LMFDB - Embedded newform 441.3.n.h.128.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(128,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("441.128");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.n (of order $6$, degree $2$, not 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			128.6
Character	$\chi$	$=$	441.128
Dual form			441.3.n.h.410.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.526549 + 0.304003i) q^{2} +(2.98425 - 0.307033i) q^{3} +(-1.81516 + 3.14396i) q^{4} -1.05593i q^{5} +(-1.47801 + 1.06889i) q^{6} -4.63929i q^{8} +(8.81146 - 1.83252i) q^{9} +O(q^{10})$	\(q+(-0.526549 + 0.304003i) q^{2} +(2.98425 - 0.307033i) q^{3} +(-1.81516 + 3.14396i) q^{4} -1.05593i q^{5} +(-1.47801 + 1.06889i) q^{6} -4.63929i q^{8} +(8.81146 - 1.83252i) q^{9} +(0.321007 + 0.556001i) q^{10} -21.8552i q^{11} +(-4.45160 + 9.93966i) q^{12} +(-8.12859 - 14.0791i) q^{13} +(-0.324207 - 3.15117i) q^{15} +(-5.85030 - 10.1330i) q^{16} +(12.2125 - 7.05090i) q^{17} +(-4.08257 + 3.64363i) q^{18} +(-10.1979 + 17.6633i) q^{19} +(3.31981 + 1.91669i) q^{20} +(6.64405 + 11.5078i) q^{22} +4.99247i q^{23} +(-1.42441 - 13.8448i) q^{24} +23.8850 q^{25} +(8.56020 + 4.94224i) q^{26} +(25.7329 - 8.17411i) q^{27} +(26.0574 + 15.0442i) q^{29} +(1.12868 + 1.56069i) q^{30} +(20.6710 - 35.8032i) q^{31} +(22.2319 + 12.8356i) q^{32} +(-6.71027 - 65.2213i) q^{33} +(-4.28699 + 7.42528i) q^{34} +(-10.2329 + 31.0292i) q^{36} +(-9.98903 + 17.3015i) q^{37} -12.4008i q^{38} +(-28.5805 - 39.5199i) q^{39} -4.89878 q^{40} +(-13.3140 + 7.68686i) q^{41} +(0.851359 - 1.47460i) q^{43} +(68.7118 + 39.6708i) q^{44} +(-1.93503 - 9.30433i) q^{45} +(-1.51773 - 2.62878i) q^{46} +(-18.6613 + 10.7741i) q^{47} +(-20.5699 - 28.4432i) q^{48} +(-12.5766 + 7.26112i) q^{50} +(34.2803 - 24.7913i) q^{51} +59.0189 q^{52} +(31.4729 - 18.1709i) q^{53} +(-11.0647 + 12.1270i) q^{54} -23.0777 q^{55} +(-25.0099 + 55.8427i) q^{57} -18.2940 q^{58} +(-67.7180 - 39.0970i) q^{59} +(10.4956 + 4.70060i) q^{60} +(-23.0131 - 39.8599i) q^{61} +25.1362i q^{62} +31.1941 q^{64} +(-14.8667 + 8.58326i) q^{65} +(23.3608 + 32.3023i) q^{66} +(-20.9530 + 36.2917i) q^{67} +51.1941i q^{68} +(1.53285 + 14.8988i) q^{69} +2.65470i q^{71} +(-8.50160 - 40.8789i) q^{72} +(-41.2692 - 71.4803i) q^{73} -12.1468i q^{74} +(71.2787 - 7.33348i) q^{75} +(-37.0217 - 64.1235i) q^{76} +(27.0632 + 12.1206i) q^{78} +(-19.4593 - 33.7045i) q^{79} +(-10.6998 + 6.17753i) q^{80} +(74.2837 - 32.2944i) q^{81} +(4.67366 - 8.09501i) q^{82} +(33.1355 + 19.1308i) q^{83} +(-7.44529 - 12.8956i) q^{85} +1.03526i q^{86} +(82.3808 + 36.8953i) q^{87} -101.393 q^{88} +(50.4792 + 29.1442i) q^{89} +(3.84743 + 4.31093i) q^{90} +(-15.6961 - 9.06216i) q^{92} +(50.6946 - 113.192i) q^{93} +(6.55071 - 11.3462i) q^{94} +(18.6513 + 10.7683i) q^{95} +(70.2864 + 31.4787i) q^{96} +(42.7655 - 74.0720i) q^{97} +(-40.0502 - 192.576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{3} + 24 q^{4} + 14 q^{6} - 16 q^{9}+O(q^{10}) $ 24 * q + 10 * q^3 + 24 * q^4 + 14 * q^6 - 16 * q^9	$ 24 q + 10 q^{3} + 24 q^{4} + 14 q^{6} - 16 q^{9} - 22 q^{12} - 10 q^{15} - 48 q^{16} - 108 q^{17} - 8 q^{18} - 12 q^{19} + 18 q^{20} - 24 q^{22} - 30 q^{24} - 108 q^{25} - 144 q^{26} + 124 q^{27} + 54 q^{29} - 38 q^{30} - 30 q^{31} - 126 q^{32} - 26 q^{33} - 60 q^{34} + 124 q^{36} - 42 q^{37} + 56 q^{39} - 120 q^{40} - 180 q^{41} - 60 q^{43} + 72 q^{44} - 98 q^{45} + 84 q^{46} + 378 q^{47} - 436 q^{48} - 378 q^{50} - 72 q^{51} - 36 q^{52} + 324 q^{53} + 446 q^{54} + 132 q^{55} - 232 q^{57} - 180 q^{58} - 90 q^{59} - 290 q^{60} + 324 q^{64} - 126 q^{65} - 28 q^{66} + 6 q^{67} + 432 q^{69} + 750 q^{72} - 36 q^{73} - 172 q^{75} - 84 q^{76} + 28 q^{78} - 6 q^{79} - 504 q^{80} - 112 q^{81} - 54 q^{82} + 558 q^{83} + 126 q^{85} + 670 q^{87} - 336 q^{88} - 522 q^{89} + 488 q^{90} + 774 q^{92} + 42 q^{93} + 354 q^{94} - 648 q^{95} + 184 q^{96} + 270 q^{97} + 296 q^{99}+O(q^{100}) $ 24 * q + 10 * q^3 + 24 * q^4 + 14 * q^6 - 16 * q^9 - 22 * q^12 - 10 * q^15 - 48 * q^16 - 108 * q^17 - 8 * q^18 - 12 * q^19 + 18 * q^20 - 24 * q^22 - 30 * q^24 - 108 * q^25 - 144 * q^26 + 124 * q^27 + 54 * q^29 - 38 * q^30 - 30 * q^31 - 126 * q^32 - 26 * q^33 - 60 * q^34 + 124 * q^36 - 42 * q^37 + 56 * q^39 - 120 * q^40 - 180 * q^41 - 60 * q^43 + 72 * q^44 - 98 * q^45 + 84 * q^46 + 378 * q^47 - 436 * q^48 - 378 * q^50 - 72 * q^51 - 36 * q^52 + 324 * q^53 + 446 * q^54 + 132 * q^55 - 232 * q^57 - 180 * q^58 - 90 * q^59 - 290 * q^60 + 324 * q^64 - 126 * q^65 - 28 * q^66 + 6 * q^67 + 432 * q^69 + 750 * q^72 - 36 * q^73 - 172 * q^75 - 84 * q^76 + 28 * q^78 - 6 * q^79 - 504 * q^80 - 112 * q^81 - 54 * q^82 + 558 * q^83 + 126 * q^85 + 670 * q^87 - 336 * q^88 - 522 * q^89 + 488 * q^90 + 774 * q^92 + 42 * q^93 + 354 * q^94 - 648 * q^95 + 184 * q^96 + 270 * q^97 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.526549	+	0.304003i	−0.263274	+	0.152002i	−0.625827	−	0.779962i	$-0.715239\pi$
$2$	−0.526549	+	0.304003i	−0.263274	+	0.152002i	0.362553	+	0.931963i	$0.381905\pi$
$3$	2.98425	−	0.307033i	0.994749	−	0.102344i
$3$	2.98425	−	0.307033i	0.994749	−	0.102344i
$4$	−1.81516	+	3.14396i	−0.453791	+	0.785989i
$5$		−	1.05593i		−	0.211187i	−0.994409	−	0.105593i	$-0.966326\pi$
$5$		−	1.05593i		−	0.211187i	0.994409	−	0.105593i	$-0.0336742\pi$
$6$	−1.47801	+	1.06889i	−0.246336	+	0.178148i
$7$		0			0
$7$		0			0
$8$		−	4.63929i		−	0.579911i
$9$	8.81146	−	1.83252i	0.979051	−	0.203614i
$10$	0.321007	+	0.556001i	0.0321007	+	0.0556001i
$11$		−	21.8552i		−	1.98684i	−0.114542	−	0.993418i	$-0.536540\pi$
$11$		−	21.8552i		−	1.98684i	0.114542	−	0.993418i	$-0.463460\pi$
$12$	−4.45160	+	9.93966i	−0.370967	+	0.828305i
$13$	−8.12859	−	14.0791i	−0.625276	−	1.08301i	−0.988487	−	0.151304i	$-0.951653\pi$
$13$	−8.12859	−	14.0791i	−0.625276	−	1.08301i	0.363211	−	0.931707i	$-0.381680\pi$
$14$		0			0
$15$	−0.324207	−	3.15117i	−0.0216138	−	0.210078i
$16$	−5.85030	−	10.1330i	−0.365644	−	0.633313i
$17$	12.2125	−	7.05090i	0.718383	−	0.414759i	−0.0957743	−	0.995403i	$-0.530533\pi$
$17$	12.2125	−	7.05090i	0.718383	−	0.414759i	0.814157	+	0.580645i	$0.197199\pi$
$18$	−4.08257	+	3.64363i	−0.226810	+	0.202424i
$19$	−10.1979	+	17.6633i	−0.536732	+	0.929647i	0.462346	+	0.886700i	$0.347008\pi$
$19$	−10.1979	+	17.6633i	−0.536732	+	0.929647i	−0.999077	+	0.0429469i	$0.986325\pi$
$20$	3.31981	+	1.91669i	0.165991	+	0.0958347i
$21$		0			0
$22$	6.64405	+	11.5078i	0.302002	+	0.523083i
$23$			4.99247i			0.217064i	0.994093	+	0.108532i	$0.0346150\pi$
$23$			4.99247i			0.217064i	−0.994093	+	0.108532i	$0.965385\pi$
$24$	−1.42441	−	13.8448i	−0.0593506	−	0.576866i
$25$	23.8850			0.955400
$26$	8.56020	+	4.94224i	0.329239	+	0.190086i
$27$	25.7329	−	8.17411i	0.953072	−	0.302745i
$28$		0			0
$29$	26.0574	+	15.0442i	0.898531	+	0.518767i	0.876723	−	0.480995i	$-0.159725\pi$
$29$	26.0574	+	15.0442i	0.898531	+	0.518767i	0.0218077	+	0.999762i	$0.493058\pi$
$30$	1.12868	+	1.56069i	0.0376225	+	0.0520228i
$31$	20.6710	−	35.8032i	0.666807	−	1.15494i	−0.311985	−	0.950087i	$-0.600994\pi$
$31$	20.6710	−	35.8032i	0.666807	−	1.15494i	0.978792	−	0.204856i	$-0.0656726\pi$
$32$	22.2319	+	12.8356i	0.694747	+	0.401112i
$33$	−6.71027	−	65.2213i	−0.203341	−	1.97640i
$34$	−4.28699	+	7.42528i	−0.126088	+	0.218391i
$35$		0			0
$36$	−10.2329	+	31.0292i	−0.284247	+	0.861922i
$37$	−9.98903	+	17.3015i	−0.269974	+	0.467608i	−0.968855	−	0.247630i	$-0.920348\pi$
$37$	−9.98903	+	17.3015i	−0.269974	+	0.467608i	0.698881	+	0.715238i	$0.253682\pi$
$38$		−	12.4008i		−	0.326336i
$39$	−28.5805	−	39.5199i	−0.732833	−	1.01333i
$40$	−4.89878			−0.122470
$41$	−13.3140	+	7.68686i	−0.324732	+	0.187484i	−0.653500	−	0.756927i	$-0.726700\pi$
$41$	−13.3140	+	7.68686i	−0.324732	+	0.187484i	0.328768	+	0.944411i	$0.393367\pi$
$42$		0			0
$43$	0.851359	−	1.47460i	0.0197991	−	0.0342930i	−0.855956	−	0.517048i	$-0.827031\pi$
$43$	0.851359	−	1.47460i	0.0197991	−	0.0342930i	0.875755	+	0.482756i	$0.160364\pi$
$44$	68.7118	+	39.6708i	1.56163	+	0.901609i
$45$	−1.93503	−	9.30433i	−0.0430006	−	0.206763i
$46$	−1.51773	−	2.62878i	−0.0329941	−	0.0571474i
$47$	−18.6613	+	10.7741i	−0.397048	+	0.229236i	−0.685209	−	0.728346i	$-0.740289\pi$
$47$	−18.6613	+	10.7741i	−0.397048	+	0.229236i	0.288162	+	0.957582i	$0.406956\pi$
$48$	−20.5699	−	28.4432i	−0.428540	−	0.592566i
$49$		0			0
$50$	−12.5766	+	7.26112i	−0.251532	+	0.145222i
$51$	34.2803	−	24.7913i	0.672163	−	0.486103i
$52$	59.0189			1.13498
$53$	31.4729	−	18.1709i	0.593829	−	0.342847i	−0.172781	−	0.984960i	$-0.555275\pi$
$53$	31.4729	−	18.1709i	0.593829	−	0.342847i	0.766610	+	0.642113i	$0.221942\pi$
$54$	−11.0647	+	12.1270i	−0.204902	+	0.224573i
$55$	−23.0777			−0.419594
$56$		0			0
$57$	−25.0099	+	55.8427i	−0.438769	+	0.979697i
$58$	−18.2940			−0.315414
$59$	−67.7180	−	39.0970i	−1.14776	−	0.662661i	−0.199422	−	0.979914i	$-0.563906\pi$
$59$	−67.7180	−	39.0970i	−1.14776	−	0.662661i	−0.948341	+	0.317252i	$0.897240\pi$
$60$	10.4956	+	4.70060i	0.174927	+	0.0783433i
$61$	−23.0131	−	39.8599i	−0.377264	−	0.653440i	0.613399	−	0.789773i	$-0.289802\pi$
$61$	−23.0131	−	39.8599i	−0.377264	−	0.653440i	−0.990663	+	0.136333i	$0.956468\pi$
$62$			25.1362i			0.405423i
$63$		0			0
$64$	31.1941			0.487409
$65$	−14.8667	+	8.58326i	−0.228718	+	0.132050i
$66$	23.3608	+	32.3023i	0.353951	+	0.489428i
$67$	−20.9530	+	36.2917i	−0.312731	+	0.541666i	−0.978953	−	0.204088i	$-0.934577\pi$
$67$	−20.9530	+	36.2917i	−0.312731	+	0.541666i	0.666221	+	0.745754i	$0.267911\pi$
$68$			51.1941i			0.752855i
$69$	1.53285	+	14.8988i	0.0222153	+	0.215924i
$70$		0			0
$71$			2.65470i			0.0373901i	0.999825	+	0.0186951i	$0.00595117\pi$
$71$			2.65470i			0.0373901i	−0.999825	+	0.0186951i	$0.994049\pi$
$72$	−8.50160	−	40.8789i	−0.118078	−	0.567763i
$73$	−41.2692	−	71.4803i	−0.565331	−	0.979183i	−0.997019	−	0.0771594i	$-0.975415\pi$
$73$	−41.2692	−	71.4803i	−0.565331	−	0.979183i	0.431687	−	0.902023i	$-0.357918\pi$
$74$		−	12.1468i		−	0.164146i
$75$	71.2787	−	7.33348i	0.950383	−	0.0977797i
$76$	−37.0217	−	64.1235i	−0.487128	−	0.843731i
$77$		0			0
$78$	27.0632	+	12.1206i	0.346964	+	0.155392i
$79$	−19.4593	−	33.7045i	−0.246320	−	0.426639i	0.716182	−	0.697914i	$-0.245888\pi$
$79$	−19.4593	−	33.7045i	−0.246320	−	0.426639i	−0.962502	+	0.271275i	$0.912555\pi$
$80$	−10.6998	+	6.17753i	−0.133748	+	0.0772192i
$81$	74.2837	−	32.2944i	0.917083	−	0.398697i
$82$	4.67366	−	8.09501i	0.0569958	−	0.0987196i
$83$	33.1355	+	19.1308i	0.399223	+	0.230492i	0.686149	−	0.727461i	$-0.259300\pi$
$83$	33.1355	+	19.1308i	0.399223	+	0.230492i	−0.286925	+	0.957953i	$0.592633\pi$
$84$		0			0
$85$	−7.44529	−	12.8956i	−0.0875916	−	0.151713i
$86$			1.03526i			0.0120379i
$87$	82.3808	+	36.8953i	0.946906	+	0.424084i
$88$	−101.393			−1.15219
$89$	50.4792	+	29.1442i	0.567182	+	0.327463i	0.756023	−	0.654545i	$-0.227140\pi$
$89$	50.4792	+	29.1442i	0.567182	+	0.327463i	−0.188841	+	0.982008i	$0.560473\pi$
$90$	3.84743	+	4.31093i	0.0427492	+	0.0478992i
$91$		0			0
$92$	−15.6961	−	9.06216i	−0.170610	−	0.0985017i
$93$	50.6946	−	113.192i	0.545103	−	1.21712i
$94$	6.55071	−	11.3462i	0.0696884	−	0.120704i
$95$	18.6513	+	10.7683i	0.196329	+	0.113351i
$96$	70.2864	+	31.4787i	0.732150	+	0.327903i
$97$	42.7655	−	74.0720i	0.440881	−	0.763629i	−0.556874	−	0.830597i	$-0.687999\pi$
$97$	42.7655	−	74.0720i	0.440881	−	0.763629i	0.997755	+	0.0669683i	$0.0213326\pi$
$98$		0			0
$99$	−40.0502	−	192.576i	−0.404547	−	1.94522i
$100$	−43.3552	+	75.0934i	−0.433552	+	0.750934i
$101$			108.237i			1.07165i	0.844329	+	0.535826i	$0.180000\pi$
$101$			108.237i			1.07165i	−0.844329	+	0.535826i	$0.820000\pi$
$102$	−10.5136	+	23.4751i	−0.103075	+	0.230148i
$103$	−107.557			−1.04424			−0.522120	−	0.852872i	$-0.674859\pi$
$103$	−107.557			−1.04424			−0.522120	+	0.852872i	$0.674859\pi$
$104$	−65.3172	+	37.7109i	−0.628050	+	0.362605i
$105$		0			0
$106$	−11.0480	+	19.1357i	−0.104227	+	0.180526i
$107$	159.081	+	91.8456i	1.48674	+	0.858370i	0.999886	−	0.0151128i	$-0.00481074\pi$
$107$	159.081	+	91.8456i	1.48674	+	0.858370i	0.486855	+	0.873483i	$0.338144\pi$
$108$	−21.0105	+	95.7406i	−0.194541	+	0.886487i
$109$	10.7322	+	18.5888i	0.0984610	+	0.170539i	0.911048	−	0.412301i	$-0.135275\pi$
$109$	10.7322	+	18.5888i	0.0984610	+	0.170539i	−0.812587	+	0.582840i	$0.801941\pi$
$110$	12.1515	−	7.01568i	0.110468	−	0.0637789i
$111$	−24.4976	+	54.6989i	−0.220699	+	0.492783i
$112$		0			0
$113$	141.157	−	81.4968i	1.24917	−	0.721211i	0.278229	−	0.960515i	$-0.410252\pi$
$113$	141.157	−	81.4968i	1.24917	−	0.721211i	0.970945	+	0.239304i	$0.0769192\pi$
$114$	−3.80745	−	37.0070i	−0.0333986	−	0.324623i
$115$	5.27172			0.0458411
$116$	−94.5969	+	54.6156i	−0.815491	+	0.470824i
$117$	−97.4251	−	109.162i	−0.832694	−	0.933008i
$118$	47.5425			0.402902
$119$		0			0
$120$	−14.6192	+	1.50409i	−0.121827	+	0.0125341i
$121$	−356.650			−2.94752
$122$	24.2350	+	13.9921i	0.198648	+	0.114689i
$123$	−37.3722	+	27.0273i	−0.303839	+	0.219734i
$124$	75.0425	+	129.977i	0.605182	+	1.04821i
$125$		−	51.6194i		−	0.412955i
$126$		0			0
$127$	−7.50601			−0.0591024			−0.0295512	−	0.999563i	$-0.509408\pi$
$127$	−7.50601			−0.0591024			−0.0295512	+	0.999563i	$0.509408\pi$
$128$	−105.353	+	60.8255i	−0.823069	+	0.475199i
$129$	2.08792	−	4.66196i	0.0161854	−	0.0361392i
$130$	5.21868	−	9.03902i	0.0401437	−	0.0695309i
$131$		−	14.0812i		−	0.107490i	−0.998555	−	0.0537451i	$-0.982884\pi$
$131$		−	14.0812i		−	0.107490i	0.998555	−	0.0537451i	$-0.0171159\pi$
$132$	217.233	+	97.2906i	1.64571	+	0.737050i
$133$		0			0
$134$		−	25.4791i		−	0.190143i
$135$	−8.63133	−	27.1723i	−0.0639358	−	0.201276i
$136$	−32.7111	−	56.6573i	−0.240523	−	0.416598i
$137$			156.776i			1.14435i	0.820132	+	0.572174i	$0.193900\pi$
$137$			156.776i			1.14435i	−0.820132	+	0.572174i	$0.806100\pi$
$138$	−5.33639	−	7.37894i	−0.0386695	−	0.0534706i
$139$	55.2338	+	95.6677i	0.397365	+	0.688257i	0.993400	−	0.114702i	$-0.0365912\pi$
$139$	55.2338	+	95.6677i	0.397365	+	0.688257i	−0.596035	+	0.802959i	$0.703258\pi$
$140$		0			0
$141$	−52.3818	+	37.8821i	−0.371502	+	0.268668i
$142$	−0.807037	−	1.39783i	−0.00568336	−	0.00984387i
$143$	−307.702	+	177.652i	−2.15177	+	1.24232i
$144$	−70.1187	−	78.5659i	−0.486935	−	0.545596i
$145$	15.8857	−	27.5149i	0.109557	−	0.189758i
$146$	43.4605	+	25.0919i	0.297675	+	0.171863i
$147$		0			0
$148$	−36.2634	−	62.8101i	−0.245023	−	0.424393i
$149$			117.418i			0.788041i	0.919102	+	0.394020i	$0.128916\pi$
$149$			117.418i			0.788041i	−0.919102	+	0.394020i	$0.871084\pi$
$150$	−35.3023	+	25.5304i	−0.235349	+	0.170203i
$151$	102.359			0.677877			0.338939	−	0.940809i	$-0.389932\pi$
$151$	102.359			0.677877			0.338939	+	0.940809i	$0.389932\pi$
$152$	81.9451	+	47.3110i	0.539112	+	0.311257i
$153$	94.6891	−	84.5084i	0.618883	−	0.552343i
$154$		0			0
$155$	−37.8059	−	21.8272i	−0.243909	−	0.140821i
$156$	176.127	−	18.1207i	1.12902	−	0.116159i
$157$	−41.7307	+	72.2797i	−0.265801	+	0.460380i	−0.967773	−	0.251824i	$-0.918970\pi$
$157$	−41.7307	+	72.2797i	−0.265801	+	0.460380i	0.701972	+	0.712204i	$0.252303\pi$
$158$	20.4925	+	11.8314i	0.129700	+	0.0748821i
$159$	88.3439	−	63.8897i	0.555622	−	0.401822i
$160$	13.5535	−	23.4754i	0.0847097	−	0.146721i
$161$		0			0
$162$	−29.2964	+	39.5871i	−0.180842	+	0.244365i
$163$	38.6691	−	66.9769i	0.237234	−	0.410901i	−0.722686	−	0.691177i	$-0.757093\pi$
$163$	38.6691	−	66.9769i	0.237234	−	0.410901i	0.959920	+	0.280276i	$0.0904259\pi$
$164$		−	55.8116i		−	0.340315i
$165$	−68.8695	+	7.08560i	−0.417391	+	0.0429430i
$166$	−23.2633			−0.140140
$167$	−276.594	+	159.692i	−1.65625	+	0.956238i	−0.681831	+	0.731510i	$0.738816\pi$
$167$	−276.594	+	159.692i	−1.65625	+	0.956238i	−0.974422	+	0.224728i	$0.927851\pi$
$168$		0			0
$169$	−47.6481	+	82.5289i	−0.281941	+	0.488337i
$170$	7.84061	+	4.52678i	0.0461213	+	0.0266281i
$171$	−57.4901	+	174.327i	−0.336199	+	1.01946i
$172$	3.09071	+	5.35327i	0.0179693	+	0.0311237i
$173$	−58.1895	+	33.5957i	−0.336356	+	0.194195i	−0.658659	−	0.752441i	$-0.728876\pi$
$173$	−58.1895	+	33.5957i	−0.336356	+	0.194195i	0.322304	+	0.946636i	$0.395543\pi$
$174$	−54.5938	+	5.61686i	−0.313757	+	0.0322808i
$175$		0			0
$176$	−221.459	+	127.859i	−1.25829	+	0.726474i
$177$	−214.091	−	95.8835i	−1.20956	−	0.541715i
$178$	−35.4397			−0.199099
$179$	238.910	−	137.935i	1.33469	−	0.770585i	0.348677	−	0.937243i	$-0.386631\pi$
$179$	238.910	−	137.935i	1.33469	−	0.770585i	0.986015	+	0.166658i	$0.0532976\pi$
$180$	32.7648	+	10.8052i	0.182027	+	0.0600292i
$181$	−274.461			−1.51636			−0.758181	−	0.652044i	$-0.773912\pi$
$181$	−274.461			−1.51636			−0.758181	+	0.652044i	$0.773912\pi$
$182$		0			0
$183$	−80.9151	−	111.886i	−0.442159	−	0.611398i
$184$	23.1615			0.125878
$185$	18.2693	+	10.5478i	0.0987527	+	0.0570149i
$186$	7.71764	+	75.0126i	0.0414927	+	0.403294i
$187$	−154.099	−	266.907i	−0.824058	−	1.42731i
$188$		−	78.2269i		−	0.416100i
$189$		0			0
$190$	−13.0944			−0.0689180
$191$	47.6864	−	27.5317i	0.249667	−	0.144145i	−0.369945	−	0.929054i	$-0.620623\pi$
$191$	47.6864	−	27.5317i	0.249667	−	0.144145i	0.619612	+	0.784908i	$0.287290\pi$
$192$	93.0910	−	9.57763i	0.484849	−	0.0498835i
$193$	−114.576	+	198.452i	−0.593660	+	1.02825i	0.400074	+	0.916483i	$0.368984\pi$
$193$	−114.576	+	198.452i	−0.593660	+	1.02825i	−0.993734	+	0.111767i	$0.964349\pi$
$194$			52.0034i			0.268059i
$195$	−41.7304	+	30.1791i	−0.214002	+	0.154765i
$196$		0			0
$197$		−	276.616i		−	1.40414i	−0.712106	−	0.702072i	$-0.752258\pi$
$197$		−	276.616i		−	1.40414i	0.712106	−	0.702072i	$-0.247742\pi$
$198$	79.6322	+	89.2255i	0.402183	+	0.450634i
$199$	68.9149	+	119.364i	0.346306	+	0.599819i	0.985590	−	0.169151i	$-0.0541026\pi$
$199$	68.9149	+	119.364i	0.346306	+	0.599819i	−0.639284	+	0.768971i	$0.720769\pi$
$200$		−	110.809i		−	0.554047i
$201$	−51.3862	+	114.737i	−0.255653	+	0.570828i
$202$	−32.9043	−	56.9920i	−0.162893	−	0.282138i
$203$		0			0
$204$	15.7183	+	152.776i	0.0770504	+	0.748902i
$205$	8.11682	+	14.0587i	0.0395942	+	0.0685792i
$206$	56.6339	−	32.6976i	0.274922	−	0.158726i
$207$	9.14882	+	43.9910i	0.0441972	+	0.212517i
$208$	−95.1094	+	164.734i	−0.457257	+	0.791992i
$209$	386.035	+	222.877i	1.84706	+	1.06640i
$210$		0			0
$211$	112.988	+	195.700i	0.535487	+	0.927490i	0.999140	+	0.0414730i	$0.0132051\pi$
$211$	112.988	+	195.700i	0.535487	+	0.927490i	−0.463653	+	0.886017i	$0.653462\pi$
$212$			131.933i			0.622324i
$213$	0.815080	+	7.92228i	0.00382667	+	0.0371938i
$214$	−111.685			−0.521894
$215$	−1.55708	−	0.898980i	−0.00724223	−	0.00418130i
$216$	−37.9220	−	119.382i	−0.175565	−	0.552697i
$217$		0			0
$218$	−11.3021	−	6.52527i	−0.0518445	−	0.0299325i
$219$	−145.104	−	200.644i	−0.662577	−	0.916183i
$220$	41.8898	−	72.5552i	0.190408	−	0.329796i
$221$	−198.541	−	114.628i	−0.898376	−	0.518678i
$222$	−3.72946	−	36.2490i	−0.0167994	−	0.163284i
$223$	−85.6801	+	148.402i	−0.384215	+	0.665481i	−0.991660	−	0.128881i	$-0.958861\pi$
$223$	−85.6801	+	148.402i	−0.384215	+	0.665481i	0.607445	+	0.794362i	$0.292195\pi$
$224$		0			0
$225$	210.462	−	43.7698i	0.935386	−	0.194533i
$226$	−49.5506	+	85.8241i	−0.219250	+	0.379753i
$227$		−	295.742i		−	1.30283i	−0.758722	−	0.651414i	$-0.774176\pi$
$227$		−	295.742i		−	1.30283i	0.758722	−	0.651414i	$-0.225824\pi$
$228$	−130.170	−	179.994i	−0.570921	−	0.789446i
$229$	7.75360			0.0338585			0.0169292	−	0.999857i	$-0.494611\pi$
$229$	7.75360			0.0338585			0.0169292	+	0.999857i	$0.494611\pi$
$230$	−2.77582	+	1.60262i	−0.0120688	+	0.00696792i
$231$		0			0
$232$	69.7946	−	120.888i	0.300839	−	0.521068i
$233$	−1.52555	−	0.880778i	−0.00654744	−	0.00378016i	0.496723	−	0.867909i	$-0.334537\pi$
$233$	−1.52555	−	0.880778i	−0.00654744	−	0.00378016i	−0.503270	+	0.864129i	$0.667870\pi$
$234$	84.4847	+	27.8615i	0.361046	+	0.119066i
$235$	11.3767	+	19.7051i	0.0484116	+	0.0838513i
$236$	245.839	−	141.935i	1.04169	−	0.601420i
$237$	−68.4197	−	94.6079i	−0.288691	−	0.399189i
$238$		0			0
$239$	−82.1746	+	47.4435i	−0.343827	+	0.198508i	−0.661963	−	0.749537i	$-0.730276\pi$
$239$	−82.1746	+	47.4435i	−0.343827	+	0.198508i	0.318136	+	0.948045i	$0.396943\pi$
$240$	−30.0341	+	21.7205i	−0.125142	+	0.0905020i
$241$	84.6102			0.351080			0.175540	−	0.984472i	$-0.443833\pi$
$241$	84.6102			0.351080			0.175540	+	0.984472i	$0.443833\pi$
$242$	187.794	−	108.423i	0.776007	−	0.448028i
$243$	211.766	−	119.182i	0.871463	−	0.490461i
$244$	167.090			0.684796
$245$		0			0
$246$	11.4619	−	25.5925i	0.0465931	−	0.104034i
$247$	331.579			1.34242
$248$	−166.101	−	95.8987i	−0.669764	−	0.386688i
$249$	104.758	+	46.9174i	0.420717	+	0.188423i
$250$	15.6924	+	27.1801i	0.0627698	+	0.108720i
$251$		−	308.555i		−	1.22930i	−0.788799	−	0.614651i	$-0.789297\pi$
$251$		−	308.555i		−	1.22930i	0.788799	−	0.614651i	$-0.210703\pi$
$252$		0			0
$253$	109.111			0.431271
$254$	3.95228	−	2.28185i	0.0155602	−	0.00898366i
$255$	−26.1779	−	36.1977i	−0.102659	−	0.141952i
$256$	−25.4060	+	44.0045i	−0.0992423	+	0.171893i
$257$			137.567i			0.535278i	0.963519	+	0.267639i	$0.0862435\pi$
$257$			137.567i			0.535278i	−0.963519	+	0.267639i	$0.913756\pi$
$258$	0.317860	+	3.08948i	0.00123202	+	0.0119747i
$259$		0			0
$260$		−	62.3201i		−	0.239693i
$261$	257.173	+	84.8110i	0.985336	+	0.324946i
$262$	4.28074	+	7.41445i	0.0163387	+	0.0282994i
$263$			292.117i			1.11071i	0.831613	+	0.555356i	$0.187418\pi$
$263$			292.117i			1.11071i	−0.831613	+	0.555356i	$0.812582\pi$
$264$	−302.581	+	31.1308i	−1.14614	+	0.117920i
$265$	−19.1873	−	33.2333i	−0.0724048	−	0.125409i
$266$		0			0
$267$	159.591	+	71.4746i	0.597717	+	0.267695i
$268$	−76.0663	−	131.751i	−0.283829	−	0.491607i
$269$	351.998	−	203.226i	1.30854	−	0.755487i	0.326689	−	0.945132i	$-0.394067\pi$
$269$	351.998	−	203.226i	1.30854	−	0.755487i	0.981853	+	0.189645i	$0.0607336\pi$
$270$	12.8053	+	11.6836i	0.0474270	+	0.0432726i
$271$	−82.4156	+	142.748i	−0.304116	+	0.526745i	−0.977064	−	0.212945i	$-0.931695\pi$
$271$	−82.4156	+	142.748i	−0.304116	+	0.526745i	0.672948	+	0.739690i	$0.265028\pi$
$272$	−142.894	−	82.4997i	−0.525344	−	0.303308i
$273$		0			0
$274$	−47.6603	−	82.5500i	−0.173943	−	0.301277i
$275$		−	522.012i		−	1.89822i
$276$	−49.6235	−	22.2245i	−0.179795	−	0.0805235i
$277$	344.356			1.24316			0.621582	−	0.783349i	$-0.286490\pi$
$277$	344.356			1.24316			0.621582	+	0.783349i	$0.286490\pi$
$278$	−58.1666	−	33.5825i	−0.209232	−	0.120800i
$279$	116.532	−	353.359i	0.417676	−	1.26652i
$280$		0			0
$281$	369.989	+	213.613i	1.31669	+	0.760189i	0.983194	−	0.182565i	$-0.0584399\pi$
$281$	369.989	+	213.613i	1.31669	+	0.760189i	0.333491	+	0.942753i	$0.391773\pi$
$282$	16.0653	−	35.8710i	0.0569691	−	0.127202i
$283$	27.7732	−	48.1045i	0.0981384	−	0.169981i	−0.812776	−	0.582577i	$-0.802045\pi$
$283$	27.7732	−	48.1045i	0.0981384	−	0.169981i	0.910914	+	0.412596i	$0.135378\pi$
$284$	−8.34626	−	4.81872i	−0.0293883	−	0.0169673i
$285$	58.9663	+	26.4088i	0.206899	+	0.0926624i
$286$	108.014	−	187.085i	0.377670	−	0.654143i
$287$		0			0
$288$	219.417	+	72.3599i	0.761865	+	0.251250i
$289$	−45.0697	+	78.0631i	−0.155951	+	0.270114i
$290$			19.3173i			0.0666112i
$291$	104.880	−	234.180i	0.360413	−	0.804741i
$292$	299.641			1.02617
$293$	−61.2947	+	35.3885i	−0.209197	+	0.120780i	−0.600938	−	0.799296i	$-0.705206\pi$
$293$	−61.2947	+	35.3885i	−0.209197	+	0.120780i	0.391741	+	0.920075i	$0.371873\pi$
$294$		0			0
$295$	−41.2839	+	71.5058i	−0.139945	+	0.242393i
$296$	80.2666	+	46.3420i	0.271171	+	0.156561i
$297$	−178.647	−	562.399i	−0.601505	−	1.89360i
$298$	−35.6955	−	61.8264i	−0.119783	−	0.207471i
$299$	70.2897	−	40.5818i	0.235083	−	0.135725i
$300$	−106.326	+	237.409i	−0.354422	+	0.791363i
$301$		0			0
$302$	−53.8973	+	31.1176i	−0.178468	+	0.103038i
$303$	33.2322	+	323.005i	0.109677	+	1.06602i
$304$	238.643			0.785010
$305$	−42.0894	+	24.3003i	−0.137998	+	0.0796732i
$306$	−24.1676	+	73.2836i	−0.0789792	+	0.239489i
$307$	56.5282			0.184131			0.0920655	−	0.995753i	$-0.470653\pi$
$307$	56.5282			0.184131			0.0920655	+	0.995753i	$0.470653\pi$
$308$		0			0
$309$	−320.976	+	33.0234i	−1.03876	+	0.106872i
$310$	26.5422			0.0856200
$311$	489.541	+	282.637i	1.57409	+	0.908800i	0.995660	+	0.0930665i	$0.0296669\pi$
$311$	489.541	+	282.637i	1.57409	+	0.908800i	0.578428	+	0.815733i	$0.303666\pi$
$312$	−183.344	+	132.593i	−0.587641	+	0.424978i
$313$	7.29712	+	12.6390i	0.0233135	+	0.0403801i	0.877447	−	0.479674i	$-0.159245\pi$
$313$	7.29712	+	12.6390i	0.0233135	+	0.0403801i	−0.854133	+	0.520054i	$0.825912\pi$
$314$		−	50.7450i		−	0.161608i
$315$		0			0
$316$	141.287			0.447112
$317$	−210.858	+	121.739i	−0.665167	+	0.384034i	−0.794243	−	0.607600i	$-0.792132\pi$
$317$	−210.858	+	121.739i	−0.665167	+	0.384034i	0.129076	+	0.991635i	$0.458799\pi$
$318$	−27.0947	+	60.4978i	−0.0852035	+	0.190245i
$319$	328.795	−	569.490i	1.03071	−	1.78523i
$320$		−	32.9390i		−	0.102934i
$321$	502.937	+	225.247i	1.56678	+	0.701703i
$322$		0			0
$323$			287.617i			0.890456i
$324$	−33.3049	+	292.164i	−0.102793	+	0.901742i
$325$	−194.151	−	336.280i	−0.597389	−	1.03471i
$326$			47.0221i			0.144240i
$327$	37.7351	+	52.1784i	0.115398	+	0.159567i
$328$	35.6615	+	61.7676i	0.108724	+	0.188316i
$329$		0			0
$330$	34.1091	−	24.6674i	0.103361	−	0.0747498i
$331$	154.134	+	266.968i	0.465661	+	0.806549i	0.999231	−	0.0392068i	$-0.0124831\pi$
$331$	154.134	+	266.968i	0.465661	+	0.806549i	−0.533570	+	0.845756i	$0.679150\pi$
$332$	−120.293	+	69.4511i	−0.362328	+	0.209190i
$333$	−56.3125	+	170.757i	−0.169107	+	0.512783i
$334$	97.0936	−	168.171i	0.290699	−	0.503506i
$335$	38.3216	+	22.1250i	0.114393	+	0.0660448i
$336$		0			0
$337$	66.3297	+	114.886i	0.196824	+	0.340909i	0.947497	−	0.319765i	$-0.103604\pi$
$337$	66.3297	+	114.886i	0.196824	+	0.340909i	−0.750673	+	0.660674i	$0.770271\pi$
$338$		−	57.9407i		−	0.171422i
$339$	396.224	−	286.546i	1.16880	−	0.845270i
$340$	54.0577			0.158993
$341$	−782.487	−	451.769i	−2.29468	−	1.32484i
$342$	−22.7247	−	109.269i	−0.0664465	−	0.319500i
$343$		0			0
$344$	−6.84108	−	3.94970i	−0.0198869	−	0.0114817i
$345$	15.7321	−	1.61859i	0.0456004	−	0.00469157i
$346$	20.4264	−	35.3796i	0.0590359	−	0.102253i
$347$	−359.479	−	207.545i	−1.03596	−	0.598113i	−0.117276	−	0.993099i	$-0.537416\pi$
$347$	−359.479	−	207.545i	−1.03596	−	0.598113i	−0.918687	+	0.394986i	$0.870749\pi$
$348$	−265.532	+	192.031i	−0.763022	+	0.551812i
$349$	−147.383	+	255.275i	−0.422302	+	0.731448i	−0.996164	−	0.0875035i	$-0.972111\pi$
$349$	−147.383	+	255.275i	−0.422302	+	0.731448i	0.573862	+	0.818952i	$0.305444\pi$
$350$		0			0
$351$	−324.257	−	295.854i	−0.923809	−	0.842887i
$352$	280.525	−	485.883i	0.796945	−	1.38035i
$353$		−	9.24695i		−	0.0261953i	−0.999914	−	0.0130977i	$-0.995831\pi$
$353$		−	9.24695i		−	0.0261953i	0.999914	−	0.0130977i	$-0.00416923\pi$
$354$	141.878	−	14.5971i	0.400787	−	0.0412347i
$355$	2.80319			0.00789631
$356$	−183.256	+	105.803i	−0.514764	+	0.297199i
$357$		0			0
$358$	−83.8652	+	145.259i	−0.234260	+	0.405751i
$359$	−89.0874	−	51.4346i	−0.248154	−	0.143272i	0.370764	−	0.928727i	$-0.379096\pi$
$359$	−89.0874	−	51.4346i	−0.248154	−	0.143272i	−0.618919	+	0.785455i	$0.712429\pi$
$360$	−43.1655	+	8.97714i	−0.119904	+	0.0249365i
$361$	−27.4945	−	47.6219i	−0.0761621	−	0.131917i
$362$	144.517	−	83.4371i	0.399219	−	0.230489i
$363$	−1064.33	+	109.503i	−2.93204	+	0.301662i
$364$		0			0
$365$	−75.4786	+	43.5776i	−0.206791	+	0.119391i
$366$	76.6194	+	34.3150i	0.209343	+	0.0937567i
$367$	−544.389			−1.48335			−0.741674	−	0.670760i	$-0.765968\pi$
$367$	−544.389			−1.48335			−0.741674	+	0.670760i	$0.765968\pi$
$368$	50.5888	−	29.2075i	0.137470	−	0.0793681i
$369$	−103.230	+	92.1307i	−0.279755	+	0.249677i
$370$	−12.8262			−0.0346654
$371$		0			0
$372$	263.853	+	364.844i	0.709282	+	0.980765i
$373$	429.429			1.15129			0.575643	−	0.817701i	$-0.304752\pi$
$373$	429.429			1.15129			0.575643	+	0.817701i	$0.304752\pi$
$374$	162.281	+	93.6930i	0.433907	+	0.250516i
$375$	−15.8488	−	154.045i	−0.0422636	−	0.410787i
$376$	49.9840	+	86.5749i	0.132936	+	0.230252i
$377$		−	489.154i		−	1.29749i
$378$		0			0
$379$	−449.221			−1.18528			−0.592639	−	0.805468i	$-0.701914\pi$
$379$	−449.221			−1.18528			−0.592639	+	0.805468i	$0.701914\pi$
$380$	−67.7103	+	39.0925i	−0.178185	+	0.102875i
$381$	−22.3998	+	2.30459i	−0.0587921	+	0.00604879i
$382$	−16.7395	+	28.9936i	−0.0438206	+	0.0758995i
$383$			415.580i			1.08507i	0.840035	+	0.542533i	$0.182534\pi$
$383$			415.580i			1.08507i	−0.840035	+	0.542533i	$0.817466\pi$
$384$	−295.723	+	213.865i	−0.770113	+	0.556940i
$385$		0			0
$386$		−	139.326i		−	0.360949i
$387$	4.79949	−	14.5535i	0.0124018	−	0.0376059i
$388$	155.253	+	268.906i	0.400136	+	0.693056i
$389$		−	211.780i		−	0.544420i	−0.962238	−	0.272210i	$-0.912245\pi$
$389$		−	211.780i		−	0.544420i	0.962238	−	0.272210i	$-0.0877546\pi$
$390$	12.7986	−	28.5770i	0.0328168	−	0.0732743i
$391$	35.2014	+	60.9706i	0.0900291	+	0.155935i
$392$		0			0
$393$	−4.32340	−	42.0219i	−0.0110010	−	0.106926i
$394$	84.0922	+	145.652i	0.213432	+	0.369675i
$395$	−35.5897	+	20.5477i	−0.0901006	+	0.0520196i
$396$	678.149	+	223.642i	1.71250	+	0.564752i
$397$	301.401	−	522.042i	0.759196	−	1.31497i	−0.184065	−	0.982914i	$-0.558926\pi$
$397$	301.401	−	522.042i	0.759196	−	1.31497i	0.943261	−	0.332052i	$-0.107741\pi$
$398$	−72.5741	−	41.9007i	−0.182347	−	0.105278i
$399$		0			0
$400$	−139.734	−	242.027i	−0.349336	−	0.605068i
$401$		−	498.735i		−	1.24373i	−0.783125	−	0.621864i	$-0.786376\pi$
$401$		−	498.735i		−	1.24373i	0.783125	−	0.621864i	$-0.213624\pi$
$402$	−7.82292	−	76.0359i	−0.0194600	−	0.189144i
$403$	−672.105			−1.66775
$404$	−340.292	−	196.468i	−0.842306	−	0.486306i
$405$	−34.1008	−	78.4387i	−0.0841995	−	0.193676i
$406$		0			0
$407$	378.128	+	218.312i	0.929061	+	0.536394i
$408$	−115.014	−	159.036i	−0.281896	−	0.389794i
$409$	−265.579	+	459.996i	−0.649338	+	1.12469i	0.333944	+	0.942593i	$0.391620\pi$
$409$	−265.579	+	459.996i	−0.649338	+	1.12469i	−0.983281	+	0.182093i	$0.941713\pi$
$410$	−8.54780	−	4.93508i	−0.0208483	−	0.0120368i
$411$	48.1353	+	467.857i	0.117117	+	1.13834i
$412$	195.233	−	338.154i	0.473867	−	0.820761i
$413$		0			0
$414$	−18.1907	−	20.3821i	−0.0439389	−	0.0492322i
$415$	20.2009	−	34.9890i	0.0486768	−	0.0843108i
$416$		−	417.341i		−	1.00322i
$417$	194.204	+	268.538i	0.465718	+	0.643975i
$418$	−271.022			−0.648377
$419$	256.304	−	147.977i	0.611704	−	0.353168i	−0.161928	−	0.986803i	$-0.551771\pi$
$419$	256.304	−	147.977i	0.611704	−	0.353168i	0.773632	+	0.633635i	$0.218438\pi$
$420$		0			0
$421$	−164.115	+	284.256i	−0.389822	+	0.675192i	−0.992425	−	0.122849i	$-0.960797\pi$
$421$	−164.115	+	284.256i	−0.389822	+	0.675192i	0.602603	+	0.798041i	$0.294130\pi$
$422$	−118.987	−	68.6972i	−0.281960	−	0.162790i
$423$	−144.689	+	129.133i	−0.342055	+	0.305278i
$424$	−84.3000	−	146.012i	−0.198821	−	0.344368i
$425$	291.696	−	168.411i	0.686343	−	0.396260i
$426$	−2.83758	−	3.92368i	−0.00666098	−	0.00921052i
$427$		0			0
$428$	−577.517	+	333.430i	−1.34934	+	0.779041i
$429$	−863.715	+	624.633i	−2.01332	+	1.45602i
$430$	1.09317			0.00254226
$431$	−298.538	+	172.361i	−0.692665	+	0.399910i	−0.804610	−	0.593804i	$-0.797625\pi$
$431$	−298.538	+	172.361i	−0.692665	+	0.399910i	0.111945	+	0.993714i	$0.464292\pi$
$432$	−233.374	−	212.931i	−0.540217	−	0.492896i
$433$	668.552			1.54400			0.772000	−	0.635622i	$-0.219256\pi$
$433$	668.552			1.54400			0.772000	+	0.635622i	$0.219256\pi$
$434$		0			0
$435$	38.9590	−	86.9887i	0.0895609	−	0.199974i
$436$	−77.9232			−0.178723
$437$	−88.1835	−	50.9127i	−0.201793	−	0.116505i
$438$	137.401	+	61.5367i	0.313701	+	0.140495i
$439$	266.985	+	462.431i	0.608165	+	1.05337i	0.991543	+	0.129782i	$0.0414276\pi$
$439$	266.985	+	462.431i	0.608165	+	1.05337i	−0.383377	+	0.923592i	$0.625239\pi$
$440$			107.064i			0.243327i
$441$		0			0
$442$	139.389			0.315359
$443$	−146.716	+	84.7067i	−0.331188	+	0.191211i	−0.656368	−	0.754441i	$-0.727908\pi$
$443$	−146.716	+	84.7067i	−0.331188	+	0.191211i	0.325181	+	0.945652i	$0.394575\pi$
$444$	−127.504	−	176.307i	−0.287171	−	0.397088i
$445$	30.7743	−	53.3027i	0.0691558	−	0.119781i
$446$		−	104.188i		−	0.233605i
$447$	36.0512	+	350.405i	0.0806515	+	0.783903i
$448$		0			0
$449$		−	253.851i		−	0.565370i	−0.959213	−	0.282685i	$-0.908775\pi$
$449$		−	253.851i		−	0.565370i	0.959213	−	0.282685i	$-0.0912251\pi$
$450$	−97.5122	+	87.0280i	−0.216694	+	0.193396i
$451$	167.998	+	290.981i	0.372501	+	0.645190i
$452$			591.721i			1.30912i
$453$	305.466	−	31.4277i	0.674318	−	0.0693768i
$454$	89.9065	+	155.723i	0.198032	+	0.343002i
$455$		0			0
$456$	259.070	+	116.028i	0.568137	+	0.254447i
$457$	118.649	+	205.507i	0.259626	+	0.449686i	0.966142	−	0.258012i	$-0.0830673\pi$
$457$	118.649	+	205.507i	0.259626	+	0.449686i	−0.706515	+	0.707698i	$0.749734\pi$
$458$	−4.08265	+	2.35712i	−0.00891408	+	0.00514654i
$459$	256.629	−	281.267i	0.559104	−	0.612781i
$460$	−9.56904	+	16.5741i	−0.0208023	+	0.0360306i
$461$	629.107	+	363.215i	1.36466	+	0.787886i	0.990240	−	0.139374i	$-0.0445092\pi$
$461$	629.107	+	363.215i	1.36466	+	0.787886i	0.374418	+	0.927260i	$0.377842\pi$
$462$		0			0
$463$	−327.616	−	567.448i	−0.707594	−	1.22559i	−0.965747	−	0.259485i	$-0.916447\pi$
$463$	−327.616	−	567.448i	−0.707594	−	1.22559i	0.258153	−	0.966104i	$-0.416886\pi$
$464$		−	352.053i		−	0.758736i
$465$	−119.524	−	53.5302i	−0.257040	−	0.115119i
$466$	1.07104			0.00229836
$467$	148.297	+	85.6192i	0.317552	+	0.183339i	0.650301	−	0.759677i	$-0.274643\pi$
$467$	148.297	+	85.6192i	0.317552	+	0.183339i	−0.332749	+	0.943015i	$0.607976\pi$
$468$	520.043	−	108.154i	1.11120	−	0.231097i
$469$		0			0
$470$	−11.9808	−	6.91712i	−0.0254911	−	0.0147173i
$471$	−102.342	+	228.513i	−0.217288	+	0.485166i
$472$	−181.382	+	314.163i	−0.384285	+	0.665600i
$473$	−32.2276	−	18.6066i	−0.0681345	−	0.0393375i
$474$	64.7874	+	29.0159i	0.136682	+	0.0612149i
$475$	−243.577	+	421.888i	−0.512794	+	0.888185i
$476$		0			0
$477$	244.024	−	217.787i	0.511580	−	0.456576i
$478$	28.8459	−	49.9626i	0.0603472	−	0.104524i
$479$			847.093i			1.76846i	0.467051	+	0.884230i	$0.345316\pi$
$479$			847.093i			1.76846i	−0.467051	+	0.884230i	$0.654684\pi$
$480$	33.2394	−	74.2179i	0.0692488	−	0.154621i
$481$	324.787			0.675233
$482$	−44.5514	+	25.7218i	−0.0924303	+	0.0533647i
$483$		0			0
$484$	647.378	−	1121.29i	1.33756	−	2.31672i
$485$	−78.2152	−	45.1576i	−0.161268	−	0.0931084i
$486$	−75.2732	+	127.133i	−0.154883	+	0.261590i
$487$	−34.8852	−	60.4229i	−0.0716328	−	0.124072i	0.827984	−	0.560751i	$-0.189488\pi$
$487$	−34.8852	−	60.4229i	−0.0716328	−	0.124072i	−0.899617	+	0.436680i	$0.856154\pi$
$488$	−184.921	+	106.764i	−0.378937	+	0.218779i
$489$	94.8341	−	211.748i	0.193935	−	0.433023i
$490$		0			0
$491$	211.867	−	122.322i	0.431501	−	0.249127i	−0.268485	−	0.963284i	$-0.586523\pi$
$491$	211.867	−	122.322i	0.431501	−	0.249127i	0.699986	+	0.714157i	$0.253190\pi$
$492$	−17.1360	−	166.556i	−0.0348293	−	0.338528i
$493$	424.302			0.860652
$494$	−174.592	+	100.801i	−0.353426	+	0.204050i
$495$	−203.348	+	42.2904i	−0.410804	+	0.0854351i
$496$	−483.726			−0.975255
$497$		0			0
$498$	−69.4235	+	7.14260i	−0.139405	+	0.0143426i
$499$	416.993			0.835658			0.417829	−	0.908526i	$-0.362791\pi$
$499$	416.993			0.835658			0.417829	+	0.908526i	$0.362791\pi$
$500$	162.289	+	93.6976i	0.324578	+	0.187395i
$501$	−776.395	+	561.483i	−1.54969	+	1.12072i
$502$	93.8016	+	162.469i	0.186856	+	0.323644i
$503$		−	691.668i		−	1.37509i	−0.726144	−	0.687543i	$-0.758689\pi$
$503$		−	691.668i		−	1.37509i	0.726144	−	0.687543i	$-0.241311\pi$
$504$		0			0
$505$	114.291			0.226319
$506$	−57.4525	+	33.1702i	−0.113543	+	0.0655538i
$507$	−116.855	+	260.916i	−0.230482	+	0.514628i
$508$	13.6246	−	23.5986i	0.0268202	−	0.0464539i
$509$			233.282i			0.458315i	0.973389	+	0.229157i	$0.0735971\pi$
$509$			233.282i			0.458315i	−0.973389	+	0.229157i	$0.926403\pi$
$510$	24.7882	+	11.1017i	0.0486043	+	0.0217680i
$511$		0			0
$512$		−	517.498i		−	1.01074i
$513$	−118.040	+	537.887i	−0.230098	+	1.04851i
$514$	−41.8207	−	72.4355i	−0.0813631	−	0.140925i
$515$			113.573i			0.220530i
$516$	10.8671	+	15.0265i	0.0210602	+	0.0291212i
$517$	235.470	+	407.845i	0.455454	+	0.788869i
$518$		0			0
$519$	−163.337	+	118.124i	−0.314715	+	0.227599i
$520$	39.8202	+	68.9707i	0.0765774	+	0.132636i
$521$	221.904	−	128.116i	0.425920	−	0.245905i	−0.271687	−	0.962386i	$-0.587582\pi$
$521$	221.904	−	128.116i	0.425920	−	0.245905i	0.697607	+	0.716481i	$0.254248\pi$
$522$	−161.197	+	33.5242i	−0.308806	+	0.0642225i
$523$	117.623	−	203.729i	0.224901	−	0.389540i	−0.731389	−	0.681961i	$-0.761127\pi$
$523$	117.623	−	203.729i	0.224901	−	0.389540i	0.956290	+	0.292421i	$0.0944608\pi$
$524$	44.2708	+	25.5597i	0.0844862	+	0.0487781i
$525$		0			0
$526$	−88.8045	−	153.814i	−0.168830	−	0.292422i
$527$		−	582.996i		−	1.10626i
$528$	−621.632	+	449.560i	−1.17733	+	0.851438i
$529$	504.075			0.952883
$530$	20.2061	+	11.6660i	0.0381247	+	0.0220113i
$531$	−668.341	−	220.407i	−1.25865	−	0.415079i
$532$		0			0
$533$	216.449	+	124.967i	0.406095	+	0.234459i
$534$	−105.761	+	10.8811i	−0.198054	+	0.0203767i
$535$	96.9830	−	167.979i	0.181277	−	0.313980i
$536$	168.367	+	97.2070i	0.314118	+	0.181356i
$537$	670.616	−	484.984i	1.24882	−	0.903137i
$538$	−123.563	+	214.017i	−0.229670	+	0.397801i
$539$		0			0
$540$	101.096	+	22.1857i	0.187214	+	0.0410846i
$541$	87.5771	−	151.688i	0.161880	−	0.280384i	−0.773663	−	0.633597i	$-0.781578\pi$
$541$	87.5771	−	151.688i	0.161880	−	0.280384i	0.935543	+	0.353213i	$0.114911\pi$
$542$		−	100.218i		−	0.184905i
$543$	−819.061	+	84.2687i	−1.50840	+	0.155191i
$544$	362.010			0.665459
$545$	19.6286	−	11.3326i	0.0360157	−	0.0207937i
$546$		0			0
$547$	−153.703	+	266.221i	−0.280992	+	0.486692i	−0.971629	−	0.236509i	$-0.923997\pi$
$547$	−153.703	+	266.221i	−0.280992	+	0.486692i	0.690637	+	0.723201i	$0.257330\pi$
$548$	−492.896	−	284.574i	−0.899445	−	0.519295i
$549$	−275.823	−	309.052i	−0.502410	−	0.562935i
$550$	158.693	+	274.865i	0.288533	+	0.499754i
$551$	−531.462	+	306.840i	−0.964540	+	0.556878i
$552$	69.1197	−	7.11134i	0.125217	−	0.0128829i
$553$		0			0
$554$	−181.320	+	104.685i	−0.327293	+	0.188963i
$555$	57.7585	+	25.8679i	0.104069	+	0.0466088i
$556$	−401.034			−0.721283
$557$	306.106	−	176.730i	0.549562	−	0.317290i	−0.199383	−	0.979922i	$-0.563894\pi$
$557$	306.106	−	176.730i	0.549562	−	0.317290i	0.748945	+	0.662632i	$0.230561\pi$
$558$	46.0627	+	221.487i	0.0825496	+	0.396930i
$559$	−27.6814			−0.0495195
$560$		0			0
$561$	−541.818	−	749.203i	−0.965808	−	1.33548i
$562$	−259.756			−0.462199
$563$	175.929	+	101.573i	0.312485	+	0.180413i	0.648038	−	0.761608i	$-0.275590\pi$
$563$	175.929	+	101.573i	0.312485	+	0.180413i	−0.335553	+	0.942021i	$0.608923\pi$
$564$	−24.0182	−	233.448i	−0.0425855	−	0.413916i
$565$	−86.0553	−	149.052i	−0.152310	−	0.263809i
$566$			33.7725i			0.0596687i
$567$		0			0
$568$	12.3159			0.0216830
$569$	−188.506	+	108.834i	−0.331294	+	0.191273i	−0.656415	−	0.754400i	$-0.727928\pi$
$569$	−188.506	+	108.834i	−0.331294	+	0.191273i	0.325122	+	0.945672i	$0.394595\pi$
$570$	−39.0770	+	4.02041i	−0.0685561	+	0.00705336i
$571$	−324.722	+	562.435i	−0.568690	+	0.985000i	0.428006	+	0.903776i	$0.359216\pi$
$571$	−324.722	+	562.435i	−0.568690	+	0.985000i	−0.996696	+	0.0812239i	$0.974117\pi$
$572$		−	1289.87i		−	2.25502i
$573$	133.855	−	96.8028i	0.233604	−	0.168940i
$574$		0			0
$575$			119.245i			0.207383i
$576$	274.866	−	57.1640i	0.477198	−	0.0992431i
$577$	310.795	+	538.313i	0.538640	+	0.932952i	0.998978	+	0.0452078i	$0.0143950\pi$
$577$	310.795	+	538.313i	0.538640	+	0.932952i	−0.460338	+	0.887744i	$0.652272\pi$
$578$		−	54.8054i		−	0.0948190i
$579$	−280.993	+	627.409i	−0.485307	+	1.08361i
$580$	57.6705	+	99.8882i	0.0994318	+	0.172221i
$581$		0			0
$582$	15.9667	+	155.191i	0.0274343	+	0.266651i
$583$	−397.129	−	687.847i	−0.681181	−	1.17984i
$584$	−331.618	+	191.460i	−0.567839	+	0.327842i
$585$	−115.268	+	102.875i	−0.197039	+	0.175854i
$586$	21.5164	−	37.2675i	0.0367174	−	0.0635965i
$587$	297.051	+	171.502i	0.506049	+	0.292168i	0.731208	−	0.682154i	$-0.238957\pi$
$587$	297.051	+	171.502i	0.506049	+	0.292168i	−0.225159	+	0.974322i	$0.572290\pi$
$588$		0			0
$589$	421.602	+	730.236i	0.715793	+	1.23979i
$590$		−	50.2017i		−	0.0850877i
$591$	−84.9303	−	825.492i	−0.143706	−	1.39677i
$592$	233.755			0.394857
$593$	654.707	+	377.995i	1.10406	+	0.637429i	0.937284	−	0.348566i	$-0.113331\pi$
$593$	654.707	+	377.995i	1.10406	+	0.637429i	0.166775	+	0.985995i	$0.446665\pi$
$594$	265.037	+	241.821i	0.446191	+	0.407106i
$595$		0			0
$596$	−369.157	−	213.133i	−0.619391	−	0.357606i
$597$	242.308	+	335.053i	0.405876	+	0.561227i
$598$	−24.6740	+	42.7366i	−0.0412608	+	0.0714658i
$599$	−594.729	−	343.367i	−0.992870	−	0.573234i	−0.0867391	−	0.996231i	$-0.527645\pi$
$599$	−594.729	−	343.367i	−0.992870	−	0.573234i	−0.906131	+	0.422997i	$0.860978\pi$
$600$	−34.0221	−	330.683i	−0.0567035	−	0.551138i
$601$	203.146	−	351.860i	0.338014	−	0.585458i	−0.646045	−	0.763299i	$-0.723578\pi$
$601$	203.146	−	351.860i	0.338014	−	0.585458i	0.984059	+	0.177842i	$0.0569115\pi$
$602$		0			0
$603$	−118.121	+	358.179i	−0.195889	+	0.593996i
$604$	−185.799	+	321.814i	−0.307615	+	0.532804i
$605$			376.599i			0.622478i
$606$	−115.693	−	159.975i	−0.190913	−	0.263986i
$607$	243.768			0.401595			0.200797	−	0.979633i	$-0.435647\pi$
$607$	243.768			0.401595			0.200797	+	0.979633i	$0.435647\pi$
$608$	−453.438	+	261.792i	−0.745785	+	0.430579i
$609$		0			0
$610$	14.7748	−	25.5906i	0.0242209	−	0.0419518i
$611$	303.379	+	175.156i	0.496529	+	0.286671i
$612$	93.8145	+	451.095i	0.153292	+	0.737084i
$613$	218.720	+	378.834i	0.356802	+	0.618000i	0.987425	−	0.158090i	$-0.0505336\pi$
$613$	218.720	+	378.834i	0.356802	+	0.618000i	−0.630622	+	0.776090i	$0.717200\pi$
$614$	−29.7649	+	17.1847i	−0.0484770	+	0.0279882i
$615$	28.5391	+	39.4626i	0.0464050	+	0.0641669i
$616$		0			0
$617$	252.875	−	145.998i	0.409846	−	0.236625i	−0.280877	−	0.959744i	$-0.590625\pi$
$617$	252.875	−	145.998i	0.409846	−	0.236625i	0.690724	+	0.723119i	$0.257292\pi$
$618$	158.970	−	114.966i	0.257233	−	0.186029i
$619$	−962.966			−1.55568			−0.777840	−	0.628462i	$-0.783685\pi$
$619$	−962.966			−1.55568			−0.777840	+	0.628462i	$0.783685\pi$
$620$	137.248	−	79.2400i	0.221367	−	0.127806i
$621$	40.8090	+	128.471i	0.0657150	+	0.206878i
$622$	−343.690			−0.552556
$623$		0			0
$624$	−233.251	+	520.810i	−0.373800	+	0.834631i
$625$	542.618			0.868189
$626$	−7.68458	−	4.43669i	−0.0122757	−	0.00708737i
$627$	1220.45	+	546.596i	1.94650	+	0.871763i
$628$	−151.496	−	262.399i	−0.241236	−	0.417833i
$629$			281.726i			0.447896i
$630$		0			0
$631$	−1093.87			−1.73355			−0.866777	−	0.498695i	$-0.833813\pi$
$631$	−1093.87			−1.73355			−0.866777	+	0.498695i	$0.833813\pi$
$632$	−156.365	+	90.2773i	−0.247413	+	0.142844i
$633$	397.270	+	549.327i	0.627598	+	0.867816i
$634$	74.0180	−	128.203i	0.116748	−	0.202213i
$635$			7.92585i			0.0124817i
$636$	40.5076	+	393.720i	0.0636913	+	0.619056i
$637$		0			0
$638$			399.819i			0.626675i
$639$	4.86480	+	23.3918i	0.00761315	+	0.0366069i
$640$	64.2277	+	111.246i	0.100356	+	0.173821i
$641$		−	610.212i		−	0.951969i	−0.879454	−	0.475985i	$-0.842092\pi$
$641$		−	610.212i		−	0.951969i	0.879454	−	0.475985i	$-0.157908\pi$
$642$	−333.297	+	34.2911i	−0.519154	+	0.0534129i
$643$	−490.571	−	849.694i	−0.762941	−	1.32145i	−0.941328	−	0.337493i	$-0.890421\pi$
$643$	−490.571	−	849.694i	−0.762941	−	1.32145i	0.178387	−	0.983960i	$-0.442912\pi$
$644$		0			0
$645$	−4.92272	−	2.20470i	−0.00763213	−	0.00341815i
$646$	−87.4366	−	151.445i	−0.135351	−	0.234434i
$647$	305.923	−	176.625i	0.472833	−	0.272990i	−0.244592	−	0.969626i	$-0.578654\pi$
$647$	305.923	−	176.625i	0.472833	−	0.272990i	0.717425	+	0.696636i	$0.245321\pi$
$648$	−149.823	−	344.624i	−0.231208	−	0.531826i
$649$	−854.473	+	1479.99i	−1.31660	+	2.28042i
$650$	204.460	+	118.045i	0.314555	+	0.181608i
$651$		0			0
$652$	140.382	+	243.148i	0.215309	+	0.372926i
$653$			582.330i			0.891777i	0.895089	+	0.445889i	$0.147112\pi$
$653$			582.330i			0.891777i	−0.895089	+	0.445889i	$0.852888\pi$
$654$	−35.7318	−	16.0029i	−0.0546357	−	0.0244693i
$655$	−14.8689			−0.0227005
$656$	155.782	+	89.9408i	0.237473	+	0.137105i
$657$	−494.631	−	554.219i	−0.752863	−	0.843561i
$658$		0			0
$659$	−531.436	−	306.824i	−0.806427	−	0.465591i	0.0392864	−	0.999228i	$-0.487492\pi$
$659$	−531.436	−	306.824i	−0.806427	−	0.465591i	−0.845714	+	0.533637i	$0.820825\pi$
$660$	102.733	−	229.384i	0.155655	−	0.347552i
$661$	−222.908	+	386.088i	−0.337228	+	0.584097i	−0.983910	−	0.178663i	$-0.942823\pi$
$661$	−222.908	+	386.088i	−0.337228	+	0.584097i	0.646682	+	0.762760i	$0.276156\pi$
$662$	−162.318	−	93.7144i	−0.245194	−	0.141563i
$663$	−627.690	−	281.119i	−0.946742	−	0.424010i
$664$	88.7533	−	153.725i	0.133665	−	0.231514i
$665$		0			0
$666$	−22.2593	−	107.031i	−0.0334223	−	0.160707i
$667$	−75.1080	+	130.091i	−0.112606	+	0.195039i
$668$		−	1159.47i		−	1.73573i
$669$	−210.126	+	469.175i	−0.314090	+	0.701309i
$670$	−26.9043			−0.0401556
$671$	−871.145	+	502.956i	−1.29828	+	0.749562i
$672$		0			0
$673$	−50.0003	+	86.6031i	−0.0742947	+	0.128682i	−0.900779	−	0.434277i	$-0.857004\pi$
$673$	−50.0003	+	86.6031i	−0.0742947	+	0.128682i	0.826485	+	0.562959i	$0.190337\pi$
$674$	−69.8516	−	40.3289i	−0.103637	−	0.0598351i
$675$	614.631	−	195.239i	0.910565	−	0.289242i
$676$	−172.978	−	299.607i	−0.255885	−	0.443206i
$677$	739.773	−	427.108i	1.09272	−	0.630884i	0.158422	−	0.987371i	$-0.449359\pi$
$677$	739.773	−	427.108i	1.09272	−	0.630884i	0.934300	+	0.356488i	$0.116026\pi$
$678$	−121.520	+	271.334i	−0.179234	+	0.400198i
$679$		0			0
$680$	−59.8265	+	34.5408i	−0.0879801	+	0.0507953i
$681$	−90.8025	−	882.568i	−0.133337	−	1.29599i
$682$	549.357			0.805509
$683$	232.215	−	134.069i	0.339992	−	0.196295i	−0.320276	−	0.947324i	$-0.603776\pi$
$683$	232.215	−	134.069i	0.339992	−	0.196295i	0.660269	+	0.751029i	$0.270442\pi$
$684$	−443.724	−	497.179i	−0.648719	−	0.726870i
$685$	165.545			0.241671
$686$		0			0
$687$	23.1386	−	2.38061i	0.0336807	−	0.00346522i
$688$	−19.9228			−0.0289576
$689$	−511.661	−	295.408i	−0.742614	−	0.428748i
$690$	−7.79168	+	5.63488i	−0.0112923	+	0.00816650i
$691$	−396.988	−	687.604i	−0.574513	−	0.995086i	−0.996094	−	0.0882951i	$-0.971858\pi$
$691$	−396.988	−	687.604i	−0.574513	−	0.995086i	0.421581	−	0.906791i	$-0.361475\pi$
$692$		−	243.927i		−	0.352496i
$693$		0			0
$694$	252.378			0.363657
$695$	101.019	−	58.3233i	0.145351	−	0.0839184i
$696$	171.168	−	382.188i	0.245931	−	0.549121i
$697$	−108.398	+	187.752i	−0.155521	+	0.269371i
$698$		−	179.220i		−	0.256762i
$699$	−4.82305	−	2.16007i	−0.00689994	−	0.00309022i
$700$		0			0
$701$			608.220i			0.867647i	0.900998	+	0.433823i	$0.142836\pi$
$701$			608.220i			0.867647i	−0.900998	+	0.433823i	$0.857164\pi$
$702$	260.678	+	57.2062i	0.371336	+	0.0814903i
$703$	−203.734	−	352.878i	−0.289807	−	0.501960i
$704$		−	681.755i		−	0.968401i
$705$	40.0011	+	55.3117i	0.0567391	+	0.0784564i
$706$	2.81110	+	4.86897i	0.00398173	+	0.00689656i
$707$		0			0
$708$	690.065	−	499.050i	0.974668	−	0.704873i
$709$	423.910	+	734.234i	0.597899	+	1.03559i	0.993131	+	0.117010i	$0.0373309\pi$
$709$	423.910	+	734.234i	0.597899	+	1.03559i	−0.395232	+	0.918581i	$0.629336\pi$
$710$	−1.47602	+	0.852179i	−0.00207890	+	0.00120025i
$711$	−233.229	−	261.326i	−0.328030	−	0.367547i
$712$	135.208	−	234.187i	0.189899	−	0.328915i
$713$	178.747	+	103.199i	0.250697	+	0.144740i
$714$		0			0
$715$	187.589	+	324.914i	0.262362	+	0.454425i
$716$			1001.50i			1.39874i
$717$	−230.662	+	166.813i	−0.321705	+	0.232655i
$718$	62.5452			0.0871103
$719$	36.4855	+	21.0649i	0.0507448	+	0.0292975i	0.525158	−	0.851005i	$-0.324006\pi$
$719$	36.4855	+	21.0649i	0.0507448	+	0.0292975i	−0.474413	+	0.880302i	$0.657340\pi$
$720$	−82.9604	+	74.0407i	−0.115223	+	0.102834i
$721$		0			0
$722$	28.9544	+	16.7168i	0.0401031	+	0.0231535i
$723$	252.498	−	25.9781i	0.349236	−	0.0359310i
$724$	498.193	−	862.895i	0.688111	−	1.19184i
$725$	622.381	+	359.332i	0.858457	+	0.495630i
$726$	527.133	−	381.219i	0.726079	−	0.525095i
$727$	−180.096	+	311.935i	−0.247725	+	0.429072i	−0.962894	−	0.269879i	$-0.913016\pi$
$727$	−180.096	+	311.935i	−0.247725	+	0.429072i	0.715169	+	0.698951i	$0.246349\pi$
$728$		0			0
$729$	595.368	−	420.688i	0.816691	−	0.577075i
$730$	26.4954	−	45.8914i	0.0362951	−	0.0628650i
$731$		−	24.0114i		−	0.0328473i
$732$	498.639	−	51.3022i	0.681200	−	0.0700849i
$733$	−367.876			−0.501877			−0.250938	−	0.968003i	$-0.580739\pi$
$733$	−367.876			−0.501877			−0.250938	+	0.968003i	$0.580739\pi$
$734$	286.647	−	165.496i	0.390528	−	0.225471i
$735$		0			0
$736$	−64.0813	+	110.992i	−0.0870670	+	0.150805i
$737$	793.162	+	457.932i	1.07620	+	0.621346i
$738$	26.3474	−	79.8935i	0.0357011	−	0.108257i
$739$	−325.456	−	563.706i	−0.440401	−	0.762796i	0.557318	−	0.830299i	$-0.311830\pi$
$739$	−325.456	−	563.706i	−0.440401	−	0.762796i	−0.997719	+	0.0675026i	$0.978497\pi$
$740$	−66.3234	+	38.2918i	−0.0896262	+	0.0517457i
$741$	989.512	−	101.805i	1.33537	−	0.137389i
$742$		0			0
$743$	845.004	−	487.864i	1.13729	−	0.656613i	0.191530	−	0.981487i	$-0.438655\pi$
$743$	845.004	−	487.864i	1.13729	−	0.656613i	0.945757	+	0.324874i	$0.105322\pi$
$744$	−525.132	−	235.187i	−0.705823	−	0.316111i
$745$	123.986			0.166424
$746$	−226.116	+	130.548i	−0.303104	+	0.174997i
$747$	327.030	+	107.849i	0.437791	+	0.144376i
$748$	1118.86			1.49580
$749$		0			0
$750$	55.1753	+	76.2941i	0.0735671	+	0.101725i
$751$	−668.826			−0.890581			−0.445290	−	0.895386i	$-0.646900\pi$
$751$	−668.826			−0.890581			−0.445290	+	0.895386i	$0.646900\pi$
$752$	218.348	+	126.063i	0.290356	+	0.167637i
$753$	−94.7364	−	920.803i	−0.125812	−	1.22285i
$754$	148.704	+	257.564i	0.197221	+	0.341596i
$755$		−	108.085i		−	0.143159i
$756$		0			0
$757$	933.487			1.23314			0.616570	−	0.787300i	$-0.288522\pi$
$757$	933.487			1.23314			0.616570	+	0.787300i	$0.288522\pi$
$758$	236.537	−	136.564i	0.312054	−	0.180164i
$759$	325.616	−	33.5008i	0.429006	−	0.0441381i
$760$	49.9573	−	86.5286i	0.0657333	−	0.113853i
$761$			950.592i			1.24914i	0.780971	+	0.624568i	$0.214725\pi$
$761$			950.592i			1.24914i	−0.780971	+	0.624568i	$0.785275\pi$
$762$	11.0940	−	8.02308i	0.0145590	−	0.0105290i
$763$		0			0
$764$			199.899i			0.261647i
$765$	−89.2354	−	99.9855i	−0.116648	−	0.130700i
$766$	−126.338	−	218.823i	−0.164932	−	0.285670i
$767$			1271.22i			1.65739i
$768$	−62.3070	+	139.121i	−0.0811289	+	0.181147i
$769$	142.532	+	246.872i	0.185347	+	0.321030i	0.943693	−	0.330822i	$-0.107326\pi$
$769$	142.532	+	246.872i	0.185347	+	0.321030i	−0.758347	+	0.651851i	$0.773993\pi$
$770$		0			0
$771$	42.2374	+	410.533i	0.0547827	+	0.532468i
$772$	−415.950	−	720.447i	−0.538795	−	0.933221i
$773$	139.541	−	80.5640i	0.180519	−	0.104223i	−0.407018	−	0.913420i	$-0.633431\pi$
$773$	139.541	−	80.5640i	0.180519	−	0.104223i	0.587536	+	0.809198i	$0.300098\pi$
$774$	1.89714	+	9.12219i	0.00245109	+	0.0117858i
$775$	493.727	−	855.160i	0.637067	−	1.10343i
$776$	−343.641	−	198.401i	−0.442837	−	0.255672i
$777$		0			0
$778$	64.3816	+	111.512i	0.0827528	+	0.143332i
$779$		−	313.559i		−	0.402515i
$780$	−19.1343	−	185.979i	−0.0245312	−	0.238434i
$781$	58.0190			0.0742881
$782$	−37.0705	−	21.4027i	−0.0474047	−	0.0273691i
$783$	793.507	+	174.137i	1.01342	+	0.222397i
$784$		0			0
$785$	76.3226	+	44.0649i	0.0972263	+	0.0561336i
$786$	15.0513	+	20.8122i	0.0191492	+	0.0264787i
$787$	775.200	−	1342.69i	0.985006	−	1.70608i	0.343096	−	0.939300i	$-0.388524\pi$
$787$	775.200	−	1342.69i	0.985006	−	1.70608i	0.641910	−	0.766780i	$-0.278142\pi$
$788$	869.670	+	502.104i	1.10364	+	0.637188i
$789$	89.6896	+	871.750i	0.113675	+	1.10488i
$790$	12.4932	−	21.6388i	0.0158141	−	0.0273909i
$791$		0			0
$792$	−893.417	+	185.804i	−1.12805	+	0.234601i
$793$	−374.128	+	648.009i	−0.471789	+	0.817162i
$794$			366.507i			0.461596i
$795$	−67.4633	−	93.2854i	−0.0848595	−	0.117340i
$796$	−500.367			−0.628602
$797$	601.600	−	347.334i	0.754831	−	0.435802i	−0.0726061	−	0.997361i	$-0.523132\pi$
$797$	601.600	−	347.334i	0.754831	−	0.435802i	0.827437	+	0.561559i	$0.189798\pi$
$798$		0			0
$799$	−151.934	+	263.157i	−0.190155	+	0.329358i
$800$	531.009	+	306.578i	0.663761	+	0.383223i
$801$	498.203	+	164.298i	0.621976	+	0.205117i
$802$	151.617	+	262.608i	0.189049	+	0.327442i
$803$	−1562.22	+	901.947i	−1.94548	+	1.12322i
$804$	−267.452	−	369.822i	−0.332652	−	0.459977i
$805$		0			0
$806$	353.896	−	204.322i	0.439077	−	0.253501i
$807$	988.051	−	714.552i	1.22435	−	0.885442i
$808$	502.142			0.621462
$809$	−58.6179	+	33.8431i	−0.0724572	+	0.0418332i	−0.535791	−	0.844351i	$-0.679986\pi$
$809$	−58.6179	+	33.8431i	−0.0724572	+	0.0418332i	0.463334	+	0.886184i	$0.346653\pi$
$810$	41.8014	+	30.9351i	0.0516066	+	0.0381915i
$811$	−951.824			−1.17364			−0.586821	−	0.809716i	$-0.699621\pi$
$811$	−951.824			−1.17364			−0.586821	+	0.809716i	$0.699621\pi$
$812$		0			0
$813$	−202.120	+	451.299i	−0.248610	+	0.555104i
$814$	−265.470			−0.326131
$815$	−70.7232	−	40.8321i	−0.0867769	−	0.0501007i
$816$	−451.760	−	202.326i	−0.553628	−	0.247949i
$817$	17.3642	+	30.0756i	0.0212536	+	0.0368123i
$818$		−	322.947i		−	0.394801i
$819$		0			0
$820$	−58.9334			−0.0718700
$821$	−209.051	+	120.695i	−0.254629	+	0.147010i	−0.621882	−	0.783111i	$-0.713632\pi$
$821$	−209.051	+	120.695i	−0.254629	+	0.147010i	0.367253	+	0.930121i	$0.380298\pi$
$822$	−167.576	−	231.716i	−0.203863	−	0.281893i
$823$	682.725	−	1182.51i	0.829556	−	1.43683i	−0.0688301	−	0.997628i	$-0.521927\pi$
$823$	682.725	−	1182.51i	0.829556	−	1.43683i	0.898387	−	0.439206i	$-0.144740\pi$
$824$			498.986i			0.605566i
$825$	−160.275	−	1557.81i	−0.194272	−	1.88826i
$826$		0			0
$827$		−	278.115i		−	0.336293i	−0.985762	−	0.168147i	$-0.946222\pi$
$827$		−	278.115i		−	0.336293i	0.985762	−	0.168147i	$-0.0537782\pi$
$828$	−154.912	−	51.0873i	−0.187092	−	0.0616997i
$829$	−192.136	−	332.789i	−0.231768	−	0.401434i	0.726561	−	0.687102i	$-0.241118\pi$
$829$	−192.136	−	332.789i	−0.231768	−	0.401434i	−0.958328	+	0.285669i	$0.907784\pi$
$830$			24.5645i			0.0295958i
$831$	1027.64	−	105.729i	1.23664	−	0.127231i
$832$	−253.565	−	439.187i	−0.304765	−	0.527869i
$833$		0			0
$834$	−183.894	−	82.3594i	−0.220497	−	0.0987523i
$835$	168.624	+	292.065i	0.201945	+	0.349779i
$836$	−1401.43	+	809.118i	−1.67636	+	0.967844i
$837$	239.266	−	1090.29i	0.285861	−	1.30262i
$838$	−89.9711	+	155.835i	−0.107364	+	0.185960i
$839$	−1380.43	−	796.989i	−1.64532	−	0.949928i	−0.978896	−	0.204358i	$-0.934489\pi$
$839$	−1380.43	−	796.989i	−1.64532	−	0.949928i	−0.666427	−	0.745570i	$-0.732177\pi$
$840$		0			0
$841$	32.1586	+	55.7004i	0.0382386	+	0.0662311i
$842$		−	199.566i		−	0.237015i
$843$	1169.72	+	523.875i	1.38757	+	0.621442i
$844$	−820.365			−0.971996
$845$	87.1451	+	50.3133i	0.103130	+	0.0595423i
$846$	36.9292	−	111.981i	0.0436515	−	0.132365i
$847$		0			0
$848$	−368.252	−	212.610i	−0.434259	−	0.250720i
$849$	68.1123	−	152.083i	0.0802265	−	0.179132i
$850$	−102.395	+	177.353i	−0.120464	+	0.208650i
$851$	−86.3773	−	49.8699i	−0.101501	−	0.0586016i
$852$	−26.3868	−	11.8177i	−0.0309704	−	0.0138705i
$853$	−22.9378	+	39.7294i	−0.0268907	+	0.0465761i	−0.879158	−	0.476531i	$-0.841894\pi$
$853$	−22.9378	+	39.7294i	−0.0268907	+	0.0465761i	0.852267	+	0.523107i	$0.175227\pi$
$854$		0			0
$855$	184.078	+	60.7057i	0.215296	+	0.0710009i
$856$	426.098	−	738.024i	0.497778	−	0.862177i
$857$		−	686.751i		−	0.801343i	−0.916222	−	0.400671i	$-0.868777\pi$
$857$		−	686.751i		−	0.801343i	0.916222	−	0.400671i	$-0.131223\pi$
$858$	264.898	−	591.472i	0.308739	−	0.689361i
$859$	−1266.73			−1.47466			−0.737331	−	0.675532i	$-0.763914\pi$
$859$	−1266.73			−1.47466			−0.737331	+	0.675532i	$0.763914\pi$
$860$	5.65271	−	3.26359i	0.00657292	−	0.00379487i
$861$		0			0
$862$	104.797	−	181.513i	0.121574	−	0.210572i
$863$	451.473	+	260.658i	0.523144	+	0.302037i	0.738220	−	0.674560i	$-0.235667\pi$
$863$	451.473	+	260.658i	0.523144	+	0.302037i	−0.215076	+	0.976597i	$0.569000\pi$
$864$	677.012	+	148.571i	0.783578	+	0.171958i
$865$	35.4749	+	61.4443i	0.0410114	+	0.0710339i
$866$	−352.025	+	203.242i	−0.406496	+	0.234690i
$867$	−110.531	+	246.797i	−0.127487	+	0.284657i
$868$		0			0
$869$	−736.618	+	425.287i	−0.847662	+	0.489398i
$870$	5.93103	+	57.6475i	0.00681728	+	0.0662615i
$871$	681.274			0.782174
$872$	86.2388	−	49.7900i	0.0988977	−	0.0570986i
$873$	241.088	−	731.051i	0.276160	−	0.837401i
$874$	61.9105			0.0708359
$875$		0			0
$876$	894.204	−	91.9997i	1.02078	−	0.105023i
$877$	−985.072			−1.12323			−0.561615	−	0.827399i	$-0.689820\pi$
$877$	−985.072			−1.12323			−0.561615	+	0.827399i	$0.689820\pi$
$878$	−281.161	−	162.328i	−0.320229	−	0.184884i
$879$	−172.053	+	124.427i	−0.195737	+	0.141556i
$880$	135.011	+	233.846i	0.153422	+	0.265735i
$881$			1229.69i			1.39579i	0.716198	+	0.697897i	$0.245881\pi$
$881$			1229.69i			1.39579i	−0.716198	+	0.697897i	$0.754119\pi$
$882$		0			0
$883$	105.285			0.119236			0.0596180	−	0.998221i	$-0.481012\pi$
$883$	105.285			0.119236			0.0596180	+	0.998221i	$0.481012\pi$
$884$	720.769	−	416.136i	0.815350	−	0.470742i
$885$	−101.247	+	226.067i	−0.114403	+	0.255442i
$886$	51.5022	−	89.2044i	0.0581289	−	0.100682i
$887$		−	650.589i		−	0.733471i	−0.930325	−	0.366736i	$-0.880475\pi$
$887$		−	650.589i		−	0.733471i	0.930325	−	0.366736i	$-0.119525\pi$
$888$	253.764	+	113.651i	0.285770	+	0.127986i
$889$		0			0
$890$			37.4220i			0.0420472i
$891$	−705.801	−	1623.49i	−0.792145	−	1.82209i
$892$	−311.047	−	538.749i	−0.348707	−	0.603978i
$893$		−	439.492i		−	0.492152i
$894$	−125.507	−	173.545i	−0.140388	−	0.194122i
$895$	−145.650	−	252.273i	−0.162737	−	0.281870i
$896$		0			0
$897$	197.302	−	142.687i	0.219958	−	0.159072i
$898$	77.1715	+	133.665i	0.0859371	+	0.148847i
$899$	1077.27	−	621.959i	1.19829	−	0.691835i
$900$	−244.412	+	741.132i	−0.271569	+	0.823480i
$901$	256.242	−	443.824i	0.284398	−	0.492591i
$902$	−176.918	−	102.144i	−0.196140	−	0.113241i
$903$		0			0
$904$	−378.087	−	654.866i	−0.418238	−	0.724410i
$905$			289.813i			0.320236i
$906$	−151.289	+	109.411i	−0.166985	+	0.120762i
$907$	−1026.62			−1.13189			−0.565945	−	0.824443i	$-0.691489\pi$
$907$	−1026.62			−1.13189			−0.565945	+	0.824443i	$0.691489\pi$
$908$	929.801	+	536.821i	1.02401	+	0.591212i
$909$	198.346	+	953.724i	0.218203	+	1.04920i
$910$		0			0
$911$	374.455	+	216.192i	0.411038	+	0.237313i	0.691235	−	0.722630i	$-0.257067\pi$
$911$	374.455	+	216.192i	0.411038	+	0.237313i	−0.280198	+	0.959942i	$0.590400\pi$
$912$	712.170	−	73.2713i	0.780888	−	0.0803413i
$913$	418.108	−	724.184i	0.457949	−	0.793192i
$914$	−124.949	−	72.1395i	−0.136706	−	0.0789272i
$915$	−118.144	+	85.4410i	−0.129119	+	0.0933782i
$916$	−14.0740	+	24.3770i	−0.0153647	+	0.0266124i
$917$		0			0
$918$	−49.6217	+	226.117i	−0.0540542	+	0.246314i
$919$	−670.390	+	1161.15i	−0.729478	+	1.26349i	0.227626	+	0.973749i	$0.426904\pi$
$919$	−670.390	+	1161.15i	−0.729478	+	1.26349i	−0.957104	+	0.289744i	$0.906430\pi$
$920$		−	24.4570i		−	0.0265837i
$921$	168.694	−	17.3560i	0.183164	−	0.0188447i
$922$	−441.674			−0.479039
$923$	37.3759	−	21.5790i	0.0404939	−	0.0233792i
$924$		0			0
$925$	−238.588	+	413.246i	−0.257933	+	0.446753i
$926$	345.012	+	199.193i	0.372583	+	0.215111i
$927$	−947.732	+	197.100i	−1.02236	+	0.212622i
$928$	386.204	+	668.924i	0.416168	+	0.720824i
$929$	959.943	−	554.223i	1.03331	−	0.596580i	0.115377	−	0.993322i	$-0.463192\pi$
$929$	959.943	−	554.223i	1.03331	−	0.596580i	0.917930	+	0.396741i	$0.129859\pi$
$930$	79.2084	−	8.14932i	0.0851704	−	0.00876271i
$931$		0			0
$932$	5.53826	−	3.19751i	0.00594234	−	0.00343081i
$933$	1547.69	+	693.153i	1.65883	+	0.742929i
$934$	−104.114			−0.111471
$935$	−281.836	+	162.718i	−0.301429	+	0.174030i
$936$	−506.434	+	451.983i	−0.541062	+	0.482888i
$937$	−862.090			−0.920053			−0.460027	−	0.887905i	$-0.652160\pi$
$937$	−862.090			−0.920053			−0.460027	+	0.887905i	$0.652160\pi$
$938$		0			0
$939$	25.6570	+	35.4774i	0.0273237	+	0.0377821i
$940$	−82.6025			−0.0878750
$941$	−1516.31	−	875.439i	−1.61138	−	0.930329i	−0.989052	−	0.147570i	$-0.952855\pi$
$941$	−1516.31	−	875.439i	−1.61138	−	0.930329i	−0.622325	−	0.782759i	$-0.713812\pi$
$942$	−15.5804	−	151.436i	−0.0165397	−	0.160760i
$943$	−38.3764	−	66.4699i	−0.0406961	−	0.0704877i
$944$			914.917i			0.969192i
$945$		0			0
$946$	22.6259			0.0239174
$947$	446.988	−	258.069i	0.472005	−	0.272512i	−0.245074	−	0.969504i	$-0.578812\pi$
$947$	446.988	−	258.069i	0.472005	−	0.272512i	0.717079	+	0.696992i	$0.245479\pi$
$948$	421.636	−	43.3798i	0.444764	−	0.0457593i
$949$	−670.921	+	1162.07i	−0.706977	+	1.22452i
$950$		−	296.193i		−	0.311782i
$951$	−591.874	+	428.039i	−0.622370	+	0.450094i
$952$		0			0
$953$		−	447.867i		−	0.469955i	−0.972001	−	0.234977i	$-0.924498\pi$
$953$		−	447.867i		−	0.469955i	0.972001	−	0.234977i	$-0.0755016\pi$
$954$	−62.2825	+	188.859i	−0.0652857	+	0.197966i
$955$	−29.0717	−	50.3537i	−0.0304416	−	0.0527264i
$956$		−	344.471i		−	0.360325i
$957$	806.354	−	1800.45i	0.842585	−	1.88135i
$958$	−257.519	−	446.036i	−0.268809	−	0.465590i
$959$		0			0
$960$	−10.1133	−	98.2981i	−0.0105347	−	0.102394i
$961$	−374.081	−	647.927i	−0.389262	−	0.674222i
$962$	−171.016	+	98.7363i	−0.177772	+	0.102636i
$963$	1570.05	+	517.774i	1.63037	+	0.537668i
$964$	−153.581	+	266.011i	−0.159317	+	0.275945i
$965$	209.553	+	120.985i	0.217153	+	0.125373i
$966$		0			0
$967$	594.482	+	1029.67i	0.614769	+	1.06481i	0.990425	+	0.138053i	$0.0440843\pi$
$967$	594.482	+	1029.67i	0.614769	+	1.06481i	−0.375655	+	0.926759i	$0.622582\pi$
$968$			1654.60i			1.70930i
$969$	88.3080	+	858.322i	0.0911331	+	0.885781i
$970$	54.9122			0.0566105
$971$	123.367	+	71.2259i	0.127051	+	0.0733531i	0.562179	−	0.827016i	$-0.309963\pi$
$971$	123.367	+	71.2259i	0.127051	+	0.0733531i	−0.435127	+	0.900369i	$0.643297\pi$
$972$	−9.68592	+	882.117i	−0.00996494	+	0.907527i
$973$		0			0
$974$	36.7375	+	21.2104i	0.0377182	+	0.0217766i
$975$	−682.645	−	943.932i	−0.700149	−	0.968136i
$976$	−269.267	+	466.384i	−0.275888	+	0.477853i
$977$	427.287	+	246.694i	0.437346	+	0.252502i	0.702471	−	0.711712i	$-0.252080\pi$
$977$	427.287	+	246.694i	0.437346	+	0.252502i	−0.265125	+	0.964214i	$0.585413\pi$
$978$	14.4373	+	140.326i	0.0147621	+	0.143482i
$979$	636.952	−	1103.23i	0.650615	−	1.12690i
$980$		0			0
$981$	128.631	+	144.127i	0.131123	+	0.146919i
$982$	−74.3722	+	128.816i	−0.0757355	+	0.131178i
$983$			1542.62i			1.56930i	0.619938	+	0.784651i	$0.287158\pi$
$983$			1542.62i			1.56930i	−0.619938	+	0.784651i	$0.712842\pi$
$984$	125.387	+	173.380i	0.127426	+	0.176200i
$985$	−292.089			−0.296537
$986$	−223.416	+	128.989i	−0.226588	+	0.130821i
$987$		0			0
$988$	−601.869	+	1042.47i	−0.609180	+	1.05513i
$989$	7.36189	+	4.25039i	0.00744377	+	0.00429766i
$990$	94.2163	−	84.0864i	0.0951679	−	0.0849357i
$991$	−114.250	−	197.887i	−0.115288	−	0.199684i	0.802607	−	0.596508i	$-0.203446\pi$
$991$	−114.250	−	197.887i	−0.115288	−	0.199684i	−0.917895	+	0.396824i	$0.870112\pi$
$992$	919.111	−	530.649i	0.926524	−	0.534929i
$993$	541.942	+	749.374i	0.545762	+	0.754656i
$994$		0			0
$995$	126.041	−	72.7696i	0.126674	−	0.0731353i
$996$	−337.660	+	244.193i	−0.339016	+	0.245174i
$997$	−972.797			−0.975724			−0.487862	−	0.872921i	$-0.662223\pi$
$997$	−972.797			−0.975724			−0.487862	+	0.872921i	$0.662223\pi$
$998$	−219.567	+	126.767i	−0.220007	+	0.127021i
$999$	−115.623	+	526.870i	−0.115738	+	0.527397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.n.h.128.6		24
7.2	even	3		441.3.r.h.344.7		24
7.3	odd	6		441.3.j.h.263.6		24
7.4	even	3		441.3.j.g.263.6		24
7.5	odd	6		63.3.r.a.29.7	✓	24
7.6	odd	2		441.3.n.g.128.6		24
9.5	odd	6		441.3.j.g.275.7		24
21.5	even	6		189.3.r.a.8.6		24
63.5	even	6		63.3.r.a.50.7	yes	24
63.23	odd	6		441.3.r.h.50.7		24
63.32	odd	6	inner	441.3.n.h.410.6		24
63.40	odd	6		189.3.r.a.71.6		24
63.41	even	6		441.3.j.h.275.7		24
63.47	even	6		567.3.b.a.323.14		24
63.59	even	6		441.3.n.g.410.6		24
63.61	odd	6		567.3.b.a.323.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.r.a.29.7	✓	24	7.5	odd	6
63.3.r.a.50.7	yes	24	63.5	even	6
189.3.r.a.8.6		24	21.5	even	6
189.3.r.a.71.6		24	63.40	odd	6
441.3.j.g.263.6		24	7.4	even	3
441.3.j.g.275.7		24	9.5	odd	6
441.3.j.h.263.6		24	7.3	odd	6
441.3.j.h.275.7		24	63.41	even	6
441.3.n.g.128.6		24	7.6	odd	2
441.3.n.g.410.6		24	63.59	even	6
441.3.n.h.128.6		24	1.1	even	1	trivial
441.3.n.h.410.6		24	63.32	odd	6	inner
441.3.r.h.50.7		24	63.23	odd	6
441.3.r.h.344.7		24	7.2	even	3
567.3.b.a.323.11		24	63.61	odd	6
567.3.b.a.323.14		24	63.47	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.526549 + 0.304003i) q^{2} +(2.98425 - 0.307033i) q^{3} +(-1.81516 + 3.14396i) q^{4} -1.05593i q^{5} +(-1.47801 + 1.06889i) q^{6} -4.63929i q^{8} +(8.81146 - 1.83252i) q^{9} +O(q^{10})\)	\(q+(-0.526549 + 0.304003i) q^{2} +(2.98425 - 0.307033i) q^{3} +(-1.81516 + 3.14396i) q^{4} -1.05593i q^{5} +(-1.47801 + 1.06889i) q^{6} -4.63929i q^{8} +(8.81146 - 1.83252i) q^{9} +(0.321007 + 0.556001i) q^{10} -21.8552i q^{11} +(-4.45160 + 9.93966i) q^{12} +(-8.12859 - 14.0791i) q^{13} +(-0.324207 - 3.15117i) q^{15} +(-5.85030 - 10.1330i) q^{16} +(12.2125 - 7.05090i) q^{17} +(-4.08257 + 3.64363i) q^{18} +(-10.1979 + 17.6633i) q^{19} +(3.31981 + 1.91669i) q^{20} +(6.64405 + 11.5078i) q^{22} +4.99247i q^{23} +(-1.42441 - 13.8448i) q^{24} +23.8850 q^{25} +(8.56020 + 4.94224i) q^{26} +(25.7329 - 8.17411i) q^{27} +(26.0574 + 15.0442i) q^{29} +(1.12868 + 1.56069i) q^{30} +(20.6710 - 35.8032i) q^{31} +(22.2319 + 12.8356i) q^{32} +(-6.71027 - 65.2213i) q^{33} +(-4.28699 + 7.42528i) q^{34} +(-10.2329 + 31.0292i) q^{36} +(-9.98903 + 17.3015i) q^{37} -12.4008i q^{38} +(-28.5805 - 39.5199i) q^{39} -4.89878 q^{40} +(-13.3140 + 7.68686i) q^{41} +(0.851359 - 1.47460i) q^{43} +(68.7118 + 39.6708i) q^{44} +(-1.93503 - 9.30433i) q^{45} +(-1.51773 - 2.62878i) q^{46} +(-18.6613 + 10.7741i) q^{47} +(-20.5699 - 28.4432i) q^{48} +(-12.5766 + 7.26112i) q^{50} +(34.2803 - 24.7913i) q^{51} +59.0189 q^{52} +(31.4729 - 18.1709i) q^{53} +(-11.0647 + 12.1270i) q^{54} -23.0777 q^{55} +(-25.0099 + 55.8427i) q^{57} -18.2940 q^{58} +(-67.7180 - 39.0970i) q^{59} +(10.4956 + 4.70060i) q^{60} +(-23.0131 - 39.8599i) q^{61} +25.1362i q^{62} +31.1941 q^{64} +(-14.8667 + 8.58326i) q^{65} +(23.3608 + 32.3023i) q^{66} +(-20.9530 + 36.2917i) q^{67} +51.1941i q^{68} +(1.53285 + 14.8988i) q^{69} +2.65470i q^{71} +(-8.50160 - 40.8789i) q^{72} +(-41.2692 - 71.4803i) q^{73} -12.1468i q^{74} +(71.2787 - 7.33348i) q^{75} +(-37.0217 - 64.1235i) q^{76} +(27.0632 + 12.1206i) q^{78} +(-19.4593 - 33.7045i) q^{79} +(-10.6998 + 6.17753i) q^{80} +(74.2837 - 32.2944i) q^{81} +(4.67366 - 8.09501i) q^{82} +(33.1355 + 19.1308i) q^{83} +(-7.44529 - 12.8956i) q^{85} +1.03526i q^{86} +(82.3808 + 36.8953i) q^{87} -101.393 q^{88} +(50.4792 + 29.1442i) q^{89} +(3.84743 + 4.31093i) q^{90} +(-15.6961 - 9.06216i) q^{92} +(50.6946 - 113.192i) q^{93} +(6.55071 - 11.3462i) q^{94} +(18.6513 + 10.7683i) q^{95} +(70.2864 + 31.4787i) q^{96} +(42.7655 - 74.0720i) q^{97} +(-40.0502 - 192.576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{3} + 24 q^{4} + 14 q^{6} - 16 q^{9}+O(q^{10}) \) 24 * q + 10 * q^3 + 24 * q^4 + 14 * q^6 - 16 * q^9	\( 24 q + 10 q^{3} + 24 q^{4} + 14 q^{6} - 16 q^{9} - 22 q^{12} - 10 q^{15} - 48 q^{16} - 108 q^{17} - 8 q^{18} - 12 q^{19} + 18 q^{20} - 24 q^{22} - 30 q^{24} - 108 q^{25} - 144 q^{26} + 124 q^{27} + 54 q^{29} - 38 q^{30} - 30 q^{31} - 126 q^{32} - 26 q^{33} - 60 q^{34} + 124 q^{36} - 42 q^{37} + 56 q^{39} - 120 q^{40} - 180 q^{41} - 60 q^{43} + 72 q^{44} - 98 q^{45} + 84 q^{46} + 378 q^{47} - 436 q^{48} - 378 q^{50} - 72 q^{51} - 36 q^{52} + 324 q^{53} + 446 q^{54} + 132 q^{55} - 232 q^{57} - 180 q^{58} - 90 q^{59} - 290 q^{60} + 324 q^{64} - 126 q^{65} - 28 q^{66} + 6 q^{67} + 432 q^{69} + 750 q^{72} - 36 q^{73} - 172 q^{75} - 84 q^{76} + 28 q^{78} - 6 q^{79} - 504 q^{80} - 112 q^{81} - 54 q^{82} + 558 q^{83} + 126 q^{85} + 670 q^{87} - 336 q^{88} - 522 q^{89} + 488 q^{90} + 774 q^{92} + 42 q^{93} + 354 q^{94} - 648 q^{95} + 184 q^{96} + 270 q^{97} + 296 q^{99}+O(q^{100}) \) 24 * q + 10 * q^3 + 24 * q^4 + 14 * q^6 - 16 * q^9 - 22 * q^12 - 10 * q^15 - 48 * q^16 - 108 * q^17 - 8 * q^18 - 12 * q^19 + 18 * q^20 - 24 * q^22 - 30 * q^24 - 108 * q^25 - 144 * q^26 + 124 * q^27 + 54 * q^29 - 38 * q^30 - 30 * q^31 - 126 * q^32 - 26 * q^33 - 60 * q^34 + 124 * q^36 - 42 * q^37 + 56 * q^39 - 120 * q^40 - 180 * q^41 - 60 * q^43 + 72 * q^44 - 98 * q^45 + 84 * q^46 + 378 * q^47 - 436 * q^48 - 378 * q^50 - 72 * q^51 - 36 * q^52 + 324 * q^53 + 446 * q^54 + 132 * q^55 - 232 * q^57 - 180 * q^58 - 90 * q^59 - 290 * q^60 + 324 * q^64 - 126 * q^65 - 28 * q^66 + 6 * q^67 + 432 * q^69 + 750 * q^72 - 36 * q^73 - 172 * q^75 - 84 * q^76 + 28 * q^78 - 6 * q^79 - 504 * q^80 - 112 * q^81 - 54 * q^82 + 558 * q^83 + 126 * q^85 + 670 * q^87 - 336 * q^88 - 522 * q^89 + 488 * q^90 + 774 * q^92 + 42 * q^93 + 354 * q^94 - 648 * q^95 + 184 * q^96 + 270 * q^97 + 296 * q^99

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