LMFDB - Embedded newform 495.2.n.g.361.4

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 5x^14 - 8x^13 + 47x^12 + 32x^11 + 171x^10 + 26x^9 + 360x^8 - 172x^7 + 471x^6 - 430x^5 + 383x^4 + 70x^3 + 17x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.4
Root			$-1.41763 - 1.02997i$ of defining polynomial
Character	$\chi$	$=$	495.361
Dual form			495.2.n.g.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.850504 - 2.61758i) q^{2} +(-4.51034 - 3.27695i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.21013 - 1.60575i) q^{7} +(-7.96046 + 5.78361i) q^{8} +O(q^{10})$	\(q+(0.850504 - 2.61758i) q^{2} +(-4.51034 - 3.27695i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.21013 - 1.60575i) q^{7} +(-7.96046 + 5.78361i) q^{8} +2.75229 q^{10} +(-3.02195 - 1.36669i) q^{11} +(-0.857468 + 2.63902i) q^{13} +(-6.08291 + 4.41949i) q^{14} +(4.92308 + 15.1517i) q^{16} +(-1.16845 - 3.59612i) q^{17} +(3.43983 - 2.49918i) q^{19} +(1.72280 - 5.30222i) q^{20} +(-6.14759 + 6.74782i) q^{22} -1.37658 q^{23} +(-0.809017 + 0.587785i) q^{25} +(6.17856 + 4.48898i) q^{26} +(4.70645 + 14.4850i) q^{28} +(-7.17384 - 5.21210i) q^{29} +(1.68946 - 5.19964i) q^{31} +24.1685 q^{32} -10.4069 q^{34} +(0.844194 - 2.59816i) q^{35} +(1.86189 + 1.35274i) q^{37} +(-3.61622 - 11.1296i) q^{38} +(-7.96046 - 5.78361i) q^{40} +(-6.97314 + 5.06629i) q^{41} +12.3981 q^{43} +(9.15144 + 16.0670i) q^{44} +(-1.17079 + 3.60332i) q^{46} +(4.52496 - 3.28757i) q^{47} +(0.143108 + 0.440442i) q^{49} +(0.850504 + 2.61758i) q^{50} +(12.5154 - 9.09297i) q^{52} +(-0.168046 + 0.517191i) q^{53} +(0.365963 - 3.29637i) q^{55} +26.8807 q^{56} +(-19.7445 + 14.3452i) q^{58} +(-0.314933 - 0.228812i) q^{59} +(-4.43173 - 13.6395i) q^{61} +(-12.1736 - 8.84462i) q^{62} +(10.7092 - 32.9596i) q^{64} -2.77482 q^{65} +3.65454 q^{67} +(-6.51421 + 20.0487i) q^{68} +(-6.08291 - 4.41949i) q^{70} +(-2.83231 - 8.71697i) q^{71} +(-6.60178 - 4.79647i) q^{73} +(5.12445 - 3.72313i) q^{74} -23.7045 q^{76} +(4.48433 + 7.87305i) q^{77} +(-1.06521 + 3.27837i) q^{79} +(-12.8888 + 9.36425i) q^{80} +(7.33073 + 22.5617i) q^{82} +(-1.43839 - 4.42691i) q^{83} +(3.05904 - 2.22252i) q^{85} +(10.5446 - 32.4530i) q^{86} +(31.9605 - 6.59832i) q^{88} +6.62318 q^{89} +(6.13272 - 4.45568i) q^{91} +(6.20886 + 4.51100i) q^{92} +(-4.75700 - 14.6405i) q^{94} +(3.43983 + 2.49918i) q^{95} +(-5.12775 + 15.7816i) q^{97} +1.27461 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8	$ 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8 + 8 * q^10 + 4 * q^11 + 2 * q^13 - 22 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 + 2 * q^20 - 28 * q^22 + 8 * q^23 - 4 * q^25 + 6 * q^26 - 2 * q^28 - 26 * q^29 - 10 * q^31 + 56 * q^32 - 4 * q^34 - 4 * q^35 + 22 * q^37 - 30 * q^38 - 6 * q^40 - 6 * q^41 + 28 * q^43 + 68 * q^44 + 16 * q^46 - 20 * q^47 + 10 * q^49 - 2 * q^50 + 30 * q^52 + 14 * q^53 - 6 * q^55 + 68 * q^56 - 6 * q^58 - 16 * q^59 - 38 * q^61 - 20 * q^62 + 10 * q^64 + 12 * q^65 + 20 * q^67 - 48 * q^68 - 22 * q^70 - 54 * q^71 + 2 * q^73 + 28 * q^74 - 44 * q^76 + 34 * q^77 - 12 * q^79 - 22 * q^80 + 30 * q^82 - 28 * q^83 - 4 * q^85 + 74 * q^86 + 46 * q^88 + 76 * q^89 - 34 * q^91 - 8 * q^92 - 10 * q^94 - 4 * q^95 - 18 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	0.850504	−	2.61758i	0.601397	−	1.85091i	0.0815129	−	0.996672i	$-0.474025\pi$
$2$	0.850504	−	2.61758i	0.601397	−	1.85091i	0.519884	−	0.854237i	$-0.325975\pi$
$3$		0			0
$3$		0			0
$4$	−4.51034	−	3.27695i	−2.25517	−	1.63848i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	−2.21013	−	1.60575i	−0.835350	−	0.606917i	0.0857178	−	0.996319i	$-0.472682\pi$
$7$	−2.21013	−	1.60575i	−0.835350	−	0.606917i	−0.921068	+	0.389402i	$0.872682\pi$
$8$	−7.96046	+	5.78361i	−2.81445	+	2.04481i
$9$		0			0
$10$	2.75229			0.870350
$11$	−3.02195	−	1.36669i	−0.911152	−	0.412072i
$11$	−3.02195	−	1.36669i	−0.911152	−	0.412072i
$12$		0			0
$13$	−0.857468	+	2.63902i	−0.237819	+	0.731931i	0.758916	+	0.651188i	$0.225729\pi$
$13$	−0.857468	+	2.63902i	−0.237819	+	0.731931i	−0.996735	+	0.0807428i	$0.974271\pi$
$14$	−6.08291	+	4.41949i	−1.62573	+	1.18116i
$15$		0			0
$16$	4.92308	+	15.1517i	1.23077	+	3.78792i
$17$	−1.16845	−	3.59612i	−0.283391	−	0.872187i	−0.986876	−	0.161477i	$-0.948374\pi$
$17$	−1.16845	−	3.59612i	−0.283391	−	0.872187i	0.703486	−	0.710709i	$-0.251626\pi$
$18$		0			0
$19$	3.43983	−	2.49918i	0.789151	−	0.573352i	−0.118561	−	0.992947i	$-0.537828\pi$
$19$	3.43983	−	2.49918i	0.789151	−	0.573352i	0.907711	+	0.419595i	$0.137828\pi$
$20$	1.72280	−	5.30222i	0.385229	−	1.18561i
$21$		0			0
$22$	−6.14759	+	6.74782i	−1.31067	+	1.43864i
$23$	−1.37658			−0.287038			−0.143519	−	0.989648i	$-0.545842\pi$
$23$	−1.37658			−0.287038			−0.143519	+	0.989648i	$0.545842\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	6.17856	+	4.48898i	1.21171	+	0.880362i
$27$		0			0
$28$	4.70645	+	14.4850i	0.889436	+	2.73740i
$29$	−7.17384	−	5.21210i	−1.33215	−	0.967862i	−0.999694	−	0.0247431i	$-0.992123\pi$
$29$	−7.17384	−	5.21210i	−1.33215	−	0.967862i	−0.332454	−	0.943119i	$-0.607877\pi$
$30$		0			0
$31$	1.68946	−	5.19964i	0.303437	−	0.933883i	−0.676819	−	0.736149i	$-0.736642\pi$
$31$	1.68946	−	5.19964i	0.303437	−	0.933883i	0.980256	−	0.197733i	$-0.0633580\pi$
$32$	24.1685			4.27243
$33$		0			0
$34$	−10.4069			−1.78477
$35$	0.844194	−	2.59816i	0.142695	−	0.439169i
$36$		0			0
$37$	1.86189	+	1.35274i	0.306093	+	0.222389i	0.730218	−	0.683214i	$-0.239418\pi$
$37$	1.86189	+	1.35274i	0.306093	+	0.222389i	−0.424125	+	0.905603i	$0.639418\pi$
$38$	−3.61622	−	11.1296i	−0.586629	−	1.80546i
$39$		0			0
$40$	−7.96046	−	5.78361i	−1.25866	−	0.914469i
$41$	−6.97314	+	5.06629i	−1.08902	+	0.791221i	−0.979234	−	0.202734i	$-0.935017\pi$
$41$	−6.97314	+	5.06629i	−1.08902	+	0.791221i	−0.109788	+	0.993955i	$0.535017\pi$
$42$		0			0
$43$	12.3981			1.89069			0.945346	−	0.326070i	$-0.105724\pi$
$43$	12.3981			1.89069			0.945346	+	0.326070i	$0.105724\pi$
$44$	9.15144	+	16.0670i	1.37963	+	2.42219i
$45$		0			0
$46$	−1.17079	+	3.60332i	−0.172623	+	0.531280i
$47$	4.52496	−	3.28757i	0.660033	−	0.479542i	−0.206641	−	0.978417i	$-0.566253\pi$
$47$	4.52496	−	3.28757i	0.660033	−	0.479542i	0.866674	+	0.498875i	$0.166253\pi$
$48$		0			0
$49$	0.143108	+	0.440442i	0.0204440	+	0.0629202i
$50$	0.850504	+	2.61758i	0.120279	+	0.370182i
$51$		0			0
$52$	12.5154	−	9.09297i	1.73557	−	1.26097i
$53$	−0.168046	+	0.517191i	−0.0230828	+	0.0710417i	−0.961934	−	0.273281i	$-0.911891\pi$
$53$	−0.168046	+	0.517191i	−0.0230828	+	0.0710417i	0.938852	+	0.344322i	$0.111891\pi$
$54$		0			0
$55$	0.365963	−	3.29637i	0.0493464	−	0.444483i
$56$	26.8807			3.59208
$57$		0			0
$58$	−19.7445	+	14.3452i	−2.59258	+	1.88362i
$59$	−0.314933	−	0.228812i	−0.0410008	−	0.0297888i	0.567096	−	0.823652i	$-0.308067\pi$
$59$	−0.314933	−	0.228812i	−0.0410008	−	0.0297888i	−0.608097	+	0.793863i	$0.708067\pi$
$60$		0			0
$61$	−4.43173	−	13.6395i	−0.567425	−	1.74635i	−0.660635	−	0.750707i	$-0.729713\pi$
$61$	−4.43173	−	13.6395i	−0.567425	−	1.74635i	0.0932105	−	0.995646i	$-0.470287\pi$
$62$	−12.1736	−	8.84462i	−1.54605	−	1.12327i
$63$		0			0
$64$	10.7092	−	32.9596i	1.33865	−	4.11996i
$65$	−2.77482			−0.344175
$66$		0			0
$67$	3.65454			0.446473			0.223237	−	0.974764i	$-0.428338\pi$
$67$	3.65454			0.446473			0.223237	+	0.974764i	$0.428338\pi$
$68$	−6.51421	+	20.0487i	−0.789964	+	2.43126i
$69$		0			0
$70$	−6.08291	−	4.41949i	−0.727047	−	0.528230i
$71$	−2.83231	−	8.71697i	−0.336134	−	1.03451i	−0.966161	−	0.257940i	$-0.916956\pi$
$71$	−2.83231	−	8.71697i	−0.336134	−	1.03451i	0.630027	−	0.776573i	$-0.283044\pi$
$72$		0			0
$73$	−6.60178	−	4.79647i	−0.772680	−	0.561385i	0.130093	−	0.991502i	$-0.458472\pi$
$73$	−6.60178	−	4.79647i	−0.772680	−	0.561385i	−0.902773	+	0.430117i	$0.858472\pi$
$74$	5.12445	−	3.72313i	0.595706	−	0.432805i
$75$		0			0
$76$	−23.7045			−2.71909
$77$	4.48433	+	7.87305i	0.511037	+	0.897218i
$78$		0			0
$79$	−1.06521	+	3.27837i	−0.119845	+	0.368845i	−0.992927	−	0.118729i	$-0.962118\pi$
$79$	−1.06521	+	3.27837i	−0.119845	+	0.368845i	0.873082	+	0.487574i	$0.162118\pi$
$80$	−12.8888	+	9.36425i	−1.44101	+	1.04695i
$81$		0			0
$82$	7.33073	+	22.5617i	0.809544	+	2.49152i
$83$	−1.43839	−	4.42691i	−0.157884	−	0.485916i	0.840558	−	0.541722i	$-0.182227\pi$
$83$	−1.43839	−	4.42691i	−0.157884	−	0.485916i	−0.998442	+	0.0558055i	$0.982227\pi$
$84$		0			0
$85$	3.05904	−	2.22252i	0.331800	−	0.241066i
$86$	10.5446	−	32.4530i	1.13706	−	3.49950i
$87$		0			0
$88$	31.9605	−	6.59832i	3.40700	−	0.703383i
$89$	6.62318			0.702056			0.351028	−	0.936365i	$-0.385832\pi$
$89$	6.62318			0.702056			0.351028	+	0.936365i	$0.385832\pi$
$90$		0			0
$91$	6.13272	−	4.45568i	0.642884	−	0.467082i
$92$	6.20886	+	4.51100i	0.647318	+	0.470304i
$93$		0			0
$94$	−4.75700	−	14.6405i	−0.490647	−	1.51006i
$95$	3.43983	+	2.49918i	0.352919	+	0.256411i
$96$		0			0
$97$	−5.12775	+	15.7816i	−0.520645	+	1.60238i	0.252126	+	0.967694i	$0.418870\pi$
$97$	−5.12775	+	15.7816i	−0.520645	+	1.60238i	−0.772771	+	0.634685i	$0.781130\pi$
$98$	1.27461			0.128755
$99$		0			0
$100$	5.57509			0.557509
$101$	0.166576	−	0.512669i	0.0165749	−	0.0510124i	−0.942427	−	0.334412i	$-0.891462\pi$
$101$	0.166576	−	0.512669i	0.0165749	−	0.0510124i	0.959002	+	0.283400i	$0.0914623\pi$
$102$		0			0
$103$	4.94360	+	3.59174i	0.487108	+	0.353905i	0.804071	−	0.594533i	$-0.202663\pi$
$103$	4.94360	+	3.59174i	0.487108	+	0.353905i	−0.316963	+	0.948438i	$0.602663\pi$
$104$	−8.43720	−	25.9670i	−0.827335	−	2.54628i
$105$		0			0
$106$	1.21087	+	0.879746i	0.117610	+	0.0854485i
$107$	−7.99070	+	5.80559i	−0.772490	+	0.561247i	−0.902716	−	0.430237i	$-0.858430\pi$
$107$	−7.99070	+	5.80559i	−0.772490	+	0.561247i	0.130225	+	0.991484i	$0.458430\pi$
$108$		0			0
$109$	−5.44683			−0.521712			−0.260856	−	0.965378i	$-0.584005\pi$
$109$	−5.44683			−0.521712			−0.260856	+	0.965378i	$0.584005\pi$
$110$	−8.31727	−	3.76151i	−0.793020	−	0.358646i
$111$		0			0
$112$	13.4492	−	41.3924i	1.27083	−	3.91121i
$113$	−0.629096	+	0.457065i	−0.0591804	+	0.0429971i	−0.616982	−	0.786977i	$-0.711645\pi$
$113$	−0.629096	+	0.457065i	−0.0591804	+	0.0429971i	0.557802	+	0.829974i	$0.311645\pi$
$114$		0			0
$115$	−0.425388	−	1.30921i	−0.0396676	−	0.122084i
$116$	15.2766	+	47.0167i	1.41840	+	4.36539i
$117$		0			0
$118$	−0.866786	+	0.629757i	−0.0797941	+	0.0579738i
$119$	−3.19205	+	9.82412i	−0.292615	+	0.900576i
$120$		0			0
$121$	7.26434	+	8.26011i	0.660394	+	0.750919i
$122$	−39.4716			−3.57359
$123$		0			0
$124$	−24.6590	+	17.9158i	−2.21445	+	1.60889i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	1.33823	+	4.11865i	0.118749	+	0.365471i	0.992710	−	0.120524i	$-0.0384574\pi$
$127$	1.33823	+	4.11865i	0.118749	+	0.365471i	−0.873962	+	0.485995i	$0.838457\pi$
$128$	−38.0608	−	27.6528i	−3.36413	−	2.44419i
$129$		0			0
$130$	−2.36000	+	7.26333i	−0.206986	+	0.637036i
$131$	−11.7312			−1.02496			−0.512478	−	0.858700i	$-0.671272\pi$
$131$	−11.7312			−1.02496			−0.512478	+	0.858700i	$0.671272\pi$
$132$		0			0
$133$	−11.6155			−1.00719
$134$	3.10820	−	9.56606i	0.268508	−	0.826381i
$135$		0			0
$136$	30.0999	+	21.8689i	2.58105	+	1.87524i
$137$	4.19773	+	12.9193i	0.358636	+	1.10377i	0.953871	+	0.300216i	$0.0970589\pi$
$137$	4.19773	+	12.9193i	0.358636	+	1.10377i	−0.595235	+	0.803552i	$0.702941\pi$
$138$		0			0
$139$	9.73424	+	7.07234i	0.825647	+	0.599868i	0.918325	−	0.395828i	$-0.129542\pi$
$139$	9.73424	+	7.07234i	0.825647	+	0.599868i	−0.0926772	+	0.995696i	$0.529542\pi$
$140$	−12.3217	+	8.95221i	−1.04137	+	0.756600i
$141$		0			0
$142$	−25.2263			−2.11694
$143$	6.19793	−	6.80308i	0.518297	−	0.568902i
$144$		0			0
$145$	2.74016	−	8.43335i	0.227558	−	0.700352i
$146$	−18.1700	+	13.2013i	−1.50376	+	1.09255i
$147$		0			0
$148$	−3.96488	−	12.2026i	−0.325911	−	1.00305i
$149$	−4.26239	−	13.1183i	−0.349188	−	1.07469i	−0.959303	−	0.282378i	$-0.908877\pi$
$149$	−4.26239	−	13.1183i	−0.349188	−	1.07469i	0.610115	−	0.792313i	$-0.291123\pi$
$150$		0			0
$151$	13.7584	−	9.99604i	1.11964	−	0.813466i	0.135486	−	0.990779i	$-0.456741\pi$
$151$	13.7584	−	9.99604i	1.11964	−	0.813466i	0.984154	+	0.177313i	$0.0567405\pi$
$152$	−12.9283	+	39.7892i	−1.04862	+	3.22733i
$153$		0			0
$154$	24.4223	−	5.04204i	1.96800	−	0.406299i
$155$	5.46722			0.439138
$156$		0			0
$157$	2.92121	−	2.12238i	0.233138	−	0.169385i	−0.465083	−	0.885267i	$-0.653975\pi$
$157$	2.92121	−	2.12238i	0.233138	−	0.169385i	0.698221	+	0.715883i	$0.253975\pi$
$158$	7.67543	+	5.57652i	0.610624	+	0.443644i
$159$		0			0
$160$	7.46848	+	22.9856i	0.590435	+	1.81717i
$161$	3.04243	+	2.21045i	0.239777	+	0.174208i
$162$		0			0
$163$	−1.11971	+	3.44612i	−0.0877027	+	0.269921i	−0.985283	−	0.170929i	$-0.945323\pi$
$163$	−1.11971	+	3.44612i	−0.0877027	+	0.269921i	0.897581	+	0.440850i	$0.145323\pi$
$164$	48.0532			3.75233
$165$		0			0
$166$	−12.8111			−0.994337
$167$	0.701987	−	2.16049i	0.0543214	−	0.167184i	−0.920215	−	0.391413i	$-0.871986\pi$
$167$	0.701987	−	2.16049i	0.0543214	−	0.167184i	0.974536	+	0.224229i	$0.0719864\pi$
$168$		0			0
$169$	4.28807	+	3.11547i	0.329852	+	0.239651i
$170$	−3.21591	−	9.89755i	−0.246649	−	0.759107i
$171$		0			0
$172$	−55.9196	−	40.6280i	−4.26383	−	3.09785i
$173$	15.5901	−	11.3269i	1.18530	−	0.861169i	0.192538	−	0.981290i	$-0.438328\pi$
$173$	15.5901	−	11.3269i	1.18530	−	0.861169i	0.992759	+	0.120121i	$0.0383282\pi$
$174$		0			0
$175$	2.73187			0.206510
$176$	5.83031	−	52.5159i	0.439476	−	3.95853i
$177$		0			0
$178$	5.63304	−	17.3367i	0.422214	−	1.29944i
$179$	5.88061	−	4.27251i	0.439537	−	0.319343i	−0.345914	−	0.938266i	$-0.612431\pi$
$179$	5.88061	−	4.27251i	0.439537	−	0.319343i	0.785451	+	0.618924i	$0.212431\pi$
$180$		0			0
$181$	−2.50887	−	7.72150i	−0.186483	−	0.573934i	0.813488	−	0.581581i	$-0.197566\pi$
$181$	−2.50887	−	7.72150i	−0.186483	−	0.573934i	−0.999971	+	0.00764707i	$0.997566\pi$
$182$	−6.44721	−	19.8425i	−0.477899	−	1.47082i
$183$		0			0
$184$	10.9582	−	7.96162i	0.807852	−	0.586939i
$185$	−0.711178	+	2.18878i	−0.0522869	+	0.160922i
$186$		0			0
$187$	−1.38377	+	12.4642i	−0.101191	+	0.911471i
$188$	−31.1823			−2.27420
$189$		0			0
$190$	9.46740	−	6.87847i	0.686837	−	0.499016i
$191$	16.1974	+	11.7681i	1.17201	+	0.851512i	0.991248	−	0.132016i	$-0.0421450\pi$
$191$	16.1974	+	11.7681i	1.17201	+	0.851512i	0.180758	+	0.983528i	$0.442145\pi$
$192$		0			0
$193$	−6.04819	−	18.6144i	−0.435359	−	1.33990i	−0.892719	−	0.450614i	$-0.851205\pi$
$193$	−6.04819	−	18.6144i	−0.435359	−	1.33990i	0.457360	−	0.889282i	$-0.348795\pi$
$194$	36.9485	+	26.8446i	2.65274	+	1.92733i
$195$		0			0
$196$	0.797840	−	2.45550i	0.0569886	−	0.175393i
$197$	22.9044			1.63187			0.815937	−	0.578141i	$-0.196222\pi$
$197$	22.9044			1.63187			0.815937	+	0.578141i	$0.196222\pi$
$198$		0			0
$199$	−17.3671			−1.23112			−0.615560	−	0.788090i	$-0.711070\pi$
$199$	−17.3671			−1.23112			−0.615560	+	0.788090i	$0.711070\pi$
$200$	3.04062	−	9.35808i	0.215005	−	0.661716i
$201$		0			0
$202$	−1.20028	−	0.872053i	−0.0844513	−	0.0613574i
$203$	7.48576	+	23.0388i	0.525398	+	1.61701i
$204$		0			0
$205$	−6.97314	−	5.06629i	−0.487026	−	0.353845i
$206$	13.6062	−	9.88550i	0.947990	−	0.688755i
$207$		0			0
$208$	−44.2069			−3.06520
$209$	−13.8106	+	2.85123i	−0.955298	+	0.197224i
$210$		0			0
$211$	5.13295	−	15.7976i	0.353367	−	1.08755i	−0.603583	−	0.797300i	$-0.706261\pi$
$211$	5.13295	−	15.7976i	0.353367	−	1.08755i	0.956950	−	0.290252i	$-0.0937391\pi$
$212$	2.45275	−	1.78203i	0.168456	−	0.122390i
$213$		0			0
$214$	8.40047	+	25.8540i	0.574244	+	1.76734i
$215$	3.83122	+	11.7913i	0.261287	+	0.804159i
$216$		0			0
$217$	−12.0833	+	8.77901i	−0.820266	+	0.595958i
$218$	−4.63255	+	14.2575i	−0.313756	+	0.965641i
$219$		0			0
$220$	−12.4527	+	13.6685i	−0.839559	+	0.921531i
$221$	10.4921			0.705776
$222$		0			0
$223$	7.24917	−	5.26683i	0.485440	−	0.352693i	−0.317988	−	0.948095i	$-0.603007\pi$
$223$	7.24917	−	5.26683i	0.485440	−	0.352693i	0.803428	+	0.595402i	$0.203007\pi$
$224$	−53.4155	−	38.8086i	−3.56897	−	2.59301i
$225$		0			0
$226$	0.661356	+	2.03545i	0.0439928	+	0.135396i
$227$	−0.858807	−	0.623960i	−0.0570010	−	0.0414137i	0.558920	−	0.829222i	$-0.311216\pi$
$227$	−0.858807	−	0.623960i	−0.0570010	−	0.0414137i	−0.615921	+	0.787808i	$0.711216\pi$
$228$		0			0
$229$	−1.80884	+	5.56705i	−0.119532	+	0.367881i	−0.992865	−	0.119242i	$-0.961954\pi$
$229$	−1.80884	+	5.56705i	−0.119532	+	0.367881i	0.873334	+	0.487123i	$0.161954\pi$
$230$	−3.78875			−0.249823
$231$		0			0
$232$	87.2518			5.72836
$233$	0.580093	−	1.78534i	0.0380031	−	0.116962i	−0.930255	−	0.366913i	$-0.880415\pi$
$233$	0.580093	−	1.78534i	0.0380031	−	0.116962i	0.968258	+	0.249951i	$0.0804146\pi$
$234$		0			0
$235$	4.52496	+	3.28757i	0.295176	+	0.214458i
$236$	0.670648	+	2.06404i	0.0436554	+	0.134358i
$237$		0			0
$238$	23.0006	+	16.7109i	1.49091	+	1.08321i
$239$	−1.65086	+	1.19942i	−0.106785	+	0.0775841i	−0.639896	−	0.768461i	$-0.721023\pi$
$239$	−1.65086	+	1.19942i	−0.106785	+	0.0775841i	0.533111	+	0.846045i	$0.321023\pi$
$240$		0			0
$241$	15.3922			0.991500			0.495750	−	0.868465i	$-0.334893\pi$
$241$	15.3922			0.991500			0.495750	+	0.868465i	$0.334893\pi$
$242$	27.7999	−	11.9897i	1.78704	−	0.770729i
$243$		0			0
$244$	−24.7073	+	76.0411i	−1.58172	+	4.86804i
$245$	−0.374662	+	0.272208i	−0.0239363	+	0.0173907i
$246$		0			0
$247$	3.64584	+	11.2207i	0.231979	+	0.713958i
$248$	16.6238	+	51.1627i	1.05561	+	3.24883i
$249$		0			0
$250$	−2.22665	+	1.61775i	−0.140826	+	0.102316i
$251$	4.14616	−	12.7606i	0.261703	−	0.805439i	−0.730732	−	0.682665i	$-0.760821\pi$
$251$	4.14616	−	12.7606i	0.261703	−	0.805439i	0.992435	−	0.122774i	$-0.0391791\pi$
$252$		0			0
$253$	4.15996	+	1.88136i	0.261535	+	0.118280i
$254$	11.9191			0.747869
$255$		0			0
$256$	−48.6801	+	35.3681i	−3.04250	+	2.21051i
$257$	−7.77754	−	5.65071i	−0.485150	−	0.352482i	0.318166	−	0.948035i	$-0.396933\pi$
$257$	−7.77754	−	5.65071i	−0.485150	−	0.352482i	−0.803316	+	0.595553i	$0.796933\pi$
$258$		0			0
$259$	−1.94285	−	5.97946i	−0.120723	−	0.371546i
$260$	12.5154	+	9.09297i	0.776172	+	0.563922i
$261$		0			0
$262$	−9.97740	+	30.7073i	−0.616406	+	1.89710i
$263$	−23.4178			−1.44400			−0.722002	−	0.691891i	$-0.756778\pi$
$263$	−23.4178			−1.44400			−0.722002	+	0.691891i	$0.756778\pi$
$264$		0			0
$265$	−0.543807			−0.0334058
$266$	−9.87905	+	30.4046i	−0.605723	+	1.86422i
$267$		0			0
$268$	−16.4832	−	11.9758i	−1.00687	−	0.731536i
$269$	2.92395	+	8.99899i	0.178276	+	0.548678i	0.999768	−	0.0215424i	$-0.00685769\pi$
$269$	2.92395	+	8.99899i	0.178276	+	0.548678i	−0.821492	+	0.570221i	$0.806858\pi$
$270$		0			0
$271$	−20.6671	−	15.0155i	−1.25544	−	0.912128i	−0.256912	−	0.966435i	$-0.582705\pi$
$271$	−20.6671	−	15.0155i	−1.25544	−	0.912128i	−0.998524	+	0.0543073i	$0.982705\pi$
$272$	48.7348	−	35.4079i	2.95498	−	2.14692i
$273$		0			0
$274$	37.3874			2.25866
$275$	3.24813	−	0.670584i	0.195869	−	0.0404377i
$276$		0			0
$277$	−1.43703	+	4.42272i	−0.0863427	+	0.265736i	−0.984901	−	0.173119i	$-0.944616\pi$
$277$	−1.43703	+	4.42272i	−0.0863427	+	0.265736i	0.898558	+	0.438854i	$0.144616\pi$
$278$	26.7914	−	19.4651i	1.60684	−	1.16744i
$279$		0			0
$280$	8.30658	+	25.5650i	0.496413	+	1.52780i
$281$	3.33872	+	10.2755i	0.199172	+	0.612987i	0.999903	+	0.0139628i	$0.00444464\pi$
$281$	3.33872	+	10.2755i	0.199172	+	0.612987i	−0.800731	+	0.599024i	$0.795555\pi$
$282$		0			0
$283$	−1.62343	+	1.17949i	−0.0965028	+	0.0701134i	−0.634990	−	0.772520i	$-0.718996\pi$
$283$	−1.62343	+	1.17949i	−0.0965028	+	0.0701134i	0.538487	+	0.842634i	$0.318996\pi$
$284$	−15.7904	+	48.5978i	−0.936987	+	2.88375i
$285$		0			0
$286$	−12.5362	−	22.0096i	−0.741283	−	1.30146i
$287$	23.5467			1.38992
$288$		0			0
$289$	2.18650	−	1.58859i	0.128618	−	0.0934462i
$290$	−19.7445	−	14.3452i	−1.15943	−	0.842379i
$291$		0			0
$292$	14.0584	+	43.2675i	0.822708	+	2.53204i
$293$	0.487479	+	0.354174i	0.0284788	+	0.0206911i	0.601934	−	0.798546i	$-0.294397\pi$
$293$	0.487479	+	0.354174i	0.0284788	+	0.0206911i	−0.573455	+	0.819237i	$0.694397\pi$
$294$		0			0
$295$	0.120294	−	0.370226i	0.00700377	−	0.0215554i
$296$	−22.6452			−1.31623
$297$		0			0
$298$	−37.9633			−2.19916
$299$	1.18038	−	3.63283i	0.0682629	−	0.210092i
$300$		0			0
$301$	−27.4014	−	19.9083i	−1.57939	−	1.14749i
$302$	−14.4639	−	44.5153i	−0.832304	−	2.56157i
$303$		0			0
$304$	54.8013	+	39.8155i	3.14307	+	2.28357i
$305$	11.6024	−	8.42965i	0.664352	−	0.482680i
$306$		0			0
$307$	30.7715			1.75622			0.878112	−	0.478454i	$-0.158803\pi$
$307$	30.7715			1.75622			0.878112	+	0.478454i	$0.158803\pi$
$308$	5.57376	−	50.2051i	0.317595	−	2.86070i
$309$		0			0
$310$	4.64989	−	14.3109i	0.264096	−	0.812804i
$311$	1.16730	−	0.848096i	0.0661917	−	0.0480911i	−0.554197	−	0.832385i	$-0.686975\pi$
$311$	1.16730	−	0.848096i	0.0661917	−	0.0480911i	0.620389	+	0.784294i	$0.286975\pi$
$312$		0			0
$313$	7.26167	+	22.3491i	0.410454	+	1.26325i	0.916255	+	0.400596i	$0.131197\pi$
$313$	7.26167	+	22.3491i	0.410454	+	1.26325i	−0.505801	+	0.862650i	$0.668803\pi$
$314$	−3.07101	−	9.45160i	−0.173307	−	0.533384i
$315$		0			0
$316$	15.5475	−	11.2959i	0.874615	−	0.635445i
$317$	−4.42454	+	13.6173i	−0.248507	+	0.764825i	0.746533	+	0.665348i	$0.231717\pi$
$317$	−4.42454	+	13.6173i	−0.248507	+	0.764825i	−0.995040	+	0.0994767i	$0.968283\pi$
$318$		0			0
$319$	14.5557	+	25.5551i	0.814960	+	1.43081i
$320$	34.6558			1.93732
$321$		0			0
$322$	8.37363	−	6.08380i	0.466644	−	0.339037i
$323$	−13.0066	−	9.44986i	−0.723707	−	0.525804i
$324$		0			0
$325$	−0.857468	−	2.63902i	−0.0475638	−	0.146386i
$326$	8.06818	+	5.86188i	0.446855	+	0.324659i
$327$		0			0
$328$	26.2080	−	80.6599i	1.44709	−	4.45370i
$329$	−15.2798			−0.842400
$330$		0			0
$331$	−4.93282			−0.271132			−0.135566	−	0.990768i	$-0.543285\pi$
$331$	−4.93282			−0.271132			−0.135566	+	0.990768i	$0.543285\pi$
$332$	−8.01914	+	24.6804i	−0.440108	+	1.35451i
$333$		0			0
$334$	−5.05823	−	3.67502i	−0.276774	−	0.201088i
$335$	1.12932	+	3.47567i	0.0617011	+	0.189896i
$336$		0			0
$337$	−6.22343	−	4.52159i	−0.339012	−	0.246306i	0.405233	−	0.914213i	$-0.367190\pi$
$337$	−6.22343	−	4.52159i	−0.339012	−	0.246306i	−0.744245	+	0.667907i	$0.767190\pi$
$338$	11.8020	−	8.57466i	0.641944	−	0.466400i
$339$		0			0
$340$	−21.0804			−1.14325
$341$	−12.2118	+	13.4041i	−0.661303	+	0.725871i
$342$		0			0
$343$	−5.51840	+	16.9839i	−0.297966	+	0.917045i
$344$	−98.6945	+	71.7057i	−5.32125	+	3.86611i
$345$		0			0
$346$	−16.3896	−	50.4420i	−0.881111	−	2.71178i
$347$	5.30460	+	16.3259i	0.284766	+	0.876420i	0.986469	+	0.163950i	$0.0524235\pi$
$347$	5.30460	+	16.3259i	0.284766	+	0.876420i	−0.701703	+	0.712470i	$0.747576\pi$
$348$		0			0
$349$	−19.6433	+	14.2717i	−1.05148	+	0.763948i	−0.972494	−	0.232927i	$-0.925170\pi$
$349$	−19.6433	+	14.2717i	−1.05148	+	0.763948i	−0.0789902	+	0.996875i	$0.525170\pi$
$350$	2.32346	−	7.15089i	0.124194	−	0.382231i
$351$		0			0
$352$	−73.0359	−	33.0308i	−3.89283	−	1.76055i
$353$	−5.84602			−0.311152			−0.155576	−	0.987824i	$-0.549723\pi$
$353$	−5.84602			−0.311152			−0.155576	+	0.987824i	$0.549723\pi$
$354$		0			0
$355$	7.41509	−	5.38738i	0.393552	−	0.285932i
$356$	−29.8728	−	21.7038i	−1.58325	−	1.15030i
$357$		0			0
$358$	−6.18217	−	19.0268i	−0.326738	−	1.00560i
$359$	−6.58896	−	4.78716i	−0.347752	−	0.252656i	0.400173	−	0.916439i	$-0.368950\pi$
$359$	−6.58896	−	4.78716i	−0.347752	−	0.252656i	−0.747925	+	0.663783i	$0.768950\pi$
$360$		0			0
$361$	−0.284813	+	0.876565i	−0.0149902	+	0.0461350i
$362$	−22.3454			−1.17445
$363$		0			0
$364$	−42.2617			−2.21512
$365$	2.52166	−	7.76086i	0.131989	−	0.406222i
$366$		0			0
$367$	−18.3442	−	13.3279i	−0.957561	−	0.695709i	−0.00497831	−	0.999988i	$-0.501585\pi$
$367$	−18.3442	−	13.3279i	−0.957561	−	0.695709i	−0.952583	+	0.304279i	$0.901585\pi$
$368$	−6.77703	−	20.8575i	−0.353277	−	1.08727i
$369$		0			0
$370$	5.12445	+	3.72313i	0.266408	+	0.193556i
$371$	1.20188	−	0.873219i	0.0623987	−	0.0453353i
$372$		0			0
$373$	−14.0566			−0.727825			−0.363913	−	0.931433i	$-0.618559\pi$
$373$	−14.0566			−0.727825			−0.363913	+	0.931433i	$0.618559\pi$
$374$	31.4491	+	14.2230i	1.62619	+	0.735452i
$375$		0			0
$376$	−17.0067	+	52.3411i	−0.877052	+	2.69929i
$377$	19.9061	−	14.4627i	1.02522	−	0.744865i
$378$		0			0
$379$	−7.79252	−	23.9829i	−0.400275	−	1.23192i	−0.924777	−	0.380511i	$-0.875748\pi$
$379$	−7.79252	−	23.9829i	−0.400275	−	1.23192i	0.524502	−	0.851410i	$-0.324252\pi$
$380$	−7.32509	−	22.5443i	−0.375769	−	1.15650i
$381$		0			0
$382$	44.5800	−	32.3893i	2.28091	−	1.65718i
$383$	−7.58065	+	23.3308i	−0.387353	+	1.19215i	0.547406	+	0.836867i	$0.315615\pi$
$383$	−7.58065	+	23.3308i	−0.387353	+	1.19215i	−0.934759	+	0.355283i	$0.884385\pi$
$384$		0			0
$385$	−6.10198	+	6.69776i	−0.310986	+	0.341349i
$386$	−53.8688			−2.74185
$387$		0			0
$388$	74.8435	−	54.3770i	3.79960	−	2.76057i
$389$	−19.5464	−	14.2013i	−0.991044	−	0.720035i	−0.0308944	−	0.999523i	$-0.509836\pi$
$389$	−19.5464	−	14.2013i	−0.991044	−	0.720035i	−0.960149	+	0.279487i	$0.909836\pi$
$390$		0			0
$391$	1.60847	+	4.95036i	0.0813437	+	0.250350i
$392$	−3.68655	−	2.67843i	−0.186199	−	0.135281i
$393$		0			0
$394$	19.4803	−	59.9542i	0.981404	−	3.02045i
$395$	−3.44708			−0.173441
$396$		0			0
$397$	−29.4680			−1.47896			−0.739479	−	0.673179i	$-0.764928\pi$
$397$	−29.4680			−1.47896			−0.739479	+	0.673179i	$0.764928\pi$
$398$	−14.7708	+	45.4597i	−0.740392	+	2.27869i
$399$		0			0
$400$	−12.8888	−	9.36425i	−0.644439	−	0.468212i
$401$	−1.41465	−	4.35386i	−0.0706444	−	0.217421i	0.909501	−	0.415702i	$-0.136464\pi$
$401$	−1.41465	−	4.35386i	−0.0706444	−	0.217421i	−0.980145	+	0.198281i	$0.936464\pi$
$402$		0			0
$403$	12.2733	+	8.91705i	0.611375	+	0.444190i
$404$	−2.43131	+	1.76645i	−0.120962	+	0.0878840i
$405$		0			0
$406$	66.6726			3.30891
$407$	−3.77776	−	6.63253i	−0.187256	−	0.328762i
$408$		0			0
$409$	−5.87483	+	18.0809i	−0.290492	+	0.894041i	0.694207	+	0.719775i	$0.255755\pi$
$409$	−5.87483	+	18.0809i	−0.290492	+	0.894041i	−0.984699	+	0.174266i	$0.944245\pi$
$410$	−19.1921	+	13.9439i	−0.947830	+	0.688639i
$411$		0			0
$412$	−10.5274	−	32.3999i	−0.518646	−	1.59623i
$413$	0.328627	+	1.01141i	0.0161707	+	0.0497682i
$414$		0			0
$415$	3.76575	−	2.73598i	0.184853	−	0.134304i
$416$	−20.7237	+	63.7810i	−1.01606	+	3.12712i
$417$		0			0
$418$	−4.28263	+	38.5753i	−0.209470	+	1.88678i
$419$	−2.54104			−0.124138			−0.0620690	−	0.998072i	$-0.519770\pi$
$419$	−2.54104			−0.124138			−0.0620690	+	0.998072i	$0.519770\pi$
$420$		0			0
$421$	−1.66151	+	1.20716i	−0.0809770	+	0.0588333i	−0.627537	−	0.778587i	$-0.715937\pi$
$421$	−1.66151	+	1.20716i	−0.0809770	+	0.0588333i	0.546560	+	0.837420i	$0.315937\pi$
$422$	−36.9859	−	26.8718i	−1.80045	−	1.30810i
$423$		0			0
$424$	−1.65351	−	5.08899i	−0.0803016	−	0.247143i
$425$	3.05904	+	2.22252i	0.148385	+	0.107808i
$426$		0			0
$427$	−12.1069	+	37.2612i	−0.585894	+	1.80320i
$428$	55.0654			2.66169
$429$		0			0
$430$	34.1231			1.64556
$431$	11.7090	−	36.0366i	0.564003	−	1.73582i	−0.106892	−	0.994271i	$-0.534090\pi$
$431$	11.7090	−	36.0366i	0.564003	−	1.73582i	0.670895	−	0.741552i	$-0.265910\pi$
$432$		0			0
$433$	−7.36735	−	5.35269i	−0.354052	−	0.257234i	0.396515	−	0.918028i	$-0.370220\pi$
$433$	−7.36735	−	5.35269i	−0.354052	−	0.257234i	−0.750567	+	0.660794i	$0.770220\pi$
$434$	12.7029	+	39.0955i	0.609759	+	1.87664i
$435$		0			0
$436$	24.5670	+	17.8490i	1.17655	+	0.854812i
$437$	−4.73521	+	3.44033i	−0.226516	+	0.164573i
$438$		0			0
$439$	31.0675			1.48277			0.741385	−	0.671079i	$-0.234169\pi$
$439$	31.0675			1.48277			0.741385	+	0.671079i	$0.234169\pi$
$440$	16.1517	+	28.3572i	0.770002	+	1.35188i
$441$		0			0
$442$	8.92358	−	27.4640i	0.424452	−	1.30633i
$443$	12.0635	−	8.76465i	0.573155	−	0.416421i	−0.263095	−	0.964770i	$-0.584743\pi$
$443$	12.0635	−	8.76465i	0.573155	−	0.416421i	0.836250	+	0.548349i	$0.184743\pi$
$444$		0			0
$445$	2.04667	+	6.29902i	0.0970217	+	0.298602i
$446$	−7.62091	−	23.4547i	−0.360861	−	1.11061i
$447$		0			0
$448$	−76.5938	+	55.6487i	−3.61872	+	2.62915i
$449$	7.91389	−	24.3565i	0.373480	−	1.14945i	−0.571019	−	0.820937i	$-0.693452\pi$
$449$	7.91389	−	24.3565i	0.373480	−	1.14945i	0.944499	−	0.328515i	$-0.106548\pi$
$450$		0			0
$451$	27.9965	−	5.77995i	1.31830	−	0.272167i
$452$	4.33522			0.203911
$453$		0			0
$454$	−2.36368	+	1.71732i	−0.110933	+	0.0805976i
$455$	6.13272	+	4.45568i	0.287506	+	0.208886i
$456$		0			0
$457$	2.48022	+	7.63332i	0.116020	+	0.357072i	0.992158	−	0.124987i	$-0.0398891\pi$
$457$	2.48022	+	7.63332i	0.116020	+	0.357072i	−0.876139	+	0.482059i	$0.839889\pi$
$458$	13.0338	+	9.46958i	0.609028	+	0.442485i
$459$		0			0
$460$	−2.37157	+	7.29895i	−0.110575	+	0.340315i
$461$	16.8858			0.786449			0.393225	−	0.919442i	$-0.371360\pi$
$461$	16.8858			0.786449			0.393225	+	0.919442i	$0.371360\pi$
$462$		0			0
$463$	−4.70959			−0.218873			−0.109437	−	0.993994i	$-0.534905\pi$
$463$	−4.70959			−0.218873			−0.109437	+	0.993994i	$0.534905\pi$
$464$	43.6547	−	134.355i	2.02662	−	6.23728i
$465$		0			0
$466$	−4.17991	−	3.03688i	−0.193630	−	0.140681i
$467$	4.76345	+	14.6604i	0.220426	+	0.678402i	0.998724	+	0.0505066i	$0.0160836\pi$
$467$	4.76345	+	14.6604i	0.220426	+	0.678402i	−0.778297	+	0.627896i	$0.783916\pi$
$468$		0			0
$469$	−8.07700	−	5.86829i	−0.372961	−	0.270972i
$470$	12.4540	−	9.04834i	0.574459	−	0.417369i
$471$		0			0
$472$	3.83037			0.176307
$473$	−37.4664	−	16.9443i	−1.72271	−	0.779100i
$474$		0			0
$475$	−1.31390	+	4.04376i	−0.0602857	+	0.185540i
$476$	46.5904	−	33.8499i	2.13547	−	1.55151i
$477$		0			0
$478$	1.73552	+	5.34138i	0.0793808	+	0.244309i
$479$	−3.04251	−	9.36388i	−0.139016	−	0.427847i	0.857177	−	0.515022i	$-0.172216\pi$
$479$	−3.04251	−	9.36388i	−0.139016	−	0.427847i	−0.996193	+	0.0871750i	$0.972216\pi$
$480$		0			0
$481$	−5.16642	+	3.75362i	−0.235568	+	0.171150i
$482$	13.0911	−	40.2904i	0.596285	−	1.83518i
$483$		0			0
$484$	−5.69662	−	61.0608i	−0.258937	−	2.77549i
$485$	−16.5938			−0.753484
$486$		0			0
$487$	6.61144	−	4.80349i	0.299593	−	0.217667i	−0.427825	−	0.903862i	$-0.640720\pi$
$487$	6.61144	−	4.80349i	0.299593	−	0.217667i	0.727418	+	0.686194i	$0.240720\pi$
$488$	114.164	+	82.9449i	5.16796	+	3.75474i
$489$		0			0
$490$	0.393875	+	1.21222i	0.0177934	+	0.0547626i
$491$	−31.2098	−	22.6752i	−1.40848	−	1.02332i	−0.993542	−	0.113468i	$-0.963804\pi$
$491$	−31.2098	−	22.6752i	−1.40848	−	1.02332i	−0.414936	−	0.909851i	$-0.636196\pi$
$492$		0			0
$493$	−10.3611	+	31.8880i	−0.466638	+	1.43617i
$494$	32.4720			1.46098
$495$		0			0
$496$	87.1006			3.91093
$497$	−7.73751	+	23.8136i	−0.347075	+	1.06819i
$498$		0			0
$499$	1.90088	+	1.38107i	0.0850950	+	0.0618251i	0.629519	−	0.776985i	$-0.283252\pi$
$499$	1.90088	+	1.38107i	0.0850950	+	0.0618251i	−0.544424	+	0.838810i	$0.683252\pi$
$500$	1.72280	+	5.30222i	0.0770458	+	0.237123i
$501$		0			0
$502$	−29.8755	−	21.7058i	−1.33341	−	0.968777i
$503$	−5.13915	+	3.73381i	−0.229143	+	0.166482i	−0.696433	−	0.717622i	$-0.745231\pi$
$503$	−5.13915	+	3.73381i	−0.229143	+	0.166482i	0.467290	+	0.884104i	$0.345231\pi$
$504$		0			0
$505$	0.539052			0.0239875
$506$	8.46267	−	9.28894i	0.376212	−	0.412944i
$507$		0			0
$508$	7.46075	−	22.9618i	0.331017	−	1.01877i
$509$	−24.2744	+	17.6364i	−1.07594	+	0.781719i	−0.976971	−	0.213371i	$-0.931556\pi$
$509$	−24.2744	+	17.6364i	−1.07594	+	0.781719i	−0.0989727	+	0.995090i	$0.531556\pi$
$510$		0			0
$511$	6.88883	+	21.2016i	0.304744	+	0.937906i
$512$	22.1005	+	68.0184i	0.976714	+	3.00602i
$513$		0			0
$514$	−21.4060	+	15.5524i	−0.944179	+	0.685986i
$515$	−1.88829	+	5.81156i	−0.0832079	+	0.256088i
$516$		0			0
$517$	−18.1673	+	3.75068i	−0.798995	+	0.164955i
$518$	−17.3041			−0.760300
$519$		0			0
$520$	22.0889	−	16.0485i	0.968661	−	0.703773i
$521$	19.3706	+	14.0736i	0.848641	+	0.616574i	0.924771	−	0.380524i	$-0.124256\pi$
$521$	19.3706	+	14.0736i	0.848641	+	0.616574i	−0.0761299	+	0.997098i	$0.524256\pi$
$522$		0			0
$523$	−5.25118	−	16.1615i	−0.229618	−	0.706692i	−0.997790	−	0.0664479i	$-0.978833\pi$
$523$	−5.25118	−	16.1615i	−0.229618	−	0.706692i	0.768172	−	0.640244i	$-0.221167\pi$
$524$	52.9115	+	38.4425i	2.31145	+	1.67937i
$525$		0			0
$526$	−19.9169	+	61.2980i	−0.868420	+	2.67272i
$527$	−20.6726			−0.900511
$528$		0			0
$529$	−21.1050			−0.917609
$530$	−0.462510	+	1.42346i	−0.0200901	+	0.0618311i
$531$		0			0
$532$	52.3900	+	38.0635i	2.27139	+	1.65026i
$533$	−7.39076	−	22.7464i	−0.320129	−	0.985257i
$534$		0			0
$535$	−7.99070	−	5.80559i	−0.345468	−	0.250997i
$536$	−29.0918	+	21.1364i	−1.25657	+	0.912955i
$537$		0			0
$538$	26.0424			1.12277
$539$	0.169480	−	1.52658i	0.00730003	−	0.0657542i
$540$		0			0
$541$	0.384841	−	1.18442i	0.0165456	−	0.0509221i	−0.942443	−	0.334367i	$-0.891477\pi$
$541$	0.384841	−	1.18442i	0.0165456	−	0.0509221i	0.958988	+	0.283445i	$0.0914774\pi$
$542$	−56.8818	+	41.3270i	−2.44328	+	1.77515i
$543$		0			0
$544$	−28.2397	−	86.9127i	−1.21077	−	3.72635i
$545$	−1.68316	−	5.18024i	−0.0720988	−	0.221897i
$546$		0			0
$547$	−6.24250	+	4.53544i	−0.266910	+	0.193922i	−0.713188	−	0.700973i	$-0.752749\pi$
$547$	−6.24250	+	4.53544i	−0.266910	+	0.193922i	0.446278	+	0.894895i	$0.352749\pi$
$548$	23.4027	−	72.0261i	0.999713	−	3.07680i
$549$		0			0
$550$	1.00724	−	9.07256i	0.0429487	−	0.386855i
$551$	−37.7027			−1.60619
$552$		0			0
$553$	7.61848	−	5.53515i	0.323971	−	0.235379i
$554$	10.3546	+	7.52308i	0.439926	+	0.319625i
$555$		0			0
$556$	−20.7290	−	63.7973i	−0.879105	−	2.70561i
$557$	−8.83599	−	6.41973i	−0.374393	−	0.272013i	0.384637	−	0.923068i	$-0.374327\pi$
$557$	−8.83599	−	6.41973i	−0.374393	−	0.272013i	−0.759030	+	0.651055i	$0.774327\pi$
$558$		0			0
$559$	−10.6310	+	32.7188i	−0.449642	+	1.38386i
$560$	43.5225			1.83916
$561$		0			0
$562$	29.7366			1.25436
$563$	3.77104	−	11.6061i	0.158930	−	0.489137i	−0.839608	−	0.543193i	$-0.817215\pi$
$563$	3.77104	−	11.6061i	0.158930	−	0.489137i	0.998538	+	0.0540564i	$0.0172151\pi$
$564$		0			0
$565$	−0.629096	−	0.457065i	−0.0264663	−	0.0192289i
$566$	1.70668	+	5.25262i	0.0717370	+	0.220784i
$567$		0			0
$568$	72.9620	+	53.0100i	3.06142	+	2.22425i
$569$	−5.39492	+	3.91964i	−0.226167	+	0.164320i	−0.695098	−	0.718915i	$-0.744639\pi$
$569$	−5.39492	+	3.91964i	−0.226167	+	0.164320i	0.468931	+	0.883235i	$0.344639\pi$
$570$		0			0
$571$	−9.35392			−0.391450			−0.195725	−	0.980659i	$-0.562706\pi$
$571$	−9.35392			−0.391450			−0.195725	+	0.980659i	$0.562706\pi$
$572$	−50.2481	+	10.3739i	−2.10098	+	0.433753i
$573$		0			0
$574$	20.0266	−	61.6355i	0.835894	−	2.57262i
$575$	1.11368	−	0.809136i	0.0464436	−	0.0337433i
$576$		0			0
$577$	−3.38517	−	10.4185i	−0.140927	−	0.433727i	0.855538	−	0.517740i	$-0.173226\pi$
$577$	−3.38517	−	10.4185i	−0.140927	−	0.433727i	−0.996465	+	0.0840124i	$0.973226\pi$
$578$	−2.29862	−	7.07444i	−0.0956102	−	0.294258i
$579$		0			0
$580$	−39.9948	+	29.0579i	−1.66069	+	1.20656i
$581$	−3.92949	+	12.0937i	−0.163023	+	0.501732i
$582$		0			0
$583$	1.21466	−	1.33326i	0.0503062	−	0.0552179i
$584$	80.2941			3.32259
$585$		0			0
$586$	1.34168	−	0.974789i	0.0554244	−	0.0402682i
$587$	19.3936	+	14.0902i	0.800458	+	0.581567i	0.911048	−	0.412299i	$-0.135274\pi$
$587$	19.3936	+	14.0902i	0.800458	+	0.581567i	−0.110590	+	0.993866i	$0.535274\pi$
$588$		0			0
$589$	−7.18337	−	22.1081i	−0.295986	−	0.910950i
$590$	−0.866786	−	0.629757i	−0.0356850	−	0.0259267i
$591$		0			0
$592$	−11.3301	+	34.8704i	−0.465663	+	1.43316i
$593$	−2.17705			−0.0894006			−0.0447003	−	0.999000i	$-0.514233\pi$
$593$	−2.17705			−0.0894006			−0.0447003	+	0.999000i	$0.514233\pi$
$594$		0			0
$595$	−10.3297			−0.423476
$596$	−23.7632	+	73.1356i	−0.973378	+	2.99575i
$597$		0			0
$598$	−8.50530	−	6.17946i	−0.347808	−	0.252697i
$599$	−8.89601	−	27.3791i	−0.363481	−	1.11868i	−0.950927	−	0.309416i	$-0.899867\pi$
$599$	−8.89601	−	27.3791i	−0.363481	−	1.11868i	0.587446	−	0.809263i	$-0.300133\pi$
$600$		0			0
$601$	8.44390	+	6.13486i	0.344434	+	0.250246i	0.746530	−	0.665351i	$-0.231718\pi$
$601$	8.44390	+	6.13486i	0.344434	+	0.250246i	−0.402096	+	0.915597i	$0.631718\pi$
$602$	−75.4165	+	54.7933i	−3.07375	+	2.23321i
$603$		0			0
$604$	−94.8115			−3.85782
$605$	−5.61103	+	9.46131i	−0.228121	+	0.384657i
$606$		0			0
$607$	9.06265	−	27.8920i	0.367842	−	1.13210i	−0.580341	−	0.814374i	$-0.697081\pi$
$607$	9.06265	−	27.8920i	0.367842	−	1.13210i	0.948182	−	0.317727i	$-0.102919\pi$
$608$	83.1355	−	60.4015i	3.37159	−	2.44960i
$609$		0			0
$610$	−12.1974	−	37.5397i	−0.493858	−	1.51994i
$611$	4.79595	+	14.7604i	0.194023	+	0.597142i
$612$		0			0
$613$	22.3217	−	16.2176i	0.901563	−	0.655024i	−0.0373040	−	0.999304i	$-0.511877\pi$
$613$	22.3217	−	16.2176i	0.901563	−	0.655024i	0.938867	+	0.344280i	$0.111877\pi$
$614$	26.1713	−	80.5470i	1.05619	−	3.25061i
$615$		0			0
$616$	−81.2320	−	36.7375i	−3.27293	−	1.48019i
$617$	46.9079			1.88844			0.944220	−	0.329315i	$-0.106818\pi$
$617$	46.9079			1.88844			0.944220	+	0.329315i	$0.106818\pi$
$618$		0			0
$619$	15.4577	−	11.2307i	0.621296	−	0.451398i	−0.232078	−	0.972697i	$-0.574552\pi$
$619$	15.4577	−	11.2307i	0.621296	−	0.451398i	0.853374	+	0.521299i	$0.174552\pi$
$620$	−24.6590	−	17.9158i	−0.990331	−	0.719517i
$621$		0			0
$622$	−1.22716	−	3.77682i	−0.0492048	−	0.151437i
$623$	−14.6381	−	10.6352i	−0.586462	−	0.426090i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	64.6767			2.58500
$627$		0			0
$628$	−20.1306			−0.803298
$629$	2.68909	−	8.27618i	0.107221	−	0.329993i
$630$		0			0
$631$	24.9280	+	18.1112i	0.992368	+	0.720997i	0.960438	−	0.278493i	$-0.0898348\pi$
$631$	24.9280	+	18.1112i	0.992368	+	0.720997i	0.0319295	+	0.999490i	$0.489835\pi$
$632$	−10.4813	−	32.2580i	−0.416922	−	1.28316i
$633$		0			0
$634$	31.8814	+	23.1632i	1.26617	+	0.919927i
$635$	−3.50353	+	2.54547i	−0.139034	+	0.101014i
$636$		0			0
$637$	−1.28504			−0.0509152
$638$	79.2721	−	16.3659i	3.13841	−	0.647933i
$639$		0			0
$640$	14.5379	−	44.7432i	0.574663	−	1.76863i
$641$	4.27097	−	3.10304i	0.168693	−	0.122563i	−0.500235	−	0.865889i	$-0.666753\pi$
$641$	4.27097	−	3.10304i	0.168693	−	0.122563i	0.668929	+	0.743327i	$0.266753\pi$
$642$		0			0
$643$	−13.5247	−	41.6249i	−0.533364	−	1.64152i	−0.747158	−	0.664646i	$-0.768582\pi$
$643$	−13.5247	−	41.6249i	−0.533364	−	1.64152i	0.213795	−	0.976879i	$-0.431418\pi$
$644$	−6.47883	−	19.9398i	−0.255302	−	0.785737i
$645$		0			0
$646$	−35.7979	+	26.0087i	−1.40845	+	1.02330i
$647$	9.70364	−	29.8647i	0.381489	−	1.17410i	−0.557506	−	0.830173i	$-0.688242\pi$
$647$	9.70364	−	29.8647i	0.381489	−	1.17410i	0.938995	−	0.343930i	$-0.111758\pi$
$648$		0			0
$649$	0.638996	+	1.12187i	0.0250828	+	0.0440374i
$650$	−7.63712			−0.299552
$651$		0			0
$652$	16.3431	−	11.8739i	0.640044	−	0.465019i
$653$	−26.0527	−	18.9284i	−1.01952	−	0.740726i	−0.0533374	−	0.998577i	$-0.516986\pi$
$653$	−26.0527	−	18.9284i	−1.01952	−	0.740726i	−0.966185	+	0.257850i	$0.916986\pi$
$654$		0			0
$655$	−3.62513	−	11.1570i	−0.141646	−	0.435940i
$656$	−111.092	−	80.7131i	−4.33742	−	3.15132i
$657$		0			0
$658$	−12.9955	+	39.9960i	−0.506617	+	1.55921i
$659$	20.7286			0.807472			0.403736	−	0.914875i	$-0.367711\pi$
$659$	20.7286			0.807472			0.403736	+	0.914875i	$0.367711\pi$
$660$		0			0
$661$	−43.6387			−1.69735			−0.848673	−	0.528917i	$-0.822598\pi$
$661$	−43.6387			−1.69735			−0.848673	+	0.528917i	$0.822598\pi$
$662$	−4.19538	+	12.9121i	−0.163058	+	0.501842i
$663$		0			0
$664$	37.0537	+	26.9211i	1.43796	+	1.04474i
$665$	−3.58940	−	11.0470i	−0.139191	−	0.428385i
$666$		0			0
$667$	9.87539	+	7.17489i	0.382377	+	0.277813i
$668$	−10.2460	+	7.44419i	−0.396431	+	0.288024i
$669$		0			0
$670$	10.0583			0.388588
$671$	−5.24841	+	47.2745i	−0.202613	+	1.82501i
$672$		0			0
$673$	−8.88682	+	27.3508i	−0.342562	+	1.05430i	0.620314	+	0.784353i	$0.287005\pi$
$673$	−8.88682	+	27.3508i	−0.342562	+	1.05430i	−0.962876	+	0.269944i	$0.912995\pi$
$674$	−17.1287	+	12.4447i	−0.659772	+	0.479352i
$675$		0			0
$676$	−9.13142	−	28.1036i	−0.351208	−	1.08091i
$677$	−4.31414	−	13.2776i	−0.165806	−	0.510298i	0.833289	−	0.552838i	$-0.186455\pi$
$677$	−4.31414	−	13.2776i	−0.165806	−	0.510298i	−0.999095	+	0.0425397i	$0.986455\pi$
$678$		0			0
$679$	36.6743	−	26.6455i	1.40743	−	1.02256i
$680$	−11.4971	+	35.3846i	−0.440896	+	1.35694i
$681$		0			0
$682$	24.7001	+	43.3655i	0.945815	+	1.66055i
$683$	12.1334			0.464272			0.232136	−	0.972683i	$-0.425429\pi$
$683$	12.1334			0.464272			0.232136	+	0.972683i	$0.425429\pi$
$684$		0			0
$685$	−10.9898	+	7.98455i	−0.419898	+	0.305074i
$686$	39.7633	+	28.8897i	1.51817	+	1.10302i
$687$		0			0
$688$	61.0368	+	187.852i	2.32700	+	7.16178i
$689$	−1.22078	−	0.886950i	−0.0465081	−	0.0337901i
$690$		0			0
$691$	−7.41129	+	22.8096i	−0.281939	+	0.867719i	0.705361	+	0.708849i	$0.250785\pi$
$691$	−7.41129	+	22.8096i	−0.281939	+	0.867719i	−0.987300	+	0.158870i	$0.949215\pi$
$692$	−107.435			−4.08405
$693$		0			0
$694$	47.2459			1.79343
$695$	−3.71815	+	11.4433i	−0.141037	+	0.434068i
$696$		0			0
$697$	26.3667	+	19.1565i	0.998711	+	0.725606i
$698$	20.6507	+	63.5562i	0.781639	+	2.40564i
$699$		0			0
$700$	−12.3217	−	8.95221i	−0.465715	−	0.338362i
$701$	34.5576	−	25.1075i	1.30522	−	0.948298i	0.305229	−	0.952279i	$-0.401267\pi$
$701$	34.5576	−	25.1075i	1.30522	−	0.948298i	0.999992	+	0.00398054i	$0.00126705\pi$
$702$		0			0
$703$	9.78532			0.369060
$704$	−77.4083	+	84.9661i	−2.91743	+	3.20228i
$705$		0			0
$706$	−4.97206	+	15.3024i	−0.187126	+	0.575914i
$707$	−1.19137	+	0.865583i	−0.0448062	+	0.0325536i
$708$		0			0
$709$	−1.28091	−	3.94224i	−0.0481057	−	0.148054i	0.924118	−	0.382106i	$-0.124801\pi$
$709$	−1.28091	−	3.94224i	−0.0481057	−	0.148054i	−0.972224	+	0.234052i	$0.924801\pi$
$710$	−7.79534	−	23.9916i	−0.292554	−	0.900388i
$711$		0			0
$712$	−52.7235	+	38.3059i	−1.97590	+	1.43557i
$713$	−2.32569	+	7.15774i	−0.0870978	+	0.268059i
$714$		0			0
$715$	8.38538	+	3.79232i	0.313595	+	0.141825i
$716$	−40.5244			−1.51447
$717$		0			0
$718$	−18.1347	+	13.1756i	−0.676781	+	0.491710i
$719$	−21.3040	−	15.4783i	−0.794505	−	0.577241i	0.114792	−	0.993390i	$-0.463380\pi$
$719$	−21.3040	−	15.4783i	−0.794505	−	0.577241i	−0.909297	+	0.416148i	$0.863380\pi$
$720$		0			0
$721$	−5.15856	−	15.8764i	−0.192115	−	0.591268i
$722$	2.05224	+	1.49104i	0.0763766	+	0.0554909i
$723$		0			0
$724$	−13.9871	+	43.0480i	−0.519828	+	1.59987i
$725$	8.86735			0.329325
$726$		0			0
$727$	14.3772			0.533220			0.266610	−	0.963804i	$-0.414096\pi$
$727$	14.3772			0.533220			0.266610	+	0.963804i	$0.414096\pi$
$728$	−23.0493	+	70.9385i	−0.854265	+	2.62916i
$729$		0			0
$730$	−18.1700	−	13.2013i	−0.672502	−	0.488601i
$731$	−14.4865	−	44.5850i	−0.535804	−	1.64904i
$732$		0			0
$733$	−27.8882	−	20.2620i	−1.03007	−	0.748393i	−0.0617509	−	0.998092i	$-0.519668\pi$
$733$	−27.8882	−	20.2620i	−1.03007	−	0.748393i	−0.968324	+	0.249699i	$0.919668\pi$
$734$	−50.4886	+	36.6821i	−1.86357	+	1.35396i
$735$		0			0
$736$	−33.2700			−1.22635
$737$	−11.0438	−	4.99461i	−0.406805	−	0.183979i
$738$		0			0
$739$	−1.55016	+	4.77090i	−0.0570235	+	0.175500i	−0.975511	−	0.219949i	$-0.929411\pi$
$739$	−1.55016	+	4.77090i	−0.0570235	+	0.175500i	0.918488	+	0.395449i	$0.129411\pi$
$740$	10.3802	−	7.54165i	0.381583	−	0.277237i
$741$		0			0
$742$	−1.26352	−	3.88870i	−0.0463851	−	0.142759i
$743$	11.9473	+	36.7700i	0.438303	+	1.34896i	0.889663	+	0.456617i	$0.150939\pi$
$743$	11.9473	+	36.7700i	0.438303	+	1.34896i	−0.451360	+	0.892342i	$0.649061\pi$
$744$		0			0
$745$	11.1591	−	8.10754i	0.408837	−	0.297037i
$746$	−11.9552	+	36.7944i	−0.437712	+	1.34714i
$747$		0			0
$748$	47.0858	−	51.6831i	1.72163	−	1.88972i
$749$	26.9828			0.985930
$750$		0			0
$751$	4.20753	−	3.05695i	0.153535	−	0.111550i	−0.508365	−	0.861141i	$-0.669750\pi$
$751$	4.20753	−	3.05695i	0.153535	−	0.111550i	0.661901	+	0.749592i	$0.269750\pi$
$752$	72.0889	+	52.3757i	2.62881	+	1.90994i
$753$		0			0
$754$	−20.9269	−	64.4065i	−0.762114	−	2.34555i
$755$	13.7584	+	9.99604i	0.500718	+	0.363793i
$756$		0			0
$757$	1.91394	−	5.89049i	0.0695632	−	0.214093i	−0.910231	−	0.414100i	$-0.864096\pi$
$757$	1.91394	−	5.89049i	0.0695632	−	0.214093i	0.979795	+	0.200007i	$0.0640964\pi$
$758$	−69.4048			−2.52090
$759$		0			0
$760$	−41.8369			−1.51758
$761$	−3.65297	+	11.2427i	−0.132420	+	0.407547i	−0.995180	−	0.0980670i	$-0.968734\pi$
$761$	−3.65297	+	11.2427i	−0.132420	+	0.407547i	0.862760	+	0.505614i	$0.168734\pi$
$762$		0			0
$763$	12.0382	+	8.74626i	0.435812	+	0.316636i
$764$	−34.4923	−	106.156i	−1.24789	−	3.84061i
$765$		0			0
$766$	54.6230	+	39.6859i	1.97361	+	1.43391i
$767$	0.873884	−	0.634914i	0.0315541	−	0.0229254i
$768$		0			0
$769$	2.73424			0.0985992			0.0492996	−	0.998784i	$-0.484301\pi$
$769$	2.73424			0.0985992			0.0492996	+	0.998784i	$0.484301\pi$
$770$	12.3422	+	21.6689i	0.444781	+	0.780893i
$771$		0			0
$772$	−33.7192	+	103.777i	−1.21358	+	3.73502i
$773$	1.24618	−	0.905406i	0.0448221	−	0.0325652i	−0.565149	−	0.824989i	$-0.691181\pi$
$773$	1.24618	−	0.905406i	0.0448221	−	0.0325652i	0.609971	+	0.792424i	$0.291181\pi$
$774$		0			0
$775$	1.68946	+	5.19964i	0.0606874	+	0.186777i
$776$	−50.4554	−	155.286i	−1.81124	−	5.57443i
$777$		0			0
$778$	−53.7974	+	39.0861i	−1.92873	+	1.40131i
$779$	−11.3249	+	34.8543i	−0.405755	+	1.24879i
$780$		0			0
$781$	−3.35426	+	30.2131i	−0.120025	+	1.08111i
$782$	14.3260			0.512296
$783$		0			0
$784$	−5.96889	+	4.33665i	−0.213175	+	0.154881i
$785$	2.92121	+	2.12238i	0.104262	+	0.0757511i
$786$		0			0
$787$	−14.6565	−	45.1080i	−0.522446	−	1.60792i	−0.769311	−	0.638875i	$-0.779400\pi$
$787$	−14.6565	−	45.1080i	−0.522446	−	1.60792i	0.246864	−	0.969050i	$-0.420600\pi$
$788$	−103.307	−	75.0568i	−3.68015	−	2.67379i
$789$		0			0
$790$	−2.93175	+	9.02301i	−0.104307	+	0.321024i
$791$	2.12432			0.0755320
$792$		0			0
$793$	39.7948			1.41315
$794$	−25.0627	+	77.1350i	−0.889441	+	2.73742i
$795$		0			0
$796$	78.3314	+	56.9111i	2.77638	+	2.01716i
$797$	15.9360	+	49.0460i	0.564483	+	1.73730i	0.669483	+	0.742828i	$0.266516\pi$
$797$	15.9360	+	49.0460i	0.564483	+	1.73730i	−0.105000	+	0.994472i	$0.533484\pi$
$798$		0			0
$799$	−17.1097	−	12.4309i	−0.605297	−	0.439774i
$800$	−19.5527	+	14.2059i	−0.691293	+	0.502254i
$801$		0			0
$802$	−12.5997			−0.444912
$803$	13.3950	+	23.5173i	0.472698	+	0.829906i
$804$		0			0
$805$	−1.16210	+	3.57659i	−0.0409588	+	0.126058i
$806$	33.7795	−	24.5423i	1.18983	−	0.864465i
$807$		0			0
$808$	1.63905	+	5.04449i	0.0576617	+	0.177464i
$809$	8.49825	+	26.1549i	0.298783	+	0.919558i	0.981925	+	0.189273i	$0.0606130\pi$
$809$	8.49825	+	26.1549i	0.298783	+	0.919558i	−0.683142	+	0.730286i	$0.739387\pi$
$810$		0			0
$811$	−14.1696	+	10.2948i	−0.497562	+	0.361500i	−0.808085	−	0.589066i	$-0.799496\pi$
$811$	−14.1696	+	10.2948i	−0.497562	+	0.361500i	0.310523	+	0.950566i	$0.399496\pi$
$812$	41.7338	−	128.443i	1.46457	−	4.50748i
$813$		0			0
$814$	−20.5742	+	4.24759i	−0.721125	+	0.148878i
$815$	−3.62347			−0.126925
$816$		0			0
$817$	42.6473	−	30.9851i	1.49204	−	1.08403i
$818$	42.3316	+	30.7557i	1.48009	+	1.07535i
$819$		0			0
$820$	14.8493	+	45.7013i	0.518559	+	1.59596i
$821$	−10.2920	−	7.47755i	−0.359192	−	0.260968i	0.393523	−	0.919315i	$-0.371256\pi$
$821$	−10.2920	−	7.47755i	−0.359192	−	0.260968i	−0.752715	+	0.658346i	$0.771256\pi$
$822$		0			0
$823$	3.88274	−	11.9498i	0.135344	−	0.416545i	−0.860300	−	0.509789i	$-0.829724\pi$
$823$	3.88274	−	11.9498i	0.135344	−	0.416545i	0.995643	+	0.0932437i	$0.0297236\pi$
$824$	−60.1266			−2.09461
$825$		0			0
$826$	2.92694			0.101841
$827$	8.54516	−	26.2993i	0.297144	−	0.914516i	−0.685348	−	0.728215i	$-0.740350\pi$
$827$	8.54516	−	26.2993i	0.297144	−	0.914516i	0.982493	−	0.186301i	$-0.0596499\pi$
$828$		0			0
$829$	−25.7708	−	18.7236i	−0.895058	−	0.650298i	0.0421336	−	0.999112i	$-0.486584\pi$
$829$	−25.7708	−	18.7236i	−0.895058	−	0.650298i	−0.937192	+	0.348814i	$0.886584\pi$
$830$	−3.95886	−	12.1841i	−0.137414	−	0.422917i
$831$		0			0
$832$	77.7982	+	56.5237i	2.69717	+	1.95961i
$833$	1.41666	−	1.02927i	0.0490845	−	0.0356620i
$834$		0			0
$835$	2.27168			0.0786147
$836$	71.6337	+	32.3966i	2.47750	+	1.12046i
$837$		0			0
$838$	−2.16116	+	6.65138i	−0.0746562	+	0.229768i
$839$	18.7145	−	13.5968i	0.646095	−	0.469415i	−0.215844	−	0.976428i	$-0.569250\pi$
$839$	18.7145	−	13.5968i	0.646095	−	0.469415i	0.861939	+	0.507013i	$0.169250\pi$
$840$		0			0
$841$	15.3365	+	47.2009i	0.528844	+	1.62762i
$842$	1.74671	+	5.37583i	0.0601957	+	0.185263i
$843$		0			0
$844$	−74.9194	+	54.4321i	−2.57883	+	1.87363i
$845$	−1.63790	+	5.04093i	−0.0563454	+	0.173413i
$846$		0			0
$847$	−2.79142	−	29.9206i	−0.0959144	−	1.02808i
$848$	−8.66361			−0.297510
$849$		0			0
$850$	8.41936	−	6.11702i	0.288782	−	0.209812i
$851$	−2.56305	−	1.86216i	−0.0878601	−	0.0638341i
$852$		0			0
$853$	−4.33989	−	13.3568i	−0.148595	−	0.457328i	0.848861	−	0.528616i	$-0.177289\pi$
$853$	−4.33989	−	13.3568i	−0.148595	−	0.457328i	−0.997456	+	0.0712883i	$0.977289\pi$
$854$	87.2373	+	63.3816i	2.98520	+	2.16887i
$855$		0			0
$856$	30.0324	−	92.4302i	1.02649	−	3.15920i
$857$	26.1013			0.891603			0.445801	−	0.895132i	$-0.352919\pi$
$857$	26.1013			0.891603			0.445801	+	0.895132i	$0.352919\pi$
$858$		0			0
$859$	1.98117			0.0675967			0.0337983	−	0.999429i	$-0.489240\pi$
$859$	1.98117			0.0675967			0.0337983	+	0.999429i	$0.489240\pi$
$860$	21.3594	−	65.7374i	0.728349	−	2.24163i
$861$		0			0
$862$	−84.3702	−	61.2986i	−2.87366	−	2.08784i
$863$	5.99993	+	18.4659i	0.204240	+	0.628586i	0.999744	+	0.0226375i	$0.00720636\pi$
$863$	5.99993	+	18.4659i	0.204240	+	0.628586i	−0.795504	+	0.605949i	$0.792794\pi$
$864$		0			0
$865$	15.5901	+	11.3269i	0.530081	+	0.385126i
$866$	−20.2771	+	14.7321i	−0.689043	+	0.500619i
$867$		0			0
$868$	83.2680			2.82630
$869$	7.69949	−	8.45125i	0.261187	−	0.286689i
$870$		0			0
$871$	−3.13365	+	9.64439i	−0.106180	+	0.326788i
$872$	43.3592	−	31.5023i	1.46833	−	1.06680i
$873$		0			0
$874$	4.97803	+	15.3208i	0.168385	+	0.518234i
$875$	0.844194	+	2.59816i	0.0285390	+	0.0878339i
$876$		0			0
$877$	8.26881	−	6.00764i	0.279218	−	0.202864i	−0.439358	−	0.898312i	$-0.644794\pi$
$877$	8.26881	−	6.00764i	0.279218	−	0.202864i	0.718576	+	0.695448i	$0.244794\pi$
$878$	26.4230	−	81.3217i	0.891734	−	2.74447i
$879$		0			0
$880$	51.7472	−	10.6833i	1.74440	−	0.360135i
$881$	−26.4278			−0.890377			−0.445188	−	0.895437i	$-0.646863\pi$
$881$	−26.4278			−0.890377			−0.445188	+	0.895437i	$0.646863\pi$
$882$		0			0
$883$	−35.7491	+	25.9732i	−1.20305	+	0.874068i	−0.994581	−	0.103961i	$-0.966848\pi$
$883$	−35.7491	+	25.9732i	−1.20305	+	0.874068i	−0.208470	+	0.978029i	$0.566848\pi$
$884$	−47.3230	−	34.3822i	−1.59165	−	1.15640i
$885$		0			0
$886$	−12.6821	−	39.0316i	−0.426065	−	1.31129i
$887$	−7.12089	−	5.17363i	−0.239096	−	0.173714i	0.461784	−	0.886992i	$-0.347209\pi$
$887$	−7.12089	−	5.17363i	−0.239096	−	0.173714i	−0.700881	+	0.713279i	$0.747209\pi$
$888$		0			0
$889$	3.65587	−	11.2516i	0.122614	−	0.377367i
$890$	18.2289			0.611034
$891$		0			0
$892$	−49.9554			−1.67263
$893$	7.34883	−	22.6174i	0.245919	−	0.756861i
$894$		0			0
$895$	5.88061	+	4.27251i	0.196567	+	0.142814i
$896$	39.7158	+	122.233i	1.32681	+	4.08350i
$897$		0			0
$898$	−57.0242	−	41.4305i	−1.90292	−	1.38255i
$899$	−39.2210	+	28.4957i	−1.30809	+	0.950385i
$900$		0			0
$901$	2.05623			0.0685031
$902$	8.68164	−	78.1990i	0.289067	−	2.60374i
$903$		0			0
$904$	2.36441	−	7.27689i	0.0786389	−	0.242026i
$905$	6.56830	−	4.77215i	0.218338	−	0.158632i
$906$		0			0
$907$	5.82018	+	17.9127i	0.193256	+	0.594781i	0.999993	+	0.00386938i	$0.00123167\pi$
$907$	5.82018	+	17.9127i	0.193256	+	0.594781i	−0.806737	+	0.590911i	$0.798768\pi$
$908$	1.82882	+	5.62854i	0.0606916	+	0.186790i
$909$		0			0
$910$	16.8790	−	12.2633i	0.559534	−	0.406525i
$911$	−6.82807	+	21.0146i	−0.226224	+	0.696246i	0.771941	+	0.635694i	$0.219286\pi$
$911$	−6.82807	+	21.0146i	−0.226224	+	0.696246i	−0.998165	+	0.0605519i	$0.980714\pi$
$912$		0			0
$913$	−1.70346	+	15.3437i	−0.0563762	+	0.507803i
$914$	22.0903			0.730681
$915$		0			0
$916$	26.4014	−	19.1818i	0.872328	−	0.633784i
$917$	25.9274	+	18.8373i	0.856198	+	0.622064i
$918$		0			0
$919$	1.25113	+	3.85059i	0.0412710	+	0.127019i	0.969569	−	0.244818i	$-0.0787281\pi$
$919$	1.25113	+	3.85059i	0.0412710	+	0.127019i	−0.928298	+	0.371837i	$0.878728\pi$
$920$	10.9582	+	7.96162i	0.361282	+	0.262487i
$921$		0			0
$922$	14.3614	−	44.1999i	0.472968	−	1.45565i
$923$	25.4328			0.837132
$924$		0			0
$925$	−2.30142			−0.0756703
$926$	−4.00552	+	12.3277i	−0.131630	+	0.405114i
$927$		0			0
$928$	−173.381	−	125.969i	−5.69151	−	4.13512i
$929$	12.4502	+	38.3178i	0.408478	+	1.25717i	0.917956	+	0.396682i	$0.129838\pi$
$929$	12.4502	+	38.3178i	0.408478	+	1.25717i	−0.509478	+	0.860484i	$0.670162\pi$
$930$		0			0
$931$	1.59301	+	1.15739i	0.0522088	+	0.0379319i
$932$	−8.46690	+	6.15156i	−0.277343	+	0.201501i
$933$		0			0
$934$	42.4261			1.38822
$935$	−12.2818	+	2.53560i	−0.401656	+	0.0829229i
$936$		0			0
$937$	11.4264	−	35.1669i	0.373285	−	1.14885i	−0.571344	−	0.820711i	$-0.693578\pi$
$937$	11.4264	−	35.1669i	0.373285	−	1.14885i	0.944629	−	0.328142i	$-0.106422\pi$
$938$	−22.2302	+	16.1512i	−0.725843	+	0.527356i
$939$		0			0
$940$	−9.63586	−	29.6561i	−0.314287	−	0.967276i
$941$	13.3298	+	41.0250i	0.434540	+	1.33738i	0.893558	+	0.448949i	$0.148201\pi$
$941$	13.3298	+	41.0250i	0.434540	+	1.33738i	−0.459018	+	0.888427i	$0.651799\pi$
$942$		0			0
$943$	9.59912	−	6.97417i	0.312590	−	0.227110i
$944$	1.91645	−	5.89822i	0.0623751	−	0.191971i
$945$		0			0
$946$	−76.2184	+	83.6601i	−2.47807	+	2.72002i
$947$	42.5933			1.38410			0.692048	−	0.721851i	$-0.256709\pi$
$947$	42.5933			1.38410			0.692048	+	0.721851i	$0.256709\pi$
$948$		0			0
$949$	18.3188	−	13.3094i	0.594653	−	0.432041i
$950$	9.46740	+	6.87847i	0.307163	+	0.223167i
$951$		0			0
$952$	−31.4087	−	96.6661i	−1.01796	−	3.13296i
$953$	−22.1144	−	16.0671i	−0.716357	−	0.520464i	0.168861	−	0.985640i	$-0.445991\pi$
$953$	−22.1144	−	16.0671i	−0.716357	−	0.520464i	−0.885218	+	0.465176i	$0.845991\pi$
$954$		0			0
$955$	−6.18687	+	19.0412i	−0.200202	+	0.616160i
$956$	11.3764			0.367939
$957$		0			0
$958$	−27.0984			−0.875509
$959$	11.4676	−	35.2938i	0.370309	−	1.13969i
$960$		0			0
$961$	0.897578	+	0.652129i	0.0289541	+	0.0210364i
$962$	5.43135	+	16.7160i	0.175114	+	0.538945i
$963$		0			0
$964$	−69.4242	−	50.4396i	−2.23600	−	1.62455i
$965$	15.8344	−	11.5043i	0.509727	−	0.370338i
$966$		0			0
$967$	20.7000			0.665668			0.332834	−	0.942985i	$-0.391995\pi$
$967$	20.7000			0.665668			0.332834	+	0.942985i	$0.391995\pi$
$968$	−105.601	−	23.7402i	−3.39413	−	0.763038i
$969$		0			0
$970$	−14.1131	+	43.4355i	−0.453143	+	1.39463i
$971$	22.2682	−	16.1788i	0.714619	−	0.519201i	−0.170041	−	0.985437i	$-0.554390\pi$
$971$	22.2682	−	16.1788i	0.714619	−	0.519201i	0.884660	+	0.466236i	$0.154390\pi$
$972$		0			0
$973$	−10.1575	−	31.2615i	−0.325634	−	1.00220i
$974$	−6.95048	−	21.3914i	−0.222708	−	0.685424i
$975$		0			0
$976$	184.843	−	134.296i	5.91668	−	4.29872i
$977$	−11.2775	+	34.7086i	−0.360799	+	1.11043i	0.591771	+	0.806106i	$0.298429\pi$
$977$	−11.2775	+	34.7086i	−0.360799	+	1.11043i	−0.952570	+	0.304320i	$0.901571\pi$
$978$		0			0
$979$	−20.0149	−	9.05181i	−0.639679	−	0.289297i
$980$	2.58186			0.0824746
$981$		0			0
$982$	−85.8983	+	62.4087i	−2.74112	+	1.99154i
$983$	39.7265	+	28.8630i	1.26708	+	0.920587i	0.999082	−	0.0428334i	$-0.0136385\pi$
$983$	39.7265	+	28.8630i	1.26708	+	0.920587i	0.267996	+	0.963420i	$0.413638\pi$
$984$		0			0
$985$	7.07786	+	21.7834i	0.225519	+	0.694077i
$986$	74.6574	+	54.2418i	2.37758	+	1.72741i
$987$		0			0
$988$	20.3258	−	62.5565i	0.646651	−	1.99019i
$989$	−17.0670			−0.542699
$990$		0			0
$991$	−5.08586			−0.161558			−0.0807788	−	0.996732i	$-0.525741\pi$
$991$	−5.08586			−0.161558			−0.0807788	+	0.996732i	$0.525741\pi$
$992$	40.8318	−	125.667i	1.29641	−	3.98994i
$993$		0			0
$994$	55.7533	+	40.5071i	1.76839	+	1.28481i
$995$	−5.36672	−	16.5171i	−0.170137	−	0.523627i
$996$		0			0
$997$	14.8334	+	10.7771i	0.469777	+	0.341313i	0.797354	−	0.603511i	$-0.206232\pi$
$997$	14.8334	+	10.7771i	0.469777	+	0.341313i	−0.327577	+	0.944824i	$0.606232\pi$
$998$	5.23176	−	3.80110i	0.165609	−	0.120322i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.g.361.4	yes	16
3.2	odd	2		495.2.n.h.361.1	yes	16
11.4	even	5		5445.2.a.cd.1.8		8
11.5	even	5	inner	495.2.n.g.181.4	✓	16
11.7	odd	10		5445.2.a.cb.1.1		8
33.5	odd	10		495.2.n.h.181.1	yes	16
33.26	odd	10		5445.2.a.ca.1.1		8
33.29	even	10		5445.2.a.cc.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.181.4	✓	16	11.5	even	5	inner
495.2.n.g.361.4	yes	16	1.1	even	1	trivial
495.2.n.h.181.1	yes	16	33.5	odd	10
495.2.n.h.361.1	yes	16	3.2	odd	2
5445.2.a.ca.1.1		8	33.26	odd	10
5445.2.a.cb.1.1		8	11.7	odd	10
5445.2.a.cc.1.8		8	33.29	even	10
5445.2.a.cd.1.8		8	11.4	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.850504 - 2.61758i) q^{2} +(-4.51034 - 3.27695i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.21013 - 1.60575i) q^{7} +(-7.96046 + 5.78361i) q^{8} +O(q^{10})\)	\(q+(0.850504 - 2.61758i) q^{2} +(-4.51034 - 3.27695i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.21013 - 1.60575i) q^{7} +(-7.96046 + 5.78361i) q^{8} +2.75229 q^{10} +(-3.02195 - 1.36669i) q^{11} +(-0.857468 + 2.63902i) q^{13} +(-6.08291 + 4.41949i) q^{14} +(4.92308 + 15.1517i) q^{16} +(-1.16845 - 3.59612i) q^{17} +(3.43983 - 2.49918i) q^{19} +(1.72280 - 5.30222i) q^{20} +(-6.14759 + 6.74782i) q^{22} -1.37658 q^{23} +(-0.809017 + 0.587785i) q^{25} +(6.17856 + 4.48898i) q^{26} +(4.70645 + 14.4850i) q^{28} +(-7.17384 - 5.21210i) q^{29} +(1.68946 - 5.19964i) q^{31} +24.1685 q^{32} -10.4069 q^{34} +(0.844194 - 2.59816i) q^{35} +(1.86189 + 1.35274i) q^{37} +(-3.61622 - 11.1296i) q^{38} +(-7.96046 - 5.78361i) q^{40} +(-6.97314 + 5.06629i) q^{41} +12.3981 q^{43} +(9.15144 + 16.0670i) q^{44} +(-1.17079 + 3.60332i) q^{46} +(4.52496 - 3.28757i) q^{47} +(0.143108 + 0.440442i) q^{49} +(0.850504 + 2.61758i) q^{50} +(12.5154 - 9.09297i) q^{52} +(-0.168046 + 0.517191i) q^{53} +(0.365963 - 3.29637i) q^{55} +26.8807 q^{56} +(-19.7445 + 14.3452i) q^{58} +(-0.314933 - 0.228812i) q^{59} +(-4.43173 - 13.6395i) q^{61} +(-12.1736 - 8.84462i) q^{62} +(10.7092 - 32.9596i) q^{64} -2.77482 q^{65} +3.65454 q^{67} +(-6.51421 + 20.0487i) q^{68} +(-6.08291 - 4.41949i) q^{70} +(-2.83231 - 8.71697i) q^{71} +(-6.60178 - 4.79647i) q^{73} +(5.12445 - 3.72313i) q^{74} -23.7045 q^{76} +(4.48433 + 7.87305i) q^{77} +(-1.06521 + 3.27837i) q^{79} +(-12.8888 + 9.36425i) q^{80} +(7.33073 + 22.5617i) q^{82} +(-1.43839 - 4.42691i) q^{83} +(3.05904 - 2.22252i) q^{85} +(10.5446 - 32.4530i) q^{86} +(31.9605 - 6.59832i) q^{88} +6.62318 q^{89} +(6.13272 - 4.45568i) q^{91} +(6.20886 + 4.51100i) q^{92} +(-4.75700 - 14.6405i) q^{94} +(3.43983 + 2.49918i) q^{95} +(-5.12775 + 15.7816i) q^{97} +1.27461 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8	\( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8 + 8 * q^10 + 4 * q^11 + 2 * q^13 - 22 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 + 2 * q^20 - 28 * q^22 + 8 * q^23 - 4 * q^25 + 6 * q^26 - 2 * q^28 - 26 * q^29 - 10 * q^31 + 56 * q^32 - 4 * q^34 - 4 * q^35 + 22 * q^37 - 30 * q^38 - 6 * q^40 - 6 * q^41 + 28 * q^43 + 68 * q^44 + 16 * q^46 - 20 * q^47 + 10 * q^49 - 2 * q^50 + 30 * q^52 + 14 * q^53 - 6 * q^55 + 68 * q^56 - 6 * q^58 - 16 * q^59 - 38 * q^61 - 20 * q^62 + 10 * q^64 + 12 * q^65 + 20 * q^67 - 48 * q^68 - 22 * q^70 - 54 * q^71 + 2 * q^73 + 28 * q^74 - 44 * q^76 + 34 * q^77 - 12 * q^79 - 22 * q^80 + 30 * q^82 - 28 * q^83 - 4 * q^85 + 74 * q^86 + 46 * q^88 + 76 * q^89 - 34 * q^91 - 8 * q^92 - 10 * q^94 - 4 * q^95 - 18 * q^97 + 8 * q^98

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