LMFDB - Embedded newform 650.2.e.d.601.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(451,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,-1,-2,0,-1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.1
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	650.601
Dual form			650.2.e.d.451.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.39564 - 2.41733i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.39564 + 2.41733i) q^{6} +(-0.895644 + 1.55130i) q^{7} +1.00000 q^{8} +(-2.39564 + 4.14938i) q^{9} +(1.89564 + 3.28335i) q^{11} +2.79129 q^{12} +(3.50000 - 0.866025i) q^{13} +1.79129 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.395644 + 0.685275i) q^{17} +4.79129 q^{18} +(-2.50000 + 4.33013i) q^{19} +5.00000 q^{21} +(1.89564 - 3.28335i) q^{22} +(2.29129 + 3.96863i) q^{23} +(-1.39564 - 2.41733i) q^{24} +(-2.50000 - 2.59808i) q^{26} +5.00000 q^{27} +(-0.895644 - 1.55130i) q^{28} +(1.89564 + 3.28335i) q^{29} +9.58258 q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.29129 - 9.16478i) q^{33} +0.791288 q^{34} +(-2.39564 - 4.14938i) q^{36} +(-3.18693 - 5.51993i) q^{37} +5.00000 q^{38} +(-6.97822 - 7.25198i) q^{39} +(-6.08258 - 10.5353i) q^{41} +(-2.50000 - 4.33013i) q^{42} +(-5.47822 + 9.48855i) q^{43} -3.79129 q^{44} +(2.29129 - 3.96863i) q^{46} -0.791288 q^{47} +(-1.39564 + 2.41733i) q^{48} +(1.89564 + 3.28335i) q^{49} +2.20871 q^{51} +(-1.00000 + 3.46410i) q^{52} -4.58258 q^{53} +(-2.50000 - 4.33013i) q^{54} +(-0.895644 + 1.55130i) q^{56} +13.9564 q^{57} +(1.89564 - 3.28335i) q^{58} +(2.29129 - 3.96863i) q^{59} +(4.29129 - 7.43273i) q^{61} +(-4.79129 - 8.29875i) q^{62} +(-4.29129 - 7.43273i) q^{63} +1.00000 q^{64} -10.5826 q^{66} +(5.50000 + 9.52628i) q^{67} +(-0.395644 - 0.685275i) q^{68} +(6.39564 - 11.0776i) q^{69} +(-3.79129 + 6.56670i) q^{71} +(-2.39564 + 4.14938i) q^{72} +7.16515 q^{73} +(-3.18693 + 5.51993i) q^{74} +(-2.50000 - 4.33013i) q^{76} -6.79129 q^{77} +(-2.79129 + 9.66930i) q^{78} +14.9564 q^{79} +(0.208712 + 0.361500i) q^{81} +(-6.08258 + 10.5353i) q^{82} +6.16515 q^{83} +(-2.50000 + 4.33013i) q^{84} +10.9564 q^{86} +(5.29129 - 9.16478i) q^{87} +(1.89564 + 3.28335i) q^{88} +(-0.313068 - 0.542250i) q^{89} +(-1.79129 + 6.20520i) q^{91} -4.58258 q^{92} +(-13.3739 - 23.1642i) q^{93} +(0.395644 + 0.685275i) q^{94} +2.79129 q^{96} +(-4.60436 + 7.97498i) q^{97} +(1.89564 - 3.28335i) q^{98} -18.1652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} + q^{7} + 4 q^{8} - 5 q^{9} + 3 q^{11} + 2 q^{12} + 14 q^{13} - 2 q^{14} - 2 q^{16} + 3 q^{17} + 10 q^{18} - 10 q^{19} + 20 q^{21} + 3 q^{22} - q^{24} - 10 q^{26}+ \cdots - 36 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 + q^7 + 4 * q^8 - 5 * q^9 + 3 * q^11 + 2 * q^12 + 14 * q^13 - 2 * q^14 - 2 * q^16 + 3 * q^17 + 10 * q^18 - 10 * q^19 + 20 * q^21 + 3 * q^22 - q^24 - 10 * q^26 + 20 * q^27 + q^28 + 3 * q^29 + 20 * q^31 - 2 * q^32 + 12 * q^33 - 6 * q^34 - 5 * q^36 + q^37 + 20 * q^38 - 5 * q^39 - 6 * q^41 - 10 * q^42 + q^43 - 6 * q^44 + 6 * q^47 - q^48 + 3 * q^49 + 18 * q^51 - 4 * q^52 - 10 * q^54 + q^56 + 10 * q^57 + 3 * q^58 + 8 * q^61 - 10 * q^62 - 8 * q^63 + 4 * q^64 - 24 * q^66 + 22 * q^67 + 3 * q^68 + 21 * q^69 - 6 * q^71 - 5 * q^72 - 8 * q^73 + q^74 - 10 * q^76 - 18 * q^77 - 2 * q^78 + 14 * q^79 + 10 * q^81 - 6 * q^82 - 12 * q^83 - 10 * q^84 - 2 * q^86 + 12 * q^87 + 3 * q^88 - 15 * q^89 + 2 * q^91 - 26 * q^93 - 3 * q^94 + 2 * q^96 - 23 * q^97 + 3 * q^98 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.39564	−	2.41733i	−0.805775	−	1.39564i	−0.915766	−	0.401711i	$-0.868416\pi$
$3$	−1.39564	−	2.41733i	−0.805775	−	1.39564i	0.109991	−	0.993933i	$-0.464918\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.39564	+	2.41733i	−0.569769	+	0.986869i
$7$	−0.895644	+	1.55130i	−0.338522	+	0.586337i	−0.984155	−	0.177311i	$-0.943260\pi$
$7$	−0.895644	+	1.55130i	−0.338522	+	0.586337i	0.645633	+	0.763648i	$0.276593\pi$
$8$	1.00000			0.353553
$9$	−2.39564	+	4.14938i	−0.798548	+	1.38313i
$10$		0			0
$11$	1.89564	+	3.28335i	0.571558	+	0.989968i	0.996406	+	0.0847031i	$0.0269942\pi$
$11$	1.89564	+	3.28335i	0.571558	+	0.989968i	−0.424848	+	0.905265i	$0.639672\pi$
$12$	2.79129			0.805775
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	1.79129			0.478742
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.395644	+	0.685275i	−0.0959577	+	0.166204i	−0.910008	−	0.414591i	$-0.863925\pi$
$17$	−0.395644	+	0.685275i	−0.0959577	+	0.166204i	0.814050	+	0.580795i	$0.197258\pi$
$18$	4.79129			1.12932
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$	5.00000			1.09109
$22$	1.89564	−	3.28335i	0.404153	−	0.700013i
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	0.999675	−	0.0254855i	$-0.00811315\pi$
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	−0.521909	+	0.853001i	$0.674780\pi$
$24$	−1.39564	−	2.41733i	−0.284885	−	0.493435i
$25$		0			0
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$	5.00000			0.962250
$28$	−0.895644	−	1.55130i	−0.169261	−	0.293168i
$29$	1.89564	+	3.28335i	0.352012	+	0.609703i	0.986602	−	0.163146i	$-0.0521642\pi$
$29$	1.89564	+	3.28335i	0.352012	+	0.609703i	−0.634590	+	0.772849i	$0.718831\pi$
$30$		0			0
$31$	9.58258			1.72108			0.860541	−	0.509382i	$-0.170126\pi$
$31$	9.58258			1.72108			0.860541	+	0.509382i	$0.170126\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.29129	−	9.16478i	0.921095	−	1.59538i
$34$	0.791288			0.135705
$35$		0			0
$36$	−2.39564	−	4.14938i	−0.399274	−	0.691563i
$37$	−3.18693	−	5.51993i	−0.523928	−	0.907471i	−0.999612	−	0.0278541i	$-0.991133\pi$
$37$	−3.18693	−	5.51993i	−0.523928	−	0.907471i	0.475684	−	0.879616i	$-0.342201\pi$
$38$	5.00000			0.811107
$39$	−6.97822	−	7.25198i	−1.11741	−	1.16125i
$40$		0			0
$41$	−6.08258	−	10.5353i	−0.949939	−	1.64534i	−0.745547	−	0.666453i	$-0.767812\pi$
$41$	−6.08258	−	10.5353i	−0.949939	−	1.64534i	−0.204392	−	0.978889i	$-0.565522\pi$
$42$	−2.50000	−	4.33013i	−0.385758	−	0.668153i
$43$	−5.47822	+	9.48855i	−0.835421	+	1.44699i	0.0582668	+	0.998301i	$0.481443\pi$
$43$	−5.47822	+	9.48855i	−0.835421	+	1.44699i	−0.893687	+	0.448690i	$0.851891\pi$
$44$	−3.79129			−0.571558
$45$		0			0
$46$	2.29129	−	3.96863i	0.337832	−	0.585142i
$47$	−0.791288			−0.115421			−0.0577106	−	0.998333i	$-0.518380\pi$
$47$	−0.791288			−0.115421			−0.0577106	+	0.998333i	$0.518380\pi$
$48$	−1.39564	+	2.41733i	−0.201444	+	0.348911i
$49$	1.89564	+	3.28335i	0.270806	+	0.469050i
$50$		0			0
$51$	2.20871			0.309282
$52$	−1.00000	+	3.46410i	−0.138675	+	0.480384i
$53$	−4.58258			−0.629465			−0.314733	−	0.949180i	$-0.601915\pi$
$53$	−4.58258			−0.629465			−0.314733	+	0.949180i	$0.601915\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$		0			0
$56$	−0.895644	+	1.55130i	−0.119685	+	0.207301i
$57$	13.9564			1.84858
$58$	1.89564	−	3.28335i	0.248910	−	0.431125i
$59$	2.29129	−	3.96863i	0.298300	−	0.516671i	−0.677447	−	0.735572i	$-0.736914\pi$
$59$	2.29129	−	3.96863i	0.298300	−	0.516671i	0.975747	+	0.218900i	$0.0702470\pi$
$60$		0			0
$61$	4.29129	−	7.43273i	0.549443	−	0.951663i	−0.448870	−	0.893597i	$-0.648173\pi$
$61$	4.29129	−	7.43273i	0.549443	−	0.951663i	0.998313	−	0.0580661i	$-0.0184934\pi$
$62$	−4.79129	−	8.29875i	−0.608494	−	1.05394i
$63$	−4.29129	−	7.43273i	−0.540651	−	0.936436i
$64$	1.00000			0.125000
$65$		0			0
$66$	−10.5826			−1.30263
$67$	5.50000	+	9.52628i	0.671932	+	1.16382i	0.977356	+	0.211604i	$0.0678686\pi$
$67$	5.50000	+	9.52628i	0.671932	+	1.16382i	−0.305424	+	0.952217i	$0.598798\pi$
$68$	−0.395644	−	0.685275i	−0.0479789	−	0.0831018i
$69$	6.39564	−	11.0776i	0.769945	−	1.33358i
$70$		0			0
$71$	−3.79129	+	6.56670i	−0.449943	+	0.779324i	−0.998382	−	0.0568665i	$-0.981889\pi$
$71$	−3.79129	+	6.56670i	−0.449943	+	0.779324i	0.548439	+	0.836191i	$0.315222\pi$
$72$	−2.39564	+	4.14938i	−0.282329	+	0.489009i
$73$	7.16515			0.838618			0.419309	−	0.907844i	$-0.362272\pi$
$73$	7.16515			0.838618			0.419309	+	0.907844i	$0.362272\pi$
$74$	−3.18693	+	5.51993i	−0.370473	+	0.641679i
$75$		0			0
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	−6.79129			−0.773939
$78$	−2.79129	+	9.66930i	−0.316051	+	1.09483i
$79$	14.9564			1.68273			0.841365	−	0.540467i	$-0.181752\pi$
$79$	14.9564			1.68273			0.841365	+	0.540467i	$0.181752\pi$
$80$		0			0
$81$	0.208712	+	0.361500i	0.0231902	+	0.0401667i
$82$	−6.08258	+	10.5353i	−0.671708	+	1.16343i
$83$	6.16515			0.676713			0.338357	−	0.941018i	$-0.390129\pi$
$83$	6.16515			0.676713			0.338357	+	0.941018i	$0.390129\pi$
$84$	−2.50000	+	4.33013i	−0.272772	+	0.472456i
$85$		0			0
$86$	10.9564			1.18146
$87$	5.29129	−	9.16478i	0.567286	−	0.982567i
$88$	1.89564	+	3.28335i	0.202076	+	0.350006i
$89$	−0.313068	−	0.542250i	−0.0331852	−	0.0574784i	0.848956	−	0.528464i	$-0.177232\pi$
$89$	−0.313068	−	0.542250i	−0.0331852	−	0.0574784i	−0.882141	+	0.470985i	$0.843898\pi$
$90$		0			0
$91$	−1.79129	+	6.20520i	−0.187778	+	0.650482i
$92$	−4.58258			−0.477767
$93$	−13.3739	−	23.1642i	−1.38681	−	2.40202i
$94$	0.395644	+	0.685275i	0.0408076	+	0.0706808i
$95$		0			0
$96$	2.79129			0.284885
$97$	−4.60436	+	7.97498i	−0.467502	+	0.809736i	−0.999311	−	0.0371279i	$-0.988179\pi$
$97$	−4.60436	+	7.97498i	−0.467502	+	0.809736i	0.531809	+	0.846864i	$0.321512\pi$
$98$	1.89564	−	3.28335i	0.191489	−	0.331669i
$99$	−18.1652			−1.82567
$100$		0			0
$101$	9.87386	+	17.1020i	0.982486	+	1.70172i	0.652614	+	0.757690i	$0.273672\pi$
$101$	9.87386	+	17.1020i	0.982486	+	1.70172i	0.329872	+	0.944026i	$0.392995\pi$
$102$	−1.10436	−	1.91280i	−0.109348	−	0.189396i
$103$	2.58258			0.254469			0.127234	−	0.991873i	$-0.459390\pi$
$103$	2.58258			0.254469			0.127234	+	0.991873i	$0.459390\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$		0			0
$106$	2.29129	+	3.96863i	0.222550	+	0.385467i
$107$	−5.20871	−	9.02175i	−0.503545	−	0.872166i	−0.999992	−	0.00409850i	$-0.998695\pi$
$107$	−5.20871	−	9.02175i	−0.503545	−	0.872166i	0.496446	−	0.868067i	$-0.334638\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	1.83485			0.175747			0.0878733	−	0.996132i	$-0.471993\pi$
$109$	1.83485			0.175747			0.0878733	+	0.996132i	$0.471993\pi$
$110$		0			0
$111$	−8.89564	+	15.4077i	−0.844337	+	1.46243i
$112$	1.79129			0.169261
$113$	−0.313068	+	0.542250i	−0.0294510	+	0.0510106i	−0.880375	−	0.474278i	$-0.842709\pi$
$113$	−0.313068	+	0.542250i	−0.0294510	+	0.0510106i	0.850924	+	0.525288i	$0.176043\pi$
$114$	−6.97822	−	12.0866i	−0.653570	−	1.13202i
$115$		0			0
$116$	−3.79129			−0.352012
$117$	−4.79129	+	16.5975i	−0.442955	+	1.53444i
$118$	−4.58258			−0.421860
$119$	−0.708712	−	1.22753i	−0.0649675	−	0.112527i
$120$		0			0
$121$	−1.68693	+	2.92185i	−0.153357	+	0.265623i
$122$	−8.58258			−0.777030
$123$	−16.9782	+	29.4071i	−1.53087	+	2.65155i
$124$	−4.79129	+	8.29875i	−0.430270	+	0.745250i
$125$		0			0
$126$	−4.29129	+	7.43273i	−0.382298	+	0.662160i
$127$	8.18693	+	14.1802i	0.726473	+	1.25829i	0.958365	+	0.285546i	$0.0921750\pi$
$127$	8.18693	+	14.1802i	0.726473	+	1.25829i	−0.231892	+	0.972741i	$0.574492\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	30.5826			2.69265
$130$		0			0
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$	5.29129	+	9.16478i	0.460547	+	0.797692i
$133$	−4.47822	−	7.75650i	−0.388311	−	0.672574i
$134$	5.50000	−	9.52628i	0.475128	−	0.822945i
$135$		0			0
$136$	−0.395644	+	0.685275i	−0.0339262	+	0.0587619i
$137$	7.58258	−	13.1334i	0.647823	−	1.12206i	−0.335819	−	0.941927i	$-0.609013\pi$
$137$	7.58258	−	13.1334i	0.647823	−	1.12206i	0.983642	−	0.180136i	$-0.0576538\pi$
$138$	−12.7913			−1.08887
$139$	−10.7913	+	18.6911i	−0.915305	+	1.58535i	−0.108851	+	0.994058i	$0.534717\pi$
$139$	−10.7913	+	18.6911i	−0.915305	+	1.58535i	−0.806454	+	0.591297i	$0.798616\pi$
$140$		0			0
$141$	1.10436	+	1.91280i	0.0930036	+	0.161087i
$142$	7.58258			0.636316
$143$	9.47822	+	9.85005i	0.792609	+	0.823703i
$144$	4.79129			0.399274
$145$		0			0
$146$	−3.58258	−	6.20520i	−0.296496	−	0.513546i
$147$	5.29129	−	9.16478i	0.436418	−	0.755898i
$148$	6.37386			0.523928
$149$	1.97822	−	3.42638i	0.162062	−	0.280700i	−0.773546	−	0.633740i	$-0.781519\pi$
$149$	1.97822	−	3.42638i	0.162062	−	0.280700i	0.935608	+	0.353040i	$0.114852\pi$
$150$		0			0
$151$	−6.37386			−0.518698			−0.259349	−	0.965784i	$-0.583508\pi$
$151$	−6.37386			−0.518698			−0.259349	+	0.965784i	$0.583508\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$	−1.89564	−	3.28335i	−0.153254	−	0.265443i
$154$	3.39564	+	5.88143i	0.273629	+	0.473939i
$155$		0			0
$156$	9.76951	−	2.41733i	0.782187	−	0.193541i
$157$	−5.16515			−0.412224			−0.206112	−	0.978528i	$-0.566081\pi$
$157$	−5.16515			−0.412224			−0.206112	+	0.978528i	$0.566081\pi$
$158$	−7.47822	−	12.9527i	−0.594935	−	1.03046i
$159$	6.39564	+	11.0776i	0.507208	+	0.878509i
$160$		0			0
$161$	−8.20871			−0.646937
$162$	0.208712	−	0.361500i	0.0163980	−	0.0284021i
$163$	−2.31307	+	4.00635i	−0.181173	+	0.313802i	−0.942280	−	0.334825i	$-0.891323\pi$
$163$	−2.31307	+	4.00635i	−0.181173	+	0.313802i	0.761107	+	0.648626i	$0.224656\pi$
$164$	12.1652			0.949939
$165$		0			0
$166$	−3.08258	−	5.33918i	−0.239254	−	0.414401i
$167$	−0.708712	−	1.22753i	−0.0548418	−	0.0949888i	0.837301	−	0.546742i	$-0.184132\pi$
$167$	−0.708712	−	1.22753i	−0.0548418	−	0.0949888i	−0.892143	+	0.451753i	$0.850799\pi$
$168$	5.00000			0.385758
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	−11.9782	−	20.7469i	−0.915997	−	1.58655i
$172$	−5.47822	−	9.48855i	−0.417710	−	0.723496i
$173$	−9.56080	+	16.5598i	−0.726894	+	1.25902i	0.231296	+	0.972883i	$0.425703\pi$
$173$	−9.56080	+	16.5598i	−0.726894	+	1.25902i	−0.958190	+	0.286134i	$0.907630\pi$
$174$	−10.5826			−0.802263
$175$		0			0
$176$	1.89564	−	3.28335i	0.142890	−	0.247492i
$177$	−12.7913			−0.961452
$178$	−0.313068	+	0.542250i	−0.0234655	+	0.0406434i
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$	7.37386			0.548095			0.274047	−	0.961716i	$-0.411637\pi$
$181$	7.37386			0.548095			0.274047	+	0.961716i	$0.411637\pi$
$182$	6.26951	−	1.55130i	0.464727	−	0.114990i
$183$	−23.9564			−1.77091
$184$	2.29129	+	3.96863i	0.168916	+	0.292571i
$185$		0			0
$186$	−13.3739	+	23.1642i	−0.980619	+	1.69848i
$187$	−3.00000			−0.219382
$188$	0.395644	−	0.685275i	0.0288553	−	0.0499788i
$189$	−4.47822	+	7.75650i	−0.325743	+	0.564203i
$190$		0			0
$191$	0.873864	−	1.51358i	0.0632305	−	0.109519i	−0.832677	−	0.553759i	$-0.813193\pi$
$191$	0.873864	−	1.51358i	0.0632305	−	0.109519i	0.895908	+	0.444240i	$0.146526\pi$
$192$	−1.39564	−	2.41733i	−0.100722	−	0.174455i
$193$	8.97822	+	15.5507i	0.646266	+	1.11937i	0.984007	+	0.178127i	$0.0570038\pi$
$193$	8.97822	+	15.5507i	0.646266	+	1.11937i	−0.337741	+	0.941239i	$0.609663\pi$
$194$	9.20871			0.661147
$195$		0			0
$196$	−3.79129			−0.270806
$197$	−4.97822	−	8.62253i	−0.354683	−	0.614330i	0.632380	−	0.774658i	$-0.282078\pi$
$197$	−4.97822	−	8.62253i	−0.354683	−	0.614330i	−0.987064	+	0.160328i	$0.948745\pi$
$198$	9.08258	+	15.7315i	0.645471	+	1.11799i
$199$	7.06080	−	12.2297i	0.500527	−	0.866937i	−0.499473	−	0.866329i	$-0.666473\pi$
$199$	7.06080	−	12.2297i	0.500527	−	0.866937i	1.00000		0.000608067i	$-0.000193554\pi$
$200$		0			0
$201$	15.3521	−	26.5906i	1.08285	−	1.87556i
$202$	9.87386	−	17.1020i	0.694723	−	1.20329i
$203$	−6.79129			−0.476655
$204$	−1.10436	+	1.91280i	−0.0773204	+	0.133923i
$205$		0			0
$206$	−1.29129	−	2.23658i	−0.0899683	−	0.155830i
$207$	−21.9564			−1.52608
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	−18.9564			−1.31124
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	2.29129	−	3.96863i	0.157366	−	0.272566i
$213$	21.1652			1.45021
$214$	−5.20871	+	9.02175i	−0.356060	+	0.616714i
$215$		0			0
$216$	5.00000			0.340207
$217$	−8.58258	+	14.8655i	−0.582623	+	1.00913i
$218$	−0.917424	−	1.58903i	−0.0621358	−	0.107622i
$219$	−10.0000	−	17.3205i	−0.675737	−	1.17041i
$220$		0			0
$221$	−0.791288	+	2.74110i	−0.0532278	+	0.184386i
$222$	17.7913			1.19407
$223$	4.87386	+	8.44178i	0.326378	+	0.565303i	0.981790	−	0.189968i	$-0.0608384\pi$
$223$	4.87386	+	8.44178i	0.326378	+	0.565303i	−0.655412	+	0.755271i	$0.727505\pi$
$224$	−0.895644	−	1.55130i	−0.0598427	−	0.103651i
$225$		0			0
$226$	0.626136			0.0416500
$227$	8.29129	−	14.3609i	0.550312	−	0.953169i	−0.447940	−	0.894064i	$-0.647842\pi$
$227$	8.29129	−	14.3609i	0.550312	−	0.953169i	0.998252	−	0.0591047i	$-0.0188246\pi$
$228$	−6.97822	+	12.0866i	−0.462144	+	0.800457i
$229$	−12.3739			−0.817688			−0.408844	−	0.912604i	$-0.634068\pi$
$229$	−12.3739			−0.817688			−0.408844	+	0.912604i	$0.634068\pi$
$230$		0			0
$231$	9.47822	+	16.4168i	0.623621	+	1.08014i
$232$	1.89564	+	3.28335i	0.124455	+	0.215563i
$233$	15.0000			0.982683			0.491341	−	0.870967i	$-0.336507\pi$
$233$	15.0000			0.982683			0.491341	+	0.870967i	$0.336507\pi$
$234$	16.7695	−	4.14938i	1.09626	−	0.271253i
$235$		0			0
$236$	2.29129	+	3.96863i	0.149150	+	0.258336i
$237$	−20.8739	−	36.1546i	−1.35590	−	2.34849i
$238$	−0.708712	+	1.22753i	−0.0459390	+	0.0795687i
$239$	−18.1652			−1.17501			−0.587503	−	0.809222i	$-0.699889\pi$
$239$	−18.1652			−1.17501			−0.587503	+	0.809222i	$0.699889\pi$
$240$		0			0
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	3.37386			0.216880
$243$	8.08258	−	13.9994i	0.518497	−	0.898064i
$244$	4.29129	+	7.43273i	0.274722	+	0.475832i
$245$		0			0
$246$	33.9564			2.16498
$247$	−5.00000	+	17.3205i	−0.318142	+	1.10208i
$248$	9.58258			0.608494
$249$	−8.60436	−	14.9032i	−0.545279	−	0.944451i
$250$		0			0
$251$	10.1869	−	17.6443i	0.642993	−	1.11370i	−0.341768	−	0.939784i	$-0.611026\pi$
$251$	10.1869	−	17.6443i	0.642993	−	1.11370i	0.984761	−	0.173913i	$-0.0556411\pi$
$252$	8.58258			0.540651
$253$	−8.68693	+	15.0462i	−0.546143	+	0.945947i
$254$	8.18693	−	14.1802i	0.513694	−	0.889744i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.4564	+	19.8431i	0.714633	+	1.23778i	0.963101	+	0.269141i	$0.0867396\pi$
$257$	11.4564	+	19.8431i	0.714633	+	1.23778i	−0.248468	+	0.968640i	$0.579927\pi$
$258$	−15.2913	−	26.4853i	−0.951994	−	1.64890i
$259$	11.4174			0.709444
$260$		0			0
$261$	−18.1652			−1.12439
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	−4.97822	−	8.62253i	−0.306970	−	0.531688i	0.670728	−	0.741704i	$-0.265982\pi$
$263$	−4.97822	−	8.62253i	−0.306970	−	0.531688i	−0.977698	+	0.210016i	$0.932649\pi$
$264$	5.29129	−	9.16478i	0.325656	−	0.564053i
$265$		0			0
$266$	−4.47822	+	7.75650i	−0.274577	+	0.475582i
$267$	−0.873864	+	1.51358i	−0.0534796	+	0.0926294i
$268$	−11.0000			−0.671932
$269$	7.66515	−	13.2764i	0.467353	−	0.809478i	−0.531952	−	0.846775i	$-0.678541\pi$
$269$	7.66515	−	13.2764i	0.467353	−	0.809478i	0.999304	+	0.0372964i	$0.0118746\pi$
$270$		0			0
$271$	−5.58258	−	9.66930i	−0.339117	−	0.587368i	0.645150	−	0.764056i	$-0.276795\pi$
$271$	−5.58258	−	9.66930i	−0.339117	−	0.587368i	−0.984267	+	0.176688i	$0.943462\pi$
$272$	0.791288			0.0479789
$273$	17.5000	−	4.33013i	1.05915	−	0.262071i
$274$	−15.1652			−0.916160
$275$		0			0
$276$	6.39564	+	11.0776i	0.384973	+	0.666792i
$277$	−3.81307	+	6.60443i	−0.229105	+	0.396822i	−0.957543	−	0.288290i	$-0.906913\pi$
$277$	−3.81307	+	6.60443i	−0.229105	+	0.396822i	0.728438	+	0.685112i	$0.240247\pi$
$278$	21.5826			1.29444
$279$	−22.9564	+	39.7617i	−1.37437	+	2.38047i
$280$		0			0
$281$	−14.5390			−0.867325			−0.433662	−	0.901075i	$-0.642779\pi$
$281$	−14.5390			−0.867325			−0.433662	+	0.901075i	$0.642779\pi$
$282$	1.10436	−	1.91280i	0.0657634	−	0.113906i
$283$	−6.26951	−	10.8591i	−0.372684	−	0.645507i	0.617294	−	0.786733i	$-0.288229\pi$
$283$	−6.26951	−	10.8591i	−0.372684	−	0.645507i	−0.989977	+	0.141226i	$0.954896\pi$
$284$	−3.79129	−	6.56670i	−0.224972	−	0.389662i
$285$		0			0
$286$	3.79129	−	13.1334i	0.224184	−	0.776595i
$287$	21.7913			1.28630
$288$	−2.39564	−	4.14938i	−0.141165	−	0.244504i
$289$	8.18693	+	14.1802i	0.481584	+	0.834128i
$290$		0			0
$291$	25.7042			1.50680
$292$	−3.58258	+	6.20520i	−0.209654	+	0.363132i
$293$	3.31307	−	5.73840i	0.193552	−	0.335241i	−0.752873	−	0.658166i	$-0.771333\pi$
$293$	3.31307	−	5.73840i	0.193552	−	0.335241i	0.946425	+	0.322925i	$0.104666\pi$
$294$	−10.5826			−0.617188
$295$		0			0
$296$	−3.18693	−	5.51993i	−0.185237	−	0.320839i
$297$	9.47822	+	16.4168i	0.549982	+	0.952597i
$298$	−3.95644			−0.229190
$299$	11.4564	+	11.9059i	0.662543	+	0.688535i
$300$		0			0
$301$	−9.81307	−	16.9967i	−0.565616	−	0.979675i
$302$	3.18693	+	5.51993i	0.183387	+	0.317636i
$303$	27.5608	−	47.7367i	1.58333	−	2.74240i
$304$	5.00000			0.286770
$305$		0			0
$306$	−1.89564	+	3.28335i	−0.108367	+	0.187697i
$307$	13.1652			0.751375			0.375687	−	0.926746i	$-0.377407\pi$
$307$	13.1652			0.751375			0.375687	+	0.926746i	$0.377407\pi$
$308$	3.39564	−	5.88143i	0.193485	−	0.335125i
$309$	−3.60436	−	6.24293i	−0.205045	−	0.355148i
$310$		0			0
$311$	−17.3739			−0.985181			−0.492591	−	0.870261i	$-0.663950\pi$
$311$	−17.3739			−0.985181			−0.492591	+	0.870261i	$0.663950\pi$
$312$	−6.97822	−	7.25198i	−0.395064	−	0.410562i
$313$	4.62614			0.261485			0.130742	−	0.991416i	$-0.458264\pi$
$313$	4.62614			0.261485			0.130742	+	0.991416i	$0.458264\pi$
$314$	2.58258	+	4.47315i	0.145743	+	0.252435i
$315$		0			0
$316$	−7.47822	+	12.9527i	−0.420683	+	0.728644i
$317$	−26.5390			−1.49058			−0.745290	−	0.666741i	$-0.767689\pi$
$317$	−26.5390			−1.49058			−0.745290	+	0.666741i	$0.767689\pi$
$318$	6.39564	−	11.0776i	0.358650	−	0.621200i
$319$	−7.18693	+	12.4481i	−0.402391	+	0.696962i
$320$		0			0
$321$	−14.5390	+	25.1823i	−0.811489	+	1.40554i
$322$	4.10436	+	7.10895i	0.228727	+	0.396166i
$323$	−1.97822	−	3.42638i	−0.110071	−	0.190649i
$324$	−0.417424			−0.0231902
$325$		0			0
$326$	4.62614			0.256218
$327$	−2.56080	−	4.43543i	−0.141612	−	0.245280i
$328$	−6.08258	−	10.5353i	−0.335854	−	0.581716i
$329$	0.708712	−	1.22753i	0.0390726	−	0.0676757i
$330$		0			0
$331$	−5.97822	+	10.3546i	−0.328593	+	0.569139i	−0.982233	−	0.187666i	$-0.939908\pi$
$331$	−5.97822	+	10.3546i	−0.328593	+	0.569139i	0.653640	+	0.756805i	$0.273241\pi$
$332$	−3.08258	+	5.33918i	−0.169178	+	0.293025i
$333$	30.5390			1.67353
$334$	−0.708712	+	1.22753i	−0.0387790	+	0.0671672i
$335$		0			0
$336$	−2.50000	−	4.33013i	−0.136386	−	0.236228i
$337$	−0.252273			−0.0137422			−0.00687109	−	0.999976i	$-0.502187\pi$
$337$	−0.252273			−0.0137422			−0.00687109	+	0.999976i	$0.502187\pi$
$338$	−11.0000	−	6.92820i	−0.598321	−	0.376845i
$339$	1.74773			0.0949235
$340$		0			0
$341$	18.1652	+	31.4630i	0.983698	+	1.70382i
$342$	−11.9782	+	20.7469i	−0.647708	+	1.12186i
$343$	−19.3303			−1.04374
$344$	−5.47822	+	9.48855i	−0.295366	+	0.511589i
$345$		0			0
$346$	19.1216			1.02798
$347$	14.2913	−	24.7532i	0.767197	−	1.32882i	−0.171881	−	0.985118i	$-0.554984\pi$
$347$	14.2913	−	24.7532i	0.767197	−	1.32882i	0.939077	−	0.343706i	$-0.111682\pi$
$348$	5.29129	+	9.16478i	0.283643	+	0.491284i
$349$	−13.4782	−	23.3450i	−0.721473	−	1.24963i	−0.960410	−	0.278592i	$-0.910132\pi$
$349$	−13.4782	−	23.3450i	−0.721473	−	1.24963i	0.238937	−	0.971035i	$-0.423201\pi$
$350$		0			0
$351$	17.5000	−	4.33013i	0.934081	−	0.231125i
$352$	−3.79129			−0.202076
$353$	−9.31307	−	16.1307i	−0.495685	−	0.858551i	0.504303	−	0.863527i	$-0.331749\pi$
$353$	−9.31307	−	16.1307i	−0.495685	−	0.858551i	−0.999988	+	0.00497584i	$0.998416\pi$
$354$	6.39564	+	11.0776i	0.339925	+	0.588767i
$355$		0			0
$356$	0.626136			0.0331852
$357$	−1.97822	+	3.42638i	−0.104698	+	0.181343i
$358$	−3.00000	+	5.19615i	−0.158555	+	0.274625i
$359$	−33.7913			−1.78344			−0.891718	−	0.452591i	$-0.850500\pi$
$359$	−33.7913			−1.78344			−0.891718	+	0.452591i	$0.850500\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−3.68693	−	6.38595i	−0.193781	−	0.335638i
$363$	9.41742			0.494287
$364$	−4.47822	−	4.65390i	−0.234722	−	0.243931i
$365$		0			0
$366$	11.9782	+	20.7469i	0.626112	+	1.08446i
$367$	12.3739	+	21.4322i	0.645910	+	1.11875i	0.984090	+	0.177668i	$0.0568554\pi$
$367$	12.3739	+	21.4322i	0.645910	+	1.11875i	−0.338180	+	0.941081i	$0.609811\pi$
$368$	2.29129	−	3.96863i	0.119442	−	0.206879i
$369$	58.2867			3.03429
$370$		0			0
$371$	4.10436	−	7.10895i	0.213088	−	0.369078i
$372$	26.7477			1.38681
$373$	−6.58258	+	11.4014i	−0.340833	+	0.590340i	−0.984588	−	0.174892i	$-0.944042\pi$
$373$	−6.58258	+	11.4014i	−0.340833	+	0.590340i	0.643755	+	0.765232i	$0.277376\pi$
$374$	1.50000	+	2.59808i	0.0775632	+	0.134343i
$375$		0			0
$376$	−0.791288			−0.0408076
$377$	9.47822	+	9.85005i	0.488153	+	0.507304i
$378$	8.95644			0.460670
$379$	−8.50000	−	14.7224i	−0.436616	−	0.756241i	0.560810	−	0.827944i	$-0.310490\pi$
$379$	−8.50000	−	14.7224i	−0.436616	−	0.756241i	−0.997426	+	0.0717038i	$0.977156\pi$
$380$		0			0
$381$	22.8521	−	39.5810i	1.17075	−	2.02779i
$382$	−1.74773			−0.0894215
$383$	0.873864	−	1.51358i	0.0446523	−	0.0773401i	−0.842835	−	0.538171i	$-0.819115\pi$
$383$	0.873864	−	1.51358i	0.0446523	−	0.0773401i	0.887488	+	0.460831i	$0.152449\pi$
$384$	−1.39564	+	2.41733i	−0.0712212	+	0.123359i
$385$		0			0
$386$	8.97822	−	15.5507i	0.456979	−	0.791511i
$387$	−26.2477	−	45.4624i	−1.33425	−	2.31098i
$388$	−4.60436	−	7.97498i	−0.233751	−	0.404868i
$389$	−6.33030			−0.320959			−0.160480	−	0.987039i	$-0.551304\pi$
$389$	−6.33030			−0.320959			−0.160480	+	0.987039i	$0.551304\pi$
$390$		0			0
$391$	−3.62614			−0.183382
$392$	1.89564	+	3.28335i	0.0957445	+	0.165834i
$393$	20.9347	+	36.2599i	1.05601	+	1.82907i
$394$	−4.97822	+	8.62253i	−0.250799	+	0.434397i
$395$		0			0
$396$	9.08258	−	15.7315i	0.456417	−	0.790537i
$397$	−3.10436	+	5.37690i	−0.155803	+	0.269859i	−0.933351	−	0.358965i	$-0.883130\pi$
$397$	−3.10436	+	5.37690i	−0.155803	+	0.269859i	0.777548	+	0.628824i	$0.216463\pi$
$398$	−14.1216			−0.707851
$399$	−12.5000	+	21.6506i	−0.625783	+	1.08389i
$400$		0			0
$401$	10.1869	+	17.6443i	0.508711	+	0.881113i	0.999949	+	0.0100881i	$0.00321119\pi$
$401$	10.1869	+	17.6443i	0.508711	+	0.881113i	−0.491238	+	0.871025i	$0.663455\pi$
$402$	−30.7042			−1.53138
$403$	33.5390	−	8.29875i	1.67070	−	0.413390i
$404$	−19.7477			−0.982486
$405$		0			0
$406$	3.39564	+	5.88143i	0.168523	+	0.291890i
$407$	12.0826	−	20.9276i	0.598911	−	1.03734i
$408$	2.20871			0.109348
$409$	11.2477	−	19.4816i	0.556164	−	0.963305i	−0.441648	−	0.897189i	$-0.645606\pi$
$409$	11.2477	−	19.4816i	0.556164	−	0.963305i	0.997812	−	0.0661162i	$-0.0210608\pi$
$410$		0			0
$411$	−42.3303			−2.08800
$412$	−1.29129	+	2.23658i	−0.0636172	+	0.110188i
$413$	4.10436	+	7.10895i	0.201962	+	0.349809i
$414$	10.9782	+	19.0148i	0.539550	+	0.934528i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	60.2432			2.95012
$418$	9.47822	+	16.4168i	0.463595	+	0.802970i
$419$	1.73049	+	2.99730i	0.0845401	+	0.146428i	0.905195	−	0.424996i	$-0.139725\pi$
$419$	1.73049	+	2.99730i	0.0845401	+	0.146428i	−0.820655	+	0.571424i	$0.806391\pi$
$420$		0			0
$421$	1.04356			0.0508600			0.0254300	−	0.999677i	$-0.491905\pi$
$421$	1.04356			0.0508600			0.0254300	+	0.999677i	$0.491905\pi$
$422$	−2.50000	+	4.33013i	−0.121698	+	0.210787i
$423$	1.89564	−	3.28335i	0.0921694	−	0.159642i
$424$	−4.58258			−0.222550
$425$		0			0
$426$	−10.5826	−	18.3296i	−0.512727	−	0.888070i
$427$	7.68693	+	13.3142i	0.371997	+	0.644317i
$428$	10.4174			0.503545
$429$	10.5826	−	36.6591i	0.510932	−	1.76992i
$430$		0			0
$431$	3.39564	+	5.88143i	0.163562	+	0.283298i	0.936144	−	0.351617i	$-0.114368\pi$
$431$	3.39564	+	5.88143i	0.163562	+	0.283298i	−0.772581	+	0.634916i	$0.781035\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	15.2913	−	26.4853i	0.734852	−	1.27280i	−0.219936	−	0.975514i	$-0.570585\pi$
$433$	15.2913	−	26.4853i	0.734852	−	1.27280i	0.954788	−	0.297287i	$-0.0960819\pi$
$434$	17.1652			0.823954
$435$		0			0
$436$	−0.917424	+	1.58903i	−0.0439367	+	0.0761005i
$437$	−22.9129			−1.09607
$438$	−10.0000	+	17.3205i	−0.477818	+	0.827606i
$439$	8.79129	+	15.2270i	0.419585	+	0.726743i	0.995898	−	0.0904865i	$-0.0288422\pi$
$439$	8.79129	+	15.2270i	0.419585	+	0.726743i	−0.576312	+	0.817229i	$0.695509\pi$
$440$		0			0
$441$	−18.1652			−0.865007
$442$	2.76951	−	0.685275i	0.131732	−	0.0325952i
$443$	−2.04356			−0.0970925			−0.0485463	−	0.998821i	$-0.515459\pi$
$443$	−2.04356			−0.0970925			−0.0485463	+	0.998821i	$0.515459\pi$
$444$	−8.89564	−	15.4077i	−0.422169	−	0.731217i
$445$		0			0
$446$	4.87386	−	8.44178i	0.230784	−	0.399730i
$447$	−11.0436			−0.522343
$448$	−0.895644	+	1.55130i	−0.0423152	+	0.0732921i
$449$	−16.1869	+	28.0366i	−0.763909	+	1.32313i	0.176913	+	0.984226i	$0.443389\pi$
$449$	−16.1869	+	28.0366i	−0.763909	+	1.32313i	−0.940822	+	0.338902i	$0.889945\pi$
$450$		0			0
$451$	23.0608	−	39.9425i	1.08589	−	1.88082i
$452$	−0.313068	−	0.542250i	−0.0147255	−	0.0255053i
$453$	8.89564	+	15.4077i	0.417954	+	0.723917i
$454$	−16.5826			−0.778259
$455$		0			0
$456$	13.9564			0.653570
$457$	3.68693	+	6.38595i	0.172467	+	0.298722i	0.939282	−	0.343146i	$-0.111493\pi$
$457$	3.68693	+	6.38595i	0.172467	+	0.298722i	−0.766815	+	0.641869i	$0.778159\pi$
$458$	6.18693	+	10.7161i	0.289096	+	0.500730i
$459$	−1.97822	+	3.42638i	−0.0923354	+	0.159930i
$460$		0			0
$461$	−14.6044	+	25.2955i	−0.680193	+	1.17813i	0.294729	+	0.955581i	$0.404771\pi$
$461$	−14.6044	+	25.2955i	−0.680193	+	1.17813i	−0.974922	+	0.222547i	$0.928563\pi$
$462$	9.47822	−	16.4168i	0.440967	−	0.763777i
$463$	−17.9564			−0.834507			−0.417253	−	0.908790i	$-0.637007\pi$
$463$	−17.9564			−0.834507			−0.417253	+	0.908790i	$0.637007\pi$
$464$	1.89564	−	3.28335i	0.0880031	−	0.152426i
$465$		0			0
$466$	−7.50000	−	12.9904i	−0.347431	−	0.601768i
$467$	8.37386			0.387496			0.193748	−	0.981051i	$-0.437936\pi$
$467$	8.37386			0.387496			0.193748	+	0.981051i	$0.437936\pi$
$468$	−11.9782	−	12.4481i	−0.553693	−	0.575415i
$469$	−19.7042			−0.909854
$470$		0			0
$471$	7.20871	+	12.4859i	0.332160	+	0.575318i
$472$	2.29129	−	3.96863i	0.105465	−	0.182671i
$473$	−41.5390			−1.90997
$474$	−20.8739	+	36.1546i	−0.958768	+	1.66064i
$475$		0			0
$476$	1.41742			0.0649675
$477$	10.9782	−	19.0148i	0.502658	−	0.870629i
$478$	9.08258	+	15.7315i	0.415427	+	0.719541i
$479$	−9.47822	−	16.4168i	−0.433071	−	0.750101i	0.564065	−	0.825730i	$-0.309237\pi$
$479$	−9.47822	−	16.4168i	−0.433071	−	0.750101i	−0.997136	+	0.0756295i	$0.975903\pi$
$480$		0			0
$481$	−15.9347	−	16.5598i	−0.726558	−	0.755061i
$482$	−7.00000			−0.318841
$483$	11.4564	+	19.8431i	0.521286	+	0.902894i
$484$	−1.68693	−	2.92185i	−0.0766787	−	0.132811i
$485$		0			0
$486$	−16.1652			−0.733266
$487$	10.5608	−	18.2918i	0.478555	−	0.828882i	−0.521142	−	0.853470i	$-0.674494\pi$
$487$	10.5608	−	18.2918i	0.478555	−	0.828882i	0.999698	+	0.0245876i	$0.00782728\pi$
$488$	4.29129	−	7.43273i	0.194257	−	0.336464i
$489$	12.9129			0.583941
$490$		0			0
$491$	−17.4564	−	30.2354i	−0.787798	−	1.36451i	−0.927313	−	0.374286i	$-0.877888\pi$
$491$	−17.4564	−	30.2354i	−0.787798	−	1.36451i	0.139515	−	0.990220i	$-0.455446\pi$
$492$	−16.9782	−	29.4071i	−0.765437	−	1.32578i
$493$	−3.00000			−0.135113
$494$	17.5000	−	4.33013i	0.787362	−	0.194822i
$495$		0			0
$496$	−4.79129	−	8.29875i	−0.215135	−	0.372625i
$497$	−6.79129	−	11.7629i	−0.304631	−	0.527636i
$498$	−8.60436	+	14.9032i	−0.385570	+	0.667828i
$499$	9.74773			0.436368			0.218184	−	0.975908i	$-0.429987\pi$
$499$	9.74773			0.436368			0.218184	+	0.975908i	$0.429987\pi$
$500$		0			0
$501$	−1.97822	+	3.42638i	−0.0883803	+	0.153079i
$502$	−20.3739			−0.909330
$503$	−21.9564	+	38.0297i	−0.978989	+	1.69566i	−0.312902	+	0.949786i	$0.601301\pi$
$503$	−21.9564	+	38.0297i	−0.978989	+	1.69566i	−0.666088	+	0.745874i	$0.732032\pi$
$504$	−4.29129	−	7.43273i	−0.191149	−	0.331080i
$505$		0			0
$506$	17.3739			0.772362
$507$	−30.7042	−	19.3386i	−1.36362	−	0.858858i
$508$	−16.3739			−0.726473
$509$	−12.9564	−	22.4412i	−0.574284	−	0.994689i	−0.996119	−	0.0880165i	$-0.971947\pi$
$509$	−12.9564	−	22.4412i	−0.574284	−	0.994689i	0.421835	−	0.906673i	$-0.361386\pi$
$510$		0			0
$511$	−6.41742	+	11.1153i	−0.283890	+	0.491712i
$512$	1.00000			0.0441942
$513$	−12.5000	+	21.6506i	−0.551888	+	0.955899i
$514$	11.4564	−	19.8431i	0.505322	−	0.875243i
$515$		0			0
$516$	−15.2913	+	26.4853i	−0.673161	+	1.16595i
$517$	−1.50000	−	2.59808i	−0.0659699	−	0.114263i
$518$	−5.70871	−	9.88778i	−0.250826	−	0.434444i
$519$	53.3739			2.34285
$520$		0			0
$521$	36.3303			1.59166			0.795830	−	0.605520i	$-0.207035\pi$
$521$	36.3303			1.59166			0.795830	+	0.605520i	$0.207035\pi$
$522$	9.08258	+	15.7315i	0.397534	+	0.688548i
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	0.977503	−	0.210921i	$-0.0676463\pi$
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	−0.671414	+	0.741082i	$0.734313\pi$
$524$	7.50000	−	12.9904i	0.327639	−	0.567487i
$525$		0			0
$526$	−4.97822	+	8.62253i	−0.217061	+	0.375960i
$527$	−3.79129	+	6.56670i	−0.165151	+	0.286050i
$528$	−10.5826			−0.460547
$529$	1.00000	−	1.73205i	0.0434783	−	0.0753066i
$530$		0			0
$531$	10.9782	+	19.0148i	0.476414	+	0.825174i
$532$	8.95644			0.388311
$533$	−30.4129	−	31.6060i	−1.31733	−	1.36901i
$534$	1.74773			0.0756315
$535$		0			0
$536$	5.50000	+	9.52628i	0.237564	+	0.411473i
$537$	−8.37386	+	14.5040i	−0.361359	+	0.625892i
$538$	−15.3303			−0.660936
$539$	−7.18693	+	12.4481i	−0.309563	+	0.536179i
$540$		0			0
$541$	27.9129			1.20007			0.600034	−	0.799974i	$-0.295154\pi$
$541$	27.9129			1.20007			0.600034	+	0.799974i	$0.295154\pi$
$542$	−5.58258	+	9.66930i	−0.239792	+	0.415332i
$543$	−10.2913	−	17.8250i	−0.441641	−	0.764945i
$544$	−0.395644	−	0.685275i	−0.0169631	−	0.0293809i
$545$		0			0
$546$	−12.5000	−	12.9904i	−0.534951	−	0.555937i
$547$	−41.3303			−1.76716			−0.883578	−	0.468284i	$-0.844872\pi$
$547$	−41.3303			−1.76716			−0.883578	+	0.468284i	$0.844872\pi$
$548$	7.58258	+	13.1334i	0.323912	+	0.561031i
$549$	20.5608	+	35.6123i	0.877513	+	1.51990i
$550$		0			0
$551$	−18.9564			−0.807571
$552$	6.39564	−	11.0776i	0.272217	−	0.471493i
$553$	−13.3956	+	23.2019i	−0.569641	+	0.986647i
$554$	7.62614			0.324003
$555$		0			0
$556$	−10.7913	−	18.6911i	−0.457653	−	0.792677i
$557$	9.62614	+	16.6730i	0.407872	+	0.706456i	0.994651	−	0.103292i	$-0.0329375\pi$
$557$	9.62614	+	16.6730i	0.407872	+	0.706456i	−0.586779	+	0.809747i	$0.699604\pi$
$558$	45.9129			1.94365
$559$	−10.9564	+	37.9542i	−0.463408	+	1.60529i
$560$		0			0
$561$	4.18693	+	7.25198i	0.176772	+	0.306179i
$562$	7.26951	+	12.5912i	0.306646	+	0.531126i
$563$	7.35208	−	12.7342i	0.309853	−	0.536682i	−0.668477	−	0.743733i	$-0.733053\pi$
$563$	7.35208	−	12.7342i	0.309853	−	0.536682i	0.978330	+	0.207051i	$0.0663867\pi$
$564$	−2.20871			−0.0930036
$565$		0			0
$566$	−6.26951	+	10.8591i	−0.263527	+	0.456442i
$567$	−0.747727			−0.0314016
$568$	−3.79129	+	6.56670i	−0.159079	+	0.275533i
$569$	−3.31307	−	5.73840i	−0.138891	−	0.240566i	0.788186	−	0.615437i	$-0.211020\pi$
$569$	−3.31307	−	5.73840i	−0.138891	−	0.240566i	−0.927077	+	0.374871i	$0.877687\pi$
$570$		0			0
$571$	−6.37386			−0.266738			−0.133369	−	0.991066i	$-0.542580\pi$
$571$	−6.37386			−0.266738			−0.133369	+	0.991066i	$0.542580\pi$
$572$	−13.2695	+	3.28335i	−0.554826	+	0.137284i
$573$	−4.87841			−0.203798
$574$	−10.8956	−	18.8718i	−0.454775	−	0.787694i
$575$		0			0
$576$	−2.39564	+	4.14938i	−0.0998185	+	0.172891i
$577$	2.25227			0.0937633			0.0468817	−	0.998900i	$-0.485072\pi$
$577$	2.25227			0.0937633			0.0468817	+	0.998900i	$0.485072\pi$
$578$	8.18693	−	14.1802i	0.340531	−	0.589818i
$579$	25.0608	−	43.4066i	1.04149	−	1.80392i
$580$		0			0
$581$	−5.52178	+	9.56400i	−0.229082	+	0.396782i
$582$	−12.8521	−	22.2605i	−0.532736	−	0.922726i
$583$	−8.68693	−	15.0462i	−0.359776	−	0.623150i
$584$	7.16515			0.296496
$585$		0			0
$586$	−6.62614			−0.273723
$587$	11.1434	+	19.3009i	0.459936	+	0.796633i	0.998957	−	0.0456596i	$-0.0145390\pi$
$587$	11.1434	+	19.3009i	0.459936	+	0.796633i	−0.539021	+	0.842292i	$0.681206\pi$
$588$	5.29129	+	9.16478i	0.218209	+	0.377949i
$589$	−23.9564	+	41.4938i	−0.987108	+	1.70972i
$590$		0			0
$591$	−13.8956	+	24.0680i	−0.571590	+	0.990024i
$592$	−3.18693	+	5.51993i	−0.130982	+	0.226868i
$593$	−1.58258			−0.0649886			−0.0324943	−	0.999472i	$-0.510345\pi$
$593$	−1.58258			−0.0649886			−0.0324943	+	0.999472i	$0.510345\pi$
$594$	9.47822	−	16.4168i	0.388896	−	0.673588i
$595$		0			0
$596$	1.97822	+	3.42638i	0.0810310	+	0.140350i
$597$	−39.4174			−1.61325
$598$	4.58258	−	15.8745i	0.187395	−	0.649157i
$599$	7.74773			0.316564			0.158282	−	0.987394i	$-0.449405\pi$
$599$	7.74773			0.316564			0.158282	+	0.987394i	$0.449405\pi$
$600$		0			0
$601$	8.87386	+	15.3700i	0.361972	+	0.626955i	0.988285	−	0.152617i	$-0.0487701\pi$
$601$	8.87386	+	15.3700i	0.361972	+	0.626955i	−0.626313	+	0.779572i	$0.715437\pi$
$602$	−9.81307	+	16.9967i	−0.399951	+	0.692735i
$603$	−52.7042			−2.14628
$604$	3.18693	−	5.51993i	0.129674	−	0.224603i
$605$		0			0
$606$	−55.1216			−2.23916
$607$	2.50000	−	4.33013i	0.101472	−	0.175754i	−0.810819	−	0.585296i	$-0.800978\pi$
$607$	2.50000	−	4.33013i	0.101472	−	0.175754i	0.912291	+	0.409542i	$0.134311\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$	9.47822	+	16.4168i	0.384077	+	0.665241i
$610$		0			0
$611$	−2.76951	+	0.685275i	−0.112042	+	0.0277233i
$612$	3.79129			0.153254
$613$	4.79129	+	8.29875i	0.193518	+	0.335184i	0.946414	−	0.322957i	$-0.104677\pi$
$613$	4.79129	+	8.29875i	0.193518	+	0.335184i	−0.752895	+	0.658140i	$0.771343\pi$
$614$	−6.58258	−	11.4014i	−0.265651	−	0.460121i
$615$		0			0
$616$	−6.79129			−0.273629
$617$	15.0826	−	26.1238i	0.607202	−	1.05170i	−0.384498	−	0.923126i	$-0.625625\pi$
$617$	15.0826	−	26.1238i	0.607202	−	1.05170i	0.991699	−	0.128578i	$-0.0410413\pi$
$618$	−3.60436	+	6.24293i	−0.144988	+	0.251127i
$619$	31.2087			1.25438			0.627192	−	0.778865i	$-0.284204\pi$
$619$	31.2087			1.25438			0.627192	+	0.778865i	$0.284204\pi$
$620$		0			0
$621$	11.4564	+	19.8431i	0.459731	+	0.796278i
$622$	8.68693	+	15.0462i	0.348314	+	0.603298i
$623$	1.12159			0.0449356
$624$	−2.79129	+	9.66930i	−0.111741	+	0.387082i
$625$		0			0
$626$	−2.31307	−	4.00635i	−0.0924488	−	0.160126i
$627$	26.4564	+	45.8239i	1.05657	+	1.83003i
$628$	2.58258	−	4.47315i	0.103056	−	0.178498i
$629$	5.04356			0.201100
$630$		0			0
$631$	−5.18693	+	8.98403i	−0.206488	+	0.357649i	−0.950606	−	0.310400i	$-0.899537\pi$
$631$	−5.18693	+	8.98403i	−0.206488	+	0.357649i	0.744117	+	0.668049i	$0.232870\pi$
$632$	14.9564			0.594935
$633$	−6.97822	+	12.0866i	−0.277359	+	0.480400i
$634$	13.2695	+	22.9835i	0.526999	+	0.912790i
$635$		0			0
$636$	−12.7913			−0.507208
$637$	9.47822	+	9.85005i	0.375541	+	0.390273i
$638$	14.3739			0.569067
$639$	−18.1652	−	31.4630i	−0.718602	−	1.24466i
$640$		0			0
$641$	1.89564	−	3.28335i	0.0748734	−	0.129685i	−0.826158	−	0.563439i	$-0.809478\pi$
$641$	1.89564	−	3.28335i	0.0748734	−	0.129685i	0.901031	+	0.433754i	$0.142811\pi$
$642$	29.0780			1.14762
$643$	−1.12614	+	1.95053i	−0.0444105	+	0.0769212i	−0.887376	−	0.461046i	$-0.847474\pi$
$643$	−1.12614	+	1.95053i	−0.0444105	+	0.0769212i	0.842966	+	0.537967i	$0.180808\pi$
$644$	4.10436	−	7.10895i	0.161734	−	0.280132i
$645$		0			0
$646$	−1.97822	+	3.42638i	−0.0778320	+	0.134809i
$647$	22.9782	+	39.7994i	0.903367	+	1.56468i	0.823094	+	0.567905i	$0.192246\pi$
$647$	22.9782	+	39.7994i	0.903367	+	1.56468i	0.0802727	+	0.996773i	$0.474421\pi$
$648$	0.208712	+	0.361500i	0.00819899	+	0.0142011i
$649$	17.3739			0.681984
$650$		0			0
$651$	47.9129			1.87785
$652$	−2.31307	−	4.00635i	−0.0905867	−	0.156901i
$653$	−15.7087	−	27.2083i	−0.614729	−	1.06474i	−0.990432	−	0.138002i	$-0.955932\pi$
$653$	−15.7087	−	27.2083i	−0.614729	−	1.06474i	0.375703	−	0.926740i	$-0.377401\pi$
$654$	−2.56080	+	4.43543i	−0.100135	+	0.173439i
$655$		0			0
$656$	−6.08258	+	10.5353i	−0.237485	+	0.411336i
$657$	−17.1652	+	29.7309i	−0.669676	+	1.15991i
$658$	−1.41742			−0.0552570
$659$	−10.7477	+	18.6156i	−0.418672	+	0.725161i	−0.995806	−	0.0914882i	$-0.970838\pi$
$659$	−10.7477	+	18.6156i	−0.418672	+	0.725161i	0.577134	+	0.816649i	$0.304171\pi$
$660$		0			0
$661$	3.97822	+	6.89048i	0.154735	+	0.268009i	0.932962	−	0.359974i	$-0.117214\pi$
$661$	3.97822	+	6.89048i	0.154735	+	0.268009i	−0.778228	+	0.627982i	$0.783881\pi$
$662$	11.9564			0.464700
$663$	7.73049	−	1.91280i	0.300227	−	0.0742870i
$664$	6.16515			0.239254
$665$		0			0
$666$	−15.2695	−	26.4476i	−0.591681	−	1.02482i
$667$	−8.68693	+	15.0462i	−0.336359	+	0.582591i
$668$	1.41742			0.0548418
$669$	13.6044	−	23.5634i	0.525975	−	0.911015i
$670$		0			0
$671$	32.5390			1.25615
$672$	−2.50000	+	4.33013i	−0.0964396	+	0.167038i
$673$	−11.9564	−	20.7092i	−0.460887	−	0.798279i	0.538119	−	0.842869i	$-0.319135\pi$
$673$	−11.9564	−	20.7092i	−0.460887	−	0.798279i	−0.999005	+	0.0445897i	$0.985802\pi$
$674$	0.126136	+	0.218475i	0.00485859	+	0.00841533i
$675$		0			0
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	4.25227			0.163428			0.0817141	−	0.996656i	$-0.473961\pi$
$677$	4.25227			0.163428			0.0817141	+	0.996656i	$0.473961\pi$
$678$	−0.873864	−	1.51358i	−0.0335605	−	0.0581285i
$679$	−8.24773	−	14.2855i	−0.316519	−	0.548226i
$680$		0			0
$681$	−46.2867			−1.77371
$682$	18.1652	−	31.4630i	0.695580	−	1.20478i
$683$	−14.4564	+	25.0393i	−0.553160	+	0.958102i	0.444884	+	0.895588i	$0.353245\pi$
$683$	−14.4564	+	25.0393i	−0.553160	+	0.958102i	−0.998044	+	0.0625134i	$0.980088\pi$
$684$	23.9564			0.915997
$685$		0			0
$686$	9.66515	+	16.7405i	0.369017	+	0.639157i
$687$	17.2695	+	29.9117i	0.658873	+	1.14120i
$688$	10.9564			0.417710
$689$	−16.0390	+	3.96863i	−0.611038	+	0.151193i
$690$		0			0
$691$	−1.62614	−	2.81655i	−0.0618611	−	0.107147i	0.833436	−	0.552616i	$-0.186370\pi$
$691$	−1.62614	−	2.81655i	−0.0618611	−	0.107147i	−0.895297	+	0.445469i	$0.853037\pi$
$692$	−9.56080	−	16.5598i	−0.363447	−	0.629509i
$693$	16.2695	−	28.1796i	0.618027	−	1.07046i
$694$	−28.5826			−1.08498
$695$		0			0
$696$	5.29129	−	9.16478i	0.200566	−	0.347390i
$697$	9.62614			0.364616
$698$	−13.4782	+	23.3450i	−0.510158	+	0.883620i
$699$	−20.9347	−	36.2599i	−0.791822	−	1.37148i
$700$		0			0
$701$	4.87841			0.184255			0.0921275	−	0.995747i	$-0.470633\pi$
$701$	4.87841			0.184255			0.0921275	+	0.995747i	$0.470633\pi$
$702$	−12.5000	−	12.9904i	−0.471782	−	0.490290i
$703$	31.8693			1.20197
$704$	1.89564	+	3.28335i	0.0714448	+	0.123746i
$705$		0			0
$706$	−9.31307	+	16.1307i	−0.350502	+	0.607087i
$707$	−35.3739			−1.33037
$708$	6.39564	−	11.0776i	0.240363	−	0.416321i
$709$	5.39564	−	9.34553i	0.202638	−	0.350979i	−0.746740	−	0.665116i	$-0.768382\pi$
$709$	5.39564	−	9.34553i	0.202638	−	0.350979i	0.949377	+	0.314138i	$0.101715\pi$
$710$		0			0
$711$	−35.8303	+	62.0599i	−1.34374	+	2.32743i
$712$	−0.313068	−	0.542250i	−0.0117327	−	0.0203217i
$713$	21.9564	+	38.0297i	0.822275	+	1.42422i
$714$	3.95644			0.148066
$715$		0			0
$716$	6.00000			0.224231
$717$	25.3521	+	43.9111i	0.946791	+	1.63989i
$718$	16.8956	+	29.2641i	0.630540	+	1.09213i
$719$	−5.76951	+	9.99308i	−0.215166	+	0.372679i	−0.953324	−	0.301949i	$-0.902363\pi$
$719$	−5.76951	+	9.99308i	−0.215166	+	0.372679i	0.738158	+	0.674628i	$0.235696\pi$
$720$		0			0
$721$	−2.31307	+	4.00635i	−0.0861432	+	0.149204i
$722$	−3.00000	+	5.19615i	−0.111648	+	0.193381i
$723$	−19.5390			−0.726664
$724$	−3.68693	+	6.38595i	−0.137024	+	0.237332i
$725$		0			0
$726$	−4.70871	−	8.15573i	−0.174757	−	0.302687i
$727$	−23.1652			−0.859148			−0.429574	−	0.903032i	$-0.641336\pi$
$727$	−23.1652			−0.859148			−0.429574	+	0.903032i	$0.641336\pi$
$728$	−1.79129	+	6.20520i	−0.0663895	+	0.229980i
$729$	−43.8693			−1.62479
$730$		0			0
$731$	−4.33485	−	7.50818i	−0.160330	−	0.277700i
$732$	11.9782	−	20.7469i	0.442728	−	0.766827i
$733$	−19.3739			−0.715590			−0.357795	−	0.933800i	$-0.616471\pi$
$733$	−19.3739			−0.715590			−0.357795	+	0.933800i	$0.616471\pi$
$734$	12.3739	−	21.4322i	0.456728	−	0.791075i
$735$		0			0
$736$	−4.58258			−0.168916
$737$	−20.8521	+	36.1169i	−0.768096	+	1.33038i
$738$	−29.1434	−	50.4778i	−1.07278	−	1.85811i
$739$	−17.1869	−	29.7686i	−0.632232	−	1.09506i	−0.987095	−	0.160139i	$-0.948806\pi$
$739$	−17.1869	−	29.7686i	−0.632232	−	1.09506i	0.354863	−	0.934918i	$-0.384528\pi$
$740$		0			0
$741$	48.8475	−	12.0866i	1.79446	−	0.444013i
$742$	−8.20871			−0.301351
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	−0.937336	−	0.348428i	$-0.886716\pi$
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	0.166920	−	0.985970i	$-0.446618\pi$
$744$	−13.3739	−	23.1642i	−0.490310	−	0.849241i
$745$		0			0
$746$	13.1652			0.482010
$747$	−14.7695	+	25.5815i	−0.540388	+	0.935980i
$748$	1.50000	−	2.59808i	0.0548454	−	0.0949951i
$749$	18.6606			0.681844
$750$		0			0
$751$	−1.24773	−	2.16113i	−0.0455302	−	0.0788606i	0.842362	−	0.538912i	$-0.181164\pi$
$751$	−1.24773	−	2.16113i	−0.0455302	−	0.0788606i	−0.887892	+	0.460051i	$0.847831\pi$
$752$	0.395644	+	0.685275i	0.0144276	+	0.0249894i
$753$	−56.8693			−2.07243
$754$	3.79129	−	13.1334i	0.138071	−	0.478290i
$755$		0			0
$756$	−4.47822	−	7.75650i	−0.162871	−	0.282101i
$757$	−23.8739	−	41.3507i	−0.867710	−	1.50292i	−0.864331	−	0.502924i	$-0.832258\pi$
$757$	−23.8739	−	41.3507i	−0.867710	−	1.50292i	−0.00337974	−	0.999994i	$-0.501076\pi$
$758$	−8.50000	+	14.7224i	−0.308734	+	0.534743i
$759$	48.4955			1.76027
$760$		0			0
$761$	5.45644	−	9.45083i	0.197796	−	0.342592i	−0.750018	−	0.661418i	$-0.769955\pi$
$761$	5.45644	−	9.45083i	0.197796	−	0.342592i	0.947813	+	0.318825i	$0.103288\pi$
$762$	−45.7042			−1.65569
$763$	−1.64337	+	2.84640i	−0.0594940	+	0.103047i
$764$	0.873864	+	1.51358i	0.0316153	+	0.0547593i
$765$		0			0
$766$	−1.74773			−0.0631479
$767$	4.58258	−	15.8745i	0.165467	−	0.573195i
$768$	2.79129			0.100722
$769$	−18.3739	−	31.8245i	−0.662578	−	1.14762i	−0.979936	−	0.199314i	$-0.936129\pi$
$769$	−18.3739	−	31.8245i	−0.662578	−	1.14762i	0.317357	−	0.948306i	$-0.397205\pi$
$770$		0			0
$771$	31.9782	−	55.3879i	1.15167	−	1.99475i
$772$	−17.9564			−0.646266
$773$	18.3303	−	31.7490i	0.659295	−	1.14193i	−0.321503	−	0.946908i	$-0.604188\pi$
$773$	18.3303	−	31.7490i	0.659295	−	1.14193i	0.980798	−	0.195024i	$-0.0624786\pi$
$774$	−26.2477	+	45.4624i	−0.943455	+	1.63411i
$775$		0			0
$776$	−4.60436	+	7.97498i	−0.165287	+	0.286285i
$777$	−15.9347	−	27.5996i	−0.571653	−	0.990132i
$778$	3.16515	+	5.48220i	0.113476	+	0.196547i
$779$	60.8258			2.17931
$780$		0			0
$781$	−28.7477			−1.02867
$782$	1.81307	+	3.14033i	0.0648352	+	0.112298i
$783$	9.47822	+	16.4168i	0.338724	+	0.586687i
$784$	1.89564	−	3.28335i	0.0677016	−	0.117263i
$785$		0			0
$786$	20.9347	−	36.2599i	0.746715	−	1.29335i
$787$	21.7695	−	37.7059i	0.775999	−	1.34407i	−0.158232	−	0.987402i	$-0.550579\pi$
$787$	21.7695	−	37.7059i	0.775999	−	1.34407i	0.934231	−	0.356668i	$-0.116087\pi$
$788$	9.95644			0.354683
$789$	−13.8956	+	24.0680i	−0.494698	+	0.856842i
$790$		0			0
$791$	−0.560795	−	0.971326i	−0.0199396	−	0.0345364i
$792$	−18.1652			−0.645471
$793$	8.58258	−	29.7309i	0.304776	−	1.05578i
$794$	6.20871			0.220339
$795$		0			0
$796$	7.06080	+	12.2297i	0.250263	+	0.433469i
$797$	22.0390	−	38.1727i	0.780662	−	1.35215i	−0.150895	−	0.988550i	$-0.548215\pi$
$797$	22.0390	−	38.1727i	0.780662	−	1.35215i	0.931557	−	0.363596i	$-0.118451\pi$
$798$	25.0000			0.884990
$799$	0.313068	−	0.542250i	0.0110756	−	0.0191834i
$800$		0			0
$801$	3.00000			0.106000
$802$	10.1869	−	17.6443i	0.359713	−	0.623041i
$803$	13.5826	+	23.5257i	0.479319	+	0.830204i
$804$	15.3521	+	26.5906i	0.541426	+	0.937778i
$805$		0			0
$806$	−23.9564	−	24.8963i	−0.843830	−	0.876933i
$807$	−42.7913			−1.50632
$808$	9.87386	+	17.1020i	0.347361	+	0.601647i
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$		0			0
$811$	−18.7042			−0.656792			−0.328396	−	0.944540i	$-0.606508\pi$
$811$	−18.7042			−0.656792			−0.328396	+	0.944540i	$0.606508\pi$
$812$	3.39564	−	5.88143i	0.119164	−	0.206398i
$813$	−15.5826	+	26.9898i	−0.546505	+	0.946574i
$814$	−24.1652			−0.846988
$815$		0			0
$816$	−1.10436	−	1.91280i	−0.0386602	−	0.0669614i
$817$	−27.3911	−	47.4428i	−0.958293	−	1.65981i
$818$	−22.4955			−0.786535
$819$	−21.4564	−	22.2982i	−0.749749	−	0.779162i
$820$		0			0
$821$	−5.45644	−	9.45083i	−0.190431	−	0.329836i	0.754962	−	0.655768i	$-0.227655\pi$
$821$	−5.45644	−	9.45083i	−0.190431	−	0.329836i	−0.945393	+	0.325932i	$0.894322\pi$
$822$	21.1652	+	36.6591i	0.738219	+	1.27863i
$823$	10.6261	−	18.4050i	0.370404	−	0.641558i	−0.619224	−	0.785215i	$-0.712553\pi$
$823$	10.6261	−	18.4050i	0.370404	−	0.641558i	0.989628	+	0.143656i	$0.0458860\pi$
$824$	2.58258			0.0899683
$825$		0			0
$826$	4.10436	−	7.10895i	0.142809	−	0.247352i
$827$	45.3303			1.57629			0.788145	−	0.615490i	$-0.211042\pi$
$827$	45.3303			1.57629			0.788145	+	0.615490i	$0.211042\pi$
$828$	10.9782	−	19.0148i	0.381520	−	0.660811i
$829$	22.1434	+	38.3534i	0.769071	+	1.33207i	0.938067	+	0.346453i	$0.112614\pi$
$829$	22.1434	+	38.3534i	0.769071	+	1.33207i	−0.168996	+	0.985617i	$0.554053\pi$
$830$		0			0
$831$	21.2867			0.738429
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	−3.00000			−0.103944
$834$	−30.1216	−	52.1721i	−1.04303	−	1.80657i
$835$		0			0
$836$	9.47822	−	16.4168i	0.327811	−	0.567785i
$837$	47.9129			1.65611
$838$	1.73049	−	2.99730i	0.0597789	−	0.103540i
$839$	2.85208	−	4.93995i	0.0984648	−	0.170546i	−0.812585	−	0.582843i	$-0.801940\pi$
$839$	2.85208	−	4.93995i	0.0984648	−	0.170546i	0.911049	+	0.412297i	$0.135273\pi$
$840$		0			0
$841$	7.31307	−	12.6666i	0.252175	−	0.436780i
$842$	−0.521780	−	0.903750i	−0.0179817	−	0.0311453i
$843$	20.2913	+	35.1455i	0.698869	+	1.21048i
$844$	5.00000			0.172107
$845$		0			0
$846$	−3.79129			−0.130347
$847$	−3.02178	−	5.23388i	−0.103830	−	0.179838i
$848$	2.29129	+	3.96863i	0.0786831	+	0.136283i
$849$	−17.5000	+	30.3109i	−0.600598	+	1.04027i
$850$		0			0
$851$	14.6044	−	25.2955i	0.500631	−	0.867118i
$852$	−10.5826	+	18.3296i	−0.362553	+	0.627960i
$853$	32.1216			1.09982			0.549911	−	0.835223i	$-0.314662\pi$
$853$	32.1216			1.09982			0.549911	+	0.835223i	$0.314662\pi$
$854$	7.68693	−	13.3142i	0.263041	−	0.455601i
$855$		0			0
$856$	−5.20871	−	9.02175i	−0.178030	−	0.308357i
$857$	24.1652			0.825466			0.412733	−	0.910852i	$-0.364574\pi$
$857$	24.1652			0.825466			0.412733	+	0.910852i	$0.364574\pi$
$858$	−37.0390	+	9.16478i	−1.26449	+	0.312880i
$859$	21.2867			0.726294			0.363147	−	0.931732i	$-0.381702\pi$
$859$	21.2867			0.726294			0.363147	+	0.931732i	$0.381702\pi$
$860$		0			0
$861$	−30.4129	−	52.6767i	−1.03647	−	1.79522i
$862$	3.39564	−	5.88143i	0.115656	−	0.200322i
$863$	22.5826			0.768720			0.384360	−	0.923183i	$-0.374422\pi$
$863$	22.5826			0.768720			0.384360	+	0.923183i	$0.374422\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$		0			0
$866$	−30.5826			−1.03924
$867$	22.8521	−	39.5810i	0.776097	−	1.34424i
$868$	−8.58258	−	14.8655i	−0.291312	−	0.504566i
$869$	28.3521	+	49.1072i	0.961779	+	1.66585i
$870$		0			0
$871$	27.5000	+	28.5788i	0.931802	+	0.968357i
$872$	1.83485			0.0621358
$873$	−22.0608	−	38.2104i	−0.746645	−	1.29323i
$874$	11.4564	+	19.8431i	0.387520	+	0.671204i
$875$		0			0
$876$	20.0000			0.675737
$877$	9.12614	−	15.8069i	0.308168	−	0.533762i	−0.669794	−	0.742547i	$-0.733618\pi$
$877$	9.12614	−	15.8069i	0.308168	−	0.533762i	0.977962	+	0.208785i	$0.0669509\pi$
$878$	8.79129	−	15.2270i	0.296692	−	0.513885i
$879$	−18.4955			−0.623836
$880$		0			0
$881$	2.52178	+	4.36785i	0.0849609	+	0.147157i	0.905375	−	0.424614i	$-0.139590\pi$
$881$	2.52178	+	4.36785i	0.0849609	+	0.147157i	−0.820414	+	0.571770i	$0.806257\pi$
$882$	9.08258	+	15.7315i	0.305826	+	0.529707i
$883$	19.9564			0.671588			0.335794	−	0.941936i	$-0.390995\pi$
$883$	19.9564			0.671588			0.335794	+	0.941936i	$0.390995\pi$
$884$	−1.97822	−	2.05583i	−0.0665347	−	0.0691449i
$885$		0			0
$886$	1.02178	+	1.76978i	0.0343274	+	0.0594568i
$887$	25.5826	+	44.3103i	0.858979	+	1.48779i	0.872904	+	0.487892i	$0.162234\pi$
$887$	25.5826	+	44.3103i	0.858979	+	1.48779i	−0.0139252	+	0.999903i	$0.504433\pi$
$888$	−8.89564	+	15.4077i	−0.298518	+	0.517049i
$889$	−29.3303			−0.983707
$890$		0			0
$891$	−0.791288	+	1.37055i	−0.0265091	+	0.0459152i
$892$	−9.74773			−0.326378
$893$	1.97822	−	3.42638i	0.0661986	−	0.114659i
$894$	5.52178	+	9.56400i	0.184676	+	0.319868i
$895$		0			0
$896$	1.79129			0.0598427
$897$	12.7913	−	44.3103i	0.427089	−	1.47948i
$898$	32.3739			1.08033
$899$	18.1652	+	31.4630i	0.605842	+	1.04935i
$900$		0			0
$901$	1.81307	−	3.14033i	0.0604021	−	0.104619i
$902$	−46.1216			−1.53568
$903$	−27.3911	+	47.4428i	−0.911519	+	1.57880i
$904$	−0.313068	+	0.542250i	−0.0104125	+	0.0180350i
$905$		0			0
$906$	8.89564	−	15.4077i	0.295538	−	0.511887i
$907$	16.2477	+	28.1419i	0.539497	+	0.934436i	0.998931	+	0.0462243i	$0.0147189\pi$
$907$	16.2477	+	28.1419i	0.539497	+	0.934436i	−0.459434	+	0.888212i	$0.651948\pi$
$908$	8.29129	+	14.3609i	0.275156	+	0.476584i
$909$	−94.6170			−3.13825
$910$		0			0
$911$	45.3303			1.50186			0.750930	−	0.660382i	$-0.229606\pi$
$911$	45.3303			1.50186			0.750930	+	0.660382i	$0.229606\pi$
$912$	−6.97822	−	12.0866i	−0.231072	−	0.400228i
$913$	11.6869	+	20.2424i	0.386781	+	0.669924i
$914$	3.68693	−	6.38595i	0.121953	−	0.211229i
$915$		0			0
$916$	6.18693	−	10.7161i	0.204422	−	0.354069i
$917$	13.4347	−	23.2695i	0.443652	−	0.768427i
$918$	3.95644			0.130582
$919$	22.3739	−	38.7527i	0.738046	−	1.27833i	−0.215328	−	0.976542i	$-0.569082\pi$
$919$	22.3739	−	38.7527i	0.738046	−	1.27833i	0.953374	−	0.301791i	$-0.0975844\pi$
$920$		0			0
$921$	−18.3739	−	31.8245i	−0.605439	−	1.04865i
$922$	29.2087			0.961938
$923$	−7.58258	+	26.2668i	−0.249584	+	0.864583i
$924$	−18.9564			−0.623621
$925$		0			0
$926$	8.97822	+	15.5507i	0.295043	+	0.511029i
$927$	−6.18693	+	10.7161i	−0.203206	+	0.351962i
$928$	−3.79129			−0.124455
$929$	11.3739	−	19.7001i	0.373164	−	0.646340i	−0.616886	−	0.787052i	$-0.711606\pi$
$929$	11.3739	−	19.7001i	0.373164	−	0.646340i	0.990050	+	0.140713i	$0.0449394\pi$
$930$		0			0
$931$	−18.9564			−0.621272
$932$	−7.50000	+	12.9904i	−0.245671	+	0.425514i
$933$	24.2477	+	41.9983i	0.793835	+	1.37496i
$934$	−4.18693	−	7.25198i	−0.137001	−	0.237292i
$935$		0			0
$936$	−4.79129	+	16.5975i	−0.156608	+	0.542507i
$937$	−32.6261			−1.06585			−0.532925	−	0.846163i	$-0.678907\pi$
$937$	−32.6261			−1.06585			−0.532925	+	0.846163i	$0.678907\pi$
$938$	9.85208	+	17.0643i	0.321682	+	0.557169i
$939$	−6.45644	−	11.1829i	−0.210698	−	0.364940i
$940$		0			0
$941$	−47.3739			−1.54434			−0.772172	−	0.635414i	$-0.780830\pi$
$941$	−47.3739			−1.54434			−0.772172	+	0.635414i	$0.780830\pi$
$942$	7.20871	−	12.4859i	0.234873	−	0.406811i
$943$	27.8739	−	48.2789i	0.907698	−	1.57218i
$944$	−4.58258			−0.149150
$945$		0			0
$946$	20.7695	+	35.9738i	0.675275	+	1.16961i
$947$	−18.3956	−	31.8622i	−0.597778	−	1.03538i	−0.993148	−	0.116860i	$-0.962717\pi$
$947$	−18.3956	−	31.8622i	−0.597778	−	1.03538i	0.395370	−	0.918522i	$-0.370616\pi$
$948$	41.7477			1.35590
$949$	25.0780	−	6.20520i	0.814067	−	0.201429i
$950$		0			0
$951$	37.0390	+	64.1535i	1.20107	+	2.08032i
$952$	−0.708712	−	1.22753i	−0.0229695	−	0.0397843i
$953$	15.2477	−	26.4098i	0.493922	−	0.855499i	−0.506053	−	0.862502i	$-0.668896\pi$
$953$	15.2477	−	26.4098i	0.493922	−	0.855499i	0.999975	+	0.00700373i	$0.00222937\pi$
$954$	−21.9564			−0.710866
$955$		0			0
$956$	9.08258	−	15.7315i	0.293751	−	0.508793i
$957$	40.1216			1.29695
$958$	−9.47822	+	16.4168i	−0.306227	+	0.530401i
$959$	13.5826	+	23.5257i	0.438604	+	0.759685i
$960$		0			0
$961$	60.8258			1.96212
$962$	−6.37386	+	22.0797i	−0.205502	+	0.711878i
$963$	49.9129			1.60842
$964$	3.50000	+	6.06218i	0.112727	+	0.195250i
$965$		0			0
$966$	11.4564	−	19.8431i	0.368605	−	0.638442i
$967$	−6.74773			−0.216992			−0.108496	−	0.994097i	$-0.534604\pi$
$967$	−6.74773			−0.216992			−0.108496	+	0.994097i	$0.534604\pi$
$968$	−1.68693	+	2.92185i	−0.0542200	+	0.0939119i
$969$	−5.52178	+	9.56400i	−0.177385	+	0.307240i
$970$		0			0
$971$	−9.24773	+	16.0175i	−0.296774	+	0.514027i	−0.975396	−	0.220460i	$-0.929244\pi$
$971$	−9.24773	+	16.0175i	−0.296774	+	0.514027i	0.678622	+	0.734487i	$0.262577\pi$
$972$	8.08258	+	13.9994i	0.259249	+	0.449032i
$973$	−19.3303	−	33.4811i	−0.619701	−	1.07335i
$974$	−21.1216			−0.676779
$975$		0			0
$976$	−8.58258			−0.274722
$977$	−5.29129	−	9.16478i	−0.169283	−	0.293207i	0.768885	−	0.639387i	$-0.220812\pi$
$977$	−5.29129	−	9.16478i	−0.169283	−	0.293207i	−0.938168	+	0.346180i	$0.887479\pi$
$978$	−6.45644	−	11.1829i	−0.206454	−	0.357589i
$979$	1.18693	−	2.05583i	0.0379345	−	0.0657045i
$980$		0			0
$981$	−4.39564	+	7.61348i	−0.140342	+	0.243080i
$982$	−17.4564	+	30.2354i	−0.557057	+	0.964852i
$983$	18.4610			0.588814			0.294407	−	0.955680i	$-0.404878\pi$
$983$	18.4610			0.588814			0.294407	+	0.955680i	$0.404878\pi$
$984$	−16.9782	+	29.4071i	−0.541246	+	0.937465i
$985$		0			0
$986$	1.50000	+	2.59808i	0.0477697	+	0.0827396i
$987$	−3.95644			−0.125935
$988$	−12.5000	−	12.9904i	−0.397678	−	0.413279i
$989$	−50.2087			−1.59654
$990$		0			0
$991$	−13.0000	−	22.5167i	−0.412959	−	0.715265i	0.582253	−	0.813008i	$-0.302171\pi$
$991$	−13.0000	−	22.5167i	−0.412959	−	0.715265i	−0.995212	+	0.0977423i	$0.968838\pi$
$992$	−4.79129	+	8.29875i	−0.152124	+	0.263486i
$993$	33.3739			1.05909
$994$	−6.79129	+	11.7629i	−0.215407	+	0.373095i
$995$		0			0
$996$	17.2087			0.545279
$997$	−2.56080	+	4.43543i	−0.0811012	+	0.140471i	−0.903723	−	0.428117i	$-0.859177\pi$
$997$	−2.56080	+	4.43543i	−0.0811012	+	0.140471i	0.822622	+	0.568589i	$0.192510\pi$
$998$	−4.87386	−	8.44178i	−0.154279	−	0.267220i
$999$	−15.9347	−	27.5996i	−0.504150	−	0.873214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.e.d.601.1	yes	4
5.2	odd	4		650.2.o.f.549.3		8
5.3	odd	4		650.2.o.f.549.2		8
5.4	even	2		650.2.e.i.601.2	yes	4
13.3	even	3		8450.2.a.bk.1.2		2
13.9	even	3	inner	650.2.e.d.451.1	✓	4
13.10	even	6		8450.2.a.be.1.2		2
65.9	even	6		650.2.e.i.451.2	yes	4
65.22	odd	12		650.2.o.f.399.2		8
65.29	even	6		8450.2.a.bb.1.1		2
65.48	odd	12		650.2.o.f.399.3		8
65.49	even	6		8450.2.a.bh.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.e.d.451.1	✓	4	13.9	even	3	inner
650.2.e.d.601.1	yes	4	1.1	even	1	trivial
650.2.e.i.451.2	yes	4	65.9	even	6
650.2.e.i.601.2	yes	4	5.4	even	2
650.2.o.f.399.2		8	65.22	odd	12
650.2.o.f.399.3		8	65.48	odd	12
650.2.o.f.549.2		8	5.3	odd	4
650.2.o.f.549.3		8	5.2	odd	4
8450.2.a.bb.1.1		2	65.29	even	6
8450.2.a.be.1.2		2	13.10	even	6
8450.2.a.bh.1.1		2	65.49	even	6
8450.2.a.bk.1.2		2	13.3	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.39564 - 2.41733i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.39564 + 2.41733i) q^{6} +(-0.895644 + 1.55130i) q^{7} +1.00000 q^{8} +(-2.39564 + 4.14938i) q^{9} +(1.89564 + 3.28335i) q^{11} +2.79129 q^{12} +(3.50000 - 0.866025i) q^{13} +1.79129 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.395644 + 0.685275i) q^{17} +4.79129 q^{18} +(-2.50000 + 4.33013i) q^{19} +5.00000 q^{21} +(1.89564 - 3.28335i) q^{22} +(2.29129 + 3.96863i) q^{23} +(-1.39564 - 2.41733i) q^{24} +(-2.50000 - 2.59808i) q^{26} +5.00000 q^{27} +(-0.895644 - 1.55130i) q^{28} +(1.89564 + 3.28335i) q^{29} +9.58258 q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.29129 - 9.16478i) q^{33} +0.791288 q^{34} +(-2.39564 - 4.14938i) q^{36} +(-3.18693 - 5.51993i) q^{37} +5.00000 q^{38} +(-6.97822 - 7.25198i) q^{39} +(-6.08258 - 10.5353i) q^{41} +(-2.50000 - 4.33013i) q^{42} +(-5.47822 + 9.48855i) q^{43} -3.79129 q^{44} +(2.29129 - 3.96863i) q^{46} -0.791288 q^{47} +(-1.39564 + 2.41733i) q^{48} +(1.89564 + 3.28335i) q^{49} +2.20871 q^{51} +(-1.00000 + 3.46410i) q^{52} -4.58258 q^{53} +(-2.50000 - 4.33013i) q^{54} +(-0.895644 + 1.55130i) q^{56} +13.9564 q^{57} +(1.89564 - 3.28335i) q^{58} +(2.29129 - 3.96863i) q^{59} +(4.29129 - 7.43273i) q^{61} +(-4.79129 - 8.29875i) q^{62} +(-4.29129 - 7.43273i) q^{63} +1.00000 q^{64} -10.5826 q^{66} +(5.50000 + 9.52628i) q^{67} +(-0.395644 - 0.685275i) q^{68} +(6.39564 - 11.0776i) q^{69} +(-3.79129 + 6.56670i) q^{71} +(-2.39564 + 4.14938i) q^{72} +7.16515 q^{73} +(-3.18693 + 5.51993i) q^{74} +(-2.50000 - 4.33013i) q^{76} -6.79129 q^{77} +(-2.79129 + 9.66930i) q^{78} +14.9564 q^{79} +(0.208712 + 0.361500i) q^{81} +(-6.08258 + 10.5353i) q^{82} +6.16515 q^{83} +(-2.50000 + 4.33013i) q^{84} +10.9564 q^{86} +(5.29129 - 9.16478i) q^{87} +(1.89564 + 3.28335i) q^{88} +(-0.313068 - 0.542250i) q^{89} +(-1.79129 + 6.20520i) q^{91} -4.58258 q^{92} +(-13.3739 - 23.1642i) q^{93} +(0.395644 + 0.685275i) q^{94} +2.79129 q^{96} +(-4.60436 + 7.97498i) q^{97} +(1.89564 - 3.28335i) q^{98} -18.1652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} + q^{7} + 4 q^{8} - 5 q^{9} + 3 q^{11} + 2 q^{12} + 14 q^{13} - 2 q^{14} - 2 q^{16} + 3 q^{17} + 10 q^{18} - 10 q^{19} + 20 q^{21} + 3 q^{22} - q^{24} - 10 q^{26}+ \cdots - 36 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 + q^7 + 4 * q^8 - 5 * q^9 + 3 * q^11 + 2 * q^12 + 14 * q^13 - 2 * q^14 - 2 * q^16 + 3 * q^17 + 10 * q^18 - 10 * q^19 + 20 * q^21 + 3 * q^22 - q^24 - 10 * q^26 + 20 * q^27 + q^28 + 3 * q^29 + 20 * q^31 - 2 * q^32 + 12 * q^33 - 6 * q^34 - 5 * q^36 + q^37 + 20 * q^38 - 5 * q^39 - 6 * q^41 - 10 * q^42 + q^43 - 6 * q^44 + 6 * q^47 - q^48 + 3 * q^49 + 18 * q^51 - 4 * q^52 - 10 * q^54 + q^56 + 10 * q^57 + 3 * q^58 + 8 * q^61 - 10 * q^62 - 8 * q^63 + 4 * q^64 - 24 * q^66 + 22 * q^67 + 3 * q^68 + 21 * q^69 - 6 * q^71 - 5 * q^72 - 8 * q^73 + q^74 - 10 * q^76 - 18 * q^77 - 2 * q^78 + 14 * q^79 + 10 * q^81 - 6 * q^82 - 12 * q^83 - 10 * q^84 - 2 * q^86 + 12 * q^87 + 3 * q^88 - 15 * q^89 + 2 * q^91 - 26 * q^93 - 3 * q^94 + 2 * q^96 - 23 * q^97 + 3 * q^98 - 36 * q^99

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