LMFDB - Embedded newform 196.3.g.i.79.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,3,Mod(67,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.67"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	196.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-2,0,-4,2,12,0,-8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34061318146$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} + \cdots + 4 $ x^12 - 3x^11 - 4x^10 + 3x^9 + 86x^8 - 163x^7 + 155x^6 - 166x^5 + 164x^4 - 116x^3 + 60x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.5
Root			$0.907369 - 0.0534805i$ of defining polynomial
Character	$\chi$	$=$	196.79
Dual form			196.3.g.i.67.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19654 + 1.60259i) q^{2} +(1.86796 - 1.07847i) q^{3} +(-1.13656 + 3.83513i) q^{4} +(-3.25304 + 5.63443i) q^{5} +(3.96343 + 1.70313i) q^{6} +(-7.50608 + 2.76746i) q^{8} +(-2.17382 + 3.76517i) q^{9} +(-12.9221 + 1.52857i) q^{10} +(-0.528732 + 0.305264i) q^{11} +(2.01300 + 8.38961i) q^{12} +10.6645 q^{13} +14.0332i q^{15} +(-13.4164 - 8.71774i) q^{16} +(-5.99069 - 10.3762i) q^{17} +(-8.63508 + 1.02145i) q^{18} +(10.5811 + 6.10898i) q^{19} +(-17.9115 - 18.8797i) q^{20} +(-1.12186 - 0.482077i) q^{22} +(34.7524 + 20.0643i) q^{23} +(-11.0364 + 13.2645i) q^{24} +(-8.66451 - 15.0074i) q^{25} +(12.7606 + 17.0908i) q^{26} +28.7900i q^{27} -9.04293 q^{29} +(-22.4894 + 16.7913i) q^{30} +(30.2408 - 17.4595i) q^{31} +(-2.08243 - 31.9322i) q^{32} +(-0.658433 + 1.14044i) q^{33} +(9.46059 - 22.0161i) q^{34} +(-11.9692 - 12.6162i) q^{36} +(25.4082 - 44.0084i) q^{37} +(2.87054 + 24.2667i) q^{38} +(19.9209 - 11.5013i) q^{39} +(8.82450 - 51.2951i) q^{40} -25.7382 q^{41} +19.8107i q^{43} +(-0.569787 - 2.37471i) q^{44} +(-14.1430 - 24.4965i) q^{45} +(9.42799 + 79.7015i) q^{46} +(-40.7870 - 23.5484i) q^{47} +(-34.4631 - 1.81520i) q^{48} +(13.6831 - 31.8426i) q^{50} +(-22.3807 - 12.9215i) q^{51} +(-12.1209 + 40.8998i) q^{52} +(13.4390 + 23.2770i) q^{53} +(-46.1384 + 34.4485i) q^{54} -3.97214i q^{55} +26.3533 q^{57} +(-10.8203 - 14.4921i) q^{58} +(39.8644 - 23.0157i) q^{59} +(-53.8190 - 15.9496i) q^{60} +(21.1035 - 36.5524i) q^{61} +(64.1648 + 27.5724i) q^{62} +(48.6823 - 41.5455i) q^{64} +(-34.6920 + 60.0884i) q^{65} +(-2.61550 + 0.309390i) q^{66} +(24.0592 - 13.8906i) q^{67} +(46.6028 - 11.1819i) q^{68} +86.5547 q^{69} -57.1882i q^{71} +(5.89691 - 34.2776i) q^{72} +(28.1645 + 48.7824i) q^{73} +(100.929 - 11.9391i) q^{74} +(-32.3699 - 18.6888i) q^{75} +(-35.4548 + 33.6365i) q^{76} +(42.2680 + 18.1631i) q^{78} +(15.9295 + 9.19688i) q^{79} +(92.7637 - 47.2348i) q^{80} +(11.4846 + 19.8919i) q^{81} +(-30.7969 - 41.2477i) q^{82} +37.3775i q^{83} +77.9517 q^{85} +(-31.7483 + 23.7043i) q^{86} +(-16.8918 + 9.75249i) q^{87} +(3.12390 - 3.75458i) q^{88} +(-12.3537 + 21.3973i) q^{89} +(22.3349 - 51.9766i) q^{90} +(-116.448 + 110.476i) q^{92} +(37.6590 - 65.2273i) q^{93} +(-11.0651 - 93.5415i) q^{94} +(-68.8412 + 39.7455i) q^{95} +(-38.3277 - 57.4021i) q^{96} -109.895 q^{97} -2.65435i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{8} + 4 q^{9} + 2 q^{10} + 24 q^{12} + 24 q^{13} + 16 q^{16} + 2 q^{17} + 56 q^{18} - 152 q^{20} + 44 q^{22} + 44 q^{24} - 56 q^{26} + 72 q^{29} - 74 q^{30}+ \cdots - 744 q^{97}+O(q^{100}) $ 12 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^8 + 4 * q^9 + 2 * q^10 + 24 * q^12 + 24 * q^13 + 16 * q^16 + 2 * q^17 + 56 * q^18 - 152 * q^20 + 44 * q^22 + 44 * q^24 - 56 * q^26 + 72 * q^29 - 74 * q^30 - 112 * q^32 + 14 * q^33 + 316 * q^34 - 160 * q^36 + 86 * q^37 + 2 * q^38 + 148 * q^40 - 8 * q^41 + 64 * q^44 - 156 * q^45 + 162 * q^46 - 512 * q^48 + 208 * q^50 + 64 * q^52 - 74 * q^53 - 182 * q^54 - 220 * q^57 - 176 * q^58 - 232 * q^60 - 86 * q^61 + 532 * q^62 - 160 * q^64 - 140 * q^65 - 102 * q^66 + 68 * q^68 + 300 * q^69 + 152 * q^72 + 234 * q^73 + 290 * q^74 - 576 * q^76 + 64 * q^78 + 146 * q^81 - 272 * q^82 + 268 * q^85 - 16 * q^86 - 188 * q^88 - 6 * q^89 + 640 * q^90 - 448 * q^92 + 162 * q^93 - 102 * q^94 + 320 * q^96 - 744 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.19654	+	1.60259i	0.598272	+	0.801293i
$2$	1.19654	+	1.60259i	0.598272	+	0.801293i
$3$	1.86796	−	1.07847i	0.622653	−	0.359489i	−0.155248	−	0.987875i	$-0.549618\pi$
$3$	1.86796	−	1.07847i	0.622653	−	0.359489i	0.777901	+	0.628387i	$0.216284\pi$
$4$	−1.13656	+	3.83513i	−0.284141	+	0.958782i
$5$	−3.25304	+	5.63443i	−0.650608	+	1.12689i	0.332368	+	0.943150i	$0.392152\pi$
$5$	−3.25304	+	5.63443i	−0.650608	+	1.12689i	−0.982976	+	0.183736i	$0.941181\pi$
$6$	3.96343	+	1.70313i	0.660572	+	0.283855i
$7$		0			0
$7$		0			0
$8$	−7.50608	+	2.76746i	−0.938259	+	0.345932i
$9$	−2.17382	+	3.76517i	−0.241536	+	0.418352i
$10$	−12.9221	+	1.52857i	−1.29221	+	0.152857i
$11$	−0.528732	+	0.305264i	−0.0480665	+	0.0277512i	−0.523841	−	0.851816i	$-0.675501\pi$
$11$	−0.528732	+	0.305264i	−0.0480665	+	0.0277512i	0.475774	+	0.879567i	$0.342168\pi$
$12$	2.01300	+	8.38961i	0.167750	+	0.699134i
$13$	10.6645			0.820347			0.410173	−	0.912008i	$-0.365468\pi$
$13$	10.6645			0.820347			0.410173	+	0.912008i	$0.365468\pi$
$14$		0			0
$15$			14.0332i			0.935544i
$16$	−13.4164	−	8.71774i	−0.838528	−	0.544859i
$17$	−5.99069	−	10.3762i	−0.352393	−	0.610363i	0.634275	−	0.773108i	$-0.281299\pi$
$17$	−5.99069	−	10.3762i	−0.352393	−	0.610363i	−0.986668	+	0.162744i	$0.947965\pi$
$18$	−8.63508	+	1.02145i	−0.479727	+	0.0567475i
$19$	10.5811	+	6.10898i	0.556898	+	0.321525i	0.751900	−	0.659278i	$-0.229138\pi$
$19$	10.5811	+	6.10898i	0.556898	+	0.321525i	−0.195001	+	0.980803i	$0.562471\pi$
$20$	−17.9115	−	18.8797i	−0.895574	−	0.943986i
$21$		0			0
$22$	−1.12186	−	0.482077i	−0.0509937	−	0.0219126i
$23$	34.7524	+	20.0643i	1.51097	+	0.872361i	0.999918	+	0.0128131i	$0.00407865\pi$
$23$	34.7524	+	20.0643i	1.51097	+	0.872361i	0.511055	+	0.859548i	$0.329255\pi$
$24$	−11.0364	+	13.2645i	−0.459851	+	0.552689i
$25$	−8.66451	−	15.0074i	−0.346580	−	0.600295i
$26$	12.7606	+	17.0908i	0.490791	+	0.657338i
$27$			28.7900i			1.06629i
$28$		0			0
$29$	−9.04293			−0.311825			−0.155913	−	0.987771i	$-0.549832\pi$
$29$	−9.04293			−0.311825			−0.155913	+	0.987771i	$0.549832\pi$
$30$	−22.4894	+	16.7913i	−0.749645	+	0.559710i
$31$	30.2408	−	17.4595i	0.975509	−	0.563210i	0.0745975	−	0.997214i	$-0.476233\pi$
$31$	30.2408	−	17.4595i	0.975509	−	0.563210i	0.900911	+	0.434004i	$0.142899\pi$
$32$	−2.08243	−	31.9322i	−0.0650759	−	0.997880i
$33$	−0.658433	+	1.14044i	−0.0199525	+	0.0345588i
$34$	9.46059	−	22.0161i	0.278253	−	0.647534i
$35$		0			0
$36$	−11.9692	−	12.6162i	−0.332478	−	0.350451i
$37$	25.4082	−	44.0084i	0.686709	−	1.18941i	−0.286187	−	0.958174i	$-0.592388\pi$
$37$	25.4082	−	44.0084i	0.686709	−	1.18941i	0.972896	−	0.231241i	$-0.0742787\pi$
$38$	2.87054	+	24.2667i	0.0755406	+	0.638598i
$39$	19.9209	−	11.5013i	0.510791	−	0.294905i
$40$	8.82450	−	51.2951i	0.220612	−	1.28238i
$41$	−25.7382			−0.627761			−0.313881	−	0.949462i	$-0.601629\pi$
$41$	−25.7382			−0.627761			−0.313881	+	0.949462i	$0.601629\pi$
$42$		0			0
$43$			19.8107i			0.460713i	0.973106	+	0.230357i	$0.0739893\pi$
$43$			19.8107i			0.460713i	−0.973106	+	0.230357i	$0.926011\pi$
$44$	−0.569787	−	2.37471i	−0.0129497	−	0.0539706i
$45$	−14.1430	−	24.4965i	−0.314290	−	0.544366i
$46$	9.42799	+	79.7015i	0.204956	+	1.73264i
$47$	−40.7870	−	23.5484i	−0.867809	−	0.501030i	−0.00118973	−	0.999999i	$-0.500379\pi$
$47$	−40.7870	−	23.5484i	−0.867809	−	0.501030i	−0.866620	+	0.498969i	$0.833712\pi$
$48$	−34.4631	−	1.81520i	−0.717982	−	0.0378167i
$49$		0			0
$50$	13.6831	−	31.8426i	0.273663	−	0.636852i
$51$	−22.3807	−	12.9215i	−0.438837	−	0.253363i
$52$	−12.1209	+	40.8998i	−0.233094	+	0.786534i
$53$	13.4390	+	23.2770i	0.253566	+	0.439190i	0.964505	−	0.264064i	$-0.0850631\pi$
$53$	13.4390	+	23.2770i	0.253566	+	0.439190i	−0.710939	+	0.703254i	$0.751730\pi$
$54$	−46.1384	+	34.4485i	−0.854415	+	0.637934i
$55$		−	3.97214i		−	0.0722207i
$56$		0			0
$57$	26.3533			0.462339
$58$	−10.8203	−	14.4921i	−0.186556	−	0.249863i
$59$	39.8644	−	23.0157i	0.675668	−	0.390097i	−0.122553	−	0.992462i	$-0.539108\pi$
$59$	39.8644	−	23.0157i	0.675668	−	0.390097i	0.798221	+	0.602365i	$0.205775\pi$
$60$	−53.8190	−	15.9496i	−0.896984	−	0.265827i
$61$	21.1035	−	36.5524i	0.345959	−	0.599219i	−0.639568	−	0.768734i	$-0.720887\pi$
$61$	21.1035	−	36.5524i	0.345959	−	0.599219i	0.985528	+	0.169515i	$0.0542202\pi$
$62$	64.1648	+	27.5724i	1.03492	+	0.444715i
$63$		0			0
$64$	48.6823	−	41.5455i	0.760661	−	0.649149i
$65$	−34.6920	+	60.0884i	−0.533724	+	0.924437i
$66$	−2.61550	+	0.309390i	−0.0396287	+	0.00468773i
$67$	24.0592	−	13.8906i	0.359092	−	0.207322i	−0.309590	−	0.950870i	$-0.600192\pi$
$67$	24.0592	−	13.8906i	0.359092	−	0.207322i	0.668683	+	0.743548i	$0.266859\pi$
$68$	46.6028	−	11.1819i	0.685335	−	0.164439i
$69$	86.5547			1.25442
$70$		0			0
$71$		−	57.1882i		−	0.805467i	−0.915317	−	0.402734i	$-0.868060\pi$
$71$		−	57.1882i		−	0.805467i	0.915317	−	0.402734i	$-0.131940\pi$
$72$	5.89691	−	34.2776i	0.0819016	−	0.476078i
$73$	28.1645	+	48.7824i	0.385815	+	0.668251i	0.991882	−	0.127162i	$-0.0405869\pi$
$73$	28.1645	+	48.7824i	0.385815	+	0.668251i	−0.606067	+	0.795414i	$0.707254\pi$
$74$	100.929	−	11.9391i	1.36391	−	0.161339i
$75$	−32.3699	−	18.6888i	−0.431598	−	0.249183i
$76$	−35.4548	+	33.6365i	−0.466510	+	0.442586i
$77$		0			0
$78$	42.2680	+	18.1631i	0.541898	+	0.232860i
$79$	15.9295	+	9.19688i	0.201639	+	0.116416i	0.597420	−	0.801929i	$-0.296193\pi$
$79$	15.9295	+	9.19688i	0.201639	+	0.116416i	−0.395781	+	0.918345i	$0.629526\pi$
$80$	92.7637	−	47.2348i	1.15955	−	0.590435i
$81$	11.4846	+	19.8919i	0.141785	+	0.245579i
$82$	−30.7969	−	41.2477i	−0.375572	−	0.503021i
$83$			37.3775i			0.450332i	0.974320	+	0.225166i	$0.0722924\pi$
$83$			37.3775i			0.450332i	−0.974320	+	0.225166i	$0.927708\pi$
$84$		0			0
$85$	77.9517			0.917079
$86$	−31.7483	+	23.7043i	−0.369166	+	0.275632i
$87$	−16.8918	+	9.75249i	−0.194159	+	0.112098i
$88$	3.12390	−	3.75458i	0.0354988	−	0.0426656i
$89$	−12.3537	+	21.3973i	−0.138806	+	0.240419i	−0.927045	−	0.374950i	$-0.877660\pi$
$89$	−12.3537	+	21.3973i	−0.138806	+	0.240419i	0.788239	+	0.615369i	$0.210993\pi$
$90$	22.3349	−	51.9766i	0.248166	−	0.577517i
$91$		0			0
$92$	−116.448	+	110.476i	−1.26573	+	1.20082i
$93$	37.6590	−	65.2273i	0.404935	−	0.701369i
$94$	−11.0651	−	93.5415i	−0.117714	−	0.995122i
$95$	−68.8412	+	39.7455i	−0.724644	+	0.418374i
$96$	−38.3277	−	57.4021i	−0.399246	−	0.597939i
$97$	−109.895			−1.13294			−0.566468	−	0.824084i	$-0.691690\pi$
$97$	−109.895			−1.13294			−0.566468	+	0.824084i	$0.691690\pi$
$98$		0			0
$99$		−	2.65435i		−	0.0268117i
$100$	67.4030	−	16.1727i	0.674030	−	0.161727i
$101$	21.5756	+	37.3700i	0.213620	+	0.370000i	0.952845	−	0.303458i	$-0.0981414\pi$
$101$	21.5756	+	37.3700i	0.213620	+	0.370000i	−0.739225	+	0.673458i	$0.764808\pi$
$102$	−6.07167	−	51.3282i	−0.0595262	−	0.503217i
$103$	130.437	+	75.3078i	1.26638	+	0.731144i	0.974301	−	0.225251i	$-0.0723202\pi$
$103$	130.437	+	75.3078i	1.26638	+	0.731144i	0.292077	+	0.956395i	$0.405654\pi$
$104$	−80.0486	+	29.5136i	−0.769698	+	0.283785i
$105$		0			0
$106$	−21.2231	+	49.3892i	−0.200218	+	0.465936i
$107$	−35.1527	−	20.2954i	−0.328530	−	0.189677i	0.326658	−	0.945143i	$-0.394077\pi$
$107$	−35.1527	−	20.2954i	−0.328530	−	0.189677i	−0.655188	+	0.755466i	$0.727411\pi$
$108$	−110.413	−	32.7216i	−1.02234	−	0.302978i
$109$	−33.2652	−	57.6170i	−0.305185	−	0.528596i	0.672117	−	0.740445i	$-0.265385\pi$
$109$	−33.2652	−	57.6170i	−0.305185	−	0.528596i	−0.977303	+	0.211848i	$0.932052\pi$
$110$	6.36569	−	4.75284i	0.0578699	−	0.0432076i
$111$		−	109.608i		−	0.987457i
$112$		0			0
$113$	−143.395			−1.26899			−0.634493	−	0.772929i	$-0.718791\pi$
$113$	−143.395			−1.26899			−0.634493	+	0.772929i	$0.718791\pi$
$114$	31.5329	+	42.2335i	0.276604	+	0.370469i
$115$	−226.102	+	130.540i	−1.96610	+	1.13513i
$116$	10.2779	−	34.6808i	0.0886023	−	0.298972i
$117$	−23.1827	+	40.1537i	−0.198143	+	0.343194i
$118$	84.5842	+	36.3468i	0.716815	+	0.308024i
$119$		0			0
$120$	−38.8362	−	105.334i	−0.323635	−	0.877783i
$121$	−60.3136	+	104.466i	−0.498460	+	0.863358i
$122$	83.8296	−	9.91631i	0.687128	−	0.0812812i
$123$	−48.0779	+	27.7578i	−0.390877	+	0.225673i
$124$	32.5889	+	135.821i	0.262814	+	1.09533i
$125$	−49.9080			−0.399264
$126$		0			0
$127$		−	83.0059i		−	0.653590i	−0.945095	−	0.326795i	$-0.894031\pi$
$127$		−	83.0059i		−	0.653590i	0.945095	−	0.326795i	$-0.105969\pi$
$128$	124.831	+	28.3066i	0.975241	+	0.221145i
$129$	21.3651	+	37.0055i	0.165621	+	0.286864i
$130$	−137.807	+	16.3014i	−1.06006	+	0.125395i
$131$	−25.5368	−	14.7437i	−0.194938	−	0.112547i	0.399354	−	0.916797i	$-0.369234\pi$
$131$	−25.5368	−	14.7437i	−0.194938	−	0.112547i	−0.594292	+	0.804249i	$0.702568\pi$
$132$	−3.62538	−	3.82136i	−0.0274650	−	0.0289497i
$133$		0			0
$134$	51.0487	+	21.9362i	0.380961	+	0.163703i
$135$	−162.215	−	93.6548i	−1.20159	−	0.693740i
$136$	73.6822	+	61.3054i	0.541781	+	0.450775i
$137$	11.7586	+	20.3664i	0.0858288	+	0.148660i	0.905744	−	0.423825i	$-0.139313\pi$
$137$	11.7586	+	20.3664i	0.0858288	+	0.148660i	−0.819915	+	0.572485i	$0.805980\pi$
$138$	103.566	+	138.711i	0.750482	+	1.00515i
$139$		−	256.175i		−	1.84299i	−0.388396	−	0.921493i	$-0.626971\pi$
$139$		−	256.175i		−	1.84299i	0.388396	−	0.921493i	$-0.373029\pi$
$140$		0			0
$141$	−101.585			−0.720459
$142$	91.6490	−	68.4282i	0.645416	−	0.481889i
$143$	−5.63867	+	3.25549i	−0.0394312	+	0.0227656i
$144$	61.9887	−	31.5644i	0.430477	−	0.219197i
$145$	29.4170	−	50.9517i	0.202876	−	0.351391i
$146$	−44.4779	+	103.506i	−0.304643	+	0.708947i
$147$		0			0
$148$	139.900	+	147.462i	0.945268	+	0.996366i
$149$	−44.7826	+	77.5658i	−0.300554	+	0.520576i	−0.976262	−	0.216595i	$-0.930505\pi$
$149$	−44.7826	+	77.5658i	−0.300554	+	0.520576i	0.675707	+	0.737170i	$0.263838\pi$
$150$	−8.78164	−	74.2374i	−0.0585443	−	0.494916i
$151$	40.8283	−	23.5722i	0.270386	−	0.156107i	−0.358677	−	0.933462i	$-0.616772\pi$
$151$	40.8283	−	23.5722i	0.270386	−	0.156107i	0.629063	+	0.777354i	$0.283439\pi$
$152$	−96.3286	−	16.5718i	−0.633741	−	0.109025i
$153$	52.0907			0.340462
$154$		0			0
$155$			227.186i			1.46572i
$156$	21.4677	+	89.4711i	0.137613	+	0.573532i
$157$	−143.897	−	249.237i	−0.916540	−	1.58749i	−0.804631	−	0.593776i	$-0.797637\pi$
$157$	−143.897	−	249.237i	−0.916540	−	1.58749i	−0.111910	−	0.993718i	$-0.535697\pi$
$158$	4.32151	+	36.5328i	0.0273513	+	0.231220i
$159$	50.2070	+	28.9870i	0.315767	+	0.182308i
$160$	186.694	+	92.1433i	1.16684	+	0.575895i
$161$		0			0
$162$	−18.1367	+	42.2067i	−0.111955	+	0.260535i
$163$	11.7940	+	6.80925i	0.0723557	+	0.0417746i	0.535741	−	0.844382i	$-0.320032\pi$
$163$	11.7940	+	6.80925i	0.0723557	+	0.0417746i	−0.463386	+	0.886157i	$0.653366\pi$
$164$	29.2531	−	98.7094i	0.178373	−	0.601887i
$165$	−4.28381	−	7.41978i	−0.0259625	−	0.0449684i
$166$	−59.9007	+	44.7238i	−0.360848	+	0.269421i
$167$			241.587i			1.44663i	0.690519	+	0.723314i	$0.257382\pi$
$167$			241.587i			1.44663i	−0.690519	+	0.723314i	$0.742618\pi$
$168$		0			0
$169$	−55.2683			−0.327031
$170$	93.2727	+	124.924i	0.548663	+	0.734849i
$171$	−46.0027	+	26.5597i	−0.269022	+	0.155320i
$172$	−75.9765	−	22.5161i	−0.441724	−	0.130908i
$173$	−57.3775	+	99.3807i	−0.331662	+	0.574455i	−0.982838	−	0.184472i	$-0.940943\pi$
$173$	−57.3775	+	99.3807i	−0.331662	+	0.574455i	0.651176	+	0.758927i	$0.274276\pi$
$174$	−35.8410	−	15.4013i	−0.205983	−	0.0885132i
$175$		0			0
$176$	9.75491	+	0.513800i	0.0554256	+	0.00291932i
$177$	49.6434	−	85.9848i	0.280471	−	0.485790i
$178$	−49.0727	+	5.80488i	−0.275689	+	0.0326117i
$179$	−23.2381	+	13.4165i	−0.129822	+	0.0749526i	−0.563504	−	0.826113i	$-0.690547\pi$
$179$	−23.2381	+	13.4165i	−0.129822	+	0.0749526i	0.433683	+	0.901066i	$0.357214\pi$
$180$	110.022	−	26.3986i	0.611231	−	0.146659i
$181$	46.5388			0.257120			0.128560	−	0.991702i	$-0.458964\pi$
$181$	46.5388			0.257120			0.128560	+	0.991702i	$0.458964\pi$
$182$		0			0
$183$		−	91.0377i		−	0.497474i
$184$	−316.381	−	54.4283i	−1.71946	−	0.295806i
$185$	165.308	+	286.322i	0.893556	+	1.54768i
$186$	149.593	−	17.6956i	0.804263	−	0.0951374i
$187$	6.33494	+	3.65748i	0.0338767	+	0.0195587i
$188$	136.668	−	129.659i	0.726959	−	0.689677i
$189$		0			0
$190$	−146.067	−	62.7667i	−0.768774	−	0.330351i
$191$	65.3175	+	37.7111i	0.341976	+	0.197440i	0.661146	−	0.750258i	$-0.270071\pi$
$191$	65.3175	+	37.7111i	0.341976	+	0.197440i	−0.319169	+	0.947698i	$0.603404\pi$
$192$	46.1311	−	130.108i	0.240266	−	0.677644i
$193$	83.0347	+	143.820i	0.430232	+	0.745183i	0.996893	−	0.0787675i	$-0.0250985\pi$
$193$	83.0347	+	143.820i	0.430232	+	0.745183i	−0.566661	+	0.823951i	$0.691765\pi$
$194$	−131.494	−	176.116i	−0.677803	−	0.907813i
$195$			149.657i			0.767471i
$196$		0			0
$197$	279.737			1.41998			0.709991	−	0.704210i	$-0.248699\pi$
$197$	279.737			1.41998			0.709991	+	0.704210i	$0.248699\pi$
$198$	4.25383	−	3.17605i	0.0214840	−	0.0160407i
$199$	0.238457	−	0.137673i	0.00119828	−	0.000691824i	−0.499401	−	0.866371i	$-0.666446\pi$
$199$	0.238457	−	0.137673i	0.00119828	−	0.000691824i	0.500599	+	0.865679i	$0.333113\pi$
$200$	106.569	+	88.6678i	0.532844	+	0.443339i
$201$	29.9610	−	51.8940i	0.149060	−	0.258179i
$202$	−34.0725	+	79.2916i	−0.168676	+	0.392533i
$203$		0			0
$204$	74.9928	−	71.1468i	0.367612	−	0.348759i
$205$	83.7274	−	145.020i	0.408426	−	0.707415i
$206$	35.3863	+	299.146i	0.171778	+	1.45216i
$207$	−151.091	+	87.2324i	−0.729908	+	0.421413i
$208$	−143.080	−	92.9705i	−0.687883	−	0.446973i
$209$	−7.45940			−0.0356909
$210$		0			0
$211$		−	301.264i		−	1.42779i	−0.700252	−	0.713896i	$-0.746929\pi$
$211$		−	301.264i		−	1.42779i	0.700252	−	0.713896i	$-0.253071\pi$
$212$	−104.545	+	25.0845i	−0.493136	+	0.118323i
$213$	−61.6755	−	106.825i	−0.289556	−	0.501527i
$214$	−9.53660	−	80.6196i	−0.0445635	−	0.376727i
$215$	−111.622	−	64.4449i	−0.519171	−	0.299744i
$216$	−79.6751	−	216.100i	−0.368866	−	1.00046i
$217$		0			0
$218$	52.5329	−	122.252i	0.240977	−	0.560787i
$219$	105.220	+	60.7489i	0.480458	+	0.277392i
$220$	15.2337	+	4.51459i	0.0692439	+	0.0205209i
$221$	−63.8877	−	110.657i	−0.289085	−	0.500709i
$222$	175.656	−	131.150i	0.791242	−	0.590768i
$223$		−	215.034i		−	0.964279i	−0.876094	−	0.482140i	$-0.839860\pi$
$223$		−	215.034i		−	0.964279i	0.876094	−	0.482140i	$-0.160140\pi$
$224$		0			0
$225$	75.3404			0.334846
$226$	−171.579	−	229.804i	−0.759199	−	1.01683i
$227$	364.944	−	210.700i	1.60768	−	0.928195i	0.617794	−	0.786340i	$-0.288027\pi$
$227$	364.944	−	210.700i	1.60768	−	0.928195i	0.989887	−	0.141855i	$-0.0453067\pi$
$228$	−29.9522	+	101.068i	−0.131369	+	0.443282i
$229$	22.7637	−	39.4278i	0.0994046	−	0.172174i	−0.812034	−	0.583610i	$-0.801640\pi$
$229$	22.7637	−	39.4278i	0.0994046	−	0.172174i	0.911438	+	0.411437i	$0.134973\pi$
$230$	−479.742	−	206.151i	−2.08583	−	0.896307i
$231$		0			0
$232$	67.8769	−	25.0259i	0.292573	−	0.107870i
$233$	−75.7232	+	131.156i	−0.324992	+	0.562903i	−0.981511	−	0.191407i	$-0.938695\pi$
$233$	−75.7232	+	131.156i	−0.324992	+	0.562903i	0.656518	+	0.754310i	$0.272028\pi$
$234$	−92.0889	+	10.8933i	−0.393542	+	0.0465526i
$235$	265.364	−	153.208i	1.12921	−	0.651948i
$236$	42.9598	+	179.044i	0.182033	+	0.758661i
$237$	39.6741			0.167401
$238$		0			0
$239$			200.986i			0.840944i	0.907306	+	0.420472i	$0.138135\pi$
$239$			200.986i			0.840944i	−0.907306	+	0.420472i	$0.861865\pi$
$240$	122.338	−	188.275i	0.509740	−	0.784480i
$241$	124.318	+	215.326i	0.515844	+	0.893468i	0.999831	+	0.0183927i	$0.00585490\pi$
$241$	124.318	+	215.326i	0.515844	+	0.893468i	−0.483987	+	0.875075i	$0.660812\pi$
$242$	−239.584	+	28.3407i	−0.990017	+	0.117110i
$243$	−181.490	−	104.783i	−0.746872	−	0.431207i
$244$	116.198	+	122.479i	0.476220	+	0.501963i
$245$		0			0
$246$	−102.012	−	43.8356i	−0.414681	−	0.178193i
$247$	112.842	+	65.1493i	0.456850	+	0.263762i
$248$	−178.671	+	214.743i	−0.720448	+	0.865897i
$249$	40.3104	+	69.8196i	0.161889	+	0.280400i
$250$	−59.7171	−	79.9819i	−0.238868	−	0.319927i
$251$			226.888i			0.903938i	0.892034	+	0.451969i	$0.149278\pi$
$251$			226.888i			0.903938i	−0.892034	+	0.451969i	$0.850722\pi$
$252$		0			0
$253$	−24.4996			−0.0968364
$254$	133.024	−	99.3202i	0.523717	−	0.391024i
$255$	145.611	−	84.0683i	0.571022	−	0.329680i
$256$	104.002	+	233.922i	0.406257	+	0.913759i
$257$	177.583	−	307.583i	0.690984	−	1.19682i	−0.280532	−	0.959845i	$-0.590511\pi$
$257$	177.583	−	307.583i	0.690984	−	1.19682i	0.971516	−	0.236975i	$-0.0761559\pi$
$258$	−33.7402	+	78.5182i	−0.130776	+	0.304334i
$259$		0			0
$260$	−191.017	−	201.343i	−0.734681	−	0.774396i
$261$	19.6577	−	34.0481i	0.0753169	−	0.130453i
$262$	−6.92790	−	58.5664i	−0.0264424	−	0.223536i
$263$	338.273	−	195.302i	1.28621	−	0.742593i	0.308232	−	0.951311i	$-0.400263\pi$
$263$	338.273	−	195.302i	1.28621	−	0.742593i	0.977976	+	0.208718i	$0.0669292\pi$
$264$	1.78613	−	10.3824i	0.00676563	−	0.0393273i
$265$	−174.870			−0.659888
$266$		0			0
$267$			53.2923i			0.199597i
$268$	25.9274	+	108.058i	0.0967439	+	0.403200i
$269$	−187.371	−	324.536i	−0.696546	−	1.20645i	−0.969657	−	0.244471i	$-0.921386\pi$
$269$	−187.371	−	324.536i	−0.696546	−	1.20645i	0.273110	−	0.961983i	$-0.411948\pi$
$270$	−44.0074	−	372.026i	−0.162990	−	1.37787i
$271$	−132.759	−	76.6485i	−0.489886	−	0.282836i	0.234641	−	0.972082i	$-0.424608\pi$
$271$	−132.759	−	76.6485i	−0.489886	−	0.282836i	−0.724527	+	0.689246i	$0.757942\pi$
$272$	−10.0831	+	191.437i	−0.0370703	+	0.703811i
$273$		0			0
$274$	−18.5693	+	43.2134i	−0.0677712	+	0.157713i
$275$	9.16241	+	5.28992i	0.0333178	+	0.0192361i
$276$	−98.3750	+	331.948i	−0.356431	+	1.20271i
$277$	−224.888	−	389.517i	−0.811869	−	1.40620i	−0.911555	−	0.411179i	$-0.865117\pi$
$277$	−224.888	−	389.517i	−0.811869	−	1.40620i	0.0996861	−	0.995019i	$-0.468216\pi$
$278$	410.542	−	306.525i	1.47677	−	1.10261i
$279$			151.815i			0.544141i
$280$		0			0
$281$	−3.27554			−0.0116567			−0.00582836	−	0.999983i	$-0.501855\pi$
$281$	−3.27554			−0.0116567			−0.00582836	+	0.999983i	$0.501855\pi$
$282$	−121.551	−	162.798i	−0.431030	−	0.577298i
$283$	296.447	−	171.154i	1.04752	−	0.604783i	0.125562	−	0.992086i	$-0.459926\pi$
$283$	296.447	−	171.154i	1.04752	−	0.604783i	0.921953	+	0.387303i	$0.126593\pi$
$284$	219.324	+	64.9981i	0.772268	+	0.228866i
$285$	−85.7283	+	148.486i	−0.300801	+	0.521003i
$286$	−11.9641	−	5.14112i	−0.0418326	−	0.0179759i
$287$		0			0
$288$	124.757	+	61.5741i	0.433183	+	0.213799i
$289$	72.7233	−	125.961i	0.251638	−	0.435850i
$290$	116.853	−	13.8227i	0.402942	−	0.0476645i
$291$	−205.279	+	118.518i	−0.705425	+	0.407277i
$292$	−219.097	+	52.5703i	−0.750334	+	0.180035i
$293$	243.752			0.831919			0.415959	−	0.909383i	$-0.363446\pi$
$293$	243.752			0.831919			0.415959	+	0.909383i	$0.363446\pi$
$294$		0			0
$295$			299.484i			1.01520i
$296$	−68.9248	+	400.646i	−0.232854	+	1.35353i
$297$	−8.78853	−	15.2222i	−0.0295910	−	0.0512531i
$298$	−177.890	+	21.0429i	−0.596947	+	0.0706136i
$299$	370.617	+	213.976i	1.23952	+	0.715638i
$300$	108.464	−	102.902i	0.361548	−	0.343006i
$301$		0			0
$302$	86.6293	+	37.2256i	0.286852	+	0.123264i
$303$	80.6046	+	46.5371i	0.266022	+	0.153588i
$304$	−88.7037	−	174.204i	−0.291789	−	0.573039i
$305$	137.301	+	237.812i	0.450167	+	0.779713i
$306$	62.3289	+	83.4799i	0.203689	+	0.272810i
$307$		−	58.4520i		−	0.190397i	−0.995458	−	0.0951987i	$-0.969651\pi$
$307$		−	58.4520i		−	0.190397i	0.995458	−	0.0951987i	$-0.0303487\pi$
$308$		0			0
$309$	324.868			1.05135
$310$	−364.085	+	271.838i	−1.17447	+	0.876896i
$311$	−107.722	+	62.1933i	−0.346373	+	0.199978i	−0.663086	−	0.748543i	$-0.730754\pi$
$311$	−107.722	+	62.1933i	−0.346373	+	0.199978i	0.316714	+	0.948521i	$0.397421\pi$
$312$	−117.698	+	141.460i	−0.377237	+	0.453397i
$313$	−240.725	+	416.948i	−0.769090	+	1.33210i	0.168967	+	0.985622i	$0.445957\pi$
$313$	−240.725	+	416.948i	−0.769090	+	1.33210i	−0.938057	+	0.346481i	$0.887376\pi$
$314$	227.244	−	528.830i	0.723708	−	1.68417i
$315$		0			0
$316$	−53.3761	+	50.6387i	−0.168912	+	0.160249i
$317$	179.573	−	311.030i	0.566478	−	0.981168i	−0.430433	−	0.902623i	$-0.641639\pi$
$317$	179.573	−	311.030i	0.566478	−	0.981168i	0.996911	−	0.0785457i	$-0.0250276\pi$
$318$	13.6207	+	115.145i	0.0428324	+	0.362092i
$319$	4.78129	−	2.76048i	0.0149884	−	0.00865353i
$320$	75.7197	+	409.446i	0.236624	+	1.27952i
$321$	−87.5517			−0.272747
$322$		0			0
$323$		−	146.388i		−	0.453214i
$324$	−89.3411	+	21.4365i	−0.275744	+	0.0661621i
$325$	−92.4027	−	160.046i	−0.284316	−	0.492450i
$326$	3.19959	+	27.0484i	0.00981470	+	0.0829706i
$327$	−124.276	−	71.7508i	−0.380049	−	0.219421i
$328$	193.193	−	71.2295i	0.589003	−	0.217163i
$329$		0			0
$330$	6.76507	−	15.7433i	0.0205002	−	0.0477069i
$331$	109.721	+	63.3476i	0.331484	+	0.191383i	0.656500	−	0.754326i	$-0.272036\pi$
$331$	109.721	+	63.3476i	0.331484	+	0.191383i	−0.325016	+	0.945709i	$0.605370\pi$
$332$	−143.348	−	42.4820i	−0.431770	−	0.127958i
$333$	110.466	+	191.333i	0.331729	+	0.574572i
$334$	−387.164	+	289.069i	−1.15917	+	0.865477i
$335$			180.746i			0.539541i
$336$		0			0
$337$	−551.430			−1.63629			−0.818146	−	0.575011i	$-0.804998\pi$
$337$	−551.430			−1.63629			−0.818146	+	0.575011i	$0.804998\pi$
$338$	−66.1309	−	88.5722i	−0.195654	−	0.262048i
$339$	−267.857	+	154.647i	−0.790138	+	0.456186i
$340$	−88.5972	+	298.955i	−0.260580	+	0.879279i
$341$	−10.6595	+	18.4628i	−0.0312596	+	0.0541431i
$342$	−97.6084	−	41.9435i	−0.285405	−	0.122642i
$343$		0			0
$344$	−54.8252	−	148.700i	−0.159376	−	0.432269i
$345$	−281.566	+	487.686i	−0.816132	+	1.41358i
$346$	−227.921	+	26.9610i	−0.658730	+	0.0779221i
$347$	−356.182	+	205.642i	−1.02646	+	0.592628i	−0.915969	−	0.401249i	$-0.868576\pi$
$347$	−356.182	+	205.642i	−1.02646	+	0.592628i	−0.110493	+	0.993877i	$0.535243\pi$
$348$	−18.2034	−	75.8666i	−0.0523087	−	0.218008i
$349$	402.535			1.15340			0.576698	−	0.816957i	$-0.304341\pi$
$349$	402.535			1.15340			0.576698	+	0.816957i	$0.304341\pi$
$350$		0			0
$351$			307.031i			0.874732i
$352$	10.8488	+	16.2479i	0.0308204	+	0.0461587i
$353$	−29.9594	−	51.8913i	−0.0848709	−	0.147001i	0.820465	−	0.571696i	$-0.193714\pi$
$353$	−29.9594	−	51.8913i	−0.0848709	−	0.147001i	−0.905336	+	0.424696i	$0.860381\pi$
$354$	197.199	−	23.3269i	0.557058	−	0.0658951i
$355$	322.223	+	186.035i	0.907669	+	0.524043i
$356$	−68.0205	−	71.6975i	−0.191069	−	0.201397i
$357$		0			0
$358$	−49.3065	−	21.1876i	−0.137728	−	0.0591832i
$359$	121.860	+	70.3559i	0.339443	+	0.195977i	0.660026	−	0.751243i	$-0.270545\pi$
$359$	121.860	+	70.3559i	0.339443	+	0.195977i	−0.320583	+	0.947221i	$0.603879\pi$
$360$	173.952	+	144.732i	0.483199	+	0.402033i
$361$	−105.861	−	183.356i	−0.293243	−	0.507912i
$362$	55.6857	+	74.5824i	0.153828	+	0.206029i
$363$			260.185i			0.716763i
$364$		0			0
$365$	−366.481			−1.00406
$366$	145.896	−	108.931i	0.398622	−	0.297625i
$367$	−288.714	+	166.689i	−0.786686	+	0.454193i	−0.838795	−	0.544448i	$-0.816739\pi$
$367$	−288.714	+	166.689i	−0.786686	+	0.454193i	0.0521085	+	0.998641i	$0.483406\pi$
$368$	−291.338	−	572.154i	−0.791679	−	1.55477i
$369$	55.9503	−	96.9087i	0.151627	−	0.262625i
$370$	−261.057	+	607.517i	−0.705559	+	1.64194i
$371$		0			0
$372$	207.353	+	218.562i	0.557401	+	0.587533i
$373$	128.721	−	222.951i	0.345095	−	0.597723i	−0.640276	−	0.768145i	$-0.721180\pi$
$373$	128.721	−	222.951i	0.345095	−	0.597723i	0.985371	+	0.170423i	$0.0545133\pi$
$374$	1.71861	+	14.5286i	0.00459521	+	0.0388466i
$375$	−93.2261	+	53.8241i	−0.248603	+	0.143531i
$376$	371.320	+	63.8796i	0.987553	+	0.169893i
$377$	−96.4384			−0.255805
$378$		0			0
$379$		−	122.957i		−	0.324426i	−0.986756	−	0.162213i	$-0.948137\pi$
$379$		−	122.957i		−	0.324426i	0.986756	−	0.162213i	$-0.0518631\pi$
$380$	−74.1866	−	309.188i	−0.195228	−	0.813653i
$381$	−89.5190	−	155.052i	−0.234958	−	0.406959i
$382$	17.7200	+	149.800i	0.0463875	+	0.392146i
$383$	−302.009	−	174.365i	−0.788535	−	0.455261i	0.0509116	−	0.998703i	$-0.483787\pi$
$383$	−302.009	−	174.365i	−0.788535	−	0.455261i	−0.839446	+	0.543442i	$0.817121\pi$
$384$	263.706	−	81.7503i	0.686736	−	0.212891i
$385$		0			0
$386$	−131.130	+	305.158i	−0.339715	+	0.790564i
$387$	−74.5905	−	43.0649i	−0.192740	−	0.111279i
$388$	124.902	−	421.461i	0.321913	−	1.08624i
$389$	176.689	+	306.035i	0.454215	+	0.786723i	0.998643	−	0.0520848i	$-0.0165866\pi$
$389$	176.689	+	306.035i	0.454215	+	0.786723i	−0.544428	+	0.838808i	$0.683253\pi$
$390$	−239.838	+	179.071i	−0.614969	+	0.459156i
$391$		−	480.796i		−	1.22966i
$392$		0			0
$393$	−63.6023			−0.161838
$394$	334.717	+	448.302i	0.849536	+	1.13782i
$395$	−103.638	+	59.8356i	−0.262375	+	0.151482i
$396$	10.1798	+	3.01684i	0.0257065	+	0.00761829i
$397$	91.1659	−	157.904i	0.229637	−	0.397743i	−0.728064	−	0.685510i	$-0.759579\pi$
$397$	91.1659	−	157.904i	0.229637	−	0.397743i	0.957701	+	0.287767i	$0.0929128\pi$
$398$	0.505957	+	0.217416i	0.00127125	+	0.000546270i
$399$		0			0
$400$	−14.5835	+	276.880i	−0.0364588	+	0.692201i
$401$	−172.934	+	299.530i	−0.431257	+	0.746959i	−0.996982	−	0.0776352i	$-0.975263\pi$
$401$	−172.934	+	299.530i	−0.431257	+	0.746959i	0.565725	+	0.824594i	$0.308596\pi$
$402$	119.014	−	14.0784i	0.296056	−	0.0350208i
$403$	322.503	−	186.197i	0.800255	−	0.462028i
$404$	−167.841	+	40.2717i	−0.415448	+	0.0996825i
$405$	−149.439			−0.368986
$406$		0			0
$407$			31.0248i			0.0762281i
$408$	203.751	+	35.0521i	0.499390	+	0.0859120i
$409$	152.896	+	264.823i	0.373828	+	0.647489i	0.990151	−	0.140005i	$-0.0447117\pi$
$409$	152.896	+	264.823i	0.373828	+	0.647489i	−0.616323	+	0.787494i	$0.711378\pi$
$410$	332.591	−	39.3426i	0.811197	−	0.0959575i
$411$	43.9290	+	25.3624i	0.106883	+	0.0617090i
$412$	−437.065	+	414.650i	−1.06084	+	1.00643i
$413$		0			0
$414$	−320.584	−	137.759i	−0.774358	−	0.332751i
$415$	−210.601	−	121.590i	−0.507472	−	0.292989i
$416$	−22.2081	−	340.541i	−0.0533848	−	0.818608i
$417$	−276.276	−	478.524i	−0.662532	−	1.14754i
$418$	−8.92550	−	11.9543i	−0.0213529	−	0.0285989i
$419$		−	749.709i		−	1.78928i	−0.446786	−	0.894641i	$-0.647431\pi$
$419$		−	749.709i		−	1.78928i	0.446786	−	0.894641i	$-0.352569\pi$
$420$		0			0
$421$	356.196			0.846070			0.423035	−	0.906113i	$-0.360965\pi$
$421$	356.196			0.846070			0.423035	+	0.906113i	$0.360965\pi$
$422$	482.801	−	360.476i	1.14408	−	0.854208i
$423$	177.327	−	102.380i	0.419214	−	0.242033i
$424$	−165.293	−	137.527i	−0.389841	−	0.324357i
$425$	−103.813	+	179.809i	−0.244265	+	0.423080i
$426$	97.3990	−	226.661i	0.228636	−	0.532069i
$427$		0			0
$428$	117.789	−	111.748i	0.275208	−	0.261094i
$429$	−7.02186	+	12.1622i	−0.0163680	+	0.0283502i
$430$	−30.2819	−	255.995i	−0.0704231	−	0.595336i
$431$	−163.925	+	94.6420i	−0.380336	+	0.219587i	−0.677964	−	0.735095i	$-0.737138\pi$
$431$	−163.925	+	94.6420i	−0.380336	+	0.219587i	0.297629	+	0.954682i	$0.403804\pi$
$432$	250.984	−	386.259i	0.580980	−	0.894118i
$433$	−771.353			−1.78142			−0.890708	−	0.454575i	$-0.849791\pi$
$433$	−771.353			−1.78142			−0.890708	+	0.454575i	$0.849791\pi$
$434$		0			0
$435$		−	126.901i		−	0.291726i
$436$	258.777	−	62.0909i	0.593525	−	0.142410i
$437$	245.145	+	424.603i	0.560972	+	0.971632i
$438$	28.5453	+	241.313i	0.0651718	+	0.550944i
$439$	695.621	+	401.617i	1.58456	+	0.914845i	0.994181	+	0.107718i	$0.0343543\pi$
$439$	695.621	+	401.617i	1.58456	+	0.914845i	0.590377	+	0.807127i	$0.298979\pi$
$440$	10.9927	+	29.8152i	0.0249835	+	0.0677617i
$441$		0			0
$442$	100.893	−	234.791i	0.228264	−	0.531202i
$443$	−627.440	−	362.253i	−1.41634	−	0.817726i	−0.420368	−	0.907354i	$-0.638099\pi$
$443$	−627.440	−	362.253i	−1.41634	−	0.817726i	−0.995975	+	0.0896276i	$0.971432\pi$
$444$	420.360	+	124.576i	0.946756	+	0.280577i
$445$	−80.3742	−	139.212i	−0.180616	−	0.312836i
$446$	344.611	−	257.298i	0.772670	−	0.576901i
$447$			193.186i			0.432184i
$448$		0			0
$449$	675.025			1.50340			0.751698	−	0.659507i	$-0.229235\pi$
$449$	675.025			1.50340			0.751698	+	0.659507i	$0.229235\pi$
$450$	90.1481	+	120.739i	0.200329	+	0.268310i
$451$	13.6086	−	7.85694i	0.0301743	−	0.0174212i
$452$	162.978	−	549.940i	0.360571	−	1.21668i
$453$	50.8437	−	88.0638i	0.112238	−	0.194401i
$454$	774.337	+	332.741i	1.70559	+	0.732911i
$455$		0			0
$456$	−197.810	+	72.9317i	−0.433794	+	0.159938i
$457$	−181.945	+	315.138i	−0.398129	+	0.689579i	−0.993495	−	0.113875i	$-0.963674\pi$
$457$	−181.945	+	315.138i	−0.398129	+	0.689579i	0.595366	+	0.803454i	$0.297007\pi$
$458$	90.4242	−	10.6964i	0.197433	−	0.0233546i
$459$	298.730	−	172.472i	0.650827	−	0.375755i
$460$	−243.658	−	1015.50i	−0.529692	−	2.20760i
$461$	233.360			0.506205			0.253102	−	0.967439i	$-0.418549\pi$
$461$	233.360			0.506205			0.253102	+	0.967439i	$0.418549\pi$
$462$		0			0
$463$		−	872.151i		−	1.88370i	−0.336040	−	0.941848i	$-0.609088\pi$
$463$		−	872.151i		−	1.88370i	0.336040	−	0.941848i	$-0.390912\pi$
$464$	121.324	+	78.8339i	0.261474	+	0.169901i
$465$	245.012	+	424.374i	0.526908	+	0.912632i
$466$	−300.796	+	35.5815i	−0.645484	+	0.0763552i
$467$	−664.940	−	383.903i	−1.42386	−	0.822063i	−0.427229	−	0.904143i	$-0.640510\pi$
$467$	−664.940	−	383.903i	−1.42386	−	0.822063i	−0.996626	+	0.0820802i	$0.973844\pi$
$468$	−127.646	−	134.546i	−0.272748	−	0.287492i
$469$		0			0
$470$	563.048	+	241.948i	1.19797	+	0.514783i
$471$	−537.586	−	310.376i	−1.14137	−	0.658972i
$472$	−235.530	+	283.081i	−0.499005	+	0.599748i
$473$	−6.04748	−	10.4745i	−0.0127854	−	0.0221449i
$474$	47.4718	+	63.5811i	0.100151	+	0.134137i
$475$		−	211.725i		−	0.445737i
$476$		0			0
$477$	−116.856			−0.244981
$478$	−322.097	+	240.488i	−0.673843	+	0.503113i
$479$	−682.194	+	393.865i	−1.42421	+	0.822265i	−0.996655	−	0.0817264i	$-0.973957\pi$
$479$	−682.194	+	393.865i	−1.42421	+	0.822265i	−0.427550	+	0.903992i	$0.640623\pi$
$480$	448.109	−	29.2231i	0.933561	−	0.0608814i
$481$	270.966	−	469.327i	0.563340	−	0.975733i
$482$	−196.326	+	456.878i	−0.407315	+	0.947879i
$483$		0			0
$484$	−332.091	−	350.043i	−0.686139	−	0.723230i
$485$	357.492	−	619.194i	0.737096	−	1.27669i
$486$	−49.2365	−	416.231i	−0.101310	−	0.856443i
$487$	−31.8410	+	18.3834i	−0.0653819	+	0.0377483i	−0.532335	−	0.846534i	$-0.678685\pi$
$487$	−31.8410	+	18.3834i	−0.0653819	+	0.0377483i	0.466953	+	0.884282i	$0.345352\pi$
$488$	−57.2474	+	332.768i	−0.117310	+	0.681902i
$489$	29.3742			0.0600699
$490$		0			0
$491$		−	413.002i		−	0.841145i	−0.907259	−	0.420573i	$-0.861829\pi$
$491$		−	413.002i		−	0.841145i	0.907259	−	0.420573i	$-0.138171\pi$
$492$	−51.8111	−	215.934i	−0.105307	−	0.438889i
$493$	54.1733	+	93.8310i	0.109885	+	0.190327i
$494$	30.6129	+	258.793i	0.0619695	+	0.523872i
$495$	14.9558	+	8.63471i	0.0302137	+	0.0174439i
$496$	−557.931	−	29.3867i	−1.12486	−	0.0592474i
$497$		0			0
$498$	−63.6588	+	148.143i	−0.127829	+	0.297476i
$499$	585.830	+	338.229i	1.17401	+	0.677814i	0.954621	−	0.297824i	$-0.0962607\pi$
$499$	585.830	+	338.229i	1.17401	+	0.677814i	0.219388	+	0.975638i	$0.429594\pi$
$500$	56.7237	−	191.404i	0.113447	−	0.382807i
$501$	260.543	+	451.274i	0.520047	+	0.900747i
$502$	−363.608	+	271.482i	−0.724319	+	0.540801i
$503$			88.3032i			0.175553i	0.996140	+	0.0877765i	$0.0279761\pi$
$503$			88.3032i			0.175553i	−0.996140	+	0.0877765i	$0.972024\pi$
$504$		0			0
$505$	−280.745			−0.555930
$506$	−29.3149	−	39.2627i	−0.0579345	−	0.0775943i
$507$	−103.239	+	59.6050i	−0.203627	+	0.117564i
$508$	318.338	+	94.3415i	0.626650	+	0.185712i
$509$	−130.134	+	225.399i	−0.255666	+	0.442827i	−0.965076	−	0.261969i	$-0.915628\pi$
$509$	−130.134	+	225.399i	−0.255666	+	0.442827i	0.709410	+	0.704796i	$0.248961\pi$
$510$	308.956	+	132.762i	0.605796	+	0.260318i
$511$		0			0
$512$	−250.438	+	446.570i	−0.489136	+	0.872207i
$513$	−175.877	+	304.628i	−0.342841	+	0.593818i
$514$	705.414	−	83.4443i	1.37240	−	0.162343i
$515$	−848.633	+	489.958i	−1.64783	+	0.951375i
$516$	−166.204	+	39.8789i	−0.322100	+	0.0772848i
$517$	28.7539			0.0556168
$518$		0			0
$519$			247.519i			0.476914i
$520$	94.1089	−	547.037i	0.180979	−	1.05199i
$521$	−296.145	−	512.939i	−0.568417	−	0.984528i	−0.996723	−	0.0808936i	$-0.974223\pi$
$521$	−296.145	−	512.939i	−0.568417	−	0.984528i	0.428305	−	0.903634i	$-0.359111\pi$
$522$	78.0864	−	9.23694i	0.149591	−	0.0176953i
$523$	−417.637	−	241.123i	−0.798541	−	0.461038i	0.0444199	−	0.999013i	$-0.485856\pi$
$523$	−417.637	−	241.123i	−0.798541	−	0.461038i	−0.842961	+	0.537975i	$0.819189\pi$
$524$	85.5682	−	81.1799i	0.163298	−	0.154923i
$525$		0			0
$526$	717.746	+	308.424i	1.36454	+	0.586357i
$527$	−362.326	−	209.189i	−0.687526	−	0.396943i
$528$	18.7759	−	9.56059i	0.0355604	−	0.0181072i
$529$	540.652	+	936.437i	1.02203	+	1.77020i
$530$	−209.240	−	280.245i	−0.394793	−	0.528764i
$531$			200.128i			0.376889i
$532$		0			0
$533$	−274.485			−0.514982
$534$	−85.4055	+	63.7666i	−0.159935	+	0.119413i
$535$	228.706	−	132.044i	0.427488	−	0.246810i
$536$	−142.148	+	170.847i	−0.265202	+	0.318744i
$537$	−28.9385	+	50.1230i	−0.0538892	+	0.0933389i
$538$	295.899	−	688.600i	0.549999	−	1.27993i
$539$		0			0
$540$	543.546	−	515.671i	1.00657	−	0.954946i
$541$	−190.830	+	330.527i	−0.352736	+	0.610956i	−0.986728	−	0.162383i	$-0.948082\pi$
$541$	−190.830	+	330.527i	−0.352736	+	0.610956i	0.633992	+	0.773340i	$0.281415\pi$
$542$	−36.0163	−	304.471i	−0.0664507	−	0.561755i
$543$	86.9325	−	50.1905i	0.160097	−	0.0924319i
$544$	−318.859	+	212.903i	−0.586137	+	0.391366i
$545$	432.852			0.794223
$546$		0			0
$547$			826.228i			1.51047i	0.655453	+	0.755236i	$0.272478\pi$
$547$			826.228i			1.51047i	−0.655453	+	0.755236i	$0.727522\pi$
$548$	−91.4722	+	21.9478i	−0.166920	+	0.0400508i
$549$	91.7505	+	158.917i	0.167123	+	0.289466i
$550$	2.48567	+	21.0132i	0.00451941	+	0.0382058i
$551$	−95.6838	−	55.2431i	−0.173655	−	0.100260i
$552$	−649.686	+	239.537i	−1.17697	+	0.433943i
$553$		0			0
$554$	355.146	−	826.476i	0.641058	−	1.49183i
$555$	617.576	+	356.558i	1.11275	+	0.642447i
$556$	982.464	+	291.159i	1.76702	+	0.523668i
$557$	−179.446	−	310.810i	−0.322165	−	0.558006i	0.658769	−	0.752345i	$-0.271077\pi$
$557$	−179.446	−	310.810i	−0.322165	−	0.558006i	−0.980935	+	0.194339i	$0.937744\pi$
$558$	−243.297	+	181.654i	−0.436017	+	0.325545i
$559$			211.271i			0.377945i
$560$		0			0
$561$	15.7779			0.0281245
$562$	−3.91933	−	5.24933i	−0.00697389	−	0.00934045i
$563$	−80.3362	+	46.3821i	−0.142693	+	0.0823839i	−0.569647	−	0.821890i	$-0.692920\pi$
$563$	−80.3362	+	46.3821i	−0.142693	+	0.0823839i	0.426954	+	0.904273i	$0.359587\pi$
$564$	115.458	−	389.590i	0.204712	−	0.690763i
$565$	466.471	−	807.951i	0.825612	−	1.43000i
$566$	629.000	+	270.289i	1.11131	+	0.477542i
$567$		0			0
$568$	158.266	+	429.259i	0.278637	+	0.755737i
$569$	188.943	−	327.259i	0.332062	−	0.575148i	−0.650854	−	0.759203i	$-0.725589\pi$
$569$	188.943	−	327.259i	0.332062	−	0.575148i	0.982916	+	0.184055i	$0.0589224\pi$
$570$	−340.539	+	40.2828i	−0.597437	+	0.0706716i
$571$	686.704	−	396.469i	1.20263	−	0.694341i	0.241494	−	0.970402i	$-0.422363\pi$
$571$	686.704	−	396.469i	1.20263	−	0.694341i	0.961140	+	0.276062i	$0.0890294\pi$
$572$	−6.07650	−	25.3251i	−0.0106233	−	0.0442746i
$573$	162.680			0.283910
$574$		0			0
$575$		−	695.389i		−	1.20937i
$576$	50.5992	+	273.610i	0.0878458	+	0.475017i
$577$	202.147	+	350.129i	0.350342	+	0.606810i	0.986309	−	0.164906i	$-0.0527320\pi$
$577$	202.147	+	350.129i	0.350342	+	0.606810i	−0.635967	+	0.771716i	$0.719399\pi$
$578$	288.879	−	34.1719i	0.499791	−	0.0591209i
$579$	310.211	+	179.100i	0.535770	+	0.309327i
$580$	161.972	+	170.728i	0.279262	+	0.294358i
$581$		0			0
$582$	−435.560	−	187.165i	−0.748385	−	0.321590i
$583$	−14.2113	−	8.20488i	−0.0243761	−	0.0140736i
$584$	−346.408	−	288.220i	−0.593165	−	0.493527i
$585$	−150.829	−	261.243i	−0.257827	−	0.446569i
$586$	291.660	+	390.634i	0.497714	+	0.666611i
$587$			252.412i			0.430003i	0.976614	+	0.215002i	$0.0689756\pi$
$587$			252.412i			0.430003i	−0.976614	+	0.215002i	$0.931024\pi$
$588$		0			0
$589$	426.639			0.724345
$590$	−479.949	+	358.346i	−0.813473	+	0.607366i
$591$	522.536	−	301.686i	0.884156	−	0.510468i
$592$	−724.542	+	368.933i	−1.22389	+	0.623198i
$593$	−221.333	+	383.360i	−0.373243	+	0.646476i	−0.990062	−	0.140629i	$-0.955088\pi$
$593$	−221.333	+	383.360i	−0.373243	+	0.646476i	0.616819	+	0.787105i	$0.288421\pi$
$594$	13.8790	−	32.2984i	0.0233653	−	0.0543744i
$595$		0			0
$596$	−246.576	−	259.906i	−0.413719	−	0.436083i
$597$	0.296952	−	0.514335i	0.000497406	−	0.000861533i
$598$	100.545	+	849.977i	0.168135	+	1.42137i
$599$	−201.082	+	116.095i	−0.335696	+	0.193814i	−0.658367	−	0.752697i	$-0.728752\pi$
$599$	−201.082	+	116.095i	−0.335696	+	0.193814i	0.322671	+	0.946511i	$0.395419\pi$
$600$	294.691	+	50.6969i	0.491152	+	0.0844948i
$601$	−127.875			−0.212770			−0.106385	−	0.994325i	$-0.533928\pi$
$601$	−127.875			−0.212770			−0.106385	+	0.994325i	$0.533928\pi$
$602$		0			0
$603$			120.783i			0.200303i
$604$	43.9985	+	183.373i	0.0728452	+	0.303598i
$605$	−392.405	−	679.665i	−0.648603	−	1.12341i
$606$	21.8673	+	184.859i	0.0360846	+	0.305049i
$607$	166.162	+	95.9334i	0.273742	+	0.158045i	0.630587	−	0.776119i	$-0.282814\pi$
$607$	166.162	+	95.9334i	0.273742	+	0.158045i	−0.356845	+	0.934164i	$0.616148\pi$
$608$	173.039	−	350.598i	0.284603	−	0.576641i
$609$		0			0
$610$	−216.828	+	504.590i	−0.355456	+	0.827197i
$611$	−434.974	−	251.132i	−0.711905	−	0.411018i
$612$	−59.2045	+	199.775i	−0.0967393	+	0.326429i
$613$	−163.435	−	283.077i	−0.266615	−	0.461790i	0.701371	−	0.712797i	$-0.252572\pi$
$613$	−163.435	−	283.077i	−0.266615	−	0.461790i	−0.967985	+	0.251006i	$0.919238\pi$
$614$	93.6744	−	69.9404i	0.152564	−	0.113909i
$615$		−	361.189i		−	0.587299i
$616$		0			0
$617$	−557.014			−0.902778			−0.451389	−	0.892327i	$-0.649071\pi$
$617$	−557.014			−0.902778			−0.451389	+	0.892327i	$0.649071\pi$
$618$	388.719	+	520.628i	0.628994	+	0.842441i
$619$	−405.320	+	234.011i	−0.654798	+	0.378048i	−0.790292	−	0.612731i	$-0.790071\pi$
$619$	−405.320	+	234.011i	−0.654798	+	0.378048i	0.135494	+	0.990778i	$0.456738\pi$
$620$	−871.287	−	258.211i	−1.40530	−	0.416470i
$621$	−577.650	+	1000.52i	−0.930194	+	1.61114i
$622$	−228.564	−	98.2166i	−0.367466	−	0.157905i
$623$		0			0
$624$	−367.533	−	19.3583i	−0.588994	−	0.0310228i
$625$	378.965	−	656.387i	0.606344	−	1.05022i
$626$	−956.234	+	113.114i	−1.52753	+	0.180694i
$627$	−13.9338	+	8.04471i	−0.0222230	+	0.0128305i
$628$	1119.40	−	268.590i	1.78249	−	0.427690i
$629$	−608.851			−0.967967
$630$		0			0
$631$			557.865i			0.884096i	0.896991	+	0.442048i	$0.145748\pi$
$631$			557.865i			0.884096i	−0.896991	+	0.442048i	$0.854252\pi$
$632$	−145.020	−	24.9483i	−0.229462	−	0.0394752i
$633$	−324.903	−	562.749i	−0.513275	−	0.889018i
$634$	713.321	−	84.3796i	1.12511	−	0.133091i
$635$	467.690	+	270.021i	0.736520	+	0.425230i
$636$	−168.233	+	159.605i	−0.264517	+	0.250951i
$637$		0			0
$638$	10.1449	+	4.35939i	0.0159011	+	0.00683290i
$639$	215.323	+	124.317i	0.336969	+	0.194549i
$640$	−565.571	+	611.268i	−0.883704	+	0.955106i
$641$	−361.777	−	626.616i	−0.564395	−	0.977560i	−0.997106	−	0.0760277i	$-0.975776\pi$
$641$	−361.777	−	626.616i	−0.564395	−	0.977560i	0.432711	−	0.901533i	$-0.357557\pi$
$642$	−104.760	−	140.309i	−0.163177	−	0.218550i
$643$		−	145.293i		−	0.225961i	−0.993597	−	0.112980i	$-0.963960\pi$
$643$		−	145.293i		−	0.225961i	0.993597	−	0.112980i	$-0.0360397\pi$
$644$		0			0
$645$	−278.006			−0.431018
$646$	234.599	−	175.160i	0.363157	−	0.271145i
$647$	294.712	−	170.152i	0.455506	−	0.262987i	−0.254647	−	0.967034i	$-0.581959\pi$
$647$	294.712	−	170.152i	0.455506	−	0.262987i	0.710153	+	0.704048i	$0.248626\pi$
$648$	−141.254	−	117.527i	−0.217985	−	0.181369i
$649$	−14.0517	+	24.3383i	−0.0216514	+	0.0375012i
$650$	145.924	−	339.586i	0.224498	−	0.522439i
$651$		0			0
$652$	−39.5190	+	37.4923i	−0.0606119	+	0.0575035i
$653$	−406.929	+	704.822i	−0.623169	+	1.07936i	0.365723	+	0.930724i	$0.380822\pi$
$653$	−406.929	+	704.822i	−0.623169	+	1.07936i	−0.988892	+	0.148637i	$0.952512\pi$
$654$	−33.7149	−	285.016i	−0.0515518	−	0.435804i
$655$	166.145	−	95.9236i	0.253656	−	0.146448i
$656$	345.315	+	224.379i	0.526395	+	0.342041i
$657$	−244.898			−0.372753
$658$		0			0
$659$			939.024i			1.42492i	0.701711	+	0.712462i	$0.252420\pi$
$659$			939.024i			1.42492i	−0.701711	+	0.712462i	$0.747580\pi$
$660$	33.3247	−	7.99592i	0.0504919	−	0.0121150i
$661$	−104.148	−	180.389i	−0.157561	−	0.272904i	0.776428	−	0.630206i	$-0.217030\pi$
$661$	−104.148	−	180.389i	−0.157561	−	0.272904i	−0.933989	+	0.357303i	$0.883696\pi$
$662$	29.7664	+	251.636i	0.0449643	+	0.380115i
$663$	−238.679	−	137.802i	−0.359999	−	0.207845i
$664$	−103.441	−	280.558i	−0.155784	−	0.422528i
$665$		0			0
$666$	−174.450	+	405.969i	−0.261936	+	0.609563i
$667$	−314.263	−	181.440i	−0.471159	−	0.272024i
$668$	−926.517	−	274.579i	−1.38700	−	0.411047i
$669$	−231.907	−	401.675i	−0.346648	−	0.600411i
$670$	−289.661	+	216.271i	−0.432331	+	0.322792i
$671$			25.7685i			0.0384032i
$672$		0			0
$673$	634.671			0.943048			0.471524	−	0.881853i	$-0.343704\pi$
$673$	634.671			0.943048			0.471524	+	0.881853i	$0.343704\pi$
$674$	−659.810	−	883.714i	−0.978947	−	1.31115i
$675$	432.062	−	249.451i	0.640091	−	0.369557i
$676$	62.8159	−	211.961i	0.0929230	−	0.313552i
$677$	145.058	−	251.248i	0.214266	−	0.371119i	−0.738780	−	0.673947i	$-0.764598\pi$
$677$	145.058	−	251.248i	0.214266	−	0.371119i	0.953045	+	0.302828i	$0.0979309\pi$
$678$	−568.338	−	244.221i	−0.838256	−	0.360208i
$679$		0			0
$680$	−585.112	+	215.728i	−0.860458	+	0.317247i
$681$	454.466	−	787.159i	0.667351	−	1.15589i
$682$	−42.3428	+	5.00879i	−0.0620862	+	0.00734426i
$683$	617.155	−	356.315i	0.903595	−	0.521691i	0.0252299	−	0.999682i	$-0.491968\pi$
$683$	617.155	−	356.315i	0.903595	−	0.521691i	0.878365	+	0.477991i	$0.158635\pi$
$684$	−49.5747	−	206.613i	−0.0724777	−	0.302066i
$685$	−153.004			−0.223364
$686$		0			0
$687$		−	98.1994i		−	0.142939i
$688$	172.704	−	265.789i	0.251024	−	0.386321i
$689$	143.320	+	248.238i	0.208012	+	0.360288i
$690$	−1118.46	+	132.305i	−1.62096	+	0.191746i
$691$	−350.022	−	202.085i	−0.506545	−	0.292454i	0.224868	−	0.974389i	$-0.427805\pi$
$691$	−350.022	−	202.085i	−0.506545	−	0.292454i	−0.731412	+	0.681936i	$0.761138\pi$
$692$	−315.925	−	333.003i	−0.456538	−	0.481218i
$693$		0			0
$694$	−755.746	−	324.753i	−1.08897	−	0.467944i
$695$	1443.40	+	833.347i	2.07683	+	1.19906i
$696$	99.8016	−	119.950i	0.143393	−	0.172342i
$697$	154.190	+	267.064i	0.221219	+	0.383162i
$698$	481.651	+	645.097i	0.690045	+	0.924208i
$699$			326.660i			0.467324i
$700$		0			0
$701$	−111.341			−0.158831			−0.0794156	−	0.996842i	$-0.525305\pi$
$701$	−111.341			−0.158831			−0.0794156	+	0.996842i	$0.525305\pi$
$702$	−492.043	+	367.376i	−0.700916	+	0.523327i
$703$	537.692	−	310.437i	0.764854	−	0.441589i
$704$	−13.0576	+	36.8274i	−0.0185477	+	0.0523116i
$705$	330.459	−	572.371i	0.468736	−	0.811874i
$706$	47.3124	−	110.103i	0.0670148	−	0.155953i
$707$		0			0
$708$	273.340	+	288.116i	0.386074	+	0.406944i
$709$	−386.373	+	669.217i	−0.544955	+	0.943889i	0.453655	+	0.891177i	$0.350120\pi$
$709$	−386.373	+	669.217i	−0.544955	+	0.943889i	−0.998610	+	0.0527117i	$0.983214\pi$
$710$	87.4160	+	738.989i	0.123121	+	1.04083i
$711$	−69.2556	+	39.9847i	−0.0974059	+	0.0562373i
$712$	33.5119	−	194.798i	0.0470672	−	0.273593i
$713$	1401.25			1.96529
$714$		0			0
$715$		−	42.3609i		−	0.0592460i
$716$	−25.0425	−	104.370i	−0.0349756	−	0.145768i
$717$	216.756	+	375.433i	0.302310	+	0.523616i
$718$	33.0595	+	279.475i	0.0460438	+	0.389241i
$719$	803.582	+	463.948i	1.11764	+	0.645269i	0.940797	−	0.338971i	$-0.110079\pi$
$719$	803.582	+	463.948i	1.11764	+	0.645269i	0.176841	+	0.984239i	$0.443412\pi$
$720$	−23.8046	+	451.951i	−0.0330620	+	0.627710i
$721$		0			0
$722$	167.177	−	389.045i	0.231547	−	0.538843i
$723$	464.443	+	268.146i	0.642383	+	0.370880i
$724$	−52.8943	+	178.482i	−0.0730585	+	0.246522i
$725$	78.3525	+	135.711i	0.108072	+	0.187187i
$726$	−416.969	+	311.323i	−0.574337	+	0.428819i
$727$			811.924i			1.11681i	0.829567	+	0.558407i	$0.188587\pi$
$727$			811.924i			1.11681i	−0.829567	+	0.558407i	$0.811413\pi$
$728$		0			0
$729$	−658.744			−0.903627
$730$	−438.510	−	587.317i	−0.600699	−	0.804544i
$731$	205.559	−	118.680i	0.281202	−	0.162352i
$732$	349.141	+	103.470i	0.476969	+	0.141353i
$733$	−495.396	+	858.052i	−0.675848	+	1.17060i	0.300373	+	0.953822i	$0.402889\pi$
$733$	−495.396	+	858.052i	−0.675848	+	1.17060i	−0.976220	+	0.216781i	$0.930444\pi$
$734$	−612.592	−	263.238i	−0.834594	−	0.358635i
$735$		0			0
$736$	568.327	−	1151.50i	0.772184	−	1.56454i
$737$	−8.48057	+	14.6888i	−0.0115069	+	0.0199305i
$738$	222.252	−	26.2904i	0.301154	−	0.0356239i
$739$	−989.673	+	571.388i	−1.33921	+	0.773191i	−0.986690	−	0.162615i	$-0.948007\pi$
$739$	−989.673	+	571.388i	−1.33921	+	0.773191i	−0.352516	+	0.935806i	$0.614674\pi$
$740$	−1285.96	+	308.554i	−1.73779	+	0.416965i
$741$	281.045			0.379278
$742$		0			0
$743$			143.488i			0.193120i	0.995327	+	0.0965601i	$0.0307840\pi$
$743$			143.488i			0.193120i	−0.995327	+	0.0965601i	$0.969216\pi$
$744$	−102.157	+	593.821i	−0.137308	+	0.798146i
$745$	−291.359	−	504.649i	−0.391086	−	0.677381i
$746$	511.317	−	60.4844i	0.685412	−	0.0810783i
$747$	−140.733	−	81.2520i	−0.188397	−	0.108771i
$748$	−21.2270	+	20.1383i	−0.0283783	+	0.0269229i
$749$		0			0
$750$	−197.807	−	84.9999i	−0.263742	−	0.113333i
$751$	1202.40	+	694.203i	1.60106	+	0.924372i	0.991276	+	0.131804i	$0.0420769\pi$
$751$	1202.40	+	694.203i	1.60106	+	0.924372i	0.609783	+	0.792568i	$0.291256\pi$
$752$	341.928	+	671.507i	0.454691	+	0.892961i
$753$	244.692	+	423.818i	0.324956	+	0.562840i
$754$	−115.393	−	154.551i	−0.153041	−	0.204975i
$755$			306.725i			0.406258i
$756$		0			0
$757$	206.398			0.272652			0.136326	−	0.990664i	$-0.456470\pi$
$757$	206.398			0.272652			0.136326	+	0.990664i	$0.456470\pi$
$758$	197.050	−	147.124i	0.259960	−	0.194095i
$759$	−45.7642	+	26.4220i	−0.0602954	+	0.0348116i
$760$	406.733	−	488.848i	0.535175	−	0.643221i
$761$	−284.867	+	493.405i	−0.374333	+	0.648363i	−0.990227	−	0.139466i	$-0.955462\pi$
$761$	−284.867	+	493.405i	−0.374333	+	0.648363i	0.615894	+	0.787829i	$0.288795\pi$
$762$	141.370	−	328.988i	0.185525	−	0.431743i
$763$		0			0
$764$	−218.864	+	207.640i	−0.286472	+	0.271780i
$765$	−169.453	+	293.501i	−0.221507	+	0.383662i
$766$	−81.9322	−	692.630i	−0.106961	−	0.904217i
$767$	425.134	−	245.451i	0.554282	−	0.320015i
$768$	446.548	+	324.794i	0.581443	+	0.422909i
$769$	945.548			1.22958			0.614791	−	0.788690i	$-0.289240\pi$
$769$	945.548			1.22958			0.614791	+	0.788690i	$0.289240\pi$
$770$		0			0
$771$		−	766.069i		−	0.993604i
$772$	−645.944	+	154.988i	−0.836715	+	0.200761i
$773$	66.4717	+	115.132i	0.0859918	+	0.148942i	0.905813	−	0.423677i	$-0.139261\pi$
$773$	66.4717	+	115.132i	0.0859918	+	0.148942i	−0.819822	+	0.572619i	$0.805927\pi$
$774$	−20.2357	−	171.067i	−0.0261443	−	0.221016i
$775$	−524.043	−	302.556i	−0.676184	−	0.390395i
$776$	824.878	−	304.129i	1.06299	−	0.391919i
$777$		0			0
$778$	−279.031	+	649.345i	−0.358652	+	0.834633i
$779$	−272.338	−	157.234i	−0.349599	−	0.201841i
$780$	−573.953	−	170.095i	−0.735838	−	0.218070i
$781$	17.4575	+	30.2372i	0.0223527	+	0.0387160i
$782$	770.517	−	575.293i	0.985315	−	0.735669i
$783$		−	260.346i		−	0.332497i
$784$		0			0
$785$	1872.41			2.38523
$786$	−76.1030	−	101.928i	−0.0968231	−	0.129680i
$787$	202.605	−	116.974i	0.257440	−	0.148633i	−0.365726	−	0.930722i	$-0.619179\pi$
$787$	202.605	−	116.974i	0.257440	−	0.148633i	0.623166	+	0.782089i	$0.285846\pi$
$788$	−317.939	+	1072.83i	−0.403475	+	1.36145i
$789$	421.253	−	729.631i	0.533907	−	0.924755i
$790$	−219.899	−	94.4933i	−0.278354	−	0.119612i
$791$		0			0
$792$	7.34582	+	19.9238i	0.00927502	+	0.0251563i
$793$	225.059	−	389.813i	0.283807	−	0.491567i
$794$	362.139	−	42.8379i	0.456094	−	0.0539520i
$795$	−326.651	+	188.592i	−0.410881	+	0.237222i
$796$	0.256973	+	1.07099i	0.000322830	+	0.00134546i
$797$	−1208.00			−1.51569			−0.757843	−	0.652437i	$-0.773747\pi$
$797$	−1208.00			−1.51569			−0.757843	+	0.652437i	$0.773747\pi$
$798$		0			0
$799$			564.285i			0.706239i
$800$	−461.175	+	307.928i	−0.576468	+	0.384910i
$801$	−53.7095	−	93.0277i	−0.0670531	−	0.116139i
$802$	−686.947	+	81.2598i	−0.856542	+	0.101321i
$803$	−29.7830	−	17.1952i	−0.0370896	−	0.0214137i
$804$	164.968	+	173.885i	0.205184	+	0.216275i
$805$		0			0
$806$	684.286	+	294.046i	0.848990	+	0.364821i
$807$	−700.002	−	404.147i	−0.867413	−	0.500801i
$808$	−265.368	−	220.792i	−0.328426	−	0.273258i
$809$	−34.7428	−	60.1763i	−0.0429453	−	0.0743835i	0.843754	−	0.536730i	$-0.180341\pi$
$809$	−34.7428	−	60.1763i	−0.0429453	−	0.0743835i	−0.886699	+	0.462347i	$0.847007\pi$
$810$	−178.811	−	239.490i	−0.220754	−	0.295666i
$811$			1095.24i			1.35048i	0.737599	+	0.675239i	$0.235959\pi$
$811$			1095.24i			1.35048i	−0.737599	+	0.675239i	$0.764041\pi$
$812$		0			0
$813$	−330.651			−0.406705
$814$	−49.7200	+	37.1226i	−0.0610810	+	0.0456051i
$815$	−76.7325	+	44.3015i	−0.0941503	+	0.0543577i
$816$	187.623	+	368.470i	0.229930	+	0.451556i
$817$	−121.023	+	209.618i	−0.148131	+	0.256570i
$818$	−241.455	+	561.901i	−0.295178	+	0.686920i
$819$		0			0
$820$	461.009	+	485.930i	0.562206	+	0.592598i
$821$	378.010	−	654.733i	0.460427	−	0.797483i	−0.538555	−	0.842590i	$-0.681030\pi$
$821$	378.010	−	654.733i	0.460427	−	0.797483i	0.998982	+	0.0451075i	$0.0143630\pi$
$822$	11.9175	+	100.747i	0.0144982	+	0.122563i
$823$	−277.186	+	160.033i	−0.336799	+	0.194451i	−0.658856	−	0.752269i	$-0.728959\pi$
$823$	−277.186	+	160.033i	−0.336799	+	0.194451i	0.322057	+	0.946720i	$0.395626\pi$
$824$	−1187.48	−	204.287i	−1.44112	−	0.247921i
$825$	22.8200			0.0276606
$826$		0			0
$827$		−	104.960i		−	0.126917i	−0.997984	−	0.0634585i	$-0.979787\pi$
$827$		−	104.960i		−	0.126917i	0.997984	−	0.0634585i	$-0.0202131\pi$
$828$	−162.823	−	678.599i	−0.196646	−	0.819564i
$829$	408.833	+	708.120i	0.493164	+	0.854186i	0.999969	−	0.00787505i	$-0.00250673\pi$
$829$	408.833	+	708.120i	0.493164	+	0.854186i	−0.506804	+	0.862061i	$0.669173\pi$
$830$	−57.1340	−	482.994i	−0.0688362	−	0.581921i
$831$	−840.161	−	485.067i	−1.01102	−	0.583715i
$832$	519.173	−	443.063i	0.624006	−	0.532527i
$833$		0			0
$834$	436.300	−	1015.33i	0.523141	−	1.21742i
$835$	−1361.20	−	785.891i	−1.63018	−	0.941187i
$836$	8.47809	−	28.6078i	0.0101413	−	0.0342198i
$837$	502.659	+	870.631i	0.600548	+	1.04018i
$838$	1201.47	−	897.060i	1.43374	−	1.07048i
$839$		−	1029.02i		−	1.22648i	−0.789896	−	0.613240i	$-0.789866\pi$
$839$		−	1029.02i		−	1.22648i	0.789896	−	0.613240i	$-0.210134\pi$
$840$		0			0
$841$	−759.225			−0.902765
$842$	426.204	+	570.834i	0.506180	+	0.677950i
$843$	−6.11857	+	3.53256i	−0.00725809	+	0.00419046i
$844$	1155.39	+	342.406i	1.36894	+	0.405694i
$845$	179.790	−	311.405i	0.212769	−	0.368527i
$846$	376.253	+	161.680i	0.444744	+	0.191111i
$847$		0			0
$848$	22.6197	−	429.453i	0.0266741	−	0.506430i
$849$	369.167	−	639.416i	0.434825	−	0.753140i
$850$	−412.376	+	48.7805i	−0.485148	+	0.0573888i
$851$	1765.99	−	1019.60i	2.07520	−	1.19812i
$852$	479.787	−	115.120i	0.563130	−	0.135117i
$853$	−583.808			−0.684417			−0.342209	−	0.939624i	$-0.611175\pi$
$853$	−583.808			−0.684417			−0.342209	+	0.939624i	$0.611175\pi$
$854$		0			0
$855$		−	345.598i		−	0.404209i
$856$	320.026	+	55.0553i	0.373862	+	0.0643169i
$857$	−549.072	−	951.020i	−0.640691	−	1.10971i	−0.985279	−	0.170955i	$-0.945315\pi$
$857$	−549.072	−	951.020i	−0.640691	−	1.10971i	0.344588	−	0.938754i	$-0.388019\pi$
$858$	−27.8930	+	3.29950i	−0.0325093	+	0.00384557i
$859$	259.092	+	149.587i	0.301620	+	0.174141i	0.643171	−	0.765723i	$-0.277619\pi$
$859$	259.092	+	149.587i	0.301620	+	0.174141i	−0.341550	+	0.939864i	$0.610952\pi$
$860$	374.020	−	354.838i	0.434907	−	0.412603i
$861$		0			0
$862$	−347.815	−	149.460i	−0.403498	−	0.173388i
$863$	−815.368	−	470.753i	−0.944807	−	0.545485i	−0.0533431	−	0.998576i	$-0.516988\pi$
$863$	−815.368	−	470.753i	−0.944807	−	0.545485i	−0.891464	+	0.453092i	$0.850321\pi$
$864$	919.326	−	59.9530i	1.06403	−	0.0693901i
$865$	−373.302	−	646.578i	−0.431563	−	0.747489i
$866$	−922.958	−	1236.16i	−1.06577	−	1.42744i
$867$		−	313.719i		−	0.361844i
$868$		0			0
$869$	−11.2299			−0.0129228
$870$	203.370	−	151.843i	0.233758	−	0.174532i
$871$	256.579	−	148.136i	0.294580	−	0.170076i
$872$	409.144	+	340.417i	0.469202	+	0.390387i
$873$	238.891	−	413.772i	0.273644	−	0.473966i
$874$	−387.137	+	900.922i	−0.442948	+	1.03080i
$875$		0			0
$876$	−352.570	+	334.488i	−0.402477	+	0.381836i
$877$	−491.695	+	851.640i	−0.560655	+	0.971084i	0.436784	+	0.899566i	$0.356117\pi$
$877$	−491.695	+	851.640i	−0.560655	+	0.971084i	−0.997439	+	0.0715173i	$0.977216\pi$
$878$	188.715	+	1595.35i	0.214938	+	1.81702i
$879$	455.319	−	262.879i	0.517996	−	0.299065i
$880$	−34.6281	+	53.2919i	−0.0393501	+	0.0605590i
$881$	155.250			0.176220			0.0881102	−	0.996111i	$-0.471917\pi$
$881$	155.250			0.176220			0.0881102	+	0.996111i	$0.471917\pi$
$882$		0			0
$883$		−	612.809i		−	0.694008i	−0.937864	−	0.347004i	$-0.887199\pi$
$883$		−	612.809i		−	0.694008i	0.937864	−	0.347004i	$-0.112801\pi$
$884$	496.996	−	119.249i	0.562212	−	0.134897i
$885$	322.984	+	559.424i	0.364953	+	0.632117i
$886$	−170.219	−	1438.98i	−0.192120	−	1.62413i
$887$	−123.796	−	71.4737i	−0.139567	−	0.0805791i	0.428591	−	0.903499i	$-0.359010\pi$
$887$	−123.796	−	71.4737i	−0.139567	−	0.0805791i	−0.568158	+	0.822920i	$0.692344\pi$
$888$	303.335	+	822.724i	0.341593	+	0.926490i
$889$		0			0
$890$	126.928	−	295.380i	0.142616	−	0.331888i
$891$	−12.1446	−	7.01167i	−0.0136303	−	0.00786944i
$892$	824.684	+	244.400i	0.924534	+	0.273991i
$893$	−287.714	−	498.335i	−0.322188	−	0.558045i
$894$	−309.597	+	231.156i	−0.346306	+	0.258563i
$895$		−	174.578i		−	0.195059i
$896$		0			0
$897$	923.063			1.02906
$898$	807.697	+	1081.79i	0.899440	+	1.20466i
$899$	−273.465	+	157.885i	−0.304188	+	0.175623i
$900$	−85.6292	+	288.940i	−0.0951435	+	0.321045i
$901$	161.018	−	278.891i	0.178710	−	0.309535i
$902$	28.8747	+	12.4078i	0.0320119	+	0.0137559i
$903$		0			0
$904$	1076.34	−	396.841i	1.19064	−	0.438984i
$905$	−151.392	+	262.219i	−0.167284	+	0.289745i
$906$	201.966	−	23.8909i	0.222921	−	0.0263696i
$907$	−1169.79	+	675.381i	−1.28974	+	0.744632i	−0.978608	−	0.205735i	$-0.934042\pi$
$907$	−1169.79	+	675.381i	−1.28974	+	0.744632i	−0.311132	+	0.950367i	$0.600708\pi$
$908$	393.281	+	1639.08i	0.433129	+	1.80516i
$909$	−187.606			−0.206387
$910$		0			0
$911$		−	215.218i		−	0.236244i	−0.992999	−	0.118122i	$-0.962313\pi$
$911$		−	215.218i		−	0.236244i	0.992999	−	0.118122i	$-0.0376874\pi$
$912$	−353.568	−	229.741i	−0.387684	−	0.251910i
$913$	−11.4100	−	19.7627i	−0.0124973	−	0.0216459i
$914$	−722.740	+	85.4939i	−0.790744	+	0.0935382i
$915$	512.945	+	296.149i	0.560596	+	0.323660i
$916$	125.338	+	132.114i	0.136832	+	0.144229i
$917$		0			0
$918$	633.844	+	272.370i	0.690462	+	0.296699i
$919$	−7.65593	−	4.42016i	−0.00833072	−	0.00480975i	0.495829	−	0.868420i	$-0.334864\pi$
$919$	−7.65593	−	4.42016i	−0.00833072	−	0.00480975i	−0.504160	+	0.863611i	$0.668198\pi$
$920$	1335.87	−	1605.57i	1.45204	−	1.74518i
$921$	−63.0385	−	109.186i	−0.0684457	−	0.118551i
$922$	279.226	+	373.980i	0.302848	+	0.405618i
$923$		−	609.884i		−	0.660763i
$924$		0			0
$925$	−880.599			−0.951999
$926$	1397.70	−	1043.57i	1.50939	−	1.12696i
$927$	−567.093	+	327.411i	−0.611751	+	0.353195i
$928$	18.8313	+	288.760i	0.0202923	+	0.311164i
$929$	712.274	−	1233.69i	0.766710	−	1.32798i	−0.172627	−	0.984987i	$-0.555226\pi$
$929$	712.274	−	1233.69i	0.766710	−	1.32798i	0.939338	−	0.342994i	$-0.111441\pi$
$930$	−386.927	+	900.435i	−0.416051	+	0.968210i
$931$		0			0
$932$	−416.938	−	439.476i	−0.447358	−	0.471541i
$933$	−134.147	+	232.349i	−0.143780	+	0.249034i
$934$	−180.392	−	1524.98i	−0.193139	−	1.63274i
$935$	−41.2156	+	23.7958i	−0.0440808	+	0.0254501i
$936$	62.8877	−	365.554i	0.0671877	−	0.390549i
$937$	−616.709			−0.658174			−0.329087	−	0.944300i	$-0.606741\pi$
$937$	−616.709			−0.658174			−0.329087	+	0.944300i	$0.606741\pi$
$938$		0			0
$939$			1038.46i			1.10592i
$940$	285.969	+	1191.83i	0.304222	+	1.26791i
$941$	467.668	+	810.025i	0.496991	+	0.860813i	0.999994	−	0.00347133i	$-0.00110496\pi$
$941$	467.668	+	810.025i	0.496991	+	0.860813i	−0.503003	+	0.864285i	$0.667772\pi$
$942$	−145.842	−	1232.91i	−0.154822	−	1.30882i
$943$	−894.464	−	516.419i	−0.948531	−	0.547634i
$944$	−735.484	−	38.7386i	−0.779114	−	0.0410366i
$945$		0			0
$946$	9.55028	−	22.2248i	0.0100954	−	0.0234935i
$947$	988.080	+	570.468i	1.04338	+	0.602395i	0.920788	−	0.390062i	$-0.127547\pi$
$947$	988.080	+	570.468i	1.04338	+	0.602395i	0.122590	+	0.992457i	$0.460880\pi$
$948$	−45.0922	+	152.155i	−0.0475656	+	0.160501i
$949$	300.361	+	520.240i	0.316502	+	0.548198i
$950$	339.308	−	253.339i	0.357166	−	0.266672i
$951$		−	774.656i		−	0.814570i
$952$		0			0
$953$	−1265.64			−1.32806			−0.664030	−	0.747706i	$-0.731155\pi$
$953$	−1265.64			−1.32806			−0.664030	+	0.747706i	$0.731155\pi$
$954$	−139.823	−	187.272i	−0.146565	−	0.196302i
$955$	−424.960	+	245.351i	−0.444985	+	0.256912i
$956$	−770.806	−	228.433i	−0.806282	−	0.238947i
$957$	5.95416	−	10.3129i	0.00622169	−	0.0107763i
$958$	−1447.48	−	621.998i	−1.51094	−	0.649267i
$959$		0			0
$960$	583.015	+	683.167i	0.607307	+	0.711633i
$961$	129.169	−	223.728i	0.134411	−	0.232807i
$962$	1076.36	−	127.324i	1.11888	−	0.132354i
$963$	152.831	−	88.2373i	0.158703	−	0.0916275i
$964$	−967.098	+	232.046i	−1.00321	+	0.240711i
$965$	−1080.46			−1.11965
$966$		0			0
$967$		−	1527.55i		−	1.57968i	−0.613313	−	0.789840i	$-0.710164\pi$
$967$		−	1527.55i		−	1.57968i	0.613313	−	0.789840i	$-0.289836\pi$
$968$	163.612	−	951.047i	0.169021	−	0.982487i
$969$	−157.874	−	273.447i	−0.162925	−	0.282195i
$970$	1420.07	−	167.981i	1.46399	−	0.173177i
$971$	−156.301	−	90.2405i	−0.160969	−	0.0929356i	0.417351	−	0.908745i	$-0.362958\pi$
$971$	−156.301	−	90.2405i	−0.160969	−	0.0929356i	−0.578321	+	0.815810i	$0.696292\pi$
$972$	608.133	−	576.945i	0.625651	−	0.593565i
$973$		0			0
$974$	−67.5601	−	29.0314i	−0.0693636	−	0.0298063i
$975$	−345.209	−	199.306i	−0.354060	−	0.204417i
$976$	−601.788	+	306.428i	−0.616586	+	0.313963i
$977$	446.888	+	774.033i	0.457408	+	0.792255i	0.998823	−	0.0485011i	$-0.0154444\pi$
$977$	446.888	+	774.033i	0.457408	+	0.792255i	−0.541415	+	0.840756i	$0.682111\pi$
$978$	35.1475	+	47.0747i	0.0359382	+	0.0481336i
$979$		−	15.0846i		−	0.0154081i
$980$		0			0
$981$	289.250			0.294852
$982$	661.872	−	494.175i	0.674004	−	0.503234i
$983$	−561.180	+	323.997i	−0.570885	+	0.329600i	−0.757503	−	0.652832i	$-0.773581\pi$
$983$	−561.180	+	323.997i	−0.570885	+	0.329600i	0.186618	+	0.982433i	$0.440247\pi$
$984$	284.058	−	341.406i	0.288677	−	0.346957i
$985$	−909.994	+	1576.16i	−0.923852	+	1.60016i
$986$	−85.5514	+	199.090i	−0.0867662	+	0.201917i
$987$		0			0
$988$	−378.108	+	358.717i	−0.382700	+	0.363074i
$989$	−397.487	+	688.468i	−0.401908	+	0.696126i
$990$	4.05736	+	34.2997i	0.00409834	+	0.0346462i
$991$	−1167.47	+	674.041i	−1.17808	+	0.680162i	−0.955569	−	0.294769i	$-0.904757\pi$
$991$	−1167.47	+	674.041i	−1.17808	+	0.680162i	−0.222507	+	0.974931i	$0.571424\pi$
$992$	−620.494	−	929.295i	−0.625498	−	0.936789i
$993$	273.273			0.275199
$994$		0			0
$995$			1.79142i			0.00180042i
$996$	−313.583	+	75.2411i	−0.314842	+	0.0755432i
$997$	256.786	+	444.766i	0.257559	+	0.446105i	0.965587	−	0.260079i	$-0.0837486\pi$
$997$	256.786	+	444.766i	0.257559	+	0.446105i	−0.708029	+	0.706184i	$0.750415\pi$
$998$	158.930	+	1343.55i	0.159249	+	1.34624i
$999$	1267.00	+	731.502i	1.26827	+	0.732234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.g.i.79.5		12
4.3	odd	2	inner	196.3.g.i.79.1		12
7.2	even	3		196.3.c.h.99.3		6
7.3	odd	6		28.3.g.a.11.1	✓	12
7.4	even	3	inner	196.3.g.i.67.1		12
7.5	odd	6		196.3.c.i.99.3		6
7.6	odd	2		28.3.g.a.23.5	yes	12
21.17	even	6		252.3.y.c.235.6		12
21.20	even	2		252.3.y.c.163.2		12
28.3	even	6		28.3.g.a.11.5	yes	12
28.11	odd	6	inner	196.3.g.i.67.5		12
28.19	even	6		196.3.c.i.99.4		6
28.23	odd	6		196.3.c.h.99.4		6
28.27	even	2		28.3.g.a.23.1	yes	12
56.3	even	6		448.3.r.h.319.5		12
56.13	odd	2		448.3.r.h.191.5		12
56.27	even	2		448.3.r.h.191.2		12
56.45	odd	6		448.3.r.h.319.2		12
84.59	odd	6		252.3.y.c.235.2		12
84.83	odd	2		252.3.y.c.163.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.g.a.11.1	✓	12	7.3	odd	6
28.3.g.a.11.5	yes	12	28.3	even	6
28.3.g.a.23.1	yes	12	28.27	even	2
28.3.g.a.23.5	yes	12	7.6	odd	2
196.3.c.h.99.3		6	7.2	even	3
196.3.c.h.99.4		6	28.23	odd	6
196.3.c.i.99.3		6	7.5	odd	6
196.3.c.i.99.4		6	28.19	even	6
196.3.g.i.67.1		12	7.4	even	3	inner
196.3.g.i.67.5		12	28.11	odd	6	inner
196.3.g.i.79.1		12	4.3	odd	2	inner
196.3.g.i.79.5		12	1.1	even	1	trivial
252.3.y.c.163.2		12	21.20	even	2
252.3.y.c.163.6		12	84.83	odd	2
252.3.y.c.235.2		12	84.59	odd	6
252.3.y.c.235.6		12	21.17	even	6
448.3.r.h.191.2		12	56.27	even	2
448.3.r.h.191.5		12	56.13	odd	2
448.3.r.h.319.2		12	56.45	odd	6
448.3.r.h.319.5		12	56.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	196.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.19654 + 1.60259i) q^{2} +(1.86796 - 1.07847i) q^{3} +(-1.13656 + 3.83513i) q^{4} +(-3.25304 + 5.63443i) q^{5} +(3.96343 + 1.70313i) q^{6} +(-7.50608 + 2.76746i) q^{8} +(-2.17382 + 3.76517i) q^{9} +(-12.9221 + 1.52857i) q^{10} +(-0.528732 + 0.305264i) q^{11} +(2.01300 + 8.38961i) q^{12} +10.6645 q^{13} +14.0332i q^{15} +(-13.4164 - 8.71774i) q^{16} +(-5.99069 - 10.3762i) q^{17} +(-8.63508 + 1.02145i) q^{18} +(10.5811 + 6.10898i) q^{19} +(-17.9115 - 18.8797i) q^{20} +(-1.12186 - 0.482077i) q^{22} +(34.7524 + 20.0643i) q^{23} +(-11.0364 + 13.2645i) q^{24} +(-8.66451 - 15.0074i) q^{25} +(12.7606 + 17.0908i) q^{26} +28.7900i q^{27} -9.04293 q^{29} +(-22.4894 + 16.7913i) q^{30} +(30.2408 - 17.4595i) q^{31} +(-2.08243 - 31.9322i) q^{32} +(-0.658433 + 1.14044i) q^{33} +(9.46059 - 22.0161i) q^{34} +(-11.9692 - 12.6162i) q^{36} +(25.4082 - 44.0084i) q^{37} +(2.87054 + 24.2667i) q^{38} +(19.9209 - 11.5013i) q^{39} +(8.82450 - 51.2951i) q^{40} -25.7382 q^{41} +19.8107i q^{43} +(-0.569787 - 2.37471i) q^{44} +(-14.1430 - 24.4965i) q^{45} +(9.42799 + 79.7015i) q^{46} +(-40.7870 - 23.5484i) q^{47} +(-34.4631 - 1.81520i) q^{48} +(13.6831 - 31.8426i) q^{50} +(-22.3807 - 12.9215i) q^{51} +(-12.1209 + 40.8998i) q^{52} +(13.4390 + 23.2770i) q^{53} +(-46.1384 + 34.4485i) q^{54} -3.97214i q^{55} +26.3533 q^{57} +(-10.8203 - 14.4921i) q^{58} +(39.8644 - 23.0157i) q^{59} +(-53.8190 - 15.9496i) q^{60} +(21.1035 - 36.5524i) q^{61} +(64.1648 + 27.5724i) q^{62} +(48.6823 - 41.5455i) q^{64} +(-34.6920 + 60.0884i) q^{65} +(-2.61550 + 0.309390i) q^{66} +(24.0592 - 13.8906i) q^{67} +(46.6028 - 11.1819i) q^{68} +86.5547 q^{69} -57.1882i q^{71} +(5.89691 - 34.2776i) q^{72} +(28.1645 + 48.7824i) q^{73} +(100.929 - 11.9391i) q^{74} +(-32.3699 - 18.6888i) q^{75} +(-35.4548 + 33.6365i) q^{76} +(42.2680 + 18.1631i) q^{78} +(15.9295 + 9.19688i) q^{79} +(92.7637 - 47.2348i) q^{80} +(11.4846 + 19.8919i) q^{81} +(-30.7969 - 41.2477i) q^{82} +37.3775i q^{83} +77.9517 q^{85} +(-31.7483 + 23.7043i) q^{86} +(-16.8918 + 9.75249i) q^{87} +(3.12390 - 3.75458i) q^{88} +(-12.3537 + 21.3973i) q^{89} +(22.3349 - 51.9766i) q^{90} +(-116.448 + 110.476i) q^{92} +(37.6590 - 65.2273i) q^{93} +(-11.0651 - 93.5415i) q^{94} +(-68.8412 + 39.7455i) q^{95} +(-38.3277 - 57.4021i) q^{96} -109.895 q^{97} -2.65435i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 4 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{8} + 4 q^{9} + 2 q^{10} + 24 q^{12} + 24 q^{13} + 16 q^{16} + 2 q^{17} + 56 q^{18} - 152 q^{20} + 44 q^{22} + 44 q^{24} - 56 q^{26} + 72 q^{29} - 74 q^{30}+ \cdots - 744 q^{97}+O(q^{100}) \) 12 * q - 2 * q^2 - 4 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^8 + 4 * q^9 + 2 * q^10 + 24 * q^12 + 24 * q^13 + 16 * q^16 + 2 * q^17 + 56 * q^18 - 152 * q^20 + 44 * q^22 + 44 * q^24 - 56 * q^26 + 72 * q^29 - 74 * q^30 - 112 * q^32 + 14 * q^33 + 316 * q^34 - 160 * q^36 + 86 * q^37 + 2 * q^38 + 148 * q^40 - 8 * q^41 + 64 * q^44 - 156 * q^45 + 162 * q^46 - 512 * q^48 + 208 * q^50 + 64 * q^52 - 74 * q^53 - 182 * q^54 - 220 * q^57 - 176 * q^58 - 232 * q^60 - 86 * q^61 + 532 * q^62 - 160 * q^64 - 140 * q^65 - 102 * q^66 + 68 * q^68 + 300 * q^69 + 152 * q^72 + 234 * q^73 + 290 * q^74 - 576 * q^76 + 64 * q^78 + 146 * q^81 - 272 * q^82 + 268 * q^85 - 16 * q^86 - 188 * q^88 - 6 * q^89 + 640 * q^90 - 448 * q^92 + 162 * q^93 - 102 * q^94 + 320 * q^96 - 744 * q^97

Introduction

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