LMFDB - Embedded newform 6018.2.a.ba.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-2.88446$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.88446 q^{5} +1.00000 q^{6} -1.31412 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.88446 q^{5} +1.00000 q^{6} -1.31412 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.88446 q^{10} -0.382903 q^{11} +1.00000 q^{12} -5.18249 q^{13} -1.31412 q^{14} +3.88446 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +7.41569 q^{19} +3.88446 q^{20} -1.31412 q^{21} -0.382903 q^{22} +5.18555 q^{23} +1.00000 q^{24} +10.0890 q^{25} -5.18249 q^{26} +1.00000 q^{27} -1.31412 q^{28} +2.99737 q^{29} +3.88446 q^{30} -5.17612 q^{31} +1.00000 q^{32} -0.382903 q^{33} -1.00000 q^{34} -5.10464 q^{35} +1.00000 q^{36} -6.75312 q^{37} +7.41569 q^{38} -5.18249 q^{39} +3.88446 q^{40} +8.40110 q^{41} -1.31412 q^{42} +7.41225 q^{43} -0.382903 q^{44} +3.88446 q^{45} +5.18555 q^{46} +6.28590 q^{47} +1.00000 q^{48} -5.27309 q^{49} +10.0890 q^{50} -1.00000 q^{51} -5.18249 q^{52} -10.6282 q^{53} +1.00000 q^{54} -1.48737 q^{55} -1.31412 q^{56} +7.41569 q^{57} +2.99737 q^{58} +1.00000 q^{59} +3.88446 q^{60} +13.1953 q^{61} -5.17612 q^{62} -1.31412 q^{63} +1.00000 q^{64} -20.1312 q^{65} -0.382903 q^{66} +11.6554 q^{67} -1.00000 q^{68} +5.18555 q^{69} -5.10464 q^{70} -8.74967 q^{71} +1.00000 q^{72} +15.5055 q^{73} -6.75312 q^{74} +10.0890 q^{75} +7.41569 q^{76} +0.503180 q^{77} -5.18249 q^{78} -12.8641 q^{79} +3.88446 q^{80} +1.00000 q^{81} +8.40110 q^{82} -9.21568 q^{83} -1.31412 q^{84} -3.88446 q^{85} +7.41225 q^{86} +2.99737 q^{87} -0.382903 q^{88} +11.4719 q^{89} +3.88446 q^{90} +6.81041 q^{91} +5.18555 q^{92} -5.17612 q^{93} +6.28590 q^{94} +28.8059 q^{95} +1.00000 q^{96} +10.9855 q^{97} -5.27309 q^{98} -0.382903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * 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
$5$	3.88446	1.73718	0.868591	−	0.495529i	$-0.165026\pi$
$5$	3.88446	1.73718	0.868591	+	0.495529i	$0.165026\pi$
$6$	1.00000	0.408248
$7$	−1.31412	−0.496690	−0.248345	−	0.968672i	$-0.579887\pi$
$7$	−1.31412	−0.496690	−0.248345	+	0.968672i	$0.579887\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.88446	1.22837
$11$	−0.382903	−0.115450	−0.0577248	−	0.998333i	$-0.518385\pi$
$11$	−0.382903	−0.115450	−0.0577248	+	0.998333i	$0.518385\pi$
$12$	1.00000	0.288675
$13$	−5.18249	−1.43736	−0.718682	−	0.695339i	$-0.755254\pi$
$13$	−5.18249	−1.43736	−0.718682	+	0.695339i	$0.755254\pi$
$14$	−1.31412	−0.351213
$15$	3.88446	1.00296
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	7.41569	1.70128	0.850638	−	0.525752i	$-0.176216\pi$
$19$	7.41569	1.70128	0.850638	+	0.525752i	$0.176216\pi$
$20$	3.88446	0.868591
$21$	−1.31412	−0.286764
$22$	−0.382903	−0.0816351
$23$	5.18555	1.08126	0.540631	−	0.841260i	$-0.318185\pi$
$23$	5.18555	1.08126	0.540631	+	0.841260i	$0.318185\pi$
$24$	1.00000	0.204124
$25$	10.0890	2.01780
$26$	−5.18249	−1.01637
$27$	1.00000	0.192450
$28$	−1.31412	−0.248345
$29$	2.99737	0.556597	0.278299	−	0.960495i	$-0.410229\pi$
$29$	2.99737	0.556597	0.278299	+	0.960495i	$0.410229\pi$
$30$	3.88446	0.709202
$31$	−5.17612	−0.929659	−0.464829	−	0.885400i	$-0.653884\pi$
$31$	−5.17612	−0.929659	−0.464829	+	0.885400i	$0.653884\pi$
$32$	1.00000	0.176777
$33$	−0.382903	−0.0666548
$34$	−1.00000	−0.171499
$35$	−5.10464	−0.862842
$36$	1.00000	0.166667
$37$	−6.75312	−1.11021	−0.555103	−	0.831782i	$-0.687321\pi$
$37$	−6.75312	−1.11021	−0.555103	+	0.831782i	$0.687321\pi$
$38$	7.41569	1.20298
$39$	−5.18249	−0.829862
$40$	3.88446	0.614187
$41$	8.40110	1.31203	0.656016	−	0.754747i	$-0.272240\pi$
$41$	8.40110	1.31203	0.656016	+	0.754747i	$0.272240\pi$
$42$	−1.31412	−0.202773
$43$	7.41225	1.13036	0.565179	−	0.824968i	$-0.308807\pi$
$43$	7.41225	1.13036	0.565179	+	0.824968i	$0.308807\pi$
$44$	−0.382903	−0.0577248
$45$	3.88446	0.579061
$46$	5.18555	0.764568
$47$	6.28590	0.916893	0.458447	−	0.888722i	$-0.348406\pi$
$47$	6.28590	0.916893	0.458447	+	0.888722i	$0.348406\pi$
$48$	1.00000	0.144338
$49$	−5.27309	−0.753299
$50$	10.0890	1.42680
$51$	−1.00000	−0.140028
$52$	−5.18249	−0.718682
$53$	−10.6282	−1.45989	−0.729947	−	0.683504i	$-0.760455\pi$
$53$	−10.6282	−1.45989	−0.729947	+	0.683504i	$0.760455\pi$
$54$	1.00000	0.136083
$55$	−1.48737	−0.200557
$56$	−1.31412	−0.175607
$57$	7.41569	0.982232
$58$	2.99737	0.393574
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	3.88446	0.501481
$61$	13.1953	1.68948	0.844742	−	0.535174i	$-0.179754\pi$
$61$	13.1953	1.68948	0.844742	+	0.535174i	$0.179754\pi$
$62$	−5.17612	−0.657368
$63$	−1.31412	−0.165563
$64$	1.00000	0.125000
$65$	−20.1312	−2.49696
$66$	−0.382903	−0.0471321
$67$	11.6554	1.42393	0.711965	−	0.702215i	$-0.247805\pi$
$67$	11.6554	1.42393	0.711965	+	0.702215i	$0.247805\pi$
$68$	−1.00000	−0.121268
$69$	5.18555	0.624267
$70$	−5.10464	−0.610121
$71$	−8.74967	−1.03839	−0.519197	−	0.854654i	$-0.673769\pi$
$71$	−8.74967	−1.03839	−0.519197	+	0.854654i	$0.673769\pi$
$72$	1.00000	0.117851
$73$	15.5055	1.81479	0.907393	−	0.420283i	$-0.138069\pi$
$73$	15.5055	1.81479	0.907393	+	0.420283i	$0.138069\pi$
$74$	−6.75312	−0.785034
$75$	10.0890	1.16498
$76$	7.41569	0.850638
$77$	0.503180	0.0573427
$78$	−5.18249	−0.586801
$79$	−12.8641	−1.44733	−0.723663	−	0.690154i	$-0.757543\pi$
$79$	−12.8641	−1.44733	−0.723663	+	0.690154i	$0.757543\pi$
$80$	3.88446	0.434296
$81$	1.00000	0.111111
$82$	8.40110	0.927746
$83$	−9.21568	−1.01155	−0.505776	−	0.862665i	$-0.668794\pi$
$83$	−9.21568	−1.01155	−0.505776	+	0.862665i	$0.668794\pi$
$84$	−1.31412	−0.143382
$85$	−3.88446	−0.421329
$86$	7.41225	0.799284
$87$	2.99737	0.321352
$88$	−0.382903	−0.0408176
$89$	11.4719	1.21602	0.608008	−	0.793931i	$-0.291969\pi$
$89$	11.4719	1.21602	0.608008	+	0.793931i	$0.291969\pi$
$90$	3.88446	0.409458
$91$	6.81041	0.713925
$92$	5.18555	0.540631
$93$	−5.17612	−0.536739
$94$	6.28590	0.648342
$95$	28.8059	2.95543
$96$	1.00000	0.102062
$97$	10.9855	1.11541	0.557704	−	0.830040i	$-0.311682\pi$
$97$	10.9855	1.11541	0.557704	+	0.830040i	$0.311682\pi$
$98$	−5.27309	−0.532663
$99$	−0.382903	−0.0384832
$100$	10.0890	1.00890
$101$	−2.34030	−0.232869	−0.116434	−	0.993198i	$-0.537146\pi$
$101$	−2.34030	−0.232869	−0.116434	+	0.993198i	$0.537146\pi$
$102$	−1.00000	−0.0990148
$103$	−13.0237	−1.28326	−0.641630	−	0.767014i	$-0.721742\pi$
$103$	−13.0237	−1.28326	−0.641630	+	0.767014i	$0.721742\pi$
$104$	−5.18249	−0.508185
$105$	−5.10464	−0.498162
$106$	−10.6282	−1.03230
$107$	−8.20946	−0.793638	−0.396819	−	0.917897i	$-0.629886\pi$
$107$	−8.20946	−0.793638	−0.396819	+	0.917897i	$0.629886\pi$
$108$	1.00000	0.0962250
$109$	−10.7616	−1.03078	−0.515389	−	0.856956i	$-0.672352\pi$
$109$	−10.7616	−1.03078	−0.515389	+	0.856956i	$0.672352\pi$
$110$	−1.48737	−0.141815
$111$	−6.75312	−0.640977
$112$	−1.31412	−0.124173
$113$	2.46701	0.232076	0.116038	−	0.993245i	$-0.462981\pi$
$113$	2.46701	0.232076	0.116038	+	0.993245i	$0.462981\pi$
$114$	7.41569	0.694543
$115$	20.1431	1.87835
$116$	2.99737	0.278299
$117$	−5.18249	−0.479121
$118$	1.00000	0.0920575
$119$	1.31412	0.120465
$120$	3.88446	0.354601
$121$	−10.8534	−0.986671
$122$	13.1953	1.19465
$123$	8.40110	0.757502
$124$	−5.17612	−0.464829
$125$	19.7681	1.76811
$126$	−1.31412	−0.117071
$127$	2.39909	0.212885	0.106442	−	0.994319i	$-0.466054\pi$
$127$	2.39909	0.212885	0.106442	+	0.994319i	$0.466054\pi$
$128$	1.00000	0.0883883
$129$	7.41225	0.652612
$130$	−20.1312	−1.76562
$131$	3.27401	0.286051	0.143026	−	0.989719i	$-0.454317\pi$
$131$	3.27401	0.286051	0.143026	+	0.989719i	$0.454317\pi$
$132$	−0.382903	−0.0333274
$133$	−9.74510	−0.845008
$134$	11.6554	1.00687
$135$	3.88446	0.334321
$136$	−1.00000	−0.0857493
$137$	12.5522	1.07241	0.536203	−	0.844089i	$-0.319858\pi$
$137$	12.5522	1.07241	0.536203	+	0.844089i	$0.319858\pi$
$138$	5.18555	0.441423
$139$	5.17150	0.438641	0.219320	−	0.975653i	$-0.429616\pi$
$139$	5.17150	0.438641	0.219320	+	0.975653i	$0.429616\pi$
$140$	−5.10464	−0.431421
$141$	6.28590	0.529369
$142$	−8.74967	−0.734256
$143$	1.98439	0.165943
$144$	1.00000	0.0833333
$145$	11.6432	0.966911
$146$	15.5055	1.28325
$147$	−5.27309	−0.434917
$148$	−6.75312	−0.555103
$149$	−13.3006	−1.08963	−0.544814	−	0.838557i	$-0.683400\pi$
$149$	−13.3006	−1.08963	−0.544814	+	0.838557i	$0.683400\pi$
$150$	10.0890	0.823765
$151$	13.3583	1.08708	0.543542	−	0.839382i	$-0.317083\pi$
$151$	13.3583	1.08708	0.543542	+	0.839382i	$0.317083\pi$
$152$	7.41569	0.601492
$153$	−1.00000	−0.0808452
$154$	0.503180	0.0405474
$155$	−20.1064	−1.61499
$156$	−5.18249	−0.414931
$157$	−5.06891	−0.404543	−0.202271	−	0.979330i	$-0.564832\pi$
$157$	−5.06891	−0.404543	−0.202271	+	0.979330i	$0.564832\pi$
$158$	−12.8641	−1.02341
$159$	−10.6282	−0.842870
$160$	3.88446	0.307093
$161$	−6.81443	−0.537053
$162$	1.00000	0.0785674
$163$	6.47859	0.507442	0.253721	−	0.967277i	$-0.418345\pi$
$163$	6.47859	0.507442	0.253721	+	0.967277i	$0.418345\pi$
$164$	8.40110	0.656016
$165$	−1.48737	−0.115792
$166$	−9.21568	−0.715276
$167$	−6.98756	−0.540714	−0.270357	−	0.962760i	$-0.587142\pi$
$167$	−6.98756	−0.540714	−0.270357	+	0.962760i	$0.587142\pi$
$168$	−1.31412	−0.101387
$169$	13.8582	1.06601
$170$	−3.88446	−0.297924
$171$	7.41569	0.567092
$172$	7.41225	0.565179
$173$	14.4690	1.10006	0.550028	−	0.835146i	$-0.314617\pi$
$173$	14.4690	1.10006	0.550028	+	0.835146i	$0.314617\pi$
$174$	2.99737	0.227230
$175$	−13.2582	−1.00222
$176$	−0.382903	−0.0288624
$177$	1.00000	0.0751646
$178$	11.4719	0.859853
$179$	15.7395	1.17643	0.588213	−	0.808706i	$-0.299832\pi$
$179$	15.7395	1.17643	0.588213	+	0.808706i	$0.299832\pi$
$180$	3.88446	0.289530
$181$	10.8865	0.809188	0.404594	−	0.914496i	$-0.367413\pi$
$181$	10.8865	0.809188	0.404594	+	0.914496i	$0.367413\pi$
$182$	6.81041	0.504821
$183$	13.1953	0.975424
$184$	5.18555	0.382284
$185$	−26.2322	−1.92863
$186$	−5.17612	−0.379532
$187$	0.382903	0.0280006
$188$	6.28590	0.458447
$189$	−1.31412	−0.0955881
$190$	28.8059	2.08980
$191$	−18.2284	−1.31896	−0.659479	−	0.751723i	$-0.729223\pi$
$191$	−18.2284	−1.31896	−0.659479	+	0.751723i	$0.729223\pi$
$192$	1.00000	0.0721688
$193$	−1.50357	−0.108230	−0.0541148	−	0.998535i	$-0.517234\pi$
$193$	−1.50357	−0.108230	−0.0541148	+	0.998535i	$0.517234\pi$
$194$	10.9855	0.788713
$195$	−20.1312	−1.44162
$196$	−5.27309	−0.376649
$197$	−20.9733	−1.49428	−0.747142	−	0.664665i	$-0.768574\pi$
$197$	−20.9733	−1.49428	−0.747142	+	0.664665i	$0.768574\pi$
$198$	−0.382903	−0.0272117
$199$	−6.59803	−0.467722	−0.233861	−	0.972270i	$-0.575136\pi$
$199$	−6.59803	−0.467722	−0.233861	+	0.972270i	$0.575136\pi$
$200$	10.0890	0.713402
$201$	11.6554	0.822107
$202$	−2.34030	−0.164663
$203$	−3.93890	−0.276457
$204$	−1.00000	−0.0700140
$205$	32.6337	2.27924
$206$	−13.0237	−0.907402
$207$	5.18555	0.360421
$208$	−5.18249	−0.359341
$209$	−2.83949	−0.196412
$210$	−5.10464	−0.352254
$211$	−21.4122	−1.47408	−0.737039	−	0.675851i	$-0.763776\pi$
$211$	−21.4122	−1.47408	−0.737039	+	0.675851i	$0.763776\pi$
$212$	−10.6282	−0.729947
$213$	−8.74967	−0.599517
$214$	−8.20946	−0.561187
$215$	28.7926	1.96364
$216$	1.00000	0.0680414
$217$	6.80204	0.461753
$218$	−10.7616	−0.728870
$219$	15.5055	1.04777
$220$	−1.48737	−0.100278
$221$	5.18249	0.348612
$222$	−6.75312	−0.453239
$223$	15.1890	1.01713	0.508566	−	0.861023i	$-0.330176\pi$
$223$	15.1890	1.01713	0.508566	+	0.861023i	$0.330176\pi$
$224$	−1.31412	−0.0878033
$225$	10.0890	0.672601
$226$	2.46701	0.164103
$227$	6.29236	0.417638	0.208819	−	0.977954i	$-0.433038\pi$
$227$	6.29236	0.417638	0.208819	+	0.977954i	$0.433038\pi$
$228$	7.41569	0.491116
$229$	4.70862	0.311154	0.155577	−	0.987824i	$-0.450276\pi$
$229$	4.70862	0.311154	0.155577	+	0.987824i	$0.450276\pi$
$230$	20.1431	1.32819
$231$	0.503180	0.0331068
$232$	2.99737	0.196787
$233$	−17.1851	−1.12583	−0.562916	−	0.826514i	$-0.690320\pi$
$233$	−17.1851	−1.12583	−0.562916	+	0.826514i	$0.690320\pi$
$234$	−5.18249	−0.338790
$235$	24.4173	1.59281
$236$	1.00000	0.0650945
$237$	−12.8641	−0.835614
$238$	1.31412	0.0851817
$239$	−26.8548	−1.73709	−0.868547	−	0.495607i	$-0.834946\pi$
$239$	−26.8548	−1.73709	−0.868547	+	0.495607i	$0.834946\pi$
$240$	3.88446	0.250741
$241$	−6.44224	−0.414981	−0.207491	−	0.978237i	$-0.566530\pi$
$241$	−6.44224	−0.414981	−0.207491	+	0.978237i	$0.566530\pi$
$242$	−10.8534	−0.697682
$243$	1.00000	0.0641500
$244$	13.1953	0.844742
$245$	−20.4831	−1.30862
$246$	8.40110	0.535635
$247$	−38.4317	−2.44535
$248$	−5.17612	−0.328684
$249$	−9.21568	−0.584020
$250$	19.7681	1.25024
$251$	−22.0124	−1.38941	−0.694705	−	0.719295i	$-0.744465\pi$
$251$	−22.0124	−1.38941	−0.694705	+	0.719295i	$0.744465\pi$
$252$	−1.31412	−0.0827817
$253$	−1.98556	−0.124831
$254$	2.39909	0.150532
$255$	−3.88446	−0.243254
$256$	1.00000	0.0625000
$257$	−30.4992	−1.90249	−0.951243	−	0.308443i	$-0.900192\pi$
$257$	−30.4992	−1.90249	−0.951243	+	0.308443i	$0.900192\pi$
$258$	7.41225	0.461467
$259$	8.87440	0.551428
$260$	−20.1312	−1.24848
$261$	2.99737	0.185532
$262$	3.27401	0.202269
$263$	−29.4401	−1.81536	−0.907678	−	0.419668i	$-0.862146\pi$
$263$	−29.4401	−1.81536	−0.907678	+	0.419668i	$0.862146\pi$
$264$	−0.382903	−0.0235660
$265$	−41.2848	−2.53610
$266$	−9.74510	−0.597511
$267$	11.4719	0.702067
$268$	11.6554	0.711965
$269$	−18.3243	−1.11725	−0.558626	−	0.829420i	$-0.688671\pi$
$269$	−18.3243	−1.11725	−0.558626	+	0.829420i	$0.688671\pi$
$270$	3.88446	0.236401
$271$	−17.7377	−1.07749	−0.538745	−	0.842469i	$-0.681101\pi$
$271$	−17.7377	−1.07749	−0.538745	+	0.842469i	$0.681101\pi$
$272$	−1.00000	−0.0606339
$273$	6.81041	0.412185
$274$	12.5522	0.758305
$275$	−3.86311	−0.232955
$276$	5.18555	0.312134
$277$	−29.2579	−1.75793	−0.878967	−	0.476882i	$-0.841767\pi$
$277$	−29.2579	−1.75793	−0.878967	+	0.476882i	$0.841767\pi$
$278$	5.17150	0.310166
$279$	−5.17612	−0.309886
$280$	−5.10464	−0.305061
$281$	−4.02762	−0.240268	−0.120134	−	0.992758i	$-0.538332\pi$
$281$	−4.02762	−0.240268	−0.120134	+	0.992758i	$0.538332\pi$
$282$	6.28590	0.374320
$283$	−2.82388	−0.167862	−0.0839310	−	0.996472i	$-0.526748\pi$
$283$	−2.82388	−0.167862	−0.0839310	+	0.996472i	$0.526748\pi$
$284$	−8.74967	−0.519197
$285$	28.8059	1.70632
$286$	1.98439	0.117339
$287$	−11.0400	−0.651673
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	11.6432	0.683710
$291$	10.9855	0.643981
$292$	15.5055	0.907393
$293$	18.1503	1.06035	0.530177	−	0.847887i	$-0.322126\pi$
$293$	18.1503	1.06035	0.530177	+	0.847887i	$0.322126\pi$
$294$	−5.27309	−0.307533
$295$	3.88446	0.226162
$296$	−6.75312	−0.392517
$297$	−0.382903	−0.0222183
$298$	−13.3006	−0.770484
$299$	−26.8741	−1.55417
$300$	10.0890	0.582490
$301$	−9.74058	−0.561438
$302$	13.3583	0.768685
$303$	−2.34030	−0.134447
$304$	7.41569	0.425319
$305$	51.2566	2.93494
$306$	−1.00000	−0.0571662
$307$	−1.94224	−0.110849	−0.0554247	−	0.998463i	$-0.517651\pi$
$307$	−1.94224	−0.110849	−0.0554247	+	0.998463i	$0.517651\pi$
$308$	0.503180	0.0286713
$309$	−13.0237	−0.740891
$310$	−20.1064	−1.14197
$311$	2.57407	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$311$	2.57407	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$312$	−5.18249	−0.293401
$313$	8.53570	0.482466	0.241233	−	0.970467i	$-0.422448\pi$
$313$	8.53570	0.482466	0.241233	+	0.970467i	$0.422448\pi$
$314$	−5.06891	−0.286055
$315$	−5.10464	−0.287614
$316$	−12.8641	−0.723663
$317$	−18.4350	−1.03541	−0.517705	−	0.855559i	$-0.673214\pi$
$317$	−18.4350	−1.03541	−0.517705	+	0.855559i	$0.673214\pi$
$318$	−10.6282	−0.595999
$319$	−1.14770	−0.0642589
$320$	3.88446	0.217148
$321$	−8.20946	−0.458207
$322$	−6.81443	−0.379754
$323$	−7.41569	−0.412620
$324$	1.00000	0.0555556
$325$	−52.2862	−2.90032
$326$	6.47859	0.358816
$327$	−10.7616	−0.595120
$328$	8.40110	0.463873
$329$	−8.26043	−0.455412
$330$	−1.48737	−0.0818770
$331$	−1.37722	−0.0756989	−0.0378494	−	0.999283i	$-0.512051\pi$
$331$	−1.37722	−0.0756989	−0.0378494	+	0.999283i	$0.512051\pi$
$332$	−9.21568	−0.505776
$333$	−6.75312	−0.370068
$334$	−6.98756	−0.382342
$335$	45.2748	2.47363
$336$	−1.31412	−0.0716911
$337$	19.9751	1.08811	0.544056	−	0.839049i	$-0.316888\pi$
$337$	19.9751	1.08811	0.544056	+	0.839049i	$0.316888\pi$
$338$	13.8582	0.753786
$339$	2.46701	0.133989
$340$	−3.88446	−0.210664
$341$	1.98195	0.107329
$342$	7.41569	0.400995
$343$	16.1283	0.870847
$344$	7.41225	0.399642
$345$	20.1431	1.08447
$346$	14.4690	0.777858
$347$	32.1251	1.72456	0.862282	−	0.506429i	$-0.169035\pi$
$347$	32.1251	1.72456	0.862282	+	0.506429i	$0.169035\pi$
$348$	2.99737	0.160676
$349$	11.5536	0.618451	0.309226	−	0.950989i	$-0.399930\pi$
$349$	11.5536	0.618451	0.309226	+	0.950989i	$0.399930\pi$
$350$	−13.2582	−0.708679
$351$	−5.18249	−0.276621
$352$	−0.382903	−0.0204088
$353$	10.2025	0.543024	0.271512	−	0.962435i	$-0.412476\pi$
$353$	10.2025	0.543024	0.271512	+	0.962435i	$0.412476\pi$
$354$	1.00000	0.0531494
$355$	−33.9877	−1.80388
$356$	11.4719	0.608008
$357$	1.31412	0.0695506
$358$	15.7395	0.831859
$359$	−1.96895	−0.103917	−0.0519587	−	0.998649i	$-0.516546\pi$
$359$	−1.96895	−0.103917	−0.0519587	+	0.998649i	$0.516546\pi$
$360$	3.88446	0.204729
$361$	35.9925	1.89434
$362$	10.8865	0.572182
$363$	−10.8534	−0.569655
$364$	6.81041	0.356962
$365$	60.2306	3.15261
$366$	13.1953	0.689729
$367$	−30.1856	−1.57568	−0.787838	−	0.615882i	$-0.788800\pi$
$367$	−30.1856	−1.57568	−0.787838	+	0.615882i	$0.788800\pi$
$368$	5.18555	0.270316
$369$	8.40110	0.437344
$370$	−26.2322	−1.36375
$371$	13.9667	0.725115
$372$	−5.17612	−0.268369
$373$	24.4533	1.26614	0.633072	−	0.774093i	$-0.281794\pi$
$373$	24.4533	1.26614	0.633072	+	0.774093i	$0.281794\pi$
$374$	0.382903	0.0197994
$375$	19.7681	1.02082
$376$	6.28590	0.324171
$377$	−15.5338	−0.800033
$378$	−1.31412	−0.0675910
$379$	−28.4217	−1.45993	−0.729963	−	0.683486i	$-0.760463\pi$
$379$	−28.4217	−1.45993	−0.729963	+	0.683486i	$0.760463\pi$
$380$	28.8059	1.47771
$381$	2.39909	0.122909
$382$	−18.2284	−0.932644
$383$	26.8022	1.36953	0.684764	−	0.728765i	$-0.259905\pi$
$383$	26.8022	1.36953	0.684764	+	0.728765i	$0.259905\pi$
$384$	1.00000	0.0510310
$385$	1.95458	0.0996147
$386$	−1.50357	−0.0765298
$387$	7.41225	0.376786
$388$	10.9855	0.557704
$389$	−22.2321	−1.12721	−0.563606	−	0.826044i	$-0.690586\pi$
$389$	−22.2321	−1.12721	−0.563606	+	0.826044i	$0.690586\pi$
$390$	−20.1312	−1.01938
$391$	−5.18555	−0.262245
$392$	−5.27309	−0.266331
$393$	3.27401	0.165152
$394$	−20.9733	−1.05662
$395$	−49.9701	−2.51427
$396$	−0.382903	−0.0192416
$397$	24.1013	1.20961	0.604806	−	0.796373i	$-0.293251\pi$
$397$	24.1013	1.20961	0.604806	+	0.796373i	$0.293251\pi$
$398$	−6.59803	−0.330729
$399$	−9.74510	−0.487865
$400$	10.0890	0.504451
$401$	−23.4861	−1.17284	−0.586421	−	0.810007i	$-0.699463\pi$
$401$	−23.4861	−1.17284	−0.586421	+	0.810007i	$0.699463\pi$
$402$	11.6554	0.581317
$403$	26.8252	1.33626
$404$	−2.34030	−0.116434
$405$	3.88446	0.193020
$406$	−3.93890	−0.195484
$407$	2.58579	0.128173
$408$	−1.00000	−0.0495074
$409$	0.583302	0.0288424	0.0144212	−	0.999896i	$-0.495409\pi$
$409$	0.583302	0.0288424	0.0144212	+	0.999896i	$0.495409\pi$
$410$	32.6337	1.61167
$411$	12.5522	0.619154
$412$	−13.0237	−0.641630
$413$	−1.31412	−0.0646636
$414$	5.18555	0.254856
$415$	−35.7979	−1.75725
$416$	−5.18249	−0.254092
$417$	5.17150	0.253249
$418$	−2.83949	−0.138884
$419$	−16.2990	−0.796256	−0.398128	−	0.917330i	$-0.630340\pi$
$419$	−16.2990	−0.796256	−0.398128	+	0.917330i	$0.630340\pi$
$420$	−5.10464	−0.249081
$421$	−30.9252	−1.50720	−0.753601	−	0.657332i	$-0.771685\pi$
$421$	−30.9252	−1.50720	−0.753601	+	0.657332i	$0.771685\pi$
$422$	−21.4122	−1.04233
$423$	6.28590	0.305631
$424$	−10.6282	−0.516151
$425$	−10.0890	−0.489389
$426$	−8.74967	−0.423923
$427$	−17.3402	−0.839150
$428$	−8.20946	−0.396819
$429$	1.98439	0.0958072
$430$	28.7926	1.38850
$431$	−7.98301	−0.384528	−0.192264	−	0.981343i	$-0.561583\pi$
$431$	−7.98301	−0.384528	−0.192264	+	0.981343i	$0.561583\pi$
$432$	1.00000	0.0481125
$433$	−23.7533	−1.14151	−0.570755	−	0.821121i	$-0.693349\pi$
$433$	−23.7533	−1.14151	−0.570755	+	0.821121i	$0.693349\pi$
$434$	6.80204	0.326508
$435$	11.6432	0.558247
$436$	−10.7616	−0.515389
$437$	38.4544	1.83953
$438$	15.5055	0.740883
$439$	−26.8861	−1.28320	−0.641601	−	0.767038i	$-0.721730\pi$
$439$	−26.8861	−1.28320	−0.641601	+	0.767038i	$0.721730\pi$
$440$	−1.48737	−0.0709076
$441$	−5.27309	−0.251100
$442$	5.18249	0.246506
$443$	19.7504	0.938370	0.469185	−	0.883100i	$-0.344548\pi$
$443$	19.7504	0.938370	0.469185	+	0.883100i	$0.344548\pi$
$444$	−6.75312	−0.320489
$445$	44.5620	2.11244
$446$	15.1890	0.719221
$447$	−13.3006	−0.629097
$448$	−1.31412	−0.0620863
$449$	33.0396	1.55924	0.779618	−	0.626255i	$-0.215413\pi$
$449$	33.0396	1.55924	0.779618	+	0.626255i	$0.215413\pi$
$450$	10.0890	0.475601
$451$	−3.21680	−0.151473
$452$	2.46701	0.116038
$453$	13.3583	0.627629
$454$	6.29236	0.295315
$455$	26.4548	1.24022
$456$	7.41569	0.347272
$457$	28.3754	1.32734	0.663672	−	0.748024i	$-0.268997\pi$
$457$	28.3754	1.32734	0.663672	+	0.748024i	$0.268997\pi$
$458$	4.70862	0.220019
$459$	−1.00000	−0.0466760
$460$	20.1431	0.939175
$461$	12.2289	0.569558	0.284779	−	0.958593i	$-0.408080\pi$
$461$	12.2289	0.569558	0.284779	+	0.958593i	$0.408080\pi$
$462$	0.503180	0.0234100
$463$	39.2456	1.82390	0.911948	−	0.410305i	$-0.134578\pi$
$463$	39.2456	1.82390	0.911948	+	0.410305i	$0.134578\pi$
$464$	2.99737	0.139149
$465$	−20.1064	−0.932413
$466$	−17.1851	−0.796083
$467$	−13.2955	−0.615244	−0.307622	−	0.951509i	$-0.599533\pi$
$467$	−13.2955	−0.615244	−0.307622	+	0.951509i	$0.599533\pi$
$468$	−5.18249	−0.239561
$469$	−15.3166	−0.707253
$470$	24.4173	1.12629
$471$	−5.06891	−0.233563
$472$	1.00000	0.0460287
$473$	−2.83817	−0.130499
$474$	−12.8641	−0.590868
$475$	74.8171	3.43284
$476$	1.31412	0.0602326
$477$	−10.6282	−0.486631
$478$	−26.8548	−1.22831
$479$	13.3055	0.607945	0.303972	−	0.952681i	$-0.401687\pi$
$479$	13.3055	0.607945	0.303972	+	0.952681i	$0.401687\pi$
$480$	3.88446	0.177300
$481$	34.9980	1.59577
$482$	−6.44224	−0.293436
$483$	−6.81443	−0.310067
$484$	−10.8534	−0.493336
$485$	42.6727	1.93767
$486$	1.00000	0.0453609
$487$	−38.5121	−1.74515	−0.872575	−	0.488480i	$-0.837552\pi$
$487$	−38.5121	−1.74515	−0.872575	+	0.488480i	$0.837552\pi$
$488$	13.1953	0.597323
$489$	6.47859	0.292972
$490$	−20.4831	−0.925332
$491$	25.4796	1.14988	0.574939	−	0.818196i	$-0.305026\pi$
$491$	25.4796	1.14988	0.574939	+	0.818196i	$0.305026\pi$
$492$	8.40110	0.378751
$493$	−2.99737	−0.134995
$494$	−38.4317	−1.72913
$495$	−1.48737	−0.0668523
$496$	−5.17612	−0.232415
$497$	11.4981	0.515761
$498$	−9.21568	−0.412965
$499$	19.9674	0.893863	0.446931	−	0.894568i	$-0.352517\pi$
$499$	19.9674	0.893863	0.446931	+	0.894568i	$0.352517\pi$
$500$	19.7681	0.884056
$501$	−6.98756	−0.312181
$502$	−22.0124	−0.982461
$503$	−5.78807	−0.258077	−0.129039	−	0.991640i	$-0.541189\pi$
$503$	−5.78807	−0.258077	−0.129039	+	0.991640i	$0.541189\pi$
$504$	−1.31412	−0.0585355
$505$	−9.09080	−0.404535
$506$	−1.98556	−0.0882690
$507$	13.8582	0.615464
$508$	2.39909	0.106442
$509$	13.6695	0.605891	0.302945	−	0.953008i	$-0.402030\pi$
$509$	13.6695	0.605891	0.302945	+	0.953008i	$0.402030\pi$
$510$	−3.88446	−0.172007
$511$	−20.3761	−0.901387
$512$	1.00000	0.0441942
$513$	7.41569	0.327411
$514$	−30.4992	−1.34526
$515$	−50.5899	−2.22926
$516$	7.41225	0.326306
$517$	−2.40689	−0.105855
$518$	8.87440	0.389919
$519$	14.4690	0.635118
$520$	−20.1312	−0.882810
$521$	−3.16369	−0.138604	−0.0693019	−	0.997596i	$-0.522077\pi$
$521$	−3.16369	−0.138604	−0.0693019	+	0.997596i	$0.522077\pi$
$522$	2.99737	0.131191
$523$	−24.4461	−1.06895	−0.534477	−	0.845183i	$-0.679492\pi$
$523$	−24.4461	−1.06895	−0.534477	+	0.845183i	$0.679492\pi$
$524$	3.27401	0.143026
$525$	−13.2582	−0.578634
$526$	−29.4401	−1.28365
$527$	5.17612	0.225475
$528$	−0.382903	−0.0166637
$529$	3.88995	0.169128
$530$	−41.2848	−1.79330
$531$	1.00000	0.0433963
$532$	−9.74510	−0.422504
$533$	−43.5386	−1.88587
$534$	11.4719	0.496436
$535$	−31.8893	−1.37869
$536$	11.6554	0.503436
$537$	15.7395	0.679210
$538$	−18.3243	−0.790016
$539$	2.01908	0.0869680
$540$	3.88446	0.167160
$541$	28.1035	1.20826	0.604132	−	0.796884i	$-0.293520\pi$
$541$	28.1035	1.20826	0.604132	+	0.796884i	$0.293520\pi$
$542$	−17.7377	−0.761901
$543$	10.8865	0.467185
$544$	−1.00000	−0.0428746
$545$	−41.8031	−1.79065
$546$	6.81041	0.291459
$547$	12.8521	0.549517	0.274759	−	0.961513i	$-0.411402\pi$
$547$	12.8521	0.549517	0.274759	+	0.961513i	$0.411402\pi$
$548$	12.5522	0.536203
$549$	13.1953	0.563161
$550$	−3.86311	−0.164724
$551$	22.2276	0.946926
$552$	5.18555	0.220712
$553$	16.9050	0.718873
$554$	−29.2579	−1.24305
$555$	−26.2322	−1.11349
$556$	5.17150	0.219320
$557$	−8.90890	−0.377482	−0.188741	−	0.982027i	$-0.560441\pi$
$557$	−8.90890	−0.377482	−0.188741	+	0.982027i	$0.560441\pi$
$558$	−5.17612	−0.219123
$559$	−38.4139	−1.62474
$560$	−5.10464	−0.215711
$561$	0.382903	0.0161662
$562$	−4.02762	−0.169895
$563$	−36.9801	−1.55853	−0.779263	−	0.626697i	$-0.784406\pi$
$563$	−36.9801	−1.55853	−0.779263	+	0.626697i	$0.784406\pi$
$564$	6.28590	0.264684
$565$	9.58298	0.403159
$566$	−2.82388	−0.118696
$567$	−1.31412	−0.0551878
$568$	−8.74967	−0.367128
$569$	27.8348	1.16690	0.583448	−	0.812150i	$-0.301703\pi$
$569$	27.8348	1.16690	0.583448	+	0.812150i	$0.301703\pi$
$570$	28.8059	1.20655
$571$	−9.18311	−0.384301	−0.192151	−	0.981365i	$-0.561546\pi$
$571$	−9.18311	−0.384301	−0.192151	+	0.981365i	$0.561546\pi$
$572$	1.98439	0.0829715
$573$	−18.2284	−0.761501
$574$	−11.0400	−0.460803
$575$	52.3171	2.18178
$576$	1.00000	0.0416667
$577$	−7.97499	−0.332003	−0.166002	−	0.986125i	$-0.553086\pi$
$577$	−7.97499	−0.332003	−0.166002	+	0.986125i	$0.553086\pi$
$578$	1.00000	0.0415945
$579$	−1.50357	−0.0624864
$580$	11.6432	0.483456
$581$	12.1105	0.502428
$582$	10.9855	0.455364
$583$	4.06956	0.168544
$584$	15.5055	0.641624
$585$	−20.1312	−0.832321
$586$	18.1503	0.749783
$587$	−17.0143	−0.702257	−0.351129	−	0.936327i	$-0.614202\pi$
$587$	−17.0143	−0.702257	−0.351129	+	0.936327i	$0.614202\pi$
$588$	−5.27309	−0.217459
$589$	−38.3845	−1.58161
$590$	3.88446	0.159921
$591$	−20.9733	−0.862725
$592$	−6.75312	−0.277551
$593$	8.17886	0.335866	0.167933	−	0.985798i	$-0.446291\pi$
$593$	8.17886	0.335866	0.167933	+	0.985798i	$0.446291\pi$
$594$	−0.382903	−0.0157107
$595$	5.10464	0.209270
$596$	−13.3006	−0.544814
$597$	−6.59803	−0.270039
$598$	−26.8741	−1.09896
$599$	−3.17743	−0.129826	−0.0649131	−	0.997891i	$-0.520677\pi$
$599$	−3.17743	−0.129826	−0.0649131	+	0.997891i	$0.520677\pi$
$600$	10.0890	0.411883
$601$	15.8495	0.646513	0.323256	−	0.946311i	$-0.395222\pi$
$601$	15.8495	0.646513	0.323256	+	0.946311i	$0.395222\pi$
$602$	−9.74058	−0.396997
$603$	11.6554	0.474644
$604$	13.3583	0.543542
$605$	−42.1595	−1.71403
$606$	−2.34030	−0.0950682
$607$	−2.69227	−0.109276	−0.0546380	−	0.998506i	$-0.517400\pi$
$607$	−2.69227	−0.109276	−0.0546380	+	0.998506i	$0.517400\pi$
$608$	7.41569	0.300746
$609$	−3.93890	−0.159612
$610$	51.2566	2.07532
$611$	−32.5766	−1.31791
$612$	−1.00000	−0.0404226
$613$	44.6930	1.80513	0.902566	−	0.430551i	$-0.141681\pi$
$613$	44.6930	1.80513	0.902566	+	0.430551i	$0.141681\pi$
$614$	−1.94224	−0.0783824
$615$	32.6337	1.31592
$616$	0.503180	0.0202737
$617$	−33.7537	−1.35887	−0.679436	−	0.733735i	$-0.737775\pi$
$617$	−33.7537	−1.35887	−0.679436	+	0.733735i	$0.737775\pi$
$618$	−13.0237	−0.523889
$619$	−8.98512	−0.361143	−0.180571	−	0.983562i	$-0.557795\pi$
$619$	−8.98512	−0.361143	−0.180571	+	0.983562i	$0.557795\pi$
$620$	−20.1064	−0.807494
$621$	5.18555	0.208089
$622$	2.57407	0.103211
$623$	−15.0754	−0.603983
$624$	−5.18249	−0.207466
$625$	26.3432	1.05373
$626$	8.53570	0.341155
$627$	−2.83949	−0.113398
$628$	−5.06891	−0.202271
$629$	6.75312	0.269264
$630$	−5.10464	−0.203374
$631$	−17.2835	−0.688046	−0.344023	−	0.938961i	$-0.611790\pi$
$631$	−17.2835	−0.688046	−0.344023	+	0.938961i	$0.611790\pi$
$632$	−12.8641	−0.511707
$633$	−21.4122	−0.851059
$634$	−18.4350	−0.732146
$635$	9.31916	0.369820
$636$	−10.6282	−0.421435
$637$	27.3277	1.08276
$638$	−1.14770	−0.0454379
$639$	−8.74967	−0.346132
$640$	3.88446	0.153547
$641$	35.8018	1.41409	0.707043	−	0.707170i	$-0.250029\pi$
$641$	35.8018	1.41409	0.707043	+	0.707170i	$0.250029\pi$
$642$	−8.20946	−0.324001
$643$	8.65698	0.341398	0.170699	−	0.985323i	$-0.445397\pi$
$643$	8.65698	0.341398	0.170699	+	0.985323i	$0.445397\pi$
$644$	−6.81443	−0.268526
$645$	28.7926	1.13371
$646$	−7.41569	−0.291766
$647$	30.0714	1.18223	0.591115	−	0.806587i	$-0.298688\pi$
$647$	30.0714	1.18223	0.591115	+	0.806587i	$0.298688\pi$
$648$	1.00000	0.0392837
$649$	−0.382903	−0.0150302
$650$	−52.2862	−2.05084
$651$	6.80204	0.266593
$652$	6.47859	0.253721
$653$	24.8020	0.970577	0.485288	−	0.874354i	$-0.338715\pi$
$653$	24.8020	0.970577	0.485288	+	0.874354i	$0.338715\pi$
$654$	−10.7616	−0.420813
$655$	12.7177	0.496923
$656$	8.40110	0.328008
$657$	15.5055	0.604929
$658$	−8.26043	−0.322025
$659$	−3.57687	−0.139335	−0.0696676	−	0.997570i	$-0.522194\pi$
$659$	−3.57687	−0.139335	−0.0696676	+	0.997570i	$0.522194\pi$
$660$	−1.48737	−0.0578958
$661$	−48.4359	−1.88394	−0.941968	−	0.335701i	$-0.891027\pi$
$661$	−48.4359	−1.88394	−0.941968	+	0.335701i	$0.891027\pi$
$662$	−1.37722	−0.0535272
$663$	5.18249	0.201271
$664$	−9.21568	−0.357638
$665$	−37.8545	−1.46793
$666$	−6.75312	−0.261678
$667$	15.5430	0.601828
$668$	−6.98756	−0.270357
$669$	15.1890	0.587241
$670$	45.2748	1.74912
$671$	−5.05251	−0.195050
$672$	−1.31412	−0.0506933
$673$	−1.08414	−0.0417906	−0.0208953	−	0.999782i	$-0.506652\pi$
$673$	−1.08414	−0.0417906	−0.0208953	+	0.999782i	$0.506652\pi$
$674$	19.9751	0.769412
$675$	10.0890	0.388327
$676$	13.8582	0.533007
$677$	9.19558	0.353415	0.176707	−	0.984263i	$-0.443455\pi$
$677$	9.19558	0.353415	0.176707	+	0.984263i	$0.443455\pi$
$678$	2.46701	0.0947448
$679$	−14.4363	−0.554013
$680$	−3.88446	−0.148962
$681$	6.29236	0.241124
$682$	1.98195	0.0758928
$683$	6.49187	0.248405	0.124202	−	0.992257i	$-0.460363\pi$
$683$	6.49187	0.248405	0.124202	+	0.992257i	$0.460363\pi$
$684$	7.41569	0.283546
$685$	48.7584	1.86296
$686$	16.1283	0.615782
$687$	4.70862	0.179645
$688$	7.41225	0.282589
$689$	55.0805	2.09840
$690$	20.1431	0.766833
$691$	−34.2816	−1.30413	−0.652067	−	0.758161i	$-0.726098\pi$
$691$	−34.2816	−1.30413	−0.652067	+	0.758161i	$0.726098\pi$
$692$	14.4690	0.550028
$693$	0.503180	0.0191142
$694$	32.1251	1.21945
$695$	20.0885	0.761999
$696$	2.99737	0.113615
$697$	−8.40110	−0.318214
$698$	11.5536	0.437311
$699$	−17.1851	−0.649999
$700$	−13.2582	−0.501112
$701$	5.54349	0.209375	0.104687	−	0.994505i	$-0.466616\pi$
$701$	5.54349	0.209375	0.104687	+	0.994505i	$0.466616\pi$
$702$	−5.18249	−0.195600
$703$	−50.0790	−1.88877
$704$	−0.382903	−0.0144312
$705$	24.4173	0.919610
$706$	10.2025	0.383976
$707$	3.07543	0.115664
$708$	1.00000	0.0375823
$709$	−31.9263	−1.19902	−0.599510	−	0.800368i	$-0.704638\pi$
$709$	−31.9263	−1.19902	−0.599510	+	0.800368i	$0.704638\pi$
$710$	−33.9877	−1.27554
$711$	−12.8641	−0.482442
$712$	11.4719	0.429926
$713$	−26.8410	−1.00521
$714$	1.31412	0.0491797
$715$	7.70828	0.288273
$716$	15.7395	0.588213
$717$	−26.8548	−1.00291
$718$	−1.96895	−0.0734807
$719$	−30.5229	−1.13831	−0.569156	−	0.822230i	$-0.692730\pi$
$719$	−30.5229	−1.13831	−0.569156	+	0.822230i	$0.692730\pi$
$720$	3.88446	0.144765
$721$	17.1147	0.637383
$722$	35.9925	1.33950
$723$	−6.44224	−0.239590
$724$	10.8865	0.404594
$725$	30.2405	1.12310
$726$	−10.8534	−0.402807
$727$	−14.2419	−0.528205	−0.264102	−	0.964495i	$-0.585076\pi$
$727$	−14.2419	−0.528205	−0.264102	+	0.964495i	$0.585076\pi$
$728$	6.81041	0.252411
$729$	1.00000	0.0370370
$730$	60.2306	2.22924
$731$	−7.41225	−0.274152
$732$	13.1953	0.487712
$733$	51.3875	1.89804	0.949021	−	0.315214i	$-0.102076\pi$
$733$	51.3875	1.89804	0.949021	+	0.315214i	$0.102076\pi$
$734$	−30.1856	−1.11417
$735$	−20.4831	−0.755531
$736$	5.18555	0.191142
$737$	−4.46288	−0.164392
$738$	8.40110	0.309249
$739$	−51.4045	−1.89095	−0.945473	−	0.325700i	$-0.894400\pi$
$739$	−51.4045	−1.89095	−0.945473	+	0.325700i	$0.894400\pi$
$740$	−26.2322	−0.964315
$741$	−38.4317	−1.41183
$742$	13.9667	0.512734
$743$	30.0489	1.10239	0.551194	−	0.834377i	$-0.314172\pi$
$743$	30.0489	1.10239	0.551194	+	0.834377i	$0.314172\pi$
$744$	−5.17612	−0.189766
$745$	−51.6657	−1.89288
$746$	24.4533	0.895299
$747$	−9.21568	−0.337184
$748$	0.382903	0.0140003
$749$	10.7882	0.394192
$750$	19.7681	0.721829
$751$	−39.0003	−1.42314	−0.711571	−	0.702614i	$-0.752016\pi$
$751$	−39.0003	−1.42314	−0.711571	+	0.702614i	$0.752016\pi$
$752$	6.28590	0.229223
$753$	−22.0124	−0.802176
$754$	−15.5338	−0.565709
$755$	51.8898	1.88846
$756$	−1.31412	−0.0477941
$757$	17.9795	0.653476	0.326738	−	0.945115i	$-0.394051\pi$
$757$	17.9795	0.653476	0.326738	+	0.945115i	$0.394051\pi$
$758$	−28.4217	−1.03232
$759$	−1.98556	−0.0720713
$760$	28.8059	1.04490
$761$	13.3033	0.482243	0.241122	−	0.970495i	$-0.422485\pi$
$761$	13.3033	0.482243	0.241122	+	0.970495i	$0.422485\pi$
$762$	2.39909	0.0869098
$763$	14.1421	0.511977
$764$	−18.2284	−0.659479
$765$	−3.88446	−0.140443
$766$	26.8022	0.968403
$767$	−5.18249	−0.187129
$768$	1.00000	0.0360844
$769$	23.3484	0.841964	0.420982	−	0.907069i	$-0.361685\pi$
$769$	23.3484	0.841964	0.420982	+	0.907069i	$0.361685\pi$
$770$	1.95458	0.0704382
$771$	−30.4992	−1.09840
$772$	−1.50357	−0.0541148
$773$	41.6909	1.49952	0.749759	−	0.661711i	$-0.230169\pi$
$773$	41.6909	1.49952	0.749759	+	0.661711i	$0.230169\pi$
$774$	7.41225	0.266428
$775$	−52.2220	−1.87587
$776$	10.9855	0.394356
$777$	8.87440	0.318367
$778$	−22.2321	−0.797060
$779$	62.3000	2.23213
$780$	−20.1312	−0.720811
$781$	3.35027	0.119882
$782$	−5.18555	−0.185435
$783$	2.99737	0.107117
$784$	−5.27309	−0.188325
$785$	−19.6900	−0.702765
$786$	3.27401	0.116780
$787$	3.44924	0.122952	0.0614761	−	0.998109i	$-0.480419\pi$
$787$	3.44924	0.122952	0.0614761	+	0.998109i	$0.480419\pi$
$788$	−20.9733	−0.747142
$789$	−29.4401	−1.04810
$790$	−49.9701	−1.77786
$791$	−3.24194	−0.115270
$792$	−0.382903	−0.0136059
$793$	−68.3844	−2.42840
$794$	24.1013	0.855324
$795$	−41.2848	−1.46422
$796$	−6.59803	−0.233861
$797$	37.8682	1.34136	0.670680	−	0.741747i	$-0.266003\pi$
$797$	37.8682	1.34136	0.670680	+	0.741747i	$0.266003\pi$
$798$	−9.74510	−0.344973
$799$	−6.28590	−0.222379
$800$	10.0890	0.356701
$801$	11.4719	0.405338
$802$	−23.4861	−0.829324
$803$	−5.93711	−0.209516
$804$	11.6554	0.411053
$805$	−26.4704	−0.932959
$806$	26.8252	0.944877
$807$	−18.3243	−0.645046
$808$	−2.34030	−0.0823315
$809$	−31.4446	−1.10553	−0.552767	−	0.833336i	$-0.686428\pi$
$809$	−31.4446	−1.10553	−0.552767	+	0.833336i	$0.686428\pi$
$810$	3.88446	0.136486
$811$	−2.34829	−0.0824596	−0.0412298	−	0.999150i	$-0.513128\pi$
$811$	−2.34829	−0.0824596	−0.0412298	+	0.999150i	$0.513128\pi$
$812$	−3.93890	−0.138228
$813$	−17.7377	−0.622089
$814$	2.58579	0.0906318
$815$	25.1658	0.881520
$816$	−1.00000	−0.0350070
$817$	54.9670	1.92305
$818$	0.583302	0.0203947
$819$	6.81041	0.237975
$820$	32.6337	1.13962
$821$	33.3826	1.16506	0.582530	−	0.812809i	$-0.302063\pi$
$821$	33.3826	1.16506	0.582530	+	0.812809i	$0.302063\pi$
$822$	12.5522	0.437808
$823$	−39.8022	−1.38742	−0.693708	−	0.720256i	$-0.744024\pi$
$823$	−39.8022	−1.38742	−0.693708	+	0.720256i	$0.744024\pi$
$824$	−13.0237	−0.453701
$825$	−3.86311	−0.134496
$826$	−1.31412	−0.0457241
$827$	31.4340	1.09307	0.546534	−	0.837437i	$-0.315947\pi$
$827$	31.4340	1.09307	0.546534	+	0.837437i	$0.315947\pi$
$828$	5.18555	0.180210
$829$	−18.4974	−0.642442	−0.321221	−	0.947004i	$-0.604093\pi$
$829$	−18.4974	−0.642442	−0.321221	+	0.947004i	$0.604093\pi$
$830$	−35.7979	−1.24256
$831$	−29.2579	−1.01494
$832$	−5.18249	−0.179670
$833$	5.27309	0.182702
$834$	5.17150	0.179074
$835$	−27.1429	−0.939319
$836$	−2.83949	−0.0982058
$837$	−5.17612	−0.178913
$838$	−16.2990	−0.563038
$839$	−2.11435	−0.0729954	−0.0364977	−	0.999334i	$-0.511620\pi$
$839$	−2.11435	−0.0729954	−0.0364977	+	0.999334i	$0.511620\pi$
$840$	−5.10464	−0.176127
$841$	−20.0158	−0.690199
$842$	−30.9252	−1.06575
$843$	−4.02762	−0.138719
$844$	−21.4122	−0.737039
$845$	53.8316	1.85186
$846$	6.28590	0.216114
$847$	14.2626	0.490070
$848$	−10.6282	−0.364974
$849$	−2.82388	−0.0969152
$850$	−10.0890	−0.346051
$851$	−35.0186	−1.20042
$852$	−8.74967	−0.299759
$853$	−29.2580	−1.00177	−0.500887	−	0.865513i	$-0.666993\pi$
$853$	−29.2580	−1.00177	−0.500887	+	0.865513i	$0.666993\pi$
$854$	−17.3402	−0.593369
$855$	28.8059	0.985143
$856$	−8.20946	−0.280593
$857$	10.6594	0.364118	0.182059	−	0.983288i	$-0.441724\pi$
$857$	10.6594	0.364118	0.182059	+	0.983288i	$0.441724\pi$
$858$	1.98439	0.0677459
$859$	−26.9255	−0.918686	−0.459343	−	0.888259i	$-0.651915\pi$
$859$	−26.9255	−0.918686	−0.459343	+	0.888259i	$0.651915\pi$
$860$	28.7926	0.981819
$861$	−11.0400	−0.376244
$862$	−7.98301	−0.271903
$863$	−5.75940	−0.196052	−0.0980262	−	0.995184i	$-0.531253\pi$
$863$	−5.75940	−0.196052	−0.0980262	+	0.995184i	$0.531253\pi$
$864$	1.00000	0.0340207
$865$	56.2042	1.91100
$866$	−23.7533	−0.807169
$867$	1.00000	0.0339618
$868$	6.80204	0.230876
$869$	4.92570	0.167093
$870$	11.6432	0.394740
$871$	−60.4039	−2.04671
$872$	−10.7616	−0.364435
$873$	10.9855	0.371803
$874$	38.4544	1.30074
$875$	−25.9776	−0.878204
$876$	15.5055	0.523884
$877$	49.9546	1.68685	0.843424	−	0.537249i	$-0.180536\pi$
$877$	49.9546	1.68685	0.843424	+	0.537249i	$0.180536\pi$
$878$	−26.8861	−0.907361
$879$	18.1503	0.612195
$880$	−1.48737	−0.0501392
$881$	5.45793	0.183882	0.0919412	−	0.995764i	$-0.470693\pi$
$881$	5.45793	0.183882	0.0919412	+	0.995764i	$0.470693\pi$
$882$	−5.27309	−0.177554
$883$	3.08222	0.103725	0.0518625	−	0.998654i	$-0.483484\pi$
$883$	3.08222	0.103725	0.0518625	+	0.998654i	$0.483484\pi$
$884$	5.18249	0.174306
$885$	3.88446	0.130575
$886$	19.7504	0.663528
$887$	−43.4404	−1.45858	−0.729292	−	0.684202i	$-0.760150\pi$
$887$	−43.4404	−1.45858	−0.729292	+	0.684202i	$0.760150\pi$
$888$	−6.75312	−0.226620
$889$	−3.15269	−0.105738
$890$	44.5620	1.49372
$891$	−0.382903	−0.0128277
$892$	15.1890	0.508566
$893$	46.6143	1.55989
$894$	−13.3006	−0.444839
$895$	61.1395	2.04367
$896$	−1.31412	−0.0439016
$897$	−26.8741	−0.897299
$898$	33.0396	1.10255
$899$	−15.5147	−0.517446
$900$	10.0890	0.336301
$901$	10.6282	0.354076
$902$	−3.21680	−0.107108
$903$	−9.74058	−0.324146
$904$	2.46701	0.0820514
$905$	42.2882	1.40571
$906$	13.3583	0.443800
$907$	−2.35053	−0.0780480	−0.0390240	−	0.999238i	$-0.512425\pi$
$907$	−2.35053	−0.0780480	−0.0390240	+	0.999238i	$0.512425\pi$
$908$	6.29236	0.208819
$909$	−2.34030	−0.0776229
$910$	26.4548	0.876967
$911$	20.5125	0.679611	0.339805	−	0.940496i	$-0.389639\pi$
$911$	20.5125	0.679611	0.339805	+	0.940496i	$0.389639\pi$
$912$	7.41569	0.245558
$913$	3.52871	0.116783
$914$	28.3754	0.938573
$915$	51.2566	1.69449
$916$	4.70862	0.155577
$917$	−4.30243	−0.142079
$918$	−1.00000	−0.0330049
$919$	−44.4269	−1.46551	−0.732754	−	0.680494i	$-0.761765\pi$
$919$	−44.4269	−1.46551	−0.732754	+	0.680494i	$0.761765\pi$
$920$	20.1431	0.664097
$921$	−1.94224	−0.0639990
$922$	12.2289	0.402739
$923$	45.3451	1.49255
$924$	0.503180	0.0165534
$925$	−68.1323	−2.24018
$926$	39.2456	1.28969
$927$	−13.0237	−0.427753
$928$	2.99737	0.0983935
$929$	17.6194	0.578074	0.289037	−	0.957318i	$-0.406665\pi$
$929$	17.6194	0.578074	0.289037	+	0.957318i	$0.406665\pi$
$930$	−20.1064	−0.659316
$931$	−39.1036	−1.28157
$932$	−17.1851	−0.562916
$933$	2.57407	0.0842712
$934$	−13.2955	−0.435043
$935$	1.48737	0.0486422
$936$	−5.18249	−0.169395
$937$	41.3937	1.35227	0.676136	−	0.736777i	$-0.263653\pi$
$937$	41.3937	1.35227	0.676136	+	0.736777i	$0.263653\pi$
$938$	−15.3166	−0.500103
$939$	8.53570	0.278552
$940$	24.4173	0.796406
$941$	15.5774	0.507809	0.253904	−	0.967229i	$-0.418285\pi$
$941$	15.5774	0.507809	0.253904	+	0.967229i	$0.418285\pi$
$942$	−5.06891	−0.165154
$943$	43.5643	1.41865
$944$	1.00000	0.0325472
$945$	−5.10464	−0.166054
$946$	−2.83817	−0.0922769
$947$	26.1739	0.850539	0.425270	−	0.905067i	$-0.360179\pi$
$947$	26.1739	0.850539	0.425270	+	0.905067i	$0.360179\pi$
$948$	−12.8641	−0.417807
$949$	−80.3573	−2.60851
$950$	74.8171	2.42739
$951$	−18.4350	−0.597795
$952$	1.31412	0.0425909
$953$	−33.7529	−1.09336	−0.546682	−	0.837341i	$-0.684109\pi$
$953$	−33.7529	−1.09336	−0.546682	+	0.837341i	$0.684109\pi$
$954$	−10.6282	−0.344100
$955$	−70.8073	−2.29127
$956$	−26.8548	−0.868547
$957$	−1.14770	−0.0370999
$958$	13.3055	0.429882
$959$	−16.4951	−0.532653
$960$	3.88446	0.125370
$961$	−4.20776	−0.135734
$962$	34.9980	1.12838
$963$	−8.20946	−0.264546
$964$	−6.44224	−0.207491
$965$	−5.84057	−0.188015
$966$	−6.81443	−0.219251
$967$	55.1187	1.77250	0.886249	−	0.463209i	$-0.153302\pi$
$967$	55.1187	1.77250	0.886249	+	0.463209i	$0.153302\pi$
$968$	−10.8534	−0.348841
$969$	−7.41569	−0.238226
$970$	42.6727	1.37014
$971$	−38.9303	−1.24933	−0.624666	−	0.780892i	$-0.714765\pi$
$971$	−38.9303	−1.24933	−0.624666	+	0.780892i	$0.714765\pi$
$972$	1.00000	0.0320750
$973$	−6.79596	−0.217869
$974$	−38.5121	−1.23401
$975$	−52.2862	−1.67450
$976$	13.1953	0.422371
$977$	10.4767	0.335181	0.167590	−	0.985857i	$-0.446401\pi$
$977$	10.4767	0.335181	0.167590	+	0.985857i	$0.446401\pi$
$978$	6.47859	0.207163
$979$	−4.39261	−0.140388
$980$	−20.4831	−0.654309
$981$	−10.7616	−0.343593
$982$	25.4796	0.813087
$983$	−20.2483	−0.645820	−0.322910	−	0.946430i	$-0.604661\pi$
$983$	−20.2483	−0.645820	−0.322910	+	0.946430i	$0.604661\pi$
$984$	8.40110	0.267817
$985$	−81.4698	−2.59584
$986$	−2.99737	−0.0954557
$987$	−8.26043	−0.262932
$988$	−38.4317	−1.22268
$989$	38.4366	1.22221
$990$	−1.48737	−0.0472717
$991$	22.4488	0.713109	0.356554	−	0.934275i	$-0.383951\pi$
$991$	22.4488	0.713109	0.356554	+	0.934275i	$0.383951\pi$
$992$	−5.17612	−0.164342
$993$	−1.37722	−0.0437048
$994$	11.4981	0.364698
$995$	−25.6298	−0.812519
$996$	−9.21568	−0.292010
$997$	−28.5299	−0.903550	−0.451775	−	0.892132i	$-0.649209\pi$
$997$	−28.5299	−0.903550	−0.451775	+	0.892132i	$0.649209\pi$
$998$	19.9674	0.632056
$999$	−6.75312	−0.213659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.11	✓	12	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.88446 q^{5} +1.00000 q^{6} -1.31412 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.88446 q^{5} +1.00000 q^{6} -1.31412 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.88446 q^{10} -0.382903 q^{11} +1.00000 q^{12} -5.18249 q^{13} -1.31412 q^{14} +3.88446 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +7.41569 q^{19} +3.88446 q^{20} -1.31412 q^{21} -0.382903 q^{22} +5.18555 q^{23} +1.00000 q^{24} +10.0890 q^{25} -5.18249 q^{26} +1.00000 q^{27} -1.31412 q^{28} +2.99737 q^{29} +3.88446 q^{30} -5.17612 q^{31} +1.00000 q^{32} -0.382903 q^{33} -1.00000 q^{34} -5.10464 q^{35} +1.00000 q^{36} -6.75312 q^{37} +7.41569 q^{38} -5.18249 q^{39} +3.88446 q^{40} +8.40110 q^{41} -1.31412 q^{42} +7.41225 q^{43} -0.382903 q^{44} +3.88446 q^{45} +5.18555 q^{46} +6.28590 q^{47} +1.00000 q^{48} -5.27309 q^{49} +10.0890 q^{50} -1.00000 q^{51} -5.18249 q^{52} -10.6282 q^{53} +1.00000 q^{54} -1.48737 q^{55} -1.31412 q^{56} +7.41569 q^{57} +2.99737 q^{58} +1.00000 q^{59} +3.88446 q^{60} +13.1953 q^{61} -5.17612 q^{62} -1.31412 q^{63} +1.00000 q^{64} -20.1312 q^{65} -0.382903 q^{66} +11.6554 q^{67} -1.00000 q^{68} +5.18555 q^{69} -5.10464 q^{70} -8.74967 q^{71} +1.00000 q^{72} +15.5055 q^{73} -6.75312 q^{74} +10.0890 q^{75} +7.41569 q^{76} +0.503180 q^{77} -5.18249 q^{78} -12.8641 q^{79} +3.88446 q^{80} +1.00000 q^{81} +8.40110 q^{82} -9.21568 q^{83} -1.31412 q^{84} -3.88446 q^{85} +7.41225 q^{86} +2.99737 q^{87} -0.382903 q^{88} +11.4719 q^{89} +3.88446 q^{90} +6.81041 q^{91} +5.18555 q^{92} -5.17612 q^{93} +6.28590 q^{94} +28.8059 q^{95} +1.00000 q^{96} +10.9855 q^{97} -5.27309 q^{98} -0.382903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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