LMFDB - Embedded newform 300.3.u.a.287.116

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(23,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 10, 11]))

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

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

chi := DirichletCharacter("300.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.u (of order $20$, degree $8$, 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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$116$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			287.116
Character	$\chi$	$=$	300.287
Dual form			300.3.u.a.23.116

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99999 + 0.00504968i) q^{2} +(2.26627 + 1.96571i) q^{3} +(3.99995 + 0.0201986i) q^{4} +(2.32110 - 4.42860i) q^{5} +(4.52260 + 3.94285i) q^{6} +(-3.36739 + 3.36739i) q^{7} +(7.99977 + 0.0605956i) q^{8} +(1.27197 + 8.90966i) q^{9} +O(q^{10})$	\(q+(1.99999 + 0.00504968i) q^{2} +(2.26627 + 1.96571i) q^{3} +(3.99995 + 0.0201986i) q^{4} +(2.32110 - 4.42860i) q^{5} +(4.52260 + 3.94285i) q^{6} +(-3.36739 + 3.36739i) q^{7} +(7.99977 + 0.0605956i) q^{8} +(1.27197 + 8.90966i) q^{9} +(4.66454 - 8.84546i) q^{10} +(1.00022 + 0.726705i) q^{11} +(9.02526 + 7.90851i) q^{12} +(-1.13771 + 7.18323i) q^{13} +(-6.75176 + 6.71775i) q^{14} +(13.9656 - 5.47381i) q^{15} +(15.9992 + 0.161587i) q^{16} +(-7.56891 - 14.8548i) q^{17} +(2.49894 + 17.8257i) q^{18} +(3.65066 - 11.2356i) q^{19} +(9.37371 - 17.6673i) q^{20} +(-14.2507 + 1.01211i) q^{21} +(1.99677 + 1.45846i) q^{22} +(8.07059 - 1.27826i) q^{23} +(18.0105 + 15.8626i) q^{24} +(-14.2250 - 20.5584i) q^{25} +(-2.31169 + 14.3607i) q^{26} +(-14.6312 + 22.6920i) q^{27} +(-13.5374 + 13.4014i) q^{28} +(0.636054 + 1.95757i) q^{29} +(27.9587 - 10.8771i) q^{30} +(-22.1772 - 7.20581i) q^{31} +(31.9975 + 0.403964i) q^{32} +(0.838287 + 3.61306i) q^{33} +(-15.0628 - 29.7478i) q^{34} +(7.09679 + 22.7288i) q^{35} +(4.90785 + 35.6639i) q^{36} +(-22.8993 - 3.62690i) q^{37} +(7.35803 - 22.4526i) q^{38} +(-16.6985 + 14.0427i) q^{39} +(18.8366 - 35.2872i) q^{40} +(18.9983 + 26.1489i) q^{41} +(-28.5065 + 1.95224i) q^{42} +(-47.1136 - 47.1136i) q^{43} +(3.98617 + 2.92699i) q^{44} +(42.4097 + 15.0471i) q^{45} +(16.1476 - 2.51575i) q^{46} +(-32.7679 + 64.3106i) q^{47} +(35.9409 + 31.8160i) q^{48} +26.3214i q^{49} +(-28.3462 - 41.1885i) q^{50} +(12.0471 - 48.5433i) q^{51} +(-4.69588 + 28.7096i) q^{52} +(-0.100916 + 0.198059i) q^{53} +(-29.3769 + 45.3100i) q^{54} +(5.53990 - 2.74284i) q^{55} +(-27.1424 + 26.7343i) q^{56} +(30.3593 - 18.2867i) q^{57} +(1.26222 + 3.91835i) q^{58} +(15.8056 + 21.7545i) q^{59} +(55.9722 - 21.6129i) q^{60} +(-44.4165 - 32.2705i) q^{61} +(-44.3179 - 14.5236i) q^{62} +(-34.2855 - 25.7191i) q^{63} +(63.9927 + 0.969502i) q^{64} +(29.1709 + 21.7114i) q^{65} +(1.65832 + 7.23033i) q^{66} +(-51.4412 - 100.959i) q^{67} +(-29.9752 - 59.5714i) q^{68} +(20.8028 + 12.9676i) q^{69} +(14.0788 + 45.4934i) q^{70} +(-29.8545 - 91.8827i) q^{71} +(9.63558 + 71.3523i) q^{72} +(109.830 - 17.3954i) q^{73} +(-45.7802 - 7.36941i) q^{74} +(8.17409 - 74.5532i) q^{75} +(14.8294 - 44.8680i) q^{76} +(-5.81524 + 0.921043i) q^{77} +(-33.4678 + 28.0010i) q^{78} +(21.9236 + 67.4738i) q^{79} +(37.8512 - 70.4790i) q^{80} +(-77.7642 + 22.6656i) q^{81} +(37.8644 + 52.3936i) q^{82} +(-60.1499 - 118.051i) q^{83} +(-57.0226 + 3.76053i) q^{84} +(-83.3542 - 0.959763i) q^{85} +(-93.9891 - 94.4649i) q^{86} +(-2.40655 + 5.68669i) q^{87} +(7.95753 + 5.87408i) q^{88} +(63.1182 + 45.8581i) q^{89} +(84.7432 + 30.3083i) q^{90} +(-20.3576 - 28.0198i) q^{91} +(32.3078 - 4.94994i) q^{92} +(-36.0950 - 59.9243i) q^{93} +(-65.8603 + 128.455i) q^{94} +(-41.2844 - 42.2462i) q^{95} +(71.7208 + 63.8132i) q^{96} +(60.2398 - 118.227i) q^{97} +(-0.132915 + 52.6426i) q^{98} +(-5.20244 + 9.83600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 20 q^{4} - 6 q^{6} - 20 q^{9}+O(q^{10}) $ 928 * q - 20 * q^4 - 6 * q^6 - 20 * q^9	$ 928 q - 20 q^{4} - 6 q^{6} - 20 q^{9} - 8 q^{10} + 10 q^{12} - 32 q^{13} - 12 q^{16} + 14 q^{18} - 12 q^{21} + 56 q^{22} - 32 q^{25} + 64 q^{28} - 78 q^{30} + 20 q^{33} - 20 q^{34} - 70 q^{36} - 124 q^{40} + 454 q^{42} + 84 q^{45} - 12 q^{46} - 76 q^{48} - 324 q^{52} - 660 q^{54} + 52 q^{57} - 200 q^{58} - 826 q^{60} - 24 q^{61} - 20 q^{64} + 138 q^{66} - 20 q^{69} + 352 q^{70} + 590 q^{72} - 144 q^{73} + 96 q^{76} + 308 q^{78} - 12 q^{81} + 20 q^{82} - 10 q^{84} + 864 q^{85} - 760 q^{88} - 538 q^{90} - 388 q^{93} - 1420 q^{94} - 6 q^{96} + 288 q^{97}+O(q^{100}) $ 928 * q - 20 * q^4 - 6 * q^6 - 20 * q^9 - 8 * q^10 + 10 * q^12 - 32 * q^13 - 12 * q^16 + 14 * q^18 - 12 * q^21 + 56 * q^22 - 32 * q^25 + 64 * q^28 - 78 * q^30 + 20 * q^33 - 20 * q^34 - 70 * q^36 - 124 * q^40 + 454 * q^42 + 84 * q^45 - 12 * q^46 - 76 * q^48 - 324 * q^52 - 660 * q^54 + 52 * q^57 - 200 * q^58 - 826 * q^60 - 24 * q^61 - 20 * q^64 + 138 * q^66 - 20 * q^69 + 352 * q^70 + 590 * q^72 - 144 * q^73 + 96 * q^76 + 308 * q^78 - 12 * q^81 + 20 * q^82 - 10 * q^84 + 864 * q^85 - 760 * q^88 - 538 * q^90 - 388 * q^93 - 1420 * q^94 - 6 * q^96 + 288 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{9}{20}\right)$

Coefficient data

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

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

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

$2$	1.99999	+	0.00504968i	0.999997	+	0.00252484i
$2$	1.99999	+	0.00504968i	0.999997	+	0.00252484i
$3$	2.26627	+	1.96571i	0.755424	+	0.655237i
$3$	2.26627	+	1.96571i	0.755424	+	0.655237i
$4$	3.99995	+	0.0201986i	0.999987	+	0.00504966i
$5$	2.32110	−	4.42860i	0.464219	−	0.885720i
$5$	2.32110	−	4.42860i	0.464219	−	0.885720i
$6$	4.52260	+	3.94285i	0.753767	+	0.657142i
$7$	−3.36739	+	3.36739i	−0.481055	+	0.481055i	−0.905469	−	0.424413i	$-0.860480\pi$
$7$	−3.36739	+	3.36739i	−0.481055	+	0.481055i	0.424413	+	0.905469i	$0.360480\pi$
$8$	7.99977	+	0.0605956i	0.999971	+	0.00757445i
$9$	1.27197	+	8.90966i	0.141330	+	0.989963i
$10$	4.66454	−	8.84546i	0.466454	−	0.884546i
$11$	1.00022	+	0.726705i	0.0909294	+	0.0660641i	0.632321	−	0.774706i	$-0.282102\pi$
$11$	1.00022	+	0.726705i	0.0909294	+	0.0660641i	−0.541392	+	0.840771i	$0.682102\pi$
$12$	9.02526	+	7.90851i	0.752105	+	0.659043i
$13$	−1.13771	+	7.18323i	−0.0875163	+	0.552556i	0.904503	+	0.426468i	$0.140242\pi$
$13$	−1.13771	+	7.18323i	−0.0875163	+	0.552556i	−0.992019	+	0.126088i	$0.959758\pi$
$14$	−6.75176	+	6.71775i	−0.482268	+	0.479839i
$15$	13.9656	−	5.47381i	0.931039	−	0.364921i
$16$	15.9992	+	0.161587i	0.999949	+	0.0100992i
$17$	−7.56891	−	14.8548i	−0.445230	−	0.873813i	−0.999149	−	0.0412425i	$-0.986868\pi$
$17$	−7.56891	−	14.8548i	−0.445230	−	0.873813i	0.553919	−	0.832570i	$-0.313132\pi$
$18$	2.49894	+	17.8257i	0.138830	+	0.990316i
$19$	3.65066	−	11.2356i	0.192140	−	0.591346i	−0.807858	−	0.589377i	$-0.799373\pi$
$19$	3.65066	−	11.2356i	0.192140	−	0.591346i	0.999998	−	0.00196896i	$-0.000626739\pi$
$20$	9.37371	−	17.6673i	0.468686	−	0.883365i
$21$	−14.2507	+	1.01211i	−0.678606	+	0.0481955i
$22$	1.99677	+	1.45846i	0.0907624	+	0.0662935i
$23$	8.07059	−	1.27826i	0.350895	−	0.0555763i	0.0215010	−	0.999769i	$-0.493156\pi$
$23$	8.07059	−	1.27826i	0.350895	−	0.0555763i	0.329394	+	0.944192i	$0.393156\pi$
$24$	18.0105	+	15.8626i	0.750439	+	0.660940i
$25$	−14.2250	−	20.5584i	−0.569001	−	0.822337i
$26$	−2.31169	+	14.3607i	−0.0889111	+	0.552333i
$27$	−14.6312	+	22.6920i	−0.541896	+	0.840446i
$28$	−13.5374	+	13.4014i	−0.483478	+	0.478620i
$29$	0.636054	+	1.95757i	0.0219329	+	0.0675026i	0.961424	−	0.275071i	$-0.0887014\pi$
$29$	0.636054	+	1.95757i	0.0219329	+	0.0675026i	−0.939491	+	0.342574i	$0.888701\pi$
$30$	27.9587	−	10.8771i	0.931957	−	0.362569i
$31$	−22.1772	−	7.20581i	−0.715394	−	0.232446i	−0.0713688	−	0.997450i	$-0.522737\pi$
$31$	−22.1772	−	7.20581i	−0.715394	−	0.232446i	−0.644025	+	0.765004i	$0.722737\pi$
$32$	31.9975	+	0.403964i	0.999920	+	0.0126239i
$33$	0.838287	+	3.61306i	0.0254026	+	0.109487i
$34$	−15.0628	−	29.7478i	−0.443022	−	0.874934i
$35$	7.09679	+	22.7288i	0.202766	+	0.649396i
$36$	4.90785	+	35.6639i	0.136329	+	0.990664i
$37$	−22.8993	−	3.62690i	−0.618901	−	0.0980243i	−0.160892	−	0.986972i	$-0.551437\pi$
$37$	−22.8993	−	3.62690i	−0.618901	−	0.0980243i	−0.458009	+	0.888948i	$0.651437\pi$
$38$	7.35803	−	22.4526i	0.193632	−	0.590859i
$39$	−16.6985	+	14.0427i	−0.428167	+	0.360070i
$40$	18.8366	−	35.2872i	0.470915	−	0.882179i
$41$	18.9983	+	26.1489i	0.463373	+	0.637778i	0.975204	−	0.221308i	$-0.0710326\pi$
$41$	18.9983	+	26.1489i	0.463373	+	0.637778i	−0.511831	+	0.859086i	$0.671033\pi$
$42$	−28.5065	+	1.95224i	−0.678725	+	0.0464820i
$43$	−47.1136	−	47.1136i	−1.09567	−	1.09567i	−0.994911	−	0.100755i	$-0.967874\pi$
$43$	−47.1136	−	47.1136i	−1.09567	−	1.09567i	−0.100755	−	0.994911i	$-0.532126\pi$
$44$	3.98617	+	2.92699i	0.0905947	+	0.0665224i
$45$	42.4097	+	15.0471i	0.942438	+	0.334381i
$46$	16.1476	−	2.51575i	0.351034	−	0.0546902i
$47$	−32.7679	+	64.3106i	−0.697189	+	1.36831i	0.222215	+	0.974998i	$0.428671\pi$
$47$	−32.7679	+	64.3106i	−0.697189	+	1.36831i	−0.919405	+	0.393313i	$0.871329\pi$
$48$	35.9409	+	31.8160i	0.748768	+	0.662832i
$49$			26.3214i			0.537172i
$50$	−28.3462	−	41.1885i	−0.566923	−	0.823771i
$51$	12.0471	−	48.5433i	0.236217	−	0.951830i
$52$	−4.69588	+	28.7096i	−0.0903054	+	0.552107i
$53$	−0.100916	+	0.198059i	−0.00190408	+	0.00373696i	−0.891957	−	0.452121i	$-0.850668\pi$
$53$	−0.100916	+	0.198059i	−0.00190408	+	0.00373696i	0.890053	+	0.455858i	$0.150668\pi$
$54$	−29.3769	+	45.3100i	−0.544016	+	0.839075i
$55$	5.53990	−	2.74284i	0.100726	−	0.0498699i
$56$	−27.1424	+	26.7343i	−0.484685	+	0.477398i
$57$	30.3593	−	18.2867i	0.532619	−	0.320820i
$58$	1.26222	+	3.91835i	0.0217624	+	0.0675577i
$59$	15.8056	+	21.7545i	0.267891	+	0.368720i	0.921676	−	0.387960i	$-0.126820\pi$
$59$	15.8056	+	21.7545i	0.267891	+	0.368720i	−0.653785	+	0.756680i	$0.726820\pi$
$60$	55.9722	−	21.6129i	0.932869	−	0.360215i
$61$	−44.4165	−	32.2705i	−0.728140	−	0.529025i	0.160834	−	0.986981i	$-0.448581\pi$
$61$	−44.4165	−	32.2705i	−0.728140	−	0.529025i	−0.888974	+	0.457957i	$0.848581\pi$
$62$	−44.3179	−	14.5236i	−0.714805	−	0.234251i
$63$	−34.2855	−	25.7191i	−0.544214	−	0.408239i
$64$	63.9927	+	0.969502i	0.999885	+	0.0151485i
$65$	29.1709	+	21.7114i	0.448783	+	0.334022i
$66$	1.65832	+	7.23033i	0.0251261	+	0.109550i
$67$	−51.4412	−	100.959i	−0.767779	−	1.50685i	−0.859539	−	0.511070i	$-0.829249\pi$
$67$	−51.4412	−	100.959i	−0.767779	−	1.50685i	0.0917598	−	0.995781i	$-0.470751\pi$
$68$	−29.9752	−	59.5714i	−0.440812	−	0.876050i
$69$	20.8028	+	12.9676i	0.301490	+	0.187936i
$70$	14.0788	+	45.4934i	0.201125	+	0.649905i
$71$	−29.8545	−	91.8827i	−0.420486	−	1.29412i	−0.907251	−	0.420590i	$-0.861823\pi$
$71$	−29.8545	−	91.8827i	−0.420486	−	1.29412i	0.486765	−	0.873533i	$-0.338177\pi$
$72$	9.63558	+	71.3523i	0.133827	+	0.991005i
$73$	109.830	−	17.3954i	1.50452	−	0.238293i	0.650891	−	0.759171i	$-0.274395\pi$
$73$	109.830	−	17.3954i	1.50452	−	0.238293i	0.853631	+	0.520878i	$0.174395\pi$
$74$	−45.7802	−	7.36941i	−0.618651	−	0.0995866i
$75$	8.17409	−	74.5532i	0.108988	−	0.994043i
$76$	14.8294	−	44.8680i	0.195124	−	0.590368i
$77$	−5.81524	+	0.921043i	−0.0755226	+	0.0119616i
$78$	−33.4678	+	28.0010i	−0.429074	+	0.358988i
$79$	21.9236	+	67.4738i	0.277514	+	0.854099i	0.988543	+	0.150937i	$0.0482291\pi$
$79$	21.9236	+	67.4738i	0.277514	+	0.854099i	−0.711030	+	0.703162i	$0.751771\pi$
$80$	37.8512	−	70.4790i	0.473140	−	0.880987i
$81$	−77.7642	+	22.6656i	−0.960052	+	0.279823i
$82$	37.8644	+	52.3936i	0.461761	+	0.638946i
$83$	−60.1499	−	118.051i	−0.724697	−	1.42230i	−0.899153	−	0.437634i	$-0.855817\pi$
$83$	−60.1499	−	118.051i	−0.724697	−	1.42230i	0.174456	−	0.984665i	$-0.444183\pi$
$84$	−57.0226	+	3.76053i	−0.678840	+	0.0447682i
$85$	−83.3542	−	0.959763i	−0.980638	−	0.0112913i
$86$	−93.9891	−	94.4649i	−1.09290	−	1.09843i
$87$	−2.40655	+	5.68669i	−0.0276615	+	0.0653643i
$88$	7.95753	+	5.87408i	0.0904264	+	0.0667510i
$89$	63.1182	+	45.8581i	0.709193	+	0.515259i	0.882913	−	0.469536i	$-0.155579\pi$
$89$	63.1182	+	45.8581i	0.709193	+	0.515259i	−0.173720	+	0.984795i	$0.555579\pi$
$90$	84.7432	+	30.3083i	0.941591	+	0.336759i
$91$	−20.3576	−	28.0198i	−0.223710	−	0.307910i
$92$	32.3078	−	4.94994i	0.351171	−	0.0538037i
$93$	−36.0950	−	59.9243i	−0.388119	−	0.644347i
$94$	−65.8603	+	128.455i	−0.700642	+	1.36655i
$95$	−41.2844	−	42.2462i	−0.434572	−	0.444696i
$96$	71.7208	+	63.8132i	0.747092	+	0.664721i
$97$	60.2398	−	118.227i	0.621029	−	1.21884i	−0.339486	−	0.940611i	$-0.610253\pi$
$97$	60.2398	−	118.227i	0.621029	−	1.21884i	0.960515	−	0.278227i	$-0.0897468\pi$
$98$	−0.132915	+	52.6426i	−0.00135627	+	0.537170i
$99$	−5.20244	+	9.83600i	−0.0525499	+	0.0993536i
$100$	−56.4842	−	82.5199i	−0.564842	−	0.825199i
$101$			121.916i			1.20709i	0.797327	+	0.603547i	$0.206246\pi$
$101$			121.916i			1.20709i	−0.797327	+	0.603547i	$0.793754\pi$
$102$	24.3392	−	97.0255i	0.238619	−	0.951230i
$103$	−87.4696	+	171.669i	−0.849220	+	1.66669i	−0.109283	+	0.994011i	$0.534855\pi$
$103$	−87.4696	+	171.669i	−0.849220	+	1.66669i	−0.739937	+	0.672677i	$0.765145\pi$
$104$	−9.53670	+	57.3952i	−0.0916991	+	0.551877i
$105$	−28.5951	+	65.4600i	−0.272334	+	0.623428i
$106$	−0.202832	+	0.395607i	−0.00191351	+	0.00373214i
$107$	92.1510	+	92.1510i	0.861224	+	0.861224i	0.991480	−	0.130256i	$-0.0415800\pi$
$107$	92.1510	+	92.1510i	0.861224	+	0.861224i	−0.130256	+	0.991480i	$0.541580\pi$
$108$	−58.9823	+	90.4714i	−0.546133	+	0.837699i
$109$	23.7896	+	32.7436i	0.218253	+	0.300400i	0.904078	−	0.427366i	$-0.140559\pi$
$109$	23.7896	+	32.7436i	0.218253	+	0.300400i	−0.685825	+	0.727766i	$0.740559\pi$
$110$	11.0936	−	5.45769i	0.100851	−	0.0496154i
$111$	−44.7667	−	53.2330i	−0.403303	−	0.479576i
$112$	−54.4196	+	53.3313i	−0.485889	+	0.476173i
$113$	−31.5843	−	5.00245i	−0.279507	−	0.0442695i	0.0151072	−	0.999886i	$-0.495191\pi$
$113$	−31.5843	−	5.00245i	−0.279507	−	0.0442695i	−0.294614	+	0.955616i	$0.595191\pi$
$114$	60.8107	−	36.4200i	0.533427	−	0.319474i
$115$	13.0717	−	38.7084i	0.113667	−	0.336595i
$116$	2.50464	+	7.84304i	0.0215918	+	0.0676124i
$117$	−65.4473	−	0.999782i	−0.559378	−	0.00854514i
$118$	31.5012	+	43.5887i	0.266959	+	0.369396i
$119$	75.5094	+	24.5345i	0.634533	+	0.206172i
$120$	112.053	−	42.9430i	0.933776	−	0.357858i
$121$	−36.9187	−	113.624i	−0.305113	−	0.939042i
$122$	−88.6698	−	64.7651i	−0.726802	−	0.530861i
$123$	−8.34588	+	96.6056i	−0.0678527	+	0.785412i
$124$	−88.5622	−	29.2708i	−0.714211	−	0.236055i
$125$	−124.063	+	15.2790i	−0.992502	+	0.122232i
$126$	−68.4409	−	51.6111i	−0.543182	−	0.409612i
$127$	−3.36089	+	0.532313i	−0.0264637	+	0.00419144i	−0.169652	−	0.985504i	$-0.554264\pi$
$127$	−3.36089	+	0.532313i	−0.0264637	+	0.00419144i	0.143189	+	0.989695i	$0.454264\pi$
$128$	127.980	+	2.26214i	0.999844	+	0.0176730i
$129$	−14.1605	−	199.384i	−0.109772	−	1.54561i
$130$	58.2320	+	43.5700i	0.447939	+	0.335154i
$131$	3.16775	−	9.74933i	0.0241813	−	0.0744224i	−0.938238	−	0.345992i	$-0.887543\pi$
$131$	3.16775	−	9.74933i	0.0241813	−	0.0744224i	0.962419	+	0.271569i	$0.0875426\pi$
$132$	3.28013	+	14.4690i	0.0248494	+	0.109614i
$133$	25.5413	+	50.1277i	0.192040	+	0.376900i
$134$	−102.372	−	202.177i	−0.763972	−	1.50879i
$135$	66.5336	+	117.466i	0.492842	+	0.870119i
$136$	−59.6494	−	119.294i	−0.438598	−	0.877160i
$137$	−22.2734	+	140.629i	−0.162580	+	1.02649i	0.762576	+	0.646899i	$0.223934\pi$
$137$	−22.2734	+	140.629i	−0.162580	+	1.02649i	−0.925156	+	0.379588i	$0.876066\pi$
$138$	41.5400	+	26.0401i	0.301015	+	0.188696i
$139$	163.252	+	118.610i	1.17448	+	0.853307i	0.991538	−	0.129818i	$-0.0414392\pi$
$139$	163.252	+	118.610i	1.17448	+	0.853307i	0.182938	+	0.983124i	$0.441439\pi$
$140$	27.9277	+	91.0576i	0.199484	+	0.650411i
$141$	−200.677	+	81.3331i	−1.42324	+	0.576831i
$142$	−59.2449	−	183.916i	−0.417217	−	1.29518i
$143$	−6.35805	+	6.35805i	−0.0444619	+	0.0444619i
$144$	18.9108	+	142.753i	0.131325	+	0.991339i
$145$	10.1457	+	1.72688i	0.0699701	+	0.0119095i
$146$	219.747	−	34.2360i	1.50512	−	0.234493i
$147$	−51.7402	+	59.6514i	−0.351974	+	0.405792i
$148$	−91.5229	−	14.9699i	−0.618398	−	0.101148i
$149$	161.066			1.08098			0.540492	−	0.841349i	$-0.318238\pi$
$149$	161.066			1.08098			0.540492	+	0.841349i	$0.318238\pi$
$150$	16.7246	−	149.065i	0.111497	−	0.993765i
$151$		−	149.468i		−	0.989857i	−0.868934	−	0.494928i	$-0.835194\pi$
$151$		−	149.468i		−	0.989857i	0.868934	−	0.494928i	$-0.164806\pi$
$152$	29.8853	−	89.6608i	0.196614	−	0.589874i
$153$	122.724	−	86.3313i	0.802118	−	0.564257i
$154$	−11.6351	+	1.81272i	−0.0755525	+	0.0117709i
$155$	−83.3871	+	81.4887i	−0.537981	+	0.525733i
$156$	−67.0768	+	55.8329i	−0.429979	+	0.357903i
$157$	−31.1794	−	31.1794i	−0.198595	−	0.198595i	0.600802	−	0.799398i	$-0.294848\pi$
$157$	−31.1794	−	31.1794i	−0.198595	−	0.198595i	−0.799398	+	0.600802i	$0.794848\pi$
$158$	43.5063	+	135.058i	0.275356	+	0.854797i
$159$	−0.618030	+	0.250484i	−0.00388698	+	0.00157537i
$160$	76.0581	−	140.766i	0.475363	−	0.879790i
$161$	−22.8724	+	31.4812i	−0.142065	+	0.195535i
$162$	−155.642	+	44.9384i	−0.960755	+	0.277398i
$163$	15.3009	+	2.42342i	0.0938706	+	0.0148676i	0.203193	−	0.979139i	$-0.434868\pi$
$163$	15.3009	+	2.42342i	0.0938706	+	0.0148676i	−0.109322	+	0.994006i	$0.534868\pi$
$164$	75.4640	+	104.978i	0.460147	+	0.640110i
$165$	17.9466	+	4.67382i	0.108767	+	0.0283262i
$166$	−119.703	−	236.405i	−0.721104	−	1.42412i
$167$	−78.2403	+	39.8654i	−0.468505	+	0.238715i	−0.672272	−	0.740304i	$-0.734681\pi$
$167$	−78.2403	+	39.8654i	−0.468505	+	0.238715i	0.203767	+	0.979019i	$0.434681\pi$
$168$	−114.064	+	7.23308i	−0.678951	+	0.0430541i
$169$	110.424	+	35.8790i	0.653398	+	0.212302i
$170$	−166.703	−	2.34043i	−0.980607	−	0.0137672i
$171$	104.749	+	18.2348i	0.612566	+	0.106636i
$172$	−187.501	−	189.404i	−1.09012	−	1.10118i
$173$	15.7252	+	99.2850i	0.0908971	+	0.573902i	0.990534	+	0.137264i	$0.0438309\pi$
$173$	15.7252	+	99.2850i	0.0908971	+	0.573902i	−0.899637	+	0.436638i	$0.856169\pi$
$174$	−4.84180	+	11.3612i	−0.0278265	+	0.0652942i
$175$	117.129	+	21.3269i	0.669311	+	0.121868i
$176$	15.8853	+	11.7883i	0.0902576	+	0.0669791i
$177$	−6.94333	+	80.3708i	−0.0392279	+	0.454072i
$178$	126.004	+	92.0346i	0.707890	+	0.517048i
$179$	332.754	−	108.118i	1.85896	−	0.604012i	0.864029	−	0.503442i	$-0.167933\pi$
$179$	332.754	−	108.118i	1.85896	−	0.604012i	0.994930	−	0.100570i	$-0.0320667\pi$
$180$	169.333	+	61.0444i	0.940738	+	0.339135i
$181$	39.8094	−	122.521i	0.219941	−	0.676910i	−0.778824	−	0.627242i	$-0.784184\pi$
$181$	39.8094	−	122.521i	0.219941	−	0.676910i	0.998766	−	0.0496681i	$-0.0158163\pi$
$182$	−40.5736	−	56.1423i	−0.222932	−	0.308474i
$183$	−37.2255	−	160.444i	−0.203418	−	0.876742i
$184$	64.6403	−	9.73671i	0.351306	−	0.0529169i
$185$	−69.2136	+	92.9937i	−0.374128	+	0.502668i
$186$	−71.8872	−	120.030i	−0.386490	−	0.645325i
$187$	3.22447	−	20.3585i	0.0172432	−	0.108869i
$188$	−132.369	+	256.577i	−0.704090	+	1.36477i
$189$	−27.1440	−	125.682i	−0.143619	−	0.664983i
$190$	−82.3551	−	84.7005i	−0.433448	−	0.445792i
$191$	281.134	−	204.256i	1.47191	−	1.06940i	0.491851	−	0.870680i	$-0.336321\pi$
$191$	281.134	−	204.256i	1.47191	−	1.06940i	0.980056	−	0.198723i	$-0.0636794\pi$
$192$	143.119	+	127.988i	0.745411	+	0.666605i
$193$	−227.781	+	227.781i	−1.18021	+	1.18021i	−0.200526	+	0.979688i	$0.564265\pi$
$193$	−227.781	+	227.781i	−1.18021	+	1.18021i	−0.979688	+	0.200526i	$0.935735\pi$
$194$	121.076	−	236.150i	0.624105	−	1.21727i
$195$	23.4308	+	106.546i	0.120158	+	0.546387i
$196$	−0.531657	+	105.284i	−0.00271253	+	0.537165i
$197$	124.853	+	63.6156i	0.633769	+	0.322922i	0.741193	−	0.671292i	$-0.234260\pi$
$197$	124.853	+	63.6156i	0.633769	+	0.322922i	−0.107424	+	0.994213i	$0.534260\pi$
$198$	−10.4545	+	19.6457i	−0.0528006	+	0.0992206i
$199$	5.59187			0.0280999			0.0140499	−	0.999901i	$-0.495528\pi$
$199$	5.59187			0.0280999			0.0140499	+	0.999901i	$0.495528\pi$
$200$	−112.551	−	165.325i	−0.562756	−	0.826623i
$201$	81.8765	−	329.919i	0.407346	−	1.64139i
$202$	−0.615639	+	243.832i	−0.00304772	+	1.20709i
$203$	−8.73375	−	4.45007i	−0.0430234	−	0.0219215i
$204$	49.1682	−	193.927i	0.241020	−	0.950625i
$205$	159.900	−	23.4418i	0.780000	−	0.114350i
$206$	−175.806	+	342.895i	−0.853425	+	1.66454i
$207$	21.6544	+	70.2803i	0.104610	+	0.339518i
$208$	−19.3632	+	114.742i	−0.0930922	+	0.551644i
$209$	11.8164	−	8.58514i	0.0565379	−	0.0410772i
$210$	−57.5205	+	130.775i	−0.273907	+	0.622739i
$211$	−36.8321	+	50.6951i	−0.174560	+	0.240261i	−0.887328	−	0.461139i	$-0.847441\pi$
$211$	−36.8321	+	50.6951i	−0.174560	+	0.240261i	0.712768	+	0.701400i	$0.247441\pi$
$212$	−0.407660	+	0.790187i	−0.00192292	+	0.00372730i
$213$	112.956	−	266.917i	0.530312	−	1.25313i
$214$	183.836	+	184.767i	0.859047	+	0.863396i
$215$	−318.003	+	99.2923i	−1.47908	+	0.461825i
$216$	−118.421	+	180.644i	−0.548246	+	0.836317i
$217$	98.9440	−	50.4145i	0.455963	−	0.232325i
$218$	47.4137	+	65.6071i	0.217494	+	0.300950i
$219$	283.099	+	176.471i	1.29269	+	0.805806i
$220$	22.2147	−	10.8593i	0.100976	−	0.0493606i
$221$	115.317	−	37.4687i	0.521795	−	0.169542i
$222$	−89.2642	−	106.692i	−0.402091	−	0.480593i
$223$	32.7540	+	206.801i	0.146879	+	0.927357i	0.945523	+	0.325554i	$0.105551\pi$
$223$	32.7540	+	206.801i	0.146879	+	0.927357i	−0.798645	+	0.601803i	$0.794449\pi$
$224$	−109.108	+	106.388i	−0.487090	+	0.474944i
$225$	165.075	−	152.890i	0.733665	−	0.679511i
$226$	−63.1430	−	10.1644i	−0.279394	−	0.0449751i
$227$	29.7558	+	187.870i	0.131083	+	0.827623i	0.962362	+	0.271769i	$0.0876087\pi$
$227$	29.7558	+	187.870i	0.131083	+	0.827623i	−0.831280	+	0.555854i	$0.812391\pi$
$228$	121.805	−	72.5327i	0.534232	−	0.318126i
$229$	−330.975	+	107.540i	−1.44531	+	0.469609i	−0.923548	−	0.383483i	$-0.874724\pi$
$229$	−330.975	+	107.540i	−1.44531	+	0.469609i	−0.521760	+	0.853092i	$0.674724\pi$
$230$	26.3388	−	77.3505i	0.114517	−	0.336307i
$231$	−14.9894	−	9.34374i	−0.0648892	−	0.0404491i
$232$	4.96967	+	15.6987i	0.0214210	+	0.0676667i
$233$	−172.601	+	87.9445i	−0.740776	+	0.377444i	−0.783294	−	0.621652i	$-0.786462\pi$
$233$	−172.601	+	87.9445i	−0.740776	+	0.377444i	0.0425181	+	0.999096i	$0.486462\pi$
$234$	−130.889	−	2.33004i	−0.559355	−	0.00995745i
$235$	208.749	+	294.387i	0.888292	+	1.25271i
$236$	62.7821	+	87.3361i	0.266026	+	0.370068i
$237$	−82.9492	+	196.009i	−0.349997	+	0.827044i
$238$	150.894	+	49.4501i	0.634010	+	0.207774i
$239$	13.9176	−	19.1560i	0.0582328	−	0.0801505i	−0.778907	−	0.627139i	$-0.784226\pi$
$239$	13.9176	−	19.1560i	0.0582328	−	0.0801505i	0.837140	+	0.546988i	$0.184226\pi$
$240$	224.322	−	85.3199i	0.934676	−	0.355500i
$241$	−0.263072	+	0.191133i	−0.00109158	+	0.000793082i	−0.588331	−	0.808620i	$-0.700215\pi$
$241$	−0.263072	+	0.191133i	−0.00109158	+	0.000793082i	0.587239	+	0.809413i	$0.300215\pi$
$242$	−73.2634	−	227.434i	−0.302741	−	0.939810i
$243$	−220.789	−	101.495i	−0.908596	−	0.417676i
$244$	−177.012	−	129.978i	−0.725459	−	0.532695i
$245$	116.567	+	61.0945i	0.475784	+	0.249365i
$246$	−17.1795	+	193.169i	−0.0698355	+	0.785238i
$247$	76.5543	+	39.0064i	0.309936	+	0.157920i
$248$	−176.976	−	58.9887i	−0.713613	−	0.237858i
$249$	95.7377	−	385.772i	0.384489	−	1.54929i
$250$	−248.202	+	29.9314i	−0.992807	+	0.119726i
$251$	417.398			1.66294			0.831470	−	0.555570i	$-0.187500\pi$
$251$	417.398			1.66294			0.831470	+	0.555570i	$0.187500\pi$
$252$	−136.621	−	103.568i	−0.542146	−	0.410982i
$253$	9.00131	+	4.58640i	0.0355783	+	0.0181281i
$254$	−6.72445	+	1.04765i	−0.0264742	+	0.00412461i
$255$	−187.017	−	166.025i	−0.733399	−	0.651080i
$256$	255.948	+	5.17052i	0.999796	+	0.0201974i
$257$	230.153	−	230.153i	0.895538	−	0.895538i	−0.0994993	−	0.995038i	$-0.531724\pi$
$257$	230.153	−	230.153i	0.895538	−	0.895538i	0.995038	+	0.0994993i	$0.0317241\pi$
$258$	−27.3141	−	398.838i	−0.105869	−	1.54588i
$259$	89.3241	−	64.8978i	0.344881	−	0.250570i
$260$	116.244	+	87.4338i	0.447091	+	0.336284i
$261$	−16.6323	+	8.15700i	−0.0637252	+	0.0312529i
$262$	6.38471	−	19.4826i	0.0243691	−	0.0743611i
$263$	−10.4491	+	65.9732i	−0.0397305	+	0.250849i	−0.999558	−	0.0297437i	$-0.990531\pi$
$263$	−10.4491	+	65.9732i	−0.0397305	+	0.250849i	0.959827	+	0.280592i	$0.0905309\pi$
$264$	6.48717	+	28.9545i	0.0245726	+	0.109676i
$265$	0.642888	+	0.906631i	0.00242599	+	0.00342125i
$266$	50.8294	+	100.384i	0.191088	+	0.377384i
$267$	52.8993	+	227.999i	0.198125	+	0.853928i
$268$	−203.723	−	404.870i	−0.760160	−	1.51071i
$269$	−26.5465	+	81.7018i	−0.0986859	+	0.303724i	−0.988197	−	0.153190i	$-0.951045\pi$
$269$	−26.5465	+	81.7018i	−0.0986859	+	0.303724i	0.889511	+	0.456914i	$0.151045\pi$
$270$	132.474	+	235.267i	0.490643	+	0.871361i
$271$	38.4072	−	12.4793i	0.141724	−	0.0460489i	−0.237296	−	0.971437i	$-0.576261\pi$
$271$	38.4072	−	12.4793i	0.141724	−	0.0460489i	0.379020	+	0.925388i	$0.376261\pi$
$272$	−118.696	−	238.888i	−0.436382	−	0.878265i
$273$	8.94302	−	103.518i	0.0327583	−	0.379185i
$274$	−45.2568	+	281.144i	−0.165171	+	1.02607i
$275$	0.711686	−	30.9004i	0.00258795	−	0.112365i
$276$	82.9483	+	52.2898i	0.300537	+	0.189456i
$277$	78.0529	+	492.807i	0.281780	+	1.77909i	0.570123	+	0.821559i	$0.306895\pi$
$277$	78.0529	+	492.807i	0.281780	+	1.77909i	−0.288344	+	0.957527i	$0.593105\pi$
$278$	325.904	+	238.043i	1.17232	+	0.856269i
$279$	35.9926	−	206.757i	0.129006	−	0.741065i
$280$	55.3954	+	182.256i	0.197841	+	0.650913i
$281$	143.607	+	46.6608i	0.511058	+	0.166053i	0.553183	−	0.833060i	$-0.313413\pi$
$281$	143.607	+	46.6608i	0.511058	+	0.166053i	−0.0421256	+	0.999112i	$0.513413\pi$
$282$	−401.763	+	161.652i	−1.42469	+	0.573235i
$283$	207.071	−	105.508i	0.731699	−	0.372819i	−0.0481058	−	0.998842i	$-0.515318\pi$
$283$	207.071	−	105.508i	0.731699	−	0.372819i	0.779804	+	0.626023i	$0.215318\pi$
$284$	−117.561	−	368.129i	−0.413946	−	1.29623i
$285$	−10.5179	−	176.894i	−0.0369048	−	0.620682i
$286$	−12.7482	+	12.6840i	−0.0445740	+	0.0443495i
$287$	−152.028	−	24.0789i	−0.529715	−	0.0838986i
$288$	37.1006	+	285.600i	0.128821	+	0.991668i
$289$	6.49265	−	8.93636i	0.0224659	−	0.0309217i
$290$	20.2825	+	3.50499i	0.0699398	+	0.0120862i
$291$	368.920	−	149.521i	1.26777	−	0.513818i
$292$	439.666	−	67.3622i	1.50571	−	0.230692i
$293$	212.794	+	212.794i	0.726260	+	0.726260i	0.969873	−	0.243612i	$-0.0783324\pi$
$293$	212.794	+	212.794i	0.726260	+	0.726260i	−0.243612	+	0.969873i	$0.578332\pi$
$294$	−103.781	+	119.041i	−0.352998	+	0.404902i
$295$	133.028	−	19.5023i	0.450943	−	0.0661095i
$296$	−182.970	−	30.4020i	−0.618141	−	0.102709i
$297$	−31.1249	+	12.0646i	−0.104798	+	0.0406214i
$298$	322.132	+	0.813334i	1.08098	+	0.00272931i
$299$			59.4271i			0.198753i
$300$	34.2018	−	298.044i	0.114006	−	0.993480i
$301$	317.300			1.05415
$302$	0.754767	−	298.936i	0.00249923	−	0.989854i
$303$	−239.652	+	276.296i	−0.790932	+	0.911867i
$304$	60.2231	−	179.170i	0.198102	−	0.589375i
$305$	−246.008	+	121.800i	−0.806584	+	0.399345i
$306$	245.883	−	172.042i	0.803540	−	0.562230i
$307$	−55.0388	+	55.0388i	−0.179279	+	0.179279i	−0.791042	−	0.611762i	$-0.790461\pi$
$307$	−55.0388	+	55.0388i	−0.179279	+	0.179279i	0.611762	+	0.791042i	$0.290461\pi$
$308$	−23.2793	+	3.56667i	−0.0755820	+	0.0115801i
$309$	−535.681	+	217.108i	−1.73360	+	0.702615i
$310$	−167.185	+	162.556i	−0.539307	+	0.524373i
$311$	−299.426	−	217.546i	−0.962784	−	0.699503i	−0.00898812	−	0.999960i	$-0.502861\pi$
$311$	−299.426	−	217.546i	−0.962784	−	0.699503i	−0.953796	+	0.300456i	$0.902861\pi$
$312$	−134.435	+	111.327i	−0.430882	+	0.356816i
$313$	−28.1242	+	177.569i	−0.0898538	+	0.567314i	0.901153	+	0.433501i	$0.142722\pi$
$313$	−28.1242	+	177.569i	−0.0898538	+	0.567314i	−0.991007	+	0.133813i	$0.957278\pi$
$314$	−62.2013	−	62.5161i	−0.198093	−	0.199096i
$315$	−193.479	+	92.1404i	−0.614220	+	0.292509i
$316$	86.3303	+	270.335i	0.273197	+	0.855490i
$317$	−271.925	−	533.682i	−0.857807	−	1.68354i	−0.720992	−	0.692944i	$-0.756314\pi$
$317$	−271.925	−	533.682i	−0.857807	−	1.68354i	−0.136815	−	0.990597i	$-0.543686\pi$
$318$	−1.23732	+	0.497845i	−0.00389094	+	0.00156555i
$319$	−0.786382	+	2.42024i	−0.00246515	+	0.00758695i
$320$	152.827	−	281.148i	0.477583	−	0.878587i
$321$	27.6970	+	389.981i	0.0862835	+	1.21489i
$322$	−45.9037	+	62.8467i	−0.142558	+	0.195176i
$323$	−194.534	+	30.8111i	−0.602272	+	0.0953905i
$324$	−311.511	+	89.0906i	−0.961452	+	0.274971i
$325$	163.860	−	78.7921i	0.504184	−	0.242437i
$326$	30.5895	+	4.92410i	0.0938327	+	0.0151046i
$327$	−10.4507	+	120.969i	−0.0319593	+	0.369937i
$328$	150.397	+	210.336i	0.458529	+	0.641270i
$329$	−106.217	−	326.901i	−0.322847	−	0.993620i
$330$	35.8694	+	9.43823i	0.108695	+	0.0286007i
$331$	−186.721	−	60.6694i	−0.564112	−	0.183291i	0.0130584	−	0.999915i	$-0.495843\pi$
$331$	−186.721	−	60.6694i	−0.564112	−	0.183291i	−0.577171	+	0.816624i	$0.695843\pi$
$332$	−238.212	−	473.412i	−0.717506	−	1.42594i
$333$	3.18719	−	208.639i	0.00957115	−	0.626543i
$334$	−156.681	+	79.3355i	−0.469106	+	0.237531i
$335$	−566.507	−	6.52292i	−1.69107	−	0.0194714i
$336$	−228.163	+	13.8901i	−0.679058	+	0.0413397i
$337$	−377.782	−	59.8347i	−1.12101	−	0.177551i	−0.431702	−	0.902016i	$-0.642087\pi$
$337$	−377.782	−	59.8347i	−1.12101	−	0.177551i	−0.689311	+	0.724465i	$0.742087\pi$
$338$	220.667	+	72.3154i	0.652860	+	0.213951i
$339$	−61.7451	−	73.4224i	−0.182139	−	0.216585i
$340$	−333.393	−	5.52265i	−0.980569	−	0.0162431i
$341$	−16.9457	−	23.3237i	−0.0496941	−	0.0683980i
$342$	209.405	+	36.9985i	0.612294	+	0.108183i
$343$	−253.636	−	253.636i	−0.739465	−	0.739465i
$344$	−374.043	−	379.753i	−1.08734	−	1.10393i
$345$	105.713	−	62.0285i	0.306416	−	0.179793i
$346$	30.9489	+	198.649i	0.0894478	+	0.574129i
$347$	−53.3966	+	104.797i	−0.153881	+	0.302008i	−0.955058	−	0.296419i	$-0.904207\pi$
$347$	−53.3966	+	104.797i	−0.153881	+	0.302008i	0.801177	+	0.598427i	$0.204207\pi$
$348$	−9.74094	+	22.6979i	−0.0279912	+	0.0652238i
$349$			317.579i			0.909968i	0.890500	+	0.454984i	$0.150355\pi$
$349$			317.579i			0.909968i	−0.890500	+	0.454984i	$0.849645\pi$
$350$	234.150	+	43.2452i	0.669001	+	0.123558i
$351$	−146.356	−	130.916i	−0.416969	−	0.372980i
$352$	31.7111	+	23.6568i	0.0900882	+	0.0672067i
$353$	−265.615	+	521.299i	−0.752451	+	1.47677i	0.122455	+	0.992474i	$0.460923\pi$
$353$	−265.615	+	521.299i	−0.752451	+	1.47677i	−0.874906	+	0.484293i	$0.839077\pi$
$354$	−14.2925	+	160.706i	−0.0403742	+	0.453972i
$355$	−476.207	−	81.0548i	−1.34143	−	0.228323i
$356$	251.543	+	184.705i	0.706582	+	0.518834i
$357$	122.897	+	204.031i	0.344249	+	0.571516i
$358$	666.051	−	214.555i	1.86048	−	0.599317i
$359$	110.020	+	151.430i	0.306464	+	0.421811i	0.934274	−	0.356555i	$-0.116049\pi$
$359$	110.020	+	151.430i	0.306464	+	0.421811i	−0.627811	+	0.778366i	$0.716049\pi$
$360$	338.356	+	122.943i	0.939878	+	0.341510i
$361$	179.144	+	130.156i	0.496245	+	0.360543i
$362$	80.2372	−	244.840i	0.221650	−	0.676353i
$363$	139.684	−	330.074i	0.384805	−	0.909296i
$364$	−80.8634	−	112.489i	−0.222152	−	0.309036i
$365$	177.889	−	526.770i	0.487367	−	1.44321i
$366$	−73.6405	−	321.074i	−0.201204	−	0.877253i
$367$	−0.694508	−	1.36305i	−0.00189239	−	0.00371403i	0.890058	−	0.455847i	$-0.150663\pi$
$367$	−0.694508	−	1.36305i	−0.00189239	−	0.00371403i	−0.891951	+	0.452132i	$0.850663\pi$
$368$	129.329	−	19.1469i	0.351439	−	0.0520297i
$369$	−208.813	+	202.529i	−0.565888	+	0.548859i
$370$	−138.896	+	185.637i	−0.375396	+	0.501722i
$371$	−0.327118	−	1.00676i	−0.000881719	−	0.00271365i
$372$	−143.168	−	240.423i	−0.384860	−	0.646299i
$373$	−406.165	+	64.3302i	−1.08891	+	0.172467i	−0.674977	−	0.737839i	$-0.735846\pi$
$373$	−406.165	+	64.3302i	−1.08891	+	0.172467i	−0.413936	+	0.910306i	$0.635846\pi$
$374$	6.55173	−	40.7006i	0.0175180	−	0.108825i
$375$	−311.194	−	209.245i	−0.829850	−	0.557986i
$376$	−266.033	+	512.485i	−0.707533	+	1.36299i
$377$	−14.7853	+	2.34177i	−0.0392184	+	0.00621159i
$378$	−53.6532	−	251.500i	−0.141940	−	0.665343i
$379$	−158.660	−	488.305i	−0.418628	−	1.28840i	−0.908965	−	0.416872i	$-0.863126\pi$
$379$	−158.660	−	488.305i	−0.418628	−	1.28840i	0.490337	−	0.871533i	$-0.336874\pi$
$380$	−164.282	−	169.816i	−0.432321	−	0.446885i
$381$	−8.66306	−	5.40017i	−0.0227377	−	0.0141737i
$382$	563.298	−	407.091i	1.47460	−	1.06568i
$383$	−306.869	−	602.265i	−0.801225	−	1.57249i	−0.819790	−	0.572665i	$-0.805910\pi$
$383$	−306.869	−	602.265i	−0.801225	−	1.57249i	0.0185646	−	0.999828i	$-0.494090\pi$
$384$	285.591	+	256.698i	0.743726	+	0.668485i
$385$	−9.41879	+	27.8912i	−0.0244644	+	0.0724447i
$386$	−456.712	+	454.411i	−1.18319	+	1.17723i
$387$	359.840	−	479.694i	0.929818	−	1.23952i
$388$	243.344	−	471.686i	0.627176	−	1.21569i
$389$	−261.838	−	190.236i	−0.673105	−	0.489040i	0.197958	−	0.980211i	$-0.436569\pi$
$389$	−261.838	−	190.236i	−0.673105	−	0.489040i	−0.871063	+	0.491171i	$0.836569\pi$
$390$	46.3235	+	213.209i	0.118778	+	0.546689i
$391$	−80.0738	−	110.212i	−0.204792	−	0.281872i
$392$	−1.59496	+	210.565i	−0.00406878	+	0.537156i
$393$	26.3433	−	15.8678i	0.0670314	−	0.0403760i
$394$	249.383	+	127.861i	0.632952	+	0.324521i
$395$	349.701	+	59.5224i	0.885320	+	0.150690i
$396$	−21.0082	+	39.2384i	−0.0530510	+	0.0990870i
$397$	140.919	−	276.568i	0.354959	−	0.696645i	−0.642621	−	0.766185i	$-0.722153\pi$
$397$	140.919	−	276.568i	0.354959	−	0.696645i	0.997579	+	0.0695391i	$0.0221528\pi$
$398$	11.1837	+	0.0282371i	0.0280998	+	7.09476e-5i
$399$	−40.6529	+	163.810i	−0.101887	+	0.410551i
$400$	−224.267	−	331.216i	−0.560667	−	0.828041i
$401$		−	124.583i		−	0.310681i	−0.987861	−	0.155340i	$-0.950353\pi$
$401$		−	124.583i		−	0.310681i	0.987861	−	0.155340i	$-0.0496474\pi$
$402$	165.418	−	659.423i	0.411489	−	1.64035i
$403$	76.9922	−	151.106i	0.191048	−	0.374952i
$404$	−2.46255	+	487.660i	−0.00609542	+	1.20708i
$405$	−80.1210	+	396.996i	−0.197830	+	0.980236i
$406$	−17.4450	−	8.94421i	−0.0429679	−	0.0220301i
$407$	−20.2688	−	20.2688i	−0.0498004	−	0.0498004i
$408$	99.3153	−	387.605i	0.243420	−	0.950013i
$409$	−59.7362	−	82.2198i	−0.146054	−	0.201027i	0.729722	−	0.683744i	$-0.239650\pi$
$409$	−59.7362	−	82.2198i	−0.146054	−	0.201027i	−0.875776	+	0.482718i	$0.839650\pi$
$410$	319.917	−	46.0760i	0.780286	−	0.112380i
$411$	−326.913	+	274.920i	−0.795408	+	0.668904i
$412$	−353.341	+	684.900i	−0.857625	+	1.66238i
$413$	−126.479	−	20.0324i	−0.306245	−	0.0485045i
$414$	42.9537	+	140.670i	0.103753	+	0.339782i
$415$	−662.413	−	7.62721i	−1.59618	−	0.0183788i
$416$	−39.3056	+	229.385i	−0.0944847	+	0.551407i
$417$	136.821	+	589.708i	0.328109	+	1.41417i
$418$	23.6761	−	17.1105i	0.0566415	−	0.0409343i
$419$	222.495	+	72.2929i	0.531013	+	0.172537i	0.562238	−	0.826976i	$-0.309941\pi$
$419$	222.495	+	72.2929i	0.531013	+	0.172537i	−0.0312243	+	0.999512i	$0.509941\pi$
$420$	−115.701	+	261.259i	−0.275479	+	0.622045i
$421$	−35.7738	−	110.100i	−0.0849733	−	0.261521i	0.899538	−	0.436843i	$-0.143903\pi$
$421$	−35.7738	−	110.100i	−0.0849733	−	0.261521i	−0.984511	+	0.175322i	$0.943903\pi$
$422$	−73.9200	+	101.204i	−0.175166	+	0.239819i
$423$	−614.666	−	210.150i	−1.45311	−	0.496808i
$424$	−0.819307	+	1.57831i	−0.00193233	+	0.00372243i
$425$	−197.724	+	366.915i	−0.465232	+	0.863330i
$426$	227.260	−	533.261i	0.533474	−	1.25179i
$427$	258.235	−	40.9004i	0.604766	−	0.0957855i
$428$	366.738	+	370.460i	0.856864	+	0.865562i
$429$	−26.9072	+	1.91098i	−0.0627207	+	0.00445451i
$430$	−636.505	+	196.978i	−1.48024	+	0.458089i
$431$	−87.4378	+	269.106i	−0.202872	+	0.624376i	0.796922	+	0.604082i	$0.206460\pi$
$431$	−87.4378	+	269.106i	−0.202872	+	0.624376i	−0.999794	+	0.0202936i	$0.993540\pi$
$432$	−237.754	+	360.690i	−0.550356	+	0.834930i
$433$	−87.0090	−	170.765i	−0.200945	−	0.394376i	0.768441	−	0.639921i	$-0.221033\pi$
$433$	−87.0090	−	170.765i	−0.200945	−	0.394376i	−0.969385	+	0.245545i	$0.921033\pi$
$434$	198.142	−	100.329i	0.456548	−	0.231173i
$435$	19.5983	+	23.8570i	0.0450535	+	0.0548437i
$436$	94.4958	+	131.453i	0.216734	+	0.301498i
$437$	15.1010	−	95.3442i	0.0345561	−	0.218179i
$438$	565.305	+	354.371i	1.29065	+	0.809067i
$439$	−179.358	−	130.311i	−0.408559	−	0.296836i	0.364459	−	0.931219i	$-0.381254\pi$
$439$	−179.358	−	130.311i	−0.408559	−	0.296836i	−0.773018	+	0.634384i	$0.781254\pi$
$440$	44.4842	−	21.6064i	0.101100	−	0.0491055i
$441$	−234.515	+	33.4800i	−0.531780	+	0.0759184i
$442$	230.822	−	74.3548i	0.522222	−	0.168224i
$443$	498.477	−	498.477i	1.12523	−	1.12523i	0.134288	−	0.990942i	$-0.457125\pi$
$443$	498.477	−	498.477i	1.12523	−	1.12523i	0.990942	−	0.134288i	$-0.0428746\pi$
$444$	−177.989	−	213.833i	−0.400876	−	0.481607i
$445$	349.591	−	173.085i	0.785597	−	0.388954i
$446$	64.4635	+	413.765i	0.144537	+	0.927725i
$447$	365.020	+	316.610i	0.816600	+	0.708300i
$448$	−218.753	+	212.223i	−0.488287	+	0.473713i
$449$	705.362			1.57096			0.785481	−	0.618886i	$-0.212416\pi$
$449$	705.362			1.57096			0.785481	+	0.618886i	$0.212416\pi$
$450$	330.920	−	304.945i	0.735379	−	0.677656i
$451$			39.9609i			0.0886051i
$452$	−126.234	−	20.6475i	−0.279280	−	0.0456804i
$453$	293.812	−	338.736i	0.648591	−	0.747761i
$454$	58.5626	+	375.890i	0.128993	+	0.827952i
$455$	−171.341	+	25.1190i	−0.376573	+	0.0552066i
$456$	243.975	−	144.450i	0.535033	−	0.316776i
$457$	−383.720	−	383.720i	−0.839651	−	0.839651i	0.149162	−	0.988813i	$-0.452342\pi$
$457$	−383.720	−	383.720i	−0.839651	−	0.839651i	−0.988813	+	0.149162i	$0.952342\pi$
$458$	−662.492	+	213.409i	−1.44649	+	0.465958i
$459$	447.828	+	45.5897i	0.975661	+	0.0993240i
$460$	53.0681	−	154.568i	0.115365	−	0.336016i
$461$	−354.561	+	488.011i	−0.769112	+	1.05859i	0.227289	+	0.973827i	$0.427014\pi$
$461$	−354.561	+	488.011i	−0.769112	+	1.05859i	−0.996401	+	0.0847647i	$0.972986\pi$
$462$	−29.9315	−	18.7631i	−0.0647869	−	0.0406128i
$463$	465.112	+	73.6666i	1.00456	+	0.159107i	0.636977	−	0.770883i	$-0.280185\pi$
$463$	465.112	+	73.6666i	1.00456	+	0.159107i	0.367585	+	0.929990i	$0.380185\pi$
$464$	9.86003	+	31.4224i	0.0212501	+	0.0677206i
$465$	−349.161	+	20.7606i	−0.750883	+	0.0446464i
$466$	−345.644	+	175.017i	−0.741726	+	0.375573i
$467$	−287.403	+	146.439i	−0.615424	+	0.313574i	−0.733770	−	0.679398i	$-0.762241\pi$
$467$	−287.403	+	146.439i	−0.615424	+	0.313574i	0.118346	+	0.992972i	$0.462241\pi$
$468$	−261.766	−	5.32102i	−0.559328	−	0.0113697i
$469$	513.191	+	166.746i	1.09422	+	0.355535i
$470$	416.010	+	589.826i	0.885127	+	1.25495i
$471$	−9.37133	−	131.951i	−0.0198967	−	0.280150i
$472$	125.123	+	174.989i	0.265090	+	0.370739i
$473$	−12.8865	−	81.3619i	−0.0272441	−	0.172012i
$474$	−166.888	+	391.599i	−0.352084	+	0.826158i
$475$	−282.916	+	84.7747i	−0.595613	+	0.178473i
$476$	301.538	+	99.6619i	0.633483	+	0.209374i
$477$	−1.89300	−	0.647203i	−0.00396855	−	0.00135682i
$478$	27.9319	−	38.2416i	0.0584350	−	0.0800033i
$479$	−494.597	+	160.704i	−1.03256	+	0.335500i	−0.775802	−	0.630976i	$-0.782655\pi$
$479$	−494.597	+	160.704i	−1.03256	+	0.335500i	−0.256759	+	0.966475i	$0.582655\pi$
$480$	449.074	−	169.506i	0.935571	−	0.353139i
$481$	52.1057	−	160.365i	0.108328	−	0.333399i
$482$	−0.527107	+	0.380936i	−0.00109358	+	0.000790323i
$483$	−113.718	+	26.3844i	−0.235441	+	0.0546260i
$484$	−145.378	−	455.236i	−0.300368	−	0.940571i
$485$	−383.759	−	541.195i	−0.791256	−	1.11587i
$486$	−441.064	−	204.105i	−0.907538	−	0.419969i
$487$	19.1933	−	121.182i	0.0394113	−	0.248833i	−0.960115	−	0.279605i	$-0.909796\pi$
$487$	19.1933	−	121.182i	0.0394113	−	0.248833i	0.999526	+	0.0307717i	$0.00979649\pi$
$488$	−353.367	−	260.848i	−0.724112	−	0.534525i
$489$	29.9122	+	35.5693i	0.0611702	+	0.0727388i
$490$	232.825	+	122.777i	0.475153	+	0.250566i
$491$	501.152	−	364.109i	1.02068	−	0.741565i	0.0542554	−	0.998527i	$-0.482721\pi$
$491$	501.152	−	364.109i	1.02068	−	0.741565i	0.966422	+	0.256962i	$0.0827215\pi$
$492$	−35.3344	+	386.249i	−0.0718179	+	0.785059i
$493$	24.2652	−	24.2652i	0.0492194	−	0.0492194i
$494$	152.911	+	78.3990i	0.309537	+	0.158702i
$495$	31.4844	+	45.8699i	0.0636048	+	0.0926664i
$496$	−353.653	−	118.871i	−0.713010	−	0.239659i
$497$	409.937	+	208.873i	0.824822	+	0.420268i
$498$	193.423	−	771.059i	0.388399	−	1.54831i
$499$	−707.290			−1.41742			−0.708708	−	0.705502i	$-0.750721\pi$
$499$	−707.290			−1.41742			−0.708708	+	0.705502i	$0.750721\pi$
$500$	−496.553	+	58.6093i	−0.993106	+	0.117219i
$501$	−255.678	−	63.4519i	−0.510334	−	0.126650i
$502$	834.793	+	2.10772i	1.66293	+	0.00419865i
$503$	247.188	+	125.949i	0.491427	+	0.250395i	0.682100	−	0.731259i	$-0.261067\pi$
$503$	247.188	+	125.949i	0.491427	+	0.250395i	−0.190673	+	0.981654i	$0.561067\pi$
$504$	−272.718	−	207.824i	−0.541106	−	0.412350i
$505$	539.920	+	282.980i	1.06915	+	0.560356i
$506$	17.9794	+	9.21822i	0.0355324	+	0.0182178i
$507$	179.723	+	298.373i	0.354484	+	0.588508i
$508$	−13.4541	+	2.06134i	−0.0264845	+	0.00405775i
$509$	424.130	−	308.148i	0.833261	−	0.605399i	−0.0872193	−	0.996189i	$-0.527798\pi$
$509$	424.130	−	308.148i	0.833261	−	0.605399i	0.920480	+	0.390790i	$0.127798\pi$
$510$	−373.194	−	332.994i	−0.731753	−	0.652929i
$511$	−311.264	+	428.417i	−0.609126	+	0.838390i
$512$	511.868	+	11.6335i	0.999742	+	0.0227216i
$513$	201.545	+	247.231i	0.392874	+	0.481931i
$514$	461.467	−	459.143i	0.897797	−	0.893274i
$515$	557.227	+	785.828i	1.08200	+	1.52588i
$516$	−52.6141	−	797.812i	−0.101965	−	1.54615i
$517$	−79.5101	+	40.5124i	−0.153791	+	0.0783606i
$518$	178.975	−	129.344i	0.345512	−	0.249699i
$519$	−159.528	+	255.918i	−0.307376	+	0.493098i
$520$	232.045	+	175.454i	0.446240	+	0.337412i
$521$	32.8247	−	10.6654i	0.0630033	−	0.0204710i	−0.277346	−	0.960770i	$-0.589455\pi$
$521$	32.8247	−	10.6654i	0.0630033	−	0.0204710i	0.340349	+	0.940299i	$0.389455\pi$
$522$	−33.3057	+	16.2300i	−0.0638039	+	0.0310919i
$523$	−25.8416	−	163.157i	−0.0494103	−	0.311964i	−0.999999	−	0.00151072i	$-0.999519\pi$
$523$	−25.8416	−	163.157i	−0.0494103	−	0.311964i	0.950589	−	0.310453i	$-0.100481\pi$
$524$	12.8678	−	38.9328i	0.0245568	−	0.0742993i
$525$	223.524	+	278.575i	0.425761	+	0.530619i
$526$	−21.2313	+	131.893i	−0.0403637	+	0.250747i
$527$	60.8162	+	383.979i	0.115401	+	0.728612i
$528$	12.8281	+	57.9415i	0.0242956	+	0.109738i
$529$	−439.608	+	142.837i	−0.831018	+	0.270014i
$530$	1.28119	+	1.81650i	0.00241735	+	0.00342736i
$531$	−173.721	+	168.493i	−0.327158	+	0.317313i
$532$	101.152	+	201.024i	0.190135	+	0.377865i
$533$	−209.448	+	106.719i	−0.392961	+	0.200224i
$534$	104.647	+	456.263i	0.195968	+	0.854426i
$535$	621.991	−	194.209i	1.16260	−	0.363007i
$536$	−405.400	−	810.766i	−0.756344	−	1.51262i
$537$	966.639	+	409.072i	1.80007	+	0.761773i
$538$	−53.5054	+	163.269i	−0.0994525	+	0.303474i
$539$	−19.1279	+	26.3273i	−0.0354878	+	0.0488447i
$540$	263.758	+	471.202i	0.488442	+	0.872597i
$541$	619.010	−	449.737i	1.14420	−	0.831308i	0.156498	−	0.987678i	$-0.449979\pi$
$541$	619.010	−	449.737i	1.14420	−	0.831308i	0.987698	+	0.156371i	$0.0499794\pi$
$542$	76.8772	−	24.7645i	0.141840	−	0.0456910i
$543$	331.059	−	199.411i	0.609685	−	0.367240i
$544$	−236.185	−	478.374i	−0.434164	−	0.879364i
$545$	200.226	−	29.3537i	0.367388	−	0.0538600i
$546$	18.4087	−	206.989i	0.0337156	−	0.379102i
$547$	959.844	+	489.065i	1.75474	+	0.894086i	0.956491	+	0.291762i	$0.0942415\pi$
$547$	959.844	+	489.065i	1.75474	+	0.894086i	0.798252	+	0.602324i	$0.205758\pi$
$548$	−91.9330	+	562.058i	−0.167761	+	1.02565i
$549$	231.023	−	436.783i	0.420807	−	0.795598i
$550$	1.57940	−	61.7971i	0.00287164	−	0.112358i
$551$	24.3165			0.0441316
$552$	165.632	+	104.998i	0.300058	+	0.190214i
$553$	−301.036	−	153.385i	−0.544368	−	0.277370i
$554$	153.617	+	986.005i	0.277287	+	1.77979i
$555$	−339.655	+	74.6950i	−0.611992	+	0.134586i
$556$	650.604	+	477.730i	1.17015	+	0.859226i
$557$	348.874	−	348.874i	0.626344	−	0.626344i	−0.320802	−	0.947146i	$-0.603952\pi$
$557$	348.874	−	348.874i	0.626344	−	0.626344i	0.947146	+	0.320802i	$0.103952\pi$
$558$	73.0291	−	413.331i	0.130876	−	0.740737i
$559$	392.030	−	284.826i	0.701305	−	0.509528i
$560$	109.870	+	364.790i	0.196197	+	0.651410i
$561$	47.3265	−	39.7995i	0.0843609	−	0.0709439i
$562$	286.978	+	94.0465i	0.510637	+	0.167342i
$563$	−117.471	+	741.685i	−0.208652	+	1.31738i	0.631647	+	0.775256i	$0.282379\pi$
$563$	−117.471	+	741.685i	−0.208652	+	1.31738i	−0.840299	+	0.542123i	$0.817621\pi$
$564$	−804.340	+	321.275i	−1.42614	+	0.569636i
$565$	−95.4639	+	128.263i	−0.168963	+	0.227014i
$566$	414.673	−	209.969i	0.732638	−	0.370970i
$567$	185.538	−	338.186i	0.327228	−	0.596448i
$568$	−233.262	−	736.850i	−0.410672	−	1.29727i
$569$	−33.1280	+	101.957i	−0.0582214	+	0.179187i	−0.975938	−	0.218049i	$-0.930031\pi$
$569$	−33.1280	+	101.957i	−0.0582214	+	0.179187i	0.917716	+	0.397236i	$0.130031\pi$
$570$	−20.1424	−	353.841i	−0.0353376	−	0.620773i
$571$	110.991	−	36.0632i	0.194380	−	0.0631579i	−0.210209	−	0.977656i	$-0.567415\pi$
$571$	110.991	−	36.0632i	0.194380	−	0.0631579i	0.404589	+	0.914499i	$0.367415\pi$
$572$	−25.5603	+	25.3035i	−0.0446859	+	0.0442368i
$573$	1038.63	+	89.7289i	1.81262	+	0.156595i
$574$	−303.934	−	48.9253i	−0.529501	−	0.0852357i
$575$	−141.083	−	147.735i	−0.245362	−	0.256931i
$576$	72.7588	+	571.386i	0.126317	+	0.991990i
$577$	−136.547	−	862.124i	−0.236650	−	1.49415i	−0.764396	−	0.644747i	$-0.776963\pi$
$577$	−136.547	−	862.124i	−0.236650	−	1.49415i	0.527746	−	0.849402i	$-0.323037\pi$
$578$	13.0304	−	17.8399i	0.0225439	−	0.0308649i
$579$	−963.966	+	68.4622i	−1.66488	+	0.118242i
$580$	40.5472	+	7.11238i	0.0699090	+	0.0122627i
$581$	600.071	+	194.975i	1.03282	+	0.335585i
$582$	738.593	−	297.178i	1.26906	−	0.510616i
$583$	−0.244869	+	0.124767i	−0.000420016	+	0.000214009i
$584$	879.670	−	132.504i	1.50628	−	0.226890i
$585$	−156.337	+	287.519i	−0.267243	+	0.491486i
$586$	424.513	+	426.662i	0.724424	+	0.728092i
$587$	412.345	+	65.3090i	0.702462	+	0.111259i	0.497440	−	0.867498i	$-0.334274\pi$
$587$	412.345	+	65.3090i	0.702462	+	0.111259i	0.205022	+	0.978757i	$0.434274\pi$
$588$	−208.163	+	237.558i	−0.354019	+	0.404010i
$589$	−161.923	+	222.868i	−0.274911	+	0.378383i
$590$	266.154	−	38.3328i	0.451109	−	0.0649708i
$591$	157.900	+	389.594i	0.267174	+	0.659212i
$592$	−365.785	−	61.7276i	−0.617879	−	0.104270i
$593$	−668.345	−	668.345i	−1.12706	−	1.12706i	−0.990653	−	0.136405i	$-0.956445\pi$
$593$	−668.345	−	668.345i	−1.12706	−	1.12706i	−0.136405	−	0.990653i	$-0.543555\pi$
$594$	−62.3105	+	23.9719i	−0.104900	+	0.0403567i
$595$	283.918	−	277.454i	0.477173	−	0.466309i
$596$	644.258	+	3.25332i	1.08097	+	0.00545860i
$597$	12.6727	+	10.9920i	0.0212273	+	0.0184121i
$598$	−0.300088	+	118.854i	−0.000501819	+	0.198752i
$599$		−	247.954i		−	0.413947i	−0.978347	−	0.206974i	$-0.933639\pi$
$599$		−	247.954i		−	0.413947i	0.978347	−	0.206974i	$-0.0663614\pi$
$600$	69.9085	−	595.913i	0.116514	−	0.993189i
$601$	−905.090			−1.50597			−0.752986	−	0.658036i	$-0.771387\pi$
$601$	−905.090			−1.50597			−0.752986	+	0.658036i	$0.771387\pi$
$602$	634.597	+	1.60226i	1.05415	+	0.00266156i
$603$	834.079	−	586.741i	1.38322	−	0.973036i
$604$	3.01906	−	597.866i	0.00499844	−	0.989844i
$605$	−588.888	−	100.234i	−0.973368	−	0.165676i
$606$	−480.699	+	551.380i	−0.793232	+	0.909868i
$607$	−766.102	+	766.102i	−1.26211	+	1.26211i	−0.312044	+	0.950067i	$0.601014\pi$
$607$	−766.102	+	766.102i	−1.26211	+	1.26211i	−0.950067	+	0.312044i	$0.898986\pi$
$608$	121.351	−	358.035i	0.199590	−	0.588873i
$609$	−11.0455	−	27.2531i	−0.0181371	−	0.0447505i
$610$	−492.630	+	242.358i	−0.807590	+	0.397307i
$611$	−424.677	−	308.546i	−0.695053	−	0.504985i
$612$	492.634	−	342.842i	0.804957	−	0.560199i
$613$	40.0607	−	252.933i	0.0653518	−	0.412615i	−0.933225	−	0.359291i	$-0.883018\pi$
$613$	40.0607	−	252.933i	0.0653518	−	0.412615i	0.998577	−	0.0533239i	$-0.0169816\pi$
$614$	−110.355	+	109.799i	−0.179732	+	0.178826i
$615$	408.456	+	261.191i	0.664157	+	0.424702i
$616$	−46.5764	+	7.01576i	−0.0756110	+	0.0113892i
$617$	−178.268	−	349.871i	−0.288927	−	0.567052i	0.700229	−	0.713918i	$-0.253081\pi$
$617$	−178.268	−	349.871i	−0.288927	−	0.567052i	−0.989156	+	0.146866i	$0.953081\pi$
$618$	−1072.45	+	431.510i	−1.73536	+	0.698236i
$619$	90.0522	−	277.152i	0.145480	−	0.447742i	−0.851592	−	0.524205i	$-0.824363\pi$
$619$	90.0522	−	277.152i	0.145480	−	0.447742i	0.997072	+	0.0764630i	$0.0243627\pi$
$620$	−335.190	+	324.266i	−0.540629	+	0.523010i
$621$	−89.0761	+	201.840i	−0.143440	+	0.325025i
$622$	−597.751	−	436.602i	−0.961014	−	0.701932i
$623$	−366.965	+	58.1216i	−0.589029	+	0.0932931i
$624$	−269.432	+	221.974i	−0.431781	+	0.355727i
$625$	−220.297	+	584.888i	−0.352475	+	0.935821i
$626$	−57.1449	+	354.996i	−0.0912859	+	0.567086i
$627$	43.6551	+	3.77142i	0.0696254	+	0.00601502i
$628$	−124.086	−	125.346i	−0.197590	−	0.199596i
$629$	119.446	+	367.617i	0.189898	+	0.584447i
$630$	−387.423	+	183.303i	−0.614957	+	0.290958i
$631$	−36.5774	−	11.8847i	−0.0579674	−	0.0188347i	0.279890	−	0.960032i	$-0.409702\pi$
$631$	−36.5774	−	11.8847i	−0.0579674	−	0.0188347i	−0.337857	+	0.941197i	$0.609702\pi$
$632$	171.295	+	541.104i	0.271036	+	0.856177i
$633$	−183.123	+	42.4875i	−0.289294	+	0.0671208i
$634$	−541.153	−	1068.73i	−0.853553	−	1.68570i
$635$	−5.44354	+	16.1196i	−0.00857251	+	0.0253852i
$636$	−2.47715	+	0.989438i	−0.00389488	+	0.00155572i
$637$	−189.073	−	29.9462i	−0.296817	−	0.0470112i
$638$	−1.58498	+	4.83649i	−0.00248430	+	0.00758070i
$639$	780.670	−	382.866i	1.22171	−	0.599164i
$640$	307.072	−	561.522i	0.479800	−	0.877378i
$641$	−484.264	−	666.532i	−0.755482	−	1.03983i	−0.997576	−	0.0695794i	$-0.977834\pi$
$641$	−484.264	−	666.532i	−0.755482	−	1.03983i	0.242094	−	0.970253i	$-0.422166\pi$
$642$	53.4246	+	780.100i	0.0832158	+	1.21511i
$643$	19.5319	+	19.5319i	0.0303761	+	0.0303761i	0.722132	−	0.691756i	$-0.243162\pi$
$643$	19.5319	+	19.5319i	0.0303761	+	0.0303761i	−0.691756	+	0.722132i	$0.743162\pi$
$644$	−92.1244	+	125.461i	−0.143050	+	0.194815i
$645$	−915.860	−	400.078i	−1.41994	−	0.620276i
$646$	−389.222	+	60.6398i	−0.602511	+	0.0938696i
$647$	323.690	−	635.278i	0.500294	−	0.981883i	−0.493405	−	0.869800i	$-0.664248\pi$
$647$	323.690	−	635.278i	0.500294	−	0.981883i	0.993699	−	0.112083i	$-0.0357522\pi$
$648$	−623.469	+	176.608i	−0.962144	+	0.272543i
$649$			33.2454i			0.0512255i
$650$	328.116	−	156.756i	0.504794	−	0.241164i
$651$	323.334	+	80.2423i	0.496673	+	0.123260i
$652$	61.1539	+	10.0026i	0.0937943	+	0.0153415i
$653$	372.404	−	730.885i	0.570298	−	1.11927i	−0.408177	−	0.912903i	$-0.633835\pi$
$653$	372.404	−	730.885i	0.570298	−	1.11927i	0.978474	−	0.206369i	$-0.0661647\pi$
$654$	−21.5122	+	241.885i	−0.0328932	+	0.369855i
$655$	−35.8233	−	36.6578i	−0.0546920	−	0.0559662i
$656$	299.732	+	421.431i	0.456908	+	0.642425i
$657$	294.687	+	956.423i	0.448535	+	1.45574i
$658$	−210.782	−	654.336i	−0.320337	−	0.994432i
$659$	−182.069	−	250.597i	−0.276281	−	0.380268i	0.648217	−	0.761456i	$-0.275515\pi$
$659$	−182.069	−	250.597i	−0.276281	−	0.380268i	−0.924498	+	0.381188i	$0.875515\pi$
$660$	71.6909	+	19.0575i	0.108623	+	0.0288750i
$661$	295.949	+	215.019i	0.447729	+	0.325294i	0.788698	−	0.614780i	$-0.210755\pi$
$661$	295.949	+	215.019i	0.447729	+	0.325294i	−0.340970	+	0.940074i	$0.610755\pi$
$662$	−373.135	−	122.281i	−0.563648	−	0.184715i
$663$	334.992	+	141.765i	0.505266	+	0.213824i
$664$	−474.032	−	948.024i	−0.713903	−	1.42775i
$665$	281.280	+	3.23873i	0.422977	+	0.00487027i
$666$	7.42792	−	417.260i	0.0111530	−	0.626516i
$667$	7.63561	+	14.9857i	0.0114477	+	0.0224674i
$668$	−313.762	+	157.879i	−0.469704	+	0.236346i
$669$	−332.281	+	533.051i	−0.496682	+	0.796788i
$670$	−1132.98	−	15.9065i	−1.69101	−	0.0237410i
$671$	−20.9753	−	64.5555i	−0.0312598	−	0.0962078i
$672$	−456.396	+	26.6280i	−0.679160	+	0.0396250i
$673$	−932.721	+	147.729i	−1.38592	+	0.219507i	−0.804429	−	0.594049i	$-0.797529\pi$
$673$	−932.721	+	147.729i	−1.38592	+	0.219507i	−0.581487	+	0.813556i	$0.697529\pi$
$674$	−755.258	−	121.577i	−1.12056	−	0.180381i
$675$	674.641	−	22.0010i	0.999469	−	0.0325941i
$676$	440.966	+	145.745i	0.652317	+	0.215598i
$677$	−1055.35	+	167.152i	−1.55887	+	0.246901i	−0.875517	−	0.483188i	$-0.839479\pi$
$677$	−1055.35	+	167.152i	−1.55887	+	0.246901i	−0.683352	+	0.730089i	$0.739479\pi$
$678$	−123.119	−	147.156i	−0.181592	−	0.217044i
$679$	195.266	+	600.968i	0.287579	+	0.885078i
$680$	−666.757	−	12.7288i	−0.980525	−	0.0187188i
$681$	−301.864	+	484.257i	−0.443266	+	0.711096i
$682$	−33.7735	−	46.7329i	−0.0495212	−	0.0685232i
$683$	79.7144	+	156.448i	0.116712	+	0.229060i	0.941971	−	0.335694i	$-0.108971\pi$
$683$	79.7144	+	156.448i	0.116712	+	0.229060i	−0.825259	+	0.564755i	$0.808971\pi$
$684$	418.621	+	75.0542i	0.612019	+	0.109728i
$685$	571.090	+	425.053i	0.833708	+	0.620515i
$686$	−505.990	−	508.552i	−0.737595	−	0.741329i
$687$	−961.473	−	406.886i	−1.39952	−	0.592265i
$688$	−746.167	−	761.393i	−1.08454	−	1.10668i
$689$	−1.30789	−	0.950237i	−0.00189824	−	0.00137915i
$690$	211.740	−	123.523i	0.306869	−	0.179018i
$691$	619.122	+	852.148i	0.895980	+	1.23321i	0.971733	+	0.236084i	$0.0758640\pi$
$691$	619.122	+	852.148i	0.895980	+	1.23321i	−0.0757530	+	0.997127i	$0.524136\pi$
$692$	60.8946	+	397.453i	0.0879980	+	0.574354i
$693$	−15.6030	−	50.6403i	−0.0225151	−	0.0730740i
$694$	−107.322	+	209.323i	−0.154643	+	0.301618i
$695$	904.199	−	447.675i	1.30101	−	0.644136i
$696$	−19.5964	+	45.3464i	−0.0281558	+	0.0651529i
$697$	244.641	−	480.135i	0.350991	−	0.688859i
$698$	−1.60367	+	635.156i	−0.00229752	+	0.909965i
$699$	−564.033	−	139.977i	−0.806915	−	0.200253i
$700$	468.081	+	87.6725i	0.668687	+	0.125246i
$701$			349.815i			0.499023i	0.968372	+	0.249511i	$0.0802700\pi$
$701$			349.815i			0.499023i	−0.968372	+	0.249511i	$0.919730\pi$
$702$	−292.050	−	262.570i	−0.416025	−	0.374032i
$703$	−124.348	+	244.047i	−0.176882	+	0.347150i
$704$	63.3024	+	47.4735i	0.0899182	+	0.0674340i
$705$	−105.598	+	1077.50i	−0.149785	+	1.52837i
$706$	−533.861	+	1041.25i	−0.756177	+	1.47486i
$707$	−410.540	−	410.540i	−0.580679	−	0.580679i
$708$	−29.3963	+	321.339i	−0.0415203	+	0.453868i
$709$	524.561	+	721.997i	0.739861	+	1.01833i	0.998627	+	0.0523910i	$0.0166842\pi$
$709$	524.561	+	721.997i	0.739861	+	1.01833i	−0.258766	+	0.965940i	$0.583316\pi$
$710$	−952.002	−	164.514i	−1.34085	−	0.231710i
$711$	−573.283	+	281.156i	−0.806305	+	0.395438i
$712$	502.152	+	370.679i	0.705270	+	0.520616i
$713$	−188.194	−	29.8070i	−0.263947	−	0.0418050i
$714$	244.763	+	408.682i	0.342805	+	0.572384i
$715$	13.3996	+	42.9149i	0.0187408	+	0.0600209i
$716$	1333.18	−	425.746i	1.86199	−	0.594618i
$717$	69.1962	−	16.0546i	0.0965080	−	0.0223914i
$718$	219.275	+	303.415i	0.305398	+	0.422583i
$719$	−837.320	−	272.062i	−1.16456	−	0.378389i	−0.337951	−	0.941164i	$-0.609734\pi$
$719$	−837.320	−	272.062i	−1.16456	−	0.378389i	−0.826611	+	0.562774i	$0.809734\pi$
$720$	676.089	+	247.595i	0.939013	+	0.343881i
$721$	−283.531	−	872.619i	−0.393247	−	1.21029i
$722$	357.630	+	261.216i	0.495333	+	0.361795i
$723$	−0.971903	−	0.0839639i	−0.00134426	−	0.000116133i
$724$	161.710	−	489.273i	0.223357	−	0.675791i
$725$	31.1967	−	40.9228i	0.0430300	−	0.0564453i
$726$	281.034	−	659.442i	0.387100	−	0.908322i
$727$	−881.678	+	139.644i	−1.21276	+	0.192083i	−0.729863	−	0.683593i	$-0.760416\pi$
$727$	−881.678	+	139.644i	−1.21276	+	0.192083i	−0.482899	+	0.875676i	$0.660416\pi$
$728$	−161.158	−	225.386i	−0.221371	−	0.309596i
$729$	−300.857	−	664.023i	−0.412698	−	0.910868i
$730$	358.437	−	1052.64i	0.491009	−	1.44197i
$731$	−343.266	+	1056.46i	−0.469584	+	1.44523i
$732$	−145.659	−	642.519i	−0.198988	−	0.877758i
$733$	172.289	+	338.136i	0.235046	+	0.461304i	0.978158	−	0.207863i	$-0.0666509\pi$
$733$	172.289	+	338.136i	0.235046	+	0.461304i	−0.743112	+	0.669167i	$0.766651\pi$
$734$	−1.38213	−	2.72960i	−0.00188301	−	0.00371879i
$735$	144.078	+	367.594i	0.196025	+	0.500127i
$736$	258.755	−	37.6407i	0.351569	−	0.0511422i
$737$	21.9147	−	138.364i	0.0297351	−	0.187740i
$738$	−418.647	+	404.002i	−0.567272	+	0.547429i
$739$	116.882	+	84.9196i	0.158162	+	0.114912i	0.664051	−	0.747687i	$-0.268836\pi$
$739$	116.882	+	84.9196i	0.158162	+	0.114912i	−0.505889	+	0.862598i	$0.668836\pi$
$740$	−278.729	+	370.572i	−0.376661	+	0.500773i
$741$	96.8176	+	238.882i	0.130658	+	0.322378i
$742$	−0.649149	−	2.01517i	−0.000874864	−	0.00271587i
$743$	75.4763	−	75.4763i	0.101583	−	0.101583i	−0.654489	−	0.756072i	$-0.727116\pi$
$743$	75.4763	−	75.4763i	0.101583	−	0.101583i	0.756072	+	0.654489i	$0.227116\pi$
$744$	−285.121	−	481.568i	−0.383227	−	0.647268i
$745$	373.851	−	713.299i	0.501813	−	0.957449i
$746$	−812.652	+	126.609i	−1.08935	+	0.169717i
$747$	975.284	−	686.072i	1.30560	−	0.918436i
$748$	13.3089	−	81.3679i	0.0177927	−	0.108781i
$749$	−620.616			−0.828593
$750$	−621.329	−	420.060i	−0.828439	−	0.560080i
$751$		−	390.338i		−	0.519758i	−0.965641	−	0.259879i	$-0.916317\pi$
$751$		−	390.338i		−	0.519758i	0.965641	−	0.259879i	$-0.0836827\pi$
$752$	−534.651	+	1023.62i	−0.710972	+	1.36120i
$753$	945.936	+	820.483i	1.25622	+	1.08962i
$754$	−29.5824	+	4.60886i	−0.0392340	+	0.00611255i
$755$	−661.936	−	346.930i	−0.876737	−	0.459510i
$756$	−106.036	−	503.269i	−0.140259	−	0.665700i
$757$	−658.520	−	658.520i	−0.869908	−	0.869908i	0.122554	−	0.992462i	$-0.460891\pi$
$757$	−658.520	−	658.520i	−0.869908	−	0.869908i	−0.992462	+	0.122554i	$0.960891\pi$
$758$	−314.853	−	977.409i	−0.415374	−	1.28946i
$759$	11.3839	+	28.0880i	0.0149985	+	0.0370066i
$760$	−327.705	−	340.461i	−0.431191	−	0.447975i
$761$	169.076	−	232.713i	0.222176	−	0.305799i	−0.683349	−	0.730092i	$-0.739477\pi$
$761$	169.076	−	232.713i	0.222176	−	0.305799i	0.905525	+	0.424293i	$0.139477\pi$
$762$	−17.2988	−	10.8441i	−0.0227018	−	0.0142310i
$763$	−190.369	−	30.1515i	−0.249501	−	0.0395170i
$764$	1128.65	−	811.335i	1.47729	−	1.06196i
$765$	−97.4729	−	743.879i	−0.127416	−	0.972391i
$766$	−610.695	−	1206.08i	−0.797252	−	1.57451i
$767$	−174.250	+	88.7846i	−0.227183	+	0.115756i
$768$	569.883	+	514.837i	0.742036	+	0.670361i
$769$	464.963	+	151.075i	0.604633	+	0.196457i	0.595306	−	0.803499i	$-0.297031\pi$
$769$	464.963	+	151.075i	0.604633	+	0.196457i	0.00932718	+	0.999957i	$0.497031\pi$
$770$	−18.9784	+	55.7347i	−0.0246472	+	0.0723827i
$771$	974.005	−	69.1752i	1.26330	−	0.0897213i
$772$	−915.715	+	906.513i	−1.18616	+	1.17424i
$773$	39.5923	+	249.976i	0.0512190	+	0.323384i	0.999973	+	0.00736789i	$0.00234529\pi$
$773$	39.5923	+	249.976i	0.0512190	+	0.323384i	−0.948754	+	0.316016i	$0.897655\pi$
$774$	722.099	−	957.567i	0.932945	−	1.23717i
$775$	167.332	+	558.431i	0.215912	+	0.720556i
$776$	489.069	−	942.141i	0.630243	−	1.21410i
$777$	330.003	+	28.5094i	0.424714	+	0.0366916i
$778$	−522.714	−	381.794i	−0.671868	−	0.490737i
$779$	363.154	−	117.996i	0.466180	−	0.151471i
$780$	91.5701	+	426.650i	0.117398	+	0.546987i
$781$	36.9105	−	113.599i	0.0472605	−	0.145453i
$782$	−159.591	−	220.828i	−0.204080	−	0.282389i
$783$	−53.7276	−	14.2083i	−0.0686176	−	0.0181459i
$784$	−4.25320	+	421.121i	−0.00542500	+	0.537144i
$785$	−210.452	+	65.7109i	−0.268092	+	0.0837082i
$786$	52.7666	−	31.6024i	0.0671331	−	0.0402066i
$787$	174.800	−	1103.65i	0.222110	−	1.40235i	−0.584563	−	0.811348i	$-0.698734\pi$
$787$	174.800	−	1103.65i	0.222110	−	1.40235i	0.806673	−	0.590998i	$-0.201266\pi$
$788$	498.119	+	256.981i	0.632131	+	0.326118i
$789$	−153.365	+	128.973i	−0.194379	+	0.163464i
$790$	699.100	+	120.810i	0.884937	+	0.152924i
$791$	123.202	−	89.5112i	0.155754	−	0.113162i
$792$	−42.2144	+	78.3705i	−0.0533010	+	0.0989527i
$793$	282.340	−	282.340i	0.356040	−	0.356040i
$794$	283.233	−	552.423i	0.356716	−	0.695747i
$795$	−0.325214	+	3.31840i	−0.000409074	+	0.00417409i
$796$	22.3672	+	0.112948i	0.0280995	+	0.000141895i
$797$	−632.431	−	322.240i	−0.793515	−	0.404316i	0.00973924	−	0.999953i	$-0.496900\pi$
$797$	−632.431	−	322.240i	−0.793515	−	0.404316i	−0.803254	+	0.595637i	$0.796900\pi$
$798$	−82.1328	+	327.413i	−0.102923	+	0.410292i
$799$	1203.34			1.50606
$800$	−446.860	−	663.563i	−0.558575	−	0.829454i
$801$	−328.295	+	620.692i	−0.409857	+	0.774896i
$802$	0.629104	−	249.165i	0.000784419	−	0.310680i
$803$	122.496	+	62.4148i	0.152548	+	0.0777271i
$804$	334.166	−	1318.01i	0.415629	−	1.63931i
$805$	86.3286	+	174.364i	0.107240	+	0.216601i
$806$	154.747	−	301.822i	0.191994	−	0.374469i
$807$	−220.764	+	132.976i	−0.273561	+	0.164778i
$808$	−7.38760	+	975.304i	−0.00914308	+	1.20706i
$809$	511.452	−	371.592i	0.632203	−	0.459322i	−0.224960	−	0.974368i	$-0.572225\pi$
$809$	511.452	−	371.592i	0.632203	−	0.459322i	0.857163	+	0.515046i	$0.172225\pi$
$810$	−162.246	+	793.584i	−0.200304	+	0.979734i
$811$	−273.905	+	376.998i	−0.337737	+	0.464855i	−0.943779	−	0.330578i	$-0.892756\pi$
$811$	−273.905	+	376.998i	−0.337737	+	0.464855i	0.606042	+	0.795433i	$0.292756\pi$
$812$	−34.8447	−	17.9765i	−0.0429122	−	0.0221385i
$813$	111.572	+	47.2161i	0.137235	+	0.0580763i
$814$	−40.4351	−	40.6398i	−0.0496745	−	0.0499260i
$815$	46.2472	−	62.1366i	0.0567451	−	0.0762412i
$816$	200.587	−	774.707i	0.245818	−	0.949396i
$817$	−701.345	+	357.353i	−0.858439	+	0.437396i
$818$	−119.057	−	164.741i	−0.145546	−	0.201395i
$819$	223.753	−	217.020i	0.273203	−	0.264981i
$820$	640.065	−	90.5362i	0.780567	−	0.110410i
$821$	381.072	−	123.818i	0.464156	−	0.150814i	−0.0675972	−	0.997713i	$-0.521533\pi$
$821$	381.072	−	123.818i	0.464156	−	0.150814i	0.531754	+	0.846899i	$0.321533\pi$
$822$	−655.212	+	548.187i	−0.797095	+	0.666894i
$823$	115.173	+	727.176i	0.139943	+	0.883568i	0.953349	+	0.301871i	$0.0976111\pi$
$823$	115.173	+	727.176i	0.139943	+	0.883568i	−0.813406	+	0.581697i	$0.802389\pi$
$824$	−710.139	+	1368.01i	−0.861819	+	1.66021i
$825$	62.3541	−	68.6298i	0.0755808	−	0.0831876i
$826$	−252.857	−	40.7033i	−0.306122	−	0.0492776i
$827$	−92.4492	−	583.702i	−0.111789	−	0.705806i	−0.978384	−	0.206795i	$-0.933697\pi$
$827$	−92.4492	−	583.702i	−0.111789	−	0.705806i	0.866596	−	0.499011i	$-0.166303\pi$
$828$	85.1968	+	281.555i	0.102895	+	0.340042i
$829$	806.527	−	262.057i	0.972892	−	0.316112i	0.220909	−	0.975294i	$-0.429098\pi$
$829$	806.527	−	262.057i	0.972892	−	0.316112i	0.751983	+	0.659183i	$0.229098\pi$
$830$	−1324.78	−	18.5993i	−1.59613	−	0.0224088i
$831$	−791.826	+	1270.26i	−0.952859	+	1.52860i
$832$	−79.7693	+	458.571i	−0.0958766	+	0.551167i
$833$	391.000	−	199.224i	0.469387	−	0.239165i
$834$	270.664	+	1180.10i	0.324538	+	1.41499i
$835$	−5.05507	+	439.027i	−0.00605397	+	0.525780i
$836$	47.4385	−	34.1014i	0.0567446	−	0.0407912i
$837$	487.993	−	397.816i	0.583027	−	0.475288i
$838$	444.623	+	145.709i	0.530576	+	0.173877i
$839$	1.00633	−	1.38510i	0.00119945	−	0.00165089i	−0.808417	−	0.588610i	$-0.799675\pi$
$839$	1.00633	−	1.38510i	0.00119945	−	0.00165089i	0.809616	+	0.586959i	$0.199675\pi$
$840$	−232.721	+	521.932i	−0.277048	+	0.621348i
$841$	676.956	−	491.837i	0.804941	−	0.584824i
$842$	−70.9913	−	220.381i	−0.0843127	−	0.261735i
$843$	233.731	+	388.036i	0.277261	+	0.460304i
$844$	−148.351	+	202.034i	−0.175771	+	0.239376i
$845$	415.199	−	405.746i	0.491360	−	0.480173i
$846$	−1228.27	−	423.402i	−1.45185	−	0.500475i
$847$	506.936	+	258.297i	0.598508	+	0.304955i
$848$	−1.64658	+	3.15247i	−0.00194172	+	0.00371754i
$849$	676.676	+	167.932i	0.797027	+	0.197799i
$850$	−397.299	+	732.829i	−0.467410	+	0.862152i
$851$	−189.447			−0.222617
$852$	457.211	−	1065.37i	0.536633	−	1.25044i
$853$	−356.405	−	181.597i	−0.417825	−	0.212892i	0.232422	−	0.972615i	$-0.425335\pi$
$853$	−356.405	−	181.597i	−0.417825	−	0.212892i	−0.650247	+	0.759722i	$0.725335\pi$
$854$	516.675	−	80.4965i	0.605006	−	0.0942582i
$855$	323.887	−	421.566i	0.378815	−	0.493059i
$856$	731.603	+	742.771i	0.854676	+	0.867723i
$857$	−29.1771	+	29.1771i	−0.0340456	+	0.0340456i	−0.723925	−	0.689879i	$-0.757664\pi$
$857$	−29.1771	+	29.1771i	−0.0340456	+	0.0340456i	0.689879	+	0.723925i	$0.257664\pi$
$858$	−53.8238	+	3.68608i	−0.0627317	+	0.00429613i
$859$	−674.966	+	490.391i	−0.785758	+	0.570886i	−0.906702	−	0.421773i	$-0.861408\pi$
$859$	−674.966	+	490.391i	−0.785758	+	0.570886i	0.120944	+	0.992659i	$0.461408\pi$
$860$	−1274.00	+	390.741i	−1.48140	+	0.454350i
$861$	−297.205	−	353.412i	−0.345186	−	0.410467i
$862$	−176.234	+	537.769i	−0.204448	+	0.623862i
$863$	−155.907	+	984.357i	−0.180657	+	1.14062i	0.716067	+	0.698031i	$0.245940\pi$
$863$	−155.907	+	984.357i	−0.180657	+	1.14062i	−0.896724	+	0.442590i	$0.854060\pi$
$864$	−477.327	+	720.177i	−0.552462	+	0.833538i
$865$	476.194	+	160.809i	0.550513	+	0.185907i
$866$	−173.155	−	341.968i	−0.199948	−	0.394882i
$867$	32.2804	−	7.48956i	0.0372323	−	0.00863848i
$868$	396.789	−	199.657i	0.457131	−	0.230019i
$869$	−27.1051	+	83.4209i	−0.0311911	+	0.0959965i
$870$	39.0759	+	47.8128i	0.0449149	+	0.0549573i
$871$	783.737	−	254.652i	0.899813	−	0.292367i
$872$	188.327	+	263.383i	0.215972	+	0.302044i
$873$	1129.99	+	386.335i	1.29437	+	0.442537i
$874$	30.6834	−	190.611i	0.0351069	−	0.218091i
$875$	366.317	−	469.217i	0.418648	−	0.536249i
$876$	1128.82	+	711.595i	1.28860	+	0.812323i
$877$	−31.1275	−	196.531i	−0.0354932	−	0.224095i	0.963566	−	0.267472i	$-0.0861883\pi$
$877$	−31.1275	−	196.531i	−0.0354932	−	0.224095i	−0.999059	+	0.0433771i	$0.986188\pi$
$878$	−358.056	−	261.527i	−0.407809	−	0.297866i
$879$	63.9577	+	900.541i	0.0727619	+	1.02451i
$880$	89.0771	−	42.9881i	0.101224	−	0.0488501i
$881$	143.559	+	46.6453i	0.162950	+	0.0529458i	0.389356	−	0.921087i	$-0.372698\pi$
$881$	143.559	+	46.6453i	0.162950	+	0.0529458i	−0.226406	+	0.974033i	$0.572698\pi$
$882$	−469.197	+	65.7756i	−0.531970	+	0.0745755i
$883$	−434.179	+	221.225i	−0.491709	+	0.250538i	−0.682220	−	0.731147i	$-0.738985\pi$
$883$	−434.179	+	221.225i	−0.491709	+	0.250538i	0.190511	+	0.981685i	$0.438985\pi$
$884$	462.018	−	147.544i	0.522645	−	0.166905i
$885$	339.814	+	217.297i	0.383971	+	0.245534i
$886$	999.468	−	994.433i	1.12807	−	1.12239i
$887$	−230.382	−	36.4890i	−0.259732	−	0.0411375i	0.0252102	−	0.999682i	$-0.491974\pi$
$887$	−230.382	−	36.4890i	−0.259732	−	0.0411375i	−0.284942	+	0.958545i	$0.591974\pi$
$888$	−354.897	−	428.564i	−0.399659	−	0.482617i
$889$	9.52492	−	13.1099i	0.0107142	−	0.0147468i
$890$	700.053	−	344.403i	0.786576	−	0.386969i
$891$	−94.2528	−	33.8409i	−0.105783	−	0.0379808i
$892$	126.837	+	827.854i	0.142194	+	0.928087i
$893$	602.942	+	602.942i	0.675187	+	0.675187i
$894$	728.440	+	635.061i	0.814809	+	0.710359i
$895$	293.540	−	1724.59i	0.327978	−	1.92691i
$896$	−438.576	+	423.341i	−0.489482	+	0.472479i
$897$	−116.817	+	134.678i	−0.130230	+	0.150143i
$898$	1410.72	+	3.56185i	1.57096	+	0.00396642i
$899$		−	47.9968i		−	0.0533891i
$900$	663.379	−	608.218i	0.737087	−	0.675797i
$901$	3.70595			0.00411316
$902$	−0.201790	+	79.9216i	−0.000223714	+	0.0886049i
$903$	719.087	+	623.719i	0.796331	+	0.690719i
$904$	−252.364	−	41.9324i	−0.279163	−	0.0463853i
$905$	−450.194	−	460.682i	−0.497452	−	0.509041i
$906$	589.332	−	675.986i	0.650476	−	0.746121i
$907$	−676.033	+	676.033i	−0.745351	+	0.745351i	−0.973602	−	0.228251i	$-0.926699\pi$
$907$	−676.033	+	676.033i	−0.745351	+	0.745351i	0.228251	+	0.973602i	$0.426699\pi$
$908$	115.227	+	752.073i	0.126902	+	0.828275i
$909$	−1086.23	+	155.074i	−1.19498	+	0.170598i
$910$	−342.807	+	49.3726i	−0.376711	+	0.0542556i
$911$	−265.310	−	192.759i	−0.291229	−	0.211590i	0.432571	−	0.901600i	$-0.357606\pi$
$911$	−265.310	−	192.759i	−0.291229	−	0.211590i	−0.723800	+	0.690009i	$0.757606\pi$
$912$	488.678	−	287.667i	0.535831	−	0.315424i
$913$	25.6248	−	161.788i	0.0280666	−	0.177205i
$914$	−765.501	−	769.376i	−0.837528	−	0.841768i
$915$	−796.945	−	207.548i	−0.870979	−	0.226829i
$916$	−1326.06	+	423.471i	−1.44766	+	0.462305i
$917$	22.1627	+	43.4968i	0.0241687	+	0.0474338i
$918$	895.423	+	93.4405i	0.975407	+	0.101787i
$919$	−141.684	+	436.060i	−0.154172	+	0.474494i	−0.998076	−	0.0620008i	$-0.980252\pi$
$919$	−141.684	+	436.060i	−0.154172	+	0.474494i	0.843904	+	0.536495i	$0.180252\pi$
$920$	106.916	−	308.866i	0.116213	−	0.335724i
$921$	−232.923	+	16.5425i	−0.252902	+	0.0179615i
$922$	−711.583	+	974.228i	−0.771782	+	1.05665i
$923$	693.980	−	109.916i	0.751875	−	0.119085i
$924$	−59.7682	−	37.6772i	−0.0646842	−	0.0407762i
$925$	251.181	+	522.367i	0.271547	+	0.564721i
$926$	929.850	+	149.681i	1.00416	+	0.161643i
$927$	−1640.77	−	560.967i	−1.76998	−	0.605143i
$928$	19.5613	+	62.8943i	0.0210790	+	0.0677741i
$929$	122.007	+	375.500i	0.131332	+	0.404198i	0.995001	−	0.0998603i	$-0.0318396\pi$
$929$	122.007	+	375.500i	0.131332	+	0.404198i	−0.863670	+	0.504059i	$0.831840\pi$
$930$	−698.424	+	39.7579i	−0.750994	+	0.0427504i
$931$	295.736	+	96.0905i	0.317654	+	0.103212i
$932$	−692.171	+	348.287i	−0.742672	+	0.373699i
$933$	−250.948	−	1081.60i	−0.268969	−	1.15927i
$934$	−575.544	+	291.426i	−0.616214	+	0.312020i
$935$	−82.6754	−	61.5339i	−0.0884229	−	0.0658117i
$936$	−523.502	−	11.9638i	−0.559298	−	0.0127819i
$937$	−519.589	−	82.2949i	−0.554524	−	0.0878281i	−0.127118	−	0.991888i	$-0.540573\pi$
$937$	−519.589	−	82.2949i	−0.554524	−	0.0878281i	−0.427407	+	0.904060i	$0.640573\pi$
$938$	1025.54	+	336.082i	1.09332	+	0.358296i
$939$	−412.787	+	347.136i	−0.439603	+	0.369687i
$940$	829.038	+	1181.75i	0.881955	+	1.25718i
$941$	295.877	+	407.240i	0.314428	+	0.432773i	0.936756	−	0.349984i	$-0.113813\pi$
$941$	295.877	+	407.240i	0.314428	+	0.432773i	−0.622328	+	0.782757i	$0.713813\pi$
$942$	−18.0763	−	263.948i	−0.0191893	−	0.280200i
$943$	186.752	+	186.752i	0.198041	+	0.198041i
$944$	249.361	+	350.608i	0.264154	+	0.371407i
$945$	−619.598	−	171.509i	−0.655660	−	0.181491i
$946$	−25.3620	−	162.788i	−0.0268097	−	0.172081i
$947$	717.974	−	1409.10i	0.758156	−	1.48796i	−0.111210	−	0.993797i	$-0.535473\pi$
$947$	717.974	−	1409.10i	0.758156	−	1.48796i	0.869366	−	0.494168i	$-0.164527\pi$
$948$	−335.752	+	782.352i	−0.354169	+	0.825266i
$949$			808.725i			0.852187i
$950$	−566.259	+	168.120i	−0.596062	+	0.176969i
$951$	432.809	−	1743.99i	0.455110	−	1.83385i
$952$	602.571	+	200.846i	0.632953	+	0.210972i
$953$	156.431	−	307.014i	0.164146	−	0.322155i	−0.794253	−	0.607588i	$-0.792137\pi$
$953$	156.431	−	307.014i	0.164146	−	0.322155i	0.958399	+	0.285433i	$0.0921373\pi$
$954$	−3.78272	−	1.30396i	−0.00396512	−	0.00136684i
$955$	−252.029	−	1719.13i	−0.263905	−	1.80013i
$956$	56.0568	−	76.3418i	0.0586368	−	0.0798555i
$957$	−6.53964	+	3.93911i	−0.00683348	+	0.00411610i
$958$	−990.002	+	318.910i	−1.03341	+	0.332891i
$959$	−398.548	−	548.554i	−0.415587	−	0.572007i
$960$	899.001	−	336.744i	0.936460	−	0.350775i
$961$	−337.560	−	245.252i	−0.351260	−	0.255205i
$962$	105.021	−	320.465i	0.109169	−	0.333124i
$963$	−703.821	+	938.247i	−0.730863	+	0.974296i
$964$	−1.05613	+	0.759207i	−0.00109557	+	0.000787559i
$965$	480.051	+	1537.46i	0.497462	+	1.59322i
$966$	−227.568	+	52.1943i	−0.235578	+	0.0540314i
$967$	−529.471	−	1039.15i	−0.547540	−	1.07461i	−0.984542	−	0.175147i	$-0.943960\pi$
$967$	−529.471	−	1039.15i	−0.547540	−	1.07461i	0.437003	−	0.899460i	$-0.356040\pi$
$968$	−288.456	−	911.204i	−0.297992	−	0.941326i
$969$	−501.432	−	312.571i	−0.517474	−	0.322571i
$970$	−764.783	−	1084.32i	−0.788437	−	1.11786i
$971$	410.356	+	1262.95i	0.422612	+	1.30066i	0.905263	+	0.424852i	$0.139674\pi$
$971$	410.356	+	1262.95i	0.422612	+	1.30066i	−0.482651	+	0.875813i	$0.660326\pi$
$972$	−881.094	−	410.436i	−0.906475	−	0.422259i
$973$	−949.138	+	150.329i	−0.975476	+	0.154500i
$974$	38.9984	−	242.266i	0.0400395	−	0.248733i
$975$	526.233	+	143.536i	0.539726	+	0.147217i
$976$	−705.414	−	523.479i	−0.722760	−	0.536351i
$977$	−130.067	+	20.6005i	−0.133128	+	0.0210855i	−0.222643	−	0.974900i	$-0.571468\pi$
$977$	−130.067	+	20.6005i	−0.133128	+	0.0210855i	0.0895146	+	0.995986i	$0.471468\pi$
$978$	59.6447	+	71.2894i	0.0609864	+	0.0728930i
$979$	29.8070	+	91.7367i	0.0304464	+	0.0937045i
$980$	465.028	+	246.729i	0.474519	+	0.251765i
$981$	−261.475	+	253.606i	−0.266539	+	0.258518i
$982$	1004.14	−	725.684i	1.02255	−	0.738986i
$983$	581.843	+	1141.93i	0.591905	+	1.16168i	0.971614	+	0.236573i	$0.0760242\pi$
$983$	581.843	+	1141.93i	0.591905	+	1.16168i	−0.379709	+	0.925106i	$0.623976\pi$
$984$	−72.6190	+	772.317i	−0.0737998	+	0.784875i
$985$	571.523	−	405.265i	0.580226	−	0.411436i
$986$	48.6527	−	48.4077i	0.0493435	−	0.0490950i
$987$	401.877	−	949.637i	0.407170	−	0.962145i
$988$	305.425	+	157.570i	0.309135	+	0.159484i
$989$	−440.458	−	320.012i	−0.445357	−	0.323571i
$990$	62.7369	+	91.8984i	0.0633706	+	0.0928267i
$991$	−807.479	−	1111.40i	−0.814812	−	1.12149i	−0.990563	−	0.137058i	$-0.956235\pi$
$991$	−807.479	−	1111.40i	−0.814812	−	1.12149i	0.175751	−	0.984435i	$-0.443765\pi$
$992$	−706.703	−	239.526i	−0.712402	−	0.241458i
$993$	−303.902	−	504.533i	−0.306045	−	0.508090i
$994$	818.816	+	419.815i	0.823758	+	0.422349i
$995$	12.9793	−	24.7642i	0.0130445	−	0.0248886i
$996$	390.738	−	1541.14i	0.392307	−	1.54732i
$997$	−699.137	+	1372.13i	−0.701241	+	1.37626i	0.215390	+	0.976528i	$0.430898\pi$
$997$	−699.137	+	1372.13i	−0.701241	+	1.37626i	−0.916631	+	0.399734i	$0.869102\pi$
$998$	−1414.58	−	3.57159i	−1.41741	−	0.00357874i
$999$	417.346	−	466.567i	0.417764	−	0.467034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.u.a.287.116	yes	928
3.2	odd	2	inner	300.3.u.a.287.1	yes	928
4.3	odd	2	inner	300.3.u.a.287.106	yes	928
12.11	even	2	inner	300.3.u.a.287.11	yes	928
25.23	odd	20	inner	300.3.u.a.23.11	yes	928
75.23	even	20	inner	300.3.u.a.23.106	yes	928
100.23	even	20	inner	300.3.u.a.23.1	✓	928
300.23	odd	20	inner	300.3.u.a.23.116	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.u.a.23.1	✓	928	100.23	even	20	inner
300.3.u.a.23.11	yes	928	25.23	odd	20	inner
300.3.u.a.23.106	yes	928	75.23	even	20	inner
300.3.u.a.23.116	yes	928	300.23	odd	20	inner
300.3.u.a.287.1	yes	928	3.2	odd	2	inner
300.3.u.a.287.11	yes	928	12.11	even	2	inner
300.3.u.a.287.106	yes	928	4.3	odd	2	inner
300.3.u.a.287.116	yes	928	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99999 + 0.00504968i) q^{2} +(2.26627 + 1.96571i) q^{3} +(3.99995 + 0.0201986i) q^{4} +(2.32110 - 4.42860i) q^{5} +(4.52260 + 3.94285i) q^{6} +(-3.36739 + 3.36739i) q^{7} +(7.99977 + 0.0605956i) q^{8} +(1.27197 + 8.90966i) q^{9} +O(q^{10})\)	\(q+(1.99999 + 0.00504968i) q^{2} +(2.26627 + 1.96571i) q^{3} +(3.99995 + 0.0201986i) q^{4} +(2.32110 - 4.42860i) q^{5} +(4.52260 + 3.94285i) q^{6} +(-3.36739 + 3.36739i) q^{7} +(7.99977 + 0.0605956i) q^{8} +(1.27197 + 8.90966i) q^{9} +(4.66454 - 8.84546i) q^{10} +(1.00022 + 0.726705i) q^{11} +(9.02526 + 7.90851i) q^{12} +(-1.13771 + 7.18323i) q^{13} +(-6.75176 + 6.71775i) q^{14} +(13.9656 - 5.47381i) q^{15} +(15.9992 + 0.161587i) q^{16} +(-7.56891 - 14.8548i) q^{17} +(2.49894 + 17.8257i) q^{18} +(3.65066 - 11.2356i) q^{19} +(9.37371 - 17.6673i) q^{20} +(-14.2507 + 1.01211i) q^{21} +(1.99677 + 1.45846i) q^{22} +(8.07059 - 1.27826i) q^{23} +(18.0105 + 15.8626i) q^{24} +(-14.2250 - 20.5584i) q^{25} +(-2.31169 + 14.3607i) q^{26} +(-14.6312 + 22.6920i) q^{27} +(-13.5374 + 13.4014i) q^{28} +(0.636054 + 1.95757i) q^{29} +(27.9587 - 10.8771i) q^{30} +(-22.1772 - 7.20581i) q^{31} +(31.9975 + 0.403964i) q^{32} +(0.838287 + 3.61306i) q^{33} +(-15.0628 - 29.7478i) q^{34} +(7.09679 + 22.7288i) q^{35} +(4.90785 + 35.6639i) q^{36} +(-22.8993 - 3.62690i) q^{37} +(7.35803 - 22.4526i) q^{38} +(-16.6985 + 14.0427i) q^{39} +(18.8366 - 35.2872i) q^{40} +(18.9983 + 26.1489i) q^{41} +(-28.5065 + 1.95224i) q^{42} +(-47.1136 - 47.1136i) q^{43} +(3.98617 + 2.92699i) q^{44} +(42.4097 + 15.0471i) q^{45} +(16.1476 - 2.51575i) q^{46} +(-32.7679 + 64.3106i) q^{47} +(35.9409 + 31.8160i) q^{48} +26.3214i q^{49} +(-28.3462 - 41.1885i) q^{50} +(12.0471 - 48.5433i) q^{51} +(-4.69588 + 28.7096i) q^{52} +(-0.100916 + 0.198059i) q^{53} +(-29.3769 + 45.3100i) q^{54} +(5.53990 - 2.74284i) q^{55} +(-27.1424 + 26.7343i) q^{56} +(30.3593 - 18.2867i) q^{57} +(1.26222 + 3.91835i) q^{58} +(15.8056 + 21.7545i) q^{59} +(55.9722 - 21.6129i) q^{60} +(-44.4165 - 32.2705i) q^{61} +(-44.3179 - 14.5236i) q^{62} +(-34.2855 - 25.7191i) q^{63} +(63.9927 + 0.969502i) q^{64} +(29.1709 + 21.7114i) q^{65} +(1.65832 + 7.23033i) q^{66} +(-51.4412 - 100.959i) q^{67} +(-29.9752 - 59.5714i) q^{68} +(20.8028 + 12.9676i) q^{69} +(14.0788 + 45.4934i) q^{70} +(-29.8545 - 91.8827i) q^{71} +(9.63558 + 71.3523i) q^{72} +(109.830 - 17.3954i) q^{73} +(-45.7802 - 7.36941i) q^{74} +(8.17409 - 74.5532i) q^{75} +(14.8294 - 44.8680i) q^{76} +(-5.81524 + 0.921043i) q^{77} +(-33.4678 + 28.0010i) q^{78} +(21.9236 + 67.4738i) q^{79} +(37.8512 - 70.4790i) q^{80} +(-77.7642 + 22.6656i) q^{81} +(37.8644 + 52.3936i) q^{82} +(-60.1499 - 118.051i) q^{83} +(-57.0226 + 3.76053i) q^{84} +(-83.3542 - 0.959763i) q^{85} +(-93.9891 - 94.4649i) q^{86} +(-2.40655 + 5.68669i) q^{87} +(7.95753 + 5.87408i) q^{88} +(63.1182 + 45.8581i) q^{89} +(84.7432 + 30.3083i) q^{90} +(-20.3576 - 28.0198i) q^{91} +(32.3078 - 4.94994i) q^{92} +(-36.0950 - 59.9243i) q^{93} +(-65.8603 + 128.455i) q^{94} +(-41.2844 - 42.2462i) q^{95} +(71.7208 + 63.8132i) q^{96} +(60.2398 - 118.227i) q^{97} +(-0.132915 + 52.6426i) q^{98} +(-5.20244 + 9.83600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 20 q^{4} - 6 q^{6} - 20 q^{9}+O(q^{10}) \) 928 * q - 20 * q^4 - 6 * q^6 - 20 * q^9	\( 928 q - 20 q^{4} - 6 q^{6} - 20 q^{9} - 8 q^{10} + 10 q^{12} - 32 q^{13} - 12 q^{16} + 14 q^{18} - 12 q^{21} + 56 q^{22} - 32 q^{25} + 64 q^{28} - 78 q^{30} + 20 q^{33} - 20 q^{34} - 70 q^{36} - 124 q^{40} + 454 q^{42} + 84 q^{45} - 12 q^{46} - 76 q^{48} - 324 q^{52} - 660 q^{54} + 52 q^{57} - 200 q^{58} - 826 q^{60} - 24 q^{61} - 20 q^{64} + 138 q^{66} - 20 q^{69} + 352 q^{70} + 590 q^{72} - 144 q^{73} + 96 q^{76} + 308 q^{78} - 12 q^{81} + 20 q^{82} - 10 q^{84} + 864 q^{85} - 760 q^{88} - 538 q^{90} - 388 q^{93} - 1420 q^{94} - 6 q^{96} + 288 q^{97}+O(q^{100}) \) 928 * q - 20 * q^4 - 6 * q^6 - 20 * q^9 - 8 * q^10 + 10 * q^12 - 32 * q^13 - 12 * q^16 + 14 * q^18 - 12 * q^21 + 56 * q^22 - 32 * q^25 + 64 * q^28 - 78 * q^30 + 20 * q^33 - 20 * q^34 - 70 * q^36 - 124 * q^40 + 454 * q^42 + 84 * q^45 - 12 * q^46 - 76 * q^48 - 324 * q^52 - 660 * q^54 + 52 * q^57 - 200 * q^58 - 826 * q^60 - 24 * q^61 - 20 * q^64 + 138 * q^66 - 20 * q^69 + 352 * q^70 + 590 * q^72 - 144 * q^73 + 96 * q^76 + 308 * q^78 - 12 * q^81 + 20 * q^82 - 10 * q^84 + 864 * q^85 - 760 * q^88 - 538 * q^90 - 388 * q^93 - 1420 * q^94 - 6 * q^96 + 288 * q^97

Introduction

L-functions

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