LMFDB - Embedded newform 6006.2.a.cg.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6006,2,Mod(1,6006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6006.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:	$47.9581514540$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 8x^{5} + 23x^{4} + 5x^{3} - 31x^{2} + 18x - 3 $ x^7 - 3x^6 - 8x^5 + 23x^4 + 5x^3 - 31x^2 + 18x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.52204$ of defining polynomial
Character	$\chi$	$=$	6006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.43215 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.43215 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.43215 q^{10} +1.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +1.43215 q^{15} +1.00000 q^{16} +1.60945 q^{17} +1.00000 q^{18} +3.77694 q^{19} +1.43215 q^{20} +1.00000 q^{21} +1.00000 q^{22} -2.24760 q^{23} +1.00000 q^{24} -2.94896 q^{25} +1.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -9.52558 q^{29} +1.43215 q^{30} +2.81545 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.60945 q^{34} +1.43215 q^{35} +1.00000 q^{36} -1.04159 q^{37} +3.77694 q^{38} +1.00000 q^{39} +1.43215 q^{40} +10.5588 q^{41} +1.00000 q^{42} +9.10068 q^{43} +1.00000 q^{44} +1.43215 q^{45} -2.24760 q^{46} +4.41962 q^{47} +1.00000 q^{48} +1.00000 q^{49} -2.94896 q^{50} +1.60945 q^{51} +1.00000 q^{52} +1.70136 q^{53} +1.00000 q^{54} +1.43215 q^{55} +1.00000 q^{56} +3.77694 q^{57} -9.52558 q^{58} +5.28919 q^{59} +1.43215 q^{60} +2.00000 q^{61} +2.81545 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.43215 q^{65} +1.00000 q^{66} -7.96497 q^{67} +1.60945 q^{68} -2.24760 q^{69} +1.43215 q^{70} -2.42490 q^{71} +1.00000 q^{72} +9.91613 q^{73} -1.04159 q^{74} -2.94896 q^{75} +3.77694 q^{76} +1.00000 q^{77} +1.00000 q^{78} +4.75281 q^{79} +1.43215 q^{80} +1.00000 q^{81} +10.5588 q^{82} -16.2469 q^{83} +1.00000 q^{84} +2.30496 q^{85} +9.10068 q^{86} -9.52558 q^{87} +1.00000 q^{88} +9.52558 q^{89} +1.43215 q^{90} +1.00000 q^{91} -2.24760 q^{92} +2.81545 q^{93} +4.41962 q^{94} +5.40913 q^{95} +1.00000 q^{96} +13.5717 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} + 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 + 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} + 7 q^{7} + 7 q^{8} + 7 q^{9} + 2 q^{10} + 7 q^{11} + 7 q^{12} + 7 q^{13} + 7 q^{14} + 2 q^{15} + 7 q^{16} + 6 q^{17} + 7 q^{18} + 4 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 2 q^{23} + 7 q^{24} + 17 q^{25} + 7 q^{26} + 7 q^{27} + 7 q^{28} + 6 q^{29} + 2 q^{30} + 10 q^{31} + 7 q^{32} + 7 q^{33} + 6 q^{34} + 2 q^{35} + 7 q^{36} + 6 q^{37} + 4 q^{38} + 7 q^{39} + 2 q^{40} - 4 q^{41} + 7 q^{42} + 6 q^{43} + 7 q^{44} + 2 q^{45} + 2 q^{46} - 2 q^{47} + 7 q^{48} + 7 q^{49} + 17 q^{50} + 6 q^{51} + 7 q^{52} - 8 q^{53} + 7 q^{54} + 2 q^{55} + 7 q^{56} + 4 q^{57} + 6 q^{58} + 6 q^{59} + 2 q^{60} + 14 q^{61} + 10 q^{62} + 7 q^{63} + 7 q^{64} + 2 q^{65} + 7 q^{66} + 18 q^{67} + 6 q^{68} + 2 q^{69} + 2 q^{70} - 2 q^{71} + 7 q^{72} + 2 q^{73} + 6 q^{74} + 17 q^{75} + 4 q^{76} + 7 q^{77} + 7 q^{78} + 16 q^{79} + 2 q^{80} + 7 q^{81} - 4 q^{82} - 2 q^{83} + 7 q^{84} - 12 q^{85} + 6 q^{86} + 6 q^{87} + 7 q^{88} - 6 q^{89} + 2 q^{90} + 7 q^{91} + 2 q^{92} + 10 q^{93} - 2 q^{94} + 20 q^{95} + 7 q^{96} - 12 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 + 7 * q^7 + 7 * q^8 + 7 * q^9 + 2 * q^10 + 7 * q^11 + 7 * q^12 + 7 * q^13 + 7 * q^14 + 2 * q^15 + 7 * q^16 + 6 * q^17 + 7 * q^18 + 4 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 2 * q^23 + 7 * q^24 + 17 * q^25 + 7 * q^26 + 7 * q^27 + 7 * q^28 + 6 * q^29 + 2 * q^30 + 10 * q^31 + 7 * q^32 + 7 * q^33 + 6 * q^34 + 2 * q^35 + 7 * q^36 + 6 * q^37 + 4 * q^38 + 7 * q^39 + 2 * q^40 - 4 * q^41 + 7 * q^42 + 6 * q^43 + 7 * q^44 + 2 * q^45 + 2 * q^46 - 2 * q^47 + 7 * q^48 + 7 * q^49 + 17 * q^50 + 6 * q^51 + 7 * q^52 - 8 * q^53 + 7 * q^54 + 2 * q^55 + 7 * q^56 + 4 * q^57 + 6 * q^58 + 6 * q^59 + 2 * q^60 + 14 * q^61 + 10 * q^62 + 7 * q^63 + 7 * q^64 + 2 * q^65 + 7 * q^66 + 18 * q^67 + 6 * q^68 + 2 * q^69 + 2 * q^70 - 2 * q^71 + 7 * q^72 + 2 * q^73 + 6 * q^74 + 17 * q^75 + 4 * q^76 + 7 * q^77 + 7 * q^78 + 16 * q^79 + 2 * q^80 + 7 * q^81 - 4 * q^82 - 2 * q^83 + 7 * q^84 - 12 * q^85 + 6 * q^86 + 6 * q^87 + 7 * q^88 - 6 * q^89 + 2 * q^90 + 7 * q^91 + 2 * q^92 + 10 * q^93 - 2 * q^94 + 20 * q^95 + 7 * q^96 - 12 * q^97 + 7 * q^98 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.43215	0.640476	0.320238	−	0.947337i	$-0.396237\pi$
$5$	1.43215	0.640476	0.320238	+	0.947337i	$0.396237\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.43215	0.452885
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.00000	0.267261
$15$	1.43215	0.369779
$16$	1.00000	0.250000
$17$	1.60945	0.390348	0.195174	−	0.980769i	$-0.437473\pi$
$17$	1.60945	0.390348	0.195174	+	0.980769i	$0.437473\pi$
$18$	1.00000	0.235702
$19$	3.77694	0.866489	0.433244	−	0.901276i	$-0.357369\pi$
$19$	3.77694	0.866489	0.433244	+	0.901276i	$0.357369\pi$
$20$	1.43215	0.320238
$21$	1.00000	0.218218
$22$	1.00000	0.213201
$23$	−2.24760	−0.468657	−0.234328	−	0.972157i	$-0.575289\pi$
$23$	−2.24760	−0.468657	−0.234328	+	0.972157i	$0.575289\pi$
$24$	1.00000	0.204124
$25$	−2.94896	−0.589791
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−9.52558	−1.76886	−0.884428	−	0.466678i	$-0.845451\pi$
$29$	−9.52558	−1.76886	−0.884428	+	0.466678i	$0.845451\pi$
$30$	1.43215	0.261473
$31$	2.81545	0.505670	0.252835	−	0.967509i	$-0.418637\pi$
$31$	2.81545	0.505670	0.252835	+	0.967509i	$0.418637\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	1.60945	0.276018
$35$	1.43215	0.242077
$36$	1.00000	0.166667
$37$	−1.04159	−0.171237	−0.0856184	−	0.996328i	$-0.527287\pi$
$37$	−1.04159	−0.171237	−0.0856184	+	0.996328i	$0.527287\pi$
$38$	3.77694	0.612700
$39$	1.00000	0.160128
$40$	1.43215	0.226442
$41$	10.5588	1.64901	0.824505	−	0.565855i	$-0.191454\pi$
$41$	10.5588	1.64901	0.824505	+	0.565855i	$0.191454\pi$
$42$	1.00000	0.154303
$43$	9.10068	1.38784	0.693920	−	0.720052i	$-0.255882\pi$
$43$	9.10068	1.38784	0.693920	+	0.720052i	$0.255882\pi$
$44$	1.00000	0.150756
$45$	1.43215	0.213492
$46$	−2.24760	−0.331391
$47$	4.41962	0.644668	0.322334	−	0.946626i	$-0.395533\pi$
$47$	4.41962	0.644668	0.322334	+	0.946626i	$0.395533\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−2.94896	−0.417045
$51$	1.60945	0.225368
$52$	1.00000	0.138675
$53$	1.70136	0.233699	0.116850	−	0.993150i	$-0.462720\pi$
$53$	1.70136	0.233699	0.116850	+	0.993150i	$0.462720\pi$
$54$	1.00000	0.136083
$55$	1.43215	0.193111
$56$	1.00000	0.133631
$57$	3.77694	0.500268
$58$	−9.52558	−1.25077
$59$	5.28919	0.688594	0.344297	−	0.938861i	$-0.388117\pi$
$59$	5.28919	0.688594	0.344297	+	0.938861i	$0.388117\pi$
$60$	1.43215	0.184889
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	2.81545	0.357563
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	1.43215	0.177636
$66$	1.00000	0.123091
$67$	−7.96497	−0.973076	−0.486538	−	0.873659i	$-0.661740\pi$
$67$	−7.96497	−0.973076	−0.486538	+	0.873659i	$0.661740\pi$
$68$	1.60945	0.195174
$69$	−2.24760	−0.270579
$70$	1.43215	0.171174
$71$	−2.42490	−0.287783	−0.143891	−	0.989593i	$-0.545962\pi$
$71$	−2.42490	−0.287783	−0.143891	+	0.989593i	$0.545962\pi$
$72$	1.00000	0.117851
$73$	9.91613	1.16060	0.580298	−	0.814405i	$-0.302936\pi$
$73$	9.91613	1.16060	0.580298	+	0.814405i	$0.302936\pi$
$74$	−1.04159	−0.121083
$75$	−2.94896	−0.340516
$76$	3.77694	0.433244
$77$	1.00000	0.113961
$78$	1.00000	0.113228
$79$	4.75281	0.534733	0.267366	−	0.963595i	$-0.413847\pi$
$79$	4.75281	0.534733	0.267366	+	0.963595i	$0.413847\pi$
$80$	1.43215	0.160119
$81$	1.00000	0.111111
$82$	10.5588	1.16603
$83$	−16.2469	−1.78333	−0.891665	−	0.452695i	$-0.850463\pi$
$83$	−16.2469	−1.78333	−0.891665	+	0.452695i	$0.850463\pi$
$84$	1.00000	0.109109
$85$	2.30496	0.250008
$86$	9.10068	0.981351
$87$	−9.52558	−1.02125
$88$	1.00000	0.106600
$89$	9.52558	1.00971	0.504855	−	0.863204i	$-0.331546\pi$
$89$	9.52558	1.00971	0.504855	+	0.863204i	$0.331546\pi$
$90$	1.43215	0.150962
$91$	1.00000	0.104828
$92$	−2.24760	−0.234328
$93$	2.81545	0.291949
$94$	4.41962	0.455849
$95$	5.40913	0.554965
$96$	1.00000	0.102062
$97$	13.5717	1.37800	0.689000	−	0.724762i	$-0.258050\pi$
$97$	13.5717	1.37800	0.689000	+	0.724762i	$0.258050\pi$
$98$	1.00000	0.101015
$99$	1.00000	0.100504
$100$	−2.94896	−0.294896
$101$	−15.9399	−1.58608	−0.793040	−	0.609169i	$-0.791503\pi$
$101$	−15.9399	−1.58608	−0.793040	+	0.609169i	$0.791503\pi$
$102$	1.60945	0.159359
$103$	−13.2224	−1.30284	−0.651421	−	0.758716i	$-0.725827\pi$
$103$	−13.2224	−1.30284	−0.651421	+	0.758716i	$0.725827\pi$
$104$	1.00000	0.0980581
$105$	1.43215	0.139763
$106$	1.70136	0.165250
$107$	−17.4776	−1.68962	−0.844812	−	0.535063i	$-0.820288\pi$
$107$	−17.4776	−1.68962	−0.844812	+	0.535063i	$0.820288\pi$
$108$	1.00000	0.0962250
$109$	−0.864294	−0.0827843	−0.0413922	−	0.999143i	$-0.513179\pi$
$109$	−0.864294	−0.0827843	−0.0413922	+	0.999143i	$0.513179\pi$
$110$	1.43215	0.136550
$111$	−1.04159	−0.0988636
$112$	1.00000	0.0944911
$113$	8.87982	0.835343	0.417671	−	0.908598i	$-0.362846\pi$
$113$	8.87982	0.835343	0.417671	+	0.908598i	$0.362846\pi$
$114$	3.77694	0.353743
$115$	−3.21889	−0.300163
$116$	−9.52558	−0.884428
$117$	1.00000	0.0924500
$118$	5.28919	0.486910
$119$	1.60945	0.147538
$120$	1.43215	0.130737
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	10.5588	0.952056
$124$	2.81545	0.252835
$125$	−11.3841	−1.01822
$126$	1.00000	0.0890871
$127$	−14.8851	−1.32084	−0.660418	−	0.750898i	$-0.729621\pi$
$127$	−14.8851	−1.32084	−0.660418	+	0.750898i	$0.729621\pi$
$128$	1.00000	0.0883883
$129$	9.10068	0.801270
$130$	1.43215	0.125608
$131$	−3.56826	−0.311760	−0.155880	−	0.987776i	$-0.549821\pi$
$131$	−3.56826	−0.311760	−0.155880	+	0.987776i	$0.549821\pi$
$132$	1.00000	0.0870388
$133$	3.77694	0.327502
$134$	−7.96497	−0.688069
$135$	1.43215	0.123260
$136$	1.60945	0.138009
$137$	11.9505	1.02100	0.510499	−	0.859878i	$-0.329461\pi$
$137$	11.9505	1.02100	0.510499	+	0.859878i	$0.329461\pi$
$138$	−2.24760	−0.191328
$139$	−7.09539	−0.601824	−0.300912	−	0.953652i	$-0.597291\pi$
$139$	−7.09539	−0.601824	−0.300912	+	0.953652i	$0.597291\pi$
$140$	1.43215	0.121038
$141$	4.41962	0.372199
$142$	−2.42490	−0.203493
$143$	1.00000	0.0836242
$144$	1.00000	0.0833333
$145$	−13.6420	−1.13291
$146$	9.91613	0.820665
$147$	1.00000	0.0824786
$148$	−1.04159	−0.0856184
$149$	−8.06216	−0.660478	−0.330239	−	0.943897i	$-0.607129\pi$
$149$	−8.06216	−0.660478	−0.330239	+	0.943897i	$0.607129\pi$
$150$	−2.94896	−0.240781
$151$	−12.9784	−1.05617	−0.528085	−	0.849192i	$-0.677090\pi$
$151$	−12.9784	−1.05617	−0.528085	+	0.849192i	$0.677090\pi$
$152$	3.77694	0.306350
$153$	1.60945	0.130116
$154$	1.00000	0.0805823
$155$	4.03214	0.323869
$156$	1.00000	0.0800641
$157$	−7.47415	−0.596502	−0.298251	−	0.954487i	$-0.596403\pi$
$157$	−7.47415	−0.596502	−0.298251	+	0.954487i	$0.596403\pi$
$158$	4.75281	0.378113
$159$	1.70136	0.134926
$160$	1.43215	0.113221
$161$	−2.24760	−0.177136
$162$	1.00000	0.0785674
$163$	−0.632872	−0.0495703	−0.0247852	−	0.999693i	$-0.507890\pi$
$163$	−0.632872	−0.0495703	−0.0247852	+	0.999693i	$0.507890\pi$
$164$	10.5588	0.824505
$165$	1.43215	0.111492
$166$	−16.2469	−1.26101
$167$	10.7176	0.829351	0.414676	−	0.909969i	$-0.363895\pi$
$167$	10.7176	0.829351	0.414676	+	0.909969i	$0.363895\pi$
$168$	1.00000	0.0771517
$169$	1.00000	0.0769231
$170$	2.30496	0.176783
$171$	3.77694	0.288830
$172$	9.10068	0.693920
$173$	−0.818147	−0.0622026	−0.0311013	−	0.999516i	$-0.509901\pi$
$173$	−0.818147	−0.0622026	−0.0311013	+	0.999516i	$0.509901\pi$
$174$	−9.52558	−0.722132
$175$	−2.94896	−0.222920
$176$	1.00000	0.0753778
$177$	5.28919	0.397560
$178$	9.52558	0.713972
$179$	13.7701	1.02923	0.514613	−	0.857423i	$-0.327936\pi$
$179$	13.7701	1.02923	0.514613	+	0.857423i	$0.327936\pi$
$180$	1.43215	0.106746
$181$	−3.91133	−0.290727	−0.145364	−	0.989378i	$-0.546435\pi$
$181$	−3.91133	−0.290727	−0.145364	+	0.989378i	$0.546435\pi$
$182$	1.00000	0.0741249
$183$	2.00000	0.147844
$184$	−2.24760	−0.165695
$185$	−1.49171	−0.109673
$186$	2.81545	0.206439
$187$	1.60945	0.117694
$188$	4.41962	0.322334
$189$	1.00000	0.0727393
$190$	5.40913	0.392419
$191$	19.1085	1.38264	0.691322	−	0.722547i	$-0.257029\pi$
$191$	19.1085	1.38264	0.691322	+	0.722547i	$0.257029\pi$
$192$	1.00000	0.0721688
$193$	4.78602	0.344505	0.172253	−	0.985053i	$-0.444895\pi$
$193$	4.78602	0.344505	0.172253	+	0.985053i	$0.444895\pi$
$194$	13.5717	0.974393
$195$	1.43215	0.102558
$196$	1.00000	0.0714286
$197$	−5.55247	−0.395597	−0.197798	−	0.980243i	$-0.563379\pi$
$197$	−5.55247	−0.395597	−0.197798	+	0.980243i	$0.563379\pi$
$198$	1.00000	0.0710669
$199$	3.63851	0.257927	0.128964	−	0.991649i	$-0.458835\pi$
$199$	3.63851	0.257927	0.128964	+	0.991649i	$0.458835\pi$
$200$	−2.94896	−0.208523
$201$	−7.96497	−0.561806
$202$	−15.9399	−1.12153
$203$	−9.52558	−0.668564
$204$	1.60945	0.112684
$205$	15.1218	1.05615
$206$	−13.2224	−0.921249
$207$	−2.24760	−0.156219
$208$	1.00000	0.0693375
$209$	3.77694	0.261256
$210$	1.43215	0.0988275
$211$	24.9174	1.71539	0.857693	−	0.514163i	$-0.171897\pi$
$211$	24.9174	1.71539	0.857693	+	0.514163i	$0.171897\pi$
$212$	1.70136	0.116850
$213$	−2.42490	−0.166151
$214$	−17.4776	−1.19474
$215$	13.0335	0.888878
$216$	1.00000	0.0680414
$217$	2.81545	0.191125
$218$	−0.864294	−0.0585373
$219$	9.91613	0.670070
$220$	1.43215	0.0965553
$221$	1.60945	0.108263
$222$	−1.04159	−0.0699072
$223$	8.40840	0.563068	0.281534	−	0.959551i	$-0.409157\pi$
$223$	8.40840	0.563068	0.281534	+	0.959551i	$0.409157\pi$
$224$	1.00000	0.0668153
$225$	−2.94896	−0.196597
$226$	8.87982	0.590677
$227$	8.08174	0.536404	0.268202	−	0.963363i	$-0.413571\pi$
$227$	8.08174	0.536404	0.268202	+	0.963363i	$0.413571\pi$
$228$	3.77694	0.250134
$229$	18.7554	1.23939	0.619695	−	0.784843i	$-0.287256\pi$
$229$	18.7554	1.23939	0.619695	+	0.784843i	$0.287256\pi$
$230$	−3.21889	−0.212248
$231$	1.00000	0.0657952
$232$	−9.52558	−0.625385
$233$	3.61969	0.237134	0.118567	−	0.992946i	$-0.462170\pi$
$233$	3.61969	0.237134	0.118567	+	0.992946i	$0.462170\pi$
$234$	1.00000	0.0653720
$235$	6.32954	0.412894
$236$	5.28919	0.344297
$237$	4.75281	0.308728
$238$	1.60945	0.104325
$239$	20.6821	1.33781	0.668906	−	0.743347i	$-0.266763\pi$
$239$	20.6821	1.33781	0.668906	+	0.743347i	$0.266763\pi$
$240$	1.43215	0.0924447
$241$	−1.15807	−0.0745979	−0.0372989	−	0.999304i	$-0.511875\pi$
$241$	−1.15807	−0.0745979	−0.0372989	+	0.999304i	$0.511875\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	1.43215	0.0914965
$246$	10.5588	0.673205
$247$	3.77694	0.240321
$248$	2.81545	0.178781
$249$	−16.2469	−1.02961
$250$	−11.3841	−0.719992
$251$	−19.8413	−1.25237	−0.626186	−	0.779673i	$-0.715385\pi$
$251$	−19.8413	−1.25237	−0.626186	+	0.779673i	$0.715385\pi$
$252$	1.00000	0.0629941
$253$	−2.24760	−0.141305
$254$	−14.8851	−0.933972
$255$	2.30496	0.144342
$256$	1.00000	0.0625000
$257$	−25.9925	−1.62137	−0.810683	−	0.585485i	$-0.800904\pi$
$257$	−25.9925	−1.62137	−0.810683	+	0.585485i	$0.800904\pi$
$258$	9.10068	0.566583
$259$	−1.04159	−0.0647215
$260$	1.43215	0.0888180
$261$	−9.52558	−0.589618
$262$	−3.56826	−0.220448
$263$	−3.67381	−0.226537	−0.113268	−	0.993564i	$-0.536132\pi$
$263$	−3.67381	−0.226537	−0.113268	+	0.993564i	$0.536132\pi$
$264$	1.00000	0.0615457
$265$	2.43659	0.149679
$266$	3.77694	0.231579
$267$	9.52558	0.582956
$268$	−7.96497	−0.486538
$269$	−20.6889	−1.26142	−0.630712	−	0.776017i	$-0.717237\pi$
$269$	−20.6889	−1.26142	−0.630712	+	0.776017i	$0.717237\pi$
$270$	1.43215	0.0871577
$271$	−17.9966	−1.09322	−0.546608	−	0.837388i	$-0.684081\pi$
$271$	−17.9966	−1.09322	−0.546608	+	0.837388i	$0.684081\pi$
$272$	1.60945	0.0975870
$273$	1.00000	0.0605228
$274$	11.9505	0.721955
$275$	−2.94896	−0.177829
$276$	−2.24760	−0.135290
$277$	−9.46887	−0.568929	−0.284465	−	0.958687i	$-0.591816\pi$
$277$	−9.46887	−0.568929	−0.284465	+	0.958687i	$0.591816\pi$
$278$	−7.09539	−0.425553
$279$	2.81545	0.168557
$280$	1.43215	0.0855871
$281$	12.6854	0.756750	0.378375	−	0.925652i	$-0.376483\pi$
$281$	12.6854	0.756750	0.378375	+	0.925652i	$0.376483\pi$
$282$	4.41962	0.263184
$283$	23.8795	1.41949	0.709746	−	0.704458i	$-0.248810\pi$
$283$	23.8795	1.41949	0.709746	+	0.704458i	$0.248810\pi$
$284$	−2.42490	−0.143891
$285$	5.40913	0.320409
$286$	1.00000	0.0591312
$287$	10.5588	0.623267
$288$	1.00000	0.0589256
$289$	−14.4097	−0.847628
$290$	−13.6420	−0.801087
$291$	13.5717	0.795588
$292$	9.91613	0.580298
$293$	−9.90847	−0.578859	−0.289430	−	0.957199i	$-0.593466\pi$
$293$	−9.90847	−0.578859	−0.289430	+	0.957199i	$0.593466\pi$
$294$	1.00000	0.0583212
$295$	7.57490	0.441028
$296$	−1.04159	−0.0605414
$297$	1.00000	0.0580259
$298$	−8.06216	−0.467028
$299$	−2.24760	−0.129982
$300$	−2.94896	−0.170258
$301$	9.10068	0.524554
$302$	−12.9784	−0.746825
$303$	−15.9399	−0.915724
$304$	3.77694	0.216622
$305$	2.86429	0.164009
$306$	1.60945	0.0920059
$307$	−13.1924	−0.752932	−0.376466	−	0.926430i	$-0.622861\pi$
$307$	−13.1924	−0.752932	−0.376466	+	0.926430i	$0.622861\pi$
$308$	1.00000	0.0569803
$309$	−13.2224	−0.752196
$310$	4.03214	0.229010
$311$	−30.1280	−1.70840	−0.854202	−	0.519941i	$-0.825954\pi$
$311$	−30.1280	−1.70840	−0.854202	+	0.519941i	$0.825954\pi$
$312$	1.00000	0.0566139
$313$	−4.86925	−0.275227	−0.137613	−	0.990486i	$-0.543943\pi$
$313$	−4.86925	−0.275227	−0.137613	+	0.990486i	$0.543943\pi$
$314$	−7.47415	−0.421791
$315$	1.43215	0.0806923
$316$	4.75281	0.267366
$317$	−21.3373	−1.19842	−0.599212	−	0.800590i	$-0.704520\pi$
$317$	−21.3373	−1.19842	−0.599212	+	0.800590i	$0.704520\pi$
$318$	1.70136	0.0954073
$319$	−9.52558	−0.533330
$320$	1.43215	0.0800594
$321$	−17.4776	−0.975505
$322$	−2.24760	−0.125254
$323$	6.07878	0.338232
$324$	1.00000	0.0555556
$325$	−2.94896	−0.163579
$326$	−0.632872	−0.0350515
$327$	−0.864294	−0.0477955
$328$	10.5588	0.583013
$329$	4.41962	0.243661
$330$	1.43215	0.0788371
$331$	4.73573	0.260299	0.130150	−	0.991494i	$-0.458454\pi$
$331$	4.73573	0.260299	0.130150	+	0.991494i	$0.458454\pi$
$332$	−16.2469	−0.891665
$333$	−1.04159	−0.0570790
$334$	10.7176	0.586440
$335$	−11.4070	−0.623231
$336$	1.00000	0.0545545
$337$	−13.4973	−0.735243	−0.367622	−	0.929975i	$-0.619828\pi$
$337$	−13.4973	−0.735243	−0.367622	+	0.929975i	$0.619828\pi$
$338$	1.00000	0.0543928
$339$	8.87982	0.482285
$340$	2.30496	0.125004
$341$	2.81545	0.152465
$342$	3.77694	0.204233
$343$	1.00000	0.0539949
$344$	9.10068	0.490676
$345$	−3.21889	−0.173299
$346$	−0.818147	−0.0439839
$347$	6.20964	0.333351	0.166676	−	0.986012i	$-0.446697\pi$
$347$	6.20964	0.333351	0.166676	+	0.986012i	$0.446697\pi$
$348$	−9.52558	−0.510624
$349$	−2.22037	−0.118854	−0.0594268	−	0.998233i	$-0.518927\pi$
$349$	−2.22037	−0.118854	−0.0594268	+	0.998233i	$0.518927\pi$
$350$	−2.94896	−0.157628
$351$	1.00000	0.0533761
$352$	1.00000	0.0533002
$353$	15.8290	0.842494	0.421247	−	0.906946i	$-0.361593\pi$
$353$	15.8290	0.842494	0.421247	+	0.906946i	$0.361593\pi$
$354$	5.28919	0.281117
$355$	−3.47281	−0.184318
$356$	9.52558	0.504855
$357$	1.60945	0.0851809
$358$	13.7701	0.727772
$359$	33.6190	1.77434	0.887171	−	0.461441i	$-0.152667\pi$
$359$	33.6190	1.77434	0.887171	+	0.461441i	$0.152667\pi$
$360$	1.43215	0.0754808
$361$	−4.73474	−0.249197
$362$	−3.91133	−0.205575
$363$	1.00000	0.0524864
$364$	1.00000	0.0524142
$365$	14.2014	0.743333
$366$	2.00000	0.104542
$367$	−12.3281	−0.643521	−0.321761	−	0.946821i	$-0.604275\pi$
$367$	−12.3281	−0.643521	−0.321761	+	0.946821i	$0.604275\pi$
$368$	−2.24760	−0.117164
$369$	10.5588	0.549670
$370$	−1.49171	−0.0775505
$371$	1.70136	0.0883300
$372$	2.81545	0.145974
$373$	1.07576	0.0557005	0.0278502	−	0.999612i	$-0.491134\pi$
$373$	1.07576	0.0557005	0.0278502	+	0.999612i	$0.491134\pi$
$374$	1.60945	0.0832225
$375$	−11.3841	−0.587871
$376$	4.41962	0.227924
$377$	−9.52558	−0.490592
$378$	1.00000	0.0514344
$379$	−15.2762	−0.784683	−0.392342	−	0.919820i	$-0.628335\pi$
$379$	−15.2762	−0.784683	−0.392342	+	0.919820i	$0.628335\pi$
$380$	5.40913	0.277482
$381$	−14.8851	−0.762585
$382$	19.1085	0.977677
$383$	−12.7804	−0.653047	−0.326523	−	0.945189i	$-0.605877\pi$
$383$	−12.7804	−0.653047	−0.326523	+	0.945189i	$0.605877\pi$
$384$	1.00000	0.0510310
$385$	1.43215	0.0729890
$386$	4.78602	0.243602
$387$	9.10068	0.462613
$388$	13.5717	0.689000
$389$	−1.91676	−0.0971838	−0.0485919	−	0.998819i	$-0.515473\pi$
$389$	−1.91676	−0.0971838	−0.0485919	+	0.998819i	$0.515473\pi$
$390$	1.43215	0.0725196
$391$	−3.61739	−0.182939
$392$	1.00000	0.0505076
$393$	−3.56826	−0.179995
$394$	−5.55247	−0.279729
$395$	6.80672	0.342483
$396$	1.00000	0.0502519
$397$	10.6057	0.532285	0.266143	−	0.963934i	$-0.414251\pi$
$397$	10.6057	0.532285	0.266143	+	0.963934i	$0.414251\pi$
$398$	3.63851	0.182382
$399$	3.77694	0.189083
$400$	−2.94896	−0.147448
$401$	−37.4896	−1.87214	−0.936072	−	0.351809i	$-0.885567\pi$
$401$	−37.4896	−1.87214	−0.936072	+	0.351809i	$0.885567\pi$
$402$	−7.96497	−0.397257
$403$	2.81545	0.140248
$404$	−15.9399	−0.793040
$405$	1.43215	0.0711639
$406$	−9.52558	−0.472746
$407$	−1.04159	−0.0516299
$408$	1.60945	0.0796795
$409$	0.0908413	0.00449181	0.00224591	−	0.999997i	$-0.499285\pi$
$409$	0.0908413	0.00449181	0.00224591	+	0.999997i	$0.499285\pi$
$410$	15.1218	0.746811
$411$	11.9505	0.589473
$412$	−13.2224	−0.651421
$413$	5.28919	0.260264
$414$	−2.24760	−0.110464
$415$	−23.2680	−1.14218
$416$	1.00000	0.0490290
$417$	−7.09539	−0.347463
$418$	3.77694	0.184736
$419$	−22.7777	−1.11276	−0.556382	−	0.830926i	$-0.687811\pi$
$419$	−22.7777	−1.11276	−0.556382	+	0.830926i	$0.687811\pi$
$420$	1.43215	0.0698816
$421$	−3.81855	−0.186105	−0.0930525	−	0.995661i	$-0.529662\pi$
$421$	−3.81855	−0.186105	−0.0930525	+	0.995661i	$0.529662\pi$
$422$	24.9174	1.21296
$423$	4.41962	0.214889
$424$	1.70136	0.0826251
$425$	−4.74619	−0.230224
$426$	−2.42490	−0.117487
$427$	2.00000	0.0967868
$428$	−17.4776	−0.844812
$429$	1.00000	0.0482805
$430$	13.0335	0.628531
$431$	−27.2163	−1.31096	−0.655482	−	0.755211i	$-0.727535\pi$
$431$	−27.2163	−1.31096	−0.655482	+	0.755211i	$0.727535\pi$
$432$	1.00000	0.0481125
$433$	−1.34458	−0.0646165	−0.0323083	−	0.999478i	$-0.510286\pi$
$433$	−1.34458	−0.0646165	−0.0323083	+	0.999478i	$0.510286\pi$
$434$	2.81545	0.135146
$435$	−13.6420	−0.654085
$436$	−0.864294	−0.0413922
$437$	−8.48904	−0.406086
$438$	9.91613	0.473811
$439$	38.0406	1.81558	0.907790	−	0.419425i	$-0.137768\pi$
$439$	38.0406	1.81558	0.907790	+	0.419425i	$0.137768\pi$
$440$	1.43215	0.0682749
$441$	1.00000	0.0476190
$442$	1.60945	0.0765536
$443$	4.46780	0.212272	0.106136	−	0.994352i	$-0.466152\pi$
$443$	4.46780	0.212272	0.106136	+	0.994352i	$0.466152\pi$
$444$	−1.04159	−0.0494318
$445$	13.6420	0.646694
$446$	8.40840	0.398149
$447$	−8.06216	−0.381327
$448$	1.00000	0.0472456
$449$	−20.8862	−0.985681	−0.492840	−	0.870120i	$-0.664041\pi$
$449$	−20.8862	−0.985681	−0.492840	+	0.870120i	$0.664041\pi$
$450$	−2.94896	−0.139015
$451$	10.5588	0.497195
$452$	8.87982	0.417671
$453$	−12.9784	−0.609780
$454$	8.08174	0.379295
$455$	1.43215	0.0671401
$456$	3.77694	0.176871
$457$	35.8799	1.67839	0.839195	−	0.543831i	$-0.183027\pi$
$457$	35.8799	1.67839	0.839195	+	0.543831i	$0.183027\pi$
$458$	18.7554	0.876381
$459$	1.60945	0.0751225
$460$	−3.21889	−0.150082
$461$	8.71899	0.406084	0.203042	−	0.979170i	$-0.434917\pi$
$461$	8.71899	0.406084	0.203042	+	0.979170i	$0.434917\pi$
$462$	1.00000	0.0465242
$463$	17.1968	0.799203	0.399602	−	0.916689i	$-0.369149\pi$
$463$	17.1968	0.799203	0.399602	+	0.916689i	$0.369149\pi$
$464$	−9.52558	−0.442214
$465$	4.03214	0.186986
$466$	3.61969	0.167679
$467$	15.0891	0.698241	0.349120	−	0.937078i	$-0.386480\pi$
$467$	15.0891	0.698241	0.349120	+	0.937078i	$0.386480\pi$
$468$	1.00000	0.0462250
$469$	−7.96497	−0.367788
$470$	6.32954	0.291960
$471$	−7.47415	−0.344391
$472$	5.28919	0.243455
$473$	9.10068	0.418450
$474$	4.75281	0.218304
$475$	−11.1380	−0.511047
$476$	1.60945	0.0737689
$477$	1.70136	0.0778997
$478$	20.6821	0.945975
$479$	25.8513	1.18118	0.590588	−	0.806973i	$-0.298896\pi$
$479$	25.8513	1.18118	0.590588	+	0.806973i	$0.298896\pi$
$480$	1.43215	0.0653683
$481$	−1.04159	−0.0474926
$482$	−1.15807	−0.0527487
$483$	−2.24760	−0.102269
$484$	1.00000	0.0454545
$485$	19.4367	0.882575
$486$	1.00000	0.0453609
$487$	16.5018	0.747769	0.373885	−	0.927475i	$-0.378026\pi$
$487$	16.5018	0.747769	0.373885	+	0.927475i	$0.378026\pi$
$488$	2.00000	0.0905357
$489$	−0.632872	−0.0286195
$490$	1.43215	0.0646978
$491$	16.5846	0.748452	0.374226	−	0.927338i	$-0.377908\pi$
$491$	16.5846	0.748452	0.374226	+	0.927338i	$0.377908\pi$
$492$	10.5588	0.476028
$493$	−15.3309	−0.690469
$494$	3.77694	0.169932
$495$	1.43215	0.0643702
$496$	2.81545	0.126418
$497$	−2.42490	−0.108772
$498$	−16.2469	−0.728042
$499$	−22.9238	−1.02621	−0.513106	−	0.858325i	$-0.671505\pi$
$499$	−22.9238	−1.02621	−0.513106	+	0.858325i	$0.671505\pi$
$500$	−11.3841	−0.509111
$501$	10.7176	0.478826
$502$	−19.8413	−0.885561
$503$	−20.9904	−0.935916	−0.467958	−	0.883751i	$-0.655010\pi$
$503$	−20.9904	−0.935916	−0.467958	+	0.883751i	$0.655010\pi$
$504$	1.00000	0.0445435
$505$	−22.8283	−1.01585
$506$	−2.24760	−0.0999180
$507$	1.00000	0.0444116
$508$	−14.8851	−0.660418
$509$	30.1848	1.33792	0.668959	−	0.743299i	$-0.266740\pi$
$509$	30.1848	1.33792	0.668959	+	0.743299i	$0.266740\pi$
$510$	2.30496	0.102065
$511$	9.91613	0.438664
$512$	1.00000	0.0441942
$513$	3.77694	0.166756
$514$	−25.9925	−1.14648
$515$	−18.9364	−0.834439
$516$	9.10068	0.400635
$517$	4.41962	0.194375
$518$	−1.04159	−0.0457650
$519$	−0.818147	−0.0359127
$520$	1.43215	0.0628038
$521$	16.2819	0.713324	0.356662	−	0.934234i	$-0.383915\pi$
$521$	16.2819	0.713324	0.356662	+	0.934234i	$0.383915\pi$
$522$	−9.52558	−0.416923
$523$	14.3709	0.628395	0.314197	−	0.949358i	$-0.398265\pi$
$523$	14.3709	0.628395	0.314197	+	0.949358i	$0.398265\pi$
$524$	−3.56826	−0.155880
$525$	−2.94896	−0.128703
$526$	−3.67381	−0.160186
$527$	4.53132	0.197387
$528$	1.00000	0.0435194
$529$	−17.9483	−0.780361
$530$	2.43659	0.105839
$531$	5.28919	0.229531
$532$	3.77694	0.163751
$533$	10.5588	0.457353
$534$	9.52558	0.412212
$535$	−25.0305	−1.08216
$536$	−7.96497	−0.344034
$537$	13.7701	0.594224
$538$	−20.6889	−0.891962
$539$	1.00000	0.0430730
$540$	1.43215	0.0616298
$541$	−14.1595	−0.608763	−0.304381	−	0.952550i	$-0.598450\pi$
$541$	−14.1595	−0.608763	−0.304381	+	0.952550i	$0.598450\pi$
$542$	−17.9966	−0.773021
$543$	−3.91133	−0.167851
$544$	1.60945	0.0690044
$545$	−1.23780	−0.0530213
$546$	1.00000	0.0427960
$547$	−0.843972	−0.0360857	−0.0180428	−	0.999837i	$-0.505744\pi$
$547$	−0.843972	−0.0360857	−0.0180428	+	0.999837i	$0.505744\pi$
$548$	11.9505	0.510499
$549$	2.00000	0.0853579
$550$	−2.94896	−0.125744
$551$	−35.9775	−1.53269
$552$	−2.24760	−0.0956642
$553$	4.75281	0.202110
$554$	−9.46887	−0.402294
$555$	−1.49171	−0.0633197
$556$	−7.09539	−0.300912
$557$	4.03997	0.171179	0.0855895	−	0.996330i	$-0.472723\pi$
$557$	4.03997	0.171179	0.0855895	+	0.996330i	$0.472723\pi$
$558$	2.81545	0.119188
$559$	9.10068	0.384918
$560$	1.43215	0.0605192
$561$	1.60945	0.0679509
$562$	12.6854	0.535103
$563$	−19.5806	−0.825223	−0.412611	−	0.910907i	$-0.635383\pi$
$563$	−19.5806	−0.825223	−0.412611	+	0.910907i	$0.635383\pi$
$564$	4.41962	0.186099
$565$	12.7172	0.535017
$566$	23.8795	1.00373
$567$	1.00000	0.0419961
$568$	−2.42490	−0.101747
$569$	−29.9841	−1.25700	−0.628499	−	0.777810i	$-0.716330\pi$
$569$	−29.9841	−1.25700	−0.628499	+	0.777810i	$0.716330\pi$
$570$	5.40913	0.226563
$571$	41.2980	1.72827	0.864135	−	0.503261i	$-0.167867\pi$
$571$	41.2980	1.72827	0.864135	+	0.503261i	$0.167867\pi$
$572$	1.00000	0.0418121
$573$	19.1085	0.798270
$574$	10.5588	0.440716
$575$	6.62807	0.276410
$576$	1.00000	0.0416667
$577$	−14.5800	−0.606973	−0.303487	−	0.952836i	$-0.598151\pi$
$577$	−14.5800	−0.606973	−0.303487	+	0.952836i	$0.598151\pi$
$578$	−14.4097	−0.599364
$579$	4.78602	0.198900
$580$	−13.6420	−0.566454
$581$	−16.2469	−0.674036
$582$	13.5717	0.562566
$583$	1.70136	0.0704630
$584$	9.91613	0.410332
$585$	1.43215	0.0592120
$586$	−9.90847	−0.409315
$587$	9.81642	0.405167	0.202584	−	0.979265i	$-0.435066\pi$
$587$	9.81642	0.405167	0.202584	+	0.979265i	$0.435066\pi$
$588$	1.00000	0.0412393
$589$	10.6338	0.438158
$590$	7.57490	0.311854
$591$	−5.55247	−0.228398
$592$	−1.04159	−0.0428092
$593$	−36.7231	−1.50804	−0.754018	−	0.656853i	$-0.771887\pi$
$593$	−36.7231	−1.50804	−0.754018	+	0.656853i	$0.771887\pi$
$594$	1.00000	0.0410305
$595$	2.30496	0.0944943
$596$	−8.06216	−0.330239
$597$	3.63851	0.148914
$598$	−2.24760	−0.0919112
$599$	−7.77146	−0.317533	−0.158767	−	0.987316i	$-0.550752\pi$
$599$	−7.77146	−0.317533	−0.158767	+	0.987316i	$0.550752\pi$
$600$	−2.94896	−0.120391
$601$	14.0502	0.573120	0.286560	−	0.958062i	$-0.407488\pi$
$601$	14.0502	0.573120	0.286560	+	0.958062i	$0.407488\pi$
$602$	9.10068	0.370916
$603$	−7.96497	−0.324359
$604$	−12.9784	−0.528085
$605$	1.43215	0.0582250
$606$	−15.9399	−0.647515
$607$	−12.9738	−0.526590	−0.263295	−	0.964715i	$-0.584809\pi$
$607$	−12.9738	−0.526590	−0.263295	+	0.964715i	$0.584809\pi$
$608$	3.77694	0.153175
$609$	−9.52558	−0.385996
$610$	2.86429	0.115972
$611$	4.41962	0.178799
$612$	1.60945	0.0650580
$613$	7.71672	0.311675	0.155838	−	0.987783i	$-0.450192\pi$
$613$	7.71672	0.311675	0.155838	+	0.987783i	$0.450192\pi$
$614$	−13.1924	−0.532403
$615$	15.1218	0.609768
$616$	1.00000	0.0402911
$617$	−16.3666	−0.658896	−0.329448	−	0.944174i	$-0.606863\pi$
$617$	−16.3666	−0.658896	−0.329448	+	0.944174i	$0.606863\pi$
$618$	−13.2224	−0.531883
$619$	−37.3389	−1.50078	−0.750389	−	0.660996i	$-0.770134\pi$
$619$	−37.3389	−1.50078	−0.750389	+	0.660996i	$0.770134\pi$
$620$	4.03214	0.161935
$621$	−2.24760	−0.0901931
$622$	−30.1280	−1.20802
$623$	9.52558	0.381634
$624$	1.00000	0.0400320
$625$	−1.55888	−0.0623553
$626$	−4.86925	−0.194615
$627$	3.77694	0.150836
$628$	−7.47415	−0.298251
$629$	−1.67639	−0.0668420
$630$	1.43215	0.0570581
$631$	14.4793	0.576410	0.288205	−	0.957569i	$-0.406941\pi$
$631$	14.4793	0.576410	0.288205	+	0.957569i	$0.406941\pi$
$632$	4.75281	0.189057
$633$	24.9174	0.990378
$634$	−21.3373	−0.847414
$635$	−21.3176	−0.845963
$636$	1.70136	0.0674631
$637$	1.00000	0.0396214
$638$	−9.52558	−0.377121
$639$	−2.42490	−0.0959275
$640$	1.43215	0.0566106
$641$	−24.9986	−0.987384	−0.493692	−	0.869637i	$-0.664353\pi$
$641$	−24.9986	−0.987384	−0.493692	+	0.869637i	$0.664353\pi$
$642$	−17.4776	−0.689786
$643$	−19.5060	−0.769240	−0.384620	−	0.923075i	$-0.625667\pi$
$643$	−19.5060	−0.769240	−0.384620	+	0.923075i	$0.625667\pi$
$644$	−2.24760	−0.0885678
$645$	13.0335	0.513194
$646$	6.07878	0.239166
$647$	7.85953	0.308990	0.154495	−	0.987994i	$-0.450625\pi$
$647$	7.85953	0.308990	0.154495	+	0.987994i	$0.450625\pi$
$648$	1.00000	0.0392837
$649$	5.28919	0.207619
$650$	−2.94896	−0.115668
$651$	2.81545	0.110346
$652$	−0.632872	−0.0247852
$653$	−15.6553	−0.612638	−0.306319	−	0.951929i	$-0.599097\pi$
$653$	−15.6553	−0.612638	−0.306319	+	0.951929i	$0.599097\pi$
$654$	−0.864294	−0.0337966
$655$	−5.11027	−0.199675
$656$	10.5588	0.412252
$657$	9.91613	0.386865
$658$	4.41962	0.172295
$659$	23.8376	0.928583	0.464291	−	0.885682i	$-0.346309\pi$
$659$	23.8376	0.928583	0.464291	+	0.885682i	$0.346309\pi$
$660$	1.43215	0.0557462
$661$	−46.6414	−1.81414	−0.907070	−	0.420979i	$-0.861686\pi$
$661$	−46.6414	−1.81414	−0.907070	+	0.420979i	$0.861686\pi$
$662$	4.73573	0.184059
$663$	1.60945	0.0625057
$664$	−16.2469	−0.630503
$665$	5.40913	0.209757
$666$	−1.04159	−0.0403609
$667$	21.4097	0.828986
$668$	10.7176	0.414676
$669$	8.40840	0.325088
$670$	−11.4070	−0.440691
$671$	2.00000	0.0772091
$672$	1.00000	0.0385758
$673$	23.0056	0.886801	0.443401	−	0.896324i	$-0.353772\pi$
$673$	23.0056	0.886801	0.443401	+	0.896324i	$0.353772\pi$
$674$	−13.4973	−0.519896
$675$	−2.94896	−0.113505
$676$	1.00000	0.0384615
$677$	−7.22444	−0.277658	−0.138829	−	0.990316i	$-0.544334\pi$
$677$	−7.22444	−0.277658	−0.138829	+	0.990316i	$0.544334\pi$
$678$	8.87982	0.341027
$679$	13.5717	0.520835
$680$	2.30496	0.0883913
$681$	8.08174	0.309693
$682$	2.81545	0.107809
$683$	−36.3632	−1.39140	−0.695699	−	0.718334i	$-0.744905\pi$
$683$	−36.3632	−1.39140	−0.695699	+	0.718334i	$0.744905\pi$
$684$	3.77694	0.144415
$685$	17.1148	0.653924
$686$	1.00000	0.0381802
$687$	18.7554	0.715562
$688$	9.10068	0.346960
$689$	1.70136	0.0648165
$690$	−3.21889	−0.122541
$691$	42.8089	1.62853	0.814263	−	0.580496i	$-0.197141\pi$
$691$	42.8089	1.62853	0.814263	+	0.580496i	$0.197141\pi$
$692$	−0.818147	−0.0311013
$693$	1.00000	0.0379869
$694$	6.20964	0.235715
$695$	−10.1616	−0.385453
$696$	−9.52558	−0.361066
$697$	16.9938	0.643688
$698$	−2.22037	−0.0840422
$699$	3.61969	0.136909
$700$	−2.94896	−0.111460
$701$	−20.9827	−0.792508	−0.396254	−	0.918141i	$-0.629690\pi$
$701$	−20.9827	−0.792508	−0.396254	+	0.918141i	$0.629690\pi$
$702$	1.00000	0.0377426
$703$	−3.93403	−0.148375
$704$	1.00000	0.0376889
$705$	6.32954	0.238384
$706$	15.8290	0.595733
$707$	−15.9399	−0.599482
$708$	5.28919	0.198780
$709$	−36.7027	−1.37840	−0.689199	−	0.724572i	$-0.742037\pi$
$709$	−36.7027	−1.37840	−0.689199	+	0.724572i	$0.742037\pi$
$710$	−3.47281	−0.130332
$711$	4.75281	0.178244
$712$	9.52558	0.356986
$713$	−6.32801	−0.236986
$714$	1.60945	0.0602320
$715$	1.43215	0.0535593
$716$	13.7701	0.514613
$717$	20.6821	0.772386
$718$	33.6190	1.25465
$719$	−3.54901	−0.132356	−0.0661778	−	0.997808i	$-0.521080\pi$
$719$	−3.54901	−0.132356	−0.0661778	+	0.997808i	$0.521080\pi$
$720$	1.43215	0.0533730
$721$	−13.2224	−0.492428
$722$	−4.73474	−0.176209
$723$	−1.15807	−0.0430691
$724$	−3.91133	−0.145364
$725$	28.0905	1.04325
$726$	1.00000	0.0371135
$727$	−16.0547	−0.595435	−0.297717	−	0.954654i	$-0.596225\pi$
$727$	−16.0547	−0.595435	−0.297717	+	0.954654i	$0.596225\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	14.2014	0.525616
$731$	14.6471	0.541741
$732$	2.00000	0.0739221
$733$	−16.1063	−0.594899	−0.297449	−	0.954738i	$-0.596136\pi$
$733$	−16.1063	−0.594899	−0.297449	+	0.954738i	$0.596136\pi$
$734$	−12.3281	−0.455038
$735$	1.43215	0.0528255
$736$	−2.24760	−0.0828476
$737$	−7.96497	−0.293393
$738$	10.5588	0.388675
$739$	26.6666	0.980946	0.490473	−	0.871456i	$-0.336824\pi$
$739$	26.6666	0.980946	0.490473	+	0.871456i	$0.336824\pi$
$740$	−1.49171	−0.0548365
$741$	3.77694	0.138749
$742$	1.70136	0.0624587
$743$	−43.1568	−1.58327	−0.791635	−	0.610994i	$-0.790770\pi$
$743$	−43.1568	−1.58327	−0.791635	+	0.610994i	$0.790770\pi$
$744$	2.81545	0.103220
$745$	−11.5462	−0.423020
$746$	1.07576	0.0393862
$747$	−16.2469	−0.594444
$748$	1.60945	0.0588472
$749$	−17.4776	−0.638618
$750$	−11.3841	−0.415688
$751$	−22.0979	−0.806362	−0.403181	−	0.915120i	$-0.632096\pi$
$751$	−22.0979	−0.806362	−0.403181	+	0.915120i	$0.632096\pi$
$752$	4.41962	0.161167
$753$	−19.8413	−0.723058
$754$	−9.52558	−0.346901
$755$	−18.5870	−0.676451
$756$	1.00000	0.0363696
$757$	−4.68005	−0.170099	−0.0850496	−	0.996377i	$-0.527105\pi$
$757$	−4.68005	−0.170099	−0.0850496	+	0.996377i	$0.527105\pi$
$758$	−15.2762	−0.554855
$759$	−2.24760	−0.0815827
$760$	5.40913	0.196210
$761$	9.11831	0.330538	0.165269	−	0.986248i	$-0.447151\pi$
$761$	9.11831	0.330538	0.165269	+	0.986248i	$0.447151\pi$
$762$	−14.8851	−0.539229
$763$	−0.864294	−0.0312895
$764$	19.1085	0.691322
$765$	2.30496	0.0833361
$766$	−12.7804	−0.461774
$767$	5.28919	0.190982
$768$	1.00000	0.0360844
$769$	11.1340	0.401502	0.200751	−	0.979642i	$-0.435662\pi$
$769$	11.1340	0.401502	0.200751	+	0.979642i	$0.435662\pi$
$770$	1.43215	0.0516110
$771$	−25.9925	−0.936096
$772$	4.78602	0.172253
$773$	3.01604	0.108479	0.0542397	−	0.998528i	$-0.482726\pi$
$773$	3.01604	0.108479	0.0542397	+	0.998528i	$0.482726\pi$
$774$	9.10068	0.327117
$775$	−8.30265	−0.298240
$776$	13.5717	0.487196
$777$	−1.04159	−0.0373669
$778$	−1.91676	−0.0687193
$779$	39.8800	1.42885
$780$	1.43215	0.0512791
$781$	−2.42490	−0.0867697
$782$	−3.61739	−0.129358
$783$	−9.52558	−0.340416
$784$	1.00000	0.0357143
$785$	−10.7041	−0.382045
$786$	−3.56826	−0.127276
$787$	15.1412	0.539725	0.269862	−	0.962899i	$-0.413022\pi$
$787$	15.1412	0.539725	0.269862	+	0.962899i	$0.413022\pi$
$788$	−5.55247	−0.197798
$789$	−3.67381	−0.130791
$790$	6.80672	0.242172
$791$	8.87982	0.315730
$792$	1.00000	0.0355335
$793$	2.00000	0.0710221
$794$	10.6057	0.376383
$795$	2.43659	0.0864170
$796$	3.63851	0.128964
$797$	−13.2676	−0.469963	−0.234982	−	0.972000i	$-0.575503\pi$
$797$	−13.2676	−0.469963	−0.234982	+	0.972000i	$0.575503\pi$
$798$	3.77694	0.133702
$799$	7.11314	0.251645
$800$	−2.94896	−0.104261
$801$	9.52558	0.336570
$802$	−37.4896	−1.32381
$803$	9.91613	0.349933
$804$	−7.96497	−0.280903
$805$	−3.21889	−0.113451
$806$	2.81545	0.0991701
$807$	−20.6889	−0.728284
$808$	−15.9399	−0.560764
$809$	18.2846	0.642854	0.321427	−	0.946934i	$-0.395838\pi$
$809$	18.2846	0.642854	0.321427	+	0.946934i	$0.395838\pi$
$810$	1.43215	0.0503205
$811$	−8.66619	−0.304311	−0.152156	−	0.988357i	$-0.548621\pi$
$811$	−8.66619	−0.304311	−0.152156	+	0.988357i	$0.548621\pi$
$812$	−9.52558	−0.334282
$813$	−17.9966	−0.631169
$814$	−1.04159	−0.0365078
$815$	−0.906365	−0.0317486
$816$	1.60945	0.0563419
$817$	34.3727	1.20255
$818$	0.0908413	0.00317619
$819$	1.00000	0.0349428
$820$	15.1218	0.528075
$821$	−26.9338	−0.939996	−0.469998	−	0.882667i	$-0.655745\pi$
$821$	−26.9338	−0.939996	−0.469998	+	0.882667i	$0.655745\pi$
$822$	11.9505	0.416821
$823$	−5.55469	−0.193624	−0.0968122	−	0.995303i	$-0.530865\pi$
$823$	−5.55469	−0.193624	−0.0968122	+	0.995303i	$0.530865\pi$
$824$	−13.2224	−0.460624
$825$	−2.94896	−0.102669
$826$	5.28919	0.184035
$827$	25.8335	0.898318	0.449159	−	0.893452i	$-0.351724\pi$
$827$	25.8335	0.898318	0.449159	+	0.893452i	$0.351724\pi$
$828$	−2.24760	−0.0781095
$829$	−56.3722	−1.95789	−0.978943	−	0.204133i	$-0.934562\pi$
$829$	−56.3722	−1.95789	−0.978943	+	0.204133i	$0.934562\pi$
$830$	−23.2680	−0.807643
$831$	−9.46887	−0.328471
$832$	1.00000	0.0346688
$833$	1.60945	0.0557640
$834$	−7.09539	−0.245693
$835$	15.3491	0.531179
$836$	3.77694	0.130628
$837$	2.81545	0.0973163
$838$	−22.7777	−0.786844
$839$	−1.20513	−0.0416058	−0.0208029	−	0.999784i	$-0.506622\pi$
$839$	−1.20513	−0.0416058	−0.0208029	+	0.999784i	$0.506622\pi$
$840$	1.43215	0.0494138
$841$	61.7366	2.12885
$842$	−3.81855	−0.131596
$843$	12.6854	0.436910
$844$	24.9174	0.857693
$845$	1.43215	0.0492673
$846$	4.41962	0.151950
$847$	1.00000	0.0343604
$848$	1.70136	0.0584248
$849$	23.8795	0.819544
$850$	−4.74619	−0.162793
$851$	2.34108	0.0802513
$852$	−2.42490	−0.0830757
$853$	29.9832	1.02661	0.513303	−	0.858208i	$-0.328422\pi$
$853$	29.9832	1.02661	0.513303	+	0.858208i	$0.328422\pi$
$854$	2.00000	0.0684386
$855$	5.40913	0.184988
$856$	−17.4776	−0.597372
$857$	−17.9974	−0.614779	−0.307389	−	0.951584i	$-0.599455\pi$
$857$	−17.9974	−0.614779	−0.307389	+	0.951584i	$0.599455\pi$
$858$	1.00000	0.0341394
$859$	24.0433	0.820345	0.410173	−	0.912008i	$-0.365468\pi$
$859$	24.0433	0.820345	0.410173	+	0.912008i	$0.365468\pi$
$860$	13.0335	0.444439
$861$	10.5588	0.359843
$862$	−27.2163	−0.926992
$863$	−55.4481	−1.88748	−0.943738	−	0.330695i	$-0.892717\pi$
$863$	−55.4481	−1.88748	−0.943738	+	0.330695i	$0.892717\pi$
$864$	1.00000	0.0340207
$865$	−1.17171	−0.0398392
$866$	−1.34458	−0.0456908
$867$	−14.4097	−0.489378
$868$	2.81545	0.0955627
$869$	4.75281	0.161228
$870$	−13.6420	−0.462508
$871$	−7.96497	−0.269883
$872$	−0.864294	−0.0292687
$873$	13.5717	0.459333
$874$	−8.48904	−0.287146
$875$	−11.3841	−0.384852
$876$	9.91613	0.335035
$877$	−0.966996	−0.0326532	−0.0163266	−	0.999867i	$-0.505197\pi$
$877$	−0.966996	−0.0326532	−0.0163266	+	0.999867i	$0.505197\pi$
$878$	38.0406	1.28381
$879$	−9.90847	−0.334205
$880$	1.43215	0.0482777
$881$	−43.4442	−1.46367	−0.731836	−	0.681480i	$-0.761336\pi$
$881$	−43.4442	−1.46367	−0.731836	+	0.681480i	$0.761336\pi$
$882$	1.00000	0.0336718
$883$	−7.63732	−0.257016	−0.128508	−	0.991708i	$-0.541019\pi$
$883$	−7.63732	−0.257016	−0.128508	+	0.991708i	$0.541019\pi$
$884$	1.60945	0.0541315
$885$	7.57490	0.254627
$886$	4.46780	0.150099
$887$	31.5086	1.05796	0.528978	−	0.848636i	$-0.322575\pi$
$887$	31.5086	1.05796	0.528978	+	0.848636i	$0.322575\pi$
$888$	−1.04159	−0.0349536
$889$	−14.8851	−0.499229
$890$	13.6420	0.457282
$891$	1.00000	0.0335013
$892$	8.40840	0.281534
$893$	16.6926	0.558597
$894$	−8.06216	−0.269639
$895$	19.7208	0.659194
$896$	1.00000	0.0334077
$897$	−2.24760	−0.0750452
$898$	−20.8862	−0.696981
$899$	−26.8188	−0.894457
$900$	−2.94896	−0.0982985
$901$	2.73824	0.0912240
$902$	10.5588	0.351570
$903$	9.10068	0.302852
$904$	8.87982	0.295338
$905$	−5.60160	−0.186204
$906$	−12.9784	−0.431179
$907$	−46.3499	−1.53902	−0.769511	−	0.638634i	$-0.779500\pi$
$907$	−46.3499	−1.53902	−0.769511	+	0.638634i	$0.779500\pi$
$908$	8.08174	0.268202
$909$	−15.9399	−0.528694
$910$	1.43215	0.0474752
$911$	22.1098	0.732531	0.366266	−	0.930510i	$-0.380636\pi$
$911$	22.1098	0.732531	0.366266	+	0.930510i	$0.380636\pi$
$912$	3.77694	0.125067
$913$	−16.2469	−0.537694
$914$	35.8799	1.18680
$915$	2.86429	0.0946906
$916$	18.7554	0.619695
$917$	−3.56826	−0.117834
$918$	1.60945	0.0531196
$919$	22.5961	0.745377	0.372689	−	0.927956i	$-0.378436\pi$
$919$	22.5961	0.745377	0.372689	+	0.927956i	$0.378436\pi$
$920$	−3.21889	−0.106124
$921$	−13.1924	−0.434706
$922$	8.71899	0.287145
$923$	−2.42490	−0.0798165
$924$	1.00000	0.0328976
$925$	3.07161	0.100994
$926$	17.1968	0.565122
$927$	−13.2224	−0.434281
$928$	−9.52558	−0.312692
$929$	−12.2870	−0.403124	−0.201562	−	0.979476i	$-0.564602\pi$
$929$	−12.2870	−0.403124	−0.201562	+	0.979476i	$0.564602\pi$
$930$	4.03214	0.132219
$931$	3.77694	0.123784
$932$	3.61969	0.118567
$933$	−30.1280	−0.986348
$934$	15.0891	0.493731
$935$	2.30496	0.0753804
$936$	1.00000	0.0326860
$937$	−28.3961	−0.927661	−0.463831	−	0.885924i	$-0.653525\pi$
$937$	−28.3961	−0.927661	−0.463831	+	0.885924i	$0.653525\pi$
$938$	−7.96497	−0.260065
$939$	−4.86925	−0.158902
$940$	6.32954	0.206447
$941$	−1.93152	−0.0629658	−0.0314829	−	0.999504i	$-0.510023\pi$
$941$	−1.93152	−0.0629658	−0.0314829	+	0.999504i	$0.510023\pi$
$942$	−7.47415	−0.243521
$943$	−23.7320	−0.772820
$944$	5.28919	0.172149
$945$	1.43215	0.0465877
$946$	9.10068	0.295889
$947$	−52.7965	−1.71565	−0.857827	−	0.513938i	$-0.828186\pi$
$947$	−52.7965	−1.71565	−0.857827	+	0.513938i	$0.828186\pi$
$948$	4.75281	0.154364
$949$	9.91613	0.321891
$950$	−11.1380	−0.361365
$951$	−21.3373	−0.691911
$952$	1.60945	0.0521625
$953$	−9.55109	−0.309390	−0.154695	−	0.987962i	$-0.549439\pi$
$953$	−9.55109	−0.309390	−0.154695	+	0.987962i	$0.549439\pi$
$954$	1.70136	0.0550834
$955$	27.3662	0.885549
$956$	20.6821	0.668906
$957$	−9.52558	−0.307918
$958$	25.8513	0.835218
$959$	11.9505	0.385901
$960$	1.43215	0.0462223
$961$	−23.0732	−0.744298
$962$	−1.04159	−0.0335823
$963$	−17.4776	−0.563208
$964$	−1.15807	−0.0372989
$965$	6.85428	0.220647
$966$	−2.24760	−0.0723153
$967$	−5.46013	−0.175586	−0.0877929	−	0.996139i	$-0.527981\pi$
$967$	−5.46013	−0.175586	−0.0877929	+	0.996139i	$0.527981\pi$
$968$	1.00000	0.0321412
$969$	6.07878	0.195279
$970$	19.4367	0.624075
$971$	1.75240	0.0562371	0.0281186	−	0.999605i	$-0.491048\pi$
$971$	1.75240	0.0562371	0.0281186	+	0.999605i	$0.491048\pi$
$972$	1.00000	0.0320750
$973$	−7.09539	−0.227468
$974$	16.5018	0.528753
$975$	−2.94896	−0.0944422
$976$	2.00000	0.0640184
$977$	15.8161	0.506003	0.253002	−	0.967466i	$-0.418582\pi$
$977$	15.8161	0.506003	0.253002	+	0.967466i	$0.418582\pi$
$978$	−0.632872	−0.0202370
$979$	9.52558	0.304439
$980$	1.43215	0.0457483
$981$	−0.864294	−0.0275948
$982$	16.5846	0.529236
$983$	14.8833	0.474703	0.237351	−	0.971424i	$-0.423721\pi$
$983$	14.8833	0.474703	0.237351	+	0.971424i	$0.423721\pi$
$984$	10.5588	0.336603
$985$	−7.95195	−0.253370
$986$	−15.3309	−0.488235
$987$	4.41962	0.140678
$988$	3.77694	0.120160
$989$	−20.4547	−0.650421
$990$	1.43215	0.0455166
$991$	27.6215	0.877426	0.438713	−	0.898627i	$-0.355435\pi$
$991$	27.6215	0.877426	0.438713	+	0.898627i	$0.355435\pi$
$992$	2.81545	0.0893907
$993$	4.73573	0.150284
$994$	−2.42490	−0.0769131
$995$	5.21088	0.165196
$996$	−16.2469	−0.514803
$997$	27.6645	0.876142	0.438071	−	0.898940i	$-0.355662\pi$
$997$	27.6645	0.876142	0.438071	+	0.898940i	$0.355662\pi$
$998$	−22.9238	−0.725641
$999$	−1.04159	−0.0329545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6006.2.a.cg.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6006.2.a.cg.1.5	✓	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.43215 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.43215 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.43215 q^{10} +1.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +1.43215 q^{15} +1.00000 q^{16} +1.60945 q^{17} +1.00000 q^{18} +3.77694 q^{19} +1.43215 q^{20} +1.00000 q^{21} +1.00000 q^{22} -2.24760 q^{23} +1.00000 q^{24} -2.94896 q^{25} +1.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -9.52558 q^{29} +1.43215 q^{30} +2.81545 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.60945 q^{34} +1.43215 q^{35} +1.00000 q^{36} -1.04159 q^{37} +3.77694 q^{38} +1.00000 q^{39} +1.43215 q^{40} +10.5588 q^{41} +1.00000 q^{42} +9.10068 q^{43} +1.00000 q^{44} +1.43215 q^{45} -2.24760 q^{46} +4.41962 q^{47} +1.00000 q^{48} +1.00000 q^{49} -2.94896 q^{50} +1.60945 q^{51} +1.00000 q^{52} +1.70136 q^{53} +1.00000 q^{54} +1.43215 q^{55} +1.00000 q^{56} +3.77694 q^{57} -9.52558 q^{58} +5.28919 q^{59} +1.43215 q^{60} +2.00000 q^{61} +2.81545 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.43215 q^{65} +1.00000 q^{66} -7.96497 q^{67} +1.60945 q^{68} -2.24760 q^{69} +1.43215 q^{70} -2.42490 q^{71} +1.00000 q^{72} +9.91613 q^{73} -1.04159 q^{74} -2.94896 q^{75} +3.77694 q^{76} +1.00000 q^{77} +1.00000 q^{78} +4.75281 q^{79} +1.43215 q^{80} +1.00000 q^{81} +10.5588 q^{82} -16.2469 q^{83} +1.00000 q^{84} +2.30496 q^{85} +9.10068 q^{86} -9.52558 q^{87} +1.00000 q^{88} +9.52558 q^{89} +1.43215 q^{90} +1.00000 q^{91} -2.24760 q^{92} +2.81545 q^{93} +4.41962 q^{94} +5.40913 q^{95} +1.00000 q^{96} +13.5717 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} + 7 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 + 7 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} + 7 q^{7} + 7 q^{8} + 7 q^{9} + 2 q^{10} + 7 q^{11} + 7 q^{12} + 7 q^{13} + 7 q^{14} + 2 q^{15} + 7 q^{16} + 6 q^{17} + 7 q^{18} + 4 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 2 q^{23} + 7 q^{24} + 17 q^{25} + 7 q^{26} + 7 q^{27} + 7 q^{28} + 6 q^{29} + 2 q^{30} + 10 q^{31} + 7 q^{32} + 7 q^{33} + 6 q^{34} + 2 q^{35} + 7 q^{36} + 6 q^{37} + 4 q^{38} + 7 q^{39} + 2 q^{40} - 4 q^{41} + 7 q^{42} + 6 q^{43} + 7 q^{44} + 2 q^{45} + 2 q^{46} - 2 q^{47} + 7 q^{48} + 7 q^{49} + 17 q^{50} + 6 q^{51} + 7 q^{52} - 8 q^{53} + 7 q^{54} + 2 q^{55} + 7 q^{56} + 4 q^{57} + 6 q^{58} + 6 q^{59} + 2 q^{60} + 14 q^{61} + 10 q^{62} + 7 q^{63} + 7 q^{64} + 2 q^{65} + 7 q^{66} + 18 q^{67} + 6 q^{68} + 2 q^{69} + 2 q^{70} - 2 q^{71} + 7 q^{72} + 2 q^{73} + 6 q^{74} + 17 q^{75} + 4 q^{76} + 7 q^{77} + 7 q^{78} + 16 q^{79} + 2 q^{80} + 7 q^{81} - 4 q^{82} - 2 q^{83} + 7 q^{84} - 12 q^{85} + 6 q^{86} + 6 q^{87} + 7 q^{88} - 6 q^{89} + 2 q^{90} + 7 q^{91} + 2 q^{92} + 10 q^{93} - 2 q^{94} + 20 q^{95} + 7 q^{96} - 12 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 + 7 * q^7 + 7 * q^8 + 7 * q^9 + 2 * q^10 + 7 * q^11 + 7 * q^12 + 7 * q^13 + 7 * q^14 + 2 * q^15 + 7 * q^16 + 6 * q^17 + 7 * q^18 + 4 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 2 * q^23 + 7 * q^24 + 17 * q^25 + 7 * q^26 + 7 * q^27 + 7 * q^28 + 6 * q^29 + 2 * q^30 + 10 * q^31 + 7 * q^32 + 7 * q^33 + 6 * q^34 + 2 * q^35 + 7 * q^36 + 6 * q^37 + 4 * q^38 + 7 * q^39 + 2 * q^40 - 4 * q^41 + 7 * q^42 + 6 * q^43 + 7 * q^44 + 2 * q^45 + 2 * q^46 - 2 * q^47 + 7 * q^48 + 7 * q^49 + 17 * q^50 + 6 * q^51 + 7 * q^52 - 8 * q^53 + 7 * q^54 + 2 * q^55 + 7 * q^56 + 4 * q^57 + 6 * q^58 + 6 * q^59 + 2 * q^60 + 14 * q^61 + 10 * q^62 + 7 * q^63 + 7 * q^64 + 2 * q^65 + 7 * q^66 + 18 * q^67 + 6 * q^68 + 2 * q^69 + 2 * q^70 - 2 * q^71 + 7 * q^72 + 2 * q^73 + 6 * q^74 + 17 * q^75 + 4 * q^76 + 7 * q^77 + 7 * q^78 + 16 * q^79 + 2 * q^80 + 7 * q^81 - 4 * q^82 - 2 * q^83 + 7 * q^84 - 12 * q^85 + 6 * q^86 + 6 * q^87 + 7 * q^88 - 6 * q^89 + 2 * q^90 + 7 * q^91 + 2 * q^92 + 10 * q^93 - 2 * q^94 + 20 * q^95 + 7 * q^96 - 12 * q^97 + 7 * q^98 + 7 * q^99

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