LMFDB - Embedded newform 4030.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1797120146$
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} - 12x^{5} + 10x^{4} + 26x^{3} - 6x^{2} - 17x - 4 $ x^7 - x^6 - 12x^5 + 10x^4 + 26x^3 - 6x^2 - 17*x - 4
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			1.3
Root			$1.09573$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.09573 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.09573 q^{6} -2.85390 q^{7} -1.00000 q^{8} -1.79939 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.09573 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.09573 q^{6} -2.85390 q^{7} -1.00000 q^{8} -1.79939 q^{9} -1.00000 q^{10} +1.42679 q^{11} -1.09573 q^{12} -1.00000 q^{13} +2.85390 q^{14} -1.09573 q^{15} +1.00000 q^{16} -4.91892 q^{17} +1.79939 q^{18} +0.556163 q^{19} +1.00000 q^{20} +3.12709 q^{21} -1.42679 q^{22} +5.09377 q^{23} +1.09573 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.25881 q^{27} -2.85390 q^{28} +8.95879 q^{29} +1.09573 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.56337 q^{33} +4.91892 q^{34} -2.85390 q^{35} -1.79939 q^{36} -0.113068 q^{37} -0.556163 q^{38} +1.09573 q^{39} -1.00000 q^{40} +10.3856 q^{41} -3.12709 q^{42} -4.19895 q^{43} +1.42679 q^{44} -1.79939 q^{45} -5.09377 q^{46} -1.73731 q^{47} -1.09573 q^{48} +1.14476 q^{49} -1.00000 q^{50} +5.38978 q^{51} -1.00000 q^{52} -5.68358 q^{53} -5.25881 q^{54} +1.42679 q^{55} +2.85390 q^{56} -0.609402 q^{57} -8.95879 q^{58} -1.56050 q^{59} -1.09573 q^{60} +6.15940 q^{61} -1.00000 q^{62} +5.13527 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.56337 q^{66} +5.47308 q^{67} -4.91892 q^{68} -5.58137 q^{69} +2.85390 q^{70} +1.02381 q^{71} +1.79939 q^{72} -1.59055 q^{73} +0.113068 q^{74} -1.09573 q^{75} +0.556163 q^{76} -4.07192 q^{77} -1.09573 q^{78} -12.5352 q^{79} +1.00000 q^{80} -0.364052 q^{81} -10.3856 q^{82} -1.21766 q^{83} +3.12709 q^{84} -4.91892 q^{85} +4.19895 q^{86} -9.81637 q^{87} -1.42679 q^{88} -16.1489 q^{89} +1.79939 q^{90} +2.85390 q^{91} +5.09377 q^{92} -1.09573 q^{93} +1.73731 q^{94} +0.556163 q^{95} +1.09573 q^{96} -14.3690 q^{97} -1.14476 q^{98} -2.56735 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9} - 7 q^{10} - 2 q^{11} - q^{12} - 7 q^{13} + 4 q^{14} - q^{15} + 7 q^{16} - 8 q^{17} - 4 q^{18} + q^{19} + 7 q^{20} - 11 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} + 7 q^{25} + 7 q^{26} - q^{27} - 4 q^{28} - 4 q^{29} + q^{30} + 7 q^{31} - 7 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} - q^{38} + q^{39} - 7 q^{40} - 6 q^{41} + 11 q^{42} - 5 q^{43} - 2 q^{44} + 4 q^{45} + 5 q^{46} - 18 q^{47} - q^{48} - 9 q^{49} - 7 q^{50} - q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 2 q^{55} + 4 q^{56} - 31 q^{57} + 4 q^{58} + 3 q^{59} - q^{60} - 7 q^{61} - 7 q^{62} - 19 q^{63} + 7 q^{64} - 7 q^{65} + 4 q^{66} + 6 q^{67} - 8 q^{68} - 10 q^{69} + 4 q^{70} + 4 q^{71} - 4 q^{72} - 31 q^{73} + 2 q^{74} - q^{75} + q^{76} - 25 q^{77} - q^{78} - 2 q^{79} + 7 q^{80} + 31 q^{81} + 6 q^{82} - 40 q^{83} - 11 q^{84} - 8 q^{85} + 5 q^{86} - 5 q^{87} + 2 q^{88} - 4 q^{90} + 4 q^{91} - 5 q^{92} - q^{93} + 18 q^{94} + q^{95} + q^{96} - 21 q^{97} + 9 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9 - 7 * q^10 - 2 * q^11 - q^12 - 7 * q^13 + 4 * q^14 - q^15 + 7 * q^16 - 8 * q^17 - 4 * q^18 + q^19 + 7 * q^20 - 11 * q^21 + 2 * q^22 - 5 * q^23 + q^24 + 7 * q^25 + 7 * q^26 - q^27 - 4 * q^28 - 4 * q^29 + q^30 + 7 * q^31 - 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^37 - q^38 + q^39 - 7 * q^40 - 6 * q^41 + 11 * q^42 - 5 * q^43 - 2 * q^44 + 4 * q^45 + 5 * q^46 - 18 * q^47 - q^48 - 9 * q^49 - 7 * q^50 - q^51 - 7 * q^52 - 12 * q^53 + q^54 - 2 * q^55 + 4 * q^56 - 31 * q^57 + 4 * q^58 + 3 * q^59 - q^60 - 7 * q^61 - 7 * q^62 - 19 * q^63 + 7 * q^64 - 7 * q^65 + 4 * q^66 + 6 * q^67 - 8 * q^68 - 10 * q^69 + 4 * q^70 + 4 * q^71 - 4 * q^72 - 31 * q^73 + 2 * q^74 - q^75 + q^76 - 25 * q^77 - q^78 - 2 * q^79 + 7 * q^80 + 31 * q^81 + 6 * q^82 - 40 * q^83 - 11 * q^84 - 8 * q^85 + 5 * q^86 - 5 * q^87 + 2 * q^88 - 4 * q^90 + 4 * q^91 - 5 * q^92 - q^93 + 18 * q^94 + q^95 + q^96 - 21 * q^97 + 9 * q^98 - 23 * 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
$3$	−1.09573	−0.632617	−0.316309	−	0.948656i	$-0.602444\pi$
$3$	−1.09573	−0.632617	−0.316309	+	0.948656i	$0.602444\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.09573	0.447328
$7$	−2.85390	−1.07867	−0.539337	−	0.842090i	$-0.681325\pi$
$7$	−2.85390	−1.07867	−0.539337	+	0.842090i	$0.681325\pi$
$8$	−1.00000	−0.353553
$9$	−1.79939	−0.599795
$10$	−1.00000	−0.316228
$11$	1.42679	0.430193	0.215097	−	0.976593i	$-0.430993\pi$
$11$	1.42679	0.430193	0.215097	+	0.976593i	$0.430993\pi$
$12$	−1.09573	−0.316309
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.85390	0.762737
$15$	−1.09573	−0.282915
$16$	1.00000	0.250000
$17$	−4.91892	−1.19301	−0.596507	−	0.802608i	$-0.703445\pi$
$17$	−4.91892	−1.19301	−0.596507	+	0.802608i	$0.703445\pi$
$18$	1.79939	0.424119
$19$	0.556163	0.127593	0.0637963	−	0.997963i	$-0.479679\pi$
$19$	0.556163	0.127593	0.0637963	+	0.997963i	$0.479679\pi$
$20$	1.00000	0.223607
$21$	3.12709	0.682388
$22$	−1.42679	−0.304193
$23$	5.09377	1.06212	0.531062	−	0.847333i	$-0.321793\pi$
$23$	5.09377	1.06212	0.531062	+	0.847333i	$0.321793\pi$
$24$	1.09573	0.223664
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	5.25881	1.01206
$28$	−2.85390	−0.539337
$29$	8.95879	1.66361	0.831803	−	0.555071i	$-0.187309\pi$
$29$	8.95879	1.66361	0.831803	+	0.555071i	$0.187309\pi$
$30$	1.09573	0.200051
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−1.56337	−0.272148
$34$	4.91892	0.843588
$35$	−2.85390	−0.482398
$36$	−1.79939	−0.299898
$37$	−0.113068	−0.0185882	−0.00929410	−	0.999957i	$-0.502958\pi$
$37$	−0.113068	−0.0185882	−0.00929410	+	0.999957i	$0.502958\pi$
$38$	−0.556163	−0.0902216
$39$	1.09573	0.175456
$40$	−1.00000	−0.158114
$41$	10.3856	1.62195	0.810977	−	0.585077i	$-0.198936\pi$
$41$	10.3856	1.62195	0.810977	+	0.585077i	$0.198936\pi$
$42$	−3.12709	−0.482521
$43$	−4.19895	−0.640334	−0.320167	−	0.947361i	$-0.603739\pi$
$43$	−4.19895	−0.640334	−0.320167	+	0.947361i	$0.603739\pi$
$44$	1.42679	0.215097
$45$	−1.79939	−0.268237
$46$	−5.09377	−0.751035
$47$	−1.73731	−0.253413	−0.126706	−	0.991940i	$-0.540441\pi$
$47$	−1.73731	−0.253413	−0.126706	+	0.991940i	$0.540441\pi$
$48$	−1.09573	−0.158154
$49$	1.14476	0.163537
$50$	−1.00000	−0.141421
$51$	5.38978	0.754721
$52$	−1.00000	−0.138675
$53$	−5.68358	−0.780700	−0.390350	−	0.920667i	$-0.627646\pi$
$53$	−5.68358	−0.780700	−0.390350	+	0.920667i	$0.627646\pi$
$54$	−5.25881	−0.715633
$55$	1.42679	0.192388
$56$	2.85390	0.381369
$57$	−0.609402	−0.0807173
$58$	−8.95879	−1.17635
$59$	−1.56050	−0.203160	−0.101580	−	0.994827i	$-0.532390\pi$
$59$	−1.56050	−0.203160	−0.101580	+	0.994827i	$0.532390\pi$
$60$	−1.09573	−0.141458
$61$	6.15940	0.788631	0.394315	−	0.918975i	$-0.370982\pi$
$61$	6.15940	0.788631	0.394315	+	0.918975i	$0.370982\pi$
$62$	−1.00000	−0.127000
$63$	5.13527	0.646983
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	1.56337	0.192437
$67$	5.47308	0.668644	0.334322	−	0.942459i	$-0.391493\pi$
$67$	5.47308	0.668644	0.334322	+	0.942459i	$0.391493\pi$
$68$	−4.91892	−0.596507
$69$	−5.58137	−0.671918
$70$	2.85390	0.341107
$71$	1.02381	0.121504	0.0607518	−	0.998153i	$-0.480650\pi$
$71$	1.02381	0.121504	0.0607518	+	0.998153i	$0.480650\pi$
$72$	1.79939	0.212060
$73$	−1.59055	−0.186160	−0.0930801	−	0.995659i	$-0.529671\pi$
$73$	−1.59055	−0.186160	−0.0930801	+	0.995659i	$0.529671\pi$
$74$	0.113068	0.0131438
$75$	−1.09573	−0.126523
$76$	0.556163	0.0637963
$77$	−4.07192	−0.464038
$78$	−1.09573	−0.124066
$79$	−12.5352	−1.41032	−0.705160	−	0.709048i	$-0.749125\pi$
$79$	−12.5352	−1.41032	−0.705160	+	0.709048i	$0.749125\pi$
$80$	1.00000	0.111803
$81$	−0.364052	−0.0404502
$82$	−10.3856	−1.14690
$83$	−1.21766	−0.133656	−0.0668278	−	0.997765i	$-0.521288\pi$
$83$	−1.21766	−0.133656	−0.0668278	+	0.997765i	$0.521288\pi$
$84$	3.12709	0.341194
$85$	−4.91892	−0.533532
$86$	4.19895	0.452785
$87$	−9.81637	−1.05243
$88$	−1.42679	−0.152096
$89$	−16.1489	−1.71178	−0.855890	−	0.517158i	$-0.826990\pi$
$89$	−16.1489	−1.71178	−0.855890	+	0.517158i	$0.826990\pi$
$90$	1.79939	0.189672
$91$	2.85390	0.299170
$92$	5.09377	0.531062
$93$	−1.09573	−0.113621
$94$	1.73731	0.179190
$95$	0.556163	0.0570612
$96$	1.09573	0.111832
$97$	−14.3690	−1.45895	−0.729474	−	0.684008i	$-0.760235\pi$
$97$	−14.3690	−1.45895	−0.729474	+	0.684008i	$0.760235\pi$
$98$	−1.14476	−0.115638
$99$	−2.56735	−0.258028
$100$	1.00000	0.100000
$101$	−14.6591	−1.45863	−0.729317	−	0.684176i	$-0.760162\pi$
$101$	−14.6591	−1.45863	−0.729317	+	0.684176i	$0.760162\pi$
$102$	−5.38978	−0.533668
$103$	17.6302	1.73716	0.868578	−	0.495553i	$-0.165034\pi$
$103$	17.6302	1.73716	0.868578	+	0.495553i	$0.165034\pi$
$104$	1.00000	0.0980581
$105$	3.12709	0.305173
$106$	5.68358	0.552038
$107$	−10.9718	−1.06069	−0.530344	−	0.847783i	$-0.677937\pi$
$107$	−10.9718	−1.06069	−0.530344	+	0.847783i	$0.677937\pi$
$108$	5.25881	0.506029
$109$	−6.50751	−0.623307	−0.311653	−	0.950196i	$-0.600883\pi$
$109$	−6.50751	−0.623307	−0.311653	+	0.950196i	$0.600883\pi$
$110$	−1.42679	−0.136039
$111$	0.123891	0.0117592
$112$	−2.85390	−0.269668
$113$	14.7913	1.39145	0.695723	−	0.718310i	$-0.255084\pi$
$113$	14.7913	1.39145	0.695723	+	0.718310i	$0.255084\pi$
$114$	0.609402	0.0570758
$115$	5.09377	0.474996
$116$	8.95879	0.831803
$117$	1.79939	0.166353
$118$	1.56050	0.143656
$119$	14.0381	1.28687
$120$	1.09573	0.100026
$121$	−8.96427	−0.814934
$122$	−6.15940	−0.557646
$123$	−11.3797	−1.02608
$124$	1.00000	0.0898027
$125$	1.00000	0.0894427
$126$	−5.13527	−0.457486
$127$	−13.4853	−1.19663	−0.598314	−	0.801262i	$-0.704162\pi$
$127$	−13.4853	−1.19663	−0.598314	+	0.801262i	$0.704162\pi$
$128$	−1.00000	−0.0883883
$129$	4.60090	0.405086
$130$	1.00000	0.0877058
$131$	5.38524	0.470511	0.235255	−	0.971934i	$-0.424407\pi$
$131$	5.38524	0.470511	0.235255	+	0.971934i	$0.424407\pi$
$132$	−1.56337	−0.136074
$133$	−1.58724	−0.137631
$134$	−5.47308	−0.472802
$135$	5.25881	0.452606
$136$	4.91892	0.421794
$137$	14.9994	1.28149	0.640745	−	0.767754i	$-0.278626\pi$
$137$	14.9994	1.28149	0.640745	+	0.767754i	$0.278626\pi$
$138$	5.58137	0.475118
$139$	7.80806	0.662271	0.331135	−	0.943583i	$-0.392568\pi$
$139$	7.80806	0.662271	0.331135	+	0.943583i	$0.392568\pi$
$140$	−2.85390	−0.241199
$141$	1.90361	0.160313
$142$	−1.02381	−0.0859160
$143$	−1.42679	−0.119314
$144$	−1.79939	−0.149949
$145$	8.95879	0.743987
$146$	1.59055	0.131635
$147$	−1.25434	−0.103456
$148$	−0.113068	−0.00929410
$149$	5.71686	0.468344	0.234172	−	0.972195i	$-0.424762\pi$
$149$	5.71686	0.468344	0.234172	+	0.972195i	$0.424762\pi$
$150$	1.09573	0.0894656
$151$	−6.56934	−0.534605	−0.267303	−	0.963613i	$-0.586132\pi$
$151$	−6.56934	−0.534605	−0.267303	+	0.963613i	$0.586132\pi$
$152$	−0.556163	−0.0451108
$153$	8.85103	0.715564
$154$	4.07192	0.328124
$155$	1.00000	0.0803219
$156$	1.09573	0.0877282
$157$	−3.57605	−0.285400	−0.142700	−	0.989766i	$-0.545578\pi$
$157$	−3.57605	−0.285400	−0.142700	+	0.989766i	$0.545578\pi$
$158$	12.5352	0.997247
$159$	6.22764	0.493884
$160$	−1.00000	−0.0790569
$161$	−14.5371	−1.14569
$162$	0.364052	0.0286026
$163$	−23.6237	−1.85035	−0.925176	−	0.379539i	$-0.876083\pi$
$163$	−23.6237	−1.85035	−0.925176	+	0.379539i	$0.876083\pi$
$164$	10.3856	0.810977
$165$	−1.56337	−0.121708
$166$	1.21766	0.0945088
$167$	−11.3565	−0.878789	−0.439395	−	0.898294i	$-0.644807\pi$
$167$	−11.3565	−0.878789	−0.439395	+	0.898294i	$0.644807\pi$
$168$	−3.12709	−0.241260
$169$	1.00000	0.0769231
$170$	4.91892	0.377264
$171$	−1.00075	−0.0765295
$172$	−4.19895	−0.320167
$173$	−18.1355	−1.37882	−0.689410	−	0.724372i	$-0.742130\pi$
$173$	−18.1355	−1.37882	−0.689410	+	0.724372i	$0.742130\pi$
$174$	9.81637	0.744177
$175$	−2.85390	−0.215735
$176$	1.42679	0.107548
$177$	1.70988	0.128523
$178$	16.1489	1.21041
$179$	8.00219	0.598112	0.299056	−	0.954236i	$-0.403328\pi$
$179$	8.00219	0.598112	0.299056	+	0.954236i	$0.403328\pi$
$180$	−1.79939	−0.134118
$181$	−6.88738	−0.511935	−0.255968	−	0.966685i	$-0.582394\pi$
$181$	−6.88738	−0.511935	−0.255968	+	0.966685i	$0.582394\pi$
$182$	−2.85390	−0.211545
$183$	−6.74901	−0.498901
$184$	−5.09377	−0.375518
$185$	−0.113068	−0.00831290
$186$	1.09573	0.0803425
$187$	−7.01826	−0.513226
$188$	−1.73731	−0.126706
$189$	−15.0081	−1.09168
$190$	−0.556163	−0.0403483
$191$	−1.55391	−0.112437	−0.0562185	−	0.998418i	$-0.517904\pi$
$191$	−1.55391	−0.112437	−0.0562185	+	0.998418i	$0.517904\pi$
$192$	−1.09573	−0.0790772
$193$	2.95951	0.213030	0.106515	−	0.994311i	$-0.466031\pi$
$193$	2.95951	0.213030	0.106515	+	0.994311i	$0.466031\pi$
$194$	14.3690	1.03163
$195$	1.09573	0.0784665
$196$	1.14476	0.0817685
$197$	−7.76332	−0.553114	−0.276557	−	0.960998i	$-0.589193\pi$
$197$	−7.76332	−0.553114	−0.276557	+	0.960998i	$0.589193\pi$
$198$	2.56735	0.182453
$199$	−0.784095	−0.0555830	−0.0277915	−	0.999614i	$-0.508847\pi$
$199$	−0.784095	−0.0555830	−0.0277915	+	0.999614i	$0.508847\pi$
$200$	−1.00000	−0.0707107
$201$	−5.99700	−0.422996
$202$	14.6591	1.03141
$203$	−25.5675	−1.79449
$204$	5.38978	0.377360
$205$	10.3856	0.725360
$206$	−17.6302	−1.22835
$207$	−9.16565	−0.637057
$208$	−1.00000	−0.0693375
$209$	0.793528	0.0548895
$210$	−3.12709	−0.215790
$211$	24.3760	1.67812	0.839058	−	0.544042i	$-0.183107\pi$
$211$	24.3760	1.67812	0.839058	+	0.544042i	$0.183107\pi$
$212$	−5.68358	−0.390350
$213$	−1.12181	−0.0768653
$214$	10.9718	0.750019
$215$	−4.19895	−0.286366
$216$	−5.25881	−0.357817
$217$	−2.85390	−0.193736
$218$	6.50751	0.440744
$219$	1.74281	0.117768
$220$	1.42679	0.0961941
$221$	4.91892	0.330882
$222$	−0.123891	−0.00831502
$223$	19.5925	1.31201	0.656006	−	0.754756i	$-0.272245\pi$
$223$	19.5925	1.31201	0.656006	+	0.754756i	$0.272245\pi$
$224$	2.85390	0.190684
$225$	−1.79939	−0.119959
$226$	−14.7913	−0.983901
$227$	−10.6523	−0.707016	−0.353508	−	0.935432i	$-0.615011\pi$
$227$	−10.6523	−0.707016	−0.353508	+	0.935432i	$0.615011\pi$
$228$	−0.609402	−0.0403587
$229$	2.63786	0.174315	0.0871574	−	0.996195i	$-0.472222\pi$
$229$	2.63786	0.174315	0.0871574	+	0.996195i	$0.472222\pi$
$230$	−5.09377	−0.335873
$231$	4.46170	0.293559
$232$	−8.95879	−0.588173
$233$	−15.3296	−1.00428	−0.502138	−	0.864788i	$-0.667453\pi$
$233$	−15.3296	−1.00428	−0.502138	+	0.864788i	$0.667453\pi$
$234$	−1.79939	−0.117630
$235$	−1.73731	−0.113330
$236$	−1.56050	−0.101580
$237$	13.7351	0.892193
$238$	−14.0381	−0.909956
$239$	4.49219	0.290576	0.145288	−	0.989389i	$-0.453589\pi$
$239$	4.49219	0.290576	0.145288	+	0.989389i	$0.453589\pi$
$240$	−1.09573	−0.0707288
$241$	8.80007	0.566862	0.283431	−	0.958993i	$-0.408527\pi$
$241$	8.80007	0.566862	0.283431	+	0.958993i	$0.408527\pi$
$242$	8.96427	0.576245
$243$	−15.3775	−0.986469
$244$	6.15940	0.394315
$245$	1.14476	0.0731360
$246$	11.3797	0.725546
$247$	−0.556163	−0.0353878
$248$	−1.00000	−0.0635001
$249$	1.33422	0.0845529
$250$	−1.00000	−0.0632456
$251$	12.6808	0.800403	0.400202	−	0.916427i	$-0.368940\pi$
$251$	12.6808	0.800403	0.400202	+	0.916427i	$0.368940\pi$
$252$	5.13527	0.323492
$253$	7.26773	0.456919
$254$	13.4853	0.846143
$255$	5.38978	0.337521
$256$	1.00000	0.0625000
$257$	8.48959	0.529566	0.264783	−	0.964308i	$-0.414700\pi$
$257$	8.48959	0.529566	0.264783	+	0.964308i	$0.414700\pi$
$258$	−4.60090	−0.286439
$259$	0.322684	0.0200506
$260$	−1.00000	−0.0620174
$261$	−16.1203	−0.997823
$262$	−5.38524	−0.332701
$263$	−3.33405	−0.205586	−0.102793	−	0.994703i	$-0.532778\pi$
$263$	−3.33405	−0.205586	−0.102793	+	0.994703i	$0.532778\pi$
$264$	1.56337	0.0962187
$265$	−5.68358	−0.349140
$266$	1.58724	0.0973197
$267$	17.6948	1.08290
$268$	5.47308	0.334322
$269$	−23.8878	−1.45647	−0.728233	−	0.685330i	$-0.759658\pi$
$269$	−23.8878	−1.45647	−0.728233	+	0.685330i	$0.759658\pi$
$270$	−5.25881	−0.320041
$271$	24.2540	1.47332	0.736662	−	0.676261i	$-0.236401\pi$
$271$	24.2540	1.47332	0.736662	+	0.676261i	$0.236401\pi$
$272$	−4.91892	−0.298253
$273$	−3.12709	−0.189260
$274$	−14.9994	−0.906150
$275$	1.42679	0.0860386
$276$	−5.58137	−0.335959
$277$	−26.7603	−1.60787	−0.803935	−	0.594717i	$-0.797264\pi$
$277$	−26.7603	−1.60787	−0.803935	+	0.594717i	$0.797264\pi$
$278$	−7.80806	−0.468296
$279$	−1.79939	−0.107726
$280$	2.85390	0.170553
$281$	−25.8934	−1.54467	−0.772335	−	0.635215i	$-0.780912\pi$
$281$	−25.8934	−1.54467	−0.772335	+	0.635215i	$0.780912\pi$
$282$	−1.90361	−0.113359
$283$	−14.7398	−0.876190	−0.438095	−	0.898929i	$-0.644347\pi$
$283$	−14.7398	−0.876190	−0.438095	+	0.898929i	$0.644347\pi$
$284$	1.02381	0.0607518
$285$	−0.609402	−0.0360979
$286$	1.42679	0.0843678
$287$	−29.6394	−1.74956
$288$	1.79939	0.106030
$289$	7.19576	0.423280
$290$	−8.95879	−0.526078
$291$	15.7445	0.922956
$292$	−1.59055	−0.0930801
$293$	−1.31696	−0.0769374	−0.0384687	−	0.999260i	$-0.512248\pi$
$293$	−1.31696	−0.0769374	−0.0384687	+	0.999260i	$0.512248\pi$
$294$	1.25434	0.0731547
$295$	−1.56050	−0.0908560
$296$	0.113068	0.00657192
$297$	7.50321	0.435381
$298$	−5.71686	−0.331169
$299$	−5.09377	−0.294580
$300$	−1.09573	−0.0632617
$301$	11.9834	0.690712
$302$	6.56934	0.378023
$303$	16.0623	0.922757
$304$	0.556163	0.0318982
$305$	6.15940	0.352686
$306$	−8.85103	−0.505980
$307$	5.69668	0.325127	0.162563	−	0.986698i	$-0.448024\pi$
$307$	5.69668	0.325127	0.162563	+	0.986698i	$0.448024\pi$
$308$	−4.07192	−0.232019
$309$	−19.3179	−1.09895
$310$	−1.00000	−0.0567962
$311$	0.993683	0.0563466	0.0281733	−	0.999603i	$-0.491031\pi$
$311$	0.993683	0.0563466	0.0281733	+	0.999603i	$0.491031\pi$
$312$	−1.09573	−0.0620332
$313$	20.6207	1.16555	0.582776	−	0.812633i	$-0.301966\pi$
$313$	20.6207	1.16555	0.582776	+	0.812633i	$0.301966\pi$
$314$	3.57605	0.201808
$315$	5.13527	0.289340
$316$	−12.5352	−0.705160
$317$	−31.8845	−1.79081	−0.895406	−	0.445252i	$-0.853114\pi$
$317$	−31.8845	−1.79081	−0.895406	+	0.445252i	$0.853114\pi$
$318$	−6.22764	−0.349229
$319$	12.7823	0.715672
$320$	1.00000	0.0559017
$321$	12.0221	0.671009
$322$	14.5371	0.810122
$323$	−2.73572	−0.152220
$324$	−0.364052	−0.0202251
$325$	−1.00000	−0.0554700
$326$	23.6237	1.30840
$327$	7.13045	0.394315
$328$	−10.3856	−0.573448
$329$	4.95811	0.273350
$330$	1.56337	0.0860607
$331$	−11.8191	−0.649637	−0.324819	−	0.945776i	$-0.605303\pi$
$331$	−11.8191	−0.649637	−0.324819	+	0.945776i	$0.605303\pi$
$332$	−1.21766	−0.0668278
$333$	0.203452	0.0111491
$334$	11.3565	0.621398
$335$	5.47308	0.299027
$336$	3.12709	0.170597
$337$	−11.8078	−0.643210	−0.321605	−	0.946874i	$-0.604222\pi$
$337$	−11.8078	−0.643210	−0.321605	+	0.946874i	$0.604222\pi$
$338$	−1.00000	−0.0543928
$339$	−16.2072	−0.880253
$340$	−4.91892	−0.266766
$341$	1.42679	0.0772650
$342$	1.00075	0.0541145
$343$	16.7103	0.902271
$344$	4.19895	0.226392
$345$	−5.58137	−0.300491
$346$	18.1355	0.974972
$347$	24.3131	1.30520	0.652598	−	0.757704i	$-0.273679\pi$
$347$	24.3131	1.30520	0.652598	+	0.757704i	$0.273679\pi$
$348$	−9.81637	−0.526213
$349$	−18.6646	−0.999095	−0.499547	−	0.866287i	$-0.666500\pi$
$349$	−18.6646	−0.999095	−0.499547	+	0.866287i	$0.666500\pi$
$350$	2.85390	0.152547
$351$	−5.25881	−0.280694
$352$	−1.42679	−0.0760481
$353$	−19.7388	−1.05059	−0.525295	−	0.850920i	$-0.676045\pi$
$353$	−19.7388	−1.05059	−0.525295	+	0.850920i	$0.676045\pi$
$354$	−1.70988	−0.0908792
$355$	1.02381	0.0543381
$356$	−16.1489	−0.855890
$357$	−15.3819	−0.814097
$358$	−8.00219	−0.422929
$359$	3.67513	0.193966	0.0969829	−	0.995286i	$-0.469081\pi$
$359$	3.67513	0.193966	0.0969829	+	0.995286i	$0.469081\pi$
$360$	1.79939	0.0948360
$361$	−18.6907	−0.983720
$362$	6.88738	0.361993
$363$	9.82238	0.515541
$364$	2.85390	0.149585
$365$	−1.59055	−0.0832533
$366$	6.74901	0.352777
$367$	−1.14874	−0.0599637	−0.0299819	−	0.999550i	$-0.509545\pi$
$367$	−1.14874	−0.0599637	−0.0299819	+	0.999550i	$0.509545\pi$
$368$	5.09377	0.265531
$369$	−18.6877	−0.972841
$370$	0.113068	0.00587811
$371$	16.2204	0.842120
$372$	−1.09573	−0.0568107
$373$	−19.4432	−1.00673	−0.503366	−	0.864073i	$-0.667905\pi$
$373$	−19.4432	−1.00673	−0.503366	+	0.864073i	$0.667905\pi$
$374$	7.01826	0.362906
$375$	−1.09573	−0.0565830
$376$	1.73731	0.0895949
$377$	−8.95879	−0.461401
$378$	15.0081	0.771935
$379$	10.4244	0.535464	0.267732	−	0.963493i	$-0.413726\pi$
$379$	10.4244	0.535464	0.267732	+	0.963493i	$0.413726\pi$
$380$	0.556163	0.0285306
$381$	14.7762	0.757007
$382$	1.55391	0.0795050
$383$	−4.61609	−0.235871	−0.117936	−	0.993021i	$-0.537628\pi$
$383$	−4.61609	−0.235871	−0.117936	+	0.993021i	$0.537628\pi$
$384$	1.09573	0.0559160
$385$	−4.07192	−0.207524
$386$	−2.95951	−0.150635
$387$	7.55554	0.384069
$388$	−14.3690	−0.729474
$389$	2.24055	0.113601	0.0568003	−	0.998386i	$-0.481910\pi$
$389$	2.24055	0.113601	0.0568003	+	0.998386i	$0.481910\pi$
$390$	−1.09573	−0.0554842
$391$	−25.0558	−1.26713
$392$	−1.14476	−0.0578191
$393$	−5.90075	−0.297653
$394$	7.76332	0.391111
$395$	−12.5352	−0.630714
$396$	−2.56735	−0.129014
$397$	−2.60027	−0.130504	−0.0652520	−	0.997869i	$-0.520785\pi$
$397$	−2.60027	−0.130504	−0.0652520	+	0.997869i	$0.520785\pi$
$398$	0.784095	0.0393031
$399$	1.73917	0.0870676
$400$	1.00000	0.0500000
$401$	−25.6158	−1.27919	−0.639595	−	0.768712i	$-0.720898\pi$
$401$	−25.6158	−1.27919	−0.639595	+	0.768712i	$0.720898\pi$
$402$	5.99700	0.299103
$403$	−1.00000	−0.0498135
$404$	−14.6591	−0.729317
$405$	−0.364052	−0.0180899
$406$	25.5675	1.26889
$407$	−0.161324	−0.00799652
$408$	−5.38978	−0.266834
$409$	−2.34201	−0.115805	−0.0579025	−	0.998322i	$-0.518441\pi$
$409$	−2.34201	−0.115805	−0.0579025	+	0.998322i	$0.518441\pi$
$410$	−10.3856	−0.512907
$411$	−16.4353	−0.810692
$412$	17.6302	0.868578
$413$	4.45352	0.219144
$414$	9.16565	0.450467
$415$	−1.21766	−0.0597726
$416$	1.00000	0.0490290
$417$	−8.55549	−0.418964
$418$	−0.793528	−0.0388127
$419$	25.9810	1.26926	0.634628	−	0.772818i	$-0.281154\pi$
$419$	25.9810	1.26926	0.634628	+	0.772818i	$0.281154\pi$
$420$	3.12709	0.152587
$421$	−32.6509	−1.59131	−0.795653	−	0.605753i	$-0.792872\pi$
$421$	−32.6509	−1.59131	−0.795653	+	0.605753i	$0.792872\pi$
$422$	−24.3760	−1.18661
$423$	3.12609	0.151996
$424$	5.68358	0.276019
$425$	−4.91892	−0.238603
$426$	1.12181	0.0543520
$427$	−17.5783	−0.850675
$428$	−10.9718	−0.530344
$429$	1.56337	0.0754802
$430$	4.19895	0.202491
$431$	−16.8295	−0.810646	−0.405323	−	0.914174i	$-0.632841\pi$
$431$	−16.8295	−0.810646	−0.405323	+	0.914174i	$0.632841\pi$
$432$	5.25881	0.253015
$433$	4.38930	0.210936	0.105468	−	0.994423i	$-0.466366\pi$
$433$	4.38930	0.210936	0.105468	+	0.994423i	$0.466366\pi$
$434$	2.85390	0.136992
$435$	−9.81637	−0.470659
$436$	−6.50751	−0.311653
$437$	2.83297	0.135519
$438$	−1.74281	−0.0832746
$439$	0.197918	0.00944610	0.00472305	−	0.999989i	$-0.498497\pi$
$439$	0.197918	0.00944610	0.00472305	+	0.999989i	$0.498497\pi$
$440$	−1.42679	−0.0680195
$441$	−2.05986	−0.0980887
$442$	−4.91892	−0.233969
$443$	1.49193	0.0708836	0.0354418	−	0.999372i	$-0.488716\pi$
$443$	1.49193	0.0708836	0.0354418	+	0.999372i	$0.488716\pi$
$444$	0.123891	0.00587961
$445$	−16.1489	−0.765531
$446$	−19.5925	−0.927732
$447$	−6.26411	−0.296282
$448$	−2.85390	−0.134834
$449$	3.85099	0.181740	0.0908698	−	0.995863i	$-0.471035\pi$
$449$	3.85099	0.181740	0.0908698	+	0.995863i	$0.471035\pi$
$450$	1.79939	0.0848239
$451$	14.8180	0.697754
$452$	14.7913	0.695723
$453$	7.19819	0.338201
$454$	10.6523	0.499936
$455$	2.85390	0.133793
$456$	0.609402	0.0285379
$457$	−24.6944	−1.15516	−0.577579	−	0.816335i	$-0.696002\pi$
$457$	−24.6944	−1.15516	−0.577579	+	0.816335i	$0.696002\pi$
$458$	−2.63786	−0.123259
$459$	−25.8677	−1.20740
$460$	5.09377	0.237498
$461$	−0.602112	−0.0280432	−0.0140216	−	0.999902i	$-0.504463\pi$
$461$	−0.602112	−0.0280432	−0.0140216	+	0.999902i	$0.504463\pi$
$462$	−4.46170	−0.207577
$463$	13.5522	0.629826	0.314913	−	0.949121i	$-0.398025\pi$
$463$	13.5522	0.629826	0.314913	+	0.949121i	$0.398025\pi$
$464$	8.95879	0.415901
$465$	−1.09573	−0.0508130
$466$	15.3296	0.710130
$467$	−31.5857	−1.46161	−0.730807	−	0.682584i	$-0.760856\pi$
$467$	−31.5857	−1.46161	−0.730807	+	0.682584i	$0.760856\pi$
$468$	1.79939	0.0831766
$469$	−15.6196	−0.721248
$470$	1.73731	0.0801361
$471$	3.91837	0.180549
$472$	1.56050	0.0718280
$473$	−5.99102	−0.275467
$474$	−13.7351	−0.630876
$475$	0.556163	0.0255185
$476$	14.0381	0.643436
$477$	10.2270	0.468260
$478$	−4.49219	−0.205468
$479$	−13.0563	−0.596556	−0.298278	−	0.954479i	$-0.596412\pi$
$479$	−13.0563	−0.596556	−0.298278	+	0.954479i	$0.596412\pi$
$480$	1.09573	0.0500128
$481$	0.113068	0.00515544
$482$	−8.80007	−0.400832
$483$	15.9287	0.724780
$484$	−8.96427	−0.407467
$485$	−14.3690	−0.652462
$486$	15.3775	0.697539
$487$	30.0862	1.36333	0.681667	−	0.731662i	$-0.261255\pi$
$487$	30.0862	1.36333	0.681667	+	0.731662i	$0.261255\pi$
$488$	−6.15940	−0.278823
$489$	25.8851	1.17056
$490$	−1.14476	−0.0517149
$491$	−18.7618	−0.846707	−0.423353	−	0.905965i	$-0.639147\pi$
$491$	−18.7618	−0.846707	−0.423353	+	0.905965i	$0.639147\pi$
$492$	−11.3797	−0.513038
$493$	−44.0676	−1.98470
$494$	0.556163	0.0250230
$495$	−2.56735	−0.115394
$496$	1.00000	0.0449013
$497$	−2.92185	−0.131063
$498$	−1.33422	−0.0597879
$499$	−28.3103	−1.26734	−0.633672	−	0.773602i	$-0.718453\pi$
$499$	−28.3103	−1.26734	−0.633672	+	0.773602i	$0.718453\pi$
$500$	1.00000	0.0447214
$501$	12.4436	0.555937
$502$	−12.6808	−0.565971
$503$	−13.9581	−0.622361	−0.311180	−	0.950351i	$-0.600724\pi$
$503$	−13.9581	−0.622361	−0.311180	+	0.950351i	$0.600724\pi$
$504$	−5.13527	−0.228743
$505$	−14.6591	−0.652321
$506$	−7.26773	−0.323090
$507$	−1.09573	−0.0486629
$508$	−13.4853	−0.598314
$509$	−19.1610	−0.849298	−0.424649	−	0.905358i	$-0.639602\pi$
$509$	−19.1610	−0.849298	−0.424649	+	0.905358i	$0.639602\pi$
$510$	−5.38978	−0.238664
$511$	4.53928	0.200806
$512$	−1.00000	−0.0441942
$513$	2.92476	0.129131
$514$	−8.48959	−0.374460
$515$	17.6302	0.776880
$516$	4.60090	0.202543
$517$	−2.47877	−0.109016
$518$	−0.322684	−0.0141779
$519$	19.8716	0.872265
$520$	1.00000	0.0438529
$521$	−12.2941	−0.538613	−0.269306	−	0.963055i	$-0.586794\pi$
$521$	−12.2941	−0.538613	−0.269306	+	0.963055i	$0.586794\pi$
$522$	16.1203	0.705567
$523$	32.1724	1.40680	0.703401	−	0.710793i	$-0.251664\pi$
$523$	32.1724	1.40680	0.703401	+	0.710793i	$0.251664\pi$
$524$	5.38524	0.235255
$525$	3.12709	0.136478
$526$	3.33405	0.145371
$527$	−4.91892	−0.214271
$528$	−1.56337	−0.0680369
$529$	2.94647	0.128107
$530$	5.68358	0.246879
$531$	2.80795	0.121855
$532$	−1.58724	−0.0688154
$533$	−10.3856	−0.449849
$534$	−17.6948	−0.765727
$535$	−10.9718	−0.474354
$536$	−5.47308	−0.236401
$537$	−8.76820	−0.378376
$538$	23.8878	1.02988
$539$	1.63333	0.0703525
$540$	5.25881	0.226303
$541$	−4.43175	−0.190536	−0.0952678	−	0.995452i	$-0.530371\pi$
$541$	−4.43175	−0.190536	−0.0952678	+	0.995452i	$0.530371\pi$
$542$	−24.2540	−1.04180
$543$	7.54668	0.323859
$544$	4.91892	0.210897
$545$	−6.50751	−0.278751
$546$	3.12709	0.133827
$547$	−12.2208	−0.522525	−0.261262	−	0.965268i	$-0.584139\pi$
$547$	−12.2208	−0.522525	−0.261262	+	0.965268i	$0.584139\pi$
$548$	14.9994	0.640745
$549$	−11.0831	−0.473017
$550$	−1.42679	−0.0608385
$551$	4.98255	0.212264
$552$	5.58137	0.237559
$553$	35.7742	1.52128
$554$	26.7603	1.13694
$555$	0.123891	0.00525888
$556$	7.80806	0.331135
$557$	−18.6407	−0.789830	−0.394915	−	0.918718i	$-0.629226\pi$
$557$	−18.6407	−0.789830	−0.394915	+	0.918718i	$0.629226\pi$
$558$	1.79939	0.0761741
$559$	4.19895	0.177597
$560$	−2.85390	−0.120599
$561$	7.69009	0.324676
$562$	25.8934	1.09225
$563$	27.4199	1.15561	0.577805	−	0.816175i	$-0.303909\pi$
$563$	27.4199	1.15561	0.577805	+	0.816175i	$0.303909\pi$
$564$	1.90361	0.0801566
$565$	14.7913	0.622273
$566$	14.7398	0.619560
$567$	1.03897	0.0436326
$568$	−1.02381	−0.0429580
$569$	9.79534	0.410642	0.205321	−	0.978695i	$-0.434176\pi$
$569$	9.79534	0.410642	0.205321	+	0.978695i	$0.434176\pi$
$570$	0.609402	0.0255251
$571$	1.58372	0.0662766	0.0331383	−	0.999451i	$-0.489450\pi$
$571$	1.58372	0.0662766	0.0331383	+	0.999451i	$0.489450\pi$
$572$	−1.42679	−0.0596571
$573$	1.70266	0.0711296
$574$	29.6394	1.23713
$575$	5.09377	0.212425
$576$	−1.79939	−0.0749744
$577$	9.24852	0.385021	0.192510	−	0.981295i	$-0.438337\pi$
$577$	9.24852	0.385021	0.192510	+	0.981295i	$0.438337\pi$
$578$	−7.19576	−0.299304
$579$	−3.24281	−0.134767
$580$	8.95879	0.371993
$581$	3.47509	0.144171
$582$	−15.7445	−0.652629
$583$	−8.10927	−0.335852
$584$	1.59055	0.0658175
$585$	1.79939	0.0743955
$586$	1.31696	0.0544030
$587$	−12.4984	−0.515865	−0.257933	−	0.966163i	$-0.583041\pi$
$587$	−12.4984	−0.515865	−0.257933	+	0.966163i	$0.583041\pi$
$588$	−1.25434	−0.0517282
$589$	0.556163	0.0229163
$590$	1.56050	0.0642449
$591$	8.50647	0.349909
$592$	−0.113068	−0.00464705
$593$	−11.1319	−0.457132	−0.228566	−	0.973528i	$-0.573404\pi$
$593$	−11.1319	−0.457132	−0.228566	+	0.973528i	$0.573404\pi$
$594$	−7.50321	−0.307861
$595$	14.0381	0.575507
$596$	5.71686	0.234172
$597$	0.859153	0.0351628
$598$	5.09377	0.208300
$599$	−3.64834	−0.149067	−0.0745336	−	0.997219i	$-0.523747\pi$
$599$	−3.64834	−0.149067	−0.0745336	+	0.997219i	$0.523747\pi$
$600$	1.09573	0.0447328
$601$	−1.58042	−0.0644666	−0.0322333	−	0.999480i	$-0.510262\pi$
$601$	−1.58042	−0.0644666	−0.0322333	+	0.999480i	$0.510262\pi$
$602$	−11.9834	−0.488407
$603$	−9.84819	−0.401049
$604$	−6.56934	−0.267303
$605$	−8.96427	−0.364449
$606$	−16.0623	−0.652488
$607$	11.2496	0.456608	0.228304	−	0.973590i	$-0.426682\pi$
$607$	11.2496	0.456608	0.228304	+	0.973590i	$0.426682\pi$
$608$	−0.556163	−0.0225554
$609$	28.0150	1.13522
$610$	−6.15940	−0.249387
$611$	1.73731	0.0702840
$612$	8.85103	0.357782
$613$	−32.2074	−1.30085	−0.650423	−	0.759572i	$-0.725408\pi$
$613$	−32.2074	−1.30085	−0.650423	+	0.759572i	$0.725408\pi$
$614$	−5.69668	−0.229899
$615$	−11.3797	−0.458875
$616$	4.07192	0.164062
$617$	−33.6639	−1.35526	−0.677628	−	0.735405i	$-0.736992\pi$
$617$	−33.6639	−1.35526	−0.677628	+	0.735405i	$0.736992\pi$
$618$	19.3179	0.777078
$619$	−21.9632	−0.882775	−0.441387	−	0.897317i	$-0.645514\pi$
$619$	−21.9632	−0.882775	−0.441387	+	0.897317i	$0.645514\pi$
$620$	1.00000	0.0401610
$621$	26.7872	1.07493
$622$	−0.993683	−0.0398431
$623$	46.0874	1.84645
$624$	1.09573	0.0438641
$625$	1.00000	0.0400000
$626$	−20.6207	−0.824170
$627$	−0.869489	−0.0347240
$628$	−3.57605	−0.142700
$629$	0.556171	0.0221760
$630$	−5.13527	−0.204594
$631$	27.0982	1.07876	0.539381	−	0.842062i	$-0.318658\pi$
$631$	27.0982	1.07876	0.539381	+	0.842062i	$0.318658\pi$
$632$	12.5352	0.498624
$633$	−26.7095	−1.06161
$634$	31.8845	1.26629
$635$	−13.4853	−0.535148
$636$	6.22764	0.246942
$637$	−1.14476	−0.0453570
$638$	−12.7823	−0.506056
$639$	−1.84222	−0.0728773
$640$	−1.00000	−0.0395285
$641$	8.13482	0.321306	0.160653	−	0.987011i	$-0.448640\pi$
$641$	8.13482	0.321306	0.160653	+	0.987011i	$0.448640\pi$
$642$	−12.0221	−0.474475
$643$	17.4004	0.686205	0.343102	−	0.939298i	$-0.388522\pi$
$643$	17.4004	0.686205	0.343102	+	0.939298i	$0.388522\pi$
$644$	−14.5371	−0.572843
$645$	4.60090	0.181160
$646$	2.73572	0.107636
$647$	−12.3281	−0.484669	−0.242334	−	0.970193i	$-0.577913\pi$
$647$	−12.3281	−0.484669	−0.242334	+	0.970193i	$0.577913\pi$
$648$	0.364052	0.0143013
$649$	−2.22651	−0.0873981
$650$	1.00000	0.0392232
$651$	3.12709	0.122560
$652$	−23.6237	−0.925176
$653$	39.7267	1.55463	0.777314	−	0.629113i	$-0.216582\pi$
$653$	39.7267	1.55463	0.777314	+	0.629113i	$0.216582\pi$
$654$	−7.13045	−0.278823
$655$	5.38524	0.210419
$656$	10.3856	0.405489
$657$	2.86202	0.111658
$658$	−4.95811	−0.193287
$659$	−0.427375	−0.0166482	−0.00832409	−	0.999965i	$-0.502650\pi$
$659$	−0.427375	−0.0166482	−0.00832409	+	0.999965i	$0.502650\pi$
$660$	−1.56337	−0.0608541
$661$	25.9335	1.00869	0.504347	−	0.863501i	$-0.331733\pi$
$661$	25.9335	1.00869	0.504347	+	0.863501i	$0.331733\pi$
$662$	11.8191	0.459363
$663$	−5.38978	−0.209322
$664$	1.21766	0.0472544
$665$	−1.58724	−0.0615504
$666$	−0.203452	−0.00788362
$667$	45.6340	1.76696
$668$	−11.3565	−0.439395
$669$	−21.4680	−0.830001
$670$	−5.47308	−0.211444
$671$	8.78817	0.339264
$672$	−3.12709	−0.120630
$673$	46.2210	1.78169	0.890845	−	0.454308i	$-0.150113\pi$
$673$	46.2210	1.78169	0.890845	+	0.454308i	$0.150113\pi$
$674$	11.8078	0.454818
$675$	5.25881	0.202412
$676$	1.00000	0.0384615
$677$	27.0925	1.04125	0.520624	−	0.853786i	$-0.325699\pi$
$677$	27.0925	1.04125	0.520624	+	0.853786i	$0.325699\pi$
$678$	16.2072	0.622433
$679$	41.0077	1.57373
$680$	4.91892	0.188632
$681$	11.6720	0.447270
$682$	−1.42679	−0.0546346
$683$	0.881729	0.0337384	0.0168692	−	0.999858i	$-0.494630\pi$
$683$	0.881729	0.0337384	0.0168692	+	0.999858i	$0.494630\pi$
$684$	−1.00075	−0.0382647
$685$	14.9994	0.573099
$686$	−16.7103	−0.638002
$687$	−2.89037	−0.110275
$688$	−4.19895	−0.160084
$689$	5.68358	0.216527
$690$	5.58137	0.212479
$691$	5.72070	0.217626	0.108813	−	0.994062i	$-0.465295\pi$
$691$	5.72070	0.217626	0.108813	+	0.994062i	$0.465295\pi$
$692$	−18.1355	−0.689410
$693$	7.32695	0.278328
$694$	−24.3131	−0.922914
$695$	7.80806	0.296176
$696$	9.81637	0.372089
$697$	−51.0858	−1.93501
$698$	18.6646	0.706467
$699$	16.7970	0.635322
$700$	−2.85390	−0.107867
$701$	0.564710	0.0213288	0.0106644	−	0.999943i	$-0.496605\pi$
$701$	0.564710	0.0213288	0.0106644	+	0.999943i	$0.496605\pi$
$702$	5.25881	0.198481
$703$	−0.0628841	−0.00237172
$704$	1.42679	0.0537742
$705$	1.90361	0.0716942
$706$	19.7388	0.742880
$707$	41.8356	1.57339
$708$	1.70988	0.0642613
$709$	26.3173	0.988366	0.494183	−	0.869358i	$-0.335467\pi$
$709$	26.3173	0.988366	0.494183	+	0.869358i	$0.335467\pi$
$710$	−1.02381	−0.0384228
$711$	22.5557	0.845904
$712$	16.1489	0.605206
$713$	5.09377	0.190763
$714$	15.3819	0.575654
$715$	−1.42679	−0.0533589
$716$	8.00219	0.299056
$717$	−4.92221	−0.183823
$718$	−3.67513	−0.137155
$719$	−22.3528	−0.833618	−0.416809	−	0.908994i	$-0.636852\pi$
$719$	−22.3528	−0.833618	−0.416809	+	0.908994i	$0.636852\pi$
$720$	−1.79939	−0.0670592
$721$	−50.3149	−1.87382
$722$	18.6907	0.695595
$723$	−9.64245	−0.358607
$724$	−6.88738	−0.255968
$725$	8.95879	0.332721
$726$	−9.82238	−0.364543
$727$	−39.9545	−1.48183	−0.740915	−	0.671598i	$-0.765608\pi$
$727$	−39.9545	−1.48183	−0.740915	+	0.671598i	$0.765608\pi$
$728$	−2.85390	−0.105773
$729$	17.9417	0.664507
$730$	1.59055	0.0588690
$731$	20.6543	0.763927
$732$	−6.74901	−0.249451
$733$	0.157500	0.00581739	0.00290870	−	0.999996i	$-0.499074\pi$
$733$	0.157500	0.00581739	0.00290870	+	0.999996i	$0.499074\pi$
$734$	1.14874	0.0424008
$735$	−1.25434	−0.0462671
$736$	−5.09377	−0.187759
$737$	7.80894	0.287646
$738$	18.6877	0.687902
$739$	44.2620	1.62820	0.814101	−	0.580723i	$-0.197230\pi$
$739$	44.2620	1.62820	0.814101	+	0.580723i	$0.197230\pi$
$740$	−0.113068	−0.00415645
$741$	0.609402	0.0223870
$742$	−16.2204	−0.595469
$743$	6.18208	0.226798	0.113399	−	0.993550i	$-0.463826\pi$
$743$	6.18208	0.226798	0.113399	+	0.993550i	$0.463826\pi$
$744$	1.09573	0.0401712
$745$	5.71686	0.209450
$746$	19.4432	0.711867
$747$	2.19104	0.0801660
$748$	−7.01826	−0.256613
$749$	31.3125	1.14414
$750$	1.09573	0.0400102
$751$	33.8223	1.23419	0.617096	−	0.786888i	$-0.288309\pi$
$751$	33.8223	1.23419	0.617096	+	0.786888i	$0.288309\pi$
$752$	−1.73731	−0.0633532
$753$	−13.8946	−0.506349
$754$	8.95879	0.326260
$755$	−6.56934	−0.239083
$756$	−15.0081	−0.545840
$757$	−3.40398	−0.123720	−0.0618599	−	0.998085i	$-0.519703\pi$
$757$	−3.40398	−0.123720	−0.0618599	+	0.998085i	$0.519703\pi$
$758$	−10.4244	−0.378630
$759$	−7.96344	−0.289055
$760$	−0.556163	−0.0201742
$761$	−5.69056	−0.206283	−0.103141	−	0.994667i	$-0.532889\pi$
$761$	−5.69056	−0.206283	−0.103141	+	0.994667i	$0.532889\pi$
$762$	−14.7762	−0.535285
$763$	18.5718	0.672345
$764$	−1.55391	−0.0562185
$765$	8.85103	0.320010
$766$	4.61609	0.166786
$767$	1.56050	0.0563465
$768$	−1.09573	−0.0395386
$769$	46.1282	1.66343	0.831713	−	0.555206i	$-0.187361\pi$
$769$	46.1282	1.66343	0.831713	+	0.555206i	$0.187361\pi$
$770$	4.07192	0.146742
$771$	−9.30225	−0.335013
$772$	2.95951	0.106515
$773$	23.0841	0.830278	0.415139	−	0.909758i	$-0.363733\pi$
$773$	23.0841	0.830278	0.415139	+	0.909758i	$0.363733\pi$
$774$	−7.55554	−0.271578
$775$	1.00000	0.0359211
$776$	14.3690	0.515816
$777$	−0.353573	−0.0126844
$778$	−2.24055	−0.0803277
$779$	5.77608	0.206949
$780$	1.09573	0.0392333
$781$	1.46076	0.0522700
$782$	25.0558	0.895995
$783$	47.1126	1.68367
$784$	1.14476	0.0408842
$785$	−3.57605	−0.127635
$786$	5.90075	0.210473
$787$	11.9131	0.424657	0.212328	−	0.977198i	$-0.431895\pi$
$787$	11.9131	0.424657	0.212328	+	0.977198i	$0.431895\pi$
$788$	−7.76332	−0.276557
$789$	3.65320	0.130057
$790$	12.5352	0.445982
$791$	−42.2128	−1.50092
$792$	2.56735	0.0912266
$793$	−6.15940	−0.218727
$794$	2.60027	0.0922803
$795$	6.22764	0.220872
$796$	−0.784095	−0.0277915
$797$	−49.0481	−1.73737	−0.868687	−	0.495362i	$-0.835035\pi$
$797$	−49.0481	−1.73737	−0.868687	+	0.495362i	$0.835035\pi$
$798$	−1.73917	−0.0615661
$799$	8.54568	0.302325
$800$	−1.00000	−0.0353553
$801$	29.0581	1.02672
$802$	25.6158	0.904524
$803$	−2.26938	−0.0800848
$804$	−5.99700	−0.211498
$805$	−14.5371	−0.512366
$806$	1.00000	0.0352235
$807$	26.1745	0.921385
$808$	14.6591	0.515705
$809$	2.43560	0.0856312	0.0428156	−	0.999083i	$-0.486367\pi$
$809$	2.43560	0.0856312	0.0428156	+	0.999083i	$0.486367\pi$
$810$	0.364052	0.0127915
$811$	−26.0116	−0.913392	−0.456696	−	0.889623i	$-0.650967\pi$
$811$	−26.0116	−0.913392	−0.456696	+	0.889623i	$0.650967\pi$
$812$	−25.5675	−0.897244
$813$	−26.5757	−0.932050
$814$	0.161324	0.00565439
$815$	−23.6237	−0.827502
$816$	5.38978	0.188680
$817$	−2.33530	−0.0817019
$818$	2.34201	0.0818865
$819$	−5.13527	−0.179441
$820$	10.3856	0.362680
$821$	−32.0382	−1.11814	−0.559070	−	0.829121i	$-0.688842\pi$
$821$	−32.0382	−1.11814	−0.559070	+	0.829121i	$0.688842\pi$
$822$	16.4353	0.573246
$823$	24.5580	0.856038	0.428019	−	0.903770i	$-0.359212\pi$
$823$	24.5580	0.856038	0.428019	+	0.903770i	$0.359212\pi$
$824$	−17.6302	−0.614177
$825$	−1.56337	−0.0544295
$826$	−4.45352	−0.154958
$827$	−48.9636	−1.70263	−0.851316	−	0.524653i	$-0.824195\pi$
$827$	−48.9636	−1.70263	−0.851316	+	0.524653i	$0.824195\pi$
$828$	−9.16565	−0.318529
$829$	9.52307	0.330750	0.165375	−	0.986231i	$-0.447117\pi$
$829$	9.52307	0.330750	0.165375	+	0.986231i	$0.447117\pi$
$830$	1.21766	0.0422656
$831$	29.3219	1.01717
$832$	−1.00000	−0.0346688
$833$	−5.63098	−0.195102
$834$	8.55549	0.296252
$835$	−11.3565	−0.393006
$836$	0.793528	0.0274447
$837$	5.25881	0.181771
$838$	−25.9810	−0.897499
$839$	−3.29458	−0.113742	−0.0568708	−	0.998382i	$-0.518112\pi$
$839$	−3.29458	−0.113742	−0.0568708	+	0.998382i	$0.518112\pi$
$840$	−3.12709	−0.107895
$841$	51.2599	1.76758
$842$	32.6509	1.12522
$843$	28.3721	0.977186
$844$	24.3760	0.839058
$845$	1.00000	0.0344010
$846$	−3.12609	−0.107477
$847$	25.5832	0.879048
$848$	−5.68358	−0.195175
$849$	16.1508	0.554293
$850$	4.91892	0.168718
$851$	−0.575940	−0.0197430
$852$	−1.12181	−0.0384326
$853$	20.3476	0.696687	0.348344	−	0.937367i	$-0.386744\pi$
$853$	20.3476	0.696687	0.348344	+	0.937367i	$0.386744\pi$
$854$	17.5783	0.601518
$855$	−1.00075	−0.0342250
$856$	10.9718	0.375010
$857$	43.3147	1.47960	0.739800	−	0.672827i	$-0.234920\pi$
$857$	43.3147	1.47960	0.739800	+	0.672827i	$0.234920\pi$
$858$	−1.56337	−0.0533725
$859$	−8.20208	−0.279851	−0.139926	−	0.990162i	$-0.544686\pi$
$859$	−8.20208	−0.279851	−0.139926	+	0.990162i	$0.544686\pi$
$860$	−4.19895	−0.143183
$861$	32.4767	1.10680
$862$	16.8295	0.573213
$863$	−11.8019	−0.401740	−0.200870	−	0.979618i	$-0.564377\pi$
$863$	−11.8019	−0.401740	−0.200870	+	0.979618i	$0.564377\pi$
$864$	−5.25881	−0.178908
$865$	−18.1355	−0.616627
$866$	−4.38930	−0.149154
$867$	−7.88458	−0.267774
$868$	−2.85390	−0.0968678
$869$	−17.8851	−0.606710
$870$	9.81637	0.332806
$871$	−5.47308	−0.185448
$872$	6.50751	0.220372
$873$	25.8553	0.875071
$874$	−2.83297	−0.0958265
$875$	−2.85390	−0.0964795
$876$	1.74281	0.0588841
$877$	20.9424	0.707175	0.353588	−	0.935401i	$-0.384962\pi$
$877$	20.9424	0.707175	0.353588	+	0.935401i	$0.384962\pi$
$878$	−0.197918	−0.00667940
$879$	1.44302	0.0486719
$880$	1.42679	0.0480971
$881$	20.5098	0.690994	0.345497	−	0.938420i	$-0.387710\pi$
$881$	20.5098	0.690994	0.345497	+	0.938420i	$0.387710\pi$
$882$	2.05986	0.0693592
$883$	−33.4763	−1.12657	−0.563284	−	0.826263i	$-0.690462\pi$
$883$	−33.4763	−1.12657	−0.563284	+	0.826263i	$0.690462\pi$
$884$	4.91892	0.165441
$885$	1.70988	0.0574771
$886$	−1.49193	−0.0501223
$887$	6.68032	0.224303	0.112152	−	0.993691i	$-0.464226\pi$
$887$	6.68032	0.224303	0.112152	+	0.993691i	$0.464226\pi$
$888$	−0.123891	−0.00415751
$889$	38.4858	1.29077
$890$	16.1489	0.541312
$891$	−0.519425	−0.0174014
$892$	19.5925	0.656006
$893$	−0.966228	−0.0323336
$894$	6.26411	0.209503
$895$	8.00219	0.267484
$896$	2.85390	0.0953422
$897$	5.58137	0.186357
$898$	−3.85099	−0.128509
$899$	8.95879	0.298792
$900$	−1.79939	−0.0599795
$901$	27.9571	0.931385
$902$	−14.8180	−0.493387
$903$	−13.1305	−0.436956
$904$	−14.7913	−0.491950
$905$	−6.88738	−0.228944
$906$	−7.19819	−0.239144
$907$	−22.2710	−0.739496	−0.369748	−	0.929132i	$-0.620556\pi$
$907$	−22.2710	−0.739496	−0.369748	+	0.929132i	$0.620556\pi$
$908$	−10.6523	−0.353508
$909$	26.3774	0.874882
$910$	−2.85390	−0.0946059
$911$	−35.6013	−1.17952	−0.589762	−	0.807577i	$-0.700779\pi$
$911$	−35.6013	−1.17952	−0.589762	+	0.807577i	$0.700779\pi$
$912$	−0.609402	−0.0201793
$913$	−1.73735	−0.0574978
$914$	24.6944	0.816819
$915$	−6.74901	−0.223116
$916$	2.63786	0.0871574
$917$	−15.3690	−0.507528
$918$	25.8677	0.853760
$919$	41.9884	1.38507	0.692535	−	0.721384i	$-0.256494\pi$
$919$	41.9884	1.38507	0.692535	+	0.721384i	$0.256494\pi$
$920$	−5.09377	−0.167937
$921$	−6.24200	−0.205681
$922$	0.602112	0.0198295
$923$	−1.02381	−0.0336990
$924$	4.46170	0.146779
$925$	−0.113068	−0.00371764
$926$	−13.5522	−0.445354
$927$	−31.7235	−1.04194
$928$	−8.95879	−0.294087
$929$	−28.2626	−0.927265	−0.463632	−	0.886028i	$-0.653454\pi$
$929$	−28.2626	−0.927265	−0.463632	+	0.886028i	$0.653454\pi$
$930$	1.09573	0.0359302
$931$	0.636673	0.0208661
$932$	−15.3296	−0.502138
$933$	−1.08880	−0.0356458
$934$	31.5857	1.03352
$935$	−7.01826	−0.229522
$936$	−1.79939	−0.0588148
$937$	59.1026	1.93080	0.965400	−	0.260775i	$-0.0839782\pi$
$937$	59.1026	1.93080	0.965400	+	0.260775i	$0.0839782\pi$
$938$	15.6196	0.510000
$939$	−22.5947	−0.737349
$940$	−1.73731	−0.0566648
$941$	−8.16247	−0.266089	−0.133044	−	0.991110i	$-0.542475\pi$
$941$	−8.16247	−0.266089	−0.133044	+	0.991110i	$0.542475\pi$
$942$	−3.91837	−0.127667
$943$	52.9017	1.72272
$944$	−1.56050	−0.0507900
$945$	−15.0081	−0.488214
$946$	5.99102	0.194785
$947$	28.5300	0.927102	0.463551	−	0.886070i	$-0.346575\pi$
$947$	28.5300	0.927102	0.463551	+	0.886070i	$0.346575\pi$
$948$	13.7351	0.446097
$949$	1.59055	0.0516315
$950$	−0.556163	−0.0180443
$951$	34.9366	1.13290
$952$	−14.0381	−0.454978
$953$	−30.3585	−0.983407	−0.491704	−	0.870763i	$-0.663626\pi$
$953$	−30.3585	−0.983407	−0.491704	+	0.870763i	$0.663626\pi$
$954$	−10.2270	−0.331110
$955$	−1.55391	−0.0502834
$956$	4.49219	0.145288
$957$	−14.0059	−0.452746
$958$	13.0563	0.421829
$959$	−42.8070	−1.38231
$960$	−1.09573	−0.0353644
$961$	1.00000	0.0322581
$962$	−0.113068	−0.00364545
$963$	19.7426	0.636195
$964$	8.80007	0.283431
$965$	2.95951	0.0952700
$966$	−15.9287	−0.512497
$967$	−11.0100	−0.354059	−0.177030	−	0.984206i	$-0.556649\pi$
$967$	−11.0100	−0.354059	−0.177030	+	0.984206i	$0.556649\pi$
$968$	8.96427	0.288123
$969$	2.99760	0.0962968
$970$	14.3690	0.461360
$971$	−57.4843	−1.84476	−0.922379	−	0.386285i	$-0.873758\pi$
$971$	−57.4843	−1.84476	−0.922379	+	0.386285i	$0.873758\pi$
$972$	−15.3775	−0.493234
$973$	−22.2834	−0.714374
$974$	−30.0862	−0.964023
$975$	1.09573	0.0350913
$976$	6.15940	0.197158
$977$	8.68649	0.277905	0.138953	−	0.990299i	$-0.455626\pi$
$977$	8.68649	0.277905	0.138953	+	0.990299i	$0.455626\pi$
$978$	−25.8851	−0.827714
$979$	−23.0411	−0.736396
$980$	1.14476	0.0365680
$981$	11.7095	0.373857
$982$	18.7618	0.598712
$983$	−18.2385	−0.581719	−0.290859	−	0.956766i	$-0.593941\pi$
$983$	−18.2385	−0.581719	−0.290859	+	0.956766i	$0.593941\pi$
$984$	11.3797	0.362773
$985$	−7.76332	−0.247360
$986$	44.0676	1.40340
$987$	−5.43273	−0.172926
$988$	−0.556163	−0.0176939
$989$	−21.3885	−0.680114
$990$	2.56735	0.0815956
$991$	−24.6706	−0.783687	−0.391843	−	0.920032i	$-0.628162\pi$
$991$	−24.6706	−0.783687	−0.391843	+	0.920032i	$0.628162\pi$
$992$	−1.00000	−0.0317500
$993$	12.9505	0.410972
$994$	2.92185	0.0926753
$995$	−0.784095	−0.0248575
$996$	1.33422	0.0422764
$997$	18.1406	0.574520	0.287260	−	0.957853i	$-0.407256\pi$
$997$	18.1406	0.574520	0.287260	+	0.957853i	$0.407256\pi$
$998$	28.3103	0.896147
$999$	−0.594601	−0.0188123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.h.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.h.1.3	✓	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.09573 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.09573 q^{6} -2.85390 q^{7} -1.00000 q^{8} -1.79939 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.09573 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.09573 q^{6} -2.85390 q^{7} -1.00000 q^{8} -1.79939 q^{9} -1.00000 q^{10} +1.42679 q^{11} -1.09573 q^{12} -1.00000 q^{13} +2.85390 q^{14} -1.09573 q^{15} +1.00000 q^{16} -4.91892 q^{17} +1.79939 q^{18} +0.556163 q^{19} +1.00000 q^{20} +3.12709 q^{21} -1.42679 q^{22} +5.09377 q^{23} +1.09573 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.25881 q^{27} -2.85390 q^{28} +8.95879 q^{29} +1.09573 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.56337 q^{33} +4.91892 q^{34} -2.85390 q^{35} -1.79939 q^{36} -0.113068 q^{37} -0.556163 q^{38} +1.09573 q^{39} -1.00000 q^{40} +10.3856 q^{41} -3.12709 q^{42} -4.19895 q^{43} +1.42679 q^{44} -1.79939 q^{45} -5.09377 q^{46} -1.73731 q^{47} -1.09573 q^{48} +1.14476 q^{49} -1.00000 q^{50} +5.38978 q^{51} -1.00000 q^{52} -5.68358 q^{53} -5.25881 q^{54} +1.42679 q^{55} +2.85390 q^{56} -0.609402 q^{57} -8.95879 q^{58} -1.56050 q^{59} -1.09573 q^{60} +6.15940 q^{61} -1.00000 q^{62} +5.13527 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.56337 q^{66} +5.47308 q^{67} -4.91892 q^{68} -5.58137 q^{69} +2.85390 q^{70} +1.02381 q^{71} +1.79939 q^{72} -1.59055 q^{73} +0.113068 q^{74} -1.09573 q^{75} +0.556163 q^{76} -4.07192 q^{77} -1.09573 q^{78} -12.5352 q^{79} +1.00000 q^{80} -0.364052 q^{81} -10.3856 q^{82} -1.21766 q^{83} +3.12709 q^{84} -4.91892 q^{85} +4.19895 q^{86} -9.81637 q^{87} -1.42679 q^{88} -16.1489 q^{89} +1.79939 q^{90} +2.85390 q^{91} +5.09377 q^{92} -1.09573 q^{93} +1.73731 q^{94} +0.556163 q^{95} +1.09573 q^{96} -14.3690 q^{97} -1.14476 q^{98} -2.56735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9} - 7 q^{10} - 2 q^{11} - q^{12} - 7 q^{13} + 4 q^{14} - q^{15} + 7 q^{16} - 8 q^{17} - 4 q^{18} + q^{19} + 7 q^{20} - 11 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} + 7 q^{25} + 7 q^{26} - q^{27} - 4 q^{28} - 4 q^{29} + q^{30} + 7 q^{31} - 7 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} - q^{38} + q^{39} - 7 q^{40} - 6 q^{41} + 11 q^{42} - 5 q^{43} - 2 q^{44} + 4 q^{45} + 5 q^{46} - 18 q^{47} - q^{48} - 9 q^{49} - 7 q^{50} - q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 2 q^{55} + 4 q^{56} - 31 q^{57} + 4 q^{58} + 3 q^{59} - q^{60} - 7 q^{61} - 7 q^{62} - 19 q^{63} + 7 q^{64} - 7 q^{65} + 4 q^{66} + 6 q^{67} - 8 q^{68} - 10 q^{69} + 4 q^{70} + 4 q^{71} - 4 q^{72} - 31 q^{73} + 2 q^{74} - q^{75} + q^{76} - 25 q^{77} - q^{78} - 2 q^{79} + 7 q^{80} + 31 q^{81} + 6 q^{82} - 40 q^{83} - 11 q^{84} - 8 q^{85} + 5 q^{86} - 5 q^{87} + 2 q^{88} - 4 q^{90} + 4 q^{91} - 5 q^{92} - q^{93} + 18 q^{94} + q^{95} + q^{96} - 21 q^{97} + 9 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9 - 7 * q^10 - 2 * q^11 - q^12 - 7 * q^13 + 4 * q^14 - q^15 + 7 * q^16 - 8 * q^17 - 4 * q^18 + q^19 + 7 * q^20 - 11 * q^21 + 2 * q^22 - 5 * q^23 + q^24 + 7 * q^25 + 7 * q^26 - q^27 - 4 * q^28 - 4 * q^29 + q^30 + 7 * q^31 - 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^37 - q^38 + q^39 - 7 * q^40 - 6 * q^41 + 11 * q^42 - 5 * q^43 - 2 * q^44 + 4 * q^45 + 5 * q^46 - 18 * q^47 - q^48 - 9 * q^49 - 7 * q^50 - q^51 - 7 * q^52 - 12 * q^53 + q^54 - 2 * q^55 + 4 * q^56 - 31 * q^57 + 4 * q^58 + 3 * q^59 - q^60 - 7 * q^61 - 7 * q^62 - 19 * q^63 + 7 * q^64 - 7 * q^65 + 4 * q^66 + 6 * q^67 - 8 * q^68 - 10 * q^69 + 4 * q^70 + 4 * q^71 - 4 * q^72 - 31 * q^73 + 2 * q^74 - q^75 + q^76 - 25 * q^77 - q^78 - 2 * q^79 + 7 * q^80 + 31 * q^81 + 6 * q^82 - 40 * q^83 - 11 * q^84 - 8 * q^85 + 5 * q^86 - 5 * q^87 + 2 * q^88 - 4 * q^90 + 4 * q^91 - 5 * q^92 - q^93 + 18 * q^94 + q^95 + q^96 - 21 * q^97 + 9 * q^98 - 23 * q^99

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