LMFDB - Embedded newform 3311.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3311,2,Mod(1,3311)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3311, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3311.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3311 = 7 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3311.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:	$26.4384681092$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 17 x^{16} + 82 x^{15} + 94 x^{14} - 662 x^{13} - 99 x^{12} + 2694 x^{11} - 849 x^{10} + \cdots + 45 $ x^18 - 4x^17 - 17x^16 + 82x^15 + 94x^14 - 662x^13 - 99x^12 + 2694x^11 - 849x^10 - 5900x^9 + 3348x^8 + 6849x^7 - 4930x^6 - 3791x^5 + 3179x^4 + 727x^3 - 788x^2 + 5*x + 45
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.495079$ of defining polynomial
Character	$\chi$	$=$	3311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.495079 q^{2} +1.43449 q^{3} -1.75490 q^{4} +2.92094 q^{5} -0.710186 q^{6} -1.00000 q^{7} +1.85897 q^{8} -0.942241 q^{9} +O(q^{10})$	\(q-0.495079 q^{2} +1.43449 q^{3} -1.75490 q^{4} +2.92094 q^{5} -0.710186 q^{6} -1.00000 q^{7} +1.85897 q^{8} -0.942241 q^{9} -1.44610 q^{10} -1.00000 q^{11} -2.51738 q^{12} -4.48934 q^{13} +0.495079 q^{14} +4.19006 q^{15} +2.58946 q^{16} +4.95877 q^{17} +0.466484 q^{18} -2.23624 q^{19} -5.12595 q^{20} -1.43449 q^{21} +0.495079 q^{22} -5.09352 q^{23} +2.66667 q^{24} +3.53189 q^{25} +2.22258 q^{26} -5.65510 q^{27} +1.75490 q^{28} +3.69702 q^{29} -2.07441 q^{30} -0.428156 q^{31} -4.99993 q^{32} -1.43449 q^{33} -2.45499 q^{34} -2.92094 q^{35} +1.65353 q^{36} -4.72967 q^{37} +1.10712 q^{38} -6.43991 q^{39} +5.42994 q^{40} -2.83629 q^{41} +0.710186 q^{42} -1.00000 q^{43} +1.75490 q^{44} -2.75223 q^{45} +2.52170 q^{46} -0.0467874 q^{47} +3.71455 q^{48} +1.00000 q^{49} -1.74856 q^{50} +7.11331 q^{51} +7.87832 q^{52} +1.04364 q^{53} +2.79972 q^{54} -2.92094 q^{55} -1.85897 q^{56} -3.20787 q^{57} -1.83032 q^{58} -4.32914 q^{59} -7.35312 q^{60} -8.64639 q^{61} +0.211971 q^{62} +0.942241 q^{63} -2.70355 q^{64} -13.1131 q^{65} +0.710186 q^{66} +7.58631 q^{67} -8.70213 q^{68} -7.30660 q^{69} +1.44610 q^{70} +2.25654 q^{71} -1.75160 q^{72} -5.58703 q^{73} +2.34156 q^{74} +5.06645 q^{75} +3.92438 q^{76} +1.00000 q^{77} +3.18826 q^{78} -2.02957 q^{79} +7.56364 q^{80} -5.28546 q^{81} +1.40419 q^{82} -13.6598 q^{83} +2.51738 q^{84} +14.4843 q^{85} +0.495079 q^{86} +5.30334 q^{87} -1.85897 q^{88} +4.00422 q^{89} +1.36257 q^{90} +4.48934 q^{91} +8.93861 q^{92} -0.614185 q^{93} +0.0231635 q^{94} -6.53193 q^{95} -7.17234 q^{96} -13.0640 q^{97} -0.495079 q^{98} +0.942241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} + 3 q^{3} + 14 q^{4} + 4 q^{5} - 4 q^{6} - 18 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 + 3 * q^3 + 14 * q^4 + 4 * q^5 - 4 * q^6 - 18 * q^7 - 6 * q^8 + 3 * q^9	\( 18 q - 4 q^{2} + 3 q^{3} + 14 q^{4} + 4 q^{5} - 4 q^{6} - 18 q^{7} - 6 q^{8} + 3 q^{9} - 8 q^{10} - 18 q^{11} + 6 q^{12} - 16 q^{13} + 4 q^{14} + 8 q^{15} + 6 q^{16} - 9 q^{17} - 17 q^{18} - 8 q^{19} + 7 q^{20} - 3 q^{21} + 4 q^{22} + 20 q^{23} - 4 q^{24} - 8 q^{25} + 9 q^{26} + 12 q^{27} - 14 q^{28} - 30 q^{29} - 28 q^{30} - 9 q^{31} - 16 q^{32} - 3 q^{33} - 4 q^{34} - 4 q^{35} - 18 q^{36} + 13 q^{37} - 6 q^{38} - 20 q^{39} - 21 q^{40} - 17 q^{41} + 4 q^{42} - 18 q^{43} - 14 q^{44} - 4 q^{45} + 7 q^{46} - 10 q^{47} + 15 q^{48} + 18 q^{49} - 3 q^{50} - 30 q^{51} - 64 q^{52} + 2 q^{53} - 9 q^{54} - 4 q^{55} + 6 q^{56} - 22 q^{57} - 21 q^{58} + 17 q^{59} - 27 q^{60} - 34 q^{61} - 10 q^{62} - 3 q^{63} + 8 q^{64} - 31 q^{65} + 4 q^{66} + 12 q^{67} - 29 q^{68} - 28 q^{69} + 8 q^{70} + 11 q^{71} - 18 q^{72} - 51 q^{73} - 67 q^{74} - 30 q^{75} - 63 q^{76} + 18 q^{77} + 6 q^{78} - 35 q^{79} + 7 q^{80} - 34 q^{81} - 10 q^{82} - 25 q^{83} - 6 q^{84} + 4 q^{85} + 4 q^{86} - 39 q^{87} + 6 q^{88} - 20 q^{89} - 17 q^{90} + 16 q^{91} + 45 q^{92} - 12 q^{93} - 15 q^{94} - 33 q^{95} - 29 q^{96} - 26 q^{97} - 4 q^{98} - 3 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 + 3 * q^3 + 14 * q^4 + 4 * q^5 - 4 * q^6 - 18 * q^7 - 6 * q^8 + 3 * q^9 - 8 * q^10 - 18 * q^11 + 6 * q^12 - 16 * q^13 + 4 * q^14 + 8 * q^15 + 6 * q^16 - 9 * q^17 - 17 * q^18 - 8 * q^19 + 7 * q^20 - 3 * q^21 + 4 * q^22 + 20 * q^23 - 4 * q^24 - 8 * q^25 + 9 * q^26 + 12 * q^27 - 14 * q^28 - 30 * q^29 - 28 * q^30 - 9 * q^31 - 16 * q^32 - 3 * q^33 - 4 * q^34 - 4 * q^35 - 18 * q^36 + 13 * q^37 - 6 * q^38 - 20 * q^39 - 21 * q^40 - 17 * q^41 + 4 * q^42 - 18 * q^43 - 14 * q^44 - 4 * q^45 + 7 * q^46 - 10 * q^47 + 15 * q^48 + 18 * q^49 - 3 * q^50 - 30 * q^51 - 64 * q^52 + 2 * q^53 - 9 * q^54 - 4 * q^55 + 6 * q^56 - 22 * q^57 - 21 * q^58 + 17 * q^59 - 27 * q^60 - 34 * q^61 - 10 * q^62 - 3 * q^63 + 8 * q^64 - 31 * q^65 + 4 * q^66 + 12 * q^67 - 29 * q^68 - 28 * q^69 + 8 * q^70 + 11 * q^71 - 18 * q^72 - 51 * q^73 - 67 * q^74 - 30 * q^75 - 63 * q^76 + 18 * q^77 + 6 * q^78 - 35 * q^79 + 7 * q^80 - 34 * q^81 - 10 * q^82 - 25 * q^83 - 6 * q^84 + 4 * q^85 + 4 * q^86 - 39 * q^87 + 6 * q^88 - 20 * q^89 - 17 * q^90 + 16 * q^91 + 45 * q^92 - 12 * q^93 - 15 * q^94 - 33 * q^95 - 29 * q^96 - 26 * q^97 - 4 * q^98 - 3 * 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 $

$2$	−0.495079	−0.350074	−0.175037	−	0.984562i	$-0.556004\pi$
$2$	−0.495079	−0.350074	−0.175037	+	0.984562i	$0.556004\pi$
$3$	1.43449	0.828203	0.414101	−	0.910231i	$-0.364096\pi$
$3$	1.43449	0.828203	0.414101	+	0.910231i	$0.364096\pi$
$4$	−1.75490	−0.877448
$5$	2.92094	1.30628	0.653142	−	0.757236i	$-0.273450\pi$
$5$	2.92094	1.30628	0.653142	+	0.757236i	$0.273450\pi$
$6$	−0.710186	−0.289932
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.85897	0.657245
$9$	−0.942241	−0.314080
$10$	−1.44610	−0.457296
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.51738	−0.726705
$13$	−4.48934	−1.24512	−0.622559	−	0.782573i	$-0.713907\pi$
$13$	−4.48934	−1.24512	−0.622559	+	0.782573i	$0.713907\pi$
$14$	0.495079	0.132315
$15$	4.19006	1.08187
$16$	2.58946	0.647364
$17$	4.95877	1.20268	0.601340	−	0.798994i	$-0.294634\pi$
$17$	4.95877	1.20268	0.601340	+	0.798994i	$0.294634\pi$
$18$	0.466484	0.109951
$19$	−2.23624	−0.513030	−0.256515	−	0.966540i	$-0.582574\pi$
$19$	−2.23624	−0.513030	−0.256515	+	0.966540i	$0.582574\pi$
$20$	−5.12595	−1.14620
$21$	−1.43449	−0.313031
$22$	0.495079	0.105551
$23$	−5.09352	−1.06207	−0.531036	−	0.847349i	$-0.678197\pi$
$23$	−5.09352	−1.06207	−0.531036	+	0.847349i	$0.678197\pi$
$24$	2.66667	0.544333
$25$	3.53189	0.706378
$26$	2.22258	0.435883
$27$	−5.65510	−1.08832
$28$	1.75490	0.331644
$29$	3.69702	0.686520	0.343260	−	0.939241i	$-0.388469\pi$
$29$	3.69702	0.686520	0.343260	+	0.939241i	$0.388469\pi$
$30$	−2.07441	−0.378734
$31$	−0.428156	−0.0768990	−0.0384495	−	0.999261i	$-0.512242\pi$
$31$	−0.428156	−0.0768990	−0.0384495	+	0.999261i	$0.512242\pi$
$32$	−4.99993	−0.883871
$33$	−1.43449	−0.249713
$34$	−2.45499	−0.421026
$35$	−2.92094	−0.493729
$36$	1.65353	0.275589
$37$	−4.72967	−0.777552	−0.388776	−	0.921332i	$-0.627102\pi$
$37$	−4.72967	−0.777552	−0.388776	+	0.921332i	$0.627102\pi$
$38$	1.10712	0.179598
$39$	−6.43991	−1.03121
$40$	5.42994	0.858549
$41$	−2.83629	−0.442954	−0.221477	−	0.975166i	$-0.571088\pi$
$41$	−2.83629	−0.442954	−0.221477	+	0.975166i	$0.571088\pi$
$42$	0.710186	0.109584
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.75490	0.264561
$45$	−2.75223	−0.410278
$46$	2.52170	0.371804
$47$	−0.0467874	−0.00682465	−0.00341233	−	0.999994i	$-0.501086\pi$
$47$	−0.0467874	−0.00682465	−0.00341233	+	0.999994i	$0.501086\pi$
$48$	3.71455	0.536149
$49$	1.00000	0.142857
$50$	−1.74856	−0.247284
$51$	7.11331	0.996062
$52$	7.87832	1.09253
$53$	1.04364	0.143355	0.0716773	−	0.997428i	$-0.477165\pi$
$53$	1.04364	0.143355	0.0716773	+	0.997428i	$0.477165\pi$
$54$	2.79972	0.380994
$55$	−2.92094	−0.393859
$56$	−1.85897	−0.248415
$57$	−3.20787	−0.424893
$58$	−1.83032	−0.240333
$59$	−4.32914	−0.563606	−0.281803	−	0.959472i	$-0.590933\pi$
$59$	−4.32914	−0.563606	−0.281803	+	0.959472i	$0.590933\pi$
$60$	−7.35312	−0.949283
$61$	−8.64639	−1.10706	−0.553528	−	0.832830i	$-0.686719\pi$
$61$	−8.64639	−1.10706	−0.553528	+	0.832830i	$0.686719\pi$
$62$	0.211971	0.0269203
$63$	0.942241	0.118711
$64$	−2.70355	−0.337944
$65$	−13.1131	−1.62648
$66$	0.710186	0.0874178
$67$	7.58631	0.926815	0.463407	−	0.886145i	$-0.346627\pi$
$67$	7.58631	0.926815	0.463407	+	0.886145i	$0.346627\pi$
$68$	−8.70213	−1.05529
$69$	−7.30660	−0.879612
$70$	1.44610	0.172842
$71$	2.25654	0.267802	0.133901	−	0.990995i	$-0.457250\pi$
$71$	2.25654	0.267802	0.133901	+	0.990995i	$0.457250\pi$
$72$	−1.75160	−0.206428
$73$	−5.58703	−0.653912	−0.326956	−	0.945040i	$-0.606023\pi$
$73$	−5.58703	−0.653912	−0.326956	+	0.945040i	$0.606023\pi$
$74$	2.34156	0.272201
$75$	5.06645	0.585024
$76$	3.92438	0.450157
$77$	1.00000	0.113961
$78$	3.18826	0.361000
$79$	−2.02957	−0.228345	−0.114172	−	0.993461i	$-0.536422\pi$
$79$	−2.02957	−0.228345	−0.114172	+	0.993461i	$0.536422\pi$
$80$	7.56364	0.845641
$81$	−5.28546	−0.587273
$82$	1.40419	0.155067
$83$	−13.6598	−1.49936	−0.749678	−	0.661803i	$-0.769792\pi$
$83$	−13.6598	−1.49936	−0.749678	+	0.661803i	$0.769792\pi$
$84$	2.51738	0.274669
$85$	14.4843	1.57104
$86$	0.495079	0.0533858
$87$	5.30334	0.568577
$88$	−1.85897	−0.198167
$89$	4.00422	0.424446	0.212223	−	0.977221i	$-0.431930\pi$
$89$	4.00422	0.424446	0.212223	+	0.977221i	$0.431930\pi$
$90$	1.36257	0.143628
$91$	4.48934	0.470610
$92$	8.93861	0.931914
$93$	−0.614185	−0.0636880
$94$	0.0231635	0.00238913
$95$	−6.53193	−0.670162
$96$	−7.17234	−0.732024
$97$	−13.0640	−1.32644	−0.663222	−	0.748423i	$-0.730811\pi$
$97$	−13.0640	−1.32644	−0.663222	+	0.748423i	$0.730811\pi$
$98$	−0.495079	−0.0500105
$99$	0.942241	0.0946987
$100$	−6.19810	−0.619810
$101$	−19.9961	−1.98969	−0.994844	−	0.101419i	$-0.967662\pi$
$101$	−19.9961	−1.98969	−0.994844	+	0.101419i	$0.967662\pi$
$102$	−3.52165	−0.348695
$103$	8.84137	0.871167	0.435583	−	0.900148i	$-0.356542\pi$
$103$	8.84137	0.871167	0.435583	+	0.900148i	$0.356542\pi$
$104$	−8.34555	−0.818348
$105$	−4.19006	−0.408908
$106$	−0.516683	−0.0501847
$107$	2.35377	0.227548	0.113774	−	0.993507i	$-0.463706\pi$
$107$	2.35377	0.227548	0.113774	+	0.993507i	$0.463706\pi$
$108$	9.92412	0.954949
$109$	−12.8302	−1.22891	−0.614457	−	0.788950i	$-0.710625\pi$
$109$	−12.8302	−1.22891	−0.614457	+	0.788950i	$0.710625\pi$
$110$	1.44610	0.137880
$111$	−6.78465	−0.643971
$112$	−2.58946	−0.244681
$113$	−9.43289	−0.887372	−0.443686	−	0.896182i	$-0.646329\pi$
$113$	−9.43289	−0.887372	−0.443686	+	0.896182i	$0.646329\pi$
$114$	1.58815	0.148744
$115$	−14.8779	−1.38737
$116$	−6.48789	−0.602385
$117$	4.23004	0.391067
$118$	2.14327	0.197304
$119$	−4.95877	−0.454570
$120$	7.78919	0.711053
$121$	1.00000	0.0909091
$122$	4.28065	0.387552
$123$	−4.06863	−0.366856
$124$	0.751369	0.0674749
$125$	−4.28827	−0.383554
$126$	−0.466484	−0.0415577
$127$	10.1861	0.903869	0.451934	−	0.892051i	$-0.350734\pi$
$127$	10.1861	0.903869	0.451934	+	0.892051i	$0.350734\pi$
$128$	11.3383	1.00218
$129$	−1.43449	−0.126300
$130$	6.49201	0.569387
$131$	−4.22453	−0.369099	−0.184549	−	0.982823i	$-0.559083\pi$
$131$	−4.22453	−0.369099	−0.184549	+	0.982823i	$0.559083\pi$
$132$	2.51738	0.219110
$133$	2.23624	0.193907
$134$	−3.75582	−0.324454
$135$	−16.5182	−1.42166
$136$	9.21822	0.790455
$137$	−5.51223	−0.470941	−0.235471	−	0.971881i	$-0.575663\pi$
$137$	−5.51223	−0.470941	−0.235471	+	0.971881i	$0.575663\pi$
$138$	3.61735	0.307929
$139$	16.6315	1.41066	0.705332	−	0.708877i	$-0.250798\pi$
$139$	16.6315	1.41066	0.705332	+	0.708877i	$0.250798\pi$
$140$	5.12595	0.433222
$141$	−0.0671161	−0.00565219
$142$	−1.11716	−0.0937503
$143$	4.48934	0.375417
$144$	−2.43989	−0.203324
$145$	10.7988	0.896789
$146$	2.76602	0.228918
$147$	1.43449	0.118315
$148$	8.30007	0.682262
$149$	4.40212	0.360636	0.180318	−	0.983608i	$-0.442287\pi$
$149$	4.40212	0.360636	0.180318	+	0.983608i	$0.442287\pi$
$150$	−2.50830	−0.204802
$151$	3.95004	0.321450	0.160725	−	0.986999i	$-0.448617\pi$
$151$	3.95004	0.321450	0.160725	+	0.986999i	$0.448617\pi$
$152$	−4.15711	−0.337186
$153$	−4.67236	−0.377738
$154$	−0.495079	−0.0398946
$155$	−1.25062	−0.100452
$156$	11.3014	0.904834
$157$	13.7226	1.09518	0.547592	−	0.836745i	$-0.315545\pi$
$157$	13.7226	1.09518	0.547592	+	0.836745i	$0.315545\pi$
$158$	1.00480	0.0799376
$159$	1.49709	0.118727
$160$	−14.6045	−1.15459
$161$	5.09352	0.401426
$162$	2.61672	0.205589
$163$	18.1525	1.42181	0.710907	−	0.703287i	$-0.248285\pi$
$163$	18.1525	1.42181	0.710907	+	0.703287i	$0.248285\pi$
$164$	4.97739	0.388669
$165$	−4.19006	−0.326195
$166$	6.76267	0.524885
$167$	19.6838	1.52318	0.761588	−	0.648061i	$-0.224420\pi$
$167$	19.6838	1.52318	0.761588	+	0.648061i	$0.224420\pi$
$168$	−2.66667	−0.205738
$169$	7.15415	0.550319
$170$	−7.17086	−0.549980
$171$	2.10708	0.161132
$172$	1.75490	0.133810
$173$	−17.2705	−1.31305	−0.656525	−	0.754304i	$-0.727974\pi$
$173$	−17.2705	−1.31305	−0.656525	+	0.754304i	$0.727974\pi$
$174$	−2.62557	−0.199044
$175$	−3.53189	−0.266986
$176$	−2.58946	−0.195188
$177$	−6.21011	−0.466780
$178$	−1.98241	−0.148588
$179$	5.44362	0.406875	0.203437	−	0.979088i	$-0.434789\pi$
$179$	5.44362	0.406875	0.203437	+	0.979088i	$0.434789\pi$
$180$	4.82988	0.359998
$181$	−1.79406	−0.133352	−0.0666758	−	0.997775i	$-0.521239\pi$
$181$	−1.79406	−0.133352	−0.0666758	+	0.997775i	$0.521239\pi$
$182$	−2.22258	−0.164748
$183$	−12.4032	−0.916867
$184$	−9.46871	−0.698043
$185$	−13.8151	−1.01570
$186$	0.304070	0.0222955
$187$	−4.95877	−0.362621
$188$	0.0821071	0.00598828
$189$	5.65510	0.411348
$190$	3.23382	0.234606
$191$	4.36193	0.315618	0.157809	−	0.987470i	$-0.449557\pi$
$191$	4.36193	0.315618	0.157809	+	0.987470i	$0.449557\pi$
$192$	−3.87822	−0.279886
$193$	−10.7847	−0.776297	−0.388148	−	0.921597i	$-0.626885\pi$
$193$	−10.7847	−0.776297	−0.388148	+	0.921597i	$0.626885\pi$
$194$	6.46769	0.464353
$195$	−18.8106	−1.34705
$196$	−1.75490	−0.125350
$197$	−10.7496	−0.765877	−0.382939	−	0.923774i	$-0.625088\pi$
$197$	−10.7496	−0.765877	−0.382939	+	0.923774i	$0.625088\pi$
$198$	−0.466484	−0.0331515
$199$	−6.11001	−0.433127	−0.216564	−	0.976269i	$-0.569485\pi$
$199$	−6.11001	−0.433127	−0.216564	+	0.976269i	$0.569485\pi$
$200$	6.56568	0.464263
$201$	10.8825	0.767590
$202$	9.89966	0.696538
$203$	−3.69702	−0.259480
$204$	−12.4831	−0.873993
$205$	−8.28463	−0.578623
$206$	−4.37718	−0.304973
$207$	4.79932	0.333576
$208$	−11.6249	−0.806045
$209$	2.23624	0.154684
$210$	2.07441	0.143148
$211$	−13.6724	−0.941248	−0.470624	−	0.882334i	$-0.655971\pi$
$211$	−13.6724	−0.941248	−0.470624	+	0.882334i	$0.655971\pi$
$212$	−1.83148	−0.125786
$213$	3.23698	0.221794
$214$	−1.16530	−0.0796584
$215$	−2.92094	−0.199206
$216$	−10.5127	−0.715297
$217$	0.428156	0.0290651
$218$	6.35199	0.430211
$219$	−8.01453	−0.541572
$220$	5.12595	0.345591
$221$	−22.2616	−1.49748
$222$	3.35894	0.225437
$223$	19.0826	1.27787	0.638934	−	0.769261i	$-0.279376\pi$
$223$	19.0826	1.27787	0.638934	+	0.769261i	$0.279376\pi$
$224$	4.99993	0.334072
$225$	−3.32789	−0.221859
$226$	4.67003	0.310646
$227$	0.570032	0.0378343	0.0189172	−	0.999821i	$-0.493978\pi$
$227$	0.570032	0.0378343	0.0189172	+	0.999821i	$0.493978\pi$
$228$	5.62948	0.372821
$229$	19.3021	1.27552	0.637761	−	0.770234i	$-0.279861\pi$
$229$	19.3021	1.27552	0.637761	+	0.770234i	$0.279861\pi$
$230$	7.36572	0.485681
$231$	1.43449	0.0943825
$232$	6.87265	0.451212
$233$	−10.7139	−0.701889	−0.350944	−	0.936396i	$-0.614139\pi$
$233$	−10.7139	−0.701889	−0.350944	+	0.936396i	$0.614139\pi$
$234$	−2.09420	−0.136902
$235$	−0.136663	−0.00891493
$236$	7.59720	0.494536
$237$	−2.91140	−0.189116
$238$	2.45499	0.159133
$239$	−23.0963	−1.49397	−0.746987	−	0.664838i	$-0.768500\pi$
$239$	−23.0963	−1.49397	−0.746987	+	0.664838i	$0.768500\pi$
$240$	10.8500	0.700362
$241$	−11.7939	−0.759712	−0.379856	−	0.925046i	$-0.624026\pi$
$241$	−11.7939	−0.759712	−0.379856	+	0.925046i	$0.624026\pi$
$242$	−0.495079	−0.0318249
$243$	9.38337	0.601943
$244$	15.1735	0.971385
$245$	2.92094	0.186612
$246$	2.01429	0.128427
$247$	10.0393	0.638783
$248$	−0.795929	−0.0505415
$249$	−19.5948	−1.24177
$250$	2.12303	0.134272
$251$	14.4643	0.912978	0.456489	−	0.889729i	$-0.349107\pi$
$251$	14.4643	0.912978	0.456489	+	0.889729i	$0.349107\pi$
$252$	−1.65353	−0.104163
$253$	5.09352	0.320227
$254$	−5.04292	−0.316421
$255$	20.7775	1.30114
$256$	−0.206265	−0.0128916
$257$	−1.08939	−0.0679543	−0.0339771	−	0.999423i	$-0.510817\pi$
$257$	−1.08939	−0.0679543	−0.0339771	+	0.999423i	$0.510817\pi$
$258$	0.710186	0.0442142
$259$	4.72967	0.293887
$260$	23.0121	1.42715
$261$	−3.48348	−0.215622
$262$	2.09148	0.129212
$263$	−25.2785	−1.55874	−0.779368	−	0.626566i	$-0.784460\pi$
$263$	−25.2785	−1.55874	−0.779368	+	0.626566i	$0.784460\pi$
$264$	−2.66667	−0.164122
$265$	3.04840	0.187262
$266$	−1.10712	−0.0678818
$267$	5.74401	0.351528
$268$	−13.3132	−0.813232
$269$	−16.6141	−1.01298	−0.506490	−	0.862246i	$-0.669057\pi$
$269$	−16.6141	−1.01298	−0.506490	+	0.862246i	$0.669057\pi$
$270$	8.17782	0.497686
$271$	−8.49295	−0.515910	−0.257955	−	0.966157i	$-0.583049\pi$
$271$	−8.49295	−0.515910	−0.257955	+	0.966157i	$0.583049\pi$
$272$	12.8405	0.778571
$273$	6.43991	0.389761
$274$	2.72899	0.164864
$275$	−3.53189	−0.212981
$276$	12.8223	0.771814
$277$	0.277616	0.0166804	0.00834018	−	0.999965i	$-0.497345\pi$
$277$	0.277616	0.0166804	0.00834018	+	0.999965i	$0.497345\pi$
$278$	−8.23390	−0.493837
$279$	0.403426	0.0241525
$280$	−5.42994	−0.324501
$281$	−26.5961	−1.58659	−0.793294	−	0.608839i	$-0.791636\pi$
$281$	−26.5961	−1.58659	−0.793294	+	0.608839i	$0.791636\pi$
$282$	0.0332278	0.00197869
$283$	−25.2043	−1.49824	−0.749119	−	0.662436i	$-0.769523\pi$
$283$	−25.2043	−1.49824	−0.749119	+	0.662436i	$0.769523\pi$
$284$	−3.95999	−0.234982
$285$	−9.36999	−0.555030
$286$	−2.22258	−0.131424
$287$	2.83629	0.167421
$288$	4.71113	0.277606
$289$	7.58943	0.446437
$290$	−5.34625	−0.313942
$291$	−18.7401	−1.09856
$292$	9.80466	0.573774
$293$	12.7442	0.744523	0.372262	−	0.928128i	$-0.378582\pi$
$293$	12.7442	0.744523	0.372262	+	0.928128i	$0.378582\pi$
$294$	−0.710186	−0.0414189
$295$	−12.6452	−0.736230
$296$	−8.79231	−0.511043
$297$	5.65510	0.328142
$298$	−2.17940	−0.126249
$299$	22.8665	1.32241
$300$	−8.89110	−0.513328
$301$	1.00000	0.0576390
$302$	−1.95558	−0.112531
$303$	−28.6842	−1.64786
$304$	−5.79066	−0.332117
$305$	−25.2556	−1.44613
$306$	2.31319	0.132236
$307$	−25.6800	−1.46563	−0.732817	−	0.680425i	$-0.761795\pi$
$307$	−25.6800	−1.46563	−0.732817	+	0.680425i	$0.761795\pi$
$308$	−1.75490	−0.0999945
$309$	12.6829	0.721503
$310$	0.619154	0.0351656
$311$	5.57197	0.315958	0.157979	−	0.987443i	$-0.449502\pi$
$311$	5.57197	0.315958	0.157979	+	0.987443i	$0.449502\pi$
$312$	−11.9716	−0.677758
$313$	21.5090	1.21576	0.607881	−	0.794028i	$-0.292020\pi$
$313$	21.5090	1.21576	0.607881	+	0.794028i	$0.292020\pi$
$314$	−6.79378	−0.383395
$315$	2.75223	0.155070
$316$	3.56169	0.200361
$317$	17.6535	0.991518	0.495759	−	0.868460i	$-0.334890\pi$
$317$	17.6535	0.991518	0.495759	+	0.868460i	$0.334890\pi$
$318$	−0.741176	−0.0415631
$319$	−3.69702	−0.206993
$320$	−7.89691	−0.441451
$321$	3.37646	0.188455
$322$	−2.52170	−0.140529
$323$	−11.0890	−0.617010
$324$	9.27544	0.515302
$325$	−15.8558	−0.879523
$326$	−8.98692	−0.497739
$327$	−18.4048	−1.01779
$328$	−5.27258	−0.291129
$329$	0.0467874	0.00257948
$330$	2.07441	0.114192
$331$	−17.8393	−0.980534	−0.490267	−	0.871572i	$-0.663101\pi$
$331$	−17.8393	−0.980534	−0.490267	+	0.871572i	$0.663101\pi$
$332$	23.9715	1.31561
$333$	4.45648	0.244214
$334$	−9.74503	−0.533224
$335$	22.1591	1.21068
$336$	−3.71455	−0.202645
$337$	6.38525	0.347827	0.173914	−	0.984761i	$-0.444359\pi$
$337$	6.38525	0.347827	0.173914	+	0.984761i	$0.444359\pi$
$338$	−3.54187	−0.192652
$339$	−13.5314	−0.734924
$340$	−25.4184	−1.37851
$341$	0.428156	0.0231859
$342$	−1.04317	−0.0564083
$343$	−1.00000	−0.0539949
$344$	−1.85897	−0.100229
$345$	−21.3421	−1.14902
$346$	8.55025	0.459665
$347$	−9.52683	−0.511427	−0.255714	−	0.966753i	$-0.582310\pi$
$347$	−9.52683	−0.511427	−0.255714	+	0.966753i	$0.582310\pi$
$348$	−9.30681	−0.498897
$349$	9.52404	0.509810	0.254905	−	0.966966i	$-0.417956\pi$
$349$	9.52404	0.509810	0.254905	+	0.966966i	$0.417956\pi$
$350$	1.74856	0.0934647
$351$	25.3877	1.35509
$352$	4.99993	0.266497
$353$	26.1564	1.39216	0.696082	−	0.717963i	$-0.254925\pi$
$353$	26.1564	1.39216	0.696082	+	0.717963i	$0.254925\pi$
$354$	3.07450	0.163408
$355$	6.59121	0.349825
$356$	−7.02699	−0.372430
$357$	−7.11331	−0.376476
$358$	−2.69502	−0.142436
$359$	−12.2709	−0.647631	−0.323816	−	0.946120i	$-0.604966\pi$
$359$	−12.2709	−0.647631	−0.323816	+	0.946120i	$0.604966\pi$
$360$	−5.11631	−0.269653
$361$	−13.9992	−0.736801
$362$	0.888203	0.0466829
$363$	1.43449	0.0752912
$364$	−7.87832	−0.412936
$365$	−16.3194	−0.854195
$366$	6.14054	0.320971
$367$	−19.9506	−1.04141	−0.520706	−	0.853736i	$-0.674331\pi$
$367$	−19.9506	−1.04141	−0.520706	+	0.853736i	$0.674331\pi$
$368$	−13.1895	−0.687548
$369$	2.67247	0.139123
$370$	6.83955	0.355571
$371$	−1.04364	−0.0541829
$372$	1.07783	0.0558829
$373$	20.4006	1.05630	0.528151	−	0.849151i	$-0.322886\pi$
$373$	20.4006	1.05630	0.528151	+	0.849151i	$0.322886\pi$
$374$	2.45499	0.126944
$375$	−6.15147	−0.317661
$376$	−0.0869765	−0.00448547
$377$	−16.5972	−0.854798
$378$	−2.79972	−0.144002
$379$	27.7093	1.42333	0.711666	−	0.702518i	$-0.247941\pi$
$379$	27.7093	1.42333	0.711666	+	0.702518i	$0.247941\pi$
$380$	11.4629	0.588033
$381$	14.6118	0.748586
$382$	−2.15950	−0.110490
$383$	−3.66520	−0.187283	−0.0936414	−	0.995606i	$-0.529851\pi$
$383$	−3.66520	−0.187283	−0.0936414	+	0.995606i	$0.529851\pi$
$384$	16.2647	0.830005
$385$	2.92094	0.148865
$386$	5.33926	0.271761
$387$	0.942241	0.0478968
$388$	22.9259	1.16389
$389$	3.72014	0.188618	0.0943092	−	0.995543i	$-0.469936\pi$
$389$	3.72014	0.188618	0.0943092	+	0.995543i	$0.469936\pi$
$390$	9.31272	0.471568
$391$	−25.2576	−1.27733
$392$	1.85897	0.0938922
$393$	−6.06004	−0.305689
$394$	5.32190	0.268114
$395$	−5.92826	−0.298283
$396$	−1.65353	−0.0830933
$397$	−20.4464	−1.02617	−0.513087	−	0.858336i	$-0.671498\pi$
$397$	−20.4464	−1.02617	−0.513087	+	0.858336i	$0.671498\pi$
$398$	3.02494	0.151626
$399$	3.20787	0.160594
$400$	9.14567	0.457283
$401$	6.40405	0.319803	0.159902	−	0.987133i	$-0.448882\pi$
$401$	6.40405	0.319803	0.159902	+	0.987133i	$0.448882\pi$
$402$	−5.38769	−0.268713
$403$	1.92214	0.0957484
$404$	35.0911	1.74585
$405$	−15.4385	−0.767146
$406$	1.83032	0.0908371
$407$	4.72967	0.234441
$408$	13.2234	0.654657
$409$	32.1617	1.59029	0.795147	−	0.606416i	$-0.207394\pi$
$409$	32.1617	1.59029	0.795147	+	0.606416i	$0.207394\pi$
$410$	4.10155	0.202561
$411$	−7.90723	−0.390035
$412$	−15.5157	−0.764404
$413$	4.32914	0.213023
$414$	−2.37605	−0.116776
$415$	−39.8994	−1.95858
$416$	22.4464	1.10052
$417$	23.8577	1.16832
$418$	−1.10712	−0.0541509
$419$	−4.43320	−0.216576	−0.108288	−	0.994120i	$-0.534537\pi$
$419$	−4.43320	−0.216576	−0.108288	+	0.994120i	$0.534537\pi$
$420$	7.35312	0.358795
$421$	30.0475	1.46442	0.732212	−	0.681077i	$-0.238488\pi$
$421$	30.0475	1.46442	0.732212	+	0.681077i	$0.238488\pi$
$422$	6.76893	0.329506
$423$	0.0440850	0.00214349
$424$	1.94009	0.0942192
$425$	17.5138	0.849546
$426$	−1.60256	−0.0776443
$427$	8.64639	0.418428
$428$	−4.13062	−0.199661
$429$	6.43991	0.310922
$430$	1.44610	0.0697369
$431$	6.45599	0.310974	0.155487	−	0.987838i	$-0.450305\pi$
$431$	6.45599	0.310974	0.155487	+	0.987838i	$0.450305\pi$
$432$	−14.6436	−0.704542
$433$	−38.0581	−1.82896	−0.914478	−	0.404635i	$-0.867398\pi$
$433$	−38.0581	−1.82896	−0.914478	+	0.404635i	$0.867398\pi$
$434$	−0.211971	−0.0101749
$435$	15.4907	0.742723
$436$	22.5158	1.07831
$437$	11.3904	0.544875
$438$	3.96783	0.189590
$439$	36.8905	1.76069	0.880343	−	0.474338i	$-0.157313\pi$
$439$	36.8905	1.76069	0.880343	+	0.474338i	$0.157313\pi$
$440$	−5.42994	−0.258862
$441$	−0.942241	−0.0448686
$442$	11.0213	0.524228
$443$	−8.03526	−0.381766	−0.190883	−	0.981613i	$-0.561135\pi$
$443$	−8.03526	−0.381766	−0.190883	+	0.981613i	$0.561135\pi$
$444$	11.9064	0.565051
$445$	11.6961	0.554447
$446$	−9.44742	−0.447348
$447$	6.31479	0.298679
$448$	2.70355	0.127731
$449$	−41.4725	−1.95721	−0.978604	−	0.205751i	$-0.934036\pi$
$449$	−41.4725	−1.95721	−0.978604	+	0.205751i	$0.934036\pi$
$450$	1.64757	0.0776671
$451$	2.83629	0.133556
$452$	16.5537	0.778623
$453$	5.66629	0.266226
$454$	−0.282211	−0.0132448
$455$	13.1131	0.614751
$456$	−5.96333	−0.279259
$457$	12.1457	0.568152	0.284076	−	0.958802i	$-0.408313\pi$
$457$	12.1457	0.568152	0.284076	+	0.958802i	$0.408313\pi$
$458$	−9.55609	−0.446527
$459$	−28.0424	−1.30891
$460$	26.1091	1.21734
$461$	1.80151	0.0839049	0.0419525	−	0.999120i	$-0.486642\pi$
$461$	1.80151	0.0839049	0.0419525	+	0.999120i	$0.486642\pi$
$462$	−0.710186	−0.0330408
$463$	−12.3379	−0.573392	−0.286696	−	0.958022i	$-0.592557\pi$
$463$	−12.3379	−0.573392	−0.286696	+	0.958022i	$0.592557\pi$
$464$	9.57327	0.444428
$465$	−1.79400	−0.0831946
$466$	5.30421	0.245713
$467$	12.5544	0.580951	0.290475	−	0.956882i	$-0.406187\pi$
$467$	12.5544	0.580951	0.290475	+	0.956882i	$0.406187\pi$
$468$	−7.42328	−0.343141
$469$	−7.58631	−0.350303
$470$	0.0676591	0.00312088
$471$	19.6849	0.907034
$472$	−8.04775	−0.370428
$473$	1.00000	0.0459800
$474$	1.44137	0.0662045
$475$	−7.89816	−0.362393
$476$	8.70213	0.398862
$477$	−0.983357	−0.0450248
$478$	11.4345	0.523001
$479$	9.57624	0.437550	0.218775	−	0.975775i	$-0.429794\pi$
$479$	9.57624	0.437550	0.218775	+	0.975775i	$0.429794\pi$
$480$	−20.9500	−0.956231
$481$	21.2331	0.968144
$482$	5.83891	0.265955
$483$	7.30660	0.332462
$484$	−1.75490	−0.0797680
$485$	−38.1590	−1.73271
$486$	−4.64551	−0.210725
$487$	5.70286	0.258421	0.129211	−	0.991617i	$-0.458756\pi$
$487$	5.70286	0.258421	0.129211	+	0.991617i	$0.458756\pi$
$488$	−16.0734	−0.727608
$489$	26.0396	1.17755
$490$	−1.44610	−0.0653280
$491$	28.4706	1.28486	0.642430	−	0.766344i	$-0.277926\pi$
$491$	28.4706	1.28486	0.642430	+	0.766344i	$0.277926\pi$
$492$	7.14002	0.321897
$493$	18.3327	0.825663
$494$	−4.97023	−0.223621
$495$	2.75223	0.123703
$496$	−1.10869	−0.0497817
$497$	−2.25654	−0.101219
$498$	9.70098	0.434711
$499$	1.62066	0.0725507	0.0362753	−	0.999342i	$-0.488451\pi$
$499$	1.62066	0.0725507	0.0362753	+	0.999342i	$0.488451\pi$
$500$	7.52547	0.336549
$501$	28.2362	1.26150
$502$	−7.16097	−0.319610
$503$	−14.1662	−0.631641	−0.315821	−	0.948819i	$-0.602280\pi$
$503$	−14.1662	−0.631641	−0.315821	+	0.948819i	$0.602280\pi$
$504$	1.75160	0.0780224
$505$	−58.4074	−2.59910
$506$	−2.52170	−0.112103
$507$	10.2626	0.455776
$508$	−17.8755	−0.793098
$509$	26.1384	1.15856	0.579281	−	0.815128i	$-0.303333\pi$
$509$	26.1384	1.15856	0.579281	+	0.815128i	$0.303333\pi$
$510$	−10.2865	−0.455495
$511$	5.58703	0.247156
$512$	−22.5745	−0.997663
$513$	12.6462	0.558343
$514$	0.539334	0.0237890
$515$	25.8251	1.13799
$516$	2.51738	0.110821
$517$	0.0467874	0.00205771
$518$	−2.34156	−0.102882
$519$	−24.7743	−1.08747
$520$	−24.3768	−1.06900
$521$	24.1248	1.05693	0.528464	−	0.848956i	$-0.322768\pi$
$521$	24.1248	1.05693	0.528464	+	0.848956i	$0.322768\pi$
$522$	1.72460	0.0754837
$523$	5.46720	0.239064	0.119532	−	0.992830i	$-0.461861\pi$
$523$	5.46720	0.239064	0.119532	+	0.992830i	$0.461861\pi$
$524$	7.41361	0.323865
$525$	−5.06645	−0.221118
$526$	12.5148	0.545673
$527$	−2.12313	−0.0924849
$528$	−3.71455	−0.161655
$529$	2.94397	0.127999
$530$	−1.50920	−0.0655555
$531$	4.07909	0.177018
$532$	−3.92438	−0.170143
$533$	12.7331	0.551530
$534$	−2.84374	−0.123061
$535$	6.87522	0.297242
$536$	14.1027	0.609145
$537$	7.80881	0.336975
$538$	8.22530	0.354618
$539$	−1.00000	−0.0430730
$540$	28.9878	1.24743
$541$	1.18740	0.0510505	0.0255252	−	0.999674i	$-0.491874\pi$
$541$	1.18740	0.0510505	0.0255252	+	0.999674i	$0.491874\pi$
$542$	4.20468	0.180606
$543$	−2.57356	−0.110442
$544$	−24.7935	−1.06301
$545$	−37.4764	−1.60531
$546$	−3.18826	−0.136445
$547$	−12.6914	−0.542647	−0.271323	−	0.962488i	$-0.587461\pi$
$547$	−12.6914	−0.542647	−0.271323	+	0.962488i	$0.587461\pi$
$548$	9.67339	0.413227
$549$	8.14698	0.347705
$550$	1.74856	0.0745590
$551$	−8.26744	−0.352205
$552$	−13.5828	−0.578121
$553$	2.02957	0.0863062
$554$	−0.137442	−0.00583936
$555$	−19.8176	−0.841209
$556$	−29.1865	−1.23779
$557$	−5.27390	−0.223462	−0.111731	−	0.993738i	$-0.535640\pi$
$557$	−5.27390	−0.223462	−0.111731	+	0.993738i	$0.535640\pi$
$558$	−0.199728	−0.00845515
$559$	4.48934	0.189879
$560$	−7.56364	−0.319622
$561$	−7.11331	−0.300324
$562$	13.1672	0.555423
$563$	30.4343	1.28265	0.641326	−	0.767268i	$-0.278385\pi$
$563$	30.4343	1.28265	0.641326	+	0.767268i	$0.278385\pi$
$564$	0.117782	0.00495951
$565$	−27.5529	−1.15916
$566$	12.4781	0.524494
$567$	5.28546	0.221968
$568$	4.19483	0.176011
$569$	27.2386	1.14190	0.570950	−	0.820985i	$-0.306575\pi$
$569$	27.2386	1.14190	0.570950	+	0.820985i	$0.306575\pi$
$570$	4.63889	0.194302
$571$	2.59875	0.108754	0.0543771	−	0.998520i	$-0.482683\pi$
$571$	2.59875	0.108754	0.0543771	+	0.998520i	$0.482683\pi$
$572$	−7.87832	−0.329409
$573$	6.25714	0.261396
$574$	−1.40419	−0.0586096
$575$	−17.9897	−0.750224
$576$	2.54740	0.106142
$577$	6.81653	0.283776	0.141888	−	0.989883i	$-0.454683\pi$
$577$	6.81653	0.283776	0.141888	+	0.989883i	$0.454683\pi$
$578$	−3.75737	−0.156286
$579$	−15.4705	−0.642931
$580$	−18.9507	−0.786886
$581$	13.6598	0.566703
$582$	9.27783	0.384578
$583$	−1.04364	−0.0432230
$584$	−10.3861	−0.429781
$585$	12.3557	0.510844
$586$	−6.30938	−0.260638
$587$	13.9247	0.574732	0.287366	−	0.957821i	$-0.407220\pi$
$587$	13.9247	0.574732	0.287366	+	0.957821i	$0.407220\pi$
$588$	−2.51738	−0.103815
$589$	0.957461	0.0394515
$590$	6.26036	0.257735
$591$	−15.4202	−0.634302
$592$	−12.2473	−0.503359
$593$	−25.2277	−1.03598	−0.517989	−	0.855387i	$-0.673319\pi$
$593$	−25.2277	−1.03598	−0.517989	+	0.855387i	$0.673319\pi$
$594$	−2.79972	−0.114874
$595$	−14.4843	−0.593797
$596$	−7.72526	−0.316439
$597$	−8.76474	−0.358717
$598$	−11.3207	−0.462940
$599$	35.3301	1.44355	0.721775	−	0.692128i	$-0.243326\pi$
$599$	35.3301	1.44355	0.721775	+	0.692128i	$0.243326\pi$
$600$	9.41839	0.384504
$601$	−34.0893	−1.39053	−0.695266	−	0.718752i	$-0.744713\pi$
$601$	−34.0893	−1.39053	−0.695266	+	0.718752i	$0.744713\pi$
$602$	−0.495079	−0.0201779
$603$	−7.14812	−0.291094
$604$	−6.93192	−0.282056
$605$	2.92094	0.118753
$606$	14.2010	0.576874
$607$	10.7073	0.434596	0.217298	−	0.976105i	$-0.430276\pi$
$607$	10.7073	0.434596	0.217298	+	0.976105i	$0.430276\pi$
$608$	11.1811	0.453452
$609$	−5.30334	−0.214902
$610$	12.5035	0.506252
$611$	0.210045	0.00849750
$612$	8.19950	0.331445
$613$	36.9142	1.49095	0.745475	−	0.666533i	$-0.232223\pi$
$613$	36.9142	1.49095	0.745475	+	0.666533i	$0.232223\pi$
$614$	12.7136	0.513080
$615$	−11.8842	−0.479218
$616$	1.85897	0.0749001
$617$	27.0187	1.08773	0.543866	−	0.839172i	$-0.316960\pi$
$617$	27.0187	1.08773	0.543866	+	0.839172i	$0.316960\pi$
$618$	−6.27902	−0.252579
$619$	−30.6959	−1.23377	−0.616887	−	0.787052i	$-0.711606\pi$
$619$	−30.6959	−1.23377	−0.616887	+	0.787052i	$0.711606\pi$
$620$	2.19470	0.0881414
$621$	28.8044	1.15588
$622$	−2.75857	−0.110608
$623$	−4.00422	−0.160426
$624$	−16.6759	−0.667568
$625$	−30.1852	−1.20741
$626$	−10.6487	−0.425607
$627$	3.20787	0.128110
$628$	−24.0818	−0.960967
$629$	−23.4533	−0.935146
$630$	−1.36257	−0.0542861
$631$	−14.7369	−0.586669	−0.293334	−	0.956010i	$-0.594765\pi$
$631$	−14.7369	−0.586669	−0.293334	+	0.956010i	$0.594765\pi$
$632$	−3.77292	−0.150079
$633$	−19.6129	−0.779544
$634$	−8.73987	−0.347104
$635$	29.7529	1.18071
$636$	−2.62723	−0.104177
$637$	−4.48934	−0.177874
$638$	1.83032	0.0724630
$639$	−2.12620	−0.0841112
$640$	33.1186	1.30913
$641$	−28.1509	−1.11190	−0.555948	−	0.831217i	$-0.687644\pi$
$641$	−28.1509	−1.11190	−0.555948	+	0.831217i	$0.687644\pi$
$642$	−1.67161	−0.0659733
$643$	2.14100	0.0844328	0.0422164	−	0.999108i	$-0.486558\pi$
$643$	2.14100	0.0844328	0.0422164	+	0.999108i	$0.486558\pi$
$644$	−8.93861	−0.352230
$645$	−4.19006	−0.164983
$646$	5.48995	0.215999
$647$	4.34299	0.170741	0.0853704	−	0.996349i	$-0.472793\pi$
$647$	4.34299	0.170741	0.0853704	+	0.996349i	$0.472793\pi$
$648$	−9.82552	−0.385983
$649$	4.32914	0.169934
$650$	7.84989	0.307898
$651$	0.614185	0.0240718
$652$	−31.8558	−1.24757
$653$	−9.59431	−0.375454	−0.187727	−	0.982221i	$-0.560112\pi$
$653$	−9.59431	−0.375454	−0.187727	+	0.982221i	$0.560112\pi$
$654$	9.11185	0.356302
$655$	−12.3396	−0.482148
$656$	−7.34444	−0.286752
$657$	5.26433	0.205381
$658$	−0.0231635	−0.000903007 0
$659$	−3.91507	−0.152509	−0.0762547	−	0.997088i	$-0.524296\pi$
$659$	−3.91507	−0.152509	−0.0762547	+	0.997088i	$0.524296\pi$
$660$	7.35312	0.286220
$661$	−25.7488	−1.00151	−0.500756	−	0.865588i	$-0.666945\pi$
$661$	−25.7488	−1.00151	−0.500756	+	0.865588i	$0.666945\pi$
$662$	8.83184	0.343259
$663$	−31.9340	−1.24022
$664$	−25.3931	−0.985445
$665$	6.53193	0.253298
$666$	−2.20631	−0.0854928
$667$	−18.8309	−0.729134
$668$	−34.5430	−1.33651
$669$	27.3739	1.05833
$670$	−10.9705	−0.423828
$671$	8.64639	0.333790
$672$	7.17234	0.276679
$673$	−9.29172	−0.358169	−0.179085	−	0.983834i	$-0.557314\pi$
$673$	−9.29172	−0.358169	−0.179085	+	0.983834i	$0.557314\pi$
$674$	−3.16121	−0.121765
$675$	−19.9732	−0.768768
$676$	−12.5548	−0.482877
$677$	−4.06273	−0.156143	−0.0780717	−	0.996948i	$-0.524876\pi$
$677$	−4.06273	−0.156143	−0.0780717	+	0.996948i	$0.524876\pi$
$678$	6.69910	0.257278
$679$	13.0640	0.501348
$680$	26.9258	1.03256
$681$	0.817704	0.0313345
$682$	−0.211971	−0.00811679
$683$	9.21792	0.352714	0.176357	−	0.984326i	$-0.443569\pi$
$683$	9.21792	0.352714	0.176357	+	0.984326i	$0.443569\pi$
$684$	−3.69771	−0.141385
$685$	−16.1009	−0.615183
$686$	0.495079	0.0189022
$687$	27.6887	1.05639
$688$	−2.58946	−0.0987221
$689$	−4.68524	−0.178493
$690$	10.5661	0.402243
$691$	36.3234	1.38181	0.690903	−	0.722947i	$-0.257213\pi$
$691$	36.3234	1.38181	0.690903	+	0.722947i	$0.257213\pi$
$692$	30.3079	1.15213
$693$	−0.942241	−0.0357928
$694$	4.71654	0.179037
$695$	48.5796	1.84273
$696$	9.85875	0.373695
$697$	−14.0645	−0.532731
$698$	−4.71515	−0.178471
$699$	−15.3689	−0.581306
$700$	6.19810	0.234266
$701$	−9.06118	−0.342236	−0.171118	−	0.985251i	$-0.554738\pi$
$701$	−9.06118	−0.342236	−0.171118	+	0.985251i	$0.554738\pi$
$702$	−12.5689	−0.474383
$703$	10.5767	0.398907
$704$	2.70355	0.101894
$705$	−0.196042	−0.00738337
$706$	−12.9495	−0.487360
$707$	19.9961	0.752031
$708$	10.8981	0.409576
$709$	13.4197	0.503989	0.251995	−	0.967729i	$-0.418913\pi$
$709$	13.4197	0.503989	0.251995	+	0.967729i	$0.418913\pi$
$710$	−3.26317	−0.122465
$711$	1.91235	0.0717186
$712$	7.44373	0.278965
$713$	2.18082	0.0816724
$714$	3.52165	0.131794
$715$	13.1131	0.490401
$716$	−9.55298	−0.357012
$717$	−33.1314	−1.23731
$718$	6.07505	0.226719
$719$	39.4590	1.47157	0.735786	−	0.677214i	$-0.236813\pi$
$719$	39.4590	1.47157	0.735786	+	0.677214i	$0.236813\pi$
$720$	−7.12677	−0.265599
$721$	−8.84137	−0.329270
$722$	6.93072	0.257935
$723$	−16.9182	−0.629195
$724$	3.14839	0.117009
$725$	13.0575	0.484942
$726$	−0.710186	−0.0263575
$727$	−31.3293	−1.16194	−0.580969	−	0.813926i	$-0.697326\pi$
$727$	−31.3293	−1.16194	−0.580969	+	0.813926i	$0.697326\pi$
$728$	8.34555	0.309307
$729$	29.3167	1.08580
$730$	8.07938	0.299031
$731$	−4.95877	−0.183407
$732$	21.7663	0.804504
$733$	−1.54646	−0.0571199	−0.0285599	−	0.999592i	$-0.509092\pi$
$733$	−1.54646	−0.0571199	−0.0285599	+	0.999592i	$0.509092\pi$
$734$	9.87712	0.364571
$735$	4.19006	0.154553
$736$	25.4672	0.938735
$737$	−7.58631	−0.279445
$738$	−1.32308	−0.0487033
$739$	39.9189	1.46844	0.734220	−	0.678912i	$-0.237548\pi$
$739$	39.9189	1.46844	0.734220	+	0.678912i	$0.237548\pi$
$740$	24.2440	0.891228
$741$	14.4012	0.529041
$742$	0.516683	0.0189680
$743$	−2.00135	−0.0734225	−0.0367113	−	0.999326i	$-0.511688\pi$
$743$	−2.00135	−0.0734225	−0.0367113	+	0.999326i	$0.511688\pi$
$744$	−1.14175	−0.0418586
$745$	12.8583	0.471092
$746$	−10.0999	−0.369783
$747$	12.8708	0.470918
$748$	8.70213	0.318182
$749$	−2.35377	−0.0860049
$750$	3.04547	0.111205
$751$	25.0082	0.912562	0.456281	−	0.889836i	$-0.349181\pi$
$751$	25.0082	0.912562	0.456281	+	0.889836i	$0.349181\pi$
$752$	−0.121154	−0.00441803
$753$	20.7489	0.756131
$754$	8.21691	0.299242
$755$	11.5378	0.419905
$756$	−9.92412	−0.360937
$757$	26.0774	0.947799	0.473900	−	0.880579i	$-0.342846\pi$
$757$	26.0774	0.947799	0.473900	+	0.880579i	$0.342846\pi$
$758$	−13.7183	−0.498271
$759$	7.30660	0.265213
$760$	−12.1427	−0.440461
$761$	23.4683	0.850725	0.425362	−	0.905023i	$-0.360147\pi$
$761$	23.4683	0.850725	0.425362	+	0.905023i	$0.360147\pi$
$762$	−7.23401	−0.262061
$763$	12.8302	0.464486
$764$	−7.65473	−0.276938
$765$	−13.6477	−0.493433
$766$	1.81456	0.0655628
$767$	19.4350	0.701757
$768$	−0.295885	−0.0106768
$769$	−12.2459	−0.441599	−0.220799	−	0.975319i	$-0.570867\pi$
$769$	−12.2459	−0.441599	−0.220799	+	0.975319i	$0.570867\pi$
$770$	−1.44610	−0.0521137
$771$	−1.56272	−0.0562799
$772$	18.9260	0.681160
$773$	−8.13555	−0.292615	−0.146308	−	0.989239i	$-0.546739\pi$
$773$	−8.13555	−0.292615	−0.146308	+	0.989239i	$0.546739\pi$
$774$	−0.466484	−0.0167674
$775$	−1.51220	−0.0543198
$776$	−24.2855	−0.871799
$777$	6.78465	0.243398
$778$	−1.84176	−0.0660304
$779$	6.34263	0.227248
$780$	33.0106	1.18197
$781$	−2.25654	−0.0807452
$782$	12.5045	0.447161
$783$	−20.9070	−0.747156
$784$	2.58946	0.0924806
$785$	40.0829	1.43062
$786$	3.00020	0.107014
$787$	37.9481	1.35270	0.676352	−	0.736579i	$-0.263560\pi$
$787$	37.9481	1.35270	0.676352	+	0.736579i	$0.263560\pi$
$788$	18.8644	0.672018
$789$	−36.2617	−1.29095
$790$	2.93496	0.104421
$791$	9.43289	0.335395
$792$	1.75160	0.0622403
$793$	38.8166	1.37842
$794$	10.1226	0.359237
$795$	4.37290	0.155091
$796$	10.7224	0.380047
$797$	47.1960	1.67177	0.835884	−	0.548906i	$-0.184955\pi$
$797$	47.1960	1.67177	0.835884	+	0.548906i	$0.184955\pi$
$798$	−1.58815	−0.0562199
$799$	−0.232008	−0.00820786
$800$	−17.6592	−0.624346
$801$	−3.77294	−0.133310
$802$	−3.17051	−0.111955
$803$	5.58703	0.197162
$804$	−19.0976	−0.673521
$805$	14.8779	0.524376
$806$	−0.951609	−0.0335190
$807$	−23.8328	−0.838953
$808$	−37.1722	−1.30771
$809$	−45.7778	−1.60946	−0.804730	−	0.593641i	$-0.797690\pi$
$809$	−45.7778	−1.60946	−0.804730	+	0.593641i	$0.797690\pi$
$810$	7.64328	0.268558
$811$	14.4168	0.506241	0.253121	−	0.967435i	$-0.418543\pi$
$811$	14.4168	0.506241	0.253121	+	0.967435i	$0.418543\pi$
$812$	6.48789	0.227680
$813$	−12.1830	−0.427278
$814$	−2.34156	−0.0820716
$815$	53.0223	1.85729
$816$	18.4196	0.644815
$817$	2.23624	0.0782363
$818$	−15.9226	−0.556720
$819$	−4.23004	−0.147809
$820$	14.5387	0.507712
$821$	23.3126	0.813616	0.406808	−	0.913514i	$-0.366642\pi$
$821$	23.3126	0.813616	0.406808	+	0.913514i	$0.366642\pi$
$822$	3.91470	0.136541
$823$	−10.3566	−0.361009	−0.180505	−	0.983574i	$-0.557773\pi$
$823$	−10.3566	−0.361009	−0.180505	+	0.983574i	$0.557773\pi$
$824$	16.4359	0.572570
$825$	−5.06645	−0.176391
$826$	−2.14327	−0.0745738
$827$	33.7943	1.17514	0.587571	−	0.809173i	$-0.300084\pi$
$827$	33.7943	1.17514	0.587571	+	0.809173i	$0.300084\pi$
$828$	−8.42232	−0.292696
$829$	23.8618	0.828756	0.414378	−	0.910105i	$-0.363999\pi$
$829$	23.8618	0.828756	0.414378	+	0.910105i	$0.363999\pi$
$830$	19.7534	0.685649
$831$	0.398238	0.0138147
$832$	12.1372	0.420780
$833$	4.95877	0.171811
$834$	−11.8114	−0.408997
$835$	57.4951	1.98970
$836$	−3.92438	−0.135727
$837$	2.42126	0.0836911
$838$	2.19479	0.0758176
$839$	2.12651	0.0734153	0.0367077	−	0.999326i	$-0.488313\pi$
$839$	2.12651	0.0734153	0.0367077	+	0.999326i	$0.488313\pi$
$840$	−7.78919	−0.268753
$841$	−15.3320	−0.528691
$842$	−14.8759	−0.512656
$843$	−38.1518	−1.31402
$844$	23.9937	0.825896
$845$	20.8968	0.718873
$846$	−0.0218256	−0.000750379 0
$847$	−1.00000	−0.0343604
$848$	2.70245	0.0928026
$849$	−36.1552	−1.24084
$850$	−8.67073	−0.297404
$851$	24.0907	0.825817
$852$	−5.68056	−0.194613
$853$	−47.4221	−1.62370	−0.811851	−	0.583864i	$-0.801540\pi$
$853$	−47.4221	−1.62370	−0.811851	+	0.583864i	$0.801540\pi$
$854$	−4.28065	−0.146481
$855$	6.15465	0.210485
$856$	4.37559	0.149555
$857$	−12.4687	−0.425922	−0.212961	−	0.977061i	$-0.568311\pi$
$857$	−12.4687	−0.425922	−0.212961	+	0.977061i	$0.568311\pi$
$858$	−3.18826	−0.108846
$859$	−26.4324	−0.901861	−0.450931	−	0.892559i	$-0.648908\pi$
$859$	−26.4324	−0.901861	−0.450931	+	0.892559i	$0.648908\pi$
$860$	5.12595	0.174793
$861$	4.06863	0.138658
$862$	−3.19622	−0.108864
$863$	48.0808	1.63669	0.818345	−	0.574728i	$-0.194892\pi$
$863$	48.0808	1.63669	0.818345	+	0.574728i	$0.194892\pi$
$864$	28.2751	0.961938
$865$	−50.4460	−1.71522
$866$	18.8418	0.640270
$867$	10.8870	0.369740
$868$	−0.751369	−0.0255031
$869$	2.02957	0.0688486
$870$	−7.66913	−0.260008
$871$	−34.0575	−1.15399
$872$	−23.8510	−0.807698
$873$	12.3094	0.416610
$874$	−5.63913	−0.190746
$875$	4.28827	0.144970
$876$	14.0647	0.475201
$877$	7.39280	0.249637	0.124819	−	0.992180i	$-0.460165\pi$
$877$	7.39280	0.249637	0.124819	+	0.992180i	$0.460165\pi$
$878$	−18.2637	−0.616370
$879$	18.2814	0.616616
$880$	−7.56364	−0.254970
$881$	−24.8822	−0.838303	−0.419152	−	0.907916i	$-0.637672\pi$
$881$	−24.8822	−0.838303	−0.419152	+	0.907916i	$0.637672\pi$
$882$	0.466484	0.0157073
$883$	−47.0313	−1.58273	−0.791365	−	0.611343i	$-0.790629\pi$
$883$	−47.0313	−1.58273	−0.791365	+	0.611343i	$0.790629\pi$
$884$	39.0668	1.31396
$885$	−18.1394	−0.609748
$886$	3.97809	0.133646
$887$	18.9268	0.635499	0.317750	−	0.948175i	$-0.397073\pi$
$887$	18.9268	0.635499	0.317750	+	0.948175i	$0.397073\pi$
$888$	−12.6125	−0.423247
$889$	−10.1861	−0.341630
$890$	−5.79049	−0.194098
$891$	5.28546	0.177070
$892$	−33.4881	−1.12126
$893$	0.104628	0.00350125
$894$	−3.12632	−0.104560
$895$	15.9005	0.531494
$896$	−11.3383	−0.378787
$897$	32.8018	1.09522
$898$	20.5322	0.685167
$899$	−1.58290	−0.0527927
$900$	5.84010	0.194670
$901$	5.17516	0.172410
$902$	−1.40419	−0.0467543
$903$	1.43449	0.0477368
$904$	−17.5355	−0.583221
$905$	−5.24035	−0.174195
$906$	−2.80526	−0.0931986
$907$	56.3498	1.87106	0.935532	−	0.353242i	$-0.114921\pi$
$907$	56.3498	1.87106	0.935532	+	0.353242i	$0.114921\pi$
$908$	−1.00035	−0.0331977
$909$	18.8412	0.624922
$910$	−6.49201	−0.215208
$911$	−19.5692	−0.648357	−0.324179	−	0.945996i	$-0.605088\pi$
$911$	−19.5692	−0.648357	−0.324179	+	0.945996i	$0.605088\pi$
$912$	−8.30663	−0.275060
$913$	13.6598	0.452073
$914$	−6.01308	−0.198895
$915$	−36.2289	−1.19769
$916$	−33.8733	−1.11920
$917$	4.22453	0.139506
$918$	13.8832	0.458214
$919$	53.7694	1.77369	0.886845	−	0.462067i	$-0.152892\pi$
$919$	53.7694	1.77369	0.886845	+	0.462067i	$0.152892\pi$
$920$	−27.6575	−0.911842
$921$	−36.8377	−1.21384
$922$	−0.891892	−0.0293729
$923$	−10.1304	−0.333445
$924$	−2.51738	−0.0828157
$925$	−16.7046	−0.549245
$926$	6.10825	0.200729
$927$	−8.33070	−0.273616
$928$	−18.4848	−0.606794
$929$	46.5902	1.52858	0.764288	−	0.644875i	$-0.223091\pi$
$929$	46.5902	1.52858	0.764288	+	0.644875i	$0.223091\pi$
$930$	0.888170	0.0291242
$931$	−2.23624	−0.0732900
$932$	18.8017	0.615871
$933$	7.99294	0.261677
$934$	−6.21545	−0.203376
$935$	−14.4843	−0.473686
$936$	7.86351	0.257027
$937$	−26.4951	−0.865559	−0.432779	−	0.901500i	$-0.642467\pi$
$937$	−26.4951	−0.865559	−0.432779	+	0.901500i	$0.642467\pi$
$938$	3.75582	0.122632
$939$	30.8545	1.00690
$940$	0.239830	0.00782239
$941$	23.2250	0.757115	0.378557	−	0.925578i	$-0.376420\pi$
$941$	23.2250	0.757115	0.378557	+	0.925578i	$0.376420\pi$
$942$	−9.74561	−0.317529
$943$	14.4467	0.470449
$944$	−11.2101	−0.364858
$945$	16.5182	0.537337
$946$	−0.495079	−0.0160964
$947$	37.3548	1.21387	0.606934	−	0.794752i	$-0.292399\pi$
$947$	37.3548	1.21387	0.606934	+	0.794752i	$0.292399\pi$
$948$	5.10921	0.165939
$949$	25.0821	0.814198
$950$	3.91022	0.126864
$951$	25.3237	0.821178
$952$	−9.21822	−0.298764
$953$	−18.6648	−0.604613	−0.302306	−	0.953211i	$-0.597757\pi$
$953$	−18.6648	−0.604613	−0.302306	+	0.953211i	$0.597757\pi$
$954$	0.486840	0.0157620
$955$	12.7409	0.412287
$956$	40.5316	1.31089
$957$	−5.30334	−0.171433
$958$	−4.74100	−0.153175
$959$	5.51223	0.177999
$960$	−11.3280	−0.365611
$961$	−30.8167	−0.994087
$962$	−10.5120	−0.338922
$963$	−2.21782	−0.0714682
$964$	20.6971	0.666608
$965$	−31.5013	−1.01406
$966$	−3.61735	−0.116386
$967$	−9.23689	−0.297038	−0.148519	−	0.988910i	$-0.547451\pi$
$967$	−9.23689	−0.297038	−0.148519	+	0.988910i	$0.547451\pi$
$968$	1.85897	0.0597496
$969$	−15.9071	−0.511009
$970$	18.8917	0.606577
$971$	17.5322	0.562636	0.281318	−	0.959615i	$-0.409228\pi$
$971$	17.5322	0.562636	0.281318	+	0.959615i	$0.409228\pi$
$972$	−16.4668	−0.528174
$973$	−16.6315	−0.533181
$974$	−2.82337	−0.0904665
$975$	−22.7450	−0.728424
$976$	−22.3894	−0.716669
$977$	−13.1812	−0.421705	−0.210853	−	0.977518i	$-0.567624\pi$
$977$	−13.1812	−0.421705	−0.210853	+	0.977518i	$0.567624\pi$
$978$	−12.8916	−0.412229
$979$	−4.00422	−0.127975
$980$	−5.12595	−0.163742
$981$	12.0892	0.385978
$982$	−14.0952	−0.449796
$983$	13.6069	0.433994	0.216997	−	0.976172i	$-0.430374\pi$
$983$	13.6069	0.433994	0.216997	+	0.976172i	$0.430374\pi$
$984$	−7.56346	−0.241114
$985$	−31.3989	−1.00045
$986$	−9.07613	−0.289043
$987$	0.0671161	0.00213633
$988$	−17.6179	−0.560499
$989$	5.09352	0.161965
$990$	−1.36257	−0.0433053
$991$	−35.1041	−1.11512	−0.557559	−	0.830137i	$-0.688262\pi$
$991$	−35.1041	−1.11512	−0.557559	+	0.830137i	$0.688262\pi$
$992$	2.14075	0.0679688
$993$	−25.5902	−0.812081
$994$	1.11716	0.0354343
$995$	−17.8470	−0.565787
$996$	34.3869	1.08959
$997$	15.7419	0.498552	0.249276	−	0.968432i	$-0.419807\pi$
$997$	15.7419	0.498552	0.249276	+	0.968432i	$0.419807\pi$
$998$	−0.802354	−0.0253981
$999$	26.7467	0.846229

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.2.a.f.1.9	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.2.a.f.1.9	✓	18	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:	\( N \)	\(=\)	\( 3311 = 7 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3311.a (trivial)

\(f(q)\)	\(=\)	\(q-0.495079 q^{2} +1.43449 q^{3} -1.75490 q^{4} +2.92094 q^{5} -0.710186 q^{6} -1.00000 q^{7} +1.85897 q^{8} -0.942241 q^{9} +O(q^{10})\)	\(q-0.495079 q^{2} +1.43449 q^{3} -1.75490 q^{4} +2.92094 q^{5} -0.710186 q^{6} -1.00000 q^{7} +1.85897 q^{8} -0.942241 q^{9} -1.44610 q^{10} -1.00000 q^{11} -2.51738 q^{12} -4.48934 q^{13} +0.495079 q^{14} +4.19006 q^{15} +2.58946 q^{16} +4.95877 q^{17} +0.466484 q^{18} -2.23624 q^{19} -5.12595 q^{20} -1.43449 q^{21} +0.495079 q^{22} -5.09352 q^{23} +2.66667 q^{24} +3.53189 q^{25} +2.22258 q^{26} -5.65510 q^{27} +1.75490 q^{28} +3.69702 q^{29} -2.07441 q^{30} -0.428156 q^{31} -4.99993 q^{32} -1.43449 q^{33} -2.45499 q^{34} -2.92094 q^{35} +1.65353 q^{36} -4.72967 q^{37} +1.10712 q^{38} -6.43991 q^{39} +5.42994 q^{40} -2.83629 q^{41} +0.710186 q^{42} -1.00000 q^{43} +1.75490 q^{44} -2.75223 q^{45} +2.52170 q^{46} -0.0467874 q^{47} +3.71455 q^{48} +1.00000 q^{49} -1.74856 q^{50} +7.11331 q^{51} +7.87832 q^{52} +1.04364 q^{53} +2.79972 q^{54} -2.92094 q^{55} -1.85897 q^{56} -3.20787 q^{57} -1.83032 q^{58} -4.32914 q^{59} -7.35312 q^{60} -8.64639 q^{61} +0.211971 q^{62} +0.942241 q^{63} -2.70355 q^{64} -13.1131 q^{65} +0.710186 q^{66} +7.58631 q^{67} -8.70213 q^{68} -7.30660 q^{69} +1.44610 q^{70} +2.25654 q^{71} -1.75160 q^{72} -5.58703 q^{73} +2.34156 q^{74} +5.06645 q^{75} +3.92438 q^{76} +1.00000 q^{77} +3.18826 q^{78} -2.02957 q^{79} +7.56364 q^{80} -5.28546 q^{81} +1.40419 q^{82} -13.6598 q^{83} +2.51738 q^{84} +14.4843 q^{85} +0.495079 q^{86} +5.30334 q^{87} -1.85897 q^{88} +4.00422 q^{89} +1.36257 q^{90} +4.48934 q^{91} +8.93861 q^{92} -0.614185 q^{93} +0.0231635 q^{94} -6.53193 q^{95} -7.17234 q^{96} -13.0640 q^{97} -0.495079 q^{98} +0.942241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} + 3 q^{3} + 14 q^{4} + 4 q^{5} - 4 q^{6} - 18 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 + 3 * q^3 + 14 * q^4 + 4 * q^5 - 4 * q^6 - 18 * q^7 - 6 * q^8 + 3 * q^9	\( 18 q - 4 q^{2} + 3 q^{3} + 14 q^{4} + 4 q^{5} - 4 q^{6} - 18 q^{7} - 6 q^{8} + 3 q^{9} - 8 q^{10} - 18 q^{11} + 6 q^{12} - 16 q^{13} + 4 q^{14} + 8 q^{15} + 6 q^{16} - 9 q^{17} - 17 q^{18} - 8 q^{19} + 7 q^{20} - 3 q^{21} + 4 q^{22} + 20 q^{23} - 4 q^{24} - 8 q^{25} + 9 q^{26} + 12 q^{27} - 14 q^{28} - 30 q^{29} - 28 q^{30} - 9 q^{31} - 16 q^{32} - 3 q^{33} - 4 q^{34} - 4 q^{35} - 18 q^{36} + 13 q^{37} - 6 q^{38} - 20 q^{39} - 21 q^{40} - 17 q^{41} + 4 q^{42} - 18 q^{43} - 14 q^{44} - 4 q^{45} + 7 q^{46} - 10 q^{47} + 15 q^{48} + 18 q^{49} - 3 q^{50} - 30 q^{51} - 64 q^{52} + 2 q^{53} - 9 q^{54} - 4 q^{55} + 6 q^{56} - 22 q^{57} - 21 q^{58} + 17 q^{59} - 27 q^{60} - 34 q^{61} - 10 q^{62} - 3 q^{63} + 8 q^{64} - 31 q^{65} + 4 q^{66} + 12 q^{67} - 29 q^{68} - 28 q^{69} + 8 q^{70} + 11 q^{71} - 18 q^{72} - 51 q^{73} - 67 q^{74} - 30 q^{75} - 63 q^{76} + 18 q^{77} + 6 q^{78} - 35 q^{79} + 7 q^{80} - 34 q^{81} - 10 q^{82} - 25 q^{83} - 6 q^{84} + 4 q^{85} + 4 q^{86} - 39 q^{87} + 6 q^{88} - 20 q^{89} - 17 q^{90} + 16 q^{91} + 45 q^{92} - 12 q^{93} - 15 q^{94} - 33 q^{95} - 29 q^{96} - 26 q^{97} - 4 q^{98} - 3 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 + 3 * q^3 + 14 * q^4 + 4 * q^5 - 4 * q^6 - 18 * q^7 - 6 * q^8 + 3 * q^9 - 8 * q^10 - 18 * q^11 + 6 * q^12 - 16 * q^13 + 4 * q^14 + 8 * q^15 + 6 * q^16 - 9 * q^17 - 17 * q^18 - 8 * q^19 + 7 * q^20 - 3 * q^21 + 4 * q^22 + 20 * q^23 - 4 * q^24 - 8 * q^25 + 9 * q^26 + 12 * q^27 - 14 * q^28 - 30 * q^29 - 28 * q^30 - 9 * q^31 - 16 * q^32 - 3 * q^33 - 4 * q^34 - 4 * q^35 - 18 * q^36 + 13 * q^37 - 6 * q^38 - 20 * q^39 - 21 * q^40 - 17 * q^41 + 4 * q^42 - 18 * q^43 - 14 * q^44 - 4 * q^45 + 7 * q^46 - 10 * q^47 + 15 * q^48 + 18 * q^49 - 3 * q^50 - 30 * q^51 - 64 * q^52 + 2 * q^53 - 9 * q^54 - 4 * q^55 + 6 * q^56 - 22 * q^57 - 21 * q^58 + 17 * q^59 - 27 * q^60 - 34 * q^61 - 10 * q^62 - 3 * q^63 + 8 * q^64 - 31 * q^65 + 4 * q^66 + 12 * q^67 - 29 * q^68 - 28 * q^69 + 8 * q^70 + 11 * q^71 - 18 * q^72 - 51 * q^73 - 67 * q^74 - 30 * q^75 - 63 * q^76 + 18 * q^77 + 6 * q^78 - 35 * q^79 + 7 * q^80 - 34 * q^81 - 10 * q^82 - 25 * q^83 - 6 * q^84 + 4 * q^85 + 4 * q^86 - 39 * q^87 + 6 * q^88 - 20 * q^89 - 17 * q^90 + 16 * q^91 + 45 * q^92 - 12 * q^93 - 15 * q^94 - 33 * q^95 - 29 * q^96 - 26 * q^97 - 4 * q^98 - 3 * q^99

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