LMFDB - Embedded newform 403.2.k.e.287.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, 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("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.16
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.773013 - 2.37909i) q^{2} +(0.384456 + 1.18324i) q^{3} +(-3.44449 - 2.50257i) q^{4} -2.86335 q^{5} +3.11221 q^{6} +(-1.19324 - 0.866941i) q^{7} +(-4.56892 + 3.31951i) q^{8} +(1.17481 - 0.853551i) q^{9} +O(q^{10})$	\(q+(0.773013 - 2.37909i) q^{2} +(0.384456 + 1.18324i) q^{3} +(-3.44449 - 2.50257i) q^{4} -2.86335 q^{5} +3.11221 q^{6} +(-1.19324 - 0.866941i) q^{7} +(-4.56892 + 3.31951i) q^{8} +(1.17481 - 0.853551i) q^{9} +(-2.21341 + 6.81217i) q^{10} +(-4.28613 - 3.11405i) q^{11} +(1.63687 - 5.03777i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-2.98492 + 2.16867i) q^{14} +(-1.10083 - 3.38802i) q^{15} +(1.73423 + 5.33742i) q^{16} +(-6.22931 + 4.52586i) q^{17} +(-1.12253 - 3.45479i) q^{18} +(0.422979 - 1.30179i) q^{19} +(9.86278 + 7.16573i) q^{20} +(0.567046 - 1.74519i) q^{21} +(-10.7218 + 7.78988i) q^{22} +(3.11255 - 2.26140i) q^{23} +(-5.68431 - 4.12989i) q^{24} +3.19879 q^{25} +2.50152 q^{26} +(4.48118 + 3.25576i) q^{27} +(1.94053 + 5.97234i) q^{28} +(-0.139754 + 0.430119i) q^{29} -8.91136 q^{30} +(3.97919 - 3.89437i) q^{31} +2.74380 q^{32} +(2.03683 - 6.26871i) q^{33} +(5.95208 + 18.3186i) q^{34} +(3.41667 + 2.48236i) q^{35} -6.18269 q^{36} -5.08045 q^{37} +(-2.77012 - 2.01261i) q^{38} +(-1.00652 + 0.731280i) q^{39} +(13.0824 - 9.50493i) q^{40} +(3.74120 - 11.5142i) q^{41} +(-3.71362 - 2.69811i) q^{42} +(2.47671 - 7.62253i) q^{43} +(6.97038 + 21.4526i) q^{44} +(-3.36390 + 2.44402i) q^{45} +(-2.97403 - 9.15314i) q^{46} +(-1.09459 - 3.36881i) q^{47} +(-5.64868 + 4.10401i) q^{48} +(-1.49088 - 4.58845i) q^{49} +(2.47270 - 7.61020i) q^{50} +(-7.75005 - 5.63074i) q^{51} +(1.31568 - 4.04924i) q^{52} +(-0.503374 + 0.365722i) q^{53} +(11.2098 - 8.14437i) q^{54} +(12.2727 + 8.91663i) q^{55} +8.32964 q^{56} +1.70295 q^{57} +(0.915260 + 0.664975i) q^{58} +(1.44138 + 4.43611i) q^{59} +(-4.68693 + 14.4249i) q^{60} +10.4459 q^{61} +(-6.18908 - 12.4772i) q^{62} -2.14181 q^{63} +(-1.34747 + 4.14709i) q^{64} +(-0.884825 - 2.72321i) q^{65} +(-13.3393 - 9.69160i) q^{66} +6.12626 q^{67} +32.7830 q^{68} +(3.87241 + 2.81347i) q^{69} +(8.54689 - 6.20968i) q^{70} +(-6.31968 + 4.59152i) q^{71} +(-2.53425 + 7.79960i) q^{72} +(-3.48822 - 2.53434i) q^{73} +(-3.92726 + 12.0868i) q^{74} +(1.22979 + 3.78492i) q^{75} +(-4.71477 + 3.42548i) q^{76} +(2.41469 + 7.43164i) q^{77} +(0.961727 + 2.95989i) q^{78} +(7.59432 - 5.51760i) q^{79} +(-4.96572 - 15.2829i) q^{80} +(-0.783304 + 2.41076i) q^{81} +(-24.5014 - 17.8013i) q^{82} +(-4.95653 + 15.2546i) q^{83} +(-6.32063 + 4.59221i) q^{84} +(17.8367 - 12.9591i) q^{85} +(-16.2202 - 11.7846i) q^{86} -0.562661 q^{87} +29.9201 q^{88} +(3.75763 + 2.73008i) q^{89} +(3.21420 + 9.89228i) q^{90} +(0.455778 - 1.40274i) q^{91} -16.3805 q^{92} +(6.13777 + 3.21110i) q^{93} -8.86083 q^{94} +(-1.21114 + 3.72750i) q^{95} +(1.05487 + 3.24656i) q^{96} +(-6.67779 - 4.85170i) q^{97} -12.0688 q^{98} -7.69340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.773013	−	2.37909i	0.546603	−	1.68227i	−0.170545	−	0.985350i	$-0.554553\pi$
$2$	0.773013	−	2.37909i	0.546603	−	1.68227i	0.717148	−	0.696921i	$-0.245447\pi$
$3$	0.384456	+	1.18324i	0.221966	+	0.683141i	0.998585	+	0.0531711i	$0.0169329\pi$
$3$	0.384456	+	1.18324i	0.221966	+	0.683141i	−0.776619	+	0.629970i	$0.783067\pi$
$4$	−3.44449	−	2.50257i	−1.72224	−	1.25128i
$5$	−2.86335			−1.28053			−0.640265	−	0.768154i	$-0.721175\pi$
$5$	−2.86335			−1.28053			−0.640265	+	0.768154i	$0.721175\pi$
$6$	3.11221			1.27056
$7$	−1.19324	−	0.866941i	−0.451003	−	0.327673i	0.338989	−	0.940790i	$-0.389915\pi$
$7$	−1.19324	−	0.866941i	−0.451003	−	0.327673i	−0.789992	+	0.613118i	$0.789915\pi$
$8$	−4.56892	+	3.31951i	−1.61536	+	1.17362i
$9$	1.17481	−	0.853551i	0.391604	−	0.284517i
$10$	−2.21341	+	6.81217i	−0.699942	+	2.15420i
$11$	−4.28613	−	3.11405i	−1.29232	−	0.938922i	−0.292467	−	0.956276i	$-0.594476\pi$
$11$	−4.28613	−	3.11405i	−1.29232	−	0.938922i	−0.999849	+	0.0173533i	$0.994476\pi$
$12$	1.63687	−	5.03777i	0.472524	−	1.45428i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	−2.98492	+	2.16867i	−0.797754	+	0.579602i
$15$	−1.10083	−	3.38802i	−0.284234	−	0.874783i
$16$	1.73423	+	5.33742i	0.433558	+	1.33435i
$17$	−6.22931	+	4.52586i	−1.51083	+	1.09768i	−0.545021	+	0.838423i	$0.683478\pi$
$17$	−6.22931	+	4.52586i	−1.51083	+	1.09768i	−0.965808	+	0.259258i	$0.916522\pi$
$18$	−1.12253	−	3.45479i	−0.264583	−	0.814302i
$19$	0.422979	−	1.30179i	0.0970379	−	0.298652i	−0.890742	−	0.454510i	$-0.849814\pi$
$19$	0.422979	−	1.30179i	0.0970379	−	0.298652i	0.987779	+	0.155858i	$0.0498143\pi$
$20$	9.86278	+	7.16573i	2.20538	+	1.60231i
$21$	0.567046	−	1.74519i	0.123740	−	0.380831i
$22$	−10.7218	+	7.78988i	−2.28591	+	1.66081i
$23$	3.11255	−	2.26140i	0.649012	−	0.471535i	−0.213922	−	0.976851i	$-0.568624\pi$
$23$	3.11255	−	2.26140i	0.649012	−	0.471535i	0.862934	+	0.505316i	$0.168624\pi$
$24$	−5.68431	−	4.12989i	−1.16031	−	0.843011i
$25$	3.19879			0.639757
$26$	2.50152			0.490589
$27$	4.48118	+	3.25576i	0.862403	+	0.626572i
$28$	1.94053	+	5.97234i	0.366726	+	1.12867i
$29$	−0.139754	+	0.430119i	−0.0259517	+	0.0798711i	−0.963194	−	0.268809i	$-0.913370\pi$
$29$	−0.139754	+	0.430119i	−0.0259517	+	0.0798711i	0.937242	+	0.348680i	$0.113370\pi$
$30$	−8.91136			−1.62699
$31$	3.97919	−	3.89437i	0.714683	−	0.699449i
$31$	3.97919	−	3.89437i	0.714683	−	0.699449i
$32$	2.74380			0.485039
$33$	2.03683	−	6.26871i	0.354566	−	1.09124i
$34$	5.95208	+	18.3186i	1.02077	+	3.14162i
$35$	3.41667	+	2.48236i	0.577523	+	0.419595i
$36$	−6.18269			−1.03045
$37$	−5.08045			−0.835221			−0.417610	−	0.908626i	$-0.637132\pi$
$37$	−5.08045			−0.835221			−0.417610	+	0.908626i	$0.637132\pi$
$38$	−2.77012	−	2.01261i	−0.449372	−	0.326488i
$39$	−1.00652	+	0.731280i	−0.161172	+	0.117098i
$40$	13.0824	−	9.50493i	2.06851	−	1.50286i
$41$	3.74120	−	11.5142i	0.584277	−	1.79822i	−0.0178751	−	0.999840i	$-0.505690\pi$
$41$	3.74120	−	11.5142i	0.584277	−	1.79822i	0.602153	−	0.798381i	$-0.294310\pi$
$42$	−3.71362	−	2.69811i	−0.573025	−	0.416327i
$43$	2.47671	−	7.62253i	0.377695	−	1.16242i	−0.563948	−	0.825810i	$-0.690718\pi$
$43$	2.47671	−	7.62253i	0.377695	−	1.16242i	0.941643	−	0.336614i	$-0.109282\pi$
$44$	6.97038	+	21.4526i	1.05082	+	3.23411i
$45$	−3.36390	+	2.44402i	−0.501461	+	0.364333i
$46$	−2.97403	−	9.15314i	−0.438497	−	1.34956i
$47$	−1.09459	−	3.36881i	−0.159663	−	0.491391i	0.838941	−	0.544223i	$-0.183175\pi$
$47$	−1.09459	−	3.36881i	−0.159663	−	0.491391i	−0.998603	+	0.0528317i	$0.983175\pi$
$48$	−5.64868	+	4.10401i	−0.815317	+	0.592362i
$49$	−1.49088	−	4.58845i	−0.212983	−	0.655494i
$50$	2.47270	−	7.61020i	0.349693	−	1.07625i
$51$	−7.75005	−	5.63074i	−1.08522	−	0.788461i
$52$	1.31568	−	4.04924i	0.182452	−	0.561528i
$53$	−0.503374	+	0.365722i	−0.0691437	+	0.0502358i	−0.621820	−	0.783160i	$-0.713607\pi$
$53$	−0.503374	+	0.365722i	−0.0691437	+	0.0502358i	0.552676	+	0.833396i	$0.313607\pi$
$54$	11.2098	−	8.14437i	1.52546	−	1.10831i
$55$	12.2727	+	8.91663i	1.65485	+	1.20232i
$56$	8.32964			1.11310
$57$	1.70295			0.225561
$58$	0.915260	+	0.664975i	0.120180	+	0.0873155i
$59$	1.44138	+	4.43611i	0.187652	+	0.577532i	0.999984	−	0.00566262i	$-0.00180248\pi$
$59$	1.44138	+	4.43611i	0.187652	+	0.577532i	−0.812332	+	0.583195i	$0.801802\pi$
$60$	−4.68693	+	14.4249i	−0.605081	+	1.86225i
$61$	10.4459			1.33746			0.668730	−	0.743506i	$-0.266838\pi$
$61$	10.4459			1.33746			0.668730	+	0.743506i	$0.266838\pi$
$62$	−6.18908	−	12.4772i	−0.786014	−	1.58461i
$63$	−2.14181			−0.269843
$64$	−1.34747	+	4.14709i	−0.168434	+	0.518387i
$65$	−0.884825	−	2.72321i	−0.109749	−	0.337773i
$66$	−13.3393	−	9.69160i	−1.64196	−	1.19295i
$67$	6.12626			0.748442			0.374221	−	0.927340i	$-0.377910\pi$
$67$	6.12626			0.748442			0.374221	+	0.927340i	$0.377910\pi$
$68$	32.7830			3.97552
$69$	3.87241	+	2.81347i	0.466184	+	0.338702i
$70$	8.54689	−	6.20968i	1.02155	−	0.742198i
$71$	−6.31968	+	4.59152i	−0.750009	+	0.544913i	−0.895830	−	0.444398i	$-0.853418\pi$
$71$	−6.31968	+	4.59152i	−0.750009	+	0.544913i	0.145821	+	0.989311i	$0.453418\pi$
$72$	−2.53425	+	7.79960i	−0.298664	+	0.919192i
$73$	−3.48822	−	2.53434i	−0.408265	−	0.296622i	0.364634	−	0.931151i	$-0.381194\pi$
$73$	−3.48822	−	2.53434i	−0.408265	−	0.296622i	−0.772899	+	0.634529i	$0.781194\pi$
$74$	−3.92726	+	12.0868i	−0.456534	+	1.40507i
$75$	1.22979	+	3.78492i	0.142004	+	0.437045i
$76$	−4.71477	+	3.42548i	−0.540821	+	0.392930i
$77$	2.41469	+	7.43164i	0.275179	+	0.846914i
$78$	0.961727	+	2.95989i	0.108894	+	0.335142i
$79$	7.59432	−	5.51760i	0.854428	−	0.620778i	−0.0719356	−	0.997409i	$-0.522918\pi$
$79$	7.59432	−	5.51760i	0.854428	−	0.620778i	0.926363	+	0.376631i	$0.122918\pi$
$80$	−4.96572	−	15.2829i	−0.555184	−	1.70868i
$81$	−0.783304	+	2.41076i	−0.0870338	+	0.267862i
$82$	−24.5014	−	17.8013i	−2.70573	−	1.96583i
$83$	−4.95653	+	15.2546i	−0.544050	+	1.67441i	0.179188	+	0.983815i	$0.442653\pi$
$83$	−4.95653	+	15.2546i	−0.544050	+	1.67441i	−0.723238	+	0.690599i	$0.757347\pi$
$84$	−6.32063	+	4.59221i	−0.689637	+	0.501051i
$85$	17.8367	−	12.9591i	1.93466	−	1.40561i
$86$	−16.2202	−	11.7846i	−1.74906	−	1.27077i
$87$	−0.562661			−0.0603236
$88$	29.9201			3.18949
$89$	3.75763	+	2.73008i	0.398308	+	0.289388i	0.768851	−	0.639428i	$-0.220829\pi$
$89$	3.75763	+	2.73008i	0.398308	+	0.289388i	−0.370544	+	0.928815i	$0.620829\pi$
$90$	3.21420	+	9.89228i	0.338806	+	1.04274i
$91$	0.455778	−	1.40274i	0.0477785	−	0.147047i
$92$	−16.3805			−1.70778
$93$	6.13777	+	3.21110i	0.636458	+	0.332975i
$94$	−8.86083			−0.913925
$95$	−1.21114	+	3.72750i	−0.124260	+	0.382433i
$96$	1.05487	+	3.24656i	0.107662	+	0.331350i
$97$	−6.67779	−	4.85170i	−0.678027	−	0.492616i	0.194675	−	0.980868i	$-0.437635\pi$
$97$	−6.67779	−	4.85170i	−0.678027	−	0.492616i	−0.872703	+	0.488252i	$0.837635\pi$
$98$	−12.0688			−1.21913
$99$	−7.69340			−0.773215
$100$	−11.0182	−	8.00518i	−1.10182	−	0.800518i
$101$	−1.35594	+	0.985151i	−0.134921	+	0.0980262i	−0.653199	−	0.757186i	$-0.726573\pi$
$101$	−1.35594	+	0.985151i	−0.134921	+	0.0980262i	0.518277	+	0.855213i	$0.326573\pi$
$102$	−19.3869	+	14.0854i	−1.91959	+	1.39467i
$103$	−4.32333	+	13.3058i	−0.425990	+	1.31106i	0.476053	+	0.879417i	$0.342067\pi$
$103$	−4.32333	+	13.3058i	−0.425990	+	1.31106i	−0.902043	+	0.431646i	$0.857933\pi$
$104$	−4.56892	−	3.31951i	−0.448019	−	0.325505i
$105$	−1.62365	+	4.99709i	−0.158452	+	0.487666i
$106$	0.480972	+	1.48028i	0.0467161	+	0.143777i
$107$	−10.2280	+	7.43106i	−0.988776	+	0.718388i	−0.959653	−	0.281188i	$-0.909272\pi$
$107$	−10.2280	+	7.43106i	−0.988776	+	0.718388i	−0.0291233	+	0.999576i	$0.509272\pi$
$108$	−7.28759	−	22.4289i	−0.701248	−	2.15822i
$109$	−2.17409	−	6.69116i	−0.208240	−	0.640897i	−0.999565	−	0.0295009i	$-0.990608\pi$
$109$	−2.17409	−	6.69116i	−0.208240	−	0.640897i	0.791325	−	0.611396i	$-0.209392\pi$
$110$	30.7004	−	22.3052i	2.92717	−	2.12671i
$111$	−1.95321	−	6.01137i	−0.185391	−	0.570574i
$112$	2.55787	−	7.87231i	0.241696	−	0.743863i
$113$	−10.0808	−	7.32411i	−0.948319	−	0.688994i	0.00208935	−	0.999998i	$-0.499335\pi$
$113$	−10.0808	−	7.32411i	−0.948319	−	0.688994i	−0.950409	+	0.311003i	$0.899335\pi$
$114$	1.31640	−	4.05146i	0.123292	−	0.379454i
$115$	−8.91233	+	6.47519i	−0.831079	+	0.603815i
$116$	1.55778	−	1.13180i	0.144636	−	0.105085i
$117$	1.17481	+	0.853551i	0.108611	+	0.0789108i
$118$	11.6681			1.07414
$119$	11.3567			1.04107
$120$	16.2762	+	11.8253i	1.48581	+	1.07950i
$121$	5.27437	+	16.2328i	0.479488	+	1.47571i
$122$	8.07481	−	24.8517i	0.731059	−	2.24997i
$123$	15.0624			1.35813
$124$	−23.4522	+	3.45592i	−2.10607	+	0.310350i
$125$	5.15751			0.461302
$126$	−1.65565	+	5.09557i	−0.147497	+	0.453949i
$127$	3.14201	+	9.67012i	0.278809	+	0.858085i	0.988186	+	0.153256i	$0.0489760\pi$
$127$	3.14201	+	9.67012i	0.278809	+	0.858085i	−0.709378	+	0.704828i	$0.751024\pi$
$128$	13.2642	+	9.63704i	1.17241	+	0.851802i
$129$	9.97143			0.877936
$130$	−7.16274			−0.628214
$131$	−6.20409	−	4.50754i	−0.542054	−	0.393825i	0.282793	−	0.959181i	$-0.408739\pi$
$131$	−6.20409	−	4.50754i	−0.542054	−	0.393825i	−0.824847	+	0.565356i	$0.808739\pi$
$132$	−22.7037	+	16.4952i	−1.97610	+	1.43572i
$133$	−1.63329	+	1.18666i	−0.141625	+	0.102896i
$134$	4.73568	−	14.5749i	0.409101	−	1.25908i
$135$	−12.8312	−	9.32240i	−1.10433	−	0.802345i
$136$	13.4375	−	41.3565i	1.15226	−	3.54629i
$137$	−4.59161	−	14.1315i	−0.392288	−	1.20734i	−0.931054	−	0.364882i	$-0.881109\pi$
$137$	−4.59161	−	14.1315i	−0.392288	−	1.20734i	0.538766	−	0.842455i	$-0.318891\pi$
$138$	9.68693	−	7.03796i	0.824606	−	0.599111i
$139$	−0.455336	−	1.40138i	−0.0386211	−	0.118864i	0.929887	−	0.367845i	$-0.119904\pi$
$139$	−0.455336	−	1.40138i	−0.0386211	−	0.118864i	−0.968508	+	0.248981i	$0.919904\pi$
$140$	−5.55642	−	17.1009i	−0.469603	−	1.44529i
$141$	3.56527	−	2.59032i	0.300250	−	0.218144i
$142$	6.03844	+	18.5844i	0.506735	+	1.55957i
$143$	1.63715	−	5.03864i	0.136906	−	0.421353i
$144$	6.59315	+	4.79021i	0.549429	+	0.399184i
$145$	0.400165	−	1.23158i	0.0332319	−	0.102277i
$146$	−8.72586	+	6.33971i	−0.722158	+	0.524678i
$147$	4.85604	−	3.52812i	0.400520	−	0.290995i
$148$	17.4995	+	12.7142i	1.43845	+	1.04510i
$149$	−6.54242			−0.535976			−0.267988	−	0.963422i	$-0.586359\pi$
$149$	−6.54242			−0.535976			−0.267988	+	0.963422i	$0.586359\pi$
$150$	9.95531			0.812847
$151$	−2.65286	−	1.92742i	−0.215887	−	0.156851i	0.474586	−	0.880209i	$-0.342598\pi$
$151$	−2.65286	−	1.92742i	−0.215887	−	0.156851i	−0.690473	+	0.723358i	$0.742598\pi$
$152$	2.38877	+	7.35187i	0.193755	+	0.596315i
$153$	−3.45522	+	10.6341i	−0.279338	+	0.859713i
$154$	19.5471			1.57515
$155$	−11.3938	+	11.1509i	−0.915173	+	0.895665i
$156$	5.29702			0.424101
$157$	4.68702	−	14.4252i	0.374065	−	1.15125i	−0.570043	−	0.821615i	$-0.693073\pi$
$157$	4.68702	−	14.4252i	0.374065	−	1.15125i	0.944107	−	0.329638i	$-0.106927\pi$
$158$	−7.25635	−	22.3327i	−0.577284	−	1.77670i
$159$	−0.626261	−	0.455005i	−0.0496657	−	0.0360843i
$160$	−7.85646			−0.621107
$161$	−5.67453			−0.447216
$162$	5.12992	+	3.72710i	0.403044	+	0.292829i
$163$	−5.60474	+	4.07208i	−0.438997	+	0.318950i	−0.785236	−	0.619196i	$-0.787459\pi$
$163$	−5.60474	+	4.07208i	−0.438997	+	0.318950i	0.346239	+	0.938146i	$0.387459\pi$
$164$	−41.7017	+	30.2980i	−3.25635	+	2.36588i
$165$	−5.83216	+	17.9495i	−0.454033	+	1.39737i
$166$	32.4607	+	23.5841i	2.51944	+	1.83048i
$167$	5.07325	−	15.6138i	0.392580	−	1.20824i	−0.538251	−	0.842785i	$-0.680915\pi$
$167$	5.07325	−	15.6138i	0.392580	−	1.20824i	0.930831	−	0.365451i	$-0.119085\pi$
$168$	3.20239	+	9.85593i	0.247069	+	0.760401i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−17.0429	−	52.4527i	−1.30713	−	4.02294i
$171$	−0.614227	−	1.89040i	−0.0469711	−	0.144562i
$172$	−27.6069	+	20.0576i	−2.10500	+	1.52938i
$173$	−1.85940	−	5.72265i	−0.141368	−	0.435085i	0.855158	−	0.518367i	$-0.173460\pi$
$173$	−1.85940	−	5.72265i	−0.141368	−	0.435085i	−0.996526	+	0.0832819i	$0.973460\pi$
$174$	−0.434945	+	1.33862i	−0.0329731	+	0.101481i
$175$	−3.81693	−	2.77316i	−0.288533	−	0.209631i
$176$	9.18786	−	28.2773i	0.692561	−	2.13148i
$177$	−4.69481	+	3.41098i	−0.352884	+	0.256385i
$178$	9.39979	−	6.82935i	0.704544	−	0.511881i
$179$	−4.65428	−	3.38153i	−0.347877	−	0.252748i	0.400101	−	0.916471i	$-0.368975\pi$
$179$	−4.65428	−	3.38153i	−0.347877	−	0.252748i	−0.747978	+	0.663724i	$0.768975\pi$
$180$	17.7032			1.31952
$181$	−5.74850			−0.427282			−0.213641	−	0.976912i	$-0.568532\pi$
$181$	−5.74850			−0.427282			−0.213641	+	0.976912i	$0.568532\pi$
$182$	−2.98492	−	2.16867i	−0.221257	−	0.160753i
$183$	4.01599	+	12.3599i	0.296871	+	0.913673i
$184$	−6.71424	+	20.6643i	−0.494980	+	1.52339i
$185$	14.5471			1.06953
$186$	12.3841	−	12.1201i	0.908044	−	0.888689i
$187$	40.7934			2.98311
$188$	−4.66035	+	14.3431i	−0.339891	+	1.04608i
$189$	−2.52457	−	7.76983i	−0.183636	−	0.565172i
$190$	7.93182	+	5.76281i	0.575435	+	0.418078i
$191$	−5.78306			−0.418448			−0.209224	−	0.977868i	$-0.567094\pi$
$191$	−5.78306			−0.418448			−0.209224	+	0.977868i	$0.567094\pi$
$192$	−5.42503			−0.391518
$193$	−6.17048	−	4.48312i	−0.444161	−	0.322702i	0.343125	−	0.939290i	$-0.388515\pi$
$193$	−6.17048	−	4.48312i	−0.444161	−	0.322702i	−0.787286	+	0.616588i	$0.788515\pi$
$194$	−16.7047	+	12.1366i	−1.19932	+	0.871360i
$195$	2.88202	−	2.09391i	0.206386	−	0.149948i
$196$	−6.34760	+	19.5359i	−0.453400	+	1.39542i
$197$	18.9758	+	13.7867i	1.35197	+	0.982262i	0.998911	+	0.0466600i	$0.0148577\pi$
$197$	18.9758	+	13.7867i	1.35197	+	0.982262i	0.353057	+	0.935602i	$0.385142\pi$
$198$	−5.94710	+	18.3033i	−0.422642	+	1.30076i
$199$	8.11873	+	24.9869i	0.575522	+	1.77127i	0.634396	+	0.773008i	$0.281249\pi$
$199$	8.11873	+	24.9869i	0.575522	+	1.77127i	−0.0588746	+	0.998265i	$0.518751\pi$
$200$	−14.6150	+	10.6184i	−1.03344	+	0.750835i
$201$	2.35528	+	7.24881i	0.166129	+	0.511292i
$202$	1.29560	+	3.98745i	0.0911581	+	0.280556i
$203$	0.539648	−	0.392077i	0.0378759	−	0.0275184i
$204$	12.6036	+	38.7900i	0.882431	+	2.71584i
$205$	−10.7124	+	32.9693i	−0.748185	+	2.30268i
$206$	28.3138	+	20.5712i	1.97271	+	1.43326i
$207$	1.72644	−	5.31344i	0.119996	−	0.369310i
$208$	−4.54028	+	3.29870i	−0.314812	+	0.228724i
$209$	−5.86680	+	4.26248i	−0.405815	+	0.294842i
$210$	10.6334	+	7.72563i	0.733775	+	0.533119i
$211$	2.97050			0.204497			0.102249	−	0.994759i	$-0.467396\pi$
$211$	2.97050			0.204497			0.102249	+	0.994759i	$0.467396\pi$
$212$	2.64911			0.181942
$213$	−7.86249	−	5.71243i	−0.538729	−	0.391410i
$214$	9.77280	+	30.0776i	0.668055	+	2.05606i
$215$	−7.09169	+	21.8260i	−0.483649	+	1.48852i
$216$	−31.2817			−2.12845
$217$	−8.12432	+	1.19720i	−0.551515	+	0.0812713i
$218$	−17.5995			−1.19199
$219$	1.65765	−	5.10173i	0.112014	−	0.344743i
$220$	−19.9587	−	61.4265i	−1.34561	−	4.14137i
$221$	−6.22931	−	4.52586i	−0.419028	−	0.304442i
$222$	−15.8114			−1.06119
$223$	18.0024			1.20553			0.602764	−	0.797919i	$-0.294066\pi$
$223$	18.0024			1.20553			0.602764	+	0.797919i	$0.294066\pi$
$224$	−3.27401	−	2.37871i	−0.218754	−	0.158934i
$225$	3.75797	−	2.73033i	0.250532	−	0.182022i
$226$	−25.2173	+	18.3214i	−1.67743	+	1.21872i
$227$	−1.98825	+	6.11920i	−0.131965	+	0.406145i	−0.995106	−	0.0988178i	$-0.968494\pi$
$227$	−1.98825	+	6.11920i	−0.131965	+	0.406145i	0.863141	+	0.504963i	$0.168494\pi$
$228$	−5.86577	−	4.26173i	−0.388470	−	0.282240i
$229$	−1.95095	+	6.00441i	−0.128922	+	0.396782i	−0.994595	−	0.103828i	$-0.966891\pi$
$229$	−1.95095	+	6.00441i	−0.128922	+	0.396782i	0.865673	+	0.500610i	$0.166891\pi$
$230$	8.51571	+	26.2087i	0.561509	+	1.72815i
$231$	−7.86504	+	5.71428i	−0.517481	+	0.375972i
$232$	−0.789260	−	2.42909i	−0.0518175	−	0.159478i
$233$	−4.09357	−	12.5987i	−0.268179	−	0.825369i	−0.990944	−	0.134276i	$-0.957129\pi$
$233$	−4.09357	−	12.5987i	−0.268179	−	0.825369i	0.722765	−	0.691094i	$-0.242871\pi$
$234$	2.93882	−	2.13518i	0.192117	−	0.139581i
$235$	3.13420	+	9.64608i	0.204453	+	0.629241i
$236$	6.13684	−	18.8873i	0.399475	−	1.22946i
$237$	9.44830	+	6.86459i	0.613733	+	0.445903i
$238$	8.77889	−	27.0187i	0.569051	−	1.75136i
$239$	13.3327	−	9.68679i	0.862422	−	0.626587i	−0.0661205	−	0.997812i	$-0.521062\pi$
$239$	13.3327	−	9.68679i	0.862422	−	0.626587i	0.928543	+	0.371225i	$0.121062\pi$
$240$	16.1742	−	11.7512i	1.04404	−	0.758538i
$241$	−13.8761	−	10.0816i	−0.893841	−	0.649413i	0.0430357	−	0.999074i	$-0.486297\pi$
$241$	−13.8761	−	10.0816i	−0.893841	−	0.649413i	−0.936877	+	0.349660i	$0.886297\pi$
$242$	42.6965			2.74464
$243$	13.4635			0.863682
$244$	−35.9807	−	26.1415i	−2.30343	−	1.67354i
$245$	4.26891	+	13.1384i	0.272731	+	0.839379i
$246$	11.6434	−	35.8348i	0.742357	−	2.28474i
$247$	1.36879			0.0870938
$248$	−5.25317	+	31.0020i	−0.333577	+	1.96863i
$249$	−19.9554			−1.26462
$250$	3.98682	−	12.2702i	0.252149	−	0.776034i
$251$	−6.23225	−	19.1809i	−0.393376	−	1.21069i	−0.930219	−	0.367006i	$-0.880383\pi$
$251$	−6.23225	−	19.1809i	−0.393376	−	1.21069i	0.536842	−	0.843683i	$-0.319617\pi$
$252$	7.37745	+	5.36003i	0.464736	+	0.337650i
$253$	−20.3829			−1.28146
$254$	25.4349			1.59593
$255$	22.1911	+	16.1228i	1.38966	+	1.00965i
$256$	26.1254	−	18.9812i	1.63284	−	1.18632i
$257$	18.9460	−	13.7651i	1.18182	−	0.858640i	0.189441	−	0.981892i	$-0.439332\pi$
$257$	18.9460	−	13.7651i	1.18182	−	0.858640i	0.992375	+	0.123252i	$0.0393323\pi$
$258$	7.70805	−	23.7229i	0.479882	−	1.47693i
$259$	6.06221	+	4.40445i	0.376687	+	0.273679i
$260$	−3.76725	+	11.5944i	−0.233635	+	0.719054i
$261$	0.202944	+	0.624596i	0.0125619	+	0.0386615i
$262$	−15.5197	+	11.2757i	−0.958809	+	0.696616i
$263$	−4.03460	−	12.4172i	−0.248784	−	0.765678i	−0.994991	−	0.0999642i	$-0.968127\pi$
$263$	−4.03460	−	12.4172i	−0.248784	−	0.765678i	0.746207	−	0.665714i	$-0.231873\pi$
$264$	11.5030	+	35.4025i	0.707959	+	2.17887i
$265$	1.44134	−	1.04719i	0.0885406	−	0.0643285i
$266$	1.56061	+	4.80306i	0.0956870	+	0.294494i
$267$	−1.78568	+	5.49575i	−0.109282	+	0.336335i
$268$	−21.1018	−	15.3314i	−1.28900	−	0.936513i
$269$	−3.00050	+	9.23459i	−0.182944	+	0.563043i	−0.999907	−	0.0136471i	$-0.995656\pi$
$269$	−3.00050	+	9.23459i	−0.182944	+	0.563043i	0.816963	+	0.576690i	$0.195656\pi$
$270$	−32.0975	+	23.3202i	−1.95339	+	1.41922i
$271$	16.6997	−	12.1331i	1.01444	−	0.737032i	0.0493022	−	0.998784i	$-0.484300\pi$
$271$	16.6997	−	12.1331i	1.01444	−	0.737032i	0.965135	+	0.261752i	$0.0843003\pi$
$272$	−34.9594	−	25.3995i	−2.11973	−	1.54007i
$273$	1.83500			0.111059
$274$	−37.1695			−2.24549
$275$	−13.7104	−	9.96119i	−0.826769	−	0.600683i
$276$	−6.29757	−	19.3819i	−0.379069	−	1.16666i
$277$	−4.62884	+	14.2461i	−0.278120	+	0.855966i	0.710257	+	0.703943i	$0.248579\pi$
$277$	−4.62884	+	14.2461i	−0.278120	+	0.855966i	−0.988377	+	0.152023i	$0.951421\pi$
$278$	−3.68599			−0.221071
$279$	1.35076	−	7.97158i	0.0808676	−	0.477246i
$280$	−23.8507			−1.42535
$281$	6.41599	−	19.7464i	0.382746	−	1.17797i	−0.555356	−	0.831613i	$-0.687418\pi$
$281$	6.41599	−	19.7464i	0.382746	−	1.17797i	0.938102	−	0.346358i	$-0.112582\pi$
$282$	−3.40660	−	10.4844i	−0.202860	−	0.624340i
$283$	4.97301	+	3.61310i	0.295615	+	0.214777i	0.725699	−	0.688012i	$-0.241516\pi$
$283$	4.97301	+	3.61310i	0.295615	+	0.214777i	−0.430085	+	0.902788i	$0.641516\pi$
$284$	33.2587			1.97354
$285$	−4.87613			−0.288837
$286$	−10.7218	−	7.78988i	−0.633996	−	0.460625i
$287$	−14.4463	+	10.4959i	−0.852739	+	0.619551i
$288$	3.22344	−	2.34197i	0.189943	−	0.138002i
$289$	13.0676	−	40.2179i	0.768682	−	2.36576i
$290$	−2.62071	−	1.90406i	−0.153894	−	0.111810i
$291$	3.17338	−	9.76667i	0.186027	−	0.572532i
$292$	5.67277	+	17.4590i	0.331974	+	1.02171i
$293$	8.86650	−	6.44189i	0.517987	−	0.376339i	−0.297858	−	0.954610i	$-0.596272\pi$
$293$	8.86650	−	6.44189i	0.517987	−	0.376339i	0.815845	+	0.578271i	$0.196272\pi$
$294$	−4.63993	−	14.2803i	−0.270606	−	0.832841i
$295$	−4.12718	−	12.7021i	−0.240293	−	0.739547i
$296$	23.2121	−	16.8646i	1.34918	−	0.980236i
$297$	−9.06826	−	27.9092i	−0.526194	−	1.61946i
$298$	−5.05738	+	15.5650i	−0.292966	+	0.901657i
$299$	3.11255	+	2.26140i	0.180004	+	0.130780i
$300$	5.23600	−	16.1147i	0.302300	−	0.930385i
$301$	−9.56360	+	6.94836i	−0.551237	+	0.400497i
$302$	−6.63619	+	4.82148i	−0.381870	+	0.277445i
$303$	−1.68697	−	1.22565i	−0.0969137	−	0.0704119i
$304$	7.68176			0.440579
$305$	−29.9103			−1.71266
$306$	22.6285	+	16.4405i	1.29358	+	0.939843i
$307$	6.49329	+	19.9843i	0.370592	+	1.14056i	0.946405	+	0.322983i	$0.104686\pi$
$307$	6.49329	+	19.9843i	0.370592	+	1.14056i	−0.575813	+	0.817581i	$0.695314\pi$
$308$	10.2808	−	31.6411i	0.585804	−	1.80292i
$309$	−17.4061			−0.990196
$310$	17.7215	+	35.7267i	1.00652	+	2.02914i
$311$	0.459578			0.0260603			0.0130301	−	0.999915i	$-0.495852\pi$
$311$	0.459578			0.0260603			0.0130301	+	0.999915i	$0.495852\pi$
$312$	2.17121	−	6.68231i	0.122921	−	0.378311i
$313$	−7.58256	−	23.3367i	−0.428592	−	1.31907i	−0.899513	−	0.436894i	$-0.856078\pi$
$313$	−7.58256	−	23.3367i	−0.428592	−	1.31907i	0.470921	−	0.882175i	$-0.343922\pi$
$314$	−30.6956	−	22.3017i	−1.73225	−	1.25856i
$315$	6.13277			0.345542
$316$	−39.9667			−2.24830
$317$	−4.75369	−	3.45376i	−0.266994	−	0.193982i	0.446231	−	0.894918i	$-0.352766\pi$
$317$	−4.75369	−	3.45376i	−0.266994	−	0.193982i	−0.713225	+	0.700936i	$0.752766\pi$
$318$	−1.56661	+	1.13821i	−0.0878509	+	0.0638274i
$319$	1.93842	−	1.40834i	0.108531	−	0.0788521i
$320$	3.85829	−	11.8746i	0.215685	−	0.663810i
$321$	−12.7249	−	9.24519i	−0.710235	−	0.516016i
$322$	−4.38649	+	13.5002i	−0.244449	+	0.752338i
$323$	3.25687	+	10.0236i	0.181217	+	0.557729i
$324$	8.73117	−	6.34357i	0.485065	−	0.352420i
$325$	0.988479	+	3.04223i	0.0548310	+	0.168752i
$326$	5.35531	+	16.4819i	0.296603	+	0.912851i
$327$	7.08137	−	5.14492i	0.391601	−	0.284515i
$328$	21.1284	+	65.0265i	1.16662	+	3.59049i
$329$	−1.61444	+	4.96875i	−0.0890072	+	0.273936i
$330$	38.1952	+	27.7505i	2.10258	+	1.52761i
$331$	−1.40745	+	4.33169i	−0.0773605	+	0.238091i	−0.982257	−	0.187541i	$-0.939948\pi$
$331$	−1.40745	+	4.33169i	−0.0773605	+	0.238091i	0.904896	+	0.425632i	$0.139948\pi$
$332$	55.2485	−	40.1404i	3.03215	−	2.20299i
$333$	−5.96857	+	4.33642i	−0.327076	+	0.237634i
$334$	−33.2251	−	24.1394i	−1.81799	−	1.32085i
$335$	−17.5416			−0.958403
$336$	10.2982			0.561812
$337$	−15.0048	−	10.9017i	−0.817366	−	0.593851i	0.0985908	−	0.995128i	$-0.468567\pi$
$337$	−15.0048	−	10.9017i	−0.817366	−	0.593851i	−0.915957	+	0.401277i	$0.868567\pi$
$338$	0.773013	+	2.37909i	0.0420464	+	0.129405i
$339$	4.79053	−	14.7437i	0.260186	−	0.800769i
$340$	−93.8693			−5.09078
$341$	−29.1826	+	4.30035i	−1.58032	+	0.232877i
$342$	−4.97223			−0.268867
$343$	−5.38939	+	16.5868i	−0.290999	+	0.895604i
$344$	13.9872	+	43.0482i	0.754139	+	2.32100i
$345$	−11.0881	−	8.05596i	−0.596962	−	0.433718i
$346$	−15.0520			−0.809203
$347$	22.5600			1.21108			0.605542	−	0.795814i	$-0.292957\pi$
$347$	22.5600			1.21108			0.605542	+	0.795814i	$0.292957\pi$
$348$	1.93808	+	1.40810i	0.103892	+	0.0754819i
$349$	14.7673	−	10.7290i	0.790473	−	0.574312i	−0.117631	−	0.993057i	$-0.537530\pi$
$349$	14.7673	−	10.7290i	0.790473	−	0.574312i	0.908104	+	0.418745i	$0.137530\pi$
$350$	−9.54813	+	6.93712i	−0.510369	+	0.370805i
$351$	−1.71166	+	5.26794i	−0.0913615	+	0.281182i
$352$	−11.7603	−	8.54433i	−0.626824	−	0.455414i
$353$	−3.76564	+	11.5895i	−0.200425	+	0.616845i	0.799445	+	0.600739i	$0.205127\pi$
$353$	−3.76564	+	11.5895i	−0.200425	+	0.616845i	−0.999870	+	0.0161058i	$0.994873\pi$
$354$	4.48588	+	13.8061i	0.238422	+	0.733787i
$355$	18.0955	−	13.1471i	0.960409	−	0.697778i
$356$	−6.11090	−	18.8074i	−0.323877	−	0.996792i
$357$	4.36616	+	13.4377i	0.231082	+	0.711197i
$358$	−11.6428	+	8.45899i	−0.615341	+	0.447071i
$359$	1.48966	+	4.58469i	0.0786210	+	0.241971i	0.982640	−	0.185521i	$-0.0593973\pi$
$359$	1.48966	+	4.58469i	0.0786210	+	0.241971i	−0.904019	+	0.427492i	$0.859397\pi$
$360$	7.25644	−	22.3330i	0.382448	−	1.17705i
$361$	13.8556	+	10.0667i	0.729240	+	0.529824i
$362$	−4.44367	+	13.6762i	−0.233554	+	0.718805i
$363$	−17.1795	+	12.4816i	−0.901690	+	0.655116i
$364$	−5.08037	+	3.69111i	−0.266284	+	0.193467i
$365$	9.98800	+	7.25671i	0.522796	+	0.379834i
$366$	32.5098			1.69932
$367$	22.5284			1.17597			0.587987	−	0.808870i	$-0.299921\pi$
$367$	22.5284			1.17597			0.587987	+	0.808870i	$0.299921\pi$
$368$	17.4679	+	12.6912i	0.910579	+	0.661574i
$369$	−5.43278	−	16.7204i	−0.282819	−	0.870428i
$370$	11.2451	−	34.6089i	0.584606	−	1.79923i
$371$	0.917706			0.0476449
$372$	−13.1055	−	26.4208i	−0.679488	−	1.36985i
$373$	19.9251			1.03168			0.515841	−	0.856684i	$-0.327480\pi$
$373$	19.9251			1.03168			0.515841	+	0.856684i	$0.327480\pi$
$374$	31.5338	−	97.0511i	1.63057	−	5.01839i
$375$	1.98284	+	6.10255i	0.102393	+	0.315134i
$376$	16.1839	+	11.7583i	0.834620	+	0.606387i
$377$	−0.452254			−0.0232923
$378$	−20.4367			−1.05115
$379$	−19.4377	−	14.1223i	−0.998447	−	0.725415i	−0.0366927	−	0.999327i	$-0.511682\pi$
$379$	−19.4377	−	14.1223i	−0.998447	−	0.725415i	−0.961755	+	0.273912i	$0.911682\pi$
$380$	13.5000	−	9.80836i	0.692538	−	0.503158i
$381$	−10.2341	+	7.43548i	−0.524307	+	0.380931i
$382$	−4.47038	+	13.7584i	−0.228725	+	0.703942i
$383$	29.5678	+	21.4823i	1.51084	+	1.09769i	0.965801	+	0.259284i	$0.0834867\pi$
$383$	29.5678	+	21.4823i	1.51084	+	1.09769i	0.545043	+	0.838408i	$0.316513\pi$
$384$	−6.30336	+	19.3997i	−0.321667	+	0.989989i
$385$	−6.91410	−	21.2794i	−0.352375	−	1.08450i
$386$	−15.4356	+	11.2146i	−0.785652	+	0.570809i
$387$	−3.59655	−	11.0690i	−0.182823	−	0.562671i
$388$	10.8599	+	33.4232i	0.551326	+	1.69681i
$389$	−17.8448	+	12.9650i	−0.904766	+	0.657351i	−0.939686	−	0.342039i	$-0.888882\pi$
$389$	−17.8448	+	12.9650i	−0.904766	+	0.657351i	0.0349199	+	0.999390i	$0.488882\pi$
$390$	−2.75376	−	8.47521i	−0.139442	−	0.429159i
$391$	−9.15426	+	28.1739i	−0.462951	+	1.42482i
$392$	22.0431	+	16.0153i	1.11335	+	0.808893i
$393$	2.94827	−	9.07385i	0.148721	−	0.457715i
$394$	47.4683	−	34.4878i	2.39142	−	1.73747i
$395$	−21.7452	+	15.7988i	−1.09412	+	0.794925i
$396$	26.4998	+	19.2532i	1.33167	+	0.967512i
$397$	−35.9526			−1.80441			−0.902205	−	0.431308i	$-0.858052\pi$
$397$	−35.9526			−1.80441			−0.902205	+	0.431308i	$0.858052\pi$
$398$	65.7219			3.29434
$399$	−2.03203	−	1.47635i	−0.101729	−	0.0739101i
$400$	5.54744	+	17.0733i	0.277372	+	0.853663i
$401$	2.47814	−	7.62693i	0.123752	−	0.380871i	−0.869919	−	0.493194i	$-0.835829\pi$
$401$	2.47814	−	7.62693i	0.123752	−	0.380871i	0.993672	+	0.112323i	$0.0358293\pi$
$402$	19.0662			0.950937
$403$	4.93340	+	2.58101i	0.245750	+	0.128569i
$404$	7.13594			0.355026
$405$	2.24288	−	6.90286i	0.111449	−	0.343006i
$406$	−0.515632	−	1.58695i	−0.0255904	−	0.0787592i
$407$	21.7755	+	15.8208i	1.07937	+	0.784208i
$408$	54.1006			2.67838
$409$	−34.3095			−1.69649			−0.848247	−	0.529600i	$-0.822342\pi$
$409$	−34.3095			−1.69649			−0.848247	+	0.529600i	$0.822342\pi$
$410$	70.1562	+	50.9714i	3.46477	+	2.51730i
$411$	14.9556	−	10.8659i	0.737707	−	0.535976i
$412$	48.1904	−	35.0124i	2.37417	−	1.72493i
$413$	2.12593	−	6.54294i	0.104610	−	0.321957i
$414$	−11.3066	−	8.21473i	−0.555689	−	0.403732i
$415$	14.1923	−	43.6794i	0.696673	−	2.14414i
$416$	0.847880	+	2.60951i	0.0415707	+	0.127942i
$417$	1.48311	−	1.07754i	0.0726280	−	0.0527674i
$418$	5.60571	+	17.2526i	0.274184	+	0.843852i
$419$	−6.59207	−	20.2883i	−0.322044	−	0.991149i	−0.972757	−	0.231826i	$-0.925530\pi$
$419$	−6.59207	−	20.2883i	−0.322044	−	0.991149i	0.650714	−	0.759323i	$-0.274470\pi$
$420$	18.0982	−	13.1491i	0.883101	−	0.641610i
$421$	11.7872	+	36.2773i	0.574473	+	1.76805i	0.637968	+	0.770063i	$0.279775\pi$
$421$	11.7872	+	36.2773i	0.574473	+	1.76805i	−0.0634951	+	0.997982i	$0.520225\pi$
$422$	2.29623	−	7.06708i	0.111779	−	0.344020i
$423$	−4.16139	−	3.02342i	−0.202334	−	0.147004i
$424$	1.08585	−	3.34191i	0.0527337	−	0.162297i
$425$	−19.9262	+	14.4772i	−0.966564	+	0.702250i
$426$	−19.6682	+	14.2898i	−0.952928	+	0.692343i
$427$	−12.4645	−	9.05597i	−0.603198	−	0.438249i
$428$	53.8269			2.60182
$429$	6.59132			0.318232
$430$	46.4440	+	33.7436i	2.23973	+	1.62726i
$431$	−9.18734	−	28.2757i	−0.442539	−	1.36199i	−0.885160	−	0.465286i	$-0.845952\pi$
$431$	−9.18734	−	28.2757i	−0.442539	−	1.36199i	0.442622	−	0.896708i	$-0.354048\pi$
$432$	−9.60597	+	29.5641i	−0.462168	+	1.42241i
$433$	7.31295			0.351438			0.175719	−	0.984440i	$-0.443775\pi$
$433$	7.31295			0.351438			0.175719	+	0.984440i	$0.443775\pi$
$434$	−3.43196	+	20.2539i	−0.164739	+	0.972220i
$435$	1.61110			0.0772462
$436$	−9.25645	+	28.4884i	−0.443304	+	1.36435i
$437$	−1.62734	−	5.00843i	−0.0778461	−	0.239586i
$438$	−10.8561	−	7.88741i	−0.518724	−	0.376875i
$439$	11.2636			0.537582			0.268791	−	0.963198i	$-0.413376\pi$
$439$	11.2636			0.537582			0.268791	+	0.963198i	$0.413376\pi$
$440$	−85.6718			−4.08424
$441$	−5.66798	−	4.11803i	−0.269904	−	0.196097i
$442$	−15.5828	+	11.3215i	−0.741196	+	0.538510i
$443$	−10.2132	+	7.42034i	−0.485245	+	0.352551i	−0.803353	−	0.595503i	$-0.796953\pi$
$443$	−10.2132	+	7.42034i	−0.485245	+	0.352551i	0.318108	+	0.948055i	$0.396953\pi$
$444$	−8.31603	+	25.5941i	−0.394662	+	1.21464i
$445$	−10.7594	−	7.81717i	−0.510045	−	0.370569i
$446$	13.9161	−	42.8293i	0.658945	−	2.02802i
$447$	−2.51528	−	7.74122i	−0.118968	−	0.366147i
$448$	5.20314	−	3.78031i	0.245825	−	0.178603i
$449$	−0.795983	−	2.44979i	−0.0375648	−	0.115613i	0.930516	−	0.366252i	$-0.119359\pi$
$449$	−0.795983	−	2.44979i	−0.0375648	−	0.115613i	−0.968081	+	0.250639i	$0.919359\pi$
$450$	−3.59073	−	11.0511i	−0.169269	−	0.520956i
$451$	−51.8912	+	37.7012i	−2.44346	+	1.77528i
$452$	16.3940	+	50.4556i	0.771110	+	2.37323i
$453$	1.26068	−	3.87997i	0.0592318	−	0.182297i
$454$	13.0212	+	9.46044i	0.611114	+	0.444000i
$455$	−1.30505	+	4.01654i	−0.0611818	+	0.188298i
$456$	−7.78061	+	5.65295i	−0.364361	+	0.264724i
$457$	15.7107	−	11.4145i	0.734916	−	0.533948i	−0.156199	−	0.987726i	$-0.549924\pi$
$457$	15.7107	−	11.4145i	0.734916	−	0.533948i	0.891115	+	0.453778i	$0.149924\pi$
$458$	12.7769	+	9.28297i	0.597026	+	0.433765i
$459$	−42.6497			−1.99072
$460$	46.9030			2.18686
$461$	−17.5427	−	12.7455i	−0.817043	−	0.593617i	0.0988208	−	0.995105i	$-0.468493\pi$
$461$	−17.5427	−	12.7455i	−0.817043	−	0.593617i	−0.915864	+	0.401489i	$0.868493\pi$
$462$	7.51502	+	23.1288i	0.349630	+	1.07605i
$463$	1.84021	−	5.66359i	0.0855219	−	0.263209i	−0.899146	−	0.437649i	$-0.855811\pi$
$463$	1.84021	−	5.66359i	0.0855219	−	0.263209i	0.984668	+	0.174439i	$0.0558113\pi$
$464$	−2.53809			−0.117828
$465$	−17.5746	−	9.19451i	−0.815003	−	0.426385i
$466$	−33.1379			−1.53508
$467$	−8.22004	+	25.2987i	−0.380378	+	1.17068i	0.559400	+	0.828898i	$0.311032\pi$
$467$	−8.22004	+	25.2987i	−0.380378	+	1.17068i	−0.939778	+	0.341786i	$0.888968\pi$
$468$	−1.91056	−	5.88009i	−0.0883155	−	0.271807i
$469$	−7.31011	−	5.31111i	−0.337550	−	0.245244i
$470$	25.3717			1.17031
$471$	18.8703			0.869498
$472$	−21.3113	−	15.4835i	−0.980930	−	0.712687i
$473$	−34.3525	+	24.9585i	−1.57953	+	1.14759i
$474$	23.6351	−	17.1719i	1.08560	−	0.788733i
$475$	1.35302	−	4.16416i	0.0620807	−	0.191065i
$476$	−39.1181	−	28.4209i	−1.79297	−	1.30267i
$477$	−0.279207	+	0.859310i	−0.0127840	+	0.0393451i
$478$	−12.7394	−	39.2078i	−0.582686	−	1.79332i
$479$	−6.43678	+	4.67660i	−0.294104	+	0.213679i	−0.725046	−	0.688701i	$-0.758181\pi$
$479$	−6.43678	+	4.67660i	−0.294104	+	0.213679i	0.430942	+	0.902380i	$0.358181\pi$
$480$	−3.02046	−	9.29603i	−0.137865	−	0.424304i
$481$	−1.56995	−	4.83180i	−0.0715833	−	0.220311i
$482$	−34.7115	+	25.2194i	−1.58107	+	1.14871i
$483$	−2.18161	−	6.71430i	−0.0992667	−	0.305511i
$484$	22.4563	−	69.1133i	1.02074	−	3.14151i
$485$	19.1209	+	13.8921i	0.868234	+	0.630809i
$486$	10.4074	−	32.0308i	0.472091	−	1.45295i
$487$	−0.818392	+	0.594597i	−0.0370849	+	0.0269437i	−0.606173	−	0.795333i	$-0.707296\pi$
$487$	−0.818392	+	0.594597i	−0.0370849	+	0.0269437i	0.569088	+	0.822276i	$0.307296\pi$
$488$	−47.7264	+	34.6753i	−2.16047	+	1.56968i
$489$	−6.97301	−	5.06618i	−0.315330	−	0.229101i
$490$	34.5573			1.56114
$491$	7.20785			0.325286			0.162643	−	0.986685i	$-0.447998\pi$
$491$	7.20785			0.325286			0.162643	+	0.986685i	$0.447998\pi$
$492$	−51.8822	−	37.6946i	−2.33903	−	1.69940i
$493$	−1.07609	−	3.31185i	−0.0484644	−	0.149158i
$494$	1.05809	−	3.25647i	0.0476058	−	0.146515i
$495$	22.0289			0.990126
$496$	27.6867	+	14.4848i	1.24317	+	0.650388i
$497$	11.5215			0.516809
$498$	−15.4258	+	47.4757i	−0.691246	+	2.12744i
$499$	−4.92752	−	15.1654i	−0.220586	−	0.678894i	−0.998710	−	0.0507831i	$-0.983828\pi$
$499$	−4.92752	−	15.1654i	−0.220586	−	0.678894i	0.778124	−	0.628111i	$-0.216172\pi$
$500$	−17.7650	−	12.9070i	−0.794474	−	0.577219i
$501$	20.4253			0.912535
$502$	−50.4507			−2.25173
$503$	−5.35795	−	3.89278i	−0.238899	−	0.173570i	0.461894	−	0.886935i	$-0.347170\pi$
$503$	−5.35795	−	3.89278i	−0.238899	−	0.173570i	−0.700793	+	0.713365i	$0.747170\pi$
$504$	9.78577	−	7.10977i	0.435893	−	0.316695i
$505$	3.88255	−	2.82083i	0.172771	−	0.125526i
$506$	−15.7563	+	48.4928i	−0.700452	+	2.15577i
$507$	−1.00652	−	0.731280i	−0.0447011	−	0.0324773i
$508$	13.3775	−	41.1717i	0.593531	−	1.82670i
$509$	4.45611	+	13.7145i	0.197514	+	0.607884i	0.999938	+	0.0111305i	$0.00354303\pi$
$509$	4.45611	+	13.7145i	0.197514	+	0.607884i	−0.802425	+	0.596754i	$0.796457\pi$
$510$	55.5116	−	40.3315i	2.45810	−	1.78591i
$511$	1.96517	+	6.04816i	0.0869339	+	0.267555i
$512$	−14.8297	−	45.6412i	−0.655388	−	2.01708i
$513$	6.13378	−	4.45645i	0.270813	−	0.196757i
$514$	−18.1028	−	55.7147i	−0.798481	−	2.45747i
$515$	12.3792	−	38.0993i	0.545493	−	1.67885i
$516$	−34.3465	−	24.9542i	−1.51202	−	1.09855i
$517$	−5.79908	+	17.8477i	−0.255043	+	0.784943i
$518$	15.1648	−	11.0178i	0.666301	−	0.484096i
$519$	6.05638	−	4.40022i	0.265846	−	0.193148i
$520$	13.0824	+	9.50493i	0.573702	+	0.416819i
$521$	27.8241			1.21900			0.609499	−	0.792787i	$-0.291371\pi$
$521$	27.8241			1.21900			0.609499	+	0.792787i	$0.291371\pi$
$522$	1.64285			0.0719055
$523$	22.9623	+	16.6831i	1.00407	+	0.729501i	0.962957	−	0.269654i	$-0.0869092\pi$
$523$	22.9623	+	16.6831i	1.00407	+	0.729501i	0.0411145	+	0.999154i	$0.486909\pi$
$524$	10.0895	+	31.0523i	0.440762	+	1.35653i
$525$	1.81386	−	5.58248i	0.0791633	−	0.243639i
$526$	−32.6605			−1.42406
$527$	−7.16223	+	42.2684i	−0.311991	+	1.84124i
$528$	36.9911			1.60983
$529$	−2.53335	+	7.79684i	−0.110145	+	0.338993i
$530$	−1.37719	−	4.23856i	−0.0598214	−	0.184111i
$531$	5.47979	+	3.98130i	0.237803	+	0.172774i
$532$	8.59555			0.372664
$533$	12.1068			0.524403
$534$	11.6945	+	8.49658i	0.506072	+	0.367683i
$535$	29.2863	−	21.2777i	1.26616	−	0.919917i
$536$	−27.9904	+	20.3362i	−1.20900	+	0.878390i
$537$	2.21178	−	6.80716i	0.0954454	−	0.293751i
$538$	19.6505	+	14.2769i	0.847193	+	0.615522i
$539$	−7.89860	+	24.3094i	−0.340217	+	1.04708i
$540$	20.8669	+	64.2218i	0.897969	+	2.76367i
$541$	19.8161	−	14.3972i	0.851959	−	0.618984i	−0.0737265	−	0.997278i	$-0.523489\pi$
$541$	19.8161	−	14.3972i	0.851959	−	0.618984i	0.925685	+	0.378294i	$0.123489\pi$
$542$	−15.9566	−	49.1092i	−0.685393	−	2.10942i
$543$	−2.21005	−	6.80183i	−0.0948422	−	0.291894i
$544$	−17.0919	+	12.4180i	−0.732811	+	0.532418i
$545$	6.22519	+	19.1592i	0.266658	+	0.820688i
$546$	1.41848	−	4.36563i	0.0607053	−	0.186832i
$547$	−14.4919	−	10.5290i	−0.619631	−	0.450188i	0.233162	−	0.972438i	$-0.425093\pi$
$547$	−14.4919	−	10.5290i	−0.619631	−	0.450188i	−0.852792	+	0.522250i	$0.825093\pi$
$548$	−19.5493	+	60.1667i	−0.835106	+	2.57019i
$549$	12.2720	−	8.91610i	0.523754	−	0.380530i
$550$	−34.2969	+	24.9182i	−1.46243	+	1.06251i
$551$	0.500813	+	0.363862i	0.0213354	+	0.0155011i
$552$	−27.0321			−1.15056
$553$	−13.8453			−0.588762
$554$	30.3146	+	22.0249i	1.28794	+	0.935747i
$555$	5.59273	+	17.2127i	0.237398	+	0.730637i
$556$	−1.93865	+	5.96655i	−0.0822170	+	0.253038i
$557$	−5.37026			−0.227545			−0.113773	−	0.993507i	$-0.536294\pi$
$557$	−5.37026			−0.227545			−0.113773	+	0.993507i	$0.536294\pi$
$558$	−17.9210	−	9.37571i	−0.758655	−	0.396905i
$559$	8.01480			0.338990
$560$	−7.32407	+	22.5412i	−0.309499	+	0.952539i
$561$	15.6833	+	48.2681i	0.662148	+	2.03788i
$562$	−42.0188	−	30.5284i	−1.77246	−	1.28776i
$563$	−19.7609			−0.832822			−0.416411	−	0.909177i	$-0.636712\pi$
$563$	−19.7609			−0.832822			−0.416411	+	0.909177i	$0.636712\pi$
$564$	−18.7630			−0.790063
$565$	28.8648	+	20.9715i	1.21435	+	0.882278i
$566$	12.4401	−	9.03826i	0.522896	−	0.379906i
$567$	3.02466	−	2.19754i	0.127024	−	0.0922882i
$568$	13.6325	−	41.9565i	0.572007	−	1.76046i
$569$	22.5092	+	16.3539i	0.943635	+	0.685591i	0.949293	−	0.314393i	$-0.101801\pi$
$569$	22.5092	+	16.3539i	0.943635	+	0.685591i	−0.00565798	+	0.999984i	$0.501801\pi$
$570$	−3.76932	+	11.6008i	−0.157879	+	0.485902i
$571$	−7.74224	−	23.8282i	−0.324002	−	0.997177i	−0.971889	−	0.235440i	$-0.924347\pi$
$571$	−7.74224	−	23.8282i	−0.324002	−	0.997177i	0.647886	−	0.761737i	$-0.275653\pi$
$572$	−18.2487	+	13.2585i	−0.763017	+	0.554364i
$573$	−2.22334	−	6.84272i	−0.0928812	−	0.285859i
$574$	13.8034	+	42.4825i	0.576143	+	1.77319i
$575$	9.95639	−	7.23374i	0.415210	−	0.301668i
$576$	1.95673	+	6.02219i	0.0815303	+	0.250925i
$577$	−1.90669	+	5.86818i	−0.0793765	+	0.244296i	−0.982868	−	0.184310i	$-0.940995\pi$
$577$	−1.90669	+	5.86818i	−0.0793765	+	0.244296i	0.903492	+	0.428606i	$0.140995\pi$
$578$	−85.5806	−	62.1780i	−3.55968	−	2.58626i
$579$	2.93230	−	9.02470i	0.121862	−	0.375054i
$580$	−4.46048	+	3.24073i	−0.185211	+	0.134564i
$581$	19.1392	−	13.9055i	0.794028	−	0.576895i
$582$	−20.7827	−	15.0995i	−0.861471	−	0.625896i
$583$	3.29640			0.136523
$584$	24.3502			1.00762
$585$	−3.36390	−	2.44402i	−0.139080	−	0.101048i
$586$	−8.47192	−	26.0739i	−0.349972	−	1.07710i
$587$	3.75895	−	11.5689i	0.155149	−	0.477498i	−0.843027	−	0.537871i	$-0.819229\pi$
$587$	3.75895	−	11.5689i	0.155149	−	0.477498i	0.998176	+	0.0603725i	$0.0192288\pi$
$588$	−25.5559			−1.05391
$589$	−3.38655	−	6.82731i	−0.139540	−	0.281315i
$590$	−33.4099			−1.37546
$591$	−9.01756	+	27.7532i	−0.370933	+	1.14161i
$592$	−8.81068	−	27.1165i	−0.362117	−	1.11448i
$593$	−12.5933	−	9.14956i	−0.517144	−	0.375727i	0.298383	−	0.954446i	$-0.403553\pi$
$593$	−12.5933	−	9.14956i	−0.517144	−	0.375727i	−0.815527	+	0.578719i	$0.803553\pi$
$594$	−73.4085			−3.01199
$595$	−32.5183			−1.33312
$596$	22.5353	+	16.3728i	0.923081	+	0.670658i
$597$	−26.4441	+	19.2127i	−1.08228	+	0.786325i
$598$	7.78612	−	5.65695i	0.318398	−	0.231330i
$599$	8.85132	−	27.2416i	0.361655	−	1.11306i	−0.590394	−	0.807115i	$-0.701028\pi$
$599$	8.85132	−	27.2416i	0.361655	−	1.11306i	0.952049	−	0.305945i	$-0.0989724\pi$
$600$	−18.1829	−	13.2107i	−0.742314	−	0.539323i
$601$	3.68436	−	11.3393i	0.150288	−	0.462539i	−0.847365	−	0.531011i	$-0.821812\pi$
$601$	3.68436	−	11.3393i	0.150288	−	0.462539i	0.997653	+	0.0684717i	$0.0218123\pi$
$602$	9.13799	+	28.1238i	0.372437	+	1.14624i
$603$	7.19721	−	5.22908i	0.293093	−	0.212944i
$604$	4.31426	+	13.2779i	0.175545	+	0.540271i
$605$	−15.1024	−	46.4803i	−0.613999	−	1.88969i
$606$	−4.21999	+	3.06600i	−0.171425	+	0.124548i
$607$	−10.6625	−	32.8157i	−0.432777	−	1.33195i	−0.895348	−	0.445368i	$-0.853073\pi$
$607$	−10.6625	−	32.8157i	−0.432777	−	1.33195i	0.462571	−	0.886582i	$-0.346927\pi$
$608$	1.16057	−	3.57186i	0.0470672	−	0.144858i
$609$	0.671391	+	0.487794i	0.0272061	+	0.0197664i
$610$	−23.1210	+	71.1592i	−0.936143	+	2.88115i
$611$	2.86568	−	2.08204i	0.115933	−	0.0842302i
$612$	38.5139	−	27.9820i	1.55683	−	1.13110i
$613$	27.3730	+	19.8876i	1.10558	+	0.803253i	0.981962	−	0.189076i	$-0.0605493\pi$
$613$	27.3730	+	19.8876i	1.10558	+	0.803253i	0.123621	+	0.992330i	$0.460549\pi$
$614$	52.5638			2.12130
$615$	−43.1289			−1.73912
$616$	−35.7019	−	25.9390i	−1.43847	−	1.04511i
$617$	10.9638	+	33.7432i	0.441387	+	1.35845i	0.886398	+	0.462924i	$0.153200\pi$
$617$	10.9638	+	33.7432i	0.441387	+	1.35845i	−0.445011	+	0.895525i	$0.646800\pi$
$618$	−13.4551	+	41.4106i	−0.541244	+	1.66578i
$619$	−7.47775			−0.300556			−0.150278	−	0.988644i	$-0.548017\pi$
$619$	−7.47775			−0.300556			−0.150278	+	0.988644i	$0.548017\pi$
$620$	67.1518	−	9.89551i	2.69688	−	0.397413i
$621$	21.3105			0.855160
$622$	0.355260	−	1.09338i	0.0142446	−	0.0438405i
$623$	−2.11694	−	6.51528i	−0.0848136	−	0.261029i
$624$	−5.64868	−	4.10401i	−0.226128	−	0.164292i
$625$	−30.7617			−1.23047
$626$	−61.3816			−2.45330
$627$	−7.29904	−	5.30306i	−0.291496	−	0.211784i
$628$	−52.2443	+	37.9577i	−2.08477	+	1.51468i
$629$	31.6477	−	22.9934i	1.26188	−	0.916806i
$630$	4.74071	−	14.5904i	0.188874	−	0.581296i
$631$	15.2468	+	11.0774i	0.606965	+	0.440986i	0.848344	−	0.529445i	$-0.177600\pi$
$631$	15.2468	+	11.0774i	0.606965	+	0.440986i	−0.241379	+	0.970431i	$0.577600\pi$
$632$	−16.3821	+	50.4189i	−0.651644	+	2.00555i
$633$	1.14203	+	3.51480i	0.0453915	+	0.139701i
$634$	−11.8915	+	8.63965i	−0.472270	+	0.343124i
$635$	−8.99669	−	27.6890i	−0.357023	−	1.09880i
$636$	1.01847	+	3.13452i	0.0403848	+	0.124292i
$637$	3.90317	−	2.83582i	0.154649	−	0.112359i
$638$	−1.85215	−	5.70034i	−0.0733274	−	0.225679i
$639$	−3.50535	+	10.7883i	−0.138669	+	0.426780i
$640$	−37.9802	−	27.5942i	−1.50130	−	1.09076i
$641$	4.07390	−	12.5382i	0.160909	−	0.495228i	−0.837802	−	0.545974i	$-0.816160\pi$
$641$	4.07390	−	12.5382i	0.160909	−	0.495228i	0.998712	+	0.0507459i	$0.0161599\pi$
$642$	−31.8317	+	23.1271i	−1.25630	+	0.912752i
$643$	−11.0764	+	8.04747i	−0.436810	+	0.317361i	−0.784366	−	0.620298i	$-0.787012\pi$
$643$	−11.0764	+	8.04747i	−0.436810	+	0.317361i	0.347556	+	0.937659i	$0.387012\pi$
$644$	19.5458	+	14.2009i	0.770214	+	0.559593i
$645$	−28.5517			−1.12422
$646$	26.3647			1.03730
$647$	3.20578	+	2.32914i	0.126032	+	0.0915678i	0.649016	−	0.760775i	$-0.275181\pi$
$647$	3.20578	+	2.32914i	0.126032	+	0.0915678i	−0.522983	+	0.852343i	$0.675181\pi$
$648$	−4.42370	−	13.6148i	−0.173779	−	0.534838i
$649$	7.63635	−	23.5023i	0.299753	−	0.922544i
$650$	8.00184			0.313858
$651$	−4.54002	−	9.15271i	−0.177937	−	0.358723i
$652$	29.4961			1.15516
$653$	−2.61660	+	8.05306i	−0.102395	+	0.315141i	−0.989110	−	0.147176i	$-0.952982\pi$
$653$	−2.61660	+	8.05306i	−0.102395	+	0.315141i	0.886715	+	0.462317i	$0.152982\pi$
$654$	−6.76623	−	20.8243i	−0.264581	−	0.814295i
$655$	17.7645	+	12.9067i	0.694116	+	0.504305i
$656$	67.9444			2.65278
$657$	−6.26119			−0.244272
$658$	10.5731	+	7.68182i	0.412183	+	0.299468i
$659$	6.06052	−	4.40323i	0.236084	−	0.171525i	−0.463453	−	0.886122i	$-0.653390\pi$
$659$	6.06052	−	4.40323i	0.236084	−	0.171525i	0.699537	+	0.714596i	$0.253390\pi$
$660$	65.0087	−	47.2316i	2.53046	−	1.83849i
$661$	−11.1667	+	34.3676i	−0.434334	+	1.33674i	0.459433	+	0.888212i	$0.348053\pi$
$661$	−11.1667	+	34.3676i	−0.434334	+	1.33674i	−0.893767	+	0.448531i	$0.851947\pi$
$662$	9.21750	+	6.69690i	0.358248	+	0.260282i
$663$	2.96026	−	9.11073i	0.114967	−	0.353831i
$664$	−27.9920	−	86.1504i	−1.08630	−	3.34329i
$665$	4.67670	−	3.39782i	0.181355	−	0.131762i
$666$	5.70295	+	17.5519i	0.220985	+	0.680122i
$667$	0.537680	+	1.65481i	0.0208190	+	0.0640744i
$668$	−56.5494	+	41.0856i	−2.18796	+	1.58965i
$669$	6.92113	+	21.3010i	0.267586	+	0.823546i
$670$	−13.5599	+	41.7332i	−0.523866	+	1.61229i
$671$	−44.7724	−	32.5291i	−1.72842	−	1.25577i
$672$	1.55586	−	4.78844i	0.0600185	−	0.184718i
$673$	−17.4198	+	12.6562i	−0.671483	+	0.487861i	−0.870521	−	0.492131i	$-0.836218\pi$
$673$	−17.4198	+	12.6562i	−0.671483	+	0.487861i	0.199038	+	0.979992i	$0.436218\pi$
$674$	−37.5350	+	27.2708i	−1.44579	+	1.05043i
$675$	14.3343	+	10.4145i	0.551728	+	0.400854i
$676$	4.25762			0.163755
$677$	−13.8227			−0.531251			−0.265625	−	0.964076i	$-0.585578\pi$
$677$	−13.8227			−0.531251			−0.265625	+	0.964076i	$0.585578\pi$
$678$	−31.3735	−	22.7942i	−1.20489	−	0.875406i
$679$	3.76208	+	11.5785i	0.144376	+	0.444342i
$680$	−38.4764	+	118.418i	−1.47550	+	4.54113i
$681$	−8.00484			−0.306746
$682$	−12.3276	+	72.7522i	−0.472048	+	2.78582i
$683$	44.6663			1.70911			0.854554	−	0.519363i	$-0.173831\pi$
$683$	44.6663			1.70911			0.854554	+	0.519363i	$0.173831\pi$
$684$	−2.61515	+	8.04859i	−0.0999926	+	0.307746i
$685$	13.1474	+	40.4635i	0.502336	+	1.54603i
$686$	35.2955	+	25.6437i	1.34759	+	0.979080i
$687$	−7.85468			−0.299675
$688$	44.9798			1.71484
$689$	−0.503374	−	0.365722i	−0.0191770	−	0.0139329i
$690$	−27.7371	+	20.1522i	−1.05593	+	0.767180i
$691$	39.2638	−	28.5268i	1.49367	−	1.08521i	0.520847	−	0.853650i	$-0.325616\pi$
$691$	39.2638	−	28.5268i	1.49367	−	1.08521i	0.972820	−	0.231562i	$-0.0743837\pi$
$692$	−7.91662	+	24.3649i	−0.300945	+	0.926213i
$693$	9.18008	+	6.66972i	0.348723	+	0.253362i
$694$	17.4392	−	53.6722i	0.661982	−	2.03737i
$695$	1.30379	+	4.01265i	0.0494555	+	0.152208i
$696$	2.57075	−	1.86776i	0.0974441	−	0.0707973i
$697$	28.8067	+	88.6578i	1.09113	+	3.35815i
$698$	−14.1101	−	43.4263i	−0.534074	−	1.64371i
$699$	13.3334	−	9.68731i	0.504317	−	0.366408i
$700$	6.20734	+	19.1042i	0.234615	+	0.722072i
$701$	13.7302	−	42.2574i	0.518584	−	1.59604i	−0.258080	−	0.966124i	$-0.583090\pi$
$701$	13.7302	−	42.2574i	0.518584	−	1.59604i	0.776664	−	0.629915i	$-0.216910\pi$
$702$	11.2098	+	8.14437i	0.423085	+	0.307390i
$703$	−2.14892	+	6.61370i	−0.0810481	+	0.249440i
$704$	18.6897	−	13.5789i	0.704395	−	0.511773i
$705$	−10.2086	+	7.41699i	−0.384479	+	0.279340i
$706$	24.6615	+	17.9176i	0.928147	+	0.674338i
$707$	2.47204			0.0929705
$708$	24.7074			0.928562
$709$	7.24457	+	5.26349i	0.272075	+	0.197674i	0.715454	−	0.698660i	$-0.246220\pi$
$709$	7.24457	+	5.26349i	0.272075	+	0.197674i	−0.443378	+	0.896335i	$0.646220\pi$
$710$	−17.2902	−	53.2137i	−0.648889	−	1.99707i
$711$	4.21235	−	12.9643i	0.157975	−	0.486198i
$712$	−26.2308			−0.983041
$713$	3.57870	−	21.1200i	0.134023	−	0.790948i
$714$	35.3445			1.32274
$715$	−4.68775	+	14.4274i	−0.175312	+	0.539555i
$716$	7.56910	+	23.2953i	0.282871	+	0.870586i
$717$	16.5876	+	12.0516i	0.619476	+	0.450075i
$718$	12.0589			0.450035
$719$	−25.6471			−0.956476			−0.478238	−	0.878230i	$-0.658724\pi$
$719$	−25.6471			−0.956476			−0.478238	+	0.878230i	$0.658724\pi$
$720$	−18.8785	−	13.7160i	−0.703561	−	0.511167i
$721$	16.6941	−	12.1290i	0.621723	−	0.451708i
$722$	34.6600	−	25.1820i	1.28991	−	0.937176i
$723$	6.59414	−	20.2947i	0.245239	−	0.754767i
$724$	19.8006	+	14.3860i	0.735884	+	0.534651i
$725$	−0.447044	+	1.37586i	−0.0166028	+	0.0510981i
$726$	16.4150	+	50.5201i	0.609216	+	1.87498i
$727$	30.8456	−	22.4107i	1.14400	−	0.831166i	0.156330	−	0.987705i	$-0.450034\pi$
$727$	30.8456	−	22.4107i	1.14400	−	0.831166i	0.987672	+	0.156539i	$0.0500337\pi$
$728$	2.57400	+	7.92196i	0.0953988	+	0.293607i
$729$	7.52603	+	23.1627i	0.278742	+	0.857879i
$730$	24.9852	−	18.1528i	0.924745	−	0.671866i
$731$	19.0703	+	58.6923i	0.705340	+	2.17081i
$732$	17.0986	−	52.6240i	0.631981	−	1.94504i
$733$	−25.2210	−	18.3241i	−0.931559	−	0.676817i	0.0148148	−	0.999890i	$-0.495284\pi$
$733$	−25.2210	−	18.3241i	−0.931559	−	0.676817i	−0.946374	+	0.323073i	$0.895284\pi$
$734$	17.4148	−	53.5972i	0.642791	−	1.97831i
$735$	−13.9046	+	10.1023i	−0.512878	+	0.372627i
$736$	8.54021	−	6.20483i	0.314796	−	0.228713i
$737$	−26.2579	−	19.0775i	−0.967224	−	0.702729i
$738$	−43.9789			−1.61888
$739$	−7.83970			−0.288388			−0.144194	−	0.989549i	$-0.546059\pi$
$739$	−7.83970			−0.288388			−0.144194	+	0.989549i	$0.546059\pi$
$740$	−50.1074	−	36.4051i	−1.84198	−	1.33828i
$741$	0.526239	+	1.61960i	0.0193319	+	0.0594974i
$742$	0.709399	−	2.18331i	0.0260429	−	0.0801517i
$743$	−23.1813			−0.850439			−0.425219	−	0.905090i	$-0.639803\pi$
$743$	−23.1813			−0.850439			−0.425219	+	0.905090i	$0.639803\pi$
$744$	−38.7023	+	5.70317i	−1.41889	+	0.209088i
$745$	18.7333			0.686333
$746$	15.4024	−	47.4036i	0.563920	−	1.73557i
$747$	7.19762	+	22.1520i	0.263347	+	0.810499i
$748$	−140.512	−	102.088i	−5.13763	−	3.73271i
$749$	18.6467			0.681337
$750$	16.0513			0.586109
$751$	13.8571	+	10.0677i	0.505651	+	0.367377i	0.811171	−	0.584808i	$-0.198830\pi$
$751$	13.8571	+	10.0677i	0.505651	+	0.367377i	−0.305520	+	0.952186i	$0.598830\pi$
$752$	16.0824	−	11.6846i	0.586466	−	0.426093i
$753$	20.2995	−	14.7484i	0.739755	−	0.537463i
$754$	−0.349598	+	1.07595i	−0.0127316	+	0.0391839i
$755$	7.59607	+	5.51887i	0.276449	+	0.200852i
$756$	−10.7487	+	33.0810i	−0.390925	+	1.20314i
$757$	−11.0045	−	33.8682i	−0.399964	−	1.23096i	−0.925028	−	0.379899i	$-0.875959\pi$
$757$	−11.0045	−	33.8682i	−0.399964	−	1.23096i	0.525064	−	0.851063i	$-0.324041\pi$
$758$	−48.6239	+	35.3273i	−1.76610	+	1.28315i
$759$	−7.83635	−	24.1178i	−0.284441	−	0.875420i
$760$	−6.83988	−	21.0510i	−0.248109	−	0.763600i
$761$	13.8041	−	10.0292i	0.500397	−	0.363559i	−0.308772	−	0.951136i	$-0.599918\pi$
$761$	13.8041	−	10.0292i	0.500397	−	0.363559i	0.809168	+	0.587577i	$0.199918\pi$
$762$	9.77862	+	30.0955i	0.354242	+	1.09024i
$763$	−3.20663	+	9.86898i	−0.116088	+	0.357281i
$764$	19.9197	+	14.4725i	0.720669	+	0.523597i
$765$	9.89350	−	30.4491i	0.357700	−	1.10089i
$766$	73.9646	−	53.7384i	2.67245	−	1.94165i
$767$	−3.77358	+	2.74167i	−0.136256	+	0.0989958i
$768$	32.5033	+	23.6150i	1.17286	+	0.852134i
$769$	−53.6950			−1.93629			−0.968145	−	0.250390i	$-0.919441\pi$
$769$	−53.6950			−1.93629			−0.968145	+	0.250390i	$0.919441\pi$
$770$	−55.9703			−2.01703
$771$	23.5712	+	17.1255i	0.848896	+	0.616759i
$772$	10.0348	+	30.8841i	0.361162	+	1.11154i
$773$	−3.74309	+	11.5201i	−0.134630	+	0.414348i	−0.995532	−	0.0944222i	$-0.969900\pi$
$773$	−3.74309	+	11.5201i	−0.134630	+	0.414348i	0.860902	+	0.508770i	$0.169900\pi$
$774$	−29.1144			−1.04650
$775$	12.7286	−	12.4572i	0.457224	−	0.447477i
$776$	46.6155			1.67340
$777$	−2.88085	+	8.86634i	−0.103350	+	0.318078i
$778$	17.0506	+	52.4764i	0.611294	+	1.88137i
$779$	−13.4067	−	9.74055i	−0.480345	−	0.348991i
$780$	−15.1672			−0.543074
$781$	41.3852			1.48088
$782$	59.9519	+	43.5576i	2.14388	+	1.55762i
$783$	−2.02663	+	1.47243i	−0.0724258	+	0.0526204i
$784$	21.9050	−	15.9149i	0.782320	−	0.568389i
$785$	−13.4206	+	41.3043i	−0.479001	+	1.47421i
$786$	−19.3085	−	14.0284i	−0.688710	−	0.500377i
$787$	3.37986	−	10.4021i	0.120479	−	0.370796i	−0.872571	−	0.488487i	$-0.837549\pi$
$787$	3.37986	−	10.4021i	0.120479	−	0.370796i	0.993050	+	0.117690i	$0.0375490\pi$
$788$	−30.8597	−	94.9762i	−1.09933	−	3.38339i
$789$	13.1414	−	9.54775i	0.467845	−	0.339909i
$790$	20.7775	+	63.9465i	0.739230	+	2.27512i
$791$	5.67923	+	17.4789i	0.201930	+	0.621477i
$792$	35.1505	−	25.5383i	1.24902	−	0.907465i
$793$	3.22796	+	9.93463i	0.114628	+	0.352789i
$794$	−27.7918	+	85.5345i	−0.986295	+	3.03551i
$795$	1.79321	+	1.30284i	0.0635984	+	0.0462070i
$796$	34.5665	−	106.385i	1.22518	−	3.77071i
$797$	−18.4024	+	13.3701i	−0.651846	+	0.473594i	−0.863900	−	0.503664i	$-0.831985\pi$
$797$	−18.4024	+	13.3701i	−0.651846	+	0.473594i	0.212053	+	0.977258i	$0.431985\pi$
$798$	−5.08316	+	3.69313i	−0.179942	+	0.130735i
$799$	22.0653	+	16.0314i	0.780613	+	0.567149i
$800$	8.77682			0.310307
$801$	6.74477			0.238315
$802$	−16.2295	−	11.7914i	−0.573084	−	0.416370i
$803$	7.05888	+	21.7250i	0.249103	+	0.766659i
$804$	10.0279	−	30.8627i	0.353656	−	1.08844i
$805$	16.2482			0.572673
$806$	9.95403	−	9.74185i	0.350616	−	0.343142i
$807$	−12.0802			−0.425245
$808$	2.92497	−	9.00215i	0.102900	−	0.316694i
$809$	−1.84410	−	5.67555i	−0.0648350	−	0.199542i	0.913391	−	0.407083i	$-0.133454\pi$
$809$	−1.84410	−	5.67555i	−0.0648350	−	0.199542i	−0.978226	+	0.207541i	$0.933454\pi$
$810$	−14.6888	−	10.6720i	−0.516110	−	0.374976i
$811$	−8.49368			−0.298253			−0.149127	−	0.988818i	$-0.547646\pi$
$811$	−8.49368			−0.298253			−0.149127	+	0.988818i	$0.547646\pi$
$812$	−2.84001			−0.0996649
$813$	20.7766	+	15.0951i	0.728667	+	0.529408i
$814$	54.4718	−	39.5761i	1.90924	−	1.38714i
$815$	16.0483	−	11.6598i	0.562149	−	0.408425i
$816$	16.6132	−	51.1302i	0.581579	−	1.78992i
$817$	−8.87537	−	6.44833i	−0.310510	−	0.225599i
$818$	−26.5217	+	81.6254i	−0.927309	+	2.85396i
$819$	−0.661857	−	2.03699i	−0.0231271	−	0.0711780i
$820$	119.407	−	86.7539i	4.16986	−	3.02958i
$821$	−5.34110	−	16.4382i	−0.186406	−	0.573697i	0.813564	−	0.581475i	$-0.197524\pi$
$821$	−5.34110	−	16.4382i	−0.186406	−	0.573697i	−0.999970	+	0.00777772i	$0.997524\pi$
$822$	−14.2901	−	43.9803i	−0.498424	−	1.53399i
$823$	−11.7437	+	8.53227i	−0.409358	+	0.297416i	−0.773342	−	0.633989i	$-0.781416\pi$
$823$	−11.7437	+	8.53227i	−0.409358	+	0.297416i	0.363984	+	0.931405i	$0.381416\pi$
$824$	−24.4159	−	75.1446i	−0.850570	−	2.61778i
$825$	6.51538	−	20.0523i	0.226836	−	0.698131i
$826$	−13.9229	−	10.1156i	−0.484439	−	0.351965i
$827$	−13.9575	+	42.9567i	−0.485349	+	1.49375i	0.346127	+	0.938188i	$0.387497\pi$
$827$	−13.9575	+	42.9567i	−0.485349	+	1.49375i	−0.831475	+	0.555561i	$0.812503\pi$
$828$	−19.2440	+	13.9816i	−0.668774	+	0.485893i
$829$	22.8790	−	16.6225i	0.794619	−	0.577325i	−0.114711	−	0.993399i	$-0.536594\pi$
$829$	22.8790	−	16.6225i	0.794619	−	0.577325i	0.909331	+	0.416074i	$0.136594\pi$
$830$	−92.9464	−	67.5295i	−3.22622	−	2.34398i
$831$	−18.6361			−0.646479
$832$	−4.36051			−0.151174
$833$	30.0538	+	21.8354i	1.04130	+	0.756551i
$834$	−1.41710	−	4.36140i	−0.0490703	−	0.151023i
$835$	−14.5265	+	44.7079i	−0.502710	+	1.54718i
$836$	30.8752			1.06784
$837$	30.5106	−	4.49604i	1.05460	−	0.155406i
$838$	−53.3635			−1.84341
$839$	−11.2011	+	34.4734i	−0.386705	+	1.19015i	0.548532	+	0.836130i	$0.315187\pi$
$839$	−11.2011	+	34.4734i	−0.386705	+	1.19015i	−0.935236	+	0.354024i	$0.884813\pi$
$840$	−9.16956	−	28.2210i	−0.316380	−	0.973717i
$841$	23.2960	+	16.9256i	0.803311	+	0.583640i
$842$	95.4185			3.28834
$843$	25.8313			0.889677
$844$	−10.2318	−	7.43387i	−0.352194	−	0.255884i
$845$	2.31650	−	1.68304i	0.0796900	−	0.0578982i
$846$	−10.4098	+	7.56317i	−0.357897	+	0.260027i
$847$	7.77932	−	23.9423i	0.267300	−	0.822666i
$848$	−2.82498	−	2.05247i	−0.0970102	−	0.0704820i
$849$	−2.36324	+	7.27332i	−0.0811063	+	0.249620i
$850$	19.0394	+	58.5974i	0.653048	+	2.00987i
$851$	−15.8132	+	11.4889i	−0.542068	+	0.393836i
$852$	12.7865	+	39.3528i	0.438058	+	1.34821i
$853$	3.03229	+	9.33243i	0.103824	+	0.319536i	0.989453	−	0.144857i	$-0.0462723\pi$
$853$	3.03229	+	9.33243i	0.103824	+	0.319536i	−0.885629	+	0.464394i	$0.846272\pi$
$854$	−31.1802	+	22.6537i	−1.06696	+	0.775195i
$855$	1.75875	+	5.41287i	0.0601479	+	0.185116i
$856$	22.0633	−	67.9038i	0.754107	−	2.32090i
$857$	23.8134	+	17.3015i	0.813452	+	0.591007i	0.914829	−	0.403841i	$-0.132325\pi$
$857$	23.8134	+	17.3015i	0.813452	+	0.591007i	−0.101377	+	0.994848i	$0.532325\pi$
$858$	5.09518	−	15.6813i	0.173946	−	0.535352i
$859$	−15.9147	+	11.5627i	−0.543004	+	0.394515i	−0.825199	−	0.564842i	$-0.808937\pi$
$859$	−15.9147	+	11.5627i	−0.543004	+	0.394515i	0.282196	+	0.959357i	$0.408937\pi$
$860$	79.0482	−	57.4319i	2.69552	−	1.95841i
$861$	−17.9731	−	13.0582i	−0.612520	−	0.445022i
$862$	−74.3725			−2.53314
$863$	19.1170			0.650749			0.325375	−	0.945585i	$-0.394510\pi$
$863$	19.1170			0.650749			0.325375	+	0.945585i	$0.394510\pi$
$864$	12.2954	+	8.93315i	0.418299	+	0.303912i
$865$	5.32412	+	16.3860i	0.181026	+	0.557139i
$866$	5.65301	−	17.3982i	0.192097	−	0.591214i
$867$	52.6112			1.78677
$868$	30.9802	+	16.2079i	1.05154	+	0.550132i
$869$	−49.7323			−1.68705
$870$	1.24540	−	3.83295i	0.0422230	−	0.129949i
$871$	1.89312	+	5.82642i	0.0641459	+	0.197421i
$872$	32.1446	+	23.3544i	1.08855	+	0.790881i
$873$	−11.9863			−0.405676
$874$	−13.1735			−0.445599
$875$	−6.15416	−	4.47126i	−0.208048	−	0.151156i
$876$	−18.4772	+	13.4245i	−0.624286	+	0.453570i
$877$	−32.1681	+	23.3715i	−1.08624	+	0.789199i	−0.978760	−	0.205009i	$-0.934278\pi$
$877$	−32.1681	+	23.3715i	−1.08624	+	0.789199i	−0.107478	+	0.994207i	$0.534278\pi$
$878$	8.70692	−	26.7971i	0.293844	−	0.904359i
$879$	11.0311	+	8.01453i	0.372068	+	0.270323i
$880$	−26.3081	+	80.9680i	−0.886845	+	2.72943i
$881$	−13.4806	−	41.4892i	−0.454174	−	1.39781i	−0.872102	−	0.489325i	$-0.837243\pi$
$881$	−13.4806	−	41.4892i	−0.454174	−	1.39781i	0.417927	−	0.908480i	$-0.362757\pi$
$882$	−14.1786	+	10.3013i	−0.477418	+	0.346864i
$883$	−15.9268	−	49.0177i	−0.535980	−	1.64958i	−0.741522	−	0.670929i	$-0.765896\pi$
$883$	−15.9268	−	49.0177i	−0.535980	−	1.64958i	0.205542	−	0.978648i	$-0.434104\pi$
$884$	10.1305	+	31.1785i	0.340726	+	1.04865i
$885$	13.4429	−	9.76684i	0.451878	−	0.328309i
$886$	9.75871	+	30.0342i	0.327850	+	1.00902i
$887$	−11.7819	+	36.2608i	−0.395596	+	1.21752i	0.532901	+	0.846178i	$0.321102\pi$
$887$	−11.7819	+	36.2608i	−0.395596	+	1.21752i	−0.928497	+	0.371341i	$0.878898\pi$
$888$	28.8789	+	20.9817i	0.969111	+	0.704101i
$889$	4.63424	−	14.2627i	0.155428	−	0.478357i
$890$	−26.9149	+	19.5548i	−0.902190	+	0.655480i
$891$	10.8646	−	7.89358i	0.363977	−	0.264445i
$892$	−62.0089	−	45.0521i	−2.07621	−	1.50846i
$893$	−4.84848			−0.162248
$894$	−20.3614			−0.680987
$895$	13.3268	+	9.68252i	0.445467	+	0.323651i
$896$	−7.47271	−	22.9986i	−0.249646	−	0.768331i
$897$	−1.47913	+	4.55229i	−0.0493867	+	0.151997i
$898$	−6.44357			−0.215025
$899$	1.11893	+	2.25578i	0.0373185	+	0.0752344i
$900$	−19.7771			−0.659237
$901$	1.48046	−	4.55639i	0.0493213	−	0.151795i
$902$	49.5819	+	152.597i	1.65090	+	5.08094i
$903$	−11.8983	−	8.64464i	−0.395952	−	0.287676i
$904$	70.3707			2.34049
$905$	16.4600			0.547148
$906$	−8.25627	−	5.99853i	−0.274296	−	0.199288i
$907$	2.85751	−	2.07610i	0.0948820	−	0.0689358i	−0.539333	−	0.842093i	$-0.681324\pi$
$907$	2.85751	−	2.07610i	0.0948820	−	0.0689358i	0.634215	+	0.773157i	$0.281324\pi$
$908$	22.1622	−	16.1018i	0.735478	−	0.534356i
$909$	−0.752103	+	2.31473i	−0.0249457	+	0.0767749i
$910$	8.54689	+	6.20968i	0.283327	+	0.205849i
$911$	9.13309	−	28.1087i	0.302593	−	0.931284i	−0.677972	−	0.735088i	$-0.737141\pi$
$911$	9.13309	−	28.1087i	0.302593	−	0.931284i	0.980565	−	0.196197i	$-0.0628591\pi$
$912$	2.95330	+	9.08933i	0.0977936	+	0.300978i
$913$	68.7481	−	49.9484i	2.27523	−	1.65305i
$914$	−15.0115	−	46.2008i	−0.496538	−	1.52819i
$915$	−11.4992	−	35.3909i	−0.380152	−	1.16999i
$916$	21.7464	−	15.7997i	0.718523	−	0.522037i
$917$	3.49521	+	10.7572i	0.115422	+	0.355233i
$918$	−32.9688	+	101.468i	−1.08813	+	3.34893i
$919$	13.2275	+	9.61033i	0.436335	+	0.317016i	0.784177	−	0.620537i	$-0.213085\pi$
$919$	13.2275	+	9.61033i	0.436335	+	0.317016i	−0.347842	+	0.937553i	$0.613085\pi$
$920$	19.2252	−	59.1692i	0.633837	−	1.95075i
$921$	−21.1497	+	15.3662i	−0.696907	+	0.506333i
$922$	−43.8834	+	31.8831i	−1.44522	+	1.05002i
$923$	−6.31968	−	4.59152i	−0.208015	−	0.151132i
$924$	41.3914			1.36168
$925$	−16.2513			−0.534339
$926$	−12.0517	−	8.75606i	−0.396043	−	0.287742i
$927$	6.27811	+	19.3220i	0.206200	+	0.634619i
$928$	−0.383457	+	1.18016i	−0.0125876	+	0.0387406i
$929$	17.1584			0.562950			0.281475	−	0.959569i	$-0.409176\pi$
$929$	17.1584			0.562950			0.281475	+	0.959569i	$0.409176\pi$
$930$	−35.4600	+	34.7041i	−1.16278	+	1.13799i
$931$	−6.60383			−0.216432
$932$	−17.4289	+	53.6405i	−0.570902	+	1.75705i
$933$	0.176688	+	0.543789i	0.00578450	+	0.0178029i
$934$	53.8337	+	39.1125i	1.76149	+	1.27980i
$935$	−116.806			−3.81996
$936$	−8.20099			−0.268058
$937$	−18.4492	−	13.4042i	−0.602711	−	0.437895i	0.244129	−	0.969743i	$-0.421498\pi$
$937$	−18.4492	−	13.4042i	−0.602711	−	0.437895i	−0.846840	+	0.531848i	$0.821498\pi$
$938$	−18.2864	+	13.2859i	−0.597073	+	0.433799i
$939$	24.6977	−	17.9439i	0.805978	−	0.585577i
$940$	13.3442	−	41.0693i	0.435241	−	1.33953i
$941$	18.7803	+	13.6447i	0.612219	+	0.444803i	0.850195	−	0.526468i	$-0.176484\pi$
$941$	18.7803	+	13.6447i	0.612219	+	0.444803i	−0.237976	+	0.971271i	$0.576484\pi$
$942$	14.5870	−	44.8942i	0.475270	−	1.46273i
$943$	−14.3936	−	44.2990i	−0.468721	−	1.44257i
$944$	−21.1777	+	15.3865i	−0.689274	+	0.500787i
$945$	7.22874	+	22.2478i	0.235151	+	0.723720i
$946$	32.8237	+	101.021i	1.06719	+	3.28447i
$947$	24.7252	−	17.9639i	0.803460	−	0.583748i	−0.108467	−	0.994100i	$-0.534594\pi$
$947$	24.7252	−	17.9639i	0.803460	−	0.583748i	0.911927	+	0.410352i	$0.134594\pi$
$948$	−15.3654	−	47.2900i	−0.499047	−	1.53591i
$949$	1.33238	−	4.10065i	0.0432509	−	0.133113i
$950$	−8.86102	−	6.43790i	−0.287489	−	0.208873i
$951$	2.25902	−	6.95255i	0.0732537	−	0.225452i
$952$	−51.8879	+	37.6988i	−1.68170	+	1.22182i
$953$	35.2719	−	25.6265i	1.14257	−	0.830124i	0.155092	−	0.987900i	$-0.450432\pi$
$953$	35.2719	−	25.6265i	1.14257	−	0.830124i	0.987475	+	0.157776i	$0.0504324\pi$
$954$	1.82855	+	1.32852i	0.0592014	+	0.0430123i
$955$	16.5589			0.535835
$956$	−70.1663			−2.26934
$957$	2.41164	+	1.75216i	0.0779572	+	0.0566392i
$958$	6.15033	+	18.9288i	0.198708	+	0.611561i
$959$	−6.77230	+	20.8430i	−0.218689	+	0.673055i
$960$	15.5338			0.501350
$961$	0.667834	−	30.9928i	0.0215430	−	0.999768i
$962$	−12.7089			−0.409750
$963$	−5.67316	+	17.4602i	−0.182815	+	0.562647i
$964$	22.5663	+	69.4519i	0.726812	+	2.23690i
$965$	17.6683	+	12.8367i	0.568762	+	0.413229i
$966$	−17.6604			−0.568212
$967$	16.6615			0.535797			0.267899	−	0.963447i	$-0.413671\pi$
$967$	16.6615			0.535797			0.267899	+	0.963447i	$0.413671\pi$
$968$	−77.9832	−	56.6581i	−2.50648	−	1.82106i
$969$	−10.6082	+	7.70728i	−0.340783	+	0.247594i
$970$	47.8313	−	34.7515i	1.53577	−	1.11580i
$971$	−18.7704	+	57.7694i	−0.602371	+	1.85391i	−0.0884285	+	0.996083i	$0.528184\pi$
$971$	−18.7704	+	57.7694i	−0.602371	+	1.85391i	−0.513942	+	0.857825i	$0.671816\pi$
$972$	−46.3747	−	33.6932i	−1.48747	−	1.08071i
$973$	−0.671588	+	2.06694i	−0.0215301	+	0.0662629i
$974$	0.781971	+	2.40666i	0.0250560	+	0.0771144i
$975$	−3.21964	+	2.33921i	−0.103111	+	0.0749146i
$976$	18.1156	+	55.7541i	0.579866	+	1.78464i
$977$	−1.55089	−	4.77314i	−0.0496173	−	0.152706i	0.923178	−	0.384373i	$-0.125582\pi$
$977$	−1.55089	−	4.77314i	−0.0496173	−	0.152706i	−0.972795	+	0.231666i	$0.925582\pi$
$978$	−17.4431	+	12.6732i	−0.557770	+	0.405244i
$979$	−7.60407	−	23.4029i	−0.243027	−	0.747960i
$980$	18.1754	−	55.9382i	0.580592	−	1.78688i
$981$	−8.26539	−	6.00516i	−0.263894	−	0.191730i
$982$	5.57177	−	17.1481i	0.177802	−	0.547219i
$983$	23.3561	−	16.9692i	0.744943	−	0.541233i	−0.149312	−	0.988790i	$-0.547706\pi$
$983$	23.3561	−	16.9692i	0.744943	−	0.541233i	0.894255	+	0.447557i	$0.147706\pi$
$984$	−68.8187	+	49.9997i	−2.19386	+	1.59393i
$985$	−54.3343	−	39.4762i	−1.73124	−	1.25782i
$986$	−8.71102			−0.277415
$987$	−6.49988			−0.206893
$988$	−4.71477	−	3.42548i	−0.149997	−	0.108979i
$989$	−9.52871	−	29.3264i	−0.302995	−	0.932524i
$990$	17.0286	−	52.4088i	0.541206	−	1.66566i
$991$	6.65162			0.211296			0.105648	−	0.994404i	$-0.466308\pi$
$991$	6.65162			0.211296			0.105648	+	0.994404i	$0.466308\pi$
$992$	10.9181	−	10.6853i	0.346649	−	0.339260i
$993$	−5.66651			−0.179821
$994$	8.90627	−	27.4107i	0.282490	−	0.869414i
$995$	−23.2468	−	71.5463i	−0.736973	−	2.26817i
$996$	68.7361	+	49.9397i	2.17799	+	1.58240i
$997$	31.1864			0.987684			0.493842	−	0.869552i	$-0.335592\pi$
$997$	31.1864			0.987684			0.493842	+	0.869552i	$0.335592\pi$
$998$	−39.8888			−1.26266
$999$	−22.7664	−	16.5408i	−0.720297	−	0.523326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.287.16	yes	68
31.4	even	5	inner	403.2.k.e.66.16	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.16	✓	68	31.4	even	5	inner
403.2.k.e.287.16	yes	68	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.773013 - 2.37909i) q^{2} +(0.384456 + 1.18324i) q^{3} +(-3.44449 - 2.50257i) q^{4} -2.86335 q^{5} +3.11221 q^{6} +(-1.19324 - 0.866941i) q^{7} +(-4.56892 + 3.31951i) q^{8} +(1.17481 - 0.853551i) q^{9} +O(q^{10})\)	\(q+(0.773013 - 2.37909i) q^{2} +(0.384456 + 1.18324i) q^{3} +(-3.44449 - 2.50257i) q^{4} -2.86335 q^{5} +3.11221 q^{6} +(-1.19324 - 0.866941i) q^{7} +(-4.56892 + 3.31951i) q^{8} +(1.17481 - 0.853551i) q^{9} +(-2.21341 + 6.81217i) q^{10} +(-4.28613 - 3.11405i) q^{11} +(1.63687 - 5.03777i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-2.98492 + 2.16867i) q^{14} +(-1.10083 - 3.38802i) q^{15} +(1.73423 + 5.33742i) q^{16} +(-6.22931 + 4.52586i) q^{17} +(-1.12253 - 3.45479i) q^{18} +(0.422979 - 1.30179i) q^{19} +(9.86278 + 7.16573i) q^{20} +(0.567046 - 1.74519i) q^{21} +(-10.7218 + 7.78988i) q^{22} +(3.11255 - 2.26140i) q^{23} +(-5.68431 - 4.12989i) q^{24} +3.19879 q^{25} +2.50152 q^{26} +(4.48118 + 3.25576i) q^{27} +(1.94053 + 5.97234i) q^{28} +(-0.139754 + 0.430119i) q^{29} -8.91136 q^{30} +(3.97919 - 3.89437i) q^{31} +2.74380 q^{32} +(2.03683 - 6.26871i) q^{33} +(5.95208 + 18.3186i) q^{34} +(3.41667 + 2.48236i) q^{35} -6.18269 q^{36} -5.08045 q^{37} +(-2.77012 - 2.01261i) q^{38} +(-1.00652 + 0.731280i) q^{39} +(13.0824 - 9.50493i) q^{40} +(3.74120 - 11.5142i) q^{41} +(-3.71362 - 2.69811i) q^{42} +(2.47671 - 7.62253i) q^{43} +(6.97038 + 21.4526i) q^{44} +(-3.36390 + 2.44402i) q^{45} +(-2.97403 - 9.15314i) q^{46} +(-1.09459 - 3.36881i) q^{47} +(-5.64868 + 4.10401i) q^{48} +(-1.49088 - 4.58845i) q^{49} +(2.47270 - 7.61020i) q^{50} +(-7.75005 - 5.63074i) q^{51} +(1.31568 - 4.04924i) q^{52} +(-0.503374 + 0.365722i) q^{53} +(11.2098 - 8.14437i) q^{54} +(12.2727 + 8.91663i) q^{55} +8.32964 q^{56} +1.70295 q^{57} +(0.915260 + 0.664975i) q^{58} +(1.44138 + 4.43611i) q^{59} +(-4.68693 + 14.4249i) q^{60} +10.4459 q^{61} +(-6.18908 - 12.4772i) q^{62} -2.14181 q^{63} +(-1.34747 + 4.14709i) q^{64} +(-0.884825 - 2.72321i) q^{65} +(-13.3393 - 9.69160i) q^{66} +6.12626 q^{67} +32.7830 q^{68} +(3.87241 + 2.81347i) q^{69} +(8.54689 - 6.20968i) q^{70} +(-6.31968 + 4.59152i) q^{71} +(-2.53425 + 7.79960i) q^{72} +(-3.48822 - 2.53434i) q^{73} +(-3.92726 + 12.0868i) q^{74} +(1.22979 + 3.78492i) q^{75} +(-4.71477 + 3.42548i) q^{76} +(2.41469 + 7.43164i) q^{77} +(0.961727 + 2.95989i) q^{78} +(7.59432 - 5.51760i) q^{79} +(-4.96572 - 15.2829i) q^{80} +(-0.783304 + 2.41076i) q^{81} +(-24.5014 - 17.8013i) q^{82} +(-4.95653 + 15.2546i) q^{83} +(-6.32063 + 4.59221i) q^{84} +(17.8367 - 12.9591i) q^{85} +(-16.2202 - 11.7846i) q^{86} -0.562661 q^{87} +29.9201 q^{88} +(3.75763 + 2.73008i) q^{89} +(3.21420 + 9.89228i) q^{90} +(0.455778 - 1.40274i) q^{91} -16.3805 q^{92} +(6.13777 + 3.21110i) q^{93} -8.86083 q^{94} +(-1.21114 + 3.72750i) q^{95} +(1.05487 + 3.24656i) q^{96} +(-6.67779 - 4.85170i) q^{97} -12.0688 q^{98} -7.69340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

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