LMFDB - Embedded newform 8030.2.a.bg.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} - 6 x^{13} + 136 x^{12} - 149 x^{11} - 876 x^{10} + 1631 x^{9} + 2142 x^{8} + \cdots - 32 $ x^15 - 7x^14 - 6x^13 + 136x^12 - 149x^11 - 876x^10 + 1631x^9 + 2142x^8 - 5473x^7 - 1914x^6 + 7517x^5 + 392x^4 - 3966x^3 - 79x^2 + 491x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.490398$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.490398 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.490398 q^{6} -1.29403 q^{7} +1.00000 q^{8} -2.75951 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.490398 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.490398 q^{6} -1.29403 q^{7} +1.00000 q^{8} -2.75951 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.490398 q^{12} +6.36293 q^{13} -1.29403 q^{14} +0.490398 q^{15} +1.00000 q^{16} -5.15983 q^{17} -2.75951 q^{18} -0.102375 q^{19} -1.00000 q^{20} +0.634591 q^{21} -1.00000 q^{22} -0.876186 q^{23} -0.490398 q^{24} +1.00000 q^{25} +6.36293 q^{26} +2.82445 q^{27} -1.29403 q^{28} +7.52730 q^{29} +0.490398 q^{30} +8.76862 q^{31} +1.00000 q^{32} +0.490398 q^{33} -5.15983 q^{34} +1.29403 q^{35} -2.75951 q^{36} -1.76958 q^{37} -0.102375 q^{38} -3.12037 q^{39} -1.00000 q^{40} -8.81403 q^{41} +0.634591 q^{42} +3.60667 q^{43} -1.00000 q^{44} +2.75951 q^{45} -0.876186 q^{46} -9.28620 q^{47} -0.490398 q^{48} -5.32548 q^{49} +1.00000 q^{50} +2.53037 q^{51} +6.36293 q^{52} -0.175296 q^{53} +2.82445 q^{54} +1.00000 q^{55} -1.29403 q^{56} +0.0502045 q^{57} +7.52730 q^{58} -5.90363 q^{59} +0.490398 q^{60} -4.20889 q^{61} +8.76862 q^{62} +3.57090 q^{63} +1.00000 q^{64} -6.36293 q^{65} +0.490398 q^{66} -10.3049 q^{67} -5.15983 q^{68} +0.429680 q^{69} +1.29403 q^{70} -4.49164 q^{71} -2.75951 q^{72} -1.00000 q^{73} -1.76958 q^{74} -0.490398 q^{75} -0.102375 q^{76} +1.29403 q^{77} -3.12037 q^{78} +3.97702 q^{79} -1.00000 q^{80} +6.89342 q^{81} -8.81403 q^{82} +8.30735 q^{83} +0.634591 q^{84} +5.15983 q^{85} +3.60667 q^{86} -3.69137 q^{87} -1.00000 q^{88} +12.1665 q^{89} +2.75951 q^{90} -8.23384 q^{91} -0.876186 q^{92} -4.30011 q^{93} -9.28620 q^{94} +0.102375 q^{95} -0.490398 q^{96} +9.09868 q^{97} -5.32548 q^{98} +2.75951 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 7 q^{3} + 15 q^{4} - 15 q^{5} + 7 q^{6} + 3 q^{7} + 15 q^{8} + 16 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 7 * q^3 + 15 * q^4 - 15 * q^5 + 7 * q^6 + 3 * q^7 + 15 * q^8 + 16 * q^9	\( 15 q + 15 q^{2} + 7 q^{3} + 15 q^{4} - 15 q^{5} + 7 q^{6} + 3 q^{7} + 15 q^{8} + 16 q^{9} - 15 q^{10} - 15 q^{11} + 7 q^{12} - q^{13} + 3 q^{14} - 7 q^{15} + 15 q^{16} + 2 q^{17} + 16 q^{18} + 23 q^{19} - 15 q^{20} + 20 q^{21} - 15 q^{22} + 7 q^{24} + 15 q^{25} - q^{26} + 19 q^{27} + 3 q^{28} + 23 q^{29} - 7 q^{30} + 9 q^{31} + 15 q^{32} - 7 q^{33} + 2 q^{34} - 3 q^{35} + 16 q^{36} + 11 q^{37} + 23 q^{38} + 7 q^{39} - 15 q^{40} + 27 q^{41} + 20 q^{42} + 7 q^{43} - 15 q^{44} - 16 q^{45} - 18 q^{47} + 7 q^{48} + 16 q^{49} + 15 q^{50} + 21 q^{51} - q^{52} - 19 q^{53} + 19 q^{54} + 15 q^{55} + 3 q^{56} + 11 q^{57} + 23 q^{58} + 2 q^{59} - 7 q^{60} + 31 q^{61} + 9 q^{62} + 20 q^{63} + 15 q^{64} + q^{65} - 7 q^{66} + 49 q^{67} + 2 q^{68} + 33 q^{69} - 3 q^{70} + 32 q^{71} + 16 q^{72} - 15 q^{73} + 11 q^{74} + 7 q^{75} + 23 q^{76} - 3 q^{77} + 7 q^{78} + 36 q^{79} - 15 q^{80} + 23 q^{81} + 27 q^{82} + 33 q^{83} + 20 q^{84} - 2 q^{85} + 7 q^{86} + 29 q^{87} - 15 q^{88} + 6 q^{89} - 16 q^{90} + 33 q^{91} + 20 q^{93} - 18 q^{94} - 23 q^{95} + 7 q^{96} + 30 q^{97} + 16 q^{98} - 16 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 7 * q^3 + 15 * q^4 - 15 * q^5 + 7 * q^6 + 3 * q^7 + 15 * q^8 + 16 * q^9 - 15 * q^10 - 15 * q^11 + 7 * q^12 - q^13 + 3 * q^14 - 7 * q^15 + 15 * q^16 + 2 * q^17 + 16 * q^18 + 23 * q^19 - 15 * q^20 + 20 * q^21 - 15 * q^22 + 7 * q^24 + 15 * q^25 - q^26 + 19 * q^27 + 3 * q^28 + 23 * q^29 - 7 * q^30 + 9 * q^31 + 15 * q^32 - 7 * q^33 + 2 * q^34 - 3 * q^35 + 16 * q^36 + 11 * q^37 + 23 * q^38 + 7 * q^39 - 15 * q^40 + 27 * q^41 + 20 * q^42 + 7 * q^43 - 15 * q^44 - 16 * q^45 - 18 * q^47 + 7 * q^48 + 16 * q^49 + 15 * q^50 + 21 * q^51 - q^52 - 19 * q^53 + 19 * q^54 + 15 * q^55 + 3 * q^56 + 11 * q^57 + 23 * q^58 + 2 * q^59 - 7 * q^60 + 31 * q^61 + 9 * q^62 + 20 * q^63 + 15 * q^64 + q^65 - 7 * q^66 + 49 * q^67 + 2 * q^68 + 33 * q^69 - 3 * q^70 + 32 * q^71 + 16 * q^72 - 15 * q^73 + 11 * q^74 + 7 * q^75 + 23 * q^76 - 3 * q^77 + 7 * q^78 + 36 * q^79 - 15 * q^80 + 23 * q^81 + 27 * q^82 + 33 * q^83 + 20 * q^84 - 2 * q^85 + 7 * q^86 + 29 * q^87 - 15 * q^88 + 6 * q^89 - 16 * q^90 + 33 * q^91 + 20 * q^93 - 18 * q^94 - 23 * q^95 + 7 * q^96 + 30 * q^97 + 16 * q^98 - 16 * 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
$3$	−0.490398	−0.283131	−0.141566	−	0.989929i	$-0.545214\pi$
$3$	−0.490398	−0.283131	−0.141566	+	0.989929i	$0.545214\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.490398	−0.200204
$7$	−1.29403	−0.489099	−0.244549	−	0.969637i	$-0.578640\pi$
$7$	−1.29403	−0.489099	−0.244549	+	0.969637i	$0.578640\pi$
$8$	1.00000	0.353553
$9$	−2.75951	−0.919837
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.490398	−0.141566
$13$	6.36293	1.76476	0.882379	−	0.470539i	$-0.155940\pi$
$13$	6.36293	1.76476	0.882379	+	0.470539i	$0.155940\pi$
$14$	−1.29403	−0.345845
$15$	0.490398	0.126620
$16$	1.00000	0.250000
$17$	−5.15983	−1.25144	−0.625721	−	0.780047i	$-0.715195\pi$
$17$	−5.15983	−1.25144	−0.625721	+	0.780047i	$0.715195\pi$
$18$	−2.75951	−0.650423
$19$	−0.102375	−0.0234864	−0.0117432	−	0.999931i	$-0.503738\pi$
$19$	−0.102375	−0.0234864	−0.0117432	+	0.999931i	$0.503738\pi$
$20$	−1.00000	−0.223607
$21$	0.634591	0.138479
$22$	−1.00000	−0.213201
$23$	−0.876186	−0.182697	−0.0913487	−	0.995819i	$-0.529118\pi$
$23$	−0.876186	−0.182697	−0.0913487	+	0.995819i	$0.529118\pi$
$24$	−0.490398	−0.100102
$25$	1.00000	0.200000
$26$	6.36293	1.24787
$27$	2.82445	0.543566
$28$	−1.29403	−0.244549
$29$	7.52730	1.39779	0.698893	−	0.715227i	$-0.253677\pi$
$29$	7.52730	1.39779	0.698893	+	0.715227i	$0.253677\pi$
$30$	0.490398	0.0895340
$31$	8.76862	1.57489	0.787445	−	0.616385i	$-0.211403\pi$
$31$	8.76862	1.57489	0.787445	+	0.616385i	$0.211403\pi$
$32$	1.00000	0.176777
$33$	0.490398	0.0853673
$34$	−5.15983	−0.884903
$35$	1.29403	0.218732
$36$	−2.75951	−0.459918
$37$	−1.76958	−0.290917	−0.145458	−	0.989364i	$-0.546466\pi$
$37$	−1.76958	−0.290917	−0.145458	+	0.989364i	$0.546466\pi$
$38$	−0.102375	−0.0166074
$39$	−3.12037	−0.499659
$40$	−1.00000	−0.158114
$41$	−8.81403	−1.37652	−0.688260	−	0.725464i	$-0.741625\pi$
$41$	−8.81403	−1.37652	−0.688260	+	0.725464i	$0.741625\pi$
$42$	0.634591	0.0979196
$43$	3.60667	0.550012	0.275006	−	0.961443i	$-0.411320\pi$
$43$	3.60667	0.550012	0.275006	+	0.961443i	$0.411320\pi$
$44$	−1.00000	−0.150756
$45$	2.75951	0.411363
$46$	−0.876186	−0.129187
$47$	−9.28620	−1.35453	−0.677265	−	0.735739i	$-0.736835\pi$
$47$	−9.28620	−1.35453	−0.677265	+	0.735739i	$0.736835\pi$
$48$	−0.490398	−0.0707828
$49$	−5.32548	−0.760782
$50$	1.00000	0.141421
$51$	2.53037	0.354323
$52$	6.36293	0.882379
$53$	−0.175296	−0.0240787	−0.0120394	−	0.999928i	$-0.503832\pi$
$53$	−0.175296	−0.0240787	−0.0120394	+	0.999928i	$0.503832\pi$
$54$	2.82445	0.384359
$55$	1.00000	0.134840
$56$	−1.29403	−0.172922
$57$	0.0502045	0.00664975
$58$	7.52730	0.988383
$59$	−5.90363	−0.768588	−0.384294	−	0.923211i	$-0.625555\pi$
$59$	−5.90363	−0.768588	−0.384294	+	0.923211i	$0.625555\pi$
$60$	0.490398	0.0633101
$61$	−4.20889	−0.538893	−0.269446	−	0.963015i	$-0.586841\pi$
$61$	−4.20889	−0.538893	−0.269446	+	0.963015i	$0.586841\pi$
$62$	8.76862	1.11362
$63$	3.57090	0.449891
$64$	1.00000	0.125000
$65$	−6.36293	−0.789224
$66$	0.490398	0.0603638
$67$	−10.3049	−1.25894	−0.629471	−	0.777024i	$-0.716728\pi$
$67$	−10.3049	−1.25894	−0.629471	+	0.777024i	$0.716728\pi$
$68$	−5.15983	−0.625721
$69$	0.429680	0.0517274
$70$	1.29403	0.154667
$71$	−4.49164	−0.533060	−0.266530	−	0.963827i	$-0.585877\pi$
$71$	−4.49164	−0.533060	−0.266530	+	0.963827i	$0.585877\pi$
$72$	−2.75951	−0.325211
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−1.76958	−0.205709
$75$	−0.490398	−0.0566263
$76$	−0.102375	−0.0117432
$77$	1.29403	0.147469
$78$	−3.12037	−0.353312
$79$	3.97702	0.447449	0.223725	−	0.974652i	$-0.428178\pi$
$79$	3.97702	0.447449	0.223725	+	0.974652i	$0.428178\pi$
$80$	−1.00000	−0.111803
$81$	6.89342	0.765936
$82$	−8.81403	−0.973347
$83$	8.30735	0.911850	0.455925	−	0.890018i	$-0.349309\pi$
$83$	8.30735	0.911850	0.455925	+	0.890018i	$0.349309\pi$
$84$	0.634591	0.0692396
$85$	5.15983	0.559662
$86$	3.60667	0.388917
$87$	−3.69137	−0.395757
$88$	−1.00000	−0.106600
$89$	12.1665	1.28964	0.644821	−	0.764333i	$-0.276932\pi$
$89$	12.1665	1.28964	0.644821	+	0.764333i	$0.276932\pi$
$90$	2.75951	0.290878
$91$	−8.23384	−0.863141
$92$	−0.876186	−0.0913487
$93$	−4.30011	−0.445901
$94$	−9.28620	−0.957798
$95$	0.102375	0.0105035
$96$	−0.490398	−0.0500510
$97$	9.09868	0.923831	0.461916	−	0.886924i	$-0.347162\pi$
$97$	9.09868	0.923831	0.461916	+	0.886924i	$0.347162\pi$
$98$	−5.32548	−0.537954
$99$	2.75951	0.277341
$100$	1.00000	0.100000
$101$	1.45738	0.145014	0.0725072	−	0.997368i	$-0.476900\pi$
$101$	1.45738	0.145014	0.0725072	+	0.997368i	$0.476900\pi$
$102$	2.53037	0.250544
$103$	14.7720	1.45552	0.727762	−	0.685830i	$-0.240561\pi$
$103$	14.7720	1.45552	0.727762	+	0.685830i	$0.240561\pi$
$104$	6.36293	0.623937
$105$	−0.634591	−0.0619298
$106$	−0.175296	−0.0170262
$107$	−7.17735	−0.693861	−0.346930	−	0.937891i	$-0.612776\pi$
$107$	−7.17735	−0.693861	−0.346930	+	0.937891i	$0.612776\pi$
$108$	2.82445	0.271783
$109$	6.34131	0.607387	0.303693	−	0.952770i	$-0.401780\pi$
$109$	6.34131	0.607387	0.303693	+	0.952770i	$0.401780\pi$
$110$	1.00000	0.0953463
$111$	0.867797	0.0823677
$112$	−1.29403	−0.122275
$113$	18.9933	1.78674	0.893371	−	0.449319i	$-0.148333\pi$
$113$	18.9933	1.78674	0.893371	+	0.449319i	$0.148333\pi$
$114$	0.0502045	0.00470208
$115$	0.876186	0.0817047
$116$	7.52730	0.698893
$117$	−17.5586	−1.62329
$118$	−5.90363	−0.543473
$119$	6.67699	0.612079
$120$	0.490398	0.0447670
$121$	1.00000	0.0909091
$122$	−4.20889	−0.381055
$123$	4.32238	0.389736
$124$	8.76862	0.787445
$125$	−1.00000	−0.0894427
$126$	3.57090	0.318121
$127$	17.6727	1.56820	0.784101	−	0.620633i	$-0.213124\pi$
$127$	17.6727	1.56820	0.784101	+	0.620633i	$0.213124\pi$
$128$	1.00000	0.0883883
$129$	−1.76870	−0.155726
$130$	−6.36293	−0.558066
$131$	15.2928	1.33613	0.668067	−	0.744101i	$-0.267122\pi$
$131$	15.2928	1.33613	0.668067	+	0.744101i	$0.267122\pi$
$132$	0.490398	0.0426837
$133$	0.132477	0.0114872
$134$	−10.3049	−0.890206
$135$	−2.82445	−0.243090
$136$	−5.15983	−0.442452
$137$	13.7754	1.17691	0.588457	−	0.808528i	$-0.299736\pi$
$137$	13.7754	1.17691	0.588457	+	0.808528i	$0.299736\pi$
$138$	0.429680	0.0365768
$139$	20.2860	1.72064	0.860318	−	0.509758i	$-0.170265\pi$
$139$	20.2860	1.72064	0.860318	+	0.509758i	$0.170265\pi$
$140$	1.29403	0.109366
$141$	4.55393	0.383510
$142$	−4.49164	−0.376930
$143$	−6.36293	−0.532095
$144$	−2.75951	−0.229959
$145$	−7.52730	−0.625109
$146$	−1.00000	−0.0827606
$147$	2.61160	0.215401
$148$	−1.76958	−0.145458
$149$	−17.5326	−1.43633	−0.718163	−	0.695875i	$-0.755017\pi$
$149$	−17.5326	−1.43633	−0.718163	+	0.695875i	$0.755017\pi$
$150$	−0.490398	−0.0400408
$151$	4.39007	0.357259	0.178629	−	0.983916i	$-0.442834\pi$
$151$	4.39007	0.357259	0.178629	+	0.983916i	$0.442834\pi$
$152$	−0.102375	−0.00830371
$153$	14.2386	1.15112
$154$	1.29403	0.104276
$155$	−8.76862	−0.704312
$156$	−3.12037	−0.249829
$157$	8.43762	0.673395	0.336698	−	0.941613i	$-0.390690\pi$
$157$	8.43762	0.673395	0.336698	+	0.941613i	$0.390690\pi$
$158$	3.97702	0.316395
$159$	0.0859647	0.00681744
$160$	−1.00000	−0.0790569
$161$	1.13381	0.0893570
$162$	6.89342	0.541599
$163$	12.5927	0.986338	0.493169	−	0.869934i	$-0.335838\pi$
$163$	12.5927	0.986338	0.493169	+	0.869934i	$0.335838\pi$
$164$	−8.81403	−0.688260
$165$	−0.490398	−0.0381774
$166$	8.30735	0.644775
$167$	−4.06251	−0.314366	−0.157183	−	0.987569i	$-0.550241\pi$
$167$	−4.06251	−0.314366	−0.157183	+	0.987569i	$0.550241\pi$
$168$	0.634591	0.0489598
$169$	27.4869	2.11437
$170$	5.15983	0.395741
$171$	0.282505	0.0216037
$172$	3.60667	0.275006
$173$	3.57767	0.272005	0.136003	−	0.990708i	$-0.456574\pi$
$173$	3.57767	0.272005	0.136003	+	0.990708i	$0.456574\pi$
$174$	−3.69137	−0.279842
$175$	−1.29403	−0.0978197
$176$	−1.00000	−0.0753778
$177$	2.89513	0.217611
$178$	12.1665	0.911915
$179$	3.68139	0.275160	0.137580	−	0.990491i	$-0.456068\pi$
$179$	3.68139	0.275160	0.137580	+	0.990491i	$0.456068\pi$
$180$	2.75951	0.205682
$181$	19.5272	1.45145	0.725723	−	0.687987i	$-0.241505\pi$
$181$	19.5272	1.45145	0.725723	+	0.687987i	$0.241505\pi$
$182$	−8.23384	−0.610333
$183$	2.06403	0.152577
$184$	−0.876186	−0.0645933
$185$	1.76958	0.130102
$186$	−4.30011	−0.315300
$187$	5.15983	0.377324
$188$	−9.28620	−0.677265
$189$	−3.65494	−0.265857
$190$	0.102375	0.00742707
$191$	9.68764	0.700973	0.350487	−	0.936568i	$-0.386016\pi$
$191$	9.68764	0.700973	0.350487	+	0.936568i	$0.386016\pi$
$192$	−0.490398	−0.0353914
$193$	−24.3293	−1.75126	−0.875631	−	0.482981i	$-0.839554\pi$
$193$	−24.3293	−1.75126	−0.875631	+	0.482981i	$0.839554\pi$
$194$	9.09868	0.653247
$195$	3.12037	0.223454
$196$	−5.32548	−0.380391
$197$	−1.15060	−0.0819771	−0.0409885	−	0.999160i	$-0.513051\pi$
$197$	−1.15060	−0.0819771	−0.0409885	+	0.999160i	$0.513051\pi$
$198$	2.75951	0.196110
$199$	−11.9831	−0.849461	−0.424731	−	0.905320i	$-0.639631\pi$
$199$	−11.9831	−0.849461	−0.424731	+	0.905320i	$0.639631\pi$
$200$	1.00000	0.0707107
$201$	5.05349	0.356446
$202$	1.45738	0.102541
$203$	−9.74058	−0.683655
$204$	2.53037	0.177161
$205$	8.81403	0.615599
$206$	14.7720	1.02921
$207$	2.41784	0.168052
$208$	6.36293	0.441190
$209$	0.102375	0.00708143
$210$	−0.634591	−0.0437910
$211$	4.05149	0.278916	0.139458	−	0.990228i	$-0.455464\pi$
$211$	4.05149	0.278916	0.139458	+	0.990228i	$0.455464\pi$
$212$	−0.175296	−0.0120394
$213$	2.20269	0.150926
$214$	−7.17735	−0.490634
$215$	−3.60667	−0.245973
$216$	2.82445	0.192180
$217$	−11.3469	−0.770277
$218$	6.34131	0.429487
$219$	0.490398	0.0331380
$220$	1.00000	0.0674200
$221$	−32.8316	−2.20849
$222$	0.867797	0.0582427
$223$	−4.55712	−0.305167	−0.152584	−	0.988291i	$-0.548759\pi$
$223$	−4.55712	−0.305167	−0.152584	+	0.988291i	$0.548759\pi$
$224$	−1.29403	−0.0864612
$225$	−2.75951	−0.183967
$226$	18.9933	1.26342
$227$	8.63098	0.572858	0.286429	−	0.958101i	$-0.407532\pi$
$227$	8.63098	0.572858	0.286429	+	0.958101i	$0.407532\pi$
$228$	0.0502045	0.00332488
$229$	23.4524	1.54978	0.774890	−	0.632096i	$-0.217805\pi$
$229$	23.4524	1.54978	0.774890	+	0.632096i	$0.217805\pi$
$230$	0.876186	0.0577740
$231$	−0.634591	−0.0417530
$232$	7.52730	0.494192
$233$	21.1211	1.38369	0.691843	−	0.722048i	$-0.256799\pi$
$233$	21.1211	1.38369	0.691843	+	0.722048i	$0.256799\pi$
$234$	−17.5586	−1.14784
$235$	9.28620	0.605765
$236$	−5.90363	−0.384294
$237$	−1.95032	−0.126687
$238$	6.67699	0.432805
$239$	4.84842	0.313618	0.156809	−	0.987629i	$-0.449879\pi$
$239$	4.84842	0.313618	0.156809	+	0.987629i	$0.449879\pi$
$240$	0.490398	0.0316551
$241$	24.1006	1.55246	0.776230	−	0.630450i	$-0.217130\pi$
$241$	24.1006	1.55246	0.776230	+	0.630450i	$0.217130\pi$
$242$	1.00000	0.0642824
$243$	−11.8539	−0.760427
$244$	−4.20889	−0.269446
$245$	5.32548	0.340232
$246$	4.32238	0.275585
$247$	−0.651405	−0.0414479
$248$	8.76862	0.556808
$249$	−4.07391	−0.258173
$250$	−1.00000	−0.0632456
$251$	4.51372	0.284903	0.142452	−	0.989802i	$-0.454501\pi$
$251$	4.51372	0.284903	0.142452	+	0.989802i	$0.454501\pi$
$252$	3.57090	0.224945
$253$	0.876186	0.0550853
$254$	17.6727	1.10889
$255$	−2.53037	−0.158458
$256$	1.00000	0.0625000
$257$	−1.44574	−0.0901828	−0.0450914	−	0.998983i	$-0.514358\pi$
$257$	−1.44574	−0.0901828	−0.0450914	+	0.998983i	$0.514358\pi$
$258$	−1.76870	−0.110115
$259$	2.28989	0.142287
$260$	−6.36293	−0.394612
$261$	−20.7717	−1.28573
$262$	15.2928	0.944790
$263$	3.80243	0.234468	0.117234	−	0.993104i	$-0.462597\pi$
$263$	3.80243	0.234468	0.117234	+	0.993104i	$0.462597\pi$
$264$	0.490398	0.0301819
$265$	0.175296	0.0107683
$266$	0.132477	0.00812267
$267$	−5.96641	−0.365138
$268$	−10.3049	−0.629471
$269$	−27.3371	−1.66677	−0.833387	−	0.552690i	$-0.813601\pi$
$269$	−27.3371	−1.66677	−0.833387	+	0.552690i	$0.813601\pi$
$270$	−2.82445	−0.171891
$271$	8.96381	0.544513	0.272256	−	0.962225i	$-0.412230\pi$
$271$	8.96381	0.544513	0.272256	+	0.962225i	$0.412230\pi$
$272$	−5.15983	−0.312861
$273$	4.03786	0.244382
$274$	13.7754	0.832204
$275$	−1.00000	−0.0603023
$276$	0.429680	0.0258637
$277$	−20.3451	−1.22242	−0.611209	−	0.791470i	$-0.709316\pi$
$277$	−20.3451	−1.22242	−0.611209	+	0.791470i	$0.709316\pi$
$278$	20.2860	1.21667
$279$	−24.1971	−1.44864
$280$	1.29403	0.0773333
$281$	−15.6416	−0.933097	−0.466549	−	0.884496i	$-0.654503\pi$
$281$	−15.6416	−0.933097	−0.466549	+	0.884496i	$0.654503\pi$
$282$	4.55393	0.271183
$283$	−13.4363	−0.798702	−0.399351	−	0.916798i	$-0.630765\pi$
$283$	−13.4363	−0.798702	−0.399351	+	0.916798i	$0.630765\pi$
$284$	−4.49164	−0.266530
$285$	−0.0502045	−0.00297386
$286$	−6.36293	−0.376248
$287$	11.4057	0.673255
$288$	−2.75951	−0.162606
$289$	9.62382	0.566107
$290$	−7.52730	−0.442018
$291$	−4.46198	−0.261566
$292$	−1.00000	−0.0585206
$293$	−25.5581	−1.49312	−0.746561	−	0.665317i	$-0.768296\pi$
$293$	−25.5581	−1.49312	−0.746561	+	0.665317i	$0.768296\pi$
$294$	2.61160	0.152312
$295$	5.90363	0.343723
$296$	−1.76958	−0.102855
$297$	−2.82445	−0.163891
$298$	−17.5326	−1.01564
$299$	−5.57511	−0.322417
$300$	−0.490398	−0.0283131
$301$	−4.66715	−0.269010
$302$	4.39007	0.252620
$303$	−0.714695	−0.0410581
$304$	−0.102375	−0.00587161
$305$	4.20889	0.241000
$306$	14.2386	0.813966
$307$	13.2476	0.756082	0.378041	−	0.925789i	$-0.376598\pi$
$307$	13.2476	0.756082	0.378041	+	0.925789i	$0.376598\pi$
$308$	1.29403	0.0737344
$309$	−7.24414	−0.412104
$310$	−8.76862	−0.498024
$311$	−9.61855	−0.545418	−0.272709	−	0.962097i	$-0.587920\pi$
$311$	−9.61855	−0.545418	−0.272709	+	0.962097i	$0.587920\pi$
$312$	−3.12037	−0.176656
$313$	21.7443	1.22906	0.614531	−	0.788893i	$-0.289345\pi$
$313$	21.7443	1.22906	0.614531	+	0.788893i	$0.289345\pi$
$314$	8.43762	0.476162
$315$	−3.57090	−0.201197
$316$	3.97702	0.223725
$317$	18.0479	1.01367	0.506836	−	0.862042i	$-0.330815\pi$
$317$	18.0479	1.01367	0.506836	+	0.862042i	$0.330815\pi$
$318$	0.0859647	0.00482066
$319$	−7.52730	−0.421448
$320$	−1.00000	−0.0559017
$321$	3.51976	0.196454
$322$	1.13381	0.0631850
$323$	0.528238	0.0293919
$324$	6.89342	0.382968
$325$	6.36293	0.352952
$326$	12.5927	0.697446
$327$	−3.10976	−0.171970
$328$	−8.81403	−0.486674
$329$	12.0166	0.662499
$330$	−0.490398	−0.0269955
$331$	−7.23130	−0.397468	−0.198734	−	0.980053i	$-0.563683\pi$
$331$	−7.23130	−0.397468	−0.198734	+	0.980053i	$0.563683\pi$
$332$	8.30735	0.455925
$333$	4.88317	0.267596
$334$	−4.06251	−0.222290
$335$	10.3049	0.563016
$336$	0.634591	0.0346198
$337$	−18.7373	−1.02069	−0.510344	−	0.859970i	$-0.670482\pi$
$337$	−18.7373	−1.02069	−0.510344	+	0.859970i	$0.670482\pi$
$338$	27.4869	1.49509
$339$	−9.31429	−0.505883
$340$	5.15983	0.279831
$341$	−8.76862	−0.474847
$342$	0.282505	0.0152761
$343$	15.9496	0.861196
$344$	3.60667	0.194459
$345$	−0.429680	−0.0231332
$346$	3.57767	0.192337
$347$	19.8149	1.06372	0.531861	−	0.846832i	$-0.321493\pi$
$347$	19.8149	1.06372	0.531861	+	0.846832i	$0.321493\pi$
$348$	−3.69137	−0.197878
$349$	−27.9387	−1.49552	−0.747762	−	0.663966i	$-0.768872\pi$
$349$	−27.9387	−1.49552	−0.747762	+	0.663966i	$0.768872\pi$
$350$	−1.29403	−0.0691690
$351$	17.9718	0.959263
$352$	−1.00000	−0.0533002
$353$	−4.18113	−0.222539	−0.111269	−	0.993790i	$-0.535492\pi$
$353$	−4.18113	−0.222539	−0.111269	+	0.993790i	$0.535492\pi$
$354$	2.89513	0.153874
$355$	4.49164	0.238392
$356$	12.1665	0.644821
$357$	−3.27438	−0.173299
$358$	3.68139	0.194568
$359$	34.3846	1.81475	0.907374	−	0.420324i	$-0.138084\pi$
$359$	34.3846	1.81475	0.907374	+	0.420324i	$0.138084\pi$
$360$	2.75951	0.145439
$361$	−18.9895	−0.999448
$362$	19.5272	1.02633
$363$	−0.490398	−0.0257392
$364$	−8.23384	−0.431571
$365$	1.00000	0.0523424
$366$	2.06403	0.107889
$367$	−9.07827	−0.473882	−0.236941	−	0.971524i	$-0.576145\pi$
$367$	−9.07827	−0.473882	−0.236941	+	0.971524i	$0.576145\pi$
$368$	−0.876186	−0.0456743
$369$	24.3224	1.26617
$370$	1.76958	0.0919959
$371$	0.226838	0.0117769
$372$	−4.30011	−0.222950
$373$	27.9255	1.44593	0.722963	−	0.690887i	$-0.242780\pi$
$373$	27.9255	1.44593	0.722963	+	0.690887i	$0.242780\pi$
$374$	5.15983	0.266808
$375$	0.490398	0.0253240
$376$	−9.28620	−0.478899
$377$	47.8957	2.46675
$378$	−3.65494	−0.187990
$379$	6.43719	0.330656	0.165328	−	0.986239i	$-0.447132\pi$
$379$	6.43719	0.330656	0.165328	+	0.986239i	$0.447132\pi$
$380$	0.102375	0.00525173
$381$	−8.66668	−0.444007
$382$	9.68764	0.495663
$383$	−25.6700	−1.31167	−0.655837	−	0.754902i	$-0.727684\pi$
$383$	−25.6700	−1.31167	−0.655837	+	0.754902i	$0.727684\pi$
$384$	−0.490398	−0.0250255
$385$	−1.29403	−0.0659501
$386$	−24.3293	−1.23833
$387$	−9.95264	−0.505921
$388$	9.09868	0.461916
$389$	−11.1168	−0.563644	−0.281822	−	0.959467i	$-0.590939\pi$
$389$	−11.1168	−0.563644	−0.281822	+	0.959467i	$0.590939\pi$
$390$	3.12037	0.158006
$391$	4.52097	0.228635
$392$	−5.32548	−0.268977
$393$	−7.49954	−0.378302
$394$	−1.15060	−0.0579666
$395$	−3.97702	−0.200105
$396$	2.75951	0.138671
$397$	−7.65871	−0.384380	−0.192190	−	0.981358i	$-0.561559\pi$
$397$	−7.65871	−0.384380	−0.192190	+	0.981358i	$0.561559\pi$
$398$	−11.9831	−0.600660
$399$	−0.0649663	−0.00325238
$400$	1.00000	0.0500000
$401$	−6.89414	−0.344277	−0.172138	−	0.985073i	$-0.555068\pi$
$401$	−6.89414	−0.344277	−0.172138	+	0.985073i	$0.555068\pi$
$402$	5.05349	0.252045
$403$	55.7941	2.77930
$404$	1.45738	0.0725072
$405$	−6.89342	−0.342537
$406$	−9.74058	−0.483417
$407$	1.76958	0.0877147
$408$	2.53037	0.125272
$409$	4.85546	0.240087	0.120044	−	0.992769i	$-0.461697\pi$
$409$	4.85546	0.240087	0.120044	+	0.992769i	$0.461697\pi$
$410$	8.81403	0.435294
$411$	−6.75544	−0.333221
$412$	14.7720	0.727762
$413$	7.63950	0.375915
$414$	2.41784	0.118830
$415$	−8.30735	−0.407792
$416$	6.36293	0.311968
$417$	−9.94821	−0.487166
$418$	0.102375	0.00500733
$419$	24.6106	1.20231	0.601154	−	0.799133i	$-0.294708\pi$
$419$	24.6106	1.20231	0.601154	+	0.799133i	$0.294708\pi$
$420$	−0.634591	−0.0309649
$421$	0.0137291	0.000669115 0	0.000334557	−	1.00000i	$-0.499894\pi$
$421$	0.0137291	0.000669115 0	0.000334557		1.00000i	$0.499894\pi$
$422$	4.05149	0.197224
$423$	25.6253	1.24595
$424$	−0.175296	−0.00851311
$425$	−5.15983	−0.250288
$426$	2.20269	0.106721
$427$	5.44644	0.263572
$428$	−7.17735	−0.346930
$429$	3.12037	0.150653
$430$	−3.60667	−0.173929
$431$	−8.67738	−0.417975	−0.208987	−	0.977918i	$-0.567017\pi$
$431$	−8.67738	−0.417975	−0.208987	+	0.977918i	$0.567017\pi$
$432$	2.82445	0.135892
$433$	4.15261	0.199562	0.0997808	−	0.995009i	$-0.468186\pi$
$433$	4.15261	0.199562	0.0997808	+	0.995009i	$0.468186\pi$
$434$	−11.3469	−0.544668
$435$	3.69137	0.176988
$436$	6.34131	0.303693
$437$	0.0896996	0.00429091
$438$	0.490398	0.0234321
$439$	32.8507	1.56788	0.783939	−	0.620838i	$-0.213208\pi$
$439$	32.8507	1.56788	0.783939	+	0.620838i	$0.213208\pi$
$440$	1.00000	0.0476731
$441$	14.6957	0.699796
$442$	−32.8316	−1.56164
$443$	−12.0554	−0.572770	−0.286385	−	0.958115i	$-0.592454\pi$
$443$	−12.0554	−0.572770	−0.286385	+	0.958115i	$0.592454\pi$
$444$	0.867797	0.0411838
$445$	−12.1665	−0.576746
$446$	−4.55712	−0.215786
$447$	8.59795	0.406669
$448$	−1.29403	−0.0611373
$449$	17.4956	0.825668	0.412834	−	0.910806i	$-0.364539\pi$
$449$	17.4956	0.825668	0.412834	+	0.910806i	$0.364539\pi$
$450$	−2.75951	−0.130085
$451$	8.81403	0.415037
$452$	18.9933	0.893371
$453$	−2.15288	−0.101151
$454$	8.63098	0.405072
$455$	8.23384	0.386008
$456$	0.0502045	0.00235104
$457$	35.7260	1.67119	0.835596	−	0.549344i	$-0.185122\pi$
$457$	35.7260	1.67119	0.835596	+	0.549344i	$0.185122\pi$
$458$	23.4524	1.09586
$459$	−14.5737	−0.680241
$460$	0.876186	0.0408524
$461$	−20.2673	−0.943941	−0.471971	−	0.881614i	$-0.656457\pi$
$461$	−20.2673	−0.943941	−0.471971	+	0.881614i	$0.656457\pi$
$462$	−0.634591	−0.0295239
$463$	26.9240	1.25126	0.625631	−	0.780119i	$-0.284842\pi$
$463$	26.9240	1.25126	0.625631	+	0.780119i	$0.284842\pi$
$464$	7.52730	0.349446
$465$	4.30011	0.199413
$466$	21.1211	0.978414
$467$	20.3630	0.942289	0.471145	−	0.882056i	$-0.343841\pi$
$467$	20.3630	0.942289	0.471145	+	0.882056i	$0.343841\pi$
$468$	−17.5586	−0.811645
$469$	13.3349	0.615747
$470$	9.28620	0.428340
$471$	−4.13779	−0.190659
$472$	−5.90363	−0.271737
$473$	−3.60667	−0.165835
$474$	−1.95032	−0.0895812
$475$	−0.102375	−0.00469729
$476$	6.67699	0.306039
$477$	0.483730	0.0221485
$478$	4.84842	0.221762
$479$	−41.5094	−1.89661	−0.948307	−	0.317354i	$-0.897206\pi$
$479$	−41.5094	−1.89661	−0.948307	+	0.317354i	$0.897206\pi$
$480$	0.490398	0.0223835
$481$	−11.2597	−0.513398
$482$	24.1006	1.09775
$483$	−0.556020	−0.0252998
$484$	1.00000	0.0454545
$485$	−9.09868	−0.413150
$486$	−11.8539	−0.537703
$487$	13.7509	0.623111	0.311556	−	0.950228i	$-0.399150\pi$
$487$	13.7509	0.623111	0.311556	+	0.950228i	$0.399150\pi$
$488$	−4.20889	−0.190527
$489$	−6.17544	−0.279263
$490$	5.32548	0.240581
$491$	7.51969	0.339359	0.169679	−	0.985499i	$-0.445727\pi$
$491$	7.51969	0.339359	0.169679	+	0.985499i	$0.445727\pi$
$492$	4.32238	0.194868
$493$	−38.8396	−1.74925
$494$	−0.651405	−0.0293081
$495$	−2.75951	−0.124031
$496$	8.76862	0.393723
$497$	5.81233	0.260719
$498$	−4.07391	−0.182556
$499$	0.126935	0.00568241	0.00284120	−	0.999996i	$-0.499096\pi$
$499$	0.126935	0.00568241	0.00284120	+	0.999996i	$0.499096\pi$
$500$	−1.00000	−0.0447214
$501$	1.99224	0.0890069
$502$	4.51372	0.201457
$503$	7.47595	0.333336	0.166668	−	0.986013i	$-0.446699\pi$
$503$	7.47595	0.333336	0.166668	+	0.986013i	$0.446699\pi$
$504$	3.57090	0.159060
$505$	−1.45738	−0.0648524
$506$	0.876186	0.0389512
$507$	−13.4795	−0.598646
$508$	17.6727	0.784101
$509$	−4.15118	−0.183998	−0.0919988	−	0.995759i	$-0.529326\pi$
$509$	−4.15118	−0.183998	−0.0919988	+	0.995759i	$0.529326\pi$
$510$	−2.53037	−0.112047
$511$	1.29403	0.0572447
$512$	1.00000	0.0441942
$513$	−0.289153	−0.0127664
$514$	−1.44574	−0.0637689
$515$	−14.7720	−0.650930
$516$	−1.76870	−0.0778628
$517$	9.28620	0.408406
$518$	2.28989	0.100612
$519$	−1.75448	−0.0770132
$520$	−6.36293	−0.279033
$521$	5.34780	0.234291	0.117146	−	0.993115i	$-0.462626\pi$
$521$	5.34780	0.234291	0.117146	+	0.993115i	$0.462626\pi$
$522$	−20.7717	−0.909151
$523$	20.9327	0.915322	0.457661	−	0.889127i	$-0.348687\pi$
$523$	20.9327	0.915322	0.457661	+	0.889127i	$0.348687\pi$
$524$	15.2928	0.668067
$525$	0.634591	0.0276958
$526$	3.80243	0.165794
$527$	−45.2446	−1.97088
$528$	0.490398	0.0213418
$529$	−22.2323	−0.966622
$530$	0.175296	0.00761436
$531$	16.2911	0.706975
$532$	0.132477	0.00574360
$533$	−56.0831	−2.42923
$534$	−5.96641	−0.258192
$535$	7.17735	0.310304
$536$	−10.3049	−0.445103
$537$	−1.80535	−0.0779065
$538$	−27.3371	−1.17859
$539$	5.32548	0.229385
$540$	−2.82445	−0.121545
$541$	−35.8244	−1.54021	−0.770105	−	0.637917i	$-0.779796\pi$
$541$	−35.8244	−1.54021	−0.770105	+	0.637917i	$0.779796\pi$
$542$	8.96381	0.385029
$543$	−9.57611	−0.410950
$544$	−5.15983	−0.221226
$545$	−6.34131	−0.271632
$546$	4.03786	0.172804
$547$	−34.1602	−1.46059	−0.730293	−	0.683134i	$-0.760616\pi$
$547$	−34.1602	−1.46059	−0.730293	+	0.683134i	$0.760616\pi$
$548$	13.7754	0.588457
$549$	11.6145	0.495693
$550$	−1.00000	−0.0426401
$551$	−0.770608	−0.0328290
$552$	0.429680	0.0182884
$553$	−5.14639	−0.218847
$554$	−20.3451	−0.864379
$555$	−0.867797	−0.0368359
$556$	20.2860	0.860318
$557$	2.40941	0.102090	0.0510449	−	0.998696i	$-0.483745\pi$
$557$	2.40941	0.102090	0.0510449	+	0.998696i	$0.483745\pi$
$558$	−24.1971	−1.02434
$559$	22.9490	0.970638
$560$	1.29403	0.0546829
$561$	−2.53037	−0.106832
$562$	−15.6416	−0.659799
$563$	−32.4527	−1.36772	−0.683859	−	0.729614i	$-0.739700\pi$
$563$	−32.4527	−1.36772	−0.683859	+	0.729614i	$0.739700\pi$
$564$	4.55393	0.191755
$565$	−18.9933	−0.799056
$566$	−13.4363	−0.564768
$567$	−8.92032	−0.374618
$568$	−4.49164	−0.188465
$569$	−4.83484	−0.202687	−0.101343	−	0.994852i	$-0.532314\pi$
$569$	−4.83484	−0.202687	−0.101343	+	0.994852i	$0.532314\pi$
$570$	−0.0502045	−0.00210284
$571$	3.33466	0.139551	0.0697755	−	0.997563i	$-0.477772\pi$
$571$	3.33466	0.139551	0.0697755	+	0.997563i	$0.477772\pi$
$572$	−6.36293	−0.266047
$573$	−4.75080	−0.198468
$574$	11.4057	0.476063
$575$	−0.876186	−0.0365395
$576$	−2.75951	−0.114980
$577$	−13.9812	−0.582046	−0.291023	−	0.956716i	$-0.593996\pi$
$577$	−13.9812	−0.582046	−0.291023	+	0.956716i	$0.593996\pi$
$578$	9.62382	0.400298
$579$	11.9310	0.495837
$580$	−7.52730	−0.312554
$581$	−10.7500	−0.445985
$582$	−4.46198	−0.184955
$583$	0.175296	0.00726001
$584$	−1.00000	−0.0413803
$585$	17.5586	0.725957
$586$	−25.5581	−1.05580
$587$	−17.5341	−0.723710	−0.361855	−	0.932234i	$-0.617857\pi$
$587$	−17.5341	−0.723710	−0.361855	+	0.932234i	$0.617857\pi$
$588$	2.61160	0.107701
$589$	−0.897688	−0.0369886
$590$	5.90363	0.243049
$591$	0.564253	0.0232103
$592$	−1.76958	−0.0727292
$593$	−2.99429	−0.122961	−0.0614804	−	0.998108i	$-0.519582\pi$
$593$	−2.99429	−0.122961	−0.0614804	+	0.998108i	$0.519582\pi$
$594$	−2.82445	−0.115889
$595$	−6.67699	−0.273730
$596$	−17.5326	−0.718163
$597$	5.87650	0.240509
$598$	−5.57511	−0.227983
$599$	6.35031	0.259467	0.129733	−	0.991549i	$-0.458588\pi$
$599$	6.35031	0.259467	0.129733	+	0.991549i	$0.458588\pi$
$600$	−0.490398	−0.0200204
$601$	−1.82218	−0.0743285	−0.0371642	−	0.999309i	$-0.511832\pi$
$601$	−1.82218	−0.0743285	−0.0371642	+	0.999309i	$0.511832\pi$
$602$	−4.66715	−0.190219
$603$	28.4364	1.15802
$604$	4.39007	0.178629
$605$	−1.00000	−0.0406558
$606$	−0.714695	−0.0290325
$607$	−45.5458	−1.84865	−0.924324	−	0.381610i	$-0.875370\pi$
$607$	−45.5458	−1.84865	−0.924324	+	0.381610i	$0.875370\pi$
$608$	−0.102375	−0.00415186
$609$	4.77676	0.193564
$610$	4.20889	0.170413
$611$	−59.0874	−2.39042
$612$	14.2386	0.575561
$613$	−16.2869	−0.657823	−0.328912	−	0.944361i	$-0.606682\pi$
$613$	−16.2869	−0.657823	−0.328912	+	0.944361i	$0.606682\pi$
$614$	13.2476	0.534631
$615$	−4.32238	−0.174295
$616$	1.29403	0.0521381
$617$	15.6312	0.629290	0.314645	−	0.949209i	$-0.398115\pi$
$617$	15.6312	0.629290	0.314645	+	0.949209i	$0.398115\pi$
$618$	−7.24414	−0.291402
$619$	0.942905	0.0378986	0.0189493	−	0.999820i	$-0.493968\pi$
$619$	0.942905	0.0378986	0.0189493	+	0.999820i	$0.493968\pi$
$620$	−8.76862	−0.352156
$621$	−2.47474	−0.0993081
$622$	−9.61855	−0.385669
$623$	−15.7438	−0.630763
$624$	−3.12037	−0.124915
$625$	1.00000	0.0400000
$626$	21.7443	0.869078
$627$	−0.0502045	−0.00200498
$628$	8.43762	0.336698
$629$	9.13071	0.364065
$630$	−3.57090	−0.142268
$631$	−20.7002	−0.824063	−0.412032	−	0.911170i	$-0.635181\pi$
$631$	−20.7002	−0.824063	−0.412032	+	0.911170i	$0.635181\pi$
$632$	3.97702	0.158197
$633$	−1.98684	−0.0789700
$634$	18.0479	0.716774
$635$	−17.6727	−0.701322
$636$	0.0859647	0.00340872
$637$	−33.8856	−1.34260
$638$	−7.52730	−0.298009
$639$	12.3947	0.490328
$640$	−1.00000	−0.0395285
$641$	−8.05818	−0.318279	−0.159139	−	0.987256i	$-0.550872\pi$
$641$	−8.05818	−0.318279	−0.159139	+	0.987256i	$0.550872\pi$
$642$	3.51976	0.138914
$643$	−38.8217	−1.53098	−0.765490	−	0.643448i	$-0.777503\pi$
$643$	−38.8217	−1.53098	−0.765490	+	0.643448i	$0.777503\pi$
$644$	1.13381	0.0446785
$645$	1.76870	0.0696426
$646$	0.528238	0.0207832
$647$	18.7733	0.738056	0.369028	−	0.929418i	$-0.379691\pi$
$647$	18.7733	0.738056	0.369028	+	0.929418i	$0.379691\pi$
$648$	6.89342	0.270799
$649$	5.90363	0.231738
$650$	6.36293	0.249575
$651$	5.56449	0.218090
$652$	12.5927	0.493169
$653$	−38.5992	−1.51050	−0.755252	−	0.655434i	$-0.772486\pi$
$653$	−38.5992	−1.51050	−0.755252	+	0.655434i	$0.772486\pi$
$654$	−3.10976	−0.121601
$655$	−15.2928	−0.597537
$656$	−8.81403	−0.344130
$657$	2.75951	0.107659
$658$	12.0166	0.468458
$659$	47.8772	1.86503	0.932516	−	0.361130i	$-0.117609\pi$
$659$	47.8772	1.86503	0.932516	+	0.361130i	$0.117609\pi$
$660$	−0.490398	−0.0190887
$661$	9.88046	0.384305	0.192153	−	0.981365i	$-0.438453\pi$
$661$	9.88046	0.384305	0.192153	+	0.981365i	$0.438453\pi$
$662$	−7.23130	−0.281052
$663$	16.1006	0.625294
$664$	8.30735	0.322388
$665$	−0.132477	−0.00513723
$666$	4.88317	0.189219
$667$	−6.59532	−0.255372
$668$	−4.06251	−0.157183
$669$	2.23480	0.0864024
$670$	10.3049	0.398112
$671$	4.20889	0.162482
$672$	0.634591	0.0244799
$673$	−7.69356	−0.296565	−0.148282	−	0.988945i	$-0.547374\pi$
$673$	−7.69356	−0.296565	−0.148282	+	0.988945i	$0.547374\pi$
$674$	−18.7373	−0.721735
$675$	2.82445	0.108713
$676$	27.4869	1.05719
$677$	−22.1022	−0.849458	−0.424729	−	0.905320i	$-0.639631\pi$
$677$	−22.1022	−0.849458	−0.424729	+	0.905320i	$0.639631\pi$
$678$	−9.31429	−0.357713
$679$	−11.7740	−0.451845
$680$	5.15983	0.197870
$681$	−4.23261	−0.162194
$682$	−8.76862	−0.335768
$683$	−21.3124	−0.815495	−0.407748	−	0.913095i	$-0.633686\pi$
$683$	−21.3124	−0.815495	−0.407748	+	0.913095i	$0.633686\pi$
$684$	0.282505	0.0108018
$685$	−13.7754	−0.526332
$686$	15.9496	0.608958
$687$	−11.5010	−0.438792
$688$	3.60667	0.137503
$689$	−1.11539	−0.0424931
$690$	−0.429680	−0.0163576
$691$	−6.90869	−0.262819	−0.131410	−	0.991328i	$-0.541950\pi$
$691$	−6.90869	−0.262819	−0.131410	+	0.991328i	$0.541950\pi$
$692$	3.57767	0.136003
$693$	−3.57090	−0.135647
$694$	19.8149	0.752165
$695$	−20.2860	−0.769492
$696$	−3.69137	−0.139921
$697$	45.4789	1.72264
$698$	−27.9387	−1.05750
$699$	−10.3577	−0.391765
$700$	−1.29403	−0.0489099
$701$	34.6702	1.30947	0.654737	−	0.755857i	$-0.272779\pi$
$701$	34.6702	1.30947	0.654737	+	0.755857i	$0.272779\pi$
$702$	17.9718	0.678301
$703$	0.181161	0.00683260
$704$	−1.00000	−0.0376889
$705$	−4.55393	−0.171511
$706$	−4.18113	−0.157359
$707$	−1.88589	−0.0709264
$708$	2.89513	0.108806
$709$	21.5828	0.810560	0.405280	−	0.914193i	$-0.367174\pi$
$709$	21.5828	0.810560	0.405280	+	0.914193i	$0.367174\pi$
$710$	4.49164	0.168568
$711$	−10.9746	−0.411580
$712$	12.1665	0.455958
$713$	−7.68294	−0.287728
$714$	−3.27438	−0.122541
$715$	6.36293	0.237960
$716$	3.68139	0.137580
$717$	−2.37766	−0.0887952
$718$	34.3846	1.28322
$719$	39.6382	1.47826	0.739128	−	0.673564i	$-0.235238\pi$
$719$	39.6382	1.47826	0.739128	+	0.673564i	$0.235238\pi$
$720$	2.75951	0.102841
$721$	−19.1154	−0.711895
$722$	−18.9895	−0.706717
$723$	−11.8189	−0.439550
$724$	19.5272	0.725723
$725$	7.52730	0.279557
$726$	−0.490398	−0.0182004
$727$	13.4396	0.498447	0.249223	−	0.968446i	$-0.419825\pi$
$727$	13.4396	0.498447	0.249223	+	0.968446i	$0.419825\pi$
$728$	−8.23384	−0.305167
$729$	−14.8672	−0.550635
$730$	1.00000	0.0370117
$731$	−18.6098	−0.688308
$732$	2.06403	0.0762887
$733$	2.79786	0.103341	0.0516707	−	0.998664i	$-0.483545\pi$
$733$	2.79786	0.103341	0.0516707	+	0.998664i	$0.483545\pi$
$734$	−9.07827	−0.335085
$735$	−2.61160	−0.0963304
$736$	−0.876186	−0.0322966
$737$	10.3049	0.379585
$738$	24.3224	0.895321
$739$	−13.2502	−0.487415	−0.243708	−	0.969849i	$-0.578364\pi$
$739$	−13.2502	−0.487415	−0.243708	+	0.969849i	$0.578364\pi$
$740$	1.76958	0.0650510
$741$	0.319448	0.0117352
$742$	0.226838	0.00832750
$743$	−13.2623	−0.486547	−0.243273	−	0.969958i	$-0.578221\pi$
$743$	−13.2623	−0.486547	−0.243273	+	0.969958i	$0.578221\pi$
$744$	−4.30011	−0.157650
$745$	17.5326	0.642345
$746$	27.9255	1.02242
$747$	−22.9242	−0.838753
$748$	5.15983	0.188662
$749$	9.28773	0.339366
$750$	0.490398	0.0179068
$751$	29.3180	1.06983	0.534914	−	0.844907i	$-0.320344\pi$
$751$	29.3180	1.06983	0.534914	+	0.844907i	$0.320344\pi$
$752$	−9.28620	−0.338633
$753$	−2.21352	−0.0806651
$754$	47.8957	1.74426
$755$	−4.39007	−0.159771
$756$	−3.65494	−0.132929
$757$	20.7404	0.753822	0.376911	−	0.926249i	$-0.376986\pi$
$757$	20.7404	0.753822	0.376911	+	0.926249i	$0.376986\pi$
$758$	6.43719	0.233809
$759$	−0.429680	−0.0155964
$760$	0.102375	0.00371353
$761$	26.0318	0.943653	0.471826	−	0.881692i	$-0.343595\pi$
$761$	26.0318	0.943653	0.471826	+	0.881692i	$0.343595\pi$
$762$	−8.66668	−0.313961
$763$	−8.20586	−0.297072
$764$	9.68764	0.350487
$765$	−14.2386	−0.514798
$766$	−25.6700	−0.927494
$767$	−37.5644	−1.35637
$768$	−0.490398	−0.0176957
$769$	40.6398	1.46551	0.732754	−	0.680493i	$-0.238234\pi$
$769$	40.6398	1.46551	0.732754	+	0.680493i	$0.238234\pi$
$770$	−1.29403	−0.0466337
$771$	0.708988	0.0255336
$772$	−24.3293	−0.875631
$773$	−31.7489	−1.14193	−0.570964	−	0.820975i	$-0.693430\pi$
$773$	−31.7489	−1.14193	−0.570964	+	0.820975i	$0.693430\pi$
$774$	−9.95264	−0.357740
$775$	8.76862	0.314978
$776$	9.09868	0.326624
$777$	−1.12296	−0.0402859
$778$	−11.1168	−0.398556
$779$	0.902337	0.0323296
$780$	3.12037	0.111727
$781$	4.49164	0.160724
$782$	4.52097	0.161669
$783$	21.2605	0.759788
$784$	−5.32548	−0.190196
$785$	−8.43762	−0.301152
$786$	−7.49954	−0.267500
$787$	8.56751	0.305399	0.152699	−	0.988273i	$-0.451203\pi$
$787$	8.56751	0.305399	0.152699	+	0.988273i	$0.451203\pi$
$788$	−1.15060	−0.0409885
$789$	−1.86471	−0.0663853
$790$	−3.97702	−0.141496
$791$	−24.5780	−0.873894
$792$	2.75951	0.0980549
$793$	−26.7808	−0.951016
$794$	−7.65871	−0.271797
$795$	−0.0859647	−0.00304885
$796$	−11.9831	−0.424731
$797$	37.8253	1.33984	0.669920	−	0.742433i	$-0.266328\pi$
$797$	37.8253	1.33984	0.669920	+	0.742433i	$0.266328\pi$
$798$	−0.0649663	−0.00229978
$799$	47.9152	1.69512
$800$	1.00000	0.0353553
$801$	−33.5735	−1.18626
$802$	−6.89414	−0.243440
$803$	1.00000	0.0352892
$804$	5.05349	0.178223
$805$	−1.13381	−0.0399617
$806$	55.7941	1.96526
$807$	13.4061	0.471916
$808$	1.45738	0.0512703
$809$	30.5125	1.07276	0.536380	−	0.843976i	$-0.319791\pi$
$809$	30.5125	1.07276	0.536380	+	0.843976i	$0.319791\pi$
$810$	−6.89342	−0.242210
$811$	−25.9853	−0.912468	−0.456234	−	0.889860i	$-0.650802\pi$
$811$	−25.9853	−0.912468	−0.456234	+	0.889860i	$0.650802\pi$
$812$	−9.74058	−0.341827
$813$	−4.39583	−0.154169
$814$	1.76958	0.0620237
$815$	−12.5927	−0.441104
$816$	2.53037	0.0885806
$817$	−0.369233	−0.0129178
$818$	4.85546	0.169767
$819$	22.7214	0.793949
$820$	8.81403	0.307799
$821$	−49.9494	−1.74324	−0.871622	−	0.490178i	$-0.836932\pi$
$821$	−49.9494	−1.74324	−0.871622	+	0.490178i	$0.836932\pi$
$822$	−6.75544	−0.235623
$823$	46.5740	1.62347	0.811734	−	0.584028i	$-0.198524\pi$
$823$	46.5740	1.62347	0.811734	+	0.584028i	$0.198524\pi$
$824$	14.7720	0.514605
$825$	0.490398	0.0170735
$826$	7.63950	0.265812
$827$	−27.6061	−0.959957	−0.479978	−	0.877280i	$-0.659356\pi$
$827$	−27.6061	−0.959957	−0.479978	+	0.877280i	$0.659356\pi$
$828$	2.41784	0.0840259
$829$	33.7873	1.17348	0.586741	−	0.809775i	$-0.300411\pi$
$829$	33.7873	1.17348	0.586741	+	0.809775i	$0.300411\pi$
$830$	−8.30735	−0.288352
$831$	9.97718	0.346105
$832$	6.36293	0.220595
$833$	27.4785	0.952075
$834$	−9.94821	−0.344478
$835$	4.06251	0.140589
$836$	0.102375	0.00354072
$837$	24.7665	0.856057
$838$	24.6106	0.850160
$839$	34.1984	1.18066	0.590330	−	0.807162i	$-0.298998\pi$
$839$	34.1984	1.18066	0.590330	+	0.807162i	$0.298998\pi$
$840$	−0.634591	−0.0218955
$841$	27.6603	0.953803
$842$	0.0137291	0.000473135 0
$843$	7.67059	0.264189
$844$	4.05149	0.139458
$845$	−27.4869	−0.945577
$846$	25.6253	0.881018
$847$	−1.29403	−0.0444635
$848$	−0.175296	−0.00601968
$849$	6.58911	0.226138
$850$	−5.15983	−0.176981
$851$	1.55048	0.0531497
$852$	2.20269	0.0754630
$853$	12.5484	0.429649	0.214825	−	0.976653i	$-0.431082\pi$
$853$	12.5484	0.429649	0.214825	+	0.976653i	$0.431082\pi$
$854$	5.44644	0.186373
$855$	−0.282505	−0.00966147
$856$	−7.17735	−0.245317
$857$	−14.9292	−0.509973	−0.254986	−	0.966945i	$-0.582071\pi$
$857$	−14.9292	−0.509973	−0.254986	+	0.966945i	$0.582071\pi$
$858$	3.12037	0.106528
$859$	−5.89687	−0.201199	−0.100599	−	0.994927i	$-0.532076\pi$
$859$	−5.89687	−0.201199	−0.100599	+	0.994927i	$0.532076\pi$
$860$	−3.60667	−0.122986
$861$	−5.59331	−0.190620
$862$	−8.67738	−0.295553
$863$	−37.4394	−1.27445	−0.637225	−	0.770677i	$-0.719918\pi$
$863$	−37.4394	−1.27445	−0.637225	+	0.770677i	$0.719918\pi$
$864$	2.82445	0.0960898
$865$	−3.57767	−0.121644
$866$	4.15261	0.141111
$867$	−4.71950	−0.160283
$868$	−11.3469	−0.385138
$869$	−3.97702	−0.134911
$870$	3.69137	0.125149
$871$	−65.5692	−2.22173
$872$	6.34131	0.214744
$873$	−25.1079	−0.849774
$874$	0.0896996	0.00303413
$875$	1.29403	0.0437463
$876$	0.490398	0.0165690
$877$	13.4842	0.455329	0.227665	−	0.973740i	$-0.426891\pi$
$877$	13.4842	0.455329	0.227665	+	0.973740i	$0.426891\pi$
$878$	32.8507	1.10866
$879$	12.5337	0.422750
$880$	1.00000	0.0337100
$881$	43.5273	1.46647	0.733237	−	0.679973i	$-0.238009\pi$
$881$	43.5273	1.46647	0.733237	+	0.679973i	$0.238009\pi$
$882$	14.6957	0.494830
$883$	−41.7948	−1.40651	−0.703254	−	0.710938i	$-0.748270\pi$
$883$	−41.7948	−1.40651	−0.703254	+	0.710938i	$0.748270\pi$
$884$	−32.8316	−1.10425
$885$	−2.89513	−0.0973187
$886$	−12.0554	−0.405010
$887$	30.9891	1.04051	0.520256	−	0.854010i	$-0.325836\pi$
$887$	30.9891	1.04051	0.520256	+	0.854010i	$0.325836\pi$
$888$	0.867797	0.0291214
$889$	−22.8691	−0.767006
$890$	−12.1665	−0.407821
$891$	−6.89342	−0.230938
$892$	−4.55712	−0.152584
$893$	0.950675	0.0318131
$894$	8.59795	0.287558
$895$	−3.68139	−0.123055
$896$	−1.29403	−0.0432306
$897$	2.73402	0.0912863
$898$	17.4956	0.583836
$899$	66.0041	2.20136
$900$	−2.75951	−0.0919837
$901$	0.904496	0.0301331
$902$	8.81403	0.293475
$903$	2.28876	0.0761652
$904$	18.9933	0.631709
$905$	−19.5272	−0.649107
$906$	−2.15288	−0.0715247
$907$	−21.0727	−0.699709	−0.349854	−	0.936804i	$-0.613769\pi$
$907$	−21.0727	−0.699709	−0.349854	+	0.936804i	$0.613769\pi$
$908$	8.63098	0.286429
$909$	−4.02165	−0.133390
$910$	8.23384	0.272949
$911$	16.1287	0.534367	0.267184	−	0.963646i	$-0.413907\pi$
$911$	16.1287	0.534367	0.267184	+	0.963646i	$0.413907\pi$
$912$	0.0502045	0.00166244
$913$	−8.30735	−0.274933
$914$	35.7260	1.18171
$915$	−2.06403	−0.0682347
$916$	23.4524	0.774890
$917$	−19.7893	−0.653501
$918$	−14.5737	−0.481003
$919$	−16.8703	−0.556499	−0.278250	−	0.960509i	$-0.589754\pi$
$919$	−16.8703	−0.556499	−0.278250	+	0.960509i	$0.589754\pi$
$920$	0.876186	0.0288870
$921$	−6.49661	−0.214071
$922$	−20.2673	−0.667467
$923$	−28.5800	−0.940722
$924$	−0.634591	−0.0208765
$925$	−1.76958	−0.0581833
$926$	26.9240	0.884776
$927$	−40.7633	−1.33884
$928$	7.52730	0.247096
$929$	9.45580	0.310235	0.155117	−	0.987896i	$-0.450424\pi$
$929$	9.45580	0.310235	0.155117	+	0.987896i	$0.450424\pi$
$930$	4.30011	0.141006
$931$	0.545196	0.0178681
$932$	21.1211	0.691843
$933$	4.71692	0.154425
$934$	20.3630	0.666299
$935$	−5.15983	−0.168744
$936$	−17.5586	−0.573920
$937$	−20.0651	−0.655497	−0.327748	−	0.944765i	$-0.606290\pi$
$937$	−20.0651	−0.655497	−0.327748	+	0.944765i	$0.606290\pi$
$938$	13.3349	0.435399
$939$	−10.6634	−0.347986
$940$	9.28620	0.302882
$941$	−49.9640	−1.62878	−0.814390	−	0.580318i	$-0.802928\pi$
$941$	−49.9640	−1.62878	−0.814390	+	0.580318i	$0.802928\pi$
$942$	−4.13779	−0.134817
$943$	7.72273	0.251487
$944$	−5.90363	−0.192147
$945$	3.65494	0.118895
$946$	−3.60667	−0.117263
$947$	8.82764	0.286860	0.143430	−	0.989660i	$-0.454187\pi$
$947$	8.82764	0.286860	0.143430	+	0.989660i	$0.454187\pi$
$948$	−1.95032	−0.0633435
$949$	−6.36293	−0.206549
$950$	−0.102375	−0.00332149
$951$	−8.85066	−0.287002
$952$	6.67699	0.216402
$953$	−21.3002	−0.689982	−0.344991	−	0.938606i	$-0.612118\pi$
$953$	−21.3002	−0.689982	−0.344991	+	0.938606i	$0.612118\pi$
$954$	0.483730	0.0156613
$955$	−9.68764	−0.313485
$956$	4.84842	0.156809
$957$	3.69137	0.119325
$958$	−41.5094	−1.34111
$959$	−17.8259	−0.575627
$960$	0.490398	0.0158275
$961$	45.8887	1.48028
$962$	−11.2597	−0.363027
$963$	19.8060	0.638239
$964$	24.1006	0.776230
$965$	24.3293	0.783188
$966$	−0.556020	−0.0178896
$967$	−10.2931	−0.331003	−0.165501	−	0.986210i	$-0.552924\pi$
$967$	−10.2931	−0.331003	−0.165501	+	0.986210i	$0.552924\pi$
$968$	1.00000	0.0321412
$969$	−0.259047	−0.00832178
$970$	−9.09868	−0.292141
$971$	43.1675	1.38531	0.692655	−	0.721269i	$-0.256441\pi$
$971$	43.1675	1.38531	0.692655	+	0.721269i	$0.256441\pi$
$972$	−11.8539	−0.380213
$973$	−26.2508	−0.841561
$974$	13.7509	0.440606
$975$	−3.12037	−0.0999317
$976$	−4.20889	−0.134723
$977$	−40.4200	−1.29315	−0.646576	−	0.762850i	$-0.723799\pi$
$977$	−40.4200	−1.29315	−0.646576	+	0.762850i	$0.723799\pi$
$978$	−6.17544	−0.197469
$979$	−12.1665	−0.388842
$980$	5.32548	0.170116
$981$	−17.4989	−0.558697
$982$	7.51969	0.239963
$983$	6.83622	0.218041	0.109021	−	0.994039i	$-0.465229\pi$
$983$	6.83622	0.218041	0.109021	+	0.994039i	$0.465229\pi$
$984$	4.32238	0.137793
$985$	1.15060	0.0366613
$986$	−38.8396	−1.23690
$987$	−5.89294	−0.187574
$988$	−0.651405	−0.0207240
$989$	−3.16011	−0.100486
$990$	−2.75951	−0.0877030
$991$	−24.5889	−0.781093	−0.390546	−	0.920583i	$-0.627714\pi$
$991$	−24.5889	−0.781093	−0.390546	+	0.920583i	$0.627714\pi$
$992$	8.76862	0.278404
$993$	3.54621	0.112536
$994$	5.81233	0.184356
$995$	11.9831	0.379891
$996$	−4.07391	−0.129087
$997$	12.1187	0.383802	0.191901	−	0.981414i	$-0.438535\pi$
$997$	12.1187	0.383802	0.191901	+	0.981414i	$0.438535\pi$
$998$	0.126935	0.00401807
$999$	−4.99809	−0.158132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bg.1.6	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bg.1.6	✓	15	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.490398 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.490398 q^{6} -1.29403 q^{7} +1.00000 q^{8} -2.75951 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.490398 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.490398 q^{6} -1.29403 q^{7} +1.00000 q^{8} -2.75951 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.490398 q^{12} +6.36293 q^{13} -1.29403 q^{14} +0.490398 q^{15} +1.00000 q^{16} -5.15983 q^{17} -2.75951 q^{18} -0.102375 q^{19} -1.00000 q^{20} +0.634591 q^{21} -1.00000 q^{22} -0.876186 q^{23} -0.490398 q^{24} +1.00000 q^{25} +6.36293 q^{26} +2.82445 q^{27} -1.29403 q^{28} +7.52730 q^{29} +0.490398 q^{30} +8.76862 q^{31} +1.00000 q^{32} +0.490398 q^{33} -5.15983 q^{34} +1.29403 q^{35} -2.75951 q^{36} -1.76958 q^{37} -0.102375 q^{38} -3.12037 q^{39} -1.00000 q^{40} -8.81403 q^{41} +0.634591 q^{42} +3.60667 q^{43} -1.00000 q^{44} +2.75951 q^{45} -0.876186 q^{46} -9.28620 q^{47} -0.490398 q^{48} -5.32548 q^{49} +1.00000 q^{50} +2.53037 q^{51} +6.36293 q^{52} -0.175296 q^{53} +2.82445 q^{54} +1.00000 q^{55} -1.29403 q^{56} +0.0502045 q^{57} +7.52730 q^{58} -5.90363 q^{59} +0.490398 q^{60} -4.20889 q^{61} +8.76862 q^{62} +3.57090 q^{63} +1.00000 q^{64} -6.36293 q^{65} +0.490398 q^{66} -10.3049 q^{67} -5.15983 q^{68} +0.429680 q^{69} +1.29403 q^{70} -4.49164 q^{71} -2.75951 q^{72} -1.00000 q^{73} -1.76958 q^{74} -0.490398 q^{75} -0.102375 q^{76} +1.29403 q^{77} -3.12037 q^{78} +3.97702 q^{79} -1.00000 q^{80} +6.89342 q^{81} -8.81403 q^{82} +8.30735 q^{83} +0.634591 q^{84} +5.15983 q^{85} +3.60667 q^{86} -3.69137 q^{87} -1.00000 q^{88} +12.1665 q^{89} +2.75951 q^{90} -8.23384 q^{91} -0.876186 q^{92} -4.30011 q^{93} -9.28620 q^{94} +0.102375 q^{95} -0.490398 q^{96} +9.09868 q^{97} -5.32548 q^{98} +2.75951 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 7 q^{3} + 15 q^{4} - 15 q^{5} + 7 q^{6} + 3 q^{7} + 15 q^{8} + 16 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 7 * q^3 + 15 * q^4 - 15 * q^5 + 7 * q^6 + 3 * q^7 + 15 * q^8 + 16 * q^9	\( 15 q + 15 q^{2} + 7 q^{3} + 15 q^{4} - 15 q^{5} + 7 q^{6} + 3 q^{7} + 15 q^{8} + 16 q^{9} - 15 q^{10} - 15 q^{11} + 7 q^{12} - q^{13} + 3 q^{14} - 7 q^{15} + 15 q^{16} + 2 q^{17} + 16 q^{18} + 23 q^{19} - 15 q^{20} + 20 q^{21} - 15 q^{22} + 7 q^{24} + 15 q^{25} - q^{26} + 19 q^{27} + 3 q^{28} + 23 q^{29} - 7 q^{30} + 9 q^{31} + 15 q^{32} - 7 q^{33} + 2 q^{34} - 3 q^{35} + 16 q^{36} + 11 q^{37} + 23 q^{38} + 7 q^{39} - 15 q^{40} + 27 q^{41} + 20 q^{42} + 7 q^{43} - 15 q^{44} - 16 q^{45} - 18 q^{47} + 7 q^{48} + 16 q^{49} + 15 q^{50} + 21 q^{51} - q^{52} - 19 q^{53} + 19 q^{54} + 15 q^{55} + 3 q^{56} + 11 q^{57} + 23 q^{58} + 2 q^{59} - 7 q^{60} + 31 q^{61} + 9 q^{62} + 20 q^{63} + 15 q^{64} + q^{65} - 7 q^{66} + 49 q^{67} + 2 q^{68} + 33 q^{69} - 3 q^{70} + 32 q^{71} + 16 q^{72} - 15 q^{73} + 11 q^{74} + 7 q^{75} + 23 q^{76} - 3 q^{77} + 7 q^{78} + 36 q^{79} - 15 q^{80} + 23 q^{81} + 27 q^{82} + 33 q^{83} + 20 q^{84} - 2 q^{85} + 7 q^{86} + 29 q^{87} - 15 q^{88} + 6 q^{89} - 16 q^{90} + 33 q^{91} + 20 q^{93} - 18 q^{94} - 23 q^{95} + 7 q^{96} + 30 q^{97} + 16 q^{98} - 16 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 7 * q^3 + 15 * q^4 - 15 * q^5 + 7 * q^6 + 3 * q^7 + 15 * q^8 + 16 * q^9 - 15 * q^10 - 15 * q^11 + 7 * q^12 - q^13 + 3 * q^14 - 7 * q^15 + 15 * q^16 + 2 * q^17 + 16 * q^18 + 23 * q^19 - 15 * q^20 + 20 * q^21 - 15 * q^22 + 7 * q^24 + 15 * q^25 - q^26 + 19 * q^27 + 3 * q^28 + 23 * q^29 - 7 * q^30 + 9 * q^31 + 15 * q^32 - 7 * q^33 + 2 * q^34 - 3 * q^35 + 16 * q^36 + 11 * q^37 + 23 * q^38 + 7 * q^39 - 15 * q^40 + 27 * q^41 + 20 * q^42 + 7 * q^43 - 15 * q^44 - 16 * q^45 - 18 * q^47 + 7 * q^48 + 16 * q^49 + 15 * q^50 + 21 * q^51 - q^52 - 19 * q^53 + 19 * q^54 + 15 * q^55 + 3 * q^56 + 11 * q^57 + 23 * q^58 + 2 * q^59 - 7 * q^60 + 31 * q^61 + 9 * q^62 + 20 * q^63 + 15 * q^64 + q^65 - 7 * q^66 + 49 * q^67 + 2 * q^68 + 33 * q^69 - 3 * q^70 + 32 * q^71 + 16 * q^72 - 15 * q^73 + 11 * q^74 + 7 * q^75 + 23 * q^76 - 3 * q^77 + 7 * q^78 + 36 * q^79 - 15 * q^80 + 23 * q^81 + 27 * q^82 + 33 * q^83 + 20 * q^84 - 2 * q^85 + 7 * q^86 + 29 * q^87 - 15 * q^88 + 6 * q^89 - 16 * q^90 + 33 * q^91 + 20 * q^93 - 18 * q^94 - 23 * q^95 + 7 * q^96 + 30 * q^97 + 16 * q^98 - 16 * q^99

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