LMFDB - Embedded newform 845.2.l.d.654.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(654,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("845.654");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.l (of order $6$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			654.3
Root			$-1.16746 + 0.312819i$ of defining polynomial
Character	$\chi$	$=$	845.654
Dual form			845.2.l.d.699.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.769594 + 1.33298i) q^{2} +(-2.74538 - 1.58504i) q^{3} +(-0.184551 - 0.319652i) q^{4} +(2.17009 + 0.539189i) q^{5} +(4.22565 - 2.43968i) q^{6} +(-0.854638 - 1.48028i) q^{7} -2.51026 q^{8} +(3.52472 + 6.10500i) q^{9} +(-2.38881 + 2.47772i) q^{10} +(-2.19900 - 1.26959i) q^{11} +1.17009i q^{12} +2.63090 q^{14} +(-5.10306 - 4.91996i) q^{15} +(2.30098 - 3.98542i) q^{16} +(0.798148 - 0.460811i) q^{17} -10.8504 q^{18} +(0.466951 - 0.269594i) q^{19} +(-0.228139 - 0.793181i) q^{20} +5.41855i q^{21} +(3.38468 - 1.95415i) q^{22} +(2.45078 + 1.41496i) q^{23} +(6.89160 + 3.97887i) q^{24} +(4.41855 + 2.34017i) q^{25} -12.8371i q^{27} +(-0.315449 + 0.546373i) q^{28} +(-2.56391 + 4.44083i) q^{29} +(10.4855 - 3.01589i) q^{30} +0.879362i q^{31} +(1.03139 + 1.78642i) q^{32} +(4.02472 + 6.97103i) q^{33} +1.41855i q^{34} +(-1.05649 - 3.67314i) q^{35} +(1.30098 - 2.25337i) q^{36} +(-3.02472 + 5.23898i) q^{37} +0.829914i q^{38} +(-5.44748 - 1.35350i) q^{40} +(-1.09275 - 0.630898i) q^{41} +(-7.22280 - 4.17009i) q^{42} +(-5.57017 + 3.21594i) q^{43} +0.937221i q^{44} +(4.35721 + 15.1489i) q^{45} +(-3.77221 + 2.17789i) q^{46} -5.70928 q^{47} +(-12.6341 + 7.29432i) q^{48} +(2.03919 - 3.53198i) q^{49} +(-6.51989 + 4.08884i) q^{50} -2.92162 q^{51} +8.49693i q^{53} +(17.1116 + 9.87936i) q^{54} +(-4.08747 - 3.94081i) q^{55} +(2.14536 + 3.71588i) q^{56} -1.70928 q^{57} +(-3.94635 - 6.83527i) q^{58} +(-4.08990 + 2.36130i) q^{59} +(-0.630898 + 2.53919i) q^{60} +(-4.02472 - 6.97103i) q^{61} +(-1.17217 - 0.676752i) q^{62} +(6.02472 - 10.4351i) q^{63} +6.02893 q^{64} -12.3896 q^{66} +(-3.93302 + 6.81218i) q^{67} +(-0.294598 - 0.170086i) q^{68} +(-4.48554 - 7.76918i) q^{69} +(5.70928 + 1.41855i) q^{70} +(-12.5412 + 7.24067i) q^{71} +(-8.84797 - 15.3251i) q^{72} -1.95055 q^{73} +(-4.65562 - 8.06377i) q^{74} +(-8.42131 - 13.4282i) q^{75} +(-0.172353 - 0.0995079i) q^{76} +4.34017i q^{77} -0.496928 q^{79} +(7.14223 - 7.40804i) q^{80} +(-9.77319 + 16.9277i) q^{81} +(1.68194 - 0.971071i) q^{82} -8.63090 q^{83} +(1.73205 - 1.00000i) q^{84} +(1.98052 - 0.569647i) q^{85} -9.89988i q^{86} +(14.0778 - 8.12783i) q^{87} +(5.52007 + 3.18701i) q^{88} +(-11.1173 - 6.41855i) q^{89} +(-23.5464 - 5.85043i) q^{90} -1.04453i q^{92} +(1.39383 - 2.41418i) q^{93} +(4.39383 - 7.61033i) q^{94} +(1.15869 - 0.333268i) q^{95} -6.53919i q^{96} +(-2.95774 - 5.12296i) q^{97} +(3.13870 + 5.43638i) q^{98} -17.8999i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 10 q^{4} + 4 q^{5} + 4 q^{7} + 36 q^{8} + 6 q^{9} + 2 q^{10} + 16 q^{14} - 4 q^{15} - 10 q^{16} - 20 q^{18} + 14 q^{20} - 4 q^{25} + 4 q^{28} + 12 q^{29} + 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 10 * q^4 + 4 * q^5 + 4 * q^7 + 36 * q^8 + 6 * q^9 + 2 * q^10 + 16 * q^14 - 4 * q^15 - 10 * q^16 - 20 * q^18 + 14 * q^20 - 4 * q^25 + 4 * q^28 + 12 * q^29 + 8 * q^30 - 22 * q^32 + 12 * q^33 - 8 * q^35 - 22 * q^36 - 68 * q^40 + 38 * q^45 - 40 * q^47 + 18 * q^49 - 22 * q^50 - 48 * q^51 + 16 * q^55 + 40 * q^56 + 8 * q^57 - 24 * q^58 + 8 * q^60 - 12 * q^61 + 36 * q^63 + 132 * q^64 - 32 * q^66 - 20 * q^67 - 24 * q^69 + 40 * q^70 - 90 * q^72 - 96 * q^73 - 4 * q^74 + 16 * q^75 + 64 * q^79 + 58 * q^80 - 46 * q^81 - 88 * q^83 - 32 * q^85 - 140 * q^90 - 4 * q^93 + 32 * q^94 + 16 * q^95 + 28 * q^97 + 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.769594	+	1.33298i	−0.544185	+	0.942557i	0.454472	+	0.890761i	$0.349828\pi$
$2$	−0.769594	+	1.33298i	−0.544185	+	0.942557i	−0.998658	+	0.0517959i	$0.983505\pi$
$3$	−2.74538	−	1.58504i	−1.58504	−	0.915125i	−0.994107	−	0.108407i	$-0.965425\pi$
$3$	−2.74538	−	1.58504i	−1.58504	−	0.915125i	−0.590937	−	0.806718i	$-0.701242\pi$
$4$	−0.184551	−	0.319652i	−0.0922756	−	0.159826i
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$6$	4.22565	−	2.43968i	1.72511	−	0.995996i
$7$	−0.854638	−	1.48028i	−0.323023	−	0.559492i	0.658088	−	0.752941i	$-0.271366\pi$
$7$	−0.854638	−	1.48028i	−0.323023	−	0.559492i	−0.981110	+	0.193450i	$0.938032\pi$
$8$	−2.51026			−0.887511
$9$	3.52472	+	6.10500i	1.17491	+	2.03500i
$10$	−2.38881	+	2.47772i	−0.755409	+	0.783523i
$11$	−2.19900	−	1.26959i	−0.663024	−	0.382797i	0.130404	−	0.991461i	$-0.458373\pi$
$11$	−2.19900	−	1.26959i	−0.663024	−	0.382797i	−0.793428	+	0.608664i	$0.791706\pi$
$12$			1.17009i			0.337775i
$13$		0			0
$13$		0			0
$14$	2.63090			0.703137
$15$	−5.10306	−	4.91996i	−1.31761	−	1.27033i
$16$	2.30098	−	3.98542i	0.575246	−	0.996355i
$17$	0.798148	−	0.460811i	0.193579	−	0.111763i	−0.400078	−	0.916481i	$-0.631017\pi$
$17$	0.798148	−	0.460811i	0.193579	−	0.111763i	0.593657	+	0.804718i	$0.297684\pi$
$18$	−10.8504			−2.55747
$19$	0.466951	−	0.269594i	0.107126	−	0.0618492i	−0.445480	−	0.895292i	$-0.646967\pi$
$19$	0.466951	−	0.269594i	0.107126	−	0.0618492i	0.552606	+	0.833443i	$0.313634\pi$
$20$	−0.228139	−	0.793181i	−0.0510135	−	0.177361i
$21$			5.41855i			1.18242i
$22$	3.38468	−	1.95415i	0.721616	−	0.416625i
$23$	2.45078	+	1.41496i	0.511022	+	0.295039i	0.733254	−	0.679955i	$-0.238001\pi$
$23$	2.45078	+	1.41496i	0.511022	+	0.295039i	−0.222231	+	0.974994i	$0.571334\pi$
$24$	6.89160	+	3.97887i	1.40674	+	0.812183i
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$		0			0
$27$		−	12.8371i		−	2.47050i
$28$	−0.315449	+	0.546373i	−0.0596142	+	0.103255i
$29$	−2.56391	+	4.44083i	−0.476107	+	0.824641i	−0.999625	−	0.0273733i	$-0.991286\pi$
$29$	−2.56391	+	4.44083i	−0.476107	+	0.824641i	0.523519	+	0.852014i	$0.324619\pi$
$30$	10.4855	−	3.01589i	1.91438	−	0.550624i
$31$			0.879362i			0.157938i	0.996877	+	0.0789690i	$0.0251628\pi$
$31$			0.879362i			0.157938i	−0.996877	+	0.0789690i	$0.974837\pi$
$32$	1.03139	+	1.78642i	0.182326	+	0.315797i
$33$	4.02472	+	6.97103i	0.700615	+	1.21350i
$34$			1.41855i			0.243279i
$35$	−1.05649	−	3.67314i	−0.178579	−	0.620874i
$36$	1.30098	−	2.25337i	0.216831	−	0.375562i
$37$	−3.02472	+	5.23898i	−0.497262	+	0.861282i	−0.999995	−	0.00315916i	$-0.998994\pi$
$37$	−3.02472	+	5.23898i	−0.497262	+	0.861282i	0.502733	+	0.864442i	$0.332328\pi$
$38$			0.829914i			0.134630i
$39$		0			0
$40$	−5.44748	−	1.35350i	−0.861322	−	0.214008i
$41$	−1.09275	−	0.630898i	−0.170658	−	0.0985297i	0.412238	−	0.911076i	$-0.364747\pi$
$41$	−1.09275	−	0.630898i	−0.170658	−	0.0985297i	−0.582896	+	0.812547i	$0.698081\pi$
$42$	−7.22280	−	4.17009i	−1.11450	−	0.643458i
$43$	−5.57017	+	3.21594i	−0.849443	+	0.490426i	−0.860463	−	0.509513i	$-0.829826\pi$
$43$	−5.57017	+	3.21594i	−0.849443	+	0.490426i	0.0110196	+	0.999939i	$0.496492\pi$
$44$			0.937221i			0.141291i
$45$	4.35721	+	15.1489i	0.649534	+	2.25826i
$46$	−3.77221	+	2.17789i	−0.556182	+	0.321112i
$47$	−5.70928			−0.832783			−0.416392	−	0.909185i	$-0.636705\pi$
$47$	−5.70928			−0.832783			−0.416392	+	0.909185i	$0.636705\pi$
$48$	−12.6341	+	7.29432i	−1.82358	+	1.05284i
$49$	2.03919	−	3.53198i	0.291313	−	0.504568i
$50$	−6.51989	+	4.08884i	−0.922051	+	0.578249i
$51$	−2.92162			−0.409109
$52$		0			0
$53$			8.49693i			1.16714i	0.812062	+	0.583571i	$0.198345\pi$
$53$			8.49693i			1.16714i	−0.812062	+	0.583571i	$0.801655\pi$
$54$	17.1116	+	9.87936i	2.32859	+	1.34441i
$55$	−4.08747	−	3.94081i	−0.551155	−	0.531378i
$56$	2.14536	+	3.71588i	0.286686	+	0.496555i
$57$	−1.70928			−0.226399
$58$	−3.94635	−	6.83527i	−0.518181	−	0.897515i
$59$	−4.08990	+	2.36130i	−0.532459	+	0.307415i	−0.742017	−	0.670381i	$-0.766131\pi$
$59$	−4.08990	+	2.36130i	−0.532459	+	0.307415i	0.209558	+	0.977796i	$0.432797\pi$
$60$	−0.630898	+	2.53919i	−0.0814485	+	0.327808i
$61$	−4.02472	−	6.97103i	−0.515313	−	0.892549i	−0.999842	−	0.0177733i	$-0.994342\pi$
$61$	−4.02472	−	6.97103i	−0.515313	−	0.892549i	0.484529	−	0.874775i	$-0.338991\pi$
$62$	−1.17217	−	0.676752i	−0.148866	−	0.0859476i
$63$	6.02472	−	10.4351i	0.759044	−	1.31470i
$64$	6.02893			0.753616
$65$		0			0
$66$	−12.3896			−1.52506
$67$	−3.93302	+	6.81218i	−0.480494	+	0.832241i	−0.999750	−	0.0223786i	$-0.992876\pi$
$67$	−3.93302	+	6.81218i	−0.480494	+	0.832241i	0.519255	+	0.854619i	$0.326209\pi$
$68$	−0.294598	−	0.170086i	−0.0357253	−	0.0206260i
$69$	−4.48554	−	7.76918i	−0.539995	−	0.935299i
$70$	5.70928	+	1.41855i	0.682389	+	0.169549i
$71$	−12.5412	+	7.24067i	−1.48837	+	0.859309i	−0.999912	−	0.0132804i	$-0.995773\pi$
$71$	−12.5412	+	7.24067i	−1.48837	+	0.859309i	−0.488455	+	0.872589i	$0.662439\pi$
$72$	−8.84797	−	15.3251i	−1.04274	−	1.80608i
$73$	−1.95055			−0.228295			−0.114147	−	0.993464i	$-0.536414\pi$
$73$	−1.95055			−0.228295			−0.114147	+	0.993464i	$0.536414\pi$
$74$	−4.65562	−	8.06377i	−0.541205	−	0.937395i
$75$	−8.42131	−	13.4282i	−0.972409	−	1.55056i
$76$	−0.172353	−	0.0995079i	−0.0197702	−	0.0114143i
$77$			4.34017i			0.494609i
$78$		0			0
$79$	−0.496928			−0.0559088			−0.0279544	−	0.999609i	$-0.508899\pi$
$79$	−0.496928			−0.0559088			−0.0279544	+	0.999609i	$0.508899\pi$
$80$	7.14223	−	7.40804i	0.798526	−	0.828245i
$81$	−9.77319	+	16.9277i	−1.08591	+	1.88085i
$82$	1.68194	−	0.971071i	0.185740	−	0.107237i
$83$	−8.63090			−0.947364			−0.473682	−	0.880696i	$-0.657075\pi$
$83$	−8.63090			−0.947364			−0.473682	+	0.880696i	$0.657075\pi$
$84$	1.73205	−	1.00000i	0.188982	−	0.109109i
$85$	1.98052	−	0.569647i	0.214817	−	0.0617869i
$86$		−	9.89988i		−	1.06753i
$87$	14.0778	−	8.12783i	1.50930	−	0.871394i
$88$	5.52007	+	3.18701i	0.588441	+	0.339737i
$89$	−11.1173	−	6.41855i	−1.17843	−	0.680365i	−0.222777	−	0.974870i	$-0.571512\pi$
$89$	−11.1173	−	6.41855i	−1.17843	−	0.680365i	−0.955650	+	0.294504i	$0.904845\pi$
$90$	−23.5464	−	5.85043i	−2.48201	−	0.616690i
$91$		0			0
$92$		−	1.04453i		−	0.108900i
$93$	1.39383	−	2.41418i	0.144533	−	0.250339i
$94$	4.39383	−	7.61033i	0.453189	−	0.784946i
$95$	1.15869	−	0.333268i	0.118879	−	0.0341926i
$96$		−	6.53919i		−	0.667403i
$97$	−2.95774	−	5.12296i	−0.300313	−	0.520157i	0.675894	−	0.736999i	$-0.263758\pi$
$97$	−2.95774	−	5.12296i	−0.300313	−	0.520157i	−0.976207	+	0.216842i	$0.930424\pi$
$98$	3.13870	+	5.43638i	0.317056	+	0.549158i
$99$		−	17.8999i		−	1.79901i
$100$	−0.0674077	−	1.84428i	−0.00674077	−	0.184428i
$101$	−8.21953	+	14.2367i	−0.817874	+	1.41660i	0.0893712	+	0.995998i	$0.471514\pi$
$101$	−8.21953	+	14.2367i	−0.817874	+	1.41660i	−0.907246	+	0.420601i	$0.861819\pi$
$102$	2.24846	−	3.89445i	0.222631	−	0.385608i
$103$			10.1906i			1.00411i	0.864836	+	0.502055i	$0.167423\pi$
$103$			10.1906i			1.00411i	−0.864836	+	0.502055i	$0.832577\pi$
$104$		0			0
$105$	−2.92162	+	11.7587i	−0.285121	+	1.14753i
$106$	−11.3262	−	6.53919i	−1.10010	−	0.635142i
$107$	8.44508	+	4.87577i	0.816416	+	0.471358i	0.849179	−	0.528105i	$-0.177097\pi$
$107$	8.44508	+	4.87577i	0.816416	+	0.471358i	−0.0327627	+	0.999463i	$0.510431\pi$
$108$	−4.10341	+	2.36910i	−0.394850	+	0.227967i
$109$			16.8638i			1.61526i	0.589693	+	0.807628i	$0.299249\pi$
$109$			16.8638i			1.61526i	−0.589693	+	0.807628i	$0.700751\pi$
$110$	8.39870	−	2.41568i	0.800785	−	0.230326i
$111$	16.6080	−	9.58864i	1.57636	−	0.910113i
$112$	−7.86603			−0.743270
$113$	−10.1834	+	5.87936i	−0.957969	+	0.553084i	−0.895547	−	0.444966i	$-0.853216\pi$
$113$	−10.1834	+	5.87936i	−0.957969	+	0.553084i	−0.0624219	+	0.998050i	$0.519882\pi$
$114$	1.31545	−	2.27842i	0.123203	−	0.213394i
$115$	4.55547	+	4.39201i	0.424800	+	0.409557i
$116$	1.89269			0.175732
$117$		0			0
$118$		−	7.26898i		−	0.669164i
$119$	−1.36426	−	0.787653i	−0.125061	−	0.0722040i
$120$	12.8100	+	12.3504i	1.16939	+	1.12743i
$121$	−2.27626	−	3.94260i	−0.206933	−	0.358418i
$122$	12.3896			1.12170
$123$	2.00000	+	3.46410i	0.180334	+	0.312348i
$124$	0.281090	−	0.162287i	0.0252426	−	0.0145738i
$125$	8.32684	+	7.46081i	0.744775	+	0.667315i
$126$	9.27319	+	16.0616i	0.826121	+	1.43088i
$127$	15.5947	+	9.00359i	1.38380	+	0.798940i	0.992608	−	0.121367i	$-0.0387279\pi$
$127$	15.5947	+	9.00359i	1.38380	+	0.798940i	0.391197	+	0.920307i	$0.372061\pi$
$128$	−6.70261	+	11.6093i	−0.592433	+	1.02612i
$129$	20.3896			1.79521
$130$		0			0
$131$	14.2557			1.24552			0.622761	−	0.782412i	$-0.286011\pi$
$131$	14.2557			1.24552			0.622761	+	0.782412i	$0.286011\pi$
$132$	1.48554	−	2.57302i	0.129299	−	0.223953i
$133$	−0.798148	−	0.460811i	−0.0692082	−	0.0399574i
$134$	−6.05365	−	10.4852i	−0.522956	−	0.905786i
$135$	6.92162	−	27.8576i	0.595718	−	2.39760i
$136$	−2.00356	+	1.15676i	−0.171804	+	0.0991910i
$137$	6.89269	+	11.9385i	0.588882	+	1.01997i	0.994379	+	0.105878i	$0.0337653\pi$
$137$	6.89269	+	11.9385i	0.588882	+	1.01997i	−0.405497	+	0.914097i	$0.632901\pi$
$138$	13.8082			1.17543
$139$	−3.32684	−	5.76226i	−0.282179	−	0.488748i	0.689742	−	0.724055i	$-0.257724\pi$
$139$	−3.32684	−	5.76226i	−0.282179	−	0.488748i	−0.971921	+	0.235307i	$0.924391\pi$
$140$	−0.979150	+	1.01559i	−0.0827532	+	0.0858331i
$141$	15.6741	+	9.04945i	1.32000	+	0.762101i
$142$		−	22.2895i		−	1.87049i
$143$		0			0
$144$	32.4413			2.70344
$145$	−7.95836	+	8.25455i	−0.660906	+	0.685503i
$146$	1.50113	−	2.60004i	0.124235	−	0.215181i
$147$	−11.1967	+	6.46441i	−0.923486	+	0.533175i
$148$	2.23287			0.183540
$149$	7.86211	−	4.53919i	0.644089	−	0.371865i	−0.142099	−	0.989852i	$-0.545385\pi$
$149$	7.86211	−	4.53919i	0.644089	−	0.371865i	0.786188	+	0.617988i	$0.212052\pi$
$150$	24.3805	−	0.891099i	1.99066	−	0.0727579i
$151$		−	3.27739i		−	0.266711i	−0.991068	−	0.133355i	$-0.957425\pi$
$151$		−	3.27739i		−	0.266711i	0.991068	−	0.133355i	$-0.0425751\pi$
$152$	−1.17217	+	0.676752i	−0.0950754	+	0.0548918i
$153$	5.62651	+	3.24846i	0.454876	+	0.262623i
$154$	−5.78535	−	3.34017i	−0.466197	−	0.269159i
$155$	−0.474142	+	1.90829i	−0.0380840	+	0.153278i
$156$		0			0
$157$		−	12.8371i		−	1.02451i	−0.858833	−	0.512256i	$-0.828810\pi$
$157$		−	12.8371i		−	1.02451i	0.858833	−	0.512256i	$-0.171190\pi$
$158$	0.382433	−	0.662394i	0.0304248	−	0.0526972i
$159$	13.4680	−	23.3273i	1.06808	−	1.84997i
$160$	1.27499	+	4.43280i	0.100797	+	0.350443i
$161$		−	4.83710i		−	0.381217i
$162$	−15.0428	−	26.0549i	−1.18187	−	2.04706i
$163$	−6.02472	−	10.4351i	−0.471893	−	0.817342i	0.527590	−	0.849499i	$-0.323096\pi$
$163$	−6.02472	−	10.4351i	−0.471893	−	0.817342i	−0.999483	+	0.0321568i	$0.989762\pi$
$164$			0.465732i			0.0363675i
$165$	4.97530	+	17.2978i	0.387327	+	1.34663i
$166$	6.64229	−	11.5048i	0.515542	−	0.892945i
$167$	4.36490	−	7.56022i	0.337766	−	0.585028i	−0.646246	−	0.763129i	$-0.723662\pi$
$167$	4.36490	−	7.56022i	0.337766	−	0.585028i	0.984012	+	0.178101i	$0.0569955\pi$
$168$		−	13.6020i		−	1.04941i
$169$		0			0
$170$	−0.764867	+	3.07838i	−0.0586626	+	0.236101i
$171$	3.29175	+	1.90049i	0.251726	+	0.145334i
$172$	2.05596	+	1.18701i	0.156766	+	0.0905088i
$173$	−0.748041	+	0.431882i	−0.0568725	+	0.0328354i	−0.528167	−	0.849141i	$-0.677120\pi$
$173$	−0.748041	+	0.431882i	−0.0568725	+	0.0328354i	0.471294	+	0.881976i	$0.343787\pi$
$174$			25.0205i			1.89680i
$175$	−0.312158	−	8.54067i	−0.0235970	−	0.645614i
$176$	−10.1197	+	5.84263i	−0.762804	+	0.440405i
$177$	14.9711			1.12529
$178$	17.1116	−	9.87936i	1.28257	−	0.740489i
$179$	−9.95774	+	17.2473i	−0.744276	+	1.28912i	0.206256	+	0.978498i	$0.433872\pi$
$179$	−9.95774	+	17.2473i	−0.744276	+	1.28912i	−0.950532	+	0.310626i	$0.899461\pi$
$180$	4.03824	−	4.18853i	0.300993	−	0.312195i
$181$	−14.3896			−1.06957			−0.534786	−	0.844987i	$-0.679608\pi$
$181$	−14.3896			−1.06957			−0.534786	+	0.844987i	$0.679608\pi$
$182$		0			0
$183$			25.5174i			1.88630i
$184$	−6.15209	−	3.55191i	−0.453538	−	0.261850i
$185$	−9.38871	+	9.73813i	−0.690272	+	0.715962i
$186$	2.14536	+	3.71588i	0.157306	+	0.272461i
$187$	−2.34017			−0.171130
$188$	1.05365	+	1.82498i	0.0768456	+	0.133100i
$189$	−19.0025	+	10.9711i	−1.38222	+	0.798028i
$190$	−0.447480	+	1.80098i	−0.0324636	+	0.130657i
$191$	−0.738205	−	1.27861i	−0.0534146	−	0.0925168i	0.838082	−	0.545545i	$-0.183677\pi$
$191$	−0.738205	−	1.27861i	−0.0534146	−	0.0925168i	−0.891496	+	0.453028i	$0.850344\pi$
$192$	−16.5517	−	9.55611i	−1.19451	−	0.689653i
$193$	8.86603	−	15.3564i	0.638191	−	1.10538i	−0.347639	−	0.937629i	$-0.613016\pi$
$193$	8.86603	−	15.3564i	0.638191	−	1.10538i	0.985829	−	0.167750i	$-0.0536503\pi$
$194$	9.10504			0.653704
$195$		0			0
$196$	−1.50534			−0.107524
$197$	−1.00000	+	1.73205i	−0.0712470	+	0.123404i	−0.899448	−	0.437028i	$-0.856031\pi$
$197$	−1.00000	+	1.73205i	−0.0712470	+	0.123404i	0.828201	+	0.560431i	$0.189365\pi$
$198$	23.8601	+	13.7756i	1.69567	+	0.978993i
$199$	2.69594	+	4.66951i	0.191110	+	0.331013i	0.945619	−	0.325278i	$-0.105458\pi$
$199$	2.69594	+	4.66951i	0.191110	+	0.331013i	−0.754508	+	0.656291i	$0.772124\pi$
$200$	−11.0917	−	5.87444i	−0.784302	−	0.415386i
$201$	21.5952	−	12.4680i	1.52321	−	0.879425i
$202$	−12.6514	−	21.9129i	−0.890151	−	1.54179i
$203$	8.76487			0.615173
$204$	0.539189	+	0.933903i	0.0377508	+	0.0653863i
$205$	−2.03118	−	1.95830i	−0.141864	−	0.136774i
$206$	−13.5838	−	7.84263i	−0.946431	−	0.546422i
$207$			19.9493i			1.38657i
$208$		0			0
$209$	−1.36910			−0.0947028
$210$	−13.4256	−	12.9439i	−0.926457	−	0.893214i
$211$	11.3763	−	19.7043i	0.783176	−	1.35650i	−0.146906	−	0.989150i	$-0.546932\pi$
$211$	11.3763	−	19.7043i	0.783176	−	1.35650i	0.930083	−	0.367350i	$-0.119735\pi$
$212$	2.71606	−	1.56812i	0.186540	−	0.107699i
$213$	45.9071			3.14550
$214$	−12.9986	+	7.50473i	−0.888564	+	0.513013i
$215$	−13.8218	+	3.97549i	−0.942636	+	0.271126i
$216$			32.2245i			2.19260i
$217$	1.30170	−	0.751536i	0.0883650	−	0.0510176i
$218$	−22.4790	−	12.9783i	−1.52247	−	0.878999i
$219$	5.35500	+	3.09171i	0.361857	+	0.208918i
$220$	−0.505339	+	2.03385i	−0.0340699	+	0.137122i
$221$		0			0
$222$			29.5174i			1.98108i
$223$	4.38050	−	7.58724i	0.293340	−	0.508079i	−0.681258	−	0.732044i	$-0.738567\pi$
$223$	4.38050	−	7.58724i	0.293340	−	0.508079i	0.974597	+	0.223965i	$0.0719000\pi$
$224$	1.76293	−	3.05348i	0.117791	−	0.204019i
$225$	1.28741	+	35.2237i	0.0858276	+	2.34825i
$226$		−	18.0989i		−	1.20392i
$227$	8.61336	+	14.9188i	0.571689	+	0.990194i	0.996393	+	0.0848618i	$0.0270449\pi$
$227$	8.61336	+	14.9188i	0.571689	+	0.990194i	−0.424704	+	0.905332i	$0.639622\pi$
$228$	0.315449	+	0.546373i	0.0208911	+	0.0361845i
$229$			3.07838i			0.203425i	0.994814	+	0.101712i	$0.0324322\pi$
$229$			3.07838i			0.203425i	−0.994814	+	0.101712i	$0.967568\pi$
$230$	−9.36031	+	2.69227i	−0.617201	+	0.177523i
$231$	6.87936	−	11.9154i	0.452629	−	0.783976i
$232$	6.43609	−	11.1476i	0.422550	−	0.731878i
$233$		−	18.9360i		−	1.24054i	−0.784389	−	0.620269i	$-0.787023\pi$
$233$		−	18.9360i		−	1.24054i	0.784389	−	0.620269i	$-0.212977\pi$
$234$		0			0
$235$	−12.3896	−	3.07838i	−0.808210	−	0.200811i
$236$	1.50959	+	0.871563i	0.0982660	+	0.0567339i
$237$	1.36426	+	0.787653i	0.0886179	+	0.0511636i
$238$	2.09985	−	1.21235i	0.136113	−	0.0785848i
$239$		−	6.63809i		−	0.429382i	−0.976682	−	0.214691i	$-0.931126\pi$
$239$		−	6.63809i		−	0.429382i	0.976682	−	0.214691i	$-0.0688745\pi$
$240$	−31.3502	+	9.01712i	−2.02364	+	0.582053i
$241$	8.20681	−	4.73820i	0.528647	−	0.305215i	−0.211818	−	0.977309i	$-0.567938\pi$
$241$	8.20681	−	4.73820i	0.528647	−	0.305215i	0.740465	+	0.672094i	$0.234605\pi$
$242$	7.00719			0.450439
$243$	20.3104	−	11.7262i	1.30291	−	0.752236i
$244$	−1.48554	+	2.57302i	−0.0951017	+	0.164721i
$245$	6.32962	−	6.56519i	0.404385	−	0.419435i
$246$	−6.15676			−0.392540
$247$		0			0
$248$		−	2.20743i		−	0.140172i
$249$	23.6951	+	13.6803i	1.50161	+	0.866957i
$250$	−16.3534	+	5.35769i	−1.03428	+	0.338850i
$251$	14.7298	+	25.5128i	0.929736	+	1.61035i	0.783761	+	0.621062i	$0.213299\pi$
$251$	14.7298	+	25.5128i	0.929736	+	1.61035i	0.145975	+	0.989288i	$0.453368\pi$
$252$	−4.44748			−0.280165
$253$	−3.59284	−	6.22299i	−0.225880	−	0.391236i
$254$	−24.0032	+	13.8582i	−1.50609	+	0.869543i
$255$	−6.34017	−	1.57531i	−0.397037	−	0.0986495i
$256$	−4.28765	−	7.42643i	−0.267978	−	0.464152i
$257$	17.7238	+	10.2329i	1.10558	+	0.638309i	0.937682	−	0.347495i	$-0.112968\pi$
$257$	17.7238	+	10.2329i	1.10558	+	0.638309i	0.167901	+	0.985804i	$0.446301\pi$
$258$	−15.6917	+	27.1789i	−0.976925	+	1.69208i
$259$	10.3402			0.642507
$260$		0			0
$261$	−36.1483			−2.23753
$262$	−10.9711	+	19.0025i	−0.677795	+	1.17398i
$263$	−7.91844	−	4.57171i	−0.488272	−	0.281904i	0.235585	−	0.971854i	$-0.424299\pi$
$263$	−7.91844	−	4.57171i	−0.488272	−	0.281904i	−0.723857	+	0.689950i	$0.757633\pi$
$264$	−10.1031	−	17.4991i	−0.621803	−	1.07699i
$265$	−4.58145	+	18.4391i	−0.281436	+	1.13270i
$266$	1.22850	−	0.709275i	0.0753242	−	0.0434885i
$267$	20.3474	+	35.2427i	1.24524	+	2.15682i
$268$	2.90337			0.177352
$269$	5.69594	+	9.86567i	0.347288	+	0.601520i	0.985767	−	0.168119i	$-0.0537693\pi$
$269$	5.69594	+	9.86567i	0.347288	+	0.601520i	−0.638479	+	0.769639i	$0.720436\pi$
$270$	31.8067	+	30.6654i	1.93570	+	1.86624i
$271$	−18.3035	−	10.5675i	−1.11186	−	0.641930i	−0.172546	−	0.985001i	$-0.555200\pi$
$271$	−18.3035	−	10.5675i	−1.11186	−	0.641930i	−0.939309	+	0.343071i	$0.888533\pi$
$272$		−	4.24128i		−	0.257165i
$273$		0			0
$274$	−21.2183			−1.28185
$275$	−6.74533	−	10.7558i	−0.406759	−	0.648600i
$276$	−1.65562	+	2.86762i	−0.0996567	+	0.172611i
$277$	−11.3262	+	6.53919i	−0.680526	+	0.392902i	−0.800053	−	0.599929i	$-0.795195\pi$
$277$	−11.3262	+	6.53919i	−0.680526	+	0.392902i	0.119527	+	0.992831i	$0.461862\pi$
$278$	10.2413			0.614231
$279$	−5.36851	+	3.09951i	−0.321404	+	0.185563i
$280$	2.65206	+	9.22053i	0.158491	+	0.551032i
$281$			0.680346i			0.0405860i	0.999794	+	0.0202930i	$0.00645991\pi$
$281$			0.680346i			0.0405860i	−0.999794	+	0.0202930i	$0.993540\pi$
$282$	−24.1254	+	13.9288i	−1.43665	+	0.829449i
$283$	−16.7105	−	9.64782i	−0.993337	−	0.573504i	−0.0870671	−	0.996202i	$-0.527749\pi$
$283$	−16.7105	−	9.64782i	−0.993337	−	0.573504i	−0.906270	+	0.422699i	$0.861083\pi$
$284$	4.62899	+	2.67255i	0.274680	+	0.158586i
$285$	−3.70928	−	0.921622i	−0.219719	−	0.0545922i
$286$		0			0
$287$			2.15676i			0.127309i
$288$	−7.27073	+	12.5933i	−0.428432	+	0.742066i
$289$	−8.07531	+	13.9868i	−0.475018	+	0.822755i
$290$	−4.87841	−	16.9610i	−0.286470	−	0.995982i
$291$			18.7526i			1.09930i
$292$	0.359977	+	0.623498i	0.0210660	+	0.0364875i
$293$	4.73400	+	8.19953i	0.276563	+	0.479022i	0.970528	−	0.240987i	$-0.0774712\pi$
$293$	4.73400	+	8.19953i	0.276563	+	0.479022i	−0.693965	+	0.720009i	$0.744138\pi$
$294$		−	19.8999i		−	1.16058i
$295$	−10.1486	+	2.91901i	−0.590875	+	0.169951i
$296$	7.59284	−	13.1512i	0.441325	−	0.764397i
$297$	−16.2979	+	28.2288i	−0.945701	+	1.63800i
$298$			13.9733i			0.809454i
$299$		0			0
$300$	−2.73820	+	5.17009i	−0.158090	+	0.298495i
$301$	9.52096	+	5.49693i	0.548779	+	0.316838i
$302$	4.36869	+	2.52226i	0.251390	+	0.145140i
$303$	45.1314	−	26.0566i	2.59273	−	1.49691i
$304$		−	2.48133i		−	0.142314i
$305$	−4.97530	−	17.2978i	−0.284885	−	0.990470i
$306$	−8.66025	+	5.00000i	−0.495074	+	0.285831i
$307$	0.264063			0.0150709			0.00753543	−	0.999972i	$-0.497601\pi$
$307$	0.264063			0.0150709			0.00753543	+	0.999972i	$0.497601\pi$
$308$	1.38735	−	0.800984i	0.0790513	−	0.0456403i
$309$	16.1526	−	27.9770i	0.918886	−	1.59156i
$310$	−2.17881	−	2.10063i	−0.123748	−	0.119308i
$311$	−13.0472			−0.739838			−0.369919	−	0.929064i	$-0.620615\pi$
$311$	−13.0472			−0.739838			−0.369919	+	0.929064i	$0.620615\pi$
$312$		0			0
$313$		−	33.7009i		−	1.90489i	−0.304718	−	0.952443i	$-0.598562\pi$
$313$		−	33.7009i		−	1.90489i	0.304718	−	0.952443i	$-0.401438\pi$
$314$	17.1116	+	9.87936i	0.965661	+	0.557525i
$315$	18.7007	−	19.3967i	1.05366	−	1.09288i
$316$	0.0917087	+	0.158844i	0.00515902	+	0.00893568i
$317$	−13.9506			−0.783541			−0.391771	−	0.920063i	$-0.628137\pi$
$317$	−13.9506			−0.783541			−0.391771	+	0.920063i	$0.628137\pi$
$318$	20.7298	+	35.9051i	1.16247	+	2.01346i
$319$	11.2761	−	6.51026i	0.631340	−	0.364505i
$320$	13.0833	+	3.25073i	0.731379	+	0.181721i
$321$	−15.4566	−	26.7716i	−0.862704	−	1.49425i
$322$	6.44774	+	3.72261i	0.359319	+	0.207453i
$323$	0.248464	−	0.430353i	0.0138249	−	0.0239455i
$324$	7.21461			0.400812
$325$		0			0
$326$	18.5464			1.02719
$327$	26.7298	−	46.2974i	1.47816	−	2.56025i
$328$	2.74308	+	1.58372i	0.151461	+	0.0874461i
$329$	4.87936	+	8.45130i	0.269008	+	0.465935i
$330$	−26.8865	−	6.68035i	−1.48006	−	0.367741i
$331$	−15.9822	+	9.22733i	−0.878462	+	0.507180i	−0.870151	−	0.492785i	$-0.835979\pi$
$331$	−15.9822	+	9.22733i	−0.878462	+	0.507180i	−0.00831086	+	0.999965i	$0.502645\pi$
$332$	1.59284	+	2.75888i	0.0874186	+	0.151413i
$333$	−42.6453			−2.33695
$334$	6.71840	+	11.6366i	0.367615	+	0.636727i
$335$	−12.2080	+	12.6624i	−0.666996	+	0.691820i
$336$	21.5952	+	12.4680i	1.17812	+	0.680185i
$337$		−	15.8576i		−	0.863820i	−0.901917	−	0.431910i	$-0.857840\pi$
$337$		−	15.8576i		−	0.863820i	0.901917	−	0.431910i	$-0.142160\pi$
$338$		0			0
$339$	37.2762			2.02456
$340$	−0.547595	−	0.527947i	−0.0296975	−	0.0286319i
$341$	1.11643	−	1.93372i	0.0604582	−	0.104717i
$342$	−5.06662	+	2.92522i	−0.273972	+	0.158178i
$343$	−18.9360			−1.02245
$344$	13.9826	−	8.07285i	0.753890	−	0.435259i
$345$	−5.54495	−	19.2783i	−0.298530	−	1.03791i
$346$		−	1.32950i		−	0.0714741i
$347$	−8.42199	+	4.86244i	−0.452116	+	0.261029i	−0.708723	−	0.705486i	$-0.750729\pi$
$347$	−8.42199	+	4.86244i	−0.452116	+	0.261029i	0.256607	+	0.966516i	$0.417395\pi$
$348$	−5.19615	−	3.00000i	−0.278543	−	0.160817i
$349$	26.7683	+	15.4547i	1.43287	+	0.827269i	0.997339	−	0.0729030i	$-0.0232264\pi$
$349$	26.7683	+	15.4547i	1.43287	+	0.827269i	0.435534	+	0.900172i	$0.356560\pi$
$350$	11.6248	+	6.15676i	0.621369	+	0.329092i
$351$		0			0
$352$		−	5.23779i		−	0.279175i
$353$	2.97528	−	5.15333i	0.158358	−	0.274284i	−0.775919	−	0.630833i	$-0.782713\pi$
$353$	2.97528	−	5.15333i	0.158358	−	0.274284i	0.934277	+	0.356549i	$0.116047\pi$
$354$	−11.5217	+	19.9561i	−0.612369	+	1.06065i
$355$	−31.1196	+	8.95079i	−1.65166	+	0.475059i
$356$			4.73820i			0.251124i
$357$	2.49693	+	4.32481i	0.132151	+	0.228893i
$358$	−15.3268	−	26.5469i	−0.810049	−	1.40305i
$359$			10.9783i			0.579410i	0.957116	+	0.289705i	$0.0935573\pi$
$359$			10.9783i			0.579410i	−0.957116	+	0.289705i	$0.906443\pi$
$360$	−10.9377	−	38.0276i	−0.576469	−	2.00423i
$361$	−9.35464	+	16.2027i	−0.492349	+	0.852774i
$362$	11.0742	−	19.1810i	0.582046	−	1.00813i
$363$			14.4319i			0.757477i
$364$		0			0
$365$	−4.23287	−	1.05172i	−0.221558	−	0.0550493i
$366$	−34.0142	−	19.6381i	−1.77795	−	1.02650i
$367$	8.98417	+	5.18701i	0.468970	+	0.270760i	0.715808	−	0.698297i	$-0.246058\pi$
$367$	8.98417	+	5.18701i	0.468970	+	0.270760i	−0.246839	+	0.969057i	$0.579392\pi$
$368$	11.2784	−	6.51159i	0.587927	−	0.339440i
$369$		−	8.89496i		−	0.463053i
$370$	−5.75520	−	20.0093i	−0.299199	−	1.04024i
$371$	12.5778	−	7.26180i	0.653007	−	0.377014i
$372$	−1.02893			−0.0533475
$373$	20.7740	−	11.9939i	1.07564	−	0.621018i	0.145920	−	0.989296i	$-0.453386\pi$
$373$	20.7740	−	11.9939i	1.07564	−	0.621018i	0.929716	+	0.368278i	$0.120053\pi$
$374$	1.80098	−	3.11940i	0.0931267	−	0.161300i
$375$	−11.0346	−	33.6811i	−0.569824	−	1.73929i
$376$	14.3318			0.739104
$377$		0			0
$378$		−	33.7731i		−	1.73710i
$379$	25.7708	+	14.8788i	1.32375	+	0.764270i	0.984325	−	0.176362i	$-0.0564328\pi$
$379$	25.7708	+	14.8788i	1.32375	+	0.764270i	0.339429	+	0.940632i	$0.389766\pi$
$380$	−0.320367	−	0.308872i	−0.0164345	−	0.0158448i
$381$	−28.5422	−	49.4365i	−1.46226	−	2.53271i
$382$	2.27247			0.116270
$383$	6.20814	+	10.7528i	0.317221	+	0.549443i	0.979907	−	0.199454i	$-0.0639169\pi$
$383$	6.20814	+	10.7528i	0.317221	+	0.549443i	−0.662686	+	0.748897i	$0.730584\pi$
$384$	36.8024	−	21.2479i	1.87806	−	1.08430i
$385$	−2.34017	+	9.41855i	−0.119266	+	0.480014i
$386$	13.6465	+	23.6364i	0.694588	+	1.20306i
$387$	−39.2666	−	22.6706i	−1.99604	−	1.15241i
$388$	−1.09171	+	1.89090i	−0.0554231	+	0.0959956i
$389$	−16.8371			−0.853675			−0.426837	−	0.904328i	$-0.640372\pi$
$389$	−16.8371			−0.853675			−0.426837	+	0.904328i	$0.640372\pi$
$390$		0			0
$391$	2.60811			0.131898
$392$	−5.11889	+	8.86618i	−0.258543	+	0.447810i
$393$	−39.1371	−	22.5958i	−1.97421	−	1.13981i
$394$	−1.53919	−	2.66595i	−0.0775432	−	0.134309i
$395$	−1.07838	−	0.267938i	−0.0542591	−	0.0134814i
$396$	−5.72173	+	3.30344i	−0.287528	+	0.166004i
$397$	−1.94635	−	3.37117i	−0.0976843	−	0.169194i	0.813041	−	0.582206i	$-0.197810\pi$
$397$	−1.94635	−	3.37117i	−0.0976843	−	0.169194i	−0.910726	+	0.413012i	$0.864477\pi$
$398$	−8.29914			−0.415998
$399$	1.46081	+	2.53020i	0.0731320	+	0.126668i
$400$	19.4936	−	12.2251i	0.974680	−	0.611254i
$401$	−7.88520	−	4.55252i	−0.393768	−	0.227342i	0.290024	−	0.957020i	$-0.406337\pi$
$401$	−7.88520	−	4.55252i	−0.393768	−	0.227342i	−0.683791	+	0.729678i	$0.739670\pi$
$402$			38.3812i			1.91428i
$403$		0			0
$404$	6.06770			0.301879
$405$	−30.3359	+	31.4649i	−1.50740	+	1.56350i
$406$	−6.74539	+	11.6834i	−0.334768	+	0.579836i
$407$	13.3027	−	7.68035i	0.659393	−	0.380701i
$408$	7.33403			0.363089
$409$	16.8170	−	9.70928i	0.831545	−	0.480093i	−0.0228363	−	0.999739i	$-0.507270\pi$
$409$	16.8170	−	9.70928i	0.831545	−	0.480093i	0.854381	+	0.519646i	$0.173936\pi$
$410$	4.17355	−	1.20042i	0.206117	−	0.0592846i
$411$		−	43.7009i		−	2.15560i
$412$	3.25745	−	1.88069i	0.160483	−	0.0926549i
$413$	6.99076	+	4.03612i	0.343993	+	0.198604i
$414$	−26.5920	−	15.3529i	−1.30693	−	0.754554i
$415$	−18.7298	−	4.65368i	−0.919409	−	0.228440i
$416$		0			0
$417$			21.0928i			1.03292i
$418$	1.05365	−	1.82498i	0.0515359	−	0.0892628i
$419$	−8.38962	+	14.5313i	−0.409860	+	0.709898i	−0.994874	−	0.101125i	$-0.967756\pi$
$419$	−8.38962	+	14.5313i	−0.409860	+	0.709898i	0.585014	+	0.811023i	$0.301089\pi$
$420$	4.29789	−	1.23618i	0.209716	−	0.0603196i
$421$		−	19.0205i		−	0.927003i	−0.886096	−	0.463502i	$-0.846593\pi$
$421$		−	19.0205i		−	0.927003i	0.886096	−	0.463502i	$-0.153407\pi$
$422$	17.5103	+	30.3287i	0.852386	+	1.47638i
$423$	−20.1236	−	34.8551i	−0.978444	−	1.69471i
$424$		−	21.3295i		−	1.03585i
$425$	4.60504	−	0.168312i	0.223377	−	0.00816435i
$426$	−35.3298	+	61.1931i	−1.71174	+	2.96481i
$427$	−6.87936	+	11.9154i	−0.332916	+	0.576627i
$428$		−	3.59932i		−	0.173979i
$429$		0			0
$430$	5.33791	−	21.4836i	0.257417	−	1.03603i
$431$	−6.95416	−	4.01499i	−0.334970	−	0.193395i	0.323075	−	0.946373i	$-0.395283\pi$
$431$	−6.95416	−	4.01499i	−0.334970	−	0.193395i	−0.658046	+	0.752978i	$0.728617\pi$
$432$	−51.1613	−	29.5380i	−2.46150	−	1.42115i
$433$	−11.2992	+	6.52359i	−0.543004	+	0.313504i	−0.746296	−	0.665615i	$-0.768170\pi$
$433$	−11.2992	+	6.52359i	−0.543004	+	0.313504i	0.203291	+	0.979118i	$0.434836\pi$
$434$			2.31351i			0.111052i
$435$	34.9325	−	10.0475i	1.67488	−	0.481740i
$436$	5.39054	−	3.11223i	0.258160	−	0.149049i
$437$	1.52586			0.0729917
$438$	−8.24235	+	4.75872i	−0.393835	+	0.227381i
$439$	3.85043	−	6.66914i	0.183771	−	0.318301i	−0.759391	−	0.650635i	$-0.774503\pi$
$439$	3.85043	−	6.66914i	0.183771	−	0.318301i	0.943162	+	0.332334i	$0.107836\pi$
$440$	10.2606	+	9.89245i	0.489156	+	0.471604i
$441$	28.7503			1.36906
$442$		0			0
$443$			6.39084i			0.303638i	0.988408	+	0.151819i	$0.0485131\pi$
$443$			6.39084i			0.303638i	−0.988408	+	0.151819i	$0.951487\pi$
$444$	−6.13005	−	3.53919i	−0.290920	−	0.167962i
$445$	−20.6646	−	19.9231i	−0.979596	−	0.944446i
$446$	6.74241	+	11.6782i	0.319262	+	0.552979i
$447$	−28.7792			−1.36121
$448$	−5.15255	−	8.92448i	−0.243435	−	0.421642i
$449$	27.3806	−	15.8082i	1.29217	−	0.746034i	0.313130	−	0.949710i	$-0.398622\pi$
$449$	27.3806	−	15.8082i	1.29217	−	0.746034i	0.979038	+	0.203676i	$0.0652891\pi$
$450$	−47.9432	−	25.3919i	−2.26006	−	1.19699i
$451$	1.60197	+	2.77469i	0.0754337	+	0.130655i
$452$	3.75870	+	2.17009i	0.176794	+	0.102072i
$453$	−5.19481	+	8.99768i	−0.244073	+	0.422748i
$454$	−26.5152			−1.24442
$455$		0			0
$456$	4.29072			0.200932
$457$	−17.8215	+	30.8677i	−0.833655	+	1.44393i	0.0614663	+	0.998109i	$0.480422\pi$
$457$	−17.8215	+	30.8677i	−0.833655	+	1.44393i	−0.895121	+	0.445823i	$0.852911\pi$
$458$	−4.10341	−	2.36910i	−0.191740	−	0.110701i
$459$	−5.91548	−	10.2459i	−0.276111	−	0.478238i
$460$	0.563198	−	2.26672i	0.0262592	−	0.105686i
$461$	−12.9726	+	7.48974i	−0.604195	+	0.348832i	−0.770690	−	0.637210i	$-0.780088\pi$
$461$	−12.9726	+	7.48974i	−0.604195	+	0.348832i	0.166495	+	0.986042i	$0.446755\pi$
$462$	10.5886	+	18.3401i	0.492628	+	0.853257i
$463$	9.09663			0.422756			0.211378	−	0.977404i	$-0.432205\pi$
$463$	9.09663			0.422756			0.211378	+	0.977404i	$0.432205\pi$
$464$	11.7990	+	20.4365i	0.547757	+	0.948743i
$465$	4.32642	−	4.48744i	0.200633	−	0.208100i
$466$	25.2412	+	14.5730i	1.16928	+	0.675083i
$467$		−	1.87709i		−	0.0868616i	−0.999056	−	0.0434308i	$-0.986171\pi$
$467$		−	1.87709i		−	0.0868616i	0.999056	−	0.0434308i	$-0.0138288\pi$
$468$		0			0
$469$	13.4452			0.620842
$470$	13.6384	−	14.1460i	0.629092	−	0.652505i
$471$	−20.3474	+	35.2427i	−0.937557	+	1.62390i
$472$	10.2667	−	5.92748i	0.472563	−	0.272835i
$473$	16.3318			0.750935
$474$	−2.09985	+	1.21235i	−0.0964491	+	0.0556849i
$475$	2.69415	−	0.0984700i	0.123616	−	0.00451811i
$476$			0.581449i			0.0266507i
$477$	−51.8738	+	29.9493i	−2.37514	+	1.37129i
$478$	8.84841	+	5.10863i	0.404717	+	0.233663i
$479$	13.6339	+	7.87156i	0.622951	+	0.359661i	0.778017	−	0.628243i	$-0.216226\pi$
$479$	13.6339	+	7.87156i	0.622951	+	0.359661i	−0.155066	+	0.987904i	$0.549559\pi$
$480$	3.52586	−	14.1906i	0.160933	−	0.647710i
$481$		0			0
$482$			14.5860i			0.664373i
$483$	−7.66701	+	13.2797i	−0.348861	+	0.604245i
$484$	−0.840173	+	1.45522i	−0.0381897	+	0.0661465i
$485$	−3.65631	−	12.7120i	−0.166024	−	0.577224i
$486$			36.0977i			1.63742i
$487$	2.47220	+	4.28198i	0.112026	+	0.194035i	0.916587	−	0.399835i	$-0.130933\pi$
$487$	2.47220	+	4.28198i	0.112026	+	0.194035i	−0.804561	+	0.593870i	$0.797599\pi$
$488$	10.1031	+	17.4991i	0.457346	+	0.792146i
$489$			38.1978i			1.72736i
$490$	3.88001	+	13.4898i	0.175281	+	0.609406i
$491$	19.7431	−	34.1961i	0.890995	−	1.54325i	0.0523101	−	0.998631i	$-0.483342\pi$
$491$	19.7431	−	34.1961i	0.890995	−	1.54325i	0.838685	−	0.544617i	$-0.183325\pi$
$492$	0.738205	−	1.27861i	0.0332808	−	0.0576441i
$493$			4.72592i			0.212845i
$494$		0			0
$495$	9.65142	−	38.8443i	0.433799	−	1.74592i
$496$	3.50463	+	2.02340i	0.157362	+	0.0908532i
$497$	21.4364	+	12.3763i	0.961552	+	0.555152i
$498$	−36.4712	+	21.0566i	−1.63431	+	0.943570i
$499$		−	1.67089i		−	0.0747993i	−0.999300	−	0.0373997i	$-0.988093\pi$
$499$		−	1.67089i		−	0.0747993i	0.999300	−	0.0373997i	$-0.0119075\pi$
$500$	0.848135	−	4.03859i	0.0379297	−	0.180611i
$501$	−23.9666	+	13.8371i	−1.07075	+	0.618196i
$502$	−45.3439			−2.02380
$503$	−7.86833	+	4.54278i	−0.350832	+	0.202553i	−0.665051	−	0.746798i	$-0.731590\pi$
$503$	−7.86833	+	4.54278i	−0.350832	+	0.202553i	0.314220	+	0.949350i	$0.398257\pi$
$504$	−15.1236	+	26.1949i	−0.673660	+	1.16681i
$505$	−25.5133	+	26.4629i	−1.13533	+	1.17758i
$506$	11.0601			0.491683
$507$		0			0
$508$		−	6.64650i		−	0.294891i
$509$	−16.9257	−	9.77205i	−0.750218	−	0.433139i	0.0755545	−	0.997142i	$-0.475927\pi$
$509$	−16.9257	−	9.77205i	−0.750218	−	0.433139i	−0.825773	+	0.564003i	$0.809261\pi$
$510$	6.97921	−	7.23896i	0.309045	−	0.320546i
$511$	1.66701	+	2.88735i	0.0737444	+	0.127729i
$512$	−13.6114			−0.601546
$513$	−3.46081	−	5.99430i	−0.152799	−	0.264655i
$514$	−27.2803	+	15.7503i	−1.20328	+	0.694717i
$515$	−5.49466	+	22.1145i	−0.242124	+	0.974481i
$516$	−3.76293	−	6.51758i	−0.165654	−	0.286921i
$517$	12.5547	+	7.24846i	0.552155	+	0.318787i
$518$	−7.95774	+	13.7832i	−0.349643	+	0.605599i
$519$	2.73820			0.120194
$520$		0			0
$521$	6.50534			0.285004			0.142502	−	0.989795i	$-0.454485\pi$
$521$	6.50534			0.285004			0.142502	+	0.989795i	$0.454485\pi$
$522$	27.8196	−	48.1849i	1.21763	−	2.10900i
$523$	31.6490	+	18.2726i	1.38392	+	0.799004i	0.992621	−	0.121261i	$-0.0386939\pi$
$523$	31.6490	+	18.2726i	1.38392	+	0.799004i	0.391295	+	0.920265i	$0.372027\pi$
$524$	−2.63090	−	4.55685i	−0.114931	−	0.199067i
$525$	−12.6803	+	23.9421i	−0.553416	+	1.04492i
$526$	12.1880	−	7.03673i	0.531421	−	0.306816i
$527$	0.405220	+	0.701861i	0.0176516	+	0.0305736i
$528$	37.0433			1.61210
$529$	−7.49579	−	12.9831i	−0.325904	−	0.564482i
$530$	−21.0530	−	20.2976i	−0.914484	−	0.881670i
$531$	−28.8315	−	16.6459i	−1.25118	−	0.722370i
$532$			0.340173i			0.0147484i
$533$		0			0
$534$	−62.6369			−2.71056
$535$	15.6976	+	15.1343i	0.678666	+	0.654314i
$536$	9.87289	−	17.1003i	0.426444	−	0.738622i
$537$	54.6755	−	31.5669i	2.35942	−	1.36221i
$538$	−17.5343			−0.755956
$539$	−8.96836	+	5.17789i	−0.386295	+	0.223027i
$540$	−10.1821	+	2.92865i	−0.438169	+	0.126029i
$541$		−	20.3402i		−	0.874492i	−0.899342	−	0.437246i	$-0.855954\pi$
$541$		−	20.3402i		−	0.874492i	0.899342	−	0.437246i	$-0.144046\pi$
$542$	28.1725	−	16.2654i	1.21011	−	0.698658i
$543$	39.5049	+	22.8082i	1.69532	+	0.978792i
$544$	1.64640	+	0.950552i	0.0705890	+	0.0407546i
$545$	−9.09275	+	36.5958i	−0.389491	+	1.56759i
$546$		0			0
$547$		−	11.5948i		−	0.495757i	−0.968791	−	0.247879i	$-0.920267\pi$
$547$		−	11.5948i		−	0.495757i	0.968791	−	0.247879i	$-0.0797334\pi$
$548$	2.54411	−	4.40653i	0.108679	−	0.188237i
$549$	28.3721	−	49.1419i	1.21089	−	2.09732i
$550$	19.5284	−	0.713756i	0.832694	−	0.0304347i
$551$			2.76487i			0.117787i
$552$	11.2599	+	19.5026i	0.479251	+	0.830088i
$553$	0.424694	+	0.735591i	0.0180598	+	0.0312805i
$554$		−	20.1301i		−	0.855246i
$555$	41.2109	−	11.8533i	1.74931	−	0.503145i
$556$	−1.22795	+	2.12686i	−0.0520765	+	0.0901991i
$557$	−5.36490	+	9.29227i	−0.227318	+	0.393726i	−0.957012	−	0.290047i	$-0.906329\pi$
$557$	−5.36490	+	9.29227i	−0.227318	+	0.393726i	0.729694	+	0.683773i	$0.239662\pi$
$558$		−	9.54146i		−	0.403922i
$559$		0			0
$560$	−17.0700	−	4.24128i	−0.721338	−	0.179227i
$561$	6.42465	+	3.70928i	0.271249	+	0.156606i
$562$	−0.906885	−	0.523590i	−0.0382546	−	0.0220863i
$563$	8.87543	−	5.12423i	0.374055	−	0.215961i	−0.301174	−	0.953569i	$-0.597378\pi$
$563$	8.87543	−	5.12423i	0.374055	−	0.215961i	0.675228	+	0.737609i	$0.264045\pi$
$564$		−	6.68035i		−	0.281293i
$565$	−25.2688	+	7.26797i	−1.06307	+	0.305766i
$566$	25.7206	−	14.8498i	1.08112	−	0.624185i
$567$	33.4101			1.40309
$568$	31.4817	−	18.1759i	1.32094	−	0.762646i
$569$	4.42276	−	7.66044i	0.185412	−	0.321142i	−0.758304	−	0.651902i	$-0.773972\pi$
$569$	4.42276	−	7.66044i	0.185412	−	0.321142i	0.943715	+	0.330759i	$0.107305\pi$
$570$	4.08314	−	4.23510i	0.171024	−	0.177389i
$571$	−9.29299			−0.388900			−0.194450	−	0.980912i	$-0.562292\pi$
$571$	−9.29299			−0.388900			−0.194450	+	0.980912i	$0.562292\pi$
$572$		0			0
$573$			4.68035i			0.195524i
$574$	−2.87490	−	1.65983i	−0.119996	−	0.0692798i
$575$	7.51764	+	11.9873i	0.313507	+	0.499905i
$576$	21.2503	+	36.8066i	0.885430	+	1.53361i
$577$	19.5259			0.812872			0.406436	−	0.913679i	$-0.366771\pi$
$577$	19.5259			0.812872			0.406436	+	0.913679i	$0.366771\pi$
$578$	−12.4294	−	21.5284i	−0.516996	−	0.895463i
$579$	−48.6812	+	28.1061i	−2.02312	+	1.16805i
$580$	4.10731	+	1.02052i	0.170547	+	0.0423747i
$581$	7.37629	+	12.7761i	0.306020	+	0.530042i
$582$	−24.9968	−	14.4319i	−1.03615	−	0.598221i
$583$	10.7877	−	18.6848i	0.446779	−	0.773844i
$584$	4.89639			0.202614
$585$		0			0
$586$	−14.5730			−0.602007
$587$	11.2514	−	19.4881i	0.464397	−	0.804359i	−0.534777	−	0.844993i	$-0.679604\pi$
$587$	11.2514	−	19.4881i	0.464397	−	0.804359i	0.999174	+	0.0406341i	$0.0129378\pi$
$588$	4.13272	+	2.38603i	0.170431	+	0.0983981i
$589$	0.237071	+	0.410619i	0.00976834	+	0.0169193i
$590$	3.91935	−	15.7743i	0.161357	−	0.649419i
$591$	5.49075	−	3.17009i	0.225859	−	0.130400i
$592$	13.9197	+	24.1096i	0.572096	+	0.990898i
$593$	−4.43907			−0.182291			−0.0911454	−	0.995838i	$-0.529053\pi$
$593$	−4.43907			−0.182291			−0.0911454	+	0.995838i	$0.529053\pi$
$594$	−25.0856	−	43.4495i	−1.02927	−	1.78275i
$595$	−2.53586	−	2.44487i	−0.103960	−	0.100230i
$596$	−2.90192	−	1.67543i	−0.118867	−	0.0686281i
$597$		−	17.0928i		−	0.699560i
$598$		0			0
$599$	−33.3607			−1.36308			−0.681540	−	0.731780i	$-0.738690\pi$
$599$	−33.3607			−1.36308			−0.681540	+	0.731780i	$0.738690\pi$
$600$	21.1397	+	33.7084i	0.863023	+	1.37614i
$601$	−6.65983	+	11.5352i	−0.271660	+	0.470529i	−0.969287	−	0.245932i	$-0.920906\pi$
$601$	−6.65983	+	11.5352i	−0.271660	+	0.470529i	0.697627	+	0.716461i	$0.254239\pi$
$602$	−14.6546	+	8.46081i	−0.597275	+	0.344837i
$603$	−55.4512			−2.25815
$604$	−1.04763	+	0.604847i	−0.0426273	+	0.0246109i
$605$	−2.81388	−	9.78311i	−0.114400	−	0.397740i
$606$			80.2122i			3.25840i
$607$	12.2269	−	7.05919i	0.496273	−	0.286523i	−0.230900	−	0.972977i	$-0.574167\pi$
$607$	12.2269	−	7.05919i	0.496273	−	0.286523i	0.727173	+	0.686454i	$0.240834\pi$
$608$	0.963217	+	0.556114i	0.0390636	+	0.0225534i
$609$	−24.0628	−	13.8927i	−0.975076	−	0.562960i
$610$	26.8865	+	6.68035i	1.08860	+	0.270479i
$611$		0			0
$612$		−	2.39803i		−	0.0969347i
$613$	13.4052	−	23.2185i	0.541432	−	0.937787i	−0.457390	−	0.889266i	$-0.651216\pi$
$613$	13.4052	−	23.2185i	0.541432	−	0.937787i	0.998822	−	0.0485213i	$-0.0154509\pi$
$614$	−0.203221	+	0.351989i	−0.00820134	+	0.0142051i
$615$	2.47237	+	8.59578i	0.0996955	+	0.346615i
$616$		−	10.8950i		−	0.438970i
$617$	7.44748	+	12.8994i	0.299824	+	0.519311i	0.976096	−	0.217342i	$-0.0697386\pi$
$617$	7.44748	+	12.8994i	0.299824	+	0.519311i	−0.676271	+	0.736653i	$0.736405\pi$
$618$	24.8618	+	43.0619i	1.00009	+	1.73221i
$619$			45.3184i			1.82150i	0.412956	+	0.910751i	$0.364496\pi$
$619$			45.3184i			1.82150i	−0.412956	+	0.910751i	$0.635504\pi$
$620$	0.697493	−	0.200617i	0.0280120	−	0.00805697i
$621$	18.1639	−	31.4609i	0.728894	−	1.26248i
$622$	10.0410	−	17.3916i	0.402609	−	0.697339i
$623$			21.9421i			0.879093i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	44.9225	+	25.9360i	1.79546	+	1.03661i
$627$	3.75870	+	2.17009i	0.150108	+	0.0866649i
$628$	−4.10341	+	2.36910i	−0.163744	+	0.0945375i
$629$			5.57531i			0.222302i
$630$	11.4634	+	39.8551i	0.456711	+	1.58787i
$631$	−32.8116	+	18.9438i	−1.30621	+	0.754141i	−0.981461	−	0.191660i	$-0.938613\pi$
$631$	−32.8116	+	18.9438i	−1.30621	+	0.754141i	−0.324749	+	0.945800i	$0.605280\pi$
$632$	1.24742			0.0496197
$633$	−62.4644	+	36.0638i	−2.48274	+	1.43341i
$634$	10.7363	−	18.5958i	0.426392	−	0.738532i
$635$	28.9872	+	27.9471i	1.15032	+	1.10905i
$636$	−9.94214			−0.394232
$637$		0			0
$638$			20.0410i			0.793432i
$639$	−88.4085	−	51.0427i	−3.49739	−	2.01922i
$640$	−20.8048	+	21.5791i	−0.822383	+	0.852990i
$641$	−4.23513	−	7.33547i	−0.167278	−	0.289733i	0.770184	−	0.637822i	$-0.220164\pi$
$641$	−4.23513	−	7.33547i	−0.167278	−	0.289733i	−0.937462	+	0.348088i	$0.886831\pi$
$642$	47.5813			1.87788
$643$	−17.0875	−	29.5964i	−0.673865	−	1.16717i	−0.976799	−	0.214157i	$-0.931299\pi$
$643$	−17.0875	−	29.5964i	−0.673865	−	1.16717i	0.302934	−	0.953012i	$-0.402034\pi$
$644$	−1.54619	+	0.892693i	−0.0609284	+	0.0351770i
$645$	44.2472	+	10.9939i	1.74223	+	0.432883i
$646$	0.382433	+	0.662394i	0.0150466	+	0.0260615i
$647$	−11.9717	−	6.91189i	−0.470658	−	0.271734i	0.245857	−	0.969306i	$-0.420931\pi$
$647$	−11.9717	−	6.91189i	−0.470658	−	0.271734i	−0.716515	+	0.697572i	$0.754264\pi$
$648$	24.5332	−	42.4928i	0.963757	−	1.66928i
$649$	11.9916			0.470711
$650$		0			0
$651$	−4.76487			−0.186750
$652$	−2.22374	+	3.85163i	−0.0870884	+	0.150842i
$653$	−37.1336	−	21.4391i	−1.45315	−	0.838976i	−0.454490	−	0.890752i	$-0.650178\pi$
$653$	−37.1336	−	21.4391i	−1.45315	−	0.838976i	−0.998659	+	0.0517764i	$0.983512\pi$
$654$	41.1422	+	71.2604i	1.60879	+	2.78650i
$655$	30.9360	+	7.68649i	1.20877	+	0.300336i
$656$	−5.02879	+	2.90337i	−0.196341	+	0.113358i
$657$	−6.87516	−	11.9081i	−0.268225	−	0.464580i
$658$	−15.0205			−0.585561
$659$	−11.6248	−	20.1347i	−0.452836	−	0.784335i	0.545725	−	0.837964i	$-0.316254\pi$
$659$	−11.6248	−	20.1347i	−0.452836	−	0.784335i	−0.998561	+	0.0536293i	$0.982921\pi$
$660$	4.61109	−	4.78270i	0.179486	−	0.186166i
$661$	23.4399	+	13.5330i	0.911707	+	0.526374i	0.880980	−	0.473153i	$-0.156884\pi$
$661$	23.4399	+	13.5330i	0.911707	+	0.526374i	0.0307272	+	0.999528i	$0.490218\pi$
$662$		−	28.4052i		−	1.10400i
$663$		0			0
$664$	21.6658			0.840796
$665$	−1.48359	−	1.43035i	−0.0575310	−	0.0554667i
$666$	32.8196	−	56.8452i	1.27173	−	2.20270i
$667$	−12.5672	+	7.25565i	−0.486602	+	0.280940i
$668$	−3.22219			−0.124670
$669$	−24.0522	+	13.8865i	−0.929912	+	0.536885i
$670$	−7.48343	−	26.0179i	−0.289110	−	1.00516i
$671$			20.4391i			0.789042i
$672$	−9.67980	+	5.58864i	−0.373407	+	0.215586i
$673$	−14.0046	−	8.08557i	−0.539838	−	0.311676i	0.205175	−	0.978725i	$-0.434224\pi$
$673$	−14.0046	−	8.08557i	−0.539838	−	0.311676i	−0.745013	+	0.667050i	$0.767557\pi$
$674$	21.1378	+	12.2039i	0.814199	+	0.470078i
$675$	30.0410	−	56.7214i	1.15628	−	2.18321i
$676$		0			0
$677$			43.1194i			1.65721i	0.559831	+	0.828607i	$0.310866\pi$
$677$			43.1194i			1.65721i	−0.559831	+	0.828607i	$0.689134\pi$
$678$	−28.6875	+	49.6883i	−1.10174	+	1.90827i
$679$	−5.05559	+	8.75654i	−0.194016	+	0.336045i
$680$	−4.97161	+	1.42996i	−0.190652	+	0.0548366i
$681$		−	54.6102i		−	2.09267i
$682$	1.71840	+	2.97636i	0.0658010	+	0.113971i
$683$	−8.85464	−	15.3367i	−0.338813	−	0.586842i	0.645396	−	0.763848i	$-0.276692\pi$
$683$	−8.85464	−	15.3367i	−0.338813	−	0.586842i	−0.984210	+	0.177006i	$0.943359\pi$
$684$		−	1.40295i		−	0.0536432i
$685$	8.52064	+	29.6240i	0.325557	+	1.13188i
$686$	14.5730	−	25.2412i	0.556401	−	0.963715i
$687$	4.87936	−	8.45130i	0.186159	−	0.322437i
$688$			29.5993i			1.12846i
$689$		0			0
$690$	29.9649	+	7.44521i	1.14075	+	0.283434i
$691$	21.5462	+	12.4397i	0.819655	+	0.473228i	0.850297	−	0.526303i	$-0.176422\pi$
$691$	21.5462	+	12.4397i	0.819655	+	0.473228i	−0.0306428	+	0.999530i	$0.509755\pi$
$692$	0.276104	+	0.159409i	0.0104959	+	0.00605980i
$693$	−26.4968	+	15.2979i	−1.00653	+	0.581120i
$694$		−	14.9684i		−	0.568193i
$695$	−4.11259	−	14.2984i	−0.155999	−	0.542369i
$696$	−35.3390	+	20.4030i	−1.33952	+	0.773372i
$697$	−1.16290			−0.0440479
$698$	−41.2014	+	23.7877i	−1.55950	+	0.900376i
$699$	−30.0144	+	51.9864i	−1.13525	+	1.96631i
$700$	−2.67243	+	1.67597i	−0.101009	+	0.0633458i
$701$	−33.0661			−1.24889			−0.624445	−	0.781069i	$-0.714675\pi$
$701$	−33.0661			−1.24889			−0.624445	+	0.781069i	$0.714675\pi$
$702$		0			0
$703$			3.26180i			0.123021i
$704$	−13.2576	−	7.65430i	−0.499666	−	0.288482i
$705$	29.1348	+	28.0894i	1.09728	+	1.05791i
$706$	4.57951	+	7.93195i	0.172352	+	0.298523i
$707$	28.0989			1.05677
$708$	−2.76293	−	4.78553i	−0.103837	−	0.179851i
$709$	1.89090	−	1.09171i	0.0710141	−	0.0410000i	−0.464073	−	0.885797i	$-0.653612\pi$
$709$	1.89090	−	1.09171i	0.0710141	−	0.0410000i	0.535087	+	0.844797i	$0.320279\pi$
$710$	12.0183	−	48.3701i	0.451037	−	1.81530i
$711$	−1.75154	−	3.03375i	−0.0656877	−	0.113774i
$712$	27.9072	+	16.1122i	1.04587	+	0.603831i
$713$	−1.24426	+	2.15512i	−0.0465979	+	0.0807099i
$714$	−7.68649			−0.287660
$715$		0			0
$716$	7.35085			0.274714
$717$	−10.5217	+	18.2240i	−0.392938	+	0.680589i
$718$	−14.6338	−	8.44881i	−0.546127	−	0.315307i
$719$	−2.60424	−	4.51067i	−0.0971216	−	0.168220i	0.813370	−	0.581746i	$-0.197630\pi$
$719$	−2.60424	−	4.51067i	−0.0971216	−	0.168220i	−0.910492	+	0.413526i	$0.864297\pi$
$720$	70.4005	+	17.4920i	2.62367	+	0.651889i
$721$	15.0849	−	8.70928i	0.561791	−	0.324350i
$722$	−14.3986	−	24.9390i	−0.535859	−	0.928134i
$723$	−30.0410			−1.11724
$724$	2.65562	+	4.59967i	0.0986954	+	0.170945i
$725$	−21.7211	+	13.6220i	−0.806701	+	0.505909i
$726$	−19.2374	−	11.1067i	−0.713965	−	0.412208i
$727$			3.52464i			0.130721i	0.997862	+	0.0653607i	$0.0208198\pi$
$727$			3.52464i			0.130721i	−0.997862	+	0.0653607i	$0.979180\pi$
$728$		0			0
$729$	−15.7070			−0.581741
$730$	4.65950	−	4.83292i	0.172456	−	0.178874i
$731$	−2.96388	+	5.13360i	−0.109623	+	0.189873i
$732$	8.15670	−	4.70928i	0.301480	−	0.174060i
$733$	−21.8310			−0.806345			−0.403172	−	0.915124i	$-0.632093\pi$
$733$	−21.8310			−0.806345			−0.403172	+	0.915124i	$0.632093\pi$
$734$	−13.8283	+	7.98379i	−0.510413	+	0.294687i
$735$	−27.7833	+	7.99119i	−1.02480	+	0.294760i
$736$			5.83749i			0.215173i
$737$	17.2974	−	9.98667i	0.637159	−	0.367864i
$738$	11.8568	+	6.84551i	0.436454	+	0.251987i
$739$	−43.6073	−	25.1767i	−1.60412	−	0.926139i	−0.990651	−	0.136419i	$-0.956441\pi$
$739$	−43.6073	−	25.1767i	−1.60412	−	0.926139i	−0.613468	−	0.789720i	$-0.710226\pi$
$740$	4.84551	+	1.20394i	0.178125	+	0.0442576i
$741$		0			0
$742$			22.3545i			0.820661i
$743$	−15.3938	+	26.6629i	−0.564745	+	0.978167i	0.432329	+	0.901716i	$0.357692\pi$
$743$	−15.3938	+	26.6629i	−0.564745	+	0.978167i	−0.997073	+	0.0764505i	$0.975641\pi$
$744$	−3.49887	+	6.06021i	−0.128275	+	0.222178i
$745$	19.5089	−	5.61127i	0.714752	−	0.205581i
$746$			36.9216i			1.35180i
$747$	−30.4215	−	52.6916i	−1.11307	−	1.92789i
$748$	0.431882	+	0.748041i	0.0157912	+	0.0273511i
$749$		−	16.6681i		−	0.609038i
$750$	53.3883	+	11.2119i	1.94947	+	0.409402i
$751$	−5.31124	+	9.19934i	−0.193810	+	0.335689i	−0.946510	−	0.322675i	$-0.895418\pi$
$751$	−5.31124	+	9.19934i	−0.193810	+	0.335689i	0.752700	+	0.658364i	$0.228751\pi$
$752$	−13.1370	+	22.7539i	−0.479055	+	0.829748i
$753$		−	93.3894i		−	3.40330i
$754$		0			0
$755$	1.76713	−	7.11223i	0.0643126	−	0.258840i
$756$	7.01385	+	4.04945i	0.255091	+	0.147277i
$757$	6.91575	+	3.99281i	0.251357	+	0.145121i	0.620386	−	0.784297i	$-0.286976\pi$
$757$	6.91575	+	3.99281i	0.251357	+	0.145121i	−0.369028	+	0.929418i	$0.620309\pi$
$758$	−39.6661	+	22.9012i	−1.44074	+	0.831809i
$759$			22.7792i			0.826834i
$760$	−2.90860	+	0.836590i	−0.105506	+	0.0303463i
$761$	42.3798	−	24.4680i	1.53627	−	0.886964i	0.537215	−	0.843446i	$-0.319477\pi$
$761$	42.3798	−	24.4680i	1.53627	−	0.886964i	0.999053	−	0.0435187i	$-0.0138568\pi$
$762$	87.8636			3.18296
$763$	24.9630	−	14.4124i	0.903722	−	0.521764i
$764$	−0.272473	+	0.471937i	−0.00985773	+	0.0170741i
$765$	10.4585	+	10.0832i	0.378127	+	0.364559i
$766$	−19.1110			−0.690509
$767$		0			0
$768$			27.1845i			0.980935i
$769$	−6.92428	−	3.99773i	−0.249696	−	0.144162i	0.369929	−	0.929060i	$-0.379382\pi$
$769$	−6.92428	−	3.99773i	−0.249696	−	0.144162i	−0.619625	+	0.784898i	$0.712715\pi$
$770$	−10.7537	−	10.3679i	−0.387537	−	0.373632i
$771$	−32.4391	−	56.1861i	−1.16826	−	2.02349i
$772$	−6.54495			−0.235558
$773$	−13.3070	−	23.0485i	−0.478621	−	0.828996i	0.521079	−	0.853509i	$-0.325530\pi$
$773$	−13.3070	−	23.0485i	−0.478621	−	0.828996i	−0.999700	+	0.0245130i	$0.992196\pi$
$774$	60.4388	−	34.8943i	2.17243	−	1.25425i
$775$	−2.05786	+	3.88550i	−0.0739205	+	0.139571i
$776$	7.42469	+	12.8599i	0.266531	+	0.461645i
$777$	−28.3877	−	16.3896i	−1.01840	−	0.587974i
$778$	12.9577	−	22.4435i	0.464557	−	0.804637i
$779$	−0.680346			−0.0243759
$780$		0			0
$781$	36.7708			1.31576
$782$	−2.00719	+	3.47655i	−0.0717769	+	0.124321i
$783$	57.0074	+	32.9132i	2.03728	+	1.17622i
$784$	−9.38428	−	16.2541i	−0.335153	−	0.580502i
$785$	6.92162	−	27.8576i	0.247043	−	0.994281i
$786$	60.2394	−	34.7792i	2.14867	−	1.24053i
$787$	−4.62896	−	8.01759i	−0.165005	−	0.285796i	0.771652	−	0.636045i	$-0.219431\pi$
$787$	−4.62896	−	8.01759i	−0.165005	−	0.285796i	−0.936657	+	0.350248i	$0.886097\pi$
$788$	0.738205			0.0262975
$789$	14.4927	+	25.1021i	0.515955	+	0.893660i
$790$	1.18707	−	1.23125i	0.0422340	−	0.0438059i
$791$	17.4062	+	10.0494i	0.618892	+	0.357317i
$792$			44.9333i			1.59664i
$793$		0			0
$794$	5.99159			0.212634
$795$	41.8045	−	43.3604i	1.48265	−	1.53783i
$796$	0.995079	−	1.72353i	0.0352697	−	0.0610888i
$797$	−13.8063	+	7.97107i	−0.489044	+	0.282350i	−0.724178	−	0.689613i	$-0.757781\pi$
$797$	−13.8063	+	7.97107i	−0.489044	+	0.282350i	0.235134	+	0.971963i	$0.424447\pi$
$798$	−4.49693			−0.159190
$799$	−4.55685	+	2.63090i	−0.161210	+	0.0930745i
$800$	0.376717	+	10.3070i	0.0133190	+	0.364408i
$801$		−	90.4945i		−	3.19747i
$802$	12.1368	−	7.00719i	0.428566	−	0.247432i
$803$	4.28927	+	2.47641i	0.151365	+	0.0873906i
$804$	−7.97084	−	4.60197i	−0.281110	−	0.162299i
$805$	2.60811	−	10.4969i	0.0919238	−	0.369968i
$806$		0			0
$807$		−	36.1133i		−	1.27125i
$808$	20.6332	−	35.7377i	0.725872	−	1.25725i
$809$	8.96194	−	15.5225i	0.315085	−	0.545744i	−0.664370	−	0.747403i	$-0.731300\pi$
$809$	8.96194	−	15.5225i	0.315085	−	0.545744i	0.979456	+	0.201660i	$0.0646336\pi$
$810$	−18.5956	−	64.6522i	−0.653384	−	2.27165i
$811$			7.43415i			0.261048i	0.991445	+	0.130524i	$0.0416660\pi$
$811$			7.43415i			0.261048i	−0.991445	+	0.130524i	$0.958334\pi$
$812$	−1.61757	−	2.80171i	−0.0567655	−	0.0983207i
$813$	33.4999	+	58.0235i	1.17489	+	2.03497i
$814$			23.6430i			0.828687i
$815$	−7.44767	−	25.8936i	−0.260880	−	0.907013i
$816$	−6.72261	+	11.6439i	−0.235338	+	0.407618i
$817$	−1.73400	+	3.00338i	−0.0606650	+	0.105075i
$818$			29.8888i			1.04504i
$819$		0			0
$820$	−0.251117	+	1.01068i	−0.00876940	+	0.0352944i
$821$	−17.7363	−	10.2401i	−0.619001	−	0.357380i	0.157479	−	0.987522i	$-0.449663\pi$
$821$	−17.7363	−	10.2401i	−0.619001	−	0.357380i	−0.776480	+	0.630142i	$0.782997\pi$
$822$	58.2522	+	33.6319i	2.03178	+	1.17305i
$823$	−3.24893	+	1.87577i	−0.113250	+	0.0653852i	−0.555555	−	0.831480i	$-0.687494\pi$
$823$	−3.24893	+	1.87577i	−0.113250	+	0.0653852i	0.442305	+	0.896865i	$0.354161\pi$
$824$		−	25.5811i		−	0.891159i
$825$	1.47004	+	40.2204i	0.0511802	+	1.40029i
$826$	−10.7601	+	6.21235i	−0.374392	+	0.216155i
$827$	−48.1483			−1.67428			−0.837141	−	0.546987i	$-0.815775\pi$
$827$	−48.1483			−1.67428			−0.837141	+	0.546987i	$0.815775\pi$
$828$	6.37684	−	3.68167i	0.221611	−	0.127947i
$829$	−18.2804	+	31.6625i	−0.634904	+	1.09969i	0.351632	+	0.936138i	$0.385627\pi$
$829$	−18.2804	+	31.6625i	−0.634904	+	1.09969i	−0.986536	+	0.163547i	$0.947706\pi$
$830$	20.6176	−	21.3849i	0.715647	−	0.742282i
$831$	41.4596			1.43822
$832$		0			0
$833$		−	3.75872i		−	0.130232i
$834$	−28.1161	−	16.2329i	−0.973583	−	0.562098i
$835$	13.5486	−	14.0528i	0.468868	−	0.486318i
$836$	0.252669	+	0.437636i	0.00873876	+	0.0151360i
$837$	11.2885			0.390186
$838$	−12.9132	−	22.3663i	−0.446079	−	0.772632i
$839$	39.1698	−	22.6147i	1.35229	−	0.780746i	0.363721	−	0.931508i	$-0.381506\pi$
$839$	39.1698	−	22.6147i	1.35229	−	0.780746i	0.988570	+	0.150762i	$0.0481728\pi$
$840$	7.33403	−	29.5174i	0.253048	−	1.01845i
$841$	1.35270	+	2.34294i	0.0466448	+	0.0807912i
$842$	25.3539	+	14.6381i	0.873753	+	0.504462i
$843$	1.07838	−	1.86781i	0.0371413	−	0.0643306i
$844$	−8.39803			−0.289072
$845$		0			0
$846$	61.9481			2.12982
$847$	−3.89076	+	6.73899i	−0.133688	+	0.231554i
$848$	33.8638	+	19.5513i	1.16289	+	0.671394i
$849$	30.5844	+	52.9738i	1.04965	+	1.81806i
$850$	−3.31965	+	6.26794i	−0.113863	+	0.214989i
$851$	−14.8258	+	8.55971i	−0.508224	+	0.293423i
$852$	−8.47220	−	14.6743i	−0.290253	−	0.502733i
$853$	37.2534			1.27553			0.637766	−	0.770230i	$-0.279859\pi$
$853$	37.2534			1.27553			0.637766	+	0.770230i	$0.279859\pi$
$854$	−10.5886	−	18.3401i	−0.362336	−	0.627584i
$855$	6.11866	+	5.89911i	0.209254	+	0.201745i
$856$	−21.1993	−	12.2394i	−0.724578	−	0.418336i
$857$		−	10.8371i		−	0.370188i	−0.982721	−	0.185094i	$-0.940741\pi$
$857$		−	10.8371i		−	0.370188i	0.982721	−	0.185094i	$-0.0592590\pi$
$858$		0			0
$859$	−14.6081			−0.498422			−0.249211	−	0.968449i	$-0.580171\pi$
$859$	−14.6081			−0.498422			−0.249211	+	0.968449i	$0.580171\pi$
$860$	3.82160	+	3.68447i	0.130315	+	0.125639i
$861$	3.41855	−	5.92110i	0.116504	−	0.201791i
$862$	10.7038	−	6.17982i	0.364572	−	0.210486i
$863$	−10.3440			−0.352116			−0.176058	−	0.984380i	$-0.556335\pi$
$863$	−10.3440			−0.352116			−0.176058	+	0.984380i	$0.556335\pi$
$864$	22.9324	−	13.2401i	0.780178	−	0.450436i
$865$	−1.85618	+	0.533885i	−0.0631120	+	0.0181526i
$866$		−	20.0821i		−	0.682417i
$867$	44.3395	−	25.5994i	1.50585	−	0.869402i
$868$	−0.480460	−	0.277394i	−0.0163079	−	0.00941535i
$869$	1.09275	+	0.630898i	0.0370689	+	0.0214017i
$870$	−13.4908	+	54.2967i	−0.457380	+	1.84083i
$871$		0			0
$872$		−	42.3324i		−	1.43356i
$873$	20.8504	−	36.1140i	0.705680	−	1.22227i
$874$	−1.17429	+	2.03393i	−0.0397210	+	0.0687988i
$875$	3.92763	−	18.7023i	0.132778	−	0.632254i
$876$		−	2.28231i		−	0.0771122i
$877$	19.0338	+	32.9676i	0.642727	+	1.11324i	0.984821	+	0.173571i	$0.0555306\pi$
$877$	19.0338	+	32.9676i	0.642727	+	1.11324i	−0.342094	+	0.939666i	$0.611136\pi$
$878$	5.92654	+	10.2651i	0.200011	+	0.346429i
$879$		−	30.0144i		−	1.01236i
$880$	−25.1110	+	7.22257i	−0.846491	+	0.243473i
$881$	6.02472	−	10.4351i	0.202978	−	0.351568i	−0.746509	−	0.665376i	$-0.768271\pi$
$881$	6.02472	−	10.4351i	0.202978	−	0.351568i	0.949487	+	0.313807i	$0.101605\pi$
$882$	−22.1261	+	38.3235i	−0.745024	+	1.29042i
$883$		−	0.320699i		−	0.0107924i	−0.999985	−	0.00539619i	$-0.998282\pi$
$883$		−	0.320699i		−	0.0107924i	0.999985	−	0.00539619i	$-0.00171767\pi$
$884$		0			0
$885$	32.4885	+	8.07223i	1.09209	+	0.271345i
$886$	−8.51885	−	4.91836i	−0.286196	−	0.165235i
$887$	−3.13626	−	1.81072i	−0.105305	−	0.0607981i	0.446422	−	0.894822i	$-0.352698\pi$
$887$	−3.13626	−	1.81072i	−0.105305	−	0.0607981i	−0.551728	+	0.834024i	$0.686031\pi$
$888$	−41.6904	+	24.0700i	−1.39904	+	0.807735i
$889$		−	30.7792i		−	1.03230i
$890$	42.4604	−	12.2127i	1.42328	−	0.409371i
$891$	42.9825	−	24.8160i	1.43997	−	0.831366i
$892$	−3.23370			−0.108272
$893$	−2.66595	+	1.53919i	−0.0892127	+	0.0515070i
$894$	22.1483	−	38.3621i	0.740751	−	1.28302i
$895$	−30.9087	+	32.0591i	−1.03316	+	1.07162i
$896$	22.9132			0.765477
$897$		0			0
$898$			48.6635i			1.62392i
$899$	−3.90509	−	2.25461i	−0.130242	−	0.0751954i
$900$	11.0217	−	6.91210i	0.367391	−	0.230403i
$901$	3.91548	+	6.78181i	0.130444	+	0.225935i
$902$	−4.93146			−0.164200
$903$	−17.4257	−	30.1823i	−0.579892	−	1.00440i
$904$	25.5629	−	14.7587i	0.850208	−	0.490868i
$905$	−31.2267	−	7.75872i	−1.03801	−	0.257909i
$906$	−7.99579	−	13.8491i	−0.265642	−	0.460106i
$907$	9.46855	+	5.46667i	0.314398	+	0.181518i	0.648893	−	0.760880i	$-0.275232\pi$
$907$	9.46855	+	5.46667i	0.314398	+	0.181518i	−0.334495	+	0.942398i	$0.608566\pi$
$908$	3.17921	−	5.50656i	0.105506	−	0.182742i
$909$	−115.886			−3.84371
$910$		0			0
$911$	−37.5897			−1.24540			−0.622701	−	0.782460i	$-0.713965\pi$
$911$	−37.5897			−1.24540			−0.622701	+	0.782460i	$0.713965\pi$
$912$	−3.93302	+	6.81218i	−0.130235	+	0.225574i
$913$	18.9794	+	10.9577i	0.628125	+	0.362648i
$914$	−27.4307	−	47.5113i	−0.907326	−	1.57153i
$915$	−13.7587	+	55.3751i	−0.454849	+	1.83064i
$916$	0.984010	−	0.568118i	0.0325126	−	0.0187712i
$917$	−12.1834	−	21.1023i	−0.402332	−	0.696859i
$918$	18.2101			0.601022
$919$	16.8371	+	29.1627i	0.555405	+	0.961989i	0.997872	+	0.0652045i	$0.0207700\pi$
$919$	16.8371	+	29.1627i	0.555405	+	0.961989i	−0.442467	+	0.896785i	$0.645897\pi$
$920$	−11.4354	−	11.0251i	−0.377014	−	0.363486i
$921$	−0.724951	−	0.418551i	−0.0238880	−	0.0137917i
$922$		−	23.0563i		−	0.759317i
$923$		0			0
$924$	−5.07838			−0.167066
$925$	−25.6250	+	16.0703i	−0.842545	+	0.528388i
$926$	−7.00072	+	12.1256i	−0.230058	+	0.398472i
$927$	−62.2137	+	35.9191i	−2.04336	+	1.17974i
$928$	−10.5776			−0.347226
$929$	37.4157	−	21.6020i	1.22757	−	0.708738i	0.261049	−	0.965326i	$-0.415932\pi$
$929$	37.4157	−	21.6020i	1.22757	−	0.708738i	0.966521	+	0.256588i	$0.0825984\pi$
$930$	2.65206	+	9.22053i	0.0869646	+	0.302353i
$931$		−	2.19902i		−	0.0720698i
$932$	−6.05293	+	3.49466i	−0.198270	+	0.114471i
$933$	35.8194	+	20.6803i	1.17267	+	0.677044i
$934$	2.50212	+	1.44460i	0.0818720	+	0.0472688i
$935$	−5.07838	−	1.26180i	−0.166081	−	0.0412651i
$936$		0			0
$937$		−	27.5630i		−	0.900445i	−0.892916	−	0.450222i	$-0.851345\pi$
$937$		−	27.5630i		−	0.900445i	0.892916	−	0.450222i	$-0.148655\pi$
$938$	−10.3474	+	17.9222i	−0.337853	+	0.585179i
$939$	−53.4173	+	92.5215i	−1.74321	+	3.01933i
$940$	1.30251	+	4.52849i	0.0424832	+	0.147703i
$941$			58.1666i			1.89618i	0.318007	+	0.948088i	$0.396987\pi$
$941$			58.1666i			1.89618i	−0.318007	+	0.948088i	$0.603013\pi$
$942$	−31.3184	−	54.2451i	−1.02041	−	1.76740i
$943$	−1.78539	−	3.09238i	−0.0581402	−	0.100702i
$944$			21.7333i			0.707358i
$945$	−47.1524	+	13.5623i	−1.53387	+	0.441180i
$946$	−12.5688	+	21.7699i	−0.408648	+	0.707799i
$947$	24.2576	−	42.0154i	0.788266	−	1.36532i	−0.138763	−	0.990326i	$-0.544313\pi$
$947$	24.2576	−	42.0154i	0.788266	−	1.36532i	0.927029	−	0.374991i	$-0.122354\pi$
$948$		−	0.581449i		−	0.0188846i
$949$		0			0
$950$	−1.94214	+	3.66701i	−0.0630114	+	0.118974i
$951$	38.2995	+	22.1122i	1.24195	+	0.717038i
$952$	3.42463	+	1.97721i	0.110993	+	0.0640819i
$953$	19.9488	−	11.5174i	0.646205	−	0.373087i	−0.140796	−	0.990039i	$-0.544966\pi$
$953$	19.9488	−	11.5174i	0.646205	−	0.373087i	0.787001	+	0.616952i	$0.211633\pi$
$954$		−	92.1953i		−	2.98493i
$955$	−0.912557	−	3.17272i	−0.0295296	−	0.102667i
$956$	−2.12188	+	1.22507i	−0.0686264	+	0.0396215i
$957$	−41.2762			−1.33427
$958$	−20.9852	+	12.1158i	−0.678002	+	0.391444i
$959$	11.7815	−	20.4062i	0.380445	−	0.658950i
$960$	−30.7660	−	29.6621i	−0.992969	−	0.957339i
$961$	30.2267			0.975056
$962$		0			0
$963$			68.7429i			2.21521i
$964$	−3.02915	−	1.74888i	−0.0975625	−	0.0563277i
$965$	27.5201	−	28.5443i	0.885902	−	0.918873i
$966$	−11.8010	−	20.4399i	−0.379690	−	0.657643i
$967$	54.9998			1.76868			0.884338	−	0.466848i	$-0.154611\pi$
$967$	54.9998			1.76868			0.884338	+	0.466848i	$0.154611\pi$
$968$	5.71400	+	9.89694i	0.183655	+	0.318100i
$969$	−1.36426	+	0.787653i	−0.0438262	+	0.0253031i
$970$	19.7587	+	4.90934i	0.634414	+	0.157629i
$971$	−4.85270	−	8.40512i	−0.155731	−	0.269733i	0.777594	−	0.628766i	$-0.216440\pi$
$971$	−4.85270	−	8.40512i	−0.155731	−	0.269733i	−0.933325	+	0.359033i	$0.883106\pi$
$972$	−7.49661	−	4.32817i	−0.240454	−	0.138826i
$973$	−5.68649	+	9.84929i	−0.182300	+	0.315754i
$974$	−7.61038			−0.243852
$975$		0			0
$976$	−37.0433			−1.18573
$977$	−16.1031	+	27.8914i	−0.515184	+	0.892325i	0.484661	+	0.874702i	$0.338943\pi$
$977$	−16.1031	+	27.8914i	−0.515184	+	0.892325i	−0.999845	+	0.0176225i	$0.994390\pi$
$978$	−50.9168	−	29.3968i	−1.62814	−	0.940006i
$979$	16.2979	+	28.2288i	0.520884	+	0.902197i
$980$	−3.26672	−	0.811662i	−0.104351	−	0.0259276i
$981$	−102.953	+	59.4401i	−3.28705	+	1.89778i
$982$	30.3884	+	52.6343i	0.969733	+	1.67963i
$983$	44.0782			1.40588			0.702938	−	0.711251i	$-0.251871\pi$
$983$	44.0782			1.40588			0.702938	+	0.711251i	$0.251871\pi$
$984$	−5.02052	−	8.69579i	−0.160048	−	0.277212i
$985$	−3.10399	+	3.21951i	−0.0989013	+	0.102582i
$986$	−6.29954	−	3.63704i	−0.200618	−	0.115827i
$987$		−	30.9360i		−	0.984704i
$988$		0			0
$989$	−18.2017			−0.578779
$990$	44.3509	+	42.7595i	1.40956	+	1.35898i
$991$	−6.03385	+	10.4509i	−0.191672	+	0.331985i	−0.945804	−	0.324737i	$-0.894724\pi$
$991$	−6.03385	+	10.4509i	−0.191672	+	0.331985i	0.754133	+	0.656722i	$0.228058\pi$
$992$	−1.57091	+	0.906965i	−0.0498764	+	0.0287962i
$993$	58.5029			1.85653
$994$	−32.9946	+	19.0494i	−1.04653	+	0.604212i
$995$	3.33268	+	11.5869i	0.105653	+	0.367328i
$996$		−	10.0989i		−	0.319996i
$997$	−39.6282	+	22.8794i	−1.25504	+	0.724597i	−0.972106	−	0.234543i	$-0.924641\pi$
$997$	−39.6282	+	22.8794i	−1.25504	+	0.724597i	−0.282933	+	0.959140i	$0.591307\pi$
$998$	2.22726	+	1.28591i	0.0705026	+	0.0407047i
$999$	67.2533	+	38.8287i	2.12780	+	1.22849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.l.d.654.3		12
5.4	even	2		845.2.l.e.654.4		12
13.2	odd	12		845.2.n.f.484.2		12
13.3	even	3	inner	845.2.l.d.699.4		12
13.4	even	6		845.2.d.a.844.4		6
13.5	odd	4		845.2.n.f.529.5		12
13.6	odd	12		65.2.b.a.14.2	✓	6
13.7	odd	12		845.2.b.c.339.5		6
13.8	odd	4		845.2.n.g.529.2		12
13.9	even	3		845.2.d.b.844.4		6
13.10	even	6		845.2.l.e.699.4		12
13.11	odd	12		845.2.n.g.484.5		12
13.12	even	2		845.2.l.e.654.3		12
39.32	even	12		585.2.c.b.469.5		6
52.19	even	12		1040.2.d.c.209.1		6
65.4	even	6		845.2.d.b.844.3		6
65.7	even	12		4225.2.a.ba.1.2		3
65.9	even	6		845.2.d.a.844.3		6
65.19	odd	12		65.2.b.a.14.5	yes	6
65.24	odd	12		845.2.n.g.484.2		12
65.29	even	6		845.2.l.e.699.3		12
65.32	even	12		325.2.a.k.1.2		3
65.33	even	12		4225.2.a.bh.1.2		3
65.34	odd	4		845.2.n.g.529.5		12
65.44	odd	4		845.2.n.f.529.2		12
65.49	even	6	inner	845.2.l.d.699.3		12
65.54	odd	12		845.2.n.f.484.5		12
65.58	even	12		325.2.a.j.1.2		3
65.59	odd	12		845.2.b.c.339.2		6
65.64	even	2	inner	845.2.l.d.654.4		12
195.32	odd	12		2925.2.a.bf.1.2		3
195.149	even	12		585.2.c.b.469.2		6
195.188	odd	12		2925.2.a.bj.1.2		3
260.19	even	12		1040.2.d.c.209.6		6
260.123	odd	12		5200.2.a.cj.1.3		3
260.227	odd	12		5200.2.a.cb.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.2	✓	6	13.6	odd	12
65.2.b.a.14.5	yes	6	65.19	odd	12
325.2.a.j.1.2		3	65.58	even	12
325.2.a.k.1.2		3	65.32	even	12
585.2.c.b.469.2		6	195.149	even	12
585.2.c.b.469.5		6	39.32	even	12
845.2.b.c.339.2		6	65.59	odd	12
845.2.b.c.339.5		6	13.7	odd	12
845.2.d.a.844.3		6	65.9	even	6
845.2.d.a.844.4		6	13.4	even	6
845.2.d.b.844.3		6	65.4	even	6
845.2.d.b.844.4		6	13.9	even	3
845.2.l.d.654.3		12	1.1	even	1	trivial
845.2.l.d.654.4		12	65.64	even	2	inner
845.2.l.d.699.3		12	65.49	even	6	inner
845.2.l.d.699.4		12	13.3	even	3	inner
845.2.l.e.654.3		12	13.12	even	2
845.2.l.e.654.4		12	5.4	even	2
845.2.l.e.699.3		12	65.29	even	6
845.2.l.e.699.4		12	13.10	even	6
845.2.n.f.484.2		12	13.2	odd	12
845.2.n.f.484.5		12	65.54	odd	12
845.2.n.f.529.2		12	65.44	odd	4
845.2.n.f.529.5		12	13.5	odd	4
845.2.n.g.484.2		12	65.24	odd	12
845.2.n.g.484.5		12	13.11	odd	12
845.2.n.g.529.2		12	13.8	odd	4
845.2.n.g.529.5		12	65.34	odd	4
1040.2.d.c.209.1		6	52.19	even	12
1040.2.d.c.209.6		6	260.19	even	12
2925.2.a.bf.1.2		3	195.32	odd	12
2925.2.a.bj.1.2		3	195.188	odd	12
4225.2.a.ba.1.2		3	65.7	even	12
4225.2.a.bh.1.2		3	65.33	even	12
5200.2.a.cb.1.1		3	260.227	odd	12
5200.2.a.cj.1.3		3	260.123	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.769594 + 1.33298i) q^{2} +(-2.74538 - 1.58504i) q^{3} +(-0.184551 - 0.319652i) q^{4} +(2.17009 + 0.539189i) q^{5} +(4.22565 - 2.43968i) q^{6} +(-0.854638 - 1.48028i) q^{7} -2.51026 q^{8} +(3.52472 + 6.10500i) q^{9} +(-2.38881 + 2.47772i) q^{10} +(-2.19900 - 1.26959i) q^{11} +1.17009i q^{12} +2.63090 q^{14} +(-5.10306 - 4.91996i) q^{15} +(2.30098 - 3.98542i) q^{16} +(0.798148 - 0.460811i) q^{17} -10.8504 q^{18} +(0.466951 - 0.269594i) q^{19} +(-0.228139 - 0.793181i) q^{20} +5.41855i q^{21} +(3.38468 - 1.95415i) q^{22} +(2.45078 + 1.41496i) q^{23} +(6.89160 + 3.97887i) q^{24} +(4.41855 + 2.34017i) q^{25} -12.8371i q^{27} +(-0.315449 + 0.546373i) q^{28} +(-2.56391 + 4.44083i) q^{29} +(10.4855 - 3.01589i) q^{30} +0.879362i q^{31} +(1.03139 + 1.78642i) q^{32} +(4.02472 + 6.97103i) q^{33} +1.41855i q^{34} +(-1.05649 - 3.67314i) q^{35} +(1.30098 - 2.25337i) q^{36} +(-3.02472 + 5.23898i) q^{37} +0.829914i q^{38} +(-5.44748 - 1.35350i) q^{40} +(-1.09275 - 0.630898i) q^{41} +(-7.22280 - 4.17009i) q^{42} +(-5.57017 + 3.21594i) q^{43} +0.937221i q^{44} +(4.35721 + 15.1489i) q^{45} +(-3.77221 + 2.17789i) q^{46} -5.70928 q^{47} +(-12.6341 + 7.29432i) q^{48} +(2.03919 - 3.53198i) q^{49} +(-6.51989 + 4.08884i) q^{50} -2.92162 q^{51} +8.49693i q^{53} +(17.1116 + 9.87936i) q^{54} +(-4.08747 - 3.94081i) q^{55} +(2.14536 + 3.71588i) q^{56} -1.70928 q^{57} +(-3.94635 - 6.83527i) q^{58} +(-4.08990 + 2.36130i) q^{59} +(-0.630898 + 2.53919i) q^{60} +(-4.02472 - 6.97103i) q^{61} +(-1.17217 - 0.676752i) q^{62} +(6.02472 - 10.4351i) q^{63} +6.02893 q^{64} -12.3896 q^{66} +(-3.93302 + 6.81218i) q^{67} +(-0.294598 - 0.170086i) q^{68} +(-4.48554 - 7.76918i) q^{69} +(5.70928 + 1.41855i) q^{70} +(-12.5412 + 7.24067i) q^{71} +(-8.84797 - 15.3251i) q^{72} -1.95055 q^{73} +(-4.65562 - 8.06377i) q^{74} +(-8.42131 - 13.4282i) q^{75} +(-0.172353 - 0.0995079i) q^{76} +4.34017i q^{77} -0.496928 q^{79} +(7.14223 - 7.40804i) q^{80} +(-9.77319 + 16.9277i) q^{81} +(1.68194 - 0.971071i) q^{82} -8.63090 q^{83} +(1.73205 - 1.00000i) q^{84} +(1.98052 - 0.569647i) q^{85} -9.89988i q^{86} +(14.0778 - 8.12783i) q^{87} +(5.52007 + 3.18701i) q^{88} +(-11.1173 - 6.41855i) q^{89} +(-23.5464 - 5.85043i) q^{90} -1.04453i q^{92} +(1.39383 - 2.41418i) q^{93} +(4.39383 - 7.61033i) q^{94} +(1.15869 - 0.333268i) q^{95} -6.53919i q^{96} +(-2.95774 - 5.12296i) q^{97} +(3.13870 + 5.43638i) q^{98} -17.8999i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 10 q^{4} + 4 q^{5} + 4 q^{7} + 36 q^{8} + 6 q^{9} + 2 q^{10} + 16 q^{14} - 4 q^{15} - 10 q^{16} - 20 q^{18} + 14 q^{20} - 4 q^{25} + 4 q^{28} + 12 q^{29} + 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 10 * q^4 + 4 * q^5 + 4 * q^7 + 36 * q^8 + 6 * q^9 + 2 * q^10 + 16 * q^14 - 4 * q^15 - 10 * q^16 - 20 * q^18 + 14 * q^20 - 4 * q^25 + 4 * q^28 + 12 * q^29 + 8 * q^30 - 22 * q^32 + 12 * q^33 - 8 * q^35 - 22 * q^36 - 68 * q^40 + 38 * q^45 - 40 * q^47 + 18 * q^49 - 22 * q^50 - 48 * q^51 + 16 * q^55 + 40 * q^56 + 8 * q^57 - 24 * q^58 + 8 * q^60 - 12 * q^61 + 36 * q^63 + 132 * q^64 - 32 * q^66 - 20 * q^67 - 24 * q^69 + 40 * q^70 - 90 * q^72 - 96 * q^73 - 4 * q^74 + 16 * q^75 + 64 * q^79 + 58 * q^80 - 46 * q^81 - 88 * q^83 - 32 * q^85 - 140 * q^90 - 4 * q^93 + 32 * q^94 + 16 * q^95 + 28 * q^97 + 50 * q^98

Introduction

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