LMFDB - Embedded newform 4017.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.38645 q^{2} -1.00000 q^{3} +3.69513 q^{4} +2.94139 q^{5} +2.38645 q^{6} -4.88857 q^{7} -4.04533 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38645 q^{2} -1.00000 q^{3} +3.69513 q^{4} +2.94139 q^{5} +2.38645 q^{6} -4.88857 q^{7} -4.04533 q^{8} +1.00000 q^{9} -7.01947 q^{10} +6.02637 q^{11} -3.69513 q^{12} -1.00000 q^{13} +11.6663 q^{14} -2.94139 q^{15} +2.26372 q^{16} +1.40834 q^{17} -2.38645 q^{18} +1.58234 q^{19} +10.8688 q^{20} +4.88857 q^{21} -14.3816 q^{22} -7.54660 q^{23} +4.04533 q^{24} +3.65177 q^{25} +2.38645 q^{26} -1.00000 q^{27} -18.0639 q^{28} +6.10846 q^{29} +7.01947 q^{30} -8.93715 q^{31} +2.68843 q^{32} -6.02637 q^{33} -3.36094 q^{34} -14.3792 q^{35} +3.69513 q^{36} +3.39436 q^{37} -3.77616 q^{38} +1.00000 q^{39} -11.8989 q^{40} -0.822765 q^{41} -11.6663 q^{42} -1.92940 q^{43} +22.2682 q^{44} +2.94139 q^{45} +18.0096 q^{46} -13.0199 q^{47} -2.26372 q^{48} +16.8981 q^{49} -8.71475 q^{50} -1.40834 q^{51} -3.69513 q^{52} -0.0799155 q^{53} +2.38645 q^{54} +17.7259 q^{55} +19.7759 q^{56} -1.58234 q^{57} -14.5775 q^{58} +9.78401 q^{59} -10.8688 q^{60} +4.27813 q^{61} +21.3280 q^{62} -4.88857 q^{63} -10.9432 q^{64} -2.94139 q^{65} +14.3816 q^{66} -1.39016 q^{67} +5.20401 q^{68} +7.54660 q^{69} +34.3152 q^{70} -1.53807 q^{71} -4.04533 q^{72} -12.7364 q^{73} -8.10047 q^{74} -3.65177 q^{75} +5.84693 q^{76} -29.4603 q^{77} -2.38645 q^{78} -15.8320 q^{79} +6.65847 q^{80} +1.00000 q^{81} +1.96349 q^{82} +8.27246 q^{83} +18.0639 q^{84} +4.14248 q^{85} +4.60442 q^{86} -6.10846 q^{87} -24.3787 q^{88} -15.5927 q^{89} -7.01947 q^{90} +4.88857 q^{91} -27.8857 q^{92} +8.93715 q^{93} +31.0713 q^{94} +4.65426 q^{95} -2.68843 q^{96} +10.7622 q^{97} -40.3265 q^{98} +6.02637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.38645	−1.68747	−0.843736	−	0.536758i	$-0.819649\pi$
$2$	−2.38645	−1.68747	−0.843736	+	0.536758i	$0.819649\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.69513	1.84756
$5$	2.94139	1.31543	0.657714	−	0.753267i	$-0.271523\pi$
$5$	2.94139	1.31543	0.657714	+	0.753267i	$0.271523\pi$
$6$	2.38645	0.974263
$7$	−4.88857	−1.84771	−0.923853	−	0.382747i	$-0.874978\pi$
$7$	−4.88857	−1.84771	−0.923853	+	0.382747i	$0.874978\pi$
$8$	−4.04533	−1.43024
$9$	1.00000	0.333333
$10$	−7.01947	−2.21975
$11$	6.02637	1.81702	0.908509	−	0.417865i	$-0.137221\pi$
$11$	6.02637	1.81702	0.908509	+	0.417865i	$0.137221\pi$
$12$	−3.69513	−1.06669
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	11.6663	3.11795
$15$	−2.94139	−0.759463
$16$	2.26372	0.565929
$17$	1.40834	0.341573	0.170787	−	0.985308i	$-0.445369\pi$
$17$	1.40834	0.341573	0.170787	+	0.985308i	$0.445369\pi$
$18$	−2.38645	−0.562491
$19$	1.58234	0.363013	0.181506	−	0.983390i	$-0.441903\pi$
$19$	1.58234	0.363013	0.181506	+	0.983390i	$0.441903\pi$
$20$	10.8688	2.43034
$21$	4.88857	1.06677
$22$	−14.3816	−3.06617
$23$	−7.54660	−1.57357	−0.786787	−	0.617224i	$-0.788257\pi$
$23$	−7.54660	−1.57357	−0.786787	+	0.617224i	$0.788257\pi$
$24$	4.04533	0.825750
$25$	3.65177	0.730353
$26$	2.38645	0.468021
$27$	−1.00000	−0.192450
$28$	−18.0639	−3.41376
$29$	6.10846	1.13431	0.567156	−	0.823610i	$-0.308044\pi$
$29$	6.10846	1.13431	0.567156	+	0.823610i	$0.308044\pi$
$30$	7.01947	1.28157
$31$	−8.93715	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$31$	−8.93715	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$32$	2.68843	0.475251
$33$	−6.02637	−1.04906
$34$	−3.36094	−0.576396
$35$	−14.3792	−2.43053
$36$	3.69513	0.615855
$37$	3.39436	0.558030	0.279015	−	0.960287i	$-0.409992\pi$
$37$	3.39436	0.558030	0.279015	+	0.960287i	$0.409992\pi$
$38$	−3.77616	−0.612574
$39$	1.00000	0.160128
$40$	−11.8989	−1.88138
$41$	−0.822765	−0.128494	−0.0642472	−	0.997934i	$-0.520465\pi$
$41$	−0.822765	−0.128494	−0.0642472	+	0.997934i	$0.520465\pi$
$42$	−11.6663	−1.80015
$43$	−1.92940	−0.294231	−0.147116	−	0.989119i	$-0.546999\pi$
$43$	−1.92940	−0.294231	−0.147116	+	0.989119i	$0.546999\pi$
$44$	22.2682	3.35706
$45$	2.94139	0.438476
$46$	18.0096	2.65536
$47$	−13.0199	−1.89915	−0.949575	−	0.313540i	$-0.898485\pi$
$47$	−13.0199	−1.89915	−0.949575	+	0.313540i	$0.898485\pi$
$48$	−2.26372	−0.326740
$49$	16.8981	2.41402
$50$	−8.71475	−1.23245
$51$	−1.40834	−0.197207
$52$	−3.69513	−0.512422
$53$	−0.0799155	−0.0109772	−0.00548862	−	0.999985i	$-0.501747\pi$
$53$	−0.0799155	−0.0109772	−0.00548862	+	0.999985i	$0.501747\pi$
$54$	2.38645	0.324754
$55$	17.7259	2.39016
$56$	19.7759	2.64267
$57$	−1.58234	−0.209585
$58$	−14.5775	−1.91412
$59$	9.78401	1.27377	0.636885	−	0.770959i	$-0.280223\pi$
$59$	9.78401	1.27377	0.636885	+	0.770959i	$0.280223\pi$
$60$	−10.8688	−1.40316
$61$	4.27813	0.547758	0.273879	−	0.961764i	$-0.411693\pi$
$61$	4.27813	0.547758	0.273879	+	0.961764i	$0.411693\pi$
$62$	21.3280	2.70866
$63$	−4.88857	−0.615902
$64$	−10.9432	−1.36790
$65$	−2.94139	−0.364834
$66$	14.3816	1.77025
$67$	−1.39016	−0.169835	−0.0849177	−	0.996388i	$-0.527063\pi$
$67$	−1.39016	−0.169835	−0.0849177	+	0.996388i	$0.527063\pi$
$68$	5.20401	0.631079
$69$	7.54660	0.908504
$70$	34.3152	4.10145
$71$	−1.53807	−0.182535	−0.0912677	−	0.995826i	$-0.529092\pi$
$71$	−1.53807	−0.182535	−0.0912677	+	0.995826i	$0.529092\pi$
$72$	−4.04533	−0.476747
$73$	−12.7364	−1.49069	−0.745344	−	0.666680i	$-0.767715\pi$
$73$	−12.7364	−1.49069	−0.745344	+	0.666680i	$0.767715\pi$
$74$	−8.10047	−0.941661
$75$	−3.65177	−0.421670
$76$	5.84693	0.670689
$77$	−29.4603	−3.35732
$78$	−2.38645	−0.270212
$79$	−15.8320	−1.78124	−0.890619	−	0.454750i	$-0.849729\pi$
$79$	−15.8320	−1.78124	−0.890619	+	0.454750i	$0.849729\pi$
$80$	6.65847	0.744440
$81$	1.00000	0.111111
$82$	1.96349	0.216831
$83$	8.27246	0.908021	0.454010	−	0.890996i	$-0.349993\pi$
$83$	8.27246	0.908021	0.454010	+	0.890996i	$0.349993\pi$
$84$	18.0639	1.97093
$85$	4.14248	0.449315
$86$	4.60442	0.496507
$87$	−6.10846	−0.654895
$88$	−24.3787	−2.59878
$89$	−15.5927	−1.65283	−0.826413	−	0.563064i	$-0.809622\pi$
$89$	−15.5927	−1.65283	−0.826413	+	0.563064i	$0.809622\pi$
$90$	−7.01947	−0.739917
$91$	4.88857	0.512462
$92$	−27.8857	−2.90728
$93$	8.93715	0.926740
$94$	31.0713	3.20476
$95$	4.65426	0.477517
$96$	−2.68843	−0.274386
$97$	10.7622	1.09274	0.546370	−	0.837544i	$-0.316009\pi$
$97$	10.7622	1.09274	0.546370	+	0.837544i	$0.316009\pi$
$98$	−40.3265	−4.07359
$99$	6.02637	0.605673
$100$	13.4937	1.34937
$101$	−10.6894	−1.06363	−0.531816	−	0.846860i	$-0.678490\pi$
$101$	−10.6894	−1.06363	−0.531816	+	0.846860i	$0.678490\pi$
$102$	3.36094	0.332782
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	4.04533	0.396678
$105$	14.3792	1.40327
$106$	0.190714	0.0185238
$107$	−9.13282	−0.882903	−0.441451	−	0.897285i	$-0.645536\pi$
$107$	−9.13282	−0.882903	−0.441451	+	0.897285i	$0.645536\pi$
$108$	−3.69513	−0.355564
$109$	−5.11237	−0.489677	−0.244838	−	0.969564i	$-0.578735\pi$
$109$	−5.11237	−0.489677	−0.244838	+	0.969564i	$0.578735\pi$
$110$	−42.3019	−4.03333
$111$	−3.39436	−0.322179
$112$	−11.0663	−1.04567
$113$	1.61210	0.151654	0.0758269	−	0.997121i	$-0.475840\pi$
$113$	1.61210	0.151654	0.0758269	+	0.997121i	$0.475840\pi$
$114$	3.77616	0.353670
$115$	−22.1975	−2.06993
$116$	22.5715	2.09571
$117$	−1.00000	−0.0924500
$118$	−23.3490	−2.14945
$119$	−6.88478	−0.631127
$120$	11.8989	1.08622
$121$	25.3171	2.30156
$122$	−10.2095	−0.924327
$123$	0.822765	0.0741862
$124$	−33.0239	−2.96564
$125$	−3.96568	−0.354701
$126$	11.6663	1.03932
$127$	5.15705	0.457614	0.228807	−	0.973472i	$-0.426517\pi$
$127$	5.15705	0.457614	0.228807	+	0.973472i	$0.426517\pi$
$128$	20.7386	1.83305
$129$	1.92940	0.169874
$130$	7.01947	0.615648
$131$	11.0863	0.968612	0.484306	−	0.874899i	$-0.339072\pi$
$131$	11.0863	0.968612	0.484306	+	0.874899i	$0.339072\pi$
$132$	−22.2682	−1.93820
$133$	−7.73536	−0.670741
$134$	3.31755	0.286593
$135$	−2.94139	−0.253154
$136$	−5.69722	−0.488532
$137$	−1.66240	−0.142028	−0.0710141	−	0.997475i	$-0.522624\pi$
$137$	−1.66240	−0.142028	−0.0710141	+	0.997475i	$0.522624\pi$
$138$	−18.0096	−1.53308
$139$	−0.703823	−0.0596975	−0.0298487	−	0.999554i	$-0.509503\pi$
$139$	−0.703823	−0.0596975	−0.0298487	+	0.999554i	$0.509503\pi$
$140$	−53.1329	−4.49055
$141$	13.0199	1.09647
$142$	3.67052	0.308024
$143$	−6.02637	−0.503950
$144$	2.26372	0.188643
$145$	17.9673	1.49211
$146$	30.3949	2.51550
$147$	−16.8981	−1.39373
$148$	12.5426	1.03100
$149$	−11.7472	−0.962369	−0.481185	−	0.876619i	$-0.659793\pi$
$149$	−11.7472	−0.962369	−0.481185	+	0.876619i	$0.659793\pi$
$150$	8.71475	0.711556
$151$	−4.66358	−0.379517	−0.189758	−	0.981831i	$-0.560770\pi$
$151$	−4.66358	−0.379517	−0.189758	+	0.981831i	$0.560770\pi$
$152$	−6.40107	−0.519196
$153$	1.40834	0.113858
$154$	70.3055	5.66538
$155$	−26.2876	−2.11147
$156$	3.69513	0.295847
$157$	16.4671	1.31422	0.657108	−	0.753796i	$-0.271779\pi$
$157$	16.4671	1.31422	0.657108	+	0.753796i	$0.271779\pi$
$158$	37.7822	3.00579
$159$	0.0799155	0.00633771
$160$	7.90771	0.625159
$161$	36.8921	2.90750
$162$	−2.38645	−0.187497
$163$	21.5466	1.68766	0.843829	−	0.536612i	$-0.180296\pi$
$163$	21.5466	1.68766	0.843829	+	0.536612i	$0.180296\pi$
$164$	−3.04022	−0.237402
$165$	−17.7259	−1.37996
$166$	−19.7418	−1.53226
$167$	1.30540	0.101015	0.0505073	−	0.998724i	$-0.483916\pi$
$167$	1.30540	0.101015	0.0505073	+	0.998724i	$0.483916\pi$
$168$	−19.7759	−1.52574
$169$	1.00000	0.0769231
$170$	−9.88582	−0.758207
$171$	1.58234	0.121004
$172$	−7.12939	−0.543611
$173$	0.662605	0.0503769	0.0251885	−	0.999683i	$-0.491981\pi$
$173$	0.662605	0.0503769	0.0251885	+	0.999683i	$0.491981\pi$
$174$	14.5775	1.10512
$175$	−17.8519	−1.34948
$176$	13.6420	1.02830
$177$	−9.78401	−0.735411
$178$	37.2112	2.78910
$179$	−13.5132	−1.01003	−0.505014	−	0.863111i	$-0.668513\pi$
$179$	−13.5132	−1.01003	−0.505014	+	0.863111i	$0.668513\pi$
$180$	10.8688	0.810113
$181$	10.1149	0.751832	0.375916	−	0.926654i	$-0.377328\pi$
$181$	10.1149	0.751832	0.375916	+	0.926654i	$0.377328\pi$
$182$	−11.6663	−0.864765
$183$	−4.27813	−0.316248
$184$	30.5285	2.25059
$185$	9.98415	0.734049
$186$	−21.3280	−1.56385
$187$	8.48719	0.620645
$188$	−48.1103	−3.50880
$189$	4.88857	0.355591
$190$	−11.1071	−0.805797
$191$	8.94429	0.647186	0.323593	−	0.946196i	$-0.395109\pi$
$191$	8.94429	0.647186	0.323593	+	0.946196i	$0.395109\pi$
$192$	10.9432	0.789759
$193$	24.3825	1.75509	0.877546	−	0.479493i	$-0.159179\pi$
$193$	24.3825	1.75509	0.877546	+	0.479493i	$0.159179\pi$
$194$	−25.6835	−1.84397
$195$	2.94139	0.210637
$196$	62.4408	4.46005
$197$	3.37569	0.240508	0.120254	−	0.992743i	$-0.461629\pi$
$197$	3.37569	0.240508	0.120254	+	0.992743i	$0.461629\pi$
$198$	−14.3816	−1.02206
$199$	−19.0112	−1.34767	−0.673833	−	0.738884i	$-0.735353\pi$
$199$	−19.0112	−1.34767	−0.673833	+	0.738884i	$0.735353\pi$
$200$	−14.7726	−1.04458
$201$	1.39016	0.0980545
$202$	25.5096	1.79485
$203$	−29.8616	−2.09588
$204$	−5.20401	−0.364353
$205$	−2.42007	−0.169025
$206$	2.38645	0.166272
$207$	−7.54660	−0.524525
$208$	−2.26372	−0.156961
$209$	9.53574	0.659601
$210$	−34.3152	−2.36797
$211$	−21.7766	−1.49917	−0.749583	−	0.661910i	$-0.769746\pi$
$211$	−21.7766	−1.49917	−0.749583	+	0.661910i	$0.769746\pi$
$212$	−0.295298	−0.0202812
$213$	1.53807	0.105387
$214$	21.7950	1.48987
$215$	−5.67512	−0.387040
$216$	4.04533	0.275250
$217$	43.6899	2.96586
$218$	12.2004	0.826316
$219$	12.7364	0.860649
$220$	65.4995	4.41597
$221$	−1.40834	−0.0947354
$222$	8.10047	0.543668
$223$	−1.16147	−0.0777775	−0.0388887	−	0.999244i	$-0.512382\pi$
$223$	−1.16147	−0.0777775	−0.0388887	+	0.999244i	$0.512382\pi$
$224$	−13.1426	−0.878124
$225$	3.65177	0.243451
$226$	−3.84720	−0.255912
$227$	8.84689	0.587189	0.293594	−	0.955930i	$-0.405148\pi$
$227$	8.84689	0.587189	0.293594	+	0.955930i	$0.405148\pi$
$228$	−5.84693	−0.387222
$229$	−15.8059	−1.04448	−0.522242	−	0.852797i	$-0.674904\pi$
$229$	−15.8059	−1.04448	−0.522242	+	0.852797i	$0.674904\pi$
$230$	52.9731	3.49294
$231$	29.4603	1.93835
$232$	−24.7108	−1.62234
$233$	−17.7013	−1.15965	−0.579825	−	0.814741i	$-0.696879\pi$
$233$	−17.7013	−1.15965	−0.579825	+	0.814741i	$0.696879\pi$
$234$	2.38645	0.156007
$235$	−38.2966	−2.49820
$236$	36.1532	2.35337
$237$	15.8320	1.02840
$238$	16.4302	1.06501
$239$	13.9030	0.899307	0.449654	−	0.893203i	$-0.351547\pi$
$239$	13.9030	0.899307	0.449654	+	0.893203i	$0.351547\pi$
$240$	−6.65847	−0.429803
$241$	−19.3070	−1.24368	−0.621838	−	0.783146i	$-0.713614\pi$
$241$	−19.3070	−1.24368	−0.621838	+	0.783146i	$0.713614\pi$
$242$	−60.4180	−3.88381
$243$	−1.00000	−0.0641500
$244$	15.8082	1.01202
$245$	49.7040	3.17547
$246$	−1.96349	−0.125187
$247$	−1.58234	−0.100682
$248$	36.1538	2.29577
$249$	−8.27246	−0.524246
$250$	9.46388	0.598548
$251$	−12.0124	−0.758214	−0.379107	−	0.925353i	$-0.623769\pi$
$251$	−12.0124	−0.758214	−0.379107	+	0.925353i	$0.623769\pi$
$252$	−18.0639	−1.13792
$253$	−45.4786	−2.85921
$254$	−12.3070	−0.772211
$255$	−4.14248	−0.259412
$256$	−27.6050	−1.72531
$257$	3.36667	0.210007	0.105003	−	0.994472i	$-0.466515\pi$
$257$	3.36667	0.210007	0.105003	+	0.994472i	$0.466515\pi$
$258$	−4.60442	−0.286658
$259$	−16.5936	−1.03108
$260$	−10.8688	−0.674055
$261$	6.10846	0.378104
$262$	−26.4568	−1.63451
$263$	−10.2809	−0.633949	−0.316975	−	0.948434i	$-0.602667\pi$
$263$	−10.2809	−0.633949	−0.316975	+	0.948434i	$0.602667\pi$
$264$	24.3787	1.50040
$265$	−0.235063	−0.0144398
$266$	18.4600	1.13186
$267$	15.5927	0.954260
$268$	−5.13683	−0.313782
$269$	−18.0704	−1.10177	−0.550885	−	0.834581i	$-0.685710\pi$
$269$	−18.0704	−1.10177	−0.550885	+	0.834581i	$0.685710\pi$
$270$	7.01947	0.427191
$271$	22.4779	1.36544	0.682718	−	0.730682i	$-0.260798\pi$
$271$	22.4779	1.36544	0.682718	+	0.730682i	$0.260798\pi$
$272$	3.18809	0.193306
$273$	−4.88857	−0.295870
$274$	3.96722	0.239669
$275$	22.0069	1.32707
$276$	27.8857	1.67852
$277$	−21.6180	−1.29890	−0.649450	−	0.760404i	$-0.725001\pi$
$277$	−21.6180	−1.29890	−0.649450	+	0.760404i	$0.725001\pi$
$278$	1.67964	0.100738
$279$	−8.93715	−0.535053
$280$	58.1686	3.47624
$281$	16.2090	0.966946	0.483473	−	0.875359i	$-0.339375\pi$
$281$	16.2090	0.966946	0.483473	+	0.875359i	$0.339375\pi$
$282$	−31.0713	−1.85027
$283$	16.2034	0.963191	0.481595	−	0.876394i	$-0.340057\pi$
$283$	16.2034	0.963191	0.481595	+	0.876394i	$0.340057\pi$
$284$	−5.68337	−0.337246
$285$	−4.65426	−0.275695
$286$	14.3816	0.850402
$287$	4.02215	0.237420
$288$	2.68843	0.158417
$289$	−15.0166	−0.883328
$290$	−42.8781	−2.51789
$291$	−10.7622	−0.630893
$292$	−47.0628	−2.75414
$293$	25.8869	1.51233	0.756164	−	0.654382i	$-0.227071\pi$
$293$	25.8869	1.51233	0.756164	+	0.654382i	$0.227071\pi$
$294$	40.3265	2.35189
$295$	28.7786	1.67555
$296$	−13.7313	−0.798118
$297$	−6.02637	−0.349685
$298$	28.0341	1.62397
$299$	7.54660	0.436431
$300$	−13.4937	−0.779062
$301$	9.43202	0.543653
$302$	11.1294	0.640424
$303$	10.6894	0.614088
$304$	3.58196	0.205440
$305$	12.5836	0.720537
$306$	−3.36094	−0.192132
$307$	14.6896	0.838378	0.419189	−	0.907899i	$-0.362315\pi$
$307$	14.6896	0.838378	0.419189	+	0.907899i	$0.362315\pi$
$308$	−108.860	−6.20286
$309$	1.00000	0.0568880
$310$	62.7341	3.56306
$311$	−13.1747	−0.747067	−0.373534	−	0.927617i	$-0.621854\pi$
$311$	−13.1747	−0.747067	−0.373534	+	0.927617i	$0.621854\pi$
$312$	−4.04533	−0.229022
$313$	−18.6901	−1.05643	−0.528214	−	0.849111i	$-0.677138\pi$
$313$	−18.6901	−1.05643	−0.528214	+	0.849111i	$0.677138\pi$
$314$	−39.2978	−2.21770
$315$	−14.3792	−0.810175
$316$	−58.5013	−3.29095
$317$	−10.9594	−0.615544	−0.307772	−	0.951460i	$-0.599583\pi$
$317$	−10.9594	−0.615544	−0.307772	+	0.951460i	$0.599583\pi$
$318$	−0.190714	−0.0106947
$319$	36.8118	2.06107
$320$	−32.1883	−1.79938
$321$	9.13282	0.509744
$322$	−88.0410	−4.90633
$323$	2.22847	0.123995
$324$	3.69513	0.205285
$325$	−3.65177	−0.202564
$326$	−51.4198	−2.84788
$327$	5.11237	0.282715
$328$	3.32836	0.183778
$329$	63.6488	3.50907
$330$	42.3019	2.32864
$331$	6.42322	0.353052	0.176526	−	0.984296i	$-0.443514\pi$
$331$	6.42322	0.353052	0.176526	+	0.984296i	$0.443514\pi$
$332$	30.5678	1.67763
$333$	3.39436	0.186010
$334$	−3.11526	−0.170460
$335$	−4.08901	−0.223406
$336$	11.0663	0.603719
$337$	−27.7359	−1.51087	−0.755435	−	0.655223i	$-0.772574\pi$
$337$	−27.7359	−1.51087	−0.755435	+	0.655223i	$0.772574\pi$
$338$	−2.38645	−0.129806
$339$	−1.61210	−0.0875574
$340$	15.3070	0.830139
$341$	−53.8586	−2.91661
$342$	−3.77616	−0.204191
$343$	−48.3877	−2.61269
$344$	7.80508	0.420822
$345$	22.1975	1.19507
$346$	−1.58127	−0.0850097
$347$	13.8749	0.744845	0.372422	−	0.928063i	$-0.378527\pi$
$347$	13.8749	0.744845	0.372422	+	0.928063i	$0.378527\pi$
$348$	−22.5715	−1.20996
$349$	−4.20617	−0.225151	−0.112576	−	0.993643i	$-0.535910\pi$
$349$	−4.20617	−0.225151	−0.112576	+	0.993643i	$0.535910\pi$
$350$	42.6027	2.27721
$351$	1.00000	0.0533761
$352$	16.2014	0.863540
$353$	1.30762	0.0695975	0.0347987	−	0.999394i	$-0.488921\pi$
$353$	1.30762	0.0695975	0.0347987	+	0.999394i	$0.488921\pi$
$354$	23.3490	1.24099
$355$	−4.52406	−0.240112
$356$	−57.6171	−3.05370
$357$	6.88478	0.364381
$358$	32.2486	1.70439
$359$	35.9799	1.89895	0.949474	−	0.313845i	$-0.101617\pi$
$359$	35.9799	1.89895	0.949474	+	0.313845i	$0.101617\pi$
$360$	−11.8989	−0.627127
$361$	−16.4962	−0.868222
$362$	−24.1386	−1.26870
$363$	−25.3171	−1.32880
$364$	18.0639	0.946806
$365$	−37.4628	−1.96089
$366$	10.2095	0.533660
$367$	−11.4402	−0.597174	−0.298587	−	0.954382i	$-0.596515\pi$
$367$	−11.4402	−0.597174	−0.298587	+	0.954382i	$0.596515\pi$
$368$	−17.0834	−0.890532
$369$	−0.822765	−0.0428314
$370$	−23.8266	−1.23869
$371$	0.390673	0.0202827
$372$	33.0239	1.71221
$373$	18.9226	0.979773	0.489886	−	0.871786i	$-0.337038\pi$
$373$	18.9226	0.979773	0.489886	+	0.871786i	$0.337038\pi$
$374$	−20.2542	−1.04732
$375$	3.96568	0.204787
$376$	52.6699	2.71624
$377$	−6.10846	−0.314602
$378$	−11.6663	−0.600051
$379$	−21.5528	−1.10709	−0.553546	−	0.832819i	$-0.686726\pi$
$379$	−21.5528	−1.10709	−0.553546	+	0.832819i	$0.686726\pi$
$380$	17.1981	0.882244
$381$	−5.15705	−0.264204
$382$	−21.3451	−1.09211
$383$	−5.27438	−0.269508	−0.134754	−	0.990879i	$-0.543024\pi$
$383$	−5.27438	−0.269508	−0.134754	+	0.990879i	$0.543024\pi$
$384$	−20.7386	−1.05831
$385$	−86.6543	−4.41631
$386$	−58.1876	−2.96167
$387$	−1.92940	−0.0980771
$388$	39.7678	2.01891
$389$	−21.5607	−1.09317	−0.546585	−	0.837404i	$-0.684072\pi$
$389$	−21.5607	−1.09317	−0.546585	+	0.837404i	$0.684072\pi$
$390$	−7.01947	−0.355445
$391$	−10.6282	−0.537491
$392$	−68.3586	−3.45263
$393$	−11.0863	−0.559228
$394$	−8.05592	−0.405851
$395$	−46.5680	−2.34309
$396$	22.2682	1.11902
$397$	7.18291	0.360500	0.180250	−	0.983621i	$-0.442309\pi$
$397$	7.18291	0.360500	0.180250	+	0.983621i	$0.442309\pi$
$398$	45.3691	2.27415
$399$	7.73536	0.387252
$400$	8.26657	0.413328
$401$	−13.8346	−0.690869	−0.345435	−	0.938443i	$-0.612268\pi$
$401$	−13.8346	−0.690869	−0.345435	+	0.938443i	$0.612268\pi$
$402$	−3.31755	−0.165464
$403$	8.93715	0.445191
$404$	−39.4986	−1.96513
$405$	2.94139	0.146159
$406$	71.2632	3.53673
$407$	20.4557	1.01395
$408$	5.69722	0.282054
$409$	−18.3983	−0.909737	−0.454869	−	0.890558i	$-0.650314\pi$
$409$	−18.3983	−0.909737	−0.454869	+	0.890558i	$0.650314\pi$
$410$	5.77537	0.285225
$411$	1.66240	0.0820000
$412$	−3.69513	−0.182046
$413$	−47.8298	−2.35355
$414$	18.0096	0.885121
$415$	24.3325	1.19444
$416$	−2.68843	−0.131811
$417$	0.703823	0.0344664
$418$	−22.7565	−1.11306
$419$	−21.9397	−1.07182	−0.535912	−	0.844274i	$-0.680032\pi$
$419$	−21.9397	−1.07182	−0.535912	+	0.844274i	$0.680032\pi$
$420$	53.1329	2.59262
$421$	−4.31520	−0.210310	−0.105155	−	0.994456i	$-0.533534\pi$
$421$	−4.31520	−0.210310	−0.105155	+	0.994456i	$0.533534\pi$
$422$	51.9688	2.52980
$423$	−13.0199	−0.633050
$424$	0.323285	0.0157001
$425$	5.14294	0.249469
$426$	−3.67052	−0.177837
$427$	−20.9139	−1.01210
$428$	−33.7469	−1.63122
$429$	6.02637	0.290956
$430$	13.5434	0.653120
$431$	−23.0722	−1.11135	−0.555674	−	0.831400i	$-0.687540\pi$
$431$	−23.0722	−1.11135	−0.555674	+	0.831400i	$0.687540\pi$
$432$	−2.26372	−0.108913
$433$	7.48088	0.359508	0.179754	−	0.983712i	$-0.442470\pi$
$433$	7.48088	0.359508	0.179754	+	0.983712i	$0.442470\pi$
$434$	−104.264	−5.00482
$435$	−17.9673	−0.861468
$436$	−18.8909	−0.904709
$437$	−11.9412	−0.571227
$438$	−30.3949	−1.45232
$439$	1.16168	0.0554439	0.0277220	−	0.999616i	$-0.491175\pi$
$439$	1.16168	0.0554439	0.0277220	+	0.999616i	$0.491175\pi$
$440$	−71.7072	−3.41850
$441$	16.8981	0.804673
$442$	3.36094	0.159863
$443$	−31.3171	−1.48792	−0.743959	−	0.668225i	$-0.767054\pi$
$443$	−31.3171	−1.48792	−0.743959	+	0.668225i	$0.767054\pi$
$444$	−12.5426	−0.595246
$445$	−45.8643	−2.17418
$446$	2.77178	0.131247
$447$	11.7472	0.555624
$448$	53.4967	2.52748
$449$	−21.7604	−1.02694	−0.513469	−	0.858108i	$-0.671640\pi$
$449$	−21.7604	−1.02694	−0.513469	+	0.858108i	$0.671640\pi$
$450$	−8.71475	−0.410817
$451$	−4.95829	−0.233477
$452$	5.95693	0.280190
$453$	4.66358	0.219114
$454$	−21.1126	−0.990865
$455$	14.3792	0.674107
$456$	6.40107	0.299758
$457$	−34.4182	−1.61002	−0.805008	−	0.593263i	$-0.797839\pi$
$457$	−34.4182	−1.61002	−0.805008	+	0.593263i	$0.797839\pi$
$458$	37.7200	1.76254
$459$	−1.40834	−0.0657358
$460$	−82.0225	−3.82432
$461$	−0.524708	−0.0244381	−0.0122190	−	0.999925i	$-0.503890\pi$
$461$	−0.524708	−0.0244381	−0.0122190	+	0.999925i	$0.503890\pi$
$462$	−70.3055	−3.27091
$463$	−16.7041	−0.776307	−0.388154	−	0.921595i	$-0.626887\pi$
$463$	−16.7041	−0.776307	−0.388154	+	0.921595i	$0.626887\pi$
$464$	13.8278	0.641941
$465$	26.2876	1.21906
$466$	42.2432	1.95688
$467$	−33.8358	−1.56574	−0.782868	−	0.622188i	$-0.786244\pi$
$467$	−33.8358	−1.56574	−0.782868	+	0.622188i	$0.786244\pi$
$468$	−3.69513	−0.170807
$469$	6.79591	0.313806
$470$	91.3929	4.21564
$471$	−16.4671	−0.758763
$472$	−39.5796	−1.82180
$473$	−11.6273	−0.534624
$474$	−37.7822	−1.73539
$475$	5.77832	0.265127
$476$	−25.4402	−1.16605
$477$	−0.0799155	−0.00365908
$478$	−33.1787	−1.51756
$479$	31.1654	1.42398	0.711991	−	0.702188i	$-0.247794\pi$
$479$	31.1654	1.42398	0.711991	+	0.702188i	$0.247794\pi$
$480$	−7.90771	−0.360936
$481$	−3.39436	−0.154770
$482$	46.0752	2.09867
$483$	−36.8921	−1.67865
$484$	93.5500	4.25227
$485$	31.6559	1.43742
$486$	2.38645	0.108251
$487$	−38.8501	−1.76047	−0.880233	−	0.474542i	$-0.842614\pi$
$487$	−38.8501	−1.76047	−0.880233	+	0.474542i	$0.842614\pi$
$488$	−17.3065	−0.783426
$489$	−21.5466	−0.974370
$490$	−118.616	−5.35852
$491$	−9.95827	−0.449410	−0.224705	−	0.974427i	$-0.572142\pi$
$491$	−9.95827	−0.449410	−0.224705	+	0.974427i	$0.572142\pi$
$492$	3.04022	0.137064
$493$	8.60280	0.387451
$494$	3.77616	0.169897
$495$	17.7259	0.796720
$496$	−20.2312	−0.908408
$497$	7.51897	0.337272
$498$	19.7418	0.884651
$499$	16.7396	0.749366	0.374683	−	0.927153i	$-0.377752\pi$
$499$	16.7396	0.749366	0.374683	+	0.927153i	$0.377752\pi$
$500$	−14.6537	−0.655333
$501$	−1.30540	−0.0583209
$502$	28.6669	1.27947
$503$	−37.4100	−1.66803	−0.834014	−	0.551743i	$-0.813963\pi$
$503$	−37.4100	−1.66803	−0.834014	+	0.551743i	$0.813963\pi$
$504$	19.7759	0.880889
$505$	−31.4416	−1.39913
$506$	108.532	4.82485
$507$	−1.00000	−0.0444116
$508$	19.0560	0.845472
$509$	−3.12200	−0.138380	−0.0691901	−	0.997603i	$-0.522042\pi$
$509$	−3.12200	−0.138380	−0.0691901	+	0.997603i	$0.522042\pi$
$510$	9.88582	0.437751
$511$	62.2630	2.75435
$512$	24.4008	1.07837
$513$	−1.58234	−0.0698618
$514$	−8.03437	−0.354381
$515$	−2.94139	−0.129613
$516$	7.12939	0.313854
$517$	−78.4628	−3.45079
$518$	39.5997	1.73991
$519$	−0.662605	−0.0290851
$520$	11.8989	0.521801
$521$	28.3531	1.24217	0.621086	−	0.783742i	$-0.286692\pi$
$521$	28.3531	1.24217	0.621086	+	0.783742i	$0.286692\pi$
$522$	−14.5775	−0.638040
$523$	−0.350943	−0.0153457	−0.00767283	−	0.999971i	$-0.502442\pi$
$523$	−0.350943	−0.0153457	−0.00767283	+	0.999971i	$0.502442\pi$
$524$	40.9652	1.78957
$525$	17.8519	0.779122
$526$	24.5349	1.06977
$527$	−12.5866	−0.548280
$528$	−13.6420	−0.593692
$529$	33.9511	1.47614
$530$	0.560964	0.0243667
$531$	9.78401	0.424590
$532$	−28.5831	−1.23924
$533$	0.822765	0.0356379
$534$	−37.2112	−1.61029
$535$	−26.8632	−1.16140
$536$	5.62367	0.242906
$537$	13.5132	0.583139
$538$	43.1240	1.85921
$539$	101.834	4.38632
$540$	−10.8688	−0.467719
$541$	−26.1039	−1.12229	−0.561146	−	0.827717i	$-0.689639\pi$
$541$	−26.1039	−1.12229	−0.561146	+	0.827717i	$0.689639\pi$
$542$	−53.6423	−2.30414
$543$	−10.1149	−0.434070
$544$	3.78623	0.162333
$545$	−15.0375	−0.644135
$546$	11.6663	0.499272
$547$	15.0261	0.642469	0.321234	−	0.947000i	$-0.395902\pi$
$547$	15.0261	0.642469	0.321234	+	0.947000i	$0.395902\pi$
$548$	−6.14277	−0.262406
$549$	4.27813	0.182586
$550$	−52.5183	−2.23939
$551$	9.66563	0.411770
$552$	−30.5285	−1.29938
$553$	77.3958	3.29121
$554$	51.5902	2.19186
$555$	−9.98415	−0.423803
$556$	−2.60072	−0.110295
$557$	−22.9034	−0.970450	−0.485225	−	0.874389i	$-0.661262\pi$
$557$	−22.9034	−0.970450	−0.485225	+	0.874389i	$0.661262\pi$
$558$	21.3280	0.902888
$559$	1.92940	0.0816050
$560$	−32.5504	−1.37551
$561$	−8.48719	−0.358330
$562$	−38.6819	−1.63170
$563$	−16.6623	−0.702234	−0.351117	−	0.936332i	$-0.614198\pi$
$563$	−16.6623	−0.702234	−0.351117	+	0.936332i	$0.614198\pi$
$564$	48.1103	2.02581
$565$	4.74182	0.199490
$566$	−38.6685	−1.62536
$567$	−4.88857	−0.205301
$568$	6.22201	0.261070
$569$	24.1559	1.01267	0.506334	−	0.862338i	$-0.331000\pi$
$569$	24.1559	1.01267	0.506334	+	0.862338i	$0.331000\pi$
$570$	11.1071	0.465227
$571$	−39.1720	−1.63930	−0.819649	−	0.572866i	$-0.805831\pi$
$571$	−39.1720	−1.63930	−0.819649	+	0.572866i	$0.805831\pi$
$572$	−22.2682	−0.931081
$573$	−8.94429	−0.373653
$574$	−9.59864	−0.400639
$575$	−27.5584	−1.14927
$576$	−10.9432	−0.455968
$577$	−6.27852	−0.261378	−0.130689	−	0.991423i	$-0.541719\pi$
$577$	−6.27852	−0.261378	−0.130689	+	0.991423i	$0.541719\pi$
$578$	35.8362	1.49059
$579$	−24.3825	−1.01330
$580$	66.3917	2.75676
$581$	−40.4405	−1.67776
$582$	25.6835	1.06462
$583$	−0.481600	−0.0199458
$584$	51.5232	2.13204
$585$	−2.94139	−0.121611
$586$	−61.7777	−2.55201
$587$	14.1272	0.583091	0.291546	−	0.956557i	$-0.405831\pi$
$587$	14.1272	0.583091	0.291546	+	0.956557i	$0.405831\pi$
$588$	−62.4408	−2.57501
$589$	−14.1416	−0.582693
$590$	−68.6785	−2.82745
$591$	−3.37569	−0.138858
$592$	7.68388	0.315806
$593$	8.31545	0.341475	0.170737	−	0.985317i	$-0.445385\pi$
$593$	8.31545	0.341475	0.170737	+	0.985317i	$0.445385\pi$
$594$	14.3816	0.590085
$595$	−20.2508	−0.830203
$596$	−43.4075	−1.77804
$597$	19.0112	0.778075
$598$	−18.0096	−0.736466
$599$	−35.6920	−1.45833	−0.729167	−	0.684336i	$-0.760092\pi$
$599$	−35.6920	−1.45833	−0.729167	+	0.684336i	$0.760092\pi$
$600$	14.7726	0.603090
$601$	8.58924	0.350362	0.175181	−	0.984536i	$-0.443949\pi$
$601$	8.58924	0.350362	0.175181	+	0.984536i	$0.443949\pi$
$602$	−22.5090	−0.917399
$603$	−1.39016	−0.0566118
$604$	−17.2325	−0.701181
$605$	74.4675	3.02753
$606$	−25.5096	−1.03626
$607$	24.2248	0.983255	0.491628	−	0.870805i	$-0.336402\pi$
$607$	24.2248	0.983255	0.491628	+	0.870805i	$0.336402\pi$
$608$	4.25399	0.172522
$609$	29.8616	1.21005
$610$	−30.0302	−1.21589
$611$	13.0199	0.526729
$612$	5.20401	0.210360
$613$	43.4482	1.75486	0.877428	−	0.479708i	$-0.159257\pi$
$613$	43.4482	1.75486	0.877428	+	0.479708i	$0.159257\pi$
$614$	−35.0559	−1.41474
$615$	2.42007	0.0975867
$616$	119.177	4.80177
$617$	9.62894	0.387647	0.193823	−	0.981036i	$-0.437911\pi$
$617$	9.62894	0.387647	0.193823	+	0.981036i	$0.437911\pi$
$618$	−2.38645	−0.0959970
$619$	−42.2992	−1.70015	−0.850074	−	0.526663i	$-0.823443\pi$
$619$	−42.2992	−1.70015	−0.850074	+	0.526663i	$0.823443\pi$
$620$	−97.1362	−3.90108
$621$	7.54660	0.302835
$622$	31.4407	1.26066
$623$	76.2262	3.05394
$624$	2.26372	0.0906212
$625$	−29.9234	−1.19694
$626$	44.6030	1.78269
$627$	−9.53574	−0.380821
$628$	60.8480	2.42810
$629$	4.78043	0.190608
$630$	34.3152	1.36715
$631$	−42.5315	−1.69315	−0.846576	−	0.532268i	$-0.821340\pi$
$631$	−42.5315	−1.69315	−0.846576	+	0.532268i	$0.821340\pi$
$632$	64.0457	2.54760
$633$	21.7766	0.865544
$634$	26.1541	1.03871
$635$	15.1689	0.601959
$636$	0.295298	0.0117093
$637$	−16.8981	−0.669528
$638$	−87.8495	−3.47799
$639$	−1.53807	−0.0608451
$640$	61.0002	2.41124
$641$	−3.46954	−0.137039	−0.0685194	−	0.997650i	$-0.521827\pi$
$641$	−3.46954	−0.137039	−0.0685194	+	0.997650i	$0.521827\pi$
$642$	−21.7950	−0.860179
$643$	46.7427	1.84335	0.921675	−	0.387962i	$-0.126821\pi$
$643$	46.7427	1.84335	0.921675	+	0.387962i	$0.126821\pi$
$644$	136.321	5.37180
$645$	5.67512	0.223458
$646$	−5.31813	−0.209239
$647$	−6.77467	−0.266340	−0.133170	−	0.991093i	$-0.542516\pi$
$647$	−6.77467	−0.266340	−0.133170	+	0.991093i	$0.542516\pi$
$648$	−4.04533	−0.158916
$649$	58.9621	2.31446
$650$	8.71475	0.341820
$651$	−43.6899	−1.71234
$652$	79.6174	3.11806
$653$	−28.0894	−1.09922	−0.549612	−	0.835420i	$-0.685224\pi$
$653$	−28.0894	−1.09922	−0.549612	+	0.835420i	$0.685224\pi$
$654$	−12.2004	−0.477074
$655$	32.6090	1.27414
$656$	−1.86251	−0.0727187
$657$	−12.7364	−0.496896
$658$	−151.894	−5.92146
$659$	35.3981	1.37892	0.689458	−	0.724326i	$-0.257849\pi$
$659$	35.3981	1.37892	0.689458	+	0.724326i	$0.257849\pi$
$660$	−65.4995	−2.54956
$661$	−7.02996	−0.273434	−0.136717	−	0.990610i	$-0.543655\pi$
$661$	−7.02996	−0.273434	−0.136717	+	0.990610i	$0.543655\pi$
$662$	−15.3287	−0.595766
$663$	1.40834	0.0546955
$664$	−33.4649	−1.29869
$665$	−22.7527	−0.882312
$666$	−8.10047	−0.313887
$667$	−46.0981	−1.78492
$668$	4.82361	0.186631
$669$	1.16147	0.0449049
$670$	9.75820	0.376992
$671$	25.7816	0.995287
$672$	13.1426	0.506985
$673$	−10.1224	−0.390188	−0.195094	−	0.980785i	$-0.562501\pi$
$673$	−10.1224	−0.390188	−0.195094	+	0.980785i	$0.562501\pi$
$674$	66.1902	2.54955
$675$	−3.65177	−0.140557
$676$	3.69513	0.142120
$677$	2.67210	0.102697	0.0513487	−	0.998681i	$-0.483648\pi$
$677$	2.67210	0.102697	0.0513487	+	0.998681i	$0.483648\pi$
$678$	3.84720	0.147751
$679$	−52.6119	−2.01906
$680$	−16.7577	−0.642630
$681$	−8.84689	−0.339014
$682$	128.531	4.92169
$683$	6.25597	0.239378	0.119689	−	0.992811i	$-0.461810\pi$
$683$	6.25597	0.239378	0.119689	+	0.992811i	$0.461810\pi$
$684$	5.84693	0.223563
$685$	−4.88976	−0.186828
$686$	115.475	4.40885
$687$	15.8059	0.603033
$688$	−4.36762	−0.166514
$689$	0.0799155	0.00304454
$690$	−52.9731	−2.01665
$691$	39.9791	1.52088	0.760439	−	0.649410i	$-0.224984\pi$
$691$	39.9791	1.52088	0.760439	+	0.649410i	$0.224984\pi$
$692$	2.44841	0.0930746
$693$	−29.4603	−1.11911
$694$	−33.1118	−1.25691
$695$	−2.07022	−0.0785278
$696$	24.7108	0.936659
$697$	−1.15874	−0.0438902
$698$	10.0378	0.379936
$699$	17.7013	0.669524
$700$	−65.9651	−2.49325
$701$	−6.29680	−0.237827	−0.118914	−	0.992905i	$-0.537941\pi$
$701$	−6.29680	−0.237827	−0.118914	+	0.992905i	$0.537941\pi$
$702$	−2.38645	−0.0900706
$703$	5.37102	0.202572
$704$	−65.9479	−2.48550
$705$	38.2966	1.44233
$706$	−3.12056	−0.117444
$707$	52.2557	1.96528
$708$	−36.1532	−1.35872
$709$	−6.99775	−0.262806	−0.131403	−	0.991329i	$-0.541948\pi$
$709$	−6.99775	−0.262806	−0.131403	+	0.991329i	$0.541948\pi$
$710$	10.7964	0.405183
$711$	−15.8320	−0.593746
$712$	63.0778	2.36394
$713$	67.4451	2.52584
$714$	−16.4302	−0.614884
$715$	−17.7259	−0.662911
$716$	−49.9332	−1.86609
$717$	−13.9030	−0.519215
$718$	−85.8642	−3.20442
$719$	−31.3658	−1.16975	−0.584873	−	0.811125i	$-0.698856\pi$
$719$	−31.3658	−1.16975	−0.584873	+	0.811125i	$0.698856\pi$
$720$	6.65847	0.248147
$721$	4.88857	0.182060
$722$	39.3673	1.46510
$723$	19.3070	0.718037
$724$	37.3757	1.38906
$725$	22.3067	0.828449
$726$	60.4180	2.24232
$727$	−1.66931	−0.0619113	−0.0309557	−	0.999521i	$-0.509855\pi$
$727$	−1.66931	−0.0619113	−0.0309557	+	0.999521i	$0.509855\pi$
$728$	−19.7759	−0.732944
$729$	1.00000	0.0370370
$730$	89.4031	3.30896
$731$	−2.71726	−0.100502
$732$	−15.8082	−0.584289
$733$	−36.2236	−1.33795	−0.668975	−	0.743285i	$-0.733267\pi$
$733$	−36.2236	−1.33795	−0.668975	+	0.743285i	$0.733267\pi$
$734$	27.3014	1.00771
$735$	−49.7040	−1.83336
$736$	−20.2885	−0.747843
$737$	−8.37763	−0.308594
$738$	1.96349	0.0722769
$739$	16.6173	0.611279	0.305639	−	0.952147i	$-0.401130\pi$
$739$	16.6173	0.611279	0.305639	+	0.952147i	$0.401130\pi$
$740$	36.8927	1.35620
$741$	1.58234	0.0581285
$742$	−0.932319	−0.0342265
$743$	5.51265	0.202239	0.101120	−	0.994874i	$-0.467757\pi$
$743$	5.51265	0.202239	0.101120	+	0.994874i	$0.467757\pi$
$744$	−36.1538	−1.32546
$745$	−34.5531	−1.26593
$746$	−45.1577	−1.65334
$747$	8.27246	0.302674
$748$	31.3613	1.14668
$749$	44.6464	1.63135
$750$	−9.46388	−0.345572
$751$	−6.32963	−0.230971	−0.115486	−	0.993309i	$-0.536842\pi$
$751$	−6.32963	−0.230971	−0.115486	+	0.993309i	$0.536842\pi$
$752$	−29.4734	−1.07478
$753$	12.0124	0.437755
$754$	14.5775	0.530882
$755$	−13.7174	−0.499227
$756$	18.0639	0.656978
$757$	10.8039	0.392675	0.196338	−	0.980536i	$-0.437095\pi$
$757$	10.8039	0.392675	0.196338	+	0.980536i	$0.437095\pi$
$758$	51.4346	1.86819
$759$	45.4786	1.65077
$760$	−18.8280	−0.682965
$761$	−9.59850	−0.347945	−0.173973	−	0.984750i	$-0.555660\pi$
$761$	−9.59850	−0.347945	−0.173973	+	0.984750i	$0.555660\pi$
$762$	12.3070	0.445837
$763$	24.9922	0.904778
$764$	33.0503	1.19572
$765$	4.14248	0.149772
$766$	12.5870	0.454788
$767$	−9.78401	−0.353280
$768$	27.6050	0.996111
$769$	29.3130	1.05705	0.528527	−	0.848917i	$-0.322745\pi$
$769$	29.3130	1.05705	0.528527	+	0.848917i	$0.322745\pi$
$770$	206.796	7.45241
$771$	−3.36667	−0.121248
$772$	90.0965	3.24264
$773$	35.7351	1.28530	0.642651	−	0.766159i	$-0.277835\pi$
$773$	35.7351	1.28530	0.642651	+	0.766159i	$0.277835\pi$
$774$	4.60442	0.165502
$775$	−32.6364	−1.17233
$776$	−43.5368	−1.56288
$777$	16.5936	0.595292
$778$	51.4534	1.84469
$779$	−1.30189	−0.0466451
$780$	10.8688	0.389166
$781$	−9.26898	−0.331670
$782$	25.3636	0.907001
$783$	−6.10846	−0.218298
$784$	38.2526	1.36616
$785$	48.4361	1.72876
$786$	26.4568	0.943682
$787$	−49.2351	−1.75504	−0.877521	−	0.479538i	$-0.840804\pi$
$787$	−49.2351	−1.75504	−0.877521	+	0.479538i	$0.840804\pi$
$788$	12.4736	0.444355
$789$	10.2809	0.366011
$790$	111.132	3.95391
$791$	−7.88088	−0.280212
$792$	−24.3787	−0.866259
$793$	−4.27813	−0.151921
$794$	−17.1416	−0.608333
$795$	0.235063	0.00833681
$796$	−70.2487	−2.48990
$797$	13.2838	0.470535	0.235267	−	0.971931i	$-0.424403\pi$
$797$	13.2838	0.470535	0.235267	+	0.971931i	$0.424403\pi$
$798$	−18.4600	−0.653478
$799$	−18.3365	−0.648699
$800$	9.81750	0.347101
$801$	−15.5927	−0.550942
$802$	33.0156	1.16582
$803$	−76.7545	−2.70861
$804$	5.13683	0.181162
$805$	108.514	3.82461
$806$	−21.3280	−0.751248
$807$	18.0704	0.636107
$808$	43.2421	1.52125
$809$	26.5364	0.932968	0.466484	−	0.884530i	$-0.345520\pi$
$809$	26.5364	0.932968	0.466484	+	0.884530i	$0.345520\pi$
$810$	−7.01947	−0.246639
$811$	−3.76959	−0.132368	−0.0661842	−	0.997807i	$-0.521082\pi$
$811$	−3.76959	−0.132368	−0.0661842	+	0.997807i	$0.521082\pi$
$812$	−110.343	−3.87227
$813$	−22.4779	−0.788335
$814$	−48.8164	−1.71102
$815$	63.3769	2.21999
$816$	−3.18809	−0.111606
$817$	−3.05296	−0.106810
$818$	43.9066	1.53516
$819$	4.88857	0.170821
$820$	−8.94248	−0.312285
$821$	25.9860	0.906919	0.453460	−	0.891277i	$-0.350190\pi$
$821$	25.9860	0.906919	0.453460	+	0.891277i	$0.350190\pi$
$822$	−3.96722	−0.138373
$823$	−46.8695	−1.63377	−0.816884	−	0.576801i	$-0.804301\pi$
$823$	−46.8695	−1.63377	−0.816884	+	0.576801i	$0.804301\pi$
$824$	4.04533	0.140926
$825$	−22.0069	−0.766182
$826$	114.143	3.97155
$827$	−36.7277	−1.27715	−0.638573	−	0.769561i	$-0.720475\pi$
$827$	−36.7277	−1.27715	−0.638573	+	0.769561i	$0.720475\pi$
$828$	−27.8857	−0.969093
$829$	2.41025	0.0837116	0.0418558	−	0.999124i	$-0.486673\pi$
$829$	2.41025	0.0837116	0.0418558	+	0.999124i	$0.486673\pi$
$830$	−58.0683	−2.01558
$831$	21.6180	0.749920
$832$	10.9432	0.379388
$833$	23.7984	0.824564
$834$	−1.67964	−0.0581610
$835$	3.83968	0.132878
$836$	35.2358	1.21865
$837$	8.93715	0.308913
$838$	52.3579	1.80868
$839$	9.13442	0.315355	0.157678	−	0.987491i	$-0.449599\pi$
$839$	9.13442	0.315355	0.157678	+	0.987491i	$0.449599\pi$
$840$	−58.1686	−2.00701
$841$	8.31325	0.286664
$842$	10.2980	0.354892
$843$	−16.2090	−0.558267
$844$	−80.4675	−2.76981
$845$	2.94139	0.101187
$846$	31.0713	1.06825
$847$	−123.765	−4.25260
$848$	−0.180906	−0.00621234
$849$	−16.2034	−0.556098
$850$	−12.2734	−0.420972
$851$	−25.6159	−0.878102
$852$	5.68337	0.194709
$853$	43.8587	1.50169	0.750847	−	0.660476i	$-0.229646\pi$
$853$	43.8587	1.50169	0.750847	+	0.660476i	$0.229646\pi$
$854$	49.9100	1.70788
$855$	4.65426	0.159172
$856$	36.9453	1.26276
$857$	−43.3976	−1.48243	−0.741217	−	0.671266i	$-0.765751\pi$
$857$	−43.3976	−1.48243	−0.741217	+	0.671266i	$0.765751\pi$
$858$	−14.3816	−0.490980
$859$	28.6209	0.976534	0.488267	−	0.872694i	$-0.337629\pi$
$859$	28.6209	0.976534	0.488267	+	0.872694i	$0.337629\pi$
$860$	−20.9703	−0.715082
$861$	−4.02215	−0.137074
$862$	55.0606	1.87537
$863$	−41.4768	−1.41189	−0.705944	−	0.708268i	$-0.749477\pi$
$863$	−41.4768	−1.41189	−0.705944	+	0.708268i	$0.749477\pi$
$864$	−2.68843	−0.0914621
$865$	1.94898	0.0662673
$866$	−17.8527	−0.606660
$867$	15.0166	0.509989
$868$	161.440	5.47963
$869$	−95.4095	−3.23654
$870$	42.8781	1.45370
$871$	1.39016	0.0471039
$872$	20.6813	0.700356
$873$	10.7622	0.364246
$874$	28.4972	0.963931
$875$	19.3865	0.655383
$876$	47.0628	1.59011
$877$	4.95090	0.167180	0.0835899	−	0.996500i	$-0.473361\pi$
$877$	4.95090	0.167180	0.0835899	+	0.996500i	$0.473361\pi$
$878$	−2.77229	−0.0935601
$879$	−25.8869	−0.873143
$880$	40.1264	1.35266
$881$	−17.8729	−0.602155	−0.301077	−	0.953600i	$-0.597346\pi$
$881$	−17.8729	−0.602155	−0.301077	+	0.953600i	$0.597346\pi$
$882$	−40.3265	−1.35786
$883$	−39.5010	−1.32932	−0.664658	−	0.747148i	$-0.731423\pi$
$883$	−39.5010	−1.32932	−0.664658	+	0.747148i	$0.731423\pi$
$884$	−5.20401	−0.175030
$885$	−28.7786	−0.967381
$886$	74.7365	2.51082
$887$	−10.5883	−0.355519	−0.177760	−	0.984074i	$-0.556885\pi$
$887$	−10.5883	−0.355519	−0.177760	+	0.984074i	$0.556885\pi$
$888$	13.7313	0.460794
$889$	−25.2106	−0.845537
$890$	109.453	3.66886
$891$	6.02637	0.201891
$892$	−4.29176	−0.143699
$893$	−20.6019	−0.689415
$894$	−28.0341	−0.937601
$895$	−39.7477	−1.32862
$896$	−101.382	−3.38693
$897$	−7.54660	−0.251974
$898$	51.9301	1.73293
$899$	−54.5922	−1.82075
$900$	13.4937	0.449792
$901$	−0.112548	−0.00374953
$902$	11.8327	0.393985
$903$	−9.43202	−0.313878
$904$	−6.52149	−0.216902
$905$	29.7517	0.988981
$906$	−11.1294	−0.369749
$907$	9.22221	0.306219	0.153109	−	0.988209i	$-0.451071\pi$
$907$	9.22221	0.306219	0.153109	+	0.988209i	$0.451071\pi$
$908$	32.6904	1.08487
$909$	−10.6894	−0.354544
$910$	−34.3152	−1.13754
$911$	0.704119	0.0233285	0.0116643	−	0.999932i	$-0.496287\pi$
$911$	0.704119	0.0233285	0.0116643	+	0.999932i	$0.496287\pi$
$912$	−3.58196	−0.118611
$913$	49.8529	1.64989
$914$	82.1373	2.71686
$915$	−12.5836	−0.416002
$916$	−58.4049	−1.92975
$917$	−54.1960	−1.78971
$918$	3.36094	0.110927
$919$	−13.9088	−0.458809	−0.229404	−	0.973331i	$-0.573678\pi$
$919$	−13.9088	−0.458809	−0.229404	+	0.973331i	$0.573678\pi$
$920$	89.7962	2.96049
$921$	−14.6896	−0.484038
$922$	1.25219	0.0412386
$923$	1.53807	0.0506262
$924$	108.860	3.58122
$925$	12.3954	0.407559
$926$	39.8635	1.31000
$927$	−1.00000	−0.0328443
$928$	16.4221	0.539083
$929$	−8.92023	−0.292663	−0.146332	−	0.989236i	$-0.546747\pi$
$929$	−8.92023	−0.292663	−0.146332	+	0.989236i	$0.546747\pi$
$930$	−62.7341	−2.05713
$931$	26.7385	0.876319
$932$	−65.4085	−2.14253
$933$	13.1747	0.431320
$934$	80.7474	2.64214
$935$	24.9641	0.816414
$936$	4.04533	0.132226
$937$	26.8726	0.877889	0.438944	−	0.898514i	$-0.355353\pi$
$937$	26.8726	0.877889	0.438944	+	0.898514i	$0.355353\pi$
$938$	−16.2181	−0.529539
$939$	18.6901	0.609929
$940$	−141.511	−4.61558
$941$	−13.8437	−0.451292	−0.225646	−	0.974209i	$-0.572449\pi$
$941$	−13.8437	−0.451292	−0.225646	+	0.974209i	$0.572449\pi$
$942$	39.2978	1.28039
$943$	6.20908	0.202195
$944$	22.1482	0.720864
$945$	14.3792	0.467755
$946$	27.7479	0.902163
$947$	−24.7639	−0.804718	−0.402359	−	0.915482i	$-0.631810\pi$
$947$	−24.7639	−0.804718	−0.402359	+	0.915482i	$0.631810\pi$
$948$	58.5013	1.90003
$949$	12.7364	0.413443
$950$	−13.7896	−0.447395
$951$	10.9594	0.355384
$952$	27.8513	0.902664
$953$	39.7935	1.28904	0.644519	−	0.764588i	$-0.277058\pi$
$953$	39.7935	1.28904	0.644519	+	0.764588i	$0.277058\pi$
$954$	0.190714	0.00617460
$955$	26.3086	0.851327
$956$	51.3732	1.66153
$957$	−36.8118	−1.18996
$958$	−74.3745	−2.40293
$959$	8.12675	0.262426
$960$	32.1883	1.03887
$961$	48.8727	1.57654
$962$	8.10047	0.261170
$963$	−9.13282	−0.294301
$964$	−71.3420	−2.29777
$965$	71.7184	2.30870
$966$	88.0410	2.83267
$967$	−21.8765	−0.703501	−0.351751	−	0.936094i	$-0.614414\pi$
$967$	−21.8765	−0.703501	−0.351751	+	0.936094i	$0.614414\pi$
$968$	−102.416	−3.29178
$969$	−2.22847	−0.0715888
$970$	−75.5451	−2.42561
$971$	−18.2100	−0.584387	−0.292194	−	0.956359i	$-0.594385\pi$
$971$	−18.2100	−0.584387	−0.292194	+	0.956359i	$0.594385\pi$
$972$	−3.69513	−0.118521
$973$	3.44069	0.110303
$974$	92.7137	2.97074
$975$	3.65177	0.116950
$976$	9.68447	0.309992
$977$	34.0217	1.08845	0.544226	−	0.838939i	$-0.316823\pi$
$977$	34.0217	1.08845	0.544226	+	0.838939i	$0.316823\pi$
$978$	51.4198	1.64422
$979$	−93.9676	−3.00322
$980$	183.663	5.86689
$981$	−5.11237	−0.163226
$982$	23.7649	0.758368
$983$	41.0307	1.30868	0.654339	−	0.756202i	$-0.272947\pi$
$983$	41.0307	1.30868	0.654339	+	0.756202i	$0.272947\pi$
$984$	−3.32836	−0.106104
$985$	9.92923	0.316372
$986$	−20.5301	−0.653813
$987$	−63.6488	−2.02596
$988$	−5.84693	−0.186016
$989$	14.5604	0.462995
$990$	−42.3019	−1.34444
$991$	−45.2566	−1.43762	−0.718812	−	0.695204i	$-0.755314\pi$
$991$	−45.2566	−1.43762	−0.718812	+	0.695204i	$0.755314\pi$
$992$	−24.0269	−0.762854
$993$	−6.42322	−0.203835
$994$	−17.9436	−0.569137
$995$	−55.9192	−1.77276
$996$	−30.5678	−0.968578
$997$	21.1390	0.669479	0.334739	−	0.942311i	$-0.391352\pi$
$997$	21.1390	0.669479	0.334739	+	0.942311i	$0.391352\pi$
$998$	−39.9481	−1.26453
$999$	−3.39436	−0.107393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.3	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.38645 q^{2} -1.00000 q^{3} +3.69513 q^{4} +2.94139 q^{5} +2.38645 q^{6} -4.88857 q^{7} -4.04533 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38645 q^{2} -1.00000 q^{3} +3.69513 q^{4} +2.94139 q^{5} +2.38645 q^{6} -4.88857 q^{7} -4.04533 q^{8} +1.00000 q^{9} -7.01947 q^{10} +6.02637 q^{11} -3.69513 q^{12} -1.00000 q^{13} +11.6663 q^{14} -2.94139 q^{15} +2.26372 q^{16} +1.40834 q^{17} -2.38645 q^{18} +1.58234 q^{19} +10.8688 q^{20} +4.88857 q^{21} -14.3816 q^{22} -7.54660 q^{23} +4.04533 q^{24} +3.65177 q^{25} +2.38645 q^{26} -1.00000 q^{27} -18.0639 q^{28} +6.10846 q^{29} +7.01947 q^{30} -8.93715 q^{31} +2.68843 q^{32} -6.02637 q^{33} -3.36094 q^{34} -14.3792 q^{35} +3.69513 q^{36} +3.39436 q^{37} -3.77616 q^{38} +1.00000 q^{39} -11.8989 q^{40} -0.822765 q^{41} -11.6663 q^{42} -1.92940 q^{43} +22.2682 q^{44} +2.94139 q^{45} +18.0096 q^{46} -13.0199 q^{47} -2.26372 q^{48} +16.8981 q^{49} -8.71475 q^{50} -1.40834 q^{51} -3.69513 q^{52} -0.0799155 q^{53} +2.38645 q^{54} +17.7259 q^{55} +19.7759 q^{56} -1.58234 q^{57} -14.5775 q^{58} +9.78401 q^{59} -10.8688 q^{60} +4.27813 q^{61} +21.3280 q^{62} -4.88857 q^{63} -10.9432 q^{64} -2.94139 q^{65} +14.3816 q^{66} -1.39016 q^{67} +5.20401 q^{68} +7.54660 q^{69} +34.3152 q^{70} -1.53807 q^{71} -4.04533 q^{72} -12.7364 q^{73} -8.10047 q^{74} -3.65177 q^{75} +5.84693 q^{76} -29.4603 q^{77} -2.38645 q^{78} -15.8320 q^{79} +6.65847 q^{80} +1.00000 q^{81} +1.96349 q^{82} +8.27246 q^{83} +18.0639 q^{84} +4.14248 q^{85} +4.60442 q^{86} -6.10846 q^{87} -24.3787 q^{88} -15.5927 q^{89} -7.01947 q^{90} +4.88857 q^{91} -27.8857 q^{92} +8.93715 q^{93} +31.0713 q^{94} +4.65426 q^{95} -2.68843 q^{96} +10.7622 q^{97} -40.3265 q^{98} +6.02637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

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