LMFDB - Embedded newform 495.2.n.d.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$-0.386111 + 0.280526i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.d.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12474 + 0.817172i) q^{2} +(-0.0207616 + 0.0638975i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.394797 - 1.21506i) q^{7} +(-0.888090 - 2.73326i) q^{8} +O(q^{10})$	\(q+(-1.12474 + 0.817172i) q^{2} +(-0.0207616 + 0.0638975i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.394797 - 1.21506i) q^{7} +(-0.888090 - 2.73326i) q^{8} +1.39026 q^{10} +(1.20381 + 3.09044i) q^{11} +(1.14748 - 0.833694i) q^{13} +(0.548870 + 1.68925i) q^{14} +(3.12371 + 2.26951i) q^{16} +(4.04508 + 2.93893i) q^{17} +(0.0488697 + 0.150406i) q^{19} +(0.0543544 - 0.0394908i) q^{20} +(-3.87940 - 2.49222i) q^{22} +5.00829 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.609348 + 1.87538i) q^{26} +(0.0694428 + 0.0504531i) q^{28} +(-1.93913 + 5.96802i) q^{29} +(-2.46735 + 1.79264i) q^{31} +0.379898 q^{32} -6.95128 q^{34} +(-1.03359 + 0.750949i) q^{35} +(-1.45235 + 4.46988i) q^{37} +(-0.177873 - 0.129232i) q^{38} +(-0.888090 + 2.73326i) q^{40} +(-2.34419 - 7.21469i) q^{41} +5.41324 q^{43} +(-0.222465 + 0.0127583i) q^{44} +(-5.63303 + 4.09264i) q^{46} +(2.54386 + 7.82920i) q^{47} +(4.34261 + 3.15509i) q^{49} +(-1.12474 - 0.817172i) q^{50} +(0.0294475 + 0.0906300i) q^{52} +(7.57764 - 5.50548i) q^{53} +(0.842610 - 3.20780i) q^{55} -3.67169 q^{56} +(-2.69588 - 8.29708i) q^{58} +(-2.50256 + 7.70209i) q^{59} +(11.5623 + 8.40047i) q^{61} +(1.31024 - 4.03250i) q^{62} +(-6.67470 + 4.84945i) q^{64} -1.41837 q^{65} -7.38362 q^{67} +(-0.271772 + 0.197454i) q^{68} +(0.548870 - 1.68925i) q^{70} +(-5.48204 - 3.98294i) q^{71} +(2.67642 - 8.23717i) q^{73} +(-2.01914 - 6.21429i) q^{74} -0.0106252 q^{76} +(4.23034 - 0.242610i) q^{77} +(2.05953 - 1.49634i) q^{79} +(-1.19315 - 3.67214i) q^{80} +(8.53225 + 6.19905i) q^{82} +(8.18897 + 5.94964i) q^{83} +(-1.54508 - 4.75528i) q^{85} +(-6.08850 + 4.42355i) q^{86} +(7.37788 - 6.03493i) q^{88} -11.0447 q^{89} +(-0.559967 - 1.72340i) q^{91} +(-0.103980 + 0.320017i) q^{92} +(-9.25900 - 6.72705i) q^{94} +(0.0488697 - 0.150406i) q^{95} +(-5.18739 + 3.76886i) q^{97} -7.46257 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8}+O(q^{10}) $ 8 * q - 2 * q^4 - 2 * q^5 + q^7 - 5 * q^8	$ 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8} - 10 q^{10} + 3 q^{11} + 6 q^{13} + 10 q^{14} - 20 q^{16} + 10 q^{17} + 6 q^{19} - 7 q^{20} - 25 q^{22} + 10 q^{23} - 2 q^{25} + 8 q^{26} + 31 q^{28} + 3 q^{31} - 60 q^{32} + 50 q^{34} + q^{35} - 19 q^{37} + 28 q^{38} - 5 q^{40} + 25 q^{41} - 4 q^{43} - 7 q^{44} - 6 q^{46} - 15 q^{47} + 21 q^{49} + 6 q^{52} - 7 q^{53} - 7 q^{55} - 20 q^{56} - 2 q^{58} - 35 q^{59} + 21 q^{61} + 19 q^{62} - 77 q^{64} + 6 q^{65} - 26 q^{67} + 35 q^{68} + 10 q^{70} - 25 q^{71} + q^{73} + 29 q^{74} - 14 q^{76} + 61 q^{77} + 30 q^{79} + 5 q^{80} + 57 q^{82} - 11 q^{83} + 10 q^{85} + 34 q^{86} - 85 q^{88} - 32 q^{89} + 37 q^{91} + 10 q^{92} - 39 q^{94} + 6 q^{95} + 5 q^{97} - 50 q^{98}+O(q^{100}) $ 8 * q - 2 * q^4 - 2 * q^5 + q^7 - 5 * q^8 - 10 * q^10 + 3 * q^11 + 6 * q^13 + 10 * q^14 - 20 * q^16 + 10 * q^17 + 6 * q^19 - 7 * q^20 - 25 * q^22 + 10 * q^23 - 2 * q^25 + 8 * q^26 + 31 * q^28 + 3 * q^31 - 60 * q^32 + 50 * q^34 + q^35 - 19 * q^37 + 28 * q^38 - 5 * q^40 + 25 * q^41 - 4 * q^43 - 7 * q^44 - 6 * q^46 - 15 * q^47 + 21 * q^49 + 6 * q^52 - 7 * q^53 - 7 * q^55 - 20 * q^56 - 2 * q^58 - 35 * q^59 + 21 * q^61 + 19 * q^62 - 77 * q^64 + 6 * q^65 - 26 * q^67 + 35 * q^68 + 10 * q^70 - 25 * q^71 + q^73 + 29 * q^74 - 14 * q^76 + 61 * q^77 + 30 * q^79 + 5 * q^80 + 57 * q^82 - 11 * q^83 + 10 * q^85 + 34 * q^86 - 85 * q^88 - 32 * q^89 + 37 * q^91 + 10 * q^92 - 39 * q^94 + 6 * q^95 + 5 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.12474	+	0.817172i	−0.795312	+	0.577828i	−0.909535	−	0.415627i	$-0.863562\pi$
$2$	−1.12474	+	0.817172i	−0.795312	+	0.577828i	0.114223	+	0.993455i	$0.463562\pi$
$3$		0			0
$3$		0			0
$4$	−0.0207616	+	0.0638975i	−0.0103808	+	0.0319487i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	0.394797	−	1.21506i	0.149219	−	0.459250i	−0.848310	−	0.529500i	$-0.822380\pi$
$7$	0.394797	−	1.21506i	0.149219	−	0.459250i	0.997529	+	0.0702498i	$0.0223796\pi$
$8$	−0.888090	−	2.73326i	−0.313987	−	0.966353i
$9$		0			0
$10$	1.39026			0.439638
$11$	1.20381	+	3.09044i	0.362964	+	0.931803i
$11$	1.20381	+	3.09044i	0.362964	+	0.931803i
$12$		0			0
$13$	1.14748	−	0.833694i	0.318254	−	0.231225i	−0.417176	−	0.908826i	$-0.636980\pi$
$13$	1.14748	−	0.833694i	0.318254	−	0.231225i	0.735430	+	0.677601i	$0.236980\pi$
$14$	0.548870	+	1.68925i	0.146692	+	0.451470i
$15$		0			0
$16$	3.12371	+	2.26951i	0.780927	+	0.567377i
$17$	4.04508	+	2.93893i	0.981077	+	0.712794i	0.957949	−	0.286938i	$-0.0926374\pi$
$17$	4.04508	+	2.93893i	0.981077	+	0.712794i	0.0231281	+	0.999733i	$0.492637\pi$
$18$		0			0
$19$	0.0488697	+	0.150406i	0.0112115	+	0.0345054i	0.956506	−	0.291713i	$-0.0942254\pi$
$19$	0.0488697	+	0.150406i	0.0112115	+	0.0345054i	−0.945294	+	0.326219i	$0.894225\pi$
$20$	0.0543544	−	0.0394908i	0.0121540	−	0.00883042i
$21$		0			0
$22$	−3.87940	−	2.49222i	−0.827092	−	0.531344i
$23$	5.00829			1.04430			0.522150	−	0.852853i	$-0.325130\pi$
$23$	5.00829			1.04430			0.522150	+	0.852853i	$0.325130\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.609348	+	1.87538i	−0.119503	+	0.367792i
$27$		0			0
$28$	0.0694428	+	0.0504531i	0.0131234	+	0.00953474i
$29$	−1.93913	+	5.96802i	−0.360087	+	1.10823i	0.592914	+	0.805266i	$0.297977\pi$
$29$	−1.93913	+	5.96802i	−0.360087	+	1.10823i	−0.953001	+	0.302967i	$0.902023\pi$
$30$		0			0
$31$	−2.46735	+	1.79264i	−0.443149	+	0.321967i	−0.786885	−	0.617100i	$-0.788308\pi$
$31$	−2.46735	+	1.79264i	−0.443149	+	0.321967i	0.343736	+	0.939066i	$0.388308\pi$
$32$	0.379898			0.0671570
$33$		0			0
$34$	−6.95128			−1.19214
$35$	−1.03359	+	0.750949i	−0.174709	+	0.126934i
$36$		0			0
$37$	−1.45235	+	4.46988i	−0.238765	+	0.734844i	0.757834	+	0.652447i	$0.226258\pi$
$37$	−1.45235	+	4.46988i	−0.238765	+	0.734844i	−0.996600	+	0.0823971i	$0.973742\pi$
$38$	−0.177873	−	0.129232i	−0.0288548	−	0.0209643i
$39$		0			0
$40$	−0.888090	+	2.73326i	−0.140419	+	0.432166i
$41$	−2.34419	−	7.21469i	−0.366101	−	1.12674i	−0.949288	−	0.314407i	$-0.898194\pi$
$41$	−2.34419	−	7.21469i	−0.366101	−	1.12674i	0.583187	−	0.812338i	$-0.301806\pi$
$42$		0			0
$43$	5.41324			0.825512			0.412756	−	0.910842i	$-0.364566\pi$
$43$	5.41324			0.825512			0.412756	+	0.910842i	$0.364566\pi$
$44$	−0.222465	+	0.0127583i	−0.0335378	+	0.00192339i
$45$		0			0
$46$	−5.63303	+	4.09264i	−0.830545	+	0.603426i
$47$	2.54386	+	7.82920i	0.371060	+	1.14201i	0.946098	+	0.323880i	$0.104987\pi$
$47$	2.54386	+	7.82920i	0.371060	+	1.14201i	−0.575038	+	0.818127i	$0.695013\pi$
$48$		0			0
$49$	4.34261	+	3.15509i	0.620373	+	0.450727i
$50$	−1.12474	−	0.817172i	−0.159062	−	0.115566i
$51$		0			0
$52$	0.0294475	+	0.0906300i	0.00408363	+	0.0125681i
$53$	7.57764	−	5.50548i	1.04087	−	0.756236i	0.0704143	−	0.997518i	$-0.477568\pi$
$53$	7.57764	−	5.50548i	1.04087	−	0.756236i	0.970455	+	0.241282i	$0.0775679\pi$
$54$		0			0
$55$	0.842610	−	3.20780i	0.113617	−	0.432540i
$56$	−3.67169			−0.490651
$57$		0			0
$58$	−2.69588	−	8.29708i	−0.353987	−	1.08946i
$59$	−2.50256	+	7.70209i	−0.325806	+	1.00273i	0.645270	+	0.763955i	$0.276745\pi$
$59$	−2.50256	+	7.70209i	−0.325806	+	1.00273i	−0.971076	+	0.238772i	$0.923255\pi$
$60$		0			0
$61$	11.5623	+	8.40047i	1.48039	+	1.07557i	0.977429	+	0.211263i	$0.0677576\pi$
$61$	11.5623	+	8.40047i	1.48039	+	1.07557i	0.502965	+	0.864307i	$0.332242\pi$
$62$	1.31024	−	4.03250i	0.166401	−	0.512128i
$63$		0			0
$64$	−6.67470	+	4.84945i	−0.834338	+	0.606182i
$65$	−1.41837			−0.175927
$66$		0			0
$67$	−7.38362			−0.902053			−0.451026	−	0.892511i	$-0.648942\pi$
$67$	−7.38362			−0.902053			−0.451026	+	0.892511i	$0.648942\pi$
$68$	−0.271772	+	0.197454i	−0.0329572	+	0.0239448i
$69$		0			0
$70$	0.548870	−	1.68925i	0.0656025	−	0.201904i
$71$	−5.48204	−	3.98294i	−0.650599	−	0.472688i	0.212876	−	0.977079i	$-0.431717\pi$
$71$	−5.48204	−	3.98294i	−0.650599	−	0.472688i	−0.863475	+	0.504391i	$0.831717\pi$
$72$		0			0
$73$	2.67642	−	8.23717i	0.313251	−	0.964087i	−0.663217	−	0.748427i	$-0.730810\pi$
$73$	2.67642	−	8.23717i	0.313251	−	0.964087i	0.976468	−	0.215661i	$-0.0691905\pi$
$74$	−2.01914	−	6.21429i	−0.234721	−	0.722396i
$75$		0			0
$76$	−0.0106252			−0.00121879
$77$	4.23034	−	0.242610i	0.482092	−	0.0276480i
$78$		0			0
$79$	2.05953	−	1.49634i	0.231716	−	0.168351i	−0.465869	−	0.884854i	$-0.654258\pi$
$79$	2.05953	−	1.49634i	0.231716	−	0.168351i	0.697585	+	0.716502i	$0.254258\pi$
$80$	−1.19315	−	3.67214i	−0.133398	−	0.410558i
$81$		0			0
$82$	8.53225	+	6.19905i	0.942230	+	0.684570i
$83$	8.18897	+	5.94964i	0.898856	+	0.653057i	0.938172	−	0.346170i	$-0.112518\pi$
$83$	8.18897	+	5.94964i	0.898856	+	0.653057i	−0.0393157	+	0.999227i	$0.512518\pi$
$84$		0			0
$85$	−1.54508	−	4.75528i	−0.167588	−	0.515783i
$86$	−6.08850	+	4.42355i	−0.656539	+	0.477004i
$87$		0			0
$88$	7.37788	−	6.03493i	0.786485	−	0.643325i
$89$	−11.0447			−1.17073			−0.585367	−	0.810768i	$-0.699050\pi$
$89$	−11.0447			−1.17073			−0.585367	+	0.810768i	$0.699050\pi$
$90$		0			0
$91$	−0.559967	−	1.72340i	−0.0587005	−	0.180661i
$92$	−0.103980	+	0.320017i	−0.0108407	+	0.0333641i
$93$		0			0
$94$	−9.25900	−	6.72705i	−0.954993	−	0.693843i
$95$	0.0488697	−	0.150406i	0.00501393	−	0.0154313i
$96$		0			0
$97$	−5.18739	+	3.76886i	−0.526699	+	0.382669i	−0.819122	−	0.573620i	$-0.805539\pi$
$97$	−5.18739	+	3.76886i	−0.526699	+	0.382669i	0.292422	+	0.956289i	$0.405539\pi$
$98$	−7.46257			−0.753833
$99$		0			0
$100$	−0.0671858			−0.00671858
$101$	7.09624	−	5.15572i	0.706102	−	0.513013i	−0.175812	−	0.984424i	$-0.556255\pi$
$101$	7.09624	−	5.15572i	0.706102	−	0.513013i	0.881914	+	0.471411i	$0.156255\pi$
$102$		0			0
$103$	3.57429	−	11.0005i	0.352185	−	1.08391i	−0.605439	−	0.795892i	$-0.707002\pi$
$103$	3.57429	−	11.0005i	0.352185	−	1.08391i	0.957624	−	0.288022i	$-0.0929977\pi$
$104$	−3.29777	−	2.39597i	−0.323373	−	0.234944i
$105$		0			0
$106$	−4.02396	+	12.3845i	−0.390842	+	1.20289i
$107$	−4.74238	−	14.5955i	−0.458463	−	1.41100i	−0.867021	−	0.498272i	$-0.833968\pi$
$107$	−4.74238	−	14.5955i	−0.458463	−	1.41100i	0.408557	−	0.912733i	$-0.366032\pi$
$108$		0			0
$109$	14.4004			1.37931			0.689656	−	0.724137i	$-0.257762\pi$
$109$	14.4004			1.37931			0.689656	+	0.724137i	$0.257762\pi$
$110$	1.67361	+	4.29651i	0.159573	+	0.409656i
$111$		0			0
$112$	3.99082	−	2.89950i	0.377097	−	0.273977i
$113$	−5.98397	−	18.4168i	−0.562924	−	1.73250i	−0.674039	−	0.738695i	$-0.735442\pi$
$113$	−5.98397	−	18.4168i	−0.562924	−	1.73250i	0.111115	−	0.993808i	$-0.464558\pi$
$114$		0			0
$115$	−4.05179	−	2.94380i	−0.377832	−	0.274511i
$116$	−0.341082	−	0.247811i	−0.0316687	−	0.0230086i
$117$		0			0
$118$	−3.47920	−	10.7079i	−0.320287	−	0.985741i
$119$	5.16796	−	3.75475i	0.473747	−	0.344197i
$120$		0			0
$121$	−8.10166	+	7.44064i	−0.736515	+	0.676422i
$122$	−19.8692			−1.79887
$123$		0			0
$124$	−0.0633189	−	0.194875i	−0.00568620	−	0.0175003i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	4.87364	+	3.54091i	0.432466	+	0.314205i	0.782634	−	0.622482i	$-0.213876\pi$
$127$	4.87364	+	3.54091i	0.432466	+	0.314205i	−0.350168	+	0.936687i	$0.613876\pi$
$128$	3.30968	−	10.1862i	0.292537	−	0.900337i
$129$		0			0
$130$	1.59529	−	1.15905i	0.139917	−	0.101655i
$131$	18.7278			1.63626			0.818130	−	0.575034i	$-0.195011\pi$
$131$	18.7278			1.63626			0.818130	+	0.575034i	$0.195011\pi$
$132$		0			0
$133$	0.202046			0.0175196
$134$	8.30467	−	6.03369i	0.717414	−	0.521232i
$135$		0			0
$136$	4.44045	−	13.6663i	0.380765	−	1.17188i
$137$	2.45714	+	1.78521i	0.209927	+	0.152521i	0.687781	−	0.725918i	$-0.258585\pi$
$137$	2.45714	+	1.78521i	0.209927	+	0.152521i	−0.477853	+	0.878440i	$0.658585\pi$
$138$		0			0
$139$	−0.683520	+	2.10366i	−0.0579754	+	0.178430i	−0.975851	−	0.218439i	$-0.929903\pi$
$139$	−0.683520	+	2.10366i	−0.0579754	+	0.178430i	0.917875	+	0.396869i	$0.129903\pi$
$140$	−0.0265248	−	0.0816349i	−0.00224175	−	0.00689941i
$141$		0			0
$142$	9.42063			0.790562
$143$	3.95784	+	2.54261i	0.330971	+	0.212624i
$144$		0			0
$145$	5.07670	−	3.68844i	0.421597	−	0.306308i
$146$	3.72091	+	11.4518i	0.307945	+	0.947756i
$147$		0			0
$148$	−0.255461	−	0.185603i	−0.0209988	−	0.0152565i
$149$	1.19833	+	0.870637i	0.0981710	+	0.0713254i	0.635788	−	0.771864i	$-0.280675\pi$
$149$	1.19833	+	0.870637i	0.0981710	+	0.0713254i	−0.537617	+	0.843189i	$0.680675\pi$
$150$		0			0
$151$	−2.79165	−	8.59180i	−0.227181	−	0.699191i	−0.998063	−	0.0622129i	$-0.980184\pi$
$151$	−2.79165	−	8.59180i	−0.227181	−	0.699191i	0.770882	−	0.636978i	$-0.219816\pi$
$152$	0.367697	−	0.267147i	0.0298242	−	0.0216685i
$153$		0			0
$154$	−4.55978	+	3.72979i	−0.367438	+	0.300555i
$155$	3.04981			0.244967
$156$		0			0
$157$	−5.45034	−	16.7744i	−0.434985	−	1.33874i	−0.893102	−	0.449853i	$-0.851476\pi$
$157$	−5.45034	−	16.7744i	−0.434985	−	1.33874i	0.458118	−	0.888891i	$-0.348524\pi$
$158$	−1.09368	+	3.36599i	−0.0870082	+	0.267784i
$159$		0			0
$160$	−0.307344	−	0.223298i	−0.0242976	−	0.0176533i
$161$	1.97726	−	6.08538i	0.155830	−	0.479595i
$162$		0			0
$163$	−19.0152	+	13.8153i	−1.48938	+	1.08210i	−0.515002	+	0.857189i	$0.672209\pi$
$163$	−19.0152	+	13.8153i	−1.48938	+	1.08210i	−0.974379	+	0.224910i	$0.927791\pi$
$164$	0.509669			0.0397985
$165$		0			0
$166$	−14.0724			−1.09223
$167$	0.487619	−	0.354276i	0.0377331	−	0.0274147i	−0.568759	−	0.822504i	$-0.692576\pi$
$167$	0.487619	−	0.354276i	0.0377331	−	0.0274147i	0.606492	+	0.795090i	$0.292576\pi$
$168$		0			0
$169$	−3.39555	+	10.4504i	−0.261196	+	0.803880i
$170$	5.62371	+	4.08586i	0.431319	+	0.313371i
$171$		0			0
$172$	−0.112387	+	0.345893i	−0.00856945	+	0.0263741i
$173$	−2.98631	−	9.19091i	−0.227045	−	0.698772i	−0.998078	−	0.0619764i	$-0.980260\pi$
$173$	−2.98631	−	9.19091i	−0.227045	−	0.698772i	0.771033	−	0.636795i	$-0.219740\pi$
$174$		0			0
$175$	1.27759			0.0965768
$176$	−3.25341	+	12.3857i	−0.245235	+	0.933607i
$177$		0			0
$178$	12.4224	−	9.02542i	0.931100	−	0.676484i
$179$	0.369495	+	1.13719i	0.0276174	+	0.0849975i	0.963915	−	0.266210i	$-0.0857713\pi$
$179$	0.369495	+	1.13719i	0.0276174	+	0.0849975i	−0.936298	+	0.351207i	$0.885771\pi$
$180$		0			0
$181$	−12.5997	−	9.15421i	−0.936527	−	0.680427i	0.0110551	−	0.999939i	$-0.496481\pi$
$181$	−12.5997	−	9.15421i	−0.936527	−	0.680427i	−0.947582	+	0.319512i	$0.896481\pi$
$182$	2.03813	+	1.48079i	0.151076	+	0.109763i
$183$		0			0
$184$	−4.44781	−	13.6890i	−0.327897	−	1.00916i
$185$	3.80231	−	2.76254i	0.279551	−	0.203106i
$186$		0			0
$187$	−4.21305	+	16.0390i	−0.308089	+	1.17289i
$188$	−0.553081			−0.0403376
$189$		0			0
$190$	0.0679415	+	0.209102i	0.00492899	+	0.0151699i
$191$	−5.68641	+	17.5010i	−0.411454	+	1.26633i	0.503930	+	0.863744i	$0.331887\pi$
$191$	−5.68641	+	17.5010i	−0.411454	+	1.26633i	−0.915384	+	0.402581i	$0.868113\pi$
$192$		0			0
$193$	−1.26853	−	0.921640i	−0.0913107	−	0.0663411i	0.541193	−	0.840898i	$-0.317973\pi$
$193$	−1.26853	−	0.921640i	−0.0913107	−	0.0663411i	−0.632504	+	0.774557i	$0.717973\pi$
$194$	2.75466	−	8.47798i	0.197773	−	0.608683i
$195$		0			0
$196$	−0.291762	+	0.211977i	−0.0208401	+	0.0151412i
$197$	−7.97000			−0.567839			−0.283920	−	0.958848i	$-0.591635\pi$
$197$	−7.97000			−0.567839			−0.283920	+	0.958848i	$0.591635\pi$
$198$		0			0
$199$	3.53141			0.250335			0.125167	−	0.992136i	$-0.460053\pi$
$199$	3.53141			0.250335			0.125167	+	0.992136i	$0.460053\pi$
$200$	2.32505	−	1.68925i	0.164406	−	0.119448i
$201$		0			0
$202$	−3.76832	+	11.5977i	−0.265138	+	0.816011i
$203$	6.48595	+	4.71232i	0.455224	+	0.330740i
$204$		0			0
$205$	−2.34419	+	7.21469i	−0.163726	+	0.503895i
$206$	4.96918	+	15.2936i	0.346219	+	1.06555i
$207$		0			0
$208$	5.47647			0.379725
$209$	−0.405990	+	0.332090i	−0.0280829	+	0.0229711i
$210$		0			0
$211$	−16.3867	+	11.9056i	−1.12810	+	0.819616i	−0.985418	−	0.170152i	$-0.945574\pi$
$211$	−16.3867	+	11.9056i	−1.12810	+	0.819616i	−0.142686	+	0.989768i	$0.545574\pi$
$212$	0.194463	+	0.598495i	0.0133558	+	0.0411048i
$213$		0			0
$214$	17.2610	+	12.5409i	1.17994	+	0.857276i
$215$	−4.37940	−	3.18182i	−0.298673	−	0.216999i
$216$		0			0
$217$	1.20406	+	3.70571i	0.0817368	+	0.251560i
$218$	−16.1968	+	11.7676i	−1.09698	+	0.797005i
$219$		0			0
$220$	0.187477	+	0.120440i	0.0126397	+	0.00812004i
$221$	7.09183			0.477048
$222$		0			0
$223$	6.96833	+	21.4463i	0.466634	+	1.43615i	0.856916	+	0.515456i	$0.172377\pi$
$223$	6.96833	+	21.4463i	0.466634	+	1.43615i	−0.390282	+	0.920695i	$0.627623\pi$
$224$	0.149983	−	0.461599i	0.0100211	−	0.0308419i
$225$		0			0
$226$	21.7801	+	15.8242i	1.44879	+	1.05261i
$227$	−5.81143	+	17.8857i	−0.385718	+	1.18712i	0.550240	+	0.835007i	$0.314536\pi$
$227$	−5.81143	+	17.8857i	−0.385718	+	1.18712i	−0.935958	+	0.352112i	$0.885464\pi$
$228$		0			0
$229$	19.2805	−	14.0081i	1.27409	−	0.925681i	0.274732	−	0.961521i	$-0.411411\pi$
$229$	19.2805	−	14.0081i	1.27409	−	0.925681i	0.999358	+	0.0358402i	$0.0114107\pi$
$230$	6.96281			0.459114
$231$		0			0
$232$	18.0343			1.18401
$233$	−8.16446	+	5.93183i	−0.534871	+	0.388607i	−0.822177	−	0.569232i	$-0.807241\pi$
$233$	−8.16446	+	5.93183i	−0.534871	+	0.388607i	0.287305	+	0.957839i	$0.407241\pi$
$234$		0			0
$235$	2.54386	−	7.82920i	0.165943	−	0.510721i
$236$	−0.440187	−	0.319815i	−0.0286538	−	0.0208182i
$237$		0			0
$238$	−2.74435	+	8.44624i	−0.177890	+	0.547488i
$239$	−0.0516759	−	0.159042i	−0.00334264	−	0.0102876i	0.949371	−	0.314156i	$-0.101722\pi$
$239$	−0.0516759	−	0.159042i	−0.00334264	−	0.0102876i	−0.952714	+	0.303869i	$0.901722\pi$
$240$		0			0
$241$	0.965256			0.0621776			0.0310888	−	0.999517i	$-0.490103\pi$
$241$	0.965256			0.0621776			0.0310888	+	0.999517i	$0.490103\pi$
$242$	3.03199	−	14.9892i	0.194904	−	0.963545i
$243$		0			0
$244$	−0.776819	+	0.564392i	−0.0497307	+	0.0361315i
$245$	−1.65873	−	5.10504i	−0.105972	−	0.326149i
$246$		0			0
$247$	0.181469	+	0.131845i	0.0115466	+	0.00838911i
$248$	7.09097	+	5.15189i	0.450277	+	0.327145i
$249$		0			0
$250$	0.429613	+	1.32221i	0.0271711	+	0.0836241i
$251$	−19.0201	+	13.8189i	−1.20054	+	0.872244i	−0.994338	−	0.106265i	$-0.966111\pi$
$251$	−19.0201	+	13.8189i	−1.20054	+	0.872244i	−0.206203	+	0.978509i	$0.566111\pi$
$252$		0			0
$253$	6.02905	+	15.4778i	0.379043	+	0.973083i
$254$	−8.37512			−0.525502
$255$		0			0
$256$	−0.497709	−	1.53179i	−0.0311068	−	0.0957369i
$257$	2.03418	−	6.26055i	0.126888	−	0.390522i	−0.867352	−	0.497695i	$-0.834180\pi$
$257$	2.03418	−	6.26055i	0.126888	−	0.390522i	0.994240	+	0.107173i	$0.0341798\pi$
$258$		0			0
$259$	4.85780	+	3.52940i	0.301849	+	0.219306i
$260$	0.0294475	−	0.0906300i	0.00182625	−	0.00562063i
$261$		0			0
$262$	−21.0640	+	15.3039i	−1.30134	+	0.945477i
$263$	−12.4538			−0.767936			−0.383968	−	0.923346i	$-0.625443\pi$
$263$	−12.4538			−0.767936			−0.383968	+	0.923346i	$0.625443\pi$
$264$		0			0
$265$	−9.36648			−0.575378
$266$	−0.227249	+	0.165106i	−0.0139335	+	0.0101233i
$267$		0			0
$268$	0.153295	−	0.471795i	0.00936401	−	0.0288195i
$269$	16.8057	+	12.2100i	1.02466	+	0.744459i	0.967233	−	0.253891i	$-0.0817105\pi$
$269$	16.8057	+	12.2100i	1.02466	+	0.744459i	0.0574266	+	0.998350i	$0.481710\pi$
$270$		0			0
$271$	4.44683	−	13.6859i	0.270126	−	0.831362i	−0.720342	−	0.693619i	$-0.756015\pi$
$271$	4.44683	−	13.6859i	0.270126	−	0.831362i	0.990468	−	0.137743i	$-0.0439848\pi$
$272$	5.96575	+	18.3607i	0.361727	+	1.11328i
$273$		0			0
$274$	−4.22247			−0.255089
$275$	−2.56719	+	2.09989i	−0.154807	+	0.126628i
$276$		0			0
$277$	14.1474	−	10.2787i	0.850038	−	0.617589i	−0.0751187	−	0.997175i	$-0.523934\pi$
$277$	14.1474	−	10.2787i	0.850038	−	0.617589i	0.925156	+	0.379586i	$0.123934\pi$
$278$	−0.950268	−	2.92462i	−0.0569933	−	0.175407i
$279$		0			0
$280$	2.97046	+	2.15817i	0.177519	+	0.128975i
$281$	−15.2791	−	11.1009i	−0.911474	−	0.662224i	0.0299134	−	0.999552i	$-0.490477\pi$
$281$	−15.2791	−	11.1009i	−0.911474	−	0.662224i	−0.941387	+	0.337328i	$0.890477\pi$
$282$		0			0
$283$	−4.19686	−	12.9166i	−0.249478	−	0.767813i	−0.994868	−	0.101185i	$-0.967737\pi$
$283$	−4.19686	−	12.9166i	−0.249478	−	0.767813i	0.745390	−	0.666629i	$-0.232263\pi$
$284$	0.368316	−	0.267597i	0.0218555	−	0.0158790i
$285$		0			0
$286$	−6.52930	+	0.374455i	−0.386085	+	0.0221420i
$287$	−9.69177			−0.572087
$288$		0			0
$289$	2.47214	+	7.60845i	0.145420	+	0.447556i
$290$	−2.69588	+	8.29708i	−0.158308	+	0.487221i
$291$		0			0
$292$	0.470768	+	0.342033i	0.0275496	+	0.0200159i
$293$	−6.15016	+	18.9282i	−0.359296	+	1.10580i	0.594180	+	0.804332i	$0.297477\pi$
$293$	−6.15016	+	18.9282i	−0.359296	+	1.10580i	−0.953476	+	0.301468i	$0.902523\pi$
$294$		0			0
$295$	6.55179	−	4.76016i	0.381460	−	0.277147i
$296$	13.5072			0.785088
$297$		0			0
$298$	−2.05927			−0.119290
$299$	5.74692	−	4.17538i	0.332353	−	0.241469i
$300$		0			0
$301$	2.13713	−	6.57742i	0.123182	−	0.379116i
$302$	10.1609	+	7.38230i	0.584692	+	0.424804i
$303$		0			0
$304$	−0.188692	+	0.580733i	−0.0108222	+	0.0333073i
$305$	−4.41639	−	13.5922i	−0.252882	−	0.778289i
$306$		0			0
$307$	−14.9354			−0.852410			−0.426205	−	0.904627i	$-0.640150\pi$
$307$	−14.9354			−0.852410			−0.426205	+	0.904627i	$0.640150\pi$
$308$	−0.0723262	+	0.275345i	−0.00412117	+	0.0156892i
$309$		0			0
$310$	−3.43025	+	2.49222i	−0.194825	+	0.141549i
$311$	1.54416	+	4.75243i	0.0875611	+	0.269485i	0.985244	−	0.171157i	$-0.0547506\pi$
$311$	1.54416	+	4.75243i	0.0875611	+	0.269485i	−0.897683	+	0.440643i	$0.854751\pi$
$312$		0			0
$313$	−7.60191	−	5.52311i	−0.429685	−	0.312185i	0.351838	−	0.936061i	$-0.385557\pi$
$313$	−7.60191	−	5.52311i	−0.429685	−	0.312185i	−0.781523	+	0.623876i	$0.785557\pi$
$314$	19.8378	+	14.4130i	1.11951	+	0.813374i
$315$		0			0
$316$	0.0528532	+	0.162665i	0.00297322	+	0.00915064i
$317$	1.74144	−	1.26523i	0.0978088	−	0.0710623i	−0.537806	−	0.843069i	$-0.680747\pi$
$317$	1.74144	−	1.26523i	0.0978088	−	0.0710623i	0.635615	+	0.772006i	$0.280747\pi$
$318$		0			0
$319$	−20.7782	+	1.19163i	−1.16335	+	0.0667183i
$320$	8.25038			0.461210
$321$		0			0
$322$	2.74890	+	8.46024i	0.153190	+	0.471471i
$323$	−0.244349	+	0.752028i	−0.0135959	+	0.0418440i
$324$		0			0
$325$	1.14748	+	0.833694i	0.0636508	+	0.0462450i
$326$	10.0976	−	31.0773i	0.559256	−	1.72121i
$327$		0			0
$328$	−17.6378	+	12.8146i	−0.973882	+	0.707567i
$329$	10.5173			0.579836
$330$		0			0
$331$	−19.5116			−1.07245			−0.536227	−	0.844074i	$-0.680151\pi$
$331$	−19.5116			−1.07245			−0.536227	+	0.844074i	$0.680151\pi$
$332$	−0.550182	+	0.399731i	−0.0301952	+	0.0219381i
$333$		0			0
$334$	−0.258941	+	0.796938i	−0.0141686	+	0.0436065i
$335$	5.97348	+	4.33998i	0.326366	+	0.237119i
$336$		0			0
$337$	9.76639	−	30.0579i	0.532009	−	1.63736i	−0.218015	−	0.975945i	$-0.569958\pi$
$337$	9.76639	−	30.0579i	0.532009	−	1.63736i	0.750024	−	0.661410i	$-0.230042\pi$
$338$	−4.72069	−	14.5288i	−0.256772	−	0.790262i
$339$		0			0
$340$	0.335929			0.0182183
$341$	−8.51027	−	5.46721i	−0.460857	−	0.296066i
$342$		0			0
$343$	12.7832	−	9.28756i	0.690230	−	0.501481i
$344$	−4.80744	−	14.7958i	−0.259200	−	0.797736i
$345$		0			0
$346$	10.8694	+	7.89707i	0.584341	+	0.424549i
$347$	7.59111	+	5.51527i	0.407512	+	0.296075i	0.772594	−	0.634900i	$-0.218959\pi$
$347$	7.59111	+	5.51527i	0.407512	+	0.296075i	−0.365082	+	0.930976i	$0.618959\pi$
$348$		0			0
$349$	−7.66768	−	23.5987i	−0.410441	−	1.26321i	−0.916265	−	0.400572i	$-0.868812\pi$
$349$	−7.66768	−	23.5987i	−0.410441	−	1.26321i	0.505824	−	0.862637i	$-0.331188\pi$
$350$	−1.43696	+	1.04401i	−0.0768087	+	0.0558048i
$351$		0			0
$352$	0.457326	+	1.17405i	0.0243756	+	0.0625771i
$353$	19.4788			1.03675			0.518375	−	0.855153i	$-0.326537\pi$
$353$	19.4788			1.03675			0.518375	+	0.855153i	$0.326537\pi$
$354$		0			0
$355$	2.09395	+	6.44453i	0.111136	+	0.342040i
$356$	0.229305	−	0.705728i	0.0121531	−	0.0374035i
$357$		0			0
$358$	−1.34487	−	0.977103i	−0.0710784	−	0.0516415i
$359$	−9.19946	+	28.3130i	−0.485529	+	1.49430i	0.345684	+	0.938351i	$0.387647\pi$
$359$	−9.19946	+	28.3130i	−0.485529	+	1.49430i	−0.831213	+	0.555954i	$0.812353\pi$
$360$		0			0
$361$	15.3511	−	11.1532i	0.807952	−	0.587012i
$362$	21.6520			1.13800
$363$		0			0
$364$	0.121747			0.00638126
$365$	−7.00695	+	5.09085i	−0.366761	+	0.266467i
$366$		0			0
$367$	−1.98882	+	6.12097i	−0.103816	+	0.319512i	−0.989451	−	0.144870i	$-0.953724\pi$
$367$	−1.98882	+	6.12097i	−0.103816	+	0.319512i	0.885635	+	0.464382i	$0.153724\pi$
$368$	15.6444	+	11.3663i	0.815523	+	0.592512i
$369$		0			0
$370$	−2.01914	+	6.21429i	−0.104970	+	0.323065i
$371$	−3.69786	−	11.3809i	−0.191983	−	0.590864i
$372$		0			0
$373$	−20.8924			−1.08177			−0.540883	−	0.841098i	$-0.681910\pi$
$373$	−20.8924			−1.08177			−0.540883	+	0.841098i	$0.681910\pi$
$374$	−8.36806	−	21.4825i	−0.432702	−	1.11084i
$375$		0			0
$376$	19.1401	−	13.9061i	0.987074	−	0.717151i
$377$	2.75039	+	8.46483i	0.141652	+	0.435961i
$378$		0			0
$379$	11.4873	+	8.34603i	0.590064	+	0.428707i	0.842338	−	0.538949i	$-0.181178\pi$
$379$	11.4873	+	8.34603i	0.590064	+	0.428707i	−0.252274	+	0.967656i	$0.581178\pi$
$380$	0.00859593	+	0.00624531i	0.000440962	+	0.000320378i
$381$		0			0
$382$	−7.90557	−	24.3308i	−0.404484	−	1.24487i
$383$	−21.4214	+	15.5635i	−1.09458	+	0.795260i	−0.980167	−	0.198173i	$-0.936499\pi$
$383$	−21.4214	+	15.5635i	−1.09458	+	0.795260i	−0.114415	+	0.993433i	$0.536499\pi$
$384$		0			0
$385$	−3.56502	−	2.29026i	−0.181690	−	0.116722i
$386$	2.17990			0.110954
$387$		0			0
$388$	−0.133122	−	0.409708i	−0.00675826	−	0.0207998i
$389$	11.2780	−	34.7102i	0.571819	−	1.75988i	−0.0749470	−	0.997188i	$-0.523879\pi$
$389$	11.2780	−	34.7102i	0.571819	−	1.75988i	0.646766	−	0.762689i	$-0.276121\pi$
$390$		0			0
$391$	20.2590	+	14.7190i	1.02454	+	0.744372i
$392$	4.76705	−	14.6715i	0.240773	−	0.741022i
$393$		0			0
$394$	8.96419	−	6.51287i	0.451610	−	0.328114i
$395$	−2.54572			−0.128089
$396$		0			0
$397$	−8.03969			−0.403500			−0.201750	−	0.979437i	$-0.564663\pi$
$397$	−8.03969			−0.403500			−0.201750	+	0.979437i	$0.564663\pi$
$398$	−3.97192	+	2.88577i	−0.199094	+	0.144651i
$399$		0			0
$400$	−1.19315	+	3.67214i	−0.0596575	+	0.183607i
$401$	−22.7255	−	16.5110i	−1.13486	−	0.824521i	−0.148461	−	0.988918i	$-0.547432\pi$
$401$	−22.7255	−	16.5110i	−1.13486	−	0.824521i	−0.986394	+	0.164397i	$0.947432\pi$
$402$		0			0
$403$	−1.33673	+	4.11403i	−0.0665873	+	0.204935i
$404$	0.182109	+	0.560473i	0.00906024	+	0.0278846i
$405$		0			0
$406$	−11.1458			−0.553156
$407$	−15.5623	+	0.892497i	−0.771393	+	0.0442394i
$408$		0			0
$409$	4.83752	−	3.51466i	0.239200	−	0.173789i	−0.461727	−	0.887022i	$-0.652770\pi$
$409$	4.83752	−	3.51466i	0.239200	−	0.173789i	0.700927	+	0.713233i	$0.252770\pi$
$410$	−3.25903	−	10.0303i	−0.160952	−	0.495360i
$411$		0			0
$412$	0.628698	+	0.456776i	0.0309737	+	0.0225037i
$413$	8.37051	+	6.08153i	0.411886	+	0.299253i
$414$		0			0
$415$	−3.12791	−	9.62671i	−0.153543	−	0.472557i
$416$	0.435925	−	0.316718i	0.0213730	−	0.0155284i
$417$		0			0
$418$	0.185259	−	0.705278i	0.00906131	−	0.0344963i
$419$	15.4707			0.755795			0.377897	−	0.925847i	$-0.376647\pi$
$419$	15.4707			0.755795			0.377897	+	0.925847i	$0.376647\pi$
$420$		0			0
$421$	10.6841	+	32.8824i	0.520713	+	1.60259i	0.772640	+	0.634844i	$0.218936\pi$
$421$	10.6841	+	32.8824i	0.520713	+	1.60259i	−0.251927	+	0.967746i	$0.581064\pi$
$422$	8.70182	−	26.7815i	0.423598	−	1.30370i
$423$		0			0
$424$	−21.7775	−	15.8223i	−1.05761	−	0.768399i
$425$	−1.54508	+	4.75528i	−0.0749476	+	0.230665i
$426$		0			0
$427$	14.7718	−	10.7324i	0.714859	−	0.519375i
$428$	1.03108			0.0498390
$429$		0			0
$430$	7.52580			0.362926
$431$	2.71871	−	1.97526i	0.130956	−	0.0951450i	−0.520379	−	0.853935i	$-0.674209\pi$
$431$	2.71871	−	1.97526i	0.130956	−	0.0951450i	0.651335	+	0.758790i	$0.274209\pi$
$432$		0			0
$433$	1.13650	−	3.49779i	0.0546167	−	0.168093i	−0.920027	−	0.391855i	$-0.871834\pi$
$433$	1.13650	−	3.49779i	0.0546167	−	0.168093i	0.974644	+	0.223761i	$0.0718337\pi$
$434$	−4.38246	−	3.18404i	−0.210365	−	0.152839i
$435$		0			0
$436$	−0.298975	+	0.920152i	−0.0143183	+	0.0440673i
$437$	0.244754	+	0.753275i	0.0117082	+	0.0360340i
$438$		0			0
$439$	−1.55432			−0.0741835			−0.0370917	−	0.999312i	$-0.511809\pi$
$439$	−1.55432			−0.0741835			−0.0370917	+	0.999312i	$0.511809\pi$
$440$	−9.51608	+	0.545747i	−0.453661	+	0.0260175i
$441$		0			0
$442$	−7.97647	+	5.79524i	−0.379402	+	0.275652i
$443$	−6.55298	−	20.1680i	−0.311342	−	0.958211i	−0.977234	−	0.212163i	$-0.931949\pi$
$443$	−6.55298	−	20.1680i	−0.311342	−	0.958211i	0.665893	−	0.746047i	$-0.268051\pi$
$444$		0			0
$445$	8.93534	+	6.49191i	0.423576	+	0.307746i
$446$	−25.3629	−	18.4272i	−1.20097	−	0.872555i
$447$		0			0
$448$	3.25723	+	10.0247i	0.153890	+	0.473624i
$449$	12.2247	−	8.88179i	0.576921	−	0.419157i	−0.260692	−	0.965422i	$-0.583951\pi$
$449$	12.2247	−	8.88179i	0.576921	−	0.419157i	0.837613	+	0.546265i	$0.183951\pi$
$450$		0			0
$451$	19.4746	−	15.9297i	0.917023	−	0.750102i
$452$	1.30102			0.0611949
$453$		0			0
$454$	−8.07938	−	24.8658i	−0.379184	−	1.16701i
$455$	−0.559967	+	1.72340i	−0.0262516	+	0.0807943i
$456$		0			0
$457$	−33.4158	−	24.2780i	−1.56312	−	1.13568i	−0.933389	−	0.358866i	$-0.883163\pi$
$457$	−33.4158	−	24.2780i	−1.56312	−	1.13568i	−0.629735	−	0.776810i	$-0.716837\pi$
$458$	−10.2385	+	31.5110i	−0.478415	+	1.47241i
$459$		0			0
$460$	0.272223	−	0.197782i	0.0126925	−	0.00922161i
$461$	16.3158			0.759901			0.379951	−	0.925007i	$-0.375941\pi$
$461$	16.3158			0.759901			0.379951	+	0.925007i	$0.375941\pi$
$462$		0			0
$463$	8.47904			0.394054			0.197027	−	0.980398i	$-0.436871\pi$
$463$	8.47904			0.394054			0.197027	+	0.980398i	$0.436871\pi$
$464$	−19.6017	+	14.2415i	−0.909987	+	0.661144i
$465$		0			0
$466$	4.33558	−	13.3435i	0.200842	−	0.618128i
$467$	−29.5833	−	21.4935i	−1.36895	−	0.994601i	−0.997818	−	0.0660214i	$-0.978969\pi$
$467$	−29.5833	−	21.4935i	−1.36895	−	0.994601i	−0.371133	−	0.928580i	$-0.621031\pi$
$468$		0			0
$469$	−2.91503	+	8.97155i	−0.134604	+	0.414268i
$470$	3.53662	+	10.8846i	0.163132	+	0.502069i
$471$		0			0
$472$	23.2743			1.07129
$473$	6.51654	+	16.7293i	0.299631	+	0.769214i
$474$		0			0
$475$	−0.127943	+	0.0929558i	−0.00587041	+	0.00426510i
$476$	0.132624	+	0.408174i	0.00607881	+	0.0187086i
$477$		0			0
$478$	0.188087	+	0.136653i	0.00860289	+	0.00625037i
$479$	−31.5123	−	22.8950i	−1.43983	−	1.04610i	−0.988077	−	0.153958i	$-0.950798\pi$
$479$	−31.5123	−	22.8950i	−1.43983	−	1.04610i	−0.451756	−	0.892142i	$-0.649202\pi$
$480$		0			0
$481$	2.05997	+	6.33993i	0.0939264	+	0.289076i
$482$	−1.08566	+	0.788781i	−0.0494506	+	0.0359280i
$483$		0			0
$484$	−0.307235	−	0.672155i	−0.0139652	−	0.0305525i
$485$	6.41196			0.291152
$486$		0			0
$487$	2.55622	+	7.86723i	0.115833	+	0.356498i	0.992120	−	0.125292i	$-0.0399868\pi$
$487$	2.55622	+	7.86723i	0.115833	+	0.356498i	−0.876287	+	0.481790i	$0.839987\pi$
$488$	12.6923	−	39.0630i	0.574555	−	1.76830i
$489$		0			0
$490$	6.03734	+	4.38639i	0.272739	+	0.198157i
$491$	3.74905	−	11.5384i	0.169192	−	0.520720i	−0.830128	−	0.557572i	$-0.811733\pi$
$491$	3.74905	−	11.5384i	0.169192	−	0.520720i	0.999321	+	0.0368519i	$0.0117330\pi$
$492$		0			0
$493$	−25.3835	+	18.4422i	−1.14322	+	0.830594i
$494$	−0.311846			−0.0140306
$495$		0			0
$496$	−11.7757			−0.528744
$497$	−7.00381	+	5.08857i	−0.314164	+	0.228253i
$498$		0			0
$499$	−8.76312	+	26.9701i	−0.392291	+	1.20735i	0.538760	+	0.842459i	$0.318893\pi$
$499$	−8.76312	+	26.9701i	−0.392291	+	1.20735i	−0.931051	+	0.364889i	$0.881107\pi$
$500$	0.0543544	+	0.0394908i	0.00243080	+	0.00176608i
$501$		0			0
$502$	10.1003	−	31.0855i	0.450798	−	1.38741i
$503$	4.72177	+	14.5321i	0.210533	+	0.647955i	0.999441	+	0.0334427i	$0.0106471\pi$
$503$	4.72177	+	14.5321i	0.210533	+	0.647955i	−0.788907	+	0.614512i	$0.789353\pi$
$504$		0			0
$505$	−8.77143			−0.390324
$506$	−19.4292	−	12.4818i	−0.863733	−	0.554883i
$507$		0			0
$508$	−0.327439	+	0.237899i	−0.0145278	+	0.0105550i
$509$	6.81363	+	20.9702i	0.302009	+	0.929488i	0.980776	+	0.195134i	$0.0625143\pi$
$509$	6.81363	+	20.9702i	0.302009	+	0.929488i	−0.678768	+	0.734353i	$0.737486\pi$
$510$		0			0
$511$	−8.95202	−	6.50402i	−0.396014	−	0.287721i
$512$	19.1413	+	13.9069i	0.845932	+	0.614605i
$513$		0			0
$514$	2.82803	+	8.70377i	0.124739	+	0.383907i
$515$	−9.35761	+	6.79870i	−0.412345	+	0.299587i
$516$		0			0
$517$	−21.1334	+	17.2866i	−0.929444	+	0.760262i
$518$	−8.34789			−0.366785
$519$		0			0
$520$	1.25964	+	3.87676i	0.0552387	+	0.170007i
$521$	7.39725	−	22.7664i	0.324079	−	0.997413i	−0.647775	−	0.761831i	$-0.724300\pi$
$521$	7.39725	−	22.7664i	0.324079	−	0.997413i	0.971855	−	0.235582i	$-0.0756996\pi$
$522$		0			0
$523$	20.5022	+	14.8957i	0.896498	+	0.651344i	0.937564	−	0.347812i	$-0.113075\pi$
$523$	20.5022	+	14.8957i	0.896498	+	0.651344i	−0.0410660	+	0.999156i	$0.513075\pi$
$524$	−0.388819	+	1.19666i	−0.0169856	+	0.0522764i
$525$		0			0
$526$	14.0073	−	10.1769i	0.610749	−	0.443735i
$527$	−15.2491			−0.664260
$528$		0			0
$529$	2.08298			0.0905642
$530$	10.5349	−	7.65403i	0.457606	−	0.332470i
$531$		0			0
$532$	−0.00419478	+	0.0129102i	−0.000181867	+	0.000559729i
$533$	−8.70476	−	6.32438i	−0.377045	−	0.273939i
$534$		0			0
$535$	−4.74238	+	14.5955i	−0.205031	+	0.631020i
$536$	6.55732	+	20.1814i	0.283233	+	0.871702i
$537$		0			0
$538$	−28.8797			−1.24509
$539$	−4.52293	+	17.2187i	−0.194816	+	0.741663i
$540$		0			0
$541$	28.3669	−	20.6097i	1.21959	−	0.886082i	0.223522	−	0.974699i	$-0.428245\pi$
$541$	28.3669	−	20.6097i	1.21959	−	0.886082i	0.996066	+	0.0886168i	$0.0282447\pi$
$542$	6.18224	+	19.0270i	0.265550	+	0.817279i
$543$		0			0
$544$	1.53672	+	1.11649i	0.0658862	+	0.0478692i
$545$	−11.6502	−	8.46436i	−0.499040	−	0.362574i
$546$		0			0
$547$	−0.342349	−	1.05364i	−0.0146378	−	0.0450505i	0.943471	−	0.331456i	$-0.107540\pi$
$547$	−0.342349	−	1.05364i	−0.0146378	−	0.0450505i	−0.958109	+	0.286405i	$0.907540\pi$
$548$	−0.165085	+	0.119941i	−0.00705207	+	0.00512363i
$549$		0			0
$550$	1.17144	−	4.45967i	0.0499505	−	0.190161i
$551$	−0.992388			−0.0422771
$552$		0			0
$553$	−1.00505	−	3.09321i	−0.0427389	−	0.131537i
$554$	−7.51273	+	23.1218i	−0.319185	+	0.982352i
$555$		0			0
$556$	−0.120228	−	0.0873504i	−0.00509878	−	0.00370448i
$557$	1.67483	−	5.15461i	0.0709650	−	0.218408i	−0.909284	−	0.416177i	$-0.863370\pi$
$557$	1.67483	−	5.15461i	0.0709650	−	0.218408i	0.980249	+	0.197769i	$0.0633697\pi$
$558$		0			0
$559$	6.21159	−	4.51299i	0.262722	−	0.190879i
$560$	−4.93293			−0.208454
$561$		0			0
$562$	26.2564			1.10756
$563$	26.4911	−	19.2469i	1.11647	−	0.811161i	0.132798	−	0.991143i	$-0.457604\pi$
$563$	26.4911	−	19.2469i	1.11647	−	0.811161i	0.983670	+	0.179982i	$0.0576038\pi$
$564$		0			0
$565$	−5.98397	+	18.4168i	−0.251747	+	0.774799i
$566$	15.2755	+	11.0983i	0.642077	+	0.466496i
$567$		0			0
$568$	−6.01786	+	18.5211i	−0.252504	+	0.777126i
$569$	1.08692	+	3.34521i	0.0455662	+	0.140238i	0.971251	−	0.238057i	$-0.0765104\pi$
$569$	1.08692	+	3.34521i	0.0455662	+	0.140238i	−0.925685	+	0.378295i	$0.876510\pi$
$570$		0			0
$571$	−36.0252			−1.50761			−0.753804	−	0.657099i	$-0.771783\pi$
$571$	−36.0252			−1.50761			−0.753804	+	0.657099i	$0.771783\pi$
$572$	−0.244637	+	0.200107i	−0.0102288	+	0.00836691i
$573$		0			0
$574$	10.9007	−	7.91984i	0.454988	−	0.330568i
$575$	1.54765	+	4.76317i	0.0645413	+	0.198638i
$576$		0			0
$577$	−12.5803	−	9.14009i	−0.523723	−	0.380507i	0.294281	−	0.955719i	$-0.404920\pi$
$577$	−12.5803	−	9.14009i	−0.523723	−	0.380507i	−0.818005	+	0.575212i	$0.804920\pi$
$578$	−8.99793	−	6.53738i	−0.374265	−	0.271919i
$579$		0			0
$580$	0.130282	+	0.400966i	0.00540966	+	0.0166492i
$581$	10.4622	−	7.60120i	0.434043	−	0.315351i
$582$		0			0
$583$	26.1364	+	16.7907i	1.08246	+	0.695399i
$584$	−24.8912			−1.03001
$585$		0			0
$586$	−8.55030	−	26.3151i	−0.353210	−	1.08707i
$587$	7.49687	−	23.0730i	0.309429	−	0.952324i	−0.668558	−	0.743660i	$-0.733088\pi$
$587$	7.49687	−	23.0730i	0.309429	−	0.952324i	0.977987	−	0.208665i	$-0.0669117\pi$
$588$		0			0
$589$	−0.390201	−	0.283498i	−0.0160780	−	0.0116813i
$590$	−3.47920	+	10.7079i	−0.143237	+	0.440837i
$591$		0			0
$592$	−14.6812	+	10.6665i	−0.603392	+	0.438390i
$593$	−27.4019			−1.12526			−0.562630	−	0.826709i	$-0.690210\pi$
$593$	−27.4019			−1.12526			−0.562630	+	0.826709i	$0.690210\pi$
$594$		0			0
$595$	−6.38796			−0.261881
$596$	−0.0805107	+	0.0584945i	−0.00329785	+	0.00239603i
$597$		0			0
$598$	−3.05179	+	9.39245i	−0.124797	+	0.384086i
$599$	8.63810	+	6.27594i	0.352943	+	0.256428i	0.750103	−	0.661321i	$-0.230004\pi$
$599$	8.63810	+	6.27594i	0.352943	+	0.256428i	−0.397160	+	0.917750i	$0.630004\pi$
$600$		0			0
$601$	3.41967	−	10.5247i	0.139491	−	0.429310i	−0.856770	−	0.515698i	$-0.827533\pi$
$601$	3.41967	−	10.5247i	0.139491	−	0.429310i	0.996262	+	0.0863885i	$0.0275326\pi$
$602$	2.97116	+	9.14430i	0.121096	+	0.372694i
$603$		0			0
$604$	0.606953			0.0246966
$605$	10.9279	−	1.25756i	0.444281	−	0.0511272i
$606$		0			0
$607$	0.416254	−	0.302426i	0.0168952	−	0.0122751i	−0.579306	−	0.815110i	$-0.696676\pi$
$607$	0.416254	−	0.302426i	0.0168952	−	0.0122751i	0.596201	+	0.802835i	$0.296676\pi$
$608$	0.0185655	+	0.0571387i	0.000752930	+	0.00231728i
$609$		0			0
$610$	16.0745	+	11.6788i	0.650837	+	0.472861i
$611$	9.44619	+	6.86306i	0.382152	+	0.277650i
$612$		0			0
$613$	5.90150	+	18.1630i	0.238360	+	0.733595i	0.996658	+	0.0816877i	$0.0260310\pi$
$613$	5.90150	+	18.1630i	0.238360	+	0.733595i	−0.758298	+	0.651908i	$0.773969\pi$
$614$	16.7985	−	12.2048i	0.677932	−	0.492546i
$615$		0			0
$616$	−4.42004	−	11.3472i	−0.178088	−	0.457190i
$617$	4.70745			0.189515			0.0947573	−	0.995500i	$-0.469792\pi$
$617$	4.70745			0.189515			0.0947573	+	0.995500i	$0.469792\pi$
$618$		0			0
$619$	11.5477	+	35.5402i	0.464141	+	1.42848i	0.860060	+	0.510194i	$0.170426\pi$
$619$	11.5477	+	35.5402i	0.464141	+	1.42848i	−0.395919	+	0.918286i	$0.629574\pi$
$620$	−0.0633189	+	0.194875i	−0.00254295	+	0.00782639i
$621$		0			0
$622$	−5.62033	−	4.08341i	−0.225355	−	0.163730i
$623$	−4.36041	+	13.4200i	−0.174696	+	0.537660i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	13.0635			0.522123
$627$		0			0
$628$	1.18500			0.0472867
$629$	−19.0115	+	13.8127i	−0.758040	+	0.550748i
$630$		0			0
$631$	10.9908	−	33.8262i	0.437536	−	1.34660i	−0.452928	−	0.891547i	$-0.649621\pi$
$631$	10.9908	−	33.8262i	0.437536	−	1.34660i	0.890465	−	0.455052i	$-0.150379\pi$
$632$	−5.91893	−	4.30036i	−0.235443	−	0.171059i
$633$		0			0
$634$	−0.924756	+	2.84611i	−0.0367268	+	0.113033i
$635$	−1.86157	−	5.72931i	−0.0738740	−	0.227361i
$636$		0			0
$637$	7.61344			0.301656
$638$	22.3963	−	18.3196i	0.886678	−	0.725281i
$639$		0			0
$640$	−8.66486	+	6.29539i	−0.342509	+	0.248847i
$641$	−3.77305	−	11.6123i	−0.149027	−	0.458657i	0.848480	−	0.529227i	$-0.177518\pi$
$641$	−3.77305	−	11.6123i	−0.149027	−	0.458657i	−0.997507	+	0.0705705i	$0.977518\pi$
$642$		0			0
$643$	16.9567	+	12.3197i	0.668705	+	0.485843i	0.869591	−	0.493772i	$-0.164382\pi$
$643$	16.9567	+	12.3197i	0.668705	+	0.485843i	−0.200886	+	0.979615i	$0.564382\pi$
$644$	0.347790	+	0.252684i	0.0137048	+	0.00995714i
$645$		0			0
$646$	−0.339707	−	1.04551i	−0.0133656	−	0.0411351i
$647$	12.0354	−	8.74424i	0.473161	−	0.343772i	−0.325511	−	0.945538i	$-0.605536\pi$
$647$	12.0354	−	8.74424i	0.473161	−	0.343772i	0.798672	+	0.601767i	$0.205536\pi$
$648$		0			0
$649$	−26.8155	+	1.53787i	−1.05260	+	0.0603666i
$650$	−1.97189			−0.0773440
$651$		0			0
$652$	−0.487980	−	1.50185i	−0.0191108	−	0.0588169i
$653$	3.74861	−	11.5370i	0.146694	−	0.451479i	−0.850531	−	0.525926i	$-0.823719\pi$
$653$	3.74861	−	11.5370i	0.146694	−	0.451479i	0.997225	+	0.0744465i	$0.0237190\pi$
$654$		0			0
$655$	−15.1511	−	11.0079i	−0.592004	−	0.430116i
$656$	9.05120	−	27.8567i	0.353390	−	1.08762i
$657$		0			0
$658$	−11.8292	+	8.59443i	−0.461151	+	0.335046i
$659$	−7.49994			−0.292156			−0.146078	−	0.989273i	$-0.546665\pi$
$659$	−7.49994			−0.292156			−0.146078	+	0.989273i	$0.546665\pi$
$660$		0			0
$661$	9.65248			0.375438			0.187719	−	0.982223i	$-0.439891\pi$
$661$	9.65248			0.375438			0.187719	+	0.982223i	$0.439891\pi$
$662$	21.9455	−	15.9443i	0.852936	−	0.619694i
$663$		0			0
$664$	8.98936	−	27.6664i	0.348855	−	1.07366i
$665$	−0.163458	−	0.118759i	−0.00633864	−	0.00460529i
$666$		0			0
$667$	−9.71171	+	29.8896i	−0.376039	+	1.15733i
$668$	0.0125136	+	0.0385130i	0.000484167	+	0.00149011i
$669$		0			0
$670$	−10.2651			−0.396577
$671$	−12.0424	+	45.8451i	−0.464890	+	1.76983i
$672$		0			0
$673$	−19.7801	+	14.3711i	−0.762469	+	0.553966i	−0.899667	−	0.436578i	$-0.856190\pi$
$673$	−19.7801	+	14.3711i	−0.762469	+	0.553966i	0.137198	+	0.990544i	$0.456190\pi$
$674$	13.5778	+	41.7881i	0.522997	+	1.60962i
$675$		0			0
$676$	−0.597260	−	0.433935i	−0.0229715	−	0.0166898i
$677$	37.8130	+	27.4728i	1.45327	+	1.05586i	0.985053	+	0.172251i	$0.0551041\pi$
$677$	37.8130	+	27.4728i	1.45327	+	1.05586i	0.468219	+	0.883613i	$0.344896\pi$
$678$		0			0
$679$	2.53143	+	7.79093i	0.0971472	+	0.298988i
$680$	−11.6252	+	8.44624i	−0.445808	+	0.323898i
$681$		0			0
$682$	14.0395	−	0.805166i	0.537600	−	0.0308314i
$683$	28.1941			1.07882			0.539408	−	0.842045i	$-0.318648\pi$
$683$	28.1941			1.07882			0.539408	+	0.842045i	$0.318648\pi$
$684$		0			0
$685$	−0.938543	−	2.88854i	−0.0358599	−	0.110365i
$686$	−6.78829	+	20.8922i	−0.259178	+	0.797668i
$687$		0			0
$688$	16.9094	+	12.2854i	0.644664	+	0.468376i
$689$	4.10532	−	12.6349i	0.156400	−	0.481350i
$690$		0			0
$691$	−9.38225	+	6.81661i	−0.356918	+	0.259316i	−0.751765	−	0.659431i	$-0.770797\pi$
$691$	−9.38225	+	6.81661i	−0.356918	+	0.259316i	0.394848	+	0.918747i	$0.370797\pi$
$692$	0.649276			0.0246818
$693$		0			0
$694$	−13.0450			−0.495180
$695$	1.78948	−	1.30013i	0.0678788	−	0.0493168i
$696$		0			0
$697$	11.7210	−	36.0734i	0.443963	−	1.36638i
$698$	27.9083	+	20.2766i	1.05635	+	0.767481i
$699$		0			0
$700$	−0.0265248	+	0.0816349i	−0.00100254	+	0.00308551i
$701$	11.3415	+	34.9056i	0.428363	+	1.31837i	0.899737	+	0.436433i	$0.143759\pi$
$701$	11.3415	+	34.9056i	0.428363	+	1.31837i	−0.471373	+	0.881934i	$0.656241\pi$
$702$		0			0
$703$	−0.743272			−0.0280330
$704$	−23.0221	−	14.7899i	−0.867676	−	0.557417i
$705$		0			0
$706$	−21.9086	+	15.9175i	−0.824540	+	0.599064i
$707$	−3.46294	−	10.6578i	−0.130237	−	0.400829i
$708$		0			0
$709$	−29.5214	−	21.4486i	−1.10870	−	0.805518i	−0.126242	−	0.991999i	$-0.540292\pi$
$709$	−29.5214	−	21.4486i	−1.10870	−	0.805518i	−0.982458	+	0.186482i	$0.940292\pi$
$710$	−7.62145	−	5.53731i	−0.286028	−	0.207811i
$711$		0			0
$712$	9.80868	+	30.1880i	0.367596	+	1.13134i
$713$	−12.3572	+	8.97804i	−0.462781	+	0.336230i
$714$		0			0
$715$	−1.70745	−	4.38337i	−0.0638549	−	0.163929i
$716$	−0.0803349			−0.00300225
$717$		0			0
$718$	−12.7896	−	39.3624i	−0.477304	−	1.46899i
$719$	2.88278	−	8.87229i	0.107510	−	0.330881i	−0.882802	−	0.469746i	$-0.844346\pi$
$719$	2.88278	−	8.87229i	0.107510	−	0.330881i	0.990311	+	0.138865i	$0.0443455\pi$
$720$		0			0
$721$	−11.9552	−	8.68596i	−0.445235	−	0.323482i
$722$	−8.15190	+	25.0890i	−0.303382	+	0.933715i
$723$		0			0
$724$	0.846520	−	0.615033i	0.0314607	−	0.0228575i
$725$	−6.27515			−0.233053
$726$		0			0
$727$	−8.46883			−0.314091			−0.157046	−	0.987591i	$-0.550197\pi$
$727$	−8.46883			−0.314091			−0.157046	+	0.987591i	$0.550197\pi$
$728$	−4.21320	+	3.06107i	−0.156152	+	0.113451i
$729$		0			0
$730$	3.72091	−	11.4518i	0.137717	−	0.423849i
$731$	21.8970	+	15.9091i	0.809891	+	0.588420i
$732$		0			0
$733$	8.97601	−	27.6253i	0.331537	−	1.02036i	−0.636866	−	0.770974i	$-0.719770\pi$
$733$	8.97601	−	27.6253i	0.331537	−	1.02036i	0.968403	−	0.249391i	$-0.0802303\pi$
$734$	−2.76498	−	8.50972i	−0.102057	−	0.314100i
$735$		0			0
$736$	1.90264			0.0701322
$737$	−8.88851	−	22.8187i	−0.327412	−	0.840536i
$738$		0			0
$739$	11.1281	−	8.08505i	0.409354	−	0.297413i	−0.363986	−	0.931404i	$-0.618584\pi$
$739$	11.1281	−	8.08505i	0.409354	−	0.297413i	0.773340	+	0.633991i	$0.218584\pi$
$740$	0.0975775	+	0.300313i	0.00358702	+	0.0110397i
$741$		0			0
$742$	13.4593	+	9.77872i	0.494105	+	0.358988i
$743$	−28.2456	−	20.5217i	−1.03623	−	0.752867i	−0.0666857	−	0.997774i	$-0.521242\pi$
$743$	−28.2456	−	20.5217i	−1.03623	−	0.752867i	−0.969547	+	0.244907i	$0.921242\pi$
$744$		0			0
$745$	−0.457721	−	1.40872i	−0.0167696	−	0.0516115i
$746$	23.4985	−	17.0727i	0.860343	−	0.625075i
$747$		0			0
$748$	−0.937384	−	0.602198i	−0.0342741	−	0.0220185i
$749$	−19.6068			−0.716416
$750$		0			0
$751$	6.82903	+	21.0176i	0.249195	+	0.766943i	0.994918	+	0.100687i	$0.0321042\pi$
$751$	6.82903	+	21.0176i	0.249195	+	0.766943i	−0.745723	+	0.666256i	$0.767896\pi$
$752$	−9.82214	+	30.2294i	−0.358177	+	1.10235i
$753$		0			0
$754$	−10.0107	−	7.27320i	−0.364568	−	0.264874i
$755$	−2.79165	+	8.59180i	−0.101598	+	0.312688i
$756$		0			0
$757$	36.4300	−	26.4680i	1.32407	−	0.961994i	0.324200	−	0.945989i	$-0.394905\pi$
$757$	36.4300	−	26.4680i	1.32407	−	0.961994i	0.999872	−	0.0160057i	$-0.00509498\pi$
$758$	−19.7404			−0.717004
$759$		0			0
$760$	−0.454498			−0.0164864
$761$	27.1831	−	19.7496i	0.985385	−	0.715924i	0.0264794	−	0.999649i	$-0.491570\pi$
$761$	27.1831	−	19.7496i	0.985385	−	0.715924i	0.958906	+	0.283725i	$0.0915704\pi$
$762$		0			0
$763$	5.68525	−	17.4974i	0.205820	−	0.633449i
$764$	−1.00021	−	0.726694i	−0.0361863	−	0.0262909i
$765$		0			0
$766$	11.3754	−	35.0099i	0.411011	−	1.26496i
$767$	3.54955	+	10.9244i	0.128167	+	0.394457i
$768$		0			0
$769$	24.6086			0.887408			0.443704	−	0.896173i	$-0.353664\pi$
$769$	24.6086			0.887408			0.443704	+	0.896173i	$0.353664\pi$
$770$	5.88126	−	0.337290i	0.211946	−	0.0121551i
$771$		0			0
$772$	0.0852271	−	0.0619211i	0.00306739	−	0.00222859i
$773$	7.31802	+	22.5225i	0.263211	+	0.810080i	0.992100	+	0.125448i	$0.0400369\pi$
$773$	7.31802	+	22.5225i	0.263211	+	0.810080i	−0.728889	+	0.684632i	$0.759963\pi$
$774$		0			0
$775$	−2.46735	−	1.79264i	−0.0886299	−	0.0643934i
$776$	14.9081	+	10.8314i	0.535171	+	0.388824i
$777$		0			0
$778$	15.6794	+	48.2561i	0.562132	+	1.73006i
$779$	0.970569	−	0.705160i	0.0347742	−	0.0252650i
$780$		0			0
$781$	5.70968	−	21.7367i	0.204308	−	0.777799i
$782$	−34.8141			−1.24495
$783$		0			0
$784$	6.40454	+	19.7112i	0.228734	+	0.703970i
$785$	−5.45034	+	16.7744i	−0.194531	+	0.598705i
$786$		0			0
$787$	14.9029	+	10.8276i	0.531232	+	0.385963i	0.820819	−	0.571189i	$-0.193518\pi$
$787$	14.9029	+	10.8276i	0.531232	+	0.385963i	−0.289586	+	0.957152i	$0.593518\pi$
$788$	0.165470	−	0.509263i	0.00589461	−	0.0181418i
$789$		0			0
$790$	2.86328	−	2.08030i	0.101871	−	0.0740136i
$791$	−24.7399			−0.879651
$792$		0			0
$793$	20.2709			0.719840
$794$	9.04257	−	6.56981i	0.320909	−	0.233154i
$795$		0			0
$796$	−0.0733175	+	0.225648i	−0.00259867	+	0.00799788i
$797$	−5.26399	−	3.82451i	−0.186460	−	0.135471i	0.490639	−	0.871363i	$-0.336763\pi$
$797$	−5.26399	−	3.82451i	−0.186460	−	0.135471i	−0.677099	+	0.735892i	$0.736763\pi$
$798$		0			0
$799$	−12.7193	+	39.1460i	−0.449977	+	1.38489i
$800$	0.117395	+	0.361304i	0.00415053	+	0.0127740i
$801$		0			0
$802$	39.0526			1.37900
$803$	28.6784	−	1.64471i	1.01204	−	0.0580404i
$804$		0			0
$805$	−5.17653	+	3.76097i	−0.182449	+	0.132557i
$806$	−1.85840	−	5.71956i	−0.0654593	−	0.201463i
$807$		0			0
$808$	−20.3940	−	14.8171i	−0.717459	−	0.521264i
$809$	9.58727	+	6.96556i	0.337071	+	0.244896i	0.743425	−	0.668819i	$-0.233200\pi$
$809$	9.58727	+	6.96556i	0.337071	+	0.244896i	−0.406354	+	0.913716i	$0.633200\pi$
$810$		0			0
$811$	2.32193	+	7.14616i	0.0815339	+	0.250936i	0.983511	−	0.180848i	$-0.0578843\pi$
$811$	2.32193	+	7.14616i	0.0815339	+	0.250936i	−0.901977	+	0.431784i	$0.857884\pi$
$812$	−0.435763	+	0.316601i	−0.0152923	+	0.0111105i
$813$		0			0
$814$	16.7742	−	13.7209i	0.587936	−	0.480917i
$815$	23.5040			0.823310
$816$		0			0
$817$	0.264544	+	0.814182i	0.00925521	+	0.0284846i
$818$	−2.56887	+	7.90618i	−0.0898185	+	0.276433i
$819$		0			0
$820$	−0.412331	−	0.299576i	−0.0143992	−	0.0104617i
$821$	11.5376	−	35.5092i	0.402666	−	1.23928i	−0.520163	−	0.854067i	$-0.674129\pi$
$821$	11.5376	−	35.5092i	0.402666	−	1.23928i	0.922829	−	0.385211i	$-0.125871\pi$
$822$		0			0
$823$	34.8280	−	25.3040i	1.21403	−	0.882043i	0.218438	−	0.975851i	$-0.429904\pi$
$823$	34.8280	−	25.3040i	1.21403	−	0.882043i	0.995590	+	0.0938075i	$0.0299038\pi$
$824$	−33.2416			−1.15803
$825$		0			0
$826$	−14.3843			−0.500495
$827$	−16.2049	+	11.7736i	−0.563500	+	0.409407i	−0.832738	−	0.553667i	$-0.813228\pi$
$827$	−16.2049	+	11.7736i	−0.563500	+	0.409407i	0.269238	+	0.963074i	$0.413228\pi$
$828$		0			0
$829$	−14.8083	+	45.5753i	−0.514314	+	1.58289i	0.270213	+	0.962800i	$0.412906\pi$
$829$	−14.8083	+	45.5753i	−0.514314	+	1.58289i	−0.784527	+	0.620094i	$0.787094\pi$
$830$	11.3848	+	8.27152i	0.395171	+	0.287109i
$831$		0			0
$832$	−3.61613	+	11.1293i	−0.125367	+	0.385840i
$833$	8.29365	+	25.5252i	0.287358	+	0.884396i
$834$		0			0
$835$	−0.602731			−0.0208584
$836$	−0.0127907	−	0.0328364i	−0.000442376	−	0.00113567i
$837$		0			0
$838$	−17.4006	+	12.6423i	−0.601093	+	0.436720i
$839$	−0.686305	−	2.11223i	−0.0236939	−	0.0729222i	0.938510	−	0.345251i	$-0.112206\pi$
$839$	−0.686305	−	2.11223i	−0.0236939	−	0.0729222i	−0.962204	+	0.272329i	$0.912206\pi$
$840$		0			0
$841$	−8.39554	−	6.09971i	−0.289501	−	0.210335i
$842$	−38.8875	−	28.2534i	−1.34015	−	0.973677i
$843$		0			0
$844$	−0.420526	−	1.29425i	−0.0144751	−	0.0445498i
$845$	8.88967	−	6.45873i	0.305814	−	0.222187i
$846$		0			0
$847$	5.84231	+	12.7816i	0.200744	+	0.439180i
$848$	36.1651			1.24191
$849$		0			0
$850$	−2.14807	−	6.61106i	−0.0736780	−	0.226758i
$851$	−7.27381	+	22.3865i	−0.249343	+	0.767398i
$852$		0			0
$853$	5.15474	+	3.74514i	0.176495	+	0.128231i	0.672525	−	0.740074i	$-0.265210\pi$
$853$	5.15474	+	3.74514i	0.176495	+	0.128231i	−0.496030	+	0.868305i	$0.665210\pi$
$854$	−7.84430	+	24.1423i	−0.268426	+	0.826131i
$855$		0			0
$856$	−35.6818	+	25.9243i	−1.21958	+	0.886075i
$857$	−35.9060			−1.22653			−0.613263	−	0.789878i	$-0.710144\pi$
$857$	−35.9060			−1.22653			−0.613263	+	0.789878i	$0.710144\pi$
$858$		0			0
$859$	56.4697			1.92672			0.963360	−	0.268212i	$-0.0864328\pi$
$859$	56.4697			1.92672			0.963360	+	0.268212i	$0.0864328\pi$
$860$	0.294234	−	0.213773i	0.0100333	−	0.00728961i
$861$		0			0
$862$	−1.44372	+	4.44332i	−0.0491733	+	0.151340i
$863$	−25.1395	−	18.2649i	−0.855759	−	0.621745i	0.0709688	−	0.997479i	$-0.477391\pi$
$863$	−25.1395	−	18.2649i	−0.855759	−	0.621745i	−0.926728	+	0.375733i	$0.877391\pi$
$864$		0			0
$865$	−2.98631	+	9.19091i	−0.101537	+	0.312500i
$866$	1.58003	+	4.86283i	0.0536915	+	0.165246i
$867$		0			0
$868$	−0.261784			−0.00888552
$869$	7.10365	+	4.56356i	0.240975	+	0.154808i
$870$		0			0
$871$	−8.47257	+	6.15568i	−0.287082	+	0.208577i
$872$	−12.7889	−	39.3601i	−0.433086	−	1.33290i
$873$		0			0
$874$	−0.890840	−	0.647233i	−0.0301331	−	0.0218930i
$875$	−1.03359	−	0.750949i	−0.0349418	−	0.0253867i
$876$		0			0
$877$	5.19841	+	15.9991i	0.175538	+	0.540250i	0.999658	−	0.0261655i	$-0.00832970\pi$
$877$	5.19841	+	15.9991i	0.175538	+	0.540250i	−0.824120	+	0.566416i	$0.808330\pi$
$878$	1.74820	−	1.27014i	0.0589990	−	0.0428653i
$879$		0			0
$880$	9.91220	−	8.10793i	0.334140	−	0.273318i
$881$	−26.5633			−0.894940			−0.447470	−	0.894299i	$-0.647675\pi$
$881$	−26.5633			−0.894940			−0.447470	+	0.894299i	$0.647675\pi$
$882$		0			0
$883$	−16.8026	−	51.7129i	−0.565451	−	1.74028i	−0.666608	−	0.745409i	$-0.732254\pi$
$883$	−16.8026	−	51.7129i	−0.565451	−	1.74028i	0.101157	−	0.994870i	$-0.467746\pi$
$884$	−0.147237	+	0.453150i	−0.00495213	+	0.0152411i
$885$		0			0
$886$	23.8511	+	17.3289i	0.801295	+	0.582175i
$887$	12.7396	−	39.2084i	0.427753	−	1.31649i	−0.472580	−	0.881288i	$-0.656677\pi$
$887$	12.7396	−	39.2084i	0.427753	−	1.31649i	0.900333	−	0.435202i	$-0.143323\pi$
$888$		0			0
$889$	6.22652	−	4.52383i	0.208831	−	0.151724i
$890$	−15.3550			−0.514699
$891$		0			0
$892$	−1.51504			−0.0507273
$893$	−1.05324	+	0.765222i	−0.0352453	+	0.0256072i
$894$		0			0
$895$	0.369495	−	1.13719i	0.0123509	−	0.0380121i
$896$	−11.0702	−	8.04293i	−0.369828	−	0.268696i
$897$		0			0
$898$	−6.49171	+	19.9794i	−0.216631	+	0.666722i
$899$	−5.91398	−	18.2013i	−0.197242	−	0.607049i
$900$		0			0
$901$	46.8324			1.56021
$902$	−8.88654	+	33.8309i	−0.295889	+	1.12645i
$903$		0			0
$904$	−45.0235	+	32.7115i	−1.49746	+	1.08797i
$905$	4.81265	+	14.8118i	0.159978	+	0.492361i
$906$		0			0
$907$	−34.3060	−	24.9248i	−1.13911	−	0.827614i	−0.152117	−	0.988362i	$-0.548609\pi$
$907$	−34.3060	−	24.9248i	−1.13911	−	0.827614i	−0.986995	+	0.160748i	$0.948609\pi$
$908$	−1.02220	−	0.742671i	−0.0339229	−	0.0246464i
$909$		0			0
$910$	−0.778498	−	2.39597i	−0.0258069	−	0.0794256i
$911$	−6.48184	+	4.70933i	−0.214753	+	0.156027i	−0.689962	−	0.723846i	$-0.742373\pi$
$911$	−6.48184	+	4.70933i	−0.214753	+	0.156027i	0.475209	+	0.879873i	$0.342373\pi$
$912$		0			0
$913$	−8.52900	+	32.4698i	−0.282269	+	1.07459i
$914$	57.4234			1.89940
$915$		0			0
$916$	0.494789	+	1.52280i	0.0163483	+	0.0503149i
$917$	7.39370	−	22.7555i	0.244162	−	0.751452i
$918$		0			0
$919$	−33.3587	−	24.2365i	−1.10040	−	0.799489i	−0.119277	−	0.992861i	$-0.538058\pi$
$919$	−33.3587	−	24.2365i	−1.10040	−	0.799489i	−0.981125	+	0.193372i	$0.938058\pi$
$920$	−4.44781	+	13.6890i	−0.146640	+	0.451312i
$921$		0			0
$922$	−18.3510	+	13.3328i	−0.604359	+	0.439092i
$923$	−9.61110			−0.316353
$924$		0			0
$925$	−4.69991			−0.154532
$926$	−9.53672	+	6.92884i	−0.313396	+	0.227696i
$927$		0			0
$928$	−0.736670	+	2.26724i	−0.0241824	+	0.0744257i
$929$	−12.2921	−	8.93073i	−0.403291	−	0.293008i	0.367589	−	0.929988i	$-0.380183\pi$
$929$	−12.2921	−	8.93073i	−0.403291	−	0.293008i	−0.770880	+	0.636980i	$0.780183\pi$
$930$		0			0
$931$	−0.262321	+	0.807341i	−0.00859723	+	0.0264595i
$932$	−0.209522	−	0.644842i	−0.00686312	−	0.0211225i
$933$		0			0
$934$	50.8375			1.66345
$935$	12.8359	−	10.4995i	0.419780	−	0.343369i
$936$		0			0
$937$	−20.6472	+	15.0011i	−0.674515	+	0.490064i	−0.871533	−	0.490336i	$-0.836874\pi$
$937$	−20.6472	+	15.0011i	−0.674515	+	0.490064i	0.197019	+	0.980400i	$0.436874\pi$
$938$	−4.05265	−	12.4728i	−0.132324	−	0.407250i
$939$		0			0
$940$	0.447452	+	0.325093i	0.0145943	+	0.0106034i
$941$	26.1857	+	19.0250i	0.853629	+	0.620198i	0.926144	−	0.377170i	$-0.123103\pi$
$941$	26.1857	+	19.0250i	0.853629	+	0.620198i	−0.0725154	+	0.997367i	$0.523103\pi$
$942$		0			0
$943$	−11.7404	−	36.1332i	−0.382320	−	1.17666i
$944$	−25.2972	+	18.3795i	−0.823354	+	0.598202i
$945$		0			0
$946$	−21.0001	−	13.4910i	−0.682774	−	0.438631i
$947$	40.1516			1.30475			0.652375	−	0.757896i	$-0.273773\pi$
$947$	40.1516			1.30475			0.652375	+	0.757896i	$0.273773\pi$
$948$		0			0
$949$	−3.79614	−	11.6833i	−0.123228	−	0.379256i
$950$	0.0679415	−	0.209102i	0.00220431	−	0.00678418i
$951$		0			0
$952$	−14.8523	−	10.7908i	−0.481366	−	0.349733i
$953$	−11.0168	+	33.9064i	−0.356871	+	1.09833i	0.598046	+	0.801461i	$0.295944\pi$
$953$	−11.0168	+	33.9064i	−0.356871	+	1.09833i	−0.954917	+	0.296873i	$0.904056\pi$
$954$		0			0
$955$	14.8872	−	10.8162i	0.481739	−	0.350004i
$956$	0.0112353			0.000363374
$957$		0			0
$958$	54.1524			1.74958
$959$	3.13922	−	2.28077i	0.101371	−	0.0736501i
$960$		0			0
$961$	−6.70525	+	20.6366i	−0.216298	+	0.665698i
$962$	−7.49774	−	5.44743i	−0.241737	−	0.175632i
$963$		0			0
$964$	−0.0200402	+	0.0616775i	−0.000645452	+	0.00198650i
$965$	0.484535	+	1.49124i	0.0155977	+	0.0480049i
$966$		0			0
$967$	−20.0622			−0.645156			−0.322578	−	0.946543i	$-0.604549\pi$
$967$	−20.0622			−0.645156			−0.322578	+	0.946543i	$0.604549\pi$
$968$	27.5322	+	15.5360i	0.884918	+	0.499346i
$969$		0			0
$970$	−7.21180	+	5.23968i	−0.231557	+	0.168236i
$971$	12.8646	+	39.5931i	0.412844	+	1.27060i	0.914165	+	0.405342i	$0.132848\pi$
$971$	12.8646	+	39.5931i	0.412844	+	1.27060i	−0.501321	+	0.865261i	$0.667152\pi$
$972$		0			0
$973$	2.28622	+	1.66104i	0.0732929	+	0.0532504i
$974$	−9.30396	−	6.75972i	−0.298118	−	0.216596i
$975$		0			0
$976$	17.0522	+	52.4812i	0.545827	+	1.67988i
$977$	15.4297	−	11.2104i	0.493641	−	0.358651i	−0.312942	−	0.949772i	$-0.601315\pi$
$977$	15.4297	−	11.2104i	0.493641	−	0.358651i	0.806583	+	0.591121i	$0.201315\pi$
$978$		0			0
$979$	−13.2958	−	34.1330i	−0.424934	−	1.09089i
$980$	0.360637			0.0115201
$981$		0			0
$982$	5.21214	+	16.0413i	0.166326	+	0.511899i
$983$	−8.20635	+	25.2566i	−0.261742	+	0.805559i	0.730684	+	0.682716i	$0.239201\pi$
$983$	−8.20635	+	25.2566i	−0.261742	+	0.805559i	−0.992426	+	0.122843i	$0.960799\pi$
$984$		0			0
$985$	6.44787	+	4.68465i	0.205446	+	0.149265i
$986$	13.4794	−	41.4854i	0.429272	−	1.32116i
$987$		0			0
$988$	−0.0121922	+	0.00885813i	−0.000387884	+	0.000281815i
$989$	27.1111			0.862082
$990$		0			0
$991$	−24.2494			−0.770307			−0.385153	−	0.922853i	$-0.625851\pi$
$991$	−24.2494			−0.770307			−0.385153	+	0.922853i	$0.625851\pi$
$992$	−0.937341	+	0.681018i	−0.0297606	+	0.0216223i
$993$		0			0
$994$	3.71924	−	11.4466i	0.117967	−	0.363065i
$995$	−2.85697	−	2.07571i	−0.0905720	−	0.0658044i
$996$		0			0
$997$	4.96330	−	15.2755i	0.157189	−	0.483779i	−0.841187	−	0.540745i	$-0.818143\pi$
$997$	4.96330	−	15.2755i	0.157189	−	0.483779i	0.998376	+	0.0569657i	$0.0181426\pi$
$998$	−12.1830	−	37.4954i	−0.385646	−	1.18690i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.d.91.1		8
3.2	odd	2		165.2.m.a.91.2	✓	8
11.2	odd	10		5445.2.a.bv.1.1		4
11.4	even	5	inner	495.2.n.d.136.1		8
11.9	even	5		5445.2.a.be.1.4		4
15.2	even	4		825.2.bx.h.124.3		16
15.8	even	4		825.2.bx.h.124.2		16
15.14	odd	2		825.2.n.k.751.1		8
33.2	even	10		1815.2.a.o.1.4		4
33.20	odd	10		1815.2.a.x.1.1		4
33.26	odd	10		165.2.m.a.136.2	yes	8
165.59	odd	10		825.2.n.k.301.1		8
165.92	even	20		825.2.bx.h.499.2		16
165.119	odd	10		9075.2.a.cl.1.4		4
165.134	even	10		9075.2.a.dj.1.1		4
165.158	even	20		825.2.bx.h.499.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.91.2	✓	8	3.2	odd	2
165.2.m.a.136.2	yes	8	33.26	odd	10
495.2.n.d.91.1		8	1.1	even	1	trivial
495.2.n.d.136.1		8	11.4	even	5	inner
825.2.n.k.301.1		8	165.59	odd	10
825.2.n.k.751.1		8	15.14	odd	2
825.2.bx.h.124.2		16	15.8	even	4
825.2.bx.h.124.3		16	15.2	even	4
825.2.bx.h.499.2		16	165.92	even	20
825.2.bx.h.499.3		16	165.158	even	20
1815.2.a.o.1.4		4	33.2	even	10
1815.2.a.x.1.1		4	33.20	odd	10
5445.2.a.be.1.4		4	11.9	even	5
5445.2.a.bv.1.1		4	11.2	odd	10
9075.2.a.cl.1.4		4	165.119	odd	10
9075.2.a.dj.1.1		4	165.134	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12474 + 0.817172i) q^{2} +(-0.0207616 + 0.0638975i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.394797 - 1.21506i) q^{7} +(-0.888090 - 2.73326i) q^{8} +O(q^{10})\)	\(q+(-1.12474 + 0.817172i) q^{2} +(-0.0207616 + 0.0638975i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.394797 - 1.21506i) q^{7} +(-0.888090 - 2.73326i) q^{8} +1.39026 q^{10} +(1.20381 + 3.09044i) q^{11} +(1.14748 - 0.833694i) q^{13} +(0.548870 + 1.68925i) q^{14} +(3.12371 + 2.26951i) q^{16} +(4.04508 + 2.93893i) q^{17} +(0.0488697 + 0.150406i) q^{19} +(0.0543544 - 0.0394908i) q^{20} +(-3.87940 - 2.49222i) q^{22} +5.00829 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.609348 + 1.87538i) q^{26} +(0.0694428 + 0.0504531i) q^{28} +(-1.93913 + 5.96802i) q^{29} +(-2.46735 + 1.79264i) q^{31} +0.379898 q^{32} -6.95128 q^{34} +(-1.03359 + 0.750949i) q^{35} +(-1.45235 + 4.46988i) q^{37} +(-0.177873 - 0.129232i) q^{38} +(-0.888090 + 2.73326i) q^{40} +(-2.34419 - 7.21469i) q^{41} +5.41324 q^{43} +(-0.222465 + 0.0127583i) q^{44} +(-5.63303 + 4.09264i) q^{46} +(2.54386 + 7.82920i) q^{47} +(4.34261 + 3.15509i) q^{49} +(-1.12474 - 0.817172i) q^{50} +(0.0294475 + 0.0906300i) q^{52} +(7.57764 - 5.50548i) q^{53} +(0.842610 - 3.20780i) q^{55} -3.67169 q^{56} +(-2.69588 - 8.29708i) q^{58} +(-2.50256 + 7.70209i) q^{59} +(11.5623 + 8.40047i) q^{61} +(1.31024 - 4.03250i) q^{62} +(-6.67470 + 4.84945i) q^{64} -1.41837 q^{65} -7.38362 q^{67} +(-0.271772 + 0.197454i) q^{68} +(0.548870 - 1.68925i) q^{70} +(-5.48204 - 3.98294i) q^{71} +(2.67642 - 8.23717i) q^{73} +(-2.01914 - 6.21429i) q^{74} -0.0106252 q^{76} +(4.23034 - 0.242610i) q^{77} +(2.05953 - 1.49634i) q^{79} +(-1.19315 - 3.67214i) q^{80} +(8.53225 + 6.19905i) q^{82} +(8.18897 + 5.94964i) q^{83} +(-1.54508 - 4.75528i) q^{85} +(-6.08850 + 4.42355i) q^{86} +(7.37788 - 6.03493i) q^{88} -11.0447 q^{89} +(-0.559967 - 1.72340i) q^{91} +(-0.103980 + 0.320017i) q^{92} +(-9.25900 - 6.72705i) q^{94} +(0.0488697 - 0.150406i) q^{95} +(-5.18739 + 3.76886i) q^{97} -7.46257 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8}+O(q^{10}) \) 8 * q - 2 * q^4 - 2 * q^5 + q^7 - 5 * q^8	\( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8} - 10 q^{10} + 3 q^{11} + 6 q^{13} + 10 q^{14} - 20 q^{16} + 10 q^{17} + 6 q^{19} - 7 q^{20} - 25 q^{22} + 10 q^{23} - 2 q^{25} + 8 q^{26} + 31 q^{28} + 3 q^{31} - 60 q^{32} + 50 q^{34} + q^{35} - 19 q^{37} + 28 q^{38} - 5 q^{40} + 25 q^{41} - 4 q^{43} - 7 q^{44} - 6 q^{46} - 15 q^{47} + 21 q^{49} + 6 q^{52} - 7 q^{53} - 7 q^{55} - 20 q^{56} - 2 q^{58} - 35 q^{59} + 21 q^{61} + 19 q^{62} - 77 q^{64} + 6 q^{65} - 26 q^{67} + 35 q^{68} + 10 q^{70} - 25 q^{71} + q^{73} + 29 q^{74} - 14 q^{76} + 61 q^{77} + 30 q^{79} + 5 q^{80} + 57 q^{82} - 11 q^{83} + 10 q^{85} + 34 q^{86} - 85 q^{88} - 32 q^{89} + 37 q^{91} + 10 q^{92} - 39 q^{94} + 6 q^{95} + 5 q^{97} - 50 q^{98}+O(q^{100}) \) 8 * q - 2 * q^4 - 2 * q^5 + q^7 - 5 * q^8 - 10 * q^10 + 3 * q^11 + 6 * q^13 + 10 * q^14 - 20 * q^16 + 10 * q^17 + 6 * q^19 - 7 * q^20 - 25 * q^22 + 10 * q^23 - 2 * q^25 + 8 * q^26 + 31 * q^28 + 3 * q^31 - 60 * q^32 + 50 * q^34 + q^35 - 19 * q^37 + 28 * q^38 - 5 * q^40 + 25 * q^41 - 4 * q^43 - 7 * q^44 - 6 * q^46 - 15 * q^47 + 21 * q^49 + 6 * q^52 - 7 * q^53 - 7 * q^55 - 20 * q^56 - 2 * q^58 - 35 * q^59 + 21 * q^61 + 19 * q^62 - 77 * q^64 + 6 * q^65 - 26 * q^67 + 35 * q^68 + 10 * q^70 - 25 * q^71 + q^73 + 29 * q^74 - 14 * q^76 + 61 * q^77 + 30 * q^79 + 5 * q^80 + 57 * q^82 - 11 * q^83 + 10 * q^85 + 34 * q^86 - 85 * q^88 - 32 * q^89 + 37 * q^91 + 10 * q^92 - 39 * q^94 + 6 * q^95 + 5 * q^97 - 50 * q^98

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