LMFDB - Embedded newform 105.3.n.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(31,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("105.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
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} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 456 x^{8} - 1050 x^{7} + 1999 x^{6} - 2844 x^{5} + 2949 x^{4} + \cdots + 36 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 456x^8 - 1050x^7 + 1999x^6 - 2844x^5 + 2949x^4 - 2136x^3 + 1020x^2 - 288*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$0.500000 - 2.96550i$ of defining polynomial
Character	$\chi$	$=$	105.31
Dual form			105.3.n.b.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25588 - 2.17524i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.15446 + 1.99958i) q^{4} +(1.93649 - 1.11803i) q^{5} -4.35049i q^{6} +(6.75110 - 1.85004i) q^{7} -4.24760 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.25588 - 2.17524i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.15446 + 1.99958i) q^{4} +(1.93649 - 1.11803i) q^{5} -4.35049i q^{6} +(6.75110 - 1.85004i) q^{7} -4.24760 q^{8} +(1.50000 + 2.59808i) q^{9} +(-4.86399 - 2.80823i) q^{10} +(9.04589 - 15.6679i) q^{11} +(-3.46337 + 1.99958i) q^{12} +3.19366i q^{13} +(-12.5028 - 12.3619i) q^{14} +3.87298 q^{15} +(9.95229 + 17.2379i) q^{16} +(-29.0590 - 16.7772i) q^{17} +(3.76763 - 6.52573i) q^{18} +(-6.07005 + 3.50455i) q^{19} +5.16288i q^{20} +(11.7288 + 3.07156i) q^{21} -45.4421 q^{22} +(11.4822 + 19.8878i) q^{23} +(-6.37140 - 3.67853i) q^{24} +(2.50000 - 4.33013i) q^{25} +(6.94698 - 4.01084i) q^{26} +5.19615i q^{27} +(-4.09455 + 15.6351i) q^{28} +33.8290 q^{29} +(-4.86399 - 8.42468i) q^{30} +(29.0932 + 16.7970i) q^{31} +(16.5025 - 28.5832i) q^{32} +(27.1377 - 15.6679i) q^{33} +84.2806i q^{34} +(11.0050 - 11.1305i) q^{35} -6.92674 q^{36} +(9.65886 + 16.7296i) q^{37} +(15.2465 + 8.80256i) q^{38} +(-2.76579 + 4.79048i) q^{39} +(-8.22544 + 4.74896i) q^{40} +76.0832i q^{41} +(-8.04858 - 29.3706i) q^{42} -45.0254 q^{43} +(20.8862 + 36.1759i) q^{44} +(5.80948 + 3.35410i) q^{45} +(28.8405 - 49.9533i) q^{46} +(-46.3954 + 26.7864i) q^{47} +34.4757i q^{48} +(42.1547 - 24.9796i) q^{49} -12.5588 q^{50} +(-29.0590 - 50.3317i) q^{51} +(-6.38596 - 3.68693i) q^{52} +(0.0636230 - 0.110198i) q^{53} +(11.3029 - 6.52573i) q^{54} -40.4544i q^{55} +(-28.6760 + 7.85823i) q^{56} -12.1401 q^{57} +(-42.4850 - 73.5863i) q^{58} +(13.7756 + 7.95335i) q^{59} +(-4.47119 + 7.74433i) q^{60} +(-6.33370 + 3.65676i) q^{61} -84.3798i q^{62} +(14.9332 + 14.7648i) q^{63} -3.28220 q^{64} +(3.57062 + 6.18449i) q^{65} +(-68.1632 - 39.3540i) q^{66} +(-14.8912 + 25.7924i) q^{67} +(67.0948 - 38.7372i) q^{68} +39.7756i q^{69} +(-38.0326 - 9.96004i) q^{70} -100.778 q^{71} +(-6.37140 - 11.0356i) q^{72} +(-5.96325 - 3.44288i) q^{73} +(24.2607 - 42.0208i) q^{74} +(7.50000 - 4.33013i) q^{75} -16.1834i q^{76} +(32.0834 - 122.511i) q^{77} +13.8940 q^{78} +(-30.7043 - 53.1813i) q^{79} +(38.5450 + 22.2540i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(165.499 - 95.5512i) q^{82} +81.0916i q^{83} +(-19.6822 + 19.9067i) q^{84} -75.0301 q^{85} +(56.5463 + 97.9411i) q^{86} +(50.7435 + 29.2968i) q^{87} +(-38.4233 + 66.5511i) q^{88} +(-23.4905 + 13.5622i) q^{89} -16.8494i q^{90} +(5.90839 + 21.5607i) q^{91} -53.0229 q^{92} +(29.0932 + 50.3909i) q^{93} +(116.534 + 67.2808i) q^{94} +(-7.83640 + 13.5730i) q^{95} +(49.5075 - 28.5832i) q^{96} -15.5200i q^{97} +(-107.278 - 60.3254i) q^{98} +54.2753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9	$ 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9} + 20 q^{11} - 66 q^{12} + 32 q^{14} - 82 q^{16} - 78 q^{17} - 6 q^{18} - 6 q^{19} + 36 q^{21} + 56 q^{22} + 2 q^{23} + 60 q^{24} + 30 q^{25} + 36 q^{26} - 128 q^{28} - 100 q^{29} + 108 q^{31} - 108 q^{32} + 60 q^{33} - 60 q^{35} - 132 q^{36} - 34 q^{37} + 126 q^{38} - 42 q^{39} - 90 q^{40} + 114 q^{42} - 124 q^{43} + 234 q^{44} + 278 q^{46} + 96 q^{47} - 60 q^{49} + 20 q^{50} - 78 q^{51} - 444 q^{52} - 76 q^{53} - 18 q^{54} + 112 q^{56} - 12 q^{57} - 52 q^{58} - 270 q^{59} + 60 q^{60} - 60 q^{61} + 42 q^{63} + 700 q^{64} - 60 q^{65} + 84 q^{66} - 18 q^{67} + 108 q^{68} - 300 q^{70} - 628 q^{71} + 60 q^{72} + 234 q^{73} + 244 q^{74} + 90 q^{75} - 196 q^{77} + 72 q^{78} + 108 q^{79} + 480 q^{80} - 54 q^{81} + 480 q^{82} - 192 q^{84} - 60 q^{85} + 130 q^{86} - 150 q^{87} - 668 q^{88} - 186 q^{89} + 444 q^{91} + 456 q^{92} + 108 q^{93} + 30 q^{94} - 324 q^{96} + 416 q^{98} + 120 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9 + 20 * q^11 - 66 * q^12 + 32 * q^14 - 82 * q^16 - 78 * q^17 - 6 * q^18 - 6 * q^19 + 36 * q^21 + 56 * q^22 + 2 * q^23 + 60 * q^24 + 30 * q^25 + 36 * q^26 - 128 * q^28 - 100 * q^29 + 108 * q^31 - 108 * q^32 + 60 * q^33 - 60 * q^35 - 132 * q^36 - 34 * q^37 + 126 * q^38 - 42 * q^39 - 90 * q^40 + 114 * q^42 - 124 * q^43 + 234 * q^44 + 278 * q^46 + 96 * q^47 - 60 * q^49 + 20 * q^50 - 78 * q^51 - 444 * q^52 - 76 * q^53 - 18 * q^54 + 112 * q^56 - 12 * q^57 - 52 * q^58 - 270 * q^59 + 60 * q^60 - 60 * q^61 + 42 * q^63 + 700 * q^64 - 60 * q^65 + 84 * q^66 - 18 * q^67 + 108 * q^68 - 300 * q^70 - 628 * q^71 + 60 * q^72 + 234 * q^73 + 244 * q^74 + 90 * q^75 - 196 * q^77 + 72 * q^78 + 108 * q^79 + 480 * q^80 - 54 * q^81 + 480 * q^82 - 192 * q^84 - 60 * q^85 + 130 * q^86 - 150 * q^87 - 668 * q^88 - 186 * q^89 + 444 * q^91 + 456 * q^92 + 108 * q^93 + 30 * q^94 - 324 * q^96 + 416 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.25588	−	2.17524i	−0.627939	−	1.08762i	−0.987965	−	0.154679i	$-0.950566\pi$
$2$	−1.25588	−	2.17524i	−0.627939	−	1.08762i	0.360026	−	0.932942i	$-0.382768\pi$
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−1.15446	+	1.99958i	−0.288614	+	0.499894i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		−	4.35049i		−	0.725081i
$7$	6.75110	−	1.85004i	0.964443	−	0.264291i
$7$	6.75110	−	1.85004i	0.964443	−	0.264291i
$8$	−4.24760			−0.530950
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−4.86399	−	2.80823i	−0.486399	−	0.280823i
$11$	9.04589	−	15.6679i	0.822353	−	1.42436i	−0.0815719	−	0.996667i	$-0.525994\pi$
$11$	9.04589	−	15.6679i	0.822353	−	1.42436i	0.903925	−	0.427690i	$-0.140673\pi$
$12$	−3.46337	+	1.99958i	−0.288614	+	0.166631i
$13$			3.19366i			0.245666i	0.992427	+	0.122833i	$0.0391979\pi$
$13$			3.19366i			0.245666i	−0.992427	+	0.122833i	$0.960802\pi$
$14$	−12.5028	−	12.3619i	−0.893060	−	0.882990i
$15$	3.87298			0.258199
$16$	9.95229	+	17.2379i	0.622018	+	1.07737i
$17$	−29.0590	−	16.7772i	−1.70935	−	0.986897i	−0.935355	−	0.353711i	$-0.884919\pi$
$17$	−29.0590	−	16.7772i	−1.70935	−	0.986897i	−0.774000	−	0.633185i	$-0.781747\pi$
$18$	3.76763	−	6.52573i	0.209313	−	0.362541i
$19$	−6.07005	+	3.50455i	−0.319476	+	0.184450i	−0.651159	−	0.758941i	$-0.725717\pi$
$19$	−6.07005	+	3.50455i	−0.319476	+	0.184450i	0.331683	+	0.943391i	$0.392384\pi$
$20$			5.16288i			0.258144i
$21$	11.7288	+	3.07156i	0.558516	+	0.146265i
$22$	−45.4421			−2.06555
$23$	11.4822	+	19.8878i	0.499227	+	0.864687i	1.00000		0.000891916i	$-0.000283906\pi$
$23$	11.4822	+	19.8878i	0.499227	+	0.864687i	−0.500772	+	0.865579i	$0.666951\pi$
$24$	−6.37140	−	3.67853i	−0.265475	−	0.153272i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	6.94698	−	4.01084i	0.267191	−	0.154263i
$27$			5.19615i			0.192450i
$28$	−4.09455	+	15.6351i	−0.146234	+	0.558397i
$29$	33.8290			1.16652			0.583258	−	0.812287i	$-0.301778\pi$
$29$	33.8290			1.16652			0.583258	+	0.812287i	$0.301778\pi$
$30$	−4.86399	−	8.42468i	−0.162133	−	0.280823i
$31$	29.0932	+	16.7970i	0.938491	+	0.541838i	0.889487	−	0.456961i	$-0.151062\pi$
$31$	29.0932	+	16.7970i	0.938491	+	0.541838i	0.0490039	+	0.998799i	$0.484395\pi$
$32$	16.5025	−	28.5832i	0.515703	−	0.893224i
$33$	27.1377	−	15.6679i	0.822353	−	0.474786i
$34$			84.2806i			2.47884i
$35$	11.0050	−	11.1305i	0.314430	−	0.318016i
$36$	−6.92674			−0.192409
$37$	9.65886	+	16.7296i	0.261050	+	0.452152i	0.966521	−	0.256586i	$-0.0825978\pi$
$37$	9.65886	+	16.7296i	0.261050	+	0.452152i	−0.705471	+	0.708739i	$0.749264\pi$
$38$	15.2465	+	8.80256i	0.401223	+	0.231646i
$39$	−2.76579	+	4.79048i	−0.0709176	+	0.122833i
$40$	−8.22544	+	4.74896i	−0.205636	+	0.118724i
$41$			76.0832i			1.85569i	0.372969	+	0.927844i	$0.378340\pi$
$41$			76.0832i			1.85569i	−0.372969	+	0.927844i	$0.621660\pi$
$42$	−8.04858	−	29.3706i	−0.191633	−	0.699299i
$43$	−45.0254			−1.04710			−0.523551	−	0.851995i	$-0.675393\pi$
$43$	−45.0254			−1.04710			−0.523551	+	0.851995i	$0.675393\pi$
$44$	20.8862	+	36.1759i	0.474685	+	0.822179i
$45$	5.80948	+	3.35410i	0.129099	+	0.0745356i
$46$	28.8405	−	49.9533i	0.626968	−	1.08594i
$47$	−46.3954	+	26.7864i	−0.987135	+	0.569923i	−0.904417	−	0.426650i	$-0.859694\pi$
$47$	−46.3954	+	26.7864i	−0.987135	+	0.569923i	−0.0827186	+	0.996573i	$0.526360\pi$
$48$			34.4757i			0.718244i
$49$	42.1547	−	24.9796i	0.860300	−	0.509788i
$50$	−12.5588			−0.251175
$51$	−29.0590	−	50.3317i	−0.569785	−	0.986897i
$52$	−6.38596	−	3.68693i	−0.122807	−	0.0709026i
$53$	0.0636230	−	0.110198i	0.00120043	−	0.00207921i	−0.865425	−	0.501039i	$-0.832951\pi$
$53$	0.0636230	−	0.110198i	0.00120043	−	0.00207921i	0.866625	+	0.498960i	$0.166285\pi$
$54$	11.3029	−	6.52573i	0.209313	−	0.120847i
$55$		−	40.4544i		−	0.735535i
$56$	−28.6760	+	7.85823i	−0.512071	+	0.140326i
$57$	−12.1401			−0.212984
$58$	−42.4850	−	73.5863i	−0.732501	−	1.26873i
$59$	13.7756	+	7.95335i	0.233485	+	0.134803i	0.612179	−	0.790719i	$-0.290293\pi$
$59$	13.7756	+	7.95335i	0.233485	+	0.134803i	−0.378694	+	0.925522i	$0.623627\pi$
$60$	−4.47119	+	7.74433i	−0.0745198	+	0.129072i
$61$	−6.33370	+	3.65676i	−0.103831	+	0.0599469i	−0.551016	−	0.834494i	$-0.685760\pi$
$61$	−6.33370	+	3.65676i	−0.103831	+	0.0599469i	0.447185	+	0.894441i	$0.352426\pi$
$62$		−	84.3798i		−	1.36096i
$63$	14.9332	+	14.7648i	0.237035	+	0.234362i
$64$	−3.28220			−0.0512844
$65$	3.57062	+	6.18449i	0.0549325	+	0.0951460i
$66$	−68.1632	−	39.3540i	−1.03278	−	0.596273i
$67$	−14.8912	+	25.7924i	−0.222257	+	0.384961i	−0.955493	−	0.295013i	$-0.904676\pi$
$67$	−14.8912	+	25.7924i	−0.222257	+	0.384961i	0.733236	+	0.679975i	$0.238009\pi$
$68$	67.0948	−	38.7372i	0.986688	−	0.569664i
$69$			39.7756i			0.576458i
$70$	−38.0326	−	9.96004i	−0.543323	−	0.142286i
$71$	−100.778			−1.41941			−0.709703	−	0.704501i	$-0.751171\pi$
$71$	−100.778			−1.41941			−0.709703	+	0.704501i	$0.751171\pi$
$72$	−6.37140	−	11.0356i	−0.0884916	−	0.153272i
$73$	−5.96325	−	3.44288i	−0.0816884	−	0.0471628i	0.458599	−	0.888643i	$-0.348351\pi$
$73$	−5.96325	−	3.44288i	−0.0816884	−	0.0471628i	−0.540288	+	0.841480i	$0.681685\pi$
$74$	24.2607	−	42.0208i	0.327847	−	0.567848i
$75$	7.50000	−	4.33013i	0.100000	−	0.0577350i
$76$		−	16.1834i		−	0.212939i
$77$	32.0834	−	122.511i	0.416667	−	1.59105i
$78$	13.8940			0.178128
$79$	−30.7043	−	53.1813i	−0.388662	−	0.673182i	0.603608	−	0.797281i	$-0.293729\pi$
$79$	−30.7043	−	53.1813i	−0.388662	−	0.673182i	−0.992270	+	0.124100i	$0.960396\pi$
$80$	38.5450	+	22.2540i	0.481813	+	0.278175i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	165.499	−	95.5512i	2.01829	−	1.16526i
$83$			81.0916i			0.977007i	0.872562	+	0.488503i	$0.162457\pi$
$83$			81.0916i			0.977007i	−0.872562	+	0.488503i	$0.837543\pi$
$84$	−19.6822	+	19.9067i	−0.234312	+	0.236985i
$85$	−75.0301			−0.882707
$86$	56.5463	+	97.9411i	0.657515	+	1.13885i
$87$	50.7435	+	29.2968i	0.583258	+	0.336744i
$88$	−38.4233	+	66.5511i	−0.436628	+	0.756263i
$89$	−23.4905	+	13.5622i	−0.263938	+	0.152385i	−0.626130	−	0.779719i	$-0.715362\pi$
$89$	−23.4905	+	13.5622i	−0.263938	+	0.152385i	0.362192	+	0.932104i	$0.382029\pi$
$90$		−	16.8494i		−	0.187215i
$91$	5.90839	+	21.5607i	0.0649274	+	0.236931i
$92$	−53.0229			−0.576336
$93$	29.0932	+	50.3909i	0.312830	+	0.541838i
$94$	116.534	+	67.2808i	1.23972	+	0.715753i
$95$	−7.83640	+	13.5730i	−0.0824884	+	0.142874i
$96$	49.5075	−	28.5832i	0.515703	−	0.297741i
$97$		−	15.5200i		−	0.160000i	−0.996795	−	0.0800002i	$-0.974508\pi$
$97$		−	15.5200i		−	0.160000i	0.996795	−	0.0800002i	$-0.0254921\pi$
$98$	−107.278	−	60.3254i	−1.09467	−	0.615565i
$99$	54.2753			0.548236
$100$	5.77228	+	9.99788i	0.0577228	+	0.0999788i
$101$	−9.04350	−	5.22127i	−0.0895396	−	0.0516957i	0.454562	−	0.890715i	$-0.349796\pi$
$101$	−9.04350	−	5.22127i	−0.0895396	−	0.0516957i	−0.544101	+	0.839020i	$0.683129\pi$
$102$	−72.9892	+	126.421i	−0.715580	+	1.23942i
$103$	58.6435	−	33.8578i	0.569354	−	0.328717i	−0.187537	−	0.982258i	$-0.560050\pi$
$103$	58.6435	−	33.8578i	0.569354	−	0.328717i	0.756891	+	0.653541i	$0.226717\pi$
$104$		−	13.5654i		−	0.130436i
$105$	26.1469	−	7.16518i	0.249018	−	0.0682398i
$106$	−0.319611			−0.00301519
$107$	36.0768	+	62.4869i	0.337167	+	0.583990i	0.983899	−	0.178728i	$-0.0571981\pi$
$107$	36.0768	+	62.4869i	0.337167	+	0.583990i	−0.646732	+	0.762717i	$0.723865\pi$
$108$	−10.3901	−	5.99873i	−0.0962047	−	0.0555438i
$109$	80.9882	−	140.276i	0.743011	−	1.28693i	−0.208107	−	0.978106i	$-0.566730\pi$
$109$	80.9882	−	140.276i	0.743011	−	1.28693i	0.951118	−	0.308827i	$-0.0999365\pi$
$110$	−87.9982	+	50.8058i	−0.799984	+	0.461871i
$111$			33.4593i			0.301435i
$112$	99.0796	+	97.9624i	0.884640	+	0.874665i
$113$	178.415			1.57889			0.789447	−	0.613819i	$-0.210367\pi$
$113$	178.415			1.57889			0.789447	+	0.613819i	$0.210367\pi$
$114$	15.2465	+	26.4077i	0.133741	+	0.231646i
$115$	44.4705	+	25.6750i	0.386700	+	0.223261i
$116$	−39.0541	+	67.6436i	−0.336673	+	0.583135i
$117$	−8.29736	+	4.79048i	−0.0709176	+	0.0409443i
$118$		−	39.9538i		−	0.338591i
$119$	−227.219	−	59.5044i	−1.90940	−	0.500037i
$120$	−16.4509			−0.137091
$121$	−103.156	−	178.672i	−0.852530	−	1.47663i
$122$	15.9087	+	9.18489i	0.130399	+	0.0752860i
$123$	−65.8900	+	114.125i	−0.535691	+	0.927844i
$124$	−67.1737	+	38.7827i	−0.541723	+	0.312764i
$125$		−	11.1803i		−	0.0894427i
$126$	13.3628	−	51.0261i	0.106054	−	0.404969i
$127$	−147.321			−1.16001			−0.580005	−	0.814613i	$-0.696949\pi$
$127$	−147.321			−1.16001			−0.580005	+	0.814613i	$0.696949\pi$
$128$	−61.8880	−	107.193i	−0.483500	−	0.837446i
$129$	−67.5380	−	38.9931i	−0.523551	−	0.302272i
$130$	8.96851	−	15.5339i	0.0689885	−	0.119492i
$131$	−55.1079	+	31.8166i	−0.420671	+	0.242875i	−0.695365	−	0.718657i	$-0.744757\pi$
$131$	−55.1079	+	31.8166i	−0.420671	+	0.242875i	0.274693	+	0.961532i	$0.411424\pi$
$132$			72.3518i			0.548119i
$133$	−34.4960	+	34.8894i	−0.259368	+	0.262326i
$134$	74.8063			0.558256
$135$	5.80948	+	10.0623i	0.0430331	+	0.0745356i
$136$	123.431	+	71.2630i	0.907582	+	0.523993i
$137$	−17.3871	+	30.1153i	−0.126913	+	0.219820i	−0.922479	−	0.386047i	$-0.873840\pi$
$137$	−17.3871	+	30.1153i	−0.126913	+	0.219820i	0.795566	+	0.605867i	$0.207174\pi$
$138$	86.5216	−	49.9533i	0.626968	−	0.361980i
$139$			34.4898i			0.248128i	0.992274	+	0.124064i	$0.0395928\pi$
$139$			34.4898i			0.248128i	−0.992274	+	0.124064i	$0.960407\pi$
$140$	9.55154	+	34.8551i	0.0682253	+	0.248965i
$141$	−92.7907			−0.658090
$142$	126.565	+	219.216i	0.891300	+	1.54378i
$143$	50.0380	+	28.8894i	0.349916	+	0.202024i
$144$	−29.8569	+	51.7136i	−0.207339	+	0.359122i
$145$	65.5095	−	37.8219i	0.451790	−	0.260841i
$146$			17.2954i			0.118461i
$147$	84.8650	−	0.962379i	0.577313	−	0.00654680i
$148$	−44.6029			−0.301371
$149$	−27.7734	−	48.1050i	−0.186399	−	0.322852i	0.757648	−	0.652663i	$-0.226348\pi$
$149$	−27.7734	−	48.1050i	−0.186399	−	0.322852i	−0.944047	+	0.329811i	$0.893015\pi$
$150$	−18.8382	−	10.8762i	−0.125588	−	0.0725081i
$151$	−21.6154	+	37.4389i	−0.143148	+	0.247940i	−0.928681	−	0.370881i	$-0.879056\pi$
$151$	−21.6154	+	37.4389i	−0.143148	+	0.247940i	0.785532	+	0.618821i	$0.212389\pi$
$152$	25.7831	−	14.8859i	0.169626	−	0.0979336i
$153$		−	100.663i		−	0.657931i
$154$	−306.784	+	84.0697i	−1.99210	+	0.545907i
$155$	75.1184			0.484635
$156$	−6.38596	−	11.0608i	−0.0409356	−	0.0709026i
$157$	37.4563	+	21.6254i	0.238575	+	0.137742i	0.614522	−	0.788900i	$-0.289349\pi$
$157$	37.4563	+	21.6254i	0.238575	+	0.137742i	−0.375946	+	0.926641i	$0.622682\pi$
$158$	−77.1216	+	133.578i	−0.488111	+	0.845434i
$159$	0.190869	−	0.110198i	0.00120043	−	0.000693071i
$160$		−	73.8015i		−	0.461259i
$161$	114.311	+	113.022i	0.710006	+	0.702000i
$162$	22.6058			0.139542
$163$	−79.8057	−	138.228i	−0.489606	−	0.848022i	0.510323	−	0.859983i	$-0.329526\pi$
$163$	−79.8057	−	138.228i	−0.489606	−	0.848022i	−0.999928	+	0.0119612i	$0.996193\pi$
$164$	−152.134	−	87.8347i	−0.927647	−	0.535577i
$165$	35.0346	−	60.6817i	0.212331	−	0.367768i
$166$	176.394	−	101.841i	1.06261	−	0.613500i
$167$		−	189.479i		−	1.13460i	−0.823510	−	0.567302i	$-0.807987\pi$
$167$		−	189.479i		−	1.13460i	0.823510	−	0.567302i	$-0.192013\pi$
$168$	−49.8194	−	13.0468i	−0.296544	−	0.0776593i
$169$	158.801			0.939648
$170$	94.2286	+	163.209i	0.554286	+	0.960051i
$171$	−18.2102	−	10.5136i	−0.106492	−	0.0614833i
$172$	51.9798	−	90.0316i	0.302208	−	0.523440i
$173$	−63.6817	+	36.7667i	−0.368103	+	0.212524i	−0.672629	−	0.739980i	$-0.734835\pi$
$173$	−63.6817	+	36.7667i	−0.368103	+	0.212524i	0.304527	+	0.952504i	$0.401502\pi$
$174$		−	147.173i		−	0.845819i
$175$	8.86684	−	33.8582i	0.0506677	−	0.193476i
$176$	360.109			2.04607
$177$	13.7756	+	23.8601i	0.0778283	+	0.134803i
$178$	59.0024	+	34.0650i	0.331474	+	0.191377i
$179$	100.561	−	174.176i	0.561792	−	0.973052i	−0.435549	−	0.900165i	$-0.643446\pi$
$179$	100.561	−	174.176i	0.561792	−	0.973052i	0.997340	−	0.0728865i	$-0.0232211\pi$
$180$	−13.4136	+	7.74433i	−0.0745198	+	0.0430240i
$181$		−	123.082i		−	0.680011i	−0.940423	−	0.340006i	$-0.889571\pi$
$181$		−	123.082i		−	0.680011i	0.940423	−	0.340006i	$-0.110429\pi$
$182$	39.4795	−	39.9298i	0.216920	−	0.219394i
$183$	−12.6674			−0.0692207
$184$	−48.7719	−	84.4754i	−0.265065	−	0.459106i
$185$	37.4086	+	21.5979i	0.202209	+	0.116745i
$186$	73.0750	−	126.570i	0.392876	−	0.680482i
$187$	−525.730	+	303.530i	−2.81139	+	1.62316i
$188$		−	123.695i		−	0.657951i
$189$	9.61309	+	35.0797i	0.0508629	+	0.185607i
$190$	39.3662			0.207191
$191$	84.4682	+	146.303i	0.442242	+	0.765985i	0.997856	−	0.0654552i	$-0.0208499\pi$
$191$	84.4682	+	146.303i	0.442242	+	0.765985i	−0.555614	+	0.831441i	$0.687517\pi$
$192$	−4.92330	−	2.84247i	−0.0256422	−	0.0148045i
$193$	99.4792	−	172.303i	0.515436	−	0.892762i	−0.484403	−	0.874845i	$-0.660963\pi$
$193$	99.4792	−	172.303i	0.515436	−	0.892762i	0.999839	−	0.0179170i	$-0.00570347\pi$
$194$	−33.7599	+	19.4913i	−0.174020	+	0.100470i
$195$			12.3690i			0.0634306i
$196$	1.28290	+	113.129i	0.00654541	+	0.577191i
$197$	33.9412			0.172290			0.0861452	−	0.996283i	$-0.472545\pi$
$197$	33.9412			0.172290			0.0861452	+	0.996283i	$0.472545\pi$
$198$	−68.1632	−	118.062i	−0.344258	−	0.596273i
$199$	−159.078	−	91.8435i	−0.799385	−	0.461525i	0.0438711	−	0.999037i	$-0.486031\pi$
$199$	−159.078	−	91.8435i	−0.799385	−	0.461525i	−0.843256	+	0.537512i	$0.819364\pi$
$200$	−10.6190	+	18.3926i	−0.0530950	+	0.0919632i
$201$	−44.6737	+	25.7924i	−0.222257	+	0.128320i
$202$			26.2291i			0.129847i
$203$	228.383	−	62.5850i	1.12504	−	0.308300i
$204$	134.190			0.657792
$205$	85.0636	+	147.334i	0.414944	+	0.718705i
$206$	−147.298	−	85.0426i	−0.715039	−	0.412828i
$207$	−34.4467	+	59.6634i	−0.166409	+	0.288229i
$208$	−55.0518	+	31.7842i	−0.264672	+	0.152809i
$209$			126.807i			0.606732i
$210$	−48.4233	−	47.8773i	−0.230587	−	0.227987i
$211$	−231.521			−1.09726			−0.548628	−	0.836067i	$-0.684850\pi$
$211$	−231.521			−1.09726			−0.548628	+	0.836067i	$0.684850\pi$
$212$	0.146900	+	0.254438i	0.000692924	+	0.00120018i
$213$	−151.167	−	87.2762i	−0.709703	−	0.409747i
$214$	90.6162	−	156.952i	0.423440	−	0.733420i
$215$	−87.1912	+	50.3399i	−0.405541	+	0.234139i
$216$		−	22.0712i		−	0.102181i
$217$	227.486	+	59.5744i	1.04832	+	0.274537i
$218$	−406.845			−1.86626
$219$	−5.96325	−	10.3287i	−0.0272295	−	0.0471628i
$220$	80.8917	+	46.7029i	0.367690	+	0.212286i
$221$	53.5807	−	92.8045i	0.242447	−	0.419930i
$222$	72.7821	−	42.0208i	0.327847	−	0.189283i
$223$			243.627i			1.09250i	0.837623	+	0.546249i	$0.183945\pi$
$223$			243.627i			1.09250i	−0.837623	+	0.546249i	$0.816055\pi$
$224$	58.5300	−	223.498i	0.261295	−	0.997760i
$225$	15.0000			0.0666667
$226$	−224.067	−	388.096i	−0.991449	−	1.71724i
$227$	35.9626	+	20.7630i	0.158426	+	0.0914670i	0.577117	−	0.816662i	$-0.304178\pi$
$227$	35.9626	+	20.7630i	0.158426	+	0.0914670i	−0.418691	+	0.908129i	$0.637511\pi$
$228$	14.0152	−	24.2751i	0.0614702	−	0.106470i
$229$	−253.106	+	146.131i	−1.10527	+	0.638126i	−0.937599	−	0.347718i	$-0.886957\pi$
$229$	−253.106	+	146.131i	−1.10527	+	0.638126i	−0.167667	+	0.985844i	$0.553623\pi$
$230$		−	128.979i		−	0.560778i
$231$	154.223	−	155.982i	0.667631	−	0.675245i
$232$	−143.692			−0.619362
$233$	−179.940	−	311.665i	−0.772273	−	1.33762i	−0.936314	−	0.351163i	$-0.885786\pi$
$233$	−179.940	−	311.665i	−0.772273	−	1.33762i	0.164041	−	0.986454i	$-0.447547\pi$
$234$	20.8409	+	12.0325i	0.0890638	+	0.0514210i
$235$	−59.8962	+	103.743i	−0.254877	+	0.441460i
$236$	−31.8067	+	18.3636i	−0.134774	+	0.0778118i
$237$		−	106.363i		−	0.448788i
$238$	155.923	+	568.987i	0.655137	+	2.39070i
$239$	178.697			0.747684			0.373842	−	0.927492i	$-0.378040\pi$
$239$	178.697			0.747684			0.373842	+	0.927492i	$0.378040\pi$
$240$	38.5450	+	66.7620i	0.160604	+	0.278175i
$241$	−28.0911	−	16.2184i	−0.116560	−	0.0672962i	0.440586	−	0.897710i	$-0.354771\pi$
$241$	−28.0911	−	16.2184i	−0.116560	−	0.0672962i	−0.557147	+	0.830414i	$0.688104\pi$
$242$	−259.103	+	448.779i	−1.07067	+	1.85446i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		−	16.8863i		−	0.0692061i
$245$	53.7042	−	95.5032i	0.219201	−	0.389809i
$246$	330.999			1.34552
$247$	−11.1923	−	19.3857i	−0.0453130	−	0.0784844i
$248$	−123.576	−	71.3468i	−0.498292	−	0.287689i
$249$	−70.2274	+	121.637i	−0.282038	+	0.488503i
$250$	−24.3200	+	14.0411i	−0.0972798	+	0.0561645i
$251$			353.330i			1.40769i	0.710354	+	0.703844i	$0.248535\pi$
$251$			353.330i			1.40769i	−0.710354	+	0.703844i	$0.751465\pi$
$252$	−46.7631	+	12.8147i	−0.185568	+	0.0508521i
$253$	415.468			1.64217
$254$	185.017	+	320.459i	0.728415	+	1.26165i
$255$	−112.545	−	64.9780i	−0.441354	−	0.254816i
$256$	−162.012	+	280.613i	−0.632859	+	1.09614i
$257$	270.082	−	155.932i	1.05090	−	0.606738i	0.128000	−	0.991774i	$-0.459144\pi$
$257$	270.082	−	155.932i	1.05090	−	0.606738i	0.922902	+	0.385036i	$0.125811\pi$
$258$			195.882i			0.759233i
$259$	96.1584	+	95.0742i	0.371268	+	0.367082i
$260$	−16.4885			−0.0634172
$261$	50.7435	+	87.8903i	0.194419	+	0.336744i
$262$	138.418	+	79.9155i	0.528312	+	0.305021i
$263$	23.8639	−	41.3334i	0.0907371	−	0.157161i	−0.817084	−	0.576518i	$-0.804411\pi$
$263$	23.8639	−	41.3334i	0.0907371	−	0.157161i	0.907821	+	0.419357i	$0.137744\pi$
$264$	−115.270	+	66.5511i	−0.436628	+	0.252088i
$265$		−	0.284531i		−	0.00107370i
$266$	119.216	+	31.2204i	0.448179	+	0.117370i
$267$	−46.9810			−0.175959
$268$	−34.3826	−	59.5524i	−0.128293	−	0.222210i
$269$	−245.854	−	141.944i	−0.913957	−	0.527673i	−0.0322549	−	0.999480i	$-0.510269\pi$
$269$	−245.854	−	141.944i	−0.913957	−	0.527673i	−0.881702	+	0.471806i	$0.843602\pi$
$270$	14.5920	−	25.2740i	0.0540444	−	0.0936076i
$271$	−141.099	+	81.4637i	−0.520661	+	0.300604i	−0.737205	−	0.675669i	$-0.763855\pi$
$271$	−141.099	+	81.4637i	−0.520661	+	0.300604i	0.216544	+	0.976273i	$0.430522\pi$
$272$		−	667.888i		−	2.45547i
$273$	−9.80952	+	37.4578i	−0.0359323	+	0.137208i
$274$	87.3441			0.318774
$275$	−45.2294	−	78.3397i	−0.164471	−	0.284872i
$276$	−79.5344	−	45.9192i	−0.288168	−	0.166374i
$277$	214.949	−	372.303i	0.775989	−	1.34405i	−0.158248	−	0.987399i	$-0.550585\pi$
$277$	214.949	−	372.303i	0.775989	−	1.34405i	0.934237	−	0.356653i	$-0.116082\pi$
$278$	75.0237	−	43.3149i	0.269869	−	0.155809i
$279$			100.782i			0.361225i
$280$	−46.7450	+	47.2781i	−0.166946	+	0.168850i
$281$	−195.866			−0.697031			−0.348516	−	0.937303i	$-0.613314\pi$
$281$	−195.866			−0.697031			−0.348516	+	0.937303i	$0.613314\pi$
$282$	116.534	+	201.842i	0.413240	+	0.715753i
$283$	22.5276	+	13.0063i	0.0796027	+	0.0459587i	0.539273	−	0.842131i	$-0.318699\pi$
$283$	22.5276	+	13.0063i	0.0796027	+	0.0459587i	−0.459670	+	0.888090i	$0.652032\pi$
$284$	116.344	−	201.513i	0.409661	−	0.709553i
$285$	−23.5092	+	13.5730i	−0.0824884	+	0.0476247i
$286$		−	145.126i		−	0.507435i
$287$	140.757	+	513.645i	0.490442	+	1.78970i
$288$	99.0150			0.343802
$289$	418.452	+	724.780i	1.44793	+	2.50789i
$290$	−164.544	−	94.9995i	−0.567393	−	0.327584i
$291$	13.4407	−	23.2801i	0.0461881	−	0.0800002i
$292$	13.7686	−	7.94932i	0.0471528	−	0.0272237i
$293$			463.992i			1.58359i	0.610787	+	0.791795i	$0.290853\pi$
$293$			463.992i			1.58359i	−0.610787	+	0.791795i	$0.709147\pi$
$294$	−108.673	−	183.393i	−0.369638	−	0.623787i
$295$	35.5685			0.120571
$296$	−41.0270	−	71.0608i	−0.138605	−	0.240070i
$297$	81.4130	+	47.0038i	0.274118	+	0.158262i
$298$	−69.7600	+	120.828i	−0.234094	+	0.405463i
$299$	−63.5148	+	36.6703i	−0.212424	+	0.122643i
$300$			19.9958i			0.0666525i
$301$	−303.971	+	83.2987i	−1.00987	+	0.276740i
$302$	108.585			0.359553
$303$	−9.04350	−	15.6638i	−0.0298465	−	0.0516957i
$304$	−120.822	−	69.7565i	−0.397440	−	0.229462i
$305$	−8.17677	+	14.1626i	−0.0268091	+	0.0464347i
$306$	−218.968	+	126.421i	−0.715580	+	0.413140i
$307$			231.106i			0.752789i	0.926460	+	0.376394i	$0.122836\pi$
$307$			231.106i			0.752789i	−0.926460	+	0.376394i	$0.877164\pi$
$308$	207.931	+	205.587i	0.675102	+	0.667490i
$309$	117.287			0.379570
$310$	−94.3395	−	163.401i	−0.304321	−	0.527099i
$311$	−312.230	−	180.266i	−1.00395	−	0.579633i	−0.0945385	−	0.995521i	$-0.530138\pi$
$311$	−312.230	−	180.266i	−1.00395	−	0.579633i	−0.909416	+	0.415888i	$0.863471\pi$
$312$	11.7480	−	20.3481i	0.0376537	−	0.0652181i
$313$	425.757	−	245.811i	1.36025	−	0.785338i	0.370589	−	0.928797i	$-0.379156\pi$
$313$	425.757	−	245.811i	1.36025	−	0.785338i	0.989656	+	0.143459i	$0.0458225\pi$
$314$		−	108.635i		−	0.345973i
$315$	45.4256	+	11.8961i	0.144208	+	0.0377654i
$316$	141.787			0.448693
$317$	−161.795	−	280.236i	−0.510393	−	0.884026i	−0.999927	−	0.0120425i	$-0.996167\pi$
$317$	−161.795	−	280.236i	−0.510393	−	0.884026i	0.489535	−	0.871984i	$-0.337167\pi$
$318$	−0.479416	−	0.276791i	−0.00150760	−	0.000870412i
$319$	306.013	−	530.030i	0.959289	−	1.66154i
$320$	−6.35596	+	3.66961i	−0.0198624	+	0.0114675i
$321$			124.974i			0.389327i
$322$	102.290	−	390.596i	0.317670	−	1.21303i
$323$	235.186			0.728131
$324$	−10.3901	−	17.9962i	−0.0320682	−	0.0555438i
$325$	13.8289	+	7.98414i	0.0425506	+	0.0245666i
$326$	−200.452	+	347.194i	−0.614884	+	1.06501i
$327$	242.965	−	140.276i	0.743011	−	0.428978i
$328$		−	323.171i		−	0.985277i
$329$	−263.664	+	266.671i	−0.801410	+	0.810549i
$330$	−175.996			−0.533323
$331$	26.3697	+	45.6737i	0.0796668	+	0.137987i	0.903106	−	0.429417i	$-0.141281\pi$
$331$	26.3697	+	45.6737i	0.0796668	+	0.137987i	−0.823439	+	0.567404i	$0.807948\pi$
$332$	−162.149	−	93.6166i	−0.488400	−	0.281978i
$333$	−28.9766	+	50.1889i	−0.0870168	+	0.150717i
$334$	−412.162	+	237.962i	−1.23402	+	0.712461i
$335$			66.5957i			0.198793i
$336$	63.7815	+	232.749i	0.189826	+	0.692706i
$337$	−276.771			−0.821280			−0.410640	−	0.911798i	$-0.634695\pi$
$337$	−276.771			−0.821280			−0.410640	+	0.911798i	$0.634695\pi$
$338$	−199.434	−	345.430i	−0.590042	−	1.02198i
$339$	267.623	+	154.512i	0.789447	+	0.455787i
$340$	86.6190	−	150.028i	0.254762	−	0.441260i
$341$	526.348	−	303.887i	1.54354	−	0.891165i
$342$			52.8154i			0.154431i
$343$	238.377	−	246.628i	0.694978	−	0.719031i
$344$	191.250			0.555958
$345$	44.4705	+	77.0251i	0.128900	+	0.223261i
$346$	159.953	+	92.3489i	0.462292	+	0.266904i
$347$	82.4712	−	142.844i	0.237669	−	0.411655i	−0.722376	−	0.691501i	$-0.756950\pi$
$347$	82.4712	−	142.844i	0.237669	−	0.411655i	0.960045	+	0.279846i	$0.0902833\pi$
$348$	−117.162	+	67.6436i	−0.336673	+	0.194378i
$349$		−	369.205i		−	1.05789i	−0.848655	−	0.528947i	$-0.822587\pi$
$349$		−	369.205i		−	1.05789i	0.848655	−	0.528947i	$-0.177413\pi$
$350$	−84.7855	+	23.2342i	−0.242244	+	0.0663835i
$351$	−16.5947			−0.0472784
$352$	−298.560	−	517.120i	−0.848181	−	1.46909i
$353$	−286.202	−	165.239i	−0.810772	−	0.468099i	0.0364522	−	0.999335i	$-0.488394\pi$
$353$	−286.202	−	165.239i	−0.810772	−	0.468099i	−0.847224	+	0.531236i	$0.821728\pi$
$354$	34.6010	−	59.9306i	0.0977428	−	0.169296i
$355$	−195.156	+	112.673i	−0.549734	+	0.317389i
$356$		−	62.6281i		−	0.175922i
$357$	−289.296	−	286.034i	−0.810353	−	0.801216i
$358$	−505.168			−1.41108
$359$	−206.424	−	357.537i	−0.574997	−	0.995924i	−0.996042	−	0.0888839i	$-0.971670\pi$
$359$	−206.424	−	357.537i	−0.574997	−	0.995924i	0.421045	−	0.907040i	$-0.361663\pi$
$360$	−24.6763	−	14.2469i	−0.0685453	−	0.0395747i
$361$	−155.936	+	270.090i	−0.431957	+	0.748171i
$362$	−267.733	+	154.576i	−0.739595	+	0.427005i
$363$		−	357.343i		−	0.984417i
$364$	−49.9332	−	13.0766i	−0.137179	−	0.0359247i
$365$	−15.3970			−0.0421837
$366$	15.9087	+	27.5547i	0.0434664	+	0.0752860i
$367$	−301.840	−	174.267i	−0.822452	−	0.474843i	0.0288095	−	0.999585i	$-0.490828\pi$
$367$	−301.840	−	174.267i	−0.822452	−	0.474843i	−0.851261	+	0.524742i	$0.824162\pi$
$368$	−228.549	+	395.858i	−0.621057	+	1.07570i
$369$	−197.670	+	114.125i	−0.535691	+	0.309281i
$370$		−	108.497i		−	0.293235i
$371$	0.225654	−	0.861664i	0.000608231	−	0.00232255i
$372$	−134.347			−0.361149
$373$	237.339	+	411.083i	0.636297	+	1.10210i	0.986239	+	0.165328i	$0.0528682\pi$
$373$	237.339	+	411.083i	0.636297	+	1.10210i	−0.349941	+	0.936772i	$0.613798\pi$
$374$	1320.50	+	762.393i	3.53076	+	2.03848i
$375$	9.68246	−	16.7705i	0.0258199	−	0.0447214i
$376$	197.069	−	113.778i	0.524119	−	0.302600i
$377$			108.038i			0.286573i
$378$	64.2341	−	64.9667i	0.169932	−	0.171870i
$379$	−74.9686			−0.197806			−0.0989031	−	0.995097i	$-0.531533\pi$
$379$	−74.9686			−0.197806			−0.0989031	+	0.995097i	$0.531533\pi$
$380$	−18.0936	−	31.3390i	−0.0476146	−	0.0824710i
$381$	−220.982	−	127.584i	−0.580005	−	0.334866i
$382$	212.163	−	367.478i	0.555402	−	0.961984i
$383$	506.173	−	292.239i	1.32160	−	0.763027i	0.337617	−	0.941284i	$-0.390379\pi$
$383$	506.173	−	292.239i	1.32160	−	0.763027i	0.983984	+	0.178257i	$0.0570459\pi$
$384$		−	214.386i		−	0.558298i
$385$	−74.8423	−	273.112i	−0.194396	−	0.709382i
$386$	−499.735			−1.29465
$387$	−67.5380	−	116.979i	−0.174517	−	0.302272i
$388$	31.0335	+	17.9172i	0.0799832	+	0.0461783i
$389$	−277.707	+	481.002i	−0.713899	+	1.23651i	0.249484	+	0.968379i	$0.419739\pi$
$389$	−277.707	+	481.002i	−0.713899	+	1.23651i	−0.963383	+	0.268130i	$0.913594\pi$
$390$	26.9055	−	15.5339i	0.0689885	−	0.0398306i
$391$		−	770.561i		−	1.97074i
$392$	−179.056	+	106.103i	−0.456776	+	0.270672i
$393$	−110.216			−0.280448
$394$	−42.6260	−	73.8304i	−0.108188	−	0.187387i
$395$	−118.917	−	68.6568i	−0.301056	−	0.173815i
$396$	−62.6585	+	108.528i	−0.158228	+	0.274060i
$397$	−9.32790	+	5.38547i	−0.0234960	+	0.0135654i	−0.511702	−	0.859163i	$-0.670985\pi$
$397$	−9.32790	+	5.38547i	−0.0234960	+	0.0135654i	0.488206	+	0.872728i	$0.337651\pi$
$398$			461.377i			1.15924i
$399$	−81.9590	+	22.4597i	−0.205411	+	0.0562899i
$400$	99.5229			0.248807
$401$	−45.8035	−	79.3339i	−0.114223	−	0.197840i	0.803246	−	0.595648i	$-0.203105\pi$
$401$	−45.8035	−	79.3339i	−0.114223	−	0.197840i	−0.917469	+	0.397807i	$0.869771\pi$
$402$	112.209	+	64.7842i	0.279128	+	0.161155i
$403$	−53.6438	+	92.9137i	−0.133111	+	0.230555i
$404$	20.8806	−	12.0554i	0.0516848	−	0.0298402i
$405$			20.1246i			0.0496904i
$406$	−422.958	−	418.189i	−1.04177	−	1.03002i
$407$	349.492			0.858702
$408$	123.431	+	213.789i	0.302527	+	0.523993i
$409$	423.556	+	244.540i	1.03559	+	0.597898i	0.918581	−	0.395233i	$-0.129336\pi$
$409$	423.556	+	244.540i	1.03559	+	0.597898i	0.117008	+	0.993131i	$0.462670\pi$
$410$	213.659	−	370.068i	0.521119	−	0.902605i
$411$	−52.1612	+	30.1153i	−0.126913	+	0.0732732i
$412$			156.350i			0.379489i
$413$	107.715	+	28.2085i	0.260810	+	0.0683013i
$414$	173.043			0.417979
$415$	90.6631	+	157.033i	0.218465	+	0.378393i
$416$	91.2848	+	52.7033i	0.219435	+	0.126691i
$417$	−29.8690	+	51.7347i	−0.0716284	+	0.124064i
$418$	275.836	−	159.254i	0.659894	−	0.380990i
$419$			602.995i			1.43913i	0.694426	+	0.719564i	$0.255658\pi$
$419$			602.995i			1.43913i	−0.694426	+	0.719564i	$0.744342\pi$
$420$	−15.8581	+	60.5546i	−0.0377574	+	0.144178i
$421$	594.085			1.41113			0.705564	−	0.708646i	$-0.250694\pi$
$421$	594.085			1.41113			0.705564	+	0.708646i	$0.250694\pi$
$422$	290.762	+	503.615i	0.689009	+	1.19340i
$423$	−139.186	−	80.3591i	−0.329045	−	0.189974i
$424$	−0.270245	+	0.468078i	−0.000637370	+	0.00110396i
$425$	−145.295	+	83.8862i	−0.341871	+	0.197379i
$426$			438.433i			1.02919i
$427$	−35.9943	+	36.4048i	−0.0842957	+	0.0852570i
$428$	−166.596			−0.389244
$429$	50.0380	+	86.6683i	0.116639	+	0.202024i
$430$	219.003	+	126.441i	0.509309	+	0.294050i
$431$	261.570	−	453.052i	0.606890	−	1.05116i	−0.384860	−	0.922975i	$-0.625750\pi$
$431$	261.570	−	453.052i	0.606890	−	1.05116i	0.991750	−	0.128189i	$-0.0409165\pi$
$432$	−89.5706	+	51.7136i	−0.207339	+	0.119707i
$433$			133.825i			0.309065i	0.987988	+	0.154532i	$0.0493871\pi$
$433$			133.825i			0.309065i	−0.987988	+	0.154532i	$0.950613\pi$
$434$	−156.106	−	569.656i	−0.359691	−	1.31257i
$435$	131.019			0.301193
$436$	186.995	+	323.884i	0.428887	+	0.742854i
$437$	−139.395	−	80.4800i	−0.318983	−	0.184165i
$438$	−14.9782	+	25.9430i	−0.0341969	+	0.0592307i
$439$	243.842	−	140.782i	0.555449	−	0.320689i	−0.195868	−	0.980630i	$-0.562752\pi$
$439$	243.842	−	140.782i	0.555449	−	0.320689i	0.751317	+	0.659942i	$0.229419\pi$
$440$			171.834i			0.390532i
$441$	128.131	+	72.0517i	0.290546	+	0.163383i
$442$	−269.163			−0.608967
$443$	137.241	+	237.709i	0.309800	+	0.536590i	0.978318	−	0.207106i	$-0.0664045\pi$
$443$	137.241	+	237.709i	0.309800	+	0.536590i	−0.668518	+	0.743696i	$0.733071\pi$
$444$	−66.9044	−	38.6273i	−0.150686	−	0.0869983i
$445$	−30.3261	+	52.5264i	−0.0681485	+	0.118037i
$446$	529.948	−	305.965i	1.18822	−	0.686021i
$447$		−	96.2099i		−	0.215235i
$448$	−22.1585	+	6.07221i	−0.0494609	+	0.0135540i
$449$	−858.846			−1.91280			−0.956399	−	0.292064i	$-0.905658\pi$
$449$	−858.846			−1.91280			−0.956399	+	0.292064i	$0.905658\pi$
$450$	−18.8382	−	32.6287i	−0.0418626	−	0.0725081i
$451$	1192.07	+	688.240i	2.64316	+	1.52603i
$452$	−205.972	+	356.754i	−0.455691	+	0.789280i
$453$	−64.8461	+	37.4389i	−0.143148	+	0.0826466i
$454$		−	104.303i		−	0.229743i
$455$	35.5471	+	35.1463i	0.0781256	+	0.0772446i
$456$	51.5663			0.113084
$457$	−89.3506	−	154.760i	−0.195515	−	0.338643i	0.751554	−	0.659672i	$-0.229305\pi$
$457$	−89.3506	−	154.760i	−0.195515	−	0.338643i	−0.947069	+	0.321029i	$0.895971\pi$
$458$	635.740	+	367.045i	1.38808	+	0.801408i
$459$	87.1771	−	150.995i	0.189928	−	0.328966i
$460$	−102.678	+	59.2814i	−0.223214	+	0.128873i
$461$		−	318.581i		−	0.691066i	−0.938407	−	0.345533i	$-0.887698\pi$
$461$		−	318.581i		−	0.691066i	0.938407	−	0.345533i	$-0.112302\pi$
$462$	−532.983	−	139.578i	−1.15364	−	0.302118i
$463$	−821.470			−1.77423			−0.887116	−	0.461546i	$-0.847295\pi$
$463$	−821.470			−1.77423			−0.887116	+	0.461546i	$0.847295\pi$
$464$	336.676	+	583.139i	0.725594	+	1.25677i
$465$	112.678	+	65.0544i	0.242317	+	0.139902i
$466$	−451.964	+	782.825i	−0.969881	+	1.67988i
$467$	−163.565	+	94.4344i	−0.350247	+	0.202215i	−0.664794	−	0.747027i	$-0.731481\pi$
$467$	−163.565	+	94.4344i	−0.350247	+	0.202215i	0.314547	+	0.949242i	$0.398147\pi$
$468$		−	22.1216i		−	0.0472684i
$469$	−52.8153	+	201.676i	−0.112613	+	0.430014i
$470$	300.889			0.640189
$471$	37.4563	+	64.8762i	0.0795251	+	0.137742i
$472$	−58.5133	−	33.7827i	−0.123969	−	0.0715734i
$473$	−407.294	+	705.454i	−0.861087	+	1.49145i
$474$	−231.365	+	133.578i	−0.488111	+	0.281811i
$475$			35.0455i			0.0737799i
$476$	381.298	−	385.647i	0.801046	−	0.810182i
$477$	0.381738			0.000800289
$478$	−224.421	−	388.709i	−0.469500	−	0.813198i
$479$	−157.920	−	91.1754i	−0.329688	−	0.190345i	0.326015	−	0.945365i	$-0.394294\pi$
$479$	−157.920	−	91.1754i	−0.329688	−	0.190345i	−0.655702	+	0.755019i	$0.727627\pi$
$480$	63.9139	−	110.702i	0.133154	−	0.230630i
$481$	−53.4287	+	30.8471i	−0.111078	+	0.0641311i
$482$			81.4732i			0.169032i
$483$	73.5865	+	268.529i	0.152353	+	0.555961i
$484$	476.357			0.984209
$485$	−17.3519	−	30.0544i	−0.0357772	−	0.0619679i
$486$	33.9087	+	19.5772i	0.0697710	+	0.0402823i
$487$	−118.253	+	204.820i	−0.242819	+	0.420575i	−0.961516	−	0.274748i	$-0.911405\pi$
$487$	−118.253	+	204.820i	−0.242819	+	0.420575i	0.718697	+	0.695323i	$0.244739\pi$
$488$	26.9030	−	15.5325i	0.0551291	−	0.0318288i
$489$		−	276.455i		−	0.565348i
$490$	−275.189	+	3.12067i	−0.561609	+	0.00636871i
$491$	−233.364			−0.475284			−0.237642	−	0.971353i	$-0.576374\pi$
$491$	−233.364			−0.475284			−0.237642	+	0.971353i	$0.576374\pi$
$492$	−152.134	−	263.504i	−0.309216	−	0.535577i
$493$	−983.037	−	567.557i	−1.99399	−	1.15123i
$494$	−28.1123	+	48.6920i	−0.0569076	+	0.0985668i
$495$	105.104	−	60.6817i	0.212331	−	0.122589i
$496$			668.673i			1.34813i
$497$	−680.362	+	186.443i	−1.36894	+	0.375137i
$498$	352.788			0.708409
$499$	127.407	+	220.675i	0.255324	+	0.442235i	0.964984	−	0.262310i	$-0.0844844\pi$
$499$	127.407	+	220.675i	0.255324	+	0.442235i	−0.709659	+	0.704545i	$0.751151\pi$
$500$	22.3559	+	12.9072i	0.0447119	+	0.0258144i
$501$	164.093	−	284.218i	0.327532	−	0.567302i
$502$	768.578	−	443.739i	1.53103	−	0.883942i
$503$		−	740.796i		−	1.47275i	−0.676571	−	0.736377i	$-0.736535\pi$
$503$		−	740.796i		−	1.47275i	0.676571	−	0.736377i	$-0.263465\pi$
$504$	−63.4302	−	62.7150i	−0.125854	−	0.124435i
$505$	−23.3502			−0.0462381
$506$	−521.777	−	903.744i	−1.03118	−	1.78605i
$507$	238.201	+	137.525i	0.469824	+	0.271253i
$508$	170.076	−	294.580i	0.334795	−	0.579882i
$509$	−104.609	+	60.3958i	−0.205518	+	0.118656i	−0.599227	−	0.800579i	$-0.704525\pi$
$509$	−104.609	+	60.3958i	−0.205518	+	0.118656i	0.393709	+	0.919235i	$0.371192\pi$
$510$			326.417i			0.640034i
$511$	−46.6280	−	12.2110i	−0.0912485	−	0.0238963i
$512$	318.764			0.622586
$513$	−18.2102	−	31.5409i	−0.0354974	−	0.0614833i
$514$	−678.379	−	391.662i	−1.31980	−	0.761989i
$515$	75.7084	−	131.131i	0.147007	−	0.254623i
$516$	155.939	−	90.0316i	0.302208	−	0.174480i
$517$			969.226i			1.87471i
$518$	86.0463	−	328.570i	0.166112	−	0.634304i
$519$	−127.363			−0.245402
$520$	−15.1665	−	26.2692i	−0.0291664	−	0.0505177i
$521$	−121.114	−	69.9254i	−0.232465	−	0.134214i	0.379244	−	0.925297i	$-0.376184\pi$
$521$	−121.114	−	69.9254i	−0.232465	−	0.134214i	−0.611709	+	0.791083i	$0.709518\pi$
$522$	127.455	−	220.759i	0.244167	−	0.422910i
$523$	−500.230	+	288.808i	−0.956463	+	0.552214i	−0.895083	−	0.445900i	$-0.852884\pi$
$523$	−500.230	+	288.808i	−0.956463	+	0.552214i	−0.0613801	+	0.998114i	$0.519550\pi$
$524$		−	146.923i		−	0.280388i
$525$	42.6223	−	43.1084i	0.0811854	−	0.0821113i
$526$	−119.880			−0.227909
$527$	−563.614	−	976.208i	−1.06948	−	1.85239i
$528$	540.164	+	311.864i	1.02304	+	0.590651i
$529$	0.816801	−	1.41474i	0.00154405	−	0.00267437i
$530$	−0.618923	+	0.357336i	−0.00116778	+	0.000674218i
$531$			47.7201i			0.0898684i
$532$	−29.9399	−	109.256i	−0.0562780	−	0.205368i
$533$	−242.984			−0.455879
$534$	59.0024	+	102.195i	0.110491	+	0.191377i
$535$	139.725	+	80.6703i	0.261168	+	0.150786i
$536$	63.2520	−	109.556i	0.118008	−	0.204395i
$537$	301.682	−	174.176i	0.561792	−	0.324351i
$538$			713.058i			1.32539i
$539$	−10.0523	−	886.440i	−0.0186500	−	1.64460i
$540$	−26.8271			−0.0496799
$541$	320.603	+	555.300i	0.592611	+	1.02643i	0.993879	+	0.110472i	$0.0352362\pi$
$541$	320.603	+	555.300i	0.592611	+	1.02643i	−0.401268	+	0.915961i	$0.631430\pi$
$542$	354.407	+	204.617i	0.653887	+	0.377522i
$543$	106.592	−	184.623i	0.196302	−	0.340006i
$544$	−959.094	+	553.733i	−1.76304	+	1.01789i
$545$		−	362.190i		−	0.664570i
$546$	93.7995	−	25.7044i	0.171794	−	0.0470776i
$547$	705.352			1.28949			0.644746	−	0.764397i	$-0.276963\pi$
$547$	705.352			1.28949			0.644746	+	0.764397i	$0.276963\pi$
$548$	−40.1452	−	69.5335i	−0.0732576	−	0.126886i
$549$	−19.0011	−	10.9703i	−0.0346104	−	0.0199823i
$550$	−113.605	+	196.770i	−0.206555	+	0.357764i
$551$	−205.344	+	118.555i	−0.372674	+	0.215164i
$552$		−	168.951i		−	0.306070i
$553$	−305.675	−	302.228i	−0.552758	−	0.546525i
$554$	−1079.80			−1.94909
$555$	37.4086	+	64.7936i	0.0674029	+	0.116745i
$556$	−68.9650	−	39.8169i	−0.124038	−	0.0716132i
$557$	−153.355	+	265.618i	−0.275323	+	0.476873i	−0.970216	−	0.242240i	$-0.922118\pi$
$557$	−153.355	+	265.618i	−0.275323	+	0.476873i	0.694894	+	0.719112i	$0.255451\pi$
$558$	219.225	−	126.570i	0.392876	−	0.226827i
$559$		−	143.795i		−	0.257237i
$560$	301.392	+	78.9290i	0.538200	+	0.140945i
$561$	−1051.46			−1.87426
$562$	245.983	+	426.056i	0.437693	+	0.758106i
$563$	53.2662	+	30.7533i	0.0946114	+	0.0546239i	0.546559	−	0.837420i	$-0.315937\pi$
$563$	53.2662	+	30.7533i	0.0946114	+	0.0546239i	−0.451948	+	0.892044i	$0.649271\pi$
$564$	107.123	−	185.542i	0.189934	−	0.328975i
$565$	345.499	−	199.474i	0.611503	−	0.353051i
$566$		−	65.3373i		−	0.115437i
$567$	−15.9603	+	60.9448i	−0.0281487	+	0.107486i
$568$	428.064			0.753634
$569$	327.810	+	567.784i	0.576117	+	0.997863i	0.995919	+	0.0902479i	$0.0287659\pi$
$569$	327.810	+	567.784i	0.576117	+	0.997863i	−0.419803	+	0.907615i	$0.637901\pi$
$570$	59.0494	+	34.0922i	0.103595	+	0.0598108i
$571$	109.570	−	189.782i	0.191892	−	0.332367i	−0.753985	−	0.656892i	$-0.771871\pi$
$571$	109.570	−	189.782i	0.191892	−	0.332367i	0.945877	+	0.324524i	$0.105204\pi$
$572$	−115.533	+	66.7032i	−0.201981	+	0.116614i
$573$			292.606i			0.510657i
$574$	940.530	−	951.256i	1.63855	−	1.65724i
$575$	114.822			0.199691
$576$	−4.92330	−	8.52741i	−0.00854740	−	0.0148045i
$577$	−430.445	−	248.517i	−0.746005	−	0.430706i	0.0782437	−	0.996934i	$-0.475069\pi$
$577$	−430.445	−	248.517i	−0.746005	−	0.430706i	−0.824249	+	0.566228i	$0.808402\pi$
$578$	1051.05	−	1820.47i	1.81842	−	3.14960i
$579$	298.438	−	172.303i	0.515436	−	0.297587i
$580$			174.655i			0.301129i
$581$	150.023	+	547.457i	0.258215	+	0.942267i
$582$	−67.5197			−0.116013
$583$	−1.15105	−	1.99368i	−0.00197436	−	0.00341969i
$584$	25.3295	+	14.6240i	0.0433724	+	0.0250411i
$585$	−10.7118	+	18.5535i	−0.0183108	+	0.0317153i
$586$	1009.30	−	582.717i	1.72235	−	0.994398i
$587$			1122.33i			1.91198i	0.293395	+	0.955991i	$0.405215\pi$
$587$			1122.33i			1.91198i	−0.293395	+	0.955991i	$0.594785\pi$
$588$	−96.0486	+	170.805i	−0.163348	+	0.290485i
$589$	−235.463			−0.399768
$590$	−44.6697	−	77.3701i	−0.0757113	−	0.131136i
$591$	50.9118	+	29.3939i	0.0861452	+	0.0497359i
$592$	−192.256	+	332.996i	−0.324756	+	0.562494i
$593$	621.851	−	359.026i	1.04865	−	0.605440i	0.126381	−	0.991982i	$-0.459664\pi$
$593$	621.851	−	359.026i	1.04865	−	0.605440i	0.922272	+	0.386542i	$0.126331\pi$
$594$		−	236.124i		−	0.397515i
$595$	−506.536	+	138.809i	−0.851321	+	0.233292i
$596$	128.253			0.215189
$597$	−159.078	−	275.530i	−0.266462	−	0.461525i
$598$	159.534	+	92.1068i	0.266779	+	0.154025i
$599$	342.069	−	592.481i	0.571067	−	0.989117i	−0.425390	−	0.905010i	$-0.639863\pi$
$599$	342.069	−	592.481i	0.571067	−	0.989117i	0.996457	−	0.0841069i	$-0.0268037\pi$
$600$	−31.8570	+	18.3926i	−0.0530950	+	0.0306544i
$601$		−	264.906i		−	0.440776i	−0.975412	−	0.220388i	$-0.929268\pi$
$601$		−	264.906i		−	0.440776i	0.975412	−	0.220388i	$-0.0707323\pi$
$602$	562.945	+	556.597i	0.935124	+	0.924580i
$603$	−89.3475			−0.148172
$604$	−49.9080	−	86.4431i	−0.0826291	−	0.143118i
$605$	−399.522	−	230.664i	−0.660367	−	0.381263i
$606$	−22.7151	+	39.3436i	−0.0374836	+	0.0649235i
$607$	249.874	−	144.265i	0.411654	−	0.237669i	−0.279846	−	0.960045i	$-0.590283\pi$
$607$	249.874	−	144.265i	0.411654	−	0.237669i	0.691500	+	0.722376i	$0.256950\pi$
$608$			231.335i			0.380485i
$609$	396.774	+	103.908i	0.651518	+	0.170620i
$610$	41.0761			0.0673378
$611$	−85.5465	−	148.171i	−0.140011	−	0.242505i
$612$	201.284	+	116.212i	0.328896	+	0.189888i
$613$	−140.450	+	243.266i	−0.229119	+	0.396845i	−0.957547	−	0.288277i	$-0.906918\pi$
$613$	−140.450	+	243.266i	−0.229119	+	0.396845i	0.728428	+	0.685122i	$0.240251\pi$
$614$	502.712	−	290.241i	0.818749	−	0.472705i
$615$			294.669i			0.479137i
$616$	−136.277	+	520.378i	−0.221229	+	0.844769i
$617$	1060.68			1.71909			0.859544	−	0.511062i	$-0.170748\pi$
$617$	1060.68			1.71909			0.859544	+	0.511062i	$0.170748\pi$
$618$	−147.298	−	255.128i	−0.238346	−	0.412828i
$619$	−625.650	−	361.219i	−1.01074	−	0.583552i	−0.0993334	−	0.995054i	$-0.531671\pi$
$619$	−625.650	−	361.219i	−1.01074	−	0.583552i	−0.911409	+	0.411502i	$0.865004\pi$
$620$	−86.7208	+	150.205i	−0.139872	+	0.242266i
$621$	−103.340	+	59.6634i	−0.166409	+	0.0960764i
$622$			905.568i			1.45590i
$623$	−133.496	+	135.018i	−0.214279	+	0.216723i
$624$	−110.104			−0.176448
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−1069.40	−	617.416i	−1.70830	−	0.986288i
$627$	−109.818	+	190.210i	−0.175148	+	0.303366i
$628$	−86.4833	+	49.9312i	−0.137712	+	0.0795082i
$629$		−	648.196i		−	1.03052i
$630$	−31.1720	−	113.752i	−0.0494794	−	0.180558i
$631$	−836.847			−1.32622			−0.663112	−	0.748520i	$-0.730765\pi$
$631$	−836.847			−1.32622			−0.663112	+	0.748520i	$0.730765\pi$
$632$	130.419	+	225.893i	0.206360	+	0.357426i
$633$	−347.282	−	200.503i	−0.548628	−	0.316751i
$634$	−406.388	+	703.885i	−0.640991	+	1.11023i
$635$	−285.286	+	164.710i	−0.449270	+	0.259386i
$636$			0.508876i			0.000800119i
$637$	79.7763	+	134.628i	0.125237	+	0.211346i
$638$	−1537.26			−2.40950
$639$	−151.167	−	261.829i	−0.236568	−	0.409747i
$640$	−239.691	−	138.386i	−0.374517	−	0.216228i
$641$	464.543	−	804.611i	0.724715	−	1.25524i	−0.234376	−	0.972146i	$-0.575305\pi$
$641$	464.543	−	804.611i	0.724715	−	1.25524i	0.959091	−	0.283098i	$-0.0913621\pi$
$642$	271.849	−	156.952i	0.423440	−	0.244473i
$643$		−	417.625i		−	0.649495i	−0.945801	−	0.324748i	$-0.894721\pi$
$643$		−	417.625i		−	0.649495i	0.945801	−	0.324748i	$-0.105279\pi$
$644$	−357.963	+	98.0945i	−0.555843	+	0.152321i
$645$	−174.382			−0.270360
$646$	−295.365	−	511.588i	−0.457222	−	0.791931i
$647$	823.277	+	475.319i	1.27245	+	0.734651i	0.975449	−	0.220225i	$-0.0706791\pi$
$647$	823.277	+	475.319i	1.27245	+	0.734651i	0.297004	+	0.954876i	$0.404012\pi$
$648$	19.1142	−	33.1068i	0.0294972	−	0.0510907i
$649$	249.225	−	143.890i	0.384014	−	0.221711i
$650$		−	40.1084i		−	0.0617052i
$651$	289.636	+	286.371i	0.444910	+	0.439893i
$652$	368.529			0.565228
$653$	478.332	+	828.495i	0.732514	+	1.26875i	0.955805	+	0.294000i	$0.0949866\pi$
$653$	478.332	+	828.495i	0.732514	+	1.26875i	−0.223291	+	0.974752i	$0.571680\pi$
$654$	−610.268	−	352.338i	−0.933131	−	0.538744i
$655$	−71.1441	+	123.225i	−0.108617	+	0.188130i
$656$	−1311.51	+	757.202i	−1.99926	+	1.15427i
$657$		−	20.6573i		−	0.0314419i
$658$	911.203	+	238.627i	1.38481	+	0.362655i
$659$	36.4849			0.0553641			0.0276820	−	0.999617i	$-0.491187\pi$
$659$	36.4849			0.0553641			0.0276820	+	0.999617i	$0.491187\pi$
$660$	80.8917	+	140.109i	0.122563	+	0.212286i
$661$	479.862	+	277.048i	0.725963	+	0.419135i	0.816944	−	0.576718i	$-0.195667\pi$
$661$	479.862	+	277.048i	0.725963	+	0.419135i	−0.0909803	+	0.995853i	$0.529000\pi$
$662$	66.2343	−	114.721i	0.100052	−	0.173295i
$663$	160.742	−	92.8045i	0.242447	−	0.139977i
$664$		−	344.444i		−	0.518742i
$665$	−27.7937	+	106.131i	−0.0417950	+	0.159595i
$666$	145.564			0.218565
$667$	388.432	+	672.784i	0.582357	+	1.00867i
$668$	378.877	+	218.745i	0.567181	+	0.327462i
$669$	−210.987	+	365.440i	−0.315377	+	0.546249i
$670$	144.862	−	83.6360i	0.216212	−	0.124830i
$671$			132.315i			0.197190i
$672$	281.350	−	284.559i	0.418676	−	0.423451i
$673$	−232.062			−0.344817			−0.172408	−	0.985026i	$-0.555155\pi$
$673$	−232.062			−0.344817			−0.172408	+	0.985026i	$0.555155\pi$
$674$	347.591	+	602.045i	0.515713	+	0.893242i
$675$	22.5000	+	12.9904i	0.0333333	+	0.0192450i
$676$	−183.328	+	317.534i	−0.271196	+	0.469725i
$677$	114.622	−	66.1769i	0.169308	−	0.0977502i	−0.412951	−	0.910753i	$-0.635502\pi$
$677$	114.622	−	66.1769i	0.169308	−	0.0977502i	0.582260	+	0.813003i	$0.302169\pi$
$678$		−	776.192i		−	1.14483i
$679$	−28.7127	−	104.777i	−0.0422867	−	0.154311i
$680$	318.698			0.468673
$681$	35.9626	+	62.2891i	0.0528085	+	0.0914670i
$682$	−1322.06	−	763.290i	−1.93850	−	1.11919i
$683$	−426.855	+	739.334i	−0.624970	+	1.08248i	0.363576	+	0.931564i	$0.381556\pi$
$683$	−426.855	+	739.334i	−0.624970	+	1.08248i	−0.988547	+	0.150916i	$0.951778\pi$
$684$	42.0456	−	24.2751i	0.0614702	−	0.0354899i
$685$			77.7573i			0.113514i
$686$	−835.848	−	208.794i	−1.21844	−	0.304365i
$687$	−506.212			−0.736844
$688$	−448.105	−	776.141i	−0.651316	−	1.12811i
$689$	0.351935	+	0.203190i	0.000510791	+	0.000294905i
$690$	111.699	−	193.468i	0.161883	−	0.280389i
$691$	−306.365	+	176.880i	−0.443364	+	0.255976i	−0.705024	−	0.709184i	$-0.749064\pi$
$691$	−306.365	+	176.880i	−0.443364	+	0.255976i	0.261659	+	0.965160i	$0.415730\pi$
$692$		−	169.782i		−	0.245350i
$693$	366.418	−	100.412i	0.528742	−	0.144894i
$694$	−414.295			−0.596966
$695$	38.5608	+	66.7892i	0.0554831	+	0.0960995i
$696$	−215.538	−	124.441i	−0.309681	−	0.178794i
$697$	1276.47	−	2210.90i	1.83137	−	3.17203i
$698$	−803.111	+	463.676i	−1.15059	+	0.664292i
$699$		−	623.329i		−	0.891745i
$700$	57.4657	+	56.8177i	0.0820939	+	0.0811682i
$701$	−338.721			−0.483196			−0.241598	−	0.970376i	$-0.577672\pi$
$701$	−338.721			−0.483196			−0.241598	+	0.970376i	$0.577672\pi$
$702$	20.8409	+	36.0976i	0.0296879	+	0.0514210i
$703$	−117.260	−	67.6998i	−0.166799	−	0.0963013i
$704$	−29.6904	+	51.4253i	−0.0421739	+	0.0730473i
$705$	−179.688	+	103.743i	−0.254877	+	0.147153i
$706$			830.080i			1.17575i
$707$	−70.7131	−	18.5185i	−0.100019	−	0.0261930i
$708$	−63.6134			−0.0898494
$709$	170.868	+	295.952i	0.240998	+	0.417421i	0.960999	−	0.276552i	$-0.0891918\pi$
$709$	170.868	+	295.952i	0.240998	+	0.417421i	−0.720001	+	0.693973i	$0.755858\pi$
$710$	490.183	+	283.007i	0.690398	+	0.398602i
$711$	92.1128	−	159.544i	0.129554	−	0.224394i
$712$	99.7782	−	57.6070i	0.140138	−	0.0809087i
$713$			771.467i			1.08200i
$714$	−258.873	+	988.513i	−0.362568	+	1.38447i
$715$	129.198			0.180696
$716$	232.186	+	402.158i	0.324282	+	0.561673i
$717$	268.045	+	154.756i	0.373842	+	0.215838i
$718$	−518.486	+	898.044i	−0.722125	+	1.25076i
$719$	529.822	−	305.893i	0.736887	−	0.425442i	−0.0840494	−	0.996462i	$-0.526785\pi$
$719$	529.822	−	305.893i	0.736887	−	0.425442i	0.820936	+	0.571020i	$0.193452\pi$
$720$			133.524i			0.185450i
$721$	333.270	−	337.071i	0.462233	−	0.467504i
$722$	783.348			1.08497
$723$	−28.0911	−	48.6552i	−0.0388535	−	0.0672962i
$724$	246.112	+	142.093i	0.339934	+	0.196261i
$725$	84.5724	−	146.484i	0.116652	−	0.202047i
$726$	−777.309	+	448.779i	−1.07067	+	0.618154i
$727$			779.914i			1.07278i	0.843969	+	0.536392i	$0.180213\pi$
$727$			779.914i			1.07278i	−0.843969	+	0.536392i	$0.819787\pi$
$728$	−25.0965	−	91.5811i	−0.0344732	−	0.125798i
$729$	−27.0000			−0.0370370
$730$	19.3368	+	33.4923i	0.0264888	+	0.0458799i
$731$	1308.39	+	755.401i	1.78987	+	1.03338i
$732$	14.6239	−	25.3294i	0.0199781	−	0.0346030i
$733$	−758.843	+	438.118i	−1.03526	+	0.597705i	−0.918486	−	0.395454i	$-0.870587\pi$
$733$	−758.843	+	438.118i	−1.03526	+	0.597705i	−0.116770	+	0.993159i	$0.537254\pi$
$734$			875.433i			1.19269i
$735$	163.264	−	96.7456i	0.222129	−	0.131627i
$736$	757.942			1.02981
$737$	269.409	+	466.630i	0.365548	+	0.633148i
$738$	496.498	+	286.654i	0.672762	+	0.388419i
$739$	−205.331	+	355.644i	−0.277850	+	0.481250i	−0.970850	−	0.239687i	$-0.922955\pi$
$739$	−205.331	+	355.644i	−0.277850	+	0.481250i	0.693000	+	0.720937i	$0.256288\pi$
$740$	−86.3732	+	49.8676i	−0.116721	+	0.0673886i
$741$		−	38.7713i		−	0.0523229i
$742$	−2.15772	+	0.591292i	−0.00290798	+	0.000796890i
$743$	938.294			1.26284			0.631422	−	0.775439i	$-0.282471\pi$
$743$	938.294			1.26284			0.631422	+	0.775439i	$0.282471\pi$
$744$	−123.576	−	214.040i	−0.166097	−	0.287689i
$745$	−107.566	−	62.1033i	−0.144384	−	0.0833601i
$746$	596.137	−	1032.54i	0.799112	−	1.38410i
$747$	−210.682	+	121.637i	−0.282038	+	0.162834i
$748$		−	1401.65i		−	1.87386i
$749$	359.162	+	355.112i	0.479522	+	0.474115i
$750$	−48.6399			−0.0648532
$751$	−416.766	−	721.860i	−0.554948	−	0.961198i	−0.997908	−	0.0646568i	$-0.979405\pi$
$751$	−416.766	−	721.860i	−0.554948	−	0.961198i	0.442959	−	0.896542i	$-0.353929\pi$
$752$	−923.480	−	533.171i	−1.22803	−	0.709004i
$753$	−305.993	+	529.995i	−0.406365	+	0.703844i
$754$	235.009	−	135.683i	0.311683	−	0.179950i
$755$			96.6668i			0.128036i
$756$	−81.2425	−	21.2759i	−0.107464	−	0.0281427i
$757$	466.398			0.616113			0.308057	−	0.951368i	$-0.400321\pi$
$757$	466.398			0.616113			0.308057	+	0.951368i	$0.400321\pi$
$758$	94.1513	+	163.075i	0.124210	+	0.215138i
$759$	623.202	+	359.806i	0.821083	+	0.474052i
$760$	33.2859	−	57.6529i	0.0437972	−	0.0758590i
$761$	−528.454	+	305.103i	−0.694420	+	0.400924i	−0.805266	−	0.592914i	$-0.797977\pi$
$761$	−528.454	+	305.103i	−0.694420	+	0.400924i	0.110846	+	0.993838i	$0.464644\pi$
$762$			640.919i			0.841101i
$763$	287.244	−	1096.85i	0.376466	−	1.43755i
$764$	−390.059			−0.510549
$765$	−112.545	−	194.934i	−0.147118	−	0.254816i
$766$	−1271.38	−	734.033i	−1.65977	−	0.958268i
$767$	−25.4003	+	43.9946i	−0.0331164	+	0.0573593i
$768$	−486.036	+	280.613i	−0.632859	+	0.365381i
$769$		−	351.836i		−	0.457524i	−0.973482	−	0.228762i	$-0.926532\pi$
$769$		−	351.836i		−	0.457524i	0.973482	−	0.228762i	$-0.0734677\pi$
$770$	−500.092	+	505.795i	−0.649470	+	0.656877i
$771$	540.163			0.700601
$772$	229.689	+	397.833i	0.297524	+	0.515327i
$773$	−16.9721	−	9.79886i	−0.0219562	−	0.0126764i	0.488982	−	0.872294i	$-0.337368\pi$
$773$	−16.9721	−	9.79886i	−0.0219562	−	0.0126764i	−0.510938	+	0.859618i	$0.670702\pi$
$774$	−169.639	+	293.823i	−0.219172	+	0.379617i
$775$	145.466	−	83.9849i	0.187698	−	0.108368i
$776$			65.9229i			0.0849522i
$777$	61.9010	+	225.887i	0.0796667	+	0.290717i
$778$	1395.06			1.79314
$779$	−266.637	−	461.829i	−0.342281	−	0.592848i
$780$	−24.7327	−	14.2794i	−0.0317086	−	0.0183070i
$781$	−911.625	+	1578.98i	−1.16725	+	2.02174i
$782$	−1676.16	+	967.730i	−2.14342	+	1.23751i
$783$			175.781i			0.224496i
$784$	850.131	+	478.053i	1.08435	+	0.609761i
$785$	96.7118			0.123200
$786$	138.418	+	239.746i	0.176104	+	0.305021i
$787$	9.99550	+	5.77090i	0.0127008	+	0.00733279i	0.506337	−	0.862336i	$-0.330999\pi$
$787$	9.99550	+	5.77090i	0.0127008	+	0.00733279i	−0.493636	+	0.869669i	$0.664333\pi$
$788$	−39.1836	+	67.8680i	−0.0497254	+	0.0861269i
$789$	71.5916	−	41.3334i	0.0907371	−	0.0523871i
$790$			344.898i			0.436580i
$791$	1204.50	−	330.075i	1.52275	−	0.417288i
$792$	−230.540			−0.291086
$793$	−11.6784	−	20.2276i	−0.0147269	−	0.0255078i
$794$	23.4294	+	13.5270i	0.0295081	+	0.0170365i
$795$	0.246411	−	0.426796i	0.000309951	−	0.000536850i
$796$	367.296	−	212.059i	0.461427	−	0.266405i
$797$		−	1503.22i		−	1.88610i	−0.332650	−	0.943050i	$-0.607943\pi$
$797$		−	1503.22i		−	1.88610i	0.332650	−	0.943050i	$-0.392057\pi$
$798$	151.786	+	150.074i	0.190208	+	0.188063i
$799$	1797.61			2.24982
$800$	−82.5125	−	142.916i	−0.103141	−	0.178645i
$801$	−70.4715	−	40.6867i	−0.0879794	−	0.0507949i
$802$	−115.047	+	199.267i	−0.143450	+	0.248463i
$803$	−107.886	+	62.2879i	−0.134353	+	0.0775690i
$804$		−	119.105i		−	0.148140i
$805$	347.725	+	91.0626i	0.431956	+	0.113121i
$806$	269.480			0.334342
$807$	−245.854	−	425.832i	−0.304652	−	0.527673i
$808$	38.4132	+	22.1778i	0.0475410	+	0.0274478i
$809$	375.558	−	650.485i	0.464224	−	0.804060i	−0.534942	−	0.844889i	$-0.679666\pi$
$809$	375.558	−	650.485i	0.464224	−	0.804060i	0.999166	+	0.0408287i	$0.0129998\pi$
$810$	43.7759	−	25.2740i	0.0540444	−	0.0312025i
$811$		−	1514.57i		−	1.86753i	−0.357889	−	0.933764i	$-0.616503\pi$
$811$		−	1514.57i		−	1.86753i	0.357889	−	0.933764i	$-0.383497\pi$
$812$	−138.514	+	528.920i	−0.170584	+	0.651380i
$813$	−282.198			−0.347108
$814$	−438.919	−	760.230i	−0.539212	−	0.933943i
$815$	−309.086	−	178.451i	−0.379247	−	0.218958i
$816$	578.408	−	1001.83i	0.708833	−	1.22773i
$817$	273.306	−	157.793i	0.334524	−	0.193138i
$818$		−	1228.45i		−	1.50177i
$819$	−47.1537	+	47.6915i	−0.0575748	+	0.0582314i
$820$	−392.809			−0.479035
$821$	514.749	+	891.572i	0.626978	+	1.08596i	0.988155	+	0.153461i	$0.0490419\pi$
$821$	514.749	+	891.572i	0.626978	+	1.08596i	−0.361177	+	0.932497i	$0.617625\pi$
$822$	131.016	+	75.6422i	0.159387	+	0.0920221i
$823$	−401.675	+	695.721i	−0.488062	+	0.845347i	−0.999906	−	0.0137309i	$-0.995629\pi$
$823$	−401.675	+	695.721i	−0.488062	+	0.845347i	0.511844	+	0.859078i	$0.328963\pi$
$824$	−249.094	+	143.815i	−0.302299	+	0.174532i
$825$		−	156.679i		−	0.189914i
$826$	−73.9161	−	269.732i	−0.0894867	−	0.326552i
$827$	661.812			0.800257			0.400128	−	0.916459i	$-0.368966\pi$
$827$	661.812			0.800257			0.400128	+	0.916459i	$0.368966\pi$
$828$	−79.5344	−	137.758i	−0.0960560	−	0.166374i
$829$	−471.540	−	272.243i	−0.568805	−	0.328400i	0.187867	−	0.982195i	$-0.439843\pi$
$829$	−471.540	−	272.243i	−0.568805	−	0.328400i	−0.756672	+	0.653795i	$0.773176\pi$
$830$	227.724	−	394.429i	0.274366	−	0.475215i
$831$	644.847	−	372.303i	0.775989	−	0.448017i
$832$		−	10.4822i		−	0.0125988i
$833$	−1644.06	+	18.6439i	−1.97367	+	0.0223816i
$834$	150.047			0.179913
$835$	−211.844	−	366.924i	−0.253705	−	0.439430i
$836$	−253.560	−	146.393i	−0.303302	−	0.175111i
$837$	−87.2796	+	151.173i	−0.104277	+	0.180613i
$838$	1311.66	−	757.288i	1.56523	−	0.903685i
$839$		−	409.350i		−	0.487903i	−0.969787	−	0.243951i	$-0.921556\pi$
$839$		−	409.350i		−	0.487903i	0.969787	−	0.243951i	$-0.0784437\pi$
$840$	−111.062	+	30.4348i	−0.132216	+	0.0362319i
$841$	303.400			0.360761
$842$	−746.098	−	1292.28i	−0.886102	−	1.53477i
$843$	−293.799	−	169.625i	−0.348516	−	0.201216i
$844$	267.281	−	462.944i	0.316683	−	0.548512i
$845$	307.516	−	177.544i	0.363924	−	0.210112i
$846$			403.685i			0.477169i
$847$	−1026.97	−	1015.39i	−1.21248	−	1.19880i
$848$	2.53278			0.00298676
$849$	22.5276	+	39.0189i	0.0265342	+	0.0459587i
$850$	364.946	+	210.702i	0.429348	+	0.247884i
$851$	−221.811	+	384.187i	−0.260647	+	0.451454i
$852$	349.031	−	201.513i	0.409661	−	0.236518i
$853$			322.928i			0.378579i	0.981921	+	0.189289i	$0.0606184\pi$
$853$			322.928i			0.378579i	−0.981921	+	0.189289i	$0.939382\pi$
$854$	124.394	+	32.5764i	0.145660	+	0.0381456i
$855$	−47.0184			−0.0549923
$856$	−153.240	−	265.419i	−0.179019	−	0.310069i
$857$	−176.838	−	102.098i	−0.206346	−	0.119134i	0.393266	−	0.919425i	$-0.371345\pi$
$857$	−176.838	−	102.098i	−0.206346	−	0.119134i	−0.599612	+	0.800291i	$0.704678\pi$
$858$	125.683	−	217.690i	0.146484	−	0.253718i
$859$	−506.168	+	292.236i	−0.589253	+	0.340205i	−0.764802	−	0.644265i	$-0.777163\pi$
$859$	−506.168	+	292.236i	−0.589253	+	0.340205i	0.175549	+	0.984471i	$0.443830\pi$
$860$		−	232.461i		−	0.270303i
$861$	−233.694	+	892.367i	−0.271422	+	1.03643i
$862$	−1314.00			−1.52436
$863$	−176.836	−	306.288i	−0.204908	−	0.354911i	0.745195	−	0.666846i	$-0.232356\pi$
$863$	−176.836	−	306.288i	−0.204908	−	0.354911i	−0.950103	+	0.311935i	$0.899023\pi$
$864$	148.523	+	85.7495i	0.171901	+	0.0992471i
$865$	−82.2128	+	142.397i	−0.0950437	+	0.164620i
$866$	291.102	−	168.068i	0.336145	−	0.194074i
$867$			1449.56i			1.67193i
$868$	−381.747	+	386.100i	−0.439800	+	0.444816i
$869$	−1110.99			−1.27847
$870$	−164.544	−	284.998i	−0.189131	−	0.327584i
$871$	−82.3720	−	47.5575i	−0.0945718	−	0.0546010i
$872$	−344.006	+	595.835i	−0.394502	+	0.683297i
$873$	40.3222	−	23.2801i	0.0461881	−	0.0266667i
$874$			404.292i			0.462577i
$875$	−20.6841	−	75.4796i	−0.0236389	−	0.0862624i
$876$	27.5372			0.0314352
$877$	−385.179	−	667.149i	−0.439200	−	0.760717i	0.558428	−	0.829553i	$-0.311405\pi$
$877$	−385.179	−	667.149i	−0.439200	−	0.760717i	−0.997628	+	0.0688360i	$0.978071\pi$
$878$	−612.472	−	353.611i	−0.697576	−	0.402746i
$879$	−401.829	+	695.988i	−0.457143	+	0.791795i
$880$	697.348	−	402.614i	0.792441	−	0.457516i
$881$		−	477.678i		−	0.542200i	−0.962551	−	0.271100i	$-0.912613\pi$
$881$		−	477.678i		−	0.542200i	0.962551	−	0.271100i	$-0.0873874\pi$
$882$	−4.18682	−	369.204i	−0.00474696	−	0.418599i
$883$	1519.53			1.72088			0.860438	−	0.509556i	$-0.170190\pi$
$883$	1519.53			1.72088			0.860438	+	0.509556i	$0.170190\pi$
$884$	123.713	+	214.278i	0.139947	+	0.242395i
$885$	53.3527	+	30.8032i	0.0602856	+	0.0348059i
$886$	344.717	−	597.067i	0.389071	−	0.673891i
$887$	−1179.73	+	681.115i	−1.33002	+	0.767887i	−0.985302	−	0.170820i	$-0.945358\pi$
$887$	−1179.73	+	681.115i	−1.33002	+	0.767887i	−0.344716	+	0.938707i	$0.612025\pi$
$888$		−	142.122i		−	0.160047i
$889$	−994.580	+	272.550i	−1.11876	+	0.306581i
$890$	152.343			0.171172
$891$	81.4130	+	141.011i	0.0913726	+	0.158262i
$892$	−487.150	−	281.256i	−0.546133	−	0.315310i
$893$	187.748	−	325.189i	0.210244	−	0.364154i
$894$	−209.280	+	120.828i	−0.234094	+	0.135154i
$895$		−	449.721i		−	0.502482i
$896$	−616.124	−	609.176i	−0.687638	−	0.679884i
$897$	−127.030			−0.141616
$898$	1078.61	+	1868.20i	1.20112	+	2.08040i
$899$	984.194	+	568.225i	1.09477	+	0.632063i
$900$	−17.3168	+	29.9936i	−0.0192409	+	0.0333263i
$901$	−3.69764	+	2.13484i	−0.00410393	+	0.00236941i
$902$		−	3457.38i		−	3.83302i
$903$	−528.095	−	138.298i	−0.584823	−	0.153154i
$904$	−757.835			−0.838314
$905$	−137.610	−	238.347i	−0.152055	−	0.263367i
$906$	162.877	+	94.0374i	0.179776	+	0.103794i
$907$	−740.973	+	1283.40i	−0.816950	+	1.41500i	0.0909699	+	0.995854i	$0.471003\pi$
$907$	−740.973	+	1283.40i	−0.816950	+	1.41500i	−0.907920	+	0.419145i	$0.862330\pi$
$908$	−83.0345	+	47.9400i	−0.0914477	+	0.0527973i
$909$		−	31.3276i		−	0.0344638i
$910$	31.8089	−	121.463i	0.0349549	−	0.133476i
$911$	78.8697			0.0865749			0.0432875	−	0.999063i	$-0.486217\pi$
$911$	78.8697			0.0865749			0.0432875	+	0.999063i	$0.486217\pi$
$912$	−120.822	−	209.269i	−0.132480	−	0.229462i
$913$	1270.54	+	733.545i	1.39161	+	0.803445i
$914$	−224.427	+	388.718i	−0.245543	+	0.425294i
$915$	−24.5303	+	14.1626i	−0.0268091	+	0.0154782i
$916$		−	674.807i		−	0.736688i
$917$	−313.177	+	316.749i	−0.341524	+	0.345419i
$918$	−437.935			−0.477053
$919$	−57.0752	−	98.8572i	−0.0621058	−	0.107570i	0.833301	−	0.552820i	$-0.186448\pi$
$919$	−57.0752	−	98.8572i	−0.0621058	−	0.107570i	−0.895407	+	0.445250i	$0.853115\pi$
$920$	−188.893	−	109.057i	−0.205318	−	0.118541i
$921$	−200.144	+	346.659i	−0.217311	+	0.376394i
$922$	−692.992	+	400.099i	−0.751618	+	0.433947i
$923$		−	321.850i		−	0.348700i
$924$	133.854	+	488.454i	0.144863	+	0.528630i
$925$	96.5886			0.104420
$926$	1031.66	+	1786.90i	1.11411	+	1.92969i
$927$	175.931	+	101.574i	0.189785	+	0.109572i
$928$	558.263	−	966.940i	0.601576	−	1.04196i
$929$	−457.113	+	263.914i	−0.492048	+	0.284084i	−0.725424	−	0.688302i	$-0.758356\pi$
$929$	−457.113	+	263.914i	−0.492048	+	0.284084i	0.233376	+	0.972387i	$0.425023\pi$
$930$		−	326.801i		−	0.351399i
$931$	−168.339	+	299.361i	−0.180815	+	0.321547i
$932$	830.930			0.891556
$933$	−312.230	−	540.798i	−0.334651	−	0.579633i
$934$	410.836	+	237.196i	0.439867	+	0.253957i
$935$	−678.714	+	1175.57i	−0.725897	+	1.25729i
$936$	35.2439	−	20.3481i	0.0376537	−	0.0217394i
$937$		−	1454.57i		−	1.55237i	−0.630506	−	0.776184i	$-0.717153\pi$
$937$		−	1454.57i		−	1.55237i	0.630506	−	0.776184i	$-0.282847\pi$
$938$	505.025	−	138.395i	0.538406	−	0.147542i
$939$	851.514			0.906830
$940$	−138.295	−	239.534i	−0.147122	−	0.254823i
$941$	707.370	+	408.400i	0.751722	+	0.434007i	0.826316	−	0.563207i	$-0.190433\pi$
$941$	707.370	+	408.400i	0.751722	+	0.434007i	−0.0745940	+	0.997214i	$0.523766\pi$
$942$	94.0811	−	162.953i	0.0998738	−	0.172986i
$943$	−1513.13	+	873.605i	−1.60459	+	0.926410i
$944$			316.616i			0.335399i
$945$	57.8360	+	57.1839i	0.0612021	+	0.0605120i
$946$	2046.05			2.16284
$947$	−387.230	−	670.701i	−0.408901	−	0.708238i	0.585866	−	0.810408i	$-0.300755\pi$
$947$	−387.230	−	670.701i	−0.408901	−	0.708238i	−0.994767	+	0.102170i	$0.967421\pi$
$948$	212.680	+	122.791i	0.224346	+	0.129526i
$949$	10.9954	−	19.0446i	0.0115863	−	0.0200680i
$950$	76.2324	−	44.0128i	0.0802446	−	0.0463293i
$951$		−	560.473i		−	0.589351i
$952$	965.135	+	252.751i	1.01380	+	0.265495i
$953$	126.147			0.132368			0.0661840	−	0.997807i	$-0.478918\pi$
$953$	126.147			0.132368			0.0661840	+	0.997807i	$0.478918\pi$
$954$	−0.479416	−	0.830373i	−0.000502532	−	0.000870412i
$955$	327.144	+	188.877i	0.342559	+	0.197777i
$956$	−206.297	+	357.317i	−0.215792	+	0.373763i
$957$	918.039	−	530.030i	0.959289	−	0.553846i
$958$			458.020i			0.478101i
$959$	−61.6673	+	235.478i	−0.0643038	+	0.245545i
$960$	−12.7119			−0.0132416
$961$	83.7768	+	145.106i	0.0871767	+	0.150995i
$962$	134.200	+	77.4803i	0.139501	+	0.0805408i
$963$	−108.231	+	187.461i	−0.112389	+	0.194663i
$964$	64.8598	−	37.4468i	0.0672819	−	0.0388452i
$965$		−	444.885i		−	0.461020i
$966$	491.701	−	497.308i	0.509007	−	0.514812i
$967$	−1344.77			−1.39066			−0.695331	−	0.718690i	$-0.744742\pi$
$967$	−1344.77			−1.39066			−0.695331	+	0.718690i	$0.744742\pi$
$968$	438.166	+	758.926i	0.452651	+	0.784014i
$969$	352.780	+	203.677i	0.364066	+	0.210193i
$970$	−43.5838	+	75.4893i	−0.0449317	+	0.0778241i
$971$	−292.296	+	168.757i	−0.301026	+	0.173797i	−0.642904	−	0.765947i	$-0.722270\pi$
$971$	−292.296	+	168.757i	−0.301026	+	0.173797i	0.341878	+	0.939744i	$0.388937\pi$
$972$		−	35.9924i		−	0.0370292i
$973$	63.8075	+	232.844i	0.0655781	+	0.239305i
$974$	594.044			0.609902
$975$	13.8289	+	23.9524i	0.0141835	+	0.0245666i
$976$	−126.070	−	72.7863i	−0.129170	−	0.0745761i
$977$	−10.4344	+	18.0729i	−0.0106800	+	0.0184984i	−0.871316	−	0.490722i	$-0.836733\pi$
$977$	−10.4344	+	18.0729i	−0.0106800	+	0.0184984i	0.860636	+	0.509221i	$0.170066\pi$
$978$	−601.357	+	347.194i	−0.614884	+	0.355004i
$979$			490.730i			0.501257i
$980$	128.967	+	217.640i	0.131599	+	0.222081i
$981$	485.929			0.495341
$982$	293.077	+	507.624i	0.298449	+	0.516929i
$983$	106.119	+	61.2679i	0.107954	+	0.0623274i	0.553005	−	0.833178i	$-0.313481\pi$
$983$	106.119	+	61.2679i	0.107954	+	0.0623274i	−0.445051	+	0.895505i	$0.646814\pi$
$984$	279.874	−	484.756i	0.284425	−	0.492639i
$985$	65.7268	−	37.9474i	0.0667278	−	0.0385253i
$986$			2851.13i			2.89161i
$987$	−626.439	+	171.667i	−0.634690	+	0.173928i
$988$	51.6841			0.0523119
$989$	−516.992	−	895.456i	−0.522742	−	0.905415i
$990$	−263.995	−	152.417i	−0.266661	−	0.153957i
$991$	248.494	−	430.404i	0.250751	−	0.434313i	−0.712982	−	0.701182i	$-0.752656\pi$
$991$	248.494	−	430.404i	0.250751	−	0.434313i	0.963733	+	0.266869i	$0.0859892\pi$
$992$	960.222	−	554.384i	0.967966	−	0.558855i
$993$			91.3474i			0.0919913i
$994$	1260.01	+	1245.80i	1.26762	+	1.25332i
$995$	−410.737			−0.412801
$996$	−162.149	−	280.850i	−0.162800	−	0.281978i
$997$	344.863	+	199.107i	0.345901	+	0.199706i	0.662878	−	0.748727i	$-0.269335\pi$
$997$	344.863	+	199.107i	0.345901	+	0.199706i	−0.316977	+	0.948433i	$0.602668\pi$
$998$	320.015	−	554.282i	0.320656	−	0.555393i
$999$	−86.9298	+	50.1889i	−0.0870168	+	0.0502392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.n.b.31.2	✓	12
3.2	odd	2		315.3.w.b.136.5		12
5.2	odd	4		525.3.s.j.199.9		24
5.3	odd	4		525.3.s.j.199.4		24
5.4	even	2		525.3.o.m.451.5		12
7.3	odd	6		735.3.h.b.391.10		12
7.4	even	3		735.3.h.b.391.9		12
7.5	odd	6	inner	105.3.n.b.61.2	yes	12
21.5	even	6		315.3.w.b.271.5		12
35.12	even	12		525.3.s.j.124.4		24
35.19	odd	6		525.3.o.m.376.5		12
35.33	even	12		525.3.s.j.124.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.b.31.2	✓	12	1.1	even	1	trivial
105.3.n.b.61.2	yes	12	7.5	odd	6	inner
315.3.w.b.136.5		12	3.2	odd	2
315.3.w.b.271.5		12	21.5	even	6
525.3.o.m.376.5		12	35.19	odd	6
525.3.o.m.451.5		12	5.4	even	2
525.3.s.j.124.4		24	35.12	even	12
525.3.s.j.124.9		24	35.33	even	12
525.3.s.j.199.4		24	5.3	odd	4
525.3.s.j.199.9		24	5.2	odd	4
735.3.h.b.391.9		12	7.4	even	3
735.3.h.b.391.10		12	7.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25588 - 2.17524i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.15446 + 1.99958i) q^{4} +(1.93649 - 1.11803i) q^{5} -4.35049i q^{6} +(6.75110 - 1.85004i) q^{7} -4.24760 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.25588 - 2.17524i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.15446 + 1.99958i) q^{4} +(1.93649 - 1.11803i) q^{5} -4.35049i q^{6} +(6.75110 - 1.85004i) q^{7} -4.24760 q^{8} +(1.50000 + 2.59808i) q^{9} +(-4.86399 - 2.80823i) q^{10} +(9.04589 - 15.6679i) q^{11} +(-3.46337 + 1.99958i) q^{12} +3.19366i q^{13} +(-12.5028 - 12.3619i) q^{14} +3.87298 q^{15} +(9.95229 + 17.2379i) q^{16} +(-29.0590 - 16.7772i) q^{17} +(3.76763 - 6.52573i) q^{18} +(-6.07005 + 3.50455i) q^{19} +5.16288i q^{20} +(11.7288 + 3.07156i) q^{21} -45.4421 q^{22} +(11.4822 + 19.8878i) q^{23} +(-6.37140 - 3.67853i) q^{24} +(2.50000 - 4.33013i) q^{25} +(6.94698 - 4.01084i) q^{26} +5.19615i q^{27} +(-4.09455 + 15.6351i) q^{28} +33.8290 q^{29} +(-4.86399 - 8.42468i) q^{30} +(29.0932 + 16.7970i) q^{31} +(16.5025 - 28.5832i) q^{32} +(27.1377 - 15.6679i) q^{33} +84.2806i q^{34} +(11.0050 - 11.1305i) q^{35} -6.92674 q^{36} +(9.65886 + 16.7296i) q^{37} +(15.2465 + 8.80256i) q^{38} +(-2.76579 + 4.79048i) q^{39} +(-8.22544 + 4.74896i) q^{40} +76.0832i q^{41} +(-8.04858 - 29.3706i) q^{42} -45.0254 q^{43} +(20.8862 + 36.1759i) q^{44} +(5.80948 + 3.35410i) q^{45} +(28.8405 - 49.9533i) q^{46} +(-46.3954 + 26.7864i) q^{47} +34.4757i q^{48} +(42.1547 - 24.9796i) q^{49} -12.5588 q^{50} +(-29.0590 - 50.3317i) q^{51} +(-6.38596 - 3.68693i) q^{52} +(0.0636230 - 0.110198i) q^{53} +(11.3029 - 6.52573i) q^{54} -40.4544i q^{55} +(-28.6760 + 7.85823i) q^{56} -12.1401 q^{57} +(-42.4850 - 73.5863i) q^{58} +(13.7756 + 7.95335i) q^{59} +(-4.47119 + 7.74433i) q^{60} +(-6.33370 + 3.65676i) q^{61} -84.3798i q^{62} +(14.9332 + 14.7648i) q^{63} -3.28220 q^{64} +(3.57062 + 6.18449i) q^{65} +(-68.1632 - 39.3540i) q^{66} +(-14.8912 + 25.7924i) q^{67} +(67.0948 - 38.7372i) q^{68} +39.7756i q^{69} +(-38.0326 - 9.96004i) q^{70} -100.778 q^{71} +(-6.37140 - 11.0356i) q^{72} +(-5.96325 - 3.44288i) q^{73} +(24.2607 - 42.0208i) q^{74} +(7.50000 - 4.33013i) q^{75} -16.1834i q^{76} +(32.0834 - 122.511i) q^{77} +13.8940 q^{78} +(-30.7043 - 53.1813i) q^{79} +(38.5450 + 22.2540i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(165.499 - 95.5512i) q^{82} +81.0916i q^{83} +(-19.6822 + 19.9067i) q^{84} -75.0301 q^{85} +(56.5463 + 97.9411i) q^{86} +(50.7435 + 29.2968i) q^{87} +(-38.4233 + 66.5511i) q^{88} +(-23.4905 + 13.5622i) q^{89} -16.8494i q^{90} +(5.90839 + 21.5607i) q^{91} -53.0229 q^{92} +(29.0932 + 50.3909i) q^{93} +(116.534 + 67.2808i) q^{94} +(-7.83640 + 13.5730i) q^{95} +(49.5075 - 28.5832i) q^{96} -15.5200i q^{97} +(-107.278 - 60.3254i) q^{98} +54.2753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9	\( 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9} + 20 q^{11} - 66 q^{12} + 32 q^{14} - 82 q^{16} - 78 q^{17} - 6 q^{18} - 6 q^{19} + 36 q^{21} + 56 q^{22} + 2 q^{23} + 60 q^{24} + 30 q^{25} + 36 q^{26} - 128 q^{28} - 100 q^{29} + 108 q^{31} - 108 q^{32} + 60 q^{33} - 60 q^{35} - 132 q^{36} - 34 q^{37} + 126 q^{38} - 42 q^{39} - 90 q^{40} + 114 q^{42} - 124 q^{43} + 234 q^{44} + 278 q^{46} + 96 q^{47} - 60 q^{49} + 20 q^{50} - 78 q^{51} - 444 q^{52} - 76 q^{53} - 18 q^{54} + 112 q^{56} - 12 q^{57} - 52 q^{58} - 270 q^{59} + 60 q^{60} - 60 q^{61} + 42 q^{63} + 700 q^{64} - 60 q^{65} + 84 q^{66} - 18 q^{67} + 108 q^{68} - 300 q^{70} - 628 q^{71} + 60 q^{72} + 234 q^{73} + 244 q^{74} + 90 q^{75} - 196 q^{77} + 72 q^{78} + 108 q^{79} + 480 q^{80} - 54 q^{81} + 480 q^{82} - 192 q^{84} - 60 q^{85} + 130 q^{86} - 150 q^{87} - 668 q^{88} - 186 q^{89} + 444 q^{91} + 456 q^{92} + 108 q^{93} + 30 q^{94} - 324 q^{96} + 416 q^{98} + 120 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9 + 20 * q^11 - 66 * q^12 + 32 * q^14 - 82 * q^16 - 78 * q^17 - 6 * q^18 - 6 * q^19 + 36 * q^21 + 56 * q^22 + 2 * q^23 + 60 * q^24 + 30 * q^25 + 36 * q^26 - 128 * q^28 - 100 * q^29 + 108 * q^31 - 108 * q^32 + 60 * q^33 - 60 * q^35 - 132 * q^36 - 34 * q^37 + 126 * q^38 - 42 * q^39 - 90 * q^40 + 114 * q^42 - 124 * q^43 + 234 * q^44 + 278 * q^46 + 96 * q^47 - 60 * q^49 + 20 * q^50 - 78 * q^51 - 444 * q^52 - 76 * q^53 - 18 * q^54 + 112 * q^56 - 12 * q^57 - 52 * q^58 - 270 * q^59 + 60 * q^60 - 60 * q^61 + 42 * q^63 + 700 * q^64 - 60 * q^65 + 84 * q^66 - 18 * q^67 + 108 * q^68 - 300 * q^70 - 628 * q^71 + 60 * q^72 + 234 * q^73 + 244 * q^74 + 90 * q^75 - 196 * q^77 + 72 * q^78 + 108 * q^79 + 480 * q^80 - 54 * q^81 + 480 * q^82 - 192 * q^84 - 60 * q^85 + 130 * q^86 - 150 * q^87 - 668 * q^88 - 186 * q^89 + 444 * q^91 + 456 * q^92 + 108 * q^93 + 30 * q^94 - 324 * q^96 + 416 * q^98 + 120 * q^99

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