LMFDB - Embedded newform 4017.2.a.g.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17908 q^{2} -1.00000 q^{3} -0.609765 q^{4} +4.22706 q^{5} +1.17908 q^{6} +3.50133 q^{7} +3.07713 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.17908 q^{2} -1.00000 q^{3} -0.609765 q^{4} +4.22706 q^{5} +1.17908 q^{6} +3.50133 q^{7} +3.07713 q^{8} +1.00000 q^{9} -4.98405 q^{10} +1.99179 q^{11} +0.609765 q^{12} -1.00000 q^{13} -4.12836 q^{14} -4.22706 q^{15} -2.40866 q^{16} -1.98864 q^{17} -1.17908 q^{18} -0.207518 q^{19} -2.57751 q^{20} -3.50133 q^{21} -2.34848 q^{22} -2.99968 q^{23} -3.07713 q^{24} +12.8680 q^{25} +1.17908 q^{26} -1.00000 q^{27} -2.13499 q^{28} +6.92896 q^{29} +4.98405 q^{30} -1.32438 q^{31} -3.31425 q^{32} -1.99179 q^{33} +2.34476 q^{34} +14.8003 q^{35} -0.609765 q^{36} +0.697456 q^{37} +0.244681 q^{38} +1.00000 q^{39} +13.0072 q^{40} -3.09452 q^{41} +4.12836 q^{42} +8.08867 q^{43} -1.21452 q^{44} +4.22706 q^{45} +3.53687 q^{46} +6.61362 q^{47} +2.40866 q^{48} +5.25931 q^{49} -15.1724 q^{50} +1.98864 q^{51} +0.609765 q^{52} -4.57877 q^{53} +1.17908 q^{54} +8.41940 q^{55} +10.7740 q^{56} +0.207518 q^{57} -8.16982 q^{58} +9.27407 q^{59} +2.57751 q^{60} -4.61883 q^{61} +1.56156 q^{62} +3.50133 q^{63} +8.72509 q^{64} -4.22706 q^{65} +2.34848 q^{66} +5.99796 q^{67} +1.21260 q^{68} +2.99968 q^{69} -17.4508 q^{70} -14.9044 q^{71} +3.07713 q^{72} +8.59077 q^{73} -0.822358 q^{74} -12.8680 q^{75} +0.126537 q^{76} +6.97391 q^{77} -1.17908 q^{78} +6.17426 q^{79} -10.1815 q^{80} +1.00000 q^{81} +3.64869 q^{82} +12.0914 q^{83} +2.13499 q^{84} -8.40607 q^{85} -9.53721 q^{86} -6.92896 q^{87} +6.12899 q^{88} -8.17030 q^{89} -4.98405 q^{90} -3.50133 q^{91} +1.82910 q^{92} +1.32438 q^{93} -7.79800 q^{94} -0.877192 q^{95} +3.31425 q^{96} -0.583380 q^{97} -6.20116 q^{98} +1.99179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * 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 $

$2$	−1.17908	−0.833737	−0.416869	−	0.908967i	$-0.636872\pi$
$2$	−1.17908	−0.833737	−0.416869	+	0.908967i	$0.636872\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.609765	−0.304882
$5$	4.22706	1.89040	0.945199	−	0.326496i	$-0.105868\pi$
$5$	4.22706	1.89040	0.945199	+	0.326496i	$0.105868\pi$
$6$	1.17908	0.481358
$7$	3.50133	1.32338	0.661689	−	0.749778i	$-0.269840\pi$
$7$	3.50133	1.32338	0.661689	+	0.749778i	$0.269840\pi$
$8$	3.07713	1.08793
$9$	1.00000	0.333333
$10$	−4.98405	−1.57609
$11$	1.99179	0.600547	0.300273	−	0.953853i	$-0.402922\pi$
$11$	1.99179	0.600547	0.300273	+	0.953853i	$0.402922\pi$
$12$	0.609765	0.176024
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.12836	−1.10335
$15$	−4.22706	−1.09142
$16$	−2.40866	−0.602164
$17$	−1.98864	−0.482315	−0.241157	−	0.970486i	$-0.577527\pi$
$17$	−1.98864	−0.482315	−0.241157	+	0.970486i	$0.577527\pi$
$18$	−1.17908	−0.277912
$19$	−0.207518	−0.0476080	−0.0238040	−	0.999717i	$-0.507578\pi$
$19$	−0.207518	−0.0476080	−0.0238040	+	0.999717i	$0.507578\pi$
$20$	−2.57751	−0.576349
$21$	−3.50133	−0.764053
$22$	−2.34848	−0.500698
$23$	−2.99968	−0.625477	−0.312739	−	0.949839i	$-0.601246\pi$
$23$	−2.99968	−0.625477	−0.312739	+	0.949839i	$0.601246\pi$
$24$	−3.07713	−0.628116
$25$	12.8680	2.57360
$26$	1.17908	0.231237
$27$	−1.00000	−0.192450
$28$	−2.13499	−0.403475
$29$	6.92896	1.28668	0.643338	−	0.765582i	$-0.277549\pi$
$29$	6.92896	1.28668	0.643338	+	0.765582i	$0.277549\pi$
$30$	4.98405	0.909959
$31$	−1.32438	−0.237866	−0.118933	−	0.992902i	$-0.537947\pi$
$31$	−1.32438	−0.237866	−0.118933	+	0.992902i	$0.537947\pi$
$32$	−3.31425	−0.585882
$33$	−1.99179	−0.346726
$34$	2.34476	0.402124
$35$	14.8003	2.50171
$36$	−0.609765	−0.101627
$37$	0.697456	0.114661	0.0573305	−	0.998355i	$-0.481741\pi$
$37$	0.697456	0.114661	0.0573305	+	0.998355i	$0.481741\pi$
$38$	0.244681	0.0396925
$39$	1.00000	0.160128
$40$	13.0072	2.05662
$41$	−3.09452	−0.483283	−0.241641	−	0.970366i	$-0.577686\pi$
$41$	−3.09452	−0.483283	−0.241641	+	0.970366i	$0.577686\pi$
$42$	4.12836	0.637019
$43$	8.08867	1.23351	0.616756	−	0.787155i	$-0.288447\pi$
$43$	8.08867	1.23351	0.616756	+	0.787155i	$0.288447\pi$
$44$	−1.21452	−0.183096
$45$	4.22706	0.630132
$46$	3.53687	0.521484
$47$	6.61362	0.964695	0.482348	−	0.875980i	$-0.339784\pi$
$47$	6.61362	0.964695	0.482348	+	0.875980i	$0.339784\pi$
$48$	2.40866	0.347660
$49$	5.25931	0.751330
$50$	−15.1724	−2.14571
$51$	1.98864	0.278465
$52$	0.609765	0.0845591
$53$	−4.57877	−0.628943	−0.314471	−	0.949267i	$-0.601827\pi$
$53$	−4.57877	−0.628943	−0.314471	+	0.949267i	$0.601827\pi$
$54$	1.17908	0.160453
$55$	8.41940	1.13527
$56$	10.7740	1.43974
$57$	0.207518	0.0274865
$58$	−8.16982	−1.07275
$59$	9.27407	1.20738	0.603690	−	0.797219i	$-0.293696\pi$
$59$	9.27407	1.20738	0.603690	+	0.797219i	$0.293696\pi$
$60$	2.57751	0.332755
$61$	−4.61883	−0.591381	−0.295691	−	0.955284i	$-0.595550\pi$
$61$	−4.61883	−0.591381	−0.295691	+	0.955284i	$0.595550\pi$
$62$	1.56156	0.198318
$63$	3.50133	0.441126
$64$	8.72509	1.09064
$65$	−4.22706	−0.524302
$66$	2.34848	0.289078
$67$	5.99796	0.732767	0.366384	−	0.930464i	$-0.380596\pi$
$67$	5.99796	0.732767	0.366384	+	0.930464i	$0.380596\pi$
$68$	1.21260	0.147049
$69$	2.99968	0.361119
$70$	−17.4508	−2.08577
$71$	−14.9044	−1.76882	−0.884412	−	0.466707i	$-0.845440\pi$
$71$	−14.9044	−1.76882	−0.884412	+	0.466707i	$0.845440\pi$
$72$	3.07713	0.362643
$73$	8.59077	1.00547	0.502737	−	0.864440i	$-0.332327\pi$
$73$	8.59077	1.00547	0.502737	+	0.864440i	$0.332327\pi$
$74$	−0.822358	−0.0955972
$75$	−12.8680	−1.48587
$76$	0.126537	0.0145148
$77$	6.97391	0.794751
$78$	−1.17908	−0.133505
$79$	6.17426	0.694658	0.347329	−	0.937743i	$-0.387089\pi$
$79$	6.17426	0.694658	0.347329	+	0.937743i	$0.387089\pi$
$80$	−10.1815	−1.13833
$81$	1.00000	0.111111
$82$	3.64869	0.402931
$83$	12.0914	1.32721	0.663604	−	0.748084i	$-0.269026\pi$
$83$	12.0914	1.32721	0.663604	+	0.748084i	$0.269026\pi$
$84$	2.13499	0.232946
$85$	−8.40607	−0.911767
$86$	−9.53721	−1.02842
$87$	−6.92896	−0.742863
$88$	6.12899	0.653352
$89$	−8.17030	−0.866050	−0.433025	−	0.901382i	$-0.642554\pi$
$89$	−8.17030	−0.866050	−0.433025	+	0.901382i	$0.642554\pi$
$90$	−4.98405	−0.525365
$91$	−3.50133	−0.367039
$92$	1.82910	0.190697
$93$	1.32438	0.137332
$94$	−7.79800	−0.804302
$95$	−0.877192	−0.0899980
$96$	3.31425	0.338259
$97$	−0.583380	−0.0592333	−0.0296166	−	0.999561i	$-0.509429\pi$
$97$	−0.583380	−0.0592333	−0.0296166	+	0.999561i	$0.509429\pi$
$98$	−6.20116	−0.626412
$99$	1.99179	0.200182
$100$	−7.84646	−0.784646
$101$	9.92184	0.987260	0.493630	−	0.869672i	$-0.335670\pi$
$101$	9.92184	0.987260	0.493630	+	0.869672i	$0.335670\pi$
$102$	−2.34476	−0.232166
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−3.07713	−0.301737
$105$	−14.8003	−1.44436
$106$	5.39875	0.524373
$107$	−17.4412	−1.68610	−0.843050	−	0.537835i	$-0.819243\pi$
$107$	−17.4412	−1.68610	−0.843050	+	0.537835i	$0.819243\pi$
$108$	0.609765	0.0586746
$109$	−0.882772	−0.0845542	−0.0422771	−	0.999106i	$-0.513461\pi$
$109$	−0.882772	−0.0845542	−0.0422771	+	0.999106i	$0.513461\pi$
$110$	−9.92717	−0.946519
$111$	−0.697456	−0.0661996
$112$	−8.43351	−0.796891
$113$	−10.5763	−0.994934	−0.497467	−	0.867483i	$-0.665736\pi$
$113$	−10.5763	−0.994934	−0.497467	+	0.867483i	$0.665736\pi$
$114$	−0.244681	−0.0229165
$115$	−12.6798	−1.18240
$116$	−4.22503	−0.392285
$117$	−1.00000	−0.0924500
$118$	−10.9349	−1.00664
$119$	−6.96287	−0.638285
$120$	−13.0072	−1.18739
$121$	−7.03278	−0.639343
$122$	5.44599	0.493057
$123$	3.09452	0.279023
$124$	0.807562	0.0725212
$125$	33.2585	2.97473
$126$	−4.12836	−0.367783
$127$	−17.2455	−1.53029	−0.765146	−	0.643857i	$-0.777333\pi$
$127$	−17.2455	−1.53029	−0.765146	+	0.643857i	$0.777333\pi$
$128$	−3.65910	−0.323422
$129$	−8.08867	−0.712168
$130$	4.98405	0.437130
$131$	19.4733	1.70139	0.850696	−	0.525658i	$-0.176181\pi$
$131$	19.4733	1.70139	0.850696	+	0.525658i	$0.176181\pi$
$132$	1.21452	0.105711
$133$	−0.726590	−0.0630034
$134$	−7.07209	−0.610935
$135$	−4.22706	−0.363807
$136$	−6.11928	−0.524724
$137$	3.25264	0.277891	0.138946	−	0.990300i	$-0.455629\pi$
$137$	3.25264	0.277891	0.138946	+	0.990300i	$0.455629\pi$
$138$	−3.53687	−0.301079
$139$	−8.10201	−0.687204	−0.343602	−	0.939115i	$-0.611647\pi$
$139$	−8.10201	−0.687204	−0.343602	+	0.939115i	$0.611647\pi$
$140$	−9.02471	−0.762727
$141$	−6.61362	−0.556967
$142$	17.5735	1.47473
$143$	−1.99179	−0.166562
$144$	−2.40866	−0.200721
$145$	29.2891	2.43233
$146$	−10.1292	−0.838300
$147$	−5.25931	−0.433781
$148$	−0.425284	−0.0349581
$149$	2.32613	0.190564	0.0952818	−	0.995450i	$-0.469625\pi$
$149$	2.32613	0.190564	0.0952818	+	0.995450i	$0.469625\pi$
$150$	15.1724	1.23882
$151$	4.42473	0.360079	0.180040	−	0.983659i	$-0.442377\pi$
$151$	4.42473	0.360079	0.180040	+	0.983659i	$0.442377\pi$
$152$	−0.638561	−0.0517941
$153$	−1.98864	−0.160772
$154$	−8.22281	−0.662613
$155$	−5.59825	−0.449662
$156$	−0.609765	−0.0488202
$157$	−6.66683	−0.532071	−0.266036	−	0.963963i	$-0.585714\pi$
$157$	−6.66683	−0.532071	−0.266036	+	0.963963i	$0.585714\pi$
$158$	−7.27996	−0.579162
$159$	4.57877	0.363120
$160$	−14.0095	−1.10755
$161$	−10.5029	−0.827743
$162$	−1.17908	−0.0926375
$163$	6.82683	0.534718	0.267359	−	0.963597i	$-0.413849\pi$
$163$	6.82683	0.534718	0.267359	+	0.963597i	$0.413849\pi$
$164$	1.88693	0.147344
$165$	−8.41940	−0.655450
$166$	−14.2568	−1.10654
$167$	−5.06609	−0.392026	−0.196013	−	0.980601i	$-0.562799\pi$
$167$	−5.06609	−0.392026	−0.196013	+	0.980601i	$0.562799\pi$
$168$	−10.7740	−0.831235
$169$	1.00000	0.0769231
$170$	9.91145	0.760174
$171$	−0.207518	−0.0158693
$172$	−4.93219	−0.376076
$173$	11.5887	0.881073	0.440536	−	0.897735i	$-0.354788\pi$
$173$	11.5887	0.881073	0.440536	+	0.897735i	$0.354788\pi$
$174$	8.16982	0.619352
$175$	45.0552	3.40585
$176$	−4.79754	−0.361628
$177$	−9.27407	−0.697082
$178$	9.63346	0.722058
$179$	2.27524	0.170059	0.0850296	−	0.996378i	$-0.472902\pi$
$179$	2.27524	0.170059	0.0850296	+	0.996378i	$0.472902\pi$
$180$	−2.57751	−0.192116
$181$	−4.22260	−0.313864	−0.156932	−	0.987609i	$-0.550160\pi$
$181$	−4.22260	−0.313864	−0.156932	+	0.987609i	$0.550160\pi$
$182$	4.12836	0.306014
$183$	4.61883	0.341434
$184$	−9.23041	−0.680475
$185$	2.94819	0.216755
$186$	−1.56156	−0.114499
$187$	−3.96094	−0.289653
$188$	−4.03275	−0.294118
$189$	−3.50133	−0.254684
$190$	1.03428	0.0750347
$191$	−4.40198	−0.318516	−0.159258	−	0.987237i	$-0.550910\pi$
$191$	−4.40198	−0.318516	−0.159258	+	0.987237i	$0.550910\pi$
$192$	−8.72509	−0.629679
$193$	−15.1376	−1.08963	−0.544814	−	0.838557i	$-0.683400\pi$
$193$	−15.1376	−1.08963	−0.544814	+	0.838557i	$0.683400\pi$
$194$	0.687853	0.0493850
$195$	4.22706	0.302706
$196$	−3.20694	−0.229067
$197$	17.5600	1.25110	0.625550	−	0.780184i	$-0.284875\pi$
$197$	17.5600	1.25110	0.625550	+	0.780184i	$0.284875\pi$
$198$	−2.34848	−0.166899
$199$	2.47122	0.175180	0.0875902	−	0.996157i	$-0.472083\pi$
$199$	2.47122	0.175180	0.0875902	+	0.996157i	$0.472083\pi$
$200$	39.5965	2.79990
$201$	−5.99796	−0.423063
$202$	−11.6987	−0.823116
$203$	24.2606	1.70276
$204$	−1.21260	−0.0848989
$205$	−13.0807	−0.913596
$206$	−1.17908	−0.0821506
$207$	−2.99968	−0.208492
$208$	2.40866	0.167010
$209$	−0.413333	−0.0285908
$210$	17.4508	1.20422
$211$	−10.4518	−0.719535	−0.359767	−	0.933042i	$-0.617144\pi$
$211$	−10.4518	−0.719535	−0.359767	+	0.933042i	$0.617144\pi$
$212$	2.79197	0.191753
$213$	14.9044	1.02123
$214$	20.5646	1.40576
$215$	34.1913	2.33183
$216$	−3.07713	−0.209372
$217$	−4.63710	−0.314787
$218$	1.04086	0.0704960
$219$	−8.59077	−0.580510
$220$	−5.13385	−0.346124
$221$	1.98864	0.133770
$222$	0.822358	0.0551930
$223$	17.7090	1.18588	0.592940	−	0.805247i	$-0.297967\pi$
$223$	17.7090	1.18588	0.592940	+	0.805247i	$0.297967\pi$
$224$	−11.6043	−0.775343
$225$	12.8680	0.857867
$226$	12.4703	0.829514
$227$	−7.89207	−0.523815	−0.261908	−	0.965093i	$-0.584352\pi$
$227$	−7.89207	−0.523815	−0.261908	+	0.965093i	$0.584352\pi$
$228$	−0.126537	−0.00838014
$229$	−10.9759	−0.725311	−0.362655	−	0.931923i	$-0.618130\pi$
$229$	−10.9759	−0.725311	−0.362655	+	0.931923i	$0.618130\pi$
$230$	14.9506	0.985811
$231$	−6.97391	−0.458850
$232$	21.3213	1.39981
$233$	−22.8302	−1.49566	−0.747828	−	0.663892i	$-0.768903\pi$
$233$	−22.8302	−1.49566	−0.747828	+	0.663892i	$0.768903\pi$
$234$	1.17908	0.0770790
$235$	27.9561	1.82366
$236$	−5.65500	−0.368109
$237$	−6.17426	−0.401061
$238$	8.20979	0.532162
$239$	−7.90484	−0.511322	−0.255661	−	0.966767i	$-0.582293\pi$
$239$	−7.90484	−0.511322	−0.255661	+	0.966767i	$0.582293\pi$
$240$	10.1815	0.657215
$241$	14.4866	0.933161	0.466580	−	0.884479i	$-0.345486\pi$
$241$	14.4866	0.933161	0.466580	+	0.884479i	$0.345486\pi$
$242$	8.29222	0.533044
$243$	−1.00000	−0.0641500
$244$	2.81640	0.180302
$245$	22.2314	1.42031
$246$	−3.64869	−0.232632
$247$	0.207518	0.0132041
$248$	−4.07530	−0.258782
$249$	−12.0914	−0.766264
$250$	−39.2145	−2.48015
$251$	22.4431	1.41660	0.708299	−	0.705912i	$-0.249463\pi$
$251$	22.4431	1.41660	0.708299	+	0.705912i	$0.249463\pi$
$252$	−2.13499	−0.134492
$253$	−5.97473	−0.375628
$254$	20.3339	1.27586
$255$	8.40607	0.526409
$256$	−13.1358	−0.820987
$257$	15.6218	0.974463	0.487232	−	0.873273i	$-0.338007\pi$
$257$	15.6218	0.974463	0.487232	+	0.873273i	$0.338007\pi$
$258$	9.53721	0.593761
$259$	2.44202	0.151740
$260$	2.57751	0.159850
$261$	6.92896	0.428892
$262$	−22.9606	−1.41851
$263$	12.7264	0.784745	0.392373	−	0.919806i	$-0.371654\pi$
$263$	12.7264	0.784745	0.392373	+	0.919806i	$0.371654\pi$
$264$	−6.12899	−0.377213
$265$	−19.3547	−1.18895
$266$	0.856710	0.0525283
$267$	8.17030	0.500014
$268$	−3.65734	−0.223408
$269$	−27.9911	−1.70665	−0.853324	−	0.521381i	$-0.825417\pi$
$269$	−27.9911	−1.70665	−0.853324	+	0.521381i	$0.825417\pi$
$270$	4.98405	0.303320
$271$	10.4866	0.637015	0.318508	−	0.947920i	$-0.396818\pi$
$271$	10.4866	0.637015	0.318508	+	0.947920i	$0.396818\pi$
$272$	4.78994	0.290433
$273$	3.50133	0.211910
$274$	−3.83512	−0.231688
$275$	25.6304	1.54557
$276$	−1.82910	−0.110099
$277$	−4.17846	−0.251060	−0.125530	−	0.992090i	$-0.540063\pi$
$277$	−4.17846	−0.251060	−0.125530	+	0.992090i	$0.540063\pi$
$278$	9.55294	0.572947
$279$	−1.32438	−0.0792888
$280$	45.5425	2.72168
$281$	30.1581	1.79908	0.899540	−	0.436838i	$-0.143902\pi$
$281$	30.1581	1.79908	0.899540	+	0.436838i	$0.143902\pi$
$282$	7.79800	0.464364
$283$	−11.4678	−0.681687	−0.340843	−	0.940120i	$-0.610713\pi$
$283$	−11.4678	−0.681687	−0.340843	+	0.940120i	$0.610713\pi$
$284$	9.08816	0.539283
$285$	0.877192	0.0519604
$286$	2.34848	0.138869
$287$	−10.8349	−0.639566
$288$	−3.31425	−0.195294
$289$	−13.0453	−0.767372
$290$	−34.5343	−2.02792
$291$	0.583380	0.0341983
$292$	−5.23834	−0.306551
$293$	8.37841	0.489472	0.244736	−	0.969590i	$-0.421299\pi$
$293$	8.37841	0.489472	0.244736	+	0.969590i	$0.421299\pi$
$294$	6.20116	0.361659
$295$	39.2020	2.28243
$296$	2.14616	0.124743
$297$	−1.99179	−0.115575
$298$	−2.74269	−0.158880
$299$	2.99968	0.173476
$300$	7.84646	0.453015
$301$	28.3211	1.63240
$302$	−5.21712	−0.300211
$303$	−9.92184	−0.569995
$304$	0.499841	0.0286678
$305$	−19.5241	−1.11795
$306$	2.34476	0.134041
$307$	15.4032	0.879108	0.439554	−	0.898216i	$-0.355136\pi$
$307$	15.4032	0.879108	0.439554	+	0.898216i	$0.355136\pi$
$308$	−4.25244	−0.242305
$309$	−1.00000	−0.0568880
$310$	6.60079	0.374900
$311$	20.9116	1.18579	0.592893	−	0.805281i	$-0.297986\pi$
$311$	20.9116	1.18579	0.592893	+	0.805281i	$0.297986\pi$
$312$	3.07713	0.174208
$313$	−30.0959	−1.70112	−0.850561	−	0.525876i	$-0.823737\pi$
$313$	−30.0959	−1.70112	−0.850561	+	0.525876i	$0.823737\pi$
$314$	7.86074	0.443607
$315$	14.8003	0.833904
$316$	−3.76484	−0.211789
$317$	3.76515	0.211472	0.105736	−	0.994394i	$-0.466280\pi$
$317$	3.76515	0.211472	0.105736	+	0.994394i	$0.466280\pi$
$318$	−5.39875	−0.302747
$319$	13.8010	0.772709
$320$	36.8814	2.06174
$321$	17.4412	0.973471
$322$	12.3838	0.690120
$323$	0.412678	0.0229620
$324$	−0.609765	−0.0338758
$325$	−12.8680	−0.713789
$326$	−8.04939	−0.445815
$327$	0.882772	0.0488174
$328$	−9.52223	−0.525777
$329$	23.1565	1.27666
$330$	9.92717	0.546473
$331$	21.1912	1.16477	0.582387	−	0.812911i	$-0.302119\pi$
$331$	21.1912	1.16477	0.582387	+	0.812911i	$0.302119\pi$
$332$	−7.37293	−0.404642
$333$	0.697456	0.0382203
$334$	5.97334	0.326846
$335$	25.3537	1.38522
$336$	8.43351	0.460085
$337$	−14.9947	−0.816811	−0.408406	−	0.912801i	$-0.633915\pi$
$337$	−14.9947	−0.816811	−0.408406	+	0.912801i	$0.633915\pi$
$338$	−1.17908	−0.0641336
$339$	10.5763	0.574426
$340$	5.12573	0.277982
$341$	−2.63789	−0.142850
$342$	0.244681	0.0132308
$343$	−6.09473	−0.329084
$344$	24.8899	1.34197
$345$	12.6798	0.682659
$346$	−13.6640	−0.734583
$347$	28.2114	1.51447	0.757233	−	0.653145i	$-0.226551\pi$
$347$	28.2114	1.51447	0.757233	+	0.653145i	$0.226551\pi$
$348$	4.22503	0.226486
$349$	−18.2243	−0.975524	−0.487762	−	0.872977i	$-0.662187\pi$
$349$	−18.2243	−0.975524	−0.487762	+	0.872977i	$0.662187\pi$
$350$	−53.1237	−2.83958
$351$	1.00000	0.0533761
$352$	−6.60128	−0.351850
$353$	−9.17865	−0.488530	−0.244265	−	0.969708i	$-0.578547\pi$
$353$	−9.17865	−0.488530	−0.244265	+	0.969708i	$0.578547\pi$
$354$	10.9349	0.581183
$355$	−63.0017	−3.34378
$356$	4.98196	0.264043
$357$	6.96287	0.368514
$358$	−2.68269	−0.141785
$359$	0.468112	0.0247060	0.0123530	−	0.999924i	$-0.496068\pi$
$359$	0.468112	0.0247060	0.0123530	+	0.999924i	$0.496068\pi$
$360$	13.0072	0.685539
$361$	−18.9569	−0.997733
$362$	4.97880	0.261680
$363$	7.03278	0.369125
$364$	2.13499	0.111904
$365$	36.3137	1.90074
$366$	−5.44599	−0.284666
$367$	−28.8847	−1.50777	−0.753883	−	0.657008i	$-0.771822\pi$
$367$	−28.8847	−1.50777	−0.753883	+	0.657008i	$0.771822\pi$
$368$	7.22521	0.376640
$369$	−3.09452	−0.161094
$370$	−3.47615	−0.180717
$371$	−16.0318	−0.832329
$372$	−0.807562	−0.0418702
$373$	−2.86205	−0.148191	−0.0740955	−	0.997251i	$-0.523607\pi$
$373$	−2.86205	−0.148191	−0.0740955	+	0.997251i	$0.523607\pi$
$374$	4.67028	0.241494
$375$	−33.2585	−1.71746
$376$	20.3509	1.04952
$377$	−6.92896	−0.356860
$378$	4.12836	0.212340
$379$	−16.8373	−0.864876	−0.432438	−	0.901664i	$-0.642347\pi$
$379$	−16.8373	−0.864876	−0.432438	+	0.901664i	$0.642347\pi$
$380$	0.534881	0.0274388
$381$	17.2455	0.883514
$382$	5.19030	0.265559
$383$	15.6265	0.798474	0.399237	−	0.916848i	$-0.369275\pi$
$383$	15.6265	0.798474	0.399237	+	0.916848i	$0.369275\pi$
$384$	3.65910	0.186728
$385$	29.4791	1.50239
$386$	17.8485	0.908463
$387$	8.08867	0.411170
$388$	0.355724	0.0180592
$389$	10.3393	0.524224	0.262112	−	0.965037i	$-0.415581\pi$
$389$	10.3393	0.524224	0.262112	+	0.965037i	$0.415581\pi$
$390$	−4.98405	−0.252377
$391$	5.96527	0.301677
$392$	16.1836	0.817394
$393$	−19.4733	−0.982299
$394$	−20.7047	−1.04309
$395$	26.0989	1.31318
$396$	−1.21452	−0.0610320
$397$	−22.5096	−1.12972	−0.564862	−	0.825185i	$-0.691071\pi$
$397$	−22.5096	−1.12972	−0.564862	+	0.825185i	$0.691071\pi$
$398$	−2.91378	−0.146054
$399$	0.726590	0.0363750
$400$	−30.9946	−1.54973
$401$	−4.38018	−0.218736	−0.109368	−	0.994001i	$-0.534883\pi$
$401$	−4.38018	−0.218736	−0.109368	+	0.994001i	$0.534883\pi$
$402$	7.07209	0.352724
$403$	1.32438	0.0659723
$404$	−6.04999	−0.300998
$405$	4.22706	0.210044
$406$	−28.6052	−1.41965
$407$	1.38918	0.0688593
$408$	6.11928	0.302950
$409$	−11.3595	−0.561689	−0.280845	−	0.959753i	$-0.590615\pi$
$409$	−11.3595	−0.561689	−0.280845	+	0.959753i	$0.590615\pi$
$410$	15.4232	0.761699
$411$	−3.25264	−0.160441
$412$	−0.609765	−0.0300409
$413$	32.4716	1.59782
$414$	3.53687	0.173828
$415$	51.1112	2.50895
$416$	3.31425	0.162494
$417$	8.10201	0.396757
$418$	0.487353	0.0238372
$419$	1.32514	0.0647371	0.0323686	−	0.999476i	$-0.489695\pi$
$419$	1.32514	0.0647371	0.0323686	+	0.999476i	$0.489695\pi$
$420$	9.02471	0.440361
$421$	24.1139	1.17524	0.587619	−	0.809138i	$-0.300066\pi$
$421$	24.1139	1.17524	0.587619	+	0.809138i	$0.300066\pi$
$422$	12.3236	0.599903
$423$	6.61362	0.321565
$424$	−14.0895	−0.684245
$425$	−25.5898	−1.24129
$426$	−17.5735	−0.851438
$427$	−16.1721	−0.782621
$428$	10.6350	0.514062
$429$	1.99179	0.0961645
$430$	−40.3143	−1.94413
$431$	24.7725	1.19325	0.596624	−	0.802521i	$-0.296508\pi$
$431$	24.7725	1.19325	0.596624	+	0.802521i	$0.296508\pi$
$432$	2.40866	0.115887
$433$	37.1375	1.78472	0.892358	−	0.451328i	$-0.149050\pi$
$433$	37.1375	1.78472	0.892358	+	0.451328i	$0.149050\pi$
$434$	5.46753	0.262450
$435$	−29.2891	−1.40431
$436$	0.538283	0.0257791
$437$	0.622489	0.0297777
$438$	10.1292	0.483993
$439$	−33.6976	−1.60830	−0.804149	−	0.594427i	$-0.797379\pi$
$439$	−33.6976	−1.60830	−0.804149	+	0.594427i	$0.797379\pi$
$440$	25.9076	1.23510
$441$	5.25931	0.250443
$442$	−2.34476	−0.111529
$443$	1.03775	0.0493050	0.0246525	−	0.999696i	$-0.492152\pi$
$443$	1.03775	0.0493050	0.0246525	+	0.999696i	$0.492152\pi$
$444$	0.425284	0.0201831
$445$	−34.5363	−1.63718
$446$	−20.8803	−0.988712
$447$	−2.32613	−0.110022
$448$	30.5494	1.44332
$449$	−26.4885	−1.25007	−0.625035	−	0.780596i	$-0.714915\pi$
$449$	−26.4885	−1.25007	−0.625035	+	0.780596i	$0.714915\pi$
$450$	−15.1724	−0.715236
$451$	−6.16363	−0.290234
$452$	6.44905	0.303338
$453$	−4.42473	−0.207892
$454$	9.30540	0.436724
$455$	−14.8003	−0.693850
$456$	0.638561	0.0299033
$457$	19.1934	0.897828	0.448914	−	0.893575i	$-0.351811\pi$
$457$	19.1934	0.897828	0.448914	+	0.893575i	$0.351811\pi$
$458$	12.9415	0.604719
$459$	1.98864	0.0928215
$460$	7.73171	0.360493
$461$	−14.1890	−0.660845	−0.330423	−	0.943833i	$-0.607191\pi$
$461$	−14.1890	−0.660845	−0.330423	+	0.943833i	$0.607191\pi$
$462$	8.22281	0.382560
$463$	2.53045	0.117600	0.0588000	−	0.998270i	$-0.481273\pi$
$463$	2.53045	0.117600	0.0588000	+	0.998270i	$0.481273\pi$
$464$	−16.6895	−0.774790
$465$	5.59825	0.259612
$466$	26.9187	1.24698
$467$	8.38406	0.387968	0.193984	−	0.981005i	$-0.437859\pi$
$467$	8.38406	0.387968	0.193984	+	0.981005i	$0.437859\pi$
$468$	0.609765	0.0281864
$469$	21.0008	0.969728
$470$	−32.9626	−1.52045
$471$	6.66683	0.307191
$472$	28.5375	1.31354
$473$	16.1109	0.740781
$474$	7.27996	0.334380
$475$	−2.67035	−0.122524
$476$	4.24571	0.194602
$477$	−4.57877	−0.209648
$478$	9.32046	0.426308
$479$	−8.54776	−0.390557	−0.195278	−	0.980748i	$-0.562561\pi$
$479$	−8.54776	−0.390557	−0.195278	+	0.980748i	$0.562561\pi$
$480$	14.0095	0.639444
$481$	−0.697456	−0.0318012
$482$	−17.0808	−0.778011
$483$	10.5029	0.477898
$484$	4.28834	0.194924
$485$	−2.46598	−0.111974
$486$	1.17908	0.0534843
$487$	20.1379	0.912534	0.456267	−	0.889843i	$-0.349186\pi$
$487$	20.1379	0.912534	0.456267	+	0.889843i	$0.349186\pi$
$488$	−14.2127	−0.643381
$489$	−6.82683	−0.308720
$490$	−26.2127	−1.18417
$491$	−15.0088	−0.677340	−0.338670	−	0.940905i	$-0.609977\pi$
$491$	−15.0088	−0.677340	−0.338670	+	0.940905i	$0.609977\pi$
$492$	−1.88693	−0.0850693
$493$	−13.7792	−0.620583
$494$	−0.244681	−0.0110087
$495$	8.41940	0.378424
$496$	3.18999	0.143235
$497$	−52.1851	−2.34082
$498$	14.2568	0.638863
$499$	−28.3286	−1.26816	−0.634081	−	0.773267i	$-0.718621\pi$
$499$	−28.3286	−1.26816	−0.634081	+	0.773267i	$0.718621\pi$
$500$	−20.2799	−0.906944
$501$	5.06609	0.226336
$502$	−26.4623	−1.18107
$503$	33.5622	1.49647	0.748233	−	0.663436i	$-0.230902\pi$
$503$	33.5622	1.49647	0.748233	+	0.663436i	$0.230902\pi$
$504$	10.7740	0.479914
$505$	41.9402	1.86631
$506$	7.04470	0.313175
$507$	−1.00000	−0.0444116
$508$	10.5157	0.466559
$509$	26.7372	1.18510	0.592552	−	0.805532i	$-0.298120\pi$
$509$	26.7372	1.18510	0.592552	+	0.805532i	$0.298120\pi$
$510$	−9.91145	−0.438887
$511$	30.0791	1.33062
$512$	22.8064	1.00791
$513$	0.207518	0.00916216
$514$	−18.4194	−0.812446
$515$	4.22706	0.186266
$516$	4.93219	0.217127
$517$	13.1729	0.579345
$518$	−2.87935	−0.126511
$519$	−11.5887	−0.508688
$520$	−13.0072	−0.570403
$521$	−14.0229	−0.614353	−0.307176	−	0.951653i	$-0.599384\pi$
$521$	−14.0229	−0.614353	−0.307176	+	0.951653i	$0.599384\pi$
$522$	−8.16982	−0.357583
$523$	17.1581	0.750273	0.375137	−	0.926970i	$-0.377596\pi$
$523$	17.1581	0.750273	0.375137	+	0.926970i	$0.377596\pi$
$524$	−11.8741	−0.518724
$525$	−45.0552	−1.96637
$526$	−15.0055	−0.654271
$527$	2.63372	0.114726
$528$	4.79754	0.208786
$529$	−14.0019	−0.608778
$530$	22.8208	0.991273
$531$	9.27407	0.402460
$532$	0.443049	0.0192086
$533$	3.09452	0.134038
$534$	−9.63346	−0.416881
$535$	−73.7248	−3.18740
$536$	18.4565	0.797199
$537$	−2.27524	−0.0981838
$538$	33.0038	1.42290
$539$	10.4754	0.451209
$540$	2.57751	0.110918
$541$	18.5148	0.796012	0.398006	−	0.917383i	$-0.369702\pi$
$541$	18.5148	0.796012	0.398006	+	0.917383i	$0.369702\pi$
$542$	−12.3646	−0.531103
$543$	4.22260	0.181209
$544$	6.59083	0.282580
$545$	−3.73153	−0.159841
$546$	−4.12836	−0.176677
$547$	−16.6619	−0.712412	−0.356206	−	0.934407i	$-0.615930\pi$
$547$	−16.6619	−0.712412	−0.356206	+	0.934407i	$0.615930\pi$
$548$	−1.98334	−0.0847242
$549$	−4.61883	−0.197127
$550$	−30.2203	−1.28860
$551$	−1.43789	−0.0612560
$552$	9.23041	0.392872
$553$	21.6181	0.919296
$554$	4.92675	0.209318
$555$	−2.94819	−0.125143
$556$	4.94032	0.209516
$557$	35.7512	1.51483	0.757413	−	0.652937i	$-0.226463\pi$
$557$	35.7512	1.51483	0.757413	+	0.652937i	$0.226463\pi$
$558$	1.56156	0.0661060
$559$	−8.08867	−0.342114
$560$	−35.6489	−1.50644
$561$	3.96094	0.167231
$562$	−35.5589	−1.49996
$563$	−35.2509	−1.48565	−0.742824	−	0.669486i	$-0.766514\pi$
$563$	−35.2509	−1.48565	−0.742824	+	0.669486i	$0.766514\pi$
$564$	4.03275	0.169809
$565$	−44.7066	−1.88082
$566$	13.5214	0.568348
$567$	3.50133	0.147042
$568$	−45.8627	−1.92436
$569$	−26.1901	−1.09794	−0.548972	−	0.835840i	$-0.684981\pi$
$569$	−26.1901	−1.09794	−0.548972	+	0.835840i	$0.684981\pi$
$570$	−1.03428	−0.0433213
$571$	23.2816	0.974303	0.487152	−	0.873317i	$-0.338036\pi$
$571$	23.2816	0.974303	0.487152	+	0.873317i	$0.338036\pi$
$572$	1.21452	0.0507817
$573$	4.40198	0.183895
$574$	12.7753	0.533230
$575$	−38.6000	−1.60973
$576$	8.72509	0.363545
$577$	8.76906	0.365061	0.182530	−	0.983200i	$-0.441571\pi$
$577$	8.76906	0.365061	0.182530	+	0.983200i	$0.441571\pi$
$578$	15.3815	0.639787
$579$	15.1376	0.629097
$580$	−17.8595	−0.741574
$581$	42.3361	1.75640
$582$	−0.687853	−0.0285124
$583$	−9.11994	−0.377709
$584$	26.4349	1.09388
$585$	−4.22706	−0.174767
$586$	−9.87883	−0.408091
$587$	−16.3229	−0.673716	−0.336858	−	0.941555i	$-0.609364\pi$
$587$	−16.3229	−0.673716	−0.336858	+	0.941555i	$0.609364\pi$
$588$	3.20694	0.132252
$589$	0.274834	0.0113243
$590$	−46.2224	−1.90295
$591$	−17.5600	−0.722323
$592$	−1.67993	−0.0690448
$593$	−23.3447	−0.958650	−0.479325	−	0.877637i	$-0.659118\pi$
$593$	−23.3447	−0.958650	−0.479325	+	0.877637i	$0.659118\pi$
$594$	2.34848	0.0963594
$595$	−29.4324	−1.20661
$596$	−1.41839	−0.0580995
$597$	−2.47122	−0.101140
$598$	−3.53687	−0.144634
$599$	−28.4845	−1.16384	−0.581922	−	0.813244i	$-0.697699\pi$
$599$	−28.4845	−1.16384	−0.581922	+	0.813244i	$0.697699\pi$
$600$	−39.5965	−1.61652
$601$	−16.8680	−0.688061	−0.344030	−	0.938959i	$-0.611792\pi$
$601$	−16.8680	−0.688061	−0.344030	+	0.938959i	$0.611792\pi$
$602$	−33.3929	−1.36099
$603$	5.99796	0.244256
$604$	−2.69804	−0.109782
$605$	−29.7280	−1.20861
$606$	11.6987	0.475226
$607$	20.1169	0.816522	0.408261	−	0.912865i	$-0.366135\pi$
$607$	20.1169	0.816522	0.408261	+	0.912865i	$0.366135\pi$
$608$	0.687768	0.0278927
$609$	−24.2606	−0.983088
$610$	23.0205	0.932073
$611$	−6.61362	−0.267558
$612$	1.21260	0.0490164
$613$	−37.6644	−1.52125	−0.760625	−	0.649192i	$-0.775107\pi$
$613$	−37.6644	−1.52125	−0.760625	+	0.649192i	$0.775107\pi$
$614$	−18.1617	−0.732945
$615$	13.0807	0.527465
$616$	21.4596	0.864632
$617$	23.6145	0.950685	0.475343	−	0.879801i	$-0.342324\pi$
$617$	23.6145	0.950685	0.475343	+	0.879801i	$0.342324\pi$
$618$	1.17908	0.0474297
$619$	2.01316	0.0809159	0.0404580	−	0.999181i	$-0.487118\pi$
$619$	2.01316	0.0809159	0.0404580	+	0.999181i	$0.487118\pi$
$620$	3.41361	0.137094
$621$	2.99968	0.120373
$622$	−24.6565	−0.988634
$623$	−28.6069	−1.14611
$624$	−2.40866	−0.0964235
$625$	76.2456	3.04983
$626$	35.4856	1.41829
$627$	0.413333	0.0165069
$628$	4.06520	0.162219
$629$	−1.38698	−0.0553027
$630$	−17.4508	−0.695256
$631$	3.72338	0.148225	0.0741127	−	0.997250i	$-0.476388\pi$
$631$	3.72338	0.148225	0.0741127	+	0.997250i	$0.476388\pi$
$632$	18.9990	0.755739
$633$	10.4518	0.415424
$634$	−4.43942	−0.176312
$635$	−72.8977	−2.89286
$636$	−2.79197	−0.110709
$637$	−5.25931	−0.208381
$638$	−16.2725	−0.644236
$639$	−14.9044	−0.589608
$640$	−15.4672	−0.611396
$641$	5.91251	0.233530	0.116765	−	0.993160i	$-0.462748\pi$
$641$	5.91251	0.233530	0.116765	+	0.993160i	$0.462748\pi$
$642$	−20.5646	−0.811619
$643$	26.4518	1.04316	0.521578	−	0.853204i	$-0.325344\pi$
$643$	26.4518	1.04316	0.521578	+	0.853204i	$0.325344\pi$
$644$	6.40428	0.252364
$645$	−34.1913	−1.34628
$646$	−0.486582	−0.0191443
$647$	9.98316	0.392479	0.196239	−	0.980556i	$-0.437127\pi$
$647$	9.98316	0.392479	0.196239	+	0.980556i	$0.437127\pi$
$648$	3.07713	0.120881
$649$	18.4720	0.725089
$650$	15.1724	0.595112
$651$	4.63710	0.181742
$652$	−4.16276	−0.163026
$653$	−49.0199	−1.91830	−0.959148	−	0.282906i	$-0.908702\pi$
$653$	−49.0199	−1.91830	−0.959148	+	0.282906i	$0.908702\pi$
$654$	−1.04086	−0.0407009
$655$	82.3148	3.21631
$656$	7.45364	0.291016
$657$	8.59077	0.335158
$658$	−27.3034	−1.06440
$659$	−5.14829	−0.200549	−0.100275	−	0.994960i	$-0.531972\pi$
$659$	−5.14829	−0.200549	−0.100275	+	0.994960i	$0.531972\pi$
$660$	5.13385	0.199835
$661$	21.7635	0.846504	0.423252	−	0.906012i	$-0.360889\pi$
$661$	21.7635	0.846504	0.423252	+	0.906012i	$0.360889\pi$
$662$	−24.9862	−0.971116
$663$	−1.98864	−0.0772322
$664$	37.2069	1.44391
$665$	−3.07134	−0.119101
$666$	−0.822358	−0.0318657
$667$	−20.7847	−0.804786
$668$	3.08912	0.119522
$669$	−17.7090	−0.684668
$670$	−29.8941	−1.15491
$671$	−9.19974	−0.355152
$672$	11.6043	0.447645
$673$	−38.0103	−1.46519	−0.732594	−	0.680666i	$-0.761690\pi$
$673$	−38.0103	−1.46519	−0.732594	+	0.680666i	$0.761690\pi$
$674$	17.6799	0.681006
$675$	−12.8680	−0.495290
$676$	−0.609765	−0.0234525
$677$	14.0708	0.540786	0.270393	−	0.962750i	$-0.412846\pi$
$677$	14.0708	0.540786	0.270393	+	0.962750i	$0.412846\pi$
$678$	−12.4703	−0.478920
$679$	−2.04261	−0.0783880
$680$	−25.8666	−0.991937
$681$	7.89207	0.302425
$682$	3.11029	0.119099
$683$	−28.0779	−1.07437	−0.537186	−	0.843464i	$-0.680513\pi$
$683$	−28.0779	−1.07437	−0.537186	+	0.843464i	$0.680513\pi$
$684$	0.126537	0.00483828
$685$	13.7491	0.525325
$686$	7.18618	0.274370
$687$	10.9759	0.418758
$688$	−19.4828	−0.742777
$689$	4.57877	0.174437
$690$	−14.9506	−0.569158
$691$	−15.2724	−0.580988	−0.290494	−	0.956877i	$-0.593820\pi$
$691$	−15.2724	−0.580988	−0.290494	+	0.956877i	$0.593820\pi$
$692$	−7.06638	−0.268624
$693$	6.97391	0.264917
$694$	−33.2635	−1.26267
$695$	−34.2477	−1.29909
$696$	−21.3213	−0.808182
$697$	6.15387	0.233094
$698$	21.4879	0.813330
$699$	22.8302	0.863518
$700$	−27.4730	−1.03838
$701$	10.1580	0.383663	0.191832	−	0.981428i	$-0.438557\pi$
$701$	10.1580	0.383663	0.191832	+	0.981428i	$0.438557\pi$
$702$	−1.17908	−0.0445016
$703$	−0.144735	−0.00545878
$704$	17.3785	0.654978
$705$	−27.9561	−1.05289
$706$	10.8224	0.407306
$707$	34.7396	1.30652
$708$	5.65500	0.212528
$709$	−5.05358	−0.189791	−0.0948957	−	0.995487i	$-0.530252\pi$
$709$	−5.05358	−0.189791	−0.0948957	+	0.995487i	$0.530252\pi$
$710$	74.2842	2.78783
$711$	6.17426	0.231553
$712$	−25.1411	−0.942201
$713$	3.97273	0.148780
$714$	−8.20979	−0.307244
$715$	−8.41940	−0.314868
$716$	−1.38736	−0.0518481
$717$	7.90484	0.295212
$718$	−0.551942	−0.0205983
$719$	49.8751	1.86003	0.930015	−	0.367523i	$-0.119794\pi$
$719$	49.8751	1.86003	0.930015	+	0.367523i	$0.119794\pi$
$720$	−10.1815	−0.379443
$721$	3.50133	0.130396
$722$	22.3518	0.831848
$723$	−14.4866	−0.538761
$724$	2.57479	0.0956915
$725$	89.1619	3.31139
$726$	−8.29222	−0.307753
$727$	−27.5521	−1.02185	−0.510925	−	0.859625i	$-0.670697\pi$
$727$	−27.5521	−1.02185	−0.510925	+	0.859625i	$0.670697\pi$
$728$	−10.7740	−0.399312
$729$	1.00000	0.0370370
$730$	−42.8168	−1.58472
$731$	−16.0854	−0.594941
$732$	−2.81640	−0.104097
$733$	−0.821960	−0.0303598	−0.0151799	−	0.999885i	$-0.504832\pi$
$733$	−0.821960	−0.0303598	−0.0151799	+	0.999885i	$0.504832\pi$
$734$	34.0574	1.25708
$735$	−22.2314	−0.820018
$736$	9.94170	0.366456
$737$	11.9467	0.440061
$738$	3.64869	0.134310
$739$	35.8423	1.31848	0.659240	−	0.751932i	$-0.270878\pi$
$739$	35.8423	1.31848	0.659240	+	0.751932i	$0.270878\pi$
$740$	−1.79770	−0.0660847
$741$	−0.207518	−0.00762338
$742$	18.9028	0.693944
$743$	46.4022	1.70233	0.851166	−	0.524896i	$-0.175896\pi$
$743$	46.4022	1.70233	0.851166	+	0.524896i	$0.175896\pi$
$744$	4.07530	0.149408
$745$	9.83267	0.360241
$746$	3.37459	0.123552
$747$	12.0914	0.442403
$748$	2.41524	0.0883100
$749$	−61.0673	−2.23135
$750$	39.2145	1.43191
$751$	26.2705	0.958625	0.479313	−	0.877644i	$-0.340886\pi$
$751$	26.2705	0.958625	0.479313	+	0.877644i	$0.340886\pi$
$752$	−15.9299	−0.580905
$753$	−22.4431	−0.817873
$754$	8.16982	0.297527
$755$	18.7036	0.680693
$756$	2.13499	0.0776487
$757$	−23.4174	−0.851120	−0.425560	−	0.904930i	$-0.639923\pi$
$757$	−23.4174	−0.851120	−0.425560	+	0.904930i	$0.639923\pi$
$758$	19.8526	0.721080
$759$	5.97473	0.216869
$760$	−2.69923	−0.0979114
$761$	−41.7647	−1.51397	−0.756984	−	0.653433i	$-0.773328\pi$
$761$	−41.7647	−1.51397	−0.756984	+	0.653433i	$0.773328\pi$
$762$	−20.3339	−0.736618
$763$	−3.09087	−0.111897
$764$	2.68417	0.0971100
$765$	−8.40607	−0.303922
$766$	−18.4249	−0.665718
$767$	−9.27407	−0.334867
$768$	13.1358	0.473997
$769$	5.12320	0.184747	0.0923736	−	0.995724i	$-0.470555\pi$
$769$	5.12320	0.184747	0.0923736	+	0.995724i	$0.470555\pi$
$770$	−34.7583	−1.25260
$771$	−15.6218	−0.562607
$772$	9.23036	0.332208
$773$	−14.7624	−0.530965	−0.265482	−	0.964116i	$-0.585531\pi$
$773$	−14.7624	−0.530965	−0.265482	+	0.964116i	$0.585531\pi$
$774$	−9.53721	−0.342808
$775$	−17.0422	−0.612173
$776$	−1.79513	−0.0644416
$777$	−2.44202	−0.0876071
$778$	−12.1909	−0.437065
$779$	0.642169	0.0230081
$780$	−2.57751	−0.0922896
$781$	−29.6864	−1.06226
$782$	−7.03355	−0.251519
$783$	−6.92896	−0.247621
$784$	−12.6679	−0.452424
$785$	−28.1811	−1.00583
$786$	22.9606	0.818979
$787$	−54.6451	−1.94789	−0.973943	−	0.226791i	$-0.927177\pi$
$787$	−54.6451	−1.94789	−0.973943	+	0.226791i	$0.927177\pi$
$788$	−10.7075	−0.381438
$789$	−12.7264	−0.453073
$790$	−30.7728	−1.09485
$791$	−37.0311	−1.31667
$792$	6.12899	0.217784
$793$	4.61883	0.164020
$794$	26.5407	0.941893
$795$	19.3547	0.686441
$796$	−1.50686	−0.0534094
$797$	−19.6475	−0.695950	−0.347975	−	0.937504i	$-0.613131\pi$
$797$	−19.6475	−0.695950	−0.347975	+	0.937504i	$0.613131\pi$
$798$	−0.856710	−0.0303272
$799$	−13.1521	−0.465287
$800$	−42.6478	−1.50783
$801$	−8.17030	−0.288683
$802$	5.16460	0.182368
$803$	17.1110	0.603834
$804$	3.65734	0.128985
$805$	−44.3963	−1.56476
$806$	−1.56156	−0.0550035
$807$	27.9911	0.985334
$808$	30.5308	1.07407
$809$	16.2787	0.572329	0.286164	−	0.958181i	$-0.407620\pi$
$809$	16.2787	0.572329	0.286164	+	0.958181i	$0.407620\pi$
$810$	−4.98405	−0.175122
$811$	−7.70388	−0.270520	−0.135260	−	0.990810i	$-0.543187\pi$
$811$	−7.70388	−0.270520	−0.135260	+	0.990810i	$0.543187\pi$
$812$	−14.7932	−0.519141
$813$	−10.4866	−0.367781
$814$	−1.63796	−0.0574106
$815$	28.8574	1.01083
$816$	−4.78994	−0.167681
$817$	−1.67855	−0.0587250
$818$	13.3937	0.468301
$819$	−3.50133	−0.122346
$820$	7.97615	0.278539
$821$	28.3645	0.989930	0.494965	−	0.868913i	$-0.335181\pi$
$821$	28.3645	0.989930	0.494965	+	0.868913i	$0.335181\pi$
$822$	3.83512	0.133765
$823$	−25.1404	−0.876339	−0.438169	−	0.898892i	$-0.644373\pi$
$823$	−25.1404	−0.876339	−0.438169	+	0.898892i	$0.644373\pi$
$824$	3.07713	0.107197
$825$	−25.6304	−0.892335
$826$	−38.2867	−1.33216
$827$	46.6770	1.62312	0.811559	−	0.584270i	$-0.198619\pi$
$827$	46.6770	1.62312	0.811559	+	0.584270i	$0.198619\pi$
$828$	1.82910	0.0635656
$829$	−16.0248	−0.556563	−0.278281	−	0.960500i	$-0.589765\pi$
$829$	−16.0248	−0.556563	−0.278281	+	0.960500i	$0.589765\pi$
$830$	−60.2643	−2.09180
$831$	4.17846	0.144949
$832$	−8.72509	−0.302488
$833$	−10.4589	−0.362378
$834$	−9.55294	−0.330791
$835$	−21.4146	−0.741085
$836$	0.252036	0.00871684
$837$	1.32438	0.0457774
$838$	−1.56244	−0.0539737
$839$	24.1433	0.833520	0.416760	−	0.909017i	$-0.363166\pi$
$839$	24.1433	0.833520	0.416760	+	0.909017i	$0.363166\pi$
$840$	−45.5425	−1.57136
$841$	19.0105	0.655534
$842$	−28.4322	−0.979839
$843$	−30.1581	−1.03870
$844$	6.37317	0.219373
$845$	4.22706	0.145415
$846$	−7.79800	−0.268101
$847$	−24.6241	−0.846093
$848$	11.0287	0.378727
$849$	11.4678	0.393572
$850$	30.1725	1.03491
$851$	−2.09215	−0.0717178
$852$	−9.08816	−0.311355
$853$	33.6628	1.15259	0.576297	−	0.817240i	$-0.304497\pi$
$853$	33.6628	1.15259	0.576297	+	0.817240i	$0.304497\pi$
$854$	19.0682	0.652500
$855$	−0.877192	−0.0299993
$856$	−53.6687	−1.83436
$857$	−37.4005	−1.27758	−0.638788	−	0.769382i	$-0.720564\pi$
$857$	−37.4005	−1.27758	−0.638788	+	0.769382i	$0.720564\pi$
$858$	−2.34848	−0.0801759
$859$	27.3262	0.932358	0.466179	−	0.884690i	$-0.345630\pi$
$859$	27.3262	0.932358	0.466179	+	0.884690i	$0.345630\pi$
$860$	−20.8486	−0.710933
$861$	10.8349	0.369253
$862$	−29.2088	−0.994855
$863$	−4.42691	−0.150694	−0.0753468	−	0.997157i	$-0.524006\pi$
$863$	−4.42691	−0.150694	−0.0753468	+	0.997157i	$0.524006\pi$
$864$	3.31425	0.112753
$865$	48.9861	1.66558
$866$	−43.7882	−1.48798
$867$	13.0453	0.443043
$868$	2.82754	0.0959730
$869$	12.2978	0.417175
$870$	34.5343	1.17082
$871$	−5.99796	−0.203233
$872$	−2.71640	−0.0919890
$873$	−0.583380	−0.0197444
$874$	−0.733966	−0.0248268
$875$	116.449	3.93670
$876$	5.23834	0.176987
$877$	53.7711	1.81572	0.907861	−	0.419272i	$-0.137715\pi$
$877$	53.7711	1.81572	0.907861	+	0.419272i	$0.137715\pi$
$878$	39.7322	1.34090
$879$	−8.37841	−0.282597
$880$	−20.2795	−0.683621
$881$	56.1223	1.89081	0.945404	−	0.325901i	$-0.105667\pi$
$881$	56.1223	1.89081	0.945404	+	0.325901i	$0.105667\pi$
$882$	−6.20116	−0.208804
$883$	32.8019	1.10387	0.551936	−	0.833886i	$-0.313889\pi$
$883$	32.8019	1.10387	0.551936	+	0.833886i	$0.313889\pi$
$884$	−1.21260	−0.0407841
$885$	−39.2020	−1.31776
$886$	−1.22359	−0.0411074
$887$	30.0304	1.00832	0.504160	−	0.863610i	$-0.331802\pi$
$887$	30.0304	1.00832	0.504160	+	0.863610i	$0.331802\pi$
$888$	−2.14616	−0.0720204
$889$	−60.3822	−2.02515
$890$	40.7212	1.36498
$891$	1.99179	0.0667274
$892$	−10.7983	−0.361554
$893$	−1.37245	−0.0459272
$894$	2.74269	0.0917294
$895$	9.61756	0.321480
$896$	−12.8117	−0.428010
$897$	−2.99968	−0.100156
$898$	31.2322	1.04223
$899$	−9.17660	−0.306057
$900$	−7.84646	−0.261549
$901$	9.10550	0.303348
$902$	7.26742	0.241979
$903$	−28.3211	−0.942468
$904$	−32.5446	−1.08242
$905$	−17.8492	−0.593327
$906$	5.21712	0.173327
$907$	2.16740	0.0719673	0.0359837	−	0.999352i	$-0.488544\pi$
$907$	2.16740	0.0719673	0.0359837	+	0.999352i	$0.488544\pi$
$908$	4.81231	0.159702
$909$	9.92184	0.329087
$910$	17.4508	0.578488
$911$	31.5330	1.04474	0.522368	−	0.852720i	$-0.325049\pi$
$911$	31.5330	1.04474	0.522368	+	0.852720i	$0.325049\pi$
$912$	−0.499841	−0.0165514
$913$	24.0836	0.797050
$914$	−22.6306	−0.748552
$915$	19.5241	0.645446
$916$	6.69274	0.221134
$917$	68.1825	2.25158
$918$	−2.34476	−0.0773888
$919$	−40.2796	−1.32870	−0.664352	−	0.747420i	$-0.731292\pi$
$919$	−40.2796	−1.32870	−0.664352	+	0.747420i	$0.731292\pi$
$920$	−39.0175	−1.28637
$921$	−15.4032	−0.507553
$922$	16.7299	0.550971
$923$	14.9044	0.490584
$924$	4.25244	0.139895
$925$	8.97487	0.295092
$926$	−2.98361	−0.0980476
$927$	1.00000	0.0328443
$928$	−22.9643	−0.753840
$929$	−13.9400	−0.457357	−0.228678	−	0.973502i	$-0.573440\pi$
$929$	−13.9400	−0.457357	−0.228678	+	0.973502i	$0.573440\pi$
$930$	−6.60079	−0.216449
$931$	−1.09140	−0.0357693
$932$	13.9211	0.455999
$933$	−20.9116	−0.684614
$934$	−9.88550	−0.323464
$935$	−16.7431	−0.547559
$936$	−3.07713	−0.100579
$937$	25.3020	0.826581	0.413291	−	0.910599i	$-0.364379\pi$
$937$	25.3020	0.826581	0.413291	+	0.910599i	$0.364379\pi$
$938$	−24.7617	−0.808499
$939$	30.0959	0.982143
$940$	−17.0467	−0.556001
$941$	−57.1738	−1.86381	−0.931906	−	0.362699i	$-0.881855\pi$
$941$	−57.1738	−1.86381	−0.931906	+	0.362699i	$0.881855\pi$
$942$	−7.86074	−0.256117
$943$	9.28257	0.302282
$944$	−22.3381	−0.727042
$945$	−14.8003	−0.481454
$946$	−18.9961	−0.617617
$947$	−1.84313	−0.0598937	−0.0299468	−	0.999551i	$-0.509534\pi$
$947$	−1.84313	−0.0598937	−0.0299468	+	0.999551i	$0.509534\pi$
$948$	3.76484	0.122276
$949$	−8.59077	−0.278868
$950$	3.14856	0.102153
$951$	−3.76515	−0.122093
$952$	−21.4256	−0.694409
$953$	35.0278	1.13466	0.567331	−	0.823490i	$-0.307976\pi$
$953$	35.0278	1.13466	0.567331	+	0.823490i	$0.307976\pi$
$954$	5.39875	0.174791
$955$	−18.6074	−0.602122
$956$	4.82009	0.155893
$957$	−13.8010	−0.446124
$958$	10.0785	0.325622
$959$	11.3885	0.367755
$960$	−36.8814	−1.19034
$961$	−29.2460	−0.943420
$962$	0.822358	0.0265139
$963$	−17.4412	−0.562034
$964$	−8.83339	−0.284504
$965$	−63.9874	−2.05983
$966$	−12.3838	−0.398441
$967$	−46.6874	−1.50137	−0.750683	−	0.660663i	$-0.770275\pi$
$967$	−46.6874	−1.50137	−0.750683	+	0.660663i	$0.770275\pi$
$968$	−21.6408	−0.695560
$969$	−0.412678	−0.0132571
$970$	2.90759	0.0933572
$971$	−5.64196	−0.181059	−0.0905295	−	0.995894i	$-0.528856\pi$
$971$	−5.64196	−0.181059	−0.0905295	+	0.995894i	$0.528856\pi$
$972$	0.609765	0.0195582
$973$	−28.3678	−0.909430
$974$	−23.7442	−0.760814
$975$	12.8680	0.412106
$976$	11.1252	0.356109
$977$	33.9996	1.08774	0.543872	−	0.839168i	$-0.316958\pi$
$977$	33.9996	1.08774	0.543872	+	0.839168i	$0.316958\pi$
$978$	8.04939	0.257391
$979$	−16.2735	−0.520104
$980$	−13.5559	−0.433028
$981$	−0.882772	−0.0281847
$982$	17.6967	0.564723
$983$	−19.1847	−0.611898	−0.305949	−	0.952048i	$-0.598974\pi$
$983$	−19.1847	−0.611898	−0.305949	+	0.952048i	$0.598974\pi$
$984$	9.52223	0.303558
$985$	74.2272	2.36507
$986$	16.2468	0.517403
$987$	−23.1565	−0.737078
$988$	−0.126537	−0.00402569
$989$	−24.2635	−0.771533
$990$	−9.92717	−0.315506
$991$	52.5804	1.67027	0.835136	−	0.550044i	$-0.185389\pi$
$991$	52.5804	1.67027	0.835136	+	0.550044i	$0.185389\pi$
$992$	4.38934	0.139362
$993$	−21.1912	−0.672483
$994$	61.5306	1.95163
$995$	10.4460	0.331160
$996$	7.37293	0.233620
$997$	−9.26075	−0.293291	−0.146645	−	0.989189i	$-0.546848\pi$
$997$	−9.26075	−0.293291	−0.146645	+	0.989189i	$0.546848\pi$
$998$	33.4018	1.05731
$999$	−0.697456	−0.0220665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.8	✓	24	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)

\(f(q)\)	\(=\)	\(q-1.17908 q^{2} -1.00000 q^{3} -0.609765 q^{4} +4.22706 q^{5} +1.17908 q^{6} +3.50133 q^{7} +3.07713 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.17908 q^{2} -1.00000 q^{3} -0.609765 q^{4} +4.22706 q^{5} +1.17908 q^{6} +3.50133 q^{7} +3.07713 q^{8} +1.00000 q^{9} -4.98405 q^{10} +1.99179 q^{11} +0.609765 q^{12} -1.00000 q^{13} -4.12836 q^{14} -4.22706 q^{15} -2.40866 q^{16} -1.98864 q^{17} -1.17908 q^{18} -0.207518 q^{19} -2.57751 q^{20} -3.50133 q^{21} -2.34848 q^{22} -2.99968 q^{23} -3.07713 q^{24} +12.8680 q^{25} +1.17908 q^{26} -1.00000 q^{27} -2.13499 q^{28} +6.92896 q^{29} +4.98405 q^{30} -1.32438 q^{31} -3.31425 q^{32} -1.99179 q^{33} +2.34476 q^{34} +14.8003 q^{35} -0.609765 q^{36} +0.697456 q^{37} +0.244681 q^{38} +1.00000 q^{39} +13.0072 q^{40} -3.09452 q^{41} +4.12836 q^{42} +8.08867 q^{43} -1.21452 q^{44} +4.22706 q^{45} +3.53687 q^{46} +6.61362 q^{47} +2.40866 q^{48} +5.25931 q^{49} -15.1724 q^{50} +1.98864 q^{51} +0.609765 q^{52} -4.57877 q^{53} +1.17908 q^{54} +8.41940 q^{55} +10.7740 q^{56} +0.207518 q^{57} -8.16982 q^{58} +9.27407 q^{59} +2.57751 q^{60} -4.61883 q^{61} +1.56156 q^{62} +3.50133 q^{63} +8.72509 q^{64} -4.22706 q^{65} +2.34848 q^{66} +5.99796 q^{67} +1.21260 q^{68} +2.99968 q^{69} -17.4508 q^{70} -14.9044 q^{71} +3.07713 q^{72} +8.59077 q^{73} -0.822358 q^{74} -12.8680 q^{75} +0.126537 q^{76} +6.97391 q^{77} -1.17908 q^{78} +6.17426 q^{79} -10.1815 q^{80} +1.00000 q^{81} +3.64869 q^{82} +12.0914 q^{83} +2.13499 q^{84} -8.40607 q^{85} -9.53721 q^{86} -6.92896 q^{87} +6.12899 q^{88} -8.17030 q^{89} -4.98405 q^{90} -3.50133 q^{91} +1.82910 q^{92} +1.32438 q^{93} -7.79800 q^{94} -0.877192 q^{95} +3.31425 q^{96} -0.583380 q^{97} -6.20116 q^{98} +1.99179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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