LMFDB - Embedded newform 475.2.e.g.201.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, degree $2$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6x^{10} + 29x^{8} + 40x^{6} + 43x^{4} + 7x^{2} + 1 $ x^12 + 6x^10 + 29x^8 + 40x^6 + 43x^4 + 7*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.5
Root			$-0.579521 + 1.00376i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.g.26.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.431391 - 0.747190i) q^{2} +(1.53957 - 2.66661i) q^{3} +(0.627804 + 1.08739i) q^{4} +(-1.32831 - 2.30070i) q^{6} -0.566520 q^{7} +2.80888 q^{8} +(-3.24054 - 5.61278i) q^{9} +O(q^{10})$	\(q+(0.431391 - 0.747190i) q^{2} +(1.53957 - 2.66661i) q^{3} +(0.627804 + 1.08739i) q^{4} +(-1.32831 - 2.30070i) q^{6} -0.566520 q^{7} +2.80888 q^{8} +(-3.24054 - 5.61278i) q^{9} -1.91223 q^{11} +3.86619 q^{12} +(0.0972656 + 0.168469i) q^{13} +(-0.244391 + 0.423298i) q^{14} +(-0.0438854 + 0.0760118i) q^{16} +(2.64775 - 4.58603i) q^{17} -5.59175 q^{18} +(-2.36834 - 3.65936i) q^{19} +(-0.872196 + 1.51069i) q^{21} +(-0.824918 + 1.42880i) q^{22} +(1.68770 + 2.92318i) q^{23} +(4.32446 - 7.49018i) q^{24} +0.167838 q^{26} -10.7187 q^{27} +(-0.355664 - 0.616027i) q^{28} +(4.36834 + 7.56619i) q^{29} +5.65662 q^{31} +(2.84674 + 4.93070i) q^{32} +(-2.94401 + 5.09917i) q^{33} +(-2.28442 - 3.95674i) q^{34} +(4.06885 - 7.04745i) q^{36} -0.955582 q^{37} +(-3.75592 + 0.190988i) q^{38} +0.598988 q^{39} +(-5.02496 + 8.70349i) q^{41} +(0.752514 + 1.30339i) q^{42} +(-2.46622 + 4.27161i) q^{43} +(-1.20051 - 2.07934i) q^{44} +2.91223 q^{46} +(4.41971 + 7.65516i) q^{47} +(0.135129 + 0.234051i) q^{48} -6.67906 q^{49} +(-8.15277 - 14.1210i) q^{51} +(-0.122128 + 0.211531i) q^{52} +(-4.10305 - 7.10669i) q^{53} +(-4.62395 + 8.00892i) q^{54} -1.59128 q^{56} +(-13.4043 + 0.681609i) q^{57} +7.53785 q^{58} +(-1.85713 + 3.21664i) q^{59} +(1.75561 + 3.04080i) q^{61} +(2.44021 - 4.22657i) q^{62} +(1.83583 + 3.17975i) q^{63} +4.73669 q^{64} +(2.54003 + 4.39947i) q^{66} +(2.02182 + 3.50190i) q^{67} +6.64906 q^{68} +10.3933 q^{69} +(-2.59767 + 4.49929i) q^{71} +(-9.10228 - 15.7656i) q^{72} +(4.30205 - 7.45136i) q^{73} +(-0.412229 + 0.714002i) q^{74} +(2.49230 - 4.87268i) q^{76} +1.08332 q^{77} +(0.258398 - 0.447558i) q^{78} +(-3.31324 + 5.73870i) q^{79} +(-6.78057 + 11.7443i) q^{81} +(4.33544 + 7.50921i) q^{82} +4.51737 q^{83} -2.19027 q^{84} +(2.12780 + 3.68547i) q^{86} +26.9014 q^{87} -5.37122 q^{88} +(-1.68676 - 2.92155i) q^{89} +(-0.0551029 - 0.0954410i) q^{91} +(-2.11909 + 3.67037i) q^{92} +(8.70875 - 15.0840i) q^{93} +7.62648 q^{94} +17.5310 q^{96} +(7.59611 - 13.1568i) q^{97} +(-2.88128 + 4.99053i) q^{98} +(6.19665 + 10.7329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^4 - 12 * q^6 - 8 * q^9	$ 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9} + 4 q^{11} - 22 q^{14} - 14 q^{16} + 12 q^{19} - 20 q^{21} - 2 q^{24} - 44 q^{26} + 12 q^{29} + 60 q^{31} - 10 q^{34} + 14 q^{36} - 4 q^{39} - 12 q^{41} - 20 q^{44} + 8 q^{46} + 4 q^{49} - 40 q^{51} + 4 q^{54} + 92 q^{56} - 20 q^{59} + 2 q^{61} - 24 q^{64} - 6 q^{66} + 36 q^{69} + 2 q^{71} + 22 q^{74} - 70 q^{76} - 24 q^{79} - 14 q^{81} + 96 q^{84} + 16 q^{86} - 36 q^{89} + 24 q^{91} + 60 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 12 * q - 2 * q^4 - 12 * q^6 - 8 * q^9 + 4 * q^11 - 22 * q^14 - 14 * q^16 + 12 * q^19 - 20 * q^21 - 2 * q^24 - 44 * q^26 + 12 * q^29 + 60 * q^31 - 10 * q^34 + 14 * q^36 - 4 * q^39 - 12 * q^41 - 20 * q^44 + 8 * q^46 + 4 * q^49 - 40 * q^51 + 4 * q^54 + 92 * q^56 - 20 * q^59 + 2 * q^61 - 24 * q^64 - 6 * q^66 + 36 * q^69 + 2 * q^71 + 22 * q^74 - 70 * q^76 - 24 * q^79 - 14 * q^81 + 96 * q^84 + 16 * q^86 - 36 * q^89 + 24 * q^91 + 60 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.431391	−	0.747190i	0.305039	−	0.528343i	−0.672231	−	0.740342i	$-0.734664\pi$
$2$	0.431391	−	0.747190i	0.305039	−	0.528343i	0.977270	+	0.211998i	$0.0679971\pi$
$3$	1.53957	−	2.66661i	0.888870	−	1.53957i	0.0476573	−	0.998864i	$-0.484824\pi$
$3$	1.53957	−	2.66661i	0.888870	−	1.53957i	0.841213	−	0.540704i	$-0.181842\pi$
$4$	0.627804	+	1.08739i	0.313902	+	0.543695i
$5$		0			0
$5$		0			0
$6$	−1.32831	−	2.30070i	−0.542280	−	0.939257i
$7$	−0.566520			−0.214124			−0.107062	−	0.994252i	$-0.534144\pi$
$7$	−0.566520			−0.214124			−0.107062	+	0.994252i	$0.534144\pi$
$8$	2.80888			0.993088
$9$	−3.24054	−	5.61278i	−1.08018	−	1.87093i
$10$		0			0
$11$	−1.91223			−0.576559			−0.288279	−	0.957546i	$-0.593083\pi$
$11$	−1.91223			−0.576559			−0.288279	+	0.957546i	$0.593083\pi$
$12$	3.86619			1.11607
$13$	0.0972656	+	0.168469i	0.0269766	+	0.0467249i	0.879199	−	0.476456i	$-0.158079\pi$
$13$	0.0972656	+	0.168469i	0.0269766	+	0.0467249i	−0.852222	+	0.523180i	$0.824745\pi$
$14$	−0.244391	+	0.423298i	−0.0653163	+	0.113131i
$15$		0			0
$16$	−0.0438854	+	0.0760118i	−0.0109714	+	0.0190029i
$17$	2.64775	−	4.58603i	0.642173	−	1.11228i	−0.342774	−	0.939418i	$-0.611367\pi$
$17$	2.64775	−	4.58603i	0.642173	−	1.11228i	0.984947	−	0.172858i	$-0.0553001\pi$
$18$	−5.59175			−1.31799
$19$	−2.36834	−	3.65936i	−0.543335	−	0.839516i
$19$	−2.36834	−	3.65936i	−0.543335	−	0.839516i
$20$		0			0
$21$	−0.872196	+	1.51069i	−0.190329	+	0.329659i
$22$	−0.824918	+	1.42880i	−0.175873	+	0.304621i
$23$	1.68770	+	2.92318i	0.351910	+	0.609525i	0.986584	−	0.163254i	$-0.0521991\pi$
$23$	1.68770	+	2.92318i	0.351910	+	0.609525i	−0.634674	+	0.772780i	$0.718866\pi$
$24$	4.32446	−	7.49018i	0.882726	−	1.52893i
$25$		0			0
$26$	0.167838			0.0329157
$27$	−10.7187			−2.06282
$28$	−0.355664	−	0.616027i	−0.0672141	−	0.116418i
$29$	4.36834	+	7.56619i	0.811181	+	1.40501i	0.912038	+	0.410106i	$0.134508\pi$
$29$	4.36834	+	7.56619i	0.811181	+	1.40501i	−0.100857	+	0.994901i	$0.532158\pi$
$30$		0			0
$31$	5.65662			1.01596			0.507980	−	0.861369i	$-0.330393\pi$
$31$	5.65662			1.01596			0.507980	+	0.861369i	$0.330393\pi$
$32$	2.84674	+	4.93070i	0.503238	+	0.871633i
$33$	−2.94401	+	5.09917i	−0.512486	+	0.887651i
$34$	−2.28442	−	3.95674i	−0.391776	−	0.678575i
$35$		0			0
$36$	4.06885	−	7.04745i	0.678142	−	1.17458i
$37$	−0.955582			−0.157097			−0.0785484	−	0.996910i	$-0.525029\pi$
$37$	−0.955582			−0.157097			−0.0785484	+	0.996910i	$0.525029\pi$
$38$	−3.75592	+	0.190988i	−0.609291	+	0.0309824i
$39$	0.598988			0.0959149
$40$		0			0
$41$	−5.02496	+	8.70349i	−0.784768	+	1.35926i	0.144370	+	0.989524i	$0.453884\pi$
$41$	−5.02496	+	8.70349i	−0.784768	+	1.35926i	−0.929138	+	0.369734i	$0.879449\pi$
$42$	0.752514	+	1.30339i	0.116115	+	0.201118i
$43$	−2.46622	+	4.27161i	−0.376094	+	0.651415i	−0.990490	−	0.137583i	$-0.956066\pi$
$43$	−2.46622	+	4.27161i	−0.376094	+	0.651415i	0.614396	+	0.788998i	$0.289400\pi$
$44$	−1.20051	−	2.07934i	−0.180983	−	0.313472i
$45$		0			0
$46$	2.91223			0.429385
$47$	4.41971	+	7.65516i	0.644681	+	1.11662i	0.984375	+	0.176084i	$0.0563430\pi$
$47$	4.41971	+	7.65516i	0.644681	+	1.11662i	−0.339694	+	0.940536i	$0.610324\pi$
$48$	0.135129	+	0.234051i	0.0195042	+	0.0337823i
$49$	−6.67906			−0.954151
$50$		0			0
$51$	−8.15277	−	14.1210i	−1.14162	−	1.97734i
$52$	−0.122128	+	0.211531i	−0.0169361	+	0.0293341i
$53$	−4.10305	−	7.10669i	−0.563597	−	0.976179i	−0.997179	−	0.0750646i	$-0.976084\pi$
$53$	−4.10305	−	7.10669i	−0.563597	−	0.976179i	0.433581	−	0.901114i	$-0.357250\pi$
$54$	−4.62395	+	8.00892i	−0.629240	+	1.08988i
$55$		0			0
$56$	−1.59128			−0.212644
$57$	−13.4043	+	0.681609i	−1.77545	+	0.0902813i
$58$	7.53785			0.989768
$59$	−1.85713	+	3.21664i	−0.241777	+	0.418770i	−0.961221	−	0.275781i	$-0.911064\pi$
$59$	−1.85713	+	3.21664i	−0.241777	+	0.418770i	0.719443	+	0.694551i	$0.244397\pi$
$60$		0			0
$61$	1.75561	+	3.04080i	0.224783	+	0.389335i	0.956254	−	0.292537i	$-0.0944995\pi$
$61$	1.75561	+	3.04080i	0.224783	+	0.389335i	−0.731472	+	0.681872i	$0.761166\pi$
$62$	2.44021	−	4.22657i	0.309907	−	0.536775i
$63$	1.83583	+	3.17975i	0.231293	+	0.400611i
$64$	4.73669			0.592086
$65$		0			0
$66$	2.54003	+	4.39947i	0.312657	+	0.541537i
$67$	2.02182	+	3.50190i	0.247005	+	0.427825i	0.962693	−	0.270594i	$-0.0872202\pi$
$67$	2.02182	+	3.50190i	0.247005	+	0.427825i	−0.715688	+	0.698420i	$0.753887\pi$
$68$	6.64906			0.806318
$69$	10.3933			1.25121
$70$		0			0
$71$	−2.59767	+	4.49929i	−0.308286	+	0.533967i	−0.977988	−	0.208663i	$-0.933089\pi$
$71$	−2.59767	+	4.49929i	−0.308286	+	0.533967i	0.669701	+	0.742631i	$0.266422\pi$
$72$	−9.10228	−	15.7656i	−1.07271	−	1.85799i
$73$	4.30205	−	7.45136i	0.503516	−	0.872116i	−0.496475	−	0.868051i	$-0.665373\pi$
$73$	4.30205	−	7.45136i	0.503516	−	0.872116i	0.999992	−	0.00406505i	$-0.00129395\pi$
$74$	−0.412229	+	0.714002i	−0.0479207	+	0.0830010i
$75$		0			0
$76$	2.49230	−	4.87268i	0.285886	−	0.558934i
$77$	1.08332			0.123455
$78$	0.258398	−	0.447558i	0.0292578	−	0.0506760i
$79$	−3.31324	+	5.73870i	−0.372769	+	0.645654i	−0.989990	−	0.141135i	$-0.954925\pi$
$79$	−3.31324	+	5.73870i	−0.372769	+	0.645654i	0.617222	+	0.786789i	$0.288258\pi$
$80$		0			0
$81$	−6.78057	+	11.7443i	−0.753397	+	1.30492i
$82$	4.33544	+	7.50921i	0.478770	+	0.829253i
$83$	4.51737			0.495845			0.247923	−	0.968780i	$-0.420252\pi$
$83$	4.51737			0.495845			0.247923	+	0.968780i	$0.420252\pi$
$84$	−2.19027			−0.238978
$85$		0			0
$86$	2.12780	+	3.68547i	0.229447	+	0.397414i
$87$	26.9014			2.88414
$88$	−5.37122			−0.572574
$89$	−1.68676	−	2.92155i	−0.178796	−	0.309684i	0.762672	−	0.646785i	$-0.223887\pi$
$89$	−1.68676	−	2.92155i	−0.178796	−	0.309684i	−0.941468	+	0.337101i	$0.890554\pi$
$90$		0			0
$91$	−0.0551029	−	0.0954410i	−0.00577635	−	0.0100049i
$92$	−2.11909	+	3.67037i	−0.220930	+	0.382663i
$93$	8.70875	−	15.0840i	0.903056	−	1.56414i
$94$	7.62648			0.786612
$95$		0			0
$96$	17.5310			1.78925
$97$	7.59611	−	13.1568i	0.771268	−	1.33588i	−0.165600	−	0.986193i	$-0.552956\pi$
$97$	7.59611	−	13.1568i	0.771268	−	1.33588i	0.936868	−	0.349683i	$-0.113711\pi$
$98$	−2.88128	+	4.99053i	−0.291053	+	0.504119i
$99$	6.19665	+	10.7329i	0.622787	+	1.07870i
$100$		0			0
$101$	−1.77068	−	3.06690i	−0.176189	−	0.305168i	0.764383	−	0.644762i	$-0.223044\pi$
$101$	−1.77068	−	3.06690i	−0.176189	−	0.305168i	−0.940572	+	0.339594i	$0.889710\pi$
$102$	−14.0681			−1.39295
$103$	−15.6919			−1.54617			−0.773086	−	0.634301i	$-0.781288\pi$
$103$	−15.6919			−1.54617			−0.773086	+	0.634301i	$0.781288\pi$
$104$	0.273207	+	0.473209i	0.0267902	+	0.0464020i
$105$		0			0
$106$	−7.08007			−0.687677
$107$	−1.05731			−0.102214			−0.0511071	−	0.998693i	$-0.516275\pi$
$107$	−1.05731			−0.102214			−0.0511071	+	0.998693i	$0.516275\pi$
$108$	−6.72926	−	11.6554i	−0.647523	−	1.12154i
$109$	3.37220	−	5.84081i	0.322998	−	0.559449i	−0.658107	−	0.752924i	$-0.728643\pi$
$109$	3.37220	−	5.84081i	0.322998	−	0.559449i	0.981105	+	0.193476i	$0.0619760\pi$
$110$		0			0
$111$	−1.47118	+	2.54817i	−0.139639	+	0.241861i
$112$	0.0248620	−	0.0430622i	0.00234923	−	0.00406899i
$113$	7.90091			0.743255			0.371627	−	0.928382i	$-0.378800\pi$
$113$	7.90091			0.743255			0.371627	+	0.928382i	$0.378800\pi$
$114$	−5.27321	+	10.3096i	−0.493881	+	0.965585i
$115$		0			0
$116$	−5.48493	+	9.50018i	−0.509263	+	0.882069i
$117$	0.630386	−	1.09186i	0.0582792	−	0.100943i
$118$	1.60229	+	2.77525i	0.147503	+	0.255483i
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	−7.34338			−0.667580
$122$	3.02941			0.274270
$123$	15.4725	+	26.7992i	1.39511	+	2.41641i
$124$	3.55125	+	6.15095i	0.318912	+	0.552371i
$125$		0			0
$126$	3.16784			0.282213
$127$	−4.23818	−	7.34074i	−0.376078	−	0.651385i	0.614410	−	0.788987i	$-0.289394\pi$
$127$	−4.23818	−	7.34074i	−0.376078	−	0.651385i	−0.990488	+	0.137601i	$0.956061\pi$
$128$	−3.65012	+	6.32219i	−0.322628	+	0.558808i
$129$	7.59381	+	13.1529i	0.668598	+	1.15805i
$130$		0			0
$131$	−0.937193	+	1.62327i	−0.0818830	+	0.141825i	−0.904059	−	0.427408i	$-0.859427\pi$
$131$	−0.937193	+	1.62327i	−0.0818830	+	0.141825i	0.822176	+	0.569234i	$0.192760\pi$
$132$	−7.39304			−0.643482
$133$	1.34171	+	2.07310i	0.116341	+	0.179761i
$134$	3.48878			0.301385
$135$		0			0
$136$	7.43719	−	12.8816i	0.637734	−	1.10459i
$137$	6.23068	+	10.7918i	0.532323	+	0.922010i	0.999288	+	0.0377341i	$0.0120140\pi$
$137$	6.23068	+	10.7918i	0.532323	+	0.922010i	−0.466965	+	0.884276i	$0.654653\pi$
$138$	4.48357	−	7.76578i	0.381667	−	0.661067i
$139$	0.156620	+	0.271275i	0.0132844	+	0.0230092i	0.872591	−	0.488451i	$-0.162438\pi$
$139$	0.156620	+	0.271275i	0.0132844	+	0.0230092i	−0.859307	+	0.511460i	$0.829105\pi$
$140$		0			0
$141$	27.2178			2.29215
$142$	2.24122	+	3.88190i	0.188079	+	0.325762i
$143$	−0.185994	−	0.322151i	−0.0155536	−	0.0269397i
$144$	0.568850			0.0474041
$145$		0			0
$146$	−3.71172	−	6.42889i	−0.307184	−	0.532059i
$147$	−10.2829	+	17.8104i	−0.848116	+	1.46898i
$148$	−0.599919	−	1.03909i	−0.0493130	−	0.0854127i
$149$	−2.18291	+	3.78091i	−0.178831	+	0.309744i	−0.941480	−	0.337068i	$-0.890565\pi$
$149$	−2.18291	+	3.78091i	−0.178831	+	0.309744i	0.762650	+	0.646812i	$0.223898\pi$
$150$		0			0
$151$	0.197977			0.0161111			0.00805555	−	0.999968i	$-0.497436\pi$
$151$	0.197977			0.0161111			0.00805555	+	0.999968i	$0.497436\pi$
$152$	−6.65239	−	10.2787i	−0.539580	−	0.833713i
$153$	−34.3205			−2.77465
$154$	0.467332	−	0.809443i	0.0376587	−	0.0652268i
$155$		0			0
$156$	0.376047	+	0.651333i	0.0301079	+	0.0521484i
$157$	7.88498	−	13.6572i	0.629290	−	1.08996i	−0.358405	−	0.933566i	$-0.616679\pi$
$157$	7.88498	−	13.6572i	0.629290	−	1.08996i	0.987695	−	0.156395i	$-0.0499874\pi$
$158$	2.85860	+	4.95124i	0.227418	+	0.393900i
$159$	−25.2677			−2.00386
$160$		0			0
$161$	−0.956115	−	1.65604i	−0.0753524	−	0.130514i
$162$	5.85015	+	10.1328i	0.459631	+	0.796105i
$163$	−9.18768			−0.719635			−0.359817	−	0.933023i	$-0.617161\pi$
$163$	−9.18768			−0.719635			−0.359817	+	0.933023i	$0.617161\pi$
$164$	−12.6188			−0.985361
$165$		0			0
$166$	1.94875	−	3.37533i	0.151252	−	0.261977i
$167$	−1.53510	−	2.65888i	−0.118790	−	0.205750i	0.800498	−	0.599335i	$-0.204568\pi$
$167$	−1.53510	−	2.65888i	−0.118790	−	0.205750i	−0.919288	+	0.393585i	$0.871235\pi$
$168$	−2.44989	+	4.24334i	−0.189013	+	0.327380i
$169$	6.48108	−	11.2256i	0.498545	−	0.863504i
$170$		0			0
$171$	−12.8645	+	25.1513i	−0.983772	+	1.92337i
$172$	−6.19320			−0.472227
$173$	5.20676	−	9.01838i	0.395863	−	0.685655i	−0.597348	−	0.801982i	$-0.703779\pi$
$173$	5.20676	−	9.01838i	0.395863	−	0.685655i	0.993211	+	0.116328i	$0.0371122\pi$
$174$	11.6050	−	20.1005i	0.879775	−	1.52382i
$175$		0			0
$176$	0.0839190	−	0.145352i	0.00632563	−	0.0109563i
$177$	5.71834	+	9.90446i	0.429817	+	0.744465i
$178$	−2.91061			−0.218159
$179$	−13.4432			−1.00479			−0.502397	−	0.864637i	$-0.667549\pi$
$179$	−13.4432			−1.00479			−0.502397	+	0.864637i	$0.667549\pi$
$180$		0			0
$181$	−3.98108	−	6.89543i	−0.295911	−	0.512533i	0.679285	−	0.733874i	$-0.262290\pi$
$181$	−3.98108	−	6.89543i	−0.295911	−	0.512533i	−0.975196	+	0.221341i	$0.928957\pi$
$182$	−0.0950835			−0.00704806
$183$	10.8115			0.799210
$184$	4.74054	+	8.21086i	0.349477	+	0.605312i
$185$		0			0
$186$	−7.51375	−	13.0142i	−0.550935	−	0.954247i
$187$	−5.06310	+	8.76954i	−0.370250	+	0.641292i
$188$	−5.54942	+	9.61189i	−0.404733	+	0.701019i
$189$	6.07236			0.441699
$190$		0			0
$191$	−14.0999			−1.02023			−0.510115	−	0.860106i	$-0.670397\pi$
$191$	−14.0999			−1.02023			−0.510115	+	0.860106i	$0.670397\pi$
$192$	7.29245	−	12.6309i	0.526287	−	0.911557i
$193$	1.98842	−	3.44405i	0.143130	−	0.247908i	−0.785544	−	0.618806i	$-0.787617\pi$
$193$	1.98842	−	3.44405i	0.143130	−	0.247908i	0.928674	+	0.370898i	$0.120950\pi$
$194$	−6.55378	−	11.3515i	−0.470534	−	0.814989i
$195$		0			0
$196$	−4.19314	−	7.26273i	−0.299510	−	0.518767i
$197$	−18.3494			−1.30734			−0.653669	−	0.756781i	$-0.726771\pi$
$197$	−18.3494			−1.30734			−0.653669	+	0.756781i	$0.726771\pi$
$198$	10.6927			0.759898
$199$	0.803346	+	1.39144i	0.0569477	+	0.0986363i	0.893094	−	0.449870i	$-0.148530\pi$
$199$	0.803346	+	1.39144i	0.0569477	+	0.0986363i	−0.836146	+	0.548507i	$0.815197\pi$
$200$		0			0
$201$	12.4509			0.878222
$202$	−3.05542			−0.214978
$203$	−2.47475	−	4.28640i	−0.173694	−	0.300846i
$204$	10.2367	−	17.7305i	0.716711	−	1.24138i
$205$		0			0
$206$	−6.76936	+	11.7249i	−0.471643	+	0.816910i
$207$	10.9381	−	18.9454i	0.760251	−	1.31679i
$208$	−0.0170742			−0.00118388
$209$	4.52882	+	6.99754i	0.313265	+	0.484030i
$210$		0			0
$211$	3.04993	−	5.28263i	0.209966	−	0.363671i	−0.741738	−	0.670690i	$-0.765998\pi$
$211$	3.04993	−	5.28263i	0.209966	−	0.363671i	0.951703	+	0.307019i	$0.0993314\pi$
$212$	5.15182	−	8.92322i	0.353829	−	0.612849i
$213$	7.99857	+	13.8539i	0.548053	+	0.949255i
$214$	−0.456115	+	0.790014i	−0.0311794	+	0.0540042i
$215$		0			0
$216$	−30.1076			−2.04856
$217$	−3.20459			−0.217542
$218$	−2.90947	−	5.03934i	−0.197054	−	0.341307i
$219$	−13.2466	−	22.9438i	−0.895121	−	1.55040i
$220$		0			0
$221$	1.03014			0.0692946
$222$	1.26931	+	2.19851i	0.0851905	+	0.147554i
$223$	8.61263	−	14.9175i	0.576744	−	0.998950i	−0.419106	−	0.907938i	$-0.637656\pi$
$223$	8.61263	−	14.9175i	0.576744	−	0.998950i	0.995850	−	0.0910127i	$-0.0290104\pi$
$224$	−1.61274	−	2.79334i	−0.107755	−	0.186638i
$225$		0			0
$226$	3.40838	−	5.90348i	0.226722	−	0.392694i
$227$	−1.18505			−0.0786542			−0.0393271	−	0.999226i	$-0.512521\pi$
$227$	−1.18505			−0.0786542			−0.0393271	+	0.999226i	$0.512521\pi$
$228$	−9.15647	−	14.1478i	−0.606402	−	0.936961i
$229$	6.24791			0.412873			0.206437	−	0.978460i	$-0.433813\pi$
$229$	6.24791			0.412873			0.206437	+	0.978460i	$0.433813\pi$
$230$		0			0
$231$	1.66784	−	2.88878i	0.109736	−	0.190068i
$232$	12.2701	+	21.2525i	0.805574	+	1.39530i
$233$	−1.37844	+	2.38752i	−0.0903043	+	0.156412i	−0.907639	−	0.419751i	$-0.862117\pi$
$233$	−1.37844	+	2.38752i	−0.0903043	+	0.156412i	0.817335	+	0.576163i	$0.195451\pi$
$234$	−0.543885	−	0.942037i	−0.0355549	−	0.0615829i
$235$		0			0
$236$	−4.66365			−0.303578
$237$	10.2019	+	17.6702i	0.662686	+	1.14781i
$238$	1.29417	+	2.24157i	0.0838887	+	0.145299i
$239$	17.3055			1.11940			0.559701	−	0.828695i	$-0.310916\pi$
$239$	17.3055			1.11940			0.559701	+	0.828695i	$0.310916\pi$
$240$		0			0
$241$	2.39331	+	4.14533i	0.154167	+	0.267024i	0.932755	−	0.360510i	$-0.117397\pi$
$241$	2.39331	+	4.14533i	0.154167	+	0.267024i	−0.778589	+	0.627535i	$0.784064\pi$
$242$	−3.16786	+	5.48690i	−0.203638	+	0.352711i
$243$	4.80023	+	8.31425i	0.307935	+	0.533359i
$244$	−2.20436	+	3.81806i	−0.141120	+	0.244426i
$245$		0			0
$246$	26.6988			1.70226
$247$	0.386131	−	0.754923i	0.0245689	−	0.0480346i
$248$	15.8888			1.00894
$249$	6.95479	−	12.0461i	0.440742	−	0.763388i
$250$		0			0
$251$	13.1240	+	22.7314i	0.828377	+	1.43479i	0.899311	+	0.437309i	$0.144068\pi$
$251$	13.1240	+	22.7314i	0.828377	+	1.43479i	−0.0709346	+	0.997481i	$0.522598\pi$
$252$	−2.30508	+	3.99252i	−0.145207	+	0.251505i
$253$	−3.22727	−	5.58979i	−0.202897	−	0.351427i
$254$	−7.31324			−0.458874
$255$		0			0
$256$	7.88594	+	13.6589i	0.492871	+	0.853678i
$257$	−11.1252	−	19.2695i	−0.693974	−	1.20200i	−0.970525	−	0.240999i	$-0.922525\pi$
$257$	−11.1252	−	19.2695i	−0.693974	−	1.20200i	0.276552	−	0.960999i	$-0.410808\pi$
$258$	13.1036			0.815794
$259$	0.541356			0.0336382
$260$		0			0
$261$	28.3116	−	49.0371i	1.75244	−	3.03532i
$262$	0.808593	+	1.40052i	0.0499550	+	0.0865246i
$263$	4.40671	−	7.63264i	0.271729	−	0.470649i	−0.697576	−	0.716511i	$-0.745738\pi$
$263$	4.40671	−	7.63264i	0.271729	−	0.470649i	0.969305	+	0.245863i	$0.0790712\pi$
$264$	−8.26936	+	14.3229i	−0.508944	+	0.881516i
$265$		0			0
$266$	2.12780	−	0.108199i	0.130464	−	0.00663409i
$267$	−10.3875			−0.635706
$268$	−2.53862	+	4.39702i	−0.155071	+	0.268591i
$269$	2.38209	−	4.12590i	0.145239	−	0.251561i	−0.784223	−	0.620479i	$-0.786938\pi$
$269$	2.38209	−	4.12590i	0.145239	−	0.251561i	0.929462	+	0.368918i	$0.120272\pi$
$270$		0			0
$271$	−1.75946	+	3.04748i	−0.106880	+	0.185121i	−0.914505	−	0.404576i	$-0.867419\pi$
$271$	−1.75946	+	3.04748i	−0.106880	+	0.185121i	0.807625	+	0.589696i	$0.200753\pi$
$272$	0.232395	+	0.402520i	0.0140910	+	0.0244063i
$273$	−0.339339			−0.0205377
$274$	10.7514			0.649517
$275$		0			0
$276$	6.52496	+	11.3016i	0.392757	+	0.680275i
$277$	−32.7724			−1.96910			−0.984551	−	0.175098i	$-0.943976\pi$
$277$	−32.7724			−1.96910			−0.984551	+	0.175098i	$0.943976\pi$
$278$	0.270258			0.0162090
$279$	−18.3305	−	31.7494i	−1.09742	−	1.90078i
$280$		0			0
$281$	−4.95997	−	8.59091i	−0.295887	−	0.512491i	0.679304	−	0.733857i	$-0.262282\pi$
$281$	−4.95997	−	8.59091i	−0.295887	−	0.512491i	−0.975191	+	0.221366i	$0.928948\pi$
$282$	11.7415	−	20.3369i	0.699195	−	1.21104i
$283$	−1.23591	+	2.14066i	−0.0734673	+	0.127249i	−0.900419	−	0.435024i	$-0.856740\pi$
$283$	−1.23591	+	2.14066i	−0.0734673	+	0.127249i	0.826951	+	0.562273i	$0.190073\pi$
$284$	−6.52330			−0.387087
$285$		0			0
$286$	−0.320945			−0.0189779
$287$	2.84674	−	4.93070i	0.168038	−	0.291050i
$288$	18.4500	−	31.9563i	1.08717	−	1.88304i
$289$	−5.52111	−	9.56285i	−0.324771	−	0.562520i
$290$		0			0
$291$	−23.3895	−	40.5117i	−1.37111	−	2.37484i
$292$	10.8034			0.632219
$293$	−17.0284			−0.994812			−0.497406	−	0.867518i	$-0.665714\pi$
$293$	−17.0284			−0.994812			−0.497406	+	0.867518i	$0.665714\pi$
$294$	8.87186	+	15.3665i	0.517417	+	0.896193i
$295$		0			0
$296$	−2.68411			−0.156011
$297$	20.4966			1.18934
$298$	1.88337	+	3.26209i	0.109101	+	0.188968i
$299$	−0.328310	+	0.568650i	−0.0189867	+	0.0328859i
$300$		0			0
$301$	1.39716	−	2.41995i	0.0805310	−	0.139484i
$302$	0.0854052	−	0.147926i	0.00491452	−	0.00851220i
$303$	−10.9043			−0.626437
$304$	0.382090	−	0.0194293i	0.0219144	−	0.00111435i
$305$		0			0
$306$	−14.8055	+	25.6439i	−0.846376	+	1.46597i
$307$	−10.4896	+	18.1686i	−0.598676	+	1.03694i	0.394341	+	0.918964i	$0.370973\pi$
$307$	−10.4896	+	18.1686i	−0.598676	+	1.03694i	−0.993017	+	0.117972i	$0.962361\pi$
$308$	0.680110	+	1.17799i	0.0387529	+	0.0671220i
$309$	−24.1588	+	41.8443i	−1.37435	+	2.38044i
$310$		0			0
$311$	−3.14805			−0.178509			−0.0892547	−	0.996009i	$-0.528449\pi$
$311$	−3.14805			−0.178509			−0.0892547	+	0.996009i	$0.528449\pi$
$312$	1.68248			0.0952520
$313$	−6.14641	−	10.6459i	−0.347416	−	0.601742i	0.638374	−	0.769726i	$-0.279607\pi$
$313$	−6.14641	−	10.6459i	−0.347416	−	0.601742i	−0.985790	+	0.167985i	$0.946274\pi$
$314$	−6.80301	−	11.7832i	−0.383916	−	0.664962i
$315$		0			0
$316$	−8.32027			−0.468052
$317$	5.73095	+	9.92630i	0.321882	+	0.557517i	0.980876	−	0.194631i	$-0.0623511\pi$
$317$	5.73095	+	9.92630i	0.321882	+	0.557517i	−0.658994	+	0.752148i	$0.729018\pi$
$318$	−10.9002	+	18.8798i	−0.611255	+	1.05873i
$319$	−8.35327	−	14.4683i	−0.467694	−	0.810069i
$320$		0			0
$321$	−1.62780	+	2.81944i	−0.0908552	+	0.157366i
$322$	−1.64984			−0.0919417
$323$	−23.0527	+	1.17223i	−1.28269	+	0.0652246i
$324$	−17.0275			−0.945972
$325$		0			0
$326$	−3.96348	+	6.86495i	−0.219517	+	0.380214i
$327$	−10.3834	−	17.9847i	−0.574206	−	0.994554i
$328$	−14.1145	+	24.4470i	−0.779343	+	1.34986i
$329$	−2.50385	−	4.33680i	−0.138042	−	0.239095i
$330$		0			0
$331$	5.85724			0.321943			0.160972	−	0.986959i	$-0.448537\pi$
$331$	5.85724			0.321943			0.160972	+	0.986959i	$0.448537\pi$
$332$	2.83602	+	4.91213i	0.155647	+	0.269588i
$333$	3.09660	+	5.36347i	0.169693	+	0.293916i
$334$	−2.64892			−0.144942
$335$		0			0
$336$	−0.0765533	−	0.132594i	−0.00417633	−	0.00723361i
$337$	4.30498	−	7.45644i	0.234507	−	0.406178i	−0.724622	−	0.689146i	$-0.757986\pi$
$337$	4.30498	−	7.45644i	0.234507	−	0.406178i	0.959129	+	0.282968i	$0.0913191\pi$
$338$	−5.59175	−	9.68520i	−0.304151	−	0.526805i
$339$	12.1640	−	21.0686i	0.660657	−	1.14429i
$340$		0			0
$341$	−10.8168			−0.585760
$342$	13.2432	+	20.4623i	0.716110	+	1.10647i
$343$	7.74945			0.418431
$344$	−6.92730	+	11.9984i	−0.373495	+	0.646912i
$345$		0			0
$346$	−4.49230	−	7.78089i	−0.241507	−	0.418303i
$347$	−6.04507	+	10.4704i	−0.324517	+	0.562079i	−0.981414	−	0.191900i	$-0.938535\pi$
$347$	−6.04507	+	10.4704i	−0.324517	+	0.562079i	0.656898	+	0.753980i	$0.271868\pi$
$348$	16.8888	+	29.2523i	0.905337	+	1.56809i
$349$	18.9819			1.01608			0.508040	−	0.861333i	$-0.330370\pi$
$349$	18.9819			1.01608			0.508040	+	0.861333i	$0.330370\pi$
$350$		0			0
$351$	−1.04256	−	1.80577i	−0.0556479	−	0.0963850i
$352$	−5.44362	−	9.42863i	−0.290146	−	0.502548i
$353$	7.71759			0.410766			0.205383	−	0.978682i	$-0.434156\pi$
$353$	7.71759			0.410766			0.205383	+	0.978682i	$0.434156\pi$
$354$	9.86736			0.524444
$355$		0			0
$356$	2.11791	−	3.66833i	0.112249	−	0.194421i
$357$	4.61870	+	7.99983i	0.244448	+	0.423396i
$358$	−5.79929	+	10.0447i	−0.306502	+	0.530877i
$359$	3.51507	−	6.08828i	0.185518	−	0.321327i	−0.758233	−	0.651984i	$-0.773937\pi$
$359$	3.51507	−	6.08828i	0.185518	−	0.321327i	0.943751	+	0.330657i	$0.107270\pi$
$360$		0			0
$361$	−7.78190	+	17.3333i	−0.409573	+	0.912277i
$362$	−6.86960			−0.361058
$363$	−11.3056	+	19.5819i	−0.593392	+	1.02778i
$364$	0.0691877	−	0.119837i	0.00362642	−	0.00628114i
$365$		0			0
$366$	4.66399	−	8.07826i	0.243790	−	0.422257i
$367$	−16.8554	−	29.1945i	−0.879847	−	1.52394i	−0.851508	−	0.524342i	$-0.824311\pi$
$367$	−16.8554	−	29.1945i	−0.879847	−	1.52394i	−0.0283394	−	0.999598i	$-0.509022\pi$
$368$	−0.296261			−0.0154437
$369$	65.1344			3.39076
$370$		0			0
$371$	2.32446	+	4.02608i	0.120680	+	0.209024i
$372$	21.8696			1.13388
$373$	−10.0097			−0.518281			−0.259141	−	0.965840i	$-0.583439\pi$
$373$	−10.0097			−0.518281			−0.259141	+	0.965840i	$0.583439\pi$
$374$	4.36834	+	7.56619i	0.225882	+	0.391239i
$375$		0			0
$376$	12.4144	+	21.5024i	0.640225	+	1.10890i
$377$	−0.849780	+	1.47186i	−0.0437659	+	0.0758047i
$378$	2.61956	−	4.53721i	0.134736	−	0.233369i
$379$	−35.8064			−1.83925			−0.919626	−	0.392796i	$-0.871508\pi$
$379$	−35.8064			−1.83925			−0.919626	+	0.392796i	$0.871508\pi$
$380$		0			0
$381$	−26.0999			−1.33714
$382$	−6.08255	+	10.5353i	−0.311210	+	0.539032i
$383$	−8.12477	+	14.0725i	−0.415156	+	0.719072i	−0.995445	−	0.0953393i	$-0.969606\pi$
$383$	−8.12477	+	14.0725i	−0.415156	+	0.719072i	0.580289	+	0.814411i	$0.302940\pi$
$384$	11.2392	+	19.4669i	0.573549	+	0.993416i
$385$		0			0
$386$	−1.71558	−	2.97146i	−0.0873205	−	0.151244i
$387$	31.9675			1.62500
$388$	19.0755			0.968411
$389$	9.69280	+	16.7884i	0.491445	+	0.851207i	0.999951	−	0.00985094i	$-0.00313570\pi$
$389$	9.69280	+	16.7884i	0.491445	+	0.851207i	−0.508507	+	0.861058i	$0.669802\pi$
$390$		0			0
$391$	17.8744			0.903947
$392$	−18.7607			−0.947556
$393$	2.88575	+	4.99826i	0.145567	+	0.252129i
$394$	−7.91574	+	13.7105i	−0.398789	+	0.690723i
$395$		0			0
$396$	−7.78057	+	13.4763i	−0.390989	+	0.677212i
$397$	2.67707	−	4.63682i	0.134358	−	0.232716i	−0.790994	−	0.611824i	$-0.790436\pi$
$397$	2.67707	−	4.63682i	0.134358	−	0.232716i	0.925352	+	0.379109i	$0.123769\pi$
$398$	1.38622			0.0694851
$399$	7.59381	−	0.386145i	0.380166	−	0.0193314i
$400$		0			0
$401$	−4.16916	+	7.22120i	−0.208198	+	0.360609i	−0.951147	−	0.308739i	$-0.900093\pi$
$401$	−4.16916	+	7.22120i	−0.208198	+	0.360609i	0.742949	+	0.669348i	$0.233426\pi$
$402$	5.37122	−	9.30322i	0.267892	−	0.464003i
$403$	0.550195	+	0.952965i	0.0274072	+	0.0474706i
$404$	2.22328	−	3.85083i	0.110612	−	0.191586i
$405$		0			0
$406$	−4.27034			−0.211933
$407$	1.82729			0.0905755
$408$	−22.9001	−	39.6642i	−1.13373	−	1.96367i
$409$	17.6613	+	30.5903i	0.873297	+	1.51259i	0.858566	+	0.512703i	$0.171356\pi$
$409$	17.6613	+	30.5903i	0.873297	+	1.51259i	0.0147313	+	0.999891i	$0.495311\pi$
$410$		0			0
$411$	38.3702			1.89266
$412$	−9.85147	−	17.0632i	−0.485347	−	0.840646i
$413$	1.05210	−	1.82229i	0.0517704	−	0.0896689i
$414$	−9.43719	−	16.3457i	−0.463813	−	0.803347i
$415$		0			0
$416$	−0.553780	+	0.959176i	−0.0271513	+	0.0470274i
$417$	0.964511			0.0472323
$418$	7.18219	−	0.365214i	0.351292	−	0.0178632i
$419$	21.2453			1.03790			0.518949	−	0.854805i	$-0.326323\pi$
$419$	21.2453			1.03790			0.518949	+	0.854805i	$0.326323\pi$
$420$		0			0
$421$	7.43719	−	12.8816i	0.362467	−	0.627811i	−0.625900	−	0.779904i	$-0.715268\pi$
$421$	7.43719	−	12.8816i	0.362467	−	0.627811i	0.988366	+	0.152093i	$0.0486013\pi$
$422$	−2.63142	−	4.55775i	−0.128096	−	0.221868i
$423$	28.6445	−	49.6137i	1.39274	−	2.41230i
$424$	−11.5250	−	19.9618i	−0.559702	−	0.969432i
$425$		0			0
$426$	13.8020			0.668710
$427$	−0.994587	−	1.72268i	−0.0481314	−	0.0833661i
$428$	−0.663785	−	1.14971i	−0.0320853	−	0.0555733i
$429$	−1.14540			−0.0553006
$430$		0			0
$431$	8.47590	+	14.6807i	0.408270	+	0.707144i	0.994696	−	0.102858i	$-0.0327989\pi$
$431$	8.47590	+	14.6807i	0.408270	+	0.707144i	−0.586426	+	0.810003i	$0.699466\pi$
$432$	0.470395	−	0.814748i	0.0226319	−	0.0391996i
$433$	11.5730	+	20.0450i	0.556161	+	0.963299i	0.997812	+	0.0661122i	$0.0210595\pi$
$433$	11.5730	+	20.0450i	0.556161	+	0.963299i	−0.441651	+	0.897187i	$0.645607\pi$
$434$	−1.38243	+	2.39444i	−0.0663587	+	0.114937i
$435$		0			0
$436$	8.46832			0.405559
$437$	6.69993	−	13.0990i	0.320501	−	0.626610i
$438$	−22.8578			−1.09219
$439$	−16.7729	+	29.0515i	−0.800525	+	1.38655i	0.118745	+	0.992925i	$0.462113\pi$
$439$	−16.7729	+	29.0515i	−0.800525	+	1.38655i	−0.919271	+	0.393626i	$0.871221\pi$
$440$		0			0
$441$	21.6437	+	37.4881i	1.03065	+	1.78515i
$442$	0.444392	−	0.769710i	0.0211376	−	0.0366114i
$443$	−15.6789	−	27.1567i	−0.744929	−	1.29025i	−0.950228	−	0.311555i	$-0.899150\pi$
$443$	−15.6789	−	27.1567i	−0.744929	−	1.29025i	0.205299	−	0.978699i	$-0.434183\pi$
$444$	−3.69446			−0.175331
$445$		0			0
$446$	−7.43081	−	12.8705i	−0.351859	−	0.609438i
$447$	6.72147	+	11.6419i	0.317915	+	0.550644i
$448$	−2.68343			−0.126780
$449$	−16.0301			−0.756509			−0.378255	−	0.925702i	$-0.623476\pi$
$449$	−16.0301			−0.756509			−0.378255	+	0.925702i	$0.623476\pi$
$450$		0			0
$451$	9.60888	−	16.6431i	0.452465	−	0.783692i
$452$	4.96022	+	8.59136i	0.233309	+	0.404104i
$453$	0.304798	−	0.527926i	0.0143207	−	0.0248041i
$454$	−0.511217	+	0.885455i	−0.0239926	+	0.0415564i
$455$		0			0
$456$	−37.6511	+	1.91456i	−1.76317	+	0.0896573i
$457$	15.3980			0.720286			0.360143	−	0.932897i	$-0.382728\pi$
$457$	15.3980			0.720286			0.360143	+	0.932897i	$0.382728\pi$
$458$	2.69529	−	4.66837i	0.125943	−	0.218139i
$459$	−28.3804	+	49.1563i	−1.32469	+	2.29442i
$460$		0			0
$461$	2.90705	−	5.03517i	0.135395	−	0.234511i	−0.790353	−	0.612651i	$-0.790103\pi$
$461$	2.90705	−	5.03517i	0.135395	−	0.234511i	0.925748	+	0.378140i	$0.123436\pi$
$462$	−1.43898	−	2.49238i	−0.0669474	−	0.115956i
$463$	32.6788			1.51871			0.759356	−	0.650675i	$-0.225514\pi$
$463$	32.6788			1.51871			0.759356	+	0.650675i	$0.225514\pi$
$464$	−0.766826			−0.0355990
$465$		0			0
$466$	1.18929	+	2.05991i	0.0550927	+	0.0954234i
$467$	−6.59041			−0.304968			−0.152484	−	0.988306i	$-0.548727\pi$
$467$	−6.59041			−0.304968			−0.152484	+	0.988306i	$0.548727\pi$
$468$	1.58304			0.0731759
$469$	−1.14540	−	1.98390i	−0.0528898	−	0.0916078i
$470$		0			0
$471$	−24.2789	−	42.0523i	−1.11871	−	1.93767i
$472$	−5.21644	+	9.03514i	−0.240106	+	0.415876i
$473$	4.71597	−	8.16830i	0.216841	−	0.375579i
$474$	17.6040			0.808581
$475$		0			0
$476$	−3.76683			−0.172652
$477$	−26.5922	+	46.0590i	−1.21757	+	2.10890i
$478$	7.46545	−	12.9305i	0.341462	−	0.591429i
$479$	18.4032	+	31.8753i	0.840864	+	1.45642i	0.889165	+	0.457586i	$0.151286\pi$
$479$	18.4032	+	31.8753i	0.840864	+	1.45642i	−0.0483016	+	0.998833i	$0.515381\pi$
$480$		0			0
$481$	−0.0929453	−	0.160986i	−0.00423794	−	0.00734033i
$482$	4.12980			0.188107
$483$	−5.88801			−0.267914
$484$	−4.61021	−	7.98511i	−0.209555	−	0.362960i
$485$		0			0
$486$	8.28310			0.375729
$487$	2.45475			0.111235			0.0556176	−	0.998452i	$-0.482287\pi$
$487$	2.45475			0.111235			0.0556176	+	0.998452i	$0.482287\pi$
$488$	4.93129	+	8.54125i	0.223229	+	0.386644i
$489$	−14.1451	+	24.5000i	−0.639662	+	1.10793i
$490$		0			0
$491$	−8.89716	+	15.4103i	−0.401523	+	0.695459i	−0.993910	−	0.110195i	$-0.964852\pi$
$491$	−8.89716	+	15.4103i	−0.401523	+	0.695459i	0.592387	+	0.805654i	$0.298186\pi$
$492$	−19.4275	+	33.6494i	−0.875858	+	1.51703i
$493$	46.2651			2.08367
$494$	−0.397498	−	0.614180i	−0.0178843	−	0.0276333i
$495$		0			0
$496$	−0.248243	+	0.429970i	−0.0111464	+	0.0193062i
$497$	1.47163	−	2.54894i	0.0660116	−	0.114335i
$498$	−6.00046	−	10.3931i	−0.268887	−	0.465726i
$499$	14.6399	−	25.3570i	0.655371	−	1.13514i	−0.326429	−	0.945222i	$-0.605845\pi$
$499$	14.6399	−	25.3570i	0.655371	−	1.13514i	0.981801	−	0.189915i	$-0.0608213\pi$
$500$		0			0
$501$	−9.45359			−0.422355
$502$	22.6462			1.01075
$503$	14.7189	+	25.4939i	0.656283	+	1.13672i	0.981571	+	0.191100i	$0.0612056\pi$
$503$	14.7189	+	25.4939i	0.656283	+	1.13672i	−0.325287	+	0.945615i	$0.605461\pi$
$504$	5.15662	+	8.93153i	0.229694	+	0.397842i
$505$		0			0
$506$	−5.56885			−0.247566
$507$	−19.9561	−	34.5650i	−0.886283	−	1.53509i
$508$	5.32149	−	9.21710i	0.236103	−	0.408943i
$509$	−3.34723	−	5.79757i	−0.148363	−	0.256973i	0.782259	−	0.622953i	$-0.214067\pi$
$509$	−3.34723	−	5.79757i	−0.148363	−	0.256973i	−0.930623	+	0.365980i	$0.880734\pi$
$510$		0			0
$511$	−2.43719	+	4.22134i	−0.107815	+	0.186741i
$512$	−0.992797			−0.0438758
$513$	25.3856	+	39.2237i	1.12080	+	1.73177i
$514$	−19.1973			−0.846757
$515$		0			0
$516$	−9.53486	+	16.5149i	−0.419749	+	0.727026i
$517$	−8.45150	−	14.6384i	−0.371696	−	0.643797i
$518$	0.233536	−	0.404496i	0.0102610	−	0.0177725i
$519$	−16.0323	−	27.7688i	−0.703741	−	1.21892i
$520$		0			0
$521$	20.0801			0.879724			0.439862	−	0.898065i	$-0.355027\pi$
$521$	20.0801			0.879724			0.439862	+	0.898065i	$0.355027\pi$
$522$	−24.4267	−	42.3083i	−1.06913	−	1.85178i
$523$	−18.2220	−	31.5615i	−0.796793	−	1.38009i	−0.921694	−	0.387918i	$-0.873195\pi$
$523$	−18.2220	−	31.5615i	−0.796793	−	1.38009i	0.124901	−	0.992169i	$-0.460139\pi$
$524$	−2.35350			−0.102813
$525$		0			0
$526$	−3.80202	−	6.58530i	−0.165776	−	0.287133i
$527$	14.9773	−	25.9414i	0.652421	−	1.13003i
$528$	−0.258398	−	0.447558i	−0.0112453	−	0.0194775i
$529$	5.80335	−	10.0517i	0.252319	−	0.437030i
$530$		0			0
$531$	24.0724			1.04465
$532$	−1.41193	+	2.76047i	−0.0612151	+	0.119681i
$533$	−1.95503			−0.0846816
$534$	−4.48108	+	7.76146i	−0.193915	+	0.335871i
$535$		0			0
$536$	5.67906	+	9.83641i	0.245298	+	0.424868i
$537$	−20.6968	+	35.8479i	−0.893132	+	1.54695i
$538$	−2.05522	−	3.55975i	−0.0886069	−	0.153472i
$539$	12.7719			0.550124
$540$		0			0
$541$	7.31456	+	12.6692i	0.314478	+	0.544691i	0.979326	−	0.202287i	$-0.0648373\pi$
$541$	7.31456	+	12.6692i	0.314478	+	0.544691i	−0.664849	+	0.746978i	$0.731504\pi$
$542$	1.51803	+	2.62930i	0.0652049	+	0.112938i
$543$	−24.5166			−1.05211
$544$	30.1498			1.29266
$545$		0			0
$546$	−0.146388	+	0.253551i	−0.00626481	+	0.0108510i
$547$	10.2093	+	17.6831i	0.436519	+	0.756073i	0.997418	−	0.0718112i	$-0.0228779\pi$
$547$	10.2093	+	17.6831i	0.436519	+	0.756073i	−0.560899	+	0.827884i	$0.689545\pi$
$548$	−7.82329	+	13.5503i	−0.334194	+	0.578842i
$549$	11.3782	−	19.7077i	0.485611	−	0.841104i
$550$		0			0
$551$	17.3417	−	33.9047i	0.738782	−	1.44439i
$552$	29.1935			1.24256
$553$	1.87702	−	3.25109i	0.0798188	−	0.138250i
$554$	−14.1377	+	24.4872i	−0.600653	+	1.04036i
$555$		0			0
$556$	−0.196654	+	0.340615i	−0.00833999	+	0.0144453i
$557$	17.9399	+	31.0728i	0.760138	+	1.31660i	0.942779	+	0.333418i	$0.108202\pi$
$557$	17.9399	+	31.0728i	0.760138	+	1.31660i	−0.182641	+	0.983180i	$0.558465\pi$
$558$	−31.6304			−1.33902
$559$	−0.959512			−0.0405830
$560$		0			0
$561$	15.5900	+	27.0026i	0.658209	+	1.14005i
$562$	−8.55873			−0.361028
$563$	−37.7708			−1.59185			−0.795925	−	0.605395i	$-0.793015\pi$
$563$	−37.7708			−1.59185			−0.795925	+	0.605395i	$0.793015\pi$
$564$	17.0874	+	29.5963i	0.719511	+	1.24623i
$565$		0			0
$566$	1.06632	+	1.84692i	0.0448208	+	0.0776319i
$567$	3.84133	−	6.65338i	0.161321	−	0.279416i
$568$	−7.29653	+	12.6380i	−0.306155	+	0.530277i
$569$	28.0844			1.17736			0.588681	−	0.808366i	$-0.299648\pi$
$569$	28.0844			1.17736			0.588681	+	0.808366i	$0.299648\pi$
$570$		0			0
$571$	20.6040			0.862253			0.431126	−	0.902292i	$-0.358116\pi$
$571$	20.6040			0.862253			0.431126	+	0.902292i	$0.358116\pi$
$572$	0.233536	−	0.404496i	0.00976463	−	0.0169128i
$573$	−21.7077	+	37.5988i	−0.906852	+	1.57071i
$574$	−2.45611	−	4.25412i	−0.102516	−	0.177563i
$575$		0			0
$576$	−15.3494	−	26.5860i	−0.639559	−	1.10775i
$577$	43.8371			1.82496			0.912481	−	0.409119i	$-0.134164\pi$
$577$	43.8371			1.82496			0.912481	+	0.409119i	$0.134164\pi$
$578$	−9.52702			−0.396272
$579$	−6.12263	−	10.6047i	−0.254448	−	0.440717i
$580$		0			0
$581$	−2.55918			−0.106173
$582$	−40.3600			−1.67297
$583$	7.84597	+	13.5896i	0.324947	+	0.562825i
$584$	12.0839	−	20.9300i	0.500036	−	0.866088i
$585$		0			0
$586$	−7.34591	+	12.7235i	−0.303457	+	0.525602i
$587$	−18.9905	+	32.8925i	−0.783821	+	1.35762i	0.145880	+	0.989302i	$0.453399\pi$
$587$	−18.9905	+	32.8925i	−0.783821	+	1.35762i	−0.929701	+	0.368315i	$0.879935\pi$
$588$	−25.8225			−1.06490
$589$	−13.3968	−	20.6996i	−0.552006	−	0.852914i
$590$		0			0
$591$	−28.2501	+	48.9306i	−1.16205	+	2.01274i
$592$	0.0419361	−	0.0726355i	0.00172356	−	0.00298530i
$593$	2.69007	+	4.65934i	0.110468	+	0.191336i	0.915959	−	0.401272i	$-0.131432\pi$
$593$	2.69007	+	4.65934i	0.110468	+	0.191336i	−0.805491	+	0.592608i	$0.798098\pi$
$594$	8.84206	−	15.3149i	0.362794	−	0.628378i
$595$		0			0
$596$	−5.48175			−0.224541
$597$	4.94722			0.202476
$598$	0.283260	+	0.490620i	0.0115834	+	0.0200630i
$599$	−11.2143	−	19.4237i	−0.458202	−	0.793629i	0.540664	−	0.841239i	$-0.318173\pi$
$599$	−11.2143	−	19.4237i	−0.458202	−	0.793629i	−0.998866	+	0.0476095i	$0.984840\pi$
$600$		0			0
$601$	−29.5732			−1.20632			−0.603159	−	0.797621i	$-0.706091\pi$
$601$	−29.5732			−1.20632			−0.603159	+	0.797621i	$0.706091\pi$
$602$	−1.20544	−	2.08789i	−0.0491302	−	0.0850960i
$603$	13.1036	−	22.6961i	0.533620	−	0.924257i
$604$	0.124291	+	0.215278i	0.00505731	+	0.00875952i
$605$		0			0
$606$	−4.70402	+	8.14760i	−0.191088	+	0.330974i
$607$	24.5915			0.998139			0.499069	−	0.866562i	$-0.333675\pi$
$607$	24.5915			0.998139			0.499069	+	0.866562i	$0.333675\pi$
$608$	11.3012	−	22.0949i	0.458323	−	0.896065i
$609$	−15.2402			−0.617564
$610$		0			0
$611$	−0.859772	+	1.48917i	−0.0347826	+	0.0602453i
$612$	−21.5466	−	37.3197i	−0.870968	−	1.50856i
$613$	−14.9450	+	25.8856i	−0.603624	+	1.04551i	0.388643	+	0.921388i	$0.372944\pi$
$613$	−14.9450	+	25.8856i	−0.603624	+	1.04551i	−0.992267	+	0.124119i	$0.960389\pi$
$614$	9.05027	+	15.6755i	0.365239	+	0.632613i
$615$		0			0
$616$	3.04290			0.122602
$617$	−20.3570	−	35.2594i	−0.819544	−	1.41949i	−0.906019	−	0.423238i	$-0.860894\pi$
$617$	−20.3570	−	35.2594i	−0.819544	−	1.41949i	0.0864749	−	0.996254i	$-0.472440\pi$
$618$	20.8438	+	36.1025i	0.838459	+	1.45225i
$619$	−28.4784			−1.14464			−0.572322	−	0.820029i	$-0.693957\pi$
$619$	−28.4784			−1.14464			−0.572322	+	0.820029i	$0.693957\pi$
$620$		0			0
$621$	−18.0900	−	31.3327i	−0.725925	−	1.25734i
$622$	−1.35804	+	2.35219i	−0.0544524	+	0.0943143i
$623$	0.955582	+	1.65512i	0.0382846	+	0.0663109i
$624$	−0.0262868	+	0.0455302i	−0.00105232	+	0.00182266i
$625$		0			0
$626$	−10.6060			−0.423902
$627$	25.6321	−	1.30339i	1.02365	−	0.0520525i
$628$	19.8009			0.790141
$629$	−2.53014	+	4.38233i	−0.100883	+	0.174735i
$630$		0			0
$631$	−21.2101	−	36.7369i	−0.844359	−	1.46247i	−0.886176	−	0.463348i	$-0.846648\pi$
$631$	−21.2101	−	36.7369i	−0.844359	−	1.46247i	0.0418172	−	0.999125i	$-0.486685\pi$
$632$	−9.30649	+	16.1193i	−0.370192	+	0.641192i
$633$	−9.39114	−	16.2659i	−0.373264	−	0.646513i
$634$	9.88912			0.392747
$635$		0			0
$636$	−15.8632	−	27.4758i	−0.629016	−	1.08949i
$637$	−0.649643	−	1.12521i	−0.0257398	−	0.0445826i
$638$	−14.4141			−0.570659
$639$	33.6714			1.33202
$640$		0			0
$641$	14.7630	−	25.5702i	0.583102	−	1.00996i	−0.412007	−	0.911181i	$-0.635172\pi$
$641$	14.7630	−	25.5702i	0.583102	−	1.00996i	0.995109	−	0.0987822i	$-0.0314947\pi$
$642$	1.40444	+	2.43256i	0.0554288	+	0.0960055i
$643$	10.7985	−	18.7036i	0.425852	−	0.737597i	−0.570648	−	0.821195i	$-0.693308\pi$
$643$	10.7985	−	18.7036i	0.425852	−	0.737597i	0.996500	+	0.0835979i	$0.0266411\pi$
$644$	1.20051	−	2.07934i	0.0473066	−	0.0819374i
$645$		0			0
$646$	−9.06885	+	17.7305i	−0.356809	+	0.697596i
$647$	12.6128			0.495861			0.247930	−	0.968778i	$-0.420250\pi$
$647$	12.6128			0.495861			0.247930	+	0.968778i	$0.420250\pi$
$648$	−19.0458	+	32.9883i	−0.748190	+	1.29590i
$649$	3.55125	−	6.15095i	0.139399	−	0.241446i
$650$		0			0
$651$	−4.93368	+	8.54538i	−0.193366	+	0.334920i
$652$	−5.76807	−	9.99059i	−0.225895	−	0.391262i
$653$	26.6312			1.04216			0.521080	−	0.853508i	$-0.325529\pi$
$653$	26.6312			1.04216			0.521080	+	0.853508i	$0.325529\pi$
$654$	−17.9173			−0.700621
$655$		0			0
$656$	−0.441045	−	0.763913i	−0.0172199	−	0.0298258i
$657$	−55.7638			−2.17555
$658$	−4.32055			−0.168433
$659$	−19.9772	−	34.6016i	−0.778202	−	1.34789i	−0.932977	−	0.359936i	$-0.882798\pi$
$659$	−19.9772	−	34.6016i	−0.778202	−	1.34789i	0.154775	−	0.987950i	$-0.450535\pi$
$660$		0			0
$661$	6.76165	+	11.7115i	0.262998	+	0.455526i	0.967037	−	0.254635i	$-0.0819555\pi$
$661$	6.76165	+	11.7115i	0.262998	+	0.455526i	−0.704039	+	0.710161i	$0.748622\pi$
$662$	2.52676	−	4.37648i	0.0982053	−	0.170097i
$663$	1.58597	−	2.74698i	0.0615939	−	0.106684i
$664$	12.6887			0.492418
$665$		0			0
$666$	5.34338			0.207052
$667$	−14.7449	+	25.5389i	−0.570925	+	0.988871i
$668$	1.92749	−	3.33851i	0.0745768	−	0.129171i
$669$	−26.5195	−	45.9330i	−1.02530	−	1.77587i
$670$		0			0
$671$	−3.35713	−	5.81471i	−0.129600	−	0.224475i
$672$	−9.93166			−0.383122
$673$	−34.4110			−1.32645			−0.663224	−	0.748421i	$-0.730812\pi$
$673$	−34.4110			−1.32645			−0.663224	+	0.748421i	$0.730812\pi$
$674$	−3.71425	−	6.43327i	−0.143068	−	0.247800i
$675$		0			0
$676$	16.2754			0.625977
$677$	29.6650			1.14012			0.570059	−	0.821604i	$-0.306920\pi$
$677$	29.6650			1.14012			0.570059	+	0.821604i	$0.306920\pi$
$678$	−10.4949	−	18.1776i	−0.403053	−	0.698108i
$679$	−4.30335	+	7.45361i	−0.165147	+	0.286043i
$680$		0			0
$681$	−1.82446	+	3.16005i	−0.0699134	+	0.121094i
$682$	−4.66625	+	8.08217i	−0.178680	+	0.309482i
$683$	27.8978			1.06748			0.533740	−	0.845648i	$-0.320786\pi$
$683$	27.8978			1.06748			0.533740	+	0.845648i	$0.320786\pi$
$684$	−35.4256	+	1.80139i	−1.35453	+	0.0688779i
$685$		0			0
$686$	3.34304	−	5.79032i	0.127638	−	0.221075i
$687$	9.61907	−	16.6607i	0.366991	−	0.635646i
$688$	−0.216462	−	0.374923i	−0.00825253	−	0.0142938i
$689$	0.798172	−	1.38247i	0.0304079	−	0.0526680i
$690$		0			0
$691$	−49.6386			−1.88834			−0.944170	−	0.329459i	$-0.893134\pi$
$691$	−49.6386			−1.88834			−0.944170	+	0.329459i	$0.893134\pi$
$692$	13.0753			0.497049
$693$	−3.51053	−	6.08041i	−0.133354	−	0.230976i
$694$	5.21558	+	9.03364i	0.197981	+	0.342912i
$695$		0			0
$696$	75.5629			2.86420
$697$	26.6097	+	46.0893i	1.00791	+	1.74576i
$698$	8.18863	−	14.1831i	0.309944	−	0.536839i
$699$	4.24439	+	7.35150i	0.160538	+	0.278059i
$700$		0			0
$701$	24.9906	−	43.2851i	0.943883	−	1.63485i	0.185911	−	0.982567i	$-0.440476\pi$
$701$	24.9906	−	43.2851i	0.943883	−	1.63485i	0.757972	−	0.652287i	$-0.226190\pi$
$702$	−1.79901			−0.0678991
$703$	2.26315	+	3.49682i	0.0853562	+	0.131885i
$704$	−9.05763			−0.341372
$705$		0			0
$706$	3.32929	−	5.76651i	0.125300	−	0.217025i
$707$	1.00312	+	1.73746i	0.0377264	+	0.0653440i
$708$	−7.18000	+	12.4361i	−0.269841	+	0.467378i
$709$	−12.5938	−	21.8131i	−0.472971	−	0.819209i	0.526551	−	0.850144i	$-0.323485\pi$
$709$	−12.5938	−	21.8131i	−0.472971	−	0.819209i	−0.999521	+	0.0309345i	$0.990152\pi$
$710$		0			0
$711$	42.9468			1.61063
$712$	−4.73790	−	8.20628i	−0.177560	−	0.307543i
$713$	9.54667	+	16.5353i	0.357526	+	0.619253i
$714$	7.96986			0.298265
$715$		0			0
$716$	−8.43972	−	14.6180i	−0.315407	−	0.546301i
$717$	26.6431	−	46.1471i	0.995003	−	1.72340i
$718$	−3.03274	−	5.25285i	−0.113181	−	0.196035i
$719$	−8.58777	+	14.8745i	−0.320270	+	0.554724i	−0.980544	−	0.196301i	$-0.937107\pi$
$719$	−8.58777	+	14.8745i	−0.320270	+	0.554724i	0.660274	+	0.751025i	$0.270440\pi$
$720$		0			0
$721$	8.88979			0.331073
$722$	9.59421	+	13.2920i	0.357060	+	0.494676i
$723$	14.7386			0.548136
$724$	4.99868	−	8.65796i	0.185774	−	0.321771i
$725$		0			0
$726$	9.75429	+	16.8949i	0.362016	+	0.627029i
$727$	−0.528264	+	0.914981i	−0.0195922	+	0.0339348i	−0.875655	−	0.482937i	$-0.839570\pi$
$727$	−0.528264	+	0.914981i	−0.0195922	+	0.0339348i	0.856063	+	0.516871i	$0.172903\pi$
$728$	−0.154777	−	0.268082i	−0.00573643	−	0.00993579i
$729$	−11.1223			−0.411937
$730$		0			0
$731$	13.0598	+	22.6203i	0.483035	+	0.836641i
$732$	6.78752	+	11.7563i	0.250874	+	0.434526i
$733$	−20.5025			−0.757277			−0.378639	−	0.925545i	$-0.623608\pi$
$733$	−20.5025			−0.757277			−0.378639	+	0.925545i	$0.623608\pi$
$734$	−29.0851			−1.07355
$735$		0			0
$736$	−9.60888	+	16.6431i	−0.354188	+	0.613472i
$737$	−3.86619	−	6.69644i	−0.142413	−	0.246666i
$738$	28.0984	−	48.6678i	1.03431	−	1.79149i
$739$	−12.4548	+	21.5723i	−0.458157	+	0.793551i	−0.998864	−	0.0476601i	$-0.984824\pi$
$739$	−12.4548	+	21.5723i	−0.458157	+	0.793551i	0.540707	+	0.841211i	$0.318157\pi$
$740$		0			0
$741$	−1.41861	−	2.19192i	−0.0521139	−	0.0805221i
$742$	4.01100			0.147248
$743$	6.62867	−	11.4812i	0.243182	−	0.421204i	−0.718437	−	0.695592i	$-0.755142\pi$
$743$	6.62867	−	11.4812i	0.243182	−	0.421204i	0.961619	+	0.274388i	$0.0884754\pi$
$744$	24.4618	−	42.3691i	0.896814	−	1.55333i
$745$		0			0
$746$	−4.31808	+	7.47913i	−0.158096	+	0.273830i
$747$	−14.6387	−	25.3550i	−0.535602	−	0.927690i
$748$	−12.7145			−0.464889
$749$	0.598988			0.0218866
$750$		0			0
$751$	−12.4183	−	21.5091i	−0.453149	−	0.784877i	0.545430	−	0.838156i	$-0.316366\pi$
$751$	−12.4183	−	21.5091i	−0.453149	−	0.784877i	−0.998580	+	0.0532786i	$0.983033\pi$
$752$	−0.775843			−0.0282921
$753$	80.8209			2.94528
$754$	0.733174	+	1.26989i	0.0267006	+	0.0462468i
$755$		0			0
$756$	3.81226	+	6.60302i	0.138650	+	0.240150i
$757$	24.2329	−	41.9726i	0.880760	−	1.52552i	0.0302631	−	0.999542i	$-0.490365\pi$
$757$	24.2329	−	41.9726i	0.880760	−	1.52552i	0.850497	−	0.525980i	$-0.176301\pi$
$758$	−15.4465	+	26.7542i	−0.561044	+	0.971756i
$759$	−19.8744			−0.721395
$760$		0			0
$761$	40.3726			1.46351			0.731753	−	0.681570i	$-0.238702\pi$
$761$	40.3726			1.46351			0.731753	+	0.681570i	$0.238702\pi$
$762$	−11.2592	+	19.5016i	−0.407879	+	0.706467i
$763$	−1.91042	+	3.30894i	−0.0691617	+	0.119792i
$764$	−8.85195	−	15.3320i	−0.320252	−	0.554693i
$765$		0			0
$766$	7.00989	+	12.1415i	0.253278	+	0.438690i
$767$	−0.722538			−0.0260893
$768$	48.5638			1.75239
$769$	22.4772	+	38.9317i	0.810550	+	1.40391i	0.912480	+	0.409121i	$0.134165\pi$
$769$	22.4772	+	38.9317i	0.810550	+	1.40391i	−0.101930	+	0.994792i	$0.532502\pi$
$770$		0			0
$771$	−68.5123			−2.46741
$772$	4.99337			0.179715
$773$	1.84323	+	3.19256i	0.0662962	+	0.114828i	0.897268	−	0.441486i	$-0.145548\pi$
$773$	1.84323	+	3.19256i	0.0662962	+	0.114828i	−0.830972	+	0.556314i	$0.812215\pi$
$774$	13.7905	−	23.8858i	0.495688	−	0.858557i
$775$		0			0
$776$	21.3365	−	36.9560i	0.765937	−	1.32664i
$777$	0.833455	−	1.44359i	0.0299000	−	0.0517884i
$778$	16.7255			0.599639
$779$	43.7501	−	2.22469i	1.56751	−	0.0797078i
$780$		0			0
$781$	4.96733	−	8.60367i	0.177745	−	0.307864i
$782$	7.71084	−	13.3556i	0.275739	−	0.477594i
$783$	−46.8230	−	81.0999i	−1.67332	−	2.89827i
$784$	0.293113	−	0.507687i	0.0104683	−	0.0181317i
$785$		0			0
$786$	4.97953			0.177614
$787$	−45.7141			−1.62953			−0.814766	−	0.579790i	$-0.803135\pi$
$787$	−45.7141			−1.62953			−0.814766	+	0.579790i	$0.803135\pi$
$788$	−11.5198	−	19.9529i	−0.410376	−	0.710793i
$789$	−13.5688	−	23.5019i	−0.483064	−	0.836691i
$790$		0			0
$791$	−4.47602			−0.159149
$792$	17.4056	+	30.1475i	0.618483	+	1.07124i
$793$	−0.341521	+	0.591531i	−0.0121278	+	0.0210059i
$794$	−2.30973	−	4.00056i	−0.0819691	−	0.141975i
$795$		0			0
$796$	−1.00869	+	1.74710i	−0.0357520	+	0.0619243i
$797$	30.3378			1.07462			0.537310	−	0.843385i	$-0.319441\pi$
$797$	30.3378			1.07462			0.537310	+	0.843385i	$0.319441\pi$
$798$	2.98738	−	5.84060i	0.105752	−	0.206755i
$799$	46.8091			1.65599
$800$		0			0
$801$	−10.9320	+	18.9348i	−0.386264	+	0.669029i
$802$	3.59707	+	6.23031i	0.127017	+	0.220000i
$803$	−8.22650	+	14.2487i	−0.290307	+	0.502826i
$804$	7.81675	+	13.5390i	0.275676	+	0.477484i
$805$		0			0
$806$	0.949395			0.0334410
$807$	−7.33478	−	12.7042i	−0.258197	−	0.447209i
$808$	−4.97362	−	8.61456i	−0.174971	−	0.303059i
$809$	34.5585			1.21501			0.607506	−	0.794315i	$-0.292170\pi$
$809$	34.5585			1.21501			0.607506	+	0.794315i	$0.292170\pi$
$810$		0			0
$811$	−16.6377	−	28.8173i	−0.584229	−	1.01191i	−0.994971	−	0.100162i	$-0.968064\pi$
$811$	−16.6377	−	28.8173i	−0.584229	−	1.01191i	0.410742	−	0.911751i	$-0.365270\pi$
$812$	3.10732	−	5.38204i	0.109046	−	0.188873i
$813$	5.41762	+	9.38359i	0.190004	+	0.329097i
$814$	0.788277	−	1.36534i	0.0276291	−	0.0478550i
$815$		0			0
$816$	1.43115			0.0501003
$817$	21.4722	−	1.09186i	0.751218	−	0.0381994i
$818$	30.4757			1.06556
$819$	−0.357126	+	0.618561i	−0.0124790	+	0.0216143i
$820$		0			0
$821$	−6.35063	−	10.9996i	−0.221638	−	0.383889i	0.733667	−	0.679509i	$-0.237807\pi$
$821$	−6.35063	−	10.9996i	−0.221638	−	0.383889i	−0.955306	+	0.295620i	$0.904474\pi$
$822$	16.5525	−	28.6698i	0.577336	−	0.999976i
$823$	−6.00454	−	10.4002i	−0.209305	−	0.362527i	0.742191	−	0.670189i	$-0.233787\pi$
$823$	−6.00454	−	10.4002i	−0.209305	−	0.362527i	−0.951496	+	0.307662i	$0.900453\pi$
$824$	−44.0767			−1.53549
$825$		0			0
$826$	−0.907731	−	1.57224i	−0.0315840	−	0.0547051i
$827$	4.27272	+	7.40057i	0.148577	+	0.257343i	0.930702	−	0.365779i	$-0.119197\pi$
$827$	4.27272	+	7.40057i	0.148577	+	0.257343i	−0.782125	+	0.623122i	$0.785864\pi$
$828$	27.4680			0.954578
$829$	−27.1042			−0.941369			−0.470685	−	0.882302i	$-0.655993\pi$
$829$	−27.1042			−0.941369			−0.470685	+	0.882302i	$0.655993\pi$
$830$		0			0
$831$	−50.4553	+	87.3912i	−1.75028	+	3.03157i
$832$	0.460717	+	0.797985i	0.0159725	+	0.0276652i
$833$	−17.6844	+	30.6303i	−0.612729	+	1.06128i
$834$	0.416081	−	0.720673i	0.0144077	−	0.0249549i
$835$		0			0
$836$	−4.76584	+	9.31767i	−0.164830	+	0.322258i
$837$	−60.6317			−2.09574
$838$	9.16500	−	15.8743i	0.316600	−	0.548367i
$839$	18.2190	−	31.5562i	0.628989	−	1.08944i	−0.358766	−	0.933427i	$-0.616802\pi$
$839$	18.2190	−	31.5562i	0.628989	−	1.08944i	0.987755	−	0.156013i	$-0.0498642\pi$
$840$		0			0
$841$	−23.6649	+	40.9887i	−0.816029	+	1.41340i
$842$	−6.41667	−	11.1140i	−0.221133	−	0.383014i
$843$	−30.5448			−1.05202
$844$	7.65903			0.263635
$845$		0			0
$846$	−24.7139	−	42.8058i	−0.849682	−	1.47169i
$847$	4.16017			0.142945
$848$	0.720256			0.0247337
$849$	3.80554	+	6.59138i	0.130606	+	0.226216i
$850$		0			0
$851$	−1.61274	−	2.79334i	−0.0552838	−	0.0957544i
$852$	−10.0431	+	17.3951i	−0.344070	+	0.595947i
$853$	−9.17354	+	15.8890i	−0.314096	+	0.544030i	−0.979245	−	0.202680i	$-0.935035\pi$
$853$	−9.17354	+	15.8890i	−0.314096	+	0.544030i	0.665149	+	0.746711i	$0.268368\pi$
$854$	−1.71622			−0.0587279
$855$		0			0
$856$	−2.96986			−0.101508
$857$	−3.92892	+	6.80508i	−0.134209	+	0.232457i	−0.925295	−	0.379248i	$-0.876183\pi$
$857$	−3.92892	+	6.80508i	−0.134209	+	0.232457i	0.791086	+	0.611705i	$0.209516\pi$
$858$	−0.494116	+	0.855834i	−0.0168688	+	0.0292177i
$859$	17.1511	+	29.7066i	0.585188	+	1.01358i	0.994852	+	0.101339i	$0.0323127\pi$
$859$	17.1511	+	29.7066i	0.585188	+	1.01358i	−0.409664	+	0.912237i	$0.634354\pi$
$860$		0			0
$861$	−8.76550	−	15.1823i	−0.298728	−	0.517411i
$862$	14.6257			0.498153
$863$	35.9451			1.22359			0.611793	−	0.791018i	$-0.290449\pi$
$863$	35.9451			1.22359			0.611793	+	0.791018i	$0.290449\pi$
$864$	−30.5134	−	52.8508i	−1.03809	−	1.79802i
$865$		0			0
$866$	19.9699			0.678604
$867$	−34.0005			−1.15472
$868$	−2.01185	−	3.48463i	−0.0682868	−	0.118276i
$869$	6.33568	−	10.9737i	0.214923	−	0.372258i
$870$		0			0
$871$	−0.393308	+	0.681229i	−0.0133267	+	0.0230826i
$872$	9.47209	−	16.4061i	0.320765	−	0.555582i
$873$	−98.4620			−3.33243
$874$	−6.89716	−	10.6569i	−0.233300	−	0.360475i
$875$		0			0
$876$	16.6325	−	28.8084i	0.561961	−	0.973345i
$877$	−12.6258	+	21.8685i	−0.426343	+	0.738448i	−0.996545	−	0.0830567i	$-0.973532\pi$
$877$	−12.6258	+	21.8685i	−0.426343	+	0.738448i	0.570202	+	0.821505i	$0.306865\pi$
$878$	14.4713	+	25.0651i	0.488383	+	0.845905i
$879$	−26.2164	+	45.4082i	−0.884259	+	1.53158i
$880$		0			0
$881$	17.7796			0.599010			0.299505	−	0.954095i	$-0.403179\pi$
$881$	17.7796			0.599010			0.299505	+	0.954095i	$0.403179\pi$
$882$	37.3476			1.25756
$883$	3.77671	+	6.54146i	0.127096	+	0.220138i	0.922550	−	0.385876i	$-0.126101\pi$
$883$	3.77671	+	6.54146i	0.127096	+	0.220138i	−0.795454	+	0.606014i	$0.792768\pi$
$884$	0.646726	+	1.12016i	0.0217517	+	0.0376751i
$885$		0			0
$886$	−27.0550			−0.908930
$887$	−8.12030	−	14.0648i	−0.272653	−	0.472249i	0.696887	−	0.717181i	$-0.254568\pi$
$887$	−8.12030	−	14.0648i	−0.272653	−	0.472249i	−0.969540	+	0.244932i	$0.921234\pi$
$888$	−4.13238	+	7.15748i	−0.138673	+	0.240189i
$889$	2.40101	+	4.15867i	0.0805273	+	0.139477i
$890$		0			0
$891$	12.9660	−	22.4578i	0.434378	−	0.752364i
$892$	21.6282			0.724165
$893$	17.5456	−	34.3034i	0.587142	−	1.14792i
$894$	11.5983			0.387906
$895$		0			0
$896$	2.06787	−	3.58165i	0.0690825	−	0.119654i
$897$	1.01091	+	1.75095i	0.0337534	+	0.0584625i
$898$	−6.91525	+	11.9776i	−0.230765	+	0.399697i
$899$	24.7101	+	42.7991i	0.824127	+	1.42743i
$900$		0			0
$901$	−43.4553			−1.44771
$902$	−8.29036	−	14.3593i	−0.276039	−	0.478113i
$903$	−4.30205	−	7.45136i	−0.143163	−	0.247966i
$904$	22.1927			0.738118
$905$		0			0
$906$	−0.262974	−	0.455485i	−0.00873674	−	0.0151325i
$907$	−9.12675	+	15.8080i	−0.303049	+	0.524896i	−0.976825	−	0.214040i	$-0.931338\pi$
$907$	−9.12675	+	15.8080i	−0.303049	+	0.524896i	0.673776	+	0.738935i	$0.264671\pi$
$908$	−0.743977	−	1.28861i	−0.0246897	−	0.0427639i
$909$	−11.4759	+	19.8768i	−0.380632	+	0.659273i
$910$		0			0
$911$	15.9019			0.526853			0.263426	−	0.964679i	$-0.415147\pi$
$911$	15.9019			0.526853			0.263426	+	0.964679i	$0.415147\pi$
$912$	0.536444	−	1.04880i	0.0177634	−	0.0347292i
$913$	−8.63824			−0.285884
$914$	6.64254	−	11.5052i	0.219716	−	0.380558i
$915$		0			0
$916$	3.92246	+	6.79390i	0.129602	+	0.224477i
$917$	0.530939	−	0.919612i	0.0175331	−	0.0303683i
$918$	24.4861	+	42.4112i	0.808162	+	1.39978i
$919$	−30.0748			−0.992075			−0.496038	−	0.868301i	$-0.665212\pi$
$919$	−30.0748			−0.992075			−0.496038	+	0.868301i	$0.665212\pi$
$920$		0			0
$921$	32.2990	+	55.9436i	1.06429	+	1.84340i
$922$	−2.50815	−	4.34425i	−0.0826016	−	0.143070i
$923$	−1.01065			−0.0332661
$924$	4.18830			0.137785
$925$		0			0
$926$	14.0973	−	24.4173i	0.463267	−	0.802402i
$927$	50.8504	+	88.0754i	1.67014	+	2.89278i
$928$	−24.8711	+	43.0780i	−0.816433	+	1.41410i
$929$	18.4221	−	31.9081i	0.604410	−	1.04687i	−0.387734	−	0.921771i	$-0.626742\pi$
$929$	18.4221	−	31.9081i	0.604410	−	1.04687i	0.992144	−	0.125098i	$-0.0399245\pi$
$930$		0			0
$931$	15.8183	+	24.4411i	0.518424	+	0.801025i
$932$	−3.46155			−0.113387
$933$	−4.84663	+	8.39462i	−0.158672	+	0.274827i
$934$	−2.84304	+	4.92429i	−0.0930272	+	0.161128i
$935$		0			0
$936$	1.77068	−	3.06690i	0.0578764	−	0.100245i
$937$	−21.6160	−	37.4401i	−0.706165	−	1.22311i	−0.966270	−	0.257533i	$-0.917090\pi$
$937$	−21.6160	−	37.4401i	−0.706165	−	1.22311i	0.260105	−	0.965580i	$-0.416243\pi$
$938$	−1.97646			−0.0645338
$939$	−37.8513			−1.23523
$940$		0			0
$941$	10.1601	+	17.5979i	0.331211	+	0.573674i	0.982750	−	0.184941i	$-0.0592095\pi$
$941$	10.1601	+	17.5979i	0.331211	+	0.573674i	−0.651539	+	0.758615i	$0.725876\pi$
$942$	−41.8948			−1.36501
$943$	−33.9225			−1.10467
$944$	−0.163001	−	0.282327i	−0.00530525	−	0.00918896i
$945$		0			0
$946$	−4.06885	−	7.04745i	−0.132290	−	0.229133i
$947$	−10.7525	+	18.6239i	−0.349409	+	0.605195i	−0.986145	−	0.165888i	$-0.946951\pi$
$947$	−10.7525	+	18.6239i	−0.349409	+	0.605195i	0.636735	+	0.771083i	$0.280284\pi$
$948$	−12.8096	+	22.1869i	−0.416037	+	0.720597i
$949$	1.67376			0.0543327
$950$		0			0
$951$	35.2928			1.14445
$952$	−4.21332	+	7.29768i	−0.136554	+	0.236519i
$953$	8.86503	−	15.3547i	0.287166	−	0.497387i	−0.685966	−	0.727634i	$-0.740620\pi$
$953$	8.86503	−	15.3547i	0.287166	−	0.497387i	0.973132	+	0.230247i	$0.0739534\pi$
$954$	22.9432	+	39.7389i	0.742815	+	1.28659i
$955$		0			0
$956$	10.8645	+	18.8179i	0.351383	+	0.608613i
$957$	−51.4417			−1.66288
$958$	31.7559			1.02599
$959$	−3.52980	−	6.11379i	−0.113983	−	0.197425i
$960$		0			0
$961$	0.997355			0.0321727
$962$	−0.160383			−0.00517095
$963$	3.42626	+	5.93446i	0.110410	+	0.191235i
$964$	−3.00506	+	5.20491i	−0.0967864	+	0.167639i
$965$		0			0
$966$	−2.54003	+	4.39947i	−0.0817242	+	0.141551i
$967$	−6.82652	+	11.8239i	−0.219526	+	0.380230i	−0.954663	−	0.297688i	$-0.903784\pi$
$967$	−6.82652	+	11.8239i	−0.219526	+	0.380230i	0.735137	+	0.677919i	$0.237118\pi$
$968$	−20.6267			−0.662966
$969$	−32.3654	+	63.2774i	−1.03973	+	2.03276i
$970$		0			0
$971$	−13.9798	+	24.2136i	−0.448632	+	0.777053i	−0.998297	−	0.0583319i	$-0.981422\pi$
$971$	−13.9798	+	24.2136i	−0.448632	+	0.777053i	0.549666	+	0.835385i	$0.314755\pi$
$972$	−6.02722	+	10.4394i	−0.193323	+	0.334845i
$973$	−0.0887286	−	0.153682i	−0.00284451	−	0.00492683i
$974$	1.05895	−	1.83416i	0.0339311	−	0.0587704i
$975$		0			0
$976$	−0.308182			−0.00986468
$977$	−17.8540			−0.571200			−0.285600	−	0.958349i	$-0.592193\pi$
$977$	−17.8540			−0.571200			−0.285600	+	0.958349i	$0.592193\pi$
$978$	12.2041	+	21.1381i	0.390244	+	0.675922i
$979$	3.22547	+	5.58668i	0.103086	+	0.178551i
$980$		0			0
$981$	−43.7109			−1.39558
$982$	7.67630	+	13.2957i	0.244961	+	0.424284i
$983$	−24.5222	+	42.4736i	−0.782136	+	1.35470i	0.148559	+	0.988903i	$0.452536\pi$
$983$	−24.5222	+	42.4736i	−0.782136	+	1.35470i	−0.930695	+	0.365795i	$0.880797\pi$
$984$	43.4605	+	75.2758i	1.38547	+	2.39970i
$985$		0			0
$986$	19.9583	−	34.5688i	0.635602	−	1.10089i
$987$	−15.4194			−0.490805
$988$	1.06331	−	0.0540692i	0.0338284	−	0.00172017i
$989$	−16.6489			−0.529405
$990$		0			0
$991$	12.5337	−	21.7089i	0.398145	−	0.689607i	−0.595352	−	0.803465i	$-0.702988\pi$
$991$	12.5337	−	21.7089i	0.398145	−	0.689607i	0.993497	+	0.113858i	$0.0363209\pi$
$992$	16.1029	+	27.8911i	0.511269	+	0.885543i
$993$	9.01762	−	15.6190i	0.286166	−	0.495653i
$994$	−1.26969	−	2.19917i	−0.0402722	−	0.0697536i
$995$		0			0
$996$	17.4650			0.553400
$997$	15.0111	+	26.0000i	0.475406	+	0.823427i	0.999603	−	0.0281699i	$-0.00896794\pi$
$997$	15.0111	+	26.0000i	0.475406	+	0.823427i	−0.524197	+	0.851597i	$0.675635\pi$
$998$	−12.6310	−	21.8776i	−0.399828	−	0.692522i
$999$	10.2426			0.324062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.g.201.5		12
5.2	odd	4		95.2.i.b.49.5	yes	12
5.3	odd	4		95.2.i.b.49.2	✓	12
5.4	even	2	inner	475.2.e.g.201.2		12
15.2	even	4		855.2.be.d.334.2		12
15.8	even	4		855.2.be.d.334.5		12
19.7	even	3	inner	475.2.e.g.26.5		12
19.8	odd	6		9025.2.a.bt.1.5		6
19.11	even	3		9025.2.a.bu.1.2		6
95.7	odd	12		95.2.i.b.64.2	yes	12
95.8	even	12		1805.2.b.g.1084.2		6
95.27	even	12		1805.2.b.g.1084.5		6
95.49	even	6		9025.2.a.bu.1.5		6
95.64	even	6	inner	475.2.e.g.26.2		12
95.68	odd	12		1805.2.b.f.1084.5		6
95.83	odd	12		95.2.i.b.64.5	yes	12
95.84	odd	6		9025.2.a.bt.1.2		6
95.87	odd	12		1805.2.b.f.1084.2		6
285.83	even	12		855.2.be.d.64.2		12
285.197	even	12		855.2.be.d.64.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.2	✓	12	5.3	odd	4
95.2.i.b.49.5	yes	12	5.2	odd	4
95.2.i.b.64.2	yes	12	95.7	odd	12
95.2.i.b.64.5	yes	12	95.83	odd	12
475.2.e.g.26.2		12	95.64	even	6	inner
475.2.e.g.26.5		12	19.7	even	3	inner
475.2.e.g.201.2		12	5.4	even	2	inner
475.2.e.g.201.5		12	1.1	even	1	trivial
855.2.be.d.64.2		12	285.83	even	12
855.2.be.d.64.5		12	285.197	even	12
855.2.be.d.334.2		12	15.2	even	4
855.2.be.d.334.5		12	15.8	even	4
1805.2.b.f.1084.2		6	95.87	odd	12
1805.2.b.f.1084.5		6	95.68	odd	12
1805.2.b.g.1084.2		6	95.8	even	12
1805.2.b.g.1084.5		6	95.27	even	12
9025.2.a.bt.1.2		6	95.84	odd	6
9025.2.a.bt.1.5		6	19.8	odd	6
9025.2.a.bu.1.2		6	19.11	even	3
9025.2.a.bu.1.5		6	95.49	even	6

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.431391 - 0.747190i) q^{2} +(1.53957 - 2.66661i) q^{3} +(0.627804 + 1.08739i) q^{4} +(-1.32831 - 2.30070i) q^{6} -0.566520 q^{7} +2.80888 q^{8} +(-3.24054 - 5.61278i) q^{9} +O(q^{10})\)	\(q+(0.431391 - 0.747190i) q^{2} +(1.53957 - 2.66661i) q^{3} +(0.627804 + 1.08739i) q^{4} +(-1.32831 - 2.30070i) q^{6} -0.566520 q^{7} +2.80888 q^{8} +(-3.24054 - 5.61278i) q^{9} -1.91223 q^{11} +3.86619 q^{12} +(0.0972656 + 0.168469i) q^{13} +(-0.244391 + 0.423298i) q^{14} +(-0.0438854 + 0.0760118i) q^{16} +(2.64775 - 4.58603i) q^{17} -5.59175 q^{18} +(-2.36834 - 3.65936i) q^{19} +(-0.872196 + 1.51069i) q^{21} +(-0.824918 + 1.42880i) q^{22} +(1.68770 + 2.92318i) q^{23} +(4.32446 - 7.49018i) q^{24} +0.167838 q^{26} -10.7187 q^{27} +(-0.355664 - 0.616027i) q^{28} +(4.36834 + 7.56619i) q^{29} +5.65662 q^{31} +(2.84674 + 4.93070i) q^{32} +(-2.94401 + 5.09917i) q^{33} +(-2.28442 - 3.95674i) q^{34} +(4.06885 - 7.04745i) q^{36} -0.955582 q^{37} +(-3.75592 + 0.190988i) q^{38} +0.598988 q^{39} +(-5.02496 + 8.70349i) q^{41} +(0.752514 + 1.30339i) q^{42} +(-2.46622 + 4.27161i) q^{43} +(-1.20051 - 2.07934i) q^{44} +2.91223 q^{46} +(4.41971 + 7.65516i) q^{47} +(0.135129 + 0.234051i) q^{48} -6.67906 q^{49} +(-8.15277 - 14.1210i) q^{51} +(-0.122128 + 0.211531i) q^{52} +(-4.10305 - 7.10669i) q^{53} +(-4.62395 + 8.00892i) q^{54} -1.59128 q^{56} +(-13.4043 + 0.681609i) q^{57} +7.53785 q^{58} +(-1.85713 + 3.21664i) q^{59} +(1.75561 + 3.04080i) q^{61} +(2.44021 - 4.22657i) q^{62} +(1.83583 + 3.17975i) q^{63} +4.73669 q^{64} +(2.54003 + 4.39947i) q^{66} +(2.02182 + 3.50190i) q^{67} +6.64906 q^{68} +10.3933 q^{69} +(-2.59767 + 4.49929i) q^{71} +(-9.10228 - 15.7656i) q^{72} +(4.30205 - 7.45136i) q^{73} +(-0.412229 + 0.714002i) q^{74} +(2.49230 - 4.87268i) q^{76} +1.08332 q^{77} +(0.258398 - 0.447558i) q^{78} +(-3.31324 + 5.73870i) q^{79} +(-6.78057 + 11.7443i) q^{81} +(4.33544 + 7.50921i) q^{82} +4.51737 q^{83} -2.19027 q^{84} +(2.12780 + 3.68547i) q^{86} +26.9014 q^{87} -5.37122 q^{88} +(-1.68676 - 2.92155i) q^{89} +(-0.0551029 - 0.0954410i) q^{91} +(-2.11909 + 3.67037i) q^{92} +(8.70875 - 15.0840i) q^{93} +7.62648 q^{94} +17.5310 q^{96} +(7.59611 - 13.1568i) q^{97} +(-2.88128 + 4.99053i) q^{98} +(6.19665 + 10.7329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^4 - 12 * q^6 - 8 * q^9	\( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9} + 4 q^{11} - 22 q^{14} - 14 q^{16} + 12 q^{19} - 20 q^{21} - 2 q^{24} - 44 q^{26} + 12 q^{29} + 60 q^{31} - 10 q^{34} + 14 q^{36} - 4 q^{39} - 12 q^{41} - 20 q^{44} + 8 q^{46} + 4 q^{49} - 40 q^{51} + 4 q^{54} + 92 q^{56} - 20 q^{59} + 2 q^{61} - 24 q^{64} - 6 q^{66} + 36 q^{69} + 2 q^{71} + 22 q^{74} - 70 q^{76} - 24 q^{79} - 14 q^{81} + 96 q^{84} + 16 q^{86} - 36 q^{89} + 24 q^{91} + 60 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 12 * q - 2 * q^4 - 12 * q^6 - 8 * q^9 + 4 * q^11 - 22 * q^14 - 14 * q^16 + 12 * q^19 - 20 * q^21 - 2 * q^24 - 44 * q^26 + 12 * q^29 + 60 * q^31 - 10 * q^34 + 14 * q^36 - 4 * q^39 - 12 * q^41 - 20 * q^44 + 8 * q^46 + 4 * q^49 - 40 * q^51 + 4 * q^54 + 92 * q^56 - 20 * q^59 + 2 * q^61 - 24 * q^64 - 6 * q^66 + 36 * q^69 + 2 * q^71 + 22 * q^74 - 70 * q^76 - 24 * q^79 - 14 * q^81 + 96 * q^84 + 16 * q^86 - 36 * q^89 + 24 * q^91 + 60 * q^94 + 52 * q^96 + 30 * q^99

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