LMFDB - Embedded newform 55.3.i.d.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,3,Mod(6,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("55.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.i (of order $10$, degree $4$, 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:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
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} + 25x^{10} + 235x^{8} + 1025x^{6} + 2090x^{4} + 1880x^{2} + 605 $ x^12 + 25x^10 + 235x^8 + 1025x^6 + 2090x^4 + 1880*x^2 + 605
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.3
Root			$2.63198i$ of defining polynomial
Character	$\chi$	$=$	55.41
Dual form			55.3.i.d.51.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.07416 + 2.85483i) q^{2} +(-0.286558 - 0.881935i) q^{3} +(-2.61187 + 8.03851i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.92341 - 2.64735i) q^{6} +(3.73363 + 1.21313i) q^{7} +(-14.9418 + 4.85489i) q^{8} +(6.58546 - 4.78462i) q^{9} +O(q^{10})$	\(q+(2.07416 + 2.85483i) q^{2} +(-0.286558 - 0.881935i) q^{3} +(-2.61187 + 8.03851i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.92341 - 2.64735i) q^{6} +(3.73363 + 1.21313i) q^{7} +(-14.9418 + 4.85489i) q^{8} +(6.58546 - 4.78462i) q^{9} -7.89056i q^{10} +(-2.87880 - 10.6166i) q^{11} +7.83789 q^{12} +(-3.37849 - 4.65009i) q^{13} +(4.28086 + 13.1751i) q^{14} +(-0.640763 + 1.97207i) q^{15} +(-17.4997 - 12.7143i) q^{16} +(-5.29106 + 7.28252i) q^{17} +(27.3186 + 8.87634i) q^{18} +(-27.7487 + 9.01609i) q^{19} +(15.2902 - 11.1090i) q^{20} -3.64045i q^{21} +(24.3376 - 30.2390i) q^{22} +36.7936 q^{23} +(8.56339 + 11.7865i) q^{24} +(1.54508 + 4.75528i) q^{25} +(6.26771 - 19.2900i) q^{26} +(-12.8588 - 9.34246i) q^{27} +(-19.5035 + 26.8443i) q^{28} +(-24.8274 - 8.06690i) q^{29} +(-6.95896 + 2.26110i) q^{30} +(-39.1642 + 28.4544i) q^{31} -13.4870i q^{32} +(-8.53822 + 5.58119i) q^{33} -31.7649 q^{34} +(-5.15975 - 7.10179i) q^{35} +(21.2608 + 65.4341i) q^{36} +(6.73919 - 20.7411i) q^{37} +(-83.2945 - 60.5170i) q^{38} +(-3.13294 + 4.31213i) q^{39} +(33.4109 + 10.8559i) q^{40} +(40.5371 - 13.1713i) q^{41} +(10.3929 - 7.55087i) q^{42} +70.3737i q^{43} +(92.8608 + 4.58797i) q^{44} -18.2018 q^{45} +(76.3156 + 105.039i) q^{46} +(-5.46351 - 16.8149i) q^{47} +(-6.19847 + 19.0769i) q^{48} +(-27.1735 - 19.7427i) q^{49} +(-10.3708 + 14.2742i) q^{50} +(7.93890 + 2.57951i) q^{51} +(46.2040 - 15.0126i) q^{52} +(50.4423 - 36.6485i) q^{53} -56.0874i q^{54} +(-8.74592 + 22.9893i) q^{55} -61.6768 q^{56} +(15.9032 + 21.8889i) q^{57} +(-28.4662 - 87.6100i) q^{58} +(-12.0295 + 37.0230i) q^{59} +(-14.1789 - 10.3016i) q^{60} +(26.4166 - 36.3594i) q^{61} +(-162.465 - 52.7881i) q^{62} +(30.3921 - 9.87498i) q^{63} +(-31.4956 + 22.8829i) q^{64} +12.8525i q^{65} +(-33.6430 - 12.7989i) q^{66} +36.2530 q^{67} +(-44.7211 - 61.5533i) q^{68} +(-10.5435 - 32.4495i) q^{69} +(9.57229 - 29.4605i) q^{70} +(1.98595 + 1.44287i) q^{71} +(-75.1699 + 103.462i) q^{72} +(125.450 + 40.7610i) q^{73} +(73.1905 - 23.7810i) q^{74} +(3.75109 - 2.72533i) q^{75} -246.607i q^{76} +(2.13097 - 43.1309i) q^{77} -18.8086 q^{78} +(-24.9427 - 34.3307i) q^{79} +(14.9465 + 46.0006i) q^{80} +(18.0841 - 55.6573i) q^{81} +(121.682 + 88.4072i) q^{82} +(-45.3846 + 62.4666i) q^{83} +(29.2638 + 9.50839i) q^{84} +(19.1432 - 6.22001i) q^{85} +(-200.905 + 145.966i) q^{86} +24.2077i q^{87} +(94.5569 + 144.655i) q^{88} +105.316 q^{89} +(-37.7533 - 51.9630i) q^{90} +(-6.97287 - 21.4603i) q^{91} +(-96.1001 + 295.766i) q^{92} +(36.3177 + 26.3864i) q^{93} +(36.6717 - 50.4742i) q^{94} +(62.0479 + 20.1606i) q^{95} +(-11.8946 + 3.86481i) q^{96} +(-45.8248 + 33.2937i) q^{97} -118.525i q^{98} +(-69.7546 - 56.1413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 5 q^{2} - 13 q^{3} + 13 q^{4} - 15 q^{5} + 20 q^{6} - 5 q^{7} - 35 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q + 5 * q^2 - 13 * q^3 + 13 * q^4 - 15 * q^5 + 20 * q^6 - 5 * q^7 - 35 * q^8 + 4 * q^9	\( 12 q + 5 q^{2} - 13 q^{3} + 13 q^{4} - 15 q^{5} + 20 q^{6} - 5 q^{7} - 35 q^{8} + 4 q^{9} + 12 q^{11} - 2 q^{12} + 70 q^{13} - 60 q^{14} + 35 q^{15} - 43 q^{16} - 15 q^{17} - 30 q^{18} - 80 q^{19} + 20 q^{20} - 10 q^{22} + 42 q^{23} + 210 q^{24} - 15 q^{25} - 120 q^{26} - 109 q^{27} + 140 q^{28} + 5 q^{29} - 20 q^{30} - 46 q^{31} + 42 q^{33} + 10 q^{34} + 20 q^{35} - 39 q^{36} - 42 q^{37} - 130 q^{38} - 285 q^{39} - 25 q^{40} + 230 q^{41} + 135 q^{42} + 488 q^{44} - 50 q^{45} + 205 q^{46} + 58 q^{47} - 323 q^{48} - 212 q^{49} - 25 q^{50} + 360 q^{51} + 410 q^{52} - 43 q^{53} - 80 q^{55} - 410 q^{56} + 270 q^{57} - 450 q^{58} - 74 q^{59} - 25 q^{60} - 290 q^{61} - 350 q^{62} + 295 q^{63} - 7 q^{64} + 185 q^{66} - 212 q^{67} + 55 q^{68} - 73 q^{69} + 160 q^{70} - 276 q^{71} - 555 q^{72} + 645 q^{73} - 100 q^{74} + 10 q^{75} - 140 q^{77} + 360 q^{78} + 235 q^{79} + 140 q^{80} - 30 q^{81} + 215 q^{82} + 60 q^{83} - 580 q^{84} + 65 q^{85} - 480 q^{86} - 165 q^{88} - 114 q^{89} + 145 q^{90} + 160 q^{91} + 33 q^{92} + 129 q^{93} + 375 q^{94} + 50 q^{95} + 265 q^{96} + 63 q^{97} + 669 q^{99}+O(q^{100}) \) 12 * q + 5 * q^2 - 13 * q^3 + 13 * q^4 - 15 * q^5 + 20 * q^6 - 5 * q^7 - 35 * q^8 + 4 * q^9 + 12 * q^11 - 2 * q^12 + 70 * q^13 - 60 * q^14 + 35 * q^15 - 43 * q^16 - 15 * q^17 - 30 * q^18 - 80 * q^19 + 20 * q^20 - 10 * q^22 + 42 * q^23 + 210 * q^24 - 15 * q^25 - 120 * q^26 - 109 * q^27 + 140 * q^28 + 5 * q^29 - 20 * q^30 - 46 * q^31 + 42 * q^33 + 10 * q^34 + 20 * q^35 - 39 * q^36 - 42 * q^37 - 130 * q^38 - 285 * q^39 - 25 * q^40 + 230 * q^41 + 135 * q^42 + 488 * q^44 - 50 * q^45 + 205 * q^46 + 58 * q^47 - 323 * q^48 - 212 * q^49 - 25 * q^50 + 360 * q^51 + 410 * q^52 - 43 * q^53 - 80 * q^55 - 410 * q^56 + 270 * q^57 - 450 * q^58 - 74 * q^59 - 25 * q^60 - 290 * q^61 - 350 * q^62 + 295 * q^63 - 7 * q^64 + 185 * q^66 - 212 * q^67 + 55 * q^68 - 73 * q^69 + 160 * q^70 - 276 * q^71 - 555 * q^72 + 645 * q^73 - 100 * q^74 + 10 * q^75 - 140 * q^77 + 360 * q^78 + 235 * q^79 + 140 * q^80 - 30 * q^81 + 215 * q^82 + 60 * q^83 - 580 * q^84 + 65 * q^85 - 480 * q^86 - 165 * q^88 - 114 * q^89 + 145 * q^90 + 160 * q^91 + 33 * q^92 + 129 * q^93 + 375 * q^94 + 50 * q^95 + 265 * q^96 + 63 * q^97 + 669 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	2.07416	+	2.85483i	1.03708	+	1.42742i	0.899498	+	0.436925i	$0.143933\pi$
$2$	2.07416	+	2.85483i	1.03708	+	1.42742i	0.137581	+	0.990491i	$0.456067\pi$
$3$	−0.286558	−	0.881935i	−0.0955193	−	0.293978i	0.891869	−	0.452293i	$-0.149394\pi$
$3$	−0.286558	−	0.881935i	−0.0955193	−	0.293978i	−0.987389	+	0.158315i	$0.949394\pi$
$4$	−2.61187	+	8.03851i	−0.652968	+	2.00963i
$5$	−1.80902	−	1.31433i	−0.361803	−	0.262866i
$5$	−1.80902	−	1.31433i	−0.361803	−	0.262866i
$6$	1.92341	−	2.64735i	0.320568	−	0.441224i
$7$	3.73363	+	1.21313i	0.533376	+	0.173304i	0.563307	−	0.826248i	$-0.309529\pi$
$7$	3.73363	+	1.21313i	0.533376	+	0.173304i	−0.0299310	+	0.999552i	$0.509529\pi$
$8$	−14.9418	+	4.85489i	−1.86773	+	0.606861i
$9$	6.58546	−	4.78462i	0.731718	−	0.531624i
$10$		−	7.89056i		−	0.789056i
$11$	−2.87880	−	10.6166i	−0.261709	−	0.965147i
$11$	−2.87880	−	10.6166i	−0.261709	−	0.965147i
$12$	7.83789			0.653158
$13$	−3.37849	−	4.65009i	−0.259884	−	0.357699i	0.659058	−	0.752092i	$-0.270955\pi$
$13$	−3.37849	−	4.65009i	−0.259884	−	0.357699i	−0.918942	+	0.394393i	$0.870955\pi$
$14$	4.28086	+	13.1751i	0.305775	+	0.941080i
$15$	−0.640763	+	1.97207i	−0.0427175	+	0.131471i
$16$	−17.4997	−	12.7143i	−1.09373	−	0.794641i
$17$	−5.29106	+	7.28252i	−0.311239	+	0.428383i	−0.935767	−	0.352619i	$-0.885291\pi$
$17$	−5.29106	+	7.28252i	−0.311239	+	0.428383i	0.624528	+	0.781002i	$0.285291\pi$
$18$	27.3186	+	8.87634i	1.51770	+	0.493130i
$19$	−27.7487	+	9.01609i	−1.46046	+	0.474531i	−0.928210	−	0.372058i	$-0.878652\pi$
$19$	−27.7487	+	9.01609i	−1.46046	+	0.474531i	−0.532247	+	0.846589i	$0.678652\pi$
$20$	15.2902	−	11.1090i	0.764508	−	0.555448i
$21$		−	3.64045i		−	0.173355i
$22$	24.3376	−	30.2390i	1.10625	−	1.37450i
$23$	36.7936			1.59972			0.799860	−	0.600186i	$-0.204907\pi$
$23$	36.7936			1.59972			0.799860	+	0.600186i	$0.204907\pi$
$24$	8.56339	+	11.7865i	0.356808	+	0.491104i
$25$	1.54508	+	4.75528i	0.0618034	+	0.190211i
$26$	6.26771	−	19.2900i	0.241066	−	0.741924i
$27$	−12.8588	−	9.34246i	−0.476252	−	0.346017i
$28$	−19.5035	+	26.8443i	−0.696555	+	0.958726i
$29$	−24.8274	−	8.06690i	−0.856116	−	0.278169i	−0.152111	−	0.988363i	$-0.548607\pi$
$29$	−24.8274	−	8.06690i	−0.856116	−	0.278169i	−0.704006	+	0.710195i	$0.748607\pi$
$30$	−6.95896	+	2.26110i	−0.231965	+	0.0753701i
$31$	−39.1642	+	28.4544i	−1.26336	+	0.917885i	−0.998918	−	0.0465167i	$-0.985188\pi$
$31$	−39.1642	+	28.4544i	−1.26336	+	0.917885i	−0.264442	+	0.964401i	$0.585188\pi$
$32$		−	13.4870i		−	0.421469i
$33$	−8.53822	+	5.58119i	−0.258734	+	0.169127i
$34$	−31.7649			−0.934261
$35$	−5.15975	−	7.10179i	−0.147422	−	0.202908i
$36$	21.2608	+	65.4341i	0.590579	+	1.81761i
$37$	6.73919	−	20.7411i	0.182140	−	0.560571i	−0.817747	−	0.575578i	$-0.804777\pi$
$37$	6.73919	−	20.7411i	0.182140	−	0.560571i	0.999887	+	0.0150073i	$0.00477717\pi$
$38$	−83.2945	−	60.5170i	−2.19196	−	1.59255i
$39$	−3.13294	+	4.31213i	−0.0803319	+	0.110567i
$40$	33.4109	+	10.8559i	0.835272	+	0.271396i
$41$	40.5371	−	13.1713i	0.988709	−	0.321251i	0.230364	−	0.973105i	$-0.426008\pi$
$41$	40.5371	−	13.1713i	0.988709	−	0.321251i	0.758345	+	0.651854i	$0.226008\pi$
$42$	10.3929	−	7.55087i	0.247450	−	0.179783i
$43$			70.3737i			1.63660i	0.574794	+	0.818298i	$0.305082\pi$
$43$			70.3737i			1.63660i	−0.574794	+	0.818298i	$0.694918\pi$
$44$	92.8608	+	4.58797i	2.11047	+	0.104272i
$45$	−18.2018			−0.404484
$46$	76.3156	+	105.039i	1.65904	+	2.28347i
$47$	−5.46351	−	16.8149i	−0.116245	−	0.357765i	0.875960	−	0.482384i	$-0.160229\pi$
$47$	−5.46351	−	16.8149i	−0.116245	−	0.357765i	−0.992205	+	0.124619i	$0.960229\pi$
$48$	−6.19847	+	19.0769i	−0.129135	+	0.397436i
$49$	−27.1735	−	19.7427i	−0.554561	−	0.402912i
$50$	−10.3708	+	14.2742i	−0.207416	+	0.285483i
$51$	7.93890	+	2.57951i	0.155665	+	0.0505785i
$52$	46.2040	−	15.0126i	0.888538	−	0.288704i
$53$	50.4423	−	36.6485i	0.951742	−	0.691481i	0.000523852	−	1.00000i	$-0.499833\pi$
$53$	50.4423	−	36.6485i	0.951742	−	0.691481i	0.951218	+	0.308519i	$0.0998333\pi$
$54$		−	56.0874i		−	1.03866i
$55$	−8.74592	+	22.9893i	−0.159017	+	0.417988i
$56$	−61.6768			−1.10137
$57$	15.9032	+	21.8889i	0.279004	+	0.384016i
$58$	−28.4662	−	87.6100i	−0.490797	−	1.51052i
$59$	−12.0295	+	37.0230i	−0.203890	+	0.627509i	0.795867	+	0.605471i	$0.207015\pi$
$59$	−12.0295	+	37.0230i	−0.203890	+	0.627509i	−0.999757	+	0.0220376i	$0.992985\pi$
$60$	−14.1789	−	10.3016i	−0.236315	−	0.171693i
$61$	26.4166	−	36.3594i	0.433060	−	0.596055i	−0.535593	−	0.844477i	$-0.679912\pi$
$61$	26.4166	−	36.3594i	0.433060	−	0.596055i	0.968652	+	0.248421i	$0.0799117\pi$
$62$	−162.465	−	52.7881i	−2.62041	−	0.851422i
$63$	30.3921	−	9.87498i	0.482414	−	0.156746i
$64$	−31.4956	+	22.8829i	−0.492118	+	0.357545i
$65$			12.8525i			0.197731i
$66$	−33.6430	−	12.7989i	−0.509742	−	0.193923i
$67$	36.2530			0.541090			0.270545	−	0.962707i	$-0.412796\pi$
$67$	36.2530			0.541090			0.270545	+	0.962707i	$0.412796\pi$
$68$	−44.7211	−	61.5533i	−0.657663	−	0.905195i
$69$	−10.5435	−	32.4495i	−0.152804	−	0.470283i
$70$	9.57229	−	29.4605i	0.136747	−	0.420864i
$71$	1.98595	+	1.44287i	0.0279711	+	0.0203222i	0.601683	−	0.798735i	$-0.294497\pi$
$71$	1.98595	+	1.44287i	0.0279711	+	0.0203222i	−0.573712	+	0.819057i	$0.694497\pi$
$72$	−75.1699	+	103.462i	−1.04403	+	1.43698i
$73$	125.450	+	40.7610i	1.71849	+	0.558370i	0.991709	−	0.128503i	$-0.0410172\pi$
$73$	125.450	+	40.7610i	1.71849	+	0.558370i	0.726777	+	0.686873i	$0.241017\pi$
$74$	73.1905	−	23.7810i	0.989061	−	0.321365i
$75$	3.75109	−	2.72533i	0.0500146	−	0.0363377i
$76$		−	246.607i		−	3.24483i
$77$	2.13097	−	43.1309i	0.0276749	−	0.560142i
$78$	−18.8086			−0.241136
$79$	−24.9427	−	34.3307i	−0.315730	−	0.434565i	0.621427	−	0.783472i	$-0.286553\pi$
$79$	−24.9427	−	34.3307i	−0.315730	−	0.434565i	−0.937158	+	0.348907i	$0.886553\pi$
$80$	14.9465	+	46.0006i	0.186831	+	0.575008i
$81$	18.0841	−	55.6573i	0.223261	−	0.687127i
$82$	121.682	+	88.4072i	1.48393	+	1.07814i
$83$	−45.3846	+	62.4666i	−0.546803	+	0.752609i	−0.989574	−	0.144025i	$-0.953995\pi$
$83$	−45.3846	+	62.4666i	−0.546803	+	0.752609i	0.442771	+	0.896635i	$0.353995\pi$
$84$	29.2638	+	9.50839i	0.348379	+	0.113195i
$85$	19.1432	−	6.22001i	0.225215	−	0.0731766i
$86$	−200.905	+	145.966i	−2.33610	+	1.69728i
$87$			24.2077i			0.278250i
$88$	94.5569	+	144.655i	1.07451	+	1.64381i
$89$	105.316			1.18332			0.591661	−	0.806187i	$-0.298472\pi$
$89$	105.316			1.18332			0.591661	+	0.806187i	$0.298472\pi$
$90$	−37.7533	−	51.9630i	−0.419481	−	0.577366i
$91$	−6.97287	−	21.4603i	−0.0766249	−	0.235827i
$92$	−96.1001	+	295.766i	−1.04457	+	3.21484i
$93$	36.3177	+	26.3864i	0.390513	+	0.283725i
$94$	36.6717	−	50.4742i	0.390124	−	0.536960i
$95$	62.0479	+	20.1606i	0.653136	+	0.212217i
$96$	−11.8946	+	3.86481i	−0.123903	+	0.0402584i
$97$	−45.8248	+	33.2937i	−0.472421	+	0.343234i	−0.798384	−	0.602149i	$-0.794311\pi$
$97$	−45.8248	+	33.2937i	−0.472421	+	0.343234i	0.325963	+	0.945382i	$0.394311\pi$
$98$		−	118.525i		−	1.20944i
$99$	−69.7546	−	56.1413i	−0.704592	−	0.567084i
$100$	−42.2610			−0.422610
$101$	−54.3720	−	74.8367i	−0.538337	−	0.740957i	0.450035	−	0.893011i	$-0.351411\pi$
$101$	−54.3720	−	74.8367i	−0.538337	−	0.740957i	−0.988372	+	0.152054i	$0.951411\pi$
$102$	9.10247	+	28.0145i	0.0892399	+	0.274652i
$103$	−13.5278	+	41.6344i	−0.131338	+	0.404218i	−0.995003	−	0.0998498i	$-0.968164\pi$
$103$	−13.5278	+	41.6344i	−0.131338	+	0.404218i	0.863664	+	0.504068i	$0.168164\pi$
$104$	73.0564	+	53.0786i	0.702465	+	0.510371i
$105$	−4.78475	+	6.58564i	−0.0455690	+	0.0627204i
$106$	209.251	+	67.9896i	1.97406	+	0.641412i
$107$	60.5320	−	19.6680i	0.565719	−	0.183813i	−0.0121737	−	0.999926i	$-0.503875\pi$
$107$	60.5320	−	19.6680i	0.565719	−	0.183813i	0.577893	+	0.816113i	$0.303875\pi$
$108$	108.685	−	78.9643i	1.00634	−	0.731151i
$109$			180.853i			1.65920i	0.558358	+	0.829600i	$0.311432\pi$
$109$			180.853i			1.65920i	−0.558358	+	0.829600i	$0.688568\pi$
$110$	−83.7711	+	22.7153i	−0.761555	+	0.206503i
$111$	−20.2235			−0.182193
$112$	−49.9133	−	68.6998i	−0.445654	−	0.613391i
$113$	−22.4996	−	69.2468i	−0.199112	−	0.612803i	−0.999904	−	0.0138608i	$-0.995588\pi$
$113$	−22.4996	−	69.2468i	−0.199112	−	0.612803i	0.800792	−	0.598942i	$-0.204412\pi$
$114$	−29.5033	+	90.8020i	−0.258801	+	0.796508i
$115$	−66.5602	−	48.3588i	−0.578784	−	0.420511i
$116$	129.692	−	178.505i	1.11803	−	1.53884i
$117$	−44.4978	−	14.4582i	−0.380323	−	0.123574i
$118$	−130.646	+	42.4493i	−1.10717	+	0.359740i
$119$	−28.5895	+	20.7715i	−0.240248	+	0.174551i
$120$		−	32.5771i		−	0.271475i
$121$	−104.425	+	61.1262i	−0.863017	+	0.505175i
$122$	158.592			1.29994
$123$	−23.2324	−	31.9767i	−0.188881	−	0.259973i
$124$	−126.440	−	389.141i	−1.01967	−	3.13823i
$125$	3.45492	−	10.6331i	0.0276393	−	0.0850651i
$126$	91.2293	+	66.2820i	0.724042	+	0.526047i
$127$	−68.7276	+	94.5954i	−0.541162	+	0.744846i	−0.988780	−	0.149379i	$-0.952273\pi$
$127$	−68.7276	+	94.5954i	−0.541162	+	0.744846i	0.447618	+	0.894225i	$0.352273\pi$
$128$	−181.961	−	59.1227i	−1.42157	−	0.461896i
$129$	62.0650	−	20.1661i	0.481124	−	0.156327i
$130$	−36.6918	+	26.6582i	−0.282245	+	0.205063i
$131$		−	41.6464i		−	0.317912i	−0.987286	−	0.158956i	$-0.949187\pi$
$131$		−	41.6464i		−	0.317912i	0.987286	−	0.158956i	$-0.0508127\pi$
$132$	−22.5637	−	83.2119i	−0.170937	−	0.630393i
$133$	−114.541			−0.861211
$134$	75.1945	+	103.496i	0.561153	+	0.772360i
$135$	10.9827	+	33.8014i	0.0813535	+	0.250380i
$136$	43.7022	−	134.502i	0.321340	−	0.988982i
$137$	−85.7502	−	62.3011i	−0.625914	−	0.454753i	0.229069	−	0.973410i	$-0.426432\pi$
$137$	−85.7502	−	62.3011i	−0.625914	−	0.454753i	−0.854982	+	0.518657i	$0.826432\pi$
$138$	70.7691	−	97.4053i	0.512819	−	0.705835i
$139$	31.5601	+	10.2545i	0.227051	+	0.0737733i	0.420333	−	0.907370i	$-0.361913\pi$
$139$	31.5601	+	10.2545i	0.227051	+	0.0737733i	−0.193282	+	0.981143i	$0.561913\pi$
$140$	70.5645	−	22.9278i	0.504032	−	0.163770i
$141$	−13.2641	+	9.63691i	−0.0940714	+	0.0683469i
$142$			8.66229i			0.0610020i
$143$	−39.6422	+	49.2548i	−0.277218	+	0.344439i
$144$	−176.076			−1.22275
$145$	34.3106	+	47.2245i	0.236625	+	0.325686i
$146$	143.836	+	442.682i	0.985179	+	3.03207i
$147$	−9.62499	+	29.6227i	−0.0654761	+	0.201515i
$148$	149.126	+	108.346i	1.00761	+	0.732069i
$149$	70.8877	−	97.5686i	0.475757	−	0.654823i	−0.501926	−	0.864911i	$-0.667375\pi$
$149$	70.8877	−	97.5686i	0.475757	−	0.654823i	0.977683	+	0.210088i	$0.0673750\pi$
$150$	15.5607	+	5.05598i	0.103738	+	0.0337065i
$151$	−65.2872	+	21.2131i	−0.432366	+	0.140484i	−0.517111	−	0.855919i	$-0.672992\pi$
$151$	−65.2872	+	21.2131i	−0.432366	+	0.140484i	0.0847449	+	0.996403i	$0.472992\pi$
$152$	370.843	−	269.433i	2.43976	−	1.77259i
$153$			73.2744i			0.478918i
$154$	127.551	−	83.3767i	0.828256	−	0.541407i
$155$	108.247			0.698368
$156$	−26.4802	−	36.4469i	−0.169745	−	0.233634i
$157$	−57.8493	−	178.042i	−0.368467	−	1.13402i	−0.947782	−	0.318920i	$-0.896680\pi$
$157$	−57.8493	−	178.042i	−0.368467	−	1.13402i	0.579315	−	0.815104i	$-0.303320\pi$
$158$	46.2732	−	142.414i	0.292868	−	0.901356i
$159$	−46.7762	−	33.9849i	−0.294190	−	0.213742i
$160$	−17.7263	+	24.3982i	−0.110790	+	0.152489i
$161$	137.374	+	44.6354i	0.853253	+	0.277239i
$162$	196.402	−	63.8147i	1.21236	−	0.393918i
$163$	−29.2151	+	21.2260i	−0.179234	+	0.130221i	−0.673785	−	0.738928i	$-0.735333\pi$
$163$	−29.2151	+	21.2260i	−0.179234	+	0.130221i	0.494551	+	0.869149i	$0.335333\pi$
$164$			360.259i			2.19670i
$165$	22.7813	+	1.12555i	0.138068	+	0.00682154i
$166$	−272.466			−1.64136
$167$	−90.2211	−	124.179i	−0.540246	−	0.743585i	0.448403	−	0.893832i	$-0.351993\pi$
$167$	−90.2211	−	124.179i	−0.540246	−	0.743585i	−0.988648	+	0.150247i	$0.951993\pi$
$168$	17.6740	+	54.3949i	0.105202	+	0.323779i
$169$	42.0147	−	129.308i	0.248608	−	0.765136i
$170$	57.4632	+	41.7494i	0.338019	+	0.245585i
$171$	−139.599	+	192.142i	−0.816370	+	1.12364i
$172$	−565.700	−	183.807i	−3.28895	−	1.06864i
$173$	−1.64642	+	0.534955i	−0.00951689	+	0.00309223i	−0.313772	−	0.949498i	$-0.601593\pi$
$173$	−1.64642	+	0.534955i	−0.00951689	+	0.00309223i	0.304255	+	0.952591i	$0.401593\pi$
$174$	−69.1090	+	50.2107i	−0.397178	+	0.288567i
$175$			19.6289i			0.112165i
$176$	−84.6043	+	222.389i	−0.480706	+	1.26357i
$177$	36.0990			0.203949
$178$	218.441	+	300.659i	1.22720	+	1.68909i
$179$	26.7282	+	82.2609i	0.149320	+	0.459558i	0.997541	−	0.0700832i	$-0.0223265\pi$
$179$	26.7282	+	82.2609i	0.149320	+	0.459558i	−0.848222	+	0.529641i	$0.822326\pi$
$180$	47.5407	−	146.315i	0.264115	−	0.812862i
$181$	−144.912	−	105.285i	−0.800619	−	0.581684i	0.110477	−	0.993879i	$-0.464762\pi$
$181$	−144.912	−	105.285i	−0.800619	−	0.581684i	−0.911096	+	0.412195i	$0.864762\pi$
$182$	46.8027	−	64.4184i	0.257158	−	0.353947i
$183$	−39.6365	−	12.8787i	−0.216593	−	0.0703753i
$184$	−549.762	+	178.629i	−2.98784	+	0.970808i
$185$	−39.4519	+	28.6635i	−0.213254	+	0.154938i
$186$			158.411i			0.851670i
$187$	92.5476	+	35.2082i	0.494907	+	0.188279i
$188$	149.437			0.794878
$189$	−36.6764	−	50.4807i	−0.194055	−	0.267094i
$190$	71.1420	+	218.953i	0.374432	+	1.15238i
$191$	104.623	−	321.997i	0.547765	−	1.68585i	−0.166559	−	0.986032i	$-0.553266\pi$
$191$	104.623	−	321.997i	0.547765	−	1.68585i	0.714324	−	0.699815i	$-0.246734\pi$
$192$	29.2065	+	21.2198i	0.152117	+	0.110520i
$193$	−5.22978	+	7.19818i	−0.0270973	+	0.0372963i	−0.822351	−	0.568981i	$-0.807338\pi$
$193$	−5.22978	+	7.19818i	−0.0270973	+	0.0372963i	0.795253	+	0.606277i	$0.207338\pi$
$194$	−190.096	−	61.7658i	−0.979874	−	0.318381i
$195$	11.3351	−	3.68300i	0.0581287	−	0.0188872i
$196$	229.676	−	166.869i	1.17181	−	0.851373i
$197$			199.660i			1.01350i	0.862093	+	0.506751i	$0.169154\pi$
$197$			199.660i			1.01350i	−0.862093	+	0.506751i	$0.830846\pi$
$198$	15.5920	−	315.584i	0.0787477	−	1.59386i
$199$	182.624			0.917706			0.458853	−	0.888512i	$-0.348260\pi$
$199$	182.624			0.917706			0.458853	+	0.888512i	$0.348260\pi$
$200$	−46.1727	−	63.5513i	−0.230864	−	0.317757i
$201$	−10.3886	−	31.9728i	−0.0516845	−	0.159069i
$202$	100.870	−	310.446i	0.499356	−	1.53686i
$203$	−82.9101	−	60.2377i	−0.408424	−	0.296737i
$204$	−41.4708	+	57.0796i	−0.203288	+	0.279802i
$205$	−90.6436	−	29.4519i	−0.442164	−	0.143668i
$206$	−146.918	+	47.7366i	−0.713195	+	0.231731i
$207$	242.303	−	176.043i	1.17054	−	0.850450i
$208$			124.330i			0.597740i
$209$	175.603	+	268.642i	0.840207	+	1.28537i
$210$	−28.7252			−0.136787
$211$	80.0829	+	110.225i	0.379540	+	0.522392i	0.955463	−	0.295112i	$-0.0953571\pi$
$211$	80.0829	+	110.225i	0.379540	+	0.522392i	−0.575923	+	0.817504i	$0.695357\pi$
$212$	162.851	+	501.202i	0.768163	+	2.36416i
$213$	0.703432	−	2.16494i	0.00330250	−	0.0101640i
$214$	181.702	+	132.014i	0.849073	+	0.616888i
$215$	92.4941	−	127.307i	0.430205	−	0.592126i
$216$	237.490	+	77.1653i	1.09949	+	0.357247i
$217$	−180.744	+	58.7271i	−0.832920	+	0.270632i
$218$	−516.305	+	375.117i	−2.36837	+	1.72072i
$219$		−	122.319i		−	0.558533i
$220$	−161.957	−	130.349i	−0.736167	−	0.592497i
$221$	51.7402			0.234118
$222$	−41.9466	−	57.7346i	−0.188949	−	0.260066i
$223$	−12.5350	−	38.5788i	−0.0562108	−	0.172999i	0.919009	−	0.394236i	$-0.128991\pi$
$223$	−12.5350	−	38.5788i	−0.0562108	−	0.172999i	−0.975220	+	0.221237i	$0.928991\pi$
$224$	16.3615	−	50.3555i	0.0730424	−	0.224801i
$225$	32.9273	+	23.9231i	0.146344	+	0.106325i
$226$	151.020	−	207.861i	0.668230	−	0.919740i
$227$	181.180	+	58.8689i	0.798148	+	0.259334i	0.679570	−	0.733611i	$-0.262166\pi$
$227$	181.180	+	58.8689i	0.798148	+	0.259334i	0.118578	+	0.992945i	$0.462166\pi$
$228$	−217.491	+	70.6672i	−0.953909	+	0.309944i
$229$	185.982	−	135.124i	0.812148	−	0.590060i	−0.102304	−	0.994753i	$-0.532622\pi$
$229$	185.982	−	135.124i	0.812148	−	0.590060i	0.914453	+	0.404693i	$0.132622\pi$
$230$		−	290.322i		−	1.26227i
$231$	−38.6493	+	10.4801i	−0.167313	+	0.0453685i
$232$	410.130			1.76780
$233$	111.299	+	153.190i	0.477678	+	0.657467i	0.978057	−	0.208340i	$-0.0668059\pi$
$233$	111.299	+	153.190i	0.477678	+	0.657467i	−0.500379	+	0.865807i	$0.666806\pi$
$234$	−51.0197	−	157.022i	−0.218033	−	0.671036i
$235$	−12.2168	+	37.5994i	−0.0519863	+	0.159997i
$236$	−266.191	−	193.399i	−1.12793	−	0.819486i
$237$	−23.1299	+	31.8355i	−0.0975944	+	0.134327i
$238$	−118.598	−	38.5349i	−0.498312	−	0.161912i
$239$	−106.671	+	34.6595i	−0.446322	+	0.145019i	−0.523551	−	0.851994i	$-0.675393\pi$
$239$	−106.671	+	34.6595i	−0.446322	+	0.145019i	0.0772283	+	0.997013i	$0.475393\pi$
$240$	36.2865	−	26.3637i	0.151194	−	0.109849i
$241$			118.124i			0.490141i	0.969505	+	0.245070i	$0.0788110\pi$
$241$			118.124i			0.490141i	−0.969505	+	0.245070i	$0.921189\pi$
$242$	−391.099	−	171.331i	−1.61611	−	0.707978i
$243$	−197.317			−0.812006
$244$	223.278	+	307.316i	0.915076	+	1.25949i
$245$	23.2089	+	71.4298i	0.0947304	+	0.291550i
$246$	43.1004	−	132.649i	0.175205	−	0.539225i
$247$	135.674	+	98.5731i	0.549288	+	0.399081i
$248$	447.040	−	615.298i	1.80258	−	2.48104i
$249$	68.0967	+	22.1260i	0.273481	+	0.0888593i
$250$	37.5218	−	12.1916i	0.150087	−	0.0487664i
$251$	148.903	−	108.184i	0.593240	−	0.431014i	−0.250233	−	0.968186i	$-0.580507\pi$
$251$	148.903	−	108.184i	0.593240	−	0.431014i	0.843473	+	0.537172i	$0.180507\pi$
$252$			270.099i			1.07182i
$253$	−105.921	−	390.623i	−0.418661	−	1.54397i
$254$	−412.606			−1.62443
$255$	−10.9713	−	15.1007i	−0.0430247	−	0.0592184i
$256$	−160.509	−	493.997i	−0.626990	−	1.92968i
$257$	−124.017	+	381.685i	−0.482557	+	1.48516i	0.352932	+	0.935649i	$0.385185\pi$
$257$	−124.017	+	381.685i	−0.482557	+	1.48516i	−0.835489	+	0.549507i	$0.814815\pi$
$258$	186.303	+	135.357i	0.722106	+	0.524641i
$259$	50.3234	−	69.2642i	0.194299	−	0.267429i
$260$	−103.315	−	33.5692i	−0.397366	−	0.129112i
$261$	−202.097	+	65.6652i	−0.774317	+	0.251591i
$262$	118.894	−	86.3812i	0.453792	−	0.329699i
$263$			72.9866i			0.277516i	0.990326	+	0.138758i	$0.0443110\pi$
$263$			72.9866i			0.277516i	−0.990326	+	0.138758i	$0.955689\pi$
$264$	100.480	−	124.845i	0.380607	−	0.472898i
$265$	−139.419			−0.526110
$266$	−237.576	−	326.996i	−0.893144	−	1.22931i
$267$	−30.1791	−	92.8816i	−0.113030	−	0.347871i
$268$	−94.6882	+	291.420i	−0.353314	+	1.08739i
$269$	−161.917	−	117.640i	−0.601923	−	0.437322i	0.244638	−	0.969614i	$-0.421331\pi$
$269$	−161.917	−	117.640i	−0.601923	−	0.437322i	−0.846561	+	0.532292i	$0.821331\pi$
$270$	−73.7173	+	101.463i	−0.273027	+	0.375789i
$271$	144.974	+	47.1049i	0.534959	+	0.173819i	0.564023	−	0.825759i	$-0.309253\pi$
$271$	144.974	+	47.1049i	0.534959	+	0.173819i	−0.0290645	+	0.999578i	$0.509253\pi$
$272$	185.184	−	60.1698i	0.680822	−	0.221213i
$273$	−16.9284	+	12.2992i	−0.0620089	+	0.0450521i
$274$		−	374.025i		−	1.36505i
$275$	46.0370	−	30.0931i	0.167407	−	0.109429i
$276$	288.384			1.04487
$277$	−121.855	−	167.719i	−0.439911	−	0.605485i	0.530281	−	0.847822i	$-0.322086\pi$
$277$	−121.855	−	167.719i	−0.439911	−	0.605485i	−0.970192	+	0.242336i	$0.922086\pi$
$278$	36.1857	+	111.368i	0.130164	+	0.400605i
$279$	−121.770	+	374.771i	−0.436453	+	1.34327i
$280$	111.574	+	81.0636i	0.398480	+	0.289513i
$281$	−72.0371	+	99.1506i	−0.256360	+	0.352849i	−0.917726	−	0.397214i	$-0.869977\pi$
$281$	−72.0371	+	99.1506i	−0.256360	+	0.352849i	0.661366	+	0.750063i	$0.269977\pi$
$282$	−55.0235	−	17.8782i	−0.195119	−	0.0633980i
$283$	158.184	−	51.3970i	0.558953	−	0.181615i	−0.0158971	−	0.999874i	$-0.505060\pi$
$283$	158.184	−	51.3970i	0.558953	−	0.181615i	0.574850	+	0.818259i	$0.305060\pi$
$284$	−16.7856	+	12.1954i	−0.0591042	+	0.0429417i
$285$		−	60.4994i		−	0.212279i
$286$	−222.838	−	11.0098i	−0.779155	−	0.0384957i
$287$	167.329			0.583028
$288$	−64.5301	−	88.8181i	−0.224063	−	0.308396i
$289$	64.2661	+	197.791i	0.222374	+	0.684397i
$290$	−63.6524	+	195.902i	−0.219491	+	0.675524i
$291$	42.4943	+	30.8739i	0.146028	+	0.106096i
$292$	−655.316	+	901.965i	−2.24423	+	3.08892i
$293$	48.4902	+	15.7554i	0.165496	+	0.0537728i	0.390593	−	0.920564i	$-0.372270\pi$
$293$	48.4902	+	15.7554i	0.165496	+	0.0537728i	−0.225097	+	0.974336i	$0.572270\pi$
$294$	−104.531	+	33.9643i	−0.355549	+	0.115525i
$295$	70.4220	−	51.1646i	0.238719	−	0.173439i
$296$			342.628i			1.15753i
$297$	−62.1675	+	163.412i	−0.209318	+	0.550209i
$298$	425.574			1.42810
$299$	−124.307	−	171.093i	−0.415741	−	0.572219i
$300$	12.1102	+	37.2714i	0.0403674	+	0.124238i
$301$	−85.3725	+	262.749i	−0.283629	+	0.872922i
$302$	−195.976	−	142.385i	−0.648927	−	0.471473i
$303$	−50.4203	+	69.3976i	−0.166404	+	0.229035i
$304$	600.226	+	195.025i	1.97443	+	0.641530i
$305$	−95.5763	+	31.0546i	−0.313365	+	0.101818i
$306$	−209.186	+	151.983i	−0.683615	+	0.496675i
$307$		−	388.897i		−	1.26676i	−0.773839	−	0.633382i	$-0.781666\pi$
$307$		−	388.897i		−	1.26676i	0.773839	−	0.633382i	$-0.218334\pi$
$308$	341.143	+	129.782i	1.10761	+	0.421371i
$309$	40.5954			0.131377
$310$	224.521	+	309.027i	0.724263	+	0.996862i
$311$	−12.6147	−	38.8239i	−0.0405616	−	0.124836i	0.928725	−	0.370769i	$-0.120906\pi$
$311$	−12.6147	−	38.8239i	−0.0405616	−	0.124836i	−0.969287	+	0.245933i	$0.920906\pi$
$312$	25.8769	−	79.6410i	0.0829389	−	0.255260i
$313$	414.787	+	301.360i	1.32520	+	0.962812i	0.999852	+	0.0172161i	$0.00548034\pi$
$313$	414.787	+	301.360i	1.32520	+	0.962812i	0.325345	+	0.945595i	$0.394520\pi$
$314$	388.291	−	534.437i	1.23660	−	1.70203i
$315$	−67.9587	−	22.0811i	−0.215742	−	0.0700988i
$316$	341.114	−	110.835i	1.07948	−	0.350743i
$317$	−142.274	+	103.368i	−0.448814	+	0.326083i	−0.789127	−	0.614230i	$-0.789467\pi$
$317$	−142.274	+	103.368i	−0.448814	+	0.326083i	0.340313	+	0.940312i	$0.389467\pi$
$318$		−	204.028i		−	0.641598i
$319$	−14.1702	+	286.806i	−0.0444207	+	0.899077i
$320$	87.0516			0.272036
$321$	−34.6918	−	47.7492i	−0.108074	−	0.148751i
$322$	157.508	+	484.760i	0.489155	+	1.50547i
$323$	81.1601	−	249.785i	0.251270	−	0.773328i
$324$	400.168	+	290.739i	1.23509	+	0.897343i
$325$	16.8924	−	23.2505i	0.0519767	−	0.0715399i
$326$	−121.193	−	39.3781i	−0.371759	−	0.120792i
$327$	159.500	−	51.8248i	0.487769	−	0.158486i
$328$	−541.752	+	393.606i	−1.65168	+	1.20002i
$329$		−	69.4088i		−	0.210969i
$330$	44.0387	+	67.3713i	0.133451	+	0.204156i
$331$	−97.5050			−0.294577			−0.147289	−	0.989094i	$-0.547055\pi$
$331$	−97.5050			−0.294577			−0.147289	+	0.989094i	$0.547055\pi$
$332$	−383.600	−	527.979i	−1.15542	−	1.59030i
$333$	−54.8576	−	168.834i	−0.164737	−	0.507010i
$334$	167.377	−	515.132i	0.501127	−	1.54231i
$335$	−65.5823	−	47.6484i	−0.195768	−	0.142234i
$336$	−46.2856	+	63.7067i	−0.137755	+	0.189603i
$337$	147.559	+	47.9448i	0.437860	+	0.142269i	0.519648	−	0.854380i	$-0.326063\pi$
$337$	147.559	+	47.9448i	0.437860	+	0.142269i	−0.0817878	+	0.996650i	$0.526063\pi$
$338$	456.298	−	148.260i	1.34999	−	0.438639i
$339$	−54.6237	+	39.6864i	−0.161132	+	0.117069i
$340$			170.129i			0.500379i
$341$	414.835	+	333.876i	1.21653	+	0.979109i
$342$	−838.084			−2.45054
$343$	−190.574	−	262.302i	−0.555608	−	0.764729i
$344$	−341.656	−	1051.51i	−0.993187	−	3.05671i
$345$	−23.5760	+	72.5593i	−0.0683361	+	0.210317i
$346$	−4.94214	−	3.59068i	−0.0142837	−	0.0103777i
$347$	29.5186	−	40.6288i	0.0850680	−	0.117086i	−0.764362	−	0.644787i	$-0.776946\pi$
$347$	29.5186	−	40.6288i	0.0850680	−	0.117086i	0.849430	+	0.527701i	$0.176946\pi$
$348$	−194.594	−	63.2275i	−0.559179	−	0.181688i
$349$	−146.948	+	47.7462i	−0.421053	+	0.136809i	−0.511878	−	0.859058i	$-0.671050\pi$
$349$	−146.948	+	47.7462i	−0.421053	+	0.136809i	0.0908242	+	0.995867i	$0.471050\pi$
$350$	−56.0371	+	40.7134i	−0.160106	+	0.116324i
$351$			91.3580i			0.260279i
$352$	−143.186	+	38.8263i	−0.406779	+	0.110302i
$353$	−559.143			−1.58397			−0.791987	−	0.610538i	$-0.790953\pi$
$353$	−559.143			−1.58397			−0.791987	+	0.610538i	$0.790953\pi$
$354$	74.8751	+	103.057i	0.211511	+	0.291121i
$355$	−1.69620	−	5.22037i	−0.00477803	−	0.0147053i
$356$	−275.071	+	846.582i	−0.772672	+	2.37804i
$357$	26.5117	+	19.2619i	0.0742624	+	0.0539548i
$358$	−179.403	+	246.927i	−0.501125	+	0.689739i
$359$	−646.648	−	210.109i	−1.80125	−	0.585261i	−0.801331	−	0.598221i	$-0.795874\pi$
$359$	−646.648	−	210.109i	−1.80125	−	0.585261i	−0.999916	+	0.0129603i	$0.995874\pi$
$360$	271.967	−	88.3675i	0.755465	−	0.245465i
$361$	396.644	−	288.179i	1.09874	−	0.798279i
$362$		−	632.077i		−	1.74607i
$363$	83.8331	+	74.5799i	0.230945	+	0.205454i
$364$	190.721			0.523959
$365$	−173.367	−	238.619i	−0.474978	−	0.653751i
$366$	−45.4458	−	139.868i	−0.124169	−	0.382153i
$367$	139.082	−	428.051i	0.378970	−	1.16635i	−0.561791	−	0.827279i	$-0.689887\pi$
$367$	139.082	−	428.051i	0.378970	−	1.16635i	0.940761	−	0.339071i	$-0.110113\pi$
$368$	−643.875	−	467.803i	−1.74966	−	1.27120i
$369$	203.936	−	280.693i	0.552671	−	0.760686i
$370$	−163.659	−	53.1760i	−0.442322	−	0.143719i
$371$	232.793	−	75.6389i	0.627473	−	0.203878i
$372$	−306.965	+	223.023i	−0.825173	+	0.599524i
$373$		−	396.273i		−	1.06239i	−0.847248	−	0.531197i	$-0.821742\pi$
$373$		−	396.273i		−	1.06239i	0.847248	−	0.531197i	$-0.178258\pi$
$374$	91.4446	+	337.235i	0.244504	+	0.901699i
$375$	−10.3678			−0.0276474
$376$	163.269	+	224.721i	0.434227	+	0.597662i
$377$	46.3672	+	142.703i	0.122990	+	0.378524i
$378$	68.0414	−	209.410i	0.180004	−	0.553995i
$379$	−429.812	−	312.277i	−1.13407	−	0.823950i	−0.147787	−	0.989019i	$-0.547215\pi$
$379$	−429.812	−	312.277i	−1.13407	−	0.823950i	−0.986282	+	0.165069i	$0.947215\pi$
$380$	−324.122	+	446.116i	−0.852954	+	1.17399i
$381$	103.121	+	33.5062i	0.270660	+	0.0879427i
$382$	1136.25	−	369.190i	2.97448	−	0.966467i
$383$	500.006	−	363.276i	1.30550	−	0.948500i	0.305506	−	0.952190i	$-0.401175\pi$
$383$	500.006	−	363.276i	1.30550	−	0.948500i	0.999993	+	0.00368998i	$0.00117456\pi$
$384$			177.420i			0.462031i
$385$	−60.5431	+	75.2238i	−0.157255	+	0.195386i
$386$	−31.3970			−0.0813393
$387$	336.711	+	463.443i	0.870054	+	1.19753i
$388$	−147.943	−	455.322i	−0.381297	−	1.17351i
$389$	3.92137	−	12.0687i	0.0100806	−	0.0310250i	−0.945890	−	0.324488i	$-0.894808\pi$
$389$	3.92137	−	12.0687i	0.0100806	−	0.0310250i	0.955970	+	0.293463i	$0.0948079\pi$
$390$	34.0251	+	24.7207i	0.0872438	+	0.0633864i
$391$	−194.677	+	267.950i	−0.497895	+	0.685294i
$392$	501.870	+	163.067i	1.28028	+	0.415988i
$393$	−36.7294	+	11.9341i	−0.0934591	+	0.0303667i
$394$	−569.995	+	414.126i	−1.44669	+	1.05108i
$395$			94.8876i			0.240222i
$396$	633.483	−	414.090i	1.59970	−	1.04568i
$397$	−240.779			−0.606497			−0.303249	−	0.952911i	$-0.598071\pi$
$397$	−240.779			−0.606497			−0.303249	+	0.952911i	$0.598071\pi$
$398$	378.790	+	521.359i	0.951733	+	1.30995i
$399$	32.8227	+	101.018i	0.0822623	+	0.253177i
$400$	33.4214	−	102.860i	0.0835535	−	0.257151i
$401$	581.860	+	422.746i	1.45102	+	1.05423i	0.985591	+	0.169145i	$0.0541008\pi$
$401$	581.860	+	422.746i	1.45102	+	1.05423i	0.465431	+	0.885084i	$0.345899\pi$
$402$	69.7294	−	95.9743i	0.173456	−	0.238742i
$403$	264.631	+	85.9839i	0.656653	+	0.213360i
$404$	743.588	−	241.606i	1.84056	−	0.598036i
$405$	−105.866	+	76.9165i	−0.261399	+	0.189917i
$406$		−	361.637i		−	0.890731i
$407$	−239.601	−	11.8380i	−0.588701	−	0.0290859i
$408$	−131.145			−0.321433
$409$	−62.9642	−	86.6628i	−0.153947	−	0.211890i	0.725077	−	0.688668i	$-0.241804\pi$
$409$	−62.9642	−	86.6628i	−0.153947	−	0.211890i	−0.879023	+	0.476779i	$0.841804\pi$
$410$	−103.929	−	319.860i	−0.253485	−	0.780147i
$411$	−30.3731	+	93.4789i	−0.0739006	+	0.227443i
$412$	−299.346	−	217.488i	−0.726568	−	0.527882i
$413$	−89.8276	+	123.637i	−0.217500	+	0.299363i
$414$	1005.15	+	326.592i	2.42789	+	0.788870i
$415$	164.203	−	53.3528i	0.395670	−	0.128561i
$416$	−62.7158	+	45.5657i	−0.150759	+	0.109533i
$417$		−	30.7724i		−	0.0737948i
$418$	−402.698	+	1058.52i	−0.963392	+	2.53235i
$419$	29.4752			0.0703464			0.0351732	−	0.999381i	$-0.488802\pi$
$419$	29.4752			0.0703464			0.0351732	+	0.999381i	$0.488802\pi$
$420$	−40.4416	−	55.6631i	−0.0962895	−	0.132531i
$421$	−127.694	−	393.002i	−0.303311	−	0.933496i	−0.980302	−	0.197504i	$-0.936716\pi$
$421$	−127.694	−	393.002i	−0.303311	−	0.933496i	0.676991	−	0.735991i	$-0.263284\pi$
$422$	−148.568	+	457.247i	−0.352058	+	1.08352i
$423$	−116.433	−	84.5934i	−0.275255	−	0.199984i
$424$	−575.775	+	792.487i	−1.35796	+	1.86907i
$425$	−42.8056	−	13.9084i	−0.100719	−	0.0327256i
$426$	7.63957	−	2.48225i	0.0179333	−	0.00582687i
$427$	142.739	−	103.706i	0.334283	−	0.242871i
$428$			537.957i			1.25691i
$429$	54.7993	+	20.8475i	0.127737	+	0.0485956i
$430$	555.288			1.29137
$431$	115.324	+	158.730i	0.267574	+	0.368284i	0.921569	−	0.388215i	$-0.126908\pi$
$431$	115.324	+	158.730i	0.267574	+	0.368284i	−0.653995	+	0.756499i	$0.726908\pi$
$432$	106.242	+	326.980i	0.245931	+	0.756898i
$433$	−25.9577	+	79.8895i	−0.0599484	+	0.184502i	−0.976546	−	0.215309i	$-0.930924\pi$
$433$	−25.9577	+	79.8895i	−0.0599484	+	0.184502i	0.916598	+	0.399811i	$0.130924\pi$
$434$	−542.547	−	394.183i	−1.25011	−	0.908256i
$435$	31.8169	−	43.7922i	0.0731423	−	0.100672i
$436$	−1453.79	−	472.364i	−3.33438	−	1.08340i
$437$	−1020.97	+	331.734i	−2.33632	+	0.759117i
$438$	349.199	−	253.708i	0.797258	−	0.579242i
$439$		−	139.738i		−	0.318309i	−0.987254	−	0.159154i	$-0.949123\pi$
$439$		−	139.738i		−	0.318309i	0.987254	−	0.159154i	$-0.0508768\pi$
$440$	19.0692	−	385.962i	0.0433392	−	0.877187i
$441$	−273.411			−0.619980
$442$	107.317	+	147.709i	0.242799	+	0.334184i
$443$	91.4047	+	281.315i	0.206331	+	0.635022i	0.999656	+	0.0262237i	$0.00834822\pi$
$443$	91.4047	+	281.315i	0.206331	+	0.635022i	−0.793325	+	0.608799i	$0.791652\pi$
$444$	52.8211	−	162.567i	0.118966	−	0.366141i
$445$	−190.518	−	138.419i	−0.428130	−	0.311055i
$446$	84.1364	−	115.804i	0.188647	−	0.259650i
$447$	−106.363	−	34.5593i	−0.237948	−	0.0773139i
$448$	−145.353	+	47.2280i	−0.324448	+	0.105420i
$449$	−532.550	+	386.920i	−1.18608	+	0.861737i	−0.992844	−	0.119415i	$-0.961898\pi$
$449$	−532.550	+	386.920i	−1.18608	+	0.861737i	−0.193235	+	0.981153i	$0.561898\pi$
$450$			143.622i			0.319160i
$451$	−256.532	−	392.449i	−0.568808	−	0.870175i
$452$	615.407			1.36152
$453$	37.4171	+	51.5003i	0.0825986	+	0.113687i
$454$	207.734	+	639.341i	0.457565	+	1.40824i
$455$	−15.5918	+	47.9867i	−0.0342677	+	0.105465i
$456$	−343.891	−	249.851i	−0.754146	−	0.547919i
$457$	87.2258	−	120.056i	0.190866	−	0.262705i	−0.702849	−	0.711339i	$-0.748089\pi$
$457$	87.2258	−	120.056i	0.190866	−	0.262705i	0.893716	+	0.448634i	$0.148089\pi$
$458$	771.512	+	250.679i	1.68452	+	0.547335i
$459$	136.073	−	44.2129i	0.296456	−	0.0963244i
$460$	562.580	−	408.738i	1.22300	−	0.888561i
$461$		−	500.817i		−	1.08637i	−0.839613	−	0.543185i	$-0.817218\pi$
$461$		−	500.817i		−	1.08637i	0.839613	−	0.543185i	$-0.182782\pi$
$462$	−110.084	−	88.5998i	−0.238276	−	0.191774i
$463$	−398.770			−0.861275			−0.430638	−	0.902525i	$-0.641711\pi$
$463$	−398.770			−0.861275			−0.430638	+	0.902525i	$0.641711\pi$
$464$	331.906	+	456.830i	0.715315	+	0.984547i
$465$	−31.0191	−	95.4668i	−0.0667076	−	0.205305i
$466$	−206.480	+	635.479i	−0.443090	+	1.36369i
$467$	508.794	+	369.661i	1.08949	+	0.791564i	0.979314	−	0.202347i	$-0.0648569\pi$
$467$	508.794	+	369.661i	1.08949	+	0.791564i	0.110181	+	0.993912i	$0.464857\pi$
$468$	232.445	−	319.933i	0.496677	−	0.683618i
$469$	135.356	+	43.9797i	0.288604	+	0.0937733i
$470$	−132.679	+	43.1101i	−0.282297	+	0.0917237i
$471$	−140.444	+	102.039i	−0.298183	+	0.216642i
$472$		−	611.593i		−	1.29575i
$473$	747.130	−	202.592i	1.57956	−	0.428312i
$474$	−138.860			−0.292954
$475$	−85.7481	−	118.022i	−0.180522	−	0.248468i
$476$	−92.2999	−	284.070i	−0.193907	−	0.596785i
$477$	156.837	−	482.694i	0.328799	−	1.01194i
$478$	−320.200	−	232.639i	−0.669874	−	0.486692i
$479$	−56.6925	+	78.0306i	−0.118356	+	0.162903i	−0.864084	−	0.503347i	$-0.832102\pi$
$479$	−56.6925	+	78.0306i	−0.118356	+	0.162903i	0.745728	+	0.666250i	$0.232102\pi$
$480$	26.5972	+	8.64197i	0.0554109	+	0.0180041i
$481$	−119.216	+	38.7357i	−0.247851	+	0.0805317i
$482$	−337.224	+	245.007i	−0.699634	+	0.508314i
$483$		−	133.945i		−	0.277319i
$484$	−218.619	−	999.076i	−0.451692	−	2.06421i
$485$	126.657			0.261148
$486$	−409.267	−	563.308i	−0.842114	−	1.15907i
$487$	247.215	+	760.849i	0.507628	+	1.56232i	0.796307	+	0.604892i	$0.206784\pi$
$487$	247.215	+	760.849i	0.507628	+	1.56232i	−0.288680	+	0.957426i	$0.593216\pi$
$488$	−218.192	+	671.525i	−0.447114	+	1.37607i
$489$	27.0918	+	19.6833i	0.0554024	+	0.0402522i
$490$	−155.781	+	214.414i	−0.317920	+	0.437580i
$491$	−800.353	−	260.050i	−1.63005	−	0.529634i	−0.655764	−	0.754966i	$-0.727653\pi$
$491$	−800.353	−	260.050i	−1.63005	−	0.529634i	−0.974282	+	0.225332i	$0.927653\pi$
$492$	317.725	−	103.235i	0.645783	−	0.209828i
$493$	190.110	−	138.123i	0.385620	−	0.280169i
$494$			591.783i			1.19794i
$495$	52.3992	+	193.241i	0.105857	+	0.390386i
$496$	1047.14			2.11116
$497$	5.66440	+	7.79638i	0.0113972	+	0.0156869i
$498$	78.0774	+	240.298i	0.156782	+	0.482525i
$499$	−220.886	+	679.818i	−0.442658	+	1.36236i	0.442374	+	0.896830i	$0.354136\pi$
$499$	−220.886	+	679.818i	−0.442658	+	1.36236i	−0.885032	+	0.465530i	$0.845864\pi$
$500$	76.4508	+	55.5448i	0.152902	+	0.111090i
$501$	−83.6639	+	115.153i	−0.166994	+	0.229847i
$502$	617.697	+	200.702i	1.23047	+	0.399805i
$503$	−660.549	+	214.625i	−1.31322	+	0.426690i	−0.880161	−	0.474676i	$-0.842565\pi$
$503$	−660.549	+	214.625i	−1.31322	+	0.426690i	−0.433057	+	0.901366i	$0.642565\pi$
$504$	−406.170	+	295.100i	−0.805894	+	0.585516i
$505$			206.843i			0.409591i
$506$	895.466	−	1112.60i	1.76970	−	2.19882i
$507$	−126.081			−0.248680
$508$	−580.899	−	799.539i	−1.14350	−	1.57390i
$509$	−7.78172	−	23.9497i	−0.0152883	−	0.0470524i	0.943121	−	0.332449i	$-0.107875\pi$
$509$	−7.78172	−	23.9497i	−0.0152883	−	0.0470524i	−0.958410	+	0.285396i	$0.907875\pi$
$510$	20.3537	−	62.6424i	0.0399093	−	0.122828i
$511$	418.934	+	304.373i	0.819832	+	0.595643i
$512$	627.525	−	863.714i	1.22563	−	1.68694i
$513$	441.047	+	143.305i	0.859741	+	0.279347i
$514$	−1346.88	+	437.627i	−2.62038	+	0.851415i
$515$	79.1934	−	57.5374i	0.153774	−	0.111723i
$516$			551.581i			1.06896i
$517$	−162.789	+	106.411i	−0.314873	+	0.205824i
$518$	302.116			0.583236
$519$	0.943590	+	1.29874i	0.00181809	+	0.00250239i
$520$	−62.3976	−	192.040i	−0.119995	−	0.369308i
$521$	144.330	−	444.202i	0.277025	−	0.852596i	−0.711651	−	0.702533i	$-0.752052\pi$
$521$	144.330	−	444.202i	0.277025	−	0.852596i	0.988676	−	0.150063i	$-0.0479476\pi$
$522$	−606.643	−	440.752i	−1.16215	−	0.844353i
$523$	−469.788	+	646.608i	−0.898257	+	1.23634i	0.0727642	+	0.997349i	$0.476818\pi$
$523$	−469.788	+	646.608i	−0.898257	+	1.23634i	−0.971021	+	0.238995i	$0.923182\pi$
$524$	334.775	+	108.775i	0.638884	+	0.207586i
$525$	17.3114	−	5.62481i	0.0329741	−	0.0107139i
$526$	−208.365	+	151.386i	−0.396130	+	0.287806i
$527$		−	435.768i		−	0.826884i
$528$	220.377	+	10.8881i	0.417380	+	0.0206215i
$529$	824.767			1.55911
$530$	−289.177	−	398.018i	−0.545617	−	0.750978i
$531$	97.9211	+	301.370i	0.184409	+	0.567552i
$532$	299.167	−	920.740i	0.562343	−	1.73071i
$533$	−198.202	−	144.002i	−0.371860	−	0.270172i
$534$	202.565	−	278.807i	0.379336	−	0.522111i
$535$	−135.354	−	43.9790i	−0.252997	−	0.0822038i
$536$	−541.686	+	176.004i	−1.01061	+	0.328366i
$537$	64.8896	−	47.1450i	0.120837	−	0.0877934i
$538$		−	706.250i		−	1.31273i
$539$	−131.374	+	345.326i	−0.243736	+	0.640679i
$540$	−300.398			−0.556293
$541$	631.800	+	869.598i	1.16784	+	1.60739i	0.676564	+	0.736383i	$0.263468\pi$
$541$	631.800	+	869.598i	1.16784	+	1.60739i	0.491272	+	0.871006i	$0.336532\pi$
$542$	166.222	+	511.579i	0.306683	+	0.943872i
$543$	−51.3286	+	157.973i	−0.0945278	+	0.290927i
$544$	98.2193	+	71.3605i	0.180550	+	0.131177i
$545$	237.700	−	327.166i	0.436147	−	0.600304i
$546$	−70.2245	−	22.8173i	−0.128616	−	0.0417899i
$547$	322.941	−	104.930i	0.590386	−	0.191828i	0.00143823	−	0.999999i	$-0.499542\pi$
$547$	322.941	−	104.930i	0.590386	−	0.191828i	0.588948	+	0.808171i	$0.299542\pi$
$548$	724.777	−	526.581i	1.32259	−	0.960915i
$549$		−	365.837i		−	0.666369i
$550$	181.399	+	69.0102i	0.329816	+	0.125473i
$551$	761.659			1.38232
$552$	315.078	+	433.667i	0.570793	+	0.785629i
$553$	−51.4792	−	158.437i	−0.0930909	−	0.286504i
$554$	226.064	−	695.753i	0.408057	−	1.25587i
$555$	36.5846	+	26.5803i	0.0659182	+	0.0478924i
$556$	−164.862	+	226.913i	−0.296514	+	0.408116i
$557$	393.990	+	128.015i	0.707344	+	0.229830i	0.640527	−	0.767935i	$-0.278716\pi$
$557$	393.990	+	128.015i	0.707344	+	0.229830i	0.0668164	+	0.997765i	$0.478716\pi$
$558$	−1322.48	+	429.700i	−2.37003	+	0.770071i
$559$	327.244	−	237.757i	0.585409	−	0.425325i
$560$			189.881i			0.339074i
$561$	4.53112	−	91.7101i	0.00807686	−	0.163476i
$562$	−432.475			−0.769528
$563$	−471.902	−	649.518i	−0.838193	−	1.15367i	−0.986342	−	0.164708i	$-0.947332\pi$
$563$	−471.902	−	649.518i	−0.838193	−	1.15367i	0.148150	−	0.988965i	$-0.452668\pi$
$564$	−42.8224	−	131.794i	−0.0759262	−	0.233677i
$565$	−50.3107	+	154.840i	−0.0890455	+	0.274054i
$566$	474.827	+	344.982i	0.838918	+	0.609509i
$567$	135.039	−	185.865i	0.238164	−	0.327805i
$568$	−36.6786	−	11.9176i	−0.0645750	−	0.0209817i
$569$	436.517	−	141.833i	0.767165	−	0.249267i	0.100814	−	0.994905i	$-0.467855\pi$
$569$	436.517	−	141.833i	0.767165	−	0.249267i	0.666351	+	0.745638i	$0.267855\pi$
$570$	172.716	−	125.485i	0.303010	−	0.220150i
$571$		−	203.201i		−	0.355869i	−0.984042	−	0.177935i	$-0.943058\pi$
$571$		−	203.201i		−	0.355869i	0.984042	−	0.177935i	$-0.0569416\pi$
$572$	−292.395	−	447.312i	−0.511180	−	0.782014i
$573$	−313.961			−0.547924
$574$	347.067	+	477.696i	0.604646	+	0.832223i
$575$	56.8492	+	174.964i	0.0988682	+	0.304285i
$576$	−97.9271	+	301.388i	−0.170012	+	0.523244i
$577$	−655.994	−	476.608i	−1.13690	−	0.826010i	−0.150220	−	0.988653i	$-0.547998\pi$
$577$	−655.994	−	476.608i	−1.13690	−	0.826010i	−0.986685	+	0.162643i	$0.947998\pi$
$578$	−431.362	+	593.718i	−0.746300	+	1.02719i
$579$	7.84696	+	2.54963i	0.0135526	+	0.00440351i
$580$	−469.229	+	152.462i	−0.809016	+	0.262865i
$581$	−245.230	+	178.170i	−0.422082	+	0.306661i
$582$			185.351i			0.318473i
$583$	−534.296	−	430.023i	−0.916460	−	0.737604i
$584$	−2072.33			−3.54851
$585$	61.4944	+	84.6398i	0.105119	+	0.144684i
$586$	55.5972	+	171.111i	0.0948758	+	0.291998i
$587$	18.3545	−	56.4895i	0.0312684	−	0.0962342i	−0.934204	−	0.356738i	$-0.883889\pi$
$587$	18.3545	−	56.4895i	0.0312684	−	0.0962342i	0.965473	+	0.260504i	$0.0838888\pi$
$588$	−212.983	−	154.741i	−0.362216	−	0.263165i
$589$	830.206	−	1142.68i	1.40952	−	1.94003i
$590$	292.132	+	94.9196i	0.495140	+	0.160881i
$591$	176.087	−	57.2141i	0.297947	−	0.0968090i
$592$	−381.641	+	277.279i	−0.644665	+	0.468376i
$593$			1164.75i			1.96416i	0.188457	+	0.982081i	$0.439651\pi$
$593$			1164.75i			1.96416i	−0.188457	+	0.982081i	$0.560349\pi$
$594$	−595.459	+	161.464i	−1.00246	+	0.271826i
$595$	79.0195			0.132806
$596$	599.157	+	824.669i	1.00530	+	1.38367i
$597$	−52.3322	−	161.062i	−0.0876586	−	0.269786i
$598$	230.612	−	709.749i	0.385638	−	1.18687i
$599$	−196.571	−	142.817i	−0.328165	−	0.238426i	0.411487	−	0.911416i	$-0.365010\pi$
$599$	−196.571	−	142.817i	−0.328165	−	0.238426i	−0.739651	+	0.672990i	$0.765010\pi$
$600$	−42.8169	+	58.9324i	−0.0713615	+	0.0982207i
$601$	−572.415	−	185.989i	−0.952438	−	0.309466i	−0.208732	−	0.977973i	$-0.566934\pi$
$601$	−572.415	−	185.989i	−0.952438	−	0.309466i	−0.743706	+	0.668507i	$0.766934\pi$
$602$	−927.181	+	301.260i	−1.54017	+	0.500431i
$603$	238.743	−	173.457i	0.395925	−	0.287656i
$604$		−	580.218i		−	0.960626i
$605$	269.247	+	26.6704i	0.445036	+	0.0440833i
$606$	−302.698			−0.499502
$607$	135.753	+	186.849i	0.223646	+	0.307823i	0.906065	−	0.423139i	$-0.139072\pi$
$607$	135.753	+	186.849i	0.223646	+	0.307823i	−0.682418	+	0.730962i	$0.739072\pi$
$608$	121.600	+	374.246i	0.200000	+	0.615537i
$609$	−29.3672	+	90.3829i	−0.0482220	+	0.148412i
$610$	−286.896	−	208.442i	−0.470321	−	0.341708i
$611$	−59.7326	+	82.2149i	−0.0977621	+	0.134558i
$612$	−589.017	−	191.383i	−0.962447	−	0.312718i
$613$	670.628	−	217.900i	1.09401	−	0.355465i	0.294215	−	0.955739i	$-0.404942\pi$
$613$	670.628	−	217.900i	1.09401	−	0.355465i	0.799794	+	0.600274i	$0.204942\pi$
$614$	1110.23	−	806.633i	1.80820	−	1.31373i
$615$			88.3814i			0.143710i
$616$	177.555	+	654.799i	0.288239	+	1.06299i
$617$	−181.458			−0.294097			−0.147049	−	0.989129i	$-0.546977\pi$
$617$	−181.458			−0.294097			−0.147049	+	0.989129i	$0.546977\pi$
$618$	84.2011	+	115.893i	0.136248	+	0.187529i
$619$	323.645	+	996.077i	0.522852	+	1.60917i	0.768526	+	0.639819i	$0.220991\pi$
$619$	323.645	+	996.077i	0.522852	+	1.60917i	−0.245674	+	0.969352i	$0.579009\pi$
$620$	−282.727	+	870.145i	−0.456012	+	1.40346i
$621$	−473.121	−	343.743i	−0.761870	−	0.553531i
$622$	84.6710	−	116.540i	0.136127	−	0.187363i
$623$	393.210	+	127.762i	0.631156	+	0.205075i
$624$	109.651	−	35.6277i	0.175723	−	0.0570958i
$625$	−20.2254	+	14.6946i	−0.0323607	+	0.0235114i
$626$			1809.21i			2.89012i
$627$	186.604	−	231.852i	0.297614	−	0.369780i
$628$	1582.29			2.51956
$629$	115.390	+	158.821i	0.183450	+	0.252497i
$630$	−77.9191	−	239.810i	−0.123681	−	0.380651i
$631$	−104.631	+	322.020i	−0.165817	+	0.510333i	−0.999096	−	0.0425205i	$-0.986461\pi$
$631$	−104.631	+	322.020i	−0.165817	+	0.510333i	0.833278	+	0.552854i	$0.186461\pi$
$632$	539.360	+	391.868i	0.853418	+	0.620044i
$633$	74.2626	−	102.214i	0.117318	−	0.161475i
$634$	−590.197	−	191.767i	−0.930911	−	0.302471i
$635$	248.659	−	80.7941i	0.391589	−	0.127235i
$636$	395.362	−	287.247i	0.621638	−	0.451646i
$637$			193.060i			0.303076i
$638$	−848.173	+	554.426i	−1.32942	+	0.869007i
$639$	19.9820			0.0312707
$640$	251.464	+	346.111i	0.392913	+	0.540798i
$641$	−218.541	−	672.600i	−0.340937	−	1.04930i	−0.963723	−	0.266905i	$-0.913999\pi$
$641$	−218.541	−	672.600i	−0.340937	−	1.04930i	0.622786	−	0.782393i	$-0.286001\pi$
$642$	64.3596	−	198.079i	0.100249	−	0.308534i
$643$	793.754	+	576.696i	1.23445	+	0.896884i	0.997216	−	0.0745679i	$-0.0237578\pi$
$643$	793.754	+	576.696i	1.23445	+	0.896884i	0.237238	+	0.971451i	$0.423758\pi$
$644$	−717.605	+	987.698i	−1.11429	+	1.53369i
$645$	−138.781	−	45.0928i	−0.215165	−	0.0699114i
$646$	881.433	−	286.395i	1.36445	−	0.443336i
$647$	−280.736	+	203.966i	−0.433904	+	0.315250i	−0.783208	−	0.621760i	$-0.786418\pi$
$647$	−280.736	+	203.966i	−0.433904	+	0.315250i	0.349304	+	0.937009i	$0.386418\pi$
$648$			919.417i			1.41885i
$649$	427.690	+	21.1309i	0.658998	+	0.0325591i
$650$	101.414			0.156021
$651$	103.587	+	142.575i	0.159120	+	0.219010i
$652$	−94.3195	−	290.286i	−0.144662	−	0.445223i
$653$	344.696	−	1060.87i	0.527866	−	1.62460i	−0.230712	−	0.973022i	$-0.574106\pi$
$653$	344.696	−	1060.87i	0.527866	−	1.62460i	0.758578	−	0.651582i	$-0.225894\pi$
$654$	478.780	+	347.854i	0.732079	+	0.531887i
$655$	−54.7371	+	75.3391i	−0.0835680	+	0.115022i
$656$	−876.848	−	284.905i	−1.33666	−	0.434307i
$657$	1021.17	−	331.798i	1.55429	−	0.505019i
$658$	198.150	−	143.965i	0.301141	−	0.218791i
$659$		−	68.8178i		−	0.104428i	−0.998636	−	0.0522138i	$-0.983372\pi$
$659$		−	68.8178i		−	0.104428i	0.998636	−	0.0522138i	$-0.0166277\pi$
$660$	−68.5496	+	180.188i	−0.103863	+	0.273012i
$661$	−56.9620			−0.0861754			−0.0430877	−	0.999071i	$-0.513719\pi$
$661$	−56.9620			−0.0861754			−0.0430877	+	0.999071i	$0.513719\pi$
$662$	−202.241	−	278.360i	−0.305500	−	0.420484i
$663$	−14.8266	−	45.6314i	−0.0223628	−	0.0688257i
$664$	374.860	−	1153.70i	0.564548	−	1.73750i
$665$	207.207	+	150.545i	0.311589	+	0.226383i
$666$	368.210	−	506.798i	0.552868	−	0.760958i
$667$	−913.487	−	296.810i	−1.36955	−	0.444993i
$668$	1233.86	−	400.905i	1.84709	−	0.600157i
$669$	−30.4320	+	22.1101i	−0.0454888	+	0.0330495i
$670$		−	286.057i		−	0.426950i
$671$	−462.062	−	175.784i	−0.688617	−	0.261973i
$672$	−49.0988			−0.0730637
$673$	220.445	+	303.417i	0.327556	+	0.450842i	0.940755	−	0.339086i	$-0.110118\pi$
$673$	220.445	+	303.417i	0.327556	+	0.450842i	−0.613199	+	0.789928i	$0.710118\pi$
$674$	169.186	+	520.701i	0.251018	+	0.772554i
$675$	24.5581	−	75.5821i	0.0363824	−	0.111974i
$676$	929.707	+	675.472i	1.37531	+	0.999218i
$677$	−341.663	+	470.259i	−0.504672	+	0.694621i	−0.983009	−	0.183555i	$-0.941240\pi$
$677$	−341.663	+	470.259i	−0.504672	+	0.694621i	0.478338	+	0.878176i	$0.341240\pi$
$678$	−226.596	−	73.6255i	−0.334212	−	0.108592i
$679$	−211.483	+	68.7149i	−0.311462	+	0.101200i
$680$	−255.837	+	185.877i	−0.376231	+	0.273348i
$681$		−	176.658i		−	0.259410i
$682$	−92.7269	+	1876.80i	−0.135963	+	2.75190i
$683$	−688.418			−1.00793			−0.503966	−	0.863723i	$-0.668126\pi$
$683$	−688.418			−1.00793			−0.503966	+	0.863723i	$0.668126\pi$
$684$	−1179.92	−	1624.02i	−1.72503	−	2.37430i
$685$	73.2394	+	225.408i	0.106919	+	0.329062i
$686$	353.549	−	1088.11i	0.515377	−	1.58617i
$687$	−172.465	−	125.303i	−0.251041	−	0.182392i
$688$	894.749	−	1231.52i	1.30051	−	1.78999i
$689$	−340.838	−	110.745i	−0.494685	−	0.160733i
$690$	−256.045	+	83.1940i	−0.371080	+	0.120571i
$691$	−479.696	+	348.519i	−0.694205	+	0.504369i	−0.878040	−	0.478588i	$-0.841149\pi$
$691$	−479.696	+	348.519i	−0.694205	+	0.504369i	0.183835	+	0.982957i	$0.441149\pi$
$692$		−	14.6320i		−	0.0211445i
$693$	−192.331	−	294.233i	−0.277535	−	0.424578i
$694$	177.215			0.255353
$695$	−43.6150	−	60.0308i	−0.0627553	−	0.0863753i
$696$	−117.526	−	361.707i	−0.168859	−	0.519695i
$697$	−118.564	+	364.902i	−0.170106	+	0.523532i
$698$	−441.100	−	320.478i	−0.631948	−	0.459137i
$699$	103.210	−	142.056i	0.147654	−	0.203228i
$700$	−157.787	−	51.2681i	−0.225410	−	0.0732401i
$701$	−563.333	+	183.038i	−0.803613	+	0.261110i	−0.681890	−	0.731455i	$-0.738842\pi$
$701$	−563.333	+	183.038i	−0.803613	+	0.261110i	−0.121723	+	0.992564i	$0.538842\pi$
$702$	−260.812	+	189.491i	−0.371527	+	0.269930i
$703$			636.300i			0.905120i
$704$	333.608	+	268.501i	0.473875	+	0.381394i
$705$	36.6610			0.0520014
$706$	−1159.75	−	1596.26i	−1.64270	−	2.26099i
$707$	−112.219	−	345.373i	−0.158725	−	0.488505i
$708$	−94.2860	+	290.183i	−0.133172	+	0.409862i
$709$	238.019	+	172.931i	0.335711	+	0.243909i	0.742850	−	0.669458i	$-0.233473\pi$
$709$	238.019	+	172.931i	0.335711	+	0.243909i	−0.407139	+	0.913366i	$0.633473\pi$
$710$	11.3851	−	15.6702i	0.0160353	−	0.0220707i
$711$	−328.518	−	106.742i	−0.462051	−	0.150129i
$712$	−1573.61	+	511.296i	−2.21012	+	0.718112i
$713$	−1440.99	+	1046.94i	−2.02102	+	1.46836i
$714$			115.638i			0.161959i
$715$	136.450	−	36.9999i	0.190840	−	0.0517480i
$716$	−731.066			−1.02104
$717$	61.1349	+	84.1449i	0.0852648	+	0.117357i
$718$	−741.424	−	2281.87i	−1.03262	−	3.17809i
$719$	184.687	−	568.407i	0.256866	−	0.790552i	−0.736590	−	0.676339i	$-0.763565\pi$
$719$	184.687	−	568.407i	0.256866	−	0.790552i	0.993456	−	0.114213i	$-0.0364346\pi$
$720$	318.525	+	231.422i	0.442396	+	0.321419i
$721$	−101.016	+	139.037i	−0.140105	+	0.192839i
$722$	1645.40	+	534.624i	2.27895	+	0.740477i
$723$	104.178	−	33.8493i	0.144091	−	0.0468179i
$724$	1224.82	−	889.887i	1.69175	−	1.22913i
$725$		−	130.525i		−	0.180035i
$726$	−39.0299	+	394.020i	−0.0537602	+	0.542727i
$727$	165.031			0.227003			0.113502	−	0.993538i	$-0.463793\pi$
$727$	165.031			0.227003			0.113502	+	0.993538i	$0.463793\pi$
$728$	208.375	+	286.803i	0.286229	+	0.393960i
$729$	−106.214	−	326.894i	−0.145699	−	0.448415i
$730$	321.627	−	989.867i	0.440585	−	1.35598i
$731$	−512.498	−	372.351i	−0.701091	−	0.509372i
$732$	207.051	−	284.981i	0.282856	−	0.389318i
$733$	−35.3224	−	11.4769i	−0.0481888	−	0.0156575i	0.284823	−	0.958580i	$-0.408065\pi$
$733$	−35.3224	−	11.4769i	−0.0481888	−	0.0156575i	−0.333012	+	0.942923i	$0.608065\pi$
$734$	1510.49	−	490.788i	2.05789	−	0.668649i
$735$	56.3457	−	40.9375i	0.0766608	−	0.0556973i
$736$		−	496.235i		−	0.674232i
$737$	−104.365	−	384.884i	−0.141608	−	0.522231i
$738$	1224.33			1.65898
$739$	−152.133	−	209.393i	−0.205864	−	0.283347i	0.693584	−	0.720376i	$-0.256031\pi$
$739$	−152.133	−	209.393i	−0.205864	−	0.283347i	−0.899447	+	0.437029i	$0.856031\pi$
$740$	−127.369	−	392.000i	−0.172120	−	0.529730i
$741$	48.0565	−	147.903i	0.0648536	−	0.199599i
$742$	698.785	+	507.697i	0.941758	+	0.684228i
$743$	−329.255	+	453.181i	−0.443143	+	0.609933i	−0.970907	−	0.239457i	$-0.923030\pi$
$743$	−329.255	+	453.181i	−0.443143	+	0.609933i	0.527764	+	0.849391i	$0.323030\pi$
$744$	−670.756	−	217.942i	−0.901553	−	0.292932i
$745$	−256.474	+	83.3335i	−0.344261	+	0.111857i
$746$	1131.29	−	821.932i	1.51648	−	1.10179i
$747$			628.519i			0.841391i
$748$	−524.744	+	651.986i	−0.701530	+	0.871639i
$749$	249.864			0.333597
$750$	−21.5044	−	29.5982i	−0.0286725	−	0.0394643i
$751$	−231.599	−	712.788i	−0.308387	−	0.949119i	−0.978391	−	0.206761i	$-0.933708\pi$
$751$	−231.599	−	712.788i	−0.308387	−	0.949119i	0.670004	−	0.742358i	$-0.266292\pi$
$752$	−118.180	+	363.720i	−0.157154	+	0.483671i
$753$	−138.081	−	100.322i	−0.183374	−	0.133229i
$754$	−311.222	+	428.360i	−0.412761	+	0.568116i
$755$	145.987	+	47.4340i	0.193360	+	0.0628264i
$756$	501.584	−	162.975i	0.663471	−	0.215575i
$757$	−692.859	+	503.392i	−0.915270	+	0.664982i	−0.942342	−	0.334651i	$-0.891382\pi$
$757$	−692.859	+	503.392i	−0.915270	+	0.664982i	0.0270725	+	0.999633i	$0.491382\pi$
$758$		−	1874.75i		−	2.47329i
$759$	−314.151	+	205.352i	−0.413902	+	0.270556i
$760$	−1024.99			−1.34867
$761$	−94.4945	−	130.061i	−0.124172	−	0.170907i	0.742405	−	0.669951i	$-0.233685\pi$
$761$	−94.4945	−	130.061i	−0.124172	−	0.170907i	−0.866577	+	0.499043i	$0.833685\pi$
$762$	118.235	+	363.891i	0.155165	+	0.477548i
$763$	−219.398	+	675.238i	−0.287547	+	0.884978i
$764$	2315.11	+	1682.03i	3.03025	+	2.20161i
$765$	96.3066	−	132.555i	0.125891	−	0.173274i
$766$	2074.18	+	673.942i	2.70781	+	0.879820i
$767$	212.802	−	69.1436i	0.277447	−	0.0901481i
$768$	−389.678	+	283.118i	−0.507393	+	0.368643i
$769$		−	81.4227i		−	0.105881i	−0.998598	−	0.0529407i	$-0.983141\pi$
$769$		−	81.4227i		−	0.105881i	0.998598	−	0.0529407i	$-0.0168594\pi$
$770$	−340.327	−	16.8145i	−0.441983	−	0.0218371i
$771$	372.159			0.482697
$772$	−44.2031	−	60.8404i	−0.0572579	−	0.0788088i
$773$	140.758	+	433.209i	0.182094	+	0.560426i	0.999886	−	0.0150867i	$-0.00480244\pi$
$773$	140.758	+	433.209i	0.182094	+	0.560426i	−0.817793	+	0.575513i	$0.804802\pi$
$774$	−624.660	+	1922.51i	−0.807055	+	2.48386i
$775$	−195.821	−	142.272i	−0.252672	−	0.183577i
$776$	523.068	−	719.942i	0.674057	−	0.927760i
$777$	−75.5070	−	24.5337i	−0.0971776	−	0.0315749i
$778$	42.5877	−	13.8376i	0.0547400	−	0.0177861i
$779$	−1006.10	+	730.972i	−1.29152	+	0.938346i
$780$			100.737i			0.129150i
$781$	9.60130	−	25.2378i	0.0122936	−	0.0323147i
$782$	−1168.74			−1.49456
$783$	243.885	+	335.679i	0.311476	+	0.428709i
$784$	224.514	+	690.982i	0.286369	+	0.881354i
$785$	−129.355	+	398.113i	−0.164783	+	0.507151i
$786$	−110.252	−	80.1031i	−0.140270	−	0.101912i
$787$	70.2003	−	96.6224i	0.0891999	−	0.122773i	−0.762085	−	0.647477i	$-0.775824\pi$
$787$	70.2003	−	96.6224i	0.0891999	−	0.122773i	0.851285	+	0.524704i	$0.175824\pi$
$788$	−1604.97	−	521.486i	−2.03676	−	0.661784i
$789$	64.3694	−	20.9149i	0.0815836	−	0.0265081i
$790$	−270.888	+	196.812i	−0.342896	+	0.249129i
$791$		−	285.837i		−	0.361362i
$792$	1314.82	+	500.202i	1.66013	+	0.631568i
$793$	−258.323			−0.325754
$794$	−499.414	−	687.385i	−0.628985	−	0.865724i
$795$	39.9517	+	122.959i	0.0502537	+	0.154665i
$796$	−476.989	+	1468.02i	−0.599233	+	1.84425i
$797$	1109.47	+	806.080i	1.39206	+	1.01139i	0.995636	+	0.0933265i	$0.0297500\pi$
$797$	1109.47	+	806.080i	1.39206	+	1.01139i	0.396427	+	0.918066i	$0.370250\pi$
$798$	−220.309	+	303.230i	−0.276077	+	0.379987i
$799$	151.363	+	49.1808i	0.189440	+	0.0615529i
$800$	64.1345	−	20.8386i	0.0801681	−	0.0260482i
$801$	693.553	−	503.895i	0.865858	−	0.629083i
$802$			2537.95i			3.16453i
$803$	71.6002	−	1449.19i	0.0891659	−	1.80472i
$804$	284.147			0.353417
$805$	−189.846	−	261.300i	−0.235833	−	0.324597i
$806$	303.417	+	933.822i	0.376448	+	1.15859i
$807$	−57.3519	+	176.511i	−0.0710680	+	0.218725i
$808$	1175.74	+	854.225i	1.45512	+	1.05721i
$809$	−7.99326	+	11.0018i	−0.00988042	+	0.0135992i	−0.813929	−	0.580965i	$-0.802675\pi$
$809$	−7.99326	+	11.0018i	−0.00988042	+	0.0135992i	0.804048	+	0.594564i	$0.202675\pi$
$810$	−439.167	−	142.694i	−0.542182	−	0.176166i
$811$	−203.261	+	66.0435i	−0.250630	+	0.0814346i	−0.431638	−	0.902047i	$-0.642064\pi$
$811$	−203.261	+	66.0435i	−0.250630	+	0.0814346i	0.181008	+	0.983482i	$0.442064\pi$
$812$	700.772	−	509.141i	0.863020	−	0.627020i
$813$		−	141.356i		−	0.173869i
$814$	−463.175	−	708.575i	−0.569011	−	0.870485i
$815$	80.7486			0.0990780
$816$	−106.132	−	146.078i	−0.130063	−	0.179017i
$817$	−634.495	−	1952.78i	−0.776616	−	2.39018i
$818$	116.810	−	359.505i	0.142800	−	0.439492i
$819$	−148.599	−	107.963i	−0.181439	−	0.131823i
$820$	473.499	−	651.715i	0.577438	−	0.794775i
$821$	1240.59	+	403.092i	1.51107	+	0.490977i	0.943224	−	0.332157i	$-0.107776\pi$
$821$	1240.59	+	403.092i	1.51107	+	0.490977i	0.567848	+	0.823134i	$0.307776\pi$
$822$	−329.865	+	107.180i	−0.401296	+	0.130389i
$823$	−231.338	+	168.077i	−0.281091	+	0.204225i	−0.719393	−	0.694603i	$-0.755580\pi$
$823$	−231.338	+	168.077i	−0.281091	+	0.204225i	0.438302	+	0.898828i	$0.355580\pi$
$824$		−	687.770i		−	0.834672i
$825$	−39.7324	−	31.9782i	−0.0481605	−	0.0387615i
$826$	−539.279			−0.652881
$827$	−328.834	−	452.602i	−0.397623	−	0.547282i	0.562522	−	0.826782i	$-0.309831\pi$
$827$	−328.834	−	452.602i	−0.397623	−	0.547282i	−0.960146	+	0.279501i	$0.909831\pi$
$828$	782.262	+	2407.55i	0.944761	+	2.90767i
$829$	−279.385	+	859.857i	−0.337014	+	1.03722i	0.628707	+	0.777642i	$0.283584\pi$
$829$	−279.385	+	859.857i	−0.337014	+	1.03722i	−0.965721	+	0.259580i	$0.916416\pi$
$830$	492.896	+	358.110i	0.593851	+	0.431458i
$831$	−112.999	+	155.530i	−0.135980	+	0.187160i
$832$	212.815	+	69.1477i	0.255787	+	0.0831103i
$833$	287.553	−	93.4317i	0.345202	−	0.112163i
$834$	87.8501	−	63.8268i	0.105336	−	0.0765310i
$835$			343.221i			0.411044i
$836$	−2618.13	+	709.932i	−3.13174	+	0.849201i
$837$	769.439			0.919281
$838$	61.1361	+	84.1466i	0.0729548	+	0.100414i
$839$	−49.7340	−	153.066i	−0.0592778	−	0.182438i	0.917033	−	0.398811i	$-0.130577\pi$
$839$	−49.7340	−	153.066i	−0.0592778	−	0.182438i	−0.976311	+	0.216373i	$0.930577\pi$
$840$	39.5202	−	121.631i	0.0470479	−	0.144799i
$841$	−129.060	−	93.7676i	−0.153460	−	0.111495i
$842$	857.096	−	1179.69i	1.01793	−	1.40106i
$843$	108.087	+	35.1196i	0.128217	+	0.0416603i
$844$	−1095.21	+	355.855i	−1.29764	+	0.421629i
$845$	−245.958	+	178.699i	−0.291075	+	0.211478i
$846$		−	507.856i		−	0.600303i
$847$	−464.039	+	101.542i	−0.547862	+	0.119884i
$848$	−1348.68			−1.59043
$849$	−90.6575	−	124.779i	−0.106782	−	0.146972i
$850$	−49.0794	−	151.051i	−0.0577405	−	0.177707i
$851$	247.959	−	763.139i	0.291374	−	0.896756i
$852$	15.5656	+	11.3091i	0.0182695	+	0.0132736i
$853$	859.656	−	1183.22i	1.00780	−	1.38712i	0.0873903	−	0.996174i	$-0.472147\pi$
$853$	859.656	−	1183.22i	1.00780	−	1.38712i	0.920413	−	0.390948i	$-0.127853\pi$
$854$	592.125	+	192.393i	0.693355	+	0.225285i
$855$	505.075	−	164.109i	0.590731	−	0.191940i
$856$	−808.971	+	587.752i	−0.945059	+	0.686626i
$857$		−	874.204i		−	1.02007i	−0.860152	−	0.510037i	$-0.829632\pi$
$857$		−	874.204i		−	1.02007i	0.860152	−	0.510037i	$-0.170368\pi$
$858$	54.1462	+	199.684i	0.0631075	+	0.232732i
$859$	984.004			1.14552			0.572761	−	0.819722i	$-0.305872\pi$
$859$	984.004			1.14552			0.572761	+	0.819722i	$0.305872\pi$
$860$	781.778	+	1076.02i	0.909044	+	1.25119i
$861$	−47.9494	−	147.573i	−0.0556904	−	0.171397i
$862$	−213.948	+	658.463i	−0.248199	+	0.763878i
$863$	1110.66	+	806.939i	1.28697	+	0.935039i	0.999740	−	0.0228217i	$-0.00726500\pi$
$863$	1110.66	+	806.939i	1.28697	+	0.935039i	0.287232	+	0.957861i	$0.407265\pi$
$864$	−126.002	+	173.427i	−0.145835	+	0.200725i
$865$	3.68151	+	1.19620i	0.00425608	+	0.00138289i
$866$	−281.911	+	91.5985i	−0.325533	+	0.105772i
$867$	156.023	−	113.357i	0.179957	−	0.130746i
$868$		−	1606.30i		−	1.85057i
$869$	−292.670	+	363.638i	−0.336790	+	0.418456i
$870$	191.013			0.219555
$871$	−122.480	−	168.580i	−0.140620	−	0.193547i
$872$	−878.020	−	2702.27i	−1.00690	−	3.09893i
$873$	−142.480	+	438.508i	−0.163207	+	0.502300i
$874$	−3064.70	−	2226.64i	−3.50653	−	2.54764i
$875$	25.7988	−	35.5090i	0.0294843	−	0.0405817i
$876$	983.260	+	319.481i	1.12244	+	0.364704i
$877$	−771.335	+	250.622i	−0.879516	+	0.285772i	−0.713756	−	0.700394i	$-0.753008\pi$
$877$	−771.335	+	250.622i	−0.879516	+	0.285772i	−0.165760	+	0.986166i	$0.553008\pi$
$878$	398.927	−	289.838i	0.454359	−	0.330111i
$879$		−	47.2800i		−	0.0537884i
$880$	445.343	−	291.108i	0.506071	−	0.330804i
$881$	−348.997			−0.396137			−0.198069	−	0.980188i	$-0.563467\pi$
$881$	−348.997			−0.396137			−0.198069	+	0.980188i	$0.563467\pi$
$882$	−567.098	−	780.543i	−0.642968	−	0.884970i
$883$	302.060	+	929.644i	0.342084	+	1.05282i	0.963127	+	0.269049i	$0.0867092\pi$
$883$	302.060	+	929.644i	0.342084	+	1.05282i	−0.621043	+	0.783776i	$0.713291\pi$
$884$	−135.139	+	415.914i	−0.152872	+	0.470491i
$885$	−65.3038	−	47.4460i	−0.0737896	−	0.0536113i
$886$	−613.519	+	844.436i	−0.692459	+	0.953088i
$887$	14.4247	+	4.68686i	0.0162623	+	0.00528395i	0.317137	−	0.948380i	$-0.397279\pi$
$887$	14.4247	+	4.68686i	0.0162623	+	0.00528395i	−0.300875	+	0.953664i	$0.597279\pi$
$888$	302.175	−	98.1827i	0.340287	−	0.110566i
$889$	−371.360	+	269.809i	−0.417728	+	0.303497i
$890$		−	831.000i		−	0.933708i
$891$	−642.952	−	31.7663i	−0.721608	−	0.0356525i
$892$	342.856			0.384368
$893$	303.210	+	417.333i	0.339541	+	0.467338i
$894$	−121.952	−	375.329i	−0.136411	−	0.419831i
$895$	59.7661	−	183.941i	0.0667777	−	0.205521i
$896$	−607.652	−	441.485i	−0.678184	−	0.492729i
$897$	−115.272	+	158.659i	−0.128509	+	0.176877i
$898$	−2209.18	−	717.807i	−2.46011	−	0.799340i
$899$	1201.88	−	390.515i	1.33691	−	0.434388i
$900$	−278.308	+	202.202i	−0.309231	+	0.224669i
$901$			561.257i			0.622926i
$902$	588.287	−	1546.36i	0.652203	−	1.71437i
$903$	256.192			0.283712
$904$	672.370	+	925.438i	0.743773	+	1.02372i
$905$	123.770	+	380.924i	0.136762	+	0.420910i
$906$	−69.4156	+	213.639i	−0.0766177	+	0.235805i
$907$	−450.207	−	327.095i	−0.496369	−	0.360634i	0.311259	−	0.950325i	$-0.399249\pi$
$907$	−450.207	−	327.095i	−0.496369	−	0.360634i	−0.807629	+	0.589692i	$0.799249\pi$
$908$	−946.436	+	1302.66i	−1.04233	+	1.43464i
$909$	−716.130	−	232.685i	−0.787821	−	0.255979i
$910$	−169.334	+	55.0199i	−0.186081	+	0.0604614i
$911$	264.619	−	192.257i	0.290471	−	0.211039i	−0.433001	−	0.901394i	$-0.642545\pi$
$911$	264.619	−	192.257i	0.290471	−	0.211039i	0.723472	+	0.690354i	$0.242545\pi$
$912$		−	585.246i		−	0.641717i
$913$	793.837	+	302.002i	0.869482	+	0.330780i
$914$	523.660			0.572932
$915$	54.7763	+	75.3931i	0.0598648	+	0.0823968i
$916$	600.434	+	1847.94i	0.655495	+	2.01741i
$917$	50.5226	−	155.492i	0.0550955	−	0.169567i
$918$	408.458	+	296.762i	0.444943	+	0.323270i
$919$	312.999	−	430.806i	0.340586	−	0.468776i	−0.604026	−	0.796964i	$-0.706438\pi$
$919$	312.999	−	430.806i	0.340586	−	0.468776i	0.944612	+	0.328188i	$0.106438\pi$
$920$	1229.31	+	399.426i	1.33620	+	0.434158i
$921$	−342.981	+	111.441i	−0.372401	+	0.121000i
$922$	1429.75	−	1038.77i	1.55070	−	1.12665i
$923$		−	14.1096i		−	0.0152866i
$924$	16.7023	−	338.056i	0.0180761	−	0.365861i
$925$	109.042			0.117884
$926$	−827.113	−	1138.42i	−0.893210	−	1.22940i
$927$	110.118	+	338.907i	0.118789	+	0.365596i
$928$	−108.798	+	334.847i	−0.117240	+	0.360826i
$929$	−617.340	−	448.524i	−0.664521	−	0.482803i	0.203666	−	0.979041i	$-0.434714\pi$
$929$	−617.340	−	448.524i	−0.664521	−	0.482803i	−0.868187	+	0.496238i	$0.834714\pi$
$930$	208.203	−	286.567i	0.223875	−	0.308137i
$931$	932.031	+	302.835i	1.00111	+	0.325279i
$932$	−1522.12	+	494.566i	−1.63317	+	0.530650i
$933$	−30.6253	+	22.2506i	−0.0328246	+	0.0238484i
$934$			2219.26i			2.37608i
$935$	−121.145	−	185.330i	−0.129567	−	0.198214i
$936$	735.071			0.785332
$937$	930.495	+	1280.72i	0.993058	+	1.36683i	0.929489	+	0.368850i	$0.120248\pi$
$937$	930.495	+	1280.72i	0.993058	+	1.36683i	0.0635691	+	0.997977i	$0.479752\pi$
$938$	155.194	+	477.638i	0.165452	+	0.509209i
$939$	146.919	−	452.172i	0.156464	−	0.481546i
$940$	−270.334	−	196.409i	−0.287590	−	0.208946i
$941$	−325.495	+	448.005i	−0.345903	+	0.476094i	−0.946154	−	0.323717i	$-0.895067\pi$
$941$	−325.495	+	448.005i	−0.345903	+	0.476094i	0.600251	+	0.799812i	$0.295067\pi$
$942$	−582.606	−	189.300i	−0.618477	−	0.200956i
$943$	1491.50	−	484.619i	1.58166	−	0.513912i
$944$	681.233	−	494.945i	0.721645	−	0.524306i
$945$			139.525i			0.147646i
$946$	2128.03	+	1712.72i	2.24950	+	1.81049i
$947$	945.630			0.998553			0.499276	−	0.866443i	$-0.333599\pi$
$947$	945.630			0.998553			0.499276	+	0.866443i	$0.333599\pi$
$948$	−195.498	−	269.080i	−0.206222	−	0.283840i
$949$	−234.287	−	721.062i	−0.246878	−	0.759813i
$950$	159.078	−	489.593i	0.167451	−	0.515361i
$951$	131.934	+	95.8555i	0.138732	+	0.100794i
$952$	326.336	−	449.163i	0.342790	−	0.471810i
$953$	−602.472	−	195.755i	−0.632185	−	0.205409i	−0.0246421	−	0.999696i	$-0.507845\pi$
$953$	−602.472	−	195.755i	−0.632185	−	0.205409i	−0.607543	+	0.794287i	$0.707845\pi$
$954$	1703.32	−	553.441i	1.78545	−	0.580127i
$955$	−612.474	+	444.989i	−0.641334	+	0.465957i
$956$		−	948.003i		−	0.991635i
$957$	257.004	−	69.6892i	0.268552	−	0.0728205i
$958$	−340.353			−0.355275
$959$	−244.580	−	336.636i	−0.255037	−	0.351028i
$960$	−24.9453	−	76.7738i	−0.0259847	−	0.0799727i
$961$	427.212	−	1314.82i	0.444549	−	1.36818i
$962$	−357.857	−	259.999i	−0.371993	−	0.270269i
$963$	304.527	−	419.145i	0.316227	−	0.435249i
$964$	−949.540	−	308.524i	−0.985000	−	0.320046i
$965$	18.9215	−	6.14798i	0.0196078	−	0.00637096i
$966$	382.391	−	277.823i	0.395850	−	0.287602i
$967$		−	855.136i		−	0.884318i	−0.896937	−	0.442159i	$-0.854213\pi$
$967$		−	855.136i		−	0.884318i	0.896937	−	0.442159i	$-0.145787\pi$
$968$	1263.54	−	1420.31i	1.30531	−	1.46726i
$969$	−243.551			−0.251343
$970$	262.706	+	361.583i	0.270831	+	0.372766i
$971$	306.329	+	942.784i	0.315478	+	0.970942i	0.975557	+	0.219746i	$0.0705227\pi$
$971$	306.329	+	942.784i	0.315478	+	0.970942i	−0.660079	+	0.751196i	$0.729477\pi$
$972$	515.368	−	1586.14i	0.530214	−	1.63183i
$973$	105.394	+	76.5730i	0.108318	+	0.0786979i
$974$	−1659.33	+	2283.88i	−1.70363	+	2.34484i
$975$	−25.3460	−	8.23543i	−0.0259959	−	0.00844659i
$976$	−924.565	+	300.409i	−0.947300	+	0.307796i
$977$	−46.4848	+	33.7732i	−0.0475791	+	0.0345682i	−0.611321	−	0.791383i	$-0.709361\pi$
$977$	−46.4848	+	33.7732i	−0.0475791	+	0.0345682i	0.563742	+	0.825951i	$0.309361\pi$
$978$			118.169i			0.120827i
$979$	−303.183	−	1118.10i	−0.309686	−	1.14208i
$980$	−634.808			−0.647763
$981$	865.312	+	1191.00i	0.882071	+	1.21407i
$982$	−917.657	−	2824.26i	−0.934477	−	2.87603i
$983$	218.826	−	673.476i	0.222610	−	0.685123i	−0.775915	−	0.630837i	$-0.782712\pi$
$983$	218.826	−	673.476i	0.222610	−	0.685123i	0.998525	−	0.0542862i	$-0.0172883\pi$
$984$	502.378	+	364.999i	0.510546	+	0.370934i
$985$	262.418	−	361.188i	0.266415	−	0.366688i
$986$	788.638	+	256.244i	0.799835	+	0.259882i
$987$	−61.2140	+	19.8896i	−0.0620203	+	0.0201516i
$988$	−1146.74	+	833.159i	−1.16067	+	0.843278i
$989$			2589.30i			2.61810i
$990$	−442.987	+	550.403i	−0.447461	+	0.555963i
$991$	1006.83			1.01598			0.507989	−	0.861363i	$-0.330389\pi$
$991$	1006.83			1.01598			0.507989	+	0.861363i	$0.330389\pi$
$992$	383.765	+	528.207i	0.386860	+	0.532467i
$993$	27.9408	+	85.9930i	0.0281378	+	0.0865992i
$994$	−10.5085	+	32.3418i	−0.0105719	+	0.0325370i
$995$	−330.369	−	240.027i	−0.332029	−	0.241233i
$996$	−355.720	+	489.606i	−0.357148	+	0.491573i
$997$	537.627	+	174.686i	0.539245	+	0.175211i	0.565961	−	0.824432i	$-0.308505\pi$
$997$	537.627	+	174.686i	0.539245	+	0.175211i	−0.0267164	+	0.999643i	$0.508505\pi$
$998$	−2398.92	+	779.456i	−2.40373	+	0.781018i
$999$	−280.431	+	203.745i	−0.280712	+	0.203949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.i.d.41.3	✓	12
5.2	odd	4		275.3.q.f.74.1		24
5.3	odd	4		275.3.q.f.74.6		24
5.4	even	2		275.3.x.f.151.1		12
11.2	odd	10		605.3.c.d.241.11		12
11.7	odd	10	inner	55.3.i.d.51.3	yes	12
11.9	even	5		605.3.c.d.241.2		12
55.7	even	20		275.3.q.f.249.6		24
55.18	even	20		275.3.q.f.249.1		24
55.29	odd	10		275.3.x.f.51.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.d.41.3	✓	12	1.1	even	1	trivial
55.3.i.d.51.3	yes	12	11.7	odd	10	inner
275.3.q.f.74.1		24	5.2	odd	4
275.3.q.f.74.6		24	5.3	odd	4
275.3.q.f.249.1		24	55.18	even	20
275.3.q.f.249.6		24	55.7	even	20
275.3.x.f.51.1		12	55.29	odd	10
275.3.x.f.151.1		12	5.4	even	2
605.3.c.d.241.2		12	11.9	even	5
605.3.c.d.241.11		12	11.2	odd	10

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.07416 + 2.85483i) q^{2} +(-0.286558 - 0.881935i) q^{3} +(-2.61187 + 8.03851i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.92341 - 2.64735i) q^{6} +(3.73363 + 1.21313i) q^{7} +(-14.9418 + 4.85489i) q^{8} +(6.58546 - 4.78462i) q^{9} +O(q^{10})\)	\(q+(2.07416 + 2.85483i) q^{2} +(-0.286558 - 0.881935i) q^{3} +(-2.61187 + 8.03851i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.92341 - 2.64735i) q^{6} +(3.73363 + 1.21313i) q^{7} +(-14.9418 + 4.85489i) q^{8} +(6.58546 - 4.78462i) q^{9} -7.89056i q^{10} +(-2.87880 - 10.6166i) q^{11} +7.83789 q^{12} +(-3.37849 - 4.65009i) q^{13} +(4.28086 + 13.1751i) q^{14} +(-0.640763 + 1.97207i) q^{15} +(-17.4997 - 12.7143i) q^{16} +(-5.29106 + 7.28252i) q^{17} +(27.3186 + 8.87634i) q^{18} +(-27.7487 + 9.01609i) q^{19} +(15.2902 - 11.1090i) q^{20} -3.64045i q^{21} +(24.3376 - 30.2390i) q^{22} +36.7936 q^{23} +(8.56339 + 11.7865i) q^{24} +(1.54508 + 4.75528i) q^{25} +(6.26771 - 19.2900i) q^{26} +(-12.8588 - 9.34246i) q^{27} +(-19.5035 + 26.8443i) q^{28} +(-24.8274 - 8.06690i) q^{29} +(-6.95896 + 2.26110i) q^{30} +(-39.1642 + 28.4544i) q^{31} -13.4870i q^{32} +(-8.53822 + 5.58119i) q^{33} -31.7649 q^{34} +(-5.15975 - 7.10179i) q^{35} +(21.2608 + 65.4341i) q^{36} +(6.73919 - 20.7411i) q^{37} +(-83.2945 - 60.5170i) q^{38} +(-3.13294 + 4.31213i) q^{39} +(33.4109 + 10.8559i) q^{40} +(40.5371 - 13.1713i) q^{41} +(10.3929 - 7.55087i) q^{42} +70.3737i q^{43} +(92.8608 + 4.58797i) q^{44} -18.2018 q^{45} +(76.3156 + 105.039i) q^{46} +(-5.46351 - 16.8149i) q^{47} +(-6.19847 + 19.0769i) q^{48} +(-27.1735 - 19.7427i) q^{49} +(-10.3708 + 14.2742i) q^{50} +(7.93890 + 2.57951i) q^{51} +(46.2040 - 15.0126i) q^{52} +(50.4423 - 36.6485i) q^{53} -56.0874i q^{54} +(-8.74592 + 22.9893i) q^{55} -61.6768 q^{56} +(15.9032 + 21.8889i) q^{57} +(-28.4662 - 87.6100i) q^{58} +(-12.0295 + 37.0230i) q^{59} +(-14.1789 - 10.3016i) q^{60} +(26.4166 - 36.3594i) q^{61} +(-162.465 - 52.7881i) q^{62} +(30.3921 - 9.87498i) q^{63} +(-31.4956 + 22.8829i) q^{64} +12.8525i q^{65} +(-33.6430 - 12.7989i) q^{66} +36.2530 q^{67} +(-44.7211 - 61.5533i) q^{68} +(-10.5435 - 32.4495i) q^{69} +(9.57229 - 29.4605i) q^{70} +(1.98595 + 1.44287i) q^{71} +(-75.1699 + 103.462i) q^{72} +(125.450 + 40.7610i) q^{73} +(73.1905 - 23.7810i) q^{74} +(3.75109 - 2.72533i) q^{75} -246.607i q^{76} +(2.13097 - 43.1309i) q^{77} -18.8086 q^{78} +(-24.9427 - 34.3307i) q^{79} +(14.9465 + 46.0006i) q^{80} +(18.0841 - 55.6573i) q^{81} +(121.682 + 88.4072i) q^{82} +(-45.3846 + 62.4666i) q^{83} +(29.2638 + 9.50839i) q^{84} +(19.1432 - 6.22001i) q^{85} +(-200.905 + 145.966i) q^{86} +24.2077i q^{87} +(94.5569 + 144.655i) q^{88} +105.316 q^{89} +(-37.7533 - 51.9630i) q^{90} +(-6.97287 - 21.4603i) q^{91} +(-96.1001 + 295.766i) q^{92} +(36.3177 + 26.3864i) q^{93} +(36.6717 - 50.4742i) q^{94} +(62.0479 + 20.1606i) q^{95} +(-11.8946 + 3.86481i) q^{96} +(-45.8248 + 33.2937i) q^{97} -118.525i q^{98} +(-69.7546 - 56.1413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 5 q^{2} - 13 q^{3} + 13 q^{4} - 15 q^{5} + 20 q^{6} - 5 q^{7} - 35 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q + 5 * q^2 - 13 * q^3 + 13 * q^4 - 15 * q^5 + 20 * q^6 - 5 * q^7 - 35 * q^8 + 4 * q^9	\( 12 q + 5 q^{2} - 13 q^{3} + 13 q^{4} - 15 q^{5} + 20 q^{6} - 5 q^{7} - 35 q^{8} + 4 q^{9} + 12 q^{11} - 2 q^{12} + 70 q^{13} - 60 q^{14} + 35 q^{15} - 43 q^{16} - 15 q^{17} - 30 q^{18} - 80 q^{19} + 20 q^{20} - 10 q^{22} + 42 q^{23} + 210 q^{24} - 15 q^{25} - 120 q^{26} - 109 q^{27} + 140 q^{28} + 5 q^{29} - 20 q^{30} - 46 q^{31} + 42 q^{33} + 10 q^{34} + 20 q^{35} - 39 q^{36} - 42 q^{37} - 130 q^{38} - 285 q^{39} - 25 q^{40} + 230 q^{41} + 135 q^{42} + 488 q^{44} - 50 q^{45} + 205 q^{46} + 58 q^{47} - 323 q^{48} - 212 q^{49} - 25 q^{50} + 360 q^{51} + 410 q^{52} - 43 q^{53} - 80 q^{55} - 410 q^{56} + 270 q^{57} - 450 q^{58} - 74 q^{59} - 25 q^{60} - 290 q^{61} - 350 q^{62} + 295 q^{63} - 7 q^{64} + 185 q^{66} - 212 q^{67} + 55 q^{68} - 73 q^{69} + 160 q^{70} - 276 q^{71} - 555 q^{72} + 645 q^{73} - 100 q^{74} + 10 q^{75} - 140 q^{77} + 360 q^{78} + 235 q^{79} + 140 q^{80} - 30 q^{81} + 215 q^{82} + 60 q^{83} - 580 q^{84} + 65 q^{85} - 480 q^{86} - 165 q^{88} - 114 q^{89} + 145 q^{90} + 160 q^{91} + 33 q^{92} + 129 q^{93} + 375 q^{94} + 50 q^{95} + 265 q^{96} + 63 q^{97} + 669 q^{99}+O(q^{100}) \) 12 * q + 5 * q^2 - 13 * q^3 + 13 * q^4 - 15 * q^5 + 20 * q^6 - 5 * q^7 - 35 * q^8 + 4 * q^9 + 12 * q^11 - 2 * q^12 + 70 * q^13 - 60 * q^14 + 35 * q^15 - 43 * q^16 - 15 * q^17 - 30 * q^18 - 80 * q^19 + 20 * q^20 - 10 * q^22 + 42 * q^23 + 210 * q^24 - 15 * q^25 - 120 * q^26 - 109 * q^27 + 140 * q^28 + 5 * q^29 - 20 * q^30 - 46 * q^31 + 42 * q^33 + 10 * q^34 + 20 * q^35 - 39 * q^36 - 42 * q^37 - 130 * q^38 - 285 * q^39 - 25 * q^40 + 230 * q^41 + 135 * q^42 + 488 * q^44 - 50 * q^45 + 205 * q^46 + 58 * q^47 - 323 * q^48 - 212 * q^49 - 25 * q^50 + 360 * q^51 + 410 * q^52 - 43 * q^53 - 80 * q^55 - 410 * q^56 + 270 * q^57 - 450 * q^58 - 74 * q^59 - 25 * q^60 - 290 * q^61 - 350 * q^62 + 295 * q^63 - 7 * q^64 + 185 * q^66 - 212 * q^67 + 55 * q^68 - 73 * q^69 + 160 * q^70 - 276 * q^71 - 555 * q^72 + 645 * q^73 - 100 * q^74 + 10 * q^75 - 140 * q^77 + 360 * q^78 + 235 * q^79 + 140 * q^80 - 30 * q^81 + 215 * q^82 + 60 * q^83 - 580 * q^84 + 65 * q^85 - 480 * q^86 - 165 * q^88 - 114 * q^89 + 145 * q^90 + 160 * q^91 + 33 * q^92 + 129 * q^93 + 375 * q^94 + 50 * q^95 + 265 * q^96 + 63 * q^97 + 669 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more