LMFDB - Embedded newform 6014.2.a.j.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.0623199 q^{3} +1.00000 q^{4} +1.97455 q^{5} +0.0623199 q^{6} -0.185636 q^{7} -1.00000 q^{8} -2.99612 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.0623199 q^{3} +1.00000 q^{4} +1.97455 q^{5} +0.0623199 q^{6} -0.185636 q^{7} -1.00000 q^{8} -2.99612 q^{9} -1.97455 q^{10} -1.12173 q^{11} -0.0623199 q^{12} -4.71384 q^{13} +0.185636 q^{14} -0.123054 q^{15} +1.00000 q^{16} +5.95039 q^{17} +2.99612 q^{18} -5.93391 q^{19} +1.97455 q^{20} +0.0115688 q^{21} +1.12173 q^{22} +5.58488 q^{23} +0.0623199 q^{24} -1.10117 q^{25} +4.71384 q^{26} +0.373677 q^{27} -0.185636 q^{28} +3.59334 q^{29} +0.123054 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.0699062 q^{33} -5.95039 q^{34} -0.366546 q^{35} -2.99612 q^{36} +5.72530 q^{37} +5.93391 q^{38} +0.293766 q^{39} -1.97455 q^{40} +6.21359 q^{41} -0.0115688 q^{42} -5.51327 q^{43} -1.12173 q^{44} -5.91597 q^{45} -5.58488 q^{46} -9.14577 q^{47} -0.0623199 q^{48} -6.96554 q^{49} +1.10117 q^{50} -0.370828 q^{51} -4.71384 q^{52} +11.2122 q^{53} -0.373677 q^{54} -2.21491 q^{55} +0.185636 q^{56} +0.369801 q^{57} -3.59334 q^{58} -4.49793 q^{59} -0.123054 q^{60} -9.23791 q^{61} +1.00000 q^{62} +0.556186 q^{63} +1.00000 q^{64} -9.30770 q^{65} -0.0699062 q^{66} +15.9950 q^{67} +5.95039 q^{68} -0.348049 q^{69} +0.366546 q^{70} +11.2449 q^{71} +2.99612 q^{72} +1.46090 q^{73} -5.72530 q^{74} +0.0686246 q^{75} -5.93391 q^{76} +0.208234 q^{77} -0.293766 q^{78} -17.4814 q^{79} +1.97455 q^{80} +8.96506 q^{81} -6.21359 q^{82} -12.4925 q^{83} +0.0115688 q^{84} +11.7493 q^{85} +5.51327 q^{86} -0.223936 q^{87} +1.12173 q^{88} +12.6942 q^{89} +5.91597 q^{90} +0.875058 q^{91} +5.58488 q^{92} +0.0623199 q^{93} +9.14577 q^{94} -11.7168 q^{95} +0.0623199 q^{96} +1.00000 q^{97} +6.96554 q^{98} +3.36084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * 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
$3$	−0.0623199	−0.0359804	−0.0179902	−	0.999838i	$-0.505727\pi$
$3$	−0.0623199	−0.0359804	−0.0179902	+	0.999838i	$0.505727\pi$
$4$	1.00000	0.500000
$5$	1.97455	0.883044	0.441522	−	0.897250i	$-0.354439\pi$
$5$	1.97455	0.883044	0.441522	+	0.897250i	$0.354439\pi$
$6$	0.0623199	0.0254420
$7$	−0.185636	−0.0701637	−0.0350819	−	0.999384i	$-0.511169\pi$
$7$	−0.185636	−0.0701637	−0.0350819	+	0.999384i	$0.511169\pi$
$8$	−1.00000	−0.353553
$9$	−2.99612	−0.998705
$10$	−1.97455	−0.624406
$11$	−1.12173	−0.338215	−0.169107	−	0.985598i	$-0.554089\pi$
$11$	−1.12173	−0.338215	−0.169107	+	0.985598i	$0.554089\pi$
$12$	−0.0623199	−0.0179902
$13$	−4.71384	−1.30738	−0.653692	−	0.756760i	$-0.726781\pi$
$13$	−4.71384	−1.30738	−0.653692	+	0.756760i	$0.726781\pi$
$14$	0.185636	0.0496132
$15$	−0.123054	−0.0317723
$16$	1.00000	0.250000
$17$	5.95039	1.44318	0.721591	−	0.692319i	$-0.243411\pi$
$17$	5.95039	1.44318	0.721591	+	0.692319i	$0.243411\pi$
$18$	2.99612	0.706191
$19$	−5.93391	−1.36133	−0.680666	−	0.732594i	$-0.738310\pi$
$19$	−5.93391	−1.36133	−0.680666	+	0.732594i	$0.738310\pi$
$20$	1.97455	0.441522
$21$	0.0115688	0.00252452
$22$	1.12173	0.239154
$23$	5.58488	1.16453	0.582264	−	0.813000i	$-0.302167\pi$
$23$	5.58488	1.16453	0.582264	+	0.813000i	$0.302167\pi$
$24$	0.0623199	0.0127210
$25$	−1.10117	−0.220233
$26$	4.71384	0.924460
$27$	0.373677	0.0719143
$28$	−0.185636	−0.0350819
$29$	3.59334	0.667266	0.333633	−	0.942703i	$-0.391725\pi$
$29$	3.59334	0.667266	0.333633	+	0.942703i	$0.391725\pi$
$30$	0.123054	0.0224664
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	0.0699062	0.0121691
$34$	−5.95039	−1.02048
$35$	−0.366546	−0.0619577
$36$	−2.99612	−0.499353
$37$	5.72530	0.941234	0.470617	−	0.882338i	$-0.344031\pi$
$37$	5.72530	0.941234	0.470617	+	0.882338i	$0.344031\pi$
$38$	5.93391	0.962607
$39$	0.293766	0.0470402
$40$	−1.97455	−0.312203
$41$	6.21359	0.970400	0.485200	−	0.874403i	$-0.338747\pi$
$41$	6.21359	0.970400	0.485200	+	0.874403i	$0.338747\pi$
$42$	−0.0115688	−0.00178511
$43$	−5.51327	−0.840766	−0.420383	−	0.907347i	$-0.638104\pi$
$43$	−5.51327	−0.840766	−0.420383	+	0.907347i	$0.638104\pi$
$44$	−1.12173	−0.169107
$45$	−5.91597	−0.881901
$46$	−5.58488	−0.823445
$47$	−9.14577	−1.33405	−0.667024	−	0.745036i	$-0.732432\pi$
$47$	−9.14577	−1.33405	−0.667024	+	0.745036i	$0.732432\pi$
$48$	−0.0623199	−0.00899510
$49$	−6.96554	−0.995077
$50$	1.10117	0.155728
$51$	−0.370828	−0.0519263
$52$	−4.71384	−0.653692
$53$	11.2122	1.54011	0.770054	−	0.637979i	$-0.220229\pi$
$53$	11.2122	1.54011	0.770054	+	0.637979i	$0.220229\pi$
$54$	−0.373677	−0.0508511
$55$	−2.21491	−0.298659
$56$	0.185636	0.0248066
$57$	0.369801	0.0489813
$58$	−3.59334	−0.471828
$59$	−4.49793	−0.585581	−0.292790	−	0.956177i	$-0.594584\pi$
$59$	−4.49793	−0.585581	−0.292790	+	0.956177i	$0.594584\pi$
$60$	−0.123054	−0.0158861
$61$	−9.23791	−1.18279	−0.591397	−	0.806381i	$-0.701423\pi$
$61$	−9.23791	−1.18279	−0.591397	+	0.806381i	$0.701423\pi$
$62$	1.00000	0.127000
$63$	0.556186	0.0700729
$64$	1.00000	0.125000
$65$	−9.30770	−1.15448
$66$	−0.0699062	−0.00860486
$67$	15.9950	1.95411	0.977053	−	0.212997i	$-0.0683224\pi$
$67$	15.9950	1.95411	0.977053	+	0.212997i	$0.0683224\pi$
$68$	5.95039	0.721591
$69$	−0.348049	−0.0419002
$70$	0.366546	0.0438107
$71$	11.2449	1.33453	0.667265	−	0.744821i	$-0.267465\pi$
$71$	11.2449	1.33453	0.667265	+	0.744821i	$0.267465\pi$
$72$	2.99612	0.353096
$73$	1.46090	0.170985	0.0854924	−	0.996339i	$-0.472754\pi$
$73$	1.46090	0.170985	0.0854924	+	0.996339i	$0.472754\pi$
$74$	−5.72530	−0.665553
$75$	0.0686246	0.00792408
$76$	−5.93391	−0.680666
$77$	0.208234	0.0237304
$78$	−0.293766	−0.0332625
$79$	−17.4814	−1.96682	−0.983408	−	0.181406i	$-0.941935\pi$
$79$	−17.4814	−1.96682	−0.983408	+	0.181406i	$0.941935\pi$
$80$	1.97455	0.220761
$81$	8.96506	0.996118
$82$	−6.21359	−0.686176
$83$	−12.4925	−1.37122	−0.685612	−	0.727967i	$-0.740465\pi$
$83$	−12.4925	−1.37122	−0.685612	+	0.727967i	$0.740465\pi$
$84$	0.0115688	0.00126226
$85$	11.7493	1.27439
$86$	5.51327	0.594511
$87$	−0.223936	−0.0240085
$88$	1.12173	0.119577
$89$	12.6942	1.34559	0.672793	−	0.739831i	$-0.265095\pi$
$89$	12.6942	1.34559	0.672793	+	0.739831i	$0.265095\pi$
$90$	5.91597	0.623598
$91$	0.875058	0.0917310
$92$	5.58488	0.582264
$93$	0.0623199	0.00646227
$94$	9.14577	0.943314
$95$	−11.7168	−1.20212
$96$	0.0623199	0.00636050
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	6.96554	0.703626
$99$	3.36084	0.337777
$100$	−1.10117	−0.110117
$101$	10.1470	1.00967	0.504833	−	0.863217i	$-0.331554\pi$
$101$	10.1470	1.00967	0.504833	+	0.863217i	$0.331554\pi$
$102$	0.370828	0.0367174
$103$	12.8162	1.26281	0.631407	−	0.775452i	$-0.282478\pi$
$103$	12.8162	1.26281	0.631407	+	0.775452i	$0.282478\pi$
$104$	4.71384	0.462230
$105$	0.0228431	0.00222926
$106$	−11.2122	−1.08902
$107$	16.8698	1.63087	0.815435	−	0.578849i	$-0.196498\pi$
$107$	16.8698	1.63087	0.815435	+	0.578849i	$0.196498\pi$
$108$	0.373677	0.0359571
$109$	11.3317	1.08538	0.542689	−	0.839934i	$-0.317406\pi$
$109$	11.3317	1.08538	0.542689	+	0.839934i	$0.317406\pi$
$110$	2.21491	0.211184
$111$	−0.356800	−0.0338660
$112$	−0.185636	−0.0175409
$113$	−10.0654	−0.946872	−0.473436	−	0.880828i	$-0.656986\pi$
$113$	−10.0654	−0.946872	−0.473436	+	0.880828i	$0.656986\pi$
$114$	−0.369801	−0.0346350
$115$	11.0276	1.02833
$116$	3.59334	0.333633
$117$	14.1232	1.30569
$118$	4.49793	0.414068
$119$	−1.10461	−0.101259
$120$	0.123054	0.0112332
$121$	−9.74172	−0.885611
$122$	9.23791	0.836362
$123$	−0.387230	−0.0349154
$124$	−1.00000	−0.0898027
$125$	−12.0470	−1.07752
$126$	−0.556186	−0.0495490
$127$	5.68353	0.504332	0.252166	−	0.967684i	$-0.418857\pi$
$127$	5.68353	0.504332	0.252166	+	0.967684i	$0.418857\pi$
$128$	−1.00000	−0.0883883
$129$	0.343587	0.0302511
$130$	9.30770	0.816339
$131$	19.6897	1.72030	0.860148	−	0.510044i	$-0.170371\pi$
$131$	19.6897	1.72030	0.860148	+	0.510044i	$0.170371\pi$
$132$	0.0699062	0.00608456
$133$	1.10155	0.0955161
$134$	−15.9950	−1.38176
$135$	0.737843	0.0635035
$136$	−5.95039	−0.510242
$137$	6.60214	0.564059	0.282029	−	0.959406i	$-0.408992\pi$
$137$	6.60214	0.564059	0.282029	+	0.959406i	$0.408992\pi$
$138$	0.348049	0.0296279
$139$	−12.4741	−1.05804	−0.529021	−	0.848609i	$-0.677441\pi$
$139$	−12.4741	−1.05804	−0.529021	+	0.848609i	$0.677441\pi$
$140$	−0.366546	−0.0309788
$141$	0.569964	0.0479996
$142$	−11.2449	−0.943655
$143$	5.28767	0.442177
$144$	−2.99612	−0.249676
$145$	7.09521	0.589225
$146$	−1.46090	−0.120905
$147$	0.434092	0.0358033
$148$	5.72530	0.470617
$149$	10.2655	0.840985	0.420492	−	0.907296i	$-0.361857\pi$
$149$	10.2655	0.840985	0.420492	+	0.907296i	$0.361857\pi$
$150$	−0.0686246	−0.00560317
$151$	−2.88805	−0.235026	−0.117513	−	0.993071i	$-0.537492\pi$
$151$	−2.88805	−0.235026	−0.117513	+	0.993071i	$0.537492\pi$
$152$	5.93391	0.481304
$153$	−17.8281	−1.44131
$154$	−0.208234	−0.0167799
$155$	−1.97455	−0.158599
$156$	0.293766	0.0235201
$157$	18.6607	1.48928	0.744642	−	0.667464i	$-0.232620\pi$
$157$	18.6607	1.48928	0.744642	+	0.667464i	$0.232620\pi$
$158$	17.4814	1.39075
$159$	−0.698741	−0.0554137
$160$	−1.97455	−0.156102
$161$	−1.03675	−0.0817076
$162$	−8.96506	−0.704362
$163$	−3.16170	−0.247644	−0.123822	−	0.992304i	$-0.539515\pi$
$163$	−3.16170	−0.247644	−0.123822	+	0.992304i	$0.539515\pi$
$164$	6.21359	0.485200
$165$	0.138033	0.0107459
$166$	12.4925	0.969602
$167$	19.3902	1.50046	0.750228	−	0.661179i	$-0.229944\pi$
$167$	19.3902	1.50046	0.750228	+	0.661179i	$0.229944\pi$
$168$	−0.0115688	−0.000892553 0
$169$	9.22031	0.709254
$170$	−11.7493	−0.901132
$171$	17.7787	1.35957
$172$	−5.51327	−0.420383
$173$	−0.420911	−0.0320013	−0.0160006	−	0.999872i	$-0.505093\pi$
$173$	−0.420911	−0.0320013	−0.0160006	+	0.999872i	$0.505093\pi$
$174$	0.223936	0.0169766
$175$	0.204416	0.0154524
$176$	−1.12173	−0.0845537
$177$	0.280311	0.0210694
$178$	−12.6942	−0.951473
$179$	19.1843	1.43390	0.716951	−	0.697124i	$-0.245537\pi$
$179$	19.1843	1.43390	0.716951	+	0.697124i	$0.245537\pi$
$180$	−5.91597	−0.440950
$181$	−12.5758	−0.934754	−0.467377	−	0.884058i	$-0.654801\pi$
$181$	−12.5758	−0.934754	−0.467377	+	0.884058i	$0.654801\pi$
$182$	−0.875058	−0.0648636
$183$	0.575706	0.0425574
$184$	−5.58488	−0.411723
$185$	11.3049	0.831151
$186$	−0.0623199	−0.00456952
$187$	−6.67475	−0.488106
$188$	−9.14577	−0.667024
$189$	−0.0693679	−0.00504577
$190$	11.7168	0.850025
$191$	4.12556	0.298515	0.149258	−	0.988798i	$-0.452312\pi$
$191$	4.12556	0.298515	0.149258	+	0.988798i	$0.452312\pi$
$192$	−0.0623199	−0.00449755
$193$	−21.1823	−1.52474	−0.762369	−	0.647143i	$-0.775964\pi$
$193$	−21.1823	−1.52474	−0.762369	+	0.647143i	$0.775964\pi$
$194$	−1.00000	−0.0717958
$195$	0.580055	0.0415386
$196$	−6.96554	−0.497539
$197$	8.67513	0.618077	0.309039	−	0.951049i	$-0.399993\pi$
$197$	8.67513	0.618077	0.309039	+	0.951049i	$0.399993\pi$
$198$	−3.36084	−0.238844
$199$	7.44389	0.527683	0.263842	−	0.964566i	$-0.415010\pi$
$199$	7.44389	0.527683	0.263842	+	0.964566i	$0.415010\pi$
$200$	1.10117	0.0778642
$201$	−0.996810	−0.0703095
$202$	−10.1470	−0.713942
$203$	−0.667052	−0.0468179
$204$	−0.370828	−0.0259632
$205$	12.2690	0.856906
$206$	−12.8162	−0.892944
$207$	−16.7329	−1.16302
$208$	−4.71384	−0.326846
$209$	6.65626	0.460423
$210$	−0.0228431	−0.00157633
$211$	−3.45020	−0.237521	−0.118761	−	0.992923i	$-0.537892\pi$
$211$	−3.45020	−0.237521	−0.118761	+	0.992923i	$0.537892\pi$
$212$	11.2122	0.770054
$213$	−0.700784	−0.0480169
$214$	−16.8698	−1.15320
$215$	−10.8862	−0.742433
$216$	−0.373677	−0.0254255
$217$	0.185636	0.0126018
$218$	−11.3317	−0.767478
$219$	−0.0910428	−0.00615211
$220$	−2.21491	−0.149329
$221$	−28.0492	−1.88679
$222$	0.356800	0.0239469
$223$	11.8942	0.796494	0.398247	−	0.917278i	$-0.369619\pi$
$223$	11.8942	0.796494	0.398247	+	0.917278i	$0.369619\pi$
$224$	0.185636	0.0124033
$225$	3.29922	0.219948
$226$	10.0654	0.669539
$227$	−7.29674	−0.484301	−0.242151	−	0.970239i	$-0.577853\pi$
$227$	−7.29674	−0.484301	−0.242151	+	0.970239i	$0.577853\pi$
$228$	0.369801	0.0244907
$229$	13.5670	0.896536	0.448268	−	0.893899i	$-0.352041\pi$
$229$	13.5670	0.896536	0.448268	+	0.893899i	$0.352041\pi$
$230$	−11.0276	−0.727138
$231$	−0.0129771	−0.000853830 0
$232$	−3.59334	−0.235914
$233$	1.09979	0.0720500	0.0360250	−	0.999351i	$-0.488530\pi$
$233$	1.09979	0.0720500	0.0360250	+	0.999351i	$0.488530\pi$
$234$	−14.1232	−0.923264
$235$	−18.0587	−1.17802
$236$	−4.49793	−0.292790
$237$	1.08944	0.0707669
$238$	1.10461	0.0716010
$239$	−2.54833	−0.164838	−0.0824190	−	0.996598i	$-0.526265\pi$
$239$	−2.54833	−0.164838	−0.0824190	+	0.996598i	$0.526265\pi$
$240$	−0.123054	−0.00794307
$241$	15.6649	1.00906	0.504531	−	0.863394i	$-0.331665\pi$
$241$	15.6649	1.00906	0.504531	+	0.863394i	$0.331665\pi$
$242$	9.74172	0.626221
$243$	−1.67973	−0.107755
$244$	−9.23791	−0.591397
$245$	−13.7538	−0.878697
$246$	0.387230	0.0246889
$247$	27.9715	1.77979
$248$	1.00000	0.0635001
$249$	0.778528	0.0493372
$250$	12.0470	0.761921
$251$	−8.86706	−0.559684	−0.279842	−	0.960046i	$-0.590282\pi$
$251$	−8.86706	−0.559684	−0.279842	+	0.960046i	$0.590282\pi$
$252$	0.556186	0.0350364
$253$	−6.26474	−0.393861
$254$	−5.68353	−0.356616
$255$	−0.732217	−0.0458532
$256$	1.00000	0.0625000
$257$	26.7031	1.66569	0.832846	−	0.553505i	$-0.186710\pi$
$257$	26.7031	1.66569	0.832846	+	0.553505i	$0.186710\pi$
$258$	−0.343587	−0.0213908
$259$	−1.06282	−0.0660405
$260$	−9.30770	−0.577239
$261$	−10.7661	−0.666402
$262$	−19.6897	−1.21643
$263$	−5.83617	−0.359874	−0.179937	−	0.983678i	$-0.557589\pi$
$263$	−5.83617	−0.359874	−0.179937	+	0.983678i	$0.557589\pi$
$264$	−0.0699062	−0.00430243
$265$	22.1389	1.35998
$266$	−1.10155	−0.0675401
$267$	−0.791103	−0.0484147
$268$	15.9950	0.977053
$269$	−22.1887	−1.35287	−0.676435	−	0.736502i	$-0.736476\pi$
$269$	−22.1887	−1.35287	−0.676435	+	0.736502i	$0.736476\pi$
$270$	−0.737843	−0.0449037
$271$	7.54853	0.458540	0.229270	−	0.973363i	$-0.426366\pi$
$271$	7.54853	0.458540	0.229270	+	0.973363i	$0.426366\pi$
$272$	5.95039	0.360796
$273$	−0.0545335	−0.00330052
$274$	−6.60214	−0.398850
$275$	1.23521	0.0744862
$276$	−0.348049	−0.0209501
$277$	12.0695	0.725184	0.362592	−	0.931948i	$-0.381892\pi$
$277$	12.0695	0.725184	0.362592	+	0.931948i	$0.381892\pi$
$278$	12.4741	0.748149
$279$	2.99612	0.179373
$280$	0.366546	0.0219053
$281$	−27.5265	−1.64209	−0.821046	−	0.570862i	$-0.806609\pi$
$281$	−27.5265	−1.64209	−0.821046	+	0.570862i	$0.806609\pi$
$282$	−0.569964	−0.0339408
$283$	−4.05664	−0.241142	−0.120571	−	0.992705i	$-0.538473\pi$
$283$	−4.05664	−0.241142	−0.120571	+	0.992705i	$0.538473\pi$
$284$	11.2449	0.667265
$285$	0.730189	0.0432527
$286$	−5.28767	−0.312666
$287$	−1.15346	−0.0680869
$288$	2.99612	0.176548
$289$	18.4072	1.08278
$290$	−7.09521	−0.416645
$291$	−0.0623199	−0.00365326
$292$	1.46090	0.0854924
$293$	19.3247	1.12896	0.564479	−	0.825447i	$-0.309077\pi$
$293$	19.3247	1.12896	0.564479	+	0.825447i	$0.309077\pi$
$294$	−0.434092	−0.0253167
$295$	−8.88137	−0.517094
$296$	−5.72530	−0.332776
$297$	−0.419166	−0.0243225
$298$	−10.2655	−0.594666
$299$	−26.3262	−1.52249
$300$	0.0686246	0.00396204
$301$	1.02346	0.0589913
$302$	2.88805	0.166189
$303$	−0.632361	−0.0363282
$304$	−5.93391	−0.340333
$305$	−18.2407	−1.04446
$306$	17.8281	1.01916
$307$	20.2038	1.15309	0.576547	−	0.817064i	$-0.304400\pi$
$307$	20.2038	1.15309	0.576547	+	0.817064i	$0.304400\pi$
$308$	0.208234	0.0118652
$309$	−0.798702	−0.0454366
$310$	1.97455	0.112147
$311$	15.8173	0.896914	0.448457	−	0.893804i	$-0.351974\pi$
$311$	15.8173	0.896914	0.448457	+	0.893804i	$0.351974\pi$
$312$	−0.293766	−0.0166312
$313$	30.3541	1.71572	0.857859	−	0.513885i	$-0.171794\pi$
$313$	30.3541	1.71572	0.857859	+	0.513885i	$0.171794\pi$
$314$	−18.6607	−1.05308
$315$	1.09822	0.0618774
$316$	−17.4814	−0.983408
$317$	−21.6640	−1.21677	−0.608387	−	0.793641i	$-0.708183\pi$
$317$	−21.6640	−1.21677	−0.608387	+	0.793641i	$0.708183\pi$
$318$	0.698741	0.0391834
$319$	−4.03076	−0.225679
$320$	1.97455	0.110381
$321$	−1.05133	−0.0586794
$322$	1.03675	0.0577760
$323$	−35.3091	−1.96465
$324$	8.96506	0.498059
$325$	5.19072	0.287930
$326$	3.16170	0.175110
$327$	−0.706189	−0.0390524
$328$	−6.21359	−0.343088
$329$	1.69778	0.0936017
$330$	−0.138033	−0.00759847
$331$	−20.9268	−1.15024	−0.575121	−	0.818068i	$-0.695045\pi$
$331$	−20.9268	−1.15024	−0.575121	+	0.818068i	$0.695045\pi$
$332$	−12.4925	−0.685612
$333$	−17.1537	−0.940015
$334$	−19.3902	−1.06098
$335$	31.5830	1.72556
$336$	0.0115688	0.000631130 0
$337$	12.1215	0.660301	0.330151	−	0.943928i	$-0.392900\pi$
$337$	12.1215	0.660301	0.330151	+	0.943928i	$0.392900\pi$
$338$	−9.22031	−0.501519
$339$	0.627274	0.0340688
$340$	11.7493	0.637197
$341$	1.12173	0.0607452
$342$	−17.7787	−0.961361
$343$	2.59250	0.139982
$344$	5.51327	0.297256
$345$	−0.687239	−0.0369997
$346$	0.420911	0.0226283
$347$	−35.8736	−1.92579	−0.962897	−	0.269870i	$-0.913019\pi$
$347$	−35.8736	−1.92579	−0.962897	+	0.269870i	$0.913019\pi$
$348$	−0.223936	−0.0120043
$349$	−30.2870	−1.62123	−0.810613	−	0.585582i	$-0.800866\pi$
$349$	−30.2870	−1.62123	−0.810613	+	0.585582i	$0.800866\pi$
$350$	−0.204416	−0.0109265
$351$	−1.76146	−0.0940196
$352$	1.12173	0.0597885
$353$	−4.49269	−0.239122	−0.119561	−	0.992827i	$-0.538149\pi$
$353$	−4.49269	−0.239122	−0.119561	+	0.992827i	$0.538149\pi$
$354$	−0.280311	−0.0148983
$355$	22.2037	1.17845
$356$	12.6942	0.672793
$357$	0.0688389	0.00364334
$358$	−19.1843	−1.01392
$359$	25.1552	1.32764	0.663820	−	0.747892i	$-0.268934\pi$
$359$	25.1552	1.32764	0.663820	+	0.747892i	$0.268934\pi$
$360$	5.91597	0.311799
$361$	16.2113	0.853226
$362$	12.5758	0.660971
$363$	0.607103	0.0318646
$364$	0.875058	0.0458655
$365$	2.88461	0.150987
$366$	−0.575706	−0.0300926
$367$	−0.564060	−0.0294437	−0.0147218	−	0.999892i	$-0.504686\pi$
$367$	−0.564060	−0.0294437	−0.0147218	+	0.999892i	$0.504686\pi$
$368$	5.58488	0.291132
$369$	−18.6166	−0.969144
$370$	−11.3049	−0.587712
$371$	−2.08138	−0.108060
$372$	0.0623199	0.00323114
$373$	24.4048	1.26363	0.631817	−	0.775117i	$-0.282309\pi$
$373$	24.4048	1.26363	0.631817	+	0.775117i	$0.282309\pi$
$374$	6.67475	0.345143
$375$	0.750770	0.0387696
$376$	9.14577	0.471657
$377$	−16.9384	−0.872373
$378$	0.0693679	0.00356790
$379$	−7.93610	−0.407650	−0.203825	−	0.979007i	$-0.565337\pi$
$379$	−7.93610	−0.407650	−0.203825	+	0.979007i	$0.565337\pi$
$380$	−11.7168	−0.601058
$381$	−0.354197	−0.0181461
$382$	−4.12556	−0.211082
$383$	−23.0598	−1.17830	−0.589151	−	0.808023i	$-0.700538\pi$
$383$	−23.0598	−1.17830	−0.589151	+	0.808023i	$0.700538\pi$
$384$	0.0623199	0.00318025
$385$	0.411167	0.0209550
$386$	21.1823	1.07815
$387$	16.5184	0.839677
$388$	1.00000	0.0507673
$389$	9.47327	0.480314	0.240157	−	0.970734i	$-0.422801\pi$
$389$	9.47327	0.480314	0.240157	+	0.970734i	$0.422801\pi$
$390$	−0.580055	−0.0293722
$391$	33.2322	1.68063
$392$	6.96554	0.351813
$393$	−1.22706	−0.0618970
$394$	−8.67513	−0.437047
$395$	−34.5179	−1.73679
$396$	3.36084	0.168889
$397$	−19.5229	−0.979828	−0.489914	−	0.871771i	$-0.662972\pi$
$397$	−19.5229	−0.979828	−0.489914	+	0.871771i	$0.662972\pi$
$398$	−7.44389	−0.373128
$399$	−0.0686482	−0.00343671
$400$	−1.10117	−0.0550583
$401$	−19.0372	−0.950672	−0.475336	−	0.879804i	$-0.657673\pi$
$401$	−19.0372	−0.950672	−0.475336	+	0.879804i	$0.657673\pi$
$402$	0.996810	0.0497164
$403$	4.71384	0.234813
$404$	10.1470	0.504833
$405$	17.7019	0.879616
$406$	0.667052	0.0331052
$407$	−6.42225	−0.318339
$408$	0.370828	0.0183587
$409$	30.6128	1.51371	0.756854	−	0.653584i	$-0.226735\pi$
$409$	30.6128	1.51371	0.756854	+	0.653584i	$0.226735\pi$
$410$	−12.2690	−0.605924
$411$	−0.411445	−0.0202951
$412$	12.8162	0.631407
$413$	0.834977	0.0410865
$414$	16.7329	0.822379
$415$	−24.6669	−1.21085
$416$	4.71384	0.231115
$417$	0.777387	0.0380688
$418$	−6.65626	−0.325568
$419$	−1.49092	−0.0728361	−0.0364180	−	0.999337i	$-0.511595\pi$
$419$	−1.49092	−0.0728361	−0.0364180	+	0.999337i	$0.511595\pi$
$420$	0.0228431	0.00111463
$421$	9.84706	0.479916	0.239958	−	0.970783i	$-0.422866\pi$
$421$	9.84706	0.479916	0.239958	+	0.970783i	$0.422866\pi$
$422$	3.45020	0.167953
$423$	27.4018	1.33232
$424$	−11.2122	−0.544510
$425$	−6.55237	−0.317837
$426$	0.700784	0.0339531
$427$	1.71489	0.0829892
$428$	16.8698	0.815435
$429$	−0.329527	−0.0159097
$430$	10.8862	0.524980
$431$	9.82788	0.473392	0.236696	−	0.971584i	$-0.423935\pi$
$431$	9.82788	0.473392	0.236696	+	0.971584i	$0.423935\pi$
$432$	0.373677	0.0179786
$433$	−4.69425	−0.225591	−0.112796	−	0.993618i	$-0.535981\pi$
$433$	−4.69425	−0.225591	−0.112796	+	0.993618i	$0.535981\pi$
$434$	−0.185636	−0.00891080
$435$	−0.442173	−0.0212006
$436$	11.3317	0.542689
$437$	−33.1402	−1.58531
$438$	0.0910428	0.00435020
$439$	−7.96634	−0.380213	−0.190106	−	0.981763i	$-0.560883\pi$
$439$	−7.96634	−0.380213	−0.190106	+	0.981763i	$0.560883\pi$
$440$	2.21491	0.105592
$441$	20.8696	0.993789
$442$	28.0492	1.33417
$443$	13.9005	0.660431	0.330215	−	0.943906i	$-0.392879\pi$
$443$	13.9005	0.660431	0.330215	+	0.943906i	$0.392879\pi$
$444$	−0.356800	−0.0169330
$445$	25.0653	1.18821
$446$	−11.8942	−0.563206
$447$	−0.639747	−0.0302590
$448$	−0.185636	−0.00877046
$449$	33.3209	1.57251	0.786254	−	0.617903i	$-0.212018\pi$
$449$	33.3209	1.57251	0.786254	+	0.617903i	$0.212018\pi$
$450$	−3.29922	−0.155527
$451$	−6.96998	−0.328204
$452$	−10.0654	−0.473436
$453$	0.179983	0.00845634
$454$	7.29674	0.342453
$455$	1.72784	0.0810025
$456$	−0.369801	−0.0173175
$457$	0.561879	0.0262836	0.0131418	−	0.999914i	$-0.495817\pi$
$457$	0.561879	0.0262836	0.0131418	+	0.999914i	$0.495817\pi$
$458$	−13.5670	−0.633946
$459$	2.22353	0.103785
$460$	11.0276	0.514165
$461$	5.35627	0.249466	0.124733	−	0.992190i	$-0.460192\pi$
$461$	5.35627	0.249466	0.124733	+	0.992190i	$0.460192\pi$
$462$	0.0129771	0.000603749 0
$463$	17.3526	0.806443	0.403222	−	0.915102i	$-0.367890\pi$
$463$	17.3526	0.806443	0.403222	+	0.915102i	$0.367890\pi$
$464$	3.59334	0.166816
$465$	0.123054	0.00570647
$466$	−1.09979	−0.0509470
$467$	41.5370	1.92210	0.961052	−	0.276366i	$-0.0891303\pi$
$467$	41.5370	1.92210	0.961052	+	0.276366i	$0.0891303\pi$
$468$	14.1232	0.652846
$469$	−2.96925	−0.137107
$470$	18.0587	0.832988
$471$	−1.16293	−0.0535851
$472$	4.49793	0.207034
$473$	6.18441	0.284360
$474$	−1.08944	−0.0500397
$475$	6.53422	0.299811
$476$	−1.10461	−0.0506295
$477$	−33.5929	−1.53811
$478$	2.54833	0.116558
$479$	25.8109	1.17933	0.589665	−	0.807648i	$-0.299260\pi$
$479$	25.8109	1.17933	0.589665	+	0.807648i	$0.299260\pi$
$480$	0.123054	0.00561660
$481$	−26.9882	−1.23055
$482$	−15.6649	−0.713515
$483$	0.0646104	0.00293987
$484$	−9.74172	−0.442805
$485$	1.97455	0.0896595
$486$	1.67973	0.0761943
$487$	−8.75913	−0.396914	−0.198457	−	0.980110i	$-0.563593\pi$
$487$	−8.75913	−0.396914	−0.198457	+	0.980110i	$0.563593\pi$
$488$	9.23791	0.418181
$489$	0.197037	0.00891032
$490$	13.7538	0.621332
$491$	19.1339	0.863500	0.431750	−	0.901993i	$-0.357896\pi$
$491$	19.1339	0.863500	0.431750	+	0.901993i	$0.357896\pi$
$492$	−0.387230	−0.0174577
$493$	21.3818	0.962986
$494$	−27.9715	−1.25850
$495$	6.63613	0.298272
$496$	−1.00000	−0.0449013
$497$	−2.08746	−0.0936356
$498$	−0.778528	−0.0348867
$499$	−37.3385	−1.67150	−0.835750	−	0.549110i	$-0.814967\pi$
$499$	−37.3385	−1.67150	−0.835750	+	0.549110i	$0.814967\pi$
$500$	−12.0470	−0.538760
$501$	−1.20839	−0.0539870
$502$	8.86706	0.395756
$503$	8.74194	0.389784	0.194892	−	0.980825i	$-0.437564\pi$
$503$	8.74194	0.389784	0.194892	+	0.980825i	$0.437564\pi$
$504$	−0.556186	−0.0247745
$505$	20.0358	0.891579
$506$	6.26474	0.278502
$507$	−0.574609	−0.0255193
$508$	5.68353	0.252166
$509$	39.5052	1.75104	0.875519	−	0.483183i	$-0.160520\pi$
$509$	39.5052	1.75104	0.875519	+	0.483183i	$0.160520\pi$
$510$	0.732217	0.0324231
$511$	−0.271194	−0.0119969
$512$	−1.00000	−0.0441942
$513$	−2.21737	−0.0978992
$514$	−26.7031	−1.17782
$515$	25.3061	1.11512
$516$	0.343587	0.0151256
$517$	10.2591	0.451195
$518$	1.06282	0.0466977
$519$	0.0262312	0.00115142
$520$	9.30770	0.408170
$521$	29.9111	1.31043	0.655215	−	0.755443i	$-0.272578\pi$
$521$	29.9111	1.31043	0.655215	+	0.755443i	$0.272578\pi$
$522$	10.7661	0.471217
$523$	8.35117	0.365171	0.182586	−	0.983190i	$-0.441553\pi$
$523$	8.35117	0.365171	0.182586	+	0.983190i	$0.441553\pi$
$524$	19.6897	0.860148
$525$	−0.0127392	−0.000555983 0
$526$	5.83617	0.254469
$527$	−5.95039	−0.259203
$528$	0.0699062	0.00304228
$529$	8.19086	0.356124
$530$	−22.1389	−0.961653
$531$	13.4763	0.584823
$532$	1.10155	0.0477581
$533$	−29.2899	−1.26869
$534$	0.791103	0.0342344
$535$	33.3103	1.44013
$536$	−15.9950	−0.690881
$537$	−1.19556	−0.0515924
$538$	22.1887	0.956624
$539$	7.81347	0.336550
$540$	0.737843	0.0317517
$541$	−7.86372	−0.338088	−0.169044	−	0.985609i	$-0.554068\pi$
$541$	−7.86372	−0.338088	−0.169044	+	0.985609i	$0.554068\pi$
$542$	−7.54853	−0.324237
$543$	0.783724	0.0336328
$544$	−5.95039	−0.255121
$545$	22.3749	0.958437
$546$	0.0545335	0.00233382
$547$	−35.6711	−1.52519	−0.762594	−	0.646878i	$-0.776074\pi$
$547$	−35.6711	−1.52519	−0.762594	+	0.646878i	$0.776074\pi$
$548$	6.60214	0.282029
$549$	27.6779	1.18126
$550$	−1.23521	−0.0526697
$551$	−21.3225	−0.908371
$552$	0.348049	0.0148140
$553$	3.24518	0.137999
$554$	−12.0695	−0.512783
$555$	−0.704519	−0.0299052
$556$	−12.4741	−0.529021
$557$	1.51184	0.0640585	0.0320293	−	0.999487i	$-0.489803\pi$
$557$	1.51184	0.0640585	0.0320293	+	0.999487i	$0.489803\pi$
$558$	−2.99612	−0.126836
$559$	25.9887	1.09920
$560$	−0.366546	−0.0154894
$561$	0.415970	0.0175623
$562$	27.5265	1.16113
$563$	−29.0523	−1.22441	−0.612205	−	0.790699i	$-0.709717\pi$
$563$	−29.0523	−1.22441	−0.612205	+	0.790699i	$0.709717\pi$
$564$	0.569964	0.0239998
$565$	−19.8746	−0.836129
$566$	4.05664	0.170513
$567$	−1.66424	−0.0698913
$568$	−11.2449	−0.471828
$569$	−36.0210	−1.51008	−0.755040	−	0.655679i	$-0.772382\pi$
$569$	−36.0210	−1.51008	−0.755040	+	0.655679i	$0.772382\pi$
$570$	−0.730189	−0.0305842
$571$	12.4144	0.519528	0.259764	−	0.965672i	$-0.416355\pi$
$571$	12.4144	0.519528	0.259764	+	0.965672i	$0.416355\pi$
$572$	5.28767	0.221089
$573$	−0.257105	−0.0107407
$574$	1.15346	0.0481447
$575$	−6.14988	−0.256468
$576$	−2.99612	−0.124838
$577$	40.5865	1.68964	0.844819	−	0.535052i	$-0.179708\pi$
$577$	40.5865	1.68964	0.844819	+	0.535052i	$0.179708\pi$
$578$	−18.4072	−0.765638
$579$	1.32008	0.0548607
$580$	7.09521	0.294613
$581$	2.31905	0.0962102
$582$	0.0623199	0.00258324
$583$	−12.5770	−0.520888
$584$	−1.46090	−0.0604523
$585$	27.8870	1.15298
$586$	−19.3247	−0.798294
$587$	−7.88150	−0.325305	−0.162652	−	0.986683i	$-0.552005\pi$
$587$	−7.88150	−0.325305	−0.162652	+	0.986683i	$0.552005\pi$
$588$	0.434092	0.0179016
$589$	5.93391	0.244503
$590$	8.88137	0.365640
$591$	−0.540633	−0.0222387
$592$	5.72530	0.235308
$593$	−25.0051	−1.02684	−0.513418	−	0.858139i	$-0.671621\pi$
$593$	−25.0051	−1.02684	−0.513418	+	0.858139i	$0.671621\pi$
$594$	0.419166	0.0171986
$595$	−2.18110	−0.0894162
$596$	10.2655	0.420492
$597$	−0.463902	−0.0189863
$598$	26.3262	1.07656
$599$	10.1596	0.415110	0.207555	−	0.978223i	$-0.433449\pi$
$599$	10.1596	0.415110	0.207555	+	0.978223i	$0.433449\pi$
$600$	−0.0686246	−0.00280159
$601$	44.4711	1.81401	0.907007	−	0.421116i	$-0.138361\pi$
$601$	44.4711	1.81401	0.907007	+	0.421116i	$0.138361\pi$
$602$	−1.02346	−0.0417131
$603$	−47.9230	−1.95158
$604$	−2.88805	−0.117513
$605$	−19.2355	−0.782033
$606$	0.632361	0.0256879
$607$	−21.3011	−0.864583	−0.432292	−	0.901734i	$-0.642295\pi$
$607$	−21.3011	−0.864583	−0.432292	+	0.901734i	$0.642295\pi$
$608$	5.93391	0.240652
$609$	0.0415706	0.00168453
$610$	18.2407	0.738544
$611$	43.1117	1.74411
$612$	−17.8281	−0.720657
$613$	−43.4074	−1.75321	−0.876605	−	0.481211i	$-0.840197\pi$
$613$	−43.4074	−1.75321	−0.876605	+	0.481211i	$0.840197\pi$
$614$	−20.2038	−0.815361
$615$	−0.764604	−0.0308318
$616$	−0.208234	−0.00838997
$617$	18.3639	0.739305	0.369652	−	0.929170i	$-0.379477\pi$
$617$	18.3639	0.739305	0.369652	+	0.929170i	$0.379477\pi$
$618$	0.798702	0.0321285
$619$	45.7901	1.84046	0.920229	−	0.391380i	$-0.128002\pi$
$619$	45.7901	1.84046	0.920229	+	0.391380i	$0.128002\pi$
$620$	−1.97455	−0.0792997
$621$	2.08694	0.0837461
$622$	−15.8173	−0.634214
$623$	−2.35650	−0.0944113
$624$	0.293766	0.0117601
$625$	−18.2816	−0.731264
$626$	−30.3541	−1.21320
$627$	−0.414817	−0.0165662
$628$	18.6607	0.744642
$629$	34.0678	1.35837
$630$	−1.09822	−0.0437540
$631$	33.6176	1.33830	0.669148	−	0.743129i	$-0.266659\pi$
$631$	33.6176	1.33830	0.669148	+	0.743129i	$0.266659\pi$
$632$	17.4814	0.695375
$633$	0.215016	0.00854612
$634$	21.6640	0.860389
$635$	11.2224	0.445347
$636$	−0.698741	−0.0277069
$637$	32.8345	1.30095
$638$	4.03076	0.159579
$639$	−33.6912	−1.33280
$640$	−1.97455	−0.0780508
$641$	−20.3977	−0.805661	−0.402831	−	0.915275i	$-0.631974\pi$
$641$	−20.3977	−0.805661	−0.402831	+	0.915275i	$0.631974\pi$
$642$	1.05133	0.0414926
$643$	−29.8402	−1.17678	−0.588391	−	0.808576i	$-0.700238\pi$
$643$	−29.8402	−1.17678	−0.588391	+	0.808576i	$0.700238\pi$
$644$	−1.03675	−0.0408538
$645$	0.678428	0.0267131
$646$	35.3091	1.38922
$647$	−34.1833	−1.34388	−0.671942	−	0.740604i	$-0.734540\pi$
$647$	−34.1833	−1.34388	−0.671942	+	0.740604i	$0.734540\pi$
$648$	−8.96506	−0.352181
$649$	5.04547	0.198052
$650$	−5.19072	−0.203597
$651$	−0.0115688	−0.000453417 0
$652$	−3.16170	−0.123822
$653$	46.9818	1.83854	0.919269	−	0.393630i	$-0.128781\pi$
$653$	46.9818	1.83854	0.919269	+	0.393630i	$0.128781\pi$
$654$	0.706189	0.0276142
$655$	38.8782	1.51910
$656$	6.21359	0.242600
$657$	−4.37701	−0.170763
$658$	−1.69778	−0.0661864
$659$	−46.5046	−1.81156	−0.905781	−	0.423745i	$-0.860715\pi$
$659$	−46.5046	−1.81156	−0.905781	+	0.423745i	$0.860715\pi$
$660$	0.138033	0.00537293
$661$	35.7881	1.39199	0.695997	−	0.718045i	$-0.254963\pi$
$661$	35.7881	1.39199	0.695997	+	0.718045i	$0.254963\pi$
$662$	20.9268	0.813344
$663$	1.74802	0.0678876
$664$	12.4925	0.484801
$665$	2.17505	0.0843450
$666$	17.1537	0.664691
$667$	20.0683	0.777049
$668$	19.3902	0.750228
$669$	−0.741244	−0.0286582
$670$	−31.5830	−1.22016
$671$	10.3625	0.400039
$672$	−0.0115688	−0.000446276 0
$673$	−4.84687	−0.186833	−0.0934165	−	0.995627i	$-0.529779\pi$
$673$	−4.84687	−0.186833	−0.0934165	+	0.995627i	$0.529779\pi$
$674$	−12.1215	−0.466903
$675$	−0.411481	−0.0158379
$676$	9.22031	0.354627
$677$	−7.97880	−0.306650	−0.153325	−	0.988176i	$-0.548998\pi$
$677$	−7.97880	−0.306650	−0.153325	+	0.988176i	$0.548998\pi$
$678$	−0.627274	−0.0240903
$679$	−0.185636	−0.00712405
$680$	−11.7493	−0.450566
$681$	0.454732	0.0174254
$682$	−1.12173	−0.0429533
$683$	27.8275	1.06479	0.532394	−	0.846497i	$-0.321292\pi$
$683$	27.8275	1.06479	0.532394	+	0.846497i	$0.321292\pi$
$684$	17.7787	0.679785
$685$	13.0362	0.498089
$686$	−2.59250	−0.0989822
$687$	−0.845497	−0.0322577
$688$	−5.51327	−0.210191
$689$	−52.8523	−2.01351
$690$	0.687239	0.0261627
$691$	−21.4495	−0.815978	−0.407989	−	0.912987i	$-0.633770\pi$
$691$	−21.4495	−0.815978	−0.407989	+	0.912987i	$0.633770\pi$
$692$	−0.420911	−0.0160006
$693$	−0.623892	−0.0236997
$694$	35.8736	1.36174
$695$	−24.6308	−0.934298
$696$	0.223936	0.00848829
$697$	36.9733	1.40046
$698$	30.2870	1.14638
$699$	−0.0685391	−0.00259239
$700$	0.204416	0.00772619
$701$	38.8670	1.46799	0.733994	−	0.679156i	$-0.237654\pi$
$701$	38.8670	1.46799	0.733994	+	0.679156i	$0.237654\pi$
$702$	1.76146	0.0664819
$703$	−33.9734	−1.28133
$704$	−1.12173	−0.0422769
$705$	1.12542	0.0423858
$706$	4.49269	0.169085
$707$	−1.88365	−0.0708419
$708$	0.280311	0.0105347
$709$	10.9299	0.410481	0.205240	−	0.978712i	$-0.434202\pi$
$709$	10.9299	0.410481	0.205240	+	0.978712i	$0.434202\pi$
$710$	−22.2037	−0.833289
$711$	52.3764	1.96427
$712$	−12.6942	−0.475736
$713$	−5.58488	−0.209155
$714$	−0.0688389	−0.00257623
$715$	10.4407	0.390462
$716$	19.1843	0.716951
$717$	0.158812	0.00593094
$718$	−25.1552	−0.938784
$719$	−31.7945	−1.18573	−0.592867	−	0.805300i	$-0.702004\pi$
$719$	−31.7945	−1.18573	−0.592867	+	0.805300i	$0.702004\pi$
$720$	−5.91597	−0.220475
$721$	−2.37914	−0.0886037
$722$	−16.2113	−0.603322
$723$	−0.976232	−0.0363065
$724$	−12.5758	−0.467377
$725$	−3.95686	−0.146954
$726$	−0.607103	−0.0225317
$727$	0.333170	0.0123566	0.00617830	−	0.999981i	$-0.498033\pi$
$727$	0.333170	0.0123566	0.00617830	+	0.999981i	$0.498033\pi$
$728$	−0.875058	−0.0324318
$729$	−26.7905	−0.992241
$730$	−2.88461	−0.106764
$731$	−32.8061	−1.21338
$732$	0.575706	0.0212787
$733$	35.4747	1.31029	0.655143	−	0.755505i	$-0.272608\pi$
$733$	35.4747	1.31029	0.655143	+	0.755505i	$0.272608\pi$
$734$	0.564060	0.0208198
$735$	0.857134	0.0316159
$736$	−5.58488	−0.205861
$737$	−17.9422	−0.660908
$738$	18.6166	0.685288
$739$	−26.0733	−0.959122	−0.479561	−	0.877509i	$-0.659204\pi$
$739$	−26.0733	−0.959122	−0.479561	+	0.877509i	$0.659204\pi$
$740$	11.3049	0.415575
$741$	−1.74318	−0.0640374
$742$	2.08138	0.0764098
$743$	21.0946	0.773885	0.386942	−	0.922104i	$-0.373531\pi$
$743$	21.0946	0.773885	0.386942	+	0.922104i	$0.373531\pi$
$744$	−0.0623199	−0.00228476
$745$	20.2698	0.742626
$746$	−24.4048	−0.893524
$747$	37.4288	1.36945
$748$	−6.67475	−0.244053
$749$	−3.13165	−0.114428
$750$	−0.750770	−0.0274143
$751$	−25.1803	−0.918842	−0.459421	−	0.888219i	$-0.651943\pi$
$751$	−25.1803	−0.918842	−0.459421	+	0.888219i	$0.651943\pi$
$752$	−9.14577	−0.333512
$753$	0.552594	0.0201377
$754$	16.9384	0.616861
$755$	−5.70259	−0.207538
$756$	−0.0693679	−0.00252289
$757$	−11.6085	−0.421917	−0.210959	−	0.977495i	$-0.567659\pi$
$757$	−11.6085	−0.421917	−0.210959	+	0.977495i	$0.567659\pi$
$758$	7.93610	0.288252
$759$	0.390418	0.0141713
$760$	11.7168	0.425012
$761$	−23.5183	−0.852539	−0.426270	−	0.904596i	$-0.640172\pi$
$761$	−23.5183	−0.852539	−0.426270	+	0.904596i	$0.640172\pi$
$762$	0.354197	0.0128312
$763$	−2.10357	−0.0761542
$764$	4.12556	0.149258
$765$	−35.2024	−1.27274
$766$	23.0598	0.833185
$767$	21.2025	0.765579
$768$	−0.0623199	−0.00224878
$769$	18.4491	0.665291	0.332646	−	0.943052i	$-0.392059\pi$
$769$	18.4491	0.665291	0.332646	+	0.943052i	$0.392059\pi$
$770$	−0.411167	−0.0148174
$771$	−1.66413	−0.0599323
$772$	−21.1823	−0.762369
$773$	45.5604	1.63869	0.819347	−	0.573298i	$-0.194336\pi$
$773$	45.5604	1.63869	0.819347	+	0.573298i	$0.194336\pi$
$774$	−16.5184	−0.593742
$775$	1.10117	0.0395551
$776$	−1.00000	−0.0358979
$777$	0.0662349	0.00237616
$778$	−9.47327	−0.339633
$779$	−36.8709	−1.32104
$780$	0.580055	0.0207693
$781$	−12.6138	−0.451358
$782$	−33.2322	−1.18838
$783$	1.34275	0.0479859
$784$	−6.96554	−0.248769
$785$	36.8464	1.31510
$786$	1.22706	0.0437678
$787$	−4.90387	−0.174804	−0.0874020	−	0.996173i	$-0.527856\pi$
$787$	−4.90387	−0.174804	−0.0874020	+	0.996173i	$0.527856\pi$
$788$	8.67513	0.309039
$789$	0.363709	0.0129484
$790$	34.5179	1.22809
$791$	1.86849	0.0664360
$792$	−3.36084	−0.119422
$793$	43.5461	1.54637
$794$	19.5229	0.692843
$795$	−1.37970	−0.0489328
$796$	7.44389	0.263842
$797$	−4.81708	−0.170630	−0.0853148	−	0.996354i	$-0.527190\pi$
$797$	−4.81708	−0.170630	−0.0853148	+	0.996354i	$0.527190\pi$
$798$	0.0686482	0.00243012
$799$	−54.4209	−1.92527
$800$	1.10117	0.0389321
$801$	−38.0334	−1.34384
$802$	19.0372	0.672226
$803$	−1.63873	−0.0578296
$804$	−0.996810	−0.0351548
$805$	−2.04712	−0.0721514
$806$	−4.71384	−0.166038
$807$	1.38280	0.0486769
$808$	−10.1470	−0.356971
$809$	5.68986	0.200045	0.100022	−	0.994985i	$-0.468109\pi$
$809$	5.68986	0.200045	0.100022	+	0.994985i	$0.468109\pi$
$810$	−17.7019	−0.621982
$811$	−8.21684	−0.288532	−0.144266	−	0.989539i	$-0.546082\pi$
$811$	−8.21684	−0.288532	−0.144266	+	0.989539i	$0.546082\pi$
$812$	−0.667052	−0.0234089
$813$	−0.470423	−0.0164985
$814$	6.42225	0.225100
$815$	−6.24293	−0.218680
$816$	−0.370828	−0.0129816
$817$	32.7153	1.14456
$818$	−30.6128	−1.07035
$819$	−2.62177	−0.0916122
$820$	12.2690	0.428453
$821$	39.9579	1.39454	0.697270	−	0.716808i	$-0.254398\pi$
$821$	39.9579	1.39454	0.697270	+	0.716808i	$0.254398\pi$
$822$	0.411445	0.0143508
$823$	−45.5213	−1.58677	−0.793387	−	0.608718i	$-0.791684\pi$
$823$	−45.5213	−1.58677	−0.793387	+	0.608718i	$0.791684\pi$
$824$	−12.8162	−0.446472
$825$	−0.0769784	−0.00268004
$826$	−0.834977	−0.0290526
$827$	−53.3423	−1.85489	−0.927447	−	0.373954i	$-0.878002\pi$
$827$	−53.3423	−1.85489	−0.927447	+	0.373954i	$0.878002\pi$
$828$	−16.7329	−0.581510
$829$	30.8470	1.07136	0.535681	−	0.844420i	$-0.320055\pi$
$829$	30.8470	1.07136	0.535681	+	0.844420i	$0.320055\pi$
$830$	24.6669	0.856201
$831$	−0.752169	−0.0260924
$832$	−4.71384	−0.163423
$833$	−41.4477	−1.43608
$834$	−0.777387	−0.0269187
$835$	38.2868	1.32497
$836$	6.65626	0.230212
$837$	−0.373677	−0.0129162
$838$	1.49092	0.0515029
$839$	29.1923	1.00783	0.503915	−	0.863753i	$-0.331892\pi$
$839$	29.1923	1.00783	0.503915	+	0.863753i	$0.331892\pi$
$840$	−0.0228431	−0.000788163 0
$841$	−16.0879	−0.554756
$842$	−9.84706	−0.339352
$843$	1.71545	0.0590831
$844$	−3.45020	−0.118761
$845$	18.2059	0.626303
$846$	−27.4018	−0.942093
$847$	1.80841	0.0621377
$848$	11.2122	0.385027
$849$	0.252810	0.00867640
$850$	6.55237	0.224745
$851$	31.9751	1.09609
$852$	−0.700784	−0.0240085
$853$	−35.1381	−1.20311	−0.601553	−	0.798833i	$-0.705451\pi$
$853$	−35.1381	−1.20311	−0.601553	+	0.798833i	$0.705451\pi$
$854$	−1.71489	−0.0586822
$855$	35.1048	1.20056
$856$	−16.8698	−0.576599
$857$	32.5741	1.11271	0.556355	−	0.830945i	$-0.312200\pi$
$857$	32.5741	1.11271	0.556355	+	0.830945i	$0.312200\pi$
$858$	0.329527	0.0112499
$859$	−11.6839	−0.398648	−0.199324	−	0.979934i	$-0.563875\pi$
$859$	−11.6839	−0.398648	−0.199324	+	0.979934i	$0.563875\pi$
$860$	−10.8862	−0.371217
$861$	0.0718838	0.00244979
$862$	−9.82788	−0.334739
$863$	16.4945	0.561480	0.280740	−	0.959784i	$-0.409420\pi$
$863$	16.4945	0.561480	0.280740	+	0.959784i	$0.409420\pi$
$864$	−0.373677	−0.0127128
$865$	−0.831109	−0.0282586
$866$	4.69425	0.159517
$867$	−1.14713	−0.0389587
$868$	0.185636	0.00630089
$869$	19.6095	0.665207
$870$	0.442173	0.0149911
$871$	−75.3981	−2.55477
$872$	−11.3317	−0.383739
$873$	−2.99612	−0.101403
$874$	33.1402	1.12098
$875$	2.23636	0.0756028
$876$	−0.0910428	−0.00307605
$877$	−23.8984	−0.806992	−0.403496	−	0.914981i	$-0.632205\pi$
$877$	−23.8984	−0.806992	−0.403496	+	0.914981i	$0.632205\pi$
$878$	7.96634	0.268851
$879$	−1.20431	−0.0406204
$880$	−2.21491	−0.0746647
$881$	16.4717	0.554945	0.277473	−	0.960734i	$-0.410503\pi$
$881$	16.4717	0.554945	0.277473	+	0.960734i	$0.410503\pi$
$882$	−20.8696	−0.702715
$883$	4.73050	0.159194	0.0795970	−	0.996827i	$-0.474637\pi$
$883$	4.73050	0.159194	0.0795970	+	0.996827i	$0.474637\pi$
$884$	−28.0492	−0.943397
$885$	0.553486	0.0186052
$886$	−13.9005	−0.466995
$887$	−6.42448	−0.215713	−0.107857	−	0.994166i	$-0.534399\pi$
$887$	−6.42448	−0.215713	−0.107857	+	0.994166i	$0.534399\pi$
$888$	0.356800	0.0119734
$889$	−1.05507	−0.0353858
$890$	−25.0653	−0.840192
$891$	−10.0564	−0.336902
$892$	11.8942	0.398247
$893$	54.2702	1.81608
$894$	0.639747	0.0213963
$895$	37.8803	1.26620
$896$	0.185636	0.00620166
$897$	1.64065	0.0547797
$898$	−33.3209	−1.11193
$899$	−3.59334	−0.119844
$900$	3.29922	0.109974
$901$	66.7167	2.22266
$902$	6.96998	0.232075
$903$	−0.0637819	−0.00212253
$904$	10.0654	0.334770
$905$	−24.8316	−0.825429
$906$	−0.179983	−0.00597953
$907$	−17.6766	−0.586942	−0.293471	−	0.955968i	$-0.594810\pi$
$907$	−17.6766	−0.586942	−0.293471	+	0.955968i	$0.594810\pi$
$908$	−7.29674	−0.242151
$909$	−30.4016	−1.00836
$910$	−1.72784	−0.0572774
$911$	−15.1075	−0.500535	−0.250267	−	0.968177i	$-0.580519\pi$
$911$	−15.1075	−0.500535	−0.250267	+	0.968177i	$0.580519\pi$
$912$	0.369801	0.0122453
$913$	14.0132	0.463769
$914$	−0.561879	−0.0185853
$915$	1.13676	0.0375801
$916$	13.5670	0.448268
$917$	−3.65511	−0.120702
$918$	−2.22353	−0.0733874
$919$	−15.5025	−0.511380	−0.255690	−	0.966759i	$-0.582303\pi$
$919$	−15.5025	−0.511380	−0.255690	+	0.966759i	$0.582303\pi$
$920$	−11.0276	−0.363569
$921$	−1.25910	−0.0414888
$922$	−5.35627	−0.176399
$923$	−53.0069	−1.74474
$924$	−0.0129771	−0.000426915 0
$925$	−6.30451	−0.207291
$926$	−17.3526	−0.570241
$927$	−38.3987	−1.26118
$928$	−3.59334	−0.117957
$929$	1.35155	0.0443428	0.0221714	−	0.999754i	$-0.492942\pi$
$929$	1.35155	0.0443428	0.0221714	+	0.999754i	$0.492942\pi$
$930$	−0.123054	−0.00403509
$931$	41.3329	1.35463
$932$	1.09979	0.0360250
$933$	−0.985730	−0.0322713
$934$	−41.5370	−1.35913
$935$	−13.1796	−0.431019
$936$	−14.1232	−0.461632
$937$	−30.0010	−0.980090	−0.490045	−	0.871697i	$-0.663020\pi$
$937$	−30.0010	−0.980090	−0.490045	+	0.871697i	$0.663020\pi$
$938$	2.96925	0.0969495
$939$	−1.89167	−0.0617322
$940$	−18.0587	−0.589011
$941$	−24.0778	−0.784913	−0.392457	−	0.919771i	$-0.628375\pi$
$941$	−24.0778	−0.784913	−0.392457	+	0.919771i	$0.628375\pi$
$942$	1.16293	0.0378904
$943$	34.7021	1.13006
$944$	−4.49793	−0.146395
$945$	−0.136970	−0.00445564
$946$	−6.18441	−0.201073
$947$	−16.2382	−0.527672	−0.263836	−	0.964568i	$-0.584988\pi$
$947$	−16.2382	−0.527672	−0.263836	+	0.964568i	$0.584988\pi$
$948$	1.08944	0.0353834
$949$	−6.88643	−0.223543
$950$	−6.53422	−0.211998
$951$	1.35010	0.0437800
$952$	1.10461	0.0358005
$953$	46.7000	1.51276	0.756381	−	0.654132i	$-0.226966\pi$
$953$	46.7000	1.51276	0.756381	+	0.654132i	$0.226966\pi$
$954$	33.5929	1.08761
$955$	8.14611	0.263602
$956$	−2.54833	−0.0824190
$957$	0.251197	0.00812004
$958$	−25.8109	−0.833913
$959$	−1.22559	−0.0395765
$960$	−0.123054	−0.00397154
$961$	1.00000	0.0322581
$962$	26.9882	0.870133
$963$	−50.5440	−1.62876
$964$	15.6649	0.504531
$965$	−41.8255	−1.34641
$966$	−0.0646104	−0.00207880
$967$	27.8395	0.895259	0.447630	−	0.894219i	$-0.352268\pi$
$967$	27.8395	0.895259	0.447630	+	0.894219i	$0.352268\pi$
$968$	9.74172	0.313111
$969$	2.20046	0.0706890
$970$	−1.97455	−0.0633989
$971$	−6.67067	−0.214072	−0.107036	−	0.994255i	$-0.534136\pi$
$971$	−6.67067	−0.214072	−0.107036	+	0.994255i	$0.534136\pi$
$972$	−1.67973	−0.0538775
$973$	2.31565	0.0742362
$974$	8.75913	0.280661
$975$	−0.323485	−0.0103598
$976$	−9.23791	−0.295698
$977$	−3.40994	−0.109094	−0.0545469	−	0.998511i	$-0.517371\pi$
$977$	−3.40994	−0.109094	−0.0545469	+	0.998511i	$0.517371\pi$
$978$	−0.197037	−0.00630055
$979$	−14.2395	−0.455097
$980$	−13.7538	−0.439348
$981$	−33.9510	−1.08397
$982$	−19.1339	−0.610587
$983$	13.9065	0.443548	0.221774	−	0.975098i	$-0.428815\pi$
$983$	13.9065	0.443548	0.221774	+	0.975098i	$0.428815\pi$
$984$	0.387230	0.0123445
$985$	17.1294	0.545790
$986$	−21.3818	−0.680934
$987$	−0.105806	−0.00336783
$988$	27.9715	0.889893
$989$	−30.7909	−0.979095
$990$	−6.63613	−0.210910
$991$	28.3884	0.901786	0.450893	−	0.892578i	$-0.351106\pi$
$991$	28.3884	0.901786	0.450893	+	0.892578i	$0.351106\pi$
$992$	1.00000	0.0317500
$993$	1.30416	0.0413862
$994$	2.08746	0.0662103
$995$	14.6983	0.465967
$996$	0.778528	0.0246686
$997$	49.8281	1.57807	0.789036	−	0.614347i	$-0.210581\pi$
$997$	49.8281	1.57807	0.789036	+	0.614347i	$0.210581\pi$
$998$	37.3385	1.18193
$999$	2.13942	0.0676881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.16	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.16	✓	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0623199 q^{3} +1.00000 q^{4} +1.97455 q^{5} +0.0623199 q^{6} -0.185636 q^{7} -1.00000 q^{8} -2.99612 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.0623199 q^{3} +1.00000 q^{4} +1.97455 q^{5} +0.0623199 q^{6} -0.185636 q^{7} -1.00000 q^{8} -2.99612 q^{9} -1.97455 q^{10} -1.12173 q^{11} -0.0623199 q^{12} -4.71384 q^{13} +0.185636 q^{14} -0.123054 q^{15} +1.00000 q^{16} +5.95039 q^{17} +2.99612 q^{18} -5.93391 q^{19} +1.97455 q^{20} +0.0115688 q^{21} +1.12173 q^{22} +5.58488 q^{23} +0.0623199 q^{24} -1.10117 q^{25} +4.71384 q^{26} +0.373677 q^{27} -0.185636 q^{28} +3.59334 q^{29} +0.123054 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.0699062 q^{33} -5.95039 q^{34} -0.366546 q^{35} -2.99612 q^{36} +5.72530 q^{37} +5.93391 q^{38} +0.293766 q^{39} -1.97455 q^{40} +6.21359 q^{41} -0.0115688 q^{42} -5.51327 q^{43} -1.12173 q^{44} -5.91597 q^{45} -5.58488 q^{46} -9.14577 q^{47} -0.0623199 q^{48} -6.96554 q^{49} +1.10117 q^{50} -0.370828 q^{51} -4.71384 q^{52} +11.2122 q^{53} -0.373677 q^{54} -2.21491 q^{55} +0.185636 q^{56} +0.369801 q^{57} -3.59334 q^{58} -4.49793 q^{59} -0.123054 q^{60} -9.23791 q^{61} +1.00000 q^{62} +0.556186 q^{63} +1.00000 q^{64} -9.30770 q^{65} -0.0699062 q^{66} +15.9950 q^{67} +5.95039 q^{68} -0.348049 q^{69} +0.366546 q^{70} +11.2449 q^{71} +2.99612 q^{72} +1.46090 q^{73} -5.72530 q^{74} +0.0686246 q^{75} -5.93391 q^{76} +0.208234 q^{77} -0.293766 q^{78} -17.4814 q^{79} +1.97455 q^{80} +8.96506 q^{81} -6.21359 q^{82} -12.4925 q^{83} +0.0115688 q^{84} +11.7493 q^{85} +5.51327 q^{86} -0.223936 q^{87} +1.12173 q^{88} +12.6942 q^{89} +5.91597 q^{90} +0.875058 q^{91} +5.58488 q^{92} +0.0623199 q^{93} +9.14577 q^{94} -11.7168 q^{95} +0.0623199 q^{96} +1.00000 q^{97} +6.96554 q^{98} +3.36084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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