LMFDB - Embedded newform 429.2.i.e.100.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 6x^{7} + 46x^{6} - 31x^{5} + 111x^{4} - 36x^{3} + 145x^{2} - 72x + 81 $ x^10 - 2x^9 + 10x^8 - 6x^7 + 46x^6 - 31x^5 + 111x^4 - 36x^3 + 145x^2 - 72*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.5
Root			$1.38472 - 2.39840i$ of defining polynomial
Character	$\chi$	$=$	429.100
Dual form			429.2.i.e.133.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38472 - 2.39840i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.83488 - 4.91015i) q^{4} +3.07670 q^{5} +(-1.38472 - 2.39840i) q^{6} +(1.16758 + 2.02232i) q^{7} -10.1631 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.38472 - 2.39840i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.83488 - 4.91015i) q^{4} +3.07670 q^{5} +(-1.38472 - 2.39840i) q^{6} +(1.16758 + 2.02232i) q^{7} -10.1631 q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.26035 - 7.37914i) q^{10} +(0.500000 - 0.866025i) q^{11} -5.66975 q^{12} +(-3.02927 + 1.95539i) q^{13} +6.46709 q^{14} +(1.53835 - 2.66450i) q^{15} +(-8.40330 + 14.5549i) q^{16} +(-0.0407573 - 0.0705938i) q^{17} -2.76943 q^{18} +(3.32173 + 5.75341i) q^{19} +(-8.72205 - 15.1070i) q^{20} +2.33517 q^{21} +(-1.38472 - 2.39840i) q^{22} +(1.19033 - 2.06171i) q^{23} +(-5.08157 + 8.80153i) q^{24} +4.46606 q^{25} +(0.495130 + 9.97305i) q^{26} -1.00000 q^{27} +(6.61991 - 11.4660i) q^{28} +(0.746689 - 1.29330i) q^{29} +(-4.26035 - 7.37914i) q^{30} -3.28968 q^{31} +(13.1092 + 22.7059i) q^{32} +(-0.500000 - 0.866025i) q^{33} -0.225749 q^{34} +(3.59230 + 6.22205i) q^{35} +(-2.83488 + 4.91015i) q^{36} +(-3.23761 + 5.60770i) q^{37} +18.3986 q^{38} +(0.178784 + 3.60112i) q^{39} -31.2689 q^{40} +(-4.47290 + 7.74730i) q^{41} +(3.23354 - 5.60066i) q^{42} +(-1.82202 - 3.15584i) q^{43} -5.66975 q^{44} +(-1.53835 - 2.66450i) q^{45} +(-3.29653 - 5.70976i) q^{46} -1.76451 q^{47} +(8.40330 + 14.5549i) q^{48} +(0.773495 - 1.33973i) q^{49} +(6.18422 - 10.7114i) q^{50} -0.0815147 q^{51} +(18.1889 + 9.33086i) q^{52} +13.3492 q^{53} +(-1.38472 + 2.39840i) q^{54} +(1.53835 - 2.66450i) q^{55} +(-11.8663 - 20.5531i) q^{56} +6.64346 q^{57} +(-2.06791 - 3.58172i) q^{58} +(-4.09311 - 7.08947i) q^{59} -17.4441 q^{60} +(-5.94189 - 10.2916i) q^{61} +(-4.55528 + 7.88997i) q^{62} +(1.16758 - 2.02232i) q^{63} +38.9970 q^{64} +(-9.32013 + 6.01614i) q^{65} -2.76943 q^{66} +(6.44987 - 11.1715i) q^{67} +(-0.231084 + 0.400249i) q^{68} +(-1.19033 - 2.06171i) q^{69} +19.8973 q^{70} +(-2.50327 - 4.33579i) q^{71} +(5.08157 + 8.80153i) q^{72} -9.99952 q^{73} +(8.96633 + 15.5301i) q^{74} +(2.23303 - 3.86772i) q^{75} +(18.8334 - 32.6204i) q^{76} +2.33517 q^{77} +(8.88448 + 4.55773i) q^{78} +11.6763 q^{79} +(-25.8544 + 44.7811i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(12.3874 + 21.4556i) q^{82} +0.656706 q^{83} +(-6.61991 - 11.4660i) q^{84} +(-0.125398 - 0.217196i) q^{85} -10.0919 q^{86} +(-0.746689 - 1.29330i) q^{87} +(-5.08157 + 8.80153i) q^{88} +(-4.64536 + 8.04600i) q^{89} -8.52070 q^{90} +(-7.49134 - 3.84305i) q^{91} -13.4977 q^{92} +(-1.64484 + 2.84895i) q^{93} +(-2.44335 + 4.23200i) q^{94} +(10.2200 + 17.7015i) q^{95} +26.2185 q^{96} +(-0.373516 - 0.646949i) q^{97} +(-2.14214 - 3.71030i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.38472	−	2.39840i	0.979142	−	1.69592i	0.313615	−	0.949550i	$-0.398460\pi$
$2$	1.38472	−	2.39840i	0.979142	−	1.69592i	0.665527	−	0.746373i	$-0.268207\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−2.83488	−	4.91015i	−1.41744	−	2.45508i
$5$	3.07670			1.37594			0.687970	−	0.725739i	$-0.258502\pi$
$5$	3.07670			1.37594			0.687970	+	0.725739i	$0.258502\pi$
$6$	−1.38472	−	2.39840i	−0.565308	−	0.979142i
$7$	1.16758	+	2.02232i	0.441305	+	0.764363i	0.997787	−	0.0664969i	$-0.0211822\pi$
$7$	1.16758	+	2.02232i	0.441305	+	0.764363i	−0.556481	+	0.830860i	$0.687849\pi$
$8$	−10.1631			−3.59321
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	4.26035	−	7.37914i	1.34724	−	2.33349i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−5.66975			−1.63672
$13$	−3.02927	+	1.95539i	−0.840167	+	0.542327i
$13$	−3.02927	+	1.95539i	−0.840167	+	0.542327i
$14$	6.46709			1.72840
$15$	1.53835	−	2.66450i	0.397200	−	0.687970i
$16$	−8.40330	+	14.5549i	−2.10082	+	3.63873i
$17$	−0.0407573	−	0.0705938i	−0.00988510	−	0.0171215i	0.861041	−	0.508536i	$-0.169813\pi$
$17$	−0.0407573	−	0.0705938i	−0.00988510	−	0.0171215i	−0.870926	+	0.491415i	$0.836480\pi$
$18$	−2.76943			−0.652761
$19$	3.32173	+	5.75341i	0.762058	+	1.31992i	0.941788	+	0.336207i	$0.109144\pi$
$19$	3.32173	+	5.75341i	0.762058	+	1.31992i	−0.179731	+	0.983716i	$0.557523\pi$
$20$	−8.72205	−	15.1070i	−1.95031	−	3.37804i
$21$	2.33517			0.509575
$22$	−1.38472	−	2.39840i	−0.295222	−	0.511340i
$23$	1.19033	−	2.06171i	0.248200	−	0.429895i	−0.714826	−	0.699302i	$-0.753494\pi$
$23$	1.19033	−	2.06171i	0.248200	−	0.429895i	0.963027	+	0.269407i	$0.0868276\pi$
$24$	−5.08157	+	8.80153i	−1.03727	+	1.79660i
$25$	4.46606			0.893212
$26$	0.495130	+	9.97305i	0.0971029	+	1.95588i
$27$	−1.00000			−0.192450
$28$	6.61991	−	11.4660i	1.25105	−	2.16688i
$29$	0.746689	−	1.29330i	0.138657	−	0.240161i	−0.788332	−	0.615251i	$-0.789055\pi$
$29$	0.746689	−	1.29330i	0.138657	−	0.240161i	0.926988	+	0.375090i	$0.122388\pi$
$30$	−4.26035	−	7.37914i	−0.777830	−	1.34724i
$31$	−3.28968			−0.590845			−0.295422	−	0.955367i	$-0.595460\pi$
$31$	−3.28968			−0.590845			−0.295422	+	0.955367i	$0.595460\pi$
$32$	13.1092	+	22.7059i	2.31741	+	4.01387i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	−0.225749			−0.0387157
$35$	3.59230	+	6.22205i	0.607210	+	1.05172i
$36$	−2.83488	+	4.91015i	−0.472479	+	0.818358i
$37$	−3.23761	+	5.60770i	−0.532259	+	0.921900i	0.467031	+	0.884241i	$0.345324\pi$
$37$	−3.23761	+	5.60770i	−0.532259	+	0.921900i	−0.999291	+	0.0376595i	$0.988010\pi$
$38$	18.3986			2.98465
$39$	0.178784	+	3.60112i	0.0286283	+	0.576640i
$40$	−31.2689			−4.94404
$41$	−4.47290	+	7.74730i	−0.698550	+	1.20992i	0.270419	+	0.962743i	$0.412838\pi$
$41$	−4.47290	+	7.74730i	−0.698550	+	1.20992i	−0.968969	+	0.247182i	$0.920496\pi$
$42$	3.23354	−	5.60066i	0.498947	−	0.864201i
$43$	−1.82202	−	3.15584i	−0.277856	−	0.481261i	0.692996	−	0.720942i	$-0.256290\pi$
$43$	−1.82202	−	3.15584i	−0.277856	−	0.481261i	−0.970852	+	0.239681i	$0.922957\pi$
$44$	−5.66975			−0.854747
$45$	−1.53835	−	2.66450i	−0.229323	−	0.397200i
$46$	−3.29653	−	5.70976i	−0.486047	−	0.841857i
$47$	−1.76451			−0.257380			−0.128690	−	0.991685i	$-0.541077\pi$
$47$	−1.76451			−0.257380			−0.128690	+	0.991685i	$0.541077\pi$
$48$	8.40330	+	14.5549i	1.21291	+	2.10082i
$49$	0.773495	−	1.33973i	0.110499	−	0.191390i
$50$	6.18422	−	10.7114i	0.874581	−	1.51482i
$51$	−0.0815147			−0.0114143
$52$	18.1889	+	9.33086i	2.52234	+	1.29396i
$53$	13.3492			1.83366			0.916830	−	0.399278i	$-0.130739\pi$
$53$	13.3492			1.83366			0.916830	+	0.399278i	$0.130739\pi$
$54$	−1.38472	+	2.39840i	−0.188436	+	0.326381i
$55$	1.53835	−	2.66450i	0.207431	−	0.359281i
$56$	−11.8663	−	20.5531i	−1.58570	−	2.74652i
$57$	6.64346			0.879948
$58$	−2.06791	−	3.58172i	−0.271529	−	0.470303i
$59$	−4.09311	−	7.08947i	−0.532877	−	0.922971i	−0.999263	−	0.0383891i	$-0.987777\pi$
$59$	−4.09311	−	7.08947i	−0.532877	−	0.922971i	0.466385	−	0.884582i	$-0.345556\pi$
$60$	−17.4441			−2.25202
$61$	−5.94189	−	10.2916i	−0.760781	−	1.31771i	−0.942449	−	0.334351i	$-0.891483\pi$
$61$	−5.94189	−	10.2916i	−0.760781	−	1.31771i	0.181668	−	0.983360i	$-0.441850\pi$
$62$	−4.55528	+	7.88997i	−0.578521	+	1.00203i
$63$	1.16758	−	2.02232i	0.147102	−	0.254788i
$64$	38.9970			4.87463
$65$	−9.32013	+	6.01614i	−1.15602	+	0.746210i
$66$	−2.76943			−0.340894
$67$	6.44987	−	11.1715i	0.787977	−	1.36482i	−0.139228	−	0.990260i	$-0.544462\pi$
$67$	6.44987	−	11.1715i	0.787977	−	1.36482i	0.927204	−	0.374556i	$-0.122205\pi$
$68$	−0.231084	+	0.400249i	−0.0280231	+	0.0485373i
$69$	−1.19033	−	2.06171i	−0.143298	−	0.248200i
$70$	19.8973			2.37818
$71$	−2.50327	−	4.33579i	−0.297083	−	0.514563i	0.678384	−	0.734707i	$-0.262681\pi$
$71$	−2.50327	−	4.33579i	−0.297083	−	0.514563i	−0.975467	+	0.220144i	$0.929347\pi$
$72$	5.08157	+	8.80153i	0.598868	+	1.03727i
$73$	−9.99952			−1.17036			−0.585178	−	0.810905i	$-0.698975\pi$
$73$	−9.99952			−1.17036			−0.585178	+	0.810905i	$0.698975\pi$
$74$	8.96633	+	15.5301i	1.04232	+	1.80534i
$75$	2.23303	−	3.86772i	0.257848	−	0.446606i
$76$	18.8334	−	32.6204i	2.16034	−	3.74182i
$77$	2.33517			0.266117
$78$	8.88448	+	4.55773i	1.00597	+	0.516061i
$79$	11.6763			1.31369			0.656843	−	0.754028i	$-0.271892\pi$
$79$	11.6763			1.31369			0.656843	+	0.754028i	$0.271892\pi$
$80$	−25.8544	+	44.7811i	−2.89061	+	5.00668i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	12.3874	+	21.4556i	1.36796	+	2.36938i
$83$	0.656706			0.0720829			0.0360414	−	0.999350i	$-0.488525\pi$
$83$	0.656706			0.0720829			0.0360414	+	0.999350i	$0.488525\pi$
$84$	−6.61991	−	11.4660i	−0.722292	−	1.25105i
$85$	−0.125398	−	0.217196i	−0.0136013	−	0.0235582i
$86$	−10.0919			−1.08824
$87$	−0.746689	−	1.29330i	−0.0800535	−	0.138657i
$88$	−5.08157	+	8.80153i	−0.541697	+	0.938246i
$89$	−4.64536	+	8.04600i	−0.492407	+	0.852874i	−0.999962	−	0.00874566i	$-0.997216\pi$
$89$	−4.64536	+	8.04600i	−0.492407	+	0.852874i	0.507555	+	0.861619i	$0.330549\pi$
$90$	−8.52070			−0.898161
$91$	−7.49134	−	3.84305i	−0.785305	−	0.402861i
$92$	−13.4977			−1.40723
$93$	−1.64484	+	2.84895i	−0.170562	+	0.295422i
$94$	−2.44335	+	4.23200i	−0.252012	+	0.436497i
$95$	10.2200	+	17.7015i	1.04855	+	1.81613i
$96$	26.2185			2.67591
$97$	−0.373516	−	0.646949i	−0.0379248	−	0.0656877i	0.846440	−	0.532484i	$-0.178741\pi$
$97$	−0.373516	−	0.646949i	−0.0379248	−	0.0656877i	−0.884365	+	0.466796i	$0.845408\pi$
$98$	−2.14214	−	3.71030i	−0.216389	−	0.374797i
$99$	−1.00000			−0.100504
$100$	−12.6607	−	21.9290i	−1.26607	−	2.19290i
$101$	−4.66308	+	8.07669i	−0.463994	+	0.803661i	−0.999156	−	0.0410887i	$-0.986917\pi$
$101$	−4.66308	+	8.07669i	−0.463994	+	0.803661i	0.535162	+	0.844750i	$0.320251\pi$
$102$	−0.112875	+	0.195505i	−0.0111763	+	0.0193578i
$103$	−10.9250			−1.07647			−0.538237	−	0.842793i	$-0.680910\pi$
$103$	−10.9250			−1.07647			−0.538237	+	0.842793i	$0.680910\pi$
$104$	30.7868	−	19.8729i	3.01890	−	1.94870i
$105$	7.18460			0.701145
$106$	18.4849	−	32.0168i	1.79541	−	3.10975i
$107$	6.47782	−	11.2199i	0.626235	−	1.08467i	−0.362066	−	0.932153i	$-0.617928\pi$
$107$	6.47782	−	11.2199i	0.626235	−	1.08467i	0.988301	−	0.152518i	$-0.0487383\pi$
$108$	2.83488	+	4.91015i	0.272786	+	0.472479i
$109$	−6.26821			−0.600386			−0.300193	−	0.953879i	$-0.597051\pi$
$109$	−6.26821			−0.600386			−0.300193	+	0.953879i	$0.597051\pi$
$110$	−4.26035	−	7.37914i	−0.406208	−	0.703574i
$111$	3.23761	+	5.60770i	0.307300	+	0.532259i
$112$	−39.2462			−3.70842
$113$	−3.60687	−	6.24728i	−0.339306	−	0.587694i	0.644997	−	0.764185i	$-0.276859\pi$
$113$	−3.60687	−	6.24728i	−0.339306	−	0.587694i	−0.984302	+	0.176491i	$0.943525\pi$
$114$	9.19931	−	15.9337i	0.861594	−	1.49233i
$115$	3.66227	−	6.34324i	0.341509	−	0.591510i
$116$	−8.46709			−0.786150
$117$	3.20805	+	1.64573i	0.296584	+	0.152147i
$118$	−22.6712			−2.08705
$119$	0.0951752	−	0.164848i	0.00872470	−	0.0151116i
$120$	−15.6344	+	27.0796i	−1.42722	+	2.47202i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−32.9113			−2.97965
$123$	4.47290	+	7.74730i	0.403308	+	0.698550i
$124$	9.32585	+	16.1528i	0.837486	+	1.45057i
$125$	−1.64278			−0.146935
$126$	−3.23354	−	5.60066i	−0.288067	−	0.498947i
$127$	2.83436	−	4.90926i	0.251509	−	0.435626i	−0.712433	−	0.701741i	$-0.752407\pi$
$127$	2.83436	−	4.90926i	0.251509	−	0.435626i	0.963941	+	0.266114i	$0.0857399\pi$
$128$	27.7814	−	48.1188i	2.45555	−	4.25314i
$129$	−3.64405			−0.320840
$130$	1.52336	+	30.6840i	0.133608	+	2.69117i
$131$	5.90135			0.515604			0.257802	−	0.966198i	$-0.417002\pi$
$131$	5.90135			0.515604			0.257802	+	0.966198i	$0.417002\pi$
$132$	−2.83488	+	4.91015i	−0.246744	+	0.427374i
$133$	−7.75680	+	13.4352i	−0.672600	+	1.16498i
$134$	−17.8625	−	30.9387i	−1.54308	−	2.67270i
$135$	−3.07670			−0.264800
$136$	0.414222	+	0.717454i	0.0355193	+	0.0615212i
$137$	9.91725	+	17.1772i	0.847288	+	1.46755i	0.883619	+	0.468206i	$0.155099\pi$
$137$	9.91725	+	17.1772i	0.847288	+	1.46755i	−0.0363315	+	0.999340i	$0.511567\pi$
$138$	−6.59306			−0.561238
$139$	7.09107	+	12.2821i	0.601456	+	1.04175i	0.992601	+	0.121424i	$0.0387460\pi$
$139$	7.09107	+	12.2821i	0.601456	+	1.04175i	−0.391144	+	0.920329i	$0.627921\pi$
$140$	20.3675	−	35.2775i	1.72136	−	2.98149i
$141$	−0.882255	+	1.52811i	−0.0742993	+	0.128690i
$142$	−13.8653			−1.16355
$143$	0.178784	+	3.60112i	0.0149507	+	0.301140i
$144$	16.8066			1.40055
$145$	2.29734	−	3.97910i	0.190783	−	0.330447i
$146$	−13.8465	+	23.9828i	−1.14594	+	1.98483i
$147$	−0.773495	−	1.33973i	−0.0637968	−	0.110499i
$148$	36.7129			3.01778
$149$	10.1724	+	17.6192i	0.833359	+	1.44342i	0.895360	+	0.445343i	$0.146918\pi$
$149$	10.1724	+	17.6192i	0.833359	+	1.44342i	−0.0620012	+	0.998076i	$0.519748\pi$
$150$	−6.18422	−	10.7114i	−0.504940	−	0.874581i
$151$	−5.65027			−0.459813			−0.229906	−	0.973213i	$-0.573842\pi$
$151$	−5.65027			−0.459813			−0.229906	+	0.973213i	$0.573842\pi$
$152$	−33.7592	−	58.4727i	−2.73823	−	4.74276i
$153$	−0.0407573	+	0.0705938i	−0.00329503	+	0.00570717i
$154$	3.23354	−	5.60066i	0.260566	−	0.451314i
$155$	−10.1214			−0.812967
$156$	17.1752	−	11.0866i	1.37512	−	0.887636i
$157$	−13.4264			−1.07155			−0.535773	−	0.844362i	$-0.679980\pi$
$157$	−13.4264			−1.07155			−0.535773	+	0.844362i	$0.679980\pi$
$158$	16.1683	−	28.0044i	1.28628	−	2.22791i
$159$	6.67462	−	11.5608i	0.529332	−	0.916830i
$160$	40.3331	+	69.8590i	3.18861	+	5.52284i
$161$	5.55923			0.438128
$162$	1.38472	+	2.39840i	0.108794	+	0.188436i
$163$	2.73189	+	4.73177i	0.213978	+	0.370621i	0.952956	−	0.303109i	$-0.0980245\pi$
$163$	2.73189	+	4.73177i	0.213978	+	0.370621i	−0.738978	+	0.673730i	$0.764691\pi$
$164$	50.7205			3.96061
$165$	−1.53835	−	2.66450i	−0.119760	−	0.207431i
$166$	0.909352	−	1.57504i	0.0705794	−	0.122247i
$167$	0.669237	−	1.15915i	0.0517871	−	0.0896980i	−0.838970	−	0.544178i	$-0.816842\pi$
$167$	0.669237	−	1.15915i	0.0517871	−	0.0896980i	0.890757	+	0.454480i	$0.150175\pi$
$168$	−23.7326			−1.83101
$169$	5.35290	−	11.8468i	0.411762	−	0.911291i
$170$	−0.694562			−0.0532705
$171$	3.32173	−	5.75341i	0.254019	−	0.439974i
$172$	−10.3304	+	17.8928i	−0.787687	+	1.36431i
$173$	8.49068	+	14.7063i	0.645534	+	1.11810i	0.984178	+	0.177183i	$0.0566986\pi$
$173$	8.49068	+	14.7063i	0.645534	+	1.11810i	−0.338644	+	0.940915i	$0.609968\pi$
$174$	−4.13581			−0.313535
$175$	5.21450	+	9.03178i	0.394179	+	0.682738i
$176$	8.40330	+	14.5549i	0.633422	+	1.09712i
$177$	−8.18622			−0.615314
$178$	12.8650	+	22.2828i	0.964273	+	1.67017i
$179$	−1.12137	+	1.94228i	−0.0838154	+	0.145173i	−0.904886	−	0.425654i	$-0.860044\pi$
$179$	−1.12137	+	1.94228i	−0.0838154	+	0.145173i	0.821070	+	0.570827i	$0.193377\pi$
$180$	−8.72205	+	15.1070i	−0.650103	+	1.12601i
$181$	−16.9181			−1.25751			−0.628754	−	0.777604i	$-0.716435\pi$
$181$	−16.9181			−1.25751			−0.628754	+	0.777604i	$0.716435\pi$
$182$	−19.5905	+	12.6457i	−1.45215	+	0.937360i
$183$	−11.8838			−0.878474
$184$	−12.0974	+	20.9534i	−0.891836	+	1.54470i
$185$	−9.96113	+	17.2532i	−0.732357	+	1.26848i
$186$	4.55528	+	7.88997i	0.334009	+	0.578521i
$187$	−0.0815147			−0.00596094
$188$	5.00217	+	8.66401i	0.364821	+	0.631888i
$189$	−1.16758	−	2.02232i	−0.0849292	−	0.147102i
$190$	56.6070			4.10670
$191$	−3.17684	−	5.50245i	−0.229868	−	0.398143i	0.727901	−	0.685682i	$-0.240496\pi$
$191$	−3.17684	−	5.50245i	−0.229868	−	0.398143i	−0.957769	+	0.287539i	$0.907163\pi$
$192$	19.4985	−	33.7724i	1.40718	−	2.43732i
$193$	5.48496	−	9.50023i	0.394816	−	0.683842i	−0.598262	−	0.801301i	$-0.704142\pi$
$193$	5.48496	−	9.50023i	0.394816	−	0.683842i	0.993078	+	0.117459i	$0.0374749\pi$
$194$	−2.06886			−0.148535
$195$	0.550064	+	11.0795i	0.0393909	+	0.793422i
$196$	−8.77105			−0.626503
$197$	−7.13087	+	12.3510i	−0.508054	+	0.879975i	0.491903	+	0.870650i	$0.336302\pi$
$197$	−7.13087	+	12.3510i	−0.508054	+	0.879975i	−0.999957	+	0.00932472i	$0.997032\pi$
$198$	−1.38472	+	2.39840i	−0.0984075	+	0.170447i
$199$	−4.46845	−	7.73958i	−0.316760	−	0.548645i	0.663050	−	0.748575i	$-0.269262\pi$
$199$	−4.46845	−	7.73958i	−0.316760	−	0.548645i	−0.979810	+	0.199931i	$0.935928\pi$
$200$	−45.3891			−3.20950
$201$	−6.44987	−	11.1715i	−0.454939	−	0.787977i
$202$	12.9141	+	22.3679i	0.908632	+	1.57380i
$203$	3.48729			0.244760
$204$	0.231084	+	0.400249i	0.0161791	+	0.0280231i
$205$	−13.7618	+	23.8361i	−0.961163	+	1.66478i
$206$	−15.1281	+	26.2026i	−1.05402	+	1.82562i
$207$	−2.38065			−0.165467
$208$	−3.00475	−	60.5225i	−0.208342	−	4.19648i
$209$	6.64346			0.459538
$210$	9.94863	−	17.2315i	0.686521	−	1.18909i
$211$	6.61661	−	11.4603i	0.455506	−	0.788960i	−0.543211	−	0.839596i	$-0.682792\pi$
$211$	6.61661	−	11.4603i	0.455506	−	0.788960i	0.998717	+	0.0506365i	$0.0161250\pi$
$212$	−37.8435	−	65.5468i	−2.59910	−	4.50177i
$213$	−5.00654			−0.343042
$214$	−17.9399	−	31.0728i	−1.22635	−	2.12409i
$215$	−5.60581	−	9.70955i	−0.382313	−	0.662186i
$216$	10.1631			0.691514
$217$	−3.84098	−	6.65278i	−0.260743	−	0.451620i
$218$	−8.67969	+	15.0337i	−0.587863	+	1.01821i
$219$	−4.99976	+	8.65984i	−0.337852	+	0.585178i
$220$	−17.4441			−1.17608
$221$	0.261503	+	0.134151i	0.0175906	+	0.00902396i
$222$	17.9327			1.20356
$223$	−3.87763	+	6.71625i	−0.259665	+	0.449754i	−0.966152	−	0.257973i	$-0.916946\pi$
$223$	−3.87763	+	6.71625i	−0.259665	+	0.449754i	0.706487	+	0.707726i	$0.250279\pi$
$224$	−30.6123	+	53.0220i	−2.04537	+	3.54268i
$225$	−2.23303	−	3.86772i	−0.148869	−	0.257848i
$226$	−19.9779			−1.32891
$227$	−5.98320	−	10.3632i	−0.397119	−	0.687830i	0.596250	−	0.802799i	$-0.296657\pi$
$227$	−5.98320	−	10.3632i	−0.397119	−	0.687830i	−0.993369	+	0.114969i	$0.963323\pi$
$228$	−18.8334	−	32.6204i	−1.24727	−	2.16034i
$229$	5.90101			0.389950			0.194975	−	0.980808i	$-0.437538\pi$
$229$	5.90101			0.389950			0.194975	+	0.980808i	$0.437538\pi$
$230$	−10.1424	−	17.5672i	−0.668771	−	1.15835i
$231$	1.16758	−	2.02232i	0.0768214	−	0.133059i
$232$	−7.58870	+	13.1440i	−0.498223	+	0.862947i
$233$	4.77824			0.313033			0.156517	−	0.987675i	$-0.449974\pi$
$233$	4.77824			0.313033			0.156517	+	0.987675i	$0.449974\pi$
$234$	8.38935	−	5.41532i	0.548429	−	0.354010i
$235$	−5.42886			−0.354140
$236$	−23.2069	+	40.1956i	−1.51064	+	2.61651i
$237$	5.83815	−	10.1120i	0.379228	−	0.656843i
$238$	−0.263581	−	0.456536i	−0.0170854	−	0.0295928i
$239$	10.7589			0.695936			0.347968	−	0.937506i	$-0.386872\pi$
$239$	10.7589			0.695936			0.347968	+	0.937506i	$0.386872\pi$
$240$	25.8544	+	44.7811i	1.66889	+	2.89061i
$241$	11.5230	+	19.9584i	0.742261	+	1.28563i	0.951464	+	0.307761i	$0.0995798\pi$
$241$	11.5230	+	19.9584i	0.742261	+	1.28563i	−0.209203	+	0.977872i	$0.567087\pi$
$242$	−2.76943			−0.178026
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−33.6890	+	58.3511i	−2.15672	+	3.73555i
$245$	2.37981	−	4.12195i	0.152040	−	0.263342i
$246$	24.7748			1.57958
$247$	−21.3126	−	10.9333i	−1.35609	−	0.695671i
$248$	33.4335			2.12303
$249$	0.328353	−	0.568724i	0.0208085	−	0.0360414i
$250$	−2.27478	+	3.94004i	−0.143870	+	0.249190i
$251$	12.5532	+	21.7428i	0.792352	+	1.37239i	0.924507	+	0.381164i	$0.124477\pi$
$251$	12.5532	+	21.7428i	0.792352	+	1.37239i	−0.132156	+	0.991229i	$0.542190\pi$
$252$	−13.2398			−0.834031
$253$	−1.19033	−	2.06171i	−0.0748352	−	0.129618i
$254$	−7.84957	−	13.5959i	−0.492526	−	0.853080i
$255$	−0.250796			−0.0157054
$256$	−37.9416	−	65.7168i	−2.37135	−	4.10730i
$257$	9.00210	−	15.5921i	0.561536	−	0.972608i	−0.435827	−	0.900030i	$-0.643544\pi$
$257$	9.00210	−	15.5921i	0.561536	−	0.972608i	0.997363	−	0.0725779i	$-0.0231226\pi$
$258$	−5.04597	+	8.73988i	−0.314148	+	0.544121i
$259$	−15.1207			−0.939556
$260$	55.9616	+	28.7082i	3.47059	+	1.78041i
$261$	−1.49338			−0.0924378
$262$	8.17170	−	14.1538i	0.504849	−	0.874424i
$263$	−3.01230	+	5.21745i	−0.185746	+	0.321722i	−0.943828	−	0.330438i	$-0.892804\pi$
$263$	−3.01230	+	5.21745i	−0.185746	+	0.321722i	0.758081	+	0.652160i	$0.226137\pi$
$264$	5.08157	+	8.80153i	0.312749	+	0.541697i
$265$	41.0716			2.52301
$266$	21.4819	+	37.2078i	1.31714	+	2.28136i
$267$	4.64536	+	8.04600i	0.284291	+	0.492407i
$268$	−73.1383			−4.46763
$269$	−2.42124	−	4.19371i	−0.147625	−	0.255695i	0.782724	−	0.622369i	$-0.213830\pi$
$269$	−2.42124	−	4.19371i	−0.147625	−	0.255695i	−0.930349	+	0.366674i	$0.880496\pi$
$270$	−4.26035	+	7.37914i	−0.259277	+	0.449080i
$271$	−3.77886	+	6.54517i	−0.229549	+	0.397591i	−0.957675	−	0.287853i	$-0.907059\pi$
$271$	−3.77886	+	6.54517i	−0.229549	+	0.397591i	0.728125	+	0.685444i	$0.240392\pi$
$272$	1.36998			0.0830675
$273$	−7.07385	+	4.56616i	−0.428129	+	0.276357i
$274$	54.9303			3.31846
$275$	2.23303	−	3.86772i	0.134657	−	0.233232i
$276$	−6.74886	+	11.6894i	−0.406234	+	0.703617i
$277$	9.89163	+	17.1328i	0.594331	+	1.02941i	0.993641	+	0.112595i	$0.0359163\pi$
$277$	9.89163	+	17.1328i	0.594331	+	1.02941i	−0.399310	+	0.916816i	$0.630750\pi$
$278$	39.2765			2.35564
$279$	1.64484	+	2.84895i	0.0984741	+	0.170562i
$280$	−36.5090	−	63.2355i	−2.18183	−	3.77904i
$281$	−10.1888			−0.607815			−0.303908	−	0.952702i	$-0.598291\pi$
$281$	−10.1888			−0.607815			−0.303908	+	0.952702i	$0.598291\pi$
$282$	2.44335	+	4.23200i	0.145499	+	0.252012i
$283$	6.31581	−	10.9393i	0.375436	−	0.650275i	−0.614956	−	0.788561i	$-0.710826\pi$
$283$	6.31581	−	10.9393i	0.375436	−	0.650275i	0.990392	+	0.138287i	$0.0441596\pi$
$284$	−14.1929	+	24.5828i	−0.842195	+	1.45872i
$285$	20.4399			1.21076
$286$	8.88448	+	4.55773i	0.525350	+	0.269504i
$287$	−20.8900			−1.23310
$288$	13.1092	−	22.7059i	0.772469	−	1.33796i
$289$	8.49668	−	14.7167i	0.499805	−	0.865687i
$290$	−6.36232	−	11.0199i	−0.373608	−	0.647108i
$291$	−0.747032			−0.0437918
$292$	28.3474	+	49.0991i	1.65891	+	2.87331i
$293$	−7.78793	−	13.4891i	−0.454976	−	0.788041i	0.543711	−	0.839273i	$-0.317019\pi$
$293$	−7.78793	−	13.4891i	−0.454976	−	0.788041i	−0.998687	+	0.0512312i	$0.983685\pi$
$294$	−4.28428			−0.249864
$295$	−12.5933	−	21.8122i	−0.733207	−	1.26995i
$296$	32.9042	−	56.9918i	1.91252	−	3.31258i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	56.3438			3.26391
$299$	0.425622	+	8.57301i	0.0246144	+	0.495790i
$300$	−25.3214			−1.46193
$301$	4.25473	−	7.36941i	0.245239	−	0.424766i
$302$	−7.82402	+	13.5516i	−0.450222	+	0.779807i
$303$	4.66308	+	8.07669i	0.267887	+	0.463994i
$304$	−111.654			−6.40380
$305$	−18.2814	−	31.6643i	−1.04679	−	1.81309i
$306$	0.112875	+	0.195505i	0.00645261	+	0.0111763i
$307$	−16.4089			−0.936508			−0.468254	−	0.883594i	$-0.655117\pi$
$307$	−16.4089			−0.936508			−0.468254	+	0.883594i	$0.655117\pi$
$308$	−6.61991	−	11.4660i	−0.377205	−	0.653338i
$309$	−5.46251	+	9.46135i	−0.310751	+	0.538237i
$310$	−14.0152	+	24.2750i	−0.796010	+	1.37873i
$311$	0.222728			0.0126297			0.00631486	−	0.999980i	$-0.497990\pi$
$311$	0.222728			0.0126297			0.00631486	+	0.999980i	$0.497990\pi$
$312$	−1.81700	−	36.5986i	−0.102868	−	2.07199i
$313$	−18.0333			−1.01930			−0.509650	−	0.860382i	$-0.670225\pi$
$313$	−18.0333			−1.01930			−0.509650	+	0.860382i	$0.670225\pi$
$314$	−18.5918	+	32.2019i	−1.04920	+	1.81726i
$315$	3.59230	−	6.22205i	0.202403	−	0.350573i
$316$	−33.1008	−	57.3323i	−1.86207	−	3.22520i
$317$	16.3907			0.920596			0.460298	−	0.887765i	$-0.347743\pi$
$317$	16.3907			0.920596			0.460298	+	0.887765i	$0.347743\pi$
$318$	−18.4849	−	32.0168i	−1.03658	−	1.79541i
$319$	−0.746689	−	1.29330i	−0.0418066	−	0.0724111i
$320$	119.982			6.70720
$321$	−6.47782	−	11.2199i	−0.361557	−	0.626235i
$322$	7.69795	−	13.3332i	0.428990	−	0.743032i
$323$	0.270770	−	0.468987i	0.0150660	−	0.0260951i
$324$	5.66975			0.314986
$325$	−13.5289	+	8.73288i	−0.750447	+	0.484413i
$326$	15.1316			0.838060
$327$	−3.13411	+	5.42843i	−0.173316	+	0.300193i
$328$	45.4587	−	78.7368i	2.51004	−	4.34751i
$329$	−2.06021	−	3.56840i	−0.113583	−	0.196732i
$330$	−8.52070			−0.469049
$331$	−8.79904	−	15.2404i	−0.483639	−	0.837687i	0.516184	−	0.856477i	$-0.327352\pi$
$331$	−8.79904	−	15.2404i	−0.483639	−	0.837687i	−0.999823	+	0.0187901i	$0.994019\pi$
$332$	−1.86168	−	3.22453i	−0.102173	−	0.176969i
$333$	6.47521			0.354840
$334$	−1.85341	−	3.21020i	−0.101414	−	0.175654i
$335$	19.8443	−	34.3713i	1.08421	−	1.87791i
$336$	−19.6231	+	33.9882i	−1.07053	+	1.85421i
$337$	−23.2778			−1.26802			−0.634012	−	0.773323i	$-0.718593\pi$
$337$	−23.2778			−1.26802			−0.634012	+	0.773323i	$0.718593\pi$
$338$	−21.0011	−	29.2428i	−1.14231	−	1.59060i
$339$	−7.21373			−0.391796
$340$	−0.710975	+	1.23145i	−0.0385580	+	0.0667845i
$341$	−1.64484	+	2.84895i	−0.0890732	+	0.154279i
$342$	−9.19931	−	15.9337i	−0.497442	−	0.861594i
$343$	19.9587			1.07767
$344$	18.5175	+	32.0732i	0.998395	+	1.72927i
$345$	−3.66227	−	6.34324i	−0.197170	−	0.341509i
$346$	47.0287			2.52828
$347$	−14.6668	−	25.4036i	−0.787353	−	1.36374i	−0.927583	−	0.373616i	$-0.878118\pi$
$347$	−14.6668	−	25.4036i	−0.787353	−	1.36374i	0.140230	−	0.990119i	$-0.455216\pi$
$348$	−4.23354	+	7.33271i	−0.226942	+	0.393075i
$349$	−3.82748	+	6.62939i	−0.204880	+	0.354863i	−0.950095	−	0.311962i	$-0.899014\pi$
$349$	−3.82748	+	6.62939i	−0.204880	+	0.354863i	0.745214	+	0.666825i	$0.232347\pi$
$350$	28.8824			1.54383
$351$	3.02927	−	1.95539i	0.161690	−	0.104371i
$352$	26.2185			1.39745
$353$	11.7343	−	20.3244i	0.624553	−	1.08176i	−0.364074	−	0.931370i	$-0.618614\pi$
$353$	11.7343	−	20.3244i	0.624553	−	1.08176i	0.988627	−	0.150388i	$-0.0480523\pi$
$354$	−11.3356	+	19.6338i	−0.602480	+	1.04353i
$355$	−7.70180	−	13.3399i	−0.408769	−	0.708008i
$356$	52.6761			2.79183
$357$	−0.0951752	−	0.164848i	−0.00503721	−	0.00872470i
$358$	3.10557	+	5.37900i	0.164134	+	0.284289i
$359$	11.4336			0.603441			0.301721	−	0.953396i	$-0.402439\pi$
$359$	11.4336			0.603441			0.301721	+	0.953396i	$0.402439\pi$
$360$	15.6344	+	27.0796i	0.824007	+	1.42722i
$361$	−12.5678	+	21.7681i	−0.661464	+	1.14569i
$362$	−23.4267	+	40.5762i	−1.23128	+	2.13264i
$363$	−1.00000			−0.0524864
$364$	2.36707	+	47.6782i	0.124068	+	2.49901i
$365$	−30.7655			−1.61034
$366$	−16.4556	+	28.5020i	−0.860151	+	1.48982i
$367$	10.7190	−	18.5659i	0.559528	−	0.969130i	−0.438008	−	0.898971i	$-0.644316\pi$
$367$	10.7190	−	18.5659i	0.559528	−	0.969130i	0.997536	−	0.0701594i	$-0.0223508\pi$
$368$	20.0053	+	34.6503i	1.04285	+	1.80627i
$369$	8.94581			0.465700
$370$	27.5867	+	47.7815i	1.43416	+	2.48404i
$371$	15.5864	+	26.9964i	0.809204	+	1.40158i
$372$	18.6517			0.967045
$373$	4.23067	+	7.32774i	0.219056	+	0.379416i	0.954520	−	0.298148i	$-0.0963690\pi$
$373$	4.23067	+	7.32774i	0.219056	+	0.379416i	−0.735464	+	0.677564i	$0.763036\pi$
$374$	−0.112875	+	0.195505i	−0.00583661	+	0.0101093i
$375$	−0.821389	+	1.42269i	−0.0424163	+	0.0734673i
$376$	17.9330			0.924821
$377$	0.266992	+	5.37783i	0.0137508	+	0.276972i
$378$	−6.46709			−0.332631
$379$	0.302515	−	0.523972i	0.0155392	−	0.0269146i	−0.858151	−	0.513397i	$-0.828387\pi$
$379$	0.302515	−	0.523972i	0.0155392	−	0.0269146i	0.873690	+	0.486482i	$0.161720\pi$
$380$	57.9446	−	100.363i	2.97250	−	5.14852i
$381$	−2.83436	−	4.90926i	−0.145209	−	0.251509i
$382$	−17.5961			−0.900294
$383$	5.11608	+	8.86131i	0.261419	+	0.452792i	0.966619	−	0.256217i	$-0.0824761\pi$
$383$	5.11608	+	8.86131i	0.261419	+	0.452792i	−0.705200	+	0.709008i	$0.749143\pi$
$384$	−27.7814	−	48.1188i	−1.41771	−	2.45555i
$385$	7.18460			0.366161
$386$	−15.1902	−	26.3102i	−0.773162	−	1.33916i
$387$	−1.82202	+	3.15584i	−0.0926187	+	0.160420i
$388$	−2.11774	+	3.66804i	−0.107512	+	0.186217i
$389$	−23.0095			−1.16663			−0.583315	−	0.812246i	$-0.698245\pi$
$389$	−23.0095			−1.16663			−0.583315	+	0.812246i	$0.698245\pi$
$390$	27.3348	+	14.0227i	1.38415	+	0.710069i
$391$	−0.194058			−0.00981394
$392$	−7.86113	+	13.6159i	−0.397047	+	0.687705i
$393$	2.95068	−	5.11072i	0.148842	−	0.257802i
$394$	19.7485	+	34.2054i	0.994914	+	1.72324i
$395$	35.9244			1.80755
$396$	2.83488	+	4.91015i	0.142458	+	0.246744i
$397$	3.25386	+	5.63586i	0.163307	+	0.282856i	0.936053	−	0.351860i	$-0.114451\pi$
$397$	3.25386	+	5.63586i	0.163307	+	0.282856i	−0.772746	+	0.634715i	$0.781117\pi$
$398$	−24.7501			−1.24061
$399$	7.75680	+	13.4352i	0.388326	+	0.672600i
$400$	−37.5296	+	65.0032i	−1.87648	+	3.25016i
$401$	−6.16517	+	10.6784i	−0.307874	+	0.533254i	−0.977897	−	0.209087i	$-0.932951\pi$
$401$	−6.16517	+	10.6784i	−0.307874	+	0.533254i	0.670023	+	0.742340i	$0.266284\pi$
$402$	−35.7249			−1.78180
$403$	9.96533	−	6.43261i	0.496408	−	0.320431i
$404$	52.8770			2.63073
$405$	−1.53835	+	2.66450i	−0.0764411	+	0.132400i
$406$	4.82891	−	8.36391i	0.239655	−	0.415094i
$407$	3.23761	+	5.60770i	0.160482	+	0.277963i
$408$	0.828444			0.0410141
$409$	−6.17787	−	10.7004i	−0.305476	−	0.529100i	0.671891	−	0.740650i	$-0.265482\pi$
$409$	−6.17787	−	10.7004i	−0.305476	−	0.529100i	−0.977367	+	0.211550i	$0.932149\pi$
$410$	38.1123	+	66.0124i	1.88223	+	3.26012i
$411$	19.8345			0.978364
$412$	30.9711	+	53.6435i	1.52584	+	2.64283i
$413$	9.55810	−	16.5551i	0.470323	−	0.814624i
$414$	−3.29653	+	5.70976i	−0.162016	+	0.280619i
$415$	2.02049			0.0991818
$416$	−84.1101	−	43.1484i	−4.12384	−	2.11553i
$417$	14.1821			0.694502
$418$	9.19931	−	15.9337i	0.449953	−	0.779341i
$419$	13.8942	−	24.0654i	0.678775	−	1.17567i	−0.296576	−	0.955009i	$-0.595845\pi$
$419$	13.8942	−	24.0654i	0.678775	−	1.17567i	0.975350	−	0.220663i	$-0.0708220\pi$
$420$	−20.3675	−	35.2775i	−0.993830	−	1.72136i
$421$	−5.37329			−0.261878			−0.130939	−	0.991390i	$-0.541799\pi$
$421$	−5.37329			−0.261878			−0.130939	+	0.991390i	$0.541799\pi$
$422$	−18.3242	−	31.7385i	−0.892010	−	1.54501i
$423$	0.882255	+	1.52811i	0.0428967	+	0.0742993i
$424$	−135.670			−6.58873
$425$	−0.182025	−	0.315276i	−0.00882949	−	0.0152931i
$426$	−6.93263	+	12.0077i	−0.335887	+	0.581774i
$427$	13.8753	−	24.0327i	0.671473	−	1.16303i
$428$	−73.4553			−3.55060
$429$	3.20805	+	1.64573i	0.154886	+	0.0794564i
$430$	−31.0498			−1.49736
$431$	−5.83737	+	10.1106i	−0.281176	+	0.487011i	−0.971675	−	0.236322i	$-0.924058\pi$
$431$	−5.83737	+	10.1106i	−0.281176	+	0.487011i	0.690499	+	0.723334i	$0.257391\pi$
$432$	8.40330	−	14.5549i	0.404304	−	0.700275i
$433$	−14.6447	−	25.3654i	−0.703781	−	1.21898i	−0.967130	−	0.254283i	$-0.918160\pi$
$433$	−14.6447	−	25.3654i	−0.703781	−	1.21898i	0.263349	−	0.964701i	$-0.415173\pi$
$434$	−21.2747			−1.02122
$435$	−2.29734	−	3.97910i	−0.110149	−	0.190783i
$436$	17.7696	+	30.7779i	0.851010	+	1.47399i
$437$	15.8158			0.756572
$438$	13.8465	+	23.9828i	0.661611	+	1.14594i
$439$	1.15879	−	2.00709i	0.0553062	−	0.0957932i	−0.837047	−	0.547131i	$-0.815720\pi$
$439$	1.15879	−	2.00709i	0.0553062	−	0.0957932i	0.892353	+	0.451338i	$0.149053\pi$
$440$	−15.6344	+	27.0796i	−0.745342	+	1.29097i
$441$	−1.54699			−0.0736662
$442$	0.683855	−	0.441428i	0.0325276	−	0.0209966i
$443$	−24.6517			−1.17124			−0.585620	−	0.810586i	$-0.699149\pi$
$443$	−24.6517			−1.17124			−0.585620	+	0.810586i	$0.699149\pi$
$444$	18.3564	−	31.7943i	0.871158	−	1.50889i
$445$	−14.2924	+	24.7551i	−0.677522	+	1.17350i
$446$	10.7388	+	18.6002i	0.508498	+	0.880745i
$447$	20.3449			0.962280
$448$	45.5323	+	78.8643i	2.15120	+	3.72599i
$449$	6.20598	+	10.7491i	0.292878	+	0.507280i	0.974489	−	0.224435i	$-0.0720535\pi$
$449$	6.20598	+	10.7491i	0.292878	+	0.507280i	−0.681611	+	0.731715i	$0.738720\pi$
$450$	−12.3684			−0.583054
$451$	4.47290	+	7.74730i	0.210621	+	0.364806i
$452$	−20.4500	+	35.4205i	−0.961889	+	1.66604i
$453$	−2.82514	+	4.89328i	−0.132736	+	0.229906i
$454$	−33.1401			−1.55534
$455$	−23.0486	−	11.8239i	−1.08053	−	0.554313i
$456$	−67.5184			−3.16184
$457$	13.1988	−	22.8610i	0.617413	−	1.06939i	−0.372543	−	0.928015i	$-0.621514\pi$
$457$	13.1988	−	22.8610i	0.617413	−	1.06939i	0.989956	−	0.141376i	$-0.0451525\pi$
$458$	8.17122	−	14.1530i	0.381816	−	0.661325i
$459$	0.0407573	+	0.0705938i	0.00190239	+	0.00329503i
$460$	−41.5284			−1.93627
$461$	−2.49907	−	4.32852i	−0.116393	−	0.201599i	0.801942	−	0.597401i	$-0.203800\pi$
$461$	−2.49907	−	4.32852i	−0.116393	−	0.201599i	−0.918336	+	0.395802i	$0.870467\pi$
$462$	−3.23354	−	5.60066i	−0.150438	−	0.260566i
$463$	24.4009			1.13401			0.567004	−	0.823715i	$-0.308103\pi$
$463$	24.4009			1.13401			0.567004	+	0.823715i	$0.308103\pi$
$464$	12.5493	+	21.7360i	0.582587	+	1.00907i
$465$	−5.06068	+	8.76535i	−0.234683	+	0.406483i
$466$	6.61651	−	11.4601i	0.306504	−	0.530880i
$467$	6.69697			0.309899			0.154949	−	0.987922i	$-0.450479\pi$
$467$	6.69697			0.309899			0.154949	+	0.987922i	$0.450479\pi$
$468$	−1.01366	−	20.4174i	−0.0468565	−	0.943796i
$469$	30.1231			1.39095
$470$	−7.51743	+	13.0206i	−0.346753	+	0.600594i
$471$	−6.71321	+	11.6276i	−0.309328	+	0.535773i
$472$	41.5988	+	72.0512i	1.91474	+	3.31643i
$473$	−3.64405			−0.167553
$474$	−16.1683	−	28.0044i	−0.742637	−	1.28628i
$475$	14.8350	+	25.6951i	0.680679	+	1.17897i
$476$	−1.07924			−0.0494669
$477$	−6.67462	−	11.5608i	−0.305610	−	0.529332i
$478$	14.8980	−	25.8042i	0.681420	−	1.18025i
$479$	13.4014	−	23.2119i	0.612326	−	1.06058i	−0.378521	−	0.925593i	$-0.623567\pi$
$479$	13.4014	−	23.2119i	0.612326	−	1.06058i	0.990847	−	0.134988i	$-0.0430994\pi$
$480$	80.6662			3.68189
$481$	−1.15766	−	23.3180i	−0.0527849	−	1.06321i
$482$	63.8243			2.90712
$483$	2.77961	−	4.81443i	0.126477	−	0.219064i
$484$	−2.83488	+	4.91015i	−0.128858	+	0.223189i
$485$	−1.14920	−	1.99047i	−0.0521823	−	0.0903824i
$486$	2.76943			0.125624
$487$	13.2674	+	22.9798i	0.601202	+	1.04131i	0.992639	+	0.121107i	$0.0386445\pi$
$487$	13.2674	+	22.9798i	0.601202	+	1.04131i	−0.391438	+	0.920205i	$0.628022\pi$
$488$	60.3882	+	104.595i	2.73364	+	4.73481i
$489$	5.46378			0.247081
$490$	−6.59072	−	11.4155i	−0.297738	−	0.515698i
$491$	0.825968	−	1.43062i	0.0372754	−	0.0645629i	−0.846786	−	0.531934i	$-0.821465\pi$
$491$	0.825968	−	1.43062i	0.0372754	−	0.0645629i	0.884061	+	0.467371i	$0.154799\pi$
$492$	25.3603	−	43.9253i	1.14333	−	1.98030i
$493$	−0.121732			−0.00548255
$494$	−55.7343	+	35.9765i	−2.50761	+	1.61866i
$495$	−3.07670			−0.138287
$496$	27.6442	−	47.8811i	1.24126	−	2.14993i
$497$	5.84555	−	10.1248i	0.262209	−	0.454159i
$498$	−0.909352	−	1.57504i	−0.0407490	−	0.0705794i
$499$	−1.34041			−0.0600050			−0.0300025	−	0.999550i	$-0.509552\pi$
$499$	−1.34041			−0.0600050			−0.0300025	+	0.999550i	$0.509552\pi$
$500$	4.65707	+	8.06629i	0.208271	+	0.360735i
$501$	−0.669237	−	1.15915i	−0.0298993	−	0.0517871i
$502$	69.5305			3.10330
$503$	7.35121	+	12.7327i	0.327774	+	0.567722i	0.982070	−	0.188517i	$-0.0603681\pi$
$503$	7.35121	+	12.7327i	0.327774	+	0.567722i	−0.654296	+	0.756239i	$0.727035\pi$
$504$	−11.8663	+	20.5531i	−0.528568	+	0.915506i
$505$	−14.3469	+	24.8495i	−0.638428	+	1.10579i
$506$	−6.59306			−0.293097
$507$	−7.58317	−	10.5591i	−0.336780	−	0.468948i
$508$	−32.1403			−1.42599
$509$	6.00714	−	10.4047i	0.266262	−	0.461179i	−0.701632	−	0.712540i	$-0.747545\pi$
$509$	6.00714	−	10.4047i	0.266262	−	0.461179i	0.967893	+	0.251361i	$0.0808781\pi$
$510$	−0.347281	+	0.601508i	−0.0153779	+	0.0266352i
$511$	−11.6753	−	20.2222i	−0.516484	−	0.894577i
$512$	−99.0278			−4.37645
$513$	−3.32173	−	5.75341i	−0.146658	−	0.254019i
$514$	−24.9307	−	43.1813i	−1.09965	−	1.90464i
$515$	−33.6130			−1.48116
$516$	10.3304	+	17.8928i	0.454772	+	0.787687i
$517$	−0.882255	+	1.52811i	−0.0388015	+	0.0672062i
$518$	−20.9379	+	36.2655i	−0.919958	+	1.59341i
$519$	16.9814			0.745399
$520$	94.7217	−	61.1428i	4.15382	−	2.68129i
$521$	−26.9428			−1.18038			−0.590192	−	0.807263i	$-0.700948\pi$
$521$	−26.9428			−1.18038			−0.590192	+	0.807263i	$0.700948\pi$
$522$	−2.06791	+	3.58172i	−0.0905098	+	0.156768i
$523$	−9.47958	+	16.4191i	−0.414513	+	0.717958i	−0.995377	−	0.0960427i	$-0.969381\pi$
$523$	−9.47958	+	16.4191i	−0.414513	+	0.717958i	0.580864	+	0.814001i	$0.302715\pi$
$524$	−16.7296	−	28.9765i	−0.730836	−	1.26585i
$525$	10.4290			0.455159
$526$	8.34236	+	14.4494i	0.363744	+	0.630023i
$527$	0.134079	+	0.232231i	0.00584056	+	0.0101161i
$528$	16.8066			0.731413
$529$	8.66624	+	15.0104i	0.376793	+	0.652625i
$530$	56.8725	−	98.5060i	2.47038	−	4.27883i
$531$	−4.09311	+	7.08947i	−0.177626	+	0.307657i
$532$	87.9583			3.81348
$533$	−1.59937	−	32.2149i	−0.0692762	−	1.39538i
$534$	25.7300			1.11345
$535$	19.9303	−	34.5203i	0.861662	−	1.49244i
$536$	−65.5509	+	113.537i	−2.83137	+	4.90407i
$537$	1.12137	+	1.94228i	0.0483908	+	0.0838154i
$538$	−13.4109			−0.578185
$539$	−0.773495	−	1.33973i	−0.0333168	−	0.0577063i
$540$	8.72205	+	15.1070i	0.375337	+	0.650103i
$541$	−3.59388			−0.154513			−0.0772565	−	0.997011i	$-0.524616\pi$
$541$	−3.59388			−0.154513			−0.0772565	+	0.997011i	$0.524616\pi$
$542$	10.4653	+	18.1264i	0.449523	+	0.778596i
$543$	−8.45903	+	14.6515i	−0.363012	+	0.628754i
$544$	1.06859	−	1.85086i	0.0458156	−	0.0793550i
$545$	−19.2854			−0.826095
$546$	1.15621	+	23.2887i	0.0494813	+	0.996666i
$547$	−7.24520			−0.309782			−0.154891	−	0.987932i	$-0.549503\pi$
$547$	−7.24520			−0.309782			−0.154891	+	0.987932i	$0.549503\pi$
$548$	56.2284	−	97.3904i	2.40196	−	4.16031i
$549$	−5.94189	+	10.2916i	−0.253594	+	0.439237i
$550$	−6.18422	−	10.7114i	−0.263696	−	0.456735i
$551$	9.92121			0.422658
$552$	12.0974	+	20.9534i	0.514902	+	0.891836i
$553$	13.6331	+	23.6131i	0.579736	+	1.00413i
$554$	54.7884			2.32774
$555$	9.96113	+	17.2532i	0.422827	+	0.732357i
$556$	40.2046	−	69.6364i	1.70505	−	2.95324i
$557$	15.3577	−	26.6003i	0.650725	−	1.12709i	−0.332222	−	0.943201i	$-0.607798\pi$
$557$	15.3577	−	26.6003i	0.650725	−	1.12709i	0.982947	−	0.183888i	$-0.0588684\pi$
$558$	9.11055			0.385680
$559$	11.6903	+	5.99711i	0.494446	+	0.253651i
$560$	−120.749			−5.10256
$561$	−0.0407573	+	0.0705938i	−0.00172078	+	0.00298047i
$562$	−14.1086	+	24.4369i	−0.595137	+	1.03081i
$563$	16.5498	+	28.6651i	0.697491	+	1.20809i	0.969334	+	0.245748i	$0.0790334\pi$
$563$	16.5498	+	28.6651i	0.697491	+	1.20809i	−0.271843	+	0.962342i	$0.587633\pi$
$564$	10.0043			0.421259
$565$	−11.0972	−	19.2210i	−0.466864	−	0.808632i
$566$	−17.4912	−	30.2957i	−0.735211	−	1.27342i
$567$	−2.33517			−0.0980678
$568$	25.4410	+	44.0652i	1.06748	+	1.84893i
$569$	15.6229	−	27.0596i	0.654946	−	1.13440i	−0.326962	−	0.945038i	$-0.606025\pi$
$569$	15.6229	−	27.0596i	0.654946	−	1.13440i	0.981907	−	0.189362i	$-0.0606418\pi$
$570$	28.3035	−	49.0231i	1.18550	−	2.05335i
$571$	2.16928			0.0907816			0.0453908	−	0.998969i	$-0.485547\pi$
$571$	2.16928			0.0907816			0.0453908	+	0.998969i	$0.485547\pi$
$572$	17.1752	−	11.0866i	0.718131	−	0.463553i
$573$	−6.35368			−0.265429
$574$	−28.9267	+	50.1025i	−1.20738	+	2.09124i
$575$	5.31607	−	9.20770i	0.221695	−	0.383988i
$576$	−19.4985	−	33.7724i	−0.812439	−	1.40718i
$577$	8.47580			0.352852			0.176426	−	0.984314i	$-0.443546\pi$
$577$	8.47580			0.352852			0.176426	+	0.984314i	$0.443546\pi$
$578$	−23.5310	−	40.7568i	−0.978759	−	1.69526i
$579$	−5.48496	−	9.50023i	−0.227947	−	0.394816i
$580$	−26.0507			−1.08169
$581$	0.766760	+	1.32807i	0.0318106	+	0.0550975i
$582$	−1.03443	+	1.79168i	−0.0428784	+	0.0742676i
$583$	6.67462	−	11.5608i	0.276435	−	0.478799i
$584$	101.626			4.20533
$585$	9.87019	+	5.06340i	0.408082	+	0.209346i
$586$	−43.1363			−1.78194
$587$	4.22782	−	7.32279i	0.174501	−	0.302244i	−0.765488	−	0.643451i	$-0.777502\pi$
$587$	4.22782	−	7.32279i	0.174501	−	0.302244i	0.939988	+	0.341207i	$0.110836\pi$
$588$	−4.38552	+	7.59595i	−0.180856	+	0.313252i
$589$	−10.9274	−	18.9269i	−0.450258	−	0.779869i
$590$	−69.7523			−2.87166
$591$	7.13087	+	12.3510i	0.293325	+	0.508054i
$592$	−54.4132	−	94.2464i	−2.23637	−	3.87350i
$593$	−18.0573			−0.741525			−0.370762	−	0.928728i	$-0.620904\pi$
$593$	−18.0573			−0.741525			−0.370762	+	0.928728i	$0.620904\pi$
$594$	1.38472	+	2.39840i	0.0568156	+	0.0984075i
$595$	0.292825	−	0.507188i	0.0120047	−	0.0207927i
$596$	57.6752	−	99.8964i	2.36247	−	4.09192i
$597$	−8.93690			−0.365763
$598$	21.1509	+	10.8504i	0.864923	+	0.443705i
$599$	25.6466			1.04789			0.523945	−	0.851752i	$-0.324460\pi$
$599$	25.6466			1.04789			0.523945	+	0.851752i	$0.324460\pi$
$600$	−22.6946	+	39.3081i	−0.926502	+	1.60475i
$601$	−21.1152	+	36.5726i	−0.861308	+	1.49183i	0.00935921	+	0.999956i	$0.497021\pi$
$601$	−21.1152	+	36.5726i	−0.861308	+	1.49183i	−0.870667	+	0.491873i	$0.836313\pi$
$602$	−11.7832	−	20.4091i	−0.480247	−	0.831812i
$603$	−12.8997			−0.525318
$604$	16.0178	+	27.7437i	0.651756	+	1.12887i
$605$	−1.53835	−	2.66450i	−0.0625427	−	0.108327i
$606$	25.8282			1.04920
$607$	−17.8076	−	30.8436i	−0.722788	−	1.25190i	−0.959878	−	0.280417i	$-0.909527\pi$
$607$	−17.8076	−	30.8436i	−0.722788	−	1.25190i	0.237091	−	0.971488i	$-0.423806\pi$
$608$	−87.0907	+	150.846i	−3.53199	+	6.11759i
$609$	1.74365	−	3.02008i	0.0706561	−	0.122380i
$610$	−101.258			−4.09982
$611$	5.34517	−	3.45030i	0.216242	−	0.139584i
$612$	0.462168			0.0186820
$613$	−6.18611	+	10.7147i	−0.249855	+	0.432761i	−0.963485	−	0.267761i	$-0.913716\pi$
$613$	−6.18611	+	10.7147i	−0.249855	+	0.432761i	0.713631	+	0.700522i	$0.247050\pi$
$614$	−22.7217	+	39.3552i	−0.916974	+	1.58825i
$615$	13.7618	+	23.8361i	0.554928	+	0.961163i
$616$	−23.7326			−0.956215
$617$	−6.53716	−	11.3227i	−0.263176	−	0.455834i	0.703908	−	0.710291i	$-0.251437\pi$
$617$	−6.53716	−	11.3227i	−0.263176	−	0.455834i	−0.967084	+	0.254457i	$0.918103\pi$
$618$	15.1281	+	26.2026i	0.608540	+	1.05402i
$619$	24.0004			0.964657			0.482329	−	0.875990i	$-0.339791\pi$
$619$	24.0004			0.964657			0.482329	+	0.875990i	$0.339791\pi$
$620$	28.6928	+	49.6974i	1.15233	+	1.99589i
$621$	−1.19033	+	2.06171i	−0.0477662	+	0.0827334i
$622$	0.308415	−	0.534190i	0.0123663	−	0.0214191i
$623$	−21.6954			−0.869207
$624$	−53.9164	−	27.6591i	−2.15838	−	1.10725i
$625$	−27.3846			−1.09538
$626$	−24.9710	+	43.2510i	−0.998040	+	1.72866i
$627$	3.32173	−	5.75341i	0.132657	−	0.229769i
$628$	38.0623	+	65.9258i	1.51885	+	2.63072i
$629$	0.527825			0.0210458
$630$	−9.94863	−	17.2315i	−0.396363	−	0.686521i
$631$	7.60019	+	13.1639i	0.302559	+	0.524048i	0.976715	−	0.214542i	$-0.0688257\pi$
$631$	7.60019	+	13.1639i	0.302559	+	0.524048i	−0.674156	+	0.738589i	$0.735492\pi$
$632$	−118.668			−4.72035
$633$	−6.61661	−	11.4603i	−0.262987	−	0.455506i
$634$	22.6965	−	39.3115i	0.901394	−	1.56126i
$635$	8.72047	−	15.1043i	0.346061	−	0.599395i
$636$	−75.6869			−3.00118
$637$	0.276577	+	5.57089i	0.0109584	+	0.220727i
$638$	−4.13581			−0.163738
$639$	−2.50327	+	4.33579i	−0.0990278	+	0.171521i
$640$	85.4748	−	148.047i	3.37869	−	5.85206i
$641$	1.43990	+	2.49397i	0.0568724	+	0.0985060i	0.893060	−	0.449938i	$-0.148554\pi$
$641$	1.43990	+	2.49397i	0.0568724	+	0.0985060i	−0.836187	+	0.548444i	$0.815221\pi$
$642$	−35.8798			−1.41606
$643$	−4.35190	−	7.53772i	−0.171622	−	0.297259i	0.767365	−	0.641211i	$-0.221568\pi$
$643$	−4.35190	−	7.53772i	−0.171622	−	0.297259i	−0.938987	+	0.343952i	$0.888234\pi$
$644$	−15.7597	−	27.2966i	−0.621020	−	1.07564i
$645$	−11.2116			−0.441457
$646$	−0.749879	−	1.29883i	−0.0295036	−	0.0511017i
$647$	7.71028	−	13.3546i	0.303122	−	0.525023i	−0.673719	−	0.738987i	$-0.735304\pi$
$647$	7.71028	−	13.3546i	0.303122	−	0.525023i	0.976842	+	0.213964i	$0.0686376\pi$
$648$	5.08157	−	8.80153i	0.199623	−	0.345757i
$649$	−8.18622			−0.321337
$650$	2.21128	+	44.5402i	0.0867335	+	1.74701i
$651$	−7.68196			−0.301080
$652$	15.4892	−	26.8280i	0.606602	−	1.05067i
$653$	18.6621	−	32.3236i	0.730303	−	1.26492i	−0.226451	−	0.974023i	$-0.572712\pi$
$653$	18.6621	−	32.3236i	0.730303	−	1.26492i	0.956754	−	0.290899i	$-0.0939544\pi$
$654$	8.67969	+	15.0337i	0.339403	+	0.587863i
$655$	18.1567			0.709440
$656$	−75.1743	−	130.206i	−2.93506	−	5.08368i
$657$	4.99976	+	8.65984i	0.195059	+	0.337852i
$658$	−11.4112			−0.444857
$659$	−3.14283	−	5.44354i	−0.122427	−	0.212050i	0.798297	−	0.602264i	$-0.205734\pi$
$659$	−3.14283	−	5.44354i	−0.122427	−	0.212050i	−0.920724	+	0.390214i	$0.872401\pi$
$660$	−8.72205	+	15.1070i	−0.339505	+	0.588041i
$661$	−8.37304	+	14.5025i	−0.325674	+	0.564083i	−0.981648	−	0.190699i	$-0.938924\pi$
$661$	−8.37304	+	14.5025i	−0.325674	+	0.564083i	0.655975	+	0.754783i	$0.272258\pi$
$662$	−48.7367			−1.89421
$663$	0.246930	−	0.159393i	0.00958995	−	0.00619031i
$664$	−6.67419			−0.259009
$665$	−23.8653	+	41.3360i	−0.925458	+	1.60294i
$666$	8.96633	−	15.5301i	0.347438	−	0.601781i
$667$	−1.77761	−	3.07891i	−0.0688293	−	0.119216i
$668$	−7.58882			−0.293620
$669$	3.87763	+	6.71625i	0.149918	+	0.259665i
$670$	−54.9574	−	95.1890i	−2.12319	−	3.67747i
$671$	−11.8838			−0.458768
$672$	30.6123	+	53.0220i	1.18089	+	2.04537i
$673$	1.78867	−	3.09807i	0.0689483	−	0.119422i	−0.829490	−	0.558521i	$-0.811369\pi$
$673$	1.78867	−	3.09807i	0.0689483	−	0.119422i	0.898439	+	0.439099i	$0.144702\pi$
$674$	−32.2332	+	55.8295i	−1.24158	+	2.15047i
$675$	−4.46606			−0.171899
$676$	−73.3443	+	7.30062i	−2.82094	+	0.280793i
$677$	−3.46862			−0.133310			−0.0666549	−	0.997776i	$-0.521233\pi$
$677$	−3.46862			−0.133310			−0.0666549	+	0.997776i	$0.521233\pi$
$678$	−9.98897	+	17.3014i	−0.383624	+	0.664457i
$679$	0.872223	−	1.51073i	0.0334729	−	0.0579767i
$680$	1.27444	+	2.20739i	0.0488724	+	0.0846494i
$681$	−11.9664			−0.458553
$682$	4.55528	+	7.88997i	0.174431	+	0.302123i
$683$	−10.9750	−	19.0093i	−0.419947	−	0.727369i	0.575987	−	0.817459i	$-0.304618\pi$
$683$	−10.9750	−	19.0093i	−0.419947	−	0.727369i	−0.995934	+	0.0900897i	$0.971285\pi$
$684$	−37.6668			−1.44023
$685$	30.5124	+	52.8490i	1.16582	+	2.01926i
$686$	27.6371	−	47.8688i	1.05519	−	1.82764i
$687$	2.95050	−	5.11042i	0.112569	−	0.194975i
$688$	61.2440			2.33491
$689$	−40.4384	+	26.1030i	−1.54058	+	0.994444i
$690$	−20.2848			−0.772230
$691$	−17.2844	+	29.9374i	−0.657529	+	1.13887i	0.323725	+	0.946151i	$0.395065\pi$
$691$	−17.2844	+	29.9374i	−0.657529	+	1.13887i	−0.981253	+	0.192722i	$0.938269\pi$
$692$	48.1400	−	83.3810i	1.83001	−	3.16967i
$693$	−1.16758	−	2.02232i	−0.0443529	−	0.0768214i
$694$	−81.2372			−3.08372
$695$	21.8171	+	37.7882i	0.827568	+	1.43339i
$696$	7.58870	+	13.1440i	0.287649	+	0.498223i
$697$	0.729214			0.0276210
$698$	10.5999	+	18.3596i	0.401214	+	0.694922i
$699$	2.38912	−	4.13808i	0.0903649	−	0.156517i
$700$	29.5649	−	51.2079i	1.11745	−	1.93548i
$701$	−15.1860			−0.573568			−0.286784	−	0.957995i	$-0.592586\pi$
$701$	−15.1860			−0.573568			−0.286784	+	0.957995i	$0.592586\pi$
$702$	−0.495130	−	9.97305i	−0.0186875	−	0.376408i
$703$	−43.0179			−1.62245
$704$	19.4985	−	33.7724i	0.734878	−	1.27285i
$705$	−2.71443	+	4.70153i	−0.102231	+	0.177070i
$706$	−32.4973	−	56.2870i	−1.22305	−	2.11839i
$707$	−21.7782			−0.819052
$708$	23.2069	+	40.1956i	0.872169	+	1.51064i
$709$	24.5698	+	42.5562i	0.922740	+	1.59823i	0.795157	+	0.606404i	$0.207389\pi$
$709$	24.5698	+	42.5562i	0.922740	+	1.59823i	0.127583	+	0.991828i	$0.459278\pi$
$710$	−42.6592			−1.60097
$711$	−5.83815	−	10.1120i	−0.218948	−	0.379228i
$712$	47.2114	−	81.7725i	1.76932	−	3.06455i
$713$	−3.91580	+	6.78236i	−0.146648	+	0.254001i
$714$	−0.527163			−0.0197286
$715$	0.550064	+	11.0795i	0.0205712	+	0.414351i
$716$	12.7158			0.475213
$717$	5.37946	−	9.31749i	0.200899	−	0.347968i
$718$	15.8323	−	27.4223i	0.590855	−	1.02339i
$719$	8.12540	+	14.0736i	0.303026	+	0.524857i	0.976820	−	0.214063i	$-0.0686697\pi$
$719$	8.12540	+	14.0736i	0.303026	+	0.524857i	−0.673794	+	0.738920i	$0.735336\pi$
$720$	51.7088			1.92707
$721$	−12.7559	−	22.0938i	−0.475054	−	0.822817i
$722$	34.8057	+	60.2852i	1.29533	+	2.24358i
$723$	23.0460			0.857089
$724$	47.9606	+	83.0702i	1.78244	+	3.08728i
$725$	3.33476	−	5.77597i	0.123850	−	0.214514i
$726$	−1.38472	+	2.39840i	−0.0513916	+	0.0890129i
$727$	47.9476			1.77828			0.889139	−	0.457637i	$-0.151304\pi$
$727$	47.9476			1.77828			0.889139	+	0.457637i	$0.151304\pi$
$728$	76.1354	+	39.0574i	2.82177	+	1.44756i
$729$	1.00000			0.0370370
$730$	−42.6015	+	73.7879i	−1.57675	+	2.73101i
$731$	−0.148522	+	0.257247i	−0.00549327	+	0.00951462i
$732$	33.6890	+	58.3511i	1.24518	+	2.15672i
$733$	15.4462			0.570520			0.285260	−	0.958450i	$-0.407920\pi$
$733$	15.4462			0.570520			0.285260	+	0.958450i	$0.407920\pi$
$734$	−29.6856	−	51.4169i	−1.09571	−	1.89783i
$735$	−2.37981	−	4.12195i	−0.0877805	−	0.152040i
$736$	62.4171			2.30072
$737$	−6.44987	−	11.1715i	−0.237584	−	0.411508i
$738$	12.3874	−	21.4556i	0.455987	−	0.789792i
$739$	−24.1926	+	41.9028i	−0.889939	+	1.54142i	−0.0499938	+	0.998750i	$0.515920\pi$
$739$	−24.1926	+	41.9028i	−0.889939	+	1.54142i	−0.839946	+	0.542671i	$0.817413\pi$
$740$	112.954			4.15228
$741$	−20.1248	+	12.9906i	−0.739304	+	0.477220i
$742$	86.3308			3.16930
$743$	−3.57031	+	6.18397i	−0.130982	+	0.226868i	−0.924055	−	0.382258i	$-0.875146\pi$
$743$	−3.57031	+	6.18397i	−0.130982	+	0.226868i	0.793073	+	0.609126i	$0.208480\pi$
$744$	16.7167	−	28.9542i	0.612866	−	1.06151i
$745$	31.2975	+	54.2089i	1.14665	+	1.98606i
$746$	23.4331			0.857947
$747$	−0.328353	−	0.568724i	−0.0120138	−	0.0208085i
$748$	0.231084	+	0.400249i	0.00844927	+	0.0146346i
$749$	30.2536			1.10544
$750$	2.27478	+	3.94004i	0.0830633	+	0.143870i
$751$	12.2205	−	21.1665i	0.445932	−	0.772376i	−0.552185	−	0.833722i	$-0.686206\pi$
$751$	12.2205	−	21.1665i	0.445932	−	0.772376i	0.998117	+	0.0613452i	$0.0195391\pi$
$752$	14.8277	−	25.6823i	0.540711	−	0.936539i
$753$	25.1064			0.914929
$754$	13.2679	+	6.80641i	0.483188	+	0.247875i
$755$	−17.3842			−0.632675
$756$	−6.61991	+	11.4660i	−0.240764	+	0.417015i
$757$	−6.13715	+	10.6299i	−0.223059	+	0.386349i	−0.955735	−	0.294228i	$-0.904937\pi$
$757$	−6.13715	+	10.6299i	−0.223059	+	0.386349i	0.732677	+	0.680577i	$0.238271\pi$
$758$	−0.837795	−	1.45110i	−0.0304301	−	0.0527065i
$759$	−2.38065			−0.0864122
$760$	−103.867	−	179.903i	−3.76764	−	6.52575i
$761$	11.1004	+	19.2264i	0.402388	+	0.696956i	0.994014	−	0.109256i	$-0.0348470\pi$
$761$	11.1004	+	19.2264i	0.402388	+	0.696956i	−0.591626	+	0.806213i	$0.701514\pi$
$762$	−15.6991			−0.568720
$763$	−7.31867	−	12.6763i	−0.264953	−	0.458913i
$764$	−18.0119	+	31.1975i	−0.651647	+	1.12869i
$765$	−0.125398	+	0.217196i	−0.00453377	+	0.00785272i
$766$	28.3373			1.02387
$767$	26.2618	+	13.4723i	0.948258	+	0.486456i
$768$	−75.8832			−2.73820
$769$	19.0798	−	33.0472i	0.688036	−	1.19171i	−0.284436	−	0.958695i	$-0.591806\pi$
$769$	19.0798	−	33.0472i	0.688036	−	1.19171i	0.972472	−	0.233019i	$-0.0748603\pi$
$770$	9.94863	−	17.2315i	0.358524	−	0.620982i
$771$	−9.00210	−	15.5921i	−0.324203	−	0.561536i
$772$	−62.1968			−2.23851
$773$	−18.6351	−	32.2769i	−0.670257	−	1.16092i	−0.977831	−	0.209395i	$-0.932851\pi$
$773$	−18.6351	−	32.2769i	−0.670257	−	1.16092i	0.307574	−	0.951524i	$-0.400483\pi$
$774$	5.04597	+	8.73988i	0.181374	+	0.314148i
$775$	−14.6919			−0.527749
$776$	3.79609	+	6.57503i	0.136272	+	0.236030i
$777$	−7.56036	+	13.0949i	−0.271226	+	0.469778i
$778$	−31.8617	+	55.1861i	−1.14230	+	1.97852i
$779$	−59.4311			−2.12934
$780$	52.8428	−	34.1100i	1.89208	−	1.22133i
$781$	−5.00654			−0.179148
$782$	−0.268715	+	0.465429i	−0.00960924	+	0.0166437i
$783$	−0.746689	+	1.29330i	−0.0266845	+	0.0462189i
$784$	12.9998	+	22.5163i	0.464279	+	0.804155i
$785$	−41.3090			−1.47438
$786$	−8.17170	−	14.1538i	−0.291475	−	0.504849i
$787$	−20.8960	−	36.1930i	−0.744863	−	1.29014i	−0.950259	−	0.311461i	$-0.899182\pi$
$787$	−20.8960	−	36.1930i	−0.744863	−	1.29014i	0.205396	−	0.978679i	$-0.434152\pi$
$788$	80.8606			2.88054
$789$	3.01230	+	5.21745i	0.107241	+	0.185746i
$790$	49.7451	−	86.1610i	1.76985	−	3.06547i
$791$	8.42264	−	14.5884i	0.299475	−	0.518705i
$792$	10.1631			0.361131
$793$	38.1237	+	19.5574i	1.35381	+	0.694505i
$794$	18.0227			0.639602
$795$	20.5358	−	35.5690i	0.728329	−	1.26150i
$796$	−25.3350	+	43.8815i	−0.897976	+	1.55534i
$797$	7.79618	+	13.5034i	0.276155	+	0.478315i	0.970426	−	0.241399i	$-0.0776063\pi$
$797$	7.79618	+	13.5034i	0.276155	+	0.478315i	−0.694271	+	0.719714i	$0.744273\pi$
$798$	42.9639			1.52090
$799$	0.0719167	+	0.124563i	0.00254423	+	0.00440674i
$800$	58.5466	+	101.406i	2.06993	+	3.58523i
$801$	9.29072			0.328271
$802$	17.0740	+	29.5731i	0.602905	+	1.04426i
$803$	−4.99976	+	8.65984i	−0.176438	+	0.305599i
$804$	−36.5692	+	63.3397i	−1.28970	+	2.23382i
$805$	17.1040			0.602838
$806$	−1.62882	−	32.8082i	−0.0573727	−	1.15562i
$807$	−4.84248			−0.170463
$808$	47.3915	−	82.0845i	1.66723	−	2.88772i
$809$	−15.9751	+	27.6696i	−0.561654	+	0.972813i	0.435699	+	0.900093i	$0.356501\pi$
$809$	−15.9751	+	27.6696i	−0.561654	+	0.972813i	−0.997352	+	0.0727201i	$0.976832\pi$
$810$	4.26035	+	7.37914i	0.149693	+	0.259277i
$811$	−30.2992			−1.06395			−0.531975	−	0.846760i	$-0.678550\pi$
$811$	−30.2992			−1.06395			−0.531975	+	0.846760i	$0.678550\pi$
$812$	−9.88604	−	17.1231i	−0.346932	−	0.600904i
$813$	3.77886	+	6.54517i	0.132530	+	0.229549i
$814$	17.9327			0.628540
$815$	8.40520	+	14.5582i	0.294421	+	0.509953i
$816$	0.684992	−	1.18644i	0.0239795	−	0.0415337i
$817$	12.1045	−	20.9657i	0.423485	−	0.733497i
$818$	−34.2184			−1.19642
$819$	0.417490	+	8.40921i	0.0145883	+	0.293842i
$820$	156.052			5.44956
$821$	−15.3212	+	26.5370i	−0.534713	+	0.926149i	0.464465	+	0.885592i	$0.346247\pi$
$821$	−15.3212	+	26.5370i	−0.534713	+	0.926149i	−0.999177	+	0.0405576i	$0.987087\pi$
$822$	27.4651	−	47.5710i	0.957957	−	1.65923i
$823$	0.236950	+	0.410410i	0.00825957	+	0.0143060i	0.870126	−	0.492830i	$-0.164038\pi$
$823$	0.236950	+	0.410410i	0.00825957	+	0.0143060i	−0.861866	+	0.507136i	$0.830704\pi$
$824$	111.032			3.86800
$825$	−2.23303	−	3.86772i	−0.0777441	−	0.134657i
$826$	−26.4705	−	45.8483i	−0.921027	−	1.59526i
$827$	4.71774			0.164052			0.0820259	−	0.996630i	$-0.473861\pi$
$827$	4.71774			0.164052			0.0820259	+	0.996630i	$0.473861\pi$
$828$	6.74886	+	11.6894i	0.234539	+	0.406234i
$829$	−0.417005	+	0.722274i	−0.0144832	+	0.0250856i	−0.873176	−	0.487405i	$-0.837944\pi$
$829$	−0.417005	+	0.722274i	−0.0144832	+	0.0250856i	0.858693	+	0.512490i	$0.171277\pi$
$830$	2.79780	−	4.84593i	0.0971130	−	0.168205i
$831$	19.7833			0.686274
$832$	−118.132	+	76.2544i	−4.09551	+	2.64365i
$833$	−0.126102			−0.00436919
$834$	19.6382	−	34.0144i	0.680016	−	1.17782i
$835$	2.05904	−	3.56636i	0.0712560	−	0.123419i
$836$	−18.8334	−	32.6204i	−0.651367	−	1.12820i
$837$	3.28968			0.113708
$838$	−38.4790	−	66.6475i	−1.32923	−	2.30230i
$839$	−2.97708	−	5.15645i	−0.102780	−	0.178020i	0.810049	−	0.586362i	$-0.199440\pi$
$839$	−2.97708	−	5.15645i	−0.102780	−	0.178020i	−0.912829	+	0.408342i	$0.866107\pi$
$840$	−73.0181			−2.51936
$841$	13.3849	+	23.1833i	0.461549	+	0.799426i
$842$	−7.44049	+	12.8873i	−0.256416	+	0.444126i
$843$	−5.09442	+	8.82379i	−0.175461	+	0.303908i
$844$	−75.0291			−2.58261
$845$	16.4693	−	36.4490i	0.566560	−	1.25388i
$846$	4.88669			0.168008
$847$	1.16758	−	2.02232i	0.0401187	−	0.0694876i
$848$	−112.178	+	194.297i	−3.85220	+	6.67220i
$849$	−6.31581	−	10.9393i	−0.216758	−	0.375436i
$850$	−1.00821			−0.0345813
$851$	7.70762	+	13.3500i	0.264214	+	0.457632i
$852$	14.1929	+	24.5828i	0.486241	+	0.842195i
$853$	−54.3262			−1.86009			−0.930046	−	0.367442i	$-0.880234\pi$
$853$	−54.3262			−1.86009			−0.930046	+	0.367442i	$0.880234\pi$
$854$	−38.4267	−	66.5570i	−1.31493	−	2.27753i
$855$	10.2200	−	17.7015i	0.349515	−	0.605378i
$856$	−65.8350	+	114.030i	−2.25019	+	3.89745i
$857$	52.3495			1.78822			0.894112	−	0.447844i	$-0.147808\pi$
$857$	52.3495			1.78822			0.894112	+	0.447844i	$0.147808\pi$
$858$	8.38935	−	5.41532i	0.286408	−	0.184876i
$859$	−2.69931			−0.0920992			−0.0460496	−	0.998939i	$-0.514663\pi$
$859$	−2.69931			−0.0920992			−0.0460496	+	0.998939i	$0.514663\pi$
$860$	−31.7836	+	55.0508i	−1.08381	+	1.87722i
$861$	−10.4450	+	18.0912i	−0.355964	+	0.616548i
$862$	16.1662	+	28.0007i	0.550623	+	0.953707i
$863$	−1.16501			−0.0396573			−0.0198286	−	0.999803i	$-0.506312\pi$
$863$	−1.16501			−0.0396573			−0.0198286	+	0.999803i	$0.506312\pi$
$864$	−13.1092	−	22.7059i	−0.445985	−	0.772469i
$865$	26.1232	+	45.2468i	0.888217	+	1.53844i
$866$	−81.1152			−2.75641
$867$	−8.49668	−	14.7167i	−0.288562	−	0.499805i
$868$	−21.7774	+	37.7196i	−0.739174	+	1.28029i
$869$	5.83815	−	10.1120i	0.198046	−	0.343025i
$870$	−12.7246			−0.431405
$871$	2.30627	+	46.4535i	0.0781448	+	1.57402i
$872$	63.7047			2.15731
$873$	−0.373516	+	0.646949i	−0.0126416	+	0.0218959i
$874$	21.9004	−	37.9326i	0.740791	−	1.28309i
$875$	−1.91808	−	3.32221i	−0.0648430	−	0.112311i
$876$	56.6948			1.91554
$877$	2.38668	+	4.13385i	0.0805924	+	0.139590i	0.903505	−	0.428579i	$-0.140985\pi$
$877$	2.38668	+	4.13385i	0.0805924	+	0.139590i	−0.822912	+	0.568169i	$0.807652\pi$
$878$	−3.20920	−	5.55850i	−0.108305	−	0.187590i
$879$	−15.5759			−0.525361
$880$	25.8544	+	44.7811i	0.871551	+	1.50957i
$881$	−13.5133	+	23.4057i	−0.455275	+	0.788559i	−0.998704	−	0.0508958i	$-0.983792\pi$
$881$	−13.5133	+	23.4057i	−0.455275	+	0.788559i	0.543429	+	0.839455i	$0.317126\pi$
$882$	−2.14214	+	3.71030i	−0.0721296	+	0.124932i
$883$	−44.1032			−1.48419			−0.742096	−	0.670294i	$-0.766168\pi$
$883$	−44.1032			−1.48419			−0.742096	+	0.670294i	$0.766168\pi$
$884$	−0.0826282	−	1.66432i	−0.00277909	−	0.0559772i
$885$	−25.1865			−0.846635
$886$	−34.1357	+	59.1247i	−1.14681	+	1.98633i
$887$	−9.61627	+	16.6559i	−0.322883	+	0.559249i	−0.981082	−	0.193595i	$-0.937985\pi$
$887$	−9.61627	+	16.6559i	−0.322883	+	0.559249i	0.658199	+	0.752844i	$0.271319\pi$
$888$	−32.9042	−	56.9918i	−1.10419	−	1.91252i
$889$	13.2374			0.443969
$890$	39.5817	+	68.5575i	1.32678	+	2.29805i
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	43.9704			1.47224
$893$	−5.86123	−	10.1519i	−0.196139	−	0.339722i
$894$	28.1719	−	48.7951i	0.942208	−	1.63195i
$895$	−3.45013	+	5.97579i	−0.115325	+	0.199749i
$896$	129.748			4.33459
$897$	7.63725	+	3.91790i	0.255001	+	0.130815i
$898$	34.3741			1.14708
$899$	−2.45637	+	4.25456i	−0.0819246	+	0.141898i
$900$	−12.6607	+	21.9290i	−0.422024	+	0.730967i
$901$	−0.544080	−	0.942374i	−0.0181259	−	0.0313950i
$902$	24.7748			0.824911
$903$	−4.25473	−	7.36941i	−0.141589	−	0.245239i
$904$	36.6571	+	63.4919i	1.21920	+	2.11171i
$905$	−52.0517			−1.73026
$906$	7.82402	+	13.5516i	0.259936	+	0.450222i
$907$	3.48650	−	6.03879i	0.115767	−	0.200515i	−0.802319	−	0.596896i	$-0.796401\pi$
$907$	3.48650	−	6.03879i	0.115767	−	0.200515i	0.918086	+	0.396381i	$0.129734\pi$
$908$	−33.9233	+	58.7568i	−1.12578	+	1.94991i
$909$	9.32616			0.309329
$910$	−60.2741	+	38.9069i	−1.99807	+	1.28975i
$911$	12.8344			0.425224			0.212612	−	0.977137i	$-0.431803\pi$
$911$	12.8344			0.425224			0.212612	+	0.977137i	$0.431803\pi$
$912$	−55.8270	+	96.6952i	−1.84862	+	3.20190i
$913$	0.328353	−	0.568724i	0.0108669	−	0.0188220i
$914$	−36.5531	−	63.3119i	−1.20907	−	2.09417i
$915$	−36.5628			−1.20873
$916$	−16.7286	−	28.9748i	−0.552729	−	0.957355i
$917$	6.89033	+	11.9344i	0.227539	+	0.394108i
$918$	0.225749			0.00745084
$919$	−17.2779	−	29.9261i	−0.569944	−	0.987172i	−0.996571	−	0.0827440i	$-0.973632\pi$
$919$	−17.2779	−	29.9261i	−0.569944	−	0.987172i	0.426627	−	0.904428i	$-0.359702\pi$
$920$	−37.2202	+	64.4672i	−1.22711	+	2.12542i
$921$	−8.20447	+	14.2106i	−0.270347	+	0.468254i
$922$	−13.8420			−0.455863
$923$	16.0612	+	8.23939i	0.528661	+	0.271203i
$924$	−13.2398			−0.435558
$925$	−14.4593	+	25.0443i	−0.475420	+	0.823452i
$926$	33.7884	−	58.5231i	1.11035	−	1.92319i
$927$	5.46251	+	9.46135i	0.179412	+	0.310751i
$928$	39.1541			1.28530
$929$	−12.2069	−	21.1430i	−0.400495	−	0.693678i	0.593291	−	0.804988i	$-0.297828\pi$
$929$	−12.2069	−	21.1430i	−0.400495	−	0.693678i	−0.993786	+	0.111311i	$0.964495\pi$
$930$	14.0152	+	24.2750i	0.459577	+	0.796010i
$931$	10.2774			0.336827
$932$	−13.5457	−	23.4619i	−0.443705	−	0.768520i
$933$	0.111364	−	0.192888i	0.00364589	−	0.00631486i
$934$	9.27340	−	16.0620i	0.303435	−	0.525565i
$935$	−0.250796			−0.00820190
$936$	−32.6038	−	16.7257i	−1.06569	−	0.546698i
$937$	23.7785			0.776808			0.388404	−	0.921489i	$-0.373026\pi$
$937$	23.7785			0.776808			0.388404	+	0.921489i	$0.373026\pi$
$938$	41.7119	−	72.2471i	1.36194	−	2.35895i
$939$	−9.01664	+	15.6173i	−0.294247	+	0.509650i
$940$	15.3902	+	26.6565i	0.501971	+	0.869440i
$941$	32.7773			1.06851			0.534254	−	0.845324i	$-0.320592\pi$
$941$	32.7773			1.06851			0.534254	+	0.845324i	$0.320592\pi$
$942$	18.5918	+	32.2019i	0.605753	+	1.04920i
$943$	10.6484	+	18.4436i	0.346761	+	0.600607i
$944$	137.582			4.47793
$945$	−3.59230	−	6.22205i	−0.116858	−	0.202403i
$946$	−5.04597	+	8.73988i	−0.164059	+	0.284158i
$947$	20.5793	−	35.6444i	0.668738	−	1.15829i	−0.309519	−	0.950893i	$-0.600168\pi$
$947$	20.5793	−	35.6444i	0.668738	−	1.15829i	0.978257	−	0.207395i	$-0.0664986\pi$
$948$	−66.2017			−2.15013
$949$	30.2912	−	19.5530i	0.983294	−	0.634716i
$950$	82.1693			2.66592
$951$	8.19537	−	14.1948i	0.265753	−	0.460298i
$952$	−0.967278	+	1.67538i	−0.0313497	+	0.0542992i
$953$	0.217160	+	0.376131i	0.00703449	+	0.0121841i	0.869521	−	0.493896i	$-0.164428\pi$
$953$	0.217160	+	0.376131i	0.00703449	+	0.0121841i	−0.862487	+	0.506080i	$0.831094\pi$
$954$	−36.9698			−1.19694
$955$	−9.77417	−	16.9294i	−0.316285	−	0.547821i
$956$	−30.5002	−	52.8279i	−0.986447	−	1.70858i
$957$	−1.49338			−0.0482741
$958$	−37.1143	−	64.2839i	−1.19911	−	2.07692i
$959$	−23.1584	+	40.1116i	−0.747825	+	1.29527i
$960$	59.9910	−	103.908i	1.93620	−	3.35360i
$961$	−20.1780			−0.650903
$962$	−57.5289	−	29.5123i	−1.85481	−	0.951514i
$963$	−12.9556			−0.417490
$964$	65.3325	−	113.159i	2.10422	−	3.64461i
$965$	16.8756	−	29.2293i	0.543243	−	0.940925i
$966$	−7.69795	−	13.3332i	−0.247677	−	0.428990i
$967$	−24.3034			−0.781545			−0.390773	−	0.920487i	$-0.627792\pi$
$967$	−24.3034			−0.781545			−0.390773	+	0.920487i	$0.627792\pi$
$968$	5.08157	+	8.80153i	0.163328	+	0.282892i
$969$	−0.270770	−	0.468987i	−0.00869838	−	0.0150660i
$970$	−6.36524			−0.204376
$971$	14.1096	+	24.4386i	0.452799	+	0.784270i	0.998559	−	0.0536711i	$-0.0170923\pi$
$971$	14.1096	+	24.4386i	0.452799	+	0.784270i	−0.545760	+	0.837942i	$0.683759\pi$
$972$	2.83488	−	4.91015i	0.0909287	−	0.157493i
$973$	−16.5588	+	28.6807i	−0.530852	+	0.919462i
$974$	73.4861			2.35465
$975$	0.798459	+	16.0828i	0.0255712	+	0.515062i
$976$	199.726			6.39307
$977$	25.0649	−	43.4138i	0.801899	−	1.38893i	−0.116466	−	0.993195i	$-0.537157\pi$
$977$	25.0649	−	43.4138i	0.801899	−	1.38893i	0.918365	−	0.395734i	$-0.129510\pi$
$978$	7.56579	−	13.1043i	0.241927	−	0.419030i
$979$	4.64536	+	8.04600i	0.148466	+	0.257151i
$980$	−26.9858			−0.862031
$981$	3.13411	+	5.42843i	0.100064	+	0.173316i
$982$	−2.28746	−	3.96200i	−0.0729958	−	0.126432i
$983$	8.18862			0.261176			0.130588	−	0.991437i	$-0.458313\pi$
$983$	8.18862			0.261176			0.130588	+	0.991437i	$0.458313\pi$
$984$	−45.4587	−	78.7368i	−1.44917	−	2.51004i
$985$	−21.9395	+	38.0004i	−0.699052	+	1.21079i
$986$	−0.168565	+	0.291962i	−0.00536819	+	0.00929798i
$987$	−4.12043			−0.131155
$988$	6.73422	+	135.643i	0.214244	+	4.31536i
$989$	−8.67521			−0.275856
$990$	−4.26035	+	7.37914i	−0.135403	+	0.234525i
$991$	18.1708	−	31.4728i	0.577215	−	0.999766i	−0.418582	−	0.908179i	$-0.637473\pi$
$991$	18.1708	−	31.4728i	0.577215	−	0.999766i	0.995797	−	0.0915870i	$-0.0291939\pi$
$992$	−43.1252	−	74.6951i	−1.36923	−	2.37157i
$993$	−17.5981			−0.558458
$994$	−16.1889	−	28.0399i	−0.513479	−	0.889373i
$995$	−13.7481	−	23.8123i	−0.435843	−	0.754902i
$996$	−3.72336			−0.117979
$997$	−2.45104	−	4.24533i	−0.0776253	−	0.134451i	0.824600	−	0.565717i	$-0.191400\pi$
$997$	−2.45104	−	4.24533i	−0.0776253	−	0.134451i	−0.902225	+	0.431266i	$0.858067\pi$
$998$	−1.85609	+	3.21484i	−0.0587534	+	0.101764i
$999$	3.23761	−	5.60770i	0.102433	−	0.177420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.e.100.5	✓	10
13.3	even	3	inner	429.2.i.e.133.5	yes	10
13.4	even	6		5577.2.a.u.1.5		5
13.9	even	3		5577.2.a.o.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.e.100.5	✓	10	1.1	even	1	trivial
429.2.i.e.133.5	yes	10	13.3	even	3	inner
5577.2.a.o.1.1		5	13.9	even	3
5577.2.a.u.1.5		5	13.4	even	6

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38472 - 2.39840i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.83488 - 4.91015i) q^{4} +3.07670 q^{5} +(-1.38472 - 2.39840i) q^{6} +(1.16758 + 2.02232i) q^{7} -10.1631 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.38472 - 2.39840i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.83488 - 4.91015i) q^{4} +3.07670 q^{5} +(-1.38472 - 2.39840i) q^{6} +(1.16758 + 2.02232i) q^{7} -10.1631 q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.26035 - 7.37914i) q^{10} +(0.500000 - 0.866025i) q^{11} -5.66975 q^{12} +(-3.02927 + 1.95539i) q^{13} +6.46709 q^{14} +(1.53835 - 2.66450i) q^{15} +(-8.40330 + 14.5549i) q^{16} +(-0.0407573 - 0.0705938i) q^{17} -2.76943 q^{18} +(3.32173 + 5.75341i) q^{19} +(-8.72205 - 15.1070i) q^{20} +2.33517 q^{21} +(-1.38472 - 2.39840i) q^{22} +(1.19033 - 2.06171i) q^{23} +(-5.08157 + 8.80153i) q^{24} +4.46606 q^{25} +(0.495130 + 9.97305i) q^{26} -1.00000 q^{27} +(6.61991 - 11.4660i) q^{28} +(0.746689 - 1.29330i) q^{29} +(-4.26035 - 7.37914i) q^{30} -3.28968 q^{31} +(13.1092 + 22.7059i) q^{32} +(-0.500000 - 0.866025i) q^{33} -0.225749 q^{34} +(3.59230 + 6.22205i) q^{35} +(-2.83488 + 4.91015i) q^{36} +(-3.23761 + 5.60770i) q^{37} +18.3986 q^{38} +(0.178784 + 3.60112i) q^{39} -31.2689 q^{40} +(-4.47290 + 7.74730i) q^{41} +(3.23354 - 5.60066i) q^{42} +(-1.82202 - 3.15584i) q^{43} -5.66975 q^{44} +(-1.53835 - 2.66450i) q^{45} +(-3.29653 - 5.70976i) q^{46} -1.76451 q^{47} +(8.40330 + 14.5549i) q^{48} +(0.773495 - 1.33973i) q^{49} +(6.18422 - 10.7114i) q^{50} -0.0815147 q^{51} +(18.1889 + 9.33086i) q^{52} +13.3492 q^{53} +(-1.38472 + 2.39840i) q^{54} +(1.53835 - 2.66450i) q^{55} +(-11.8663 - 20.5531i) q^{56} +6.64346 q^{57} +(-2.06791 - 3.58172i) q^{58} +(-4.09311 - 7.08947i) q^{59} -17.4441 q^{60} +(-5.94189 - 10.2916i) q^{61} +(-4.55528 + 7.88997i) q^{62} +(1.16758 - 2.02232i) q^{63} +38.9970 q^{64} +(-9.32013 + 6.01614i) q^{65} -2.76943 q^{66} +(6.44987 - 11.1715i) q^{67} +(-0.231084 + 0.400249i) q^{68} +(-1.19033 - 2.06171i) q^{69} +19.8973 q^{70} +(-2.50327 - 4.33579i) q^{71} +(5.08157 + 8.80153i) q^{72} -9.99952 q^{73} +(8.96633 + 15.5301i) q^{74} +(2.23303 - 3.86772i) q^{75} +(18.8334 - 32.6204i) q^{76} +2.33517 q^{77} +(8.88448 + 4.55773i) q^{78} +11.6763 q^{79} +(-25.8544 + 44.7811i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(12.3874 + 21.4556i) q^{82} +0.656706 q^{83} +(-6.61991 - 11.4660i) q^{84} +(-0.125398 - 0.217196i) q^{85} -10.0919 q^{86} +(-0.746689 - 1.29330i) q^{87} +(-5.08157 + 8.80153i) q^{88} +(-4.64536 + 8.04600i) q^{89} -8.52070 q^{90} +(-7.49134 - 3.84305i) q^{91} -13.4977 q^{92} +(-1.64484 + 2.84895i) q^{93} +(-2.44335 + 4.23200i) q^{94} +(10.2200 + 17.7015i) q^{95} +26.2185 q^{96} +(-0.373516 - 0.646949i) q^{97} +(-2.14214 - 3.71030i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Introduction

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