LMFDB - Embedded newform 495.2.n.d.136.2

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			136.2
Root			$1.69513 + 1.23158i$ of defining polynomial
Character	$\chi$	$=$	495.136
Dual form			495.2.n.d.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24278 + 1.62947i) q^{2} +(1.75683 + 5.40697i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.703814 - 2.16612i) q^{7} +(-3.15700 + 9.71623i) q^{8} +O(q^{10})$	\(q+(2.24278 + 1.62947i) q^{2} +(1.75683 + 5.40697i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.703814 - 2.16612i) q^{7} +(-3.15700 + 9.71623i) q^{8} -2.77222 q^{10} +(0.105203 + 3.31496i) q^{11} +(0.352519 + 0.256120i) q^{13} +(1.95113 - 6.00496i) q^{14} +(-13.7139 + 9.96371i) q^{16} +(4.04508 - 2.93893i) q^{17} +(1.45113 - 4.46612i) q^{19} +(-4.59944 - 3.34169i) q^{20} +(-5.16568 + 7.60613i) q^{22} +0.845811 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.373280 + 1.14884i) q^{26} +(10.4756 - 7.61100i) q^{28} +(0.821093 + 2.52706i) q^{29} +(3.77637 + 2.74369i) q^{31} -26.5602 q^{32} +13.8611 q^{34} +(1.84261 + 1.33873i) q^{35} +(-2.73863 - 8.42864i) q^{37} +(10.5320 - 7.65193i) q^{38} +(-3.15700 - 9.71623i) q^{40} +(1.32697 - 4.08400i) q^{41} +7.00317 q^{43} +(-17.7390 + 6.39264i) q^{44} +(1.89696 + 1.37823i) q^{46} +(-0.144675 + 0.445265i) q^{47} +(1.46641 - 1.06541i) q^{49} +(2.24278 - 1.62947i) q^{50} +(-0.765515 + 2.35601i) q^{52} +(-8.76863 - 6.37078i) q^{53} +(-2.03359 - 2.62002i) q^{55} +23.2684 q^{56} +(-2.27625 + 7.00558i) q^{58} +(-1.21629 - 3.74334i) q^{59} +(-2.39913 + 1.74307i) q^{61} +(3.99878 + 12.3070i) q^{62} +(-32.1409 - 23.3517i) q^{64} -0.435737 q^{65} -2.47048 q^{67} +(22.9972 + 16.7084i) q^{68} +(1.95113 + 6.00496i) q^{70} +(-9.15321 + 6.65020i) q^{71} +(2.60474 + 8.01655i) q^{73} +(7.59209 - 23.3661i) q^{74} +26.6975 q^{76} +(7.10654 - 2.56099i) q^{77} +(8.79457 + 6.38963i) q^{79} +(5.23823 - 16.1216i) q^{80} +(9.63087 - 6.99723i) q^{82} +(-4.78978 + 3.47998i) q^{83} +(-1.54508 + 4.75528i) q^{85} +(15.7065 + 11.4115i) q^{86} +(-32.5410 - 9.44313i) q^{88} -5.89958 q^{89} +(0.306678 - 0.943857i) q^{91} +(1.48595 + 4.57327i) q^{92} +(-1.05002 + 0.762885i) q^{94} +(1.45113 + 4.46612i) q^{95} +(6.99640 + 5.08318i) q^{97} +5.02487 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.24278	+	1.62947i	1.58588	+	1.15221i	0.909535	+	0.415627i	$0.136438\pi$
$2$	2.24278	+	1.62947i	1.58588	+	1.15221i	0.676347	+	0.736584i	$0.263562\pi$
$3$		0			0
$3$		0			0
$4$	1.75683	+	5.40697i	0.878415	+	2.70348i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	−0.703814	−	2.16612i	−0.266017	−	0.818716i	−0.991457	−	0.130431i	$-0.958364\pi$
$7$	−0.703814	−	2.16612i	−0.266017	−	0.818716i	0.725441	−	0.688285i	$-0.241636\pi$
$8$	−3.15700	+	9.71623i	−1.11617	+	3.43521i
$9$		0			0
$10$	−2.77222			−0.876654
$11$	0.105203	+	3.31496i	0.0317198	+	0.999497i
$11$	0.105203	+	3.31496i	0.0317198	+	0.999497i
$12$		0			0
$13$	0.352519	+	0.256120i	0.0977711	+	0.0710348i	0.635597	−	0.772021i	$-0.280754\pi$
$13$	0.352519	+	0.256120i	0.0977711	+	0.0710348i	−0.537826	+	0.843056i	$0.680754\pi$
$14$	1.95113	−	6.00496i	0.521461	−	1.60489i
$15$		0			0
$16$	−13.7139	+	9.96371i	−3.42847	+	2.49093i
$17$	4.04508	−	2.93893i	0.981077	−	0.712794i	0.0231281	−	0.999733i	$-0.492637\pi$
$17$	4.04508	−	2.93893i	0.981077	−	0.712794i	0.957949	+	0.286938i	$0.0926374\pi$
$18$		0			0
$19$	1.45113	−	4.46612i	0.332912	−	1.02460i	−0.634829	−	0.772652i	$-0.718930\pi$
$19$	1.45113	−	4.46612i	0.332912	−	1.02460i	0.967741	−	0.251946i	$-0.0810704\pi$
$20$	−4.59944	−	3.34169i	−1.02847	−	0.747224i
$21$		0			0
$22$	−5.16568	+	7.60613i	−1.10133	+	1.62163i
$23$	0.845811			0.176364			0.0881819	−	0.996104i	$-0.471894\pi$
$23$	0.845811			0.176364			0.0881819	+	0.996104i	$0.471894\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.373280	+	1.14884i	0.0732063	+	0.225306i
$27$		0			0
$28$	10.4756	−	7.61100i	1.97971	−	1.43834i
$29$	0.821093	+	2.52706i	0.152473	+	0.469264i	0.997896	−	0.0648334i	$-0.0206516\pi$
$29$	0.821093	+	2.52706i	0.152473	+	0.469264i	−0.845423	+	0.534097i	$0.820652\pi$
$30$		0			0
$31$	3.77637	+	2.74369i	0.678256	+	0.492782i	0.872779	−	0.488116i	$-0.162316\pi$
$31$	3.77637	+	2.74369i	0.678256	+	0.492782i	−0.194523	+	0.980898i	$0.562316\pi$
$32$	−26.5602			−4.69523
$33$		0			0
$34$	13.8611			2.37716
$35$	1.84261	+	1.33873i	0.311458	+	0.226287i
$36$		0			0
$37$	−2.73863	−	8.42864i	−0.450228	−	1.38566i	−0.876647	−	0.481134i	$-0.840225\pi$
$37$	−2.73863	−	8.42864i	−0.450228	−	1.38566i	0.426419	−	0.904526i	$-0.359775\pi$
$38$	10.5320	−	7.65193i	1.70851	−	1.24131i
$39$		0			0
$40$	−3.15700	−	9.71623i	−0.499165	−	1.53627i
$41$	1.32697	−	4.08400i	0.207238	−	0.637814i	−0.792376	−	0.610033i	$-0.791156\pi$
$41$	1.32697	−	4.08400i	0.207238	−	0.637814i	0.999614	−	0.0277805i	$-0.00884395\pi$
$42$		0			0
$43$	7.00317			1.06797			0.533986	−	0.845493i	$-0.320693\pi$
$43$	7.00317			1.06797			0.533986	+	0.845493i	$0.320693\pi$
$44$	−17.7390	+	6.39264i	−2.67426	+	0.963727i
$45$		0			0
$46$	1.89696	+	1.37823i	0.279692	+	0.203208i
$47$	−0.144675	+	0.445265i	−0.0211031	+	0.0649485i	−0.961053	−	0.276363i	$-0.910871\pi$
$47$	−0.144675	+	0.445265i	−0.0211031	+	0.0649485i	0.939950	+	0.341311i	$0.110871\pi$
$48$		0			0
$49$	1.46641	−	1.06541i	0.209487	−	0.152201i
$50$	2.24278	−	1.62947i	0.317176	−	0.230442i
$51$		0			0
$52$	−0.765515	+	2.35601i	−0.106158	+	0.326720i
$53$	−8.76863	−	6.37078i	−1.20446	−	0.875094i	−0.209747	−	0.977756i	$-0.567264\pi$
$53$	−8.76863	−	6.37078i	−1.20446	−	0.875094i	−0.994716	+	0.102662i	$0.967264\pi$
$54$		0			0
$55$	−2.03359	−	2.62002i	−0.274210	−	0.353283i
$56$	23.2684			3.10938
$57$		0			0
$58$	−2.27625	+	7.00558i	−0.298887	+	0.919878i
$59$	−1.21629	−	3.74334i	−0.158347	−	0.487341i	0.840138	−	0.542373i	$-0.182474\pi$
$59$	−1.21629	−	3.74334i	−0.158347	−	0.487341i	−0.998485	+	0.0550316i	$0.982474\pi$
$60$		0			0
$61$	−2.39913	+	1.74307i	−0.307177	+	0.223177i	−0.730684	−	0.682715i	$-0.760799\pi$
$61$	−2.39913	+	1.74307i	−0.307177	+	0.223177i	0.423507	+	0.905893i	$0.360799\pi$
$62$	3.99878	+	12.3070i	0.507845	+	1.56299i
$63$		0			0
$64$	−32.1409	−	23.3517i	−4.01761	−	2.91897i
$65$	−0.435737			−0.0540465
$66$		0			0
$67$	−2.47048			−0.301817			−0.150909	−	0.988548i	$-0.548220\pi$
$67$	−2.47048			−0.301817			−0.150909	+	0.988548i	$0.548220\pi$
$68$	22.9972	+	16.7084i	2.78882	+	2.02620i
$69$		0			0
$70$	1.95113	+	6.00496i	0.233205	+	0.717730i
$71$	−9.15321	+	6.65020i	−1.08629	+	0.789233i	−0.978768	−	0.204970i	$-0.934290\pi$
$71$	−9.15321	+	6.65020i	−1.08629	+	0.789233i	−0.107518	+	0.994203i	$0.534290\pi$
$72$		0			0
$73$	2.60474	+	8.01655i	0.304861	+	0.938266i	0.979729	+	0.200328i	$0.0642007\pi$
$73$	2.60474	+	8.01655i	0.304861	+	0.938266i	−0.674868	+	0.737939i	$0.735799\pi$
$74$	7.59209	−	23.3661i	0.882563	−	2.71625i
$75$		0			0
$76$	26.6975			3.06242
$77$	7.10654	−	2.56099i	0.809866	−	0.291852i
$78$		0			0
$79$	8.79457	+	6.38963i	0.989466	+	0.718889i	0.959804	−	0.280671i	$-0.0905569\pi$
$79$	8.79457	+	6.38963i	0.989466	+	0.718889i	0.0296621	+	0.999560i	$0.490557\pi$
$80$	5.23823	−	16.1216i	0.585652	−	1.80245i
$81$		0			0
$82$	9.63087	−	6.99723i	1.06355	−	0.772715i
$83$	−4.78978	+	3.47998i	−0.525747	+	0.381978i	−0.818764	−	0.574130i	$-0.805341\pi$
$83$	−4.78978	+	3.47998i	−0.525747	+	0.381978i	0.293017	+	0.956107i	$0.405341\pi$
$84$		0			0
$85$	−1.54508	+	4.75528i	−0.167588	+	0.515783i
$86$	15.7065	+	11.4115i	1.69368	+	1.23053i
$87$		0			0
$88$	−32.5410	−	9.44313i	−3.46888	−	1.00664i
$89$	−5.89958			−0.625354			−0.312677	−	0.949859i	$-0.601226\pi$
$89$	−5.89958			−0.625354			−0.312677	+	0.949859i	$0.601226\pi$
$90$		0			0
$91$	0.306678	−	0.943857i	0.0321486	−	0.0989431i
$92$	1.48595	+	4.57327i	0.154921	+	0.476796i
$93$		0			0
$94$	−1.05002	+	0.762885i	−0.108301	+	0.0786855i
$95$	1.45113	+	4.46612i	0.148883	+	0.458214i
$96$		0			0
$97$	6.99640	+	5.08318i	0.710377	+	0.516119i	0.883295	−	0.468817i	$-0.155320\pi$
$97$	6.99640	+	5.08318i	0.710377	+	0.516119i	−0.172918	+	0.984936i	$0.555320\pi$
$98$	5.02487			0.507589
$99$		0			0
$100$	5.68522			0.568522
$101$	−4.59624	−	3.33936i	−0.457343	−	0.332279i	0.335145	−	0.942166i	$-0.391215\pi$
$101$	−4.59624	−	3.33936i	−0.457343	−	0.332279i	−0.792488	+	0.609887i	$0.791215\pi$
$102$		0			0
$103$	−0.400526	−	1.23269i	−0.0394650	−	0.121461i	0.929383	−	0.369117i	$-0.120340\pi$
$103$	−0.400526	−	1.23269i	−0.0394650	−	0.121461i	−0.968848	+	0.247656i	$0.920340\pi$
$104$	−3.60142	+	2.61658i	−0.353148	+	0.256577i
$105$		0			0
$106$	−9.28505	−	28.5765i	−0.901844	−	2.77559i
$107$	3.77024	−	11.6036i	0.364483	−	1.12176i	−0.585821	−	0.810441i	$-0.699228\pi$
$107$	3.77024	−	11.6036i	0.364483	−	1.12176i	0.950304	−	0.311324i	$-0.100772\pi$
$108$		0			0
$109$	−12.1644			−1.16514			−0.582568	−	0.812782i	$-0.697952\pi$
$109$	−12.1644			−1.16514			−0.582568	+	0.812782i	$0.697952\pi$
$110$	−0.291645	−	9.18980i	−0.0278073	−	0.876213i
$111$		0			0
$112$	31.2346	+	22.6933i	2.95139	+	2.14431i
$113$	−0.0438966	+	0.135100i	−0.00412944	+	0.0127091i	−0.953100	−	0.302656i	$-0.902127\pi$
$113$	−0.0438966	+	0.135100i	−0.00412944	+	0.0127091i	0.948971	+	0.315365i	$0.102127\pi$
$114$		0			0
$115$	−0.684276	+	0.497155i	−0.0638090	+	0.0463600i
$116$	−12.2212	+	8.87924i	−1.13471	+	0.824417i
$117$		0			0
$118$	3.37181	−	10.3774i	0.310401	−	0.955315i
$119$	−9.21305	−	6.69367i	−0.844559	−	0.613608i
$120$		0			0
$121$	−10.9779	+	0.697484i	−0.997988	+	0.0634077i
$122$	−8.22100			−0.744294
$123$		0			0
$124$	−8.20061	+	25.2389i	−0.736437	+	2.26652i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	0.407512	−	0.296075i	0.0361609	−	0.0262724i	−0.569558	−	0.821951i	$-0.692886\pi$
$127$	0.407512	−	0.296075i	0.0361609	−	0.0262724i	0.605719	+	0.795679i	$0.292886\pi$
$128$	−17.6187	−	54.2248i	−1.55729	−	4.79284i
$129$		0			0
$130$	−0.977260	−	0.710021i	−0.0857114	−	0.0622730i
$131$	−19.1098			−1.66963			−0.834816	−	0.550529i	$-0.814426\pi$
$131$	−19.1098			−1.66963			−0.834816	+	0.550529i	$0.814426\pi$
$132$		0			0
$133$	−10.6955			−0.927415
$134$	−5.54073	−	4.02558i	−0.478646	−	0.347757i
$135$		0			0
$136$	15.7850	+	48.5812i	1.35355	+	4.16580i
$137$	9.98713	−	7.25608i	0.853258	−	0.619929i	−0.0727841	−	0.997348i	$-0.523188\pi$
$137$	9.98713	−	7.25608i	0.853258	−	0.619929i	0.926043	+	0.377419i	$0.123188\pi$
$138$		0			0
$139$	−2.38943	−	7.35391i	−0.202669	−	0.623750i	−0.999801	−	0.0199456i	$-0.993651\pi$
$139$	−2.38943	−	7.35391i	−0.202669	−	0.623750i	0.797132	−	0.603805i	$-0.206349\pi$
$140$	−4.00134	+	12.3149i	−0.338175	+	1.04080i
$141$		0			0
$142$	−31.3649			−2.63208
$143$	−0.811940	+	1.19553i	−0.0678978	+	0.0999751i
$144$		0			0
$145$	−2.14965	−	1.56181i	−0.178519	−	0.129701i
$146$	−7.22091	+	22.2237i	−0.597607	+	1.83924i
$147$		0			0
$148$	40.7620	−	29.6154i	3.35062	−	2.43437i
$149$	6.15577	−	4.47243i	0.504301	−	0.366396i	−0.306357	−	0.951917i	$-0.599110\pi$
$149$	6.15577	−	4.47243i	0.504301	−	0.366396i	0.810657	+	0.585521i	$0.199110\pi$
$150$		0			0
$151$	−0.826389	+	2.54336i	−0.0672506	+	0.206976i	−0.979035	−	0.203694i	$-0.934705\pi$
$151$	−0.826389	+	2.54336i	−0.0672506	+	0.206976i	0.911784	+	0.410670i	$0.134705\pi$
$152$	38.8126	+	28.1990i	3.14812	+	2.28724i
$153$		0			0
$154$	20.1114	+	5.83617i	1.62063	+	0.470292i
$155$	−4.66785			−0.374931
$156$		0			0
$157$	6.24214	−	19.2113i	0.498177	−	1.53323i	−0.313770	−	0.949499i	$-0.601592\pi$
$157$	6.24214	−	19.2113i	0.498177	−	1.53323i	0.811947	−	0.583731i	$-0.198408\pi$
$158$	9.31252	+	28.6610i	0.740865	+	2.28015i
$159$		0			0
$160$	21.4877	−	15.6117i	1.69875	−	1.23421i
$161$	−0.595294	−	1.83213i	−0.0469157	−	0.144392i
$162$		0			0
$163$	7.92498	+	5.75784i	0.620733	+	0.450989i	0.853177	−	0.521621i	$-0.174672\pi$
$163$	7.92498	+	5.75784i	0.620733	+	0.450989i	−0.232445	+	0.972610i	$0.574672\pi$
$164$	24.4133			1.90636
$165$		0			0
$166$	−16.4129			−1.27389
$167$	20.6927	+	15.0341i	1.60125	+	1.16338i	0.885065	+	0.465467i	$0.154114\pi$
$167$	20.6927	+	15.0341i	1.60125	+	1.16338i	0.716185	+	0.697910i	$0.245886\pi$
$168$		0			0
$169$	−3.95855	−	12.1832i	−0.304504	−	0.937166i
$170$	−11.2139	+	8.14736i	−0.860065	+	0.624874i
$171$		0			0
$172$	12.3034	+	37.8659i	0.938123	+	2.88725i
$173$	2.08712	−	6.42349i	0.158681	−	0.488369i	−0.839834	−	0.542843i	$-0.817348\pi$
$173$	2.08712	−	6.42349i	0.158681	−	0.488369i	0.998515	+	0.0544734i	$0.0173480\pi$
$174$		0			0
$175$	−2.27759			−0.172170
$176$	−34.4720	−	44.4127i	−2.59843	−	3.34773i
$177$		0			0
$178$	−13.2314	−	9.61320i	−0.991738	−	0.720540i
$179$	−2.01539	+	6.20274i	−0.150638	+	0.463615i	−0.997693	−	0.0678901i	$-0.978373\pi$
$179$	−2.01539	+	6.20274i	−0.150638	+	0.463615i	0.847055	+	0.531505i	$0.178373\pi$
$180$		0			0
$181$	−11.1257	+	8.08332i	−0.826970	+	0.600829i	−0.918700	−	0.394955i	$-0.870760\pi$
$181$	−11.1257	+	8.08332i	−0.826970	+	0.600829i	0.0917306	+	0.995784i	$0.470760\pi$
$182$	2.22580	−	1.61714i	0.164987	−	0.119870i
$183$		0			0
$184$	−2.67022	+	8.21810i	−0.196851	+	0.605846i
$185$	7.16983	+	5.20918i	0.527136	+	0.382987i
$186$		0			0
$187$	10.1680	+	13.1001i	0.743555	+	0.957974i
$188$	−2.66170			−0.194124
$189$		0			0
$190$	−4.02286	+	12.3811i	−0.291849	+	0.898218i
$191$	6.00607	+	18.4848i	0.434584	+	1.33751i	0.893512	+	0.449038i	$0.148233\pi$
$191$	6.00607	+	18.4848i	0.434584	+	1.33751i	−0.458929	+	0.888473i	$0.651767\pi$
$192$		0			0
$193$	−18.2938	+	13.2912i	−1.31681	+	0.956722i	−0.316849	+	0.948476i	$0.602625\pi$
$193$	−18.2938	+	13.2912i	−1.31681	+	0.956722i	−0.999966	+	0.00824604i	$0.997375\pi$
$194$	7.40846	+	22.8009i	0.531896	+	1.63701i
$195$		0			0
$196$	8.33685	+	6.05707i	0.595489	+	0.432648i
$197$	−23.0300			−1.64082			−0.820410	−	0.571776i	$-0.806255\pi$
$197$	−23.0300			−1.64082			−0.820410	+	0.571776i	$0.806255\pi$
$198$		0			0
$199$	−19.6216			−1.39094			−0.695468	−	0.718557i	$-0.744803\pi$
$199$	−19.6216			−1.39094			−0.695468	+	0.718557i	$0.744803\pi$
$200$	8.26512	+	6.00496i	0.584432	+	0.424615i
$201$		0			0
$202$	−4.86693	−	14.9789i	−0.342436	−	1.05391i
$203$	4.89602	−	3.55717i	0.343633	−	0.249664i
$204$		0			0
$205$	1.32697	+	4.08400i	0.0926798	+	0.285239i
$206$	1.11035	−	3.41730i	0.0773616	−	0.238095i
$207$		0			0
$208$	−7.38630			−0.512148
$209$	14.9577	+	4.34059i	1.03464	+	0.300245i
$210$		0			0
$211$	−0.0403903	−	0.0293453i	−0.00278059	−	0.00202021i	0.586394	−	0.810026i	$-0.300547\pi$
$211$	−0.0403903	−	0.0293453i	−0.00278059	−	0.00202021i	−0.589175	+	0.808006i	$0.700547\pi$
$212$	19.0416	−	58.6040i	1.30778	−	4.02494i
$213$		0			0
$214$	27.3636	−	19.8808i	1.87054	−	1.35902i
$215$	−5.66568	+	4.11636i	−0.386396	+	0.280733i
$216$		0			0
$217$	3.28530	−	10.1111i	0.223021	−	0.686387i
$218$	−27.2819	−	19.8215i	−1.84777	−	1.34248i
$219$		0			0
$220$	10.5937	−	15.5985i	0.714226	−	1.05165i
$221$	2.17868			0.146554
$222$		0			0
$223$	0.233296	−	0.718012i	0.0156227	−	0.0480816i	−0.942941	−	0.332959i	$-0.891953\pi$
$223$	0.233296	−	0.718012i	0.0156227	−	0.0480816i	0.958564	+	0.284877i	$0.0919529\pi$
$224$	18.6935	+	57.5326i	1.24901	+	3.84406i
$225$		0			0
$226$	−0.318592	+	0.231470i	−0.0211924	+	0.0153972i
$227$	−2.55989	−	7.87855i	−0.169906	−	0.522917i	0.829458	−	0.558569i	$-0.188649\pi$
$227$	−2.55989	−	7.87855i	−0.169906	−	0.522917i	−0.999364	+	0.0356515i	$0.988649\pi$
$228$		0			0
$229$	2.32691	+	1.69060i	0.153767	+	0.111718i	0.662008	−	0.749496i	$-0.269704\pi$
$229$	2.32691	+	1.69060i	0.153767	+	0.111718i	−0.508242	+	0.861214i	$0.669704\pi$
$230$	−2.34478			−0.154610
$231$		0			0
$232$	−27.1457			−1.78220
$233$	−4.18964	−	3.04395i	−0.274473	−	0.199416i	0.442030	−	0.897000i	$-0.354258\pi$
$233$	−4.18964	−	3.04395i	−0.274473	−	0.199416i	−0.716503	+	0.697584i	$0.754258\pi$
$234$		0			0
$235$	−0.144675	−	0.445265i	−0.00943757	−	0.0290459i
$236$	18.1033	−	13.1528i	1.17842	−	0.856176i
$237$		0			0
$238$	−9.75565	−	30.0248i	−0.632365	−	1.94622i
$239$	−3.34751	+	10.3026i	−0.216532	+	0.666418i	0.782509	+	0.622640i	$0.213940\pi$
$239$	−3.34751	+	10.3026i	−0.216532	+	0.666418i	−0.999041	+	0.0437789i	$0.986060\pi$
$240$		0			0
$241$	−2.96526			−0.191009			−0.0955045	−	0.995429i	$-0.530446\pi$
$241$	−2.96526			−0.191009			−0.0955045	+	0.995429i	$0.530446\pi$
$242$	−25.7574	−	16.3238i	−1.65575	−	1.04933i
$243$		0			0
$244$	−13.6396	−	9.90974i	−0.873185	−	0.634406i
$245$	−0.560118	+	1.72386i	−0.0357846	+	0.110134i
$246$		0			0
$247$	1.65541	−	1.20273i	0.105331	−	0.0765277i
$248$	−38.5803	+	28.0302i	−2.44985	+	1.77992i
$249$		0			0
$250$	−0.856664	+	2.63654i	−0.0541802	+	0.166749i
$251$	−14.2504	−	10.3535i	−0.899475	−	0.653507i	0.0388560	−	0.999245i	$-0.487629\pi$
$251$	−14.2504	−	10.3535i	−0.899475	−	0.653507i	−0.938331	+	0.345738i	$0.887629\pi$
$252$		0			0
$253$	0.0889816	+	2.80383i	0.00559422	+	0.176275i
$254$	1.39640			0.0876182
$255$		0			0
$256$	24.2895	−	74.7554i	1.51809	−	4.67221i
$257$	−6.47845	−	19.9386i	−0.404115	−	1.24374i	−0.921632	−	0.388064i	$-0.873144\pi$
$257$	−6.47845	−	19.9386i	−0.404115	−	1.24374i	0.517518	−	0.855672i	$-0.326856\pi$
$258$		0			0
$259$	−16.3299	+	11.8644i	−1.01469	+	0.737217i
$260$	−0.765515	−	2.35601i	−0.0474753	−	0.146114i
$261$		0			0
$262$	−42.8590	−	31.1389i	−2.64784	−	1.92377i
$263$	−8.43471			−0.520107			−0.260053	−	0.965594i	$-0.583740\pi$
$263$	−8.43471			−0.520107			−0.260053	+	0.965594i	$0.583740\pi$
$264$		0			0
$265$	10.8386			0.665811
$266$	−23.9875	−	17.4280i	−1.47077	−	1.06858i
$267$		0			0
$268$	−4.34021	−	13.3578i	−0.265121	−	0.815958i
$269$	7.80173	−	5.66829i	0.475680	−	0.345601i	−0.323971	−	0.946067i	$-0.605018\pi$
$269$	7.80173	−	5.66829i	0.475680	−	0.345601i	0.799651	+	0.600466i	$0.205018\pi$
$270$		0			0
$271$	3.16056	+	9.72719i	0.191990	+	0.590885i	0.999999	+	0.00171395i	$0.000545568\pi$
$271$	3.16056	+	9.72719i	0.191990	+	0.590885i	−0.808008	+	0.589171i	$0.799454\pi$
$272$	−26.1912	+	80.6081i	−1.58807	+	4.88759i
$273$		0			0
$274$	34.2225			2.06746
$275$	3.18522	+	0.924324i	0.192076	+	0.0557388i
$276$		0			0
$277$	4.72388	+	3.43210i	0.283830	+	0.206215i	0.720586	−	0.693365i	$-0.243873\pi$
$277$	4.72388	+	3.43210i	0.283830	+	0.206215i	−0.436756	+	0.899580i	$0.643873\pi$
$278$	6.62403	−	20.3867i	0.397283	−	1.22271i
$279$		0			0
$280$	−18.8246	+	13.6768i	−1.12498	+	0.817348i
$281$	11.6611	−	8.47225i	0.695640	−	0.505412i	−0.182869	−	0.983137i	$-0.558539\pi$
$281$	11.6611	−	8.47225i	0.695640	−	0.505412i	0.878509	+	0.477725i	$0.158539\pi$
$282$		0			0
$283$	−3.28592	+	10.1130i	−0.195327	+	0.601156i	0.804645	+	0.593756i	$0.202356\pi$
$283$	−3.28592	+	10.1130i	−0.195327	+	0.601156i	−0.999973	+	0.00740011i	$0.997644\pi$
$284$	−52.0380	−	37.8078i	−3.08789	−	2.24348i
$285$		0			0
$286$	−3.76908	+	1.35827i	−0.222870	+	0.0803161i
$287$	−9.78037			−0.577317
$288$		0			0
$289$	2.47214	−	7.60845i	0.145420	−	0.447556i
$290$	−2.27625	−	7.00558i	−0.133666	−	0.411382i
$291$		0			0
$292$	−38.7691	+	28.1674i	−2.26879	+	1.64837i
$293$	2.59443	+	7.98484i	0.151568	+	0.466479i	0.997797	−	0.0663405i	$-0.0211323\pi$
$293$	2.59443	+	7.98484i	0.151568	+	0.466479i	−0.846229	+	0.532820i	$0.821132\pi$
$294$		0			0
$295$	3.18428	+	2.31351i	0.185396	+	0.134698i
$296$	90.5404			5.26256
$297$		0			0
$298$	21.0937			1.22193
$299$	0.298164	+	0.216629i	0.0172433	+	0.0125280i
$300$		0			0
$301$	−4.92893	−	15.1697i	−0.284099	−	0.874366i
$302$	−5.99774	+	4.35762i	−0.345131	+	0.250753i
$303$		0			0
$304$	24.5985	+	75.7065i	1.41082	+	4.34206i
$305$	0.916387	−	2.82035i	0.0524721	−	0.161493i
$306$		0			0
$307$	4.51902			0.257914			0.128957	−	0.991650i	$-0.458837\pi$
$307$	4.51902			0.257914			0.128957	+	0.991650i	$0.458837\pi$
$308$	26.3322	+	33.9256i	1.50042	+	1.93309i
$309$		0			0
$310$	−10.4689	−	7.60613i	−0.594596	−	0.431999i
$311$	−7.41548	+	22.8225i	−0.420493	+	1.29415i	0.486751	+	0.873541i	$0.338182\pi$
$311$	−7.41548	+	22.8225i	−0.420493	+	1.29415i	−0.907244	+	0.420604i	$0.861818\pi$
$312$		0			0
$313$	20.9281	−	15.2052i	1.18293	−	0.859448i	0.190430	−	0.981701i	$-0.439012\pi$
$313$	20.9281	−	15.2052i	1.18293	−	0.859448i	0.992499	+	0.122253i	$0.0390118\pi$
$314$	45.3040	−	32.9153i	2.55665	−	1.85752i
$315$		0			0
$316$	−19.0979	+	58.7774i	−1.07434	+	3.30649i
$317$	2.34873	+	1.70645i	0.131918	+	0.0958441i	0.651787	−	0.758402i	$-0.274019\pi$
$317$	2.34873	+	1.70645i	0.131918	+	0.0958441i	−0.519869	+	0.854246i	$0.674019\pi$
$318$		0			0
$319$	−8.29072	+	2.98774i	−0.464191	+	0.167281i
$320$	39.7283			2.22088
$321$		0			0
$322$	1.65029	−	5.07906i	0.0919669	−	0.283045i
$323$	−7.25565	−	22.3306i	−0.403715	−	1.24251i
$324$		0			0
$325$	0.352519	−	0.256120i	0.0195542	−	0.0142070i
$326$	8.39172	+	25.8271i	0.464775	+	1.43043i
$327$		0			0
$328$	35.4919	+	25.7863i	1.95971	+	1.42381i
$329$	1.06632			0.0587881
$330$		0			0
$331$	10.9837			0.603720			0.301860	−	0.953352i	$-0.402392\pi$
$331$	10.9837			0.603720			0.301860	+	0.953352i	$0.402392\pi$
$332$	−27.2310	−	19.7845i	−1.49449	−	1.08581i
$333$		0			0
$334$	21.9114	+	67.4364i	1.19894	+	3.68996i
$335$	1.99866	−	1.45211i	0.109199	−	0.0793374i
$336$		0			0
$337$	3.96968	+	12.2174i	0.216242	+	0.665525i	0.999063	+	0.0432780i	$0.0137801\pi$
$337$	3.96968	+	12.2174i	0.216242	+	0.665525i	−0.782821	+	0.622247i	$0.786220\pi$
$338$	10.9740	−	33.7744i	0.596906	−	1.83709i
$339$		0			0
$340$	−28.4261			−1.54162
$341$	−8.69793	+	12.8071i	−0.471020	+	0.693545i
$342$		0			0
$343$	−16.2381	−	11.7977i	−0.876777	−	0.637016i
$344$	−22.1090	+	68.0444i	−1.19204	+	3.66871i
$345$		0			0
$346$	15.1478	−	11.0056i	0.814353	−	0.591662i
$347$	−1.52881	+	1.11074i	−0.0820707	+	0.0596279i	−0.628064	−	0.778162i	$-0.716152\pi$
$347$	−1.52881	+	1.11074i	−0.0820707	+	0.0596279i	0.545993	+	0.837790i	$0.316152\pi$
$348$		0			0
$349$	7.34802	−	22.6149i	0.393330	−	1.21055i	−0.536924	−	0.843631i	$-0.680414\pi$
$349$	7.34802	−	22.6149i	0.393330	−	1.21055i	0.930254	−	0.366915i	$-0.119586\pi$
$350$	−5.10813	−	3.71127i	−0.273041	−	0.198376i
$351$		0			0
$352$	−2.79421	−	88.0460i	−0.148932	−	4.69287i
$353$	20.2294			1.07670			0.538352	−	0.842720i	$-0.319047\pi$
$353$	20.2294			1.07670			0.538352	+	0.842720i	$0.319047\pi$
$354$		0			0
$355$	3.49622	−	10.7602i	0.185560	−	0.571094i
$356$	−10.3646	−	31.8988i	−0.549321	−	1.69063i
$357$		0			0
$358$	−14.6273	+	10.6273i	−0.773075	+	0.561672i
$359$	5.74455	+	17.6799i	0.303186	+	0.933109i	0.980348	+	0.197276i	$0.0632094\pi$
$359$	5.74455	+	17.6799i	0.303186	+	0.933109i	−0.677162	+	0.735834i	$0.736791\pi$
$360$		0			0
$361$	−2.46912	−	1.79392i	−0.129954	−	0.0944170i
$362$	−38.1241			−2.00376
$363$		0			0
$364$	5.64219			0.295731
$365$	−6.81929	−	4.95450i	−0.356938	−	0.259330i
$366$		0			0
$367$	1.82571	+	5.61894i	0.0953010	+	0.293306i	0.987332	−	0.158668i	$-0.0507199\pi$
$367$	1.82571	+	5.61894i	0.0953010	+	0.293306i	−0.892031	+	0.451974i	$0.850720\pi$
$368$	−11.5993	+	8.42742i	−0.604658	+	0.439310i
$369$		0			0
$370$	7.59209	+	23.3661i	0.394694	+	1.21474i
$371$	−7.62838	+	23.4777i	−0.396046	+	1.21890i
$372$		0			0
$373$	−1.66992			−0.0864650			−0.0432325	−	0.999065i	$-0.513766\pi$
$373$	−1.66992			−0.0864650			−0.0432325	+	0.999065i	$0.513766\pi$
$374$	1.45823	+	45.9490i	0.0754031	+	2.37597i
$375$		0			0
$376$	−3.86956	−	2.81140i	−0.199557	−	0.144987i
$377$	−0.357780	+	1.10113i	−0.0184266	+	0.0567113i
$378$		0			0
$379$	−6.82420	+	4.95807i	−0.350536	+	0.254679i	−0.749094	−	0.662464i	$-0.769511\pi$
$379$	−6.82420	+	4.95807i	−0.350536	+	0.254679i	0.398558	+	0.917143i	$0.369511\pi$
$380$	−21.5988	+	15.6924i	−1.10799	+	0.805004i
$381$		0			0
$382$	−16.6502	+	51.2439i	−0.851896	+	2.62187i
$383$	17.7025	+	12.8616i	0.904558	+	0.657199i	0.939633	−	0.342185i	$-0.111167\pi$
$383$	17.7025	+	12.8616i	0.904558	+	0.657199i	−0.0350750	+	0.999385i	$0.511167\pi$
$384$		0			0
$385$	−4.24400	+	6.24901i	−0.216294	+	0.318479i
$386$	−62.6865			−3.19066
$387$		0			0
$388$	−15.1931	+	46.7596i	−0.771314	+	2.37386i
$389$	0.121163	+	0.372902i	0.00614322	+	0.0189069i	0.954081	−	0.299548i	$-0.0968360\pi$
$389$	0.121163	+	0.372902i	0.00614322	+	0.0189069i	−0.947938	+	0.318455i	$0.896836\pi$
$390$		0			0
$391$	3.42138	−	2.48578i	0.173027	−	0.125711i
$392$	5.72230	+	17.6114i	0.289020	+	0.889512i
$393$		0			0
$394$	−51.6511	−	37.5267i	−2.60215	−	1.89057i
$395$	−10.8707			−0.546963
$396$		0			0
$397$	35.7823			1.79586			0.897932	−	0.440134i	$-0.145069\pi$
$397$	35.7823			1.79586			0.897932	+	0.440134i	$0.145069\pi$
$398$	−44.0068	−	31.9728i	−2.20586	−	1.60265i
$399$		0			0
$400$	5.23823	+	16.1216i	0.261912	+	0.806081i
$401$	24.6074	−	17.8783i	1.22884	−	0.892802i	0.232034	−	0.972708i	$-0.425462\pi$
$401$	24.6074	−	17.8783i	1.22884	−	0.892802i	0.996802	+	0.0799056i	$0.0254619\pi$
$402$		0			0
$403$	0.628526	+	1.93440i	0.0313091	+	0.0963596i
$404$	9.98101	−	30.7184i	0.496574	−	1.52830i
$405$		0			0
$406$	16.7770			0.832627
$407$	27.6524	−	9.96515i	1.37068	−	0.493954i
$408$		0			0
$409$	13.1625	+	9.56310i	0.650843	+	0.472865i	0.863558	−	0.504249i	$-0.168231\pi$
$409$	13.1625	+	9.56310i	0.650843	+	0.472865i	−0.212715	+	0.977114i	$0.568231\pi$
$410$	−3.67866	+	11.3218i	−0.181676	+	0.559142i
$411$		0			0
$412$	5.96147	−	4.33126i	0.293701	−	0.213386i
$413$	−7.25248	+	5.26923i	−0.356871	+	0.259282i
$414$		0			0
$415$	1.82953	−	5.63073i	0.0898083	−	0.276402i
$416$	−9.36298	−	6.80260i	−0.459058	−	0.333525i
$417$		0			0
$418$	26.4738	+	34.1080i	1.29488	+	1.66828i
$419$	40.0703			1.95756			0.978781	−	0.204910i	$-0.0656903\pi$
$419$	40.0703			1.95756			0.978781	+	0.204910i	$0.0656903\pi$
$420$		0			0
$421$	−5.99316	+	18.4450i	−0.292089	+	0.898956i	0.692095	+	0.721806i	$0.256688\pi$
$421$	−5.99316	+	18.4450i	−0.292089	+	0.898956i	−0.984184	+	0.177150i	$0.943312\pi$
$422$	−0.0427691	−	0.131630i	−0.00208197	−	0.00640764i
$423$		0			0
$424$	89.5825	−	65.0855i	4.35051	−	3.16083i
$425$	−1.54508	−	4.75528i	−0.0749476	−	0.230665i
$426$		0			0
$427$	5.46424	+	3.97000i	0.264433	+	0.192122i
$428$	69.3640			3.35284
$429$		0			0
$430$	−19.4143			−0.936243
$431$	27.4616	+	19.9520i	1.32278	+	0.961056i	0.999893	+	0.0146183i	$0.00465332\pi$
$431$	27.4616	+	19.9520i	1.32278	+	0.961056i	0.322887	+	0.946438i	$0.395347\pi$
$432$		0			0
$433$	−4.05291	−	12.4736i	−0.194770	−	0.599442i	−0.999979	−	0.00645020i	$-0.997947\pi$
$433$	−4.05291	−	12.4736i	−0.194770	−	0.599442i	0.805209	−	0.592991i	$-0.202053\pi$
$434$	23.8440	−	17.3236i	1.14455	−	0.831562i
$435$		0			0
$436$	−21.3707	−	65.7723i	−1.02347	−	3.14992i
$437$	1.22738	−	3.77749i	0.0587136	−	0.180702i
$438$		0			0
$439$	−9.64731			−0.460441			−0.230220	−	0.973138i	$-0.573945\pi$
$439$	−9.64731			−0.460441			−0.230220	+	0.973138i	$0.573945\pi$
$440$	31.8768	−	11.4875i	1.51966	−	0.547644i
$441$		0			0
$442$	4.88630	+	3.55010i	0.232418	+	0.168861i
$443$	2.75461	−	8.47781i	0.130875	−	0.402793i	−0.864050	−	0.503405i	$-0.832080\pi$
$443$	2.75461	−	8.47781i	0.130875	−	0.402793i	0.994926	+	0.100613i	$0.0320802\pi$
$444$		0			0
$445$	4.77286	−	3.46769i	0.226255	−	0.164384i
$446$	1.69321	−	1.23019i	0.0801759	−	0.0582512i
$447$		0			0
$448$	−27.9614	+	86.0562i	−1.32105	+	4.06578i
$449$	−10.0616	−	7.31019i	−0.474837	−	0.344989i	0.324487	−	0.945890i	$-0.394809\pi$
$449$	−10.0616	−	7.31019i	−0.474837	−	0.344989i	−0.799323	+	0.600901i	$0.794809\pi$
$450$		0			0
$451$	13.6779	+	3.96921i	0.644066	+	0.186903i
$452$	−0.807599			−0.0379863
$453$		0			0
$454$	7.09660	−	21.8411i	0.333060	−	1.02505i
$455$	0.306678	+	0.943857i	0.0143773	+	0.0442487i
$456$		0			0
$457$	30.8707	−	22.4289i	1.44407	−	1.04918i	0.456898	−	0.889519i	$-0.348960\pi$
$457$	30.8707	−	22.4289i	1.44407	−	1.04918i	0.987172	−	0.159659i	$-0.0510395\pi$
$458$	2.46395	+	7.58327i	0.115133	+	0.354343i
$459$		0			0
$460$	−3.89026	−	2.82644i	−0.181384	−	0.131783i
$461$	−34.3847			−1.60145			−0.800726	−	0.599030i	$-0.795553\pi$
$461$	−34.3847			−1.60145			−0.800726	+	0.599030i	$0.795553\pi$
$462$		0			0
$463$	−40.2561			−1.87086			−0.935430	−	0.353511i	$-0.884988\pi$
$463$	−40.2561			−1.87086			−0.935430	+	0.353511i	$0.884988\pi$
$464$	−36.4393	−	26.4747i	−1.69165	−	1.22906i
$465$		0			0
$466$	−4.43639	−	13.6538i	−0.205512	−	0.632501i
$467$	12.2292	−	8.88502i	0.565899	−	0.411150i	−0.267714	−	0.963498i	$-0.586268\pi$
$467$	12.2292	−	8.88502i	0.565899	−	0.411150i	0.833613	+	0.552349i	$0.186268\pi$
$468$		0			0
$469$	1.73876	+	5.35135i	0.0802885	+	0.247102i
$470$	0.401072	−	1.23437i	0.0185001	−	0.0569374i
$471$		0			0
$472$	40.2110			1.85086
$473$	0.736752	+	23.2152i	0.0338759	+	1.06744i
$474$		0			0
$475$	−3.79911	−	2.76021i	−0.174315	−	0.126647i
$476$	20.0067	−	61.5743i	0.917005	−	2.82225i
$477$		0			0
$478$	−24.2955	+	17.6517i	−1.11125	+	0.807370i
$479$	−23.3033	+	16.9308i	−1.06476	+	0.773590i	−0.974962	−	0.222370i	$-0.928621\pi$
$479$	−23.3033	+	16.9308i	−1.06476	+	0.773590i	−0.0897931	+	0.995960i	$0.528621\pi$
$480$		0			0
$481$	1.19332	−	3.67267i	0.0544108	−	0.167459i
$482$	−6.65040	−	4.83180i	−0.302918	−	0.220083i
$483$		0			0
$484$	−23.0575	−	58.1316i	−1.04807	−	2.64234i
$485$	−8.64803			−0.392687
$486$		0			0
$487$	8.91592	−	27.4404i	0.404019	−	1.24344i	−0.517693	−	0.855567i	$-0.673209\pi$
$487$	8.91592	−	27.4404i	0.404019	−	1.24344i	0.921712	−	0.387876i	$-0.126791\pi$
$488$	−9.36204	−	28.8134i	−0.423799	−	1.30432i
$489$		0			0
$490$	−4.06521	+	2.95355i	−0.183647	+	0.133428i
$491$	4.61569	+	14.2056i	0.208303	+	0.641092i	0.999562	+	0.0296097i	$0.00942643\pi$
$491$	4.61569	+	14.2056i	0.208303	+	0.641092i	−0.791258	+	0.611482i	$0.790574\pi$
$492$		0			0
$493$	10.7482	+	7.80906i	0.484076	+	0.351702i
$494$	5.67253			0.255219
$495$		0			0
$496$	−79.1260			−3.55286
$497$	20.8473	+	15.1464i	0.935128	+	0.679410i
$498$		0			0
$499$	6.85987	+	21.1125i	0.307090	+	0.945125i	0.978889	+	0.204392i	$0.0655218\pi$
$499$	6.85987	+	21.1125i	0.307090	+	0.945125i	−0.671799	+	0.740733i	$0.734478\pi$
$500$	−4.59944	+	3.34169i	−0.205693	+	0.149445i
$501$		0			0
$502$	−15.0896	−	46.4411i	−0.673484	−	2.07277i
$503$	−0.0480077	+	0.147752i	−0.00214056	+	0.00658795i	−0.952121	−	0.305721i	$-0.901102\pi$
$503$	−0.0480077	+	0.147752i	−0.00214056	+	0.00658795i	0.949981	+	0.312309i	$0.101102\pi$
$504$		0			0
$505$	5.68126			0.252813
$506$	−4.36919	+	6.43335i	−0.194234	+	0.285997i
$507$		0			0
$508$	2.31680	+	1.68325i	0.102791	+	0.0746822i
$509$	5.75932	−	17.7254i	0.255277	−	0.785663i	−0.738498	−	0.674256i	$-0.764464\pi$
$509$	5.75932	−	17.7254i	0.255277	−	0.785663i	0.993775	−	0.111407i	$-0.0355356\pi$
$510$		0			0
$511$	15.5315	−	11.2843i	0.687075	−	0.499189i
$512$	84.0350	−	61.0550i	3.71386	−	2.69828i
$513$		0			0
$514$	17.9597	−	55.2743i	0.792169	−	2.43804i
$515$	1.04859	+	0.761846i	0.0462065	+	0.0335710i
$516$		0			0
$517$	−1.49125	−	0.432749i	−0.0655852	−	0.0190323i
$518$	−55.9571			−2.45861
$519$		0			0
$520$	1.37562	−	4.23372i	0.0603249	−	0.185661i
$521$	−9.69969	−	29.8526i	−0.424951	−	1.30786i	−0.903041	−	0.429554i	$-0.858671\pi$
$521$	−9.69969	−	29.8526i	−0.424951	−	1.30786i	0.478090	−	0.878311i	$-0.341329\pi$
$522$		0			0
$523$	19.4036	−	14.0975i	0.848459	−	0.616442i	−0.0762616	−	0.997088i	$-0.524298\pi$
$523$	19.4036	−	14.0975i	0.848459	−	0.616442i	0.924721	+	0.380646i	$0.124298\pi$
$524$	−33.5727	−	103.326i	−1.46663	−	4.51382i
$525$		0			0
$526$	−18.9172	−	13.7441i	−0.824828	−	0.599272i
$527$	23.3392			1.01667
$528$		0			0
$529$	−22.2846			−0.968896
$530$	24.3086	+	17.6612i	1.05590	+	0.767154i
$531$		0			0
$532$	−18.7901	−	57.8300i	−0.814655	−	2.50725i
$533$	1.51378	−	1.09982i	0.0655689	−	0.0476386i
$534$		0			0
$535$	3.77024	+	11.6036i	0.163002	+	0.501668i
$536$	7.79929	−	24.0038i	0.336878	−	1.03680i
$537$		0			0
$538$	26.7338			1.15258
$539$	3.68605	+	4.74899i	0.158769	+	0.204554i
$540$		0			0
$541$	−8.06851	−	5.86211i	−0.346892	−	0.252032i	0.400672	−	0.916222i	$-0.368777\pi$
$541$	−8.06851	−	5.86211i	−0.346892	−	0.252032i	−0.747564	+	0.664190i	$0.768777\pi$
$542$	−8.76177	+	26.9660i	−0.376350	+	1.15829i
$543$		0			0
$544$	−107.438	+	78.0586i	−4.60638	+	3.34673i
$545$	9.84118	−	7.15004i	0.421550	−	0.306274i
$546$		0			0
$547$	−12.3659	+	38.0582i	−0.528726	+	1.62725i	0.228103	+	0.973637i	$0.426748\pi$
$547$	−12.3659	+	38.0582i	−0.528726	+	1.62725i	−0.756829	+	0.653614i	$0.773252\pi$
$548$	56.7791	+	41.2524i	2.42548	+	1.76222i
$549$		0			0
$550$	5.63757	+	7.26328i	0.240387	+	0.309707i
$551$	12.4777			0.531567
$552$		0			0
$553$	7.65094	−	23.5472i	0.325351	−	1.00133i
$554$	5.00209	+	15.3948i	0.212518	+	0.654064i
$555$		0			0
$556$	35.5645	−	25.8391i	1.50827	−	1.09582i
$557$	2.39812	+	7.38064i	0.101611	+	0.312728i	0.988920	−	0.148448i	$-0.0474278\pi$
$557$	2.39812	+	7.38064i	0.101611	+	0.312728i	−0.887309	+	0.461176i	$0.847428\pi$
$558$		0			0
$559$	2.46875	+	1.79365i	0.104417	+	0.0758633i
$560$	−38.6081			−1.63149
$561$		0			0
$562$	39.9584			1.68554
$563$	14.9146	+	10.8361i	0.628577	+	0.456688i	0.855907	−	0.517130i	$-0.173000\pi$
$563$	14.9146	+	10.8361i	0.628577	+	0.456688i	−0.227330	+	0.973818i	$0.573000\pi$
$564$		0			0
$565$	−0.0438966	−	0.135100i	−0.00184674	−	0.00568369i
$566$	−23.8484	+	17.3269i	−1.00242	+	0.728304i
$567$		0			0
$568$	−35.7182	−	109.929i	−1.49870	−	4.61253i
$569$	−3.40658	+	10.4844i	−0.142811	+	0.439528i	−0.996723	−	0.0808896i	$-0.974224\pi$
$569$	−3.40658	+	10.4844i	−0.142811	+	0.439528i	0.853912	+	0.520418i	$0.174224\pi$
$570$		0			0
$571$	−38.1338			−1.59585			−0.797926	−	0.602756i	$-0.794069\pi$
$571$	−38.1338			−1.59585			−0.797926	+	0.602756i	$0.794069\pi$
$572$	−7.89062	−	2.28979i	−0.329923	−	0.0957410i
$573$		0			0
$574$	−21.9352	−	15.9368i	−0.915556	−	0.665191i
$575$	0.261370	−	0.804414i	0.0108999	−	0.0335464i
$576$		0			0
$577$	−8.90910	+	6.47284i	−0.370891	+	0.269468i	−0.757580	−	0.652742i	$-0.773618\pi$
$577$	−8.90910	+	6.47284i	−0.370891	+	0.269468i	0.386690	+	0.922210i	$0.373618\pi$
$578$	17.9422	−	13.0358i	0.746297	−	0.542217i
$579$		0			0
$580$	4.66809	−	14.3669i	0.193832	−	0.596553i
$581$	10.9092	+	7.92597i	0.452589	+	0.328825i
$582$		0			0
$583$	20.1964	−	29.7378i	0.836448	−	1.23162i
$584$	−86.1138			−3.56341
$585$		0			0
$586$	−7.19234	+	22.1358i	−0.297113	+	0.914420i
$587$	−3.65999	−	11.2643i	−0.151064	−	0.464927i	0.846677	−	0.532107i	$-0.178600\pi$
$587$	−3.65999	−	11.2643i	−0.151064	−	0.464927i	−0.997741	+	0.0671803i	$0.978600\pi$
$588$		0			0
$589$	17.7337	−	12.8843i	0.730703	−	0.530887i
$590$	3.37181	+	10.3774i	0.138815	+	0.427230i
$591$		0			0
$592$	121.538	+	88.3024i	4.99517	+	3.62920i
$593$	−9.25062			−0.379877			−0.189939	−	0.981796i	$-0.560829\pi$
$593$	−9.25062			−0.379877			−0.189939	+	0.981796i	$0.560829\pi$
$594$		0			0
$595$	11.3880			0.466861
$596$	34.9969	+	25.4267i	1.43353	+	1.04152i
$597$		0			0
$598$	0.315724	+	0.971700i	0.0129109	+	0.0397358i
$599$	19.1603	−	13.9208i	0.782868	−	0.568787i	−0.122971	−	0.992410i	$-0.539242\pi$
$599$	19.1603	−	13.9208i	0.782868	−	0.568787i	0.905838	+	0.423624i	$0.139242\pi$
$600$		0			0
$601$	11.2090	+	34.4978i	0.457225	+	1.40719i	0.868503	+	0.495684i	$0.165083\pi$
$601$	11.2090	+	34.4978i	0.457225	+	1.40719i	−0.411278	+	0.911510i	$0.634917\pi$
$602$	13.6641	−	42.0537i	0.556907	−	1.71398i
$603$		0			0
$604$	−15.2037			−0.618630
$605$	8.47131	−	7.01690i	0.344408	−	0.285278i
$606$		0			0
$607$	19.8264	+	14.4047i	0.804728	+	0.584669i	0.912297	−	0.409528i	$-0.134307\pi$
$607$	19.8264	+	14.4047i	0.804728	+	0.584669i	−0.107569	+	0.994198i	$0.534307\pi$
$608$	−38.5424	+	118.621i	−1.56310	+	4.81072i
$609$		0			0
$610$	6.65093	−	4.83218i	0.269288	−	0.195649i
$611$	−0.165042	+	0.119910i	−0.00667688	+	0.00485103i
$612$		0			0
$613$	1.43538	−	4.41763i	0.0579743	−	0.178427i	−0.917876	−	0.396868i	$-0.870097\pi$
$613$	1.43538	−	4.41763i	0.0579743	−	0.178427i	0.975850	+	0.218441i	$0.0700972\pi$
$614$	10.1351	+	7.36361i	0.409021	+	0.297171i
$615$		0			0
$616$	2.44790	+	77.1339i	0.0986288	+	3.10781i
$617$	−41.7419			−1.68047			−0.840233	−	0.542226i	$-0.817582\pi$
$617$	−41.7419			−1.68047			−0.840233	+	0.542226i	$0.817582\pi$
$618$		0			0
$619$	−13.6592	+	42.0385i	−0.549008	+	1.68967i	0.162258	+	0.986748i	$0.448122\pi$
$619$	−13.6592	+	42.0385i	−0.549008	+	1.68967i	−0.711266	+	0.702923i	$0.751878\pi$
$620$	−8.20061	−	25.2389i	−0.329345	−	1.01362i
$621$		0			0
$622$	−53.8199	+	39.1024i	−2.15798	+	1.56786i
$623$	4.15221	+	12.7792i	0.166355	+	0.511987i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	71.7136			2.86625
$627$		0			0
$628$	114.841			4.58267
$629$	−35.8491	−	26.0459i	−1.42940	−	1.03852i
$630$		0			0
$631$	−4.98015	−	15.3273i	−0.198257	−	0.610171i	−0.999923	−	0.0123995i	$-0.996053\pi$
$631$	−4.98015	−	15.3273i	−0.198257	−	0.610171i	0.801667	−	0.597771i	$-0.203947\pi$
$632$	−89.8475	+	65.2780i	−3.57394	+	2.59662i
$633$		0			0
$634$	2.48706	+	7.65439i	0.0987739	+	0.303995i
$635$	−0.155656	+	0.479059i	−0.00617701	+	0.0190109i
$636$		0			0
$637$	0.789807			0.0312933
$638$	−23.4627	−	6.80867i	−0.928896	−	0.269558i
$639$		0			0
$640$	46.1264	+	33.5128i	1.82330	+	1.32471i
$641$	2.84600	−	8.75909i	0.112410	−	0.345963i	−0.878988	−	0.476844i	$-0.841781\pi$
$641$	2.84600	−	8.75909i	0.112410	−	0.345963i	0.991398	+	0.130881i	$0.0417806\pi$
$642$		0			0
$643$	−3.24845	+	2.36014i	−0.128106	+	0.0930747i	−0.649993	−	0.759940i	$-0.725228\pi$
$643$	−3.24845	+	2.36014i	−0.128106	+	0.0930747i	0.521887	+	0.853015i	$0.325228\pi$
$644$	8.86041	−	6.43747i	0.349149	−	0.253672i
$645$		0			0
$646$	20.1143	−	61.9054i	0.791386	−	2.43564i
$647$	11.5441	+	8.38728i	0.453846	+	0.329738i	0.791112	−	0.611671i	$-0.209502\pi$
$647$	11.5441	+	8.38728i	0.453846	+	0.329738i	−0.337267	+	0.941409i	$0.609502\pi$
$648$		0			0
$649$	12.2811	−	4.42574i	0.482073	−	0.173726i
$650$	1.20796			0.0473801
$651$		0			0
$652$	−17.2096	+	52.9656i	−0.673979	+	2.07429i
$653$	2.01532	+	6.20252i	0.0788656	+	0.242723i	0.982714	−	0.185129i	$-0.0592703\pi$
$653$	2.01532	+	6.20252i	0.0788656	+	0.242723i	−0.903849	+	0.427852i	$0.859270\pi$
$654$		0			0
$655$	15.4602	−	11.2325i	0.604078	−	0.438889i
$656$	22.4939	+	69.2291i	0.878239	+	2.70294i
$657$		0			0
$658$	2.39152	+	1.73754i	0.0932311	+	0.0677363i
$659$	−6.74928			−0.262915			−0.131457	−	0.991322i	$-0.541966\pi$
$659$	−6.74928			−0.262915			−0.131457	+	0.991322i	$0.541966\pi$
$660$		0			0
$661$	9.65248			0.375438			0.187719	−	0.982223i	$-0.439891\pi$
$661$	9.65248			0.375438			0.187719	+	0.982223i	$0.439891\pi$
$662$	24.6340	+	17.8977i	0.957429	+	0.695613i
$663$		0			0
$664$	−18.6910	−	57.5249i	−0.725351	−	2.23240i
$665$	8.65282	−	6.28664i	0.335542	−	0.243785i
$666$		0			0
$667$	0.694489	+	2.13742i	0.0268907	+	0.0827612i
$668$	−44.9355	+	138.297i	−1.73861	+	5.35088i
$669$		0			0
$670$	6.84872			0.264589
$671$	−6.03060	−	7.76964i	−0.232809	−	0.299944i
$672$		0			0
$673$	22.9433	+	16.6693i	0.884398	+	0.642553i	0.934411	−	0.356196i	$-0.115926\pi$
$673$	22.9433	+	16.6693i	0.884398	+	0.642553i	−0.0500135	+	0.998749i	$0.515926\pi$
$674$	−11.0048	+	33.8694i	−0.423891	+	1.30460i
$675$		0			0
$676$	58.9194	−	42.8075i	2.26613	−	1.64644i
$677$	−4.11544	+	2.99004i	−0.158169	+	0.114917i	−0.664055	−	0.747684i	$-0.731166\pi$
$677$	−4.11544	+	2.99004i	−0.158169	+	0.114917i	0.505885	+	0.862601i	$0.331166\pi$
$678$		0			0
$679$	6.08661	−	18.7327i	0.233583	−	0.718893i
$680$	−41.3256	−	30.0248i	−1.58476	−	1.15140i
$681$		0			0
$682$	−40.3764	+	14.5505i	−1.54609	+	0.557167i
$683$	−17.3612			−0.664310			−0.332155	−	0.943225i	$-0.607776\pi$
$683$	−17.3612			−0.664310			−0.332155	+	0.943225i	$0.607776\pi$
$684$		0			0
$685$	−3.81475	+	11.7406i	−0.145754	+	0.448585i
$686$	−17.1945	−	52.9192i	−0.656489	−	2.02046i
$687$		0			0
$688$	−96.0406	+	69.7776i	−3.66151	+	2.66024i
$689$	−1.45942	−	4.49164i	−0.0555995	−	0.171118i
$690$		0			0
$691$	34.7708	+	25.2625i	1.32274	+	0.961029i	0.999894	+	0.0145791i	$0.00464085\pi$
$691$	34.7708	+	25.2625i	1.32274	+	0.961029i	0.322850	+	0.946450i	$0.395359\pi$
$692$	38.3983			1.45969
$693$		0			0
$694$	−5.23870			−0.198858
$695$	6.25561	+	4.54496i	0.237289	+	0.172400i
$696$		0			0
$697$	−6.63486	−	20.4200i	−0.251313	−	0.773463i
$698$	53.3302	−	38.7467i	2.01858	−	1.46658i
$699$		0			0
$700$	−4.00134	−	12.3149i	−0.151236	−	0.465458i
$701$	4.44621	−	13.6840i	0.167931	−	0.516838i	−0.831309	−	0.555810i	$-0.812408\pi$
$701$	4.44621	−	13.6840i	0.167931	−	0.516838i	0.999240	+	0.0389718i	$0.0124082\pi$
$702$		0			0
$703$	−41.6174			−1.56963
$704$	74.0286	−	109.002i	2.79006	−	4.10818i
$705$		0			0
$706$	45.3701	+	32.9633i	1.70753	+	1.24059i
$707$	−3.99855	+	12.3063i	−0.150381	+	0.462825i
$708$		0			0
$709$	−41.4016	+	30.0800i	−1.55487	+	1.12968i	−0.614805	+	0.788680i	$0.710765\pi$
$709$	−41.4016	+	30.0800i	−1.55487	+	1.12968i	−0.940064	+	0.340998i	$0.889235\pi$
$710$	25.3747	−	18.4358i	0.952297	−	0.691884i
$711$		0			0
$712$	18.6250	−	57.3217i	0.698000	−	2.14822i
$713$	3.19409	+	2.32065i	0.119620	+	0.0869088i
$714$		0			0
$715$	−0.0458407	−	1.44445i	−0.00171434	−	0.0540193i
$716$	−37.0787			−1.38570
$717$		0			0
$718$	−15.9252	+	49.0126i	−0.594322	+	1.82913i
$719$	−16.0803	−	49.4902i	−0.599696	−	1.84567i	−0.529806	−	0.848119i	$-0.677735\pi$
$719$	−16.0803	−	49.4902i	−0.599696	−	1.84567i	−0.0698891	−	0.997555i	$-0.522265\pi$
$720$		0			0
$721$	−2.38826	+	1.73517i	−0.0889435	+	0.0646213i
$722$	−2.61454	−	8.04673i	−0.0973032	−	0.299468i
$723$		0			0
$724$	−63.2523	−	45.9555i	−2.35075	−	1.70792i
$725$	2.65711			0.0986826
$726$		0			0
$727$	−18.2951			−0.678528			−0.339264	−	0.940691i	$-0.610178\pi$
$727$	−18.2951			−0.678528			−0.339264	+	0.940691i	$0.610178\pi$
$728$	8.20256	+	5.95951i	0.304007	+	0.220874i
$729$		0			0
$730$	−7.22091	−	22.2237i	−0.267258	−	0.822535i
$731$	28.3284	−	20.5818i	1.04776	−	0.761245i
$732$		0			0
$733$	11.5929	+	35.6792i	0.428192	+	1.31784i	0.899904	+	0.436088i	$0.143636\pi$
$733$	11.5929	+	35.6792i	0.428192	+	1.31784i	−0.471712	+	0.881753i	$0.656364\pi$
$734$	−5.06126	+	15.5770i	−0.186815	+	0.574956i
$735$		0			0
$736$	−22.4649			−0.828069
$737$	−0.259901	−	8.18953i	−0.00957358	−	0.301665i
$738$		0			0
$739$	22.0973	+	16.0546i	0.812863	+	0.590579i	0.914659	−	0.404226i	$-0.132459\pi$
$739$	22.0973	+	16.0546i	0.812863	+	0.590579i	−0.101796	+	0.994805i	$0.532459\pi$
$740$	−15.5697	+	47.9187i	−0.572354	+	1.76152i
$741$		0			0
$742$	−55.3650	+	40.2250i	−2.03251	+	1.47671i
$743$	15.2284	−	11.0641i	0.558677	−	0.405902i	−0.272298	−	0.962213i	$-0.587784\pi$
$743$	15.2284	−	11.0641i	0.558677	−	0.405902i	0.830974	+	0.556311i	$0.187784\pi$
$744$		0			0
$745$	−2.35130	+	7.23654i	−0.0861448	+	0.265126i
$746$	−3.74525	−	2.72108i	−0.137123	−	0.0996259i
$747$		0			0
$748$	−52.9684	+	77.9925i	−1.93672	+	2.85169i
$749$	−27.7884			−1.01536
$750$		0			0
$751$	−7.78395	+	23.9565i	−0.284040	+	0.874186i	0.702644	+	0.711541i	$0.252003\pi$
$751$	−7.78395	+	23.9565i	−0.284040	+	0.874186i	−0.986685	+	0.162645i	$0.947997\pi$
$752$	−2.45243	−	7.54781i	−0.0894310	−	0.275240i
$753$		0			0
$754$	−2.59669	+	1.88660i	−0.0945658	+	0.0687061i
$755$	−0.826389	−	2.54336i	−0.0300754	−	0.0925625i
$756$		0			0
$757$	−37.0481	−	26.9170i	−1.34653	−	0.978315i	−0.999176	−	0.0405820i	$-0.987079\pi$
$757$	−37.0481	−	26.9170i	−1.34653	−	0.978315i	−0.347358	−	0.937733i	$-0.612921\pi$
$758$	−23.3842			−0.849352
$759$		0			0
$760$	−47.9751			−1.74024
$761$	6.48664	+	4.71282i	0.235141	+	0.170840i	0.699116	−	0.715009i	$-0.253577\pi$
$761$	6.48664	+	4.71282i	0.235141	+	0.170840i	−0.463975	+	0.885848i	$0.653577\pi$
$762$		0			0
$763$	8.56146	+	26.3495i	0.309946	+	0.953914i
$764$	−89.3949	+	64.9492i	−3.23419	+	2.34978i
$765$		0			0
$766$	18.7451	+	57.6916i	0.677289	+	2.08448i
$767$	0.529980	−	1.63111i	0.0191365	−	0.0588960i
$768$		0			0
$769$	40.0439			1.44402			0.722010	−	0.691883i	$-0.243218\pi$
$769$	40.0439			1.44402			0.722010	+	0.691883i	$0.243218\pi$
$770$	−19.7009	+	7.09965i	−0.709972	+	0.255854i
$771$		0			0
$772$	−104.004	−	75.5634i	−3.74319	−	2.71959i
$773$	7.36232	−	22.6589i	0.264804	−	0.814984i	−0.726934	−	0.686707i	$-0.759055\pi$
$773$	7.36232	−	22.6589i	0.264804	−	0.814984i	0.991738	−	0.128277i	$-0.0409445\pi$
$774$		0			0
$775$	3.77637	−	2.74369i	0.135651	−	0.0985563i
$776$	−71.4770	+	51.9311i	−2.56588	+	1.86422i
$777$		0			0
$778$	−0.335891	+	1.03377i	−0.0120423	+	0.0370624i
$779$	−16.3140	−	11.8528i	−0.584511	−	0.424672i
$780$		0			0
$781$	−23.0081	−	29.6429i	−0.823293	−	1.06071i
$782$	11.7239			0.419245
$783$		0			0
$784$	−9.49471	+	29.2217i	−0.339097	+	1.04363i
$785$	6.24214	+	19.2113i	0.222791	+	0.685681i
$786$		0			0
$787$	7.67659	−	5.57737i	0.273641	−	0.198812i	−0.442498	−	0.896769i	$-0.645908\pi$
$787$	7.67659	−	5.57737i	0.273641	−	0.198812i	0.716139	+	0.697958i	$0.245908\pi$
$788$	−40.4598	−	124.522i	−1.44132	−	4.43593i
$789$		0			0
$790$	−24.3805	−	17.7135i	−0.867419	−	0.630217i
$791$	0.323537			0.0115037
$792$		0			0
$793$	−1.29217			−0.0458864
$794$	80.2517	+	58.3063i	2.84803	+	2.06921i
$795$		0			0
$796$	−34.4718	−	106.093i	−1.22182	−	3.76037i
$797$	−19.2254	+	13.9680i	−0.680998	+	0.494774i	−0.873688	−	0.486486i	$-0.838279\pi$
$797$	−19.2254	+	13.9680i	−0.680998	+	0.494774i	0.192691	+	0.981259i	$0.438279\pi$
$798$		0			0
$799$	0.723376	+	2.22632i	0.0255912	+	0.0787617i
$800$	−8.20756	+	25.2603i	−0.290181	+	0.893086i
$801$		0			0
$802$	84.3212			2.97749
$803$	−26.3005	+	9.47795i	−0.928124	+	0.334469i
$804$		0			0
$805$	1.55850	+	1.13232i	0.0549299	+	0.0399089i
$806$	−1.74241	+	5.36260i	−0.0613739	+	0.188890i
$807$		0			0
$808$	46.9563	−	34.1158i	1.65192	−	1.20019i
$809$	−14.8963	+	10.8228i	−0.523726	+	0.380509i	−0.818006	−	0.575210i	$-0.804920\pi$
$809$	−14.8963	+	10.8228i	−0.523726	+	0.380509i	0.294280	+	0.955719i	$0.404920\pi$
$810$		0			0
$811$	7.30675	−	22.4879i	0.256575	−	0.789656i	−0.736941	−	0.675957i	$-0.763730\pi$
$811$	7.30675	−	22.4879i	0.256575	−	0.789656i	0.993515	−	0.113698i	$-0.0362697\pi$
$812$	27.8350	+	20.2233i	0.976815	+	0.709698i
$813$		0			0
$814$	78.2562	+	22.7093i	2.74288	+	0.795960i
$815$	−9.79582			−0.343133
$816$		0			0
$817$	10.1625	−	31.2770i	0.355541	−	1.09424i
$818$	13.9377	+	42.8958i	0.487320	+	1.49982i
$819$		0			0
$820$	−19.7508	+	14.3498i	−0.689727	+	0.501116i
$821$	−8.13186	−	25.0273i	−0.283804	−	0.873459i	−0.986755	−	0.162220i	$-0.948135\pi$
$821$	−8.13186	−	25.0273i	−0.283804	−	0.873459i	0.702951	−	0.711239i	$-0.251865\pi$
$822$		0			0
$823$	−32.7100	−	23.7652i	−1.14020	−	0.828403i	−0.153051	−	0.988218i	$-0.548910\pi$
$823$	−32.7100	−	23.7652i	−1.14020	−	0.828403i	−0.987147	+	0.159816i	$0.948910\pi$
$824$	13.2416			0.461293
$825$		0			0
$826$	−24.8517			−0.864703
$827$	13.4238	+	9.75293i	0.466790	+	0.339143i	0.796189	−	0.605048i	$-0.206846\pi$
$827$	13.4238	+	9.75293i	0.466790	+	0.339143i	−0.329399	+	0.944191i	$0.606846\pi$
$828$		0			0
$829$	−10.6015	−	32.6281i	−0.368206	−	1.13322i	−0.947949	−	0.318422i	$-0.896847\pi$
$829$	−10.6015	−	32.6281i	−0.368206	−	1.13322i	0.579743	−	0.814800i	$-0.303153\pi$
$830$	13.2783	−	9.64728i	0.460898	−	0.334862i
$831$		0			0
$832$	−5.34942	−	16.4638i	−0.185458	−	0.570781i
$833$	2.80059	−	8.61932i	0.0970346	−	0.298642i
$834$		0			0
$835$	−25.5776			−0.885150
$836$	2.80865	+	88.5012i	0.0971393	+	3.06088i
$837$		0			0
$838$	89.8686	+	65.2934i	3.10446	+	2.25552i
$839$	1.04698	−	3.22229i	0.0361459	−	0.111246i	−0.931356	−	0.364111i	$-0.881373\pi$
$839$	1.04698	−	3.22229i	0.0361459	−	0.111246i	0.967502	+	0.252865i	$0.0813729\pi$
$840$		0			0
$841$	17.7496	−	12.8959i	0.612056	−	0.444685i
$842$	−43.4970	+	31.6024i	−1.49901	+	1.08909i
$843$		0			0
$844$	0.0877101	−	0.269944i	0.00301910	−	0.00929185i
$845$	10.3636	+	7.52961i	0.356519	+	0.259026i
$846$		0			0
$847$	9.23721	+	23.2884i	0.317394	+	0.800201i
$848$	183.729			6.30926
$849$		0			0
$850$	4.28332	−	13.1827i	0.146917	−	0.452163i
$851$	−2.31636	−	7.12903i	−0.0794039	−	0.244380i
$852$		0			0
$853$	−13.2728	+	9.64323i	−0.454451	+	0.330178i	−0.791351	−	0.611363i	$-0.790622\pi$
$853$	−13.2728	+	9.64323i	−0.454451	+	0.330178i	0.336900	+	0.941541i	$0.390622\pi$
$854$	5.78606	+	17.8076i	0.197995	+	0.609365i
$855$		0			0
$856$	100.841	+	73.2651i	3.44667	+	2.50415i
$857$	3.37817			0.115396			0.0576981	−	0.998334i	$-0.481624\pi$
$857$	3.37817			0.115396			0.0576981	+	0.998334i	$0.481624\pi$
$858$		0			0
$859$	−2.32376			−0.0792855			−0.0396428	−	0.999214i	$-0.512622\pi$
$859$	−2.32376			−0.0792855			−0.0396428	+	0.999214i	$0.512622\pi$
$860$	−32.2106	−	23.4024i	−1.09837	−	0.798015i
$861$		0			0
$862$	29.0790	+	89.4959i	0.990434	+	3.04824i
$863$	−16.3949	+	11.9116i	−0.558090	+	0.405476i	−0.830759	−	0.556632i	$-0.812093\pi$
$863$	−16.3949	+	11.9116i	−0.558090	+	0.405476i	0.272670	+	0.962108i	$0.412093\pi$
$864$		0			0
$865$	2.08712	+	6.42349i	0.0709642	+	0.218405i
$866$	11.2356	−	34.5795i	0.381800	−	1.17506i
$867$		0			0
$868$	60.4421			2.05154
$869$	−20.2561	+	29.8258i	−0.687142	+	1.01177i
$870$		0			0
$871$	−0.870890	−	0.632739i	−0.0295090	−	0.0214395i
$872$	38.4029	−	118.192i	1.30048	−	4.00248i
$873$		0			0
$874$	8.90806	−	6.47209i	0.301320	−	0.218922i
$875$	1.84261	−	1.33873i	0.0622916	−	0.0452575i
$876$		0			0
$877$	−5.13611	+	15.8073i	−0.173434	+	0.533775i	−0.999558	−	0.0297127i	$-0.990541\pi$
$877$	−5.13611	+	15.8073i	−0.173434	+	0.533775i	0.826125	+	0.563488i	$0.190541\pi$
$878$	−21.6367	−	15.7200i	−0.730205	−	0.530525i
$879$		0			0
$880$	53.9936	+	15.6685i	1.82012	+	0.528184i
$881$	29.8895			1.00700			0.503502	−	0.863994i	$-0.332045\pi$
$881$	29.8895			1.00700			0.503502	+	0.863994i	$0.332045\pi$
$882$		0			0
$883$	4.33042	−	13.3277i	0.145730	−	0.448511i	−0.851374	−	0.524559i	$-0.824230\pi$
$883$	4.33042	−	13.3277i	0.145730	−	0.448511i	0.997104	+	0.0760479i	$0.0242302\pi$
$884$	3.82758	+	11.7801i	0.128735	+	0.396207i
$885$		0			0
$886$	19.9923	−	14.5253i	0.671655	−	0.487986i
$887$	−8.84040	−	27.2079i	−0.296831	−	0.913553i	−0.982600	−	0.185734i	$-0.940534\pi$
$887$	−8.84040	−	27.2079i	−0.296831	−	0.913553i	0.685769	−	0.727820i	$-0.259466\pi$
$888$		0			0
$889$	−0.928146	−	0.674338i	−0.0311290	−	0.0226166i
$890$	16.3550			0.548219
$891$		0			0
$892$	4.29213			0.143711
$893$	1.77866	+	1.29227i	0.0595207	+	0.0432443i
$894$		0			0
$895$	−2.01539	−	6.20274i	−0.0673672	−	0.207335i
$896$	−105.057	+	76.3284i	−3.50971	+	2.54995i
$897$		0			0
$898$	−10.6542	−	32.7902i	−0.355535	−	1.09422i
$899$	−3.83274	+	11.7959i	−0.127829	+	0.393417i
$900$		0			0
$901$	−54.1931			−1.80543
$902$	24.2087	+	31.1898i	0.806062	+	1.03851i
$903$		0			0
$904$	−1.17408	−	0.853019i	−0.0390493	−	0.0283710i
$905$	4.24966	−	13.0791i	0.141263	−	0.434764i
$906$		0			0
$907$	−21.8186	+	15.8521i	−0.724474	+	0.526361i	−0.887811	−	0.460209i	$-0.847774\pi$
$907$	−21.8186	+	15.8521i	−0.724474	+	0.526361i	0.163336	+	0.986570i	$0.447774\pi$
$908$	38.1017	−	27.6825i	1.26445	−	0.918677i
$909$		0			0
$910$	−0.850179	+	2.61658i	−0.0281832	+	0.0867389i
$911$	5.77363	+	4.19479i	0.191289	+	0.138980i	0.679308	−	0.733854i	$-0.262280\pi$
$911$	5.77363	+	4.19479i	0.191289	+	0.138980i	−0.488019	+	0.872833i	$0.662280\pi$
$912$		0			0
$913$	−12.0399	−	15.5118i	−0.398462	−	0.513366i
$914$	105.783			3.49900
$915$		0			0
$916$	−5.05303	+	15.5516i	−0.166957	+	0.513840i
$917$	13.4498	+	41.3941i	0.444150	+	1.36695i
$918$		0			0
$919$	5.57755	−	4.05233i	0.183987	−	0.133674i	−0.491980	−	0.870607i	$-0.663727\pi$
$919$	5.57755	−	4.05233i	0.183987	−	0.133674i	0.675966	+	0.736933i	$0.263727\pi$
$920$	−2.67022	−	8.21810i	−0.0880346	−	0.270943i
$921$		0			0
$922$	−77.1171	−	56.0288i	−2.53971	−	1.84521i
$923$	−4.92992			−0.162270
$924$		0			0
$925$	−8.86239			−0.291394
$926$	−90.2854	−	65.5962i	−2.96696	−	2.15563i
$927$		0			0
$928$	−21.8084	−	67.1194i	−0.715896	−	2.20330i
$929$	−29.4333	+	21.3846i	−0.965676	+	0.701605i	−0.954462	−	0.298332i	$-0.903570\pi$
$929$	−29.4333	+	21.3846i	−0.965676	+	0.701605i	−0.0112141	+	0.999937i	$0.503570\pi$
$930$		0			0
$931$	−2.63029	−	8.09519i	−0.0862042	−	0.265309i
$932$	9.09807	−	28.0010i	0.298017	−	0.917202i
$933$		0			0
$934$	41.9052			1.37118
$935$	−15.9261	−	4.62162i	−0.520839	−	0.151143i
$936$		0			0
$937$	−42.6299	−	30.9724i	−1.39266	−	1.01183i	−0.995568	−	0.0940454i	$-0.970020\pi$
$937$	−42.6299	−	30.9724i	−1.39266	−	1.01183i	−0.397090	−	0.917780i	$-0.629980\pi$
$938$	−4.82023	+	14.8351i	−0.157386	+	0.484385i
$939$		0			0
$940$	2.15336	−	1.56451i	0.0702349	−	0.0510286i
$941$	−16.4217	+	11.9311i	−0.535334	+	0.388943i	−0.822349	−	0.568983i	$-0.807337\pi$
$941$	−16.4217	+	11.9311i	−0.535334	+	0.388943i	0.287015	+	0.957926i	$0.407337\pi$
$942$		0			0
$943$	1.12237	−	3.45429i	0.0365493	−	0.112487i
$944$	53.9776	+	39.2170i	1.75682	+	1.27640i
$945$		0			0
$946$	−36.1761	+	53.2670i	−1.17619	+	1.73186i
$947$	−14.5680			−0.473395			−0.236698	−	0.971583i	$-0.576065\pi$
$947$	−14.5680			−0.473395			−0.236698	+	0.971583i	$0.576065\pi$
$948$		0			0
$949$	−1.13498	+	3.49311i	−0.0368430	+	0.113391i
$950$	−4.02286	−	12.3811i	−0.130519	−	0.401695i
$951$		0			0
$952$	94.1228	−	68.3842i	3.05054	−	2.21635i
$953$	12.2078	+	37.5718i	0.395450	+	1.21707i	0.928610	+	0.371056i	$0.121004\pi$
$953$	12.2078	+	37.5718i	0.395450	+	1.21707i	−0.533160	+	0.846014i	$0.678996\pi$
$954$		0			0
$955$	−15.7241	−	11.4242i	−0.508820	−	0.369679i
$956$	−61.5867			−1.99186
$957$		0			0
$958$	−79.8524			−2.57991
$959$	−22.7466	−	16.5264i	−0.734526	−	0.533665i
$960$		0			0
$961$	−2.84642	−	8.76037i	−0.0918199	−	0.282592i
$962$	8.66086	−	6.29248i	0.279237	−	0.202878i
$963$		0			0
$964$	−5.20945	−	16.0330i	−0.167785	−	0.516389i
$965$	6.98760	−	21.5056i	0.224939	−	0.692291i
$966$		0			0
$967$	−44.8051			−1.44083			−0.720417	−	0.693541i	$-0.756050\pi$
$967$	−44.8051			−1.44083			−0.720417	+	0.693541i	$0.756050\pi$
$968$	27.8801	−	108.865i	0.896102	−	3.49907i
$969$		0			0
$970$	−19.3956	−	14.0917i	−0.622755	−	0.452458i
$971$	−5.60723	+	17.2573i	−0.179945	+	0.553812i	−0.999825	−	0.0187228i	$-0.994040\pi$
$971$	−5.60723	+	17.2573i	−0.179945	+	0.553812i	0.819880	+	0.572535i	$0.194040\pi$
$972$		0			0
$973$	−14.2477	+	10.3516i	−0.456761	+	0.331856i
$974$	64.7097	−	47.0144i	2.07343	−	1.50644i
$975$		0			0
$976$	15.5339	−	47.8085i	0.497229	−	1.53031i
$977$	42.0662	+	30.5629i	1.34582	+	0.977794i	0.999208	+	0.0397838i	$0.0126669\pi$
$977$	42.0662	+	30.5629i	1.34582	+	0.977794i	0.346609	+	0.938010i	$0.387333\pi$
$978$		0			0
$979$	−0.620652	−	19.5569i	−0.0198361	−	0.625040i
$980$	−10.3049			−0.329178
$981$		0			0
$982$	−12.7957	+	39.3812i	−0.408328	+	1.25671i
$983$	−13.6994	−	42.1625i	−0.436943	−	1.34477i	−0.891082	−	0.453842i	$-0.850053\pi$
$983$	−13.6994	−	42.1625i	−0.436943	−	1.34477i	0.454139	−	0.890931i	$-0.349947\pi$
$984$		0			0
$985$	18.6317	−	13.5367i	0.593654	−	0.431315i
$986$	11.3813	+	35.0279i	0.362453	+	1.11552i
$987$		0			0
$988$	9.41138	+	6.83777i	0.299416	+	0.217538i
$989$	5.92336			0.188352
$990$		0			0
$991$	10.4084			0.330635			0.165317	−	0.986240i	$-0.447135\pi$
$991$	10.4084			0.330635			0.165317	+	0.986240i	$0.447135\pi$
$992$	−100.301	−	72.8731i	−3.18457	−	2.31372i
$993$		0			0
$994$	22.0751	+	67.9401i	0.700179	+	2.15493i
$995$	15.8742	−	11.5333i	0.503246	−	0.365629i
$996$		0			0
$997$	2.01541	+	6.20281i	0.0638288	+	0.196445i	0.977885	−	0.209142i	$-0.0670671\pi$
$997$	2.01541	+	6.20281i	0.0638288	+	0.196445i	−0.914056	+	0.405587i	$0.867067\pi$
$998$	−19.0171	+	58.5286i	−0.601975	+	1.85269i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.d.136.2		8
3.2	odd	2		165.2.m.a.136.1	yes	8
11.3	even	5	inner	495.2.n.d.91.2		8
11.5	even	5		5445.2.a.be.1.1		4
11.6	odd	10		5445.2.a.bv.1.4		4
15.2	even	4		825.2.bx.h.499.4		16
15.8	even	4		825.2.bx.h.499.1		16
15.14	odd	2		825.2.n.k.301.2		8
33.5	odd	10		1815.2.a.x.1.4		4
33.14	odd	10		165.2.m.a.91.1	✓	8
33.17	even	10		1815.2.a.o.1.1		4
165.14	odd	10		825.2.n.k.751.2		8
165.47	even	20		825.2.bx.h.124.1		16
165.104	odd	10		9075.2.a.cl.1.1		4
165.113	even	20		825.2.bx.h.124.4		16
165.149	even	10		9075.2.a.dj.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.91.1	✓	8	33.14	odd	10
165.2.m.a.136.1	yes	8	3.2	odd	2
495.2.n.d.91.2		8	11.3	even	5	inner
495.2.n.d.136.2		8	1.1	even	1	trivial
825.2.n.k.301.2		8	15.14	odd	2
825.2.n.k.751.2		8	165.14	odd	10
825.2.bx.h.124.1		16	165.47	even	20
825.2.bx.h.124.4		16	165.113	even	20
825.2.bx.h.499.1		16	15.8	even	4
825.2.bx.h.499.4		16	15.2	even	4
1815.2.a.o.1.1		4	33.17	even	10
1815.2.a.x.1.4		4	33.5	odd	10
5445.2.a.be.1.1		4	11.5	even	5
5445.2.a.bv.1.4		4	11.6	odd	10
9075.2.a.cl.1.1		4	165.104	odd	10
9075.2.a.dj.1.4		4	165.149	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)

\(f(q)\)	\(=\)	\(q+(2.24278 + 1.62947i) q^{2} +(1.75683 + 5.40697i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.703814 - 2.16612i) q^{7} +(-3.15700 + 9.71623i) q^{8} +O(q^{10})\)	\(q+(2.24278 + 1.62947i) q^{2} +(1.75683 + 5.40697i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.703814 - 2.16612i) q^{7} +(-3.15700 + 9.71623i) q^{8} -2.77222 q^{10} +(0.105203 + 3.31496i) q^{11} +(0.352519 + 0.256120i) q^{13} +(1.95113 - 6.00496i) q^{14} +(-13.7139 + 9.96371i) q^{16} +(4.04508 - 2.93893i) q^{17} +(1.45113 - 4.46612i) q^{19} +(-4.59944 - 3.34169i) q^{20} +(-5.16568 + 7.60613i) q^{22} +0.845811 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.373280 + 1.14884i) q^{26} +(10.4756 - 7.61100i) q^{28} +(0.821093 + 2.52706i) q^{29} +(3.77637 + 2.74369i) q^{31} -26.5602 q^{32} +13.8611 q^{34} +(1.84261 + 1.33873i) q^{35} +(-2.73863 - 8.42864i) q^{37} +(10.5320 - 7.65193i) q^{38} +(-3.15700 - 9.71623i) q^{40} +(1.32697 - 4.08400i) q^{41} +7.00317 q^{43} +(-17.7390 + 6.39264i) q^{44} +(1.89696 + 1.37823i) q^{46} +(-0.144675 + 0.445265i) q^{47} +(1.46641 - 1.06541i) q^{49} +(2.24278 - 1.62947i) q^{50} +(-0.765515 + 2.35601i) q^{52} +(-8.76863 - 6.37078i) q^{53} +(-2.03359 - 2.62002i) q^{55} +23.2684 q^{56} +(-2.27625 + 7.00558i) q^{58} +(-1.21629 - 3.74334i) q^{59} +(-2.39913 + 1.74307i) q^{61} +(3.99878 + 12.3070i) q^{62} +(-32.1409 - 23.3517i) q^{64} -0.435737 q^{65} -2.47048 q^{67} +(22.9972 + 16.7084i) q^{68} +(1.95113 + 6.00496i) q^{70} +(-9.15321 + 6.65020i) q^{71} +(2.60474 + 8.01655i) q^{73} +(7.59209 - 23.3661i) q^{74} +26.6975 q^{76} +(7.10654 - 2.56099i) q^{77} +(8.79457 + 6.38963i) q^{79} +(5.23823 - 16.1216i) q^{80} +(9.63087 - 6.99723i) q^{82} +(-4.78978 + 3.47998i) q^{83} +(-1.54508 + 4.75528i) q^{85} +(15.7065 + 11.4115i) q^{86} +(-32.5410 - 9.44313i) q^{88} -5.89958 q^{89} +(0.306678 - 0.943857i) q^{91} +(1.48595 + 4.57327i) q^{92} +(-1.05002 + 0.762885i) q^{94} +(1.45113 + 4.46612i) q^{95} +(6.99640 + 5.08318i) q^{97} +5.02487 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8}+O(q^{10}) \) 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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