LMFDB - Embedded newform 4017.2.a.l.1.12

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:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-0.772884 q^{2} +1.00000 q^{3} -1.40265 q^{4} -0.606956 q^{5} -0.772884 q^{6} +1.27278 q^{7} +2.62985 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.772884 q^{2} +1.00000 q^{3} -1.40265 q^{4} -0.606956 q^{5} -0.772884 q^{6} +1.27278 q^{7} +2.62985 q^{8} +1.00000 q^{9} +0.469107 q^{10} +4.00775 q^{11} -1.40265 q^{12} -1.00000 q^{13} -0.983715 q^{14} -0.606956 q^{15} +0.772728 q^{16} +3.13137 q^{17} -0.772884 q^{18} +4.09021 q^{19} +0.851347 q^{20} +1.27278 q^{21} -3.09753 q^{22} +3.48672 q^{23} +2.62985 q^{24} -4.63160 q^{25} +0.772884 q^{26} +1.00000 q^{27} -1.78527 q^{28} -3.95898 q^{29} +0.469107 q^{30} +9.68232 q^{31} -5.85694 q^{32} +4.00775 q^{33} -2.42019 q^{34} -0.772524 q^{35} -1.40265 q^{36} +1.53970 q^{37} -3.16126 q^{38} -1.00000 q^{39} -1.59621 q^{40} +4.48439 q^{41} -0.983715 q^{42} -6.59199 q^{43} -5.62148 q^{44} -0.606956 q^{45} -2.69483 q^{46} +6.73458 q^{47} +0.772728 q^{48} -5.38002 q^{49} +3.57969 q^{50} +3.13137 q^{51} +1.40265 q^{52} -4.30387 q^{53} -0.772884 q^{54} -2.43253 q^{55} +3.34724 q^{56} +4.09021 q^{57} +3.05983 q^{58} +6.98038 q^{59} +0.851347 q^{60} -3.41481 q^{61} -7.48331 q^{62} +1.27278 q^{63} +2.98128 q^{64} +0.606956 q^{65} -3.09753 q^{66} -3.32975 q^{67} -4.39222 q^{68} +3.48672 q^{69} +0.597072 q^{70} -8.68267 q^{71} +2.62985 q^{72} +6.09985 q^{73} -1.19001 q^{74} -4.63160 q^{75} -5.73713 q^{76} +5.10101 q^{77} +0.772884 q^{78} -0.457304 q^{79} -0.469012 q^{80} +1.00000 q^{81} -3.46592 q^{82} -13.6264 q^{83} -1.78527 q^{84} -1.90061 q^{85} +5.09484 q^{86} -3.95898 q^{87} +10.5398 q^{88} +1.35366 q^{89} +0.469107 q^{90} -1.27278 q^{91} -4.89065 q^{92} +9.68232 q^{93} -5.20505 q^{94} -2.48258 q^{95} -5.85694 q^{96} +14.7659 q^{97} +4.15813 q^{98} +4.00775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	−0.772884	−0.546512	−0.273256	−	0.961941i	$-0.588101\pi$
$2$	−0.772884	−0.546512	−0.273256	+	0.961941i	$0.588101\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.40265	−0.701325
$5$	−0.606956	−0.271439	−0.135720	−	0.990747i	$-0.543335\pi$
$5$	−0.606956	−0.271439	−0.135720	+	0.990747i	$0.543335\pi$
$6$	−0.772884	−0.315529
$7$	1.27278	0.481067	0.240534	−	0.970641i	$-0.422678\pi$
$7$	1.27278	0.481067	0.240534	+	0.970641i	$0.422678\pi$
$8$	2.62985	0.929794
$9$	1.00000	0.333333
$10$	0.469107	0.148345
$11$	4.00775	1.20838	0.604192	−	0.796839i	$-0.293496\pi$
$11$	4.00775	1.20838	0.604192	+	0.796839i	$0.293496\pi$
$12$	−1.40265	−0.404910
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.983715	−0.262909
$15$	−0.606956	−0.156715
$16$	0.772728	0.193182
$17$	3.13137	0.759470	0.379735	−	0.925095i	$-0.376015\pi$
$17$	3.13137	0.759470	0.379735	+	0.925095i	$0.376015\pi$
$18$	−0.772884	−0.182171
$19$	4.09021	0.938358	0.469179	−	0.883103i	$-0.344550\pi$
$19$	4.09021	0.938358	0.469179	+	0.883103i	$0.344550\pi$
$20$	0.851347	0.190367
$21$	1.27278	0.277744
$22$	−3.09753	−0.660395
$23$	3.48672	0.727032	0.363516	−	0.931588i	$-0.381576\pi$
$23$	3.48672	0.727032	0.363516	+	0.931588i	$0.381576\pi$
$24$	2.62985	0.536817
$25$	−4.63160	−0.926321
$26$	0.772884	0.151575
$27$	1.00000	0.192450
$28$	−1.78527	−0.337385
$29$	−3.95898	−0.735164	−0.367582	−	0.929991i	$-0.619814\pi$
$29$	−3.95898	−0.735164	−0.367582	+	0.929991i	$0.619814\pi$
$30$	0.469107	0.0856468
$31$	9.68232	1.73900	0.869498	−	0.493936i	$-0.164442\pi$
$31$	9.68232	1.73900	0.869498	+	0.493936i	$0.164442\pi$
$32$	−5.85694	−1.03537
$33$	4.00775	0.697660
$34$	−2.42019	−0.415059
$35$	−0.772524	−0.130580
$36$	−1.40265	−0.233775
$37$	1.53970	0.253126	0.126563	−	0.991959i	$-0.459605\pi$
$37$	1.53970	0.253126	0.126563	+	0.991959i	$0.459605\pi$
$38$	−3.16126	−0.512824
$39$	−1.00000	−0.160128
$40$	−1.59621	−0.252382
$41$	4.48439	0.700344	0.350172	−	0.936685i	$-0.386123\pi$
$41$	4.48439	0.700344	0.350172	+	0.936685i	$0.386123\pi$
$42$	−0.983715	−0.151791
$43$	−6.59199	−1.00527	−0.502634	−	0.864499i	$-0.667636\pi$
$43$	−6.59199	−1.00527	−0.502634	+	0.864499i	$0.667636\pi$
$44$	−5.62148	−0.847470
$45$	−0.606956	−0.0904797
$46$	−2.69483	−0.397331
$47$	6.73458	0.982339	0.491170	−	0.871064i	$-0.336570\pi$
$47$	6.73458	0.982339	0.491170	+	0.871064i	$0.336570\pi$
$48$	0.772728	0.111534
$49$	−5.38002	−0.768574
$50$	3.57969	0.506245
$51$	3.13137	0.438480
$52$	1.40265	0.194513
$53$	−4.30387	−0.591182	−0.295591	−	0.955315i	$-0.595517\pi$
$53$	−4.30387	−0.591182	−0.295591	+	0.955315i	$0.595517\pi$
$54$	−0.772884	−0.105176
$55$	−2.43253	−0.328002
$56$	3.34724	0.447293
$57$	4.09021	0.541761
$58$	3.05983	0.401776
$59$	6.98038	0.908769	0.454384	−	0.890806i	$-0.349859\pi$
$59$	6.98038	0.908769	0.454384	+	0.890806i	$0.349859\pi$
$60$	0.851347	0.109908
$61$	−3.41481	−0.437222	−0.218611	−	0.975812i	$-0.570153\pi$
$61$	−3.41481	−0.437222	−0.218611	+	0.975812i	$0.570153\pi$
$62$	−7.48331	−0.950382
$63$	1.27278	0.160356
$64$	2.98128	0.372660
$65$	0.606956	0.0752836
$66$	−3.09753	−0.381279
$67$	−3.32975	−0.406794	−0.203397	−	0.979096i	$-0.565198\pi$
$67$	−3.32975	−0.406794	−0.203397	+	0.979096i	$0.565198\pi$
$68$	−4.39222	−0.532635
$69$	3.48672	0.419752
$70$	0.597072	0.0713637
$71$	−8.68267	−1.03044	−0.515222	−	0.857057i	$-0.672291\pi$
$71$	−8.68267	−1.03044	−0.515222	+	0.857057i	$0.672291\pi$
$72$	2.62985	0.309931
$73$	6.09985	0.713934	0.356967	−	0.934117i	$-0.383811\pi$
$73$	6.09985	0.713934	0.356967	+	0.934117i	$0.383811\pi$
$74$	−1.19001	−0.138336
$75$	−4.63160	−0.534812
$76$	−5.73713	−0.658094
$77$	5.10101	0.581314
$78$	0.772884	0.0875119
$79$	−0.457304	−0.0514508	−0.0257254	−	0.999669i	$-0.508190\pi$
$79$	−0.457304	−0.0514508	−0.0257254	+	0.999669i	$0.508190\pi$
$80$	−0.469012	−0.0524372
$81$	1.00000	0.111111
$82$	−3.46592	−0.382746
$83$	−13.6264	−1.49569	−0.747844	−	0.663875i	$-0.768911\pi$
$83$	−13.6264	−1.49569	−0.747844	+	0.663875i	$0.768911\pi$
$84$	−1.78527	−0.194789
$85$	−1.90061	−0.206150
$86$	5.09484	0.549391
$87$	−3.95898	−0.424447
$88$	10.5398	1.12355
$89$	1.35366	0.143488	0.0717441	−	0.997423i	$-0.477144\pi$
$89$	1.35366	0.143488	0.0717441	+	0.997423i	$0.477144\pi$
$90$	0.469107	0.0494482
$91$	−1.27278	−0.133424
$92$	−4.89065	−0.509886
$93$	9.68232	1.00401
$94$	−5.20505	−0.536860
$95$	−2.48258	−0.254707
$96$	−5.85694	−0.597771
$97$	14.7659	1.49925	0.749627	−	0.661860i	$-0.230233\pi$
$97$	14.7659	1.49925	0.749627	+	0.661860i	$0.230233\pi$
$98$	4.15813	0.420035
$99$	4.00775	0.402794
$100$	6.49652	0.649652
$101$	16.4197	1.63382	0.816909	−	0.576767i	$-0.195686\pi$
$101$	16.4197	1.63382	0.816909	+	0.576767i	$0.195686\pi$
$102$	−2.42019	−0.239634
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.62985	−0.257878
$105$	−0.772524	−0.0753907
$106$	3.32639	0.323088
$107$	−17.3459	−1.67689	−0.838447	−	0.544983i	$-0.816536\pi$
$107$	−17.3459	−1.67689	−0.838447	+	0.544983i	$0.816536\pi$
$108$	−1.40265	−0.134970
$109$	1.48152	0.141904	0.0709520	−	0.997480i	$-0.477396\pi$
$109$	1.48152	0.141904	0.0709520	+	0.997480i	$0.477396\pi$
$110$	1.88006	0.179257
$111$	1.53970	0.146142
$112$	0.983517	0.0929336
$113$	17.2511	1.62285	0.811425	−	0.584456i	$-0.198692\pi$
$113$	17.2511	1.62285	0.811425	+	0.584456i	$0.198692\pi$
$114$	−3.16126	−0.296079
$115$	−2.11629	−0.197345
$116$	5.55306	0.515589
$117$	−1.00000	−0.0924500
$118$	−5.39503	−0.496653
$119$	3.98556	0.365356
$120$	−1.59621	−0.145713
$121$	5.06209	0.460190
$122$	2.63926	0.238947
$123$	4.48439	0.404344
$124$	−13.5809	−1.21960
$125$	5.84596	0.522879
$126$	−0.983715	−0.0876363
$127$	15.8777	1.40891	0.704457	−	0.709746i	$-0.251190\pi$
$127$	15.8777	1.40891	0.704457	+	0.709746i	$0.251190\pi$
$128$	9.40969	0.831707
$129$	−6.59199	−0.580392
$130$	−0.469107	−0.0411434
$131$	−15.9803	−1.39621	−0.698103	−	0.715998i	$-0.745972\pi$
$131$	−15.9803	−1.39621	−0.698103	+	0.715998i	$0.745972\pi$
$132$	−5.62148	−0.489287
$133$	5.20595	0.451414
$134$	2.57351	0.222318
$135$	−0.606956	−0.0522385
$136$	8.23506	0.706150
$137$	1.46088	0.124811	0.0624055	−	0.998051i	$-0.480123\pi$
$137$	1.46088	0.124811	0.0624055	+	0.998051i	$0.480123\pi$
$138$	−2.69483	−0.229399
$139$	−15.5178	−1.31621	−0.658103	−	0.752928i	$-0.728641\pi$
$139$	−15.5178	−1.31621	−0.658103	+	0.752928i	$0.728641\pi$
$140$	1.08358	0.0915794
$141$	6.73458	0.567154
$142$	6.71070	0.563149
$143$	−4.00775	−0.335145
$144$	0.772728	0.0643940
$145$	2.40293	0.199552
$146$	−4.71448	−0.390173
$147$	−5.38002	−0.443736
$148$	−2.15967	−0.177523
$149$	−13.5258	−1.10808	−0.554040	−	0.832490i	$-0.686915\pi$
$149$	−13.5258	−1.10808	−0.554040	+	0.832490i	$0.686915\pi$
$150$	3.57969	0.292281
$151$	−13.8082	−1.12370	−0.561850	−	0.827239i	$-0.689910\pi$
$151$	−13.8082	−1.12370	−0.561850	+	0.827239i	$0.689910\pi$
$152$	10.7567	0.872480
$153$	3.13137	0.253157
$154$	−3.94249	−0.317695
$155$	−5.87674	−0.472031
$156$	1.40265	0.112302
$157$	16.0167	1.27827	0.639136	−	0.769094i	$-0.279292\pi$
$157$	16.0167	1.27827	0.639136	+	0.769094i	$0.279292\pi$
$158$	0.353443	0.0281184
$159$	−4.30387	−0.341319
$160$	3.55490	0.281040
$161$	4.43785	0.349751
$162$	−0.772884	−0.0607235
$163$	−3.90157	−0.305594	−0.152797	−	0.988258i	$-0.548828\pi$
$163$	−3.90157	−0.305594	−0.152797	+	0.988258i	$0.548828\pi$
$164$	−6.29003	−0.491169
$165$	−2.43253	−0.189372
$166$	10.5316	0.817411
$167$	−1.87892	−0.145395	−0.0726975	−	0.997354i	$-0.523161\pi$
$167$	−1.87892	−0.145395	−0.0726975	+	0.997354i	$0.523161\pi$
$168$	3.34724	0.258245
$169$	1.00000	0.0769231
$170$	1.46895	0.112663
$171$	4.09021	0.312786
$172$	9.24625	0.705020
$173$	−2.34384	−0.178199	−0.0890996	−	0.996023i	$-0.528399\pi$
$173$	−2.34384	−0.178199	−0.0890996	+	0.996023i	$0.528399\pi$
$174$	3.05983	0.231965
$175$	−5.89504	−0.445623
$176$	3.09691	0.233438
$177$	6.98038	0.524678
$178$	−1.04623	−0.0784179
$179$	6.24793	0.466992	0.233496	−	0.972358i	$-0.424983\pi$
$179$	6.24793	0.466992	0.233496	+	0.972358i	$0.424983\pi$
$180$	0.851347	0.0634557
$181$	−3.09258	−0.229869	−0.114935	−	0.993373i	$-0.536666\pi$
$181$	−3.09258	−0.229869	−0.114935	+	0.993373i	$0.536666\pi$
$182$	0.983715	0.0729178
$183$	−3.41481	−0.252430
$184$	9.16957	0.675990
$185$	−0.934533	−0.0687082
$186$	−7.48331	−0.548703
$187$	12.5498	0.917730
$188$	−9.44626	−0.688939
$189$	1.27278	0.0925815
$190$	1.91874	0.139200
$191$	5.38145	0.389388	0.194694	−	0.980864i	$-0.437629\pi$
$191$	5.38145	0.389388	0.194694	+	0.980864i	$0.437629\pi$
$192$	2.98128	0.215155
$193$	23.2759	1.67543	0.837717	−	0.546105i	$-0.183890\pi$
$193$	23.2759	1.67543	0.837717	+	0.546105i	$0.183890\pi$
$194$	−11.4124	−0.819360
$195$	0.606956	0.0434650
$196$	7.54629	0.539020
$197$	3.40753	0.242777	0.121388	−	0.992605i	$-0.461265\pi$
$197$	3.40753	0.242777	0.121388	+	0.992605i	$0.461265\pi$
$198$	−3.09753	−0.220132
$199$	23.9335	1.69660	0.848302	−	0.529512i	$-0.177625\pi$
$199$	23.9335	1.69660	0.848302	+	0.529512i	$0.177625\pi$
$200$	−12.1804	−0.861287
$201$	−3.32975	−0.234863
$202$	−12.6905	−0.892900
$203$	−5.03893	−0.353663
$204$	−4.39222	−0.307517
$205$	−2.72183	−0.190101
$206$	0.772884	0.0538494
$207$	3.48672	0.242344
$208$	−0.772728	−0.0535791
$209$	16.3925	1.13390
$210$	0.597072	0.0412019
$211$	13.5613	0.933598	0.466799	−	0.884364i	$-0.345407\pi$
$211$	13.5613	0.933598	0.466799	+	0.884364i	$0.345407\pi$
$212$	6.03683	0.414611
$213$	−8.68267	−0.594927
$214$	13.4064	0.916442
$215$	4.00105	0.272869
$216$	2.62985	0.178939
$217$	12.3235	0.836574
$218$	−1.14504	−0.0775522
$219$	6.09985	0.412190
$220$	3.41199	0.230036
$221$	−3.13137	−0.210639
$222$	−1.19001	−0.0798684
$223$	27.2976	1.82798	0.913991	−	0.405736i	$-0.132985\pi$
$223$	27.2976	1.82798	0.913991	+	0.405736i	$0.132985\pi$
$224$	−7.45462	−0.498083
$225$	−4.63160	−0.308774
$226$	−13.3331	−0.886907
$227$	3.00205	0.199253	0.0996267	−	0.995025i	$-0.468235\pi$
$227$	3.00205	0.199253	0.0996267	+	0.995025i	$0.468235\pi$
$228$	−5.73713	−0.379951
$229$	12.4340	0.821665	0.410832	−	0.911711i	$-0.365238\pi$
$229$	12.4340	0.821665	0.410832	+	0.911711i	$0.365238\pi$
$230$	1.63565	0.107851
$231$	5.10101	0.335622
$232$	−10.4115	−0.683551
$233$	6.39552	0.418985	0.209492	−	0.977810i	$-0.432819\pi$
$233$	6.39552	0.418985	0.209492	+	0.977810i	$0.432819\pi$
$234$	0.772884	0.0505250
$235$	−4.08759	−0.266645
$236$	−9.79104	−0.637342
$237$	−0.457304	−0.0297051
$238$	−3.08038	−0.199671
$239$	−16.1260	−1.04310	−0.521552	−	0.853220i	$-0.674647\pi$
$239$	−16.1260	−1.04310	−0.521552	+	0.853220i	$0.674647\pi$
$240$	−0.469012	−0.0302746
$241$	28.8301	1.85711	0.928554	−	0.371197i	$-0.121053\pi$
$241$	28.8301	1.85711	0.928554	+	0.371197i	$0.121053\pi$
$242$	−3.91241	−0.251499
$243$	1.00000	0.0641500
$244$	4.78979	0.306635
$245$	3.26544	0.208621
$246$	−3.46592	−0.220979
$247$	−4.09021	−0.260254
$248$	25.4631	1.61691
$249$	−13.6264	−0.863536
$250$	−4.51825	−0.285759
$251$	28.4113	1.79330	0.896651	−	0.442738i	$-0.145993\pi$
$251$	28.4113	1.79330	0.896651	+	0.442738i	$0.145993\pi$
$252$	−1.78527	−0.112462
$253$	13.9739	0.878533
$254$	−12.2716	−0.769988
$255$	−1.90061	−0.119021
$256$	−13.2352	−0.827197
$257$	−9.02812	−0.563159	−0.281579	−	0.959538i	$-0.590858\pi$
$257$	−9.02812	−0.563159	−0.281579	+	0.959538i	$0.590858\pi$
$258$	5.09484	0.317191
$259$	1.95971	0.121771
$260$	−0.851347	−0.0527983
$261$	−3.95898	−0.245055
$262$	12.3509	0.763042
$263$	−7.30490	−0.450439	−0.225220	−	0.974308i	$-0.572310\pi$
$263$	−7.30490	−0.450439	−0.225220	+	0.974308i	$0.572310\pi$
$264$	10.5398	0.648680
$265$	2.61226	0.160470
$266$	−4.02360	−0.246703
$267$	1.35366	0.0828429
$268$	4.67048	0.285295
$269$	−0.804006	−0.0490211	−0.0245106	−	0.999700i	$-0.507803\pi$
$269$	−0.804006	−0.0490211	−0.0245106	+	0.999700i	$0.507803\pi$
$270$	0.469107	0.0285489
$271$	8.14992	0.495072	0.247536	−	0.968879i	$-0.420379\pi$
$271$	8.14992	0.495072	0.247536	+	0.968879i	$0.420379\pi$
$272$	2.41970	0.146716
$273$	−1.27278	−0.0770324
$274$	−1.12909	−0.0682107
$275$	−18.5623	−1.11935
$276$	−4.89065	−0.294383
$277$	−11.3518	−0.682065	−0.341033	−	0.940051i	$-0.610777\pi$
$277$	−11.3518	−0.682065	−0.341033	+	0.940051i	$0.610777\pi$
$278$	11.9935	0.719321
$279$	9.68232	0.579665
$280$	−2.03163	−0.121413
$281$	−8.72177	−0.520297	−0.260149	−	0.965569i	$-0.583772\pi$
$281$	−8.72177	−0.520297	−0.260149	+	0.965569i	$0.583772\pi$
$282$	−5.20505	−0.309956
$283$	1.08021	0.0642117	0.0321058	−	0.999484i	$-0.489779\pi$
$283$	1.08021	0.0642117	0.0321058	+	0.999484i	$0.489779\pi$
$284$	12.1788	0.722676
$285$	−2.48258	−0.147055
$286$	3.09753	0.183161
$287$	5.70767	0.336913
$288$	−5.85694	−0.345123
$289$	−7.19450	−0.423206
$290$	−1.85718	−0.109058
$291$	14.7659	0.865595
$292$	−8.55596	−0.500700
$293$	−14.7704	−0.862896	−0.431448	−	0.902138i	$-0.641997\pi$
$293$	−14.7704	−0.862896	−0.431448	+	0.902138i	$0.641997\pi$
$294$	4.15813	0.242507
$295$	−4.23679	−0.246675
$296$	4.04920	0.235355
$297$	4.00775	0.232553
$298$	10.4539	0.605579
$299$	−3.48672	−0.201642
$300$	6.49652	0.375077
$301$	−8.39018	−0.483602
$302$	10.6722	0.614115
$303$	16.4197	0.943285
$304$	3.16062	0.181274
$305$	2.07264	0.118679
$306$	−2.42019	−0.138353
$307$	25.5416	1.45773	0.728867	−	0.684655i	$-0.240047\pi$
$307$	25.5416	1.45773	0.728867	+	0.684655i	$0.240047\pi$
$308$	−7.15493	−0.407690
$309$	−1.00000	−0.0568880
$310$	4.54204	0.257971
$311$	7.22994	0.409972	0.204986	−	0.978765i	$-0.434285\pi$
$311$	7.22994	0.409972	0.204986	+	0.978765i	$0.434285\pi$
$312$	−2.62985	−0.148886
$313$	−5.83718	−0.329937	−0.164969	−	0.986299i	$-0.552752\pi$
$313$	−5.83718	−0.329937	−0.164969	+	0.986299i	$0.552752\pi$
$314$	−12.3791	−0.698590
$315$	−0.772524	−0.0435268
$316$	0.641438	0.0360837
$317$	−14.6189	−0.821081	−0.410540	−	0.911842i	$-0.634660\pi$
$317$	−14.6189	−0.821081	−0.410540	+	0.911842i	$0.634660\pi$
$318$	3.32639	0.186535
$319$	−15.8666	−0.888360
$320$	−1.80950	−0.101154
$321$	−17.3459	−0.968156
$322$	−3.42994	−0.191143
$323$	12.8080	0.712655
$324$	−1.40265	−0.0779250
$325$	4.63160	0.256915
$326$	3.01546	0.167011
$327$	1.48152	0.0819284
$328$	11.7933	0.651176
$329$	8.57167	0.472571
$330$	1.88006	0.103494
$331$	11.5853	0.636786	0.318393	−	0.947959i	$-0.396857\pi$
$331$	11.5853	0.636786	0.318393	+	0.947959i	$0.396857\pi$
$332$	19.1130	1.04896
$333$	1.53970	0.0843752
$334$	1.45218	0.0794600
$335$	2.02102	0.110420
$336$	0.983517	0.0536552
$337$	7.79456	0.424597	0.212298	−	0.977205i	$-0.431905\pi$
$337$	7.79456	0.424597	0.212298	+	0.977205i	$0.431905\pi$
$338$	−0.772884	−0.0420393
$339$	17.2511	0.936953
$340$	2.66589	0.144578
$341$	38.8044	2.10137
$342$	−3.16126	−0.170941
$343$	−15.7571	−0.850803
$344$	−17.3360	−0.934693
$345$	−2.11629	−0.113937
$346$	1.81152	0.0973879
$347$	−3.60199	−0.193365	−0.0966824	−	0.995315i	$-0.530823\pi$
$347$	−3.60199	−0.193365	−0.0966824	+	0.995315i	$0.530823\pi$
$348$	5.55306	0.297675
$349$	−5.86737	−0.314073	−0.157037	−	0.987593i	$-0.550194\pi$
$349$	−5.86737	−0.314073	−0.157037	+	0.987593i	$0.550194\pi$
$350$	4.55618	0.243538
$351$	−1.00000	−0.0533761
$352$	−23.4732	−1.25112
$353$	−10.5922	−0.563765	−0.281883	−	0.959449i	$-0.590959\pi$
$353$	−10.5922	−0.563765	−0.281883	+	0.959449i	$0.590959\pi$
$354$	−5.39503	−0.286742
$355$	5.27000	0.279703
$356$	−1.89872	−0.100632
$357$	3.98556	0.210938
$358$	−4.82892	−0.255217
$359$	−9.70644	−0.512286	−0.256143	−	0.966639i	$-0.582452\pi$
$359$	−9.70644	−0.512286	−0.256143	+	0.966639i	$0.582452\pi$
$360$	−1.59621	−0.0841274
$361$	−2.27020	−0.119484
$362$	2.39020	0.125626
$363$	5.06209	0.265691
$364$	1.78527	0.0935737
$365$	−3.70234	−0.193789
$366$	2.63926	0.137956
$367$	−12.6410	−0.659853	−0.329927	−	0.944007i	$-0.607024\pi$
$367$	−12.6410	−0.659853	−0.329927	+	0.944007i	$0.607024\pi$
$368$	2.69429	0.140450
$369$	4.48439	0.233448
$370$	0.722285	0.0375498
$371$	−5.47790	−0.284399
$372$	−13.5809	−0.704137
$373$	−12.0481	−0.623827	−0.311913	−	0.950111i	$-0.600970\pi$
$373$	−12.0481	−0.623827	−0.311913	+	0.950111i	$0.600970\pi$
$374$	−9.69952	−0.501550
$375$	5.84596	0.301884
$376$	17.7110	0.913373
$377$	3.95898	0.203898
$378$	−0.983715	−0.0505968
$379$	−16.6903	−0.857326	−0.428663	−	0.903465i	$-0.641015\pi$
$379$	−16.6903	−0.857326	−0.428663	+	0.903465i	$0.641015\pi$
$380$	3.48219	0.178632
$381$	15.8777	0.813437
$382$	−4.15924	−0.212805
$383$	5.34938	0.273341	0.136670	−	0.990617i	$-0.456360\pi$
$383$	5.34938	0.273341	0.136670	+	0.990617i	$0.456360\pi$
$384$	9.40969	0.480186
$385$	−3.09609	−0.157791
$386$	−17.9895	−0.915644
$387$	−6.59199	−0.335090
$388$	−20.7115	−1.05146
$389$	15.7926	0.800715	0.400357	−	0.916359i	$-0.368886\pi$
$389$	15.7926	0.800715	0.400357	+	0.916359i	$0.368886\pi$
$390$	−0.469107	−0.0237541
$391$	10.9182	0.552159
$392$	−14.1487	−0.714615
$393$	−15.9803	−0.806099
$394$	−2.63363	−0.132680
$395$	0.277564	0.0139657
$396$	−5.62148	−0.282490
$397$	39.1271	1.96374	0.981868	−	0.189568i	$-0.0607086\pi$
$397$	39.1271	1.96374	0.981868	+	0.189568i	$0.0607086\pi$
$398$	−18.4979	−0.927214
$399$	5.20595	0.260624
$400$	−3.57897	−0.178949
$401$	−14.1208	−0.705160	−0.352580	−	0.935782i	$-0.614696\pi$
$401$	−14.1208	−0.705160	−0.352580	+	0.935782i	$0.614696\pi$
$402$	2.57351	0.128355
$403$	−9.68232	−0.482311
$404$	−23.0310	−1.14584
$405$	−0.606956	−0.0301599
$406$	3.89451	0.193281
$407$	6.17075	0.305873
$408$	8.23506	0.407696
$409$	8.07670	0.399367	0.199683	−	0.979860i	$-0.436009\pi$
$409$	8.07670	0.399367	0.199683	+	0.979860i	$0.436009\pi$
$410$	2.10366	0.103892
$411$	1.46088	0.0720597
$412$	1.40265	0.0691036
$413$	8.88453	0.437179
$414$	−2.69483	−0.132444
$415$	8.27061	0.405988
$416$	5.85694	0.287160
$417$	−15.5178	−0.759912
$418$	−12.6695	−0.619687
$419$	−28.5542	−1.39496	−0.697481	−	0.716603i	$-0.745696\pi$
$419$	−28.5542	−1.39496	−0.697481	+	0.716603i	$0.745696\pi$
$420$	1.08358	0.0528734
$421$	−12.1957	−0.594382	−0.297191	−	0.954818i	$-0.596050\pi$
$421$	−12.1957	−0.594382	−0.297191	+	0.954818i	$0.596050\pi$
$422$	−10.4813	−0.510222
$423$	6.73458	0.327446
$424$	−11.3186	−0.549678
$425$	−14.5033	−0.703513
$426$	6.71070	0.325134
$427$	−4.34632	−0.210333
$428$	24.3303	1.17605
$429$	−4.00775	−0.193496
$430$	−3.09235	−0.149126
$431$	25.7108	1.23844	0.619222	−	0.785216i	$-0.287448\pi$
$431$	25.7108	1.23844	0.619222	+	0.785216i	$0.287448\pi$
$432$	0.772728	0.0371779
$433$	11.7502	0.564678	0.282339	−	0.959315i	$-0.408890\pi$
$433$	11.7502	0.564678	0.282339	+	0.959315i	$0.408890\pi$
$434$	−9.52464	−0.457198
$435$	2.40293	0.115212
$436$	−2.07806	−0.0995209
$437$	14.2614	0.682216
$438$	−4.71448	−0.225266
$439$	3.54374	0.169133	0.0845667	−	0.996418i	$-0.473049\pi$
$439$	3.54374	0.169133	0.0845667	+	0.996418i	$0.473049\pi$
$440$	−6.39720	−0.304975
$441$	−5.38002	−0.256191
$442$	2.42019	0.115117
$443$	−33.0772	−1.57154	−0.785772	−	0.618516i	$-0.787734\pi$
$443$	−33.0772	−1.57154	−0.785772	+	0.618516i	$0.787734\pi$
$444$	−2.15967	−0.102493
$445$	−0.821615	−0.0389483
$446$	−21.0979	−0.999013
$447$	−13.5258	−0.639751
$448$	3.79452	0.179274
$449$	7.49986	0.353940	0.176970	−	0.984216i	$-0.443370\pi$
$449$	7.49986	0.353940	0.176970	+	0.984216i	$0.443370\pi$
$450$	3.57969	0.168748
$451$	17.9723	0.846285
$452$	−24.1973	−1.13815
$453$	−13.8082	−0.648768
$454$	−2.32024	−0.108894
$455$	0.772524	0.0362165
$456$	10.7567	0.503726
$457$	−12.5135	−0.585357	−0.292679	−	0.956211i	$-0.594547\pi$
$457$	−12.5135	−0.585357	−0.292679	+	0.956211i	$0.594547\pi$
$458$	−9.61007	−0.449049
$459$	3.13137	0.146160
$460$	2.96841	0.138403
$461$	−0.788566	−0.0367272	−0.0183636	−	0.999831i	$-0.505846\pi$
$461$	−0.788566	−0.0367272	−0.0183636	+	0.999831i	$0.505846\pi$
$462$	−3.94249	−0.183421
$463$	−18.0010	−0.836579	−0.418289	−	0.908314i	$-0.637370\pi$
$463$	−18.0010	−0.836579	−0.418289	+	0.908314i	$0.637370\pi$
$464$	−3.05922	−0.142021
$465$	−5.87674	−0.272527
$466$	−4.94300	−0.228980
$467$	19.6407	0.908865	0.454433	−	0.890781i	$-0.349842\pi$
$467$	19.6407	0.908865	0.454433	+	0.890781i	$0.349842\pi$
$468$	1.40265	0.0648375
$469$	−4.23806	−0.195695
$470$	3.15924	0.145725
$471$	16.0167	0.738011
$472$	18.3574	0.844967
$473$	−26.4191	−1.21475
$474$	0.353443	0.0162342
$475$	−18.9442	−0.869221
$476$	−5.59035	−0.256233
$477$	−4.30387	−0.197061
$478$	12.4635	0.570068
$479$	−4.40203	−0.201134	−0.100567	−	0.994930i	$-0.532066\pi$
$479$	−4.40203	−0.201134	−0.100567	+	0.994930i	$0.532066\pi$
$480$	3.55490	0.162258
$481$	−1.53970	−0.0702044
$482$	−22.2823	−1.01493
$483$	4.43785	0.201929
$484$	−7.10034	−0.322743
$485$	−8.96228	−0.406956
$486$	−0.772884	−0.0350587
$487$	−0.226889	−0.0102813	−0.00514067	−	0.999987i	$-0.501636\pi$
$487$	−0.226889	−0.0102813	−0.00514067	+	0.999987i	$0.501636\pi$
$488$	−8.98046	−0.406526
$489$	−3.90157	−0.176435
$490$	−2.52380	−0.114014
$491$	−22.2930	−1.00607	−0.503034	−	0.864267i	$-0.667783\pi$
$491$	−22.2930	−1.00607	−0.503034	+	0.864267i	$0.667783\pi$
$492$	−6.29003	−0.283577
$493$	−12.3970	−0.558335
$494$	3.16126	0.142232
$495$	−2.43253	−0.109334
$496$	7.48181	0.335943
$497$	−11.0512	−0.495713
$498$	10.5316	0.471932
$499$	11.2834	0.505113	0.252557	−	0.967582i	$-0.418729\pi$
$499$	11.2834	0.505113	0.252557	+	0.967582i	$0.418729\pi$
$500$	−8.19984	−0.366708
$501$	−1.87892	−0.0839438
$502$	−21.9586	−0.980060
$503$	31.1216	1.38764	0.693821	−	0.720148i	$-0.255926\pi$
$503$	31.1216	1.38764	0.693821	+	0.720148i	$0.255926\pi$
$504$	3.34724	0.149098
$505$	−9.96602	−0.443482
$506$	−10.8002	−0.480129
$507$	1.00000	0.0444116
$508$	−22.2708	−0.988107
$509$	−9.85761	−0.436931	−0.218466	−	0.975845i	$-0.570105\pi$
$509$	−9.85761	−0.436931	−0.218466	+	0.975845i	$0.570105\pi$
$510$	1.46895	0.0650461
$511$	7.76380	0.343450
$512$	−8.59015	−0.379634
$513$	4.09021	0.180587
$514$	6.97769	0.307773
$515$	0.606956	0.0267457
$516$	9.24625	0.407044
$517$	26.9905	1.18704
$518$	−1.51463	−0.0665490
$519$	−2.34384	−0.102883
$520$	1.59621	0.0699983
$521$	−13.3832	−0.586329	−0.293165	−	0.956062i	$-0.594708\pi$
$521$	−13.3832	−0.586329	−0.293165	+	0.956062i	$0.594708\pi$
$522$	3.05983	0.133925
$523$	−7.51607	−0.328655	−0.164327	−	0.986406i	$-0.552545\pi$
$523$	−7.51607	−0.328655	−0.164327	+	0.986406i	$0.552545\pi$
$524$	22.4148	0.979194
$525$	−5.89504	−0.257280
$526$	5.64584	0.246170
$527$	30.3190	1.32071
$528$	3.09691	0.134776
$529$	−10.8428	−0.471424
$530$	−2.01898	−0.0876987
$531$	6.98038	0.302923
$532$	−7.30213	−0.316588
$533$	−4.48439	−0.194241
$534$	−1.04623	−0.0452746
$535$	10.5282	0.455175
$536$	−8.75677	−0.378235
$537$	6.24793	0.269618
$538$	0.621403	0.0267906
$539$	−21.5618	−0.928732
$540$	0.851347	0.0366362
$541$	39.2350	1.68685	0.843423	−	0.537251i	$-0.180537\pi$
$541$	39.2350	1.68685	0.843423	+	0.537251i	$0.180537\pi$
$542$	−6.29894	−0.270563
$543$	−3.09258	−0.132715
$544$	−18.3403	−0.786332
$545$	−0.899219	−0.0385183
$546$	0.983715	0.0420991
$547$	23.7981	1.01753	0.508766	−	0.860905i	$-0.330102\pi$
$547$	23.7981	1.01753	0.508766	+	0.860905i	$0.330102\pi$
$548$	−2.04910	−0.0875331
$549$	−3.41481	−0.145741
$550$	14.3465	0.611738
$551$	−16.1931	−0.689847
$552$	9.16957	0.390283
$553$	−0.582050	−0.0247513
$554$	8.77364	0.372756
$555$	−0.934533	−0.0396687
$556$	21.7661	0.923088
$557$	−14.9787	−0.634670	−0.317335	−	0.948314i	$-0.602788\pi$
$557$	−14.9787	−0.634670	−0.317335	+	0.948314i	$0.602788\pi$
$558$	−7.48331	−0.316794
$559$	6.59199	0.278811
$560$	−0.596952	−0.0252258
$561$	12.5498	0.529852
$562$	6.74092	0.284348
$563$	−11.0921	−0.467475	−0.233738	−	0.972300i	$-0.575096\pi$
$563$	−11.0921	−0.467475	−0.233738	+	0.972300i	$0.575096\pi$
$564$	−9.44626	−0.397759
$565$	−10.4707	−0.440505
$566$	−0.834875	−0.0350924
$567$	1.27278	0.0534519
$568$	−22.8342	−0.958100
$569$	5.98715	0.250994	0.125497	−	0.992094i	$-0.459947\pi$
$569$	5.98715	0.250994	0.125497	+	0.992094i	$0.459947\pi$
$570$	1.91874	0.0803673
$571$	−4.25895	−0.178232	−0.0891158	−	0.996021i	$-0.528404\pi$
$571$	−4.25895	−0.178232	−0.0891158	+	0.996021i	$0.528404\pi$
$572$	5.62148	0.235046
$573$	5.38145	0.224813
$574$	−4.41136	−0.184127
$575$	−16.1491	−0.673465
$576$	2.98128	0.124220
$577$	35.9720	1.49753	0.748766	−	0.662834i	$-0.230647\pi$
$577$	35.9720	1.49753	0.748766	+	0.662834i	$0.230647\pi$
$578$	5.56051	0.231287
$579$	23.2759	0.967312
$580$	−3.37047	−0.139951
$581$	−17.3434	−0.719527
$582$	−11.4124	−0.473058
$583$	−17.2489	−0.714375
$584$	16.0417	0.663811
$585$	0.606956	0.0250945
$586$	11.4158	0.471583
$587$	16.1436	0.666320	0.333160	−	0.942870i	$-0.391885\pi$
$587$	16.1436	0.666320	0.333160	+	0.942870i	$0.391885\pi$
$588$	7.54629	0.311204
$589$	39.6027	1.63180
$590$	3.27454	0.134811
$591$	3.40753	0.140167
$592$	1.18977	0.0488994
$593$	−8.27410	−0.339777	−0.169888	−	0.985463i	$-0.554341\pi$
$593$	−8.27410	−0.339777	−0.169888	+	0.985463i	$0.554341\pi$
$594$	−3.09753	−0.127093
$595$	−2.41906	−0.0991719
$596$	18.9720	0.777125
$597$	23.9335	0.979535
$598$	2.69483	0.110200
$599$	2.18933	0.0894535	0.0447268	−	0.998999i	$-0.485758\pi$
$599$	2.18933	0.0894535	0.0447268	+	0.998999i	$0.485758\pi$
$600$	−12.1804	−0.497265
$601$	−24.1627	−0.985618	−0.492809	−	0.870138i	$-0.664030\pi$
$601$	−24.1627	−0.985618	−0.492809	+	0.870138i	$0.664030\pi$
$602$	6.48464	0.264294
$603$	−3.32975	−0.135598
$604$	19.3681	0.788079
$605$	−3.07247	−0.124914
$606$	−12.6905	−0.515516
$607$	24.3725	0.989249	0.494624	−	0.869107i	$-0.335306\pi$
$607$	24.3725	0.989249	0.494624	+	0.869107i	$0.335306\pi$
$608$	−23.9561	−0.971548
$609$	−5.03893	−0.204188
$610$	−1.60191	−0.0648595
$611$	−6.73458	−0.272452
$612$	−4.39222	−0.177545
$613$	9.53118	0.384961	0.192480	−	0.981301i	$-0.438347\pi$
$613$	9.53118	0.384961	0.192480	+	0.981301i	$0.438347\pi$
$614$	−19.7407	−0.796668
$615$	−2.72183	−0.109755
$616$	13.4149	0.540502
$617$	35.2156	1.41773	0.708863	−	0.705346i	$-0.249208\pi$
$617$	35.2156	1.41773	0.708863	+	0.705346i	$0.249208\pi$
$618$	0.772884	0.0310900
$619$	−33.2229	−1.33534	−0.667671	−	0.744457i	$-0.732708\pi$
$619$	−33.2229	−1.33534	−0.667671	+	0.744457i	$0.732708\pi$
$620$	8.24302	0.331048
$621$	3.48672	0.139917
$622$	−5.58791	−0.224055
$623$	1.72292	0.0690275
$624$	−0.772728	−0.0309339
$625$	19.6098	0.784391
$626$	4.51147	0.180314
$627$	16.3925	0.654655
$628$	−22.4658	−0.896484
$629$	4.82139	0.192241
$630$	0.597072	0.0237879
$631$	28.8587	1.14885	0.574424	−	0.818558i	$-0.305226\pi$
$631$	28.8587	1.14885	0.574424	+	0.818558i	$0.305226\pi$
$632$	−1.20264	−0.0478386
$633$	13.5613	0.539013
$634$	11.2987	0.448730
$635$	−9.63704	−0.382434
$636$	6.03683	0.239376
$637$	5.38002	0.213164
$638$	12.2631	0.485499
$639$	−8.68267	−0.343481
$640$	−5.71127	−0.225758
$641$	−30.9902	−1.22404	−0.612020	−	0.790842i	$-0.709643\pi$
$641$	−30.9902	−1.22404	−0.612020	+	0.790842i	$0.709643\pi$
$642$	13.4064	0.529108
$643$	−22.4138	−0.883914	−0.441957	−	0.897036i	$-0.645716\pi$
$643$	−22.4138	−0.883914	−0.441957	+	0.897036i	$0.645716\pi$
$644$	−6.22475	−0.245289
$645$	4.00105	0.157541
$646$	−9.89908	−0.389474
$647$	−11.0593	−0.434788	−0.217394	−	0.976084i	$-0.569756\pi$
$647$	−11.0593	−0.434788	−0.217394	+	0.976084i	$0.569756\pi$
$648$	2.62985	0.103310
$649$	27.9757	1.09814
$650$	−3.57969	−0.140407
$651$	12.3235	0.482996
$652$	5.47254	0.214321
$653$	4.40547	0.172399	0.0861997	−	0.996278i	$-0.472528\pi$
$653$	4.40547	0.172399	0.0861997	+	0.996278i	$0.472528\pi$
$654$	−1.14504	−0.0447748
$655$	9.69934	0.378985
$656$	3.46522	0.135294
$657$	6.09985	0.237978
$658$	−6.62491	−0.258266
$659$	−39.7111	−1.54692	−0.773462	−	0.633842i	$-0.781477\pi$
$659$	−39.7111	−1.54692	−0.773462	+	0.633842i	$0.781477\pi$
$660$	3.41199	0.132812
$661$	−14.3086	−0.556538	−0.278269	−	0.960503i	$-0.589761\pi$
$661$	−14.3086	−0.556538	−0.278269	+	0.960503i	$0.589761\pi$
$662$	−8.95410	−0.348011
$663$	−3.13137	−0.121612
$664$	−35.8353	−1.39068
$665$	−3.15979	−0.122531
$666$	−1.19001	−0.0461120
$667$	−13.8039	−0.534488
$668$	2.63546	0.101969
$669$	27.2976	1.05539
$670$	−1.56201	−0.0603457
$671$	−13.6857	−0.528332
$672$	−7.45462	−0.287568
$673$	−11.3738	−0.438428	−0.219214	−	0.975677i	$-0.570349\pi$
$673$	−11.3738	−0.438428	−0.219214	+	0.975677i	$0.570349\pi$
$674$	−6.02429	−0.232047
$675$	−4.63160	−0.178271
$676$	−1.40265	−0.0539481
$677$	48.9594	1.88166	0.940831	−	0.338877i	$-0.110047\pi$
$677$	48.9594	1.88166	0.940831	+	0.338877i	$0.110047\pi$
$678$	−13.3331	−0.512056
$679$	18.7939	0.721242
$680$	−4.99832	−0.191677
$681$	3.00205	0.115039
$682$	−29.9913	−1.14843
$683$	−14.0043	−0.535859	−0.267929	−	0.963439i	$-0.586339\pi$
$683$	−14.0043	−0.535859	−0.267929	+	0.963439i	$0.586339\pi$
$684$	−5.73713	−0.219365
$685$	−0.886687	−0.0338786
$686$	12.1784	0.464974
$687$	12.4340	0.474388
$688$	−5.09382	−0.194200
$689$	4.30387	0.163964
$690$	1.63565	0.0622679
$691$	−5.95929	−0.226702	−0.113351	−	0.993555i	$-0.536158\pi$
$691$	−5.95929	−0.226702	−0.113351	+	0.993555i	$0.536158\pi$
$692$	3.28759	0.124976
$693$	5.10101	0.193771
$694$	2.78392	0.105676
$695$	9.41864	0.357270
$696$	−10.4115	−0.394648
$697$	14.0423	0.531890
$698$	4.53480	0.171645
$699$	6.39552	0.241901
$700$	8.26867	0.312526
$701$	−17.3264	−0.654411	−0.327205	−	0.944953i	$-0.606107\pi$
$701$	−17.3264	−0.654411	−0.327205	+	0.944953i	$0.606107\pi$
$702$	0.772884	0.0291706
$703$	6.29771	0.237523
$704$	11.9482	0.450316
$705$	−4.08759	−0.153948
$706$	8.18653	0.308104
$707$	20.8987	0.785976
$708$	−9.79104	−0.367970
$709$	1.41209	0.0530323	0.0265162	−	0.999648i	$-0.491559\pi$
$709$	1.41209	0.0530323	0.0265162	+	0.999648i	$0.491559\pi$
$710$	−4.07310	−0.152861
$711$	−0.457304	−0.0171503
$712$	3.55994	0.133414
$713$	33.7596	1.26431
$714$	−3.08038	−0.115280
$715$	2.43253	0.0909715
$716$	−8.76366	−0.327513
$717$	−16.1260	−0.602236
$718$	7.50195	0.279970
$719$	46.0903	1.71888	0.859440	−	0.511237i	$-0.170813\pi$
$719$	46.0903	1.71888	0.859440	+	0.511237i	$0.170813\pi$
$720$	−0.469012	−0.0174791
$721$	−1.27278	−0.0474010
$722$	1.75460	0.0652994
$723$	28.8301	1.07220
$724$	4.33780	0.161213
$725$	18.3364	0.680998
$726$	−3.91241	−0.145203
$727$	−23.9649	−0.888809	−0.444404	−	0.895826i	$-0.646585\pi$
$727$	−23.9649	−0.888809	−0.444404	+	0.895826i	$0.646585\pi$
$728$	−3.34724	−0.124057
$729$	1.00000	0.0370370
$730$	2.86148	0.105908
$731$	−20.6420	−0.763471
$732$	4.78979	0.177036
$733$	−31.8622	−1.17686	−0.588429	−	0.808549i	$-0.700253\pi$
$733$	−31.8622	−1.17686	−0.588429	+	0.808549i	$0.700253\pi$
$734$	9.77000	0.360617
$735$	3.26544	0.120447
$736$	−20.4215	−0.752747
$737$	−13.3448	−0.491563
$738$	−3.46592	−0.127582
$739$	14.0372	0.516366	0.258183	−	0.966096i	$-0.416876\pi$
$739$	14.0372	0.516366	0.258183	+	0.966096i	$0.416876\pi$
$740$	1.31082	0.0481868
$741$	−4.09021	−0.150258
$742$	4.23378	0.155427
$743$	−6.50547	−0.238663	−0.119331	−	0.992854i	$-0.538075\pi$
$743$	−6.50547	−0.238663	−0.119331	+	0.992854i	$0.538075\pi$
$744$	25.4631	0.933522
$745$	8.20960	0.300776
$746$	9.31178	0.340928
$747$	−13.6264	−0.498563
$748$	−17.6029	−0.643627
$749$	−22.0776	−0.806699
$750$	−4.51825	−0.164983
$751$	45.8981	1.67485	0.837423	−	0.546555i	$-0.184061\pi$
$751$	45.8981	1.67485	0.837423	+	0.546555i	$0.184061\pi$
$752$	5.20400	0.189770
$753$	28.4113	1.03536
$754$	−3.05983	−0.111433
$755$	8.38100	0.305016
$756$	−1.78527	−0.0649297
$757$	−29.1172	−1.05828	−0.529141	−	0.848534i	$-0.677486\pi$
$757$	−29.1172	−1.05828	−0.529141	+	0.848534i	$0.677486\pi$
$758$	12.8997	0.468538
$759$	13.9739	0.507221
$760$	−6.52882	−0.236825
$761$	−37.3960	−1.35561	−0.677803	−	0.735244i	$-0.737068\pi$
$761$	−37.3960	−1.35561	−0.677803	+	0.735244i	$0.737068\pi$
$762$	−12.2716	−0.444553
$763$	1.88566	0.0682654
$764$	−7.54829	−0.273088
$765$	−1.90061	−0.0687166
$766$	−4.13445	−0.149384
$767$	−6.98038	−0.252047
$768$	−13.2352	−0.477583
$769$	−22.8499	−0.823990	−0.411995	−	0.911186i	$-0.635168\pi$
$769$	−22.8499	−0.823990	−0.411995	+	0.911186i	$0.635168\pi$
$770$	2.39292	0.0862347
$771$	−9.02812	−0.325140
$772$	−32.6479	−1.17502
$773$	9.26165	0.333118	0.166559	−	0.986031i	$-0.446734\pi$
$773$	9.26165	0.333118	0.166559	+	0.986031i	$0.446734\pi$
$774$	5.09484	0.183130
$775$	−44.8447	−1.61087
$776$	38.8323	1.39400
$777$	1.95971	0.0703042
$778$	−12.2058	−0.437600
$779$	18.3421	0.657174
$780$	−0.851347	−0.0304831
$781$	−34.7980	−1.24517
$782$	−8.43853	−0.301761
$783$	−3.95898	−0.141482
$784$	−4.15729	−0.148475
$785$	−9.72144	−0.346973
$786$	12.3509	0.440543
$787$	−5.55401	−0.197979	−0.0989896	−	0.995088i	$-0.531561\pi$
$787$	−5.55401	−0.197979	−0.0989896	+	0.995088i	$0.531561\pi$
$788$	−4.77958	−0.170265
$789$	−7.30490	−0.260061
$790$	−0.214525	−0.00763244
$791$	21.9570	0.780701
$792$	10.5398	0.374516
$793$	3.41481	0.121264
$794$	−30.2407	−1.07320
$795$	2.61226	0.0926474
$796$	−33.5704	−1.18987
$797$	41.8858	1.48367	0.741836	−	0.670582i	$-0.233955\pi$
$797$	41.8858	1.48367	0.741836	+	0.670582i	$0.233955\pi$
$798$	−4.02360	−0.142434
$799$	21.0885	0.746057
$800$	27.1270	0.959085
$801$	1.35366	0.0478294
$802$	10.9138	0.385378
$803$	24.4467	0.862705
$804$	4.67048	0.164715
$805$	−2.69358	−0.0949362
$806$	7.48331	0.263588
$807$	−0.804006	−0.0283023
$808$	43.1813	1.51911
$809$	−12.3027	−0.432540	−0.216270	−	0.976334i	$-0.569389\pi$
$809$	−12.3027	−0.432540	−0.216270	+	0.976334i	$0.569389\pi$
$810$	0.469107	0.0164827
$811$	18.2900	0.642250	0.321125	−	0.947037i	$-0.395939\pi$
$811$	18.2900	0.642250	0.321125	+	0.947037i	$0.395939\pi$
$812$	7.06785	0.248033
$813$	8.14992	0.285830
$814$	−4.76928	−0.167163
$815$	2.36808	0.0829503
$816$	2.41970	0.0847065
$817$	−26.9626	−0.943302
$818$	−6.24235	−0.218259
$819$	−1.27278	−0.0444747
$820$	3.81778	0.133322
$821$	−30.4449	−1.06253	−0.531267	−	0.847204i	$-0.678284\pi$
$821$	−30.4449	−1.06253	−0.531267	+	0.847204i	$0.678284\pi$
$822$	−1.12909	−0.0393814
$823$	4.80948	0.167648	0.0838239	−	0.996481i	$-0.473287\pi$
$823$	4.80948	0.167648	0.0838239	+	0.996481i	$0.473287\pi$
$824$	−2.62985	−0.0916153
$825$	−18.5623	−0.646257
$826$	−6.86671	−0.238923
$827$	−57.0816	−1.98492	−0.992461	−	0.122560i	$-0.960890\pi$
$827$	−57.0816	−1.98492	−0.992461	+	0.122560i	$0.960890\pi$
$828$	−4.89065	−0.169962
$829$	−6.18649	−0.214866	−0.107433	−	0.994212i	$-0.534263\pi$
$829$	−6.18649	−0.214866	−0.107433	+	0.994212i	$0.534263\pi$
$830$	−6.39222	−0.221877
$831$	−11.3518	−0.393790
$832$	−2.98128	−0.103357
$833$	−16.8469	−0.583709
$834$	11.9935	0.415300
$835$	1.14042	0.0394659
$836$	−22.9930	−0.795230
$837$	9.68232	0.334670
$838$	22.0691	0.762363
$839$	−38.8161	−1.34008	−0.670041	−	0.742325i	$-0.733723\pi$
$839$	−38.8161	−1.34008	−0.670041	+	0.742325i	$0.733723\pi$
$840$	−2.03163	−0.0700978
$841$	−13.3265	−0.459534
$842$	9.42587	0.324837
$843$	−8.72177	−0.300394
$844$	−19.0217	−0.654756
$845$	−0.606956	−0.0208799
$846$	−5.20505	−0.178953
$847$	6.44295	0.221382
$848$	−3.32572	−0.114206
$849$	1.08021	0.0370726
$850$	11.2094	0.384478
$851$	5.36852	0.184030
$852$	12.1788	0.417237
$853$	5.05341	0.173025	0.0865127	−	0.996251i	$-0.472428\pi$
$853$	5.05341	0.173025	0.0865127	+	0.996251i	$0.472428\pi$
$854$	3.35920	0.114950
$855$	−2.48258	−0.0849023
$856$	−45.6173	−1.55917
$857$	−4.98603	−0.170319	−0.0851597	−	0.996367i	$-0.527140\pi$
$857$	−4.98603	−0.170319	−0.0851597	+	0.996367i	$0.527140\pi$
$858$	3.09753	0.105748
$859$	46.4552	1.58503	0.792515	−	0.609853i	$-0.208771\pi$
$859$	46.4552	1.58503	0.792515	+	0.609853i	$0.208771\pi$
$860$	−5.61207	−0.191370
$861$	5.70767	0.194517
$862$	−19.8714	−0.676824
$863$	−15.0401	−0.511969	−0.255985	−	0.966681i	$-0.582400\pi$
$863$	−15.0401	−0.511969	−0.255985	+	0.966681i	$0.582400\pi$
$864$	−5.85694	−0.199257
$865$	1.42261	0.0483702
$866$	−9.08154	−0.308603
$867$	−7.19450	−0.244338
$868$	−17.2856	−0.586711
$869$	−1.83276	−0.0621722
$870$	−1.85718	−0.0629644
$871$	3.32975	0.112824
$872$	3.89619	0.131942
$873$	14.7659	0.499752
$874$	−11.0224	−0.372839
$875$	7.44065	0.251540
$876$	−8.55596	−0.289079
$877$	26.4332	0.892586	0.446293	−	0.894887i	$-0.352744\pi$
$877$	26.4332	0.892586	0.446293	+	0.894887i	$0.352744\pi$
$878$	−2.73890	−0.0924333
$879$	−14.7704	−0.498193
$880$	−1.87969	−0.0633642
$881$	−8.36412	−0.281794	−0.140897	−	0.990024i	$-0.544999\pi$
$881$	−8.36412	−0.281794	−0.140897	+	0.990024i	$0.544999\pi$
$882$	4.15813	0.140012
$883$	−25.0647	−0.843496	−0.421748	−	0.906713i	$-0.638583\pi$
$883$	−25.0647	−0.843496	−0.421748	+	0.906713i	$0.638583\pi$
$884$	4.39222	0.147726
$885$	−4.23679	−0.142418
$886$	25.5648	0.858867
$887$	−51.0752	−1.71494	−0.857469	−	0.514536i	$-0.827964\pi$
$887$	−51.0752	−1.71494	−0.857469	+	0.514536i	$0.827964\pi$
$888$	4.04920	0.135882
$889$	20.2088	0.677783
$890$	0.635013	0.0212857
$891$	4.00775	0.134265
$892$	−38.2890	−1.28201
$893$	27.5458	0.921786
$894$	10.4539	0.349631
$895$	−3.79222	−0.126760
$896$	11.9765	0.400107
$897$	−3.48672	−0.116418
$898$	−5.79652	−0.193433
$899$	−38.3321	−1.27845
$900$	6.49652	0.216551
$901$	−13.4770	−0.448985
$902$	−13.8905	−0.462504
$903$	−8.39018	−0.279208
$904$	45.3680	1.50892
$905$	1.87706	0.0623955
$906$	10.6722	0.354559
$907$	−21.0145	−0.697777	−0.348888	−	0.937164i	$-0.613441\pi$
$907$	−21.0145	−0.697777	−0.348888	+	0.937164i	$0.613441\pi$
$908$	−4.21083	−0.139741
$909$	16.4197	0.544606
$910$	−0.597072	−0.0197927
$911$	28.1271	0.931894	0.465947	−	0.884813i	$-0.345714\pi$
$911$	28.1271	0.931894	0.465947	+	0.884813i	$0.345714\pi$
$912$	3.16062	0.104659
$913$	−54.6111	−1.80736
$914$	9.67149	0.319904
$915$	2.07264	0.0685194
$916$	−17.4406	−0.576254
$917$	−20.3395	−0.671669
$918$	−2.42019	−0.0798781
$919$	52.3296	1.72619	0.863097	−	0.505039i	$-0.168522\pi$
$919$	52.3296	1.72619	0.863097	+	0.505039i	$0.168522\pi$
$920$	−5.56553	−0.183490
$921$	25.5416	0.841623
$922$	0.609470	0.0200718
$923$	8.68267	0.285794
$924$	−7.15493	−0.235380
$925$	−7.13130	−0.234476
$926$	13.9127	0.457200
$927$	−1.00000	−0.0328443
$928$	23.1875	0.761167
$929$	−12.0529	−0.395442	−0.197721	−	0.980258i	$-0.563354\pi$
$929$	−12.0529	−0.395442	−0.197721	+	0.980258i	$0.563354\pi$
$930$	4.54204	0.148939
$931$	−22.0054	−0.721198
$932$	−8.97068	−0.293845
$933$	7.22994	0.236698
$934$	−15.1800	−0.496705
$935$	−7.61716	−0.249108
$936$	−2.62985	−0.0859595
$937$	28.3240	0.925304	0.462652	−	0.886540i	$-0.346898\pi$
$937$	28.3240	0.925304	0.462652	+	0.886540i	$0.346898\pi$
$938$	3.27553	0.106950
$939$	−5.83718	−0.190489
$940$	5.73346	0.187005
$941$	−29.1928	−0.951659	−0.475829	−	0.879538i	$-0.657852\pi$
$941$	−29.1928	−0.951659	−0.475829	+	0.879538i	$0.657852\pi$
$942$	−12.3791	−0.403331
$943$	15.6358	0.509173
$944$	5.39394	0.175558
$945$	−0.772524	−0.0251302
$946$	20.4189	0.663875
$947$	9.40865	0.305740	0.152870	−	0.988246i	$-0.451148\pi$
$947$	9.40865	0.305740	0.152870	+	0.988246i	$0.451148\pi$
$948$	0.641438	0.0208329
$949$	−6.09985	−0.198010
$950$	14.6417	0.475039
$951$	−14.6189	−0.474051
$952$	10.4815	0.339706
$953$	−37.8187	−1.22507	−0.612535	−	0.790444i	$-0.709850\pi$
$953$	−37.8187	−1.22507	−0.612535	+	0.790444i	$0.709850\pi$
$954$	3.32639	0.107696
$955$	−3.26630	−0.105695
$956$	22.6191	0.731555
$957$	−15.8666	−0.512895
$958$	3.40226	0.109922
$959$	1.85938	0.0600425
$960$	−1.80950	−0.0584015
$961$	62.7473	2.02411
$962$	1.19001	0.0383675
$963$	−17.3459	−0.558965
$964$	−40.4385	−1.30244
$965$	−14.1274	−0.454778
$966$	−3.42994	−0.110357
$967$	−35.8366	−1.15243	−0.576214	−	0.817299i	$-0.695471\pi$
$967$	−35.8366	−1.15243	−0.576214	+	0.817299i	$0.695471\pi$
$968$	13.3126	0.427882
$969$	12.8080	0.411451
$970$	6.92680	0.222406
$971$	44.5646	1.43015	0.715073	−	0.699050i	$-0.246393\pi$
$971$	44.5646	1.43015	0.715073	+	0.699050i	$0.246393\pi$
$972$	−1.40265	−0.0449900
$973$	−19.7509	−0.633184
$974$	0.175359	0.00561887
$975$	4.63160	0.148330
$976$	−2.63872	−0.0844635
$977$	−48.8863	−1.56401	−0.782006	−	0.623271i	$-0.785803\pi$
$977$	−48.8863	−1.56401	−0.782006	+	0.623271i	$0.785803\pi$
$978$	3.01546	0.0964238
$979$	5.42516	0.173389
$980$	−4.58026	−0.146311
$981$	1.48152	0.0473014
$982$	17.2299	0.549828
$983$	−24.6708	−0.786875	−0.393437	−	0.919351i	$-0.628714\pi$
$983$	−24.6708	−0.786875	−0.393437	+	0.919351i	$0.628714\pi$
$984$	11.7933	0.375957
$985$	−2.06822	−0.0658990
$986$	9.58148	0.305136
$987$	8.57167	0.272839
$988$	5.73713	0.182522
$989$	−22.9844	−0.730862
$990$	1.88006	0.0597524
$991$	−27.8775	−0.885559	−0.442779	−	0.896631i	$-0.646008\pi$
$991$	−27.8775	−0.885559	−0.442779	+	0.896631i	$0.646008\pi$
$992$	−56.7088	−1.80050
$993$	11.5853	0.367649
$994$	8.54128	0.270913
$995$	−14.5266	−0.460525
$996$	19.1130	0.605619
$997$	1.81875	0.0576004	0.0288002	−	0.999585i	$-0.490831\pi$
$997$	1.81875	0.0576004	0.0288002	+	0.999585i	$0.490831\pi$
$998$	−8.72074	−0.276050
$999$	1.53970	0.0487141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.12	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.12	✓	32	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)

\(f(q)\)	\(=\)	\(q-0.772884 q^{2} +1.00000 q^{3} -1.40265 q^{4} -0.606956 q^{5} -0.772884 q^{6} +1.27278 q^{7} +2.62985 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.772884 q^{2} +1.00000 q^{3} -1.40265 q^{4} -0.606956 q^{5} -0.772884 q^{6} +1.27278 q^{7} +2.62985 q^{8} +1.00000 q^{9} +0.469107 q^{10} +4.00775 q^{11} -1.40265 q^{12} -1.00000 q^{13} -0.983715 q^{14} -0.606956 q^{15} +0.772728 q^{16} +3.13137 q^{17} -0.772884 q^{18} +4.09021 q^{19} +0.851347 q^{20} +1.27278 q^{21} -3.09753 q^{22} +3.48672 q^{23} +2.62985 q^{24} -4.63160 q^{25} +0.772884 q^{26} +1.00000 q^{27} -1.78527 q^{28} -3.95898 q^{29} +0.469107 q^{30} +9.68232 q^{31} -5.85694 q^{32} +4.00775 q^{33} -2.42019 q^{34} -0.772524 q^{35} -1.40265 q^{36} +1.53970 q^{37} -3.16126 q^{38} -1.00000 q^{39} -1.59621 q^{40} +4.48439 q^{41} -0.983715 q^{42} -6.59199 q^{43} -5.62148 q^{44} -0.606956 q^{45} -2.69483 q^{46} +6.73458 q^{47} +0.772728 q^{48} -5.38002 q^{49} +3.57969 q^{50} +3.13137 q^{51} +1.40265 q^{52} -4.30387 q^{53} -0.772884 q^{54} -2.43253 q^{55} +3.34724 q^{56} +4.09021 q^{57} +3.05983 q^{58} +6.98038 q^{59} +0.851347 q^{60} -3.41481 q^{61} -7.48331 q^{62} +1.27278 q^{63} +2.98128 q^{64} +0.606956 q^{65} -3.09753 q^{66} -3.32975 q^{67} -4.39222 q^{68} +3.48672 q^{69} +0.597072 q^{70} -8.68267 q^{71} +2.62985 q^{72} +6.09985 q^{73} -1.19001 q^{74} -4.63160 q^{75} -5.73713 q^{76} +5.10101 q^{77} +0.772884 q^{78} -0.457304 q^{79} -0.469012 q^{80} +1.00000 q^{81} -3.46592 q^{82} -13.6264 q^{83} -1.78527 q^{84} -1.90061 q^{85} +5.09484 q^{86} -3.95898 q^{87} +10.5398 q^{88} +1.35366 q^{89} +0.469107 q^{90} -1.27278 q^{91} -4.89065 q^{92} +9.68232 q^{93} -5.20505 q^{94} -2.48258 q^{95} -5.85694 q^{96} +14.7659 q^{97} +4.15813 q^{98} +4.00775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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