LMFDB - Embedded newform 4022.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.17262 q^{3} +1.00000 q^{4} +4.25415 q^{5} +3.17262 q^{6} +4.60982 q^{7} -1.00000 q^{8} +7.06553 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.17262 q^{3} +1.00000 q^{4} +4.25415 q^{5} +3.17262 q^{6} +4.60982 q^{7} -1.00000 q^{8} +7.06553 q^{9} -4.25415 q^{10} -1.37868 q^{11} -3.17262 q^{12} +5.86718 q^{13} -4.60982 q^{14} -13.4968 q^{15} +1.00000 q^{16} -2.42902 q^{17} -7.06553 q^{18} -0.898901 q^{19} +4.25415 q^{20} -14.6252 q^{21} +1.37868 q^{22} -6.07725 q^{23} +3.17262 q^{24} +13.0978 q^{25} -5.86718 q^{26} -12.8984 q^{27} +4.60982 q^{28} +7.50485 q^{29} +13.4968 q^{30} +4.64005 q^{31} -1.00000 q^{32} +4.37403 q^{33} +2.42902 q^{34} +19.6109 q^{35} +7.06553 q^{36} +3.44327 q^{37} +0.898901 q^{38} -18.6144 q^{39} -4.25415 q^{40} -1.97823 q^{41} +14.6252 q^{42} -3.35381 q^{43} -1.37868 q^{44} +30.0578 q^{45} +6.07725 q^{46} +10.5237 q^{47} -3.17262 q^{48} +14.2505 q^{49} -13.0978 q^{50} +7.70635 q^{51} +5.86718 q^{52} -3.30715 q^{53} +12.8984 q^{54} -5.86511 q^{55} -4.60982 q^{56} +2.85187 q^{57} -7.50485 q^{58} -10.9135 q^{59} -13.4968 q^{60} -5.55303 q^{61} -4.64005 q^{62} +32.5708 q^{63} +1.00000 q^{64} +24.9599 q^{65} -4.37403 q^{66} +14.4776 q^{67} -2.42902 q^{68} +19.2808 q^{69} -19.6109 q^{70} -2.40981 q^{71} -7.06553 q^{72} +5.63237 q^{73} -3.44327 q^{74} -41.5542 q^{75} -0.898901 q^{76} -6.35548 q^{77} +18.6144 q^{78} +5.97538 q^{79} +4.25415 q^{80} +19.7251 q^{81} +1.97823 q^{82} +0.557012 q^{83} -14.6252 q^{84} -10.3334 q^{85} +3.35381 q^{86} -23.8100 q^{87} +1.37868 q^{88} -13.3822 q^{89} -30.0578 q^{90} +27.0467 q^{91} -6.07725 q^{92} -14.7211 q^{93} -10.5237 q^{94} -3.82405 q^{95} +3.17262 q^{96} +6.28902 q^{97} -14.2505 q^{98} -9.74111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.17262	−1.83171	−0.915857	−	0.401505i	$-0.868487\pi$
$3$	−3.17262	−1.83171	−0.915857	+	0.401505i	$0.868487\pi$
$4$	1.00000	0.500000
$5$	4.25415	1.90251	0.951256	−	0.308403i	$-0.0997944\pi$
$5$	4.25415	1.90251	0.951256	+	0.308403i	$0.0997944\pi$
$6$	3.17262	1.29522
$7$	4.60982	1.74235	0.871175	−	0.490973i	$-0.163359\pi$
$7$	4.60982	1.74235	0.871175	+	0.490973i	$0.163359\pi$
$8$	−1.00000	−0.353553
$9$	7.06553	2.35518
$10$	−4.25415	−1.34528
$11$	−1.37868	−0.415688	−0.207844	−	0.978162i	$-0.566645\pi$
$11$	−1.37868	−0.415688	−0.207844	+	0.978162i	$0.566645\pi$
$12$	−3.17262	−0.915857
$13$	5.86718	1.62726	0.813632	−	0.581380i	$-0.197487\pi$
$13$	5.86718	1.62726	0.813632	+	0.581380i	$0.197487\pi$
$14$	−4.60982	−1.23203
$15$	−13.4968	−3.48486
$16$	1.00000	0.250000
$17$	−2.42902	−0.589123	−0.294562	−	0.955632i	$-0.595174\pi$
$17$	−2.42902	−0.589123	−0.294562	+	0.955632i	$0.595174\pi$
$18$	−7.06553	−1.66536
$19$	−0.898901	−0.206222	−0.103111	−	0.994670i	$-0.532880\pi$
$19$	−0.898901	−0.206222	−0.103111	+	0.994670i	$0.532880\pi$
$20$	4.25415	0.951256
$21$	−14.6252	−3.19149
$22$	1.37868	0.293936
$23$	−6.07725	−1.26719	−0.633597	−	0.773663i	$-0.718422\pi$
$23$	−6.07725	−1.26719	−0.633597	+	0.773663i	$0.718422\pi$
$24$	3.17262	0.647609
$25$	13.0978	2.61955
$26$	−5.86718	−1.15065
$27$	−12.8984	−2.48229
$28$	4.60982	0.871175
$29$	7.50485	1.39362	0.696808	−	0.717258i	$-0.254603\pi$
$29$	7.50485	1.39362	0.696808	+	0.717258i	$0.254603\pi$
$30$	13.4968	2.46417
$31$	4.64005	0.833378	0.416689	−	0.909049i	$-0.363190\pi$
$31$	4.64005	0.833378	0.416689	+	0.909049i	$0.363190\pi$
$32$	−1.00000	−0.176777
$33$	4.37403	0.761421
$34$	2.42902	0.416573
$35$	19.6109	3.31484
$36$	7.06553	1.17759
$37$	3.44327	0.566069	0.283035	−	0.959110i	$-0.408659\pi$
$37$	3.44327	0.566069	0.283035	+	0.959110i	$0.408659\pi$
$38$	0.898901	0.145821
$39$	−18.6144	−2.98068
$40$	−4.25415	−0.672639
$41$	−1.97823	−0.308948	−0.154474	−	0.987997i	$-0.549368\pi$
$41$	−1.97823	−0.308948	−0.154474	+	0.987997i	$0.549368\pi$
$42$	14.6252	2.25672
$43$	−3.35381	−0.511452	−0.255726	−	0.966749i	$-0.582314\pi$
$43$	−3.35381	−0.511452	−0.255726	+	0.966749i	$0.582314\pi$
$44$	−1.37868	−0.207844
$45$	30.0578	4.48075
$46$	6.07725	0.896042
$47$	10.5237	1.53504	0.767521	−	0.641024i	$-0.221490\pi$
$47$	10.5237	1.53504	0.767521	+	0.641024i	$0.221490\pi$
$48$	−3.17262	−0.457928
$49$	14.2505	2.03578
$50$	−13.0978	−1.85230
$51$	7.70635	1.07911
$52$	5.86718	0.813632
$53$	−3.30715	−0.454273	−0.227136	−	0.973863i	$-0.572936\pi$
$53$	−3.30715	−0.454273	−0.227136	+	0.973863i	$0.572936\pi$
$54$	12.8984	1.75525
$55$	−5.86511	−0.790851
$56$	−4.60982	−0.616014
$57$	2.85187	0.377740
$58$	−7.50485	−0.985435
$59$	−10.9135	−1.42082	−0.710411	−	0.703787i	$-0.751491\pi$
$59$	−10.9135	−1.42082	−0.710411	+	0.703787i	$0.751491\pi$
$60$	−13.4968	−1.74243
$61$	−5.55303	−0.710993	−0.355496	−	0.934678i	$-0.615688\pi$
$61$	−5.55303	−0.710993	−0.355496	+	0.934678i	$0.615688\pi$
$62$	−4.64005	−0.589287
$63$	32.5708	4.10354
$64$	1.00000	0.125000
$65$	24.9599	3.09589
$66$	−4.37403	−0.538406
$67$	14.4776	1.76872	0.884362	−	0.466802i	$-0.154594\pi$
$67$	14.4776	1.76872	0.884362	+	0.466802i	$0.154594\pi$
$68$	−2.42902	−0.294562
$69$	19.2808	2.32114
$70$	−19.6109	−2.34395
$71$	−2.40981	−0.285991	−0.142996	−	0.989723i	$-0.545673\pi$
$71$	−2.40981	−0.285991	−0.142996	+	0.989723i	$0.545673\pi$
$72$	−7.06553	−0.832680
$73$	5.63237	0.659219	0.329609	−	0.944117i	$-0.393083\pi$
$73$	5.63237	0.659219	0.329609	+	0.944117i	$0.393083\pi$
$74$	−3.44327	−0.400272
$75$	−41.5542	−4.79827
$76$	−0.898901	−0.103111
$77$	−6.35548	−0.724274
$78$	18.6144	2.10766
$79$	5.97538	0.672283	0.336141	−	0.941812i	$-0.390878\pi$
$79$	5.97538	0.672283	0.336141	+	0.941812i	$0.390878\pi$
$80$	4.25415	0.475628
$81$	19.7251	2.19168
$82$	1.97823	0.218459
$83$	0.557012	0.0611400	0.0305700	−	0.999533i	$-0.490268\pi$
$83$	0.557012	0.0611400	0.0305700	+	0.999533i	$0.490268\pi$
$84$	−14.6252	−1.59574
$85$	−10.3334	−1.12081
$86$	3.35381	0.361651
$87$	−23.8100	−2.55270
$88$	1.37868	0.146968
$89$	−13.3822	−1.41851	−0.709257	−	0.704950i	$-0.750969\pi$
$89$	−13.3822	−1.41851	−0.709257	+	0.704950i	$0.750969\pi$
$90$	−30.0578	−3.16837
$91$	27.0467	2.83526
$92$	−6.07725	−0.633597
$93$	−14.7211	−1.52651
$94$	−10.5237	−1.08544
$95$	−3.82405	−0.392340
$96$	3.17262	0.323804
$97$	6.28902	0.638553	0.319276	−	0.947662i	$-0.396560\pi$
$97$	6.28902	0.638553	0.319276	+	0.947662i	$0.396560\pi$
$98$	−14.2505	−1.43951
$99$	−9.74111	−0.979018
$100$	13.0978	1.30978
$101$	10.4145	1.03628	0.518142	−	0.855295i	$-0.326624\pi$
$101$	10.4145	1.03628	0.518142	+	0.855295i	$0.326624\pi$
$102$	−7.70635	−0.763043
$103$	9.59669	0.945590	0.472795	−	0.881173i	$-0.343245\pi$
$103$	9.59669	0.945590	0.472795	+	0.881173i	$0.343245\pi$
$104$	−5.86718	−0.575325
$105$	−62.2178	−6.07184
$106$	3.30715	0.321219
$107$	−1.38035	−0.133443	−0.0667217	−	0.997772i	$-0.521254\pi$
$107$	−1.38035	−0.133443	−0.0667217	+	0.997772i	$0.521254\pi$
$108$	−12.8984	−1.24115
$109$	1.63183	0.156301	0.0781503	−	0.996942i	$-0.475099\pi$
$109$	1.63183	0.156301	0.0781503	+	0.996942i	$0.475099\pi$
$110$	5.86511	0.559216
$111$	−10.9242	−1.03688
$112$	4.60982	0.435587
$113$	−17.2113	−1.61910	−0.809551	−	0.587050i	$-0.800289\pi$
$113$	−17.2113	−1.61910	−0.809551	+	0.587050i	$0.800289\pi$
$114$	−2.85187	−0.267102
$115$	−25.8535	−2.41085
$116$	7.50485	0.696808
$117$	41.4547	3.83249
$118$	10.9135	1.00467
$119$	−11.1973	−1.02646
$120$	13.4968	1.23208
$121$	−9.09924	−0.827203
$122$	5.55303	0.502748
$123$	6.27617	0.565903
$124$	4.64005	0.416689
$125$	34.4490	3.08121
$126$	−32.5708	−2.90164
$127$	−18.1468	−1.61027	−0.805133	−	0.593094i	$-0.797906\pi$
$127$	−18.1468	−1.61027	−0.805133	+	0.593094i	$0.797906\pi$
$128$	−1.00000	−0.0883883
$129$	10.6404	0.936833
$130$	−24.9599	−2.18912
$131$	−7.03656	−0.614787	−0.307394	−	0.951582i	$-0.599457\pi$
$131$	−7.03656	−0.614787	−0.307394	+	0.951582i	$0.599457\pi$
$132$	4.37403	0.380711
$133$	−4.14377	−0.359311
$134$	−14.4776	−1.25068
$135$	−54.8716	−4.72259
$136$	2.42902	0.208287
$137$	−21.1388	−1.80601	−0.903006	−	0.429629i	$-0.858644\pi$
$137$	−21.1388	−1.80601	−0.903006	+	0.429629i	$0.858644\pi$
$138$	−19.2808	−1.64129
$139$	−12.5912	−1.06797	−0.533987	−	0.845493i	$-0.679307\pi$
$139$	−12.5912	−1.06797	−0.533987	+	0.845493i	$0.679307\pi$
$140$	19.6109	1.65742
$141$	−33.3878	−2.81176
$142$	2.40981	0.202226
$143$	−8.08898	−0.676434
$144$	7.06553	0.588794
$145$	31.9267	2.65137
$146$	−5.63237	−0.466138
$147$	−45.2113	−3.72897
$148$	3.44327	0.283035
$149$	6.08674	0.498645	0.249322	−	0.968421i	$-0.419792\pi$
$149$	6.08674	0.498645	0.249322	+	0.968421i	$0.419792\pi$
$150$	41.5542	3.39289
$151$	−14.6543	−1.19255	−0.596276	−	0.802779i	$-0.703354\pi$
$151$	−14.6543	−1.19255	−0.596276	+	0.802779i	$0.703354\pi$
$152$	0.898901	0.0729105
$153$	−17.1623	−1.38749
$154$	6.35548	0.512139
$155$	19.7395	1.58551
$156$	−18.6144	−1.49034
$157$	12.4671	0.994981	0.497491	−	0.867469i	$-0.334255\pi$
$157$	12.4671	0.994981	0.497491	+	0.867469i	$0.334255\pi$
$158$	−5.97538	−0.475376
$159$	10.4923	0.832097
$160$	−4.25415	−0.336320
$161$	−28.0151	−2.20790
$162$	−19.7251	−1.54975
$163$	12.8517	1.00662	0.503311	−	0.864105i	$-0.332115\pi$
$163$	12.8517	1.00662	0.503311	+	0.864105i	$0.332115\pi$
$164$	−1.97823	−0.154474
$165$	18.6078	1.44861
$166$	−0.557012	−0.0432325
$167$	7.59083	0.587396	0.293698	−	0.955898i	$-0.405114\pi$
$167$	7.59083	0.587396	0.293698	+	0.955898i	$0.405114\pi$
$168$	14.6252	1.12836
$169$	21.4239	1.64799
$170$	10.3334	0.792535
$171$	−6.35121	−0.485689
$172$	−3.35381	−0.255726
$173$	2.40888	0.183144	0.0915719	−	0.995798i	$-0.470811\pi$
$173$	2.40888	0.183144	0.0915719	+	0.995798i	$0.470811\pi$
$174$	23.8100	1.80503
$175$	60.3783	4.56417
$176$	−1.37868	−0.103922
$177$	34.6245	2.60254
$178$	13.3822	1.00304
$179$	15.5442	1.16182	0.580912	−	0.813966i	$-0.302696\pi$
$179$	15.5442	1.16182	0.580912	+	0.813966i	$0.302696\pi$
$180$	30.0578	2.24037
$181$	−25.3380	−1.88336	−0.941678	−	0.336515i	$-0.890752\pi$
$181$	−25.3380	−1.88336	−0.941678	+	0.336515i	$0.890752\pi$
$182$	−27.0467	−2.00483
$183$	17.6177	1.30234
$184$	6.07725	0.448021
$185$	14.6482	1.07695
$186$	14.7211	1.07941
$187$	3.34884	0.244892
$188$	10.5237	0.767521
$189$	−59.4592	−4.32502
$190$	3.82405	0.277426
$191$	17.2750	1.24998	0.624989	−	0.780634i	$-0.285103\pi$
$191$	17.2750	1.24998	0.624989	+	0.780634i	$0.285103\pi$
$192$	−3.17262	−0.228964
$193$	−24.0784	−1.73320	−0.866601	−	0.499001i	$-0.833700\pi$
$193$	−24.0784	−1.73320	−0.866601	+	0.499001i	$0.833700\pi$
$194$	−6.28902	−0.451525
$195$	−79.1882	−5.67078
$196$	14.2505	1.01789
$197$	14.4923	1.03253	0.516265	−	0.856429i	$-0.327322\pi$
$197$	14.4923	1.03253	0.516265	+	0.856429i	$0.327322\pi$
$198$	9.74111	0.692270
$199$	14.3070	1.01420	0.507099	−	0.861888i	$-0.330718\pi$
$199$	14.3070	1.01420	0.507099	+	0.861888i	$0.330718\pi$
$200$	−13.0978	−0.926151
$201$	−45.9320	−3.23980
$202$	−10.4145	−0.732763
$203$	34.5960	2.42817
$204$	7.70635	0.539553
$205$	−8.41568	−0.587776
$206$	−9.59669	−0.668633
$207$	−42.9390	−2.98447
$208$	5.86718	0.406816
$209$	1.23930	0.0857240
$210$	62.2178	4.29344
$211$	−2.62981	−0.181043	−0.0905217	−	0.995894i	$-0.528853\pi$
$211$	−2.62981	−0.181043	−0.0905217	+	0.995894i	$0.528853\pi$
$212$	−3.30715	−0.227136
$213$	7.64540	0.523854
$214$	1.38035	0.0943588
$215$	−14.2676	−0.973043
$216$	12.8984	0.877623
$217$	21.3898	1.45204
$218$	−1.63183	−0.110521
$219$	−17.8694	−1.20750
$220$	−5.86511	−0.395426
$221$	−14.2515	−0.958659
$222$	10.9242	0.733183
$223$	−12.6390	−0.846369	−0.423184	−	0.906044i	$-0.639088\pi$
$223$	−12.6390	−0.846369	−0.423184	+	0.906044i	$0.639088\pi$
$224$	−4.60982	−0.308007
$225$	92.5425	6.16950
$226$	17.2113	1.14488
$227$	−17.8242	−1.18303	−0.591517	−	0.806292i	$-0.701471\pi$
$227$	−17.8242	−1.18303	−0.591517	+	0.806292i	$0.701471\pi$
$228$	2.85187	0.188870
$229$	4.55380	0.300923	0.150462	−	0.988616i	$-0.451924\pi$
$229$	4.55380	0.300923	0.150462	+	0.988616i	$0.451924\pi$
$230$	25.8535	1.70473
$231$	20.1635	1.32666
$232$	−7.50485	−0.492718
$233$	23.7987	1.55910	0.779552	−	0.626337i	$-0.215447\pi$
$233$	23.7987	1.55910	0.779552	+	0.626337i	$0.215447\pi$
$234$	−41.4547	−2.70998
$235$	44.7694	2.92043
$236$	−10.9135	−0.710411
$237$	−18.9576	−1.23143
$238$	11.1973	0.725816
$239$	17.3939	1.12512	0.562559	−	0.826757i	$-0.309817\pi$
$239$	17.3939	1.12512	0.562559	+	0.826757i	$0.309817\pi$
$240$	−13.4968	−0.871214
$241$	−4.55831	−0.293626	−0.146813	−	0.989164i	$-0.546902\pi$
$241$	−4.55831	−0.293626	−0.146813	+	0.989164i	$0.546902\pi$
$242$	9.09924	0.584921
$243$	−23.8851	−1.53223
$244$	−5.55303	−0.355496
$245$	60.6236	3.87310
$246$	−6.27617	−0.400154
$247$	−5.27402	−0.335578
$248$	−4.64005	−0.294644
$249$	−1.76719	−0.111991
$250$	−34.4490	−2.17875
$251$	−18.1843	−1.14778	−0.573891	−	0.818932i	$-0.694567\pi$
$251$	−18.1843	−1.14778	−0.573891	+	0.818932i	$0.694567\pi$
$252$	32.5708	2.05177
$253$	8.37859	0.526758
$254$	18.1468	1.13863
$255$	32.7840	2.05301
$256$	1.00000	0.0625000
$257$	−11.5845	−0.722619	−0.361309	−	0.932446i	$-0.617670\pi$
$257$	−11.5845	−0.722619	−0.361309	+	0.932446i	$0.617670\pi$
$258$	−10.6404	−0.662441
$259$	15.8728	0.986291
$260$	24.9599	1.54794
$261$	53.0257	3.28221
$262$	7.03656	0.434720
$263$	−6.34875	−0.391481	−0.195740	−	0.980656i	$-0.562711\pi$
$263$	−6.34875	−0.391481	−0.195740	+	0.980656i	$0.562711\pi$
$264$	−4.37403	−0.269203
$265$	−14.0691	−0.864259
$266$	4.14377	0.254071
$267$	42.4568	2.59831
$268$	14.4776	0.884362
$269$	6.21690	0.379051	0.189525	−	0.981876i	$-0.439305\pi$
$269$	6.21690	0.379051	0.189525	+	0.981876i	$0.439305\pi$
$270$	54.8716	3.33938
$271$	17.3888	1.05629	0.528147	−	0.849153i	$-0.322887\pi$
$271$	17.3888	1.05629	0.528147	+	0.849153i	$0.322887\pi$
$272$	−2.42902	−0.147281
$273$	−85.8089	−5.19339
$274$	21.1388	1.27704
$275$	−18.0576	−1.08892
$276$	19.2808	1.16057
$277$	12.3875	0.744292	0.372146	−	0.928174i	$-0.378622\pi$
$277$	12.3875	0.744292	0.372146	+	0.928174i	$0.378622\pi$
$278$	12.5912	0.755171
$279$	32.7844	1.96275
$280$	−19.6109	−1.17197
$281$	−26.6964	−1.59258	−0.796288	−	0.604918i	$-0.793206\pi$
$281$	−26.6964	−1.59258	−0.796288	+	0.604918i	$0.793206\pi$
$282$	33.3878	1.98821
$283$	−19.5466	−1.16193	−0.580963	−	0.813930i	$-0.697324\pi$
$283$	−19.5466	−1.16193	−0.580963	+	0.813930i	$0.697324\pi$
$284$	−2.40981	−0.142996
$285$	12.1323	0.718654
$286$	8.08898	0.478311
$287$	−9.11929	−0.538295
$288$	−7.06553	−0.416340
$289$	−11.0999	−0.652934
$290$	−31.9267	−1.87480
$291$	−19.9527	−1.16965
$292$	5.63237	0.329609
$293$	11.5515	0.674847	0.337423	−	0.941353i	$-0.390445\pi$
$293$	11.5515	0.674847	0.337423	+	0.941353i	$0.390445\pi$
$294$	45.2113	2.63678
$295$	−46.4278	−2.70313
$296$	−3.44327	−0.200136
$297$	17.7827	1.03186
$298$	−6.08674	−0.352595
$299$	−35.6564	−2.06206
$300$	−41.5542	−2.39913
$301$	−15.4605	−0.891127
$302$	14.6543	0.843262
$303$	−33.0413	−1.89818
$304$	−0.898901	−0.0515555
$305$	−23.6234	−1.35267
$306$	17.1623	0.981103
$307$	−15.5205	−0.885803	−0.442901	−	0.896570i	$-0.646051\pi$
$307$	−15.5205	−0.885803	−0.442901	+	0.896570i	$0.646051\pi$
$308$	−6.35548	−0.362137
$309$	−30.4467	−1.73205
$310$	−19.7395	−1.12113
$311$	−12.6984	−0.720062	−0.360031	−	0.932940i	$-0.617234\pi$
$311$	−12.6984	−0.720062	−0.360031	+	0.932940i	$0.617234\pi$
$312$	18.6144	1.05383
$313$	−3.69100	−0.208627	−0.104314	−	0.994544i	$-0.533265\pi$
$313$	−3.69100	−0.208627	−0.104314	+	0.994544i	$0.533265\pi$
$314$	−12.4671	−0.703558
$315$	138.561	7.80703
$316$	5.97538	0.336141
$317$	13.1249	0.737170	0.368585	−	0.929594i	$-0.379842\pi$
$317$	13.1249	0.737170	0.368585	+	0.929594i	$0.379842\pi$
$318$	−10.4923	−0.588382
$319$	−10.3468	−0.579309
$320$	4.25415	0.237814
$321$	4.37933	0.244430
$322$	28.0151	1.56122
$323$	2.18345	0.121490
$324$	19.7251	1.09584
$325$	76.8469	4.26270
$326$	−12.8517	−0.711789
$327$	−5.17716	−0.286298
$328$	1.97823	0.109229
$329$	48.5125	2.67458
$330$	−18.6078	−1.02432
$331$	8.13173	0.446960	0.223480	−	0.974709i	$-0.428258\pi$
$331$	8.13173	0.446960	0.223480	+	0.974709i	$0.428258\pi$
$332$	0.557012	0.0305700
$333$	24.3285	1.33319
$334$	−7.59083	−0.415352
$335$	61.5900	3.36502
$336$	−14.6252	−0.797871
$337$	0.152366	0.00829991	0.00414995	−	0.999991i	$-0.498679\pi$
$337$	0.152366	0.00829991	0.00414995	+	0.999991i	$0.498679\pi$
$338$	−21.4239	−1.16530
$339$	54.6049	2.96573
$340$	−10.3334	−0.560407
$341$	−6.39715	−0.346425
$342$	6.35121	0.343434
$343$	33.4234	1.80469
$344$	3.35381	0.180825
$345$	82.0234	4.41599
$346$	−2.40888	−0.129502
$347$	1.01705	0.0545979	0.0272989	−	0.999627i	$-0.491309\pi$
$347$	1.01705	0.0545979	0.0272989	+	0.999627i	$0.491309\pi$
$348$	−23.8100	−1.27635
$349$	−28.0248	−1.50013	−0.750067	−	0.661361i	$-0.769979\pi$
$349$	−28.0248	−1.50013	−0.750067	+	0.661361i	$0.769979\pi$
$350$	−60.3783	−3.22736
$351$	−75.6771	−4.03935
$352$	1.37868	0.0734839
$353$	6.69622	0.356404	0.178202	−	0.983994i	$-0.442972\pi$
$353$	6.69622	0.356404	0.178202	+	0.983994i	$0.442972\pi$
$354$	−34.6245	−1.84027
$355$	−10.2517	−0.544102
$356$	−13.3822	−0.709257
$357$	35.5249	1.88018
$358$	−15.5442	−0.821534
$359$	17.8944	0.944431	0.472216	−	0.881483i	$-0.343454\pi$
$359$	17.8944	0.944431	0.472216	+	0.881483i	$0.343454\pi$
$360$	−30.0578	−1.58418
$361$	−18.1920	−0.957473
$362$	25.3380	1.33173
$363$	28.8684	1.51520
$364$	27.0467	1.41763
$365$	23.9609	1.25417
$366$	−17.6177	−0.920890
$367$	4.04177	0.210978	0.105489	−	0.994420i	$-0.466359\pi$
$367$	4.04177	0.210978	0.105489	+	0.994420i	$0.466359\pi$
$368$	−6.07725	−0.316799
$369$	−13.9772	−0.727626
$370$	−14.6482	−0.761521
$371$	−15.2454	−0.791501
$372$	−14.7211	−0.763255
$373$	3.11177	0.161122	0.0805608	−	0.996750i	$-0.474329\pi$
$373$	3.11177	0.161122	0.0805608	+	0.996750i	$0.474329\pi$
$374$	−3.34884	−0.173164
$375$	−109.294	−5.64390
$376$	−10.5237	−0.542719
$377$	44.0323	2.26778
$378$	59.4592	3.05825
$379$	−20.9982	−1.07861	−0.539303	−	0.842111i	$-0.681312\pi$
$379$	−20.9982	−1.07861	−0.539303	+	0.842111i	$0.681312\pi$
$380$	−3.82405	−0.196170
$381$	57.5728	2.94955
$382$	−17.2750	−0.883868
$383$	−22.6410	−1.15690	−0.578452	−	0.815717i	$-0.696343\pi$
$383$	−22.6410	−1.15690	−0.578452	+	0.815717i	$0.696343\pi$
$384$	3.17262	0.161902
$385$	−27.0371	−1.37794
$386$	24.0784	1.22556
$387$	−23.6964	−1.20456
$388$	6.28902	0.319276
$389$	29.2610	1.48359	0.741797	−	0.670625i	$-0.233974\pi$
$389$	29.2610	1.48359	0.741797	+	0.670625i	$0.233974\pi$
$390$	79.1882	4.00985
$391$	14.7618	0.746534
$392$	−14.2505	−0.719757
$393$	22.3244	1.12611
$394$	−14.4923	−0.730110
$395$	25.4201	1.27903
$396$	−9.74111	−0.489509
$397$	−10.4684	−0.525392	−0.262696	−	0.964879i	$-0.584612\pi$
$397$	−10.4684	−0.525392	−0.262696	+	0.964879i	$0.584612\pi$
$398$	−14.3070	−0.717147
$399$	13.1466	0.658154
$400$	13.0978	0.654888
$401$	−10.8419	−0.541416	−0.270708	−	0.962661i	$-0.587258\pi$
$401$	−10.8419	−0.541416	−0.270708	+	0.962661i	$0.587258\pi$
$402$	45.9320	2.29088
$403$	27.2240	1.35613
$404$	10.4145	0.518142
$405$	83.9133	4.16969
$406$	−34.5960	−1.71697
$407$	−4.74717	−0.235308
$408$	−7.70635	−0.381521
$409$	10.8422	0.536114	0.268057	−	0.963403i	$-0.413618\pi$
$409$	10.8422	0.536114	0.268057	+	0.963403i	$0.413618\pi$
$410$	8.41568	0.415621
$411$	67.0655	3.30810
$412$	9.59669	0.472795
$413$	−50.3095	−2.47557
$414$	42.9390	2.11034
$415$	2.36961	0.116320
$416$	−5.86718	−0.287662
$417$	39.9472	1.95622
$418$	−1.23930	−0.0606160
$419$	−10.5711	−0.516433	−0.258216	−	0.966087i	$-0.583135\pi$
$419$	−10.5711	−0.516433	−0.258216	+	0.966087i	$0.583135\pi$
$420$	−62.2178	−3.03592
$421$	−37.5167	−1.82845	−0.914227	−	0.405203i	$-0.867201\pi$
$421$	−37.5167	−1.82845	−0.914227	+	0.405203i	$0.867201\pi$
$422$	2.62981	0.128017
$423$	74.3556	3.61529
$424$	3.30715	0.160610
$425$	−31.8147	−1.54324
$426$	−7.64540	−0.370421
$427$	−25.5985	−1.23880
$428$	−1.38035	−0.0667217
$429$	25.6633	1.23903
$430$	14.2676	0.688045
$431$	−5.70191	−0.274651	−0.137326	−	0.990526i	$-0.543851\pi$
$431$	−5.70191	−0.274651	−0.137326	+	0.990526i	$0.543851\pi$
$432$	−12.8984	−0.620573
$433$	−8.01978	−0.385406	−0.192703	−	0.981257i	$-0.561725\pi$
$433$	−8.01978	−0.385406	−0.192703	+	0.981257i	$0.561725\pi$
$434$	−21.3898	−1.02674
$435$	−101.291	−4.85655
$436$	1.63183	0.0781503
$437$	5.46285	0.261323
$438$	17.8694	0.853831
$439$	−20.1072	−0.959663	−0.479831	−	0.877361i	$-0.659302\pi$
$439$	−20.1072	−0.959663	−0.479831	+	0.877361i	$0.659302\pi$
$440$	5.86511	0.279608
$441$	100.687	4.79462
$442$	14.2515	0.677875
$443$	16.7454	0.795599	0.397799	−	0.917472i	$-0.369774\pi$
$443$	16.7454	0.795599	0.397799	+	0.917472i	$0.369774\pi$
$444$	−10.9242	−0.518439
$445$	−56.9300	−2.69874
$446$	12.6390	0.598473
$447$	−19.3109	−0.913375
$448$	4.60982	0.217794
$449$	−13.6802	−0.645610	−0.322805	−	0.946465i	$-0.604626\pi$
$449$	−13.6802	−0.645610	−0.322805	+	0.946465i	$0.604626\pi$
$450$	−92.5425	−4.36250
$451$	2.72735	0.128426
$452$	−17.2113	−0.809551
$453$	46.4926	2.18441
$454$	17.8242	0.836532
$455$	115.061	5.39412
$456$	−2.85187	−0.133551
$457$	−14.2990	−0.668881	−0.334440	−	0.942417i	$-0.608547\pi$
$457$	−14.2990	−0.668881	−0.334440	+	0.942417i	$0.608547\pi$
$458$	−4.55380	−0.212785
$459$	31.3304	1.46238
$460$	−25.8535	−1.20543
$461$	0.530861	0.0247247	0.0123623	−	0.999924i	$-0.496065\pi$
$461$	0.530861	0.0247247	0.0123623	+	0.999924i	$0.496065\pi$
$462$	−20.1635	−0.938092
$463$	18.5087	0.860172	0.430086	−	0.902788i	$-0.358483\pi$
$463$	18.5087	0.860172	0.430086	+	0.902788i	$0.358483\pi$
$464$	7.50485	0.348404
$465$	−62.6258	−2.90420
$466$	−23.7987	−1.10245
$467$	−19.4400	−0.899578	−0.449789	−	0.893135i	$-0.648501\pi$
$467$	−19.4400	−0.899578	−0.449789	+	0.893135i	$0.648501\pi$
$468$	41.4547	1.91625
$469$	66.7393	3.08174
$470$	−44.7694	−2.06506
$471$	−39.5533	−1.82252
$472$	10.9135	0.502336
$473$	4.62384	0.212604
$474$	18.9576	0.870752
$475$	−11.7736	−0.540209
$476$	−11.1973	−0.513229
$477$	−23.3668	−1.06989
$478$	−17.3939	−0.795578
$479$	25.4261	1.16175	0.580874	−	0.813994i	$-0.302711\pi$
$479$	25.4261	1.16175	0.580874	+	0.813994i	$0.302711\pi$
$480$	13.4968	0.616041
$481$	20.2023	0.921144
$482$	4.55831	0.207625
$483$	88.8812	4.04423
$484$	−9.09924	−0.413602
$485$	26.7544	1.21485
$486$	23.8851	1.08345
$487$	35.2753	1.59848	0.799238	−	0.601014i	$-0.205236\pi$
$487$	35.2753	1.59848	0.799238	+	0.601014i	$0.205236\pi$
$488$	5.55303	0.251374
$489$	−40.7735	−1.84384
$490$	−60.6236	−2.73869
$491$	−20.9361	−0.944835	−0.472417	−	0.881375i	$-0.656619\pi$
$491$	−20.9361	−0.944835	−0.472417	+	0.881375i	$0.656619\pi$
$492$	6.27617	0.282952
$493$	−18.2294	−0.821012
$494$	5.27402	0.237289
$495$	−41.4401	−1.86259
$496$	4.64005	0.208344
$497$	−11.1088	−0.498297
$498$	1.76719	0.0791896
$499$	−38.2346	−1.71162	−0.855809	−	0.517293i	$-0.826940\pi$
$499$	−38.2346	−1.71162	−0.855809	+	0.517293i	$0.826940\pi$
$500$	34.4490	1.54061
$501$	−24.0828	−1.07594
$502$	18.1843	0.811604
$503$	33.6341	1.49967	0.749836	−	0.661624i	$-0.230133\pi$
$503$	33.6341	1.49967	0.749836	+	0.661624i	$0.230133\pi$
$504$	−32.5708	−1.45082
$505$	44.3049	1.97154
$506$	−8.37859	−0.372474
$507$	−67.9698	−3.01864
$508$	−18.1468	−0.805133
$509$	3.76941	0.167076	0.0835382	−	0.996505i	$-0.473378\pi$
$509$	3.76941	0.167076	0.0835382	+	0.996505i	$0.473378\pi$
$510$	−32.7840	−1.45170
$511$	25.9642	1.14859
$512$	−1.00000	−0.0441942
$513$	11.5944	0.511903
$514$	11.5845	0.510969
$515$	40.8257	1.79900
$516$	10.6404	0.468416
$517$	−14.5088	−0.638098
$518$	−15.8728	−0.697413
$519$	−7.64246	−0.335467
$520$	−24.9599	−1.09456
$521$	1.90776	0.0835807	0.0417903	−	0.999126i	$-0.486694\pi$
$521$	1.90776	0.0835807	0.0417903	+	0.999126i	$0.486694\pi$
$522$	−53.0257	−2.32087
$523$	36.7415	1.60659	0.803296	−	0.595580i	$-0.203078\pi$
$523$	36.7415	1.60659	0.803296	+	0.595580i	$0.203078\pi$
$524$	−7.03656	−0.307394
$525$	−191.558	−8.36026
$526$	6.34875	0.276819
$527$	−11.2708	−0.490962
$528$	4.37403	0.190355
$529$	13.9330	0.605783
$530$	14.0691	0.611123
$531$	−77.1099	−3.34629
$532$	−4.14377	−0.179655
$533$	−11.6066	−0.502739
$534$	−42.4568	−1.83728
$535$	−5.87221	−0.253878
$536$	−14.4776	−0.625338
$537$	−49.3157	−2.12813
$538$	−6.21690	−0.268029
$539$	−19.6469	−0.846250
$540$	−54.8716	−2.36130
$541$	24.9597	1.07310	0.536551	−	0.843868i	$-0.319727\pi$
$541$	24.9597	1.07310	0.536551	+	0.843868i	$0.319727\pi$
$542$	−17.3888	−0.746912
$543$	80.3878	3.44977
$544$	2.42902	0.104143
$545$	6.94202	0.297364
$546$	85.8089	3.67228
$547$	37.0976	1.58618	0.793089	−	0.609106i	$-0.208471\pi$
$547$	37.0976	1.58618	0.793089	+	0.609106i	$0.208471\pi$
$548$	−21.1388	−0.903006
$549$	−39.2351	−1.67451
$550$	18.0576	0.769980
$551$	−6.74611	−0.287394
$552$	−19.2808	−0.820646
$553$	27.5454	1.17135
$554$	−12.3875	−0.526294
$555$	−46.4730	−1.97267
$556$	−12.5912	−0.533987
$557$	−15.0276	−0.636740	−0.318370	−	0.947967i	$-0.603135\pi$
$557$	−15.0276	−0.636740	−0.318370	+	0.947967i	$0.603135\pi$
$558$	−32.7844	−1.38787
$559$	−19.6774	−0.832267
$560$	19.6109	0.828710
$561$	−10.6246	−0.448571
$562$	26.6964	1.12612
$563$	−2.98488	−0.125798	−0.0628989	−	0.998020i	$-0.520035\pi$
$563$	−2.98488	−0.125798	−0.0628989	+	0.998020i	$0.520035\pi$
$564$	−33.3878	−1.40588
$565$	−73.2193	−3.08036
$566$	19.5466	0.821606
$567$	90.9291	3.81866
$568$	2.40981	0.101113
$569$	−40.5063	−1.69811	−0.849056	−	0.528303i	$-0.822829\pi$
$569$	−40.5063	−1.69811	−0.849056	+	0.528303i	$0.822829\pi$
$570$	−12.1323	−0.508165
$571$	−30.1993	−1.26380	−0.631901	−	0.775049i	$-0.717725\pi$
$571$	−30.1993	−1.26380	−0.631901	+	0.775049i	$0.717725\pi$
$572$	−8.08898	−0.338217
$573$	−54.8072	−2.28960
$574$	9.11929	0.380632
$575$	−79.5984	−3.31948
$576$	7.06553	0.294397
$577$	24.1588	1.00574	0.502871	−	0.864361i	$-0.332277\pi$
$577$	24.1588	1.00574	0.502871	+	0.864361i	$0.332277\pi$
$578$	11.0999	0.461694
$579$	76.3917	3.17473
$580$	31.9267	1.32569
$581$	2.56773	0.106527
$582$	19.9527	0.827065
$583$	4.55951	0.188836
$584$	−5.63237	−0.233069
$585$	176.355	7.29136
$586$	−11.5515	−0.477189
$587$	23.4041	0.965990	0.482995	−	0.875623i	$-0.339549\pi$
$587$	23.4041	0.965990	0.482995	+	0.875623i	$0.339549\pi$
$588$	−45.2113	−1.86448
$589$	−4.17095	−0.171861
$590$	46.4278	1.91140
$591$	−45.9785	−1.89130
$592$	3.44327	0.141517
$593$	24.3755	1.00098	0.500492	−	0.865741i	$-0.333153\pi$
$593$	24.3755	1.00098	0.500492	+	0.865741i	$0.333153\pi$
$594$	−17.7827	−0.729635
$595$	−47.6351	−1.95285
$596$	6.08674	0.249322
$597$	−45.3908	−1.85772
$598$	35.6564	1.45810
$599$	−20.2645	−0.827985	−0.413993	−	0.910280i	$-0.635866\pi$
$599$	−20.2645	−0.827985	−0.413993	+	0.910280i	$0.635866\pi$
$600$	41.5542	1.69644
$601$	−35.8741	−1.46334	−0.731668	−	0.681661i	$-0.761258\pi$
$601$	−35.8741	−1.46334	−0.731668	+	0.681661i	$0.761258\pi$
$602$	15.4605	0.630122
$603$	102.292	4.16566
$604$	−14.6543	−0.596276
$605$	−38.7095	−1.57376
$606$	33.0413	1.34221
$607$	−0.0692887	−0.00281234	−0.00140617	−	0.999999i	$-0.500448\pi$
$607$	−0.0692887	−0.00281234	−0.00140617	+	0.999999i	$0.500448\pi$
$608$	0.898901	0.0364552
$609$	−109.760	−4.44770
$610$	23.6234	0.956484
$611$	61.7446	2.49792
$612$	−17.1623	−0.693744
$613$	19.2014	0.775536	0.387768	−	0.921757i	$-0.373246\pi$
$613$	19.2014	0.775536	0.387768	+	0.921757i	$0.373246\pi$
$614$	15.5205	0.626357
$615$	26.6998	1.07664
$616$	6.35548	0.256069
$617$	48.0538	1.93457	0.967287	−	0.253684i	$-0.0816422\pi$
$617$	48.0538	1.93457	0.967287	+	0.253684i	$0.0816422\pi$
$618$	30.4467	1.22474
$619$	26.4358	1.06254	0.531271	−	0.847202i	$-0.321714\pi$
$619$	26.4358	1.06254	0.531271	+	0.847202i	$0.321714\pi$
$620$	19.7395	0.792756
$621$	78.3867	3.14555
$622$	12.6984	0.509161
$623$	−61.6897	−2.47155
$624$	−18.6144	−0.745171
$625$	81.0624	3.24250
$626$	3.69100	0.147522
$627$	−3.93182	−0.157022
$628$	12.4671	0.497491
$629$	−8.36375	−0.333485
$630$	−138.561	−5.52040
$631$	−4.29515	−0.170987	−0.0854936	−	0.996339i	$-0.527247\pi$
$631$	−4.29515	−0.170987	−0.0854936	+	0.996339i	$0.527247\pi$
$632$	−5.97538	−0.237688
$633$	8.34338	0.331620
$634$	−13.1249	−0.521258
$635$	−77.1990	−3.06355
$636$	10.4923	0.416049
$637$	83.6101	3.31275
$638$	10.3468	0.409634
$639$	−17.0265	−0.673560
$640$	−4.25415	−0.168160
$641$	−19.2306	−0.759563	−0.379781	−	0.925076i	$-0.624001\pi$
$641$	−19.2306	−0.759563	−0.379781	+	0.925076i	$0.624001\pi$
$642$	−4.37933	−0.172838
$643$	33.9517	1.33892	0.669462	−	0.742846i	$-0.266525\pi$
$643$	33.9517	1.33892	0.669462	+	0.742846i	$0.266525\pi$
$644$	−28.0151	−1.10395
$645$	45.2657	1.78234
$646$	−2.18345	−0.0859065
$647$	26.7544	1.05183	0.525913	−	0.850538i	$-0.323724\pi$
$647$	26.7544	1.05183	0.525913	+	0.850538i	$0.323724\pi$
$648$	−19.7251	−0.774874
$649$	15.0463	0.590619
$650$	−76.8469	−3.01419
$651$	−67.8618	−2.65971
$652$	12.8517	0.503311
$653$	36.1200	1.41349	0.706743	−	0.707470i	$-0.250164\pi$
$653$	36.1200	1.41349	0.706743	+	0.707470i	$0.250164\pi$
$654$	5.17716	0.202443
$655$	−29.9346	−1.16964
$656$	−1.97823	−0.0772369
$657$	39.7956	1.55258
$658$	−48.5125	−1.89121
$659$	8.80837	0.343125	0.171563	−	0.985173i	$-0.445118\pi$
$659$	8.80837	0.343125	0.171563	+	0.985173i	$0.445118\pi$
$660$	18.6078	0.724307
$661$	33.6098	1.30727	0.653635	−	0.756810i	$-0.273243\pi$
$661$	33.6098	1.30727	0.653635	+	0.756810i	$0.273243\pi$
$662$	−8.13173	−0.316049
$663$	45.2146	1.75599
$664$	−0.557012	−0.0216163
$665$	−17.6282	−0.683593
$666$	−24.3285	−0.942710
$667$	−45.6089	−1.76598
$668$	7.59083	0.293698
$669$	40.0987	1.55031
$670$	−61.5900	−2.37943
$671$	7.65586	0.295551
$672$	14.6252	0.564180
$673$	19.3754	0.746868	0.373434	−	0.927657i	$-0.378180\pi$
$673$	19.3754	0.746868	0.373434	+	0.927657i	$0.378180\pi$
$674$	−0.152366	−0.00586892
$675$	−168.940	−6.50249
$676$	21.4239	0.823994
$677$	−0.543172	−0.0208758	−0.0104379	−	0.999946i	$-0.503323\pi$
$677$	−0.543172	−0.0208758	−0.0104379	+	0.999946i	$0.503323\pi$
$678$	−54.6049	−2.09709
$679$	28.9913	1.11258
$680$	10.3334	0.396268
$681$	56.5495	2.16698
$682$	6.39715	0.244960
$683$	5.56779	0.213046	0.106523	−	0.994310i	$-0.466028\pi$
$683$	5.56779	0.213046	0.106523	+	0.994310i	$0.466028\pi$
$684$	−6.35121	−0.242844
$685$	−89.9276	−3.43596
$686$	−33.4234	−1.27611
$687$	−14.4475	−0.551206
$688$	−3.35381	−0.127863
$689$	−19.4037	−0.739221
$690$	−82.0234	−3.12258
$691$	14.2880	0.543541	0.271770	−	0.962362i	$-0.412391\pi$
$691$	14.2880	0.543541	0.271770	+	0.962362i	$0.412391\pi$
$692$	2.40888	0.0915719
$693$	−44.9048	−1.70579
$694$	−1.01705	−0.0386065
$695$	−53.5649	−2.03183
$696$	23.8100	0.902517
$697$	4.80515	0.182008
$698$	28.0248	1.06076
$699$	−75.5043	−2.85583
$700$	60.3783	2.28209
$701$	36.7057	1.38635	0.693177	−	0.720767i	$-0.256210\pi$
$701$	36.7057	1.38635	0.693177	+	0.720767i	$0.256210\pi$
$702$	75.6771	2.85625
$703$	−3.09515	−0.116736
$704$	−1.37868	−0.0519610
$705$	−142.036	−5.34940
$706$	−6.69622	−0.252016
$707$	48.0091	1.80557
$708$	34.6245	1.30127
$709$	−9.20060	−0.345536	−0.172768	−	0.984963i	$-0.555271\pi$
$709$	−9.20060	−0.345536	−0.172768	+	0.984963i	$0.555271\pi$
$710$	10.2517	0.384738
$711$	42.2192	1.58334
$712$	13.3822	0.501520
$713$	−28.1988	−1.05605
$714$	−35.5249	−1.32949
$715$	−34.4117	−1.28692
$716$	15.5442	0.580912
$717$	−55.1842	−2.06089
$718$	−17.8944	−0.667814
$719$	−26.0249	−0.970565	−0.485282	−	0.874357i	$-0.661283\pi$
$719$	−26.0249	−0.970565	−0.485282	+	0.874357i	$0.661283\pi$
$720$	30.0578	1.12019
$721$	44.2390	1.64755
$722$	18.1920	0.677035
$723$	14.4618	0.537840
$724$	−25.3380	−0.941678
$725$	98.2967	3.65065
$726$	−28.8684	−1.07141
$727$	−23.3792	−0.867087	−0.433544	−	0.901133i	$-0.642737\pi$
$727$	−23.3792	−0.867087	−0.433544	+	0.901133i	$0.642737\pi$
$728$	−27.0467	−1.00242
$729$	16.6031	0.614929
$730$	−23.9609	−0.886833
$731$	8.14647	0.301308
$732$	17.6177	0.651168
$733$	−40.2495	−1.48665	−0.743324	−	0.668931i	$-0.766752\pi$
$733$	−40.2495	−1.48665	−0.743324	+	0.668931i	$0.766752\pi$
$734$	−4.04177	−0.149184
$735$	−192.336	−7.09441
$736$	6.07725	0.224011
$737$	−19.9600	−0.735237
$738$	13.9772	0.514509
$739$	−11.6452	−0.428377	−0.214188	−	0.976792i	$-0.568711\pi$
$739$	−11.6452	−0.428377	−0.214188	+	0.976792i	$0.568711\pi$
$740$	14.6482	0.538477
$741$	16.7325	0.614682
$742$	15.2454	0.559676
$743$	−19.9070	−0.730317	−0.365158	−	0.930945i	$-0.618985\pi$
$743$	−19.9070	−0.730317	−0.365158	+	0.930945i	$0.618985\pi$
$744$	14.7211	0.539703
$745$	25.8939	0.948678
$746$	−3.11177	−0.113930
$747$	3.93558	0.143995
$748$	3.34884	0.122446
$749$	−6.36317	−0.232505
$750$	109.294	3.99084
$751$	37.9372	1.38435	0.692174	−	0.721731i	$-0.256653\pi$
$751$	37.9372	1.38435	0.692174	+	0.721731i	$0.256653\pi$
$752$	10.5237	0.383760
$753$	57.6918	2.10241
$754$	−44.0323	−1.60356
$755$	−62.3416	−2.26884
$756$	−59.4592	−2.16251
$757$	17.1504	0.623341	0.311670	−	0.950190i	$-0.399111\pi$
$757$	17.1504	0.623341	0.311670	+	0.950190i	$0.399111\pi$
$758$	20.9982	0.762690
$759$	−26.5821	−0.964869
$760$	3.82405	0.138713
$761$	−4.53120	−0.164256	−0.0821280	−	0.996622i	$-0.526172\pi$
$761$	−4.53120	−0.164256	−0.0821280	+	0.996622i	$0.526172\pi$
$762$	−57.5728	−2.08564
$763$	7.52243	0.272330
$764$	17.2750	0.624989
$765$	−73.0109	−2.63971
$766$	22.6410	0.818054
$767$	−64.0318	−2.31205
$768$	−3.17262	−0.114482
$769$	−24.4769	−0.882658	−0.441329	−	0.897345i	$-0.645493\pi$
$769$	−24.4769	−0.882658	−0.441329	+	0.897345i	$0.645493\pi$
$770$	27.0371	0.974350
$771$	36.7531	1.32363
$772$	−24.0784	−0.866601
$773$	18.9408	0.681253	0.340627	−	0.940199i	$-0.389361\pi$
$773$	18.9408	0.681253	0.340627	+	0.940199i	$0.389361\pi$
$774$	23.6964	0.851751
$775$	60.7743	2.18308
$776$	−6.28902	−0.225763
$777$	−50.3585	−1.80660
$778$	−29.2610	−1.04906
$779$	1.77823	0.0637118
$780$	−79.1882	−2.83539
$781$	3.32235	0.118883
$782$	−14.7618	−0.527879
$783$	−96.8004	−3.45936
$784$	14.2505	0.508945
$785$	53.0368	1.89296
$786$	−22.3244	−0.796283
$787$	−12.7151	−0.453244	−0.226622	−	0.973983i	$-0.572768\pi$
$787$	−12.7151	−0.453244	−0.226622	+	0.973983i	$0.572768\pi$
$788$	14.4923	0.516265
$789$	20.1422	0.717080
$790$	−25.4201	−0.904408
$791$	−79.3410	−2.82104
$792$	9.74111	0.346135
$793$	−32.5807	−1.15697
$794$	10.4684	0.371509
$795$	44.6360	1.58307
$796$	14.3070	0.507099
$797$	−1.96099	−0.0694619	−0.0347310	−	0.999397i	$-0.511057\pi$
$797$	−1.96099	−0.0694619	−0.0347310	+	0.999397i	$0.511057\pi$
$798$	−13.1466	−0.465385
$799$	−25.5623	−0.904329
$800$	−13.0978	−0.463076
$801$	−94.5525	−3.34085
$802$	10.8419	0.382839
$803$	−7.76524	−0.274029
$804$	−45.9320	−1.61990
$805$	−119.180	−4.20055
$806$	−27.2240	−0.958926
$807$	−19.7239	−0.694313
$808$	−10.4145	−0.366382
$809$	−31.4680	−1.10636	−0.553178	−	0.833063i	$-0.686585\pi$
$809$	−31.4680	−1.10636	−0.553178	+	0.833063i	$0.686585\pi$
$810$	−83.9133	−2.94841
$811$	−40.4171	−1.41924	−0.709618	−	0.704587i	$-0.751132\pi$
$811$	−40.4171	−1.41924	−0.709618	+	0.704587i	$0.751132\pi$
$812$	34.5960	1.21408
$813$	−55.1680	−1.93483
$814$	4.74717	0.166388
$815$	54.6729	1.91511
$816$	7.70635	0.269776
$817$	3.01474	0.105473
$818$	−10.8422	−0.379090
$819$	191.099	6.67754
$820$	−8.41568	−0.293888
$821$	−28.8386	−1.00648	−0.503238	−	0.864148i	$-0.667858\pi$
$821$	−28.8386	−1.00648	−0.503238	+	0.864148i	$0.667858\pi$
$822$	−67.0655	−2.33918
$823$	32.3501	1.12765	0.563827	−	0.825893i	$-0.309328\pi$
$823$	32.3501	1.12765	0.563827	+	0.825893i	$0.309328\pi$
$824$	−9.59669	−0.334316
$825$	57.2900	1.99458
$826$	50.3095	1.75049
$827$	19.5278	0.679050	0.339525	−	0.940597i	$-0.389734\pi$
$827$	19.5278	0.679050	0.339525	+	0.940597i	$0.389734\pi$
$828$	−42.9390	−1.49223
$829$	29.4802	1.02389	0.511945	−	0.859018i	$-0.328925\pi$
$829$	29.4802	1.02389	0.511945	+	0.859018i	$0.328925\pi$
$830$	−2.36961	−0.0822503
$831$	−39.3008	−1.36333
$832$	5.86718	0.203408
$833$	−34.6146	−1.19933
$834$	−39.9472	−1.38326
$835$	32.2925	1.11753
$836$	1.23930	0.0428620
$837$	−59.8491	−2.06869
$838$	10.5711	0.365173
$839$	−38.5832	−1.33204	−0.666021	−	0.745933i	$-0.732004\pi$
$839$	−38.5832	−1.33204	−0.666021	+	0.745933i	$0.732004\pi$
$840$	62.2178	2.14672
$841$	27.3228	0.942164
$842$	37.5167	1.29291
$843$	84.6976	2.91714
$844$	−2.62981	−0.0905217
$845$	91.1402	3.13532
$846$	−74.3556	−2.55640
$847$	−41.9459	−1.44128
$848$	−3.30715	−0.113568
$849$	62.0140	2.12832
$850$	31.8147	1.09123
$851$	−20.9256	−0.717320
$852$	7.64540	0.261927
$853$	13.7380	0.470378	0.235189	−	0.971950i	$-0.424429\pi$
$853$	13.7380	0.470378	0.235189	+	0.971950i	$0.424429\pi$
$854$	25.5985	0.875962
$855$	−27.0190	−0.924029
$856$	1.38035	0.0471794
$857$	−49.2928	−1.68381	−0.841905	−	0.539625i	$-0.818566\pi$
$857$	−49.2928	−1.68381	−0.841905	+	0.539625i	$0.818566\pi$
$858$	−25.6633	−0.876129
$859$	39.6012	1.35118	0.675589	−	0.737279i	$-0.263890\pi$
$859$	39.6012	1.35118	0.675589	+	0.737279i	$0.263890\pi$
$860$	−14.2676	−0.486521
$861$	28.9320	0.986001
$862$	5.70191	0.194208
$863$	−26.9501	−0.917392	−0.458696	−	0.888593i	$-0.651683\pi$
$863$	−26.9501	−0.917392	−0.458696	+	0.888593i	$0.651683\pi$
$864$	12.8984	0.438812
$865$	10.2477	0.348433
$866$	8.01978	0.272523
$867$	35.2157	1.19599
$868$	21.3898	0.726018
$869$	−8.23814	−0.279460
$870$	101.291	3.43410
$871$	84.9429	2.87818
$872$	−1.63183	−0.0552606
$873$	44.4352	1.50390
$874$	−5.46285	−0.184784
$875$	158.804	5.36855
$876$	−17.8694	−0.603750
$877$	−26.1884	−0.884321	−0.442160	−	0.896936i	$-0.645788\pi$
$877$	−26.1884	−0.884321	−0.442160	+	0.896936i	$0.645788\pi$
$878$	20.1072	0.678584
$879$	−36.6486	−1.23613
$880$	−5.86511	−0.197713
$881$	−55.0785	−1.85564	−0.927821	−	0.373026i	$-0.878320\pi$
$881$	−55.0785	−1.85564	−0.927821	+	0.373026i	$0.878320\pi$
$882$	−100.687	−3.39031
$883$	−48.9537	−1.64742	−0.823711	−	0.567009i	$-0.808100\pi$
$883$	−48.9537	−1.64742	−0.823711	+	0.567009i	$0.808100\pi$
$884$	−14.2515	−0.479330
$885$	147.298	4.95136
$886$	−16.7454	−0.562573
$887$	34.6157	1.16228	0.581141	−	0.813803i	$-0.302606\pi$
$887$	34.6157	1.16228	0.581141	+	0.813803i	$0.302606\pi$
$888$	10.9242	0.366591
$889$	−83.6534	−2.80565
$890$	56.9300	1.90830
$891$	−27.1946	−0.911053
$892$	−12.6390	−0.423184
$893$	−9.45977	−0.316559
$894$	19.3109	0.645853
$895$	66.1271	2.21038
$896$	−4.60982	−0.154003
$897$	113.124	3.77711
$898$	13.6802	0.456516
$899$	34.8229	1.16141
$900$	92.5425	3.08475
$901$	8.03314	0.267623
$902$	−2.72735	−0.0908107
$903$	49.0503	1.63229
$904$	17.2113	0.572439
$905$	−107.791	−3.58311
$906$	−46.4926	−1.54461
$907$	52.6874	1.74946	0.874728	−	0.484614i	$-0.161040\pi$
$907$	52.6874	1.74946	0.874728	+	0.484614i	$0.161040\pi$
$908$	−17.8242	−0.591517
$909$	73.5841	2.44063
$910$	−115.061	−3.81422
$911$	8.17737	0.270928	0.135464	−	0.990782i	$-0.456747\pi$
$911$	8.17737	0.270928	0.135464	+	0.990782i	$0.456747\pi$
$912$	2.85187	0.0944349
$913$	−0.767942	−0.0254152
$914$	14.2990	0.472970
$915$	74.9481	2.47771
$916$	4.55380	0.150462
$917$	−32.4373	−1.07117
$918$	−31.3304	−1.03406
$919$	−38.5776	−1.27256	−0.636279	−	0.771459i	$-0.719527\pi$
$919$	−38.5776	−1.27256	−0.636279	+	0.771459i	$0.719527\pi$
$920$	25.8535	0.852365
$921$	49.2407	1.62254
$922$	−0.530861	−0.0174830
$923$	−14.1388	−0.465383
$924$	20.1635	0.663331
$925$	45.0991	1.48285
$926$	−18.5087	−0.608234
$927$	67.8056	2.22703
$928$	−7.50485	−0.246359
$929$	23.3030	0.764546	0.382273	−	0.924050i	$-0.375141\pi$
$929$	23.3030	0.764546	0.382273	+	0.924050i	$0.375141\pi$
$930$	62.6258	2.05358
$931$	−12.8098	−0.419823
$932$	23.7987	0.779552
$933$	40.2873	1.31895
$934$	19.4400	0.636098
$935$	14.2465	0.465909
$936$	−41.4547	−1.35499
$937$	1.01873	0.0332806	0.0166403	−	0.999862i	$-0.494703\pi$
$937$	1.01873	0.0332806	0.0166403	+	0.999862i	$0.494703\pi$
$938$	−66.7393	−2.17912
$939$	11.7101	0.382146
$940$	44.7694	1.46022
$941$	17.0718	0.556525	0.278262	−	0.960505i	$-0.410241\pi$
$941$	17.0718	0.556525	0.278262	+	0.960505i	$0.410241\pi$
$942$	39.5533	1.28872
$943$	12.0222	0.391497
$944$	−10.9135	−0.355206
$945$	−252.948	−8.22841
$946$	−4.62384	−0.150334
$947$	−9.97719	−0.324215	−0.162108	−	0.986773i	$-0.551829\pi$
$947$	−9.97719	−0.324215	−0.162108	+	0.986773i	$0.551829\pi$
$948$	−18.9576	−0.615715
$949$	33.0461	1.07272
$950$	11.7736	0.381985
$951$	−41.6405	−1.35029
$952$	11.1973	0.362908
$953$	−0.0271504	−0.000879488 0	−0.000439744	−	1.00000i	$-0.500140\pi$
$953$	−0.0271504	−0.000879488 0	−0.000439744		1.00000i	$0.500140\pi$
$954$	23.3668	0.756527
$955$	73.4905	2.37810
$956$	17.3939	0.562559
$957$	32.8265	1.06113
$958$	−25.4261	−0.821480
$959$	−97.4462	−3.14670
$960$	−13.4968	−0.435607
$961$	−9.46991	−0.305481
$962$	−20.2023	−0.651348
$963$	−9.75290	−0.314283
$964$	−4.55831	−0.146813
$965$	−102.433	−3.29744
$966$	−88.8812	−2.85971
$967$	−28.5205	−0.917159	−0.458579	−	0.888653i	$-0.651642\pi$
$967$	−28.5205	−0.917159	−0.458579	+	0.888653i	$0.651642\pi$
$968$	9.09924	0.292461
$969$	−6.92725	−0.222535
$970$	−26.7544	−0.859032
$971$	−24.6875	−0.792259	−0.396130	−	0.918195i	$-0.629647\pi$
$971$	−24.6875	−0.792259	−0.396130	+	0.918195i	$0.629647\pi$
$972$	−23.8851	−0.766114
$973$	−58.0433	−1.86078
$974$	−35.2753	−1.13029
$975$	−243.806	−7.80805
$976$	−5.55303	−0.177748
$977$	17.3688	0.555676	0.277838	−	0.960628i	$-0.410382\pi$
$977$	17.3688	0.555676	0.277838	+	0.960628i	$0.410382\pi$
$978$	40.7735	1.30379
$979$	18.4498	0.589659
$980$	60.6236	1.93655
$981$	11.5297	0.368115
$982$	20.9361	0.668099
$983$	−21.8465	−0.696796	−0.348398	−	0.937347i	$-0.613274\pi$
$983$	−21.8465	−0.696796	−0.348398	+	0.937347i	$0.613274\pi$
$984$	−6.27617	−0.200077
$985$	61.6522	1.96440
$986$	18.2294	0.580543
$987$	−153.912	−4.89906
$988$	−5.27402	−0.167789
$989$	20.3820	0.648109
$990$	41.4401	1.31705
$991$	−28.0068	−0.889664	−0.444832	−	0.895614i	$-0.646737\pi$
$991$	−28.0068	−0.889664	−0.444832	+	0.895614i	$0.646737\pi$
$992$	−4.64005	−0.147322
$993$	−25.7989	−0.818703
$994$	11.1088	0.352349
$995$	60.8642	1.92953
$996$	−1.76719	−0.0559955
$997$	−4.12120	−0.130520	−0.0652599	−	0.997868i	$-0.520788\pi$
$997$	−4.12120	−0.130520	−0.0652599	+	0.997868i	$0.520788\pi$
$998$	38.2346	1.21030
$999$	−44.4125	−1.40515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.1	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.1	✓	46	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.17262 q^{3} +1.00000 q^{4} +4.25415 q^{5} +3.17262 q^{6} +4.60982 q^{7} -1.00000 q^{8} +7.06553 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.17262 q^{3} +1.00000 q^{4} +4.25415 q^{5} +3.17262 q^{6} +4.60982 q^{7} -1.00000 q^{8} +7.06553 q^{9} -4.25415 q^{10} -1.37868 q^{11} -3.17262 q^{12} +5.86718 q^{13} -4.60982 q^{14} -13.4968 q^{15} +1.00000 q^{16} -2.42902 q^{17} -7.06553 q^{18} -0.898901 q^{19} +4.25415 q^{20} -14.6252 q^{21} +1.37868 q^{22} -6.07725 q^{23} +3.17262 q^{24} +13.0978 q^{25} -5.86718 q^{26} -12.8984 q^{27} +4.60982 q^{28} +7.50485 q^{29} +13.4968 q^{30} +4.64005 q^{31} -1.00000 q^{32} +4.37403 q^{33} +2.42902 q^{34} +19.6109 q^{35} +7.06553 q^{36} +3.44327 q^{37} +0.898901 q^{38} -18.6144 q^{39} -4.25415 q^{40} -1.97823 q^{41} +14.6252 q^{42} -3.35381 q^{43} -1.37868 q^{44} +30.0578 q^{45} +6.07725 q^{46} +10.5237 q^{47} -3.17262 q^{48} +14.2505 q^{49} -13.0978 q^{50} +7.70635 q^{51} +5.86718 q^{52} -3.30715 q^{53} +12.8984 q^{54} -5.86511 q^{55} -4.60982 q^{56} +2.85187 q^{57} -7.50485 q^{58} -10.9135 q^{59} -13.4968 q^{60} -5.55303 q^{61} -4.64005 q^{62} +32.5708 q^{63} +1.00000 q^{64} +24.9599 q^{65} -4.37403 q^{66} +14.4776 q^{67} -2.42902 q^{68} +19.2808 q^{69} -19.6109 q^{70} -2.40981 q^{71} -7.06553 q^{72} +5.63237 q^{73} -3.44327 q^{74} -41.5542 q^{75} -0.898901 q^{76} -6.35548 q^{77} +18.6144 q^{78} +5.97538 q^{79} +4.25415 q^{80} +19.7251 q^{81} +1.97823 q^{82} +0.557012 q^{83} -14.6252 q^{84} -10.3334 q^{85} +3.35381 q^{86} -23.8100 q^{87} +1.37868 q^{88} -13.3822 q^{89} -30.0578 q^{90} +27.0467 q^{91} -6.07725 q^{92} -14.7211 q^{93} -10.5237 q^{94} -3.82405 q^{95} +3.17262 q^{96} +6.28902 q^{97} -14.2505 q^{98} -9.74111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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