LMFDB - Embedded newform 363.3.h.k.269.2

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			269.2
Root			$2.44862 + 1.32134i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.k.251.2

$q$-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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−2.51626	+	0.817582i	−1.25813	+	0.408791i	−0.860828	−	0.508897i	$-0.830053\pi$
$2$	−2.51626	+	0.817582i	−1.25813	+	0.408791i	−0.397302	+	0.917688i	$0.630053\pi$
$3$	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	0.565398	−	0.824818i	$-0.308723\pi$
$5$	2.68999	+	0.874032i	0.537999	+	0.174806i	−0.0273993	+	0.999625i	$0.508723\pi$
$6$	−4.82873	+	6.29947i	−0.804788	+	1.04991i
$7$	−6.05413	+	4.39858i	−0.864876	+	0.628369i	−0.929207	−	0.369560i	$-0.879509\pi$
$7$	−6.05413	+	4.39858i	−0.864876	+	0.628369i	0.0643314	+	0.997929i	$0.479509\pi$
$8$	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	−0.746554	−	0.665325i	$-0.768293\pi$
$13$	−6.93741	−	21.3512i	−0.533647	−	1.64240i	0.212907	−	0.977073i	$-0.431707\pi$
$14$	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	$-0.186105\pi$
$17$	20.1301	+	6.54066i	1.18412	+	0.384745i	0.350225	+	0.936665i	$0.386105\pi$
$18$	−1.22232	+	23.7804i	−0.0679068	+	1.32113i
$19$	12.1083	+	8.79716i	0.637277	+	0.463009i	0.858914	−	0.512121i	$-0.171140\pi$
$19$	12.1083	+	8.79716i	0.637277	+	0.463009i	−0.221637	+	0.975129i	$0.571140\pi$
$20$	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	$-0.763555\pi$
$23$		−	31.1127i		−	1.35273i	0.736568	−	0.676363i	$-0.236445\pi$
$24$	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	$-0.318907\pi$
$29$	−12.4411	−	17.1237i	−0.429002	−	0.590471i	−0.967724	+	0.252013i	$0.918907\pi$
$30$	−18.4952	+	12.7251i	−0.616507	+	0.424169i
$31$	9.27051	+	28.5317i	0.299049	+	0.920377i	0.981831	+	0.189756i	$0.0607696\pi$
$31$	9.27051	+	28.5317i	0.299049	+	0.920377i	−0.682783	+	0.730622i	$0.739230\pi$
$32$		−	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	−0.473067	−	0.881026i	$-0.656853\pi$
$37$	8.09017	−	5.87785i	0.218653	−	0.158861i	0.691720	+	0.722166i	$0.256853\pi$
$38$	−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	$-0.627330\pi$
$41$	24.8821	−	34.2473i	0.606881	−	0.835301i	0.996316	+	0.0857534i	$0.0273297\pi$
$42$	1.52501	−	59.3774i	0.0363097	−	1.41375i
$43$	14.9666			0.348061			0.174031	−	0.984740i	$-0.444321\pi$
$43$	14.9666			0.348061			0.174031	+	0.984740i	$0.444321\pi$
$44$		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	−0.514634	−	0.857410i	$-0.672072\pi$
$47$	21.6126	−	29.7472i	0.459843	−	0.632919i	0.974476	+	0.224491i	$0.0720720\pi$
$48$	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	0.0974744	−	0.995238i	$-0.468924\pi$
$53$	40.3499	−	13.1105i	0.761319	−	0.247368i	0.663845	+	0.747870i	$0.268924\pi$
$54$	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	0.605759	−	0.795648i	$-0.292870\pi$
$59$	−19.9501	−	27.4589i	−0.338137	−	0.465406i	−0.943896	+	0.330242i	$0.892870\pi$
$60$	15.4864	−	20.2033i	0.258107	−	0.336721i
$61$	30.0621	−	92.5217i	0.492822	−	1.51675i	−0.327502	−	0.944850i	$-0.606207\pi$
$61$	30.0621	−	92.5217i	0.492822	−	1.51675i	0.820324	−	0.571899i	$-0.193793\pi$
$62$	−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	0.710385	−	0.703814i	$-0.248521\pi$
$71$	61.8699	+	20.1027i	0.871407	+	0.283137i	0.161022	+	0.986951i	$0.448521\pi$
$72$	−12.9889	−	19.9572i	−0.180401	−	0.277183i
$73$	60.5413	−	43.9858i	0.829333	−	0.602545i	−0.0900377	−	0.995938i	$-0.528699\pi$
$73$	60.5413	−	43.9858i	0.829333	−	0.602545i	0.919370	+	0.393393i	$0.128699\pi$
$74$	−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	$-0.145382\pi$
$79$	−6.93741	−	21.3512i	−0.0878154	−	0.270268i	−0.985315	+	0.170748i	$0.945382\pi$
$80$	−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	$-0.359303\pi$
$83$	20.1301	+	6.54066i	0.242531	+	0.0788031i	−0.185229	+	0.982695i	$0.559303\pi$
$84$	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	$-0.886324\pi$
$89$		−	62.2254i		−	0.699162i	0.936906	−	0.349581i	$-0.113676\pi$
$90$	−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	0.997022	+	0.0771212i	$0.0245728\pi$
$97$	22.8673	+	70.3782i	0.235745	+	0.725548i	−0.761277	+	0.648427i	$0.775427\pi$
$98$			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	$-0.862103\pi$
$101$	−140.911	+	45.7846i	−1.39515	+	0.453313i	−0.487533	+	0.873105i	$0.662103\pi$
$102$	−138.405	+	95.2258i	−1.35692	+	0.933586i
$103$	−27.5066	+	19.9847i	−0.267054	+	0.194026i	−0.713251	−	0.700909i	$-0.752778\pi$
$103$	−27.5066	+	19.9847i	−0.267054	+	0.194026i	0.446197	+	0.894935i	$0.352778\pi$
$104$	−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	$-0.736616\pi$
$107$	24.8821	−	34.2473i	0.232543	−	0.320068i	0.909302	+	0.416136i	$0.136616\pi$
$108$	−61.6721	−	52.5124i	−0.571038	−	0.486226i
$109$	−67.3498			−0.617888			−0.308944	−	0.951080i	$-0.599976\pi$
$109$	−67.3498			−0.617888			−0.308944	+	0.951080i	$0.599976\pi$
$110$		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	−0.997200	−	0.0747850i	$-0.976173\pi$
$113$	−69.8253	+	96.1063i	−0.617923	+	0.850498i	0.379276	+	0.925283i	$0.376173\pi$
$114$	−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	$-0.985424\pi$
$127$	−20.8122	+	64.0535i	−0.163876	+	0.504358i	0.835076	+	0.550135i	$0.185424\pi$
$128$	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	0.801933	−	0.597414i	$-0.203805\pi$
$137$	150.640	+	48.9458i	1.09956	+	0.357269i	0.297626	+	0.954682i	$0.403805\pi$
$138$	195.994	+	150.235i	1.42024	+	1.08866i
$139$	−72.6495	+	52.7830i	−0.522659	+	0.379734i	−0.817604	−	0.575780i	$-0.804698\pi$
$139$	−72.6495	+	52.7830i	−0.522659	+	0.379734i	0.294946	+	0.955514i	$0.404698\pi$
$140$	−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	$-0.377372\pi$
$149$	20.1301	+	6.54066i	0.135101	+	0.0438970i	−0.240686	+	0.970603i	$0.577372\pi$
$150$	129.357	−	38.3881i	0.862383	−	0.255921i
$151$	−54.4872	−	39.5872i	−0.360842	−	0.262167i	0.392561	−	0.919726i	$-0.371589\pi$
$151$	−54.4872	−	39.5872i	−0.360842	−	0.262167i	−0.753403	+	0.657559i	$0.771589\pi$
$152$	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	0.343732	−	0.939068i	$-0.388309\pi$
$157$	−69.5755	−	50.5495i	−0.443156	−	0.321972i	−0.786888	+	0.617096i	$0.788309\pi$
$158$	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	0.936908	−	0.349575i	$-0.113674\pi$
$163$	−4.32624	−	13.3148i	−0.0265413	−	0.0816858i	−0.963450	+	0.267889i	$0.913674\pi$
$164$		−	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	$-0.518423\pi$
$167$	80.5203	−	26.1626i	0.482157	−	0.156662i	0.540003	+	0.841663i	$0.318423\pi$
$168$	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	$-0.985586\pi$
$173$	−111.970	+	154.113i	−0.647223	+	0.890826i	0.351752	+	0.936093i	$0.385586\pi$
$174$	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	0.143245	−	0.989687i	$-0.454246\pi$
$179$	186.201	−	256.284i	1.04023	−	1.43175i	0.896983	−	0.442064i	$-0.145754\pi$
$180$	3.92015	−	76.2668i	0.0217786	−	0.423705i
$181$	−80.9625	+	249.177i	−0.447306	+	1.37667i	0.432628	+	0.901572i	$0.357586\pi$
$181$	−80.9625	+	249.177i	−0.447306	+	1.37667i	−0.879935	+	0.475095i	$0.842414\pi$
$182$	−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	0.890572	−	0.454843i	$-0.150305\pi$
$191$	34.9127	+	48.0532i	0.182789	+	0.251587i	−0.707783	+	0.706430i	$0.750305\pi$
$192$	69.0483	+	52.9276i	0.359627	+	0.275664i
$193$	−46.2494	+	142.341i	−0.239634	+	0.737519i	0.756838	+	0.653602i	$0.226743\pi$
$193$	−46.2494	+	142.341i	−0.239634	+	0.737519i	−0.996473	+	0.0839167i	$0.973257\pi$
$194$	−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	0.652929	+	0.757419i	$0.273540\pi$
$211$	120.249	+	370.087i	0.569898	+	1.75397i	−0.0830307	+	0.996547i	$0.526460\pi$
$212$	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	0.668092	−	0.744079i	$-0.267111\pi$
$223$	37.2148	+	27.0381i	0.166882	+	0.121247i	−0.501209	+	0.865326i	$0.667111\pi$
$224$	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	$-0.0456185\pi$
$227$	124.411	+	171.237i	0.548065	+	0.754346i	−0.441683	+	0.897171i	$0.645619\pi$
$228$	110.971	−	76.3505i	0.486716	−	0.334871i
$229$	36.4640	+	112.225i	0.159231	+	0.490064i	0.998565	−	0.0535527i	$-0.0170545\pi$
$229$	36.4640	+	112.225i	0.159231	+	0.490064i	−0.839334	+	0.543617i	$0.817055\pi$
$230$			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	$-0.541846\pi$
$233$	80.5203	−	26.1626i	0.345581	−	0.112286i	0.476664	+	0.879085i	$0.341846\pi$
$234$	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	$-0.771773\pi$
$239$	24.8821	−	34.2473i	0.104109	−	0.143294i	0.857893	+	0.513829i	$0.171773\pi$
$240$	−4.13930	+	161.167i	−0.0172471	+	0.671530i
$241$	−149.666			−0.621022			−0.310511	−	0.950570i	$-0.600500\pi$
$241$	−149.666			−0.621022			−0.310511	+	0.950570i	$0.600500\pi$
$242$		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	−0.403878	−	0.914813i	$-0.632338\pi$
$251$	−48.4199	+	15.7326i	−0.192908	+	0.0626796i	0.210970	+	0.977493i	$0.432338\pi$
$252$	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	0.684760	−	0.728769i	$-0.259907\pi$
$257$	−56.5253	−	77.8004i	−0.219943	−	0.302725i	−0.904703	+	0.426044i	$0.859907\pi$
$258$	−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	−0.430949	−	0.902376i	$-0.641821\pi$
$269$	−352.389	−	114.498i	−1.31000	−	0.425644i	−0.879048	+	0.476733i	$0.841821\pi$
$270$	47.4635	+	196.396i	0.175791	+	0.727391i
$271$	−272.436	+	197.936i	−1.00530	+	0.730392i	−0.963218	−	0.268722i	$-0.913399\pi$
$271$	−272.436	+	197.936i	−1.00530	+	0.730392i	−0.0420805	+	0.999114i	$0.513399\pi$
$272$	−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	$-0.112903\pi$
$277$	−6.93741	−	21.3512i	−0.0250448	−	0.0770800i	−0.962798	+	0.270223i	$0.912903\pi$
$278$	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	$-0.388009\pi$
$281$	20.1301	+	6.54066i	0.0716373	+	0.0232764i	−0.272979	+	0.962020i	$0.588009\pi$
$282$	83.0302	+	279.789i	0.294433	+	0.992160i
$283$	145.299	+	105.566i	0.513424	+	0.373025i	0.814121	−	0.580695i	$-0.197219\pi$
$283$	145.299	+	105.566i	0.513424	+	0.373025i	−0.300697	+	0.953720i	$0.597219\pi$
$284$	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	$-0.211500\pi$
$293$	−12.4411	−	17.1237i	−0.0424610	−	0.0584425i	−0.829720	+	0.558180i	$0.811500\pi$
$294$	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	$-0.578380\pi$
$307$	−149.666			−0.487512			−0.243756	+	0.969837i	$0.578380\pi$
$308$		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	−0.832395	−	0.554183i	$-0.813031\pi$
$311$	−14.9626	+	20.5942i	−0.0481112	+	0.0662193i	0.784284	+	0.620402i	$0.213031\pi$
$312$	−170.828	+	50.6948i	−0.547524	+	0.162483i
$313$	122.989	−	378.520i	0.392935	−	1.20933i	−0.537622	−	0.843186i	$-0.680677\pi$
$313$	122.989	−	378.520i	0.392935	−	1.20933i	0.930558	−	0.366145i	$-0.119323\pi$
$314$	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	0.390418	−	0.920638i	$-0.372330\pi$
$317$	395.429	−	128.483i	1.24741	−	0.405308i	0.856992	+	0.515329i	$0.172330\pi$
$318$	−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	$-0.823215\pi$
$337$	−205.840	+	149.552i	−0.610802	+	0.443774i	0.238894	+	0.971046i	$0.423215\pi$
$338$	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	$-0.152529\pi$
$347$	462.992	+	150.435i	1.33427	+	0.433531i	0.446898	+	0.894585i	$0.352529\pi$
$348$	−182.622	+	54.1950i	−0.524777	+	0.155733i
$349$	−54.4872	−	39.5872i	−0.156124	−	0.113430i	0.506981	−	0.861957i	$-0.330761\pi$
$349$	−54.4872	−	39.5872i	−0.156124	−	0.113430i	−0.663104	+	0.748527i	$0.730761\pi$
$350$	−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	$0.0564051\pi$
$353$			124.451i			0.352552i	−0.984341	+	0.176276i	$0.943595\pi$
$354$	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	$-0.315093\pi$
$359$	−149.293	−	205.484i	−0.415857	−	0.572379i	−0.964635	+	0.263590i	$0.915093\pi$
$360$	−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	−0.420168	−	0.907446i	$-0.638029\pi$
$367$	114.880	−	83.4655i	0.313026	−	0.227426i	0.733194	+	0.680020i	$0.238029\pi$
$368$	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	$-0.306253\pi$
$373$	426.549			1.14356			0.571781	+	0.820406i	$0.306253\pi$
$374$		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	0.700915	+	0.713245i	$0.252775\pi$
$379$	−108.156	+	332.870i	−0.285372	+	0.878284i	−0.986287	+	0.165040i	$0.947225\pi$
$380$	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	−0.870443	−	0.492269i	$-0.836168\pi$
$383$	−492.269	+	159.948i	−1.28530	+	0.417618i	−0.414854	+	0.909888i	$0.636168\pi$
$384$	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	0.337120	−	0.941462i	$-0.390547\pi$
$389$	−257.689	−	354.678i	−0.662439	−	0.911769i	−0.999559	+	0.0296928i	$0.990547\pi$
$390$	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	−0.390622	−	0.920551i	$-0.627740\pi$
$401$	−500.339	−	162.570i	−1.24773	−	0.405411i	−0.857106	+	0.515140i	$0.827740\pi$
$402$	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	$-0.0115045\pi$
$409$	69.3741	+	213.512i	0.169619	+	0.522033i	−0.829728	+	0.558168i	$0.811504\pi$
$410$	−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	$0.304255\pi$
$419$			684.479i			1.63360i	−0.576919	+	0.816801i	$0.695745\pi$
$420$	−4.89090	+	190.431i	−0.0116450	+	0.453408i
$421$	215.199	+	156.351i	0.511160	+	0.371380i	0.813264	−	0.581895i	$-0.197689\pi$
$421$	215.199	+	156.351i	0.511160	+	0.371380i	−0.302103	+	0.953275i	$0.597689\pi$
$422$	−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	$-0.379589\pi$
$431$	523.382	−	170.057i	1.21434	−	0.394564i	0.845019	+	0.534737i	$0.179589\pi$
$432$	511.479	+	39.4788i	1.18398	+	0.0913862i
$433$	−597.055	+	433.786i	−1.37888	+	1.00181i	−0.381895	+	0.924206i	$0.624728\pi$
$433$	−597.055	+	433.786i	−1.37888	+	1.00181i	−0.996984	+	0.0776084i	$0.975272\pi$
$434$	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	$-0.338521\pi$
$439$	426.549			0.971638			0.485819	+	0.874060i	$0.338521\pi$
$440$		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	−0.880522	−	0.474006i	$-0.842808\pi$
$443$	−69.8253	+	96.1063i	−0.157619	+	0.216944i	0.722902	+	0.690950i	$0.242808\pi$
$444$	−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	0.284643	−	0.958634i	$-0.408125\pi$
$449$	484.199	−	157.326i	1.07839	−	0.350391i	0.793751	+	0.608242i	$0.208125\pi$
$450$	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	−0.415243	−	0.909711i	$-0.636303\pi$
$457$	208.122	−	640.535i	0.455410	−	1.40161i	0.870653	−	0.491898i	$-0.163697\pi$
$458$	−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	0.795503	−	0.605950i	$-0.207207\pi$
$467$	505.719	+	164.318i	1.08291	+	0.351859i	0.287407	+	0.957809i	$0.407207\pi$
$468$	−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	$-0.649955\pi$
$479$	−644.162	−	209.301i	−1.34481	−	0.436954i	−0.890942	+	0.454117i	$0.849955\pi$
$480$	−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	0.257810	−	0.966196i	$-0.416999\pi$
$487$	−283.156	−	205.725i	−0.581429	−	0.422433i	−0.839239	+	0.543763i	$0.816999\pi$
$488$	−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	$-0.283277\pi$
$491$	−149.293	−	205.484i	−0.304059	−	0.418501i	−0.933517	+	0.358533i	$0.883277\pi$
$492$	−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	−0.505502	−	0.862825i	$-0.668693\pi$
$499$	79.2837	−	57.6030i	0.158885	−	0.115437i	0.664387	+	0.747389i	$0.268693\pi$
$500$	−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	$-0.631509\pi$
$503$	298.586	−	410.968i	0.593610	−	0.817034i	0.995105	+	0.0988277i	$0.0315093\pi$
$504$	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	−0.705720	−	0.708491i	$-0.749376\pi$
$509$	94.7629	−	130.430i	0.186175	−	0.256248i	0.891894	+	0.452244i	$0.149376\pi$
$510$	−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	0.886436	−	0.462852i	$-0.153174\pi$
$521$	89.7754	+	123.565i	0.172314	+	0.237169i	−0.714122	+	0.700021i	$0.753174\pi$
$522$	422.414	−	274.923i	0.809222	−	0.526672i
$523$	4.62494	−	14.2341i	0.00884310	−	0.0272163i	−0.946538	−	0.322593i	$-0.895445\pi$
$523$	4.62494	−	14.2341i	0.00884310	−	0.0272163i	0.955381	+	0.295377i	$0.0954453\pi$
$524$	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	−0.983243	−	0.182301i	$-0.941646\pi$
$541$	−159.561	−	491.077i	−0.294936	−	0.907721i	0.688307	−	0.725420i	$-0.258354\pi$
$542$	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	$-0.0889019\pi$
$547$	544.872	+	395.872i	0.996109	+	0.723716i	0.0348585	+	0.999392i	$0.488902\pi$
$548$	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	$-0.0693573\pi$
$557$	261.262	+	359.597i	0.469053	+	0.645596i	−0.507302	+	0.861768i	$0.669357\pi$
$558$	−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	$-0.437458\pi$
$563$	523.382	−	170.057i	0.929630	−	0.302055i	0.734411	+	0.678704i	$0.237458\pi$
$564$	−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	−0.443389	+	0.896329i	$0.646224\pi$
$569$	−659.377	+	907.554i	−1.15883	+	1.59500i	−0.715445	+	0.698669i	$0.753776\pi$
$570$	−335.889	−	8.62674i	−0.589279	−	0.0151346i
$571$	−808.198			−1.41541			−0.707704	−	0.706509i	$-0.750269\pi$
$571$	−808.198			−1.41541			−0.707704	+	0.706509i	$0.750269\pi$
$572$		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	−0.833087	−	0.553142i	$-0.813429\pi$
$577$	95.7953	−	294.828i	0.166023	−	0.510966i	0.999110	+	0.0421754i	$0.0134288\pi$
$578$	−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	0.945528	+	0.325541i	$0.105546\pi$
$587$	565.253	+	778.004i	0.962952	+	1.32539i	0.0174238	+	0.999848i	$0.494454\pi$
$588$	−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	0.905180	−	0.425029i	$-0.139736\pi$
$599$	831.208	+	270.076i	1.38766	+	0.450878i	0.482480	+	0.875907i	$0.339736\pi$
$600$	−82.0884	+	107.091i	−0.136814	+	0.178485i
$601$	−472.222	+	343.089i	−0.785727	+	0.570864i	−0.906692	−	0.421793i	$-0.861401\pi$
$601$	−472.222	+	343.089i	−0.785727	+	0.570864i	0.120965	+	0.992657i	$0.461401\pi$
$602$	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	−0.897635	−	0.440739i	$-0.854716\pi$
$607$	−261.309	−	804.227i	−0.430493	−	1.32492i	0.467142	−	0.884182i	$-0.345284\pi$
$608$	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	$-0.139836\pi$
$613$	478.276	+	347.488i	0.780222	+	0.566865i	−0.124824	+	0.992179i	$0.539836\pi$
$614$	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	$-0.885168\pi$
$617$		−	435.578i		−	0.705961i	0.935631	−	0.352980i	$-0.114832\pi$
$618$	6.92878	−	269.778i	0.0112116	−	0.436533i
$619$	677.956	+	492.564i	1.09524	+	0.795742i	0.980277	−	0.197628i	$-0.0633237\pi$
$619$	677.956	+	492.564i	1.09524	+	0.795742i	0.114967	+	0.993369i	$0.463324\pi$
$620$	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	−0.738586	−	0.674159i	$-0.764506\pi$
$631$	−205.490	+	149.297i	−0.325658	+	0.236605i	0.412928	+	0.910764i	$0.364506\pi$
$632$	−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	−0.860002	−	0.510290i	$-0.829538\pi$
$641$	−69.8253	+	96.1063i	−0.108932	+	0.149932i	0.751070	+	0.660222i	$0.229538\pi$
$642$	95.5910	+	322.115i	0.148896	+	0.501737i
$643$	−135.349	+	416.563i	−0.210497	+	0.647843i	0.788946	+	0.614463i	$0.210627\pi$
$643$	−135.349	+	416.563i	−0.210497	+	0.647843i	−0.999443	+	0.0333799i	$0.989373\pi$
$644$	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	−0.541963	−	0.840402i	$-0.682319\pi$
$647$	−314.729	+	102.262i	−0.486444	+	0.158055i	0.0555189	+	0.998458i	$0.482319\pi$
$648$	−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	0.429005	−	0.903302i	$-0.358864\pi$
$653$	−367.414	−	505.702i	−0.562656	−	0.774429i	−0.991661	+	0.128873i	$0.958864\pi$
$654$	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	0.920514	+	0.390709i	$0.127770\pi$
$673$	272.872	+	839.813i	0.405456	+	1.24786i	−0.515059	+	0.857155i	$0.672230\pi$
$674$	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	$-0.634644\pi$
$677$	−865.593	−	281.248i	−1.27857	−	0.415433i	−0.868077	+	0.496430i	$0.834644\pi$
$678$	−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	$0.103304\pi$
$683$			435.578i			0.637742i	−0.947798	+	0.318871i	$0.896696\pi$
$684$	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	1.00000		0.000807501i	$-0.000257036\pi$
$691$	131.641	+	405.150i	0.190508	+	0.586324i	−0.809491	+	0.587132i	$0.800257\pi$
$692$			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	$-0.737120\pi$
$701$	161.734	−	222.608i	0.230719	−	0.317557i	0.908642	+	0.417575i	$0.137120\pi$
$702$	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	−0.959792	−	0.280712i	$-0.909429\pi$
$709$	−12.9787	+	39.9444i	−0.0183057	+	0.0563390i	0.941486	+	0.337051i	$0.109429\pi$
$710$	−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	0.948401	−	0.317073i	$-0.102700\pi$
$719$	254.364	+	350.102i	0.353774	+	0.486928i	−0.594627	+	0.804002i	$0.702700\pi$
$720$	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	$-0.592345\pi$
$733$	393.518	−	285.908i	0.536860	−	0.390052i	0.822918	+	0.568161i	$0.192345\pi$
$734$	−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	0.889890	+	0.456175i	$0.150781\pi$
$739$	323.746	+	996.388i	0.438087	+	1.34829i	−0.451804	+	0.892117i	$0.649219\pi$
$740$	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	$-0.345325\pi$
$743$	241.561	+	78.4879i	0.325116	+	0.105636i	−0.141912	+	0.989879i	$0.545325\pi$
$744$	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	0.383085	−	0.923713i	$-0.374862\pi$
$751$	−283.156	−	205.725i	−0.377039	−	0.273935i	−0.760124	+	0.649779i	$0.774862\pi$
$752$	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	0.992960	−	0.118451i	$-0.0377930\pi$
$757$	90.8510	+	279.611i	0.120015	+	0.369367i	−0.872945	+	0.487818i	$0.837793\pi$
$758$		−	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	$-0.427960\pi$
$761$	744.813	−	242.004i	0.978729	−	0.318008i	0.754335	+	0.656490i	$0.227960\pi$
$762$	−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	$-0.316549\pi$
$769$	838.131			1.08990			0.544949	+	0.838469i	$0.316549\pi$
$770$		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	−0.624104	−	0.781341i	$-0.714536\pi$
$773$	241.064	−	331.796i	0.311855	−	0.429231i	0.935959	+	0.352110i	$0.114536\pi$
$774$	−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	$-0.963991\pi$
$787$	−97.1238	+	298.916i	−0.123410	+	0.379817i	0.870198	+	0.492702i	$0.163991\pi$
$788$	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	0.158494	−	0.987360i	$-0.449336\pi$
$797$	−234.029	−	76.0408i	−0.293638	−	0.0954088i	−0.452132	+	0.891951i	$0.649336\pi$
$798$	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	$-0.349824\pi$
$809$	241.561	+	78.4879i	0.298592	+	0.0970184i	−0.155890	+	0.987774i	$0.549824\pi$
$810$	451.270	+	404.687i	0.557124	+	0.499613i
$811$	−787.037	−	571.816i	−0.970452	−	0.705075i	−0.0148976	−	0.999889i	$-0.504742\pi$
$811$	−787.037	−	571.816i	−0.970452	−	0.705075i	−0.955555	+	0.294814i	$0.904742\pi$
$812$	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	$-0.295812\pi$
$821$	−286.145	−	393.844i	−0.348532	−	0.479713i	−0.946909	+	0.321502i	$0.895812\pi$
$822$	−1035.73	+	712.604i	−1.26001	+	0.866915i
$823$	321.996	+	991.001i	0.391246	+	1.20413i	0.931847	+	0.362853i	$0.118197\pi$
$823$	321.996	+	991.001i	0.391246	+	1.20413i	−0.540600	+	0.841280i	$0.681803\pi$
$824$			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	$-0.327630\pi$
$827$	1187.67	−	385.899i	1.43612	−	0.466625i	0.920687	+	0.390303i	$0.127630\pi$
$828$	−811.200	+	218.234i	−0.979710	+	0.263568i
$829$	−953.022	+	692.411i	−1.14960	+	0.835236i	−0.988428	−	0.151689i	$-0.951529\pi$
$829$	−953.022	+	692.411i	−1.14960	+	0.835236i	−0.161176	+	0.986926i	$0.551529\pi$
$830$	−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	0.284332	+	0.958726i	$0.408228\pi$
$839$	−600.165	+	826.057i	−0.715334	+	0.984573i	−0.999666	+	0.0258470i	$0.991772\pi$
$840$	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	−0.785044	−	0.619440i	$-0.787360\pi$
$853$	182.685	−	562.247i	0.214168	−	0.659141i	0.999212	−	0.0397007i	$-0.0126405\pi$
$854$	−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	0.0232978	−	0.999729i	$-0.492583\pi$
$863$	−470.749	−	152.956i	−0.545480	−	0.177237i	−0.568777	+	0.822491i	$0.692583\pi$
$864$	−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	$-0.282336\pi$
$877$	78.7037	+	57.1816i	0.0897419	+	0.0652013i	−0.542010	+	0.840372i	$0.682336\pi$
$878$	−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	$-0.678068\pi$
$881$		−	1493.41i		−	1.69513i	0.530692	−	0.847565i	$-0.321932\pi$
$882$	155.671	+	59.5773i	0.176498	+	0.0675479i
$883$	−69.5755	−	50.5495i	−0.0787944	−	0.0572475i	0.547691	−	0.836681i	$-0.315507\pi$
$883$	−69.5755	−	50.5495i	−0.0787944	−	0.0572475i	−0.626485	+	0.779433i	$0.715507\pi$
$884$	−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	$-0.245731\pi$
$887$	−149.293	−	205.484i	−0.168312	−	0.231662i	−0.884838	+	0.465899i	$0.845731\pi$
$888$	−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	0.640429	+	0.768018i	$0.278757\pi$
$907$	−298.510	+	918.721i	−0.329118	+	1.01292i	−0.969547	+	0.244905i	$0.921243\pi$
$908$	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	−0.944288	−	0.329119i	$-0.893248\pi$
$911$	−1379.97	+	448.378i	−1.51478	+	0.492183i	−0.570494	+	0.821302i	$0.693248\pi$
$912$	−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	$-0.969232\pi$
$919$	−122.561	+	377.204i	−0.133363	+	0.410450i	0.861968	+	0.506962i	$0.169232\pi$
$920$	−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	0.957770	−	0.287535i	$-0.0928358\pi$
$929$	1452.60	+	471.977i	1.56361	+	0.508049i	0.605843	+	0.795584i	$0.292836\pi$
$930$	−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	−0.912594	−	0.408867i	$-0.865924\pi$
$937$	−388.495	−	1195.67i	−0.414616	−	1.27606i	0.497978	−	0.867190i	$-0.334076\pi$
$938$	−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	$-0.316716\pi$
$941$	462.992	+	150.435i	0.492021	+	0.159867i	−0.0524893	+	0.998621i	$0.516716\pi$
$942$	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	$-0.926135\pi$
$947$		−	435.578i		−	0.459955i	0.973196	−	0.229978i	$-0.0738653\pi$
$948$	−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	0.930018	+	0.367513i	$0.119791\pi$
$953$	945.521	+	1301.40i	0.992152	+	1.36558i	0.0621339	+	0.998068i	$0.480209\pi$
$954$	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	$-0.683690\pi$
$967$	−1055.15			−1.09116			−0.545578	+	0.838060i	$0.683690\pi$
$968$		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	−0.724989	−	0.688760i	$-0.758155\pi$
$971$	149.626	−	205.942i	0.154094	−	0.212093i	0.879084	+	0.476667i	$0.158155\pi$
$972$	−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	0.493649	−	0.869661i	$-0.335663\pi$
$977$	1371.90	−	445.756i	1.40419	−	0.456250i	0.910544	+	0.413411i	$0.135663\pi$
$978$	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	0.552480	−	0.833526i	$-0.313682\pi$
$983$	−403.989	−	556.044i	−0.410976	−	0.565660i	−0.963456	+	0.267866i	$0.913682\pi$
$984$	−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	$-0.931256\pi$
$997$	−1071.58	+	778.549i	−1.07481	+	0.780892i	−0.0980354	+	0.995183i	$0.531256\pi$
$998$	−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.269.2		16
3.2	odd	2	inner	363.3.h.k.269.3		16
11.2	odd	10	inner	363.3.h.k.251.1		16
11.3	even	5		363.3.b.i.122.4	yes	4
11.4	even	5	inner	363.3.h.k.245.1		16
11.5	even	5	inner	363.3.h.k.323.4		16
11.6	odd	10	inner	363.3.h.k.323.2		16
11.7	odd	10	inner	363.3.h.k.245.3		16
11.8	odd	10		363.3.b.i.122.2	yes	4
11.9	even	5	inner	363.3.h.k.251.3		16
11.10	odd	2	inner	363.3.h.k.269.4		16
33.2	even	10	inner	363.3.h.k.251.4		16
33.5	odd	10	inner	363.3.h.k.323.1		16
33.8	even	10		363.3.b.i.122.3	yes	4
33.14	odd	10		363.3.b.i.122.1	✓	4
33.17	even	10	inner	363.3.h.k.323.3		16
33.20	odd	10	inner	363.3.h.k.251.2		16
33.26	odd	10	inner	363.3.h.k.245.4		16
33.29	even	10	inner	363.3.h.k.245.2		16
33.32	even	2	inner	363.3.h.k.269.1		16

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

Related objects

Downloads

Learn more