LMFDB - Embedded newform 8030.2.a.bc.1.5

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:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 10 x^{9} + 71 x^{8} + 28 x^{7} - 360 x^{6} - 60 x^{5} + 788 x^{4} + 309 x^{3} + \cdots - 95 $ x^11 - 5x^10 - 10x^9 + 71x^8 + 28x^7 - 360x^6 - 60x^5 + 788x^4 + 309x^3 - 632x^2 - 503x - 95
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			1.5
Root			$1.62999$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.62999 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.62999 q^{6} -2.80536 q^{7} -1.00000 q^{8} -0.343117 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.62999 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.62999 q^{6} -2.80536 q^{7} -1.00000 q^{8} -0.343117 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.62999 q^{12} +1.03896 q^{13} +2.80536 q^{14} -1.62999 q^{15} +1.00000 q^{16} +2.39983 q^{17} +0.343117 q^{18} +0.827853 q^{19} +1.00000 q^{20} +4.57272 q^{21} -1.00000 q^{22} -2.07936 q^{23} +1.62999 q^{24} +1.00000 q^{25} -1.03896 q^{26} +5.44926 q^{27} -2.80536 q^{28} -2.69143 q^{29} +1.62999 q^{30} -0.0184575 q^{31} -1.00000 q^{32} -1.62999 q^{33} -2.39983 q^{34} -2.80536 q^{35} -0.343117 q^{36} -1.13872 q^{37} -0.827853 q^{38} -1.69350 q^{39} -1.00000 q^{40} -9.31899 q^{41} -4.57272 q^{42} -0.487235 q^{43} +1.00000 q^{44} -0.343117 q^{45} +2.07936 q^{46} +4.18788 q^{47} -1.62999 q^{48} +0.870036 q^{49} -1.00000 q^{50} -3.91171 q^{51} +1.03896 q^{52} -6.96334 q^{53} -5.44926 q^{54} +1.00000 q^{55} +2.80536 q^{56} -1.34940 q^{57} +2.69143 q^{58} +10.7221 q^{59} -1.62999 q^{60} +4.23633 q^{61} +0.0184575 q^{62} +0.962565 q^{63} +1.00000 q^{64} +1.03896 q^{65} +1.62999 q^{66} -15.2857 q^{67} +2.39983 q^{68} +3.38935 q^{69} +2.80536 q^{70} +6.09341 q^{71} +0.343117 q^{72} -1.00000 q^{73} +1.13872 q^{74} -1.62999 q^{75} +0.827853 q^{76} -2.80536 q^{77} +1.69350 q^{78} +6.97948 q^{79} +1.00000 q^{80} -7.85292 q^{81} +9.31899 q^{82} +15.2789 q^{83} +4.57272 q^{84} +2.39983 q^{85} +0.487235 q^{86} +4.38702 q^{87} -1.00000 q^{88} +9.27703 q^{89} +0.343117 q^{90} -2.91465 q^{91} -2.07936 q^{92} +0.0300857 q^{93} -4.18788 q^{94} +0.827853 q^{95} +1.62999 q^{96} +9.74078 q^{97} -0.870036 q^{98} -0.343117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * 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
$3$	−1.62999	−0.941078	−0.470539	−	0.882379i	$-0.655940\pi$
$3$	−1.62999	−0.941078	−0.470539	+	0.882379i	$0.655940\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.62999	0.665443
$7$	−2.80536	−1.06033	−0.530163	−	0.847896i	$-0.677869\pi$
$7$	−2.80536	−1.06033	−0.530163	+	0.847896i	$0.677869\pi$
$8$	−1.00000	−0.353553
$9$	−0.343117	−0.114372
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.62999	−0.470539
$13$	1.03896	0.288156	0.144078	−	0.989566i	$-0.453978\pi$
$13$	1.03896	0.288156	0.144078	+	0.989566i	$0.453978\pi$
$14$	2.80536	0.749764
$15$	−1.62999	−0.420863
$16$	1.00000	0.250000
$17$	2.39983	0.582044	0.291022	−	0.956716i	$-0.406005\pi$
$17$	2.39983	0.582044	0.291022	+	0.956716i	$0.406005\pi$
$18$	0.343117	0.0808734
$19$	0.827853	0.189923	0.0949613	−	0.995481i	$-0.469727\pi$
$19$	0.827853	0.189923	0.0949613	+	0.995481i	$0.469727\pi$
$20$	1.00000	0.223607
$21$	4.57272	0.997849
$22$	−1.00000	−0.213201
$23$	−2.07936	−0.433577	−0.216788	−	0.976219i	$-0.569558\pi$
$23$	−2.07936	−0.433577	−0.216788	+	0.976219i	$0.569558\pi$
$24$	1.62999	0.332721
$25$	1.00000	0.200000
$26$	−1.03896	−0.203757
$27$	5.44926	1.04871
$28$	−2.80536	−0.530163
$29$	−2.69143	−0.499787	−0.249893	−	0.968273i	$-0.580396\pi$
$29$	−2.69143	−0.499787	−0.249893	+	0.968273i	$0.580396\pi$
$30$	1.62999	0.297595
$31$	−0.0184575	−0.00331507	−0.00165753	−	0.999999i	$-0.500528\pi$
$31$	−0.0184575	−0.00331507	−0.00165753	+	0.999999i	$0.500528\pi$
$32$	−1.00000	−0.176777
$33$	−1.62999	−0.283746
$34$	−2.39983	−0.411567
$35$	−2.80536	−0.474192
$36$	−0.343117	−0.0571861
$37$	−1.13872	−0.187205	−0.0936026	−	0.995610i	$-0.529838\pi$
$37$	−1.13872	−0.187205	−0.0936026	+	0.995610i	$0.529838\pi$
$38$	−0.827853	−0.134296
$39$	−1.69350	−0.271177
$40$	−1.00000	−0.158114
$41$	−9.31899	−1.45538	−0.727691	−	0.685905i	$-0.759407\pi$
$41$	−9.31899	−1.45538	−0.727691	+	0.685905i	$0.759407\pi$
$42$	−4.57272	−0.705586
$43$	−0.487235	−0.0743026	−0.0371513	−	0.999310i	$-0.511828\pi$
$43$	−0.487235	−0.0743026	−0.0371513	+	0.999310i	$0.511828\pi$
$44$	1.00000	0.150756
$45$	−0.343117	−0.0511488
$46$	2.07936	0.306585
$47$	4.18788	0.610865	0.305433	−	0.952214i	$-0.401199\pi$
$47$	4.18788	0.610865	0.305433	+	0.952214i	$0.401199\pi$
$48$	−1.62999	−0.235269
$49$	0.870036	0.124291
$50$	−1.00000	−0.141421
$51$	−3.91171	−0.547749
$52$	1.03896	0.144078
$53$	−6.96334	−0.956488	−0.478244	−	0.878227i	$-0.658727\pi$
$53$	−6.96334	−0.956488	−0.478244	+	0.878227i	$0.658727\pi$
$54$	−5.44926	−0.741551
$55$	1.00000	0.134840
$56$	2.80536	0.374882
$57$	−1.34940	−0.178732
$58$	2.69143	0.353403
$59$	10.7221	1.39590	0.697948	−	0.716148i	$-0.254097\pi$
$59$	10.7221	1.39590	0.697948	+	0.716148i	$0.254097\pi$
$60$	−1.62999	−0.210431
$61$	4.23633	0.542406	0.271203	−	0.962522i	$-0.412578\pi$
$61$	4.23633	0.542406	0.271203	+	0.962522i	$0.412578\pi$
$62$	0.0184575	0.00234411
$63$	0.962565	0.121272
$64$	1.00000	0.125000
$65$	1.03896	0.128867
$66$	1.62999	0.200638
$67$	−15.2857	−1.86744	−0.933721	−	0.358000i	$-0.883459\pi$
$67$	−15.2857	−1.86744	−0.933721	+	0.358000i	$0.883459\pi$
$68$	2.39983	0.291022
$69$	3.38935	0.408029
$70$	2.80536	0.335304
$71$	6.09341	0.723155	0.361578	−	0.932342i	$-0.382238\pi$
$71$	6.09341	0.723155	0.361578	+	0.932342i	$0.382238\pi$
$72$	0.343117	0.0404367
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	1.13872	0.132374
$75$	−1.62999	−0.188216
$76$	0.827853	0.0949613
$77$	−2.80536	−0.319700
$78$	1.69350	0.191751
$79$	6.97948	0.785252	0.392626	−	0.919698i	$-0.371567\pi$
$79$	6.97948	0.785252	0.392626	+	0.919698i	$0.371567\pi$
$80$	1.00000	0.111803
$81$	−7.85292	−0.872547
$82$	9.31899	1.02911
$83$	15.2789	1.67708	0.838541	−	0.544838i	$-0.183409\pi$
$83$	15.2789	1.67708	0.838541	+	0.544838i	$0.183409\pi$
$84$	4.57272	0.498925
$85$	2.39983	0.260298
$86$	0.487235	0.0525399
$87$	4.38702	0.470338
$88$	−1.00000	−0.106600
$89$	9.27703	0.983363	0.491682	−	0.870775i	$-0.336382\pi$
$89$	9.27703	0.983363	0.491682	+	0.870775i	$0.336382\pi$
$90$	0.343117	0.0361677
$91$	−2.91465	−0.305539
$92$	−2.07936	−0.216788
$93$	0.0300857	0.00311974
$94$	−4.18788	−0.431947
$95$	0.827853	0.0849359
$96$	1.62999	0.166361
$97$	9.74078	0.989026	0.494513	−	0.869170i	$-0.335346\pi$
$97$	9.74078	0.989026	0.494513	+	0.869170i	$0.335346\pi$
$98$	−0.870036	−0.0878869
$99$	−0.343117	−0.0344845
$100$	1.00000	0.100000
$101$	−3.57007	−0.355235	−0.177618	−	0.984100i	$-0.556839\pi$
$101$	−3.57007	−0.355235	−0.177618	+	0.984100i	$0.556839\pi$
$102$	3.91171	0.387317
$103$	0.407672	0.0401691	0.0200846	−	0.999798i	$-0.493606\pi$
$103$	0.407672	0.0401691	0.0200846	+	0.999798i	$0.493606\pi$
$104$	−1.03896	−0.101878
$105$	4.57272	0.446252
$106$	6.96334	0.676339
$107$	−12.4937	−1.20781	−0.603906	−	0.797056i	$-0.706390\pi$
$107$	−12.4937	−1.20781	−0.603906	+	0.797056i	$0.706390\pi$
$108$	5.44926	0.524356
$109$	14.3087	1.37053	0.685264	−	0.728294i	$-0.259687\pi$
$109$	14.3087	1.37053	0.685264	+	0.728294i	$0.259687\pi$
$110$	−1.00000	−0.0953463
$111$	1.85612	0.176175
$112$	−2.80536	−0.265081
$113$	−9.75578	−0.917747	−0.458873	−	0.888502i	$-0.651747\pi$
$113$	−9.75578	−0.917747	−0.458873	+	0.888502i	$0.651747\pi$
$114$	1.34940	0.126383
$115$	−2.07936	−0.193901
$116$	−2.69143	−0.249893
$117$	−0.356484	−0.0329570
$118$	−10.7221	−0.987048
$119$	−6.73238	−0.617156
$120$	1.62999	0.148797
$121$	1.00000	0.0909091
$122$	−4.23633	−0.383539
$123$	15.1899	1.36963
$124$	−0.0184575	−0.00165753
$125$	1.00000	0.0894427
$126$	−0.962565	−0.0857521
$127$	−7.11044	−0.630950	−0.315475	−	0.948934i	$-0.602164\pi$
$127$	−7.11044	−0.630950	−0.315475	+	0.948934i	$0.602164\pi$
$128$	−1.00000	−0.0883883
$129$	0.794191	0.0699246
$130$	−1.03896	−0.0911228
$131$	21.4107	1.87067	0.935333	−	0.353769i	$-0.115100\pi$
$131$	21.4107	1.87067	0.935333	+	0.353769i	$0.115100\pi$
$132$	−1.62999	−0.141873
$133$	−2.32242	−0.201380
$134$	15.2857	1.32048
$135$	5.44926	0.468998
$136$	−2.39983	−0.205784
$137$	−13.8697	−1.18497	−0.592483	−	0.805583i	$-0.701852\pi$
$137$	−13.8697	−1.18497	−0.592483	+	0.805583i	$0.701852\pi$
$138$	−3.38935	−0.288520
$139$	4.50120	0.381787	0.190893	−	0.981611i	$-0.438862\pi$
$139$	4.50120	0.381787	0.190893	+	0.981611i	$0.438862\pi$
$140$	−2.80536	−0.237096
$141$	−6.82623	−0.574872
$142$	−6.09341	−0.511348
$143$	1.03896	0.0868822
$144$	−0.343117	−0.0285931
$145$	−2.69143	−0.223511
$146$	1.00000	0.0827606
$147$	−1.41815	−0.116967
$148$	−1.13872	−0.0936026
$149$	3.60119	0.295021	0.147510	−	0.989061i	$-0.452874\pi$
$149$	3.60119	0.295021	0.147510	+	0.989061i	$0.452874\pi$
$150$	1.62999	0.133089
$151$	12.5261	1.01936	0.509679	−	0.860365i	$-0.329764\pi$
$151$	12.5261	1.01936	0.509679	+	0.860365i	$0.329764\pi$
$152$	−0.827853	−0.0671478
$153$	−0.823421	−0.0665697
$154$	2.80536	0.226062
$155$	−0.0184575	−0.00148254
$156$	−1.69350	−0.135588
$157$	−13.4188	−1.07094	−0.535470	−	0.844554i	$-0.679866\pi$
$157$	−13.4188	−1.07094	−0.535470	+	0.844554i	$0.679866\pi$
$158$	−6.97948	−0.555257
$159$	11.3502	0.900130
$160$	−1.00000	−0.0790569
$161$	5.83335	0.459733
$162$	7.85292	0.616984
$163$	−8.40369	−0.658228	−0.329114	−	0.944290i	$-0.606750\pi$
$163$	−8.40369	−0.658228	−0.329114	+	0.944290i	$0.606750\pi$
$164$	−9.31899	−0.727691
$165$	−1.62999	−0.126895
$166$	−15.2789	−1.18588
$167$	−7.40498	−0.573015	−0.286507	−	0.958078i	$-0.592494\pi$
$167$	−7.40498	−0.573015	−0.286507	+	0.958078i	$0.592494\pi$
$168$	−4.57272	−0.352793
$169$	−11.9206	−0.916966
$170$	−2.39983	−0.184058
$171$	−0.284050	−0.0217219
$172$	−0.487235	−0.0371513
$173$	−8.07299	−0.613778	−0.306889	−	0.951745i	$-0.599288\pi$
$173$	−8.07299	−0.613778	−0.306889	+	0.951745i	$0.599288\pi$
$174$	−4.38702	−0.332580
$175$	−2.80536	−0.212065
$176$	1.00000	0.0753778
$177$	−17.4769	−1.31365
$178$	−9.27703	−0.695343
$179$	−6.68039	−0.499316	−0.249658	−	0.968334i	$-0.580318\pi$
$179$	−6.68039	−0.499316	−0.249658	+	0.968334i	$0.580318\pi$
$180$	−0.343117	−0.0255744
$181$	17.6574	1.31246	0.656231	−	0.754560i	$-0.272150\pi$
$181$	17.6574	1.31246	0.656231	+	0.754560i	$0.272150\pi$
$182$	2.91465	0.216049
$183$	−6.90519	−0.510447
$184$	2.07936	0.153293
$185$	−1.13872	−0.0837207
$186$	−0.0300857	−0.00220599
$187$	2.39983	0.175493
$188$	4.18788	0.305433
$189$	−15.2871	−1.11198
$190$	−0.827853	−0.0600588
$191$	−8.73843	−0.632291	−0.316145	−	0.948711i	$-0.602389\pi$
$191$	−8.73843	−0.632291	−0.316145	+	0.948711i	$0.602389\pi$
$192$	−1.62999	−0.117635
$193$	24.8453	1.78840	0.894200	−	0.447667i	$-0.147745\pi$
$193$	24.8453	1.78840	0.894200	+	0.447667i	$0.147745\pi$
$194$	−9.74078	−0.699347
$195$	−1.69350	−0.121274
$196$	0.870036	0.0621454
$197$	−16.0166	−1.14114	−0.570568	−	0.821251i	$-0.693277\pi$
$197$	−16.0166	−1.14114	−0.570568	+	0.821251i	$0.693277\pi$
$198$	0.343117	0.0243842
$199$	13.4097	0.950588	0.475294	−	0.879827i	$-0.342342\pi$
$199$	13.4097	0.950588	0.475294	+	0.879827i	$0.342342\pi$
$200$	−1.00000	−0.0707107
$201$	24.9156	1.75741
$202$	3.57007	0.251189
$203$	7.55044	0.529937
$204$	−3.91171	−0.273874
$205$	−9.31899	−0.650867
$206$	−0.407672	−0.0284039
$207$	0.713464	0.0495891
$208$	1.03896	0.0720389
$209$	0.827853	0.0572638
$210$	−4.57272	−0.315548
$211$	−15.4861	−1.06611	−0.533055	−	0.846080i	$-0.678956\pi$
$211$	−15.4861	−1.06611	−0.533055	+	0.846080i	$0.678956\pi$
$212$	−6.96334	−0.478244
$213$	−9.93223	−0.680545
$214$	12.4937	0.854052
$215$	−0.487235	−0.0332292
$216$	−5.44926	−0.370775
$217$	0.0517800	0.00351505
$218$	−14.3087	−0.969110
$219$	1.62999	0.110145
$220$	1.00000	0.0674200
$221$	2.49332	0.167719
$222$	−1.85612	−0.124574
$223$	−14.2415	−0.953685	−0.476842	−	0.878989i	$-0.658219\pi$
$223$	−14.2415	−0.953685	−0.476842	+	0.878989i	$0.658219\pi$
$224$	2.80536	0.187441
$225$	−0.343117	−0.0228745
$226$	9.75578	0.648945
$227$	17.1287	1.13687	0.568436	−	0.822728i	$-0.307549\pi$
$227$	17.1287	1.13687	0.568436	+	0.822728i	$0.307549\pi$
$228$	−1.34940	−0.0893660
$229$	−11.1143	−0.734455	−0.367227	−	0.930131i	$-0.619693\pi$
$229$	−11.1143	−0.734455	−0.367227	+	0.930131i	$0.619693\pi$
$230$	2.07936	0.137109
$231$	4.57272	0.300863
$232$	2.69143	0.176701
$233$	−4.14908	−0.271815	−0.135908	−	0.990722i	$-0.543395\pi$
$233$	−4.14908	−0.271815	−0.135908	+	0.990722i	$0.543395\pi$
$234$	0.356484	0.0233041
$235$	4.18788	0.273187
$236$	10.7221	0.697948
$237$	−11.3765	−0.738984
$238$	6.73238	0.436395
$239$	9.56496	0.618706	0.309353	−	0.950947i	$-0.399888\pi$
$239$	9.56496	0.618706	0.309353	+	0.950947i	$0.399888\pi$
$240$	−1.62999	−0.105216
$241$	2.33564	0.150452	0.0752258	−	0.997167i	$-0.476032\pi$
$241$	2.33564	0.150452	0.0752258	+	0.997167i	$0.476032\pi$
$242$	−1.00000	−0.0642824
$243$	−3.54757	−0.227577
$244$	4.23633	0.271203
$245$	0.870036	0.0555846
$246$	−15.1899	−0.968473
$247$	0.860106	0.0547272
$248$	0.0184575	0.00117205
$249$	−24.9046	−1.57827
$250$	−1.00000	−0.0632456
$251$	20.9485	1.32226	0.661129	−	0.750272i	$-0.270078\pi$
$251$	20.9485	1.32226	0.661129	+	0.750272i	$0.270078\pi$
$252$	0.962565	0.0606359
$253$	−2.07936	−0.130728
$254$	7.11044	0.446149
$255$	−3.91171	−0.244961
$256$	1.00000	0.0625000
$257$	3.91726	0.244352	0.122176	−	0.992508i	$-0.461013\pi$
$257$	3.91726	0.244352	0.122176	+	0.992508i	$0.461013\pi$
$258$	−0.794191	−0.0494441
$259$	3.19453	0.198498
$260$	1.03896	0.0644335
$261$	0.923476	0.0571618
$262$	−21.4107	−1.32276
$263$	2.22017	0.136902	0.0684508	−	0.997654i	$-0.478194\pi$
$263$	2.22017	0.136902	0.0684508	+	0.997654i	$0.478194\pi$
$264$	1.62999	0.100319
$265$	−6.96334	−0.427754
$266$	2.32242	0.142397
$267$	−15.1215	−0.925421
$268$	−15.2857	−0.933721
$269$	0.364682	0.0222350	0.0111175	−	0.999938i	$-0.496461\pi$
$269$	0.364682	0.0222350	0.0111175	+	0.999938i	$0.496461\pi$
$270$	−5.44926	−0.331632
$271$	−4.33630	−0.263411	−0.131706	−	0.991289i	$-0.542045\pi$
$271$	−4.33630	−0.263411	−0.131706	+	0.991289i	$0.542045\pi$
$272$	2.39983	0.145511
$273$	4.75087	0.287536
$274$	13.8697	0.837897
$275$	1.00000	0.0603023
$276$	3.38935	0.204015
$277$	−20.9510	−1.25883	−0.629413	−	0.777071i	$-0.716704\pi$
$277$	−20.9510	−1.25883	−0.629413	+	0.777071i	$0.716704\pi$
$278$	−4.50120	−0.269964
$279$	0.00633308	0.000379152 0
$280$	2.80536	0.167652
$281$	−11.4115	−0.680754	−0.340377	−	0.940289i	$-0.610555\pi$
$281$	−11.4115	−0.680754	−0.340377	+	0.940289i	$0.610555\pi$
$282$	6.82623	0.406496
$283$	14.0837	0.837190	0.418595	−	0.908173i	$-0.362523\pi$
$283$	14.0837	0.837190	0.418595	+	0.908173i	$0.362523\pi$
$284$	6.09341	0.361578
$285$	−1.34940	−0.0799313
$286$	−1.03896	−0.0614350
$287$	26.1431	1.54318
$288$	0.343117	0.0202183
$289$	−11.2408	−0.661225
$290$	2.69143	0.158046
$291$	−15.8774	−0.930751
$292$	−1.00000	−0.0585206
$293$	−24.7896	−1.44822	−0.724111	−	0.689684i	$-0.757750\pi$
$293$	−24.7896	−1.44822	−0.724111	+	0.689684i	$0.757750\pi$
$294$	1.41815	0.0827084
$295$	10.7221	0.624264
$296$	1.13872	0.0661870
$297$	5.44926	0.316198
$298$	−3.60119	−0.208611
$299$	−2.16037	−0.124938
$300$	−1.62999	−0.0941078
$301$	1.36687	0.0787850
$302$	−12.5261	−0.720795
$303$	5.81919	0.334304
$304$	0.827853	0.0474806
$305$	4.23633	0.242571
$306$	0.823421	0.0470719
$307$	−17.1446	−0.978493	−0.489247	−	0.872145i	$-0.662728\pi$
$307$	−17.1446	−0.978493	−0.489247	+	0.872145i	$0.662728\pi$
$308$	−2.80536	−0.159850
$309$	−0.664503	−0.0378023
$310$	0.0184575	0.00104832
$311$	31.3745	1.77909	0.889543	−	0.456852i	$-0.151023\pi$
$311$	31.3745	1.77909	0.889543	+	0.456852i	$0.151023\pi$
$312$	1.69350	0.0958755
$313$	14.5767	0.823925	0.411963	−	0.911201i	$-0.364843\pi$
$313$	14.5767	0.823925	0.411963	+	0.911201i	$0.364843\pi$
$314$	13.4188	0.757269
$315$	0.962565	0.0542344
$316$	6.97948	0.392626
$317$	−12.7879	−0.718240	−0.359120	−	0.933291i	$-0.616923\pi$
$317$	−12.7879	−0.718240	−0.359120	+	0.933291i	$0.616923\pi$
$318$	−11.3502	−0.636488
$319$	−2.69143	−0.150691
$320$	1.00000	0.0559017
$321$	20.3647	1.13664
$322$	−5.83335	−0.325080
$323$	1.98670	0.110543
$324$	−7.85292	−0.436273
$325$	1.03896	0.0576311
$326$	8.40369	0.465437
$327$	−23.3232	−1.28977
$328$	9.31899	0.514555
$329$	−11.7485	−0.647716
$330$	1.62999	0.0897283
$331$	−11.2884	−0.620468	−0.310234	−	0.950660i	$-0.600407\pi$
$331$	−11.2884	−0.620468	−0.310234	+	0.950660i	$0.600407\pi$
$332$	15.2789	0.838541
$333$	0.390715	0.0214111
$334$	7.40498	0.405183
$335$	−15.2857	−0.835146
$336$	4.57272	0.249462
$337$	12.4254	0.676856	0.338428	−	0.940992i	$-0.390105\pi$
$337$	12.4254	0.676856	0.338428	+	0.940992i	$0.390105\pi$
$338$	11.9206	0.648393
$339$	15.9019	0.863671
$340$	2.39983	0.130149
$341$	−0.0184575	−0.000999531 0
$342$	0.284050	0.0153597
$343$	17.1967	0.928537
$344$	0.487235	0.0262700
$345$	3.38935	0.182476
$346$	8.07299	0.434006
$347$	−21.4909	−1.15369	−0.576845	−	0.816854i	$-0.695716\pi$
$347$	−21.4909	−1.15369	−0.576845	+	0.816854i	$0.695716\pi$
$348$	4.38702	0.235169
$349$	−18.6092	−0.996127	−0.498063	−	0.867141i	$-0.665955\pi$
$349$	−18.6092	−0.996127	−0.498063	+	0.867141i	$0.665955\pi$
$350$	2.80536	0.149953
$351$	5.66156	0.302192
$352$	−1.00000	−0.0533002
$353$	−16.3515	−0.870303	−0.435151	−	0.900357i	$-0.643305\pi$
$353$	−16.3515	−0.870303	−0.435151	+	0.900357i	$0.643305\pi$
$354$	17.4769	0.928889
$355$	6.09341	0.323405
$356$	9.27703	0.491682
$357$	10.9737	0.580792
$358$	6.68039	0.353069
$359$	−0.405707	−0.0214124	−0.0107062	−	0.999943i	$-0.503408\pi$
$359$	−0.405707	−0.0214124	−0.0107062	+	0.999943i	$0.503408\pi$
$360$	0.343117	0.0180838
$361$	−18.3147	−0.963929
$362$	−17.6574	−0.928051
$363$	−1.62999	−0.0855525
$364$	−2.91465	−0.152769
$365$	−1.00000	−0.0523424
$366$	6.90519	0.360940
$367$	8.35996	0.436386	0.218193	−	0.975906i	$-0.429984\pi$
$367$	8.35996	0.436386	0.218193	+	0.975906i	$0.429984\pi$
$368$	−2.07936	−0.108394
$369$	3.19750	0.166455
$370$	1.13872	0.0591995
$371$	19.5347	1.01419
$372$	0.0300857	0.00155987
$373$	19.2497	0.996713	0.498357	−	0.866972i	$-0.333937\pi$
$373$	19.2497	0.996713	0.498357	+	0.866972i	$0.333937\pi$
$374$	−2.39983	−0.124092
$375$	−1.62999	−0.0841726
$376$	−4.18788	−0.215973
$377$	−2.79629	−0.144016
$378$	15.2871	0.786285
$379$	15.0990	0.775584	0.387792	−	0.921747i	$-0.373238\pi$
$379$	15.0990	0.775584	0.387792	+	0.921747i	$0.373238\pi$
$380$	0.827853	0.0424680
$381$	11.5900	0.593773
$382$	8.73843	0.447097
$383$	−5.93220	−0.303121	−0.151561	−	0.988448i	$-0.548430\pi$
$383$	−5.93220	−0.303121	−0.151561	+	0.988448i	$0.548430\pi$
$384$	1.62999	0.0831803
$385$	−2.80536	−0.142974
$386$	−24.8453	−1.26459
$387$	0.167179	0.00849816
$388$	9.74078	0.494513
$389$	−10.6892	−0.541963	−0.270981	−	0.962585i	$-0.587348\pi$
$389$	−10.6892	−0.541963	−0.270981	+	0.962585i	$0.587348\pi$
$390$	1.69350	0.0857536
$391$	−4.99011	−0.252361
$392$	−0.870036	−0.0439434
$393$	−34.8994	−1.76044
$394$	16.0166	0.806904
$395$	6.97948	0.351176
$396$	−0.343117	−0.0172423
$397$	−24.9302	−1.25121	−0.625606	−	0.780139i	$-0.715148\pi$
$397$	−24.9302	−1.25121	−0.625606	+	0.780139i	$0.715148\pi$
$398$	−13.4097	−0.672167
$399$	3.78554	0.189514
$400$	1.00000	0.0500000
$401$	2.34766	0.117236	0.0586182	−	0.998280i	$-0.481331\pi$
$401$	2.34766	0.117236	0.0586182	+	0.998280i	$0.481331\pi$
$402$	−24.9156	−1.24268
$403$	−0.0191766	−0.000955255 0
$404$	−3.57007	−0.177618
$405$	−7.85292	−0.390215
$406$	−7.55044	−0.374722
$407$	−1.13872	−0.0564445
$408$	3.91171	0.193658
$409$	−4.28995	−0.212124	−0.106062	−	0.994360i	$-0.533824\pi$
$409$	−4.28995	−0.212124	−0.106062	+	0.994360i	$0.533824\pi$
$410$	9.31899	0.460232
$411$	22.6075	1.11514
$412$	0.407672	0.0200846
$413$	−30.0793	−1.48010
$414$	−0.713464	−0.0350648
$415$	15.2789	0.750014
$416$	−1.03896	−0.0509392
$417$	−7.33693	−0.359291
$418$	−0.827853	−0.0404916
$419$	5.68645	0.277801	0.138901	−	0.990306i	$-0.455643\pi$
$419$	5.68645	0.277801	0.138901	+	0.990306i	$0.455643\pi$
$420$	4.57272	0.223126
$421$	26.3072	1.28214	0.641068	−	0.767484i	$-0.278492\pi$
$421$	26.3072	1.28214	0.641068	+	0.767484i	$0.278492\pi$
$422$	15.4861	0.753854
$423$	−1.43693	−0.0698660
$424$	6.96334	0.338170
$425$	2.39983	0.116409
$426$	9.93223	0.481218
$427$	−11.8844	−0.575127
$428$	−12.4937	−0.603906
$429$	−1.69350	−0.0817629
$430$	0.487235	0.0234966
$431$	−23.9045	−1.15144	−0.575718	−	0.817648i	$-0.695278\pi$
$431$	−23.9045	−1.15144	−0.575718	+	0.817648i	$0.695278\pi$
$432$	5.44926	0.262178
$433$	−28.0480	−1.34790	−0.673950	−	0.738777i	$-0.735404\pi$
$433$	−28.0480	−1.34790	−0.673950	+	0.738777i	$0.735404\pi$
$434$	−0.0517800	−0.00248552
$435$	4.38702	0.210342
$436$	14.3087	0.685264
$437$	−1.72141	−0.0823460
$438$	−1.62999	−0.0778842
$439$	−18.0340	−0.860714	−0.430357	−	0.902659i	$-0.641612\pi$
$439$	−18.0340	−0.860714	−0.430357	+	0.902659i	$0.641612\pi$
$440$	−1.00000	−0.0476731
$441$	−0.298524	−0.0142154
$442$	−2.49332	−0.118595
$443$	−11.5903	−0.550672	−0.275336	−	0.961348i	$-0.588789\pi$
$443$	−11.5903	−0.550672	−0.275336	+	0.961348i	$0.588789\pi$
$444$	1.85612	0.0880873
$445$	9.27703	0.439773
$446$	14.2415	0.674357
$447$	−5.86992	−0.277637
$448$	−2.80536	−0.132541
$449$	−9.07449	−0.428252	−0.214126	−	0.976806i	$-0.568690\pi$
$449$	−9.07449	−0.428252	−0.214126	+	0.976806i	$0.568690\pi$
$450$	0.343117	0.0161747
$451$	−9.31899	−0.438814
$452$	−9.75578	−0.458873
$453$	−20.4175	−0.959296
$454$	−17.1287	−0.803889
$455$	−2.91465	−0.136641
$456$	1.34940	0.0631913
$457$	−17.5709	−0.821932	−0.410966	−	0.911651i	$-0.634809\pi$
$457$	−17.5709	−0.821932	−0.410966	+	0.911651i	$0.634809\pi$
$458$	11.1143	0.519338
$459$	13.0773	0.610396
$460$	−2.07936	−0.0969507
$461$	−39.8456	−1.85580	−0.927898	−	0.372835i	$-0.878386\pi$
$461$	−39.8456	−1.85580	−0.927898	+	0.372835i	$0.878386\pi$
$462$	−4.57272	−0.212742
$463$	25.8213	1.20002	0.600009	−	0.799993i	$-0.295164\pi$
$463$	25.8213	1.20002	0.600009	+	0.799993i	$0.295164\pi$
$464$	−2.69143	−0.124947
$465$	0.0300857	0.00139519
$466$	4.14908	0.192202
$467$	−1.44354	−0.0667993	−0.0333996	−	0.999442i	$-0.510633\pi$
$467$	−1.44354	−0.0667993	−0.0333996	+	0.999442i	$0.510633\pi$
$468$	−0.356484	−0.0164785
$469$	42.8818	1.98010
$470$	−4.18788	−0.193173
$471$	21.8726	1.00784
$472$	−10.7221	−0.493524
$473$	−0.487235	−0.0224031
$474$	11.3765	0.522540
$475$	0.827853	0.0379845
$476$	−6.73238	−0.308578
$477$	2.38924	0.109396
$478$	−9.56496	−0.437491
$479$	−5.10272	−0.233149	−0.116575	−	0.993182i	$-0.537191\pi$
$479$	−5.10272	−0.233149	−0.116575	+	0.993182i	$0.537191\pi$
$480$	1.62999	0.0743987
$481$	−1.18309	−0.0539442
$482$	−2.33564	−0.106385
$483$	−9.50833	−0.432644
$484$	1.00000	0.0454545
$485$	9.74078	0.442306
$486$	3.54757	0.160921
$487$	−15.1846	−0.688081	−0.344040	−	0.938955i	$-0.611796\pi$
$487$	−15.1846	−0.688081	−0.344040	+	0.938955i	$0.611796\pi$
$488$	−4.23633	−0.191770
$489$	13.6980	0.619444
$490$	−0.870036	−0.0393042
$491$	−8.20529	−0.370300	−0.185150	−	0.982710i	$-0.559277\pi$
$491$	−8.20529	−0.370300	−0.185150	+	0.982710i	$0.559277\pi$
$492$	15.1899	0.684814
$493$	−6.45898	−0.290898
$494$	−0.860106	−0.0386980
$495$	−0.343117	−0.0154220
$496$	−0.0184575	−0.000828767 0
$497$	−17.0942	−0.766780
$498$	24.9046	1.11600
$499$	−40.2349	−1.80116	−0.900580	−	0.434690i	$-0.856858\pi$
$499$	−40.2349	−1.80116	−0.900580	+	0.434690i	$0.856858\pi$
$500$	1.00000	0.0447214
$501$	12.0701	0.539252
$502$	−20.9485	−0.934977
$503$	33.3189	1.48561	0.742807	−	0.669505i	$-0.233494\pi$
$503$	33.3189	1.48561	0.742807	+	0.669505i	$0.233494\pi$
$504$	−0.962565	−0.0428761
$505$	−3.57007	−0.158866
$506$	2.07936	0.0924389
$507$	19.4305	0.862937
$508$	−7.11044	−0.315475
$509$	27.5676	1.22191	0.610957	−	0.791664i	$-0.290785\pi$
$509$	27.5676	1.22191	0.610957	+	0.791664i	$0.290785\pi$
$510$	3.91171	0.173213
$511$	2.80536	0.124102
$512$	−1.00000	−0.0441942
$513$	4.51119	0.199174
$514$	−3.91726	−0.172783
$515$	0.407672	0.0179642
$516$	0.794191	0.0349623
$517$	4.18788	0.184183
$518$	−3.19453	−0.140360
$519$	13.1589	0.577613
$520$	−1.03896	−0.0455614
$521$	−39.4485	−1.72827	−0.864136	−	0.503259i	$-0.832134\pi$
$521$	−39.4485	−1.72827	−0.864136	+	0.503259i	$0.832134\pi$
$522$	−0.923476	−0.0404195
$523$	−3.50208	−0.153135	−0.0765676	−	0.997064i	$-0.524396\pi$
$523$	−3.50208	−0.153135	−0.0765676	+	0.997064i	$0.524396\pi$
$524$	21.4107	0.935333
$525$	4.57272	0.199570
$526$	−2.22017	−0.0968040
$527$	−0.0442949	−0.00192951
$528$	−1.62999	−0.0709364
$529$	−18.6763	−0.812011
$530$	6.96334	0.302468
$531$	−3.67893	−0.159652
$532$	−2.32242	−0.100690
$533$	−9.68206	−0.419377
$534$	15.1215	0.654372
$535$	−12.4937	−0.540150
$536$	15.2857	0.660241
$537$	10.8890	0.469895
$538$	−0.364682	−0.0157225
$539$	0.870036	0.0374751
$540$	5.44926	0.234499
$541$	−39.3216	−1.69057	−0.845284	−	0.534317i	$-0.820569\pi$
$541$	−39.3216	−1.69057	−0.845284	+	0.534317i	$0.820569\pi$
$542$	4.33630	0.186260
$543$	−28.7814	−1.23513
$544$	−2.39983	−0.102892
$545$	14.3087	0.612919
$546$	−4.75087	−0.203319
$547$	3.59397	0.153667	0.0768336	−	0.997044i	$-0.475519\pi$
$547$	3.59397	0.153667	0.0768336	+	0.997044i	$0.475519\pi$
$548$	−13.8697	−0.592483
$549$	−1.45355	−0.0620362
$550$	−1.00000	−0.0426401
$551$	−2.22811	−0.0949208
$552$	−3.38935	−0.144260
$553$	−19.5799	−0.832623
$554$	20.9510	0.890124
$555$	1.85612	0.0787877
$556$	4.50120	0.190893
$557$	17.9280	0.759636	0.379818	−	0.925061i	$-0.375987\pi$
$557$	17.9280	0.759636	0.379818	+	0.925061i	$0.375987\pi$
$558$	−0.00633308	−0.000268101 0
$559$	−0.506218	−0.0214107
$560$	−2.80536	−0.118548
$561$	−3.91171	−0.165152
$562$	11.4115	0.481366
$563$	26.3835	1.11193	0.555966	−	0.831205i	$-0.312348\pi$
$563$	26.3835	1.11193	0.555966	+	0.831205i	$0.312348\pi$
$564$	−6.82623	−0.287436
$565$	−9.75578	−0.410429
$566$	−14.0837	−0.591983
$567$	22.0303	0.925184
$568$	−6.09341	−0.255674
$569$	15.6943	0.657938	0.328969	−	0.944341i	$-0.393299\pi$
$569$	15.6943	0.657938	0.328969	+	0.944341i	$0.393299\pi$
$570$	1.34940	0.0565200
$571$	−10.1351	−0.424139	−0.212070	−	0.977255i	$-0.568020\pi$
$571$	−10.1351	−0.424139	−0.212070	+	0.977255i	$0.568020\pi$
$572$	1.03896	0.0434411
$573$	14.2436	0.595035
$574$	−26.1431	−1.09119
$575$	−2.07936	−0.0867153
$576$	−0.343117	−0.0142965
$577$	−3.18065	−0.132412	−0.0662062	−	0.997806i	$-0.521089\pi$
$577$	−3.18065	−0.132412	−0.0662062	+	0.997806i	$0.521089\pi$
$578$	11.2408	0.467557
$579$	−40.4976	−1.68302
$580$	−2.69143	−0.111756
$581$	−42.8629	−1.77825
$582$	15.8774	0.658140
$583$	−6.96334	−0.288392
$584$	1.00000	0.0413803
$585$	−0.356484	−0.0147388
$586$	24.7896	1.02405
$587$	−25.8141	−1.06546	−0.532731	−	0.846285i	$-0.678834\pi$
$587$	−25.8141	−1.06546	−0.532731	+	0.846285i	$0.678834\pi$
$588$	−1.41815	−0.0584837
$589$	−0.0152801	−0.000629606 0
$590$	−10.7221	−0.441421
$591$	26.1070	1.07390
$592$	−1.13872	−0.0468013
$593$	13.3970	0.550151	0.275075	−	0.961423i	$-0.411297\pi$
$593$	13.3970	0.550151	0.275075	+	0.961423i	$0.411297\pi$
$594$	−5.44926	−0.223586
$595$	−6.73238	−0.276001
$596$	3.60119	0.147510
$597$	−21.8577	−0.894578
$598$	2.16037	0.0883442
$599$	−6.17150	−0.252160	−0.126080	−	0.992020i	$-0.540240\pi$
$599$	−6.17150	−0.252160	−0.126080	+	0.992020i	$0.540240\pi$
$600$	1.62999	0.0665443
$601$	13.8895	0.566565	0.283282	−	0.959037i	$-0.408577\pi$
$601$	13.8895	0.566565	0.283282	+	0.959037i	$0.408577\pi$
$602$	−1.36687	−0.0557094
$603$	5.24477	0.213584
$604$	12.5261	0.509679
$605$	1.00000	0.0406558
$606$	−5.81919	−0.236389
$607$	23.2900	0.945310	0.472655	−	0.881248i	$-0.343296\pi$
$607$	23.2900	0.945310	0.472655	+	0.881248i	$0.343296\pi$
$608$	−0.827853	−0.0335739
$609$	−12.3072	−0.498712
$610$	−4.23633	−0.171524
$611$	4.35104	0.176024
$612$	−0.823421	−0.0332848
$613$	−11.1227	−0.449242	−0.224621	−	0.974446i	$-0.572114\pi$
$613$	−11.1227	−0.449242	−0.224621	+	0.974446i	$0.572114\pi$
$614$	17.1446	0.691899
$615$	15.1899	0.612516
$616$	2.80536	0.113031
$617$	−24.0718	−0.969095	−0.484547	−	0.874765i	$-0.661016\pi$
$617$	−24.0718	−0.969095	−0.484547	+	0.874765i	$0.661016\pi$
$618$	0.664503	0.0267302
$619$	−38.2656	−1.53802	−0.769012	−	0.639234i	$-0.779252\pi$
$619$	−38.2656	−1.53802	−0.769012	+	0.639234i	$0.779252\pi$
$620$	−0.0184575	−0.000741272 0
$621$	−11.3310	−0.454697
$622$	−31.3745	−1.25800
$623$	−26.0254	−1.04269
$624$	−1.69350	−0.0677942
$625$	1.00000	0.0400000
$626$	−14.5767	−0.582603
$627$	−1.34940	−0.0538897
$628$	−13.4188	−0.535470
$629$	−2.73274	−0.108962
$630$	−0.962565	−0.0383495
$631$	−21.0203	−0.836806	−0.418403	−	0.908261i	$-0.637410\pi$
$631$	−21.0203	−0.836806	−0.418403	+	0.908261i	$0.637410\pi$
$632$	−6.97948	−0.277629
$633$	25.2423	1.00329
$634$	12.7879	0.507873
$635$	−7.11044	−0.282169
$636$	11.3502	0.450065
$637$	0.903932	0.0358151
$638$	2.69143	0.106555
$639$	−2.09075	−0.0827089
$640$	−1.00000	−0.0395285
$641$	−9.12932	−0.360586	−0.180293	−	0.983613i	$-0.557705\pi$
$641$	−9.12932	−0.360586	−0.180293	+	0.983613i	$0.557705\pi$
$642$	−20.3647	−0.803729
$643$	43.9626	1.73372	0.866858	−	0.498555i	$-0.166136\pi$
$643$	43.9626	1.73372	0.866858	+	0.498555i	$0.166136\pi$
$644$	5.83335	0.229866
$645$	0.794191	0.0312712
$646$	−1.98670	−0.0781659
$647$	18.4920	0.726996	0.363498	−	0.931595i	$-0.381582\pi$
$647$	18.4920	0.726996	0.363498	+	0.931595i	$0.381582\pi$
$648$	7.85292	0.308492
$649$	10.7221	0.420878
$650$	−1.03896	−0.0407513
$651$	−0.0844011	−0.00330794
$652$	−8.40369	−0.329114
$653$	−6.00141	−0.234853	−0.117427	−	0.993082i	$-0.537464\pi$
$653$	−6.00141	−0.234853	−0.117427	+	0.993082i	$0.537464\pi$
$654$	23.3232	0.912008
$655$	21.4107	0.836587
$656$	−9.31899	−0.363846
$657$	0.343117	0.0133863
$658$	11.7485	0.458005
$659$	−0.0268917	−0.00104755	−0.000523775	−	1.00000i	$-0.500167\pi$
$659$	−0.0268917	−0.00104755	−0.000523775		1.00000i	$0.500167\pi$
$660$	−1.62999	−0.0634475
$661$	4.69924	0.182779	0.0913896	−	0.995815i	$-0.470869\pi$
$661$	4.69924	0.182779	0.0913896	+	0.995815i	$0.470869\pi$
$662$	11.2884	0.438737
$663$	−4.06411	−0.157837
$664$	−15.2789	−0.592938
$665$	−2.32242	−0.0900598
$666$	−0.390715	−0.0151399
$667$	5.59646	0.216696
$668$	−7.40498	−0.286507
$669$	23.2136	0.897491
$670$	15.2857	0.590537
$671$	4.23633	0.163542
$672$	−4.57272	−0.176396
$673$	23.3789	0.901190	0.450595	−	0.892728i	$-0.351212\pi$
$673$	23.3789	0.901190	0.450595	+	0.892728i	$0.351212\pi$
$674$	−12.4254	−0.478609
$675$	5.44926	0.209742
$676$	−11.9206	−0.458483
$677$	8.73337	0.335651	0.167825	−	0.985817i	$-0.446326\pi$
$677$	8.73337	0.335651	0.167825	+	0.985817i	$0.446326\pi$
$678$	−15.9019	−0.610708
$679$	−27.3264	−1.04869
$680$	−2.39983	−0.0920292
$681$	−27.9197	−1.06988
$682$	0.0184575	0.000706775 0
$683$	−47.8024	−1.82911	−0.914555	−	0.404462i	$-0.867459\pi$
$683$	−47.8024	−1.82911	−0.914555	+	0.404462i	$0.867459\pi$
$684$	−0.284050	−0.0108609
$685$	−13.8697	−0.529933
$686$	−17.1967	−0.656575
$687$	18.1163	0.691179
$688$	−0.487235	−0.0185757
$689$	−7.23463	−0.275617
$690$	−3.38935	−0.129030
$691$	−13.2431	−0.503793	−0.251896	−	0.967754i	$-0.581054\pi$
$691$	−13.2431	−0.503793	−0.251896	+	0.967754i	$0.581054\pi$
$692$	−8.07299	−0.306889
$693$	0.962565	0.0365648
$694$	21.4909	0.815782
$695$	4.50120	0.170740
$696$	−4.38702	−0.166290
$697$	−22.3640	−0.847096
$698$	18.6092	0.704368
$699$	6.76297	0.255799
$700$	−2.80536	−0.106033
$701$	−5.16088	−0.194924	−0.0974619	−	0.995239i	$-0.531072\pi$
$701$	−5.16088	−0.194924	−0.0974619	+	0.995239i	$0.531072\pi$
$702$	−5.66156	−0.213682
$703$	−0.942697	−0.0355545
$704$	1.00000	0.0376889
$705$	−6.82623	−0.257091
$706$	16.3515	0.615397
$707$	10.0153	0.376665
$708$	−17.4769	−0.656823
$709$	34.1571	1.28280	0.641399	−	0.767207i	$-0.278354\pi$
$709$	34.1571	1.28280	0.641399	+	0.767207i	$0.278354\pi$
$710$	−6.09341	−0.228682
$711$	−2.39477	−0.0898111
$712$	−9.27703	−0.347671
$713$	0.0383798	0.00143734
$714$	−10.9737	−0.410682
$715$	1.03896	0.0388549
$716$	−6.68039	−0.249658
$717$	−15.5908	−0.582251
$718$	0.405707	0.0151408
$719$	−45.8912	−1.71145	−0.855727	−	0.517427i	$-0.826890\pi$
$719$	−45.8912	−1.71145	−0.855727	+	0.517427i	$0.826890\pi$
$720$	−0.343117	−0.0127872
$721$	−1.14367	−0.0425924
$722$	18.3147	0.681601
$723$	−3.80708	−0.141587
$724$	17.6574	0.656231
$725$	−2.69143	−0.0999574
$726$	1.62999	0.0604948
$727$	−16.8443	−0.624722	−0.312361	−	0.949964i	$-0.601120\pi$
$727$	−16.8443	−0.624722	−0.312361	+	0.949964i	$0.601120\pi$
$728$	2.91465	0.108024
$729$	29.3413	1.08671
$730$	1.00000	0.0370117
$731$	−1.16928	−0.0432474
$732$	−6.90519	−0.255223
$733$	−2.42616	−0.0896123	−0.0448061	−	0.998996i	$-0.514267\pi$
$733$	−2.42616	−0.0896123	−0.0448061	+	0.998996i	$0.514267\pi$
$734$	−8.35996	−0.308572
$735$	−1.41815	−0.0523094
$736$	2.07936	0.0766463
$737$	−15.2857	−0.563055
$738$	−3.19750	−0.117702
$739$	−30.2547	−1.11294	−0.556469	−	0.830869i	$-0.687844\pi$
$739$	−30.2547	−1.11294	−0.556469	+	0.830869i	$0.687844\pi$
$740$	−1.13872	−0.0418603
$741$	−1.40197	−0.0515026
$742$	−19.5347	−0.717140
$743$	−32.4913	−1.19199	−0.595995	−	0.802988i	$-0.703242\pi$
$743$	−32.4913	−1.19199	−0.595995	+	0.802988i	$0.703242\pi$
$744$	−0.0300857	−0.00110299
$745$	3.60119	0.131937
$746$	−19.2497	−0.704783
$747$	−5.24246	−0.191812
$748$	2.39983	0.0877464
$749$	35.0493	1.28067
$750$	1.62999	0.0595190
$751$	−20.3257	−0.741696	−0.370848	−	0.928694i	$-0.620933\pi$
$751$	−20.3257	−0.741696	−0.370848	+	0.928694i	$0.620933\pi$
$752$	4.18788	0.152716
$753$	−34.1459	−1.24435
$754$	2.79629	0.101835
$755$	12.5261	0.455871
$756$	−15.2871	−0.555988
$757$	5.62380	0.204400	0.102200	−	0.994764i	$-0.467412\pi$
$757$	5.62380	0.204400	0.102200	+	0.994764i	$0.467412\pi$
$758$	−15.0990	−0.548420
$759$	3.38935	0.123026
$760$	−0.827853	−0.0300294
$761$	−29.0554	−1.05326	−0.526629	−	0.850095i	$-0.676544\pi$
$761$	−29.0554	−1.05326	−0.526629	+	0.850095i	$0.676544\pi$
$762$	−11.5900	−0.419861
$763$	−40.1411	−1.45321
$764$	−8.73843	−0.316145
$765$	−0.823421	−0.0297709
$766$	5.93220	0.214339
$767$	11.1398	0.402235
$768$	−1.62999	−0.0588174
$769$	−33.7582	−1.21735	−0.608676	−	0.793419i	$-0.708299\pi$
$769$	−33.7582	−1.21735	−0.608676	+	0.793419i	$0.708299\pi$
$770$	2.80536	0.101098
$771$	−6.38511	−0.229954
$772$	24.8453	0.894200
$773$	33.2871	1.19726	0.598628	−	0.801027i	$-0.295713\pi$
$773$	33.2871	1.19726	0.598628	+	0.801027i	$0.295713\pi$
$774$	−0.167179	−0.00600911
$775$	−0.0184575	−0.000663014 0
$776$	−9.74078	−0.349673
$777$	−5.20707	−0.186803
$778$	10.6892	0.383226
$779$	−7.71476	−0.276410
$780$	−1.69350	−0.0606370
$781$	6.09341	0.218040
$782$	4.99011	0.178446
$783$	−14.6663	−0.524132
$784$	0.870036	0.0310727
$785$	−13.4188	−0.478939
$786$	34.8994	1.24482
$787$	−16.3762	−0.583748	−0.291874	−	0.956457i	$-0.594279\pi$
$787$	−16.3762	−0.583748	−0.291874	+	0.956457i	$0.594279\pi$
$788$	−16.0166	−0.570568
$789$	−3.61887	−0.128835
$790$	−6.97948	−0.248319
$791$	27.3685	0.973111
$792$	0.343117	0.0121921
$793$	4.40137	0.156297
$794$	24.9302	0.884740
$795$	11.3502	0.402550
$796$	13.4097	0.475294
$797$	−1.53073	−0.0542213	−0.0271106	−	0.999632i	$-0.508631\pi$
$797$	−1.53073	−0.0542213	−0.0271106	+	0.999632i	$0.508631\pi$
$798$	−3.78554	−0.134007
$799$	10.0502	0.355550
$800$	−1.00000	−0.0353553
$801$	−3.18310	−0.112469
$802$	−2.34766	−0.0828987
$803$	−1.00000	−0.0352892
$804$	24.9156	0.878705
$805$	5.83335	0.205599
$806$	0.0191766	0.000675467 0
$807$	−0.594429	−0.0209249
$808$	3.57007	0.125595
$809$	24.2814	0.853687	0.426844	−	0.904325i	$-0.359625\pi$
$809$	24.2814	0.853687	0.426844	+	0.904325i	$0.359625\pi$
$810$	7.85292	0.275924
$811$	−14.8828	−0.522605	−0.261302	−	0.965257i	$-0.584152\pi$
$811$	−14.8828	−0.522605	−0.261302	+	0.965257i	$0.584152\pi$
$812$	7.55044	0.264968
$813$	7.06814	0.247891
$814$	1.13872	0.0399123
$815$	−8.40369	−0.294368
$816$	−3.91171	−0.136937
$817$	−0.403359	−0.0141117
$818$	4.28995	0.149995
$819$	1.00007	0.0349452
$820$	−9.31899	−0.325433
$821$	5.32438	0.185822	0.0929111	−	0.995674i	$-0.470383\pi$
$821$	5.32438	0.185822	0.0929111	+	0.995674i	$0.470383\pi$
$822$	−22.6075	−0.788527
$823$	−13.1505	−0.458397	−0.229198	−	0.973380i	$-0.573610\pi$
$823$	−13.1505	−0.458397	−0.229198	+	0.973380i	$0.573610\pi$
$824$	−0.407672	−0.0142019
$825$	−1.62999	−0.0567491
$826$	30.0793	1.04659
$827$	−10.7242	−0.372916	−0.186458	−	0.982463i	$-0.559701\pi$
$827$	−10.7242	−0.372916	−0.186458	+	0.982463i	$0.559701\pi$
$828$	0.713464	0.0247946
$829$	−52.9646	−1.83954	−0.919768	−	0.392461i	$-0.871624\pi$
$829$	−52.9646	−1.83954	−0.919768	+	0.392461i	$0.871624\pi$
$830$	−15.2789	−0.530340
$831$	34.1501	1.18465
$832$	1.03896	0.0360194
$833$	2.08794	0.0723427
$834$	7.33693	0.254057
$835$	−7.40498	−0.256260
$836$	0.827853	0.0286319
$837$	−0.100580	−0.00347655
$838$	−5.68645	−0.196435
$839$	29.3304	1.01260	0.506299	−	0.862358i	$-0.331013\pi$
$839$	29.3304	1.01260	0.506299	+	0.862358i	$0.331013\pi$
$840$	−4.57272	−0.157774
$841$	−21.7562	−0.750213
$842$	−26.3072	−0.906607
$843$	18.6007	0.640643
$844$	−15.4861	−0.533055
$845$	−11.9206	−0.410080
$846$	1.43693	0.0494028
$847$	−2.80536	−0.0963933
$848$	−6.96334	−0.239122
$849$	−22.9564	−0.787862
$850$	−2.39983	−0.0823134
$851$	2.36782	0.0811678
$852$	−9.93223	−0.340273
$853$	3.30227	0.113068	0.0565338	−	0.998401i	$-0.481995\pi$
$853$	3.30227	0.113068	0.0565338	+	0.998401i	$0.481995\pi$
$854$	11.8844	0.406676
$855$	−0.284050	−0.00971431
$856$	12.4937	0.427026
$857$	11.9301	0.407524	0.203762	−	0.979020i	$-0.434683\pi$
$857$	11.9301	0.407524	0.203762	+	0.979020i	$0.434683\pi$
$858$	1.69350	0.0578151
$859$	−42.3720	−1.44571	−0.722857	−	0.690998i	$-0.757171\pi$
$859$	−42.3720	−1.44571	−0.722857	+	0.690998i	$0.757171\pi$
$860$	−0.487235	−0.0166146
$861$	−42.6131	−1.45225
$862$	23.9045	0.814189
$863$	−13.9498	−0.474858	−0.237429	−	0.971405i	$-0.576305\pi$
$863$	−13.9498	−0.474858	−0.237429	+	0.971405i	$0.576305\pi$
$864$	−5.44926	−0.185388
$865$	−8.07299	−0.274490
$866$	28.0480	0.953109
$867$	18.3225	0.622264
$868$	0.0517800	0.00175753
$869$	6.97948	0.236762
$870$	−4.38702	−0.148734
$871$	−15.8812	−0.538114
$872$	−14.3087	−0.484555
$873$	−3.34222	−0.113117
$874$	1.72141	0.0582274
$875$	−2.80536	−0.0948384
$876$	1.62999	0.0550724
$877$	−52.1672	−1.76156	−0.880781	−	0.473523i	$-0.842982\pi$
$877$	−52.1672	−1.76156	−0.880781	+	0.473523i	$0.842982\pi$
$878$	18.0340	0.608616
$879$	40.4068	1.36289
$880$	1.00000	0.0337100
$881$	20.1391	0.678504	0.339252	−	0.940695i	$-0.389826\pi$
$881$	20.1391	0.678504	0.339252	+	0.940695i	$0.389826\pi$
$882$	0.298524	0.0100518
$883$	−12.6455	−0.425554	−0.212777	−	0.977101i	$-0.568251\pi$
$883$	−12.6455	−0.425554	−0.212777	+	0.977101i	$0.568251\pi$
$884$	2.49332	0.0838596
$885$	−17.4769	−0.587481
$886$	11.5903	0.389384
$887$	2.24997	0.0755467	0.0377734	−	0.999286i	$-0.487974\pi$
$887$	2.24997	0.0755467	0.0377734	+	0.999286i	$0.487974\pi$
$888$	−1.85612	−0.0622871
$889$	19.9473	0.669012
$890$	−9.27703	−0.310967
$891$	−7.85292	−0.263083
$892$	−14.2415	−0.476842
$893$	3.46695	0.116017
$894$	5.86992	0.196319
$895$	−6.68039	−0.223301
$896$	2.80536	0.0937204
$897$	3.52140	0.117576
$898$	9.07449	0.302820
$899$	0.0496772	0.00165683
$900$	−0.343117	−0.0114372
$901$	−16.7108	−0.556718
$902$	9.31899	0.310289
$903$	−2.22799	−0.0741428
$904$	9.75578	0.324472
$905$	17.6574	0.586951
$906$	20.4175	0.678324
$907$	−48.1665	−1.59934	−0.799671	−	0.600438i	$-0.794993\pi$
$907$	−48.1665	−1.59934	−0.799671	+	0.600438i	$0.794993\pi$
$908$	17.1287	0.568436
$909$	1.22495	0.0406290
$910$	2.91465	0.0966198
$911$	46.7652	1.54940	0.774700	−	0.632330i	$-0.217901\pi$
$911$	46.7652	1.54940	0.774700	+	0.632330i	$0.217901\pi$
$912$	−1.34940	−0.0446830
$913$	15.2789	0.505659
$914$	17.5709	0.581194
$915$	−6.90519	−0.228279
$916$	−11.1143	−0.367227
$917$	−60.0648	−1.98352
$918$	−13.0773	−0.431615
$919$	9.65186	0.318385	0.159193	−	0.987248i	$-0.449111\pi$
$919$	9.65186	0.318385	0.159193	+	0.987248i	$0.449111\pi$
$920$	2.07936	0.0685545
$921$	27.9456	0.920839
$922$	39.8456	1.31225
$923$	6.33081	0.208381
$924$	4.57272	0.150431
$925$	−1.13872	−0.0374410
$926$	−25.8213	−0.848541
$927$	−0.139879	−0.00459423
$928$	2.69143	0.0883507
$929$	−34.5222	−1.13264	−0.566318	−	0.824187i	$-0.691632\pi$
$929$	−34.5222	−1.13264	−0.566318	+	0.824187i	$0.691632\pi$
$930$	−0.0300857	−0.000986548 0
$931$	0.720262	0.0236056
$932$	−4.14908	−0.135908
$933$	−51.1403	−1.67426
$934$	1.44354	0.0472342
$935$	2.39983	0.0784828
$936$	0.356484	0.0116521
$937$	−58.3190	−1.90520	−0.952600	−	0.304225i	$-0.901602\pi$
$937$	−58.3190	−1.90520	−0.952600	+	0.304225i	$0.901602\pi$
$938$	−42.8818	−1.40014
$939$	−23.7600	−0.775378
$940$	4.18788	0.136594
$941$	−48.9672	−1.59629	−0.798143	−	0.602468i	$-0.794184\pi$
$941$	−48.9672	−1.59629	−0.798143	+	0.602468i	$0.794184\pi$
$942$	−21.8726	−0.712649
$943$	19.3776	0.631020
$944$	10.7221	0.348974
$945$	−15.2871	−0.497291
$946$	0.487235	0.0158414
$947$	−38.0664	−1.23699	−0.618496	−	0.785788i	$-0.712258\pi$
$947$	−38.0664	−1.23699	−0.618496	+	0.785788i	$0.712258\pi$
$948$	−11.3765	−0.369492
$949$	−1.03896	−0.0337261
$950$	−0.827853	−0.0268591
$951$	20.8442	0.675920
$952$	6.73238	0.218198
$953$	8.21341	0.266058	0.133029	−	0.991112i	$-0.457530\pi$
$953$	8.21341	0.266058	0.133029	+	0.991112i	$0.457530\pi$
$954$	−2.38924	−0.0773544
$955$	−8.73843	−0.282769
$956$	9.56496	0.309353
$957$	4.38702	0.141812
$958$	5.10272	0.164862
$959$	38.9094	1.25645
$960$	−1.62999	−0.0526079
$961$	−30.9997	−0.999989
$962$	1.18309	0.0381443
$963$	4.28680	0.138140
$964$	2.33564	0.0752258
$965$	24.8453	0.799797
$966$	9.50833	0.305926
$967$	−6.46712	−0.207969	−0.103984	−	0.994579i	$-0.533159\pi$
$967$	−6.46712	−0.207969	−0.103984	+	0.994579i	$0.533159\pi$
$968$	−1.00000	−0.0321412
$969$	−3.23832	−0.104030
$970$	−9.74078	−0.312757
$971$	51.4443	1.65093	0.825463	−	0.564457i	$-0.190914\pi$
$971$	51.4443	1.65093	0.825463	+	0.564457i	$0.190914\pi$
$972$	−3.54757	−0.113788
$973$	−12.6275	−0.404819
$974$	15.1846	0.486547
$975$	−1.69350	−0.0542354
$976$	4.23633	0.135602
$977$	−11.2062	−0.358517	−0.179258	−	0.983802i	$-0.557370\pi$
$977$	−11.2062	−0.358517	−0.179258	+	0.983802i	$0.557370\pi$
$978$	−13.6980	−0.438013
$979$	9.27703	0.296495
$980$	0.870036	0.0277923
$981$	−4.90957	−0.156750
$982$	8.20529	0.261841
$983$	−12.0187	−0.383336	−0.191668	−	0.981460i	$-0.561390\pi$
$983$	−12.0187	−0.383336	−0.191668	+	0.981460i	$0.561390\pi$
$984$	−15.1899	−0.484237
$985$	−16.0166	−0.510331
$986$	6.45898	0.205696
$987$	19.1500	0.609551
$988$	0.860106	0.0273636
$989$	1.01314	0.0322159
$990$	0.343117	0.0109050
$991$	15.9911	0.507973	0.253987	−	0.967208i	$-0.418258\pi$
$991$	15.9911	0.507973	0.253987	+	0.967208i	$0.418258\pi$
$992$	0.0184575	0.000586027 0
$993$	18.4001	0.583909
$994$	17.0942	0.542195
$995$	13.4097	0.425116
$996$	−24.9046	−0.789133
$997$	−17.3825	−0.550509	−0.275255	−	0.961371i	$-0.588762\pi$
$997$	−17.3825	−0.550509	−0.275255	+	0.961371i	$0.588762\pi$
$998$	40.2349	1.27361
$999$	−6.20521	−0.196324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bc.1.5	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bc.1.5	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.62999 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.62999 q^{6} -2.80536 q^{7} -1.00000 q^{8} -0.343117 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.62999 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.62999 q^{6} -2.80536 q^{7} -1.00000 q^{8} -0.343117 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.62999 q^{12} +1.03896 q^{13} +2.80536 q^{14} -1.62999 q^{15} +1.00000 q^{16} +2.39983 q^{17} +0.343117 q^{18} +0.827853 q^{19} +1.00000 q^{20} +4.57272 q^{21} -1.00000 q^{22} -2.07936 q^{23} +1.62999 q^{24} +1.00000 q^{25} -1.03896 q^{26} +5.44926 q^{27} -2.80536 q^{28} -2.69143 q^{29} +1.62999 q^{30} -0.0184575 q^{31} -1.00000 q^{32} -1.62999 q^{33} -2.39983 q^{34} -2.80536 q^{35} -0.343117 q^{36} -1.13872 q^{37} -0.827853 q^{38} -1.69350 q^{39} -1.00000 q^{40} -9.31899 q^{41} -4.57272 q^{42} -0.487235 q^{43} +1.00000 q^{44} -0.343117 q^{45} +2.07936 q^{46} +4.18788 q^{47} -1.62999 q^{48} +0.870036 q^{49} -1.00000 q^{50} -3.91171 q^{51} +1.03896 q^{52} -6.96334 q^{53} -5.44926 q^{54} +1.00000 q^{55} +2.80536 q^{56} -1.34940 q^{57} +2.69143 q^{58} +10.7221 q^{59} -1.62999 q^{60} +4.23633 q^{61} +0.0184575 q^{62} +0.962565 q^{63} +1.00000 q^{64} +1.03896 q^{65} +1.62999 q^{66} -15.2857 q^{67} +2.39983 q^{68} +3.38935 q^{69} +2.80536 q^{70} +6.09341 q^{71} +0.343117 q^{72} -1.00000 q^{73} +1.13872 q^{74} -1.62999 q^{75} +0.827853 q^{76} -2.80536 q^{77} +1.69350 q^{78} +6.97948 q^{79} +1.00000 q^{80} -7.85292 q^{81} +9.31899 q^{82} +15.2789 q^{83} +4.57272 q^{84} +2.39983 q^{85} +0.487235 q^{86} +4.38702 q^{87} -1.00000 q^{88} +9.27703 q^{89} +0.343117 q^{90} -2.91465 q^{91} -2.07936 q^{92} +0.0300857 q^{93} -4.18788 q^{94} +0.827853 q^{95} +1.62999 q^{96} +9.74078 q^{97} -0.870036 q^{98} -0.343117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

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