LMFDB - Embedded newform 4030.2.a.i.1.6

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} - 3x^{6} - 8x^{5} + 24x^{4} + 18x^{3} - 48x^{2} - 9x + 4 $ x^7 - 3x^6 - 8x^5 + 24x^4 + 18x^3 - 48x^2 - 9x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.37188$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.37188 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.37188 q^{6} +3.55078 q^{7} -1.00000 q^{8} +2.62583 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.37188 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.37188 q^{6} +3.55078 q^{7} -1.00000 q^{8} +2.62583 q^{9} +1.00000 q^{10} -5.43982 q^{11} +2.37188 q^{12} -1.00000 q^{13} -3.55078 q^{14} -2.37188 q^{15} +1.00000 q^{16} -3.03519 q^{17} -2.62583 q^{18} -0.377758 q^{19} -1.00000 q^{20} +8.42205 q^{21} +5.43982 q^{22} -4.43826 q^{23} -2.37188 q^{24} +1.00000 q^{25} +1.00000 q^{26} -0.887478 q^{27} +3.55078 q^{28} -4.53222 q^{29} +2.37188 q^{30} -1.00000 q^{31} -1.00000 q^{32} -12.9026 q^{33} +3.03519 q^{34} -3.55078 q^{35} +2.62583 q^{36} -2.61659 q^{37} +0.377758 q^{38} -2.37188 q^{39} +1.00000 q^{40} -2.39970 q^{41} -8.42205 q^{42} +9.77299 q^{43} -5.43982 q^{44} -2.62583 q^{45} +4.43826 q^{46} -4.09111 q^{47} +2.37188 q^{48} +5.60806 q^{49} -1.00000 q^{50} -7.19912 q^{51} -1.00000 q^{52} -4.74112 q^{53} +0.887478 q^{54} +5.43982 q^{55} -3.55078 q^{56} -0.895998 q^{57} +4.53222 q^{58} -12.5930 q^{59} -2.37188 q^{60} +4.42698 q^{61} +1.00000 q^{62} +9.32377 q^{63} +1.00000 q^{64} +1.00000 q^{65} +12.9026 q^{66} -4.83488 q^{67} -3.03519 q^{68} -10.5270 q^{69} +3.55078 q^{70} +1.51430 q^{71} -2.62583 q^{72} -7.17662 q^{73} +2.61659 q^{74} +2.37188 q^{75} -0.377758 q^{76} -19.3156 q^{77} +2.37188 q^{78} -4.16965 q^{79} -1.00000 q^{80} -9.98250 q^{81} +2.39970 q^{82} +6.45610 q^{83} +8.42205 q^{84} +3.03519 q^{85} -9.77299 q^{86} -10.7499 q^{87} +5.43982 q^{88} +7.18911 q^{89} +2.62583 q^{90} -3.55078 q^{91} -4.43826 q^{92} -2.37188 q^{93} +4.09111 q^{94} +0.377758 q^{95} -2.37188 q^{96} -9.88020 q^{97} -5.60806 q^{98} -14.2841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	$ 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} + 7 q^{10} - 6 q^{11} + 3 q^{12} - 7 q^{13} - 2 q^{14} - 3 q^{15} + 7 q^{16} - 4 q^{18} - 9 q^{19} - 7 q^{20} + q^{21} + 6 q^{22} + 7 q^{23} - 3 q^{24} + 7 q^{25} + 7 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} + 3 q^{30} - 7 q^{31} - 7 q^{32} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 9 q^{38} - 3 q^{39} + 7 q^{40} - 14 q^{41} - q^{42} + 9 q^{43} - 6 q^{44} - 4 q^{45} - 7 q^{46} - 8 q^{47} + 3 q^{48} - q^{49} - 7 q^{50} - 7 q^{51} - 7 q^{52} - 6 q^{53} - 9 q^{54} + 6 q^{55} - 2 q^{56} - 11 q^{57} + 4 q^{58} - 15 q^{59} - 3 q^{60} + q^{61} + 7 q^{62} - 17 q^{63} + 7 q^{64} + 7 q^{65} + 14 q^{67} - 14 q^{69} + 2 q^{70} - 16 q^{71} - 4 q^{72} - 13 q^{73} - 2 q^{74} + 3 q^{75} - 9 q^{76} - 5 q^{77} + 3 q^{78} - 14 q^{79} - 7 q^{80} - 25 q^{81} + 14 q^{82} - 10 q^{83} + q^{84} - 9 q^{86} - 9 q^{87} + 6 q^{88} - 26 q^{89} + 4 q^{90} - 2 q^{91} + 7 q^{92} - 3 q^{93} + 8 q^{94} + 9 q^{95} - 3 q^{96} - 5 q^{97} + q^{98} - 37 q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 + 7 * q^10 - 6 * q^11 + 3 * q^12 - 7 * q^13 - 2 * q^14 - 3 * q^15 + 7 * q^16 - 4 * q^18 - 9 * q^19 - 7 * q^20 + q^21 + 6 * q^22 + 7 * q^23 - 3 * q^24 + 7 * q^25 + 7 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 + 3 * q^30 - 7 * q^31 - 7 * q^32 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 9 * q^38 - 3 * q^39 + 7 * q^40 - 14 * q^41 - q^42 + 9 * q^43 - 6 * q^44 - 4 * q^45 - 7 * q^46 - 8 * q^47 + 3 * q^48 - q^49 - 7 * q^50 - 7 * q^51 - 7 * q^52 - 6 * q^53 - 9 * q^54 + 6 * q^55 - 2 * q^56 - 11 * q^57 + 4 * q^58 - 15 * q^59 - 3 * q^60 + q^61 + 7 * q^62 - 17 * q^63 + 7 * q^64 + 7 * q^65 + 14 * q^67 - 14 * q^69 + 2 * q^70 - 16 * q^71 - 4 * q^72 - 13 * q^73 - 2 * q^74 + 3 * q^75 - 9 * q^76 - 5 * q^77 + 3 * q^78 - 14 * q^79 - 7 * q^80 - 25 * q^81 + 14 * q^82 - 10 * q^83 + q^84 - 9 * q^86 - 9 * q^87 + 6 * q^88 - 26 * q^89 + 4 * q^90 - 2 * q^91 + 7 * q^92 - 3 * q^93 + 8 * q^94 + 9 * q^95 - 3 * q^96 - 5 * q^97 + q^98 - 37 * 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
$3$	2.37188	1.36941	0.684704	−	0.728821i	$-0.259931\pi$
$3$	2.37188	1.36941	0.684704	+	0.728821i	$0.259931\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.37188	−0.968318
$7$	3.55078	1.34207	0.671035	−	0.741426i	$-0.265850\pi$
$7$	3.55078	1.34207	0.671035	+	0.741426i	$0.265850\pi$
$8$	−1.00000	−0.353553
$9$	2.62583	0.875278
$10$	1.00000	0.316228
$11$	−5.43982	−1.64017	−0.820083	−	0.572244i	$-0.806073\pi$
$11$	−5.43982	−1.64017	−0.820083	+	0.572244i	$0.806073\pi$
$12$	2.37188	0.684704
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.55078	−0.948987
$15$	−2.37188	−0.612418
$16$	1.00000	0.250000
$17$	−3.03519	−0.736142	−0.368071	−	0.929798i	$-0.619982\pi$
$17$	−3.03519	−0.736142	−0.368071	+	0.929798i	$0.619982\pi$
$18$	−2.62583	−0.618915
$19$	−0.377758	−0.0866636	−0.0433318	−	0.999061i	$-0.513797\pi$
$19$	−0.377758	−0.0866636	−0.0433318	+	0.999061i	$0.513797\pi$
$20$	−1.00000	−0.223607
$21$	8.42205	1.83784
$22$	5.43982	1.15977
$23$	−4.43826	−0.925441	−0.462721	−	0.886504i	$-0.653127\pi$
$23$	−4.43826	−0.925441	−0.462721	+	0.886504i	$0.653127\pi$
$24$	−2.37188	−0.484159
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−0.887478	−0.170795
$28$	3.55078	0.671035
$29$	−4.53222	−0.841612	−0.420806	−	0.907151i	$-0.638253\pi$
$29$	−4.53222	−0.841612	−0.420806	+	0.907151i	$0.638253\pi$
$30$	2.37188	0.433045
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−12.9026	−2.24606
$34$	3.03519	0.520531
$35$	−3.55078	−0.600192
$36$	2.62583	0.437639
$37$	−2.61659	−0.430164	−0.215082	−	0.976596i	$-0.569002\pi$
$37$	−2.61659	−0.430164	−0.215082	+	0.976596i	$0.569002\pi$
$38$	0.377758	0.0612805
$39$	−2.37188	−0.379805
$40$	1.00000	0.158114
$41$	−2.39970	−0.374770	−0.187385	−	0.982287i	$-0.560001\pi$
$41$	−2.39970	−0.374770	−0.187385	+	0.982287i	$0.560001\pi$
$42$	−8.42205	−1.29955
$43$	9.77299	1.49037	0.745183	−	0.666860i	$-0.232362\pi$
$43$	9.77299	1.49037	0.745183	+	0.666860i	$0.232362\pi$
$44$	−5.43982	−0.820083
$45$	−2.62583	−0.391436
$46$	4.43826	0.654386
$47$	−4.09111	−0.596750	−0.298375	−	0.954449i	$-0.596445\pi$
$47$	−4.09111	−0.596750	−0.298375	+	0.954449i	$0.596445\pi$
$48$	2.37188	0.342352
$49$	5.60806	0.801152
$50$	−1.00000	−0.141421
$51$	−7.19912	−1.00808
$52$	−1.00000	−0.138675
$53$	−4.74112	−0.651243	−0.325622	−	0.945500i	$-0.605574\pi$
$53$	−4.74112	−0.651243	−0.325622	+	0.945500i	$0.605574\pi$
$54$	0.887478	0.120770
$55$	5.43982	0.733505
$56$	−3.55078	−0.474493
$57$	−0.895998	−0.118678
$58$	4.53222	0.595110
$59$	−12.5930	−1.63947	−0.819735	−	0.572743i	$-0.805879\pi$
$59$	−12.5930	−1.63947	−0.819735	+	0.572743i	$0.805879\pi$
$60$	−2.37188	−0.306209
$61$	4.42698	0.566816	0.283408	−	0.958999i	$-0.408535\pi$
$61$	4.42698	0.566816	0.283408	+	0.958999i	$0.408535\pi$
$62$	1.00000	0.127000
$63$	9.32377	1.17468
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	12.9026	1.58820
$67$	−4.83488	−0.590675	−0.295337	−	0.955393i	$-0.595432\pi$
$67$	−4.83488	−0.590675	−0.295337	+	0.955393i	$0.595432\pi$
$68$	−3.03519	−0.368071
$69$	−10.5270	−1.26731
$70$	3.55078	0.424400
$71$	1.51430	0.179715	0.0898574	−	0.995955i	$-0.471359\pi$
$71$	1.51430	0.179715	0.0898574	+	0.995955i	$0.471359\pi$
$72$	−2.62583	−0.309458
$73$	−7.17662	−0.839960	−0.419980	−	0.907533i	$-0.637963\pi$
$73$	−7.17662	−0.839960	−0.419980	+	0.907533i	$0.637963\pi$
$74$	2.61659	0.304172
$75$	2.37188	0.273882
$76$	−0.377758	−0.0433318
$77$	−19.3156	−2.20122
$78$	2.37188	0.268563
$79$	−4.16965	−0.469122	−0.234561	−	0.972101i	$-0.575365\pi$
$79$	−4.16965	−0.469122	−0.234561	+	0.972101i	$0.575365\pi$
$80$	−1.00000	−0.111803
$81$	−9.98250	−1.10917
$82$	2.39970	0.265002
$83$	6.45610	0.708649	0.354324	−	0.935123i	$-0.384711\pi$
$83$	6.45610	0.708649	0.354324	+	0.935123i	$0.384711\pi$
$84$	8.42205	0.918921
$85$	3.03519	0.329213
$86$	−9.77299	−1.05385
$87$	−10.7499	−1.15251
$88$	5.43982	0.579886
$89$	7.18911	0.762044	0.381022	−	0.924566i	$-0.375572\pi$
$89$	7.18911	0.762044	0.381022	+	0.924566i	$0.375572\pi$
$90$	2.62583	0.276787
$91$	−3.55078	−0.372223
$92$	−4.43826	−0.462721
$93$	−2.37188	−0.245953
$94$	4.09111	0.421966
$95$	0.377758	0.0387572
$96$	−2.37188	−0.242079
$97$	−9.88020	−1.00318	−0.501591	−	0.865105i	$-0.667252\pi$
$97$	−9.88020	−1.00318	−0.501591	+	0.865105i	$0.667252\pi$
$98$	−5.60806	−0.566500
$99$	−14.2841	−1.43560
$100$	1.00000	0.100000
$101$	10.4058	1.03542	0.517710	−	0.855556i	$-0.326785\pi$
$101$	10.4058	1.03542	0.517710	+	0.855556i	$0.326785\pi$
$102$	7.19912	0.712819
$103$	−14.3504	−1.41399	−0.706995	−	0.707218i	$-0.749950\pi$
$103$	−14.3504	−1.41399	−0.706995	+	0.707218i	$0.749950\pi$
$104$	1.00000	0.0980581
$105$	−8.42205	−0.821908
$106$	4.74112	0.460498
$107$	3.52828	0.341092	0.170546	−	0.985350i	$-0.445447\pi$
$107$	3.52828	0.341092	0.170546	+	0.985350i	$0.445447\pi$
$108$	−0.887478	−0.0853976
$109$	−1.72151	−0.164891	−0.0824456	−	0.996596i	$-0.526273\pi$
$109$	−1.72151	−0.164891	−0.0824456	+	0.996596i	$0.526273\pi$
$110$	−5.43982	−0.518666
$111$	−6.20624	−0.589070
$112$	3.55078	0.335518
$113$	0.427129	0.0401809	0.0200904	−	0.999798i	$-0.493605\pi$
$113$	0.427129	0.0401809	0.0200904	+	0.999798i	$0.493605\pi$
$114$	0.895998	0.0839179
$115$	4.43826	0.413870
$116$	−4.53222	−0.420806
$117$	−2.62583	−0.242758
$118$	12.5930	1.15928
$119$	−10.7773	−0.987954
$120$	2.37188	0.216522
$121$	18.5916	1.69015
$122$	−4.42698	−0.400800
$123$	−5.69180	−0.513212
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	−9.32377	−0.830627
$127$	13.4785	1.19603	0.598013	−	0.801486i	$-0.295957\pi$
$127$	13.4785	1.19603	0.598013	+	0.801486i	$0.295957\pi$
$128$	−1.00000	−0.0883883
$129$	23.1804	2.04092
$130$	−1.00000	−0.0877058
$131$	4.33240	0.378524	0.189262	−	0.981927i	$-0.439391\pi$
$131$	4.33240	0.378524	0.189262	+	0.981927i	$0.439391\pi$
$132$	−12.9026	−1.12303
$133$	−1.34134	−0.116309
$134$	4.83488	0.417670
$135$	0.887478	0.0763819
$136$	3.03519	0.260265
$137$	−16.8154	−1.43663	−0.718317	−	0.695716i	$-0.755087\pi$
$137$	−16.8154	−1.43663	−0.718317	+	0.695716i	$0.755087\pi$
$138$	10.5270	0.896121
$139$	11.7125	0.993441	0.496720	−	0.867911i	$-0.334537\pi$
$139$	11.7125	0.993441	0.496720	+	0.867911i	$0.334537\pi$
$140$	−3.55078	−0.300096
$141$	−9.70365	−0.817195
$142$	−1.51430	−0.127078
$143$	5.43982	0.454900
$144$	2.62583	0.218820
$145$	4.53222	0.376380
$146$	7.17662	0.593941
$147$	13.3017	1.09710
$148$	−2.61659	−0.215082
$149$	15.2745	1.25134	0.625668	−	0.780089i	$-0.284826\pi$
$149$	15.2745	1.25134	0.625668	+	0.780089i	$0.284826\pi$
$150$	−2.37188	−0.193664
$151$	−15.5274	−1.26360	−0.631799	−	0.775132i	$-0.717683\pi$
$151$	−15.5274	−1.26360	−0.631799	+	0.775132i	$0.717683\pi$
$152$	0.377758	0.0306402
$153$	−7.96991	−0.644329
$154$	19.3156	1.55650
$155$	1.00000	0.0803219
$156$	−2.37188	−0.189903
$157$	−15.4415	−1.23237	−0.616183	−	0.787603i	$-0.711322\pi$
$157$	−15.4415	−1.23237	−0.616183	+	0.787603i	$0.711322\pi$
$158$	4.16965	0.331720
$159$	−11.2454	−0.891817
$160$	1.00000	0.0790569
$161$	−15.7593	−1.24201
$162$	9.98250	0.784299
$163$	−0.125517	−0.00983123	−0.00491562	−	0.999988i	$-0.501565\pi$
$163$	−0.125517	−0.00983123	−0.00491562	+	0.999988i	$0.501565\pi$
$164$	−2.39970	−0.187385
$165$	12.9026	1.00447
$166$	−6.45610	−0.501090
$167$	17.3852	1.34531	0.672654	−	0.739957i	$-0.265154\pi$
$167$	17.3852	1.34531	0.672654	+	0.739957i	$0.265154\pi$
$168$	−8.42205	−0.649775
$169$	1.00000	0.0769231
$170$	−3.03519	−0.232788
$171$	−0.991930	−0.0758548
$172$	9.77299	0.745183
$173$	−6.26546	−0.476354	−0.238177	−	0.971222i	$-0.576550\pi$
$173$	−6.26546	−0.476354	−0.238177	+	0.971222i	$0.576550\pi$
$174$	10.7499	0.814948
$175$	3.55078	0.268414
$176$	−5.43982	−0.410042
$177$	−29.8692	−2.24510
$178$	−7.18911	−0.538846
$179$	21.5659	1.61191	0.805955	−	0.591977i	$-0.201652\pi$
$179$	21.5659	1.61191	0.805955	+	0.591977i	$0.201652\pi$
$180$	−2.62583	−0.195718
$181$	3.68654	0.274018	0.137009	−	0.990570i	$-0.456251\pi$
$181$	3.68654	0.274018	0.137009	+	0.990570i	$0.456251\pi$
$182$	3.55078	0.263202
$183$	10.5003	0.776203
$184$	4.43826	0.327193
$185$	2.61659	0.192375
$186$	2.37188	0.173915
$187$	16.5109	1.20740
$188$	−4.09111	−0.298375
$189$	−3.15124	−0.229219
$190$	−0.377758	−0.0274055
$191$	−2.74539	−0.198649	−0.0993246	−	0.995055i	$-0.531668\pi$
$191$	−2.74539	−0.198649	−0.0993246	+	0.995055i	$0.531668\pi$
$192$	2.37188	0.171176
$193$	4.22905	0.304414	0.152207	−	0.988349i	$-0.451362\pi$
$193$	4.22905	0.304414	0.152207	+	0.988349i	$0.451362\pi$
$194$	9.88020	0.709357
$195$	2.37188	0.169854
$196$	5.60806	0.400576
$197$	−15.8092	−1.12636	−0.563178	−	0.826336i	$-0.690421\pi$
$197$	−15.8092	−1.12636	−0.563178	+	0.826336i	$0.690421\pi$
$198$	14.2841	1.01512
$199$	9.06004	0.642249	0.321125	−	0.947037i	$-0.395939\pi$
$199$	9.06004	0.642249	0.321125	+	0.947037i	$0.395939\pi$
$200$	−1.00000	−0.0707107
$201$	−11.4678	−0.808875
$202$	−10.4058	−0.732152
$203$	−16.0929	−1.12950
$204$	−7.19912	−0.504039
$205$	2.39970	0.167602
$206$	14.3504	0.999842
$207$	−11.6541	−0.810019
$208$	−1.00000	−0.0693375
$209$	2.05493	0.142143
$210$	8.42205	0.581176
$211$	−7.29572	−0.502258	−0.251129	−	0.967954i	$-0.580802\pi$
$211$	−7.29572	−0.502258	−0.251129	+	0.967954i	$0.580802\pi$
$212$	−4.74112	−0.325622
$213$	3.59175	0.246103
$214$	−3.52828	−0.241189
$215$	−9.77299	−0.666512
$216$	0.887478	0.0603852
$217$	−3.55078	−0.241043
$218$	1.72151	0.116596
$219$	−17.0221	−1.15025
$220$	5.43982	0.366752
$221$	3.03519	0.204169
$222$	6.20624	0.416535
$223$	−10.5506	−0.706518	−0.353259	−	0.935525i	$-0.614927\pi$
$223$	−10.5506	−0.706518	−0.353259	+	0.935525i	$0.614927\pi$
$224$	−3.55078	−0.237247
$225$	2.62583	0.175056
$226$	−0.427129	−0.0284122
$227$	−9.69310	−0.643354	−0.321677	−	0.946849i	$-0.604246\pi$
$227$	−9.69310	−0.643354	−0.321677	+	0.946849i	$0.604246\pi$
$228$	−0.895998	−0.0593389
$229$	−7.37303	−0.487224	−0.243612	−	0.969873i	$-0.578332\pi$
$229$	−7.37303	−0.487224	−0.243612	+	0.969873i	$0.578332\pi$
$230$	−4.43826	−0.292650
$231$	−45.8144	−3.01437
$232$	4.53222	0.297555
$233$	19.1553	1.25491	0.627454	−	0.778654i	$-0.284097\pi$
$233$	19.1553	1.25491	0.627454	+	0.778654i	$0.284097\pi$
$234$	2.62583	0.171656
$235$	4.09111	0.266875
$236$	−12.5930	−0.819735
$237$	−9.88993	−0.642420
$238$	10.7773	0.698589
$239$	2.80145	0.181211	0.0906053	−	0.995887i	$-0.471120\pi$
$239$	2.80145	0.181211	0.0906053	+	0.995887i	$0.471120\pi$
$240$	−2.37188	−0.153104
$241$	−5.14611	−0.331490	−0.165745	−	0.986169i	$-0.553003\pi$
$241$	−5.14611	−0.331490	−0.165745	+	0.986169i	$0.553003\pi$
$242$	−18.5916	−1.19511
$243$	−21.0149	−1.34811
$244$	4.42698	0.283408
$245$	−5.60806	−0.358286
$246$	5.69180	0.362896
$247$	0.377758	0.0240362
$248$	1.00000	0.0635001
$249$	15.3131	0.970429
$250$	1.00000	0.0632456
$251$	23.9512	1.51179	0.755893	−	0.654695i	$-0.227203\pi$
$251$	23.9512	1.51179	0.755893	+	0.654695i	$0.227203\pi$
$252$	9.32377	0.587342
$253$	24.1433	1.51788
$254$	−13.4785	−0.845719
$255$	7.19912	0.450826
$256$	1.00000	0.0625000
$257$	31.8211	1.98495	0.992473	−	0.122461i	$-0.0390787\pi$
$257$	31.8211	1.98495	0.992473	+	0.122461i	$0.0390787\pi$
$258$	−23.1804	−1.44315
$259$	−9.29093	−0.577310
$260$	1.00000	0.0620174
$261$	−11.9009	−0.736645
$262$	−4.33240	−0.267657
$263$	−27.3736	−1.68793	−0.843965	−	0.536398i	$-0.819785\pi$
$263$	−27.3736	−1.68793	−0.843965	+	0.536398i	$0.819785\pi$
$264$	12.9026	0.794101
$265$	4.74112	0.291245
$266$	1.34134	0.0822427
$267$	17.0517	1.04355
$268$	−4.83488	−0.295337
$269$	11.6046	0.707548	0.353774	−	0.935331i	$-0.384898\pi$
$269$	11.6046	0.707548	0.353774	+	0.935331i	$0.384898\pi$
$270$	−0.887478	−0.0540102
$271$	−15.5964	−0.947415	−0.473708	−	0.880682i	$-0.657085\pi$
$271$	−15.5964	−0.947415	−0.473708	+	0.880682i	$0.657085\pi$
$272$	−3.03519	−0.184035
$273$	−8.42205	−0.509725
$274$	16.8154	1.01585
$275$	−5.43982	−0.328033
$276$	−10.5270	−0.633653
$277$	6.05416	0.363759	0.181880	−	0.983321i	$-0.441782\pi$
$277$	6.05416	0.363759	0.181880	+	0.983321i	$0.441782\pi$
$278$	−11.7125	−0.702469
$279$	−2.62583	−0.157205
$280$	3.55078	0.212200
$281$	−23.9438	−1.42837	−0.714183	−	0.699959i	$-0.753202\pi$
$281$	−23.9438	−1.42837	−0.714183	+	0.699959i	$0.753202\pi$
$282$	9.70365	0.577844
$283$	−24.3707	−1.44869	−0.724343	−	0.689440i	$-0.757857\pi$
$283$	−24.3707	−1.44869	−0.724343	+	0.689440i	$0.757857\pi$
$284$	1.51430	0.0898574
$285$	0.895998	0.0530744
$286$	−5.43982	−0.321663
$287$	−8.52080	−0.502967
$288$	−2.62583	−0.154729
$289$	−7.78762	−0.458095
$290$	−4.53222	−0.266141
$291$	−23.4347	−1.37377
$292$	−7.17662	−0.419980
$293$	3.47575	0.203056	0.101528	−	0.994833i	$-0.467627\pi$
$293$	3.47575	0.203056	0.101528	+	0.994833i	$0.467627\pi$
$294$	−13.3017	−0.775770
$295$	12.5930	0.733193
$296$	2.61659	0.152086
$297$	4.82772	0.280132
$298$	−15.2745	−0.884828
$299$	4.43826	0.256671
$300$	2.37188	0.136941
$301$	34.7018	2.00018
$302$	15.5274	0.893499
$303$	24.6814	1.41791
$304$	−0.377758	−0.0216659
$305$	−4.42698	−0.253488
$306$	7.96991	0.455609
$307$	−15.0856	−0.860979	−0.430489	−	0.902596i	$-0.641659\pi$
$307$	−15.0856	−0.860979	−0.430489	+	0.902596i	$0.641659\pi$
$308$	−19.3156	−1.10061
$309$	−34.0376	−1.93633
$310$	−1.00000	−0.0567962
$311$	−22.8227	−1.29415	−0.647077	−	0.762424i	$-0.724009\pi$
$311$	−22.8227	−1.29415	−0.647077	+	0.762424i	$0.724009\pi$
$312$	2.37188	0.134281
$313$	26.3309	1.48831	0.744156	−	0.668006i	$-0.232852\pi$
$313$	26.3309	1.48831	0.744156	+	0.668006i	$0.232852\pi$
$314$	15.4415	0.871414
$315$	−9.32377	−0.525335
$316$	−4.16965	−0.234561
$317$	18.2838	1.02692	0.513460	−	0.858113i	$-0.328363\pi$
$317$	18.2838	1.02692	0.513460	+	0.858113i	$0.328363\pi$
$318$	11.2454	0.630610
$319$	24.6545	1.38038
$320$	−1.00000	−0.0559017
$321$	8.36868	0.467094
$322$	15.7593	0.878232
$323$	1.14657	0.0637967
$324$	−9.98250	−0.554583
$325$	−1.00000	−0.0554700
$326$	0.125517	0.00695173
$327$	−4.08323	−0.225803
$328$	2.39970	0.132501
$329$	−14.5267	−0.800881
$330$	−12.9026	−0.710266
$331$	−13.3237	−0.732335	−0.366167	−	0.930549i	$-0.619330\pi$
$331$	−13.3237	−0.732335	−0.366167	+	0.930549i	$0.619330\pi$
$332$	6.45610	0.354324
$333$	−6.87072	−0.376513
$334$	−17.3852	−0.951277
$335$	4.83488	0.264158
$336$	8.42205	0.459460
$337$	28.8467	1.57138	0.785691	−	0.618619i	$-0.212308\pi$
$337$	28.8467	1.57138	0.785691	+	0.618619i	$0.212308\pi$
$338$	−1.00000	−0.0543928
$339$	1.01310	0.0550240
$340$	3.03519	0.164606
$341$	5.43982	0.294583
$342$	0.991930	0.0536374
$343$	−4.94246	−0.266868
$344$	−9.77299	−0.526924
$345$	10.5270	0.566757
$346$	6.26546	0.336833
$347$	−12.7284	−0.683297	−0.341648	−	0.939828i	$-0.610985\pi$
$347$	−12.7284	−0.683297	−0.341648	+	0.939828i	$0.610985\pi$
$348$	−10.7499	−0.576255
$349$	−9.41862	−0.504167	−0.252084	−	0.967705i	$-0.581116\pi$
$349$	−9.41862	−0.504167	−0.252084	+	0.967705i	$0.581116\pi$
$350$	−3.55078	−0.189797
$351$	0.887478	0.0473700
$352$	5.43982	0.289943
$353$	29.9959	1.59652	0.798260	−	0.602313i	$-0.205754\pi$
$353$	29.9959	1.59652	0.798260	+	0.602313i	$0.205754\pi$
$354$	29.8692	1.58753
$355$	−1.51430	−0.0803709
$356$	7.18911	0.381022
$357$	−25.5625	−1.35291
$358$	−21.5659	−1.13979
$359$	−1.97077	−0.104013	−0.0520065	−	0.998647i	$-0.516562\pi$
$359$	−1.97077	−0.104013	−0.0520065	+	0.998647i	$0.516562\pi$
$360$	2.62583	0.138394
$361$	−18.8573	−0.992489
$362$	−3.68654	−0.193760
$363$	44.0972	2.31450
$364$	−3.55078	−0.186112
$365$	7.17662	0.375641
$366$	−10.5003	−0.548858
$367$	23.6466	1.23434	0.617171	−	0.786829i	$-0.288279\pi$
$367$	23.6466	1.23434	0.617171	+	0.786829i	$0.288279\pi$
$368$	−4.43826	−0.231360
$369$	−6.30120	−0.328028
$370$	−2.61659	−0.136030
$371$	−16.8347	−0.874014
$372$	−2.37188	−0.122976
$373$	9.51439	0.492636	0.246318	−	0.969189i	$-0.420779\pi$
$373$	9.51439	0.492636	0.246318	+	0.969189i	$0.420779\pi$
$374$	−16.5109	−0.853757
$375$	−2.37188	−0.122484
$376$	4.09111	0.210983
$377$	4.53222	0.233421
$378$	3.15124	0.162082
$379$	19.2902	0.990871	0.495435	−	0.868645i	$-0.335008\pi$
$379$	19.2902	0.990871	0.495435	+	0.868645i	$0.335008\pi$
$380$	0.377758	0.0193786
$381$	31.9695	1.63785
$382$	2.74539	0.140466
$383$	30.3267	1.54962	0.774810	−	0.632194i	$-0.217845\pi$
$383$	30.3267	1.54962	0.774810	+	0.632194i	$0.217845\pi$
$384$	−2.37188	−0.121040
$385$	19.3156	0.984415
$386$	−4.22905	−0.215253
$387$	25.6622	1.30449
$388$	−9.88020	−0.501591
$389$	−1.16687	−0.0591626	−0.0295813	−	0.999562i	$-0.509417\pi$
$389$	−1.16687	−0.0591626	−0.0295813	+	0.999562i	$0.509417\pi$
$390$	−2.37188	−0.120105
$391$	13.4710	0.681256
$392$	−5.60806	−0.283250
$393$	10.2760	0.518353
$394$	15.8092	0.796454
$395$	4.16965	0.209798
$396$	−14.2841	−0.717801
$397$	27.4050	1.37542	0.687708	−	0.725987i	$-0.258617\pi$
$397$	27.4050	1.37542	0.687708	+	0.725987i	$0.258617\pi$
$398$	−9.06004	−0.454139
$399$	−3.18150	−0.159274
$400$	1.00000	0.0500000
$401$	−22.9615	−1.14664	−0.573322	−	0.819330i	$-0.694345\pi$
$401$	−22.9615	−1.14664	−0.573322	+	0.819330i	$0.694345\pi$
$402$	11.4678	0.571961
$403$	1.00000	0.0498135
$404$	10.4058	0.517710
$405$	9.98250	0.496034
$406$	16.0929	0.798679
$407$	14.2337	0.705541
$408$	7.19912	0.356410
$409$	14.8861	0.736071	0.368035	−	0.929812i	$-0.380031\pi$
$409$	14.8861	0.736071	0.368035	+	0.929812i	$0.380031\pi$
$410$	−2.39970	−0.118513
$411$	−39.8841	−1.96734
$412$	−14.3504	−0.706995
$413$	−44.7150	−2.20028
$414$	11.6541	0.572770
$415$	−6.45610	−0.316917
$416$	1.00000	0.0490290
$417$	27.7807	1.36043
$418$	−2.05493	−0.100510
$419$	−18.1353	−0.885966	−0.442983	−	0.896530i	$-0.646080\pi$
$419$	−18.1353	−0.885966	−0.442983	+	0.896530i	$0.646080\pi$
$420$	−8.42205	−0.410954
$421$	10.2244	0.498307	0.249154	−	0.968464i	$-0.419848\pi$
$421$	10.2244	0.498307	0.249154	+	0.968464i	$0.419848\pi$
$422$	7.29572	0.355150
$423$	−10.7426	−0.522323
$424$	4.74112	0.230249
$425$	−3.03519	−0.147228
$426$	−3.59175	−0.174021
$427$	15.7192	0.760707
$428$	3.52828	0.170546
$429$	12.9026	0.622944
$430$	9.77299	0.471295
$431$	9.44596	0.454996	0.227498	−	0.973779i	$-0.426946\pi$
$431$	9.44596	0.454996	0.227498	+	0.973779i	$0.426946\pi$
$432$	−0.887478	−0.0426988
$433$	−33.5718	−1.61336	−0.806679	−	0.590990i	$-0.798737\pi$
$433$	−33.5718	−1.61336	−0.806679	+	0.590990i	$0.798737\pi$
$434$	3.55078	0.170443
$435$	10.7499	0.515418
$436$	−1.72151	−0.0824456
$437$	1.67659	0.0802021
$438$	17.0221	0.813348
$439$	−27.9505	−1.33401	−0.667003	−	0.745055i	$-0.732423\pi$
$439$	−27.9505	−1.33401	−0.667003	+	0.745055i	$0.732423\pi$
$440$	−5.43982	−0.259333
$441$	14.7258	0.701231
$442$	−3.03519	−0.144369
$443$	−10.6214	−0.504636	−0.252318	−	0.967644i	$-0.581193\pi$
$443$	−10.6214	−0.504636	−0.252318	+	0.967644i	$0.581193\pi$
$444$	−6.20624	−0.294535
$445$	−7.18911	−0.340796
$446$	10.5506	0.499584
$447$	36.2294	1.71359
$448$	3.55078	0.167759
$449$	−18.8941	−0.891670	−0.445835	−	0.895115i	$-0.647093\pi$
$449$	−18.8941	−0.891670	−0.445835	+	0.895115i	$0.647093\pi$
$450$	−2.62583	−0.123783
$451$	13.0539	0.614684
$452$	0.427129	0.0200904
$453$	−36.8291	−1.73038
$454$	9.69310	0.454920
$455$	3.55078	0.166463
$456$	0.895998	0.0419590
$457$	11.4670	0.536403	0.268202	−	0.963363i	$-0.413571\pi$
$457$	11.4670	0.536403	0.268202	+	0.963363i	$0.413571\pi$
$458$	7.37303	0.344519
$459$	2.69366	0.125729
$460$	4.43826	0.206935
$461$	−23.2531	−1.08300	−0.541501	−	0.840700i	$-0.682144\pi$
$461$	−23.2531	−1.08300	−0.541501	+	0.840700i	$0.682144\pi$
$462$	45.8144	2.13148
$463$	−6.36720	−0.295909	−0.147954	−	0.988994i	$-0.547269\pi$
$463$	−6.36720	−0.295909	−0.147954	+	0.988994i	$0.547269\pi$
$464$	−4.53222	−0.210403
$465$	2.37188	0.109993
$466$	−19.1553	−0.887354
$467$	25.5759	1.18351	0.591755	−	0.806118i	$-0.298435\pi$
$467$	25.5759	1.18351	0.591755	+	0.806118i	$0.298435\pi$
$468$	−2.62583	−0.121379
$469$	−17.1676	−0.792727
$470$	−4.09111	−0.188709
$471$	−36.6255	−1.68761
$472$	12.5930	0.579640
$473$	−53.1633	−2.44445
$474$	9.88993	0.454259
$475$	−0.377758	−0.0173327
$476$	−10.7773	−0.493977
$477$	−12.4494	−0.570019
$478$	−2.80145	−0.128135
$479$	−40.7821	−1.86338	−0.931690	−	0.363255i	$-0.881665\pi$
$479$	−40.7821	−1.86338	−0.931690	+	0.363255i	$0.881665\pi$
$480$	2.37188	0.108261
$481$	2.61659	0.119306
$482$	5.14611	0.234399
$483$	−37.3792	−1.70081
$484$	18.5916	0.845073
$485$	9.88020	0.448637
$486$	21.0149	0.953255
$487$	5.45766	0.247310	0.123655	−	0.992325i	$-0.460538\pi$
$487$	5.45766	0.247310	0.123655	+	0.992325i	$0.460538\pi$
$488$	−4.42698	−0.200400
$489$	−0.297711	−0.0134630
$490$	5.60806	0.253347
$491$	−3.02840	−0.136670	−0.0683350	−	0.997662i	$-0.521769\pi$
$491$	−3.02840	−0.136670	−0.0683350	+	0.997662i	$0.521769\pi$
$492$	−5.69180	−0.256606
$493$	13.7562	0.619546
$494$	−0.377758	−0.0169961
$495$	14.2841	0.642021
$496$	−1.00000	−0.0449013
$497$	5.37697	0.241190
$498$	−15.3131	−0.686197
$499$	−15.0661	−0.674452	−0.337226	−	0.941424i	$-0.609489\pi$
$499$	−15.0661	−0.674452	−0.337226	+	0.941424i	$0.609489\pi$
$500$	−1.00000	−0.0447214
$501$	41.2357	1.84228
$502$	−23.9512	−1.06899
$503$	4.71669	0.210307	0.105153	−	0.994456i	$-0.466467\pi$
$503$	4.71669	0.210307	0.105153	+	0.994456i	$0.466467\pi$
$504$	−9.32377	−0.415314
$505$	−10.4058	−0.463054
$506$	−24.1433	−1.07330
$507$	2.37188	0.105339
$508$	13.4785	0.598013
$509$	7.48607	0.331814	0.165907	−	0.986141i	$-0.446945\pi$
$509$	7.48607	0.331814	0.165907	+	0.986141i	$0.446945\pi$
$510$	−7.19912	−0.318782
$511$	−25.4826	−1.12728
$512$	−1.00000	−0.0441942
$513$	0.335252	0.0148017
$514$	−31.8211	−1.40357
$515$	14.3504	0.632356
$516$	23.1804	1.02046
$517$	22.2549	0.978770
$518$	9.29093	0.408220
$519$	−14.8609	−0.652323
$520$	−1.00000	−0.0438529
$521$	5.37236	0.235367	0.117684	−	0.993051i	$-0.462453\pi$
$521$	5.37236	0.235367	0.117684	+	0.993051i	$0.462453\pi$
$522$	11.9009	0.520887
$523$	−23.6298	−1.03326	−0.516629	−	0.856209i	$-0.672813\pi$
$523$	−23.6298	−1.03326	−0.516629	+	0.856209i	$0.672813\pi$
$524$	4.33240	0.189262
$525$	8.42205	0.367568
$526$	27.3736	1.19355
$527$	3.03519	0.132215
$528$	−12.9026	−0.561514
$529$	−3.30184	−0.143558
$530$	−4.74112	−0.205941
$531$	−33.0671	−1.43499
$532$	−1.34134	−0.0581543
$533$	2.39970	0.103942
$534$	−17.0517	−0.737900
$535$	−3.52828	−0.152541
$536$	4.83488	0.208835
$537$	51.1518	2.20736
$538$	−11.6046	−0.500312
$539$	−30.5068	−1.31402
$540$	0.887478	0.0381910
$541$	−13.1649	−0.566004	−0.283002	−	0.959119i	$-0.591330\pi$
$541$	−13.1649	−0.566004	−0.283002	+	0.959119i	$0.591330\pi$
$542$	15.5964	0.669924
$543$	8.74404	0.375243
$544$	3.03519	0.130133
$545$	1.72151	0.0737416
$546$	8.42205	0.360430
$547$	−13.0895	−0.559665	−0.279833	−	0.960049i	$-0.590279\pi$
$547$	−13.0895	−0.559665	−0.279833	+	0.960049i	$0.590279\pi$
$548$	−16.8154	−0.718317
$549$	11.6245	0.496122
$550$	5.43982	0.231955
$551$	1.71208	0.0729372
$552$	10.5270	0.448061
$553$	−14.8055	−0.629595
$554$	−6.05416	−0.257217
$555$	6.20624	0.263440
$556$	11.7125	0.496720
$557$	21.7334	0.920873	0.460437	−	0.887693i	$-0.347693\pi$
$557$	21.7334	0.920873	0.460437	+	0.887693i	$0.347693\pi$
$558$	2.62583	0.111160
$559$	−9.77299	−0.413353
$560$	−3.55078	−0.150048
$561$	39.1619	1.65342
$562$	23.9438	1.01001
$563$	0.433490	0.0182694	0.00913470	−	0.999958i	$-0.497092\pi$
$563$	0.433490	0.0182694	0.00913470	+	0.999958i	$0.497092\pi$
$564$	−9.70365	−0.408597
$565$	−0.427129	−0.0179694
$566$	24.3707	1.02438
$567$	−35.4457	−1.48858
$568$	−1.51430	−0.0635388
$569$	24.3317	1.02004	0.510019	−	0.860163i	$-0.329638\pi$
$569$	24.3317	1.02004	0.510019	+	0.860163i	$0.329638\pi$
$570$	−0.895998	−0.0375292
$571$	−43.8443	−1.83483	−0.917414	−	0.397934i	$-0.869727\pi$
$571$	−43.8443	−1.83483	−0.917414	+	0.397934i	$0.869727\pi$
$572$	5.43982	0.227450
$573$	−6.51174	−0.272032
$574$	8.52080	0.355651
$575$	−4.43826	−0.185088
$576$	2.62583	0.109410
$577$	−24.4237	−1.01677	−0.508386	−	0.861129i	$-0.669758\pi$
$577$	−24.4237	−1.01677	−0.508386	+	0.861129i	$0.669758\pi$
$578$	7.78762	0.323922
$579$	10.0308	0.416867
$580$	4.53222	0.188190
$581$	22.9242	0.951056
$582$	23.4347	0.971399
$583$	25.7908	1.06815
$584$	7.17662	0.296971
$585$	2.62583	0.108565
$586$	−3.47575	−0.143582
$587$	−11.0776	−0.457223	−0.228611	−	0.973518i	$-0.573419\pi$
$587$	−11.0776	−0.457223	−0.228611	+	0.973518i	$0.573419\pi$
$588$	13.3017	0.548552
$589$	0.377758	0.0155653
$590$	−12.5930	−0.518446
$591$	−37.4975	−1.54244
$592$	−2.61659	−0.107541
$593$	−37.8578	−1.55463	−0.777317	−	0.629109i	$-0.783420\pi$
$593$	−37.8578	−1.55463	−0.777317	+	0.629109i	$0.783420\pi$
$594$	−4.82772	−0.198084
$595$	10.7773	0.441826
$596$	15.2745	0.625668
$597$	21.4894	0.879501
$598$	−4.43826	−0.181494
$599$	−21.7693	−0.889469	−0.444734	−	0.895663i	$-0.646702\pi$
$599$	−21.7693	−0.889469	−0.444734	+	0.895663i	$0.646702\pi$
$600$	−2.37188	−0.0968318
$601$	−32.0391	−1.30690	−0.653451	−	0.756969i	$-0.726679\pi$
$601$	−32.0391	−1.30690	−0.653451	+	0.756969i	$0.726679\pi$
$602$	−34.7018	−1.41434
$603$	−12.6956	−0.517005
$604$	−15.5274	−0.631799
$605$	−18.5916	−0.755857
$606$	−24.6814	−1.00261
$607$	−5.44488	−0.221001	−0.110500	−	0.993876i	$-0.535245\pi$
$607$	−5.44488	−0.221001	−0.110500	+	0.993876i	$0.535245\pi$
$608$	0.377758	0.0153201
$609$	−38.1706	−1.54675
$610$	4.42698	0.179243
$611$	4.09111	0.165509
$612$	−7.96991	−0.322164
$613$	−39.1396	−1.58083	−0.790417	−	0.612569i	$-0.790136\pi$
$613$	−39.1396	−1.58083	−0.790417	+	0.612569i	$0.790136\pi$
$614$	15.0856	0.608804
$615$	5.69180	0.229516
$616$	19.3156	0.778248
$617$	−36.0288	−1.45046	−0.725232	−	0.688504i	$-0.758268\pi$
$617$	−36.0288	−1.45046	−0.725232	+	0.688504i	$0.758268\pi$
$618$	34.0376	1.36919
$619$	32.6937	1.31407	0.657035	−	0.753860i	$-0.271810\pi$
$619$	32.6937	1.31407	0.657035	+	0.753860i	$0.271810\pi$
$620$	1.00000	0.0401610
$621$	3.93886	0.158061
$622$	22.8227	0.915106
$623$	25.5270	1.02272
$624$	−2.37188	−0.0949514
$625$	1.00000	0.0400000
$626$	−26.3309	−1.05240
$627$	4.87407	0.194652
$628$	−15.4415	−0.616183
$629$	7.94183	0.316662
$630$	9.32377	0.371468
$631$	−25.7369	−1.02457	−0.512285	−	0.858815i	$-0.671201\pi$
$631$	−25.7369	−1.02457	−0.512285	+	0.858815i	$0.671201\pi$
$632$	4.16965	0.165860
$633$	−17.3046	−0.687797
$634$	−18.2838	−0.726143
$635$	−13.4785	−0.534879
$636$	−11.2454	−0.445909
$637$	−5.60806	−0.222200
$638$	−24.6545	−0.976079
$639$	3.97631	0.157300
$640$	1.00000	0.0395285
$641$	9.44269	0.372964	0.186482	−	0.982458i	$-0.440291\pi$
$641$	9.44269	0.372964	0.186482	+	0.982458i	$0.440291\pi$
$642$	−8.36868	−0.330286
$643$	−32.0713	−1.26477	−0.632384	−	0.774655i	$-0.717923\pi$
$643$	−32.0713	−1.26477	−0.632384	+	0.774655i	$0.717923\pi$
$644$	−15.7593	−0.621004
$645$	−23.1804	−0.912727
$646$	−1.14657	−0.0451111
$647$	42.9296	1.68774	0.843868	−	0.536550i	$-0.180273\pi$
$647$	42.9296	1.68774	0.843868	+	0.536550i	$0.180273\pi$
$648$	9.98250	0.392150
$649$	68.5037	2.68900
$650$	1.00000	0.0392232
$651$	−8.42205	−0.330086
$652$	−0.125517	−0.00491562
$653$	19.2834	0.754618	0.377309	−	0.926087i	$-0.376850\pi$
$653$	19.2834	0.754618	0.377309	+	0.926087i	$0.376850\pi$
$654$	4.08323	0.159667
$655$	−4.33240	−0.169281
$656$	−2.39970	−0.0936924
$657$	−18.8446	−0.735198
$658$	14.5267	0.566308
$659$	15.4900	0.603405	0.301702	−	0.953402i	$-0.402445\pi$
$659$	15.4900	0.603405	0.301702	+	0.953402i	$0.402445\pi$
$660$	12.9026	0.502234
$661$	−11.5250	−0.448272	−0.224136	−	0.974558i	$-0.571956\pi$
$661$	−11.5250	−0.448272	−0.224136	+	0.974558i	$0.571956\pi$
$662$	13.3237	0.517839
$663$	7.19912	0.279591
$664$	−6.45610	−0.250545
$665$	1.34134	0.0520148
$666$	6.87072	0.266235
$667$	20.1152	0.778863
$668$	17.3852	0.672654
$669$	−25.0247	−0.967512
$670$	−4.83488	−0.186788
$671$	−24.0819	−0.929673
$672$	−8.42205	−0.324888
$673$	−17.1665	−0.661720	−0.330860	−	0.943680i	$-0.607339\pi$
$673$	−17.1665	−0.661720	−0.330860	+	0.943680i	$0.607339\pi$
$674$	−28.8467	−1.11113
$675$	−0.887478	−0.0341590
$676$	1.00000	0.0384615
$677$	21.8493	0.839735	0.419868	−	0.907585i	$-0.362076\pi$
$677$	21.8493	0.839735	0.419868	+	0.907585i	$0.362076\pi$
$678$	−1.01310	−0.0389079
$679$	−35.0825	−1.34634
$680$	−3.03519	−0.116394
$681$	−22.9909	−0.881014
$682$	−5.43982	−0.208301
$683$	0.430831	0.0164853	0.00824264	−	0.999966i	$-0.497376\pi$
$683$	0.430831	0.0164853	0.00824264	+	0.999966i	$0.497376\pi$
$684$	−0.991930	−0.0379274
$685$	16.8154	0.642482
$686$	4.94246	0.188704
$687$	−17.4880	−0.667208
$688$	9.77299	0.372592
$689$	4.74112	0.180622
$690$	−10.5270	−0.400758
$691$	−22.2037	−0.844670	−0.422335	−	0.906440i	$-0.638789\pi$
$691$	−22.2037	−0.844670	−0.422335	+	0.906440i	$0.638789\pi$
$692$	−6.26546	−0.238177
$693$	−50.7196	−1.92668
$694$	12.7284	0.483164
$695$	−11.7125	−0.444280
$696$	10.7499	0.407474
$697$	7.28353	0.275883
$698$	9.41862	0.356500
$699$	45.4342	1.71848
$700$	3.55078	0.134207
$701$	29.5353	1.11553	0.557767	−	0.829998i	$-0.311658\pi$
$701$	29.5353	1.11553	0.557767	+	0.829998i	$0.311658\pi$
$702$	−0.887478	−0.0334957
$703$	0.988436	0.0372796
$704$	−5.43982	−0.205021
$705$	9.70365	0.365461
$706$	−29.9959	−1.12891
$707$	36.9489	1.38961
$708$	−29.8692	−1.12255
$709$	26.0487	0.978280	0.489140	−	0.872205i	$-0.337311\pi$
$709$	26.0487	0.978280	0.489140	+	0.872205i	$0.337311\pi$
$710$	1.51430	0.0568308
$711$	−10.9488	−0.410613
$712$	−7.18911	−0.269423
$713$	4.43826	0.166214
$714$	25.5625	0.956653
$715$	−5.43982	−0.203438
$716$	21.5659	0.805955
$717$	6.64471	0.248151
$718$	1.97077	0.0735483
$719$	46.3975	1.73033	0.865167	−	0.501485i	$-0.167213\pi$
$719$	46.3975	1.73033	0.865167	+	0.501485i	$0.167213\pi$
$720$	−2.62583	−0.0978591
$721$	−50.9553	−1.89767
$722$	18.8573	0.701796
$723$	−12.2060	−0.453945
$724$	3.68654	0.137009
$725$	−4.53222	−0.168322
$726$	−44.0972	−1.63660
$727$	−39.4955	−1.46481	−0.732404	−	0.680871i	$-0.761602\pi$
$727$	−39.4955	−1.46481	−0.732404	+	0.680871i	$0.761602\pi$
$728$	3.55078	0.131601
$729$	−19.8974	−0.736941
$730$	−7.17662	−0.265619
$731$	−29.6629	−1.09712
$732$	10.5003	0.388101
$733$	48.1997	1.78030	0.890148	−	0.455672i	$-0.150601\pi$
$733$	48.1997	1.78030	0.890148	+	0.455672i	$0.150601\pi$
$734$	−23.6466	−0.872811
$735$	−13.3017	−0.490640
$736$	4.43826	0.163596
$737$	26.3009	0.968805
$738$	6.30120	0.231951
$739$	19.0107	0.699320	0.349660	−	0.936877i	$-0.386297\pi$
$739$	19.0107	0.699320	0.349660	+	0.936877i	$0.386297\pi$
$740$	2.61659	0.0961876
$741$	0.895998	0.0329153
$742$	16.8347	0.618021
$743$	31.6073	1.15956	0.579779	−	0.814774i	$-0.303139\pi$
$743$	31.6073	1.15956	0.579779	+	0.814774i	$0.303139\pi$
$744$	2.37188	0.0869575
$745$	−15.2745	−0.559615
$746$	−9.51439	−0.348346
$747$	16.9526	0.620265
$748$	16.5109	0.603698
$749$	12.5282	0.457770
$750$	2.37188	0.0866090
$751$	−26.0463	−0.950444	−0.475222	−	0.879866i	$-0.657632\pi$
$751$	−26.0463	−0.950444	−0.475222	+	0.879866i	$0.657632\pi$
$752$	−4.09111	−0.149188
$753$	56.8095	2.07025
$754$	−4.53222	−0.165054
$755$	15.5274	0.565098
$756$	−3.15124	−0.114610
$757$	43.8109	1.59233	0.796167	−	0.605077i	$-0.206858\pi$
$757$	43.8109	1.59233	0.796167	+	0.605077i	$0.206858\pi$
$758$	−19.2902	−0.700652
$759$	57.2652	2.07859
$760$	−0.377758	−0.0137027
$761$	−40.4409	−1.46598	−0.732990	−	0.680239i	$-0.761876\pi$
$761$	−40.4409	−1.46598	−0.732990	+	0.680239i	$0.761876\pi$
$762$	−31.9695	−1.15813
$763$	−6.11273	−0.221296
$764$	−2.74539	−0.0993246
$765$	7.96991	0.288153
$766$	−30.3267	−1.09575
$767$	12.5930	0.454707
$768$	2.37188	0.0855880
$769$	8.12354	0.292942	0.146471	−	0.989215i	$-0.453208\pi$
$769$	8.12354	0.292942	0.146471	+	0.989215i	$0.453208\pi$
$770$	−19.3156	−0.696086
$771$	75.4760	2.71820
$772$	4.22905	0.152207
$773$	3.76109	0.135277	0.0676385	−	0.997710i	$-0.478454\pi$
$773$	3.76109	0.135277	0.0676385	+	0.997710i	$0.478454\pi$
$774$	−25.6622	−0.922410
$775$	−1.00000	−0.0359211
$776$	9.88020	0.354679
$777$	−22.0370	−0.790573
$778$	1.16687	0.0418342
$779$	0.906504	0.0324789
$780$	2.37188	0.0849271
$781$	−8.23754	−0.294762
$782$	−13.4710	−0.481721
$783$	4.02224	0.143743
$784$	5.60806	0.200288
$785$	15.4415	0.551131
$786$	−10.2760	−0.366531
$787$	54.8927	1.95671	0.978357	−	0.206925i	$-0.0663457\pi$
$787$	54.8927	1.95671	0.978357	+	0.206925i	$0.0663457\pi$
$788$	−15.8092	−0.563178
$789$	−64.9271	−2.31147
$790$	−4.16965	−0.148350
$791$	1.51664	0.0539256
$792$	14.2841	0.507562
$793$	−4.42698	−0.157207
$794$	−27.4050	−0.972566
$795$	11.2454	0.398833
$796$	9.06004	0.321125
$797$	−51.7869	−1.83439	−0.917193	−	0.398442i	$-0.869551\pi$
$797$	−51.7869	−1.83439	−0.917193	+	0.398442i	$0.869551\pi$
$798$	3.18150	0.112624
$799$	12.4173	0.439293
$800$	−1.00000	−0.0353553
$801$	18.8774	0.667000
$802$	22.9615	0.810799
$803$	39.0395	1.37767
$804$	−11.4678	−0.404437
$805$	15.7593	0.555443
$806$	−1.00000	−0.0352235
$807$	27.5249	0.968921
$808$	−10.4058	−0.366076
$809$	−17.9994	−0.632823	−0.316412	−	0.948622i	$-0.602478\pi$
$809$	−17.9994	−0.632823	−0.316412	+	0.948622i	$0.602478\pi$
$810$	−9.98250	−0.350749
$811$	−26.8138	−0.941560	−0.470780	−	0.882251i	$-0.656028\pi$
$811$	−26.8138	−0.941560	−0.470780	+	0.882251i	$0.656028\pi$
$812$	−16.0929	−0.564751
$813$	−36.9929	−1.29740
$814$	−14.2337	−0.498893
$815$	0.125517	0.00439666
$816$	−7.19912	−0.252020
$817$	−3.69182	−0.129161
$818$	−14.8861	−0.520481
$819$	−9.32377	−0.325799
$820$	2.39970	0.0838010
$821$	38.9943	1.36091	0.680455	−	0.732790i	$-0.261782\pi$
$821$	38.9943	1.36091	0.680455	+	0.732790i	$0.261782\pi$
$822$	39.8841	1.39112
$823$	30.7157	1.07068	0.535342	−	0.844635i	$-0.320183\pi$
$823$	30.7157	1.07068	0.535342	+	0.844635i	$0.320183\pi$
$824$	14.3504	0.499921
$825$	−12.9026	−0.449211
$826$	44.7150	1.55584
$827$	2.39137	0.0831561	0.0415780	−	0.999135i	$-0.486761\pi$
$827$	2.39137	0.0831561	0.0415780	+	0.999135i	$0.486761\pi$
$828$	−11.6541	−0.405009
$829$	31.5760	1.09668	0.548340	−	0.836255i	$-0.315260\pi$
$829$	31.5760	1.09668	0.548340	+	0.836255i	$0.315260\pi$
$830$	6.45610	0.224094
$831$	14.3598	0.498135
$832$	−1.00000	−0.0346688
$833$	−17.0215	−0.589761
$834$	−27.7807	−0.961966
$835$	−17.3852	−0.601640
$836$	2.05493	0.0710714
$837$	0.887478	0.0306757
$838$	18.1353	0.626472
$839$	−27.2878	−0.942081	−0.471040	−	0.882112i	$-0.656121\pi$
$839$	−27.2878	−0.942081	−0.471040	+	0.882112i	$0.656121\pi$
$840$	8.42205	0.290588
$841$	−8.45897	−0.291689
$842$	−10.2244	−0.352356
$843$	−56.7919	−1.95602
$844$	−7.29572	−0.251129
$845$	−1.00000	−0.0344010
$846$	10.7426	0.369338
$847$	66.0148	2.26830
$848$	−4.74112	−0.162811
$849$	−57.8044	−1.98384
$850$	3.03519	0.104106
$851$	11.6131	0.398092
$852$	3.59175	0.123051
$853$	21.0799	0.721762	0.360881	−	0.932612i	$-0.382476\pi$
$853$	21.0799	0.721762	0.360881	+	0.932612i	$0.382476\pi$
$854$	−15.7192	−0.537901
$855$	0.991930	0.0339233
$856$	−3.52828	−0.120594
$857$	16.1742	0.552500	0.276250	−	0.961086i	$-0.410908\pi$
$857$	16.1742	0.552500	0.276250	+	0.961086i	$0.410908\pi$
$858$	−12.9026	−0.440488
$859$	23.5748	0.804362	0.402181	−	0.915560i	$-0.368252\pi$
$859$	23.5748	0.804362	0.402181	+	0.915560i	$0.368252\pi$
$860$	−9.77299	−0.333256
$861$	−20.2104	−0.688767
$862$	−9.44596	−0.321731
$863$	−15.7242	−0.535259	−0.267629	−	0.963522i	$-0.586240\pi$
$863$	−15.7242	−0.535259	−0.267629	+	0.963522i	$0.586240\pi$
$864$	0.887478	0.0301926
$865$	6.26546	0.213032
$866$	33.5718	1.14082
$867$	−18.4713	−0.627319
$868$	−3.55078	−0.120521
$869$	22.6821	0.769439
$870$	−10.7499	−0.364456
$871$	4.83488	0.163824
$872$	1.72151	0.0582978
$873$	−25.9438	−0.878064
$874$	−1.67659	−0.0567115
$875$	−3.55078	−0.120038
$876$	−17.0221	−0.575124
$877$	−46.2039	−1.56019	−0.780097	−	0.625659i	$-0.784830\pi$
$877$	−46.2039	−1.56019	−0.780097	+	0.625659i	$0.784830\pi$
$878$	27.9505	0.943285
$879$	8.24408	0.278066
$880$	5.43982	0.183376
$881$	−19.1259	−0.644369	−0.322185	−	0.946677i	$-0.604417\pi$
$881$	−19.1259	−0.644369	−0.322185	+	0.946677i	$0.604417\pi$
$882$	−14.7258	−0.495845
$883$	−8.50120	−0.286088	−0.143044	−	0.989716i	$-0.545689\pi$
$883$	−8.50120	−0.286088	−0.143044	+	0.989716i	$0.545689\pi$
$884$	3.03519	0.102084
$885$	29.8692	1.00404
$886$	10.6214	0.356831
$887$	5.70808	0.191659	0.0958293	−	0.995398i	$-0.469450\pi$
$887$	5.70808	0.191659	0.0958293	+	0.995398i	$0.469450\pi$
$888$	6.20624	0.208268
$889$	47.8594	1.60515
$890$	7.18911	0.240979
$891$	54.3030	1.81922
$892$	−10.5506	−0.353259
$893$	1.54545	0.0517166
$894$	−36.2294	−1.21169
$895$	−21.5659	−0.720868
$896$	−3.55078	−0.118623
$897$	10.5270	0.351488
$898$	18.8941	0.630506
$899$	4.53222	0.151158
$900$	2.62583	0.0875278
$901$	14.3902	0.479407
$902$	−13.0539	−0.434648
$903$	82.3086	2.73906
$904$	−0.427129	−0.0142061
$905$	−3.68654	−0.122545
$906$	36.8291	1.22356
$907$	12.7519	0.423420	0.211710	−	0.977333i	$-0.432097\pi$
$907$	12.7519	0.423420	0.211710	+	0.977333i	$0.432097\pi$
$908$	−9.69310	−0.321677
$909$	27.3240	0.906280
$910$	−3.55078	−0.117707
$911$	−10.7875	−0.357405	−0.178702	−	0.983903i	$-0.557190\pi$
$911$	−10.7875	−0.357405	−0.178702	+	0.983903i	$0.557190\pi$
$912$	−0.895998	−0.0296695
$913$	−35.1200	−1.16230
$914$	−11.4670	−0.379294
$915$	−10.5003	−0.347128
$916$	−7.37303	−0.243612
$917$	15.3834	0.508005
$918$	−2.69366	−0.0889041
$919$	22.6790	0.748111	0.374055	−	0.927406i	$-0.377967\pi$
$919$	22.6790	0.748111	0.374055	+	0.927406i	$0.377967\pi$
$920$	−4.43826	−0.146325
$921$	−35.7812	−1.17903
$922$	23.2531	0.765799
$923$	−1.51430	−0.0498439
$924$	−45.8144	−1.50718
$925$	−2.61659	−0.0860328
$926$	6.36720	0.209239
$927$	−37.6819	−1.23764
$928$	4.53222	0.148777
$929$	7.90204	0.259257	0.129629	−	0.991563i	$-0.458621\pi$
$929$	7.90204	0.259257	0.129629	+	0.991563i	$0.458621\pi$
$930$	−2.37188	−0.0777771
$931$	−2.11849	−0.0694308
$932$	19.1553	0.627454
$933$	−54.1327	−1.77223
$934$	−25.5759	−0.836869
$935$	−16.5109	−0.539964
$936$	2.62583	0.0858281
$937$	−46.1752	−1.50848	−0.754239	−	0.656600i	$-0.771994\pi$
$937$	−46.1752	−1.50848	−0.754239	+	0.656600i	$0.771994\pi$
$938$	17.1676	0.560543
$939$	62.4539	2.03811
$940$	4.09111	0.133437
$941$	58.4130	1.90421	0.952104	−	0.305773i	$-0.0989150\pi$
$941$	58.4130	1.90421	0.952104	+	0.305773i	$0.0989150\pi$
$942$	36.6255	1.19332
$943$	10.6505	0.346827
$944$	−12.5930	−0.409867
$945$	3.15124	0.102510
$946$	53.1633	1.72849
$947$	38.5068	1.25130	0.625651	−	0.780103i	$-0.284833\pi$
$947$	38.5068	1.25130	0.625651	+	0.780103i	$0.284833\pi$
$948$	−9.88993	−0.321210
$949$	7.17662	0.232963
$950$	0.377758	0.0122561
$951$	43.3671	1.40627
$952$	10.7773	0.349294
$953$	−15.4547	−0.500628	−0.250314	−	0.968165i	$-0.580534\pi$
$953$	−15.4547	−0.500628	−0.250314	+	0.968165i	$0.580534\pi$
$954$	12.4494	0.403064
$955$	2.74539	0.0888386
$956$	2.80145	0.0906053
$957$	58.4775	1.89031
$958$	40.7821	1.31761
$959$	−59.7077	−1.92806
$960$	−2.37188	−0.0765522
$961$	1.00000	0.0322581
$962$	−2.61659	−0.0843621
$963$	9.26469	0.298551
$964$	−5.14611	−0.165745
$965$	−4.22905	−0.136138
$966$	37.3792	1.20266
$967$	−4.31769	−0.138847	−0.0694237	−	0.997587i	$-0.522116\pi$
$967$	−4.31769	−0.138847	−0.0694237	+	0.997587i	$0.522116\pi$
$968$	−18.5916	−0.597557
$969$	2.71953	0.0873637
$970$	−9.88020	−0.317234
$971$	9.58530	0.307607	0.153803	−	0.988101i	$-0.450848\pi$
$971$	9.58530	0.307607	0.153803	+	0.988101i	$0.450848\pi$
$972$	−21.0149	−0.674053
$973$	41.5885	1.33327
$974$	−5.45766	−0.174875
$975$	−2.37188	−0.0759611
$976$	4.42698	0.141704
$977$	−0.159038	−0.00508807	−0.00254404	−	0.999997i	$-0.500810\pi$
$977$	−0.159038	−0.00508807	−0.00254404	+	0.999997i	$0.500810\pi$
$978$	0.297711	0.00951976
$979$	−39.1074	−1.24988
$980$	−5.60806	−0.179143
$981$	−4.52041	−0.144326
$982$	3.02840	0.0966402
$983$	−6.26496	−0.199821	−0.0999106	−	0.994996i	$-0.531856\pi$
$983$	−6.26496	−0.199821	−0.0999106	+	0.994996i	$0.531856\pi$
$984$	5.69180	0.181448
$985$	15.8092	0.503722
$986$	−13.7562	−0.438085
$987$	−34.4556	−1.09673
$988$	0.377758	0.0120181
$989$	−43.3751	−1.37925
$990$	−14.2841	−0.453977
$991$	39.9297	1.26841	0.634204	−	0.773166i	$-0.281328\pi$
$991$	39.9297	1.26841	0.634204	+	0.773166i	$0.281328\pi$
$992$	1.00000	0.0317500
$993$	−31.6022	−1.00286
$994$	−5.37697	−0.170547
$995$	−9.06004	−0.287223
$996$	15.3131	0.485215
$997$	39.7858	1.26003	0.630015	−	0.776583i	$-0.283049\pi$
$997$	39.7858	1.26003	0.630015	+	0.776583i	$0.283049\pi$
$998$	15.0661	0.476909
$999$	2.32216	0.0734699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.i.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.i.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.37188 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.37188 q^{6} +3.55078 q^{7} -1.00000 q^{8} +2.62583 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.37188 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.37188 q^{6} +3.55078 q^{7} -1.00000 q^{8} +2.62583 q^{9} +1.00000 q^{10} -5.43982 q^{11} +2.37188 q^{12} -1.00000 q^{13} -3.55078 q^{14} -2.37188 q^{15} +1.00000 q^{16} -3.03519 q^{17} -2.62583 q^{18} -0.377758 q^{19} -1.00000 q^{20} +8.42205 q^{21} +5.43982 q^{22} -4.43826 q^{23} -2.37188 q^{24} +1.00000 q^{25} +1.00000 q^{26} -0.887478 q^{27} +3.55078 q^{28} -4.53222 q^{29} +2.37188 q^{30} -1.00000 q^{31} -1.00000 q^{32} -12.9026 q^{33} +3.03519 q^{34} -3.55078 q^{35} +2.62583 q^{36} -2.61659 q^{37} +0.377758 q^{38} -2.37188 q^{39} +1.00000 q^{40} -2.39970 q^{41} -8.42205 q^{42} +9.77299 q^{43} -5.43982 q^{44} -2.62583 q^{45} +4.43826 q^{46} -4.09111 q^{47} +2.37188 q^{48} +5.60806 q^{49} -1.00000 q^{50} -7.19912 q^{51} -1.00000 q^{52} -4.74112 q^{53} +0.887478 q^{54} +5.43982 q^{55} -3.55078 q^{56} -0.895998 q^{57} +4.53222 q^{58} -12.5930 q^{59} -2.37188 q^{60} +4.42698 q^{61} +1.00000 q^{62} +9.32377 q^{63} +1.00000 q^{64} +1.00000 q^{65} +12.9026 q^{66} -4.83488 q^{67} -3.03519 q^{68} -10.5270 q^{69} +3.55078 q^{70} +1.51430 q^{71} -2.62583 q^{72} -7.17662 q^{73} +2.61659 q^{74} +2.37188 q^{75} -0.377758 q^{76} -19.3156 q^{77} +2.37188 q^{78} -4.16965 q^{79} -1.00000 q^{80} -9.98250 q^{81} +2.39970 q^{82} +6.45610 q^{83} +8.42205 q^{84} +3.03519 q^{85} -9.77299 q^{86} -10.7499 q^{87} +5.43982 q^{88} +7.18911 q^{89} +2.62583 q^{90} -3.55078 q^{91} -4.43826 q^{92} -2.37188 q^{93} +4.09111 q^{94} +0.377758 q^{95} -2.37188 q^{96} -9.88020 q^{97} -5.60806 q^{98} -14.2841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} + 7 q^{10} - 6 q^{11} + 3 q^{12} - 7 q^{13} - 2 q^{14} - 3 q^{15} + 7 q^{16} - 4 q^{18} - 9 q^{19} - 7 q^{20} + q^{21} + 6 q^{22} + 7 q^{23} - 3 q^{24} + 7 q^{25} + 7 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} + 3 q^{30} - 7 q^{31} - 7 q^{32} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 9 q^{38} - 3 q^{39} + 7 q^{40} - 14 q^{41} - q^{42} + 9 q^{43} - 6 q^{44} - 4 q^{45} - 7 q^{46} - 8 q^{47} + 3 q^{48} - q^{49} - 7 q^{50} - 7 q^{51} - 7 q^{52} - 6 q^{53} - 9 q^{54} + 6 q^{55} - 2 q^{56} - 11 q^{57} + 4 q^{58} - 15 q^{59} - 3 q^{60} + q^{61} + 7 q^{62} - 17 q^{63} + 7 q^{64} + 7 q^{65} + 14 q^{67} - 14 q^{69} + 2 q^{70} - 16 q^{71} - 4 q^{72} - 13 q^{73} - 2 q^{74} + 3 q^{75} - 9 q^{76} - 5 q^{77} + 3 q^{78} - 14 q^{79} - 7 q^{80} - 25 q^{81} + 14 q^{82} - 10 q^{83} + q^{84} - 9 q^{86} - 9 q^{87} + 6 q^{88} - 26 q^{89} + 4 q^{90} - 2 q^{91} + 7 q^{92} - 3 q^{93} + 8 q^{94} + 9 q^{95} - 3 q^{96} - 5 q^{97} + q^{98} - 37 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 + 7 * q^10 - 6 * q^11 + 3 * q^12 - 7 * q^13 - 2 * q^14 - 3 * q^15 + 7 * q^16 - 4 * q^18 - 9 * q^19 - 7 * q^20 + q^21 + 6 * q^22 + 7 * q^23 - 3 * q^24 + 7 * q^25 + 7 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 + 3 * q^30 - 7 * q^31 - 7 * q^32 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 9 * q^38 - 3 * q^39 + 7 * q^40 - 14 * q^41 - q^42 + 9 * q^43 - 6 * q^44 - 4 * q^45 - 7 * q^46 - 8 * q^47 + 3 * q^48 - q^49 - 7 * q^50 - 7 * q^51 - 7 * q^52 - 6 * q^53 - 9 * q^54 + 6 * q^55 - 2 * q^56 - 11 * q^57 + 4 * q^58 - 15 * q^59 - 3 * q^60 + q^61 + 7 * q^62 - 17 * q^63 + 7 * q^64 + 7 * q^65 + 14 * q^67 - 14 * q^69 + 2 * q^70 - 16 * q^71 - 4 * q^72 - 13 * q^73 - 2 * q^74 + 3 * q^75 - 9 * q^76 - 5 * q^77 + 3 * q^78 - 14 * q^79 - 7 * q^80 - 25 * q^81 + 14 * q^82 - 10 * q^83 + q^84 - 9 * q^86 - 9 * q^87 + 6 * q^88 - 26 * q^89 + 4 * q^90 - 2 * q^91 + 7 * q^92 - 3 * q^93 + 8 * q^94 + 9 * q^95 - 3 * q^96 - 5 * q^97 + q^98 - 37 * q^99

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