LMFDB - Embedded newform 6010.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
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			1.10
Root			$1.27770$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.277700 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.277700 q^{6} +2.55233 q^{7} +1.00000 q^{8} -2.92288 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.277700 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.277700 q^{6} +2.55233 q^{7} +1.00000 q^{8} -2.92288 q^{9} +1.00000 q^{10} -4.94159 q^{11} +0.277700 q^{12} +4.28763 q^{13} +2.55233 q^{14} +0.277700 q^{15} +1.00000 q^{16} -3.28799 q^{17} -2.92288 q^{18} -3.94209 q^{19} +1.00000 q^{20} +0.708781 q^{21} -4.94159 q^{22} -6.03884 q^{23} +0.277700 q^{24} +1.00000 q^{25} +4.28763 q^{26} -1.64479 q^{27} +2.55233 q^{28} -7.47038 q^{29} +0.277700 q^{30} -4.60144 q^{31} +1.00000 q^{32} -1.37228 q^{33} -3.28799 q^{34} +2.55233 q^{35} -2.92288 q^{36} -1.65521 q^{37} -3.94209 q^{38} +1.19068 q^{39} +1.00000 q^{40} -8.01358 q^{41} +0.708781 q^{42} +1.78175 q^{43} -4.94159 q^{44} -2.92288 q^{45} -6.03884 q^{46} -3.33231 q^{47} +0.277700 q^{48} -0.485632 q^{49} +1.00000 q^{50} -0.913075 q^{51} +4.28763 q^{52} -8.76375 q^{53} -1.64479 q^{54} -4.94159 q^{55} +2.55233 q^{56} -1.09472 q^{57} -7.47038 q^{58} +6.61220 q^{59} +0.277700 q^{60} +10.0369 q^{61} -4.60144 q^{62} -7.46015 q^{63} +1.00000 q^{64} +4.28763 q^{65} -1.37228 q^{66} -5.12837 q^{67} -3.28799 q^{68} -1.67699 q^{69} +2.55233 q^{70} +2.50077 q^{71} -2.92288 q^{72} +2.44565 q^{73} -1.65521 q^{74} +0.277700 q^{75} -3.94209 q^{76} -12.6126 q^{77} +1.19068 q^{78} +10.1143 q^{79} +1.00000 q^{80} +8.31189 q^{81} -8.01358 q^{82} +1.46001 q^{83} +0.708781 q^{84} -3.28799 q^{85} +1.78175 q^{86} -2.07453 q^{87} -4.94159 q^{88} -7.59665 q^{89} -2.92288 q^{90} +10.9434 q^{91} -6.03884 q^{92} -1.27782 q^{93} -3.33231 q^{94} -3.94209 q^{95} +0.277700 q^{96} -0.655528 q^{97} -0.485632 q^{98} +14.4437 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * 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
$3$	0.277700	0.160330	0.0801651	−	0.996782i	$-0.474455\pi$
$3$	0.277700	0.160330	0.0801651	+	0.996782i	$0.474455\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.277700	0.113371
$7$	2.55233	0.964689	0.482344	−	0.875982i	$-0.339785\pi$
$7$	2.55233	0.964689	0.482344	+	0.875982i	$0.339785\pi$
$8$	1.00000	0.353553
$9$	−2.92288	−0.974294
$10$	1.00000	0.316228
$11$	−4.94159	−1.48995	−0.744973	−	0.667094i	$-0.767538\pi$
$11$	−4.94159	−1.48995	−0.744973	+	0.667094i	$0.767538\pi$
$12$	0.277700	0.0801651
$13$	4.28763	1.18918	0.594588	−	0.804031i	$-0.297315\pi$
$13$	4.28763	1.18918	0.594588	+	0.804031i	$0.297315\pi$
$14$	2.55233	0.682138
$15$	0.277700	0.0717019
$16$	1.00000	0.250000
$17$	−3.28799	−0.797455	−0.398727	−	0.917070i	$-0.630548\pi$
$17$	−3.28799	−0.797455	−0.398727	+	0.917070i	$0.630548\pi$
$18$	−2.92288	−0.688930
$19$	−3.94209	−0.904377	−0.452189	−	0.891922i	$-0.649357\pi$
$19$	−3.94209	−0.904377	−0.452189	+	0.891922i	$0.649357\pi$
$20$	1.00000	0.223607
$21$	0.708781	0.154669
$22$	−4.94159	−1.05355
$23$	−6.03884	−1.25918	−0.629592	−	0.776926i	$-0.716778\pi$
$23$	−6.03884	−1.25918	−0.629592	+	0.776926i	$0.716778\pi$
$24$	0.277700	0.0566853
$25$	1.00000	0.200000
$26$	4.28763	0.840874
$27$	−1.64479	−0.316539
$28$	2.55233	0.482344
$29$	−7.47038	−1.38721	−0.693607	−	0.720353i	$-0.743980\pi$
$29$	−7.47038	−1.38721	−0.693607	+	0.720353i	$0.743980\pi$
$30$	0.277700	0.0507009
$31$	−4.60144	−0.826443	−0.413222	−	0.910630i	$-0.635597\pi$
$31$	−4.60144	−0.826443	−0.413222	+	0.910630i	$0.635597\pi$
$32$	1.00000	0.176777
$33$	−1.37228	−0.238884
$34$	−3.28799	−0.563886
$35$	2.55233	0.431422
$36$	−2.92288	−0.487147
$37$	−1.65521	−0.272115	−0.136058	−	0.990701i	$-0.543443\pi$
$37$	−1.65521	−0.272115	−0.136058	+	0.990701i	$0.543443\pi$
$38$	−3.94209	−0.639491
$39$	1.19068	0.190661
$40$	1.00000	0.158114
$41$	−8.01358	−1.25151	−0.625755	−	0.780019i	$-0.715209\pi$
$41$	−8.01358	−1.25151	−0.625755	+	0.780019i	$0.715209\pi$
$42$	0.708781	0.109367
$43$	1.78175	0.271715	0.135857	−	0.990728i	$-0.456621\pi$
$43$	1.78175	0.271715	0.135857	+	0.990728i	$0.456621\pi$
$44$	−4.94159	−0.744973
$45$	−2.92288	−0.435718
$46$	−6.03884	−0.890378
$47$	−3.33231	−0.486068	−0.243034	−	0.970018i	$-0.578143\pi$
$47$	−3.33231	−0.486068	−0.243034	+	0.970018i	$0.578143\pi$
$48$	0.277700	0.0400826
$49$	−0.485632	−0.0693761
$50$	1.00000	0.141421
$51$	−0.913075	−0.127856
$52$	4.28763	0.594588
$53$	−8.76375	−1.20379	−0.601896	−	0.798574i	$-0.705588\pi$
$53$	−8.76375	−1.20379	−0.601896	+	0.798574i	$0.705588\pi$
$54$	−1.64479	−0.223827
$55$	−4.94159	−0.666324
$56$	2.55233	0.341069
$57$	−1.09472	−0.144999
$58$	−7.47038	−0.980909
$59$	6.61220	0.860836	0.430418	−	0.902630i	$-0.358366\pi$
$59$	6.61220	0.860836	0.430418	+	0.902630i	$0.358366\pi$
$60$	0.277700	0.0358509
$61$	10.0369	1.28509	0.642547	−	0.766246i	$-0.277878\pi$
$61$	10.0369	1.28509	0.642547	+	0.766246i	$0.277878\pi$
$62$	−4.60144	−0.584384
$63$	−7.46015	−0.939890
$64$	1.00000	0.125000
$65$	4.28763	0.531816
$66$	−1.37228	−0.168916
$67$	−5.12837	−0.626530	−0.313265	−	0.949666i	$-0.601423\pi$
$67$	−5.12837	−0.626530	−0.313265	+	0.949666i	$0.601423\pi$
$68$	−3.28799	−0.398727
$69$	−1.67699	−0.201885
$70$	2.55233	0.305061
$71$	2.50077	0.296787	0.148394	−	0.988928i	$-0.452590\pi$
$71$	2.50077	0.296787	0.148394	+	0.988928i	$0.452590\pi$
$72$	−2.92288	−0.344465
$73$	2.44565	0.286241	0.143121	−	0.989705i	$-0.454286\pi$
$73$	2.44565	0.286241	0.143121	+	0.989705i	$0.454286\pi$
$74$	−1.65521	−0.192415
$75$	0.277700	0.0320661
$76$	−3.94209	−0.452189
$77$	−12.6126	−1.43733
$78$	1.19068	0.134818
$79$	10.1143	1.13795	0.568975	−	0.822355i	$-0.307340\pi$
$79$	10.1143	1.13795	0.568975	+	0.822355i	$0.307340\pi$
$80$	1.00000	0.111803
$81$	8.31189	0.923543
$82$	−8.01358	−0.884952
$83$	1.46001	0.160257	0.0801287	−	0.996785i	$-0.474467\pi$
$83$	1.46001	0.160257	0.0801287	+	0.996785i	$0.474467\pi$
$84$	0.708781	0.0773344
$85$	−3.28799	−0.356633
$86$	1.78175	0.192131
$87$	−2.07453	−0.222412
$88$	−4.94159	−0.526776
$89$	−7.59665	−0.805243	−0.402622	−	0.915367i	$-0.631901\pi$
$89$	−7.59665	−0.805243	−0.402622	+	0.915367i	$0.631901\pi$
$90$	−2.92288	−0.308099
$91$	10.9434	1.14718
$92$	−6.03884	−0.629592
$93$	−1.27782	−0.132504
$94$	−3.33231	−0.343702
$95$	−3.94209	−0.404450
$96$	0.277700	0.0283427
$97$	−0.655528	−0.0665588	−0.0332794	−	0.999446i	$-0.510595\pi$
$97$	−0.655528	−0.0665588	−0.0332794	+	0.999446i	$0.510595\pi$
$98$	−0.485632	−0.0490563
$99$	14.4437	1.45165
$100$	1.00000	0.100000
$101$	−6.14651	−0.611601	−0.305800	−	0.952096i	$-0.598924\pi$
$101$	−6.14651	−0.611601	−0.305800	+	0.952096i	$0.598924\pi$
$102$	−0.913075	−0.0904079
$103$	−2.00406	−0.197465	−0.0987327	−	0.995114i	$-0.531479\pi$
$103$	−2.00406	−0.197465	−0.0987327	+	0.995114i	$0.531479\pi$
$104$	4.28763	0.420437
$105$	0.708781	0.0691700
$106$	−8.76375	−0.851210
$107$	−5.83270	−0.563869	−0.281934	−	0.959434i	$-0.590976\pi$
$107$	−5.83270	−0.563869	−0.281934	+	0.959434i	$0.590976\pi$
$108$	−1.64479	−0.158270
$109$	2.38596	0.228534	0.114267	−	0.993450i	$-0.463548\pi$
$109$	2.38596	0.228534	0.114267	+	0.993450i	$0.463548\pi$
$110$	−4.94159	−0.471162
$111$	−0.459653	−0.0436283
$112$	2.55233	0.241172
$113$	2.53256	0.238243	0.119121	−	0.992880i	$-0.461992\pi$
$113$	2.53256	0.238243	0.119121	+	0.992880i	$0.461992\pi$
$114$	−1.09472	−0.102530
$115$	−6.03884	−0.563125
$116$	−7.47038	−0.693607
$117$	−12.5323	−1.15861
$118$	6.61220	0.608703
$119$	−8.39202	−0.769295
$120$	0.277700	0.0253504
$121$	13.4193	1.21994
$122$	10.0369	0.908699
$123$	−2.22537	−0.200655
$124$	−4.60144	−0.413222
$125$	1.00000	0.0894427
$126$	−7.46015	−0.664603
$127$	4.39330	0.389842	0.194921	−	0.980819i	$-0.437555\pi$
$127$	4.39330	0.389842	0.194921	+	0.980819i	$0.437555\pi$
$128$	1.00000	0.0883883
$129$	0.494793	0.0435641
$130$	4.28763	0.376050
$131$	12.5579	1.09719	0.548596	−	0.836087i	$-0.315162\pi$
$131$	12.5579	1.09719	0.548596	+	0.836087i	$0.315162\pi$
$132$	−1.37228	−0.119442
$133$	−10.0615	−0.872442
$134$	−5.12837	−0.443024
$135$	−1.64479	−0.141561
$136$	−3.28799	−0.281943
$137$	6.12044	0.522905	0.261452	−	0.965216i	$-0.415799\pi$
$137$	6.12044	0.522905	0.261452	+	0.965216i	$0.415799\pi$
$138$	−1.67699	−0.142755
$139$	8.54580	0.724846	0.362423	−	0.932014i	$-0.381950\pi$
$139$	8.54580	0.724846	0.362423	+	0.932014i	$0.381950\pi$
$140$	2.55233	0.215711
$141$	−0.925383	−0.0779313
$142$	2.50077	0.209860
$143$	−21.1877	−1.77181
$144$	−2.92288	−0.243574
$145$	−7.47038	−0.620381
$146$	2.44565	0.202403
$147$	−0.134860	−0.0111231
$148$	−1.65521	−0.136058
$149$	4.25428	0.348524	0.174262	−	0.984699i	$-0.444246\pi$
$149$	4.25428	0.348524	0.174262	+	0.984699i	$0.444246\pi$
$150$	0.277700	0.0226741
$151$	−1.20287	−0.0978879	−0.0489440	−	0.998802i	$-0.515586\pi$
$151$	−1.20287	−0.0978879	−0.0489440	+	0.998802i	$0.515586\pi$
$152$	−3.94209	−0.319746
$153$	9.61041	0.776955
$154$	−12.6126	−1.01635
$155$	−4.60144	−0.369597
$156$	1.19068	0.0953304
$157$	−10.1536	−0.810349	−0.405175	−	0.914239i	$-0.632789\pi$
$157$	−10.1536	−0.810349	−0.405175	+	0.914239i	$0.632789\pi$
$158$	10.1143	0.804652
$159$	−2.43369	−0.193004
$160$	1.00000	0.0790569
$161$	−15.4131	−1.21472
$162$	8.31189	0.653044
$163$	−7.04820	−0.552058	−0.276029	−	0.961149i	$-0.589019\pi$
$163$	−7.04820	−0.552058	−0.276029	+	0.961149i	$0.589019\pi$
$164$	−8.01358	−0.625755
$165$	−1.37228	−0.106832
$166$	1.46001	0.113319
$167$	13.1292	1.01597	0.507984	−	0.861367i	$-0.330391\pi$
$167$	13.1292	1.01597	0.507984	+	0.861367i	$0.330391\pi$
$168$	0.708781	0.0546837
$169$	5.38380	0.414139
$170$	−3.28799	−0.252177
$171$	11.5223	0.881129
$172$	1.78175	0.135857
$173$	9.66095	0.734508	0.367254	−	0.930121i	$-0.380298\pi$
$173$	9.66095	0.734508	0.367254	+	0.930121i	$0.380298\pi$
$174$	−2.07453	−0.157269
$175$	2.55233	0.192938
$176$	−4.94159	−0.372487
$177$	1.83621	0.138018
$178$	−7.59665	−0.569393
$179$	−12.4660	−0.931756	−0.465878	−	0.884849i	$-0.654261\pi$
$179$	−12.4660	−0.931756	−0.465878	+	0.884849i	$0.654261\pi$
$180$	−2.92288	−0.217859
$181$	−5.60337	−0.416495	−0.208248	−	0.978076i	$-0.566776\pi$
$181$	−5.60337	−0.416495	−0.208248	+	0.978076i	$0.566776\pi$
$182$	10.9434	0.811182
$183$	2.78725	0.206039
$184$	−6.03884	−0.445189
$185$	−1.65521	−0.121694
$186$	−1.27782	−0.0936944
$187$	16.2479	1.18816
$188$	−3.33231	−0.243034
$189$	−4.19803	−0.305362
$190$	−3.94209	−0.285989
$191$	13.5010	0.976895	0.488448	−	0.872593i	$-0.337563\pi$
$191$	13.5010	0.976895	0.488448	+	0.872593i	$0.337563\pi$
$192$	0.277700	0.0200413
$193$	0.481989	0.0346943	0.0173472	−	0.999850i	$-0.494478\pi$
$193$	0.481989	0.0346943	0.0173472	+	0.999850i	$0.494478\pi$
$194$	−0.655528	−0.0470642
$195$	1.19068	0.0852661
$196$	−0.485632	−0.0346880
$197$	−9.40948	−0.670397	−0.335199	−	0.942147i	$-0.608803\pi$
$197$	−9.40948	−0.670397	−0.335199	+	0.942147i	$0.608803\pi$
$198$	14.4437	1.02647
$199$	18.8322	1.33498	0.667490	−	0.744619i	$-0.267369\pi$
$199$	18.8322	1.33498	0.667490	+	0.744619i	$0.267369\pi$
$200$	1.00000	0.0707107
$201$	−1.42415	−0.100452
$202$	−6.14651	−0.432467
$203$	−19.0668	−1.33823
$204$	−0.913075	−0.0639281
$205$	−8.01358	−0.559693
$206$	−2.00406	−0.139629
$207$	17.6508	1.22682
$208$	4.28763	0.297294
$209$	19.4802	1.34747
$210$	0.708781	0.0489106
$211$	−0.421081	−0.0289884	−0.0144942	−	0.999895i	$-0.504614\pi$
$211$	−0.421081	−0.0289884	−0.0144942	+	0.999895i	$0.504614\pi$
$212$	−8.76375	−0.601896
$213$	0.694465	0.0475840
$214$	−5.83270	−0.398715
$215$	1.78175	0.121514
$216$	−1.64479	−0.111913
$217$	−11.7444	−0.797260
$218$	2.38596	0.161598
$219$	0.679157	0.0458932
$220$	−4.94159	−0.333162
$221$	−14.0977	−0.948314
$222$	−0.459653	−0.0308499
$223$	7.75783	0.519503	0.259751	−	0.965676i	$-0.416359\pi$
$223$	7.75783	0.519503	0.259751	+	0.965676i	$0.416359\pi$
$224$	2.55233	0.170534
$225$	−2.92288	−0.194859
$226$	2.53256	0.168463
$227$	−1.26402	−0.0838958	−0.0419479	−	0.999120i	$-0.513356\pi$
$227$	−1.26402	−0.0838958	−0.0419479	+	0.999120i	$0.513356\pi$
$228$	−1.09472	−0.0724995
$229$	17.1590	1.13390	0.566950	−	0.823752i	$-0.308123\pi$
$229$	17.1590	1.13390	0.566950	+	0.823752i	$0.308123\pi$
$230$	−6.03884	−0.398189
$231$	−3.50251	−0.230448
$232$	−7.47038	−0.490454
$233$	−11.0937	−0.726769	−0.363385	−	0.931639i	$-0.618379\pi$
$233$	−11.0937	−0.726769	−0.363385	+	0.931639i	$0.618379\pi$
$234$	−12.5323	−0.819259
$235$	−3.33231	−0.217376
$236$	6.61220	0.430418
$237$	2.80875	0.182448
$238$	−8.39202	−0.543974
$239$	−12.0870	−0.781845	−0.390922	−	0.920424i	$-0.627844\pi$
$239$	−12.0870	−0.781845	−0.390922	+	0.920424i	$0.627844\pi$
$240$	0.277700	0.0179255
$241$	−25.6218	−1.65044	−0.825222	−	0.564809i	$-0.808950\pi$
$241$	−25.6218	−1.65044	−0.825222	+	0.564809i	$0.808950\pi$
$242$	13.4193	0.862628
$243$	7.24257	0.464611
$244$	10.0369	0.642547
$245$	−0.485632	−0.0310259
$246$	−2.22537	−0.141885
$247$	−16.9022	−1.07546
$248$	−4.60144	−0.292192
$249$	0.405446	0.0256941
$250$	1.00000	0.0632456
$251$	−18.7449	−1.18317	−0.591583	−	0.806244i	$-0.701497\pi$
$251$	−18.7449	−1.18317	−0.591583	+	0.806244i	$0.701497\pi$
$252$	−7.46015	−0.469945
$253$	29.8415	1.87612
$254$	4.39330	0.275660
$255$	−0.913075	−0.0571790
$256$	1.00000	0.0625000
$257$	−11.5427	−0.720015	−0.360008	−	0.932949i	$-0.617226\pi$
$257$	−11.5427	−0.720015	−0.360008	+	0.932949i	$0.617226\pi$
$258$	0.494793	0.0308045
$259$	−4.22464	−0.262506
$260$	4.28763	0.265908
$261$	21.8350	1.35156
$262$	12.5579	0.775832
$263$	−1.04321	−0.0643271	−0.0321635	−	0.999483i	$-0.510240\pi$
$263$	−1.04321	−0.0643271	−0.0321635	+	0.999483i	$0.510240\pi$
$264$	−1.37228	−0.0844581
$265$	−8.76375	−0.538353
$266$	−10.0615	−0.616910
$267$	−2.10959	−0.129105
$268$	−5.12837	−0.313265
$269$	2.08721	0.127260	0.0636299	−	0.997974i	$-0.479732\pi$
$269$	2.08721	0.127260	0.0636299	+	0.997974i	$0.479732\pi$
$270$	−1.64479	−0.100098
$271$	32.6766	1.98496	0.992480	−	0.122405i	$-0.0390607\pi$
$271$	32.6766	1.98496	0.992480	+	0.122405i	$0.0390607\pi$
$272$	−3.28799	−0.199364
$273$	3.03900	0.183928
$274$	6.12044	0.369749
$275$	−4.94159	−0.297989
$276$	−1.67699	−0.100943
$277$	−22.1396	−1.33024	−0.665120	−	0.746737i	$-0.731620\pi$
$277$	−22.1396	−1.33024	−0.665120	+	0.746737i	$0.731620\pi$
$278$	8.54580	0.512543
$279$	13.4495	0.805199
$280$	2.55233	0.152531
$281$	8.01321	0.478028	0.239014	−	0.971016i	$-0.423176\pi$
$281$	8.01321	0.478028	0.239014	+	0.971016i	$0.423176\pi$
$282$	−0.925383	−0.0551058
$283$	23.1815	1.37799	0.688997	−	0.724764i	$-0.258051\pi$
$283$	23.1815	1.37799	0.688997	+	0.724764i	$0.258051\pi$
$284$	2.50077	0.148394
$285$	−1.09472	−0.0648455
$286$	−21.1877	−1.25286
$287$	−20.4533	−1.20732
$288$	−2.92288	−0.172233
$289$	−6.18912	−0.364066
$290$	−7.47038	−0.438676
$291$	−0.182040	−0.0106714
$292$	2.44565	0.143121
$293$	2.75354	0.160864	0.0804319	−	0.996760i	$-0.474370\pi$
$293$	2.75354	0.160864	0.0804319	+	0.996760i	$0.474370\pi$
$294$	−0.134860	−0.00786521
$295$	6.61220	0.384977
$296$	−1.65521	−0.0962073
$297$	8.12786	0.471626
$298$	4.25428	0.246444
$299$	−25.8923	−1.49739
$300$	0.277700	0.0160330
$301$	4.54761	0.262120
$302$	−1.20287	−0.0692172
$303$	−1.70689	−0.0980581
$304$	−3.94209	−0.226094
$305$	10.0369	0.574712
$306$	9.61041	0.549390
$307$	−10.2302	−0.583866	−0.291933	−	0.956439i	$-0.594298\pi$
$307$	−10.2302	−0.583866	−0.291933	+	0.956439i	$0.594298\pi$
$308$	−12.6126	−0.718667
$309$	−0.556527	−0.0316597
$310$	−4.60144	−0.261344
$311$	−2.39920	−0.136046	−0.0680231	−	0.997684i	$-0.521669\pi$
$311$	−2.39920	−0.136046	−0.0680231	+	0.997684i	$0.521669\pi$
$312$	1.19068	0.0674088
$313$	−15.1268	−0.855015	−0.427508	−	0.904012i	$-0.640608\pi$
$313$	−15.1268	−0.855015	−0.427508	+	0.904012i	$0.640608\pi$
$314$	−10.1536	−0.573003
$315$	−7.46015	−0.420332
$316$	10.1143	0.568975
$317$	−20.8116	−1.16890	−0.584448	−	0.811431i	$-0.698689\pi$
$317$	−20.8116	−1.16890	−0.584448	+	0.811431i	$0.698689\pi$
$318$	−2.43369	−0.136475
$319$	36.9156	2.06688
$320$	1.00000	0.0559017
$321$	−1.61974	−0.0904052
$322$	−15.4131	−0.858938
$323$	12.9615	0.721200
$324$	8.31189	0.461772
$325$	4.28763	0.237835
$326$	−7.04820	−0.390364
$327$	0.662583	0.0366409
$328$	−8.01358	−0.442476
$329$	−8.50514	−0.468904
$330$	−1.37228	−0.0755416
$331$	−8.14597	−0.447743	−0.223872	−	0.974619i	$-0.571870\pi$
$331$	−8.14597	−0.447743	−0.223872	+	0.974619i	$0.571870\pi$
$332$	1.46001	0.0801287
$333$	4.83799	0.265120
$334$	13.1292	0.718398
$335$	−5.12837	−0.280193
$336$	0.708781	0.0386672
$337$	−9.14403	−0.498107	−0.249053	−	0.968490i	$-0.580119\pi$
$337$	−9.14403	−0.498107	−0.249053	+	0.968490i	$0.580119\pi$
$338$	5.38380	0.292840
$339$	0.703291	0.0381975
$340$	−3.28799	−0.178316
$341$	22.7385	1.23136
$342$	11.5223	0.623053
$343$	−19.1058	−1.03161
$344$	1.78175	0.0960656
$345$	−1.67699	−0.0902859
$346$	9.66095	0.519376
$347$	−5.88331	−0.315833	−0.157916	−	0.987452i	$-0.550478\pi$
$347$	−5.88331	−0.315833	−0.157916	+	0.987452i	$0.550478\pi$
$348$	−2.07453	−0.111206
$349$	3.32250	0.177850	0.0889248	−	0.996038i	$-0.471657\pi$
$349$	3.32250	0.177850	0.0889248	+	0.996038i	$0.471657\pi$
$350$	2.55233	0.136428
$351$	−7.05224	−0.376421
$352$	−4.94159	−0.263388
$353$	22.7150	1.20900	0.604499	−	0.796606i	$-0.293373\pi$
$353$	22.7150	1.20900	0.604499	+	0.796606i	$0.293373\pi$
$354$	1.83621	0.0975935
$355$	2.50077	0.132727
$356$	−7.59665	−0.402622
$357$	−2.33047	−0.123341
$358$	−12.4660	−0.658851
$359$	15.2694	0.805888	0.402944	−	0.915225i	$-0.367987\pi$
$359$	15.2694	0.805888	0.402944	+	0.915225i	$0.367987\pi$
$360$	−2.92288	−0.154049
$361$	−3.45994	−0.182102
$362$	−5.60337	−0.294507
$363$	3.72656	0.195593
$364$	10.9434	0.573592
$365$	2.44565	0.128011
$366$	2.78725	0.145692
$367$	26.3432	1.37511	0.687553	−	0.726134i	$-0.258685\pi$
$367$	26.3432	1.37511	0.687553	+	0.726134i	$0.258685\pi$
$368$	−6.03884	−0.314796
$369$	23.4227	1.21934
$370$	−1.65521	−0.0860504
$371$	−22.3679	−1.16129
$372$	−1.27782	−0.0662519
$373$	25.4950	1.32008	0.660040	−	0.751230i	$-0.270539\pi$
$373$	25.4950	1.32008	0.660040	+	0.751230i	$0.270539\pi$
$374$	16.2479	0.840159
$375$	0.277700	0.0143404
$376$	−3.33231	−0.171851
$377$	−32.0302	−1.64964
$378$	−4.19803	−0.215923
$379$	−19.8048	−1.01730	−0.508652	−	0.860972i	$-0.669856\pi$
$379$	−19.8048	−1.01730	−0.508652	+	0.860972i	$0.669856\pi$
$380$	−3.94209	−0.202225
$381$	1.22002	0.0625035
$382$	13.5010	0.690769
$383$	−12.7968	−0.653884	−0.326942	−	0.945044i	$-0.606018\pi$
$383$	−12.7968	−0.653884	−0.326942	+	0.945044i	$0.606018\pi$
$384$	0.277700	0.0141713
$385$	−12.6126	−0.642795
$386$	0.481989	0.0245326
$387$	−5.20785	−0.264730
$388$	−0.655528	−0.0332794
$389$	1.10510	0.0560307	0.0280154	−	0.999607i	$-0.491081\pi$
$389$	1.10510	0.0560307	0.0280154	+	0.999607i	$0.491081\pi$
$390$	1.19068	0.0602923
$391$	19.8556	1.00414
$392$	−0.485632	−0.0245281
$393$	3.48734	0.175913
$394$	−9.40948	−0.474043
$395$	10.1143	0.508906
$396$	14.4437	0.725823
$397$	−10.7718	−0.540619	−0.270310	−	0.962773i	$-0.587126\pi$
$397$	−10.7718	−0.540619	−0.270310	+	0.962773i	$0.587126\pi$
$398$	18.8322	0.943973
$399$	−2.79408	−0.139879
$400$	1.00000	0.0500000
$401$	−4.30494	−0.214978	−0.107489	−	0.994206i	$-0.534281\pi$
$401$	−4.30494	−0.214978	−0.107489	+	0.994206i	$0.534281\pi$
$402$	−1.42415	−0.0710301
$403$	−19.7293	−0.982786
$404$	−6.14651	−0.305800
$405$	8.31189	0.413021
$406$	−19.0668	−0.946271
$407$	8.17939	0.405437
$408$	−0.913075	−0.0452040
$409$	28.0375	1.38636	0.693182	−	0.720763i	$-0.256208\pi$
$409$	28.0375	1.38636	0.693182	+	0.720763i	$0.256208\pi$
$410$	−8.01358	−0.395762
$411$	1.69965	0.0838374
$412$	−2.00406	−0.0987327
$413$	16.8765	0.830438
$414$	17.6508	0.867490
$415$	1.46001	0.0716693
$416$	4.28763	0.210219
$417$	2.37317	0.116215
$418$	19.4802	0.952808
$419$	9.83699	0.480569	0.240284	−	0.970703i	$-0.422759\pi$
$419$	9.83699	0.480569	0.240284	+	0.970703i	$0.422759\pi$
$420$	0.708781	0.0345850
$421$	−11.3117	−0.551296	−0.275648	−	0.961259i	$-0.588892\pi$
$421$	−11.3117	−0.551296	−0.275648	+	0.961259i	$0.588892\pi$
$422$	−0.421081	−0.0204979
$423$	9.73995	0.473573
$424$	−8.76375	−0.425605
$425$	−3.28799	−0.159491
$426$	0.694465	0.0336469
$427$	25.6175	1.23972
$428$	−5.83270	−0.281934
$429$	−5.88384	−0.284074
$430$	1.78175	0.0859237
$431$	−20.3784	−0.981594	−0.490797	−	0.871274i	$-0.663294\pi$
$431$	−20.3784	−0.981594	−0.490797	+	0.871274i	$0.663294\pi$
$432$	−1.64479	−0.0791348
$433$	−16.2983	−0.783246	−0.391623	−	0.920126i	$-0.628086\pi$
$433$	−16.2983	−0.783246	−0.391623	+	0.920126i	$0.628086\pi$
$434$	−11.7444	−0.563748
$435$	−2.07453	−0.0994659
$436$	2.38596	0.114267
$437$	23.8056	1.13878
$438$	0.679157	0.0324514
$439$	16.3355	0.779650	0.389825	−	0.920889i	$-0.372535\pi$
$439$	16.3355	0.779650	0.389825	+	0.920889i	$0.372535\pi$
$440$	−4.94159	−0.235581
$441$	1.41945	0.0675927
$442$	−14.0977	−0.670559
$443$	−30.3955	−1.44413	−0.722066	−	0.691824i	$-0.756807\pi$
$443$	−30.3955	−1.44413	−0.722066	+	0.691824i	$0.756807\pi$
$444$	−0.459653	−0.0218142
$445$	−7.59665	−0.360116
$446$	7.75783	0.367344
$447$	1.18141	0.0558789
$448$	2.55233	0.120586
$449$	11.9134	0.562230	0.281115	−	0.959674i	$-0.409296\pi$
$449$	11.9134	0.562230	0.281115	+	0.959674i	$0.409296\pi$
$450$	−2.92288	−0.137786
$451$	39.5998	1.86468
$452$	2.53256	0.119121
$453$	−0.334036	−0.0156944
$454$	−1.26402	−0.0593233
$455$	10.9434	0.513036
$456$	−1.09472	−0.0512649
$457$	−35.3128	−1.65186	−0.825931	−	0.563771i	$-0.809350\pi$
$457$	−35.3128	−1.65186	−0.825931	+	0.563771i	$0.809350\pi$
$458$	17.1590	0.801788
$459$	5.40804	0.252426
$460$	−6.03884	−0.281562
$461$	37.5505	1.74890	0.874450	−	0.485116i	$-0.161223\pi$
$461$	37.5505	1.74890	0.874450	+	0.485116i	$0.161223\pi$
$462$	−3.50251	−0.162951
$463$	29.2633	1.35998	0.679992	−	0.733220i	$-0.261983\pi$
$463$	29.2633	1.35998	0.679992	+	0.733220i	$0.261983\pi$
$464$	−7.47038	−0.346804
$465$	−1.27782	−0.0592575
$466$	−11.0937	−0.513904
$467$	−2.05376	−0.0950366	−0.0475183	−	0.998870i	$-0.515131\pi$
$467$	−2.05376	−0.0950366	−0.0475183	+	0.998870i	$0.515131\pi$
$468$	−12.5323	−0.579303
$469$	−13.0893	−0.604406
$470$	−3.33231	−0.153708
$471$	−2.81967	−0.129924
$472$	6.61220	0.304351
$473$	−8.80469	−0.404840
$474$	2.80875	0.129010
$475$	−3.94209	−0.180875
$476$	−8.39202	−0.384648
$477$	25.6154	1.17285
$478$	−12.0870	−0.552848
$479$	−22.3022	−1.01901	−0.509506	−	0.860467i	$-0.670172\pi$
$479$	−22.3022	−1.01901	−0.509506	+	0.860467i	$0.670172\pi$
$480$	0.277700	0.0126752
$481$	−7.09695	−0.323593
$482$	−25.6218	−1.16704
$483$	−4.28022	−0.194757
$484$	13.4193	0.609970
$485$	−0.655528	−0.0297660
$486$	7.24257	0.328530
$487$	−22.7781	−1.03218	−0.516088	−	0.856536i	$-0.672612\pi$
$487$	−22.7781	−1.03218	−0.516088	+	0.856536i	$0.672612\pi$
$488$	10.0369	0.454349
$489$	−1.95729	−0.0885116
$490$	−0.485632	−0.0219386
$491$	−18.0674	−0.815372	−0.407686	−	0.913122i	$-0.633664\pi$
$491$	−18.0674	−0.815372	−0.407686	+	0.913122i	$0.633664\pi$
$492$	−2.22537	−0.100328
$493$	24.5625	1.10624
$494$	−16.9022	−0.760467
$495$	14.4437	0.649196
$496$	−4.60144	−0.206611
$497$	6.38279	0.286307
$498$	0.405446	0.0181685
$499$	−37.4965	−1.67857	−0.839286	−	0.543690i	$-0.817027\pi$
$499$	−37.4965	−1.67857	−0.839286	+	0.543690i	$0.817027\pi$
$500$	1.00000	0.0447214
$501$	3.64598	0.162890
$502$	−18.7449	−0.836624
$503$	19.0805	0.850757	0.425378	−	0.905016i	$-0.360141\pi$
$503$	19.0805	0.850757	0.425378	+	0.905016i	$0.360141\pi$
$504$	−7.46015	−0.332301
$505$	−6.14651	−0.273516
$506$	29.8415	1.32662
$507$	1.49508	0.0663990
$508$	4.39330	0.194921
$509$	−32.0076	−1.41871	−0.709356	−	0.704851i	$-0.751014\pi$
$509$	−32.0076	−1.41871	−0.709356	+	0.704851i	$0.751014\pi$
$510$	−0.913075	−0.0404317
$511$	6.24209	0.276134
$512$	1.00000	0.0441942
$513$	6.48389	0.286271
$514$	−11.5427	−0.509128
$515$	−2.00406	−0.0883092
$516$	0.494793	0.0217820
$517$	16.4669	0.724215
$518$	−4.22464	−0.185620
$519$	2.68285	0.117764
$520$	4.28763	0.188025
$521$	−18.1180	−0.793765	−0.396882	−	0.917870i	$-0.629908\pi$
$521$	−18.1180	−0.793765	−0.396882	+	0.917870i	$0.629908\pi$
$522$	21.8350	0.955694
$523$	−10.0446	−0.439219	−0.219610	−	0.975588i	$-0.570478\pi$
$523$	−10.0446	−0.439219	−0.219610	+	0.975588i	$0.570478\pi$
$524$	12.5579	0.548596
$525$	0.708781	0.0309338
$526$	−1.04321	−0.0454861
$527$	15.1295	0.659051
$528$	−1.37228	−0.0597209
$529$	13.4676	0.585546
$530$	−8.76375	−0.380673
$531$	−19.3267	−0.838707
$532$	−10.0615	−0.436221
$533$	−34.3593	−1.48827
$534$	−2.10959	−0.0912909
$535$	−5.83270	−0.252170
$536$	−5.12837	−0.221512
$537$	−3.46182	−0.149389
$538$	2.08721	0.0899862
$539$	2.39980	0.103367
$540$	−1.64479	−0.0707803
$541$	13.4911	0.580028	0.290014	−	0.957022i	$-0.406340\pi$
$541$	13.4911	0.580028	0.290014	+	0.957022i	$0.406340\pi$
$542$	32.6766	1.40358
$543$	−1.55606	−0.0667768
$544$	−3.28799	−0.140971
$545$	2.38596	0.102203
$546$	3.03900	0.130057
$547$	−12.1566	−0.519777	−0.259889	−	0.965639i	$-0.583686\pi$
$547$	−12.1566	−0.519777	−0.259889	+	0.965639i	$0.583686\pi$
$548$	6.12044	0.261452
$549$	−29.3367	−1.25206
$550$	−4.94159	−0.210710
$551$	29.4489	1.25456
$552$	−1.67699	−0.0713773
$553$	25.8150	1.09777
$554$	−22.1396	−0.940621
$555$	−0.459653	−0.0195112
$556$	8.54580	0.362423
$557$	−15.8398	−0.671152	−0.335576	−	0.942013i	$-0.608931\pi$
$557$	−15.8398	−0.671152	−0.335576	+	0.942013i	$0.608931\pi$
$558$	13.4495	0.569362
$559$	7.63950	0.323116
$560$	2.55233	0.107855
$561$	4.51205	0.190499
$562$	8.01321	0.338017
$563$	10.3672	0.436927	0.218464	−	0.975845i	$-0.429895\pi$
$563$	10.3672	0.436927	0.218464	+	0.975845i	$0.429895\pi$
$564$	−0.925383	−0.0389657
$565$	2.53256	0.106545
$566$	23.1815	0.974389
$567$	21.2147	0.890932
$568$	2.50077	0.104930
$569$	−30.1146	−1.26247	−0.631235	−	0.775592i	$-0.717452\pi$
$569$	−30.1146	−1.26247	−0.631235	+	0.775592i	$0.717452\pi$
$570$	−1.09472	−0.0458527
$571$	−30.8585	−1.29139	−0.645695	−	0.763596i	$-0.723432\pi$
$571$	−30.8585	−1.29139	−0.645695	+	0.763596i	$0.723432\pi$
$572$	−21.1877	−0.885904
$573$	3.74922	0.156626
$574$	−20.4533	−0.853703
$575$	−6.03884	−0.251837
$576$	−2.92288	−0.121787
$577$	−25.0135	−1.04132	−0.520662	−	0.853763i	$-0.674315\pi$
$577$	−25.0135	−1.04132	−0.520662	+	0.853763i	$0.674315\pi$
$578$	−6.18912	−0.257434
$579$	0.133848	0.00556255
$580$	−7.47038	−0.310191
$581$	3.72643	0.154598
$582$	−0.182040	−0.00754581
$583$	43.3069	1.79359
$584$	2.44565	0.101202
$585$	−12.5323	−0.518145
$586$	2.75354	0.113748
$587$	11.1035	0.458291	0.229145	−	0.973392i	$-0.426407\pi$
$587$	11.1035	0.458291	0.229145	+	0.973392i	$0.426407\pi$
$588$	−0.134860	−0.00556154
$589$	18.1393	0.747416
$590$	6.61220	0.272220
$591$	−2.61301	−0.107485
$592$	−1.65521	−0.0680288
$593$	−12.1577	−0.499256	−0.249628	−	0.968342i	$-0.580308\pi$
$593$	−12.1577	−0.499256	−0.249628	+	0.968342i	$0.580308\pi$
$594$	8.12786	0.333490
$595$	−8.39202	−0.344039
$596$	4.25428	0.174262
$597$	5.22971	0.214038
$598$	−25.8923	−1.05882
$599$	−44.2078	−1.80628	−0.903141	−	0.429345i	$-0.858744\pi$
$599$	−44.2078	−1.80628	−0.903141	+	0.429345i	$0.858744\pi$
$600$	0.277700	0.0113371
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	4.54761	0.185347
$603$	14.9896	0.610425
$604$	−1.20287	−0.0489440
$605$	13.4193	0.545574
$606$	−1.70689	−0.0693376
$607$	−28.9368	−1.17451	−0.587255	−	0.809402i	$-0.699791\pi$
$607$	−28.9368	−1.17451	−0.587255	+	0.809402i	$0.699791\pi$
$608$	−3.94209	−0.159873
$609$	−5.29487	−0.214559
$610$	10.0369	0.406382
$611$	−14.2877	−0.578020
$612$	9.61041	0.388478
$613$	3.16304	0.127754	0.0638770	−	0.997958i	$-0.479653\pi$
$613$	3.16304	0.127754	0.0638770	+	0.997958i	$0.479653\pi$
$614$	−10.2302	−0.412856
$615$	−2.22537	−0.0897357
$616$	−12.6126	−0.508174
$617$	18.2934	0.736465	0.368232	−	0.929734i	$-0.379963\pi$
$617$	18.2934	0.736465	0.368232	+	0.929734i	$0.379963\pi$
$618$	−0.556527	−0.0223868
$619$	0.884234	0.0355404	0.0177702	−	0.999842i	$-0.494343\pi$
$619$	0.884234	0.0355404	0.0177702	+	0.999842i	$0.494343\pi$
$620$	−4.60144	−0.184798
$621$	9.93259	0.398581
$622$	−2.39920	−0.0961992
$623$	−19.3891	−0.776809
$624$	1.19068	0.0476652
$625$	1.00000	0.0400000
$626$	−15.1268	−0.604587
$627$	5.40965	0.216041
$628$	−10.1536	−0.405175
$629$	5.44232	0.217000
$630$	−7.46015	−0.297219
$631$	−12.5644	−0.500183	−0.250091	−	0.968222i	$-0.580461\pi$
$631$	−12.5644	−0.500183	−0.250091	+	0.968222i	$0.580461\pi$
$632$	10.1143	0.402326
$633$	−0.116934	−0.00464772
$634$	−20.8116	−0.826534
$635$	4.39330	0.174343
$636$	−2.43369	−0.0965022
$637$	−2.08221	−0.0825003
$638$	36.9156	1.46150
$639$	−7.30947	−0.289158
$640$	1.00000	0.0395285
$641$	4.36246	0.172307	0.0861535	−	0.996282i	$-0.472542\pi$
$641$	4.36246	0.172307	0.0861535	+	0.996282i	$0.472542\pi$
$642$	−1.61974	−0.0639262
$643$	29.1984	1.15147	0.575736	−	0.817636i	$-0.304716\pi$
$643$	29.1984	1.15147	0.575736	+	0.817636i	$0.304716\pi$
$644$	−15.4131	−0.607361
$645$	0.494793	0.0194824
$646$	12.9615	0.509965
$647$	−32.3343	−1.27119	−0.635595	−	0.772022i	$-0.719245\pi$
$647$	−32.3343	−1.27119	−0.635595	+	0.772022i	$0.719245\pi$
$648$	8.31189	0.326522
$649$	−32.6748	−1.28260
$650$	4.28763	0.168175
$651$	−3.26142	−0.127825
$652$	−7.04820	−0.276029
$653$	24.9559	0.976598	0.488299	−	0.872676i	$-0.337617\pi$
$653$	24.9559	0.976598	0.488299	+	0.872676i	$0.337617\pi$
$654$	0.662583	0.0259090
$655$	12.5579	0.490680
$656$	−8.01358	−0.312878
$657$	−7.14834	−0.278883
$658$	−8.50514	−0.331565
$659$	−44.1975	−1.72169	−0.860844	−	0.508868i	$-0.830064\pi$
$659$	−44.1975	−1.72169	−0.860844	+	0.508868i	$0.830064\pi$
$660$	−1.37228	−0.0534160
$661$	−25.1576	−0.978516	−0.489258	−	0.872139i	$-0.662732\pi$
$661$	−25.1576	−0.978516	−0.489258	+	0.872139i	$0.662732\pi$
$662$	−8.14597	−0.316602
$663$	−3.91493	−0.152043
$664$	1.46001	0.0566595
$665$	−10.0615	−0.390168
$666$	4.83799	0.187468
$667$	45.1124	1.74676
$668$	13.1292	0.507984
$669$	2.15435	0.0832920
$670$	−5.12837	−0.198126
$671$	−49.5983	−1.91472
$672$	0.708781	0.0273418
$673$	−13.0385	−0.502598	−0.251299	−	0.967910i	$-0.580858\pi$
$673$	−13.0385	−0.502598	−0.251299	+	0.967910i	$0.580858\pi$
$674$	−9.14403	−0.352215
$675$	−1.64479	−0.0633078
$676$	5.38380	0.207069
$677$	14.6706	0.563835	0.281918	−	0.959439i	$-0.409030\pi$
$677$	14.6706	0.563835	0.281918	+	0.959439i	$0.409030\pi$
$678$	0.703291	0.0270097
$679$	−1.67312	−0.0642085
$680$	−3.28799	−0.126089
$681$	−0.351018	−0.0134510
$682$	22.7385	0.870701
$683$	23.0514	0.882039	0.441019	−	0.897498i	$-0.354617\pi$
$683$	23.0514	0.882039	0.441019	+	0.897498i	$0.354617\pi$
$684$	11.5223	0.440565
$685$	6.12044	0.233850
$686$	−19.1058	−0.729462
$687$	4.76506	0.181798
$688$	1.78175	0.0679286
$689$	−37.5757	−1.43152
$690$	−1.67699	−0.0638418
$691$	−12.3973	−0.471614	−0.235807	−	0.971800i	$-0.575773\pi$
$691$	−12.3973	−0.471614	−0.235807	+	0.971800i	$0.575773\pi$
$692$	9.66095	0.367254
$693$	36.8650	1.40039
$694$	−5.88331	−0.223328
$695$	8.54580	0.324161
$696$	−2.07453	−0.0786347
$697$	26.3486	0.998023
$698$	3.32250	0.125759
$699$	−3.08071	−0.116523
$700$	2.55233	0.0964689
$701$	44.9218	1.69667	0.848337	−	0.529456i	$-0.177604\pi$
$701$	44.9218	1.69667	0.848337	+	0.529456i	$0.177604\pi$
$702$	−7.05224	−0.266170
$703$	6.52499	0.246095
$704$	−4.94159	−0.186243
$705$	−0.925383	−0.0348520
$706$	22.7150	0.854891
$707$	−15.6879	−0.590004
$708$	1.83621	0.0690090
$709$	−10.9410	−0.410899	−0.205449	−	0.978668i	$-0.565866\pi$
$709$	−10.9410	−0.410899	−0.205449	+	0.978668i	$0.565866\pi$
$710$	2.50077	0.0938523
$711$	−29.5630	−1.10870
$712$	−7.59665	−0.284696
$713$	27.7874	1.04064
$714$	−2.33047	−0.0872155
$715$	−21.1877	−0.792377
$716$	−12.4660	−0.465878
$717$	−3.35657	−0.125353
$718$	15.2694	0.569849
$719$	15.7049	0.585693	0.292847	−	0.956159i	$-0.405397\pi$
$719$	15.7049	0.585693	0.292847	+	0.956159i	$0.405397\pi$
$720$	−2.92288	−0.108929
$721$	−5.11500	−0.190493
$722$	−3.45994	−0.128766
$723$	−7.11517	−0.264616
$724$	−5.60337	−0.208248
$725$	−7.47038	−0.277443
$726$	3.72656	0.138305
$727$	−11.8864	−0.440841	−0.220421	−	0.975405i	$-0.570743\pi$
$727$	−11.8864	−0.440841	−0.220421	+	0.975405i	$0.570743\pi$
$728$	10.9434	0.405591
$729$	−22.9244	−0.849052
$730$	2.44565	0.0905175
$731$	−5.85838	−0.216680
$732$	2.78725	0.103020
$733$	45.6422	1.68583	0.842916	−	0.538045i	$-0.180837\pi$
$733$	45.6422	1.68583	0.842916	+	0.538045i	$0.180837\pi$
$734$	26.3432	0.972347
$735$	−0.134860	−0.00497439
$736$	−6.03884	−0.222595
$737$	25.3423	0.933497
$738$	23.4227	0.862203
$739$	−11.0877	−0.407869	−0.203934	−	0.978985i	$-0.565373\pi$
$739$	−11.0877	−0.407869	−0.203934	+	0.978985i	$0.565373\pi$
$740$	−1.65521	−0.0608468
$741$	−4.69375	−0.172429
$742$	−22.3679	−0.821153
$743$	11.3725	0.417217	0.208609	−	0.977999i	$-0.433107\pi$
$743$	11.3725	0.417217	0.208609	+	0.977999i	$0.433107\pi$
$744$	−1.27782	−0.0468472
$745$	4.25428	0.155865
$746$	25.4950	0.933438
$747$	−4.26745	−0.156138
$748$	16.2479	0.594082
$749$	−14.8870	−0.543958
$750$	0.277700	0.0101402
$751$	−3.67148	−0.133974	−0.0669870	−	0.997754i	$-0.521339\pi$
$751$	−3.67148	−0.133974	−0.0669870	+	0.997754i	$0.521339\pi$
$752$	−3.33231	−0.121517
$753$	−5.20545	−0.189697
$754$	−32.0302	−1.16647
$755$	−1.20287	−0.0437768
$756$	−4.19803	−0.152681
$757$	−11.4260	−0.415286	−0.207643	−	0.978205i	$-0.566579\pi$
$757$	−11.4260	−0.415286	−0.207643	+	0.978205i	$0.566579\pi$
$758$	−19.8048	−0.719343
$759$	8.28699	0.300799
$760$	−3.94209	−0.142995
$761$	22.6045	0.819414	0.409707	−	0.912217i	$-0.365631\pi$
$761$	22.6045	0.819414	0.409707	+	0.912217i	$0.365631\pi$
$762$	1.22002	0.0441967
$763$	6.08976	0.220464
$764$	13.5010	0.488448
$765$	9.61041	0.347465
$766$	−12.7968	−0.462366
$767$	28.3507	1.02368
$768$	0.277700	0.0100206
$769$	0.658801	0.0237570	0.0118785	−	0.999929i	$-0.496219\pi$
$769$	0.658801	0.0237570	0.0118785	+	0.999929i	$0.496219\pi$
$770$	−12.6126	−0.454525
$771$	−3.20542	−0.115440
$772$	0.481989	0.0173472
$773$	−35.8459	−1.28929	−0.644644	−	0.764483i	$-0.722994\pi$
$773$	−35.8459	−1.28929	−0.644644	+	0.764483i	$0.722994\pi$
$774$	−5.20785	−0.187192
$775$	−4.60144	−0.165289
$776$	−0.655528	−0.0235321
$777$	−1.17318	−0.0420877
$778$	1.10510	0.0396197
$779$	31.5902	1.13184
$780$	1.19068	0.0426331
$781$	−12.3578	−0.442197
$782$	19.8556	0.710036
$783$	12.2872	0.439108
$784$	−0.485632	−0.0173440
$785$	−10.1536	−0.362399
$786$	3.48734	0.124389
$787$	14.7576	0.526053	0.263026	−	0.964789i	$-0.415279\pi$
$787$	14.7576	0.526053	0.263026	+	0.964789i	$0.415279\pi$
$788$	−9.40948	−0.335199
$789$	−0.289700	−0.0103136
$790$	10.1143	0.359851
$791$	6.46391	0.229830
$792$	14.4437	0.513234
$793$	43.0346	1.52820
$794$	−10.7718	−0.382275
$795$	−2.43369	−0.0863142
$796$	18.8322	0.667490
$797$	−3.04398	−0.107823	−0.0539116	−	0.998546i	$-0.517169\pi$
$797$	−3.04398	−0.107823	−0.0539116	+	0.998546i	$0.517169\pi$
$798$	−2.79408	−0.0989093
$799$	10.9566	0.387617
$800$	1.00000	0.0353553
$801$	22.2041	0.784544
$802$	−4.30494	−0.152013
$803$	−12.0854	−0.426484
$804$	−1.42415	−0.0502259
$805$	−15.4131	−0.543240
$806$	−19.7293	−0.694935
$807$	0.579620	0.0204036
$808$	−6.14651	−0.216234
$809$	0.954037	0.0335422	0.0167711	−	0.999859i	$-0.494661\pi$
$809$	0.954037	0.0335422	0.0167711	+	0.999859i	$0.494661\pi$
$810$	8.31189	0.292050
$811$	−3.29009	−0.115531	−0.0577654	−	0.998330i	$-0.518398\pi$
$811$	−3.29009	−0.115531	−0.0577654	+	0.998330i	$0.518398\pi$
$812$	−19.0668	−0.669115
$813$	9.07429	0.318249
$814$	8.17939	0.286687
$815$	−7.04820	−0.246888
$816$	−0.913075	−0.0319640
$817$	−7.02382	−0.245732
$818$	28.0375	0.980307
$819$	−31.9864	−1.11769
$820$	−8.01358	−0.279846
$821$	23.2855	0.812670	0.406335	−	0.913724i	$-0.366807\pi$
$821$	23.2855	0.812670	0.406335	+	0.913724i	$0.366807\pi$
$822$	1.69965	0.0592820
$823$	−40.0869	−1.39734	−0.698670	−	0.715444i	$-0.746225\pi$
$823$	−40.0869	−1.39734	−0.698670	+	0.715444i	$0.746225\pi$
$824$	−2.00406	−0.0698146
$825$	−1.37228	−0.0477767
$826$	16.8765	0.587208
$827$	−17.1194	−0.595301	−0.297651	−	0.954675i	$-0.596203\pi$
$827$	−17.1194	−0.595301	−0.297651	+	0.954675i	$0.596203\pi$
$828$	17.6508	0.613408
$829$	6.44906	0.223985	0.111993	−	0.993709i	$-0.464277\pi$
$829$	6.44906	0.223985	0.111993	+	0.993709i	$0.464277\pi$
$830$	1.46001	0.0506778
$831$	−6.14817	−0.213278
$832$	4.28763	0.148647
$833$	1.59675	0.0553243
$834$	2.37317	0.0821762
$835$	13.1292	0.454355
$836$	19.4802	0.673737
$837$	7.56839	0.261602
$838$	9.83699	0.339813
$839$	−8.16787	−0.281986	−0.140993	−	0.990011i	$-0.545030\pi$
$839$	−8.16787	−0.281986	−0.140993	+	0.990011i	$0.545030\pi$
$840$	0.708781	0.0244553
$841$	26.8066	0.924364
$842$	−11.3117	−0.389825
$843$	2.22527	0.0766424
$844$	−0.421081	−0.0144942
$845$	5.38380	0.185209
$846$	9.73995	0.334867
$847$	34.2505	1.17686
$848$	−8.76375	−0.300948
$849$	6.43749	0.220934
$850$	−3.28799	−0.112777
$851$	9.99556	0.342643
$852$	0.694465	0.0237920
$853$	46.9574	1.60779	0.803895	−	0.594772i	$-0.202757\pi$
$853$	46.9574	1.60779	0.803895	+	0.594772i	$0.202757\pi$
$854$	25.6175	0.876611
$855$	11.5223	0.394053
$856$	−5.83270	−0.199358
$857$	33.5470	1.14594	0.572971	−	0.819576i	$-0.305791\pi$
$857$	33.5470	1.14594	0.572971	+	0.819576i	$0.305791\pi$
$858$	−5.88384	−0.200871
$859$	37.2655	1.27148	0.635741	−	0.771902i	$-0.280695\pi$
$859$	37.2655	1.27148	0.635741	+	0.771902i	$0.280695\pi$
$860$	1.78175	0.0607572
$861$	−5.67987	−0.193570
$862$	−20.3784	−0.694092
$863$	24.6009	0.837425	0.418712	−	0.908119i	$-0.362482\pi$
$863$	24.6009	0.837425	0.418712	+	0.908119i	$0.362482\pi$
$864$	−1.64479	−0.0559567
$865$	9.66095	0.328482
$866$	−16.2983	−0.553839
$867$	−1.71872	−0.0583708
$868$	−11.7444	−0.398630
$869$	−49.9808	−1.69548
$870$	−2.07453	−0.0703330
$871$	−21.9886	−0.745054
$872$	2.38596	0.0807989
$873$	1.91603	0.0648478
$874$	23.8056	0.805238
$875$	2.55233	0.0862844
$876$	0.679157	0.0229466
$877$	−15.4347	−0.521194	−0.260597	−	0.965448i	$-0.583919\pi$
$877$	−15.4347	−0.521194	−0.260597	+	0.965448i	$0.583919\pi$
$878$	16.3355	0.551296
$879$	0.764660	0.0257913
$880$	−4.94159	−0.166581
$881$	21.1992	0.714218	0.357109	−	0.934063i	$-0.383762\pi$
$881$	21.1992	0.714218	0.357109	+	0.934063i	$0.383762\pi$
$882$	1.41945	0.0477952
$883$	−0.952077	−0.0320400	−0.0160200	−	0.999872i	$-0.505100\pi$
$883$	−0.952077	−0.0320400	−0.0160200	+	0.999872i	$0.505100\pi$
$884$	−14.0977	−0.474157
$885$	1.83621	0.0617235
$886$	−30.3955	−1.02116
$887$	38.0504	1.27761	0.638804	−	0.769370i	$-0.279430\pi$
$887$	38.0504	1.27761	0.638804	+	0.769370i	$0.279430\pi$
$888$	−0.459653	−0.0154249
$889$	11.2131	0.376076
$890$	−7.59665	−0.254640
$891$	−41.0740	−1.37603
$892$	7.75783	0.259751
$893$	13.1363	0.439588
$894$	1.18141	0.0395124
$895$	−12.4660	−0.416694
$896$	2.55233	0.0852672
$897$	−7.19030	−0.240077
$898$	11.9134	0.397556
$899$	34.3745	1.14645
$900$	−2.92288	−0.0974294
$901$	28.8151	0.959970
$902$	39.5998	1.31853
$903$	1.26287	0.0420258
$904$	2.53256	0.0842316
$905$	−5.60337	−0.186262
$906$	−0.334036	−0.0110976
$907$	−1.49117	−0.0495136	−0.0247568	−	0.999694i	$-0.507881\pi$
$907$	−1.49117	−0.0495136	−0.0247568	+	0.999694i	$0.507881\pi$
$908$	−1.26402	−0.0419479
$909$	17.9655	0.595879
$910$	10.9434	0.362771
$911$	40.7106	1.34880	0.674401	−	0.738365i	$-0.264402\pi$
$911$	40.7106	1.34880	0.674401	+	0.738365i	$0.264402\pi$
$912$	−1.09472	−0.0362498
$913$	−7.21480	−0.238775
$914$	−35.3128	−1.16804
$915$	2.78725	0.0921437
$916$	17.1590	0.566950
$917$	32.0520	1.05845
$918$	5.40804	0.178492
$919$	35.6676	1.17656	0.588282	−	0.808655i	$-0.299804\pi$
$919$	35.6676	1.17656	0.588282	+	0.808655i	$0.299804\pi$
$920$	−6.03884	−0.199095
$921$	−2.84092	−0.0936114
$922$	37.5505	1.23666
$923$	10.7224	0.352932
$924$	−3.50251	−0.115224
$925$	−1.65521	−0.0544231
$926$	29.2633	0.961653
$927$	5.85762	0.192389
$928$	−7.47038	−0.245227
$929$	35.6442	1.16945	0.584724	−	0.811232i	$-0.301203\pi$
$929$	35.6442	1.16945	0.584724	+	0.811232i	$0.301203\pi$
$930$	−1.27782	−0.0419014
$931$	1.91441	0.0627421
$932$	−11.0937	−0.363385
$933$	−0.666259	−0.0218123
$934$	−2.05376	−0.0672010
$935$	16.2479	0.531363
$936$	−12.5323	−0.409629
$937$	4.74195	0.154913	0.0774564	−	0.996996i	$-0.475320\pi$
$937$	4.74195	0.154913	0.0774564	+	0.996996i	$0.475320\pi$
$938$	−13.0893	−0.427380
$939$	−4.20070	−0.137085
$940$	−3.33231	−0.108688
$941$	17.7737	0.579407	0.289703	−	0.957116i	$-0.406443\pi$
$941$	17.7737	0.579407	0.289703	+	0.957116i	$0.406443\pi$
$942$	−2.81967	−0.0918698
$943$	48.3927	1.57588
$944$	6.61220	0.215209
$945$	−4.19803	−0.136562
$946$	−8.80469	−0.286265
$947$	37.4217	1.21604	0.608020	−	0.793921i	$-0.291964\pi$
$947$	37.4217	1.21604	0.608020	+	0.793921i	$0.291964\pi$
$948$	2.80875	0.0912239
$949$	10.4860	0.340391
$950$	−3.94209	−0.127898
$951$	−5.77939	−0.187409
$952$	−8.39202	−0.271987
$953$	−9.13396	−0.295878	−0.147939	−	0.988997i	$-0.547264\pi$
$953$	−9.13396	−0.295878	−0.147939	+	0.988997i	$0.547264\pi$
$954$	25.6154	0.829329
$955$	13.5010	0.436881
$956$	−12.0870	−0.390922
$957$	10.2515	0.331383
$958$	−22.3022	−0.720550
$959$	15.6214	0.504440
$960$	0.277700	0.00896273
$961$	−9.82673	−0.316991
$962$	−7.09695	−0.228815
$963$	17.0483	0.549374
$964$	−25.6218	−0.825222
$965$	0.481989	0.0155158
$966$	−4.28022	−0.137714
$967$	43.0359	1.38394	0.691970	−	0.721926i	$-0.256743\pi$
$967$	43.0359	1.38394	0.691970	+	0.721926i	$0.256743\pi$
$968$	13.4193	0.431314
$969$	3.59942	0.115630
$970$	−0.655528	−0.0210477
$971$	23.5469	0.755657	0.377829	−	0.925876i	$-0.376671\pi$
$971$	23.5469	0.755657	0.377829	+	0.925876i	$0.376671\pi$
$972$	7.24257	0.232306
$973$	21.8117	0.699250
$974$	−22.7781	−0.729859
$975$	1.19068	0.0381322
$976$	10.0369	0.321274
$977$	−43.6340	−1.39597	−0.697987	−	0.716110i	$-0.745921\pi$
$977$	−43.6340	−1.39597	−0.697987	+	0.716110i	$0.745921\pi$
$978$	−1.95729	−0.0625872
$979$	37.5395	1.19977
$980$	−0.485632	−0.0155130
$981$	−6.97389	−0.222659
$982$	−18.0674	−0.576555
$983$	17.4569	0.556790	0.278395	−	0.960467i	$-0.410198\pi$
$983$	17.4569	0.556790	0.278395	+	0.960467i	$0.410198\pi$
$984$	−2.22537	−0.0709423
$985$	−9.40948	−0.299811
$986$	24.5625	0.782230
$987$	−2.36188	−0.0751795
$988$	−16.9022	−0.537732
$989$	−10.7597	−0.342139
$990$	14.4437	0.459051
$991$	23.6777	0.752146	0.376073	−	0.926590i	$-0.377274\pi$
$991$	23.6777	0.752146	0.376073	+	0.926590i	$0.377274\pi$
$992$	−4.60144	−0.146096
$993$	−2.26214	−0.0717868
$994$	6.38279	0.202450
$995$	18.8322	0.597021
$996$	0.405446	0.0128471
$997$	−33.3445	−1.05603	−0.528015	−	0.849235i	$-0.677064\pi$
$997$	−33.3445	−1.05603	−0.528015	+	0.849235i	$0.677064\pi$
$998$	−37.4965	−1.18693
$999$	2.72247	0.0861351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.10	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.10	✓	16	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.277700 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.277700 q^{6} +2.55233 q^{7} +1.00000 q^{8} -2.92288 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.277700 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.277700 q^{6} +2.55233 q^{7} +1.00000 q^{8} -2.92288 q^{9} +1.00000 q^{10} -4.94159 q^{11} +0.277700 q^{12} +4.28763 q^{13} +2.55233 q^{14} +0.277700 q^{15} +1.00000 q^{16} -3.28799 q^{17} -2.92288 q^{18} -3.94209 q^{19} +1.00000 q^{20} +0.708781 q^{21} -4.94159 q^{22} -6.03884 q^{23} +0.277700 q^{24} +1.00000 q^{25} +4.28763 q^{26} -1.64479 q^{27} +2.55233 q^{28} -7.47038 q^{29} +0.277700 q^{30} -4.60144 q^{31} +1.00000 q^{32} -1.37228 q^{33} -3.28799 q^{34} +2.55233 q^{35} -2.92288 q^{36} -1.65521 q^{37} -3.94209 q^{38} +1.19068 q^{39} +1.00000 q^{40} -8.01358 q^{41} +0.708781 q^{42} +1.78175 q^{43} -4.94159 q^{44} -2.92288 q^{45} -6.03884 q^{46} -3.33231 q^{47} +0.277700 q^{48} -0.485632 q^{49} +1.00000 q^{50} -0.913075 q^{51} +4.28763 q^{52} -8.76375 q^{53} -1.64479 q^{54} -4.94159 q^{55} +2.55233 q^{56} -1.09472 q^{57} -7.47038 q^{58} +6.61220 q^{59} +0.277700 q^{60} +10.0369 q^{61} -4.60144 q^{62} -7.46015 q^{63} +1.00000 q^{64} +4.28763 q^{65} -1.37228 q^{66} -5.12837 q^{67} -3.28799 q^{68} -1.67699 q^{69} +2.55233 q^{70} +2.50077 q^{71} -2.92288 q^{72} +2.44565 q^{73} -1.65521 q^{74} +0.277700 q^{75} -3.94209 q^{76} -12.6126 q^{77} +1.19068 q^{78} +10.1143 q^{79} +1.00000 q^{80} +8.31189 q^{81} -8.01358 q^{82} +1.46001 q^{83} +0.708781 q^{84} -3.28799 q^{85} +1.78175 q^{86} -2.07453 q^{87} -4.94159 q^{88} -7.59665 q^{89} -2.92288 q^{90} +10.9434 q^{91} -6.03884 q^{92} -1.27782 q^{93} -3.33231 q^{94} -3.94209 q^{95} +0.277700 q^{96} -0.655528 q^{97} -0.485632 q^{98} +14.4437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

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