LMFDB - Embedded newform 6018.2.a.t.1.6

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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 15x^{6} + 14x^{5} + 84x^{4} + 9x^{3} - 158x^{2} - 142x - 35 $ x^8 - 2x^7 - 15x^6 + 14x^5 + 84x^4 + 9x^3 - 158x^2 - 142*x - 35
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.70183$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.876977 q^{5} -1.00000 q^{6} -4.57880 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.876977 q^{5} -1.00000 q^{6} -4.57880 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.876977 q^{10} +3.41569 q^{11} +1.00000 q^{12} -5.45772 q^{13} +4.57880 q^{14} +0.876977 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -0.613540 q^{19} +0.876977 q^{20} -4.57880 q^{21} -3.41569 q^{22} +8.17716 q^{23} -1.00000 q^{24} -4.23091 q^{25} +5.45772 q^{26} +1.00000 q^{27} -4.57880 q^{28} +0.557506 q^{29} -0.876977 q^{30} +3.43787 q^{31} -1.00000 q^{32} +3.41569 q^{33} -1.00000 q^{34} -4.01550 q^{35} +1.00000 q^{36} -4.45253 q^{37} +0.613540 q^{38} -5.45772 q^{39} -0.876977 q^{40} +1.14148 q^{41} +4.57880 q^{42} +0.576218 q^{43} +3.41569 q^{44} +0.876977 q^{45} -8.17716 q^{46} +2.49766 q^{47} +1.00000 q^{48} +13.9654 q^{49} +4.23091 q^{50} +1.00000 q^{51} -5.45772 q^{52} -1.84764 q^{53} -1.00000 q^{54} +2.99548 q^{55} +4.57880 q^{56} -0.613540 q^{57} -0.557506 q^{58} -1.00000 q^{59} +0.876977 q^{60} -11.0673 q^{61} -3.43787 q^{62} -4.57880 q^{63} +1.00000 q^{64} -4.78630 q^{65} -3.41569 q^{66} +0.345571 q^{67} +1.00000 q^{68} +8.17716 q^{69} +4.01550 q^{70} +5.75711 q^{71} -1.00000 q^{72} -6.22835 q^{73} +4.45253 q^{74} -4.23091 q^{75} -0.613540 q^{76} -15.6398 q^{77} +5.45772 q^{78} -13.8088 q^{79} +0.876977 q^{80} +1.00000 q^{81} -1.14148 q^{82} -5.00190 q^{83} -4.57880 q^{84} +0.876977 q^{85} -0.576218 q^{86} +0.557506 q^{87} -3.41569 q^{88} +8.09150 q^{89} -0.876977 q^{90} +24.9898 q^{91} +8.17716 q^{92} +3.43787 q^{93} -2.49766 q^{94} -0.538061 q^{95} -1.00000 q^{96} +6.31864 q^{97} -13.9654 q^{98} +3.41569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{10} + q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} - q^{22} - 11 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 4 q^{28} - 12 q^{29} + 6 q^{30} - 9 q^{31} - 8 q^{32} + q^{33} - 8 q^{34} - 28 q^{35} + 8 q^{36} - 22 q^{37} - 4 q^{38} - 2 q^{39} + 6 q^{40} - 19 q^{41} + 4 q^{42} - 5 q^{43} + q^{44} - 6 q^{45} + 11 q^{46} - 26 q^{47} + 8 q^{48} - 6 q^{50} + 8 q^{51} - 2 q^{52} - 21 q^{53} - 8 q^{54} - 13 q^{55} + 4 q^{56} + 4 q^{57} + 12 q^{58} - 8 q^{59} - 6 q^{60} + 9 q^{61} + 9 q^{62} - 4 q^{63} + 8 q^{64} + 14 q^{65} - q^{66} + 26 q^{67} + 8 q^{68} - 11 q^{69} + 28 q^{70} - 14 q^{71} - 8 q^{72} + 17 q^{73} + 22 q^{74} + 6 q^{75} + 4 q^{76} - 18 q^{77} + 2 q^{78} - 39 q^{79} - 6 q^{80} + 8 q^{81} + 19 q^{82} - 11 q^{83} - 4 q^{84} - 6 q^{85} + 5 q^{86} - 12 q^{87} - q^{88} + 6 q^{90} + 11 q^{91} - 11 q^{92} - 9 q^{93} + 26 q^{94} - 15 q^{95} - 8 q^{96} + 16 q^{97} + q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^10 + q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 4 * q^19 - 6 * q^20 - 4 * q^21 - q^22 - 11 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 4 * q^28 - 12 * q^29 + 6 * q^30 - 9 * q^31 - 8 * q^32 + q^33 - 8 * q^34 - 28 * q^35 + 8 * q^36 - 22 * q^37 - 4 * q^38 - 2 * q^39 + 6 * q^40 - 19 * q^41 + 4 * q^42 - 5 * q^43 + q^44 - 6 * q^45 + 11 * q^46 - 26 * q^47 + 8 * q^48 - 6 * q^50 + 8 * q^51 - 2 * q^52 - 21 * q^53 - 8 * q^54 - 13 * q^55 + 4 * q^56 + 4 * q^57 + 12 * q^58 - 8 * q^59 - 6 * q^60 + 9 * q^61 + 9 * q^62 - 4 * q^63 + 8 * q^64 + 14 * q^65 - q^66 + 26 * q^67 + 8 * q^68 - 11 * q^69 + 28 * q^70 - 14 * q^71 - 8 * q^72 + 17 * q^73 + 22 * q^74 + 6 * q^75 + 4 * q^76 - 18 * q^77 + 2 * q^78 - 39 * q^79 - 6 * q^80 + 8 * q^81 + 19 * q^82 - 11 * q^83 - 4 * q^84 - 6 * q^85 + 5 * q^86 - 12 * q^87 - q^88 + 6 * q^90 + 11 * q^91 - 11 * q^92 - 9 * q^93 + 26 * q^94 - 15 * q^95 - 8 * q^96 + 16 * q^97 + 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
$5$	0.876977	0.392196	0.196098	−	0.980584i	$-0.437173\pi$
$5$	0.876977	0.392196	0.196098	+	0.980584i	$0.437173\pi$
$6$	−1.00000	−0.408248
$7$	−4.57880	−1.73062	−0.865312	−	0.501233i	$-0.832880\pi$
$7$	−4.57880	−1.73062	−0.865312	+	0.501233i	$0.832880\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.876977	−0.277324
$11$	3.41569	1.02987	0.514934	−	0.857230i	$-0.327816\pi$
$11$	3.41569	1.02987	0.514934	+	0.857230i	$0.327816\pi$
$12$	1.00000	0.288675
$13$	−5.45772	−1.51370	−0.756850	−	0.653588i	$-0.773263\pi$
$13$	−5.45772	−1.51370	−0.756850	+	0.653588i	$0.773263\pi$
$14$	4.57880	1.22374
$15$	0.876977	0.226434
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−0.613540	−0.140756	−0.0703779	−	0.997520i	$-0.522421\pi$
$19$	−0.613540	−0.140756	−0.0703779	+	0.997520i	$0.522421\pi$
$20$	0.876977	0.196098
$21$	−4.57880	−0.999177
$22$	−3.41569	−0.728227
$23$	8.17716	1.70505	0.852527	−	0.522682i	$-0.175069\pi$
$23$	8.17716	1.70505	0.852527	+	0.522682i	$0.175069\pi$
$24$	−1.00000	−0.204124
$25$	−4.23091	−0.846182
$26$	5.45772	1.07035
$27$	1.00000	0.192450
$28$	−4.57880	−0.865312
$29$	0.557506	0.103526	0.0517631	−	0.998659i	$-0.483516\pi$
$29$	0.557506	0.103526	0.0517631	+	0.998659i	$0.483516\pi$
$30$	−0.876977	−0.160113
$31$	3.43787	0.617459	0.308730	−	0.951150i	$-0.400096\pi$
$31$	3.43787	0.617459	0.308730	+	0.951150i	$0.400096\pi$
$32$	−1.00000	−0.176777
$33$	3.41569	0.594595
$34$	−1.00000	−0.171499
$35$	−4.01550	−0.678744
$36$	1.00000	0.166667
$37$	−4.45253	−0.731991	−0.365996	−	0.930617i	$-0.619271\pi$
$37$	−4.45253	−0.731991	−0.365996	+	0.930617i	$0.619271\pi$
$38$	0.613540	0.0995294
$39$	−5.45772	−0.873935
$40$	−0.876977	−0.138662
$41$	1.14148	0.178269	0.0891345	−	0.996020i	$-0.471590\pi$
$41$	1.14148	0.178269	0.0891345	+	0.996020i	$0.471590\pi$
$42$	4.57880	0.706525
$43$	0.576218	0.0878724	0.0439362	−	0.999034i	$-0.486010\pi$
$43$	0.576218	0.0878724	0.0439362	+	0.999034i	$0.486010\pi$
$44$	3.41569	0.514934
$45$	0.876977	0.130732
$46$	−8.17716	−1.20566
$47$	2.49766	0.364321	0.182160	−	0.983269i	$-0.441691\pi$
$47$	2.49766	0.364321	0.182160	+	0.983269i	$0.441691\pi$
$48$	1.00000	0.144338
$49$	13.9654	1.99506
$50$	4.23091	0.598341
$51$	1.00000	0.140028
$52$	−5.45772	−0.756850
$53$	−1.84764	−0.253793	−0.126897	−	0.991916i	$-0.540502\pi$
$53$	−1.84764	−0.253793	−0.126897	+	0.991916i	$0.540502\pi$
$54$	−1.00000	−0.136083
$55$	2.99548	0.403910
$56$	4.57880	0.611868
$57$	−0.613540	−0.0812654
$58$	−0.557506	−0.0732041
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0.876977	0.113217
$61$	−11.0673	−1.41702	−0.708512	−	0.705698i	$-0.750633\pi$
$61$	−11.0673	−1.41702	−0.708512	+	0.705698i	$0.750633\pi$
$62$	−3.43787	−0.436610
$63$	−4.57880	−0.576875
$64$	1.00000	0.125000
$65$	−4.78630	−0.593667
$66$	−3.41569	−0.420442
$67$	0.345571	0.0422182	0.0211091	−	0.999777i	$-0.493280\pi$
$67$	0.345571	0.0422182	0.0211091	+	0.999777i	$0.493280\pi$
$68$	1.00000	0.121268
$69$	8.17716	0.984414
$70$	4.01550	0.479945
$71$	5.75711	0.683244	0.341622	−	0.939838i	$-0.389024\pi$
$71$	5.75711	0.683244	0.341622	+	0.939838i	$0.389024\pi$
$72$	−1.00000	−0.117851
$73$	−6.22835	−0.728974	−0.364487	−	0.931209i	$-0.618756\pi$
$73$	−6.22835	−0.728974	−0.364487	+	0.931209i	$0.618756\pi$
$74$	4.45253	0.517596
$75$	−4.23091	−0.488544
$76$	−0.613540	−0.0703779
$77$	−15.6398	−1.78232
$78$	5.45772	0.617966
$79$	−13.8088	−1.55361	−0.776804	−	0.629743i	$-0.783160\pi$
$79$	−13.8088	−1.55361	−0.776804	+	0.629743i	$0.783160\pi$
$80$	0.876977	0.0980490
$81$	1.00000	0.111111
$82$	−1.14148	−0.126055
$83$	−5.00190	−0.549030	−0.274515	−	0.961583i	$-0.588517\pi$
$83$	−5.00190	−0.549030	−0.274515	+	0.961583i	$0.588517\pi$
$84$	−4.57880	−0.499588
$85$	0.876977	0.0951215
$86$	−0.576218	−0.0621351
$87$	0.557506	0.0597709
$88$	−3.41569	−0.364114
$89$	8.09150	0.857697	0.428849	−	0.903376i	$-0.358919\pi$
$89$	8.09150	0.857697	0.428849	+	0.903376i	$0.358919\pi$
$90$	−0.876977	−0.0924415
$91$	24.9898	2.61965
$92$	8.17716	0.852527
$93$	3.43787	0.356490
$94$	−2.49766	−0.257614
$95$	−0.538061	−0.0552039
$96$	−1.00000	−0.102062
$97$	6.31864	0.641561	0.320780	−	0.947154i	$-0.396055\pi$
$97$	6.31864	0.641561	0.320780	+	0.947154i	$0.396055\pi$
$98$	−13.9654	−1.41072
$99$	3.41569	0.343290
$100$	−4.23091	−0.423091
$101$	11.2895	1.12334	0.561672	−	0.827360i	$-0.310158\pi$
$101$	11.2895	1.12334	0.561672	+	0.827360i	$0.310158\pi$
$102$	−1.00000	−0.0990148
$103$	−13.7799	−1.35778	−0.678889	−	0.734241i	$-0.737538\pi$
$103$	−13.7799	−1.35778	−0.678889	+	0.734241i	$0.737538\pi$
$104$	5.45772	0.535174
$105$	−4.01550	−0.391873
$106$	1.84764	0.179459
$107$	5.39783	0.521828	0.260914	−	0.965362i	$-0.415976\pi$
$107$	5.39783	0.521828	0.260914	+	0.965362i	$0.415976\pi$
$108$	1.00000	0.0962250
$109$	−16.9388	−1.62244	−0.811222	−	0.584738i	$-0.801197\pi$
$109$	−16.9388	−1.62244	−0.811222	+	0.584738i	$0.801197\pi$
$110$	−2.99548	−0.285608
$111$	−4.45253	−0.422615
$112$	−4.57880	−0.432656
$113$	−3.88297	−0.365279	−0.182639	−	0.983180i	$-0.558464\pi$
$113$	−3.88297	−0.365279	−0.182639	+	0.983180i	$0.558464\pi$
$114$	0.613540	0.0574633
$115$	7.17118	0.668716
$116$	0.557506	0.0517631
$117$	−5.45772	−0.504567
$118$	1.00000	0.0920575
$119$	−4.57880	−0.419738
$120$	−0.876977	−0.0800567
$121$	0.666921	0.0606292
$122$	11.0673	1.00199
$123$	1.14148	0.102924
$124$	3.43787	0.308730
$125$	−8.09530	−0.724065
$126$	4.57880	0.407912
$127$	−8.68617	−0.770773	−0.385386	−	0.922755i	$-0.625932\pi$
$127$	−8.68617	−0.770773	−0.385386	+	0.922755i	$0.625932\pi$
$128$	−1.00000	−0.0883883
$129$	0.576218	0.0507331
$130$	4.78630	0.419786
$131$	−6.95411	−0.607583	−0.303792	−	0.952738i	$-0.598253\pi$
$131$	−6.95411	−0.607583	−0.303792	+	0.952738i	$0.598253\pi$
$132$	3.41569	0.297297
$133$	2.80928	0.243596
$134$	−0.345571	−0.0298528
$135$	0.876977	0.0754781
$136$	−1.00000	−0.0857493
$137$	−5.37063	−0.458844	−0.229422	−	0.973327i	$-0.573684\pi$
$137$	−5.37063	−0.458844	−0.229422	+	0.973327i	$0.573684\pi$
$138$	−8.17716	−0.696086
$139$	11.9539	1.01392	0.506959	−	0.861970i	$-0.330769\pi$
$139$	11.9539	1.01392	0.506959	+	0.861970i	$0.330769\pi$
$140$	−4.01550	−0.339372
$141$	2.49766	0.210341
$142$	−5.75711	−0.483126
$143$	−18.6419	−1.55891
$144$	1.00000	0.0833333
$145$	0.488920	0.0406026
$146$	6.22835	0.515462
$147$	13.9654	1.15185
$148$	−4.45253	−0.365996
$149$	−0.442568	−0.0362566	−0.0181283	−	0.999836i	$-0.505771\pi$
$149$	−0.442568	−0.0362566	−0.0181283	+	0.999836i	$0.505771\pi$
$150$	4.23091	0.345452
$151$	−0.336830	−0.0274108	−0.0137054	−	0.999906i	$-0.504363\pi$
$151$	−0.336830	−0.0274108	−0.0137054	+	0.999906i	$0.504363\pi$
$152$	0.613540	0.0497647
$153$	1.00000	0.0808452
$154$	15.6398	1.26029
$155$	3.01493	0.242165
$156$	−5.45772	−0.436968
$157$	−7.36786	−0.588019	−0.294010	−	0.955802i	$-0.594990\pi$
$157$	−7.36786	−0.588019	−0.294010	+	0.955802i	$0.594990\pi$
$158$	13.8088	1.09857
$159$	−1.84764	−0.146528
$160$	−0.876977	−0.0693311
$161$	−37.4416	−2.95081
$162$	−1.00000	−0.0785674
$163$	0.473427	0.0370817	0.0185408	−	0.999828i	$-0.494098\pi$
$163$	0.473427	0.0370817	0.0185408	+	0.999828i	$0.494098\pi$
$164$	1.14148	0.0891345
$165$	2.99548	0.233198
$166$	5.00190	0.388223
$167$	−13.2391	−1.02447	−0.512235	−	0.858846i	$-0.671182\pi$
$167$	−13.2391	−1.02447	−0.512235	+	0.858846i	$0.671182\pi$
$168$	4.57880	0.353262
$169$	16.7868	1.29129
$170$	−0.876977	−0.0672611
$171$	−0.613540	−0.0469186
$172$	0.576218	0.0439362
$173$	−21.4182	−1.62840	−0.814198	−	0.580587i	$-0.802823\pi$
$173$	−21.4182	−1.62840	−0.814198	+	0.580587i	$0.802823\pi$
$174$	−0.557506	−0.0422644
$175$	19.3725	1.46442
$176$	3.41569	0.257467
$177$	−1.00000	−0.0751646
$178$	−8.09150	−0.606484
$179$	−24.8883	−1.86024	−0.930121	−	0.367253i	$-0.880298\pi$
$179$	−24.8883	−1.86024	−0.930121	+	0.367253i	$0.880298\pi$
$180$	0.876977	0.0653660
$181$	−1.56220	−0.116117	−0.0580586	−	0.998313i	$-0.518491\pi$
$181$	−1.56220	−0.116117	−0.0580586	+	0.998313i	$0.518491\pi$
$182$	−24.9898	−1.85237
$183$	−11.0673	−0.818120
$184$	−8.17716	−0.602828
$185$	−3.90476	−0.287084
$186$	−3.43787	−0.252077
$187$	3.41569	0.249780
$188$	2.49766	0.182160
$189$	−4.57880	−0.333059
$190$	0.538061	0.0390350
$191$	−7.09372	−0.513283	−0.256642	−	0.966507i	$-0.582616\pi$
$191$	−7.09372	−0.513283	−0.256642	+	0.966507i	$0.582616\pi$
$192$	1.00000	0.0721688
$193$	−5.88891	−0.423893	−0.211946	−	0.977281i	$-0.567980\pi$
$193$	−5.88891	−0.423893	−0.211946	+	0.977281i	$0.567980\pi$
$194$	−6.31864	−0.453652
$195$	−4.78630	−0.342754
$196$	13.9654	0.997531
$197$	−12.5163	−0.891751	−0.445875	−	0.895095i	$-0.647108\pi$
$197$	−12.5163	−0.891751	−0.445875	+	0.895095i	$0.647108\pi$
$198$	−3.41569	−0.242742
$199$	−10.7928	−0.765083	−0.382542	−	0.923938i	$-0.624951\pi$
$199$	−10.7928	−0.765083	−0.382542	+	0.923938i	$0.624951\pi$
$200$	4.23091	0.299171
$201$	0.345571	0.0243747
$202$	−11.2895	−0.794325
$203$	−2.55271	−0.179165
$204$	1.00000	0.0700140
$205$	1.00105	0.0699164
$206$	13.7799	0.960094
$207$	8.17716	0.568352
$208$	−5.45772	−0.378425
$209$	−2.09566	−0.144960
$210$	4.01550	0.277096
$211$	6.29242	0.433188	0.216594	−	0.976262i	$-0.430505\pi$
$211$	6.29242	0.433188	0.216594	+	0.976262i	$0.430505\pi$
$212$	−1.84764	−0.126897
$213$	5.75711	0.394471
$214$	−5.39783	−0.368988
$215$	0.505329	0.0344632
$216$	−1.00000	−0.0680414
$217$	−15.7413	−1.06859
$218$	16.9388	1.14724
$219$	−6.22835	−0.420873
$220$	2.99548	0.201955
$221$	−5.45772	−0.367126
$222$	4.45253	0.298834
$223$	−11.7149	−0.784486	−0.392243	−	0.919862i	$-0.628301\pi$
$223$	−11.7149	−0.784486	−0.392243	+	0.919862i	$0.628301\pi$
$224$	4.57880	0.305934
$225$	−4.23091	−0.282061
$226$	3.88297	0.258291
$227$	17.1444	1.13791	0.568956	−	0.822368i	$-0.307347\pi$
$227$	17.1444	1.13791	0.568956	+	0.822368i	$0.307347\pi$
$228$	−0.613540	−0.0406327
$229$	19.3413	1.27811	0.639053	−	0.769163i	$-0.279326\pi$
$229$	19.3413	1.27811	0.639053	+	0.769163i	$0.279326\pi$
$230$	−7.17118	−0.472853
$231$	−15.6398	−1.02902
$232$	−0.557506	−0.0366020
$233$	−14.1022	−0.923868	−0.461934	−	0.886914i	$-0.652844\pi$
$233$	−14.1022	−0.923868	−0.461934	+	0.886914i	$0.652844\pi$
$234$	5.45772	0.356783
$235$	2.19039	0.142885
$236$	−1.00000	−0.0650945
$237$	−13.8088	−0.896976
$238$	4.57880	0.296800
$239$	−18.0178	−1.16547	−0.582737	−	0.812661i	$-0.698018\pi$
$239$	−18.0178	−1.16547	−0.582737	+	0.812661i	$0.698018\pi$
$240$	0.876977	0.0566086
$241$	−9.58238	−0.617255	−0.308628	−	0.951183i	$-0.599870\pi$
$241$	−9.58238	−0.617255	−0.308628	+	0.951183i	$0.599870\pi$
$242$	−0.666921	−0.0428713
$243$	1.00000	0.0641500
$244$	−11.0673	−0.708512
$245$	12.2474	0.782455
$246$	−1.14148	−0.0727780
$247$	3.34853	0.213062
$248$	−3.43787	−0.218305
$249$	−5.00190	−0.316983
$250$	8.09530	0.511991
$251$	−6.95721	−0.439135	−0.219567	−	0.975597i	$-0.570465\pi$
$251$	−6.95721	−0.439135	−0.219567	+	0.975597i	$0.570465\pi$
$252$	−4.57880	−0.288437
$253$	27.9306	1.75598
$254$	8.68617	0.545018
$255$	0.876977	0.0549184
$256$	1.00000	0.0625000
$257$	25.7425	1.60577	0.802886	−	0.596132i	$-0.203297\pi$
$257$	25.7425	1.60577	0.802886	+	0.596132i	$0.203297\pi$
$258$	−0.576218	−0.0358737
$259$	20.3872	1.26680
$260$	−4.78630	−0.296834
$261$	0.557506	0.0345087
$262$	6.95411	0.429626
$263$	−0.181820	−0.0112115	−0.00560576	−	0.999984i	$-0.501784\pi$
$263$	−0.181820	−0.0112115	−0.00560576	+	0.999984i	$0.501784\pi$
$264$	−3.41569	−0.210221
$265$	−1.62034	−0.0995367
$266$	−2.80928	−0.172248
$267$	8.09150	0.495192
$268$	0.345571	0.0211091
$269$	13.4058	0.817366	0.408683	−	0.912676i	$-0.365988\pi$
$269$	13.4058	0.817366	0.408683	+	0.912676i	$0.365988\pi$
$270$	−0.876977	−0.0533711
$271$	−1.48537	−0.0902296	−0.0451148	−	0.998982i	$-0.514365\pi$
$271$	−1.48537	−0.0902296	−0.0451148	+	0.998982i	$0.514365\pi$
$272$	1.00000	0.0606339
$273$	24.9898	1.51245
$274$	5.37063	0.324451
$275$	−14.4515	−0.871457
$276$	8.17716	0.492207
$277$	8.24428	0.495351	0.247675	−	0.968843i	$-0.420333\pi$
$277$	8.24428	0.495351	0.247675	+	0.968843i	$0.420333\pi$
$278$	−11.9539	−0.716949
$279$	3.43787	0.205820
$280$	4.01550	0.239972
$281$	−22.0526	−1.31555	−0.657775	−	0.753215i	$-0.728502\pi$
$281$	−22.0526	−1.31555	−0.657775	+	0.753215i	$0.728502\pi$
$282$	−2.49766	−0.148733
$283$	−24.5950	−1.46202	−0.731011	−	0.682366i	$-0.760951\pi$
$283$	−24.5950	−1.46202	−0.731011	+	0.682366i	$0.760951\pi$
$284$	5.75711	0.341622
$285$	−0.538061	−0.0318720
$286$	18.6419	1.10232
$287$	−5.22661	−0.308517
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−0.488920	−0.0287104
$291$	6.31864	0.370405
$292$	−6.22835	−0.364487
$293$	−3.75788	−0.219538	−0.109769	−	0.993957i	$-0.535011\pi$
$293$	−3.75788	−0.219538	−0.109769	+	0.993957i	$0.535011\pi$
$294$	−13.9654	−0.814481
$295$	−0.876977	−0.0510596
$296$	4.45253	0.258798
$297$	3.41569	0.198198
$298$	0.442568	0.0256373
$299$	−44.6287	−2.58094
$300$	−4.23091	−0.244272
$301$	−2.63839	−0.152074
$302$	0.336830	0.0193824
$303$	11.2895	0.648563
$304$	−0.613540	−0.0351890
$305$	−9.70578	−0.555751
$306$	−1.00000	−0.0571662
$307$	11.2231	0.640537	0.320268	−	0.947327i	$-0.396227\pi$
$307$	11.2231	0.640537	0.320268	+	0.947327i	$0.396227\pi$
$308$	−15.6398	−0.891158
$309$	−13.7799	−0.783914
$310$	−3.01493	−0.171237
$311$	−1.71050	−0.0969936	−0.0484968	−	0.998823i	$-0.515443\pi$
$311$	−1.71050	−0.0969936	−0.0484968	+	0.998823i	$0.515443\pi$
$312$	5.45772	0.308983
$313$	−27.0813	−1.53073	−0.765363	−	0.643599i	$-0.777441\pi$
$313$	−27.0813	−1.53073	−0.765363	+	0.643599i	$0.777441\pi$
$314$	7.36786	0.415792
$315$	−4.01550	−0.226248
$316$	−13.8088	−0.776804
$317$	6.51308	0.365811	0.182906	−	0.983130i	$-0.441450\pi$
$317$	6.51308	0.365811	0.182906	+	0.983130i	$0.441450\pi$
$318$	1.84764	0.103611
$319$	1.90427	0.106618
$320$	0.876977	0.0490245
$321$	5.39783	0.301277
$322$	37.4416	2.08654
$323$	−0.613540	−0.0341383
$324$	1.00000	0.0555556
$325$	23.0911	1.28087
$326$	−0.473427	−0.0262207
$327$	−16.9388	−0.936718
$328$	−1.14148	−0.0630276
$329$	−11.4363	−0.630503
$330$	−2.99548	−0.164896
$331$	16.8361	0.925397	0.462698	−	0.886516i	$-0.346881\pi$
$331$	16.8361	0.925397	0.462698	+	0.886516i	$0.346881\pi$
$332$	−5.00190	−0.274515
$333$	−4.45253	−0.243997
$334$	13.2391	0.724409
$335$	0.303058	0.0165578
$336$	−4.57880	−0.249794
$337$	14.2541	0.776469	0.388234	−	0.921561i	$-0.373085\pi$
$337$	14.2541	0.776469	0.388234	+	0.921561i	$0.373085\pi$
$338$	−16.7868	−0.913079
$339$	−3.88297	−0.210894
$340$	0.876977	0.0475607
$341$	11.7427	0.635902
$342$	0.613540	0.0331765
$343$	−31.8933	−1.72208
$344$	−0.576218	−0.0310676
$345$	7.17118	0.386083
$346$	21.4182	1.15145
$347$	8.28372	0.444693	0.222347	−	0.974968i	$-0.428628\pi$
$347$	8.28372	0.444693	0.222347	+	0.974968i	$0.428628\pi$
$348$	0.557506	0.0298854
$349$	−6.43980	−0.344715	−0.172357	−	0.985034i	$-0.555138\pi$
$349$	−6.43980	−0.344715	−0.172357	+	0.985034i	$0.555138\pi$
$350$	−19.3725	−1.03550
$351$	−5.45772	−0.291312
$352$	−3.41569	−0.182057
$353$	−8.69953	−0.463029	−0.231515	−	0.972831i	$-0.574368\pi$
$353$	−8.69953	−0.463029	−0.231515	+	0.972831i	$0.574368\pi$
$354$	1.00000	0.0531494
$355$	5.04885	0.267965
$356$	8.09150	0.428849
$357$	−4.57880	−0.242336
$358$	24.8883	1.31539
$359$	−7.75814	−0.409459	−0.204729	−	0.978819i	$-0.565631\pi$
$359$	−7.75814	−0.409459	−0.204729	+	0.978819i	$0.565631\pi$
$360$	−0.876977	−0.0462207
$361$	−18.6236	−0.980188
$362$	1.56220	0.0821072
$363$	0.666921	0.0350043
$364$	24.9898	1.30982
$365$	−5.46212	−0.285900
$366$	11.0673	0.578498
$367$	−7.14293	−0.372858	−0.186429	−	0.982468i	$-0.559691\pi$
$367$	−7.14293	−0.372858	−0.186429	+	0.982468i	$0.559691\pi$
$368$	8.17716	0.426264
$369$	1.14148	0.0594230
$370$	3.90476	0.202999
$371$	8.45999	0.439221
$372$	3.43787	0.178245
$373$	21.1613	1.09569	0.547845	−	0.836580i	$-0.315448\pi$
$373$	21.1613	1.09569	0.547845	+	0.836580i	$0.315448\pi$
$374$	−3.41569	−0.176621
$375$	−8.09530	−0.418039
$376$	−2.49766	−0.128807
$377$	−3.04271	−0.156708
$378$	4.57880	0.235508
$379$	−9.39999	−0.482845	−0.241423	−	0.970420i	$-0.577614\pi$
$379$	−9.39999	−0.482845	−0.241423	+	0.970420i	$0.577614\pi$
$380$	−0.538061	−0.0276019
$381$	−8.68617	−0.445006
$382$	7.09372	0.362946
$383$	−3.23718	−0.165412	−0.0827060	−	0.996574i	$-0.526356\pi$
$383$	−3.23718	−0.165412	−0.0827060	+	0.996574i	$0.526356\pi$
$384$	−1.00000	−0.0510310
$385$	−13.7157	−0.699017
$386$	5.88891	0.299737
$387$	0.576218	0.0292908
$388$	6.31864	0.320780
$389$	36.7209	1.86183	0.930913	−	0.365242i	$-0.119014\pi$
$389$	36.7209	1.86183	0.930913	+	0.365242i	$0.119014\pi$
$390$	4.78630	0.242364
$391$	8.17716	0.413537
$392$	−13.9654	−0.705361
$393$	−6.95411	−0.350788
$394$	12.5163	0.630563
$395$	−12.1100	−0.609318
$396$	3.41569	0.171645
$397$	−18.8951	−0.948317	−0.474159	−	0.880439i	$-0.657248\pi$
$397$	−18.8951	−0.948317	−0.474159	+	0.880439i	$0.657248\pi$
$398$	10.7928	0.540995
$399$	2.80928	0.140640
$400$	−4.23091	−0.211546
$401$	2.86642	0.143142	0.0715711	−	0.997435i	$-0.477199\pi$
$401$	2.86642	0.143142	0.0715711	+	0.997435i	$0.477199\pi$
$402$	−0.345571	−0.0172355
$403$	−18.7629	−0.934648
$404$	11.2895	0.561672
$405$	0.876977	0.0435773
$406$	2.55271	0.126689
$407$	−15.2084	−0.753855
$408$	−1.00000	−0.0495074
$409$	24.2343	1.19831	0.599155	−	0.800633i	$-0.295503\pi$
$409$	24.2343	1.19831	0.599155	+	0.800633i	$0.295503\pi$
$410$	−1.00105	−0.0494384
$411$	−5.37063	−0.264914
$412$	−13.7799	−0.678889
$413$	4.57880	0.225308
$414$	−8.17716	−0.401885
$415$	−4.38655	−0.215327
$416$	5.45772	0.267587
$417$	11.9539	0.585386
$418$	2.09566	0.102502
$419$	−9.41548	−0.459976	−0.229988	−	0.973193i	$-0.573869\pi$
$419$	−9.41548	−0.459976	−0.229988	+	0.973193i	$0.573869\pi$
$420$	−4.01550	−0.195937
$421$	−20.0322	−0.976311	−0.488155	−	0.872757i	$-0.662330\pi$
$421$	−20.0322	−0.976311	−0.488155	+	0.872757i	$0.662330\pi$
$422$	−6.29242	−0.306310
$423$	2.49766	0.121440
$424$	1.84764	0.0897295
$425$	−4.23091	−0.205229
$426$	−5.75711	−0.278933
$427$	50.6751	2.45234
$428$	5.39783	0.260914
$429$	−18.6419	−0.900038
$430$	−0.505329	−0.0243692
$431$	28.5764	1.37648	0.688239	−	0.725484i	$-0.258384\pi$
$431$	28.5764	1.37648	0.688239	+	0.725484i	$0.258384\pi$
$432$	1.00000	0.0481125
$433$	20.2149	0.971464	0.485732	−	0.874108i	$-0.338553\pi$
$433$	20.2149	0.971464	0.485732	+	0.874108i	$0.338553\pi$
$434$	15.7413	0.755607
$435$	0.488920	0.0234419
$436$	−16.9388	−0.811222
$437$	−5.01702	−0.239996
$438$	6.22835	0.297602
$439$	5.42325	0.258838	0.129419	−	0.991590i	$-0.458689\pi$
$439$	5.42325	0.258838	0.129419	+	0.991590i	$0.458689\pi$
$440$	−2.99548	−0.142804
$441$	13.9654	0.665021
$442$	5.45772	0.259597
$443$	−23.7513	−1.12846	−0.564229	−	0.825619i	$-0.690826\pi$
$443$	−23.7513	−1.12846	−0.564229	+	0.825619i	$0.690826\pi$
$444$	−4.45253	−0.211308
$445$	7.09606	0.336385
$446$	11.7149	0.554716
$447$	−0.442568	−0.0209328
$448$	−4.57880	−0.216328
$449$	28.0600	1.32423	0.662117	−	0.749400i	$-0.269658\pi$
$449$	28.0600	1.32423	0.662117	+	0.749400i	$0.269658\pi$
$450$	4.23091	0.199447
$451$	3.89893	0.183594
$452$	−3.88297	−0.182639
$453$	−0.336830	−0.0158256
$454$	−17.1444	−0.804625
$455$	21.9155	1.02742
$456$	0.613540	0.0287317
$457$	18.4364	0.862417	0.431209	−	0.902252i	$-0.358087\pi$
$457$	18.4364	0.862417	0.431209	+	0.902252i	$0.358087\pi$
$458$	−19.3413	−0.903758
$459$	1.00000	0.0466760
$460$	7.17118	0.334358
$461$	29.0663	1.35375	0.676875	−	0.736098i	$-0.263334\pi$
$461$	29.0663	1.35375	0.676875	+	0.736098i	$0.263334\pi$
$462$	15.6398	0.727627
$463$	7.17331	0.333372	0.166686	−	0.986010i	$-0.446693\pi$
$463$	7.17331	0.333372	0.166686	+	0.986010i	$0.446693\pi$
$464$	0.557506	0.0258816
$465$	3.01493	0.139814
$466$	14.1022	0.653273
$467$	−9.35700	−0.432990	−0.216495	−	0.976284i	$-0.569463\pi$
$467$	−9.35700	−0.432990	−0.216495	+	0.976284i	$0.569463\pi$
$468$	−5.45772	−0.252283
$469$	−1.58230	−0.0730639
$470$	−2.19039	−0.101035
$471$	−7.36786	−0.339493
$472$	1.00000	0.0460287
$473$	1.96818	0.0904970
$474$	13.8088	0.634257
$475$	2.59584	0.119105
$476$	−4.57880	−0.209869
$477$	−1.84764	−0.0845978
$478$	18.0178	0.824114
$479$	28.4658	1.30064	0.650318	−	0.759662i	$-0.274636\pi$
$479$	28.4658	1.30064	0.650318	+	0.759662i	$0.274636\pi$
$480$	−0.876977	−0.0400283
$481$	24.3007	1.10802
$482$	9.58238	0.436465
$483$	−37.4416	−1.70365
$484$	0.666921	0.0303146
$485$	5.54130	0.251618
$486$	−1.00000	−0.0453609
$487$	−18.4304	−0.835161	−0.417580	−	0.908640i	$-0.637122\pi$
$487$	−18.4304	−0.835161	−0.417580	+	0.908640i	$0.637122\pi$
$488$	11.0673	0.500994
$489$	0.473427	0.0214091
$490$	−12.2474	−0.553279
$491$	−24.0743	−1.08646	−0.543229	−	0.839585i	$-0.682798\pi$
$491$	−24.0743	−1.08646	−0.543229	+	0.839585i	$0.682798\pi$
$492$	1.14148	0.0514618
$493$	0.557506	0.0251088
$494$	−3.34853	−0.150658
$495$	2.99548	0.134637
$496$	3.43787	0.154365
$497$	−26.3607	−1.18244
$498$	5.00190	0.224141
$499$	−26.3569	−1.17990	−0.589948	−	0.807441i	$-0.700852\pi$
$499$	−26.3569	−1.17990	−0.589948	+	0.807441i	$0.700852\pi$
$500$	−8.09530	−0.362033
$501$	−13.2391	−0.591478
$502$	6.95721	0.310515
$503$	−42.3047	−1.88627	−0.943137	−	0.332405i	$-0.892140\pi$
$503$	−42.3047	−1.88627	−0.943137	+	0.332405i	$0.892140\pi$
$504$	4.57880	0.203956
$505$	9.90061	0.440571
$506$	−27.9306	−1.24167
$507$	16.7868	0.745526
$508$	−8.68617	−0.385386
$509$	32.6118	1.44549	0.722747	−	0.691112i	$-0.242879\pi$
$509$	32.6118	1.44549	0.722747	+	0.691112i	$0.242879\pi$
$510$	−0.876977	−0.0388332
$511$	28.5184	1.26158
$512$	−1.00000	−0.0441942
$513$	−0.613540	−0.0270885
$514$	−25.7425	−1.13545
$515$	−12.0847	−0.532515
$516$	0.576218	0.0253666
$517$	8.53122	0.375203
$518$	−20.3872	−0.895764
$519$	−21.4182	−0.940155
$520$	4.78630	0.209893
$521$	2.40611	0.105414	0.0527068	−	0.998610i	$-0.483215\pi$
$521$	2.40611	0.105414	0.0527068	+	0.998610i	$0.483215\pi$
$522$	−0.557506	−0.0244014
$523$	−19.8954	−0.869965	−0.434982	−	0.900439i	$-0.643245\pi$
$523$	−19.8954	−0.869965	−0.434982	+	0.900439i	$0.643245\pi$
$524$	−6.95411	−0.303792
$525$	19.3725	0.845486
$526$	0.181820	0.00792774
$527$	3.43787	0.149756
$528$	3.41569	0.148649
$529$	43.8659	1.90721
$530$	1.62034	0.0703831
$531$	−1.00000	−0.0433963
$532$	2.80928	0.121798
$533$	−6.22987	−0.269846
$534$	−8.09150	−0.350153
$535$	4.73377	0.204659
$536$	−0.345571	−0.0149264
$537$	−24.8883	−1.07401
$538$	−13.4058	−0.577965
$539$	47.7016	2.05465
$540$	0.876977	0.0377391
$541$	11.4711	0.493180	0.246590	−	0.969120i	$-0.420690\pi$
$541$	11.4711	0.493180	0.246590	+	0.969120i	$0.420690\pi$
$542$	1.48537	0.0638020
$543$	−1.56220	−0.0670403
$544$	−1.00000	−0.0428746
$545$	−14.8549	−0.636316
$546$	−24.9898	−1.06947
$547$	5.73695	0.245294	0.122647	−	0.992450i	$-0.460862\pi$
$547$	5.73695	0.245294	0.122647	+	0.992450i	$0.460862\pi$
$548$	−5.37063	−0.229422
$549$	−11.0673	−0.472342
$550$	14.4515	0.616213
$551$	−0.342052	−0.0145719
$552$	−8.17716	−0.348043
$553$	63.2276	2.68871
$554$	−8.24428	−0.350266
$555$	−3.90476	−0.165748
$556$	11.9539	0.506959
$557$	37.5641	1.59164	0.795821	−	0.605531i	$-0.207039\pi$
$557$	37.5641	1.59164	0.795821	+	0.605531i	$0.207039\pi$
$558$	−3.43787	−0.145537
$559$	−3.14484	−0.133012
$560$	−4.01550	−0.169686
$561$	3.41569	0.144210
$562$	22.0526	0.930234
$563$	25.0272	1.05477	0.527386	−	0.849626i	$-0.323172\pi$
$563$	25.0272	1.05477	0.527386	+	0.849626i	$0.323172\pi$
$564$	2.49766	0.105170
$565$	−3.40527	−0.143261
$566$	24.5950	1.03381
$567$	−4.57880	−0.192292
$568$	−5.75711	−0.241563
$569$	14.8044	0.620632	0.310316	−	0.950633i	$-0.399565\pi$
$569$	14.8044	0.620632	0.310316	+	0.950633i	$0.399565\pi$
$570$	0.538061	0.0225369
$571$	15.6867	0.656468	0.328234	−	0.944596i	$-0.393546\pi$
$571$	15.6867	0.656468	0.328234	+	0.944596i	$0.393546\pi$
$572$	−18.6419	−0.779456
$573$	−7.09372	−0.296344
$574$	5.22661	0.218154
$575$	−34.5968	−1.44279
$576$	1.00000	0.0416667
$577$	−28.9362	−1.20463	−0.602315	−	0.798259i	$-0.705755\pi$
$577$	−28.9362	−1.20463	−0.602315	+	0.798259i	$0.705755\pi$
$578$	−1.00000	−0.0415945
$579$	−5.88891	−0.244735
$580$	0.488920	0.0203013
$581$	22.9027	0.950165
$582$	−6.31864	−0.261916
$583$	−6.31097	−0.261374
$584$	6.22835	0.257731
$585$	−4.78630	−0.197889
$586$	3.75788	0.155237
$587$	−17.2669	−0.712679	−0.356340	−	0.934357i	$-0.615975\pi$
$587$	−17.2669	−0.712679	−0.356340	+	0.934357i	$0.615975\pi$
$588$	13.9654	0.575925
$589$	−2.10927	−0.0869110
$590$	0.876977	0.0361046
$591$	−12.5163	−0.514853
$592$	−4.45253	−0.182998
$593$	−3.82567	−0.157101	−0.0785507	−	0.996910i	$-0.525029\pi$
$593$	−3.82567	−0.157101	−0.0785507	+	0.996910i	$0.525029\pi$
$594$	−3.41569	−0.140147
$595$	−4.01550	−0.164620
$596$	−0.442568	−0.0181283
$597$	−10.7928	−0.441721
$598$	44.6287	1.82500
$599$	−33.1372	−1.35395	−0.676976	−	0.736005i	$-0.736710\pi$
$599$	−33.1372	−1.35395	−0.676976	+	0.736005i	$0.736710\pi$
$600$	4.23091	0.172726
$601$	−41.6017	−1.69697	−0.848485	−	0.529220i	$-0.822485\pi$
$601$	−41.6017	−1.69697	−0.848485	+	0.529220i	$0.822485\pi$
$602$	2.63839	0.107533
$603$	0.345571	0.0140727
$604$	−0.336830	−0.0137054
$605$	0.584875	0.0237785
$606$	−11.2895	−0.458604
$607$	−24.3294	−0.987501	−0.493751	−	0.869604i	$-0.664374\pi$
$607$	−24.3294	−0.987501	−0.493751	+	0.869604i	$0.664374\pi$
$608$	0.613540	0.0248824
$609$	−2.55271	−0.103441
$610$	9.70578	0.392976
$611$	−13.6315	−0.551472
$612$	1.00000	0.0404226
$613$	−26.3402	−1.06387	−0.531935	−	0.846785i	$-0.678535\pi$
$613$	−26.3402	−1.06387	−0.531935	+	0.846785i	$0.678535\pi$
$614$	−11.2231	−0.452928
$615$	1.00105	0.0403662
$616$	15.6398	0.630144
$617$	−22.0578	−0.888014	−0.444007	−	0.896023i	$-0.646443\pi$
$617$	−22.0578	−0.888014	−0.444007	+	0.896023i	$0.646443\pi$
$618$	13.7799	0.554311
$619$	22.1783	0.891423	0.445711	−	0.895177i	$-0.352951\pi$
$619$	22.1783	0.891423	0.445711	+	0.895177i	$0.352951\pi$
$620$	3.01493	0.121082
$621$	8.17716	0.328138
$622$	1.71050	0.0685848
$623$	−37.0494	−1.48435
$624$	−5.45772	−0.218484
$625$	14.0552	0.562207
$626$	27.0813	1.08239
$627$	−2.09566	−0.0836927
$628$	−7.36786	−0.294010
$629$	−4.45253	−0.177534
$630$	4.01550	0.159982
$631$	−41.6080	−1.65639	−0.828194	−	0.560441i	$-0.810632\pi$
$631$	−41.6080	−1.65639	−0.828194	+	0.560441i	$0.810632\pi$
$632$	13.8088	0.549283
$633$	6.29242	0.250101
$634$	−6.51308	−0.258668
$635$	−7.61757	−0.302294
$636$	−1.84764	−0.0732638
$637$	−76.2195	−3.01993
$638$	−1.90427	−0.0753906
$639$	5.75711	0.227748
$640$	−0.876977	−0.0346656
$641$	−7.17731	−0.283487	−0.141743	−	0.989903i	$-0.545271\pi$
$641$	−7.17731	−0.283487	−0.141743	+	0.989903i	$0.545271\pi$
$642$	−5.39783	−0.213035
$643$	−31.3276	−1.23544	−0.617721	−	0.786397i	$-0.711944\pi$
$643$	−31.3276	−1.23544	−0.617721	+	0.786397i	$0.711944\pi$
$644$	−37.4416	−1.47541
$645$	0.505329	0.0198973
$646$	0.613540	0.0241394
$647$	12.7956	0.503045	0.251523	−	0.967851i	$-0.419069\pi$
$647$	12.7956	0.503045	0.251523	+	0.967851i	$0.419069\pi$
$648$	−1.00000	−0.0392837
$649$	−3.41569	−0.134077
$650$	−23.0911	−0.905709
$651$	−15.7413	−0.616951
$652$	0.473427	0.0185408
$653$	−43.1452	−1.68840	−0.844201	−	0.536026i	$-0.819925\pi$
$653$	−43.1452	−1.68840	−0.844201	+	0.536026i	$0.819925\pi$
$654$	16.9388	0.662360
$655$	−6.09859	−0.238292
$656$	1.14148	0.0445673
$657$	−6.22835	−0.242991
$658$	11.4363	0.445833
$659$	16.2184	0.631778	0.315889	−	0.948796i	$-0.397697\pi$
$659$	16.2184	0.631778	0.315889	+	0.948796i	$0.397697\pi$
$660$	2.99548	0.116599
$661$	42.3296	1.64643	0.823215	−	0.567729i	$-0.192178\pi$
$661$	42.3296	1.64643	0.823215	+	0.567729i	$0.192178\pi$
$662$	−16.8361	−0.654354
$663$	−5.45772	−0.211960
$664$	5.00190	0.194112
$665$	2.46367	0.0955372
$666$	4.45253	0.172532
$667$	4.55881	0.176518
$668$	−13.2391	−0.512235
$669$	−11.7149	−0.452923
$670$	−0.303058	−0.0117081
$671$	−37.8025	−1.45935
$672$	4.57880	0.176631
$673$	−35.9016	−1.38391	−0.691953	−	0.721943i	$-0.743249\pi$
$673$	−35.9016	−1.38391	−0.691953	+	0.721943i	$0.743249\pi$
$674$	−14.2541	−0.549046
$675$	−4.23091	−0.162848
$676$	16.7868	0.645644
$677$	12.0288	0.462306	0.231153	−	0.972917i	$-0.425750\pi$
$677$	12.0288	0.462306	0.231153	+	0.972917i	$0.425750\pi$
$678$	3.88297	0.149125
$679$	−28.9318	−1.11030
$680$	−0.876977	−0.0336305
$681$	17.1444	0.656974
$682$	−11.7427	−0.449650
$683$	−14.0759	−0.538598	−0.269299	−	0.963057i	$-0.586792\pi$
$683$	−14.0759	−0.538598	−0.269299	+	0.963057i	$0.586792\pi$
$684$	−0.613540	−0.0234593
$685$	−4.70992	−0.179957
$686$	31.8933	1.21769
$687$	19.3413	0.737915
$688$	0.576218	0.0219681
$689$	10.0839	0.384167
$690$	−7.17118	−0.273002
$691$	3.34874	0.127392	0.0636961	−	0.997969i	$-0.479711\pi$
$691$	3.34874	0.127392	0.0636961	+	0.997969i	$0.479711\pi$
$692$	−21.4182	−0.814198
$693$	−15.6398	−0.594105
$694$	−8.28372	−0.314446
$695$	10.4833	0.397655
$696$	−0.557506	−0.0211322
$697$	1.14148	0.0432366
$698$	6.43980	0.243750
$699$	−14.1022	−0.533395
$700$	19.3725	0.732212
$701$	2.25591	0.0852045	0.0426023	−	0.999092i	$-0.486435\pi$
$701$	2.25591	0.0852045	0.0426023	+	0.999092i	$0.486435\pi$
$702$	5.45772	0.205989
$703$	2.73181	0.103032
$704$	3.41569	0.128734
$705$	2.19039	0.0824948
$706$	8.69953	0.327411
$707$	−51.6923	−1.94409
$708$	−1.00000	−0.0375823
$709$	31.4557	1.18134	0.590672	−	0.806912i	$-0.298863\pi$
$709$	31.4557	1.18134	0.590672	+	0.806912i	$0.298863\pi$
$710$	−5.04885	−0.189480
$711$	−13.8088	−0.517869
$712$	−8.09150	−0.303242
$713$	28.1120	1.05280
$714$	4.57880	0.171357
$715$	−16.3485	−0.611399
$716$	−24.8883	−0.930121
$717$	−18.0178	−0.672886
$718$	7.75814	0.289531
$719$	−7.84247	−0.292475	−0.146237	−	0.989250i	$-0.546716\pi$
$719$	−7.84247	−0.292475	−0.146237	+	0.989250i	$0.546716\pi$
$720$	0.876977	0.0326830
$721$	63.0956	2.34980
$722$	18.6236	0.693097
$723$	−9.58238	−0.356372
$724$	−1.56220	−0.0580586
$725$	−2.35876	−0.0876021
$726$	−0.666921	−0.0247518
$727$	−37.3804	−1.38636	−0.693181	−	0.720763i	$-0.743791\pi$
$727$	−37.3804	−1.38636	−0.693181	+	0.720763i	$0.743791\pi$
$728$	−24.9898	−0.926185
$729$	1.00000	0.0370370
$730$	5.46212	0.202162
$731$	0.576218	0.0213122
$732$	−11.0673	−0.409060
$733$	20.7959	0.768113	0.384057	−	0.923310i	$-0.374527\pi$
$733$	20.7959	0.768113	0.384057	+	0.923310i	$0.374527\pi$
$734$	7.14293	0.263650
$735$	12.2474	0.451751
$736$	−8.17716	−0.301414
$737$	1.18036	0.0434792
$738$	−1.14148	−0.0420184
$739$	−8.12786	−0.298988	−0.149494	−	0.988763i	$-0.547764\pi$
$739$	−8.12786	−0.298988	−0.149494	+	0.988763i	$0.547764\pi$
$740$	−3.90476	−0.143542
$741$	3.34853	0.123011
$742$	−8.45999	−0.310576
$743$	8.50467	0.312006	0.156003	−	0.987757i	$-0.450139\pi$
$743$	8.50467	0.312006	0.156003	+	0.987757i	$0.450139\pi$
$744$	−3.43787	−0.126038
$745$	−0.388122	−0.0142197
$746$	−21.1613	−0.774770
$747$	−5.00190	−0.183010
$748$	3.41569	0.124890
$749$	−24.7156	−0.903088
$750$	8.09530	0.295598
$751$	8.71378	0.317970	0.158985	−	0.987281i	$-0.449178\pi$
$751$	8.71378	0.317970	0.158985	+	0.987281i	$0.449178\pi$
$752$	2.49766	0.0910802
$753$	−6.95721	−0.253535
$754$	3.04271	0.110809
$755$	−0.295392	−0.0107504
$756$	−4.57880	−0.166529
$757$	−26.4785	−0.962379	−0.481190	−	0.876617i	$-0.659795\pi$
$757$	−26.4785	−0.962379	−0.481190	+	0.876617i	$0.659795\pi$
$758$	9.39999	0.341423
$759$	27.9306	1.01382
$760$	0.538061	0.0195175
$761$	−13.9329	−0.505066	−0.252533	−	0.967588i	$-0.581264\pi$
$761$	−13.9329	−0.505066	−0.252533	+	0.967588i	$0.581264\pi$
$762$	8.68617	0.314667
$763$	77.5595	2.80784
$764$	−7.09372	−0.256642
$765$	0.876977	0.0317072
$766$	3.23718	0.116964
$767$	5.45772	0.197067
$768$	1.00000	0.0360844
$769$	11.9902	0.432379	0.216190	−	0.976351i	$-0.430637\pi$
$769$	11.9902	0.432379	0.216190	+	0.976351i	$0.430637\pi$
$770$	13.7157	0.494280
$771$	25.7425	0.927093
$772$	−5.88891	−0.211946
$773$	7.82773	0.281544	0.140772	−	0.990042i	$-0.455042\pi$
$773$	7.82773	0.281544	0.140772	+	0.990042i	$0.455042\pi$
$774$	−0.576218	−0.0207117
$775$	−14.5453	−0.522483
$776$	−6.31864	−0.226826
$777$	20.3872	0.731388
$778$	−36.7209	−1.31651
$779$	−0.700343	−0.0250924
$780$	−4.78630	−0.171377
$781$	19.6645	0.703651
$782$	−8.17716	−0.292415
$783$	0.557506	0.0199236
$784$	13.9654	0.498765
$785$	−6.46144	−0.230619
$786$	6.95411	0.248045
$787$	−7.83354	−0.279235	−0.139618	−	0.990205i	$-0.544587\pi$
$787$	−7.83354	−0.279235	−0.139618	+	0.990205i	$0.544587\pi$
$788$	−12.5163	−0.445875
$789$	−0.181820	−0.00647297
$790$	12.1100	0.430853
$791$	17.7793	0.632161
$792$	−3.41569	−0.121371
$793$	60.4024	2.14495
$794$	18.8951	0.670562
$795$	−1.62034	−0.0574675
$796$	−10.7928	−0.382542
$797$	−17.8536	−0.632406	−0.316203	−	0.948692i	$-0.602408\pi$
$797$	−17.8536	−0.632406	−0.316203	+	0.948692i	$0.602408\pi$
$798$	−2.80928	−0.0994475
$799$	2.49766	0.0883608
$800$	4.23091	0.149585
$801$	8.09150	0.285899
$802$	−2.86642	−0.101217
$803$	−21.2741	−0.750747
$804$	0.345571	0.0121873
$805$	−32.8354	−1.15730
$806$	18.7629	0.660896
$807$	13.4058	0.471906
$808$	−11.2895	−0.397162
$809$	23.2016	0.815726	0.407863	−	0.913043i	$-0.366274\pi$
$809$	23.2016	0.815726	0.407863	+	0.913043i	$0.366274\pi$
$810$	−0.876977	−0.0308138
$811$	−15.4652	−0.543056	−0.271528	−	0.962431i	$-0.587529\pi$
$811$	−15.4652	−0.543056	−0.271528	+	0.962431i	$0.587529\pi$
$812$	−2.55271	−0.0895825
$813$	−1.48537	−0.0520941
$814$	15.2084	0.533056
$815$	0.415185	0.0145433
$816$	1.00000	0.0350070
$817$	−0.353533	−0.0123685
$818$	−24.2343	−0.847333
$819$	24.9898	0.873216
$820$	1.00105	0.0349582
$821$	−26.0352	−0.908634	−0.454317	−	0.890840i	$-0.650117\pi$
$821$	−26.0352	−0.908634	−0.454317	+	0.890840i	$0.650117\pi$
$822$	5.37063	0.187322
$823$	13.8883	0.484116	0.242058	−	0.970262i	$-0.422177\pi$
$823$	13.8883	0.484116	0.242058	+	0.970262i	$0.422177\pi$
$824$	13.7799	0.480047
$825$	−14.4515	−0.503136
$826$	−4.57880	−0.159317
$827$	40.5668	1.41064	0.705322	−	0.708887i	$-0.250802\pi$
$827$	40.5668	1.41064	0.705322	+	0.708887i	$0.250802\pi$
$828$	8.17716	0.284176
$829$	−45.0135	−1.56338	−0.781692	−	0.623664i	$-0.785643\pi$
$829$	−45.0135	−1.56338	−0.781692	+	0.623664i	$0.785643\pi$
$830$	4.38655	0.152260
$831$	8.24428	0.285991
$832$	−5.45772	−0.189213
$833$	13.9654	0.483874
$834$	−11.9539	−0.413930
$835$	−11.6103	−0.401793
$836$	−2.09566	−0.0724800
$837$	3.43787	0.118830
$838$	9.41548	0.325252
$839$	−47.5398	−1.64126	−0.820628	−	0.571462i	$-0.806376\pi$
$839$	−47.5398	−1.64126	−0.820628	+	0.571462i	$0.806376\pi$
$840$	4.01550	0.138548
$841$	−28.6892	−0.989282
$842$	20.0322	0.690356
$843$	−22.0526	−0.759533
$844$	6.29242	0.216594
$845$	14.7216	0.506438
$846$	−2.49766	−0.0858712
$847$	−3.05370	−0.104926
$848$	−1.84764	−0.0634483
$849$	−24.5950	−0.844098
$850$	4.23091	0.145119
$851$	−36.4090	−1.24809
$852$	5.75711	0.197235
$853$	−26.3179	−0.901107	−0.450553	−	0.892749i	$-0.648773\pi$
$853$	−26.3179	−0.901107	−0.450553	+	0.892749i	$0.648773\pi$
$854$	−50.6751	−1.73406
$855$	−0.538061	−0.0184013
$856$	−5.39783	−0.184494
$857$	42.3409	1.44634	0.723169	−	0.690671i	$-0.242685\pi$
$857$	42.3409	1.44634	0.723169	+	0.690671i	$0.242685\pi$
$858$	18.6419	0.636423
$859$	39.9167	1.36194	0.680971	−	0.732311i	$-0.261558\pi$
$859$	39.9167	1.36194	0.680971	+	0.732311i	$0.261558\pi$
$860$	0.505329	0.0172316
$861$	−5.22661	−0.178122
$862$	−28.5764	−0.973317
$863$	41.0923	1.39880	0.699400	−	0.714731i	$-0.253451\pi$
$863$	41.0923	1.39880	0.699400	+	0.714731i	$0.253451\pi$
$864$	−1.00000	−0.0340207
$865$	−18.7833	−0.638651
$866$	−20.2149	−0.686929
$867$	1.00000	0.0339618
$868$	−15.7413	−0.534295
$869$	−47.1664	−1.60001
$870$	−0.488920	−0.0165759
$871$	−1.88603	−0.0639057
$872$	16.9388	0.573621
$873$	6.31864	0.213854
$874$	5.01702	0.169703
$875$	37.0668	1.25309
$876$	−6.22835	−0.210437
$877$	−50.1184	−1.69238	−0.846190	−	0.532882i	$-0.821109\pi$
$877$	−50.1184	−1.69238	−0.846190	+	0.532882i	$0.821109\pi$
$878$	−5.42325	−0.183026
$879$	−3.75788	−0.126750
$880$	2.99548	0.100978
$881$	49.5222	1.66844	0.834222	−	0.551429i	$-0.185917\pi$
$881$	49.5222	1.66844	0.834222	+	0.551429i	$0.185917\pi$
$882$	−13.9654	−0.470241
$883$	−34.8985	−1.17443	−0.587213	−	0.809432i	$-0.699775\pi$
$883$	−34.8985	−1.17443	−0.587213	+	0.809432i	$0.699775\pi$
$884$	−5.45772	−0.183563
$885$	−0.876977	−0.0294793
$886$	23.7513	0.797940
$887$	−39.8364	−1.33758	−0.668788	−	0.743453i	$-0.733187\pi$
$887$	−39.8364	−1.33758	−0.668788	+	0.743453i	$0.733187\pi$
$888$	4.45253	0.149417
$889$	39.7722	1.33392
$890$	−7.09606	−0.237860
$891$	3.41569	0.114430
$892$	−11.7149	−0.392243
$893$	−1.53241	−0.0512803
$894$	0.442568	0.0148017
$895$	−21.8265	−0.729580
$896$	4.57880	0.152967
$897$	−44.6287	−1.49011
$898$	−28.0600	−0.936375
$899$	1.91663	0.0639232
$900$	−4.23091	−0.141030
$901$	−1.84764	−0.0615539
$902$	−3.89893	−0.129820
$903$	−2.63839	−0.0878000
$904$	3.88297	0.129146
$905$	−1.37001	−0.0455407
$906$	0.336830	0.0111904
$907$	−5.40197	−0.179369	−0.0896847	−	0.995970i	$-0.528586\pi$
$907$	−5.40197	−0.179369	−0.0896847	+	0.995970i	$0.528586\pi$
$908$	17.1444	0.568956
$909$	11.2895	0.374448
$910$	−21.9155	−0.726492
$911$	−43.2817	−1.43399	−0.716994	−	0.697080i	$-0.754482\pi$
$911$	−43.2817	−1.43399	−0.716994	+	0.697080i	$0.754482\pi$
$912$	−0.613540	−0.0203164
$913$	−17.0849	−0.565429
$914$	−18.4364	−0.609821
$915$	−9.70578	−0.320863
$916$	19.3413	0.639053
$917$	31.8415	1.05150
$918$	−1.00000	−0.0330049
$919$	14.7289	0.485863	0.242931	−	0.970044i	$-0.421891\pi$
$919$	14.7289	0.485863	0.242931	+	0.970044i	$0.421891\pi$
$920$	−7.17118	−0.236427
$921$	11.2231	0.369814
$922$	−29.0663	−0.957246
$923$	−31.4207	−1.03423
$924$	−15.6398	−0.514510
$925$	18.8383	0.619398
$926$	−7.17331	−0.235729
$927$	−13.7799	−0.452593
$928$	−0.557506	−0.0183010
$929$	12.1211	0.397680	0.198840	−	0.980032i	$-0.436283\pi$
$929$	12.1211	0.397680	0.198840	+	0.980032i	$0.436283\pi$
$930$	−3.01493	−0.0988634
$931$	−8.56836	−0.280817
$932$	−14.1022	−0.461934
$933$	−1.71050	−0.0559993
$934$	9.35700	0.306170
$935$	2.99548	0.0979626
$936$	5.45772	0.178391
$937$	31.0788	1.01530	0.507651	−	0.861563i	$-0.330514\pi$
$937$	31.0788	1.01530	0.507651	+	0.861563i	$0.330514\pi$
$938$	1.58230	0.0516640
$939$	−27.0813	−0.883765
$940$	2.19039	0.0714426
$941$	−18.8298	−0.613834	−0.306917	−	0.951736i	$-0.599297\pi$
$941$	−18.8298	−0.613834	−0.306917	+	0.951736i	$0.599297\pi$
$942$	7.36786	0.240058
$943$	9.33405	0.303958
$944$	−1.00000	−0.0325472
$945$	−4.01550	−0.130624
$946$	−1.96818	−0.0639910
$947$	43.1243	1.40135	0.700675	−	0.713480i	$-0.252882\pi$
$947$	43.1243	1.40135	0.700675	+	0.713480i	$0.252882\pi$
$948$	−13.8088	−0.448488
$949$	33.9926	1.10345
$950$	−2.59584	−0.0842200
$951$	6.51308	0.211201
$952$	4.57880	0.148400
$953$	10.9406	0.354400	0.177200	−	0.984175i	$-0.443296\pi$
$953$	10.9406	0.354400	0.177200	+	0.984175i	$0.443296\pi$
$954$	1.84764	0.0598196
$955$	−6.22102	−0.201308
$956$	−18.0178	−0.582737
$957$	1.90427	0.0615562
$958$	−28.4658	−0.919688
$959$	24.5910	0.794086
$960$	0.876977	0.0283043
$961$	−19.1811	−0.618744
$962$	−24.3007	−0.783485
$963$	5.39783	0.173943
$964$	−9.58238	−0.308628
$965$	−5.16444	−0.166249
$966$	37.4416	1.20466
$967$	−5.54694	−0.178377	−0.0891887	−	0.996015i	$-0.528427\pi$
$967$	−5.54694	−0.178377	−0.0891887	+	0.996015i	$0.528427\pi$
$968$	−0.666921	−0.0214357
$969$	−0.613540	−0.0197098
$970$	−5.54130	−0.177920
$971$	−43.5697	−1.39822	−0.699109	−	0.715015i	$-0.746420\pi$
$971$	−43.5697	−1.39822	−0.699109	+	0.715015i	$0.746420\pi$
$972$	1.00000	0.0320750
$973$	−54.7346	−1.75471
$974$	18.4304	0.590548
$975$	23.0911	0.739509
$976$	−11.0673	−0.354256
$977$	−5.82107	−0.186232	−0.0931162	−	0.995655i	$-0.529683\pi$
$977$	−5.82107	−0.186232	−0.0931162	+	0.995655i	$0.529683\pi$
$978$	−0.473427	−0.0151385
$979$	27.6380	0.883315
$980$	12.2474	0.391228
$981$	−16.9388	−0.540815
$982$	24.0743	0.768241
$983$	39.8971	1.27252	0.636261	−	0.771474i	$-0.280480\pi$
$983$	39.8971	1.27252	0.636261	+	0.771474i	$0.280480\pi$
$984$	−1.14148	−0.0363890
$985$	−10.9765	−0.349741
$986$	−0.557506	−0.0177546
$987$	−11.4363	−0.364021
$988$	3.34853	0.106531
$989$	4.71182	0.149827
$990$	−2.99548	−0.0952026
$991$	23.7916	0.755766	0.377883	−	0.925853i	$-0.376652\pi$
$991$	23.7916	0.755766	0.377883	+	0.925853i	$0.376652\pi$
$992$	−3.43787	−0.109152
$993$	16.8361	0.534278
$994$	26.3607	0.836110
$995$	−9.46506	−0.300063
$996$	−5.00190	−0.158491
$997$	26.5130	0.839675	0.419837	−	0.907599i	$-0.362087\pi$
$997$	26.5130	0.839675	0.419837	+	0.907599i	$0.362087\pi$
$998$	26.3569	0.834313
$999$	−4.45253	−0.140872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.t.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.t.1.6	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.876977 q^{5} -1.00000 q^{6} -4.57880 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.876977 q^{5} -1.00000 q^{6} -4.57880 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.876977 q^{10} +3.41569 q^{11} +1.00000 q^{12} -5.45772 q^{13} +4.57880 q^{14} +0.876977 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -0.613540 q^{19} +0.876977 q^{20} -4.57880 q^{21} -3.41569 q^{22} +8.17716 q^{23} -1.00000 q^{24} -4.23091 q^{25} +5.45772 q^{26} +1.00000 q^{27} -4.57880 q^{28} +0.557506 q^{29} -0.876977 q^{30} +3.43787 q^{31} -1.00000 q^{32} +3.41569 q^{33} -1.00000 q^{34} -4.01550 q^{35} +1.00000 q^{36} -4.45253 q^{37} +0.613540 q^{38} -5.45772 q^{39} -0.876977 q^{40} +1.14148 q^{41} +4.57880 q^{42} +0.576218 q^{43} +3.41569 q^{44} +0.876977 q^{45} -8.17716 q^{46} +2.49766 q^{47} +1.00000 q^{48} +13.9654 q^{49} +4.23091 q^{50} +1.00000 q^{51} -5.45772 q^{52} -1.84764 q^{53} -1.00000 q^{54} +2.99548 q^{55} +4.57880 q^{56} -0.613540 q^{57} -0.557506 q^{58} -1.00000 q^{59} +0.876977 q^{60} -11.0673 q^{61} -3.43787 q^{62} -4.57880 q^{63} +1.00000 q^{64} -4.78630 q^{65} -3.41569 q^{66} +0.345571 q^{67} +1.00000 q^{68} +8.17716 q^{69} +4.01550 q^{70} +5.75711 q^{71} -1.00000 q^{72} -6.22835 q^{73} +4.45253 q^{74} -4.23091 q^{75} -0.613540 q^{76} -15.6398 q^{77} +5.45772 q^{78} -13.8088 q^{79} +0.876977 q^{80} +1.00000 q^{81} -1.14148 q^{82} -5.00190 q^{83} -4.57880 q^{84} +0.876977 q^{85} -0.576218 q^{86} +0.557506 q^{87} -3.41569 q^{88} +8.09150 q^{89} -0.876977 q^{90} +24.9898 q^{91} +8.17716 q^{92} +3.43787 q^{93} -2.49766 q^{94} -0.538061 q^{95} -1.00000 q^{96} +6.31864 q^{97} -13.9654 q^{98} +3.41569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 8 q^{9} + 6 q^{10} + q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} - q^{22} - 11 q^{23} - 8 q^{24} + 6 q^{25} + 2 q^{26} + 8 q^{27} - 4 q^{28} - 12 q^{29} + 6 q^{30} - 9 q^{31} - 8 q^{32} + q^{33} - 8 q^{34} - 28 q^{35} + 8 q^{36} - 22 q^{37} - 4 q^{38} - 2 q^{39} + 6 q^{40} - 19 q^{41} + 4 q^{42} - 5 q^{43} + q^{44} - 6 q^{45} + 11 q^{46} - 26 q^{47} + 8 q^{48} - 6 q^{50} + 8 q^{51} - 2 q^{52} - 21 q^{53} - 8 q^{54} - 13 q^{55} + 4 q^{56} + 4 q^{57} + 12 q^{58} - 8 q^{59} - 6 q^{60} + 9 q^{61} + 9 q^{62} - 4 q^{63} + 8 q^{64} + 14 q^{65} - q^{66} + 26 q^{67} + 8 q^{68} - 11 q^{69} + 28 q^{70} - 14 q^{71} - 8 q^{72} + 17 q^{73} + 22 q^{74} + 6 q^{75} + 4 q^{76} - 18 q^{77} + 2 q^{78} - 39 q^{79} - 6 q^{80} + 8 q^{81} + 19 q^{82} - 11 q^{83} - 4 q^{84} - 6 q^{85} + 5 q^{86} - 12 q^{87} - q^{88} + 6 q^{90} + 11 q^{91} - 11 q^{92} - 9 q^{93} + 26 q^{94} - 15 q^{95} - 8 q^{96} + 16 q^{97} + q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 8 * q^9 + 6 * q^10 + q^11 + 8 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 4 * q^19 - 6 * q^20 - 4 * q^21 - q^22 - 11 * q^23 - 8 * q^24 + 6 * q^25 + 2 * q^26 + 8 * q^27 - 4 * q^28 - 12 * q^29 + 6 * q^30 - 9 * q^31 - 8 * q^32 + q^33 - 8 * q^34 - 28 * q^35 + 8 * q^36 - 22 * q^37 - 4 * q^38 - 2 * q^39 + 6 * q^40 - 19 * q^41 + 4 * q^42 - 5 * q^43 + q^44 - 6 * q^45 + 11 * q^46 - 26 * q^47 + 8 * q^48 - 6 * q^50 + 8 * q^51 - 2 * q^52 - 21 * q^53 - 8 * q^54 - 13 * q^55 + 4 * q^56 + 4 * q^57 + 12 * q^58 - 8 * q^59 - 6 * q^60 + 9 * q^61 + 9 * q^62 - 4 * q^63 + 8 * q^64 + 14 * q^65 - q^66 + 26 * q^67 + 8 * q^68 - 11 * q^69 + 28 * q^70 - 14 * q^71 - 8 * q^72 + 17 * q^73 + 22 * q^74 + 6 * q^75 + 4 * q^76 - 18 * q^77 + 2 * q^78 - 39 * q^79 - 6 * q^80 + 8 * q^81 + 19 * q^82 - 11 * q^83 - 4 * q^84 - 6 * q^85 + 5 * q^86 - 12 * q^87 - q^88 + 6 * q^90 + 11 * q^91 - 11 * q^92 - 9 * q^93 + 26 * q^94 - 15 * q^95 - 8 * q^96 + 16 * q^97 + q^99

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