LMFDB - Embedded newform 369.2.u.a.118.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, minimal)

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:	no
Analytic conductor:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.3
Character	$\chi$	$=$	369.118
Dual form			369.2.u.a.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61018 + 2.21623i) q^{2} +(-1.70094 + 5.23496i) q^{4} +(1.15434 + 0.375067i) q^{5} +(1.19485 - 0.189245i) q^{7} +(-9.13005 + 2.96653i) q^{8} +O(q^{10})$	\(q+(1.61018 + 2.21623i) q^{2} +(-1.70094 + 5.23496i) q^{4} +(1.15434 + 0.375067i) q^{5} +(1.19485 - 0.189245i) q^{7} +(-9.13005 + 2.96653i) q^{8} +(1.02746 + 3.16221i) q^{10} +(-0.836104 - 0.426016i) q^{11} +(0.289312 - 1.82664i) q^{13} +(2.34333 + 2.34333i) q^{14} +(-12.3693 - 8.98684i) q^{16} +(1.02572 - 2.01309i) q^{17} +(0.815977 + 5.15188i) q^{19} +(-3.92693 + 5.40495i) q^{20} +(-0.402132 - 2.53896i) q^{22} +(5.31348 - 3.86047i) q^{23} +(-2.85326 - 2.07302i) q^{25} +(4.51411 - 2.30005i) q^{26} +(-1.04167 + 6.57687i) q^{28} +(0.689088 + 1.35241i) q^{29} +(-0.515703 - 1.58717i) q^{31} -22.6839i q^{32} +(6.11308 - 0.968216i) q^{34} +(1.45024 + 0.229695i) q^{35} +(1.97146 - 6.06752i) q^{37} +(-10.1039 + 10.1039i) q^{38} -11.6518 q^{40} +(-4.89143 + 4.13206i) q^{41} +(0.714124 + 0.982908i) q^{43} +(3.65235 - 3.65235i) q^{44} +(17.1114 + 5.55982i) q^{46} +(5.36365 + 0.849519i) q^{47} +(-5.26555 + 1.71088i) q^{49} -9.66143i q^{50} +(9.07032 + 4.62156i) q^{52} +(4.56121 + 8.95188i) q^{53} +(-0.805362 - 0.805362i) q^{55} +(-10.3476 + 5.27237i) q^{56} +(-1.88770 + 3.70481i) q^{58} +(6.23053 - 4.52674i) q^{59} +(0.982392 - 1.35215i) q^{61} +(2.68716 - 3.69855i) q^{62} +(25.5342 - 18.5517i) q^{64} +(1.01908 - 2.00005i) q^{65} +(13.1161 - 6.68301i) q^{67} +(8.79377 + 8.79377i) q^{68} +(1.82609 + 3.58391i) q^{70} +(-2.77828 - 1.41561i) q^{71} +0.596826i q^{73} +(16.6214 - 5.40063i) q^{74} +(-28.3578 - 4.49144i) q^{76} +(-1.07964 - 0.350796i) q^{77} +(-5.89711 + 5.89711i) q^{79} +(-10.9077 - 15.0132i) q^{80} +(-17.0337 - 4.18715i) q^{82} -11.1844 q^{83} +(1.93908 - 1.93908i) q^{85} +(-1.02848 + 3.16533i) q^{86} +(8.89746 + 1.40922i) q^{88} +(-6.08909 + 0.964418i) q^{89} -2.23731i q^{91} +(11.1715 + 34.3823i) q^{92} +(6.75374 + 13.2550i) q^{94} +(-0.990387 + 6.25306i) q^{95} +(-15.0243 + 7.65525i) q^{97} +(-12.2702 - 8.91483i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	1.61018	+	2.21623i	1.13857	+	1.56711i	0.770655	+	0.637252i	$0.219929\pi$
$2$	1.61018	+	2.21623i	1.13857	+	1.56711i	0.367917	+	0.929858i	$0.380071\pi$
$3$		0			0
$3$		0			0
$4$	−1.70094	+	5.23496i	−0.850472	+	2.61748i
$5$	1.15434	+	0.375067i	0.516236	+	0.167735i	0.555536	−	0.831492i	$-0.312513\pi$
$5$	1.15434	+	0.375067i	0.516236	+	0.167735i	−0.0393006	+	0.999227i	$0.512513\pi$
$6$		0			0
$7$	1.19485	−	0.189245i	0.451609	−	0.0715279i	0.0735133	−	0.997294i	$-0.476579\pi$
$7$	1.19485	−	0.189245i	0.451609	−	0.0715279i	0.378096	+	0.925766i	$0.376579\pi$
$8$	−9.13005	+	2.96653i	−3.22796	+	1.04883i
$9$		0			0
$10$	1.02746	+	3.16221i	0.324912	+	0.999977i
$11$	−0.836104	−	0.426016i	−0.252095	−	0.128449i	0.323377	−	0.946270i	$-0.395182\pi$
$11$	−0.836104	−	0.426016i	−0.252095	−	0.128449i	−0.575472	+	0.817821i	$0.695182\pi$
$12$		0			0
$13$	0.289312	−	1.82664i	0.0802407	−	0.506620i	−0.914533	−	0.404512i	$-0.867441\pi$
$13$	0.289312	−	1.82664i	0.0802407	−	0.506620i	0.994773	−	0.102108i	$-0.0325587\pi$
$14$	2.34333	+	2.34333i	0.626282	+	0.626282i
$15$		0			0
$16$	−12.3693	−	8.98684i	−3.09233	−	2.24671i
$17$	1.02572	−	2.01309i	0.248774	−	0.488247i	−0.732524	−	0.680741i	$-0.761658\pi$
$17$	1.02572	−	2.01309i	0.248774	−	0.488247i	0.981298	+	0.192495i	$0.0616578\pi$
$18$		0			0
$19$	0.815977	+	5.15188i	0.187198	+	1.18192i	0.884986	+	0.465618i	$0.154168\pi$
$19$	0.815977	+	5.15188i	0.187198	+	1.18192i	−0.697788	+	0.716304i	$0.745832\pi$
$20$	−3.92693	+	5.40495i	−0.878088	+	1.20858i
$21$		0			0
$22$	−0.402132	−	2.53896i	−0.0857349	−	0.541309i
$23$	5.31348	−	3.86047i	1.10794	−	0.804963i	0.125599	−	0.992081i	$-0.459915\pi$
$23$	5.31348	−	3.86047i	1.10794	−	0.804963i	0.982337	+	0.187118i	$0.0599148\pi$
$24$		0			0
$25$	−2.85326	−	2.07302i	−0.570653	−	0.414603i
$26$	4.51411	−	2.30005i	0.885290	−	0.451078i
$27$		0			0
$28$	−1.04167	+	6.57687i	−0.196858	+	1.24291i
$29$	0.689088	+	1.35241i	0.127961	+	0.251137i	0.946094	−	0.323891i	$-0.104991\pi$
$29$	0.689088	+	1.35241i	0.127961	+	0.251137i	−0.818134	+	0.575028i	$0.804991\pi$
$30$		0			0
$31$	−0.515703	−	1.58717i	−0.0926230	−	0.285064i	0.894004	−	0.448059i	$-0.147885\pi$
$31$	−0.515703	−	1.58717i	−0.0926230	−	0.285064i	−0.986627	+	0.162995i	$0.947885\pi$
$32$		−	22.6839i		−	4.00999i
$33$		0			0
$34$	6.11308	−	0.968216i	1.04838	−	0.166048i
$35$	1.45024	+	0.229695i	0.245135	+	0.0388255i
$36$		0			0
$37$	1.97146	−	6.06752i	0.324105	−	0.997494i	−0.647737	−	0.761864i	$-0.724285\pi$
$37$	1.97146	−	6.06752i	0.324105	−	0.997494i	0.971843	−	0.235630i	$-0.0757154\pi$
$38$	−10.1039	+	10.1039i	−1.63906	+	1.63906i
$39$		0			0
$40$	−11.6518			−1.84231
$41$	−4.89143	+	4.13206i	−0.763913	+	0.645319i
$41$	−4.89143	+	4.13206i	−0.763913	+	0.645319i
$42$		0			0
$43$	0.714124	+	0.982908i	0.108903	+	0.149892i	0.859990	−	0.510312i	$-0.170470\pi$
$43$	0.714124	+	0.982908i	0.108903	+	0.149892i	−0.751087	+	0.660204i	$0.770470\pi$
$44$	3.65235	−	3.65235i	0.550612	−	0.550612i
$45$		0			0
$46$	17.1114	+	5.55982i	2.52293	+	0.819750i
$47$	5.36365	+	0.849519i	0.782369	+	0.123915i	0.534826	−	0.844962i	$-0.320377\pi$
$47$	5.36365	+	0.849519i	0.782369	+	0.123915i	0.247542	+	0.968877i	$0.420377\pi$
$48$		0			0
$49$	−5.26555	+	1.71088i	−0.752222	+	0.244412i
$50$		−	9.66143i		−	1.36633i
$51$		0			0
$52$	9.07032	+	4.62156i	1.25783	+	0.640895i
$53$	4.56121	+	8.95188i	0.626530	+	1.22963i	0.958162	+	0.286226i	$0.0924008\pi$
$53$	4.56121	+	8.95188i	0.626530	+	1.22963i	−0.331632	+	0.943409i	$0.607599\pi$
$54$		0			0
$55$	−0.805362	−	0.805362i	−0.108595	−	0.108595i
$56$	−10.3476	+	5.27237i	−1.38276	+	0.704550i
$57$		0			0
$58$	−1.88770	+	3.70481i	−0.247867	+	0.486466i
$59$	6.23053	−	4.52674i	0.811146	−	0.589332i	−0.103017	−	0.994680i	$-0.532850\pi$
$59$	6.23053	−	4.52674i	0.811146	−	0.589332i	0.914163	+	0.405348i	$0.132850\pi$
$60$		0			0
$61$	0.982392	−	1.35215i	0.125782	−	0.173125i	−0.741481	−	0.670973i	$-0.765876\pi$
$61$	0.982392	−	1.35215i	0.125782	−	0.173125i	0.867264	+	0.497849i	$0.165876\pi$
$62$	2.68716	−	3.69855i	0.341269	−	0.469717i
$63$		0			0
$64$	25.5342	−	18.5517i	3.19177	−	2.31896i
$65$	1.01908	−	2.00005i	0.126401	−	0.248076i
$66$		0			0
$67$	13.1161	−	6.68301i	1.60239	−	0.816460i	0.602561	−	0.798073i	$-0.294147\pi$
$67$	13.1161	−	6.68301i	1.60239	−	0.816460i	0.999831	−	0.0183870i	$-0.00585310\pi$
$68$	8.79377	+	8.79377i	1.06640	+	1.06640i
$69$		0			0
$70$	1.82609	+	3.58391i	0.218260	+	0.428359i
$71$	−2.77828	−	1.41561i	−0.329722	−	0.168001i	0.281291	−	0.959623i	$-0.409237\pi$
$71$	−2.77828	−	1.41561i	−0.329722	−	0.168001i	−0.611012	+	0.791621i	$0.709237\pi$
$72$		0			0
$73$			0.596826i			0.0698532i	0.999390	+	0.0349266i	$0.0111197\pi$
$73$			0.596826i			0.0698532i	−0.999390	+	0.0349266i	$0.988880\pi$
$74$	16.6214	−	5.40063i	1.93220	−	0.627810i
$75$		0			0
$76$	−28.3578	−	4.49144i	−3.25287	−	0.515203i
$77$	−1.07964	−	0.350796i	−0.123036	−	0.0399769i
$78$		0			0
$79$	−5.89711	+	5.89711i	−0.663477	+	0.663477i	−0.956198	−	0.292721i	$-0.905439\pi$
$79$	−5.89711	+	5.89711i	−0.663477	+	0.663477i	0.292721	+	0.956198i	$0.405439\pi$
$80$	−10.9077	−	15.0132i	−1.21952	−	1.67853i
$81$		0			0
$82$	−17.0337	−	4.18715i	−1.88106	−	0.462394i
$83$	−11.1844			−1.22765			−0.613823	−	0.789443i	$-0.710369\pi$
$83$	−11.1844			−1.22765			−0.613823	+	0.789443i	$0.710369\pi$
$84$		0			0
$85$	1.93908	−	1.93908i	0.210322	−	0.210322i
$86$	−1.02848	+	3.16533i	−0.110903	+	0.341326i
$87$		0			0
$88$	8.89746	+	1.40922i	0.948473	+	0.150223i
$89$	−6.08909	+	0.964418i	−0.645443	+	0.102228i	−0.470570	−	0.882363i	$-0.655952\pi$
$89$	−6.08909	+	0.964418i	−0.645443	+	0.102228i	−0.174873	+	0.984591i	$0.555952\pi$
$90$		0			0
$91$		−	2.23731i		−	0.234534i
$92$	11.1715	+	34.3823i	1.16471	+	3.58460i
$93$		0			0
$94$	6.75374	+	13.2550i	0.696595	+	1.36714i
$95$	−0.990387	+	6.25306i	−0.101612	+	0.641550i
$96$		0			0
$97$	−15.0243	+	7.65525i	−1.52548	+	0.777273i	−0.997410	−	0.0719256i	$-0.977086\pi$
$97$	−15.0243	+	7.65525i	−1.52548	+	0.777273i	−0.528074	+	0.849198i	$0.677086\pi$
$98$	−12.2702	−	8.91483i	−1.23948	−	0.900534i
$99$		0			0
$100$	15.7054	−	11.4106i	1.57054	−	1.14106i
$101$	−1.46960	−	9.27866i	−0.146230	−	0.923262i	−0.946285	−	0.323334i	$-0.895196\pi$
$101$	−1.46960	−	9.27866i	−0.146230	−	0.923262i	0.800055	−	0.599927i	$-0.204804\pi$
$102$		0			0
$103$	6.15464	−	8.47113i	0.606435	−	0.834686i	−0.389844	−	0.920881i	$-0.627471\pi$
$103$	6.15464	−	8.47113i	0.606435	−	0.834686i	0.996278	+	0.0861955i	$0.0274710\pi$
$104$	2.77737	+	17.5356i	0.272343	+	1.71951i
$105$		0			0
$106$	−12.4950	+	24.5229i	−1.21362	+	2.38187i
$107$	−4.04469	−	2.93864i	−0.391014	−	0.284089i	0.374857	−	0.927083i	$-0.377692\pi$
$107$	−4.04469	−	2.93864i	−0.391014	−	0.284089i	−0.765871	+	0.642994i	$0.777692\pi$
$108$		0			0
$109$	−5.70768	−	5.70768i	−0.546697	−	0.546697i	0.378787	−	0.925484i	$-0.376341\pi$
$109$	−5.70768	−	5.70768i	−0.546697	−	0.546697i	−0.925484	+	0.378787i	$0.876341\pi$
$110$	0.488085	−	3.08165i	0.0465371	−	0.293824i
$111$		0			0
$112$	−16.4802	−	8.39706i	−1.55723	−	0.793448i
$113$	−0.593004	−	1.82508i	−0.0557851	−	0.171689i	0.919282	−	0.393600i	$-0.128771\pi$
$113$	−0.593004	−	1.82508i	−0.0557851	−	0.171689i	−0.975067	+	0.221911i	$0.928771\pi$
$114$		0			0
$115$	7.58148	−	2.46337i	0.706977	−	0.229711i
$116$	−8.25193	+	1.30698i	−0.766173	+	0.121350i
$117$		0			0
$118$	20.0646	+	6.51939i	1.84710	+	0.600158i
$119$	0.844612	−	2.59945i	0.0774255	−	0.238291i
$120$		0			0
$121$	−5.94806	−	8.18680i	−0.540733	−	0.744254i
$122$	4.57850			0.414518
$123$		0			0
$124$	9.18597			0.824924
$125$	−6.08321	−	8.37282i	−0.544099	−	0.748888i
$126$		0			0
$127$	1.11004	−	3.41634i	0.0984997	−	0.303151i	−0.889650	−	0.456643i	$-0.849052\pi$
$127$	1.11004	−	3.41634i	0.0984997	−	0.303151i	0.988150	+	0.153492i	$0.0490518\pi$
$128$	39.0820	+	12.6985i	3.45439	+	1.12240i
$129$		0			0
$130$	6.07348	−	0.961945i	0.532680	−	0.0843682i
$131$	−7.54778	+	2.45242i	−0.659453	+	0.214269i	−0.619578	−	0.784935i	$-0.712696\pi$
$131$	−7.54778	+	2.45242i	−0.659453	+	0.214269i	−0.0398754	+	0.999205i	$0.512696\pi$
$132$		0			0
$133$	1.94994	+	6.00128i	0.169081	+	0.520377i
$134$	35.9305	+	18.3075i	3.10392	+	1.58153i
$135$		0			0
$136$	−3.39299	+	21.4225i	−0.290946	+	1.83696i
$137$	5.27127	+	5.27127i	0.450355	+	0.450355i	0.895472	−	0.445117i	$-0.146838\pi$
$137$	5.27127	+	5.27127i	0.450355	+	0.450355i	−0.445117	+	0.895472i	$0.646838\pi$
$138$		0			0
$139$	−1.71214	−	1.24394i	−0.145221	−	0.105510i	0.512802	−	0.858507i	$-0.328607\pi$
$139$	−1.71214	−	1.24394i	−0.145221	−	0.105510i	−0.658024	+	0.752997i	$0.728607\pi$
$140$	−3.66921	+	7.20124i	−0.310105	+	0.608616i
$141$		0			0
$142$	−1.33624	−	8.43670i	−0.112135	−	0.707992i
$143$	−1.02008	+	1.40401i	−0.0853030	+	0.117409i
$144$		0			0
$145$	0.288196	+	1.81960i	0.0239333	+	0.151109i
$146$	−1.32270	+	0.961000i	−0.109468	+	0.0795329i
$147$		0			0
$148$	28.4099	+	20.6410i	2.33528	+	1.69668i
$149$	−7.89085	+	4.02059i	−0.646444	+	0.329379i	−0.746288	−	0.665624i	$-0.768166\pi$
$149$	−7.89085	+	4.02059i	−0.646444	+	0.329379i	0.0998440	+	0.995003i	$0.468166\pi$
$150$		0			0
$151$	−0.837422	+	5.28728i	−0.0681485	+	0.430272i	0.929899	+	0.367815i	$0.119894\pi$
$151$	−0.837422	+	5.28728i	−0.0681485	+	0.430272i	−0.998048	+	0.0624578i	$0.980106\pi$
$152$	−22.7331	−	44.6163i	−1.84390	−	3.61886i
$153$		0			0
$154$	−0.960973	−	2.95757i	−0.0774374	−	0.238328i
$155$		−	2.02556i		−	0.162697i
$156$		0			0
$157$	−8.26051	+	1.30834i	−0.659260	+	0.104417i	−0.477095	−	0.878851i	$-0.658310\pi$
$157$	−8.26051	+	1.30834i	−0.659260	+	0.104417i	−0.182165	+	0.983268i	$0.558310\pi$
$158$	−22.5648	−	3.57391i	−1.79516	−	0.284325i
$159$		0			0
$160$	8.50800	−	26.1849i	0.672617	−	2.07010i
$161$	5.61821	−	5.61821i	0.442777	−	0.442777i
$162$		0			0
$163$	−0.165656			−0.0129752			−0.00648760	−	0.999979i	$-0.502065\pi$
$163$	−0.165656			−0.0129752			−0.00648760	+	0.999979i	$0.502065\pi$
$164$	−13.3111	−	32.6349i	−1.03943	−	2.54835i
$165$		0			0
$166$	−18.0089	−	24.7872i	−1.39776	−	1.92386i
$167$	−4.32550	+	4.32550i	−0.334717	+	0.334717i	−0.854375	−	0.519657i	$-0.826060\pi$
$167$	−4.32550	+	4.32550i	−0.334717	+	0.334717i	0.519657	+	0.854375i	$0.326060\pi$
$168$		0			0
$169$	9.11081	+	2.96028i	0.700831	+	0.227714i
$170$	7.41971	+	1.17517i	0.569065	+	0.0901311i
$171$		0			0
$172$	−6.36017	+	2.06654i	−0.484959	+	0.157573i
$173$		−	19.1289i		−	1.45434i	−0.686456	−	0.727171i	$-0.740835\pi$
$173$		−	19.1289i		−	1.45434i	0.686456	−	0.727171i	$-0.259165\pi$
$174$		0			0
$175$	−3.80152	−	1.93697i	−0.287368	−	0.146421i
$176$	6.51350	+	12.7835i	0.490974	+	0.963590i
$177$		0			0
$178$	−11.9419	−	11.9419i	−0.895086	−	0.895086i
$179$	11.6175	−	5.91943i	0.868335	−	0.442439i	0.0377216	−	0.999288i	$-0.487990\pi$
$179$	11.6175	−	5.91943i	0.868335	−	0.442439i	0.830613	+	0.556850i	$0.187990\pi$
$180$		0			0
$181$	−5.39400	+	10.5863i	−0.400933	+	0.786875i	−0.999903	−	0.0138960i	$-0.995577\pi$
$181$	−5.39400	+	10.5863i	−0.400933	+	0.786875i	0.598971	+	0.800771i	$0.295577\pi$
$182$	4.95839	−	3.60248i	0.367541	−	0.267034i
$183$		0			0
$184$	−37.0601	+	51.0088i	−2.73211	+	3.76042i
$185$	4.55145	−	6.26454i	0.334630	−	0.460578i
$186$		0			0
$187$	−1.71522	+	1.24618i	−0.125429	+	0.0911298i
$188$	−13.5705	+	26.6335i	−0.989728	+	1.94245i
$189$		0			0
$190$	−15.4529	+	7.87365i	−1.12107	+	0.571215i
$191$	0.305210	+	0.305210i	0.0220842	+	0.0220842i	0.718063	−	0.695978i	$-0.245029\pi$
$191$	0.305210	+	0.305210i	0.0220842	+	0.0220842i	−0.695978	+	0.718063i	$0.745029\pi$
$192$		0			0
$193$	−9.62661	−	18.8933i	−0.692938	−	1.35997i	−0.922242	−	0.386613i	$-0.873645\pi$
$193$	−9.62661	−	18.8933i	−0.692938	−	1.35997i	0.229304	−	0.973355i	$-0.426355\pi$
$194$	−41.1576	−	20.9709i	−2.95495	−	1.50562i
$195$		0			0
$196$		−	30.4751i		−	2.17679i
$197$	−22.2882	+	7.24188i	−1.58797	+	0.515963i	−0.964094	−	0.265561i	$-0.914443\pi$
$197$	−22.2882	+	7.24188i	−1.58797	+	0.515963i	−0.623876	+	0.781524i	$0.714443\pi$
$198$		0			0
$199$	5.20701	+	0.824709i	0.369115	+	0.0584621i	0.338237	−	0.941061i	$-0.390170\pi$
$199$	5.20701	+	0.824709i	0.369115	+	0.0584621i	0.0308784	+	0.999523i	$0.490170\pi$
$200$	32.2001	+	10.4624i	2.27689	+	0.739807i
$201$		0			0
$202$	18.1973	−	18.1973i	1.28036	−	1.28036i
$203$	1.07929	+	1.48552i	0.0757515	+	0.104263i
$204$		0			0
$205$	−7.19617	+	2.93518i	−0.502602	+	0.205002i
$206$	28.6841			1.99851
$207$		0			0
$208$	−19.9944	+	19.9944i	−1.38636	+	1.38636i
$209$	1.51254	−	4.65513i	0.104625	−	0.322002i
$210$		0			0
$211$	21.8950	+	3.46783i	1.50731	+	0.238735i	0.854766	−	0.519013i	$-0.173701\pi$
$211$	21.8950	+	3.46783i	1.50731	+	0.238735i	0.652547	+	0.757748i	$0.273701\pi$
$212$	−54.6211	+	8.65113i	−3.75139	+	0.594162i
$213$		0			0
$214$		−	13.6957i		−	0.936219i
$215$	0.455684	+	1.40245i	0.0310774	+	0.0956465i
$216$		0			0
$217$	−0.916550	−	1.79883i	−0.0622195	−	0.122113i
$218$	3.45911	−	21.8400i	0.234280	−	1.47919i
$219$		0			0
$220$	5.58592	−	2.84617i	0.376603	−	0.191889i
$221$	−3.38045	−	2.45604i	−0.227394	−	0.165211i
$222$		0			0
$223$	−19.1614	+	13.9216i	−1.28314	+	0.932258i	−0.999643	−	0.0267138i	$-0.991496\pi$
$223$	−19.1614	+	13.9216i	−1.28314	+	0.932258i	−0.283500	+	0.958972i	$0.591496\pi$
$224$	−4.29282	−	27.1038i	−0.286826	−	1.81095i
$225$		0			0
$226$	3.08995	−	4.25295i	0.205540	−	0.282902i
$227$	2.24211	+	14.1561i	0.148814	+	0.939575i	0.943215	+	0.332182i	$0.107785\pi$
$227$	2.24211	+	14.1561i	0.148814	+	0.939575i	−0.794401	+	0.607393i	$0.792215\pi$
$228$		0			0
$229$	9.37117	−	18.3920i	0.619264	−	1.21537i	−0.341988	−	0.939704i	$-0.611100\pi$
$229$	9.37117	−	18.3920i	0.619264	−	1.21537i	0.961252	−	0.275670i	$-0.0888997\pi$
$230$	17.6670	+	12.8358i	1.16493	+	0.846369i
$231$		0			0
$232$	−10.3034	−	10.3034i	−0.676450	−	0.676450i
$233$	−2.82151	+	17.8143i	−0.184843	+	1.16705i	0.704462	+	0.709741i	$0.251188\pi$
$233$	−2.82151	+	17.8143i	−0.184843	+	1.16705i	−0.889306	+	0.457313i	$0.848812\pi$
$234$		0			0
$235$	5.87284	+	2.99236i	0.383102	+	0.195200i
$236$	13.0996	+	40.3163i	0.852709	+	2.62437i
$237$		0			0
$238$	7.12096	−	2.31374i	0.461583	−	0.149977i
$239$	22.4231	−	3.55147i	1.45043	−	0.229725i	0.619015	−	0.785379i	$-0.287532\pi$
$239$	22.4231	−	3.55147i	1.45043	−	0.229725i	0.831414	+	0.555653i	$0.187532\pi$
$240$		0			0
$241$	−2.97068	−	0.965234i	−0.191359	−	0.0621762i	0.211770	−	0.977320i	$-0.432077\pi$
$241$	−2.97068	−	0.965234i	−0.191359	−	0.0621762i	−0.403129	+	0.915143i	$0.632077\pi$
$242$	8.56635	−	26.3645i	0.550666	−	1.69478i
$243$		0			0
$244$	5.40745	+	7.44271i	0.346176	+	0.476471i
$245$	−6.71992			−0.429320
$246$		0			0
$247$	9.64672			0.613806
$248$	9.41679	+	12.9611i	0.597967	+	0.823030i
$249$		0			0
$250$	8.76100	−	26.9636i	0.554094	−	1.70533i
$251$	−6.26375	−	2.03521i	−0.395364	−	0.128462i	0.104586	−	0.994516i	$-0.466648\pi$
$251$	−6.26375	−	2.03521i	−0.395364	−	0.128462i	−0.499950	+	0.866054i	$0.666648\pi$
$252$		0			0
$253$	−6.08724	+	0.964124i	−0.382702	+	0.0606140i
$254$	9.35875	−	3.04084i	0.587220	−	0.190799i
$255$		0			0
$256$	15.2801	+	47.0273i	0.955005	+	2.93920i
$257$	6.08184	+	3.09885i	0.379375	+	0.193301i	0.633270	−	0.773931i	$-0.281712\pi$
$257$	6.08184	+	3.09885i	0.379375	+	0.193301i	−0.253896	+	0.967232i	$0.581712\pi$
$258$		0			0
$259$	1.20734	−	7.62284i	0.0750204	−	0.473660i
$260$	8.73682	+	8.73682i	0.541834	+	0.541834i
$261$		0			0
$262$	−17.5885	−	12.7788i	−1.08662	−	0.789475i
$263$	−5.84108	+	11.4638i	−0.360177	+	0.706887i	−0.997995	−	0.0633007i	$-0.979837\pi$
$263$	−5.84108	+	11.4638i	−0.360177	+	0.706887i	0.637818	+	0.770187i	$0.279837\pi$
$264$		0			0
$265$	1.90762	+	12.0443i	0.117184	+	0.739873i
$266$	−10.1605	+	13.9847i	−0.622978	+	0.857456i
$267$		0			0
$268$	12.6755	+	80.0300i	0.774280	+	4.88861i
$269$	−13.0297	+	9.46664i	−0.794435	+	0.577191i	−0.909276	−	0.416193i	$-0.863364\pi$
$269$	−13.0297	+	9.46664i	−0.794435	+	0.577191i	0.114841	+	0.993384i	$0.463364\pi$
$270$		0			0
$271$	16.7793	+	12.1909i	1.01927	+	0.740544i	0.966133	−	0.258043i	$-0.0830776\pi$
$271$	16.7793	+	12.1909i	1.01927	+	0.740544i	0.0531382	+	0.998587i	$0.483078\pi$
$272$	−30.7788	+	15.6826i	−1.86624	+	0.950897i
$273$		0			0
$274$	−3.19463	+	20.1701i	−0.192994	+	1.21852i
$275$	1.50249	+	2.94880i	0.0906033	+	0.177819i
$276$		0			0
$277$	1.50210	+	4.62298i	0.0902524	+	0.277768i	0.985987	−	0.166820i	$-0.0533499\pi$
$277$	1.50210	+	4.62298i	0.0902524	+	0.277768i	−0.895735	+	0.444588i	$0.853350\pi$
$278$		−	5.79746i		−	0.347708i
$279$		0			0
$280$	−13.9221	+	2.20505i	−0.832006	+	0.131777i
$281$	−5.74924	−	0.910591i	−0.342971	−	0.0543213i	−0.0174270	−	0.999848i	$-0.505547\pi$
$281$	−5.74924	−	0.910591i	−0.342971	−	0.0543213i	−0.325544	+	0.945527i	$0.605547\pi$
$282$		0			0
$283$	−4.46953	+	13.7558i	−0.265686	+	0.817697i	0.725849	+	0.687854i	$0.241447\pi$
$283$	−4.46953	+	13.7558i	−0.265686	+	0.817697i	−0.991535	+	0.129843i	$0.958553\pi$
$284$	12.1363	−	12.1363i	0.720160	−	0.720160i
$285$		0			0
$286$	−4.75413			−0.281117
$287$	−5.06254	+	5.86285i	−0.298832	+	0.346073i
$288$		0			0
$289$	6.99191	+	9.62354i	0.411289	+	0.566091i
$290$	−3.56859	+	3.56859i	−0.209555	+	0.209555i
$291$		0			0
$292$	−3.12436	−	1.01517i	−0.182839	−	0.0594081i
$293$	19.4615	+	3.08239i	1.13695	+	0.180075i	0.696401	−	0.717653i	$-0.254784\pi$
$293$	19.4615	+	3.08239i	1.13695	+	0.180075i	0.440550	+	0.897728i	$0.354784\pi$
$294$		0			0
$295$	8.88997	−	2.88853i	0.517594	−	0.168177i
$296$			61.2451i			3.55980i
$297$		0			0
$298$	−21.6163	−	11.0140i	−1.25220	−	0.638026i
$299$	−5.51445	−	10.8227i	−0.318909	−	0.625893i
$300$		0			0
$301$	1.03928	+	1.03928i	0.0599031	+	0.0599031i
$302$	−13.0662	+	6.65757i	−0.751877	+	0.383100i
$303$		0			0
$304$	36.2060	−	71.0583i	2.07656	−	4.07547i
$305$	1.64116	−	1.19237i	0.0939725	−	0.0682750i
$306$		0			0
$307$	5.79055	−	7.97001i	0.330484	−	0.454872i	−0.611148	−	0.791516i	$-0.709292\pi$
$307$	5.79055	−	7.97001i	0.330484	−	0.454872i	0.941632	+	0.336644i	$0.109292\pi$
$308$	3.67280	−	5.05518i	0.209277	−	0.288046i
$309$		0			0
$310$	4.48910	−	3.26152i	0.254963	−	0.185242i
$311$	11.5241	−	22.6173i	0.653472	−	1.28251i	−0.291879	−	0.956455i	$-0.594280\pi$
$311$	11.5241	−	22.6173i	0.653472	−	1.28251i	0.945351	−	0.326056i	$-0.105720\pi$
$312$		0			0
$313$	−23.3678	+	11.9065i	−1.32083	+	0.672995i	−0.965170	−	0.261622i	$-0.915743\pi$
$313$	−23.3678	+	11.9065i	−1.32083	+	0.672995i	−0.355656	+	0.934617i	$0.615743\pi$
$314$	−16.2005	−	16.2005i	−0.914248	−	0.914248i
$315$		0			0
$316$	−20.8405	−	40.9018i	−1.17237	−	2.30091i
$317$	18.5064	+	9.42948i	1.03942	+	0.529612i	0.888473	−	0.458929i	$-0.151767\pi$
$317$	18.5064	+	9.42948i	1.03942	+	0.529612i	0.150950	+	0.988541i	$0.451767\pi$
$318$		0			0
$319$		−	1.42432i		−	0.0797466i
$320$	36.4332	−	11.8379i	2.03668	−	0.661756i
$321$		0			0
$322$	21.4976	+	3.40489i	1.19801	+	0.189747i
$323$	11.2082	+	3.64176i	0.623640	+	0.202633i
$324$		0			0
$325$	−4.61215	+	4.61215i	−0.255836	+	0.255836i
$326$	−0.266737	−	0.367132i	−0.0147732	−	0.0203336i
$327$		0			0
$328$	32.4011	−	52.2365i	1.78905	−	2.88428i
$329$	6.56951			0.362189
$330$		0			0
$331$	−4.50312	+	4.50312i	−0.247514	+	0.247514i	−0.819949	−	0.572436i	$-0.805999\pi$
$331$	−4.50312	+	4.50312i	−0.247514	+	0.247514i	0.572436	+	0.819949i	$0.305999\pi$
$332$	19.0240	−	58.5499i	1.04408	−	3.21334i
$333$		0			0
$334$	−16.5512	−	2.62145i	−0.905639	−	0.143439i
$335$	17.6470	−	2.79502i	0.964161	−	0.152708i
$336$		0			0
$337$			11.0639i			0.602688i	0.953515	+	0.301344i	$0.0974353\pi$
$337$			11.0639i			0.602688i	−0.953515	+	0.301344i	$0.902565\pi$
$338$	8.10942	+	24.9582i	0.441094	+	1.35755i
$339$		0			0
$340$	6.85273	+	13.4492i	0.371642	+	0.729388i
$341$	−0.244979	+	1.54674i	−0.0132664	+	0.0837606i
$342$		0			0
$343$	−13.5130	+	6.88519i	−0.729631	+	0.371766i
$344$	−9.43581	−	6.85552i	−0.508745	−	0.369625i
$345$		0			0
$346$	42.3940	−	30.8010i	2.27912	−	1.65587i
$347$	−0.198212	−	1.25146i	−0.0106406	−	0.0671819i	0.981797	−	0.189935i	$-0.0608277\pi$
$347$	−0.198212	−	1.25146i	−0.0106406	−	0.0671819i	−0.992437	+	0.122753i	$0.960828\pi$
$348$		0			0
$349$	−8.34115	+	11.4806i	−0.446491	+	0.614543i	−0.971639	−	0.236468i	$-0.924010\pi$
$349$	−8.34115	+	11.4806i	−0.446491	+	0.614543i	0.525148	+	0.851011i	$0.324010\pi$
$350$	−1.82838	−	11.5439i	−0.0977309	−	0.617049i
$351$		0			0
$352$	−9.66373	+	18.9661i	−0.515078	+	1.01090i
$353$	0.827363	+	0.601115i	0.0440361	+	0.0319941i	0.609586	−	0.792720i	$-0.291336\pi$
$353$	0.827363	+	0.601115i	0.0440361	+	0.0319941i	−0.565549	+	0.824714i	$0.691336\pi$
$354$		0			0
$355$	−2.67613	−	2.67613i	−0.142034	−	0.142034i
$356$	5.30851	−	33.5166i	0.281350	−	1.77638i
$357$		0			0
$358$	31.8252	+	16.2157i	1.68201	+	0.857028i
$359$	3.46550	+	10.6657i	0.182902	+	0.562915i	0.999906	−	0.0137176i	$-0.00436659\pi$
$359$	3.46550	+	10.6657i	0.182902	+	0.562915i	−0.817004	+	0.576632i	$0.804367\pi$
$360$		0			0
$361$	−7.80596	+	2.53631i	−0.410840	+	0.133490i
$362$	−32.1471	+	5.09159i	−1.68961	+	0.267608i
$363$		0			0
$364$	11.7122	+	3.80554i	0.613888	+	0.199464i
$365$	−0.223850	+	0.688939i	−0.0117168	+	0.0360607i
$366$		0			0
$367$	16.8756	+	23.2272i	0.880897	+	1.21245i	0.976172	+	0.217000i	$0.0696271\pi$
$367$	16.8756	+	23.2272i	0.880897	+	1.21245i	−0.0952746	+	0.995451i	$0.530373\pi$
$368$	−100.417			−5.23462
$369$		0			0
$370$	21.2123			1.10278
$371$	7.14404	+	9.83293i	0.370900	+	0.510500i
$372$		0			0
$373$	10.5118	−	32.3520i	0.544281	−	1.67512i	−0.178414	−	0.983956i	$-0.557097\pi$
$373$	10.5118	−	32.3520i	0.544281	−	1.67512i	0.722694	−	0.691168i	$-0.242903\pi$
$374$	−5.52365	−	1.79474i	−0.285621	−	0.0928039i
$375$		0			0
$376$	−51.4905	+	8.15530i	−2.65542	+	0.420577i
$377$	2.66974	−	0.867450i	0.137498	−	0.0446760i
$378$		0			0
$379$	−2.16181	−	6.65338i	−0.111045	−	0.341761i	0.880057	−	0.474869i	$-0.157504\pi$
$379$	−2.16181	−	6.65338i	−0.111045	−	0.341761i	−0.991102	+	0.133108i	$0.957504\pi$
$380$	−31.0499	−	15.8207i	−1.59283	−	0.811587i
$381$		0			0
$382$	−0.184971	+	1.16786i	−0.00946392	+	0.0597528i
$383$	−13.4809	−	13.4809i	−0.688840	−	0.688840i	0.273136	−	0.961976i	$-0.411939\pi$
$383$	−13.4809	−	13.4809i	−0.688840	−	0.688840i	−0.961976	+	0.273136i	$0.911939\pi$
$384$		0			0
$385$	−1.11470	−	0.809873i	−0.0568101	−	0.0412750i
$386$	26.3712	−	51.7564i	1.34226	−	2.63433i
$387$		0			0
$388$	−14.5195	−	91.6727i	−0.737117	−	4.65398i
$389$	−10.7762	+	14.8322i	−0.546377	+	0.752024i	−0.989515	−	0.144430i	$-0.953865\pi$
$389$	−10.7762	+	14.8322i	−0.546377	+	0.752024i	0.443138	+	0.896453i	$0.353865\pi$
$390$		0			0
$391$	−2.32133	−	14.6563i	−0.117395	−	0.741200i
$392$	42.9994	−	31.2409i	2.17180	−	1.57790i
$393$		0			0
$394$	−51.9378	−	37.7350i	−2.61659	−	1.90106i
$395$	−9.01908	+	4.59545i	−0.453799	+	0.231222i
$396$		0			0
$397$	−1.30237	+	8.22286i	−0.0653642	+	0.412694i	0.933211	+	0.359329i	$0.116994\pi$
$397$	−1.30237	+	8.22286i	−0.0653642	+	0.412694i	−0.998575	+	0.0533644i	$0.983006\pi$
$398$	6.55650	+	12.8679i	0.328648	+	0.645008i
$399$		0			0
$400$	16.6631	+	51.2837i	0.833153	+	2.56418i
$401$		−	4.20180i		−	0.209828i	−0.994481	−	0.104914i	$-0.966543\pi$
$401$		−	4.20180i		−	0.209828i	0.994481	−	0.104914i	$-0.0334567\pi$
$402$		0			0
$403$	−3.04840	+	0.482819i	−0.151851	+	0.0240509i
$404$	51.0732	+	8.08920i	2.54099	+	0.402453i
$405$		0			0
$406$	−1.55439	+	4.78392i	−0.0771430	+	0.237422i
$407$	−4.23321	+	4.23321i	−0.209832	+	0.209832i
$408$		0			0
$409$	38.6631			1.91177			0.955883	−	0.293746i	$-0.0949020\pi$
$409$	38.6631			1.91177			0.955883	+	0.293746i	$0.0949020\pi$
$410$	−18.0922	−	11.2222i	−0.893509	−	0.554224i
$411$		0			0
$412$	33.8774	+	46.6282i	1.66902	+	2.29721i
$413$	6.58786	−	6.58786i	0.324167	−	0.324167i
$414$		0			0
$415$	−12.9106	−	4.19490i	−0.633755	−	0.205919i
$416$	−41.4355	−	6.56274i	−2.03154	−	0.321765i
$417$		0			0
$418$	12.7523	−	4.14347i	0.623735	−	0.202664i
$419$		−	8.92254i		−	0.435895i	−0.975961	−	0.217947i	$-0.930064\pi$
$419$		−	8.92254i		−	0.435895i	0.975961	−	0.217947i	$-0.0699361\pi$
$420$		0			0
$421$	17.2160	+	8.77197i	0.839054	+	0.427520i	0.820045	−	0.572300i	$-0.193949\pi$
$421$	17.2160	+	8.77197i	0.839054	+	0.427520i	0.0190099	+	0.999819i	$0.493949\pi$
$422$	27.5695	+	54.1081i	1.34206	+	2.63394i
$423$		0			0
$424$	−68.2001	−	68.2001i	−3.31209	−	3.31209i
$425$	−7.09983	+	3.61754i	−0.344392	+	0.175477i
$426$		0			0
$427$	0.917921	−	1.80152i	0.0444213	−	0.0871817i
$428$	22.2634	−	16.1753i	1.07614	−	0.781864i
$429$		0			0
$430$	−2.37442	+	3.26811i	−0.114505	+	0.157602i
$431$	−11.6004	+	15.9666i	−0.558773	+	0.769085i	−0.991170	−	0.132598i	$-0.957668\pi$
$431$	−11.6004	+	15.9666i	−0.558773	+	0.769085i	0.432397	+	0.901683i	$0.357668\pi$
$432$		0			0
$433$	−8.46295	+	6.14869i	−0.406703	+	0.295487i	−0.772266	−	0.635299i	$-0.780877\pi$
$433$	−8.46295	+	6.14869i	−0.406703	+	0.295487i	0.365562	+	0.930787i	$0.380877\pi$
$434$	2.51081	−	4.92774i	0.120523	−	0.236539i
$435$		0			0
$436$	39.5880	−	20.1711i	1.89592	−	0.966019i
$437$	24.2243	+	24.2243i	1.15881	+	1.15881i
$438$		0			0
$439$	13.6513	+	26.7922i	0.651540	+	1.27872i	0.946344	+	0.323162i	$0.104746\pi$
$439$	13.6513	+	26.7922i	0.651540	+	1.27872i	−0.294803	+	0.955558i	$0.595254\pi$
$440$	9.74213	+	4.96386i	0.464438	+	0.236643i
$441$		0			0
$442$		−	11.4465i		−	0.544456i
$443$	20.8472	−	6.77365i	0.990479	−	0.321826i	0.231424	−	0.972853i	$-0.425662\pi$
$443$	20.8472	−	6.77365i	0.990479	−	0.321826i	0.759055	+	0.651027i	$0.225662\pi$
$444$		0			0
$445$	−7.39059	−	1.17056i	−0.350348	−	0.0554896i
$446$	−61.7069	−	20.0498i	−2.92190	−	0.949384i
$447$		0			0
$448$	26.9986	−	26.9986i	1.27556	−	1.27556i
$449$	2.93496	+	4.03963i	0.138509	+	0.190642i	0.872637	−	0.488370i	$-0.162408\pi$
$449$	2.93496	+	4.03963i	0.138509	+	0.190642i	−0.734127	+	0.679012i	$0.762408\pi$
$450$		0			0
$451$	5.85007	−	1.37100i	0.275469	−	0.0645580i
$452$	10.5629			0.496836
$453$		0			0
$454$	−27.7630	+	27.7630i	−1.30298	+	1.30298i
$455$	0.839142	−	2.58261i	0.0393396	−	0.121075i
$456$		0			0
$457$	12.1280	+	1.92089i	0.567326	+	0.0898556i	0.433507	−	0.901150i	$-0.357276\pi$
$457$	12.1280	+	1.92089i	0.567326	+	0.0898556i	0.133819	+	0.991006i	$0.457276\pi$
$458$	55.8501	−	8.84579i	2.60970	−	0.413336i
$459$		0			0
$460$			43.8788i			2.04586i
$461$	−9.09708	−	27.9979i	−0.423693	−	1.30399i	−0.904240	−	0.427025i	$-0.859562\pi$
$461$	−9.09708	−	27.9979i	−0.423693	−	1.30399i	0.480547	−	0.876969i	$-0.340438\pi$
$462$		0			0
$463$	8.27308	+	16.2368i	0.384483	+	0.754590i	0.999422	−	0.0339843i	$-0.0108196\pi$
$463$	8.27308	+	16.2368i	0.384483	+	0.754590i	−0.614940	+	0.788574i	$0.710820\pi$
$464$	3.63035	−	22.9212i	0.168535	−	1.06409i
$465$		0			0
$466$	−44.0238	+	22.4312i	−2.03936	+	1.03911i
$467$	13.9475	+	10.1335i	0.645414	+	0.468921i	0.861706	−	0.507408i	$-0.169396\pi$
$467$	13.9475	+	10.1335i	0.645414	+	0.468921i	−0.216292	+	0.976329i	$0.569396\pi$
$468$		0			0
$469$	14.4071	−	10.4673i	0.665256	−	0.483337i
$470$	2.82460	+	17.8338i	0.130289	+	0.822613i
$471$		0			0
$472$	−43.4563	+	59.8125i	−2.00024	+	2.75309i
$473$	−0.178347	−	1.12604i	−0.00820043	−	0.0517755i
$474$		0			0
$475$	8.35174	−	16.3912i	0.383204	−	0.752080i
$476$	12.1714	+	8.84303i	0.557875	+	0.405320i
$477$		0			0
$478$	43.9762	+	43.9762i	2.01142	+	2.01142i
$479$	−3.50656	+	22.1396i	−0.160219	+	1.01158i	0.768244	+	0.640157i	$0.221131\pi$
$479$	−3.50656	+	22.1396i	−0.160219	+	1.01158i	−0.928463	+	0.371425i	$0.878869\pi$
$480$		0			0
$481$	−10.5128	−	5.35656i	−0.479344	−	0.244238i
$482$	−2.64417	−	8.13792i	−0.120439	−	0.370672i
$483$		0			0
$484$	52.9749	−	17.2126i	2.40795	−	0.782391i
$485$	−20.2143	+	3.20163i	−0.917885	+	0.145379i
$486$		0			0
$487$	−0.367574	−	0.119432i	−0.0166564	−	0.00541198i	0.300677	−	0.953726i	$-0.402787\pi$
$487$	−0.367574	−	0.119432i	−0.0166564	−	0.00541198i	−0.317333	+	0.948314i	$0.602787\pi$
$488$	−4.95810	+	15.2595i	−0.224443	+	0.690764i
$489$		0			0
$490$	−10.8203	−	14.8929i	−0.488812	−	0.672792i
$491$	26.9030			1.21411			0.607057	−	0.794658i	$-0.292350\pi$
$491$	26.9030			1.21411			0.607057	+	0.794658i	$0.292350\pi$
$492$		0			0
$493$	3.42934			0.154450
$494$	15.5330	+	21.3793i	0.698863	+	0.961902i
$495$		0			0
$496$	−7.88475	+	24.2668i	−0.354036	+	1.08961i
$497$	−3.58752	−	1.16566i	−0.160922	−	0.0522868i
$498$		0			0
$499$	−9.04346	+	1.43234i	−0.404841	+	0.0641205i	−0.355534	−	0.934663i	$-0.615701\pi$
$499$	−9.04346	+	1.43234i	−0.404841	+	0.0641205i	−0.0493065	+	0.998784i	$0.515701\pi$
$500$	54.1786	−	17.6037i	2.42294	−	0.787262i
$501$		0			0
$502$	−5.57529	−	17.1590i	−0.248837	−	0.765842i
$503$	−8.04239	−	4.09780i	−0.358592	−	0.182712i	0.265408	−	0.964136i	$-0.414493\pi$
$503$	−8.04239	−	4.09780i	−0.358592	−	0.182712i	−0.624000	+	0.781424i	$0.714493\pi$
$504$		0			0
$505$	1.78371	−	11.2619i	0.0793741	−	0.501149i
$506$	−11.9383	−	11.9383i	−0.530722	−	0.530722i
$507$		0			0
$508$	15.9963	+	11.6220i	0.709721	+	0.515643i
$509$	−5.82573	+	11.4336i	−0.258221	+	0.506787i	−0.983326	−	0.181851i	$-0.941791\pi$
$509$	−5.82573	+	11.4336i	−0.258221	+	0.506787i	0.725105	+	0.688638i	$0.241791\pi$
$510$		0			0
$511$	0.112946	+	0.713115i	0.00499645	+	0.0315463i
$512$	−31.3114	+	43.0965i	−1.38378	+	1.90461i
$513$		0			0
$514$	2.92512	+	18.4685i	0.129021	+	0.814609i
$515$	10.2818	−	7.47015i	0.453069	−	0.329174i
$516$		0			0
$517$	−4.12266	−	2.99529i	−0.181314	−	0.131733i
$518$	18.8380	−	9.59844i	0.827694	−	0.421731i
$519$		0			0
$520$	−3.37101	+	21.2837i	−0.147829	+	0.933353i
$521$	−17.5110	−	34.3672i	−0.767169	−	1.50565i	−0.860181	−	0.509989i	$-0.829649\pi$
$521$	−17.5110	−	34.3672i	−0.767169	−	1.50565i	0.0930117	−	0.995665i	$-0.470351\pi$
$522$		0			0
$523$	−5.49317	−	16.9063i	−0.240200	−	0.739259i	−0.996389	−	0.0849058i	$-0.972941\pi$
$523$	−5.49317	−	16.9063i	−0.240200	−	0.739259i	0.756189	−	0.654353i	$-0.227059\pi$
$524$		−	43.6838i		−	1.90834i
$525$		0			0
$526$	−34.8116	+	5.51361i	−1.51786	+	0.240405i
$527$	−3.72409	−	0.589838i	−0.162224	−	0.0256937i
$528$		0			0
$529$	6.22243	−	19.1507i	0.270541	−	0.832638i
$530$	−23.6212	+	23.6212i	−1.02604	+	1.02604i
$531$		0			0
$532$	−34.7332			−1.50588
$533$	6.13265	+	10.1304i	0.265635	+	0.438795i
$534$		0			0
$535$	−3.56675	−	4.90921i	−0.154204	−	0.212244i
$536$	−99.9257	+	99.9257i	−4.31613	+	4.31613i
$537$		0			0
$538$	−41.9605	−	13.6338i	−1.80904	−	0.587794i
$539$	5.13141	+	0.812736i	0.221026	+	0.0350070i
$540$		0			0
$541$	−23.9953	+	7.79656i	−1.03164	+	0.335200i	−0.775439	−	0.631423i	$-0.782471\pi$
$541$	−23.9953	+	7.79656i	−1.03164	+	0.335200i	−0.256202	+	0.966623i	$0.582471\pi$
$542$			56.8164i			2.44047i
$543$		0			0
$544$	−45.6649	−	23.2674i	−1.95787	−	0.997582i
$545$	−4.44783	−	8.72936i	−0.190524	−	0.373925i
$546$		0			0
$547$	2.04384	+	2.04384i	0.0873882	+	0.0873882i	0.749450	−	0.662061i	$-0.230318\pi$
$547$	2.04384	+	2.04384i	0.0873882	+	0.0873882i	−0.662061	+	0.749450i	$0.730318\pi$
$548$	−36.5611	+	18.6288i	−1.56181	+	0.795783i
$549$		0			0
$550$	−4.11593	+	8.07796i	−0.175504	+	0.344445i
$551$	−6.40518	+	4.65364i	−0.272870	+	0.198252i
$552$		0			0
$553$	−5.93014	+	8.16214i	−0.252175	+	0.347090i
$554$	−7.82694	+	10.7729i	−0.332535	+	0.457695i
$555$		0			0
$556$	9.42423	−	6.84710i	0.399676	−	0.290382i
$557$	−2.79864	+	5.49264i	−0.118582	+	0.232731i	−0.942666	−	0.333737i	$-0.891690\pi$
$557$	−2.79864	+	5.49264i	−0.118582	+	0.232731i	0.824084	+	0.566468i	$0.191690\pi$
$558$		0			0
$559$	2.00203	−	1.02008i	0.0846767	−	0.0431450i
$560$	−15.8742	−	15.8742i	−0.670808	−	0.670808i
$561$		0			0
$562$	−7.23927	−	14.2079i	−0.305370	−	0.599323i
$563$	26.9664	+	13.7401i	1.13650	+	0.579075i	0.917928	−	0.396746i	$-0.129861\pi$
$563$	26.9664	+	13.7401i	1.13650	+	0.579075i	0.218570	+	0.975821i	$0.429861\pi$
$564$		0			0
$565$		−	2.32917i		−	0.0979891i
$566$	−37.6828	+	12.2439i	−1.58392	+	0.514648i
$567$		0			0
$568$	29.5653	+	4.68268i	1.24053	+	0.196481i
$569$	−19.3960	−	6.30213i	−0.813121	−	0.264199i	−0.127202	−	0.991877i	$-0.540600\pi$
$569$	−19.3960	−	6.30213i	−0.813121	−	0.264199i	−0.685919	+	0.727678i	$0.740600\pi$
$570$		0			0
$571$	20.9716	−	20.9716i	0.877633	−	0.877633i	−0.115656	−	0.993289i	$-0.536897\pi$
$571$	20.9716	−	20.9716i	0.877633	−	0.877633i	0.993289	+	0.115656i	$0.0368971\pi$
$572$	−5.61487	−	7.72821i	−0.234770	−	0.323133i
$573$		0			0
$574$	−21.1450	−	1.77946i	−0.882577	−	0.0742733i
$575$	−23.1636			−0.965987
$576$		0			0
$577$	−22.9911	+	22.9911i	−0.957132	+	0.957132i	−0.999118	−	0.0419858i	$-0.986632\pi$
$577$	−22.9911	+	22.9911i	−0.957132	+	0.957132i	0.0419858	+	0.999118i	$0.486632\pi$
$578$	−10.0697	+	30.9914i	−0.418844	+	1.28907i
$579$		0			0
$580$	−10.0157	−	1.58633i	−0.415880	−	0.0658690i
$581$	−13.3636	+	2.11659i	−0.554417	+	0.0878110i
$582$		0			0
$583$		−	9.42785i		−	0.390462i
$584$	−1.77050	−	5.44905i	−0.0732639	−	0.225483i
$585$		0			0
$586$	24.5053	+	48.0943i	1.01230	+	1.98676i
$587$	−3.81641	+	24.0959i	−0.157520	+	0.994543i	0.774615	+	0.632433i	$0.217944\pi$
$587$	−3.81641	+	24.0959i	−0.157520	+	0.994543i	−0.932135	+	0.362110i	$0.882056\pi$
$588$		0			0
$589$	7.75611	−	3.95194i	0.319585	−	0.162837i
$590$	20.7161	+	15.0512i	0.852870	+	0.619646i
$591$		0			0
$592$	−78.9134	+	57.3340i	−3.24332	+	2.35641i
$593$	−2.72495	−	17.2047i	−0.111900	−	0.706512i	−0.978305	−	0.207169i	$-0.933575\pi$
$593$	−2.72495	−	17.2047i	−0.111900	−	0.706512i	0.866405	−	0.499342i	$-0.166425\pi$
$594$		0			0
$595$	1.94994	−	2.68386i	0.0799396	−	0.110027i
$596$	−7.62575	−	48.1471i	−0.312363	−	1.97218i
$597$		0			0
$598$	15.1063	−	29.6478i	0.617744	−	1.21239i
$599$	−11.5445	−	8.38758i	−0.471696	−	0.342707i	0.326406	−	0.945230i	$-0.394162\pi$
$599$	−11.5445	−	8.38758i	−0.471696	−	0.342707i	−0.798102	+	0.602522i	$0.794162\pi$
$600$		0			0
$601$	−28.1452	−	28.1452i	−1.14807	−	1.14807i	−0.986933	−	0.161133i	$-0.948485\pi$
$601$	−28.1452	−	28.1452i	−1.14807	−	1.14807i	−0.161133	−	0.986933i	$-0.551515\pi$
$602$	−0.629849	+	3.97671i	−0.0256707	+	0.162079i
$603$		0			0
$604$	−26.2543	−	13.3772i	−1.06827	−	0.544312i
$605$	−3.79547	−	11.6813i	−0.154308	−	0.474911i
$606$		0			0
$607$	−10.7097	+	3.47978i	−0.434691	+	0.141240i	−0.518185	−	0.855269i	$-0.673392\pi$
$607$	−10.7097	+	3.47978i	−0.434691	+	0.141240i	0.0834937	+	0.996508i	$0.473392\pi$
$608$	116.865	−	18.5096i	4.73950	−	0.750663i
$609$		0			0
$610$	5.28514	+	1.71725i	0.213989	+	0.0695292i
$611$	3.10354	−	9.55171i	0.125556	−	0.386421i
$612$		0			0
$613$	22.6203	+	31.1342i	0.913625	+	1.25750i	0.965913	+	0.258865i	$0.0833485\pi$
$613$	22.6203	+	31.1342i	0.913625	+	1.25750i	−0.0522884	+	0.998632i	$0.516652\pi$
$614$	26.9872			1.08912
$615$		0			0
$616$	10.8978			0.439084
$617$	12.9147	+	17.7756i	0.519928	+	0.715619i	0.985554	−	0.169362i	$-0.0541708\pi$
$617$	12.9147	+	17.7756i	0.519928	+	0.715619i	−0.465626	+	0.884982i	$0.654171\pi$
$618$		0			0
$619$	6.35485	−	19.5582i	0.255423	−	0.786111i	−0.738323	−	0.674447i	$-0.764382\pi$
$619$	6.35485	−	19.5582i	0.255423	−	0.786111i	0.993746	−	0.111664i	$-0.0356180\pi$
$620$	10.6037	+	3.44535i	0.425855	+	0.138369i
$621$		0			0
$622$	68.6811	−	10.8780i	2.75386	−	0.436169i
$623$	−7.09302	+	2.30466i	−0.284176	+	0.0923343i
$624$		0			0
$625$	1.56754	+	4.82438i	0.0627014	+	0.192975i
$626$	−64.0140	−	32.6168i	−2.55851	−	1.30363i
$627$		0			0
$628$	7.20156	−	45.4689i	0.287374	−	1.81440i
$629$	−10.1923	−	10.1923i	−0.406394	−	0.406394i
$630$		0			0
$631$	−29.0459	−	21.1031i	−1.15630	−	0.840102i	−0.166995	−	0.985958i	$-0.553406\pi$
$631$	−29.0459	−	21.1031i	−1.15630	−	0.840102i	−0.989306	+	0.145856i	$0.953406\pi$
$632$	36.3469	−	71.3349i	1.44580	−	2.83755i
$633$		0			0
$634$	8.90083	+	56.1976i	0.353497	+	2.23189i
$635$	2.56271	−	3.52727i	0.101698	−	0.139976i
$636$		0			0
$637$	1.60178	+	10.1133i	0.0634650	+	0.400702i
$638$	3.15662	−	2.29342i	0.124972	−	0.0907973i
$639$		0			0
$640$	40.3511	+	29.3168i	1.59502	+	1.15885i
$641$	23.1194	−	11.7799i	0.913160	−	0.465278i	0.0667257	−	0.997771i	$-0.478745\pi$
$641$	23.1194	−	11.7799i	0.913160	−	0.465278i	0.846434	+	0.532493i	$0.178745\pi$
$642$		0			0
$643$	6.58370	−	41.5679i	0.259636	−	1.63928i	−0.421291	−	0.906926i	$-0.638423\pi$
$643$	6.58370	−	41.5679i	0.259636	−	1.63928i	0.680927	−	0.732351i	$-0.261577\pi$
$644$	19.8549	+	38.9674i	0.782392	+	1.53553i
$645$		0			0
$646$	9.97627	+	30.7038i	0.392511	+	1.20802i
$647$			25.3408i			0.996251i	0.867105	+	0.498125i	$0.165978\pi$
$647$			25.3408i			0.996251i	−0.867105	+	0.498125i	$0.834022\pi$
$648$		0			0
$649$	−7.13784	+	1.13052i	−0.280185	+	0.0443769i
$650$	−17.6480	−	2.79517i	−0.692211	−	0.109635i
$651$		0			0
$652$	0.281772	−	0.867204i	0.0110350	−	0.0339623i
$653$	10.0983	−	10.0983i	0.395178	−	0.395178i	−0.481350	−	0.876528i	$-0.659853\pi$
$653$	10.0983	−	10.0983i	0.395178	−	0.395178i	0.876528	+	0.481350i	$0.159853\pi$
$654$		0			0
$655$	−9.63252			−0.376374
$656$	97.6379	−	7.15227i	3.81212	−	0.279249i
$657$		0			0
$658$	10.5781	+	14.5595i	0.412378	+	0.567590i
$659$	−3.30690	+	3.30690i	−0.128818	+	0.128818i	−0.768576	−	0.639758i	$-0.779035\pi$
$659$	−3.30690	+	3.30690i	−0.128818	+	0.128818i	0.639758	+	0.768576i	$0.279035\pi$
$660$		0			0
$661$	−16.5128	−	5.36534i	−0.642274	−	0.208688i	−0.0302696	−	0.999542i	$-0.509637\pi$
$661$	−16.5128	−	5.36534i	−0.642274	−	0.208688i	−0.612005	+	0.790854i	$0.709637\pi$
$662$	−17.2308	−	2.72909i	−0.669693	−	0.106069i
$663$		0			0
$664$	102.114	−	33.1789i	3.96279	−	1.28759i
$665$			7.65887i			0.296998i
$666$		0			0
$667$	8.88240	+	4.52581i	0.343928	+	0.175240i
$668$	−15.2864	−	30.0013i	−0.591449	−	1.16078i
$669$		0			0
$670$	34.6094	+	34.6094i	1.33708	+	1.33708i
$671$	−1.39742	+	0.712021i	−0.0539468	+	0.0274872i
$672$		0			0
$673$	−1.92976	+	3.78737i	−0.0743869	+	0.145992i	−0.925205	−	0.379468i	$-0.876107\pi$
$673$	−1.92976	+	3.78737i	−0.0743869	+	0.145992i	0.850818	+	0.525461i	$0.176107\pi$
$674$	−24.5201	+	17.8149i	−0.944479	+	0.686205i
$675$		0			0
$676$	−30.9939	+	42.6595i	−1.19207	+	1.64075i
$677$	20.9582	−	28.8465i	0.805490	−	1.10866i	−0.186514	−	0.982452i	$-0.559719\pi$
$677$	20.9582	−	28.8465i	0.805490	−	1.10866i	0.992004	−	0.126209i	$-0.0402811\pi$
$678$		0			0
$679$	−16.5030	+	11.9901i	−0.633326	+	0.460138i
$680$	−11.9515	+	23.4562i	−0.458320	+	0.899503i
$681$		0			0
$682$	−3.82239	+	1.94760i	−0.146367	+	0.0745776i
$683$	−33.1183	−	33.1183i	−1.26724	−	1.26724i	−0.947510	−	0.319726i	$-0.896409\pi$
$683$	−33.1183	−	33.1183i	−1.26724	−	1.26724i	−0.319726	−	0.947510i	$-0.603591\pi$
$684$		0			0
$685$	4.10775	+	8.06191i	0.156949	+	0.308030i
$686$	−37.0175	−	18.8614i	−1.41334	−	0.720130i
$687$		0			0
$688$		−	18.5756i		−	0.708189i
$689$	17.6715	−	5.74182i	0.673231	−	0.218746i
$690$		0			0
$691$	−33.4395	−	5.29630i	−1.27210	−	0.201481i	−0.516371	−	0.856365i	$-0.672717\pi$
$691$	−33.4395	−	5.29630i	−1.27210	−	0.201481i	−0.755729	+	0.654884i	$0.772717\pi$
$692$	100.139	+	32.5371i	3.80672	+	1.23688i
$693$		0			0
$694$	2.45436	−	2.45436i	0.0931664	−	0.0931664i
$695$	−1.50982	−	2.07809i	−0.0572708	−	0.0788266i
$696$		0			0
$697$	3.30097	+	14.0852i	0.125033	+	0.533517i
$698$	−38.8744			−1.47142
$699$		0			0
$700$	16.6061	−	16.6061i	0.627653	−	0.627653i
$701$	2.77956	−	8.55460i	0.104982	−	0.323103i	−0.884744	−	0.466078i	$-0.845667\pi$
$701$	2.77956	−	8.55460i	0.104982	−	0.323103i	0.989726	+	0.142975i	$0.0456668\pi$
$702$		0			0
$703$	32.8678	+	5.20575i	1.23963	+	0.196338i
$704$	−29.2525	+	4.63314i	−1.10250	+	0.174618i
$705$		0			0
$706$			2.80153i			0.105437i
$707$	−3.51188	−	10.8085i	−0.132078	−	0.406494i
$708$		0			0
$709$	−6.86482	−	13.4730i	−0.257814	−	0.505988i	0.725427	−	0.688299i	$-0.241642\pi$
$709$	−6.86482	−	13.4730i	−0.257814	−	0.505988i	−0.983241	+	0.182311i	$0.941642\pi$
$710$	1.62185	−	10.2400i	0.0608671	−	0.384300i
$711$		0			0
$712$	52.7327	−	26.8687i	1.97624	−	1.00695i
$713$	−8.86739	−	6.44254i	−0.332087	−	0.241275i
$714$		0			0
$715$	−1.70411	+	1.23811i	−0.0637302	+	0.0463027i
$716$	11.2272	+	70.8860i	0.419581	+	2.64913i
$717$		0			0
$718$	−18.0576	+	24.8541i	−0.673902	+	0.927547i
$719$	−6.05643	−	38.2388i	−0.225867	−	1.42607i	−0.796389	−	0.604785i	$-0.793259\pi$
$719$	−6.05643	−	38.2388i	−0.225867	−	1.42607i	0.570522	−	0.821282i	$-0.306741\pi$
$720$		0			0
$721$	5.75073	−	11.2864i	0.214168	−	0.420329i
$722$	−18.1901	−	13.2159i	−0.676965	−	0.491844i
$723$		0			0
$724$	−46.2441	−	46.2441i	−1.71865	−	1.71865i
$725$	0.837423	−	5.28728i	0.0311011	−	0.196365i
$726$		0			0
$727$	23.9407	+	12.1984i	0.887912	+	0.452414i	0.837577	−	0.546319i	$-0.183971\pi$
$727$	23.9407	+	12.1984i	0.887912	+	0.452414i	0.0503346	+	0.998732i	$0.483971\pi$
$728$	6.63705	+	20.4268i	0.245986	+	0.757066i
$729$		0			0
$730$	−1.88729	+	0.613216i	−0.0698516	+	0.0226962i
$731$	2.71118	−	0.429408i	0.100277	−	0.0158822i
$732$		0			0
$733$	4.87811	+	1.58499i	0.180177	+	0.0585431i	0.397716	−	0.917509i	$-0.369803\pi$
$733$	4.87811	+	1.58499i	0.180177	+	0.0585431i	−0.217539	+	0.976052i	$0.569803\pi$
$734$	−24.3041	+	74.8002i	−0.897079	+	2.76093i
$735$		0			0
$736$	−87.5706	−	120.531i	−3.22789	−	4.44281i
$737$	−13.8135			−0.508828
$738$		0			0
$739$	1.40461			0.0516695			0.0258348	−	0.999666i	$-0.491776\pi$
$739$	1.40461			0.0516695			0.0258348	+	0.999666i	$0.491776\pi$
$740$	25.0529	+	34.4823i	0.920962	+	1.26760i
$741$		0			0
$742$	−10.2888	+	31.6657i	−0.377714	+	1.16248i
$743$	8.77872	+	2.85238i	0.322060	+	0.104644i	0.465585	−	0.885003i	$-0.345844\pi$
$743$	8.77872	+	2.85238i	0.322060	+	0.104644i	−0.143525	+	0.989647i	$0.545844\pi$
$744$		0			0
$745$	−10.6167	+	1.68152i	−0.388966	+	0.0616061i
$746$	88.6254	−	28.7961i	3.24481	−	1.05430i
$747$		0			0
$748$	−3.60622	−	11.0988i	−0.131856	−	0.405812i
$749$	−5.38890	−	2.74578i	−0.196906	−	0.100329i
$750$		0			0
$751$	−4.42188	+	27.9186i	−0.161357	+	1.01877i	0.765523	+	0.643408i	$0.222480\pi$
$751$	−4.42188	+	27.9186i	−0.161357	+	1.01877i	−0.926880	+	0.375358i	$0.877520\pi$
$752$	−58.7103	−	58.7103i	−2.14094	−	2.14094i
$753$		0			0
$754$	6.22124	+	4.52000i	0.226564	+	0.164609i
$755$	−2.94975	+	5.78922i	−0.107352	+	0.210691i
$756$		0			0
$757$	2.19110	+	13.8341i	0.0796371	+	0.502809i	0.994975	+	0.100122i	$0.0319234\pi$
$757$	2.19110	+	13.8341i	0.0796371	+	0.502809i	−0.915338	+	0.402686i	$0.868077\pi$
$758$	11.2645	−	15.5042i	0.409145	−	0.563139i
$759$		0			0
$760$	−9.50762	−	60.0287i	−0.344877	−	2.17747i
$761$	−38.0493	+	27.6444i	−1.37929	+	1.00211i	−0.382339	+	0.924022i	$0.624881\pi$
$761$	−38.0493	+	27.6444i	−1.37929	+	1.00211i	−0.996946	+	0.0780880i	$0.975119\pi$
$762$		0			0
$763$	−7.89995	−	5.73965i	−0.285998	−	0.207789i
$764$	−2.11691	+	1.07862i	−0.0765870	+	0.0390230i
$765$		0			0
$766$	8.17000	−	51.5834i	0.295194	−	1.86378i
$767$	−6.46619	−	12.6906i	−0.233480	−	0.458231i
$768$		0			0
$769$	−6.58433	−	20.2645i	−0.237437	−	0.730756i	−0.996789	−	0.0800756i	$-0.974484\pi$
$769$	−6.58433	−	20.2645i	−0.237437	−	0.730756i	0.759352	−	0.650680i	$-0.225516\pi$
$770$		−	3.77447i		−	0.136022i
$771$		0			0
$772$	115.280	−	18.2586i	4.14902	−	0.657140i
$773$	−39.6933	−	6.28681i	−1.42767	−	0.226121i	−0.605719	−	0.795679i	$-0.707114\pi$
$773$	−39.6933	−	6.28681i	−1.42767	−	0.226121i	−0.821951	+	0.569558i	$0.807114\pi$
$774$		0			0
$775$	−1.81880	+	5.59768i	−0.0653331	+	0.201075i
$776$	114.463	−	114.463i	4.10897	−	4.10897i
$777$		0			0
$778$	−50.2234			−1.80059
$779$	−25.2792	−	21.8284i	−0.905720	−	0.782083i
$780$		0			0
$781$	1.71986	+	2.36719i	0.0615415	+	0.0847046i
$782$	28.7439	−	28.7439i	1.02788	−	1.02788i
$783$		0			0
$784$	80.5067	+	26.1582i	2.87524	+	0.934222i
$785$	−10.0261	−	1.58798i	−0.357848	−	0.0566775i
$786$		0			0
$787$	−16.3451	+	5.31086i	−0.582642	+	0.189312i	−0.585484	−	0.810684i	$-0.699095\pi$
$787$	−16.3451	+	5.31086i	−0.582642	+	0.189312i	0.00284204	+	0.999996i	$0.499095\pi$
$788$		−	128.996i		−	4.59529i
$789$		0			0
$790$	−24.7070	−	12.5888i	−0.879034	−	0.447890i
$791$	−1.05394	−	2.06846i	−0.0374736	−	0.0735461i
$792$		0			0
$793$	−2.18567	−	2.18567i	−0.0776156	−	0.0776156i
$794$	−20.3208	+	10.3540i	−0.721158	+	0.367449i
$795$		0			0
$796$	−13.1742	+	25.8557i	−0.466946	+	0.916432i
$797$	−26.3389	+	19.1363i	−0.932971	+	0.677843i	−0.946719	−	0.322062i	$-0.895624\pi$
$797$	−26.3389	+	19.1363i	−0.932971	+	0.677843i	0.0137472	+	0.999906i	$0.495624\pi$
$798$		0			0
$799$	7.21177	−	9.92616i	0.255134	−	0.351162i
$800$	−47.0242	+	64.7233i	−1.66256	+	2.28831i
$801$		0			0
$802$	9.31216	−	6.76568i	0.328824	−	0.238904i
$803$	0.254257	−	0.499008i	0.00897255	−	0.0176096i
$804$		0			0
$805$	8.59253	−	4.37811i	0.302847	−	0.154308i
$806$	−5.97852	−	5.97852i	−0.210584	−	0.210584i
$807$		0			0
$808$	40.9429	+	80.3550i	1.44037	+	2.82688i
$809$	29.0682	+	14.8110i	1.02198	+	0.520727i	0.882904	−	0.469554i	$-0.155585\pi$
$809$	29.0682	+	14.8110i	1.02198	+	0.520727i	0.139081	+	0.990281i	$0.455585\pi$
$810$		0			0
$811$		−	7.47871i		−	0.262613i	−0.991342	−	0.131306i	$-0.958083\pi$
$811$		−	7.47871i		−	0.262613i	0.991342	−	0.131306i	$-0.0419172\pi$
$812$	−9.61245	+	3.12327i	−0.337331	+	0.109605i
$813$		0			0
$814$	−16.1980	−	2.56551i	−0.567739	−	0.0899211i
$815$	−0.191223	−	0.0621322i	−0.00669826	−	0.00217640i
$816$		0			0
$817$	−4.48111	+	4.48111i	−0.156774	+	0.156774i
$818$	62.2547	+	85.6863i	2.17669	+	2.99595i
$819$		0			0
$820$	−3.12529	−	42.6642i	−0.109140	−	1.48990i
$821$	31.8344			1.11103			0.555514	−	0.831507i	$-0.312521\pi$
$821$	31.8344			1.11103			0.555514	+	0.831507i	$0.312521\pi$
$822$		0			0
$823$	−26.9979	+	26.9979i	−0.941087	+	0.941087i	−0.998359	−	0.0572719i	$-0.981760\pi$
$823$	−26.9979	+	26.9979i	−0.941087	+	0.941087i	0.0572719	+	0.998359i	$0.481760\pi$
$824$	−31.0623	+	95.5998i	−1.08210	+	3.33038i
$825$		0			0
$826$	25.2079	+	3.99254i	0.877094	+	0.138918i
$827$	26.4709	−	4.19258i	0.920485	−	0.145790i	0.321830	−	0.946798i	$-0.395702\pi$
$827$	26.4709	−	4.19258i	0.920485	−	0.145790i	0.598655	+	0.801007i	$0.295702\pi$
$828$		0			0
$829$		−	38.1519i		−	1.32507i	−0.749031	−	0.662535i	$-0.769481\pi$
$829$		−	38.1519i		−	1.32507i	0.749031	−	0.662535i	$-0.230519\pi$
$830$	−11.4915	−	35.3674i	−0.398877	−	1.22762i
$831$		0			0
$832$	−26.4999	−	52.0090i	−0.918720	−	1.80309i
$833$	−1.95683	+	12.3549i	−0.0678001	+	0.428073i
$834$		0			0
$835$	−6.61544	+	3.37074i	−0.228937	+	0.116649i
$836$	21.7967	+	15.8362i	0.753854	+	0.547707i
$837$		0			0
$838$	19.7744	−	14.3669i	0.683095	−	0.496298i
$839$	8.25907	+	52.1457i	0.285135	+	1.80027i	0.549120	+	0.835743i	$0.314963\pi$
$839$	8.25907	+	52.1457i	0.285135	+	1.80027i	−0.263986	+	0.964527i	$0.585037\pi$
$840$		0			0
$841$	15.6916	−	21.5976i	0.541090	−	0.744746i
$842$	8.28018	+	52.2790i	0.285354	+	1.80165i
$843$		0			0
$844$	−55.3961	+	108.721i	−1.90681	+	3.74233i
$845$	9.40665	+	6.83433i	0.323599	+	0.235108i
$846$		0			0
$847$	−8.65633	−	8.65633i	−0.297435	−	0.297435i
$848$	24.0300	−	151.720i	0.825194	−	5.21007i
$849$		0			0
$850$	−19.4494	−	9.90994i	−0.667107	−	0.339908i
$851$	−12.9482	−	39.8503i	−0.443857	−	1.36605i
$852$		0			0
$853$	10.6787	−	3.46971i	0.365631	−	0.118801i	−0.120439	−	0.992721i	$-0.538430\pi$
$853$	10.6787	−	3.46971i	0.365631	−	0.118801i	0.486069	+	0.873920i	$0.338430\pi$
$854$	5.47061	−	0.866459i	0.187200	−	0.0296496i
$855$		0			0
$856$	45.6457	+	14.8312i	1.56014	+	0.506920i
$857$	2.69200	−	8.28512i	0.0919569	−	0.283014i	−0.894492	−	0.447084i	$-0.852462\pi$
$857$	2.69200	−	8.28512i	0.0919569	−	0.283014i	0.986449	+	0.164070i	$0.0524624\pi$
$858$		0			0
$859$	16.6627	+	22.9343i	0.568525	+	0.782508i	0.992379	−	0.123223i	$-0.0393230\pi$
$859$	16.6627	+	22.9343i	0.568525	+	0.782508i	−0.423854	+	0.905731i	$0.639323\pi$
$860$	−8.11688			−0.276783
$861$		0			0
$862$	−54.0645			−1.84145
$863$	−21.9985	−	30.2783i	−0.748836	−	1.03068i	−0.998061	−	0.0622388i	$-0.980176\pi$
$863$	−21.9985	−	30.2783i	−0.748836	−	1.03068i	0.249225	−	0.968446i	$-0.419824\pi$
$864$		0			0
$865$	7.17462	−	22.0812i	0.243944	−	0.750784i
$866$	−27.2538	−	8.85531i	−0.926123	−	0.300916i
$867$		0			0
$868$	10.9758	−	1.73840i	0.372544	−	0.0590051i
$869$	7.44287	−	2.41833i	0.252482	−	0.0820364i
$870$		0			0
$871$	−8.41282	−	25.8920i	−0.285058	−	0.877317i
$872$	69.0434	+	35.1794i	2.33811	+	1.19132i
$873$		0			0
$874$	−14.6810	+	92.6923i	−0.496593	+	3.13536i
$875$	−8.85302	−	8.85302i	−0.299287	−	0.299287i
$876$		0			0
$877$	−23.6500	−	17.1827i	−0.798604	−	0.580219i	0.111901	−	0.993719i	$-0.464306\pi$
$877$	−23.6500	−	17.1827i	−0.798604	−	0.580219i	−0.910504	+	0.413500i	$0.864306\pi$
$878$	−37.3965	+	73.3947i	−1.26207	+	2.47695i
$879$		0			0
$880$	2.72413	+	17.1995i	0.0918303	+	0.579793i
$881$	10.9101	−	15.0165i	0.367571	−	0.505918i	−0.584668	−	0.811273i	$-0.698775\pi$
$881$	10.9101	−	15.0165i	0.367571	−	0.505918i	0.952239	+	0.305355i	$0.0987752\pi$
$882$		0			0
$883$	−7.30514	−	46.1228i	−0.245838	−	1.55216i	−0.733844	−	0.679318i	$-0.762276\pi$
$883$	−7.30514	−	46.1228i	−0.245838	−	1.55216i	0.488007	−	0.872840i	$-0.337724\pi$
$884$	18.6072	−	13.5190i	0.625829	−	0.454692i
$885$		0			0
$886$	48.5798	+	35.2953i	1.63207	+	1.18577i
$887$	0.882451	−	0.449631i	0.0296298	−	0.0150971i	−0.439113	−	0.898432i	$-0.644707\pi$
$887$	0.882451	−	0.449631i	0.0296298	−	0.0150971i	0.468743	+	0.883335i	$0.344707\pi$
$888$		0			0
$889$	0.679797	−	4.29207i	0.0227997	−	0.143951i
$890$	−9.30600	−	18.2641i	−0.311938	−	0.612213i
$891$		0			0
$892$	−40.2865	−	123.989i	−1.34889	−	4.15146i
$893$			28.3261i			0.947896i
$894$		0			0
$895$	15.6307	−	2.47567i	0.522478	−	0.0827524i
$896$	49.1001	+	7.77670i	1.64032	+	0.259801i
$897$		0			0
$898$	−4.22691	+	13.0091i	−0.141054	+	0.434119i
$899$	1.79114	−	1.79114i	0.0597380	−	0.0597380i
$900$		0			0
$901$	22.6995			0.756230
$902$	12.4581	+	10.7575i	0.414811	+	0.358187i
$903$		0			0
$904$	10.8283	+	14.9039i	0.360144	+	0.495696i
$905$	−10.1971	+	10.1971i	−0.338962	+	0.338962i
$906$		0			0
$907$	−5.02782	−	1.63364i	−0.166946	−	0.0542440i	0.224352	−	0.974508i	$-0.427974\pi$
$907$	−5.02782	−	1.63364i	−0.166946	−	0.0542440i	−0.391297	+	0.920264i	$0.627974\pi$
$908$	−77.9205	−	12.3414i	−2.58588	−	0.409564i
$909$		0			0
$910$	7.07484	−	2.29875i	0.234529	−	0.0762029i
$911$			16.7723i			0.555691i	0.960626	+	0.277845i	$0.0896203\pi$
$911$			16.7723i			0.555691i	−0.960626	+	0.277845i	$0.910380\pi$
$912$		0			0
$913$	9.35132	+	4.76473i	0.309483	+	0.157690i
$914$	15.2713	+	29.9715i	0.505128	+	0.991370i
$915$		0			0
$916$	80.3414	+	80.3414i	2.65455	+	2.65455i
$917$	−8.55433	+	4.35865i	−0.282489	+	0.143935i
$918$		0			0
$919$	−20.4457	+	40.1269i	−0.674440	+	1.32366i	0.259330	+	0.965789i	$0.416498\pi$
$919$	−20.4457	+	40.1269i	−0.674440	+	1.32366i	−0.933770	+	0.357874i	$0.883502\pi$
$920$	−61.9116	+	44.9814i	−2.04117	+	1.48299i
$921$		0			0
$922$	47.4019	−	65.2431i	1.56110	−	2.14867i
$923$	−3.38960	+	4.66538i	−0.111570	+	0.153563i
$924$		0			0
$925$	−18.2032	+	13.2254i	−0.598516	+	0.434847i
$926$	−22.6634	+	44.4794i	−0.744764	+	1.46168i
$927$		0			0
$928$	30.6780	−	15.6312i	1.00706	−	0.513121i
$929$	9.65576	+	9.65576i	0.316795	+	0.316795i	0.847535	−	0.530740i	$-0.178086\pi$
$929$	9.65576	+	9.65576i	0.316795	+	0.316795i	−0.530740	+	0.847535i	$0.678086\pi$
$930$		0			0
$931$	−13.1108	−	25.7314i	−0.429690	−	0.843314i
$932$	−88.4581	−	45.0717i	−2.89754	−	1.47637i
$933$		0			0
$934$			47.2276i			1.54533i
$935$	−2.44735	+	0.795191i	−0.0800368	+	0.0260055i
$936$		0			0
$937$	18.4731	+	2.92586i	0.603491	+	0.0955836i	0.450701	−	0.892675i	$-0.351174\pi$
$937$	18.4731	+	2.92586i	0.603491	+	0.0955836i	0.152790	+	0.988259i	$0.451174\pi$
$938$	46.3960	+	15.0750i	1.51488	+	0.492216i
$939$		0			0
$940$	−25.6543	+	25.6543i	−0.836750	+	0.836750i
$941$	−16.6302	−	22.8895i	−0.542129	−	0.746176i	0.446789	−	0.894639i	$-0.352567\pi$
$941$	−16.6302	−	22.8895i	−0.542129	−	0.746176i	−0.988918	+	0.148463i	$0.952567\pi$
$942$		0			0
$943$	−10.0388	+	40.8388i	−0.326909	+	1.32989i
$944$	−117.749			−3.83239
$945$		0			0
$946$	2.20839	−	2.20839i	0.0718011	−	0.0718011i
$947$	3.74796	−	11.5350i	0.121792	−	0.374839i	−0.871511	−	0.490377i	$-0.836859\pi$
$947$	3.74796	−	11.5350i	0.121792	−	0.374839i	0.993303	+	0.115538i	$0.0368592\pi$
$948$		0			0
$949$	1.09019	+	0.172669i	0.0353890	+	0.00560507i
$950$	49.7745	−	7.88351i	1.61490	−	0.255775i
$951$		0			0
$952$			26.2387i			0.850400i
$953$	9.89902	+	30.4661i	0.320661	+	0.986892i	0.973361	+	0.229276i	$0.0736359\pi$
$953$	9.89902	+	30.4661i	0.320661	+	0.986892i	−0.652701	+	0.757616i	$0.726364\pi$
$954$		0			0
$955$	0.237841	+	0.466789i	0.00769636	+	0.0151049i
$956$	−19.5486	+	123.425i	−0.632247	+	3.99185i
$957$		0			0
$958$	−54.7125	+	27.8774i	−1.76768	+	0.900679i
$959$	7.29592	+	5.30080i	0.235598	+	0.171172i
$960$		0			0
$961$	22.8264	−	16.5843i	0.736334	−	0.534978i
$962$	−5.05625	−	31.9239i	−0.163020	−	1.02927i
$963$		0			0
$964$	10.1059	−	13.9096i	0.325490	−	0.447999i
$965$	−4.02611	−	25.4199i	−0.129605	−	0.818294i
$966$		0			0
$967$	−18.5414	+	36.3896i	−0.596252	+	1.17021i	0.373845	+	0.927491i	$0.378039\pi$
$967$	−18.5414	+	36.3896i	−0.596252	+	1.17021i	−0.970097	+	0.242719i	$0.921961\pi$
$968$	78.5925	+	57.1008i	2.52606	+	1.83529i
$969$		0			0
$970$	−39.6444	−	39.6444i	−1.27290	−	1.27290i
$971$	2.17456	−	13.7297i	0.0697851	−	0.440606i	−0.927913	−	0.372796i	$-0.878399\pi$
$971$	2.17456	−	13.7297i	0.0697851	−	0.440606i	0.997698	−	0.0678093i	$-0.0216010\pi$
$972$		0			0
$973$	−2.28115	−	1.16230i	−0.0731303	−	0.0372617i
$974$	−0.327173	−	1.00694i	−0.0104833	−	0.0322643i
$975$		0			0
$976$	−24.3031	+	7.89654i	−0.777922	+	0.252762i
$977$	45.5148	−	7.20884i	1.45615	−	0.230631i	0.622367	−	0.782726i	$-0.286171\pi$
$977$	45.5148	−	7.20884i	1.45615	−	0.230631i	0.833781	+	0.552095i	$0.186171\pi$
$978$		0			0
$979$	5.50197	+	1.78770i	0.175844	+	0.0571351i
$980$	11.4302	−	35.1786i	0.365125	−	1.12374i
$981$		0			0
$982$	43.3188	+	59.6232i	1.38236	+	1.90265i
$983$	25.4016			0.810185			0.405093	−	0.914276i	$-0.367239\pi$
$983$	25.4016			0.810185			0.405093	+	0.914276i	$0.367239\pi$
$984$		0			0
$985$	−28.4443			−0.906312
$986$	5.52188	+	7.60021i	0.175852	+	0.242040i
$987$		0			0
$988$	−16.4085	+	50.5003i	−0.522025	+	1.60663i
$989$	7.58896	+	2.46580i	0.241315	+	0.0784080i
$990$		0			0
$991$	27.6423	−	4.37811i	0.878087	−	0.139075i	0.298914	−	0.954280i	$-0.403376\pi$
$991$	27.6423	−	4.37811i	0.878087	−	0.139075i	0.579173	+	0.815205i	$0.303376\pi$
$992$	−36.0033	+	11.6982i	−1.14311	+	0.371418i
$993$		0			0
$994$	−3.19321	−	9.82768i	−0.101282	−	0.311715i
$995$	5.70133	+	2.90497i	0.180744	+	0.0920938i
$996$		0			0
$997$	−4.76664	+	30.0954i	−0.150961	+	0.953130i	0.789629	+	0.613585i	$0.210273\pi$
$997$	−4.76664	+	30.0954i	−0.150961	+	0.953130i	−0.940590	+	0.339545i	$0.889727\pi$
$998$	−17.7360	−	17.7360i	−0.561425	−	0.561425i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.118.3		24
3.2	odd	2		41.2.g.a.36.1	yes	24
12.11	even	2		656.2.bs.d.241.1		24
41.8	even	20	inner	369.2.u.a.172.3		24
123.8	odd	20		41.2.g.a.8.1	✓	24
123.89	even	40		1681.2.a.m.1.23		24
123.116	even	40		1681.2.a.m.1.24		24
492.131	even	20		656.2.bs.d.49.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.8.1	✓	24	123.8	odd	20
41.2.g.a.36.1	yes	24	3.2	odd	2
369.2.u.a.118.3		24	1.1	even	1	trivial
369.2.u.a.172.3		24	41.8	even	20	inner
656.2.bs.d.49.1		24	492.131	even	20
656.2.bs.d.241.1		24	12.11	even	2
1681.2.a.m.1.23		24	123.89	even	40
1681.2.a.m.1.24		24	123.116	even	40

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61018 + 2.21623i) q^{2} +(-1.70094 + 5.23496i) q^{4} +(1.15434 + 0.375067i) q^{5} +(1.19485 - 0.189245i) q^{7} +(-9.13005 + 2.96653i) q^{8} +O(q^{10})\)	\(q+(1.61018 + 2.21623i) q^{2} +(-1.70094 + 5.23496i) q^{4} +(1.15434 + 0.375067i) q^{5} +(1.19485 - 0.189245i) q^{7} +(-9.13005 + 2.96653i) q^{8} +(1.02746 + 3.16221i) q^{10} +(-0.836104 - 0.426016i) q^{11} +(0.289312 - 1.82664i) q^{13} +(2.34333 + 2.34333i) q^{14} +(-12.3693 - 8.98684i) q^{16} +(1.02572 - 2.01309i) q^{17} +(0.815977 + 5.15188i) q^{19} +(-3.92693 + 5.40495i) q^{20} +(-0.402132 - 2.53896i) q^{22} +(5.31348 - 3.86047i) q^{23} +(-2.85326 - 2.07302i) q^{25} +(4.51411 - 2.30005i) q^{26} +(-1.04167 + 6.57687i) q^{28} +(0.689088 + 1.35241i) q^{29} +(-0.515703 - 1.58717i) q^{31} -22.6839i q^{32} +(6.11308 - 0.968216i) q^{34} +(1.45024 + 0.229695i) q^{35} +(1.97146 - 6.06752i) q^{37} +(-10.1039 + 10.1039i) q^{38} -11.6518 q^{40} +(-4.89143 + 4.13206i) q^{41} +(0.714124 + 0.982908i) q^{43} +(3.65235 - 3.65235i) q^{44} +(17.1114 + 5.55982i) q^{46} +(5.36365 + 0.849519i) q^{47} +(-5.26555 + 1.71088i) q^{49} -9.66143i q^{50} +(9.07032 + 4.62156i) q^{52} +(4.56121 + 8.95188i) q^{53} +(-0.805362 - 0.805362i) q^{55} +(-10.3476 + 5.27237i) q^{56} +(-1.88770 + 3.70481i) q^{58} +(6.23053 - 4.52674i) q^{59} +(0.982392 - 1.35215i) q^{61} +(2.68716 - 3.69855i) q^{62} +(25.5342 - 18.5517i) q^{64} +(1.01908 - 2.00005i) q^{65} +(13.1161 - 6.68301i) q^{67} +(8.79377 + 8.79377i) q^{68} +(1.82609 + 3.58391i) q^{70} +(-2.77828 - 1.41561i) q^{71} +0.596826i q^{73} +(16.6214 - 5.40063i) q^{74} +(-28.3578 - 4.49144i) q^{76} +(-1.07964 - 0.350796i) q^{77} +(-5.89711 + 5.89711i) q^{79} +(-10.9077 - 15.0132i) q^{80} +(-17.0337 - 4.18715i) q^{82} -11.1844 q^{83} +(1.93908 - 1.93908i) q^{85} +(-1.02848 + 3.16533i) q^{86} +(8.89746 + 1.40922i) q^{88} +(-6.08909 + 0.964418i) q^{89} -2.23731i q^{91} +(11.1715 + 34.3823i) q^{92} +(6.75374 + 13.2550i) q^{94} +(-0.990387 + 6.25306i) q^{95} +(-15.0243 + 7.65525i) q^{97} +(-12.2702 - 8.91483i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

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