LMFDB - Embedded newform 231.2.i.f.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.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:	$1.84454428669$
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} + 15x^{8} + 72x^{6} + 120x^{4} + 72x^{2} + 12 $ x^10 + 15x^8 + 72x^6 + 120x^4 + 72x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-0.518255i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.f.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29725 - 2.24690i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.36571 + 4.09752i) q^{4} +(-1.09601 - 1.89835i) q^{5} -2.59450 q^{6} +(-2.61329 + 0.413178i) q^{7} +7.08664 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.29725 - 2.24690i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.36571 + 4.09752i) q^{4} +(-1.09601 - 1.89835i) q^{5} -2.59450 q^{6} +(-2.61329 + 0.413178i) q^{7} +7.08664 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.84359 + 4.92525i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(2.36571 + 4.09752i) q^{12} -2.95275 q^{13} +(4.31846 + 5.33581i) q^{14} -2.19202 q^{15} +(-4.46172 - 7.72792i) q^{16} +(-1.29725 + 2.24690i) q^{17} +(-1.29725 + 2.24690i) q^{18} +(1.17913 + 2.04231i) q^{19} +10.3713 q^{20} +(-0.948822 + 2.46976i) q^{21} +2.59450 q^{22} +(-4.46172 - 7.72792i) q^{23} +(3.54332 - 6.13721i) q^{24} +(0.0975238 - 0.168916i) q^{25} +(3.83045 + 6.63453i) q^{26} -1.00000 q^{27} +(4.48927 - 11.6855i) q^{28} +4.48640 q^{29} +(2.84359 + 4.92525i) q^{30} +(0.865706 - 1.49945i) q^{31} +(-4.48927 + 7.77564i) q^{32} +(0.500000 + 0.866025i) q^{33} +6.73141 q^{34} +(3.64855 + 4.50808i) q^{35} +4.73141 q^{36} +(2.19051 + 3.79407i) q^{37} +(3.05924 - 5.29876i) q^{38} +(-1.47637 + 2.55716i) q^{39} +(-7.76703 - 13.4529i) q^{40} -9.68719 q^{41} +(6.78017 - 1.07199i) q^{42} -10.3132 q^{43} +(-2.36571 - 4.09752i) q^{44} +(-1.09601 + 1.89835i) q^{45} +(-11.5759 + 20.0501i) q^{46} +(-5.55470 - 9.62102i) q^{47} -8.92343 q^{48} +(6.65857 - 2.15951i) q^{49} -0.506050 q^{50} +(1.29725 + 2.24690i) q^{51} +(6.98534 - 12.0990i) q^{52} +(4.58815 - 7.94691i) q^{53} +(1.29725 + 2.24690i) q^{54} +2.19202 q^{55} +(-18.5194 + 2.92804i) q^{56} +2.35825 q^{57} +(-5.81997 - 10.0805i) q^{58} +(-4.46172 + 7.72792i) q^{59} +(5.18567 - 8.98185i) q^{60} +(-6.73821 - 11.6709i) q^{61} -4.49214 q^{62} +(1.66447 + 2.05659i) q^{63} +5.44792 q^{64} +(3.23624 + 5.60534i) q^{65} +(1.29725 - 2.24690i) q^{66} +(1.62644 - 2.81707i) q^{67} +(-6.13781 - 10.6310i) q^{68} -8.92343 q^{69} +(5.39613 - 14.0460i) q^{70} +0.994758 q^{71} +(-3.54332 - 6.13721i) q^{72} +(-0.147439 + 0.255373i) q^{73} +(5.68326 - 9.84370i) q^{74} +(-0.0975238 - 0.168916i) q^{75} -11.1579 q^{76} +(0.948822 - 2.46976i) q^{77} +7.66090 q^{78} +(7.53672 + 13.0540i) q^{79} +(-9.78017 + 16.9398i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(12.5667 + 21.7661i) q^{82} -6.26778 q^{83} +(-7.87528 - 9.73056i) q^{84} +5.68719 q^{85} +(13.3788 + 23.1728i) q^{86} +(2.24320 - 3.88533i) q^{87} +(-3.54332 + 6.13721i) q^{88} +(1.30012 + 2.25188i) q^{89} +5.68719 q^{90} +(7.71639 - 1.22001i) q^{91} +42.2204 q^{92} +(-0.865706 - 1.49945i) q^{93} +(-14.4116 + 24.9617i) q^{94} +(2.58467 - 4.47678i) q^{95} +(4.48927 + 7.77564i) q^{96} +7.51704 q^{97} +(-13.4900 - 12.1597i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.29725	−	2.24690i	−0.917293	−	1.58880i	−0.803509	−	0.595293i	$-0.797036\pi$
$2$	−1.29725	−	2.24690i	−0.917293	−	1.58880i	−0.113784	−	0.993506i	$-0.536297\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−2.36571	+	4.09752i	−1.18285	+	2.04876i
$5$	−1.09601	−	1.89835i	−0.490151	−	0.848966i	0.509785	−	0.860302i	$-0.329725\pi$
$5$	−1.09601	−	1.89835i	−0.490151	−	0.848966i	−0.999936	+	0.0113360i	$0.996392\pi$
$6$	−2.59450			−1.05920
$7$	−2.61329	+	0.413178i	−0.987731	+	0.156167i
$7$	−2.61329	+	0.413178i	−0.987731	+	0.156167i
$8$	7.08664			2.50550
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.84359	+	4.92525i	−0.899223	+	1.55750i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	2.36571	+	4.09752i	0.682920	+	1.18285i
$13$	−2.95275			−0.818945			−0.409473	−	0.912322i	$-0.634287\pi$
$13$	−2.95275			−0.818945			−0.409473	+	0.912322i	$0.634287\pi$
$14$	4.31846	+	5.33581i	1.15416	+	1.42605i
$15$	−2.19202			−0.565977
$16$	−4.46172	−	7.72792i	−1.11543	−	1.93198i
$17$	−1.29725	+	2.24690i	−0.314629	+	0.544953i	−0.979359	−	0.202131i	$-0.935213\pi$
$17$	−1.29725	+	2.24690i	−0.314629	+	0.544953i	0.664730	+	0.747084i	$0.268547\pi$
$18$	−1.29725	+	2.24690i	−0.305764	+	0.529599i
$19$	1.17913	+	2.04231i	0.270510	+	0.468537i	0.968993	−	0.247090i	$-0.0794743\pi$
$19$	1.17913	+	2.04231i	0.270510	+	0.468537i	−0.698482	+	0.715627i	$0.746141\pi$
$20$	10.3713			2.31910
$21$	−0.948822	+	2.46976i	−0.207050	+	0.538947i
$22$	2.59450			0.553148
$23$	−4.46172	−	7.72792i	−0.930332	−	1.61138i	−0.782753	−	0.622332i	$-0.786185\pi$
$23$	−4.46172	−	7.72792i	−0.930332	−	1.61138i	−0.147579	−	0.989050i	$-0.547148\pi$
$24$	3.54332	−	6.13721i	0.723277	−	1.25275i
$25$	0.0975238	−	0.168916i	0.0195048	−	0.0337832i
$26$	3.83045	+	6.63453i	0.751213	+	1.30114i
$27$	−1.00000			−0.192450
$28$	4.48927	−	11.6855i	0.848392	−	2.20835i
$29$	4.48640			0.833103			0.416551	−	0.909112i	$-0.363239\pi$
$29$	4.48640			0.833103			0.416551	+	0.909112i	$0.363239\pi$
$30$	2.84359	+	4.92525i	0.519167	+	0.899223i
$31$	0.865706	−	1.49945i	0.155485	−	0.269309i	−0.777750	−	0.628573i	$-0.783639\pi$
$31$	0.865706	−	1.49945i	0.155485	−	0.269309i	0.933236	+	0.359265i	$0.116973\pi$
$32$	−4.48927	+	7.77564i	−0.793598	+	1.37455i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	6.73141			1.15443
$35$	3.64855	+	4.50808i	0.616717	+	0.762004i
$36$	4.73141			0.788569
$37$	2.19051	+	3.79407i	0.360117	+	0.623741i	0.987980	−	0.154583i	$-0.0494034\pi$
$37$	2.19051	+	3.79407i	0.360117	+	0.623741i	−0.627863	+	0.778324i	$0.716070\pi$
$38$	3.05924	−	5.29876i	0.496274	−	0.859572i
$39$	−1.47637	+	2.55716i	−0.236409	+	0.409473i
$40$	−7.76703	−	13.4529i	−1.22807	−	2.12709i
$41$	−9.68719			−1.51288			−0.756442	−	0.654060i	$-0.773064\pi$
$41$	−9.68719			−1.51288			−0.756442	+	0.654060i	$0.773064\pi$
$42$	6.78017	−	1.07199i	1.04620	−	0.165411i
$43$	−10.3132			−1.57275			−0.786375	−	0.617749i	$-0.788045\pi$
$43$	−10.3132			−1.57275			−0.786375	+	0.617749i	$0.788045\pi$
$44$	−2.36571	−	4.09752i	−0.356644	−	0.617725i
$45$	−1.09601	+	1.89835i	−0.163384	+	0.282989i
$46$	−11.5759	+	20.0501i	−1.70677	+	2.95622i
$47$	−5.55470	−	9.62102i	−0.810236	−	1.40337i	−0.912699	−	0.408633i	$-0.866006\pi$
$47$	−5.55470	−	9.62102i	−0.810236	−	1.40337i	0.102463	−	0.994737i	$-0.467328\pi$
$48$	−8.92343			−1.28799
$49$	6.65857	−	2.15951i	0.951224	−	0.308501i
$50$	−0.506050			−0.0715663
$51$	1.29725	+	2.24690i	0.181651	+	0.314629i
$52$	6.98534	−	12.0990i	0.968692	−	1.67782i
$53$	4.58815	−	7.94691i	0.630231	−	1.09159i	−0.357273	−	0.934000i	$-0.616294\pi$
$53$	4.58815	−	7.94691i	0.630231	−	1.09159i	0.987504	−	0.157592i	$-0.0503732\pi$
$54$	1.29725	+	2.24690i	0.176533	+	0.305764i
$55$	2.19202			0.295572
$56$	−18.5194	+	2.92804i	−2.47476	+	0.391276i
$57$	2.35825			0.312358
$58$	−5.81997	−	10.0805i	−0.764199	−	1.32363i
$59$	−4.46172	+	7.72792i	−0.580866	+	1.00609i	0.414511	+	0.910044i	$0.363953\pi$
$59$	−4.46172	+	7.72792i	−0.580866	+	1.00609i	−0.995377	+	0.0960450i	$0.969381\pi$
$60$	5.18567	−	8.98185i	0.669468	−	1.15955i
$61$	−6.73821	−	11.6709i	−0.862740	−	1.49431i	−0.869274	−	0.494330i	$-0.835413\pi$
$61$	−6.73821	−	11.6709i	−0.862740	−	1.49431i	0.00653474	−	0.999979i	$-0.497920\pi$
$62$	−4.49214			−0.570502
$63$	1.66447	+	2.05659i	0.209703	+	0.259106i
$64$	5.44792			0.680990
$65$	3.23624	+	5.60534i	0.401407	+	0.695257i
$66$	1.29725	−	2.24690i	0.159680	−	0.276574i
$67$	1.62644	−	2.81707i	0.198701	−	0.344160i	−0.749407	−	0.662110i	$-0.769661\pi$
$67$	1.62644	−	2.81707i	0.198701	−	0.344160i	0.948107	+	0.317950i	$0.102995\pi$
$68$	−6.13781	−	10.6310i	−0.744319	−	1.28920i
$69$	−8.92343			−1.07425
$70$	5.39613	−	14.0460i	0.644961	−	1.67882i
$71$	0.994758			0.118056			0.0590280	−	0.998256i	$-0.481200\pi$
$71$	0.994758			0.118056			0.0590280	+	0.998256i	$0.481200\pi$
$72$	−3.54332	−	6.13721i	−0.417584	−	0.723277i
$73$	−0.147439	+	0.255373i	−0.0172565	+	0.0298891i	−0.874525	−	0.484981i	$-0.838827\pi$
$73$	−0.147439	+	0.255373i	−0.0172565	+	0.0298891i	0.857268	+	0.514870i	$0.172160\pi$
$74$	5.68326	−	9.84370i	0.660666	−	1.14431i
$75$	−0.0975238	−	0.168916i	−0.0112611	−	0.0195048i
$76$	−11.1579			−1.27990
$77$	0.948822	−	2.46976i	0.108128	−	0.281456i
$78$	7.66090			0.867426
$79$	7.53672	+	13.0540i	0.847947	+	1.46869i	0.883037	+	0.469304i	$0.155495\pi$
$79$	7.53672	+	13.0540i	0.847947	+	1.46869i	−0.0350893	+	0.999384i	$0.511172\pi$
$80$	−9.78017	+	16.9398i	−1.09346	+	1.89392i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	12.5667	+	21.7661i	1.38776	+	2.40367i
$83$	−6.26778			−0.687978			−0.343989	−	0.938974i	$-0.611778\pi$
$83$	−6.26778			−0.687978			−0.343989	+	0.938974i	$0.611778\pi$
$84$	−7.87528	−	9.73056i	−0.859264	−	1.06169i
$85$	5.68719			0.616862
$86$	13.3788	+	23.1728i	1.44267	+	2.49878i
$87$	2.24320	−	3.88533i	0.240496	−	0.416551i
$88$	−3.54332	+	6.13721i	−0.377719	+	0.654229i
$89$	1.30012	+	2.25188i	0.137813	+	0.238698i	0.926668	−	0.375880i	$-0.122660\pi$
$89$	1.30012	+	2.25188i	0.137813	+	0.238698i	−0.788856	+	0.614578i	$0.789326\pi$
$90$	5.68719			0.599482
$91$	7.71639	−	1.22001i	0.808898	−	0.127892i
$92$	42.2204			4.40178
$93$	−0.865706	−	1.49945i	−0.0897695	−	0.155485i
$94$	−14.4116	+	24.9617i	−1.48645	+	2.57460i
$95$	2.58467	−	4.47678i	0.265181	−	0.459308i
$96$	4.48927	+	7.77564i	0.458184	+	0.793598i
$97$	7.51704			0.763239			0.381620	−	0.924319i	$-0.375366\pi$
$97$	7.51704			0.763239			0.381620	+	0.924319i	$0.375366\pi$
$98$	−13.4900	−	12.1597i	−1.36270	−	1.22832i
$99$	1.00000			0.100504
$100$	0.461425	+	0.799212i	0.0461425	+	0.0799212i
$101$	6.68023	−	11.5705i	0.664708	−	1.15131i	−0.314656	−	0.949206i	$-0.601889\pi$
$101$	6.68023	−	11.5705i	0.664708	−	1.15131i	0.979364	−	0.202103i	$-0.0647774\pi$
$102$	3.36571	−	5.82957i	0.333255	−	0.577214i
$103$	2.66431	+	4.61472i	0.262523	+	0.454702i	0.966912	−	0.255112i	$-0.0821123\pi$
$103$	2.66431	+	4.61472i	0.262523	+	0.454702i	−0.704389	+	0.709814i	$0.748779\pi$
$104$	−20.9251			−2.05187
$105$	5.72838	−	0.905695i	0.559033	−	0.0883867i
$106$	−23.8079			−2.31243
$107$	−2.94595	−	5.10253i	−0.284796	−	0.493281i	0.687764	−	0.725934i	$-0.258592\pi$
$107$	−2.94595	−	5.10253i	−0.284796	−	0.493281i	−0.972560	+	0.232654i	$0.925259\pi$
$108$	2.36571	−	4.09752i	0.227640	−	0.394284i
$109$	8.39981	−	14.5489i	0.804556	−	1.39353i	−0.112035	−	0.993704i	$-0.535737\pi$
$109$	8.39981	−	14.5489i	0.804556	−	1.39353i	0.916591	−	0.399827i	$-0.130930\pi$
$110$	−2.84359	−	4.92525i	−0.271126	−	0.469604i
$111$	4.38101			0.415827
$112$	14.8528	+	18.3518i	1.40345	+	1.73408i
$113$	12.9025			1.21376			0.606881	−	0.794793i	$-0.292420\pi$
$113$	12.9025			1.21376			0.606881	+	0.794793i	$0.292420\pi$
$114$	−3.05924	−	5.29876i	−0.286524	−	0.496274i
$115$	−9.78017	+	16.9398i	−0.912006	+	1.57964i
$116$	−10.6135	+	18.3831i	−0.985438	+	1.70683i
$117$	1.47637	+	2.55716i	0.136491	+	0.236409i
$118$	23.1518			2.13130
$119$	2.46172	−	6.40779i	0.225665	−	0.587402i
$120$	−15.5341			−1.41806
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−17.4823	+	30.2802i	−1.58277	+	2.74144i
$123$	−4.84359	+	8.38935i	−0.436732	+	0.756442i
$124$	4.09601	+	7.09450i	0.367833	+	0.637105i
$125$	−11.3876			−1.01854
$126$	2.46172	−	6.40779i	0.219307	−	0.570852i
$127$	14.6951			1.30398			0.651992	−	0.758226i	$-0.273934\pi$
$127$	14.6951			1.30398			0.651992	+	0.758226i	$0.273934\pi$
$128$	1.91124	+	3.31036i	0.168931	+	0.292597i
$129$	−5.15661	+	8.93151i	−0.454014	+	0.786375i
$130$	8.39642	−	14.5430i	0.736415	−	1.27551i
$131$	−5.38299	−	9.32360i	−0.470314	−	0.814607i	0.529110	−	0.848553i	$-0.322526\pi$
$131$	−5.38299	−	9.32360i	−0.470314	−	0.814607i	−0.999424	+	0.0339461i	$0.989193\pi$
$132$	−4.73141			−0.411817
$133$	−3.92524	−	4.84995i	−0.340361	−	0.420544i
$134$	−8.43956			−0.729067
$135$	1.09601	+	1.89835i	0.0943295	+	0.163384i
$136$	−9.19313	+	15.9230i	−0.788304	+	1.36538i
$137$	−1.30618	+	2.26236i	−0.111594	+	0.193287i	−0.916413	−	0.400234i	$-0.868929\pi$
$137$	−1.30618	+	2.26236i	−0.111594	+	0.193287i	0.804819	+	0.593520i	$0.202262\pi$
$138$	11.5759	+	20.0501i	0.985407	+	1.70677i
$139$	6.25015			0.530131			0.265066	−	0.964230i	$-0.414606\pi$
$139$	6.25015			0.530131			0.265066	+	0.964230i	$0.414606\pi$
$140$	−27.1033	+	4.28521i	−2.29065	+	0.362167i
$141$	−11.1094			−0.935580
$142$	−1.29045	−	2.23512i	−0.108292	−	0.187567i
$143$	1.47637	−	2.55716i	0.123461	−	0.213840i
$144$	−4.46172	+	7.72792i	−0.371810	+	0.643993i
$145$	−4.91714	−	8.51673i	−0.408346	−	0.707276i
$146$	0.765062			0.0633170
$147$	1.45909	−	6.84624i	0.120344	−	0.564669i
$148$	−20.7284			−1.70386
$149$	2.06100	+	3.56977i	0.168844	+	0.292447i	0.938014	−	0.346598i	$-0.112663\pi$
$149$	2.06100	+	3.56977i	0.168844	+	0.292447i	−0.769170	+	0.639045i	$0.779330\pi$
$150$	−0.253025	+	0.438252i	−0.0206594	+	0.0357832i
$151$	−6.21765	+	10.7693i	−0.505985	+	0.876392i	0.493991	+	0.869467i	$0.335538\pi$
$151$	−6.21765	+	10.7693i	−0.505985	+	0.876392i	−0.999976	+	0.00692517i	$0.997796\pi$
$152$	8.35604	+	14.4731i	0.677765	+	1.17392i
$153$	2.59450			0.209753
$154$	−6.78017	+	1.07199i	−0.546362	+	0.0863833i
$155$	−3.79529			−0.304845
$156$	−6.98534	−	12.0990i	−0.559275	−	0.968692i
$157$	9.34667	−	16.1889i	0.745945	−	1.29202i	−0.203806	−	0.979011i	$-0.565331\pi$
$157$	9.34667	−	16.1889i	0.745945	−	1.29202i	0.949752	−	0.313004i	$-0.101335\pi$
$158$	19.5540	−	33.8685i	1.55563	−	2.69443i
$159$	−4.58815	−	7.94691i	−0.363864	−	0.630231i
$160$	19.6811			1.55593
$161$	14.8528	+	18.3518i	1.17056	+	1.44633i
$162$	2.59450			0.203843
$163$	0.632374	+	1.09530i	0.0495314	+	0.0857908i	0.889728	−	0.456491i	$-0.150894\pi$
$163$	0.632374	+	1.09530i	0.0495314	+	0.0857908i	−0.840197	+	0.542282i	$0.817561\pi$
$164$	22.9170	−	39.6935i	1.78952	−	3.09954i
$165$	1.09601	−	1.89835i	0.0853243	−	0.147786i
$166$	8.13086	+	14.0831i	0.631077	+	1.09306i
$167$	−6.11021			−0.472822			−0.236411	−	0.971653i	$-0.575971\pi$
$167$	−6.11021			−0.472822			−0.236411	+	0.971653i	$0.575971\pi$
$168$	−6.72396	+	17.5023i	−0.518765	+	1.35033i
$169$	−4.28127			−0.329328
$170$	−7.37769	−	12.7785i	−0.565843	−	0.980069i
$171$	1.17913	−	2.04231i	0.0901701	−	0.156179i
$172$	24.3980	−	42.2586i	1.86033	−	3.22219i
$173$	8.73247	+	15.1251i	0.663917	+	1.14994i	0.979578	+	0.201066i	$0.0644406\pi$
$173$	8.73247	+	15.1251i	0.663917	+	1.14994i	−0.315661	+	0.948872i	$0.602226\pi$
$174$	−11.6399			−0.882421
$175$	−0.185065	+	0.481722i	−0.0139896	+	0.0364147i
$176$	8.92343			0.672629
$177$	4.46172	+	7.72792i	0.335363	+	0.580866i
$178$	3.37316	−	5.84248i	0.252829	−	0.437913i
$179$	−0.211273	+	0.365935i	−0.0157912	+	0.0273512i	−0.873813	−	0.486262i	$-0.838360\pi$
$179$	−0.211273	+	0.365935i	−0.0157912	+	0.0273512i	0.858022	+	0.513613i	$0.171693\pi$
$180$	−5.18567	−	8.98185i	−0.386517	−	0.669468i
$181$	2.40197			0.178537			0.0892686	−	0.996008i	$-0.471547\pi$
$181$	2.40197			0.178537			0.0892686	+	0.996008i	$0.471547\pi$
$182$	−12.7513	−	15.7553i	−0.945190	−	1.16786i
$183$	−13.4764			−0.996206
$184$	−31.6186	−	54.7650i	−2.33095	−	4.03733i
$185$	4.80163	−	8.31667i	0.353023	−	0.611454i
$186$	−2.24607	+	3.89031i	−0.164690	+	0.285251i
$187$	−1.29725	−	2.24690i	−0.0948642	−	0.164310i
$188$	52.5631			3.83356
$189$	2.61329	−	0.413178i	0.190089	−	0.0300543i
$190$	−13.4118			−0.972996
$191$	4.34645	+	7.52828i	0.314498	+	0.544727i	0.979331	−	0.202265i	$-0.0648304\pi$
$191$	4.34645	+	7.52828i	0.314498	+	0.544727i	−0.664832	+	0.746993i	$0.731497\pi$
$192$	2.72396	−	4.71804i	0.196585	−	0.340495i
$193$	4.02257	−	6.96729i	0.289551	−	0.501516i	−0.684152	−	0.729340i	$-0.739827\pi$
$193$	4.02257	−	6.96729i	0.289551	−	0.501516i	0.973703	+	0.227823i	$0.0731608\pi$
$194$	−9.75146	−	16.8900i	−0.700114	−	1.21263i
$195$	6.47249			0.463504
$196$	−6.90358	+	32.3924i	−0.493113	+	2.31374i
$197$	−4.79921			−0.341929			−0.170965	−	0.985277i	$-0.554688\pi$
$197$	−4.79921			−0.341929			−0.170965	+	0.985277i	$0.554688\pi$
$198$	−1.29725	−	2.24690i	−0.0921914	−	0.159680i
$199$	−1.46061	+	2.52985i	−0.103540	+	0.179336i	−0.913141	−	0.407645i	$-0.866350\pi$
$199$	−1.46061	+	2.52985i	−0.103540	+	0.179336i	0.809601	+	0.586981i	$0.199684\pi$
$200$	0.691116	−	1.19705i	0.0488693	−	0.0846440i
$201$	−1.62644	−	2.81707i	−0.114720	−	0.198701i
$202$	−34.6637			−2.43893
$203$	−11.7243	+	1.85368i	−0.822881	+	0.130103i
$204$	−12.2756			−0.859466
$205$	10.6173	+	18.3896i	0.741541	+	1.28439i
$206$	6.91255	−	11.9729i	0.481620	−	0.834191i
$207$	−4.46172	+	7.72792i	−0.310111	+	0.537127i
$208$	13.1743	+	22.8186i	0.913475	+	1.58219i
$209$	−2.35825			−0.163124
$210$	−9.46614	−	11.6962i	−0.653226	−	0.807114i
$211$	−9.82721			−0.676533			−0.338266	−	0.941050i	$-0.609841\pi$
$211$	−9.82721			−0.676533			−0.338266	+	0.941050i	$0.609841\pi$
$212$	21.7084	+	37.6001i	1.49094	+	2.58239i
$213$	0.497379	−	0.861486i	0.0340799	−	0.0590280i
$214$	−7.64326	+	13.2385i	−0.522482	+	0.904966i
$215$	11.3034	+	19.5780i	0.770885	+	1.33521i
$216$	−7.08664			−0.482185
$217$	−1.64280	+	4.27618i	−0.111521	+	0.290286i
$218$	−43.5865			−2.95205
$219$	0.147439	+	0.255373i	0.00996304	+	0.0172565i
$220$	−5.18567	+	8.98185i	−0.349618	+	0.605556i
$221$	3.83045	−	6.63453i	0.257664	−	0.446287i
$222$	−5.68326	−	9.84370i	−0.381436	−	0.660666i
$223$	−16.3127			−1.09238			−0.546190	−	0.837661i	$-0.683922\pi$
$223$	−16.3127			−1.09238			−0.546190	+	0.837661i	$0.683922\pi$
$224$	8.51904	−	22.1749i	0.569202	−	1.48162i
$225$	−0.195048			−0.0130032
$226$	−16.7377	−	28.9906i	−1.11338	−	1.92842i
$227$	−11.3044	+	19.5799i	−0.750302	+	1.29956i	0.197374	+	0.980328i	$0.436759\pi$
$227$	−11.3044	+	19.5799i	−0.750302	+	1.29956i	−0.947676	+	0.319233i	$0.896575\pi$
$228$	−5.57893	+	9.66300i	−0.369474	+	0.639948i
$229$	1.85362	+	3.21056i	0.122490	+	0.212160i	0.920749	−	0.390155i	$-0.127579\pi$
$229$	1.85362	+	3.21056i	0.122490	+	0.212160i	−0.798259	+	0.602315i	$0.794245\pi$
$230$	50.7492			3.34631
$231$	−1.66447	−	2.05659i	−0.109514	−	0.135313i
$232$	31.7935			2.08734
$233$	3.84949	+	6.66752i	0.252189	+	0.436804i	0.964128	−	0.265437i	$-0.0855163\pi$
$233$	3.84949	+	6.66752i	0.252189	+	0.436804i	−0.711939	+	0.702241i	$0.752183\pi$
$234$	3.83045	−	6.63453i	0.250404	−	0.433713i
$235$	−12.1760	+	21.0895i	−0.794275	+	1.37573i
$236$	−21.1102	−	36.5640i	−1.37416	−	2.38011i
$237$	15.0734			0.979125
$238$	−17.5911	+	2.78127i	−1.14026	+	0.180283i
$239$	−4.12986			−0.267139			−0.133569	−	0.991039i	$-0.542644\pi$
$239$	−4.12986			−0.267139			−0.133569	+	0.991039i	$0.542644\pi$
$240$	9.78017	+	16.9398i	0.631307	+	1.09346i
$241$	7.37799	−	12.7790i	0.475258	−	0.823171i	−0.524341	−	0.851509i	$-0.675688\pi$
$241$	7.37799	−	12.7790i	0.475258	−	0.823171i	0.999598	+	0.0283379i	$0.00902145\pi$
$242$	−1.29725	+	2.24690i	−0.0833903	+	0.144436i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	63.7625			4.08198
$245$	−11.3973	−	10.2734i	−0.728150	−	0.656345i
$246$	25.1334			1.60245
$247$	−3.48167	−	6.03042i	−0.221533	−	0.383707i
$248$	6.13494	−	10.6260i	0.389569	−	0.674754i
$249$	−3.13389	+	5.42805i	−0.198602	+	0.343989i
$250$	14.7726	+	25.5869i	0.934302	+	1.61826i
$251$	−13.5521			−0.855399			−0.427700	−	0.903921i	$-0.640676\pi$
$251$	−13.5521			−0.855399			−0.427700	+	0.903921i	$0.640676\pi$
$252$	−12.3645	+	1.95492i	−0.778893	+	0.123148i
$253$	8.92343			0.561011
$254$	−19.0633	−	33.0185i	−1.19613	−	2.07177i
$255$	2.84359	−	4.92525i	0.178073	−	0.308431i
$256$	10.4066	−	18.0248i	0.650413	−	1.12655i
$257$	−4.26556	−	7.38817i	−0.266078	−	0.460861i	0.701767	−	0.712406i	$-0.252395\pi$
$257$	−4.26556	−	7.38817i	−0.266078	−	0.460861i	−0.967846	+	0.251545i	$0.919061\pi$
$258$	26.7576			1.66586
$259$	−7.29205	−	9.00993i	−0.453106	−	0.559850i
$260$	−30.6240			−1.89922
$261$	−2.24320	−	3.88533i	−0.138850	−	0.240496i
$262$	−13.9661	+	24.1901i	−0.862831	+	1.49447i
$263$	−1.77645	+	3.07690i	−0.109540	+	0.189730i	−0.915584	−	0.402126i	$-0.868271\pi$
$263$	−1.77645	+	3.07690i	−0.109540	+	0.189730i	0.806044	+	0.591856i	$0.201605\pi$
$264$	3.54332	+	6.13721i	0.218076	+	0.377719i
$265$	−20.1146			−1.23563
$266$	−5.80535	+	15.1112i	−0.355949	+	0.926527i
$267$	2.60024			0.159132
$268$	7.69533	+	13.3287i	0.470067	+	0.814180i
$269$	−5.81170	+	10.0662i	−0.354346	+	0.613745i	−0.987006	−	0.160685i	$-0.948630\pi$
$269$	−5.81170	+	10.0662i	−0.354346	+	0.613745i	0.632660	+	0.774430i	$0.281963\pi$
$270$	2.84359	−	4.92525i	0.173056	−	0.299741i
$271$	−4.93989	−	8.55615i	−0.300077	−	0.519749i	0.676076	−	0.736832i	$-0.263679\pi$
$271$	−4.93989	−	8.55615i	−0.300077	−	0.519749i	−0.976153	+	0.217083i	$0.930346\pi$
$272$	23.1518			1.40378
$273$	2.80163	−	7.29260i	0.169563	−	0.441368i
$274$	6.77774			0.409458
$275$	0.0975238	+	0.168916i	0.00588091	+	0.0101860i
$276$	21.1102	−	36.5640i	1.27069	−	2.20089i
$277$	0.641050	−	1.11033i	0.0385169	−	0.0667133i	−0.846124	−	0.532986i	$-0.821070\pi$
$277$	0.641050	−	1.11033i	0.0385169	−	0.0667133i	0.884641	+	0.466272i	$0.154403\pi$
$278$	−8.10800	−	14.0435i	−0.486285	−	0.842271i
$279$	−1.73141			−0.103657
$280$	25.8559	+	31.9471i	1.54519	+	1.90921i
$281$	25.5914			1.52665			0.763327	−	0.646013i	$-0.223565\pi$
$281$	25.5914			1.52665			0.763327	+	0.646013i	$0.223565\pi$
$282$	14.4116	+	24.9617i	0.858201	+	1.48645i
$283$	6.00397	−	10.3992i	0.356899	−	0.618167i	−0.630542	−	0.776155i	$-0.717167\pi$
$283$	6.00397	−	10.3992i	0.356899	−	0.618167i	0.987441	+	0.157988i	$0.0505008\pi$
$284$	−2.35331	+	4.07604i	−0.139643	+	0.241869i
$285$	−2.58467	−	4.47678i	−0.153103	−	0.265181i
$286$	−7.66090			−0.452998
$287$	25.3154	−	4.00253i	1.49432	−	0.236262i
$288$	8.97854			0.529065
$289$	5.13429	+	8.89286i	0.302017	+	0.523109i
$290$	−12.7575	+	22.0966i	−0.749146	+	1.29756i
$291$	3.75852	−	6.50994i	0.220328	−	0.381620i
$292$	−0.697597	−	1.20827i	−0.0408238	−	0.0707088i
$293$	−17.6972			−1.03388			−0.516939	−	0.856022i	$-0.672929\pi$
$293$	−17.6972			−1.03388			−0.516939	+	0.856022i	$0.672929\pi$
$294$	−17.2756	+	5.60284i	−1.00754	+	0.326764i
$295$	19.5603			1.13885
$296$	15.5233	+	26.8872i	0.902275	+	1.56279i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	5.34727	−	9.26174i	0.309759	−	0.536518i
$299$	13.1743	+	22.8186i	0.761891	+	1.31963i
$300$	0.922850			0.0532808
$301$	26.9514	−	4.26120i	1.55345	−	0.245611i
$302$	32.2634			1.85655
$303$	−6.68023	−	11.5705i	−0.383769	−	0.664708i
$304$	10.5219	−	18.2244i	0.603470	−	1.04524i
$305$	−14.7703	+	25.5829i	−0.845745	+	1.46487i
$306$	−3.36571	−	5.82957i	−0.192405	−	0.333255i
$307$	−8.08311			−0.461327			−0.230664	−	0.973034i	$-0.574090\pi$
$307$	−8.08311			−0.461327			−0.230664	+	0.973034i	$0.574090\pi$
$308$	7.87528	+	9.73056i	0.448736	+	0.554450i
$309$	5.32863			0.303135
$310$	4.92343	+	8.52763i	0.279632	+	0.484337i
$311$	−5.79337	+	10.0344i	−0.328512	+	0.568999i	−0.982217	−	0.187750i	$-0.939880\pi$
$311$	−5.79337	+	10.0344i	−0.328512	+	0.568999i	0.653705	+	0.756749i	$0.273214\pi$
$312$	−10.4625	+	18.1216i	−0.592324	+	1.02594i
$313$	−0.777961	−	1.34747i	−0.0439730	−	0.0761634i	0.843201	−	0.537598i	$-0.180668\pi$
$313$	−0.777961	−	1.34747i	−0.0439730	−	0.0761634i	−0.887174	+	0.461435i	$0.847335\pi$
$314$	−48.4998			−2.73700
$315$	2.07984	−	5.41377i	0.117186	−	0.305032i
$316$	−71.3187			−4.01199
$317$	−5.24955	−	9.09249i	−0.294844	−	0.510685i	0.680104	−	0.733115i	$-0.261934\pi$
$317$	−5.24955	−	9.09249i	−0.294844	−	0.510685i	−0.974949	+	0.222430i	$0.928601\pi$
$318$	−11.9039	+	20.6182i	−0.667540	+	1.15621i
$319$	−2.24320	+	3.88533i	−0.125595	+	0.217537i
$320$	−5.97097	−	10.3420i	−0.333788	−	0.578137i
$321$	−5.89190			−0.328854
$322$	21.9670	−	57.1795i	1.22417	−	3.18649i
$323$	−6.11848			−0.340441
$324$	−2.36571	−	4.09752i	−0.131428	−	0.227640i
$325$	−0.287963	+	0.498767i	−0.0159733	+	0.0276666i
$326$	1.64069	−	2.84176i	0.0908695	−	0.157391i
$327$	−8.39981	−	14.5489i	−0.464510	−	0.804556i
$328$	−68.6496			−3.79054
$329$	18.4912	+	22.8474i	1.01945	+	1.25962i
$330$	−5.68719			−0.313069
$331$	−14.4905	−	25.0983i	−0.796471	−	1.37953i	−0.921901	−	0.387426i	$-0.873364\pi$
$331$	−14.4905	−	25.0983i	−0.796471	−	1.37953i	0.125429	−	0.992103i	$-0.459969\pi$
$332$	14.8277	−	25.6824i	0.813776	−	1.40950i
$333$	2.19051	−	3.79407i	0.120039	−	0.207914i
$334$	7.92646	+	13.7290i	0.433717	+	0.751219i
$335$	−7.13036			−0.389573
$336$	23.3195	−	3.68697i	1.27218	−	0.201141i
$337$	13.9865			0.761893			0.380946	−	0.924597i	$-0.375598\pi$
$337$	13.9865			0.761893			0.380946	+	0.924597i	$0.375598\pi$
$338$	5.55387	+	9.61959i	0.302091	+	0.523236i
$339$	6.45124	−	11.1739i	0.350383	−	0.606881i
$340$	−13.4542	+	23.3034i	−0.729657	+	1.26380i
$341$	0.865706	+	1.49945i	0.0468806	+	0.0811996i
$342$	−6.11848			−0.330849
$343$	−16.5085	+	8.39459i	−0.891376	+	0.453266i
$344$	−73.0860			−3.94053
$345$	9.78017	+	16.9398i	0.526547	+	0.912006i
$346$	22.6564	−	39.2420i	1.21801	−	2.10966i
$347$	4.47044	−	7.74302i	0.239986	−	0.415667i	−0.720724	−	0.693222i	$-0.756191\pi$
$347$	4.47044	−	7.74302i	0.239986	−	0.415667i	0.960710	+	0.277555i	$0.0895240\pi$
$348$	10.6135	+	18.3831i	0.568943	+	0.985438i
$349$	0.353903			0.0189440			0.00947199	−	0.999955i	$-0.496985\pi$
$349$	0.353903			0.0189440			0.00947199	+	0.999955i	$0.496985\pi$
$350$	1.32246	−	0.209089i	0.0706882	−	0.0111763i
$351$	2.95275			0.157606
$352$	−4.48927	−	7.77564i	−0.239279	−	0.414443i
$353$	−10.3020	+	17.8437i	−0.548322	+	0.949722i	0.450067	+	0.892995i	$0.351400\pi$
$353$	−10.3020	+	17.8437i	−0.548322	+	0.949722i	−0.998390	+	0.0567277i	$0.981933\pi$
$354$	11.5759	−	20.0501i	0.615252	−	1.06565i
$355$	−1.09027	−	1.88839i	−0.0578653	−	0.100226i
$356$	−12.3028			−0.652048
$357$	−4.31846	−	5.33581i	−0.228557	−	0.282401i
$358$	1.09629			0.0579408
$359$	−5.29332	−	9.16830i	−0.279371	−	0.483884i	0.691858	−	0.722034i	$-0.256793\pi$
$359$	−5.29332	−	9.16830i	−0.279371	−	0.483884i	−0.971229	+	0.238149i	$0.923459\pi$
$360$	−7.76703	+	13.4529i	−0.409358	+	0.709029i
$361$	6.71932	−	11.6382i	0.353648	−	0.612537i
$362$	−3.11596	−	5.39699i	−0.163771	−	0.283660i
$363$	−1.00000			−0.0524864
$364$	−13.2557	+	34.5043i	−0.694787	+	1.80852i
$365$	0.646381			0.0338331
$366$	17.4823	+	30.2802i	0.913813	+	1.58277i
$367$	−5.43966	+	9.42176i	−0.283948	+	0.491812i	−0.972353	−	0.233514i	$-0.924978\pi$
$367$	−5.43966	+	9.42176i	−0.283948	+	0.491812i	0.688406	+	0.725326i	$0.258311\pi$
$368$	−39.8138	+	68.9596i	−2.07544	+	3.59477i
$369$	4.84359	+	8.38935i	0.252147	+	0.436732i
$370$	−24.9156			−1.29530
$371$	−8.70668	+	22.6633i	−0.452028	+	1.17662i
$372$	8.19202			0.424736
$373$	−7.37834	−	12.7797i	−0.382036	−	0.661706i	0.609317	−	0.792927i	$-0.291444\pi$
$373$	−7.37834	−	12.7797i	−0.382036	−	0.661706i	−0.991353	+	0.131221i	$0.958110\pi$
$374$	−3.36571	+	5.82957i	−0.174037	+	0.301440i
$375$	−5.69382	+	9.86199i	−0.294028	+	0.509271i
$376$	−39.3641	−	68.1807i	−2.03005	−	3.51615i
$377$	−13.2472			−0.682266
$378$	−4.31846	−	5.33581i	−0.222117	−	0.274444i
$379$	12.8452			0.659815			0.329908	−	0.944013i	$-0.392982\pi$
$379$	12.8452			0.659815			0.329908	+	0.944013i	$0.392982\pi$
$380$	12.2291	+	21.1815i	0.627341	+	1.08659i
$381$	7.34757	−	12.7264i	0.376428	−	0.651992i
$382$	11.2769	−	19.5321i	0.576974	−	0.999349i
$383$	−6.22769	−	10.7867i	−0.318220	−	0.551173i	0.661897	−	0.749595i	$-0.269752\pi$
$383$	−6.22769	−	10.7867i	−0.318220	−	0.551173i	−0.980117	+	0.198422i	$0.936418\pi$
$384$	3.82247			0.195065
$385$	−5.72838	+	0.905695i	−0.291945	+	0.0461585i
$386$	−20.8731			−1.06241
$387$	5.15661	+	8.93151i	0.262125	+	0.454014i
$388$	−17.7831	+	30.8012i	−0.902800	+	1.56370i
$389$	−6.60538	+	11.4409i	−0.334906	+	0.580074i	−0.983467	−	0.181089i	$-0.942038\pi$
$389$	−6.60538	+	11.4409i	−0.334906	+	0.580074i	0.648561	+	0.761163i	$0.275371\pi$
$390$	−8.39642	−	14.5430i	−0.425169	−	0.736415i
$391$	23.1518			1.17084
$392$	47.1869	−	15.3037i	2.38330	−	0.772951i
$393$	−10.7660			−0.543071
$394$	6.22576	+	10.7833i	0.313649	+	0.543257i
$395$	16.5206	−	28.6146i	0.831244	−	1.43976i
$396$	−2.36571	+	4.09752i	−0.118881	+	0.205908i
$397$	−9.34708	−	16.1896i	−0.469116	−	0.812533i	0.530260	−	0.847835i	$-0.322094\pi$
$397$	−9.34708	−	16.1896i	−0.469116	−	0.812533i	−0.999377	+	0.0353016i	$0.988761\pi$
$398$	7.57909			0.379905
$399$	−6.16280	+	0.974378i	−0.308526	+	0.0487799i
$400$	−1.74049			−0.0870247
$401$	3.58604	+	6.21121i	0.179078	+	0.310173i	0.941565	−	0.336831i	$-0.109355\pi$
$401$	3.58604	+	6.21121i	0.179078	+	0.310173i	−0.762487	+	0.647004i	$0.776022\pi$
$402$	−4.21978	+	7.30887i	−0.210463	+	0.364533i
$403$	−2.55621	+	4.42749i	−0.127334	+	0.220549i
$404$	31.6069	+	54.7448i	1.57250	+	2.72366i
$405$	2.19202			0.108922
$406$	19.3743	+	23.9385i	0.961530	+	1.18805i
$407$	−4.38101			−0.217159
$408$	9.19313	+	15.9230i	0.455128	+	0.788304i
$409$	−1.52060	+	2.63375i	−0.0751887	+	0.130231i	−0.901168	−	0.433469i	$-0.857289\pi$
$409$	−1.52060	+	2.63375i	−0.0751887	+	0.130231i	0.825980	+	0.563700i	$0.190623\pi$
$410$	27.5464	−	47.7118i	1.36042	−	2.35632i
$411$	1.30618	+	2.26236i	0.0644289	+	0.111594i
$412$	−25.2119			−1.24210
$413$	8.46675	−	22.0388i	0.416622	−	1.08446i
$414$	23.1518			1.13785
$415$	6.86955	+	11.8984i	0.337213	+	0.584070i
$416$	13.2557	−	22.9595i	0.649913	−	1.12568i
$417$	3.12508	−	5.41279i	0.153036	−	0.265066i
$418$	3.05924	+	5.29876i	0.149632	+	0.259171i
$419$	24.9508			1.21893			0.609464	−	0.792814i	$-0.291385\pi$
$419$	24.9508			1.21893			0.609464	+	0.792814i	$0.291385\pi$
$420$	−9.84057	+	25.6148i	−0.480170	+	1.24987i
$421$	−11.9958			−0.584638			−0.292319	−	0.956321i	$-0.594427\pi$
$421$	−11.9958			−0.584638			−0.292319	+	0.956321i	$0.594427\pi$
$422$	12.7483	+	22.0808i	0.620579	+	1.07487i
$423$	−5.55470	+	9.62102i	−0.270079	+	0.467790i
$424$	32.5146	−	56.3169i	1.57905	−	2.73499i
$425$	0.253025	+	0.438252i	0.0122735	+	0.0212584i
$426$	−2.58090			−0.125045
$427$	22.4311	+	27.7154i	1.08552	+	1.34124i
$428$	27.8770			1.34749
$429$	−1.47637	−	2.55716i	−0.0712800	−	0.123461i
$430$	29.3266	−	50.7952i	1.41425	−	2.44956i
$431$	8.58507	−	14.8698i	0.413528	−	0.716252i	−0.581744	−	0.813372i	$-0.697630\pi$
$431$	8.58507	−	14.8698i	0.413528	−	0.716252i	0.995273	+	0.0971194i	$0.0309629\pi$
$432$	4.46172	+	7.72792i	0.214664	+	0.371810i
$433$	7.02235			0.337472			0.168736	−	0.985661i	$-0.446031\pi$
$433$	7.02235			0.337472			0.168736	+	0.985661i	$0.446031\pi$
$434$	11.7393	−	1.85605i	0.563503	−	0.0890934i
$435$	−9.83427			−0.471517
$436$	39.7429	+	68.8368i	1.90334	+	3.29668i
$437$	10.5219	−	18.2244i	0.503329	−	0.871791i
$438$	0.382531	−	0.662564i	0.0182780	−	0.0316585i
$439$	−19.8760	−	34.4263i	−0.948631	−	1.64308i	−0.748313	−	0.663346i	$-0.769136\pi$
$439$	−19.8760	−	34.4263i	−0.948631	−	1.64308i	−0.200318	−	0.979731i	$-0.564198\pi$
$440$	15.5341			0.740557
$441$	−5.19947	−	4.68673i	−0.247594	−	0.223178i
$442$	−19.8762			−0.945413
$443$	−17.5006	−	30.3119i	−0.831479	−	1.44016i	−0.896866	−	0.442303i	$-0.854162\pi$
$443$	−17.5006	−	30.3119i	−0.831479	−	1.44016i	0.0653870	−	0.997860i	$-0.479172\pi$
$444$	−10.3642	+	17.9513i	−0.491863	+	0.851931i
$445$	2.84989	−	4.93616i	0.135098	−	0.233996i
$446$	21.1616	+	36.6530i	1.00203	+	1.73557i
$447$	4.12201			0.194964
$448$	−14.2370	+	2.25096i	−0.672634	+	0.106348i
$449$	−10.3780			−0.489767			−0.244884	−	0.969552i	$-0.578750\pi$
$449$	−10.3780			−0.489767			−0.244884	+	0.969552i	$0.578750\pi$
$450$	0.253025	+	0.438252i	0.0119277	+	0.0206594i
$451$	4.84359	−	8.38935i	0.228076	−	0.395039i
$452$	−30.5235	+	52.8682i	−1.43570	+	2.48671i
$453$	6.21765	+	10.7693i	0.292131	+	0.505985i
$454$	58.6587			2.75299
$455$	−10.7732	−	13.3112i	−0.505057	−	0.624040i
$456$	16.7121			0.782615
$457$	9.30137	+	16.1104i	0.435100	+	0.753615i	0.997304	−	0.0733837i	$-0.0233798\pi$
$457$	9.30137	+	16.1104i	0.435100	+	0.753615i	−0.562204	+	0.826999i	$0.690046\pi$
$458$	4.80920	−	8.32978i	0.224719	−	0.389225i
$459$	1.29725	−	2.24690i	0.0605504	−	0.104876i
$460$	−46.2740	−	80.1489i	−2.15754	−	3.73696i
$461$	−17.0730			−0.795171			−0.397585	−	0.917565i	$-0.630152\pi$
$461$	−17.0730			−0.795171			−0.397585	+	0.917565i	$0.630152\pi$
$462$	−2.46172	+	6.40779i	−0.114529	+	0.298118i
$463$	32.3530			1.50357			0.751786	−	0.659408i	$-0.229193\pi$
$463$	32.3530			1.50357			0.751786	+	0.659408i	$0.229193\pi$
$464$	−20.0170	−	34.6705i	−0.929267	−	1.60954i
$465$	−1.89764	+	3.28682i	−0.0880012	+	0.152422i
$466$	9.98750	−	17.2989i	0.462662	−	0.801354i
$467$	0.108704	+	0.188281i	0.00503024	+	0.00871263i	0.868530	−	0.495637i	$-0.165065\pi$
$467$	0.108704	+	0.188281i	0.00503024	+	0.00871263i	−0.863499	+	0.504350i	$0.831732\pi$
$468$	−13.9707			−0.645795
$469$	−3.08640	+	8.03382i	−0.142517	+	0.370967i
$470$	63.1812			2.91433
$471$	−9.34667	−	16.1889i	−0.430672	−	0.745945i
$472$	−31.6186	+	54.7650i	−1.45536	+	2.52076i
$473$	5.15661	−	8.93151i	0.237101	−	0.410671i
$474$	−19.5540	−	33.8685i	−0.898145	−	1.55563i
$475$	0.459972			0.0211049
$476$	20.4324	+	25.2459i	0.936517	+	1.15714i
$477$	−9.17630			−0.420154
$478$	5.35746	+	9.27939i	0.245044	+	0.424429i
$479$	10.7306	−	18.5859i	0.490294	−	0.849213i	−0.509644	−	0.860385i	$-0.670223\pi$
$479$	10.7306	−	18.5859i	0.490294	−	0.849213i	0.999938	+	0.0111720i	$0.00355623\pi$
$480$	9.84057	−	17.0444i	0.449158	−	0.777965i
$481$	−6.46802	−	11.2029i	−0.294916	−	0.510810i
$482$	−38.2843			−1.74380
$483$	23.3195	−	3.68697i	1.06107	−	0.167763i
$484$	4.73141			0.215064
$485$	−8.23875	−	14.2699i	−0.374102	−	0.647964i
$486$	1.29725	−	2.24690i	0.0588444	−	0.101921i
$487$	−18.0445	+	31.2540i	−0.817676	+	1.41626i	0.0897147	+	0.995968i	$0.471404\pi$
$487$	−18.0445	+	31.2540i	−0.817676	+	1.41626i	−0.907391	+	0.420288i	$0.861929\pi$
$488$	−47.7513	−	82.7076i	−2.16160	−	3.74400i
$489$	1.26475			0.0571939
$490$	−8.29815	+	38.9359i	−0.374872	+	1.75894i
$491$	−5.10627			−0.230443			−0.115221	−	0.993340i	$-0.536758\pi$
$491$	−5.10627			−0.230443			−0.115221	+	0.993340i	$0.536758\pi$
$492$	−22.9170	−	39.6935i	−1.03318	−	1.78952i
$493$	−5.81997	+	10.0805i	−0.262118	+	0.454002i
$494$	−9.03317	+	15.6459i	−0.406421	+	0.703943i
$495$	−1.09601	−	1.89835i	−0.0492620	−	0.0853243i
$496$	−15.4501			−0.693731
$497$	−2.59959	+	0.411012i	−0.116608	+	0.0184364i
$498$	16.2617			0.728705
$499$	−3.86571	−	6.69560i	−0.173053	−	0.299736i	0.766433	−	0.642324i	$-0.222030\pi$
$499$	−3.86571	−	6.69560i	−0.173053	−	0.299736i	−0.939486	+	0.342588i	$0.888696\pi$
$500$	26.9398	−	46.6611i	1.20479	−	2.08675i
$501$	−3.05511	+	5.29160i	−0.136492	+	0.236411i
$502$	17.5804	+	30.4502i	0.784652	+	1.35906i
$503$	34.5655			1.54120			0.770599	−	0.637320i	$-0.219957\pi$
$503$	34.5655			1.54120			0.770599	+	0.637320i	$0.219957\pi$
$504$	11.7955	+	14.5743i	0.525412	+	0.649190i
$505$	−29.2864			−1.30323
$506$	−11.5759	−	20.0501i	−0.514612	−	0.891334i
$507$	−2.14064	+	3.70769i	−0.0950689	+	0.164664i
$508$	−34.7644	+	60.2137i	−1.54242	+	2.67155i
$509$	14.2704	+	24.7170i	0.632524	+	1.09556i	0.987034	+	0.160511i	$0.0513143\pi$
$509$	14.2704	+	24.7170i	0.632524	+	1.09556i	−0.354510	+	0.935052i	$0.615352\pi$
$510$	−14.7554			−0.653380
$511$	0.279788	−	0.728282i	0.0123771	−	0.0322173i
$512$	−46.3549			−2.04862
$513$	−1.17913	−	2.04231i	−0.0520597	−	0.0901701i
$514$	−11.0670	+	19.1686i	−0.488144	+	0.845490i
$515$	5.84023	−	10.1156i	0.257351	−	0.445745i
$516$	−24.3980	−	42.2586i	−1.07406	−	1.86033i
$517$	11.1094			0.488591
$518$	−10.7848	+	28.0726i	−0.473857	+	1.23344i
$519$	17.4649			0.766625
$520$	22.9341	+	39.7230i	1.00573	+	1.74197i
$521$	14.0889	−	24.4026i	0.617244	−	1.06910i	−0.372743	−	0.927935i	$-0.621583\pi$
$521$	14.0889	−	24.4026i	0.617244	−	1.06910i	0.989986	−	0.141163i	$-0.0450841\pi$
$522$	−5.81997	+	10.0805i	−0.254733	+	0.441211i
$523$	−15.7257	−	27.2377i	−0.687637	−	1.19102i	−0.972600	−	0.232484i	$-0.925315\pi$
$523$	−15.7257	−	27.2377i	−0.687637	−	1.19102i	0.284963	−	0.958539i	$-0.408019\pi$
$524$	50.9382			2.22525
$525$	0.324650	+	0.401132i	0.0141689	+	0.0175068i
$526$	9.21797			0.401923
$527$	2.24607	+	3.89031i	0.0978404	+	0.169464i
$528$	4.46172	−	7.72792i	0.194171	−	0.336314i
$529$	−28.3138	+	49.0410i	−1.23104	+	2.13222i
$530$	26.0937	+	45.1956i	1.13344	+	1.96317i
$531$	8.92343			0.387244
$532$	29.1587	−	4.61019i	1.26419	−	0.199877i
$533$	28.6038			1.23897
$534$	−3.37316	−	5.84248i	−0.145971	−	0.252829i
$535$	−6.45758	+	11.1849i	−0.279186	+	0.483564i
$536$	11.5260	−	19.9635i	0.497845	−	0.862294i
$537$	0.211273	+	0.365935i	0.00911708	+	0.0157912i
$538$	30.1569			1.30016
$539$	−1.45909	+	6.84624i	−0.0628477	+	0.294889i
$540$	−10.3713			−0.446312
$541$	−18.6395	−	32.2845i	−0.801374	−	1.38802i	−0.918712	−	0.394928i	$-0.870769\pi$
$541$	−18.6395	−	32.2845i	−0.801374	−	1.38802i	0.117338	−	0.993092i	$-0.462564\pi$
$542$	−12.8165	+	22.1989i	−0.550518	+	0.953524i
$543$	1.20099	−	2.08017i	0.0515393	−	0.0892686i
$544$	−11.6474	−	20.1739i	−0.499378	−	0.864948i
$545$	−36.8251			−1.57741
$546$	−20.0201	+	3.16532i	−0.856783	+	0.135463i
$547$	−10.7602			−0.460074			−0.230037	−	0.973182i	$-0.573885\pi$
$547$	−10.7602			−0.460074			−0.230037	+	0.973182i	$0.573885\pi$
$548$	−6.18005	−	10.7042i	−0.263999	−	0.457259i
$549$	−6.73821	+	11.6709i	−0.287580	+	0.498103i
$550$	0.253025	−	0.438252i	0.0107890	−	0.0186871i
$551$	5.29003	+	9.16260i	0.225363	+	0.390340i
$552$	−63.2371			−2.69155
$553$	−25.0893	−	30.9998i	−1.06690	−	1.31825i
$554$	−3.32640			−0.141325
$555$	−4.80163	−	8.31667i	−0.203818	−	0.353023i
$556$	−14.7860	+	25.6101i	−0.627067	+	1.08611i
$557$	5.47134	−	9.47663i	0.231828	−	0.401538i	−0.726518	−	0.687147i	$-0.758863\pi$
$557$	5.47134	−	9.47663i	0.231828	−	0.401538i	0.958346	+	0.285610i	$0.0921960\pi$
$558$	2.24607	+	3.89031i	0.0950837	+	0.164690i
$559$	30.4523			1.28800
$560$	18.5593	−	48.3094i	0.784273	−	2.04145i
$561$	−2.59450			−0.109540
$562$	−33.1984	−	57.5012i	−1.40039	−	2.42554i
$563$	−1.22250	+	2.11743i	−0.0515221	+	0.0892389i	−0.890636	−	0.454716i	$-0.849741\pi$
$563$	−1.22250	+	2.11743i	−0.0515221	+	0.0892389i	0.839114	+	0.543955i	$0.183074\pi$
$564$	26.2816	−	45.5210i	1.10665	−	1.91678i
$565$	−14.1412	−	24.4933i	−0.594926	−	1.03044i
$566$	−31.1545			−1.30952
$567$	0.948822	−	2.46976i	0.0398468	−	0.103720i
$568$	7.04949			0.295790
$569$	−14.2985	−	24.7658i	−0.599426	−	1.03824i	−0.992906	−	0.118903i	$-0.962062\pi$
$569$	−14.2985	−	24.7658i	−0.599426	−	1.03824i	0.393480	−	0.919333i	$-0.371271\pi$
$570$	−6.70591	+	11.6150i	−0.280880	+	0.486498i
$571$	0.981361	−	1.69977i	0.0410687	−	0.0711331i	−0.844760	−	0.535145i	$-0.820257\pi$
$571$	0.981361	−	1.69977i	0.0410687	−	0.0711331i	0.885829	+	0.464012i	$0.153590\pi$
$572$	6.98534	+	12.0990i	0.292072	+	0.505883i
$573$	8.69291			0.363151
$574$	−41.8337	−	51.6890i	−1.74610	−	2.15746i
$575$	−1.74049			−0.0725836
$576$	−2.72396	−	4.71804i	−0.113498	−	0.196585i
$577$	−20.6975	+	35.8490i	−0.861646	+	1.49241i	0.00869302	+	0.999962i	$0.497233\pi$
$577$	−20.6975	+	35.8490i	−0.861646	+	1.49241i	−0.870339	+	0.492453i	$0.836100\pi$
$578$	13.3209	−	23.0725i	0.554077	−	0.959689i
$579$	−4.02257	−	6.96729i	−0.167172	−	0.289551i
$580$	46.5300			1.93205
$581$	16.3795	−	2.58971i	0.679537	−	0.107439i
$582$	−19.5029			−0.808422
$583$	4.58815	+	7.94691i	0.190022	+	0.329127i
$584$	−1.04485	+	1.80973i	−0.0432362	+	0.0748873i
$585$	3.23624	−	5.60534i	0.133802	−	0.231752i
$586$	22.9576	+	39.7637i	0.948370	+	1.64262i
$587$	22.5301			0.929917			0.464959	−	0.885332i	$-0.346069\pi$
$587$	22.5301			0.929917			0.464959	+	0.885332i	$0.346069\pi$
$588$	24.6008	+	22.1749i	1.01452	+	0.914476i
$589$	4.08311			0.168241
$590$	−25.3746	−	43.9501i	−1.04466	−	1.80940i
$591$	−2.39960	+	4.15624i	−0.0987065	+	0.170965i
$592$	19.5468	−	33.8561i	0.803370	−	1.39148i
$593$	9.35654	+	16.2060i	0.384227	+	0.665501i	0.991662	−	0.128869i	$-0.0411346\pi$
$593$	9.35654	+	16.2060i	0.384227	+	0.665501i	−0.607435	+	0.794370i	$0.707801\pi$
$594$	−2.59450			−0.106453
$595$	−14.8623	+	2.34982i	−0.609294	+	0.0963333i
$596$	−19.5029			−0.798871
$597$	1.46061	+	2.52985i	0.0597787	+	0.103540i
$598$	34.1807	−	59.2028i	1.39775	−	2.42098i
$599$	−22.7235	+	39.3583i	−0.928459	+	1.60814i	−0.142557	+	0.989787i	$0.545533\pi$
$599$	−22.7235	+	39.3583i	−0.928459	+	1.60814i	−0.785902	+	0.618352i	$0.787801\pi$
$600$	−0.691116	−	1.19705i	−0.0282147	−	0.0488693i
$601$	13.6085			0.555103			0.277551	−	0.960711i	$-0.410477\pi$
$601$	13.6085			0.555103			0.277551	+	0.960711i	$0.410477\pi$
$602$	−44.5372	−	55.0293i	−1.81520	−	2.24283i
$603$	−3.25287			−0.132467
$604$	−29.4183	−	50.9539i	−1.19701	−	2.07329i
$605$	−1.09601	+	1.89835i	−0.0445591	+	0.0771787i
$606$	−17.3318	+	30.0196i	−0.704058	+	1.21946i
$607$	14.5765	+	25.2473i	0.591643	+	1.02476i	0.994011	+	0.109278i	$0.0348537\pi$
$607$	14.5765	+	25.2473i	0.591643	+	1.02476i	−0.402368	+	0.915478i	$0.631813\pi$
$608$	−21.1737			−0.858705
$609$	−4.25679	+	11.0803i	−0.172494	+	0.448998i
$610$	76.6430			3.10318
$611$	16.4016	+	28.4085i	0.663539	+	1.14928i
$612$	−6.13781	+	10.6310i	−0.248106	+	0.429733i
$613$	−10.1212	+	17.5304i	−0.408791	+	0.708047i	−0.994755	−	0.102290i	$-0.967383\pi$
$613$	−10.1212	+	17.5304i	−0.408791	+	0.708047i	0.585963	+	0.810338i	$0.300716\pi$
$614$	10.4858	+	18.1619i	0.423172	+	0.732956i
$615$	21.2345			0.856258
$616$	6.72396	−	17.5023i	0.270916	−	0.705189i
$617$	−6.70281			−0.269845			−0.134922	−	0.990856i	$-0.543079\pi$
$617$	−6.70281			−0.269845			−0.134922	+	0.990856i	$0.543079\pi$
$618$	−6.91255	−	11.9729i	−0.278064	−	0.481620i
$619$	−2.77120	+	4.79987i	−0.111384	+	0.192923i	−0.916329	−	0.400427i	$-0.868862\pi$
$619$	−2.77120	+	4.79987i	−0.111384	+	0.192923i	0.804944	+	0.593350i	$0.202195\pi$
$620$	8.97854	−	15.5513i	0.360587	−	0.624555i
$621$	4.46172	+	7.72792i	0.179042	+	0.310111i
$622$	30.0617			1.20537
$623$	−4.32802	−	5.34762i	−0.173398	−	0.214248i
$624$	26.3487			1.05479
$625$	11.9934	+	20.7731i	0.479734	+	0.830924i
$626$	−2.01842	+	3.49600i	−0.0806722	+	0.139728i
$627$	−1.17913	+	2.04231i	−0.0470898	+	0.0815619i
$628$	44.2229	+	76.5964i	1.76469	+	3.05653i
$629$	−11.3665			−0.453213
$630$	−14.8623	+	2.34982i	−0.592127	+	0.0936191i
$631$	−34.6139			−1.37796			−0.688979	−	0.724782i	$-0.741941\pi$
$631$	−34.6139			−1.37796			−0.688979	+	0.724782i	$0.741941\pi$
$632$	53.4100	+	92.5089i	2.12454	+	3.67980i
$633$	−4.91360	+	8.51061i	−0.195298	+	0.338266i
$634$	−13.6199	+	23.5904i	−0.540917	+	0.936896i
$635$	−16.1060	−	27.8965i	−0.639148	−	1.10704i
$636$	43.4169			1.72159
$637$	−19.6611	+	6.37649i	−0.779000	+	0.252646i
$638$	11.6399			0.460830
$639$	−0.497379	−	0.861486i	−0.0196760	−	0.0340799i
$640$	4.18947	−	7.25637i	0.165603	−	0.286833i
$641$	7.00029	−	12.1249i	0.276495	−	0.478903i	−0.694016	−	0.719959i	$-0.744160\pi$
$641$	7.00029	−	12.1249i	0.276495	−	0.478903i	0.970511	+	0.241056i	$0.0774938\pi$
$642$	7.64326	+	13.2385i	0.301655	+	0.522482i
$643$	9.03547			0.356324			0.178162	−	0.984001i	$-0.442985\pi$
$643$	9.03547			0.356324			0.178162	+	0.984001i	$0.442985\pi$
$644$	−110.334	+	17.4446i	−4.34778	+	0.687412i
$645$	22.6068			0.890141
$646$	7.93719	+	13.7476i	0.312284	+	0.540892i
$647$	19.7703	−	34.2432i	0.777250	−	1.34624i	−0.156270	−	0.987714i	$-0.549947\pi$
$647$	19.7703	−	34.2432i	0.777250	−	1.34624i	0.933521	−	0.358523i	$-0.116720\pi$
$648$	−3.54332	+	6.13721i	−0.139195	+	0.241092i
$649$	−4.46172	−	7.72792i	−0.175138	−	0.303347i
$650$	1.49424			0.0586089
$651$	2.88188	+	3.56080i	0.112950	+	0.139559i
$652$	−5.98404			−0.234353
$653$	−10.8407	−	18.7767i	−0.424231	−	0.734789i	0.572118	−	0.820172i	$-0.306122\pi$
$653$	−10.8407	−	18.7767i	−0.424231	−	0.734789i	−0.996348	+	0.0853827i	$0.972789\pi$
$654$	−21.7933	+	37.7470i	−0.852184	+	1.47603i
$655$	−11.7996	+	20.4375i	−0.461049	+	0.798560i
$656$	43.2215	+	74.8618i	1.68752	+	2.92286i
$657$	0.294879			0.0115043
$658$	27.3482	−	71.1867i	1.06614	−	2.77515i
$659$	9.66475			0.376485			0.188243	−	0.982123i	$-0.439721\pi$
$659$	9.66475			0.376485			0.188243	+	0.982123i	$0.439721\pi$
$660$	5.18567	+	8.98185i	0.201852	+	0.349618i
$661$	2.89068	−	5.00680i	0.112434	−	0.194742i	−0.804317	−	0.594201i	$-0.797469\pi$
$661$	2.89068	−	5.00680i	0.112434	−	0.194742i	0.916751	+	0.399459i	$0.130802\pi$
$662$	−37.5956	+	65.1175i	−1.46120	+	2.53086i
$663$	−3.83045	−	6.63453i	−0.148762	−	0.257664i
$664$	−44.4175			−1.72373
$665$	−4.90478	+	12.7670i	−0.190199	+	0.495085i
$666$	−11.3665			−0.440444
$667$	−20.0170	−	34.6705i	−0.775062	−	1.34245i
$668$	14.4550	−	25.0367i	0.559279	−	0.968700i
$669$	−8.15636	+	14.1272i	−0.315343	+	0.546190i
$670$	9.24984	+	16.0212i	0.357353	+	0.618953i
$671$	13.4764			0.520252
$672$	−14.9445	−	18.4651i	−0.576496	−	0.712308i
$673$	−4.33155			−0.166969			−0.0834846	−	0.996509i	$-0.526605\pi$
$673$	−4.33155			−0.166969			−0.0834846	+	0.996509i	$0.526605\pi$
$674$	−18.1440	−	31.4263i	−0.698879	−	1.21049i
$675$	−0.0975238	+	0.168916i	−0.00375369	+	0.00650159i
$676$	10.1282	−	17.5426i	0.389547	−	0.674715i
$677$	−10.3422	−	17.9132i	−0.397483	−	0.688460i	0.595932	−	0.803035i	$-0.296783\pi$
$677$	−10.3422	−	17.9132i	−0.397483	−	0.688460i	−0.993415	+	0.114575i	$0.963449\pi$
$678$	−33.4754			−1.28562
$679$	−19.6442	+	3.10587i	−0.753875	+	0.119193i
$680$	40.3030			1.54555
$681$	11.3044	+	19.5799i	0.433187	+	0.750302i
$682$	2.24607	−	3.89031i	0.0860065	−	0.148968i
$683$	2.73223	−	4.73236i	0.104546	−	0.181079i	−0.809007	−	0.587799i	$-0.799994\pi$
$683$	2.73223	−	4.73236i	0.104546	−	0.181079i	0.913553	+	0.406721i	$0.133328\pi$
$684$	5.57893	+	9.66300i	0.213316	+	0.369474i
$685$	5.72633			0.218792
$686$	40.2774	+	26.2031i	1.53780	+	1.00044i
$687$	3.70723			0.141440
$688$	46.0146	+	79.6997i	1.75429	+	3.03852i
$689$	−13.5477	+	23.4652i	−0.516125	+	0.893954i
$690$	25.3746	−	43.9501i	0.965995	−	1.67315i
$691$	21.7111	+	37.6046i	0.825927	+	1.43055i	0.901209	+	0.433386i	$0.142681\pi$
$691$	21.7111	+	37.6046i	0.825927	+	1.43055i	−0.0752812	+	0.997162i	$0.523985\pi$
$692$	−82.6338			−3.14127
$693$	−2.61329	+	0.413178i	−0.0992707	+	0.0156953i
$694$	−23.1971			−0.880548
$695$	−6.85023	−	11.8649i	−0.259844	−	0.450063i
$696$	15.8967	−	27.5339i	0.602564	−	1.04367i
$697$	12.5667	−	21.7661i	0.475997	−	0.824451i
$698$	−0.459100	−	0.795184i	−0.0173772	−	0.0300981i
$699$	7.69899			0.291202
$700$	−1.53605	−	1.89792i	−0.0580574	−	0.0717347i
$701$	−30.4055			−1.14840			−0.574200	−	0.818715i	$-0.694687\pi$
$701$	−30.4055			−1.14840			−0.574200	+	0.818715i	$0.694687\pi$
$702$	−3.83045	−	6.63453i	−0.144571	−	0.250404i
$703$	−5.16577	+	8.94737i	−0.194831	+	0.337457i
$704$	−2.72396	+	4.71804i	−0.102663	+	0.177818i
$705$	12.1760	+	21.0895i	0.458575	+	0.794275i
$706$	53.4572			2.01189
$707$	−12.6767	+	32.9972i	−0.476757	+	1.24099i
$708$	−42.2204			−1.58674
$709$	−9.34424	−	16.1847i	−0.350930	−	0.607829i	0.635482	−	0.772115i	$-0.280801\pi$
$709$	−9.34424	−	16.1847i	−0.350930	−	0.607829i	−0.986413	+	0.164286i	$0.947468\pi$
$710$	−2.82869	+	4.89943i	−0.106159	+	0.183872i
$711$	7.53672	−	13.0540i	0.282649	−	0.489563i
$712$	9.21348	+	15.9582i	0.345290	+	0.598060i
$713$	−15.4501			−0.578612
$714$	−6.38691	+	16.6250i	−0.239024	+	0.622175i
$715$	−6.47249			−0.242057
$716$	−0.999617	−	1.73139i	−0.0373574	−	0.0647050i
$717$	−2.06493	+	3.57657i	−0.0771163	+	0.133569i
$718$	−13.7335	+	23.7871i	−0.512530	+	0.887728i
$719$	16.2616	+	28.1660i	0.606456	+	1.05041i	0.991820	+	0.127648i	$0.0407427\pi$
$719$	16.2616	+	28.1660i	0.606456	+	1.05041i	−0.385363	+	0.922765i	$0.625924\pi$
$720$	19.5603			0.728971
$721$	−8.86932	−	10.9588i	−0.330311	−	0.408126i
$722$	−34.8665			−1.29760
$723$	−7.37799	−	12.7790i	−0.274390	−	0.475258i
$724$	−5.68236	+	9.84214i	−0.211183	+	0.365780i
$725$	0.437530	−	0.757825i	0.0162495	−	0.0281449i
$726$	1.29725	+	2.24690i	0.0481454	+	0.0833903i
$727$	−23.7302			−0.880103			−0.440051	−	0.897973i	$-0.645040\pi$
$727$	−23.7302			−0.880103			−0.440051	+	0.897973i	$0.645040\pi$
$728$	54.6833	−	8.64578i	2.02670	−	0.320434i
$729$	1.00000			0.0370370
$730$	−0.838516	−	1.45235i	−0.0310349	−	0.0537540i
$731$	13.3788	−	23.1728i	0.494833	−	0.857076i
$732$	31.8813	−	55.2199i	1.17836	−	2.04099i
$733$	−17.9943	−	31.1670i	−0.664635	−	1.15118i	−0.979384	−	0.202006i	$-0.935254\pi$
$733$	−17.9943	−	31.1670i	−0.664635	−	1.15118i	0.314749	−	0.949175i	$-0.398079\pi$
$734$	28.2263			1.04185
$735$	−14.5957	+	4.73369i	−0.538371	+	0.174605i
$736$	80.1194			2.95324
$737$	1.62644	+	2.81707i	0.0599105	+	0.103768i
$738$	12.5667	−	21.7661i	0.462586	−	0.801223i
$739$	−0.619926	+	1.07374i	−0.0228043	+	0.0394983i	−0.877202	−	0.480121i	$-0.840593\pi$
$739$	−0.619926	+	1.07374i	−0.0228043	+	0.0394983i	0.854398	+	0.519619i	$0.173926\pi$
$740$	22.7185	+	39.3496i	0.835149	+	1.44652i
$741$	−6.96333			−0.255804
$742$	62.2169	−	9.83689i	2.28405	−	0.361124i
$743$	18.6353			0.683662			0.341831	−	0.939761i	$-0.388953\pi$
$743$	18.6353			0.683662			0.341831	+	0.939761i	$0.388953\pi$
$744$	−6.13494	−	10.6260i	−0.224918	−	0.389569i
$745$	4.51776	−	7.82500i	0.165518	−	0.286686i
$746$	−19.1431	+	33.1568i	−0.700878	+	1.21396i
$747$	3.13389	+	5.42805i	0.114663	+	0.198602i
$748$	12.2756			0.448841
$749$	9.80688	+	12.1172i	0.358335	+	0.442753i
$750$	29.5452			1.07884
$751$	22.6905	+	39.3011i	0.827988	+	1.43412i	0.899614	+	0.436686i	$0.143848\pi$
$751$	22.6905	+	39.3011i	0.827988	+	1.43412i	−0.0716256	+	0.997432i	$0.522819\pi$
$752$	−49.5670	+	85.8525i	−1.80752	+	3.13072i
$753$	−6.77604	+	11.7364i	−0.246932	+	0.427700i
$754$	17.1849	+	29.7651i	0.625838	+	1.08398i
$755$	27.2584			0.992036
$756$	−4.48927	+	11.6855i	−0.163273	+	0.424997i
$757$	35.8708			1.30375			0.651874	−	0.758327i	$-0.273983\pi$
$757$	35.8708			1.30375			0.651874	+	0.758327i	$0.273983\pi$
$758$	−16.6635	−	28.8619i	−0.605244	−	1.04831i
$759$	4.46172	−	7.72792i	0.161950	−	0.280506i
$760$	18.3166	−	31.7253i	0.664413	−	1.15080i
$761$	−9.36063	−	16.2131i	−0.339323	−	0.587724i	0.644983	−	0.764197i	$-0.276864\pi$
$761$	−9.36063	−	16.2131i	−0.339323	−	0.587724i	−0.984305	+	0.176473i	$0.943531\pi$
$762$	−38.1265			−1.38118
$763$	−15.9398	+	41.4911i	−0.577061	+	1.50208i
$764$	−41.1297			−1.48802
$765$	−2.84359	−	4.92525i	−0.102810	−	0.178073i
$766$	−16.1577	+	27.9860i	−0.583802	+	1.01117i
$767$	13.1743	−	22.8186i	0.475697	−	0.823932i
$768$	−10.4066	−	18.0248i	−0.375516	−	0.650413i
$769$	6.00582			0.216576			0.108288	−	0.994120i	$-0.465463\pi$
$769$	6.00582			0.216576			0.108288	+	0.994120i	$0.465463\pi$
$770$	9.46614	+	11.6962i	0.341136	+	0.421502i
$771$	−8.53112			−0.307241
$772$	19.0324	+	32.9651i	0.684992	+	1.18644i
$773$	7.07123	−	12.2477i	0.254334	−	0.440520i	−0.710380	−	0.703818i	$-0.751477\pi$
$773$	7.07123	−	12.2477i	0.254334	−	0.440520i	0.964715	+	0.263298i	$0.0848103\pi$
$774$	13.3788	−	23.1728i	0.480891	−	0.832928i
$775$	−0.168854	−	0.292463i	−0.00606541	−	0.0105056i
$776$	53.2705			1.91230
$777$	−11.4489	+	1.81014i	−0.410725	+	0.0649384i
$778$	34.2753			1.22883
$779$	−11.4224	−	19.7842i	−0.409251	−	0.708843i
$780$	−15.3120	+	26.5212i	−0.548257	+	0.949610i
$781$	−0.497379	+	0.861486i	−0.0177976	+	0.0308264i
$782$	−30.0336	−	52.0198i	−1.07400	−	1.86022i
$783$	−4.48640			−0.160331
$784$	−46.3971	−	41.8218i	−1.65704	−	1.49363i
$785$	−40.9762			−1.46250
$786$	13.9661	+	24.1901i	0.498156	+	0.862831i
$787$	−25.0145	+	43.3265i	−0.891672	+	1.54442i	−0.0538026	+	0.998552i	$0.517134\pi$
$787$	−25.0145	+	43.3265i	−0.891672	+	1.54442i	−0.837870	+	0.545870i	$0.816199\pi$
$788$	11.3535	−	19.6649i	0.404452	−	0.700532i
$789$	1.77645	+	3.07690i	0.0632432	+	0.109540i
$790$	−85.7255			−3.04998
$791$	−33.7179	+	5.33102i	−1.19887	+	0.189549i
$792$	7.08664			0.251813
$793$	19.8962	+	34.4613i	0.706537	+	1.22376i
$794$	−24.2510	+	42.0039i	−0.860634	+	1.49066i
$795$	−10.0573	+	17.4198i	−0.356696	+	0.617816i
$796$	−6.91074	−	11.9698i	−0.244945	−	0.424257i
$797$	−7.24763			−0.256724			−0.128362	−	0.991727i	$-0.540972\pi$
$797$	−7.24763			−0.256724			−0.128362	+	0.991727i	$0.540972\pi$
$798$	10.1840	+	12.5832i	0.360510	+	0.445440i
$799$	28.8233			1.01969
$800$	0.875621	+	1.51662i	0.0309579	+	0.0536206i
$801$	1.30012	−	2.25188i	0.0459375	−	0.0795661i
$802$	9.30397	−	16.1150i	0.328535	−	0.569039i
$803$	−0.147439	−	0.255373i	−0.00520303	−	0.00901191i
$804$	15.3907			0.542787
$805$	18.5593	−	48.3094i	0.654129	−	1.70268i
$806$	13.2642			0.467210
$807$	5.81170	+	10.0662i	0.204582	+	0.354346i
$808$	47.3404	−	81.9960i	1.66543	−	2.88461i
$809$	−0.256139	+	0.443646i	−0.00900538	+	0.0155978i	−0.870493	−	0.492181i	$-0.836200\pi$
$809$	−0.256139	+	0.443646i	−0.00900538	+	0.0155978i	0.861488	+	0.507779i	$0.169533\pi$
$810$	−2.84359	−	4.92525i	−0.0999137	−	0.173056i
$811$	40.5892			1.42528			0.712640	−	0.701530i	$-0.247499\pi$
$811$	40.5892			1.42528			0.712640	+	0.701530i	$0.247499\pi$
$812$	20.1406	−	52.4257i	0.706798	−	1.83978i
$813$	−9.87979			−0.346499
$814$	5.68326	+	9.84370i	0.199198	+	0.345021i
$815$	1.38618	−	2.40093i	0.0485556	−	0.0841008i
$816$	11.5759	−	20.0501i	0.405238	−	0.701892i
$817$	−12.1606	−	21.0628i	−0.425445	−	0.736893i
$818$	7.89037			0.275880
$819$	−4.91476	−	6.07258i	−0.171735	−	0.212193i
$820$	−100.469			−3.50854
$821$	11.3094	+	19.5885i	0.394702	+	0.683645i	0.993063	−	0.117582i	$-0.0375144\pi$
$821$	11.3094	+	19.5885i	0.394702	+	0.683645i	−0.598361	+	0.801227i	$0.704181\pi$
$822$	3.38887	−	5.86969i	0.118200	−	0.204729i
$823$	−3.01815	+	5.22758i	−0.105206	+	0.182222i	−0.913822	−	0.406114i	$-0.866884\pi$
$823$	−3.01815	+	5.22758i	−0.105206	+	0.182222i	0.808616	+	0.588336i	$0.200217\pi$
$824$	18.8810	+	32.7029i	0.657751	+	1.13926i
$825$	0.195048			0.00679068
$826$	−60.5024	+	9.56582i	−2.10515	+	0.332837i
$827$	4.54161			0.157927			0.0789636	−	0.996878i	$-0.474839\pi$
$827$	4.54161			0.157927			0.0789636	+	0.996878i	$0.474839\pi$
$828$	−21.1102	−	36.5640i	−0.733631	−	1.27069i
$829$	−12.9358	+	22.4055i	−0.449280	+	0.778176i	−0.998339	−	0.0576078i	$-0.981653\pi$
$829$	−12.9358	+	22.4055i	−0.449280	+	0.778176i	0.549059	+	0.835783i	$0.314986\pi$
$830$	17.8230	−	30.8704i	0.618646	−	1.07153i
$831$	−0.641050	−	1.11033i	−0.0222378	−	0.0385169i
$832$	−16.0863			−0.557693
$833$	−3.78562	+	17.7626i	−0.131164	+	0.615436i
$834$	−16.2160			−0.561514
$835$	6.69685	+	11.5993i	0.231754	+	0.401410i
$836$	5.57893	−	9.66300i	0.192951	−	0.334202i
$837$	−0.865706	+	1.49945i	−0.0299232	+	0.0518284i
$838$	−32.3674	−	56.0620i	−1.11811	−	1.93663i
$839$	−28.9458			−0.999319			−0.499660	−	0.866222i	$-0.666542\pi$
$839$	−28.9458			−0.999319			−0.499660	+	0.866222i	$0.666542\pi$
$840$	40.5950	−	6.41833i	1.40066	−	0.221453i
$841$	−8.87225			−0.305940
$842$	15.5615	+	26.9533i	0.536284	+	0.928872i
$843$	12.7957	−	22.1628i	0.440707	−	0.763327i
$844$	23.2483	−	40.2672i	0.800239	−	1.38605i
$845$	4.69232	+	8.12733i	0.161421	+	0.279589i
$846$	28.8233			0.990965
$847$	1.66447	+	2.05659i	0.0571918	+	0.0706651i
$848$	−81.8841			−2.81191
$849$	−6.00397	−	10.3992i	−0.206056	−	0.356899i
$850$	0.656473	−	1.13704i	0.0225168	−	0.0390003i
$851$	19.5468	−	33.8561i	0.670057	−	1.16057i
$852$	2.35331	+	4.07604i	0.0806229	+	0.139643i
$853$	−4.72334			−0.161724			−0.0808620	−	0.996725i	$-0.525767\pi$
$853$	−4.72334			−0.161724			−0.0808620	+	0.996725i	$0.525767\pi$
$854$	33.1751	−	86.3542i	1.13523	−	2.95498i
$855$	−5.16934			−0.176788
$856$	−20.8769	−	36.1598i	−0.713557	−	1.23592i
$857$	−14.1046	+	24.4298i	−0.481803	+	0.834508i	−0.999782	−	0.0208859i	$-0.993351\pi$
$857$	−14.1046	+	24.4298i	−0.481803	+	0.834508i	0.517979	+	0.855394i	$0.326685\pi$
$858$	−3.83045	+	6.63453i	−0.130769	+	0.226499i
$859$	3.71790	+	6.43959i	0.126853	+	0.219716i	0.922456	−	0.386103i	$-0.126179\pi$
$859$	3.71790	+	6.43959i	0.126853	+	0.219716i	−0.795603	+	0.605819i	$0.792846\pi$
$860$	−106.962			−3.64737
$861$	9.19142	−	23.9251i	0.313243	−	0.815364i
$862$	−44.5479			−1.51731
$863$	−22.8001	−	39.4910i	−0.776125	−	1.34429i	−0.934160	−	0.356854i	$-0.883849\pi$
$863$	−22.8001	−	39.4910i	−0.776125	−	1.34429i	0.158035	−	0.987434i	$-0.449484\pi$
$864$	4.48927	−	7.77564i	0.152728	−	0.264533i
$865$	19.1417	−	33.1545i	0.650839	−	1.12729i
$866$	−9.10972	−	15.7785i	−0.309561	−	0.536175i
$867$	10.2686			0.348740
$868$	−13.6354	−	16.8476i	−0.462814	−	0.571845i
$869$	−15.0734			−0.511332
$870$	12.7575	+	22.0966i	0.432519	+	0.749146i
$871$	−4.80246	+	8.31810i	−0.162725	+	0.281848i
$872$	59.5264	−	103.103i	2.01582	−	3.49150i
$873$	−3.75852	−	6.50994i	−0.127207	−	0.220328i
$874$	−54.5978			−1.84680
$875$	29.7592	−	4.70513i	1.00605	−	0.159062i
$876$	−1.39519			−0.0471392
$877$	19.8682	+	34.4127i	0.670900	+	1.16203i	0.977649	+	0.210242i	$0.0674253\pi$
$877$	19.8682	+	34.4127i	0.670900	+	1.16203i	−0.306749	+	0.951790i	$0.599241\pi$
$878$	−51.5683	+	89.3189i	−1.74035	+	3.01437i
$879$	−8.84858	+	15.3262i	−0.298455	+	0.516939i
$880$	−9.78017	−	16.9398i	−0.329690	−	0.571039i
$881$	28.1813			0.949452			0.474726	−	0.880134i	$-0.342547\pi$
$881$	28.1813			0.949452			0.474726	+	0.880134i	$0.342547\pi$
$882$	−3.78562	+	17.7626i	−0.127468	+	0.598096i
$883$	40.6909			1.36936			0.684679	−	0.728845i	$-0.259942\pi$
$883$	40.6909			1.36936			0.684679	+	0.728845i	$0.259942\pi$
$884$	18.1234	+	31.3907i	0.609557	+	1.05578i
$885$	9.78017	−	16.9398i	0.328757	−	0.569424i
$886$	−45.4052	+	78.6442i	−1.52542	+	2.64210i
$887$	9.24688	+	16.0161i	0.310480	+	0.537767i	0.978466	−	0.206406i	$-0.0661769\pi$
$887$	9.24688	+	16.0161i	0.310480	+	0.537767i	−0.667986	+	0.744173i	$0.732844\pi$
$888$	31.0466			1.04186
$889$	−38.4027	+	6.07171i	−1.28798	+	0.203639i
$890$	−14.7881			−0.495697
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	38.5911	−	66.8417i	1.29212	−	2.23803i
$893$	13.0994	−	22.6888i	0.438354	−	0.759252i
$894$	−5.34727	−	9.26174i	−0.178839	−	0.309759i
$895$	0.926227			0.0309604
$896$	−6.36238	−	7.86124i	−0.212552	−	0.262626i
$897$	26.3487			0.879756
$898$	13.4628	+	23.3183i	0.449260	+	0.778142i
$899$	3.88390	−	6.72711i	0.129535	−	0.224362i
$900$	0.461425	−	0.799212i	0.0153808	−	0.0266404i
$901$	11.9039	+	20.6182i	0.396578	+	0.686893i
$902$	−25.1334			−0.836850
$903$	9.78541	−	25.4712i	0.325638	−	0.847629i
$904$	91.4351			3.04109
$905$	−2.63259	−	4.55977i	−0.0875101	−	0.151572i
$906$	16.1317	−	27.9409i	0.535939	−	0.928274i
$907$	23.9826	−	41.5390i	0.796328	−	1.37928i	−0.125665	−	0.992073i	$-0.540106\pi$
$907$	23.9826	−	41.5390i	0.796328	−	1.37928i	0.921993	−	0.387207i	$-0.126560\pi$
$908$	−53.4860	−	92.6404i	−1.77499	−	3.07438i
$909$	−13.3605			−0.443139
$910$	−15.9334	+	41.4744i	−0.528188	+	1.37486i
$911$	11.9369			0.395489			0.197744	−	0.980254i	$-0.436638\pi$
$911$	11.9369			0.395489			0.197744	+	0.980254i	$0.436638\pi$
$912$	−10.5219	−	18.2244i	−0.348413	−	0.603470i
$913$	3.13389	−	5.42805i	0.103717	−	0.179642i
$914$	24.1324	−	41.7985i	0.798228	−	1.38257i
$915$	14.7703	+	25.5829i	0.488291	+	0.845745i
$916$	−17.5404			−0.579552
$917$	17.9196	+	22.1411i	0.591758	+	0.731165i
$918$	−6.73141			−0.222170
$919$	−29.5225	−	51.1344i	−0.973856	−	1.68677i	−0.683660	−	0.729801i	$-0.739613\pi$
$919$	−29.5225	−	51.1344i	−0.973856	−	1.68677i	−0.290196	−	0.956967i	$-0.593720\pi$
$920$	−69.3085	+	120.046i	−2.28503	+	3.95780i
$921$	−4.04155	+	7.00018i	−0.133174	+	0.230664i
$922$	22.1480	+	38.3614i	0.729404	+	1.26337i
$923$	−2.93727			−0.0966815
$924$	12.3645	−	1.95492i	0.406764	−	0.0643120i
$925$	0.854506			0.0280960
$926$	−41.9699	−	72.6939i	−1.37922	−	2.38887i
$927$	2.66431	−	4.61472i	0.0875075	−	0.151567i
$928$	−20.1406	+	34.8846i	−0.661149	+	1.14514i
$929$	19.0374	+	32.9737i	0.624597	+	1.08183i	0.988619	+	0.150443i	$0.0480699\pi$
$929$	19.0374	+	32.9737i	0.624597	+	1.08183i	−0.364022	+	0.931390i	$0.618597\pi$
$930$	9.84686			0.322891
$931$	12.2617	+	11.0525i	0.401860	+	0.362231i
$932$	−36.4271			−1.19321
$933$	5.79337	+	10.0344i	0.189666	+	0.328512i
$934$	0.282033	−	0.488496i	0.00922841	−	0.0159841i
$935$	−2.84359	+	4.92525i	−0.0929955	+	0.161073i
$936$	10.4625	+	18.1216i	0.341979	+	0.592324i
$937$	−19.4407			−0.635099			−0.317550	−	0.948242i	$-0.602860\pi$
$937$	−19.4407			−0.635099			−0.317550	+	0.948242i	$0.602860\pi$
$938$	22.0550	−	3.48704i	0.720122	−	0.113856i
$939$	−1.55592			−0.0507756
$940$	−57.6097	−	99.7830i	−1.87902	−	3.25456i
$941$	19.8767	−	34.4274i	0.647961	−	1.12230i	−0.335648	−	0.941988i	$-0.608955\pi$
$941$	19.8767	−	34.4274i	0.647961	−	1.12230i	0.983609	−	0.180314i	$-0.0577115\pi$
$942$	−24.2499	+	42.0021i	−0.790104	+	1.36850i
$943$	43.2215	+	74.8618i	1.40749	+	2.43784i
$944$	79.6276			2.59166
$945$	−3.64855	−	4.50808i	−0.118687	−	0.146648i
$946$	−26.7576			−0.869965
$947$	−16.1771	−	28.0196i	−0.525686	−	0.910514i	−0.999552	−	0.0299177i	$-0.990475\pi$
$947$	−16.1771	−	28.0196i	−0.525686	−	0.910514i	0.473867	−	0.880597i	$-0.342858\pi$
$948$	−35.6593	+	61.7638i	−1.15816	+	2.00599i
$949$	0.435352	−	0.754052i	0.0141321	−	0.0244775i
$950$	−0.596697	−	1.03351i	−0.0193594	−	0.0335315i
$951$	−10.4991			−0.340457
$952$	17.4453	−	45.4097i	0.565405	−	1.47174i
$953$	8.56486			0.277443			0.138722	−	0.990331i	$-0.455701\pi$
$953$	8.56486			0.277443			0.138722	+	0.990331i	$0.455701\pi$
$954$	11.9039	+	20.6182i	0.385404	+	0.667540i
$955$	9.52751	−	16.5021i	0.308303	−	0.533997i
$956$	9.77004	−	16.9222i	0.315986	−	0.547303i
$957$	2.24320	+	3.88533i	0.0725123	+	0.125595i
$958$	−55.6810			−1.79897
$959$	2.47866	−	6.45189i	0.0800400	−	0.208342i
$960$	−11.9419			−0.385425
$961$	14.0011	+	24.2506i	0.451649	+	0.782278i
$962$	−16.7812	+	29.0660i	−0.541049	+	0.937125i
$963$	−2.94595	+	5.10253i	−0.0949319	+	0.164427i
$964$	34.9083	+	60.4629i	1.12432	+	1.94738i
$965$	−17.6351			−0.567694
$966$	−38.5354	−	47.6137i	−1.23986	−	1.53195i
$967$	11.2215			0.360858			0.180429	−	0.983588i	$-0.442251\pi$
$967$	11.2215			0.360858			0.180429	+	0.983588i	$0.442251\pi$
$968$	−3.54332	−	6.13721i	−0.113887	−	0.197257i
$969$	−3.05924	+	5.29876i	−0.0982769	+	0.170221i
$970$	−21.3754	+	37.0233i	−0.686323	+	1.18875i
$971$	21.3822	+	37.0351i	0.686188	+	1.18851i	0.973062	+	0.230545i	$0.0740508\pi$
$971$	21.3822	+	37.0351i	0.686188	+	1.18851i	−0.286873	+	0.957969i	$0.592616\pi$
$972$	−4.73141			−0.151760
$973$	−16.3335	+	2.58243i	−0.523627	+	0.0827888i
$974$	93.6329			3.00019
$975$	0.287963	+	0.498767i	0.00922221	+	0.0159733i
$976$	−60.1280	+	104.145i	−1.92465	+	3.33359i
$977$	−12.3598	+	21.4077i	−0.395424	+	0.684894i	−0.993155	−	0.116802i	$-0.962736\pi$
$977$	−12.3598	+	21.4077i	−0.395424	+	0.684894i	0.597731	+	0.801696i	$0.296069\pi$
$978$	−1.64069	−	2.84176i	−0.0524635	−	0.0908695i
$979$	−2.60024			−0.0831041
$980$	69.0583	−	22.3970i	2.20599	−	0.715446i
$981$	−16.7996			−0.536370
$982$	6.62410	+	11.4733i	0.211384	+	0.366127i
$983$	20.3629	−	35.2695i	0.649475	−	1.12492i	−0.333774	−	0.942653i	$-0.608322\pi$
$983$	20.3629	−	35.2695i	0.649475	−	1.12492i	0.983249	−	0.182270i	$-0.0583445\pi$
$984$	−34.3248	+	59.4523i	−1.09423	+	1.89527i
$985$	5.25998	+	9.11055i	0.167597	+	0.290286i
$986$	30.1998			0.961757
$987$	29.0321	−	4.59016i	0.924101	−	0.146106i
$988$	32.9464			1.04816
$989$	46.0146	+	79.6997i	1.46318	+	2.53430i
$990$	−2.84359	+	4.92525i	−0.0903754	+	0.156535i
$991$	28.7562	−	49.8072i	0.913471	−	1.58218i	0.104345	−	0.994541i	$-0.466725\pi$
$991$	28.7562	−	49.8072i	0.913471	−	1.58218i	0.809125	−	0.587636i	$-0.199941\pi$
$992$	7.77277	+	13.4628i	0.246786	+	0.427445i
$993$	−28.9811			−0.919686
$994$	4.29582	+	5.30784i	0.136255	+	0.168354i
$995$	6.40337			0.203000
$996$	−14.8277	−	25.6824i	−0.469834	−	0.813776i
$997$	18.9091	−	32.7516i	0.598858	−	1.03725i	−0.394132	−	0.919054i	$-0.628955\pi$
$997$	18.9091	−	32.7516i	0.598858	−	1.03725i	0.992990	−	0.118199i	$-0.0377120\pi$
$998$	−10.0296	+	17.3717i	−0.317480	+	0.549892i
$999$	−2.19051	−	3.79407i	−0.0693046	−	0.120039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.f.67.1	✓	10
3.2	odd	2		693.2.i.j.298.5		10
7.2	even	3	inner	231.2.i.f.100.1	yes	10
7.3	odd	6		1617.2.a.bb.1.5		5
7.4	even	3		1617.2.a.ba.1.5		5
21.2	odd	6		693.2.i.j.100.5		10
21.11	odd	6		4851.2.a.ca.1.1		5
21.17	even	6		4851.2.a.bz.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.1	✓	10	1.1	even	1	trivial
231.2.i.f.100.1	yes	10	7.2	even	3	inner
693.2.i.j.100.5		10	21.2	odd	6
693.2.i.j.298.5		10	3.2	odd	2
1617.2.a.ba.1.5		5	7.4	even	3
1617.2.a.bb.1.5		5	7.3	odd	6
4851.2.a.bz.1.1		5	21.17	even	6
4851.2.a.ca.1.1		5	21.11	odd	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29725 - 2.24690i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.36571 + 4.09752i) q^{4} +(-1.09601 - 1.89835i) q^{5} -2.59450 q^{6} +(-2.61329 + 0.413178i) q^{7} +7.08664 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.29725 - 2.24690i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.36571 + 4.09752i) q^{4} +(-1.09601 - 1.89835i) q^{5} -2.59450 q^{6} +(-2.61329 + 0.413178i) q^{7} +7.08664 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.84359 + 4.92525i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(2.36571 + 4.09752i) q^{12} -2.95275 q^{13} +(4.31846 + 5.33581i) q^{14} -2.19202 q^{15} +(-4.46172 - 7.72792i) q^{16} +(-1.29725 + 2.24690i) q^{17} +(-1.29725 + 2.24690i) q^{18} +(1.17913 + 2.04231i) q^{19} +10.3713 q^{20} +(-0.948822 + 2.46976i) q^{21} +2.59450 q^{22} +(-4.46172 - 7.72792i) q^{23} +(3.54332 - 6.13721i) q^{24} +(0.0975238 - 0.168916i) q^{25} +(3.83045 + 6.63453i) q^{26} -1.00000 q^{27} +(4.48927 - 11.6855i) q^{28} +4.48640 q^{29} +(2.84359 + 4.92525i) q^{30} +(0.865706 - 1.49945i) q^{31} +(-4.48927 + 7.77564i) q^{32} +(0.500000 + 0.866025i) q^{33} +6.73141 q^{34} +(3.64855 + 4.50808i) q^{35} +4.73141 q^{36} +(2.19051 + 3.79407i) q^{37} +(3.05924 - 5.29876i) q^{38} +(-1.47637 + 2.55716i) q^{39} +(-7.76703 - 13.4529i) q^{40} -9.68719 q^{41} +(6.78017 - 1.07199i) q^{42} -10.3132 q^{43} +(-2.36571 - 4.09752i) q^{44} +(-1.09601 + 1.89835i) q^{45} +(-11.5759 + 20.0501i) q^{46} +(-5.55470 - 9.62102i) q^{47} -8.92343 q^{48} +(6.65857 - 2.15951i) q^{49} -0.506050 q^{50} +(1.29725 + 2.24690i) q^{51} +(6.98534 - 12.0990i) q^{52} +(4.58815 - 7.94691i) q^{53} +(1.29725 + 2.24690i) q^{54} +2.19202 q^{55} +(-18.5194 + 2.92804i) q^{56} +2.35825 q^{57} +(-5.81997 - 10.0805i) q^{58} +(-4.46172 + 7.72792i) q^{59} +(5.18567 - 8.98185i) q^{60} +(-6.73821 - 11.6709i) q^{61} -4.49214 q^{62} +(1.66447 + 2.05659i) q^{63} +5.44792 q^{64} +(3.23624 + 5.60534i) q^{65} +(1.29725 - 2.24690i) q^{66} +(1.62644 - 2.81707i) q^{67} +(-6.13781 - 10.6310i) q^{68} -8.92343 q^{69} +(5.39613 - 14.0460i) q^{70} +0.994758 q^{71} +(-3.54332 - 6.13721i) q^{72} +(-0.147439 + 0.255373i) q^{73} +(5.68326 - 9.84370i) q^{74} +(-0.0975238 - 0.168916i) q^{75} -11.1579 q^{76} +(0.948822 - 2.46976i) q^{77} +7.66090 q^{78} +(7.53672 + 13.0540i) q^{79} +(-9.78017 + 16.9398i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(12.5667 + 21.7661i) q^{82} -6.26778 q^{83} +(-7.87528 - 9.73056i) q^{84} +5.68719 q^{85} +(13.3788 + 23.1728i) q^{86} +(2.24320 - 3.88533i) q^{87} +(-3.54332 + 6.13721i) q^{88} +(1.30012 + 2.25188i) q^{89} +5.68719 q^{90} +(7.71639 - 1.22001i) q^{91} +42.2204 q^{92} +(-0.865706 - 1.49945i) q^{93} +(-14.4116 + 24.9617i) q^{94} +(2.58467 - 4.47678i) q^{95} +(4.48927 + 7.77564i) q^{96} +7.51704 q^{97} +(-13.4900 - 12.1597i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more