LMFDB - Embedded newform 363.3.h.k.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, 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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.23612624896000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 5 x^{14} + 20 x^{13} + 19 x^{12} + 88 x^{11} - 497 x^{10} + 10 x^{9} + 3711 x^{8} + \cdots + 16 $ x^16 - 2x^15 - 5x^14 + 20x^13 + 19x^12 + 88x^11 - 497x^10 + 10x^9 + 3711x^8 - 3712x^7 + 2758x^6 - 1816x^5 + 1084x^4 - 464x^3 + 184x^2 - 64*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			251.4
Root			$-0.0676410 - 0.503753i$ of defining polynomial
Character	$\chi$	$=$	363.251
Dual form			363.3.h.k.269.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.51626 + 0.817582i) q^{2} +(2.47152 + 1.70046i) q^{3} +(2.42705 + 1.76336i) q^{4} +(2.68999 - 0.874032i) q^{5} +(4.82873 + 6.29947i) q^{6} +(6.05413 + 4.39858i) q^{7} +(-1.55513 - 2.14046i) q^{8} +(3.21687 + 8.40546i) q^{9} +7.48331 q^{10} +(3.00000 + 8.48528i) q^{12} +(6.93741 - 21.3512i) q^{13} +(11.6376 + 16.0177i) q^{14} +(8.13464 + 2.41404i) q^{15} +(-5.87132 - 18.0701i) q^{16} +(-20.1301 + 6.54066i) q^{17} +(1.22232 + 23.7804i) q^{18} +(-12.1083 + 8.79716i) q^{19} +(8.06998 + 2.62210i) q^{20} +(7.48331 + 21.1660i) q^{21} +31.1127i q^{23} +(-0.203788 - 7.93464i) q^{24} +(-13.7533 + 9.99235i) q^{25} +(34.9127 - 48.0532i) q^{26} +(-6.34258 + 26.2445i) q^{27} +(6.93741 + 21.3512i) q^{28} +(12.4411 - 17.1237i) q^{29} +(18.4952 + 12.7251i) q^{30} +(9.27051 - 28.5317i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(20.1301 + 6.54066i) q^{35} +(-7.01431 + 26.0730i) q^{36} +(8.09017 + 5.87785i) q^{37} +(-37.6599 + 12.2364i) q^{38} +(53.4528 - 40.9731i) q^{39} +(-6.05413 - 4.39858i) q^{40} +(-24.8821 - 34.2473i) q^{41} +(1.52501 + 59.3774i) q^{42} -14.9666 q^{43} +(16.0000 + 19.7990i) q^{45} +(-25.4372 + 78.2876i) q^{46} +(21.6126 + 29.7472i) q^{47} +(16.2163 - 54.6446i) q^{48} +(2.16312 + 6.65740i) q^{49} +(-42.7764 + 13.8989i) q^{50} +(-60.8741 - 18.0650i) q^{51} +(54.4872 - 39.5872i) q^{52} +(40.3499 + 13.1105i) q^{53} +(-37.4166 + 60.8523i) q^{54} -19.7990i q^{56} +(-44.8851 + 1.15280i) q^{57} +(45.3050 - 32.9160i) q^{58} +(-19.9501 + 27.4589i) q^{59} +(15.4864 + 20.2033i) q^{60} +(-30.0621 - 92.5217i) q^{61} +(46.6540 - 64.2137i) q^{62} +(-17.4968 + 65.0374i) q^{63} +(8.96149 - 27.5806i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(-60.3902 - 19.6220i) q^{68} +(-52.9059 + 76.8958i) q^{69} +(45.3050 + 32.9160i) q^{70} +(61.8699 - 20.1027i) q^{71} +(12.9889 - 19.9572i) q^{72} +(-60.5413 - 43.9858i) q^{73} +(15.5513 + 21.4046i) q^{74} +(-50.9832 + 1.30942i) q^{75} -44.8999 q^{76} +(168.000 - 59.3970i) q^{78} +(6.93741 - 21.3512i) q^{79} +(-31.5876 - 43.4767i) q^{80} +(-60.3035 + 54.0785i) q^{81} +(-34.6099 - 106.518i) q^{82} +(-20.1301 + 6.54066i) q^{83} +(-19.1608 + 64.5667i) q^{84} +(-48.4330 + 35.1887i) q^{85} +(-37.6599 - 12.2364i) q^{86} +(59.8665 - 21.1660i) q^{87} +62.2254i q^{89} +(24.0728 + 62.9007i) q^{90} +(135.915 - 98.7479i) q^{91} +(-54.8628 + 75.5121i) q^{92} +(71.4293 - 54.7527i) q^{93} +(30.0621 + 92.5217i) q^{94} +(-24.8821 + 34.2473i) q^{95} +(67.4849 - 98.0856i) q^{96} +(22.8673 - 70.3782i) q^{97} +18.5203i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 12 q^{4} + 28 q^{9} + 48 q^{12} + 32 q^{15} + 76 q^{16} - 68 q^{25} - 92 q^{27} - 120 q^{31} - 896 q^{34} - 84 q^{36} + 40 q^{37} + 224 q^{42} + 256 q^{45} - 76 q^{48} - 28 q^{49} + 224 q^{58}+ \cdots - 296 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 + 12 * q^4 + 28 * q^9 + 48 * q^12 + 32 * q^15 + 76 * q^16 - 68 * q^25 - 92 * q^27 - 120 * q^31 - 896 * q^34 - 84 * q^36 + 40 * q^37 + 224 * q^42 + 256 * q^45 - 76 * q^48 - 28 * q^49 + 224 * q^58 - 96 * q^60 - 116 * q^64 - 672 * q^67 - 352 * q^69 + 224 * q^70 + 68 * q^75 + 2688 * q^78 - 68 * q^81 + 448 * q^82 + 672 * q^91 + 120 * q^93 - 296 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	2.51626	+	0.817582i	1.25813	+	0.408791i	0.860828	−	0.508897i	$-0.169947\pi$
$2$	2.51626	+	0.817582i	1.25813	+	0.408791i	0.397302	+	0.917688i	$0.369947\pi$
$3$	2.47152	+	1.70046i	0.823842	+	0.566820i
$3$	2.47152	+	1.70046i	0.823842	+	0.566820i
$4$	2.42705	+	1.76336i	0.606763	+	0.440839i
$5$	2.68999	−	0.874032i	0.537999	−	0.174806i	−0.0273993	−	0.999625i	$-0.508723\pi$
$5$	2.68999	−	0.874032i	0.537999	−	0.174806i	0.565398	+	0.824818i	$0.308723\pi$
$6$	4.82873	+	6.29947i	0.804788	+	1.04991i
$7$	6.05413	+	4.39858i	0.864876	+	0.628369i	0.929207	−	0.369560i	$-0.120491\pi$
$7$	6.05413	+	4.39858i	0.864876	+	0.628369i	−0.0643314	+	0.997929i	$0.520491\pi$
$8$	−1.55513	−	2.14046i	−0.194392	−	0.267557i
$9$	3.21687	+	8.40546i	0.357430	+	0.933940i
$10$	7.48331			0.748331
$11$		0			0
$11$		0			0
$12$	3.00000	+	8.48528i	0.250000	+	0.707107i
$13$	6.93741	−	21.3512i	0.533647	−	1.64240i	−0.212907	−	0.977073i	$-0.568293\pi$
$13$	6.93741	−	21.3512i	0.533647	−	1.64240i	0.746554	−	0.665325i	$-0.231707\pi$
$14$	11.6376	+	16.0177i	0.831254	+	1.14412i
$15$	8.13464	+	2.41404i	0.542310	+	0.160936i
$16$	−5.87132	−	18.0701i	−0.366958	−	1.12938i
$17$	−20.1301	+	6.54066i	−1.18412	+	0.384745i	−0.833896	−	0.551921i	$-0.813895\pi$
$17$	−20.1301	+	6.54066i	−1.18412	+	0.384745i	−0.350225	+	0.936665i	$0.613895\pi$
$18$	1.22232	+	23.7804i	0.0679068	+	1.32113i
$19$	−12.1083	+	8.79716i	−0.637277	+	0.463009i	−0.858914	−	0.512121i	$-0.828860\pi$
$19$	−12.1083	+	8.79716i	−0.637277	+	0.463009i	0.221637	+	0.975129i	$0.428860\pi$
$20$	8.06998	+	2.62210i	0.403499	+	0.131105i
$21$	7.48331	+	21.1660i	0.356348	+	1.00791i
$22$		0			0
$23$			31.1127i			1.35273i	0.736568	+	0.676363i	$0.236445\pi$
$23$			31.1127i			1.35273i	−0.736568	+	0.676363i	$0.763555\pi$
$24$	−0.203788	−	7.93464i	−0.00849115	−	0.330610i
$25$	−13.7533	+	9.99235i	−0.550132	+	0.399694i
$26$	34.9127	−	48.0532i	1.34279	−	1.84820i
$27$	−6.34258	+	26.2445i	−0.234910	+	0.972017i
$28$	6.93741	+	21.3512i	0.247765	+	0.762542i
$29$	12.4411	−	17.1237i	0.429002	−	0.590471i	−0.538722	−	0.842484i	$-0.681093\pi$
$29$	12.4411	−	17.1237i	0.429002	−	0.590471i	0.967724	+	0.252013i	$0.0810925\pi$
$30$	18.4952	+	12.7251i	0.616507	+	0.424169i
$31$	9.27051	−	28.5317i	0.299049	−	0.920377i	−0.682783	−	0.730622i	$-0.739230\pi$
$31$	9.27051	−	28.5317i	0.299049	−	0.920377i	0.981831	−	0.189756i	$-0.0607696\pi$
$32$		−	39.6863i		−	1.24020i
$33$		0			0
$34$	−56.0000			−1.64706
$35$	20.1301	+	6.54066i	0.575145	+	0.186876i
$36$	−7.01431	+	26.0730i	−0.194842	+	0.724249i
$37$	8.09017	+	5.87785i	0.218653	+	0.158861i	0.691720	−	0.722166i	$-0.256853\pi$
$37$	8.09017	+	5.87785i	0.218653	+	0.158861i	−0.473067	+	0.881026i	$0.656853\pi$
$38$	−37.6599	+	12.2364i	−0.991050	+	0.322012i
$39$	53.4528	−	40.9731i	1.37058	−	1.05059i
$40$	−6.05413	−	4.39858i	−0.151353	−	0.109965i
$41$	−24.8821	−	34.2473i	−0.606881	−	0.835301i	0.389435	−	0.921054i	$-0.372670\pi$
$41$	−24.8821	−	34.2473i	−0.606881	−	0.835301i	−0.996316	+	0.0857534i	$0.972670\pi$
$42$	1.52501	+	59.3774i	0.0363097	+	1.41375i
$43$	−14.9666			−0.348061			−0.174031	−	0.984740i	$-0.555679\pi$
$43$	−14.9666			−0.348061			−0.174031	+	0.984740i	$0.555679\pi$
$44$		0			0
$45$	16.0000	+	19.7990i	0.355556	+	0.439978i
$46$	−25.4372	+	78.2876i	−0.552982	+	1.70190i
$47$	21.6126	+	29.7472i	0.459843	+	0.632919i	0.974476	−	0.224491i	$-0.0720720\pi$
$47$	21.6126	+	29.7472i	0.459843	+	0.632919i	−0.514634	+	0.857410i	$0.672072\pi$
$48$	16.2163	−	54.6446i	0.337840	−	1.13843i
$49$	2.16312	+	6.65740i	0.0441453	+	0.135865i
$50$	−42.7764	+	13.8989i	−0.855528	+	0.277978i
$51$	−60.8741	−	18.0650i	−1.19361	−	0.354216i
$52$	54.4872	−	39.5872i	1.04783	−	0.761293i
$53$	40.3499	+	13.1105i	0.761319	+	0.247368i	0.663845	−	0.747870i	$-0.268924\pi$
$53$	40.3499	+	13.1105i	0.761319	+	0.247368i	0.0974744	+	0.995238i	$0.468924\pi$
$54$	−37.4166	+	60.8523i	−0.692900	+	1.12689i
$55$		0			0
$56$		−	19.7990i		−	0.353553i
$57$	−44.8851	+	1.15280i	−0.787458	+	0.0202245i
$58$	45.3050	−	32.9160i	0.781120	−	0.567517i
$59$	−19.9501	+	27.4589i	−0.338137	+	0.465406i	−0.943896	−	0.330242i	$-0.892870\pi$
$59$	−19.9501	+	27.4589i	−0.338137	+	0.465406i	0.605759	+	0.795648i	$0.292870\pi$
$60$	15.4864	+	20.2033i	0.258107	+	0.336721i
$61$	−30.0621	−	92.5217i	−0.492822	−	1.51675i	−0.820324	−	0.571899i	$-0.806207\pi$
$61$	−30.0621	−	92.5217i	−0.492822	−	1.51675i	0.327502	−	0.944850i	$-0.393793\pi$
$62$	46.6540	−	64.2137i	0.752484	−	1.03571i
$63$	−17.4968	+	65.0374i	−0.277726	+	1.03234i
$64$	8.96149	−	27.5806i	0.140023	−	0.430947i
$65$		−	63.4980i		−	0.976893i
$66$		0			0
$67$	−42.0000			−0.626866			−0.313433	−	0.949610i	$-0.601479\pi$
$67$	−42.0000			−0.626866			−0.313433	+	0.949610i	$0.601479\pi$
$68$	−60.3902	−	19.6220i	−0.888091	−	0.288558i
$69$	−52.9059	+	76.8958i	−0.766752	+	1.11443i
$70$	45.3050	+	32.9160i	0.647214	+	0.470228i
$71$	61.8699	−	20.1027i	0.871407	−	0.283137i	0.161022	−	0.986951i	$-0.448521\pi$
$71$	61.8699	−	20.1027i	0.871407	−	0.283137i	0.710385	+	0.703814i	$0.248521\pi$
$72$	12.9889	−	19.9572i	0.180401	−	0.277183i
$73$	−60.5413	−	43.9858i	−0.829333	−	0.602545i	0.0900377	−	0.995938i	$-0.471301\pi$
$73$	−60.5413	−	43.9858i	−0.829333	−	0.602545i	−0.919370	+	0.393393i	$0.871301\pi$
$74$	15.5513	+	21.4046i	0.210153	+	0.289251i
$75$	−50.9832	+	1.30942i	−0.679776	+	0.0174589i
$76$	−44.8999			−0.590788
$77$		0			0
$78$	168.000	−	59.3970i	2.15385	−	0.761500i
$79$	6.93741	−	21.3512i	0.0878154	−	0.270268i	−0.897499	−	0.441016i	$-0.854618\pi$
$79$	6.93741	−	21.3512i	0.0878154	−	0.270268i	0.985315	+	0.170748i	$0.0546183\pi$
$80$	−31.5876	−	43.4767i	−0.394846	−	0.543458i
$81$	−60.3035	+	54.0785i	−0.744488	+	0.667636i
$82$	−34.6099	−	106.518i	−0.422072	−	1.29900i
$83$	−20.1301	+	6.54066i	−0.242531	+	0.0788031i	−0.427760	−	0.903892i	$-0.640697\pi$
$83$	−20.1301	+	6.54066i	−0.242531	+	0.0788031i	0.185229	+	0.982695i	$0.440697\pi$
$84$	−19.1608	+	64.5667i	−0.228105	+	0.768652i
$85$	−48.4330	+	35.1887i	−0.569800	+	0.413984i
$86$	−37.6599	−	12.2364i	−0.437906	−	0.142284i
$87$	59.8665	−	21.1660i	0.688121	−	0.243287i
$88$		0			0
$89$			62.2254i			0.699162i	0.936906	+	0.349581i	$0.113676\pi$
$89$			62.2254i			0.699162i	−0.936906	+	0.349581i	$0.886324\pi$
$90$	24.0728	+	62.9007i	0.267476	+	0.698897i
$91$	135.915	−	98.7479i	1.49357	−	1.08514i
$92$	−54.8628	+	75.5121i	−0.596334	+	0.820784i
$93$	71.4293	−	54.7527i	0.768057	−	0.588738i
$94$	30.0621	+	92.5217i	0.319810	+	0.984274i
$95$	−24.8821	+	34.2473i	−0.261917	+	0.360498i
$96$	67.4849	−	98.0856i	0.702968	−	1.02172i
$97$	22.8673	−	70.3782i	0.235745	−	0.725548i	−0.761277	−	0.648427i	$-0.775427\pi$
$97$	22.8673	−	70.3782i	0.235745	−	0.725548i	0.997022	−	0.0771212i	$-0.0245728\pi$
$98$			18.5203i			0.188982i
$99$		0			0
$100$	−51.0000			−0.510000
$101$	140.911	+	45.7846i	1.39515	+	0.453313i	0.907620	−	0.419792i	$-0.137897\pi$
$101$	140.911	+	45.7846i	1.39515	+	0.453313i	0.487533	+	0.873105i	$0.337897\pi$
$102$	−138.405	−	95.2258i	−1.35692	−	0.933586i
$103$	−27.5066	−	19.9847i	−0.267054	−	0.194026i	0.446197	−	0.894935i	$-0.352778\pi$
$103$	−27.5066	−	19.9847i	−0.267054	−	0.194026i	−0.713251	+	0.700909i	$0.752778\pi$
$104$	−56.4899	+	18.3547i	−0.543172	+	0.176487i
$105$	38.6298	+	50.3958i	0.367903	+	0.479960i
$106$	90.8119	+	65.9787i	0.856716	+	0.622441i
$107$	−24.8821	−	34.2473i	−0.232543	−	0.320068i	0.676759	−	0.736205i	$-0.263384\pi$
$107$	−24.8821	−	34.2473i	−0.232543	−	0.320068i	−0.909302	+	0.416136i	$0.863384\pi$
$108$	−61.6721	+	52.5124i	−0.571038	+	0.486226i
$109$	67.3498			0.617888			0.308944	−	0.951080i	$-0.400024\pi$
$109$	67.3498			0.617888			0.308944	+	0.951080i	$0.400024\pi$
$110$		0			0
$111$	10.0000	+	28.2843i	0.0900901	+	0.254813i
$112$	43.9370	−	135.224i	0.392294	−	1.20736i
$113$	−69.8253	−	96.1063i	−0.617923	−	0.850498i	0.379276	−	0.925283i	$-0.376173\pi$
$113$	−69.8253	−	96.1063i	−0.617923	−	0.850498i	−0.997200	+	0.0747850i	$0.976173\pi$
$114$	−113.885	−	33.7965i	−0.998991	−	0.296461i
$115$	27.1935	+	83.6930i	0.236465	+	0.727765i
$116$	60.3902	−	19.6220i	0.520605	−	0.169155i
$117$	201.783	−	10.3717i	1.72464	−	0.0886474i
$118$	−72.6495	+	52.7830i	−0.615674	+	0.447313i
$119$	−150.640	−	48.9458i	−1.26588	−	0.411309i
$120$	−7.48331	−	21.1660i	−0.0623610	−	0.176383i
$121$		0			0
$122$		−	257.387i		−	2.10973i
$123$	−3.26060	−	126.954i	−0.0265090	−	1.03215i
$124$	72.8115	−	52.9007i	0.587190	−	0.426618i
$125$	−69.8253	+	96.1063i	−0.558603	+	0.768851i
$126$	−97.1998	+	149.346i	−0.771427	+	1.18528i
$127$	20.8122	+	64.0535i	0.163876	+	0.504358i	0.998952	−	0.0457767i	$-0.0145763\pi$
$127$	20.8122	+	64.0535i	0.163876	+	0.504358i	−0.835076	+	0.550135i	$0.814576\pi$
$128$	−48.2091	+	66.3542i	−0.376634	+	0.518392i
$129$	−36.9904	−	25.4502i	−0.286747	−	0.197288i
$130$	51.9149	−	159.777i	0.399345	−	1.22906i
$131$			232.826i			1.77730i	0.458587	+	0.888649i	$0.348356\pi$
$131$			232.826i			1.77730i	−0.458587	+	0.888649i	$0.651644\pi$
$132$		0			0
$133$	−112.000			−0.842105
$134$	−105.683	−	34.3384i	−0.788678	−	0.256257i
$135$	5.87700	+	76.1411i	0.0435333	+	0.564008i
$136$	45.3050	+	32.9160i	0.333125	+	0.242029i
$137$	150.640	−	48.9458i	1.09956	−	0.357269i	0.297626	−	0.954682i	$-0.403805\pi$
$137$	150.640	−	48.9458i	1.09956	−	0.357269i	0.801933	+	0.597414i	$0.203805\pi$
$138$	−195.994	+	150.235i	−1.42024	+	1.08866i
$139$	72.6495	+	52.7830i	0.522659	+	0.379734i	0.817604	−	0.575780i	$-0.195302\pi$
$139$	72.6495	+	52.7830i	0.522659	+	0.379734i	−0.294946	+	0.955514i	$0.595302\pi$
$140$	37.3232	+	51.3710i	0.266594	+	0.366936i
$141$	2.83216	+	110.272i	0.0200862	+	0.782073i
$142$	172.116			1.21209
$143$		0			0
$144$	133.000	−	107.480i	0.923611	−	0.746390i
$145$	18.4998	−	56.9364i	0.127585	−	0.392665i
$146$	−116.376	−	160.177i	−0.797093	−	1.09710i
$147$	−5.97444	+	20.1322i	−0.0406424	+	0.136954i
$148$	9.27051	+	28.5317i	0.0626386	+	0.192782i
$149$	−20.1301	+	6.54066i	−0.135101	+	0.0438970i	−0.375787	−	0.926706i	$-0.622628\pi$
$149$	−20.1301	+	6.54066i	−0.135101	+	0.0438970i	0.240686	+	0.970603i	$0.422628\pi$
$150$	−129.357	−	38.3881i	−0.862383	−	0.255921i
$151$	54.4872	−	39.5872i	0.360842	−	0.262167i	−0.392561	−	0.919726i	$-0.628411\pi$
$151$	54.4872	−	39.5872i	0.360842	−	0.262167i	0.753403	+	0.657559i	$0.228411\pi$
$152$	37.6599	+	12.2364i	0.247763	+	0.0805030i
$153$	−119.733	−	148.162i	−0.782569	−	0.968380i
$154$		0			0
$155$		−	84.8528i		−	0.547438i
$156$	201.983	−	5.18759i	1.29476	−	0.0332538i
$157$	−69.5755	+	50.5495i	−0.443156	+	0.321972i	−0.786888	−	0.617096i	$-0.788309\pi$
$157$	−69.5755	+	50.5495i	−0.443156	+	0.321972i	0.343732	+	0.939068i	$0.388309\pi$
$158$	34.9127	−	48.0532i	0.220966	−	0.304134i
$159$	77.4320	+	101.016i	0.486993	+	0.635323i
$160$	−34.6871	−	106.756i	−0.216794	−	0.667224i
$161$	−136.852	+	188.360i	−0.850011	+	1.16994i
$162$	−195.953	+	86.7725i	−1.20959	+	0.535633i
$163$	−4.32624	+	13.3148i	−0.0265413	+	0.0816858i	−0.963450	−	0.267889i	$-0.913674\pi$
$163$	−4.32624	+	13.3148i	−0.0265413	+	0.0816858i	0.936908	+	0.349575i	$0.113674\pi$
$164$		−	126.996i		−	0.774366i
$165$		0			0
$166$	−56.0000			−0.337349
$167$	−80.5203	−	26.1626i	−0.482157	−	0.156662i	0.0578456	−	0.998326i	$-0.481577\pi$
$167$	−80.5203	−	26.1626i	−0.482157	−	0.156662i	−0.540003	+	0.841663i	$0.681577\pi$
$168$	33.6674	−	48.9337i	0.200401	−	0.291272i
$169$	−271.021	−	196.908i	−1.60367	−	1.16514i
$170$	−150.640	+	48.9458i	−0.886116	+	0.287916i
$171$	−112.895	−	73.4761i	−0.660204	−	0.429685i
$172$	−36.3248	−	26.3915i	−0.211191	−	0.153439i
$173$	111.970	+	154.113i	0.647223	+	0.890826i	0.998975	−	0.0452670i	$-0.0144139\pi$
$173$	111.970	+	154.113i	0.647223	+	0.890826i	−0.351752	+	0.936093i	$0.614414\pi$
$174$	167.945	−	4.31337i	0.965199	−	0.0247895i
$175$	−127.216			−0.726951
$176$		0			0
$177$	−96.0000	+	33.9411i	−0.542373	+	0.191758i
$178$	−50.8744	+	156.575i	−0.285811	+	0.879636i
$179$	186.201	+	256.284i	1.04023	+	1.43175i	0.896983	+	0.442064i	$0.145754\pi$
$179$	186.201	+	256.284i	1.04023	+	1.43175i	0.143245	+	0.989687i	$0.454246\pi$
$180$	3.92015	+	76.2668i	0.0217786	+	0.423705i
$181$	−80.9625	−	249.177i	−0.447306	−	1.37667i	−0.879935	−	0.475095i	$-0.842414\pi$
$181$	−80.9625	−	249.177i	−0.447306	−	1.37667i	0.432628	−	0.901572i	$-0.357586\pi$
$182$	422.732	−	137.354i	2.32270	−	0.754691i
$183$	83.0302	−	279.789i	0.453717	−	1.52890i
$184$	66.5954	−	48.3844i	0.361932	−	0.262959i
$185$	26.8999	+	8.74032i	0.145405	+	0.0472450i
$186$	224.499	−	79.3725i	1.20699	−	0.426734i
$187$		0			0
$188$			110.309i			0.586748i
$189$	−153.837	+	130.989i	−0.813953	+	0.693063i
$190$	−90.6099	+	65.8319i	−0.476894	+	0.346484i
$191$	34.9127	−	48.0532i	0.182789	−	0.251587i	−0.707783	−	0.706430i	$-0.750305\pi$
$191$	34.9127	−	48.0532i	0.182789	−	0.251587i	0.890572	+	0.454843i	$0.150305\pi$
$192$	69.0483	−	52.9276i	0.359627	−	0.275664i
$193$	46.2494	+	142.341i	0.239634	+	0.737519i	0.996473	+	0.0839167i	$0.0267430\pi$
$193$	46.2494	+	142.341i	0.239634	+	0.737519i	−0.756838	+	0.653602i	$0.773257\pi$
$194$	115.080	−	158.394i	0.593195	−	0.816463i
$195$	107.976	−	156.937i	0.553722	−	0.804805i
$196$	−6.48936	+	19.9722i	−0.0331090	+	0.101899i
$197$			232.826i			1.18186i	0.806723	+	0.590929i	$0.201239\pi$
$197$			232.826i			1.18186i	−0.806723	+	0.590929i	$0.798761\pi$
$198$		0			0
$199$	222.000			1.11558			0.557789	−	0.829983i	$-0.311650\pi$
$199$	222.000			1.11558			0.557789	+	0.829983i	$0.311650\pi$
$200$	42.7764	+	13.8989i	0.213882	+	0.0694945i
$201$	−103.804	−	71.4193i	−0.516438	−	0.355320i
$202$	317.135	+	230.412i	1.56997	+	1.14065i
$203$	150.640	−	48.9458i	0.742067	−	0.241112i
$204$	−115.890	−	151.187i	−0.568086	−	0.741114i
$205$	−96.8661	−	70.3773i	−0.472517	−	0.343304i
$206$	−52.8745	−	72.7756i	−0.256673	−	0.353279i
$207$	−261.517	+	100.085i	−1.26336	+	0.483505i
$208$	−426.549			−2.05072
$209$		0			0
$210$	56.0000	+	158.392i	0.266667	+	0.754247i
$211$	−120.249	+	370.087i	−0.569898	+	1.75397i	0.0830307	+	0.996547i	$0.473540\pi$
$211$	−120.249	+	370.087i	−0.569898	+	1.75397i	−0.652929	+	0.757419i	$0.726460\pi$
$212$	74.8128	+	102.971i	0.352891	+	0.485713i
$213$	187.097	+	55.5228i	0.878389	+	0.260671i
$214$	−34.6099	−	106.518i	−0.161729	−	0.497749i
$215$	−40.2601	+	13.0813i	−0.187256	+	0.0608433i
$216$	66.0387	−	27.2376i	0.305735	−	0.126100i
$217$	181.624	−	131.957i	0.836976	−	0.608099i
$218$	169.470	+	55.0640i	0.777384	+	0.252587i
$219$	−74.8331	−	211.660i	−0.341704	−	0.966484i
$220$		0			0
$221$			475.176i			2.15012i
$222$	2.03788	+	79.3464i	0.00917962	+	0.357416i
$223$	37.2148	−	27.0381i	0.166882	−	0.121247i	−0.501209	−	0.865326i	$-0.667111\pi$
$223$	37.2148	−	27.0381i	0.166882	−	0.121247i	0.668092	+	0.744079i	$0.267111\pi$
$224$	174.563	−	240.266i	0.779301	−	1.07262i
$225$	−128.233	−	83.4586i	−0.569924	−	0.370927i
$226$	−97.1238	−	298.916i	−0.429751	−	1.32264i
$227$	−124.411	+	171.237i	−0.548065	+	0.754346i	−0.989748	−	0.142825i	$-0.954381\pi$
$227$	−124.411	+	171.237i	−0.548065	+	0.754346i	0.441683	+	0.897171i	$0.354381\pi$
$228$	−110.971	−	76.3505i	−0.486716	−	0.334871i
$229$	36.4640	−	112.225i	0.159231	−	0.490064i	−0.839334	−	0.543617i	$-0.817055\pi$
$229$	36.4640	−	112.225i	0.159231	−	0.490064i	0.998565	+	0.0535527i	$0.0170545\pi$
$230$			232.826i			1.01229i
$231$		0			0
$232$	−56.0000			−0.241379
$233$	−80.5203	−	26.1626i	−0.345581	−	0.112286i	0.131084	−	0.991371i	$-0.458154\pi$
$233$	−80.5203	−	26.1626i	−0.345581	−	0.112286i	−0.476664	+	0.879085i	$0.658154\pi$
$234$	516.218	+	138.876i	2.20606	+	0.593488i
$235$	84.1378	+	61.1297i	0.358033	+	0.260126i
$236$	−96.8398	+	31.4652i	−0.410338	+	0.133327i
$237$	53.4528	−	40.9731i	0.225539	−	0.172882i
$238$	−339.031	−	246.321i	−1.42450	−	1.03496i
$239$	−24.8821	−	34.2473i	−0.104109	−	0.143294i	0.753784	−	0.657123i	$-0.228227\pi$
$239$	−24.8821	−	34.2473i	−0.104109	−	0.143294i	−0.857893	+	0.513829i	$0.828227\pi$
$240$	−4.13930	−	161.167i	−0.0172471	−	0.671530i
$241$	149.666			0.621022			0.310511	−	0.950570i	$-0.399500\pi$
$241$	149.666			0.621022			0.310511	+	0.950570i	$0.399500\pi$
$242$		0			0
$243$	−241.000	+	31.1127i	−0.991770	+	0.128036i
$244$	90.1864	−	277.565i	0.369616	−	1.13756i
$245$	11.6376	+	16.0177i	0.0475002	+	0.0653784i
$246$	95.5910	−	322.115i	0.388581	−	1.30941i
$247$	103.830	+	319.555i	0.420363	+	1.29374i
$248$	−75.4878	+	24.5275i	−0.304386	+	0.0989011i
$249$	−60.8741	−	18.0650i	−0.244474	−	0.0725502i
$250$	−254.273	+	184.740i	−1.01709	+	0.738962i
$251$	−48.4199	−	15.7326i	−0.192908	−	0.0626796i	0.210970	−	0.977493i	$-0.432338\pi$
$251$	−48.4199	−	15.7326i	−0.192908	−	0.0626796i	−0.403878	+	0.914813i	$0.632338\pi$
$252$	−157.150	+	126.996i	−0.623610	+	0.503953i
$253$		0			0
$254$			178.191i			0.701539i
$255$	−179.540	+	4.61119i	−0.704080	+	0.0180831i
$256$	−269.403	+	195.732i	−1.05235	+	0.764580i
$257$	−56.5253	+	77.8004i	−0.219943	+	0.302725i	−0.904703	−	0.426044i	$-0.859907\pi$
$257$	−56.5253	+	77.8004i	−0.219943	+	0.302725i	0.684760	+	0.728769i	$0.259907\pi$
$258$	−72.2698	−	94.2819i	−0.280116	−	0.365434i
$259$	23.1247	+	71.1706i	0.0892846	+	0.274790i
$260$	111.970	−	154.113i	0.430652	−	0.592742i
$261$	183.954	+	49.4883i	0.704803	+	0.189610i
$262$	−190.354	+	585.851i	−0.726544	+	2.23607i
$263$		−	465.652i		−	1.77054i	−0.465077	−	0.885270i	$-0.653973\pi$
$263$		−	465.652i		−	1.77054i	0.465077	−	0.885270i	$-0.346027\pi$
$264$		0			0
$265$	120.000			0.452830
$266$	−281.821	−	91.5692i	−1.05948	−	0.344245i
$267$	−105.812	+	153.792i	−0.396299	+	0.575999i
$268$	−101.936	−	74.0609i	−0.380359	−	0.276347i
$269$	−352.389	+	114.498i	−1.31000	+	0.425644i	−0.879048	−	0.476733i	$-0.841821\pi$
$269$	−352.389	+	114.498i	−1.31000	+	0.425644i	−0.430949	+	0.902376i	$0.641821\pi$
$270$	−47.4635	+	196.396i	−0.175791	+	0.727391i
$271$	272.436	+	197.936i	1.00530	+	0.730392i	0.963218	−	0.268722i	$-0.0866014\pi$
$271$	272.436	+	197.936i	1.00530	+	0.730392i	0.0420805	+	0.999114i	$0.486601\pi$
$272$	236.380	+	325.350i	0.869045	+	1.19614i
$273$	503.834	−	12.9401i	1.84555	−	0.0473997i
$274$	419.066			1.52944
$275$		0			0
$276$	−264.000	+	93.3381i	−0.956522	+	0.338182i
$277$	6.93741	−	21.3512i	0.0250448	−	0.0770800i	−0.937753	−	0.347303i	$-0.887097\pi$
$277$	6.93741	−	21.3512i	0.0250448	−	0.0770800i	0.962798	+	0.270223i	$0.0870975\pi$
$278$	139.651	+	192.213i	0.502340	+	0.691412i
$279$	269.644	−	13.8598i	0.966466	−	0.0496768i
$280$	−17.3050	−	53.2592i	−0.0618034	−	0.190211i
$281$	−20.1301	+	6.54066i	−0.0716373	+	0.0232764i	−0.344616	−	0.938744i	$-0.611991\pi$
$281$	−20.1301	+	6.54066i	−0.0716373	+	0.0232764i	0.272979	+	0.962020i	$0.411991\pi$
$282$	−83.0302	+	279.789i	−0.294433	+	0.992160i
$283$	−145.299	+	105.566i	−0.513424	+	0.373025i	−0.814121	−	0.580695i	$-0.802781\pi$
$283$	−145.299	+	105.566i	−0.513424	+	0.373025i	0.300697	+	0.953720i	$0.402781\pi$
$284$	185.610	+	60.3082i	0.653555	+	0.212353i
$285$	−119.733	+	42.3320i	−0.420116	+	0.148533i
$286$		0			0
$287$		−	316.784i		−	1.10378i
$288$	333.581	−	127.666i	1.15827	−	0.443283i
$289$	128.634	−	93.4579i	0.445099	−	0.323384i
$290$	93.1004	−	128.142i	0.321036	−	0.441868i
$291$	176.192	−	135.057i	0.605472	−	0.464112i
$292$	−69.3741	−	213.512i	−0.237583	−	0.731204i
$293$	12.4411	−	17.1237i	0.0424610	−	0.0584425i	−0.787259	−	0.616623i	$-0.788500\pi$
$293$	12.4411	−	17.1237i	0.0424610	−	0.0584425i	0.829720	+	0.558180i	$0.188500\pi$
$294$	−31.4930	+	45.7733i	−0.107119	+	0.155691i
$295$	−29.6656	+	91.3014i	−0.100561	+	0.309496i
$296$		−	26.4575i		−	0.0893835i
$297$		0			0
$298$	−56.0000			−0.187919
$299$	664.292	+	215.842i	2.22171	+	0.721879i
$300$	−126.048	−	86.7235i	−0.420159	−	0.289078i
$301$	−90.6099	−	65.8319i	−0.301030	−	0.218711i
$302$	169.470	−	55.0640i	0.561158	−	0.182331i
$303$	270.409	+	352.770i	0.892439	+	1.16426i
$304$	230.057	+	167.146i	0.756766	+	0.549823i
$305$	−161.734	−	222.608i	−0.530275	−	0.729861i
$306$	−180.145	−	470.706i	−0.588708	−	1.53825i
$307$	149.666			0.487512			0.243756	−	0.969837i	$-0.421620\pi$
$307$	149.666			0.487512			0.243756	+	0.969837i	$0.421620\pi$
$308$		0			0
$309$	−34.0000	−	96.1665i	−0.110032	−	0.311219i
$310$	69.3741	−	213.512i	0.223788	−	0.688747i
$311$	−14.9626	−	20.5942i	−0.0481112	−	0.0662193i	0.784284	−	0.620402i	$-0.213031\pi$
$311$	−14.9626	−	20.5942i	−0.0481112	−	0.0662193i	−0.832395	+	0.554183i	$0.813031\pi$
$312$	−170.828	−	50.6948i	−0.547524	−	0.162483i
$313$	122.989	+	378.520i	0.392935	+	1.20933i	0.930558	+	0.366145i	$0.119323\pi$
$313$	122.989	+	378.520i	0.392935	+	1.20933i	−0.537622	+	0.843186i	$0.680677\pi$
$314$	−216.398	+	70.3121i	−0.689166	+	0.223924i
$315$	9.77858	+	190.243i	0.0310431	+	0.603946i
$316$	54.4872	−	39.5872i	0.172428	−	0.125276i
$317$	395.429	+	128.483i	1.24741	+	0.405308i	0.856992	−	0.515329i	$-0.172330\pi$
$317$	395.429	+	128.483i	1.24741	+	0.405308i	0.390418	+	0.920638i	$0.372330\pi$
$318$	112.250	+	317.490i	0.352987	+	0.998397i
$319$		0			0
$320$		−	82.0244i		−	0.256326i
$321$	−3.26060	−	126.954i	−0.0101576	−	0.395496i
$322$	−498.354	+	362.076i	−1.54768	+	1.12446i
$323$	186.201	−	256.284i	0.576473	−	0.793447i
$324$	−241.719	+	24.9148i	−0.746047	+	0.0768976i
$325$	117.936	+	362.970i	0.362880	+	1.11683i
$326$	−21.7719	+	29.9664i	−0.0667849	+	0.0919215i
$327$	166.457	+	114.526i	0.509042	+	0.350232i
$328$	−34.6099	+	106.518i	−0.105518	+	0.324751i
$329$			275.158i			0.836347i
$330$		0			0
$331$	178.000			0.537764			0.268882	−	0.963173i	$-0.413346\pi$
$331$	178.000			0.537764			0.268882	+	0.963173i	$0.413346\pi$
$332$	−60.3902	−	19.6220i	−0.181898	−	0.0591023i
$333$	−23.3810	+	86.9099i	−0.0702133	+	0.260991i
$334$	−181.220	−	131.664i	−0.542574	−	0.394203i
$335$	−112.980	+	36.7093i	−0.337253	+	0.109580i
$336$	338.534	−	259.497i	1.00754	−	0.772311i
$337$	205.840	+	149.552i	0.610802	+	0.443774i	0.849697	−	0.527272i	$-0.176785\pi$
$337$	205.840	+	149.552i	0.610802	+	0.443774i	−0.238894	+	0.971046i	$0.576785\pi$
$338$	−520.970	−	717.053i	−1.54133	−	2.12146i
$339$	−9.15004	−	356.264i	−0.0269913	−	1.05093i
$340$	−179.600			−0.528234
$341$		0			0
$342$	−224.000	−	277.186i	−0.654971	−	0.810485i
$343$	97.1238	−	298.916i	0.283160	−	0.871476i
$344$	23.2751	+	32.0354i	0.0676602	+	0.0931263i
$345$	−75.1072	+	253.091i	−0.217702	+	0.733596i
$346$	155.745	+	479.332i	0.450129	+	1.38535i
$347$	−462.992	+	150.435i	−1.33427	+	0.433531i	−0.887372	−	0.461054i	$-0.847471\pi$
$347$	−462.992	+	150.435i	−1.33427	+	0.433531i	−0.446898	+	0.894585i	$0.647471\pi$
$348$	182.622	+	54.1950i	0.524777	+	0.155733i
$349$	54.4872	−	39.5872i	0.156124	−	0.113430i	−0.506981	−	0.861957i	$-0.669239\pi$
$349$	54.4872	−	39.5872i	0.156124	−	0.113430i	0.663104	+	0.748527i	$0.269239\pi$
$350$	−320.109	−	104.010i	−0.914598	−	0.297171i
$351$	516.349	+	317.490i	1.47108	+	0.904530i
$352$		0			0
$353$		−	124.451i		−	0.352552i	−0.984341	−	0.176276i	$-0.943595\pi$
$353$		−	124.451i		−	0.352552i	0.984341	−	0.176276i	$-0.0564051\pi$
$354$	−269.311	+	6.91678i	−0.760764	+	0.0195389i
$355$	148.859	−	108.152i	0.419321	−	0.304655i
$356$	−109.726	+	151.024i	−0.308218	+	0.424225i
$357$	−289.079	−	377.128i	−0.809746	−	1.05638i
$358$	258.997	+	797.110i	0.723455	+	2.22656i
$359$	149.293	−	205.484i	0.415857	−	0.572379i	−0.548777	−	0.835969i	$-0.684907\pi$
$359$	149.293	−	205.484i	0.415857	−	0.572379i	0.964635	+	0.263590i	$0.0849065\pi$
$360$	17.4968	−	65.0374i	0.0486021	−	0.180659i
$361$	−42.3353	+	130.295i	−0.117272	+	0.360927i
$362$		−	693.187i		−	1.91488i
$363$		0			0
$364$	504.000			1.38462
$365$	−201.301	−	65.4066i	−0.551509	−	0.179196i
$366$	437.676	−	636.138i	1.19584	−	1.73808i
$367$	114.880	+	83.4655i	0.313026	+	0.227426i	0.733194	−	0.680020i	$-0.238029\pi$
$367$	114.880	+	83.4655i	0.313026	+	0.227426i	−0.420168	+	0.907446i	$0.638029\pi$
$368$	562.209	−	182.673i	1.52774	−	0.496393i
$369$	207.822	−	319.315i	0.563203	−	0.865352i
$370$	60.5413	+	43.9858i	0.163625	+	0.118881i
$371$	186.616	+	256.855i	0.503008	+	0.692331i
$372$	269.911	−	6.93220i	0.725567	−	0.0186350i
$373$	−426.549			−1.14356			−0.571781	−	0.820406i	$-0.693747\pi$
$373$	−426.549			−1.14356			−0.571781	+	0.820406i	$0.693747\pi$
$374$		0			0
$375$	−336.000	+	118.794i	−0.896000	+	0.316784i
$376$	30.0621	−	92.5217i	0.0799525	−	0.246068i
$377$	−279.301	−	384.425i	−0.740852	−	1.01970i
$378$	−494.189	+	203.828i	−1.30738	+	0.539227i
$379$	−108.156	−	332.870i	−0.285372	−	0.878284i	−0.986287	−	0.165040i	$-0.947225\pi$
$379$	−108.156	−	332.870i	−0.285372	−	0.878284i	0.700915	−	0.713245i	$-0.252775\pi$
$380$	−120.780	+	39.2439i	−0.317843	+	0.103274i
$381$	−57.4825	+	193.700i	−0.150873	+	0.508399i
$382$	127.137	−	92.3702i	0.332819	−	0.241807i
$383$	−492.269	−	159.948i	−1.28530	−	0.417618i	−0.414854	−	0.909888i	$-0.636168\pi$
$383$	−492.269	−	159.948i	−1.28530	−	0.417618i	−0.870443	+	0.492269i	$0.836168\pi$
$384$	−231.983	+	82.0183i	−0.604122	+	0.213589i
$385$		0			0
$386$			395.980i			1.02585i
$387$	−48.1457	−	125.801i	−0.124407	−	0.325068i
$388$	179.602	−	130.488i	0.462891	−	0.336310i
$389$	−257.689	+	354.678i	−0.662439	+	0.911769i	−0.999559	−	0.0296928i	$-0.990547\pi$
$389$	−257.689	+	354.678i	−0.662439	+	0.911769i	0.337120	+	0.941462i	$0.390547\pi$
$390$	400.004	−	306.615i	1.02565	−	0.786192i
$391$	−203.497	−	626.301i	−0.520454	−	1.60179i
$392$	10.8859	−	14.9832i	0.0277702	−	0.0382225i
$393$	−395.912	+	575.436i	−1.00741	+	1.46421i
$394$	−190.354	+	585.851i	−0.483133	+	1.48693i
$395$		−	63.4980i		−	0.160755i
$396$		0			0
$397$	442.000			1.11335			0.556675	−	0.830730i	$-0.312077\pi$
$397$	442.000			1.11335			0.556675	+	0.830730i	$0.312077\pi$
$398$	558.610	+	181.503i	1.40354	+	0.456038i
$399$	−276.811	−	190.452i	−0.693761	−	0.477322i
$400$	261.312	+	189.855i	0.653281	+	0.474637i
$401$	−500.339	+	162.570i	−1.24773	+	0.405411i	−0.857106	−	0.515140i	$-0.827740\pi$
$401$	−500.339	+	162.570i	−1.24773	+	0.405411i	−0.390622	+	0.920551i	$0.627740\pi$
$402$	−202.807	−	264.578i	−0.504494	−	0.658154i
$403$	−544.872	−	395.872i	−1.35204	−	0.982314i
$404$	261.262	+	359.597i	0.646689	+	0.890091i
$405$	−114.950	+	198.178i	−0.283826	+	0.489329i
$406$	419.066			1.03218
$407$		0			0
$408$	56.0000	+	158.392i	0.137255	+	0.388215i
$409$	−69.3741	+	213.512i	−0.169619	+	0.522033i	−0.999347	−	0.0361345i	$-0.988496\pi$
$409$	−69.3741	+	213.512i	−0.169619	+	0.522033i	0.829728	+	0.558168i	$0.188496\pi$
$410$	−186.201	−	256.284i	−0.454148	−	0.625082i
$411$	455.540	+	135.186i	1.10837	+	0.328920i
$412$	−31.5197	−	97.0078i	−0.0765042	−	0.235456i
$413$	−241.561	+	78.4879i	−0.584893	+	0.190043i
$414$	−739.871	+	38.0297i	−1.78713	+	0.0918593i
$415$	−48.4330	+	35.1887i	−0.116706	+	0.0847919i
$416$	−847.348	−	275.320i	−2.03689	−	0.661827i
$417$	89.7998	+	253.992i	0.215347	+	0.609094i
$418$		0			0
$419$		−	684.479i		−	1.63360i	−0.576919	−	0.816801i	$-0.695745\pi$
$419$		−	684.479i		−	1.63360i	0.576919	−	0.816801i	$-0.304255\pi$
$420$	4.89090	+	190.431i	0.0116450	+	0.453408i
$421$	215.199	−	156.351i	0.511160	−	0.371380i	−0.302103	−	0.953275i	$-0.597689\pi$
$421$	215.199	−	156.351i	0.511160	−	0.371380i	0.813264	+	0.581895i	$0.197689\pi$
$422$	−605.153	+	832.921i	−1.43401	+	1.97375i
$423$	−180.514	+	277.357i	−0.426747	+	0.655690i
$424$	−34.6871	−	106.756i	−0.0818091	−	0.251783i
$425$	211.498	−	291.102i	0.497643	−	0.684946i
$426$	425.390	+	292.677i	0.998567	+	0.687035i
$427$	224.964	−	692.369i	0.526849	−	1.62147i
$428$		−	126.996i		−	0.296720i
$429$		0			0
$430$	−112.000			−0.260465
$431$	−523.382	−	170.057i	−1.21434	−	0.394564i	−0.369324	−	0.929301i	$-0.620411\pi$
$431$	−523.382	−	170.057i	−1.21434	−	0.394564i	−0.845019	+	0.534737i	$0.820411\pi$
$432$	511.479	−	39.4788i	1.18398	−	0.0913862i
$433$	−597.055	−	433.786i	−1.37888	−	1.00181i	−0.996984	−	0.0776084i	$-0.975272\pi$
$433$	−597.055	−	433.786i	−1.37888	−	1.00181i	−0.381895	−	0.924206i	$-0.624728\pi$
$434$	564.899	−	183.547i	1.30161	−	0.422919i
$435$	142.541	−	109.262i	0.327680	−	0.251176i
$436$	163.461	+	118.762i	0.374912	+	0.272389i
$437$	−273.704	−	376.721i	−0.626324	−	0.862061i
$438$	−15.2501	−	593.774i	−0.0348175	−	1.35565i
$439$	−426.549			−0.971638			−0.485819	−	0.874060i	$-0.661479\pi$
$439$	−426.549			−0.971638			−0.485819	+	0.874060i	$0.661479\pi$
$440$		0			0
$441$	−49.0000	+	39.5980i	−0.111111	+	0.0897913i
$442$	−388.495	+	1195.67i	−0.878948	+	2.70513i
$443$	−69.8253	−	96.1063i	−0.157619	−	0.216944i	0.722902	−	0.690950i	$-0.242808\pi$
$443$	−69.8253	−	96.1063i	−0.157619	−	0.216944i	−0.880522	+	0.474006i	$0.842808\pi$
$444$	−25.6047	+	86.2809i	−0.0576683	+	0.194326i
$445$	54.3870	+	167.386i	0.122218	+	0.376148i
$446$	115.748	−	37.6088i	0.259524	−	0.0843246i
$447$	−60.8741	−	18.0650i	−0.136184	−	0.0404139i
$448$	175.570	−	127.559i	0.391897	−	0.284730i
$449$	484.199	+	157.326i	1.07839	+	0.350391i	0.793751	−	0.608242i	$-0.208125\pi$
$449$	484.199	+	157.326i	1.07839	+	0.350391i	0.284643	+	0.958634i	$0.408125\pi$
$450$	−254.433	−	314.844i	−0.565406	−	0.699654i
$451$		0			0
$452$		−	356.382i		−	0.788455i
$453$	201.983	−	5.18759i	0.445878	−	0.0114516i
$454$	−453.050	+	329.160i	−0.997906	+	0.725021i
$455$	279.301	−	384.425i	0.613849	−	0.844891i
$456$	72.2698	+	94.2819i	0.158486	+	0.206759i
$457$	−208.122	−	640.535i	−0.455410	−	1.40161i	−0.870653	−	0.491898i	$-0.836303\pi$
$457$	−208.122	−	640.535i	−0.455410	−	1.40161i	0.415243	−	0.909711i	$-0.363697\pi$
$458$	183.506	−	252.574i	0.400668	−	0.551472i
$459$	−43.9794	−	569.788i	−0.0958158	−	1.24137i
$460$	−81.5805	+	251.079i	−0.177349	+	0.545824i
$461$		−	698.478i		−	1.51514i	−0.652755	−	0.757569i	$-0.726387\pi$
$461$		−	698.478i		−	1.51514i	0.652755	−	0.757569i	$-0.273613\pi$
$462$		0			0
$463$	882.000			1.90497			0.952484	−	0.304589i	$-0.0985192\pi$
$463$	882.000			1.90497			0.952484	+	0.304589i	$0.0985192\pi$
$464$	−382.471	−	124.272i	−0.824292	−	0.267829i
$465$	144.289	−	209.716i	0.310299	−	0.451002i
$466$	−181.220	−	131.664i	−0.388884	−	0.282541i
$467$	505.719	−	164.318i	1.08291	−	0.351859i	0.287407	−	0.957809i	$-0.407207\pi$
$467$	505.719	−	164.318i	1.08291	−	0.351859i	0.795503	+	0.605950i	$0.207207\pi$
$468$	508.027	+	330.643i	1.08553	+	0.706501i
$469$	−254.273	−	184.740i	−0.542161	−	0.393903i
$470$	161.734	+	222.608i	0.344115	+	0.473633i
$471$	−257.915	+	6.62410i	−0.547590	+	0.0140639i
$472$	89.7998			0.190254
$473$		0			0
$474$	168.000	−	59.3970i	0.354430	−	0.125310i
$475$	78.6240	−	241.980i	0.165524	−	0.509431i
$476$	−279.301	−	384.425i	−0.586767	−	0.807616i
$477$	19.6008	+	381.334i	0.0410918	+	0.799443i
$478$	−34.6099	−	106.518i	−0.0724057	−	0.222842i
$479$	644.162	−	209.301i	1.34481	−	0.436954i	0.453864	−	0.891071i	$-0.350045\pi$
$479$	644.162	−	209.301i	1.34481	−	0.436954i	0.890942	+	0.454117i	$0.150045\pi$
$480$	95.8041	−	322.834i	0.199592	−	0.672570i
$481$	181.624	−	131.957i	0.377596	−	0.274340i
$482$	376.599	+	122.364i	0.781326	+	0.253868i
$483$	−658.532	+	232.826i	−1.36342	+	0.482042i
$484$		0			0
$485$		−	209.304i		−	0.431554i
$486$	−631.856	−	118.750i	−1.30011	−	0.244341i
$487$	−283.156	+	205.725i	−0.581429	+	0.422433i	−0.839239	−	0.543763i	$-0.816999\pi$
$487$	−283.156	+	205.725i	−0.581429	+	0.422433i	0.257810	+	0.966196i	$0.416999\pi$
$488$	−151.288	+	208.230i	−0.310017	+	0.426702i
$489$	−33.3337	+	25.5512i	−0.0681670	+	0.0522520i
$490$	16.1873	+	49.8194i	0.0330353	+	0.101672i
$491$	149.293	−	205.484i	0.304059	−	0.418501i	−0.629458	−	0.777034i	$-0.716723\pi$
$491$	149.293	−	205.484i	0.304059	−	0.418501i	0.933517	+	0.358533i	$0.116723\pi$
$492$	215.952	−	313.874i	0.438926	−	0.637955i
$493$	−138.440	+	426.073i	−0.280811	+	0.864246i
$494$			888.972i			1.79954i
$495$		0			0
$496$	−570.000			−1.14919
$497$	462.992	+	150.435i	0.931573	+	0.302686i
$498$	−138.405	−	95.2258i	−0.277922	−	0.191216i
$499$	79.2837	+	57.6030i	0.158885	+	0.115437i	0.664387	−	0.747389i	$-0.268693\pi$
$499$	79.2837	+	57.6030i	0.158885	+	0.115437i	−0.505502	+	0.862825i	$0.668693\pi$
$500$	−338.939	+	110.128i	−0.677879	+	0.220256i
$501$	−154.519	−	201.583i	−0.308422	−	0.402362i
$502$	−108.974	−	79.1745i	−0.217080	−	0.157718i
$503$	−298.586	−	410.968i	−0.593610	−	0.817034i	0.401495	−	0.915861i	$-0.368491\pi$
$503$	−298.586	−	410.968i	−0.593610	−	0.817034i	−0.995105	+	0.0988277i	$0.968491\pi$
$504$	166.420	−	63.6908i	0.330198	−	0.126371i
$505$	419.066			0.829833
$506$		0			0
$507$	−335.000	−	947.523i	−0.660750	−	1.86888i
$508$	−62.4367	+	192.160i	−0.122907	+	0.378269i
$509$	94.7629	+	130.430i	0.186175	+	0.256248i	0.891894	−	0.452244i	$-0.149376\pi$
$509$	94.7629	+	130.430i	0.186175	+	0.256248i	−0.705720	+	0.708491i	$0.749376\pi$
$510$	−455.540	−	135.186i	−0.893216	−	0.265071i
$511$	−173.050	−	532.592i	−0.338649	−	1.04225i
$512$	−525.898	+	170.875i	−1.02714	+	0.333740i
$513$	−154.079	−	373.571i	−0.300349	−	0.728209i
$514$	−205.840	+	149.552i	−0.400468	+	0.290957i
$515$	−91.4598	−	29.7171i	−0.177592	−	0.0577031i
$516$	−44.8999	−	126.996i	−0.0870153	−	0.246116i
$517$		0			0
$518$			197.990i			0.382220i
$519$	14.6727	+	571.294i	0.0282711	+	1.10076i
$520$	−135.915	+	98.7479i	−0.261375	+	0.189900i
$521$	89.7754	−	123.565i	0.172314	−	0.237169i	−0.714122	−	0.700021i	$-0.753174\pi$
$521$	89.7754	−	123.565i	0.172314	−	0.237169i	0.886436	+	0.462852i	$0.153174\pi$
$522$	422.414	+	274.923i	0.809222	+	0.526672i
$523$	−4.62494	−	14.2341i	−0.00884310	−	0.0272163i	0.946538	−	0.322593i	$-0.104555\pi$
$523$	−4.62494	−	14.2341i	−0.00884310	−	0.0272163i	−0.955381	+	0.295377i	$0.904555\pi$
$524$	−410.555	+	565.081i	−0.783502	+	1.07840i
$525$	−314.418	−	216.326i	−0.598892	−	0.412050i
$526$	380.709	−	1171.70i	0.723781	−	2.22757i
$527$			634.980i			1.20490i
$528$		0			0
$529$	−439.000			−0.829868
$530$	301.951	+	98.1099i	0.569719	+	0.185113i
$531$	−294.982	−	79.3579i	−0.555521	−	0.149450i
$532$	−271.830	−	197.496i	−0.510958	−	0.371233i
$533$	−903.838	+	293.675i	−1.69576	+	0.550985i
$534$	−391.987	+	300.470i	−0.734058	+	0.562677i
$535$	−96.8661	−	70.3773i	−0.181058	−	0.131546i
$536$	65.3156	+	89.8992i	0.121857	+	0.167722i
$537$	24.4001	+	950.038i	0.0454378	+	1.76916i
$538$	−980.314			−1.82215
$539$		0			0
$540$	−120.000	+	195.161i	−0.222222	+	0.361410i
$541$	159.561	−	491.077i	0.294936	−	0.907721i	−0.688307	−	0.725420i	$-0.741646\pi$
$541$	159.561	−	491.077i	0.294936	−	0.907721i	0.983243	−	0.182301i	$-0.0583544\pi$
$542$	523.690	+	720.797i	0.966218	+	1.32988i
$543$	223.615	−	753.520i	0.411813	−	1.38770i
$544$	259.574	+	798.887i	0.477159	+	1.46854i
$545$	181.171	−	58.8659i	0.332423	−	0.108011i
$546$	1278.36	+	379.365i	2.34131	+	0.694807i
$547$	−544.872	+	395.872i	−0.996109	+	0.723716i	−0.961250	−	0.275677i	$-0.911098\pi$
$547$	−544.872	+	395.872i	−0.996109	+	0.723716i	−0.0348585	+	0.999392i	$0.511098\pi$
$548$	451.919	+	146.837i	0.824670	+	0.267951i
$549$	680.982	−	550.316i	1.24040	−	1.00240i
$550$		0			0
$551$			316.784i			0.574925i
$552$	246.868	−	6.34038i	0.447225	−	0.0114862i
$553$	135.915	−	98.7479i	0.245777	−	0.178568i
$554$	34.9127	−	48.0532i	0.0630192	−	0.0867386i
$555$	51.6213	+	67.3442i	0.0930114	+	0.121341i
$556$	83.2490	+	256.214i	0.149728	+	0.460817i
$557$	−261.262	+	359.597i	−0.469053	+	0.645596i	−0.976355	−	0.216172i	$-0.930643\pi$
$557$	−261.262	+	359.597i	−0.469053	+	0.645596i	0.507302	+	0.861768i	$0.330643\pi$
$558$	689.826	+	185.581i	1.23625	+	0.332583i
$559$	−103.830	+	319.555i	−0.185742	+	0.571655i
$560$		−	402.154i		−	0.718132i
$561$		0			0
$562$	−56.0000			−0.0996441
$563$	−523.382	−	170.057i	−0.929630	−	0.302055i	−0.195219	−	0.980760i	$-0.562542\pi$
$563$	−523.382	−	170.057i	−0.929630	−	0.302055i	−0.734411	+	0.678704i	$0.762542\pi$
$564$	−187.575	+	272.631i	−0.332581	+	0.483388i
$565$	−271.830	−	197.496i	−0.481115	−	0.349550i
$566$	−451.919	+	146.837i	−0.798443	+	0.259430i
$567$	−602.954	+	62.1485i	−1.06341	+	0.109609i
$568$	−139.245	−	101.167i	−0.245150	−	0.178112i
$569$	659.377	+	907.554i	1.15883	+	1.59500i	0.715445	+	0.698669i	$0.246224\pi$
$569$	659.377	+	907.554i	1.15883	+	1.59500i	0.443389	+	0.896329i	$0.353776\pi$
$570$	−335.889	+	8.62674i	−0.589279	+	0.0151346i
$571$	808.198			1.41541			0.707704	−	0.706509i	$-0.249731\pi$
$571$	808.198			1.41541			0.707704	+	0.706509i	$0.249731\pi$
$572$		0			0
$573$	168.000	−	59.3970i	0.293194	−	0.103660i
$574$	258.997	−	797.110i	0.451214	−	1.38869i
$575$	−310.889	−	427.902i	−0.540676	−	0.744177i
$576$	260.656	−	13.3978i	0.452528	−	0.0232601i
$577$	95.7953	+	294.828i	0.166023	+	0.510966i	0.999110	−	0.0421754i	$-0.0134288\pi$
$577$	95.7953	+	294.828i	0.166023	+	0.510966i	−0.833087	+	0.553142i	$0.813429\pi$
$578$	400.085	−	129.996i	0.692189	−	0.224906i
$579$	−127.739	+	430.445i	−0.220620	+	0.743428i
$580$	145.299	−	105.566i	0.250516	−	0.182010i
$581$	−150.640	−	48.9458i	−0.259277	−	0.0842441i
$582$	553.765	−	195.786i	0.951487	−	0.336401i
$583$		0			0
$584$			197.990i			0.339024i
$585$	533.730	−	204.265i	0.912359	−	0.349171i
$586$	45.3050	−	32.9160i	0.0773122	−	0.0561706i
$587$	565.253	−	778.004i	0.962952	−	1.32539i	0.0174238	−	0.999848i	$-0.494454\pi$
$587$	565.253	−	778.004i	0.962952	−	1.32539i	0.945528	−	0.325541i	$-0.105546\pi$
$588$	−50.0005	+	38.3269i	−0.0850349	+	0.0651817i
$589$	138.748	+	427.023i	0.235566	+	0.724997i
$590$	−149.293	+	205.484i	−0.253039	+	0.348278i
$591$	−395.912	+	575.436i	−0.669901	+	0.973664i
$592$	58.7132	−	180.701i	0.0991778	−	0.305238i
$593$		−	232.826i		−	0.392624i	−0.980541	−	0.196312i	$-0.937103\pi$
$593$		−	232.826i		−	0.392624i	0.980541	−	0.196312i	$-0.0628966\pi$
$594$		0			0
$595$	−448.000			−0.752941
$596$	−60.3902	−	19.6220i	−0.101326	−	0.0329228i
$597$	548.678	+	377.502i	0.919059	+	0.632332i
$598$	1495.06	+	1086.23i	2.50011	+	1.81643i
$599$	831.208	−	270.076i	1.38766	−	0.450878i	0.482480	−	0.875907i	$-0.339736\pi$
$599$	831.208	−	270.076i	1.38766	−	0.450878i	0.905180	+	0.425029i	$0.139736\pi$
$600$	82.0884	+	107.091i	0.136814	+	0.178485i
$601$	472.222	+	343.089i	0.785727	+	0.570864i	0.906692	−	0.421793i	$-0.138599\pi$
$601$	472.222	+	343.089i	0.785727	+	0.570864i	−0.120965	+	0.992657i	$0.538599\pi$
$602$	−174.175	−	239.731i	−0.289327	−	0.398225i
$603$	−135.109	−	353.029i	−0.224061	−	0.585455i
$604$	202.049			0.334519
$605$		0			0
$606$	392.000	+	1108.74i	0.646865	+	1.82961i
$607$	261.309	−	804.227i	0.430493	−	1.32492i	−0.467142	−	0.884182i	$-0.654716\pi$
$607$	261.309	−	804.227i	0.430493	−	1.32492i	0.897635	−	0.440739i	$-0.145284\pi$
$608$	349.127	+	480.532i	0.574221	+	0.790348i
$609$	455.540	+	135.186i	0.748013	+	0.221980i
$610$	−224.964	−	692.369i	−0.368794	−	1.13503i
$611$	785.073	−	255.086i	1.28490	−	0.417489i
$612$	−29.3357	−	570.729i	−0.0479342	−	0.932563i
$613$	−478.276	+	347.488i	−0.780222	+	0.566865i	−0.905046	−	0.425314i	$-0.860164\pi$
$613$	−478.276	+	347.488i	−0.780222	+	0.566865i	0.124824	+	0.992179i	$0.460164\pi$
$614$	376.599	+	122.364i	0.613354	+	0.199291i
$615$	−119.733	−	338.656i	−0.194688	−	0.550660i
$616$		0			0
$617$			435.578i			0.705961i	0.935631	+	0.352980i	$0.114832\pi$
$617$			435.578i			0.705961i	−0.935631	+	0.352980i	$0.885168\pi$
$618$	−6.92878	−	269.778i	−0.0112116	−	0.436533i
$619$	677.956	−	492.564i	1.09524	−	0.795742i	0.114967	−	0.993369i	$-0.463324\pi$
$619$	677.956	−	492.564i	1.09524	−	0.795742i	0.980277	+	0.197628i	$0.0633237\pi$
$620$	149.626	−	205.942i	0.241332	−	0.332165i
$621$	−816.536	−	197.335i	−1.31487	−	0.317769i
$622$	−20.8122	−	64.0535i	−0.0334602	−	0.102980i
$623$	−273.704	+	376.721i	−0.439331	+	0.604688i
$624$	−1054.23	−	725.330i	−1.68947	−	1.16239i
$625$	27.5025	−	84.6440i	0.0440040	−	0.135430i
$626$			1053.01i			1.68212i
$627$		0			0
$628$	−258.000			−0.410828
$629$	−201.301	−	65.4066i	−0.320033	−	0.103985i
$630$	−130.934	+	486.695i	−0.207831	+	0.772532i
$631$	−205.490	−	149.297i	−0.325658	−	0.236605i	0.412928	−	0.910764i	$-0.364506\pi$
$631$	−205.490	−	149.297i	−0.325658	−	0.236605i	−0.738586	+	0.674159i	$0.764506\pi$
$632$	−56.4899	+	18.3547i	−0.0893827	+	0.0290422i
$633$	−926.515	+	710.201i	−1.46369	+	1.12196i
$634$	889.957	+	646.592i	1.40372	+	1.01986i
$635$	111.970	+	154.113i	0.176330	+	0.242698i
$636$	9.80361	+	381.712i	0.0154145	+	0.600176i
$637$	157.150			0.246703
$638$		0			0
$639$	368.000	+	455.377i	0.575900	+	0.712640i
$640$	−71.6866	+	220.629i	−0.112010	+	0.344732i
$641$	−69.8253	−	96.1063i	−0.108932	−	0.149932i	0.751070	−	0.660222i	$-0.229538\pi$
$641$	−69.8253	−	96.1063i	−0.108932	−	0.149932i	−0.860002	+	0.510290i	$0.829538\pi$
$642$	95.5910	−	322.115i	0.148896	−	0.501737i
$643$	−135.349	−	416.563i	−0.210497	−	0.647843i	−0.999443	−	0.0333799i	$-0.989373\pi$
$643$	−135.349	−	416.563i	−0.210497	−	0.647843i	0.788946	−	0.614463i	$-0.210627\pi$
$644$	−664.292	+	215.842i	−1.03151	+	0.335158i
$645$	−121.748	−	36.1300i	−0.188757	−	0.0560155i
$646$	678.062	−	492.641i	1.04963	−	0.762602i
$647$	−314.729	−	102.262i	−0.486444	−	0.158055i	0.0555189	−	0.998458i	$-0.482319\pi$
$647$	−314.729	−	102.262i	−0.486444	−	0.158055i	−0.541963	+	0.840402i	$0.682319\pi$
$648$	209.533	+	44.9778i	0.323353	+	0.0694101i
$649$		0			0
$650$			1009.75i			1.55346i
$651$	673.276	−	17.2920i	1.03422	−	0.0265621i
$652$	−33.9787	+	24.6870i	−0.0521146	+	0.0378635i
$653$	−367.414	+	505.702i	−0.562656	+	0.774429i	−0.991661	−	0.128873i	$-0.958864\pi$
$653$	−367.414	+	505.702i	−0.562656	+	0.774429i	0.429005	+	0.903302i	$0.358864\pi$
$654$	325.214	+	424.268i	0.497269	+	0.648729i
$655$	203.497	+	626.301i	0.310683	+	0.956185i
$656$	−472.761	+	650.699i	−0.720672	+	0.991919i
$657$	174.968	−	650.374i	0.266313	−	0.989915i
$658$	−224.964	+	692.369i	−0.341891	+	1.05223i
$659$			465.652i			0.706604i	0.935509	+	0.353302i	$0.114941\pi$
$659$			465.652i			0.706604i	−0.935509	+	0.353302i	$0.885059\pi$
$660$		0			0
$661$	−394.000			−0.596067			−0.298033	−	0.954555i	$-0.596331\pi$
$661$	−394.000			−0.596067			−0.298033	+	0.954555i	$0.596331\pi$
$662$	447.894	+	145.530i	0.676577	+	0.219833i
$663$	−808.018	+	1174.41i	−1.21873	+	1.77136i
$664$	45.3050	+	32.9160i	0.0682303	+	0.0495723i
$665$	−301.279	+	97.8916i	−0.453052	+	0.147205i
$666$	−129.889	+	199.572i	−0.195028	+	0.299657i
$667$	532.763	+	387.075i	0.798746	+	0.580323i
$668$	−149.293	−	205.484i	−0.223492	−	0.307611i
$669$	137.955	−	3.54313i	0.206210	−	0.00529615i
$670$	−314.299			−0.469103
$671$		0			0
$672$	840.000	−	296.985i	1.25000	−	0.441942i
$673$	−272.872	+	839.813i	−0.405456	+	1.24786i	0.515059	+	0.857155i	$0.327770\pi$
$673$	−272.872	+	839.813i	−0.405456	+	1.24786i	−0.920514	+	0.390709i	$0.872230\pi$
$674$	395.677	+	544.602i	0.587058	+	0.808016i
$675$	−175.012	−	424.325i	−0.259278	−	0.628629i
$676$	−310.562	−	955.812i	−0.459411	−	1.41392i
$677$	865.593	−	281.248i	1.27857	−	0.415433i	0.410495	−	0.911863i	$-0.365356\pi$
$677$	865.593	−	281.248i	1.27857	−	0.415433i	0.868077	+	0.496430i	$0.165356\pi$
$678$	268.251	−	903.934i	0.395651	−	1.33324i
$679$	448.006	−	325.495i	0.659802	−	0.479374i
$680$	150.640	+	48.9458i	0.221529	+	0.0719791i
$681$	−598.665	+	211.660i	−0.879097	+	0.310808i
$682$		0			0
$683$		−	435.578i		−	0.637742i	−0.947798	−	0.318871i	$-0.896696\pi$
$683$		−	435.578i		−	0.637742i	0.947798	−	0.318871i	$-0.103304\pi$
$684$	−144.437	−	377.404i	−0.211165	−	0.551761i
$685$	362.440	−	263.328i	0.529109	−	0.384420i
$686$	488.777	−	672.744i	0.712503	−	0.980677i
$687$	280.955	−	215.360i	0.408960	−	0.313480i
$688$	87.8739	+	270.448i	0.127724	+	0.393093i
$689$	559.848	−	770.565i	0.812552	−	1.11838i
$690$	−395.912	+	575.436i	−0.573785	+	0.833965i
$691$	131.641	−	405.150i	0.190508	−	0.586324i	−0.809491	−	0.587132i	$-0.800257\pi$
$691$	131.641	−	405.150i	0.190508	−	0.586324i	1.00000		0.000807501i	$0.000257036\pi$
$692$			571.482i			0.825841i
$693$		0			0
$694$	−1288.00			−1.85591
$695$	241.561	+	78.4879i	0.347570	+	0.112932i
$696$	−138.405	−	95.2258i	−0.198858	−	0.136819i
$697$	724.879	+	526.656i	1.04000	+	0.755603i
$698$	169.470	−	55.0640i	0.242793	−	0.0788883i
$699$	−154.519	−	201.583i	−0.221058	−	0.288388i
$700$	−308.761	−	224.328i	−0.441087	−	0.320468i
$701$	−161.734	−	222.608i	−0.230719	−	0.317557i	0.677924	−	0.735132i	$-0.262880\pi$
$701$	−161.734	−	222.608i	−0.230719	−	0.317557i	−0.908642	+	0.417575i	$0.862880\pi$
$702$	1039.69	+	1221.04i	1.48104	+	1.73938i
$703$	−149.666			−0.212897
$704$		0			0
$705$	104.000	+	294.156i	0.147518	+	0.417243i
$706$	101.749	−	313.150i	0.144120	−	0.443556i
$707$	651.703	+	896.992i	0.921786	+	1.26873i
$708$	−292.847	−	86.9053i	−0.413626	−	0.122748i
$709$	−12.9787	−	39.9444i	−0.0183057	−	0.0563390i	0.941486	−	0.337051i	$-0.109429\pi$
$709$	−12.9787	−	39.9444i	−0.0183057	−	0.0563390i	−0.959792	+	0.280712i	$0.909429\pi$
$710$	462.992	−	150.435i	0.652101	−	0.211880i
$711$	201.783	−	10.3717i	0.283802	−	0.0145876i
$712$	133.191	−	96.7688i	0.187066	−	0.135911i
$713$	887.698	+	288.431i	1.24502	+	0.404531i
$714$	−419.066	−	1185.30i	−0.586927	−	1.66008i
$715$		0			0
$716$			950.352i			1.32731i
$717$	−3.26060	−	126.954i	−0.00454756	−	0.177063i
$718$	543.659	−	394.992i	0.757186	−	0.550128i
$719$	254.364	−	350.102i	0.353774	−	0.486928i	−0.594627	−	0.804002i	$-0.702700\pi$
$719$	254.364	−	350.102i	0.353774	−	0.486928i	0.948401	+	0.317073i	$0.102700\pi$
$720$	263.828	−	405.367i	0.366428	−	0.563010i
$721$	−78.6240	−	241.980i	−0.109049	−	0.335617i
$722$	−213.053	+	293.243i	−0.295088	+	0.406153i
$723$	369.904	+	254.502i	0.511624	+	0.352008i
$724$	242.887	−	747.530i	0.335480	−	1.03250i
$725$			359.822i			0.496306i
$726$		0			0
$727$	1102.00			1.51582			0.757909	−	0.652360i	$-0.226221\pi$
$727$	1102.00			1.51582			0.757909	+	0.652360i	$0.226221\pi$
$728$	−422.732	−	137.354i	−0.580675	−	0.188673i
$729$	−648.543	−	332.915i	−0.889634	−	0.456674i
$730$	−453.050	−	329.160i	−0.620616	−	0.450904i
$731$	301.279	−	97.8916i	0.412147	−	0.133915i
$732$	694.886	−	532.651i	0.949298	−	0.727665i
$733$	−393.518	−	285.908i	−0.536860	−	0.390052i	0.286058	−	0.958212i	$-0.407655\pi$
$733$	−393.518	−	285.908i	−0.536860	−	0.390052i	−0.822918	+	0.568161i	$0.807655\pi$
$734$	220.829	+	303.945i	0.300857	+	0.414094i
$735$	1.52501	+	59.3774i	0.00207484	+	0.0807856i
$736$	1234.75			1.67765
$737$		0			0
$738$	784.000	−	633.568i	1.06233	−	0.858493i
$739$	−323.746	+	996.388i	−0.438087	+	1.34829i	0.451804	+	0.892117i	$0.350781\pi$
$739$	−323.746	+	996.388i	−0.438087	+	1.34829i	−0.889890	+	0.456175i	$0.849219\pi$
$740$	49.8752	+	68.6474i	0.0673990	+	0.0927667i
$741$	−286.773	+	966.346i	−0.387008	+	1.30411i
$742$	259.574	+	798.887i	0.349831	+	1.07667i
$743$	−241.561	+	78.4879i	−0.325116	+	0.105636i	−0.467027	−	0.884243i	$-0.654675\pi$
$743$	−241.561	+	78.4879i	−0.325116	+	0.105636i	0.141912	+	0.989879i	$0.454675\pi$
$744$	−228.278	−	67.7437i	−0.306825	−	0.0910534i
$745$	−48.4330	+	35.1887i	−0.0650108	+	0.0472331i
$746$	−1073.31	−	348.739i	−1.43875	−	0.467478i
$747$	−119.733	−	148.162i	−0.160285	−	0.198343i
$748$		0			0
$749$		−	316.784i		−	0.422942i
$750$	−942.587	+	24.2087i	−1.25678	+	0.0322783i
$751$	−283.156	+	205.725i	−0.377039	+	0.273935i	−0.760124	−	0.649779i	$-0.774862\pi$
$751$	−283.156	+	205.725i	−0.377039	+	0.273935i	0.383085	+	0.923713i	$0.374862\pi$
$752$	410.639	−	565.197i	0.546063	−	0.751591i
$753$	−92.9183	−	121.220i	−0.123398	−	0.160982i
$754$	−388.495	−	1195.67i	−0.515246	−	1.58576i
$755$	111.970	−	154.113i	0.148304	−	0.204123i
$756$	−604.351	+	46.6472i	−0.799406	+	0.0617027i
$757$	90.8510	−	279.611i	0.120015	−	0.369367i	−0.872945	−	0.487818i	$-0.837793\pi$
$757$	90.8510	−	279.611i	0.120015	−	0.369367i	0.992960	+	0.118451i	$0.0377930\pi$
$758$		−	926.013i		−	1.22165i
$759$		0			0
$760$	112.000			0.147368
$761$	−744.813	−	242.004i	−0.978729	−	0.318008i	−0.224394	−	0.974498i	$-0.572040\pi$
$761$	−744.813	−	242.004i	−0.978729	−	0.318008i	−0.754335	+	0.656490i	$0.772040\pi$
$762$	−303.007	+	440.403i	−0.397646	+	0.577957i
$763$	407.745	+	296.244i	0.534397	+	0.388262i
$764$	169.470	−	55.0640i	0.221819	−	0.0720733i
$765$	−451.580	−	293.905i	−0.590300	−	0.384189i
$766$	−1107.91	−	804.941i	−1.44635	−	1.05084i
$767$	447.878	+	616.452i	0.583935	+	0.803718i
$768$	−998.671	+	25.6491i	−1.30035	+	0.0333973i
$769$	−838.131			−1.08990			−0.544949	−	0.838469i	$-0.683451\pi$
$769$	−838.131			−1.08990			−0.544949	+	0.838469i	$0.683451\pi$
$770$		0			0
$771$	−272.000	+	96.1665i	−0.352789	+	0.124730i
$772$	−138.748	+	427.023i	−0.179726	+	0.553139i
$773$	241.064	+	331.796i	0.311855	+	0.429231i	0.935959	−	0.352110i	$-0.114536\pi$
$773$	241.064	+	331.796i	0.311855	+	0.429231i	−0.624104	+	0.781341i	$0.714536\pi$
$774$	−18.2940	−	355.912i	−0.0236357	−	0.459835i
$775$	157.599	+	485.039i	0.203353	+	0.625857i
$776$	−186.203	+	60.5011i	−0.239953	+	0.0779653i
$777$	−63.8694	+	215.222i	−0.0822000	+	0.276992i
$778$	−938.390	+	681.780i	−1.20616	+	0.876324i
$779$	602.559	+	195.783i	0.773503	+	0.251326i
$780$	538.799	−	190.494i	0.690768	−	0.244223i
$781$		0			0
$782$		−	1742.31i		−	2.22802i
$783$	370.493	+	435.117i	0.473171	+	0.555705i
$784$	107.599	−	78.1754i	0.137244	−	0.0997136i
$785$	−142.976	+	196.789i	−0.182135	+	0.250687i
$786$	−1466.68	+	1124.25i	−1.86601	+	1.43035i
$787$	97.1238	+	298.916i	0.123410	+	0.379817i	0.993608	−	0.112885i	$-0.0360091\pi$
$787$	97.1238	+	298.916i	0.123410	+	0.379817i	−0.870198	+	0.492702i	$0.836009\pi$
$788$	−410.555	+	565.081i	−0.521009	+	0.717108i
$789$	791.823	−	1150.87i	1.00358	−	1.45865i
$790$	51.9149	−	159.777i	0.0657150	−	0.202250i
$791$		−	888.972i		−	1.12386i
$792$		0			0
$793$	−2184.00			−2.75410
$794$	1112.19	+	361.371i	1.40074	+	0.455128i
$795$	296.583	+	204.055i	0.373060	+	0.256673i
$796$	538.805	+	391.465i	0.676891	+	0.491790i
$797$	−234.029	+	76.0408i	−0.293638	+	0.0954088i	−0.452132	−	0.891951i	$-0.649336\pi$
$797$	−234.029	+	76.0408i	−0.293638	+	0.0954088i	0.158494	+	0.987360i	$0.449336\pi$
$798$	−540.818	−	705.541i	−0.677717	−	0.884137i
$799$	−629.629	−	457.453i	−0.788022	−	0.572531i
$800$	396.559	+	545.817i	0.495699	+	0.682271i
$801$	−523.033	+	200.171i	−0.652975	+	0.249901i
$802$	−1391.90			−1.73553
$803$		0			0
$804$	−126.000	−	356.382i	−0.156716	−	0.443261i
$805$	−203.497	+	626.301i	−0.252792	+	0.778013i
$806$	−1047.38	−	1441.59i	−1.29948	−	1.78858i
$807$	−1065.64	−	316.239i	−1.32049	−	0.391870i
$808$	−121.135	−	372.814i	−0.149919	−	0.461404i
$809$	−241.561	+	78.4879i	−0.298592	+	0.0970184i	−0.454482	−	0.890756i	$-0.650176\pi$
$809$	−241.561	+	78.4879i	−0.298592	+	0.0970184i	0.155890	+	0.987774i	$0.450176\pi$
$810$	−451.270	+	404.687i	−0.557124	+	0.499613i
$811$	787.037	−	571.816i	0.970452	−	0.705075i	0.0148976	−	0.999889i	$-0.495258\pi$
$811$	787.037	−	571.816i	0.970452	−	0.705075i	0.955555	+	0.294814i	$0.0952578\pi$
$812$	451.919	+	146.837i	0.556550	+	0.180834i
$813$	336.749	+	952.470i	0.414206	+	1.17155i
$814$		0			0
$815$			39.5980i			0.0485865i
$816$	30.9757	+	1206.06i	0.0379604	+	1.47802i
$817$	181.220	−	131.664i	0.221811	−	0.161155i
$818$	−349.127	+	480.532i	−0.426805	+	0.587447i
$819$	1267.24	+	824.768i	1.54730	+	1.00704i
$820$	−110.999	−	341.619i	−0.135364	−	0.416608i
$821$	286.145	−	393.844i	0.348532	−	0.479713i	−0.598377	−	0.801215i	$-0.704188\pi$
$821$	286.145	−	393.844i	0.348532	−	0.479713i	0.946909	+	0.321502i	$0.104188\pi$
$822$	1035.73	+	712.604i	1.26001	+	0.866915i
$823$	321.996	−	991.001i	0.391246	−	1.20413i	−0.540600	−	0.841280i	$-0.681803\pi$
$823$	321.996	−	991.001i	0.391246	−	1.20413i	0.931847	−	0.362853i	$-0.118197\pi$
$824$			89.9555i			0.109169i
$825$		0			0
$826$	−672.000			−0.813559
$827$	−1187.67	−	385.899i	−1.43612	−	0.466625i	−0.515437	−	0.856927i	$-0.672370\pi$
$827$	−1187.67	−	385.899i	−1.43612	−	0.466625i	−0.920687	+	0.390303i	$0.872370\pi$
$828$	−811.200	−	218.234i	−0.979710	−	0.263568i
$829$	−953.022	−	692.411i	−1.14960	−	0.835236i	−0.161176	−	0.986926i	$-0.551529\pi$
$829$	−953.022	−	692.411i	−1.14960	−	0.835236i	−0.988428	+	0.151689i	$0.951529\pi$
$830$	−150.640	+	48.9458i	−0.181494	+	0.0589708i
$831$	53.4528	−	40.9731i	0.0643235	−	0.0493058i
$832$	−526.709	−	382.677i	−0.633064	−	0.459948i
$833$	−87.0875	−	119.866i	−0.104547	−	0.143896i
$834$	18.3001	+	712.529i	0.0219425	+	0.854351i
$835$	−239.466			−0.286786
$836$		0			0
$837$	690.000	+	424.264i	0.824373	+	0.506887i
$838$	559.618	−	1722.33i	0.667802	−	2.05528i
$839$	−600.165	−	826.057i	−0.715334	−	0.984573i	−0.999666	−	0.0258470i	$-0.991772\pi$
$839$	−600.165	−	826.057i	−0.715334	−	0.984573i	0.284332	−	0.958726i	$-0.408228\pi$
$840$	47.7955	−	161.058i	0.0568994	−	0.191735i
$841$	121.444	+	373.765i	0.144404	+	0.444430i
$842$	669.325	−	217.477i	0.794923	−	0.258286i
$843$	−60.8741	−	18.0650i	−0.0722113	−	0.0214294i
$844$	−944.444	+	686.179i	−1.11901	+	0.813008i
$845$	−901.148	−	292.801i	−1.06645	−	0.346510i
$846$	−680.982	+	550.316i	−0.804943	+	0.650492i
$847$		0			0
$848$		−	806.102i		−	0.950592i
$849$	−538.621	+	13.8336i	−0.634418	+	0.0162939i
$850$	770.184	−	559.572i	0.906099	−	0.658319i
$851$	−182.876	+	251.707i	−0.214895	+	0.295778i
$852$	356.187	+	464.675i	0.418060	+	0.545393i
$853$	−182.685	−	562.247i	−0.214168	−	0.659141i	−0.999212	−	0.0397007i	$-0.987360\pi$
$853$	−182.685	−	562.247i	−0.214168	−	0.659141i	0.785044	−	0.619440i	$-0.212640\pi$
$854$	1132.14	−	1558.25i	1.32569	−	1.82465i
$855$	−367.907	−	98.9766i	−0.430301	−	0.115762i
$856$	−34.6099	+	106.518i	−0.0404321	+	0.124437i
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	706.000			0.821886			0.410943	−	0.911661i	$-0.365200\pi$
$859$	706.000			0.821886			0.410943	+	0.911661i	$0.365200\pi$
$860$	−120.780	−	39.2439i	−0.140442	−	0.0456325i
$861$	538.678	−	782.939i	0.625643	−	0.909337i
$862$	−1177.93	−	855.815i	−1.36651	−	0.992825i
$863$	−470.749	+	152.956i	−0.545480	+	0.177237i	−0.568777	−	0.822491i	$-0.692583\pi$
$863$	−470.749	+	152.956i	−0.545480	+	0.177237i	0.0232978	+	0.999729i	$0.492583\pi$
$864$	1041.54	+	251.713i	1.20549	+	0.291335i
$865$	435.897	+	316.698i	0.503927	+	0.366125i
$866$	−1147.69	−	1579.66i	−1.32528	−	1.82409i
$867$	476.843	−	12.2469i	0.549992	−	0.0141256i
$868$	673.498			0.775920
$869$		0			0
$870$	448.000	−	158.392i	0.514943	−	0.182060i
$871$	−291.371	+	896.749i	−0.334525	+	1.02956i
$872$	−104.738	−	144.159i	−0.120112	−	0.165320i
$873$	665.122	−	34.1876i	0.761881	−	0.0391610i
$874$	−380.709	−	1171.70i	−0.435594	−	1.34062i
$875$	−845.463	+	274.708i	−0.966243	+	0.313952i
$876$	191.608	−	645.667i	0.218731	−	0.737063i
$877$	−78.7037	+	57.1816i	−0.0897419	+	0.0652013i	−0.631751	−	0.775171i	$-0.717664\pi$
$877$	−78.7037	+	57.1816i	−0.0897419	+	0.0652013i	0.542010	+	0.840372i	$0.317664\pi$
$878$	−1073.31	−	348.739i	−1.22245	−	0.397197i
$879$	59.8665	−	21.1660i	0.0681075	−	0.0240796i
$880$		0			0
$881$			1493.41i			1.69513i	0.530692	+	0.847565i	$0.321932\pi$
$881$			1493.41i			1.69513i	−0.530692	+	0.847565i	$0.678068\pi$
$882$	−155.671	+	59.5773i	−0.176498	+	0.0675479i
$883$	−69.5755	+	50.5495i	−0.0787944	+	0.0572475i	−0.626485	−	0.779433i	$-0.715507\pi$
$883$	−69.5755	+	50.5495i	−0.0787944	+	0.0572475i	0.547691	+	0.836681i	$0.315507\pi$
$884$	−837.904	+	1153.28i	−0.947855	+	1.30461i
$885$	−228.574	+	175.209i	−0.258275	+	0.197976i
$886$	−97.1238	−	298.916i	−0.109621	−	0.337377i
$887$	149.293	−	205.484i	0.168312	−	0.231662i	−0.716526	−	0.697560i	$-0.754269\pi$
$887$	149.293	−	205.484i	0.168312	−	0.231662i	0.884838	+	0.465899i	$0.154269\pi$
$888$	44.9900	−	65.3904i	0.0506644	−	0.0736378i
$889$	−155.745	+	479.332i	−0.175191	+	0.539182i
$890$			465.652i			0.523205i
$891$		0			0
$892$	138.000			0.154709
$893$	−523.382	−	170.057i	−0.586094	−	0.190433i
$894$	−138.405	−	95.2258i	−0.154816	−	0.106517i
$895$	724.879	+	526.656i	0.809921	+	0.588442i
$896$	−583.729	+	189.665i	−0.651483	+	0.211680i
$897$	1274.78	+	1663.06i	1.42116	+	1.85403i
$898$	1089.74	+	791.745i	1.21352	+	0.881676i
$899$	−373.232	−	513.710i	−0.415164	−	0.571424i
$900$	−164.060	−	428.678i	−0.182289	−	0.476309i
$901$	−897.998			−0.996668
$902$		0			0
$903$	−112.000	−	316.784i	−0.124031	−	0.350813i
$904$	−97.1238	+	298.916i	−0.107438	+	0.330660i
$905$	−435.577	−	599.520i	−0.481301	−	0.662453i
$906$	512.483	+	152.084i	0.565654	+	0.167863i
$907$	−298.510	−	918.721i	−0.329118	−	1.01292i	−0.969547	−	0.244905i	$-0.921243\pi$
$907$	−298.510	−	918.721i	−0.329118	−	1.01292i	0.640429	−	0.768018i	$-0.278757\pi$
$908$	−603.902	+	196.220i	−0.665090	+	0.216101i
$909$	68.4501	+	1331.70i	0.0753026	+	1.46502i
$910$	1017.09	−	738.962i	1.11769	−	0.812046i
$911$	−1379.97	−	448.378i	−1.51478	−	0.492183i	−0.570494	−	0.821302i	$-0.693248\pi$
$911$	−1379.97	−	448.378i	−1.51478	−	0.492183i	−0.944288	+	0.329119i	$0.893248\pi$
$912$	284.366	+	804.308i	0.311805	+	0.881917i
$913$		0			0
$914$		−	1781.91i		−	1.94957i
$915$	−21.1939	−	825.202i	−0.0231627	−	0.901860i
$916$	286.392	−	208.076i	0.312655	−	0.227157i
$917$	−1024.10	+	1409.56i	−1.11680	+	1.53714i
$918$	355.184	−	1469.69i	0.386911	−	1.60097i
$919$	122.561	+	377.204i	0.133363	+	0.410450i	0.995332	−	0.0965115i	$-0.0307685\pi$
$919$	122.561	+	377.204i	0.133363	+	0.410450i	−0.861968	+	0.506962i	$0.830768\pi$
$920$	136.852	−	188.360i	0.148752	−	0.204739i
$921$	369.904	+	254.502i	0.401633	+	0.276332i
$922$	571.063	−	1757.55i	0.619375	−	1.90624i
$923$		−	1460.45i		−	1.58229i
$924$		0			0
$925$	−170.000			−0.183784
$926$	2219.34	+	721.107i	2.39670	+	0.778734i
$927$	79.4955	−	295.494i	0.0857557	−	0.318763i
$928$	−679.574	−	493.740i	−0.732300	−	0.532047i
$929$	1452.60	−	471.977i	1.56361	−	0.508049i	0.605843	−	0.795584i	$-0.292836\pi$
$929$	1452.60	−	471.977i	1.56361	−	0.508049i	0.957770	+	0.287535i	$0.0928358\pi$
$930$	534.528	−	409.731i	0.574761	−	0.440571i
$931$	−84.7578	−	61.5801i	−0.0910395	−	0.0661441i
$932$	−149.293	−	205.484i	−0.160185	−	0.220476i
$933$	−1.96072	−	76.3424i	−0.00210153	−	0.0818246i
$934$	1406.86			1.50628
$935$		0			0
$936$	−336.000	−	415.779i	−0.358974	−	0.444208i
$937$	388.495	−	1195.67i	0.414616	−	1.27606i	−0.497978	−	0.867190i	$-0.665924\pi$
$937$	388.495	−	1195.67i	0.414616	−	1.27606i	0.912594	−	0.408867i	$-0.134076\pi$
$938$	−488.777	−	672.744i	−0.521085	−	0.717211i
$939$	−339.689	+	1144.66i	−0.361756	+	1.21902i
$940$	96.4133	+	296.730i	0.102567	+	0.315670i
$941$	−462.992	+	150.435i	−0.492021	+	0.159867i	−0.544510	−	0.838754i	$-0.683284\pi$
$941$	−462.992	+	150.435i	−0.492021	+	0.159867i	0.0524893	+	0.998621i	$0.483284\pi$
$942$	−654.397	−	194.199i	−0.694689	−	0.206156i
$943$	1065.53	−	774.150i	1.12993	−	0.820944i
$944$	613.319	+	199.279i	0.649702	+	0.211101i
$945$	−299.333	+	486.818i	−0.316754	+	0.515152i
$946$		0			0
$947$			435.578i			0.459955i	0.973196	+	0.229978i	$0.0738653\pi$
$947$			435.578i			0.459955i	−0.973196	+	0.229978i	$0.926135\pi$
$948$	201.983	−	5.18759i	0.213062	−	0.00547214i
$949$	−1359.15	+	987.479i	−1.43219	+	1.04055i
$950$	395.677	−	544.602i	0.416502	−	0.573266i
$951$	758.833	+	989.960i	0.797932	+	1.04097i
$952$	129.498	+	398.555i	0.136028	+	0.418650i
$953$	−945.521	+	1301.40i	−0.992152	+	1.36558i	−0.0621339	+	0.998068i	$0.519791\pi$
$953$	−945.521	+	1301.40i	−0.992152	+	1.36558i	−0.930018	+	0.367513i	$0.880209\pi$
$954$	−262.451	+	975.561i	−0.275106	+	1.02260i
$955$	51.9149	−	159.777i	0.0543611	−	0.167306i
$956$		−	126.996i		−	0.132841i
$957$		0			0
$958$	1792.00			1.87056
$959$	1127.28	+	366.277i	1.17548	+	0.381936i
$960$	139.479	−	202.725i	0.145291	−	0.211172i
$961$	49.3500	+	35.8549i	0.0513528	+	0.0373100i
$962$	564.899	−	183.547i	0.587213	−	0.190797i
$963$	207.822	−	319.315i	0.215807	−	0.331584i
$964$	363.248	+	263.915i	0.376813	+	0.273771i
$965$	248.821	+	342.473i	0.257846	+	0.354895i
$966$	−1847.39	+	47.4471i	−1.91241	+	0.0491171i
$967$	1055.15			1.09116			0.545578	−	0.838060i	$-0.316310\pi$
$967$	1055.15			1.09116			0.545578	+	0.838060i	$0.316310\pi$
$968$		0			0
$969$	896.000	−	316.784i	0.924665	−	0.326918i
$970$	171.123	−	526.662i	0.176415	−	0.542951i
$971$	149.626	+	205.942i	0.154094	+	0.212093i	0.879084	−	0.476667i	$-0.158155\pi$
$971$	149.626	+	205.942i	0.154094	+	0.212093i	−0.724989	+	0.688760i	$0.758155\pi$
$972$	−639.782	−	349.457i	−0.658212	−	0.359523i
$973$	207.659	+	639.110i	0.213422	+	0.656845i
$974$	−880.691	+	286.154i	−0.904200	+	0.293792i
$975$	−325.734	+	1097.63i	−0.334086	+	1.12578i
$976$	−1495.37	+	1086.45i	−1.53214	+	1.11317i
$977$	1371.90	+	445.756i	1.40419	+	0.456250i	0.910544	−	0.413411i	$-0.135663\pi$
$977$	1371.90	+	445.756i	1.40419	+	0.456250i	0.493649	+	0.869661i	$0.335663\pi$
$978$	−104.766	+	37.0405i	−0.107123	+	0.0378737i
$979$		0			0
$980$			59.3970i			0.0606092i
$981$	216.656	+	566.106i	0.220852	+	0.577071i
$982$	543.659	−	394.992i	0.553625	−	0.402232i
$983$	−403.989	+	556.044i	−0.410976	+	0.565660i	−0.963456	−	0.267866i	$-0.913682\pi$
$983$	−403.989	+	556.044i	−0.410976	+	0.565660i	0.552480	+	0.833526i	$0.313682\pi$
$984$	−266.669	+	204.410i	−0.271006	+	0.207734i
$985$	203.497	+	626.301i	0.206596	+	0.635838i
$986$	−696.700	+	958.925i	−0.706592	+	0.972541i
$987$	−467.896	+	680.060i	−0.474058	+	0.689017i
$988$	−311.489	+	958.665i	−0.315272	+	0.970309i
$989$		−	465.652i		−	0.470831i
$990$		0			0
$991$	574.000			0.579213			0.289606	−	0.957146i	$-0.406476\pi$
$991$	574.000			0.579213			0.289606	+	0.957146i	$0.406476\pi$
$992$	−1132.32	−	367.912i	−1.14145	−	0.370879i
$993$	439.931	+	302.682i	0.443033	+	0.304816i
$994$	1042.01	+	757.067i	1.04830	+	0.761637i
$995$	597.179	−	194.035i	0.600180	−	0.195010i
$996$	−115.890	−	151.187i	−0.116355	−	0.151795i
$997$	1071.58	+	778.549i	1.07481	+	0.780892i	0.976770	−	0.214291i	$-0.0687442\pi$
$997$	1071.58	+	778.549i	1.07481	+	0.780892i	0.0980354	+	0.995183i	$0.468744\pi$
$998$	152.403	+	209.765i	0.152709	+	0.210185i
$999$	−205.574	+	175.041i	−0.205779	+	0.175217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.k.251.4		16
3.2	odd	2	inner	363.3.h.k.251.1		16
11.2	odd	10	inner	363.3.h.k.245.4		16
11.3	even	5	inner	363.3.h.k.323.3		16
11.4	even	5		363.3.b.i.122.3	yes	4
11.5	even	5	inner	363.3.h.k.269.1		16
11.6	odd	10	inner	363.3.h.k.269.3		16
11.7	odd	10		363.3.b.i.122.1	✓	4
11.8	odd	10	inner	363.3.h.k.323.1		16
11.9	even	5	inner	363.3.h.k.245.2		16
11.10	odd	2	inner	363.3.h.k.251.2		16
33.2	even	10	inner	363.3.h.k.245.1		16
33.5	odd	10	inner	363.3.h.k.269.4		16
33.8	even	10	inner	363.3.h.k.323.4		16
33.14	odd	10	inner	363.3.h.k.323.2		16
33.17	even	10	inner	363.3.h.k.269.2		16
33.20	odd	10	inner	363.3.h.k.245.3		16
33.26	odd	10		363.3.b.i.122.2	yes	4
33.29	even	10		363.3.b.i.122.4	yes	4
33.32	even	2	inner	363.3.h.k.251.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.i.122.1	✓	4	11.7	odd	10
363.3.b.i.122.2	yes	4	33.26	odd	10
363.3.b.i.122.3	yes	4	11.4	even	5
363.3.b.i.122.4	yes	4	33.29	even	10
363.3.h.k.245.1		16	33.2	even	10	inner
363.3.h.k.245.2		16	11.9	even	5	inner
363.3.h.k.245.3		16	33.20	odd	10	inner
363.3.h.k.245.4		16	11.2	odd	10	inner
363.3.h.k.251.1		16	3.2	odd	2	inner
363.3.h.k.251.2		16	11.10	odd	2	inner
363.3.h.k.251.3		16	33.32	even	2	inner
363.3.h.k.251.4		16	1.1	even	1	trivial
363.3.h.k.269.1		16	11.5	even	5	inner
363.3.h.k.269.2		16	33.17	even	10	inner
363.3.h.k.269.3		16	11.6	odd	10	inner
363.3.h.k.269.4		16	33.5	odd	10	inner
363.3.h.k.323.1		16	11.8	odd	10	inner
363.3.h.k.323.2		16	33.14	odd	10	inner
363.3.h.k.323.3		16	11.3	even	5	inner
363.3.h.k.323.4		16	33.8	even	10	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.51626 + 0.817582i) q^{2} +(2.47152 + 1.70046i) q^{3} +(2.42705 + 1.76336i) q^{4} +(2.68999 - 0.874032i) q^{5} +(4.82873 + 6.29947i) q^{6} +(6.05413 + 4.39858i) q^{7} +(-1.55513 - 2.14046i) q^{8} +(3.21687 + 8.40546i) q^{9} +7.48331 q^{10} +(3.00000 + 8.48528i) q^{12} +(6.93741 - 21.3512i) q^{13} +(11.6376 + 16.0177i) q^{14} +(8.13464 + 2.41404i) q^{15} +(-5.87132 - 18.0701i) q^{16} +(-20.1301 + 6.54066i) q^{17} +(1.22232 + 23.7804i) q^{18} +(-12.1083 + 8.79716i) q^{19} +(8.06998 + 2.62210i) q^{20} +(7.48331 + 21.1660i) q^{21} +31.1127i q^{23} +(-0.203788 - 7.93464i) q^{24} +(-13.7533 + 9.99235i) q^{25} +(34.9127 - 48.0532i) q^{26} +(-6.34258 + 26.2445i) q^{27} +(6.93741 + 21.3512i) q^{28} +(12.4411 - 17.1237i) q^{29} +(18.4952 + 12.7251i) q^{30} +(9.27051 - 28.5317i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(20.1301 + 6.54066i) q^{35} +(-7.01431 + 26.0730i) q^{36} +(8.09017 + 5.87785i) q^{37} +(-37.6599 + 12.2364i) q^{38} +(53.4528 - 40.9731i) q^{39} +(-6.05413 - 4.39858i) q^{40} +(-24.8821 - 34.2473i) q^{41} +(1.52501 + 59.3774i) q^{42} -14.9666 q^{43} +(16.0000 + 19.7990i) q^{45} +(-25.4372 + 78.2876i) q^{46} +(21.6126 + 29.7472i) q^{47} +(16.2163 - 54.6446i) q^{48} +(2.16312 + 6.65740i) q^{49} +(-42.7764 + 13.8989i) q^{50} +(-60.8741 - 18.0650i) q^{51} +(54.4872 - 39.5872i) q^{52} +(40.3499 + 13.1105i) q^{53} +(-37.4166 + 60.8523i) q^{54} -19.7990i q^{56} +(-44.8851 + 1.15280i) q^{57} +(45.3050 - 32.9160i) q^{58} +(-19.9501 + 27.4589i) q^{59} +(15.4864 + 20.2033i) q^{60} +(-30.0621 - 92.5217i) q^{61} +(46.6540 - 64.2137i) q^{62} +(-17.4968 + 65.0374i) q^{63} +(8.96149 - 27.5806i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(-60.3902 - 19.6220i) q^{68} +(-52.9059 + 76.8958i) q^{69} +(45.3050 + 32.9160i) q^{70} +(61.8699 - 20.1027i) q^{71} +(12.9889 - 19.9572i) q^{72} +(-60.5413 - 43.9858i) q^{73} +(15.5513 + 21.4046i) q^{74} +(-50.9832 + 1.30942i) q^{75} -44.8999 q^{76} +(168.000 - 59.3970i) q^{78} +(6.93741 - 21.3512i) q^{79} +(-31.5876 - 43.4767i) q^{80} +(-60.3035 + 54.0785i) q^{81} +(-34.6099 - 106.518i) q^{82} +(-20.1301 + 6.54066i) q^{83} +(-19.1608 + 64.5667i) q^{84} +(-48.4330 + 35.1887i) q^{85} +(-37.6599 - 12.2364i) q^{86} +(59.8665 - 21.1660i) q^{87} +62.2254i q^{89} +(24.0728 + 62.9007i) q^{90} +(135.915 - 98.7479i) q^{91} +(-54.8628 + 75.5121i) q^{92} +(71.4293 - 54.7527i) q^{93} +(30.0621 + 92.5217i) q^{94} +(-24.8821 + 34.2473i) q^{95} +(67.4849 - 98.0856i) q^{96} +(22.8673 - 70.3782i) q^{97} +18.5203i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 12 q^{4} + 28 q^{9} + 48 q^{12} + 32 q^{15} + 76 q^{16} - 68 q^{25} - 92 q^{27} - 120 q^{31} - 896 q^{34} - 84 q^{36} + 40 q^{37} + 224 q^{42} + 256 q^{45} - 76 q^{48} - 28 q^{49} + 224 q^{58}+ \cdots - 296 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 + 12 * q^4 + 28 * q^9 + 48 * q^12 + 32 * q^15 + 76 * q^16 - 68 * q^25 - 92 * q^27 - 120 * q^31 - 896 * q^34 - 84 * q^36 + 40 * q^37 + 224 * q^42 + 256 * q^45 - 76 * q^48 - 28 * q^49 + 224 * q^58 - 96 * q^60 - 116 * q^64 - 672 * q^67 - 352 * q^69 + 224 * q^70 + 68 * q^75 + 2688 * q^78 - 68 * q^81 + 448 * q^82 + 672 * q^91 + 120 * q^93 - 296 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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