LMFDB - Embedded newform 41.3.e.b.14.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,3,Mod(3,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(8))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("41.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	41.e (of order $8$, 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:	$1.11716908388$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 66 x^{18} + 1853 x^{16} + 28868 x^{14} + 272678 x^{12} + 1600296 x^{10} + 5739482 x^{8} + \cdots + 776161 $ x^20 + 66x^18 + 1853x^16 + 28868x^14 + 272678x^12 + 1600296x^10 + 5739482x^8 + 11863964x^6 + 12547553x^4 + 5476470*x^2 + 776161
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			14.3
Root			$1.38143i$ of defining polynomial
Character	$\chi$	$=$	41.14
Dual form			41.3.e.b.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.976817 - 0.976817i) q^{2} +(0.355101 + 0.857291i) q^{3} -2.09166i q^{4} +(4.54303 - 4.54303i) q^{5} +(0.490547 - 1.18428i) q^{6} +(0.392560 + 0.947724i) q^{7} +(-5.95043 + 5.95043i) q^{8} +(5.75511 - 5.75511i) q^{9} +O(q^{10})$	\(q+(-0.976817 - 0.976817i) q^{2} +(0.355101 + 0.857291i) q^{3} -2.09166i q^{4} +(4.54303 - 4.54303i) q^{5} +(0.490547 - 1.18428i) q^{6} +(0.392560 + 0.947724i) q^{7} +(-5.95043 + 5.95043i) q^{8} +(5.75511 - 5.75511i) q^{9} -8.87541 q^{10} +(-12.1914 + 5.04984i) q^{11} +(1.79316 - 0.742751i) q^{12} +(9.50068 + 22.9367i) q^{13} +(0.542293 - 1.30921i) q^{14} +(5.50793 + 2.28146i) q^{15} +3.25833 q^{16} +(0.0103812 - 0.0250625i) q^{17} -11.2434 q^{18} +(-4.10513 + 9.91065i) q^{19} +(-9.50246 - 9.50246i) q^{20} +(-0.673076 + 0.673076i) q^{21} +(16.8415 + 6.97599i) q^{22} -26.1898i q^{23} +(-7.21426 - 2.98824i) q^{24} -16.2782i q^{25} +(13.1245 - 31.6853i) q^{26} +(14.6931 + 6.08607i) q^{27} +(1.98231 - 0.821101i) q^{28} +(-9.09988 - 21.9691i) q^{29} +(-3.15167 - 7.60881i) q^{30} +34.6509i q^{31} +(20.6189 + 20.6189i) q^{32} +(-8.65836 - 8.65836i) q^{33} +(-0.0346220 + 0.0143409i) q^{34} +(6.08895 + 2.52212i) q^{35} +(-12.0377 - 12.0377i) q^{36} +31.8640 q^{37} +(13.6909 - 5.67094i) q^{38} +(-16.2897 + 16.2897i) q^{39} +54.0660i q^{40} +(-36.9925 + 17.6792i) q^{41} +1.31494 q^{42} +(-26.6842 - 26.6842i) q^{43} +(10.5625 + 25.5002i) q^{44} -52.2913i q^{45} +(-25.5826 + 25.5826i) q^{46} +(-5.31373 + 12.8285i) q^{47} +(1.15704 + 2.79334i) q^{48} +(33.9042 - 33.9042i) q^{49} +(-15.9008 + 15.9008i) q^{50} +0.0251722 q^{51} +(47.9757 - 19.8722i) q^{52} +(-44.5080 + 18.4358i) q^{53} +(-8.40746 - 20.2974i) q^{54} +(-32.4443 + 78.3274i) q^{55} +(-7.97527 - 3.30347i) q^{56} -9.95405 q^{57} +(-12.5708 + 30.3487i) q^{58} -2.86012 q^{59} +(4.77203 - 11.5207i) q^{60} +(-29.7057 - 29.7057i) q^{61} +(33.8476 - 33.8476i) q^{62} +(7.71348 + 3.19503i) q^{63} -53.3152i q^{64} +(147.364 + 61.0401i) q^{65} +16.9153i q^{66} +(14.9886 - 36.1856i) q^{67} +(-0.0524222 - 0.0217140i) q^{68} +(22.4523 - 9.30003i) q^{69} +(-3.48413 - 8.41144i) q^{70} +(-22.4314 - 54.1541i) q^{71} +68.4908i q^{72} +(-56.7726 - 56.7726i) q^{73} +(-31.1253 - 31.1253i) q^{74} +(13.9552 - 5.78042i) q^{75} +(20.7297 + 8.58652i) q^{76} +(-9.57171 - 9.57171i) q^{77} +31.8241 q^{78} +(-134.955 + 55.9004i) q^{79} +(14.8027 - 14.8027i) q^{80} -58.4932i q^{81} +(53.4042 + 18.8656i) q^{82} +127.971 q^{83} +(1.40785 + 1.40785i) q^{84} +(-0.0666974 - 0.161022i) q^{85} +52.1311i q^{86} +(15.6025 - 15.6025i) q^{87} +(42.4953 - 102.593i) q^{88} +(-39.5582 - 95.5019i) q^{89} +(-51.0790 + 51.0790i) q^{90} +(-18.0080 + 18.0080i) q^{91} -54.7801 q^{92} +(-29.7059 + 12.3046i) q^{93} +(17.7216 - 7.34054i) q^{94} +(26.3747 + 63.6741i) q^{95} +(-10.3546 + 24.9982i) q^{96} +(109.949 + 45.5425i) q^{97} -66.2363 q^{98} +(-41.1004 + 99.2252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{2} + 4 q^{3} - 12 q^{5} - 16 q^{6} - 4 q^{7} + 36 q^{8} + 4 q^{9}+O(q^{10}) $ 20 * q - 8 * q^2 + 4 * q^3 - 12 * q^5 - 16 * q^6 - 4 * q^7 + 36 * q^8 + 4 * q^9	\( 20 q - 8 q^{2} + 4 q^{3} - 12 q^{5} - 16 q^{6} - 4 q^{7} + 36 q^{8} + 4 q^{9} + 16 q^{10} - 12 q^{11} - 100 q^{12} - 48 q^{13} + 88 q^{14} + 40 q^{15} - 36 q^{16} - 28 q^{17} - 12 q^{18} + 76 q^{19} - 16 q^{20} - 88 q^{21} - 116 q^{22} + 268 q^{24} + 40 q^{26} - 80 q^{27} + 72 q^{28} - 24 q^{29} - 216 q^{30} + 176 q^{32} + 176 q^{33} + 80 q^{34} + 60 q^{35} + 48 q^{36} + 208 q^{37} - 380 q^{38} - 68 q^{39} - 116 q^{41} + 280 q^{42} - 40 q^{43} + 116 q^{44} - 176 q^{46} - 64 q^{47} - 480 q^{48} + 168 q^{49} - 148 q^{50} - 72 q^{51} - 184 q^{52} - 120 q^{53} - 284 q^{54} + 20 q^{55} + 188 q^{56} + 560 q^{57} + 36 q^{58} - 512 q^{59} + 500 q^{60} - 460 q^{61} + 68 q^{62} - 520 q^{63} + 432 q^{65} + 300 q^{67} + 120 q^{68} + 300 q^{69} + 308 q^{70} - 108 q^{71} + 60 q^{73} + 140 q^{74} + 52 q^{75} + 872 q^{76} + 112 q^{77} + 1072 q^{78} - 208 q^{79} - 68 q^{80} - 376 q^{82} - 120 q^{83} - 1604 q^{84} + 172 q^{85} + 200 q^{87} + 316 q^{88} + 268 q^{89} - 512 q^{90} - 800 q^{91} - 448 q^{92} + 312 q^{93} - 212 q^{94} - 184 q^{95} - 612 q^{96} - 120 q^{97} - 20 q^{98} + 164 q^{99}+O(q^{100}) \) 20 * q - 8 * q^2 + 4 * q^3 - 12 * q^5 - 16 * q^6 - 4 * q^7 + 36 * q^8 + 4 * q^9 + 16 * q^10 - 12 * q^11 - 100 * q^12 - 48 * q^13 + 88 * q^14 + 40 * q^15 - 36 * q^16 - 28 * q^17 - 12 * q^18 + 76 * q^19 - 16 * q^20 - 88 * q^21 - 116 * q^22 + 268 * q^24 + 40 * q^26 - 80 * q^27 + 72 * q^28 - 24 * q^29 - 216 * q^30 + 176 * q^32 + 176 * q^33 + 80 * q^34 + 60 * q^35 + 48 * q^36 + 208 * q^37 - 380 * q^38 - 68 * q^39 - 116 * q^41 + 280 * q^42 - 40 * q^43 + 116 * q^44 - 176 * q^46 - 64 * q^47 - 480 * q^48 + 168 * q^49 - 148 * q^50 - 72 * q^51 - 184 * q^52 - 120 * q^53 - 284 * q^54 + 20 * q^55 + 188 * q^56 + 560 * q^57 + 36 * q^58 - 512 * q^59 + 500 * q^60 - 460 * q^61 + 68 * q^62 - 520 * q^63 + 432 * q^65 + 300 * q^67 + 120 * q^68 + 300 * q^69 + 308 * q^70 - 108 * q^71 + 60 * q^73 + 140 * q^74 + 52 * q^75 + 872 * q^76 + 112 * q^77 + 1072 * q^78 - 208 * q^79 - 68 * q^80 - 376 * q^82 - 120 * q^83 - 1604 * q^84 + 172 * q^85 + 200 * q^87 + 316 * q^88 + 268 * q^89 - 512 * q^90 - 800 * q^91 - 448 * q^92 + 312 * q^93 - 212 * q^94 - 184 * q^95 - 612 * q^96 - 120 * q^97 - 20 * q^98 + 164 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−0.976817	−	0.976817i	−0.488408	−	0.488408i	0.419395	−	0.907804i	$-0.362242\pi$
$2$	−0.976817	−	0.976817i	−0.488408	−	0.488408i	−0.907804	+	0.419395i	$0.862242\pi$
$3$	0.355101	+	0.857291i	0.118367	+	0.285764i	0.971948	−	0.235197i	$-0.0755737\pi$
$3$	0.355101	+	0.857291i	0.118367	+	0.285764i	−0.853580	+	0.520961i	$0.825574\pi$
$4$		−	2.09166i		−	0.522915i
$5$	4.54303	−	4.54303i	0.908606	−	0.908606i	−0.0875541	−	0.996160i	$-0.527905\pi$
$5$	4.54303	−	4.54303i	0.908606	−	0.908606i	0.996160	+	0.0875541i	$0.0279051\pi$
$6$	0.490547	−	1.18428i	0.0817578	−	0.197381i
$7$	0.392560	+	0.947724i	0.0560800	+	0.135389i	0.949436	−	0.313960i	$-0.101656\pi$
$7$	0.392560	+	0.947724i	0.0560800	+	0.135389i	−0.893356	+	0.449349i	$0.851656\pi$
$8$	−5.95043	+	5.95043i	−0.743804	+	0.743804i
$9$	5.75511	−	5.75511i	0.639457	−	0.639457i
$10$	−8.87541			−0.887541
$11$	−12.1914	+	5.04984i	−1.10831	+	0.459076i	−0.860355	−	0.509696i	$-0.829758\pi$
$11$	−12.1914	+	5.04984i	−1.10831	+	0.459076i	−0.247953	+	0.968772i	$0.579758\pi$
$12$	1.79316	−	0.742751i	0.149430	−	0.0618959i
$13$	9.50068	+	22.9367i	0.730821	+	1.76436i	0.639842	+	0.768506i	$0.279000\pi$
$13$	9.50068	+	22.9367i	0.730821	+	1.76436i	0.0909790	+	0.995853i	$0.471000\pi$
$14$	0.542293	−	1.30921i	0.0387352	−	0.0935151i
$15$	5.50793	+	2.28146i	0.367195	+	0.152097i
$16$	3.25833			0.203646
$17$	0.0103812	−	0.0250625i	0.000610660	−	0.00147426i	−0.923574	−	0.383420i	$-0.874746\pi$
$17$	0.0103812	−	0.0250625i	0.000610660	−	0.00147426i	0.924185	+	0.381946i	$0.124746\pi$
$18$	−11.2434			−0.624632
$19$	−4.10513	+	9.91065i	−0.216059	+	0.521613i	−0.994333	−	0.106312i	$-0.966096\pi$
$19$	−4.10513	+	9.91065i	−0.216059	+	0.521613i	0.778273	+	0.627925i	$0.216096\pi$
$20$	−9.50246	−	9.50246i	−0.475123	−	0.475123i
$21$	−0.673076	+	0.673076i	−0.0320512	+	0.0320512i
$22$	16.8415	+	6.97599i	0.765524	+	0.317090i
$23$		−	26.1898i		−	1.13869i	−0.822100	−	0.569343i	$-0.807197\pi$
$23$		−	26.1898i		−	1.13869i	0.822100	−	0.569343i	$-0.192803\pi$
$24$	−7.21426	−	2.98824i	−0.300594	−	0.124510i
$25$		−	16.2782i		−	0.651128i
$26$	13.1245	−	31.6853i	0.504788	−	1.21867i
$27$	14.6931	+	6.08607i	0.544188	+	0.225410i
$28$	1.98231	−	0.821101i	0.0707969	−	0.0293251i
$29$	−9.09988	−	21.9691i	−0.313789	−	0.757554i	−0.999558	−	0.0297342i	$-0.990534\pi$
$29$	−9.09988	−	21.9691i	−0.313789	−	0.757554i	0.685769	−	0.727819i	$-0.259466\pi$
$30$	−3.15167	−	7.60881i	−0.105056	−	0.253627i
$31$			34.6509i			1.11777i	0.829245	+	0.558886i	$0.188771\pi$
$31$			34.6509i			1.11777i	−0.829245	+	0.558886i	$0.811229\pi$
$32$	20.6189	+	20.6189i	0.644342	+	0.644342i
$33$	−8.65836	−	8.65836i	−0.262375	−	0.262375i
$34$	−0.0346220	+	0.0143409i	−0.00101829	+	0.000421792i
$35$	6.08895	+	2.52212i	0.173970	+	0.0720607i
$36$	−12.0377	−	12.0377i	−0.334381	−	0.334381i
$37$	31.8640			0.861190			0.430595	−	0.902545i	$-0.358304\pi$
$37$	31.8640			0.861190			0.430595	+	0.902545i	$0.358304\pi$
$38$	13.6909	−	5.67094i	0.360286	−	0.149235i
$39$	−16.2897	+	16.2897i	−0.417684	+	0.417684i
$40$			54.0660i			1.35165i
$41$	−36.9925	+	17.6792i	−0.902256	+	0.431200i
$41$	−36.9925	+	17.6792i	−0.902256	+	0.431200i
$42$	1.31494			0.0313082
$43$	−26.6842	−	26.6842i	−0.620562	−	0.620562i	0.325113	−	0.945675i	$-0.394598\pi$
$43$	−26.6842	−	26.6842i	−0.620562	−	0.620562i	−0.945675	+	0.325113i	$0.894598\pi$
$44$	10.5625	+	25.5002i	0.240058	+	0.579550i
$45$		−	52.2913i		−	1.16203i
$46$	−25.5826	+	25.5826i	−0.556144	+	0.556144i
$47$	−5.31373	+	12.8285i	−0.113058	+	0.272947i	−0.970273	−	0.242012i	$-0.922193\pi$
$47$	−5.31373	+	12.8285i	−0.113058	+	0.272947i	0.857215	+	0.514958i	$0.172193\pi$
$48$	1.15704	+	2.79334i	0.0241050	+	0.0581946i
$49$	33.9042	−	33.9042i	0.691922	−	0.691922i
$50$	−15.9008	+	15.9008i	−0.318017	+	0.318017i
$51$	0.0251722			0.000493573
$52$	47.9757	−	19.8722i	0.922609	−	0.382157i
$53$	−44.5080	+	18.4358i	−0.839773	+	0.347845i	−0.760764	−	0.649029i	$-0.775176\pi$
$53$	−44.5080	+	18.4358i	−0.839773	+	0.347845i	−0.0790089	+	0.996874i	$0.525176\pi$
$54$	−8.40746	−	20.2974i	−0.155694	−	0.375878i
$55$	−32.4443	+	78.3274i	−0.589896	+	1.42413i
$56$	−7.97527	−	3.30347i	−0.142416	−	0.0589904i
$57$	−9.95405			−0.174632
$58$	−12.5708	+	30.3487i	−0.216738	+	0.523253i
$59$	−2.86012			−0.0484766			−0.0242383	−	0.999706i	$-0.507716\pi$
$59$	−2.86012			−0.0484766			−0.0242383	+	0.999706i	$0.507716\pi$
$60$	4.77203	−	11.5207i	0.0795339	−	0.192012i
$61$	−29.7057	−	29.7057i	−0.486979	−	0.486979i	0.420373	−	0.907351i	$-0.361899\pi$
$61$	−29.7057	−	29.7057i	−0.486979	−	0.486979i	−0.907351	+	0.420373i	$0.861899\pi$
$62$	33.8476	−	33.8476i	0.545929	−	0.545929i
$63$	7.71348	+	3.19503i	0.122436	+	0.0507147i
$64$		−	53.3152i		−	0.833050i
$65$	147.364	+	61.0401i	2.26713	+	0.939078i
$66$			16.9153i			0.256292i
$67$	14.9886	−	36.1856i	0.223710	−	0.540083i	−0.771678	−	0.636013i	$-0.780582\pi$
$67$	14.9886	−	36.1856i	0.223710	−	0.540083i	0.995388	+	0.0959298i	$0.0305824\pi$
$68$	−0.0524222	−	0.0217140i	−0.000770914	−	0.000319323i
$69$	22.4523	−	9.30003i	0.325395	−	0.134783i
$70$	−3.48413	−	8.41144i	−0.0497733	−	0.120163i
$71$	−22.4314	−	54.1541i	−0.315935	−	0.762734i	−0.999462	−	0.0328086i	$-0.989555\pi$
$71$	−22.4314	−	54.1541i	−0.315935	−	0.762734i	0.683527	−	0.729925i	$-0.260445\pi$
$72$			68.4908i			0.951261i
$73$	−56.7726	−	56.7726i	−0.777707	−	0.777707i	0.201734	−	0.979440i	$-0.435342\pi$
$73$	−56.7726	−	56.7726i	−0.777707	−	0.777707i	−0.979440	+	0.201734i	$0.935342\pi$
$74$	−31.1253	−	31.1253i	−0.420612	−	0.420612i
$75$	13.9552	−	5.78042i	0.186069	−	0.0770722i
$76$	20.7297	+	8.58652i	0.272759	+	0.112981i
$77$	−9.57171	−	9.57171i	−0.124308	−	0.124308i
$78$	31.8241			0.408001
$79$	−134.955	+	55.9004i	−1.70830	+	0.707600i	−0.708299	+	0.705913i	$0.750537\pi$
$79$	−134.955	+	55.9004i	−1.70830	+	0.707600i	−0.999999	+	0.00168717i	$0.999463\pi$
$80$	14.8027	−	14.8027i	0.185034	−	0.185034i
$81$		−	58.4932i		−	0.722138i
$82$	53.4042	+	18.8656i	0.651271	+	0.230068i
$83$	127.971			1.54182			0.770910	−	0.636944i	$-0.219802\pi$
$83$	127.971			1.54182			0.770910	+	0.636944i	$0.219802\pi$
$84$	1.40785	+	1.40785i	0.0167601	+	0.0167601i
$85$	−0.0666974	−	0.161022i	−0.000784676	−	0.00189437i
$86$			52.1311i			0.606175i
$87$	15.6025	−	15.6025i	0.179339	−	0.179339i
$88$	42.4953	−	102.593i	0.482901	−	1.16583i
$89$	−39.5582	−	95.5019i	−0.444474	−	1.07306i	−0.974362	−	0.224987i	$-0.927766\pi$
$89$	−39.5582	−	95.5019i	−0.444474	−	1.07306i	0.529888	−	0.848068i	$-0.322234\pi$
$90$	−51.0790	+	51.0790i	−0.567544	+	0.567544i
$91$	−18.0080	+	18.0080i	−0.197891	+	0.197891i
$92$	−54.7801			−0.595436
$93$	−29.7059	+	12.3046i	−0.319418	+	0.132307i
$94$	17.7216	−	7.34054i	0.188528	−	0.0780908i
$95$	26.3747	+	63.6741i	0.277628	+	0.670254i
$96$	−10.3546	+	24.9982i	−0.107861	+	0.260398i
$97$	109.949	+	45.5425i	1.13350	+	0.469511i	0.868969	−	0.494867i	$-0.164783\pi$
$97$	109.949	+	45.5425i	1.13350	+	0.469511i	0.264530	+	0.964377i	$0.414783\pi$
$98$	−66.2363			−0.675881
$99$	−41.1004	+	99.2252i	−0.415156	+	1.00227i
$100$	−34.0485			−0.340485
$101$	5.69079	−	13.7388i	0.0563444	−	0.136028i	−0.893200	−	0.449659i	$-0.851546\pi$
$101$	5.69079	−	13.7388i	0.0563444	−	0.136028i	0.949545	+	0.313631i	$0.101546\pi$
$102$	−0.0245887	−	0.0245887i	−0.000241065	−	0.000241065i
$103$	−19.3162	+	19.3162i	−0.187536	+	0.187536i	−0.794630	−	0.607094i	$-0.792335\pi$
$103$	−19.3162	+	19.3162i	−0.187536	+	0.187536i	0.607094	+	0.794630i	$0.292335\pi$
$104$	−193.016	−	79.9500i	−1.85593	−	0.768750i
$105$			6.11561i			0.0582439i
$106$	61.4845	+	25.4677i	0.580043	+	0.240262i
$107$			186.847i			1.74623i	0.487513	+	0.873115i	$0.337904\pi$
$107$			186.847i			1.74623i	−0.487513	+	0.873115i	$0.662096\pi$
$108$	12.7300	−	30.7329i	0.117870	−	0.284564i
$109$	−44.4400	−	18.4077i	−0.407706	−	0.168878i	0.169398	−	0.985548i	$-0.445818\pi$
$109$	−44.4400	−	18.4077i	−0.407706	−	0.168878i	−0.577105	+	0.816670i	$0.695818\pi$
$110$	108.204	−	44.8194i	0.983669	−	0.407449i
$111$	11.3150	+	27.3167i	0.101937	+	0.246097i
$112$	1.27909	+	3.08800i	0.0114205	+	0.0275714i
$113$			126.114i			1.11605i	0.829824	+	0.558025i	$0.188441\pi$
$113$			126.114i			1.11605i	−0.829824	+	0.558025i	$0.811559\pi$
$114$	9.72328	+	9.72328i	0.0852919	+	0.0852919i
$115$	−118.981	−	118.981i	−1.03462	−	1.03462i
$116$	−45.9518	+	19.0338i	−0.396136	+	0.164085i
$117$	186.681	+	77.3256i	1.59556	+	0.660903i
$118$	2.79381	+	2.79381i	0.0236764	+	0.0236764i
$119$	0.0278276			0.000233845
$120$	−46.3503	+	19.1989i	−0.386252	+	0.159991i
$121$	37.5692	−	37.5692i	0.310489	−	0.310489i
$122$			58.0340i			0.475689i
$123$	−28.2923	−	25.4354i	−0.230019	−	0.206792i
$124$	72.4779			0.584499
$125$	39.6233	+	39.6233i	0.316987	+	0.316987i
$126$	−4.41370	−	10.6556i	−0.0350294	−	0.0845684i
$127$		−	134.706i		−	1.06068i	−0.847786	−	0.530338i	$-0.822065\pi$
$127$		−	134.706i		−	1.06068i	0.847786	−	0.530338i	$-0.177935\pi$
$128$	30.3966	−	30.3966i	0.237473	−	0.237473i
$129$	13.4005	−	32.3517i	0.103880	−	0.250788i
$130$	−84.3224	−	203.572i	−0.648634	−	1.56594i
$131$	59.5935	−	59.5935i	0.454912	−	0.454912i	−0.442069	−	0.896981i	$-0.645755\pi$
$131$	59.5935	−	59.5935i	0.454912	−	0.454912i	0.896981	+	0.442069i	$0.145755\pi$
$132$	−18.1103	+	18.1103i	−0.137199	+	0.137199i
$133$	−11.0041			−0.0827374
$134$	−49.9878	+	20.7056i	−0.373043	+	0.154519i
$135$	94.4002	−	39.1018i	0.699261	−	0.289643i
$136$	0.0873599	+	0.210906i	0.000642352	+	0.00155078i
$137$	−19.9933	+	48.2682i	−0.145937	+	0.352323i	−0.979898	−	0.199501i	$-0.936068\pi$
$137$	−19.9933	+	48.2682i	−0.145937	+	0.352323i	0.833961	+	0.551824i	$0.186068\pi$
$138$	−31.0162	−	12.8473i	−0.224755	−	0.0930965i
$139$	197.683			1.42218			0.711090	−	0.703101i	$-0.248202\pi$
$139$	197.683			1.42218			0.711090	+	0.703101i	$0.248202\pi$
$140$	5.27542	−	12.7360i	0.0376816	−	0.0909714i
$141$	−12.8847			−0.0913805
$142$	−30.9873	+	74.8100i	−0.218220	+	0.526831i
$143$	−231.653	−	231.653i	−1.61995	−	1.61995i
$144$	18.7521	−	18.7521i	0.130223	−	0.130223i
$145$	−141.147	−	58.4650i	−0.973428	−	0.403207i
$146$			110.913i			0.759677i
$147$	41.1051	+	17.0263i	0.279627	+	0.115825i
$148$		−	66.6486i		−	0.450329i
$149$	16.0243	−	38.6861i	0.107546	−	0.259639i	−0.860940	−	0.508706i	$-0.830124\pi$
$149$	16.0243	−	38.6861i	0.107546	−	0.259639i	0.968486	+	0.249067i	$0.0801241\pi$
$150$	−19.2780	−	7.98522i	−0.128520	−	0.0532348i
$151$	205.755	−	85.2263i	1.36261	−	0.564413i	0.422838	−	0.906205i	$-0.361034\pi$
$151$	205.755	−	85.2263i	1.36261	−	0.564413i	0.939775	+	0.341793i	$0.111034\pi$
$152$	−34.5454	−	83.4000i	−0.227272	−	0.548684i
$153$	−0.0844923	−	0.203983i	−0.000552238	−	0.00133322i
$154$			18.6996i			0.121426i
$155$	157.420	+	157.420i	1.01561	+	1.01561i
$156$	34.0725	+	34.0725i	0.218413	+	0.218413i
$157$	−49.9163	+	20.6760i	−0.317938	+	0.131694i	−0.535945	−	0.844253i	$-0.680045\pi$
$157$	−49.9163	+	20.6760i	−0.317938	+	0.131694i	0.218007	+	0.975947i	$0.430045\pi$
$158$	186.431	+	77.2223i	1.17994	+	0.488749i
$159$	−31.6097	−	31.6097i	−0.198803	−	0.198803i
$160$	187.345			1.17091
$161$	24.8207	−	10.2811i	0.154166	−	0.0638576i
$162$	−57.1371	+	57.1371i	−0.352698	+	0.352698i
$163$			173.848i			1.06655i	0.845942	+	0.533275i	$0.179039\pi$
$163$			173.848i			1.06655i	−0.845942	+	0.533275i	$0.820961\pi$
$164$	36.9789	+	77.3757i	0.225481	+	0.471803i
$165$	−78.6703			−0.476790
$166$	−125.004	−	125.004i	−0.753038	−	0.753038i
$167$	−109.618	−	264.642i	−0.656397	−	1.58468i	−0.803328	−	0.595537i	$-0.796939\pi$
$167$	−109.618	−	264.642i	−0.656397	−	1.58468i	0.146931	−	0.989147i	$-0.453061\pi$
$168$		−	8.01019i		−	0.0476797i
$169$	−316.327	+	316.327i	−1.87176	+	1.87176i
$170$	−0.0921377	+	0.222440i	−0.000541986	+	0.00130847i
$171$	33.4115	+	80.6624i	0.195389	+	0.471710i
$172$	−55.8141	+	55.8141i	−0.324501	+	0.324501i
$173$	−146.640	+	146.640i	−0.847633	+	0.847633i	−0.989837	−	0.142205i	$-0.954581\pi$
$173$	−146.640	+	146.640i	−0.847633	+	0.847633i	0.142205	+	0.989837i	$0.454581\pi$
$174$	−30.4815			−0.175181
$175$	15.4272	−	6.39018i	0.0881557	−	0.0365153i
$176$	−39.7236	+	16.4541i	−0.225702	+	0.0934890i
$177$	−1.01563	−	2.45195i	−0.00573804	−	0.0138528i
$178$	−54.6468	+	131.929i	−0.307004	+	0.741174i
$179$	76.2003	+	31.5632i	0.425700	+	0.176331i	0.585239	−	0.810861i	$-0.301001\pi$
$179$	76.2003	+	31.5632i	0.425700	+	0.176331i	−0.159539	+	0.987192i	$0.551001\pi$
$180$	−109.375			−0.607641
$181$	9.24361	−	22.3160i	0.0510697	−	0.123293i	−0.896286	−	0.443477i	$-0.853745\pi$
$181$	9.24361	−	22.3160i	0.0510697	−	0.123293i	0.947355	+	0.320184i	$0.103745\pi$
$182$	35.1811			0.193303
$183$	14.9179	−	36.0149i	0.0815185	−	0.196803i
$184$	155.841	+	155.841i	0.846960	+	0.846960i
$185$	144.759	−	144.759i	0.782482	−	0.782482i
$186$	41.0366	+	16.9979i	0.220627	+	0.0913865i
$187$			0.357970i			0.00191428i
$188$	26.8328	+	11.1145i	0.142728	+	0.0591197i
$189$			16.3141i			0.0863181i
$190$	36.4347	−	87.9611i	0.191762	−	0.462953i
$191$	29.2722	+	12.1249i	0.153258	+	0.0634814i	0.457994	−	0.888955i	$-0.348568\pi$
$191$	29.2722	+	12.1249i	0.153258	+	0.0634814i	−0.304736	+	0.952437i	$0.598568\pi$
$192$	45.7066	−	18.9323i	0.238055	−	0.0986057i
$193$	−11.5961	−	27.9955i	−0.0600836	−	0.145055i	0.890987	−	0.454030i	$-0.150014\pi$
$193$	−11.5961	−	27.9955i	−0.0600836	−	0.145055i	−0.951070	+	0.308975i	$0.900014\pi$
$194$	−62.9137	−	151.887i	−0.324298	−	0.782923i
$195$			148.009i			0.759021i
$196$	−70.9159	−	70.9159i	−0.361816	−	0.361816i
$197$	−20.2031	−	20.2031i	−0.102554	−	0.102554i	0.653968	−	0.756522i	$-0.273103\pi$
$197$	−20.2031	−	20.2031i	−0.102554	−	0.102554i	−0.756522	+	0.653968i	$0.773103\pi$
$198$	137.072	−	56.7772i	0.692285	−	0.286754i
$199$	−340.170	−	140.903i	−1.70940	−	0.708055i	−0.999995	−	0.00325106i	$-0.998965\pi$
$199$	−340.170	−	140.903i	−1.70940	−	0.708055i	−0.709402	−	0.704804i	$-0.751035\pi$
$200$	96.8624	+	96.8624i	0.484312	+	0.484312i
$201$	36.3440			0.180816
$202$	−18.9791	+	7.86141i	−0.0939561	+	0.0389179i
$203$	17.2483	−	17.2483i	0.0849672	−	0.0849672i
$204$		−	0.0526517i		−	0.000258097i
$205$	−87.7409	+	248.375i	−0.428004	+	1.21159i
$206$	37.7367			0.183188
$207$	−150.725	−	150.725i	−0.728141	−	0.728141i
$208$	30.9564	+	74.7353i	0.148829	+	0.359304i
$209$		−	141.555i		−	0.677296i
$210$	5.97383	−	5.97383i	0.0284468	−	0.0284468i
$211$	125.807	−	303.724i	0.596240	−	1.43945i	−0.281147	−	0.959665i	$-0.590715\pi$
$211$	125.807	−	303.724i	0.596240	−	1.43945i	0.877386	−	0.479785i	$-0.159285\pi$
$212$	38.5614	+	93.0955i	0.181893	+	0.439129i
$213$	38.4604	−	38.4604i	0.180565	−	0.180565i
$214$	182.515	−	182.515i	0.852874	−	0.852874i
$215$	−242.454			−1.12769
$216$	−123.645	+	51.2154i	−0.572430	+	0.237108i
$217$	−32.8395	+	13.6026i	−0.151334	+	0.0626846i
$218$	25.4288	+	61.3906i	0.116646	+	0.281608i
$219$	28.5106	−	68.8306i	0.130185	−	0.314295i
$220$	163.834	+	67.8623i	0.744701	+	0.308465i
$221$	0.673479			0.00304742
$222$	15.6308	−	37.7361i	0.0704090	−	0.169982i
$223$	−58.2357			−0.261147			−0.130573	−	0.991439i	$-0.541682\pi$
$223$	−58.2357			−0.261147			−0.130573	+	0.991439i	$0.541682\pi$
$224$	−11.4469	+	27.6352i	−0.0511022	+	0.123372i
$225$	−93.6829	−	93.6829i	−0.416368	−	0.416368i
$226$	123.190	−	123.190i	0.545088	−	0.545088i
$227$	126.084	+	52.2256i	0.555435	+	0.230069i	0.642702	−	0.766116i	$-0.277813\pi$
$227$	126.084	+	52.2256i	0.555435	+	0.230069i	−0.0872669	+	0.996185i	$0.527813\pi$
$228$			20.8205i			0.0913178i
$229$	237.862	+	98.5256i	1.03870	+	0.430243i	0.835845	−	0.548966i	$-0.184978\pi$
$229$	237.862	+	98.5256i	1.03870	+	0.430243i	0.202854	+	0.979209i	$0.434978\pi$
$230$			232.445i			1.01063i
$231$	4.80681	−	11.6047i	0.0208087	−	0.0502366i
$232$	184.874	+	76.5772i	0.796869	+	0.330074i
$233$	−18.3963	+	7.61999i	−0.0789540	+	0.0327038i	−0.421811	−	0.906684i	$-0.638605\pi$
$233$	−18.3963	+	7.61999i	−0.0789540	+	0.0327038i	0.342857	+	0.939388i	$0.388605\pi$
$234$	−106.820	−	257.886i	−0.456494	−	1.10208i
$235$	34.1397	+	82.4206i	0.145275	+	0.350726i
$236$			5.98239i			0.0253491i
$237$	−95.8458	−	95.8458i	−0.404413	−	0.404413i
$238$	−0.0271824	−	0.0271824i	−0.000114212	−	0.000114212i
$239$	270.876	−	112.201i	1.13337	−	0.469458i	0.264446	−	0.964400i	$-0.414811\pi$
$239$	270.876	−	112.201i	1.13337	−	0.469458i	0.868926	+	0.494942i	$0.164811\pi$
$240$	17.9467	+	7.43376i	0.0747778	+	0.0309740i
$241$	202.230	+	202.230i	0.839130	+	0.839130i	0.988744	−	0.149614i	$-0.0478032\pi$
$241$	202.230	+	202.230i	0.839130	+	0.839130i	−0.149614	+	0.988744i	$0.547803\pi$
$242$	−73.3964			−0.303291
$243$	182.383	−	75.5456i	0.750548	−	0.310887i
$244$	−62.1341	+	62.1341i	−0.254648	+	0.254648i
$245$		−	308.055i		−	1.25737i
$246$	2.79066	+	52.4821i	0.0113442	+	0.213342i
$247$	−266.319			−1.07821
$248$	−206.188	−	206.188i	−0.831403	−	0.831403i
$249$	45.4427	+	109.708i	0.182501	+	0.440596i
$250$		−	77.4095i		−	0.309638i
$251$	−66.1533	+	66.1533i	−0.263559	+	0.263559i	−0.826498	−	0.562939i	$-0.809670\pi$
$251$	−66.1533	+	66.1533i	−0.263559	+	0.263559i	0.562939	+	0.826498i	$0.309670\pi$
$252$	6.68291	−	16.1340i	0.0265195	−	0.0640237i
$253$	132.254	+	319.290i	0.522744	+	1.26202i
$254$	−131.583	+	131.583i	−0.518043	+	0.518043i
$255$	0.114358	−	0.114358i	0.000448463	−	0.000448463i
$256$	−272.645			−1.06502
$257$	−85.0452	+	35.2269i	−0.330915	+	0.137070i	−0.541954	−	0.840408i	$-0.682315\pi$
$257$	−85.0452	+	35.2269i	−0.330915	+	0.137070i	0.211039	+	0.977478i	$0.432315\pi$
$258$	−44.6915	+	18.5118i	−0.173223	+	0.0717512i
$259$	12.5085	+	30.1983i	0.0482955	+	0.116596i
$260$	127.675	−	308.235i	0.491058	−	1.18552i
$261$	−178.805	−	74.0635i	−0.685077	−	0.283768i
$262$	−116.424			−0.444366
$263$	−64.9572	+	156.821i	−0.246986	+	0.596276i	−0.997945	−	0.0640720i	$-0.979591\pi$
$263$	−64.9572	+	156.821i	−0.246986	+	0.596276i	0.750960	+	0.660348i	$0.229591\pi$
$264$	103.042			0.390311
$265$	−118.447	+	285.955i	−0.446968	+	1.07908i
$266$	10.7490	+	10.7490i	0.0404096	+	0.0404096i
$267$	67.8257	−	67.8257i	0.254029	−	0.254029i
$268$	−75.6879	−	31.3509i	−0.282417	−	0.116981i
$269$		−	48.3404i		−	0.179704i	−0.995955	−	0.0898521i	$-0.971361\pi$
$269$		−	48.3404i		−	0.179704i	0.995955	−	0.0898521i	$-0.0286394\pi$
$270$	−130.407	−	54.0164i	−0.482989	−	0.200061i
$271$		−	34.7684i		−	0.128297i	−0.997940	−	0.0641484i	$-0.979567\pi$
$271$		−	34.7684i		−	0.128297i	0.997940	−	0.0641484i	$-0.0204331\pi$
$272$	0.0338255	−	0.0816620i	0.000124358	−	0.000300228i
$273$	−21.8328	−	9.04344i	−0.0799736	−	0.0331262i
$274$	66.6790	−	27.6193i	0.243354	−	0.100801i
$275$	82.2023	+	198.454i	0.298918	+	0.721651i
$276$	−19.4525	−	46.9625i	−0.0704800	−	0.170154i
$277$		−	282.188i		−	1.01873i	−0.860551	−	0.509364i	$-0.829881\pi$
$277$		−	282.188i		−	1.01873i	0.860551	−	0.509364i	$-0.170119\pi$
$278$	−193.100	−	193.100i	−0.694605	−	0.694605i
$279$	199.420	+	199.420i	0.714766	+	0.714766i
$280$	−51.2396	+	21.2241i	−0.182999	+	0.0758005i
$281$	171.362	+	70.9804i	0.609829	+	0.252599i	0.666155	−	0.745813i	$-0.267939\pi$
$281$	171.362	+	70.9804i	0.609829	+	0.252599i	−0.0563266	+	0.998412i	$0.517939\pi$
$282$	12.5859	+	12.5859i	0.0446310	+	0.0446310i
$283$	39.0466			0.137974			0.0689869	−	0.997618i	$-0.478023\pi$
$283$	39.0466			0.137974			0.0689869	+	0.997618i	$0.478023\pi$
$284$	−113.272	+	46.9188i	−0.398845	+	0.165207i
$285$	−45.2215	+	45.2215i	−0.158672	+	0.158672i
$286$			452.565i			1.58239i
$287$	−31.2768	−	28.1185i	−0.108978	−	0.0979740i
$288$	237.329			0.824058
$289$	204.353	+	204.353i	0.707105	+	0.707105i
$290$	80.7652	+	194.984i	0.278501	+	0.672360i
$291$			110.431i			0.379487i
$292$	−118.749	+	118.749i	−0.406674	+	0.406674i
$293$	6.24629	−	15.0799i	0.0213184	−	0.0514672i	−0.912862	−	0.408269i	$-0.866133\pi$
$293$	6.24629	−	15.0799i	0.0213184	−	0.0514672i	0.934180	+	0.356801i	$0.116133\pi$
$294$	−23.5206	−	56.7838i	−0.0800020	−	0.193142i
$295$	−12.9936	+	12.9936i	−0.0440461	+	0.0440461i
$296$	−189.605	+	189.605i	−0.640556	+	0.640556i
$297$	−209.863			−0.706608
$298$	−53.4421	+	22.1364i	−0.179336	+	0.0742834i
$299$	600.707	−	248.821i	2.00905	−	0.832177i
$300$	−12.0907	−	29.1894i	−0.0403022	−	0.0972981i
$301$	14.8141	−	35.7644i	0.0492162	−	0.118818i
$302$	−284.235	−	117.734i	−0.941176	−	0.389848i
$303$	13.7989			0.0455410
$304$	−13.3759	+	32.2922i	−0.0439996	+	0.106224i
$305$	−269.908			−0.884943
$306$	−0.116720	+	0.281787i	−0.000381438	+	0.000920873i
$307$	61.0974	+	61.0974i	0.199014	+	0.199014i	0.799577	−	0.600563i	$-0.205057\pi$
$307$	61.0974	+	61.0974i	0.199014	+	0.199014i	−0.600563	+	0.799577i	$0.705057\pi$
$308$	−20.0207	+	20.0207i	−0.0650024	+	0.0650024i
$309$	−23.4188	−	9.70037i	−0.0757889	−	0.0313928i
$310$		−	307.541i		−	0.992068i
$311$	−186.824	−	77.3851i	−0.600720	−	0.248827i	0.0615347	−	0.998105i	$-0.480401\pi$
$311$	−186.824	−	77.3851i	−0.600720	−	0.248827i	−0.662255	+	0.749278i	$0.730401\pi$
$312$		−	193.861i		−	0.621351i
$313$	120.502	−	290.918i	0.384991	−	0.929451i	−0.605993	−	0.795470i	$-0.707224\pi$
$313$	120.502	−	290.918i	0.384991	−	0.929451i	0.990984	−	0.133981i	$-0.0427760\pi$
$314$	68.9558	+	28.5624i	0.219604	+	0.0909631i
$315$	49.5577	−	20.5275i	0.157326	−	0.0651665i
$316$	116.925	+	282.281i	0.370014	+	0.893294i
$317$	134.543	+	324.816i	0.424427	+	1.02466i	0.981026	+	0.193876i	$0.0621059\pi$
$317$	134.543	+	324.816i	0.424427	+	1.02466i	−0.556599	+	0.830781i	$0.687894\pi$
$318$			61.7537i			0.194194i
$319$	221.880	+	221.880i	0.695550	+	0.695550i
$320$	−242.212	−	242.212i	−0.756914	−	0.756914i
$321$	−160.182	+	66.3495i	−0.499009	+	0.206696i
$322$	−34.2880	−	14.2026i	−0.106484	−	0.0441073i
$323$	0.205770	+	0.205770i	0.000637057	+	0.000637057i
$324$	−122.348			−0.377617
$325$	373.368	−	154.654i	1.14882	−	0.475859i
$326$	169.817	−	169.817i	0.520912	−	0.520912i
$327$		−	44.6346i		−	0.136497i
$328$	114.922	−	325.320i	0.350373	−	0.991831i
$329$	−14.2438			−0.0432943
$330$	76.8465	+	76.8465i	0.232868	+	0.232868i
$331$	−211.171	−	509.812i	−0.637979	−	1.54022i	−0.829367	−	0.558704i	$-0.811299\pi$
$331$	−211.171	−	509.812i	−0.637979	−	1.54022i	0.191388	−	0.981515i	$-0.438701\pi$
$332$		−	267.672i		−	0.806240i
$333$	183.381	−	183.381i	0.550694	−	0.550694i
$334$	−151.430	+	365.584i	−0.453383	+	1.09456i
$335$	−96.2987	−	232.486i	−0.287459	−	0.693987i
$336$	−2.19311	+	2.19311i	−0.00652710	+	0.00652710i
$337$	−53.5413	+	53.5413i	−0.158876	+	0.158876i	−0.782069	−	0.623192i	$-0.785835\pi$
$337$	−53.5413	+	53.5413i	−0.158876	+	0.158876i	0.623192	+	0.782069i	$0.285835\pi$
$338$	617.986			1.82836
$339$	−108.116	+	44.7831i	−0.318926	+	0.132104i
$340$	−0.336803	+	0.139508i	−0.000990596	+	0.000410318i
$341$	−174.982	−	422.443i	−0.513142	−	1.23884i
$342$	46.1555	−	111.429i	0.134958	−	0.325816i
$343$	91.8797	+	38.0578i	0.267871	+	0.110956i
$344$	317.565			0.923153
$345$	59.7510	−	144.252i	0.173191	−	0.418121i
$346$	286.482			0.827982
$347$	3.37585	−	8.15002i	0.00972867	−	0.0234871i	−0.918941	−	0.394396i	$-0.870954\pi$
$347$	3.37585	−	8.15002i	0.00972867	−	0.0234871i	0.928669	+	0.370909i	$0.120954\pi$
$348$	−32.6351	−	32.6351i	−0.0937789	−	0.0937789i
$349$	−260.720	+	260.720i	−0.747049	+	0.747049i	−0.973924	−	0.226875i	$-0.927149\pi$
$349$	−260.720	+	260.720i	−0.747049	+	0.747049i	0.226875	+	0.973924i	$0.427149\pi$
$350$	−21.3116	−	8.82756i	−0.0608904	−	0.0252216i
$351$			394.832i			1.12488i
$352$	−355.496	−	147.251i	−1.00993	−	0.418327i
$353$			60.9340i			0.172618i	0.996268	+	0.0863088i	$0.0275072\pi$
$353$			60.9340i			0.172618i	−0.996268	+	0.0863088i	$0.972493\pi$
$354$	−1.40302	+	3.38720i	−0.00396334	+	0.00956835i
$355$	−347.930	−	144.117i	−0.980084	−	0.405964i
$356$	−199.757	+	82.7422i	−0.561116	+	0.232422i
$357$	0.00988161	+	0.0238563i	2.76796e−5	+	6.68244e-5i
$358$	−43.6023	−	105.265i	−0.121794	−	0.294037i
$359$			86.3019i			0.240395i	0.992750	+	0.120198i	$0.0383528\pi$
$359$			86.3019i			0.240395i	−0.992750	+	0.120198i	$0.961647\pi$
$360$	311.156	+	311.156i	0.864321	+	0.864321i
$361$	173.897	+	173.897i	0.481708	+	0.481708i
$362$	−30.8280	+	12.7694i	−0.0851602	+	0.0352745i
$363$	45.5486	+	18.8668i	0.125478	+	0.0519748i
$364$	37.6667	+	37.6667i	0.103480	+	0.103480i
$365$	−515.839			−1.41326
$366$	−49.7520	+	20.6080i	−0.135935	+	0.0563059i
$367$	306.208	−	306.208i	0.834354	−	0.834354i	−0.153755	−	0.988109i	$-0.549137\pi$
$367$	306.208	−	306.208i	0.834354	−	0.834354i	0.988109	+	0.153755i	$0.0491366\pi$
$368$		−	85.3351i		−	0.231889i
$369$	−111.150	+	314.642i	−0.301220	+	0.852688i
$370$	−282.806			−0.764341
$371$	−34.9441	−	34.9441i	−0.0941890	−	0.0941890i
$372$	25.7370	+	62.1346i	0.0691855	+	0.167028i
$373$			478.326i			1.28238i	0.767384	+	0.641188i	$0.221558\pi$
$373$			478.326i			1.28238i	−0.767384	+	0.641188i	$0.778442\pi$
$374$	0.349671	−	0.349671i	0.000934950	−	0.000934950i
$375$	−19.8984	+	48.0390i	−0.0530624	+	0.128104i
$376$	−44.7160	−	107.954i	−0.118926	−	0.287112i
$377$	417.442	−	417.442i	1.10727	−	1.10727i
$378$	15.9359	−	15.9359i	0.0421585	−	0.0421585i
$379$	40.5044			0.106872			0.0534358	−	0.998571i	$-0.482983\pi$
$379$	40.5044			0.106872			0.0534358	+	0.998571i	$0.482983\pi$
$380$	133.184	−	55.1668i	0.350485	−	0.145176i
$381$	115.482	−	47.8342i	0.303103	−	0.125549i
$382$	−16.7497	−	40.4374i	−0.0438475	−	0.105857i
$383$	−198.505	+	479.232i	−0.518289	+	1.25126i	0.420665	+	0.907216i	$0.361797\pi$
$383$	−198.505	+	479.232i	−0.518289	+	1.25126i	−0.938954	+	0.344043i	$0.888203\pi$
$384$	36.8526	+	15.2648i	0.0959703	+	0.0397522i
$385$	−86.9691			−0.225894
$386$	−16.0192	+	38.6738i	−0.0415006	+	0.100191i
$387$	−307.141			−0.793645
$388$	95.2594	−	229.977i	0.245514	−	0.592723i
$389$	233.701	+	233.701i	0.600774	+	0.600774i	0.940518	−	0.339744i	$-0.110341\pi$
$389$	233.701	+	233.701i	0.600774	+	0.600774i	−0.339744	+	0.940518i	$0.610341\pi$
$390$	144.578	−	144.578i	0.370712	−	0.370712i
$391$	−0.656382	−	0.271882i	−0.00167873	−	0.000695351i
$392$			403.489i			1.02931i
$393$	72.2506	+	29.9272i	0.183844	+	0.0761506i
$394$			39.4695i			0.100176i
$395$	−359.150	+	867.064i	−0.909239	+	2.19510i
$396$	207.545	+	85.9680i	0.524104	+	0.217091i
$397$	118.294	−	48.9989i	0.297970	−	0.123423i	−0.228690	−	0.973499i	$-0.573444\pi$
$397$	118.294	−	48.9989i	0.297970	−	0.123423i	0.526660	+	0.850076i	$0.323444\pi$
$398$	194.647	+	469.920i	0.489063	+	1.18070i
$399$	−3.90756	−	9.43369i	−0.00979339	−	0.0236433i
$400$		−	53.0398i		−	0.132600i
$401$	−440.267	−	440.267i	−1.09792	−	1.09792i	−0.994653	−	0.103270i	$-0.967070\pi$
$401$	−440.267	−	440.267i	−1.09792	−	1.09792i	−0.103270	−	0.994653i	$-0.532930\pi$
$402$	−35.5014	−	35.5014i	−0.0883121	−	0.0883121i
$403$	−794.776	+	329.207i	−1.97215	+	0.816891i
$404$	−28.7368	−	11.9032i	−0.0711308	−	0.0294633i
$405$	−265.736	−	265.736i	−0.656139	−	0.656139i
$406$	−33.6969			−0.0829974
$407$	−388.467	+	160.908i	−0.954463	+	0.395352i
$408$	−0.149786	+	0.149786i	−0.000367122	+	0.000367122i
$409$		−	444.887i		−	1.08774i	−0.839169	−	0.543871i	$-0.816958\pi$
$409$		−	444.887i		−	1.08774i	0.839169	−	0.543871i	$-0.183042\pi$
$410$	328.324	−	156.910i	0.800790	−	0.382708i
$411$	−48.4795			−0.117955
$412$	40.4028	+	40.4028i	0.0980650	+	0.0980650i
$413$	−1.12277	−	2.71060i	−0.00271857	−	0.00656320i
$414$			294.462i			0.711260i
$415$	581.376	−	581.376i	1.40091	−	1.40091i
$416$	−277.036	+	668.824i	−0.665952	+	1.60775i
$417$	70.1975	+	169.472i	0.168339	+	0.406407i
$418$	−138.273	+	138.273i	−0.330797	+	0.330797i
$419$	434.530	−	434.530i	1.03706	−	1.03706i	0.0377779	−	0.999286i	$-0.487972\pi$
$419$	434.530	−	434.530i	1.03706	−	1.03706i	0.999286	−	0.0377779i	$-0.0120279\pi$
$420$	12.7918			0.0304566
$421$	390.608	−	161.795i	0.927811	−	0.384312i	0.132963	−	0.991121i	$-0.457551\pi$
$421$	390.608	−	161.795i	0.927811	−	0.384312i	0.794848	+	0.606809i	$0.207551\pi$
$422$	−419.572	+	173.793i	−0.994248	+	0.411831i
$423$	43.2482	+	104.410i	0.102242	+	0.246833i
$424$	155.141	−	374.543i	0.365898	−	0.883355i
$425$	−0.407973	−	0.168988i	−0.000959936	−	0.000397618i
$426$	−75.1375			−0.176379
$427$	16.4915	−	39.8141i	0.0386218	−	0.0932414i
$428$	390.819			0.913130
$429$	116.334	−	280.854i	0.271174	−	0.654672i
$430$	236.833	+	236.833i	0.550774	+	0.550774i
$431$	−487.076	+	487.076i	−1.13011	+	1.13011i	−0.139949	+	0.990159i	$0.544694\pi$
$431$	−487.076	+	487.076i	−1.13011	+	1.13011i	−0.990159	+	0.139949i	$0.955306\pi$
$432$	47.8749	+	19.8304i	0.110822	+	0.0459038i
$433$		−	461.455i		−	1.06572i	−0.846204	−	0.532858i	$-0.821118\pi$
$433$		−	461.455i		−	1.06572i	0.846204	−	0.532858i	$-0.178882\pi$
$434$	45.3654	+	18.7910i	0.104529	+	0.0432971i
$435$		−	141.765i		−	0.325897i
$436$	−38.5025	+	92.9533i	−0.0883085	+	0.213196i
$437$	259.558	+	107.512i	0.593954	+	0.246024i
$438$	−95.0845	+	39.3853i	−0.217088	+	0.0899208i
$439$	−168.872	−	407.694i	−0.384675	−	0.928688i	−0.991048	−	0.133508i	$-0.957376\pi$
$439$	−168.872	−	407.694i	−0.384675	−	0.928688i	0.606373	−	0.795181i	$-0.292624\pi$
$440$	−273.024	−	659.139i	−0.620510	−	1.49804i
$441$		−	390.244i		−	0.884908i
$442$	−0.657865	−	0.657865i	−0.00148838	−	0.00148838i
$443$	330.755	+	330.755i	0.746625	+	0.746625i	0.973844	−	0.227219i	$-0.0729633\pi$
$443$	330.755	+	330.755i	0.746625	+	0.746625i	−0.227219	+	0.973844i	$0.572963\pi$
$444$	57.1373	−	23.6670i	0.128688	−	0.0533041i
$445$	−613.582	−	254.154i	−1.37884	−	0.571132i
$446$	56.8856	+	56.8856i	0.127546	+	0.127546i
$447$	38.8555			0.0869251
$448$	50.5281	−	20.9294i	0.112786	−	0.0467174i
$449$	52.0447	−	52.0447i	0.115912	−	0.115912i	−0.646771	−	0.762684i	$-0.723881\pi$
$449$	52.0447	−	52.0447i	0.115912	−	0.115912i	0.762684	+	0.646771i	$0.223881\pi$
$450$			183.022i			0.406716i
$451$	361.713	−	402.340i	0.802024	−	0.892107i
$452$	263.786			0.583598
$453$	146.127	+	146.127i	0.322577	+	0.322577i
$454$	−72.1459	−	174.176i	−0.158912	−	0.383647i
$455$			163.622i			0.359609i
$456$	59.2309	−	59.2309i	0.129892	−	0.129892i
$457$	248.956	−	601.032i	0.544761	−	1.31517i	−0.376570	−	0.926388i	$-0.622897\pi$
$457$	248.956	−	601.032i	0.544761	−	1.31517i	0.921331	−	0.388780i	$-0.127103\pi$
$458$	−136.106	−	328.589i	−0.297175	−	0.717443i
$459$	0.305064	−	0.305064i	0.000664628	−	0.000664628i
$460$	−248.868	+	248.868i	−0.541016	+	0.541016i
$461$	484.023			1.04994			0.524971	−	0.851120i	$-0.324076\pi$
$461$	484.023			1.04994			0.524971	+	0.851120i	$0.324076\pi$
$462$	−16.0310	+	6.64026i	−0.0346991	+	0.0143728i
$463$	−565.792	+	234.359i	−1.22201	+	0.506174i	−0.898049	−	0.439895i	$-0.855016\pi$
$463$	−565.792	+	234.359i	−1.22201	+	0.506174i	−0.323964	+	0.946070i	$0.605016\pi$
$464$	−29.6504	−	71.5825i	−0.0639018	−	0.154273i
$465$	−79.0547	+	190.855i	−0.170010	+	0.410441i
$466$	25.4131	+	10.5265i	0.0545346	+	0.0225890i
$467$	−47.4463			−0.101598			−0.0507990	−	0.998709i	$-0.516177\pi$
$467$	−47.4463			−0.101598			−0.0507990	+	0.998709i	$0.516177\pi$
$468$	161.739	−	390.472i	0.345596	−	0.834341i
$469$	40.1778			0.0856671
$470$	47.1616	−	113.858i	0.100344	−	0.242251i
$471$	−35.4507	−	35.4507i	−0.0752669	−	0.0752669i
$472$	17.0189	−	17.0189i	0.0360571	−	0.0360571i
$473$	460.068	+	190.566i	0.972659	+	0.402889i
$474$			187.248i			0.395037i
$475$	161.328	+	66.8241i	0.339637	+	0.140682i
$476$		−	0.0582058i		−	0.000122281i
$477$	−150.048	+	362.248i	−0.314566	+	0.759431i
$478$	−374.196	−	154.997i	−0.782836	−	0.324261i
$479$	−525.724	+	217.762i	−1.09754	+	0.454618i	−0.856631	−	0.515929i	$-0.827447\pi$
$479$	−525.724	+	217.762i	−1.09754	+	0.454618i	−0.240913	+	0.970547i	$0.577447\pi$
$480$	66.5264	+	160.609i	0.138597	+	0.334602i
$481$	302.730	+	730.854i	0.629376	+	1.51945i
$482$		−	395.084i		−	0.819676i
$483$	17.6277	+	17.6277i	0.0364963	+	0.0364963i
$484$	−78.5819	−	78.5819i	−0.162359	−	0.162359i
$485$	706.404	−	292.602i	1.45650	−	0.603304i
$486$	−251.949	−	104.361i	−0.518414	−	0.214734i
$487$	−383.555	−	383.555i	−0.787588	−	0.787588i	0.193510	−	0.981098i	$-0.438013\pi$
$487$	−383.555	−	383.555i	−0.787588	−	0.787588i	−0.981098	+	0.193510i	$0.938013\pi$
$488$	353.523			0.724433
$489$	−149.038	+	61.7336i	−0.304781	+	0.126244i
$490$	−300.913	+	300.913i	−0.614109	+	0.614109i
$491$		−	413.228i		−	0.841604i	−0.907152	−	0.420802i	$-0.861749\pi$
$491$		−	413.228i		−	0.841604i	0.907152	−	0.420802i	$-0.138251\pi$
$492$	−53.2022	+	59.1778i	−0.108135	+	0.120280i
$493$	−0.645067			−0.00130845
$494$	260.145	+	260.145i	0.526609	+	0.526609i
$495$	264.062	+	637.503i	0.533459	+	1.28789i
$496$			112.904i			0.227630i
$497$	42.5175	−	42.5175i	0.0855483	−	0.0855483i
$498$	62.7758	−	151.554i	0.126056	−	0.304326i
$499$	279.118	+	673.850i	0.559354	+	1.35040i	0.910279	+	0.413996i	$0.135867\pi$
$499$	279.118	+	673.850i	0.559354	+	1.35040i	−0.350925	+	0.936404i	$0.614133\pi$
$500$	82.8785	−	82.8785i	0.165757	−	0.165757i
$501$	187.950	−	187.950i	0.375149	−	0.375149i
$502$	129.239			0.257449
$503$	−57.0309	+	23.6230i	−0.113381	+	0.0469641i	−0.438653	−	0.898657i	$-0.644544\pi$
$503$	−57.0309	+	23.6230i	−0.113381	+	0.0469641i	0.325272	+	0.945621i	$0.394544\pi$
$504$	−64.9104	+	26.8868i	−0.128790	+	0.0533467i
$505$	−36.5623	−	88.2691i	−0.0724005	−	0.174790i
$506$	182.700	−	441.076i	0.361067	−	0.871692i
$507$	−383.512	−	158.856i	−0.756434	−	0.313325i
$508$	−281.759			−0.554643
$509$	−122.461	+	295.647i	−0.240591	+	0.580838i	−0.997342	−	0.0728654i	$-0.976786\pi$
$509$	−122.461	+	295.647i	−0.240591	+	0.580838i	0.756751	+	0.653703i	$0.226786\pi$
$510$	−0.223414			−0.000438067
$511$	31.5181	−	76.0914i	0.0616792	−	0.148907i
$512$	144.737	+	144.737i	0.282690	+	0.282690i
$513$	−120.634	+	120.634i	−0.235154	+	0.235154i
$514$	117.484	+	48.6634i	0.228568	+	0.0946758i
$515$			175.508i			0.340792i
$516$	−67.6686	−	28.0293i	−0.131141	−	0.0543203i
$517$		−	183.231i		−	0.354411i
$518$	17.2796	−	41.7167i	0.0333584	−	0.0805343i
$519$	−177.786	−	73.6412i	−0.342554	−	0.141891i
$520$	−1240.09	+	513.663i	−2.38479	+	0.987814i
$521$	−35.0257	−	84.5595i	−0.0672278	−	0.162302i	0.886695	−	0.462355i	$-0.152996\pi$
$521$	−35.0257	−	84.5595i	−0.0672278	−	0.162302i	−0.953922	+	0.300053i	$0.902996\pi$
$522$	102.313	+	247.006i	0.196003	+	0.473192i
$523$		−	273.269i		−	0.522502i	−0.965271	−	0.261251i	$-0.915865\pi$
$523$		−	273.269i		−	0.522502i	0.965271	−	0.261251i	$-0.0841351\pi$
$524$	−124.649	−	124.649i	−0.237880	−	0.237880i
$525$	10.9565	+	10.9565i	0.0208695	+	0.0208695i
$526$	216.636	−	89.7337i	0.411856	−	0.170596i
$527$	0.868439	+	0.359719i	0.00164789	+	0.000682579i
$528$	−28.2118	−	28.2118i	−0.0534315	−	0.0534315i
$529$	−156.906			−0.296608
$530$	395.027	−	163.625i	0.745333	−	0.308727i
$531$	−16.4603	+	16.4603i	−0.0309987	+	0.0309987i
$532$			23.0168i			0.0432646i
$533$	−756.956	−	680.520i	−1.42018	−	1.27677i
$534$	−132.507			−0.248140
$535$	848.850	+	848.850i	1.58664	+	1.58664i
$536$	126.131	+	304.508i	0.235320	+	0.568113i
$537$			76.5340i			0.142521i
$538$	−47.2197	+	47.2197i	−0.0877690	+	0.0877690i
$539$	−242.128	+	584.549i	−0.449218	+	1.08451i
$540$	−81.7877	−	197.453i	−0.151459	−	0.365654i
$541$	−280.642	+	280.642i	−0.518746	+	0.518746i	−0.917192	−	0.398446i	$-0.869550\pi$
$541$	−280.642	+	280.642i	−0.518746	+	0.518746i	0.398446	+	0.917192i	$0.369550\pi$
$542$	−33.9624	+	33.9624i	−0.0626612	+	0.0626612i
$543$	22.4138			0.0412776
$544$	0.730812	−	0.302712i	0.00134340	−	0.000556456i
$545$	−285.519	+	118.266i	−0.523887	+	0.217001i
$546$	12.4929	+	30.1604i	0.0228807	+	0.0552389i
$547$	59.5360	−	143.733i	0.108841	−	0.262765i	−0.860070	−	0.510177i	$-0.829580\pi$
$547$	59.5360	−	143.733i	0.108841	−	0.262765i	0.968910	+	0.247412i	$0.0795800\pi$
$548$	100.961	+	41.8192i	0.184235	+	0.0763125i
$549$	−341.919			−0.622803
$550$	113.557	−	274.150i	0.206466	−	0.498454i
$551$	255.084			0.462947
$552$	−78.2615	+	188.940i	−0.141778	+	0.342283i
$553$	−105.956	−	105.956i	−0.191603	−	0.191603i
$554$	−275.646	+	275.646i	−0.497555	+	0.497555i
$555$	175.505	+	72.6965i	0.316225	+	0.130985i
$556$		−	413.485i		−	0.743679i
$557$	−457.414	−	189.467i	−0.821210	−	0.340156i	−0.0677932	−	0.997699i	$-0.521596\pi$
$557$	−457.414	−	189.467i	−0.821210	−	0.340156i	−0.753417	+	0.657543i	$0.771596\pi$
$558$		−	389.593i		−	0.698196i
$559$	358.528	−	865.563i	0.641374	−	1.54841i
$560$	19.8398	+	8.21792i	0.0354283	+	0.0146749i
$561$	−0.306885	+	0.127116i	−0.000547031	+	0.000226588i
$562$	−98.0543	−	236.724i	−0.174474	−	0.421217i
$563$	283.085	+	683.428i	0.502816	+	1.21390i	0.947944	+	0.318438i	$0.103158\pi$
$563$	283.085	+	683.428i	0.502816	+	1.21390i	−0.445128	+	0.895467i	$0.646842\pi$
$564$			26.9503i			0.0477842i
$565$	572.937	+	572.937i	1.01405	+	1.01405i
$566$	−38.1413	−	38.1413i	−0.0673875	−	0.0673875i
$567$	55.4354	−	22.9621i	0.0977697	−	0.0404975i
$568$	455.717	+	188.764i	0.802318	+	0.332331i
$569$	−414.050	−	414.050i	−0.727679	−	0.727679i	0.242478	−	0.970157i	$-0.422040\pi$
$569$	−414.050	−	414.050i	−0.727679	−	0.727679i	−0.970157	+	0.242478i	$0.922040\pi$
$570$	88.3463			0.154993
$571$	311.694	−	129.108i	0.545875	−	0.226109i	−0.0926654	−	0.995697i	$-0.529539\pi$
$571$	311.694	−	129.108i	0.545875	−	0.226109i	0.638540	+	0.769589i	$0.279539\pi$
$572$	−484.539	+	484.539i	−0.847096	+	0.847096i
$573$			29.4004i			0.0513095i
$574$	3.08504	+	58.0183i	0.00537464	+	0.101077i
$575$	−426.323			−0.741431
$576$	−306.835	−	306.835i	−0.532699	−	0.532699i
$577$	328.629	+	793.380i	0.569547	+	1.37501i	0.901937	+	0.431867i	$0.142145\pi$
$577$	328.629	+	793.380i	0.569547	+	1.37501i	−0.332390	+	0.943142i	$0.607855\pi$
$578$		−	399.232i		−	0.690712i
$579$	19.8825	−	19.8825i	0.0343394	−	0.0343394i
$580$	−122.289	+	295.231i	−0.210843	+	0.509020i
$581$	50.2363	+	121.281i	0.0864653	+	0.208746i
$582$	107.871	−	107.871i	0.185345	−	0.185345i
$583$	449.516	−	449.516i	0.771040	−	0.771040i
$584$	675.643			1.15692
$585$	1199.39	−	496.802i	2.05023	−	0.849235i
$586$	−20.8318	+	8.62880i	−0.0355491	+	0.0147249i
$587$	370.983	+	895.633i	0.631999	+	1.52578i	0.837106	+	0.547041i	$0.184246\pi$
$587$	370.983	+	895.633i	0.631999	+	1.52578i	−0.205107	+	0.978740i	$0.565754\pi$
$588$	35.6132	−	85.9779i	0.0605667	−	0.146221i
$589$	−343.413	−	142.246i	−0.583045	−	0.241505i
$590$	25.3847			0.0430250
$591$	10.1458	−	24.4941i	0.0171672	−	0.0414452i
$592$	103.824			0.175378
$593$	−15.7851	+	38.1085i	−0.0266190	+	0.0642639i	−0.936630	−	0.350320i	$-0.886073\pi$
$593$	−15.7851	+	38.1085i	−0.0266190	+	0.0642639i	0.910011	+	0.414584i	$0.136073\pi$
$594$	204.997	+	204.997i	0.345113	+	0.345113i
$595$	0.126421	−	0.126421i	0.000212473	−	0.000212473i
$596$	−80.9182	−	33.5174i	−0.135769	−	0.0562373i
$597$		−	341.659i		−	0.572294i
$598$	−829.833	−	343.728i	−1.38768	−	0.574796i
$599$		−	845.159i		−	1.41095i	−0.708734	−	0.705475i	$-0.750734\pi$
$599$		−	845.159i		−	1.41095i	0.708734	−	0.705475i	$-0.249266\pi$
$600$	−48.6433	+	117.435i	−0.0810721	+	0.195725i
$601$	−357.015	−	147.880i	−0.594034	−	0.246057i	0.0653509	−	0.997862i	$-0.479183\pi$
$601$	−357.015	−	147.880i	−0.594034	−	0.246057i	−0.659385	+	0.751805i	$0.729183\pi$
$602$	−49.4059	+	20.4646i	−0.0820695	+	0.0339943i
$603$	−121.991	−	294.513i	−0.202307	−	0.488413i
$604$	−178.264	−	430.368i	−0.295140	−	0.712530i
$605$		−	341.356i		−	0.564224i
$606$	−13.4790	−	13.4790i	−0.0222426	−	0.0222426i
$607$	295.420	+	295.420i	0.486689	+	0.486689i	0.907260	−	0.420571i	$-0.138170\pi$
$607$	295.420	+	295.420i	0.486689	+	0.486689i	−0.420571	+	0.907260i	$0.638170\pi$
$608$	−288.991	+	119.704i	−0.475313	+	0.196881i
$609$	20.9118	+	8.66193i	0.0343379	+	0.0142232i
$610$	263.650	+	263.650i	0.432213	+	0.432213i
$611$	−344.727			−0.564201
$612$	−0.426662	+	0.176729i	−0.000697160	+	0.000288773i
$613$	−830.468	+	830.468i	−1.35476	+	1.35476i	−0.474512	+	0.880249i	$0.657375\pi$
$613$	−830.468	+	830.468i	−1.35476	+	1.35476i	−0.880249	+	0.474512i	$0.842625\pi$
$614$		−	119.362i		−	0.194400i
$615$	−244.087	+	12.9790i	−0.396889	+	0.0211040i
$616$	113.912			0.184921
$617$	−42.2366	−	42.2366i	−0.0684548	−	0.0684548i	0.672050	−	0.740505i	$-0.265414\pi$
$617$	−42.2366	−	42.2366i	−0.0684548	−	0.0684548i	−0.740505	+	0.672050i	$0.765414\pi$
$618$	13.4004	+	32.3513i	0.0216834	+	0.0523484i
$619$			304.461i			0.491860i	0.969288	+	0.245930i	$0.0790933\pi$
$619$			304.461i			0.491860i	−0.969288	+	0.245930i	$0.920907\pi$
$620$	329.269	−	329.269i	0.531079	−	0.531079i
$621$	159.393	−	384.808i	0.256671	−	0.619659i
$622$	106.902	+	258.084i	0.171868	+	0.414926i
$623$	74.9805	−	74.9805i	0.120354	−	0.120354i
$624$	−53.0772	+	53.0772i	−0.0850597	+	0.0850597i
$625$	766.975			1.22716
$626$	−401.882	+	166.465i	−0.641984	+	0.265919i
$627$	121.354	−	50.2663i	0.193547	−	0.0801696i
$628$	43.2471	+	104.408i	0.0688649	+	0.166255i
$629$	0.330788	−	0.798592i	0.000525894	−	0.00126962i
$630$	−68.4603	−	28.3572i	−0.108667	−	0.0450114i
$631$	822.716			1.30383			0.651914	−	0.758292i	$-0.273966\pi$
$631$	822.716			1.30383			0.651914	+	0.758292i	$0.273966\pi$
$632$	470.412	−	1135.68i	0.744323	−	1.79695i
$633$	305.054			0.481917
$634$	185.862	−	448.710i	0.293157	−	0.707745i
$635$	−611.972	−	611.972i	−0.963736	−	0.963736i
$636$	−66.1167	+	66.1167i	−0.103957	+	0.103957i
$637$	1099.76	+	455.536i	1.72647	+	0.715127i
$638$		−	433.473i		−	0.679425i
$639$	−440.758	−	182.568i	−0.689762	−	0.285709i
$640$		−	276.185i		−	0.431539i
$641$	−199.884	+	482.562i	−0.311831	+	0.752827i	0.687806	+	0.725894i	$0.258574\pi$
$641$	−199.884	+	482.562i	−0.311831	+	0.752827i	−0.999637	+	0.0269325i	$0.991426\pi$
$642$	221.280	+	91.6571i	0.344672	+	0.142768i
$643$	−84.4747	+	34.9906i	−0.131376	+	0.0544177i	−0.447403	−	0.894333i	$-0.647651\pi$
$643$	−84.4747	+	34.9906i	−0.131376	+	0.0544177i	0.316027	+	0.948750i	$0.397651\pi$
$644$	−21.5045	−	51.9164i	−0.0333921	−	0.0806155i
$645$	−86.0957	−	207.853i	−0.133482	−	0.322253i
$646$		−	0.401998i		−	0.000622288i
$647$	9.46916	+	9.46916i	0.0146355	+	0.0146355i	0.714387	−	0.699751i	$-0.246706\pi$
$647$	9.46916	+	9.46916i	0.0146355	+	0.0146355i	−0.699751	+	0.714387i	$0.746706\pi$
$648$	348.060	+	348.060i	0.537129	+	0.537129i
$649$	34.8688	−	14.4431i	0.0537270	−	0.0222545i
$650$	−515.781	−	213.643i	−0.793509	−	0.328682i
$651$	−23.3227	−	23.3227i	−0.0358260	−	0.0358260i
$652$	363.630			0.557715
$653$	24.5236	−	10.1580i	0.0375552	−	0.0155559i	−0.363827	−	0.931467i	$-0.618530\pi$
$653$	24.5236	−	10.1580i	0.0375552	−	0.0155559i	0.401382	+	0.915911i	$0.368530\pi$
$654$	−43.5998	+	43.5998i	−0.0666664	+	0.0666664i
$655$		−	541.470i		−	0.826671i
$656$	−120.534	+	57.6048i	−0.183741	+	0.0878121i
$657$	−653.465			−0.994620
$658$	13.9136	+	13.9136i	0.0211453	+	0.0211453i
$659$	−261.932	−	632.360i	−0.397469	−	0.959576i	−0.988264	−	0.152754i	$-0.951186\pi$
$659$	−261.932	−	632.360i	−0.397469	−	0.959576i	0.590795	−	0.806822i	$-0.298814\pi$
$660$			164.551i			0.249320i
$661$	173.459	−	173.459i	0.262419	−	0.262419i	−0.563617	−	0.826036i	$-0.690591\pi$
$661$	173.459	−	173.459i	0.262419	−	0.262419i	0.826036	+	0.563617i	$0.190591\pi$
$662$	−291.718	+	704.269i	−0.440661	+	1.06385i
$663$	0.239153	+	0.577367i	0.000360714	+	0.000870840i
$664$	−761.483	+	761.483i	−1.14681	+	1.14681i
$665$	−49.9918	+	49.9918i	−0.0751757	+	0.0751757i
$666$	−358.259			−0.537927
$667$	−575.365	+	238.324i	−0.862616	+	0.357307i
$668$	−553.541	+	229.284i	−0.828654	+	0.343240i
$669$	−20.6796	−	49.9250i	−0.0309112	−	0.0746262i
$670$	−133.030	+	321.162i	−0.198552	+	0.479346i
$671$	512.163	+	212.145i	0.763283	+	0.316162i
$672$	−27.7562			−0.0413039
$673$	−395.832	+	955.624i	−0.588161	+	1.41995i	0.297098	+	0.954847i	$0.403981\pi$
$673$	−395.832	+	955.624i	−0.588161	+	1.41995i	−0.885259	+	0.465099i	$0.846019\pi$
$674$	104.600			0.155193
$675$	99.0703	−	239.177i	0.146771	−	0.354336i
$676$	661.647	+	661.647i	0.978768	+	0.978768i
$677$	−147.000	+	147.000i	−0.217134	+	0.217134i	−0.807289	−	0.590156i	$-0.799066\pi$
$677$	−147.000	+	147.000i	−0.217134	+	0.217134i	0.590156	+	0.807289i	$0.299066\pi$
$678$	149.354	+	61.8646i	0.220287	+	0.0912457i
$679$			122.080i			0.179794i
$680$	1.35503	+	0.561271i	0.00199269	+	0.000825399i
$681$			126.636i			0.185956i
$682$	−241.724	+	583.574i	−0.354434	+	0.855680i
$683$	−89.3993	−	37.0304i	−0.130892	−	0.0542173i	0.316276	−	0.948667i	$-0.397567\pi$
$683$	−89.3993	−	37.0304i	−0.130892	−	0.0542173i	−0.447168	+	0.894450i	$0.647567\pi$
$684$	168.718	−	69.8853i	0.246664	−	0.102172i
$685$	128.453	+	310.114i	0.187523	+	0.452721i
$686$	−52.5741	−	126.925i	−0.0766386	−	0.185022i
$687$			238.903i			0.347749i
$688$	−86.9459	−	86.9459i	−0.126375	−	0.126375i
$689$	−845.712	−	845.712i	−1.22745	−	1.22745i
$690$	−199.273	+	82.5416i	−0.288802	+	0.119626i
$691$	−313.507	−	129.859i	−0.453700	−	0.187929i	0.144118	−	0.989561i	$-0.453966\pi$
$691$	−313.507	−	129.859i	−0.453700	−	0.187929i	−0.597818	+	0.801632i	$0.703966\pi$
$692$	306.722	+	306.722i	0.443239	+	0.443239i
$693$	−110.172			−0.158979
$694$	−11.2587	+	4.66349i	−0.0162228	+	0.00671972i
$695$	898.080	−	898.080i	1.29220	−	1.29220i
$696$			185.683i			0.266786i
$697$	0.0590576	+	1.11066i	8.47311e−5	+	0.00159348i
$698$	509.351			0.729730
$699$	−13.0651	−	13.0651i	−0.0186911	−	0.0186911i
$700$	−13.3661	−	32.2685i	−0.0190944	−	0.0460979i
$701$			300.567i			0.428769i	0.976749	+	0.214384i	$0.0687745\pi$
$701$			300.567i			0.428769i	−0.976749	+	0.214384i	$0.931226\pi$
$702$	385.678	−	385.678i	0.549399	−	0.549399i
$703$	−130.806	+	315.793i	−0.186068	+	0.449208i
$704$	269.233	+	649.986i	0.382433	+	0.923276i
$705$	−58.5354	+	58.5354i	−0.0830289	+	0.0830289i
$706$	59.5214	−	59.5214i	0.0843079	−	0.0843079i
$707$	15.2545			0.0215764
$708$	−5.12865	+	2.12436i	−0.00724385	+	0.00300050i
$709$	−57.2248	+	23.7033i	−0.0807121	+	0.0334320i	−0.422674	−	0.906282i	$-0.638909\pi$
$709$	−57.2248	+	23.7033i	−0.0807121	+	0.0334320i	0.341962	+	0.939714i	$0.388909\pi$
$710$	199.088	+	480.640i	0.280405	+	0.676958i
$711$	−454.971	+	1098.40i	−0.639903	+	1.54486i
$712$	803.666	+	332.889i	1.12874	+	0.467541i
$713$	907.500			1.27279
$714$	0.0136507	−	0.0329558i	1.91187e−5	−	4.61566e-5i
$715$	−2104.81			−2.94379
$716$	66.0194	−	159.385i	0.0922059	−	0.222605i
$717$	192.377	+	192.377i	0.268308	+	0.268308i
$718$	84.3011	−	84.3011i	0.117411	−	0.117411i
$719$	594.299	+	246.167i	0.826564	+	0.342374i	0.755541	−	0.655101i	$-0.227374\pi$
$719$	594.299	+	246.167i	0.826564	+	0.342374i	0.0710222	+	0.997475i	$0.477374\pi$
$720$		−	170.382i		−	0.236642i
$721$	−25.8891	−	10.7236i	−0.0359073	−	0.0148733i
$722$		−	339.730i		−	0.470540i
$723$	−101.558	+	245.183i	−0.140467	+	0.339118i
$724$	−46.6775	−	19.3345i	−0.0644717	−	0.0267051i
$725$	−357.617	+	148.130i	−0.493265	+	0.204317i
$726$	−26.0632	−	62.9221i	−0.0358997	−	0.0866695i
$727$	−43.6860	−	105.467i	−0.0600907	−	0.145072i	0.890982	−	0.454038i	$-0.150017\pi$
$727$	−43.6860	−	105.467i	−0.0600907	−	0.145072i	−0.951073	+	0.308966i	$0.900017\pi$
$728$		−	214.311i		−	0.294384i
$729$	−242.719	−	242.719i	−0.332948	−	0.332948i
$730$	503.880	+	503.880i	0.690247	+	0.690247i
$731$	−0.945786	+	0.391757i	−0.00129383	+	0.000535920i
$732$	−75.3310	−	31.2031i	−0.102911	−	0.0426272i
$733$	−527.305	−	527.305i	−0.719380	−	0.719380i	0.249098	−	0.968478i	$-0.419866\pi$
$733$	−527.305	−	527.305i	−0.719380	−	0.719380i	−0.968478	+	0.249098i	$0.919866\pi$
$734$	−598.218			−0.815011
$735$	264.093	−	109.391i	0.359310	−	0.148831i
$736$	540.006	−	540.006i	0.733704	−	0.733704i
$737$			516.842i			0.701279i
$738$	415.921	−	198.774i	0.563578	−	0.269341i
$739$	164.452			0.222533			0.111267	−	0.993791i	$-0.464509\pi$
$739$	164.452			0.222533			0.111267	+	0.993791i	$0.464509\pi$
$740$	−302.787	−	302.787i	−0.409171	−	0.409171i
$741$	−94.5702	−	228.313i	−0.127625	−	0.308114i
$742$			68.2680i			0.0920053i
$743$	82.4432	−	82.4432i	0.110960	−	0.110960i	−0.649447	−	0.760407i	$-0.725000\pi$
$743$	82.4432	−	82.4432i	0.110960	−	0.110960i	0.760407	+	0.649447i	$0.225000\pi$
$744$	103.545	−	249.981i	0.139174	−	0.335996i
$745$	−102.953	−	248.551i	−0.138192	−	0.333626i
$746$	467.237	−	467.237i	0.626323	−	0.626323i
$747$	736.488	−	736.488i	0.985927	−	0.985927i
$748$	0.748751			0.00100100
$749$	−177.079	+	73.3486i	−0.236421	+	0.0979286i
$750$	66.3624	−	27.4882i	0.0884832	−	0.0366510i
$751$	−302.607	−	730.559i	−0.402939	−	0.972781i	−0.986949	−	0.161034i	$-0.948517\pi$
$751$	−302.607	−	730.559i	−0.402939	−	0.972781i	0.584010	−	0.811747i	$-0.301483\pi$
$752$	−17.3139	+	41.7995i	−0.0230238	+	0.0555844i
$753$	−80.2037	−	33.2215i	−0.106512	−	0.0441188i
$754$	−815.528			−1.08160
$755$	547.563	−	1321.93i	0.725249	−	1.75091i
$756$	34.1236			0.0451370
$757$	−82.7473	+	199.770i	−0.109309	+	0.263896i	−0.969063	−	0.246812i	$-0.920617\pi$
$757$	−82.7473	+	199.770i	−0.109309	+	0.263896i	0.859754	+	0.510709i	$0.170617\pi$
$758$	−39.5653	−	39.5653i	−0.0521970	−	0.0521970i
$759$	−226.761	+	226.761i	−0.298762	+	0.298762i
$760$	−535.829	−	221.948i	−0.705038	−	0.292036i
$761$			638.280i			0.838739i	0.907816	+	0.419370i	$0.137749\pi$
$761$			638.280i			0.838739i	−0.907816	+	0.419370i	$0.862251\pi$
$762$	−159.530	−	66.0795i	−0.209357	−	0.0867185i
$763$		−	49.3430i		−	0.0646697i
$764$	25.3612	−	61.2274i	0.0331953	−	0.0801406i
$765$	−1.31055	−	0.542847i	−0.00171314	−	0.000709605i
$766$	662.025	−	274.220i	0.864262	−	0.357989i
$767$	−27.1731	−	65.6016i	−0.0354277	−	0.0855301i
$768$	−96.8165	−	233.736i	−0.126063	−	0.304343i
$769$			321.513i			0.418092i	0.977906	+	0.209046i	$0.0670359\pi$
$769$			321.513i			0.418092i	−0.977906	+	0.209046i	$0.932964\pi$
$770$	84.9528	+	84.9528i	0.110328	+	0.110328i
$771$	−60.3993	−	60.3993i	−0.0783390	−	0.0783390i
$772$	−58.5571	+	24.2552i	−0.0758512	+	0.0314186i
$773$	−644.760	−	267.068i	−0.834101	−	0.345496i	−0.0755763	−	0.997140i	$-0.524080\pi$
$773$	−644.760	−	267.068i	−0.834101	−	0.345496i	−0.758525	+	0.651644i	$0.774080\pi$
$774$	300.020	+	300.020i	0.387623	+	0.387623i
$775$	564.055			0.727813
$776$	−925.245	+	383.249i	−1.19233	+	0.493877i
$777$	−21.4469	+	21.4469i	−0.0276022	+	0.0276022i
$778$		−	456.566i		−	0.586846i
$779$	−23.3536	−	439.195i	−0.0299789	−	0.563794i
$780$	309.584			0.396903
$781$	546.939	+	546.939i	0.700306	+	0.700306i
$782$	0.375586	+	0.906744i	0.000480288	+	0.00115952i
$783$		−	378.175i		−	0.482982i
$784$	110.471	−	110.471i	0.140907	−	0.140907i
$785$	−132.839	+	320.703i	−0.169222	+	0.408539i
$786$	−41.3423	−	99.8090i	−0.0525983	−	0.126983i
$787$	−38.3399	+	38.3399i	−0.0487165	+	0.0487165i	−0.731045	−	0.682329i	$-0.760967\pi$
$787$	−38.3399	+	38.3399i	−0.0487165	+	0.0487165i	0.682329	+	0.731045i	$0.260967\pi$
$788$	−42.2581	+	42.2581i	−0.0536270	+	0.0536270i
$789$	−157.507			−0.199629
$790$	1197.79	−	496.139i	1.51618	−	0.628024i
$791$	−119.521	+	49.5071i	−0.151101	+	0.0625881i
$792$	−345.868	−	834.998i	−0.436701	−	1.05429i
$793$	399.125	−	963.574i	0.503311	−	1.21510i
$794$	−163.414	−	67.6885i	−0.205812	−	0.0852500i
$795$	−287.207			−0.361267
$796$	−294.721	+	711.519i	−0.370252	+	0.893868i
$797$	1549.66			1.94437			0.972186	−	0.234209i	$-0.0752500\pi$
$797$	1549.66			1.94437			0.972186	+	0.234209i	$0.0752500\pi$
$798$	−5.39801	+	13.0320i	−0.00676443	+	0.0163308i
$799$	0.266351	+	0.266351i	0.000333355	+	0.000333355i
$800$	335.639	−	335.639i	0.419549	−	0.419549i
$801$	−777.286	−	321.962i	−0.970394	−	0.401950i
$802$			860.121i			1.07247i
$803$	978.829	+	405.444i	1.21897	+	0.504912i
$804$		−	76.0193i		−	0.0945513i
$805$	66.0539	−	159.468i	0.0820546	−	0.198097i
$806$	1097.93	+	454.776i	1.36219	+	0.564238i
$807$	41.4418	−	17.1658i	0.0513529	−	0.0212711i
$808$	47.8890	+	115.614i	0.0592686	+	0.143087i
$809$	−22.2664	−	53.7559i	−0.0275234	−	0.0664474i	0.909520	−	0.415660i	$-0.136449\pi$
$809$	−22.2664	−	53.7559i	−0.0275234	−	0.0664474i	−0.937044	+	0.349212i	$0.886449\pi$
$810$			519.151i			0.640927i
$811$	−661.326	−	661.326i	−0.815446	−	0.815446i	0.169999	−	0.985444i	$-0.445624\pi$
$811$	−661.326	−	661.326i	−0.815446	−	0.815446i	−0.985444	+	0.169999i	$0.945624\pi$
$812$	−36.0776	−	36.0776i	−0.0444306	−	0.0444306i
$813$	29.8066	−	12.3463i	0.0366625	−	0.0151861i
$814$	536.638	+	222.283i	0.659261	+	0.273075i
$815$	789.795	+	789.795i	0.969073	+	0.969073i
$816$	0.0820195			0.000100514
$817$	373.999	−	154.916i	0.457772	−	0.189615i
$818$	−434.573	+	434.573i	−0.531262	+	0.531262i
$819$			207.277i			0.253085i
$820$	519.516	+	183.524i	0.633556	+	0.223810i
$821$	−394.722			−0.480783			−0.240391	−	0.970676i	$-0.577276\pi$
$821$	−394.722			−0.480783			−0.240391	+	0.970676i	$0.577276\pi$
$822$	47.3556	+	47.3556i	0.0576102	+	0.0576102i
$823$	−83.3051	−	201.116i	−0.101221	−	0.244370i	0.865154	−	0.501507i	$-0.167221\pi$
$823$	−83.3051	−	201.116i	−0.101221	−	0.244370i	−0.966375	+	0.257137i	$0.917221\pi$
$824$		−	229.879i		−	0.278979i
$825$	−140.943	+	140.943i	−0.170840	+	0.170840i
$826$	−1.55102	+	3.74450i	−0.00187775	+	0.00453330i
$827$	−142.591	−	344.244i	−0.172419	−	0.416256i	0.813922	−	0.580975i	$-0.197328\pi$
$827$	−142.591	−	344.244i	−0.172419	−	0.416256i	−0.986341	+	0.164718i	$0.947328\pi$
$828$	−315.266	+	315.266i	−0.380756	+	0.380756i
$829$	−1023.38	+	1023.38i	−1.23448	+	1.23448i	−0.272256	+	0.962225i	$0.587770\pi$
$829$	−1023.38	+	1023.38i	−1.23448	+	1.23448i	−0.962225	+	0.272256i	$0.912230\pi$
$830$	−1135.80			−1.36843
$831$	241.917	−	100.205i	0.291115	−	0.120584i
$832$	1222.87	−	506.530i	1.46980	−	0.608811i
$833$	−0.497756	−	1.20169i	−0.000597546	−	0.00144260i
$834$	96.9728	−	234.113i	0.116274	−	0.280711i
$835$	−1700.28	−	704.277i	−2.03626	−	0.843446i
$836$	−296.084			−0.354168
$837$	−210.888	+	509.128i	−0.251957	+	0.608277i
$838$	−848.912			−1.01302
$839$	−478.975	+	1156.35i	−0.570888	+	1.37825i	0.329912	+	0.944012i	$0.392981\pi$
$839$	−478.975	+	1156.35i	−0.570888	+	1.37825i	−0.900800	+	0.434234i	$0.857019\pi$
$840$	−36.3905	−	36.3905i	−0.0433220	−	0.0433220i
$841$	194.845	−	194.845i	0.231683	−	0.231683i
$842$	−539.597	−	223.509i	−0.640852	−	0.265450i
$843$			172.112i			0.204166i
$844$	−635.287	−	263.144i	−0.752709	−	0.311782i
$845$			2874.16i			3.40138i
$846$	59.7443	−	144.236i	0.0706197	−	0.170491i
$847$	50.3534	+	20.8571i	0.0594491	+	0.0246246i
$848$	−145.022	+	60.0700i	−0.171016	+	0.0708373i
$849$	13.8655	+	33.4743i	0.0163316	+	0.0394279i
$850$	0.233444	+	0.563585i	0.000274640	+	0.000663041i
$851$		−	834.512i		−	0.980625i
$852$	−80.4460	−	80.4460i	−0.0944202	−	0.0944202i
$853$	−422.076	−	422.076i	−0.494814	−	0.494814i	0.415005	−	0.909819i	$-0.363780\pi$
$853$	−422.076	−	422.076i	−0.494814	−	0.494814i	−0.909819	+	0.415005i	$0.863780\pi$
$854$	−55.0002	+	22.7818i	−0.0644031	+	0.0266766i
$855$	518.241	+	214.662i	0.606129	+	0.251067i
$856$	−1111.82	−	1111.82i	−1.29885	−	1.29885i
$857$	−619.431			−0.722790			−0.361395	−	0.932413i	$-0.617699\pi$
$857$	−619.431			−0.722790			−0.361395	+	0.932413i	$0.617699\pi$
$858$	−387.980	+	160.706i	−0.452191	+	0.187304i
$859$	788.572	−	788.572i	0.918012	−	0.918012i	−0.0788731	−	0.996885i	$-0.525132\pi$
$859$	788.572	−	788.572i	0.918012	−	0.918012i	0.996885	+	0.0788731i	$0.0251322\pi$
$860$			507.130i			0.589687i
$861$	12.9993	−	36.7982i	0.0150979	−	0.0427389i
$862$	951.569			1.10391
$863$	755.576	+	755.576i	0.875522	+	0.875522i	0.993068	−	0.117545i	$-0.0375025\pi$
$863$	755.576	+	755.576i	0.875522	+	0.875522i	−0.117545	+	0.993068i	$0.537502\pi$
$864$	177.467	+	428.444i	0.205402	+	0.495884i
$865$			1332.38i			1.54033i
$866$	−450.757	+	450.757i	−0.520505	+	0.520505i
$867$	−102.624	+	247.756i	−0.118367	+	0.285763i
$868$	28.4519	+	68.6890i	0.0327787	+	0.0791348i
$869$	1363.01	−	1363.01i	1.56848	−	1.56848i
$870$	−138.478	+	138.478i	−0.159171	+	0.159171i
$871$	972.378			1.11639
$872$	373.971	−	154.904i	0.428866	−	0.177642i
$873$	894.873	−	370.669i	1.02506	−	0.424592i
$874$	−148.521	−	358.561i	−0.169932	−	0.410252i
$875$	−21.9974	+	53.1065i	−0.0251399	+	0.0606932i
$876$	−143.970	−	59.6344i	−0.164349	−	0.0680758i
$877$	83.1296			0.0947886			0.0473943	−	0.998876i	$-0.484908\pi$
$877$	83.1296			0.0947886			0.0473943	+	0.998876i	$0.484908\pi$
$878$	−233.285	+	563.200i	−0.265700	+	0.641458i
$879$	15.1459			0.0172308
$880$	−105.714	+	255.217i	−0.120130	+	0.290019i
$881$	−456.680	−	456.680i	−0.518365	−	0.518365i	0.398711	−	0.917076i	$-0.369458\pi$
$881$	−456.680	−	456.680i	−0.518365	−	0.518365i	−0.917076	+	0.398711i	$0.869458\pi$
$882$	−381.197	+	381.197i	−0.432196	+	0.432196i
$883$	−834.298	−	345.578i	−0.944845	−	0.391368i	−0.143554	−	0.989642i	$-0.545853\pi$
$883$	−834.298	−	345.578i	−0.944845	−	0.391368i	−0.801291	+	0.598275i	$0.795853\pi$
$884$		−	1.40869i		−	0.00159354i
$885$	−15.7533	−	6.52525i	−0.0178004	−	0.00737316i
$886$		−	646.174i		−	0.729316i
$887$	210.758	−	508.814i	0.237607	−	0.573635i	−0.759427	−	0.650593i	$-0.774521\pi$
$887$	210.758	−	508.814i	0.237607	−	0.573635i	0.997034	+	0.0769576i	$0.0245206\pi$
$888$	−229.875	−	95.2175i	−0.258869	−	0.107227i
$889$	127.664	−	52.8801i	0.143604	−	0.0594827i
$890$	351.095	+	847.619i	0.394489	+	0.952381i
$891$	295.381	+	713.113i	0.331517	+	0.800352i
$892$			121.809i			0.136557i
$893$	−105.325	−	105.325i	−0.117945	−	0.117945i
$894$	−37.9547	−	37.9547i	−0.0424550	−	0.0424550i
$895$	489.573	−	202.788i	0.547009	−	0.226578i
$896$	40.7401	+	16.8751i	0.0454688	+	0.0188338i
$897$	426.624	+	426.624i	0.475612	+	0.475612i
$898$	−101.676			−0.113225
$899$	761.248	−	315.319i	0.846772	−	0.350744i
$900$	−195.953	+	195.953i	−0.217725	+	0.217725i
$901$			1.30687i			0.00145046i
$902$	−746.340	+	39.6856i	−0.827428	+	0.0439973i
$903$	35.9209			0.0397796
$904$	−750.430	−	750.430i	−0.830122	−	0.830122i
$905$	−59.3884	−	143.376i	−0.0656226	−	0.158427i
$906$		−	285.480i		−	0.315099i
$907$	−406.812	+	406.812i	−0.448525	+	0.448525i	−0.894864	−	0.446339i	$-0.852727\pi$
$907$	−406.812	+	406.812i	−0.448525	+	0.448525i	0.446339	+	0.894864i	$0.352727\pi$
$908$	109.238	−	263.724i	0.120306	−	0.290445i
$909$	−46.3171	−	111.819i	−0.0509539	−	0.123014i
$910$	159.829	−	159.829i	0.175636	−	0.175636i
$911$	−797.009	+	797.009i	−0.874873	+	0.874873i	−0.992999	−	0.118126i	$-0.962311\pi$
$911$	−797.009	+	797.009i	−0.874873	+	0.874873i	0.118126	+	0.992999i	$0.462311\pi$
$912$	−32.4336			−0.0355632
$913$	−1560.15	+	646.233i	−1.70881	+	0.707813i
$914$	−830.282	+	343.914i	−0.908405	+	0.376274i
$915$	−95.8446	−	231.389i	−0.104748	−	0.252884i
$916$	206.082	−	497.526i	0.224980	−	0.543150i
$917$	79.8722	+	33.0841i	0.0871016	+	0.0360787i
$918$	−0.595983			−0.000649219
$919$	−292.232	+	705.510i	−0.317989	+	0.767693i	0.681372	+	0.731937i	$0.261384\pi$
$919$	−292.232	+	705.510i	−0.317989	+	0.767693i	−0.999361	+	0.0357553i	$0.988616\pi$
$920$	1415.98			1.53911
$921$	−30.6824	+	74.0739i	−0.0333143	+	0.0804277i
$922$	−472.802	−	472.802i	−0.512800	−	0.512800i
$923$	1029.00	−	1029.00i	1.11484	−	1.11484i
$924$	−24.2730	−	10.0542i	−0.0262695	−	0.0108812i
$925$		−	518.689i		−	0.560745i
$926$	781.600	+	323.749i	0.844061	+	0.349621i
$927$			222.333i			0.239842i
$928$	265.349	−	640.609i	0.285936	−	0.690311i
$929$	−405.195	−	167.837i	−0.436163	−	0.180665i	0.153788	−	0.988104i	$-0.450853\pi$
$929$	−405.195	−	167.837i	−0.436163	−	0.180665i	−0.589951	+	0.807439i	$0.700853\pi$
$930$	263.652	−	109.208i	0.283497	−	0.117428i
$931$	196.831	+	475.193i	0.211419	+	0.510412i
$932$	15.9384	+	38.4787i	0.0171013	+	0.0412862i
$933$		−	187.642i		−	0.201117i
$934$	46.3463	+	46.3463i	0.0496213	+	0.0496213i
$935$	1.62627	+	1.62627i	0.00173932	+	0.00173932i
$936$	−1570.95	+	650.709i	−1.67837	+	0.695202i
$937$	712.976	+	295.324i	0.760914	+	0.315181i	0.729186	−	0.684316i	$-0.239899\pi$
$937$	712.976	+	295.324i	0.760914	+	0.315181i	0.0317279	+	0.999497i	$0.489899\pi$
$938$	−39.2464	−	39.2464i	−0.0418405	−	0.0418405i
$939$	292.192			0.311173
$940$	172.396	−	71.4087i	0.183400	−	0.0759667i
$941$	236.692	−	236.692i	0.251532	−	0.251532i	−0.570067	−	0.821599i	$-0.693083\pi$
$941$	236.692	−	236.692i	0.251532	−	0.251532i	0.821599	+	0.570067i	$0.193083\pi$
$942$			69.2577i			0.0735220i
$943$	463.015	+	968.826i	0.491002	+	1.02739i
$944$	−9.31922			−0.00987206
$945$	74.1155	+	74.1155i	0.0784291	+	0.0784291i
$946$	−263.254	−	635.550i	−0.278281	−	0.671829i
$947$		−	1505.59i		−	1.58985i	−0.606705	−	0.794927i	$-0.707509\pi$
$947$		−	1505.59i		−	1.58985i	0.606705	−	0.794927i	$-0.292491\pi$
$948$	−200.477	+	200.477i	−0.211473	+	0.211473i
$949$	762.796	−	1841.55i	0.803789	−	1.94052i
$950$	−92.3127	−	222.863i	−0.0971713	−	0.234592i
$951$	−230.685	+	230.685i	−0.242571	+	0.242571i
$952$	−0.165586	+	0.165586i	−0.000173935	+	0.000173935i
$953$	−1012.29			−1.06221			−0.531107	−	0.847305i	$-0.678224\pi$
$953$	−1012.29			−1.06221			−0.531107	+	0.847305i	$0.678224\pi$
$954$	500.420	−	207.281i	0.524549	−	0.217275i
$955$	188.068	−	77.9005i	0.196930	−	0.0815712i
$956$	−234.685	−	566.580i	−0.245487	−	0.592657i
$957$	−111.426	+	269.006i	−0.116433	+	0.281093i
$958$	726.249	+	300.822i	0.758089	+	0.314011i
$959$	−53.5935			−0.0558848
$960$	121.636	−	293.656i	0.126705	−	0.305892i
$961$	−239.686			−0.249413
$962$	418.199	−	1009.62i	0.434719	−	1.04950i
$963$	1075.32	+	1075.32i	1.11664	+	1.11664i
$964$	422.997	−	422.997i	0.438793	−	0.438793i
$965$	−179.866	−	74.5030i	−0.186390	−	0.0772052i
$966$		−	34.4381i		−	0.0356502i
$967$	1357.57	+	562.326i	1.40390	+	0.581516i	0.950762	−	0.309922i	$-0.100303\pi$
$967$	1357.57	+	562.326i	1.40390	+	0.581516i	0.453142	+	0.891438i	$0.350303\pi$
$968$			447.106i			0.461886i
$969$	−0.103335	+	0.249473i	−0.000106641	+	0.000257454i
$970$	−975.846	−	404.209i	−1.00603	−	0.416710i
$971$	705.780	−	292.344i	0.726859	−	0.301075i	0.0115983	−	0.999933i	$-0.496308\pi$
$971$	705.780	−	292.344i	0.726859	−	0.301075i	0.715260	+	0.698858i	$0.246308\pi$
$972$	−158.016	−	381.483i	−0.162568	−	0.392473i
$973$	77.6025	+	187.349i	0.0797559	+	0.192548i
$974$			749.327i			0.769329i
$975$	265.167	+	265.167i	0.271966	+	0.271966i
$976$	−96.7910	−	96.7910i	−0.0991712	−	0.0991712i
$977$	826.431	−	342.319i	0.845887	−	0.350378i	0.0827148	−	0.996573i	$-0.473641\pi$
$977$	826.431	−	342.319i	0.845887	−	0.350378i	0.763172	+	0.646196i	$0.223641\pi$
$978$	205.885	+	85.2804i	0.210517	+	0.0871988i
$979$	964.539	+	964.539i	0.985228	+	0.985228i
$980$	−644.346			−0.657496
$981$	−361.695	+	149.819i	−0.368701	+	0.152721i
$982$	−403.648	+	403.648i	−0.411046	+	0.411046i
$983$		−	991.810i		−	1.00896i	−0.863423	−	0.504481i	$-0.831684\pi$
$983$		−	991.810i		−	1.00896i	0.863423	−	0.504481i	$-0.168316\pi$
$984$	319.703	−	16.9998i	0.324902	−	0.0172762i
$985$	−183.567			−0.186362
$986$	0.630113	+	0.630113i	0.000639059	+	0.000639059i
$987$	−5.05800	−	12.2111i	−0.00512462	−	0.0123719i
$988$			557.048i			0.563814i
$989$	−698.853	+	698.853i	−0.706626	+	0.706626i
$990$	364.783	−	880.664i	0.368468	−	0.889560i
$991$	−194.045	−	468.466i	−0.195807	−	0.472720i	0.795230	−	0.606308i	$-0.207350\pi$
$991$	−194.045	−	468.466i	−0.195807	−	0.472720i	−0.991037	+	0.133588i	$0.957350\pi$
$992$	−714.465	+	714.465i	−0.720227	+	0.720227i
$993$	362.070	−	362.070i	0.364623	−	0.364623i
$994$	−83.0636			−0.0835650
$995$	−2185.53	+	905.275i	−2.19651	+	0.909824i
$996$	229.473	−	95.0506i	0.230394	−	0.0954324i
$997$	−93.4694	−	225.655i	−0.0937507	−	0.226334i	0.870047	−	0.492969i	$-0.164088\pi$
$997$	−93.4694	−	225.655i	−0.0937507	−	0.226334i	−0.963798	+	0.266635i	$0.914088\pi$
$998$	385.581	−	930.874i	0.386353	−	0.932740i
$999$	468.180	+	193.927i	0.468649	+	0.194121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.3.e.b.14.3	yes	20
3.2	odd	2		369.3.l.b.55.3		20
41.3	odd	8	inner	41.3.e.b.3.3	✓	20
123.44	even	8		369.3.l.b.208.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.3.e.b.3.3	✓	20	41.3	odd	8	inner
41.3.e.b.14.3	yes	20	1.1	even	1	trivial
369.3.l.b.55.3		20	3.2	odd	2
369.3.l.b.208.3		20	123.44	even	8

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	41.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.976817 - 0.976817i) q^{2} +(0.355101 + 0.857291i) q^{3} -2.09166i q^{4} +(4.54303 - 4.54303i) q^{5} +(0.490547 - 1.18428i) q^{6} +(0.392560 + 0.947724i) q^{7} +(-5.95043 + 5.95043i) q^{8} +(5.75511 - 5.75511i) q^{9} +O(q^{10})\)	\(q+(-0.976817 - 0.976817i) q^{2} +(0.355101 + 0.857291i) q^{3} -2.09166i q^{4} +(4.54303 - 4.54303i) q^{5} +(0.490547 - 1.18428i) q^{6} +(0.392560 + 0.947724i) q^{7} +(-5.95043 + 5.95043i) q^{8} +(5.75511 - 5.75511i) q^{9} -8.87541 q^{10} +(-12.1914 + 5.04984i) q^{11} +(1.79316 - 0.742751i) q^{12} +(9.50068 + 22.9367i) q^{13} +(0.542293 - 1.30921i) q^{14} +(5.50793 + 2.28146i) q^{15} +3.25833 q^{16} +(0.0103812 - 0.0250625i) q^{17} -11.2434 q^{18} +(-4.10513 + 9.91065i) q^{19} +(-9.50246 - 9.50246i) q^{20} +(-0.673076 + 0.673076i) q^{21} +(16.8415 + 6.97599i) q^{22} -26.1898i q^{23} +(-7.21426 - 2.98824i) q^{24} -16.2782i q^{25} +(13.1245 - 31.6853i) q^{26} +(14.6931 + 6.08607i) q^{27} +(1.98231 - 0.821101i) q^{28} +(-9.09988 - 21.9691i) q^{29} +(-3.15167 - 7.60881i) q^{30} +34.6509i q^{31} +(20.6189 + 20.6189i) q^{32} +(-8.65836 - 8.65836i) q^{33} +(-0.0346220 + 0.0143409i) q^{34} +(6.08895 + 2.52212i) q^{35} +(-12.0377 - 12.0377i) q^{36} +31.8640 q^{37} +(13.6909 - 5.67094i) q^{38} +(-16.2897 + 16.2897i) q^{39} +54.0660i q^{40} +(-36.9925 + 17.6792i) q^{41} +1.31494 q^{42} +(-26.6842 - 26.6842i) q^{43} +(10.5625 + 25.5002i) q^{44} -52.2913i q^{45} +(-25.5826 + 25.5826i) q^{46} +(-5.31373 + 12.8285i) q^{47} +(1.15704 + 2.79334i) q^{48} +(33.9042 - 33.9042i) q^{49} +(-15.9008 + 15.9008i) q^{50} +0.0251722 q^{51} +(47.9757 - 19.8722i) q^{52} +(-44.5080 + 18.4358i) q^{53} +(-8.40746 - 20.2974i) q^{54} +(-32.4443 + 78.3274i) q^{55} +(-7.97527 - 3.30347i) q^{56} -9.95405 q^{57} +(-12.5708 + 30.3487i) q^{58} -2.86012 q^{59} +(4.77203 - 11.5207i) q^{60} +(-29.7057 - 29.7057i) q^{61} +(33.8476 - 33.8476i) q^{62} +(7.71348 + 3.19503i) q^{63} -53.3152i q^{64} +(147.364 + 61.0401i) q^{65} +16.9153i q^{66} +(14.9886 - 36.1856i) q^{67} +(-0.0524222 - 0.0217140i) q^{68} +(22.4523 - 9.30003i) q^{69} +(-3.48413 - 8.41144i) q^{70} +(-22.4314 - 54.1541i) q^{71} +68.4908i q^{72} +(-56.7726 - 56.7726i) q^{73} +(-31.1253 - 31.1253i) q^{74} +(13.9552 - 5.78042i) q^{75} +(20.7297 + 8.58652i) q^{76} +(-9.57171 - 9.57171i) q^{77} +31.8241 q^{78} +(-134.955 + 55.9004i) q^{79} +(14.8027 - 14.8027i) q^{80} -58.4932i q^{81} +(53.4042 + 18.8656i) q^{82} +127.971 q^{83} +(1.40785 + 1.40785i) q^{84} +(-0.0666974 - 0.161022i) q^{85} +52.1311i q^{86} +(15.6025 - 15.6025i) q^{87} +(42.4953 - 102.593i) q^{88} +(-39.5582 - 95.5019i) q^{89} +(-51.0790 + 51.0790i) q^{90} +(-18.0080 + 18.0080i) q^{91} -54.7801 q^{92} +(-29.7059 + 12.3046i) q^{93} +(17.7216 - 7.34054i) q^{94} +(26.3747 + 63.6741i) q^{95} +(-10.3546 + 24.9982i) q^{96} +(109.949 + 45.5425i) q^{97} -66.2363 q^{98} +(-41.1004 + 99.2252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{2} + 4 q^{3} - 12 q^{5} - 16 q^{6} - 4 q^{7} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) 20 * q - 8 * q^2 + 4 * q^3 - 12 * q^5 - 16 * q^6 - 4 * q^7 + 36 * q^8 + 4 * q^9	\( 20 q - 8 q^{2} + 4 q^{3} - 12 q^{5} - 16 q^{6} - 4 q^{7} + 36 q^{8} + 4 q^{9} + 16 q^{10} - 12 q^{11} - 100 q^{12} - 48 q^{13} + 88 q^{14} + 40 q^{15} - 36 q^{16} - 28 q^{17} - 12 q^{18} + 76 q^{19} - 16 q^{20} - 88 q^{21} - 116 q^{22} + 268 q^{24} + 40 q^{26} - 80 q^{27} + 72 q^{28} - 24 q^{29} - 216 q^{30} + 176 q^{32} + 176 q^{33} + 80 q^{34} + 60 q^{35} + 48 q^{36} + 208 q^{37} - 380 q^{38} - 68 q^{39} - 116 q^{41} + 280 q^{42} - 40 q^{43} + 116 q^{44} - 176 q^{46} - 64 q^{47} - 480 q^{48} + 168 q^{49} - 148 q^{50} - 72 q^{51} - 184 q^{52} - 120 q^{53} - 284 q^{54} + 20 q^{55} + 188 q^{56} + 560 q^{57} + 36 q^{58} - 512 q^{59} + 500 q^{60} - 460 q^{61} + 68 q^{62} - 520 q^{63} + 432 q^{65} + 300 q^{67} + 120 q^{68} + 300 q^{69} + 308 q^{70} - 108 q^{71} + 60 q^{73} + 140 q^{74} + 52 q^{75} + 872 q^{76} + 112 q^{77} + 1072 q^{78} - 208 q^{79} - 68 q^{80} - 376 q^{82} - 120 q^{83} - 1604 q^{84} + 172 q^{85} + 200 q^{87} + 316 q^{88} + 268 q^{89} - 512 q^{90} - 800 q^{91} - 448 q^{92} + 312 q^{93} - 212 q^{94} - 184 q^{95} - 612 q^{96} - 120 q^{97} - 20 q^{98} + 164 q^{99}+O(q^{100}) \) 20 * q - 8 * q^2 + 4 * q^3 - 12 * q^5 - 16 * q^6 - 4 * q^7 + 36 * q^8 + 4 * q^9 + 16 * q^10 - 12 * q^11 - 100 * q^12 - 48 * q^13 + 88 * q^14 + 40 * q^15 - 36 * q^16 - 28 * q^17 - 12 * q^18 + 76 * q^19 - 16 * q^20 - 88 * q^21 - 116 * q^22 + 268 * q^24 + 40 * q^26 - 80 * q^27 + 72 * q^28 - 24 * q^29 - 216 * q^30 + 176 * q^32 + 176 * q^33 + 80 * q^34 + 60 * q^35 + 48 * q^36 + 208 * q^37 - 380 * q^38 - 68 * q^39 - 116 * q^41 + 280 * q^42 - 40 * q^43 + 116 * q^44 - 176 * q^46 - 64 * q^47 - 480 * q^48 + 168 * q^49 - 148 * q^50 - 72 * q^51 - 184 * q^52 - 120 * q^53 - 284 * q^54 + 20 * q^55 + 188 * q^56 + 560 * q^57 + 36 * q^58 - 512 * q^59 + 500 * q^60 - 460 * q^61 + 68 * q^62 - 520 * q^63 + 432 * q^65 + 300 * q^67 + 120 * q^68 + 300 * q^69 + 308 * q^70 - 108 * q^71 + 60 * q^73 + 140 * q^74 + 52 * q^75 + 872 * q^76 + 112 * q^77 + 1072 * q^78 - 208 * q^79 - 68 * q^80 - 376 * q^82 - 120 * q^83 - 1604 * q^84 + 172 * q^85 + 200 * q^87 + 316 * q^88 + 268 * q^89 - 512 * q^90 - 800 * q^91 - 448 * q^92 + 312 * q^93 - 212 * q^94 - 184 * q^95 - 612 * q^96 - 120 * q^97 - 20 * q^98 + 164 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more