LMFDB - Embedded newform 6010.2.a.c.1.5

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			1.5
Root			$-0.981279$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.98128 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.98128 q^{6} -4.22080 q^{7} +1.00000 q^{8} +0.925466 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.98128 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.98128 q^{6} -4.22080 q^{7} +1.00000 q^{8} +0.925466 q^{9} +1.00000 q^{10} +0.530338 q^{11} -1.98128 q^{12} -0.100776 q^{13} -4.22080 q^{14} -1.98128 q^{15} +1.00000 q^{16} -3.01879 q^{17} +0.925466 q^{18} -1.24304 q^{19} +1.00000 q^{20} +8.36259 q^{21} +0.530338 q^{22} +8.77835 q^{23} -1.98128 q^{24} +1.00000 q^{25} -0.100776 q^{26} +4.11023 q^{27} -4.22080 q^{28} +1.18004 q^{29} -1.98128 q^{30} +3.73228 q^{31} +1.00000 q^{32} -1.05075 q^{33} -3.01879 q^{34} -4.22080 q^{35} +0.925466 q^{36} +5.95866 q^{37} -1.24304 q^{38} +0.199665 q^{39} +1.00000 q^{40} -10.4027 q^{41} +8.36259 q^{42} +9.82863 q^{43} +0.530338 q^{44} +0.925466 q^{45} +8.77835 q^{46} -2.60238 q^{47} -1.98128 q^{48} +10.8152 q^{49} +1.00000 q^{50} +5.98106 q^{51} -0.100776 q^{52} +6.07027 q^{53} +4.11023 q^{54} +0.530338 q^{55} -4.22080 q^{56} +2.46280 q^{57} +1.18004 q^{58} -11.8884 q^{59} -1.98128 q^{60} -9.97802 q^{61} +3.73228 q^{62} -3.90621 q^{63} +1.00000 q^{64} -0.100776 q^{65} -1.05075 q^{66} -7.26948 q^{67} -3.01879 q^{68} -17.3924 q^{69} -4.22080 q^{70} +15.6832 q^{71} +0.925466 q^{72} -15.2789 q^{73} +5.95866 q^{74} -1.98128 q^{75} -1.24304 q^{76} -2.23845 q^{77} +0.199665 q^{78} -8.86443 q^{79} +1.00000 q^{80} -10.9199 q^{81} -10.4027 q^{82} -10.8435 q^{83} +8.36259 q^{84} -3.01879 q^{85} +9.82863 q^{86} -2.33799 q^{87} +0.530338 q^{88} -12.3021 q^{89} +0.925466 q^{90} +0.425356 q^{91} +8.77835 q^{92} -7.39468 q^{93} -2.60238 q^{94} -1.24304 q^{95} -1.98128 q^{96} +9.19718 q^{97} +10.8152 q^{98} +0.490810 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.98128	−1.14389	−0.571946	−	0.820291i	$-0.693811\pi$
$3$	−1.98128	−1.14389	−0.571946	+	0.820291i	$0.693811\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.98128	−0.808854
$7$	−4.22080	−1.59531	−0.797657	−	0.603111i	$-0.793927\pi$
$7$	−4.22080	−1.59531	−0.797657	+	0.603111i	$0.793927\pi$
$8$	1.00000	0.353553
$9$	0.925466	0.308489
$10$	1.00000	0.316228
$11$	0.530338	0.159903	0.0799515	−	0.996799i	$-0.474523\pi$
$11$	0.530338	0.159903	0.0799515	+	0.996799i	$0.474523\pi$
$12$	−1.98128	−0.571946
$13$	−0.100776	−0.0279502	−0.0139751	−	0.999902i	$-0.504449\pi$
$13$	−0.100776	−0.0279502	−0.0139751	+	0.999902i	$0.504449\pi$
$14$	−4.22080	−1.12806
$15$	−1.98128	−0.511564
$16$	1.00000	0.250000
$17$	−3.01879	−0.732163	−0.366082	−	0.930583i	$-0.619301\pi$
$17$	−3.01879	−0.732163	−0.366082	+	0.930583i	$0.619301\pi$
$18$	0.925466	0.218134
$19$	−1.24304	−0.285172	−0.142586	−	0.989782i	$-0.545542\pi$
$19$	−1.24304	−0.285172	−0.142586	+	0.989782i	$0.545542\pi$
$20$	1.00000	0.223607
$21$	8.36259	1.82487
$22$	0.530338	0.113069
$23$	8.77835	1.83041	0.915206	−	0.402986i	$-0.132028\pi$
$23$	8.77835	1.83041	0.915206	+	0.402986i	$0.132028\pi$
$24$	−1.98128	−0.404427
$25$	1.00000	0.200000
$26$	−0.100776	−0.0197638
$27$	4.11023	0.791014
$28$	−4.22080	−0.797657
$29$	1.18004	0.219128	0.109564	−	0.993980i	$-0.465054\pi$
$29$	1.18004	0.219128	0.109564	+	0.993980i	$0.465054\pi$
$30$	−1.98128	−0.361730
$31$	3.73228	0.670337	0.335168	−	0.942158i	$-0.391207\pi$
$31$	3.73228	0.670337	0.335168	+	0.942158i	$0.391207\pi$
$32$	1.00000	0.176777
$33$	−1.05075	−0.182912
$34$	−3.01879	−0.517717
$35$	−4.22080	−0.713446
$36$	0.925466	0.154244
$37$	5.95866	0.979597	0.489798	−	0.871836i	$-0.337070\pi$
$37$	5.95866	0.979597	0.489798	+	0.871836i	$0.337070\pi$
$38$	−1.24304	−0.201647
$39$	0.199665	0.0319720
$40$	1.00000	0.158114
$41$	−10.4027	−1.62463	−0.812317	−	0.583216i	$-0.801794\pi$
$41$	−10.4027	−1.62463	−0.812317	+	0.583216i	$0.801794\pi$
$42$	8.36259	1.29038
$43$	9.82863	1.49885	0.749426	−	0.662088i	$-0.230329\pi$
$43$	9.82863	1.49885	0.749426	+	0.662088i	$0.230329\pi$
$44$	0.530338	0.0799515
$45$	0.925466	0.137960
$46$	8.77835	1.29430
$47$	−2.60238	−0.379596	−0.189798	−	0.981823i	$-0.560783\pi$
$47$	−2.60238	−0.379596	−0.189798	+	0.981823i	$0.560783\pi$
$48$	−1.98128	−0.285973
$49$	10.8152	1.54503
$50$	1.00000	0.141421
$51$	5.98106	0.837515
$52$	−0.100776	−0.0139751
$53$	6.07027	0.833815	0.416908	−	0.908949i	$-0.363114\pi$
$53$	6.07027	0.833815	0.416908	+	0.908949i	$0.363114\pi$
$54$	4.11023	0.559332
$55$	0.530338	0.0715108
$56$	−4.22080	−0.564029
$57$	2.46280	0.326206
$58$	1.18004	0.154947
$59$	−11.8884	−1.54773	−0.773866	−	0.633349i	$-0.781680\pi$
$59$	−11.8884	−1.54773	−0.773866	+	0.633349i	$0.781680\pi$
$60$	−1.98128	−0.255782
$61$	−9.97802	−1.27755	−0.638777	−	0.769392i	$-0.720559\pi$
$61$	−9.97802	−1.27755	−0.638777	+	0.769392i	$0.720559\pi$
$62$	3.73228	0.474000
$63$	−3.90621	−0.492136
$64$	1.00000	0.125000
$65$	−0.100776	−0.0124997
$66$	−1.05075	−0.129338
$67$	−7.26948	−0.888109	−0.444054	−	0.896000i	$-0.646460\pi$
$67$	−7.26948	−0.888109	−0.444054	+	0.896000i	$0.646460\pi$
$68$	−3.01879	−0.366082
$69$	−17.3924	−2.09379
$70$	−4.22080	−0.504483
$71$	15.6832	1.86125	0.930624	−	0.365976i	$-0.119265\pi$
$71$	15.6832	1.86125	0.930624	+	0.365976i	$0.119265\pi$
$72$	0.925466	0.109067
$73$	−15.2789	−1.78826	−0.894128	−	0.447812i	$-0.852203\pi$
$73$	−15.2789	−1.78826	−0.894128	+	0.447812i	$0.852203\pi$
$74$	5.95866	0.692680
$75$	−1.98128	−0.228778
$76$	−1.24304	−0.142586
$77$	−2.23845	−0.255096
$78$	0.199665	0.0226076
$79$	−8.86443	−0.997326	−0.498663	−	0.866796i	$-0.666175\pi$
$79$	−8.86443	−0.997326	−0.498663	+	0.866796i	$0.666175\pi$
$80$	1.00000	0.111803
$81$	−10.9199	−1.21332
$82$	−10.4027	−1.14879
$83$	−10.8435	−1.19022	−0.595112	−	0.803643i	$-0.702892\pi$
$83$	−10.8435	−1.19022	−0.595112	+	0.803643i	$0.702892\pi$
$84$	8.36259	0.912433
$85$	−3.01879	−0.327433
$86$	9.82863	1.05985
$87$	−2.33799	−0.250659
$88$	0.530338	0.0565343
$89$	−12.3021	−1.30402	−0.652012	−	0.758209i	$-0.726075\pi$
$89$	−12.3021	−1.30402	−0.652012	+	0.758209i	$0.726075\pi$
$90$	0.925466	0.0975527
$91$	0.425356	0.0445894
$92$	8.77835	0.915206
$93$	−7.39468	−0.766793
$94$	−2.60238	−0.268415
$95$	−1.24304	−0.127533
$96$	−1.98128	−0.202213
$97$	9.19718	0.933832	0.466916	−	0.884302i	$-0.345365\pi$
$97$	9.19718	0.933832	0.466916	+	0.884302i	$0.345365\pi$
$98$	10.8152	1.09250
$99$	0.490810	0.0493283
$100$	1.00000	0.100000
$101$	−0.696428	−0.0692972	−0.0346486	−	0.999400i	$-0.511031\pi$
$101$	−0.696428	−0.0692972	−0.0346486	+	0.999400i	$0.511031\pi$
$102$	5.98106	0.592213
$103$	−0.109262	−0.0107659	−0.00538294	−	0.999986i	$-0.501713\pi$
$103$	−0.109262	−0.0107659	−0.00538294	+	0.999986i	$0.501713\pi$
$104$	−0.100776	−0.00988190
$105$	8.36259	0.816105
$106$	6.07027	0.589596
$107$	−11.7250	−1.13350	−0.566749	−	0.823890i	$-0.691799\pi$
$107$	−11.7250	−1.13350	−0.566749	+	0.823890i	$0.691799\pi$
$108$	4.11023	0.395507
$109$	−7.56174	−0.724283	−0.362141	−	0.932123i	$-0.617954\pi$
$109$	−7.56174	−0.724283	−0.362141	+	0.932123i	$0.617954\pi$
$110$	0.530338	0.0505658
$111$	−11.8058	−1.12055
$112$	−4.22080	−0.398828
$113$	−9.90909	−0.932169	−0.466084	−	0.884740i	$-0.654336\pi$
$113$	−9.90909	−0.932169	−0.466084	+	0.884740i	$0.654336\pi$
$114$	2.46280	0.230662
$115$	8.77835	0.818585
$116$	1.18004	0.109564
$117$	−0.0932647	−0.00862233
$118$	−11.8884	−1.09441
$119$	12.7417	1.16803
$120$	−1.98128	−0.180865
$121$	−10.7187	−0.974431
$122$	−9.97802	−0.903367
$123$	20.6107	1.85841
$124$	3.73228	0.335168
$125$	1.00000	0.0894427
$126$	−3.90621	−0.347993
$127$	10.1010	0.896323	0.448162	−	0.893953i	$-0.352079\pi$
$127$	10.1010	0.896323	0.448162	+	0.893953i	$0.352079\pi$
$128$	1.00000	0.0883883
$129$	−19.4733	−1.71453
$130$	−0.100776	−0.00883864
$131$	15.1653	1.32499	0.662497	−	0.749064i	$-0.269497\pi$
$131$	15.1653	1.32499	0.662497	+	0.749064i	$0.269497\pi$
$132$	−1.05075	−0.0914559
$133$	5.24661	0.454939
$134$	−7.26948	−0.627988
$135$	4.11023	0.353752
$136$	−3.01879	−0.258859
$137$	6.86463	0.586485	0.293242	−	0.956038i	$-0.405266\pi$
$137$	6.86463	0.586485	0.293242	+	0.956038i	$0.405266\pi$
$138$	−17.3924	−1.48054
$139$	−5.33765	−0.452734	−0.226367	−	0.974042i	$-0.572685\pi$
$139$	−5.33765	−0.452734	−0.226367	+	0.974042i	$0.572685\pi$
$140$	−4.22080	−0.356723
$141$	5.15604	0.434217
$142$	15.6832	1.31610
$143$	−0.0534454	−0.00446933
$144$	0.925466	0.0771222
$145$	1.18004	0.0979972
$146$	−15.2789	−1.26449
$147$	−21.4279	−1.76734
$148$	5.95866	0.489798
$149$	2.94235	0.241046	0.120523	−	0.992711i	$-0.461543\pi$
$149$	2.94235	0.241046	0.120523	+	0.992711i	$0.461543\pi$
$150$	−1.98128	−0.161771
$151$	10.3478	0.842094	0.421047	−	0.907039i	$-0.361663\pi$
$151$	10.3478	0.842094	0.421047	+	0.907039i	$0.361663\pi$
$152$	−1.24304	−0.100823
$153$	−2.79378	−0.225864
$154$	−2.23845	−0.180380
$155$	3.73228	0.299784
$156$	0.199665	0.0159860
$157$	10.7164	0.855264	0.427632	−	0.903953i	$-0.359348\pi$
$157$	10.7164	0.855264	0.427632	+	0.903953i	$0.359348\pi$
$158$	−8.86443	−0.705216
$159$	−12.0269	−0.953795
$160$	1.00000	0.0790569
$161$	−37.0517	−2.92008
$162$	−10.9199	−0.857949
$163$	−0.373966	−0.0292913	−0.0146457	−	0.999893i	$-0.504662\pi$
$163$	−0.373966	−0.0292913	−0.0146457	+	0.999893i	$0.504662\pi$
$164$	−10.4027	−0.812317
$165$	−1.05075	−0.0818006
$166$	−10.8435	−0.841615
$167$	−5.64002	−0.436438	−0.218219	−	0.975900i	$-0.570025\pi$
$167$	−5.64002	−0.436438	−0.218219	+	0.975900i	$0.570025\pi$
$168$	8.36259	0.645188
$169$	−12.9898	−0.999219
$170$	−3.01879	−0.231530
$171$	−1.15039	−0.0879723
$172$	9.82863	0.749426
$173$	−7.93500	−0.603287	−0.301643	−	0.953421i	$-0.597535\pi$
$173$	−7.93500	−0.603287	−0.301643	+	0.953421i	$0.597535\pi$
$174$	−2.33799	−0.177243
$175$	−4.22080	−0.319063
$176$	0.530338	0.0399758
$177$	23.5542	1.77044
$178$	−12.3021	−0.922084
$179$	−20.4271	−1.52679	−0.763395	−	0.645932i	$-0.776469\pi$
$179$	−20.4271	−1.52679	−0.763395	+	0.645932i	$0.776469\pi$
$180$	0.925466	0.0689802
$181$	−16.1239	−1.19848	−0.599238	−	0.800571i	$-0.704530\pi$
$181$	−16.1239	−1.19848	−0.599238	+	0.800571i	$0.704530\pi$
$182$	0.425356	0.0315295
$183$	19.7692	1.46138
$184$	8.77835	0.647148
$185$	5.95866	0.438089
$186$	−7.39468	−0.542204
$187$	−1.60098	−0.117075
$188$	−2.60238	−0.189798
$189$	−17.3485	−1.26192
$190$	−1.24304	−0.0901792
$191$	−9.40217	−0.680317	−0.340158	−	0.940368i	$-0.610481\pi$
$191$	−9.40217	−0.680317	−0.340158	+	0.940368i	$0.610481\pi$
$192$	−1.98128	−0.142986
$193$	10.0203	0.721276	0.360638	−	0.932706i	$-0.382559\pi$
$193$	10.0203	0.721276	0.360638	+	0.932706i	$0.382559\pi$
$194$	9.19718	0.660319
$195$	0.199665	0.0142983
$196$	10.8152	0.772513
$197$	−3.88607	−0.276871	−0.138436	−	0.990371i	$-0.544207\pi$
$197$	−3.88607	−0.276871	−0.138436	+	0.990371i	$0.544207\pi$
$198$	0.490810	0.0348804
$199$	−12.8979	−0.914310	−0.457155	−	0.889387i	$-0.651132\pi$
$199$	−12.8979	−0.914310	−0.457155	+	0.889387i	$0.651132\pi$
$200$	1.00000	0.0707107
$201$	14.4029	1.01590
$202$	−0.696428	−0.0490005
$203$	−4.98073	−0.349579
$204$	5.98106	0.418758
$205$	−10.4027	−0.726559
$206$	−0.109262	−0.00761262
$207$	8.12406	0.564661
$208$	−0.100776	−0.00698756
$209$	−0.659229	−0.0455998
$210$	8.36259	0.577073
$211$	−18.4433	−1.26969	−0.634843	−	0.772641i	$-0.718935\pi$
$211$	−18.4433	−1.26969	−0.634843	+	0.772641i	$0.718935\pi$
$212$	6.07027	0.416908
$213$	−31.0727	−2.12907
$214$	−11.7250	−0.801504
$215$	9.82863	0.670307
$216$	4.11023	0.279666
$217$	−15.7532	−1.06940
$218$	−7.56174	−0.512145
$219$	30.2717	2.04557
$220$	0.530338	0.0357554
$221$	0.304221	0.0204641
$222$	−11.8058	−0.792351
$223$	22.0052	1.47358	0.736789	−	0.676122i	$-0.236341\pi$
$223$	22.0052	1.47358	0.736789	+	0.676122i	$0.236341\pi$
$224$	−4.22080	−0.282014
$225$	0.925466	0.0616977
$226$	−9.90909	−0.659143
$227$	−14.6503	−0.972376	−0.486188	−	0.873854i	$-0.661613\pi$
$227$	−14.6503	−0.972376	−0.486188	+	0.873854i	$0.661613\pi$
$228$	2.46280	0.163103
$229$	−17.3362	−1.14561	−0.572805	−	0.819692i	$-0.694145\pi$
$229$	−17.3362	−1.14561	−0.572805	+	0.819692i	$0.694145\pi$
$230$	8.77835	0.578827
$231$	4.43500	0.291802
$232$	1.18004	0.0774736
$233$	12.0048	0.786459	0.393230	−	0.919440i	$-0.371358\pi$
$233$	12.0048	0.786459	0.393230	+	0.919440i	$0.371358\pi$
$234$	−0.0932647	−0.00609691
$235$	−2.60238	−0.169761
$236$	−11.8884	−0.773866
$237$	17.5629	1.14083
$238$	12.7417	0.825922
$239$	27.5016	1.77893	0.889467	−	0.457000i	$-0.151076\pi$
$239$	27.5016	1.77893	0.889467	+	0.457000i	$0.151076\pi$
$240$	−1.98128	−0.127891
$241$	−13.2419	−0.852983	−0.426491	−	0.904492i	$-0.640251\pi$
$241$	−13.2419	−0.852983	−0.426491	+	0.904492i	$0.640251\pi$
$242$	−10.7187	−0.689027
$243$	9.30470	0.596897
$244$	−9.97802	−0.638777
$245$	10.8152	0.690957
$246$	20.6107	1.31409
$247$	0.125268	0.00797062
$248$	3.73228	0.237000
$249$	21.4839	1.36149
$250$	1.00000	0.0632456
$251$	−3.04529	−0.192217	−0.0961084	−	0.995371i	$-0.530640\pi$
$251$	−3.04529	−0.192217	−0.0961084	+	0.995371i	$0.530640\pi$
$252$	−3.90621	−0.246068
$253$	4.65549	0.292688
$254$	10.1010	0.633796
$255$	5.98106	0.374548
$256$	1.00000	0.0625000
$257$	−17.9678	−1.12080	−0.560401	−	0.828222i	$-0.689353\pi$
$257$	−17.9678	−1.12080	−0.560401	+	0.828222i	$0.689353\pi$
$258$	−19.4733	−1.21235
$259$	−25.1503	−1.56276
$260$	−0.100776	−0.00624986
$261$	1.09209	0.0675986
$262$	15.1653	0.936913
$263$	0.207779	0.0128122	0.00640610	−	0.999979i	$-0.497961\pi$
$263$	0.207779	0.0128122	0.00640610	+	0.999979i	$0.497961\pi$
$264$	−1.05075	−0.0646691
$265$	6.07027	0.372894
$266$	5.24661	0.321690
$267$	24.3740	1.49166
$268$	−7.26948	−0.444054
$269$	32.4104	1.97610	0.988048	−	0.154148i	$-0.0492633\pi$
$269$	32.4104	1.97610	0.988048	+	0.154148i	$0.0492633\pi$
$270$	4.11023	0.250141
$271$	2.36018	0.143371	0.0716853	−	0.997427i	$-0.477162\pi$
$271$	2.36018	0.143371	0.0716853	+	0.997427i	$0.477162\pi$
$272$	−3.01879	−0.183041
$273$	−0.842748	−0.0510054
$274$	6.86463	0.414707
$275$	0.530338	0.0319806
$276$	−17.3924	−1.04690
$277$	−7.91946	−0.475834	−0.237917	−	0.971285i	$-0.576465\pi$
$277$	−7.91946	−0.475834	−0.237917	+	0.971285i	$0.576465\pi$
$278$	−5.33765	−0.320131
$279$	3.45409	0.206791
$280$	−4.22080	−0.252241
$281$	15.4693	0.922820	0.461410	−	0.887187i	$-0.347344\pi$
$281$	15.4693	0.922820	0.461410	+	0.887187i	$0.347344\pi$
$282$	5.15604	0.307038
$283$	30.3044	1.80141	0.900706	−	0.434429i	$-0.143050\pi$
$283$	30.3044	1.80141	0.900706	+	0.434429i	$0.143050\pi$
$284$	15.6832	0.930624
$285$	2.46280	0.145884
$286$	−0.0534454	−0.00316029
$287$	43.9079	2.59180
$288$	0.925466	0.0545336
$289$	−7.88693	−0.463937
$290$	1.18004	0.0692945
$291$	−18.2222	−1.06820
$292$	−15.2789	−0.894128
$293$	11.2466	0.657034	0.328517	−	0.944498i	$-0.393451\pi$
$293$	11.2466	0.657034	0.328517	+	0.944498i	$0.393451\pi$
$294$	−21.4279	−1.24970
$295$	−11.8884	−0.692167
$296$	5.95866	0.346340
$297$	2.17981	0.126486
$298$	2.94235	0.170446
$299$	−0.884647	−0.0511604
$300$	−1.98128	−0.114389
$301$	−41.4847	−2.39114
$302$	10.3478	0.595451
$303$	1.37982	0.0792685
$304$	−1.24304	−0.0712929
$305$	−9.97802	−0.571340
$306$	−2.79378	−0.159710
$307$	−13.5263	−0.771986	−0.385993	−	0.922502i	$-0.626141\pi$
$307$	−13.5263	−0.771986	−0.385993	+	0.922502i	$0.626141\pi$
$308$	−2.23845	−0.127548
$309$	0.216478	0.0123150
$310$	3.73228	0.211979
$311$	−19.4234	−1.10140	−0.550699	−	0.834704i	$-0.685639\pi$
$311$	−19.4234	−1.10140	−0.550699	+	0.834704i	$0.685639\pi$
$312$	0.199665	0.0113038
$313$	−24.8018	−1.40188	−0.700942	−	0.713219i	$-0.747237\pi$
$313$	−24.8018	−1.40188	−0.700942	+	0.713219i	$0.747237\pi$
$314$	10.7164	0.604763
$315$	−3.90621	−0.220090
$316$	−8.86443	−0.498663
$317$	−18.3022	−1.02795	−0.513977	−	0.857804i	$-0.671828\pi$
$317$	−18.3022	−1.02795	−0.513977	+	0.857804i	$0.671828\pi$
$318$	−12.0269	−0.674435
$319$	0.625822	0.0350393
$320$	1.00000	0.0559017
$321$	23.2305	1.29660
$322$	−37.0517	−2.06481
$323$	3.75246	0.208792
$324$	−10.9199	−0.606662
$325$	−0.100776	−0.00559005
$326$	−0.373966	−0.0207121
$327$	14.9819	0.828501
$328$	−10.4027	−0.574395
$329$	10.9841	0.605575
$330$	−1.05075	−0.0578418
$331$	−8.11182	−0.445866	−0.222933	−	0.974834i	$-0.571563\pi$
$331$	−8.11182	−0.445866	−0.222933	+	0.974834i	$0.571563\pi$
$332$	−10.8435	−0.595112
$333$	5.51453	0.302195
$334$	−5.64002	−0.308608
$335$	−7.26948	−0.397174
$336$	8.36259	0.456217
$337$	−5.34930	−0.291395	−0.145697	−	0.989329i	$-0.546543\pi$
$337$	−5.34930	−0.291395	−0.145697	+	0.989329i	$0.546543\pi$
$338$	−12.9898	−0.706554
$339$	19.6327	1.06630
$340$	−3.01879	−0.163717
$341$	1.97937	0.107189
$342$	−1.15039	−0.0622058
$343$	−16.1031	−0.869488
$344$	9.82863	0.529924
$345$	−17.3924	−0.936373
$346$	−7.93500	−0.426588
$347$	−5.05294	−0.271256	−0.135628	−	0.990760i	$-0.543305\pi$
$347$	−5.05294	−0.271256	−0.135628	+	0.990760i	$0.543305\pi$
$348$	−2.33799	−0.125330
$349$	−21.1201	−1.13053	−0.565267	−	0.824908i	$-0.691227\pi$
$349$	−21.1201	−1.13053	−0.565267	+	0.824908i	$0.691227\pi$
$350$	−4.22080	−0.225611
$351$	−0.414213	−0.0221090
$352$	0.530338	0.0282671
$353$	18.4134	0.980044	0.490022	−	0.871710i	$-0.336989\pi$
$353$	18.4134	0.980044	0.490022	+	0.871710i	$0.336989\pi$
$354$	23.5542	1.25189
$355$	15.6832	0.832376
$356$	−12.3021	−0.652012
$357$	−25.2449	−1.33610
$358$	−20.4271	−1.07960
$359$	−2.92099	−0.154164	−0.0770819	−	0.997025i	$-0.524560\pi$
$359$	−2.92099	−0.154164	−0.0770819	+	0.997025i	$0.524560\pi$
$360$	0.925466	0.0487763
$361$	−17.4549	−0.918677
$362$	−16.1239	−0.847451
$363$	21.2368	1.11464
$364$	0.425356	0.0222947
$365$	−15.2789	−0.799732
$366$	19.7692	1.03335
$367$	13.5315	0.706339	0.353169	−	0.935559i	$-0.385104\pi$
$367$	13.5315	0.706339	0.353169	+	0.935559i	$0.385104\pi$
$368$	8.77835	0.457603
$369$	−9.62738	−0.501181
$370$	5.95866	0.309776
$371$	−25.6214	−1.33020
$372$	−7.39468	−0.383396
$373$	11.7727	0.609569	0.304785	−	0.952421i	$-0.401416\pi$
$373$	11.7727	0.609569	0.304785	+	0.952421i	$0.401416\pi$
$374$	−1.60098	−0.0827846
$375$	−1.98128	−0.102313
$376$	−2.60238	−0.134207
$377$	−0.118920	−0.00612469
$378$	−17.3485	−0.892309
$379$	16.1520	0.829674	0.414837	−	0.909896i	$-0.363839\pi$
$379$	16.1520	0.829674	0.414837	+	0.909896i	$0.363839\pi$
$380$	−1.24304	−0.0637664
$381$	−20.0130	−1.02530
$382$	−9.40217	−0.481057
$383$	5.99445	0.306302	0.153151	−	0.988203i	$-0.451058\pi$
$383$	5.99445	0.306302	0.153151	+	0.988203i	$0.451058\pi$
$384$	−1.98128	−0.101107
$385$	−2.23845	−0.114082
$386$	10.0203	0.510019
$387$	9.09606	0.462379
$388$	9.19718	0.466916
$389$	7.07504	0.358719	0.179360	−	0.983784i	$-0.442597\pi$
$389$	7.07504	0.358719	0.179360	+	0.983784i	$0.442597\pi$
$390$	0.199665	0.0101104
$391$	−26.4999	−1.34016
$392$	10.8152	0.546249
$393$	−30.0466	−1.51565
$394$	−3.88607	−0.195778
$395$	−8.86443	−0.446018
$396$	0.490810	0.0246641
$397$	1.12705	0.0565649	0.0282824	−	0.999600i	$-0.490996\pi$
$397$	1.12705	0.0565649	0.0282824	+	0.999600i	$0.490996\pi$
$398$	−12.8979	−0.646515
$399$	−10.3950	−0.520400
$400$	1.00000	0.0500000
$401$	−18.1263	−0.905184	−0.452592	−	0.891718i	$-0.649501\pi$
$401$	−18.1263	−0.905184	−0.452592	+	0.891718i	$0.649501\pi$
$402$	14.4029	0.718350
$403$	−0.376124	−0.0187361
$404$	−0.696428	−0.0346486
$405$	−10.9199	−0.542615
$406$	−4.98073	−0.247189
$407$	3.16010	0.156641
$408$	5.98106	0.296106
$409$	−8.94909	−0.442504	−0.221252	−	0.975217i	$-0.571014\pi$
$409$	−8.94909	−0.442504	−0.221252	+	0.975217i	$0.571014\pi$
$410$	−10.4027	−0.513755
$411$	−13.6007	−0.670875
$412$	−0.109262	−0.00538294
$413$	50.1784	2.46912
$414$	8.12406	0.399276
$415$	−10.8435	−0.532284
$416$	−0.100776	−0.00494095
$417$	10.5754	0.517878
$418$	−0.659229	−0.0322440
$419$	18.7687	0.916911	0.458456	−	0.888717i	$-0.348403\pi$
$419$	18.7687	0.916911	0.458456	+	0.888717i	$0.348403\pi$
$420$	8.36259	0.408053
$421$	−15.5120	−0.756010	−0.378005	−	0.925803i	$-0.623390\pi$
$421$	−15.5120	−0.756010	−0.378005	+	0.925803i	$0.623390\pi$
$422$	−18.4433	−0.897804
$423$	−2.40841	−0.117101
$424$	6.07027	0.294798
$425$	−3.01879	−0.146433
$426$	−31.0727	−1.50548
$427$	42.1153	2.03810
$428$	−11.7250	−0.566749
$429$	0.105890	0.00511243
$430$	9.82863	0.473979
$431$	6.46497	0.311407	0.155703	−	0.987804i	$-0.450236\pi$
$431$	6.46497	0.311407	0.155703	+	0.987804i	$0.450236\pi$
$432$	4.11023	0.197754
$433$	−20.4238	−0.981507	−0.490754	−	0.871298i	$-0.663278\pi$
$433$	−20.4238	−0.981507	−0.490754	+	0.871298i	$0.663278\pi$
$434$	−15.7532	−0.756178
$435$	−2.33799	−0.112098
$436$	−7.56174	−0.362141
$437$	−10.9118	−0.521982
$438$	30.2717	1.44644
$439$	18.6018	0.887816	0.443908	−	0.896072i	$-0.353592\pi$
$439$	18.6018	0.887816	0.443908	+	0.896072i	$0.353592\pi$
$440$	0.530338	0.0252829
$441$	10.0091	0.476623
$442$	0.304221	0.0144703
$443$	12.2738	0.583147	0.291573	−	0.956548i	$-0.405821\pi$
$443$	12.2738	0.583147	0.291573	+	0.956548i	$0.405821\pi$
$444$	−11.8058	−0.560276
$445$	−12.3021	−0.583177
$446$	22.0052	1.04198
$447$	−5.82961	−0.275731
$448$	−4.22080	−0.199414
$449$	−27.2626	−1.28660	−0.643301	−	0.765613i	$-0.722436\pi$
$449$	−27.2626	−1.28660	−0.643301	+	0.765613i	$0.722436\pi$
$450$	0.925466	0.0436269
$451$	−5.51697	−0.259784
$452$	−9.90909	−0.466084
$453$	−20.5019	−0.963265
$454$	−14.6503	−0.687573
$455$	0.425356	0.0199410
$456$	2.46280	0.115331
$457$	−19.2314	−0.899606	−0.449803	−	0.893128i	$-0.648506\pi$
$457$	−19.2314	−0.899606	−0.449803	+	0.893128i	$0.648506\pi$
$458$	−17.3362	−0.810069
$459$	−12.4079	−0.579151
$460$	8.77835	0.409293
$461$	11.5699	0.538862	0.269431	−	0.963020i	$-0.413164\pi$
$461$	11.5699	0.538862	0.269431	+	0.963020i	$0.413164\pi$
$462$	4.43500	0.206335
$463$	−0.00174954	−8.13082e−5 0	−4.06541e−5	−	1.00000i	$-0.500013\pi$
$463$	−0.00174954	−8.13082e−5 0	−4.06541e−5		1.00000i	$0.500013\pi$
$464$	1.18004	0.0547821
$465$	−7.39468	−0.342920
$466$	12.0048	0.556111
$467$	−32.4183	−1.50014	−0.750070	−	0.661358i	$-0.769980\pi$
$467$	−32.4183	−1.50014	−0.750070	+	0.661358i	$0.769980\pi$
$468$	−0.0932647	−0.00431116
$469$	30.6831	1.41681
$470$	−2.60238	−0.120039
$471$	−21.2322	−0.978329
$472$	−11.8884	−0.547206
$473$	5.21250	0.239671
$474$	17.5629	0.806691
$475$	−1.24304	−0.0570344
$476$	12.7417	0.584015
$477$	5.61783	0.257223
$478$	27.5016	1.25790
$479$	6.16045	0.281478	0.140739	−	0.990047i	$-0.455052\pi$
$479$	6.16045	0.281478	0.140739	+	0.990047i	$0.455052\pi$
$480$	−1.98128	−0.0904326
$481$	−0.600489	−0.0273800
$482$	−13.2419	−0.603150
$483$	73.4097	3.34026
$484$	−10.7187	−0.487216
$485$	9.19718	0.417622
$486$	9.30470	0.422070
$487$	−24.9602	−1.13105	−0.565527	−	0.824730i	$-0.691327\pi$
$487$	−24.9602	−1.13105	−0.565527	+	0.824730i	$0.691327\pi$
$488$	−9.97802	−0.451684
$489$	0.740932	0.0335061
$490$	10.8152	0.488580
$491$	15.8961	0.717382	0.358691	−	0.933456i	$-0.383223\pi$
$491$	15.8961	0.717382	0.358691	+	0.933456i	$0.383223\pi$
$492$	20.6107	0.929203
$493$	−3.56230	−0.160438
$494$	0.125268	0.00563608
$495$	0.490810	0.0220603
$496$	3.73228	0.167584
$497$	−66.1955	−2.96928
$498$	21.4839	0.962717
$499$	−3.29567	−0.147535	−0.0737673	−	0.997275i	$-0.523502\pi$
$499$	−3.29567	−0.147535	−0.0737673	+	0.997275i	$0.523502\pi$
$500$	1.00000	0.0447214
$501$	11.1745	0.499238
$502$	−3.04529	−0.135918
$503$	25.1867	1.12302	0.561509	−	0.827471i	$-0.310221\pi$
$503$	25.1867	1.12302	0.561509	+	0.827471i	$0.310221\pi$
$504$	−3.90621	−0.173996
$505$	−0.696428	−0.0309907
$506$	4.65549	0.206962
$507$	25.7365	1.14300
$508$	10.1010	0.448162
$509$	20.5352	0.910207	0.455104	−	0.890438i	$-0.349602\pi$
$509$	20.5352	0.910207	0.455104	+	0.890438i	$0.349602\pi$
$510$	5.98106	0.264846
$511$	64.4891	2.85283
$512$	1.00000	0.0441942
$513$	−5.10916	−0.225575
$514$	−17.9678	−0.792526
$515$	−0.109262	−0.00481464
$516$	−19.4733	−0.857263
$517$	−1.38014	−0.0606986
$518$	−25.1503	−1.10504
$519$	15.7215	0.690095
$520$	−0.100776	−0.00441932
$521$	−0.894877	−0.0392053	−0.0196026	−	0.999808i	$-0.506240\pi$
$521$	−0.894877	−0.0392053	−0.0196026	+	0.999808i	$0.506240\pi$
$522$	1.09209	0.0477995
$523$	22.9521	1.00362	0.501812	−	0.864977i	$-0.332667\pi$
$523$	22.9521	1.00362	0.501812	+	0.864977i	$0.332667\pi$
$524$	15.1653	0.662497
$525$	8.36259	0.364973
$526$	0.207779	0.00905959
$527$	−11.2669	−0.490796
$528$	−1.05075	−0.0457279
$529$	54.0594	2.35041
$530$	6.07027	0.263676
$531$	−11.0023	−0.477458
$532$	5.24661	0.227469
$533$	1.04835	0.0454089
$534$	24.3740	1.05476
$535$	−11.7250	−0.506916
$536$	−7.26948	−0.313994
$537$	40.4717	1.74648
$538$	32.4104	1.39731
$539$	5.73571	0.247054
$540$	4.11023	0.176876
$541$	−34.2710	−1.47343	−0.736714	−	0.676205i	$-0.763623\pi$
$541$	−34.2710	−1.47343	−0.736714	+	0.676205i	$0.763623\pi$
$542$	2.36018	0.101378
$543$	31.9459	1.37093
$544$	−3.01879	−0.129429
$545$	−7.56174	−0.323909
$546$	−0.842748	−0.0360663
$547$	−28.2684	−1.20867	−0.604334	−	0.796731i	$-0.706561\pi$
$547$	−28.2684	−1.20867	−0.604334	+	0.796731i	$0.706561\pi$
$548$	6.86463	0.293242
$549$	−9.23431	−0.394111
$550$	0.530338	0.0226137
$551$	−1.46683	−0.0624893
$552$	−17.3924	−0.740268
$553$	37.4150	1.59105
$554$	−7.91946	−0.336466
$555$	−11.8058	−0.501126
$556$	−5.33765	−0.226367
$557$	−32.4389	−1.37448	−0.687241	−	0.726430i	$-0.741178\pi$
$557$	−32.4389	−1.37448	−0.687241	+	0.726430i	$0.741178\pi$
$558$	3.45409	0.146223
$559$	−0.990490	−0.0418933
$560$	−4.22080	−0.178362
$561$	3.17198	0.133921
$562$	15.4693	0.652532
$563$	−19.8704	−0.837437	−0.418718	−	0.908116i	$-0.637521\pi$
$563$	−19.8704	−0.837437	−0.418718	+	0.908116i	$0.637521\pi$
$564$	5.15604	0.217108
$565$	−9.90909	−0.416878
$566$	30.3044	1.27379
$567$	46.0908	1.93563
$568$	15.6832	0.658051
$569$	−19.7541	−0.828136	−0.414068	−	0.910246i	$-0.635893\pi$
$569$	−19.7541	−0.828136	−0.414068	+	0.910246i	$0.635893\pi$
$570$	2.46280	0.103155
$571$	−44.2621	−1.85231	−0.926156	−	0.377140i	$-0.876908\pi$
$571$	−44.2621	−1.85231	−0.926156	+	0.377140i	$0.876908\pi$
$572$	−0.0534454	−0.00223466
$573$	18.6283	0.778209
$574$	43.9079	1.83268
$575$	8.77835	0.366082
$576$	0.925466	0.0385611
$577$	−46.1403	−1.92085	−0.960423	−	0.278544i	$-0.910148\pi$
$577$	−46.1403	−1.92085	−0.960423	+	0.278544i	$0.910148\pi$
$578$	−7.88693	−0.328053
$579$	−19.8530	−0.825062
$580$	1.18004	0.0489986
$581$	45.7681	1.89878
$582$	−18.2222	−0.755333
$583$	3.21930	0.133330
$584$	−15.2789	−0.632244
$585$	−0.0932647	−0.00385602
$586$	11.2466	0.464593
$587$	−10.3313	−0.426419	−0.213210	−	0.977006i	$-0.568392\pi$
$587$	−10.3313	−0.426419	−0.213210	+	0.977006i	$0.568392\pi$
$588$	−21.4279	−0.883672
$589$	−4.63935	−0.191161
$590$	−11.8884	−0.489436
$591$	7.69939	0.316711
$592$	5.95866	0.244899
$593$	−14.6996	−0.603640	−0.301820	−	0.953365i	$-0.597594\pi$
$593$	−14.6996	−0.603640	−0.301820	+	0.953365i	$0.597594\pi$
$594$	2.17981	0.0894388
$595$	12.7417	0.522359
$596$	2.94235	0.120523
$597$	25.5544	1.04587
$598$	−0.884647	−0.0361759
$599$	−16.2736	−0.664922	−0.332461	−	0.943117i	$-0.607879\pi$
$599$	−16.2736	−0.664922	−0.332461	+	0.943117i	$0.607879\pi$
$600$	−1.98128	−0.0808854
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−41.4847	−1.69079
$603$	−6.72766	−0.273971
$604$	10.3478	0.421047
$605$	−10.7187	−0.435779
$606$	1.37982	0.0560513
$607$	8.74412	0.354913	0.177456	−	0.984129i	$-0.443213\pi$
$607$	8.74412	0.354913	0.177456	+	0.984129i	$0.443213\pi$
$608$	−1.24304	−0.0504117
$609$	9.86822	0.399880
$610$	−9.97802	−0.403998
$611$	0.262257	0.0106098
$612$	−2.79378	−0.112932
$613$	30.3287	1.22497	0.612483	−	0.790484i	$-0.290171\pi$
$613$	30.3287	1.22497	0.612483	+	0.790484i	$0.290171\pi$
$614$	−13.5263	−0.545877
$615$	20.6107	0.831105
$616$	−2.23845	−0.0901899
$617$	21.6643	0.872172	0.436086	−	0.899905i	$-0.356364\pi$
$617$	21.6643	0.872172	0.436086	+	0.899905i	$0.356364\pi$
$618$	0.216478	0.00870801
$619$	−8.68872	−0.349229	−0.174615	−	0.984637i	$-0.555868\pi$
$619$	−8.68872	−0.349229	−0.174615	+	0.984637i	$0.555868\pi$
$620$	3.73228	0.149892
$621$	36.0810	1.44788
$622$	−19.4234	−0.778806
$623$	51.9249	2.08033
$624$	0.199665	0.00799301
$625$	1.00000	0.0400000
$626$	−24.8018	−0.991281
$627$	1.30612	0.0521613
$628$	10.7164	0.427632
$629$	−17.9879	−0.717225
$630$	−3.90621	−0.155627
$631$	20.6798	0.823248	0.411624	−	0.911354i	$-0.364962\pi$
$631$	20.6798	0.823248	0.411624	+	0.911354i	$0.364962\pi$
$632$	−8.86443	−0.352608
$633$	36.5412	1.45238
$634$	−18.3022	−0.726874
$635$	10.1010	0.400848
$636$	−12.0269	−0.476897
$637$	−1.08991	−0.0431838
$638$	0.625822	0.0247765
$639$	14.5142	0.574174
$640$	1.00000	0.0395285
$641$	−0.615269	−0.0243016	−0.0121508	−	0.999926i	$-0.503868\pi$
$641$	−0.615269	−0.0243016	−0.0121508	+	0.999926i	$0.503868\pi$
$642$	23.2305	0.916834
$643$	−8.45656	−0.333494	−0.166747	−	0.986000i	$-0.553326\pi$
$643$	−8.45656	−0.333494	−0.166747	+	0.986000i	$0.553326\pi$
$644$	−37.0517	−1.46004
$645$	−19.4733	−0.766759
$646$	3.75246	0.147638
$647$	33.2576	1.30749	0.653745	−	0.756715i	$-0.273197\pi$
$647$	33.2576	1.30749	0.653745	+	0.756715i	$0.273197\pi$
$648$	−10.9199	−0.428975
$649$	−6.30485	−0.247487
$650$	−0.100776	−0.00395276
$651$	31.2115	1.22328
$652$	−0.373966	−0.0146457
$653$	−28.3789	−1.11055	−0.555277	−	0.831666i	$-0.687388\pi$
$653$	−28.3789	−1.11055	−0.555277	+	0.831666i	$0.687388\pi$
$654$	14.9819	0.585839
$655$	15.1653	0.592556
$656$	−10.4027	−0.406159
$657$	−14.1401	−0.551656
$658$	10.9841	0.428206
$659$	−33.8124	−1.31714	−0.658572	−	0.752518i	$-0.728839\pi$
$659$	−33.8124	−1.31714	−0.658572	+	0.752518i	$0.728839\pi$
$660$	−1.05075	−0.0409003
$661$	−34.6501	−1.34773	−0.673866	−	0.738853i	$-0.735368\pi$
$661$	−34.6501	−1.34773	−0.673866	+	0.738853i	$0.735368\pi$
$662$	−8.11182	−0.315275
$663$	−0.602747	−0.0234087
$664$	−10.8435	−0.420808
$665$	5.24661	0.203455
$666$	5.51453	0.213684
$667$	10.3588	0.401095
$668$	−5.64002	−0.218219
$669$	−43.5985	−1.68562
$670$	−7.26948	−0.280845
$671$	−5.29173	−0.204285
$672$	8.36259	0.322594
$673$	33.9018	1.30682	0.653409	−	0.757005i	$-0.273338\pi$
$673$	33.9018	1.30682	0.653409	+	0.757005i	$0.273338\pi$
$674$	−5.34930	−0.206047
$675$	4.11023	0.158203
$676$	−12.9898	−0.499609
$677$	−8.49652	−0.326548	−0.163274	−	0.986581i	$-0.552205\pi$
$677$	−8.49652	−0.326548	−0.163274	+	0.986581i	$0.552205\pi$
$678$	19.6327	0.753988
$679$	−38.8195	−1.48975
$680$	−3.01879	−0.115765
$681$	29.0264	1.11229
$682$	1.97937	0.0757940
$683$	42.8371	1.63912	0.819558	−	0.572996i	$-0.194219\pi$
$683$	42.8371	1.63912	0.819558	+	0.572996i	$0.194219\pi$
$684$	−1.15039	−0.0439861
$685$	6.86463	0.262284
$686$	−16.1031	−0.614821
$687$	34.3479	1.31045
$688$	9.82863	0.374713
$689$	−0.611737	−0.0233053
$690$	−17.3924	−0.662116
$691$	24.9210	0.948040	0.474020	−	0.880514i	$-0.342802\pi$
$691$	24.9210	0.948040	0.474020	+	0.880514i	$0.342802\pi$
$692$	−7.93500	−0.301643
$693$	−2.07161	−0.0786941
$694$	−5.05294	−0.191807
$695$	−5.33765	−0.202469
$696$	−2.33799	−0.0886214
$697$	31.4036	1.18950
$698$	−21.1201	−0.799409
$699$	−23.7848	−0.899624
$700$	−4.22080	−0.159531
$701$	12.9906	0.490647	0.245323	−	0.969441i	$-0.421106\pi$
$701$	12.9906	0.490647	0.245323	+	0.969441i	$0.421106\pi$
$702$	−0.414213	−0.0156334
$703$	−7.40682	−0.279353
$704$	0.530338	0.0199879
$705$	5.15604	0.194188
$706$	18.4134	0.692996
$707$	2.93949	0.110551
$708$	23.5542	0.885220
$709$	35.0433	1.31608	0.658039	−	0.752984i	$-0.271386\pi$
$709$	35.0433	1.31608	0.658039	+	0.752984i	$0.271386\pi$
$710$	15.6832	0.588578
$711$	−8.20372	−0.307664
$712$	−12.3021	−0.461042
$713$	32.7632	1.22699
$714$	−25.2449	−0.944765
$715$	−0.0534454	−0.00199874
$716$	−20.4271	−0.763395
$717$	−54.4884	−2.03491
$718$	−2.92099	−0.109010
$719$	−16.5186	−0.616039	−0.308019	−	0.951380i	$-0.599666\pi$
$719$	−16.5186	−0.616039	−0.308019	+	0.951380i	$0.599666\pi$
$720$	0.925466	0.0344901
$721$	0.461172	0.0171749
$722$	−17.4549	−0.649603
$723$	26.2358	0.975720
$724$	−16.1239	−0.599238
$725$	1.18004	0.0438257
$726$	21.2368	0.788172
$727$	32.1976	1.19414	0.597072	−	0.802187i	$-0.296331\pi$
$727$	32.1976	1.19414	0.597072	+	0.802187i	$0.296331\pi$
$728$	0.425356	0.0157647
$729$	14.3245	0.530538
$730$	−15.2789	−0.565496
$731$	−29.6705	−1.09740
$732$	19.7692	0.730692
$733$	−48.4593	−1.78989	−0.894943	−	0.446181i	$-0.852784\pi$
$733$	−48.4593	−1.78989	−0.894943	+	0.446181i	$0.852784\pi$
$734$	13.5315	0.499457
$735$	−21.4279	−0.790380
$736$	8.77835	0.323574
$737$	−3.85529	−0.142011
$738$	−9.62738	−0.354389
$739$	29.2098	1.07450	0.537250	−	0.843423i	$-0.319463\pi$
$739$	29.2098	1.07450	0.537250	+	0.843423i	$0.319463\pi$
$740$	5.95866	0.219045
$741$	−0.248191	−0.00911752
$742$	−25.6214	−0.940591
$743$	−32.6377	−1.19736	−0.598681	−	0.800988i	$-0.704308\pi$
$743$	−32.6377	−1.19736	−0.598681	+	0.800988i	$0.704308\pi$
$744$	−7.39468	−0.271102
$745$	2.94235	0.107799
$746$	11.7727	0.431031
$747$	−10.0352	−0.367170
$748$	−1.60098	−0.0585375
$749$	49.4889	1.80829
$750$	−1.98128	−0.0723461
$751$	38.0341	1.38789	0.693943	−	0.720030i	$-0.255872\pi$
$751$	38.0341	1.38789	0.693943	+	0.720030i	$0.255872\pi$
$752$	−2.60238	−0.0948990
$753$	6.03356	0.219875
$754$	−0.118920	−0.00433081
$755$	10.3478	0.376596
$756$	−17.3485	−0.630958
$757$	−13.0065	−0.472730	−0.236365	−	0.971664i	$-0.575956\pi$
$757$	−13.0065	−0.472730	−0.236365	+	0.971664i	$0.575956\pi$
$758$	16.1520	0.586668
$759$	−9.22383	−0.334804
$760$	−1.24304	−0.0450896
$761$	−11.1052	−0.402564	−0.201282	−	0.979533i	$-0.564511\pi$
$761$	−11.1052	−0.402564	−0.201282	+	0.979533i	$0.564511\pi$
$762$	−20.0130	−0.724994
$763$	31.9166	1.15546
$764$	−9.40217	−0.340158
$765$	−2.79378	−0.101009
$766$	5.99445	0.216588
$767$	1.19806	0.0432595
$768$	−1.98128	−0.0714932
$769$	38.0655	1.37268	0.686338	−	0.727283i	$-0.259217\pi$
$769$	38.0655	1.37268	0.686338	+	0.727283i	$0.259217\pi$
$770$	−2.23845	−0.0806683
$771$	35.5992	1.28208
$772$	10.0203	0.360638
$773$	13.3518	0.480231	0.240115	−	0.970744i	$-0.422815\pi$
$773$	13.3518	0.480231	0.240115	+	0.970744i	$0.422815\pi$
$774$	9.09606	0.326951
$775$	3.73228	0.134067
$776$	9.19718	0.330159
$777$	49.8298	1.78763
$778$	7.07504	0.253653
$779$	12.9310	0.463300
$780$	0.199665	0.00714917
$781$	8.31738	0.297619
$782$	−26.4999	−0.947636
$783$	4.85025	0.173334
$784$	10.8152	0.386257
$785$	10.7164	0.382486
$786$	−30.0466	−1.07173
$787$	−42.7857	−1.52515	−0.762573	−	0.646903i	$-0.776064\pi$
$787$	−42.7857	−1.52515	−0.762573	+	0.646903i	$0.776064\pi$
$788$	−3.88607	−0.138436
$789$	−0.411668	−0.0146558
$790$	−8.86443	−0.315382
$791$	41.8243	1.48710
$792$	0.490810	0.0174402
$793$	1.00554	0.0357079
$794$	1.12705	0.0399974
$795$	−12.0269	−0.426550
$796$	−12.8979	−0.457155
$797$	25.1817	0.891981	0.445991	−	0.895038i	$-0.352851\pi$
$797$	25.1817	0.891981	0.445991	+	0.895038i	$0.352851\pi$
$798$	−10.3950	−0.367979
$799$	7.85602	0.277926
$800$	1.00000	0.0353553
$801$	−11.3852	−0.402277
$802$	−18.1263	−0.640062
$803$	−8.10296	−0.285947
$804$	14.4029	0.507950
$805$	−37.0517	−1.30590
$806$	−0.376124	−0.0132484
$807$	−64.2140	−2.26044
$808$	−0.696428	−0.0245003
$809$	−40.4736	−1.42298	−0.711488	−	0.702699i	$-0.751978\pi$
$809$	−40.4736	−1.42298	−0.711488	+	0.702699i	$0.751978\pi$
$810$	−10.9199	−0.383687
$811$	31.3771	1.10180	0.550899	−	0.834572i	$-0.314285\pi$
$811$	31.3771	1.10180	0.550899	+	0.834572i	$0.314285\pi$
$812$	−4.98073	−0.174789
$813$	−4.67617	−0.164000
$814$	3.16010	0.110762
$815$	−0.373966	−0.0130995
$816$	5.98106	0.209379
$817$	−12.2173	−0.427430
$818$	−8.94909	−0.312897
$819$	0.393652	0.0137553
$820$	−10.4027	−0.363279
$821$	−42.4491	−1.48148	−0.740742	−	0.671789i	$-0.765526\pi$
$821$	−42.4491	−1.48148	−0.740742	+	0.671789i	$0.765526\pi$
$822$	−13.6007	−0.474380
$823$	−51.7268	−1.80308	−0.901541	−	0.432693i	$-0.857563\pi$
$823$	−51.7268	−1.80308	−0.901541	+	0.432693i	$0.857563\pi$
$824$	−0.109262	−0.00380631
$825$	−1.05075	−0.0365824
$826$	50.1784	1.74593
$827$	−31.4371	−1.09318	−0.546588	−	0.837401i	$-0.684074\pi$
$827$	−31.4371	−1.09318	−0.546588	+	0.837401i	$0.684074\pi$
$828$	8.12406	0.282331
$829$	−18.9051	−0.656601	−0.328300	−	0.944573i	$-0.606476\pi$
$829$	−18.9051	−0.656601	−0.328300	+	0.944573i	$0.606476\pi$
$830$	−10.8435	−0.376382
$831$	15.6907	0.544303
$832$	−0.100776	−0.00349378
$833$	−32.6487	−1.13121
$834$	10.5754	0.366195
$835$	−5.64002	−0.195181
$836$	−0.659229	−0.0227999
$837$	15.3405	0.530246
$838$	18.7687	0.648354
$839$	−3.25070	−0.112227	−0.0561133	−	0.998424i	$-0.517871\pi$
$839$	−3.25070	−0.112227	−0.0561133	+	0.998424i	$0.517871\pi$
$840$	8.36259	0.288537
$841$	−27.6075	−0.951983
$842$	−15.5120	−0.534580
$843$	−30.6490	−1.05561
$844$	−18.4433	−0.634843
$845$	−12.9898	−0.446864
$846$	−2.40841	−0.0828030
$847$	45.2417	1.55452
$848$	6.07027	0.208454
$849$	−60.0416	−2.06062
$850$	−3.01879	−0.103543
$851$	52.3071	1.79307
$852$	−31.0727	−1.06453
$853$	24.1730	0.827668	0.413834	−	0.910352i	$-0.364189\pi$
$853$	24.1730	0.827668	0.413834	+	0.910352i	$0.364189\pi$
$854$	42.1153	1.44115
$855$	−1.15039	−0.0393424
$856$	−11.7250	−0.400752
$857$	39.8298	1.36056	0.680279	−	0.732953i	$-0.261858\pi$
$857$	39.8298	1.36056	0.680279	+	0.732953i	$0.261858\pi$
$858$	0.105890	0.00361503
$859$	−43.0036	−1.46726	−0.733632	−	0.679547i	$-0.762176\pi$
$859$	−43.0036	−1.46726	−0.733632	+	0.679547i	$0.762176\pi$
$860$	9.82863	0.335154
$861$	−86.9938	−2.96474
$862$	6.46497	0.220198
$863$	−7.04963	−0.239972	−0.119986	−	0.992776i	$-0.538285\pi$
$863$	−7.04963	−0.239972	−0.119986	+	0.992776i	$0.538285\pi$
$864$	4.11023	0.139833
$865$	−7.93500	−0.269798
$866$	−20.4238	−0.694030
$867$	15.6262	0.530694
$868$	−15.7532	−0.534699
$869$	−4.70115	−0.159475
$870$	−2.33799	−0.0792654
$871$	0.732589	0.0248228
$872$	−7.56174	−0.256073
$873$	8.51167	0.288076
$874$	−10.9118	−0.369097
$875$	−4.22080	−0.142689
$876$	30.2717	1.02279
$877$	−12.8520	−0.433980	−0.216990	−	0.976174i	$-0.569624\pi$
$877$	−12.8520	−0.433980	−0.216990	+	0.976174i	$0.569624\pi$
$878$	18.6018	0.627781
$879$	−22.2827	−0.751575
$880$	0.530338	0.0178777
$881$	43.2443	1.45694	0.728469	−	0.685079i	$-0.240232\pi$
$881$	43.2443	1.45694	0.728469	+	0.685079i	$0.240232\pi$
$882$	10.0091	0.337023
$883$	−12.6452	−0.425544	−0.212772	−	0.977102i	$-0.568249\pi$
$883$	−12.6452	−0.425544	−0.212772	+	0.977102i	$0.568249\pi$
$884$	0.304221	0.0102321
$885$	23.5542	0.791764
$886$	12.2738	0.412347
$887$	38.0927	1.27903	0.639514	−	0.768780i	$-0.279136\pi$
$887$	38.0927	1.27903	0.639514	+	0.768780i	$0.279136\pi$
$888$	−11.8058	−0.396175
$889$	−42.6345	−1.42992
$890$	−12.3021	−0.412369
$891$	−5.79125	−0.194014
$892$	22.0052	0.736789
$893$	3.23485	0.108250
$894$	−5.82961	−0.194971
$895$	−20.4271	−0.682801
$896$	−4.22080	−0.141007
$897$	1.75273	0.0585220
$898$	−27.2626	−0.909765
$899$	4.40425	0.146890
$900$	0.925466	0.0308489
$901$	−18.3248	−0.610489
$902$	−5.51697	−0.183695
$903$	82.1928	2.73521
$904$	−9.90909	−0.329571
$905$	−16.1239	−0.535975
$906$	−20.5019	−0.681131
$907$	32.2222	1.06992	0.534960	−	0.844877i	$-0.320327\pi$
$907$	32.2222	1.06992	0.534960	+	0.844877i	$0.320327\pi$
$908$	−14.6503	−0.486188
$909$	−0.644521	−0.0213774
$910$	0.425356	0.0141004
$911$	−13.2276	−0.438250	−0.219125	−	0.975697i	$-0.570320\pi$
$911$	−13.2276	−0.438250	−0.219125	+	0.975697i	$0.570320\pi$
$912$	2.46280	0.0815514
$913$	−5.75070	−0.190320
$914$	−19.2314	−0.636118
$915$	19.7692	0.653551
$916$	−17.3362	−0.572805
$917$	−64.0096	−2.11378
$918$	−12.4079	−0.409522
$919$	59.8759	1.97512	0.987561	−	0.157235i	$-0.0502579\pi$
$919$	59.8759	1.97512	0.987561	+	0.157235i	$0.0502579\pi$
$920$	8.77835	0.289414
$921$	26.7994	0.883069
$922$	11.5699	0.381033
$923$	−1.58049	−0.0520223
$924$	4.43500	0.145901
$925$	5.95866	0.195919
$926$	−0.00174954	−5.74936e−5 0
$927$	−0.101118	−0.00332115
$928$	1.18004	0.0387368
$929$	1.14314	0.0375051	0.0187526	−	0.999824i	$-0.494031\pi$
$929$	1.14314	0.0375051	0.0187526	+	0.999824i	$0.494031\pi$
$930$	−7.39468	−0.242481
$931$	−13.4437	−0.440598
$932$	12.0048	0.393230
$933$	38.4831	1.25988
$934$	−32.4183	−1.06076
$935$	−1.60098	−0.0523576
$936$	−0.0932647	−0.00304845
$937$	−7.60417	−0.248418	−0.124209	−	0.992256i	$-0.539639\pi$
$937$	−7.60417	−0.248418	−0.124209	+	0.992256i	$0.539639\pi$
$938$	30.6831	1.00184
$939$	49.1394	1.60360
$940$	−2.60238	−0.0848803
$941$	35.7215	1.16449	0.582244	−	0.813014i	$-0.302175\pi$
$941$	35.7215	1.16449	0.582244	+	0.813014i	$0.302175\pi$
$942$	−21.2322	−0.691783
$943$	−91.3189	−2.97375
$944$	−11.8884	−0.386933
$945$	−17.3485	−0.564346
$946$	5.21250	0.169473
$947$	−20.1569	−0.655013	−0.327506	−	0.944849i	$-0.606208\pi$
$947$	−20.1569	−0.655013	−0.327506	+	0.944849i	$0.606208\pi$
$948$	17.5629	0.570416
$949$	1.53974	0.0499821
$950$	−1.24304	−0.0403294
$951$	36.2618	1.17587
$952$	12.7417	0.412961
$953$	46.2528	1.49827	0.749137	−	0.662415i	$-0.230468\pi$
$953$	46.2528	1.49827	0.749137	+	0.662415i	$0.230468\pi$
$954$	5.61783	0.181884
$955$	−9.40217	−0.304247
$956$	27.5016	0.889467
$957$	−1.23993	−0.0400812
$958$	6.16045	0.199035
$959$	−28.9742	−0.935627
$960$	−1.98128	−0.0639455
$961$	−17.0701	−0.550649
$962$	−0.600489	−0.0193606
$963$	−10.8511	−0.349671
$964$	−13.2419	−0.426491
$965$	10.0203	0.322565
$966$	73.4097	2.36192
$967$	−20.8826	−0.671538	−0.335769	−	0.941944i	$-0.608996\pi$
$967$	−20.8826	−0.671538	−0.335769	+	0.941944i	$0.608996\pi$
$968$	−10.7187	−0.344513
$969$	−7.43466	−0.238836
$970$	9.19718	0.295304
$971$	−43.3521	−1.39123	−0.695617	−	0.718413i	$-0.744869\pi$
$971$	−43.3521	−1.39123	−0.695617	+	0.718413i	$0.744869\pi$
$972$	9.30470	0.298448
$973$	22.5292	0.722252
$974$	−24.9602	−0.799776
$975$	0.199665	0.00639441
$976$	−9.97802	−0.319389
$977$	−40.2151	−1.28659	−0.643297	−	0.765617i	$-0.722434\pi$
$977$	−40.2151	−1.28659	−0.643297	+	0.765617i	$0.722434\pi$
$978$	0.740932	0.0236924
$979$	−6.52430	−0.208517
$980$	10.8152	0.345478
$981$	−6.99813	−0.223433
$982$	15.8961	0.507266
$983$	−13.3486	−0.425754	−0.212877	−	0.977079i	$-0.568283\pi$
$983$	−13.3486	−0.425754	−0.212877	+	0.977079i	$0.568283\pi$
$984$	20.6107	0.657046
$985$	−3.88607	−0.123821
$986$	−3.56230	−0.113447
$987$	−21.7626	−0.692712
$988$	0.125268	0.00398531
$989$	86.2792	2.74352
$990$	0.490810	0.0155990
$991$	−35.3546	−1.12308	−0.561538	−	0.827451i	$-0.689790\pi$
$991$	−35.3546	−1.12308	−0.561538	+	0.827451i	$0.689790\pi$
$992$	3.73228	0.118500
$993$	16.0718	0.510023
$994$	−66.1955	−2.09959
$995$	−12.8979	−0.408892
$996$	21.4839	0.680744
$997$	46.6368	1.47700	0.738501	−	0.674253i	$-0.235534\pi$
$997$	46.6368	1.47700	0.738501	+	0.674253i	$0.235534\pi$
$998$	−3.29567	−0.104323
$999$	24.4914	0.774875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.98128 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.98128 q^{6} -4.22080 q^{7} +1.00000 q^{8} +0.925466 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.98128 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.98128 q^{6} -4.22080 q^{7} +1.00000 q^{8} +0.925466 q^{9} +1.00000 q^{10} +0.530338 q^{11} -1.98128 q^{12} -0.100776 q^{13} -4.22080 q^{14} -1.98128 q^{15} +1.00000 q^{16} -3.01879 q^{17} +0.925466 q^{18} -1.24304 q^{19} +1.00000 q^{20} +8.36259 q^{21} +0.530338 q^{22} +8.77835 q^{23} -1.98128 q^{24} +1.00000 q^{25} -0.100776 q^{26} +4.11023 q^{27} -4.22080 q^{28} +1.18004 q^{29} -1.98128 q^{30} +3.73228 q^{31} +1.00000 q^{32} -1.05075 q^{33} -3.01879 q^{34} -4.22080 q^{35} +0.925466 q^{36} +5.95866 q^{37} -1.24304 q^{38} +0.199665 q^{39} +1.00000 q^{40} -10.4027 q^{41} +8.36259 q^{42} +9.82863 q^{43} +0.530338 q^{44} +0.925466 q^{45} +8.77835 q^{46} -2.60238 q^{47} -1.98128 q^{48} +10.8152 q^{49} +1.00000 q^{50} +5.98106 q^{51} -0.100776 q^{52} +6.07027 q^{53} +4.11023 q^{54} +0.530338 q^{55} -4.22080 q^{56} +2.46280 q^{57} +1.18004 q^{58} -11.8884 q^{59} -1.98128 q^{60} -9.97802 q^{61} +3.73228 q^{62} -3.90621 q^{63} +1.00000 q^{64} -0.100776 q^{65} -1.05075 q^{66} -7.26948 q^{67} -3.01879 q^{68} -17.3924 q^{69} -4.22080 q^{70} +15.6832 q^{71} +0.925466 q^{72} -15.2789 q^{73} +5.95866 q^{74} -1.98128 q^{75} -1.24304 q^{76} -2.23845 q^{77} +0.199665 q^{78} -8.86443 q^{79} +1.00000 q^{80} -10.9199 q^{81} -10.4027 q^{82} -10.8435 q^{83} +8.36259 q^{84} -3.01879 q^{85} +9.82863 q^{86} -2.33799 q^{87} +0.530338 q^{88} -12.3021 q^{89} +0.925466 q^{90} +0.425356 q^{91} +8.77835 q^{92} -7.39468 q^{93} -2.60238 q^{94} -1.24304 q^{95} -1.98128 q^{96} +9.19718 q^{97} +10.8152 q^{98} +0.490810 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 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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