LMFDB - Embedded newform 287.3.i.a.40.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(40,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("287.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			40.6
Character	$\chi$	$=$	287.40
Dual form			287.3.i.a.122.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75354 + 3.03722i) q^{2} +(2.52990 + 4.38192i) q^{3} +(-4.14980 - 7.18766i) q^{4} +(-1.03847 - 0.599559i) q^{5} -17.7451 q^{6} +(-6.93494 - 0.952149i) q^{7} +15.0790 q^{8} +(-8.30079 + 14.3774i) q^{9} +O(q^{10})$	\(q+(-1.75354 + 3.03722i) q^{2} +(2.52990 + 4.38192i) q^{3} +(-4.14980 - 7.18766i) q^{4} +(-1.03847 - 0.599559i) q^{5} -17.7451 q^{6} +(-6.93494 - 0.952149i) q^{7} +15.0790 q^{8} +(-8.30079 + 14.3774i) q^{9} +(3.64198 - 2.10270i) q^{10} +(-10.6048 + 6.12269i) q^{11} +(20.9972 - 36.3681i) q^{12} +2.71749 q^{13} +(15.0526 - 19.3933i) q^{14} -6.06730i q^{15} +(-9.84248 + 17.0477i) q^{16} +(2.67168 + 4.62748i) q^{17} +(-29.1115 - 50.4226i) q^{18} +(5.30352 - 9.18597i) q^{19} +9.95220i q^{20} +(-13.3725 - 32.7972i) q^{21} -42.9455i q^{22} +(13.5552 - 23.4783i) q^{23} +(38.1485 + 66.0751i) q^{24} +(-11.7811 - 20.4054i) q^{25} +(-4.76523 + 8.25361i) q^{26} -38.4625 q^{27} +(21.9349 + 53.7973i) q^{28} +31.5638i q^{29} +(18.4277 + 10.6392i) q^{30} +(-30.6575 + 17.7001i) q^{31} +(-4.36028 - 7.55222i) q^{32} +(-53.6583 - 30.9796i) q^{33} -18.7396 q^{34} +(6.63084 + 5.14668i) q^{35} +137.786 q^{36} +(-8.15975 + 14.1331i) q^{37} +(18.5999 + 32.2159i) q^{38} +(6.87498 + 11.9078i) q^{39} +(-15.6591 - 9.04077i) q^{40} +(37.8493 - 15.7616i) q^{41} +(123.061 + 16.8960i) q^{42} -60.6607 q^{43} +(88.0157 + 50.8159i) q^{44} +(17.2402 - 9.95363i) q^{45} +(47.5391 + 82.3402i) q^{46} +(23.0711 - 39.9602i) q^{47} -99.6020 q^{48} +(47.1868 + 13.2062i) q^{49} +82.6342 q^{50} +(-13.5182 + 23.4141i) q^{51} +(-11.2770 - 19.5324i) q^{52} +(-84.0927 + 48.5509i) q^{53} +(67.4455 - 116.819i) q^{54} +14.6837 q^{55} +(-104.572 - 14.3575i) q^{56} +53.6695 q^{57} +(-95.8662 - 55.3484i) q^{58} +(-24.1999 + 13.9718i) q^{59} +(-43.6097 + 25.1781i) q^{60} +(-60.0851 - 34.6901i) q^{61} -124.151i q^{62} +(71.2549 - 91.8028i) q^{63} -48.1562 q^{64} +(-2.82202 - 1.62930i) q^{65} +(188.184 - 108.648i) q^{66} +(-33.2786 + 19.2134i) q^{67} +(22.1739 - 38.4063i) q^{68} +137.173 q^{69} +(-27.2590 + 11.1144i) q^{70} +51.1309i q^{71} +(-125.168 + 216.797i) q^{72} +(-124.559 + 71.9143i) q^{73} +(-28.6169 - 49.5659i) q^{74} +(59.6098 - 103.247i) q^{75} -88.0342 q^{76} +(79.3735 - 32.3632i) q^{77} -48.2222 q^{78} +(95.8844 + 55.3589i) q^{79} +(20.4422 - 11.8023i) q^{80} +(-22.5991 - 39.1428i) q^{81} +(-18.4989 + 142.595i) q^{82} -99.6298i q^{83} +(-180.242 + 232.219i) q^{84} -6.40732i q^{85} +(106.371 - 184.240i) q^{86} +(-138.310 + 79.8533i) q^{87} +(-159.910 + 92.3243i) q^{88} +(-22.5612 + 39.0772i) q^{89} +69.8163i q^{90} +(-18.8456 - 2.58746i) q^{91} -225.005 q^{92} +(-155.121 - 89.5589i) q^{93} +(80.9120 + 140.144i) q^{94} +(-11.0151 + 6.35955i) q^{95} +(22.0621 - 38.2127i) q^{96} -81.1123 q^{97} +(-122.854 + 120.159i) q^{98} -203.293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{2} - 106 q^{4} - 6 q^{5} + 20 q^{8} - 136 q^{9}+O(q^{10}) $ 108 * q - 2 * q^2 - 106 * q^4 - 6 * q^5 + 20 * q^8 - 136 * q^9	$ 108 q - 2 q^{2} - 106 q^{4} - 6 q^{5} + 20 q^{8} - 136 q^{9} - 60 q^{10} - 202 q^{16} - 4 q^{18} - 56 q^{21} + 12 q^{23} + 208 q^{25} + 30 q^{31} - 152 q^{32} + 24 q^{33} + 284 q^{36} - 52 q^{37} + 30 q^{39} + 24 q^{40} - 78 q^{42} - 112 q^{43} - 210 q^{45} - 264 q^{46} + 380 q^{49} - 48 q^{50} + 180 q^{51} + 168 q^{57} - 138 q^{59} - 294 q^{61} + 268 q^{64} - 612 q^{66} + 74 q^{72} + 48 q^{73} - 194 q^{74} + 256 q^{77} + 184 q^{78} + 12 q^{80} - 314 q^{81} + 474 q^{82} + 828 q^{84} - 496 q^{86} + 1122 q^{87} - 786 q^{91} + 160 q^{92} - 176 q^{98}+O(q^{100}) $ 108 * q - 2 * q^2 - 106 * q^4 - 6 * q^5 + 20 * q^8 - 136 * q^9 - 60 * q^10 - 202 * q^16 - 4 * q^18 - 56 * q^21 + 12 * q^23 + 208 * q^25 + 30 * q^31 - 152 * q^32 + 24 * q^33 + 284 * q^36 - 52 * q^37 + 30 * q^39 + 24 * q^40 - 78 * q^42 - 112 * q^43 - 210 * q^45 - 264 * q^46 + 380 * q^49 - 48 * q^50 + 180 * q^51 + 168 * q^57 - 138 * q^59 - 294 * q^61 + 268 * q^64 - 612 * q^66 + 74 * q^72 + 48 * q^73 - 194 * q^74 + 256 * q^77 + 184 * q^78 + 12 * q^80 - 314 * q^81 + 474 * q^82 + 828 * q^84 - 496 * q^86 + 1122 * q^87 - 786 * q^91 + 160 * q^92 - 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.75354	+	3.03722i	−0.876770	+	1.51861i	−0.0219040	+	0.999760i	$0.506973\pi$
$2$	−1.75354	+	3.03722i	−0.876770	+	1.51861i	−0.854866	+	0.518849i	$0.826361\pi$
$3$	2.52990	+	4.38192i	0.843300	+	1.46064i	0.887089	+	0.461598i	$0.152724\pi$
$3$	2.52990	+	4.38192i	0.843300	+	1.46064i	−0.0437893	+	0.999041i	$0.513943\pi$
$4$	−4.14980	−	7.18766i	−1.03745	−	1.79692i
$5$	−1.03847	−	0.599559i	−0.207693	−	0.119912i	0.392546	−	0.919733i	$-0.371595\pi$
$5$	−1.03847	−	0.599559i	−0.207693	−	0.119912i	−0.600239	+	0.799821i	$0.704928\pi$
$6$	−17.7451			−2.95752
$7$	−6.93494	−	0.952149i	−0.990706	−	0.136021i
$7$	−6.93494	−	0.952149i	−0.990706	−	0.136021i
$8$	15.0790			1.88488
$9$	−8.30079	+	14.3774i	−0.922310	+	1.59749i
$10$	3.64198	−	2.10270i	0.364198	−	0.210270i
$11$	−10.6048	+	6.12269i	−0.964074	+	0.556609i	−0.897425	−	0.441168i	$-0.854564\pi$
$11$	−10.6048	+	6.12269i	−0.964074	+	0.556609i	−0.0666497	+	0.997776i	$0.521231\pi$
$12$	20.9972	−	36.3681i	1.74976	−	3.03068i
$13$	2.71749			0.209038			0.104519	−	0.994523i	$-0.466670\pi$
$13$	2.71749			0.209038			0.104519	+	0.994523i	$0.466670\pi$
$14$	15.0526	−	19.3933i	1.07518	−	1.38524i
$15$		−	6.06730i		−	0.404487i
$16$	−9.84248	+	17.0477i	−0.615155	+	1.06548i
$17$	2.67168	+	4.62748i	0.157158	+	0.272205i	0.933843	−	0.357684i	$-0.116434\pi$
$17$	2.67168	+	4.62748i	0.157158	+	0.272205i	−0.776685	+	0.629889i	$0.783100\pi$
$18$	−29.1115	−	50.4226i	−1.61731	−	2.80126i
$19$	5.30352	−	9.18597i	0.279133	−	0.483472i	−0.692037	−	0.721862i	$-0.743286\pi$
$19$	5.30352	−	9.18597i	0.279133	−	0.483472i	0.971169	+	0.238390i	$0.0766197\pi$
$20$			9.95220i			0.497610i
$21$	−13.3725	−	32.7972i	−0.636784	−	1.56177i
$22$		−	42.9455i		−	1.95207i
$23$	13.5552	−	23.4783i	0.589356	−	1.02080i	−0.404960	−	0.914334i	$-0.632715\pi$
$23$	13.5552	−	23.4783i	0.589356	−	1.02080i	0.994317	−	0.106461i	$-0.0339519\pi$
$24$	38.1485	+	66.0751i	1.58952	+	2.75313i
$25$	−11.7811	−	20.4054i	−0.471242	−	0.816216i
$26$	−4.76523	+	8.25361i	−0.183278	+	0.317447i
$27$	−38.4625			−1.42454
$28$	21.9349	+	53.7973i	0.783389	+	1.92133i
$29$			31.5638i			1.08841i	0.838953	+	0.544203i	$0.183168\pi$
$29$			31.5638i			1.08841i	−0.838953	+	0.544203i	$0.816832\pi$
$30$	18.4277	+	10.6392i	0.614257	+	0.354642i
$31$	−30.6575	+	17.7001i	−0.988950	+	0.570971i	−0.904960	−	0.425496i	$-0.860100\pi$
$31$	−30.6575	+	17.7001i	−0.988950	+	0.570971i	−0.0839900	+	0.996467i	$0.526766\pi$
$32$	−4.36028	−	7.55222i	−0.136259	−	0.236007i
$33$	−53.6583	−	30.9796i	−1.62601	−	0.938776i
$34$	−18.7396			−0.551164
$35$	6.63084	+	5.14668i	0.189452	+	0.147048i
$36$	137.786			3.82740
$37$	−8.15975	+	14.1331i	−0.220534	+	0.381976i	−0.954970	−	0.296702i	$-0.904113\pi$
$37$	−8.15975	+	14.1331i	−0.220534	+	0.381976i	0.734436	+	0.678678i	$0.237447\pi$
$38$	18.5999	+	32.2159i	0.489470	+	0.847787i
$39$	6.87498	+	11.9078i	0.176282	+	0.305329i
$40$	−15.6591	−	9.04077i	−0.391477	−	0.226019i
$41$	37.8493	−	15.7616i	0.923155	−	0.384429i
$41$	37.8493	−	15.7616i	0.923155	−	0.384429i
$42$	123.061	+	16.8960i	2.93003	+	0.402286i
$43$	−60.6607			−1.41071			−0.705357	−	0.708852i	$-0.749214\pi$
$43$	−60.6607			−1.41071			−0.705357	+	0.708852i	$0.749214\pi$
$44$	88.0157	+	50.8159i	2.00036	+	1.15491i
$45$	17.2402	−	9.95363i	0.383115	−	0.221192i
$46$	47.5391	+	82.3402i	1.03346	+	1.79000i
$47$	23.0711	−	39.9602i	0.490874	−	0.850218i	−0.509071	−	0.860724i	$-0.670011\pi$
$47$	23.0711	−	39.9602i	0.490874	−	0.850218i	0.999945	+	0.0105065i	$0.00334439\pi$
$48$	−99.6020			−2.07504
$49$	47.1868	+	13.2062i	0.962996	+	0.269514i
$50$	82.6342			1.65268
$51$	−13.5182	+	23.4141i	−0.265062	+	0.459101i
$52$	−11.2770	−	19.5324i	−0.216866	−	0.375623i
$53$	−84.0927	+	48.5509i	−1.58665	+	0.916056i	−0.592802	+	0.805348i	$0.701978\pi$
$53$	−84.0927	+	48.5509i	−1.58665	+	0.916056i	−0.993853	+	0.110707i	$0.964688\pi$
$54$	67.4455	−	116.819i	1.24899	−	2.16331i
$55$	14.6837			0.266976
$56$	−104.572	−	14.3575i	−1.86736	−	0.256384i
$57$	53.6695			0.941570
$58$	−95.8662	−	55.3484i	−1.65287	−	0.954282i
$59$	−24.1999	+	13.9718i	−0.410167	+	0.236810i	−0.690862	−	0.722987i	$-0.742769\pi$
$59$	−24.1999	+	13.9718i	−0.410167	+	0.236810i	0.280694	+	0.959797i	$0.409435\pi$
$60$	−43.6097	+	25.1781i	−0.726828	+	0.419635i
$61$	−60.0851	−	34.6901i	−0.985002	−	0.568691i	−0.0812251	−	0.996696i	$-0.525883\pi$
$61$	−60.0851	−	34.6901i	−0.985002	−	0.568691i	−0.903776	+	0.428005i	$0.859217\pi$
$62$		−	124.151i		−	2.00244i
$63$	71.2549	−	91.8028i	1.13103	−	1.45719i
$64$	−48.1562			−0.752440
$65$	−2.82202	−	1.62930i	−0.0434157	−	0.0250661i
$66$	188.184	−	108.648i	2.85127	−	1.64618i
$67$	−33.2786	+	19.2134i	−0.496695	+	0.286767i	−0.727348	−	0.686269i	$-0.759247\pi$
$67$	−33.2786	+	19.2134i	−0.496695	+	0.286767i	0.230652	+	0.973036i	$0.425914\pi$
$68$	22.1739	−	38.4063i	0.326086	−	0.564798i
$69$	137.173			1.98802
$70$	−27.2590	+	11.1144i	−0.389415	+	0.158777i
$71$			51.1309i			0.720153i	0.932923	+	0.360077i	$0.117249\pi$
$71$			51.1309i			0.720153i	−0.932923	+	0.360077i	$0.882751\pi$
$72$	−125.168	+	216.797i	−1.73844	+	3.01107i
$73$	−124.559	+	71.9143i	−1.70629	+	0.985128i	−0.767234	+	0.641367i	$0.778368\pi$
$73$	−124.559	+	71.9143i	−1.70629	+	0.985128i	−0.939057	+	0.343761i	$0.888299\pi$
$74$	−28.6169	−	49.5659i	−0.386715	−	0.669810i
$75$	59.6098	−	103.247i	0.794797	−	1.37663i
$76$	−88.0342			−1.15834
$77$	79.3735	−	32.3632i	1.03082	−	0.420301i
$78$	−48.2222			−0.618233
$79$	95.8844	+	55.3589i	1.21373	+	0.700746i	0.963569	−	0.267459i	$-0.0861841\pi$
$79$	95.8844	+	55.3589i	1.21373	+	0.700746i	0.250158	+	0.968205i	$0.419517\pi$
$80$	20.4422	−	11.8023i	0.255527	−	0.147529i
$81$	−22.5991	−	39.1428i	−0.279002	−	0.483245i
$82$	−18.4989	+	142.595i	−0.225596	+	1.73897i
$83$		−	99.6298i		−	1.20036i	−0.799865	−	0.600180i	$-0.795096\pi$
$83$		−	99.6298i		−	1.20036i	0.799865	−	0.600180i	$-0.204904\pi$
$84$	−180.242	+	232.219i	−2.14574	+	2.76451i
$85$		−	6.40732i		−	0.0753802i
$86$	106.371	−	184.240i	1.23687	−	2.14233i
$87$	−138.310	+	79.8533i	−1.58977	+	0.917854i
$88$	−159.910	+	92.3243i	−1.81716	+	1.04914i
$89$	−22.5612	+	39.0772i	−0.253497	+	0.439069i	−0.964486	−	0.264134i	$-0.914914\pi$
$89$	−22.5612	+	39.0772i	−0.253497	+	0.439069i	0.710989	+	0.703203i	$0.248247\pi$
$90$			69.8163i			0.775737i
$91$	−18.8456	−	2.58746i	−0.207095	−	0.0284336i
$92$	−225.005			−2.44571
$93$	−155.121	−	89.5589i	−1.66796	−	0.962999i
$94$	80.9120	+	140.144i	0.860766	+	1.49089i
$95$	−11.0151	+	6.35955i	−0.115948	+	0.0669426i
$96$	22.0621	−	38.2127i	0.229814	−	0.398049i
$97$	−81.1123			−0.836209			−0.418105	−	0.908399i	$-0.637305\pi$
$97$	−81.1123			−0.836209			−0.418105	+	0.908399i	$0.637305\pi$
$98$	−122.854	+	120.159i	−1.25361	+	1.22611i
$99$		−	203.293i		−	2.05346i
$100$	−97.7781	+	169.357i	−0.977781	+	1.69357i
$101$	16.3401	+	28.3019i	0.161783	+	0.280216i	0.935508	−	0.353305i	$-0.114942\pi$
$101$	16.3401	+	28.3019i	0.161783	+	0.280216i	−0.773725	+	0.633521i	$0.781609\pi$
$102$	−47.4093	−	82.1152i	−0.464797	−	0.805051i
$103$	95.2827	+	55.0115i	0.925075	+	0.534092i	0.885251	−	0.465114i	$-0.153987\pi$
$103$	95.2827	+	55.0115i	0.925075	+	0.534092i	0.0398245	+	0.999207i	$0.487320\pi$
$104$	40.9771			0.394011
$105$	−5.77697	+	42.0764i	−0.0550188	+	0.400727i
$106$		−	340.544i		−	3.21268i
$107$	13.4591	−	23.3119i	0.125786	−	0.217868i	−0.796254	−	0.604963i	$-0.793188\pi$
$107$	13.4591	−	23.3119i	0.125786	−	0.217868i	0.922040	+	0.387095i	$0.126521\pi$
$108$	159.612	+	276.455i	1.47789	+	2.55977i
$109$	−12.6851	+	7.32372i	−0.116377	+	0.0671901i	−0.557058	−	0.830473i	$-0.688070\pi$
$109$	−12.6851	+	7.32372i	−0.116377	+	0.0671901i	0.440682	+	0.897663i	$0.354737\pi$
$110$	−25.7484	+	44.5975i	−0.234076	+	0.405432i
$111$	−82.5734			−0.743905
$112$	84.4889	−	108.853i	0.754365	−	0.971903i
$113$	−191.914			−1.69835			−0.849175	−	0.528112i	$-0.822900\pi$
$113$	−191.914			−1.69835			−0.849175	+	0.528112i	$0.822900\pi$
$114$	−94.1116	+	163.006i	−0.825540	+	1.42988i
$115$	−28.1532	+	16.2543i	−0.244811	+	0.141342i
$116$	226.870	−	130.983i	1.95578	−	1.12917i
$117$	−22.5573	+	39.0704i	−0.192798	+	0.333935i
$118$		−	98.0004i		−	0.830512i
$119$	−14.1219	−	34.6352i	−0.118671	−	0.291052i
$120$		−	91.4890i		−	0.762408i
$121$	14.4748	−	25.0710i	0.119626	−	0.207199i
$122$	210.723	−	121.661i	1.72724	−	0.997222i
$123$	164.821	+	125.977i	1.34001	+	1.02421i
$124$	254.445	+	146.904i	2.05197	+	1.18471i
$125$			58.2317i			0.465854i
$126$	153.877	+	377.397i	1.22124	+	2.99521i
$127$	163.929			1.29078			0.645391	−	0.763852i	$-0.276694\pi$
$127$	163.929			1.29078			0.645391	+	0.763852i	$0.276694\pi$
$128$	101.885	−	176.470i	0.795975	−	1.37867i
$129$	−153.466	−	265.810i	−1.18966	−	2.06054i
$130$	9.89706	−	5.71407i	0.0761312	−	0.0439544i
$131$	−2.41297	−	1.39313i	−0.0184196	−	0.0106346i	0.490762	−	0.871294i	$-0.336718\pi$
$131$	−2.41297	−	1.39313i	−0.0184196	−	0.0106346i	−0.509182	+	0.860659i	$0.670052\pi$
$132$			514.237i			3.89573i
$133$	−45.5260	+	58.6544i	−0.342301	+	0.441011i
$134$		−	134.766i		−	1.00572i
$135$	39.9420	+	23.0605i	0.295867	+	0.170819i
$136$	40.2863	+	69.7780i	0.296223	+	0.513073i
$137$	15.7016	−	9.06531i	0.114610	−	0.0661702i	−0.441599	−	0.897212i	$-0.645589\pi$
$137$	15.7016	−	9.06531i	0.114610	−	0.0661702i	0.556209	+	0.831042i	$0.312255\pi$
$138$	−240.539	+	416.625i	−1.74303	+	3.01902i
$139$		−	83.1858i		−	0.598459i	−0.954181	−	0.299229i	$-0.903270\pi$
$139$		−	83.1858i		−	0.598459i	0.954181	−	0.299229i	$-0.0967296\pi$
$140$	9.47598	−	69.0179i	0.0676856	−	0.492985i
$141$	233.470			1.65581
$142$	−155.296	−	89.6600i	−1.09363	−	0.631408i
$143$	−28.8185	+	16.6384i	−0.201528	+	0.116352i
$144$	−163.401	−	283.018i	−1.13473	−	1.96540i
$145$	18.9244	−	32.7780i	0.130513	−	0.226055i
$146$		−	504.418i		−	3.45492i
$147$	61.5095	+	240.179i	0.418432	+	1.63387i
$148$	135.445			0.915171
$149$	−128.054	−	73.9319i	−0.859421	−	0.496187i	0.00439707	−	0.999990i	$-0.498600\pi$
$149$	−128.054	−	73.9319i	−0.859421	−	0.496187i	−0.863818	+	0.503803i	$0.831934\pi$
$150$	209.056	+	362.096i	1.39371	+	2.41397i
$151$	43.8247	−	25.3022i	0.290230	−	0.167564i	−0.347816	−	0.937563i	$-0.613076\pi$
$151$	43.8247	−	25.3022i	0.290230	−	0.167564i	0.638046	+	0.769999i	$0.279743\pi$
$152$	79.9720	−	138.516i	0.526131	−	0.911286i
$153$	−88.7082			−0.579792
$154$	−40.8906	+	297.825i	−0.265523	+	1.93393i
$155$	42.4490			0.273865
$156$	57.0596	−	98.8301i	0.365767	−	0.633526i
$157$	23.3953	+	40.5219i	0.149015	+	0.258101i	0.930864	−	0.365367i	$-0.119056\pi$
$157$	23.3953	+	40.5219i	0.149015	+	0.258101i	−0.781849	+	0.623468i	$0.785723\pi$
$158$	−336.274	+	194.148i	−2.12832	+	1.22879i
$159$	−425.492	−	245.658i	−2.67605	−	1.54502i
$160$			10.4570i			0.0653561i
$161$	−116.359	+	149.914i	−0.722729	+	0.931143i
$162$	158.514			0.978480
$163$	52.7913	−	91.4372i	0.323873	−	0.560965i	−0.657411	−	0.753533i	$-0.728348\pi$
$163$	52.7913	−	91.4372i	0.323873	−	0.560965i	0.981284	+	0.192568i	$0.0616816\pi$
$164$	−270.356	−	206.641i	−1.64851	−	1.26001i
$165$	37.1482	+	64.3426i	0.225141	+	0.389955i
$166$	302.598	+	174.705i	1.82288	+	1.05244i
$167$	34.7752			0.208235			0.104117	−	0.994565i	$-0.466798\pi$
$167$	34.7752			0.208235			0.104117	+	0.994565i	$0.466798\pi$
$168$	−201.644	−	494.550i	−1.20026	−	2.94375i
$169$	−161.615			−0.956303
$170$	19.4604	+	11.2355i	0.114473	+	0.0660911i
$171$	88.0468	+	152.502i	0.514894	+	0.891822i
$172$	251.730	+	436.009i	1.46355	+	2.53494i
$173$	222.685	+	128.567i	1.28720	+	0.743163i	0.978153	−	0.207885i	$-0.0666579\pi$
$173$	222.685	+	128.567i	1.28720	+	0.743163i	0.309043	+	0.951048i	$0.399991\pi$
$174$		−	560.103i		−	3.21898i
$175$	62.2720	+	152.728i	0.355840	+	0.872729i
$176$		−	241.050i		−	1.36960i
$177$	−122.446	−	70.6945i	−0.691788	−	0.399404i
$178$	−79.1239	−	137.047i	−0.444516	−	0.769925i
$179$	206.613	−	119.288i	1.15426	−	0.666414i	0.204340	−	0.978900i	$-0.434495\pi$
$179$	206.613	−	119.288i	1.15426	−	0.666414i	0.949922	+	0.312486i	$0.101162\pi$
$180$	−143.087	−	82.6111i	−0.794926	−	0.458951i
$181$	−17.2227			−0.0951528			−0.0475764	−	0.998868i	$-0.515150\pi$
$181$	−17.2227			−0.0951528			−0.0475764	+	0.998868i	$0.515150\pi$
$182$	40.9052	−	52.7011i	0.224754	−	0.289567i
$183$		−	351.050i		−	1.91831i
$184$	204.399	−	354.030i	1.11087	−	1.92408i
$185$	16.9473	−	9.78451i	0.0916068	−	0.0528892i
$186$	544.020	−	314.090i	2.92484	−	1.68866i
$187$	−56.6653	−	32.7157i	−0.303023	−	0.174950i
$188$	−382.961			−2.03703
$189$	266.735	+	36.6220i	1.41130	+	0.193767i
$190$		−	44.6069i		−	0.234773i
$191$	296.480	+	171.173i	1.55225	+	0.896191i	0.997958	+	0.0638681i	$0.0203437\pi$
$191$	296.480	+	171.173i	1.55225	+	0.896191i	0.554291	+	0.832323i	$0.312990\pi$
$192$	−121.830	−	211.016i	−0.634533	−	1.09904i
$193$	−296.804	+	171.360i	−1.53784	+	0.887875i	−0.538880	+	0.842383i	$0.681152\pi$
$193$	−296.804	+	171.360i	−1.53784	+	0.887875i	−0.998965	+	0.0454922i	$0.985514\pi$
$194$	142.234	−	246.356i	0.733163	−	1.26988i
$195$		−	16.4878i		−	0.0845530i
$196$	−100.894	−	393.966i	−0.514766	−	2.01003i
$197$	236.409			1.20004			0.600022	−	0.799983i	$-0.295158\pi$
$197$	236.409			1.20004			0.600022	+	0.799983i	$0.295158\pi$
$198$	617.445	+	356.482i	3.11841	+	1.80041i
$199$	163.018	+	282.355i	0.819186	+	1.41887i	0.906283	+	0.422672i	$0.138908\pi$
$199$	163.018	+	282.355i	0.819186	+	1.41887i	−0.0870971	+	0.996200i	$0.527759\pi$
$200$	−177.647	−	307.694i	−0.888235	−	1.53847i
$201$	−168.383	−	97.2160i	−0.837727	−	0.483662i
$202$	−114.612			−0.567386
$203$	30.0534	−	218.893i	0.148047	−	1.07829i
$204$	224.391			1.09995
$205$	−48.7553	−	6.32503i	−0.237831	−	0.0308538i
$206$	−334.164	+	192.930i	−1.62216	+	0.936552i
$207$	225.038	+	389.777i	1.08714	+	1.88298i
$208$	−26.7468	+	46.3269i	−0.128591	+	0.222725i
$209$			129.887i			0.621470i
$210$	−117.665	−	91.3285i	−0.560309	−	0.434898i
$211$		−	244.263i		−	1.15765i	−0.815453	−	0.578823i	$-0.803512\pi$
$211$		−	244.263i		−	1.15765i	0.815453	−	0.578823i	$-0.196488\pi$
$212$	697.936	+	402.953i	3.29215	+	1.90072i
$213$	−224.051	+	129.356i	−1.05188	+	0.607305i
$214$	47.2022	+	81.7566i	0.220571	+	0.382040i
$215$	62.9942	+	36.3697i	0.292996	+	0.169161i
$216$	−579.977			−2.68508
$217$	229.461	−	93.5586i	1.05742	−	0.431146i
$218$		−	51.3697i		−	0.235641i
$219$	−630.245	−	363.872i	−2.87783	−	1.66152i
$220$	−60.9343	−	105.541i	−0.276974	−	0.479733i
$221$	7.26026	+	12.5751i	0.0328519	+	0.0569011i
$222$	144.796	−	250.794i	0.652233	−	1.12970i
$223$			285.158i			1.27873i	0.768902	+	0.639367i	$0.220803\pi$
$223$			285.158i			1.27873i	−0.768902	+	0.639367i	$0.779197\pi$
$224$	23.0474	+	56.5258i	0.102890	+	0.252347i
$225$	391.168			1.73853
$226$	336.528	−	582.883i	1.48906	−	2.57913i
$227$	−120.011	−	207.865i	−0.528682	−	0.915703i	−0.999441	−	0.0334415i	$-0.989353\pi$
$227$	−120.011	−	207.865i	−0.528682	−	0.915703i	0.470759	−	0.882262i	$-0.343980\pi$
$228$	−222.718	−	385.758i	−0.976832	−	1.69192i
$229$	−198.859	+	344.433i	−0.868378	+	1.50408i	−0.00472493	+	0.999989i	$0.501504\pi$
$229$	−198.859	+	344.433i	−0.868378	+	1.50408i	−0.863653	+	0.504086i	$0.831829\pi$
$230$		−	114.010i		−	0.495696i
$231$	342.620	+	265.932i	1.48320	+	1.15122i
$232$			475.952i			2.05152i
$233$	78.9593	+	45.5872i	0.338881	+	0.195653i	0.659777	−	0.751461i	$-0.270651\pi$
$233$	78.9593	+	45.5872i	0.338881	+	0.195653i	−0.320896	+	0.947114i	$0.603984\pi$
$234$	−79.1103	−	137.023i	−0.338078	−	0.585569i
$235$	−47.9170	+	27.6649i	−0.203902	+	0.117723i
$236$	200.849	+	115.960i	0.851056	+	0.491357i
$237$			560.210i			2.36376i
$238$	129.958	+	17.8429i	0.546041	+	0.0749700i
$239$			234.493i			0.981144i	0.871401	+	0.490572i	$0.163212\pi$
$239$			234.493i			0.981144i	−0.871401	+	0.490572i	$0.836788\pi$
$240$	103.433	+	59.7173i	0.430972	+	0.248822i
$241$	−98.0371	+	56.6017i	−0.406793	+	0.234862i	−0.689411	−	0.724371i	$-0.742130\pi$
$241$	−98.0371	+	56.6017i	−0.406793	+	0.234862i	0.282618	+	0.959233i	$0.408797\pi$
$242$	50.7641	+	87.9261i	0.209769	+	0.363331i
$243$	−58.7341	+	101.730i	−0.241704	+	0.418644i
$244$			575.829i			2.35995i
$245$	−41.0841	−	42.0055i	−0.167690	−	0.171451i
$246$	−671.641	+	279.691i	−2.73025	+	1.13696i
$247$	14.4123	−	24.9628i	0.0583493	−	0.101064i
$248$	−462.285	+	266.900i	−1.86405	+	1.07621i
$249$	436.569	−	252.054i	1.75329	−	1.01226i
$250$	−176.862	−	102.112i	−0.707450	−	0.408446i
$251$			387.101i			1.54224i	0.636692	+	0.771118i	$0.280302\pi$
$251$			387.101i			1.54224i	−0.636692	+	0.771118i	$0.719698\pi$
$252$	−955.541	−	131.193i	−3.79183	−	0.520608i
$253$			331.977i			1.31216i
$254$	−287.457	+	497.889i	−1.13172	+	1.96019i
$255$	28.0763	−	16.2099i	0.110103	−	0.0635681i
$256$	261.006	+	452.075i	1.01955	+	1.76592i
$257$	−180.389	+	312.444i	−0.701904	+	1.21573i	0.265893	+	0.964003i	$0.414333\pi$
$257$	−180.389	+	312.444i	−0.701904	+	1.21573i	−0.967797	+	0.251731i	$0.919000\pi$
$258$	1076.43			4.17222
$259$	70.0442	−	90.2430i	0.270441	−	0.348428i
$260$			27.0450i			0.104019i
$261$	−453.805	−	262.004i	−1.73872	−	1.00385i
$262$	8.46249	−	4.88582i	0.0322996	−	0.0186482i
$263$	188.027	−	108.557i	0.714931	−	0.412765i	−0.0979534	−	0.995191i	$-0.531230\pi$
$263$	188.027	−	108.557i	0.714931	−	0.412765i	0.812884	+	0.582426i	$0.197896\pi$
$264$	−809.115	−	467.143i	−3.06483	−	1.76948i
$265$	116.437			0.439384
$266$	−98.3146	−	241.125i	−0.369604	−	0.906486i
$267$	−228.310			−0.855095
$268$	276.199	+	159.464i	1.03059	+	0.595013i
$269$	150.889	−	87.1155i	0.560924	−	0.323850i	−0.192592	−	0.981279i	$-0.561689\pi$
$269$	150.889	−	87.1155i	0.560924	−	0.323850i	0.753516	+	0.657429i	$0.228356\pi$
$270$	−140.080	+	80.8751i	−0.518814	+	0.299537i
$271$	−372.759	−	215.213i	−1.37550	−	0.794143i	−0.383883	−	0.923382i	$-0.625413\pi$
$271$	−372.759	−	215.213i	−1.37550	−	0.794143i	−0.991614	+	0.129239i	$0.958747\pi$
$272$	−105.184			−0.386705
$273$	−36.3396	−	89.1260i	−0.133112	−	0.326469i
$274$			63.5855i			0.232064i
$275$	249.872	+	144.264i	0.908625	+	0.524595i
$276$	−569.241	−	985.955i	−2.06247	−	3.57230i
$277$	−131.489	−	227.746i	−0.474690	−	0.822186i	0.524890	−	0.851170i	$-0.324106\pi$
$277$	−131.489	−	227.746i	−0.474690	−	0.822186i	−0.999580	+	0.0289834i	$0.990773\pi$
$278$	252.653	+	145.869i	0.908825	+	0.524710i
$279$		−	587.699i		−	2.10645i
$280$	99.9866	+	77.6070i	0.357095	+	0.277168i
$281$			158.133i			0.562752i	0.959598	+	0.281376i	$0.0907908\pi$
$281$			158.133i			0.562752i	−0.959598	+	0.281376i	$0.909209\pi$
$282$	−409.399	+	709.099i	−1.45177	+	2.51454i
$283$	290.755	−	167.867i	1.02740	−	0.593171i	0.111163	−	0.993802i	$-0.464542\pi$
$283$	290.755	−	167.867i	1.02740	−	0.593171i	0.916239	+	0.400631i	$0.131209\pi$
$284$	367.512	−	212.183i	1.29405	−	0.747123i
$285$	−55.7340	−	32.1780i	−0.195558	−	0.112905i
$286$		−	116.704i		−	0.408056i
$287$	−277.490	+	73.2675i	−0.966865	+	0.255287i
$288$	144.775			0.502691
$289$	130.224	−	225.555i	0.450603	−	0.780467i
$290$	66.3692	+	114.955i	0.228859	+	0.396396i
$291$	−205.206	−	355.427i	−0.705175	−	1.22140i
$292$	1033.79	+	596.860i	3.54038	+	2.04404i
$293$	−172.524			−0.588819			−0.294409	−	0.955679i	$-0.595123\pi$
$293$	−172.524			−0.588819			−0.294409	+	0.955679i	$0.595123\pi$
$294$	−837.336	−	234.346i	−2.84808	−	0.797094i
$295$	33.5077			0.113585
$296$	−123.041	+	213.114i	−0.415680	+	0.719978i
$297$	407.888	−	235.494i	1.37336	−	0.792909i
$298$	449.095	−	259.285i	1.50703	−	0.870084i
$299$	36.8361	−	63.8020i	0.123198	−	0.213385i
$300$	−989.475			−3.29825
$301$	420.679	+	57.7581i	1.39760	+	0.191887i
$302$			177.474i			0.587662i
$303$	−82.6776	+	143.202i	−0.272863	+	0.472613i
$304$	104.400	+	180.825i	0.343420	+	0.594820i
$305$	41.5976	+	72.0491i	0.136386	+	0.236227i
$306$	155.553	−	269.426i	0.508344	−	0.880478i
$307$			269.367i			0.877418i	0.898629	+	0.438709i	$0.144564\pi$
$307$			269.367i			0.877418i	−0.898629	+	0.438709i	$0.855436\pi$
$308$	−562.000	−	436.209i	−1.82467	−	1.41626i
$309$			556.695i			1.80160i
$310$	−74.4360	+	128.927i	−0.240116	+	0.415893i
$311$	54.5714	+	94.5204i	0.175471	+	0.303924i	0.940324	−	0.340280i	$-0.110522\pi$
$311$	54.5714	+	94.5204i	0.175471	+	0.303924i	−0.764853	+	0.644204i	$0.777189\pi$
$312$	103.668	+	179.558i	0.332269	+	0.575507i
$313$	−25.6700	+	44.4617i	−0.0820126	+	0.142050i	−0.904114	−	0.427291i	$-0.859468\pi$
$313$	−25.6700	+	44.4617i	−0.0820126	+	0.142050i	0.822102	+	0.569341i	$0.192801\pi$
$314$	−164.099			−0.522607
$315$	−129.037	+	52.6126i	−0.409641	+	0.167024i
$316$		−	918.914i		−	2.90795i
$317$	75.4507	+	43.5615i	0.238015	+	0.137418i	0.614264	−	0.789101i	$-0.289453\pi$
$317$	75.4507	+	43.5615i	0.238015	+	0.137418i	−0.376249	+	0.926519i	$0.622786\pi$
$318$	1492.24	−	861.542i	4.69256	−	2.70925i
$319$	−193.255	−	334.728i	−0.605817	−	1.04931i
$320$	50.0086	+	28.8725i	0.156277	+	0.0902265i
$321$	136.201			0.424302
$322$	−251.281	−	616.289i	−0.780376	−	1.91394i
$323$	56.6772			0.175471
$324$	−187.564	+	324.870i	−0.578900	+	1.00268i
$325$	−32.0149	−	55.4515i	−0.0985074	−	0.170620i
$326$	185.143	+	320.678i	0.567924	+	0.983673i
$327$	−64.1838	−	37.0566i	−0.196281	−	0.113323i
$328$	570.731	−	237.669i	1.74003	−	0.724602i
$329$	−198.045	+	255.155i	−0.601959	+	0.775547i
$330$	−260.563			−0.789586
$331$	−260.743	−	150.540i	−0.787744	−	0.454804i	0.0514239	−	0.998677i	$-0.483624\pi$
$331$	−260.743	−	150.540i	−0.787744	−	0.454804i	−0.839168	+	0.543873i	$0.816957\pi$
$332$	−716.106	+	413.444i	−2.15694	+	1.24531i
$333$	−135.465	−	234.632i	−0.406801	−	0.704600i
$334$	−60.9797	+	105.620i	−0.182574	+	0.316228i
$335$	46.0783			0.137547
$336$	690.734	+	94.8359i	2.05576	+	0.282250i
$337$	126.434			0.375176			0.187588	−	0.982248i	$-0.439933\pi$
$337$	126.434			0.375176			0.187588	+	0.982248i	$0.439933\pi$
$338$	283.399	−	490.861i	0.838458	−	1.45225i
$339$	−485.522	−	840.949i	−1.43222	−	2.48068i
$340$	−46.0536	+	26.5891i	−0.135452	+	0.0782032i
$341$	216.745	−	375.413i	0.635614	−	1.10092i
$342$	−617.574			−1.80577
$343$	−314.664	−	136.513i	−0.917387	−	0.397997i
$344$	−914.705			−2.65903
$345$	−142.450	−	82.2434i	−0.412898	−	0.238387i
$346$	−780.974	+	450.895i	−2.25715	+	1.30317i
$347$	−13.3697	+	7.71902i	−0.0385295	+	0.0222450i	−0.519141	−	0.854689i	$-0.673748\pi$
$347$	−13.3697	+	7.71902i	−0.0385295	+	0.0222450i	0.480612	+	0.876934i	$0.340415\pi$
$348$	1147.92	+	662.750i	3.29861	+	1.90445i
$349$		−	94.8589i		−	0.271802i	−0.990722	−	0.135901i	$-0.956607\pi$
$349$		−	94.8589i		−	0.271802i	0.990722	−	0.135901i	$-0.0433929\pi$
$350$	−573.063	−	78.6801i	−1.63732	−	0.224800i
$351$	−104.521			−0.297782
$352$	92.4799	+	53.3933i	0.262727	+	0.151685i
$353$	14.6841	−	8.47787i	0.0415980	−	0.0240166i	−0.479057	−	0.877784i	$-0.659021\pi$
$353$	14.6841	−	8.47787i	0.0415980	−	0.0240166i	0.520655	+	0.853767i	$0.325688\pi$
$354$	429.429	−	247.931i	1.21308	−	0.700371i
$355$	30.6560	−	53.0977i	0.0863549	−	0.149571i
$356$	374.498			1.05196
$357$	116.041	−	149.504i	0.325046	−	0.418780i
$358$			836.705i			2.33717i
$359$	−234.588	+	406.318i	−0.653449	+	1.13181i	0.328832	+	0.944389i	$0.393345\pi$
$359$	−234.588	+	406.318i	−0.653449	+	1.13181i	−0.982280	+	0.187418i	$0.939988\pi$
$360$	259.965	−	150.091i	0.722126	−	0.416920i
$361$	124.245	+	215.199i	0.344170	+	0.596120i
$362$	30.2006	−	52.3090i	0.0834271	−	0.144500i
$363$	146.479			0.403523
$364$	59.6079	+	146.194i	0.163758	+	0.401631i
$365$	172.468			0.472514
$366$	1066.22	+	615.581i	2.91316	+	1.68191i
$367$	−209.385	+	120.888i	−0.570531	+	0.329396i	−0.757362	−	0.652996i	$-0.773512\pi$
$367$	−209.385	+	120.888i	−0.570531	+	0.329396i	0.186830	+	0.982392i	$0.440179\pi$
$368$	266.833	+	462.169i	0.725091	+	1.25589i
$369$	−87.5689	+	675.008i	−0.237314	+	1.82929i
$370$			68.6301i			0.185487i
$371$	629.406	−	256.629i	1.69651	−	0.691723i
$372$			1486.61i			3.99625i
$373$	151.113	−	261.735i	0.405128	−	0.701703i	−0.589208	−	0.807981i	$-0.700560\pi$
$373$	151.113	−	261.735i	0.405128	−	0.701703i	0.994336	+	0.106279i	$0.0338935\pi$
$374$	198.730	−	114.737i	0.531363	−	0.306783i
$375$	−255.166	+	147.320i	−0.680444	+	0.392854i
$376$	347.889	−	602.562i	0.925237	−	1.60256i
$377$			85.7743i			0.227518i
$378$	−578.959	+	745.915i	−1.53164	+	1.97332i
$379$	−136.519			−0.360209			−0.180105	−	0.983647i	$-0.557644\pi$
$379$	−136.519			−0.360209			−0.180105	+	0.983647i	$0.557644\pi$
$380$	91.4206	+	52.7817i	0.240580	+	0.138899i
$381$	414.725	+	718.325i	1.08852	+	1.88537i
$382$	−1039.78	+	600.316i	−2.72193	+	1.57151i
$383$	−288.135	+	499.065i	−0.752312	+	1.30304i	0.194388	+	0.980925i	$0.437728\pi$
$383$	−288.135	+	499.065i	−0.752312	+	1.30304i	−0.946700	+	0.322117i	$0.895605\pi$
$384$	1031.03			2.68498
$385$	−101.830	−	13.9810i	−0.264494	−	0.0363144i
$386$		−	1201.94i		−	3.11385i
$387$	503.532	−	872.143i	1.30112	−	2.25360i
$388$	336.600	+	583.008i	0.867525	+	1.50260i
$389$	−158.753	−	274.968i	−0.408105	−	0.706858i	0.586573	−	0.809897i	$-0.300477\pi$
$389$	−158.753	−	274.968i	−0.408105	−	0.706858i	−0.994677	+	0.103039i	$0.967143\pi$
$390$	50.0771	+	28.9121i	0.128403	+	0.0741335i
$391$	144.861			0.370487
$392$	711.532	+	199.137i	1.81513	+	0.508002i
$393$		−	14.0979i		−	0.0358726i
$394$	−414.552	+	718.025i	−1.05216	+	1.82240i
$395$	−66.3819	−	114.977i	−0.168055	−	0.291080i
$396$	−1461.20	+	843.624i	−3.68990	+	2.13036i
$397$	72.9565	−	126.364i	0.183770	−	0.318298i	−0.759392	−	0.650634i	$-0.774503\pi$
$397$	72.9565	−	126.364i	0.183770	−	0.318298i	0.943161	+	0.332336i	$0.107837\pi$
$398$	−1143.43			−2.87295
$399$	−372.195	−	51.1014i	−0.932819	−	0.128074i
$400$	463.819			1.15955
$401$	232.320	−	402.391i	0.579353	−	1.00347i	−0.416201	−	0.909273i	$-0.636639\pi$
$401$	232.320	−	402.391i	0.579353	−	1.00347i	0.995554	−	0.0941957i	$-0.0300279\pi$
$402$	590.533	−	340.944i	1.46899	−	0.848120i
$403$	−83.3114	+	48.0998i	−0.206728	+	0.119354i
$404$	135.616	−	234.894i	0.335683	−	0.581421i
$405$			54.1980i			0.133822i
$406$	612.126	+	475.117i	1.50770	+	1.17024i
$407$		−	199.839i		−	0.491004i
$408$	−203.841	+	353.063i	−0.499610	+	0.865350i
$409$	359.956	−	207.821i	0.880089	−	0.508120i	0.00940125	−	0.999956i	$-0.497007\pi$
$409$	359.956	−	207.821i	0.880089	−	0.508120i	0.870688	+	0.491836i	$0.163674\pi$
$410$	104.705	−	136.989i	0.255378	−	0.334120i
$411$	79.4469	+	45.8687i	0.193301	+	0.111603i
$412$		−	913.147i		−	2.21638i
$413$	181.128	−	73.8517i	0.438566	−	0.178818i
$414$	−1578.45			−3.81268
$415$	−59.7340	+	103.462i	−0.143937	+	0.249307i
$416$	−11.8490	−	20.5231i	−0.0284832	−	0.0493343i
$417$	364.513	−	210.452i	0.874132	−	0.504680i
$418$	−394.496	−	227.763i	−0.943771	−	0.544886i
$419$		−	565.355i		−	1.34930i	−0.738139	−	0.674649i	$-0.764295\pi$
$419$		−	565.355i		−	1.34930i	0.738139	−	0.674649i	$-0.235705\pi$
$420$	326.404	−	133.086i	0.777152	−	0.316870i
$421$		−	314.372i		−	0.746728i	−0.927685	−	0.373364i	$-0.878204\pi$
$421$		−	314.372i		−	0.746728i	0.927685	−	0.373364i	$-0.121796\pi$
$422$	741.882	+	428.326i	1.75801	+	1.01499i
$423$	383.016	+	663.403i	0.905475	+	1.56833i
$424$	−1268.04	+	732.101i	−2.99065	+	1.72665i
$425$	62.9504	−	109.033i	0.148119	−	0.256549i
$426$		−	907.323i		−	2.12987i
$427$	383.656	+	297.784i	0.898493	+	0.697387i
$428$	−223.411			−0.521987
$429$	−145.816	−	84.1868i	−0.339897	−	0.196240i
$430$	−220.925	+	127.551i	−0.513780	+	0.296631i
$431$	207.376	+	359.186i	0.481151	+	0.833378i	0.999766	−	0.0216300i	$-0.00688557\pi$
$431$	207.376	+	359.186i	0.481151	+	0.833378i	−0.518615	+	0.855008i	$0.673552\pi$
$432$	378.566	−	655.696i	0.876310	−	1.51781i
$433$			317.708i			0.733737i	0.930273	+	0.366868i	$0.119570\pi$
$433$			317.708i			0.733737i	−0.930273	+	0.366868i	$0.880430\pi$
$434$	−118.210	+	860.982i	−0.272374	+	1.98383i
$435$	191.507			0.440246
$436$	105.281	+	60.7839i	0.241470	+	0.139413i
$437$	−143.781	−	249.035i	−0.329017	−	0.569875i
$438$	2210.32	−	1276.13i	5.04639	−	2.91353i
$439$	370.209	−	641.221i	0.843300	−	1.46064i	−0.0437885	−	0.999041i	$-0.513943\pi$
$439$	370.209	−	641.221i	0.843300	−	1.46064i	0.887089	−	0.461598i	$-0.152724\pi$
$440$	221.416			0.503217
$441$	−581.559	+	568.802i	−1.31873	+	1.28980i
$442$	−50.9246			−0.115214
$443$	−246.664	+	427.234i	−0.556803	+	0.964412i	0.440958	+	0.897528i	$0.354639\pi$
$443$	−246.664	+	427.234i	−0.556803	+	0.964412i	−0.997761	+	0.0668836i	$0.978694\pi$
$444$	342.663	+	593.510i	0.771764	+	1.33673i
$445$	46.8581	−	27.0536i	0.105299	−	0.0607945i
$446$	−866.086	−	500.035i	−1.94190	−	1.12115i
$447$		−	748.161i		−	1.67374i
$448$	333.960	+	45.8518i	0.745447	+	0.102348i
$449$	611.060			1.36094			0.680468	−	0.732778i	$-0.261777\pi$
$449$	611.060			1.36094			0.680468	+	0.732778i	$0.261777\pi$
$450$	−685.929	+	1188.06i	−1.52429	+	2.64014i
$451$	−304.882	+	398.889i	−0.676013	+	0.884454i
$452$	796.403	+	1379.41i	1.76195	+	3.05179i
$453$	221.744	+	128.024i	0.489502	+	0.282614i
$454$	841.774			1.85413
$455$	18.0192	+	13.9861i	0.0396027	+	0.0307386i
$456$	809.284			1.77475
$457$	34.8990	+	20.1490i	0.0763655	+	0.0440896i	0.537697	−	0.843138i	$-0.319295\pi$
$457$	34.8990	+	20.1490i	0.0763655	+	0.0440896i	−0.461331	+	0.887228i	$0.652628\pi$
$458$	−697.413	−	1207.95i	−1.52274	−	2.63745i
$459$	−102.759	−	177.984i	−0.223877	−	0.387766i
$460$	233.661	+	134.904i	0.507958	+	0.293270i
$461$			503.558i			1.09232i	0.837682	+	0.546159i	$0.183910\pi$
$461$			503.558i			1.09232i	−0.837682	+	0.546159i	$0.816090\pi$
$462$	−1408.49	+	574.288i	−3.04868	+	1.24305i
$463$		−	726.075i		−	1.56820i	−0.620636	−	0.784099i	$-0.713126\pi$
$463$		−	726.075i		−	1.56820i	0.620636	−	0.784099i	$-0.286874\pi$
$464$	−538.089	−	310.666i	−1.15968	−	0.669539i
$465$	107.392	+	186.008i	0.230950	+	0.400017i
$466$	−276.917	+	159.878i	−0.594242	+	0.343086i
$467$	−73.5829	−	42.4831i	−0.157565	−	0.0909703i	0.419144	−	0.907920i	$-0.362330\pi$
$467$	−73.5829	−	42.4831i	−0.157565	−	0.0909703i	−0.576709	+	0.816949i	$0.695663\pi$
$468$	374.433			0.800071
$469$	249.079	−	101.558i	0.531086	−	0.216541i
$470$		−	194.046i		−	0.412864i
$471$	−118.376	+	205.033i	−0.251329	+	0.435314i
$472$	−364.911	+	210.681i	−0.773116	+	0.446359i
$473$	643.296	−	371.407i	1.36003	−	0.785216i
$474$	−1701.48	−	982.350i	−3.58962	−	2.07247i
$475$	−249.924			−0.526156
$476$	−190.343	+	245.232i	−0.399880	+	0.515194i
$477$		−	1612.04i		−	3.37955i
$478$	−712.208	−	411.194i	−1.48997	−	0.860237i
$479$	173.638	+	300.750i	0.362501	+	0.627870i	0.988372	−	0.152057i	$-0.0485896\pi$
$479$	173.638	+	300.750i	0.362501	+	0.627870i	−0.625871	+	0.779927i	$0.715256\pi$
$480$	−45.8216	+	26.4551i	−0.0954616	+	0.0551148i
$481$	−22.1740	+	38.4066i	−0.0460999	+	0.0798474i
$482$		−	397.013i		−	0.823679i
$483$	−951.288	−	130.609i	−1.96954	−	0.270413i
$484$	−240.270			−0.496425
$485$	84.2324	+	48.6316i	0.173675	+	0.100271i
$486$	−205.985	−	356.777i	−0.423838	−	0.734108i
$487$	−384.955	−	666.761i	−0.790462	−	1.36912i	−0.925681	−	0.378304i	$-0.876507\pi$
$487$	−384.955	−	666.761i	−0.790462	−	1.36912i	0.135220	−	0.990816i	$-0.456826\pi$
$488$	−906.025	−	523.094i	−1.85661	−	1.07191i
$489$	534.227			1.09249
$490$	199.622	−	51.1230i	0.407393	−	0.104333i
$491$	709.790			1.44560			0.722800	−	0.691057i	$-0.242855\pi$
$491$	709.790			1.44560			0.722800	+	0.691057i	$0.242855\pi$
$492$	221.509	−	1707.46i	0.450221	−	3.47044i
$493$	−146.061	+	84.3283i	−0.296270	+	0.171051i
$494$	50.5449	+	87.5464i	0.102318	+	0.177219i
$495$	−121.886	+	211.113i	−0.246234	+	0.426491i
$496$		−	696.851i		−	1.40494i
$497$	48.6842	−	354.590i	0.0979562	−	0.713460i
$498$			1767.94i			3.55009i
$499$	68.2391	+	39.3979i	0.136752	+	0.0789537i	0.566815	−	0.823845i	$-0.308175\pi$
$499$	68.2391	+	39.3979i	0.136752	+	0.0789537i	−0.430063	+	0.902799i	$0.641509\pi$
$500$	418.550	−	241.650i	0.837100	−	0.483300i
$501$	87.9779	+	152.382i	0.175605	+	0.304156i
$502$	−1175.71	−	678.797i	−2.34206	−	1.35219i
$503$	−852.227			−1.69429			−0.847144	−	0.531363i	$-0.821680\pi$
$503$	−852.227			−1.69429			−0.847144	+	0.531363i	$0.821680\pi$
$504$	1074.46	−	1384.30i	2.13186	−	2.74662i
$505$		−	39.1874i		−	0.0775988i
$506$	−1008.29	−	582.135i	−1.99266	−	1.15046i
$507$	−408.870	−	708.184i	−0.806451	−	1.39681i
$508$	−680.274	−	1178.27i	−1.33912	−	2.31943i
$509$	−2.34424	+	4.06034i	−0.00460557	+	0.00797708i	−0.868319	−	0.496006i	$-0.834799\pi$
$509$	−2.34424	+	4.06034i	−0.00460557	+	0.00797708i	0.863713	+	0.503983i	$0.168133\pi$
$510$			113.699i			0.222938i
$511$	932.284	−	380.123i	1.82443	−	0.743880i
$512$	−1015.66			−1.98370
$513$	−203.987	+	353.315i	−0.397635	+	0.688723i
$514$	−632.640	−	1095.76i	−1.23082	−	2.13184i
$515$	−65.9653	−	114.255i	−0.128088	−	0.221855i
$516$	−1273.70	+	2206.12i	−2.46842	+	4.27542i
$517$			565.028i			1.09290i
$518$	151.262	+	370.984i	0.292012	+	0.716186i
$519$			1301.05i			2.50684i
$520$	−42.5534	−	24.5682i	−0.0818334	−	0.0472466i
$521$	410.468	+	710.951i	0.787846	+	1.36459i	0.927284	+	0.374358i	$0.122137\pi$
$521$	410.468	+	710.951i	0.787846	+	1.36459i	−0.139438	+	0.990231i	$0.544530\pi$
$522$	1591.53	−	918.870i	3.04891	−	1.76029i
$523$	−58.5045	−	33.7776i	−0.111863	−	0.0645843i	0.443024	−	0.896510i	$-0.353905\pi$
$523$	−58.5045	−	33.7776i	−0.111863	−	0.0645843i	−0.554888	+	0.831925i	$0.687239\pi$
$524$			23.1249i			0.0441314i
$525$	−511.697	+	659.256i	−0.974661	+	1.25573i
$526$			761.438i			1.44760i
$527$	−163.814	−	94.5779i	−0.310842	−	0.179465i
$528$	1056.26	−	609.832i	2.00049	−	1.15499i
$529$	−102.987	−	178.378i	−0.194682	−	0.337199i
$530$	−204.176	+	353.644i	−0.385238	+	0.667252i
$531$		−	463.908i		−	0.873650i
$532$	610.512	+	83.8217i	1.14758	+	0.157560i
$533$	102.855	−	42.8320i	0.192974	−	0.0803601i
$534$	400.351	−	693.429i	0.749722	−	1.29856i
$535$	−27.9537	+	16.1391i	−0.0522499	+	0.0301665i
$536$	−501.809	+	289.720i	−0.936211	+	0.540522i
$537$	1045.42	+	603.574i	1.94678	+	1.12397i
$538$			611.042i			1.13577i
$539$	−581.265	+	148.861i	−1.07841	+	0.276180i
$540$		−	382.786i		−	0.708864i
$541$	−91.7198	+	158.863i	−0.169538	+	0.293648i	−0.938257	−	0.345938i	$-0.887561\pi$
$541$	−91.7198	+	158.863i	−0.169538	+	0.293648i	0.768720	+	0.639586i	$0.220894\pi$
$542$	1307.30	−	754.768i	2.41199	−	1.39256i
$543$	−43.5716	−	75.4683i	−0.0802424	−	0.138984i
$544$	23.2985	−	40.3542i	0.0428282	−	0.0741805i
$545$	17.5640			0.0322275
$546$	334.418	+	45.9147i	0.612487	+	0.0840929i
$547$		−	529.463i		−	0.967940i	−0.875085	−	0.483970i	$-0.839194\pi$
$547$		−	529.463i		−	0.967940i	0.875085	−	0.483970i	$-0.160806\pi$
$548$	−130.317	−	75.2385i	−0.237804	−	0.137296i
$549$	997.508	−	575.911i	1.81695	−	1.04902i
$550$	−876.320	+	505.944i	−1.59331	+	0.919898i
$551$	289.944	+	167.399i	0.526214	+	0.303810i
$552$	2068.44			3.74717
$553$	−612.243	−	475.207i	−1.10713	−	0.859326i
$554$	922.285			1.66477
$555$	85.7498	+	49.5077i	0.154504	+	0.0892030i
$556$	−597.911	+	345.204i	−1.07538	+	0.620871i
$557$	212.985	−	122.967i	0.382379	−	0.220767i	−0.296474	−	0.955041i	$-0.595811\pi$
$557$	212.985	−	122.967i	0.382379	−	0.220767i	0.678853	+	0.734274i	$0.262477\pi$
$558$	1784.97	+	1030.55i	3.19887	+	1.84687i
$559$	−164.845			−0.294893
$560$	−153.003	+	62.3842i	−0.273219	+	0.111400i
$561$		−	331.070i		−	0.590143i
$562$	−480.286	−	277.293i	−0.854601	−	0.493404i
$563$	−360.621	−	624.613i	−0.640534	−	1.10944i	−0.985314	−	0.170754i	$-0.945380\pi$
$563$	−360.621	−	624.613i	−0.640534	−	1.10944i	0.344780	−	0.938684i	$-0.387954\pi$
$564$	−968.853	−	1678.10i	−1.71782	−	2.97536i
$565$	199.296	+	115.063i	0.352736	+	0.203652i
$566$			1177.45i			2.08030i
$567$	119.454	+	292.971i	0.210677	+	0.516704i
$568$			771.004i			1.35740i
$569$	64.1183	−	111.056i	0.112686	−	0.195178i	−0.804166	−	0.594404i	$-0.797388\pi$
$569$	64.1183	−	111.056i	0.112686	−	0.195178i	0.916852	+	0.399226i	$0.130721\pi$
$570$	195.464	−	112.851i	0.342918	−	0.197984i
$571$	326.437	−	188.468i	0.571693	−	0.330067i	−0.186132	−	0.982525i	$-0.559595\pi$
$571$	326.437	−	188.468i	0.571693	−	0.330067i	0.757825	+	0.652457i	$0.226262\pi$
$572$	239.182	+	138.092i	0.418150	+	0.241419i
$573$			1732.20i			3.02303i
$574$	264.061	−	971.276i	0.460036	−	1.69212i
$575$	−638.778			−1.11092
$576$	399.734	−	692.360i	0.693983	−	1.20201i
$577$	38.2701	+	66.2857i	0.0663259	+	0.114880i	0.897281	−	0.441459i	$-0.145539\pi$
$577$	38.2701	+	66.2857i	0.0663259	+	0.114880i	−0.830955	+	0.556339i	$0.812206\pi$
$578$	456.707	+	791.039i	0.790150	+	1.36858i
$579$	−1501.77	−	867.047i	−2.59373	−	1.49749i
$580$	−314.129			−0.541602
$581$	−94.8624	+	690.927i	−0.163274	+	1.18920i
$582$	1439.35			2.47311
$583$	594.525	−	1029.75i	1.01977	−	1.76629i
$584$	−1878.23	+	1084.40i	−3.21615	+	1.85685i
$585$	46.8501	−	27.0489i	0.0800856	−	0.0462374i
$586$	302.527	−	523.993i	0.516258	−	0.894186i
$587$	−417.344			−0.710978			−0.355489	−	0.934680i	$-0.615686\pi$
$587$	−417.344			−0.710978			−0.355489	+	0.934680i	$0.615686\pi$
$588$	1471.07	−	1438.80i	2.50183	−	2.44695i
$589$			375.491i			0.637506i
$590$	−58.7570	+	101.770i	−0.0995882	+	0.172492i
$591$	598.090	+	1035.92i	1.01200	+	1.75283i
$592$	−160.624	−	278.210i	−0.271325	−	0.469949i
$593$	−274.793	+	475.955i	−0.463394	+	0.802622i	−0.999127	−	0.0417649i	$-0.986702\pi$
$593$	−274.793	+	475.955i	−0.463394	+	0.802622i	0.535733	+	0.844387i	$0.320035\pi$
$594$			1651.79i			2.78079i
$595$	−6.10072	+	44.4344i	−0.0102533	+	0.0746796i
$596$			1227.21i			2.05908i
$597$	−824.838	+	1428.66i	−1.38164	+	2.39307i
$598$	129.187	+	223.759i	0.216032	+	0.374178i
$599$	373.178	+	646.364i	0.623002	+	1.07907i	0.988924	+	0.148425i	$0.0474205\pi$
$599$	373.178	+	646.364i	0.623002	+	1.07907i	−0.365922	+	0.930646i	$0.619246\pi$
$600$	898.858	−	1556.87i	1.49810	−	2.59478i
$601$	69.7823			0.116110			0.0580551	−	0.998313i	$-0.481510\pi$
$601$	69.7823			0.116110			0.0580551	+	0.998313i	$0.481510\pi$
$602$	−913.101	+	1176.41i	−1.51678	+	1.95417i
$603$		−	637.946i		−	1.05795i
$604$	−363.728	−	209.998i	−0.602198	−	0.347679i
$605$	−30.0631	+	17.3570i	−0.0496911	+	0.0286892i
$606$	−289.957	−	502.220i	−0.478476	−	0.828745i
$607$	88.9332	+	51.3456i	0.146513	+	0.0845891i	0.571464	−	0.820627i	$-0.306376\pi$
$607$	88.9332	+	51.3456i	0.146513	+	0.0845891i	−0.424952	+	0.905216i	$0.639709\pi$
$608$	−92.4993			−0.152137
$609$	1035.20	−	422.086i	1.69984	−	0.693081i
$610$	−291.772			−0.478315
$611$	62.6954	−	108.592i	0.102611	−	0.177728i
$612$	368.121	+	637.605i	0.601505	+	1.04184i
$613$	−117.790	−	204.019i	−0.192154	−	0.332820i	0.753810	−	0.657092i	$-0.228214\pi$
$613$	−117.790	−	204.019i	−0.192154	−	0.332820i	−0.945964	+	0.324272i	$0.894881\pi$
$614$	−818.128	−	472.346i	−1.33246	−	0.769293i
$615$	−95.6303	−	229.643i	−0.155496	−	0.373404i
$616$	1196.88	−	488.005i	1.94298	−	0.792216i
$617$	651.265			1.05554			0.527768	−	0.849389i	$-0.323029\pi$
$617$	651.265			1.05554			0.527768	+	0.849389i	$0.323029\pi$
$618$	−1690.80	−	976.186i	−2.73593	−	1.57959i
$619$	549.727	−	317.385i	0.888089	−	0.512738i	0.0147719	−	0.999891i	$-0.495298\pi$
$619$	549.727	−	317.385i	0.888089	−	0.512738i	0.873317	+	0.487153i	$0.161964\pi$
$620$	−176.155	−	305.109i	−0.284121	−	0.492112i
$621$	−521.366	+	903.033i	−0.839560	+	1.45416i
$622$	−382.772			−0.615389
$623$	193.668	−	249.516i	0.310863	−	0.400508i
$624$	−270.667			−0.433762
$625$	−259.613	+	449.663i	−0.415381	+	0.719461i
$626$	−90.0266	−	155.931i	−0.143812	−	0.249090i
$627$	−569.155	+	328.602i	−0.907744	+	0.524086i
$628$	194.172	−	336.316i	0.309191	−	0.535534i
$629$	−87.2009			−0.138634
$630$	66.4755	−	484.172i	0.105517	−	0.768527i
$631$	1067.80			1.69224			0.846119	−	0.532993i	$-0.178933\pi$
$631$	1067.80			1.69224			0.846119	+	0.532993i	$0.178933\pi$
$632$	1445.84	+	834.759i	2.28773	+	1.32082i
$633$	1070.34	−	617.962i	1.69090	−	0.976243i
$634$	−264.612	+	152.774i	−0.417369	+	0.240968i
$635$	−170.235	−	98.2853i	−0.268087	−	0.154780i
$636$			4077.73i			6.41152i
$637$	128.230	+	35.8877i	0.201303	+	0.0563386i
$638$	1355.52			2.12465
$639$	−735.128	−	424.427i	−1.15044	−	0.664204i
$640$	−211.608	+	122.172i	−0.330638	+	0.190894i
$641$	−804.230	+	464.322i	−1.25465	+	0.724372i	−0.972029	−	0.234860i	$-0.924537\pi$
$641$	−804.230	+	464.322i	−1.25465	+	0.724372i	−0.282619	+	0.959232i	$0.591203\pi$
$642$	−238.834	+	413.672i	−0.372015	+	0.644349i
$643$	−946.223			−1.47158			−0.735788	−	0.677212i	$-0.763188\pi$
$643$	−946.223			−1.47158			−0.735788	+	0.677212i	$0.763188\pi$
$644$	1560.40	+	214.239i	2.42298	+	0.332669i
$645$			368.047i			0.570615i
$646$	−99.3857	+	172.141i	−0.153848	+	0.266472i
$647$	−556.707	+	321.415i	−0.860444	+	0.496777i	−0.864161	−	0.503216i	$-0.832150\pi$
$647$	−556.707	+	321.415i	−0.860444	+	0.496777i	0.00371720	+	0.999993i	$0.498817\pi$
$648$	−340.773	−	590.236i	−0.525884	−	0.910858i
$649$	171.090	−	296.337i	0.263621	−	0.456605i
$650$	224.558			0.345473
$651$	990.479	+	768.784i	1.52147	+	1.18093i
$652$	−876.293			−1.34401
$653$	−683.059	−	394.364i	−1.04603	−	0.603927i	−0.124496	−	0.992220i	$-0.539731\pi$
$653$	−683.059	−	394.364i	−1.04603	−	0.603927i	−0.921536	+	0.388293i	$0.873065\pi$
$654$	225.098	−	129.960i	0.344186	−	0.198716i
$655$	1.67053	+	2.89344i	0.00255043	+	0.00441747i
$656$	−103.833	+	800.376i	−0.158282	+	1.22009i
$657$		−	2387.78i		−	3.63437i
$658$	−427.682	−	1048.93i	−0.649973	−	1.59412i
$659$		−	34.3955i		−	0.0521935i	−0.999659	−	0.0260968i	$-0.991692\pi$
$659$		−	34.3955i		−	0.0521935i	0.999659	−	0.0260968i	$-0.00830780\pi$
$660$	308.315	−	534.018i	0.467144	−	0.809118i
$661$	−791.930	+	457.221i	−1.19808	+	0.691711i	−0.960126	−	0.279566i	$-0.909809\pi$
$661$	−791.930	+	457.221i	−1.19808	+	0.691711i	−0.237952	+	0.971277i	$0.576476\pi$
$662$	914.447	−	527.956i	1.38134	−	0.797517i
$663$	−36.7355	+	63.6277i	−0.0554080	+	0.0959694i
$664$		−	1502.32i		−	2.26253i
$665$	82.4440	−	33.6151i	0.123976	−	0.0505490i
$666$	950.171			1.42668
$667$	741.064	+	427.854i	1.11104	+	0.641460i
$668$	−144.310	−	249.953i	−0.216033	−	0.374181i
$669$	−1249.54	+	721.420i	−1.86777	+	1.07836i
$670$	−80.8001	+	139.950i	−0.120597	+	0.208880i
$671$	849.589			1.26615
$672$	−189.384	+	243.997i	−0.281821	+	0.363090i
$673$		−	307.942i		−	0.457567i	−0.973477	−	0.228783i	$-0.926525\pi$
$673$		−	307.942i		−	0.457567i	0.973477	−	0.228783i	$-0.0734747\pi$
$674$	−221.707	+	384.008i	−0.328943	+	0.569745i
$675$	453.129	+	784.842i	0.671302	+	1.16273i
$676$	670.671	+	1161.64i	0.992117	+	1.71840i
$677$	71.3247	+	41.1793i	0.105354	+	0.0608262i	0.551751	−	0.834009i	$-0.313960\pi$
$677$	71.3247	+	41.1793i	0.105354	+	0.0608262i	−0.446397	+	0.894835i	$0.647293\pi$
$678$	3405.53			5.02290
$679$	562.509	+	77.2310i	0.828438	+	0.113742i
$680$		−	96.6162i		−	0.142083i
$681$	607.230	−	1051.75i	0.891674	−	1.54443i
$682$	760.140	+	1316.60i	1.11457	+	1.93050i
$683$	−188.300	+	108.715i	−0.275695	+	0.159173i	−0.631473	−	0.775398i	$-0.717549\pi$
$683$	−188.300	+	108.715i	−0.275695	+	0.159173i	0.355778	+	0.934571i	$0.384216\pi$
$684$	730.753	−	1265.70i	1.06835	−	1.85044i
$685$	−21.7408			−0.0317383
$686$	966.395	−	716.321i	1.40874	−	1.04420i
$687$	−2012.37			−2.92921
$688$	597.052	−	1034.12i	0.867808	−	1.50309i
$689$	−228.521	+	131.937i	−0.331671	+	0.191490i
$690$	499.583	−	288.434i	0.724033	−	0.418021i
$691$	−88.5898	+	153.442i	−0.128205	+	0.222058i	−0.922981	−	0.384845i	$-0.874255\pi$
$691$	−88.5898	+	153.442i	−0.128205	+	0.222058i	0.794776	+	0.606903i	$0.207588\pi$
$692$		−	2134.11i		−	3.08398i
$693$	−193.565	+	1409.82i	−0.279315	+	2.03438i
$694$		−	54.1424i		−	0.0780150i
$695$	−49.8748	+	86.3856i	−0.0717623	+	0.124296i
$696$	−2085.58	+	1204.11i	−2.99652	+	1.73004i
$697$	174.058	+	133.037i	0.249724	+	0.190871i
$698$	288.107	+	166.339i	0.412761	+	0.238308i
$699$			461.324i			0.659977i
$700$	839.338	−	1081.38i	1.19905	−	1.54483i
$701$	−39.2671			−0.0560158			−0.0280079	−	0.999608i	$-0.508916\pi$
$701$	−39.2671			−0.0560158			−0.0280079	+	0.999608i	$0.508916\pi$
$702$	183.282	−	317.454i	0.261086	−	0.452214i
$703$	86.5508	+	149.910i	0.123116	+	0.213244i
$704$	510.687	−	294.845i	0.725408	−	0.418815i
$705$	−242.451	−	139.979i	−0.343902	−	0.198552i
$706$			59.4651i			0.0842282i
$707$	−86.3699	−	211.830i	−0.122164	−	0.299618i
$708$			1173.47i			1.65745i
$709$	−1057.23	−	610.390i	−1.49115	−	0.860916i	−0.491202	−	0.871046i	$-0.663442\pi$
$709$	−1057.23	−	610.390i	−1.49115	−	0.860916i	−0.999949	+	0.0101294i	$0.996776\pi$
$710$	107.513	+	186.218i	0.151427	+	0.262279i
$711$	−1591.83	+	919.045i	−2.23887	+	1.29261i
$712$	−340.201	+	589.246i	−0.477811	+	0.827592i
$713$			959.713i			1.34602i
$714$	250.594	+	614.605i	0.350973	+	0.860791i
$715$	39.9027			0.0558080
$716$	−1714.81	−	990.043i	−2.39498	−	1.38274i
$717$	−1027.53	+	593.245i	−1.43310	+	0.827399i
$718$	−822.719	−	1424.99i	−1.14585	−	1.98467i
$719$	−68.2207	+	118.162i	−0.0948827	+	0.164342i	−0.909560	−	0.415573i	$-0.863581\pi$
$719$	−68.2207	+	118.162i	−0.0948827	+	0.164342i	0.814677	+	0.579915i	$0.196914\pi$
$720$			391.873i			0.544269i
$721$	−608.401	−	472.225i	−0.843829	−	0.654958i
$722$	−871.476			−1.20703
$723$	−496.048	−	286.393i	−0.686097	−	0.396118i
$724$	71.4706	+	123.791i	0.0987163	+	0.170982i
$725$	644.072	−	371.855i	0.888375	−	0.512903i
$726$	−256.856	+	444.888i	−0.353797	+	0.612794i
$727$	1094.35			1.50529			0.752645	−	0.658426i	$-0.228777\pi$
$727$	1094.35			1.50529			0.752645	+	0.658426i	$0.228777\pi$
$728$	−284.174	−	39.0163i	−0.390349	−	0.0535939i
$729$	−1001.15			−1.37332
$730$	−302.429	+	523.822i	−0.414286	+	0.717564i
$731$	−162.066	−	280.707i	−0.221705	−	0.384004i
$732$	−2523.23	+	1456.79i	−3.44704	+	1.99015i
$733$	−535.163	−	308.977i	−0.730100	−	0.421523i	0.0883587	−	0.996089i	$-0.471838\pi$
$733$	−535.163	−	308.977i	−0.730100	−	0.421523i	−0.818459	+	0.574565i	$0.805171\pi$
$734$		−	847.931i		−	1.15522i
$735$	80.1259	−	286.297i	0.109015	−	0.389519i
$736$	−236.418			−0.321220
$737$	235.276	−	407.509i	0.319234	−	0.552930i
$738$	−1896.59	−	1449.62i	−2.56991	−	1.96425i
$739$	601.415	+	1041.68i	0.813822	+	1.40958i	0.910171	+	0.414234i	$0.135950\pi$
$739$	601.415	+	1041.68i	0.813822	+	1.40958i	−0.0963483	+	0.995348i	$0.530716\pi$
$740$	−140.655	−	81.2075i	−0.190075	−	0.109740i
$741$	145.846			0.196824
$742$	−324.249	+	2361.65i	−0.436993	+	3.18282i
$743$	587.085			0.790154			0.395077	−	0.918648i	$-0.370718\pi$
$743$	587.085			0.790154			0.395077	+	0.918648i	$0.370718\pi$
$744$	−2339.07	−	1350.46i	−3.14391	−	1.81514i
$745$	88.6531	+	153.552i	0.118997	+	0.206110i
$746$	529.965	+	917.926i	0.710408	+	1.23046i
$747$	1432.42	+	827.006i	1.91756	+	1.10710i
$748$			543.055i			0.726010i
$749$	−115.535	+	148.851i	−0.154252	+	0.198733i
$750$		−	1033.33i		−	1.37777i
$751$	93.8189	+	54.1664i	0.124925	+	0.0721257i	0.561160	−	0.827707i	$-0.310355\pi$
$751$	93.8189	+	54.1664i	0.124925	+	0.0721257i	−0.436235	+	0.899833i	$0.643688\pi$
$752$	454.153	+	786.616i	0.603926	+	1.04603i
$753$	−1696.25	+	979.328i	−2.25265	+	1.30057i
$754$	−260.515	−	150.409i	−0.345511	−	0.199481i
$755$	−60.6807			−0.0803718
$756$	−843.670	−	2069.18i	−1.11597	−	2.73701i
$757$			909.279i			1.20116i	0.799564	+	0.600580i	$0.205064\pi$
$757$			909.279i			1.20116i	−0.799564	+	0.600580i	$0.794936\pi$
$758$	239.392	−	414.639i	0.315821	−	0.547017i
$759$	−1454.70	+	839.869i	−1.91660	+	1.10655i
$760$	−166.096	+	95.8958i	−0.218548	+	0.126179i
$761$	−525.039	−	303.132i	−0.689934	−	0.398333i	0.113654	−	0.993520i	$-0.463745\pi$
$761$	−525.039	−	303.132i	−0.689934	−	0.398333i	−0.803587	+	0.595187i	$0.797078\pi$
$762$	−2908.95			−3.81751
$763$	94.9434	−	38.7115i	0.124434	−	0.0507359i
$764$		−	2841.33i		−	3.71901i
$765$	92.1205	+	53.1858i	0.120419	+	0.0695239i
$766$	−1010.51	−	1750.26i	−1.31921	−	2.28494i
$767$	−65.7629	+	37.9682i	−0.0857404	+	0.0495023i
$768$	−1320.64	+	2287.41i	−1.71958	+	2.97840i
$769$			459.969i			0.598139i	0.954231	+	0.299069i	$0.0966762\pi$
$769$			459.969i			0.598139i	−0.954231	+	0.299069i	$0.903324\pi$
$770$	221.027	−	284.765i	0.287048	−	0.369824i
$771$	−1825.47			−2.36766
$772$	2463.35	+	1422.22i	3.19087	+	1.84225i
$773$	521.910	+	903.974i	0.675174	+	1.16944i	0.976418	+	0.215889i	$0.0692650\pi$
$773$	521.910	+	903.974i	0.675174	+	1.16944i	−0.301244	+	0.953547i	$0.597402\pi$
$774$	1765.93	+	3058.67i	2.28156	+	3.95178i
$775$	722.355	+	417.052i	0.932071	+	0.538131i
$776$	−1223.10			−1.57615
$777$	572.642	+	78.6222i	0.736991	+	0.101187i
$778$	1113.52			1.43126
$779$	55.9493	−	431.275i	0.0718220	−	0.553626i
$780$	−118.509	+	68.4212i	−0.151935	+	0.0877195i
$781$	−313.059	−	542.234i	−0.400843	−	0.694281i
$782$	−254.019	+	439.973i	−0.324832	+	0.562626i
$783$		−	1214.02i		−	1.55048i
$784$	−689.570	+	674.444i	−0.879554	+	0.860260i
$785$		−	56.1075i		−	0.0714746i
$786$	42.8185	+	24.7213i	0.0544765	+	0.0314520i
$787$	−835.893	+	482.603i	−1.06213	+	0.613219i	−0.926020	−	0.377476i	$-0.876792\pi$
$787$	−835.893	+	482.603i	−1.06213	+	0.613219i	−0.136106	+	0.990694i	$0.543459\pi$
$788$	−981.049	−	1699.23i	−1.24499	−	2.15638i
$789$	951.378	+	549.278i	1.20580	+	0.696170i
$790$	465.613			0.589383
$791$	1330.91	+	182.730i	1.68257	+	0.231012i
$792$		−	3065.46i		−	3.87053i
$793$	−163.281	−	94.2701i	−0.205902	−	0.118878i
$794$	255.864	+	443.170i	0.322247	+	0.558148i
$795$	294.573	+	510.216i	0.370532	+	0.641781i
$796$	1352.98	−	2343.44i	1.69973	−	2.94402i
$797$		−	1223.37i		−	1.53497i	−0.641068	−	0.767484i	$-0.721508\pi$
$797$		−	1223.37i		−	1.53497i	0.641068	−	0.767484i	$-0.278492\pi$
$798$	807.864	−	1040.83i	1.01236	−	1.30430i
$799$	246.554			0.308578
$800$	−102.737	+	177.946i	−0.128422	+	0.222433i
$801$	−374.552	−	648.743i	−0.467605	−	0.809916i
$802$	814.766	+	1411.22i	1.01592	+	1.75962i
$803$	880.619	−	1525.28i	1.09666	−	1.89947i
$804$			1613.71i			2.00710i
$805$	210.718	−	85.9164i	0.261761	−	0.106728i
$806$		−	337.380i		−	0.418585i
$807$	763.466	+	440.787i	0.946054	+	0.546205i
$808$	246.393	+	426.765i	0.304941	+	0.528174i
$809$	1051.00	−	606.798i	1.29914	−	0.750059i	0.318884	−	0.947794i	$-0.396692\pi$
$809$	1051.00	−	606.798i	1.29914	−	0.750059i	0.980256	+	0.197735i	$0.0633585\pi$
$810$	−164.611	−	95.0384i	−0.203224	−	0.117331i
$811$		−	1557.59i		−	1.92059i	−0.278995	−	0.960293i	$-0.590001\pi$
$811$		−	1557.59i		−	1.92059i	0.278995	−	0.960293i	$-0.409999\pi$
$812$	−1698.05	+	692.348i	−2.09119	+	0.852646i
$813$		−	2177.87i		−	2.67880i
$814$	606.954	+	350.425i	0.745643	+	0.430497i
$815$	−109.644	+	63.3030i	−0.134533	+	0.0776724i
$816$	−266.104	−	460.906i	−0.326108	−	0.564836i
$817$	−321.715	+	557.228i	−0.393777	+	0.682041i
$818$			1457.69i			1.78202i
$819$	193.635	−	249.473i	0.236428	−	0.304607i
$820$	156.862	+	376.684i	0.191296	+	0.459371i
$821$	−322.425	+	558.457i	−0.392723	+	0.680216i	−0.992808	−	0.119721i	$-0.961800\pi$
$821$	−322.425	+	558.457i	−0.392723	+	0.680216i	0.600085	+	0.799936i	$0.295133\pi$
$822$	−278.626	+	160.865i	−0.338962	+	0.195700i
$823$	−740.325	+	427.427i	−0.899544	+	0.519352i	−0.877052	−	0.480395i	$-0.840493\pi$
$823$	−740.325	+	427.427i	−0.899544	+	0.519352i	−0.0224920	+	0.999747i	$0.507160\pi$
$824$	1436.77	+	829.521i	1.74365	+	1.00670i
$825$			1459.89i			1.76956i
$826$	−93.3110	+	679.627i	−0.112967	+	0.822793i
$827$			76.8617i			0.0929404i	0.998920	+	0.0464702i	$0.0147972\pi$
$827$			76.8617i			0.0929404i	−0.998920	+	0.0464702i	$0.985203\pi$
$828$	1867.72	−	3234.99i	2.25570	−	3.90699i
$829$	989.076	−	571.044i	1.19310	−	0.688834i	0.234088	−	0.972215i	$-0.424789\pi$
$829$	989.076	−	571.044i	1.19310	−	0.688834i	0.959007	+	0.283381i	$0.0914561\pi$
$830$	−209.492	−	362.850i	−0.252400	−	0.437169i
$831$	665.308	−	1152.35i	0.800611	−	1.38670i
$832$	−130.864			−0.157288
$833$	64.9566	+	253.639i	0.0779791	+	0.304489i
$834$			1476.14i			1.76995i
$835$	−36.1129	−	20.8498i	−0.0432490	−	0.0249698i
$836$	933.587	−	539.006i	1.11673	−	0.644745i
$837$	1179.16	−	680.789i	1.40880	−	0.813369i
$838$	1717.11	+	991.373i	2.04906	+	1.18302i
$839$	366.100			0.436353			0.218177	−	0.975909i	$-0.429989\pi$
$839$	366.100			0.436353			0.218177	+	0.975909i	$0.429989\pi$
$840$	−87.1112	+	634.471i	−0.103704	+	0.755322i
$841$	−155.273			−0.184630
$842$	954.818	+	551.265i	1.13399	+	0.654708i
$843$	−692.927	+	400.062i	−0.821978	+	0.474569i
$844$	−1755.68	+	1013.64i	−2.08019	+	1.20100i
$845$	167.832	+	96.8979i	0.198618	+	0.114672i
$846$	−2686.53			−3.17557
$847$	−124.253	+	160.084i	−0.146698	+	0.189001i
$848$		−	1911.45i		−	2.25406i
$849$	1471.16	+	849.376i	1.73282	+	1.00044i
$850$	220.772	+	382.388i	0.259732	+	0.449869i
$851$	221.214	+	383.154i	0.259946	+	0.450240i
$852$	1859.53	+	1073.60i	2.18255	+	1.26010i
$853$		−	422.641i		−	0.495476i	−0.968827	−	0.247738i	$-0.920313\pi$
$853$		−	422.641i		−	0.495476i	0.968827	−	0.247738i	$-0.0796872\pi$
$854$	−1577.19	+	643.073i	−1.84683	+	0.753012i
$855$		−	211.157i		−	0.246967i
$856$	202.950	−	351.521i	0.237092	−	0.410655i
$857$	1004.49	−	579.945i	1.17211	−	0.676716i	0.217931	−	0.975964i	$-0.430069\pi$
$857$	1004.49	−	579.945i	1.17211	−	0.676716i	0.954175	+	0.299249i	$0.0967360\pi$
$858$	511.387	−	295.250i	0.596023	−	0.344114i
$859$	−271.596	−	156.806i	−0.316177	−	0.182545i	0.333510	−	0.942746i	$-0.391767\pi$
$859$	−271.596	−	156.806i	−0.316177	−	0.182545i	−0.649687	+	0.760202i	$0.725100\pi$
$860$		−	603.708i		−	0.701986i
$861$	−1023.07	−	1030.58i	−1.18824	−	1.19696i
$862$	−1454.57			−1.68743
$863$	−8.01538	+	13.8830i	−0.00928781	+	0.0160870i	−0.870632	−	0.491935i	$-0.836290\pi$
$863$	−8.01538	+	13.8830i	−0.00928781	+	0.0160870i	0.861344	+	0.508022i	$0.169623\pi$
$864$	167.707	+	290.477i	0.194105	+	0.336200i
$865$	−154.167	−	267.026i	−0.178228	−	0.308700i
$866$	−964.949	−	557.114i	−1.11426	−	0.643318i
$867$	1317.82			1.51997
$868$	−1624.68	−	1261.04i	−1.87176	−	1.45281i
$869$	−1355.78			−1.56016
$870$	−335.815	+	581.649i	−0.385994	+	0.668562i
$871$	−90.4343	+	52.2122i	−0.103828	+	0.0599452i
$872$	−191.278	+	110.435i	−0.219356	+	0.126645i
$873$	673.296	−	1166.18i	0.771244	−	1.33583i
$874$	1008.50			1.15389
$875$	55.4453	−	403.834i	0.0633660	−	0.461524i
$876$			6039.99i			6.89496i
$877$	−2.77665	+	4.80931i	−0.00316608	+	0.00548382i	−0.867604	−	0.497256i	$-0.834341\pi$
$877$	−2.77665	+	4.80931i	−0.00316608	+	0.00548382i	0.864438	+	0.502739i	$0.167674\pi$
$878$	1298.35	+	2248.81i	1.47876	+	2.56129i
$879$	−436.468	−	755.985i	−0.496551	−	0.860051i
$880$	−144.524	+	250.322i	−0.164231	+	0.284457i
$881$		−	534.781i		−	0.607016i	−0.952829	−	0.303508i	$-0.901842\pi$
$881$		−	534.781i		−	0.607016i	0.952829	−	0.303508i	$-0.0981579\pi$
$882$	−707.789	−	2763.74i	−0.802482	−	3.13349i
$883$			843.664i			0.955452i	0.878509	+	0.477726i	$0.158539\pi$
$883$			843.664i			0.955452i	−0.878509	+	0.477726i	$0.841461\pi$
$884$	60.2573	−	104.369i	0.0681643	−	0.118064i
$885$	84.7711	+	146.828i	0.0957865	+	0.165907i
$886$	−865.069	−	1498.34i	−0.976376	−	1.69113i
$887$	274.682	−	475.764i	0.309676	−	0.536374i	−0.668616	−	0.743608i	$-0.733113\pi$
$887$	274.682	−	475.764i	0.309676	−	0.536374i	0.978291	+	0.207234i	$0.0664462\pi$
$888$	−1245.13			−1.40217
$889$	−1136.84	−	156.085i	−1.27879	−	0.175574i
$890$			189.758i			0.213211i
$891$	479.319	+	276.735i	0.537956	+	0.310589i
$892$	2049.62	−	1183.35i	2.29778	−	1.32662i
$893$	−244.716	−	423.860i	−0.274038	−	0.474647i
$894$	2272.33	+	1311.93i	2.54176	+	1.46748i
$895$	−286.081			−0.319644
$896$	−874.591	+	1126.80i	−0.976106	+	1.25759i
$897$	372.767			0.415571
$898$	−1071.52	+	1855.92i	−1.19323	+	2.06673i
$899$	−558.682	−	967.666i	−0.621448	−	1.07638i
$900$	−1623.27	−	2811.59i	−1.80363	−	3.12399i
$901$	−449.337	−	259.425i	−0.498710	−	0.287930i
$902$	−676.890	−	1625.46i	−0.750432	−	1.80206i
$903$	811.184	+	1989.50i	0.898321	+	2.20321i
$904$	−2893.87			−3.20118
$905$	17.8852	+	10.3260i	0.0197626	+	0.0114099i
$906$	−777.675	+	448.991i	−0.858361	+	0.495575i
$907$	77.1784	+	133.677i	0.0850919	+	0.147384i	0.905430	−	0.424495i	$-0.139548\pi$
$907$	77.1784	+	133.677i	0.0850919	+	0.147384i	−0.820338	+	0.571878i	$0.806215\pi$
$908$	−996.041	+	1725.19i	−1.09696	+	1.89999i
$909$	−542.542			−0.596856
$910$	−74.0762	+	30.2033i	−0.0814024	+	0.0331904i
$911$	−850.465			−0.933551			−0.466776	−	0.884376i	$-0.654584\pi$
$911$	−850.465			−0.933551			−0.466776	+	0.884376i	$0.654584\pi$
$912$	−528.241	+	914.940i	−0.579212	+	1.00322i
$913$	610.003	+	1056.56i	0.668130	+	1.15724i
$914$	−122.394	+	70.6640i	−0.133910	+	0.0773129i
$915$	−210.475	+	364.554i	−0.230028	+	0.398420i
$916$	3300.89			3.60360
$917$	15.4074	+	11.9588i	0.0168019	+	0.0130412i
$918$	720.770			0.785153
$919$	502.357	+	290.036i	0.546634	+	0.315600i	0.747763	−	0.663965i	$-0.231128\pi$
$919$	502.357	+	290.036i	0.546634	+	0.315600i	−0.201129	+	0.979565i	$0.564461\pi$
$920$	−424.524	+	245.099i	−0.461439	+	0.266412i
$921$	−1180.34	+	681.472i	−1.28159	+	0.739927i
$922$	−1529.42	−	883.009i	−1.65880	−	0.957711i
$923$			138.948i			0.150539i
$924$	489.630	−	3566.20i	0.529903	−	3.85953i
$925$	384.522			0.415699
$926$	2205.25	+	1273.20i	2.38148	+	1.37495i
$927$	−1581.84	+	913.278i	−1.70641	+	0.985198i
$928$	238.377	−	137.627i	0.256872	−	0.148305i
$929$	−264.540	+	458.197i	−0.284758	+	0.493215i	−0.972550	−	0.232692i	$-0.925246\pi$
$929$	−264.540	+	458.197i	−0.284758	+	0.493215i	0.687793	+	0.725907i	$0.258580\pi$
$930$	−753.263			−0.809960
$931$	371.568	−	363.417i	0.399106	−	0.390352i
$932$		−	756.711i		−	0.811922i
$933$	−276.120	+	478.254i	−0.295949	+	0.512598i
$934$	258.061	−	148.992i	0.276297	−	0.159520i
$935$	39.2300	+	67.9484i	0.0419573	+	0.0726721i
$936$	−340.143	+	589.144i	−0.363400	+	0.629428i
$937$	67.1075			0.0716196			0.0358098	−	0.999359i	$-0.488599\pi$
$937$	67.1075			0.0716196			0.0358098	+	0.999359i	$0.488599\pi$
$938$	−128.317	+	934.593i	−0.136799	+	0.996368i
$939$	−259.770			−0.276645
$940$	397.692	+	229.608i	0.423077	+	0.244264i
$941$	1254.79	−	724.453i	1.33346	−	0.769876i	0.347635	−	0.937630i	$-0.386985\pi$
$941$	1254.79	−	724.453i	1.33346	−	0.769876i	0.985829	+	0.167754i	$0.0536515\pi$
$942$	−415.153	−	719.066i	−0.440714	−	0.763340i
$943$	143.000	−	1102.29i	0.151644	−	1.16892i
$944$		−	550.069i		−	0.582700i
$945$	−255.038	−	197.954i	−0.269882	−	0.209475i
$946$			2605.11i			2.75381i
$947$	210.727	−	364.990i	0.222521	−	0.385417i	−0.733052	−	0.680172i	$-0.761905\pi$
$947$	210.727	−	364.990i	0.222521	−	0.385417i	0.955573	+	0.294756i	$0.0952382\pi$
$948$	4026.60	−	2324.76i	4.24747	−	2.45228i
$949$	−338.489	+	195.427i	−0.356679	+	0.205929i
$950$	438.252	−	759.075i	0.461318	−	0.799026i
$951$			440.825i			0.463538i
$952$	−212.944	−	522.265i	−0.223681	−	0.548597i
$953$	−242.664			−0.254631			−0.127316	−	0.991862i	$-0.540636\pi$
$953$	−242.664			−0.254631			−0.127316	+	0.991862i	$0.540636\pi$
$954$	4896.13	+	2826.78i	5.13222	+	2.96309i
$955$	−205.256	−	355.514i	−0.214928	−	0.372266i
$956$	1685.46	−	973.101i	1.76303	−	1.01789i
$957$	977.834	−	1693.66i	1.02177	−	1.76976i
$958$	−1217.92			−1.27132
$959$	−117.521	+	47.9172i	−0.122545	+	0.0499658i
$960$			292.178i			0.304352i
$961$	146.087	−	253.029i	0.152015	−	0.263298i
$962$	−77.7661	−	134.695i	−0.0808380	−	0.140015i
$963$	223.443	+	387.014i	0.232028	+	0.401884i
$964$	813.669	+	469.772i	0.844055	+	0.487315i
$965$	410.961			0.425867
$966$	2064.81	−	2660.24i	2.13748	−	2.75387i
$967$		−	1694.27i		−	1.75209i	−0.482228	−	0.876046i	$-0.660172\pi$
$967$		−	1694.27i		−	1.75209i	0.482228	−	0.876046i	$-0.339828\pi$
$968$	218.265	−	378.047i	0.225481	−	0.390544i
$969$	143.388	+	248.355i	0.147975	+	0.256300i
$970$	−295.410	+	170.555i	−0.304546	+	0.175830i
$971$	−414.466	+	717.876i	−0.426844	+	0.739316i	−0.996591	−	0.0825046i	$-0.973708\pi$
$971$	−414.466	+	717.876i	−0.426844	+	0.739316i	0.569746	+	0.821821i	$0.307041\pi$
$972$	974.939			1.00302
$973$	−79.2052	+	576.888i	−0.0814031	+	0.592897i
$974$	2700.13			2.77221
$975$	161.989	−	280.573i	0.166143	−	0.287767i
$976$	1182.77	−	682.874i	1.21186	−	0.699666i
$977$	509.291	−	294.039i	0.521280	−	0.300961i	−0.216178	−	0.976354i	$-0.569359\pi$
$977$	509.291	−	294.039i	0.521280	−	0.300961i	0.737458	+	0.675393i	$0.236026\pi$
$978$	−936.788	+	1622.56i	−0.957861	+	1.65906i
$979$		−	552.542i		−	0.564394i
$980$	−131.431	+	469.613i	−0.134113	+	0.479197i
$981$		−	243.171i		−	0.247880i
$982$	−1244.64	+	2155.79i	−1.26746	+	2.19530i
$983$	−656.665	+	379.126i	−0.668021	+	0.385682i	−0.795326	−	0.606181i	$-0.792701\pi$
$983$	−656.665	+	379.126i	−0.668021	+	0.385682i	0.127305	+	0.991864i	$0.459367\pi$
$984$	2485.34	+	1899.62i	2.52575	+	1.93051i
$985$	−245.503	−	141.741i	−0.249241	−	0.143899i
$986$		−	591.492i		−	0.599891i
$987$	−1619.10	−	222.298i	−1.64043	−	0.225226i
$988$	−239.232			−0.242138
$989$	−822.268	+	1424.21i	−0.831414	+	1.44005i
$990$	−427.464	−	740.389i	−0.431782	−	0.747868i
$991$	−91.4080	+	52.7744i	−0.0922381	+	0.0532537i	−0.545410	−	0.838170i	$-0.683626\pi$
$991$	−91.4080	+	52.7744i	−0.0922381	+	0.0532537i	0.453171	+	0.891423i	$0.350293\pi$
$992$	267.350	+	154.355i	0.269506	+	0.155599i
$993$		−	1523.41i		−	1.53415i
$994$	991.597	+	769.651i	0.997582	+	0.774297i
$995$		−	390.956i		−	0.392920i
$996$	−3623.35	−	2091.94i	−3.63790	−	2.10034i
$997$	440.966	+	763.775i	0.442293	+	0.766074i	0.997859	−	0.0653986i	$-0.0208319\pi$
$997$	440.966	+	763.775i	0.442293	+	0.766074i	−0.555566	+	0.831472i	$0.687499\pi$
$998$	−239.320	+	138.171i	−0.239800	+	0.138448i
$999$	313.844	−	543.594i	0.314158	−	0.544138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.i.a.40.6	yes	108
7.3	odd	6	inner	287.3.i.a.122.5	yes	108
41.40	even	2	inner	287.3.i.a.40.5	✓	108
287.122	odd	6	inner	287.3.i.a.122.6	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.i.a.40.5	✓	108	41.40	even	2	inner
287.3.i.a.40.6	yes	108	1.1	even	1	trivial
287.3.i.a.122.5	yes	108	7.3	odd	6	inner
287.3.i.a.122.6	yes	108	287.122	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75354 + 3.03722i) q^{2} +(2.52990 + 4.38192i) q^{3} +(-4.14980 - 7.18766i) q^{4} +(-1.03847 - 0.599559i) q^{5} -17.7451 q^{6} +(-6.93494 - 0.952149i) q^{7} +15.0790 q^{8} +(-8.30079 + 14.3774i) q^{9} +O(q^{10})\)	\(q+(-1.75354 + 3.03722i) q^{2} +(2.52990 + 4.38192i) q^{3} +(-4.14980 - 7.18766i) q^{4} +(-1.03847 - 0.599559i) q^{5} -17.7451 q^{6} +(-6.93494 - 0.952149i) q^{7} +15.0790 q^{8} +(-8.30079 + 14.3774i) q^{9} +(3.64198 - 2.10270i) q^{10} +(-10.6048 + 6.12269i) q^{11} +(20.9972 - 36.3681i) q^{12} +2.71749 q^{13} +(15.0526 - 19.3933i) q^{14} -6.06730i q^{15} +(-9.84248 + 17.0477i) q^{16} +(2.67168 + 4.62748i) q^{17} +(-29.1115 - 50.4226i) q^{18} +(5.30352 - 9.18597i) q^{19} +9.95220i q^{20} +(-13.3725 - 32.7972i) q^{21} -42.9455i q^{22} +(13.5552 - 23.4783i) q^{23} +(38.1485 + 66.0751i) q^{24} +(-11.7811 - 20.4054i) q^{25} +(-4.76523 + 8.25361i) q^{26} -38.4625 q^{27} +(21.9349 + 53.7973i) q^{28} +31.5638i q^{29} +(18.4277 + 10.6392i) q^{30} +(-30.6575 + 17.7001i) q^{31} +(-4.36028 - 7.55222i) q^{32} +(-53.6583 - 30.9796i) q^{33} -18.7396 q^{34} +(6.63084 + 5.14668i) q^{35} +137.786 q^{36} +(-8.15975 + 14.1331i) q^{37} +(18.5999 + 32.2159i) q^{38} +(6.87498 + 11.9078i) q^{39} +(-15.6591 - 9.04077i) q^{40} +(37.8493 - 15.7616i) q^{41} +(123.061 + 16.8960i) q^{42} -60.6607 q^{43} +(88.0157 + 50.8159i) q^{44} +(17.2402 - 9.95363i) q^{45} +(47.5391 + 82.3402i) q^{46} +(23.0711 - 39.9602i) q^{47} -99.6020 q^{48} +(47.1868 + 13.2062i) q^{49} +82.6342 q^{50} +(-13.5182 + 23.4141i) q^{51} +(-11.2770 - 19.5324i) q^{52} +(-84.0927 + 48.5509i) q^{53} +(67.4455 - 116.819i) q^{54} +14.6837 q^{55} +(-104.572 - 14.3575i) q^{56} +53.6695 q^{57} +(-95.8662 - 55.3484i) q^{58} +(-24.1999 + 13.9718i) q^{59} +(-43.6097 + 25.1781i) q^{60} +(-60.0851 - 34.6901i) q^{61} -124.151i q^{62} +(71.2549 - 91.8028i) q^{63} -48.1562 q^{64} +(-2.82202 - 1.62930i) q^{65} +(188.184 - 108.648i) q^{66} +(-33.2786 + 19.2134i) q^{67} +(22.1739 - 38.4063i) q^{68} +137.173 q^{69} +(-27.2590 + 11.1144i) q^{70} +51.1309i q^{71} +(-125.168 + 216.797i) q^{72} +(-124.559 + 71.9143i) q^{73} +(-28.6169 - 49.5659i) q^{74} +(59.6098 - 103.247i) q^{75} -88.0342 q^{76} +(79.3735 - 32.3632i) q^{77} -48.2222 q^{78} +(95.8844 + 55.3589i) q^{79} +(20.4422 - 11.8023i) q^{80} +(-22.5991 - 39.1428i) q^{81} +(-18.4989 + 142.595i) q^{82} -99.6298i q^{83} +(-180.242 + 232.219i) q^{84} -6.40732i q^{85} +(106.371 - 184.240i) q^{86} +(-138.310 + 79.8533i) q^{87} +(-159.910 + 92.3243i) q^{88} +(-22.5612 + 39.0772i) q^{89} +69.8163i q^{90} +(-18.8456 - 2.58746i) q^{91} -225.005 q^{92} +(-155.121 - 89.5589i) q^{93} +(80.9120 + 140.144i) q^{94} +(-11.0151 + 6.35955i) q^{95} +(22.0621 - 38.2127i) q^{96} -81.1123 q^{97} +(-122.854 + 120.159i) q^{98} -203.293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{2} - 106 q^{4} - 6 q^{5} + 20 q^{8} - 136 q^{9}+O(q^{10}) \) 108 * q - 2 * q^2 - 106 * q^4 - 6 * q^5 + 20 * q^8 - 136 * q^9	\( 108 q - 2 q^{2} - 106 q^{4} - 6 q^{5} + 20 q^{8} - 136 q^{9} - 60 q^{10} - 202 q^{16} - 4 q^{18} - 56 q^{21} + 12 q^{23} + 208 q^{25} + 30 q^{31} - 152 q^{32} + 24 q^{33} + 284 q^{36} - 52 q^{37} + 30 q^{39} + 24 q^{40} - 78 q^{42} - 112 q^{43} - 210 q^{45} - 264 q^{46} + 380 q^{49} - 48 q^{50} + 180 q^{51} + 168 q^{57} - 138 q^{59} - 294 q^{61} + 268 q^{64} - 612 q^{66} + 74 q^{72} + 48 q^{73} - 194 q^{74} + 256 q^{77} + 184 q^{78} + 12 q^{80} - 314 q^{81} + 474 q^{82} + 828 q^{84} - 496 q^{86} + 1122 q^{87} - 786 q^{91} + 160 q^{92} - 176 q^{98}+O(q^{100}) \) 108 * q - 2 * q^2 - 106 * q^4 - 6 * q^5 + 20 * q^8 - 136 * q^9 - 60 * q^10 - 202 * q^16 - 4 * q^18 - 56 * q^21 + 12 * q^23 + 208 * q^25 + 30 * q^31 - 152 * q^32 + 24 * q^33 + 284 * q^36 - 52 * q^37 + 30 * q^39 + 24 * q^40 - 78 * q^42 - 112 * q^43 - 210 * q^45 - 264 * q^46 + 380 * q^49 - 48 * q^50 + 180 * q^51 + 168 * q^57 - 138 * q^59 - 294 * q^61 + 268 * q^64 - 612 * q^66 + 74 * q^72 + 48 * q^73 - 194 * q^74 + 256 * q^77 + 184 * q^78 + 12 * q^80 - 314 * q^81 + 474 * q^82 + 828 * q^84 - 496 * q^86 + 1122 * q^87 - 786 * q^91 + 160 * q^92 - 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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