LMFDB - Embedded newform 4017.2.a.l.1.15

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			1.15
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)

$f(q)$	$=$	$q-0.163737 q^{2} +1.00000 q^{3} -1.97319 q^{4} +3.16137 q^{5} -0.163737 q^{6} +4.62100 q^{7} +0.650558 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.163737 q^{2} +1.00000 q^{3} -1.97319 q^{4} +3.16137 q^{5} -0.163737 q^{6} +4.62100 q^{7} +0.650558 q^{8} +1.00000 q^{9} -0.517632 q^{10} -5.10770 q^{11} -1.97319 q^{12} -1.00000 q^{13} -0.756628 q^{14} +3.16137 q^{15} +3.83986 q^{16} +3.51961 q^{17} -0.163737 q^{18} +4.63697 q^{19} -6.23798 q^{20} +4.62100 q^{21} +0.836318 q^{22} -2.82465 q^{23} +0.650558 q^{24} +4.99424 q^{25} +0.163737 q^{26} +1.00000 q^{27} -9.11811 q^{28} -9.76478 q^{29} -0.517632 q^{30} +8.00926 q^{31} -1.92984 q^{32} -5.10770 q^{33} -0.576290 q^{34} +14.6087 q^{35} -1.97319 q^{36} +3.97116 q^{37} -0.759243 q^{38} -1.00000 q^{39} +2.05665 q^{40} -2.15785 q^{41} -0.756628 q^{42} +3.44910 q^{43} +10.0785 q^{44} +3.16137 q^{45} +0.462500 q^{46} +0.639740 q^{47} +3.83986 q^{48} +14.3536 q^{49} -0.817741 q^{50} +3.51961 q^{51} +1.97319 q^{52} +10.0134 q^{53} -0.163737 q^{54} -16.1473 q^{55} +3.00623 q^{56} +4.63697 q^{57} +1.59886 q^{58} -4.29554 q^{59} -6.23798 q^{60} +4.13769 q^{61} -1.31141 q^{62} +4.62100 q^{63} -7.36373 q^{64} -3.16137 q^{65} +0.836318 q^{66} -1.56966 q^{67} -6.94487 q^{68} -2.82465 q^{69} -2.39198 q^{70} +2.75380 q^{71} +0.650558 q^{72} +10.2384 q^{73} -0.650226 q^{74} +4.99424 q^{75} -9.14963 q^{76} -23.6027 q^{77} +0.163737 q^{78} +0.404050 q^{79} +12.1392 q^{80} +1.00000 q^{81} +0.353319 q^{82} +11.3957 q^{83} -9.11811 q^{84} +11.1268 q^{85} -0.564744 q^{86} -9.76478 q^{87} -3.32285 q^{88} -14.2326 q^{89} -0.517632 q^{90} -4.62100 q^{91} +5.57358 q^{92} +8.00926 q^{93} -0.104749 q^{94} +14.6592 q^{95} -1.92984 q^{96} -7.64785 q^{97} -2.35022 q^{98} -5.10770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.163737	−0.115779	−0.0578897	−	0.998323i	$-0.518437\pi$
$2$	−0.163737	−0.115779	−0.0578897	+	0.998323i	$0.518437\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.97319	−0.986595
$5$	3.16137	1.41381	0.706903	−	0.707310i	$-0.250092\pi$
$5$	3.16137	1.41381	0.706903	+	0.707310i	$0.250092\pi$
$6$	−0.163737	−0.0668453
$7$	4.62100	1.74657	0.873287	−	0.487206i	$-0.161984\pi$
$7$	4.62100	1.74657	0.873287	+	0.487206i	$0.161984\pi$
$8$	0.650558	0.230007
$9$	1.00000	0.333333
$10$	−0.517632	−0.163690
$11$	−5.10770	−1.54003	−0.770014	−	0.638027i	$-0.779751\pi$
$11$	−5.10770	−1.54003	−0.770014	+	0.638027i	$0.779751\pi$
$12$	−1.97319	−0.569611
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.756628	−0.202217
$15$	3.16137	0.816261
$16$	3.83986	0.959965
$17$	3.51961	0.853631	0.426816	−	0.904339i	$-0.359635\pi$
$17$	3.51961	0.853631	0.426816	+	0.904339i	$0.359635\pi$
$18$	−0.163737	−0.0385931
$19$	4.63697	1.06379	0.531897	−	0.846809i	$-0.321479\pi$
$19$	4.63697	1.06379	0.531897	+	0.846809i	$0.321479\pi$
$20$	−6.23798	−1.39485
$21$	4.62100	1.00839
$22$	0.836318	0.178304
$23$	−2.82465	−0.588981	−0.294490	−	0.955654i	$-0.595150\pi$
$23$	−2.82465	−0.588981	−0.294490	+	0.955654i	$0.595150\pi$
$24$	0.650558	0.132795
$25$	4.99424	0.998848
$26$	0.163737	0.0321114
$27$	1.00000	0.192450
$28$	−9.11811	−1.72316
$29$	−9.76478	−1.81328	−0.906638	−	0.421910i	$-0.861360\pi$
$29$	−9.76478	−1.81328	−0.906638	+	0.421910i	$0.861360\pi$
$30$	−0.517632	−0.0945063
$31$	8.00926	1.43851	0.719253	−	0.694748i	$-0.244484\pi$
$31$	8.00926	1.43851	0.719253	+	0.694748i	$0.244484\pi$
$32$	−1.92984	−0.341151
$33$	−5.10770	−0.889136
$34$	−0.576290	−0.0988330
$35$	14.6087	2.46932
$36$	−1.97319	−0.328865
$37$	3.97116	0.652855	0.326428	−	0.945222i	$-0.394155\pi$
$37$	3.97116	0.652855	0.326428	+	0.945222i	$0.394155\pi$
$38$	−0.759243	−0.123166
$39$	−1.00000	−0.160128
$40$	2.05665	0.325185
$41$	−2.15785	−0.336999	−0.168500	−	0.985702i	$-0.553892\pi$
$41$	−2.15785	−0.336999	−0.168500	+	0.985702i	$0.553892\pi$
$42$	−0.756628	−0.116750
$43$	3.44910	0.525982	0.262991	−	0.964798i	$-0.415291\pi$
$43$	3.44910	0.525982	0.262991	+	0.964798i	$0.415291\pi$
$44$	10.0785	1.51938
$45$	3.16137	0.471269
$46$	0.462500	0.0681918
$47$	0.639740	0.0933157	0.0466579	−	0.998911i	$-0.485143\pi$
$47$	0.639740	0.0933157	0.0466579	+	0.998911i	$0.485143\pi$
$48$	3.83986	0.554236
$49$	14.3536	2.05052
$50$	−0.817741	−0.115646
$51$	3.51961	0.492844
$52$	1.97319	0.273632
$53$	10.0134	1.37545	0.687723	−	0.725974i	$-0.258611\pi$
$53$	10.0134	1.37545	0.687723	+	0.725974i	$0.258611\pi$
$54$	−0.163737	−0.0222818
$55$	−16.1473	−2.17730
$56$	3.00623	0.401724
$57$	4.63697	0.614182
$58$	1.59886	0.209940
$59$	−4.29554	−0.559231	−0.279616	−	0.960112i	$-0.590207\pi$
$59$	−4.29554	−0.559231	−0.279616	+	0.960112i	$0.590207\pi$
$60$	−6.23798	−0.805319
$61$	4.13769	0.529777	0.264889	−	0.964279i	$-0.414665\pi$
$61$	4.13769	0.529777	0.264889	+	0.964279i	$0.414665\pi$
$62$	−1.31141	−0.166549
$63$	4.62100	0.582191
$64$	−7.36373	−0.920467
$65$	−3.16137	−0.392119
$66$	0.836318	0.102944
$67$	−1.56966	−0.191765	−0.0958824	−	0.995393i	$-0.530567\pi$
$67$	−1.56966	−0.191765	−0.0958824	+	0.995393i	$0.530567\pi$
$68$	−6.94487	−0.842189
$69$	−2.82465	−0.340048
$70$	−2.39198	−0.285896
$71$	2.75380	0.326816	0.163408	−	0.986559i	$-0.447751\pi$
$71$	2.75380	0.326816	0.163408	+	0.986559i	$0.447751\pi$
$72$	0.650558	0.0766690
$73$	10.2384	1.19831	0.599156	−	0.800632i	$-0.295503\pi$
$73$	10.2384	1.19831	0.599156	+	0.800632i	$0.295503\pi$
$74$	−0.650226	−0.0755872
$75$	4.99424	0.576685
$76$	−9.14963	−1.04953
$77$	−23.6027	−2.68977
$78$	0.163737	0.0185395
$79$	0.404050	0.0454592	0.0227296	−	0.999742i	$-0.492764\pi$
$79$	0.404050	0.0454592	0.0227296	+	0.999742i	$0.492764\pi$
$80$	12.1392	1.35720
$81$	1.00000	0.111111
$82$	0.353319	0.0390176
$83$	11.3957	1.25084	0.625421	−	0.780288i	$-0.284927\pi$
$83$	11.3957	1.25084	0.625421	+	0.780288i	$0.284927\pi$
$84$	−9.11811	−0.994868
$85$	11.1268	1.20687
$86$	−0.564744	−0.0608979
$87$	−9.76478	−1.04689
$88$	−3.32285	−0.354217
$89$	−14.2326	−1.50865	−0.754325	−	0.656501i	$-0.772036\pi$
$89$	−14.2326	−1.50865	−0.754325	+	0.656501i	$0.772036\pi$
$90$	−0.517632	−0.0545632
$91$	−4.62100	−0.484412
$92$	5.57358	0.581085
$93$	8.00926	0.830522
$94$	−0.104749	−0.0108040
$95$	14.6592	1.50400
$96$	−1.92984	−0.196964
$97$	−7.64785	−0.776521	−0.388261	−	0.921550i	$-0.626924\pi$
$97$	−7.64785	−0.776521	−0.388261	+	0.921550i	$0.626924\pi$
$98$	−2.35022	−0.237408
$99$	−5.10770	−0.513343
$100$	−9.85458	−0.985458
$101$	3.17832	0.316254	0.158127	−	0.987419i	$-0.449454\pi$
$101$	3.17832	0.316254	0.158127	+	0.987419i	$0.449454\pi$
$102$	−0.576290	−0.0570612
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−0.650558	−0.0637924
$105$	14.6087	1.42566
$106$	−1.63956	−0.159248
$107$	−3.63640	−0.351545	−0.175772	−	0.984431i	$-0.556242\pi$
$107$	−3.63640	−0.351545	−0.175772	+	0.984431i	$0.556242\pi$
$108$	−1.97319	−0.189870
$109$	7.66759	0.734422	0.367211	−	0.930138i	$-0.380313\pi$
$109$	7.66759	0.734422	0.367211	+	0.930138i	$0.380313\pi$
$110$	2.64391	0.252087
$111$	3.97116	0.376926
$112$	17.7440	1.67665
$113$	2.66411	0.250619	0.125309	−	0.992118i	$-0.460008\pi$
$113$	2.66411	0.250619	0.125309	+	0.992118i	$0.460008\pi$
$114$	−0.759243	−0.0711096
$115$	−8.92976	−0.832704
$116$	19.2678	1.78897
$117$	−1.00000	−0.0924500
$118$	0.703338	0.0647475
$119$	16.2641	1.49093
$120$	2.05665	0.187746
$121$	15.0886	1.37169
$122$	−0.677493	−0.0613373
$123$	−2.15785	−0.194566
$124$	−15.8038	−1.41922
$125$	−0.0182133	−0.00162905
$126$	−0.756628	−0.0674058
$127$	−15.6822	−1.39157	−0.695786	−	0.718249i	$-0.744944\pi$
$127$	−15.6822	−1.39157	−0.695786	+	0.718249i	$0.744944\pi$
$128$	5.06540	0.447722
$129$	3.44910	0.303676
$130$	0.517632	0.0453993
$131$	−0.467446	−0.0408410	−0.0204205	−	0.999791i	$-0.506500\pi$
$131$	−0.467446	−0.0408410	−0.0204205	+	0.999791i	$0.506500\pi$
$132$	10.0785	0.877217
$133$	21.4275	1.85800
$134$	0.257012	0.0222024
$135$	3.16137	0.272087
$136$	2.28971	0.196341
$137$	6.83168	0.583670	0.291835	−	0.956469i	$-0.405734\pi$
$137$	6.83168	0.583670	0.291835	+	0.956469i	$0.405734\pi$
$138$	0.462500	0.0393706
$139$	−8.48495	−0.719684	−0.359842	−	0.933013i	$-0.617169\pi$
$139$	−8.48495	−0.719684	−0.359842	+	0.933013i	$0.617169\pi$
$140$	−28.8257	−2.43622
$141$	0.639740	0.0538759
$142$	−0.450898	−0.0378386
$143$	5.10770	0.427127
$144$	3.83986	0.319988
$145$	−30.8701	−2.56362
$146$	−1.67640	−0.138740
$147$	14.3536	1.18387
$148$	−7.83586	−0.644104
$149$	−8.96853	−0.734731	−0.367365	−	0.930077i	$-0.619740\pi$
$149$	−8.96853	−0.734731	−0.367365	+	0.930077i	$0.619740\pi$
$150$	−0.817741	−0.0667683
$151$	−6.57949	−0.535431	−0.267716	−	0.963498i	$-0.586269\pi$
$151$	−6.57949	−0.535431	−0.267716	+	0.963498i	$0.586269\pi$
$152$	3.01662	0.244680
$153$	3.51961	0.284544
$154$	3.86463	0.311421
$155$	25.3202	2.03377
$156$	1.97319	0.157982
$157$	−15.6957	−1.25265	−0.626325	−	0.779562i	$-0.715442\pi$
$157$	−15.6957	−1.25265	−0.626325	+	0.779562i	$0.715442\pi$
$158$	−0.0661579	−0.00526324
$159$	10.0134	0.794114
$160$	−6.10094	−0.482321
$161$	−13.0527	−1.02870
$162$	−0.163737	−0.0128644
$163$	17.4107	1.36371	0.681855	−	0.731487i	$-0.261173\pi$
$163$	17.4107	1.36371	0.681855	+	0.731487i	$0.261173\pi$
$164$	4.25784	0.332482
$165$	−16.1473	−1.25707
$166$	−1.86590	−0.144822
$167$	−1.55283	−0.120162	−0.0600808	−	0.998194i	$-0.519136\pi$
$167$	−1.55283	−0.120162	−0.0600808	+	0.998194i	$0.519136\pi$
$168$	3.00623	0.231935
$169$	1.00000	0.0769231
$170$	−1.82186	−0.139731
$171$	4.63697	0.354598
$172$	−6.80572	−0.518932
$173$	−1.84736	−0.140452	−0.0702262	−	0.997531i	$-0.522372\pi$
$173$	−1.84736	−0.140452	−0.0702262	+	0.997531i	$0.522372\pi$
$174$	1.59886	0.121209
$175$	23.0784	1.74456
$176$	−19.6128	−1.47837
$177$	−4.29554	−0.322872
$178$	2.33040	0.174671
$179$	6.51002	0.486582	0.243291	−	0.969953i	$-0.421773\pi$
$179$	6.51002	0.486582	0.243291	+	0.969953i	$0.421773\pi$
$180$	−6.23798	−0.464951
$181$	−1.47565	−0.109685	−0.0548423	−	0.998495i	$-0.517466\pi$
$181$	−1.47565	−0.109685	−0.0548423	+	0.998495i	$0.517466\pi$
$182$	0.756628	0.0560850
$183$	4.13769	0.305867
$184$	−1.83760	−0.135470
$185$	12.5543	0.923011
$186$	−1.31141	−0.0961573
$187$	−17.9771	−1.31462
$188$	−1.26233	−0.0920649
$189$	4.62100	0.336128
$190$	−2.40025	−0.174132
$191$	−10.6553	−0.770991	−0.385495	−	0.922710i	$-0.625969\pi$
$191$	−10.6553	−0.770991	−0.385495	+	0.922710i	$0.625969\pi$
$192$	−7.36373	−0.531432
$193$	−14.9986	−1.07962	−0.539812	−	0.841785i	$-0.681505\pi$
$193$	−14.9986	−1.07962	−0.539812	+	0.841785i	$0.681505\pi$
$194$	1.25223	0.0899052
$195$	−3.16137	−0.226390
$196$	−28.3225	−2.02303
$197$	27.4620	1.95659	0.978293	−	0.207228i	$-0.0664442\pi$
$197$	27.4620	1.95659	0.978293	+	0.207228i	$0.0664442\pi$
$198$	0.836318	0.0594346
$199$	−0.264401	−0.0187429	−0.00937144	−	0.999956i	$-0.502983\pi$
$199$	−0.264401	−0.0187429	−0.00937144	+	0.999956i	$0.502983\pi$
$200$	3.24904	0.229742
$201$	−1.56966	−0.110715
$202$	−0.520408	−0.0366158
$203$	−45.1231	−3.16702
$204$	−6.94487	−0.486238
$205$	−6.82174	−0.476451
$206$	0.163737	0.0114081
$207$	−2.82465	−0.196327
$208$	−3.83986	−0.266246
$209$	−23.6843	−1.63827
$210$	−2.39198	−0.165062
$211$	−24.5468	−1.68987	−0.844935	−	0.534869i	$-0.820361\pi$
$211$	−24.5468	−1.68987	−0.844935	+	0.534869i	$0.820361\pi$
$212$	−19.7583	−1.35701
$213$	2.75380	0.188687
$214$	0.595413	0.0407016
$215$	10.9039	0.743637
$216$	0.650558	0.0442648
$217$	37.0108	2.51246
$218$	−1.25547	−0.0850310
$219$	10.2384	0.691846
$220$	31.8617	2.14812
$221$	−3.51961	−0.236755
$222$	−0.650226	−0.0436403
$223$	9.17938	0.614697	0.307348	−	0.951597i	$-0.400558\pi$
$223$	9.17938	0.614697	0.307348	+	0.951597i	$0.400558\pi$
$224$	−8.91780	−0.595846
$225$	4.99424	0.332949
$226$	−0.436213	−0.0290165
$227$	−11.5520	−0.766735	−0.383367	−	0.923596i	$-0.625236\pi$
$227$	−11.5520	−0.766735	−0.383367	+	0.923596i	$0.625236\pi$
$228$	−9.14963	−0.605949
$229$	14.9537	0.988167	0.494084	−	0.869414i	$-0.335504\pi$
$229$	14.9537	0.988167	0.494084	+	0.869414i	$0.335504\pi$
$230$	1.46213	0.0964101
$231$	−23.6027	−1.55294
$232$	−6.35256	−0.417066
$233$	22.2265	1.45611	0.728054	−	0.685520i	$-0.240425\pi$
$233$	22.2265	1.45611	0.728054	+	0.685520i	$0.240425\pi$
$234$	0.163737	0.0107038
$235$	2.02245	0.131930
$236$	8.47591	0.551735
$237$	0.404050	0.0262459
$238$	−2.66304	−0.172619
$239$	5.67158	0.366864	0.183432	−	0.983032i	$-0.441279\pi$
$239$	5.67158	0.366864	0.183432	+	0.983032i	$0.441279\pi$
$240$	12.1392	0.783582
$241$	−1.57447	−0.101421	−0.0507103	−	0.998713i	$-0.516149\pi$
$241$	−1.57447	−0.101421	−0.0507103	+	0.998713i	$0.516149\pi$
$242$	−2.47056	−0.158813
$243$	1.00000	0.0641500
$244$	−8.16446	−0.522676
$245$	45.3771	2.89904
$246$	0.353319	0.0225268
$247$	−4.63697	−0.295043
$248$	5.21049	0.330866
$249$	11.3957	0.722174
$250$	0.00298219	0.000188610 0
$251$	3.66787	0.231514	0.115757	−	0.993278i	$-0.463071\pi$
$251$	3.66787	0.231514	0.115757	+	0.993278i	$0.463071\pi$
$252$	−9.11811	−0.574387
$253$	14.4275	0.907047
$254$	2.56776	0.161115
$255$	11.1268	0.696786
$256$	13.8981	0.868630
$257$	−21.9753	−1.37078	−0.685391	−	0.728175i	$-0.740369\pi$
$257$	−21.9753	−1.37078	−0.685391	+	0.728175i	$0.740369\pi$
$258$	−0.564744	−0.0351594
$259$	18.3508	1.14026
$260$	6.23798	0.386863
$261$	−9.76478	−0.604425
$262$	0.0765382	0.00472854
$263$	2.09368	0.129102	0.0645509	−	0.997914i	$-0.479439\pi$
$263$	2.09368	0.129102	0.0645509	+	0.997914i	$0.479439\pi$
$264$	−3.32285	−0.204507
$265$	31.6560	1.94461
$266$	−3.50846	−0.215118
$267$	−14.2326	−0.871020
$268$	3.09724	0.189194
$269$	15.4804	0.943859	0.471930	−	0.881636i	$-0.343558\pi$
$269$	15.4804	0.943859	0.471930	+	0.881636i	$0.343558\pi$
$270$	−0.517632	−0.0315021
$271$	21.9723	1.33472	0.667360	−	0.744736i	$-0.267424\pi$
$271$	21.9723	1.33472	0.667360	+	0.744736i	$0.267424\pi$
$272$	13.5148	0.819456
$273$	−4.62100	−0.279676
$274$	−1.11860	−0.0675770
$275$	−25.5091	−1.53825
$276$	5.57358	0.335490
$277$	2.61236	0.156962	0.0784809	−	0.996916i	$-0.474993\pi$
$277$	2.61236	0.156962	0.0784809	+	0.996916i	$0.474993\pi$
$278$	1.38930	0.0833246
$279$	8.00926	0.479502
$280$	9.50379	0.567960
$281$	−15.6924	−0.936128	−0.468064	−	0.883694i	$-0.655048\pi$
$281$	−15.6924	−0.936128	−0.468064	+	0.883694i	$0.655048\pi$
$282$	−0.104749	−0.00623772
$283$	27.9524	1.66160	0.830798	−	0.556573i	$-0.187884\pi$
$283$	27.9524	1.66160	0.830798	+	0.556573i	$0.187884\pi$
$284$	−5.43377	−0.322435
$285$	14.6592	0.868334
$286$	−0.836318	−0.0494525
$287$	−9.97141	−0.588594
$288$	−1.92984	−0.113717
$289$	−4.61233	−0.271313
$290$	5.05457	0.296814
$291$	−7.64785	−0.448325
$292$	−20.2023	−1.18225
$293$	6.94962	0.406001	0.203001	−	0.979179i	$-0.434931\pi$
$293$	6.94962	0.406001	0.203001	+	0.979179i	$0.434931\pi$
$294$	−2.35022	−0.137068
$295$	−13.5798	−0.790645
$296$	2.58347	0.150161
$297$	−5.10770	−0.296379
$298$	1.46848	0.0850667
$299$	2.82465	0.163354
$300$	−9.85458	−0.568955
$301$	15.9383	0.918667
$302$	1.07730	0.0619919
$303$	3.17832	0.182590
$304$	17.8053	1.02121
$305$	13.0808	0.749003
$306$	−0.576290	−0.0329443
$307$	−1.88843	−0.107778	−0.0538892	−	0.998547i	$-0.517162\pi$
$307$	−1.88843	−0.107778	−0.0538892	+	0.998547i	$0.517162\pi$
$308$	46.5726	2.65372
$309$	−1.00000	−0.0568880
$310$	−4.14585	−0.235469
$311$	23.1462	1.31250	0.656250	−	0.754544i	$-0.272142\pi$
$311$	23.1462	1.31250	0.656250	+	0.754544i	$0.272142\pi$
$312$	−0.650558	−0.0368306
$313$	−27.4461	−1.55134	−0.775671	−	0.631137i	$-0.782589\pi$
$313$	−27.4461	−1.55134	−0.775671	+	0.631137i	$0.782589\pi$
$314$	2.56996	0.145031
$315$	14.6087	0.823106
$316$	−0.797267	−0.0448498
$317$	14.6789	0.824446	0.412223	−	0.911083i	$-0.364752\pi$
$317$	14.6789	0.824446	0.412223	+	0.911083i	$0.364752\pi$
$318$	−1.63956	−0.0919420
$319$	49.8756	2.79250
$320$	−23.2795	−1.30136
$321$	−3.63640	−0.202964
$322$	2.13721	0.119102
$323$	16.3203	0.908088
$324$	−1.97319	−0.109622
$325$	−4.99424	−0.277031
$326$	−2.85077	−0.157890
$327$	7.66759	0.424019
$328$	−1.40380	−0.0775121
$329$	2.95624	0.162983
$330$	2.64391	0.145542
$331$	17.9238	0.985179	0.492589	−	0.870262i	$-0.336050\pi$
$331$	17.9238	0.985179	0.492589	+	0.870262i	$0.336050\pi$
$332$	−22.4859	−1.23407
$333$	3.97116	0.217618
$334$	0.254256	0.0139123
$335$	−4.96228	−0.271118
$336$	17.7440	0.968014
$337$	−28.5296	−1.55411	−0.777053	−	0.629436i	$-0.783286\pi$
$337$	−28.5296	−1.55411	−0.777053	+	0.629436i	$0.783286\pi$
$338$	−0.163737	−0.00890611
$339$	2.66411	0.144695
$340$	−21.9553	−1.19069
$341$	−40.9089	−2.21534
$342$	−0.759243	−0.0410552
$343$	33.9812	1.83481
$344$	2.24384	0.120980
$345$	−8.92976	−0.480762
$346$	0.302482	0.0162615
$347$	−30.7177	−1.64901	−0.824507	−	0.565852i	$-0.808547\pi$
$347$	−30.7177	−1.64901	−0.824507	+	0.565852i	$0.808547\pi$
$348$	19.2678	1.03286
$349$	24.5749	1.31546	0.657732	−	0.753252i	$-0.271516\pi$
$349$	24.5749	1.31546	0.657732	+	0.753252i	$0.271516\pi$
$350$	−3.77878	−0.201984
$351$	−1.00000	−0.0533761
$352$	9.85705	0.525382
$353$	31.9232	1.69910	0.849550	−	0.527508i	$-0.176873\pi$
$353$	31.9232	1.69910	0.849550	+	0.527508i	$0.176873\pi$
$354$	0.703338	0.0373820
$355$	8.70577	0.462054
$356$	28.0836	1.48843
$357$	16.2641	0.860789
$358$	−1.06593	−0.0563361
$359$	−10.1552	−0.535973	−0.267986	−	0.963423i	$-0.586358\pi$
$359$	−10.1552	−0.535973	−0.267986	+	0.963423i	$0.586358\pi$
$360$	2.05665	0.108395
$361$	2.50151	0.131659
$362$	0.241619	0.0126992
$363$	15.0886	0.791945
$364$	9.11811	0.477919
$365$	32.3673	1.69418
$366$	−0.677493	−0.0354131
$367$	29.8497	1.55814	0.779070	−	0.626937i	$-0.215692\pi$
$367$	29.8497	1.55814	0.779070	+	0.626937i	$0.215692\pi$
$368$	−10.8463	−0.565401
$369$	−2.15785	−0.112333
$370$	−2.05560	−0.106866
$371$	46.2719	2.40232
$372$	−15.8038	−0.819389
$373$	−30.5655	−1.58262	−0.791311	−	0.611414i	$-0.790601\pi$
$373$	−30.5655	−1.58262	−0.791311	+	0.611414i	$0.790601\pi$
$374$	2.94352	0.152206
$375$	−0.0182133	−0.000940532 0
$376$	0.416188	0.0214633
$377$	9.76478	0.502912
$378$	−0.756628	−0.0389168
$379$	25.2064	1.29476	0.647382	−	0.762166i	$-0.275864\pi$
$379$	25.2064	1.29476	0.647382	+	0.762166i	$0.275864\pi$
$380$	−28.9253	−1.48384
$381$	−15.6822	−0.803425
$382$	1.74467	0.0892649
$383$	−19.5303	−0.997954	−0.498977	−	0.866615i	$-0.666291\pi$
$383$	−19.5303	−0.997954	−0.498977	+	0.866615i	$0.666291\pi$
$384$	5.06540	0.258493
$385$	−74.6167	−3.80282
$386$	2.45583	0.124998
$387$	3.44910	0.175327
$388$	15.0907	0.766112
$389$	−34.8370	−1.76630	−0.883152	−	0.469087i	$-0.844583\pi$
$389$	−34.8370	−1.76630	−0.883152	+	0.469087i	$0.844583\pi$
$390$	0.517632	0.0262113
$391$	−9.94168	−0.502772
$392$	9.33788	0.471634
$393$	−0.467446	−0.0235795
$394$	−4.49654	−0.226532
$395$	1.27735	0.0642704
$396$	10.0785	0.506462
$397$	−4.71579	−0.236679	−0.118339	−	0.992973i	$-0.537757\pi$
$397$	−4.71579	−0.236679	−0.118339	+	0.992973i	$0.537757\pi$
$398$	0.0432922	0.00217004
$399$	21.4275	1.07271
$400$	19.1772	0.958859
$401$	33.9128	1.69352	0.846761	−	0.531973i	$-0.178549\pi$
$401$	33.9128	1.69352	0.846761	+	0.531973i	$0.178549\pi$
$402$	0.257012	0.0128186
$403$	−8.00926	−0.398970
$404$	−6.27143	−0.312015
$405$	3.16137	0.157090
$406$	7.38831	0.366676
$407$	−20.2835	−1.00542
$408$	2.28971	0.113358
$409$	34.8115	1.72132	0.860659	−	0.509181i	$-0.170052\pi$
$409$	34.8115	1.72132	0.860659	+	0.509181i	$0.170052\pi$
$410$	1.11697	0.0551633
$411$	6.83168	0.336982
$412$	1.97319	0.0972121
$413$	−19.8497	−0.976739
$414$	0.462500	0.0227306
$415$	36.0260	1.76845
$416$	1.92984	0.0946183
$417$	−8.48495	−0.415510
$418$	3.87799	0.189678
$419$	−32.7606	−1.60046	−0.800231	−	0.599693i	$-0.795290\pi$
$419$	−32.7606	−1.60046	−0.800231	+	0.599693i	$0.795290\pi$
$420$	−28.8257	−1.40655
$421$	−14.0772	−0.686083	−0.343042	−	0.939320i	$-0.611457\pi$
$421$	−14.0772	−0.686083	−0.343042	+	0.939320i	$0.611457\pi$
$422$	4.01921	0.195652
$423$	0.639740	0.0311052
$424$	6.51429	0.316362
$425$	17.5778	0.852648
$426$	−0.450898	−0.0218461
$427$	19.1203	0.925296
$428$	7.17532	0.346832
$429$	5.10770	0.246602
$430$	−1.78536	−0.0860979
$431$	0.738363	0.0355657	0.0177829	−	0.999842i	$-0.494339\pi$
$431$	0.738363	0.0355657	0.0177829	+	0.999842i	$0.494339\pi$
$432$	3.83986	0.184745
$433$	−22.2057	−1.06714	−0.533569	−	0.845757i	$-0.679150\pi$
$433$	−22.2057	−1.06714	−0.533569	+	0.845757i	$0.679150\pi$
$434$	−6.06003	−0.290891
$435$	−30.8701	−1.48011
$436$	−15.1296	−0.724577
$437$	−13.0978	−0.626554
$438$	−1.67640	−0.0801015
$439$	−2.98914	−0.142664	−0.0713320	−	0.997453i	$-0.522725\pi$
$439$	−2.98914	−0.142664	−0.0713320	+	0.997453i	$0.522725\pi$
$440$	−10.5048	−0.500794
$441$	14.3536	0.683507
$442$	0.576290	0.0274113
$443$	36.3150	1.72538	0.862690	−	0.505733i	$-0.168778\pi$
$443$	36.3150	1.72538	0.862690	+	0.505733i	$0.168778\pi$
$444$	−7.83586	−0.371874
$445$	−44.9944	−2.13294
$446$	−1.50300	−0.0711692
$447$	−8.96853	−0.424197
$448$	−34.0278	−1.60766
$449$	−34.0848	−1.60856	−0.804280	−	0.594251i	$-0.797449\pi$
$449$	−34.0848	−1.60856	−0.804280	+	0.594251i	$0.797449\pi$
$450$	−0.817741	−0.0385487
$451$	11.0216	0.518988
$452$	−5.25680	−0.247259
$453$	−6.57949	−0.309131
$454$	1.89149	0.0887721
$455$	−14.6087	−0.684865
$456$	3.01662	0.141266
$457$	23.9523	1.12044	0.560221	−	0.828343i	$-0.310716\pi$
$457$	23.9523	1.12044	0.560221	+	0.828343i	$0.310716\pi$
$458$	−2.44847	−0.114409
$459$	3.51961	0.164281
$460$	17.6201	0.821542
$461$	−18.0733	−0.841756	−0.420878	−	0.907117i	$-0.638278\pi$
$461$	−18.0733	−0.841756	−0.420878	+	0.907117i	$0.638278\pi$
$462$	3.86463	0.179799
$463$	8.61844	0.400533	0.200266	−	0.979741i	$-0.435819\pi$
$463$	8.61844	0.400533	0.200266	+	0.979741i	$0.435819\pi$
$464$	−37.4954	−1.74068
$465$	25.3202	1.17420
$466$	−3.63930	−0.168587
$467$	11.4001	0.527536	0.263768	−	0.964586i	$-0.415035\pi$
$467$	11.4001	0.527536	0.263768	+	0.964586i	$0.415035\pi$
$468$	1.97319	0.0912108
$469$	−7.25341	−0.334931
$470$	−0.331150	−0.0152748
$471$	−15.6957	−0.723218
$472$	−2.79449	−0.128627
$473$	−17.6169	−0.810028
$474$	−0.0661579	−0.00303873
$475$	23.1581	1.06257
$476$	−32.0922	−1.47094
$477$	10.0134	0.458482
$478$	−0.928647	−0.0424753
$479$	−25.7379	−1.17599	−0.587997	−	0.808863i	$-0.700083\pi$
$479$	−25.7379	−1.17599	−0.587997	+	0.808863i	$0.700083\pi$
$480$	−6.10094	−0.278468
$481$	−3.97116	−0.181070
$482$	0.257799	0.0117424
$483$	−13.0527	−0.593919
$484$	−29.7726	−1.35330
$485$	−24.1777	−1.09785
$486$	−0.163737	−0.00742725
$487$	−4.10989	−0.186237	−0.0931185	−	0.995655i	$-0.529684\pi$
$487$	−4.10989	−0.186237	−0.0931185	+	0.995655i	$0.529684\pi$
$488$	2.69181	0.121852
$489$	17.4107	0.787339
$490$	−7.42991	−0.335649
$491$	8.65215	0.390466	0.195233	−	0.980757i	$-0.437454\pi$
$491$	8.65215	0.390466	0.195233	+	0.980757i	$0.437454\pi$
$492$	4.25784	0.191958
$493$	−34.3683	−1.54787
$494$	0.759243	0.0341600
$495$	−16.1473	−0.725767
$496$	30.7544	1.38092
$497$	12.7253	0.570808
$498$	−1.86590	−0.0836129
$499$	−18.8523	−0.843945	−0.421973	−	0.906609i	$-0.638662\pi$
$499$	−18.8523	−0.843945	−0.421973	+	0.906609i	$0.638662\pi$
$500$	0.0359384	0.00160721
$501$	−1.55283	−0.0693754
$502$	−0.600566	−0.0268046
$503$	−4.75159	−0.211863	−0.105931	−	0.994373i	$-0.533782\pi$
$503$	−4.75159	−0.211863	−0.105931	+	0.994373i	$0.533782\pi$
$504$	3.00623	0.133908
$505$	10.0478	0.447122
$506$	−2.36231	−0.105017
$507$	1.00000	0.0444116
$508$	30.9440	1.37292
$509$	10.4490	0.463142	0.231571	−	0.972818i	$-0.425613\pi$
$509$	10.4490	0.463142	0.231571	+	0.972818i	$0.425613\pi$
$510$	−1.82186	−0.0806735
$511$	47.3116	2.09294
$512$	−12.4064	−0.548292
$513$	4.63697	0.204727
$514$	3.59817	0.158708
$515$	−3.16137	−0.139306
$516$	−6.80572	−0.299605
$517$	−3.26760	−0.143709
$518$	−3.00469	−0.132019
$519$	−1.84736	−0.0810903
$520$	−2.05665	−0.0901901
$521$	−26.7892	−1.17366	−0.586828	−	0.809712i	$-0.699624\pi$
$521$	−26.7892	−1.17366	−0.586828	+	0.809712i	$0.699624\pi$
$522$	1.59886	0.0699800
$523$	−35.9081	−1.57015	−0.785077	−	0.619398i	$-0.787377\pi$
$523$	−35.9081	−1.57015	−0.785077	+	0.619398i	$0.787377\pi$
$524$	0.922360	0.0402935
$525$	23.0784	1.00722
$526$	−0.342812	−0.0149473
$527$	28.1895	1.22795
$528$	−19.6128	−0.853540
$529$	−15.0213	−0.653102
$530$	−5.18325	−0.225146
$531$	−4.29554	−0.186410
$532$	−42.2804	−1.83309
$533$	2.15785	0.0934667
$534$	2.33040	0.100846
$535$	−11.4960	−0.497016
$536$	−1.02116	−0.0441072
$537$	6.51002	0.280928
$538$	−2.53472	−0.109279
$539$	−73.3141	−3.15786
$540$	−6.23798	−0.268440
$541$	−31.8049	−1.36740	−0.683701	−	0.729763i	$-0.739631\pi$
$541$	−31.8049	−1.36740	−0.683701	+	0.729763i	$0.739631\pi$
$542$	−3.59767	−0.154533
$543$	−1.47565	−0.0633264
$544$	−6.79230	−0.291217
$545$	24.2401	1.03833
$546$	0.756628	0.0323807
$547$	−31.5433	−1.34869	−0.674347	−	0.738415i	$-0.735575\pi$
$547$	−31.5433	−1.34869	−0.674347	+	0.738415i	$0.735575\pi$
$548$	−13.4802	−0.575846
$549$	4.13769	0.176592
$550$	4.17677	0.178098
$551$	−45.2790	−1.92895
$552$	−1.83760	−0.0782134
$553$	1.86711	0.0793978
$554$	−0.427740	−0.0181729
$555$	12.5543	0.532901
$556$	16.7424	0.710037
$557$	−36.5136	−1.54713	−0.773565	−	0.633717i	$-0.781529\pi$
$557$	−36.5136	−1.54713	−0.773565	+	0.633717i	$0.781529\pi$
$558$	−1.31141	−0.0555165
$559$	−3.44910	−0.145881
$560$	56.0953	2.37046
$561$	−17.9771	−0.758994
$562$	2.56942	0.108384
$563$	−0.789780	−0.0332853	−0.0166426	−	0.999862i	$-0.505298\pi$
$563$	−0.789780	−0.0332853	−0.0166426	+	0.999862i	$0.505298\pi$
$564$	−1.26233	−0.0531537
$565$	8.42224	0.354326
$566$	−4.57684	−0.192379
$567$	4.62100	0.194064
$568$	1.79151	0.0751699
$569$	−41.4502	−1.73768	−0.868841	−	0.495091i	$-0.835135\pi$
$569$	−41.4502	−1.73768	−0.868841	+	0.495091i	$0.835135\pi$
$570$	−2.40025	−0.100535
$571$	46.8954	1.96251	0.981257	−	0.192705i	$-0.0617261\pi$
$571$	46.8954	1.96251	0.981257	+	0.192705i	$0.0617261\pi$
$572$	−10.0785	−0.421402
$573$	−10.6553	−0.445132
$574$	1.63269	0.0681471
$575$	−14.1070	−0.588302
$576$	−7.36373	−0.306822
$577$	−2.65928	−0.110707	−0.0553537	−	0.998467i	$-0.517629\pi$
$577$	−2.65928	−0.110707	−0.0553537	+	0.998467i	$0.517629\pi$
$578$	0.755208	0.0314125
$579$	−14.9986	−0.623322
$580$	60.9125	2.52925
$581$	52.6596	2.18469
$582$	1.25223	0.0519068
$583$	−51.1454	−2.11823
$584$	6.66066	0.275620
$585$	−3.16137	−0.130706
$586$	−1.13791	−0.0470066
$587$	−16.6129	−0.685689	−0.342844	−	0.939392i	$-0.611390\pi$
$587$	−16.6129	−0.685689	−0.342844	+	0.939392i	$0.611390\pi$
$588$	−28.3225	−1.16800
$589$	37.1387	1.53027
$590$	2.22351	0.0915404
$591$	27.4620	1.12964
$592$	15.2487	0.626718
$593$	10.8083	0.443845	0.221922	−	0.975064i	$-0.428767\pi$
$593$	10.8083	0.443845	0.221922	+	0.975064i	$0.428767\pi$
$594$	0.836318	0.0343146
$595$	51.4169	2.10789
$596$	17.6966	0.724882
$597$	−0.264401	−0.0108212
$598$	−0.462500	−0.0189130
$599$	25.1902	1.02924	0.514622	−	0.857417i	$-0.327932\pi$
$599$	25.1902	1.02924	0.514622	+	0.857417i	$0.327932\pi$
$600$	3.24904	0.132642
$601$	11.3331	0.462287	0.231144	−	0.972920i	$-0.425753\pi$
$601$	11.3331	0.462287	0.231144	+	0.972920i	$0.425753\pi$
$602$	−2.60968	−0.106363
$603$	−1.56966	−0.0639216
$604$	12.9826	0.528254
$605$	47.7005	1.93930
$606$	−0.520408	−0.0211401
$607$	−38.1653	−1.54908	−0.774540	−	0.632525i	$-0.782019\pi$
$607$	−38.1653	−1.54908	−0.774540	+	0.632525i	$0.782019\pi$
$608$	−8.94862	−0.362915
$609$	−45.1231	−1.82848
$610$	−2.14180	−0.0867191
$611$	−0.639740	−0.0258811
$612$	−6.94487	−0.280730
$613$	−33.8327	−1.36649	−0.683245	−	0.730189i	$-0.739432\pi$
$613$	−33.8327	−1.36649	−0.683245	+	0.730189i	$0.739432\pi$
$614$	0.309206	0.0124785
$615$	−6.82174	−0.275079
$616$	−15.3549	−0.618667
$617$	−14.0893	−0.567213	−0.283606	−	0.958941i	$-0.591531\pi$
$617$	−14.0893	−0.567213	−0.283606	+	0.958941i	$0.591531\pi$
$618$	0.163737	0.00658646
$619$	−18.8760	−0.758690	−0.379345	−	0.925255i	$-0.623851\pi$
$619$	−18.8760	−0.758690	−0.379345	+	0.925255i	$0.623851\pi$
$620$	−49.9616	−2.00651
$621$	−2.82465	−0.113349
$622$	−3.78988	−0.151960
$623$	−65.7688	−2.63497
$624$	−3.83986	−0.153717
$625$	−25.0288	−1.00115
$626$	4.49393	0.179614
$627$	−23.6843	−0.945858
$628$	30.9705	1.23586
$629$	13.9770	0.557298
$630$	−2.39198	−0.0952987
$631$	39.4154	1.56910	0.784552	−	0.620063i	$-0.212893\pi$
$631$	39.4154	1.56910	0.784552	+	0.620063i	$0.212893\pi$
$632$	0.262858	0.0104559
$633$	−24.5468	−0.975647
$634$	−2.40347	−0.0954539
$635$	−49.5773	−1.96741
$636$	−19.7583	−0.783469
$637$	−14.3536	−0.568712
$638$	−8.16647	−0.323314
$639$	2.75380	0.108939
$640$	16.0136	0.632992
$641$	23.0971	0.912282	0.456141	−	0.889907i	$-0.349231\pi$
$641$	23.0971	0.912282	0.456141	+	0.889907i	$0.349231\pi$
$642$	0.595413	0.0234991
$643$	37.7990	1.49065	0.745323	−	0.666703i	$-0.232295\pi$
$643$	37.7990	1.49065	0.745323	+	0.666703i	$0.232295\pi$
$644$	25.7555	1.01491
$645$	10.9039	0.429339
$646$	−2.67224	−0.105138
$647$	−2.68365	−0.105505	−0.0527526	−	0.998608i	$-0.516799\pi$
$647$	−2.68365	−0.105505	−0.0527526	+	0.998608i	$0.516799\pi$
$648$	0.650558	0.0255563
$649$	21.9403	0.861232
$650$	0.817741	0.0320744
$651$	37.0108	1.45057
$652$	−34.3546	−1.34543
$653$	−21.5517	−0.843384	−0.421692	−	0.906739i	$-0.638564\pi$
$653$	−21.5517	−0.843384	−0.421692	+	0.906739i	$0.638564\pi$
$654$	−1.25547	−0.0490927
$655$	−1.47777	−0.0577412
$656$	−8.28583	−0.323507
$657$	10.2384	0.399437
$658$	−0.484046	−0.0188701
$659$	36.7745	1.43253	0.716266	−	0.697828i	$-0.245850\pi$
$659$	36.7745	1.43253	0.716266	+	0.697828i	$0.245850\pi$
$660$	31.8617	1.24022
$661$	−39.4866	−1.53585	−0.767925	−	0.640539i	$-0.778711\pi$
$661$	−39.4866	−1.53585	−0.767925	+	0.640539i	$0.778711\pi$
$662$	−2.93478	−0.114063
$663$	−3.51961	−0.136690
$664$	7.41357	0.287702
$665$	67.7400	2.62685
$666$	−0.650226	−0.0251957
$667$	27.5821	1.06798
$668$	3.06403	0.118551
$669$	9.17938	0.354895
$670$	0.812508	0.0313899
$671$	−21.1341	−0.815872
$672$	−8.91780	−0.344012
$673$	20.2798	0.781730	0.390865	−	0.920448i	$-0.372176\pi$
$673$	20.2798	0.781730	0.390865	+	0.920448i	$0.372176\pi$
$674$	4.67134	0.179933
$675$	4.99424	0.192228
$676$	−1.97319	−0.0758919
$677$	−26.8502	−1.03194	−0.515969	−	0.856607i	$-0.672568\pi$
$677$	−26.8502	−1.03194	−0.515969	+	0.856607i	$0.672568\pi$
$678$	−0.436213	−0.0167527
$679$	−35.3407	−1.35625
$680$	7.23862	0.277588
$681$	−11.5520	−0.442674
$682$	6.69829	0.256491
$683$	−37.3122	−1.42771	−0.713856	−	0.700293i	$-0.753053\pi$
$683$	−37.3122	−1.42771	−0.713856	+	0.700293i	$0.753053\pi$
$684$	−9.14963	−0.349845
$685$	21.5974	0.825196
$686$	−5.56398	−0.212434
$687$	14.9537	0.570518
$688$	13.2440	0.504925
$689$	−10.0134	−0.381480
$690$	1.46213	0.0556624
$691$	−33.3056	−1.26700	−0.633502	−	0.773741i	$-0.718383\pi$
$691$	−33.3056	−1.26700	−0.633502	+	0.773741i	$0.718383\pi$
$692$	3.64520	0.138570
$693$	−23.6027	−0.896591
$694$	5.02962	0.190922
$695$	−26.8240	−1.01749
$696$	−6.35256	−0.240793
$697$	−7.59478	−0.287673
$698$	−4.02382	−0.152304
$699$	22.2265	0.840684
$700$	−45.5380	−1.72118
$701$	14.0850	0.531984	0.265992	−	0.963975i	$-0.414301\pi$
$701$	14.0850	0.531984	0.265992	+	0.963975i	$0.414301\pi$
$702$	0.163737	0.00617985
$703$	18.4142	0.694504
$704$	37.6117	1.41755
$705$	2.02245	0.0761700
$706$	−5.22700	−0.196721
$707$	14.6870	0.552362
$708$	8.47591	0.318544
$709$	0.299300	0.0112405	0.00562023	−	0.999984i	$-0.498211\pi$
$709$	0.299300	0.0112405	0.00562023	+	0.999984i	$0.498211\pi$
$710$	−1.42546	−0.0534964
$711$	0.404050	0.0151531
$712$	−9.25911	−0.347000
$713$	−22.6234	−0.847252
$714$	−2.66304	−0.0996617
$715$	16.1473	0.603875
$716$	−12.8455	−0.480059
$717$	5.67158	0.211809
$718$	1.66279	0.0620546
$719$	−21.4038	−0.798227	−0.399113	−	0.916902i	$-0.630682\pi$
$719$	−21.4038	−0.798227	−0.399113	+	0.916902i	$0.630682\pi$
$720$	12.1392	0.452401
$721$	−4.62100	−0.172095
$722$	−0.409590	−0.0152434
$723$	−1.57447	−0.0585552
$724$	2.91175	0.108214
$725$	−48.7677	−1.81119
$726$	−2.47056	−0.0916909
$727$	−10.8226	−0.401387	−0.200693	−	0.979654i	$-0.564319\pi$
$727$	−10.8226	−0.401387	−0.200693	+	0.979654i	$0.564319\pi$
$728$	−3.00623	−0.111418
$729$	1.00000	0.0370370
$730$	−5.29972	−0.196151
$731$	12.1395	0.448995
$732$	−8.16446	−0.301767
$733$	17.0481	0.629686	0.314843	−	0.949144i	$-0.398048\pi$
$733$	17.0481	0.629686	0.314843	+	0.949144i	$0.398048\pi$
$734$	−4.88749	−0.180401
$735$	45.3771	1.67376
$736$	5.45113	0.200931
$737$	8.01736	0.295323
$738$	0.353319	0.0130059
$739$	13.1572	0.483997	0.241998	−	0.970277i	$-0.422197\pi$
$739$	13.1572	0.483997	0.241998	+	0.970277i	$0.422197\pi$
$740$	−24.7720	−0.910638
$741$	−4.63697	−0.170343
$742$	−7.57641	−0.278139
$743$	−32.7708	−1.20224	−0.601122	−	0.799157i	$-0.705279\pi$
$743$	−32.7708	−1.20224	−0.601122	+	0.799157i	$0.705279\pi$
$744$	5.21049	0.191026
$745$	−28.3528	−1.03877
$746$	5.00470	0.183235
$747$	11.3957	0.416947
$748$	35.4723	1.29699
$749$	−16.8038	−0.613999
$750$	0.00298219	0.000108894 0
$751$	47.9910	1.75121	0.875607	−	0.483023i	$-0.160461\pi$
$751$	47.9910	1.75121	0.875607	+	0.483023i	$0.160461\pi$
$752$	2.45651	0.0895798
$753$	3.66787	0.133665
$754$	−1.59886	−0.0582269
$755$	−20.8002	−0.756996
$756$	−9.11811	−0.331623
$757$	−46.8287	−1.70202	−0.851009	−	0.525151i	$-0.824009\pi$
$757$	−46.8287	−1.70202	−0.851009	+	0.525151i	$0.824009\pi$
$758$	−4.12721	−0.149907
$759$	14.4275	0.523684
$760$	9.53664	0.345930
$761$	10.5546	0.382604	0.191302	−	0.981531i	$-0.438729\pi$
$761$	10.5546	0.382604	0.191302	+	0.981531i	$0.438729\pi$
$762$	2.56776	0.0930201
$763$	35.4319	1.28272
$764$	21.0249	0.760656
$765$	11.1268	0.402290
$766$	3.19784	0.115543
$767$	4.29554	0.155103
$768$	13.8981	0.501504
$769$	25.9742	0.936655	0.468328	−	0.883555i	$-0.344857\pi$
$769$	25.9742	0.936655	0.468328	+	0.883555i	$0.344857\pi$
$770$	12.2175	0.440288
$771$	−21.9753	−0.791422
$772$	29.5951	1.06515
$773$	−48.0880	−1.72961	−0.864803	−	0.502112i	$-0.832557\pi$
$773$	−48.0880	−1.72961	−0.864803	+	0.502112i	$0.832557\pi$
$774$	−0.564744	−0.0202993
$775$	40.0002	1.43685
$776$	−4.97537	−0.178605
$777$	18.3508	0.658330
$778$	5.70409	0.204502
$779$	−10.0059	−0.358498
$780$	6.23798	0.223355
$781$	−14.0656	−0.503306
$782$	1.62782	0.0582107
$783$	−9.76478	−0.348965
$784$	55.1160	1.96843
$785$	−49.6197	−1.77100
$786$	0.0765382	0.00273003
$787$	10.1803	0.362887	0.181444	−	0.983401i	$-0.441923\pi$
$787$	10.1803	0.362887	0.181444	+	0.983401i	$0.441923\pi$
$788$	−54.1877	−1.93036
$789$	2.09368	0.0745369
$790$	−0.209149	−0.00744120
$791$	12.3109	0.437724
$792$	−3.32285	−0.118072
$793$	−4.13769	−0.146934
$794$	0.772149	0.0274025
$795$	31.6560	1.12272
$796$	0.521713	0.0184916
$797$	−12.8505	−0.455189	−0.227595	−	0.973756i	$-0.573086\pi$
$797$	−12.8505	−0.455189	−0.227595	+	0.973756i	$0.573086\pi$
$798$	−3.50846	−0.124198
$799$	2.25164	0.0796572
$800$	−9.63809	−0.340758
$801$	−14.2326	−0.502883
$802$	−5.55277	−0.196075
$803$	−52.2946	−1.84544
$804$	3.09724	0.109231
$805$	−41.2644	−1.45438
$806$	1.31141	0.0461925
$807$	15.4804	0.544937
$808$	2.06768	0.0727407
$809$	−29.0969	−1.02299	−0.511496	−	0.859285i	$-0.670909\pi$
$809$	−29.0969	−1.02299	−0.511496	+	0.859285i	$0.670909\pi$
$810$	−0.517632	−0.0181877
$811$	33.3699	1.17178	0.585888	−	0.810392i	$-0.300746\pi$
$811$	33.3699	1.17178	0.585888	+	0.810392i	$0.300746\pi$
$812$	89.0364	3.12457
$813$	21.9723	0.770601
$814$	3.32116	0.116407
$815$	55.0416	1.92802
$816$	13.5148	0.473113
$817$	15.9934	0.559537
$818$	−5.69993	−0.199293
$819$	−4.62100	−0.161471
$820$	13.4606	0.470064
$821$	−27.9169	−0.974305	−0.487153	−	0.873317i	$-0.661964\pi$
$821$	−27.9169	−0.974305	−0.487153	+	0.873317i	$0.661964\pi$
$822$	−1.11860	−0.0390156
$823$	−15.5983	−0.543724	−0.271862	−	0.962336i	$-0.587639\pi$
$823$	−15.5983	−0.543724	−0.271862	+	0.962336i	$0.587639\pi$
$824$	−0.650558	−0.0226633
$825$	−25.5091	−0.888112
$826$	3.25012	0.113086
$827$	−9.10735	−0.316694	−0.158347	−	0.987384i	$-0.550616\pi$
$827$	−9.10735	−0.316694	−0.158347	+	0.987384i	$0.550616\pi$
$828$	5.57358	0.193695
$829$	42.4522	1.47442	0.737212	−	0.675661i	$-0.236142\pi$
$829$	42.4522	1.47442	0.737212	+	0.675661i	$0.236142\pi$
$830$	−5.89879	−0.204750
$831$	2.61236	0.0906219
$832$	7.36373	0.255292
$833$	50.5193	1.75039
$834$	1.38930	0.0481075
$835$	−4.90907	−0.169885
$836$	46.7335	1.61631
$837$	8.00926	0.276841
$838$	5.36412	0.185300
$839$	−23.8258	−0.822558	−0.411279	−	0.911510i	$-0.634918\pi$
$839$	−23.8258	−0.822558	−0.411279	+	0.911510i	$0.634918\pi$
$840$	9.50379	0.327912
$841$	66.3510	2.28797
$842$	2.30496	0.0794343
$843$	−15.6924	−0.540474
$844$	48.4355	1.66722
$845$	3.16137	0.108754
$846$	−0.104749	−0.00360135
$847$	69.7243	2.39576
$848$	38.4500	1.32038
$849$	27.9524	0.959323
$850$	−2.87813	−0.0987191
$851$	−11.2172	−0.384519
$852$	−5.43377	−0.186158
$853$	−24.7476	−0.847341	−0.423670	−	0.905816i	$-0.639259\pi$
$853$	−24.7476	−0.847341	−0.423670	+	0.905816i	$0.639259\pi$
$854$	−3.13070	−0.107130
$855$	14.6592	0.501333
$856$	−2.36569	−0.0808577
$857$	35.8358	1.22413	0.612064	−	0.790808i	$-0.290339\pi$
$857$	35.8358	1.22413	0.612064	+	0.790808i	$0.290339\pi$
$858$	−0.836318	−0.0285514
$859$	−12.2365	−0.417505	−0.208752	−	0.977969i	$-0.566940\pi$
$859$	−12.2365	−0.417505	−0.208752	+	0.977969i	$0.566940\pi$
$860$	−21.5154	−0.733669
$861$	−9.97141	−0.339825
$862$	−0.120897	−0.00411778
$863$	30.9389	1.05317	0.526586	−	0.850122i	$-0.323472\pi$
$863$	30.9389	1.05317	0.526586	+	0.850122i	$0.323472\pi$
$864$	−1.92984	−0.0656546
$865$	−5.84019	−0.198573
$866$	3.63589	0.123553
$867$	−4.61233	−0.156643
$868$	−73.0294	−2.47878
$869$	−2.06376	−0.0700084
$870$	5.05457	0.171366
$871$	1.56966	0.0531860
$872$	4.98821	0.168922
$873$	−7.64785	−0.258840
$874$	2.14460	0.0725421
$875$	−0.0841638	−0.00284526
$876$	−20.2023	−0.682572
$877$	−44.0615	−1.48785	−0.743926	−	0.668262i	$-0.767039\pi$
$877$	−44.0615	−1.48785	−0.743926	+	0.668262i	$0.767039\pi$
$878$	0.489433	0.0165176
$879$	6.94962	0.234405
$880$	−62.0034	−2.09013
$881$	20.6822	0.696800	0.348400	−	0.937346i	$-0.386725\pi$
$881$	20.6822	0.696800	0.348400	+	0.937346i	$0.386725\pi$
$882$	−2.35022	−0.0791361
$883$	−14.7864	−0.497604	−0.248802	−	0.968554i	$-0.580037\pi$
$883$	−14.7864	−0.497604	−0.248802	+	0.968554i	$0.580037\pi$
$884$	6.94487	0.233581
$885$	−13.5798	−0.456479
$886$	−5.94611	−0.199763
$887$	25.7404	0.864278	0.432139	−	0.901807i	$-0.357759\pi$
$887$	25.7404	0.864278	0.432139	+	0.901807i	$0.357759\pi$
$888$	2.58347	0.0866956
$889$	−72.4676	−2.43048
$890$	7.36724	0.246951
$891$	−5.10770	−0.171114
$892$	−18.1127	−0.606457
$893$	2.96646	0.0992688
$894$	1.46848	0.0491133
$895$	20.5806	0.687932
$896$	23.4072	0.781980
$897$	2.82465	0.0943124
$898$	5.58093	0.186238
$899$	−78.2087	−2.60841
$900$	−9.85458	−0.328486
$901$	35.2433	1.17412
$902$	−1.80465	−0.0600882
$903$	15.9383	0.530393
$904$	1.73316	0.0576440
$905$	−4.66509	−0.155073
$906$	1.07730	0.0357911
$907$	−51.7087	−1.71696	−0.858480	−	0.512847i	$-0.828591\pi$
$907$	−51.7087	−1.71696	−0.858480	+	0.512847i	$0.828591\pi$
$908$	22.7943	0.756457
$909$	3.17832	0.105418
$910$	2.39198	0.0792933
$911$	5.39304	0.178679	0.0893397	−	0.996001i	$-0.471524\pi$
$911$	5.39304	0.178679	0.0893397	+	0.996001i	$0.471524\pi$
$912$	17.8053	0.589593
$913$	−58.2058	−1.92633
$914$	−3.92187	−0.129724
$915$	13.0808	0.432437
$916$	−29.5065	−0.974921
$917$	−2.16007	−0.0713318
$918$	−0.576290	−0.0190204
$919$	3.39772	0.112080	0.0560402	−	0.998429i	$-0.482152\pi$
$919$	3.39772	0.112080	0.0560402	+	0.998429i	$0.482152\pi$
$920$	−5.80932	−0.191528
$921$	−1.88843	−0.0622259
$922$	2.95926	0.0974581
$923$	−2.75380	−0.0906424
$924$	46.5726	1.53212
$925$	19.8329	0.652103
$926$	−1.41116	−0.0463735
$927$	−1.00000	−0.0328443
$928$	18.8445	0.618601
$929$	40.7258	1.33617	0.668084	−	0.744085i	$-0.267114\pi$
$929$	40.7258	1.33617	0.668084	+	0.744085i	$0.267114\pi$
$930$	−4.14585	−0.135948
$931$	66.5575	2.18133
$932$	−43.8571	−1.43659
$933$	23.1462	0.757772
$934$	−1.86662	−0.0610778
$935$	−56.8323	−1.85861
$936$	−0.650558	−0.0212641
$937$	−41.0198	−1.34006	−0.670028	−	0.742335i	$-0.733718\pi$
$937$	−41.0198	−1.34006	−0.670028	+	0.742335i	$0.733718\pi$
$938$	1.18765	0.0387782
$939$	−27.4461	−0.895668
$940$	−3.99069	−0.130162
$941$	−49.2415	−1.60523	−0.802614	−	0.596499i	$-0.796558\pi$
$941$	−49.2415	−1.60523	−0.802614	+	0.596499i	$0.796558\pi$
$942$	2.56996	0.0837337
$943$	6.09517	0.198486
$944$	−16.4943	−0.536842
$945$	14.6087	0.475220
$946$	2.88454	0.0937846
$947$	−8.84801	−0.287522	−0.143761	−	0.989612i	$-0.545920\pi$
$947$	−8.84801	−0.287522	−0.143761	+	0.989612i	$0.545920\pi$
$948$	−0.797267	−0.0258940
$949$	−10.2384	−0.332352
$950$	−3.79184	−0.123024
$951$	14.6789	0.475994
$952$	10.5808	0.342924
$953$	−19.2054	−0.622124	−0.311062	−	0.950390i	$-0.600685\pi$
$953$	−19.2054	−0.622124	−0.311062	+	0.950390i	$0.600685\pi$
$954$	−1.63956	−0.0530828
$955$	−33.6853	−1.09003
$956$	−11.1911	−0.361946
$957$	49.8756	1.61225
$958$	4.21424	0.136156
$959$	31.5692	1.01942
$960$	−23.2795	−0.751341
$961$	33.1483	1.06930
$962$	0.650226	0.0209641
$963$	−3.63640	−0.117182
$964$	3.10673	0.100061
$965$	−47.4162	−1.52638
$966$	2.13721	0.0687636
$967$	10.3844	0.333940	0.166970	−	0.985962i	$-0.446602\pi$
$967$	10.3844	0.333940	0.166970	+	0.985962i	$0.446602\pi$
$968$	9.81599	0.315498
$969$	16.3203	0.524285
$970$	3.95877	0.127109
$971$	−13.3722	−0.429135	−0.214567	−	0.976709i	$-0.568834\pi$
$971$	−13.3722	−0.429135	−0.214567	+	0.976709i	$0.568834\pi$
$972$	−1.97319	−0.0632901
$973$	−39.2090	−1.25698
$974$	0.672941	0.0215624
$975$	−4.99424	−0.159944
$976$	15.8882	0.508568
$977$	−5.49368	−0.175758	−0.0878791	−	0.996131i	$-0.528009\pi$
$977$	−5.49368	−0.175758	−0.0878791	+	0.996131i	$0.528009\pi$
$978$	−2.85077	−0.0911576
$979$	72.6957	2.32337
$980$	−89.5377	−2.86018
$981$	7.66759	0.244807
$982$	−1.41668	−0.0452080
$983$	−54.1702	−1.72776	−0.863881	−	0.503695i	$-0.831973\pi$
$983$	−54.1702	−1.72776	−0.863881	+	0.503695i	$0.831973\pi$
$984$	−1.40380	−0.0447516
$985$	86.8174	2.76623
$986$	5.62735	0.179211
$987$	2.95624	0.0940982
$988$	9.14963	0.291088
$989$	−9.74250	−0.309793
$990$	2.64391	0.0840289
$991$	−33.7232	−1.07125	−0.535626	−	0.844455i	$-0.679924\pi$
$991$	−33.7232	−1.07125	−0.535626	+	0.844455i	$0.679924\pi$
$992$	−15.4566	−0.490748
$993$	17.9238	0.568793
$994$	−2.08360	−0.0660878
$995$	−0.835868	−0.0264988
$996$	−22.4859	−0.712493
$997$	−28.0740	−0.889114	−0.444557	−	0.895751i	$-0.646639\pi$
$997$	−28.0740	−0.889114	−0.444557	+	0.895751i	$0.646639\pi$
$998$	3.08682	0.0977115
$999$	3.97116	0.125642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.15	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-0.163737 q^{2} +1.00000 q^{3} -1.97319 q^{4} +3.16137 q^{5} -0.163737 q^{6} +4.62100 q^{7} +0.650558 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.163737 q^{2} +1.00000 q^{3} -1.97319 q^{4} +3.16137 q^{5} -0.163737 q^{6} +4.62100 q^{7} +0.650558 q^{8} +1.00000 q^{9} -0.517632 q^{10} -5.10770 q^{11} -1.97319 q^{12} -1.00000 q^{13} -0.756628 q^{14} +3.16137 q^{15} +3.83986 q^{16} +3.51961 q^{17} -0.163737 q^{18} +4.63697 q^{19} -6.23798 q^{20} +4.62100 q^{21} +0.836318 q^{22} -2.82465 q^{23} +0.650558 q^{24} +4.99424 q^{25} +0.163737 q^{26} +1.00000 q^{27} -9.11811 q^{28} -9.76478 q^{29} -0.517632 q^{30} +8.00926 q^{31} -1.92984 q^{32} -5.10770 q^{33} -0.576290 q^{34} +14.6087 q^{35} -1.97319 q^{36} +3.97116 q^{37} -0.759243 q^{38} -1.00000 q^{39} +2.05665 q^{40} -2.15785 q^{41} -0.756628 q^{42} +3.44910 q^{43} +10.0785 q^{44} +3.16137 q^{45} +0.462500 q^{46} +0.639740 q^{47} +3.83986 q^{48} +14.3536 q^{49} -0.817741 q^{50} +3.51961 q^{51} +1.97319 q^{52} +10.0134 q^{53} -0.163737 q^{54} -16.1473 q^{55} +3.00623 q^{56} +4.63697 q^{57} +1.59886 q^{58} -4.29554 q^{59} -6.23798 q^{60} +4.13769 q^{61} -1.31141 q^{62} +4.62100 q^{63} -7.36373 q^{64} -3.16137 q^{65} +0.836318 q^{66} -1.56966 q^{67} -6.94487 q^{68} -2.82465 q^{69} -2.39198 q^{70} +2.75380 q^{71} +0.650558 q^{72} +10.2384 q^{73} -0.650226 q^{74} +4.99424 q^{75} -9.14963 q^{76} -23.6027 q^{77} +0.163737 q^{78} +0.404050 q^{79} +12.1392 q^{80} +1.00000 q^{81} +0.353319 q^{82} +11.3957 q^{83} -9.11811 q^{84} +11.1268 q^{85} -0.564744 q^{86} -9.76478 q^{87} -3.32285 q^{88} -14.2326 q^{89} -0.517632 q^{90} -4.62100 q^{91} +5.57358 q^{92} +8.00926 q^{93} -0.104749 q^{94} +14.6592 q^{95} -1.92984 q^{96} -7.64785 q^{97} -2.35022 q^{98} -5.10770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 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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