LMFDB - Embedded newform 4017.2.a.j.1.8

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			1.8
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)

$f(q)$	$=$	$q-0.925244 q^{2} -1.00000 q^{3} -1.14392 q^{4} +3.08995 q^{5} +0.925244 q^{6} -0.0396192 q^{7} +2.90890 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.925244 q^{2} -1.00000 q^{3} -1.14392 q^{4} +3.08995 q^{5} +0.925244 q^{6} -0.0396192 q^{7} +2.90890 q^{8} +1.00000 q^{9} -2.85895 q^{10} +3.49434 q^{11} +1.14392 q^{12} +1.00000 q^{13} +0.0366574 q^{14} -3.08995 q^{15} -0.403588 q^{16} +4.97266 q^{17} -0.925244 q^{18} +5.15461 q^{19} -3.53467 q^{20} +0.0396192 q^{21} -3.23311 q^{22} +5.51853 q^{23} -2.90890 q^{24} +4.54778 q^{25} -0.925244 q^{26} -1.00000 q^{27} +0.0453214 q^{28} -6.50685 q^{29} +2.85895 q^{30} +6.23092 q^{31} -5.44437 q^{32} -3.49434 q^{33} -4.60092 q^{34} -0.122421 q^{35} -1.14392 q^{36} +10.4013 q^{37} -4.76927 q^{38} -1.00000 q^{39} +8.98834 q^{40} +8.28965 q^{41} -0.0366574 q^{42} +8.81740 q^{43} -3.99726 q^{44} +3.08995 q^{45} -5.10598 q^{46} -10.5346 q^{47} +0.403588 q^{48} -6.99843 q^{49} -4.20781 q^{50} -4.97266 q^{51} -1.14392 q^{52} -0.138518 q^{53} +0.925244 q^{54} +10.7973 q^{55} -0.115248 q^{56} -5.15461 q^{57} +6.02042 q^{58} +12.9656 q^{59} +3.53467 q^{60} +1.88482 q^{61} -5.76512 q^{62} -0.0396192 q^{63} +5.84455 q^{64} +3.08995 q^{65} +3.23311 q^{66} +5.01033 q^{67} -5.68834 q^{68} -5.51853 q^{69} +0.113269 q^{70} -14.7803 q^{71} +2.90890 q^{72} -7.21359 q^{73} -9.62371 q^{74} -4.54778 q^{75} -5.89649 q^{76} -0.138443 q^{77} +0.925244 q^{78} -16.9142 q^{79} -1.24707 q^{80} +1.00000 q^{81} -7.66995 q^{82} -11.0487 q^{83} -0.0453214 q^{84} +15.3653 q^{85} -8.15824 q^{86} +6.50685 q^{87} +10.1647 q^{88} +2.35669 q^{89} -2.85895 q^{90} -0.0396192 q^{91} -6.31278 q^{92} -6.23092 q^{93} +9.74704 q^{94} +15.9275 q^{95} +5.44437 q^{96} -14.7503 q^{97} +6.47525 q^{98} +3.49434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.925244	−0.654246	−0.327123	−	0.944982i	$-0.606079\pi$
$2$	−0.925244	−0.654246	−0.327123	+	0.944982i	$0.606079\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.14392	−0.571962
$5$	3.08995	1.38187	0.690934	−	0.722918i	$-0.257200\pi$
$5$	3.08995	1.38187	0.690934	+	0.722918i	$0.257200\pi$
$6$	0.925244	0.377729
$7$	−0.0396192	−0.0149746	−0.00748732	−	0.999972i	$-0.502383\pi$
$7$	−0.0396192	−0.0149746	−0.00748732	+	0.999972i	$0.502383\pi$
$8$	2.90890	1.02845
$9$	1.00000	0.333333
$10$	−2.85895	−0.904081
$11$	3.49434	1.05358	0.526791	−	0.849995i	$-0.323395\pi$
$11$	3.49434	1.05358	0.526791	+	0.849995i	$0.323395\pi$
$12$	1.14392	0.330223
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.0366574	0.00979710
$15$	−3.08995	−0.797821
$16$	−0.403588	−0.100897
$17$	4.97266	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$17$	4.97266	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$18$	−0.925244	−0.218082
$19$	5.15461	1.18255	0.591275	−	0.806470i	$-0.298625\pi$
$19$	5.15461	1.18255	0.591275	+	0.806470i	$0.298625\pi$
$20$	−3.53467	−0.790376
$21$	0.0396192	0.00864562
$22$	−3.23311	−0.689302
$23$	5.51853	1.15069	0.575346	−	0.817910i	$-0.304867\pi$
$23$	5.51853	1.15069	0.575346	+	0.817910i	$0.304867\pi$
$24$	−2.90890	−0.593776
$25$	4.54778	0.909556
$26$	−0.925244	−0.181455
$27$	−1.00000	−0.192450
$28$	0.0453214	0.00856493
$29$	−6.50685	−1.20829	−0.604146	−	0.796874i	$-0.706486\pi$
$29$	−6.50685	−1.20829	−0.604146	+	0.796874i	$0.706486\pi$
$30$	2.85895	0.521971
$31$	6.23092	1.11911	0.559553	−	0.828794i	$-0.310973\pi$
$31$	6.23092	1.11911	0.559553	+	0.828794i	$0.310973\pi$
$32$	−5.44437	−0.962438
$33$	−3.49434	−0.608286
$34$	−4.60092	−0.789051
$35$	−0.122421	−0.0206930
$36$	−1.14392	−0.190654
$37$	10.4013	1.70996	0.854980	−	0.518662i	$-0.173570\pi$
$37$	10.4013	1.70996	0.854980	+	0.518662i	$0.173570\pi$
$38$	−4.76927	−0.773678
$39$	−1.00000	−0.160128
$40$	8.98834	1.42118
$41$	8.28965	1.29463	0.647313	−	0.762224i	$-0.275893\pi$
$41$	8.28965	1.29463	0.647313	+	0.762224i	$0.275893\pi$
$42$	−0.0366574	−0.00565636
$43$	8.81740	1.34464	0.672321	−	0.740260i	$-0.265298\pi$
$43$	8.81740	1.34464	0.672321	+	0.740260i	$0.265298\pi$
$44$	−3.99726	−0.602609
$45$	3.08995	0.460622
$46$	−5.10598	−0.752836
$47$	−10.5346	−1.53662	−0.768312	−	0.640076i	$-0.778903\pi$
$47$	−10.5346	−1.53662	−0.768312	+	0.640076i	$0.778903\pi$
$48$	0.403588	0.0582529
$49$	−6.99843	−0.999776
$50$	−4.20781	−0.595074
$51$	−4.97266	−0.696311
$52$	−1.14392	−0.158634
$53$	−0.138518	−0.0190269	−0.00951344	−	0.999955i	$-0.503028\pi$
$53$	−0.138518	−0.0190269	−0.00951344	+	0.999955i	$0.503028\pi$
$54$	0.925244	0.125910
$55$	10.7973	1.45591
$56$	−0.115248	−0.0154007
$57$	−5.15461	−0.682745
$58$	6.02042	0.790520
$59$	12.9656	1.68798	0.843991	−	0.536358i	$-0.180200\pi$
$59$	12.9656	1.68798	0.843991	+	0.536358i	$0.180200\pi$
$60$	3.53467	0.456324
$61$	1.88482	0.241327	0.120663	−	0.992693i	$-0.461498\pi$
$61$	1.88482	0.241327	0.120663	+	0.992693i	$0.461498\pi$
$62$	−5.76512	−0.732171
$63$	−0.0396192	−0.00499155
$64$	5.84455	0.730569
$65$	3.08995	0.383261
$66$	3.23311	0.397968
$67$	5.01033	0.612110	0.306055	−	0.952014i	$-0.400991\pi$
$67$	5.01033	0.612110	0.306055	+	0.952014i	$0.400991\pi$
$68$	−5.68834	−0.689813
$69$	−5.51853	−0.664353
$70$	0.113269	0.0135383
$71$	−14.7803	−1.75410	−0.877050	−	0.480399i	$-0.840492\pi$
$71$	−14.7803	−1.75410	−0.877050	+	0.480399i	$0.840492\pi$
$72$	2.90890	0.342817
$73$	−7.21359	−0.844287	−0.422143	−	0.906529i	$-0.638722\pi$
$73$	−7.21359	−0.844287	−0.422143	+	0.906529i	$0.638722\pi$
$74$	−9.62371	−1.11873
$75$	−4.54778	−0.525133
$76$	−5.89649	−0.676374
$77$	−0.138443	−0.0157770
$78$	0.925244	0.104763
$79$	−16.9142	−1.90299	−0.951497	−	0.307658i	$-0.900455\pi$
$79$	−16.9142	−1.90299	−0.951497	+	0.307658i	$0.900455\pi$
$80$	−1.24707	−0.139426
$81$	1.00000	0.111111
$82$	−7.66995	−0.847004
$83$	−11.0487	−1.21276	−0.606379	−	0.795176i	$-0.707378\pi$
$83$	−11.0487	−1.21276	−0.606379	+	0.795176i	$0.707378\pi$
$84$	−0.0453214	−0.00494497
$85$	15.3653	1.66660
$86$	−8.15824	−0.879726
$87$	6.50685	0.697608
$88$	10.1647	1.08356
$89$	2.35669	0.249809	0.124905	−	0.992169i	$-0.460138\pi$
$89$	2.35669	0.249809	0.124905	+	0.992169i	$0.460138\pi$
$90$	−2.85895	−0.301360
$91$	−0.0396192	−0.00415322
$92$	−6.31278	−0.658153
$93$	−6.23092	−0.646116
$94$	9.74704	1.00533
$95$	15.9275	1.63413
$96$	5.44437	0.555664
$97$	−14.7503	−1.49767	−0.748835	−	0.662756i	$-0.769387\pi$
$97$	−14.7503	−1.49767	−0.748835	+	0.662756i	$0.769387\pi$
$98$	6.47525	0.654099
$99$	3.49434	0.351194
$100$	−5.20232	−0.520232
$101$	0.117677	0.0117093	0.00585465	−	0.999983i	$-0.498136\pi$
$101$	0.117677	0.0117093	0.00585465	+	0.999983i	$0.498136\pi$
$102$	4.60092	0.455559
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.90890	0.285241
$105$	0.122421	0.0119471
$106$	0.128163	0.0124483
$107$	7.92558	0.766195	0.383097	−	0.923708i	$-0.374857\pi$
$107$	7.92558	0.766195	0.383097	+	0.923708i	$0.374857\pi$
$108$	1.14392	0.110074
$109$	14.0736	1.34801	0.674004	−	0.738728i	$-0.264573\pi$
$109$	14.0736	1.34801	0.674004	+	0.738728i	$0.264573\pi$
$110$	−9.99015	−0.952523
$111$	−10.4013	−0.987245
$112$	0.0159898	0.00151090
$113$	−12.0428	−1.13289	−0.566444	−	0.824100i	$-0.691681\pi$
$113$	−12.0428	−1.13289	−0.566444	+	0.824100i	$0.691681\pi$
$114$	4.76927	0.446683
$115$	17.0520	1.59010
$116$	7.44335	0.691097
$117$	1.00000	0.0924500
$118$	−11.9964	−1.10436
$119$	−0.197013	−0.0180601
$120$	−8.98834	−0.820519
$121$	1.21038	0.110035
$122$	−1.74392	−0.157887
$123$	−8.28965	−0.747453
$124$	−7.12770	−0.640086
$125$	−1.39733	−0.124981
$126$	0.0366574	0.00326570
$127$	3.37378	0.299375	0.149687	−	0.988733i	$-0.452173\pi$
$127$	3.37378	0.299375	0.149687	+	0.988733i	$0.452173\pi$
$128$	5.48112	0.484467
$129$	−8.81740	−0.776329
$130$	−2.85895	−0.250747
$131$	6.99071	0.610781	0.305391	−	0.952227i	$-0.401213\pi$
$131$	6.99071	0.610781	0.305391	+	0.952227i	$0.401213\pi$
$132$	3.99726	0.347916
$133$	−0.204222	−0.0177083
$134$	−4.63578	−0.400470
$135$	−3.08995	−0.265940
$136$	14.4649	1.24036
$137$	−0.643737	−0.0549981	−0.0274991	−	0.999622i	$-0.508754\pi$
$137$	−0.643737	−0.0549981	−0.0274991	+	0.999622i	$0.508754\pi$
$138$	5.10598	0.434650
$139$	−3.97850	−0.337452	−0.168726	−	0.985663i	$-0.553965\pi$
$139$	−3.97850	−0.337452	−0.168726	+	0.985663i	$0.553965\pi$
$140$	0.140041	0.0118356
$141$	10.5346	0.887170
$142$	13.6754	1.14761
$143$	3.49434	0.292211
$144$	−0.403588	−0.0336323
$145$	−20.1058	−1.66970
$146$	6.67433	0.552371
$147$	6.99843	0.577221
$148$	−11.8983	−0.978032
$149$	−13.2124	−1.08240	−0.541202	−	0.840893i	$-0.682031\pi$
$149$	−13.2124	−1.08240	−0.541202	+	0.840893i	$0.682031\pi$
$150$	4.20781	0.343566
$151$	−5.11702	−0.416417	−0.208209	−	0.978084i	$-0.566763\pi$
$151$	−5.11702	−0.416417	−0.208209	+	0.978084i	$0.566763\pi$
$152$	14.9942	1.21619
$153$	4.97266	0.402016
$154$	0.128093	0.0103220
$155$	19.2532	1.54646
$156$	1.14392	0.0915873
$157$	−13.0212	−1.03921	−0.519604	−	0.854407i	$-0.673920\pi$
$157$	−13.0212	−1.03921	−0.519604	+	0.854407i	$0.673920\pi$
$158$	15.6497	1.24503
$159$	0.138518	0.0109852
$160$	−16.8228	−1.32996
$161$	−0.218640	−0.0172312
$162$	−0.925244	−0.0726940
$163$	−22.2970	−1.74644	−0.873218	−	0.487330i	$-0.837971\pi$
$163$	−22.2970	−1.74644	−0.873218	+	0.487330i	$0.837971\pi$
$164$	−9.48274	−0.740477
$165$	−10.7973	−0.840570
$166$	10.2228	0.793441
$167$	12.9274	1.00036	0.500178	−	0.865923i	$-0.333268\pi$
$167$	12.9274	1.00036	0.500178	+	0.865923i	$0.333268\pi$
$168$	0.115248	0.00889158
$169$	1.00000	0.0769231
$170$	−14.2166	−1.09036
$171$	5.15461	0.394183
$172$	−10.0864	−0.769084
$173$	−24.2997	−1.84747	−0.923737	−	0.383028i	$-0.874881\pi$
$173$	−24.2997	−1.84747	−0.923737	+	0.383028i	$0.874881\pi$
$174$	−6.02042	−0.456407
$175$	−0.180179	−0.0136203
$176$	−1.41027	−0.106303
$177$	−12.9656	−0.974557
$178$	−2.18052	−0.163437
$179$	−14.0277	−1.04848	−0.524240	−	0.851570i	$-0.675651\pi$
$179$	−14.0277	−1.04848	−0.524240	+	0.851570i	$0.675651\pi$
$180$	−3.53467	−0.263459
$181$	24.2888	1.80537	0.902686	−	0.430300i	$-0.141592\pi$
$181$	24.2888	1.80537	0.902686	+	0.430300i	$0.141592\pi$
$182$	0.0366574	0.00271723
$183$	−1.88482	−0.139330
$184$	16.0528	1.18343
$185$	32.1394	2.36294
$186$	5.76512	0.422719
$187$	17.3761	1.27067
$188$	12.0507	0.878891
$189$	0.0396192	0.00288187
$190$	−14.7368	−1.06912
$191$	18.9728	1.37283	0.686413	−	0.727212i	$-0.259184\pi$
$191$	18.9728	1.37283	0.686413	+	0.727212i	$0.259184\pi$
$192$	−5.84455	−0.421794
$193$	−2.82839	−0.203592	−0.101796	−	0.994805i	$-0.532459\pi$
$193$	−2.82839	−0.203592	−0.101796	+	0.994805i	$0.532459\pi$
$194$	13.6477	0.979845
$195$	−3.08995	−0.221276
$196$	8.00568	0.571834
$197$	4.88664	0.348159	0.174079	−	0.984732i	$-0.444305\pi$
$197$	4.88664	0.348159	0.174079	+	0.984732i	$0.444305\pi$
$198$	−3.23311	−0.229767
$199$	−18.9501	−1.34334	−0.671669	−	0.740851i	$-0.734422\pi$
$199$	−18.9501	−1.34334	−0.671669	+	0.740851i	$0.734422\pi$
$200$	13.2290	0.935433
$201$	−5.01033	−0.353402
$202$	−0.108880	−0.00766077
$203$	0.257796	0.0180937
$204$	5.68834	0.398264
$205$	25.6146	1.78900
$206$	0.925244	0.0644648
$207$	5.51853	0.383564
$208$	−0.403588	−0.0279838
$209$	18.0119	1.24591
$210$	−0.113269	−0.00781634
$211$	4.22079	0.290571	0.145286	−	0.989390i	$-0.453590\pi$
$211$	4.22079	0.290571	0.145286	+	0.989390i	$0.453590\pi$
$212$	0.158454	0.0108827
$213$	14.7803	1.01273
$214$	−7.33309	−0.501280
$215$	27.2453	1.85812
$216$	−2.90890	−0.197925
$217$	−0.246864	−0.0167582
$218$	−13.0215	−0.881929
$219$	7.21359	0.487449
$220$	−12.3513	−0.832725
$221$	4.97266	0.334497
$222$	9.62371	0.645901
$223$	−6.30900	−0.422482	−0.211241	−	0.977434i	$-0.567750\pi$
$223$	−6.30900	−0.422482	−0.211241	+	0.977434i	$0.567750\pi$
$224$	0.215702	0.0144122
$225$	4.54778	0.303185
$226$	11.1425	0.741188
$227$	7.02933	0.466553	0.233277	−	0.972410i	$-0.425055\pi$
$227$	7.02933	0.466553	0.233277	+	0.972410i	$0.425055\pi$
$228$	5.89649	0.390504
$229$	−2.10554	−0.139138	−0.0695691	−	0.997577i	$-0.522162\pi$
$229$	−2.10554	−0.139138	−0.0695691	+	0.997577i	$0.522162\pi$
$230$	−15.7772	−1.04032
$231$	0.138443	0.00910886
$232$	−18.9278	−1.24267
$233$	−2.25624	−0.147811	−0.0739054	−	0.997265i	$-0.523546\pi$
$233$	−2.25624	−0.147811	−0.0739054	+	0.997265i	$0.523546\pi$
$234$	−0.925244	−0.0604851
$235$	−32.5513	−2.12341
$236$	−14.8317	−0.965462
$237$	16.9142	1.09869
$238$	0.182285	0.0118158
$239$	−9.86302	−0.637986	−0.318993	−	0.947757i	$-0.603345\pi$
$239$	−9.86302	−0.637986	−0.318993	+	0.947757i	$0.603345\pi$
$240$	1.24707	0.0804978
$241$	−27.9348	−1.79944	−0.899720	−	0.436467i	$-0.856230\pi$
$241$	−27.9348	−1.79944	−0.899720	+	0.436467i	$0.856230\pi$
$242$	−1.11990	−0.0719897
$243$	−1.00000	−0.0641500
$244$	−2.15609	−0.138030
$245$	−21.6248	−1.38156
$246$	7.66995	0.489018
$247$	5.15461	0.327980
$248$	18.1251	1.15094
$249$	11.0487	0.700186
$250$	1.29287	0.0817683
$251$	−8.79781	−0.555313	−0.277656	−	0.960680i	$-0.589558\pi$
$251$	−8.79781	−0.555313	−0.277656	+	0.960680i	$0.589558\pi$
$252$	0.0453214	0.00285498
$253$	19.2836	1.21235
$254$	−3.12157	−0.195865
$255$	−15.3653	−0.962210
$256$	−16.7605	−1.04753
$257$	8.62454	0.537984	0.268992	−	0.963142i	$-0.413309\pi$
$257$	8.62454	0.537984	0.268992	+	0.963142i	$0.413309\pi$
$258$	8.15824	0.507910
$259$	−0.412090	−0.0256060
$260$	−3.53467	−0.219211
$261$	−6.50685	−0.402764
$262$	−6.46811	−0.399601
$263$	22.6581	1.39716	0.698581	−	0.715531i	$-0.253815\pi$
$263$	22.6581	1.39716	0.698581	+	0.715531i	$0.253815\pi$
$264$	−10.1647	−0.625591
$265$	−0.428013	−0.0262926
$266$	0.188955	0.0115856
$267$	−2.35669	−0.144227
$268$	−5.73144	−0.350104
$269$	−2.34779	−0.143147	−0.0715737	−	0.997435i	$-0.522802\pi$
$269$	−2.34779	−0.143147	−0.0715737	+	0.997435i	$0.522802\pi$
$270$	2.85895	0.173990
$271$	4.60693	0.279851	0.139926	−	0.990162i	$-0.455314\pi$
$271$	4.60693	0.279851	0.139926	+	0.990162i	$0.455314\pi$
$272$	−2.00691	−0.121687
$273$	0.0396192	0.00239786
$274$	0.595613	0.0359823
$275$	15.8915	0.958292
$276$	6.31278	0.379985
$277$	7.68137	0.461529	0.230764	−	0.973010i	$-0.425877\pi$
$277$	7.68137	0.461529	0.230764	+	0.973010i	$0.425877\pi$
$278$	3.68109	0.220777
$279$	6.23092	0.373035
$280$	−0.356111	−0.0212817
$281$	3.05880	0.182473	0.0912365	−	0.995829i	$-0.470918\pi$
$281$	3.05880	0.182473	0.0912365	+	0.995829i	$0.470918\pi$
$282$	−9.74704	−0.580428
$283$	20.9541	1.24559	0.622797	−	0.782383i	$-0.285996\pi$
$283$	20.9541	1.24559	0.622797	+	0.782383i	$0.285996\pi$
$284$	16.9076	1.00328
$285$	−15.9275	−0.943463
$286$	−3.23311	−0.191178
$287$	−0.328429	−0.0193866
$288$	−5.44437	−0.320813
$289$	7.72733	0.454549
$290$	18.6028	1.09239
$291$	14.7503	0.864681
$292$	8.25180	0.482900
$293$	15.9826	0.933714	0.466857	−	0.884333i	$-0.345386\pi$
$293$	15.9826	0.933714	0.466857	+	0.884333i	$0.345386\pi$
$294$	−6.47525	−0.377644
$295$	40.0631	2.33257
$296$	30.2562	1.75861
$297$	−3.49434	−0.202762
$298$	12.2247	0.708158
$299$	5.51853	0.319145
$300$	5.20232	0.300356
$301$	−0.349338	−0.0201355
$302$	4.73449	0.272439
$303$	−0.117677	−0.00676037
$304$	−2.08034	−0.119316
$305$	5.82400	0.333481
$306$	−4.60092	−0.263017
$307$	−0.519759	−0.0296642	−0.0148321	−	0.999890i	$-0.504721\pi$
$307$	−0.519759	−0.0296642	−0.0148321	+	0.999890i	$0.504721\pi$
$308$	0.158368	0.00902386
$309$	1.00000	0.0568880
$310$	−17.8139	−1.01176
$311$	8.79637	0.498796	0.249398	−	0.968401i	$-0.419767\pi$
$311$	8.79637	0.498796	0.249398	+	0.968401i	$0.419767\pi$
$312$	−2.90890	−0.164684
$313$	19.0398	1.07619	0.538097	−	0.842883i	$-0.319143\pi$
$313$	19.0398	1.07619	0.538097	+	0.842883i	$0.319143\pi$
$314$	12.0478	0.679897
$315$	−0.122421	−0.00689766
$316$	19.3485	1.08844
$317$	−22.5286	−1.26533	−0.632666	−	0.774425i	$-0.718039\pi$
$317$	−22.5286	−1.26533	−0.632666	+	0.774425i	$0.718039\pi$
$318$	−0.128163	−0.00718701
$319$	−22.7371	−1.27303
$320$	18.0594	1.00955
$321$	−7.92558	−0.442363
$322$	0.202295	0.0112735
$323$	25.6321	1.42621
$324$	−1.14392	−0.0635514
$325$	4.54778	0.252266
$326$	20.6302	1.14260
$327$	−14.0736	−0.778273
$328$	24.1137	1.33146
$329$	0.417371	0.0230104
$330$	9.99015	0.549940
$331$	12.3109	0.676670	0.338335	−	0.941026i	$-0.390136\pi$
$331$	12.3109	0.676670	0.338335	+	0.941026i	$0.390136\pi$
$332$	12.6389	0.693651
$333$	10.4013	0.569986
$334$	−11.9610	−0.654479
$335$	15.4817	0.845854
$336$	−0.0159898	−0.000872317 0
$337$	−25.2345	−1.37461	−0.687305	−	0.726369i	$-0.741206\pi$
$337$	−25.2345	−1.37461	−0.687305	+	0.726369i	$0.741206\pi$
$338$	−0.925244	−0.0503266
$339$	12.0428	0.654073
$340$	−17.5767	−0.953230
$341$	21.7729	1.17907
$342$	−4.76927	−0.257893
$343$	0.554606	0.0299459
$344$	25.6489	1.38290
$345$	−17.0520	−0.918047
$346$	22.4832	1.20870
$347$	20.5346	1.10235	0.551176	−	0.834389i	$-0.314179\pi$
$347$	20.5346	1.10235	0.551176	+	0.834389i	$0.314179\pi$
$348$	−7.44335	−0.399005
$349$	3.83016	0.205024	0.102512	−	0.994732i	$-0.467312\pi$
$349$	3.83016	0.205024	0.102512	+	0.994732i	$0.467312\pi$
$350$	0.166710	0.00891102
$351$	−1.00000	−0.0533761
$352$	−19.0245	−1.01401
$353$	3.43213	0.182674	0.0913369	−	0.995820i	$-0.470886\pi$
$353$	3.43213	0.182674	0.0913369	+	0.995820i	$0.470886\pi$
$354$	11.9964	0.637600
$355$	−45.6704	−2.42393
$356$	−2.69588	−0.142881
$357$	0.197013	0.0104270
$358$	12.9790	0.685964
$359$	−28.7278	−1.51619	−0.758097	−	0.652142i	$-0.773871\pi$
$359$	−28.7278	−1.51619	−0.758097	+	0.652142i	$0.773871\pi$
$360$	8.98834	0.473727
$361$	7.57003	0.398423
$362$	−22.4730	−1.18116
$363$	−1.21038	−0.0635285
$364$	0.0453214	0.00237548
$365$	−22.2896	−1.16669
$366$	1.74392	0.0911561
$367$	33.4088	1.74392	0.871962	−	0.489574i	$-0.162848\pi$
$367$	33.4088	1.74392	0.871962	+	0.489574i	$0.162848\pi$
$368$	−2.22721	−0.116101
$369$	8.28965	0.431542
$370$	−29.7368	−1.54594
$371$	0.00548796	0.000284921 0
$372$	7.12770	0.369554
$373$	22.8382	1.18252	0.591260	−	0.806481i	$-0.298631\pi$
$373$	22.8382	1.18252	0.591260	+	0.806481i	$0.298631\pi$
$374$	−16.0772	−0.831330
$375$	1.39733	0.0721578
$376$	−30.6439	−1.58034
$377$	−6.50685	−0.335120
$378$	−0.0366574	−0.00188545
$379$	24.4997	1.25847	0.629233	−	0.777216i	$-0.283369\pi$
$379$	24.4997	1.25847	0.629233	+	0.777216i	$0.283369\pi$
$380$	−18.2198	−0.934658
$381$	−3.37378	−0.172844
$382$	−17.5545	−0.898165
$383$	9.37695	0.479140	0.239570	−	0.970879i	$-0.422994\pi$
$383$	9.37695	0.479140	0.239570	+	0.970879i	$0.422994\pi$
$384$	−5.48112	−0.279707
$385$	−0.427781	−0.0218017
$386$	2.61695	0.133199
$387$	8.81740	0.448214
$388$	16.8733	0.856611
$389$	−1.69589	−0.0859848	−0.0429924	−	0.999075i	$-0.513689\pi$
$389$	−1.69589	−0.0859848	−0.0429924	+	0.999075i	$0.513689\pi$
$390$	2.85895	0.144769
$391$	27.4417	1.38779
$392$	−20.3577	−1.02822
$393$	−6.99071	−0.352635
$394$	−4.52134	−0.227782
$395$	−52.2640	−2.62968
$396$	−3.99726	−0.200870
$397$	3.85526	0.193490	0.0967449	−	0.995309i	$-0.469157\pi$
$397$	3.85526	0.193490	0.0967449	+	0.995309i	$0.469157\pi$
$398$	17.5335	0.878874
$399$	0.204222	0.0102239
$400$	−1.83543	−0.0917716
$401$	6.36716	0.317961	0.158980	−	0.987282i	$-0.449179\pi$
$401$	6.36716	0.317961	0.158980	+	0.987282i	$0.449179\pi$
$402$	4.63578	0.231212
$403$	6.23092	0.310384
$404$	−0.134614	−0.00669728
$405$	3.08995	0.153541
$406$	−0.238524	−0.0118378
$407$	36.3455	1.80158
$408$	−14.4649	−0.716121
$409$	−39.8948	−1.97267	−0.986335	−	0.164751i	$-0.947318\pi$
$409$	−39.8948	−1.97267	−0.986335	+	0.164751i	$0.947318\pi$
$410$	−23.6997	−1.17045
$411$	0.643737	0.0317532
$412$	1.14392	0.0563571
$413$	−0.513688	−0.0252769
$414$	−5.10598	−0.250945
$415$	−34.1400	−1.67587
$416$	−5.44437	−0.266932
$417$	3.97850	0.194828
$418$	−16.6654	−0.815133
$419$	−3.00337	−0.146724	−0.0733621	−	0.997305i	$-0.523373\pi$
$419$	−3.00337	−0.146724	−0.0733621	+	0.997305i	$0.523373\pi$
$420$	−0.140041	−0.00683328
$421$	−3.79669	−0.185039	−0.0925197	−	0.995711i	$-0.529492\pi$
$421$	−3.79669	−0.185039	−0.0925197	+	0.995711i	$0.529492\pi$
$422$	−3.90526	−0.190105
$423$	−10.5346	−0.512208
$424$	−0.402934	−0.0195682
$425$	22.6146	1.09697
$426$	−13.6754	−0.662575
$427$	−0.0746751	−0.00361378
$428$	−9.06626	−0.438234
$429$	−3.49434	−0.168708
$430$	−25.2086	−1.21566
$431$	−11.6764	−0.562431	−0.281215	−	0.959645i	$-0.590738\pi$
$431$	−11.6764	−0.562431	−0.281215	+	0.959645i	$0.590738\pi$
$432$	0.403588	0.0194176
$433$	−24.5667	−1.18060	−0.590300	−	0.807184i	$-0.700990\pi$
$433$	−24.5667	−1.18060	−0.590300	+	0.807184i	$0.700990\pi$
$434$	0.228409	0.0109640
$435$	20.1058	0.964001
$436$	−16.0992	−0.771010
$437$	28.4459	1.36075
$438$	−6.67433	−0.318912
$439$	28.0249	1.33755	0.668777	−	0.743463i	$-0.266818\pi$
$439$	28.0249	1.33755	0.668777	+	0.743463i	$0.266818\pi$
$440$	31.4083	1.49733
$441$	−6.99843	−0.333259
$442$	−4.60092	−0.218843
$443$	25.5952	1.21606	0.608032	−	0.793913i	$-0.291959\pi$
$443$	25.5952	1.21606	0.608032	+	0.793913i	$0.291959\pi$
$444$	11.8983	0.564667
$445$	7.28206	0.345203
$446$	5.83736	0.276407
$447$	13.2124	0.624926
$448$	−0.231556	−0.0109400
$449$	−10.5815	−0.499372	−0.249686	−	0.968327i	$-0.580327\pi$
$449$	−10.5815	−0.499372	−0.249686	+	0.968327i	$0.580327\pi$
$450$	−4.20781	−0.198358
$451$	28.9668	1.36399
$452$	13.7760	0.647969
$453$	5.11702	0.240419
$454$	−6.50384	−0.305241
$455$	−0.122421	−0.00573920
$456$	−14.9942	−0.702169
$457$	−36.0492	−1.68631	−0.843154	−	0.537671i	$-0.819304\pi$
$457$	−36.0492	−1.68631	−0.843154	+	0.537671i	$0.819304\pi$
$458$	1.94814	0.0910306
$459$	−4.97266	−0.232104
$460$	−19.5062	−0.909479
$461$	1.19909	0.0558473	0.0279236	−	0.999610i	$-0.491110\pi$
$461$	1.19909	0.0558473	0.0279236	+	0.999610i	$0.491110\pi$
$462$	−0.128093	−0.00595944
$463$	−0.451840	−0.0209988	−0.0104994	−	0.999945i	$-0.503342\pi$
$463$	−0.451840	−0.0209988	−0.0104994	+	0.999945i	$0.503342\pi$
$464$	2.62609	0.121913
$465$	−19.2532	−0.892847
$466$	2.08757	0.0967047
$467$	32.9385	1.52421	0.762107	−	0.647451i	$-0.224165\pi$
$467$	32.9385	1.52421	0.762107	+	0.647451i	$0.224165\pi$
$468$	−1.14392	−0.0528779
$469$	−0.198505	−0.00916612
$470$	30.1178	1.38923
$471$	13.0212	0.599987
$472$	37.7157	1.73600
$473$	30.8110	1.41669
$474$	−15.6497	−0.718816
$475$	23.4421	1.07560
$476$	0.225368	0.0103297
$477$	−0.138518	−0.00634230
$478$	9.12569	0.417400
$479$	5.49293	0.250978	0.125489	−	0.992095i	$-0.459950\pi$
$479$	5.49293	0.250978	0.125489	+	0.992095i	$0.459950\pi$
$480$	16.8228	0.767854
$481$	10.4013	0.474257
$482$	25.8465	1.17728
$483$	0.218640	0.00994844
$484$	−1.38458	−0.0629356
$485$	−45.5778	−2.06958
$486$	0.925244	0.0419699
$487$	−3.07810	−0.139482	−0.0697411	−	0.997565i	$-0.522217\pi$
$487$	−3.07810	−0.139482	−0.0697411	+	0.997565i	$0.522217\pi$
$488$	5.48275	0.248192
$489$	22.2970	1.00831
$490$	20.0082	0.903878
$491$	2.37188	0.107041	0.0535207	−	0.998567i	$-0.482956\pi$
$491$	2.37188	0.107041	0.0535207	+	0.998567i	$0.482956\pi$
$492$	9.48274	0.427515
$493$	−32.3563	−1.45726
$494$	−4.76927	−0.214580
$495$	10.7973	0.485303
$496$	−2.51473	−0.112915
$497$	0.585584	0.0262670
$498$	−10.2228	−0.458094
$499$	0.0437236	0.00195733	0.000978667	−	1.00000i	$-0.499688\pi$
$499$	0.0437236	0.00195733	0.000978667		1.00000i	$0.499688\pi$
$500$	1.59844	0.0714844
$501$	−12.9274	−0.577556
$502$	8.14012	0.363311
$503$	44.0778	1.96533	0.982666	−	0.185384i	$-0.0593529\pi$
$503$	44.0778	1.96533	0.982666	+	0.185384i	$0.0593529\pi$
$504$	−0.115248	−0.00513356
$505$	0.363616	0.0161807
$506$	−17.8420	−0.793174
$507$	−1.00000	−0.0444116
$508$	−3.85935	−0.171231
$509$	7.51536	0.333113	0.166556	−	0.986032i	$-0.446735\pi$
$509$	7.51536	0.333113	0.166556	+	0.986032i	$0.446735\pi$
$510$	14.2166	0.629522
$511$	0.285797	0.0126429
$512$	4.54528	0.200875
$513$	−5.15461	−0.227582
$514$	−7.97980	−0.351974
$515$	−3.08995	−0.136159
$516$	10.0864	0.444031
$517$	−36.8113	−1.61896
$518$	0.381284	0.0167526
$519$	24.2997	1.06664
$520$	8.98834	0.394165
$521$	−20.0023	−0.876317	−0.438158	−	0.898898i	$-0.644369\pi$
$521$	−20.0023	−0.876317	−0.438158	+	0.898898i	$0.644369\pi$
$522$	6.02042	0.263507
$523$	−24.5126	−1.07186	−0.535930	−	0.844262i	$-0.680039\pi$
$523$	−24.5126	−1.07186	−0.535930	+	0.844262i	$0.680039\pi$
$524$	−7.99684	−0.349344
$525$	0.180179	0.00786368
$526$	−20.9643	−0.914087
$527$	30.9842	1.34969
$528$	1.41027	0.0613742
$529$	7.45414	0.324093
$530$	0.396016	0.0172018
$531$	12.9656	0.562661
$532$	0.233614	0.0101285
$533$	8.28965	0.359065
$534$	2.18052	0.0943602
$535$	24.4896	1.05878
$536$	14.5745	0.629524
$537$	14.0277	0.605340
$538$	2.17228	0.0936537
$539$	−24.4549	−1.05335
$540$	3.53467	0.152108
$541$	−19.7988	−0.851215	−0.425607	−	0.904908i	$-0.639940\pi$
$541$	−19.7988	−0.851215	−0.425607	+	0.904908i	$0.639940\pi$
$542$	−4.26253	−0.183091
$543$	−24.2888	−1.04233
$544$	−27.0730	−1.16075
$545$	43.4868	1.86277
$546$	−0.0366574	−0.00156879
$547$	0.233397	0.00997933	0.00498966	−	0.999988i	$-0.498412\pi$
$547$	0.233397	0.00997933	0.00498966	+	0.999988i	$0.498412\pi$
$548$	0.736386	0.0314568
$549$	1.88482	0.0804422
$550$	−14.7035	−0.626959
$551$	−33.5403	−1.42886
$552$	−16.0528	−0.683253
$553$	0.670126	0.0284967
$554$	−7.10714	−0.301953
$555$	−32.1394	−1.36424
$556$	4.55111	0.193010
$557$	4.92999	0.208890	0.104445	−	0.994531i	$-0.466693\pi$
$557$	4.92999	0.208890	0.104445	+	0.994531i	$0.466693\pi$
$558$	−5.76512	−0.244057
$559$	8.81740	0.372936
$560$	0.0494078	0.00208786
$561$	−17.3761	−0.733621
$562$	−2.83014	−0.119382
$563$	−7.79291	−0.328432	−0.164216	−	0.986424i	$-0.552509\pi$
$563$	−7.79291	−0.328432	−0.164216	+	0.986424i	$0.552509\pi$
$564$	−12.0507	−0.507428
$565$	−37.2115	−1.56550
$566$	−19.3877	−0.814925
$567$	−0.0396192	−0.00166385
$568$	−42.9944	−1.80400
$569$	−24.2543	−1.01679	−0.508397	−	0.861123i	$-0.669762\pi$
$569$	−24.2543	−1.01679	−0.508397	+	0.861123i	$0.669762\pi$
$570$	14.7368	0.617257
$571$	−23.3775	−0.978317	−0.489159	−	0.872195i	$-0.662696\pi$
$571$	−23.3775	−0.978317	−0.489159	+	0.872195i	$0.662696\pi$
$572$	−3.99726	−0.167134
$573$	−18.9728	−0.792601
$574$	0.303877	0.0126836
$575$	25.0971	1.04662
$576$	5.84455	0.243523
$577$	−6.43457	−0.267875	−0.133937	−	0.990990i	$-0.542762\pi$
$577$	−6.43457	−0.267875	−0.133937	+	0.990990i	$0.542762\pi$
$578$	−7.14966	−0.297387
$579$	2.82839	0.117544
$580$	22.9996	0.955005
$581$	0.437742	0.0181606
$582$	−13.6477	−0.565714
$583$	−0.484028	−0.0200464
$584$	−20.9836	−0.868307
$585$	3.08995	0.127754
$586$	−14.7878	−0.610878
$587$	−4.46109	−0.184129	−0.0920644	−	0.995753i	$-0.529347\pi$
$587$	−4.46109	−0.184129	−0.0920644	+	0.995753i	$0.529347\pi$
$588$	−8.00568	−0.330148
$589$	32.1180	1.32340
$590$	−37.0682	−1.52607
$591$	−4.88664	−0.201010
$592$	−4.19783	−0.172530
$593$	−31.3446	−1.28717	−0.643584	−	0.765376i	$-0.722553\pi$
$593$	−31.3446	−1.28717	−0.643584	+	0.765376i	$0.722553\pi$
$594$	3.23311	0.132656
$595$	−0.608759	−0.0249567
$596$	15.1140	0.619094
$597$	18.9501	0.775577
$598$	−5.10598	−0.208799
$599$	25.5143	1.04249	0.521244	−	0.853408i	$-0.325468\pi$
$599$	25.5143	1.04249	0.521244	+	0.853408i	$0.325468\pi$
$600$	−13.2290	−0.540073
$601$	37.8392	1.54350	0.771748	−	0.635929i	$-0.219383\pi$
$601$	37.8392	1.54350	0.771748	+	0.635929i	$0.219383\pi$
$602$	0.323223	0.0131736
$603$	5.01033	0.204037
$604$	5.85349	0.238175
$605$	3.74001	0.152053
$606$	0.108880	0.00442295
$607$	−28.2513	−1.14668	−0.573342	−	0.819316i	$-0.694353\pi$
$607$	−28.2513	−1.14668	−0.573342	+	0.819316i	$0.694353\pi$
$608$	−28.0636	−1.13813
$609$	−0.257796	−0.0104464
$610$	−5.38862	−0.218179
$611$	−10.5346	−0.426183
$612$	−5.68834	−0.229938
$613$	18.9449	0.765176	0.382588	−	0.923919i	$-0.375033\pi$
$613$	18.9449	0.765176	0.382588	+	0.923919i	$0.375033\pi$
$614$	0.480904	0.0194077
$615$	−25.6146	−1.03288
$616$	−0.402715	−0.0162259
$617$	−12.1713	−0.489998	−0.244999	−	0.969523i	$-0.578788\pi$
$617$	−12.1713	−0.489998	−0.244999	+	0.969523i	$0.578788\pi$
$618$	−0.925244	−0.0372188
$619$	−16.5244	−0.664171	−0.332086	−	0.943249i	$-0.607752\pi$
$619$	−16.5244	−0.664171	−0.332086	+	0.943249i	$0.607752\pi$
$620$	−22.0242	−0.884514
$621$	−5.51853	−0.221451
$622$	−8.13878	−0.326335
$623$	−0.0933703	−0.00374080
$624$	0.403588	0.0161565
$625$	−27.0566	−1.08226
$626$	−17.6165	−0.704095
$627$	−18.0119	−0.719328
$628$	14.8953	0.594387
$629$	51.7220	2.06229
$630$	0.113269	0.00451276
$631$	35.0905	1.39693	0.698465	−	0.715645i	$-0.253867\pi$
$631$	35.0905	1.39693	0.698465	+	0.715645i	$0.253867\pi$
$632$	−49.2016	−1.95713
$633$	−4.22079	−0.167761
$634$	20.8444	0.827838
$635$	10.4248	0.413696
$636$	−0.158454	−0.00628311
$637$	−6.99843	−0.277288
$638$	21.0374	0.832878
$639$	−14.7803	−0.584700
$640$	16.9364	0.669469
$641$	−3.37099	−0.133146	−0.0665731	−	0.997782i	$-0.521207\pi$
$641$	−3.37099	−0.133146	−0.0665731	+	0.997782i	$0.521207\pi$
$642$	7.33309	0.289414
$643$	0.0969389	0.00382290	0.00191145	−	0.999998i	$-0.499392\pi$
$643$	0.0969389	0.00382290	0.00191145	+	0.999998i	$0.499392\pi$
$644$	0.250107	0.00985560
$645$	−27.2453	−1.07278
$646$	−23.7160	−0.933092
$647$	−26.9288	−1.05868	−0.529340	−	0.848410i	$-0.677560\pi$
$647$	−26.9288	−1.05868	−0.529340	+	0.848410i	$0.677560\pi$
$648$	2.90890	0.114272
$649$	45.3063	1.77843
$650$	−4.20781	−0.165044
$651$	0.246864	0.00967536
$652$	25.5061	0.998895
$653$	−16.9084	−0.661678	−0.330839	−	0.943687i	$-0.607332\pi$
$653$	−16.9084	−0.661678	−0.330839	+	0.943687i	$0.607332\pi$
$654$	13.0215	0.509182
$655$	21.6009	0.844018
$656$	−3.34561	−0.130624
$657$	−7.21359	−0.281429
$658$	−0.386170	−0.0150545
$659$	−8.44346	−0.328910	−0.164455	−	0.986385i	$-0.552587\pi$
$659$	−8.44346	−0.328910	−0.164455	+	0.986385i	$0.552587\pi$
$660$	12.3513	0.480774
$661$	−39.3098	−1.52897	−0.764487	−	0.644640i	$-0.777007\pi$
$661$	−39.3098	−1.52897	−0.764487	+	0.644640i	$0.777007\pi$
$662$	−11.3906	−0.442709
$663$	−4.97266	−0.193122
$664$	−32.1396	−1.24726
$665$	−0.631034	−0.0244705
$666$	−9.62371	−0.372911
$667$	−35.9082	−1.39037
$668$	−14.7880	−0.572166
$669$	6.30900	0.243920
$670$	−14.3243	−0.553397
$671$	6.58620	0.254257
$672$	−0.215702	−0.00832087
$673$	−46.0127	−1.77366	−0.886830	−	0.462097i	$-0.847097\pi$
$673$	−46.0127	−1.77366	−0.886830	+	0.462097i	$0.847097\pi$
$674$	23.3481	0.899333
$675$	−4.54778	−0.175044
$676$	−1.14392	−0.0439971
$677$	26.4026	1.01473	0.507367	−	0.861730i	$-0.330619\pi$
$677$	26.4026	1.01473	0.507367	+	0.861730i	$0.330619\pi$
$678$	−11.1425	−0.427925
$679$	0.584397	0.0224271
$680$	44.6959	1.71401
$681$	−7.02933	−0.269365
$682$	−20.1453	−0.771402
$683$	−35.7303	−1.36718	−0.683590	−	0.729866i	$-0.739582\pi$
$683$	−35.7303	−1.36718	−0.683590	+	0.729866i	$0.739582\pi$
$684$	−5.89649	−0.225458
$685$	−1.98911	−0.0760001
$686$	−0.513146	−0.0195920
$687$	2.10554	0.0803315
$688$	−3.55860	−0.135670
$689$	−0.138518	−0.00527711
$690$	15.7772	0.600628
$691$	−32.8307	−1.24894	−0.624469	−	0.781049i	$-0.714685\pi$
$691$	−32.8307	−1.24894	−0.624469	+	0.781049i	$0.714685\pi$
$692$	27.7970	1.05668
$693$	−0.138443	−0.00525900
$694$	−18.9995	−0.721210
$695$	−12.2934	−0.466314
$696$	18.9278	0.717455
$697$	41.2216	1.56138
$698$	−3.54383	−0.134136
$699$	2.25624	0.0853387
$700$	0.206112	0.00779029
$701$	−8.30140	−0.313540	−0.156770	−	0.987635i	$-0.550108\pi$
$701$	−8.30140	−0.313540	−0.156770	+	0.987635i	$0.550108\pi$
$702$	0.925244	0.0349211
$703$	53.6145	2.02211
$704$	20.4228	0.769714
$705$	32.5513	1.22595
$706$	−3.17555	−0.119514
$707$	−0.00466227	−0.000175343 0
$708$	14.8317	0.557410
$709$	2.15128	0.0807929	0.0403965	−	0.999184i	$-0.487138\pi$
$709$	2.15128	0.0807929	0.0403965	+	0.999184i	$0.487138\pi$
$710$	42.2562	1.58585
$711$	−16.9142	−0.634331
$712$	6.85538	0.256916
$713$	34.3855	1.28775
$714$	−0.182285	−0.00682183
$715$	10.7973	0.403797
$716$	16.0466	0.599691
$717$	9.86302	0.368341
$718$	26.5802	0.991964
$719$	24.6132	0.917919	0.458960	−	0.888457i	$-0.348222\pi$
$719$	24.6132	0.917919	0.458960	+	0.888457i	$0.348222\pi$
$720$	−1.24707	−0.0464754
$721$	0.0396192	0.00147550
$722$	−7.00413	−0.260667
$723$	27.9348	1.03891
$724$	−27.7845	−1.03260
$725$	−29.5917	−1.09901
$726$	1.11990	0.0415633
$727$	−3.34696	−0.124132	−0.0620659	−	0.998072i	$-0.519769\pi$
$727$	−3.34696	−0.124132	−0.0620659	+	0.998072i	$0.519769\pi$
$728$	−0.115248	−0.00427138
$729$	1.00000	0.0370370
$730$	20.6233	0.763304
$731$	43.8459	1.62170
$732$	2.15609	0.0796915
$733$	−37.8232	−1.39703	−0.698517	−	0.715594i	$-0.746156\pi$
$733$	−37.8232	−1.39703	−0.698517	+	0.715594i	$0.746156\pi$
$734$	−30.9112	−1.14095
$735$	21.6248	0.797642
$736$	−30.0449	−1.10747
$737$	17.5078	0.644907
$738$	−7.66995	−0.282335
$739$	−38.8721	−1.42993	−0.714966	−	0.699159i	$-0.753558\pi$
$739$	−38.8721	−1.42993	−0.714966	+	0.699159i	$0.753558\pi$
$740$	−36.7650	−1.35151
$741$	−5.15461	−0.189359
$742$	−0.00507770	−0.000186408 0
$743$	−34.6307	−1.27048	−0.635239	−	0.772316i	$-0.719098\pi$
$743$	−34.6307	−1.27048	−0.635239	+	0.772316i	$0.719098\pi$
$744$	−18.1251	−0.664498
$745$	−40.8257	−1.49574
$746$	−21.1309	−0.773659
$747$	−11.0487	−0.404252
$748$	−19.8770	−0.726775
$749$	−0.314005	−0.0114735
$750$	−1.29287	−0.0472089
$751$	−3.59727	−0.131266	−0.0656332	−	0.997844i	$-0.520907\pi$
$751$	−3.59727	−0.131266	−0.0656332	+	0.997844i	$0.520907\pi$
$752$	4.25162	0.155041
$753$	8.79781	0.320610
$754$	6.02042	0.219251
$755$	−15.8113	−0.575434
$756$	−0.0453214	−0.00164832
$757$	−23.0015	−0.836005	−0.418002	−	0.908446i	$-0.637270\pi$
$757$	−23.0015	−0.836005	−0.418002	+	0.908446i	$0.637270\pi$
$758$	−22.6682	−0.823347
$759$	−19.2836	−0.699950
$760$	46.3314	1.68062
$761$	−27.6866	−1.00364	−0.501819	−	0.864973i	$-0.667336\pi$
$761$	−27.6866	−1.00364	−0.501819	+	0.864973i	$0.667336\pi$
$762$	3.12157	0.113083
$763$	−0.557585	−0.0201859
$764$	−21.7035	−0.785204
$765$	15.3653	0.555532
$766$	−8.67596	−0.313475
$767$	12.9656	0.468162
$768$	16.7605	0.604791
$769$	28.4884	1.02732	0.513659	−	0.857994i	$-0.328290\pi$
$769$	28.4884	1.02732	0.513659	+	0.857994i	$0.328290\pi$
$770$	0.395802	0.0142637
$771$	−8.62454	−0.310605
$772$	3.23546	0.116447
$773$	15.0656	0.541872	0.270936	−	0.962597i	$-0.412667\pi$
$773$	15.0656	0.541872	0.270936	+	0.962597i	$0.412667\pi$
$774$	−8.15824	−0.293242
$775$	28.3369	1.01789
$776$	−42.9072	−1.54028
$777$	0.412090	0.0147836
$778$	1.56911	0.0562552
$779$	42.7300	1.53096
$780$	3.53467	0.126561
$781$	−51.6474	−1.84809
$782$	−25.3903	−0.907955
$783$	6.50685	0.232536
$784$	2.82448	0.100874
$785$	−40.2349	−1.43605
$786$	6.46811	0.230710
$787$	22.1315	0.788902	0.394451	−	0.918917i	$-0.370935\pi$
$787$	22.1315	0.788902	0.394451	+	0.918917i	$0.370935\pi$
$788$	−5.58995	−0.199134
$789$	−22.6581	−0.806651
$790$	48.3569	1.72046
$791$	0.477125	0.0169646
$792$	10.1647	0.361185
$793$	1.88482	0.0669320
$794$	−3.56705	−0.126590
$795$	0.428013	0.0151801
$796$	21.6775	0.768339
$797$	8.43733	0.298866	0.149433	−	0.988772i	$-0.452255\pi$
$797$	8.43733	0.298866	0.149433	+	0.988772i	$0.452255\pi$
$798$	−0.188955	−0.00668892
$799$	−52.3848	−1.85324
$800$	−24.7598	−0.875392
$801$	2.35669	0.0832697
$802$	−5.89117	−0.208024
$803$	−25.2067	−0.889525
$804$	5.73144	0.202132
$805$	−0.675585	−0.0238112
$806$	−5.76512	−0.203068
$807$	2.34779	0.0826462
$808$	0.342310	0.0120424
$809$	6.14722	0.216125	0.108062	−	0.994144i	$-0.465535\pi$
$809$	6.14722	0.216125	0.108062	+	0.994144i	$0.465535\pi$
$810$	−2.85895	−0.100453
$811$	23.7060	0.832431	0.416215	−	0.909266i	$-0.363356\pi$
$811$	23.7060	0.832431	0.416215	+	0.909266i	$0.363356\pi$
$812$	−0.294899	−0.0103489
$813$	−4.60693	−0.161572
$814$	−33.6285	−1.17868
$815$	−68.8966	−2.41334
$816$	2.00691	0.0702558
$817$	45.4503	1.59010
$818$	36.9124	1.29061
$819$	−0.0396192	−0.00138441
$820$	−29.3012	−1.02324
$821$	19.4745	0.679663	0.339832	−	0.940486i	$-0.389630\pi$
$821$	19.4745	0.679663	0.339832	+	0.940486i	$0.389630\pi$
$822$	−0.595613	−0.0207744
$823$	39.5484	1.37857	0.689285	−	0.724490i	$-0.257925\pi$
$823$	39.5484	1.37857	0.689285	+	0.724490i	$0.257925\pi$
$824$	−2.90890	−0.101336
$825$	−15.8915	−0.553270
$826$	0.475286	0.0165373
$827$	−18.5588	−0.645352	−0.322676	−	0.946509i	$-0.604582\pi$
$827$	−18.5588	−0.645352	−0.322676	+	0.946509i	$0.604582\pi$
$828$	−6.31278	−0.219384
$829$	−48.2351	−1.67527	−0.837637	−	0.546227i	$-0.816064\pi$
$829$	−48.2351	−1.67527	−0.837637	+	0.546227i	$0.816064\pi$
$830$	31.5879	1.09643
$831$	−7.68137	−0.266464
$832$	5.84455	0.202623
$833$	−34.8008	−1.20578
$834$	−3.68109	−0.127466
$835$	39.9451	1.38236
$836$	−20.6043	−0.712615
$837$	−6.23092	−0.215372
$838$	2.77885	0.0959937
$839$	26.9694	0.931087	0.465544	−	0.885025i	$-0.345859\pi$
$839$	26.9694	0.931087	0.465544	+	0.885025i	$0.345859\pi$
$840$	0.356111	0.0122870
$841$	13.3391	0.459969
$842$	3.51287	0.121061
$843$	−3.05880	−0.105351
$844$	−4.82827	−0.166196
$845$	3.08995	0.106297
$846$	9.74704	0.335110
$847$	−0.0479543	−0.00164773
$848$	0.0559042	0.00191976
$849$	−20.9541	−0.719144
$850$	−20.9240	−0.717687
$851$	57.3997	1.96764
$852$	−16.9076	−0.579243
$853$	23.2990	0.797742	0.398871	−	0.917007i	$-0.369402\pi$
$853$	23.2990	0.797742	0.398871	+	0.917007i	$0.369402\pi$
$854$	0.0690926	0.00236430
$855$	15.9275	0.544709
$856$	23.0547	0.787993
$857$	−17.0309	−0.581764	−0.290882	−	0.956759i	$-0.593949\pi$
$857$	−17.0309	−0.581764	−0.290882	+	0.956759i	$0.593949\pi$
$858$	3.23311	0.110377
$859$	−41.3719	−1.41159	−0.705795	−	0.708416i	$-0.749410\pi$
$859$	−41.3719	−1.41159	−0.705795	+	0.708416i	$0.749410\pi$
$860$	−31.1666	−1.06277
$861$	0.328429	0.0111928
$862$	10.8035	0.367968
$863$	40.2530	1.37023	0.685114	−	0.728436i	$-0.259752\pi$
$863$	40.2530	1.37023	0.685114	+	0.728436i	$0.259752\pi$
$864$	5.44437	0.185221
$865$	−75.0849	−2.55296
$866$	22.7302	0.772403
$867$	−7.72733	−0.262434
$868$	0.282394	0.00958507
$869$	−59.1038	−2.00496
$870$	−18.6028	−0.630694
$871$	5.01033	0.169769
$872$	40.9387	1.38636
$873$	−14.7503	−0.499224
$874$	−26.3194	−0.890266
$875$	0.0553610	0.00187154
$876$	−8.25180	−0.278803
$877$	14.0124	0.473166	0.236583	−	0.971611i	$-0.423973\pi$
$877$	14.0124	0.473166	0.236583	+	0.971611i	$0.423973\pi$
$878$	−25.9298	−0.875089
$879$	−15.9826	−0.539080
$880$	−4.35767	−0.146897
$881$	−13.3109	−0.448456	−0.224228	−	0.974537i	$-0.571986\pi$
$881$	−13.3109	−0.448456	−0.224228	+	0.974537i	$0.571986\pi$
$882$	6.47525	0.218033
$883$	54.7584	1.84277	0.921384	−	0.388653i	$-0.127060\pi$
$883$	54.7584	1.84277	0.921384	+	0.388653i	$0.127060\pi$
$884$	−5.68834	−0.191320
$885$	−40.0631	−1.34671
$886$	−23.6818	−0.795604
$887$	−19.7016	−0.661514	−0.330757	−	0.943716i	$-0.607304\pi$
$887$	−19.7016	−0.661514	−0.330757	+	0.943716i	$0.607304\pi$
$888$	−30.2562	−1.01533
$889$	−0.133667	−0.00448303
$890$	−6.73768	−0.225848
$891$	3.49434	0.117065
$892$	7.21702	0.241644
$893$	−54.3016	−1.81713
$894$	−12.2247	−0.408855
$895$	−43.3449	−1.44886
$896$	−0.217157	−0.00725472
$897$	−5.51853	−0.184258
$898$	9.79046	0.326712
$899$	−40.5437	−1.35221
$900$	−5.20232	−0.173411
$901$	−0.688802	−0.0229473
$902$	−26.8014	−0.892388
$903$	0.349338	0.0116253
$904$	−35.0312	−1.16512
$905$	75.0511	2.49478
$906$	−4.73449	−0.157293
$907$	−46.7872	−1.55354	−0.776771	−	0.629783i	$-0.783144\pi$
$907$	−46.7872	−1.55354	−0.776771	+	0.629783i	$0.783144\pi$
$908$	−8.04103	−0.266851
$909$	0.117677	0.00390310
$910$	0.113269	0.00375485
$911$	−39.0032	−1.29223	−0.646117	−	0.763239i	$-0.723608\pi$
$911$	−39.0032	−1.29223	−0.646117	+	0.763239i	$0.723608\pi$
$912$	2.08034	0.0688870
$913$	−38.6080	−1.27774
$914$	33.3543	1.10326
$915$	−5.82400	−0.192536
$916$	2.40858	0.0795818
$917$	−0.276966	−0.00914623
$918$	4.60092	0.151853
$919$	3.26717	0.107774	0.0538869	−	0.998547i	$-0.482839\pi$
$919$	3.26717	0.107774	0.0538869	+	0.998547i	$0.482839\pi$
$920$	49.6024	1.63534
$921$	0.519759	0.0171266
$922$	−1.10945	−0.0365379
$923$	−14.7803	−0.486500
$924$	−0.158368	−0.00520993
$925$	47.3027	1.55530
$926$	0.418062	0.0137384
$927$	−1.00000	−0.0328443
$928$	35.4257	1.16291
$929$	−34.3270	−1.12623	−0.563117	−	0.826377i	$-0.690398\pi$
$929$	−34.3270	−1.12623	−0.563117	+	0.826377i	$0.690398\pi$
$930$	17.8139	0.584141
$931$	−36.0742	−1.18228
$932$	2.58096	0.0845422
$933$	−8.79637	−0.287980
$934$	−30.4762	−0.997211
$935$	53.6914	1.75590
$936$	2.90890	0.0950802
$937$	−48.6897	−1.59062	−0.795312	−	0.606200i	$-0.792693\pi$
$937$	−48.6897	−1.59062	−0.795312	+	0.606200i	$0.792693\pi$
$938$	0.183666	0.00599690
$939$	−19.0398	−0.621341
$940$	37.2362	1.21451
$941$	40.9092	1.33360	0.666801	−	0.745236i	$-0.267663\pi$
$941$	40.9092	1.33360	0.666801	+	0.745236i	$0.267663\pi$
$942$	−12.0478	−0.392539
$943$	45.7467	1.48972
$944$	−5.23278	−0.170312
$945$	0.122421	0.00398236
$946$	−28.5076	−0.926863
$947$	15.7819	0.512842	0.256421	−	0.966565i	$-0.417457\pi$
$947$	15.7819	0.512842	0.256421	+	0.966565i	$0.417457\pi$
$948$	−19.3485	−0.628412
$949$	−7.21359	−0.234163
$950$	−21.6896	−0.703704
$951$	22.5286	0.730539
$952$	−0.573089	−0.0185739
$953$	8.51027	0.275675	0.137837	−	0.990455i	$-0.455985\pi$
$953$	8.51027	0.275675	0.137837	+	0.990455i	$0.455985\pi$
$954$	0.128163	0.00414942
$955$	58.6250	1.89706
$956$	11.2825	0.364904
$957$	22.7371	0.734987
$958$	−5.08230	−0.164202
$959$	0.0255043	0.000823577 0
$960$	−18.0594	−0.582863
$961$	7.82436	0.252399
$962$	−9.62371	−0.310281
$963$	7.92558	0.255398
$964$	31.9553	1.02921
$965$	−8.73957	−0.281337
$966$	−0.202295	−0.00650873
$967$	−28.5713	−0.918793	−0.459396	−	0.888231i	$-0.651934\pi$
$967$	−28.5713	−0.918793	−0.459396	+	0.888231i	$0.651934\pi$
$968$	3.52087	0.113165
$969$	−25.6321	−0.823423
$970$	42.1706	1.35402
$971$	51.1769	1.64235	0.821173	−	0.570679i	$-0.193320\pi$
$971$	51.1769	1.64235	0.821173	+	0.570679i	$0.193320\pi$
$972$	1.14392	0.0366914
$973$	0.157625	0.00505323
$974$	2.84800	0.0912557
$975$	−4.54778	−0.145646
$976$	−0.760692	−0.0243491
$977$	22.2794	0.712780	0.356390	−	0.934337i	$-0.384007\pi$
$977$	22.2794	0.712780	0.356390	+	0.934337i	$0.384007\pi$
$978$	−20.6302	−0.659680
$979$	8.23508	0.263194
$980$	24.7371	0.790198
$981$	14.0736	0.449336
$982$	−2.19457	−0.0700314
$983$	6.64162	0.211835	0.105917	−	0.994375i	$-0.466222\pi$
$983$	6.64162	0.211835	0.105917	+	0.994375i	$0.466222\pi$
$984$	−24.1137	−0.768718
$985$	15.0995	0.481109
$986$	29.9375	0.953404
$987$	−0.417371	−0.0132851
$988$	−5.89649	−0.187592
$989$	48.6591	1.54727
$990$	−9.99015	−0.317508
$991$	36.9847	1.17486	0.587429	−	0.809276i	$-0.300140\pi$
$991$	36.9847	1.17486	0.587429	+	0.809276i	$0.300140\pi$
$992$	−33.9235	−1.07707
$993$	−12.3109	−0.390676
$994$	−0.541808	−0.0171851
$995$	−58.5549	−1.85631
$996$	−12.6389	−0.400480
$997$	48.2436	1.52789	0.763945	−	0.645281i	$-0.223260\pi$
$997$	48.2436	1.52789	0.763945	+	0.645281i	$0.223260\pi$
$998$	−0.0404549	−0.00128058
$999$	−10.4013	−0.329082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.8	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-0.925244 q^{2} -1.00000 q^{3} -1.14392 q^{4} +3.08995 q^{5} +0.925244 q^{6} -0.0396192 q^{7} +2.90890 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.925244 q^{2} -1.00000 q^{3} -1.14392 q^{4} +3.08995 q^{5} +0.925244 q^{6} -0.0396192 q^{7} +2.90890 q^{8} +1.00000 q^{9} -2.85895 q^{10} +3.49434 q^{11} +1.14392 q^{12} +1.00000 q^{13} +0.0366574 q^{14} -3.08995 q^{15} -0.403588 q^{16} +4.97266 q^{17} -0.925244 q^{18} +5.15461 q^{19} -3.53467 q^{20} +0.0396192 q^{21} -3.23311 q^{22} +5.51853 q^{23} -2.90890 q^{24} +4.54778 q^{25} -0.925244 q^{26} -1.00000 q^{27} +0.0453214 q^{28} -6.50685 q^{29} +2.85895 q^{30} +6.23092 q^{31} -5.44437 q^{32} -3.49434 q^{33} -4.60092 q^{34} -0.122421 q^{35} -1.14392 q^{36} +10.4013 q^{37} -4.76927 q^{38} -1.00000 q^{39} +8.98834 q^{40} +8.28965 q^{41} -0.0366574 q^{42} +8.81740 q^{43} -3.99726 q^{44} +3.08995 q^{45} -5.10598 q^{46} -10.5346 q^{47} +0.403588 q^{48} -6.99843 q^{49} -4.20781 q^{50} -4.97266 q^{51} -1.14392 q^{52} -0.138518 q^{53} +0.925244 q^{54} +10.7973 q^{55} -0.115248 q^{56} -5.15461 q^{57} +6.02042 q^{58} +12.9656 q^{59} +3.53467 q^{60} +1.88482 q^{61} -5.76512 q^{62} -0.0396192 q^{63} +5.84455 q^{64} +3.08995 q^{65} +3.23311 q^{66} +5.01033 q^{67} -5.68834 q^{68} -5.51853 q^{69} +0.113269 q^{70} -14.7803 q^{71} +2.90890 q^{72} -7.21359 q^{73} -9.62371 q^{74} -4.54778 q^{75} -5.89649 q^{76} -0.138443 q^{77} +0.925244 q^{78} -16.9142 q^{79} -1.24707 q^{80} +1.00000 q^{81} -7.66995 q^{82} -11.0487 q^{83} -0.0453214 q^{84} +15.3653 q^{85} -8.15824 q^{86} +6.50685 q^{87} +10.1647 q^{88} +2.35669 q^{89} -2.85895 q^{90} -0.0396192 q^{91} -6.31278 q^{92} -6.23092 q^{93} +9.74704 q^{94} +15.9275 q^{95} +5.44437 q^{96} -14.7503 q^{97} +6.47525 q^{98} +3.49434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 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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