LMFDB - Embedded newform 4970.2.a.x.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4970,2,Mod(1,4970)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4970, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4970.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4970 = 2 \cdot 5 \cdot 7 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4970.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:	$39.6856498046$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 11x^{5} + 9x^{4} + 35x^{3} - 24x^{2} - 33x + 22 $ x^7 - x^6 - 11x^5 + 9x^4 + 35x^3 - 24x^2 - 33*x + 22
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.18572$ of defining polynomial
Character	$\chi$	$=$	4970.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.18572 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.18572 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.59407 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.18572 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.18572 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.59407 q^{9} -1.00000 q^{10} -0.587553 q^{11} +1.18572 q^{12} -2.40667 q^{13} -1.00000 q^{14} -1.18572 q^{15} +1.00000 q^{16} +6.36761 q^{17} -1.59407 q^{18} -0.642216 q^{19} -1.00000 q^{20} -1.18572 q^{21} -0.587553 q^{22} -1.33585 q^{23} +1.18572 q^{24} +1.00000 q^{25} -2.40667 q^{26} -5.44727 q^{27} -1.00000 q^{28} -6.07993 q^{29} -1.18572 q^{30} -3.09097 q^{31} +1.00000 q^{32} -0.696672 q^{33} +6.36761 q^{34} +1.00000 q^{35} -1.59407 q^{36} -3.09931 q^{37} -0.642216 q^{38} -2.85363 q^{39} -1.00000 q^{40} -4.99455 q^{41} -1.18572 q^{42} -6.71968 q^{43} -0.587553 q^{44} +1.59407 q^{45} -1.33585 q^{46} -8.98806 q^{47} +1.18572 q^{48} +1.00000 q^{49} +1.00000 q^{50} +7.55019 q^{51} -2.40667 q^{52} -0.800800 q^{53} -5.44727 q^{54} +0.587553 q^{55} -1.00000 q^{56} -0.761487 q^{57} -6.07993 q^{58} +8.29714 q^{59} -1.18572 q^{60} -12.4108 q^{61} -3.09097 q^{62} +1.59407 q^{63} +1.00000 q^{64} +2.40667 q^{65} -0.696672 q^{66} +7.30117 q^{67} +6.36761 q^{68} -1.58394 q^{69} +1.00000 q^{70} +1.00000 q^{71} -1.59407 q^{72} +11.7771 q^{73} -3.09931 q^{74} +1.18572 q^{75} -0.642216 q^{76} +0.587553 q^{77} -2.85363 q^{78} +12.4497 q^{79} -1.00000 q^{80} -1.67671 q^{81} -4.99455 q^{82} -10.4117 q^{83} -1.18572 q^{84} -6.36761 q^{85} -6.71968 q^{86} -7.20908 q^{87} -0.587553 q^{88} +1.30582 q^{89} +1.59407 q^{90} +2.40667 q^{91} -1.33585 q^{92} -3.66502 q^{93} -8.98806 q^{94} +0.642216 q^{95} +1.18572 q^{96} -6.78780 q^{97} +1.00000 q^{98} +0.936603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + q^{3} + 7 q^{4} - 7 q^{5} + q^{6} - 7 q^{7} + 7 q^{8} + 2 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + q^3 + 7 * q^4 - 7 * q^5 + q^6 - 7 * q^7 + 7 * q^8 + 2 * q^9	$ 7 q + 7 q^{2} + q^{3} + 7 q^{4} - 7 q^{5} + q^{6} - 7 q^{7} + 7 q^{8} + 2 q^{9} - 7 q^{10} - 9 q^{11} + q^{12} - 7 q^{14} - q^{15} + 7 q^{16} - 5 q^{17} + 2 q^{18} + 2 q^{19} - 7 q^{20} - q^{21} - 9 q^{22} - 8 q^{23} + q^{24} + 7 q^{25} + q^{27} - 7 q^{28} - 19 q^{29} - q^{30} - 6 q^{31} + 7 q^{32} - 6 q^{33} - 5 q^{34} + 7 q^{35} + 2 q^{36} - 10 q^{37} + 2 q^{38} - 19 q^{39} - 7 q^{40} - 19 q^{41} - q^{42} - 22 q^{43} - 9 q^{44} - 2 q^{45} - 8 q^{46} + 2 q^{47} + q^{48} + 7 q^{49} + 7 q^{50} - 22 q^{51} - 3 q^{53} + q^{54} + 9 q^{55} - 7 q^{56} - 25 q^{57} - 19 q^{58} + 13 q^{59} - q^{60} - 4 q^{61} - 6 q^{62} - 2 q^{63} + 7 q^{64} - 6 q^{66} - 23 q^{67} - 5 q^{68} - 19 q^{69} + 7 q^{70} + 7 q^{71} + 2 q^{72} - 10 q^{74} + q^{75} + 2 q^{76} + 9 q^{77} - 19 q^{78} - 40 q^{79} - 7 q^{80} - 33 q^{81} - 19 q^{82} + 24 q^{83} - q^{84} + 5 q^{85} - 22 q^{86} - 6 q^{87} - 9 q^{88} - 4 q^{89} - 2 q^{90} - 8 q^{92} - 12 q^{93} + 2 q^{94} - 2 q^{95} + q^{96} - 35 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) $ 7 * q + 7 * q^2 + q^3 + 7 * q^4 - 7 * q^5 + q^6 - 7 * q^7 + 7 * q^8 + 2 * q^9 - 7 * q^10 - 9 * q^11 + q^12 - 7 * q^14 - q^15 + 7 * q^16 - 5 * q^17 + 2 * q^18 + 2 * q^19 - 7 * q^20 - q^21 - 9 * q^22 - 8 * q^23 + q^24 + 7 * q^25 + q^27 - 7 * q^28 - 19 * q^29 - q^30 - 6 * q^31 + 7 * q^32 - 6 * q^33 - 5 * q^34 + 7 * q^35 + 2 * q^36 - 10 * q^37 + 2 * q^38 - 19 * q^39 - 7 * q^40 - 19 * q^41 - q^42 - 22 * q^43 - 9 * q^44 - 2 * q^45 - 8 * q^46 + 2 * q^47 + q^48 + 7 * q^49 + 7 * q^50 - 22 * q^51 - 3 * q^53 + q^54 + 9 * q^55 - 7 * q^56 - 25 * q^57 - 19 * q^58 + 13 * q^59 - q^60 - 4 * q^61 - 6 * q^62 - 2 * q^63 + 7 * q^64 - 6 * q^66 - 23 * q^67 - 5 * q^68 - 19 * q^69 + 7 * q^70 + 7 * q^71 + 2 * q^72 - 10 * q^74 + q^75 + 2 * q^76 + 9 * q^77 - 19 * q^78 - 40 * q^79 - 7 * q^80 - 33 * q^81 - 19 * q^82 + 24 * q^83 - q^84 + 5 * q^85 - 22 * q^86 - 6 * q^87 - 9 * q^88 - 4 * q^89 - 2 * q^90 - 8 * q^92 - 12 * q^93 + 2 * q^94 - 2 * q^95 + q^96 - 35 * q^97 + 7 * q^98 - 24 * 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
$3$	1.18572	0.684574	0.342287	−	0.939595i	$-0.388798\pi$
$3$	1.18572	0.684574	0.342287	+	0.939595i	$0.388798\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.18572	0.484067
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.59407	−0.531358
$10$	−1.00000	−0.316228
$11$	−0.587553	−0.177154	−0.0885770	−	0.996069i	$-0.528232\pi$
$11$	−0.587553	−0.177154	−0.0885770	+	0.996069i	$0.528232\pi$
$12$	1.18572	0.342287
$13$	−2.40667	−0.667490	−0.333745	−	0.942663i	$-0.608312\pi$
$13$	−2.40667	−0.667490	−0.333745	+	0.942663i	$0.608312\pi$
$14$	−1.00000	−0.267261
$15$	−1.18572	−0.306151
$16$	1.00000	0.250000
$17$	6.36761	1.54437	0.772186	−	0.635396i	$-0.219163\pi$
$17$	6.36761	1.54437	0.772186	+	0.635396i	$0.219163\pi$
$18$	−1.59407	−0.375727
$19$	−0.642216	−0.147334	−0.0736672	−	0.997283i	$-0.523470\pi$
$19$	−0.642216	−0.147334	−0.0736672	+	0.997283i	$0.523470\pi$
$20$	−1.00000	−0.223607
$21$	−1.18572	−0.258745
$22$	−0.587553	−0.125267
$23$	−1.33585	−0.278544	−0.139272	−	0.990254i	$-0.544476\pi$
$23$	−1.33585	−0.278544	−0.139272	+	0.990254i	$0.544476\pi$
$24$	1.18572	0.242034
$25$	1.00000	0.200000
$26$	−2.40667	−0.471987
$27$	−5.44727	−1.04833
$28$	−1.00000	−0.188982
$29$	−6.07993	−1.12901	−0.564507	−	0.825428i	$-0.690934\pi$
$29$	−6.07993	−1.12901	−0.564507	+	0.825428i	$0.690934\pi$
$30$	−1.18572	−0.216481
$31$	−3.09097	−0.555155	−0.277577	−	0.960703i	$-0.589531\pi$
$31$	−3.09097	−0.555155	−0.277577	+	0.960703i	$0.589531\pi$
$32$	1.00000	0.176777
$33$	−0.696672	−0.121275
$34$	6.36761	1.09204
$35$	1.00000	0.169031
$36$	−1.59407	−0.265679
$37$	−3.09931	−0.509524	−0.254762	−	0.967004i	$-0.581997\pi$
$37$	−3.09931	−0.509524	−0.254762	+	0.967004i	$0.581997\pi$
$38$	−0.642216	−0.104181
$39$	−2.85363	−0.456946
$40$	−1.00000	−0.158114
$41$	−4.99455	−0.780018	−0.390009	−	0.920811i	$-0.627528\pi$
$41$	−4.99455	−0.780018	−0.390009	+	0.920811i	$0.627528\pi$
$42$	−1.18572	−0.182960
$43$	−6.71968	−1.02474	−0.512371	−	0.858764i	$-0.671233\pi$
$43$	−6.71968	−1.02474	−0.512371	+	0.858764i	$0.671233\pi$
$44$	−0.587553	−0.0885770
$45$	1.59407	0.237630
$46$	−1.33585	−0.196960
$47$	−8.98806	−1.31104	−0.655522	−	0.755176i	$-0.727551\pi$
$47$	−8.98806	−1.31104	−0.655522	+	0.755176i	$0.727551\pi$
$48$	1.18572	0.171144
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	7.55019	1.05724
$52$	−2.40667	−0.333745
$53$	−0.800800	−0.109998	−0.0549991	−	0.998486i	$-0.517516\pi$
$53$	−0.800800	−0.109998	−0.0549991	+	0.998486i	$0.517516\pi$
$54$	−5.44727	−0.741280
$55$	0.587553	0.0792257
$56$	−1.00000	−0.133631
$57$	−0.761487	−0.100861
$58$	−6.07993	−0.798334
$59$	8.29714	1.08020	0.540098	−	0.841602i	$-0.318387\pi$
$59$	8.29714	1.08020	0.540098	+	0.841602i	$0.318387\pi$
$60$	−1.18572	−0.153075
$61$	−12.4108	−1.58904	−0.794520	−	0.607239i	$-0.792277\pi$
$61$	−12.4108	−1.58904	−0.794520	+	0.607239i	$0.792277\pi$
$62$	−3.09097	−0.392554
$63$	1.59407	0.200834
$64$	1.00000	0.125000
$65$	2.40667	0.298511
$66$	−0.696672	−0.0857544
$67$	7.30117	0.891980	0.445990	−	0.895038i	$-0.352852\pi$
$67$	7.30117	0.891980	0.445990	+	0.895038i	$0.352852\pi$
$68$	6.36761	0.772186
$69$	−1.58394	−0.190684
$70$	1.00000	0.119523
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−1.59407	−0.187863
$73$	11.7771	1.37841	0.689203	−	0.724569i	$-0.257961\pi$
$73$	11.7771	1.37841	0.689203	+	0.724569i	$0.257961\pi$
$74$	−3.09931	−0.360288
$75$	1.18572	0.136915
$76$	−0.642216	−0.0736672
$77$	0.587553	0.0669579
$78$	−2.85363	−0.323110
$79$	12.4497	1.40070	0.700348	−	0.713801i	$-0.253028\pi$
$79$	12.4497	1.40070	0.700348	+	0.713801i	$0.253028\pi$
$80$	−1.00000	−0.111803
$81$	−1.67671	−0.186301
$82$	−4.99455	−0.551556
$83$	−10.4117	−1.14284	−0.571418	−	0.820659i	$-0.693606\pi$
$83$	−10.4117	−1.14284	−0.571418	+	0.820659i	$0.693606\pi$
$84$	−1.18572	−0.129372
$85$	−6.36761	−0.690664
$86$	−6.71968	−0.724602
$87$	−7.20908	−0.772894
$88$	−0.587553	−0.0626334
$89$	1.30582	0.138416	0.0692081	−	0.997602i	$-0.477953\pi$
$89$	1.30582	0.138416	0.0692081	+	0.997602i	$0.477953\pi$
$90$	1.59407	0.168030
$91$	2.40667	0.252287
$92$	−1.33585	−0.139272
$93$	−3.66502	−0.380045
$94$	−8.98806	−0.927048
$95$	0.642216	0.0658900
$96$	1.18572	0.121017
$97$	−6.78780	−0.689197	−0.344598	−	0.938750i	$-0.611985\pi$
$97$	−6.78780	−0.689197	−0.344598	+	0.938750i	$0.611985\pi$
$98$	1.00000	0.101015
$99$	0.936603	0.0941322
$100$	1.00000	0.100000
$101$	−12.8613	−1.27975	−0.639876	−	0.768478i	$-0.721014\pi$
$101$	−12.8613	−1.27975	−0.639876	+	0.768478i	$0.721014\pi$
$102$	7.55019	0.747580
$103$	−10.8539	−1.06947	−0.534733	−	0.845021i	$-0.679588\pi$
$103$	−10.8539	−1.06947	−0.534733	+	0.845021i	$0.679588\pi$
$104$	−2.40667	−0.235993
$105$	1.18572	0.115714
$106$	−0.800800	−0.0777805
$107$	−4.44072	−0.429300	−0.214650	−	0.976691i	$-0.568861\pi$
$107$	−4.44072	−0.429300	−0.214650	+	0.976691i	$0.568861\pi$
$108$	−5.44727	−0.524164
$109$	0.688375	0.0659344	0.0329672	−	0.999456i	$-0.489504\pi$
$109$	0.688375	0.0659344	0.0329672	+	0.999456i	$0.489504\pi$
$110$	0.587553	0.0560210
$111$	−3.67491	−0.348807
$112$	−1.00000	−0.0944911
$113$	−1.09154	−0.102683	−0.0513416	−	0.998681i	$-0.516350\pi$
$113$	−1.09154	−0.102683	−0.0513416	+	0.998681i	$0.516350\pi$
$114$	−0.761487	−0.0713198
$115$	1.33585	0.124568
$116$	−6.07993	−0.564507
$117$	3.83641	0.354676
$118$	8.29714	0.763814
$119$	−6.36761	−0.583718
$120$	−1.18572	−0.108241
$121$	−10.6548	−0.968616
$122$	−12.4108	−1.12362
$123$	−5.92213	−0.533980
$124$	−3.09097	−0.277577
$125$	−1.00000	−0.0894427
$126$	1.59407	0.142011
$127$	−9.17343	−0.814010	−0.407005	−	0.913426i	$-0.633427\pi$
$127$	−9.17343	−0.814010	−0.407005	+	0.913426i	$0.633427\pi$
$128$	1.00000	0.0883883
$129$	−7.96764	−0.701512
$130$	2.40667	0.211079
$131$	4.47439	0.390929	0.195465	−	0.980711i	$-0.437379\pi$
$131$	4.47439	0.390929	0.195465	+	0.980711i	$0.437379\pi$
$132$	−0.696672	−0.0606375
$133$	0.642216	0.0556872
$134$	7.30117	0.630725
$135$	5.44727	0.468827
$136$	6.36761	0.546018
$137$	−11.9519	−1.02112	−0.510560	−	0.859842i	$-0.670562\pi$
$137$	−11.9519	−1.02112	−0.510560	+	0.859842i	$0.670562\pi$
$138$	−1.58394	−0.134834
$139$	12.2070	1.03538	0.517692	−	0.855567i	$-0.326791\pi$
$139$	12.2070	1.03538	0.517692	+	0.855567i	$0.326791\pi$
$140$	1.00000	0.0845154
$141$	−10.6573	−0.897507
$142$	1.00000	0.0839181
$143$	1.41405	0.118248
$144$	−1.59407	−0.132839
$145$	6.07993	0.504911
$146$	11.7771	0.974680
$147$	1.18572	0.0977963
$148$	−3.09931	−0.254762
$149$	−6.77100	−0.554702	−0.277351	−	0.960769i	$-0.589456\pi$
$149$	−6.77100	−0.554702	−0.277351	+	0.960769i	$0.589456\pi$
$150$	1.18572	0.0968134
$151$	−0.0544337	−0.00442975	−0.00221487	−	0.999998i	$-0.500705\pi$
$151$	−0.0544337	−0.00442975	−0.00221487	+	0.999998i	$0.500705\pi$
$152$	−0.642216	−0.0520906
$153$	−10.1504	−0.820615
$154$	0.587553	0.0473464
$155$	3.09097	0.248273
$156$	−2.85363	−0.228473
$157$	−4.07072	−0.324879	−0.162439	−	0.986719i	$-0.551936\pi$
$157$	−4.07072	−0.324879	−0.162439	+	0.986719i	$0.551936\pi$
$158$	12.4497	0.990442
$159$	−0.949522	−0.0753020
$160$	−1.00000	−0.0790569
$161$	1.33585	0.105280
$162$	−1.67671	−0.131735
$163$	−1.54206	−0.120783	−0.0603917	−	0.998175i	$-0.519235\pi$
$163$	−1.54206	−0.120783	−0.0603917	+	0.998175i	$0.519235\pi$
$164$	−4.99455	−0.390009
$165$	0.696672	0.0542358
$166$	−10.4117	−0.808107
$167$	−15.4028	−1.19190	−0.595951	−	0.803021i	$-0.703225\pi$
$167$	−15.4028	−1.19190	−0.595951	+	0.803021i	$0.703225\pi$
$168$	−1.18572	−0.0914801
$169$	−7.20794	−0.554457
$170$	−6.36761	−0.488373
$171$	1.02374	0.0782873
$172$	−6.71968	−0.512371
$173$	10.6566	0.810203	0.405101	−	0.914272i	$-0.367236\pi$
$173$	10.6566	0.810203	0.405101	+	0.914272i	$0.367236\pi$
$174$	−7.20908	−0.546519
$175$	−1.00000	−0.0755929
$176$	−0.587553	−0.0442885
$177$	9.83807	0.739475
$178$	1.30582	0.0978750
$179$	14.1406	1.05692	0.528461	−	0.848958i	$-0.322769\pi$
$179$	14.1406	1.05692	0.528461	+	0.848958i	$0.322769\pi$
$180$	1.59407	0.118815
$181$	22.3405	1.66056	0.830280	−	0.557347i	$-0.188181\pi$
$181$	22.3405	1.66056	0.830280	+	0.557347i	$0.188181\pi$
$182$	2.40667	0.178394
$183$	−14.7157	−1.08782
$184$	−1.33585	−0.0984800
$185$	3.09931	0.227866
$186$	−3.66502	−0.268732
$187$	−3.74131	−0.273592
$188$	−8.98806	−0.655522
$189$	5.44727	0.396231
$190$	0.642216	0.0465912
$191$	−26.4530	−1.91407	−0.957035	−	0.289973i	$-0.906354\pi$
$191$	−26.4530	−1.91407	−0.957035	+	0.289973i	$0.906354\pi$
$192$	1.18572	0.0855718
$193$	−15.9184	−1.14584	−0.572918	−	0.819613i	$-0.694188\pi$
$193$	−15.9184	−1.14584	−0.572918	+	0.819613i	$0.694188\pi$
$194$	−6.78780	−0.487336
$195$	2.85363	0.204353
$196$	1.00000	0.0714286
$197$	14.8456	1.05771	0.528853	−	0.848714i	$-0.322622\pi$
$197$	14.8456	1.05771	0.528853	+	0.848714i	$0.322622\pi$
$198$	0.936603	0.0665615
$199$	−9.97284	−0.706956	−0.353478	−	0.935443i	$-0.615001\pi$
$199$	−9.97284	−0.706956	−0.353478	+	0.935443i	$0.615001\pi$
$200$	1.00000	0.0707107
$201$	8.65713	0.610627
$202$	−12.8613	−0.904921
$203$	6.07993	0.426727
$204$	7.55019	0.528619
$205$	4.99455	0.348835
$206$	−10.8539	−0.756227
$207$	2.12944	0.148006
$208$	−2.40667	−0.166872
$209$	0.377336	0.0261009
$210$	1.18572	0.0818223
$211$	−8.11696	−0.558795	−0.279397	−	0.960176i	$-0.590135\pi$
$211$	−8.11696	−0.558795	−0.279397	+	0.960176i	$0.590135\pi$
$212$	−0.800800	−0.0549991
$213$	1.18572	0.0812440
$214$	−4.44072	−0.303561
$215$	6.71968	0.458278
$216$	−5.44727	−0.370640
$217$	3.09097	0.209829
$218$	0.688375	0.0466226
$219$	13.9643	0.943621
$220$	0.587553	0.0396128
$221$	−15.3247	−1.03085
$222$	−3.67491	−0.246644
$223$	13.6343	0.913023	0.456512	−	0.889717i	$-0.349099\pi$
$223$	13.6343	0.913023	0.456512	+	0.889717i	$0.349099\pi$
$224$	−1.00000	−0.0668153
$225$	−1.59407	−0.106272
$226$	−1.09154	−0.0726080
$227$	−0.303911	−0.0201712	−0.0100856	−	0.999949i	$-0.503210\pi$
$227$	−0.303911	−0.0201712	−0.0100856	+	0.999949i	$0.503210\pi$
$228$	−0.761487	−0.0504307
$229$	−14.1709	−0.936442	−0.468221	−	0.883612i	$-0.655105\pi$
$229$	−14.1709	−0.936442	−0.468221	+	0.883612i	$0.655105\pi$
$230$	1.33585	0.0880832
$231$	0.696672	0.0458377
$232$	−6.07993	−0.399167
$233$	14.9531	0.979610	0.489805	−	0.871832i	$-0.337068\pi$
$233$	14.9531	0.979610	0.489805	+	0.871832i	$0.337068\pi$
$234$	3.83641	0.250794
$235$	8.98806	0.586317
$236$	8.29714	0.540098
$237$	14.7618	0.958881
$238$	−6.36761	−0.412751
$239$	−22.0210	−1.42442	−0.712209	−	0.701968i	$-0.752305\pi$
$239$	−22.0210	−1.42442	−0.712209	+	0.701968i	$0.752305\pi$
$240$	−1.18572	−0.0765377
$241$	25.6816	1.65429	0.827147	−	0.561985i	$-0.189962\pi$
$241$	25.6816	1.65429	0.827147	+	0.561985i	$0.189962\pi$
$242$	−10.6548	−0.684915
$243$	14.3537	0.920792
$244$	−12.4108	−0.794520
$245$	−1.00000	−0.0638877
$246$	−5.92213	−0.377581
$247$	1.54560	0.0983443
$248$	−3.09097	−0.196277
$249$	−12.3454	−0.782356
$250$	−1.00000	−0.0632456
$251$	28.1618	1.77756	0.888778	−	0.458339i	$-0.151555\pi$
$251$	28.1618	1.77756	0.888778	+	0.458339i	$0.151555\pi$
$252$	1.59407	0.100417
$253$	0.784882	0.0493451
$254$	−9.17343	−0.575592
$255$	−7.55019	−0.472811
$256$	1.00000	0.0625000
$257$	−24.2265	−1.51121	−0.755603	−	0.655030i	$-0.772656\pi$
$257$	−24.2265	−1.51121	−0.755603	+	0.655030i	$0.772656\pi$
$258$	−7.96764	−0.496044
$259$	3.09931	0.192582
$260$	2.40667	0.149255
$261$	9.69186	0.599911
$262$	4.47439	0.276429
$263$	14.2993	0.881730	0.440865	−	0.897573i	$-0.354672\pi$
$263$	14.2993	0.881730	0.440865	+	0.897573i	$0.354672\pi$
$264$	−0.696672	−0.0428772
$265$	0.800800	0.0491927
$266$	0.642216	0.0393768
$267$	1.54833	0.0947562
$268$	7.30117	0.445990
$269$	7.74806	0.472408	0.236204	−	0.971704i	$-0.424097\pi$
$269$	7.74806	0.472408	0.236204	+	0.971704i	$0.424097\pi$
$270$	5.44727	0.331511
$271$	2.12146	0.128870	0.0644349	−	0.997922i	$-0.479476\pi$
$271$	2.12146	0.128870	0.0644349	+	0.997922i	$0.479476\pi$
$272$	6.36761	0.386093
$273$	2.85363	0.172710
$274$	−11.9519	−0.722041
$275$	−0.587553	−0.0354308
$276$	−1.58394	−0.0953419
$277$	4.84124	0.290882	0.145441	−	0.989367i	$-0.453540\pi$
$277$	4.84124	0.290882	0.145441	+	0.989367i	$0.453540\pi$
$278$	12.2070	0.732127
$279$	4.92724	0.294986
$280$	1.00000	0.0597614
$281$	−12.6204	−0.752870	−0.376435	−	0.926443i	$-0.622850\pi$
$281$	−12.6204	−0.752870	−0.376435	+	0.926443i	$0.622850\pi$
$282$	−10.6573	−0.634633
$283$	20.1096	1.19539	0.597695	−	0.801723i	$-0.296083\pi$
$283$	20.1096	1.19539	0.597695	+	0.801723i	$0.296083\pi$
$284$	1.00000	0.0593391
$285$	0.761487	0.0451066
$286$	1.41405	0.0836143
$287$	4.99455	0.294819
$288$	−1.59407	−0.0939317
$289$	23.5465	1.38509
$290$	6.07993	0.357026
$291$	−8.04842	−0.471807
$292$	11.7771	0.689203
$293$	28.9524	1.69142	0.845710	−	0.533643i	$-0.179178\pi$
$293$	28.9524	1.69142	0.845710	+	0.533643i	$0.179178\pi$
$294$	1.18572	0.0691525
$295$	−8.29714	−0.483078
$296$	−3.09931	−0.180144
$297$	3.20056	0.185716
$298$	−6.77100	−0.392233
$299$	3.21494	0.185925
$300$	1.18572	0.0684574
$301$	6.71968	0.387316
$302$	−0.0544337	−0.00313231
$303$	−15.2499	−0.876085
$304$	−0.642216	−0.0368336
$305$	12.4108	0.710640
$306$	−10.1504	−0.580262
$307$	−31.5852	−1.80266	−0.901332	−	0.433128i	$-0.857410\pi$
$307$	−31.5852	−1.80266	−0.901332	+	0.433128i	$0.857410\pi$
$308$	0.587553	0.0334789
$309$	−12.8697	−0.732129
$310$	3.09097	0.175555
$311$	0.291418	0.0165248	0.00826241	−	0.999966i	$-0.497370\pi$
$311$	0.291418	0.0165248	0.00826241	+	0.999966i	$0.497370\pi$
$312$	−2.85363	−0.161555
$313$	16.6957	0.943698	0.471849	−	0.881679i	$-0.343587\pi$
$313$	16.6957	0.943698	0.471849	+	0.881679i	$0.343587\pi$
$314$	−4.07072	−0.229724
$315$	−1.59407	−0.0898159
$316$	12.4497	0.700348
$317$	15.0324	0.844302	0.422151	−	0.906526i	$-0.361275\pi$
$317$	15.0324	0.844302	0.422151	+	0.906526i	$0.361275\pi$
$318$	−0.949522	−0.0532466
$319$	3.57228	0.200009
$320$	−1.00000	−0.0559017
$321$	−5.26544	−0.293888
$322$	1.33585	0.0744439
$323$	−4.08938	−0.227539
$324$	−1.67671	−0.0931504
$325$	−2.40667	−0.133498
$326$	−1.54206	−0.0854068
$327$	0.816219	0.0451370
$328$	−4.99455	−0.275778
$329$	8.98806	0.495528
$330$	0.696672	0.0383505
$331$	17.6999	0.972873	0.486437	−	0.873716i	$-0.338296\pi$
$331$	17.6999	0.972873	0.486437	+	0.873716i	$0.338296\pi$
$332$	−10.4117	−0.571418
$333$	4.94053	0.270739
$334$	−15.4028	−0.842802
$335$	−7.30117	−0.398906
$336$	−1.18572	−0.0646862
$337$	8.34243	0.454441	0.227220	−	0.973843i	$-0.427036\pi$
$337$	8.34243	0.454441	0.227220	+	0.973843i	$0.427036\pi$
$338$	−7.20794	−0.392060
$339$	−1.29426	−0.0702943
$340$	−6.36761	−0.345332
$341$	1.81611	0.0983478
$342$	1.02374	0.0553575
$343$	−1.00000	−0.0539949
$344$	−6.71968	−0.362301
$345$	1.58394	0.0852764
$346$	10.6566	0.572900
$347$	−6.68900	−0.359084	−0.179542	−	0.983750i	$-0.557462\pi$
$347$	−6.68900	−0.359084	−0.179542	+	0.983750i	$0.557462\pi$
$348$	−7.20908	−0.386447
$349$	−8.37105	−0.448092	−0.224046	−	0.974579i	$-0.571927\pi$
$349$	−8.37105	−0.448092	−0.224046	+	0.974579i	$0.571927\pi$
$350$	−1.00000	−0.0534522
$351$	13.1098	0.699749
$352$	−0.587553	−0.0313167
$353$	−5.53523	−0.294611	−0.147305	−	0.989091i	$-0.547060\pi$
$353$	−5.53523	−0.294611	−0.147305	+	0.989091i	$0.547060\pi$
$354$	9.83807	0.522887
$355$	−1.00000	−0.0530745
$356$	1.30582	0.0692081
$357$	−7.55019	−0.399598
$358$	14.1406	0.747356
$359$	13.7069	0.723425	0.361713	−	0.932290i	$-0.382192\pi$
$359$	13.7069	0.723425	0.361713	+	0.932290i	$0.382192\pi$
$360$	1.59407	0.0840151
$361$	−18.5876	−0.978293
$362$	22.3405	1.17419
$363$	−12.6336	−0.663090
$364$	2.40667	0.126144
$365$	−11.7771	−0.616441
$366$	−14.7157	−0.769202
$367$	15.1571	0.791195	0.395598	−	0.918424i	$-0.370537\pi$
$367$	15.1571	0.791195	0.395598	+	0.918424i	$0.370537\pi$
$368$	−1.33585	−0.0696359
$369$	7.96169	0.414469
$370$	3.09931	0.161126
$371$	0.800800	0.0415754
$372$	−3.66502	−0.190022
$373$	−29.7469	−1.54023	−0.770117	−	0.637902i	$-0.779802\pi$
$373$	−29.7469	−1.54023	−0.770117	+	0.637902i	$0.779802\pi$
$374$	−3.74131	−0.193459
$375$	−1.18572	−0.0612302
$376$	−8.98806	−0.463524
$377$	14.6324	0.753606
$378$	5.44727	0.280178
$379$	−8.92535	−0.458464	−0.229232	−	0.973372i	$-0.573622\pi$
$379$	−8.92535	−0.458464	−0.229232	+	0.973372i	$0.573622\pi$
$380$	0.642216	0.0329450
$381$	−10.8771	−0.557251
$382$	−26.4530	−1.35345
$383$	9.98011	0.509960	0.254980	−	0.966946i	$-0.417931\pi$
$383$	9.98011	0.509960	0.254980	+	0.966946i	$0.417931\pi$
$384$	1.18572	0.0605084
$385$	−0.587553	−0.0299445
$386$	−15.9184	−0.810228
$387$	10.7117	0.544505
$388$	−6.78780	−0.344598
$389$	−33.9537	−1.72152	−0.860759	−	0.509012i	$-0.830011\pi$
$389$	−33.9537	−1.72152	−0.860759	+	0.509012i	$0.830011\pi$
$390$	2.85363	0.144499
$391$	−8.50616	−0.430175
$392$	1.00000	0.0505076
$393$	5.30536	0.267620
$394$	14.8456	0.747911
$395$	−12.4497	−0.626411
$396$	0.936603	0.0470661
$397$	13.3718	0.671111	0.335556	−	0.942020i	$-0.391076\pi$
$397$	13.3718	0.671111	0.335556	+	0.942020i	$0.391076\pi$
$398$	−9.97284	−0.499894
$399$	0.761487	0.0381220
$400$	1.00000	0.0500000
$401$	26.0594	1.30134	0.650672	−	0.759359i	$-0.274487\pi$
$401$	26.0594	1.30134	0.650672	+	0.759359i	$0.274487\pi$
$402$	8.65713	0.431778
$403$	7.43894	0.370560
$404$	−12.8613	−0.639876
$405$	1.67671	0.0833162
$406$	6.07993	0.301742
$407$	1.82101	0.0902641
$408$	7.55019	0.373790
$409$	27.8624	1.37771	0.688854	−	0.724900i	$-0.258114\pi$
$409$	27.8624	1.37771	0.688854	+	0.724900i	$0.258114\pi$
$410$	4.99455	0.246663
$411$	−14.1716	−0.699033
$412$	−10.8539	−0.534733
$413$	−8.29714	−0.408276
$414$	2.12944	0.104656
$415$	10.4117	0.511092
$416$	−2.40667	−0.117997
$417$	14.4741	0.708797
$418$	0.377336	0.0184561
$419$	−35.2732	−1.72321	−0.861605	−	0.507579i	$-0.830541\pi$
$419$	−35.2732	−1.72321	−0.861605	+	0.507579i	$0.830541\pi$
$420$	1.18572	0.0578571
$421$	24.1815	1.17853	0.589267	−	0.807939i	$-0.299417\pi$
$421$	24.1815	1.17853	0.589267	+	0.807939i	$0.299417\pi$
$422$	−8.11696	−0.395128
$423$	14.3276	0.696634
$424$	−0.800800	−0.0388903
$425$	6.36761	0.308875
$426$	1.18572	0.0574482
$427$	12.4108	0.600600
$428$	−4.44072	−0.214650
$429$	1.67666	0.0809499
$430$	6.71968	0.324052
$431$	−25.7289	−1.23932	−0.619658	−	0.784872i	$-0.712729\pi$
$431$	−25.7289	−1.23932	−0.619658	+	0.784872i	$0.712729\pi$
$432$	−5.44727	−0.262082
$433$	6.40226	0.307673	0.153836	−	0.988096i	$-0.450837\pi$
$433$	6.40226	0.307673	0.153836	+	0.988096i	$0.450837\pi$
$434$	3.09097	0.148371
$435$	7.20908	0.345649
$436$	0.688375	0.0329672
$437$	0.857903	0.0410391
$438$	13.9643	0.667241
$439$	16.1086	0.768820	0.384410	−	0.923163i	$-0.374405\pi$
$439$	16.1086	0.768820	0.384410	+	0.923163i	$0.374405\pi$
$440$	0.587553	0.0280105
$441$	−1.59407	−0.0759083
$442$	−15.3247	−0.728923
$443$	32.7017	1.55371	0.776854	−	0.629681i	$-0.216815\pi$
$443$	32.7017	1.55371	0.776854	+	0.629681i	$0.216815\pi$
$444$	−3.67491	−0.174403
$445$	−1.30582	−0.0619016
$446$	13.6343	0.645605
$447$	−8.02849	−0.379735
$448$	−1.00000	−0.0472456
$449$	15.1026	0.712737	0.356369	−	0.934345i	$-0.384015\pi$
$449$	15.1026	0.712737	0.356369	+	0.934345i	$0.384015\pi$
$450$	−1.59407	−0.0751454
$451$	2.93456	0.138183
$452$	−1.09154	−0.0513416
$453$	−0.0645429	−0.00303249
$454$	−0.303911	−0.0142632
$455$	−2.40667	−0.112826
$456$	−0.761487	−0.0356599
$457$	−28.7792	−1.34624	−0.673118	−	0.739535i	$-0.735045\pi$
$457$	−28.7792	−1.34624	−0.673118	+	0.739535i	$0.735045\pi$
$458$	−14.1709	−0.662164
$459$	−34.6861	−1.61901
$460$	1.33585	0.0622842
$461$	11.6725	0.543641	0.271820	−	0.962348i	$-0.412374\pi$
$461$	11.6725	0.543641	0.271820	+	0.962348i	$0.412374\pi$
$462$	0.696672	0.0324121
$463$	−15.4221	−0.716724	−0.358362	−	0.933583i	$-0.616665\pi$
$463$	−15.4221	−0.716724	−0.358362	+	0.933583i	$0.616665\pi$
$464$	−6.07993	−0.282254
$465$	3.66502	0.169961
$466$	14.9531	0.692689
$467$	−27.0357	−1.25106	−0.625532	−	0.780199i	$-0.715118\pi$
$467$	−27.0357	−1.25106	−0.625532	+	0.780199i	$0.715118\pi$
$468$	3.83641	0.177338
$469$	−7.30117	−0.337137
$470$	8.98806	0.414588
$471$	−4.82673	−0.222404
$472$	8.29714	0.381907
$473$	3.94817	0.181537
$474$	14.7618	0.678031
$475$	−0.642216	−0.0294669
$476$	−6.36761	−0.291859
$477$	1.27653	0.0584485
$478$	−22.0210	−1.00722
$479$	−9.41754	−0.430298	−0.215149	−	0.976581i	$-0.569024\pi$
$479$	−9.41754	−0.430298	−0.215149	+	0.976581i	$0.569024\pi$
$480$	−1.18572	−0.0541204
$481$	7.45902	0.340102
$482$	25.6816	1.16976
$483$	1.58394	0.0720717
$484$	−10.6548	−0.484308
$485$	6.78780	0.308218
$486$	14.3537	0.651098
$487$	−37.4134	−1.69536	−0.847682	−	0.530505i	$-0.822002\pi$
$487$	−37.4134	−1.69536	−0.847682	+	0.530505i	$0.822002\pi$
$488$	−12.4108	−0.561810
$489$	−1.82845	−0.0826853
$490$	−1.00000	−0.0451754
$491$	−1.69391	−0.0764450	−0.0382225	−	0.999269i	$-0.512170\pi$
$491$	−1.69391	−0.0764450	−0.0382225	+	0.999269i	$0.512170\pi$
$492$	−5.92213	−0.266990
$493$	−38.7146	−1.74362
$494$	1.54560	0.0695399
$495$	−0.936603	−0.0420972
$496$	−3.09097	−0.138789
$497$	−1.00000	−0.0448561
$498$	−12.3454	−0.553209
$499$	1.42444	0.0637668	0.0318834	−	0.999492i	$-0.489849\pi$
$499$	1.42444	0.0637668	0.0318834	+	0.999492i	$0.489849\pi$
$500$	−1.00000	−0.0447214
$501$	−18.2633	−0.815945
$502$	28.1618	1.25692
$503$	23.2754	1.03780	0.518900	−	0.854835i	$-0.326342\pi$
$503$	23.2754	1.03780	0.518900	+	0.854835i	$0.326342\pi$
$504$	1.59407	0.0710057
$505$	12.8613	0.572322
$506$	0.784882	0.0348923
$507$	−8.54659	−0.379567
$508$	−9.17343	−0.407005
$509$	39.5861	1.75462	0.877311	−	0.479923i	$-0.159335\pi$
$509$	39.5861	1.75462	0.877311	+	0.479923i	$0.159335\pi$
$510$	−7.55019	−0.334328
$511$	−11.7771	−0.520988
$512$	1.00000	0.0441942
$513$	3.49833	0.154455
$514$	−24.2265	−1.06858
$515$	10.8539	0.478280
$516$	−7.96764	−0.350756
$517$	5.28097	0.232257
$518$	3.09931	0.136176
$519$	12.6357	0.554644
$520$	2.40667	0.105539
$521$	−35.2223	−1.54312	−0.771558	−	0.636159i	$-0.780522\pi$
$521$	−35.2223	−1.54312	−0.771558	+	0.636159i	$0.780522\pi$
$522$	9.69186	0.424201
$523$	42.9944	1.88001	0.940006	−	0.341157i	$-0.110819\pi$
$523$	42.9944	1.88001	0.940006	+	0.341157i	$0.110819\pi$
$524$	4.47439	0.195465
$525$	−1.18572	−0.0517490
$526$	14.2993	0.623478
$527$	−19.6821	−0.857366
$528$	−0.696672	−0.0303188
$529$	−21.2155	−0.922413
$530$	0.800800	0.0347845
$531$	−13.2263	−0.573971
$532$	0.642216	0.0278436
$533$	12.0202	0.520654
$534$	1.54833	0.0670027
$535$	4.44072	0.191989
$536$	7.30117	0.315363
$537$	16.7668	0.723541
$538$	7.74806	0.334043
$539$	−0.587553	−0.0253077
$540$	5.44727	0.234413
$541$	4.53498	0.194974	0.0974870	−	0.995237i	$-0.468920\pi$
$541$	4.53498	0.194974	0.0974870	+	0.995237i	$0.468920\pi$
$542$	2.12146	0.0911247
$543$	26.4896	1.13678
$544$	6.36761	0.273009
$545$	−0.688375	−0.0294868
$546$	2.85363	0.122124
$547$	−31.1603	−1.33232	−0.666159	−	0.745809i	$-0.732063\pi$
$547$	−31.1603	−1.33232	−0.666159	+	0.745809i	$0.732063\pi$
$548$	−11.9519	−0.510560
$549$	19.7837	0.844349
$550$	−0.587553	−0.0250534
$551$	3.90463	0.166343
$552$	−1.58394	−0.0674169
$553$	−12.4497	−0.529414
$554$	4.84124	0.205685
$555$	3.67491	0.155991
$556$	12.2070	0.517692
$557$	33.1050	1.40270	0.701351	−	0.712816i	$-0.252580\pi$
$557$	33.1050	1.40270	0.701351	+	0.712816i	$0.252580\pi$
$558$	4.92724	0.208586
$559$	16.1720	0.684005
$560$	1.00000	0.0422577
$561$	−4.43614	−0.187294
$562$	−12.6204	−0.532359
$563$	32.8714	1.38537	0.692683	−	0.721243i	$-0.256429\pi$
$563$	32.8714	1.38537	0.692683	+	0.721243i	$0.256429\pi$
$564$	−10.6573	−0.448754
$565$	1.09154	0.0459213
$566$	20.1096	0.845269
$567$	1.67671	0.0704151
$568$	1.00000	0.0419591
$569$	12.9504	0.542910	0.271455	−	0.962451i	$-0.412495\pi$
$569$	12.9504	0.542910	0.271455	+	0.962451i	$0.412495\pi$
$570$	0.761487	0.0318952
$571$	−6.54989	−0.274104	−0.137052	−	0.990564i	$-0.543763\pi$
$571$	−6.54989	−0.274104	−0.137052	+	0.990564i	$0.543763\pi$
$572$	1.41405	0.0591242
$573$	−31.3657	−1.31032
$574$	4.99455	0.208469
$575$	−1.33585	−0.0557087
$576$	−1.59407	−0.0664197
$577$	16.4287	0.683937	0.341968	−	0.939711i	$-0.388906\pi$
$577$	16.4287	0.683937	0.341968	+	0.939711i	$0.388906\pi$
$578$	23.5465	0.979404
$579$	−18.8748	−0.784409
$580$	6.07993	0.252455
$581$	10.4117	0.431951
$582$	−8.04842	−0.333618
$583$	0.470512	0.0194866
$584$	11.7771	0.487340
$585$	−3.83641	−0.158616
$586$	28.9524	1.19601
$587$	42.0592	1.73597	0.867984	−	0.496592i	$-0.165416\pi$
$587$	42.0592	1.73597	0.867984	+	0.496592i	$0.165416\pi$
$588$	1.18572	0.0488982
$589$	1.98507	0.0817934
$590$	−8.29714	−0.341588
$591$	17.6027	0.724078
$592$	−3.09931	−0.127381
$593$	−32.0851	−1.31758	−0.658789	−	0.752327i	$-0.728931\pi$
$593$	−32.0851	−1.31758	−0.658789	+	0.752327i	$0.728931\pi$
$594$	3.20056	0.131321
$595$	6.36761	0.261047
$596$	−6.77100	−0.277351
$597$	−11.8250	−0.483964
$598$	3.21494	0.131469
$599$	24.5985	1.00507	0.502534	−	0.864557i	$-0.332401\pi$
$599$	24.5985	1.00507	0.502534	+	0.864557i	$0.332401\pi$
$600$	1.18572	0.0484067
$601$	−10.9248	−0.445632	−0.222816	−	0.974861i	$-0.571525\pi$
$601$	−10.9248	−0.445632	−0.222816	+	0.974861i	$0.571525\pi$
$602$	6.71968	0.273874
$603$	−11.6386	−0.473961
$604$	−0.0544337	−0.00221487
$605$	10.6548	0.433178
$606$	−15.2499	−0.619486
$607$	−11.9260	−0.484061	−0.242031	−	0.970269i	$-0.577813\pi$
$607$	−11.9260	−0.484061	−0.242031	+	0.970269i	$0.577813\pi$
$608$	−0.642216	−0.0260453
$609$	7.20908	0.292127
$610$	12.4108	0.502498
$611$	21.6313	0.875109
$612$	−10.1504	−0.410307
$613$	18.2266	0.736164	0.368082	−	0.929793i	$-0.380015\pi$
$613$	18.2266	0.736164	0.368082	+	0.929793i	$0.380015\pi$
$614$	−31.5852	−1.27468
$615$	5.92213	0.238803
$616$	0.587553	0.0236732
$617$	−2.93421	−0.118127	−0.0590633	−	0.998254i	$-0.518811\pi$
$617$	−2.93421	−0.118127	−0.0590633	+	0.998254i	$0.518811\pi$
$618$	−12.8697	−0.517693
$619$	40.2560	1.61802	0.809012	−	0.587792i	$-0.200003\pi$
$619$	40.2560	1.61802	0.809012	+	0.587792i	$0.200003\pi$
$620$	3.09097	0.124136
$621$	7.27673	0.292005
$622$	0.291418	0.0116848
$623$	−1.30582	−0.0523164
$624$	−2.85363	−0.114237
$625$	1.00000	0.0400000
$626$	16.6957	0.667295
$627$	0.447414	0.0178680
$628$	−4.07072	−0.162439
$629$	−19.7352	−0.786895
$630$	−1.59407	−0.0635094
$631$	−4.62962	−0.184302	−0.0921511	−	0.995745i	$-0.529374\pi$
$631$	−4.62962	−0.184302	−0.0921511	+	0.995745i	$0.529374\pi$
$632$	12.4497	0.495221
$633$	−9.62442	−0.382537
$634$	15.0324	0.597011
$635$	9.17343	0.364037
$636$	−0.949522	−0.0376510
$637$	−2.40667	−0.0953557
$638$	3.57228	0.141428
$639$	−1.59407	−0.0630606
$640$	−1.00000	−0.0395285
$641$	−14.8071	−0.584846	−0.292423	−	0.956289i	$-0.594462\pi$
$641$	−14.8071	−0.584846	−0.292423	+	0.956289i	$0.594462\pi$
$642$	−5.26544	−0.207810
$643$	17.9957	0.709679	0.354840	−	0.934927i	$-0.384535\pi$
$643$	17.9957	0.709679	0.354840	+	0.934927i	$0.384535\pi$
$644$	1.33585	0.0526398
$645$	7.96764	0.313726
$646$	−4.08938	−0.160895
$647$	28.9294	1.13733	0.568665	−	0.822569i	$-0.307460\pi$
$647$	28.9294	1.13733	0.568665	+	0.822569i	$0.307460\pi$
$648$	−1.67671	−0.0658673
$649$	−4.87501	−0.191361
$650$	−2.40667	−0.0943973
$651$	3.66502	0.143643
$652$	−1.54206	−0.0603917
$653$	−39.6035	−1.54981	−0.774903	−	0.632080i	$-0.782201\pi$
$653$	−39.6035	−1.54981	−0.774903	+	0.632080i	$0.782201\pi$
$654$	0.816219	0.0319167
$655$	−4.47439	−0.174829
$656$	−4.99455	−0.195005
$657$	−18.7736	−0.732426
$658$	8.98806	0.350391
$659$	43.3941	1.69039	0.845197	−	0.534454i	$-0.179483\pi$
$659$	43.3941	1.69039	0.845197	+	0.534454i	$0.179483\pi$
$660$	0.696672	0.0271179
$661$	−37.3071	−1.45108	−0.725540	−	0.688180i	$-0.758410\pi$
$661$	−37.3071	−1.45108	−0.725540	+	0.688180i	$0.758410\pi$
$662$	17.6999	0.687925
$663$	−18.1708	−0.705696
$664$	−10.4117	−0.404054
$665$	−0.642216	−0.0249041
$666$	4.94053	0.191442
$667$	8.12186	0.314480
$668$	−15.4028	−0.595951
$669$	16.1665	0.625032
$670$	−7.30117	−0.282069
$671$	7.29200	0.281505
$672$	−1.18572	−0.0457400
$673$	−7.81144	−0.301109	−0.150555	−	0.988602i	$-0.548106\pi$
$673$	−7.81144	−0.301109	−0.150555	+	0.988602i	$0.548106\pi$
$674$	8.34243	0.321338
$675$	−5.44727	−0.209666
$676$	−7.20794	−0.277229
$677$	31.9336	1.22731	0.613653	−	0.789576i	$-0.289699\pi$
$677$	31.9336	1.22731	0.613653	+	0.789576i	$0.289699\pi$
$678$	−1.29426	−0.0497056
$679$	6.78780	0.260492
$680$	−6.36761	−0.244187
$681$	−0.360352	−0.0138087
$682$	1.81611	0.0695424
$683$	13.2801	0.508150	0.254075	−	0.967185i	$-0.418229\pi$
$683$	13.2801	0.508150	0.254075	+	0.967185i	$0.418229\pi$
$684$	1.02374	0.0391437
$685$	11.9519	0.456659
$686$	−1.00000	−0.0381802
$687$	−16.8027	−0.641064
$688$	−6.71968	−0.256185
$689$	1.92726	0.0734228
$690$	1.58394	0.0602995
$691$	−18.6471	−0.709369	−0.354685	−	0.934986i	$-0.615412\pi$
$691$	−18.6471	−0.709369	−0.354685	+	0.934986i	$0.615412\pi$
$692$	10.6566	0.405101
$693$	−0.936603	−0.0355786
$694$	−6.68900	−0.253911
$695$	−12.2070	−0.463038
$696$	−7.20908	−0.273259
$697$	−31.8034	−1.20464
$698$	−8.37105	−0.316849
$699$	17.7302	0.670616
$700$	−1.00000	−0.0377964
$701$	−38.3114	−1.44700	−0.723501	−	0.690323i	$-0.757468\pi$
$701$	−38.3114	−1.44700	−0.723501	+	0.690323i	$0.757468\pi$
$702$	13.1098	0.494797
$703$	1.99043	0.0750704
$704$	−0.587553	−0.0221442
$705$	10.6573	0.401377
$706$	−5.53523	−0.208321
$707$	12.8613	0.483701
$708$	9.83807	0.369737
$709$	27.4573	1.03118	0.515589	−	0.856836i	$-0.327573\pi$
$709$	27.4573	1.03118	0.515589	+	0.856836i	$0.327573\pi$
$710$	−1.00000	−0.0375293
$711$	−19.8457	−0.744271
$712$	1.30582	0.0489375
$713$	4.12907	0.154635
$714$	−7.55019	−0.282559
$715$	−1.41405	−0.0528823
$716$	14.1406	0.528461
$717$	−26.1106	−0.975120
$718$	13.7069	0.511539
$719$	−18.9742	−0.707619	−0.353809	−	0.935318i	$-0.615114\pi$
$719$	−18.9742	−0.707619	−0.353809	+	0.935318i	$0.615114\pi$
$720$	1.59407	0.0594076
$721$	10.8539	0.404220
$722$	−18.5876	−0.691757
$723$	30.4511	1.13249
$724$	22.3405	0.830280
$725$	−6.07993	−0.225803
$726$	−12.6336	−0.468875
$727$	−25.5340	−0.947002	−0.473501	−	0.880793i	$-0.657010\pi$
$727$	−25.5340	−0.947002	−0.473501	+	0.880793i	$0.657010\pi$
$728$	2.40667	0.0891971
$729$	22.0496	0.816651
$730$	−11.7771	−0.435890
$731$	−42.7883	−1.58258
$732$	−14.7157	−0.543908
$733$	−54.1131	−1.99871	−0.999357	−	0.0358530i	$-0.988585\pi$
$733$	−54.1131	−1.99871	−0.999357	+	0.0358530i	$0.988585\pi$
$734$	15.1571	0.559460
$735$	−1.18572	−0.0437359
$736$	−1.33585	−0.0492400
$737$	−4.28983	−0.158018
$738$	7.96169	0.293074
$739$	−30.9775	−1.13952	−0.569762	−	0.821809i	$-0.692965\pi$
$739$	−30.9775	−1.13952	−0.569762	+	0.821809i	$0.692965\pi$
$740$	3.09931	0.113933
$741$	1.83265	0.0673240
$742$	0.800800	0.0293983
$743$	52.9102	1.94109	0.970544	−	0.240925i	$-0.0774509\pi$
$743$	52.9102	1.94109	0.970544	+	0.240925i	$0.0774509\pi$
$744$	−3.66502	−0.134366
$745$	6.77100	0.248070
$746$	−29.7469	−1.08911
$747$	16.5971	0.607255
$748$	−3.74131	−0.136796
$749$	4.44072	0.162260
$750$	−1.18572	−0.0432963
$751$	−15.7213	−0.573679	−0.286840	−	0.957979i	$-0.592605\pi$
$751$	−15.7213	−0.573679	−0.286840	+	0.957979i	$0.592605\pi$
$752$	−8.98806	−0.327761
$753$	33.3919	1.21687
$754$	14.6324	0.532880
$755$	0.0544337	0.00198104
$756$	5.44727	0.198115
$757$	0.986916	0.0358701	0.0179350	−	0.999839i	$-0.494291\pi$
$757$	0.986916	0.0358701	0.0179350	+	0.999839i	$0.494291\pi$
$758$	−8.92535	−0.324183
$759$	0.930648	0.0337804
$760$	0.642216	0.0232956
$761$	−27.0377	−0.980116	−0.490058	−	0.871690i	$-0.663024\pi$
$761$	−27.0377	−0.980116	−0.490058	+	0.871690i	$0.663024\pi$
$762$	−10.8771	−0.394036
$763$	−0.688375	−0.0249209
$764$	−26.4530	−0.957035
$765$	10.1504	0.366990
$766$	9.98011	0.360596
$767$	−19.9685	−0.721020
$768$	1.18572	0.0427859
$769$	−11.1720	−0.402872	−0.201436	−	0.979502i	$-0.564561\pi$
$769$	−11.1720	−0.402872	−0.201436	+	0.979502i	$0.564561\pi$
$770$	−0.587553	−0.0211739
$771$	−28.7258	−1.03453
$772$	−15.9184	−0.572918
$773$	49.6702	1.78651	0.893257	−	0.449547i	$-0.148414\pi$
$773$	49.6702	1.78651	0.893257	+	0.449547i	$0.148414\pi$
$774$	10.7117	0.385023
$775$	−3.09097	−0.111031
$776$	−6.78780	−0.243668
$777$	3.67491	0.131837
$778$	−33.9537	−1.21730
$779$	3.20758	0.114924
$780$	2.85363	0.102176
$781$	−0.587553	−0.0210243
$782$	−8.50616	−0.304180
$783$	33.1190	1.18358
$784$	1.00000	0.0357143
$785$	4.07072	0.145290
$786$	5.30536	0.189236
$787$	−8.90408	−0.317396	−0.158698	−	0.987327i	$-0.550730\pi$
$787$	−8.90408	−0.317396	−0.158698	+	0.987327i	$0.550730\pi$
$788$	14.8456	0.528853
$789$	16.9549	0.603610
$790$	−12.4497	−0.442939
$791$	1.09154	0.0388106
$792$	0.936603	0.0332807
$793$	29.8687	1.06067
$794$	13.3718	0.474547
$795$	0.949522	0.0336761
$796$	−9.97284	−0.353478
$797$	12.6081	0.446600	0.223300	−	0.974750i	$-0.428317\pi$
$797$	12.6081	0.446600	0.223300	+	0.974750i	$0.428317\pi$
$798$	0.761487	0.0269563
$799$	−57.2325	−2.02474
$800$	1.00000	0.0353553
$801$	−2.08157	−0.0735485
$802$	26.0594	0.920189
$803$	−6.91967	−0.244190
$804$	8.65713	0.305313
$805$	−1.33585	−0.0470825
$806$	7.43894	0.262026
$807$	9.18701	0.323398
$808$	−12.8613	−0.452461
$809$	−14.7586	−0.518886	−0.259443	−	0.965758i	$-0.583539\pi$
$809$	−14.7586	−0.518886	−0.259443	+	0.965758i	$0.583539\pi$
$810$	1.67671	0.0589135
$811$	−14.8783	−0.522448	−0.261224	−	0.965278i	$-0.584126\pi$
$811$	−14.8783	−0.522448	−0.261224	+	0.965278i	$0.584126\pi$
$812$	6.07993	0.213364
$813$	2.51546	0.0882210
$814$	1.82101	0.0638264
$815$	1.54206	0.0540160
$816$	7.55019	0.264309
$817$	4.31549	0.150980
$818$	27.8624	0.974187
$819$	−3.83641	−0.134055
$820$	4.99455	0.174417
$821$	−0.292129	−0.0101954	−0.00509768	−	0.999987i	$-0.501623\pi$
$821$	−0.292129	−0.0101954	−0.00509768	+	0.999987i	$0.501623\pi$
$822$	−14.1716	−0.494291
$823$	−32.3653	−1.12818	−0.564092	−	0.825712i	$-0.690774\pi$
$823$	−32.3653	−1.12818	−0.564092	+	0.825712i	$0.690774\pi$
$824$	−10.8539	−0.378113
$825$	−0.696672	−0.0242550
$826$	−8.29714	−0.288695
$827$	−14.6883	−0.510761	−0.255381	−	0.966841i	$-0.582201\pi$
$827$	−14.6883	−0.510761	−0.255381	+	0.966841i	$0.582201\pi$
$828$	2.12944	0.0740032
$829$	57.2282	1.98762	0.993809	−	0.111098i	$-0.0354368\pi$
$829$	57.2282	1.98762	0.993809	+	0.111098i	$0.0354368\pi$
$830$	10.4117	0.361396
$831$	5.74035	0.199130
$832$	−2.40667	−0.0834362
$833$	6.36761	0.220625
$834$	14.4741	0.501195
$835$	15.4028	0.533035
$836$	0.377336	0.0130504
$837$	16.8374	0.581984
$838$	−35.2732	−1.21849
$839$	37.1484	1.28251	0.641253	−	0.767329i	$-0.278415\pi$
$839$	37.1484	1.28251	0.641253	+	0.767329i	$0.278415\pi$
$840$	1.18572	0.0409111
$841$	7.96554	0.274674
$842$	24.1815	0.833349
$843$	−14.9642	−0.515395
$844$	−8.11696	−0.279397
$845$	7.20794	0.247961
$846$	14.3276	0.492594
$847$	10.6548	0.366103
$848$	−0.800800	−0.0274996
$849$	23.8443	0.818334
$850$	6.36761	0.218407
$851$	4.14021	0.141925
$852$	1.18572	0.0406220
$853$	−2.67762	−0.0916800	−0.0458400	−	0.998949i	$-0.514596\pi$
$853$	−2.67762	−0.0916800	−0.0458400	+	0.998949i	$0.514596\pi$
$854$	12.4108	0.424689
$855$	−1.02374	−0.0350112
$856$	−4.44072	−0.151781
$857$	14.0243	0.479060	0.239530	−	0.970889i	$-0.423007\pi$
$857$	14.0243	0.479060	0.239530	+	0.970889i	$0.423007\pi$
$858$	1.67666	0.0572402
$859$	−4.90892	−0.167490	−0.0837451	−	0.996487i	$-0.526688\pi$
$859$	−4.90892	−0.167490	−0.0837451	+	0.996487i	$0.526688\pi$
$860$	6.71968	0.229139
$861$	5.92213	0.201826
$862$	−25.7289	−0.876329
$863$	4.09210	0.139297	0.0696484	−	0.997572i	$-0.477812\pi$
$863$	4.09210	0.139297	0.0696484	+	0.997572i	$0.477812\pi$
$864$	−5.44727	−0.185320
$865$	−10.6566	−0.362334
$866$	6.40226	0.217558
$867$	27.9195	0.948195
$868$	3.09097	0.104914
$869$	−7.31484	−0.248139
$870$	7.20908	0.244411
$871$	−17.5715	−0.595388
$872$	0.688375	0.0233113
$873$	10.8203	0.366210
$874$	0.857903	0.0290190
$875$	1.00000	0.0338062
$876$	13.9643	0.471810
$877$	8.76992	0.296139	0.148070	−	0.988977i	$-0.452694\pi$
$877$	8.76992	0.296139	0.148070	+	0.988977i	$0.452694\pi$
$878$	16.1086	0.543638
$879$	34.3294	1.15790
$880$	0.587553	0.0198064
$881$	14.3912	0.484852	0.242426	−	0.970170i	$-0.422057\pi$
$881$	14.3912	0.484852	0.242426	+	0.970170i	$0.422057\pi$
$882$	−1.59407	−0.0536753
$883$	−23.9016	−0.804353	−0.402177	−	0.915562i	$-0.631746\pi$
$883$	−23.9016	−0.804353	−0.402177	+	0.915562i	$0.631746\pi$
$884$	−15.3247	−0.515427
$885$	−9.83807	−0.330703
$886$	32.7017	1.09864
$887$	12.2803	0.412334	0.206167	−	0.978517i	$-0.433901\pi$
$887$	12.2803	0.412334	0.206167	+	0.978517i	$0.433901\pi$
$888$	−3.67491	−0.123322
$889$	9.17343	0.307667
$890$	−1.30582	−0.0437710
$891$	0.985155	0.0330039
$892$	13.6343	0.456512
$893$	5.77228	0.193162
$894$	−8.02849	−0.268513
$895$	−14.1406	−0.472670
$896$	−1.00000	−0.0334077
$897$	3.81202	0.127280
$898$	15.1026	0.503981
$899$	18.7929	0.626778
$900$	−1.59407	−0.0531358
$901$	−5.09918	−0.169878
$902$	2.93456	0.0977103
$903$	7.96764	0.265147
$904$	−1.09154	−0.0363040
$905$	−22.3405	−0.742625
$906$	−0.0645429	−0.00214430
$907$	−9.82058	−0.326087	−0.163043	−	0.986619i	$-0.552131\pi$
$907$	−9.82058	−0.326087	−0.163043	+	0.986619i	$0.552131\pi$
$908$	−0.303911	−0.0100856
$909$	20.5019	0.680006
$910$	−2.40667	−0.0797803
$911$	−14.9203	−0.494332	−0.247166	−	0.968973i	$-0.579499\pi$
$911$	−14.9203	−0.494332	−0.247166	+	0.968973i	$0.579499\pi$
$912$	−0.761487	−0.0252153
$913$	6.11745	0.202458
$914$	−28.7792	−0.951932
$915$	14.7157	0.486486
$916$	−14.1709	−0.468221
$917$	−4.47439	−0.147757
$918$	−34.6861	−1.14481
$919$	15.2966	0.504589	0.252294	−	0.967650i	$-0.418815\pi$
$919$	15.2966	0.504589	0.252294	+	0.967650i	$0.418815\pi$
$920$	1.33585	0.0440416
$921$	−37.4512	−1.23406
$922$	11.6725	0.384412
$923$	−2.40667	−0.0792165
$924$	0.696672	0.0229188
$925$	−3.09931	−0.101905
$926$	−15.4221	−0.506800
$927$	17.3019	0.568269
$928$	−6.07993	−0.199583
$929$	−38.8354	−1.27415	−0.637074	−	0.770802i	$-0.719856\pi$
$929$	−38.8354	−1.27415	−0.637074	+	0.770802i	$0.719856\pi$
$930$	3.66502	0.120181
$931$	−0.642216	−0.0210478
$932$	14.9531	0.489805
$933$	0.345540	0.0113125
$934$	−27.0357	−0.884635
$935$	3.74131	0.122354
$936$	3.83641	0.125397
$937$	−11.2177	−0.366466	−0.183233	−	0.983069i	$-0.558656\pi$
$937$	−11.2177	−0.366466	−0.183233	+	0.983069i	$0.558656\pi$
$938$	−7.30117	−0.238392
$939$	19.7964	0.646032
$940$	8.98806	0.293158
$941$	−28.5180	−0.929662	−0.464831	−	0.885399i	$-0.653885\pi$
$941$	−28.5180	−0.929662	−0.464831	+	0.885399i	$0.653885\pi$
$942$	−4.82673	−0.157263
$943$	6.67196	0.217269
$944$	8.29714	0.270049
$945$	−5.44727	−0.177200
$946$	3.94817	0.128366
$947$	−26.8072	−0.871118	−0.435559	−	0.900160i	$-0.643449\pi$
$947$	−26.8072	−0.871118	−0.435559	+	0.900160i	$0.643449\pi$
$948$	14.7618	0.479440
$949$	−28.3436	−0.920071
$950$	−0.642216	−0.0208362
$951$	17.8241	0.577987
$952$	−6.36761	−0.206375
$953$	19.2121	0.622341	0.311170	−	0.950354i	$-0.399279\pi$
$953$	19.2121	0.622341	0.311170	+	0.950354i	$0.399279\pi$
$954$	1.27653	0.0413293
$955$	26.4530	0.855998
$956$	−22.0210	−0.712209
$957$	4.23572	0.136921
$958$	−9.41754	−0.304267
$959$	11.9519	0.385947
$960$	−1.18572	−0.0382689
$961$	−21.4459	−0.691803
$962$	7.45902	0.240488
$963$	7.07883	0.228112
$964$	25.6816	0.827147
$965$	15.9184	0.512433
$966$	1.58394	0.0509624
$967$	−3.37465	−0.108522	−0.0542608	−	0.998527i	$-0.517280\pi$
$967$	−3.37465	−0.108522	−0.0542608	+	0.998527i	$0.517280\pi$
$968$	−10.6548	−0.342458
$969$	−4.84885	−0.155768
$970$	6.78780	0.217943
$971$	0.642890	0.0206313	0.0103157	−	0.999947i	$-0.496716\pi$
$971$	0.642890	0.0206313	0.0103157	+	0.999947i	$0.496716\pi$
$972$	14.3537	0.460396
$973$	−12.2070	−0.391338
$974$	−37.4134	−1.19880
$975$	−2.85363	−0.0913893
$976$	−12.4108	−0.397260
$977$	39.5079	1.26397	0.631984	−	0.774981i	$-0.282241\pi$
$977$	39.5079	1.26397	0.631984	+	0.774981i	$0.282241\pi$
$978$	−1.82845	−0.0584673
$979$	−0.767236	−0.0245210
$980$	−1.00000	−0.0319438
$981$	−1.09732	−0.0350348
$982$	−1.69391	−0.0540547
$983$	−59.4410	−1.89587	−0.947937	−	0.318459i	$-0.896835\pi$
$983$	−59.4410	−1.89587	−0.947937	+	0.318459i	$0.896835\pi$
$984$	−5.92213	−0.188791
$985$	−14.8456	−0.473020
$986$	−38.7146	−1.23292
$987$	10.6573	0.339226
$988$	1.54560	0.0491721
$989$	8.97647	0.285435
$990$	−0.936603	−0.0297672
$991$	20.3081	0.645107	0.322554	−	0.946551i	$-0.395459\pi$
$991$	20.3081	0.645107	0.322554	+	0.946551i	$0.395459\pi$
$992$	−3.09097	−0.0981384
$993$	20.9871	0.666004
$994$	−1.00000	−0.0317181
$995$	9.97284	0.316160
$996$	−12.3454	−0.391178
$997$	−39.7888	−1.26013	−0.630063	−	0.776544i	$-0.716971\pi$
$997$	−39.7888	−1.26013	−0.630063	+	0.776544i	$0.716971\pi$
$998$	1.42444	0.0450900
$999$	16.8828	0.534148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4970.2.a.x.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4970.2.a.x.1.5	✓	7	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:	\( N \)	\(=\)	\( 4970 = 2 \cdot 5 \cdot 7 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4970.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.18572 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.18572 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.59407 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.18572 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.18572 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.59407 q^{9} -1.00000 q^{10} -0.587553 q^{11} +1.18572 q^{12} -2.40667 q^{13} -1.00000 q^{14} -1.18572 q^{15} +1.00000 q^{16} +6.36761 q^{17} -1.59407 q^{18} -0.642216 q^{19} -1.00000 q^{20} -1.18572 q^{21} -0.587553 q^{22} -1.33585 q^{23} +1.18572 q^{24} +1.00000 q^{25} -2.40667 q^{26} -5.44727 q^{27} -1.00000 q^{28} -6.07993 q^{29} -1.18572 q^{30} -3.09097 q^{31} +1.00000 q^{32} -0.696672 q^{33} +6.36761 q^{34} +1.00000 q^{35} -1.59407 q^{36} -3.09931 q^{37} -0.642216 q^{38} -2.85363 q^{39} -1.00000 q^{40} -4.99455 q^{41} -1.18572 q^{42} -6.71968 q^{43} -0.587553 q^{44} +1.59407 q^{45} -1.33585 q^{46} -8.98806 q^{47} +1.18572 q^{48} +1.00000 q^{49} +1.00000 q^{50} +7.55019 q^{51} -2.40667 q^{52} -0.800800 q^{53} -5.44727 q^{54} +0.587553 q^{55} -1.00000 q^{56} -0.761487 q^{57} -6.07993 q^{58} +8.29714 q^{59} -1.18572 q^{60} -12.4108 q^{61} -3.09097 q^{62} +1.59407 q^{63} +1.00000 q^{64} +2.40667 q^{65} -0.696672 q^{66} +7.30117 q^{67} +6.36761 q^{68} -1.58394 q^{69} +1.00000 q^{70} +1.00000 q^{71} -1.59407 q^{72} +11.7771 q^{73} -3.09931 q^{74} +1.18572 q^{75} -0.642216 q^{76} +0.587553 q^{77} -2.85363 q^{78} +12.4497 q^{79} -1.00000 q^{80} -1.67671 q^{81} -4.99455 q^{82} -10.4117 q^{83} -1.18572 q^{84} -6.36761 q^{85} -6.71968 q^{86} -7.20908 q^{87} -0.587553 q^{88} +1.30582 q^{89} +1.59407 q^{90} +2.40667 q^{91} -1.33585 q^{92} -3.66502 q^{93} -8.98806 q^{94} +0.642216 q^{95} +1.18572 q^{96} -6.78780 q^{97} +1.00000 q^{98} +0.936603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + q^{3} + 7 q^{4} - 7 q^{5} + q^{6} - 7 q^{7} + 7 q^{8} + 2 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + q^3 + 7 * q^4 - 7 * q^5 + q^6 - 7 * q^7 + 7 * q^8 + 2 * q^9	\( 7 q + 7 q^{2} + q^{3} + 7 q^{4} - 7 q^{5} + q^{6} - 7 q^{7} + 7 q^{8} + 2 q^{9} - 7 q^{10} - 9 q^{11} + q^{12} - 7 q^{14} - q^{15} + 7 q^{16} - 5 q^{17} + 2 q^{18} + 2 q^{19} - 7 q^{20} - q^{21} - 9 q^{22} - 8 q^{23} + q^{24} + 7 q^{25} + q^{27} - 7 q^{28} - 19 q^{29} - q^{30} - 6 q^{31} + 7 q^{32} - 6 q^{33} - 5 q^{34} + 7 q^{35} + 2 q^{36} - 10 q^{37} + 2 q^{38} - 19 q^{39} - 7 q^{40} - 19 q^{41} - q^{42} - 22 q^{43} - 9 q^{44} - 2 q^{45} - 8 q^{46} + 2 q^{47} + q^{48} + 7 q^{49} + 7 q^{50} - 22 q^{51} - 3 q^{53} + q^{54} + 9 q^{55} - 7 q^{56} - 25 q^{57} - 19 q^{58} + 13 q^{59} - q^{60} - 4 q^{61} - 6 q^{62} - 2 q^{63} + 7 q^{64} - 6 q^{66} - 23 q^{67} - 5 q^{68} - 19 q^{69} + 7 q^{70} + 7 q^{71} + 2 q^{72} - 10 q^{74} + q^{75} + 2 q^{76} + 9 q^{77} - 19 q^{78} - 40 q^{79} - 7 q^{80} - 33 q^{81} - 19 q^{82} + 24 q^{83} - q^{84} + 5 q^{85} - 22 q^{86} - 6 q^{87} - 9 q^{88} - 4 q^{89} - 2 q^{90} - 8 q^{92} - 12 q^{93} + 2 q^{94} - 2 q^{95} + q^{96} - 35 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + q^3 + 7 * q^4 - 7 * q^5 + q^6 - 7 * q^7 + 7 * q^8 + 2 * q^9 - 7 * q^10 - 9 * q^11 + q^12 - 7 * q^14 - q^15 + 7 * q^16 - 5 * q^17 + 2 * q^18 + 2 * q^19 - 7 * q^20 - q^21 - 9 * q^22 - 8 * q^23 + q^24 + 7 * q^25 + q^27 - 7 * q^28 - 19 * q^29 - q^30 - 6 * q^31 + 7 * q^32 - 6 * q^33 - 5 * q^34 + 7 * q^35 + 2 * q^36 - 10 * q^37 + 2 * q^38 - 19 * q^39 - 7 * q^40 - 19 * q^41 - q^42 - 22 * q^43 - 9 * q^44 - 2 * q^45 - 8 * q^46 + 2 * q^47 + q^48 + 7 * q^49 + 7 * q^50 - 22 * q^51 - 3 * q^53 + q^54 + 9 * q^55 - 7 * q^56 - 25 * q^57 - 19 * q^58 + 13 * q^59 - q^60 - 4 * q^61 - 6 * q^62 - 2 * q^63 + 7 * q^64 - 6 * q^66 - 23 * q^67 - 5 * q^68 - 19 * q^69 + 7 * q^70 + 7 * q^71 + 2 * q^72 - 10 * q^74 + q^75 + 2 * q^76 + 9 * q^77 - 19 * q^78 - 40 * q^79 - 7 * q^80 - 33 * q^81 - 19 * q^82 + 24 * q^83 - q^84 + 5 * q^85 - 22 * q^86 - 6 * q^87 - 9 * q^88 - 4 * q^89 - 2 * q^90 - 8 * q^92 - 12 * q^93 + 2 * q^94 - 2 * q^95 + q^96 - 35 * q^97 + 7 * q^98 - 24 * q^99

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