LMFDB - Embedded newform 8030.2.a.bg.1.13

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			1.13
Root			$2.74529$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.74529 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.74529 q^{6} -3.29124 q^{7} +1.00000 q^{8} +4.53661 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.74529 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.74529 q^{6} -3.29124 q^{7} +1.00000 q^{8} +4.53661 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.74529 q^{12} +0.737696 q^{13} -3.29124 q^{14} -2.74529 q^{15} +1.00000 q^{16} +5.18746 q^{17} +4.53661 q^{18} -2.64062 q^{19} -1.00000 q^{20} -9.03541 q^{21} -1.00000 q^{22} +4.87120 q^{23} +2.74529 q^{24} +1.00000 q^{25} +0.737696 q^{26} +4.21844 q^{27} -3.29124 q^{28} +3.38366 q^{29} -2.74529 q^{30} -2.98474 q^{31} +1.00000 q^{32} -2.74529 q^{33} +5.18746 q^{34} +3.29124 q^{35} +4.53661 q^{36} +3.61347 q^{37} -2.64062 q^{38} +2.02519 q^{39} -1.00000 q^{40} +4.96478 q^{41} -9.03541 q^{42} +4.42392 q^{43} -1.00000 q^{44} -4.53661 q^{45} +4.87120 q^{46} +9.96845 q^{47} +2.74529 q^{48} +3.83229 q^{49} +1.00000 q^{50} +14.2411 q^{51} +0.737696 q^{52} -2.85733 q^{53} +4.21844 q^{54} +1.00000 q^{55} -3.29124 q^{56} -7.24927 q^{57} +3.38366 q^{58} -12.6304 q^{59} -2.74529 q^{60} +12.2057 q^{61} -2.98474 q^{62} -14.9311 q^{63} +1.00000 q^{64} -0.737696 q^{65} -2.74529 q^{66} -7.92749 q^{67} +5.18746 q^{68} +13.3728 q^{69} +3.29124 q^{70} +10.1709 q^{71} +4.53661 q^{72} -1.00000 q^{73} +3.61347 q^{74} +2.74529 q^{75} -2.64062 q^{76} +3.29124 q^{77} +2.02519 q^{78} +10.6114 q^{79} -1.00000 q^{80} -2.02900 q^{81} +4.96478 q^{82} +11.2130 q^{83} -9.03541 q^{84} -5.18746 q^{85} +4.42392 q^{86} +9.28913 q^{87} -1.00000 q^{88} +2.54215 q^{89} -4.53661 q^{90} -2.42794 q^{91} +4.87120 q^{92} -8.19396 q^{93} +9.96845 q^{94} +2.64062 q^{95} +2.74529 q^{96} +9.07019 q^{97} +3.83229 q^{98} -4.53661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.74529	1.58499	0.792497	−	0.609876i	$-0.208781\pi$
$3$	2.74529	1.58499	0.792497	+	0.609876i	$0.208781\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.74529	1.12076
$7$	−3.29124	−1.24397	−0.621987	−	0.783028i	$-0.713674\pi$
$7$	−3.29124	−1.24397	−0.621987	+	0.783028i	$0.713674\pi$
$8$	1.00000	0.353553
$9$	4.53661	1.51220
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.74529	0.792497
$13$	0.737696	0.204600	0.102300	−	0.994754i	$-0.467380\pi$
$13$	0.737696	0.204600	0.102300	+	0.994754i	$0.467380\pi$
$14$	−3.29124	−0.879622
$15$	−2.74529	−0.708830
$16$	1.00000	0.250000
$17$	5.18746	1.25814	0.629072	−	0.777347i	$-0.283435\pi$
$17$	5.18746	1.25814	0.629072	+	0.777347i	$0.283435\pi$
$18$	4.53661	1.06929
$19$	−2.64062	−0.605800	−0.302900	−	0.953022i	$-0.597955\pi$
$19$	−2.64062	−0.605800	−0.302900	+	0.953022i	$0.597955\pi$
$20$	−1.00000	−0.223607
$21$	−9.03541	−1.97169
$22$	−1.00000	−0.213201
$23$	4.87120	1.01572	0.507858	−	0.861441i	$-0.330438\pi$
$23$	4.87120	1.01572	0.507858	+	0.861441i	$0.330438\pi$
$24$	2.74529	0.560380
$25$	1.00000	0.200000
$26$	0.737696	0.144674
$27$	4.21844	0.811839
$28$	−3.29124	−0.621987
$29$	3.38366	0.628330	0.314165	−	0.949368i	$-0.398275\pi$
$29$	3.38366	0.628330	0.314165	+	0.949368i	$0.398275\pi$
$30$	−2.74529	−0.501219
$31$	−2.98474	−0.536075	−0.268037	−	0.963409i	$-0.586375\pi$
$31$	−2.98474	−0.536075	−0.268037	+	0.963409i	$0.586375\pi$
$32$	1.00000	0.176777
$33$	−2.74529	−0.477893
$34$	5.18746	0.889642
$35$	3.29124	0.556322
$36$	4.53661	0.756102
$37$	3.61347	0.594051	0.297026	−	0.954870i	$-0.404005\pi$
$37$	3.61347	0.594051	0.297026	+	0.954870i	$0.404005\pi$
$38$	−2.64062	−0.428366
$39$	2.02519	0.324290
$40$	−1.00000	−0.158114
$41$	4.96478	0.775369	0.387685	−	0.921792i	$-0.373275\pi$
$41$	4.96478	0.775369	0.387685	+	0.921792i	$0.373275\pi$
$42$	−9.03541	−1.39419
$43$	4.42392	0.674642	0.337321	−	0.941390i	$-0.390479\pi$
$43$	4.42392	0.674642	0.337321	+	0.941390i	$0.390479\pi$
$44$	−1.00000	−0.150756
$45$	−4.53661	−0.676278
$46$	4.87120	0.718219
$47$	9.96845	1.45405	0.727024	−	0.686612i	$-0.240903\pi$
$47$	9.96845	1.45405	0.727024	+	0.686612i	$0.240903\pi$
$48$	2.74529	0.396248
$49$	3.83229	0.547469
$50$	1.00000	0.141421
$51$	14.2411	1.99415
$52$	0.737696	0.102300
$53$	−2.85733	−0.392484	−0.196242	−	0.980556i	$-0.562874\pi$
$53$	−2.85733	−0.392484	−0.196242	+	0.980556i	$0.562874\pi$
$54$	4.21844	0.574057
$55$	1.00000	0.134840
$56$	−3.29124	−0.439811
$57$	−7.24927	−0.960189
$58$	3.38366	0.444297
$59$	−12.6304	−1.64434	−0.822171	−	0.569240i	$-0.807238\pi$
$59$	−12.6304	−1.64434	−0.822171	+	0.569240i	$0.807238\pi$
$60$	−2.74529	−0.354415
$61$	12.2057	1.56277	0.781387	−	0.624046i	$-0.214512\pi$
$61$	12.2057	1.56277	0.781387	+	0.624046i	$0.214512\pi$
$62$	−2.98474	−0.379062
$63$	−14.9311	−1.88114
$64$	1.00000	0.125000
$65$	−0.737696	−0.0915000
$66$	−2.74529	−0.337922
$67$	−7.92749	−0.968497	−0.484249	−	0.874930i	$-0.660907\pi$
$67$	−7.92749	−0.968497	−0.484249	+	0.874930i	$0.660907\pi$
$68$	5.18746	0.629072
$69$	13.3728	1.60990
$70$	3.29124	0.393379
$71$	10.1709	1.20706	0.603532	−	0.797339i	$-0.293760\pi$
$71$	10.1709	1.20706	0.603532	+	0.797339i	$0.293760\pi$
$72$	4.53661	0.534645
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	3.61347	0.420058
$75$	2.74529	0.316999
$76$	−2.64062	−0.302900
$77$	3.29124	0.375072
$78$	2.02519	0.229308
$79$	10.6114	1.19388	0.596938	−	0.802287i	$-0.296384\pi$
$79$	10.6114	1.19388	0.596938	+	0.802287i	$0.296384\pi$
$80$	−1.00000	−0.111803
$81$	−2.02900	−0.225445
$82$	4.96478	0.548269
$83$	11.2130	1.23078	0.615392	−	0.788221i	$-0.288998\pi$
$83$	11.2130	1.23078	0.615392	+	0.788221i	$0.288998\pi$
$84$	−9.03541	−0.985845
$85$	−5.18746	−0.562659
$86$	4.42392	0.477044
$87$	9.28913	0.995899
$88$	−1.00000	−0.106600
$89$	2.54215	0.269467	0.134733	−	0.990882i	$-0.456982\pi$
$89$	2.54215	0.269467	0.134733	+	0.990882i	$0.456982\pi$
$90$	−4.53661	−0.478201
$91$	−2.42794	−0.254517
$92$	4.87120	0.507858
$93$	−8.19396	−0.849675
$94$	9.96845	1.02817
$95$	2.64062	0.270922
$96$	2.74529	0.280190
$97$	9.07019	0.920938	0.460469	−	0.887676i	$-0.347681\pi$
$97$	9.07019	0.920938	0.460469	+	0.887676i	$0.347681\pi$
$98$	3.83229	0.387119
$99$	−4.53661	−0.455946
$100$	1.00000	0.100000
$101$	5.24337	0.521734	0.260867	−	0.965375i	$-0.415992\pi$
$101$	5.24337	0.521734	0.260867	+	0.965375i	$0.415992\pi$
$102$	14.2411	1.41008
$103$	6.57733	0.648084	0.324042	−	0.946043i	$-0.394958\pi$
$103$	6.57733	0.648084	0.324042	+	0.946043i	$0.394958\pi$
$104$	0.737696	0.0723371
$105$	9.03541	0.881766
$106$	−2.85733	−0.277528
$107$	−1.68210	−0.162615	−0.0813074	−	0.996689i	$-0.525910\pi$
$107$	−1.68210	−0.162615	−0.0813074	+	0.996689i	$0.525910\pi$
$108$	4.21844	0.405919
$109$	−16.3730	−1.56825	−0.784125	−	0.620603i	$-0.786888\pi$
$109$	−16.3730	−1.56825	−0.784125	+	0.620603i	$0.786888\pi$
$110$	1.00000	0.0953463
$111$	9.92002	0.941567
$112$	−3.29124	−0.310993
$113$	0.336828	0.0316861	0.0158431	−	0.999874i	$-0.494957\pi$
$113$	0.336828	0.0316861	0.0158431	+	0.999874i	$0.494957\pi$
$114$	−7.24927	−0.678956
$115$	−4.87120	−0.454242
$116$	3.38366	0.314165
$117$	3.34664	0.309397
$118$	−12.6304	−1.16273
$119$	−17.0732	−1.56510
$120$	−2.74529	−0.250609
$121$	1.00000	0.0909091
$122$	12.2057	1.10505
$123$	13.6298	1.22895
$124$	−2.98474	−0.268037
$125$	−1.00000	−0.0894427
$126$	−14.9311	−1.33017
$127$	20.1178	1.78517	0.892583	−	0.450883i	$-0.148891\pi$
$127$	20.1178	1.78517	0.892583	+	0.450883i	$0.148891\pi$
$128$	1.00000	0.0883883
$129$	12.1449	1.06930
$130$	−0.737696	−0.0647002
$131$	7.02918	0.614142	0.307071	−	0.951687i	$-0.400651\pi$
$131$	7.02918	0.614142	0.307071	+	0.951687i	$0.400651\pi$
$132$	−2.74529	−0.238947
$133$	8.69093	0.753599
$134$	−7.92749	−0.684831
$135$	−4.21844	−0.363065
$136$	5.18746	0.444821
$137$	2.36953	0.202442	0.101221	−	0.994864i	$-0.467725\pi$
$137$	2.36953	0.202442	0.101221	+	0.994864i	$0.467725\pi$
$138$	13.3728	1.13837
$139$	−19.2048	−1.62893	−0.814465	−	0.580213i	$-0.802969\pi$
$139$	−19.2048	−1.62893	−0.814465	+	0.580213i	$0.802969\pi$
$140$	3.29124	0.278161
$141$	27.3663	2.30466
$142$	10.1709	0.853522
$143$	−0.737696	−0.0616893
$144$	4.53661	0.378051
$145$	−3.38366	−0.280998
$146$	−1.00000	−0.0827606
$147$	10.5207	0.867735
$148$	3.61347	0.297026
$149$	−1.22640	−0.100471	−0.0502353	−	0.998737i	$-0.515997\pi$
$149$	−1.22640	−0.100471	−0.0502353	+	0.998737i	$0.515997\pi$
$150$	2.74529	0.224152
$151$	−16.1063	−1.31071	−0.655355	−	0.755321i	$-0.727481\pi$
$151$	−16.1063	−1.31071	−0.655355	+	0.755321i	$0.727481\pi$
$152$	−2.64062	−0.214183
$153$	23.5335	1.90257
$154$	3.29124	0.265216
$155$	2.98474	0.239740
$156$	2.02519	0.162145
$157$	1.28408	0.102481	0.0512404	−	0.998686i	$-0.483683\pi$
$157$	1.28408	0.102481	0.0512404	+	0.998686i	$0.483683\pi$
$158$	10.6114	0.844198
$159$	−7.84418	−0.622084
$160$	−1.00000	−0.0790569
$161$	−16.0323	−1.26352
$162$	−2.02900	−0.159413
$163$	21.5300	1.68636	0.843181	−	0.537629i	$-0.180680\pi$
$163$	21.5300	1.68636	0.843181	+	0.537629i	$0.180680\pi$
$164$	4.96478	0.387685
$165$	2.74529	0.213720
$166$	11.2130	0.870296
$167$	−8.03923	−0.622094	−0.311047	−	0.950394i	$-0.600680\pi$
$167$	−8.03923	−0.622094	−0.311047	+	0.950394i	$0.600680\pi$
$168$	−9.03541	−0.697097
$169$	−12.4558	−0.958139
$170$	−5.18746	−0.397860
$171$	−11.9795	−0.916093
$172$	4.42392	0.337321
$173$	7.13343	0.542345	0.271172	−	0.962531i	$-0.412589\pi$
$173$	7.13343	0.542345	0.271172	+	0.962531i	$0.412589\pi$
$174$	9.28913	0.704207
$175$	−3.29124	−0.248795
$176$	−1.00000	−0.0753778
$177$	−34.6742	−2.60627
$178$	2.54215	0.190542
$179$	14.3644	1.07364	0.536822	−	0.843695i	$-0.319625\pi$
$179$	14.3644	1.07364	0.536822	+	0.843695i	$0.319625\pi$
$180$	−4.53661	−0.338139
$181$	−0.906153	−0.0673538	−0.0336769	−	0.999433i	$-0.510722\pi$
$181$	−0.906153	−0.0673538	−0.0336769	+	0.999433i	$0.510722\pi$
$182$	−2.42794	−0.179971
$183$	33.5081	2.47699
$184$	4.87120	0.359109
$185$	−3.61347	−0.265668
$186$	−8.19396	−0.600811
$187$	−5.18746	−0.379345
$188$	9.96845	0.727024
$189$	−13.8839	−1.00991
$190$	2.64062	0.191571
$191$	7.00930	0.507175	0.253588	−	0.967312i	$-0.418389\pi$
$191$	7.00930	0.507175	0.253588	+	0.967312i	$0.418389\pi$
$192$	2.74529	0.198124
$193$	−18.1506	−1.30651	−0.653253	−	0.757140i	$-0.726596\pi$
$193$	−18.1506	−1.30651	−0.653253	+	0.757140i	$0.726596\pi$
$194$	9.07019	0.651202
$195$	−2.02519	−0.145027
$196$	3.83229	0.273735
$197$	−12.0382	−0.857686	−0.428843	−	0.903379i	$-0.641079\pi$
$197$	−12.0382	−0.857686	−0.428843	+	0.903379i	$0.641079\pi$
$198$	−4.53661	−0.322403
$199$	−26.3854	−1.87041	−0.935205	−	0.354108i	$-0.884785\pi$
$199$	−26.3854	−1.87041	−0.935205	+	0.354108i	$0.884785\pi$
$200$	1.00000	0.0707107
$201$	−21.7633	−1.53506
$202$	5.24337	0.368922
$203$	−11.1365	−0.781626
$204$	14.2411	0.997074
$205$	−4.96478	−0.346756
$206$	6.57733	0.458264
$207$	22.0987	1.53597
$208$	0.737696	0.0511500
$209$	2.64062	0.182656
$210$	9.03541	0.623503
$211$	6.13067	0.422053	0.211026	−	0.977480i	$-0.432319\pi$
$211$	6.13067	0.422053	0.211026	+	0.977480i	$0.432319\pi$
$212$	−2.85733	−0.196242
$213$	27.9220	1.91319
$214$	−1.68210	−0.114986
$215$	−4.42392	−0.301709
$216$	4.21844	0.287028
$217$	9.82350	0.666862
$218$	−16.3730	−1.10892
$219$	−2.74529	−0.185509
$220$	1.00000	0.0674200
$221$	3.82677	0.257416
$222$	9.92002	0.665788
$223$	−10.3665	−0.694192	−0.347096	−	0.937830i	$-0.612832\pi$
$223$	−10.3665	−0.694192	−0.347096	+	0.937830i	$0.612832\pi$
$224$	−3.29124	−0.219905
$225$	4.53661	0.302441
$226$	0.336828	0.0224055
$227$	5.78513	0.383972	0.191986	−	0.981398i	$-0.438507\pi$
$227$	5.78513	0.383972	0.191986	+	0.981398i	$0.438507\pi$
$228$	−7.24927	−0.480095
$229$	−21.7798	−1.43925	−0.719626	−	0.694361i	$-0.755687\pi$
$229$	−21.7798	−1.43925	−0.719626	+	0.694361i	$0.755687\pi$
$230$	−4.87120	−0.321197
$231$	9.03541	0.594487
$232$	3.38366	0.222148
$233$	−18.5493	−1.21521	−0.607603	−	0.794241i	$-0.707869\pi$
$233$	−18.5493	−1.21521	−0.607603	+	0.794241i	$0.707869\pi$
$234$	3.34664	0.218777
$235$	−9.96845	−0.650270
$236$	−12.6304	−0.822171
$237$	29.1314	1.89229
$238$	−17.0732	−1.10669
$239$	26.3067	1.70164	0.850821	−	0.525456i	$-0.176105\pi$
$239$	26.3067	1.70164	0.850821	+	0.525456i	$0.176105\pi$
$240$	−2.74529	−0.177208
$241$	−14.4428	−0.930341	−0.465170	−	0.885221i	$-0.654007\pi$
$241$	−14.4428	−0.930341	−0.465170	+	0.885221i	$0.654007\pi$
$242$	1.00000	0.0642824
$243$	−18.2255	−1.16917
$244$	12.2057	0.781387
$245$	−3.83229	−0.244836
$246$	13.6298	0.869002
$247$	−1.94798	−0.123947
$248$	−2.98474	−0.189531
$249$	30.7829	1.95078
$250$	−1.00000	−0.0632456
$251$	19.2149	1.21284	0.606418	−	0.795146i	$-0.292606\pi$
$251$	19.2149	1.21284	0.606418	+	0.795146i	$0.292606\pi$
$252$	−14.9311	−0.940570
$253$	−4.87120	−0.306250
$254$	20.1178	1.26230
$255$	−14.2411	−0.891810
$256$	1.00000	0.0625000
$257$	−24.3753	−1.52049	−0.760243	−	0.649638i	$-0.774920\pi$
$257$	−24.3753	−1.52049	−0.760243	+	0.649638i	$0.774920\pi$
$258$	12.1449	0.756111
$259$	−11.8928	−0.738984
$260$	−0.737696	−0.0457500
$261$	15.3504	0.950163
$262$	7.02918	0.434264
$263$	27.7459	1.71088	0.855442	−	0.517898i	$-0.173285\pi$
$263$	27.7459	1.71088	0.855442	+	0.517898i	$0.173285\pi$
$264$	−2.74529	−0.168961
$265$	2.85733	0.175524
$266$	8.69093	0.532875
$267$	6.97892	0.427103
$268$	−7.92749	−0.484249
$269$	20.9904	1.27981	0.639903	−	0.768456i	$-0.278975\pi$
$269$	20.9904	1.27981	0.639903	+	0.768456i	$0.278975\pi$
$270$	−4.21844	−0.256726
$271$	3.04633	0.185051	0.0925257	−	0.995710i	$-0.470506\pi$
$271$	3.04633	0.185051	0.0925257	+	0.995710i	$0.470506\pi$
$272$	5.18746	0.314536
$273$	−6.66539	−0.403408
$274$	2.36953	0.143148
$275$	−1.00000	−0.0603023
$276$	13.3728	0.804951
$277$	−10.5320	−0.632808	−0.316404	−	0.948625i	$-0.602475\pi$
$277$	−10.5320	−0.632808	−0.316404	+	0.948625i	$0.602475\pi$
$278$	−19.2048	−1.15183
$279$	−13.5406	−0.810654
$280$	3.29124	0.196689
$281$	−6.87508	−0.410133	−0.205067	−	0.978748i	$-0.565741\pi$
$281$	−6.87508	−0.410133	−0.205067	+	0.978748i	$0.565741\pi$
$282$	27.3663	1.62964
$283$	30.5139	1.81386	0.906932	−	0.421278i	$-0.138418\pi$
$283$	30.5139	1.81386	0.906932	+	0.421278i	$0.138418\pi$
$284$	10.1709	0.603532
$285$	7.24927	0.429410
$286$	−0.737696	−0.0436209
$287$	−16.3403	−0.964538
$288$	4.53661	0.267322
$289$	9.90972	0.582925
$290$	−3.38366	−0.198696
$291$	24.9003	1.45968
$292$	−1.00000	−0.0585206
$293$	16.2867	0.951478	0.475739	−	0.879586i	$-0.342181\pi$
$293$	16.2867	0.951478	0.475739	+	0.879586i	$0.342181\pi$
$294$	10.5207	0.613582
$295$	12.6304	0.735372
$296$	3.61347	0.210029
$297$	−4.21844	−0.244779
$298$	−1.22640	−0.0710434
$299$	3.59346	0.207815
$300$	2.74529	0.158499
$301$	−14.5602	−0.839236
$302$	−16.1063	−0.926812
$303$	14.3946	0.826945
$304$	−2.64062	−0.151450
$305$	−12.2057	−0.698894
$306$	23.5335	1.34532
$307$	2.69622	0.153881	0.0769407	−	0.997036i	$-0.475485\pi$
$307$	2.69622	0.153881	0.0769407	+	0.997036i	$0.475485\pi$
$308$	3.29124	0.187536
$309$	18.0567	1.02721
$310$	2.98474	0.169522
$311$	−5.33684	−0.302625	−0.151312	−	0.988486i	$-0.548350\pi$
$311$	−5.33684	−0.302625	−0.151312	+	0.988486i	$0.548350\pi$
$312$	2.02519	0.114654
$313$	−12.8426	−0.725908	−0.362954	−	0.931807i	$-0.618232\pi$
$313$	−12.8426	−0.725908	−0.362954	+	0.931807i	$0.618232\pi$
$314$	1.28408	0.0724649
$315$	14.9311	0.841272
$316$	10.6114	0.596938
$317$	−32.4577	−1.82300	−0.911502	−	0.411295i	$-0.865077\pi$
$317$	−32.4577	−1.82300	−0.911502	+	0.411295i	$0.865077\pi$
$318$	−7.84418	−0.439880
$319$	−3.38366	−0.189449
$320$	−1.00000	−0.0559017
$321$	−4.61785	−0.257743
$322$	−16.0323	−0.893445
$323$	−13.6981	−0.762184
$324$	−2.02900	−0.112722
$325$	0.737696	0.0409200
$326$	21.5300	1.19244
$327$	−44.9486	−2.48567
$328$	4.96478	0.274134
$329$	−32.8086	−1.80880
$330$	2.74529	0.151123
$331$	9.23595	0.507654	0.253827	−	0.967250i	$-0.418311\pi$
$331$	9.23595	0.507654	0.253827	+	0.967250i	$0.418311\pi$
$332$	11.2130	0.615392
$333$	16.3929	0.898326
$334$	−8.03923	−0.439887
$335$	7.92749	0.433125
$336$	−9.03541	−0.492922
$337$	8.08127	0.440215	0.220107	−	0.975476i	$-0.429359\pi$
$337$	8.08127	0.440215	0.220107	+	0.975476i	$0.429359\pi$
$338$	−12.4558	−0.677506
$339$	0.924691	0.0502223
$340$	−5.18746	−0.281329
$341$	2.98474	0.161633
$342$	−11.9795	−0.647776
$343$	10.4257	0.562936
$344$	4.42392	0.238522
$345$	−13.3728	−0.719970
$346$	7.13343	0.383496
$347$	2.47466	0.132847	0.0664234	−	0.997792i	$-0.478841\pi$
$347$	2.47466	0.132847	0.0664234	+	0.997792i	$0.478841\pi$
$348$	9.28913	0.497950
$349$	−26.2810	−1.40679	−0.703394	−	0.710801i	$-0.748333\pi$
$349$	−26.2810	−1.40679	−0.703394	+	0.710801i	$0.748333\pi$
$350$	−3.29124	−0.175924
$351$	3.11193	0.166102
$352$	−1.00000	−0.0533002
$353$	20.2649	1.07859	0.539297	−	0.842116i	$-0.318690\pi$
$353$	20.2649	1.07859	0.539297	+	0.842116i	$0.318690\pi$
$354$	−34.6742	−1.84291
$355$	−10.1709	−0.539815
$356$	2.54215	0.134733
$357$	−46.8708	−2.48067
$358$	14.3644	0.759181
$359$	7.64775	0.403633	0.201816	−	0.979423i	$-0.435316\pi$
$359$	7.64775	0.403633	0.201816	+	0.979423i	$0.435316\pi$
$360$	−4.53661	−0.239100
$361$	−12.0271	−0.633006
$362$	−0.906153	−0.0476263
$363$	2.74529	0.144090
$364$	−2.42794	−0.127259
$365$	1.00000	0.0523424
$366$	33.5081	1.75149
$367$	2.28127	0.119081	0.0595407	−	0.998226i	$-0.481036\pi$
$367$	2.28127	0.119081	0.0595407	+	0.998226i	$0.481036\pi$
$368$	4.87120	0.253929
$369$	22.5233	1.17252
$370$	−3.61347	−0.187855
$371$	9.40416	0.488240
$372$	−8.19396	−0.424837
$373$	−10.2848	−0.532527	−0.266263	−	0.963900i	$-0.585789\pi$
$373$	−10.2848	−0.532527	−0.266263	+	0.963900i	$0.585789\pi$
$374$	−5.18746	−0.268237
$375$	−2.74529	−0.141766
$376$	9.96845	0.514084
$377$	2.49612	0.128556
$378$	−13.8839	−0.714111
$379$	−33.0345	−1.69687	−0.848433	−	0.529302i	$-0.822454\pi$
$379$	−33.0345	−1.69687	−0.848433	+	0.529302i	$0.822454\pi$
$380$	2.64062	0.135461
$381$	55.2292	2.82948
$382$	7.00930	0.358627
$383$	−25.7396	−1.31523	−0.657616	−	0.753353i	$-0.728435\pi$
$383$	−25.7396	−1.31523	−0.657616	+	0.753353i	$0.728435\pi$
$384$	2.74529	0.140095
$385$	−3.29124	−0.167737
$386$	−18.1506	−0.923839
$387$	20.0696	1.02020
$388$	9.07019	0.460469
$389$	18.9435	0.960474	0.480237	−	0.877139i	$-0.340551\pi$
$389$	18.9435	0.960474	0.480237	+	0.877139i	$0.340551\pi$
$390$	−2.02519	−0.102549
$391$	25.2691	1.27792
$392$	3.83229	0.193560
$393$	19.2971	0.973411
$394$	−12.0382	−0.606476
$395$	−10.6114	−0.533918
$396$	−4.53661	−0.227973
$397$	−4.16940	−0.209256	−0.104628	−	0.994511i	$-0.533365\pi$
$397$	−4.16940	−0.209256	−0.104628	+	0.994511i	$0.533365\pi$
$398$	−26.3854	−1.32258
$399$	23.8591	1.19445
$400$	1.00000	0.0500000
$401$	−27.3581	−1.36620	−0.683098	−	0.730327i	$-0.739368\pi$
$401$	−27.3581	−1.36620	−0.683098	+	0.730327i	$0.739368\pi$
$402$	−21.7633	−1.08545
$403$	−2.20183	−0.109681
$404$	5.24337	0.260867
$405$	2.02900	0.100822
$406$	−11.1365	−0.552693
$407$	−3.61347	−0.179113
$408$	14.2411	0.705038
$409$	−21.1303	−1.04482	−0.522412	−	0.852693i	$-0.674968\pi$
$409$	−21.1303	−1.04482	−0.522412	+	0.852693i	$0.674968\pi$
$410$	−4.96478	−0.245193
$411$	6.50504	0.320870
$412$	6.57733	0.324042
$413$	41.5698	2.04552
$414$	22.0987	1.08609
$415$	−11.2130	−0.550423
$416$	0.737696	0.0361685
$417$	−52.7227	−2.58184
$418$	2.64062	0.129157
$419$	5.69708	0.278321	0.139160	−	0.990270i	$-0.455560\pi$
$419$	5.69708	0.278321	0.139160	+	0.990270i	$0.455560\pi$
$420$	9.03541	0.440883
$421$	4.13825	0.201686	0.100843	−	0.994902i	$-0.467846\pi$
$421$	4.13825	0.201686	0.100843	+	0.994902i	$0.467846\pi$
$422$	6.13067	0.298436
$423$	45.2230	2.19882
$424$	−2.85733	−0.138764
$425$	5.18746	0.251629
$426$	27.9220	1.35283
$427$	−40.1718	−1.94405
$428$	−1.68210	−0.0813074
$429$	−2.02519	−0.0977771
$430$	−4.42392	−0.213340
$431$	26.8368	1.29268	0.646342	−	0.763048i	$-0.276298\pi$
$431$	26.8368	1.29268	0.646342	+	0.763048i	$0.276298\pi$
$432$	4.21844	0.202960
$433$	−5.39483	−0.259259	−0.129629	−	0.991563i	$-0.541379\pi$
$433$	−5.39483	−0.259259	−0.129629	+	0.991563i	$0.541379\pi$
$434$	9.82350	0.471543
$435$	−9.28913	−0.445380
$436$	−16.3730	−0.784125
$437$	−12.8630	−0.615320
$438$	−2.74529	−0.131175
$439$	−11.9250	−0.569148	−0.284574	−	0.958654i	$-0.591852\pi$
$439$	−11.9250	−0.569148	−0.284574	+	0.958654i	$0.591852\pi$
$440$	1.00000	0.0476731
$441$	17.3856	0.827885
$442$	3.82677	0.182021
$443$	−20.2752	−0.963304	−0.481652	−	0.876363i	$-0.659963\pi$
$443$	−20.2752	−0.963304	−0.481652	+	0.876363i	$0.659963\pi$
$444$	9.92002	0.470784
$445$	−2.54215	−0.120509
$446$	−10.3665	−0.490868
$447$	−3.36682	−0.159245
$448$	−3.29124	−0.155497
$449$	−11.9408	−0.563520	−0.281760	−	0.959485i	$-0.590918\pi$
$449$	−11.9408	−0.563520	−0.281760	+	0.959485i	$0.590918\pi$
$450$	4.53661	0.213858
$451$	−4.96478	−0.233783
$452$	0.336828	0.0158431
$453$	−44.2164	−2.07747
$454$	5.78513	0.271509
$455$	2.42794	0.113824
$456$	−7.24927	−0.339478
$457$	27.0198	1.26394	0.631968	−	0.774995i	$-0.282248\pi$
$457$	27.0198	1.26394	0.631968	+	0.774995i	$0.282248\pi$
$458$	−21.7798	−1.01771
$459$	21.8830	1.02141
$460$	−4.87120	−0.227121
$461$	8.74585	0.407335	0.203667	−	0.979040i	$-0.434714\pi$
$461$	8.74585	0.407335	0.203667	+	0.979040i	$0.434714\pi$
$462$	9.03541	0.420366
$463$	−7.07953	−0.329014	−0.164507	−	0.986376i	$-0.552603\pi$
$463$	−7.07953	−0.329014	−0.164507	+	0.986376i	$0.552603\pi$
$464$	3.38366	0.157083
$465$	8.19396	0.379986
$466$	−18.5493	−0.859280
$467$	−0.262299	−0.0121378	−0.00606889	−	0.999982i	$-0.501932\pi$
$467$	−0.262299	−0.0121378	−0.00606889	+	0.999982i	$0.501932\pi$
$468$	3.34664	0.154698
$469$	26.0913	1.20478
$470$	−9.96845	−0.459810
$471$	3.52517	0.162431
$472$	−12.6304	−0.581363
$473$	−4.42392	−0.203412
$474$	29.1314	1.33805
$475$	−2.64062	−0.121160
$476$	−17.0732	−0.782548
$477$	−12.9626	−0.593515
$478$	26.3067	1.20324
$479$	22.2620	1.01718	0.508588	−	0.861010i	$-0.330167\pi$
$479$	22.2620	1.01718	0.508588	+	0.861010i	$0.330167\pi$
$480$	−2.74529	−0.125305
$481$	2.66565	0.121543
$482$	−14.4428	−0.657850
$483$	−44.0133	−2.00267
$484$	1.00000	0.0454545
$485$	−9.07019	−0.411856
$486$	−18.2255	−0.826726
$487$	−5.87584	−0.266260	−0.133130	−	0.991099i	$-0.542503\pi$
$487$	−5.87584	−0.266260	−0.133130	+	0.991099i	$0.542503\pi$
$488$	12.2057	0.552524
$489$	59.1062	2.67287
$490$	−3.83229	−0.173125
$491$	26.5135	1.19654	0.598269	−	0.801296i	$-0.295856\pi$
$491$	26.5135	1.19654	0.598269	+	0.801296i	$0.295856\pi$
$492$	13.6298	0.614477
$493$	17.5526	0.790530
$494$	−1.94798	−0.0876436
$495$	4.53661	0.203905
$496$	−2.98474	−0.134019
$497$	−33.4749	−1.50155
$498$	30.7829	1.37941
$499$	7.26808	0.325364	0.162682	−	0.986679i	$-0.447986\pi$
$499$	7.26808	0.325364	0.162682	+	0.986679i	$0.447986\pi$
$500$	−1.00000	−0.0447214
$501$	−22.0700	−0.986015
$502$	19.2149	0.857604
$503$	36.4238	1.62406	0.812030	−	0.583616i	$-0.198363\pi$
$503$	36.4238	1.62406	0.812030	+	0.583616i	$0.198363\pi$
$504$	−14.9311	−0.665084
$505$	−5.24337	−0.233327
$506$	−4.87120	−0.216551
$507$	−34.1948	−1.51864
$508$	20.1178	0.892583
$509$	−30.6266	−1.35750	−0.678749	−	0.734370i	$-0.737478\pi$
$509$	−30.6266	−1.35750	−0.678749	+	0.734370i	$0.737478\pi$
$510$	−14.2411	−0.630605
$511$	3.29124	0.145596
$512$	1.00000	0.0441942
$513$	−11.1393	−0.491812
$514$	−24.3753	−1.07515
$515$	−6.57733	−0.289832
$516$	12.1449	0.534651
$517$	−9.96845	−0.438412
$518$	−11.8928	−0.522540
$519$	19.5833	0.859613
$520$	−0.737696	−0.0323501
$521$	−17.2265	−0.754706	−0.377353	−	0.926070i	$-0.623166\pi$
$521$	−17.2265	−0.754706	−0.377353	+	0.926070i	$0.623166\pi$
$522$	15.3504	0.671867
$523$	5.74481	0.251203	0.125601	−	0.992081i	$-0.459914\pi$
$523$	5.74481	0.251203	0.125601	+	0.992081i	$0.459914\pi$
$524$	7.02918	0.307071
$525$	−9.03541	−0.394338
$526$	27.7459	1.20978
$527$	−15.4832	−0.674459
$528$	−2.74529	−0.119473
$529$	0.728570	0.0316770
$530$	2.85733	0.124114
$531$	−57.2994	−2.48658
$532$	8.69093	0.376800
$533$	3.66250	0.158641
$534$	6.97892	0.302008
$535$	1.68210	0.0727235
$536$	−7.92749	−0.342416
$537$	39.4344	1.70172
$538$	20.9904	0.904959
$539$	−3.83229	−0.165068
$540$	−4.21844	−0.181533
$541$	−22.3078	−0.959088	−0.479544	−	0.877518i	$-0.659198\pi$
$541$	−22.3078	−0.959088	−0.479544	+	0.877518i	$0.659198\pi$
$542$	3.04633	0.130851
$543$	−2.48765	−0.106755
$544$	5.18746	0.222410
$545$	16.3730	0.701343
$546$	−6.66539	−0.285252
$547$	−16.4380	−0.702840	−0.351420	−	0.936218i	$-0.614301\pi$
$547$	−16.4380	−0.702840	−0.351420	+	0.936218i	$0.614301\pi$
$548$	2.36953	0.101221
$549$	55.3723	2.36323
$550$	−1.00000	−0.0426401
$551$	−8.93498	−0.380643
$552$	13.3728	0.569186
$553$	−34.9247	−1.48515
$554$	−10.5320	−0.447463
$555$	−9.92002	−0.421082
$556$	−19.2048	−0.814465
$557$	39.6688	1.68082	0.840409	−	0.541952i	$-0.182315\pi$
$557$	39.6688	1.68082	0.840409	+	0.541952i	$0.182315\pi$
$558$	−13.5406	−0.573219
$559$	3.26351	0.138032
$560$	3.29124	0.139080
$561$	−14.2411	−0.601258
$562$	−6.87508	−0.290008
$563$	−4.17653	−0.176020	−0.0880098	−	0.996120i	$-0.528051\pi$
$563$	−4.17653	−0.176020	−0.0880098	+	0.996120i	$0.528051\pi$
$564$	27.3663	1.15233
$565$	−0.336828	−0.0141705
$566$	30.5139	1.28260
$567$	6.67794	0.280447
$568$	10.1709	0.426761
$569$	1.05842	0.0443715	0.0221857	−	0.999754i	$-0.492937\pi$
$569$	1.05842	0.0443715	0.0221857	+	0.999754i	$0.492937\pi$
$570$	7.24927	0.303639
$571$	27.6095	1.15542	0.577711	−	0.816241i	$-0.303946\pi$
$571$	27.6095	1.15542	0.577711	+	0.816241i	$0.303946\pi$
$572$	−0.737696	−0.0308446
$573$	19.2426	0.803869
$574$	−16.3403	−0.682032
$575$	4.87120	0.203143
$576$	4.53661	0.189025
$577$	−16.4677	−0.685559	−0.342779	−	0.939416i	$-0.611368\pi$
$577$	−16.4677	−0.685559	−0.342779	+	0.939416i	$0.611368\pi$
$578$	9.90972	0.412190
$579$	−49.8285	−2.07080
$580$	−3.38366	−0.140499
$581$	−36.9046	−1.53106
$582$	24.9003	1.03215
$583$	2.85733	0.118338
$584$	−1.00000	−0.0413803
$585$	−3.34664	−0.138367
$586$	16.2867	0.672797
$587$	5.89367	0.243258	0.121629	−	0.992576i	$-0.461188\pi$
$587$	5.89367	0.243258	0.121629	+	0.992576i	$0.461188\pi$
$588$	10.5207	0.433868
$589$	7.88156	0.324754
$590$	12.6304	0.519987
$591$	−33.0483	−1.35943
$592$	3.61347	0.148513
$593$	−35.3948	−1.45349	−0.726746	−	0.686906i	$-0.758968\pi$
$593$	−35.3948	−1.45349	−0.726746	+	0.686906i	$0.758968\pi$
$594$	−4.21844	−0.173085
$595$	17.0732	0.699933
$596$	−1.22640	−0.0502353
$597$	−72.4354	−2.96459
$598$	3.59346	0.146948
$599$	−2.65018	−0.108283	−0.0541416	−	0.998533i	$-0.517242\pi$
$599$	−2.65018	−0.108283	−0.0541416	+	0.998533i	$0.517242\pi$
$600$	2.74529	0.112076
$601$	8.17204	0.333344	0.166672	−	0.986012i	$-0.446698\pi$
$601$	8.17204	0.333344	0.166672	+	0.986012i	$0.446698\pi$
$602$	−14.5602	−0.593430
$603$	−35.9639	−1.46456
$604$	−16.1063	−0.655355
$605$	−1.00000	−0.0406558
$606$	14.3946	0.584739
$607$	12.5695	0.510181	0.255091	−	0.966917i	$-0.417895\pi$
$607$	12.5695	0.510181	0.255091	+	0.966917i	$0.417895\pi$
$608$	−2.64062	−0.107091
$609$	−30.5728	−1.23887
$610$	−12.2057	−0.494193
$611$	7.35369	0.297498
$612$	23.5335	0.951284
$613$	−0.414695	−0.0167494	−0.00837469	−	0.999965i	$-0.502666\pi$
$613$	−0.414695	−0.0167494	−0.00837469	+	0.999965i	$0.502666\pi$
$614$	2.69622	0.108811
$615$	−13.6298	−0.549605
$616$	3.29124	0.132608
$617$	−23.0364	−0.927409	−0.463705	−	0.885990i	$-0.653480\pi$
$617$	−23.0364	−0.927409	−0.463705	+	0.885990i	$0.653480\pi$
$618$	18.0567	0.726346
$619$	1.81721	0.0730400	0.0365200	−	0.999333i	$-0.488373\pi$
$619$	1.81721	0.0730400	0.0365200	+	0.999333i	$0.488373\pi$
$620$	2.98474	0.119870
$621$	20.5488	0.824597
$622$	−5.33684	−0.213988
$623$	−8.36682	−0.335210
$624$	2.02519	0.0810725
$625$	1.00000	0.0400000
$626$	−12.8426	−0.513295
$627$	7.24927	0.289508
$628$	1.28408	0.0512404
$629$	18.7447	0.747402
$630$	14.9311	0.594869
$631$	−15.3018	−0.609153	−0.304577	−	0.952488i	$-0.598515\pi$
$631$	−15.3018	−0.609153	−0.304577	+	0.952488i	$0.598515\pi$
$632$	10.6114	0.422099
$633$	16.8305	0.668951
$634$	−32.4577	−1.28906
$635$	−20.1178	−0.798350
$636$	−7.84418	−0.311042
$637$	2.82706	0.112012
$638$	−3.38366	−0.133960
$639$	46.1414	1.82532
$640$	−1.00000	−0.0395285
$641$	−23.6287	−0.933278	−0.466639	−	0.884448i	$-0.654535\pi$
$641$	−23.6287	−0.933278	−0.466639	+	0.884448i	$0.654535\pi$
$642$	−4.61785	−0.182252
$643$	29.5048	1.16356	0.581778	−	0.813348i	$-0.302357\pi$
$643$	29.5048	1.16356	0.581778	+	0.813348i	$0.302357\pi$
$644$	−16.0323	−0.631761
$645$	−12.1449	−0.478207
$646$	−13.6981	−0.538945
$647$	−39.4953	−1.55272	−0.776360	−	0.630290i	$-0.782936\pi$
$647$	−39.4953	−1.55272	−0.776360	+	0.630290i	$0.782936\pi$
$648$	−2.02900	−0.0797067
$649$	12.6304	0.495788
$650$	0.737696	0.0289348
$651$	26.9683	1.05697
$652$	21.5300	0.843181
$653$	−29.6759	−1.16131	−0.580654	−	0.814150i	$-0.697203\pi$
$653$	−29.6759	−1.16131	−0.580654	+	0.814150i	$0.697203\pi$
$654$	−44.9486	−1.75763
$655$	−7.02918	−0.274653
$656$	4.96478	0.193842
$657$	−4.53661	−0.176990
$658$	−32.8086	−1.27901
$659$	−4.88121	−0.190145	−0.0950725	−	0.995470i	$-0.530308\pi$
$659$	−4.88121	−0.190145	−0.0950725	+	0.995470i	$0.530308\pi$
$660$	2.74529	0.106860
$661$	30.1854	1.17408	0.587039	−	0.809559i	$-0.300294\pi$
$661$	30.1854	1.17408	0.587039	+	0.809559i	$0.300294\pi$
$662$	9.23595	0.358965
$663$	10.5056	0.408003
$664$	11.2130	0.435148
$665$	−8.69093	−0.337020
$666$	16.3929	0.635212
$667$	16.4825	0.638205
$668$	−8.03923	−0.311047
$669$	−28.4590	−1.10029
$670$	7.92749	0.306266
$671$	−12.2057	−0.471194
$672$	−9.03541	−0.348549
$673$	−20.8693	−0.804454	−0.402227	−	0.915540i	$-0.631764\pi$
$673$	−20.8693	−0.804454	−0.402227	+	0.915540i	$0.631764\pi$
$674$	8.08127	0.311279
$675$	4.21844	0.162368
$676$	−12.4558	−0.479069
$677$	−42.5543	−1.63550	−0.817748	−	0.575577i	$-0.804778\pi$
$677$	−42.5543	−1.63550	−0.817748	+	0.575577i	$0.804778\pi$
$678$	0.924691	0.0355125
$679$	−29.8522	−1.14562
$680$	−5.18746	−0.198930
$681$	15.8818	0.608594
$682$	2.98474	0.114291
$683$	−36.4811	−1.39591	−0.697956	−	0.716141i	$-0.745907\pi$
$683$	−36.4811	−1.39591	−0.697956	+	0.716141i	$0.745907\pi$
$684$	−11.9795	−0.458047
$685$	−2.36953	−0.0905350
$686$	10.4257	0.398056
$687$	−59.7920	−2.28121
$688$	4.42392	0.168660
$689$	−2.10784	−0.0803023
$690$	−13.3728	−0.509095
$691$	32.6460	1.24191	0.620955	−	0.783846i	$-0.286745\pi$
$691$	32.6460	1.24191	0.620955	+	0.783846i	$0.286745\pi$
$692$	7.13343	0.271172
$693$	14.9311	0.567185
$694$	2.47466	0.0939369
$695$	19.2048	0.728479
$696$	9.28913	0.352104
$697$	25.7546	0.975526
$698$	−26.2810	−0.994749
$699$	−50.9232	−1.92609
$700$	−3.29124	−0.124397
$701$	−34.1353	−1.28927	−0.644636	−	0.764490i	$-0.722991\pi$
$701$	−34.1353	−1.28927	−0.644636	+	0.764490i	$0.722991\pi$
$702$	3.11193	0.117452
$703$	−9.54182	−0.359876
$704$	−1.00000	−0.0376889
$705$	−27.3663	−1.03067
$706$	20.2649	0.762681
$707$	−17.2572	−0.649024
$708$	−34.6742	−1.30314
$709$	27.2017	1.02158	0.510791	−	0.859705i	$-0.329352\pi$
$709$	27.2017	1.02158	0.510791	+	0.859705i	$0.329352\pi$
$710$	−10.1709	−0.381707
$711$	48.1398	1.80538
$712$	2.54215	0.0952710
$713$	−14.5392	−0.544499
$714$	−46.8708	−1.75410
$715$	0.737696	0.0275883
$716$	14.3644	0.536822
$717$	72.2196	2.69709
$718$	7.64775	0.285412
$719$	−14.3223	−0.534130	−0.267065	−	0.963678i	$-0.586054\pi$
$719$	−14.3223	−0.534130	−0.267065	+	0.963678i	$0.586054\pi$
$720$	−4.53661	−0.169069
$721$	−21.6476	−0.806199
$722$	−12.0271	−0.447603
$723$	−39.6496	−1.47458
$724$	−0.906153	−0.0336769
$725$	3.38366	0.125666
$726$	2.74529	0.101887
$727$	16.6249	0.616582	0.308291	−	0.951292i	$-0.400243\pi$
$727$	16.6249	0.616582	0.308291	+	0.951292i	$0.400243\pi$
$728$	−2.42794	−0.0899854
$729$	−43.9473	−1.62768
$730$	1.00000	0.0370117
$731$	22.9489	0.848796
$732$	33.5081	1.23849
$733$	−11.9434	−0.441140	−0.220570	−	0.975371i	$-0.570792\pi$
$733$	−11.9434	−0.441140	−0.220570	+	0.975371i	$0.570792\pi$
$734$	2.28127	0.0842033
$735$	−10.5207	−0.388063
$736$	4.87120	0.179555
$737$	7.92749	0.292013
$738$	22.5233	0.829094
$739$	−17.6946	−0.650908	−0.325454	−	0.945558i	$-0.605517\pi$
$739$	−17.6946	−0.650908	−0.325454	+	0.945558i	$0.605517\pi$
$740$	−3.61347	−0.132834
$741$	−5.34776	−0.196455
$742$	9.40416	0.345237
$743$	17.3169	0.635295	0.317648	−	0.948209i	$-0.397107\pi$
$743$	17.3169	0.635295	0.317648	+	0.948209i	$0.397107\pi$
$744$	−8.19396	−0.300405
$745$	1.22640	0.0449318
$746$	−10.2848	−0.376553
$747$	50.8689	1.86120
$748$	−5.18746	−0.189672
$749$	5.53620	0.202288
$750$	−2.74529	−0.100244
$751$	41.2065	1.50365	0.751823	−	0.659365i	$-0.229175\pi$
$751$	41.2065	1.50365	0.751823	+	0.659365i	$0.229175\pi$
$752$	9.96845	0.363512
$753$	52.7505	1.92234
$754$	2.49612	0.0909032
$755$	16.1063	0.586168
$756$	−13.8839	−0.504953
$757$	−25.1549	−0.914271	−0.457136	−	0.889397i	$-0.651125\pi$
$757$	−25.1549	−0.914271	−0.457136	+	0.889397i	$0.651125\pi$
$758$	−33.0345	−1.19987
$759$	−13.3728	−0.485404
$760$	2.64062	0.0957854
$761$	−51.3761	−1.86238	−0.931192	−	0.364529i	$-0.881230\pi$
$761$	−51.3761	−1.86238	−0.931192	+	0.364529i	$0.881230\pi$
$762$	55.2292	2.00074
$763$	53.8876	1.95086
$764$	7.00930	0.253588
$765$	−23.5335	−0.850855
$766$	−25.7396	−0.930010
$767$	−9.31743	−0.336433
$768$	2.74529	0.0990621
$769$	15.9654	0.575727	0.287863	−	0.957672i	$-0.407055\pi$
$769$	15.9654	0.575727	0.287863	+	0.957672i	$0.407055\pi$
$770$	−3.29124	−0.118608
$771$	−66.9171	−2.40996
$772$	−18.1506	−0.653253
$773$	−5.51743	−0.198448	−0.0992240	−	0.995065i	$-0.531636\pi$
$773$	−5.51743	−0.198448	−0.0992240	+	0.995065i	$0.531636\pi$
$774$	20.0696	0.721387
$775$	−2.98474	−0.107215
$776$	9.07019	0.325601
$777$	−32.6492	−1.17128
$778$	18.9435	0.679157
$779$	−13.1101	−0.469719
$780$	−2.02519	−0.0725134
$781$	−10.1709	−0.363943
$782$	25.2691	0.903622
$783$	14.2738	0.510103
$784$	3.83229	0.136867
$785$	−1.28408	−0.0458308
$786$	19.2971	0.688305
$787$	−46.1883	−1.64643	−0.823217	−	0.567726i	$-0.807823\pi$
$787$	−46.1883	−1.64643	−0.823217	+	0.567726i	$0.807823\pi$
$788$	−12.0382	−0.428843
$789$	76.1705	2.71174
$790$	−10.6114	−0.377537
$791$	−1.10858	−0.0394167
$792$	−4.53661	−0.161201
$793$	9.00407	0.319744
$794$	−4.16940	−0.147966
$795$	7.84418	0.278205
$796$	−26.3854	−0.935205
$797$	24.3686	0.863181	0.431591	−	0.902070i	$-0.357952\pi$
$797$	24.3686	0.863181	0.431591	+	0.902070i	$0.357952\pi$
$798$	23.8591	0.844604
$799$	51.7109	1.82940
$800$	1.00000	0.0353553
$801$	11.5327	0.407489
$802$	−27.3581	−0.966046
$803$	1.00000	0.0352892
$804$	−21.7633	−0.767531
$805$	16.0323	0.565064
$806$	−2.20183	−0.0775561
$807$	57.6246	2.02848
$808$	5.24337	0.184461
$809$	−42.2381	−1.48501	−0.742507	−	0.669839i	$-0.766363\pi$
$809$	−42.2381	−1.48501	−0.742507	+	0.669839i	$0.766363\pi$
$810$	2.02900	0.0712919
$811$	−18.5360	−0.650887	−0.325444	−	0.945561i	$-0.605514\pi$
$811$	−18.5360	−0.650887	−0.325444	+	0.945561i	$0.605514\pi$
$812$	−11.1365	−0.390813
$813$	8.36305	0.293305
$814$	−3.61347	−0.126652
$815$	−21.5300	−0.754164
$816$	14.2411	0.498537
$817$	−11.6819	−0.408698
$818$	−21.1303	−0.738803
$819$	−11.0146	−0.384882
$820$	−4.96478	−0.173378
$821$	41.9417	1.46378	0.731888	−	0.681425i	$-0.238639\pi$
$821$	41.9417	1.46378	0.731888	+	0.681425i	$0.238639\pi$
$822$	6.50504	0.226889
$823$	−42.5003	−1.48147	−0.740735	−	0.671798i	$-0.765522\pi$
$823$	−42.5003	−1.48147	−0.740735	+	0.671798i	$0.765522\pi$
$824$	6.57733	0.229132
$825$	−2.74529	−0.0955787
$826$	41.5698	1.44640
$827$	31.2207	1.08565	0.542825	−	0.839846i	$-0.317355\pi$
$827$	31.2207	1.08565	0.542825	+	0.839846i	$0.317355\pi$
$828$	22.0987	0.767984
$829$	46.2006	1.60461	0.802306	−	0.596912i	$-0.203606\pi$
$829$	46.2006	1.60461	0.802306	+	0.596912i	$0.203606\pi$
$830$	−11.2130	−0.389208
$831$	−28.9134	−1.00300
$832$	0.737696	0.0255750
$833$	19.8798	0.688795
$834$	−52.7227	−1.82564
$835$	8.03923	0.278209
$836$	2.64062	0.0913278
$837$	−12.5909	−0.435206
$838$	5.69708	0.196802
$839$	8.67347	0.299442	0.149721	−	0.988728i	$-0.452163\pi$
$839$	8.67347	0.299442	0.149721	+	0.988728i	$0.452163\pi$
$840$	9.03541	0.311751
$841$	−17.5508	−0.605201
$842$	4.13825	0.142613
$843$	−18.8741	−0.650058
$844$	6.13067	0.211026
$845$	12.4558	0.428493
$846$	45.2230	1.55480
$847$	−3.29124	−0.113088
$848$	−2.85733	−0.0981210
$849$	83.7695	2.87496
$850$	5.18746	0.177928
$851$	17.6019	0.603387
$852$	27.9220	0.956593
$853$	35.2173	1.20582	0.602908	−	0.797811i	$-0.294009\pi$
$853$	35.2173	1.20582	0.602908	+	0.797811i	$0.294009\pi$
$854$	−40.1718	−1.37465
$855$	11.9795	0.409689
$856$	−1.68210	−0.0574930
$857$	−26.8958	−0.918744	−0.459372	−	0.888244i	$-0.651926\pi$
$857$	−26.8958	−0.918744	−0.459372	+	0.888244i	$0.651926\pi$
$858$	−2.02519	−0.0691388
$859$	18.1423	0.619008	0.309504	−	0.950898i	$-0.399837\pi$
$859$	18.1423	0.619008	0.309504	+	0.950898i	$0.399837\pi$
$860$	−4.42392	−0.150854
$861$	−44.8589	−1.52879
$862$	26.8368	0.914066
$863$	−6.49338	−0.221037	−0.110519	−	0.993874i	$-0.535251\pi$
$863$	−6.49338	−0.221037	−0.110519	+	0.993874i	$0.535251\pi$
$864$	4.21844	0.143514
$865$	−7.13343	−0.242544
$866$	−5.39483	−0.183324
$867$	27.2051	0.923932
$868$	9.82350	0.333431
$869$	−10.6114	−0.359967
$870$	−9.28913	−0.314931
$871$	−5.84808	−0.198155
$872$	−16.3730	−0.554460
$873$	41.1479	1.39265
$874$	−12.8630	−0.435097
$875$	3.29124	0.111264
$876$	−2.74529	−0.0927547
$877$	−11.9185	−0.402458	−0.201229	−	0.979544i	$-0.564494\pi$
$877$	−11.9185	−0.402458	−0.201229	+	0.979544i	$0.564494\pi$
$878$	−11.9250	−0.402448
$879$	44.7117	1.50809
$880$	1.00000	0.0337100
$881$	38.9529	1.31236	0.656178	−	0.754606i	$-0.272172\pi$
$881$	38.9529	1.31236	0.656178	+	0.754606i	$0.272172\pi$
$882$	17.3856	0.585403
$883$	−43.2987	−1.45712	−0.728559	−	0.684984i	$-0.759809\pi$
$883$	−43.2987	−1.45712	−0.728559	+	0.684984i	$0.759809\pi$
$884$	3.82677	0.128708
$885$	34.6742	1.16556
$886$	−20.2752	−0.681159
$887$	21.0708	0.707487	0.353744	−	0.935342i	$-0.384909\pi$
$887$	21.0708	0.707487	0.353744	+	0.935342i	$0.384909\pi$
$888$	9.92002	0.332894
$889$	−66.2126	−2.22070
$890$	−2.54215	−0.0852129
$891$	2.02900	0.0679741
$892$	−10.3665	−0.347096
$893$	−26.3229	−0.880863
$894$	−3.36682	−0.112603
$895$	−14.3644	−0.480148
$896$	−3.29124	−0.109953
$897$	9.86510	0.329386
$898$	−11.9408	−0.398469
$899$	−10.0993	−0.336832
$900$	4.53661	0.151220
$901$	−14.8223	−0.493801
$902$	−4.96478	−0.165309
$903$	−39.9720	−1.33018
$904$	0.336828	0.0112027
$905$	0.906153	0.0301215
$906$	−44.2164	−1.46899
$907$	−41.4330	−1.37576	−0.687881	−	0.725824i	$-0.741459\pi$
$907$	−41.4330	−1.37576	−0.687881	+	0.725824i	$0.741459\pi$
$908$	5.78513	0.191986
$909$	23.7871	0.788968
$910$	2.42794	0.0804854
$911$	−51.4238	−1.70375	−0.851873	−	0.523748i	$-0.824533\pi$
$911$	−51.4238	−1.70375	−0.851873	+	0.523748i	$0.824533\pi$
$912$	−7.24927	−0.240047
$913$	−11.2130	−0.371095
$914$	27.0198	0.893737
$915$	−33.5081	−1.10774
$916$	−21.7798	−0.719626
$917$	−23.1347	−0.763976
$918$	21.8830	0.722245
$919$	−33.5526	−1.10680	−0.553398	−	0.832917i	$-0.686669\pi$
$919$	−33.5526	−1.10680	−0.553398	+	0.832917i	$0.686669\pi$
$920$	−4.87120	−0.160599
$921$	7.40190	0.243901
$922$	8.74585	0.288029
$923$	7.50303	0.246965
$924$	9.03541	0.297243
$925$	3.61347	0.118810
$926$	−7.07953	−0.232648
$927$	29.8388	0.980034
$928$	3.38366	0.111074
$929$	−1.55217	−0.0509251	−0.0254625	−	0.999676i	$-0.508106\pi$
$929$	−1.55217	−0.0509251	−0.0254625	+	0.999676i	$0.508106\pi$
$930$	8.19396	0.268691
$931$	−10.1196	−0.331657
$932$	−18.5493	−0.607603
$933$	−14.6512	−0.479658
$934$	−0.262299	−0.00858270
$935$	5.18746	0.169648
$936$	3.34664	0.109388
$937$	−36.3304	−1.18686	−0.593431	−	0.804885i	$-0.702227\pi$
$937$	−36.3304	−1.18686	−0.593431	+	0.804885i	$0.702227\pi$
$938$	26.0913	0.851912
$939$	−35.2567	−1.15056
$940$	−9.96845	−0.325135
$941$	−1.39664	−0.0455291	−0.0227645	−	0.999741i	$-0.507247\pi$
$941$	−1.39664	−0.0455291	−0.0227645	+	0.999741i	$0.507247\pi$
$942$	3.52517	0.114856
$943$	24.1844	0.787554
$944$	−12.6304	−0.411086
$945$	13.8839	0.451643
$946$	−4.42392	−0.143834
$947$	27.7727	0.902491	0.451246	−	0.892400i	$-0.350980\pi$
$947$	27.7727	0.902491	0.451246	+	0.892400i	$0.350980\pi$
$948$	29.1314	0.946143
$949$	−0.737696	−0.0239466
$950$	−2.64062	−0.0856731
$951$	−89.1057	−2.88945
$952$	−17.0732	−0.553345
$953$	−33.8248	−1.09569	−0.547847	−	0.836579i	$-0.684552\pi$
$953$	−33.8248	−1.09569	−0.547847	+	0.836579i	$0.684552\pi$
$954$	−12.9626	−0.419679
$955$	−7.00930	−0.226816
$956$	26.3067	0.850821
$957$	−9.28913	−0.300275
$958$	22.2620	0.719253
$959$	−7.79869	−0.251833
$960$	−2.74529	−0.0886038
$961$	−22.0913	−0.712624
$962$	2.66565	0.0859438
$963$	−7.63103	−0.245907
$964$	−14.4428	−0.465170
$965$	18.1506	0.584287
$966$	−44.0133	−1.41610
$967$	−8.36831	−0.269107	−0.134553	−	0.990906i	$-0.542960\pi$
$967$	−8.36831	−0.269107	−0.134553	+	0.990906i	$0.542960\pi$
$968$	1.00000	0.0321412
$969$	−37.6053	−1.20806
$970$	−9.07019	−0.291226
$971$	−56.3650	−1.80884	−0.904419	−	0.426645i	$-0.859695\pi$
$971$	−56.3650	−1.80884	−0.904419	+	0.426645i	$0.859695\pi$
$972$	−18.2255	−0.584583
$973$	63.2077	2.02634
$974$	−5.87584	−0.188274
$975$	2.02519	0.0648580
$976$	12.2057	0.390694
$977$	−7.69162	−0.246077	−0.123038	−	0.992402i	$-0.539264\pi$
$977$	−7.69162	−0.246077	−0.123038	+	0.992402i	$0.539264\pi$
$978$	59.1062	1.89001
$979$	−2.54215	−0.0812473
$980$	−3.83229	−0.122418
$981$	−74.2780	−2.37151
$982$	26.5135	0.846080
$983$	−10.3793	−0.331048	−0.165524	−	0.986206i	$-0.552931\pi$
$983$	−10.3793	−0.331048	−0.165524	+	0.986206i	$0.552931\pi$
$984$	13.6298	0.434501
$985$	12.0382	0.383569
$986$	17.5526	0.558989
$987$	−90.0691	−2.86693
$988$	−1.94798	−0.0619734
$989$	21.5498	0.685244
$990$	4.53661	0.144183
$991$	−24.6114	−0.781805	−0.390903	−	0.920432i	$-0.627837\pi$
$991$	−24.6114	−0.781805	−0.390903	+	0.920432i	$0.627837\pi$
$992$	−2.98474	−0.0947655
$993$	25.3553	0.804628
$994$	−33.4749	−1.06176
$995$	26.3854	0.836472
$996$	30.7829	0.975392
$997$	32.6757	1.03485	0.517425	−	0.855729i	$-0.326891\pi$
$997$	32.6757	1.03485	0.517425	+	0.855729i	$0.326891\pi$
$998$	7.26808	0.230067
$999$	15.2432	0.482274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bg.1.13	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bg.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.74529 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.74529 q^{6} -3.29124 q^{7} +1.00000 q^{8} +4.53661 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.74529 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.74529 q^{6} -3.29124 q^{7} +1.00000 q^{8} +4.53661 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.74529 q^{12} +0.737696 q^{13} -3.29124 q^{14} -2.74529 q^{15} +1.00000 q^{16} +5.18746 q^{17} +4.53661 q^{18} -2.64062 q^{19} -1.00000 q^{20} -9.03541 q^{21} -1.00000 q^{22} +4.87120 q^{23} +2.74529 q^{24} +1.00000 q^{25} +0.737696 q^{26} +4.21844 q^{27} -3.29124 q^{28} +3.38366 q^{29} -2.74529 q^{30} -2.98474 q^{31} +1.00000 q^{32} -2.74529 q^{33} +5.18746 q^{34} +3.29124 q^{35} +4.53661 q^{36} +3.61347 q^{37} -2.64062 q^{38} +2.02519 q^{39} -1.00000 q^{40} +4.96478 q^{41} -9.03541 q^{42} +4.42392 q^{43} -1.00000 q^{44} -4.53661 q^{45} +4.87120 q^{46} +9.96845 q^{47} +2.74529 q^{48} +3.83229 q^{49} +1.00000 q^{50} +14.2411 q^{51} +0.737696 q^{52} -2.85733 q^{53} +4.21844 q^{54} +1.00000 q^{55} -3.29124 q^{56} -7.24927 q^{57} +3.38366 q^{58} -12.6304 q^{59} -2.74529 q^{60} +12.2057 q^{61} -2.98474 q^{62} -14.9311 q^{63} +1.00000 q^{64} -0.737696 q^{65} -2.74529 q^{66} -7.92749 q^{67} +5.18746 q^{68} +13.3728 q^{69} +3.29124 q^{70} +10.1709 q^{71} +4.53661 q^{72} -1.00000 q^{73} +3.61347 q^{74} +2.74529 q^{75} -2.64062 q^{76} +3.29124 q^{77} +2.02519 q^{78} +10.6114 q^{79} -1.00000 q^{80} -2.02900 q^{81} +4.96478 q^{82} +11.2130 q^{83} -9.03541 q^{84} -5.18746 q^{85} +4.42392 q^{86} +9.28913 q^{87} -1.00000 q^{88} +2.54215 q^{89} -4.53661 q^{90} -2.42794 q^{91} +4.87120 q^{92} -8.19396 q^{93} +9.96845 q^{94} +2.64062 q^{95} +2.74529 q^{96} +9.07019 q^{97} +3.83229 q^{98} -4.53661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 7 q^{3} + 15 q^{4} - 15 q^{5} + 7 q^{6} + 3 q^{7} + 15 q^{8} + 16 q^{9}+O(q^{10}) \) 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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