LMFDB - Embedded newform 93.2.f.b.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(4,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("93.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 13 x^{14} - 28 x^{13} + 90 x^{12} - 119 x^{11} + 382 x^{10} - 356 x^{9} + 1869 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 13x^14 - 28x^13 + 90x^12 - 119x^11 + 382x^10 - 356x^9 + 1869x^8 - 2812x^7 + 5846x^6 - 4987x^5 + 4006x^4 - 1014x^3 + 2493x^2 + 729*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$2.19791 + 1.59688i$ of defining polynomial
Character	$\chi$	$=$	93.64
Dual form			93.2.f.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19791 - 1.59688i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.66277 + 5.11749i) q^{4} +2.08737 q^{5} +2.71677 q^{6} +(0.145034 + 0.446368i) q^{7} +(2.83832 - 8.73545i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-2.19791 - 1.59688i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.66277 + 5.11749i) q^{4} +2.08737 q^{5} +2.71677 q^{6} +(0.145034 + 0.446368i) q^{7} +(2.83832 - 8.73545i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-4.58787 - 3.33328i) q^{10} +(0.836668 + 2.57500i) q^{11} +(-4.35320 - 3.16278i) q^{12} +(5.23460 - 3.80316i) q^{13} +(0.394024 - 1.21268i) q^{14} +(-1.68872 + 1.22693i) q^{15} +(-11.4814 + 8.34175i) q^{16} +(-0.511367 + 1.57383i) q^{17} +(-2.19791 + 1.59688i) q^{18} +(4.92388 + 3.57741i) q^{19} +(3.47083 + 10.6821i) q^{20} +(-0.379703 - 0.275871i) q^{21} +(2.27303 - 6.99568i) q^{22} +(-0.207019 + 0.637139i) q^{23} +(2.83832 + 8.73545i) q^{24} -0.642874 q^{25} -17.5784 q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.04313 + 1.48442i) q^{28} +(-2.70711 - 1.96683i) q^{29} +5.67092 q^{30} +(-4.69782 - 2.98839i) q^{31} +20.1860 q^{32} +(-2.19042 - 1.59144i) q^{33} +(3.63715 - 2.64254i) q^{34} +(0.302739 + 0.931736i) q^{35} +5.38085 q^{36} -6.41211 q^{37} +(-5.10958 - 15.7257i) q^{38} +(-1.99944 + 6.15365i) q^{39} +(5.92463 - 18.2341i) q^{40} +(4.58787 + 3.33328i) q^{41} +(0.394024 + 1.21268i) q^{42} +(-4.04679 - 2.94016i) q^{43} +(-11.7863 + 8.56328i) q^{44} +(0.645034 - 1.98521i) q^{45} +(1.47244 - 1.06979i) q^{46} +(-1.59535 + 1.15909i) q^{47} +(4.38552 - 13.4972i) q^{48} +(5.48491 - 3.98502i) q^{49} +(1.41298 + 1.02659i) q^{50} +(-0.511367 - 1.57383i) q^{51} +(28.1666 + 20.4642i) q^{52} +(0.772728 - 2.37821i) q^{53} +(0.839529 - 2.58380i) q^{54} +(1.74644 + 5.37498i) q^{55} +4.31088 q^{56} -6.08625 q^{57} +(2.80921 + 8.64585i) q^{58} +(-3.65498 + 2.65550i) q^{59} +(-9.08675 - 6.60191i) q^{60} -6.51961 q^{61} +(5.55333 + 14.0701i) q^{62} +0.469339 q^{63} +(-21.4042 - 15.5511i) q^{64} +(10.9266 - 7.93862i) q^{65} +(2.27303 + 6.99568i) q^{66} -8.64185 q^{67} -8.90433 q^{68} +(-0.207019 - 0.637139i) q^{69} +(0.822474 - 2.53131i) q^{70} +(2.71702 - 8.36213i) q^{71} +(-7.43082 - 5.39880i) q^{72} +(0.0564511 + 0.173738i) q^{73} +(14.0933 + 10.2394i) q^{74} +(0.520096 - 0.377872i) q^{75} +(-10.1201 + 31.1463i) q^{76} +(-1.02805 + 0.746923i) q^{77} +(14.2212 - 10.3323i) q^{78} +(0.0403226 - 0.124100i) q^{79} +(-23.9660 + 17.4123i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-4.76090 - 14.6525i) q^{82} +(-6.85491 - 4.98038i) q^{83} +(0.780404 - 2.40184i) q^{84} +(-1.06741 + 3.28516i) q^{85} +(4.19941 + 12.9245i) q^{86} +3.34617 q^{87} +24.8685 q^{88} +(-1.07379 - 3.30479i) q^{89} +(-4.58787 + 3.33328i) q^{90} +(2.45680 + 1.78497i) q^{91} -3.60478 q^{92} +(5.55715 - 0.343657i) q^{93} +5.35736 q^{94} +(10.2780 + 7.46739i) q^{95} +(-16.3308 + 11.8650i) q^{96} +(-0.790123 - 2.43175i) q^{97} -18.4190 q^{98} +2.70751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + 6 * q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 - 4 * q^9	\( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9} - 3 q^{10} + 10 q^{11} - 4 q^{12} - 3 q^{13} - 4 q^{14} - 4 q^{15} - 17 q^{16} - q^{17} - 3 q^{18} - 4 q^{19} + 7 q^{20} + 8 q^{21} + 10 q^{22} + 7 q^{23} - 2 q^{24} + 30 q^{25} - 16 q^{26} - 4 q^{27} + 9 q^{28} - 2 q^{29} + 12 q^{30} - 13 q^{31} + 108 q^{32} - 5 q^{33} - 4 q^{34} - 33 q^{35} + 26 q^{36} - 28 q^{37} - 62 q^{38} + 7 q^{39} - 27 q^{40} + 3 q^{41} - 4 q^{42} - 13 q^{43} - 64 q^{44} + q^{45} - q^{46} - 20 q^{47} - 2 q^{48} + q^{49} - 44 q^{50} - q^{51} + 88 q^{52} - 4 q^{53} + 2 q^{54} - 8 q^{55} + 104 q^{56} - 14 q^{57} - 31 q^{58} + 49 q^{59} - 8 q^{60} - 13 q^{62} - 2 q^{63} - 26 q^{64} - q^{65} + 10 q^{66} + 60 q^{67} - 30 q^{68} + 7 q^{69} + 85 q^{70} + 23 q^{71} - 7 q^{72} - 17 q^{73} + 70 q^{74} - 5 q^{75} + 7 q^{76} + 2 q^{77} + 19 q^{78} - 13 q^{79} - 94 q^{80} - 4 q^{81} - 9 q^{82} - 49 q^{83} - 6 q^{84} - 4 q^{85} + 24 q^{86} - 2 q^{87} - 32 q^{88} + 3 q^{89} - 3 q^{90} - 2 q^{91} - 70 q^{92} + 17 q^{93} + 74 q^{94} - 10 q^{95} - 32 q^{96} + 3 q^{97} - 82 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + 6 * q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 - 4 * q^9 - 3 * q^10 + 10 * q^11 - 4 * q^12 - 3 * q^13 - 4 * q^14 - 4 * q^15 - 17 * q^16 - q^17 - 3 * q^18 - 4 * q^19 + 7 * q^20 + 8 * q^21 + 10 * q^22 + 7 * q^23 - 2 * q^24 + 30 * q^25 - 16 * q^26 - 4 * q^27 + 9 * q^28 - 2 * q^29 + 12 * q^30 - 13 * q^31 + 108 * q^32 - 5 * q^33 - 4 * q^34 - 33 * q^35 + 26 * q^36 - 28 * q^37 - 62 * q^38 + 7 * q^39 - 27 * q^40 + 3 * q^41 - 4 * q^42 - 13 * q^43 - 64 * q^44 + q^45 - q^46 - 20 * q^47 - 2 * q^48 + q^49 - 44 * q^50 - q^51 + 88 * q^52 - 4 * q^53 + 2 * q^54 - 8 * q^55 + 104 * q^56 - 14 * q^57 - 31 * q^58 + 49 * q^59 - 8 * q^60 - 13 * q^62 - 2 * q^63 - 26 * q^64 - q^65 + 10 * q^66 + 60 * q^67 - 30 * q^68 + 7 * q^69 + 85 * q^70 + 23 * q^71 - 7 * q^72 - 17 * q^73 + 70 * q^74 - 5 * q^75 + 7 * q^76 + 2 * q^77 + 19 * q^78 - 13 * q^79 - 94 * q^80 - 4 * q^81 - 9 * q^82 - 49 * q^83 - 6 * q^84 - 4 * q^85 + 24 * q^86 - 2 * q^87 - 32 * q^88 + 3 * q^89 - 3 * q^90 - 2 * q^91 - 70 * q^92 + 17 * q^93 + 74 * q^94 - 10 * q^95 - 32 * q^96 + 3 * q^97 - 82 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.19791	−	1.59688i	−1.55416	−	1.12916i	−0.940601	−	0.339515i	$-0.889737\pi$
$2$	−2.19791	−	1.59688i	−1.55416	−	1.12916i	−0.613560	−	0.789648i	$-0.710263\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	1.66277	+	5.11749i	0.831387	+	2.55875i
$5$	2.08737			0.933502			0.466751	−	0.884389i	$-0.345425\pi$
$5$	2.08737			0.933502			0.466751	+	0.884389i	$0.345425\pi$
$6$	2.71677			1.10912
$7$	0.145034	+	0.446368i	0.0548176	+	0.168711i	0.974717	−	0.223443i	$-0.0717298\pi$
$7$	0.145034	+	0.446368i	0.0548176	+	0.168711i	−0.919899	+	0.392155i	$0.871730\pi$
$8$	2.83832	−	8.73545i	1.00350	−	3.08845i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−4.58787	−	3.33328i	−1.45081	−	1.05408i
$11$	0.836668	+	2.57500i	0.252265	+	0.776391i	0.994356	+	0.106093i	$0.0338340\pi$
$11$	0.836668	+	2.57500i	0.252265	+	0.776391i	−0.742091	+	0.670299i	$0.766166\pi$
$12$	−4.35320	−	3.16278i	−1.25666	−	0.913017i
$13$	5.23460	−	3.80316i	1.45182	−	1.05481i	0.466416	−	0.884566i	$-0.345545\pi$
$13$	5.23460	−	3.80316i	1.45182	−	1.05481i	0.985402	−	0.170242i	$-0.0544550\pi$
$14$	0.394024	−	1.21268i	0.105307	−	0.324102i
$15$	−1.68872	+	1.22693i	−0.436026	+	0.316791i
$16$	−11.4814	+	8.34175i	−2.87036	+	2.08544i
$17$	−0.511367	+	1.57383i	−0.124025	+	0.381709i	−0.993722	−	0.111876i	$-0.964314\pi$
$17$	−0.511367	+	1.57383i	−0.124025	+	0.381709i	0.869697	+	0.493585i	$0.164314\pi$
$18$	−2.19791	+	1.59688i	−0.518053	+	0.376388i
$19$	4.92388	+	3.57741i	1.12962	+	0.820714i	0.985639	−	0.168867i	$-0.0540109\pi$
$19$	4.92388	+	3.57741i	1.12962	+	0.820714i	0.143977	+	0.989581i	$0.454011\pi$
$20$	3.47083	+	10.6821i	0.776101	+	2.38859i
$21$	−0.379703	−	0.275871i	−0.0828580	−	0.0601999i
$22$	2.27303	−	6.99568i	0.484613	−	1.49148i
$23$	−0.207019	+	0.637139i	−0.0431664	+	0.132853i	−0.970317	−	0.241836i	$-0.922250\pi$
$23$	−0.207019	+	0.637139i	−0.0431664	+	0.132853i	0.927151	+	0.374689i	$0.122250\pi$
$24$	2.83832	+	8.73545i	0.579369	+	1.78312i
$25$	−0.642874			−0.128575
$26$	−17.5784			−3.44741
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−2.04313	+	1.48442i	−0.386114	+	0.280529i
$29$	−2.70711	−	1.96683i	−0.502697	−	0.365231i	0.307349	−	0.951597i	$-0.400558\pi$
$29$	−2.70711	−	1.96683i	−0.502697	−	0.365231i	−0.810046	+	0.586366i	$0.800558\pi$
$30$	5.67092			1.03536
$31$	−4.69782	−	2.98839i	−0.843754	−	0.536730i
$31$	−4.69782	−	2.98839i	−0.843754	−	0.536730i
$32$	20.1860			3.56841
$33$	−2.19042	−	1.59144i	−0.381304	−	0.277034i
$34$	3.63715	−	2.64254i	0.623766	−	0.453192i
$35$	0.302739	+	0.931736i	0.0511723	+	0.157492i
$36$	5.38085			0.896808
$37$	−6.41211			−1.05414			−0.527072	−	0.849820i	$-0.676710\pi$
$37$	−6.41211			−1.05414			−0.527072	+	0.849820i	$0.676710\pi$
$38$	−5.10958	−	15.7257i	−0.828884	−	2.55104i
$39$	−1.99944	+	6.15365i	−0.320167	+	0.985372i
$40$	5.92463	−	18.2341i	0.936766	−	2.88307i
$41$	4.58787	+	3.33328i	0.716504	+	0.520571i	0.885265	−	0.465086i	$-0.153977\pi$
$41$	4.58787	+	3.33328i	0.716504	+	0.520571i	−0.168761	+	0.985657i	$0.553977\pi$
$42$	0.394024	+	1.21268i	0.0607991	+	0.187121i
$43$	−4.04679	−	2.94016i	−0.617130	−	0.448371i	0.234788	−	0.972047i	$-0.424560\pi$
$43$	−4.04679	−	2.94016i	−0.617130	−	0.448371i	−0.851918	+	0.523676i	$0.824560\pi$
$44$	−11.7863	+	8.56328i	−1.77686	+	1.29096i
$45$	0.645034	−	1.98521i	0.0961560	−	0.295938i
$46$	1.47244	−	1.06979i	0.217100	−	0.157732i
$47$	−1.59535	+	1.15909i	−0.232705	+	0.169070i	−0.698027	−	0.716071i	$-0.745939\pi$
$47$	−1.59535	+	1.15909i	−0.232705	+	0.169070i	0.465322	+	0.885142i	$0.345939\pi$
$48$	4.38552	−	13.4972i	0.632995	−	1.94816i
$49$	5.48491	−	3.98502i	0.783558	−	0.569289i
$50$	1.41298	+	1.02659i	0.199826	+	0.145182i
$51$	−0.511367	−	1.57383i	−0.0716057	−	0.220380i
$52$	28.1666	+	20.4642i	3.90601	+	2.83788i
$53$	0.772728	−	2.37821i	0.106142	−	0.326673i	−0.883854	−	0.467762i	$-0.845060\pi$
$53$	0.772728	−	2.37821i	0.106142	−	0.326673i	0.989997	+	0.141089i	$0.0450604\pi$
$54$	0.839529	−	2.58380i	0.114245	−	0.351611i
$55$	1.74644	+	5.37498i	0.235490	+	0.724762i
$56$	4.31088			0.576065
$57$	−6.08625			−0.806144
$58$	2.80921	+	8.64585i	0.368867	+	1.13526i
$59$	−3.65498	+	2.65550i	−0.475838	+	0.345717i	−0.799712	−	0.600384i	$-0.795015\pi$
$59$	−3.65498	+	2.65550i	−0.475838	+	0.345717i	0.323874	+	0.946100i	$0.395015\pi$
$60$	−9.08675	−	6.60191i	−1.17309	−	0.852303i
$61$	−6.51961			−0.834751			−0.417376	−	0.908734i	$-0.637050\pi$
$61$	−6.51961			−0.834751			−0.417376	+	0.908734i	$0.637050\pi$
$62$	5.55333	+	14.0701i	0.705273	+	1.78690i
$63$	0.469339			0.0591312
$64$	−21.4042	−	15.5511i	−2.67552	−	1.94388i
$65$	10.9266	−	7.93862i	1.35527	−	0.984665i
$66$	2.27303	+	6.99568i	0.279791	+	0.861109i
$67$	−8.64185			−1.05577			−0.527885	−	0.849316i	$-0.677015\pi$
$67$	−8.64185			−1.05577			−0.527885	+	0.849316i	$0.677015\pi$
$68$	−8.90433			−1.07981
$69$	−0.207019	−	0.637139i	−0.0249221	−	0.0767025i
$70$	0.822474	−	2.53131i	0.0983044	−	0.302550i
$71$	2.71702	−	8.36213i	0.322451	−	0.992403i	−0.650127	−	0.759826i	$-0.725284\pi$
$71$	2.71702	−	8.36213i	0.322451	−	0.992403i	0.972578	−	0.232577i	$-0.0747157\pi$
$72$	−7.43082	−	5.39880i	−0.875730	−	0.636255i
$73$	0.0564511	+	0.173738i	0.00660710	+	0.0203346i	0.954306	−	0.298832i	$-0.0965970\pi$
$73$	0.0564511	+	0.173738i	0.00660710	+	0.0203346i	−0.947699	+	0.319167i	$0.896597\pi$
$74$	14.0933	+	10.2394i	1.63831	+	1.19030i
$75$	0.520096	−	0.377872i	0.0600555	−	0.0436329i
$76$	−10.1201	+	31.1463i	−1.16085	+	3.57273i
$77$	−1.02805	+	0.746923i	−0.117157	+	0.0851198i
$78$	14.2212	−	10.3323i	1.61024	−	1.16991i
$79$	0.0403226	−	0.124100i	0.00453665	−	0.0139624i	−0.948763	−	0.315990i	$-0.897663\pi$
$79$	0.0403226	−	0.124100i	0.00453665	−	0.0139624i	0.953299	+	0.302027i	$0.0976634\pi$
$80$	−23.9660	+	17.4123i	−2.67948	+	1.94676i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−4.76090	−	14.6525i	−0.525753	−	1.61810i
$83$	−6.85491	−	4.98038i	−0.752424	−	0.546668i	0.144154	−	0.989555i	$-0.453954\pi$
$83$	−6.85491	−	4.98038i	−0.752424	−	0.546668i	−0.896577	+	0.442888i	$0.853954\pi$
$84$	0.780404	−	2.40184i	0.0851491	−	0.262062i
$85$	−1.06741	+	3.28516i	−0.115777	+	0.356326i
$86$	4.19941	+	12.9245i	0.452834	+	1.39368i
$87$	3.34617			0.358747
$88$	24.8685			2.65099
$89$	−1.07379	−	3.30479i	−0.113822	−	0.350307i	0.877878	−	0.478885i	$-0.158959\pi$
$89$	−1.07379	−	3.30479i	−0.113822	−	0.350307i	−0.991699	+	0.128578i	$0.958959\pi$
$90$	−4.58787	+	3.33328i	−0.483604	+	0.351359i
$91$	2.45680	+	1.78497i	0.257543	+	0.187116i
$92$	−3.60478			−0.375824
$93$	5.55715	−	0.343657i	0.576249	−	0.0356356i
$94$	5.35736			0.552570
$95$	10.2780	+	7.46739i	1.05450	+	0.766138i
$96$	−16.3308	+	11.8650i	−1.66676	+	1.21097i
$97$	−0.790123	−	2.43175i	−0.0802248	−	0.246907i	0.902898	−	0.429856i	$-0.141436\pi$
$97$	−0.790123	−	2.43175i	−0.0802248	−	0.246907i	−0.983122	+	0.182949i	$0.941436\pi$
$98$	−18.4190			−1.86060
$99$	2.70751			0.272115
$100$	−1.06895	−	3.28990i	−0.106895	−	0.328990i
$101$	1.22009	−	3.75505i	0.121403	−	0.373641i	−0.871825	−	0.489817i	$-0.837064\pi$
$101$	1.22009	−	3.75505i	0.121403	−	0.373641i	0.993229	+	0.116176i	$0.0370635\pi$
$102$	−1.38927	+	4.27572i	−0.137558	+	0.423360i
$103$	5.41942	+	3.93744i	0.533991	+	0.387967i	0.821849	−	0.569706i	$-0.192943\pi$
$103$	5.41942	+	3.93744i	0.533991	+	0.387967i	−0.287857	+	0.957673i	$0.592943\pi$
$104$	−18.3649	−	56.5212i	−1.80082	−	5.54236i
$105$	−0.792582	−	0.575845i	−0.0773481	−	0.0561967i
$106$	−5.49611	+	3.99316i	−0.533829	+	0.387850i
$107$	3.02600	−	9.31308i	0.292535	−	0.900329i	−0.691504	−	0.722373i	$-0.743051\pi$
$107$	3.02600	−	9.31308i	0.292535	−	0.900329i	0.984038	−	0.177956i	$-0.0569486\pi$
$108$	−4.35320	+	3.16278i	−0.418887	+	0.304339i
$109$	0.486224	−	0.353262i	0.0465718	−	0.0338364i	−0.564256	−	0.825600i	$-0.690837\pi$
$109$	0.486224	−	0.353262i	0.0465718	−	0.0338364i	0.610828	+	0.791764i	$0.290837\pi$
$110$	4.74467	−	14.6026i	0.452387	−	1.39230i
$111$	5.18751	−	3.76894i	0.492376	−	0.357732i
$112$	−5.38868	−	3.91511i	−0.509183	−	0.369943i
$113$	5.31182	+	16.3481i	0.499694	+	1.53790i	0.809511	+	0.587104i	$0.199732\pi$
$113$	5.31182	+	16.3481i	0.499694	+	1.53790i	−0.309817	+	0.950796i	$0.600268\pi$
$114$	13.3771	+	9.71900i	1.25288	+	0.910268i
$115$	−0.432126	+	1.32995i	−0.0402959	+	0.124018i
$116$	5.56392	−	17.1240i	0.516597	−	1.58992i
$117$	−1.99944	−	6.15365i	−0.184848	−	0.568905i
$118$	12.2738			1.12990
$119$	−0.776671			−0.0711973
$120$	5.92463	+	18.2341i	0.540842	+	1.66454i
$121$	2.96858	−	2.15680i	0.269871	−	0.196073i
$122$	14.3296	+	10.4110i	1.29734	+	0.942570i
$123$	−5.67092			−0.511329
$124$	7.48162	−	29.0101i	0.671869	−	2.60518i
$125$	−11.7788			−1.05353
$126$	−1.03157	−	0.749477i	−0.0918993	−	0.0667687i
$127$	0.626742	−	0.455354i	0.0556143	−	0.0404062i	−0.559631	−	0.828742i	$-0.689057\pi$
$127$	0.626742	−	0.455354i	0.0556143	−	0.0404062i	0.615245	+	0.788336i	$0.289057\pi$
$128$	9.73582	+	29.9638i	0.860533	+	2.64845i
$129$	5.00211			0.440411
$130$	−36.6927			−3.21816
$131$	0.754897	+	2.32333i	0.0659556	+	0.202991i	0.978603	−	0.205757i	$-0.0659657\pi$
$131$	0.754897	+	2.32333i	0.0659556	+	0.202991i	−0.912647	+	0.408748i	$0.865966\pi$
$132$	4.50198	−	13.8557i	0.391847	−	1.20598i
$133$	−0.882712	+	2.71671i	−0.0765408	+	0.235568i
$134$	18.9940	+	13.8000i	1.64083	+	1.19214i
$135$	0.645034	+	1.98521i	0.0555157	+	0.170860i
$136$	12.2966	+	8.93404i	1.05443	+	0.766087i
$137$	−13.7836	+	10.0144i	−1.17762	+	0.855588i	−0.991901	−	0.127015i	$-0.959460\pi$
$137$	−13.7836	+	10.0144i	−1.17762	+	0.855588i	−0.185716	+	0.982604i	$0.559460\pi$
$138$	−0.562423	+	1.73096i	−0.0478766	+	0.147349i
$139$	−9.38209	+	6.81648i	−0.795778	+	0.578167i	−0.909673	−	0.415326i	$-0.863667\pi$
$139$	−9.38209	+	6.81648i	−0.795778	+	0.578167i	0.113894	+	0.993493i	$0.463667\pi$
$140$	−4.26476	+	3.09853i	−0.360438	+	0.261874i
$141$	0.609369	−	1.87544i	0.0513181	−	0.157941i
$142$	−19.3251	+	14.0405i	−1.62173	+	1.17825i
$143$	14.1728	+	10.2971i	1.18519	+	0.861088i
$144$	4.38552	+	13.4972i	0.365460	+	1.12477i
$145$	−5.65075	−	4.10551i	−0.469269	−	0.340944i
$146$	0.153365	−	0.472008i	0.0126925	−	0.0390636i
$147$	−2.09505	+	6.44790i	−0.172797	+	0.531814i
$148$	−10.6619	−	32.8139i	−0.876402	−	2.69729i
$149$	17.3713			1.42311			0.711556	−	0.702630i	$-0.247991\pi$
$149$	17.3713			1.42311			0.711556	+	0.702630i	$0.247991\pi$
$150$	−1.74654			−0.142605
$151$	1.35435	+	4.16827i	0.110216	+	0.339209i	0.990919	−	0.134459i	$-0.0429297\pi$
$151$	1.35435	+	4.16827i	0.110216	+	0.339209i	−0.880704	+	0.473668i	$0.842930\pi$
$152$	45.2258	−	32.8585i	3.66830	−	2.66517i
$153$	1.33878	+	0.972678i	0.108234	+	0.0786363i
$154$	3.45231			0.278195
$155$	−9.80611	−	6.23787i	−0.787646	−	0.501038i
$156$	−34.8159			−2.78750
$157$	−8.09617	−	5.88221i	−0.646145	−	0.469452i	0.215811	−	0.976435i	$-0.430761\pi$
$157$	−8.09617	−	5.88221i	−0.646145	−	0.469452i	−0.861956	+	0.506983i	$0.830761\pi$
$158$	−0.286799	+	0.208371i	−0.0228165	+	0.0165771i
$159$	0.772728	+	2.37821i	0.0612814	+	0.188605i
$160$	42.1357			3.33112
$161$	−0.314423			−0.0247800
$162$	0.839529	+	2.58380i	0.0659596	+	0.203003i
$163$	−7.62310	+	23.4615i	−0.597088	+	1.83765i	−0.0530394	+	0.998592i	$0.516891\pi$
$163$	−7.62310	+	23.4615i	−0.597088	+	1.83765i	−0.544048	+	0.839054i	$0.683109\pi$
$164$	−9.42945	+	29.0209i	−0.736316	+	2.26615i
$165$	−4.57223	−	3.32192i	−0.355948	−	0.258611i
$166$	7.11343	+	21.8929i	0.552110	+	1.69922i
$167$	−18.0722	−	13.1302i	−1.39847	−	1.01605i	−0.994875	−	0.101111i	$-0.967760\pi$
$167$	−18.0722	−	13.1302i	−1.39847	−	1.01605i	−0.403595	−	0.914938i	$-0.632240\pi$
$168$	−3.48757	+	2.53387i	−0.269072	+	0.195492i
$169$	8.91982	−	27.4524i	0.686140	−	2.11172i
$170$	7.59209	−	5.51597i	0.582286	−	0.423056i
$171$	4.92388	−	3.57741i	0.376539	−	0.273571i
$172$	8.31737	−	25.5982i	0.634194	−	1.95185i
$173$	10.4326	−	7.57974i	0.793177	−	0.576277i	−0.115727	−	0.993281i	$-0.536920\pi$
$173$	10.4326	−	7.57974i	0.793177	−	0.576277i	0.908905	+	0.417004i	$0.136920\pi$
$174$	−7.35460	−	5.34343i	−0.557551	−	0.405084i
$175$	−0.0932384	−	0.286958i	−0.00704816	−	0.0216920i
$176$	−31.0861	−	22.5854i	−2.34321	−	1.70244i
$177$	1.39608	−	4.29669i	0.104936	−	0.322959i
$178$	−2.91724	+	8.97835i	−0.218657	+	0.672956i
$179$	−5.31458	−	16.3566i	−0.397231	−	1.22255i	−0.927211	−	0.374540i	$-0.877801\pi$
$179$	−5.31458	−	16.3566i	−0.397231	−	1.22255i	0.529980	−	0.848010i	$-0.322199\pi$
$180$	11.2318			0.837172
$181$	−10.6819			−0.793976			−0.396988	−	0.917824i	$-0.629945\pi$
$181$	−10.6819			−0.793976			−0.396988	+	0.917824i	$0.629945\pi$
$182$	−2.54946	−	7.84643i	−0.188979	−	0.581616i
$183$	5.27448	−	3.83213i	0.389901	−	0.283279i
$184$	4.97811	+	3.61681i	0.366991	+	0.266634i
$185$	−13.3845			−0.984046
$186$	−12.7629	−	8.11876i	−0.935822	−	0.595296i
$187$	−4.48044			−0.327642
$188$	−8.58432	−	6.23688i	−0.626076	−	0.454871i
$189$	−0.379703	+	0.275871i	−0.0276193	+	0.0200666i
$190$	−10.6656	−	32.8254i	−0.773764	−	2.38140i
$191$	3.75799			0.271919			0.135959	−	0.990714i	$-0.456588\pi$
$191$	3.75799			0.271919			0.135959	+	0.990714i	$0.456588\pi$
$192$	26.4570			1.90937
$193$	5.60121	+	17.2388i	0.403184	+	1.24087i	0.922402	+	0.386231i	$0.126223\pi$
$193$	5.60121	+	17.2388i	0.403184	+	1.24087i	−0.519218	+	0.854642i	$0.673777\pi$
$194$	−2.14658	+	6.60651i	−0.154116	+	0.474319i
$195$	−4.17358	+	12.8450i	−0.298876	+	0.919846i
$196$	29.5135	+	21.4428i	2.10810	+	1.53163i
$197$	6.57970	+	20.2502i	0.468785	+	1.44277i	0.854160	+	0.520011i	$0.174072\pi$
$197$	6.57970	+	20.2502i	0.468785	+	1.44277i	−0.385375	+	0.922760i	$0.625928\pi$
$198$	−5.95088	−	4.32357i	−0.422911	−	0.307263i
$199$	5.09768	−	3.70368i	0.361365	−	0.262547i	−0.392256	−	0.919856i	$-0.628305\pi$
$199$	5.09768	−	3.70368i	0.361365	−	0.262547i	0.753621	+	0.657309i	$0.228305\pi$
$200$	−1.82468	+	5.61579i	−0.129024	+	0.397096i
$201$	6.99140	−	5.07955i	0.493135	−	0.358284i
$202$	−8.67801	+	6.30494i	−0.610583	+	0.443614i
$203$	0.485308	−	1.49362i	0.0340619	−	0.104832i
$204$	7.20375	−	5.23383i	0.504363	−	0.366441i
$205$	9.57659	+	6.95780i	0.668858	+	0.485954i
$206$	−5.62381	−	17.3083i	−0.391829	−	1.20593i
$207$	0.541983	+	0.393773i	0.0376704	+	0.0273691i
$208$	−28.3757	+	87.3315i	−1.96750	+	6.05535i
$209$	−5.09217	+	15.6721i	−0.352233	+	1.08406i
$210$	0.822474	+	2.53131i	0.0567561	+	0.174677i
$211$	14.6074			1.00562			0.502808	−	0.864398i	$-0.332300\pi$
$211$	14.6074			1.00562			0.502808	+	0.864398i	$0.332300\pi$
$212$	13.4554			0.924118
$213$	2.71702	+	8.36213i	0.186167	+	0.572964i
$214$	−21.5227	+	15.6372i	−1.47126	+	1.06894i
$215$	−8.44716	−	6.13722i	−0.576091	−	0.418555i
$216$	9.18499			0.624960
$217$	0.652576	−	2.53037i	0.0442998	−	0.171773i
$218$	−1.63279			−0.110587
$219$	−0.147791	−	0.107376i	−0.00998678	−	0.00725582i
$220$	−24.6025	+	17.8748i	−1.65870	+	1.20512i
$221$	3.30871	+	10.1832i	0.222568	+	0.684994i
$222$	−17.4202			−1.16917
$223$	14.0716			0.942307			0.471154	−	0.882051i	$-0.343838\pi$
$223$	14.0716			0.942307			0.471154	+	0.882051i	$0.343838\pi$
$224$	2.92765	+	9.01037i	0.195612	+	0.602031i
$225$	−0.198659	+	0.611410i	−0.0132439	+	0.0407606i
$226$	14.4310	−	44.4141i	0.959936	−	2.95438i
$227$	−15.5025	−	11.2632i	−1.02894	−	0.747567i	−0.0608421	−	0.998147i	$-0.519379\pi$
$227$	−15.5025	−	11.2632i	−1.02894	−	0.747567i	−0.968096	+	0.250580i	$0.919379\pi$
$228$	−10.1201	−	31.1463i	−0.670217	−	2.06272i
$229$	−14.8650	−	10.8000i	−0.982306	−	0.713687i	−0.0240834	−	0.999710i	$-0.507667\pi$
$229$	−14.8650	−	10.8000i	−0.982306	−	0.713687i	−0.958223	+	0.286023i	$0.907667\pi$
$230$	3.07354	−	2.23306i	0.202663	−	0.147243i
$231$	0.392681	−	1.20855i	0.0258365	−	0.0795166i
$232$	−24.8648	+	18.0653i	−1.63245	+	1.18605i
$233$	−3.46572	+	2.51800i	−0.227047	+	0.164959i	−0.695493	−	0.718533i	$-0.744814\pi$
$233$	−3.46572	+	2.51800i	−0.227047	+	0.164959i	0.468446	+	0.883492i	$0.344814\pi$
$234$	−5.43203	+	16.7181i	−0.355103	+	1.09289i
$235$	−3.33009	+	2.41945i	−0.217231	+	0.157827i
$236$	−19.6669	−	14.2888i	−1.28021	−	0.930124i
$237$	0.0403226	+	0.124100i	0.00261924	+	0.00806118i
$238$	1.70706	+	1.24025i	0.110652	+	0.0803934i
$239$	1.14221	−	3.51535i	0.0738832	−	0.227389i	−0.907295	−	0.420496i	$-0.861856\pi$
$239$	1.14221	−	3.51535i	0.0738832	−	0.227389i	0.981178	+	0.193106i	$0.0618562\pi$
$240$	9.15421	−	28.1738i	0.590902	−	1.81861i
$241$	1.70680	+	5.25299i	0.109945	+	0.338375i	0.990859	−	0.134901i	$-0.0430716\pi$
$241$	1.70680	+	5.25299i	0.109945	+	0.338375i	−0.880915	+	0.473275i	$0.843072\pi$
$242$	−9.96885			−0.640822
$243$	1.00000			0.0641500
$244$	−10.8406	−	33.3641i	−0.694001	−	2.13592i
$245$	11.4491	−	8.31822i	0.731453	−	0.531432i
$246$	12.4642	+	9.05576i	0.794688	+	0.577374i
$247$	39.3800			2.50569
$248$	−39.4388	+	32.5556i	−2.50437	+	2.06728i
$249$	8.47313			0.536963
$250$	25.8888	+	18.8093i	1.63735	+	1.18960i
$251$	−7.95940	+	5.78284i	−0.502393	+	0.365010i	−0.809930	−	0.586526i	$-0.800495\pi$
$251$	−7.95940	+	5.78284i	−0.502393	+	0.365010i	0.307537	+	0.951536i	$0.400495\pi$
$252$	0.780404	+	2.40184i	0.0491609	+	0.151302i
$253$	−1.81384			−0.114035
$254$	−2.10467			−0.132059
$255$	−1.06741	−	3.28516i	−0.0668440	−	0.205725i
$256$	10.0986	−	31.0804i	0.631165	−	1.94253i
$257$	−9.26584	+	28.5173i	−0.577987	+	1.77886i	0.0477869	+	0.998858i	$0.484783\pi$
$257$	−9.26584	+	28.5173i	−0.577987	+	1.77886i	−0.625774	+	0.780004i	$0.715217\pi$
$258$	−10.9942	−	7.98775i	−0.684469	−	0.497296i
$259$	−0.929972	−	2.86216i	−0.0577857	−	0.177846i
$260$	58.7942	+	42.7165i	3.64626	+	2.64917i
$261$	−2.70711	+	1.96683i	−0.167566	+	0.121744i
$262$	2.05088	−	6.31196i	0.126704	−	0.389954i
$263$	25.7355	−	18.6980i	1.58692	−	1.15297i	0.678749	−	0.734370i	$-0.262523\pi$
$263$	25.7355	−	18.6980i	1.58692	−	1.15297i	0.908173	−	0.418596i	$-0.137477\pi$
$264$	−20.1190	+	14.6173i	−1.23824	+	0.899635i
$265$	1.61297	−	4.96422i	0.0990841	−	0.304950i
$266$	6.27838	−	4.56151i	0.384952	−	0.279684i
$267$	2.81122	+	2.04247i	0.172044	+	0.124997i
$268$	−14.3694	−	44.2246i	−0.877753	−	2.70145i
$269$	11.3809	+	8.26869i	0.693904	+	0.504151i	0.877941	−	0.478768i	$-0.158917\pi$
$269$	11.3809	+	8.26869i	0.693904	+	0.504151i	−0.184037	+	0.982919i	$0.558917\pi$
$270$	1.75241	−	5.39336i	0.106648	−	0.328230i
$271$	−0.222994	+	0.686304i	−0.0135459	+	0.0416900i	−0.957601	−	0.288098i	$-0.906977\pi$
$271$	−0.222994	+	0.686304i	−0.0135459	+	0.0416900i	0.944055	+	0.329788i	$0.106977\pi$
$272$	−7.25723	−	22.3355i	−0.440034	−	1.35429i
$273$	−3.03678			−0.183794
$274$	46.2871			2.79630
$275$	−0.537872	−	1.65540i	−0.0324349	−	0.0998243i
$276$	2.91633	−	2.11883i	0.175542	−	0.127539i
$277$	7.80502	+	5.67068i	0.468958	+	0.340718i	0.797035	−	0.603933i	$-0.206401\pi$
$277$	7.80502	+	5.67068i	0.468958	+	0.340718i	−0.328077	+	0.944651i	$0.606401\pi$
$278$	31.5061			1.88961
$279$	−4.29383	+	3.54443i	−0.257065	+	0.212200i
$280$	8.99840			0.537758
$281$	−10.1685	−	7.38784i	−0.606601	−	0.440722i	0.241615	−	0.970372i	$-0.422323\pi$
$281$	−10.1685	−	7.38784i	−0.606601	−	0.440722i	−0.848216	+	0.529651i	$0.822323\pi$
$282$	−4.33420	+	3.14898i	−0.258098	+	0.187519i
$283$	−8.01923	−	24.6806i	−0.476694	−	1.46711i	−0.843660	−	0.536878i	$-0.819604\pi$
$283$	−8.01923	−	24.6806i	−0.476694	−	1.46711i	0.366967	−	0.930234i	$-0.380396\pi$
$284$	47.3109			2.80739
$285$	−12.7043			−0.752536
$286$	−14.7073	−	45.2644i	−0.869660	−	2.67654i
$287$	−0.822474	+	2.53131i	−0.0485491	+	0.149419i
$288$	6.23781	−	19.1980i	0.367567	−	1.13125i
$289$	11.5379	+	8.38274i	0.678698	+	0.493103i
$290$	5.86386	+	18.0471i	0.344338	+	1.05976i
$291$	2.06857	+	1.50290i	0.121262	+	0.0881017i
$292$	−0.795240	+	0.577776i	−0.0465379	+	0.0338118i
$293$	−1.19039	+	3.66363i	−0.0695432	+	0.214032i	−0.979788	−	0.200039i	$-0.935893\pi$
$293$	−1.19039	+	3.66363i	−0.0695432	+	0.214032i	0.910245	+	0.414070i	$0.135893\pi$
$294$	14.9012	−	10.8264i	0.869058	−	0.631408i
$295$	−7.62931	+	5.54302i	−0.444196	+	0.322727i
$296$	−18.1996	+	56.0127i	−1.05783	+	3.25567i
$297$	−2.19042	+	1.59144i	−0.127101	+	0.0923445i
$298$	−38.1806	−	27.7398i	−2.21174	−	1.60693i
$299$	1.33948	+	4.12250i	0.0774641	+	0.238410i
$300$	2.79856	+	2.03327i	0.161575	+	0.117391i
$301$	0.725474	−	2.23278i	0.0418156	−	0.128695i
$302$	3.67946	−	11.3242i	0.211729	−	0.651636i
$303$	1.22009	+	3.75505i	0.0700923	+	0.215722i
$304$	−86.3751			−4.95395
$305$	−13.6089			−0.779241
$306$	−1.38927	−	4.27572i	−0.0794191	−	0.244427i
$307$	10.0638	−	7.31179i	0.574372	−	0.417306i	−0.262319	−	0.964981i	$-0.584487\pi$
$307$	10.0638	−	7.31179i	0.574372	−	0.417306i	0.836691	+	0.547675i	$0.184487\pi$
$308$	−5.53179	−	4.01908i	−0.315203	−	0.229008i
$309$	−6.69877			−0.381080
$310$	11.5919	+	29.3695i	0.658374	+	1.66807i
$311$	−5.77766			−0.327621			−0.163810	−	0.986492i	$-0.552379\pi$
$311$	−5.77766			−0.327621			−0.163810	+	0.986492i	$0.552379\pi$
$312$	48.0798	+	34.9320i	2.72198	+	1.97764i
$313$	17.6783	−	12.8441i	0.999238	−	0.725989i	0.0373134	−	0.999304i	$-0.488120\pi$
$313$	17.6783	−	12.8441i	0.999238	−	0.725989i	0.961925	+	0.273315i	$0.0881200\pi$
$314$	8.40151	+	25.8572i	0.474125	+	1.45921i
$315$	0.979686			0.0551990
$316$	0.702129			0.0394979
$317$	−4.53975	−	13.9719i	−0.254978	−	0.784740i	−0.993834	−	0.110877i	$-0.964634\pi$
$317$	−4.53975	−	13.9719i	−0.254978	−	0.784740i	0.738857	−	0.673863i	$-0.235366\pi$
$318$	2.09933	−	6.46106i	0.117724	−	0.362318i
$319$	2.79963	−	8.61638i	0.156749	−	0.482425i
$320$	−44.6785	−	32.4609i	−2.49761	−	1.81462i
$321$	3.02600	+	9.31308i	0.168895	+	0.519805i
$322$	0.691075	+	0.502095i	0.0385121	+	0.0279807i
$323$	−8.14813	+	5.91996i	−0.453374	+	0.329395i
$324$	1.66277	−	5.11749i	0.0923763	−	0.284305i
$325$	−3.36519	+	2.44495i	−0.186667	+	0.135622i
$326$	54.2201	−	39.3932i	3.00297	−	2.18179i
$327$	−0.185721	+	0.571590i	−0.0102704	+	0.0316090i
$328$	42.1395	−	30.6162i	2.32677	−	1.69049i
$329$	−0.748759	−	0.544005i	−0.0412804	−	0.0299920i
$330$	4.74467	+	14.6026i	0.261186	+	0.803847i
$331$	−11.3031	−	8.21220i	−0.621276	−	0.451383i	0.232091	−	0.972694i	$-0.425443\pi$
$331$	−11.3031	−	8.21220i	−0.621276	−	0.451383i	−0.853367	+	0.521311i	$0.825443\pi$
$332$	14.0889	−	43.3612i	0.773229	−	2.37975i
$333$	−1.98145	+	6.09828i	−0.108583	+	0.334184i
$334$	18.7538	+	57.7183i	1.02616	+	3.15820i
$335$	−18.0388			−0.985562
$336$	6.66078			0.363375
$337$	−2.89952	−	8.92381i	−0.157947	−	0.486111i	0.840500	−	0.541811i	$-0.182261\pi$
$337$	−2.89952	−	8.92381i	−0.157947	−	0.486111i	−0.998448	+	0.0556997i	$0.982261\pi$
$338$	−63.4431	+	46.0941i	−3.45085	+	2.50719i
$339$	−13.9065	−	10.1037i	−0.755299	−	0.548757i
$340$	−18.5866			−1.00800
$341$	3.76457	−	14.5972i	0.203863	−	0.790481i
$342$	−16.5350			−0.894108
$343$	5.23220	+	3.80142i	0.282512	+	0.205257i
$344$	−37.1697	+	27.0054i	−2.00406	+	1.45603i
$345$	−0.432126	−	1.32995i	−0.0232649	−	0.0716019i
$346$	−35.0339			−1.88344
$347$	−17.5300			−0.941059			−0.470529	−	0.882384i	$-0.655937\pi$
$347$	−17.5300			−0.941059			−0.470529	+	0.882384i	$0.655937\pi$
$348$	5.56392	+	17.1240i	0.298258	+	0.917943i
$349$	−6.76403	+	20.8175i	−0.362070	+	1.11434i	0.589725	+	0.807604i	$0.299236\pi$
$349$	−6.76403	+	20.8175i	−0.362070	+	1.11434i	−0.951796	+	0.306733i	$0.900764\pi$
$350$	−0.253307	+	0.779600i	−0.0135399	+	0.0416714i
$351$	5.23460	+	3.80316i	0.279403	+	0.202998i
$352$	16.8890	+	51.9789i	0.900184	+	2.77048i
$353$	−18.0235	−	13.0948i	−0.959292	−	0.696966i	−0.00630570	−	0.999980i	$-0.502007\pi$
$353$	−18.0235	−	13.0948i	−0.959292	−	0.696966i	−0.952986	+	0.303014i	$0.902007\pi$
$354$	−9.92975	+	7.21439i	−0.527760	+	0.383440i
$355$	5.67144	−	17.4549i	0.301009	−	0.926409i
$356$	15.1267	−	10.9902i	0.801716	−	0.582481i
$357$	0.628340	−	0.456516i	0.0332553	−	0.0241614i
$358$	−14.4385	+	44.4372i	−0.763099	+	2.34858i
$359$	26.6808	−	19.3847i	1.40816	−	1.02309i	0.414571	−	0.910017i	$-0.363932\pi$
$359$	26.6808	−	19.3847i	1.40816	−	1.02309i	0.993587	−	0.113070i	$-0.0360683\pi$
$360$	−15.5109	−	11.2693i	−0.817495	−	0.593945i
$361$	5.57542	+	17.1594i	0.293443	+	0.903126i
$362$	23.4778	+	17.0576i	1.23397	+	0.896529i
$363$	−1.13390	+	3.48978i	−0.0595142	+	0.183166i
$364$	−5.04947	+	15.5407i	−0.264664	+	0.814553i
$365$	0.117834	+	0.362657i	0.00616773	+	0.0189823i
$366$	−17.7123			−0.925837
$367$	2.73812			0.142928			0.0714642	−	0.997443i	$-0.477233\pi$
$367$	2.73812			0.142928			0.0714642	+	0.997443i	$0.477233\pi$
$368$	−2.93798	−	9.04217i	−0.153153	−	0.471355i
$369$	4.58787	−	3.33328i	0.238835	−	0.173524i
$370$	29.4179	+	21.3734i	1.52936	+	1.11115i
$371$	1.17363			0.0609318
$372$	10.9989	+	27.8672i	0.570269	+	1.44485i
$373$	17.8820			0.925897			0.462949	−	0.886385i	$-0.346791\pi$
$373$	17.8820			0.925897			0.462949	+	0.886385i	$0.346791\pi$
$374$	9.84763	+	7.15472i	0.509209	+	0.369962i
$375$	9.52924	−	6.92339i	0.492088	−	0.357523i
$376$	5.59705	+	17.2259i	0.288646	+	0.888360i
$377$	−21.6508			−1.11507
$378$	1.27509			0.0655834
$379$	−3.88233	−	11.9486i	−0.199422	−	0.613757i	−0.999896	−	0.0143907i	$-0.995419\pi$
$379$	−3.88233	−	11.9486i	−0.199422	−	0.613757i	0.800475	−	0.599367i	$-0.204581\pi$
$380$	−21.1243	+	65.0140i	−1.08366	+	3.33515i
$381$	−0.239394	+	0.736779i	−0.0122645	+	0.0377463i
$382$	−8.25974	−	6.00105i	−0.422605	−	0.307041i
$383$	9.73665	+	29.9663i	0.497520	+	1.53121i	0.812993	+	0.582274i	$0.197837\pi$
$383$	9.73665	+	29.9663i	0.497520	+	1.53121i	−0.315473	+	0.948935i	$0.602163\pi$
$384$	−25.4887	−	18.5186i	−1.30071	−	0.945025i
$385$	−2.14593	+	1.55911i	−0.109367	+	0.0794595i
$386$	15.2172	−	46.8338i	0.774536	−	2.38378i
$387$	−4.04679	+	2.94016i	−0.205710	+	0.149457i
$388$	11.1307	−	8.08689i	0.565073	−	0.410550i
$389$	−3.58348	+	11.0288i	−0.181690	+	0.559183i	−0.999876	−	0.0157703i	$-0.994980\pi$
$389$	−3.58348	+	11.0288i	−0.181690	+	0.559183i	0.818186	+	0.574954i	$0.194980\pi$
$390$	29.6850	−	21.5674i	1.50316	−	1.09211i
$391$	−0.896883	−	0.651623i	−0.0453573	−	0.0329540i
$392$	−19.2430	−	59.2239i	−0.971919	−	2.99126i
$393$	−1.97634	−	1.43590i	−0.0996934	−	0.0724315i
$394$	17.8756	−	55.0153i	0.900557	−	2.77163i
$395$	0.0841683	−	0.259044i	0.00423497	−	0.0130339i
$396$	4.50198	+	13.8557i	0.226233	+	0.696274i
$397$	1.25151			0.0628114			0.0314057	−	0.999507i	$-0.490002\pi$
$397$	1.25151			0.0628114			0.0314057	+	0.999507i	$0.490002\pi$
$398$	−17.1186			−0.858077
$399$	−0.882712	−	2.71671i	−0.0441909	−	0.136005i
$400$	7.38112	−	5.36269i	0.369056	−	0.268135i
$401$	22.7657	+	16.5403i	1.13687	+	0.825982i	0.986680	−	0.162676i	$-0.0520125\pi$
$401$	22.7657	+	16.5403i	1.13687	+	0.825982i	0.150187	+	0.988658i	$0.452012\pi$
$402$	−23.4779			−1.17097
$403$	−35.9566	+	2.22358i	−1.79112	+	0.110764i
$404$	21.2452			1.05699
$405$	−1.68872	−	1.22693i	−0.0839132	−	0.0609665i
$406$	−3.45180	+	2.50788i	−0.171310	+	0.124464i
$407$	−5.36481	−	16.5112i	−0.265924	−	0.818428i
$408$	−15.1995			−0.752487
$409$	−22.1853			−1.09699			−0.548495	−	0.836154i	$-0.684799\pi$
$409$	−22.1853			−1.09699			−0.548495	+	0.836154i	$0.684799\pi$
$410$	−9.93777	−	30.5853i	−0.490791	−	1.51050i
$411$	5.26488	−	16.2036i	0.259698	−	0.799267i
$412$	−11.1385	+	34.2809i	−0.548756	+	1.68890i
$413$	−1.71543	−	1.24633i	−0.0844106	−	0.0613279i
$414$	−0.562423	−	1.73096i	−0.0276416	−	0.0850721i
$415$	−14.3087	−	10.3959i	−0.702389	−	0.510315i
$416$	105.666	−	76.7706i	5.18068	−	3.76399i
$417$	3.58364	−	11.0293i	0.175492	−	0.540107i
$418$	36.2186	−	26.3143i	1.77151	−	1.28708i
$419$	−9.72113	+	7.06281i	−0.474908	+	0.345041i	−0.799351	−	0.600864i	$-0.794823\pi$
$419$	−9.72113	+	7.06281i	−0.474908	+	0.345041i	0.324443	+	0.945905i	$0.394823\pi$
$420$	1.62900	−	5.01353i	0.0794868	−	0.244635i
$421$	−25.3245	+	18.3993i	−1.23424	+	0.896728i	−0.997201	−	0.0747716i	$-0.976177\pi$
$421$	−25.3245	+	18.3993i	−1.23424	+	0.896728i	−0.237040	+	0.971500i	$0.576177\pi$
$422$	−32.1058	−	23.3263i	−1.56289	−	1.13550i
$423$	0.609369	+	1.87544i	0.0296285	+	0.0911872i
$424$	−18.5815	−	13.5003i	−0.902398	−	0.655630i
$425$	0.328745	−	1.01177i	0.0159465	−	0.0490781i
$426$	7.38153	−	22.7180i	0.357636	−	1.10069i
$427$	−0.945564	−	2.91015i	−0.0457590	−	0.140832i
$428$	52.6911			2.54692
$429$	−17.5185			−0.845801
$430$	8.76574	+	26.9782i	0.422721	+	1.30100i
$431$	21.8984	−	15.9101i	1.05481	−	0.766364i	0.0816883	−	0.996658i	$-0.473969\pi$
$431$	21.8984	−	15.9101i	1.05481	−	0.766364i	0.973121	+	0.230294i	$0.0739688\pi$
$432$	−11.4814	−	8.34175i	−0.552401	−	0.401343i
$433$	−7.30272			−0.350946			−0.175473	−	0.984484i	$-0.556146\pi$
$433$	−7.30272			−0.350946			−0.175473	+	0.984484i	$0.556146\pi$
$434$	−5.47501	+	4.51946i	−0.262809	+	0.216941i
$435$	6.98471			0.334891
$436$	2.61630	+	1.90085i	0.125298	+	0.0910342i
$437$	−3.29864	+	2.39660i	−0.157795	+	0.114645i
$438$	0.153365	+	0.472008i	0.00732805	+	0.0225534i
$439$	2.44245			0.116572			0.0582858	−	0.998300i	$-0.481437\pi$
$439$	2.44245			0.116572			0.0582858	+	0.998300i	$0.481437\pi$
$440$	51.9098			2.47470
$441$	−2.09505	−	6.44790i	−0.0997642	−	0.307043i
$442$	8.98901	−	27.6653i	0.427564	−	1.31591i
$443$	6.65277	−	20.4751i	0.316082	−	0.972802i	−0.659224	−	0.751946i	$-0.729115\pi$
$443$	6.65277	−	20.4751i	0.316082	−	0.972802i	0.975307	−	0.220855i	$-0.0708848\pi$
$444$	27.9132	+	20.2801i	1.32470	+	0.962452i
$445$	−2.24140	−	6.89832i	−0.106253	−	0.327012i
$446$	−30.9283	−	22.4707i	−1.46450	−	1.06402i
$447$	−14.0537	+	10.2106i	−0.664716	+	0.482944i
$448$	3.83716	−	11.8096i	0.181289	−	0.557950i
$449$	−26.2296	+	19.0569i	−1.23785	+	0.899351i	−0.997453	−	0.0713242i	$-0.977278\pi$
$449$	−26.2296	+	19.0569i	−1.23785	+	0.899351i	−0.240397	+	0.970675i	$0.577278\pi$
$450$	1.41298	−	1.02659i	0.0666086	−	0.0483940i
$451$	−4.74467	+	14.6026i	−0.223418	+	0.687609i
$452$	−74.8289	+	54.3664i	−3.51966	+	2.55718i
$453$	−3.54574	−	2.57613i	−0.166593	−	0.121037i
$454$	16.0872	+	49.5113i	0.755009	+	2.32368i
$455$	5.12827	+	3.72590i	0.240417	+	0.174673i
$456$	−17.2747	+	53.1661i	−0.808963	+	2.48973i
$457$	10.1120	−	31.1216i	0.473020	−	1.45581i	−0.375590	−	0.926786i	$-0.622560\pi$
$457$	10.1120	−	31.1216i	0.473020	−	1.45581i	0.848610	−	0.529020i	$-0.177440\pi$
$458$	15.4256	+	47.4752i	0.720792	+	2.21837i
$459$	−1.65482			−0.0772403
$460$	−7.52451			−0.350832
$461$	10.1375	+	31.1999i	0.472149	+	1.45313i	0.849764	+	0.527163i	$0.176744\pi$
$461$	10.1375	+	31.1999i	0.472149	+	1.45313i	−0.377615	+	0.925963i	$0.623256\pi$
$462$	−2.79298	+	2.02922i	−0.129941	+	0.0944078i
$463$	23.8018	+	17.2930i	1.10617	+	0.803676i	0.982055	−	0.188592i	$-0.0603925\pi$
$463$	23.8018	+	17.2930i	1.10617	+	0.803676i	0.124110	+	0.992268i	$0.460392\pi$
$464$	47.4883			2.20459
$465$	11.5998	−	0.717341i	0.537930	−	0.0332659i
$466$	11.6383			0.539134
$467$	−6.12463	−	4.44980i	−0.283414	−	0.205912i	0.436991	−	0.899466i	$-0.356044\pi$
$467$	−6.12463	−	4.44980i	−0.283414	−	0.205912i	−0.720405	+	0.693554i	$0.756044\pi$
$468$	28.1666	−	20.4642i	1.30200	−	0.945960i
$469$	−1.25336	−	3.85744i	−0.0578747	−	0.178120i
$470$	11.1828			0.515825
$471$	10.0074			0.461118
$472$	12.8230	+	39.4651i	0.590225	+	1.81653i
$473$	4.18510	−	12.8804i	0.192431	−	0.592242i
$474$	0.109547	−	0.337152i	0.00503168	−	0.0154859i
$475$	−3.16543	−	2.29982i	−0.145240	−	0.105523i
$476$	−1.29143	−	3.97461i	−0.0591925	−	0.182176i
$477$	−2.02303	−	1.46982i	−0.0926282	−	0.0672983i
$478$	−8.12406	+	5.90248i	−0.371586	+	0.269973i
$479$	−1.22601	+	3.77328i	−0.0560180	+	0.172406i	−0.975151	−	0.221542i	$-0.928891\pi$
$479$	−1.22601	+	3.77328i	−0.0560180	+	0.172406i	0.919133	+	0.393948i	$0.128891\pi$
$480$	−34.0885	+	24.7667i	−1.55592	+	1.13044i
$481$	−33.5649	+	24.3863i	−1.53043	+	1.11192i
$482$	4.63698	−	14.2712i	0.211209	−	0.650034i
$483$	0.254374	−	0.184813i	0.0115744	−	0.00840929i
$484$	15.9735	+	11.6054i	0.726068	+	0.527520i
$485$	−1.64928	−	5.07597i	−0.0748900	−	0.230488i
$486$	−2.19791	−	1.59688i	−0.0996994	−	0.0724359i
$487$	−8.98193	+	27.6435i	−0.407010	+	1.25265i	0.512195	+	0.858869i	$0.328832\pi$
$487$	−8.98193	+	27.6435i	−0.407010	+	1.25265i	−0.919205	+	0.393779i	$0.871168\pi$
$488$	−18.5047	+	56.9518i	−0.837670	+	2.57808i
$489$	−7.62310	−	23.4615i	−0.344729	−	1.06097i
$490$	−38.4472			−1.73687
$491$	−0.108367			−0.00489053			−0.00244527	−	0.999997i	$-0.500778\pi$
$491$	−0.108367			−0.00489053			−0.00244527	+	0.999997i	$0.500778\pi$
$492$	−9.42945	−	29.0209i	−0.425112	−	1.30836i
$493$	4.47977	−	3.25475i	0.201759	−	0.146586i
$494$	−86.5540	−	62.8851i	−3.89425	−	2.82934i
$495$	5.65159			0.254020
$496$	78.8661	−	4.87713i	3.54119	−	0.218990i
$497$	4.12665			0.185105
$498$	−18.6232	−	13.5306i	−0.834526	−	0.606319i
$499$	3.17651	−	2.30787i	0.142200	−	0.103314i	−0.514411	−	0.857544i	$-0.671989\pi$
$499$	3.17651	−	2.30787i	0.142200	−	0.103314i	0.656611	+	0.754229i	$0.271989\pi$
$500$	−19.5854	−	60.2778i	−0.875888	−	2.69571i
$501$	22.3385			0.998010
$502$	26.7286			1.19295
$503$	5.91537	+	18.2056i	0.263753	+	0.811749i	0.991978	+	0.126411i	$0.0403458\pi$
$503$	5.91537	+	18.2056i	0.263753	+	0.811749i	−0.728225	+	0.685339i	$0.759654\pi$
$504$	1.33213	−	4.09989i	0.0593380	−	0.182623i
$505$	2.54678	−	7.83819i	0.113330	−	0.348795i
$506$	3.98666	+	2.89648i	0.177229	+	0.128764i
$507$	8.91982	+	27.4524i	0.396143	+	1.21920i
$508$	3.37240	+	2.45019i	0.149626	+	0.108710i
$509$	33.3561	−	24.2346i	1.47848	−	1.07418i	0.500441	−	0.865770i	$-0.333171\pi$
$509$	33.3561	−	24.2346i	1.47848	−	1.07418i	0.978041	−	0.208410i	$-0.0668289\pi$
$510$	−2.89992	+	8.92503i	−0.128411	+	0.395207i
$511$	−0.0693640	+	0.0503959i	−0.00306848	+	0.00222938i
$512$	−20.8502	+	15.1486i	−0.921459	+	0.669479i
$513$	−1.88075	+	5.78837i	−0.0830374	+	0.255563i
$514$	65.9042	−	47.8822i	2.90691	−	2.11199i
$515$	11.3123	+	8.21890i	0.498482	+	0.362168i
$516$	8.31737	+	25.5982i	0.366152	+	1.12690i
$517$	−4.31943	−	3.13825i	−0.189968	−	0.138020i
$518$	−2.52652	+	7.77584i	−0.111009	+	0.341651i
$519$	−3.98491	+	12.2643i	−0.174918	+	0.538342i
$520$	−38.3343	−	117.981i	−1.68107	−	5.17380i
$521$	15.7725			0.691006			0.345503	−	0.938418i	$-0.387708\pi$
$521$	15.7725			0.691006			0.345503	+	0.938418i	$0.387708\pi$
$522$	9.09078			0.397893
$523$	2.15849	+	6.64315i	0.0943842	+	0.290485i	0.987093	−	0.160150i	$-0.0511978\pi$
$523$	2.15849	+	6.64315i	0.0943842	+	0.290485i	−0.892709	+	0.450635i	$0.851198\pi$
$524$	−10.6344	+	7.72635i	−0.464566	+	0.337527i
$525$	0.244101	+	0.177350i	0.0106535	+	0.00774019i
$526$	−86.4229			−3.76822
$527$	7.10551	−	5.86539i	0.309521	−	0.255501i
$528$	38.4246			1.67221
$529$	18.2443	+	13.2553i	0.793231	+	0.576316i
$530$	−11.4724	+	8.33521i	−0.498330	+	0.362058i
$531$	1.39608	+	4.29669i	0.0605847	+	0.186460i
$532$	−15.3705			−0.666395
$533$	36.6927			1.58934
$534$	−2.91724	−	8.97835i	−0.126241	−	0.388531i
$535$	6.31640	−	19.4399i	0.273082	−	0.840459i
$536$	−24.5283	+	75.4904i	−1.05946	+	3.26069i
$537$	13.9138	+	10.1089i	0.600423	+	0.436233i
$538$	−11.8101	−	36.3477i	−0.509169	−	1.56706i
$539$	14.8505	+	10.7895i	0.639655	+	0.464736i
$540$	−9.08675	+	6.60191i	−0.391031	+	0.284101i
$541$	−7.10668	+	21.8721i	−0.305540	+	0.940356i	0.673935	+	0.738791i	$0.264603\pi$
$541$	−7.10668	+	21.8721i	−0.305540	+	0.940356i	−0.979475	+	0.201565i	$0.935397\pi$
$542$	1.58607	−	1.15234i	0.0681273	−	0.0494974i
$543$	8.64181	−	6.27864i	0.370855	−	0.269442i
$544$	−10.3224	+	31.7692i	−0.442571	+	1.36209i
$545$	1.01493	−	0.737390i	0.0434748	−	0.0315863i
$546$	6.67458	+	4.84936i	0.285645	+	0.207534i
$547$	2.16030	+	6.64872i	0.0923678	+	0.284279i	0.986559	−	0.163407i	$-0.0522483\pi$
$547$	2.16030	+	6.64872i	0.0923678	+	0.284279i	−0.894191	+	0.447686i	$0.852248\pi$
$548$	−74.1677	−	53.8860i	−3.16829	−	2.30190i
$549$	−2.01467	+	6.20052i	−0.0859841	+	0.264632i
$550$	−1.46128	+	4.49734i	−0.0623090	+	0.191767i
$551$	−6.29333	−	19.3689i	−0.268105	−	0.825141i
$552$	−6.15328			−0.261901
$553$	0.0612425			0.00260430
$554$	−8.09938	−	24.9273i	−0.344110	−	1.05906i
$555$	10.8283	−	7.86719i	0.459634	−	0.333944i
$556$	−50.4836	−	36.6785i	−2.14098	−	1.55551i
$557$	11.8384			0.501607			0.250804	−	0.968038i	$-0.419305\pi$
$557$	11.8384			0.501607			0.250804	+	0.968038i	$0.419305\pi$
$558$	15.0975	−	0.933639i	0.639128	−	0.0395241i
$559$	−32.3653			−1.36890
$560$	−11.2482	−	8.17229i	−0.475323	−	0.345342i
$561$	3.62475	−	2.63354i	0.153037	−	0.111188i
$562$	10.5520	+	32.4757i	0.445109	+	1.36990i
$563$	38.6718			1.62982			0.814910	−	0.579587i	$-0.196786\pi$
$563$	38.6718			1.62982			0.814910	+	0.579587i	$0.196786\pi$
$564$	10.6108			0.446796
$565$	11.0878	+	34.1246i	0.466465	+	1.43563i
$566$	−21.7864	+	67.0517i	−0.915751	+	2.81839i
$567$	0.145034	−	0.446368i	0.00609084	−	0.0187457i
$568$	−65.3352	−	47.4688i	−2.74140	−	1.99175i
$569$	−10.2914	−	31.6736i	−0.431437	−	1.32783i	−0.896694	−	0.442651i	$-0.854038\pi$
$569$	−10.2914	−	31.6736i	−0.431437	−	1.32783i	0.465257	−	0.885175i	$-0.345962\pi$
$570$	27.9229	+	20.2872i	1.16956	+	0.849737i
$571$	9.98443	−	7.25412i	0.417836	−	0.303575i	−0.358931	−	0.933364i	$-0.616859\pi$
$571$	9.98443	−	7.25412i	0.417836	−	0.303575i	0.776766	+	0.629789i	$0.216859\pi$
$572$	−29.1293	+	89.6507i	−1.21796	+	3.74849i
$573$	−3.04028	+	2.20889i	−0.127009	+	0.0922778i
$574$	5.84993	−	4.25022i	0.244171	−	0.177401i
$575$	0.133087	−	0.409600i	0.00555012	−	0.0170815i
$576$	−21.4042	+	15.5511i	−0.891841	+	0.647961i
$577$	31.8887	+	23.1685i	1.32754	+	0.964516i	0.999805	+	0.0197470i	$0.00628608\pi$
$577$	31.8887	+	23.1685i	1.32754	+	0.964516i	0.327737	+	0.944769i	$0.393714\pi$
$578$	−11.9730	−	36.8491i	−0.498011	−	1.53272i
$579$	−14.6642	−	10.6541i	−0.609422	−	0.442771i
$580$	11.6140	−	35.7442i	0.482244	−	1.48420i
$581$	1.22889	−	3.78213i	0.0509829	−	0.156909i
$582$	−2.14658	−	6.60651i	−0.0889788	−	0.273848i
$583$	6.77041			0.280402
$584$	1.67791			0.0694324
$585$	−4.17358	−	12.8450i	−0.172556	−	0.531074i
$586$	8.46675	−	6.15145i	0.349758	−	0.254114i
$587$	22.1555	+	16.0969i	0.914456	+	0.664391i	0.942138	−	0.335225i	$-0.108812\pi$
$587$	22.1555	+	16.0969i	0.914456	+	0.664391i	−0.0276816	+	0.999617i	$0.508812\pi$
$588$	−36.4806			−1.50444
$589$	−12.4409	−	31.5205i	−0.512616	−	1.29878i
$590$	25.6201			1.05476
$591$	−17.2259	−	12.5153i	−0.708578	−	0.514812i
$592$	73.6202	−	53.4882i	3.02577	−	2.19835i
$593$	4.10121	+	12.6222i	0.168416	+	0.518332i	0.999272	−	0.0381560i	$-0.0121484\pi$
$593$	4.10121	+	12.6222i	0.168416	+	0.518332i	−0.830855	+	0.556488i	$0.812148\pi$
$594$	7.35570			0.301808
$595$	−1.62120			−0.0664628
$596$	28.8845	+	88.8974i	1.18316	+	3.64138i
$597$	−1.94714	+	5.99268i	−0.0796911	+	0.245264i
$598$	3.63906	−	11.1999i	0.148812	−	0.457997i
$599$	−7.20130	−	5.23205i	−0.294237	−	0.213776i	0.430866	−	0.902416i	$-0.358208\pi$
$599$	−7.20130	−	5.23205i	−0.294237	−	0.213776i	−0.725103	+	0.688640i	$0.758208\pi$
$600$	−1.82468	−	5.61579i	−0.0744923	−	0.229264i
$601$	−20.3412	−	14.7788i	−0.829736	−	0.602839i	0.0897484	−	0.995964i	$-0.471394\pi$
$601$	−20.3412	−	14.7788i	−0.829736	−	0.602839i	−0.919485	+	0.393126i	$0.871394\pi$
$602$	−5.16001	+	3.74896i	−0.210306	+	0.152796i
$603$	−2.67048	+	8.21888i	−0.108750	+	0.334699i
$604$	−19.0791	+	13.8618i	−0.776317	+	0.564027i
$605$	6.19654	−	4.50205i	0.251925	−	0.183034i
$606$	3.31471	−	10.2016i	0.134651	−	0.414412i
$607$	−17.7911	+	12.9260i	−0.722118	+	0.524649i	−0.887060	−	0.461654i	$-0.847256\pi$
$607$	−17.7911	+	12.9260i	−0.722118	+	0.524649i	0.164942	+	0.986303i	$0.447256\pi$
$608$	99.3934	+	72.2135i	4.03093	+	2.92864i
$609$	0.485308	+	1.49362i	0.0196657	+	0.0605247i
$610$	29.9111	+	21.7317i	1.21107	+	0.879891i
$611$	−3.94281	+	12.1347i	−0.159509	+	0.490919i
$612$	−2.75159	+	8.46852i	−0.111226	+	0.342320i
$613$	11.0344	+	33.9605i	0.445677	+	1.37165i	0.881740	+	0.471736i	$0.156373\pi$
$613$	11.0344	+	33.9605i	0.445677	+	1.37165i	−0.436063	+	0.899916i	$0.643627\pi$
$614$	−33.7954			−1.36387
$615$	−11.8373			−0.477327
$616$	3.60677	+	11.1005i	0.145321	+	0.447252i
$617$	7.80776	−	5.67267i	0.314329	−	0.228373i	−0.419423	−	0.907791i	$-0.637768\pi$
$617$	7.80776	−	5.67267i	0.314329	−	0.228373i	0.733752	+	0.679418i	$0.237768\pi$
$618$	14.7233	+	10.6971i	0.592259	+	0.430301i
$619$	22.7986			0.916354			0.458177	−	0.888861i	$-0.348503\pi$
$619$	22.7986			0.916354			0.458177	+	0.888861i	$0.348503\pi$
$620$	15.6169	−	60.5549i	0.627191	−	2.43194i
$621$	−0.669927			−0.0268833
$622$	12.6988	+	9.22622i	0.509176	+	0.369938i
$623$	1.31941	−	0.958611i	0.0528612	−	0.0384059i
$624$	−28.3757	−	87.3315i	−1.13594	−	3.49606i
$625$	−21.3723			−0.854894
$626$	−59.3658			−2.37274
$627$	−5.09217	−	15.6721i	−0.203362	−	0.625883i
$628$	16.6401	−	51.2129i	0.664011	−	2.04362i
$629$	3.27894	−	10.0915i	0.130740	−	0.402376i
$630$	−2.15326	−	1.56444i	−0.0857881	−	0.0623287i
$631$	−4.97473	−	15.3106i	−0.198041	−	0.609507i	−0.999928	−	0.0120311i	$-0.996170\pi$
$631$	−4.97473	−	15.3106i	−0.198041	−	0.609507i	0.801887	−	0.597476i	$-0.203830\pi$
$632$	−0.969623	−	0.704472i	−0.0385695	−	0.0280224i
$633$	−11.8176	+	8.58602i	−0.469709	+	0.341264i
$634$	−12.3335	+	37.9585i	−0.489824	+	1.50752i
$635$	1.30824	−	0.950494i	0.0519161	−	0.0377192i
$636$	−10.8856	+	7.90886i	−0.431643	+	0.313607i
$637$	13.5557	−	41.7200i	0.537095	−	1.65301i
$638$	−19.9127	+	14.4674i	−0.788350	+	0.572770i
$639$	−7.11326	−	5.16808i	−0.281396	−	0.204446i
$640$	20.3223	+	62.5456i	0.803309	+	2.47233i
$641$	21.3851	+	15.5372i	0.844662	+	0.613683i	0.923669	−	0.383191i	$-0.125175\pi$
$641$	21.3851	+	15.5372i	0.844662	+	0.613683i	−0.0790073	+	0.996874i	$0.525175\pi$
$642$	8.22096	−	25.3015i	0.324455	−	0.998571i
$643$	−1.61222	+	4.96189i	−0.0635796	+	0.195678i	−0.977800	−	0.209538i	$-0.932804\pi$
$643$	−1.61222	+	4.96189i	−0.0635796	+	0.195678i	0.914221	+	0.405216i	$0.132804\pi$
$644$	−0.522814	−	1.60906i	−0.0206018	−	0.0634057i
$645$	10.4413			0.411124
$646$	27.3623			1.07656
$647$	11.9745	+	36.8539i	0.470768	+	1.44888i	0.851581	+	0.524223i	$0.175644\pi$
$647$	11.9745	+	36.8539i	0.470768	+	1.44888i	−0.380813	+	0.924652i	$0.624356\pi$
$648$	−7.43082	+	5.39880i	−0.291910	+	0.212085i
$649$	−9.89591	−	7.18980i	−0.388449	−	0.282224i
$650$	11.3007			0.443250
$651$	0.959372	+	2.43069i	0.0376007	+	0.0952663i
$652$	−132.740			−5.19848
$653$	−32.0208	−	23.2645i	−1.25307	−	0.910409i	−0.254674	−	0.967027i	$-0.581968\pi$
$653$	−32.0208	−	23.2645i	−1.25307	−	0.910409i	−0.998396	+	0.0566181i	$0.981968\pi$
$654$	1.32096	−	0.959733i	0.0516536	−	0.0375285i
$655$	1.57575	+	4.84966i	0.0615697	+	0.189492i
$656$	−80.4807			−3.14224
$657$	0.182679			0.00712700
$658$	0.776998	+	2.39135i	0.0302905	+	0.0932247i
$659$	−4.69375	+	14.4459i	−0.182843	+	0.562732i	−0.999905	−	0.0138182i	$-0.995601\pi$
$659$	−4.69375	+	14.4459i	−0.182843	+	0.562732i	0.817062	+	0.576550i	$0.195601\pi$
$660$	9.39731	−	28.9220i	0.365790	−	1.12579i
$661$	−4.92823	−	3.58057i	−0.191686	−	0.139268i	0.487803	−	0.872954i	$-0.337798\pi$
$661$	−4.92823	−	3.58057i	−0.191686	−	0.139268i	−0.679489	+	0.733686i	$0.737798\pi$
$662$	11.7294	+	36.0994i	0.455877	+	1.40304i
$663$	−8.66232	−	6.29354i	−0.336417	−	0.244421i
$664$	−62.9623	+	45.7448i	−2.44341	+	1.77524i
$665$	−1.84255	+	5.67078i	−0.0714510	+	0.219903i
$666$	14.0933	−	10.2394i	0.546103	−	0.396767i
$667$	1.81357	−	1.31763i	0.0702216	−	0.0510189i
$668$	37.1439	−	114.317i	1.43714	−	4.42306i
$669$	−11.3842	+	8.27111i	−0.440139	+	0.319779i
$670$	39.6476	+	28.8057i	1.53172	+	1.11286i
$671$	−5.45475	−	16.7880i	−0.210578	−	0.648093i
$672$	−7.66468	−	5.56872i	−0.295672	−	0.214818i
$673$	6.21198	−	19.1185i	0.239454	−	0.736964i	−0.757045	−	0.653362i	$-0.773358\pi$
$673$	6.21198	−	19.1185i	0.239454	−	0.736964i	0.996499	−	0.0836013i	$-0.0266422\pi$
$674$	−7.87734	+	24.2440i	−0.303424	+	0.933843i
$675$	−0.198659	−	0.611410i	−0.00764639	−	0.0235332i
$676$	155.319			5.97381
$677$	−17.1344			−0.658528			−0.329264	−	0.944238i	$-0.606801\pi$
$677$	−17.1344			−0.658528			−0.329264	+	0.944238i	$0.606801\pi$
$678$	14.4310	+	44.4141i	0.554219	+	1.70571i
$679$	0.970860	−	0.705371i	0.0372582	−	0.0270697i
$680$	25.6677	+	18.6487i	0.984311	+	0.715144i
$681$	19.1622			0.734296
$682$	−31.5841	+	26.0718i	−1.20942	+	0.998340i
$683$	−28.8142			−1.10255			−0.551273	−	0.834325i	$-0.685858\pi$
$683$	−28.8142			−1.10255			−0.551273	+	0.834325i	$0.685858\pi$
$684$	26.4947	+	19.2495i	1.01305	+	0.736023i
$685$	−28.7716	+	20.9038i	−1.09931	+	0.798693i
$686$	−5.42953	−	16.7104i	−0.207301	−	0.638006i
$687$	18.3741			0.701017
$688$	70.9891			2.70643
$689$	−4.99981	−	15.3878i	−0.190477	−	0.586229i
$690$	−1.17399	+	3.61316i	−0.0446929	+	0.137551i
$691$	−6.19598	+	19.0693i	−0.235706	+	0.725429i	0.761321	+	0.648375i	$0.224551\pi$
$691$	−6.19598	+	19.0693i	−0.235706	+	0.725429i	−0.997027	+	0.0770533i	$0.975449\pi$
$692$	56.1363	+	40.7854i	2.13398	+	1.55043i
$693$	0.392681	+	1.20855i	0.0149167	+	0.0459089i
$694$	38.5294	+	27.9933i	1.46256	+	1.06261i
$695$	−19.5839	+	14.2285i	−0.742860	+	0.539720i
$696$	9.49750	−	29.2303i	0.360002	−	1.10797i
$697$	−7.59209	+	5.51597i	−0.287571	+	0.208932i
$698$	48.1098	−	34.9538i	1.82098	−	1.32302i
$699$	1.32379	−	4.07420i	0.0500703	−	0.154100i
$700$	1.31347	−	0.954294i	0.0496446	−	0.0360689i
$701$	−15.5350	−	11.2868i	−0.586747	−	0.426297i	0.254403	−	0.967098i	$-0.418121\pi$
$701$	−15.5350	−	11.2868i	−0.586747	−	0.426297i	−0.841150	+	0.540801i	$0.818121\pi$
$702$	−5.43203	−	16.7181i	−0.205019	−	0.630982i
$703$	−31.5725	−	22.9387i	−1.19078	−	0.865151i
$704$	22.1357	−	68.1268i	0.834272	−	2.56763i
$705$	1.27198	−	3.91475i	0.0479055	−	0.147438i
$706$	18.7032	+	57.5625i	0.703904	+	2.16639i
$707$	1.85309			0.0696926
$708$	24.3096			0.913612
$709$	6.94423	+	21.3721i	0.260796	+	0.802648i	0.992632	+	0.121167i	$0.0386637\pi$
$709$	6.94423	+	21.3721i	0.260796	+	0.802648i	−0.731836	+	0.681481i	$0.761336\pi$
$710$	−40.3387	+	29.3078i	−1.51388	+	1.09990i
$711$	−0.105566	−	0.0766982i	−0.00395903	−	0.00287641i
$712$	−31.9165			−1.19612
$713$	2.87655	−	2.37451i	0.107728	−	0.0889262i
$714$	−2.11004			−0.0789661
$715$	29.5838	+	21.4939i	1.10637	+	0.803827i
$716$	74.8678	−	54.3947i	2.79794	−	2.03282i
$717$	1.14221	+	3.51535i	0.0426565	+	0.131283i
$718$	−89.5971			−3.34374
$719$	−22.8126			−0.850766			−0.425383	−	0.905014i	$-0.639861\pi$
$719$	−22.8126			−0.850766			−0.425383	+	0.905014i	$0.639861\pi$
$720$	9.15421	+	28.1738i	0.341157	+	1.04997i
$721$	−0.971548	+	2.99012i	−0.0361823	+	0.111358i
$722$	15.1472	−	46.6181i	0.563719	−	1.73495i
$723$	−4.46846	−	3.24652i	−0.166184	−	0.120740i
$724$	−17.7615	−	54.6643i	−0.660102	−	2.03158i
$725$	1.74033	+	1.26442i	0.0646342	+	0.0469595i
$726$	8.06497	−	5.85954i	0.299319	−	0.217468i
$727$	3.65235	−	11.2408i	0.135458	−	0.416898i	−0.860203	−	0.509952i	$-0.829663\pi$
$727$	3.65235	−	11.2408i	0.135458	−	0.416898i	0.995661	+	0.0930545i	$0.0296631\pi$
$728$	22.5657	−	16.3950i	0.836342	−	0.607638i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	0.320129	−	0.985256i	0.0118485	−	0.0364660i
$731$	6.69670	−	4.86544i	0.247686	−	0.179955i
$732$	28.3812	+	20.6201i	1.04900	+	0.762142i
$733$	−10.0545	−	30.9444i	−0.371370	−	1.14296i	−0.945895	−	0.324472i	$-0.894814\pi$
$733$	−10.0545	−	30.9444i	−0.371370	−	1.14296i	0.574526	−	0.818486i	$-0.305186\pi$
$734$	−6.01814	−	4.37244i	−0.222134	−	0.161390i
$735$	−4.37315	+	13.4592i	−0.161306	+	0.496449i
$736$	−4.17888	+	12.8613i	−0.154036	+	0.474073i
$737$	−7.23035	−	22.2527i	−0.266333	−	0.819690i
$738$	−15.4066			−0.567124
$739$	−19.0166			−0.699537			−0.349769	−	0.936836i	$-0.613740\pi$
$739$	−19.0166			−0.699537			−0.349769	+	0.936836i	$0.613740\pi$
$740$	−22.2553	−	68.4949i	−0.818123	−	2.51792i
$741$	−31.8591	+	23.1470i	−1.17037	+	0.850326i
$742$	−2.57954	−	1.87414i	−0.0946978	−	0.0688020i
$743$	−38.2094			−1.40177			−0.700883	−	0.713276i	$-0.747211\pi$
$743$	−38.2094			−1.40177			−0.700883	+	0.713276i	$0.747211\pi$
$744$	12.7710	−	49.5196i	0.468206	−	1.81548i
$745$	36.2604			1.32848
$746$	−39.3032	−	28.5554i	−1.43899	−	1.04549i
$747$	−6.85491	+	4.98038i	−0.250808	+	0.182223i
$748$	−7.44996	−	22.9286i	−0.272398	−	0.838353i
$749$	4.59593			0.167932
$750$	−32.0003			−1.16848
$751$	−5.39829	−	16.6142i	−0.196986	−	0.606262i	−0.999948	−	0.0102306i	$-0.996743\pi$
$751$	−5.39829	−	16.6142i	−0.196986	−	0.606262i	0.802961	−	0.596031i	$-0.203257\pi$
$752$	8.64806	−	26.6160i	0.315362	−	0.970585i
$753$	3.04022	−	9.35684i	0.110792	−	0.340982i
$754$	47.5866	+	34.5737i	1.73300	+	1.25910i
$755$	2.82704	+	8.70073i	0.102886	+	0.316652i
$756$	−2.04313	−	1.48442i	−0.0743078	−	0.0539877i
$757$	38.9811	−	28.3214i	1.41679	−	1.02936i	0.424503	−	0.905427i	$-0.360449\pi$
$757$	38.9811	−	28.3214i	1.41679	−	1.02936i	0.992290	−	0.123934i	$-0.0395511\pi$
$758$	−10.5474	+	32.4616i	−0.383099	+	1.17906i
$759$	1.46742	−	1.06615i	0.0532641	−	0.0386987i
$760$	94.4031	−	68.5879i	3.42436	−	2.48794i
$761$	−2.16340	+	6.65827i	−0.0784233	+	0.241362i	−0.982580	−	0.185838i	$-0.940500\pi$
$761$	−2.16340	+	6.65827i	−0.0784233	+	0.241362i	0.904157	+	0.427200i	$0.140500\pi$
$762$	1.70271	−	1.23709i	0.0616828	−	0.0448152i
$763$	0.228204	+	0.165800i	0.00826153	+	0.00600235i
$764$	6.24869	+	19.2315i	0.226070	+	0.695771i
$765$	2.79452	+	2.03034i	0.101036	+	0.0734071i
$766$	26.4523	−	81.4117i	0.955759	−	2.94152i
$767$	−9.03309	+	27.8010i	−0.326166	+	1.00384i
$768$	10.0986	+	31.0804i	0.364404	+	1.12152i
$769$	13.0887			0.471989			0.235995	−	0.971754i	$-0.424165\pi$
$769$	13.0887			0.471989			0.235995	+	0.971754i	$0.424165\pi$
$770$	7.20627			0.259696
$771$	−9.26584	−	28.5173i	−0.333701	−	1.02703i
$772$	−78.9056	+	57.3283i	−2.83987	+	2.06329i
$773$	−14.2618	−	10.3618i	−0.512961	−	0.372688i	0.300985	−	0.953629i	$-0.402685\pi$
$773$	−14.2618	−	10.3618i	−0.512961	−	0.372688i	−0.813946	+	0.580941i	$0.802685\pi$
$774$	13.5896			0.488467
$775$	3.02011	+	1.92116i	0.108486	+	0.0690099i
$776$	−23.4850			−0.843063
$777$	2.43470	+	1.76891i	0.0873443	+	0.0634594i
$778$	25.4879	−	18.5180i	0.913784	−	0.663903i
$779$	10.6656	+	32.8254i	0.382135	+	1.17609i
$780$	−72.6737			−2.60213
$781$	23.8057			0.851836
$782$	0.930708	+	2.86442i	0.0332820	+	0.102432i
$783$	1.03402	−	3.18240i	0.0369530	−	0.113730i
$784$	−29.7326	+	91.5075i	−1.06188	+	3.26812i
$785$	−16.8997	−	12.2784i	−0.603177	−	0.438234i
$786$	2.05088	+	6.31196i	0.0731525	+	0.225140i
$787$	35.5662	+	25.8404i	1.26780	+	0.921110i	0.999113	−	0.0421183i	$-0.0134106\pi$
$787$	35.5662	+	25.8404i	1.26780	+	0.921110i	0.268686	+	0.963228i	$0.413411\pi$
$788$	−92.6899	+	67.3432i	−3.30194	+	2.39900i
$789$	−9.83010	+	30.2539i	−0.349961	+	1.07707i
$790$	−0.598656	+	0.434949i	−0.0212992	+	0.0154748i
$791$	−6.52688	+	4.74205i	−0.232069	+	0.168608i
$792$	7.68479	−	23.6513i	0.273067	−	0.840414i
$793$	−34.1276	+	24.7952i	−1.21191	+	0.880502i
$794$	−2.75071	−	1.99851i	−0.0976190	−	0.0709243i
$795$	1.61297	+	4.96422i	0.0572062	+	0.176063i
$796$	27.4298	+	19.9289i	0.972224	+	0.706362i
$797$	12.8654	−	39.5955i	0.455715	−	1.40255i	−0.414580	−	0.910013i	$-0.636071\pi$
$797$	12.8654	−	39.5955i	0.455715	−	1.40255i	0.870294	−	0.492532i	$-0.163929\pi$
$798$	−2.39813	+	7.38067i	−0.0848927	+	0.261273i
$799$	−1.00839	−	3.10352i	−0.0356744	−	0.109795i
$800$	−12.9770			−0.458808
$801$	−3.47486			−0.122778
$802$	−23.6243	−	72.7082i	−0.834204	−	2.56742i
$803$	−0.400145	+	0.290723i	−0.0141208	+	0.0102594i
$804$	37.6197	+	27.3323i	1.32674	+	0.963935i
$805$	−0.656318			−0.0231322
$806$	82.5802	+	52.5310i	2.90877	+	1.85033i
$807$	−14.0675			−0.495201
$808$	−29.3390	−	21.3161i	−1.03214	−	0.749896i
$809$	21.6261	−	15.7123i	0.760335	−	0.552416i	−0.138678	−	0.990337i	$-0.544285\pi$
$809$	21.6261	−	15.7123i	0.760335	−	0.552416i	0.899013	+	0.437922i	$0.144285\pi$
$810$	1.75241	+	5.39336i	0.0615734	+	0.189503i
$811$	−10.2239			−0.359010			−0.179505	−	0.983757i	$-0.557450\pi$
$811$	−10.2239			−0.359010			−0.179505	+	0.983757i	$0.557450\pi$
$812$	8.45056			0.296556
$813$	−0.222994	−	0.686304i	−0.00782073	−	0.0240697i
$814$	−14.5750	+	44.8571i	−0.510852	+	1.57224i
$815$	−15.9123	+	48.9729i	−0.557382	+	1.71545i
$816$	18.9997	+	13.8041i	0.665122	+	0.483239i
$817$	−9.40774	−	28.9540i	−0.329135	−	1.01297i
$818$	48.7613	+	35.4272i	1.70490	+	1.23868i
$819$	2.45680	−	1.78497i	0.0858477	−	0.0623720i
$820$	−19.6828	+	60.5774i	−0.687352	+	2.11545i
$821$	−9.68374	+	7.03565i	−0.337965	+	0.245546i	−0.743803	−	0.668399i	$-0.766980\pi$
$821$	−9.68374	+	7.03565i	−0.337965	+	0.245546i	0.405838	+	0.913945i	$0.366980\pi$
$822$	−37.4470	+	27.2069i	−1.30611	+	0.948948i
$823$	−0.687505	+	2.11592i	−0.0239649	+	0.0737564i	−0.962324	−	0.271906i	$-0.912346\pi$
$823$	−0.687505	+	2.11592i	−0.0239649	+	0.0737564i	0.938359	+	0.345663i	$0.112346\pi$
$824$	49.7773	−	36.1653i	1.73408	−	1.25988i
$825$	1.40817	+	1.02309i	0.0490261	+	0.0356195i
$826$	1.78012	+	5.47865i	0.0619384	+	0.190627i
$827$	3.59012	+	2.60837i	0.124841	+	0.0907020i	0.648453	−	0.761254i	$-0.275416\pi$
$827$	3.59012	+	2.60837i	0.124841	+	0.0907020i	−0.523613	+	0.851956i	$0.675416\pi$
$828$	−1.11394	+	3.42835i	−0.0387120	+	0.119143i
$829$	13.3869	−	41.2007i	0.464947	−	1.43096i	−0.394102	−	0.919067i	$-0.628944\pi$
$829$	13.3869	−	41.2007i	0.464947	−	1.43096i	0.859049	−	0.511893i	$-0.171056\pi$
$830$	14.8484	+	45.6986i	0.515395	+	1.58622i
$831$	−9.64753			−0.334669
$832$	−171.186			−5.93480
$833$	3.46693	+	10.6701i	0.120122	+	0.369697i
$834$	−25.4890	+	18.5188i	−0.882611	+	0.641255i
$835$	−37.7235	−	27.4077i	−1.30547	−	0.948483i
$836$	−88.6689			−3.06668
$837$	1.39042	−	5.39136i	0.0480598	−	0.186353i
$838$	32.6447			1.12769
$839$	11.5333	+	8.37941i	0.398173	+	0.289289i	0.768796	−	0.639494i	$-0.220856\pi$
$839$	11.5333	+	8.37941i	0.398173	+	0.289289i	−0.370624	+	0.928783i	$0.620856\pi$
$840$	−7.27986	+	5.28913i	−0.251179	+	0.182492i
$841$	−5.50147	−	16.9318i	−0.189706	−	0.583855i
$842$	85.0426			2.93076
$843$	12.5689			0.432897
$844$	24.2888	+	74.7533i	0.836056	+	2.57311i
$845$	18.6190	−	57.3034i	0.640513	−	1.97130i
$846$	1.65552	−	5.09515i	0.0569178	−	0.175175i
$847$	1.39327	+	1.01227i	0.0478734	+	0.0347821i
$848$	10.9664	+	33.7512i	0.376589	+	1.15902i
$849$	20.9946	+	15.2535i	0.720533	+	0.523498i
$850$	−2.33823	+	1.69882i	−0.0802006	+	0.0582691i
$851$	1.32743	−	4.08540i	0.0455037	−	0.140046i
$852$	−38.2753	+	27.8087i	−1.31129	+	0.952709i
$853$	6.07563	−	4.41421i	0.208026	−	0.151140i	−0.478894	−	0.877873i	$-0.658962\pi$
$853$	6.07563	−	4.41421i	0.208026	−	0.151140i	0.686920	+	0.726733i	$0.258962\pi$
$854$	−2.56888	+	7.90620i	−0.0879053	+	0.270545i
$855$	10.2780	−	7.46739i	0.351499	−	0.255379i
$856$	−72.7651	−	52.8670i	−2.48706	−	1.80696i
$857$	10.3322	+	31.7991i	0.352940	+	1.08624i	0.957194	+	0.289446i	$0.0934710\pi$
$857$	10.3322	+	31.7991i	0.352940	+	1.08624i	−0.604255	+	0.796791i	$0.706529\pi$
$858$	38.5042	+	27.9749i	1.31451	+	0.955048i
$859$	−8.92391	+	27.4650i	−0.304480	+	0.937093i	0.675391	+	0.737460i	$0.263975\pi$
$859$	−8.92391	+	27.4650i	−0.304480	+	0.937093i	−0.979871	+	0.199633i	$0.936025\pi$
$860$	17.3615	−	53.4331i	0.592021	−	1.82205i
$861$	−0.822474	−	2.53131i	−0.0280298	−	0.0862670i
$862$	−73.5374			−2.50469
$863$	31.6205			1.07638			0.538188	−	0.842825i	$-0.319109\pi$
$863$	31.6205			1.07638			0.538188	+	0.842825i	$0.319109\pi$
$864$	6.23781	+	19.1980i	0.212215	+	0.653130i
$865$	21.7768	−	15.8217i	0.740432	−	0.537956i
$866$	16.0508	+	11.6616i	0.545427	+	0.396276i
$867$	−14.2616			−0.484349
$868$	14.0343	−	0.867887i	0.476354	−	0.0294580i
$869$	0.353295			0.0119847
$870$	−15.3518	−	11.1537i	−0.520474	−	0.378147i
$871$	−45.2366	+	32.8663i	−1.53279	+	1.11363i
$872$	−1.70585	−	5.25005i	−0.0577672	−	0.177789i
$873$	−2.55689			−0.0865377
$874$	11.0772			0.374692
$875$	−1.70832	−	5.25767i	−0.0577518	−	0.177742i
$876$	0.303755	−	0.934860i	0.0102629	−	0.0315860i
$877$	7.10997	−	21.8822i	0.240087	−	0.738911i	−0.756319	−	0.654203i	$-0.773004\pi$
$877$	7.10997	−	21.8822i	0.240087	−	0.738911i	0.996406	−	0.0847079i	$-0.0269957\pi$
$878$	−5.36829	−	3.90029i	−0.181171	−	0.131628i
$879$	−1.19039	−	3.66363i	−0.0401508	−	0.123571i
$880$	−64.8884	−	47.1441i	−2.18739	−	1.58923i
$881$	8.00368	−	5.81501i	0.269651	−	0.195913i	−0.444740	−	0.895660i	$-0.646704\pi$
$881$	8.00368	−	5.81501i	0.269651	−	0.195913i	0.714391	+	0.699747i	$0.246704\pi$
$882$	−5.69177	+	17.5175i	−0.191652	+	0.589844i
$883$	12.4095	−	9.01603i	0.417613	−	0.303413i	−0.359064	−	0.933313i	$-0.616904\pi$
$883$	12.4095	−	9.01603i	0.417613	−	0.303413i	0.776677	+	0.629900i	$0.216904\pi$
$884$	−46.6106	+	33.8646i	−1.56769	+	1.13899i
$885$	2.91414	−	8.96879i	0.0979577	−	0.301483i
$886$	−47.3185	+	34.3789i	−1.58969	+	1.15498i
$887$	−17.7630	−	12.9056i	−0.596423	−	0.433327i	0.248184	−	0.968713i	$-0.420166\pi$
$887$	−17.7630	−	12.9056i	−0.596423	−	0.433327i	−0.844607	+	0.535386i	$0.820166\pi$
$888$	−18.1996	−	56.0127i	−0.610739	−	1.87966i
$889$	0.294154	+	0.213716i	0.00986562	+	0.00716779i
$890$	−6.08937	+	18.7412i	−0.204116	+	0.628205i
$891$	0.836668	−	2.57500i	0.0280294	−	0.0862657i
$892$	23.3980	+	72.0115i	0.783422	+	2.41112i
$893$	−12.0018			−0.401626
$894$	47.1938			1.57840
$895$	−11.0935	−	34.1423i	−0.370815	−	1.14125i
$896$	−11.9628	+	8.69151i	−0.399651	+	0.290363i
$897$	−3.50680	−	2.54784i	−0.117089	−	0.0850700i
$898$	88.0819			2.93933
$899$	6.83988	+	17.3297i	0.228123	+	0.577978i
$900$	−3.45921			−0.115307
$901$	3.34775	+	2.43228i	0.111530	+	0.0810310i
$902$	33.7470	−	24.5186i	1.12365	−	0.816380i
$903$	0.725474	+	2.23278i	0.0241423	+	0.0743023i
$904$	157.885			5.25116
$905$	−22.2970			−0.741178
$906$	3.67946	+	11.3242i	0.122242	+	0.376222i
$907$	7.77128	−	23.9176i	0.258041	−	0.794169i	−0.735174	−	0.677878i	$-0.762900\pi$
$907$	7.77128	−	23.9176i	0.258041	−	0.794169i	0.993215	−	0.116291i	$-0.0371005\pi$
$908$	31.8623	−	98.0622i	1.05739	−	3.25431i
$909$	−3.19424	−	2.32075i	−0.105946	−	0.0769744i
$910$	−5.32168	−	16.3784i	−0.176412	−	0.542940i
$911$	32.2250	+	23.4128i	1.06766	+	0.775702i	0.975491	−	0.220041i	$-0.0706191\pi$
$911$	32.2250	+	23.4128i	1.06766	+	0.775702i	0.0921717	+	0.995743i	$0.470619\pi$
$912$	69.8789	−	50.7700i	2.31392	−	1.68116i
$913$	7.08919	−	21.8183i	0.234618	−	0.722080i
$914$	−71.9227	+	52.2549i	−2.37899	+	1.72844i
$915$	11.0098	−	7.99909i	0.363973	−	0.264442i
$916$	30.5520	−	94.0295i	1.00947	−	3.10682i
$917$	−0.927576	+	0.673923i	−0.0306312	+	0.0222549i
$918$	3.63715	+	2.64254i	0.120044	+	0.0872169i
$919$	10.8955	+	33.5330i	0.359411	+	1.10615i	0.953408	+	0.301685i	$0.0975491\pi$
$919$	10.8955	+	33.5330i	0.359411	+	1.10615i	−0.593997	+	0.804467i	$0.702451\pi$
$920$	10.3912	+	7.54962i	0.342587	+	0.248904i
$921$	−3.84403	+	11.8307i	−0.126665	+	0.389836i
$922$	27.5412	−	84.7631i	0.907021	−	2.79152i
$923$	−17.5800	−	54.1057i	−0.578653	−	1.78091i
$924$	6.83767			0.224943
$925$	4.12218			0.135536
$926$	−24.6995	−	76.0173i	−0.811676	−	2.49808i
$927$	5.41942	−	3.93744i	0.177997	−	0.129322i
$928$	−54.6456	−	39.7024i	−1.79383	−	1.30329i
$929$	−29.8698			−0.979996			−0.489998	−	0.871724i	$-0.663002\pi$
$929$	−29.8698			−0.979996			−0.489998	+	0.871724i	$0.663002\pi$
$930$	−26.6410	−	16.9469i	−0.873592	−	0.555710i
$931$	41.2631			1.35234
$932$	−18.6485	−	13.5490i	−0.610853	−	0.443811i
$933$	4.67422	−	3.39602i	0.153027	−	0.111181i
$934$	6.35561	+	19.5606i	0.207962	+	0.640041i
$935$	−9.35235			−0.305855
$936$	−59.4299			−1.94253
$937$	6.34978	+	19.5426i	0.207438	+	0.638429i	0.999604	+	0.0281236i	$0.00895321\pi$
$937$	6.34978	+	19.5426i	0.207438	+	0.638429i	−0.792166	+	0.610305i	$0.791047\pi$
$938$	−3.40509	+	10.4798i	−0.111180	+	0.342177i
$939$	−6.75252	+	20.7821i	−0.220360	+	0.678199i
$940$	−17.9187	−	13.0187i	−0.584443	−	0.424623i
$941$	−17.2391	−	53.0565i	−0.561979	−	1.72959i	−0.676762	−	0.736202i	$-0.736617\pi$
$941$	−17.2391	−	53.0565i	−0.561979	−	1.72959i	0.114784	−	0.993391i	$-0.463383\pi$
$942$	−21.9954	−	15.9806i	−0.716650	−	0.520677i
$943$	−3.07354	+	2.23306i	−0.100088	+	0.0727183i
$944$	19.8129	−	60.9779i	0.644856	−	1.98466i
$945$	−0.792582	+	0.575845i	−0.0257827	+	0.0187322i
$946$	−29.7669	+	21.6270i	−0.967807	+	0.703153i
$947$	−16.2792	+	50.1021i	−0.529001	+	1.62810i	0.227264	+	0.973833i	$0.427022\pi$
$947$	−16.2792	+	50.1021i	−0.529001	+	1.62810i	−0.756265	+	0.654265i	$0.772978\pi$
$948$	−0.568035	+	0.412701i	−0.0184489	+	0.0134039i
$949$	0.956255	+	0.694760i	0.0310413	+	0.0225529i
$950$	3.28482	+	10.1096i	0.106574	+	0.328000i
$951$	11.8852	+	8.63511i	0.385404	+	0.280013i
$952$	−2.20444	+	6.78457i	−0.0714463	+	0.219889i
$953$	−4.12141	+	12.6844i	−0.133506	+	0.410888i	−0.995355	−	0.0962771i	$-0.969307\pi$
$953$	−4.12141	+	12.6844i	−0.133506	+	0.410888i	0.861849	+	0.507165i	$0.169307\pi$
$954$	2.09933	+	6.46106i	0.0679682	+	0.209185i
$955$	7.84433			0.253837
$956$	19.8890			0.643257
$957$	2.79963	+	8.61638i	0.0904993	+	0.278528i
$958$	8.72015	−	6.33556i	0.281735	−	0.204693i
$959$	−6.46920	−	4.70015i	−0.208901	−	0.151776i
$960$	55.2257			1.78240
$961$	13.1391	+	28.0778i	0.423842	+	0.905736i
$962$	112.715			3.63407
$963$	−7.92218	−	5.75580i	−0.255289	−	0.185478i
$964$	−24.0441	+	17.4691i	−0.774408	+	0.562640i
$965$	11.6918	+	35.9837i	0.376373	+	1.15836i
$966$	−0.854215			−0.0274839
$967$	53.3774			1.71650			0.858251	−	0.513230i	$-0.171551\pi$
$967$	53.3774			1.71650			0.858251	+	0.513230i	$0.171551\pi$
$968$	−10.4148	−	32.0536i	−0.334746	−	1.03024i
$969$	3.11231	−	9.57870i	0.0999817	−	0.307712i
$970$	−4.48072	+	13.7902i	−0.143867	+	0.442778i
$971$	−6.60417	−	4.79821i	−0.211938	−	0.153982i	0.476752	−	0.879038i	$-0.341814\pi$
$971$	−6.60417	−	4.79821i	−0.211938	−	0.153982i	−0.688690	+	0.725056i	$0.741814\pi$
$972$	1.66277	+	5.11749i	0.0533335	+	0.164144i
$973$	−4.40338	−	3.19924i	−0.141166	−	0.102563i
$974$	63.8849	−	46.4151i	2.04700	−	1.48723i
$975$	1.28539	−	3.95602i	0.0411654	−	0.126694i
$976$	74.8545	−	54.3850i	2.39603	−	1.74082i
$977$	−16.5145	+	11.9985i	−0.528345	+	0.383865i	−0.819738	−	0.572738i	$-0.805881\pi$
$977$	−16.5145	+	11.9985i	−0.528345	+	0.383865i	0.291394	+	0.956603i	$0.405881\pi$
$978$	−20.7102	+	63.7395i	−0.662240	+	2.03817i
$979$	7.61141	−	5.53001i	0.243262	−	0.176740i
$980$	61.6056	+	44.7591i	1.96792	+	1.42978i
$981$	−0.185721	−	0.571590i	−0.00592961	−	0.0182495i
$982$	0.238181	+	0.173049i	0.00760067	+	0.00552221i
$983$	−17.7726	+	54.6984i	−0.566858	+	1.74461i	0.0955085	+	0.995429i	$0.469552\pi$
$983$	−17.7726	+	54.6984i	−0.566858	+	1.74461i	−0.662366	+	0.749180i	$0.730448\pi$
$984$	−16.0959	+	49.5380i	−0.513118	+	1.57921i
$985$	13.7343	+	42.2698i	0.437611	+	1.34683i
$986$	−15.0436			−0.479085
$987$	0.925517			0.0294595
$988$	65.4801	+	201.527i	2.08320	+	6.41143i
$989$	2.71105	−	1.96970i	0.0862065	−	0.0626327i
$990$	−12.4217	−	9.02490i	−0.394788	−	0.286830i
$991$	34.7071			1.10251			0.551254	−	0.834338i	$-0.314150\pi$
$991$	34.7071			1.10251			0.551254	+	0.834338i	$0.314150\pi$
$992$	−94.8302	−	60.3235i	−3.01086	−	1.91527i
$993$	13.9714			0.443370
$994$	−9.07002	−	6.58975i	−0.287684	−	0.209014i
$995$	10.6408	−	7.73096i	0.337334	−	0.245088i
$996$	14.0889	+	43.3612i	0.446424	+	1.37395i
$997$	18.7715			0.594499			0.297250	−	0.954800i	$-0.403931\pi$
$997$	18.7715			0.594499			0.297250	+	0.954800i	$0.403931\pi$
$998$	−10.6671			−0.337660
$999$	−1.98145	−	6.09828i	−0.0626903	−	0.192941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.f.b.64.1	yes	16
3.2	odd	2		279.2.i.c.64.4		16
31.4	even	5		2883.2.a.p.1.8		8
31.16	even	5	inner	93.2.f.b.16.1	✓	16
31.27	odd	10		2883.2.a.o.1.8		8
93.35	odd	10		8649.2.a.bh.1.1		8
93.47	odd	10		279.2.i.c.109.4		16
93.89	even	10		8649.2.a.bg.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.f.b.16.1	✓	16	31.16	even	5	inner
93.2.f.b.64.1	yes	16	1.1	even	1	trivial
279.2.i.c.64.4		16	3.2	odd	2
279.2.i.c.109.4		16	93.47	odd	10
2883.2.a.o.1.8		8	31.27	odd	10
2883.2.a.p.1.8		8	31.4	even	5
8649.2.a.bg.1.1		8	93.89	even	10
8649.2.a.bh.1.1		8	93.35	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19791 - 1.59688i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.66277 + 5.11749i) q^{4} +2.08737 q^{5} +2.71677 q^{6} +(0.145034 + 0.446368i) q^{7} +(2.83832 - 8.73545i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-2.19791 - 1.59688i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.66277 + 5.11749i) q^{4} +2.08737 q^{5} +2.71677 q^{6} +(0.145034 + 0.446368i) q^{7} +(2.83832 - 8.73545i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-4.58787 - 3.33328i) q^{10} +(0.836668 + 2.57500i) q^{11} +(-4.35320 - 3.16278i) q^{12} +(5.23460 - 3.80316i) q^{13} +(0.394024 - 1.21268i) q^{14} +(-1.68872 + 1.22693i) q^{15} +(-11.4814 + 8.34175i) q^{16} +(-0.511367 + 1.57383i) q^{17} +(-2.19791 + 1.59688i) q^{18} +(4.92388 + 3.57741i) q^{19} +(3.47083 + 10.6821i) q^{20} +(-0.379703 - 0.275871i) q^{21} +(2.27303 - 6.99568i) q^{22} +(-0.207019 + 0.637139i) q^{23} +(2.83832 + 8.73545i) q^{24} -0.642874 q^{25} -17.5784 q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.04313 + 1.48442i) q^{28} +(-2.70711 - 1.96683i) q^{29} +5.67092 q^{30} +(-4.69782 - 2.98839i) q^{31} +20.1860 q^{32} +(-2.19042 - 1.59144i) q^{33} +(3.63715 - 2.64254i) q^{34} +(0.302739 + 0.931736i) q^{35} +5.38085 q^{36} -6.41211 q^{37} +(-5.10958 - 15.7257i) q^{38} +(-1.99944 + 6.15365i) q^{39} +(5.92463 - 18.2341i) q^{40} +(4.58787 + 3.33328i) q^{41} +(0.394024 + 1.21268i) q^{42} +(-4.04679 - 2.94016i) q^{43} +(-11.7863 + 8.56328i) q^{44} +(0.645034 - 1.98521i) q^{45} +(1.47244 - 1.06979i) q^{46} +(-1.59535 + 1.15909i) q^{47} +(4.38552 - 13.4972i) q^{48} +(5.48491 - 3.98502i) q^{49} +(1.41298 + 1.02659i) q^{50} +(-0.511367 - 1.57383i) q^{51} +(28.1666 + 20.4642i) q^{52} +(0.772728 - 2.37821i) q^{53} +(0.839529 - 2.58380i) q^{54} +(1.74644 + 5.37498i) q^{55} +4.31088 q^{56} -6.08625 q^{57} +(2.80921 + 8.64585i) q^{58} +(-3.65498 + 2.65550i) q^{59} +(-9.08675 - 6.60191i) q^{60} -6.51961 q^{61} +(5.55333 + 14.0701i) q^{62} +0.469339 q^{63} +(-21.4042 - 15.5511i) q^{64} +(10.9266 - 7.93862i) q^{65} +(2.27303 + 6.99568i) q^{66} -8.64185 q^{67} -8.90433 q^{68} +(-0.207019 - 0.637139i) q^{69} +(0.822474 - 2.53131i) q^{70} +(2.71702 - 8.36213i) q^{71} +(-7.43082 - 5.39880i) q^{72} +(0.0564511 + 0.173738i) q^{73} +(14.0933 + 10.2394i) q^{74} +(0.520096 - 0.377872i) q^{75} +(-10.1201 + 31.1463i) q^{76} +(-1.02805 + 0.746923i) q^{77} +(14.2212 - 10.3323i) q^{78} +(0.0403226 - 0.124100i) q^{79} +(-23.9660 + 17.4123i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-4.76090 - 14.6525i) q^{82} +(-6.85491 - 4.98038i) q^{83} +(0.780404 - 2.40184i) q^{84} +(-1.06741 + 3.28516i) q^{85} +(4.19941 + 12.9245i) q^{86} +3.34617 q^{87} +24.8685 q^{88} +(-1.07379 - 3.30479i) q^{89} +(-4.58787 + 3.33328i) q^{90} +(2.45680 + 1.78497i) q^{91} -3.60478 q^{92} +(5.55715 - 0.343657i) q^{93} +5.35736 q^{94} +(10.2780 + 7.46739i) q^{95} +(-16.3308 + 11.8650i) q^{96} +(-0.790123 - 2.43175i) q^{97} -18.4190 q^{98} +2.70751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + 6 * q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 - 4 * q^9	\( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9} - 3 q^{10} + 10 q^{11} - 4 q^{12} - 3 q^{13} - 4 q^{14} - 4 q^{15} - 17 q^{16} - q^{17} - 3 q^{18} - 4 q^{19} + 7 q^{20} + 8 q^{21} + 10 q^{22} + 7 q^{23} - 2 q^{24} + 30 q^{25} - 16 q^{26} - 4 q^{27} + 9 q^{28} - 2 q^{29} + 12 q^{30} - 13 q^{31} + 108 q^{32} - 5 q^{33} - 4 q^{34} - 33 q^{35} + 26 q^{36} - 28 q^{37} - 62 q^{38} + 7 q^{39} - 27 q^{40} + 3 q^{41} - 4 q^{42} - 13 q^{43} - 64 q^{44} + q^{45} - q^{46} - 20 q^{47} - 2 q^{48} + q^{49} - 44 q^{50} - q^{51} + 88 q^{52} - 4 q^{53} + 2 q^{54} - 8 q^{55} + 104 q^{56} - 14 q^{57} - 31 q^{58} + 49 q^{59} - 8 q^{60} - 13 q^{62} - 2 q^{63} - 26 q^{64} - q^{65} + 10 q^{66} + 60 q^{67} - 30 q^{68} + 7 q^{69} + 85 q^{70} + 23 q^{71} - 7 q^{72} - 17 q^{73} + 70 q^{74} - 5 q^{75} + 7 q^{76} + 2 q^{77} + 19 q^{78} - 13 q^{79} - 94 q^{80} - 4 q^{81} - 9 q^{82} - 49 q^{83} - 6 q^{84} - 4 q^{85} + 24 q^{86} - 2 q^{87} - 32 q^{88} + 3 q^{89} - 3 q^{90} - 2 q^{91} - 70 q^{92} + 17 q^{93} + 74 q^{94} - 10 q^{95} - 32 q^{96} + 3 q^{97} - 82 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 4 * q^3 - 9 * q^4 + 6 * q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 - 4 * q^9 - 3 * q^10 + 10 * q^11 - 4 * q^12 - 3 * q^13 - 4 * q^14 - 4 * q^15 - 17 * q^16 - q^17 - 3 * q^18 - 4 * q^19 + 7 * q^20 + 8 * q^21 + 10 * q^22 + 7 * q^23 - 2 * q^24 + 30 * q^25 - 16 * q^26 - 4 * q^27 + 9 * q^28 - 2 * q^29 + 12 * q^30 - 13 * q^31 + 108 * q^32 - 5 * q^33 - 4 * q^34 - 33 * q^35 + 26 * q^36 - 28 * q^37 - 62 * q^38 + 7 * q^39 - 27 * q^40 + 3 * q^41 - 4 * q^42 - 13 * q^43 - 64 * q^44 + q^45 - q^46 - 20 * q^47 - 2 * q^48 + q^49 - 44 * q^50 - q^51 + 88 * q^52 - 4 * q^53 + 2 * q^54 - 8 * q^55 + 104 * q^56 - 14 * q^57 - 31 * q^58 + 49 * q^59 - 8 * q^60 - 13 * q^62 - 2 * q^63 - 26 * q^64 - q^65 + 10 * q^66 + 60 * q^67 - 30 * q^68 + 7 * q^69 + 85 * q^70 + 23 * q^71 - 7 * q^72 - 17 * q^73 + 70 * q^74 - 5 * q^75 + 7 * q^76 + 2 * q^77 + 19 * q^78 - 13 * q^79 - 94 * q^80 - 4 * q^81 - 9 * q^82 - 49 * q^83 - 6 * q^84 - 4 * q^85 + 24 * q^86 - 2 * q^87 - 32 * q^88 + 3 * q^89 - 3 * q^90 - 2 * q^91 - 70 * q^92 + 17 * q^93 + 74 * q^94 - 10 * q^95 - 32 * q^96 + 3 * q^97 - 82 * q^98 - 10 * q^99

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