LMFDB - Embedded newform 1334.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.207184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 2x^{2} + 7x - 1 $ x^5 - x^4 - 6x^3 + 2x^2 + 7*x - 1
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			1.4
Root			$1.22974$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.85405 q^{3} +1.00000 q^{4} -2.05025 q^{5} -1.85405 q^{6} +1.71748 q^{7} -1.00000 q^{8} +0.437490 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.85405 q^{3} +1.00000 q^{4} -2.05025 q^{5} -1.85405 q^{6} +1.71748 q^{7} -1.00000 q^{8} +0.437490 q^{9} +2.05025 q^{10} +3.33025 q^{11} +1.85405 q^{12} -6.00902 q^{13} -1.71748 q^{14} -3.80127 q^{15} +1.00000 q^{16} -6.27962 q^{17} -0.437490 q^{18} -8.28901 q^{19} -2.05025 q^{20} +3.18429 q^{21} -3.33025 q^{22} +1.00000 q^{23} -1.85405 q^{24} -0.796458 q^{25} +6.00902 q^{26} -4.75101 q^{27} +1.71748 q^{28} +1.00000 q^{29} +3.80127 q^{30} -1.14390 q^{31} -1.00000 q^{32} +6.17443 q^{33} +6.27962 q^{34} -3.52128 q^{35} +0.437490 q^{36} +0.0544646 q^{37} +8.28901 q^{38} -11.1410 q^{39} +2.05025 q^{40} +11.7722 q^{41} -3.18429 q^{42} +7.24778 q^{43} +3.33025 q^{44} -0.896966 q^{45} -1.00000 q^{46} -4.22721 q^{47} +1.85405 q^{48} -4.05025 q^{49} +0.796458 q^{50} -11.6427 q^{51} -6.00902 q^{52} +5.12625 q^{53} +4.75101 q^{54} -6.82785 q^{55} -1.71748 q^{56} -15.3682 q^{57} -1.00000 q^{58} -13.3832 q^{59} -3.80127 q^{60} -9.10737 q^{61} +1.14390 q^{62} +0.751382 q^{63} +1.00000 q^{64} +12.3200 q^{65} -6.17443 q^{66} +4.74896 q^{67} -6.27962 q^{68} +1.85405 q^{69} +3.52128 q^{70} +5.37843 q^{71} -0.437490 q^{72} +11.8448 q^{73} -0.0544646 q^{74} -1.47667 q^{75} -8.28901 q^{76} +5.71964 q^{77} +11.1410 q^{78} -15.5791 q^{79} -2.05025 q^{80} -10.1211 q^{81} -11.7722 q^{82} -10.0448 q^{83} +3.18429 q^{84} +12.8748 q^{85} -7.24778 q^{86} +1.85405 q^{87} -3.33025 q^{88} +1.89386 q^{89} +0.896966 q^{90} -10.3204 q^{91} +1.00000 q^{92} -2.12084 q^{93} +4.22721 q^{94} +16.9946 q^{95} -1.85405 q^{96} -8.63370 q^{97} +4.05025 q^{98} +1.45695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + q^3 + 5 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 5 q^{10} + q^{11} + q^{12} - 11 q^{13} + 2 q^{14} + 5 q^{15} + 5 q^{16} + 4 q^{17} - 2 q^{18} - 12 q^{19} - 5 q^{20} - 8 q^{21} - q^{22} + 5 q^{23} - q^{24} - 4 q^{25} + 11 q^{26} - 5 q^{27} - 2 q^{28} + 5 q^{29} - 5 q^{30} - 5 q^{31} - 5 q^{32} - 11 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 12 q^{38} - 9 q^{39} + 5 q^{40} - 6 q^{41} + 8 q^{42} - 7 q^{43} + q^{44} + 6 q^{45} - 5 q^{46} + 5 q^{47} + q^{48} - 15 q^{49} + 4 q^{50} - 42 q^{51} - 11 q^{52} - q^{53} + 5 q^{54} - 31 q^{55} + 2 q^{56} - 4 q^{57} - 5 q^{58} - 12 q^{59} + 5 q^{60} - 20 q^{61} + 5 q^{62} + 10 q^{63} + 5 q^{64} + 3 q^{65} + 11 q^{66} - 4 q^{67} + 4 q^{68} + q^{69} + 4 q^{70} - 4 q^{71} - 2 q^{72} + 4 q^{73} - 12 q^{75} - 12 q^{76} + 14 q^{77} + 9 q^{78} - q^{79} - 5 q^{80} - 23 q^{81} + 6 q^{82} + 22 q^{83} - 8 q^{84} - 16 q^{85} + 7 q^{86} + q^{87} - q^{88} + 8 q^{89} - 6 q^{90} - 18 q^{91} + 5 q^{92} - 37 q^{93} - 5 q^{94} + 18 q^{95} - q^{96} - 46 q^{97} + 15 q^{98} - 24 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 + 5 * q^10 + q^11 + q^12 - 11 * q^13 + 2 * q^14 + 5 * q^15 + 5 * q^16 + 4 * q^17 - 2 * q^18 - 12 * q^19 - 5 * q^20 - 8 * q^21 - q^22 + 5 * q^23 - q^24 - 4 * q^25 + 11 * q^26 - 5 * q^27 - 2 * q^28 + 5 * q^29 - 5 * q^30 - 5 * q^31 - 5 * q^32 - 11 * q^33 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 12 * q^38 - 9 * q^39 + 5 * q^40 - 6 * q^41 + 8 * q^42 - 7 * q^43 + q^44 + 6 * q^45 - 5 * q^46 + 5 * q^47 + q^48 - 15 * q^49 + 4 * q^50 - 42 * q^51 - 11 * q^52 - q^53 + 5 * q^54 - 31 * q^55 + 2 * q^56 - 4 * q^57 - 5 * q^58 - 12 * q^59 + 5 * q^60 - 20 * q^61 + 5 * q^62 + 10 * q^63 + 5 * q^64 + 3 * q^65 + 11 * q^66 - 4 * q^67 + 4 * q^68 + q^69 + 4 * q^70 - 4 * q^71 - 2 * q^72 + 4 * q^73 - 12 * q^75 - 12 * q^76 + 14 * q^77 + 9 * q^78 - q^79 - 5 * q^80 - 23 * q^81 + 6 * q^82 + 22 * q^83 - 8 * q^84 - 16 * q^85 + 7 * q^86 + q^87 - q^88 + 8 * q^89 - 6 * q^90 - 18 * q^91 + 5 * q^92 - 37 * q^93 - 5 * q^94 + 18 * q^95 - q^96 - 46 * q^97 + 15 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.85405	1.07043	0.535217	−	0.844714i	$-0.320230\pi$
$3$	1.85405	1.07043	0.535217	+	0.844714i	$0.320230\pi$
$4$	1.00000	0.500000
$5$	−2.05025	−0.916901	−0.458451	−	0.888720i	$-0.651595\pi$
$5$	−2.05025	−0.916901	−0.458451	+	0.888720i	$0.651595\pi$
$6$	−1.85405	−0.756912
$7$	1.71748	0.649147	0.324574	−	0.945860i	$-0.394779\pi$
$7$	1.71748	0.649147	0.324574	+	0.945860i	$0.394779\pi$
$8$	−1.00000	−0.353553
$9$	0.437490	0.145830
$10$	2.05025	0.648347
$11$	3.33025	1.00411	0.502054	−	0.864837i	$-0.332578\pi$
$11$	3.33025	1.00411	0.502054	+	0.864837i	$0.332578\pi$
$12$	1.85405	0.535217
$13$	−6.00902	−1.66660	−0.833301	−	0.552819i	$-0.813552\pi$
$13$	−6.00902	−1.66660	−0.833301	+	0.552819i	$0.813552\pi$
$14$	−1.71748	−0.459016
$15$	−3.80127	−0.981483
$16$	1.00000	0.250000
$17$	−6.27962	−1.52303	−0.761516	−	0.648146i	$-0.775545\pi$
$17$	−6.27962	−1.52303	−0.761516	+	0.648146i	$0.775545\pi$
$18$	−0.437490	−0.103117
$19$	−8.28901	−1.90163	−0.950815	−	0.309760i	$-0.899751\pi$
$19$	−8.28901	−1.90163	−0.950815	+	0.309760i	$0.899751\pi$
$20$	−2.05025	−0.458451
$21$	3.18429	0.694870
$22$	−3.33025	−0.710011
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.85405	−0.378456
$25$	−0.796458	−0.159292
$26$	6.00902	1.17847
$27$	−4.75101	−0.914333
$28$	1.71748	0.324574
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.80127	0.694013
$31$	−1.14390	−0.205450	−0.102725	−	0.994710i	$-0.532756\pi$
$31$	−1.14390	−0.205450	−0.102725	+	0.994710i	$0.532756\pi$
$32$	−1.00000	−0.176777
$33$	6.17443	1.07483
$34$	6.27962	1.07695
$35$	−3.52128	−0.595204
$36$	0.437490	0.0729151
$37$	0.0544646	0.00895393	0.00447696	−	0.999990i	$-0.498575\pi$
$37$	0.0544646	0.00895393	0.00447696	+	0.999990i	$0.498575\pi$
$38$	8.28901	1.34466
$39$	−11.1410	−1.78399
$40$	2.05025	0.324174
$41$	11.7722	1.83851	0.919253	−	0.393668i	$-0.128794\pi$
$41$	11.7722	1.83851	0.919253	+	0.393668i	$0.128794\pi$
$42$	−3.18429	−0.491347
$43$	7.24778	1.10528	0.552638	−	0.833421i	$-0.313621\pi$
$43$	7.24778	1.10528	0.552638	+	0.833421i	$0.313621\pi$
$44$	3.33025	0.502054
$45$	−0.896966	−0.133712
$46$	−1.00000	−0.147442
$47$	−4.22721	−0.616602	−0.308301	−	0.951289i	$-0.599760\pi$
$47$	−4.22721	−0.616602	−0.308301	+	0.951289i	$0.599760\pi$
$48$	1.85405	0.267609
$49$	−4.05025	−0.578608
$50$	0.796458	0.112636
$51$	−11.6427	−1.63031
$52$	−6.00902	−0.833301
$53$	5.12625	0.704145	0.352072	−	0.935973i	$-0.385477\pi$
$53$	5.12625	0.704145	0.352072	+	0.935973i	$0.385477\pi$
$54$	4.75101	0.646531
$55$	−6.82785	−0.920667
$56$	−1.71748	−0.229508
$57$	−15.3682	−2.03557
$58$	−1.00000	−0.131306
$59$	−13.3832	−1.74235	−0.871175	−	0.490973i	$-0.836641\pi$
$59$	−13.3832	−1.74235	−0.871175	+	0.490973i	$0.836641\pi$
$60$	−3.80127	−0.490742
$61$	−9.10737	−1.16608	−0.583040	−	0.812444i	$-0.698137\pi$
$61$	−9.10737	−1.16608	−0.583040	+	0.812444i	$0.698137\pi$
$62$	1.14390	0.145275
$63$	0.751382	0.0946652
$64$	1.00000	0.125000
$65$	12.3200	1.52811
$66$	−6.17443	−0.760020
$67$	4.74896	0.580178	0.290089	−	0.957000i	$-0.406315\pi$
$67$	4.74896	0.580178	0.290089	+	0.957000i	$0.406315\pi$
$68$	−6.27962	−0.761516
$69$	1.85405	0.223201
$70$	3.52128	0.420873
$71$	5.37843	0.638302	0.319151	−	0.947704i	$-0.396602\pi$
$71$	5.37843	0.638302	0.319151	+	0.947704i	$0.396602\pi$
$72$	−0.437490	−0.0515587
$73$	11.8448	1.38633	0.693164	−	0.720780i	$-0.256216\pi$
$73$	11.8448	1.38633	0.693164	+	0.720780i	$0.256216\pi$
$74$	−0.0544646	−0.00633138
$75$	−1.47667	−0.170511
$76$	−8.28901	−0.950815
$77$	5.71964	0.651813
$78$	11.1410	1.26147
$79$	−15.5791	−1.75278	−0.876391	−	0.481599i	$-0.840056\pi$
$79$	−15.5791	−1.75278	−0.876391	+	0.481599i	$0.840056\pi$
$80$	−2.05025	−0.229225
$81$	−10.1211	−1.12456
$82$	−11.7722	−1.30002
$83$	−10.0448	−1.10256	−0.551282	−	0.834319i	$-0.685861\pi$
$83$	−10.0448	−1.10256	−0.551282	+	0.834319i	$0.685861\pi$
$84$	3.18429	0.347435
$85$	12.8748	1.39647
$86$	−7.24778	−0.781548
$87$	1.85405	0.198775
$88$	−3.33025	−0.355005
$89$	1.89386	0.200749	0.100374	−	0.994950i	$-0.467996\pi$
$89$	1.89386	0.200749	0.100374	+	0.994950i	$0.467996\pi$
$90$	0.896966	0.0945486
$91$	−10.3204	−1.08187
$92$	1.00000	0.104257
$93$	−2.12084	−0.219921
$94$	4.22721	0.436004
$95$	16.9946	1.74361
$96$	−1.85405	−0.189228
$97$	−8.63370	−0.876619	−0.438310	−	0.898824i	$-0.644423\pi$
$97$	−8.63370	−0.876619	−0.438310	+	0.898824i	$0.644423\pi$
$98$	4.05025	0.409137
$99$	1.45695	0.146429
$100$	−0.796458	−0.0796458
$101$	−3.29361	−0.327726	−0.163863	−	0.986483i	$-0.552396\pi$
$101$	−3.29361	−0.327726	−0.163863	+	0.986483i	$0.552396\pi$
$102$	11.6427	1.15280
$103$	−3.57464	−0.352219	−0.176110	−	0.984371i	$-0.556351\pi$
$103$	−3.57464	−0.352219	−0.176110	+	0.984371i	$0.556351\pi$
$104$	6.00902	0.589233
$105$	−6.52861	−0.637127
$106$	−5.12625	−0.497906
$107$	11.6662	1.12782	0.563908	−	0.825837i	$-0.309297\pi$
$107$	11.6662	1.12782	0.563908	+	0.825837i	$0.309297\pi$
$108$	−4.75101	−0.457166
$109$	−4.49241	−0.430295	−0.215147	−	0.976582i	$-0.569023\pi$
$109$	−4.49241	−0.430295	−0.215147	+	0.976582i	$0.569023\pi$
$110$	6.82785	0.651010
$111$	0.100980	0.00958459
$112$	1.71748	0.162287
$113$	16.0998	1.51454	0.757270	−	0.653102i	$-0.226533\pi$
$113$	16.0998	1.51454	0.757270	+	0.653102i	$0.226533\pi$
$114$	15.3682	1.43937
$115$	−2.05025	−0.191187
$116$	1.00000	0.0928477
$117$	−2.62889	−0.243041
$118$	13.3832	1.23203
$119$	−10.7851	−0.988672
$120$	3.80127	0.347007
$121$	0.0905396	0.00823087
$122$	9.10737	0.824543
$123$	21.8262	1.96800
$124$	−1.14390	−0.102725
$125$	11.8842	1.06296
$126$	−0.751382	−0.0669384
$127$	−5.94346	−0.527397	−0.263699	−	0.964605i	$-0.584942\pi$
$127$	−5.94346	−0.527397	−0.263699	+	0.964605i	$0.584942\pi$
$128$	−1.00000	−0.0883883
$129$	13.4377	1.18313
$130$	−12.3200	−1.08054
$131$	5.13199	0.448384	0.224192	−	0.974545i	$-0.428026\pi$
$131$	5.13199	0.448384	0.224192	+	0.974545i	$0.428026\pi$
$132$	6.17443	0.537415
$133$	−14.2362	−1.23444
$134$	−4.74896	−0.410248
$135$	9.74078	0.838353
$136$	6.27962	0.538473
$137$	9.29107	0.793789	0.396895	−	0.917864i	$-0.370088\pi$
$137$	9.29107	0.793789	0.396895	+	0.917864i	$0.370088\pi$
$138$	−1.85405	−0.157827
$139$	1.66575	0.141287	0.0706437	−	0.997502i	$-0.477495\pi$
$139$	1.66575	0.141287	0.0706437	+	0.997502i	$0.477495\pi$
$140$	−3.52128	−0.297602
$141$	−7.83745	−0.660032
$142$	−5.37843	−0.451348
$143$	−20.0115	−1.67345
$144$	0.437490	0.0364575
$145$	−2.05025	−0.170264
$146$	−11.8448	−0.980281
$147$	−7.50936	−0.619362
$148$	0.0544646	0.00447696
$149$	−17.6455	−1.44557	−0.722787	−	0.691071i	$-0.757139\pi$
$149$	−17.6455	−1.44557	−0.722787	+	0.691071i	$0.757139\pi$
$150$	1.47667	0.120570
$151$	−9.71475	−0.790575	−0.395287	−	0.918558i	$-0.629355\pi$
$151$	−9.71475	−0.790575	−0.395287	+	0.918558i	$0.629355\pi$
$152$	8.28901	0.672328
$153$	−2.74727	−0.222104
$154$	−5.71964	−0.460902
$155$	2.34528	0.188378
$156$	−11.1410	−0.891994
$157$	−6.22618	−0.496903	−0.248452	−	0.968644i	$-0.579922\pi$
$157$	−6.22618	−0.496903	−0.248452	+	0.968644i	$0.579922\pi$
$158$	15.5791	1.23940
$159$	9.50431	0.753741
$160$	2.05025	0.162087
$161$	1.71748	0.135357
$162$	10.1211	0.795187
$163$	−5.34876	−0.418947	−0.209474	−	0.977814i	$-0.567175\pi$
$163$	−5.34876	−0.418947	−0.209474	+	0.977814i	$0.567175\pi$
$164$	11.7722	0.919253
$165$	−12.6592	−0.985514
$166$	10.0448	0.779630
$167$	16.5411	1.27999	0.639995	−	0.768379i	$-0.278936\pi$
$167$	16.5411	1.27999	0.639995	+	0.768379i	$0.278936\pi$
$168$	−3.18429	−0.245674
$169$	23.1083	1.77756
$170$	−12.8748	−0.987454
$171$	−3.62636	−0.277315
$172$	7.24778	0.552638
$173$	−24.5102	−1.86348	−0.931739	−	0.363129i	$-0.881708\pi$
$173$	−24.5102	−1.86348	−0.931739	+	0.363129i	$0.881708\pi$
$174$	−1.85405	−0.140555
$175$	−1.36790	−0.103404
$176$	3.33025	0.251027
$177$	−24.8132	−1.86507
$178$	−1.89386	−0.141951
$179$	11.8656	0.886875	0.443437	−	0.896305i	$-0.353759\pi$
$179$	11.8656	0.886875	0.443437	+	0.896305i	$0.353759\pi$
$180$	−0.896966	−0.0668559
$181$	9.30079	0.691322	0.345661	−	0.938359i	$-0.387655\pi$
$181$	9.30079	0.691322	0.345661	+	0.938359i	$0.387655\pi$
$182$	10.3204	0.764998
$183$	−16.8855	−1.24821
$184$	−1.00000	−0.0737210
$185$	−0.111666	−0.00820987
$186$	2.12084	0.155508
$187$	−20.9127	−1.52929
$188$	−4.22721	−0.308301
$189$	−8.15978	−0.593537
$190$	−16.9946	−1.23292
$191$	−12.6721	−0.916923	−0.458461	−	0.888714i	$-0.651599\pi$
$191$	−12.6721	−0.916923	−0.458461	+	0.888714i	$0.651599\pi$
$192$	1.85405	0.133804
$193$	−18.0752	−1.30108	−0.650542	−	0.759470i	$-0.725458\pi$
$193$	−18.0752	−1.30108	−0.650542	+	0.759470i	$0.725458\pi$
$194$	8.63370	0.619863
$195$	22.8419	1.63574
$196$	−4.05025	−0.289304
$197$	−5.03808	−0.358948	−0.179474	−	0.983763i	$-0.557440\pi$
$197$	−5.03808	−0.358948	−0.179474	+	0.983763i	$0.557440\pi$
$198$	−1.45695	−0.103541
$199$	19.1820	1.35977	0.679887	−	0.733317i	$-0.262029\pi$
$199$	19.1820	1.35977	0.679887	+	0.733317i	$0.262029\pi$
$200$	0.796458	0.0563181
$201$	8.80479	0.621042
$202$	3.29361	0.231738
$203$	1.71748	0.120544
$204$	−11.6427	−0.815153
$205$	−24.1360	−1.68573
$206$	3.57464	0.249057
$207$	0.437490	0.0304077
$208$	−6.00902	−0.416651
$209$	−27.6045	−1.90944
$210$	6.52861	0.450517
$211$	−15.6022	−1.07410	−0.537049	−	0.843551i	$-0.680461\pi$
$211$	−15.6022	−1.07410	−0.537049	+	0.843551i	$0.680461\pi$
$212$	5.12625	0.352072
$213$	9.97186	0.683260
$214$	−11.6662	−0.797487
$215$	−14.8598	−1.01343
$216$	4.75101	0.323266
$217$	−1.96463	−0.133368
$218$	4.49241	0.304264
$219$	21.9608	1.48397
$220$	−6.82785	−0.460334
$221$	37.7344	2.53829
$222$	−0.100980	−0.00677733
$223$	−9.98619	−0.668725	−0.334362	−	0.942445i	$-0.608521\pi$
$223$	−9.98619	−0.668725	−0.334362	+	0.942445i	$0.608521\pi$
$224$	−1.71748	−0.114754
$225$	−0.348443	−0.0232295
$226$	−16.0998	−1.07094
$227$	12.8281	0.851434	0.425717	−	0.904856i	$-0.360022\pi$
$227$	12.8281	0.851434	0.425717	+	0.904856i	$0.360022\pi$
$228$	−15.3682	−1.01779
$229$	4.37132	0.288865	0.144433	−	0.989515i	$-0.453864\pi$
$229$	4.37132	0.288865	0.144433	+	0.989515i	$0.453864\pi$
$230$	2.05025	0.135190
$231$	10.6045	0.697724
$232$	−1.00000	−0.0656532
$233$	20.6122	1.35035	0.675174	−	0.737659i	$-0.264069\pi$
$233$	20.6122	1.35035	0.675174	+	0.737659i	$0.264069\pi$
$234$	2.62889	0.171856
$235$	8.66686	0.565364
$236$	−13.3832	−0.871175
$237$	−28.8843	−1.87624
$238$	10.7851	0.699097
$239$	3.33026	0.215417	0.107708	−	0.994183i	$-0.465649\pi$
$239$	3.33026	0.215417	0.107708	+	0.994183i	$0.465649\pi$
$240$	−3.80127	−0.245371
$241$	18.8854	1.21651	0.608257	−	0.793740i	$-0.291869\pi$
$241$	18.8854	1.21651	0.608257	+	0.793740i	$0.291869\pi$
$242$	−0.0905396	−0.00582010
$243$	−4.51191	−0.289439
$244$	−9.10737	−0.583040
$245$	8.30405	0.530526
$246$	−21.8262	−1.39159
$247$	49.8088	3.16926
$248$	1.14390	0.0726377
$249$	−18.6236	−1.18022
$250$	−11.8842	−0.751624
$251$	8.23547	0.519818	0.259909	−	0.965633i	$-0.416307\pi$
$251$	8.23547	0.519818	0.259909	+	0.965633i	$0.416307\pi$
$252$	0.751382	0.0473326
$253$	3.33025	0.209371
$254$	5.94346	0.372926
$255$	23.8705	1.49483
$256$	1.00000	0.0625000
$257$	5.04038	0.314410	0.157205	−	0.987566i	$-0.449752\pi$
$257$	5.04038	0.314410	0.157205	+	0.987566i	$0.449752\pi$
$258$	−13.4377	−0.836596
$259$	0.0935420	0.00581242
$260$	12.3200	0.764055
$261$	0.437490	0.0270800
$262$	−5.13199	−0.317055
$263$	3.97728	0.245249	0.122625	−	0.992453i	$-0.460869\pi$
$263$	3.97728	0.245249	0.122625	+	0.992453i	$0.460869\pi$
$264$	−6.17443	−0.380010
$265$	−10.5101	−0.645631
$266$	14.2362	0.872879
$267$	3.51131	0.214888
$268$	4.74896	0.290089
$269$	−1.44133	−0.0878796	−0.0439398	−	0.999034i	$-0.513991\pi$
$269$	−1.44133	−0.0878796	−0.0439398	+	0.999034i	$0.513991\pi$
$270$	−9.74078	−0.592805
$271$	−30.2851	−1.83969	−0.919845	−	0.392282i	$-0.871686\pi$
$271$	−30.2851	−1.83969	−0.919845	+	0.392282i	$0.871686\pi$
$272$	−6.27962	−0.380758
$273$	−19.1345	−1.15807
$274$	−9.29107	−0.561294
$275$	−2.65240	−0.159946
$276$	1.85405	0.111601
$277$	23.3316	1.40186	0.700929	−	0.713231i	$-0.252769\pi$
$277$	23.3316	1.40186	0.700929	+	0.713231i	$0.252769\pi$
$278$	−1.66575	−0.0999053
$279$	−0.500445	−0.0299609
$280$	3.52128	0.210436
$281$	−0.0277966	−0.00165821	−0.000829103	−	1.00000i	$-0.500264\pi$
$281$	−0.0277966	−0.00165821	−0.000829103		1.00000i	$0.500264\pi$
$282$	7.83745	0.466713
$283$	10.8544	0.645229	0.322615	−	0.946530i	$-0.395438\pi$
$283$	10.8544	0.645229	0.322615	+	0.946530i	$0.395438\pi$
$284$	5.37843	0.319151
$285$	31.5088	1.86642
$286$	20.0115	1.18331
$287$	20.2185	1.19346
$288$	−0.437490	−0.0257794
$289$	22.4337	1.31963
$290$	2.05025	0.120395
$291$	−16.0073	−0.938363
$292$	11.8448	0.693164
$293$	−6.49931	−0.379694	−0.189847	−	0.981814i	$-0.560799\pi$
$293$	−6.49931	−0.379694	−0.189847	+	0.981814i	$0.560799\pi$
$294$	7.50936	0.437955
$295$	27.4390	1.59756
$296$	−0.0544646	−0.00316569
$297$	−15.8220	−0.918088
$298$	17.6455	1.02217
$299$	−6.00902	−0.347511
$300$	−1.47667	−0.0852556
$301$	12.4479	0.717487
$302$	9.71475	0.559021
$303$	−6.10651	−0.350810
$304$	−8.28901	−0.475407
$305$	18.6724	1.06918
$306$	2.74727	0.157051
$307$	−32.4410	−1.85150	−0.925751	−	0.378133i	$-0.876566\pi$
$307$	−32.4410	−1.85150	−0.925751	+	0.378133i	$0.876566\pi$
$308$	5.71964	0.325907
$309$	−6.62754	−0.377028
$310$	−2.34528	−0.133203
$311$	−20.2843	−1.15022	−0.575108	−	0.818078i	$-0.695040\pi$
$311$	−20.2843	−1.15022	−0.575108	+	0.818078i	$0.695040\pi$
$312$	11.1410	0.630735
$313$	3.56191	0.201331	0.100666	−	0.994920i	$-0.467903\pi$
$313$	3.56191	0.201331	0.100666	+	0.994920i	$0.467903\pi$
$314$	6.22618	0.351364
$315$	−1.54052	−0.0867987
$316$	−15.5791	−0.876391
$317$	−6.33185	−0.355632	−0.177816	−	0.984064i	$-0.556903\pi$
$317$	−6.33185	−0.355632	−0.177816	+	0.984064i	$0.556903\pi$
$318$	−9.50431	−0.532975
$319$	3.33025	0.186458
$320$	−2.05025	−0.114613
$321$	21.6297	1.20725
$322$	−1.71748	−0.0957116
$323$	52.0519	2.89624
$324$	−10.1211	−0.562282
$325$	4.78593	0.265476
$326$	5.34876	0.296240
$327$	−8.32914	−0.460602
$328$	−11.7722	−0.650010
$329$	−7.26016	−0.400266
$330$	12.6592	0.696864
$331$	19.0205	1.04546	0.522732	−	0.852497i	$-0.324913\pi$
$331$	19.0205	1.04546	0.522732	+	0.852497i	$0.324913\pi$
$332$	−10.0448	−0.551282
$333$	0.0238277	0.00130575
$334$	−16.5411	−0.905090
$335$	−9.73657	−0.531966
$336$	3.18429	0.173717
$337$	34.0013	1.85217	0.926085	−	0.377315i	$-0.123153\pi$
$337$	34.0013	1.85217	0.926085	+	0.377315i	$0.123153\pi$
$338$	−23.1083	−1.25693
$339$	29.8497	1.62121
$340$	12.8748	0.698235
$341$	−3.80947	−0.206294
$342$	3.62636	0.196091
$343$	−18.9786	−1.02475
$344$	−7.24778	−0.390774
$345$	−3.80127	−0.204653
$346$	24.5102	1.31768
$347$	20.7408	1.11343	0.556713	−	0.830705i	$-0.312062\pi$
$347$	20.7408	1.11343	0.556713	+	0.830705i	$0.312062\pi$
$348$	1.85405	0.0993874
$349$	−11.8780	−0.635813	−0.317906	−	0.948122i	$-0.602980\pi$
$349$	−11.8780	−0.635813	−0.317906	+	0.948122i	$0.602980\pi$
$350$	1.36790	0.0731175
$351$	28.5489	1.52383
$352$	−3.33025	−0.177503
$353$	−17.7205	−0.943168	−0.471584	−	0.881821i	$-0.656318\pi$
$353$	−17.7205	−0.943168	−0.471584	+	0.881821i	$0.656318\pi$
$354$	24.8132	1.31880
$355$	−11.0271	−0.585260
$356$	1.89386	0.100374
$357$	−19.9962	−1.05831
$358$	−11.8656	−0.627115
$359$	−7.06061	−0.372645	−0.186322	−	0.982489i	$-0.559657\pi$
$359$	−7.06061	−0.372645	−0.186322	+	0.982489i	$0.559657\pi$
$360$	0.896966	0.0472743
$361$	49.7077	2.61620
$362$	−9.30079	−0.488839
$363$	0.167865	0.00881061
$364$	−10.3204	−0.540935
$365$	−24.2848	−1.27113
$366$	16.8855	0.882619
$367$	6.31856	0.329826	0.164913	−	0.986308i	$-0.447266\pi$
$367$	6.31856	0.329826	0.164913	+	0.986308i	$0.447266\pi$
$368$	1.00000	0.0521286
$369$	5.15021	0.268109
$370$	0.111666	0.00580526
$371$	8.80425	0.457094
$372$	−2.12084	−0.109961
$373$	−8.70660	−0.450811	−0.225405	−	0.974265i	$-0.572371\pi$
$373$	−8.70660	−0.450811	−0.225405	+	0.974265i	$0.572371\pi$
$374$	20.9127	1.08137
$375$	22.0339	1.13783
$376$	4.22721	0.218002
$377$	−6.00902	−0.309480
$378$	8.15978	0.419694
$379$	0.658388	0.0338191	0.0169096	−	0.999857i	$-0.494617\pi$
$379$	0.658388	0.0338191	0.0169096	+	0.999857i	$0.494617\pi$
$380$	16.9946	0.871804
$381$	−11.0195	−0.564544
$382$	12.6721	0.648362
$383$	35.2904	1.80326	0.901628	−	0.432513i	$-0.142373\pi$
$383$	35.2904	1.80326	0.901628	+	0.432513i	$0.142373\pi$
$384$	−1.85405	−0.0946139
$385$	−11.7267	−0.597649
$386$	18.0752	0.920006
$387$	3.17083	0.161182
$388$	−8.63370	−0.438310
$389$	−1.02932	−0.0521886	−0.0260943	−	0.999659i	$-0.508307\pi$
$389$	−1.02932	−0.0521886	−0.0260943	+	0.999659i	$0.508307\pi$
$390$	−22.8419	−1.15664
$391$	−6.27962	−0.317574
$392$	4.05025	0.204569
$393$	9.51494	0.479965
$394$	5.03808	0.253815
$395$	31.9411	1.60713
$396$	1.45695	0.0732145
$397$	−25.2760	−1.26857	−0.634283	−	0.773101i	$-0.718705\pi$
$397$	−25.2760	−1.26857	−0.634283	+	0.773101i	$0.718705\pi$
$398$	−19.1820	−0.961506
$399$	−26.3946	−1.32138
$400$	−0.796458	−0.0398229
$401$	−26.8823	−1.34244	−0.671219	−	0.741259i	$-0.734229\pi$
$401$	−26.8823	−1.34244	−0.671219	+	0.741259i	$0.734229\pi$
$402$	−8.80479	−0.439143
$403$	6.87371	0.342404
$404$	−3.29361	−0.163863
$405$	20.7508	1.03111
$406$	−1.71748	−0.0852372
$407$	0.181381	0.00899070
$408$	11.6427	0.576400
$409$	13.7154	0.678183	0.339091	−	0.940753i	$-0.389880\pi$
$409$	13.7154	0.678183	0.339091	+	0.940753i	$0.389880\pi$
$410$	24.1360	1.19199
$411$	17.2261	0.849699
$412$	−3.57464	−0.176110
$413$	−22.9855	−1.13104
$414$	−0.437490	−0.0215015
$415$	20.5945	1.01094
$416$	6.00902	0.294616
$417$	3.08839	0.151239
$418$	27.6045	1.35018
$419$	−40.2908	−1.96833	−0.984166	−	0.177247i	$-0.943281\pi$
$419$	−40.2908	−1.96833	−0.984166	+	0.177247i	$0.943281\pi$
$420$	−6.52861	−0.318564
$421$	27.4402	1.33735	0.668677	−	0.743553i	$-0.266861\pi$
$421$	27.4402	1.33735	0.668677	+	0.743553i	$0.266861\pi$
$422$	15.6022	0.759502
$423$	−1.84936	−0.0899192
$424$	−5.12625	−0.248953
$425$	5.00146	0.242606
$426$	−9.97186	−0.483138
$427$	−15.6417	−0.756957
$428$	11.6662	0.563908
$429$	−37.1023	−1.79132
$430$	14.8598	0.716602
$431$	−12.7213	−0.612764	−0.306382	−	0.951909i	$-0.599118\pi$
$431$	−12.7213	−0.612764	−0.306382	+	0.951909i	$0.599118\pi$
$432$	−4.75101	−0.228583
$433$	37.8059	1.81684	0.908419	−	0.418062i	$-0.137290\pi$
$433$	37.8059	1.81684	0.908419	+	0.418062i	$0.137290\pi$
$434$	1.96463	0.0943051
$435$	−3.80127	−0.182257
$436$	−4.49241	−0.215147
$437$	−8.28901	−0.396517
$438$	−21.9608	−1.04933
$439$	−18.9628	−0.905047	−0.452523	−	0.891753i	$-0.649476\pi$
$439$	−18.9628	−0.905047	−0.452523	+	0.891753i	$0.649476\pi$
$440$	6.82785	0.325505
$441$	−1.77195	−0.0843784
$442$	−37.7344	−1.79484
$443$	2.59472	0.123279	0.0616395	−	0.998098i	$-0.480367\pi$
$443$	2.59472	0.123279	0.0616395	+	0.998098i	$0.480367\pi$
$444$	0.100980	0.00479230
$445$	−3.88290	−0.184067
$446$	9.98619	0.472860
$447$	−32.7155	−1.54739
$448$	1.71748	0.0811434
$449$	13.5491	0.639421	0.319711	−	0.947515i	$-0.396414\pi$
$449$	13.5491	0.639421	0.319711	+	0.947515i	$0.396414\pi$
$450$	0.348443	0.0164257
$451$	39.2042	1.84606
$452$	16.0998	0.757270
$453$	−18.0116	−0.846259
$454$	−12.8281	−0.602055
$455$	21.1594	0.991969
$456$	15.3682	0.719683
$457$	−36.2176	−1.69419	−0.847094	−	0.531444i	$-0.821650\pi$
$457$	−36.2176	−1.69419	−0.847094	+	0.531444i	$0.821650\pi$
$458$	−4.37132	−0.204259
$459$	29.8346	1.39256
$460$	−2.05025	−0.0955936
$461$	−19.1712	−0.892890	−0.446445	−	0.894811i	$-0.647310\pi$
$461$	−19.1712	−0.892890	−0.446445	+	0.894811i	$0.647310\pi$
$462$	−10.6045	−0.493365
$463$	10.7807	0.501021	0.250510	−	0.968114i	$-0.419402\pi$
$463$	10.7807	0.501021	0.250510	+	0.968114i	$0.419402\pi$
$464$	1.00000	0.0464238
$465$	4.34827	0.201646
$466$	−20.6122	−0.954840
$467$	38.7417	1.79275	0.896376	−	0.443295i	$-0.146190\pi$
$467$	38.7417	1.79275	0.896376	+	0.443295i	$0.146190\pi$
$468$	−2.62889	−0.121520
$469$	8.15625	0.376621
$470$	−8.66686	−0.399772
$471$	−11.5436	−0.531902
$472$	13.3832	0.616013
$473$	24.1369	1.10982
$474$	28.8843	1.32670
$475$	6.60185	0.302914
$476$	−10.7851	−0.494336
$477$	2.24269	0.102686
$478$	−3.33026	−0.152323
$479$	10.6629	0.487199	0.243600	−	0.969876i	$-0.421672\pi$
$479$	10.6629	0.487199	0.243600	+	0.969876i	$0.421672\pi$
$480$	3.80127	0.173503
$481$	−0.327279	−0.0149226
$482$	−18.8854	−0.860205
$483$	3.18429	0.144890
$484$	0.0905396	0.00411543
$485$	17.7013	0.803773
$486$	4.51191	0.204664
$487$	−1.99207	−0.0902692	−0.0451346	−	0.998981i	$-0.514372\pi$
$487$	−1.99207	−0.0902692	−0.0451346	+	0.998981i	$0.514372\pi$
$488$	9.10737	0.412271
$489$	−9.91685	−0.448455
$490$	−8.30405	−0.375139
$491$	−18.8737	−0.851758	−0.425879	−	0.904780i	$-0.640035\pi$
$491$	−18.8737	−0.851758	−0.425879	+	0.904780i	$0.640035\pi$
$492$	21.8262	0.984000
$493$	−6.27962	−0.282820
$494$	−49.8088	−2.24101
$495$	−2.98712	−0.134261
$496$	−1.14390	−0.0513626
$497$	9.23736	0.414352
$498$	18.6236	0.834543
$499$	−33.5753	−1.50304	−0.751519	−	0.659711i	$-0.770679\pi$
$499$	−33.5753	−1.50304	−0.751519	+	0.659711i	$0.770679\pi$
$500$	11.8842	0.531478
$501$	30.6680	1.37015
$502$	−8.23547	−0.367567
$503$	−11.5753	−0.516118	−0.258059	−	0.966129i	$-0.583083\pi$
$503$	−11.5753	−0.516118	−0.258059	+	0.966129i	$0.583083\pi$
$504$	−0.751382	−0.0334692
$505$	6.75274	0.300493
$506$	−3.33025	−0.148048
$507$	42.8439	1.90276
$508$	−5.94346	−0.263699
$509$	4.47371	0.198294	0.0991468	−	0.995073i	$-0.468389\pi$
$509$	4.47371	0.198294	0.0991468	+	0.995073i	$0.468389\pi$
$510$	−23.8705	−1.05700
$511$	20.3432	0.899931
$512$	−1.00000	−0.0441942
$513$	39.3812	1.73872
$514$	−5.04038	−0.222321
$515$	7.32891	0.322950
$516$	13.4377	0.591563
$517$	−14.0777	−0.619135
$518$	−0.0935420	−0.00411000
$519$	−45.4431	−1.99473
$520$	−12.3200	−0.540269
$521$	−23.1765	−1.01538	−0.507691	−	0.861539i	$-0.669501\pi$
$521$	−23.1765	−1.01538	−0.507691	+	0.861539i	$0.669501\pi$
$522$	−0.437490	−0.0191484
$523$	−9.26699	−0.405217	−0.202609	−	0.979260i	$-0.564942\pi$
$523$	−9.26699	−0.405217	−0.202609	+	0.979260i	$0.564942\pi$
$524$	5.13199	0.224192
$525$	−2.53616	−0.110687
$526$	−3.97728	−0.173418
$527$	7.18326	0.312908
$528$	6.17443	0.268708
$529$	1.00000	0.0434783
$530$	10.5101	0.456530
$531$	−5.85504	−0.254087
$532$	−14.2362	−0.617219
$533$	−70.7392	−3.06406
$534$	−3.51131	−0.151949
$535$	−23.9187	−1.03410
$536$	−4.74896	−0.205124
$537$	21.9993	0.949341
$538$	1.44133	0.0621403
$539$	−13.4883	−0.580984
$540$	9.74078	0.419177
$541$	33.6778	1.44792	0.723961	−	0.689841i	$-0.242319\pi$
$541$	33.6778	1.44792	0.723961	+	0.689841i	$0.242319\pi$
$542$	30.2851	1.30086
$543$	17.2441	0.740015
$544$	6.27962	0.269237
$545$	9.21058	0.394538
$546$	19.1345	0.818880
$547$	−34.1089	−1.45839	−0.729196	−	0.684305i	$-0.760106\pi$
$547$	−34.1089	−1.45839	−0.729196	+	0.684305i	$0.760106\pi$
$548$	9.29107	0.396895
$549$	−3.98439	−0.170049
$550$	2.65240	0.113099
$551$	−8.28901	−0.353124
$552$	−1.85405	−0.0789135
$553$	−26.7568	−1.13781
$554$	−23.3316	−0.991263
$555$	−0.207035	−0.00878813
$556$	1.66575	0.0706437
$557$	−42.6960	−1.80909	−0.904544	−	0.426380i	$-0.859789\pi$
$557$	−42.6960	−1.80909	−0.904544	+	0.426380i	$0.859789\pi$
$558$	0.500445	0.0211855
$559$	−43.5520	−1.84205
$560$	−3.52128	−0.148801
$561$	−38.7731	−1.63700
$562$	0.0277966	0.00117253
$563$	15.4347	0.650495	0.325248	−	0.945629i	$-0.394552\pi$
$563$	15.4347	0.650495	0.325248	+	0.945629i	$0.394552\pi$
$564$	−7.83745	−0.330016
$565$	−33.0086	−1.38868
$566$	−10.8544	−0.456246
$567$	−17.3828	−0.730008
$568$	−5.37843	−0.225674
$569$	33.3193	1.39682	0.698409	−	0.715699i	$-0.253892\pi$
$569$	33.3193	1.39682	0.698409	+	0.715699i	$0.253892\pi$
$570$	−31.5088	−1.31976
$571$	31.8036	1.33094	0.665469	−	0.746426i	$-0.268232\pi$
$571$	31.8036	1.33094	0.665469	+	0.746426i	$0.268232\pi$
$572$	−20.0115	−0.836723
$573$	−23.4947	−0.981506
$574$	−20.2185	−0.843904
$575$	−0.796458	−0.0332146
$576$	0.437490	0.0182288
$577$	−12.2978	−0.511966	−0.255983	−	0.966681i	$-0.582399\pi$
$577$	−12.2978	−0.511966	−0.255983	+	0.966681i	$0.582399\pi$
$578$	−22.4337	−0.933118
$579$	−33.5123	−1.39273
$580$	−2.05025	−0.0851322
$581$	−17.2518	−0.715726
$582$	16.0073	0.663523
$583$	17.0717	0.707037
$584$	−11.8448	−0.490141
$585$	5.38989	0.222844
$586$	6.49931	0.268484
$587$	−15.0930	−0.622955	−0.311478	−	0.950253i	$-0.600824\pi$
$587$	−15.0930	−0.622955	−0.311478	+	0.950253i	$0.600824\pi$
$588$	−7.50936	−0.309681
$589$	9.48180	0.390691
$590$	−27.4390	−1.12965
$591$	−9.34083	−0.384230
$592$	0.0544646	0.00223848
$593$	−13.2130	−0.542593	−0.271296	−	0.962496i	$-0.587452\pi$
$593$	−13.2130	−0.542593	−0.271296	+	0.962496i	$0.587452\pi$
$594$	15.8220	0.649186
$595$	22.1123	0.906515
$596$	−17.6455	−0.722787
$597$	35.5643	1.45555
$598$	6.00902	0.245727
$599$	−19.4822	−0.796023	−0.398011	−	0.917380i	$-0.630300\pi$
$599$	−19.4822	−0.796023	−0.398011	+	0.917380i	$0.630300\pi$
$600$	1.47667	0.0602848
$601$	−7.93270	−0.323581	−0.161791	−	0.986825i	$-0.551727\pi$
$601$	−7.93270	−0.323581	−0.161791	+	0.986825i	$0.551727\pi$
$602$	−12.4479	−0.507340
$603$	2.07762	0.0846074
$604$	−9.71475	−0.395287
$605$	−0.185629	−0.00754690
$606$	6.10651	0.248060
$607$	−28.3900	−1.15232	−0.576158	−	0.817338i	$-0.695449\pi$
$607$	−28.3900	−1.15232	−0.576158	+	0.817338i	$0.695449\pi$
$608$	8.28901	0.336164
$609$	3.18429	0.129034
$610$	−18.6724	−0.756024
$611$	25.4014	1.02763
$612$	−2.74727	−0.111052
$613$	−24.3858	−0.984932	−0.492466	−	0.870332i	$-0.663904\pi$
$613$	−24.3858	−0.984932	−0.492466	+	0.870332i	$0.663904\pi$
$614$	32.4410	1.30921
$615$	−44.7492	−1.80446
$616$	−5.71964	−0.230451
$617$	−1.56477	−0.0629955	−0.0314977	−	0.999504i	$-0.510028\pi$
$617$	−1.56477	−0.0629955	−0.0314977	+	0.999504i	$0.510028\pi$
$618$	6.62754	0.266599
$619$	18.1208	0.728337	0.364168	−	0.931333i	$-0.381353\pi$
$619$	18.1208	0.728337	0.364168	+	0.931333i	$0.381353\pi$
$620$	2.34528	0.0941889
$621$	−4.75101	−0.190652
$622$	20.2843	0.813325
$623$	3.25267	0.130316
$624$	−11.1410	−0.445997
$625$	−20.3834	−0.815335
$626$	−3.56191	−0.142363
$627$	−51.1799	−2.04393
$628$	−6.22618	−0.248452
$629$	−0.342017	−0.0136371
$630$	1.54052	0.0613759
$631$	21.5458	0.857724	0.428862	−	0.903370i	$-0.358915\pi$
$631$	21.5458	0.857724	0.428862	+	0.903370i	$0.358915\pi$
$632$	15.5791	0.619702
$633$	−28.9271	−1.14975
$634$	6.33185	0.251470
$635$	12.1856	0.483571
$636$	9.50431	0.376870
$637$	24.3381	0.964309
$638$	−3.33025	−0.131846
$639$	2.35301	0.0930837
$640$	2.05025	0.0810434
$641$	−30.7163	−1.21322	−0.606610	−	0.795000i	$-0.707471\pi$
$641$	−30.7163	−1.21322	−0.606610	+	0.795000i	$0.707471\pi$
$642$	−21.6297	−0.853657
$643$	27.4217	1.08141	0.540703	−	0.841213i	$-0.318158\pi$
$643$	27.4217	1.08141	0.540703	+	0.841213i	$0.318158\pi$
$644$	1.71748	0.0676783
$645$	−27.5507	−1.08481
$646$	−52.0519	−2.04795
$647$	26.4754	1.04086	0.520428	−	0.853905i	$-0.325772\pi$
$647$	26.4754	1.04086	0.520428	+	0.853905i	$0.325772\pi$
$648$	10.1211	0.397593
$649$	−44.5695	−1.74950
$650$	−4.78593	−0.187720
$651$	−3.64251	−0.142761
$652$	−5.34876	−0.209474
$653$	−39.2369	−1.53546	−0.767729	−	0.640775i	$-0.778613\pi$
$653$	−39.2369	−1.53546	−0.767729	+	0.640775i	$0.778613\pi$
$654$	8.32914	0.325695
$655$	−10.5219	−0.411124
$656$	11.7722	0.459626
$657$	5.18198	0.202168
$658$	7.26016	0.283031
$659$	12.7892	0.498196	0.249098	−	0.968478i	$-0.419866\pi$
$659$	12.7892	0.498196	0.249098	+	0.968478i	$0.419866\pi$
$660$	−12.6592	−0.492757
$661$	−21.7536	−0.846118	−0.423059	−	0.906102i	$-0.639044\pi$
$661$	−21.7536	−0.846118	−0.423059	+	0.906102i	$0.639044\pi$
$662$	−19.0205	−0.739255
$663$	69.9613	2.71707
$664$	10.0448	0.389815
$665$	29.1879	1.13186
$666$	−0.0238277	−0.000923306 0
$667$	1.00000	0.0387202
$668$	16.5411	0.639995
$669$	−18.5149	−0.715826
$670$	9.73657	0.376157
$671$	−30.3298	−1.17087
$672$	−3.18429	−0.122837
$673$	22.8719	0.881646	0.440823	−	0.897594i	$-0.354687\pi$
$673$	22.8719	0.881646	0.440823	+	0.897594i	$0.354687\pi$
$674$	−34.0013	−1.30968
$675$	3.78398	0.145646
$676$	23.1083	0.888781
$677$	7.60671	0.292350	0.146175	−	0.989259i	$-0.453304\pi$
$677$	7.60671	0.292350	0.146175	+	0.989259i	$0.453304\pi$
$678$	−29.8497	−1.14637
$679$	−14.8282	−0.569055
$680$	−12.8748	−0.493727
$681$	23.7840	0.911404
$682$	3.80947	0.145872
$683$	−35.7968	−1.36973	−0.684864	−	0.728671i	$-0.740138\pi$
$683$	−35.7968	−1.36973	−0.684864	+	0.728671i	$0.740138\pi$
$684$	−3.62636	−0.138657
$685$	−19.0490	−0.727827
$686$	18.9786	0.724607
$687$	8.10464	0.309211
$688$	7.24778	0.276319
$689$	−30.8037	−1.17353
$690$	3.80127	0.144712
$691$	−0.732133	−0.0278517	−0.0139258	−	0.999903i	$-0.504433\pi$
$691$	−0.732133	−0.0278517	−0.0139258	+	0.999903i	$0.504433\pi$
$692$	−24.5102	−0.931739
$693$	2.50229	0.0950540
$694$	−20.7408	−0.787311
$695$	−3.41522	−0.129547
$696$	−1.85405	−0.0702775
$697$	−73.9248	−2.80010
$698$	11.8780	0.449587
$699$	38.2159	1.44546
$700$	−1.36790	−0.0517019
$701$	−25.8936	−0.977990	−0.488995	−	0.872287i	$-0.662636\pi$
$701$	−25.8936	−0.977990	−0.488995	+	0.872287i	$0.662636\pi$
$702$	−28.5489	−1.07751
$703$	−0.451458	−0.0170271
$704$	3.33025	0.125513
$705$	16.0688	0.605185
$706$	17.7205	0.666921
$707$	−5.65672	−0.212743
$708$	−24.8132	−0.932535
$709$	−24.9985	−0.938840	−0.469420	−	0.882975i	$-0.655537\pi$
$709$	−24.9985	−0.938840	−0.469420	+	0.882975i	$0.655537\pi$
$710$	11.0271	0.413841
$711$	−6.81570	−0.255609
$712$	−1.89386	−0.0709754
$713$	−1.14390	−0.0428394
$714$	19.9962	0.748338
$715$	41.0287	1.53439
$716$	11.8656	0.443437
$717$	6.17447	0.230590
$718$	7.06061	0.263500
$719$	38.1965	1.42449	0.712244	−	0.701932i	$-0.247679\pi$
$719$	38.1965	1.42449	0.712244	+	0.701932i	$0.247679\pi$
$720$	−0.896966	−0.0334280
$721$	−6.13937	−0.228642
$722$	−49.7077	−1.84993
$723$	35.0144	1.30220
$724$	9.30079	0.345661
$725$	−0.796458	−0.0295797
$726$	−0.167865	−0.00623004
$727$	−6.22245	−0.230778	−0.115389	−	0.993320i	$-0.536811\pi$
$727$	−6.22245	−0.230778	−0.115389	+	0.993320i	$0.536811\pi$
$728$	10.3204	0.382499
$729$	21.9979	0.814738
$730$	24.2848	0.898822
$731$	−45.5133	−1.68337
$732$	−16.8855	−0.624106
$733$	41.4619	1.53143	0.765715	−	0.643180i	$-0.222385\pi$
$733$	41.4619	1.53143	0.765715	+	0.643180i	$0.222385\pi$
$734$	−6.31856	−0.233222
$735$	15.3961	0.567894
$736$	−1.00000	−0.0368605
$737$	15.8152	0.582561
$738$	−5.15021	−0.189582
$739$	1.96300	0.0722100	0.0361050	−	0.999348i	$-0.488505\pi$
$739$	1.96300	0.0722100	0.0361050	+	0.999348i	$0.488505\pi$
$740$	−0.111666	−0.00410494
$741$	92.3479	3.39249
$742$	−8.80425	−0.323214
$743$	49.8228	1.82782	0.913910	−	0.405917i	$-0.133048\pi$
$743$	49.8228	1.82782	0.913910	+	0.405917i	$0.133048\pi$
$744$	2.12084	0.0777539
$745$	36.1777	1.32545
$746$	8.70660	0.318771
$747$	−4.39452	−0.160787
$748$	−20.9127	−0.764644
$749$	20.0365	0.732119
$750$	−22.0339	−0.804564
$751$	0.959752	0.0350218	0.0175109	−	0.999847i	$-0.494426\pi$
$751$	0.959752	0.0350218	0.0175109	+	0.999847i	$0.494426\pi$
$752$	−4.22721	−0.154151
$753$	15.2690	0.556432
$754$	6.00902	0.218836
$755$	19.9177	0.724879
$756$	−8.15978	−0.296768
$757$	27.4905	0.999159	0.499579	−	0.866268i	$-0.333488\pi$
$757$	27.4905	0.999159	0.499579	+	0.866268i	$0.333488\pi$
$758$	−0.658388	−0.0239137
$759$	6.17443	0.224118
$760$	−16.9946	−0.616458
$761$	−4.30483	−0.156050	−0.0780250	−	0.996951i	$-0.524861\pi$
$761$	−4.30483	−0.156050	−0.0780250	+	0.996951i	$0.524861\pi$
$762$	11.0195	0.399193
$763$	−7.71563	−0.279325
$764$	−12.6721	−0.458461
$765$	5.63261	0.203647
$766$	−35.2904	−1.27509
$767$	80.4201	2.90380
$768$	1.85405	0.0669022
$769$	−23.8431	−0.859803	−0.429902	−	0.902876i	$-0.641452\pi$
$769$	−23.8431	−0.859803	−0.429902	+	0.902876i	$0.641452\pi$
$770$	11.7267	0.422601
$771$	9.34509	0.336555
$772$	−18.0752	−0.650542
$773$	9.37853	0.337322	0.168661	−	0.985674i	$-0.446056\pi$
$773$	9.37853	0.337322	0.168661	+	0.985674i	$0.446056\pi$
$774$	−3.17083	−0.113973
$775$	0.911068	0.0327265
$776$	8.63370	0.309932
$777$	0.173431	0.00622181
$778$	1.02932	0.0369029
$779$	−97.5797	−3.49616
$780$	22.8419	0.817871
$781$	17.9115	0.640923
$782$	6.27962	0.224559
$783$	−4.75101	−0.169787
$784$	−4.05025	−0.144652
$785$	12.7652	0.455611
$786$	−9.51494	−0.339387
$787$	−17.8120	−0.634928	−0.317464	−	0.948270i	$-0.602831\pi$
$787$	−17.8120	−0.634928	−0.317464	+	0.948270i	$0.602831\pi$
$788$	−5.03808	−0.179474
$789$	7.37406	0.262524
$790$	−31.9411	−1.13641
$791$	27.6511	0.983159
$792$	−1.45695	−0.0517705
$793$	54.7264	1.94339
$794$	25.2760	0.897011
$795$	−19.4863	−0.691106
$796$	19.1820	0.679887
$797$	−23.2743	−0.824418	−0.412209	−	0.911089i	$-0.635243\pi$
$797$	−23.2743	−0.824418	−0.412209	+	0.911089i	$0.635243\pi$
$798$	26.3946	0.934360
$799$	26.5453	0.939105
$800$	0.796458	0.0281590
$801$	0.828546	0.0292752
$802$	26.8823	0.949247
$803$	39.4461	1.39202
$804$	8.80479	0.310521
$805$	−3.52128	−0.124109
$806$	−6.87371	−0.242116
$807$	−2.67230	−0.0940694
$808$	3.29361	0.115869
$809$	−29.6387	−1.04204	−0.521020	−	0.853544i	$-0.674448\pi$
$809$	−29.6387	−1.04204	−0.521020	+	0.853544i	$0.674448\pi$
$810$	−20.7508	−0.729108
$811$	20.8427	0.731885	0.365942	−	0.930638i	$-0.380747\pi$
$811$	20.8427	0.731885	0.365942	+	0.930638i	$0.380747\pi$
$812$	1.71748	0.0602718
$813$	−56.1500	−1.96927
$814$	−0.181381	−0.00635739
$815$	10.9663	0.384133
$816$	−11.6427	−0.407577
$817$	−60.0769	−2.10183
$818$	−13.7154	−0.479548
$819$	−4.51507	−0.157769
$820$	−24.1360	−0.842864
$821$	−30.8248	−1.07579	−0.537897	−	0.843011i	$-0.680781\pi$
$821$	−30.8248	−1.07579	−0.537897	+	0.843011i	$0.680781\pi$
$822$	−17.2261	−0.600828
$823$	22.0369	0.768159	0.384080	−	0.923300i	$-0.374519\pi$
$823$	22.0369	0.768159	0.384080	+	0.923300i	$0.374519\pi$
$824$	3.57464	0.124528
$825$	−4.91768	−0.171212
$826$	22.9855	0.799767
$827$	5.05443	0.175760	0.0878799	−	0.996131i	$-0.471991\pi$
$827$	5.05443	0.175760	0.0878799	+	0.996131i	$0.471991\pi$
$828$	0.437490	0.0152038
$829$	−55.1464	−1.91532	−0.957658	−	0.287909i	$-0.907040\pi$
$829$	−55.1464	−1.91532	−0.957658	+	0.287909i	$0.907040\pi$
$830$	−20.5945	−0.714844
$831$	43.2578	1.50060
$832$	−6.00902	−0.208325
$833$	25.4341	0.881238
$834$	−3.08839	−0.106942
$835$	−33.9135	−1.17363
$836$	−27.6045	−0.954720
$837$	5.43468	0.187850
$838$	40.2908	1.39182
$839$	−28.0024	−0.966751	−0.483376	−	0.875413i	$-0.660589\pi$
$839$	−28.0024	−0.966751	−0.483376	+	0.875413i	$0.660589\pi$
$840$	6.52861	0.225258
$841$	1.00000	0.0344828
$842$	−27.4402	−0.945652
$843$	−0.0515362	−0.00177500
$844$	−15.6022	−0.537049
$845$	−47.3779	−1.62985
$846$	1.84936	0.0635825
$847$	0.155500	0.00534305
$848$	5.12625	0.176036
$849$	20.1246	0.690676
$850$	−5.00146	−0.171549
$851$	0.0544646	0.00186702
$852$	9.97186	0.341630
$853$	9.85091	0.337289	0.168644	−	0.985677i	$-0.446061\pi$
$853$	9.85091	0.337289	0.168644	+	0.985677i	$0.446061\pi$
$854$	15.6417	0.535250
$855$	7.43496	0.254270
$856$	−11.6662	−0.398743
$857$	−33.2358	−1.13531	−0.567656	−	0.823266i	$-0.692150\pi$
$857$	−33.2358	−1.13531	−0.567656	+	0.823266i	$0.692150\pi$
$858$	37.1023	1.26665
$859$	−2.26489	−0.0772770	−0.0386385	−	0.999253i	$-0.512302\pi$
$859$	−2.26489	−0.0772770	−0.0386385	+	0.999253i	$0.512302\pi$
$860$	−14.8598	−0.506714
$861$	37.4861	1.27752
$862$	12.7213	0.433289
$863$	1.36260	0.0463835	0.0231918	−	0.999731i	$-0.492617\pi$
$863$	1.36260	0.0463835	0.0231918	+	0.999731i	$0.492617\pi$
$864$	4.75101	0.161633
$865$	50.2522	1.70863
$866$	−37.8059	−1.28470
$867$	41.5931	1.41258
$868$	−1.96463	−0.0666838
$869$	−51.8822	−1.75998
$870$	3.80127	0.128875
$871$	−28.5366	−0.966926
$872$	4.49241	0.152132
$873$	−3.77716	−0.127837
$874$	8.28901	0.280380
$875$	20.4109	0.690015
$876$	21.9608	0.741986
$877$	−16.2042	−0.547179	−0.273589	−	0.961847i	$-0.588211\pi$
$877$	−16.2042	−0.547179	−0.273589	+	0.961847i	$0.588211\pi$
$878$	18.9628	0.639965
$879$	−12.0500	−0.406437
$880$	−6.82785	−0.230167
$881$	44.3768	1.49509	0.747546	−	0.664210i	$-0.231232\pi$
$881$	44.3768	1.49509	0.747546	+	0.664210i	$0.231232\pi$
$882$	1.77195	0.0596646
$883$	−9.37482	−0.315488	−0.157744	−	0.987480i	$-0.550422\pi$
$883$	−9.37482	−0.315488	−0.157744	+	0.987480i	$0.550422\pi$
$884$	37.7344	1.26914
$885$	50.8733	1.71009
$886$	−2.59472	−0.0871715
$887$	−1.20897	−0.0405931	−0.0202965	−	0.999794i	$-0.506461\pi$
$887$	−1.20897	−0.0405931	−0.0202965	+	0.999794i	$0.506461\pi$
$888$	−0.100980	−0.00338867
$889$	−10.2078	−0.342358
$890$	3.88290	0.130155
$891$	−33.7057	−1.12918
$892$	−9.98619	−0.334362
$893$	35.0394	1.17255
$894$	32.7155	1.09417
$895$	−24.3274	−0.813177
$896$	−1.71748	−0.0573771
$897$	−11.1410	−0.371987
$898$	−13.5491	−0.452139
$899$	−1.14390	−0.0381512
$900$	−0.348443	−0.0116148
$901$	−32.1909	−1.07244
$902$	−39.2042	−1.30536
$903$	23.0790	0.768023
$904$	−16.0998	−0.535470
$905$	−19.0690	−0.633874
$906$	18.0116	0.598395
$907$	−50.0512	−1.66192	−0.830962	−	0.556330i	$-0.812209\pi$
$907$	−50.0512	−1.66192	−0.830962	+	0.556330i	$0.812209\pi$
$908$	12.8281	0.425717
$909$	−1.44092	−0.0477924
$910$	−21.1594	−0.701428
$911$	−34.4543	−1.14152	−0.570761	−	0.821116i	$-0.693352\pi$
$911$	−34.4543	−1.14152	−0.570761	+	0.821116i	$0.693352\pi$
$912$	−15.3682	−0.508893
$913$	−33.4518	−1.10709
$914$	36.2176	1.19797
$915$	34.6196	1.14449
$916$	4.37132	0.144433
$917$	8.81409	0.291067
$918$	−29.8346	−0.984688
$919$	−12.8877	−0.425126	−0.212563	−	0.977147i	$-0.568181\pi$
$919$	−12.8877	−0.425126	−0.212563	+	0.977147i	$0.568181\pi$
$920$	2.05025	0.0675949
$921$	−60.1471	−1.98191
$922$	19.1712	0.631369
$923$	−32.3191	−1.06380
$924$	10.6045	0.348862
$925$	−0.0433788	−0.00142629
$926$	−10.7807	−0.354275
$927$	−1.56387	−0.0513642
$928$	−1.00000	−0.0328266
$929$	−15.6952	−0.514942	−0.257471	−	0.966286i	$-0.582889\pi$
$929$	−15.6952	−0.514942	−0.257471	+	0.966286i	$0.582889\pi$
$930$	−4.34827	−0.142585
$931$	33.5726	1.10030
$932$	20.6122	0.675174
$933$	−37.6080	−1.23123
$934$	−38.7417	−1.26767
$935$	42.8763	1.40221
$936$	2.62889	0.0859279
$937$	1.12854	0.0368679	0.0184339	−	0.999830i	$-0.494132\pi$
$937$	1.12854	0.0368679	0.0184339	+	0.999830i	$0.494132\pi$
$938$	−8.15625	−0.266311
$939$	6.60395	0.215512
$940$	8.66686	0.282682
$941$	22.8032	0.743362	0.371681	−	0.928360i	$-0.378781\pi$
$941$	22.8032	0.743362	0.371681	+	0.928360i	$0.378781\pi$
$942$	11.5436	0.376112
$943$	11.7722	0.383355
$944$	−13.3832	−0.435587
$945$	16.7296	0.544215
$946$	−24.1369	−0.784758
$947$	48.4834	1.57550	0.787749	−	0.615997i	$-0.211246\pi$
$947$	48.4834	1.57550	0.787749	+	0.615997i	$0.211246\pi$
$948$	−28.8843	−0.938120
$949$	−71.1756	−2.31046
$950$	−6.60185	−0.214192
$951$	−11.7395	−0.380681
$952$	10.7851	0.349548
$953$	24.5537	0.795374	0.397687	−	0.917521i	$-0.369813\pi$
$953$	24.5537	0.795374	0.397687	+	0.917521i	$0.369813\pi$
$954$	−2.24269	−0.0726096
$955$	25.9811	0.840728
$956$	3.33026	0.107708
$957$	6.17443	0.199591
$958$	−10.6629	−0.344502
$959$	15.9572	0.515286
$960$	−3.80127	−0.122685
$961$	−29.6915	−0.957790
$962$	0.327279	0.0105519
$963$	5.10386	0.164470
$964$	18.8854	0.608257
$965$	37.0588	1.19297
$966$	−3.18429	−0.102453
$967$	18.6842	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$967$	18.6842	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$968$	−0.0905396	−0.00291005
$969$	96.5066	3.10024
$970$	−17.7013	−0.568354
$971$	8.86542	0.284505	0.142252	−	0.989830i	$-0.454566\pi$
$971$	8.86542	0.284505	0.142252	+	0.989830i	$0.454566\pi$
$972$	−4.51191	−0.144719
$973$	2.86090	0.0917164
$974$	1.99207	0.0638299
$975$	8.87335	0.284174
$976$	−9.10737	−0.291520
$977$	3.20862	0.102653	0.0513264	−	0.998682i	$-0.483655\pi$
$977$	3.20862	0.102653	0.0513264	+	0.998682i	$0.483655\pi$
$978$	9.91685	0.317106
$979$	6.30702	0.201573
$980$	8.30405	0.265263
$981$	−1.96539	−0.0627499
$982$	18.8737	0.602284
$983$	10.6830	0.340736	0.170368	−	0.985381i	$-0.445504\pi$
$983$	10.6830	0.340736	0.170368	+	0.985381i	$0.445504\pi$
$984$	−21.8262	−0.695793
$985$	10.3293	0.329120
$986$	6.27962	0.199984
$987$	−13.4607	−0.428458
$988$	49.8088	1.58463
$989$	7.24778	0.230466
$990$	2.98712	0.0949369
$991$	−33.5380	−1.06537	−0.532685	−	0.846313i	$-0.678817\pi$
$991$	−33.5380	−1.06537	−0.532685	+	0.846313i	$0.678817\pi$
$992$	1.14390	0.0363188
$993$	35.2650	1.11910
$994$	−9.23736	−0.292991
$995$	−39.3279	−1.24678
$996$	−18.6236	−0.590111
$997$	60.5395	1.91731	0.958653	−	0.284579i	$-0.0918539\pi$
$997$	60.5395	1.91731	0.958653	+	0.284579i	$0.0918539\pi$
$998$	33.5753	1.06281
$999$	−0.258762	−0.00818687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.f.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.f.1.4	✓	5	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.85405 q^{3} +1.00000 q^{4} -2.05025 q^{5} -1.85405 q^{6} +1.71748 q^{7} -1.00000 q^{8} +0.437490 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.85405 q^{3} +1.00000 q^{4} -2.05025 q^{5} -1.85405 q^{6} +1.71748 q^{7} -1.00000 q^{8} +0.437490 q^{9} +2.05025 q^{10} +3.33025 q^{11} +1.85405 q^{12} -6.00902 q^{13} -1.71748 q^{14} -3.80127 q^{15} +1.00000 q^{16} -6.27962 q^{17} -0.437490 q^{18} -8.28901 q^{19} -2.05025 q^{20} +3.18429 q^{21} -3.33025 q^{22} +1.00000 q^{23} -1.85405 q^{24} -0.796458 q^{25} +6.00902 q^{26} -4.75101 q^{27} +1.71748 q^{28} +1.00000 q^{29} +3.80127 q^{30} -1.14390 q^{31} -1.00000 q^{32} +6.17443 q^{33} +6.27962 q^{34} -3.52128 q^{35} +0.437490 q^{36} +0.0544646 q^{37} +8.28901 q^{38} -11.1410 q^{39} +2.05025 q^{40} +11.7722 q^{41} -3.18429 q^{42} +7.24778 q^{43} +3.33025 q^{44} -0.896966 q^{45} -1.00000 q^{46} -4.22721 q^{47} +1.85405 q^{48} -4.05025 q^{49} +0.796458 q^{50} -11.6427 q^{51} -6.00902 q^{52} +5.12625 q^{53} +4.75101 q^{54} -6.82785 q^{55} -1.71748 q^{56} -15.3682 q^{57} -1.00000 q^{58} -13.3832 q^{59} -3.80127 q^{60} -9.10737 q^{61} +1.14390 q^{62} +0.751382 q^{63} +1.00000 q^{64} +12.3200 q^{65} -6.17443 q^{66} +4.74896 q^{67} -6.27962 q^{68} +1.85405 q^{69} +3.52128 q^{70} +5.37843 q^{71} -0.437490 q^{72} +11.8448 q^{73} -0.0544646 q^{74} -1.47667 q^{75} -8.28901 q^{76} +5.71964 q^{77} +11.1410 q^{78} -15.5791 q^{79} -2.05025 q^{80} -10.1211 q^{81} -11.7722 q^{82} -10.0448 q^{83} +3.18429 q^{84} +12.8748 q^{85} -7.24778 q^{86} +1.85405 q^{87} -3.33025 q^{88} +1.89386 q^{89} +0.896966 q^{90} -10.3204 q^{91} +1.00000 q^{92} -2.12084 q^{93} +4.22721 q^{94} +16.9946 q^{95} -1.85405 q^{96} -8.63370 q^{97} +4.05025 q^{98} +1.45695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9	\( 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 5 q^{10} + q^{11} + q^{12} - 11 q^{13} + 2 q^{14} + 5 q^{15} + 5 q^{16} + 4 q^{17} - 2 q^{18} - 12 q^{19} - 5 q^{20} - 8 q^{21} - q^{22} + 5 q^{23} - q^{24} - 4 q^{25} + 11 q^{26} - 5 q^{27} - 2 q^{28} + 5 q^{29} - 5 q^{30} - 5 q^{31} - 5 q^{32} - 11 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 12 q^{38} - 9 q^{39} + 5 q^{40} - 6 q^{41} + 8 q^{42} - 7 q^{43} + q^{44} + 6 q^{45} - 5 q^{46} + 5 q^{47} + q^{48} - 15 q^{49} + 4 q^{50} - 42 q^{51} - 11 q^{52} - q^{53} + 5 q^{54} - 31 q^{55} + 2 q^{56} - 4 q^{57} - 5 q^{58} - 12 q^{59} + 5 q^{60} - 20 q^{61} + 5 q^{62} + 10 q^{63} + 5 q^{64} + 3 q^{65} + 11 q^{66} - 4 q^{67} + 4 q^{68} + q^{69} + 4 q^{70} - 4 q^{71} - 2 q^{72} + 4 q^{73} - 12 q^{75} - 12 q^{76} + 14 q^{77} + 9 q^{78} - q^{79} - 5 q^{80} - 23 q^{81} + 6 q^{82} + 22 q^{83} - 8 q^{84} - 16 q^{85} + 7 q^{86} + q^{87} - q^{88} + 8 q^{89} - 6 q^{90} - 18 q^{91} + 5 q^{92} - 37 q^{93} - 5 q^{94} + 18 q^{95} - q^{96} - 46 q^{97} + 15 q^{98} - 24 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + q^3 + 5 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 + 5 * q^10 + q^11 + q^12 - 11 * q^13 + 2 * q^14 + 5 * q^15 + 5 * q^16 + 4 * q^17 - 2 * q^18 - 12 * q^19 - 5 * q^20 - 8 * q^21 - q^22 + 5 * q^23 - q^24 - 4 * q^25 + 11 * q^26 - 5 * q^27 - 2 * q^28 + 5 * q^29 - 5 * q^30 - 5 * q^31 - 5 * q^32 - 11 * q^33 - 4 * q^34 - 4 * q^35 + 2 * q^36 + 12 * q^38 - 9 * q^39 + 5 * q^40 - 6 * q^41 + 8 * q^42 - 7 * q^43 + q^44 + 6 * q^45 - 5 * q^46 + 5 * q^47 + q^48 - 15 * q^49 + 4 * q^50 - 42 * q^51 - 11 * q^52 - q^53 + 5 * q^54 - 31 * q^55 + 2 * q^56 - 4 * q^57 - 5 * q^58 - 12 * q^59 + 5 * q^60 - 20 * q^61 + 5 * q^62 + 10 * q^63 + 5 * q^64 + 3 * q^65 + 11 * q^66 - 4 * q^67 + 4 * q^68 + q^69 + 4 * q^70 - 4 * q^71 - 2 * q^72 + 4 * q^73 - 12 * q^75 - 12 * q^76 + 14 * q^77 + 9 * q^78 - q^79 - 5 * q^80 - 23 * q^81 + 6 * q^82 + 22 * q^83 - 8 * q^84 - 16 * q^85 + 7 * q^86 + q^87 - q^88 + 8 * q^89 - 6 * q^90 - 18 * q^91 + 5 * q^92 - 37 * q^93 - 5 * q^94 + 18 * q^95 - q^96 - 46 * q^97 + 15 * q^98 - 24 * q^99

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