LMFDB - Embedded newform 210.3.s.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(11,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("210.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.s (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	210.11
Dual form			210.3.s.a.191.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-1.44013 + 2.63174i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(0.0971326 + 4.24153i) q^{6} +(1.98659 - 6.71219i) q^{7} -2.82843i q^{8} +(-4.85208 - 7.58006i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-1.44013 + 2.63174i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(0.0971326 + 4.24153i) q^{6} +(1.98659 - 6.71219i) q^{7} -2.82843i q^{8} +(-4.85208 - 7.58006i) q^{9} +(1.58114 - 2.73861i) q^{10} +(11.3546 + 6.55561i) q^{11} +(3.11818 + 5.12611i) q^{12} +20.0024 q^{13} +(-2.31317 - 9.62545i) q^{14} +(0.153580 + 6.70645i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(7.44339 + 4.29745i) q^{17} +(-11.3025 - 5.85271i) q^{18} +(3.25218 + 5.63294i) q^{19} -4.47214i q^{20} +(14.8038 + 14.8946i) q^{21} +18.5421 q^{22} +(-33.1042 + 19.1127i) q^{23} +(7.44368 + 4.07329i) q^{24} +(2.50000 - 4.33013i) q^{25} +(24.4978 - 14.1438i) q^{26} +(26.9363 - 1.85315i) q^{27} +(-9.63926 - 10.1531i) q^{28} -23.6222i q^{29} +(4.93027 + 8.10509i) q^{30} +(22.0875 - 38.2567i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-33.6048 + 20.4415i) q^{33} +12.1550 q^{34} +(-3.65744 - 15.2192i) q^{35} +(-17.9811 + 0.823981i) q^{36} +(-9.37387 - 16.2360i) q^{37} +(7.96618 + 4.59928i) q^{38} +(-28.8060 + 52.6410i) q^{39} +(-3.16228 - 5.47723i) q^{40} +14.7844i q^{41} +(28.6629 + 7.77420i) q^{42} -36.8805 q^{43} +(22.7093 - 13.1112i) q^{44} +(-17.8708 - 9.25394i) q^{45} +(-27.0295 + 46.8165i) q^{46} +(-69.0243 + 39.8512i) q^{47} +(11.9969 - 0.274732i) q^{48} +(-41.1069 - 26.6687i) q^{49} -7.07107i q^{50} +(-22.0292 + 13.4002i) q^{51} +(20.0024 - 34.6452i) q^{52} +(-22.0573 - 12.7348i) q^{53} +(31.6798 - 21.3165i) q^{54} +29.3176 q^{55} +(-18.9849 - 5.61892i) q^{56} +(-19.5080 + 0.446740i) q^{57} +(-16.7034 - 28.9311i) q^{58} +(87.3032 + 50.4045i) q^{59} +(11.7695 + 6.44044i) q^{60} +(-24.7419 - 42.8542i) q^{61} -62.4729i q^{62} +(-60.5179 + 17.5096i) q^{63} -8.00000 q^{64} +(38.7345 - 22.3634i) q^{65} +(-26.7029 + 48.7978i) q^{66} +(-29.3214 + 50.7862i) q^{67} +(14.8868 - 8.59489i) q^{68} +(-2.62544 - 114.646i) q^{69} +(-15.2410 - 16.0534i) q^{70} +82.7346i q^{71} +(-21.4397 + 13.7237i) q^{72} +(-34.8005 + 60.2763i) q^{73} +(-22.9612 - 13.2567i) q^{74} +(7.79544 + 12.8153i) q^{75} +13.0087 q^{76} +(66.5595 - 63.1912i) q^{77} +(1.94288 + 84.8407i) q^{78} +(-0.932103 - 1.61445i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-33.9147 + 73.5581i) q^{81} +(10.4542 + 18.1071i) q^{82} +123.057i q^{83} +(40.6019 - 10.7463i) q^{84} +19.2188 q^{85} +(-45.1692 + 26.0785i) q^{86} +(62.1673 + 34.0189i) q^{87} +(18.5421 - 32.1158i) q^{88} +(53.2502 - 30.7440i) q^{89} +(-28.4307 + 1.30283i) q^{90} +(39.7365 - 134.260i) q^{91} +76.4510i q^{92} +(68.8727 + 113.223i) q^{93} +(-56.3581 + 97.6151i) q^{94} +(12.5956 + 7.27210i) q^{95} +(14.4988 - 8.81953i) q^{96} +113.892 q^{97} +(-69.2031 - 3.59539i) q^{98} +(-5.40170 - 117.877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} - 8 q^{6} + 20 q^{7} - 4 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 - 8 * q^6 + 20 * q^7 - 4 * q^9	$ 40 q + 40 q^{4} - 8 q^{6} + 20 q^{7} - 4 q^{9} + 136 q^{13} + 40 q^{15} - 80 q^{16} + 16 q^{18} - 140 q^{19} + 36 q^{21} - 8 q^{24} + 100 q^{25} - 120 q^{27} - 16 q^{28} - 20 q^{30} + 4 q^{31} + 232 q^{33} + 32 q^{34} - 16 q^{36} - 76 q^{37} - 4 q^{39} + 128 q^{42} - 104 q^{43} - 20 q^{45} - 56 q^{46} + 100 q^{49} + 168 q^{51} + 136 q^{52} + 40 q^{54} + 80 q^{55} + 200 q^{57} + 144 q^{58} + 40 q^{60} - 120 q^{61} - 324 q^{63} - 320 q^{64} - 288 q^{66} - 20 q^{67} - 416 q^{69} - 120 q^{70} - 32 q^{72} - 476 q^{73} - 560 q^{76} - 192 q^{78} - 508 q^{79} - 304 q^{81} + 224 q^{82} + 144 q^{84} - 240 q^{85} - 324 q^{87} + 468 q^{91} + 204 q^{93} + 400 q^{94} + 16 q^{96} - 512 q^{97} + 208 q^{99}+O(q^{100}) $ 40 * q + 40 * q^4 - 8 * q^6 + 20 * q^7 - 4 * q^9 + 136 * q^13 + 40 * q^15 - 80 * q^16 + 16 * q^18 - 140 * q^19 + 36 * q^21 - 8 * q^24 + 100 * q^25 - 120 * q^27 - 16 * q^28 - 20 * q^30 + 4 * q^31 + 232 * q^33 + 32 * q^34 - 16 * q^36 - 76 * q^37 - 4 * q^39 + 128 * q^42 - 104 * q^43 - 20 * q^45 - 56 * q^46 + 100 * q^49 + 168 * q^51 + 136 * q^52 + 40 * q^54 + 80 * q^55 + 200 * q^57 + 144 * q^58 + 40 * q^60 - 120 * q^61 - 324 * q^63 - 320 * q^64 - 288 * q^66 - 20 * q^67 - 416 * q^69 - 120 * q^70 - 32 * q^72 - 476 * q^73 - 560 * q^76 - 192 * q^78 - 508 * q^79 - 304 * q^81 + 224 * q^82 + 144 * q^84 - 240 * q^85 - 324 * q^87 + 468 * q^91 + 204 * q^93 + 400 * q^94 + 16 * q^96 - 512 * q^97 + 208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	−1.44013	+	2.63174i	−0.480042	+	0.877246i
$3$	−1.44013	+	2.63174i	−0.480042	+	0.877246i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$	0.0971326	+	4.24153i	0.0161888	+	0.706921i
$7$	1.98659	−	6.71219i	0.283798	−	0.958884i
$7$	1.98659	−	6.71219i	0.283798	−	0.958884i
$8$		−	2.82843i		−	0.353553i
$9$	−4.85208	−	7.58006i	−0.539120	−	0.842229i
$10$	1.58114	−	2.73861i	0.158114	−	0.273861i
$11$	11.3546	+	6.55561i	1.03224	+	0.595965i	0.917626	−	0.397445i	$-0.130103\pi$
$11$	11.3546	+	6.55561i	1.03224	+	0.595965i	0.114615	+	0.993410i	$0.463437\pi$
$12$	3.11818	+	5.12611i	0.259848	+	0.427176i
$13$	20.0024			1.53865			0.769323	−	0.638860i	$-0.220594\pi$
$13$	20.0024			1.53865			0.769323	+	0.638860i	$0.220594\pi$
$14$	−2.31317	−	9.62545i	−0.165226	−	0.687532i
$15$	0.153580	+	6.70645i	0.0102387	+	0.447096i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	7.44339	+	4.29745i	0.437847	+	0.252791i	0.702684	−	0.711502i	$-0.251985\pi$
$17$	7.44339	+	4.29745i	0.437847	+	0.252791i	−0.264837	+	0.964293i	$0.585318\pi$
$18$	−11.3025	−	5.85271i	−0.627915	−	0.325150i
$19$	3.25218	+	5.63294i	0.171167	+	0.296471i	0.938828	−	0.344386i	$-0.111913\pi$
$19$	3.25218	+	5.63294i	0.171167	+	0.296471i	−0.767661	+	0.640856i	$0.778579\pi$
$20$		−	4.47214i		−	0.223607i
$21$	14.8038	+	14.8946i	0.704942	+	0.709265i
$22$	18.5421			0.842821
$23$	−33.1042	+	19.1127i	−1.43931	+	0.830989i	−0.997802	−	0.0662661i	$-0.978891\pi$
$23$	−33.1042	+	19.1127i	−1.43931	+	0.830989i	−0.441513	+	0.897255i	$0.645558\pi$
$24$	7.44368	+	4.07329i	0.310153	+	0.169720i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	24.4978	−	14.1438i	0.942224	−	0.543993i
$27$	26.9363	−	1.85315i	0.997642	−	0.0686351i
$28$	−9.63926	−	10.1531i	−0.344259	−	0.362609i
$29$		−	23.6222i		−	0.814557i	−0.913304	−	0.407279i	$-0.866478\pi$
$29$		−	23.6222i		−	0.814557i	0.913304	−	0.407279i	$-0.133522\pi$
$30$	4.93027	+	8.10509i	0.164342	+	0.270170i
$31$	22.0875	−	38.2567i	0.712500	−	1.23409i	−0.251416	−	0.967879i	$-0.580896\pi$
$31$	22.0875	−	38.2567i	0.712500	−	1.23409i	0.963916	−	0.266207i	$-0.0857706\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	−33.6048	+	20.4415i	−1.01833	+	0.619441i
$34$	12.1550			0.357500
$35$	−3.65744	−	15.2192i	−0.104498	−	0.434833i
$36$	−17.9811	+	0.823981i	−0.499476	+	0.0228884i
$37$	−9.37387	−	16.2360i	−0.253348	−	0.438811i	0.711098	−	0.703093i	$-0.248198\pi$
$37$	−9.37387	−	16.2360i	−0.253348	−	0.438811i	−0.964445	+	0.264282i	$0.914865\pi$
$38$	7.96618	+	4.59928i	0.209636	+	0.121034i
$39$	−28.8060	+	52.6410i	−0.738614	+	1.34977i
$40$	−3.16228	−	5.47723i	−0.0790569	−	0.136931i
$41$			14.7844i			0.360595i	0.983612	+	0.180298i	$0.0577061\pi$
$41$			14.7844i			0.360595i	−0.983612	+	0.180298i	$0.942294\pi$
$42$	28.6629	+	7.77420i	0.682450	+	0.185100i
$43$	−36.8805			−0.857687			−0.428843	−	0.903379i	$-0.641079\pi$
$43$	−36.8805			−0.857687			−0.428843	+	0.903379i	$0.641079\pi$
$44$	22.7093	−	13.1112i	0.516120	−	0.297982i
$45$	−17.8708	−	9.25394i	−0.397128	−	0.205643i
$46$	−27.0295	+	46.8165i	−0.587598	+	1.01775i
$47$	−69.0243	+	39.8512i	−1.46860	+	0.847898i	−0.999381	−	0.0351824i	$-0.988799\pi$
$47$	−69.0243	+	39.8512i	−1.46860	+	0.847898i	−0.469222	+	0.883080i	$0.655465\pi$
$48$	11.9969	−	0.274732i	0.249934	−	0.00572359i
$49$	−41.1069	−	26.6687i	−0.838917	−	0.544260i
$50$		−	7.07107i		−	0.141421i
$51$	−22.0292	+	13.4002i	−0.431944	+	0.262749i
$52$	20.0024	−	34.6452i	0.384661	−	0.666253i
$53$	−22.0573	−	12.7348i	−0.416175	−	0.240279i	0.277264	−	0.960794i	$-0.410572\pi$
$53$	−22.0573	−	12.7348i	−0.416175	−	0.240279i	−0.693440	+	0.720515i	$0.743906\pi$
$54$	31.6798	−	21.3165i	0.586662	−	0.394750i
$55$	29.3176			0.533047
$56$	−18.9849	−	5.61892i	−0.339017	−	0.100338i
$57$	−19.5080	+	0.446740i	−0.342245	+	0.00783754i
$58$	−16.7034	−	28.9311i	−0.287990	−	0.498813i
$59$	87.3032	+	50.4045i	1.47972	+	0.854314i	0.999736	−	0.0229662i	$-0.00731103\pi$
$59$	87.3032	+	50.4045i	1.47972	+	0.854314i	0.479979	+	0.877280i	$0.340644\pi$
$60$	11.7695	+	6.44044i	0.196158	+	0.107341i
$61$	−24.7419	−	42.8542i	−0.405605	−	0.702529i	0.588787	−	0.808289i	$-0.299606\pi$
$61$	−24.7419	−	42.8542i	−0.405605	−	0.702529i	−0.994392	+	0.105760i	$0.966273\pi$
$62$		−	62.4729i		−	1.00763i
$63$	−60.5179	+	17.5096i	−0.960601	+	0.277930i
$64$	−8.00000			−0.125000
$65$	38.7345	−	22.3634i	0.595915	−	0.344052i
$66$	−26.7029	+	48.7978i	−0.404589	+	0.739361i
$67$	−29.3214	+	50.7862i	−0.437633	+	0.758003i	−0.997506	−	0.0705754i	$-0.977516\pi$
$67$	−29.3214	+	50.7862i	−0.437633	+	0.758003i	0.559873	+	0.828578i	$0.310850\pi$
$68$	14.8868	−	8.59489i	0.218923	−	0.126395i
$69$	−2.62544	−	114.646i	−0.0380499	−	1.66154i
$70$	−15.2410	−	16.0534i	−0.217729	−	0.229334i
$71$			82.7346i			1.16528i	0.812732	+	0.582638i	$0.197980\pi$
$71$			82.7346i			1.16528i	−0.812732	+	0.582638i	$0.802020\pi$
$72$	−21.4397	+	13.7237i	−0.297773	+	0.190608i
$73$	−34.8005	+	60.2763i	−0.476719	+	0.825702i	−0.999644	−	0.0266767i	$-0.991508\pi$
$73$	−34.8005	+	60.2763i	−0.476719	+	0.825702i	0.522925	+	0.852379i	$0.324841\pi$
$74$	−22.9612	−	13.2567i	−0.310286	−	0.179144i
$75$	7.79544	+	12.8153i	0.103939	+	0.170870i
$76$	13.0087			0.171167
$77$	66.5595	−	63.1912i	0.864409	−	0.820665i
$78$	1.94288	+	84.8407i	0.0249088	+	1.08770i
$79$	−0.932103	−	1.61445i	−0.0117988	−	0.0204361i	0.860066	−	0.510183i	$-0.170422\pi$
$79$	−0.932103	−	1.61445i	−0.0117988	−	0.0204361i	−0.871865	+	0.489747i	$0.837089\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$	−33.9147	+	73.5581i	−0.418700	+	0.908125i
$82$	10.4542	+	18.1071i	0.127490	+	0.220819i
$83$			123.057i			1.48262i	0.671164	+	0.741309i	$0.265795\pi$
$83$			123.057i			1.48262i	−0.671164	+	0.741309i	$0.734205\pi$
$84$	40.6019	−	10.7463i	0.483356	−	0.127932i
$85$	19.2188			0.226103
$86$	−45.1692	+	26.0785i	−0.525224	+	0.303238i
$87$	62.1673	+	34.0189i	0.714567	+	0.391022i
$88$	18.5421	−	32.1158i	0.210705	−	0.364952i
$89$	53.2502	−	30.7440i	0.598316	−	0.345438i	−0.170063	−	0.985433i	$-0.554397\pi$
$89$	53.2502	−	30.7440i	0.598316	−	0.345438i	0.768379	+	0.639995i	$0.221064\pi$
$90$	−28.4307	+	1.30283i	−0.315896	+	0.0144759i
$91$	39.7365	−	134.260i	0.436665	−	1.47538i
$92$			76.4510i			0.830989i
$93$	68.8727	+	113.223i	0.740567	+	1.21745i
$94$	−56.3581	+	97.6151i	−0.599554	+	1.03846i
$95$	12.5956	+	7.27210i	0.132586	+	0.0765484i
$96$	14.4988	−	8.81953i	0.151029	−	0.0918701i
$97$	113.892			1.17414			0.587071	−	0.809535i	$-0.300281\pi$
$97$	113.892			1.17414			0.587071	+	0.809535i	$0.300281\pi$
$98$	−69.2031	−	3.59539i	−0.706154	−	0.0366877i
$99$	−5.40170	−	117.877i	−0.0545626	−	1.19068i
$100$	−5.00000	−	8.66025i	−0.0500000	−	0.0866025i
$101$	−145.485	−	83.9958i	−1.44044	−	0.831641i	−0.442566	−	0.896736i	$-0.645932\pi$
$101$	−145.485	−	83.9958i	−1.44044	−	0.831641i	−0.997879	+	0.0650949i	$0.979265\pi$
$102$	−17.5047	+	31.9888i	−0.171615	+	0.313616i
$103$	−36.3361	−	62.9360i	−0.352778	−	0.611029i	0.633957	−	0.773368i	$-0.281429\pi$
$103$	−36.3361	−	62.9360i	−0.352778	−	0.611029i	−0.986735	+	0.162339i	$0.948096\pi$
$104$		−	56.5753i		−	0.543993i
$105$	45.3200	+	12.2921i	0.431619	+	0.117068i
$106$	−36.0194			−0.339806
$107$	−30.0146	+	17.3289i	−0.280510	+	0.161953i	−0.633654	−	0.773616i	$-0.718446\pi$
$107$	−30.0146	+	17.3289i	−0.280510	+	0.161953i	0.353144	+	0.935569i	$0.385113\pi$
$108$	23.7266	−	48.5082i	0.219691	−	0.449150i
$109$	3.05757	−	5.29587i	0.0280511	−	0.0485860i	−0.851659	−	0.524096i	$-0.824403\pi$
$109$	3.05757	−	5.29587i	0.0280511	−	0.0485860i	0.879710	+	0.475510i	$0.157737\pi$
$110$	35.9066	−	20.7307i	0.326423	−	0.188461i
$111$	56.2285	−	1.28765i	0.506563	−	0.0116005i
$112$	−27.2249	+	6.54263i	−0.243079	+	0.0584163i
$113$			27.4456i			0.242881i	0.992599	+	0.121440i	$0.0387514\pi$
$113$			27.4456i			0.242881i	−0.992599	+	0.121440i	$0.961249\pi$
$114$	−23.5764	+	14.3414i	−0.206810	+	0.125801i
$115$	−42.7374	+	74.0233i	−0.371629	+	0.643681i
$116$	−40.9148	−	23.6222i	−0.352714	−	0.203639i
$117$	−97.0531	−	151.619i	−0.829514	−	1.29589i
$118$	142.566			1.20818
$119$	43.6322	−	41.4242i	0.366657	−	0.348102i
$120$	18.9687	−	0.434390i	0.158072	−	0.00361992i
$121$	25.4520	+	44.0842i	0.210347	+	0.364332i
$122$	−60.6051	−	34.9903i	−0.496763	−	0.286806i
$123$	−38.9087	−	21.2914i	−0.316331	−	0.173101i
$124$	−44.1750	−	76.5134i	−0.356250	−	0.617043i
$125$		−	11.1803i		−	0.0894427i
$126$	−61.7378	+	64.2374i	−0.489983	+	0.509820i
$127$	−128.097			−1.00864			−0.504319	−	0.863517i	$-0.668257\pi$
$127$	−128.097			−1.00864			−0.504319	+	0.863517i	$0.668257\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	53.1126	−	97.0598i	0.411725	−	0.752402i
$130$	31.6266	−	54.7788i	0.243281	−	0.421375i
$131$	−105.833	+	61.1026i	−0.807883	+	0.466432i	−0.846220	−	0.532833i	$-0.821127\pi$
$131$	−105.833	+	61.1026i	−0.807883	+	0.466432i	0.0383369	+	0.999265i	$0.487794\pi$
$132$	1.80104	+	78.6467i	0.0136442	+	0.595808i
$133$	44.2701	−	10.6389i	0.332858	−	0.0799918i
$134$			82.9335i			0.618907i
$135$	50.0901	−	33.7043i	0.371038	−	0.249662i
$136$	12.1550	−	21.0531i	0.0893751	−	0.154802i
$137$	−48.6319	−	28.0776i	−0.354977	−	0.204946i	0.311898	−	0.950116i	$-0.399035\pi$
$137$	−48.6319	−	28.0776i	−0.354977	−	0.204946i	−0.666875	+	0.745169i	$0.732369\pi$
$138$	−84.2827	−	138.556i	−0.610745	−	1.00403i
$139$	111.879			0.804887			0.402443	−	0.915445i	$-0.368161\pi$
$139$	111.879			0.804887			0.402443	+	0.915445i	$0.368161\pi$
$140$	−30.0178	−	8.88430i	−0.214413	−	0.0634593i
$141$	−5.47421	−	239.045i	−0.0388242	−	1.69535i
$142$	58.5022	+	101.329i	0.411988	+	0.713583i
$143$	227.120	+	131.128i	1.58825	+	0.916978i
$144$	−16.5540	+	31.9682i	−0.114958	+	0.222001i
$145$	−26.4104	−	45.7441i	−0.182141	−	0.315477i
$146$			98.4307i			0.674183i
$147$	129.384	−	69.7763i	0.880165	−	0.474669i
$148$	−37.4955			−0.253348
$149$	39.2878	−	22.6828i	0.263676	−	0.152234i	−0.362334	−	0.932048i	$-0.618020\pi$
$149$	39.2878	−	22.6828i	0.263676	−	0.152234i	0.626010	+	0.779815i	$0.284687\pi$
$150$	18.6092	+	10.1832i	0.124061	+	0.0678882i
$151$	86.9526	−	150.606i	0.575845	−	0.997393i	−0.420104	−	0.907476i	$-0.638007\pi$
$151$	86.9526	−	150.606i	0.575845	−	0.997393i	0.995949	−	0.0899168i	$-0.0286601\pi$
$152$	15.9324	−	9.19856i	0.104818	−	0.0605168i
$153$	−3.54101	−	77.2729i	−0.0231439	−	0.505052i
$154$	36.8355	−	124.458i	0.239191	−	0.808168i
$155$		−	98.7783i		−	0.637280i
$156$	62.3710	+	102.534i	0.399814	+	0.657272i
$157$	−55.1355	+	95.4974i	−0.351181	+	0.608264i	−0.986457	−	0.164022i	$-0.947553\pi$
$157$	−55.1355	+	95.4974i	−0.351181	+	0.608264i	0.635275	+	0.772286i	$0.280887\pi$
$158$	−2.28318	−	1.31819i	−0.0144505	−	0.00834299i
$159$	65.2799	−	39.7093i	0.410565	−	0.249744i
$160$	−12.6491			−0.0790569
$161$	62.5238	+	260.171i	0.388346	+	1.61597i
$162$	10.4766	+	114.071i	0.0646702	+	0.704143i
$163$	120.047	+	207.927i	0.736482	+	1.27562i	0.954070	+	0.299584i	$0.0968479\pi$
$163$	120.047	+	207.927i	0.736482	+	1.27562i	−0.217588	+	0.976041i	$0.569819\pi$
$164$	25.6074	+	14.7844i	0.156142	+	0.0901488i
$165$	−42.2210	+	77.1561i	−0.255885	+	0.467613i
$166$	87.0146	+	150.714i	0.524184	+	0.907914i
$167$		−	133.617i		−	0.800105i	−0.916492	−	0.400052i	$-0.868992\pi$
$167$		−	133.617i		−	0.800105i	0.916492	−	0.400052i	$-0.131008\pi$
$168$	42.1282	−	41.8714i	0.250763	−	0.249234i
$169$	231.096			1.36743
$170$	23.5381	−	13.5897i	0.138459	−	0.0799395i
$171$	26.9182	−	51.9832i	0.157416	−	0.303995i
$172$	−36.8805	+	63.8789i	−0.214422	+	0.371389i
$173$	−128.125	+	73.9730i	−0.740607	+	0.427590i	−0.822290	−	0.569069i	$-0.807304\pi$
$173$	−128.125	+	73.9730i	−0.740607	+	0.427590i	0.0816829	+	0.996658i	$0.473971\pi$
$174$	100.194	−	2.29448i	0.575828	−	0.0131867i
$175$	−24.0982	−	25.3827i	−0.137704	−	0.145044i
$176$		−	52.4449i		−	0.297982i
$177$	−258.379	+	157.170i	−1.45977	+	0.887967i
$178$	43.4786	−	75.3071i	0.244262	−	0.423074i
$179$	1.49715	+	0.864379i	0.00836396	+	0.00482893i	0.504176	−	0.863601i	$-0.331796\pi$
$179$	1.49715	+	0.864379i	0.00836396	+	0.00482893i	−0.495812	+	0.868430i	$0.665130\pi$
$180$	−33.8991	+	21.6991i	−0.188328	+	0.120551i
$181$	31.5886			0.174523			0.0872613	−	0.996185i	$-0.472189\pi$
$181$	31.5886			0.174523			0.0872613	+	0.996185i	$0.472189\pi$
$182$	−46.2689	−	192.532i	−0.254225	−	1.05787i
$183$	148.413	−	3.39870i	0.810998	−	0.0185721i
$184$	54.0590	+	93.6329i	0.293799	+	0.508875i
$185$	−36.3048	−	20.9606i	−0.196242	−	0.113301i
$186$	164.412	+	89.9688i	0.883937	+	0.483703i
$187$	56.3448	+	97.5920i	0.301309	+	0.521882i
$188$			159.405i			0.847898i
$189$	41.0727	−	184.483i	0.217316	−	0.976101i
$190$	20.5686			0.108256
$191$	328.104	−	189.431i	1.71782	−	0.991785i	0.794953	−	0.606670i	$-0.207495\pi$
$191$	328.104	−	189.431i	1.71782	−	0.991785i	0.922869	−	0.385115i	$-0.125838\pi$
$192$	11.5210	−	21.0539i	0.0600052	−	0.109656i
$193$	−94.5534	+	163.771i	−0.489914	+	0.848556i	−0.999933	−	0.0116071i	$-0.996305\pi$
$193$	−94.5534	+	163.771i	−0.489914	+	0.848556i	0.510018	+	0.860163i	$0.329639\pi$
$194$	139.488	−	80.5337i	0.719012	−	0.415122i
$195$	3.07197	+	134.145i	0.0157537	+	0.687923i
$196$	−87.2985	+	44.5306i	−0.445401	+	0.227197i
$197$		−	283.115i		−	1.43713i	−0.695460	−	0.718565i	$-0.744799\pi$
$197$		−	283.115i		−	1.43713i	0.695460	−	0.718565i	$-0.255201\pi$
$198$	−89.9675	−	140.550i	−0.454381	−	0.709849i
$199$	−152.021	+	263.308i	−0.763923	+	1.32315i	0.176891	+	0.984230i	$0.443396\pi$
$199$	−152.021	+	263.308i	−0.763923	+	1.32315i	−0.940814	+	0.338923i	$0.889937\pi$
$200$	−12.2474	−	7.07107i	−0.0612372	−	0.0353553i
$201$	−91.4294	−	150.305i	−0.454872	−	0.747785i
$202$	−237.576			−1.17612
$203$	−158.556	−	46.9275i	−0.781066	−	0.231170i
$204$	1.18065	+	51.5558i	0.00578749	+	0.252725i
$205$	16.5295	+	28.6299i	0.0806316	+	0.139658i
$206$	−89.0049	−	51.3870i	−0.432063	−	0.249451i
$207$	305.500	+	158.196i	1.47585	+	0.764231i
$208$	−40.0048	−	69.2903i	−0.192331	−	0.333126i
$209$			85.2801i			0.408039i
$210$	64.1973	−	16.9914i	0.305701	−	0.0809115i
$211$	−323.760			−1.53441			−0.767204	−	0.641403i	$-0.778353\pi$
$211$	−323.760			−1.53441			−0.767204	+	0.641403i	$0.778353\pi$
$212$	−44.1146	+	25.4696i	−0.208088	+	0.120139i
$213$	−217.736	−	119.148i	−1.02223	−	0.559382i
$214$	−24.5068	+	42.4471i	−0.114518	+	0.198351i
$215$	−71.4188	+	41.2337i	−0.332181	+	0.191785i
$216$	−5.24149	−	76.1874i	−0.0242662	−	0.352720i
$217$	−212.907	−	224.256i	−0.981139	−	1.03344i
$218$		−	8.64812i		−	0.0396703i
$219$	−108.514	−	178.391i	−0.495498	−	0.814572i
$220$	29.3176	−	50.7795i	0.133262	−	0.230816i
$221$	148.886	+	85.9592i	0.673691	+	0.388956i
$222$	67.9550	−	41.3366i	0.306104	−	0.186201i
$223$	10.7780			0.0483320			0.0241660	−	0.999708i	$-0.492307\pi$
$223$	10.7780			0.0483320			0.0241660	+	0.999708i	$0.492307\pi$
$224$	−28.7172	+	27.2639i	−0.128202	+	0.121714i
$225$	−44.9528	+	2.05995i	−0.199790	+	0.00915535i
$226$	19.4069	+	33.6138i	0.0858714	+	0.148734i
$227$	44.8515	+	25.8950i	0.197584	+	0.114075i	0.595528	−	0.803335i	$-0.296943\pi$
$227$	44.8515	+	25.8950i	0.197584	+	0.114075i	−0.397944	+	0.917410i	$0.630276\pi$
$228$	−18.7342	+	34.2355i	−0.0821675	+	0.150156i
$229$	114.704	+	198.673i	0.500890	+	0.867566i	0.999999	+	0.00102744i	$0.000327044\pi$
$229$	114.704	+	198.673i	0.500890	+	0.867566i	−0.499110	+	0.866539i	$0.666340\pi$
$230$			120.880i			0.525563i
$231$	70.4486	+	266.170i	0.304972	+	1.15225i
$232$	−66.8136			−0.287990
$233$	293.322	−	169.349i	1.25889	−	0.726821i	0.286032	−	0.958220i	$-0.407664\pi$
$233$	293.322	−	169.349i	1.25889	−	0.726821i	0.972859	+	0.231399i	$0.0743303\pi$
$234$	−226.076	−	117.068i	−0.966139	−	0.500291i
$235$	−89.1100	+	154.343i	−0.379192	+	0.656779i
$236$	174.606	−	100.809i	0.739858	−	0.427157i
$237$	5.59115	−	0.128039i	0.0235914	−	0.000540251i
$238$	24.1470	−	81.5867i	0.101458	−	0.342801i
$239$			355.227i			1.48630i	0.669123	+	0.743152i	$0.266670\pi$
$239$			355.227i			1.48630i	−0.669123	+	0.743152i	$0.733330\pi$
$240$	22.9246	−	13.9449i	0.0955194	−	0.0581038i
$241$	44.1435	−	76.4588i	0.183168	−	0.317256i	−0.759790	−	0.650169i	$-0.774698\pi$
$241$	44.1435	−	76.4588i	0.183168	−	0.317256i	0.942958	+	0.332913i	$0.108031\pi$
$242$	62.3445	+	35.9946i	0.257622	+	0.148738i
$243$	−144.744	−	195.187i	−0.595655	−	0.803241i
$244$	−98.9676			−0.405605
$245$	−109.420	−	5.68481i	−0.446611	−	0.0232033i
$246$	−62.7085	+	1.43605i	−0.254913	+	0.00583759i
$247$	65.0514	+	112.672i	0.263366	+	0.456163i
$248$	−108.206	−	62.4729i	−0.436316	−	0.251907i
$249$	−323.854	−	177.218i	−1.30062	−	0.711718i
$250$	−7.90569	−	13.6931i	−0.0316228	−	0.0547723i
$251$		−	39.8390i		−	0.158721i	−0.996846	−	0.0793605i	$-0.974712\pi$
$251$		−	39.8390i		−	0.158721i	0.996846	−	0.0793605i	$-0.0252878\pi$
$252$	−30.1904	+	122.330i	−0.119803	+	0.485435i
$253$	−501.183			−1.98096
$254$	−156.886	+	90.5783i	−0.617662	+	0.356608i
$255$	−27.6774	+	50.5787i	−0.108539	+	0.198348i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−2.52145	+	1.45576i	−0.00981109	+	0.00566444i	−0.504898	−	0.863179i	$-0.668470\pi$
$257$	−2.52145	+	1.45576i	−0.00981109	+	0.00566444i	0.495086	+	0.868844i	$0.335136\pi$
$258$	−3.58230	−	156.430i	−0.0138849	−	0.606317i
$259$	−127.601	+	30.6649i	−0.492669	+	0.118397i
$260$		−	89.4534i		−	0.344052i
$261$	−179.057	+	114.617i	−0.686044	+	0.439144i
$262$	−86.4121	+	149.670i	−0.329817	+	0.571260i
$263$	−354.063	−	204.418i	−1.34625	−	0.777256i	−0.358531	−	0.933518i	$-0.616722\pi$
$263$	−354.063	−	204.418i	−1.34625	−	0.777256i	−0.987716	+	0.156262i	$0.950056\pi$
$264$	57.8174	+	95.0486i	0.219005	+	0.360033i
$265$	−56.9517			−0.214912
$266$	46.6967	−	44.3336i	0.175552	−	0.166668i
$267$	4.22318	+	184.416i	0.0158172	+	0.690695i
$268$	58.6428	+	101.572i	0.218817	+	0.379001i
$269$	95.1603	+	54.9408i	0.353756	+	0.204241i	0.666338	−	0.745650i	$-0.267861\pi$
$269$	95.1603	+	54.9408i	0.353756	+	0.204241i	−0.312582	+	0.949891i	$0.601194\pi$
$270$	37.5150	−	76.6983i	0.138945	−	0.284068i
$271$	−7.87856	−	13.6461i	−0.0290722	−	0.0503545i	0.851123	−	0.524966i	$-0.175922\pi$
$271$	−7.87856	−	13.6461i	−0.0290722	−	0.0503545i	−0.880195	+	0.474611i	$0.842589\pi$
$272$		−	34.3796i		−	0.126395i
$273$	296.111	+	297.927i	1.08466	+	1.09131i
$274$	−79.4156			−0.289838
$275$	56.7732	−	32.7780i	0.206448	−	0.119193i
$276$	−201.199	−	110.099i	−0.728981	−	0.398909i
$277$	70.1762	−	121.549i	0.253344	−	0.438804i	−0.711101	−	0.703090i	$-0.751803\pi$
$277$	70.1762	−	121.549i	0.253344	−	0.438804i	0.964444	+	0.264286i	$0.0851363\pi$
$278$	137.024	−	79.1106i	0.492890	−	0.284570i
$279$	−397.158	+	18.1997i	−1.42351	+	0.0652319i
$280$	−43.0463	+	10.3448i	−0.153737	+	0.0369457i
$281$		−	239.808i		−	0.853409i	−0.904391	−	0.426705i	$-0.859674\pi$
$281$		−	239.808i		−	0.853409i	0.904391	−	0.426705i	$-0.140326\pi$
$282$	−175.735	−	288.898i	−0.623172	−	1.02446i
$283$	97.5048	−	168.883i	0.344540	−	0.596761i	−0.640730	−	0.767766i	$-0.721368\pi$
$283$	97.5048	−	168.883i	0.344540	−	0.596761i	0.985270	+	0.171005i	$0.0547016\pi$
$284$	143.301	+	82.7346i	0.504580	+	0.291319i
$285$	−37.2775	+	22.6757i	−0.130798	+	0.0795638i
$286$	370.886			1.29680
$287$	99.2357	+	29.3706i	0.345769	+	0.102336i
$288$	2.33057	+	50.8583i	0.00809226	+	0.176591i
$289$	−107.564	−	186.306i	−0.372194	−	0.644658i
$290$	−64.6920	−	37.3499i	−0.223076	−	0.128793i
$291$	−164.019	+	299.733i	−0.563638	+	1.03001i
$292$	69.6010	+	120.553i	0.238360	+	0.412851i
$293$			208.907i			0.712992i	0.934297	+	0.356496i	$0.116029\pi$
$293$			208.907i			0.712992i	−0.934297	+	0.356496i	$0.883971\pi$
$294$	109.123	−	176.947i	0.371168	−	0.601859i
$295$	225.416			0.764122
$296$	−45.9224	+	26.5133i	−0.155143	+	0.0895720i
$297$	318.001	+	155.542i	1.07071	+	0.523711i
$298$	32.0783	−	55.5613i	0.107645	−	0.186447i
$299$	−662.164	+	382.301i	−2.21460	+	1.27860i
$300$	29.9921	−	0.686831i	0.0999738	−	0.00228944i
$301$	−73.2665	+	247.549i	−0.243410	+	0.822422i
$302$		−	245.939i		−	0.814368i
$303$	430.571	−	261.914i	1.42103	−	0.864401i
$304$	13.0087	−	22.5318i	0.0427918	−	0.0741177i
$305$	−95.8250	−	55.3246i	−0.314180	−	0.181392i
$306$	−58.9770	−	92.1357i	−0.192735	−	0.301097i
$307$	482.422			1.57141			0.785704	−	0.618603i	$-0.212301\pi$
$307$	482.422			1.57141			0.785704	+	0.618603i	$0.212301\pi$
$308$	−42.8909	−	178.476i	−0.139256	−	0.579466i
$309$	217.959	−	4.99135i	0.705370	−	0.0161532i
$310$	−69.8468	−	120.978i	−0.225312	−	0.390252i
$311$	−377.222	−	217.789i	−1.21293	−	0.700286i	−0.249535	−	0.968366i	$-0.580278\pi$
$311$	−377.222	−	217.789i	−1.21293	−	0.700286i	−0.963397	+	0.268079i	$0.913611\pi$
$312$	148.891	+	81.4755i	0.477216	+	0.261140i
$313$	261.365	+	452.697i	0.835031	+	1.44632i	0.894005	+	0.448056i	$0.147884\pi$
$313$	261.365	+	452.697i	0.835031	+	1.44632i	−0.0589747	+	0.998259i	$0.518783\pi$
$314$			155.947i			0.496645i
$315$	−97.6161	+	101.568i	−0.309892	+	0.322439i
$316$	−3.72841			−0.0117988
$317$	−98.4192	+	56.8224i	−0.310471	+	0.179250i	−0.647137	−	0.762374i	$-0.724034\pi$
$317$	−98.4192	+	56.8224i	−0.310471	+	0.179250i	0.336666	+	0.941624i	$0.390701\pi$
$318$	51.8725	−	94.7936i	0.163121	−	0.298093i
$319$	154.858	−	268.221i	0.485447	−	0.840819i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$	−2.38041	−	103.946i	−0.00741561	−	0.323821i
$322$	260.544	+	274.432i	0.809144	+	0.852274i
$323$			55.9043i			0.173078i
$324$	93.4917	+	132.300i	0.288554	+	0.408334i
$325$	50.0060	−	86.6129i	0.153865	−	0.266501i
$326$	294.053	+	169.772i	0.902003	+	0.520772i
$327$	9.53405	+	15.6734i	0.0291561	+	0.0479310i
$328$	41.8166			0.127490
$329$	130.366	+	542.472i	0.396249	+	1.64885i
$330$	2.84769	+	124.351i	0.00862937	+	0.376822i
$331$	−145.862	−	252.640i	−0.440670	−	0.763263i	0.557069	−	0.830466i	$-0.311926\pi$
$331$	−145.862	−	252.640i	−0.440670	−	0.763263i	−0.997739	+	0.0672033i	$0.978592\pi$
$332$	213.141	+	123.057i	0.641992	+	0.370654i
$333$	−77.5873	+	149.833i	−0.232995	+	0.449949i
$334$	−94.4818	−	163.647i	−0.282880	−	0.489962i
$335$			131.129i			0.391431i
$336$	21.9888	−	81.0709i	0.0654428	−	0.241283i
$337$	9.57538			0.0284136			0.0142068	−	0.999899i	$-0.495478\pi$
$337$	9.57538			0.0284136			0.0142068	+	0.999899i	$0.495478\pi$
$338$	283.033	−	163.409i	0.837376	−	0.483459i
$339$	−72.2295	−	39.5250i	−0.213066	−	0.116593i
$340$	19.2188	−	33.2879i	0.0565258	−	0.0979055i
$341$	501.592	−	289.594i	1.47094	−	0.849250i
$342$	−3.78972	−	82.7002i	−0.0110810	−	0.241813i
$343$	−260.668	+	222.938i	−0.759965	+	0.649964i
$344$			104.314i			0.303238i
$345$	−133.263	−	219.076i	−0.386269	−	0.635004i
$346$	−104.614	+	181.196i	−0.302352	+	0.523688i
$347$	−529.877	−	305.925i	−1.52702	−	0.881628i	−0.999485	−	0.0320976i	$-0.989781\pi$
$347$	−529.877	−	305.925i	−1.52702	−	0.881628i	−0.527540	−	0.849530i	$-0.676885\pi$
$348$	121.090	−	73.6581i	0.347959	−	0.211661i
$349$	95.9163			0.274832			0.137416	−	0.990513i	$-0.456120\pi$
$349$	95.9163			0.274832			0.137416	+	0.990513i	$0.456120\pi$
$350$	−47.4623	−	14.0473i	−0.135607	−	0.0401352i
$351$	538.791	−	37.0674i	1.53502	−	0.105605i
$352$	−37.0841	−	64.2316i	−0.105353	−	0.182476i
$353$	353.916	+	204.334i	1.00260	+	0.578849i	0.909015	−	0.416763i	$-0.136836\pi$
$353$	353.916	+	204.334i	1.00260	+	0.578849i	0.0935800	+	0.995612i	$0.470169\pi$
$354$	−205.312	+	375.195i	−0.579978	+	1.05987i
$355$	92.5001	+	160.215i	0.260564	+	0.451310i
$356$		−	122.976i		−	0.345438i
$357$	46.1817	+	174.485i	0.129361	+	0.488752i
$358$	2.44483			0.00682914
$359$	−44.3302	+	25.5941i	−0.123483	+	0.0712927i	−0.560469	−	0.828175i	$-0.689379\pi$
$359$	−44.3302	+	25.5941i	−0.123483	+	0.0712927i	0.436986	+	0.899468i	$0.356046\pi$
$360$	−26.1741	+	50.5462i	−0.0727058	+	0.140406i
$361$	159.347	−	275.996i	0.441403	−	0.764533i
$362$	38.6879	−	22.3365i	0.106873	−	0.0617030i
$363$	−152.672	+	3.49625i	−0.420585	+	0.00963154i
$364$	−192.808	−	203.085i	−0.529693	−	0.557927i
$365$			155.633i			0.426391i
$366$	179.364	−	109.106i	0.490066	−	0.298104i
$367$	283.270	−	490.638i	0.771853	−	1.33689i	−0.164694	−	0.986345i	$-0.552664\pi$
$367$	283.270	−	490.638i	0.771853	−	1.33689i	0.936547	−	0.350543i	$-0.114003\pi$
$368$	132.417	+	76.4510i	0.359829	+	0.207747i
$369$	112.067	−	71.7351i	0.303704	−	0.194404i
$370$	−59.2855			−0.160231
$371$	−129.297	+	122.754i	−0.348510	+	0.330873i
$372$	264.981	−	6.06815i	0.712314	−	0.0163122i
$373$	−202.115	−	350.074i	−0.541863	−	0.938535i	−0.998797	−	0.0490343i	$-0.984386\pi$
$373$	−202.115	−	350.074i	−0.541863	−	0.938535i	0.456934	−	0.889501i	$-0.348948\pi$
$374$	138.016	+	79.6835i	0.369026	+	0.213058i
$375$	29.4237	+	16.1011i	0.0784632	+	0.0429362i
$376$	112.716	+	195.230i	0.299777	+	0.519229i
$377$		−	472.500i		−	1.25332i
$378$	−80.1456	−	254.988i	−0.212026	−	0.674570i
$379$	21.5074			0.0567478			0.0283739	−	0.999597i	$-0.490967\pi$
$379$	21.5074			0.0567478			0.0283739	+	0.999597i	$0.490967\pi$
$380$	25.1913	−	14.5442i	0.0662928	−	0.0382742i
$381$	184.476	−	337.118i	0.484189	−	0.884824i
$382$	267.896	−	464.009i	0.701298	−	1.21468i
$383$	−56.1254	+	32.4040i	−0.146542	+	0.0846058i	−0.571478	−	0.820617i	$-0.693630\pi$
$383$	−56.1254	+	32.4040i	−0.146542	+	0.0846058i	0.424936	+	0.905223i	$0.360296\pi$
$384$	−0.777060	−	33.9322i	−0.00202360	−	0.0883652i
$385$	58.2420	−	196.785i	0.151278	−	0.511130i
$386$			267.438i			0.692843i
$387$	178.947	+	279.557i	0.462396	+	0.722369i
$388$	113.892	−	197.266i	0.293536	−	0.508419i
$389$	45.0181	+	25.9912i	0.115728	+	0.0668154i	0.556747	−	0.830682i	$-0.312049\pi$
$389$	45.0181	+	25.9912i	0.115728	+	0.0668154i	−0.441019	+	0.897498i	$0.645383\pi$
$390$	98.6172	+	162.121i	0.252865	+	0.415695i
$391$	−328.544			−0.840266
$392$	−75.4305	+	116.268i	−0.192425	+	0.296602i
$393$	−8.39342	−	366.519i	−0.0213573	−	0.932619i
$394$	−200.192	−	346.743i	−0.508102	−	0.880058i
$395$	−3.61002	−	2.08425i	−0.00913929	−	0.00527657i
$396$	−209.571	−	108.521i	−0.529220	−	0.274044i
$397$	−129.977	−	225.128i	−0.327399	−	0.567072i	0.654596	−	0.755979i	$-0.272839\pi$
$397$	−129.977	−	225.128i	−0.327399	−	0.567072i	−0.981995	+	0.188907i	$0.939505\pi$
$398$			429.979i			1.08035i
$399$	−35.7557	+	131.829i	−0.0896133	+	0.330398i
$400$	−20.0000			−0.0500000
$401$	−595.094	+	343.578i	−1.48403	+	0.856802i	−0.999835	−	0.0181603i	$-0.994219\pi$
$401$	−595.094	+	343.578i	−1.48403	+	0.856802i	−0.484190	+	0.874963i	$0.660886\pi$
$402$	−218.259	−	119.435i	−0.542933	−	0.297101i
$403$	441.803	−	765.225i	1.09629	−	1.89882i
$404$	−290.970	+	167.992i	−0.720222	+	0.415821i
$405$	16.5649	+	180.362i	0.0409010	+	0.445339i
$406$	−227.374	+	54.6420i	−0.560034	+	0.134586i
$407$		−	245.806i		−	0.603945i
$408$	37.9015	+	62.3079i	0.0928958	+	0.152715i
$409$	−195.907	+	339.321i	−0.478990	+	0.829635i	−0.999710	−	0.0240926i	$-0.992330\pi$
$409$	−195.907	+	339.321i	−0.478990	+	0.829635i	0.520720	+	0.853728i	$0.325664\pi$
$410$	40.4888	+	23.3762i	0.0987531	+	0.0570151i
$411$	143.929	−	87.5510i	0.350192	−	0.213020i
$412$	−145.344			−0.352778
$413$	511.760	−	485.862i	1.23913	−	1.17642i
$414$	486.021	−	22.2718i	1.17396	−	0.0537966i
$415$	137.582	+	238.299i	0.331523	+	0.574215i
$416$	−97.9913	−	56.5753i	−0.235556	−	0.135998i
$417$	−161.120	+	294.437i	−0.386379	+	0.706083i
$418$	60.3021	+	104.446i	0.144263	+	0.249872i
$419$		−	357.594i		−	0.853446i	−0.904382	−	0.426723i	$-0.859668\pi$
$419$		−	357.594i		−	0.853446i	0.904382	−	0.426723i	$-0.140332\pi$
$420$	66.6106	−	66.2045i	0.158597	−	0.157630i
$421$	446.974			1.06170			0.530848	−	0.847467i	$-0.321873\pi$
$421$	446.974			1.06170			0.530848	+	0.847467i	$0.321873\pi$
$422$	−396.523	+	228.933i	−0.939629	+	0.542495i
$423$	636.986	+	329.848i	1.50588	+	0.779781i
$424$	−36.0194	+	62.3874i	−0.0849514	+	0.147140i
$425$	37.2170	−	21.4872i	0.0875693	−	0.0505582i
$426$	−350.921	+	8.03623i	−0.823759	+	0.0188644i
$427$	−336.798	+	80.9386i	−0.788754	+	0.189552i
$428$			69.3158i			0.161953i
$429$	−672.176	+	408.880i	−1.56684	+	0.953100i
$430$	−58.3132	+	101.001i	−0.135612	+	0.234887i
$431$	237.583	+	137.168i	0.551236	+	0.318256i	0.749620	−	0.661868i	$-0.230236\pi$
$431$	237.583	+	137.168i	0.551236	+	0.318256i	−0.198384	+	0.980124i	$0.563569\pi$
$432$	−60.2922	−	89.6039i	−0.139565	−	0.207416i
$433$	89.7341			0.207238			0.103619	−	0.994617i	$-0.466958\pi$
$433$	89.7341			0.207238			0.103619	+	0.994617i	$0.466958\pi$
$434$	−419.330	−	124.108i	−0.966198	−	0.285963i
$435$	158.421	−	3.62789i	0.364186	−	0.00833999i
$436$	−6.11515	−	10.5917i	−0.0140256	−	0.0242930i
$437$	−215.322	−	124.316i	−0.492728	−	0.284476i
$438$	−259.044	−	141.753i	−0.591424	−	0.323636i
$439$	288.403	+	499.528i	0.656954	+	1.13788i	0.981400	+	0.191973i	$0.0614887\pi$
$439$	288.403	+	499.528i	0.656954	+	1.13788i	−0.324446	+	0.945904i	$0.605178\pi$
$440$		−	82.9226i		−	0.188461i
$441$	−2.69660	+	440.992i	−0.00611475	+	0.999981i
$442$	243.129			0.550066
$443$	616.665	−	356.031i	1.39202	−	0.803683i	0.398481	−	0.917177i	$-0.369538\pi$
$443$	616.665	−	356.031i	1.39202	−	0.803683i	0.993539	+	0.113494i	$0.0362043\pi$
$444$	53.9982	−	98.6782i	0.121618	−	0.222248i
$445$	68.7457	−	119.071i	0.154485	−	0.267575i
$446$	13.2003	−	7.62122i	0.0295972	−	0.0170879i
$447$	3.11585	+	136.061i	0.00697058	+	0.304387i
$448$	−15.8927	+	53.6975i	−0.0354748	+	0.119860i
$449$			162.372i			0.361630i	0.983517	+	0.180815i	$0.0578735\pi$
$449$			162.372i			0.361630i	−0.983517	+	0.180815i	$0.942126\pi$
$450$	−53.5991	+	34.3094i	−0.119109	+	0.0762430i
$451$	−96.9208	+	167.872i	−0.214902	+	0.372221i
$452$	47.5371	+	27.4456i	0.105171	+	0.0607202i
$453$	271.133	+	445.728i	0.598529	+	0.983947i
$454$	73.2421			0.161326
$455$	−73.1575	−	304.420i	−0.160786	−	0.669054i
$456$	1.26357	+	55.1769i	0.00277099	+	0.121002i
$457$	43.1763	+	74.7836i	0.0944777	+	0.163640i	0.909391	−	0.415943i	$-0.136549\pi$
$457$	43.1763	+	74.7836i	0.0944777	+	0.163640i	−0.814913	+	0.579584i	$0.803215\pi$
$458$	280.966	+	162.216i	0.613462	+	0.354182i
$459$	208.462	+	101.964i	0.454165	+	0.222143i
$460$	85.4748	+	148.047i	0.185815	+	0.321841i
$461$		−	177.631i		−	0.385317i	−0.981266	−	0.192659i	$-0.938289\pi$
$461$		−	177.631i		−	0.385317i	0.981266	−	0.192659i	$-0.0617110\pi$
$462$	274.493	+	276.176i	0.594140	+	0.597784i
$463$	−540.217			−1.16677			−0.583387	−	0.812194i	$-0.698273\pi$
$463$	−540.217			−1.16677			−0.583387	+	0.812194i	$0.698273\pi$
$464$	−81.8296	+	47.2443i	−0.176357	+	0.101820i
$465$	259.959	+	142.253i	0.559051	+	0.305921i
$466$	239.496	−	414.819i	0.513940	−	0.890170i
$467$	−250.535	+	144.646i	−0.536477	+	0.309735i	−0.743650	−	0.668569i	$-0.766907\pi$
$467$	−250.535	+	144.646i	−0.536477	+	0.309735i	0.207173	+	0.978304i	$0.433574\pi$
$468$	−359.666	+	16.4816i	−0.768516	+	0.0352171i
$469$	282.637	+	297.702i	0.602637	+	0.634759i
$470$			252.041i			0.536258i
$471$	−171.922	−	282.630i	−0.365015	−	0.600064i
$472$	142.566	−	246.931i	0.302046	−	0.523158i
$473$	−418.765	−	241.774i	−0.885339	−	0.511151i
$474$	6.75720	−	4.11036i	0.0142557	−	0.00867164i
$475$	32.5218			0.0684670
$476$	−28.1166	−	116.997i	−0.0590685	−	0.245793i
$477$	10.4932	+	228.986i	0.0219984	+	0.480054i
$478$	251.183	+	435.062i	0.525488	+	0.910171i
$479$	48.5536	+	28.0325i	0.101365	+	0.0585229i	0.549825	−	0.835280i	$-0.314694\pi$
$479$	48.5536	+	28.0325i	0.101365	+	0.0585229i	−0.448461	+	0.893803i	$0.648028\pi$
$480$	18.2163	−	33.2891i	0.0379506	−	0.0693524i
$481$	−187.500	−	324.759i	−0.389812	−	0.675175i
$482$		−	124.857i		−	0.259039i
$483$	−774.744	−	210.133i	−1.60402	−	0.435058i
$484$	101.808			0.210347
$485$	220.551	−	127.335i	0.454743	−	0.262546i
$486$	−315.293	−	136.705i	−0.648751	−	0.281287i
$487$	192.035	−	332.614i	0.394322	−	0.682986i	−0.598692	−	0.800979i	$-0.704313\pi$
$487$	192.035	−	332.614i	0.394322	−	0.682986i	0.993014	+	0.117993i	$0.0376461\pi$
$488$	−121.210	+	69.9807i	−0.248381	+	0.143403i
$489$	−720.091	+	16.4903i	−1.47258	+	0.0337226i
$490$	−138.031	+	70.4090i	−0.281696	+	0.143692i
$491$		−	323.097i		−	0.658039i	−0.944323	−	0.329019i	$-0.893282\pi$
$491$		−	323.097i		−	0.658039i	0.944323	−	0.329019i	$-0.106718\pi$
$492$	−75.7865	+	46.1004i	−0.154038	+	0.0937000i
$493$	101.515	−	175.829i	0.205913	−	0.356651i
$494$	159.343	+	91.9965i	0.322556	+	0.186228i
$495$	−142.251	−	222.229i	−0.287376	−	0.448948i
$496$	−176.700			−0.356250
$497$	555.330	+	164.360i	1.11737	+	0.330704i
$498$	−521.951	+	11.9529i	−1.04809	+	0.0240017i
$499$	−246.401	−	426.778i	−0.493789	−	0.855267i	0.506186	−	0.862425i	$-0.331055\pi$
$499$	−246.401	−	426.778i	−0.493789	−	0.855267i	−0.999974	+	0.00715734i	$0.997722\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$	351.646	+	192.426i	0.701888	+	0.384084i
$502$	−28.1704	−	48.7926i	−0.0561163	−	0.0971964i
$503$			62.5907i			0.124435i	0.998063	+	0.0622174i	$0.0198172\pi$
$503$			62.5907i			0.124435i	−0.998063	+	0.0622174i	$0.980183\pi$
$504$	49.5246	+	171.170i	0.0982630	+	0.339624i
$505$	−375.640			−0.743842
$506$	−613.821	+	354.390i	−1.21308	+	0.700375i
$507$	−332.807	+	608.183i	−0.656423	+	1.19957i
$508$	−128.097	+	221.871i	−0.252160	+	0.436753i
$509$	129.840	−	74.9633i	0.255089	−	0.147276i	−0.367003	−	0.930220i	$-0.619616\pi$
$509$	129.840	−	74.9633i	0.255089	−	0.147276i	0.622092	+	0.782944i	$0.286283\pi$
$510$	1.86677	+	81.5169i	0.00366033	+	0.159837i
$511$	335.451	+	353.332i	0.656460	+	0.691452i
$512$			22.6274i			0.0441942i
$513$	98.0405	+	145.704i	0.191112	+	0.284023i
$514$	−2.05876	+	3.56587i	−0.00400536	+	0.00693749i
$515$	−140.729	−	81.2500i	−0.273260	−	0.157767i
$516$	−115.000	−	189.054i	−0.222868	−	0.366383i
$517$	−1045.00			−2.02127
$518$	−134.596	+	127.784i	−0.259837	+	0.246688i
$519$	−10.1614	−	443.722i	−0.0195788	−	0.854955i
$520$	−63.2531	−	109.558i	−0.121641	−	0.210688i
$521$	95.6820	+	55.2420i	0.183651	+	0.106031i	0.589007	−	0.808128i	$-0.299519\pi$
$521$	95.6820	+	55.2420i	0.183651	+	0.106031i	−0.405356	+	0.914159i	$0.632852\pi$
$522$	−138.254	+	266.989i	−0.264854	+	0.511473i
$523$	−184.136	−	318.933i	−0.352076	−	0.609814i	0.634537	−	0.772893i	$-0.281191\pi$
$523$	−184.136	−	318.933i	−0.352076	−	0.609814i	−0.986613	+	0.163079i	$0.947858\pi$
$524$			244.410i			0.466432i
$525$	101.505	−	26.8658i	0.193343	−	0.0511729i
$526$	−578.182			−1.09921
$527$	328.812	−	189.840i	0.623932	−	0.360227i
$528$	138.021	+	75.5272i	0.261404	+	0.143044i
$529$	466.094	−	807.298i	0.881085	−	1.52608i
$530$	−69.7513	+	40.2709i	−0.131606	+	0.0759829i
$531$	−41.5324	−	906.330i	−0.0782154	−	1.70684i
$532$	25.8430	−	87.3170i	0.0485770	−	0.164130i
$533$			295.724i			0.554828i
$534$	135.574	+	222.876i	0.253884	+	0.417370i
$535$	−38.7487	+	67.1147i	−0.0724275	+	0.125448i
$536$	143.645	+	82.9335i	0.267994	+	0.154727i
$537$	−4.43090	+	2.69529i	−0.00825121	+	0.00501916i
$538$	155.396			0.288840
$539$	−291.925	−	572.295i	−0.541605	−	1.06177i
$540$	−8.28753	−	120.463i	−0.0153473	−	0.223079i
$541$	460.911	+	798.320i	0.851960	+	1.47564i	0.879437	+	0.476016i	$0.157920\pi$
$541$	460.911	+	798.320i	0.851960	+	1.47564i	−0.0274763	+	0.999622i	$0.508747\pi$
$542$	−19.2985	−	11.1420i	−0.0356060	−	0.0205571i
$543$	−45.4915	+	83.1328i	−0.0837781	+	0.153099i
$544$	−24.3100	−	42.1062i	−0.0446875	−	0.0774011i
$545$		−	13.6739i		−	0.0250897i
$546$	573.326	+	155.503i	1.05005	+	0.284803i
$547$	−106.461			−0.194627			−0.0973135	−	0.995254i	$-0.531025\pi$
$547$	−106.461			−0.194627			−0.0973135	+	0.995254i	$0.531025\pi$
$548$	−97.2638	+	56.1553i	−0.177489	+	0.102473i
$549$	−204.788	+	395.477i	−0.373020	+	0.720359i
$550$	46.3552	−	80.2895i	0.0842821	−	0.145981i
$551$	133.062	−	76.8235i	0.241492	−	0.139426i
$552$	−324.269	+	7.42588i	−0.587444	+	0.0134527i
$553$	−12.6882	+	3.04920i	−0.0229443	+	0.00551393i
$554$		−	198.488i		−	0.358282i
$555$	107.446	−	65.3589i	0.193597	−	0.117764i
$556$	111.879	−	193.781i	0.201222	−	0.348526i
$557$	360.459	+	208.111i	0.647144	+	0.373629i	0.787361	−	0.616492i	$-0.211447\pi$
$557$	360.459	+	208.111i	0.647144	+	0.373629i	−0.140217	+	0.990121i	$0.544780\pi$
$558$	−473.549	+	303.123i	−0.848653	+	0.543232i
$559$	−737.699			−1.31968
$560$	−45.4059	+	43.1081i	−0.0810819	+	0.0769787i
$561$	−337.980	+	7.73986i	−0.602460	+	0.0137965i
$562$	−169.570	−	293.704i	−0.301726	−	0.522604i
$563$	−415.893	−	240.116i	−0.738709	−	0.426494i	0.0828906	−	0.996559i	$-0.473585\pi$
$563$	−415.893	−	240.116i	−0.738709	−	0.426494i	−0.821600	+	0.570065i	$0.806918\pi$
$564$	−419.512	−	229.563i	−0.743815	−	0.407027i
$565$	30.6851	+	53.1481i	0.0543098	+	0.0940674i
$566$		−	275.785i		−	0.487253i
$567$	426.361	+	373.772i	0.751960	+	0.659209i
$568$	234.009			0.411988
$569$	281.825	−	162.712i	0.495299	−	0.285961i	−0.231471	−	0.972842i	$-0.574354\pi$
$569$	281.825	−	162.712i	0.495299	−	0.285961i	0.726770	+	0.686881i	$0.241020\pi$
$570$	−29.6214	+	54.1311i	−0.0519673	+	0.0949669i
$571$	−294.936	+	510.844i	−0.516525	+	0.894648i	0.483291	+	0.875460i	$0.339441\pi$
$571$	−294.936	+	510.844i	−0.516525	+	0.894648i	−0.999816	+	0.0191878i	$0.993892\pi$
$572$	454.240	−	262.256i	0.794126	−	0.458489i
$573$	26.0214	+	1136.29i	0.0454126	+	1.98305i
$574$	142.307	−	34.1988i	0.247921	−	0.0595798i
$575$			191.127i			0.332396i
$576$	38.8166	+	60.6405i	0.0673900	+	0.105279i
$577$	−188.103	+	325.803i	−0.326001	+	0.564651i	−0.981714	−	0.190359i	$-0.939035\pi$
$577$	−188.103	+	325.803i	−0.326001	+	0.564651i	0.655713	+	0.755010i	$0.272368\pi$
$578$	−263.477	−	152.118i	−0.455842	−	0.263181i
$579$	−294.834	−	484.691i	−0.509213	−	0.837118i
$580$	−105.642			−0.182141
$581$	825.983	+	244.464i	1.42166	+	0.420765i
$582$	11.0626	+	483.075i	0.0190079	+	0.830026i
$583$	−166.969	−	289.198i	−0.286395	−	0.496051i
$584$	170.487	+	98.4307i	0.291930	+	0.168546i
$585$	−357.458	−	185.101i	−0.611040	−	0.316412i
$586$	147.719	+	255.857i	0.252081	+	0.436616i
$587$		−	673.410i		−	1.14721i	−0.819133	−	0.573603i	$-0.805545\pi$
$587$		−	673.410i		−	1.14721i	0.819133	−	0.573603i	$-0.194455\pi$
$588$	8.52808	−	293.876i	0.0145035	−	0.499790i
$589$	287.330			0.487827
$590$	276.077	−	159.393i	0.467927	−	0.270158i
$591$	745.083	+	407.720i	1.26072	+	0.689882i
$592$	−37.4955	+	64.9441i	−0.0633369	+	0.109703i
$593$	−367.422	+	212.131i	−0.619598	+	0.357725i	−0.776712	−	0.629855i	$-0.783114\pi$
$593$	−367.422	+	212.131i	−0.619598	+	0.357725i	0.157114	+	0.987580i	$0.449781\pi$
$594$	499.455	−	34.3612i	0.840834	−	0.0578471i
$595$	38.1798	−	129.000i	0.0641677	−	0.216807i
$596$		−	90.7312i		−	0.152234i
$597$	−474.027	−	779.274i	−0.794016	−	1.30532i
$598$	−540.655	+	936.441i	−0.904105	+	1.56596i
$599$	831.974	+	480.341i	1.38894	+	0.801904i	0.993196	−	0.116457i	$-0.0371537\pi$
$599$	831.974	+	480.341i	1.38894	+	0.801904i	0.395743	+	0.918361i	$0.370487\pi$
$600$	36.2471	−	22.0488i	0.0604118	−	0.0367481i
$601$	−225.097			−0.374537			−0.187268	−	0.982309i	$-0.559963\pi$
$601$	−225.097			−0.374537			−0.187268	+	0.982309i	$0.559963\pi$
$602$	85.3109	+	354.992i	0.141712	+	0.589687i
$603$	527.232	−	24.1603i	0.874349	−	0.0400668i
$604$	−173.905	−	301.213i	−0.287922	−	0.498696i
$605$	98.5753	+	56.9125i	0.162934	+	0.0940702i
$606$	342.139	−	625.237i	0.564586	−	1.03174i
$607$	535.314	+	927.191i	0.881901	+	1.52750i	0.849225	+	0.528031i	$0.177070\pi$
$607$	535.314	+	927.191i	0.881901	+	1.52750i	0.0326761	+	0.999466i	$0.489597\pi$
$608$		−	36.7942i		−	0.0605168i
$609$	351.842	−	349.697i	0.577737	−	0.574215i
$610$	−156.482			−0.256527
$611$	−1380.65	+	797.119i	−2.25966	+	1.30461i
$612$	−137.382	−	71.1397i	−0.224480	−	0.116241i
$613$	442.814	−	766.976i	0.722372	−	1.25118i	−0.237675	−	0.971345i	$-0.576385\pi$
$613$	442.814	−	766.976i	0.722372	−	1.25118i	0.960047	−	0.279840i	$-0.0902813\pi$
$614$	590.844	−	341.124i	0.962287	−	0.555576i
$615$	−99.1508	+	2.27059i	−0.161221	+	0.00369202i
$616$	−178.732	−	188.259i	−0.290149	−	0.305615i
$617$			850.429i			1.37833i	0.724605	+	0.689165i	$0.242022\pi$
$617$			850.429i			1.37833i	−0.724605	+	0.689165i	$0.757978\pi$
$618$	263.415	−	160.234i	0.426238	−	0.259278i
$619$	92.9772	−	161.041i	0.150205	−	0.260163i	−0.781097	−	0.624409i	$-0.785340\pi$
$619$	92.9772	−	161.041i	0.150205	−	0.260163i	0.931303	+	0.364246i	$0.118673\pi$
$620$	−171.089	−	98.7783i	−0.275950	−	0.159320i
$621$	−856.288	+	576.174i	−1.37889	+	0.927817i
$622$	−616.000			−0.990354
$623$	−100.573	−	418.501i	−0.161434	−	0.671751i
$624$	239.966	−	5.49530i	0.384561	−	0.00880658i
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	640.210	+	369.625i	1.02270	+	0.590456i
$627$	−224.435	−	122.814i	−0.357950	−	0.195876i
$628$	110.271	+	190.995i	0.175591	+	0.304132i
$629$		−	161.135i		−	0.256176i
$630$	−47.7352	+	193.420i	−0.0757702	+	0.307016i
$631$	62.9834			0.0998153			0.0499076	−	0.998754i	$-0.484107\pi$
$631$	62.9834			0.0998153			0.0499076	+	0.998754i	$0.484107\pi$
$632$	−4.56635	+	2.63639i	−0.00722525	+	0.00417150i
$633$	466.255	−	852.051i	0.736580	−	1.34605i
$634$	−80.3590	+	139.186i	−0.126749	+	0.219536i
$635$	−248.059	+	143.217i	−0.390644	+	0.225538i
$636$	−3.49866	−	152.777i	−0.00550103	−	0.240216i
$637$	−822.237	−	533.438i	−1.29080	−	0.837423i
$638$		−	438.004i		−	0.686526i
$639$	627.134	−	401.435i	0.981430	−	0.628224i
$640$	−12.6491	+	21.9089i	−0.0197642	+	0.0342327i
$641$	98.1569	+	56.6709i	0.153131	+	0.0884102i	0.574608	−	0.818429i	$-0.305155\pi$
$641$	98.1569	+	56.6709i	0.153131	+	0.0884102i	−0.421477	+	0.906839i	$0.638488\pi$
$642$	−76.4166	−	125.625i	−0.119029	−	0.195677i
$643$	−633.163			−0.984702			−0.492351	−	0.870397i	$-0.663862\pi$
$643$	−633.163			−0.984702			−0.492351	+	0.870397i	$0.663862\pi$
$644$	513.153	+	151.877i	0.796822	+	0.235833i
$645$	−5.66411	−	247.337i	−0.00878157	−	0.383469i
$646$	39.5303	+	68.4685i	0.0611924	+	0.105988i
$647$	−717.969	−	414.520i	−1.10969	−	0.640680i	−0.170941	−	0.985281i	$-0.554681\pi$
$647$	−717.969	−	414.520i	−1.10969	−	0.640680i	−0.938749	+	0.344602i	$0.888014\pi$
$648$	208.054	+	95.9253i	0.321071	+	0.148033i
$649$	660.865	+	1144.65i	1.01828	+	1.76372i
$650$		−	141.438i		−	0.217597i
$651$	896.795	−	237.359i	1.37757	−	0.364607i
$652$	480.186			0.736482
$653$	−88.6154	+	51.1621i	−0.135705	+	0.0783494i	−0.566316	−	0.824189i	$-0.691632\pi$
$653$	−88.6154	+	51.1621i	−0.135705	+	0.0783494i	0.430610	+	0.902538i	$0.358298\pi$
$654$	22.7596	+	12.4544i	0.0348006	+	0.0190434i
$655$	−136.629	+	236.649i	−0.208595	+	0.361296i
$656$	51.2147	−	29.5688i	0.0780712	−	0.0450744i
$657$	625.753	−	28.6750i	0.952439	−	0.0436453i
$658$	543.251	+	572.207i	0.825609	+	0.869616i
$659$		−	853.723i		−	1.29548i	−0.761861	−	0.647741i	$-0.775714\pi$
$659$		−	853.723i		−	1.29548i	0.761861	−	0.647741i	$-0.224286\pi$
$660$	91.4174	+	150.285i	0.138511	+	0.227705i
$661$	6.30926	−	10.9280i	0.00954503	−	0.0165325i	−0.861213	−	0.508243i	$-0.830295\pi$
$661$	6.30926	−	10.9280i	0.00954503	−	0.0165325i	0.870758	+	0.491711i	$0.163628\pi$
$662$	−357.287	−	206.280i	−0.539708	−	0.311601i
$663$	−440.636	+	268.036i	−0.664609	+	0.404277i
$664$	348.058			0.524184
$665$	73.8340	−	70.0976i	0.111029	−	0.105410i
$666$	10.9232	+	238.370i	0.0164012	+	0.357912i
$667$	451.484	+	781.994i	0.676888	+	1.17240i
$668$	−231.432	−	133.617i	−0.346455	−	0.200026i
$669$	−15.5217	+	28.3649i	−0.0232014	+	0.0423990i
$670$	92.7225	+	160.600i	0.138392	+	0.239702i
$671$		−	648.793i		−	0.966905i
$672$	−30.3952	−	114.840i	−0.0452309	−	0.170892i
$673$	620.345			0.921761			0.460880	−	0.887462i	$-0.347534\pi$
$673$	620.345			0.921761			0.460880	+	0.887462i	$0.347534\pi$
$674$	11.7274	−	6.77082i	0.0173997	−	0.0100457i
$675$	59.3165	−	121.271i	0.0878762	−	0.179660i
$676$	231.096	−	400.269i	0.341857	−	0.592114i
$677$	730.400	−	421.696i	1.07888	−	0.622890i	0.148284	−	0.988945i	$-0.452625\pi$
$677$	730.400	−	421.696i	1.07888	−	0.622890i	0.930593	+	0.366055i	$0.119292\pi$
$678$	−116.411	+	2.66586i	−0.171698	+	0.00393194i
$679$	226.256	−	764.463i	0.333220	−	1.12587i
$680$		−	54.3589i		−	0.0799395i
$681$	−132.741	+	80.7452i	−0.194920	+	0.118569i
$682$	409.548	−	709.358i	0.600510	−	1.04011i
$683$	−490.448	−	283.160i	−0.718079	−	0.414583i	0.0959662	−	0.995385i	$-0.469406\pi$
$683$	−490.448	−	283.160i	−0.718079	−	0.414583i	−0.814045	+	0.580801i	$0.802739\pi$
$684$	−63.1193	−	98.6069i	−0.0922797	−	0.144162i
$685$	−125.567			−0.183310
$686$	−161.611	+	457.362i	−0.235585	+	0.666708i
$687$	−688.042	+	15.7564i	−1.00152	+	0.0229351i
$688$	73.7611	+	127.758i	0.107211	+	0.185695i
$689$	−441.199	−	254.726i	−0.640346	−	0.369704i
$690$	−318.123	−	174.082i	−0.461048	−	0.252292i
$691$	74.5939	+	129.200i	0.107951	+	0.186976i	0.914940	−	0.403590i	$-0.132238\pi$
$691$	74.5939	+	129.200i	0.107951	+	0.186976i	−0.806989	+	0.590566i	$0.798904\pi$
$692$			295.892i			0.427590i
$693$	−801.945	−	197.917i	−1.15721	−	0.285594i
$694$	−865.286			−1.24681
$695$	216.653	−	125.085i	0.311731	−	0.179978i
$696$	96.2199	−	175.836i	0.138247	−	0.252638i
$697$	−63.5352	+	110.046i	−0.0911552	+	0.157885i
$698$	117.473	−	67.8231i	0.168299	−	0.0971678i
$699$	23.2629	+	1015.83i	0.0332802	+	1.45326i
$700$	−68.0622	+	16.3566i	−0.0972317	+	0.0233665i
$701$			516.735i			0.737140i	0.929600	+	0.368570i	$0.120152\pi$
$701$			516.735i			0.737140i	−0.929600	+	0.368570i	$0.879848\pi$
$702$	633.671	−	426.381i	0.902665	−	0.607380i
$703$	60.9710	−	105.605i	0.0867297	−	0.150220i
$704$	−90.8372	−	52.4449i	−0.129030	−	0.0744956i
$705$	−277.861	−	456.787i	−0.394129	−	0.647926i
$706$	577.942			0.818615
$707$	−852.814	+	809.657i	−1.20624	+	1.14520i
$708$	13.8478	+	604.696i	0.0195590	+	0.854090i
$709$	579.028	+	1002.91i	0.816683	+	1.41454i	0.908113	+	0.418724i	$0.137523\pi$
$709$	579.028	+	1002.91i	0.816683	+	1.41454i	−0.0914307	+	0.995811i	$0.529144\pi$
$710$	226.578	+	130.815i	0.319124	+	0.184246i
$711$	−7.71500	+	14.8988i	−0.0108509	+	0.0209548i
$712$	−86.9571	−	150.614i	−0.122131	−	0.211537i
$713$			1688.61i			2.36832i
$714$	179.940	+	181.044i	0.252017	+	0.253563i
$715$	586.422			0.820170
$716$	2.99430	−	1.72876i	0.00418198	−	0.00241447i
$717$	−934.863	−	511.571i	−1.30385	−	0.713488i
$718$	−36.1955	+	62.6924i	−0.0504115	+	0.0873153i
$719$	307.523	−	177.548i	0.427709	−	0.246938i	−0.270661	−	0.962675i	$-0.587242\pi$
$719$	307.523	−	177.548i	0.427709	−	0.246938i	0.698370	+	0.715737i	$0.253909\pi$
$720$	3.68496	+	80.4141i	0.00511799	+	0.111686i
$721$	−494.623	+	118.867i	−0.686023	+	0.164864i
$722$		−	450.700i		−	0.624239i
$723$	137.647	+	226.284i	0.190383	+	0.312980i
$724$	31.5886	−	54.7130i	0.0436306	−	0.0755705i
$725$	−102.287	−	59.0554i	−0.141085	−	0.0814557i
$726$	−184.512	+	112.238i	−0.254149	+	0.154597i
$727$	1445.45			1.98825			0.994123	−	0.108258i	$-0.0345273\pi$
$727$	1445.45			1.98825			0.994123	+	0.108258i	$0.0345273\pi$
$728$	−379.744	−	112.392i	−0.521626	−	0.154384i
$729$	722.132	−	99.8340i	0.990578	−	0.136946i
$730$	110.049	+	190.610i	0.150752	+	0.261110i
$731$	−274.516	−	158.492i	−0.375535	−	0.216815i
$732$	142.526	−	260.457i	0.194707	−	0.355815i
$733$	−260.661	−	451.479i	−0.355609	−	0.615933i	0.631613	−	0.775284i	$-0.282393\pi$
$733$	−260.661	−	451.479i	−0.355609	−	0.615933i	−0.987222	+	0.159351i	$0.949060\pi$
$734$		−	801.208i		−	1.09156i
$735$	172.539	−	279.777i	0.234747	−	0.380649i
$736$	216.236			0.293799
$737$	−665.869	+	384.440i	−0.903486	+	0.521628i
$738$	86.5288	−	167.100i	0.117248	−	0.226423i
$739$	44.5450	−	77.1543i	0.0602775	−	0.104404i	−0.834312	−	0.551293i	$-0.814135\pi$
$739$	44.5450	−	77.1543i	0.0602775	−	0.104404i	0.894589	+	0.446889i	$0.147468\pi$
$740$	−72.6097	+	41.9212i	−0.0981212	+	0.0566503i
$741$	−390.206	+	8.93586i	−0.526594	+	0.0120592i
$742$	−71.5558	+	241.769i	−0.0964363	+	0.325834i
$743$			1229.58i			1.65489i	0.561549	+	0.827444i	$0.310206\pi$
$743$			1229.58i			1.65489i	−0.561549	+	0.827444i	$0.689794\pi$
$744$	320.243	−	194.802i	0.430434	−	0.261830i
$745$	50.7203	−	87.8501i	0.0680809	−	0.117920i
$746$	−495.079	−	285.834i	−0.663645	−	0.383155i
$747$	932.782	−	597.083i	1.24870	−	0.799308i
$748$	225.379			0.301309
$749$	56.6884	+	235.889i	0.0756855	+	0.314939i
$750$	47.4217	−	1.08598i	0.0632290	−	0.00144797i
$751$	−304.602	−	527.587i	−0.405596	−	0.702512i	0.588795	−	0.808282i	$-0.299603\pi$
$751$	−304.602	−	527.587i	−0.405596	−	0.702512i	−0.994391	+	0.105770i	$0.966269\pi$
$752$	276.097	+	159.405i	0.367151	+	0.211975i
$753$	104.846	+	57.3731i	0.139237	+	0.0761927i
$754$	−334.108	−	578.692i	−0.443114	−	0.767496i
$755$		−	388.864i		−	0.515051i
$756$	−278.461	−	255.623i	−0.368335	−	0.338126i
$757$	−902.666			−1.19243			−0.596213	−	0.802827i	$-0.703328\pi$
$757$	−902.666			−1.19243			−0.596213	+	0.802827i	$0.703328\pi$
$758$	26.3411	−	15.2080i	0.0347508	−	0.0200634i
$759$	721.766	−	1318.98i	0.950943	−	1.73779i
$760$	20.5686	−	35.6259i	0.0270639	−	0.0468761i
$761$	300.964	−	173.762i	0.395485	−	0.228333i	−0.289049	−	0.957314i	$-0.593339\pi$
$761$	300.964	−	173.762i	0.395485	−	0.228333i	0.684534	+	0.728981i	$0.260006\pi$
$762$	−12.4424	−	543.328i	−0.0163286	−	0.713028i
$763$	−29.4727	−	31.0437i	−0.0386274	−	0.0406864i
$764$		−	757.724i		−	0.991785i
$765$	−93.2509	−	145.679i	−0.121897	−	0.190431i
$766$	−45.8262	+	79.3733i	−0.0598253	+	0.103621i
$767$	1746.27	+	1008.21i	2.27676	+	1.31449i
$768$	−24.9454	−	41.0089i	−0.0324810	−	0.0533970i
$769$	1165.67			1.51582			0.757911	−	0.652358i	$-0.226220\pi$
$769$	1165.67			1.51582			0.757911	+	0.652358i	$0.226220\pi$
$770$	−67.8165	−	282.195i	−0.0880734	−	0.366487i
$771$	−0.199972	−	8.73227i	−0.000259367	−	0.0113259i
$772$	189.107	+	327.543i	0.244957	+	0.424278i
$773$	176.604	+	101.962i	0.228465	+	0.131905i	0.609864	−	0.792506i	$-0.291224\pi$
$773$	176.604	+	101.962i	0.228465	+	0.131905i	−0.381399	+	0.924411i	$0.624557\pi$
$774$	416.841	+	215.851i	0.538554	+	0.278877i
$775$	−110.438	−	191.283i	−0.142500	−	0.246817i
$776$		−	322.135i		−	0.415122i
$777$	103.060	−	379.974i	0.132638	−	0.489027i
$778$	73.5142			0.0944913
$779$	−83.2797	+	48.0816i	−0.106906	+	0.0617222i
$780$	235.418	+	128.824i	0.301818	+	0.165159i
$781$	−542.376	+	939.423i	−0.694464	+	1.20285i
$782$	−402.382	+	232.316i	−0.514556	+	0.297079i
$783$	−43.7754	−	636.294i	−0.0559072	−	0.812637i
$784$	−10.1693	+	195.736i	−0.0129711	+	0.249663i
$785$			246.573i			0.314106i
$786$	−269.448	−	442.957i	−0.342809	−	0.563559i
$787$	−122.838	+	212.762i	−0.156084	+	0.270346i	−0.933453	−	0.358699i	$-0.883220\pi$
$787$	−122.838	+	212.762i	−0.156084	+	0.270346i	0.777369	+	0.629045i	$0.216554\pi$
$788$	−490.369	−	283.115i	−0.622295	−	0.359282i
$789$	1047.87	−	637.412i	1.32810	−	0.807874i
$790$	−5.89514			−0.00746220
$791$	184.220	+	54.5230i	0.232895	+	0.0689293i
$792$	−333.407	+	15.2783i	−0.420969	+	0.0192908i
$793$	−494.897	−	857.187i	−0.624082	−	1.08094i
$794$	−318.378	−	183.816i	−0.400980	−	0.231506i
$795$	82.0176	−	149.882i	0.103167	−	0.188531i
$796$	304.041	+	526.615i	0.381961	+	0.661577i
$797$			1409.91i			1.76902i	0.466519	+	0.884511i	$0.345508\pi$
$797$			1409.91i			1.76902i	−0.466519	+	0.884511i	$0.654492\pi$
$798$	49.4253	+	186.740i	0.0619364	+	0.234009i
$799$	−685.034			−0.857364
$800$	−24.4949	+	14.1421i	−0.0306186	+	0.0176777i
$801$	−491.415	−	254.467i	−0.613502	−	0.317687i
$802$	−485.892	+	841.590i	−0.605851	+	1.04936i
$803$	−790.295	+	456.277i	−0.984178	+	0.568216i
$804$	−351.765	+	8.05554i	−0.437518	+	0.0100193i
$805$	411.957	+	433.915i	0.511748	+	0.539025i
$806$		−	1249.61i		−	1.55038i
$807$	−281.633	+	171.315i	−0.348987	+	0.212286i
$808$	−237.576	+	411.493i	−0.294030	+	0.509274i
$809$	17.5057	+	10.1069i	0.0216387	+	0.0124931i	0.510780	−	0.859711i	$-0.329357\pi$
$809$	17.5057	+	10.1069i	0.0216387	+	0.0124931i	−0.489142	+	0.872204i	$0.662690\pi$
$810$	147.823	+	209.185i	0.182498	+	0.258253i
$811$	−394.038			−0.485867			−0.242934	−	0.970043i	$-0.578110\pi$
$811$	−394.038			−0.485867			−0.242934	+	0.970043i	$0.578110\pi$
$812$	−239.837	+	227.700i	−0.295366	+	0.280419i
$813$	47.2590	−	1.08225i	0.0581291	−	0.00133118i
$814$	−173.811	−	301.049i	−0.213527	−	0.369839i
$815$	464.939	+	268.432i	0.570477	+	0.329365i
$816$	90.4780	+	49.5109i	0.110880	+	0.0606751i
$817$	−119.942	−	207.746i	−0.146808	−	0.254279i
$818$			554.109i			0.677394i
$819$	−1210.50	+	350.233i	−1.47802	+	0.427635i
$820$	66.1179			0.0806316
$821$	−708.233	+	408.898i	−0.862646	+	0.498049i	−0.864898	−	0.501948i	$-0.832617\pi$
$821$	−708.233	+	408.898i	−0.862646	+	0.498049i	0.00225117	+	0.999997i	$0.499283\pi$
$822$	114.368	−	209.001i	0.139134	−	0.254259i
$823$	−529.872	+	917.766i	−0.643830	+	1.11515i	0.340740	+	0.940158i	$0.389322\pi$
$823$	−529.872	+	917.766i	−0.643830	+	1.11515i	−0.984570	+	0.174989i	$0.944011\pi$
$824$	−178.010	+	102.774i	−0.216031	+	0.124726i
$825$	4.50260	+	196.617i	0.00545769	+	0.238323i
$826$	283.219	−	956.926i	0.342880	−	1.15851i
$827$		−	148.413i		−	0.179459i	−0.995966	−	0.0897295i	$-0.971400\pi$
$827$		−	148.413i		−	0.179459i	0.995966	−	0.0897295i	$-0.0286002\pi$
$828$	579.503	−	370.946i	0.699883	−	0.448002i
$829$	−204.365	+	353.970i	−0.246520	+	0.426985i	−0.962558	−	0.271076i	$-0.912620\pi$
$829$	−204.365	+	353.970i	−0.246520	+	0.426985i	0.716038	+	0.698061i	$0.245954\pi$
$830$	337.006	+	194.571i	0.406032	+	0.234422i
$831$	218.822	+	359.731i	0.263323	+	0.432889i
$832$	−160.019			−0.192331
$833$	−191.368	−	375.161i	−0.229733	−	0.450373i
$834$	10.8671	+	474.539i	0.0130301	+	0.568992i
$835$	−149.389	−	258.749i	−0.178909	−	0.309879i
$836$	147.709	+	85.2801i	0.176686	+	0.102010i
$837$	524.061	−	1071.43i	0.626118	−	1.28008i
$838$	−252.857	−	437.961i	−0.301739	−	0.522627i
$839$		−	1477.73i		−	1.76130i	−0.473765	−	0.880651i	$-0.657105\pi$
$839$		−	1477.73i		−	1.76130i	0.473765	−	0.880651i	$-0.342895\pi$
$840$	34.7673	−	128.184i	0.0413896	−	0.152600i
$841$	282.993			0.336496
$842$	547.430	−	316.059i	0.650154	−	0.375367i
$843$	631.111	+	345.354i	0.748649	+	0.409672i
$844$	−323.760	+	560.769i	−0.383602	+	0.664418i
$845$	447.515	−	258.373i	0.529603	−	0.305767i
$846$	1013.38	−	46.4380i	1.19785	−	0.0548913i
$847$	346.464	−	83.2616i	0.409049	−	0.0983018i
$848$			101.878i			0.120139i
$849$	304.037	+	499.820i	0.358112	+	0.588716i
$850$	30.3875	−	52.6327i	0.0357500	−	0.0619209i
$851$	620.630	+	358.321i	0.729294	+	0.421058i
$852$	−424.107	+	257.981i	−0.497778	+	0.302795i
$853$	976.115			1.14433			0.572166	−	0.820138i	$-0.306103\pi$
$853$	976.115			1.14433			0.572166	+	0.820138i	$0.306103\pi$
$854$	−355.259	+	337.281i	−0.415994	+	0.394943i
$855$	−5.99207	−	130.761i	−0.00700827	−	0.152936i
$856$	49.0137	+	84.8942i	0.0572590	+	0.0991754i
$857$	−358.745	−	207.122i	−0.418606	−	0.241682i	0.275875	−	0.961194i	$-0.411032\pi$
$857$	−358.745	−	207.122i	−0.418606	−	0.241682i	−0.694481	+	0.719511i	$0.744366\pi$
$858$	−534.122	+	976.073i	−0.622520	+	1.13761i
$859$	−168.231	−	291.384i	−0.195845	−	0.339214i	0.751332	−	0.659924i	$-0.229412\pi$
$859$	−168.231	−	291.384i	−0.195845	−	0.339214i	−0.947177	+	0.320711i	$0.896078\pi$
$860$			164.935i			0.191785i
$861$	−220.207	+	218.865i	−0.255758	+	0.254199i
$862$	387.971			0.450082
$863$	1361.70	−	786.179i	1.57787	−	0.910984i	0.582714	−	0.812677i	$-0.301991\pi$
$863$	1361.70	−	786.179i	1.57787	−	0.910984i	0.995156	−	0.0983071i	$-0.0313427\pi$
$864$	−137.202	−	67.1089i	−0.158799	−	0.0776724i
$865$	−165.409	+	286.496i	−0.191224	+	0.331210i
$866$	109.901	−	63.4516i	0.126907	−	0.0732697i
$867$	645.214	−	14.7756i	0.744192	−	0.0170423i
$868$	−601.330	+	144.510i	−0.692776	+	0.166487i
$869$		−	24.4420i		−	0.0281266i
$870$	191.460	−	116.464i	0.220069	−	0.133866i
$871$	−586.499	+	1015.85i	−0.673362	+	1.16630i
$872$	−14.9790	−	8.64812i	−0.0171777	−	0.00991757i
$873$	−552.612	−	863.307i	−0.633003	−	0.988897i
$874$	−351.619			−0.402310
$875$	−75.0445	−	22.2107i	−0.0857652	−	0.0253837i
$876$	−417.497	+	9.56083i	−0.476594	+	0.0109142i
$877$	−213.356	−	369.544i	−0.243280	−	0.421372i	0.718367	−	0.695664i	$-0.244890\pi$
$877$	−213.356	−	369.544i	−0.243280	−	0.421372i	−0.961646	+	0.274292i	$0.911557\pi$
$878$	706.440	+	407.863i	0.804601	+	0.464537i
$879$	−549.787	−	300.852i	−0.625469	−	0.342266i
$880$	−58.6352	−	101.559i	−0.0666309	−	0.115408i
$881$		−	284.614i		−	0.323058i	−0.986868	−	0.161529i	$-0.948358\pi$
$881$		−	284.614i		−	0.323058i	0.986868	−	0.161529i	$-0.0516425\pi$
$882$	308.526	+	542.009i	0.349802	+	0.614523i
$883$	383.725			0.434569			0.217285	−	0.976108i	$-0.430280\pi$
$883$	383.725			0.434569			0.217285	+	0.976108i	$0.430280\pi$
$884$	297.771	−	171.918i	0.336845	−	0.194478i
$885$	−324.627	+	593.235i	−0.366810	+	0.670322i
$886$	503.504	−	872.095i	0.568289	−	0.984306i
$887$	−512.484	+	295.883i	−0.577772	+	0.333577i	−0.760248	−	0.649633i	$-0.774922\pi$
$887$	−512.484	+	295.883i	−0.577772	+	0.333577i	0.182475	+	0.983210i	$0.441589\pi$
$888$	−3.64203	−	159.038i	−0.00410139	−	0.179097i
$889$	−254.476	+	859.812i	−0.286250	+	0.967167i
$890$		−	194.442i		−	0.218474i
$891$	−867.308	+	612.895i	−0.973409	+	0.687873i
$892$	10.7780	−	18.6681i	0.0120830	−	0.0209284i
$893$	−448.959	−	259.207i	−0.502754	−	0.290265i
$894$	100.026	+	164.437i	0.111886	+	0.183934i
$895$	3.86562			0.00431913
$896$	18.5053	+	77.0036i	0.0206533	+	0.0859415i
$897$	−52.5152	−	2293.20i	−0.0585453	−	2.55652i
$898$	114.814	+	198.864i	0.127855	+	0.221452i
$899$	−903.706	−	521.755i	−1.00523	−	0.580372i
$900$	−41.3849	+	79.9205i	−0.0459832	+	0.0888006i
$901$	−109.454	−	189.580i	−0.121481	−	0.210411i
$902$			274.133i			0.303917i
$903$	−545.971	−	549.320i	−0.604619	−	0.608327i
$904$	77.6277			0.0858714
$905$	61.1710	−	35.3171i	0.0675923	−	0.0390244i
$906$	647.247	+	354.183i	0.714400	+	0.390931i
$907$	−191.350	+	331.427i	−0.210970	+	0.365411i	−0.952018	−	0.306041i	$-0.900996\pi$
$907$	−191.350	+	331.427i	−0.210970	+	0.365411i	0.741048	+	0.671452i	$0.234329\pi$
$908$	89.7029	−	51.7900i	0.0987918	−	0.0570375i
$909$	69.2109	+	1510.34i	0.0761396	+	1.66154i
$910$	−304.857	−	321.106i	−0.335007	−	0.352864i
$911$			1329.32i			1.45919i	0.683881	+	0.729593i	$0.260291\pi$
$911$			1329.32i			1.45919i	−0.683881	+	0.729593i	$0.739709\pi$
$912$	40.5635	+	66.6841i	0.0444775	+	0.0731185i
$913$	−806.715	+	1397.27i	−0.883587	+	1.53042i
$914$	105.760	+	61.0605i	0.115711	+	0.0668058i
$915$	283.600	−	172.512i	0.309945	−	0.188538i
$916$	458.815			0.500890
$917$	199.886	+	831.755i	0.217978	+	0.907039i
$918$	327.411	−	22.5250i	0.356657	−	0.0245371i
$919$	−440.677	−	763.276i	−0.479518	−	0.830550i	0.520206	−	0.854041i	$-0.325855\pi$
$919$	−440.677	−	763.276i	−0.479518	−	0.830550i	−0.999724	+	0.0234909i	$0.992522\pi$
$920$	209.370	+	120.880i	0.227576	+	0.131391i
$921$	−694.748	+	1269.61i	−0.754341	+	1.37851i
$922$	−125.604	−	217.553i	−0.136230	−	0.235958i
$923$			1654.89i			1.79295i
$924$	531.469	+	144.150i	0.575183	+	0.156006i
$925$	−93.7387			−0.101339
$926$	−661.627	+	381.991i	−0.714500	+	0.412517i
$927$	−300.753	+	580.800i	−0.324437	+	0.626537i
$928$	−66.8136	+	115.725i	−0.0719974	+	0.124703i
$929$	−242.640	+	140.088i	−0.261184	+	0.150795i	−0.624875	−	0.780725i	$-0.714850\pi$
$929$	−242.640	+	140.088i	−0.261184	+	0.150795i	0.363690	+	0.931520i	$0.381517\pi$
$930$	418.971	−	9.59459i	0.450507	−	0.0103168i
$931$	16.5362	−	318.284i	0.0177618	−	0.341874i
$932$		−	677.397i		−	0.726821i
$933$	1116.41	−	679.105i	1.19658	−	0.727872i
$934$	−204.561	+	354.310i	−0.219016	+	0.379347i
$935$	218.222	+	125.991i	0.233393	+	0.134749i
$936$	−428.844	+	274.508i	−0.458167	+	0.293277i
$937$	339.558			0.362389			0.181194	−	0.983447i	$-0.442004\pi$
$937$	339.558			0.362389			0.181194	+	0.983447i	$0.442004\pi$
$938$	556.665	+	164.755i	0.593460	+	0.175645i
$939$	−1567.78	+	35.9027i	−1.66962	+	0.0382350i
$940$	178.220	+	308.686i	0.189596	+	0.328390i
$941$	−723.539	−	417.736i	−0.768905	−	0.443927i	0.0635791	−	0.997977i	$-0.479748\pi$
$941$	−723.539	−	417.736i	−0.768905	−	0.443927i	−0.832484	+	0.554050i	$0.813082\pi$
$942$	−410.411	−	224.583i	−0.435680	−	0.238411i
$943$	−282.571	−	489.427i	−0.299651	−	0.519010i
$944$		−	403.236i		−	0.427157i
$945$	−126.721	−	403.171i	−0.134097	−	0.426636i
$946$	−683.841			−0.722876
$947$	−225.867	+	130.405i	−0.238508	+	0.137703i	−0.614491	−	0.788924i	$-0.710639\pi$
$947$	−225.867	+	130.405i	−0.238508	+	0.137703i	0.375983	+	0.926627i	$0.377305\pi$
$948$	5.36938	−	9.81220i	0.00566391	−	0.0103504i
$949$	−696.093	+	1205.67i	−0.733502	+	1.27046i
$950$	39.8309	−	22.9964i	0.0419273	−	0.0242067i
$951$	−7.80547	−	340.845i	−0.00820765	−	0.358407i
$952$	−117.165	−	123.411i	−0.123073	−	0.129633i
$953$		−	1040.19i		−	1.09149i	−0.837952	−	0.545743i	$-0.816247\pi$
$953$		−	1040.19i		−	1.09149i	0.837952	−	0.545743i	$-0.183753\pi$
$954$	174.769	+	273.029i	0.183196	+	0.286194i
$955$	423.580	−	733.663i	0.443540	−	0.768233i
$956$	615.270	+	355.227i	0.643588	+	0.371576i
$957$	482.874	+	793.817i	0.504570	+	0.829485i
$958$	79.2878			0.0827638
$959$	−285.074	+	270.648i	−0.297262	+	0.282219i
$960$	−1.22864	−	53.6516i	−0.00127983	−	0.0558870i
$961$	−495.216	−	857.739i	−0.515313	−	0.892549i
$962$	−459.279	−	265.165i	−0.477421	−	0.275639i
$963$	276.988	+	143.431i	0.287630	+	0.148942i
$964$	−88.2870	−	152.918i	−0.0915841	−	0.158628i
$965$			422.856i			0.438193i
$966$	−1097.45	+	290.467i	−1.13608	+	0.300691i
$967$	1038.39			1.07382			0.536912	−	0.843638i	$-0.319591\pi$
$967$	1038.39			1.07382			0.536912	+	0.843638i	$0.319591\pi$
$968$	124.689	−	71.9892i	0.128811	−	0.0743690i
$969$	−147.125	−	80.5092i	−0.151832	−	0.0830848i
$970$	180.079	−	311.906i	0.185648	−	0.321552i
$971$	167.790	−	96.8739i	0.172802	−	0.0997671i	−0.411105	−	0.911588i	$-0.634857\pi$
$971$	167.790	−	96.8739i	0.172802	−	0.0997671i	0.583906	+	0.811821i	$0.301524\pi$
$972$	−482.819	+	55.5167i	−0.496727	+	0.0571160i
$973$	222.258	−	750.954i	0.228426	−	0.771793i
$974$		−	543.157i		−	0.557656i
$975$	155.927	+	256.336i	0.159926	+	0.262909i
$976$	−98.9676	+	171.417i	−0.101401	+	0.175632i
$977$	−897.727	−	518.303i	−0.918860	−	0.530504i	−0.0355891	−	0.999367i	$-0.511331\pi$
$977$	−897.727	−	518.303i	−0.918860	−	0.530504i	−0.883271	+	0.468862i	$0.844664\pi$
$978$	−870.267	+	529.378i	−0.889844	+	0.541286i
$979$	806.182			0.823475
$980$	−119.266	+	183.836i	−0.121700	+	0.187588i
$981$	−54.9786	+	2.51938i	−0.0560434	+	0.00256818i
$982$	−228.464	−	395.711i	−0.232652	−	0.402965i
$983$	−1214.52	−	701.201i	−1.23552	−	0.713328i	−0.267344	−	0.963601i	$-0.586146\pi$
$983$	−1214.52	−	701.201i	−1.23552	−	0.713328i	−0.968175	+	0.250273i	$0.919479\pi$
$984$	−60.2212	+	110.050i	−0.0612004	+	0.111840i
$985$	−316.532	−	548.249i	−0.321352	−	0.556598i
$986$		−	287.128i		−	0.291205i
$987$	−1615.39	−	438.139i	−1.63666	−	0.443910i
$988$	260.206			0.263366
$989$	1220.90	−	704.888i	1.23448	−	0.712728i
$990$	−331.361	−	171.587i	−0.334708	−	0.173320i
$991$	−259.980	+	450.299i	−0.262341	+	0.454388i	−0.966864	−	0.255293i	$-0.917828\pi$
$991$	−259.980	+	450.299i	−0.262341	+	0.454388i	0.704522	+	0.709682i	$0.251161\pi$
$992$	−216.412	+	124.946i	−0.218158	+	0.125953i
$993$	874.941	−	20.0365i	0.881109	−	0.0201777i
$994$	796.358	−	191.379i	0.801165	−	0.192534i
$995$			679.857i			0.683273i
$996$	−630.805	+	383.714i	−0.633338	+	0.385255i
$997$	434.194	−	752.046i	0.435501	−	0.754309i	−0.561836	−	0.827249i	$-0.689905\pi$
$997$	434.194	−	752.046i	0.435501	−	0.754309i	0.997336	+	0.0729397i	$0.0232381\pi$
$998$	−603.556	−	348.463i	−0.604765	−	0.349161i
$999$	−282.585	−	419.967i	−0.282868	−	0.420388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.s.a.11.15	yes	40
3.2	odd	2	inner	210.3.s.a.11.3	✓	40
7.2	even	3	inner	210.3.s.a.191.3	yes	40
21.2	odd	6	inner	210.3.s.a.191.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.s.a.11.3	✓	40	3.2	odd	2	inner
210.3.s.a.11.15	yes	40	1.1	even	1	trivial
210.3.s.a.191.3	yes	40	7.2	even	3	inner
210.3.s.a.191.15	yes	40	21.2	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-1.44013 + 2.63174i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(0.0971326 + 4.24153i) q^{6} +(1.98659 - 6.71219i) q^{7} -2.82843i q^{8} +(-4.85208 - 7.58006i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-1.44013 + 2.63174i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(0.0971326 + 4.24153i) q^{6} +(1.98659 - 6.71219i) q^{7} -2.82843i q^{8} +(-4.85208 - 7.58006i) q^{9} +(1.58114 - 2.73861i) q^{10} +(11.3546 + 6.55561i) q^{11} +(3.11818 + 5.12611i) q^{12} +20.0024 q^{13} +(-2.31317 - 9.62545i) q^{14} +(0.153580 + 6.70645i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(7.44339 + 4.29745i) q^{17} +(-11.3025 - 5.85271i) q^{18} +(3.25218 + 5.63294i) q^{19} -4.47214i q^{20} +(14.8038 + 14.8946i) q^{21} +18.5421 q^{22} +(-33.1042 + 19.1127i) q^{23} +(7.44368 + 4.07329i) q^{24} +(2.50000 - 4.33013i) q^{25} +(24.4978 - 14.1438i) q^{26} +(26.9363 - 1.85315i) q^{27} +(-9.63926 - 10.1531i) q^{28} -23.6222i q^{29} +(4.93027 + 8.10509i) q^{30} +(22.0875 - 38.2567i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-33.6048 + 20.4415i) q^{33} +12.1550 q^{34} +(-3.65744 - 15.2192i) q^{35} +(-17.9811 + 0.823981i) q^{36} +(-9.37387 - 16.2360i) q^{37} +(7.96618 + 4.59928i) q^{38} +(-28.8060 + 52.6410i) q^{39} +(-3.16228 - 5.47723i) q^{40} +14.7844i q^{41} +(28.6629 + 7.77420i) q^{42} -36.8805 q^{43} +(22.7093 - 13.1112i) q^{44} +(-17.8708 - 9.25394i) q^{45} +(-27.0295 + 46.8165i) q^{46} +(-69.0243 + 39.8512i) q^{47} +(11.9969 - 0.274732i) q^{48} +(-41.1069 - 26.6687i) q^{49} -7.07107i q^{50} +(-22.0292 + 13.4002i) q^{51} +(20.0024 - 34.6452i) q^{52} +(-22.0573 - 12.7348i) q^{53} +(31.6798 - 21.3165i) q^{54} +29.3176 q^{55} +(-18.9849 - 5.61892i) q^{56} +(-19.5080 + 0.446740i) q^{57} +(-16.7034 - 28.9311i) q^{58} +(87.3032 + 50.4045i) q^{59} +(11.7695 + 6.44044i) q^{60} +(-24.7419 - 42.8542i) q^{61} -62.4729i q^{62} +(-60.5179 + 17.5096i) q^{63} -8.00000 q^{64} +(38.7345 - 22.3634i) q^{65} +(-26.7029 + 48.7978i) q^{66} +(-29.3214 + 50.7862i) q^{67} +(14.8868 - 8.59489i) q^{68} +(-2.62544 - 114.646i) q^{69} +(-15.2410 - 16.0534i) q^{70} +82.7346i q^{71} +(-21.4397 + 13.7237i) q^{72} +(-34.8005 + 60.2763i) q^{73} +(-22.9612 - 13.2567i) q^{74} +(7.79544 + 12.8153i) q^{75} +13.0087 q^{76} +(66.5595 - 63.1912i) q^{77} +(1.94288 + 84.8407i) q^{78} +(-0.932103 - 1.61445i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-33.9147 + 73.5581i) q^{81} +(10.4542 + 18.1071i) q^{82} +123.057i q^{83} +(40.6019 - 10.7463i) q^{84} +19.2188 q^{85} +(-45.1692 + 26.0785i) q^{86} +(62.1673 + 34.0189i) q^{87} +(18.5421 - 32.1158i) q^{88} +(53.2502 - 30.7440i) q^{89} +(-28.4307 + 1.30283i) q^{90} +(39.7365 - 134.260i) q^{91} +76.4510i q^{92} +(68.8727 + 113.223i) q^{93} +(-56.3581 + 97.6151i) q^{94} +(12.5956 + 7.27210i) q^{95} +(14.4988 - 8.81953i) q^{96} +113.892 q^{97} +(-69.2031 - 3.59539i) q^{98} +(-5.40170 - 117.877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} - 8 q^{6} + 20 q^{7} - 4 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 - 8 * q^6 + 20 * q^7 - 4 * q^9	\( 40 q + 40 q^{4} - 8 q^{6} + 20 q^{7} - 4 q^{9} + 136 q^{13} + 40 q^{15} - 80 q^{16} + 16 q^{18} - 140 q^{19} + 36 q^{21} - 8 q^{24} + 100 q^{25} - 120 q^{27} - 16 q^{28} - 20 q^{30} + 4 q^{31} + 232 q^{33} + 32 q^{34} - 16 q^{36} - 76 q^{37} - 4 q^{39} + 128 q^{42} - 104 q^{43} - 20 q^{45} - 56 q^{46} + 100 q^{49} + 168 q^{51} + 136 q^{52} + 40 q^{54} + 80 q^{55} + 200 q^{57} + 144 q^{58} + 40 q^{60} - 120 q^{61} - 324 q^{63} - 320 q^{64} - 288 q^{66} - 20 q^{67} - 416 q^{69} - 120 q^{70} - 32 q^{72} - 476 q^{73} - 560 q^{76} - 192 q^{78} - 508 q^{79} - 304 q^{81} + 224 q^{82} + 144 q^{84} - 240 q^{85} - 324 q^{87} + 468 q^{91} + 204 q^{93} + 400 q^{94} + 16 q^{96} - 512 q^{97} + 208 q^{99}+O(q^{100}) \) 40 * q + 40 * q^4 - 8 * q^6 + 20 * q^7 - 4 * q^9 + 136 * q^13 + 40 * q^15 - 80 * q^16 + 16 * q^18 - 140 * q^19 + 36 * q^21 - 8 * q^24 + 100 * q^25 - 120 * q^27 - 16 * q^28 - 20 * q^30 + 4 * q^31 + 232 * q^33 + 32 * q^34 - 16 * q^36 - 76 * q^37 - 4 * q^39 + 128 * q^42 - 104 * q^43 - 20 * q^45 - 56 * q^46 + 100 * q^49 + 168 * q^51 + 136 * q^52 + 40 * q^54 + 80 * q^55 + 200 * q^57 + 144 * q^58 + 40 * q^60 - 120 * q^61 - 324 * q^63 - 320 * q^64 - 288 * q^66 - 20 * q^67 - 416 * q^69 - 120 * q^70 - 32 * q^72 - 476 * q^73 - 560 * q^76 - 192 * q^78 - 508 * q^79 - 304 * q^81 + 224 * q^82 + 144 * q^84 - 240 * q^85 - 324 * q^87 + 468 * q^91 + 204 * q^93 + 400 * q^94 + 16 * q^96 - 512 * q^97 + 208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more