LMFDB - Embedded newform 210.3.s.a.11.11

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			11.11
Character	$\chi$	$=$	210.11
Dual form			210.3.s.a.191.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-2.95566 + 0.513907i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.25654 + 2.71937i) q^{6} +(5.52236 + 4.30158i) q^{7} -2.82843i q^{8} +(8.47180 - 3.03786i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-2.95566 + 0.513907i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.25654 + 2.71937i) q^{6} +(5.52236 + 4.30158i) q^{7} -2.82843i q^{8} +(8.47180 - 3.03786i) q^{9} +(-1.58114 + 2.73861i) q^{10} +(1.44901 + 0.836586i) q^{11} +(-2.06554 + 5.63325i) q^{12} +20.4748 q^{13} +(9.80515 + 1.36344i) q^{14} +(5.14904 - 4.29970i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.30178 + 1.90628i) q^{17} +(8.22770 - 9.71108i) q^{18} +(8.08695 + 14.0070i) q^{19} +4.47214i q^{20} +(-18.5328 - 9.87600i) q^{21} +2.36622 q^{22} +(26.8291 - 15.4898i) q^{23} +(1.45355 + 8.35986i) q^{24} +(2.50000 - 4.33013i) q^{25} +(25.0764 - 14.4779i) q^{26} +(-23.4785 + 13.3326i) q^{27} +(12.9729 - 5.26343i) q^{28} -15.5223i q^{29} +(3.26591 - 8.90695i) q^{30} +(-21.5713 + 37.3626i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-4.71270 - 1.72800i) q^{33} +5.39179 q^{34} +(-15.5033 - 2.15579i) q^{35} +(3.21006 - 17.7115i) q^{36} +(-15.1002 - 26.1544i) q^{37} +(19.8089 + 11.4367i) q^{38} +(-60.5166 + 10.5222i) q^{39} +(3.16228 + 5.47723i) q^{40} +45.4889i q^{41} +(-29.6813 + 1.00908i) q^{42} +33.1142 q^{43} +(2.89802 - 1.67317i) q^{44} +(-13.0091 + 15.3546i) q^{45} +(21.9059 - 37.9421i) q^{46} +(-18.0911 + 10.4449i) q^{47} +(7.69154 + 9.21088i) q^{48} +(11.9929 + 47.5097i) q^{49} -7.07107i q^{50} +(-10.7386 - 3.93751i) q^{51} +(20.4748 - 35.4635i) q^{52} +(-29.2139 - 16.8666i) q^{53} +(-19.3276 + 32.9309i) q^{54} -3.74133 q^{55} +(12.1667 - 15.6196i) q^{56} +(-31.1005 - 37.2439i) q^{57} +(-10.9759 - 19.0109i) q^{58} +(-67.5287 - 38.9877i) q^{59} +(-2.29826 - 13.2181i) q^{60} +(-44.2007 - 76.5579i) q^{61} +61.0129i q^{62} +(59.8519 + 19.6659i) q^{63} -8.00000 q^{64} +(-39.6493 + 22.8916i) q^{65} +(-6.99374 + 1.21602i) q^{66} +(17.6918 - 30.6431i) q^{67} +(6.60356 - 3.81257i) q^{68} +(-71.3374 + 59.5702i) q^{69} +(-20.5120 + 8.32221i) q^{70} +111.536i q^{71} +(-8.59238 - 23.9619i) q^{72} +(65.5428 - 113.523i) q^{73} +(-36.9879 - 21.3550i) q^{74} +(-5.16386 + 14.0831i) q^{75} +32.3478 q^{76} +(4.40331 + 10.8530i) q^{77} +(-66.6770 + 55.6786i) q^{78} +(26.0969 + 45.2012i) q^{79} +(7.74597 + 4.47214i) q^{80} +(62.5428 - 51.4724i) q^{81} +(32.1655 + 55.7122i) q^{82} +72.2094i q^{83} +(-35.6385 + 22.2237i) q^{84} -8.52517 q^{85} +(40.5564 - 23.4153i) q^{86} +(7.97703 + 45.8786i) q^{87} +(2.36622 - 4.09842i) q^{88} +(79.2245 - 45.7403i) q^{89} +(-5.07555 + 28.0043i) q^{90} +(113.069 + 88.0741i) q^{91} -61.9592i q^{92} +(44.5565 - 121.517i) q^{93} +(-14.7713 + 25.5847i) q^{94} +(-31.3206 - 18.0830i) q^{95} +(15.9332 + 5.84224i) q^{96} -34.3269 q^{97} +(48.2826 + 49.7070i) q^{98} +(14.8172 + 2.68549i) 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
$3$	−2.95566	+	0.513907i	−0.985219	+	0.171302i
$3$	−2.95566	+	0.513907i	−0.985219	+	0.171302i
$4$	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
$6$	−3.25654	+	2.71937i	−0.542756	+	0.453228i
$7$	5.52236	+	4.30158i	0.788908	+	0.614511i
$7$	5.52236	+	4.30158i	0.788908	+	0.614511i
$8$		−	2.82843i		−	0.353553i
$9$	8.47180	−	3.03786i	0.941311	−	0.337541i
$10$	−1.58114	+	2.73861i	−0.158114	+	0.273861i
$11$	1.44901	+	0.836586i	0.131728	+	0.0760533i	0.564416	−	0.825491i	$-0.309101\pi$
$11$	1.44901	+	0.836586i	0.131728	+	0.0760533i	−0.432688	+	0.901544i	$0.642435\pi$
$12$	−2.06554	+	5.63325i	−0.172129	+	0.469438i
$13$	20.4748			1.57499			0.787494	−	0.616323i	$-0.211378\pi$
$13$	20.4748			1.57499			0.787494	+	0.616323i	$0.211378\pi$
$14$	9.80515	+	1.36344i	0.700368	+	0.0973885i
$15$	5.14904	−	4.29970i	0.343269	−	0.286647i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	3.30178	+	1.90628i	0.194222	+	0.112134i	0.593958	−	0.804496i	$-0.297565\pi$
$17$	3.30178	+	1.90628i	0.194222	+	0.112134i	−0.399735	+	0.916631i	$0.630898\pi$
$18$	8.22770	−	9.71108i	0.457094	−	0.539504i
$19$	8.08695	+	14.0070i	0.425629	+	0.737211i	0.996479	−	0.0838435i	$-0.0267196\pi$
$19$	8.08695	+	14.0070i	0.425629	+	0.737211i	−0.570850	+	0.821054i	$0.693386\pi$
$20$			4.47214i			0.223607i
$21$	−18.5328	−	9.87600i	−0.882514	−	0.470286i
$22$	2.36622			0.107556
$23$	26.8291	−	15.4898i	1.16648	−	0.673470i	0.213635	−	0.976914i	$-0.431470\pi$
$23$	26.8291	−	15.4898i	1.16648	−	0.673470i	0.952849	+	0.303444i	$0.0981364\pi$
$24$	1.45355	+	8.35986i	0.0605645	+	0.348327i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	25.0764	−	14.4779i	0.964479	−	0.556842i
$27$	−23.4785	+	13.3326i	−0.869576	+	0.493800i
$28$	12.9729	−	5.26343i	0.463318	−	0.187979i
$29$		−	15.5223i		−	0.535252i	−0.963523	−	0.267626i	$-0.913761\pi$
$29$		−	15.5223i		−	0.535252i	0.963523	−	0.267626i	$-0.0862392\pi$
$30$	3.26591	−	8.90695i	0.108864	−	0.296898i
$31$	−21.5713	+	37.3626i	−0.695849	+	1.20525i	0.274045	+	0.961717i	$0.411638\pi$
$31$	−21.5713	+	37.3626i	−0.695849	+	1.20525i	−0.969894	+	0.243528i	$0.921695\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	−4.71270	−	1.72800i	−0.142809	−	0.0523638i
$34$	5.39179			0.158582
$35$	−15.5033	−	2.15579i	−0.442952	−	0.0615939i
$36$	3.21006	−	17.7115i	0.0891684	−	0.491985i
$37$	−15.1002	−	26.1544i	−0.408115	−	0.706875i	0.586564	−	0.809903i	$-0.300480\pi$
$37$	−15.1002	−	26.1544i	−0.408115	−	0.706875i	−0.994678	+	0.103028i	$0.967147\pi$
$38$	19.8089	+	11.4367i	0.521287	+	0.300965i
$39$	−60.5166	+	10.5222i	−1.55171	+	0.269799i
$40$	3.16228	+	5.47723i	0.0790569	+	0.136931i
$41$			45.4889i			1.10948i	0.832022	+	0.554742i	$0.187183\pi$
$41$			45.4889i			1.10948i	−0.832022	+	0.554742i	$0.812817\pi$
$42$	−29.6813	+	1.00908i	−0.706698	+	0.0240258i
$43$	33.1142			0.770098			0.385049	−	0.922896i	$-0.374185\pi$
$43$	33.1142			0.770098			0.385049	+	0.922896i	$0.374185\pi$
$44$	2.89802	−	1.67317i	0.0658641	−	0.0380267i
$45$	−13.0091	+	15.3546i	−0.289092	+	0.341212i
$46$	21.9059	−	37.9421i	0.476215	−	0.824829i
$47$	−18.0911	+	10.4449i	−0.384918	+	0.222232i	−0.679956	−	0.733253i	$-0.738001\pi$
$47$	−18.0911	+	10.4449i	−0.384918	+	0.222232i	0.295038	+	0.955486i	$0.404668\pi$
$48$	7.69154	+	9.21088i	0.160240	+	0.191893i
$49$	11.9929	+	47.5097i	0.244752	+	0.969586i
$50$		−	7.07107i		−	0.141421i
$51$	−10.7386	−	3.93751i	−0.210560	−	0.0772061i
$52$	20.4748	−	35.4635i	0.393747	−	0.681989i
$53$	−29.2139	−	16.8666i	−0.551205	−	0.318238i	0.198403	−	0.980121i	$-0.436425\pi$
$53$	−29.2139	−	16.8666i	−0.551205	−	0.318238i	−0.749608	+	0.661882i	$0.769758\pi$
$54$	−19.3276	+	32.9309i	−0.357919	+	0.609831i
$55$	−3.74133			−0.0680241
$56$	12.1667	−	15.6196i	0.217262	−	0.278921i
$57$	−31.1005	−	37.2439i	−0.545623	−	0.653403i
$58$	−10.9759	−	19.0109i	−0.189240	−	0.327774i
$59$	−67.5287	−	38.9877i	−1.14455	−	0.660809i	−0.197000	−	0.980403i	$-0.563120\pi$
$59$	−67.5287	−	38.9877i	−1.14455	−	0.660809i	−0.947554	+	0.319594i	$0.896453\pi$
$60$	−2.29826	−	13.2181i	−0.0383044	−	0.220302i
$61$	−44.2007	−	76.5579i	−0.724602	−	1.25505i	−0.959138	−	0.282940i	$-0.908690\pi$
$61$	−44.2007	−	76.5579i	−0.724602	−	1.25505i	0.234536	−	0.972107i	$-0.424643\pi$
$62$			61.0129i			0.984079i
$63$	59.8519	+	19.6659i	0.950030	+	0.312158i
$64$	−8.00000			−0.125000
$65$	−39.6493	+	22.8916i	−0.609990	+	0.352178i
$66$	−6.99374	+	1.21602i	−0.105966	+	0.0184245i
$67$	17.6918	−	30.6431i	0.264056	−	0.457359i	−0.703260	−	0.710933i	$-0.748273\pi$
$67$	17.6918	−	30.6431i	0.264056	−	0.457359i	0.967316	+	0.253574i	$0.0816062\pi$
$68$	6.60356	−	3.81257i	0.0971112	−	0.0560672i
$69$	−71.3374	+	59.5702i	−1.03387	+	0.863337i
$70$	−20.5120	+	8.32221i	−0.293028	+	0.118889i
$71$			111.536i			1.57093i	0.618905	+	0.785466i	$0.287577\pi$
$71$			111.536i			1.57093i	−0.618905	+	0.785466i	$0.712423\pi$
$72$	−8.59238	−	23.9619i	−0.119339	−	0.332804i
$73$	65.5428	−	113.523i	0.897847	−	1.55512i	0.0676053	−	0.997712i	$-0.478464\pi$
$73$	65.5428	−	113.523i	0.897847	−	1.55512i	0.830241	−	0.557404i	$-0.188203\pi$
$74$	−36.9879	−	21.3550i	−0.499836	−	0.288581i
$75$	−5.16386	+	14.0831i	−0.0688514	+	0.187775i
$76$	32.3478			0.425629
$77$	4.40331	+	10.8530i	0.0571858	+	0.140948i
$78$	−66.6770	+	55.6786i	−0.854834	+	0.713829i
$79$	26.0969	+	45.2012i	0.330341	+	0.572167i	0.982579	−	0.185848i	$-0.0595031\pi$
$79$	26.0969	+	45.2012i	0.330341	+	0.572167i	−0.652238	+	0.758014i	$0.726170\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$	62.5428	−	51.4724i	0.772133	−	0.635461i
$82$	32.1655	+	55.7122i	0.392262	+	0.679418i
$83$			72.2094i			0.869992i	0.900432	+	0.434996i	$0.143250\pi$
$83$			72.2094i			0.869992i	−0.900432	+	0.434996i	$0.856750\pi$
$84$	−35.6385	+	22.2237i	−0.424268	+	0.264568i
$85$	−8.52517			−0.100296
$86$	40.5564	−	23.4153i	0.471587	−	0.272271i
$87$	7.97703	+	45.8786i	0.0916900	+	0.527341i
$88$	2.36622	−	4.09842i	0.0268889	−	0.0465729i
$89$	79.2245	−	45.7403i	0.890163	−	0.513936i	0.0161671	−	0.999869i	$-0.494854\pi$
$89$	79.2245	−	45.7403i	0.890163	−	0.513936i	0.873996	+	0.485934i	$0.161520\pi$
$90$	−5.07555	+	28.0043i	−0.0563951	+	0.311158i
$91$	113.069	+	88.0741i	1.24252	+	0.967847i
$92$		−	61.9592i		−	0.673470i
$93$	44.5565	−	121.517i	0.479102	−	1.30663i
$94$	−14.7713	+	25.5847i	−0.157142	+	0.272178i
$95$	−31.3206	−	18.0830i	−0.329691	−	0.190347i
$96$	15.9332	+	5.84224i	0.165971	+	0.0608566i
$97$	−34.3269			−0.353885			−0.176943	−	0.984221i	$-0.556621\pi$
$97$	−34.3269			−0.353885			−0.176943	+	0.984221i	$0.556621\pi$
$98$	48.2826	+	49.7070i	0.492680	+	0.507215i
$99$	14.8172	+	2.68549i	0.149668	+	0.0271262i
$100$	−5.00000	−	8.66025i	−0.0500000	−	0.0866025i
$101$	−87.7879	−	50.6844i	−0.869187	−	0.501825i	−0.00210892	−	0.999998i	$-0.500671\pi$
$101$	−87.7879	−	50.6844i	−0.869187	−	0.501825i	−0.867078	+	0.498173i	$0.834005\pi$
$102$	−15.9363	+	2.77088i	−0.156238	+	0.0271655i
$103$	−25.0852	−	43.4488i	−0.243545	−	0.421833i	0.718176	−	0.695861i	$-0.244977\pi$
$103$	−25.0852	−	43.4488i	−0.243545	−	0.421833i	−0.961722	+	0.274028i	$0.911644\pi$
$104$		−	57.9116i		−	0.556842i
$105$	46.9303	−	1.59550i	0.446955	−	0.0151952i
$106$	−47.7060			−0.450057
$107$	−143.798	+	83.0220i	−1.34391	+	0.775906i	−0.987379	−	0.158377i	$-0.949374\pi$
$107$	−143.798	+	83.0220i	−1.34391	+	0.775906i	−0.356531	+	0.934284i	$0.616040\pi$
$108$	−0.385799	+	53.9986i	−0.00357221	+	0.499987i
$109$	−10.0485	+	17.4045i	−0.0921878	+	0.159674i	−0.908431	−	0.418034i	$-0.862719\pi$
$109$	−10.0485	+	17.4045i	−0.0921878	+	0.159674i	0.816244	+	0.577708i	$0.196053\pi$
$110$	−4.58217	+	2.64552i	−0.0416561	+	0.0240502i
$111$	58.0720	+	69.5432i	0.523171	+	0.626516i
$112$	3.85639	−	27.7332i	0.0344320	−	0.247618i
$113$		−	121.396i		−	1.07430i	−0.843487	−	0.537150i	$-0.819501\pi$
$113$		−	121.396i		−	1.07430i	0.843487	−	0.537150i	$-0.180499\pi$
$114$	−64.4257	−	23.6229i	−0.565137	−	0.207219i
$115$	−34.6363	+	59.9918i	−0.301185	+	0.521668i
$116$	−26.8854	−	15.5223i	−0.231771	−	0.133813i
$117$	173.459	−	62.1998i	1.48255	−	0.531622i
$118$	−110.274			−0.934525
$119$	10.0336	+	24.7301i	0.0843159	+	0.207816i
$120$	−12.1614	−	14.5637i	−0.101345	−	0.121364i
$121$	−59.1002	−	102.365i	−0.488432	−	0.845989i
$122$	−108.269	−	62.5092i	−0.887452	−	0.512371i
$123$	−23.3770	−	134.449i	−0.190057	−	1.09308i
$124$	43.1426	+	74.7252i	0.347924	+	0.602623i
$125$			11.1803i			0.0894427i
$126$	87.2092	−	18.2360i	0.692137	−	0.144730i
$127$	157.106			1.23706			0.618528	−	0.785763i	$-0.287729\pi$
$127$	157.106			1.23706			0.618528	+	0.785763i	$0.287729\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−97.8741	+	17.0176i	−0.758714	+	0.131920i
$130$	−32.3736	+	56.0726i	−0.249027	+	0.431328i
$131$	155.596	−	89.8336i	1.18776	−	0.685752i	0.229962	−	0.973200i	$-0.426140\pi$
$131$	155.596	−	89.8336i	1.18776	−	0.685752i	0.957796	+	0.287447i	$0.0928066\pi$
$132$	−7.70569	+	6.43464i	−0.0583765	+	0.0487472i
$133$	−15.5932	+	112.138i	−0.117242	+	0.843145i
$134$		−	50.0399i		−	0.373432i
$135$	30.5597	−	52.0683i	0.226368	−	0.385691i
$136$	5.39179	−	9.33885i	0.0396455	−	0.0686680i
$137$	121.407	+	70.0946i	0.886185	+	0.511639i	0.872693	−	0.488270i	$-0.162372\pi$
$137$	121.407	+	70.0946i	0.886185	+	0.511639i	0.0134923	+	0.999909i	$0.495705\pi$
$138$	−45.2476	+	123.401i	−0.327881	+	0.894213i
$139$	−180.216			−1.29652			−0.648260	−	0.761419i	$-0.724503\pi$
$139$	−180.216			−1.29652			−0.648260	+	0.761419i	$0.724503\pi$
$140$	−19.2372	+	24.6967i	−0.137409	+	0.176405i
$141$	48.1034	−	40.1687i	0.341159	−	0.284885i
$142$	78.8680	+	136.603i	0.555408	+	0.961995i
$143$	29.6682	+	17.1290i	0.207470	+	0.119783i
$144$	−27.4671	−	23.2714i	−0.190744	−	0.161607i
$145$	17.3545	+	30.0588i	0.119686	+	0.207302i
$146$		−	185.383i		−	1.26975i
$147$	−59.8623	−	134.259i	−0.407227	−	0.913327i
$148$	−60.4010			−0.408115
$149$	−162.127	+	93.6039i	−1.08810	+	0.628214i	−0.933069	−	0.359696i	$-0.882880\pi$
$149$	−162.127	+	93.6039i	−1.08810	+	0.628214i	−0.155029	+	0.987910i	$0.549547\pi$
$150$	3.63387	+	20.8996i	0.0242258	+	0.139331i
$151$	13.4408	−	23.2802i	0.0890121	−	0.154173i	−0.818082	−	0.575102i	$-0.804962\pi$
$151$	13.4408	−	23.2802i	0.0890121	−	0.154173i	0.907094	+	0.420929i	$0.138296\pi$
$152$	39.6178	−	22.8733i	0.260643	−	0.150483i
$153$	33.7631	+	6.11929i	0.220674	+	0.0399954i
$154$	13.0671	+	10.1785i	0.0848515	+	0.0660941i
$155$		−	96.4698i		−	0.622386i
$156$	−42.2916	+	115.340i	−0.271100	+	0.739358i
$157$	60.6099	−	104.980i	0.386051	−	0.668659i	−0.605864	−	0.795568i	$-0.707172\pi$
$157$	60.6099	−	104.980i	0.386051	−	0.668659i	0.991914	+	0.126909i	$0.0405057\pi$
$158$	63.9241	+	36.9066i	0.404583	+	0.233586i
$159$	95.0140	+	34.8387i	0.597572	+	0.219112i
$160$	12.6491			0.0790569
$161$	214.791	+	29.8673i	1.33410	+	0.185511i
$162$	40.2025	−	107.265i	0.248163	−	0.662129i
$163$	−23.1412	−	40.0818i	−0.141971	−	0.245901i	0.786268	−	0.617886i	$-0.212011\pi$
$163$	−23.1412	−	40.0818i	−0.141971	−	0.245901i	−0.928239	+	0.371985i	$0.878677\pi$
$164$	78.7890	+	45.4889i	0.480421	+	0.277371i
$165$	11.0581	−	1.92269i	0.0670186	−	0.0116527i
$166$	51.0597	+	88.4380i	0.307589	+	0.532759i
$167$			54.3323i			0.325343i	0.986680	+	0.162671i	$0.0520111\pi$
$167$			54.3323i			0.325343i	−0.986680	+	0.162671i	$0.947989\pi$
$168$	−27.9336	+	52.4187i	−0.166271	+	0.312016i
$169$	250.219			1.48058
$170$	−10.4412	+	6.02820i	−0.0614185	+	0.0354600i
$171$	111.062	+	94.0975i	0.649488	+	0.550278i
$172$	33.1142	−	57.3555i	0.192524	−	0.333462i
$173$	176.525	−	101.917i	1.02038	−	0.589116i	0.106165	−	0.994349i	$-0.466143\pi$
$173$	176.525	−	101.917i	1.02038	−	0.589116i	0.914213	+	0.405233i	$0.132810\pi$
$174$	42.2109	+	50.5490i	0.242591	+	0.290511i
$175$	32.4323	−	13.1586i	0.185327	−	0.0751918i
$176$		−	6.69269i		−	0.0380267i
$177$	219.628	+	80.5308i	1.24083	+	0.454976i
$178$	64.6865	−	112.040i	0.363407	−	0.629440i
$179$	3.27150	+	1.88880i	0.0182765	+	0.0105520i	0.509110	−	0.860701i	$-0.329974\pi$
$179$	3.27150	+	1.88880i	0.0182765	+	0.0105520i	−0.490834	+	0.871253i	$0.663308\pi$
$180$	13.5857	+	37.8870i	0.0754764	+	0.210484i
$181$	−316.261			−1.74730			−0.873649	−	0.486558i	$-0.838252\pi$
$181$	−316.261			−1.74730			−0.873649	+	0.486558i	$0.838252\pi$
$182$	200.759	+	27.9162i	1.10307	+	0.153386i
$183$	169.986	+	203.564i	0.928884	+	1.11237i
$184$	−43.8118	−	75.8843i	−0.238108	−	0.412414i
$185$	58.4830	+	33.7652i	0.316124	+	0.182514i
$186$	−31.3550	−	180.333i	−0.168575	−	0.969533i
$187$	3.18954	+	5.52445i	0.0170564	+	0.0295425i
$188$			41.7797i			0.222232i
$189$	−187.008	−	27.3674i	−0.989461	−	0.144801i
$190$	−51.1464			−0.269191
$191$	−239.612	+	138.340i	−1.25451	+	0.724292i	−0.972002	−	0.234972i	$-0.924500\pi$
$191$	−239.612	+	138.340i	−1.25451	+	0.724292i	−0.282509	+	0.959265i	$0.591167\pi$
$192$	23.6452	−	4.11126i	0.123152	−	0.0214128i
$193$	−54.5397	+	94.4655i	−0.282589	+	0.489459i	−0.972022	−	0.234891i	$-0.924527\pi$
$193$	−54.5397	+	94.4655i	−0.282589	+	0.489459i	0.689433	+	0.724350i	$0.257860\pi$
$194$	−42.0417	+	24.2728i	−0.216710	+	0.125117i
$195$	105.426	−	88.0356i	0.540644	−	0.451465i
$196$	94.2821	+	26.7375i	0.481031	+	0.136416i
$197$			233.615i			1.18586i	0.805253	+	0.592931i	$0.202029\pi$
$197$			233.615i			1.18586i	−0.805253	+	0.592931i	$0.797971\pi$
$198$	20.0462	−	7.18827i	0.101243	−	0.0363044i
$199$	−5.50239	+	9.53042i	−0.0276502	+	0.0478916i	−0.879519	−	0.475863i	$-0.842136\pi$
$199$	−5.50239	+	9.53042i	−0.0276502	+	0.0478916i	0.851869	+	0.523755i	$0.175469\pi$
$200$	−12.2474	−	7.07107i	−0.0612372	−	0.0353553i
$201$	−36.5431	+	99.6622i	−0.181807	+	0.495832i
$202$	−143.357			−0.709688
$203$	66.7705	−	85.7198i	0.328919	−	0.422265i
$204$	−17.5586	+	14.6623i	−0.0860714	+	0.0718738i
$205$	−50.8581	−	88.0888i	−0.248088	−	0.429701i
$206$	−61.4458	−	35.4758i	−0.298281	−	0.172212i
$207$	180.235	−	212.730i	0.870701	−	1.02768i
$208$	−40.9497	−	70.9269i	−0.196873	−	0.340995i
$209$			27.0617i			0.129482i
$210$	56.3495	−	35.1388i	0.268331	−	0.167328i
$211$	−257.057			−1.21828			−0.609140	−	0.793063i	$-0.708485\pi$
$211$	−257.057			−1.21828			−0.609140	+	0.793063i	$0.708485\pi$
$212$	−58.4277	+	33.7333i	−0.275602	+	0.159119i
$213$	−57.3192	−	329.662i	−0.269104	−	1.54771i
$214$	−117.411	+	203.362i	−0.548649	+	0.950287i
$215$	−64.1254	+	37.0228i	−0.298257	+	0.172199i
$216$	37.7103	+	66.4073i	0.174585	+	0.307441i
$217$	−279.843	+	113.539i	−1.28960	+	0.523221i
$218$			28.4214i			0.130373i
$219$	−135.381	+	369.219i	−0.618180	+	1.68593i
$220$	−3.74133	+	6.48017i	−0.0170060	+	0.0294553i
$221$	67.6034	+	39.0309i	0.305898	+	0.176610i
$222$	120.298	+	44.1096i	0.541883	+	0.198692i
$223$	229.988			1.03134			0.515668	−	0.856788i	$-0.327544\pi$
$223$	229.988			1.03134			0.515668	+	0.856788i	$0.327544\pi$
$224$	−14.8872	−	36.6929i	−0.0664608	−	0.163808i
$225$	8.02516	−	44.2786i	0.0356674	−	0.196794i
$226$	−85.8399	−	148.679i	−0.379822	−	0.657872i
$227$	−223.709	−	129.159i	−0.985503	−	0.568980i	−0.0815757	−	0.996667i	$-0.525995\pi$
$227$	−223.709	−	129.159i	−0.985503	−	0.568980i	−0.903927	+	0.427687i	$0.859329\pi$
$228$	−95.6089	+	16.6238i	−0.419337	+	0.0729112i
$229$	−187.423	−	324.626i	−0.818440	−	1.41758i	−0.906831	−	0.421494i	$-0.861506\pi$
$229$	−187.423	−	324.626i	−0.818440	−	1.41758i	0.0883907	−	0.996086i	$-0.471828\pi$
$230$			97.9661i			0.425940i
$231$	−18.5921	−	29.8147i	−0.0804852	−	0.129068i
$232$	−43.9037			−0.189240
$233$	−34.6846	+	20.0252i	−0.148861	+	0.0859450i	−0.572580	−	0.819849i	$-0.694058\pi$
$233$	−34.6846	+	20.0252i	−0.148861	+	0.0859450i	0.423719	+	0.905793i	$0.360724\pi$
$234$	168.461	−	198.833i	0.719918	−	0.849712i
$235$	23.3555	−	40.4530i	0.0993853	−	0.172140i
$236$	−135.057	+	77.9755i	−0.572277	+	0.330404i
$237$	−100.363	−	120.188i	−0.423471	−	0.507121i
$238$	29.7754	+	23.1932i	0.125107	+	0.0974504i
$239$		−	319.971i		−	1.33879i	−0.742906	−	0.669396i	$-0.766553\pi$
$239$		−	319.971i		−	1.33879i	0.742906	−	0.669396i	$-0.233447\pi$
$240$	−25.1927	−	9.23739i	−0.104969	−	0.0384891i
$241$	−215.310	+	372.929i	−0.893404	+	1.54742i	−0.0576368	+	0.998338i	$0.518357\pi$
$241$	−215.310	+	372.929i	−0.893404	+	1.54742i	−0.835767	+	0.549084i	$0.814977\pi$
$242$	−144.765	−	83.5804i	−0.598204	−	0.345373i
$243$	−158.403	+	184.276i	−0.651863	+	0.758336i
$244$	−176.803			−0.724602
$245$	−76.3415	−	78.5937i	−0.311598	−	0.320791i
$246$	−123.701	−	148.136i	−0.502850	−	0.602179i
$247$	165.579	+	286.791i	0.670360	+	1.16110i
$248$	105.677	+	61.0129i	0.426119	+	0.246020i
$249$	−37.1089	−	213.426i	−0.149032	−	0.857132i
$250$	7.90569	+	13.6931i	0.0316228	+	0.0547723i
$251$		−	45.2522i		−	0.180287i	−0.995929	−	0.0901437i	$-0.971267\pi$
$251$		−	45.2522i		−	0.180287i	0.995929	−	0.0901437i	$-0.0287326\pi$
$252$	93.9143	−	84.0006i	0.372676	−	0.333336i
$253$	51.8342			0.204878
$254$	192.415	−	111.091i	0.757539	−	0.437365i
$255$	25.1975	−	4.38114i	0.0988135	−	0.0171810i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−335.580	+	193.747i	−1.30576	+	0.753880i	−0.981385	−	0.192049i	$-0.938487\pi$
$257$	−335.580	+	193.747i	−1.30576	+	0.753880i	−0.324373	+	0.945929i	$0.605153\pi$
$258$	−107.838	+	90.0497i	−0.417975	+	0.349030i
$259$	29.1162	−	209.389i	0.112418	−	0.808451i
$260$			91.5662i			0.352178i
$261$	−47.1547	−	131.502i	−0.180669	−	0.503839i
$262$	127.044	−	220.046i	0.484900	−	0.839872i
$263$	−292.570	−	168.916i	−1.11244	−	0.642265i	−0.172976	−	0.984926i	$-0.555338\pi$
$263$	−292.570	−	168.916i	−1.11244	−	0.642265i	−0.939459	+	0.342661i	$0.888672\pi$
$264$	−4.88753	+	13.3295i	−0.0185134	+	0.0504907i
$265$	75.4299			0.284641
$266$	60.1961	+	148.367i	0.226301	+	0.557770i
$267$	−210.654	+	175.907i	−0.788967	+	0.658826i
$268$	−35.3836	−	61.2861i	−0.132028	−	0.228680i
$269$	438.124	+	252.951i	1.62871	+	0.940339i	0.984477	+	0.175514i	$0.0561586\pi$
$269$	438.124	+	252.951i	1.62871	+	0.940339i	0.644238	+	0.764825i	$0.277175\pi$
$270$	0.610002	−	85.3793i	0.00225927	−	0.316220i
$271$	−149.385	−	258.742i	−0.551236	−	0.954768i	−0.998186	−	0.0602092i	$-0.980823\pi$
$271$	−149.385	−	258.742i	−0.551236	−	0.954768i	0.446950	−	0.894559i	$-0.352510\pi$
$272$		−	15.2503i		−	0.0560672i
$273$	−379.456	−	202.210i	−1.38995	−	0.740694i
$274$	198.257			0.723567
$275$	7.24505	−	4.18293i	0.0263456	−	0.0152107i
$276$	31.8413	+	183.130i	0.115367	+	0.663515i
$277$	−108.773	+	188.401i	−0.392683	+	0.680147i	−0.992802	−	0.119764i	$-0.961786\pi$
$277$	−108.773	+	188.401i	−0.392683	+	0.680147i	0.600120	+	0.799910i	$0.295120\pi$
$278$	−220.719	+	127.432i	−0.793953	+	0.458389i
$279$	−69.2453	+	382.059i	−0.248191	+	1.36939i
$280$	−6.09748	+	43.8500i	−0.0217767	+	0.156607i
$281$			17.2556i			0.0614079i	0.999529	+	0.0307040i	$0.00977491\pi$
$281$			17.2556i			0.0614079i	−0.999529	+	0.0307040i	$0.990225\pi$
$282$	30.5108	−	83.2107i	0.108194	−	0.295073i
$283$	−63.6733	+	110.285i	−0.224994	+	0.389701i	−0.956318	−	0.292330i	$-0.905570\pi$
$283$	−63.6733	+	110.285i	−0.224994	+	0.389701i	0.731324	+	0.682031i	$0.238903\pi$
$284$	193.186	+	111.536i	0.680233	+	0.392733i
$285$	101.866	+	37.3511i	0.357424	+	0.131057i
$286$	48.4480			0.169399
$287$	−195.674	+	251.206i	−0.681790	+	0.875281i
$288$	−50.0955	−	9.07943i	−0.173943	−	0.0315258i
$289$	−137.232	−	237.693i	−0.474852	−	0.822467i
$290$	42.5096	+	24.5429i	0.146585	+	0.0846308i
$291$	101.458	−	17.6408i	0.348654	−	0.0606214i
$292$	−131.086	−	227.047i	−0.448923	−	0.777558i
$293$		−	86.6441i		−	0.295714i	−0.989009	−	0.147857i	$-0.952763\pi$
$293$		−	86.6441i		−	0.295714i	0.989009	−	0.147857i	$-0.0472375\pi$
$294$	−168.252	−	122.104i	−0.572284	−	0.415320i
$295$	174.358			0.591045
$296$	−73.9758	+	42.7099i	−0.249918	+	0.144290i
$297$	−45.1745	−	0.322754i	−0.152103	−	0.00108671i
$298$	−132.376	+	229.282i	−0.444214	+	0.769402i
$299$	549.322	−	317.151i	1.83720	−	1.06071i
$300$	19.2288	+	23.0272i	0.0640961	+	0.0767573i
$301$	182.868	+	142.443i	0.607536	+	0.473233i
$302$		−	38.0164i		−	0.125882i
$303$	285.518	+	104.691i	0.942303	+	0.345514i
$304$	32.3478	−	56.0280i	0.106407	−	0.184303i
$305$	171.189	+	98.8358i	0.561274	+	0.324052i
$306$	45.6781	−	16.3795i	0.149275	−	0.0535279i
$307$	−420.365			−1.36927			−0.684634	−	0.728887i	$-0.740038\pi$
$307$	−420.365			−1.36927			−0.684634	+	0.728887i	$0.740038\pi$
$308$	23.2012	+	3.22620i	0.0753285	+	0.0104747i
$309$	96.4717	+	115.528i	0.312206	+	0.373877i
$310$	−68.2145	−	118.151i	−0.220047	−	0.381132i
$311$	−109.195	−	63.0437i	−0.351109	−	0.202713i	0.314065	−	0.949402i	$-0.398309\pi$
$311$	−109.195	−	63.0437i	−0.351109	−	0.202713i	−0.665174	+	0.746689i	$0.731642\pi$
$312$	29.7612	+	171.167i	0.0953884	+	0.548611i
$313$	96.7106	+	167.508i	0.308980	+	0.535168i	0.978139	−	0.207950i	$-0.0666792\pi$
$313$	96.7106	+	167.508i	0.308980	+	0.535168i	−0.669160	+	0.743119i	$0.733346\pi$
$314$		−	171.431i		−	0.545958i
$315$	−137.890	+	28.8336i	−0.437746	+	0.0915351i
$316$	104.388			0.330341
$317$	33.2695	−	19.2081i	0.104951	−	0.0605935i	−0.446606	−	0.894731i	$-0.647367\pi$
$317$	33.2695	−	19.2081i	0.104951	−	0.0605935i	0.551557	+	0.834137i	$0.314034\pi$
$318$	141.003	−	24.5165i	0.443404	−	0.0770958i
$319$	12.9858	−	22.4920i	0.0407077	−	0.0705078i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$	382.353	−	319.283i	1.19113	−	0.994652i
$322$	284.183	−	115.300i	0.882556	−	0.358075i
$323$			61.6641i			0.190911i
$324$	−26.6100	−	159.800i	−0.0821296	−	0.493209i
$325$	51.1871	−	88.6586i	0.157499	−	0.272796i
$326$	−56.6842	−	32.7266i	−0.173878	−	0.100388i
$327$	20.7555	−	56.6056i	0.0634726	−	0.173106i
$328$	128.662			0.392262
$329$	−144.835	−	20.1398i	−0.440229	−	0.0612153i
$330$	12.1838	−	10.1741i	0.0369205	−	0.0308305i
$331$	314.486	+	544.705i	0.950108	+	1.64564i	0.745185	+	0.666858i	$0.232361\pi$
$331$	314.486	+	544.705i	0.950108	+	1.64564i	0.204923	+	0.978778i	$0.434306\pi$
$332$	125.070	+	72.2094i	0.376718	+	0.217498i
$333$	−207.380	−	175.702i	−0.622762	−	0.527634i
$334$	38.4187	+	66.5432i	0.115026	+	0.199231i
$335$			79.1200i			0.236179i
$336$	2.85412	+	83.9515i	0.00849440	+	0.249856i
$337$	128.986			0.382749			0.191374	−	0.981517i	$-0.438706\pi$
$337$	128.986			0.382749			0.191374	+	0.981517i	$0.438706\pi$
$338$	306.454	−	176.931i	0.906669	−	0.523466i
$339$	62.3862	+	358.805i	0.184030	+	1.05842i
$340$	−8.52517	+	14.7660i	−0.0250740	+	0.0434295i
$341$	−62.5141	+	36.0925i	−0.183326	+	0.105843i
$342$	202.560	+	36.7124i	0.592281	+	0.107346i
$343$	−138.138	+	313.954i	−0.402734	+	0.915317i
$344$		−	93.6611i		−	0.272271i
$345$	71.5427	−	195.115i	0.207370	−	0.565550i
$346$	144.132	−	249.645i	0.416568	−	0.721516i
$347$	−207.033	−	119.530i	−0.596636	−	0.344468i	0.171081	−	0.985257i	$-0.445274\pi$
$347$	−207.033	−	119.530i	−0.596636	−	0.344468i	−0.767717	+	0.640789i	$0.778607\pi$
$348$	87.4411	+	32.0620i	0.251268	+	0.0921322i
$349$	324.427			0.929590			0.464795	−	0.885418i	$-0.346128\pi$
$349$	324.427			0.929590			0.464795	+	0.885418i	$0.346128\pi$
$350$	30.4167	−	39.0490i	0.0869050	−	0.111568i
$351$	−480.719	+	272.983i	−1.36957	+	0.777729i
$352$	−4.73245	−	8.19684i	−0.0134445	−	0.0232865i
$353$	−163.619	−	94.4652i	−0.463509	−	0.267607i	0.250010	−	0.968243i	$-0.419566\pi$
$353$	−163.619	−	94.4652i	−0.463509	−	0.267607i	−0.713518	+	0.700637i	$0.752899\pi$
$354$	325.932	−	56.6706i	0.920711	−	0.160086i
$355$	−124.701	−	215.989i	−0.351271	−	0.608419i
$356$		−	182.961i		−	0.513936i
$357$	−42.3648	−	67.9372i	−0.118669	−	0.190300i
$358$	5.34234			0.0149227
$359$	360.254	−	207.993i	1.00349	−	0.579367i	0.0942134	−	0.995552i	$-0.469966\pi$
$359$	360.254	−	207.993i	1.00349	−	0.579367i	0.909280	+	0.416185i	$0.136633\pi$
$360$	43.4293	+	36.7954i	0.120637	+	0.102209i
$361$	49.7025	−	86.0873i	0.137680	−	0.238469i
$362$	−387.339	+	223.630i	−1.07000	+	0.617763i
$363$	227.286	+	272.183i	0.626132	+	0.749814i
$364$	265.618	−	107.768i	0.729720	−	0.296065i
$365$			293.116i			0.803059i
$366$	352.130	+	129.115i	0.962105	+	0.352775i
$367$	160.552	−	278.085i	0.437472	−	0.757724i	−0.560022	−	0.828478i	$-0.689207\pi$
$367$	160.552	−	278.085i	0.437472	−	0.757724i	0.997494	+	0.0707542i	$0.0225406\pi$
$368$	−107.317	−	61.9592i	−0.291621	−	0.168367i
$369$	138.189	+	385.372i	0.374496	+	1.04437i
$370$	95.5023			0.258114
$371$	−88.7763	−	218.809i	−0.239289	−	0.589782i
$372$	−165.917	−	198.691i	−0.446012	−	0.534115i
$373$	−130.564	−	226.144i	−0.350038	−	0.606283i	0.636218	−	0.771509i	$-0.280498\pi$
$373$	−130.564	−	226.144i	−0.350038	−	0.606283i	−0.986256	+	0.165226i	$0.947165\pi$
$374$	7.81275	+	4.51070i	0.0208897	+	0.0120607i
$375$	−5.74566	−	33.0452i	−0.0153217	−	0.0881206i
$376$	29.5427	+	51.1694i	0.0785710	+	0.136089i
$377$		−	317.817i		−	0.843016i
$378$	−248.389	+	98.7166i	−0.657113	+	0.261155i
$379$	345.474			0.911540			0.455770	−	0.890098i	$-0.349364\pi$
$379$	345.474			0.911540			0.455770	+	0.890098i	$0.349364\pi$
$380$	−62.6412	+	36.1659i	−0.164845	+	0.0951735i
$381$	−464.352	+	80.7380i	−1.21877	+	0.211911i
$382$	−195.642	+	338.862i	−0.512152	+	0.887073i
$383$	95.9587	−	55.4018i	0.250545	−	0.144652i	−0.369469	−	0.929243i	$-0.620460\pi$
$383$	95.9587	−	55.4018i	0.250545	−	0.144652i	0.620014	+	0.784591i	$0.287127\pi$
$384$	26.0523	−	21.7550i	0.0678445	−	0.0566535i
$385$	−20.6609	−	16.0936i	−0.0536648	−	0.0418016i
$386$			154.262i			0.399641i
$387$	280.537	−	100.596i	0.724901	−	0.259939i
$388$	−34.3269	+	59.4559i	−0.0884713	+	0.153237i
$389$	255.551	+	147.543i	0.656944	+	0.379287i	0.791112	−	0.611672i	$-0.209503\pi$
$389$	255.551	+	147.543i	0.656944	+	0.379287i	−0.134168	+	0.990959i	$0.542836\pi$
$390$	66.8689	−	182.368i	0.171459	−	0.467611i
$391$	118.112			0.302077
$392$	134.378	−	33.9209i	0.342800	−	0.0865330i
$393$	−413.723	+	345.479i	−1.05273	+	0.879082i
$394$	165.191	+	286.119i	0.419266	+	0.726189i
$395$	−101.073	−	58.3545i	−0.255881	−	0.147733i
$396$	19.4686	−	22.9786i	0.0491631	−	0.0580267i
$397$	56.4875	+	97.8392i	0.142286	+	0.246446i	0.928357	−	0.371690i	$-0.121221\pi$
$397$	56.4875	+	97.8392i	0.142286	+	0.246446i	−0.786071	+	0.618136i	$0.787888\pi$
$398$			15.5631i			0.0391033i
$399$	−11.5406	−	339.456i	−0.0289237	−	0.850766i
$400$	−20.0000			−0.0500000
$401$	−198.174	+	114.416i	−0.494199	+	0.285326i	−0.726315	−	0.687362i	$-0.758768\pi$
$401$	−198.174	+	114.416i	−0.494199	+	0.285326i	0.232116	+	0.972688i	$0.425435\pi$
$402$	25.7159	+	147.901i	0.0639698	+	0.367912i
$403$	−441.669	+	764.993i	−1.09595	+	1.89825i
$404$	−175.576	+	101.369i	−0.434593	+	0.250913i
$405$	−63.5657	+	169.601i	−0.156952	+	0.418767i
$406$	21.1637	−	152.199i	0.0521274	−	0.374874i
$407$		−	50.5306i		−	0.124154i
$408$	−11.1370	+	30.3733i	−0.0272965	+	0.0744444i
$409$	132.142	−	228.877i	0.323086	−	0.559602i	−0.658037	−	0.752986i	$-0.728613\pi$
$409$	132.142	−	228.877i	0.323086	−	0.559602i	0.981123	+	0.193384i	$0.0619463\pi$
$410$	−124.576	−	71.9242i	−0.303845	−	0.175425i
$411$	−394.860	−	144.783i	−0.960731	−	0.352271i
$412$	−100.341			−0.243545
$413$	−205.209	−	505.784i	−0.496874	−	1.22466i
$414$	70.3193	−	387.985i	0.169853	−	0.937162i
$415$	−80.7325	−	139.833i	−0.194536	−	0.336947i
$416$	−100.306	−	57.9116i	−0.241120	−	0.139211i
$417$	532.657	−	92.6144i	1.27735	−	0.222097i
$418$	19.1355	+	33.1437i	0.0457788	+	0.0792912i
$419$		−	267.587i		−	0.638632i	−0.947648	−	0.319316i	$-0.896547\pi$
$419$		−	267.587i		−	0.638632i	0.947648	−	0.319316i	$-0.103453\pi$
$420$	44.1668	−	82.8812i	0.105159	−	0.197336i
$421$	683.379			1.62323			0.811614	−	0.584195i	$-0.198590\pi$
$421$	683.379			1.62323			0.811614	+	0.584195i	$0.198590\pi$
$422$	−314.829	+	181.767i	−0.746041	+	0.430727i
$423$	−121.534	+	143.446i	−0.287315	+	0.339115i
$424$	−47.7060	+	82.6293i	−0.112514	+	0.194880i
$425$	16.5089	−	9.53142i	0.0388445	−	0.0224269i
$426$	−303.308	−	363.222i	−0.711990	−	0.852633i
$427$	85.2275	−	612.913i	0.199596	−	1.43539i
$428$			332.088i			0.775906i
$429$	−96.4918	−	35.3806i	−0.224923	−	0.0824723i
$430$	−52.3581	+	90.6870i	−0.121763	+	0.210900i
$431$	542.014	+	312.932i	1.25757	+	0.726060i	0.972602	−	0.232477i	$-0.0746829\pi$
$431$	542.014	+	312.932i	1.25757	+	0.726060i	0.284970	+	0.958536i	$0.408016\pi$
$432$	93.1426	+	54.6668i	0.215608	+	0.126544i
$433$	494.039			1.14097			0.570483	−	0.821309i	$-0.306756\pi$
$433$	494.039			1.14097			0.570483	+	0.821309i	$0.306756\pi$
$434$	−262.452	+	336.935i	−0.604727	+	0.776348i
$435$	−66.7413	−	79.9250i	−0.153428	−	0.183736i
$436$	20.0969	+	34.8089i	0.0460939	+	0.0798370i
$437$	433.932	+	250.531i	0.992979	+	0.573296i
$438$	95.2697	+	547.928i	0.217511	+	1.25098i
$439$	−3.46878	−	6.00810i	−0.00790155	−	0.0136859i	0.862048	−	0.506827i	$-0.169182\pi$
$439$	−3.46878	−	6.00810i	−0.00790155	−	0.0136859i	−0.869949	+	0.493141i	$0.835848\pi$
$440$			10.5821i			0.0240502i
$441$	245.929	+	366.060i	0.557662	+	0.830068i
$442$	110.396			0.249765
$443$	714.996	−	412.803i	1.61399	−	0.931835i	0.625551	−	0.780183i	$-0.284874\pi$
$443$	714.996	−	412.803i	1.61399	−	0.931835i	0.988434	−	0.151652i	$-0.0484593\pi$
$444$	178.524	−	31.0405i	0.402082	−	0.0699110i
$445$	−102.278	+	177.151i	−0.229839	+	0.398093i
$446$	281.677	−	162.626i	0.631562	−	0.364632i
$447$	431.087	−	359.979i	0.964400	−	0.805322i
$448$	−44.1789	−	34.4126i	−0.0986135	−	0.0768139i
$449$		−	270.521i		−	0.602497i	−0.953546	−	0.301249i	$-0.902597\pi$
$449$		−	270.521i		−	0.602497i	0.953546	−	0.301249i	$-0.0974034\pi$
$450$	−21.4809	−	59.9047i	−0.0477354	−	0.133121i
$451$	−38.0554	+	65.9138i	−0.0843799	+	0.146150i
$452$	−210.264	−	121.396i	−0.465186	−	0.268575i
$453$	−27.7626	+	75.7156i	−0.0612861	+	0.167143i
$454$	−365.315			−0.804660
$455$	−317.428	−	44.1394i	−0.697643	−	0.0970096i
$456$	−105.342	+	87.9656i	−0.231013	+	0.192907i
$457$	171.702	+	297.397i	0.375717	+	0.650760i	0.990434	−	0.137987i	$-0.0440633\pi$
$457$	171.702	+	297.397i	0.375717	+	0.650760i	−0.614717	+	0.788747i	$0.710730\pi$
$458$	−459.090	−	265.056i	−1.00238	−	0.578725i
$459$	−102.937	−	0.735443i	−0.224263	−	0.00160227i
$460$	69.2725	+	119.984i	0.150592	+	0.260834i
$461$		−	254.080i		−	0.551149i	−0.961280	−	0.275575i	$-0.911132\pi$
$461$		−	254.080i		−	0.551149i	0.961280	−	0.275575i	$-0.0888681\pi$
$462$	−43.8527	−	23.3688i	−0.0949193	−	0.0505819i
$463$	−224.706			−0.485327			−0.242663	−	0.970111i	$-0.578021\pi$
$463$	−224.706			−0.485327			−0.242663	+	0.970111i	$0.578021\pi$
$464$	−53.7709	+	31.0446i	−0.115886	+	0.0669065i
$465$	49.5765	+	285.132i	0.106616	+	0.613186i
$466$	−28.3199	+	49.0515i	−0.0607723	+	0.105261i
$467$	173.853	−	100.374i	0.372276	−	0.214934i	−0.302176	−	0.953252i	$-0.597713\pi$
$467$	173.853	−	100.374i	0.372276	−	0.214934i	0.674452	+	0.738318i	$0.264380\pi$
$468$	65.7255	−	362.639i	0.140439	−	0.774870i
$469$	229.514	−	93.1194i	0.489368	−	0.198549i
$470$		−	66.0595i		−	0.140552i
$471$	−125.192	+	341.431i	−0.265801	+	0.724907i
$472$	−110.274	+	191.000i	−0.233631	+	0.404661i
$473$	47.9828	+	27.7029i	0.101444	+	0.0585685i
$474$	−207.904	−	76.2321i	−0.438616	−	0.160827i
$475$	80.8695			0.170252
$476$	52.8673	+	7.35137i	0.111066	+	0.0154441i
$477$	−298.733	−	54.1429i	−0.626274	−	0.113507i
$478$	−226.254	−	391.883i	−0.473334	−	0.819839i
$479$	223.631	+	129.113i	0.466870	+	0.269548i	0.714929	−	0.699198i	$-0.246459\pi$
$479$	223.631	+	129.113i	0.466870	+	0.269548i	−0.248059	+	0.968745i	$0.579793\pi$
$480$	−37.3864	+	6.50047i	−0.0778884	+	0.0135426i
$481$	−309.175	−	535.507i	−0.642775	−	1.11332i
$482$			608.990i			1.26346i
$483$	−650.196	+	22.1049i	−1.34616	+	0.0457658i
$484$	−236.401			−0.488432
$485$	66.4737	−	38.3786i	0.137059	−	0.0791312i
$486$	−63.7004	+	337.698i	−0.131071	+	0.694853i
$487$	7.47365	−	12.9447i	0.0153463	−	0.0265806i	−0.858250	−	0.513231i	$-0.828448\pi$
$487$	7.47365	−	12.9447i	0.0153463	−	0.0265806i	0.873597	+	0.486651i	$0.161782\pi$
$488$	−216.538	+	125.018i	−0.443726	+	0.256185i
$489$	88.9958	+	106.576i	0.181996	+	0.217946i
$490$	−149.073	−	42.2756i	−0.304231	−	0.0862768i
$491$		−	630.261i		−	1.28363i	−0.766861	−	0.641814i	$-0.778182\pi$
$491$		−	630.261i		−	1.28363i	0.766861	−	0.641814i	$-0.221818\pi$
$492$	−256.250	−	93.9591i	−0.520834	−	0.190974i
$493$	29.5900	−	51.2513i	0.0600202	−	0.103958i
$494$	405.584	+	234.164i	0.821020	+	0.474016i
$495$	−31.6958	+	11.3656i	−0.0640319	+	0.0229609i
$496$	172.570			0.347924
$497$	−479.781	+	615.942i	−0.965355	+	1.23932i
$498$	−196.364	−	235.152i	−0.394305	−	0.472194i
$499$	−398.102	−	689.534i	−0.797800	−	1.38183i	−0.921046	−	0.389455i	$-0.872664\pi$
$499$	−398.102	−	689.534i	−0.797800	−	1.38183i	0.123245	−	0.992376i	$-0.460670\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$	−27.9217	−	160.587i	−0.0557320	−	0.320534i
$502$	−31.9981	−	55.4223i	−0.0637412	−	0.110403i
$503$			566.364i			1.12597i	0.826466	+	0.562986i	$0.190348\pi$
$503$			566.364i			1.12597i	−0.826466	+	0.562986i	$0.809652\pi$
$504$	55.6236	−	169.287i	0.110364	−	0.335886i
$505$	226.667			0.448846
$506$	63.4837	−	36.6523i	0.125462	−	0.0724355i
$507$	−739.561	+	128.589i	−1.45870	+	0.253628i
$508$	157.106	−	272.116i	0.309264	−	0.535661i
$509$	−353.980	+	204.370i	−0.695442	+	0.401514i	−0.805648	−	0.592395i	$-0.798182\pi$
$509$	−353.980	+	204.370i	−0.695442	+	0.401514i	0.110205	+	0.993909i	$0.464849\pi$
$510$	27.7625	−	23.1831i	0.0544363	−	0.0454570i
$511$	850.281	−	344.980i	1.66395	−	0.675107i
$512$			22.6274i			0.0441942i
$513$	−376.620	−	221.044i	−0.734151	−	0.430885i
$514$	−274.000	+	474.582i	−0.533074	+	0.923311i
$515$	97.1544	+	56.0921i	0.188649	+	0.108917i
$516$	−68.3988	+	186.541i	−0.132556	+	0.361513i
$517$	−34.9523			−0.0676060
$518$	−112.400	−	277.036i	−0.216989	−	0.534819i
$519$	−469.372	+	391.949i	−0.904379	+	0.755201i
$520$	64.7471	+	112.145i	0.124514	+	0.215664i
$521$	−145.525	−	84.0190i	−0.279319	−	0.161265i	0.353796	−	0.935323i	$-0.384891\pi$
$521$	−145.525	−	84.0190i	−0.279319	−	0.161265i	−0.633115	+	0.774058i	$0.718224\pi$
$522$	−150.738	−	127.713i	−0.288771	−	0.244661i
$523$	−364.335	−	631.047i	−0.696626	−	1.20659i	−0.969630	−	0.244578i	$-0.921350\pi$
$523$	−364.335	−	631.047i	−0.696626	−	1.20659i	0.273004	−	0.962013i	$-0.411983\pi$
$524$		−	359.334i		−	0.685752i
$525$	−89.0963	+	55.5594i	−0.169707	+	0.105827i
$526$	−477.766			−0.908300
$527$	−142.448	+	82.2421i	−0.270299	+	0.156057i
$528$	3.43942	+	19.7813i	0.00651406	+	0.0374646i
$529$	215.368	−	373.029i	0.407123	−	0.705158i
$530$	92.3823	−	53.3370i	0.174306	−	0.100636i
$531$	−690.529	−	125.153i	−1.30043	−	0.235693i
$532$	178.636	+	139.147i	0.335782	+	0.261554i
$533$			931.377i			1.74742i
$534$	−133.613	+	364.396i	−0.250211	+	0.682389i
$535$	185.643	−	321.543i	0.346996	−	0.601015i
$536$	−86.6716	−	50.0399i	−0.161701	−	0.0933580i
$537$	−10.6401	−	3.90140i	−0.0198140	−	0.00726518i
$538$	715.454			1.32984
$539$	−22.3682	+	78.8751i	−0.0414994	+	0.146336i
$540$	−59.6252	−	104.999i	−0.110417	−	0.194443i
$541$	194.748	+	337.313i	0.359977	+	0.623499i	0.987957	−	0.154731i	$-0.0494512\pi$
$541$	194.748	+	337.313i	0.359977	+	0.623499i	−0.627980	+	0.778230i	$0.716118\pi$
$542$	−365.917	−	211.262i	−0.675123	−	0.389782i
$543$	934.758	−	162.529i	1.72147	−	0.299316i
$544$	−10.7836	−	18.6777i	−0.0198228	−	0.0343340i
$545$		−	44.9381i		−	0.0824553i
$546$	−607.720	+	20.6608i	−1.11304	+	0.0378403i
$547$	−70.9470			−0.129702			−0.0648510	−	0.997895i	$-0.520657\pi$
$547$	−70.9470			−0.129702			−0.0648510	+	0.997895i	$0.520657\pi$
$548$	242.815	−	140.189i	0.443093	−	0.255820i
$549$	−607.032	−	514.307i	−1.10571	−	0.936807i
$550$	5.91556	−	10.2460i	0.0107556	−	0.0186292i
$551$	217.421	−	125.528i	0.394594	−	0.227819i
$552$	168.490	+	201.773i	0.305236	+	0.365530i
$553$	−50.3199	+	361.875i	−0.0909944	+	0.654385i
$554$			307.657i			0.555338i
$555$	−190.208	−	69.7434i	−0.342717	−	0.125664i
$556$	−180.216	+	312.144i	−0.324130	+	0.561409i
$557$	731.932	+	422.581i	1.31406	+	0.758674i	0.982766	−	0.184853i	$-0.0591811\pi$
$557$	731.932	+	422.581i	1.31406	+	0.758674i	0.331295	+	0.943527i	$0.392514\pi$
$558$	185.349	+	516.889i	0.332166	+	0.926324i
$559$	678.008			1.21289
$560$	23.5388	+	58.0166i	0.0420335	+	0.103601i
$561$	−12.2662	−	14.6892i	−0.0218650	−	0.0261840i
$562$	12.2016	+	21.1337i	0.0217110	+	0.0376045i
$563$	97.0699	+	56.0433i	0.172415	+	0.0995441i	0.583724	−	0.811952i	$-0.301595\pi$
$563$	97.0699	+	56.0433i	0.172415	+	0.0995441i	−0.411309	+	0.911496i	$0.634928\pi$
$564$	−21.4709	−	123.486i	−0.0380689	−	0.218947i
$565$	135.725	+	235.082i	0.240221	+	0.416075i
$566$			180.095i			0.318189i
$567$	566.796	−	15.2163i	0.999640	−	0.0268364i
$568$	315.472			0.555408
$569$	−225.554	+	130.224i	−0.396405	+	0.228864i	−0.684931	−	0.728607i	$-0.740168\pi$
$569$	−225.554	+	130.224i	−0.396405	+	0.228864i	0.288527	+	0.957472i	$0.406835\pi$
$570$	151.171	−	26.2845i	0.265212	−	0.0461131i
$571$	−78.9901	+	136.815i	−0.138336	+	0.239606i	−0.926867	−	0.375390i	$-0.877509\pi$
$571$	−78.9901	+	136.815i	−0.138336	+	0.239606i	0.788531	+	0.614996i	$0.210842\pi$
$572$	59.3365	−	34.2579i	0.103735	−	0.0598915i
$573$	637.116	−	532.023i	1.11189	−	0.928487i
$574$	−62.0213	+	446.025i	−0.108051	+	0.777047i
$575$		−	154.898i		−	0.269388i
$576$	−67.7744	+	24.3029i	−0.117664	+	0.0421926i
$577$	−271.801	+	470.773i	−0.471058	+	0.815897i	−0.999452	−	0.0331025i	$-0.989461\pi$
$577$	−271.801	+	470.773i	−0.471058	+	0.815897i	0.528394	+	0.849000i	$0.322795\pi$
$578$	−336.149	−	194.076i	−0.581572	−	0.335771i
$579$	112.654	−	307.236i	0.194567	−	0.530632i
$580$	69.4179			0.119686
$581$	−310.614	+	398.766i	−0.534620	+	0.686344i
$582$	111.787	−	93.3475i	0.192073	−	0.160391i
$583$	−28.2208	−	48.8798i	−0.0484062	−	0.0838419i
$584$	−321.093	−	185.383i	−0.549817	−	0.317437i
$585$	−266.360	+	314.382i	−0.455316	+	0.537405i
$586$	−61.2666	−	106.117i	−0.104551	−	0.181087i
$587$		−	976.217i		−	1.66306i	−0.555479	−	0.831530i	$-0.687465\pi$
$587$		−	976.217i		−	1.66306i	0.555479	−	0.831530i	$-0.312535\pi$
$588$	−292.406	−	30.5745i	−0.497289	−	0.0519974i
$589$	−697.784			−1.18469
$590$	213.545	−	123.290i	0.361940	−	0.208966i
$591$	−120.056	−	690.485i	−0.203141	−	1.16833i
$592$	−60.4010	+	104.618i	−0.102029	+	0.176719i
$593$	−558.275	+	322.320i	−0.941441	+	0.543541i	−0.890412	−	0.455156i	$-0.849584\pi$
$593$	−558.275	+	322.320i	−0.941441	+	0.543541i	−0.0510295	+	0.998697i	$0.516250\pi$
$594$	−55.5555	+	31.5479i	−0.0935277	+	0.0531110i
$595$	−47.0790	−	36.6717i	−0.0791244	−	0.0616330i
$596$			374.415i			0.628214i
$597$	11.3654	−	30.9964i	0.0190376	−	0.0519202i
$598$	448.520	−	776.859i	0.750033	−	1.29909i
$599$	221.153	+	127.683i	0.369203	+	0.213160i	0.673110	−	0.739542i	$-0.264958\pi$
$599$	221.153	+	127.683i	0.369203	+	0.213160i	−0.303907	+	0.952702i	$0.598291\pi$
$600$	39.8331	+	14.6056i	0.0663885	+	0.0243426i
$601$	−719.562			−1.19728			−0.598638	−	0.801020i	$-0.704291\pi$
$601$	−719.562			−1.19728			−0.598638	+	0.801020i	$0.704291\pi$
$602$	324.690	+	45.1492i	0.539352	+	0.0749986i
$603$	56.7917	−	313.347i	0.0941819	−	0.519647i
$604$	−26.8817	−	46.5604i	−0.0445060	−	0.0770867i
$605$	228.894	+	132.152i	0.378338	+	0.218433i
$606$	423.714	−	73.6722i	0.699198	−	0.121571i
$607$	−475.679	−	823.901i	−0.783656	−	1.35733i	−0.929799	−	0.368069i	$-0.880019\pi$
$607$	−475.679	−	823.901i	−0.783656	−	1.35733i	0.146143	−	0.989264i	$-0.453314\pi$
$608$		−	91.4934i		−	0.150483i
$609$	−153.298	+	287.672i	−0.251722	+	0.472368i
$610$	279.550			0.458278
$611$	−370.413	+	213.858i	−0.606240	+	0.350013i
$612$	44.3620	−	52.3601i	0.0724869	−	0.0855557i
$613$	−258.282	+	447.358i	−0.421342	+	0.729785i	−0.996071	−	0.0885585i	$-0.971774\pi$
$613$	−258.282	+	447.358i	−0.421342	+	0.729785i	0.574729	+	0.818344i	$0.305107\pi$
$614$	−514.840	+	297.243i	−0.838502	+	0.484109i
$615$	195.588	+	234.224i	0.318030	+	0.380852i
$616$	30.6968	−	12.4544i	0.0498325	−	0.0202182i
$617$		−	392.429i		−	0.636027i	−0.948086	−	0.318013i	$-0.896984\pi$
$617$		−	392.429i		−	0.636027i	0.948086	−	0.318013i	$-0.103016\pi$
$618$	199.844	+	73.2767i	0.323372	+	0.118571i
$619$	−570.473	+	988.089i	−0.921605	+	1.59627i	−0.124673	+	0.992198i	$0.539788\pi$
$619$	−570.473	+	988.089i	−0.921605	+	1.59627i	−0.796932	+	0.604069i	$0.793545\pi$
$620$	−167.091	−	96.4698i	−0.269501	−	0.155597i
$621$	−423.389	+	721.380i	−0.681787	+	1.16164i
$622$	−178.314			−0.286679
$623$	634.261	+	88.1961i	1.01808	+	0.141567i
$624$	157.483	+	188.591i	0.252377	+	0.302229i
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	236.892	+	136.769i	0.378421	+	0.218482i
$627$	−13.9072	−	79.9851i	−0.0221806	−	0.127568i
$628$	−121.220	−	209.959i	−0.193025	−	0.334330i
$629$		−	115.141i		−	0.183055i
$630$	−148.492	+	132.817i	−0.235701	+	0.210820i
$631$	−254.058			−0.402627			−0.201314	−	0.979527i	$-0.564521\pi$
$631$	−254.058			−0.402627			−0.201314	+	0.979527i	$0.564521\pi$
$632$	127.848	−	73.8132i	0.202291	−	0.116793i
$633$	759.772	−	132.103i	1.20027	−	0.208694i
$634$	27.1644	−	47.0501i	0.0428461	−	0.0742116i
$635$	−304.235	+	175.650i	−0.479110	+	0.276614i
$636$	155.356	−	129.730i	0.244271	−	0.203979i
$637$	245.552	+	972.753i	0.385482	+	1.52708i
$638$		−	36.7293i		−	0.0575694i
$639$	338.832	+	944.912i	0.530253	+	1.47874i
$640$	12.6491	−	21.9089i	0.0197642	−	0.0342327i
$641$	747.919	+	431.811i	1.16680	+	0.673652i	0.952924	−	0.303209i	$-0.0980580\pi$
$641$	747.919	+	431.811i	1.16680	+	0.673652i	0.213876	+	0.976861i	$0.431391\pi$
$642$	242.517	−	661.405i	0.377752	−	1.03023i
$643$	−27.2102			−0.0423176			−0.0211588	−	0.999776i	$-0.506736\pi$
$643$	−27.2102			−0.0423176			−0.0211588	+	0.999776i	$0.506736\pi$
$644$	266.522	−	342.161i	0.413855	−	0.531306i
$645$	170.506	−	142.381i	0.264351	−	0.220746i
$646$	43.6031	+	75.5228i	0.0674971	+	0.116908i
$647$	316.642	+	182.814i	0.489401	+	0.282556i	0.724326	−	0.689458i	$-0.242151\pi$
$647$	316.642	+	182.814i	0.489401	+	0.282556i	−0.234925	+	0.972014i	$0.575484\pi$
$648$	−145.586	−	176.898i	−0.224669	−	0.272990i
$649$	−65.2332	−	112.987i	−0.100513	−	0.174094i
$650$		−	144.779i		−	0.222737i
$651$	768.770	−	479.395i	1.18091	−	0.736398i
$652$	−92.5649			−0.141971
$653$	85.7492	−	49.5073i	0.131316	−	0.0758152i	−0.432903	−	0.901440i	$-0.642511\pi$
$653$	85.7492	−	49.5073i	0.131316	−	0.0758152i	0.564219	+	0.825625i	$0.309177\pi$
$654$	−14.6059	−	84.0038i	−0.0223332	−	0.128446i
$655$	−200.874	+	347.924i	−0.306678	+	0.531182i
$656$	157.578	−	90.9777i	0.240210	−	0.138686i
$657$	210.397	−	1160.86i	0.320238	−	1.76691i
$658$	−191.627	+	77.7479i	−0.291227	+	0.118158i
$659$			13.5370i			0.0205417i	0.999947	+	0.0102709i	$0.00326938\pi$
$659$			13.5370i			0.0205417i	−0.999947	+	0.0102709i	$0.996731\pi$
$660$	7.72787	−	21.0758i	0.0117089	−	0.0319331i
$661$	332.325	−	575.605i	0.502762	−	0.870809i	−0.497233	−	0.867617i	$-0.665651\pi$
$661$	332.325	−	575.605i	0.502762	−	0.870809i	0.999995	−	0.00319184i	$-0.00101600\pi$
$662$	770.330	+	444.750i	1.16364	+	0.671828i
$663$	−219.871	−	80.6199i	−0.331630	−	0.121599i
$664$	204.239			0.307589
$665$	−95.1784	−	234.589i	−0.143125	−	0.352765i
$666$	−378.227	−	68.5508i	−0.567909	−	0.102929i
$667$	−240.438	−	416.450i	−0.360476	−	0.624363i
$668$	94.1063	+	54.3323i	0.140878	+	0.0813357i
$669$	−679.765	+	118.192i	−1.01609	+	0.176670i
$670$	55.9463	+	96.9018i	0.0835020	+	0.144630i
$671$		−	147.911i		−	0.220433i
$672$	62.8582	+	100.801i	0.0935390	+	0.150001i
$673$	83.7667			0.124468			0.0622338	−	0.998062i	$-0.480178\pi$
$673$	83.7667			0.124468			0.0622338	+	0.998062i	$0.480178\pi$
$674$	157.975	−	91.2072i	0.234385	−	0.135322i
$675$	−0.964498	+	134.997i	−0.00142889	+	0.199995i
$676$	250.219	−	433.392i	0.370146	−	0.641112i
$677$	855.496	−	493.921i	1.26366	−	0.729573i	0.289877	−	0.957064i	$-0.406386\pi$
$677$	855.496	−	493.921i	1.26366	−	0.729573i	0.973780	+	0.227492i	$0.0730524\pi$
$678$	330.120	+	395.330i	0.486903	+	0.583083i
$679$	−189.565	−	147.660i	−0.279183	−	0.217466i
$680$			24.1128i			0.0354600i
$681$	727.582	+	266.782i	1.06840	+	0.391751i
$682$	−51.0425	+	88.4083i	−0.0748424	+	0.129631i
$683$	−899.204	−	519.155i	−1.31655	−	0.760110i	−0.333378	−	0.942793i	$-0.608189\pi$
$683$	−899.204	−	519.155i	−1.31655	−	0.760110i	−0.983172	+	0.182683i	$0.941522\pi$
$684$	274.044	−	98.2682i	0.400649	−	0.143667i
$685$	−313.472			−0.457624
$686$	52.8153	+	482.191i	0.0769902	+	0.702903i
$687$	720.785	+	863.164i	1.04918	+	1.25643i
$688$	−66.2284	−	114.711i	−0.0962622	−	0.166731i
$689$	−598.149	−	345.341i	−0.868141	−	0.501221i
$690$	−50.3455	−	289.554i	−0.0729645	−	0.419644i
$691$	1.72674	+	2.99080i	0.00249890	+	0.00432822i	0.867272	−	0.497834i	$-0.165871\pi$
$691$	1.72674	+	2.99080i	0.00249890	+	0.00432822i	−0.864773	+	0.502163i	$0.832538\pi$
$692$		−	407.668i		−	0.589116i
$693$	70.2738	+	78.5674i	0.101405	+	0.113373i
$694$	−338.083			−0.487152
$695$	348.987	−	201.488i	0.502140	−	0.289911i
$696$	129.764	−	22.5624i	0.186443	−	0.0324173i
$697$	−86.7147	+	150.194i	−0.124411	+	0.215487i
$698$	397.340	−	229.405i	0.569256	−	0.328660i
$699$	92.2247	−	77.0122i	0.131938	−	0.110175i
$700$	9.64097	−	69.3329i	0.0137728	−	0.0990470i
$701$		−	694.193i		−	0.990289i	−0.868811	−	0.495145i	$-0.835115\pi$
$701$		−	694.193i		−	0.990289i	0.868811	−	0.495145i	$-0.164885\pi$
$702$	−395.730	+	674.254i	−0.563718	+	0.960476i
$703$	244.230	−	423.018i	0.347411	−	0.601733i
$704$	−11.5921	−	6.69269i	−0.0164660	−	0.00950666i
$705$	−48.2419	+	131.568i	−0.0684282	+	0.186621i
$706$	−267.188			−0.378453
$707$	−266.773	−	657.523i	−0.377331	−	0.930019i
$708$	359.111	−	299.876i	0.507219	−	0.423553i
$709$	314.037	+	543.928i	0.442929	+	0.767176i	0.997905	−	0.0646905i	$-0.0206060\pi$
$709$	314.037	+	543.928i	0.442929	+	0.767176i	−0.554976	+	0.831866i	$0.687273\pi$
$710$	−305.454	−	176.354i	−0.430217	−	0.248386i
$711$	358.403	+	303.656i	0.504083	+	0.427083i
$712$	−129.373	−	224.081i	−0.181704	−	0.314720i
$713$			1336.54i			1.87453i
$714$	−99.9249	−	53.2493i	−0.139951	−	0.0745789i
$715$	−76.6031			−0.107137
$716$	6.54300	−	3.77761i	0.00913827	−	0.00527598i
$717$	164.436	+	945.725i	0.229338	+	1.31900i
$718$	294.146	−	509.476i	0.409674	−	0.709577i
$719$	−403.521	+	232.973i	−0.561226	+	0.324024i	−0.753637	−	0.657290i	$-0.771703\pi$
$719$	−403.521	+	232.973i	−0.561226	+	0.324024i	0.192411	+	0.981314i	$0.438369\pi$
$720$	79.2080	+	14.3558i	0.110011	+	0.0199387i
$721$	48.3690	−	347.845i	0.0670860	−	0.482448i
$722$		−	140.580i		−	0.194709i
$723$	444.733	−	1212.90i	0.615121	−	1.67759i
$724$	−316.261	+	547.780i	−0.436824	+	0.756602i
$725$	−67.2136	−	38.8058i	−0.0927084	−	0.0535252i
$726$	470.829	+	172.639i	0.648525	+	0.237794i
$727$	−34.2722			−0.0471420			−0.0235710	−	0.999722i	$-0.507504\pi$
$727$	−34.2722			−0.0471420			−0.0235710	+	0.999722i	$0.507504\pi$
$728$	249.111	−	319.808i	0.342186	−	0.439297i
$729$	373.484	−	626.060i	0.512323	−	0.858793i
$730$	207.265	+	358.993i	0.283924	+	0.491771i
$731$	109.336	+	63.1251i	0.149570	+	0.0863544i
$732$	522.568	−	90.8602i	0.713891	−	0.124126i
$733$	531.976	+	921.410i	0.725752	+	1.25704i	0.958664	+	0.284542i	$0.0918414\pi$
$733$	531.976	+	921.410i	0.725752	+	1.25704i	−0.232912	+	0.972498i	$0.574825\pi$
$734$		−	454.110i		−	0.618679i
$735$	266.029	+	193.063i	0.361944	+	0.262671i
$736$	−175.247			−0.238108
$737$	51.2711	−	29.6014i	0.0695673	−	0.0401647i
$738$	441.746	+	374.269i	0.598571	+	0.507139i
$739$	−590.359	+	1022.53i	−0.798862	+	1.38367i	0.121496	+	0.992592i	$0.461231\pi$
$739$	−590.359	+	1022.53i	−0.798862	+	1.38367i	−0.920358	+	0.391077i	$0.872103\pi$
$740$	116.966	−	67.5303i	0.158062	−	0.0912572i
$741$	−636.778	−	762.564i	−0.859350	−	1.02910i
$742$	−263.450	−	205.211i	−0.355054	−	0.276565i
$743$		−	797.549i		−	1.07342i	−0.843768	−	0.536709i	$-0.819667\pi$
$743$		−	797.549i		−	1.07342i	0.843768	−	0.536709i	$-0.180333\pi$
$744$	−343.701	−	126.025i	−0.461964	−	0.169388i
$745$	209.305	−	362.526i	0.280946	−	0.486612i
$746$	−319.815	−	184.646i	−0.428707	−	0.247514i
$747$	219.362	+	611.743i	0.293658	+	0.818933i
$748$	12.7582			0.0170564
$749$	−1151.23	−	160.082i	−1.53702	−	0.213728i
$750$	−30.4035	−	36.4092i	−0.0405380	−	0.0485456i
$751$	689.987	+	1195.09i	0.918757	+	1.59133i	0.801305	+	0.598256i	$0.204139\pi$
$751$	689.987	+	1195.09i	0.918757	+	1.59133i	0.117452	+	0.993079i	$0.462527\pi$
$752$	72.3645	+	41.7797i	0.0962294	+	0.0555581i
$753$	23.2554	+	133.750i	0.0308837	+	0.177623i
$754$	−224.730	−	389.245i	−0.298051	−	0.516240i
$755$			60.1092i			0.0796148i
$756$	−234.410	+	296.540i	−0.310066	+	0.392249i
$757$	147.674			0.195077			0.0975387	−	0.995232i	$-0.468903\pi$
$757$	147.674			0.195077			0.0975387	+	0.995232i	$0.468903\pi$
$758$	423.117	−	244.287i	0.558202	−	0.322278i
$759$	−153.204	+	26.6380i	−0.201850	+	0.0350962i
$760$	−51.1464	+	88.5881i	−0.0672978	+	0.116563i
$761$	59.3764	−	34.2810i	0.0780242	−	0.0450473i	−0.460480	−	0.887670i	$-0.652323\pi$
$761$	59.3764	−	34.2810i	0.0780242	−	0.0450473i	0.538505	+	0.842623i	$0.318989\pi$
$762$	−511.622	+	427.230i	−0.671420	+	0.560669i
$763$	−130.358	+	52.8894i	−0.170849	+	0.0693177i
$764$			553.359i			0.724292i
$765$	−72.2235	+	25.8983i	−0.0944098	+	0.0338540i
$766$	78.3500	−	135.706i	0.102285	−	0.177162i
$767$	−1382.64	−	798.267i	−1.80266	−	1.04077i
$768$	16.5243	−	45.0660i	0.0215161	−	0.0586797i
$769$	−724.295			−0.941866			−0.470933	−	0.882169i	$-0.656083\pi$
$769$	−724.295			−0.941866			−0.470933	+	0.882169i	$0.656083\pi$
$770$	−36.6843	−	5.10107i	−0.0476419	−	0.00662477i
$771$	892.291	−	745.107i	1.15732	−	0.966416i
$772$	109.079	+	188.931i	0.141295	+	0.244729i
$773$	973.317	+	561.945i	1.25914	+	0.726966i	0.972908	−	0.231193i	$-0.0742629\pi$
$773$	973.317	+	561.945i	1.25914	+	0.726966i	0.286235	+	0.958160i	$0.407596\pi$
$774$	272.454	−	321.574i	0.352007	−	0.415471i
$775$	107.857	+	186.813i	0.139170	+	0.241049i
$776$			97.0911i			0.125117i
$777$	21.5489	+	633.844i	0.0277335	+	0.815758i
$778$	417.313			0.536392
$779$	−637.163	+	367.866i	−0.817924	+	0.472229i
$780$	−47.0565	−	270.638i	−0.0603289	−	0.346972i
$781$	−93.3096	+	161.617i	−0.119475	+	0.206936i
$782$	144.657	−	83.5178i	0.184983	−	0.106800i
$783$	206.953	+	364.441i	0.264308	+	0.465442i
$784$	140.593	−	136.564i	0.179327	−	0.174189i
$785$			271.056i			0.345294i
$786$	−262.414	+	715.670i	−0.333861	+	0.910522i
$787$	86.9083	−	150.530i	0.110430	−	0.191270i	−0.805514	−	0.592577i	$-0.798111\pi$
$787$	86.9083	−	150.530i	0.110430	−	0.191270i	0.915944	+	0.401307i	$0.131444\pi$
$788$	404.633	+	233.615i	0.513493	+	0.296466i
$789$	951.545	+	348.902i	1.20601	+	0.442208i
$790$	−165.051			−0.208926
$791$	522.194	−	670.392i	0.660169	−	0.847524i
$792$	7.59573	−	41.9093i	0.00959056	−	0.0529157i
$793$	−905.002	−	1567.51i	−1.14124	−	1.97668i
$794$	138.365	+	79.8854i	0.174264	+	0.100611i
$795$	−222.945	+	38.7639i	−0.280434	+	0.0487597i
$796$	11.0048	+	19.0608i	0.0138251	+	0.0239458i
$797$			812.224i			1.01910i	0.860441	+	0.509551i	$0.170188\pi$
$797$			812.224i			1.01910i	−0.860441	+	0.509551i	$0.829812\pi$
$798$	−254.166	−	407.586i	−0.318503	−	0.510760i
$799$	−79.6440			−0.0996796
$800$	−24.4949	+	14.1421i	−0.0306186	+	0.0176777i
$801$	532.221	−	628.176i	0.664446	−	0.784239i
$802$	−161.808	+	280.260i	−0.201756	+	0.349451i
$803$	189.944	−	109.664i	0.236543	−	0.136568i
$804$	136.077	+	162.957i	0.169250	+	0.202683i
$805$	−449.333	+	182.305i	−0.558178	+	0.226466i
$806$			1249.23i			1.54991i
$807$	−1424.94	−	522.481i	−1.76572	−	0.647437i
$808$	−143.357	+	248.302i	−0.177422	+	0.307304i
$809$	−1154.35	−	666.465i	−1.42689	−	0.823813i	−0.430012	−	0.902823i	$-0.641491\pi$
$809$	−1154.35	−	666.465i	−1.42689	−	0.823813i	−0.996874	+	0.0790105i	$0.974824\pi$
$810$	42.0741	+	252.665i	0.0519433	+	0.311933i
$811$	−561.748			−0.692661			−0.346331	−	0.938112i	$-0.612572\pi$
$811$	−561.748			−0.692661			−0.346331	+	0.938112i	$0.612572\pi$
$812$	−81.7006	−	201.370i	−0.100616	−	0.247992i
$813$	574.500	+	687.983i	0.706642	+	0.846227i
$814$	−35.7305	−	61.8871i	−0.0438950	−	0.0760284i
$815$	89.6256	+	51.7454i	0.109970	+	0.0634913i
$816$	7.83723	+	45.0746i	0.00960445	+	0.0552384i
$817$	267.793	+	463.831i	0.327776	+	0.567724i
$818$		−	373.755i		−	0.456913i
$819$	1225.46	+	402.657i	1.49629	+	0.491644i
$820$	−203.432			−0.248088
$821$	−309.801	+	178.864i	−0.377346	+	0.217861i	−0.676663	−	0.736293i	$-0.736575\pi$
$821$	−309.801	+	178.864i	−0.377346	+	0.217861i	0.299317	+	0.954154i	$0.403241\pi$
$822$	−585.980	+	101.886i	−0.712872	+	0.123949i
$823$	−267.842	+	463.916i	−0.325446	+	0.563689i	−0.981603	−	0.190936i	$-0.938848\pi$
$823$	−267.842	+	463.916i	−0.325446	+	0.563689i	0.656156	+	0.754625i	$0.272181\pi$
$824$	−122.892	+	70.9515i	−0.149140	+	0.0861062i
$825$	−19.2642	+	16.0866i	−0.0233506	+	0.0194989i
$826$	−608.972	−	474.352i	−0.737254	−	0.574276i
$827$		−	102.293i		−	0.123692i	−0.998086	−	0.0618458i	$-0.980301\pi$
$827$		−	102.293i		−	0.123692i	0.998086	−	0.0618458i	$-0.0196987\pi$
$828$	−188.224	−	524.906i	−0.227323	−	0.633945i
$829$	172.923	−	299.511i	0.208592	−	0.361292i	−0.742679	−	0.669647i	$-0.766445\pi$
$829$	172.923	−	299.511i	0.208592	−	0.361292i	0.951271	+	0.308356i	$0.0997786\pi$
$830$	−197.753	−	114.173i	−0.238257	−	0.137558i
$831$	224.676	−	612.747i	0.270368	−	0.737361i
$832$	−163.799			−0.196873
$833$	−50.9692	+	179.728i	−0.0611875	+	0.215760i
$834$	586.881	−	490.074i	0.703694	−	0.587619i
$835$	−60.7453	−	105.214i	−0.0727489	−	0.126005i
$836$	46.8723	+	27.0617i	0.0560673	+	0.0323705i
$837$	8.32219	−	1164.82i	0.00994288	−	1.39166i
$838$	−189.212	−	327.725i	−0.225790	−	0.391080i
$839$			807.052i			0.961921i	0.876742	+	0.480961i	$0.159712\pi$
$839$			807.052i			0.961921i	−0.876742	+	0.480961i	$0.840288\pi$
$840$	−4.51276	−	132.739i	−0.00537233	−	0.158023i
$841$	600.058			0.713505
$842$	836.964	−	483.222i	0.994020	−	0.573897i
$843$	−8.86779	−	51.0017i	−0.0105193	−	0.0605002i
$844$	−257.057	+	445.236i	−0.304570	+	0.527531i
$845$	−484.547	+	279.753i	−0.573428	+	0.331069i
$846$	−47.4169	+	261.622i	−0.0560484	+	0.309246i
$847$	113.957	−	819.518i	0.134542	−	0.967554i
$848$			134.933i			0.159119i
$849$	131.520	−	358.688i	0.154911	−	0.422483i
$850$	13.4795	−	23.3471i	0.0158582	−	0.0274672i
$851$	−810.253	−	467.800i	−0.952118	−	0.549706i
$852$	−628.311	−	230.383i	−0.737454	−	0.270402i
$853$	−748.874			−0.877930			−0.438965	−	0.898504i	$-0.644655\pi$
$853$	−748.874			−0.877930			−0.438965	+	0.898504i	$0.644655\pi$
$854$	−329.013	−	810.927i	−0.385261	−	0.949563i
$855$	−320.276	−	58.0475i	−0.374591	−	0.0678918i
$856$	234.822	+	406.723i	0.274324	+	0.475144i
$857$	452.535	+	261.271i	0.528046	+	0.304867i	0.740220	−	0.672364i	$-0.234721\pi$
$857$	452.535	+	261.271i	0.528046	+	0.304867i	−0.212174	+	0.977232i	$0.568055\pi$
$858$	−143.196	+	24.8978i	−0.166895	+	0.0290184i
$859$	230.794	+	399.747i	0.268678	+	0.465363i	0.968521	−	0.248933i	$-0.0800801\pi$
$859$	230.794	+	399.747i	0.268678	+	0.465363i	−0.699843	+	0.714297i	$0.746747\pi$
$860$			148.091i			0.172199i
$861$	449.248	−	843.036i	0.521775	−	0.979136i
$862$	885.105			1.02680
$863$	−73.1245	+	42.2184i	−0.0847329	+	0.0489205i	−0.541768	−	0.840528i	$-0.682245\pi$
$863$	−73.1245	+	42.2184i	−0.0847329	+	0.0489205i	0.457035	+	0.889449i	$0.348911\pi$
$864$	152.731	+	1.09120i	0.176772	+	0.00126297i
$865$	−227.893	+	394.723i	−0.263461	+	0.456327i
$866$	605.071	−	349.338i	0.698697	−	0.403393i
$867$	527.763	+	632.014i	0.608723	+	0.728967i
$868$	−83.1873	+	598.241i	−0.0958379	+	0.689217i
$869$			87.3293i			0.100494i
$870$	−138.257	−	50.6945i	−0.158916	−	0.0582695i
$871$	362.236	−	627.411i	0.415885	−	0.720335i
$872$	49.2272	+	28.4214i	0.0564533	+	0.0325933i
$873$	−290.810	+	104.280i	−0.333116	+	0.119451i
$874$	708.607			0.810764
$875$	−48.0931	+	61.7418i	−0.0549635	+	0.0705621i
$876$	504.125	+	603.707i	0.575485	+	0.689163i
$877$	515.796	+	893.385i	0.588137	+	1.01868i	0.994476	+	0.104961i	$0.0334716\pi$
$877$	515.796	+	893.385i	0.588137	+	1.01868i	−0.406340	+	0.913722i	$0.633195\pi$
$878$	−8.49674	−	4.90559i	−0.00967738	−	0.00558724i
$879$	44.5270	+	256.090i	0.0506565	+	0.291343i
$880$	7.48266	+	12.9603i	0.00850302	+	0.0147277i
$881$			943.891i			1.07139i	0.844413	+	0.535693i	$0.179950\pi$
$881$			943.891i			1.07139i	−0.844413	+	0.535693i	$0.820050\pi$
$882$	560.044	+	274.432i	0.634970	+	0.311147i
$883$	−704.364			−0.797695			−0.398847	−	0.917017i	$-0.630590\pi$
$883$	−704.364			−0.797695			−0.398847	+	0.917017i	$0.630590\pi$
$884$	135.207	−	78.0617i	0.152949	−	0.0883051i
$885$	−515.343	+	89.6040i	−0.582309	+	0.101247i
$886$	583.791	−	1011.16i	0.658907	−	1.14126i
$887$	−546.896	+	315.750i	−0.616568	+	0.355976i	−0.775532	−	0.631309i	$-0.782518\pi$
$887$	−546.896	+	315.750i	−0.616568	+	0.355976i	0.158964	+	0.987284i	$0.449185\pi$
$888$	196.698	−	164.253i	0.221507	−	0.184969i
$889$	867.596	+	675.804i	0.975924	+	0.760185i
$890$			289.287i			0.325042i
$891$	133.686	−	22.2616i	0.150041	−	0.0249849i
$892$	229.988	−	398.351i	0.257834	−	0.446582i
$893$	−292.604	−	168.935i	−0.327664	−	0.189177i
$894$	273.428	−	745.707i	0.305848	−	0.834124i
$895$	−8.44698			−0.00943797
$896$	−78.4412	−	10.9075i	−0.0875460	−	0.0121736i
$897$	−1460.62	+	1219.69i	−1.62834	+	1.35974i
$898$	−191.287	−	331.319i	−0.213015	−	0.368953i
$899$	579.954	+	334.837i	0.645110	+	0.372455i
$900$	−68.6677	−	58.1786i	−0.0762974	−	0.0646429i
$901$	−64.3052	−	111.380i	−0.0713709	−	0.123618i
$902$			107.637i			0.119331i
$903$	−613.699	−	327.036i	−0.679622	−	0.362166i
$904$	−343.360			−0.379822
$905$	612.436	−	353.590i	0.676725	−	0.390708i
$906$	19.5369	+	112.363i	0.0215639	+	0.124021i
$907$	598.379	−	1036.42i	0.659735	−	1.14269i	−0.320949	−	0.947096i	$-0.604002\pi$
$907$	598.379	−	1036.42i	0.659735	−	1.14269i	0.980684	−	0.195598i	$-0.0626647\pi$
$908$	−447.418	+	258.317i	−0.492751	+	0.284490i
$909$	−897.693	−	162.700i	−0.987562	−	0.178988i
$910$	−419.979	+	170.396i	−0.461516	+	0.187248i
$911$			79.1644i			0.0868983i	0.999056	+	0.0434492i	$0.0138347\pi$
$911$			79.1644i			0.0868983i	−0.999056	+	0.0434492i	$0.986165\pi$
$912$	−66.8157	+	182.223i	−0.0732629	+	0.199806i
$913$	−60.4094	+	104.632i	−0.0661658	+	0.114602i
$914$	420.583	+	242.824i	0.460157	+	0.265672i
$915$	−556.767	−	204.150i	−0.608489	−	0.223114i
$916$	−749.691			−0.818440
$917$	1245.68	+	173.217i	1.35843	+	0.188895i
$918$	−126.591	+	71.8866i	−0.137899	+	0.0783078i
$919$	−94.1564	−	163.084i	−0.102455	−	0.177458i	0.810240	−	0.586098i	$-0.199337\pi$
$919$	−94.1564	−	163.084i	−0.102455	−	0.177458i	−0.912696	+	0.408640i	$0.866003\pi$
$920$	169.682	+	97.9661i	0.184437	+	0.106485i
$921$	1242.45	−	216.029i	1.34903	−	0.234559i
$922$	−179.661	−	311.183i	−0.194861	−	0.337509i
$923$			2283.68i			2.47420i
$924$	−70.2327	+	2.38772i	−0.0760094	+	0.00258411i
$925$	−151.002			−0.163246
$926$	−275.208	+	158.891i	−0.297201	+	0.171589i
$927$	−344.508	−	291.884i	−0.371637	−	0.314869i
$928$	−43.9037	+	76.0435i	−0.0473101	+	0.0819434i
$929$	−883.748	+	510.232i	−0.951290	+	0.549227i	−0.893481	−	0.449100i	$-0.851745\pi$
$929$	−883.748	+	510.232i	−0.951290	+	0.549227i	−0.0578085	+	0.998328i	$0.518411\pi$
$930$	262.337	+	314.158i	0.282083	+	0.337804i
$931$	−568.483	+	552.193i	−0.610615	+	0.593118i
$932$			80.1007i			0.0859450i
$933$	355.141	+	130.219i	0.380644	+	0.139571i
$934$	141.950	−	245.865i	0.151981	−	0.263239i
$935$	−12.3531	−	7.13204i	−0.0132118	−	0.00762785i
$936$	−175.928	−	490.615i	−0.187957	−	0.524162i
$937$	−373.998			−0.399144			−0.199572	−	0.979883i	$-0.563955\pi$
$937$	−373.998			−0.399144			−0.199572	+	0.979883i	$0.563955\pi$
$938$	215.251	−	276.338i	0.229478	−	0.294604i
$939$	−371.927	−	445.395i	−0.396088	−	0.474329i
$940$	−46.7111	−	80.9060i	−0.0496927	−	0.0860702i
$941$	−1364.32	−	787.691i	−1.44986	−	0.837078i	−0.451390	−	0.892327i	$-0.649072\pi$
$941$	−1364.32	−	787.691i	−1.44986	−	0.837078i	−0.998473	+	0.0552486i	$0.982405\pi$
$942$	88.0995	+	506.690i	0.0935239	+	0.537888i
$943$	704.614	+	1220.43i	0.747204	+	1.29420i
$944$			311.902i			0.330404i
$945$	392.737	−	156.085i	0.415595	−	0.165169i
$946$	78.3556			0.0828283
$947$	−633.047	+	365.490i	−0.668477	+	0.385945i	−0.795499	−	0.605955i	$-0.792791\pi$
$947$	−633.047	+	365.490i	−0.668477	+	0.385945i	0.127023	+	0.991900i	$0.459458\pi$
$948$	−308.534	+	53.6455i	−0.325458	+	0.0565881i
$949$	1341.98	−	2324.37i	1.41410	−	2.44929i
$950$	99.0445	−	57.1834i	0.104257	−	0.0601930i
$951$	−88.4619	+	73.8701i	−0.0930199	+	0.0776762i
$952$	69.9472	−	28.3793i	0.0734739	−	0.0298102i
$953$		−	1112.88i		−	1.16776i	−0.811838	−	0.583882i	$-0.801533\pi$
$953$		−	1112.88i		−	1.16776i	0.811838	−	0.583882i	$-0.198467\pi$
$954$	−404.156	+	144.924i	−0.423644	+	0.151912i
$955$	309.337	−	535.788i	0.323913	−	0.561034i
$956$	−554.207	−	319.971i	−0.579714	−	0.334698i
$957$	−26.8226	+	73.1521i	−0.0280278	+	0.0764389i
$958$	365.187			0.381198
$959$	368.938	+	909.330i	0.384711	+	0.948207i
$960$	−41.1923	+	34.3976i	−0.0429086	+	0.0358308i
$961$	−450.143	−	779.670i	−0.468411	−	0.811311i
$962$	−757.321	−	437.239i	−0.787236	−	0.454511i
$963$	−966.021	+	1140.19i	−1.00314	+	1.18399i
$964$	430.621	+	745.857i	0.446702	+	0.773711i
$965$		−	243.909i		−	0.252755i
$966$	−780.694	+	486.831i	−0.808172	+	0.503966i
$967$	−1522.47			−1.57443			−0.787213	−	0.616682i	$-0.788477\pi$
$967$	−1522.47			−1.57443			−0.787213	+	0.616682i	$0.788477\pi$
$968$	−289.531	+	167.161i	−0.299102	+	0.172687i
$969$	−31.6896	−	182.258i	−0.0327034	−	0.188089i
$970$	54.2756	−	94.0080i	0.0559542	−	0.0969155i
$971$	841.847	−	486.040i	0.866989	−	0.500557i	0.000642738	−	1.00000i	$-0.499795\pi$
$971$	841.847	−	486.040i	0.866989	−	0.500557i	0.866347	+	0.499443i	$0.166462\pi$
$972$	160.772	+	458.637i	0.165403	+	0.471849i
$973$	−995.218	−	775.214i	−1.02283	−	0.796725i
$974$		−	21.1387i		−	0.0217029i
$975$	−105.729	+	288.350i	−0.108440	+	0.295743i
$976$	−176.803	+	306.232i	−0.181150	+	0.313762i
$977$	−343.320	−	198.216i	−0.351402	−	0.202882i	0.313901	−	0.949456i	$-0.398364\pi$
$977$	−343.320	−	198.216i	−0.351402	−	0.202882i	−0.665303	+	0.746574i	$0.731697\pi$
$978$	184.357	+	67.5983i	0.188505	+	0.0691189i
$979$	153.063			0.156346
$980$	−212.470	+	53.6337i	−0.216806	+	0.0547283i
$981$	−32.2562	+	177.973i	−0.0328810	+	0.181420i
$982$	−445.662	−	771.909i	−0.453831	−	0.786058i
$983$	1106.16	+	638.641i	1.12529	+	0.649686i	0.942746	−	0.333512i	$-0.108234\pi$
$983$	1106.16	+	638.641i	1.12529	+	0.649686i	0.182543	+	0.983198i	$0.441567\pi$
$984$	−380.280	+	66.1203i	−0.386464	+	0.0671954i
$985$	−261.189	−	452.393i	−0.265167	−	0.459283i
$986$		−	83.6931i		−	0.0848814i
$987$	438.433	−	14.9055i	0.444208	−	0.0151018i
$988$	662.316			0.670360
$989$	888.425	−	512.932i	0.898307	−	0.518638i
$990$	−30.7825	+	36.3323i	−0.0310934	+	0.0366993i
$991$	−419.225	+	726.118i	−0.423032	+	0.732713i	−0.996234	−	0.0867011i	$-0.972368\pi$
$991$	−419.225	+	726.118i	−0.423032	+	0.732713i	0.573203	+	0.819414i	$0.305701\pi$
$992$	211.355	−	122.026i	0.213059	−	0.123010i
$993$	−1209.44	−	1448.35i	−1.21797	−	1.45856i
$994$	−152.073	+	1093.63i	−0.152991	+	1.10023i
$995$		−	24.6074i		−	0.0247311i
$996$	−406.774	−	149.151i	−0.408407	−	0.149750i
$997$	231.377	−	400.757i	0.232073	−	0.401963i	−0.726345	−	0.687331i	$-0.758782\pi$
$997$	231.377	−	400.757i	0.232073	−	0.401963i	0.958418	+	0.285368i	$0.0921157\pi$
$998$	−975.148	−	563.002i	−0.977102	−	0.564130i
$999$	703.238	+	412.741i	0.703941	+	0.413154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.s.a.11.11	yes	40
3.2	odd	2	inner	210.3.s.a.11.6	✓	40
7.2	even	3	inner	210.3.s.a.191.6	yes	40
21.2	odd	6	inner	210.3.s.a.191.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.s.a.11.6	✓	40	3.2	odd	2	inner
210.3.s.a.11.11	yes	40	1.1	even	1	trivial
210.3.s.a.191.6	yes	40	7.2	even	3	inner
210.3.s.a.191.11	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)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-2.95566 + 0.513907i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.25654 + 2.71937i) q^{6} +(5.52236 + 4.30158i) q^{7} -2.82843i q^{8} +(8.47180 - 3.03786i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-2.95566 + 0.513907i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.25654 + 2.71937i) q^{6} +(5.52236 + 4.30158i) q^{7} -2.82843i q^{8} +(8.47180 - 3.03786i) q^{9} +(-1.58114 + 2.73861i) q^{10} +(1.44901 + 0.836586i) q^{11} +(-2.06554 + 5.63325i) q^{12} +20.4748 q^{13} +(9.80515 + 1.36344i) q^{14} +(5.14904 - 4.29970i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.30178 + 1.90628i) q^{17} +(8.22770 - 9.71108i) q^{18} +(8.08695 + 14.0070i) q^{19} +4.47214i q^{20} +(-18.5328 - 9.87600i) q^{21} +2.36622 q^{22} +(26.8291 - 15.4898i) q^{23} +(1.45355 + 8.35986i) q^{24} +(2.50000 - 4.33013i) q^{25} +(25.0764 - 14.4779i) q^{26} +(-23.4785 + 13.3326i) q^{27} +(12.9729 - 5.26343i) q^{28} -15.5223i q^{29} +(3.26591 - 8.90695i) q^{30} +(-21.5713 + 37.3626i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-4.71270 - 1.72800i) q^{33} +5.39179 q^{34} +(-15.5033 - 2.15579i) q^{35} +(3.21006 - 17.7115i) q^{36} +(-15.1002 - 26.1544i) q^{37} +(19.8089 + 11.4367i) q^{38} +(-60.5166 + 10.5222i) q^{39} +(3.16228 + 5.47723i) q^{40} +45.4889i q^{41} +(-29.6813 + 1.00908i) q^{42} +33.1142 q^{43} +(2.89802 - 1.67317i) q^{44} +(-13.0091 + 15.3546i) q^{45} +(21.9059 - 37.9421i) q^{46} +(-18.0911 + 10.4449i) q^{47} +(7.69154 + 9.21088i) q^{48} +(11.9929 + 47.5097i) q^{49} -7.07107i q^{50} +(-10.7386 - 3.93751i) q^{51} +(20.4748 - 35.4635i) q^{52} +(-29.2139 - 16.8666i) q^{53} +(-19.3276 + 32.9309i) q^{54} -3.74133 q^{55} +(12.1667 - 15.6196i) q^{56} +(-31.1005 - 37.2439i) q^{57} +(-10.9759 - 19.0109i) q^{58} +(-67.5287 - 38.9877i) q^{59} +(-2.29826 - 13.2181i) q^{60} +(-44.2007 - 76.5579i) q^{61} +61.0129i q^{62} +(59.8519 + 19.6659i) q^{63} -8.00000 q^{64} +(-39.6493 + 22.8916i) q^{65} +(-6.99374 + 1.21602i) q^{66} +(17.6918 - 30.6431i) q^{67} +(6.60356 - 3.81257i) q^{68} +(-71.3374 + 59.5702i) q^{69} +(-20.5120 + 8.32221i) q^{70} +111.536i q^{71} +(-8.59238 - 23.9619i) q^{72} +(65.5428 - 113.523i) q^{73} +(-36.9879 - 21.3550i) q^{74} +(-5.16386 + 14.0831i) q^{75} +32.3478 q^{76} +(4.40331 + 10.8530i) q^{77} +(-66.6770 + 55.6786i) q^{78} +(26.0969 + 45.2012i) q^{79} +(7.74597 + 4.47214i) q^{80} +(62.5428 - 51.4724i) q^{81} +(32.1655 + 55.7122i) q^{82} +72.2094i q^{83} +(-35.6385 + 22.2237i) q^{84} -8.52517 q^{85} +(40.5564 - 23.4153i) q^{86} +(7.97703 + 45.8786i) q^{87} +(2.36622 - 4.09842i) q^{88} +(79.2245 - 45.7403i) q^{89} +(-5.07555 + 28.0043i) q^{90} +(113.069 + 88.0741i) q^{91} -61.9592i q^{92} +(44.5565 - 121.517i) q^{93} +(-14.7713 + 25.5847i) q^{94} +(-31.3206 - 18.0830i) q^{95} +(15.9332 + 5.84224i) q^{96} -34.3269 q^{97} +(48.2826 + 49.7070i) q^{98} +(14.8172 + 2.68549i) 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

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