LMFDB - Embedded newform 6014.2.a.k.1.11

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:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.30157 q^{3} +1.00000 q^{4} +3.71801 q^{5} -1.30157 q^{6} +4.36912 q^{7} +1.00000 q^{8} -1.30591 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.30157 q^{3} +1.00000 q^{4} +3.71801 q^{5} -1.30157 q^{6} +4.36912 q^{7} +1.00000 q^{8} -1.30591 q^{9} +3.71801 q^{10} -5.30204 q^{11} -1.30157 q^{12} +1.31472 q^{13} +4.36912 q^{14} -4.83926 q^{15} +1.00000 q^{16} +4.67229 q^{17} -1.30591 q^{18} +4.22918 q^{19} +3.71801 q^{20} -5.68673 q^{21} -5.30204 q^{22} -6.77558 q^{23} -1.30157 q^{24} +8.82358 q^{25} +1.31472 q^{26} +5.60445 q^{27} +4.36912 q^{28} -2.07671 q^{29} -4.83926 q^{30} +1.00000 q^{31} +1.00000 q^{32} +6.90099 q^{33} +4.67229 q^{34} +16.2444 q^{35} -1.30591 q^{36} -6.96695 q^{37} +4.22918 q^{38} -1.71121 q^{39} +3.71801 q^{40} -5.38465 q^{41} -5.68673 q^{42} +5.29109 q^{43} -5.30204 q^{44} -4.85537 q^{45} -6.77558 q^{46} +2.60751 q^{47} -1.30157 q^{48} +12.0892 q^{49} +8.82358 q^{50} -6.08133 q^{51} +1.31472 q^{52} +1.06719 q^{53} +5.60445 q^{54} -19.7130 q^{55} +4.36912 q^{56} -5.50459 q^{57} -2.07671 q^{58} +12.1246 q^{59} -4.83926 q^{60} +6.07495 q^{61} +1.00000 q^{62} -5.70565 q^{63} +1.00000 q^{64} +4.88814 q^{65} +6.90099 q^{66} +10.4967 q^{67} +4.67229 q^{68} +8.81892 q^{69} +16.2444 q^{70} +3.54226 q^{71} -1.30591 q^{72} +5.43368 q^{73} -6.96695 q^{74} -11.4845 q^{75} +4.22918 q^{76} -23.1652 q^{77} -1.71121 q^{78} +16.3616 q^{79} +3.71801 q^{80} -3.37690 q^{81} -5.38465 q^{82} +3.36109 q^{83} -5.68673 q^{84} +17.3716 q^{85} +5.29109 q^{86} +2.70299 q^{87} -5.30204 q^{88} -8.51706 q^{89} -4.85537 q^{90} +5.74417 q^{91} -6.77558 q^{92} -1.30157 q^{93} +2.60751 q^{94} +15.7241 q^{95} -1.30157 q^{96} +1.00000 q^{97} +12.0892 q^{98} +6.92396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * 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
$3$	−1.30157	−0.751464	−0.375732	−	0.926728i	$-0.622609\pi$
$3$	−1.30157	−0.751464	−0.375732	+	0.926728i	$0.622609\pi$
$4$	1.00000	0.500000
$5$	3.71801	1.66274	0.831372	−	0.555717i	$-0.187556\pi$
$5$	3.71801	1.66274	0.831372	+	0.555717i	$0.187556\pi$
$6$	−1.30157	−0.531365
$7$	4.36912	1.65137	0.825686	−	0.564130i	$-0.190789\pi$
$7$	4.36912	1.65137	0.825686	+	0.564130i	$0.190789\pi$
$8$	1.00000	0.353553
$9$	−1.30591	−0.435302
$10$	3.71801	1.17574
$11$	−5.30204	−1.59862	−0.799312	−	0.600916i	$-0.794803\pi$
$11$	−5.30204	−1.59862	−0.799312	+	0.600916i	$0.794803\pi$
$12$	−1.30157	−0.375732
$13$	1.31472	0.364638	0.182319	−	0.983239i	$-0.441640\pi$
$13$	1.31472	0.364638	0.182319	+	0.983239i	$0.441640\pi$
$14$	4.36912	1.16770
$15$	−4.83926	−1.24949
$16$	1.00000	0.250000
$17$	4.67229	1.13320	0.566598	−	0.823994i	$-0.308259\pi$
$17$	4.67229	1.13320	0.566598	+	0.823994i	$0.308259\pi$
$18$	−1.30591	−0.307805
$19$	4.22918	0.970240	0.485120	−	0.874448i	$-0.338776\pi$
$19$	4.22918	0.970240	0.485120	+	0.874448i	$0.338776\pi$
$20$	3.71801	0.831372
$21$	−5.68673	−1.24095
$22$	−5.30204	−1.13040
$23$	−6.77558	−1.41281	−0.706403	−	0.707809i	$-0.749684\pi$
$23$	−6.77558	−1.41281	−0.706403	+	0.707809i	$0.749684\pi$
$24$	−1.30157	−0.265683
$25$	8.82358	1.76472
$26$	1.31472	0.257838
$27$	5.60445	1.07858
$28$	4.36912	0.825686
$29$	−2.07671	−0.385635	−0.192817	−	0.981235i	$-0.561763\pi$
$29$	−2.07671	−0.385635	−0.192817	+	0.981235i	$0.561763\pi$
$30$	−4.83926	−0.883524
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	6.90099	1.20131
$34$	4.67229	0.801291
$35$	16.2444	2.74581
$36$	−1.30591	−0.217651
$37$	−6.96695	−1.14536	−0.572680	−	0.819779i	$-0.694096\pi$
$37$	−6.96695	−1.14536	−0.572680	+	0.819779i	$0.694096\pi$
$38$	4.22918	0.686063
$39$	−1.71121	−0.274012
$40$	3.71801	0.587869
$41$	−5.38465	−0.840941	−0.420470	−	0.907306i	$-0.638135\pi$
$41$	−5.38465	−0.840941	−0.420470	+	0.907306i	$0.638135\pi$
$42$	−5.68673	−0.877481
$43$	5.29109	0.806884	0.403442	−	0.915005i	$-0.367814\pi$
$43$	5.29109	0.806884	0.403442	+	0.915005i	$0.367814\pi$
$44$	−5.30204	−0.799312
$45$	−4.85537	−0.723795
$46$	−6.77558	−0.999005
$47$	2.60751	0.380345	0.190172	−	0.981751i	$-0.439095\pi$
$47$	2.60751	0.380345	0.190172	+	0.981751i	$0.439095\pi$
$48$	−1.30157	−0.187866
$49$	12.0892	1.72703
$50$	8.82358	1.24784
$51$	−6.08133	−0.851556
$52$	1.31472	0.182319
$53$	1.06719	0.146589	0.0732947	−	0.997310i	$-0.476649\pi$
$53$	1.06719	0.146589	0.0732947	+	0.997310i	$0.476649\pi$
$54$	5.60445	0.762670
$55$	−19.7130	−2.65810
$56$	4.36912	0.583848
$57$	−5.50459	−0.729100
$58$	−2.07671	−0.272685
$59$	12.1246	1.57849	0.789245	−	0.614079i	$-0.210472\pi$
$59$	12.1246	1.57849	0.789245	+	0.614079i	$0.210472\pi$
$60$	−4.83926	−0.624746
$61$	6.07495	0.777817	0.388909	−	0.921276i	$-0.372852\pi$
$61$	6.07495	0.777817	0.388909	+	0.921276i	$0.372852\pi$
$62$	1.00000	0.127000
$63$	−5.70565	−0.718845
$64$	1.00000	0.125000
$65$	4.88814	0.606300
$66$	6.90099	0.849453
$67$	10.4967	1.28238	0.641188	−	0.767384i	$-0.278442\pi$
$67$	10.4967	1.28238	0.641188	+	0.767384i	$0.278442\pi$
$68$	4.67229	0.566598
$69$	8.81892	1.06167
$70$	16.2444	1.94158
$71$	3.54226	0.420388	0.210194	−	0.977660i	$-0.432590\pi$
$71$	3.54226	0.420388	0.210194	+	0.977660i	$0.432590\pi$
$72$	−1.30591	−0.153902
$73$	5.43368	0.635964	0.317982	−	0.948097i	$-0.396995\pi$
$73$	5.43368	0.635964	0.317982	+	0.948097i	$0.396995\pi$
$74$	−6.96695	−0.809892
$75$	−11.4845	−1.32612
$76$	4.22918	0.485120
$77$	−23.1652	−2.63992
$78$	−1.71121	−0.193756
$79$	16.3616	1.84082	0.920409	−	0.390957i	$-0.127856\pi$
$79$	16.3616	1.84082	0.920409	+	0.390957i	$0.127856\pi$
$80$	3.71801	0.415686
$81$	−3.37690	−0.375211
$82$	−5.38465	−0.594635
$83$	3.36109	0.368927	0.184464	−	0.982839i	$-0.440945\pi$
$83$	3.36109	0.368927	0.184464	+	0.982839i	$0.440945\pi$
$84$	−5.68673	−0.620473
$85$	17.3716	1.88421
$86$	5.29109	0.570553
$87$	2.70299	0.289791
$88$	−5.30204	−0.565199
$89$	−8.51706	−0.902807	−0.451403	−	0.892320i	$-0.649076\pi$
$89$	−8.51706	−0.902807	−0.451403	+	0.892320i	$0.649076\pi$
$90$	−4.85537	−0.511800
$91$	5.74417	0.602153
$92$	−6.77558	−0.706403
$93$	−1.30157	−0.134967
$94$	2.60751	0.268944
$95$	15.7241	1.61326
$96$	−1.30157	−0.132841
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	12.0892	1.22119
$99$	6.92396	0.695884
$100$	8.82358	0.882358
$101$	−8.85362	−0.880968	−0.440484	−	0.897760i	$-0.645193\pi$
$101$	−8.85362	−0.880968	−0.440484	+	0.897760i	$0.645193\pi$
$102$	−6.08133	−0.602141
$103$	−2.24124	−0.220836	−0.110418	−	0.993885i	$-0.535219\pi$
$103$	−2.24124	−0.220836	−0.110418	+	0.993885i	$0.535219\pi$
$104$	1.31472	0.128919
$105$	−21.1433	−2.06338
$106$	1.06719	0.103654
$107$	11.6917	1.13028	0.565141	−	0.824994i	$-0.308822\pi$
$107$	11.6917	1.13028	0.565141	+	0.824994i	$0.308822\pi$
$108$	5.60445	0.539289
$109$	−14.9053	−1.42767	−0.713834	−	0.700315i	$-0.753043\pi$
$109$	−14.9053	−1.42767	−0.713834	+	0.700315i	$0.753043\pi$
$110$	−19.7130	−1.87956
$111$	9.06801	0.860697
$112$	4.36912	0.412843
$113$	−1.46032	−0.137375	−0.0686875	−	0.997638i	$-0.521881\pi$
$113$	−1.46032	−0.137375	−0.0686875	+	0.997638i	$0.521881\pi$
$114$	−5.50459	−0.515552
$115$	−25.1917	−2.34914
$116$	−2.07671	−0.192817
$117$	−1.71690	−0.158728
$118$	12.1246	1.11616
$119$	20.4138	1.87133
$120$	−4.83926	−0.441762
$121$	17.1116	1.55560
$122$	6.07495	0.550000
$123$	7.00852	0.631937
$124$	1.00000	0.0898027
$125$	14.2161	1.27153
$126$	−5.70565	−0.508300
$127$	18.5039	1.64195	0.820976	−	0.570963i	$-0.193430\pi$
$127$	18.5039	1.64195	0.820976	+	0.570963i	$0.193430\pi$
$128$	1.00000	0.0883883
$129$	−6.88674	−0.606344
$130$	4.88814	0.428719
$131$	−1.00497	−0.0878043	−0.0439022	−	0.999036i	$-0.513979\pi$
$131$	−1.00497	−0.0878043	−0.0439022	+	0.999036i	$0.513979\pi$
$132$	6.90099	0.600654
$133$	18.4778	1.60223
$134$	10.4967	0.906777
$135$	20.8374	1.79340
$136$	4.67229	0.400645
$137$	−18.9471	−1.61876	−0.809382	−	0.587283i	$-0.800198\pi$
$137$	−18.9471	−1.61876	−0.809382	+	0.587283i	$0.800198\pi$
$138$	8.81892	0.750717
$139$	−1.88879	−0.160205	−0.0801025	−	0.996787i	$-0.525525\pi$
$139$	−1.88879	−0.160205	−0.0801025	+	0.996787i	$0.525525\pi$
$140$	16.2444	1.37290
$141$	−3.39387	−0.285815
$142$	3.54226	0.297260
$143$	−6.97070	−0.582919
$144$	−1.30591	−0.108825
$145$	−7.72122	−0.641212
$146$	5.43368	0.449694
$147$	−15.7350	−1.29780
$148$	−6.96695	−0.572680
$149$	10.9166	0.894323	0.447162	−	0.894453i	$-0.352435\pi$
$149$	10.9166	0.894323	0.447162	+	0.894453i	$0.352435\pi$
$150$	−11.4845	−0.937709
$151$	−22.2780	−1.81296	−0.906478	−	0.422253i	$-0.861239\pi$
$151$	−22.2780	−1.81296	−0.906478	+	0.422253i	$0.861239\pi$
$152$	4.22918	0.343032
$153$	−6.10157	−0.493282
$154$	−23.1652	−1.86671
$155$	3.71801	0.298638
$156$	−1.71121	−0.137006
$157$	3.58098	0.285793	0.142896	−	0.989738i	$-0.454358\pi$
$157$	3.58098	0.285793	0.142896	+	0.989738i	$0.454358\pi$
$158$	16.3616	1.30166
$159$	−1.38902	−0.110157
$160$	3.71801	0.293934
$161$	−29.6033	−2.33307
$162$	−3.37690	−0.265314
$163$	−22.9081	−1.79430	−0.897152	−	0.441722i	$-0.854368\pi$
$163$	−22.9081	−1.79430	−0.897152	+	0.441722i	$0.854368\pi$
$164$	−5.38465	−0.420470
$165$	25.6579	1.99747
$166$	3.36109	0.260871
$167$	−10.3112	−0.797907	−0.398954	−	0.916971i	$-0.630627\pi$
$167$	−10.3112	−0.797907	−0.398954	+	0.916971i	$0.630627\pi$
$168$	−5.68673	−0.438741
$169$	−11.2715	−0.867039
$170$	17.3716	1.33234
$171$	−5.52291	−0.422347
$172$	5.29109	0.403442
$173$	−7.36957	−0.560298	−0.280149	−	0.959956i	$-0.590384\pi$
$173$	−7.36957	−0.560298	−0.280149	+	0.959956i	$0.590384\pi$
$174$	2.70299	0.204913
$175$	38.5513	2.91420
$176$	−5.30204	−0.399656
$177$	−15.7811	−1.18618
$178$	−8.51706	−0.638381
$179$	−8.32570	−0.622292	−0.311146	−	0.950362i	$-0.600713\pi$
$179$	−8.32570	−0.622292	−0.311146	+	0.950362i	$0.600713\pi$
$180$	−4.85537	−0.361898
$181$	−17.4424	−1.29649	−0.648243	−	0.761433i	$-0.724496\pi$
$181$	−17.4424	−1.29649	−0.648243	+	0.761433i	$0.724496\pi$
$182$	5.74417	0.425786
$183$	−7.90699	−0.584502
$184$	−6.77558	−0.499503
$185$	−25.9032	−1.90444
$186$	−1.30157	−0.0954360
$187$	−24.7726	−1.81155
$188$	2.60751	0.190172
$189$	24.4865	1.78113
$190$	15.7241	1.14075
$191$	−2.77439	−0.200748	−0.100374	−	0.994950i	$-0.532004\pi$
$191$	−2.77439	−0.200748	−0.100374	+	0.994950i	$0.532004\pi$
$192$	−1.30157	−0.0939330
$193$	24.9290	1.79443	0.897213	−	0.441598i	$-0.145588\pi$
$193$	24.9290	1.79443	0.897213	+	0.441598i	$0.145588\pi$
$194$	1.00000	0.0717958
$195$	−6.36228	−0.455612
$196$	12.0892	0.863514
$197$	−2.72550	−0.194184	−0.0970918	−	0.995275i	$-0.530954\pi$
$197$	−2.72550	−0.194184	−0.0970918	+	0.995275i	$0.530954\pi$
$198$	6.92396	0.492064
$199$	20.5356	1.45573	0.727864	−	0.685721i	$-0.240513\pi$
$199$	20.5356	1.45573	0.727864	+	0.685721i	$0.240513\pi$
$200$	8.82358	0.623921
$201$	−13.6622	−0.963660
$202$	−8.85362	−0.622939
$203$	−9.07338	−0.636827
$204$	−6.08133	−0.425778
$205$	−20.0202	−1.39827
$206$	−2.24124	−0.156155
$207$	8.84827	0.614997
$208$	1.31472	0.0911595
$209$	−22.4233	−1.55105
$210$	−21.1433	−1.45903
$211$	−26.3161	−1.81168	−0.905838	−	0.423623i	$-0.860758\pi$
$211$	−26.3161	−1.81168	−0.905838	+	0.423623i	$0.860758\pi$
$212$	1.06719	0.0732947
$213$	−4.61051	−0.315907
$214$	11.6917	0.799230
$215$	19.6723	1.34164
$216$	5.60445	0.381335
$217$	4.36912	0.296595
$218$	−14.9053	−1.00951
$219$	−7.07233	−0.477904
$220$	−19.7130	−1.32905
$221$	6.14276	0.413207
$222$	9.06801	0.608605
$223$	2.97648	0.199320	0.0996600	−	0.995022i	$-0.468224\pi$
$223$	2.97648	0.199320	0.0996600	+	0.995022i	$0.468224\pi$
$224$	4.36912	0.291924
$225$	−11.5228	−0.768184
$226$	−1.46032	−0.0971387
$227$	10.0238	0.665305	0.332653	−	0.943049i	$-0.392056\pi$
$227$	10.0238	0.665305	0.332653	+	0.943049i	$0.392056\pi$
$228$	−5.50459	−0.364550
$229$	19.9591	1.31894	0.659469	−	0.751732i	$-0.270781\pi$
$229$	19.9591	1.31894	0.659469	+	0.751732i	$0.270781\pi$
$230$	−25.1917	−1.66109
$231$	30.1512	1.98381
$232$	−2.07671	−0.136343
$233$	15.7321	1.03065	0.515323	−	0.856996i	$-0.327672\pi$
$233$	15.7321	1.03065	0.515323	+	0.856996i	$0.327672\pi$
$234$	−1.71690	−0.112237
$235$	9.69475	0.632416
$236$	12.1246	0.789245
$237$	−21.2958	−1.38331
$238$	20.4138	1.32323
$239$	15.4091	0.996731	0.498365	−	0.866967i	$-0.333934\pi$
$239$	15.4091	0.996731	0.498365	+	0.866967i	$0.333934\pi$
$240$	−4.83926	−0.312373
$241$	−9.79047	−0.630660	−0.315330	−	0.948982i	$-0.602115\pi$
$241$	−9.79047	−0.630660	−0.315330	+	0.948982i	$0.602115\pi$
$242$	17.1116	1.09997
$243$	−12.4181	−0.796620
$244$	6.07495	0.388909
$245$	44.9477	2.87160
$246$	7.00852	0.446847
$247$	5.56019	0.353786
$248$	1.00000	0.0635001
$249$	−4.37470	−0.277235
$250$	14.2161	0.899105
$251$	9.17400	0.579057	0.289529	−	0.957169i	$-0.406501\pi$
$251$	9.17400	0.579057	0.289529	+	0.957169i	$0.406501\pi$
$252$	−5.70565	−0.359422
$253$	35.9244	2.25855
$254$	18.5039	1.16104
$255$	−22.6104	−1.41592
$256$	1.00000	0.0625000
$257$	−16.7993	−1.04791	−0.523955	−	0.851746i	$-0.675544\pi$
$257$	−16.7993	−1.04791	−0.523955	+	0.851746i	$0.675544\pi$
$258$	−6.88674	−0.428750
$259$	−30.4394	−1.89142
$260$	4.88814	0.303150
$261$	2.71198	0.167868
$262$	−1.00497	−0.0620870
$263$	10.6054	0.653954	0.326977	−	0.945032i	$-0.393970\pi$
$263$	10.6054	0.653954	0.326977	+	0.945032i	$0.393970\pi$
$264$	6.90099	0.424727
$265$	3.96781	0.243741
$266$	18.4778	1.13295
$267$	11.0856	0.678427
$268$	10.4967	0.641188
$269$	−13.2244	−0.806307	−0.403154	−	0.915132i	$-0.632086\pi$
$269$	−13.2244	−0.806307	−0.403154	+	0.915132i	$0.632086\pi$
$270$	20.8374	1.26812
$271$	0.886583	0.0538561	0.0269280	−	0.999637i	$-0.491428\pi$
$271$	0.886583	0.0538561	0.0269280	+	0.999637i	$0.491428\pi$
$272$	4.67229	0.283299
$273$	−7.47646	−0.452496
$274$	−18.9471	−1.14464
$275$	−46.7829	−2.82112
$276$	8.81892	0.530837
$277$	10.1024	0.606992	0.303496	−	0.952833i	$-0.401846\pi$
$277$	10.1024	0.606992	0.303496	+	0.952833i	$0.401846\pi$
$278$	−1.88879	−0.113282
$279$	−1.30591	−0.0781825
$280$	16.2444	0.970789
$281$	−25.1294	−1.49909	−0.749547	−	0.661951i	$-0.769729\pi$
$281$	−25.1294	−1.49909	−0.749547	+	0.661951i	$0.769729\pi$
$282$	−3.39387	−0.202102
$283$	10.6998	0.636035	0.318017	−	0.948085i	$-0.396983\pi$
$283$	10.6998	0.636035	0.318017	+	0.948085i	$0.396983\pi$
$284$	3.54226	0.210194
$285$	−20.4661	−1.21231
$286$	−6.97070	−0.412186
$287$	−23.5262	−1.38871
$288$	−1.30591	−0.0769512
$289$	4.83028	0.284134
$290$	−7.72122	−0.453405
$291$	−1.30157	−0.0762996
$292$	5.43368	0.317982
$293$	−28.6442	−1.67341	−0.836707	−	0.547651i	$-0.815522\pi$
$293$	−28.6442	−1.67341	−0.836707	+	0.547651i	$0.815522\pi$
$294$	−15.7350	−0.917682
$295$	45.0794	2.62462
$296$	−6.96695	−0.404946
$297$	−29.7150	−1.72424
$298$	10.9166	0.632382
$299$	−8.90800	−0.515163
$300$	−11.4845	−0.663060
$301$	23.1174	1.33246
$302$	−22.2780	−1.28195
$303$	11.5236	0.662016
$304$	4.22918	0.242560
$305$	22.5867	1.29331
$306$	−6.10157	−0.348803
$307$	15.2732	0.871686	0.435843	−	0.900023i	$-0.356450\pi$
$307$	15.2732	0.871686	0.435843	+	0.900023i	$0.356450\pi$
$308$	−23.1652	−1.31996
$309$	2.91714	0.165950
$310$	3.71801	0.211169
$311$	3.55560	0.201619	0.100810	−	0.994906i	$-0.467857\pi$
$311$	3.55560	0.201619	0.100810	+	0.994906i	$0.467857\pi$
$312$	−1.71121	−0.0968780
$313$	26.9424	1.52288	0.761438	−	0.648238i	$-0.224494\pi$
$313$	26.9424	1.52288	0.761438	+	0.648238i	$0.224494\pi$
$314$	3.58098	0.202086
$315$	−21.2137	−1.19525
$316$	16.3616	0.920409
$317$	7.02666	0.394657	0.197328	−	0.980337i	$-0.436774\pi$
$317$	7.02666	0.394657	0.197328	+	0.980337i	$0.436774\pi$
$318$	−1.38902	−0.0778926
$319$	11.0108	0.616485
$320$	3.71801	0.207843
$321$	−15.2176	−0.849366
$322$	−29.6033	−1.64973
$323$	19.7599	1.09947
$324$	−3.37690	−0.187605
$325$	11.6005	0.643482
$326$	−22.9081	−1.26876
$327$	19.4003	1.07284
$328$	−5.38465	−0.297317
$329$	11.3925	0.628091
$330$	25.6579	1.41242
$331$	29.7661	1.63609	0.818045	−	0.575154i	$-0.195058\pi$
$331$	29.7661	1.63609	0.818045	+	0.575154i	$0.195058\pi$
$332$	3.36109	0.184464
$333$	9.09818	0.498577
$334$	−10.3112	−0.564206
$335$	39.0268	2.13226
$336$	−5.68673	−0.310237
$337$	9.19861	0.501080	0.250540	−	0.968106i	$-0.419392\pi$
$337$	9.19861	0.501080	0.250540	+	0.968106i	$0.419392\pi$
$338$	−11.2715	−0.613089
$339$	1.90071	0.103232
$340$	17.3716	0.942107
$341$	−5.30204	−0.287121
$342$	−5.52291	−0.298645
$343$	22.2353	1.20059
$344$	5.29109	0.285276
$345$	32.7888	1.76529
$346$	−7.36957	−0.396191
$347$	1.15726	0.0621247	0.0310624	−	0.999517i	$-0.490111\pi$
$347$	1.15726	0.0621247	0.0310624	+	0.999517i	$0.490111\pi$
$348$	2.70299	0.144895
$349$	−14.5329	−0.777928	−0.388964	−	0.921253i	$-0.627167\pi$
$349$	−14.5329	−0.777928	−0.388964	+	0.921253i	$0.627167\pi$
$350$	38.5513	2.06065
$351$	7.36829	0.393290
$352$	−5.30204	−0.282599
$353$	−14.9986	−0.798294	−0.399147	−	0.916887i	$-0.630694\pi$
$353$	−14.9986	−0.798294	−0.399147	+	0.916887i	$0.630694\pi$
$354$	−15.7811	−0.838755
$355$	13.1701	0.698998
$356$	−8.51706	−0.451403
$357$	−26.5700	−1.40624
$358$	−8.32570	−0.440027
$359$	−26.3661	−1.39155	−0.695775	−	0.718260i	$-0.744939\pi$
$359$	−26.3661	−1.39155	−0.695775	+	0.718260i	$0.744939\pi$
$360$	−4.85537	−0.255900
$361$	−1.11406	−0.0586346
$362$	−17.4424	−0.916754
$363$	−22.2720	−1.16898
$364$	5.74417	0.301076
$365$	20.2025	1.05744
$366$	−7.90699	−0.413305
$367$	−13.0722	−0.682366	−0.341183	−	0.939997i	$-0.610828\pi$
$367$	−13.0722	−0.682366	−0.341183	+	0.939997i	$0.610828\pi$
$368$	−6.77558	−0.353202
$369$	7.03184	0.366063
$370$	−25.9032	−1.34664
$371$	4.66267	0.242074
$372$	−1.30157	−0.0674835
$373$	29.8942	1.54787	0.773933	−	0.633268i	$-0.218287\pi$
$373$	29.8942	1.54787	0.773933	+	0.633268i	$0.218287\pi$
$374$	−24.7726	−1.28096
$375$	−18.5033	−0.955506
$376$	2.60751	0.134472
$377$	−2.73029	−0.140617
$378$	24.4865	1.25945
$379$	−2.40368	−0.123469	−0.0617344	−	0.998093i	$-0.519663\pi$
$379$	−2.40368	−0.123469	−0.0617344	+	0.998093i	$0.519663\pi$
$380$	15.7241	0.806630
$381$	−24.0841	−1.23387
$382$	−2.77439	−0.141950
$383$	−21.5924	−1.10332	−0.551659	−	0.834070i	$-0.686005\pi$
$383$	−21.5924	−1.10332	−0.551659	+	0.834070i	$0.686005\pi$
$384$	−1.30157	−0.0664207
$385$	−86.1285	−4.38951
$386$	24.9290	1.26885
$387$	−6.90966	−0.351238
$388$	1.00000	0.0507673
$389$	−20.8316	−1.05621	−0.528103	−	0.849180i	$-0.677097\pi$
$389$	−20.8316	−1.05621	−0.528103	+	0.849180i	$0.677097\pi$
$390$	−6.36228	−0.322167
$391$	−31.6575	−1.60099
$392$	12.0892	0.610596
$393$	1.30804	0.0659818
$394$	−2.72550	−0.137309
$395$	60.8324	3.06081
$396$	6.92396	0.347942
$397$	5.57586	0.279844	0.139922	−	0.990163i	$-0.455315\pi$
$397$	5.57586	0.279844	0.139922	+	0.990163i	$0.455315\pi$
$398$	20.5356	1.02936
$399$	−24.0502	−1.20402
$400$	8.82358	0.441179
$401$	−33.9478	−1.69527	−0.847636	−	0.530578i	$-0.821975\pi$
$401$	−33.9478	−1.69527	−0.847636	+	0.530578i	$0.821975\pi$
$402$	−13.6622	−0.681410
$403$	1.31472	0.0654909
$404$	−8.85362	−0.440484
$405$	−12.5553	−0.623879
$406$	−9.07338	−0.450304
$407$	36.9390	1.83100
$408$	−6.08133	−0.301071
$409$	−6.68708	−0.330655	−0.165327	−	0.986239i	$-0.552868\pi$
$409$	−6.68708	−0.330655	−0.165327	+	0.986239i	$0.552868\pi$
$410$	−20.0202	−0.988725
$411$	24.6611	1.21644
$412$	−2.24124	−0.110418
$413$	52.9738	2.60667
$414$	8.84827	0.434869
$415$	12.4965	0.613431
$416$	1.31472	0.0644595
$417$	2.45840	0.120388
$418$	−22.4233	−1.09676
$419$	−23.7848	−1.16197	−0.580983	−	0.813916i	$-0.697332\pi$
$419$	−23.7848	−1.16197	−0.580983	+	0.813916i	$0.697332\pi$
$420$	−21.1433	−1.03169
$421$	2.81231	0.137063	0.0685317	−	0.997649i	$-0.478169\pi$
$421$	2.81231	0.137063	0.0685317	+	0.997649i	$0.478169\pi$
$422$	−26.3161	−1.28105
$423$	−3.40517	−0.165565
$424$	1.06719	0.0518272
$425$	41.2263	1.99977
$426$	−4.61051	−0.223380
$427$	26.5422	1.28446
$428$	11.6917	0.565141
$429$	9.07288	0.438043
$430$	19.6723	0.948683
$431$	9.39038	0.452319	0.226159	−	0.974090i	$-0.427383\pi$
$431$	9.39038	0.452319	0.226159	+	0.974090i	$0.427383\pi$
$432$	5.60445	0.269644
$433$	−10.2059	−0.490465	−0.245232	−	0.969464i	$-0.578864\pi$
$433$	−10.2059	−0.490465	−0.245232	+	0.969464i	$0.578864\pi$
$434$	4.36912	0.209724
$435$	10.0497	0.481848
$436$	−14.9053	−0.713834
$437$	−28.6551	−1.37076
$438$	−7.07233	−0.337929
$439$	−22.2812	−1.06342	−0.531711	−	0.846926i	$-0.678451\pi$
$439$	−22.2812	−1.06342	−0.531711	+	0.846926i	$0.678451\pi$
$440$	−19.7130	−0.939781
$441$	−15.7873	−0.751778
$442$	6.14276	0.292181
$443$	23.6032	1.12142	0.560710	−	0.828012i	$-0.310528\pi$
$443$	23.6032	1.12142	0.560710	+	0.828012i	$0.310528\pi$
$444$	9.06801	0.430349
$445$	−31.6665	−1.50114
$446$	2.97648	0.140941
$447$	−14.2088	−0.672052
$448$	4.36912	0.206421
$449$	25.6019	1.20823	0.604115	−	0.796897i	$-0.293527\pi$
$449$	25.6019	1.20823	0.604115	+	0.796897i	$0.293527\pi$
$450$	−11.5228	−0.543188
$451$	28.5496	1.34435
$452$	−1.46032	−0.0686875
$453$	28.9964	1.36237
$454$	10.0238	0.470442
$455$	21.3569	1.00123
$456$	−5.50459	−0.257776
$457$	13.9317	0.651698	0.325849	−	0.945422i	$-0.394350\pi$
$457$	13.9317	0.651698	0.325849	+	0.945422i	$0.394350\pi$
$458$	19.9591	0.932630
$459$	26.1856	1.22224
$460$	−25.1917	−1.17457
$461$	−24.7660	−1.15347	−0.576735	−	0.816932i	$-0.695673\pi$
$461$	−24.7660	−1.15347	−0.576735	+	0.816932i	$0.695673\pi$
$462$	30.1512	1.40276
$463$	25.6699	1.19298	0.596492	−	0.802619i	$-0.296561\pi$
$463$	25.6699	1.19298	0.596492	+	0.802619i	$0.296561\pi$
$464$	−2.07671	−0.0964087
$465$	−4.83926	−0.224415
$466$	15.7321	0.728777
$467$	6.96035	0.322087	0.161043	−	0.986947i	$-0.448514\pi$
$467$	6.96035	0.322087	0.161043	+	0.986947i	$0.448514\pi$
$468$	−1.71690	−0.0793638
$469$	45.8613	2.11768
$470$	9.69475	0.447186
$471$	−4.66090	−0.214763
$472$	12.1246	0.558080
$473$	−28.0535	−1.28990
$474$	−21.2958	−0.978147
$475$	37.3165	1.71220
$476$	20.4138	0.935664
$477$	−1.39365	−0.0638107
$478$	15.4091	0.704795
$479$	−13.6736	−0.624763	−0.312382	−	0.949957i	$-0.601127\pi$
$479$	−13.6736	−0.624763	−0.312382	+	0.949957i	$0.601127\pi$
$480$	−4.83926	−0.220881
$481$	−9.15960	−0.417642
$482$	−9.79047	−0.445944
$483$	38.5309	1.75322
$484$	17.1116	0.777799
$485$	3.71801	0.168826
$486$	−12.4181	−0.563296
$487$	−24.8369	−1.12547	−0.562734	−	0.826638i	$-0.690250\pi$
$487$	−24.8369	−1.12547	−0.562734	+	0.826638i	$0.690250\pi$
$488$	6.07495	0.275000
$489$	29.8166	1.34836
$490$	44.9477	2.03053
$491$	−9.00123	−0.406220	−0.203110	−	0.979156i	$-0.565105\pi$
$491$	−9.00123	−0.406220	−0.203110	+	0.979156i	$0.565105\pi$
$492$	7.00852	0.315968
$493$	−9.70298	−0.437000
$494$	5.56019	0.250165
$495$	25.7433	1.15708
$496$	1.00000	0.0449013
$497$	15.4765	0.694217
$498$	−4.37470	−0.196035
$499$	−41.9620	−1.87848	−0.939239	−	0.343263i	$-0.888468\pi$
$499$	−41.9620	−1.87848	−0.939239	+	0.343263i	$0.888468\pi$
$500$	14.2161	0.635763
$501$	13.4208	0.599599
$502$	9.17400	0.409455
$503$	4.00159	0.178422	0.0892110	−	0.996013i	$-0.471565\pi$
$503$	4.00159	0.178422	0.0892110	+	0.996013i	$0.471565\pi$
$504$	−5.70565	−0.254150
$505$	−32.9178	−1.46482
$506$	35.9244	1.59703
$507$	14.6707	0.651549
$508$	18.5039	0.820976
$509$	−6.78119	−0.300571	−0.150286	−	0.988643i	$-0.548019\pi$
$509$	−6.78119	−0.300571	−0.150286	+	0.988643i	$0.548019\pi$
$510$	−22.6104	−1.00121
$511$	23.7404	1.05021
$512$	1.00000	0.0441942
$513$	23.7022	1.04648
$514$	−16.7993	−0.740985
$515$	−8.33294	−0.367193
$516$	−6.88674	−0.303172
$517$	−13.8251	−0.608028
$518$	−30.4394	−1.33743
$519$	9.59205	0.421044
$520$	4.88814	0.214359
$521$	−5.77407	−0.252966	−0.126483	−	0.991969i	$-0.540369\pi$
$521$	−5.77407	−0.252966	−0.126483	+	0.991969i	$0.540369\pi$
$522$	2.71198	0.118700
$523$	17.9514	0.784960	0.392480	−	0.919760i	$-0.371617\pi$
$523$	17.9514	0.784960	0.392480	+	0.919760i	$0.371617\pi$
$524$	−1.00497	−0.0439022
$525$	−50.1773	−2.18992
$526$	10.6054	0.462415
$527$	4.67229	0.203528
$528$	6.90099	0.300327
$529$	22.9085	0.996023
$530$	3.96781	0.172351
$531$	−15.8336	−0.687119
$532$	18.4778	0.801113
$533$	−7.07931	−0.306639
$534$	11.0856	0.479720
$535$	43.4699	1.87937
$536$	10.4967	0.453389
$537$	10.8365	0.467630
$538$	−13.2244	−0.570145
$539$	−64.0973	−2.76087
$540$	20.8374	0.896699
$541$	−27.3583	−1.17623	−0.588113	−	0.808779i	$-0.700129\pi$
$541$	−27.3583	−1.17623	−0.588113	+	0.808779i	$0.700129\pi$
$542$	0.886583	0.0380820
$543$	22.7026	0.974263
$544$	4.67229	0.200323
$545$	−55.4180	−2.37385
$546$	−7.47646	−0.319963
$547$	−43.6375	−1.86580	−0.932902	−	0.360131i	$-0.882732\pi$
$547$	−43.6375	−1.86580	−0.932902	+	0.360131i	$0.882732\pi$
$548$	−18.9471	−0.809382
$549$	−7.93330	−0.338585
$550$	−46.7829	−1.99483
$551$	−8.78277	−0.374158
$552$	8.81892	0.375358
$553$	71.4855	3.03987
$554$	10.1024	0.429208
$555$	33.7149	1.43112
$556$	−1.88879	−0.0801025
$557$	41.3223	1.75088	0.875441	−	0.483325i	$-0.160571\pi$
$557$	41.3223	1.75088	0.875441	+	0.483325i	$0.160571\pi$
$558$	−1.30591	−0.0552834
$559$	6.95631	0.294220
$560$	16.2444	0.686452
$561$	32.2434	1.36132
$562$	−25.1294	−1.06002
$563$	38.0762	1.60472	0.802361	−	0.596839i	$-0.203577\pi$
$563$	38.0762	1.60472	0.802361	+	0.596839i	$0.203577\pi$
$564$	−3.39387	−0.142908
$565$	−5.42946	−0.228419
$566$	10.6998	0.449745
$567$	−14.7541	−0.619612
$568$	3.54226	0.148630
$569$	−5.11131	−0.214277	−0.107139	−	0.994244i	$-0.534169\pi$
$569$	−5.11131	−0.214277	−0.107139	+	0.994244i	$0.534169\pi$
$570$	−20.4661	−0.857230
$571$	43.2753	1.81102	0.905508	−	0.424330i	$-0.139490\pi$
$571$	43.2753	1.81102	0.905508	+	0.424330i	$0.139490\pi$
$572$	−6.97070	−0.291460
$573$	3.61107	0.150855
$574$	−23.5262	−0.981963
$575$	−59.7849	−2.49320
$576$	−1.30591	−0.0544127
$577$	6.95934	0.289721	0.144861	−	0.989452i	$-0.453727\pi$
$577$	6.95934	0.289721	0.144861	+	0.989452i	$0.453727\pi$
$578$	4.83028	0.200913
$579$	−32.4469	−1.34845
$580$	−7.72122	−0.320606
$581$	14.6850	0.609236
$582$	−1.30157	−0.0539520
$583$	−5.65827	−0.234341
$584$	5.43368	0.224847
$585$	−6.38345	−0.263923
$586$	−28.6442	−1.18328
$587$	−20.8643	−0.861164	−0.430582	−	0.902552i	$-0.641692\pi$
$587$	−20.8643	−0.861164	−0.430582	+	0.902552i	$0.641692\pi$
$588$	−15.7350	−0.648899
$589$	4.22918	0.174260
$590$	45.0794	1.85589
$591$	3.54744	0.145922
$592$	−6.96695	−0.286340
$593$	27.8536	1.14381	0.571904	−	0.820320i	$-0.306205\pi$
$593$	27.8536	1.14381	0.571904	+	0.820320i	$0.306205\pi$
$594$	−29.7150	−1.21922
$595$	75.8986	3.11154
$596$	10.9166	0.447162
$597$	−26.7286	−1.09393
$598$	−8.90800	−0.364275
$599$	12.8728	0.525967	0.262984	−	0.964800i	$-0.415293\pi$
$599$	12.8728	0.525967	0.262984	+	0.964800i	$0.415293\pi$
$600$	−11.4845	−0.468854
$601$	11.7299	0.478472	0.239236	−	0.970961i	$-0.423103\pi$
$601$	11.7299	0.478472	0.239236	+	0.970961i	$0.423103\pi$
$602$	23.1174	0.942195
$603$	−13.7077	−0.558221
$604$	−22.2780	−0.906478
$605$	63.6210	2.58656
$606$	11.5236	0.468116
$607$	−33.2815	−1.35086	−0.675428	−	0.737426i	$-0.736041\pi$
$607$	−33.2815	−1.35086	−0.675428	+	0.737426i	$0.736041\pi$
$608$	4.22918	0.171516
$609$	11.8097	0.478552
$610$	22.5867	0.914508
$611$	3.42815	0.138688
$612$	−6.10157	−0.246641
$613$	−22.5038	−0.908918	−0.454459	−	0.890768i	$-0.650167\pi$
$613$	−22.5038	−0.908918	−0.454459	+	0.890768i	$0.650167\pi$
$614$	15.2732	0.616375
$615$	26.0577	1.05075
$616$	−23.1652	−0.933353
$617$	34.4104	1.38531	0.692656	−	0.721268i	$-0.256440\pi$
$617$	34.4104	1.38531	0.692656	+	0.721268i	$0.256440\pi$
$618$	2.91714	0.117345
$619$	−21.6475	−0.870088	−0.435044	−	0.900409i	$-0.643267\pi$
$619$	−21.6475	−0.870088	−0.435044	+	0.900409i	$0.643267\pi$
$620$	3.71801	0.149319
$621$	−37.9734	−1.52382
$622$	3.55560	0.142566
$623$	−37.2121	−1.49087
$624$	−1.71121	−0.0685031
$625$	8.73764	0.349506
$626$	26.9424	1.07684
$627$	29.1855	1.16556
$628$	3.58098	0.142896
$629$	−32.5516	−1.29792
$630$	−21.2137	−0.845173
$631$	−28.5184	−1.13530	−0.567650	−	0.823270i	$-0.692147\pi$
$631$	−28.5184	−1.13530	−0.567650	+	0.823270i	$0.692147\pi$
$632$	16.3616	0.650828
$633$	34.2524	1.36141
$634$	7.02666	0.279064
$635$	68.7975	2.73014
$636$	−1.38902	−0.0550784
$637$	15.8939	0.629740
$638$	11.0108	0.435921
$639$	−4.62585	−0.182996
$640$	3.71801	0.146967
$641$	−5.86156	−0.231518	−0.115759	−	0.993277i	$-0.536930\pi$
$641$	−5.86156	−0.231518	−0.115759	+	0.993277i	$0.536930\pi$
$642$	−15.2176	−0.600592
$643$	−39.5813	−1.56093	−0.780467	−	0.625197i	$-0.785019\pi$
$643$	−39.5813	−1.56093	−0.780467	+	0.625197i	$0.785019\pi$
$644$	−29.6033	−1.16653
$645$	−25.6050	−1.00819
$646$	19.7599	0.777444
$647$	9.72594	0.382366	0.191183	−	0.981554i	$-0.438768\pi$
$647$	9.72594	0.382366	0.191183	+	0.981554i	$0.438768\pi$
$648$	−3.37690	−0.132657
$649$	−64.2851	−2.52341
$650$	11.6005	0.455011
$651$	−5.68673	−0.222881
$652$	−22.9081	−0.897152
$653$	39.7622	1.55601	0.778007	−	0.628255i	$-0.216231\pi$
$653$	39.7622	1.55601	0.778007	+	0.628255i	$0.216231\pi$
$654$	19.4003	0.758613
$655$	−3.73647	−0.145996
$656$	−5.38465	−0.210235
$657$	−7.09587	−0.276836
$658$	11.3925	0.444127
$659$	21.3177	0.830421	0.415211	−	0.909725i	$-0.363708\pi$
$659$	21.3177	0.830421	0.415211	+	0.909725i	$0.363708\pi$
$660$	25.6579	0.998734
$661$	19.5316	0.759693	0.379846	−	0.925050i	$-0.375977\pi$
$661$	19.5316	0.759693	0.379846	+	0.925050i	$0.375977\pi$
$662$	29.7661	1.15689
$663$	−7.99525	−0.310510
$664$	3.36109	0.130435
$665$	68.7005	2.66409
$666$	9.09818	0.352547
$667$	14.0709	0.544828
$668$	−10.3112	−0.398954
$669$	−3.87411	−0.149782
$670$	39.0268	1.50774
$671$	−32.2096	−1.24344
$672$	−5.68673	−0.219370
$673$	−20.4602	−0.788681	−0.394341	−	0.918964i	$-0.629027\pi$
$673$	−20.4602	−0.788681	−0.394341	+	0.918964i	$0.629027\pi$
$674$	9.19861	0.354317
$675$	49.4513	1.90338
$676$	−11.2715	−0.433520
$677$	48.1804	1.85172	0.925862	−	0.377862i	$-0.123341\pi$
$677$	48.1804	1.85172	0.925862	+	0.377862i	$0.123341\pi$
$678$	1.90071	0.0729963
$679$	4.36912	0.167671
$680$	17.3716	0.666171
$681$	−13.0468	−0.499953
$682$	−5.30204	−0.203025
$683$	−8.41458	−0.321975	−0.160987	−	0.986956i	$-0.551468\pi$
$683$	−8.41458	−0.321975	−0.160987	+	0.986956i	$0.551468\pi$
$684$	−5.52291	−0.211174
$685$	−70.4456	−2.69159
$686$	22.2353	0.848947
$687$	−25.9783	−0.991134
$688$	5.29109	0.201721
$689$	1.40305	0.0534521
$690$	32.7888	1.24825
$691$	−15.3566	−0.584194	−0.292097	−	0.956389i	$-0.594353\pi$
$691$	−15.3566	−0.584194	−0.292097	+	0.956389i	$0.594353\pi$
$692$	−7.36957	−0.280149
$693$	30.2516	1.14916
$694$	1.15726	0.0439288
$695$	−7.02253	−0.266380
$696$	2.70299	0.102457
$697$	−25.1586	−0.952951
$698$	−14.5329	−0.550078
$699$	−20.4765	−0.774493
$700$	38.5513	1.45710
$701$	6.00919	0.226964	0.113482	−	0.993540i	$-0.463800\pi$
$701$	6.00919	0.226964	0.113482	+	0.993540i	$0.463800\pi$
$702$	7.36829	0.278098
$703$	−29.4645	−1.11127
$704$	−5.30204	−0.199828
$705$	−12.6184	−0.475238
$706$	−14.9986	−0.564479
$707$	−38.6825	−1.45481
$708$	−15.7811	−0.593089
$709$	10.8162	0.406211	0.203105	−	0.979157i	$-0.434897\pi$
$709$	10.8162	0.406211	0.203105	+	0.979157i	$0.434897\pi$
$710$	13.1701	0.494266
$711$	−21.3666	−0.801311
$712$	−8.51706	−0.319190
$713$	−6.77558	−0.253748
$714$	−26.5700	−0.994359
$715$	−25.9171	−0.969245
$716$	−8.32570	−0.311146
$717$	−20.0561	−0.749008
$718$	−26.3661	−0.983974
$719$	−30.4669	−1.13622	−0.568112	−	0.822951i	$-0.692326\pi$
$719$	−30.4669	−1.13622	−0.568112	+	0.822951i	$0.692326\pi$
$720$	−4.85537	−0.180949
$721$	−9.79224	−0.364682
$722$	−1.11406	−0.0414609
$723$	12.7430	0.473918
$724$	−17.4424	−0.648243
$725$	−18.3240	−0.680536
$726$	−22.2720	−0.826591
$727$	−4.06767	−0.150862	−0.0754308	−	0.997151i	$-0.524033\pi$
$727$	−4.06767	−0.150862	−0.0754308	+	0.997151i	$0.524033\pi$
$728$	5.74417	0.212893
$729$	26.2937	0.973842
$730$	20.2025	0.747726
$731$	24.7215	0.914358
$732$	−7.90699	−0.292251
$733$	−0.293185	−0.0108290	−0.00541451	−	0.999985i	$-0.501724\pi$
$733$	−0.293185	−0.0108290	−0.00541451	+	0.999985i	$0.501724\pi$
$734$	−13.0722	−0.482505
$735$	−58.5028	−2.15791
$736$	−6.77558	−0.249751
$737$	−55.6539	−2.05004
$738$	7.03184	0.258846
$739$	−46.3491	−1.70498	−0.852490	−	0.522744i	$-0.824909\pi$
$739$	−46.3491	−1.70498	−0.852490	+	0.522744i	$0.824909\pi$
$740$	−25.9032	−0.952220
$741$	−7.23700	−0.265858
$742$	4.66267	0.171172
$743$	8.66126	0.317751	0.158875	−	0.987299i	$-0.449213\pi$
$743$	8.66126	0.317751	0.158875	+	0.987299i	$0.449213\pi$
$744$	−1.30157	−0.0477180
$745$	40.5880	1.48703
$746$	29.8942	1.09451
$747$	−4.38926	−0.160595
$748$	−24.7726	−0.905777
$749$	51.0825	1.86651
$750$	−18.5033	−0.675645
$751$	−12.9039	−0.470872	−0.235436	−	0.971890i	$-0.575652\pi$
$751$	−12.9039	−0.470872	−0.235436	+	0.971890i	$0.575652\pi$
$752$	2.60751	0.0950862
$753$	−11.9406	−0.435141
$754$	−2.73029	−0.0994314
$755$	−82.8297	−3.01448
$756$	24.4865	0.890566
$757$	44.1675	1.60529	0.802647	−	0.596454i	$-0.203424\pi$
$757$	44.1675	1.60529	0.802647	+	0.596454i	$0.203424\pi$
$758$	−2.40368	−0.0873057
$759$	−46.7582	−1.69722
$760$	15.7241	0.570374
$761$	−22.2076	−0.805025	−0.402512	−	0.915415i	$-0.631863\pi$
$761$	−22.2076	−0.805025	−0.402512	+	0.915415i	$0.631863\pi$
$762$	−24.0841	−0.872476
$763$	−65.1230	−2.35761
$764$	−2.77439	−0.100374
$765$	−22.6857	−0.820202
$766$	−21.5924	−0.780164
$767$	15.9405	0.575577
$768$	−1.30157	−0.0469665
$769$	−13.1742	−0.475074	−0.237537	−	0.971378i	$-0.576340\pi$
$769$	−13.1742	−0.475074	−0.237537	+	0.971378i	$0.576340\pi$
$770$	−86.1285	−3.10385
$771$	21.8655	0.787467
$772$	24.9290	0.897213
$773$	−9.50075	−0.341718	−0.170859	−	0.985295i	$-0.554654\pi$
$773$	−9.50075	−0.341718	−0.170859	+	0.985295i	$0.554654\pi$
$774$	−6.90966	−0.248363
$775$	8.82358	0.316952
$776$	1.00000	0.0358979
$777$	39.6192	1.42133
$778$	−20.8316	−0.746850
$779$	−22.7726	−0.815914
$780$	−6.36228	−0.227806
$781$	−18.7812	−0.672043
$782$	−31.6575	−1.13207
$783$	−11.6388	−0.415937
$784$	12.0892	0.431757
$785$	13.3141	0.475200
$786$	1.30804	0.0466562
$787$	43.5049	1.55078	0.775391	−	0.631481i	$-0.217553\pi$
$787$	43.5049	1.55078	0.775391	+	0.631481i	$0.217553\pi$
$788$	−2.72550	−0.0970918
$789$	−13.8037	−0.491423
$790$	60.8324	2.16432
$791$	−6.38029	−0.226857
$792$	6.92396	0.246032
$793$	7.98686	0.283622
$794$	5.57586	0.197880
$795$	−5.16440	−0.183162
$796$	20.5356	0.727864
$797$	−31.5193	−1.11647	−0.558236	−	0.829682i	$-0.688522\pi$
$797$	−31.5193	−1.11647	−0.558236	+	0.829682i	$0.688522\pi$
$798$	−24.0502	−0.851367
$799$	12.1831	0.431005
$800$	8.82358	0.311961
$801$	11.1225	0.392993
$802$	−33.9478	−1.19874
$803$	−28.8096	−1.01667
$804$	−13.6622	−0.481830
$805$	−110.065	−3.87929
$806$	1.31472	0.0463091
$807$	17.2126	0.605911
$808$	−8.85362	−0.311469
$809$	23.0711	0.811135	0.405568	−	0.914065i	$-0.367074\pi$
$809$	23.0711	0.811135	0.405568	+	0.914065i	$0.367074\pi$
$810$	−12.5553	−0.441149
$811$	24.0932	0.846028	0.423014	−	0.906123i	$-0.360972\pi$
$811$	24.0932	0.846028	0.423014	+	0.906123i	$0.360972\pi$
$812$	−9.07338	−0.318413
$813$	−1.15395	−0.0404709
$814$	36.9390	1.29471
$815$	−85.1726	−2.98347
$816$	−6.08133	−0.212889
$817$	22.3770	0.782871
$818$	−6.68708	−0.233808
$819$	−7.50134	−0.262118
$820$	−20.0202	−0.699134
$821$	8.31392	0.290158	0.145079	−	0.989420i	$-0.453656\pi$
$821$	8.31392	0.290158	0.145079	+	0.989420i	$0.453656\pi$
$822$	24.6611	0.860155
$823$	−43.5291	−1.51733	−0.758664	−	0.651482i	$-0.774148\pi$
$823$	−43.5291	−1.51733	−0.758664	+	0.651482i	$0.774148\pi$
$824$	−2.24124	−0.0780773
$825$	60.8914	2.11997
$826$	52.9738	1.84320
$827$	18.7554	0.652191	0.326095	−	0.945337i	$-0.394267\pi$
$827$	18.7554	0.652191	0.326095	+	0.945337i	$0.394267\pi$
$828$	8.84827	0.307499
$829$	43.8799	1.52401	0.762006	−	0.647569i	$-0.224214\pi$
$829$	43.8799	1.52401	0.762006	+	0.647569i	$0.224214\pi$
$830$	12.4965	0.433761
$831$	−13.1490	−0.456132
$832$	1.31472	0.0455798
$833$	56.4842	1.95706
$834$	2.45840	0.0851274
$835$	−38.3372	−1.32671
$836$	−22.4233	−0.775524
$837$	5.60445	0.193718
$838$	−23.7848	−0.821634
$839$	−8.44611	−0.291592	−0.145796	−	0.989315i	$-0.546574\pi$
$839$	−8.44611	−0.291592	−0.145796	+	0.989315i	$0.546574\pi$
$840$	−21.1433	−0.729513
$841$	−24.6873	−0.851286
$842$	2.81231	0.0969185
$843$	32.7078	1.12652
$844$	−26.3161	−0.905838
$845$	−41.9075	−1.44166
$846$	−3.40517	−0.117072
$847$	74.7625	2.56887
$848$	1.06719	0.0366474
$849$	−13.9265	−0.477957
$850$	41.2263	1.41405
$851$	47.2052	1.61817
$852$	−4.61051	−0.157953
$853$	−13.1882	−0.451554	−0.225777	−	0.974179i	$-0.572492\pi$
$853$	−13.1882	−0.451554	−0.225777	+	0.974179i	$0.572492\pi$
$854$	26.5422	0.908254
$855$	−20.5342	−0.702255
$856$	11.6917	0.399615
$857$	−36.9230	−1.26127	−0.630633	−	0.776081i	$-0.717205\pi$
$857$	−36.9230	−1.26127	−0.630633	+	0.776081i	$0.717205\pi$
$858$	9.07288	0.309743
$859$	21.2944	0.726557	0.363278	−	0.931681i	$-0.381657\pi$
$859$	21.2944	0.726557	0.363278	+	0.931681i	$0.381657\pi$
$860$	19.6723	0.670820
$861$	30.6210	1.04356
$862$	9.39038	0.319838
$863$	36.0405	1.22683	0.613417	−	0.789759i	$-0.289795\pi$
$863$	36.0405	1.22683	0.613417	+	0.789759i	$0.289795\pi$
$864$	5.60445	0.190667
$865$	−27.4001	−0.931632
$866$	−10.2059	−0.346811
$867$	−6.28696	−0.213516
$868$	4.36912	0.148298
$869$	−86.7495	−2.94278
$870$	10.0497	0.340718
$871$	13.8002	0.467603
$872$	−14.9053	−0.504757
$873$	−1.30591	−0.0441982
$874$	−28.6551	−0.969275
$875$	62.1118	2.09976
$876$	−7.07233	−0.238952
$877$	−31.0082	−1.04707	−0.523536	−	0.852004i	$-0.675387\pi$
$877$	−31.0082	−1.04707	−0.523536	+	0.852004i	$0.675387\pi$
$878$	−22.2812	−0.751954
$879$	37.2826	1.25751
$880$	−19.7130	−0.664525
$881$	−43.9156	−1.47955	−0.739777	−	0.672852i	$-0.765069\pi$
$881$	−43.9156	−1.47955	−0.739777	+	0.672852i	$0.765069\pi$
$882$	−15.7873	−0.531587
$883$	−2.58677	−0.0870519	−0.0435259	−	0.999052i	$-0.513859\pi$
$883$	−2.58677	−0.0870519	−0.0435259	+	0.999052i	$0.513859\pi$
$884$	6.14276	0.206603
$885$	−58.6742	−1.97231
$886$	23.6032	0.792964
$887$	−12.6782	−0.425691	−0.212846	−	0.977086i	$-0.568273\pi$
$887$	−12.6782	−0.425691	−0.212846	+	0.977086i	$0.568273\pi$
$888$	9.06801	0.304302
$889$	80.8455	2.71147
$890$	−31.6665	−1.06146
$891$	17.9044	0.599821
$892$	2.97648	0.0996600
$893$	11.0276	0.369026
$894$	−14.2088	−0.475212
$895$	−30.9550	−1.03471
$896$	4.36912	0.145962
$897$	11.5944	0.387127
$898$	25.6019	0.854348
$899$	−2.07671	−0.0692621
$900$	−11.5228	−0.384092
$901$	4.98621	0.166115
$902$	28.5496	0.950598
$903$	−30.0890	−1.00130
$904$	−1.46032	−0.0485694
$905$	−64.8511	−2.15572
$906$	28.9964	0.963342
$907$	−6.11917	−0.203184	−0.101592	−	0.994826i	$-0.532394\pi$
$907$	−6.11917	−0.203184	−0.101592	+	0.994826i	$0.532394\pi$
$908$	10.0238	0.332653
$909$	11.5620	0.383487
$910$	21.3569	0.707973
$911$	30.3193	1.00452	0.502261	−	0.864716i	$-0.332502\pi$
$911$	30.3193	1.00452	0.502261	+	0.864716i	$0.332502\pi$
$912$	−5.50459	−0.182275
$913$	−17.8206	−0.589776
$914$	13.9317	0.460820
$915$	−29.3982	−0.971876
$916$	19.9591	0.659469
$917$	−4.39082	−0.144998
$918$	26.1856	0.864254
$919$	34.5130	1.13848	0.569239	−	0.822172i	$-0.307238\pi$
$919$	34.5130	1.13848	0.569239	+	0.822172i	$0.307238\pi$
$920$	−25.1917	−0.830545
$921$	−19.8792	−0.655041
$922$	−24.7660	−0.815626
$923$	4.65708	0.153290
$924$	30.1512	0.991903
$925$	−61.4735	−2.02124
$926$	25.6699	0.843567
$927$	2.92685	0.0961303
$928$	−2.07671	−0.0681713
$929$	−20.2156	−0.663252	−0.331626	−	0.943411i	$-0.607597\pi$
$929$	−20.2156	−0.663252	−0.331626	+	0.943411i	$0.607597\pi$
$930$	−4.83926	−0.158686
$931$	51.1273	1.67563
$932$	15.7321	0.515323
$933$	−4.62787	−0.151510
$934$	6.96035	0.227750
$935$	−92.1049	−3.01215
$936$	−1.71690	−0.0561187
$937$	−54.4387	−1.77843	−0.889217	−	0.457485i	$-0.848750\pi$
$937$	−54.4387	−1.77843	−0.889217	+	0.457485i	$0.848750\pi$
$938$	45.8613	1.49743
$939$	−35.0675	−1.14439
$940$	9.69475	0.316208
$941$	1.96258	0.0639784	0.0319892	−	0.999488i	$-0.489816\pi$
$941$	1.96258	0.0639784	0.0319892	+	0.999488i	$0.489816\pi$
$942$	−4.66090	−0.151860
$943$	36.4841	1.18809
$944$	12.1246	0.394622
$945$	91.0411	2.96157
$946$	−28.0535	−0.912100
$947$	−38.6452	−1.25580	−0.627900	−	0.778294i	$-0.716085\pi$
$947$	−38.6452	−1.25580	−0.627900	+	0.778294i	$0.716085\pi$
$948$	−21.2958	−0.691654
$949$	7.14377	0.231897
$950$	37.3165	1.21071
$951$	−9.14572	−0.296570
$952$	20.4138	0.661614
$953$	−39.2593	−1.27173	−0.635866	−	0.771799i	$-0.719357\pi$
$953$	−39.2593	−1.27173	−0.635866	+	0.771799i	$0.719357\pi$
$954$	−1.39365	−0.0451209
$955$	−10.3152	−0.333792
$956$	15.4091	0.498365
$957$	−14.3313	−0.463267
$958$	−13.6736	−0.441774
$959$	−82.7823	−2.67318
$960$	−4.83926	−0.156186
$961$	1.00000	0.0322581
$962$	−9.15960	−0.295317
$963$	−15.2683	−0.492014
$964$	−9.79047	−0.315330
$965$	92.6861	2.98367
$966$	38.5309	1.23971
$967$	32.4305	1.04290	0.521448	−	0.853283i	$-0.325392\pi$
$967$	32.4305	1.04290	0.521448	+	0.853283i	$0.325392\pi$
$968$	17.1116	0.549987
$969$	−25.7190	−0.826214
$970$	3.71801	0.119378
$971$	−51.7917	−1.66207	−0.831037	−	0.556217i	$-0.812252\pi$
$971$	−51.7917	−1.66207	−0.831037	+	0.556217i	$0.812252\pi$
$972$	−12.4181	−0.398310
$973$	−8.25234	−0.264558
$974$	−24.8369	−0.795826
$975$	−15.0990	−0.483554
$976$	6.07495	0.194454
$977$	−31.8002	−1.01738	−0.508690	−	0.860950i	$-0.669870\pi$
$977$	−31.8002	−1.01738	−0.508690	+	0.860950i	$0.669870\pi$
$978$	29.8166	0.953431
$979$	45.1578	1.44325
$980$	44.9477	1.43580
$981$	19.4649	0.621466
$982$	−9.00123	−0.287241
$983$	−2.81652	−0.0898331	−0.0449166	−	0.998991i	$-0.514302\pi$
$983$	−2.81652	−0.0898331	−0.0449166	+	0.998991i	$0.514302\pi$
$984$	7.00852	0.223423
$985$	−10.1334	−0.322878
$986$	−9.70298	−0.309006
$987$	−14.8282	−0.471987
$988$	5.56019	0.176893
$989$	−35.8502	−1.13997
$990$	25.7433	0.818177
$991$	2.12669	0.0675567	0.0337783	−	0.999429i	$-0.489246\pi$
$991$	2.12669	0.0675567	0.0337783	+	0.999429i	$0.489246\pi$
$992$	1.00000	0.0317500
$993$	−38.7427	−1.22946
$994$	15.4765	0.490886
$995$	76.3514	2.42050
$996$	−4.37470	−0.138618
$997$	−49.7829	−1.57664	−0.788321	−	0.615264i	$-0.789049\pi$
$997$	−49.7829	−1.57664	−0.788321	+	0.615264i	$0.789049\pi$
$998$	−41.9620	−1.32829
$999$	−39.0460	−1.23536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.11	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.11	✓	37	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.30157 q^{3} +1.00000 q^{4} +3.71801 q^{5} -1.30157 q^{6} +4.36912 q^{7} +1.00000 q^{8} -1.30591 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.30157 q^{3} +1.00000 q^{4} +3.71801 q^{5} -1.30157 q^{6} +4.36912 q^{7} +1.00000 q^{8} -1.30591 q^{9} +3.71801 q^{10} -5.30204 q^{11} -1.30157 q^{12} +1.31472 q^{13} +4.36912 q^{14} -4.83926 q^{15} +1.00000 q^{16} +4.67229 q^{17} -1.30591 q^{18} +4.22918 q^{19} +3.71801 q^{20} -5.68673 q^{21} -5.30204 q^{22} -6.77558 q^{23} -1.30157 q^{24} +8.82358 q^{25} +1.31472 q^{26} +5.60445 q^{27} +4.36912 q^{28} -2.07671 q^{29} -4.83926 q^{30} +1.00000 q^{31} +1.00000 q^{32} +6.90099 q^{33} +4.67229 q^{34} +16.2444 q^{35} -1.30591 q^{36} -6.96695 q^{37} +4.22918 q^{38} -1.71121 q^{39} +3.71801 q^{40} -5.38465 q^{41} -5.68673 q^{42} +5.29109 q^{43} -5.30204 q^{44} -4.85537 q^{45} -6.77558 q^{46} +2.60751 q^{47} -1.30157 q^{48} +12.0892 q^{49} +8.82358 q^{50} -6.08133 q^{51} +1.31472 q^{52} +1.06719 q^{53} +5.60445 q^{54} -19.7130 q^{55} +4.36912 q^{56} -5.50459 q^{57} -2.07671 q^{58} +12.1246 q^{59} -4.83926 q^{60} +6.07495 q^{61} +1.00000 q^{62} -5.70565 q^{63} +1.00000 q^{64} +4.88814 q^{65} +6.90099 q^{66} +10.4967 q^{67} +4.67229 q^{68} +8.81892 q^{69} +16.2444 q^{70} +3.54226 q^{71} -1.30591 q^{72} +5.43368 q^{73} -6.96695 q^{74} -11.4845 q^{75} +4.22918 q^{76} -23.1652 q^{77} -1.71121 q^{78} +16.3616 q^{79} +3.71801 q^{80} -3.37690 q^{81} -5.38465 q^{82} +3.36109 q^{83} -5.68673 q^{84} +17.3716 q^{85} +5.29109 q^{86} +2.70299 q^{87} -5.30204 q^{88} -8.51706 q^{89} -4.85537 q^{90} +5.74417 q^{91} -6.77558 q^{92} -1.30157 q^{93} +2.60751 q^{94} +15.7241 q^{95} -1.30157 q^{96} +1.00000 q^{97} +12.0892 q^{98} +6.92396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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