	1.66585	0.832924	+	0.553388i	$0.186665\pi$
$588$	2.94153	0.121307
$589$	−0.00984545	−0.000405675 0
$590$	40.9838	1.68728
$591$	−14.1993	−0.584079
$592$	36.6405	1.50592
$593$	−25.0594	−1.02906	−0.514532	−	0.857471i	$-0.672034\pi$
$593$	−25.0594	−1.02906	−0.514532	+	0.857471i	$0.672034\pi$
$594$	−7.61509	−0.312451
$595$	−0.0364350	−0.00149369
$596$	5.69246	0.233172
$597$	−18.5251	−0.758183
$598$	−14.0900	−0.576181
$599$	25.6823	1.04935	0.524675	−	0.851303i	$-0.324187\pi$
$599$	25.6823	1.04935	0.524675	+	0.851303i	$0.324187\pi$
$600$	3.40773	0.139120
$601$	−18.3879	−0.750057	−0.375029	−	0.927013i	$-0.622367\pi$
$601$	−18.3879	−0.750057	−0.375029	+	0.927013i	$0.622367\pi$
$602$	0.680207	0.0277232
$603$	−8.32506	−0.339023
$604$	−5.06884	−0.206248
$605$	−24.6350	−1.00155
$606$	−17.2846	−0.702137
$607$	−3.58164	−0.145374	−0.0726872	−	0.997355i	$-0.523157\pi$
$607$	−3.58164	−0.145374	−0.0726872	+	0.997355i	$0.523157\pi$
$608$	0.589592	0.0239111
$609$	−0.0392672	−0.00159119
$610$	−14.7211	−0.596039
$611$	0.236387	0.00956318
$612$	0.224596	0.00907876
$613$	−42.2637	−1.70701	−0.853507	−	0.521081i	$-0.825529\pi$
$613$	−42.2637	−1.70701	−0.853507	+	0.521081i	$0.825529\pi$
$614$	−33.9748	−1.37111
$615$	9.06005	0.365337
$616$	−0.431485	−0.0173850
$617$	−24.0812	−0.969473	−0.484737	−	0.874660i	$-0.661085\pi$
$617$	−24.0812	−0.969473	−0.484737	+	0.874660i	$0.661085\pi$
$618$	−1.55573	−0.0625806
$619$	−30.3097	−1.21825	−0.609124	−	0.793075i	$-0.708479\pi$
$619$	−30.3097	−1.21825	−0.609124	+	0.793075i	$0.708479\pi$
$620$	0.0312272	0.00125412
$621$	−9.05681	−0.363437
$622$	−48.2774	−1.93575
$623$	0.463223	0.0185586
$624$	4.66394	0.186707
$625$	−16.1442	−0.645770
$626$	−28.8533	−1.15321
$627$	1.23298	0.0492404
$628$	−9.45283	−0.377209
$629$	−4.19812	−0.167390
$630$	0.106073	0.00422606
$631$	26.8025	1.06699	0.533496	−	0.845802i	$-0.320878\pi$
$631$	26.8025	1.06699	0.533496	+	0.845802i	$0.320878\pi$
$632$	2.72871	0.108542
$633$	−19.0545	−0.757350
$634$	−49.7298	−1.97502
$635$	−4.70346	−0.186651
$636$	1.80477	0.0715636
$637$	−6.99871	−0.277299
$638$	8.33662	0.330050
$639$	−1.08614	−0.0429669
$640$	25.7151	1.01648
$641$	24.3105	0.960207	0.480103	−	0.877212i	$-0.340599\pi$
$641$	24.3105	0.960207	0.480103	+	0.877212i	$0.340599\pi$
$642$	−8.86023	−0.349685
$643$	42.2245	1.66517	0.832585	−	0.553897i	$-0.186860\pi$
$643$	42.2245	1.66517	0.832585	+	0.553897i	$0.186860\pi$
$644$	0.136535	0.00538025
$645$	−23.1712	−0.912367
$646$	−0.209409	−0.00823910
$647$	−10.5044	−0.412969	−0.206484	−	0.978450i	$-0.566202\pi$
$647$	−10.5044	−0.412969	−0.206484	+	0.978450i	$0.566202\pi$
$648$	2.45759	0.0965434
$649$	−67.8363	−2.66281
$650$	2.15720	0.0846122
$651$	0.00140196	5.49471e−5 0
$652$	−0.200673	−0.00785896
$653$	4.46492	0.174726	0.0873628	−	0.996177i	$-0.472156\pi$
$653$	4.46492	0.174726	0.0873628	+	0.996177i	$0.472156\pi$
$654$	−23.1351	−0.904654
$655$	29.4390	1.15028
$656$	−22.2294	−0.867910
$657$	7.48444	0.291996
$658$	−0.0131908	−0.000514232 0
$659$	−3.42365	−0.133367	−0.0666833	−	0.997774i	$-0.521242\pi$
$659$	−3.42365	−0.133367	−0.0666833	+	0.997774i	$0.521242\pi$
$660$	−3.91069	−0.152223
$661$	21.8750	0.850837	0.425419	−	0.904997i	$-0.360127\pi$
$661$	21.8750	0.850837	0.425419	+	0.904997i	$0.360127\pi$
$662$	−11.2792	−0.438380
$663$	−0.534376	−0.0207534
$664$	−30.2532	−1.17405
$665$	−0.0171746	−0.000666003 0
$666$	12.2220	0.473593
$667$	9.91494	0.383908
$668$	−4.99442	−0.193240
$669$	−25.1849	−0.973705
$670$	−24.6195	−0.951133
$671$	24.3663	0.940650
$672$	−0.0839560	−0.00323867
$673$	6.84061	0.263686	0.131843	−	0.991271i	$-0.457910\pi$
$673$	6.84061	0.263686	0.131843	+	0.991271i	$0.457910\pi$
$674$	28.1163	1.08300
$675$	1.38661	0.0533707
$676$	0.420296	0.0161652
$677$	4.03421	0.155047	0.0775236	−	0.996991i	$-0.475299\pi$
$677$	4.03421	0.155047	0.0775236	+	0.996991i	$0.475299\pi$
$678$	−29.2717	−1.12417
$679$	0.699568	0.0268469
$680$	−2.49640	−0.0957326
$681$	−29.0343	−1.11260
$682$	−0.297643	−0.0113973
$683$	−30.7886	−1.17809	−0.589046	−	0.808099i	$-0.700496\pi$
$683$	−30.7886	−1.17809	−0.589046	+	0.808099i	$0.700496\pi$
$684$	0.105869	0.00404801
$685$	0.753875	0.0288041
$686$	0.781155	0.0298246
$687$	−1.96397	−0.0749300
$688$	56.8519	2.16746
$689$	−4.29403	−0.163590
$690$	−26.7835	−1.01963
$691$	39.0616	1.48597	0.742986	−	0.669307i	$-0.233409\pi$
$691$	39.0616	1.48597	0.742986	+	0.669307i	$0.233409\pi$
$692$	−2.41834	−0.0919314
$693$	−0.175572	−0.00666943
$694$	−55.0870	−2.09108
$695$	10.3103	0.391091
$696$	−2.69045	−0.101981
$697$	2.54695	0.0964726
$698$	8.21761	0.311041
$699$	−7.21438	−0.272873
$700$	−0.0209038	−0.000790090 0
$701$	8.50990	0.321415	0.160707	−	0.987002i	$-0.448622\pi$
$701$	8.50990	0.321415	0.160707	+	0.987002i	$0.448622\pi$
$702$	1.55573	0.0587172
$703$	−1.97890	−0.0746355
$704$	−27.8345	−1.04905
$705$	0.449345	0.0169233
$706$	41.3073	1.55462
$707$	−0.398509	−0.0149875
$708$	−5.82474	−0.218907
$709$	0.789559	0.0296525	0.0148262	−	0.999890i	$-0.495280\pi$
$709$	0.789559	0.0296525	0.0148262	+	0.999890i	$0.495280\pi$
$710$	−3.21200	−0.120544
$711$	1.11032	0.0416402
$712$	31.7384	1.18945
$713$	−0.353994	−0.0132572
$714$	0.0298192	0.00111596
$715$	9.30461	0.347973
$716$	2.66178	0.0994753
$717$	13.4023	0.500517
$718$	−0.681584	−0.0254365
$719$	−47.0102	−1.75318	−0.876591	−	0.481235i	$-0.840188\pi$
$719$	−47.0102	−1.75318	−0.876591	+	0.481235i	$0.840188\pi$
$720$	8.86565	0.330403
$721$	−0.0358686	−0.00133582
$722$	29.4602	1.09639
$723$	11.8626	0.441175
$724$	0.447849	0.0166442
$725$	−1.51799	−0.0563769
$726$	20.1618	0.748275
$727$	−38.8714	−1.44166	−0.720831	−	0.693111i	$-0.756240\pi$
$727$	−38.8714	−1.44166	−0.720831	+	0.693111i	$0.756240\pi$
$728$	0.0881505	0.00326707
$729$	1.00000	0.0370370
$730$	22.1335	0.819199
$731$	−6.51387	−0.240924
$732$	2.09220	0.0773300
$733$	16.1652	0.597075	0.298538	−	0.954398i	$-0.403501\pi$
$733$	16.1652	0.597075	0.298538	+	0.954398i	$0.403501\pi$
$734$	5.54251	0.204578
$735$	−13.3038	−0.490718
$736$	21.1988	0.781399
$737$	40.7500	1.50105
$738$	−7.41494	−0.272948
$739$	−43.6800	−1.60680	−0.803398	−	0.595443i	$-0.796977\pi$
$739$	−43.6800	−1.60680	−0.803398	+	0.595443i	$0.796977\pi$
$740$	6.27655	0.230731
$741$	−0.251892	−0.00925349
$742$	0.239615	0.00879656
$743$	−13.1409	−0.482092	−0.241046	−	0.970514i	$-0.577490\pi$
$743$	−13.1409	−0.482092	−0.241046	+	0.970514i	$0.577490\pi$
$744$	0.0960574	0.00352163
$745$	−25.7456	−0.943244
$746$	−53.5279	−1.95979
$747$	−12.3101	−0.450403
$748$	−1.09937	−0.0401969
$749$	−0.204280	−0.00746422
$750$	18.8870	0.689654
$751$	−23.7021	−0.864900	−0.432450	−	0.901658i	$-0.642351\pi$
$751$	−23.7021	−0.864900	−0.432450	+	0.901658i	$0.642351\pi$
$752$	−1.10249	−0.0402038
$753$	−1.30407	−0.0475229
$754$	−1.70314	−0.0620245
$755$	22.9250	0.834328
$756$	−0.0150754	−0.000548289 0
$757$	19.5982	0.712309	0.356155	−	0.934427i	$-0.384088\pi$
$757$	19.5982	0.712309	0.356155	+	0.934427i	$0.384088\pi$
$758$	−36.8235	−1.33749
$759$	44.3319	1.60914
$760$	−1.17674	−0.0426850
$761$	−34.3378	−1.24474	−0.622372	−	0.782722i	$-0.713831\pi$
$761$	−34.3378	−1.24474	−0.622372	+	0.782722i	$0.713831\pi$
$762$	3.84942	0.139450
$763$	−0.533399	−0.0193103
$764$	2.76924	0.100188
$765$	−1.01579	−0.0367260
$766$	−49.9136	−1.80345
$767$	13.8587	0.500407
$768$	−9.67284	−0.349039
$769$	21.9549	0.791715	0.395858	−	0.918312i	$-0.370447\pi$
$769$	21.9549	0.791715	0.395858	+	0.918312i	$0.370447\pi$
$770$	−0.519215	−0.0187112
$771$	−19.9765	−0.719435
$772$	−1.86323	−0.0670591
$773$	−37.6754	−1.35509	−0.677546	−	0.735481i	$-0.736956\pi$
$773$	−37.6754	−1.35509	−0.677546	+	0.735481i	$0.736956\pi$
$774$	18.9638	0.681641
$775$	0.0541971	0.00194682
$776$	47.9319	1.72066
$777$	0.281789	0.0101091
$778$	42.3807	1.51942
$779$	1.20057	0.0430150
$780$	0.798937	0.0286065
$781$	5.31649	0.190239
$782$	−7.52933	−0.269248
$783$	−1.09475	−0.0391232
$784$	32.6416	1.16577
$785$	42.7527	1.52591
$786$	−24.0935	−0.859388
$787$	28.6748	1.02215	0.511073	−	0.859537i	$-0.329248\pi$
$787$	28.6748	1.02215	0.511073	+	0.859537i	$0.329248\pi$
$788$	5.96789	0.212597
$789$	−26.2345	−0.933974
$790$	3.28352	0.116822
$791$	−0.674882	−0.0239960
$792$	−12.0296	−0.427453
$793$	−4.97793	−0.176771
$794$	4.98459	0.176897
$795$	−8.16249	−0.289494
$796$	7.78604	0.275969
$797$	8.48894	0.300694	0.150347	−	0.988633i	$-0.451961\pi$
$797$	8.48894	0.300694	0.150347	+	0.988633i	$0.451961\pi$
$798$	0.0140561	0.000497579 0
$799$	0.126319	0.00446886
$800$	−3.24558	−0.114748
$801$	12.9144	0.456309
$802$	−8.97299	−0.316847
$803$	−36.6353	−1.29283
$804$	3.49899	0.123400
$805$	−0.617515	−0.0217645
$806$	0.0608072	0.00214184
$807$	1.20388	0.0423787
$808$	−27.3045	−0.960568
$809$	26.8291	0.943262	0.471631	−	0.881796i	$-0.343665\pi$
$809$	26.8291	0.943262	0.471631	+	0.881796i	$0.343665\pi$
$810$	2.95727	0.103908
$811$	21.9442	0.770567	0.385283	−	0.922798i	$-0.374104\pi$
$811$	21.9442	0.770567	0.385283	+	0.922798i	$0.374104\pi$
$812$	0.0165038	0.000579171 0
$813$	−26.2188	−0.919534
$814$	−59.8251	−2.09687
$815$	0.907592	0.0317916
$816$	2.49230	0.0872479
$817$	−3.07048	−0.107423
$818$	−50.2068	−1.75544
$819$	0.0358686	0.00125335
$820$	−3.80791	−0.132978
$821$	14.0185	0.489248	0.244624	−	0.969618i	$-0.421335\pi$
$821$	14.0185	0.489248	0.244624	+	0.969618i	$0.421335\pi$
$822$	−0.616987	−0.0215199
$823$	36.5432	1.27381	0.636907	−	0.770941i	$-0.280213\pi$
$823$	36.5432	1.27381	0.636907	+	0.770941i	$0.280213\pi$
$824$	−2.45759	−0.0856143
$825$	−6.78728	−0.236303
$826$	−0.773340	−0.0269079
$827$	47.9632	1.66784	0.833921	−	0.551883i	$-0.186091\pi$
$827$	47.9632	1.66784	0.833921	+	0.551883i	$0.186091\pi$
$828$	3.80654	0.132286
$829$	−40.0084	−1.38955	−0.694775	−	0.719227i	$-0.744496\pi$
$829$	−40.0084	−1.38955	−0.694775	+	0.719227i	$0.744496\pi$
$830$	−36.4044	−1.26361
$831$	5.26115	0.182507
$832$	5.68646	0.197143
$833$	−3.73994	−0.129581
$834$	−8.43816	−0.292189
$835$	22.5885	0.781706
$836$	−0.518216	−0.0179229
$837$	0.0390860	0.00135101
$838$	−47.2005	−1.63051
$839$	−9.88436	−0.341246	−0.170623	−	0.985336i	$-0.554578\pi$
$839$	−9.88436	−0.341246	−0.170623	+	0.985336i	$0.554578\pi$
$840$	0.167565	0.00578152
$841$	−27.8015	−0.958673
$842$	−13.0999	−0.451453
$843$	7.49919	0.258286
$844$	8.00855	0.275666
$845$	−1.90089	−0.0653926
$846$	−0.367754	−0.0126436
$847$	0.464847	0.0159723
$848$	20.0271	0.687735
$849$	9.16187	0.314435
$850$	1.15275	0.0395391
$851$	−71.1514	−2.43904
$852$	0.456499	0.0156394
$853$	−8.22993	−0.281787	−0.140894	−	0.990025i	$-0.544998\pi$
$853$	−8.22993	−0.281787	−0.140894	+	0.990025i	$0.544998\pi$
$854$	0.277778	0.00950536
$855$	−0.478820	−0.0163753
$856$	−13.9965	−0.478392
$857$	−22.8180	−0.779447	−0.389724	−	0.920932i	$-0.627429\pi$
$857$	−22.8180	−0.779447	−0.389724	+	0.920932i	$0.627429\pi$
$858$	−7.61509	−0.259975
$859$	8.09768	0.276289	0.138145	−	0.990412i	$-0.455886\pi$
$859$	8.09768	0.276289	0.138145	+	0.990412i	$0.455886\pi$
$860$	9.73878	0.332090
$861$	−0.170958	−0.00582622
$862$	52.4910	1.78785
$863$	4.85749	0.165351	0.0826755	−	0.996577i	$-0.473654\pi$
$863$	4.85749	0.165351	0.0826755	+	0.996577i	$0.473654\pi$
$864$	−2.34065	−0.0796306
$865$	10.9375	0.371887
$866$	−46.9057	−1.59392
$867$	16.7144	0.567652
$868$	−0.000589238 0	−2.00000e−5 0
$869$	−5.43487	−0.184365
$870$	−3.23748	−0.109761
$871$	−8.32506	−0.282084
$872$	−36.5466	−1.23762
$873$	19.5036	0.660097
$874$	−3.54915	−0.120052
$875$	0.435454	0.0147210
$876$	−3.14568	−0.106283
$877$	26.9048	0.908510	0.454255	−	0.890872i	$-0.349906\pi$
$877$	26.9048	0.908510	0.454255	+	0.890872i	$0.349906\pi$
$878$	41.7337	1.40845
$879$	−9.32109	−0.314393
$880$	−43.3962	−1.46288
$881$	−18.5516	−0.625018	−0.312509	−	0.949915i	$-0.601169\pi$
$881$	−18.5516	−0.625018	−0.312509	+	0.949915i	$0.601169\pi$
$882$	10.8881	0.366622
$883$	−1.72428	−0.0580267	−0.0290133	−	0.999579i	$-0.509237\pi$
$883$	−1.72428	−0.0580267	−0.0290133	+	0.999579i	$0.509237\pi$
$884$	0.224596	0.00755399
$885$	26.3438	0.885537
$886$	−3.82331	−0.128447
$887$	48.2328	1.61950	0.809749	−	0.586777i	$-0.199603\pi$
$887$	48.2328	1.61950	0.809749	+	0.586777i	$0.199603\pi$
$888$	19.3072	0.647906
$889$	0.0887514	0.00297663
$890$	38.1915	1.28018
$891$	−4.89487	−0.163984
$892$	10.5851	0.354416
$893$	0.0595439	0.00199256
$894$	21.0707	0.704710
$895$	−12.0385	−0.402404
$896$	−0.485228	−0.0162103
$897$	−9.05681	−0.302398
$898$	27.0032	0.901107
$899$	−0.0427893	−0.00142710
$900$	−0.582788	−0.0194263
$901$	−2.29463	−0.0764452
$902$	36.2951	1.20850
$903$	0.437227	0.0145500
$904$	−46.2406	−1.53794
$905$	−2.02551	−0.0673301
$906$	−18.7624	−0.623337
$907$	34.3124	1.13932	0.569661	−	0.821879i	$-0.307074\pi$
$907$	34.3124	1.13932	0.569661	+	0.821879i	$0.307074\pi$
$908$	12.2030	0.404970
$909$	−11.1103	−0.368504
$910$	0.106073	0.00351630
$911$	−27.6516	−0.916140	−0.458070	−	0.888916i	$-0.651459\pi$
$911$	−27.6516	−0.916140	−0.458070	+	0.888916i	$0.651459\pi$
$912$	1.17481	0.0389019
$913$	60.2563	1.99419
$914$	15.6347	0.517151
$915$	−9.46250	−0.312820
$916$	0.825448	0.0272736
$917$	−0.555496	−0.0183441
$918$	0.831345	0.0274385
$919$	48.3144	1.59375	0.796873	−	0.604147i	$-0.206486\pi$
$919$	48.3144	1.59375	0.796873	+	0.604147i	$0.206486\pi$
$920$	−42.3099	−1.39492
$921$	−21.8385	−0.719603
$922$	13.8583	0.456397
$923$	−1.08614	−0.0357506
$924$	0.0737923	0.00242759
$925$	10.8934	0.358173
$926$	−18.9453	−0.622582
$927$	−1.00000	−0.0328443
$928$	2.56243	0.0841158
$929$	20.0230	0.656935	0.328467	−	0.944515i	$-0.393468\pi$
$929$	20.0230	0.656935	0.328467	+	0.944515i	$0.393468\pi$
$930$	0.115588	0.00379028
$931$	−1.76292	−0.0577774
$932$	3.03218	0.0993222
$933$	−31.0320	−1.01594
$934$	47.1798	1.54377
$935$	4.97216	0.162607
$936$	2.45759	0.0803289
$937$	−31.1058	−1.01618	−0.508090	−	0.861304i	$-0.669648\pi$
$937$	−31.1058	−1.01618	−0.508090	+	0.861304i	$0.669648\pi$
$938$	0.464554	0.0151682
$939$	−18.5465	−0.605242
$940$	−0.188858	−0.00615987
$941$	−6.22850	−0.203043	−0.101522	−	0.994833i	$-0.532371\pi$
$941$	−6.22850	−0.203043	−0.101522	+	0.994833i	$0.532371\pi$
$942$	−34.9898	−1.14003
$943$	43.1667	1.40570
$944$	−64.6360	−2.10372
$945$	0.0681824	0.00221797
$946$	−92.8254	−3.01802
$947$	−5.73933	−0.186503	−0.0932515	−	0.995643i	$-0.529726\pi$
$947$	−5.73933	−0.186503	−0.0932515	+	0.995643i	$0.529726\pi$
$948$	−0.466663	−0.0151565
$949$	7.48444	0.242955
$950$	0.543381	0.0176296
$951$	−31.9655	−1.03655
$952$	0.0471055	0.00152670
$953$	−16.8709	−0.546502	−0.273251	−	0.961943i	$-0.588099\pi$
$953$	−16.8709	−0.546502	−0.273251	+	0.961943i	$0.588099\pi$
$954$	6.68036	0.216285
$955$	−12.5246	−0.405285
$956$	−5.63292	−0.182182
$957$	5.35865	0.173221
$958$	44.8990	1.45062
$959$	−0.0142252	−0.000459354 0
$960$	10.8094	0.348870
$961$	−30.9985	−0.999951
$962$	12.2220	0.394053
$963$	−5.69522	−0.183526
$964$	−4.98580	−0.160582
$965$	8.42691	0.271272
$966$	0.505387	0.0162606
$967$	−1.69416	−0.0544806	−0.0272403	−	0.999629i	$-0.508672\pi$
$967$	−1.69416	−0.0544806	−0.0272403	+	0.999629i	$0.508672\pi$
$968$	31.8497	1.02369
$969$	−0.134605	−0.00432414
$970$	57.6775	1.85191
$971$	42.3831	1.36014	0.680069	−	0.733148i	$-0.261950\pi$
$971$	42.3831	1.36014	0.680069	+	0.733148i	$0.261950\pi$
$972$	−0.420296	−0.0134810
$973$	−0.194549	−0.00623694
$974$	46.2383	1.48157
$975$	1.38661	0.0444071
$976$	23.2168	0.743151
$977$	50.4319	1.61346	0.806729	−	0.590921i	$-0.201236\pi$
$977$	50.4319	1.61346	0.806729	+	0.590921i	$0.201236\pi$
$978$	−0.742793	−0.0237519
$979$	−63.2144	−2.02034
$980$	5.59153	0.178615
$981$	−14.8709	−0.474791
$982$	−42.2549	−1.34841
$983$	−30.4746	−0.971988	−0.485994	−	0.873962i	$-0.661542\pi$
$983$	−30.4746	−0.971988	−0.485994	+	0.873962i	$0.661542\pi$
$984$	−11.7134	−0.373410
$985$	−26.9912	−0.860012
$986$	−0.910115	−0.0289840
$987$	−0.00847887	−0.000269885 0
$988$	0.105869	0.00336815
$989$	−110.400	−3.51050
$990$	−14.4755	−0.460060
$991$	23.1748	0.736170	0.368085	−	0.929792i	$-0.380013\pi$
$991$	23.1748	0.736170	0.368085	+	0.929792i	$0.380013\pi$
$992$	−0.0914866	−0.00290470
$993$	−7.25012	−0.230075
$994$	0.0606085	0.00192238
$995$	−35.2142	−1.11637
$996$	5.17389	0.163941
$997$	36.6688	1.16131	0.580656	−	0.814149i	$-0.302796\pi$
$997$	36.6688	1.16131	0.580656	+	0.814149i	$0.302796\pi$
$998$	1.11561	0.0353139
$999$	7.85613	0.248557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.6	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.55573 q^{2} -1.00000 q^{3} +0.420296 q^{4} -1.90089 q^{5} +1.55573 q^{6} +0.0358686 q^{7} +2.45759 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.55573 q^{2} -1.00000 q^{3} +0.420296 q^{4} -1.90089 q^{5} +1.55573 q^{6} +0.0358686 q^{7} +2.45759 q^{8} +1.00000 q^{9} +2.95727 q^{10} -4.89487 q^{11} -0.420296 q^{12} +1.00000 q^{13} -0.0558019 q^{14} +1.90089 q^{15} -4.66394 q^{16} +0.534376 q^{17} -1.55573 q^{18} +0.251892 q^{19} -0.798937 q^{20} -0.0358686 q^{21} +7.61509 q^{22} +9.05681 q^{23} -2.45759 q^{24} -1.38661 q^{25} -1.55573 q^{26} -1.00000 q^{27} +0.0150754 q^{28} +1.09475 q^{29} -2.95727 q^{30} -0.0390860 q^{31} +2.34065 q^{32} +4.89487 q^{33} -0.831345 q^{34} -0.0681824 q^{35} +0.420296 q^{36} -7.85613 q^{37} -0.391876 q^{38} -1.00000 q^{39} -4.67162 q^{40} +4.76621 q^{41} +0.0558019 q^{42} -12.1897 q^{43} -2.05729 q^{44} -1.90089 q^{45} -14.0900 q^{46} +0.236387 q^{47} +4.66394 q^{48} -6.99871 q^{49} +2.15720 q^{50} -0.534376 q^{51} +0.420296 q^{52} -4.29403 q^{53} +1.55573 q^{54} +9.30461 q^{55} +0.0881505 q^{56} -0.251892 q^{57} -1.70314 q^{58} +13.8587 q^{59} +0.798937 q^{60} -4.97793 q^{61} +0.0608072 q^{62} +0.0358686 q^{63} +5.68646 q^{64} -1.90089 q^{65} -7.61509 q^{66} -8.32506 q^{67} +0.224596 q^{68} -9.05681 q^{69} +0.106073 q^{70} -1.08614 q^{71} +2.45759 q^{72} +7.48444 q^{73} +12.2220 q^{74} +1.38661 q^{75} +0.105869 q^{76} -0.175572 q^{77} +1.55573 q^{78} +1.11032 q^{79} +8.86565 q^{80} +1.00000 q^{81} -7.41494 q^{82} -12.3101 q^{83} -0.0150754 q^{84} -1.01579 q^{85} +18.9638 q^{86} -1.09475 q^{87} -12.0296 q^{88} +12.9144 q^{89} +2.95727 q^{90} +0.0358686 q^{91} +3.80654 q^{92} +0.0390860 q^{93} -0.367754 q^{94} -0.478820 q^{95} -2.34065 q^{96} +19.5036 q^{97} +10.8881 q^{98} -4.89487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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