LMFDB - Embedded newform 450.2.h.a.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

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("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	450.91
Dual form			450.2.h.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} -3.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} -3.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.690983 + 2.12663i) q^{10} +(-0.190983 - 0.138757i) q^{11} +(-0.809017 + 0.587785i) q^{13} +(2.42705 + 1.76336i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-2.42705 + 7.46969i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(1.80902 - 1.31433i) q^{20} +(0.0729490 + 0.224514i) q^{22} +(-5.04508 - 3.66547i) q^{23} +(-4.04508 + 2.93893i) q^{25} +1.00000 q^{26} +(-0.927051 - 2.85317i) q^{28} +(0.163119 + 0.502029i) q^{29} +(1.30902 - 4.02874i) q^{31} +1.00000 q^{32} +(6.35410 - 4.61653i) q^{34} +(2.07295 + 6.37988i) q^{35} +(-5.92705 + 4.30625i) q^{37} +(0.690983 - 0.502029i) q^{38} -2.23607 q^{40} +(-6.04508 + 4.39201i) q^{41} -1.76393 q^{43} +(0.0729490 - 0.224514i) q^{44} +(1.92705 + 5.93085i) q^{46} +(-1.83688 - 5.65334i) q^{47} +2.00000 q^{49} +5.00000 q^{50} +(-0.809017 - 0.587785i) q^{52} +(-0.472136 - 1.45309i) q^{53} +(-0.163119 + 0.502029i) q^{55} +(-0.927051 + 2.85317i) q^{56} +(0.163119 - 0.502029i) q^{58} +(3.61803 - 2.62866i) q^{59} +(1.73607 + 1.26133i) q^{61} +(-3.42705 + 2.48990i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(1.80902 + 1.31433i) q^{65} +(-1.78115 + 5.48183i) q^{67} -7.85410 q^{68} +(2.07295 - 6.37988i) q^{70} +(0.927051 + 2.85317i) q^{71} +(4.61803 + 3.35520i) q^{73} +7.32624 q^{74} -0.854102 q^{76} +(0.572949 + 0.416272i) q^{77} +(-0.854102 - 2.62866i) q^{79} +(1.80902 + 1.31433i) q^{80} +7.47214 q^{82} +(4.16312 - 12.8128i) q^{83} +17.5623 q^{85} +(1.42705 + 1.03681i) q^{86} +(-0.190983 + 0.138757i) q^{88} +(-3.61803 - 2.62866i) q^{89} +(2.42705 - 1.76336i) q^{91} +(1.92705 - 5.93085i) q^{92} +(-1.83688 + 5.65334i) q^{94} +1.90983 q^{95} +(-3.26393 - 10.0453i) q^{97} +(-1.61803 - 1.17557i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 5 q^{5} - 12 q^{7} - q^{8}+O(q^{10}) $ 4 * q - q^2 - q^4 - 5 * q^5 - 12 * q^7 - q^8	$ 4 q - q^{2} - q^{4} - 5 q^{5} - 12 q^{7} - q^{8} - 5 q^{10} - 3 q^{11} - q^{13} + 3 q^{14} - q^{16} - 3 q^{17} - 10 q^{19} + 5 q^{20} + 7 q^{22} - 9 q^{23} - 5 q^{25} + 4 q^{26} + 3 q^{28} - 15 q^{29} + 3 q^{31} + 4 q^{32} + 12 q^{34} + 15 q^{35} - 17 q^{37} + 5 q^{38} - 13 q^{41} - 16 q^{43} + 7 q^{44} + q^{46} - 23 q^{47} + 8 q^{49} + 20 q^{50} - q^{52} + 16 q^{53} + 15 q^{55} + 3 q^{56} - 15 q^{58} + 10 q^{59} - 2 q^{61} - 7 q^{62} - q^{64} + 5 q^{65} + 13 q^{67} - 18 q^{68} + 15 q^{70} - 3 q^{71} + 14 q^{73} - 2 q^{74} + 10 q^{76} + 9 q^{77} + 10 q^{79} + 5 q^{80} + 12 q^{82} + q^{83} + 30 q^{85} - q^{86} - 3 q^{88} - 10 q^{89} + 3 q^{91} + q^{92} - 23 q^{94} + 30 q^{95} - 22 q^{97} - 2 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 5 * q^5 - 12 * q^7 - q^8 - 5 * q^10 - 3 * q^11 - q^13 + 3 * q^14 - q^16 - 3 * q^17 - 10 * q^19 + 5 * q^20 + 7 * q^22 - 9 * q^23 - 5 * q^25 + 4 * q^26 + 3 * q^28 - 15 * q^29 + 3 * q^31 + 4 * q^32 + 12 * q^34 + 15 * q^35 - 17 * q^37 + 5 * q^38 - 13 * q^41 - 16 * q^43 + 7 * q^44 + q^46 - 23 * q^47 + 8 * q^49 + 20 * q^50 - q^52 + 16 * q^53 + 15 * q^55 + 3 * q^56 - 15 * q^58 + 10 * q^59 - 2 * q^61 - 7 * q^62 - q^64 + 5 * q^65 + 13 * q^67 - 18 * q^68 + 15 * q^70 - 3 * q^71 + 14 * q^73 - 2 * q^74 + 10 * q^76 + 9 * q^77 + 10 * q^79 + 5 * q^80 + 12 * q^82 + q^83 + 30 * q^85 - q^86 - 3 * q^88 - 10 * q^89 + 3 * q^91 + q^92 - 23 * q^94 + 30 * q^95 - 22 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$6$		0			0
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$	−0.690983	+	2.12663i	−0.218508	+	0.672499i
$11$	−0.190983	−	0.138757i	−0.0575835	−	0.0418369i	0.558621	−	0.829423i	$-0.311331\pi$
$11$	−0.190983	−	0.138757i	−0.0575835	−	0.0418369i	−0.616205	+	0.787586i	$0.711331\pi$
$12$		0			0
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i	−0.694297	−	0.719689i	$-0.744284\pi$
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i	0.469916	+	0.882711i	$0.344284\pi$
$14$	2.42705	+	1.76336i	0.648657	+	0.471277i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.42705	+	7.46969i	−0.588646	+	1.81167i	−0.00454037	+	0.999990i	$0.501445\pi$
$17$	−2.42705	+	7.46969i	−0.588646	+	1.81167i	−0.584106	+	0.811677i	$0.698555\pi$
$18$		0			0
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	−0.976756	−	0.214353i	$-0.931236\pi$
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	0.916206	+	0.400707i	$0.131236\pi$
$20$	1.80902	−	1.31433i	0.404508	−	0.293893i
$21$		0			0
$22$	0.0729490	+	0.224514i	0.0155528	+	0.0478665i
$23$	−5.04508	−	3.66547i	−1.05197	−	0.764303i	−0.0793863	−	0.996844i	$-0.525296\pi$
$23$	−5.04508	−	3.66547i	−1.05197	−	0.764303i	−0.972587	+	0.232541i	$0.925296\pi$
$24$		0			0
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	1.00000			0.196116
$27$		0			0
$28$	−0.927051	−	2.85317i	−0.175196	−	0.539198i
$29$	0.163119	+	0.502029i	0.0302904	+	0.0932244i	0.965059	−	0.262033i	$-0.0843931\pi$
$29$	0.163119	+	0.502029i	0.0302904	+	0.0932244i	−0.934768	+	0.355258i	$0.884393\pi$
$30$		0			0
$31$	1.30902	−	4.02874i	0.235106	−	0.723583i	−0.762001	−	0.647576i	$-0.775783\pi$
$31$	1.30902	−	4.02874i	0.235106	−	0.723583i	0.997107	−	0.0760071i	$-0.0242172\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	6.35410	−	4.61653i	1.08972	−	0.791728i
$35$	2.07295	+	6.37988i	0.350392	+	1.07840i
$36$		0			0
$37$	−5.92705	+	4.30625i	−0.974401	+	0.707944i	−0.956450	−	0.291895i	$-0.905714\pi$
$37$	−5.92705	+	4.30625i	−0.974401	+	0.707944i	−0.0179508	+	0.999839i	$0.505714\pi$
$38$	0.690983	−	0.502029i	0.112092	−	0.0814398i
$39$		0			0
$40$	−2.23607			−0.353553
$41$	−6.04508	+	4.39201i	−0.944084	+	0.685917i	−0.949400	−	0.314069i	$-0.898308\pi$
$41$	−6.04508	+	4.39201i	−0.944084	+	0.685917i	0.00531652	+	0.999986i	$0.498308\pi$
$42$		0			0
$43$	−1.76393			−0.268997			−0.134499	−	0.990914i	$-0.542942\pi$
$43$	−1.76393			−0.268997			−0.134499	+	0.990914i	$0.542942\pi$
$44$	0.0729490	−	0.224514i	0.0109975	−	0.0338468i
$45$		0			0
$46$	1.92705	+	5.93085i	0.284128	+	0.874457i
$47$	−1.83688	−	5.65334i	−0.267937	−	0.824624i	−0.991002	−	0.133845i	$-0.957268\pi$
$47$	−1.83688	−	5.65334i	−0.267937	−	0.824624i	0.723066	−	0.690779i	$-0.242732\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$	5.00000			0.707107
$51$		0			0
$52$	−0.809017	−	0.587785i	−0.112190	−	0.0815111i
$53$	−0.472136	−	1.45309i	−0.0648529	−	0.199597i	0.913379	−	0.407109i	$-0.133463\pi$
$53$	−0.472136	−	1.45309i	−0.0648529	−	0.199597i	−0.978232	+	0.207513i	$0.933463\pi$
$54$		0			0
$55$	−0.163119	+	0.502029i	−0.0219950	+	0.0676935i
$56$	−0.927051	+	2.85317i	−0.123882	+	0.381271i
$57$		0			0
$58$	0.163119	−	0.502029i	0.0214186	−	0.0659196i
$59$	3.61803	−	2.62866i	0.471028	−	0.342222i	−0.326814	−	0.945089i	$-0.605975\pi$
$59$	3.61803	−	2.62866i	0.471028	−	0.342222i	0.797842	+	0.602867i	$0.205975\pi$
$60$		0			0
$61$	1.73607	+	1.26133i	0.222281	+	0.161496i	0.693353	−	0.720598i	$-0.256133\pi$
$61$	1.73607	+	1.26133i	0.222281	+	0.161496i	−0.471072	+	0.882095i	$0.656133\pi$
$62$	−3.42705	+	2.48990i	−0.435236	+	0.316217i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.80902	+	1.31433i	0.224381	+	0.163022i
$66$		0			0
$67$	−1.78115	+	5.48183i	−0.217602	+	0.669712i	0.781356	+	0.624085i	$0.214528\pi$
$67$	−1.78115	+	5.48183i	−0.217602	+	0.669712i	−0.998959	+	0.0456261i	$0.985472\pi$
$68$	−7.85410			−0.952450
$69$		0			0
$70$	2.07295	−	6.37988i	0.247765	−	0.762542i
$71$	0.927051	+	2.85317i	0.110021	+	0.338609i	0.990876	−	0.134777i	$-0.0430317\pi$
$71$	0.927051	+	2.85317i	0.110021	+	0.338609i	−0.880855	+	0.473386i	$0.843032\pi$
$72$		0			0
$73$	4.61803	+	3.35520i	0.540500	+	0.392696i	0.824271	−	0.566196i	$-0.191585\pi$
$73$	4.61803	+	3.35520i	0.540500	+	0.392696i	−0.283771	+	0.958892i	$0.591585\pi$
$74$	7.32624			0.851658
$75$		0			0
$76$	−0.854102			−0.0979722
$77$	0.572949	+	0.416272i	0.0652936	+	0.0474386i
$78$		0			0
$79$	−0.854102	−	2.62866i	−0.0960940	−	0.295747i	0.891443	−	0.453132i	$-0.149693\pi$
$79$	−0.854102	−	2.62866i	−0.0960940	−	0.295747i	−0.987537	+	0.157385i	$0.949693\pi$
$80$	1.80902	+	1.31433i	0.202254	+	0.146946i
$81$		0			0
$82$	7.47214			0.825159
$83$	4.16312	−	12.8128i	0.456962	−	1.40638i	−0.411855	−	0.911249i	$-0.635119\pi$
$83$	4.16312	−	12.8128i	0.456962	−	1.40638i	0.868817	−	0.495134i	$-0.164881\pi$
$84$		0			0
$85$	17.5623			1.90490
$86$	1.42705	+	1.03681i	0.153883	+	0.111802i
$87$		0			0
$88$	−0.190983	+	0.138757i	−0.0203589	+	0.0147916i
$89$	−3.61803	−	2.62866i	−0.383511	−	0.278637i	0.379280	−	0.925282i	$-0.376172\pi$
$89$	−3.61803	−	2.62866i	−0.383511	−	0.278637i	−0.762791	+	0.646645i	$0.776172\pi$
$90$		0			0
$91$	2.42705	−	1.76336i	0.254424	−	0.184850i
$92$	1.92705	−	5.93085i	0.200909	−	0.618334i
$93$		0			0
$94$	−1.83688	+	5.65334i	−0.189460	+	0.583097i
$95$	1.90983			0.195944
$96$		0			0
$97$	−3.26393	−	10.0453i	−0.331402	−	1.01995i	−0.968467	−	0.249141i	$-0.919852\pi$
$97$	−3.26393	−	10.0453i	−0.331402	−	1.01995i	0.637065	−	0.770810i	$-0.280148\pi$
$98$	−1.61803	−	1.17557i	−0.163446	−	0.118751i
$99$		0			0
$100$	−4.04508	−	2.93893i	−0.404508	−	0.293893i
$101$	1.61803			0.161000			0.0805002	−	0.996755i	$-0.474348\pi$
$101$	1.61803			0.161000			0.0805002	+	0.996755i	$0.474348\pi$
$102$		0			0
$103$	−6.13525	−	18.8824i	−0.604525	−	1.86054i	−0.500026	−	0.866010i	$-0.666676\pi$
$103$	−6.13525	−	18.8824i	−0.604525	−	1.86054i	−0.104499	−	0.994525i	$-0.533324\pi$
$104$	0.309017	+	0.951057i	0.0303016	+	0.0932588i
$105$		0			0
$106$	−0.472136	+	1.45309i	−0.0458579	+	0.141136i
$107$	−10.0902			−0.975454			−0.487727	−	0.872996i	$-0.662174\pi$
$107$	−10.0902			−0.975454			−0.487727	+	0.872996i	$0.662174\pi$
$108$		0			0
$109$	12.1353	−	8.81678i	1.16235	−	0.844494i	0.172274	−	0.985049i	$-0.444889\pi$
$109$	12.1353	−	8.81678i	1.16235	−	0.844494i	0.990073	+	0.140555i	$0.0448886\pi$
$110$	0.427051	−	0.310271i	0.0407177	−	0.0295832i
$111$		0			0
$112$	2.42705	−	1.76336i	0.229335	−	0.166621i
$113$	6.66312	−	4.84104i	0.626814	−	0.455407i	−0.228481	−	0.973548i	$-0.573376\pi$
$113$	6.66312	−	4.84104i	0.626814	−	0.455407i	0.855295	+	0.518142i	$0.173376\pi$
$114$		0			0
$115$	−4.30902	+	13.2618i	−0.401818	+	1.23667i
$116$	−0.427051	+	0.310271i	−0.0396507	+	0.0288079i
$117$		0			0
$118$	−4.47214			−0.411693
$119$	7.28115	−	22.4091i	0.667462	−	2.05424i
$120$		0			0
$121$	−3.38197	−	10.4086i	−0.307451	−	0.946238i
$122$	−0.663119	−	2.04087i	−0.0600360	−	0.184772i
$123$		0			0
$124$	4.23607			0.380410
$125$	9.04508	+	6.57164i	0.809017	+	0.587785i
$126$		0			0
$127$	10.0902	+	7.33094i	0.895358	+	0.650516i	0.937269	−	0.348606i	$-0.113345\pi$
$127$	10.0902	+	7.33094i	0.895358	+	0.650516i	−0.0419116	+	0.999121i	$0.513345\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	−0.690983	−	2.12663i	−0.0606032	−	0.186518i
$131$	−3.21885	+	9.90659i	−0.281232	+	0.865543i	0.706271	+	0.707942i	$0.250376\pi$
$131$	−3.21885	+	9.90659i	−0.281232	+	0.865543i	−0.987503	+	0.157601i	$0.949624\pi$
$132$		0			0
$133$	0.791796	−	2.43690i	0.0686574	−	0.211306i
$134$	4.66312	−	3.38795i	0.402832	−	0.292675i
$135$		0			0
$136$	6.35410	+	4.61653i	0.544860	+	0.395864i
$137$	−4.92705	+	3.57971i	−0.420946	+	0.305835i	−0.778018	−	0.628241i	$-0.783775\pi$
$137$	−4.92705	+	3.57971i	−0.420946	+	0.305835i	0.357072	+	0.934077i	$0.383775\pi$
$138$		0			0
$139$	−8.35410	−	6.06961i	−0.708586	−	0.514818i	0.174131	−	0.984722i	$-0.444288\pi$
$139$	−8.35410	−	6.06961i	−0.708586	−	0.514818i	−0.882717	+	0.469905i	$0.844288\pi$
$140$	−5.42705	+	3.94298i	−0.458670	+	0.333243i
$141$		0			0
$142$	0.927051	−	2.85317i	0.0777964	−	0.239433i
$143$	0.236068			0.0197410
$144$		0			0
$145$	0.954915	−	0.693786i	0.0793014	−	0.0576158i
$146$	−1.76393	−	5.42882i	−0.145984	−	0.449293i
$147$		0			0
$148$	−5.92705	−	4.30625i	−0.487201	−	0.353972i
$149$	2.23607			0.183186			0.0915929	−	0.995797i	$-0.470804\pi$
$149$	2.23607			0.183186			0.0915929	+	0.995797i	$0.470804\pi$
$150$		0			0
$151$	3.70820			0.301769			0.150885	−	0.988551i	$-0.451788\pi$
$151$	3.70820			0.301769			0.150885	+	0.988551i	$0.451788\pi$
$152$	0.690983	+	0.502029i	0.0560461	+	0.0407199i
$153$		0			0
$154$	−0.218847	−	0.673542i	−0.0176352	−	0.0542756i
$155$	−9.47214			−0.760820
$156$		0			0
$157$	−15.5623			−1.24201			−0.621004	−	0.783808i	$-0.713275\pi$
$157$	−15.5623			−1.24201			−0.621004	+	0.783808i	$0.713275\pi$
$158$	−0.854102	+	2.62866i	−0.0679487	+	0.209125i
$159$		0			0
$160$	−0.690983	−	2.12663i	−0.0546270	−	0.168125i
$161$	15.1353	+	10.9964i	1.19283	+	0.866638i
$162$		0			0
$163$	3.92705	−	2.85317i	0.307590	−	0.223477i	−0.423271	−	0.906003i	$-0.639118\pi$
$163$	3.92705	−	2.85317i	0.307590	−	0.223477i	0.730862	+	0.682525i	$0.239118\pi$
$164$	−6.04508	−	4.39201i	−0.472042	−	0.342958i
$165$		0			0
$166$	−10.8992	+	7.91872i	−0.845941	+	0.614612i
$167$	−4.82624	+	14.8536i	−0.373466	+	1.14941i	0.571043	+	0.820920i	$0.306539\pi$
$167$	−4.82624	+	14.8536i	−0.373466	+	1.14941i	−0.944508	+	0.328488i	$0.893461\pi$
$168$		0			0
$169$	−3.70820	+	11.4127i	−0.285246	+	0.877898i
$170$	−14.2082	−	10.3229i	−1.08972	−	0.791728i
$171$		0			0
$172$	−0.545085	−	1.67760i	−0.0415623	−	0.127916i
$173$	2.61803	+	1.90211i	0.199045	+	0.144615i	0.682843	−	0.730565i	$-0.260743\pi$
$173$	2.61803	+	1.90211i	0.199045	+	0.144615i	−0.483798	+	0.875180i	$0.660743\pi$
$174$		0			0
$175$	12.1353	−	8.81678i	0.917339	−	0.666486i
$176$	0.236068			0.0177943
$177$		0			0
$178$	1.38197	+	4.25325i	0.103583	+	0.318795i
$179$	3.45492	+	10.6331i	0.258232	+	0.794758i	0.993176	+	0.116629i	$0.0372089\pi$
$179$	3.45492	+	10.6331i	0.258232	+	0.794758i	−0.734943	+	0.678129i	$0.762791\pi$
$180$		0			0
$181$	−6.61803	+	20.3682i	−0.491915	+	1.51396i	0.329796	+	0.944052i	$0.393020\pi$
$181$	−6.61803	+	20.3682i	−0.491915	+	1.51396i	−0.821710	+	0.569905i	$0.806980\pi$
$182$	−3.00000			−0.222375
$183$		0			0
$184$	−5.04508	+	3.66547i	−0.371929	+	0.270222i
$185$	13.2533	+	9.62908i	0.974401	+	0.707944i
$186$		0			0
$187$	1.50000	−	1.08981i	0.109691	−	0.0796951i
$188$	4.80902	−	3.49396i	0.350734	−	0.254823i
$189$		0			0
$190$	−1.54508	−	1.12257i	−0.112092	−	0.0814398i
$191$	14.2812	−	10.3759i	1.03335	−	0.750771i	0.0643719	−	0.997926i	$-0.479496\pi$
$191$	14.2812	−	10.3759i	1.03335	−	0.750771i	0.968976	+	0.247155i	$0.0794956\pi$
$192$		0			0
$193$	16.6525			1.19867			0.599336	−	0.800498i	$-0.295431\pi$
$193$	16.6525			1.19867			0.599336	+	0.800498i	$0.295431\pi$
$194$	−3.26393	+	10.0453i	−0.234337	+	0.721214i
$195$		0			0
$196$	0.618034	+	1.90211i	0.0441453	+	0.135865i
$197$	−3.70820	−	11.4127i	−0.264199	−	0.813120i	−0.991877	−	0.127201i	$-0.959401\pi$
$197$	−3.70820	−	11.4127i	−0.264199	−	0.813120i	0.727678	−	0.685919i	$-0.240599\pi$
$198$		0			0
$199$	−17.5623			−1.24496			−0.622479	−	0.782636i	$-0.713875\pi$
$199$	−17.5623			−1.24496			−0.622479	+	0.782636i	$0.713875\pi$
$200$	1.54508	+	4.75528i	0.109254	+	0.336249i
$201$		0			0
$202$	−1.30902	−	0.951057i	−0.0921021	−	0.0669161i
$203$	−0.489357	−	1.50609i	−0.0343461	−	0.105706i
$204$		0			0
$205$	13.5172	+	9.82084i	0.944084	+	0.685917i
$206$	−6.13525	+	18.8824i	−0.427463	+	1.31560i
$207$		0			0
$208$	0.309017	−	0.951057i	0.0214265	−	0.0659439i
$209$	0.163119	−	0.118513i	0.0112832	−	0.00819771i
$210$		0			0
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	0.227895	−	0.973686i	$-0.426816\pi$
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	−0.855607	+	0.517627i	$0.826816\pi$
$212$	1.23607	−	0.898056i	0.0848935	−	0.0616787i
$213$		0			0
$214$	8.16312	+	5.93085i	0.558019	+	0.405425i
$215$	1.21885	+	3.75123i	0.0831247	+	0.255831i
$216$		0			0
$217$	−3.92705	+	12.0862i	−0.266586	+	0.820466i
$218$	−15.0000			−1.01593
$219$		0			0
$220$	−0.527864			−0.0355886
$221$	−2.42705	−	7.46969i	−0.163261	−	0.502466i
$222$		0			0
$223$	7.28115	+	5.29007i	0.487582	+	0.354249i	0.804254	−	0.594286i	$-0.202565\pi$
$223$	7.28115	+	5.29007i	0.487582	+	0.354249i	−0.316672	+	0.948535i	$0.602565\pi$
$224$	−3.00000			−0.200446
$225$		0			0
$226$	−8.23607			−0.547855
$227$	−12.4271	−	9.02878i	−0.824812	−	0.599261i	0.0932746	−	0.995640i	$-0.470267\pi$
$227$	−12.4271	−	9.02878i	−0.824812	−	0.599261i	−0.918087	+	0.396379i	$0.870267\pi$
$228$		0			0
$229$	5.42705	+	16.7027i	0.358630	+	1.10375i	0.953875	+	0.300204i	$0.0970549\pi$
$229$	5.42705	+	16.7027i	0.358630	+	1.10375i	−0.595245	+	0.803544i	$0.702945\pi$
$230$	11.2812	−	8.19624i	0.743857	−	0.540444i
$231$		0			0
$232$	0.527864			0.0346560
$233$	−8.56231	+	26.3521i	−0.560935	+	1.72638i	0.118795	+	0.992919i	$0.462097\pi$
$233$	−8.56231	+	26.3521i	−0.560935	+	1.72638i	−0.679730	+	0.733463i	$0.737903\pi$
$234$		0			0
$235$	−10.7533	+	7.81272i	−0.701467	+	0.509646i
$236$	3.61803	+	2.62866i	0.235514	+	0.171111i
$237$		0			0
$238$	−19.0623	+	13.8496i	−1.23563	+	0.897735i
$239$	−14.6353	−	10.6331i	−0.946676	−	0.687800i	0.00334240	−	0.999994i	$-0.498936\pi$
$239$	−14.6353	−	10.6331i	−0.946676	−	0.687800i	−0.950018	+	0.312194i	$0.898936\pi$
$240$		0			0
$241$	−10.8262	+	7.86572i	−0.697379	+	0.506676i	−0.879078	−	0.476679i	$-0.841841\pi$
$241$	−10.8262	+	7.86572i	−0.697379	+	0.506676i	0.181698	+	0.983354i	$0.441841\pi$
$242$	−3.38197	+	10.4086i	−0.217401	+	0.669092i
$243$		0			0
$244$	−0.663119	+	2.04087i	−0.0424518	+	0.130653i
$245$	−1.38197	−	4.25325i	−0.0882906	−	0.271730i
$246$		0			0
$247$	−0.263932	−	0.812299i	−0.0167936	−	0.0516854i
$248$	−3.42705	−	2.48990i	−0.217618	−	0.158109i
$249$		0			0
$250$	−3.45492	−	10.6331i	−0.218508	−	0.672499i
$251$	−23.1803			−1.46313			−0.731565	−	0.681772i	$-0.761210\pi$
$251$	−23.1803			−1.46313			−0.731565	+	0.681772i	$0.761210\pi$
$252$		0			0
$253$	0.454915	+	1.40008i	0.0286003	+	0.0880226i
$254$	−3.85410	−	11.8617i	−0.241828	−	0.744270i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	16.7426			1.04438			0.522189	−	0.852830i	$-0.325116\pi$
$257$	16.7426			1.04438			0.522189	+	0.852830i	$0.325116\pi$
$258$		0			0
$259$	17.7812	−	12.9188i	1.10487	−	0.802733i
$260$	−0.690983	+	2.12663i	−0.0428529	+	0.131888i
$261$		0			0
$262$	8.42705	−	6.12261i	0.520625	−	0.378256i
$263$	1.92705	−	1.40008i	0.118827	−	0.0863329i	−0.526785	−	0.849999i	$-0.676603\pi$
$263$	1.92705	−	1.40008i	0.118827	−	0.0863329i	0.645612	+	0.763666i	$0.276603\pi$
$264$		0			0
$265$	−2.76393	+	2.00811i	−0.169787	+	0.123357i
$266$	−2.07295	+	1.50609i	−0.127101	+	0.0923440i
$267$		0			0
$268$	−5.76393			−0.352088
$269$	−4.04508	+	12.4495i	−0.246633	+	0.759059i	0.748730	+	0.662875i	$0.230664\pi$
$269$	−4.04508	+	12.4495i	−0.246633	+	0.759059i	−0.995364	+	0.0961842i	$0.969336\pi$
$270$		0			0
$271$	−2.93769	−	9.04129i	−0.178452	−	0.549219i	0.821322	−	0.570465i	$-0.193237\pi$
$271$	−2.93769	−	9.04129i	−0.178452	−	0.549219i	−0.999774	+	0.0212453i	$0.993237\pi$
$272$	−2.42705	−	7.46969i	−0.147162	−	0.452917i
$273$		0			0
$274$	6.09017			0.367921
$275$	1.18034			0.0711772
$276$		0			0
$277$	−11.0902	−	8.05748i	−0.666344	−	0.484127i	0.202456	−	0.979291i	$-0.435108\pi$
$277$	−11.0902	−	8.05748i	−0.666344	−	0.484127i	−0.868799	+	0.495164i	$0.835108\pi$
$278$	3.19098	+	9.82084i	0.191382	+	0.589015i
$279$		0			0
$280$	6.70820			0.400892
$281$	5.92705	−	18.2416i	0.353578	−	1.08820i	−0.603251	−	0.797551i	$-0.706128\pi$
$281$	5.92705	−	18.2416i	0.353578	−	1.08820i	0.956829	−	0.290651i	$-0.0938717\pi$
$282$		0			0
$283$	−7.94427	+	24.4500i	−0.472238	+	1.45340i	0.377409	+	0.926047i	$0.376815\pi$
$283$	−7.94427	+	24.4500i	−0.472238	+	1.45340i	−0.849647	+	0.527352i	$0.823185\pi$
$284$	−2.42705	+	1.76336i	−0.144019	+	0.104636i
$285$		0			0
$286$	−0.190983	−	0.138757i	−0.0112931	−	0.00820489i
$287$	18.1353	−	13.1760i	1.07049	−	0.777757i
$288$		0			0
$289$	−36.1525	−	26.2663i	−2.12662	−	1.54508i
$290$	−1.18034			−0.0693119
$291$		0			0
$292$	−1.76393	+	5.42882i	−0.103226	+	0.317698i
$293$	11.5623			0.675477			0.337739	−	0.941240i	$-0.390338\pi$
$293$	11.5623			0.675477			0.337739	+	0.941240i	$0.390338\pi$
$294$		0			0
$295$	−8.09017	−	5.87785i	−0.471028	−	0.342222i
$296$	2.26393	+	6.96767i	0.131588	+	0.404987i
$297$		0			0
$298$	−1.80902	−	1.31433i	−0.104794	−	0.0761370i
$299$	6.23607			0.360641
$300$		0			0
$301$	5.29180			0.305014
$302$	−3.00000	−	2.17963i	−0.172631	−	0.125423i
$303$		0			0
$304$	−0.263932	−	0.812299i	−0.0151375	−	0.0465886i
$305$	1.48278	−	4.56352i	0.0849037	−	0.261307i
$306$		0			0
$307$	17.1246			0.977353			0.488677	−	0.872465i	$-0.337480\pi$
$307$	17.1246			0.977353			0.488677	+	0.872465i	$0.337480\pi$
$308$	−0.218847	+	0.673542i	−0.0124700	+	0.0383786i
$309$		0			0
$310$	7.66312	+	5.56758i	0.435236	+	0.316217i
$311$	−17.0623	−	12.3965i	−0.967515	−	0.702941i	−0.0126308	−	0.999920i	$-0.504021\pi$
$311$	−17.0623	−	12.3965i	−0.967515	−	0.702941i	−0.954884	+	0.296980i	$0.904021\pi$
$312$		0			0
$313$	−2.88197	+	2.09387i	−0.162898	+	0.118353i	−0.666248	−	0.745730i	$-0.732101\pi$
$313$	−2.88197	+	2.09387i	−0.162898	+	0.118353i	0.503350	+	0.864083i	$0.332101\pi$
$314$	12.5902	+	9.14729i	0.710504	+	0.516212i
$315$		0			0
$316$	2.23607	−	1.62460i	0.125789	−	0.0913908i
$317$	−3.28115	+	10.0984i	−0.184288	+	0.567180i	−0.999935	−	0.0113694i	$-0.996381\pi$
$317$	−3.28115	+	10.0984i	−0.184288	+	0.567180i	0.815647	+	0.578549i	$0.196381\pi$
$318$		0			0
$319$	0.0385072	−	0.118513i	0.00215599	−	0.00663545i
$320$	−0.690983	+	2.12663i	−0.0386271	+	0.118882i
$321$		0			0
$322$	−5.78115	−	17.7926i	−0.322171	−	0.991541i
$323$	−5.42705	−	3.94298i	−0.301969	−	0.219393i
$324$		0			0
$325$	1.54508	−	4.75528i	0.0857059	−	0.263776i
$326$	−4.85410			−0.268844
$327$		0			0
$328$	2.30902	+	7.10642i	0.127494	+	0.392387i
$329$	5.51064	+	16.9600i	0.303812	+	0.935036i
$330$		0			0
$331$	1.40983	−	4.33901i	0.0774913	−	0.238494i	−0.904805	−	0.425825i	$-0.859984\pi$
$331$	1.40983	−	4.33901i	0.0774913	−	0.238494i	0.982297	+	0.187332i	$0.0599839\pi$
$332$	13.4721			0.739380
$333$		0			0
$334$	12.6353	−	9.18005i	0.691370	−	0.502310i
$335$	12.8885			0.704176
$336$		0			0
$337$	25.4164	−	18.4661i	1.38452	−	1.00591i	0.388078	−	0.921626i	$-0.373139\pi$
$337$	25.4164	−	18.4661i	1.38452	−	1.00591i	0.996442	−	0.0842863i	$-0.0268610\pi$
$338$	9.70820	−	7.05342i	0.528057	−	0.383656i
$339$		0			0
$340$	5.42705	+	16.7027i	0.294323	+	0.905834i
$341$	−0.809017	+	0.587785i	−0.0438107	+	0.0318304i
$342$		0			0
$343$	15.0000			0.809924
$344$	−0.545085	+	1.67760i	−0.0293890	+	0.0904501i
$345$		0			0
$346$	−1.00000	−	3.07768i	−0.0537603	−	0.165457i
$347$	3.06231	+	9.42481i	0.164393	+	0.505950i	0.998991	−	0.0449095i	$-0.0142999\pi$
$347$	3.06231	+	9.42481i	0.164393	+	0.505950i	−0.834598	+	0.550860i	$0.814300\pi$
$348$		0			0
$349$	−22.2361			−1.19027			−0.595135	−	0.803626i	$-0.702901\pi$
$349$	−22.2361			−1.19027			−0.595135	+	0.803626i	$0.702901\pi$
$350$	−15.0000			−0.801784
$351$		0			0
$352$	−0.190983	−	0.138757i	−0.0101794	−	0.00739579i
$353$	5.18034	+	15.9434i	0.275722	+	0.848584i	0.989028	+	0.147731i	$0.0471970\pi$
$353$	5.18034	+	15.9434i	0.275722	+	0.848584i	−0.713306	+	0.700853i	$0.752803\pi$
$354$		0			0
$355$	5.42705	−	3.94298i	0.288038	−	0.209272i
$356$	1.38197	−	4.25325i	0.0732441	−	0.225422i
$357$		0			0
$358$	3.45492	−	10.6331i	0.182598	−	0.561979i
$359$	2.50000	−	1.81636i	0.131945	−	0.0958636i	−0.519855	−	0.854254i	$-0.674014\pi$
$359$	2.50000	−	1.81636i	0.131945	−	0.0958636i	0.651800	+	0.758391i	$0.274014\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	17.3262	−	12.5882i	0.910647	−	0.661624i
$363$		0			0
$364$	2.42705	+	1.76336i	0.127212	+	0.0924250i
$365$	3.94427	−	12.1392i	0.206453	−	0.635396i
$366$		0			0
$367$	−9.74671	+	29.9973i	−0.508774	+	1.56585i	0.285557	+	0.958362i	$0.407821\pi$
$367$	−9.74671	+	29.9973i	−0.508774	+	1.56585i	−0.794332	+	0.607484i	$0.792179\pi$
$368$	6.23607			0.325078
$369$		0			0
$370$	−5.06231	−	15.5802i	−0.263177	−	0.809975i
$371$	1.41641	+	4.35926i	0.0735362	+	0.226321i
$372$		0			0
$373$	13.1353	+	9.54332i	0.680118	+	0.494134i	0.873397	−	0.487009i	$-0.161912\pi$
$373$	13.1353	+	9.54332i	0.680118	+	0.494134i	−0.193279	+	0.981144i	$0.561912\pi$
$374$	−1.85410			−0.0958733
$375$		0			0
$376$	−5.94427			−0.306552
$377$	−0.427051	−	0.310271i	−0.0219942	−	0.0159798i
$378$		0			0
$379$	0.163119	+	0.502029i	0.00837886	+	0.0257875i	0.955159	−	0.296095i	$-0.0956845\pi$
$379$	0.163119	+	0.502029i	0.00837886	+	0.0257875i	−0.946780	+	0.321882i	$0.895684\pi$
$380$	0.590170	+	1.81636i	0.0302751	+	0.0931771i
$381$		0			0
$382$	−17.6525			−0.903179
$383$	1.33688	−	4.11450i	0.0683114	−	0.210241i	−0.911073	−	0.412244i	$-0.864745\pi$
$383$	1.33688	−	4.11450i	0.0683114	−	0.210241i	0.979385	+	0.202003i	$0.0647451\pi$
$384$		0			0
$385$	0.489357	−	1.50609i	0.0249399	−	0.0767572i
$386$	−13.4721	−	9.78808i	−0.685714	−	0.498200i
$387$		0			0
$388$	8.54508	−	6.20837i	0.433811	−	0.315182i
$389$	−26.8713	−	19.5232i	−1.36243	−	0.989863i	−0.998286	−	0.0585208i	$-0.981362\pi$
$389$	−26.8713	−	19.5232i	−1.36243	−	0.989863i	−0.364144	−	0.931343i	$-0.618638\pi$
$390$		0			0
$391$	39.6246	−	28.7890i	2.00390	−	1.45592i
$392$	0.618034	−	1.90211i	0.0312154	−	0.0960712i
$393$		0			0
$394$	−3.70820	+	11.4127i	−0.186817	+	0.574962i
$395$	−5.00000	+	3.63271i	−0.251577	+	0.182782i
$396$		0			0
$397$	−1.78115	−	5.48183i	−0.0893935	−	0.275125i	0.896359	−	0.443330i	$-0.146203\pi$
$397$	−1.78115	−	5.48183i	−0.0893935	−	0.275125i	−0.985752	+	0.168205i	$0.946203\pi$
$398$	14.2082	+	10.3229i	0.712193	+	0.517438i
$399$		0			0
$400$	1.54508	−	4.75528i	0.0772542	−	0.237764i
$401$	−8.18034			−0.408507			−0.204253	−	0.978918i	$-0.565477\pi$
$401$	−8.18034			−0.408507			−0.204253	+	0.978918i	$0.565477\pi$
$402$		0			0
$403$	1.30902	+	4.02874i	0.0652068	+	0.200686i
$404$	0.500000	+	1.53884i	0.0248759	+	0.0765602i
$405$		0			0
$406$	−0.489357	+	1.50609i	−0.0242864	+	0.0747458i
$407$	1.72949			0.0857276
$408$		0			0
$409$	−5.42705	+	3.94298i	−0.268350	+	0.194968i	−0.713820	−	0.700329i	$-0.753037\pi$
$409$	−5.42705	+	3.94298i	−0.268350	+	0.194968i	0.445470	+	0.895297i	$0.353037\pi$
$410$	−5.16312	−	15.8904i	−0.254988	−	0.784773i
$411$		0			0
$412$	16.0623	−	11.6699i	0.791333	−	0.574937i
$413$	−10.8541	+	7.88597i	−0.534095	+	0.388043i
$414$		0			0
$415$	−30.1246			−1.47876
$416$	−0.809017	+	0.587785i	−0.0396653	+	0.0288185i
$417$		0			0
$418$	−0.201626			−0.00986186
$419$	−8.41641	+	25.9030i	−0.411168	+	1.26545i	0.504465	+	0.863432i	$0.331690\pi$
$419$	−8.41641	+	25.9030i	−0.411168	+	1.26545i	−0.915633	+	0.402014i	$0.868310\pi$
$420$		0			0
$421$	−3.79180	−	11.6699i	−0.184801	−	0.568758i	0.815144	−	0.579258i	$-0.196658\pi$
$421$	−3.79180	−	11.6699i	−0.184801	−	0.568758i	−0.999945	+	0.0104998i	$0.996658\pi$
$422$	3.48278	+	10.7189i	0.169539	+	0.521787i
$423$		0			0
$424$	−1.52786			−0.0741996
$425$	−12.1353	−	37.3485i	−0.588646	−	1.81167i
$426$		0			0
$427$	−5.20820	−	3.78398i	−0.252043	−	0.183120i
$428$	−3.11803	−	9.59632i	−0.150716	−	0.463856i
$429$		0			0
$430$	1.21885	−	3.75123i	0.0587780	−	0.180900i
$431$	9.90983	−	30.4993i	0.477340	−	1.46910i	−0.365436	−	0.930836i	$-0.619080\pi$
$431$	9.90983	−	30.4993i	0.477340	−	1.46910i	0.842776	−	0.538264i	$-0.180920\pi$
$432$		0			0
$433$	7.21885	−	22.2173i	0.346916	−	1.06770i	−0.613635	−	0.789590i	$-0.710293\pi$
$433$	7.21885	−	22.2173i	0.346916	−	1.06770i	0.960550	−	0.278106i	$-0.0897068\pi$
$434$	10.2812	−	7.46969i	0.493511	−	0.358557i
$435$		0			0
$436$	12.1353	+	8.81678i	0.581173	+	0.422247i
$437$	4.30902	−	3.13068i	0.206128	−	0.149761i
$438$		0			0
$439$	4.57295	+	3.32244i	0.218255	+	0.158572i	0.691541	−	0.722337i	$-0.256932\pi$
$439$	4.57295	+	3.32244i	0.218255	+	0.158572i	−0.473286	+	0.880909i	$0.656932\pi$
$440$	0.427051	+	0.310271i	0.0203589	+	0.0147916i
$441$		0			0
$442$	−2.42705	+	7.46969i	−0.115443	+	0.355297i
$443$	7.41641			0.352364			0.176182	−	0.984358i	$-0.443625\pi$
$443$	7.41641			0.352364			0.176182	+	0.984358i	$0.443625\pi$
$444$		0			0
$445$	−3.09017	+	9.51057i	−0.146488	+	0.450844i
$446$	−2.78115	−	8.55951i	−0.131691	−	0.405304i
$447$		0			0
$448$	2.42705	+	1.76336i	0.114667	+	0.0833107i
$449$	−13.9443			−0.658071			−0.329035	−	0.944318i	$-0.606724\pi$
$449$	−13.9443			−0.658071			−0.329035	+	0.944318i	$0.606724\pi$
$450$		0			0
$451$	1.76393			0.0830603
$452$	6.66312	+	4.84104i	0.313407	+	0.227703i
$453$		0			0
$454$	4.74671	+	14.6089i	0.222774	+	0.685628i
$455$	−5.42705	−	3.94298i	−0.254424	−	0.184850i
$456$		0			0
$457$	−11.2148			−0.524605			−0.262303	−	0.964986i	$-0.584482\pi$
$457$	−11.2148			−0.524605			−0.262303	+	0.964986i	$0.584482\pi$
$458$	5.42705	−	16.7027i	0.253589	−	0.780468i
$459$		0			0
$460$	−13.9443			−0.650155
$461$	22.7984	+	16.5640i	1.06183	+	0.771462i	0.974425	−	0.224711i	$-0.0721439\pi$
$461$	22.7984	+	16.5640i	1.06183	+	0.771462i	0.0874008	+	0.996173i	$0.472144\pi$
$462$		0			0
$463$	−9.69098	+	7.04091i	−0.450378	+	0.327219i	−0.789745	−	0.613435i	$-0.789787\pi$
$463$	−9.69098	+	7.04091i	−0.450378	+	0.327219i	0.339367	+	0.940654i	$0.389787\pi$
$464$	−0.427051	−	0.310271i	−0.0198253	−	0.0144040i
$465$		0			0
$466$	22.4164	−	16.2865i	1.03842	−	0.754456i
$467$	−0.982779	+	3.02468i	−0.0454776	+	0.139966i	−0.971217	−	0.238196i	$-0.923444\pi$
$467$	−0.982779	+	3.02468i	−0.0454776	+	0.139966i	0.925739	+	0.378162i	$0.123444\pi$
$468$		0			0
$469$	5.34346	−	16.4455i	0.246738	−	0.759381i
$470$	13.2918			0.613105
$471$		0			0
$472$	−1.38197	−	4.25325i	−0.0636101	−	0.195772i
$473$	0.336881	+	0.244758i	0.0154898	+	0.0112540i
$474$		0			0
$475$	−1.31966	−	4.06150i	−0.0605502	−	0.186354i
$476$	23.5623			1.07998
$477$		0			0
$478$	5.59017	+	17.2048i	0.255688	+	0.786928i
$479$	12.2984	+	37.8505i	0.561927	+	1.72943i	0.676910	+	0.736066i	$0.263319\pi$
$479$	12.2984	+	37.8505i	0.561927	+	1.72943i	−0.114983	+	0.993368i	$0.536681\pi$
$480$		0			0
$481$	2.26393	−	6.96767i	0.103226	−	0.317698i
$482$	13.3820			0.609532
$483$		0			0
$484$	8.85410	−	6.43288i	0.402459	−	0.292404i
$485$	−19.1074	+	13.8823i	−0.867622	+	0.630364i
$486$		0			0
$487$	14.6631	−	10.6534i	0.664449	−	0.482751i	−0.203713	−	0.979031i	$-0.565301\pi$
$487$	14.6631	−	10.6534i	0.664449	−	0.482751i	0.868163	+	0.496280i	$0.165301\pi$
$488$	1.73607	−	1.26133i	0.0785881	−	0.0570976i
$489$		0			0
$490$	−1.38197	+	4.25325i	−0.0624309	+	0.192142i
$491$	11.9443	−	8.67802i	0.539037	−	0.391634i	−0.284690	−	0.958620i	$-0.591891\pi$
$491$	11.9443	−	8.67802i	0.539037	−	0.391634i	0.823727	+	0.566986i	$0.191891\pi$
$492$		0			0
$493$	−4.14590			−0.186722
$494$	−0.263932	+	0.812299i	−0.0118749	+	0.0365471i
$495$		0			0
$496$	1.30902	+	4.02874i	0.0587766	+	0.180896i
$497$	−2.78115	−	8.55951i	−0.124752	−	0.383946i
$498$		0			0
$499$	40.8541			1.82888			0.914440	−	0.404721i	$-0.132631\pi$
$499$	40.8541			1.82888			0.914440	+	0.404721i	$0.132631\pi$
$500$	−3.45492	+	10.6331i	−0.154508	+	0.475528i
$501$		0			0
$502$	18.7533	+	13.6251i	0.837000	+	0.608116i
$503$	−2.31966	−	7.13918i	−0.103429	−	0.318320i	0.885930	−	0.463819i	$-0.153521\pi$
$503$	−2.31966	−	7.13918i	−0.103429	−	0.318320i	−0.989358	+	0.145499i	$0.953521\pi$
$504$		0			0
$505$	−1.11803	−	3.44095i	−0.0497519	−	0.153120i
$506$	0.454915	−	1.40008i	0.0202234	−	0.0622413i
$507$		0			0
$508$	−3.85410	+	11.8617i	−0.170998	+	0.526278i
$509$	−10.5902	+	7.69421i	−0.469401	+	0.341040i	−0.797208	−	0.603705i	$-0.793690\pi$
$509$	−10.5902	+	7.69421i	−0.469401	+	0.341040i	0.327807	+	0.944745i	$0.393690\pi$
$510$		0			0
$511$	−13.8541	−	10.0656i	−0.612869	−	0.445276i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	−13.5451	−	9.84108i	−0.597448	−	0.434071i
$515$	−35.9164	+	26.0948i	−1.58267	+	1.14987i
$516$		0			0
$517$	−0.433629	+	1.33457i	−0.0190710	+	0.0586944i
$518$	−21.9787			−0.965689
$519$		0			0
$520$	1.80902	−	1.31433i	0.0793306	−	0.0576371i
$521$	−10.0279	−	30.8626i	−0.439329	−	1.35211i	−0.888585	−	0.458712i	$-0.848311\pi$
$521$	−10.0279	−	30.8626i	−0.439329	−	1.35211i	0.449256	−	0.893403i	$-0.351689\pi$
$522$		0			0
$523$	−21.5623	−	15.6659i	−0.942854	−	0.685023i	0.00625211	−	0.999980i	$-0.498010\pi$
$523$	−21.5623	−	15.6659i	−0.942854	−	0.685023i	−0.949106	+	0.314957i	$0.898010\pi$
$524$	−10.4164			−0.455043
$525$		0			0
$526$	−2.38197			−0.103859
$527$	26.9164	+	19.5559i	1.17250	+	0.851869i
$528$		0			0
$529$	4.90983	+	15.1109i	0.213471	+	0.656996i
$530$	3.41641			0.148399
$531$		0			0
$532$	2.56231			0.111090
$533$	2.30902	−	7.10642i	0.100015	−	0.307813i
$534$		0			0
$535$	6.97214	+	21.4580i	0.301432	+	0.927711i
$536$	4.66312	+	3.38795i	0.201416	+	0.146337i
$537$		0			0
$538$	10.5902	−	7.69421i	0.456575	−	0.331721i
$539$	−0.381966	−	0.277515i	−0.0164524	−	0.0119534i
$540$		0			0
$541$	−23.2254	+	16.8743i	−0.998539	+	0.725481i	−0.961774	−	0.273843i	$-0.911705\pi$
$541$	−23.2254	+	16.8743i	−0.998539	+	0.725481i	−0.0367646	+	0.999324i	$0.511705\pi$
$542$	−2.93769	+	9.04129i	−0.126185	+	0.388357i
$543$		0			0
$544$	−2.42705	+	7.46969i	−0.104059	+	0.320261i
$545$	−27.1353	−	19.7149i	−1.16235	−	0.844494i
$546$		0			0
$547$	3.28115	+	10.0984i	0.140292	+	0.431774i	0.996376	−	0.0850631i	$-0.0271092\pi$
$547$	3.28115	+	10.0984i	0.140292	+	0.431774i	−0.856084	+	0.516837i	$0.827109\pi$
$548$	−4.92705	−	3.57971i	−0.210473	−	0.152918i
$549$		0			0
$550$	−0.954915	−	0.693786i	−0.0407177	−	0.0295832i
$551$	−0.450850			−0.0192068
$552$		0			0
$553$	2.56231	+	7.88597i	0.108960	+	0.335345i
$554$	4.23607	+	13.0373i	0.179973	+	0.553901i
$555$		0			0
$556$	3.19098	−	9.82084i	0.135328	−	0.416496i
$557$	10.8885			0.461362			0.230681	−	0.973029i	$-0.425905\pi$
$557$	10.8885			0.461362			0.230681	+	0.973029i	$0.425905\pi$
$558$		0			0
$559$	1.42705	−	1.03681i	0.0603578	−	0.0438525i
$560$	−5.42705	−	3.94298i	−0.229335	−	0.166621i
$561$		0			0
$562$	−15.5172	+	11.2739i	−0.654554	+	0.475562i
$563$	−28.1976	+	20.4867i	−1.18839	+	0.863413i	−0.993093	−	0.117332i	$-0.962566\pi$
$563$	−28.1976	+	20.4867i	−1.18839	+	0.863413i	−0.195293	+	0.980745i	$0.562566\pi$
$564$		0			0
$565$	−14.8992	−	10.8249i	−0.626814	−	0.455407i
$566$	20.7984	−	15.1109i	0.874221	−	0.635159i
$567$		0			0
$568$	3.00000			0.125877
$569$	−6.87132	+	21.1478i	−0.288061	+	0.886560i	0.697404	+	0.716679i	$0.254339\pi$
$569$	−6.87132	+	21.1478i	−0.288061	+	0.886560i	−0.985464	+	0.169882i	$0.945661\pi$
$570$		0			0
$571$	0.517221	+	1.59184i	0.0216450	+	0.0666165i	0.961296	−	0.275519i	$-0.0888497\pi$
$571$	0.517221	+	1.59184i	0.0216450	+	0.0666165i	−0.939651	+	0.342136i	$0.888850\pi$
$572$	0.0729490	+	0.224514i	0.00305015	+	0.00938740i
$573$		0			0
$574$	−22.4164			−0.935643
$575$	31.1803			1.30031
$576$		0			0
$577$	34.7877	+	25.2748i	1.44823	+	1.05220i	0.986240	+	0.165318i	$0.0528651\pi$
$577$	34.7877	+	25.2748i	1.44823	+	1.05220i	0.461992	+	0.886884i	$0.347135\pi$
$578$	13.8090	+	42.4998i	0.574379	+	1.76776i
$579$		0			0
$580$	0.954915	+	0.693786i	0.0396507	+	0.0288079i
$581$	−12.4894	+	38.4383i	−0.518146	+	1.59469i
$582$		0			0
$583$	−0.111456	+	0.343027i	−0.00461604	+	0.0142067i
$584$	4.61803	−	3.35520i	0.191096	−	0.138839i
$585$		0			0
$586$	−9.35410	−	6.79615i	−0.386414	−	0.280746i
$587$	−9.56231	+	6.94742i	−0.394679	+	0.286751i	−0.767370	−	0.641205i	$-0.778435\pi$
$587$	−9.56231	+	6.94742i	−0.394679	+	0.286751i	0.372691	+	0.927955i	$0.378435\pi$
$588$		0			0
$589$	2.92705	+	2.12663i	0.120607	+	0.0876261i
$590$	3.09017	+	9.51057i	0.127220	+	0.391544i
$591$		0			0
$592$	2.26393	−	6.96767i	0.0930470	−	0.286369i
$593$	47.0132			1.93060			0.965299	−	0.261145i	$-0.0841002\pi$
$593$	47.0132			1.93060			0.965299	+	0.261145i	$0.0841002\pi$
$594$		0			0
$595$	−52.6869			−2.15995
$596$	0.690983	+	2.12663i	0.0283038	+	0.0871100i
$597$		0			0
$598$	−5.04508	−	3.66547i	−0.206309	−	0.149892i
$599$	8.94427			0.365453			0.182727	−	0.983164i	$-0.441508\pi$
$599$	8.94427			0.365453			0.182727	+	0.983164i	$0.441508\pi$
$600$		0			0
$601$	−14.8328			−0.605043			−0.302522	−	0.953143i	$-0.597828\pi$
$601$	−14.8328			−0.605043			−0.302522	+	0.953143i	$0.597828\pi$
$602$	−4.28115	−	3.11044i	−0.174487	−	0.126772i
$603$		0			0
$604$	1.14590	+	3.52671i	0.0466259	+	0.143500i
$605$	−19.7984	+	14.3844i	−0.804918	+	0.584807i
$606$		0			0
$607$	−27.1459			−1.10182			−0.550909	−	0.834565i	$-0.685719\pi$
$607$	−27.1459			−1.10182			−0.550909	+	0.834565i	$0.685719\pi$
$608$	−0.263932	+	0.812299i	−0.0107039	+	0.0329431i
$609$		0			0
$610$	−3.88197	+	2.82041i	−0.157176	+	0.114195i
$611$	4.80902	+	3.49396i	0.194552	+	0.141350i
$612$		0			0
$613$	33.6246	−	24.4297i	1.35809	−	0.986707i	0.359521	−	0.933137i	$-0.382940\pi$
$613$	33.6246	−	24.4297i	1.35809	−	0.986707i	0.998564	−	0.0535698i	$-0.0170600\pi$
$614$	−13.8541	−	10.0656i	−0.559106	−	0.406214i
$615$		0			0
$616$	0.572949	−	0.416272i	0.0230848	−	0.0167721i
$617$	9.38197	−	28.8747i	0.377704	−	1.16245i	−0.563933	−	0.825821i	$-0.690712\pi$
$617$	9.38197	−	28.8747i	0.377704	−	1.16245i	0.941636	−	0.336632i	$-0.109288\pi$
$618$		0			0
$619$	−14.5106	+	44.6592i	−0.583232	+	1.79500i	0.0230252	+	0.999735i	$0.492670\pi$
$619$	−14.5106	+	44.6592i	−0.583232	+	1.79500i	−0.606257	+	0.795269i	$0.707330\pi$
$620$	−2.92705	−	9.00854i	−0.117553	−	0.361792i
$621$		0			0
$622$	6.51722	+	20.0579i	0.261317	+	0.804250i
$623$	10.8541	+	7.88597i	0.434860	+	0.315945i
$624$		0			0
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	3.56231			0.142378
$627$		0			0
$628$	−4.80902	−	14.8006i	−0.191901	−	0.590610i
$629$	−17.7812	−	54.7248i	−0.708981	−	2.18202i
$630$		0			0
$631$	2.72949	−	8.40051i	0.108659	−	0.334419i	−0.881913	−	0.471413i	$-0.843744\pi$
$631$	2.72949	−	8.40051i	0.108659	−	0.334419i	0.990572	+	0.136994i	$0.0437441\pi$
$632$	−2.76393			−0.109943
$633$		0			0
$634$	8.59017	−	6.24112i	0.341159	−	0.247867i
$635$	8.61803	−	26.5236i	0.341996	−	1.05256i
$636$		0			0
$637$	−1.61803	+	1.17557i	−0.0641088	+	0.0465778i
$638$	−0.100813	+	0.0732450i	−0.00399123	+	0.00289980i
$639$		0			0
$640$	1.80902	−	1.31433i	0.0715077	−	0.0519534i
$641$	11.6180	−	8.44100i	0.458885	−	0.333399i	−0.334209	−	0.942499i	$-0.608469\pi$
$641$	11.6180	−	8.44100i	0.458885	−	0.333399i	0.793094	+	0.609100i	$0.208469\pi$
$642$		0			0
$643$	−36.2361			−1.42901			−0.714506	−	0.699630i	$-0.753348\pi$
$643$	−36.2361			−1.42901			−0.714506	+	0.699630i	$0.753348\pi$
$644$	−5.78115	+	17.7926i	−0.227809	+	0.701125i
$645$		0			0
$646$	2.07295	+	6.37988i	0.0815591	+	0.251013i
$647$	−2.36475	−	7.27794i	−0.0929677	−	0.286125i	0.893751	−	0.448563i	$-0.148064\pi$
$647$	−2.36475	−	7.27794i	−0.0929677	−	0.286125i	−0.986719	+	0.162438i	$0.948064\pi$
$648$		0			0
$649$	−1.05573			−0.0414410
$650$	−4.04508	+	2.93893i	−0.158661	+	0.115274i
$651$		0			0
$652$	3.92705	+	2.85317i	0.153795	+	0.111739i
$653$	−12.5451	−	38.6098i	−0.490927	−	1.51092i	−0.823209	−	0.567738i	$-0.807819\pi$
$653$	−12.5451	−	38.6098i	−0.490927	−	1.51092i	0.332282	−	0.943180i	$-0.392181\pi$
$654$		0			0
$655$	23.2918			0.910086
$656$	2.30902	−	7.10642i	0.0901520	−	0.277459i
$657$		0			0
$658$	5.51064	−	16.9600i	0.214827	−	0.661170i
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	−0.495144	−	0.868811i	$-0.664885\pi$
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	0.673281	+	0.739387i	$0.264885\pi$
$660$		0			0
$661$	−5.07295	−	3.68571i	−0.197315	−	0.143358i	0.484741	−	0.874658i	$-0.338914\pi$
$661$	−5.07295	−	3.68571i	−0.197315	−	0.143358i	−0.682056	+	0.731300i	$0.738914\pi$
$662$	−3.69098	+	2.68166i	−0.143454	+	0.104226i
$663$		0			0
$664$	−10.8992	−	7.91872i	−0.422970	−	0.307306i
$665$	−5.72949			−0.222180
$666$		0			0
$667$	1.01722	−	3.13068i	0.0393870	−	0.121221i
$668$	−15.6180			−0.604280
$669$		0			0
$670$	−10.4271	−	7.57570i	−0.402832	−	0.292675i
$671$	−0.156541	−	0.481784i	−0.00604320	−	0.0185991i
$672$		0			0
$673$	1.00000	+	0.726543i	0.0385472	+	0.0280062i	0.606892	−	0.794784i	$-0.292416\pi$
$673$	1.00000	+	0.726543i	0.0385472	+	0.0280062i	−0.568345	+	0.822790i	$0.692416\pi$
$674$	−31.4164			−1.21011
$675$		0			0
$676$	−12.0000			−0.461538
$677$	8.59017	+	6.24112i	0.330147	+	0.239866i	0.740493	−	0.672064i	$-0.234592\pi$
$677$	8.59017	+	6.24112i	0.330147	+	0.239866i	−0.410346	+	0.911930i	$0.634592\pi$
$678$		0			0
$679$	9.79180	+	30.1360i	0.375775	+	1.15652i
$680$	5.42705	−	16.7027i	0.208118	−	0.640521i
$681$		0			0
$682$	1.00000			0.0382920
$683$	−10.3090	+	31.7279i	−0.394464	+	1.21403i	0.534915	+	0.844906i	$0.320344\pi$
$683$	−10.3090	+	31.7279i	−0.394464	+	1.21403i	−0.929379	+	0.369128i	$0.879656\pi$
$684$		0			0
$685$	11.0172	+	8.00448i	0.420946	+	0.305835i
$686$	−12.1353	−	8.81678i	−0.463326	−	0.336626i
$687$		0			0
$688$	1.42705	−	1.03681i	0.0544058	−	0.0395281i
$689$	1.23607	+	0.898056i	0.0470904	+	0.0342132i
$690$		0			0
$691$	−1.02786	+	0.746787i	−0.0391018	+	0.0284091i	−0.607164	−	0.794576i	$-0.707693\pi$
$691$	−1.02786	+	0.746787i	−0.0391018	+	0.0284091i	0.568063	+	0.822985i	$0.307693\pi$
$692$	−1.00000	+	3.07768i	−0.0380143	+	0.116996i
$693$		0			0
$694$	3.06231	−	9.42481i	0.116244	−	0.357761i
$695$	−7.13525	+	21.9601i	−0.270656	+	0.832992i
$696$		0			0
$697$	−18.1353	−	55.8146i	−0.686922	−	2.11413i
$698$	17.9894	+	13.0700i	0.680907	+	0.494708i
$699$		0			0
$700$	12.1353	+	8.81678i	0.458670	+	0.333243i
$701$	4.18034			0.157889			0.0789446	−	0.996879i	$-0.474845\pi$
$701$	4.18034			0.157889			0.0789446	+	0.996879i	$0.474845\pi$
$702$		0			0
$703$	−1.93363	−	5.95110i	−0.0729282	−	0.224450i
$704$	0.0729490	+	0.224514i	0.00274937	+	0.00846169i
$705$		0			0
$706$	5.18034	−	15.9434i	0.194965	−	0.600040i
$707$	−4.85410			−0.182557
$708$		0			0
$709$	−6.28115	+	4.56352i	−0.235894	+	0.171387i	−0.699452	−	0.714680i	$-0.746572\pi$
$709$	−6.28115	+	4.56352i	−0.235894	+	0.171387i	0.463558	+	0.886066i	$0.346572\pi$
$710$	−6.70820			−0.251754
$711$		0			0
$712$	−3.61803	+	2.62866i	−0.135592	+	0.0985130i
$713$	−21.3713	+	15.5272i	−0.800362	+	0.581497i
$714$		0			0
$715$	−0.163119	−	0.502029i	−0.00610030	−	0.0187748i
$716$	−9.04508	+	6.57164i	−0.338031	+	0.245594i
$717$		0			0
$718$	−3.09017			−0.115324
$719$	8.19098	−	25.2093i	0.305472	−	0.940147i	−0.674028	−	0.738705i	$-0.735438\pi$
$719$	8.19098	−	25.2093i	0.305472	−	0.940147i	0.979501	−	0.201441i	$-0.0645625\pi$
$720$		0			0
$721$	18.4058	+	56.6471i	0.685466	+	2.10965i
$722$	−5.64590	−	17.3763i	−0.210119	−	0.646678i
$723$		0			0
$724$	−21.4164			−0.795935
$725$	−2.13525	−	1.55135i	−0.0793014	−	0.0576158i
$726$		0			0
$727$	23.1803	+	16.8415i	0.859711	+	0.624617i	0.927806	−	0.373062i	$-0.121692\pi$
$727$	23.1803	+	16.8415i	0.859711	+	0.624617i	−0.0680952	+	0.997679i	$0.521692\pi$
$728$	−0.927051	−	2.85317i	−0.0343588	−	0.105745i
$729$		0			0
$730$	−10.3262	+	7.50245i	−0.382191	+	0.277678i
$731$	4.28115	−	13.1760i	0.158344	−	0.487333i
$732$		0			0
$733$	−12.2918	+	37.8303i	−0.454008	+	1.39729i	0.418288	+	0.908314i	$0.362630\pi$
$733$	−12.2918	+	37.8303i	−0.454008	+	1.39729i	−0.872296	+	0.488978i	$0.837370\pi$
$734$	25.5172	−	18.5393i	0.941858	−	0.684300i
$735$		0			0
$736$	−5.04508	−	3.66547i	−0.185964	−	0.135111i
$737$	1.10081	−	0.799788i	0.0405490	−	0.0294606i
$738$		0			0
$739$	−24.2705	−	17.6336i	−0.892805	−	0.648661i	0.0438028	−	0.999040i	$-0.486053\pi$
$739$	−24.2705	−	17.6336i	−0.892805	−	0.648661i	−0.936608	+	0.350379i	$0.886053\pi$
$740$	−5.06231	+	15.5802i	−0.186094	+	0.572739i
$741$		0			0
$742$	1.41641	−	4.35926i	0.0519980	−	0.160033i
$743$	18.2705			0.670280			0.335140	−	0.942168i	$-0.391216\pi$
$743$	18.2705			0.670280			0.335140	+	0.942168i	$0.391216\pi$
$744$		0			0
$745$	−1.54508	−	4.75528i	−0.0566075	−	0.174220i
$746$	−5.01722	−	15.4414i	−0.183694	−	0.565350i
$747$		0			0
$748$	1.50000	+	1.08981i	0.0548454	+	0.0398475i
$749$	30.2705			1.10606
$750$		0			0
$751$	1.14590			0.0418144			0.0209072	−	0.999781i	$-0.493345\pi$
$751$	1.14590			0.0418144			0.0209072	+	0.999781i	$0.493345\pi$
$752$	4.80902	+	3.49396i	0.175367	+	0.127411i
$753$		0			0
$754$	0.163119	+	0.502029i	0.00594044	+	0.0182828i
$755$	−2.56231	−	7.88597i	−0.0932519	−	0.287000i
$756$		0			0
$757$	10.4164			0.378591			0.189295	−	0.981920i	$-0.439380\pi$
$757$	10.4164			0.378591			0.189295	+	0.981920i	$0.439380\pi$
$758$	0.163119	−	0.502029i	0.00592475	−	0.0182345i
$759$		0			0
$760$	0.590170	−	1.81636i	0.0214077	−	0.0658862i
$761$	−30.6803	−	22.2906i	−1.11216	−	0.808033i	−0.129159	−	0.991624i	$-0.541228\pi$
$761$	−30.6803	−	22.2906i	−1.11216	−	0.808033i	−0.983003	+	0.183591i	$0.941228\pi$
$762$		0			0
$763$	−36.4058	+	26.4503i	−1.31798	+	0.957566i
$764$	14.2812	+	10.3759i	0.516674	+	0.375386i
$765$		0			0
$766$	−3.50000	+	2.54290i	−0.126460	+	0.0918787i
$767$	−1.38197	+	4.25325i	−0.0498999	+	0.153576i
$768$		0			0
$769$	−7.23607	+	22.2703i	−0.260939	+	0.803089i	0.731662	+	0.681668i	$0.238745\pi$
$769$	−7.23607	+	22.2703i	−0.260939	+	0.803089i	−0.992601	+	0.121421i	$0.961255\pi$
$770$	−1.28115	+	0.930812i	−0.0461695	+	0.0335441i
$771$		0			0
$772$	5.14590	+	15.8374i	0.185205	+	0.570002i
$773$	5.01722	+	3.64522i	0.180457	+	0.131110i	0.674347	−	0.738415i	$-0.264425\pi$
$773$	5.01722	+	3.64522i	0.180457	+	0.131110i	−0.493890	+	0.869525i	$0.664425\pi$
$774$		0			0
$775$	6.54508	+	20.1437i	0.235106	+	0.723583i
$776$	−10.5623			−0.379165
$777$		0			0
$778$	10.2639	+	31.5891i	0.367980	+	1.13253i
$779$	−1.97214	−	6.06961i	−0.0706591	−	0.217466i
$780$		0			0
$781$	0.218847	−	0.673542i	0.00783096	−	0.0241012i
$782$	−48.9787			−1.75148
$783$		0			0
$784$	−1.61803	+	1.17557i	−0.0577869	+	0.0419847i
$785$	10.7533	+	33.0952i	0.383801	+	1.18122i
$786$		0			0
$787$	−12.4721	+	9.06154i	−0.444584	+	0.323009i	−0.787454	−	0.616374i	$-0.788601\pi$
$787$	−12.4721	+	9.06154i	−0.444584	+	0.323009i	0.342870	+	0.939383i	$0.388601\pi$
$788$	9.70820	−	7.05342i	0.345840	−	0.251268i
$789$		0			0
$790$	6.18034			0.219887
$791$	−19.9894	+	14.5231i	−0.710740	+	0.516383i
$792$		0			0
$793$	−2.14590			−0.0762031
$794$	−1.78115	+	5.48183i	−0.0632108	+	0.194543i
$795$		0			0
$796$	−5.42705	−	16.7027i	−0.192357	−	0.592013i
$797$	−1.04508	−	3.21644i	−0.0370188	−	0.113932i	0.930840	−	0.365428i	$-0.119077\pi$
$797$	−1.04508	−	3.21644i	−0.0370188	−	0.113932i	−0.967858	+	0.251496i	$0.919077\pi$
$798$		0			0
$799$	46.6869			1.65166
$800$	−4.04508	+	2.93893i	−0.143015	+	0.103907i
$801$		0			0
$802$	6.61803	+	4.80828i	0.233691	+	0.169786i
$803$	−0.416408	−	1.28157i	−0.0146947	−	0.0452257i
$804$		0			0
$805$	12.9271	−	39.7854i	0.455619	−	1.40225i
$806$	1.30902	−	4.02874i	0.0461082	−	0.141906i
$807$		0			0
$808$	0.500000	−	1.53884i	0.0175899	−	0.0541363i
$809$	1.80902	−	1.31433i	0.0636017	−	0.0462093i	−0.555530	−	0.831496i	$-0.687485\pi$
$809$	1.80902	−	1.31433i	0.0636017	−	0.0462093i	0.619132	+	0.785287i	$0.287485\pi$
$810$		0			0
$811$	−18.6525	−	13.5518i	−0.654977	−	0.475869i	0.209986	−	0.977704i	$-0.432658\pi$
$811$	−18.6525	−	13.5518i	−0.654977	−	0.475869i	−0.864963	+	0.501836i	$0.832658\pi$
$812$	1.28115	−	0.930812i	0.0449597	−	0.0326651i
$813$		0			0
$814$	−1.39919	−	1.01657i	−0.0490415	−	0.0356307i
$815$	−8.78115	−	6.37988i	−0.307590	−	0.223477i
$816$		0			0
$817$	0.465558	−	1.43284i	0.0162878	−	0.0501287i
$818$	6.70820			0.234547
$819$		0			0
$820$	−5.16312	+	15.8904i	−0.180304	+	0.554918i
$821$	9.31966	+	28.6830i	0.325258	+	1.00104i	0.971324	+	0.237760i	$0.0764133\pi$
$821$	9.31966	+	28.6830i	0.325258	+	1.00104i	−0.646065	+	0.763282i	$0.723587\pi$
$822$		0			0
$823$	−26.5623	−	19.2986i	−0.925904	−	0.672708i	0.0190827	−	0.999818i	$-0.493925\pi$
$823$	−26.5623	−	19.2986i	−0.925904	−	0.672708i	−0.944986	+	0.327109i	$0.893925\pi$
$824$	−19.8541			−0.691650
$825$		0			0
$826$	13.4164			0.466817
$827$	19.4443	+	14.1271i	0.676144	+	0.491247i	0.872076	−	0.489370i	$-0.162773\pi$
$827$	19.4443	+	14.1271i	0.676144	+	0.491247i	−0.195932	+	0.980617i	$0.562773\pi$
$828$		0			0
$829$	8.21478	+	25.2825i	0.285311	+	0.878097i	0.986305	+	0.164930i	$0.0527399\pi$
$829$	8.21478	+	25.2825i	0.285311	+	0.878097i	−0.700994	+	0.713167i	$0.747260\pi$
$830$	24.3713	+	17.7068i	0.845941	+	0.614612i
$831$		0			0
$832$	1.00000			0.0346688
$833$	−4.85410	+	14.9394i	−0.168185	+	0.517619i
$834$		0			0
$835$	34.9230			1.20856
$836$	0.163119	+	0.118513i	0.00564159	+	0.00409885i
$837$		0			0
$838$	22.0344	−	16.0090i	0.761167	−	0.553020i
$839$	20.4271	+	14.8411i	0.705220	+	0.512372i	0.881628	−	0.471945i	$-0.156448\pi$
$839$	20.4271	+	14.8411i	0.705220	+	0.512372i	−0.176408	+	0.984317i	$0.556448\pi$
$840$		0			0
$841$	23.2361	−	16.8820i	0.801244	−	0.582138i
$842$	−3.79180	+	11.6699i	−0.130674	+	0.402173i
$843$		0			0
$844$	3.48278	−	10.7189i	0.119882	−	0.368959i
$845$	26.8328			0.923077
$846$		0			0
$847$	10.1459	+	31.2259i	0.348617	+	1.07293i
$848$	1.23607	+	0.898056i	0.0424467	+	0.0308394i
$849$		0			0
$850$	−12.1353	+	37.3485i	−0.416236	+	1.28104i
$851$	45.6869			1.56613
$852$		0			0
$853$	−7.68034	−	23.6377i	−0.262970	−	0.809338i	−0.992154	−	0.125021i	$-0.960100\pi$
$853$	−7.68034	−	23.6377i	−0.262970	−	0.809338i	0.729184	−	0.684317i	$-0.239900\pi$
$854$	1.98936	+	6.12261i	0.0680744	+	0.209511i
$855$		0			0
$856$	−3.11803	+	9.59632i	−0.106572	+	0.327996i
$857$	−35.3394			−1.20717			−0.603585	−	0.797298i	$-0.706262\pi$
$857$	−35.3394			−1.20717			−0.603585	+	0.797298i	$0.706262\pi$
$858$		0			0
$859$	31.8713	−	23.1559i	1.08744	−	0.790068i	0.108471	−	0.994100i	$-0.465404\pi$
$859$	31.8713	−	23.1559i	1.08744	−	0.790068i	0.978964	+	0.204031i	$0.0654045\pi$
$860$	−3.19098	+	2.31838i	−0.108812	+	0.0790563i
$861$		0			0
$862$	−25.9443	+	18.8496i	−0.883665	+	0.642020i
$863$	−5.47214	+	3.97574i	−0.186274	+	0.135336i	−0.677014	−	0.735970i	$-0.736726\pi$
$863$	−5.47214	+	3.97574i	−0.186274	+	0.135336i	0.490740	+	0.871306i	$0.336726\pi$
$864$		0			0
$865$	2.23607	−	6.88191i	0.0760286	−	0.233992i
$866$	−18.8992	+	13.7311i	−0.642221	+	0.466601i
$867$		0			0
$868$	−12.7082			−0.431345
$869$	−0.201626	+	0.620541i	−0.00683970	+	0.0210504i
$870$		0			0
$871$	−1.78115	−	5.48183i	−0.0603521	−	0.185745i
$872$	−4.63525	−	14.2658i	−0.156970	−	0.483103i
$873$		0			0
$874$	−5.32624			−0.180163
$875$	−27.1353	−	19.7149i	−0.917339	−	0.666486i
$876$		0			0
$877$	−19.8713	−	14.4374i	−0.671007	−	0.487515i	0.199355	−	0.979927i	$-0.436115\pi$
$877$	−19.8713	−	14.4374i	−0.671007	−	0.487515i	−0.870362	+	0.492412i	$0.836115\pi$
$878$	−1.74671	−	5.37582i	−0.0589486	−	0.181425i
$879$		0			0
$880$	−0.163119	−	0.502029i	−0.00549874	−	0.0169234i
$881$	−4.88854	+	15.0454i	−0.164699	+	0.506892i	−0.999014	−	0.0443963i	$-0.985864\pi$
$881$	−4.88854	+	15.0454i	−0.164699	+	0.506892i	0.834315	+	0.551288i	$0.185864\pi$
$882$		0			0
$883$	5.77458	−	17.7723i	0.194330	−	0.598086i	−0.805654	−	0.592387i	$-0.798186\pi$
$883$	5.77458	−	17.7723i	0.194330	−	0.598086i	0.999984	−	0.00569940i	$-0.00181418\pi$
$884$	6.35410	−	4.61653i	0.213712	−	0.155271i
$885$		0			0
$886$	−6.00000	−	4.35926i	−0.201574	−	0.146452i
$887$	8.75329	−	6.35964i	0.293907	−	0.213536i	−0.431054	−	0.902326i	$-0.641858\pi$
$887$	8.75329	−	6.35964i	0.293907	−	0.213536i	0.724960	+	0.688791i	$0.241858\pi$
$888$		0			0
$889$	−30.2705	−	21.9928i	−1.01524	−	0.737615i
$890$	8.09017	−	5.87785i	0.271183	−	0.197026i
$891$		0			0
$892$	−2.78115	+	8.55951i	−0.0931199	+	0.286594i
$893$	5.07701			0.169896
$894$		0			0
$895$	20.2254	−	14.6946i	0.676061	−	0.491187i
$896$	−0.927051	−	2.85317i	−0.0309706	−	0.0953177i
$897$		0			0
$898$	11.2812	+	8.19624i	0.376457	+	0.273512i
$899$	2.23607			0.0745770
$900$		0			0
$901$	12.0000			0.399778
$902$	−1.42705	−	1.03681i	−0.0475156	−	0.0345221i
$903$		0			0
$904$	−2.54508	−	7.83297i	−0.0846483	−	0.260521i
$905$	47.8885			1.59187
$906$		0			0
$907$	23.3820			0.776385			0.388193	−	0.921578i	$-0.373099\pi$
$907$	23.3820			0.776385			0.388193	+	0.921578i	$0.373099\pi$
$908$	4.74671	−	14.6089i	0.157525	−	0.484813i
$909$		0			0
$910$	2.07295	+	6.37988i	0.0687176	+	0.211491i
$911$	8.42705	+	6.12261i	0.279201	+	0.202851i	0.718569	−	0.695456i	$-0.244798\pi$
$911$	8.42705	+	6.12261i	0.279201	+	0.202851i	−0.439368	+	0.898307i	$0.644798\pi$
$912$		0			0
$913$	−2.57295	+	1.86936i	−0.0851522	+	0.0618667i
$914$	9.07295	+	6.59188i	0.300106	+	0.218040i
$915$		0			0
$916$	−14.2082	+	10.3229i	−0.469452	+	0.341077i
$917$	9.65654	−	29.7198i	0.318887	−	0.981434i
$918$		0			0
$919$	7.92705	−	24.3970i	0.261489	−	0.804781i	−0.730992	−	0.682386i	$-0.760942\pi$
$919$	7.92705	−	24.3970i	0.261489	−	0.804781i	0.992481	−	0.122395i	$-0.0390576\pi$
$920$	11.2812	+	8.19624i	0.371929	+	0.270222i
$921$		0			0
$922$	−8.70820	−	26.8011i	−0.286789	−	0.882647i
$923$	−2.42705	−	1.76336i	−0.0798874	−	0.0580416i
$924$		0			0
$925$	11.3197	−	34.8383i	0.372188	−	1.14548i
$926$	11.9787			0.393645
$927$		0			0
$928$	0.163119	+	0.502029i	0.00535464	+	0.0164799i
$929$	5.28773	+	16.2740i	0.173485	+	0.533931i	0.999561	−	0.0296271i	$-0.00943197\pi$
$929$	5.28773	+	16.2740i	0.173485	+	0.533931i	−0.826076	+	0.563558i	$0.809432\pi$
$930$		0			0
$931$	−0.527864	+	1.62460i	−0.0173000	+	0.0532441i
$932$	−27.7082			−0.907612
$933$		0			0
$934$	2.57295	−	1.86936i	0.0841895	−	0.0611672i
$935$	−3.35410	−	2.43690i	−0.109691	−	0.0796951i
$936$		0			0
$937$	18.5451	−	13.4738i	0.605842	−	0.440170i	−0.242106	−	0.970250i	$-0.577838\pi$
$937$	18.5451	−	13.4738i	0.605842	−	0.440170i	0.847948	+	0.530080i	$0.177838\pi$
$938$	−13.9894	+	10.1639i	−0.456769	+	0.331862i
$939$		0			0
$940$	−10.7533	−	7.81272i	−0.350734	−	0.254823i
$941$	−9.39919	+	6.82891i	−0.306405	+	0.222616i	−0.730352	−	0.683071i	$-0.760644\pi$
$941$	−9.39919	+	6.82891i	−0.306405	+	0.222616i	0.423948	+	0.905687i	$0.360644\pi$
$942$		0			0
$943$	46.5967			1.51740
$944$	−1.38197	+	4.25325i	−0.0449792	+	0.138432i
$945$		0			0
$946$	−0.128677	−	0.396027i	−0.00418365	−	0.0128760i
$947$	12.8607	+	39.5811i	0.417916	+	1.28621i	0.909617	+	0.415449i	$0.136375\pi$
$947$	12.8607	+	39.5811i	0.417916	+	1.28621i	−0.491701	+	0.870764i	$0.663625\pi$
$948$		0			0
$949$	−5.70820			−0.185296
$950$	−1.31966	+	4.06150i	−0.0428154	+	0.131772i
$951$		0			0
$952$	−19.0623	−	13.8496i	−0.617813	−	0.448867i
$953$	−13.0967	−	40.3076i	−0.424245	−	1.30569i	−0.903715	−	0.428134i	$-0.859171\pi$
$953$	−13.0967	−	40.3076i	−0.424245	−	1.30569i	0.479470	−	0.877558i	$-0.340829\pi$
$954$		0			0
$955$	−31.9336	−	23.2011i	−1.03335	−	0.750771i
$956$	5.59017	−	17.2048i	0.180799	−	0.556442i
$957$		0			0
$958$	12.2984	−	37.8505i	0.397342	−	1.22289i
$959$	14.7812	−	10.7391i	0.477308	−	0.346785i
$960$		0			0
$961$	10.5623	+	7.67396i	0.340720	+	0.247547i
$962$	−5.92705	+	4.30625i	−0.191096	+	0.138839i
$963$		0			0
$964$	−10.8262	−	7.86572i	−0.348690	−	0.253338i
$965$	−11.5066	−	35.4136i	−0.370410	−	1.14000i
$966$		0			0
$967$	8.38197	−	25.7970i	0.269546	−	0.829577i	−0.721065	−	0.692867i	$-0.756347\pi$
$967$	8.38197	−	25.7970i	0.269546	−	0.829577i	0.990611	−	0.136710i	$-0.0436528\pi$
$968$	−10.9443			−0.351762
$969$		0			0
$970$	23.6180			0.758329
$971$	16.0902	+	49.5205i	0.516358	+	1.58919i	0.780797	+	0.624785i	$0.214813\pi$
$971$	16.0902	+	49.5205i	0.516358	+	1.58919i	−0.264439	+	0.964402i	$0.585187\pi$
$972$		0			0
$973$	25.0623	+	18.2088i	0.803461	+	0.583748i
$974$	−18.1246			−0.580750
$975$		0			0
$976$	−2.14590			−0.0686885
$977$	−21.0451	−	15.2901i	−0.673292	−	0.489175i	0.197834	−	0.980236i	$-0.436609\pi$
$977$	−21.0451	−	15.2901i	−0.673292	−	0.489175i	−0.871126	+	0.491060i	$0.836609\pi$
$978$		0			0
$979$	0.326238	+	1.00406i	0.0104266	+	0.0320898i
$980$	3.61803	−	2.62866i	0.115574	−	0.0839693i
$981$		0			0
$982$	−14.7639			−0.471136
$983$	14.3647	−	44.2101i	0.458164	−	1.41008i	−0.409216	−	0.912438i	$-0.634198\pi$
$983$	14.3647	−	44.2101i	0.458164	−	1.41008i	0.867380	−	0.497647i	$-0.165802\pi$
$984$		0			0
$985$	−21.7082	+	15.7719i	−0.691681	+	0.502536i
$986$	3.35410	+	2.43690i	0.106816	+	0.0776066i
$987$		0			0
$988$	0.690983	−	0.502029i	0.0219831	−	0.0159717i
$989$	8.89919	+	6.46564i	0.282978	+	0.205595i
$990$		0			0
$991$	−42.4336	+	30.8298i	−1.34795	+	0.979342i	−0.348838	+	0.937183i	$0.613424\pi$
$991$	−42.4336	+	30.8298i	−1.34795	+	0.979342i	−0.999111	+	0.0421589i	$0.986576\pi$
$992$	1.30902	−	4.02874i	0.0415613	−	0.127913i
$993$		0			0
$994$	−2.78115	+	8.55951i	−0.0882128	+	0.271491i
$995$	12.1353	+	37.3485i	0.384713	+	1.18403i
$996$		0			0
$997$	−16.4549	−	50.6430i	−0.521132	−	1.60388i	−0.771839	−	0.635818i	$-0.780663\pi$
$997$	−16.4549	−	50.6430i	−0.521132	−	1.60388i	0.250707	−	0.968063i	$-0.419337\pi$
$998$	−33.0517	−	24.0134i	−1.04623	−	0.760132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.a.91.1		4
3.2	odd	2		50.2.d.a.41.1	yes	4
12.11	even	2		400.2.u.c.241.1		4
15.2	even	4		250.2.e.b.49.1		8
15.8	even	4		250.2.e.b.49.2		8
15.14	odd	2		250.2.d.a.201.1		4
25.11	even	5	inner	450.2.h.a.361.1		4
75.2	even	20		250.2.e.b.199.2		8
75.8	even	20		1250.2.b.b.1249.3		4
75.11	odd	10		50.2.d.a.11.1	✓	4
75.14	odd	10		250.2.d.a.51.1		4
75.17	even	20		1250.2.b.b.1249.2		4
75.23	even	20		250.2.e.b.199.1		8
75.44	odd	10		1250.2.a.d.1.2		2
75.56	odd	10		1250.2.a.a.1.1		2
300.11	even	10		400.2.u.c.161.1		4
300.119	even	10		10000.2.a.a.1.1		2
300.131	even	10		10000.2.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.a.11.1	✓	4	75.11	odd	10
50.2.d.a.41.1	yes	4	3.2	odd	2
250.2.d.a.51.1		4	75.14	odd	10
250.2.d.a.201.1		4	15.14	odd	2
250.2.e.b.49.1		8	15.2	even	4
250.2.e.b.49.2		8	15.8	even	4
250.2.e.b.199.1		8	75.23	even	20
250.2.e.b.199.2		8	75.2	even	20
400.2.u.c.161.1		4	300.11	even	10
400.2.u.c.241.1		4	12.11	even	2
450.2.h.a.91.1		4	1.1	even	1	trivial
450.2.h.a.361.1		4	25.11	even	5	inner
1250.2.a.a.1.1		2	75.56	odd	10
1250.2.a.d.1.2		2	75.44	odd	10
1250.2.b.b.1249.2		4	75.17	even	20
1250.2.b.b.1249.3		4	75.8	even	20
10000.2.a.a.1.1		2	300.119	even	10
10000.2.a.n.1.2		2	300.131	even	10

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} -3.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} -3.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.690983 + 2.12663i) q^{10} +(-0.190983 - 0.138757i) q^{11} +(-0.809017 + 0.587785i) q^{13} +(2.42705 + 1.76336i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-2.42705 + 7.46969i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(1.80902 - 1.31433i) q^{20} +(0.0729490 + 0.224514i) q^{22} +(-5.04508 - 3.66547i) q^{23} +(-4.04508 + 2.93893i) q^{25} +1.00000 q^{26} +(-0.927051 - 2.85317i) q^{28} +(0.163119 + 0.502029i) q^{29} +(1.30902 - 4.02874i) q^{31} +1.00000 q^{32} +(6.35410 - 4.61653i) q^{34} +(2.07295 + 6.37988i) q^{35} +(-5.92705 + 4.30625i) q^{37} +(0.690983 - 0.502029i) q^{38} -2.23607 q^{40} +(-6.04508 + 4.39201i) q^{41} -1.76393 q^{43} +(0.0729490 - 0.224514i) q^{44} +(1.92705 + 5.93085i) q^{46} +(-1.83688 - 5.65334i) q^{47} +2.00000 q^{49} +5.00000 q^{50} +(-0.809017 - 0.587785i) q^{52} +(-0.472136 - 1.45309i) q^{53} +(-0.163119 + 0.502029i) q^{55} +(-0.927051 + 2.85317i) q^{56} +(0.163119 - 0.502029i) q^{58} +(3.61803 - 2.62866i) q^{59} +(1.73607 + 1.26133i) q^{61} +(-3.42705 + 2.48990i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(1.80902 + 1.31433i) q^{65} +(-1.78115 + 5.48183i) q^{67} -7.85410 q^{68} +(2.07295 - 6.37988i) q^{70} +(0.927051 + 2.85317i) q^{71} +(4.61803 + 3.35520i) q^{73} +7.32624 q^{74} -0.854102 q^{76} +(0.572949 + 0.416272i) q^{77} +(-0.854102 - 2.62866i) q^{79} +(1.80902 + 1.31433i) q^{80} +7.47214 q^{82} +(4.16312 - 12.8128i) q^{83} +17.5623 q^{85} +(1.42705 + 1.03681i) q^{86} +(-0.190983 + 0.138757i) q^{88} +(-3.61803 - 2.62866i) q^{89} +(2.42705 - 1.76336i) q^{91} +(1.92705 - 5.93085i) q^{92} +(-1.83688 + 5.65334i) q^{94} +1.90983 q^{95} +(-3.26393 - 10.0453i) q^{97} +(-1.61803 - 1.17557i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 5 q^{5} - 12 q^{7} - q^{8}+O(q^{10}) \) 4 * q - q^2 - q^4 - 5 * q^5 - 12 * q^7 - q^8	\( 4 q - q^{2} - q^{4} - 5 q^{5} - 12 q^{7} - q^{8} - 5 q^{10} - 3 q^{11} - q^{13} + 3 q^{14} - q^{16} - 3 q^{17} - 10 q^{19} + 5 q^{20} + 7 q^{22} - 9 q^{23} - 5 q^{25} + 4 q^{26} + 3 q^{28} - 15 q^{29} + 3 q^{31} + 4 q^{32} + 12 q^{34} + 15 q^{35} - 17 q^{37} + 5 q^{38} - 13 q^{41} - 16 q^{43} + 7 q^{44} + q^{46} - 23 q^{47} + 8 q^{49} + 20 q^{50} - q^{52} + 16 q^{53} + 15 q^{55} + 3 q^{56} - 15 q^{58} + 10 q^{59} - 2 q^{61} - 7 q^{62} - q^{64} + 5 q^{65} + 13 q^{67} - 18 q^{68} + 15 q^{70} - 3 q^{71} + 14 q^{73} - 2 q^{74} + 10 q^{76} + 9 q^{77} + 10 q^{79} + 5 q^{80} + 12 q^{82} + q^{83} + 30 q^{85} - q^{86} - 3 q^{88} - 10 q^{89} + 3 q^{91} + q^{92} - 23 q^{94} + 30 q^{95} - 22 q^{97} - 2 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 5 * q^5 - 12 * q^7 - q^8 - 5 * q^10 - 3 * q^11 - q^13 + 3 * q^14 - q^16 - 3 * q^17 - 10 * q^19 + 5 * q^20 + 7 * q^22 - 9 * q^23 - 5 * q^25 + 4 * q^26 + 3 * q^28 - 15 * q^29 + 3 * q^31 + 4 * q^32 + 12 * q^34 + 15 * q^35 - 17 * q^37 + 5 * q^38 - 13 * q^41 - 16 * q^43 + 7 * q^44 + q^46 - 23 * q^47 + 8 * q^49 + 20 * q^50 - q^52 + 16 * q^53 + 15 * q^55 + 3 * q^56 - 15 * q^58 + 10 * q^59 - 2 * q^61 - 7 * q^62 - q^64 + 5 * q^65 + 13 * q^67 - 18 * q^68 + 15 * q^70 - 3 * q^71 + 14 * q^73 - 2 * q^74 + 10 * q^76 + 9 * q^77 + 10 * q^79 + 5 * q^80 + 12 * q^82 + q^83 + 30 * q^85 - q^86 - 3 * q^88 - 10 * q^89 + 3 * q^91 + q^92 - 23 * q^94 + 30 * q^95 - 22 * q^97 - 2 * q^98

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