LMFDB - Embedded newform 63.4.f.c.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, 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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + \cdots + 387420489 $ x^18 - 3x^17 + 6x^16 - 23x^15 - 6x^14 + 255x^13 - 56x^12 - 81x^11 + 5832x^10 - 32373x^9 + 52488x^8 - 6561x^7 - 40824x^6 + 1673055x^5 - 354294x^4 - 12223143x^3 + 28697814x^2 - 129140163*x + 387420489
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.7
Root			$-2.61694 - 1.46684i$ of defining polynomial
Character	$\chi$	$=$	63.43
Dual form			63.4.f.c.22.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66614 - 2.88585i) q^{2} +(-2.65509 + 4.46660i) q^{3} +(-1.55207 - 2.68826i) q^{4} +(8.37356 + 14.5034i) q^{5} +(8.46616 + 15.1042i) q^{6} +(-3.50000 + 6.06218i) q^{7} +16.3144 q^{8} +(-12.9010 - 23.7184i) q^{9} +O(q^{10})$	\(q+(1.66614 - 2.88585i) q^{2} +(-2.65509 + 4.46660i) q^{3} +(-1.55207 - 2.68826i) q^{4} +(8.37356 + 14.5034i) q^{5} +(8.46616 + 15.1042i) q^{6} +(-3.50000 + 6.06218i) q^{7} +16.3144 q^{8} +(-12.9010 - 23.7184i) q^{9} +55.8062 q^{10} +(4.84647 - 8.39434i) q^{11} +(16.1283 + 0.205095i) q^{12} +(7.83475 + 13.5702i) q^{13} +(11.6630 + 20.2009i) q^{14} +(-87.0135 - 1.10651i) q^{15} +(39.5987 - 68.5870i) q^{16} -104.212 q^{17} +(-89.9427 - 2.28788i) q^{18} +162.015 q^{19} +(25.9927 - 45.0206i) q^{20} +(-17.7845 - 31.7287i) q^{21} +(-16.1498 - 27.9723i) q^{22} +(-36.0714 - 62.4776i) q^{23} +(-43.3162 + 72.8700i) q^{24} +(-77.7329 + 134.637i) q^{25} +52.2153 q^{26} +(140.194 + 5.35064i) q^{27} +21.7290 q^{28} +(-32.8753 + 56.9417i) q^{29} +(-148.170 + 249.264i) q^{30} +(-98.8118 - 171.147i) q^{31} +(-66.6966 - 115.522i) q^{32} +(24.6263 + 43.9349i) q^{33} +(-173.631 + 300.739i) q^{34} -117.230 q^{35} +(-43.7380 + 71.4940i) q^{36} +123.920 q^{37} +(269.940 - 467.550i) q^{38} +(-81.4145 - 1.03531i) q^{39} +(136.610 + 236.615i) q^{40} +(-202.236 - 350.283i) q^{41} +(-121.196 - 1.54118i) q^{42} +(115.569 - 200.171i) q^{43} -30.0882 q^{44} +(235.971 - 385.717i) q^{45} -240.401 q^{46} +(101.835 - 176.383i) q^{47} +(201.213 + 358.976i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(259.028 + 448.650i) q^{50} +(276.691 - 465.472i) q^{51} +(24.3202 - 42.1237i) q^{52} -137.989 q^{53} +(249.025 - 395.663i) q^{54} +162.329 q^{55} +(-57.1005 + 98.9009i) q^{56} +(-430.164 + 723.657i) q^{57} +(109.550 + 189.746i) q^{58} +(390.060 + 675.603i) q^{59} +(132.076 + 235.633i) q^{60} +(-37.6075 + 65.1381i) q^{61} -658.538 q^{62} +(188.939 + 4.80606i) q^{63} +189.075 q^{64} +(-131.209 + 227.261i) q^{65} +(167.820 + 2.13409i) q^{66} +(67.9686 + 117.725i) q^{67} +(161.744 + 280.148i) q^{68} +(374.835 + 4.76659i) q^{69} +(-195.322 + 338.307i) q^{70} +226.751 q^{71} +(-210.473 - 386.952i) q^{72} +148.354 q^{73} +(206.469 - 357.615i) q^{74} +(-394.983 - 704.675i) q^{75} +(-251.459 - 435.539i) q^{76} +(33.9253 + 58.7603i) q^{77} +(-138.636 + 233.225i) q^{78} +(459.815 - 796.423i) q^{79} +1326.33 q^{80} +(-396.126 + 611.984i) q^{81} -1347.82 q^{82} +(-482.940 + 836.477i) q^{83} +(-57.6923 + 97.0546i) q^{84} +(-872.622 - 1511.42i) q^{85} +(-385.109 - 667.028i) q^{86} +(-167.049 - 298.026i) q^{87} +(79.0674 - 136.949i) q^{88} -1251.98 q^{89} +(-719.958 - 1323.63i) q^{90} -109.686 q^{91} +(-111.971 + 193.939i) q^{92} +(1026.80 + 13.0573i) q^{93} +(-339.343 - 587.760i) q^{94} +(1356.64 + 2349.77i) q^{95} +(693.076 + 8.81350i) q^{96} +(-415.364 + 719.431i) q^{97} -163.282 q^{98} +(-261.625 - 6.65498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) $ 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.66614	−	2.88585i	0.589071	−	1.02030i	−0.405284	−	0.914191i	$-0.632827\pi$
$2$	1.66614	−	2.88585i	0.589071	−	1.02030i	0.994354	−	0.106109i	$-0.0338394\pi$
$3$	−2.65509	+	4.46660i	−0.510971	+	0.859598i
$3$	−2.65509	+	4.46660i	−0.510971	+	0.859598i
$4$	−1.55207	−	2.68826i	−0.194009	−	0.336033i
$5$	8.37356	+	14.5034i	0.748954	+	1.29723i	0.948325	+	0.317302i	$0.102777\pi$
$5$	8.37356	+	14.5034i	0.748954	+	1.29723i	−0.199371	+	0.979924i	$0.563890\pi$
$6$	8.46616	+	15.1042i	0.576050	+	1.02771i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$	16.3144			0.721002
$9$	−12.9010	−	23.7184i	−0.477816	−	0.878460i
$10$	55.8062			1.76475
$11$	4.84647	−	8.39434i	0.132842	−	0.230090i	−0.791929	−	0.610613i	$-0.790923\pi$
$11$	4.84647	−	8.39434i	0.132842	−	0.230090i	0.924771	+	0.380524i	$0.124256\pi$
$12$	16.1283	+	0.205095i	0.387986	+	0.00493382i
$13$	7.83475	+	13.5702i	0.167151	+	0.289515i	0.937417	−	0.348208i	$-0.113210\pi$
$13$	7.83475	+	13.5702i	0.167151	+	0.289515i	−0.770266	+	0.637723i	$0.779876\pi$
$14$	11.6630	+	20.2009i	0.222648	+	0.385637i
$15$	−87.0135	−	1.10651i	−1.49779	−	0.0190466i
$16$	39.5987	−	68.5870i	0.618730	−	1.07167i
$17$	−104.212			−1.48677			−0.743383	−	0.668866i	$-0.766780\pi$
$17$	−104.212			−1.48677			−0.743383	+	0.668866i	$0.766780\pi$
$18$	−89.9427	−	2.28788i	−1.17776	−	0.0299588i
$19$	162.015			1.95625			0.978126	−	0.208011i	$-0.0666991\pi$
$19$	162.015			1.95625			0.978126	+	0.208011i	$0.0666991\pi$
$20$	25.9927	−	45.0206i	0.290607	−	0.503346i
$21$	−17.7845	−	31.7287i	−0.184805	−	0.329703i
$22$	−16.1498	−	27.9723i	−0.156507	−	0.271078i
$23$	−36.0714	−	62.4776i	−0.327018	−	0.566412i	0.654901	−	0.755715i	$-0.272710\pi$
$23$	−36.0714	−	62.4776i	−0.327018	−	0.566412i	−0.981919	+	0.189303i	$0.939377\pi$
$24$	−43.3162	+	72.8700i	−0.368412	+	0.619772i
$25$	−77.7329	+	134.637i	−0.621863	+	1.07710i
$26$	52.2153			0.393856
$27$	140.194	+	5.35064i	0.999272	+	0.0381382i
$28$	21.7290			0.146657
$29$	−32.8753	+	56.9417i	−0.210510	+	0.364614i	−0.951874	−	0.306489i	$-0.900846\pi$
$29$	−32.8753	+	56.9417i	−0.210510	+	0.364614i	0.741364	+	0.671103i	$0.234179\pi$
$30$	−148.170	+	249.264i	−0.901735	+	1.51697i
$31$	−98.8118	−	171.147i	−0.572488	−	0.991578i	−0.996310	−	0.0858321i	$-0.972645\pi$
$31$	−98.8118	−	171.147i	−0.572488	−	0.991578i	0.423822	−	0.905745i	$-0.360688\pi$
$32$	−66.6966	−	115.522i	−0.368450	−	0.638175i
$33$	24.6263	+	43.9349i	0.129906	+	0.231760i
$34$	−173.631	+	300.739i	−0.875810	+	1.51695i
$35$	−117.230			−0.566156
$36$	−43.7380	+	71.4940i	−0.202491	+	0.330991i
$37$	123.920			0.550605			0.275303	−	0.961358i	$-0.411222\pi$
$37$	123.920			0.550605			0.275303	+	0.961358i	$0.411222\pi$
$38$	269.940	−	467.550i	1.15237	−	1.99597i
$39$	−81.4145	−	1.03531i	−0.334276	−	0.00425082i
$40$	136.610	+	236.615i	0.539997	+	0.935302i
$41$	−202.236	−	350.283i	−0.770341	−	1.33427i	−0.937376	−	0.348319i	$-0.886752\pi$
$41$	−202.236	−	350.283i	−0.770341	−	1.33427i	0.167035	−	0.985951i	$-0.446581\pi$
$42$	−121.196	−	1.54118i	−0.445260	−	0.00566214i
$43$	115.569	−	200.171i	0.409863	−	0.709903i	−0.585011	−	0.811025i	$-0.698910\pi$
$43$	115.569	−	200.171i	0.409863	−	0.709903i	0.994874	+	0.101122i	$0.0322433\pi$
$44$	−30.0882			−0.103090
$45$	235.971	−	385.717i	0.781698	−	1.27776i
$46$	−240.401			−0.770547
$47$	101.835	−	176.383i	0.316046	−	0.547407i	−0.663614	−	0.748076i	$-0.730978\pi$
$47$	101.835	−	176.383i	0.316046	−	0.547407i	0.979659	+	0.200668i	$0.0643114\pi$
$48$	201.213	+	358.976i	0.605053	+	1.07945i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	259.028	+	448.650i	0.732642	+	1.26897i
$51$	276.691	−	465.472i	0.759695	−	1.27802i
$52$	24.3202	−	42.1237i	0.0648577	−	0.112337i
$53$	−137.989			−0.357627			−0.178813	−	0.983883i	$-0.557226\pi$
$53$	−137.989			−0.357627			−0.178813	+	0.983883i	$0.557226\pi$
$54$	249.025	−	395.663i	0.627555	−	0.997092i
$55$	162.329			0.397971
$56$	−57.1005	+	98.9009i	−0.136257	+	0.236003i
$57$	−430.164	+	723.657i	−0.999589	+	1.68159i
$58$	109.550	+	189.746i	0.248010	+	0.429567i
$59$	390.060	+	675.603i	0.860703	+	1.49078i	0.871252	+	0.490836i	$0.163309\pi$
$59$	390.060	+	675.603i	0.860703	+	1.49078i	−0.0105494	+	0.999944i	$0.503358\pi$
$60$	132.076	+	235.633i	0.284183	+	0.507001i
$61$	−37.6075	+	65.1381i	−0.0789369	+	0.136723i	−0.902792	−	0.430078i	$-0.858486\pi$
$61$	−37.6075	+	65.1381i	−0.0789369	+	0.136723i	0.823855	+	0.566801i	$0.191819\pi$
$62$	−658.538			−1.34894
$63$	188.939	+	4.80606i	0.377842	+	0.00961121i
$64$	189.075			0.369287
$65$	−131.209	+	227.261i	−0.250377	+	0.433666i
$66$	167.820	+	2.13409i	0.312989	+	0.00398012i
$67$	67.9686	+	117.725i	0.123936	+	0.214663i	0.921316	−	0.388814i	$-0.127115\pi$
$67$	67.9686	+	117.725i	0.123936	+	0.214663i	−0.797381	+	0.603476i	$0.793782\pi$
$68$	161.744	+	280.148i	0.288446	+	0.499602i
$69$	374.835	+	4.76659i	0.653983	+	0.00831637i
$70$	−195.322	+	338.307i	−0.333506	+	0.577649i
$71$	226.751			0.379019			0.189510	−	0.981879i	$-0.439310\pi$
$71$	226.751			0.379019			0.189510	+	0.981879i	$0.439310\pi$
$72$	−210.473	−	386.952i	−0.344507	−	0.633371i
$73$	148.354			0.237856			0.118928	−	0.992903i	$-0.462054\pi$
$73$	148.354			0.237856			0.118928	+	0.992903i	$0.462054\pi$
$74$	206.469	−	357.615i	0.324346	−	0.561783i
$75$	−394.983	−	704.675i	−0.608117	−	1.08492i
$76$	−251.459	−	435.539i	−0.379530	−	0.657365i
$77$	33.9253	+	58.7603i	0.0502097	+	0.0869658i
$78$	−138.636	+	233.225i	−0.201249	+	0.338558i
$79$	459.815	−	796.423i	0.654851	−	1.13423i	−0.327081	−	0.944996i	$-0.606065\pi$
$79$	459.815	−	796.423i	0.654851	−	1.13423i	0.981931	−	0.189238i	$-0.0606018\pi$
$80$	1326.33			1.85360
$81$	−396.126	+	611.984i	−0.543383	+	0.839485i
$82$	−1347.82			−1.81514
$83$	−482.940	+	836.477i	−0.638670	+	1.10621i	0.347055	+	0.937845i	$0.387182\pi$
$83$	−482.940	+	836.477i	−0.638670	+	1.10621i	−0.985725	+	0.168364i	$0.946152\pi$
$84$	−57.6923	+	97.0546i	−0.0749374	+	0.126066i
$85$	−872.622	−	1511.42i	−1.11352	−	1.92867i
$86$	−385.109	−	667.028i	−0.482876	−	0.836366i
$87$	−167.049	−	298.026i	−0.205857	−	0.367261i
$88$	79.0674	−	136.949i	0.0957796	−	0.165895i
$89$	−1251.98			−1.49111			−0.745557	−	0.666442i	$-0.767816\pi$
$89$	−1251.98			−1.49111			−0.745557	+	0.666442i	$0.767816\pi$
$90$	−719.958	−	1323.63i	−0.843225	−	1.55026i
$91$	−109.686			−0.126355
$92$	−111.971	+	193.939i	−0.126889	+	0.219778i
$93$	1026.80	+	13.0573i	1.14488	+	0.0145589i
$94$	−339.343	−	587.760i	−0.372347	−	0.644923i
$95$	1356.64	+	2349.77i	1.46514	+	2.53770i
$96$	693.076	+	8.81350i	0.736841	+	0.00937004i
$97$	−415.364	+	719.431i	−0.434782	+	0.753064i	−0.997278	−	0.0737361i	$-0.976508\pi$
$97$	−415.364	+	719.431i	−0.434782	+	0.753064i	0.562496	+	0.826800i	$0.309841\pi$
$98$	−163.282			−0.168306
$99$	−261.625	−	6.65498i	−0.265599	−	0.00675607i
$100$	482.587			0.482587
$101$	103.463	−	179.203i	0.101930	−	0.176548i	−0.810550	−	0.585670i	$-0.800831\pi$
$101$	103.463	−	179.203i	0.101930	−	0.176548i	0.912480	+	0.409122i	$0.134165\pi$
$102$	−882.273	−	1574.03i	−0.856451	−	1.52796i
$103$	493.955	+	855.556i	0.472533	+	0.818451i	0.999506	−	0.0314311i	$-0.0100065\pi$
$103$	493.955	+	855.556i	0.472533	+	0.818451i	−0.526973	+	0.849882i	$0.676673\pi$
$104$	127.819	+	221.390i	0.120517	+	0.208741i
$105$	311.255	−	523.619i	0.289289	−	0.486666i
$106$	−229.909	+	398.214i	−0.210668	+	0.364887i
$107$	−1715.88			−1.55028			−0.775140	−	0.631790i	$-0.782321\pi$
$107$	−1715.88			−1.55028			−0.775140	+	0.631790i	$0.782321\pi$
$108$	−203.207	−	385.183i	−0.181052	−	0.343188i
$109$	−1050.09			−0.922753			−0.461377	−	0.887204i	$-0.652644\pi$
$109$	−1050.09			−0.922753			−0.461377	+	0.887204i	$0.652644\pi$
$110$	270.463	−	468.456i	0.234433	−	0.406050i
$111$	−329.020	+	553.503i	−0.281344	+	0.473299i
$112$	277.191	+	480.109i	0.233858	+	0.405054i
$113$	147.086	+	254.761i	0.122449	+	0.212088i	0.920733	−	0.390194i	$-0.127592\pi$
$113$	147.086	+	254.761i	0.122449	+	0.212088i	−0.798284	+	0.602281i	$0.794259\pi$
$114$	1371.65	+	2447.10i	1.12690	+	2.01046i
$115$	604.092	−	1046.32i	0.489843	−	0.848432i
$116$	204.099			0.163363
$117$	220.787	−	360.897i	0.174459	−	0.285171i
$118$	2599.58			2.02806
$119$	364.741	−	631.749i	0.280972	−	0.486658i
$120$	−1419.57	−	18.0520i	−1.07991	−	0.0137326i
$121$	618.523	+	1071.31i	0.464706	+	0.804894i
$122$	125.319	+	217.059i	0.0929988	+	0.161079i
$123$	2101.53	+	26.7241i	1.54056	+	0.0195905i
$124$	−306.725	+	531.264i	−0.222135	+	0.384749i
$125$	−510.213			−0.365079
$126$	328.669	−	537.241i	0.232382	−	0.379851i
$127$	−1491.03			−1.04179			−0.520897	−	0.853620i	$-0.674402\pi$
$127$	−1491.03			−1.04179			−0.520897	+	0.853620i	$0.674402\pi$
$128$	848.599	−	1469.82i	0.585986	−	1.01496i
$129$	587.239	+	1047.67i	0.400803	+	0.715057i
$130$	437.227	+	757.300i	0.294980	+	0.510920i
$131$	−773.712	−	1340.11i	−0.516027	−	0.893785i	−0.999827	−	0.0186062i	$-0.994077\pi$
$131$	−773.712	−	1340.11i	−0.516027	−	0.893785i	0.483800	−	0.875179i	$-0.339256\pi$
$132$	79.8869	−	134.392i	0.0526762	−	0.0886162i
$133$	−567.053	+	982.164i	−0.369697	+	0.640334i
$134$	452.982			0.292027
$135$	1096.32	+	2078.10i	0.698935	+	1.32485i
$136$	−1700.15			−1.07196
$137$	10.2897	−	17.8223i	0.00641687	−	0.0111143i	−0.862799	−	0.505547i	$-0.831291\pi$
$137$	10.2897	−	17.8223i	0.00641687	−	0.0111143i	0.869216	+	0.494433i	$0.164624\pi$
$138$	638.285	−	1073.77i	0.393728	−	0.662360i
$139$	59.2567	+	102.636i	0.0361589	+	0.0626291i	0.883539	−	0.468358i	$-0.155154\pi$
$139$	59.2567	+	102.636i	0.0361589	+	0.0626291i	−0.847380	+	0.530988i	$0.821821\pi$
$140$	181.949	+	315.144i	0.109839	+	0.190247i
$141$	517.453	+	923.168i	0.309060	+	0.551382i
$142$	377.799	−	654.367i	0.223269	−	0.386713i
$143$	151.884			0.0888192
$144$	−2137.64	−	54.3754i	−1.23706	−	0.0314672i
$145$	−1101.13			−0.630649
$146$	247.179	−	428.126i	0.140114	−	0.242685i
$147$	254.591	+	3.23750i	0.142846	+	0.00181650i
$148$	−192.333	−	333.131i	−0.106822	−	0.185022i
$149$	−447.254	−	774.666i	−0.245909	−	0.425927i	0.716478	−	0.697610i	$-0.245753\pi$
$149$	−447.254	−	774.666i	−0.245909	−	0.425927i	−0.962387	+	0.271683i	$0.912420\pi$
$150$	−2691.68	−	34.2288i	−1.46517	−	0.0186318i
$151$	1362.56	−	2360.02i	0.734328	−	1.27189i	−0.220689	−	0.975344i	$-0.570831\pi$
$151$	1362.56	−	2360.02i	0.734328	−	1.27189i	0.955017	−	0.296550i	$-0.0958361\pi$
$152$	2643.18			1.41046
$153$	1344.44	+	2471.73i	0.710401	+	1.30606i
$154$	226.098			0.118308
$155$	1654.81	−	2866.22i	0.857533	−	1.48529i
$156$	123.578	+	220.471i	0.0634240	+	0.113152i
$157$	1609.93	+	2788.47i	0.818383	+	1.41748i	0.906873	+	0.421404i	$0.138462\pi$
$157$	1609.93	+	2788.47i	0.818383	+	1.41748i	−0.0884901	+	0.996077i	$0.528204\pi$
$158$	−1532.23	−	2653.91i	−0.771507	−	1.33629i
$159$	366.372	−	616.341i	0.182737	−	0.307415i
$160$	1116.98	−	1934.66i	0.551904	−	0.955926i
$161$	505.000			0.247202
$162$	1106.09	+	2162.81i	0.536436	+	1.04893i
$163$	−110.379			−0.0530401			−0.0265200	−	0.999648i	$-0.508443\pi$
$163$	−110.379			−0.0530401			−0.0265200	+	0.999648i	$0.508443\pi$
$164$	−627.769	+	1087.33i	−0.298906	+	0.517720i
$165$	−430.997	+	725.058i	−0.203352	+	0.342095i
$166$	1609.30	+	2787.38i	0.752443	+	1.30327i
$167$	−1089.44	−	1886.97i	−0.504811	−	0.874358i	−0.999985	−	0.00556385i	$-0.998229\pi$
$167$	−1089.44	−	1886.97i	−0.504811	−	0.874358i	0.495174	−	0.868794i	$-0.335104\pi$
$168$	−290.144	−	517.635i	−0.133245	−	0.237717i
$169$	975.733	−	1690.02i	0.444121	−	0.769240i
$170$	−5815.65			−2.62377
$171$	−2090.16	−	3842.74i	−0.934729	−	1.71849i
$172$	−717.484			−0.318068
$173$	−1503.35	+	2603.88i	−0.660680	+	1.14433i	0.319757	+	0.947500i	$0.396399\pi$
$173$	−1503.35	+	2603.88i	−0.660680	+	1.14433i	−0.980437	+	0.196832i	$0.936935\pi$
$174$	−1138.38	−	14.4763i	−0.495981	−	0.00630714i
$175$	−544.130	−	942.461i	−0.235042	−	0.407105i
$176$	−383.828	−	664.810i	−0.164387	−	0.284727i
$177$	−4053.29	−	51.5437i	−1.72127	−	0.0218885i
$178$	−2085.97	+	3613.01i	−0.878371	+	1.52138i
$179$	2473.72			1.03293			0.516465	−	0.856309i	$-0.327248\pi$
$179$	2473.72			1.03293			0.516465	+	0.856309i	$0.327248\pi$
$180$	−1403.15	−	35.6921i	−0.581026	−	0.0147796i
$181$	500.939			0.205716			0.102858	−	0.994696i	$-0.467201\pi$
$181$	500.939			0.205716			0.102858	+	0.994696i	$0.467201\pi$
$182$	−182.753	+	316.538i	−0.0744318	+	0.128920i
$183$	−191.095	−	340.925i	−0.0771920	−	0.137715i
$184$	−588.484	−	1019.28i	−0.235781	−	0.408384i
$185$	1037.66	+	1797.27i	0.412378	+	0.714260i
$186$	1748.48	−	2941.43i	0.689271	−	1.15955i
$187$	−505.059	+	874.787i	−0.197506	+	0.342090i
$188$	−632.219			−0.245262
$189$	−523.116	+	831.154i	−0.201328	+	0.319881i
$190$	9041.44			3.45229
$191$	−163.388	+	282.996i	−0.0618969	+	0.107209i	−0.895313	−	0.445437i	$-0.853048\pi$
$191$	−163.388	+	282.996i	−0.0618969	+	0.107209i	0.833416	+	0.552646i	$0.186382\pi$
$192$	−502.010	+	844.521i	−0.188695	+	0.317438i
$193$	−366.899	−	635.488i	−0.136839	−	0.237012i	0.789459	−	0.613803i	$-0.210361\pi$
$193$	−366.899	−	635.488i	−0.136839	−	0.237012i	−0.926299	+	0.376790i	$0.877028\pi$
$194$	1384.11	+	2397.35i	0.512234	+	0.887216i
$195$	−666.714	−	1189.46i	−0.244843	−	0.436815i
$196$	−76.0514	+	131.725i	−0.0277155	+	0.0480047i
$197$	−1257.59			−0.454821			−0.227410	−	0.973799i	$-0.573026\pi$
$197$	−1257.59			−0.454821			−0.227410	+	0.973799i	$0.573026\pi$
$198$	−455.110	+	743.921i	−0.163350	+	0.267011i
$199$	−4755.99			−1.69419			−0.847093	−	0.531445i	$-0.821649\pi$
$199$	−4755.99			−1.69419			−0.847093	+	0.531445i	$0.821649\pi$
$200$	−1268.17	+	2196.53i	−0.448364	+	0.776590i
$201$	−706.293	−	8.98157i	−0.247851	−	0.00315180i
$202$	−344.769	−	597.157i	−0.120088	−	0.207999i
$203$	−230.127	−	398.592i	−0.0795653	−	0.137811i
$204$	−1680.75	−	21.3733i	−0.576844	−	0.00733544i
$205$	3386.87	−	5866.24i	1.15390	−	1.99861i
$206$	3292.00			1.11342
$207$	−1016.51	+	1661.58i	−0.341315	+	0.557913i
$208$	1240.98			0.413686
$209$	785.201	−	1360.01i	0.259873	−	0.450114i
$210$	−992.487	−	1770.66i	−0.326134	−	0.581843i
$211$	−537.060	−	930.215i	−0.175226	−	0.303501i	0.765013	−	0.644014i	$-0.222732\pi$
$211$	−537.060	−	930.215i	−0.175226	−	0.303501i	−0.940240	+	0.340514i	$0.889399\pi$
$212$	214.168	+	370.950i	0.0693827	+	0.120174i
$213$	−602.043	+	1012.80i	−0.193668	+	0.325804i
$214$	−2858.90	+	4951.75i	−0.913224	+	1.58175i
$215$	3870.89			1.22787
$216$	2287.18	+	87.2925i	0.720478	+	0.0274977i
$217$	1383.36			0.432760
$218$	−1749.60	+	3030.39i	−0.543567	+	0.941486i
$219$	−393.892	+	662.638i	−0.121538	+	0.204461i
$220$	−251.946	−	436.383i	−0.0772099	−	0.133731i
$221$	−816.472	−	1414.17i	−0.248515	−	0.430441i
$222$	1049.13	+	1871.72i	0.317176	+	0.565862i
$223$	−458.994	+	795.001i	−0.137832	+	0.238732i	−0.926676	−	0.375862i	$-0.877347\pi$
$223$	−458.994	+	795.001i	−0.137832	+	0.238732i	0.788844	+	0.614594i	$0.210680\pi$
$224$	933.753			0.278522
$225$	4196.22	+	106.740i	1.24332	+	0.0316266i
$226$	980.268			0.288524
$227$	−494.284	+	856.125i	−0.144523	+	0.250322i	−0.929195	−	0.369590i	$-0.879498\pi$
$227$	−494.284	+	856.125i	−0.144523	+	0.250322i	0.784672	+	0.619912i	$0.212832\pi$
$228$	2613.02	+	33.2285i	0.758999	+	0.00965180i
$229$	−3163.91	−	5480.05i	−0.913000	−	1.58136i	−0.809804	−	0.586700i	$-0.800427\pi$
$229$	−3163.91	−	5480.05i	−0.913000	−	1.58136i	−0.103196	−	0.994661i	$-0.532907\pi$
$230$	−2013.01	−	3486.63i	−0.577104	−	0.999573i
$231$	−352.534	−	4.48299i	−0.100411	−	0.00127688i
$232$	−536.341	+	928.970i	−0.151778	+	0.262887i
$233$	−2136.96			−0.600846			−0.300423	−	0.953806i	$-0.597128\pi$
$233$	−2136.96			−0.600846			−0.300423	+	0.953806i	$0.597128\pi$
$234$	−673.631	−	1238.46i	−0.188191	−	0.345987i
$235$	3410.88			0.946814
$236$	1210.80	−	2097.17i	0.333968	−	0.578449i
$237$	2336.45	+	4168.38i	0.640375	+	1.14247i
$238$	−1215.42	−	2105.17i	−0.331025	−	0.573353i
$239$	633.541	+	1097.33i	0.171466	+	0.296988i	0.938933	−	0.344101i	$-0.111816\pi$
$239$	633.541	+	1097.33i	0.171466	+	0.296988i	−0.767467	+	0.641089i	$0.778483\pi$
$240$	−3521.52	+	5924.18i	−0.947137	+	1.59335i
$241$	−1327.72	+	2299.67i	−0.354878	+	0.614668i	−0.987097	−	0.160122i	$-0.948811\pi$
$241$	−1327.72	+	2299.67i	−0.354878	+	0.614668i	0.632219	+	0.774790i	$0.282144\pi$
$242$	4122.20			1.09498
$243$	−1681.74	−	3394.21i	−0.443966	−	0.896044i
$244$	233.478			0.0612578
$245$	410.304	−	710.668i	0.106993	−	0.185318i
$246$	3578.57	−	6020.17i	0.927486	−	1.56029i
$247$	1269.35	+	2198.57i	0.326990	+	0.566364i
$248$	−1612.06	−	2792.16i	−0.412765	−	0.714930i
$249$	−2453.96	−	4378.02i	−0.624552	−	1.11424i
$250$	−850.088	+	1472.40i	−0.215057	+	0.372490i
$251$	2968.88			0.746590			0.373295	−	0.927713i	$-0.378228\pi$
$251$	2968.88			0.746590			0.373295	+	0.927713i	$0.378228\pi$
$252$	−280.326	−	515.377i	−0.0700750	−	0.128832i
$253$	−699.277			−0.173767
$254$	−2484.28	+	4302.89i	−0.613690	+	1.06294i
$255$	9067.82	+	115.311i	2.22686	+	0.0283178i
$256$	−2071.48	−	3587.90i	−0.505731	−	0.875953i
$257$	1676.71	+	2904.15i	0.406967	+	0.704887i	0.994548	−	0.104278i	$-0.0332531\pi$
$257$	1676.71	+	2904.15i	0.406967	+	0.704887i	−0.587581	+	0.809165i	$0.699920\pi$
$258$	4001.84	+	50.8894i	0.965674	+	0.0122800i
$259$	−433.722	+	751.228i	−0.104055	+	0.180228i
$260$	814.585			0.194301
$261$	1774.69	+	45.1430i	0.420884	+	0.0107061i
$262$	−5156.46			−1.21591
$263$	1739.04	−	3012.11i	0.407734	−	0.706216i	−0.586902	−	0.809658i	$-0.699652\pi$
$263$	1739.04	−	3012.11i	0.407734	−	0.706216i	0.994635	+	0.103443i	$0.0329858\pi$
$264$	401.764	+	716.773i	0.0936625	+	0.167100i
$265$	−1155.46	−	2001.31i	−0.267846	−	0.463923i
$266$	1889.58	+	3272.85i	0.435555	+	0.754404i
$267$	3324.10	−	5592.07i	0.761917	−	1.28176i
$268$	210.984	−	365.435i	0.0480892	−	0.0832929i
$269$	−4629.31			−1.04927			−0.524636	−	0.851326i	$-0.675799\pi$
$269$	−4629.31			−1.04927			−0.524636	+	0.851326i	$0.675799\pi$
$270$	7823.69	+	298.599i	1.76346	+	0.0673042i
$271$	−3299.94			−0.739693			−0.369847	−	0.929093i	$-0.620590\pi$
$271$	−3299.94			−0.739693			−0.369847	+	0.929093i	$0.620590\pi$
$272$	−4126.65	+	7147.56i	−0.919907	+	1.59333i
$273$	291.227	−	489.926i	0.0645636	−	0.108614i
$274$	−34.2883	−	59.3891i	−0.00755998	−	0.0130943i
$275$	753.460	+	1305.03i	0.165219	+	0.286169i
$276$	−568.956	−	1015.05i	−0.124084	−	0.221373i
$277$	−3291.51	+	5701.07i	−0.713964	+	1.23662i	0.249394	+	0.968402i	$0.419769\pi$
$277$	−3291.51	+	5701.07i	−0.713964	+	1.23662i	−0.963358	+	0.268219i	$0.913565\pi$
$278$	394.921			0.0852007
$279$	−2784.56	+	4551.63i	−0.597517	+	0.976699i
$280$	−1912.54			−0.408199
$281$	−897.176	+	1553.95i	−0.190466	+	0.329897i	−0.945405	−	0.325898i	$-0.894333\pi$
$281$	−897.176	+	1553.95i	−0.190466	+	0.329897i	0.754939	+	0.655796i	$0.227667\pi$
$282$	3526.27	+	44.8418i	0.744633	+	0.00946912i
$283$	4135.33	+	7162.61i	0.868622	+	1.50450i	0.863405	+	0.504511i	$0.168327\pi$
$283$	4135.33	+	7162.61i	0.868622	+	1.50450i	0.00521722	+	0.999986i	$0.498339\pi$
$284$	−351.933	−	609.566i	−0.0735330	−	0.127363i
$285$	−14097.5	−	179.271i	−2.93005	−	0.0372599i
$286$	253.060	−	438.313i	0.0523208	−	0.0906222i
$287$	2831.31			0.582323
$288$	−1879.54	+	3072.29i	−0.384559	+	0.628599i
$289$	5947.06			1.21047
$290$	−1834.64	+	3177.70i	−0.371497	+	0.643451i
$291$	−2110.59	−	3765.42i	−0.425171	−	0.758531i
$292$	−230.256	−	398.814i	−0.0461462	−	0.0799275i
$293$	−1973.47	−	3418.15i	−0.393486	−	0.681538i	0.599420	−	0.800434i	$-0.295398\pi$
$293$	−1973.47	−	3418.15i	−0.393486	−	0.681538i	−0.992907	+	0.118896i	$0.962064\pi$
$294$	433.528	−	729.316i	0.0859995	−	0.144675i
$295$	−6532.37	+	11314.4i	−1.28925	+	2.23305i
$296$	2021.69			0.396988
$297$	724.362	−	1150.90i	0.141521	−	0.224856i
$298$	−2980.76			−0.579431
$299$	565.221	−	978.992i	0.109323	−	0.189353i
$300$	−1281.31	+	2155.52i	−0.246588	+	0.414831i
$301$	808.982	+	1401.20i	0.154914	+	0.268318i
$302$	−4540.44	−	7864.28i	−0.865143	−	1.49847i
$303$	525.726	+	937.928i	0.0996771	+	0.177830i
$304$	6415.59	−	11112.1i	1.21039	−	2.09646i
$305$	−1259.63			−0.236480
$306$	9373.07	+	238.424i	1.75105	+	0.0445418i
$307$	−4332.94			−0.805518			−0.402759	−	0.915306i	$-0.631949\pi$
$307$	−4332.94			−0.805518			−0.402759	+	0.915306i	$0.631949\pi$
$308$	105.309	−	182.400i	0.0194822	−	0.0337442i
$309$	−5132.92	−	65.2728i	−0.944989	−	0.0120170i
$310$	−5514.31	−	9551.06i	−1.01030	−	1.74988i
$311$	−445.794	−	772.137i	−0.0812818	−	0.140784i	0.822519	−	0.568738i	$-0.192568\pi$
$311$	−445.794	−	772.137i	−0.0812818	−	0.140784i	−0.903801	+	0.427953i	$0.859235\pi$
$312$	−1328.23	−	16.8904i	−0.241014	−	0.00306485i
$313$	1775.48	−	3075.22i	0.320626	−	0.555341i	−0.659991	−	0.751273i	$-0.729440\pi$
$313$	1775.48	−	3075.22i	0.320626	−	0.555341i	0.980617	+	0.195932i	$0.0627733\pi$
$314$	10729.5			1.92834
$315$	1512.39	+	2780.50i	0.270518	+	0.497345i
$316$	−2854.66			−0.508187
$317$	1953.28	−	3383.18i	0.346080	−	0.599427i	−0.639470	−	0.768816i	$-0.720846\pi$
$317$	1953.28	−	3383.18i	0.346080	−	0.599427i	0.985549	+	0.169389i	$0.0541794\pi$
$318$	−1168.24	−	2084.21i	−0.206011	−	0.367536i
$319$	318.658	+	551.932i	0.0559293	+	0.0968724i
$320$	1583.23	+	2742.23i	0.276578	+	0.479048i
$321$	4555.80	−	7664.13i	0.792149	−	1.33262i
$322$	841.403	−	1457.35i	0.145620	−	0.252221i
$323$	−16883.8			−2.90849
$324$	2259.99	+	115.050i	0.387516	+	0.0197273i
$325$	−2436.07			−0.415781
$326$	−183.907	+	318.536i	−0.0312443	+	0.0541168i
$327$	2788.07	−	4690.32i	0.471501	−	0.793197i
$328$	−3299.37	−	5714.67i	−0.555418	−	0.962012i
$329$	712.844	+	1234.68i	0.119454	+	0.206900i
$330$	1374.30	+	2451.84i	0.229251	+	0.408998i
$331$	1855.99	−	3214.66i	0.308200	−	0.533818i	−0.669769	−	0.742570i	$-0.733607\pi$
$331$	1855.99	−	3214.66i	0.308200	−	0.533818i	0.977969	+	0.208752i	$0.0669401\pi$
$332$	2998.23			0.495630
$333$	−1598.70	−	2939.20i	−0.263088	−	0.483685i
$334$	−7260.65			−1.18948
$335$	−1138.28	+	1971.55i	−0.185644	+	0.321545i
$336$	−2880.42	−	36.6289i	−0.467678	−	0.00594723i
$337$	648.466	+	1123.18i	0.104819	+	0.181553i	0.913664	−	0.406469i	$-0.133240\pi$
$337$	648.466	+	1123.18i	0.104819	+	0.181553i	−0.808845	+	0.588022i	$0.799907\pi$
$338$	−3251.42	−	5631.63i	−0.523237	−	0.906273i
$339$	−1528.44	−	19.4364i	−0.244878	−	0.00311399i
$340$	−2708.74	+	4691.67i	−0.432065	+	0.748358i
$341$	−1915.55			−0.304202
$342$	−14572.1	−	370.671i	−2.30400	−	0.0586070i
$343$	343.000			0.0539949
$344$	1885.44	−	3265.68i	0.295512	−	0.511841i
$345$	3069.57	+	5476.30i	0.479015	+	0.854592i
$346$	5009.60	+	8676.88i	0.778375	+	1.34818i
$347$	6198.09	+	10735.4i	0.958879	+	1.66083i	0.725232	+	0.688505i	$0.241733\pi$
$347$	6198.09	+	10735.4i	0.958879	+	1.66083i	0.233647	+	0.972321i	$0.424934\pi$
$348$	−541.900	+	911.628i	−0.0834738	+	0.140426i
$349$	4847.43	−	8395.99i	0.743486	−	1.28776i	−0.207412	−	0.978254i	$-0.566504\pi$
$349$	4847.43	−	8395.99i	0.743486	−	1.28776i	0.950899	−	0.309502i	$-0.100163\pi$
$350$	−3626.40			−0.553826
$351$	1025.78	+	1944.38i	0.155988	+	0.295679i
$352$	−1292.97			−0.195783
$353$	2458.64	−	4258.48i	0.370708	−	0.642086i	−0.618966	−	0.785417i	$-0.712448\pi$
$353$	2458.64	−	4258.48i	0.370708	−	0.642086i	0.989675	+	0.143332i	$0.0457816\pi$
$354$	−6902.11	+	11611.3i	−1.03628	+	1.74331i
$355$	1898.71	+	3288.66i	0.283868	+	0.491673i
$356$	1943.15	+	3365.64i	0.289289	+	0.501063i
$357$	1853.35	+	3306.50i	0.274762	+	0.490192i
$358$	4121.57	−	7138.77i	0.608468	−	1.05390i
$359$	9291.73			1.36601			0.683007	−	0.730412i	$-0.260672\pi$
$359$	9291.73			1.36601			0.683007	+	0.730412i	$0.260672\pi$
$360$	3849.72	−	6292.74i	0.563606	−	0.921268i
$361$	19389.9			2.82693
$362$	834.637	−	1445.63i	0.121181	−	0.209892i
$363$	−6427.36	−	81.7336i	−0.929336	−	0.0118179i
$364$	170.241	+	294.866i	0.0245139	+	0.0424593i
$365$	1242.25	+	2151.64i	0.178143	+	0.308553i
$366$	−1302.25	−	16.5600i	−0.185983	−	0.00236505i
$367$	609.600	−	1055.86i	0.0867053	−	0.150178i	−0.819411	−	0.573206i	$-0.805699\pi$
$367$	609.600	−	1055.86i	0.0867053	−	0.150178i	0.906117	+	0.423028i	$0.139033\pi$
$368$	−5713.53			−0.809343
$369$	−5699.11	+	9315.74i	−0.804021	+	1.31425i
$370$	6915.53			0.971679
$371$	482.961	−	836.513i	0.0675851	−	0.117061i
$372$	−1558.56	−	2780.57i	−0.217225	−	0.387543i
$373$	5836.18	+	10108.6i	0.810149	+	1.40322i	0.912759	+	0.408498i	$0.133947\pi$
$373$	5836.18	+	10108.6i	0.810149	+	1.40322i	−0.102610	+	0.994722i	$0.532719\pi$
$374$	1683.00	+	2915.04i	0.232690	+	0.403030i
$375$	1354.66	−	2278.92i	0.186545	−	0.313821i
$376$	1661.38	−	2877.59i	0.227870	−	0.394682i
$377$	−1030.28			−0.140748
$378$	1527.00	+	2894.45i	0.207778	+	0.393848i
$379$	768.573			0.104166			0.0520830	−	0.998643i	$-0.483414\pi$
$379$	768.573			0.104166			0.0520830	+	0.998643i	$0.483414\pi$
$380$	4211.21	−	7294.02i	0.568501	−	0.984672i
$381$	3958.82	−	6659.85i	0.532327	−	0.895523i
$382$	544.454	+	943.023i	0.0729233	+	0.126307i
$383$	−938.584	−	1625.68i	−0.125220	−	0.216888i	0.796599	−	0.604509i	$-0.206630\pi$
$383$	−938.584	−	1625.68i	−0.125220	−	0.216888i	−0.921819	+	0.387620i	$0.873297\pi$
$384$	4311.98	+	7692.84i	0.573033	+	1.02233i
$385$	−568.151	+	984.066i	−0.0752095	+	0.130267i
$386$	−2445.23			−0.322432
$387$	−6238.70	−	158.695i	−0.819460	−	0.0208447i
$388$	2578.69			0.337406
$389$	−6159.48	+	10668.5i	−0.802823	+	1.39053i	0.114929	+	0.993374i	$0.463336\pi$
$389$	−6159.48	+	10668.5i	−0.802823	+	1.39053i	−0.917751	+	0.397156i	$0.869997\pi$
$390$	−4543.43	−	57.7766i	−0.589912	−	0.00750162i
$391$	3759.06	+	6510.89i	0.486199	+	0.842122i
$392$	−399.703	−	692.306i	−0.0515002	−	0.0892009i
$393$	8040.00	+	102.241i	1.03197	+	0.0131230i
$394$	−2095.33	+	3629.22i	−0.267922	+	0.464054i
$395$	15401.1			1.96181
$396$	388.170	+	713.645i	0.0492582	+	0.0905607i
$397$	12120.2			1.53223			0.766115	−	0.642703i	$-0.222187\pi$
$397$	12120.2			1.53223			0.766115	+	0.642703i	$0.222187\pi$
$398$	−7924.15	+	13725.0i	−0.997995	+	1.72858i
$399$	−2881.36	−	5140.53i	−0.361525	−	0.644983i
$400$	6156.24	+	10662.9i	0.769530	+	1.33287i
$401$	1647.68	+	2853.86i	0.205190	+	0.355399i	0.950193	−	0.311662i	$-0.100886\pi$
$401$	1647.68	+	2853.86i	0.205190	+	0.355399i	−0.745003	+	0.667061i	$0.767552\pi$
$402$	−1202.71	+	2023.29i	−0.149218	+	0.251026i
$403$	1548.33	−	2681.79i	0.191384	−	0.331487i
$404$	−642.327			−0.0791014
$405$	−12192.9	−	620.704i	−1.49597	−	0.0761556i
$406$	−1533.70			−0.187478
$407$	600.577	−	1040.23i	0.0731437	−	0.126689i
$408$	4514.05	−	7593.90i	0.547742	−	0.921456i
$409$	−2442.58	−	4230.67i	−0.295300	−	0.511474i	0.679755	−	0.733439i	$-0.262086\pi$
$409$	−2442.58	−	4230.67i	−0.295300	−	0.511474i	−0.975055	+	0.221965i	$0.928753\pi$
$410$	−11286.0	−	19548.0i	−1.35946	−	2.35465i
$411$	52.2851	+	93.2799i	0.00627502	+	0.0111950i
$412$	1533.31	−	2655.76i	0.183351	−	0.317573i
$413$	−5460.84			−0.650630
$414$	3101.42	+	5701.93i	0.368180	+	0.676895i
$415$	−16175.7			−1.91334
$416$	1045.10	−	1810.17i	0.123174	−	0.213344i
$417$	−615.764	−	7.83036i	−0.0723120	−	0.000919555i
$418$	−2616.52	−	4531.94i	−0.306168	−	0.530298i
$419$	−3408.41	−	5903.55i	−0.397403	−	0.688323i	0.596002	−	0.802983i	$-0.296755\pi$
$419$	−3408.41	−	5903.55i	−0.397403	−	0.688323i	−0.993405	+	0.114661i	$0.963422\pi$
$420$	−1890.71	−	24.0433i	−0.219660	−	0.00279331i
$421$	−5180.66	+	8973.17i	−0.599739	+	1.03878i	0.393121	+	0.919487i	$0.371395\pi$
$421$	−5180.66	+	8973.17i	−0.599739	+	1.03878i	−0.992859	+	0.119291i	$0.961938\pi$
$422$	−3579.28			−0.412883
$423$	−5497.31	−	139.836i	−0.631887	−	0.0160734i
$424$	−2251.21			−0.257850
$425$	8100.67	−	14030.8i	0.924565	−	1.60139i
$426$	1919.71	+	3424.88i	0.218334	+	0.389521i
$427$	−263.253	−	455.967i	−0.0298353	−	0.0516763i
$428$	2663.16	+	4612.72i	0.300768	+	0.520945i
$429$	−403.264	+	678.403i	−0.0453841	+	0.0763488i
$430$	6449.46	−	11170.8i	0.723304	−	1.25280i
$431$	3794.95			0.424121			0.212060	−	0.977257i	$-0.431983\pi$
$431$	3794.95			0.424121			0.212060	+	0.977257i	$0.431983\pi$
$432$	5918.49	−	9403.61i	0.659151	−	1.04729i
$433$	2805.84			0.311409			0.155704	−	0.987804i	$-0.450235\pi$
$433$	2805.84			0.311409			0.155704	+	0.987804i	$0.450235\pi$
$434$	2304.88	−	3992.18i	0.254926	−	0.441545i
$435$	2923.60	−	4918.32i	0.322243	−	0.542104i
$436$	1629.81	+	2822.91i	0.179022	+	0.310075i
$437$	−5844.12	−	10122.3i	−0.639730	−	1.10804i
$438$	1255.99	+	2240.76i	0.137017	+	0.244447i
$439$	−2233.37	+	3868.31i	−0.242808	+	0.420556i	−0.961513	−	0.274759i	$-0.911402\pi$
$439$	−2233.37	+	3868.31i	−0.242808	+	0.420556i	0.718705	+	0.695315i	$0.244735\pi$
$440$	2648.30			0.286938
$441$	−690.421	+	1128.56i	−0.0745515	+	0.121862i
$442$	−5441.44			−0.585572
$443$	1143.57	−	1980.72i	0.122647	−	0.212430i	−0.798164	−	0.602440i	$-0.794195\pi$
$443$	1143.57	−	1980.72i	0.122647	−	0.212430i	0.920811	+	0.390010i	$0.127528\pi$
$444$	1998.62	+	25.4155i	0.213627	+	0.00271659i
$445$	−10483.5	−	18157.9i	−1.11677	−	1.93431i
$446$	1529.50	+	2649.17i	0.162385	+	0.281260i
$447$	4647.62	+	59.1015i	0.491778	+	0.00625370i
$448$	−661.762	+	1146.20i	−0.0697886	+	0.120877i
$449$	8325.23			0.875037			0.437519	−	0.899209i	$-0.355857\pi$
$449$	8325.23			0.875037			0.437519	+	0.899209i	$0.355857\pi$
$450$	7299.53	−	11931.8i	0.764674	−	1.24993i
$451$	−3920.53			−0.409336
$452$	456.576	−	790.814i	0.0475123	−	0.0822937i
$453$	6923.57	+	12352.1i	0.718096	+	1.28113i
$454$	1647.10	+	2852.85i	0.170269	+	0.294914i
$455$	−918.466	−	1590.83i	−0.0946337	−	0.163910i
$456$	−7017.87	+	11806.0i	−0.720706	+	1.21243i
$457$	259.994	−	450.323i	0.0266127	−	0.0460946i	−0.852412	−	0.522870i	$-0.824861\pi$
$457$	259.994	−	450.323i	0.0266127	−	0.0460946i	0.879025	+	0.476776i	$0.158195\pi$
$458$	−21086.1			−2.15129
$459$	−14609.8	−	557.599i	−1.48568	−	0.0567026i
$460$	−3750.37			−0.380135
$461$	7792.55	−	13497.1i	0.787278	−	1.36361i	−0.140350	−	0.990102i	$-0.544823\pi$
$461$	7792.55	−	13497.1i	0.787278	−	1.36361i	0.927628	−	0.373504i	$-0.121844\pi$
$462$	−600.309	+	1009.89i	−0.0604522	+	0.101698i
$463$	−2048.69	−	3548.43i	−0.205639	−	0.356176i	0.744697	−	0.667402i	$-0.232594\pi$
$463$	−2048.69	−	3548.43i	−0.205639	−	0.356176i	−0.950336	+	0.311226i	$0.899260\pi$
$464$	2603.64	+	4509.63i	0.260498	+	0.451195i
$465$	8408.58	+	15001.4i	0.838578	+	1.49607i
$466$	−3560.49	+	6166.95i	−0.353941	+	0.613044i
$467$	−17081.4			−1.69257			−0.846287	−	0.532728i	$-0.821167\pi$
$467$	−17081.4			−1.69257			−0.846287	+	0.532728i	$0.821167\pi$
$468$	−1312.86	−	33.3955i	−0.129673	−	0.00329852i
$469$	−951.560			−0.0936865
$470$	5683.02	−	9843.28i	0.557741	−	0.966035i
$471$	−16729.5	−	212.741i	−1.63663	−	0.0208122i
$472$	6363.60	+	11022.1i	0.620568	+	1.07486i
$473$	−1120.20	−	1940.25i	−0.108894	−	0.188610i
$474$	15922.2	+	202.474i	1.54289	+	0.0196201i
$475$	−12593.9	+	21813.3i	−1.21652	+	2.10708i
$476$	−2264.41			−0.218044
$477$	1780.20	+	3272.88i	0.170880	+	0.314161i
$478$	4222.28			0.404022
$479$	3919.34	−	6788.49i	0.373860	−	0.647545i	−0.616295	−	0.787515i	$-0.711367\pi$
$479$	3919.34	−	6788.49i	0.373860	−	0.647545i	0.990156	+	0.139970i	$0.0447006\pi$
$480$	5675.68	+	10125.8i	0.539705	+	0.962867i
$481$	970.886	+	1681.62i	0.0920345	+	0.159408i
$482$	4424.33	+	7663.17i	0.418097	+	0.724165i
$483$	−1340.82	+	2255.63i	−0.126313	+	0.212495i
$484$	1919.98	−	3325.51i	0.180314	−	0.312313i
$485$	−13912.3			−1.30252
$486$	−12597.2	−	801.998i	−1.17576	−	0.0748547i
$487$	−13120.9			−1.22088			−0.610438	−	0.792064i	$-0.709007\pi$
$487$	−13120.9			−1.22088			−0.610438	+	0.792064i	$0.709007\pi$
$488$	−613.545	+	1062.69i	−0.0569137	+	0.0985774i
$489$	293.065	−	493.018i	0.0271020	−	0.0455931i
$490$	−1367.25	−	2368.15i	−0.126053	−	0.218331i
$491$	9069.53	+	15708.9i	0.833609	+	1.44385i	0.895158	+	0.445749i	$0.147063\pi$
$491$	9069.53	+	15708.9i	0.833609	+	1.44385i	−0.0615491	+	0.998104i	$0.519604\pi$
$492$	−3189.88	−	5690.95i	−0.292299	−	0.521479i
$493$	3425.99	−	5933.98i	0.312979	−	0.542096i
$494$	8459.66			0.770482
$495$	−2094.21	−	3850.18i	−0.190157	−	0.349602i
$496$	−15651.3			−1.41686
$497$	−793.627	+	1374.60i	−0.0716279	+	0.124063i
$498$	−16722.9	−	212.657i	−1.50476	−	0.0191353i
$499$	−173.693	−	300.844i	−0.0155823	−	0.0269893i	0.858129	−	0.513434i	$-0.171627\pi$
$499$	−173.693	−	300.844i	−0.0155823	−	0.0269893i	−0.873711	+	0.486445i	$0.838294\pi$
$500$	791.886	+	1371.59i	0.0708284	+	0.122678i
$501$	11320.9	+	143.962i	1.00954	+	0.0128378i
$502$	4946.58	−	8567.74i	0.439795	−	0.761747i
$503$	−1130.27			−0.100191			−0.0500955	−	0.998744i	$-0.515953\pi$
$503$	−1130.27			−0.100191			−0.0500955	+	0.998744i	$0.515953\pi$
$504$	3082.43	+	78.4080i	0.272425	+	0.00692971i
$505$	3465.41			0.305364
$506$	−1165.10	+	2018.00i	−0.102361	+	0.177295i
$507$	4957.99	+	8845.36i	0.434304	+	0.774825i
$508$	2314.19	+	4008.29i	0.202117	+	0.350077i
$509$	4243.80	+	7350.47i	0.369554	+	0.640086i	0.989496	−	0.144561i	$-0.0461771\pi$
$509$	4243.80	+	7350.47i	0.369554	+	0.640086i	−0.619942	+	0.784648i	$0.712844\pi$
$510$	15441.1	−	25976.2i	1.34067	−	2.25538i
$511$	−519.239	+	899.348i	−0.0449506	+	0.0778568i
$512$	−227.927			−0.0196739
$513$	22713.5	+	866.884i	1.95483	+	0.0746079i
$514$	11174.6			0.958929
$515$	−8272.33	+	14328.1i	−0.707810	+	1.22596i
$516$	1904.98	−	3204.71i	0.162523	−	0.273410i
$517$	−987.080	−	1709.67i	−0.0839685	−	0.145438i
$518$	1445.29	+	2503.31i	0.122591	+	0.212334i
$519$	−7638.97	−	13628.4i	−0.646076	−	1.15264i
$520$	−2140.61	+	3707.64i	−0.180523	+	0.312674i
$521$	−1651.02			−0.138834			−0.0694170	−	0.997588i	$-0.522114\pi$
$521$	−1651.02			−0.138834			−0.0694170	+	0.997588i	$0.522114\pi$
$522$	3087.17	−	5046.27i	0.258854	−	0.423121i
$523$	20152.9			1.68494			0.842471	−	0.538742i	$-0.181100\pi$
$523$	20152.9			1.68494			0.842471	+	0.538742i	$0.181100\pi$
$524$	−2401.71	+	4159.88i	−0.200227	+	0.346804i
$525$	5654.31	+	71.9030i	0.470046	+	0.00597734i
$526$	−5794.99	−	10037.2i	−0.480368	−	0.832022i
$527$	10297.3	+	17835.5i	0.851155	+	1.47424i
$528$	3988.54	+	50.7202i	0.328748	+	0.00418052i
$529$	3481.20	−	6029.62i	0.286118	−	0.495572i
$530$	−7700.63			−0.631121
$531$	10992.1	−	17967.6i	0.898333	−	1.46841i
$532$	3520.42			0.286898
$533$	3168.94	−	5488.77i	0.257527	−	0.446050i
$534$	−10599.4	−	18910.0i	−0.858955	−	1.53243i
$535$	−14368.0	−	24886.1i	−1.16109	−	2.01106i
$536$	1108.87	+	1920.61i	0.0893578	+	0.154772i
$537$	−6567.93	+	11049.1i	−0.527797	+	0.887904i
$538$	−7713.10	+	13359.5i	−0.618096	+	1.07057i
$539$	−474.954			−0.0379550
$540$	3884.91	−	6172.55i	0.309592	−	0.491897i
$541$	−12019.3			−0.955174			−0.477587	−	0.878585i	$-0.658488\pi$
$541$	−12019.3			−0.955174			−0.477587	+	0.878585i	$0.658488\pi$
$542$	−5498.17	+	9523.11i	−0.435732	+	0.754710i
$543$	−1330.04	+	2237.50i	−0.105115	+	0.176833i
$544$	6950.56	+	12038.7i	0.547800	+	0.948817i
$545$	−8792.96	−	15229.9i	−0.691099	−	1.19702i
$546$	−928.624	−	1656.72i	−0.0727865	−	0.129856i
$547$	8156.69	−	14127.8i	0.637577	−	1.10432i	−0.348386	−	0.937351i	$-0.613270\pi$
$547$	8156.69	−	14127.8i	0.637577	−	1.10432i	0.985963	−	0.166965i	$-0.0533966\pi$
$548$	−63.8815			−0.00497971
$549$	2030.15	+	51.6411i	0.157823	+	0.00401455i
$550$	5021.49			0.389304
$551$	−5326.29	+	9225.41i	−0.411811	+	0.713277i
$552$	6115.21	+	77.7641i	0.471523	+	0.00599612i
$553$	3218.70	+	5574.96i	0.247510	+	0.428700i
$554$	10968.3	+	18997.6i	0.841150	+	1.45691i
$555$	−10782.8	−	137.119i	−0.824689	−	0.0104872i
$556$	183.941	−	318.595i	0.0140303	−	0.0243012i
$557$	−1307.87			−0.0994909			−0.0497455	−	0.998762i	$-0.515841\pi$
$557$	−1307.87			−0.0994909			−0.0497455	+	0.998762i	$0.515841\pi$
$558$	8495.83	+	15619.5i	0.644547	+	1.18499i
$559$	3621.81			0.274036
$560$	−4642.15	+	8040.44i	−0.350297	+	0.606733i
$561$	−2566.35	−	4578.53i	−0.193140	−	0.344573i
$562$	2989.65	+	5178.22i	0.224396	+	0.388666i
$563$	1674.91	+	2901.03i	0.125380	+	0.217165i	0.921882	−	0.387472i	$-0.126652\pi$
$563$	1674.91	+	2901.03i	0.125380	+	0.217165i	−0.796501	+	0.604637i	$0.793318\pi$
$564$	1678.60	−	2823.87i	0.125322	−	0.210827i
$565$	−2463.27	+	4266.51i	−0.183417	+	0.317688i
$566$	27560.2			2.04672
$567$	−2323.52	−	4543.33i	−0.172096	−	0.336512i
$568$	3699.30			0.273274
$569$	8218.38	−	14234.7i	0.605505	−	1.04877i	−0.386466	−	0.922304i	$-0.626304\pi$
$569$	8218.38	−	14234.7i	0.605505	−	1.04877i	0.991971	−	0.126462i	$-0.0403623\pi$
$570$	−24005.8	+	40384.5i	−1.76402	+	2.96758i
$571$	3797.00	+	6576.59i	0.278283	+	0.482000i	0.970958	−	0.239250i	$-0.0769015\pi$
$571$	3797.00	+	6576.59i	0.278283	+	0.482000i	−0.692675	+	0.721249i	$0.743568\pi$
$572$	−235.734	−	408.303i	−0.0172317	−	0.0298462i
$573$	−830.220	−	1481.16i	−0.0605287	−	0.107987i
$574$	4717.36	−	8170.72i	0.343030	−	0.594145i
$575$	11215.7			0.813441
$576$	−2439.26	−	4484.55i	−0.176451	−	0.324403i
$577$	−17732.2			−1.27938			−0.639689	−	0.768634i	$-0.720937\pi$
$577$	−17732.2			−1.27938			−0.639689	+	0.768634i	$0.720937\pi$
$578$	9908.65	−	17162.3i	0.713055	−	1.23505i
$579$	3812.62	+	48.4831i	0.273656	+	0.00347995i
$580$	1709.03	+	2960.13i	0.122351	+	0.211919i
$581$	−3380.58	−	5855.34i	−0.241394	−	0.418107i
$582$	−14382.9	−	182.901i	−1.02439	−	0.0130266i
$583$	−668.759	+	1158.32i	−0.0475080	+	0.0822863i
$584$	2420.31			0.171495
$585$	7083.02	+	180.171i	0.500593	+	0.0127336i
$586$	−13152.4			−0.927165
$587$	−2473.27	+	4283.83i	−0.173906	+	0.301214i	−0.939782	−	0.341774i	$-0.888972\pi$
$587$	−2473.27	+	4283.83i	−0.173906	+	0.301214i	0.765876	+	0.642988i	$0.222306\pi$
$588$	−386.439	−	689.432i	−0.0271029	−	0.0483532i
$589$	−16009.0	−	27728.4i	−1.11993	−	1.93978i
$590$	21767.7	+	37702.8i	1.51892	+	2.63085i
$591$	3339.01	−	5617.16i	0.232400	−	0.390963i
$592$	4907.09	−	8499.33i	0.340676	−	0.590068i
$593$	−3812.97			−0.264047			−0.132024	−	0.991247i	$-0.542147\pi$
$593$	−3812.97			−0.264047			−0.132024	+	0.991247i	$0.542147\pi$
$594$	−2114.44	−	4007.97i	−0.146055	−	0.276850i
$595$	12216.7			0.841741
$596$	−1388.34	+	2404.67i	−0.0954170	+	0.165267i
$597$	12627.5	−	21243.1i	0.865680	−	1.45632i
$598$	−1883.48	−	3262.28i	−0.128798	−	0.223085i
$599$	268.293	+	464.697i	0.0183007	+	0.0316978i	0.875031	−	0.484067i	$-0.160841\pi$
$599$	268.293	+	464.697i	0.0183007	+	0.0316978i	−0.856730	+	0.515765i	$0.827508\pi$
$600$	−6443.92	−	11496.4i	−0.438453	−	0.782228i
$601$	5518.20	−	9557.81i	0.374529	−	0.648704i	−0.615727	−	0.787960i	$-0.711138\pi$
$601$	5518.20	−	9557.81i	0.374529	−	0.648704i	0.990256	+	0.139255i	$0.0444709\pi$
$602$	5391.52			0.365020
$603$	1915.39	−	3130.88i	0.129354	−	0.211442i
$604$	−8459.15			−0.569864
$605$	−10358.5	+	17941.4i	−0.696086	+	1.20566i
$606$	3582.65	+	45.5588i	0.240157	+	0.00305396i
$607$	−5839.20	−	10113.8i	−0.390454	−	0.676287i	0.602055	−	0.798455i	$-0.294349\pi$
$607$	−5839.20	−	10113.8i	−0.390454	−	0.676287i	−0.992509	+	0.122168i	$0.961015\pi$
$608$	−10805.9	−	18716.3i	−0.720782	−	1.24843i
$609$	2391.36	+	30.4097i	0.159118	+	0.00202342i
$610$	−2098.73	+	3635.11i	−0.139304	+	0.241281i
$611$	3191.40			0.211310
$612$	4558.01	−	7450.51i	0.301057	−	0.492106i
$613$	12313.1			0.811291			0.405646	−	0.914030i	$-0.367047\pi$
$613$	12313.1			0.811291			0.405646	+	0.914030i	$0.367047\pi$
$614$	−7219.31	+	12504.2i	−0.474507	+	0.821871i
$615$	17209.7	+	30703.2i	1.12839	+	2.01312i
$616$	553.471	+	958.641i	0.0362013	+	0.0627025i
$617$	8406.85	+	14561.1i	0.548537	+	0.950094i	0.998375	+	0.0569836i	$0.0181483\pi$
$617$	8406.85	+	14561.1i	0.548537	+	0.950094i	−0.449838	+	0.893110i	$0.648518\pi$
$618$	−8740.55	+	14704.1i	−0.568926	+	0.957094i
$619$	−12914.9	+	22369.2i	−0.838599	+	1.45250i	0.0524669	+	0.998623i	$0.483292\pi$
$619$	−12914.9	+	22369.2i	−0.838599	+	1.45250i	−0.891066	+	0.453874i	$0.850042\pi$
$620$	−10273.5			−0.665476
$621$	−4722.71	−	8951.99i	−0.305178	−	0.578472i
$622$	−2971.03			−0.191523
$623$	4381.91	−	7589.70i	0.281794	−	0.488082i
$624$	−3294.92	+	5542.98i	−0.211382	+	0.355604i
$625$	5444.31	+	9429.83i	0.348436	+	0.603509i
$626$	−5916.41	−	10247.5i	−0.377743	−	0.654271i
$627$	3989.84	+	7118.12i	0.254129	+	0.453382i
$628$	4997.44	−	8655.81i	0.317547	−	0.550007i
$629$	−12914.0			−0.818622
$630$	10544.0	+	268.208i	0.666796	+	0.0169614i
$631$	−20126.5			−1.26977			−0.634885	−	0.772607i	$-0.718952\pi$
$631$	−20126.5			−1.26977			−0.634885	+	0.772607i	$0.718952\pi$
$632$	7501.61	−	12993.2i	0.472149	−	0.817786i
$633$	5580.84	+	70.9687i	0.350424	+	0.00445617i
$634$	−6508.90	−	11273.7i	−0.407731	−	0.706210i
$635$	−12485.2	−	21625.1i	−0.780255	−	1.35144i
$636$	−2225.52	−	28.3008i	−0.138754	−	0.00176447i
$637$	383.903	−	664.939i	0.0238788	−	0.0413593i
$638$	2123.72			0.131785
$639$	−2925.32	−	5378.17i	−0.181101	−	0.332953i
$640$	28423.2			1.75551
$641$	1434.82	−	2485.19i	0.0884121	−	0.153134i	−0.818428	−	0.574609i	$-0.805154\pi$
$641$	1434.82	−	2485.19i	0.0884121	−	0.153134i	0.906840	+	0.421475i	$0.138487\pi$
$642$	−14526.9	−	25916.9i	−0.893038	−	1.59324i
$643$	5473.05	+	9479.60i	0.335670	+	0.581398i	0.983613	−	0.180291i	$-0.0577039\pi$
$643$	5473.05	+	9479.60i	0.335670	+	0.581398i	−0.647943	+	0.761689i	$0.724371\pi$
$644$	−783.795	−	1357.57i	−0.0479594	−	0.0830681i
$645$	−10277.5	+	17289.7i	−0.627408	+	1.05548i
$646$	−28130.9	+	48724.2i	−1.71331	+	2.96753i
$647$	5124.07			0.311357			0.155679	−	0.987808i	$-0.450244\pi$
$647$	5124.07			0.311357			0.155679	+	0.987808i	$0.450244\pi$
$648$	−6462.57	+	9984.17i	−0.391780	+	0.605270i
$649$	7561.65			0.457351
$650$	−4058.84	+	7030.12i	−0.244924	+	0.424222i
$651$	−3672.95	+	6178.94i	−0.221128	+	0.371999i
$652$	171.315	+	296.727i	0.0102902	+	0.0178232i
$653$	1389.98	+	2407.52i	0.0832990	+	0.144278i	0.904665	−	0.426123i	$-0.140121\pi$
$653$	1389.98	+	2407.52i	0.0832990	+	0.144278i	−0.821366	+	0.570401i	$0.806788\pi$
$654$	−8890.21	−	15860.7i	−0.531552	−	0.948321i
$655$	12957.4	−	22442.9i	0.772960	−	1.33881i
$656$	−32033.2			−1.90653
$657$	−1913.92	−	3518.72i	−0.113652	−	0.208947i
$658$	4750.80			0.281468
$659$	976.058	−	1690.58i	0.0576962	−	0.0999328i	−0.835735	−	0.549133i	$-0.814958\pi$
$659$	976.058	−	1690.58i	0.0576962	−	0.0999328i	0.893431	+	0.449201i	$0.148291\pi$
$660$	2618.08	+	33.2929i	0.154407	+	0.00196352i
$661$	−4447.09	−	7702.58i	−0.261682	−	0.453246i	0.705007	−	0.709200i	$-0.250944\pi$
$661$	−4447.09	−	7702.58i	−0.261682	−	0.453246i	−0.966689	+	0.255954i	$0.917610\pi$
$662$	−6184.68	−	10712.2i	−0.363103	−	0.628913i
$663$	8484.34	+	107.891i	0.496990	+	0.00631997i
$664$	−7878.89	+	13646.6i	−0.460482	+	0.797578i
$665$	−18993.0			−1.10754
$666$	−11145.7	−	283.515i	−0.648481	−	0.0164955i
$667$	4743.44			0.275362
$668$	−3381.77	+	5857.40i	−0.195875	+	0.339266i
$669$	−2332.28	−	4160.94i	−0.134785	−	0.240465i
$670$	3793.07	+	6569.78i	0.218715	+	0.378825i
$671$	364.528	+	631.380i	0.0209723	+	0.0363251i
$672$	−2479.19	+	4170.70i	−0.142317	+	0.239417i
$673$	7548.45	−	13074.3i	0.432349	−	0.748851i	−0.564726	−	0.825279i	$-0.691018\pi$
$673$	7548.45	−	13074.3i	0.432349	−	0.748851i	0.997075	+	0.0764274i	$0.0243514\pi$
$674$	4321.75			0.246984
$675$	−11618.1	+	18459.4i	−0.662489	+	1.05260i
$676$	−6057.62			−0.344653
$677$	8158.89	−	14131.6i	0.463178	−	0.802248i	−0.535939	−	0.844257i	$-0.680042\pi$
$677$	8158.89	−	14131.6i	0.463178	−	0.802248i	0.999117	+	0.0420086i	$0.0133757\pi$
$678$	−2602.70	+	4378.46i	−0.147428	+	0.248015i
$679$	−2907.55	−	5036.02i	−0.164332	−	0.284631i
$680$	−14236.3	−	24658.0i	−0.802849	−	1.39058i
$681$	−2511.60	−	4480.85i	−0.141329	−	0.252139i
$682$	−3191.59	+	5527.99i	−0.179197	+	0.310378i
$683$	13408.8			0.751207			0.375603	−	0.926781i	$-0.377436\pi$
$683$	13408.8			0.751207			0.375603	+	0.926781i	$0.377436\pi$
$684$	−7086.22	+	11583.1i	−0.396123	+	0.647502i
$685$	344.646			0.0192237
$686$	571.487	−	989.845i	0.0318068	−	0.0550910i
$687$	32877.6	+	418.088i	1.82585	+	0.0232184i
$688$	−9152.76	−	15853.0i	−0.507189	−	0.878476i
$689$	−1081.11	−	1872.53i	−0.0597778	−	0.103538i
$690$	20918.1	+	266.005i	1.15411	+	0.0146763i
$691$	−7770.34	+	13458.6i	−0.427782	+	0.740941i	−0.996676	−	0.0814705i	$-0.974038\pi$
$691$	−7770.34	+	13458.6i	−0.427782	+	0.740941i	0.568893	+	0.822411i	$0.307372\pi$
$692$	9333.22			0.512711
$693$	956.031	−	1562.72i	0.0524049	−	0.0856609i
$694$	41307.6			2.25939
$695$	−992.379	+	1718.85i	−0.0541627	+	0.0938126i
$696$	−2725.31	−	4862.12i	−0.148423	−	0.264796i
$697$	21075.4	+	36503.6i	1.14532	+	1.98375i
$698$	−16153.0	−	27977.8i	−0.875932	−	1.51716i
$699$	5673.82	−	9544.96i	0.307015	−	0.516486i
$700$	−1689.06	+	2925.53i	−0.0912004	+	0.157964i
$701$	−4623.00			−0.249085			−0.124542	−	0.992214i	$-0.539746\pi$
$701$	−4623.00			−0.249085			−0.124542	+	0.992214i	$0.539746\pi$
$702$	7320.27	+	279.385i	0.393570	+	0.0150210i
$703$	20077.0			1.07712
$704$	916.345	−	1587.16i	0.0490569	−	0.0849691i
$705$	−9056.18	+	15235.0i	−0.483795	+	0.813879i
$706$	−8192.88	−	14190.5i	−0.436747	−	0.756468i
$707$	724.241	+	1254.42i	0.0385260	+	0.0667290i
$708$	6152.43	+	10976.3i	0.326585	+	0.582649i
$709$	−6188.65	+	10719.1i	−0.327813	+	0.567789i	−0.982078	−	0.188477i	$-0.939645\pi$
$709$	−6188.65	+	10719.1i	−0.327813	+	0.567789i	0.654264	+	0.756266i	$0.272978\pi$
$710$	12654.1			0.668873
$711$	−24822.0	−	631.399i	−1.30928	−	0.0333042i
$712$	−20425.2			−1.07510
$713$	−7128.56	+	12347.0i	−0.374427	+	0.648527i
$714$	12630.0	+	160.609i	0.661997	+	0.00841828i
$715$	1271.81	+	2202.83i	0.0665214	+	0.115219i
$716$	−3839.38	−	6650.00i	−0.200397	−	0.347098i
$717$	−6583.42	−	83.7180i	−0.342904	−	0.00436054i
$718$	15481.4	−	26814.5i	0.804679	−	1.39374i
$719$	−8518.11			−0.441824			−0.220912	−	0.975294i	$-0.570903\pi$
$719$	−8518.11			−0.441824			−0.220912	+	0.975294i	$0.570903\pi$
$720$	−17111.0	−	31458.4i	−0.885680	−	1.62831i
$721$	−6915.38			−0.357201
$722$	32306.3	−	55956.2i	1.66526	−	2.88431i
$723$	−6746.52	−	12036.2i	−0.347034	−	0.619130i
$724$	−777.493	−	1346.66i	−0.0399106	−	0.0691272i
$725$	−5110.98	−	8852.48i	−0.261817	−	0.453480i
$726$	−10944.8	+	18412.2i	−0.559503	+	0.941241i
$727$	−5421.50	+	9390.32i	−0.276578	+	0.479048i	−0.970532	−	0.240972i	$-0.922534\pi$
$727$	−5421.50	+	9390.32i	−0.276578	+	0.479048i	0.693954	+	0.720020i	$0.255867\pi$
$728$	−1789.47			−0.0911019
$729$	19625.7	+	1500.26i	0.997091	+	0.0762209i
$730$	8279.07			0.419756
$731$	−12043.6	+	20860.2i	−0.609370	+	1.05546i
$732$	−619.904	+	1042.85i	−0.0313010	+	0.0526570i
$733$	−321.879	−	557.511i	−0.0162195	−	0.0280930i	0.857802	−	0.513981i	$-0.171830\pi$
$733$	−321.879	−	557.511i	−0.0162195	−	0.0280930i	−0.874021	+	0.485888i	$0.838496\pi$
$734$	−2031.36	−	3518.42i	−0.102151	−	0.176931i
$735$	2084.88	+	3719.55i	0.104628	+	0.186663i
$736$	−4811.69	+	8334.09i	−0.240980	+	0.417389i
$737$	1317.63			0.0658556
$738$	17388.3	+	31968.1i	0.867304	+	1.59453i
$739$	−28541.8			−1.42074			−0.710370	−	0.703829i	$-0.751472\pi$
$739$	−28541.8			−1.42074			−0.710370	+	0.703829i	$0.751472\pi$
$740$	3221.03	−	5578.98i	0.160010	−	0.277145i
$741$	−13190.4	−	167.735i	−0.653928	−	0.00831567i
$742$	−1609.36	−	2787.50i	−0.0796248	−	0.137914i
$743$	7799.67	+	13509.4i	0.385117	+	0.667042i	0.991785	−	0.127913i	$-0.0408277\pi$
$743$	7799.67	+	13509.4i	0.385117	+	0.667042i	−0.606668	+	0.794955i	$0.707494\pi$
$744$	16751.6	+	213.022i	0.825463	+	0.0104970i
$745$	7490.21	−	12973.4i	0.368349	−	0.637999i
$746$	38895.6			1.90894
$747$	26070.3	+	663.154i	1.27693	+	0.0324813i
$748$	3135.54			0.153271
$749$	6005.56	−	10401.9i	0.292975	−	0.507448i
$750$	−4319.54	−	7706.34i	−0.210303	−	0.375194i
$751$	−1291.64	−	2237.18i	−0.0627597	−	0.108703i	0.832938	−	0.553366i	$-0.186657\pi$
$751$	−1291.64	−	2237.18i	−0.0627597	−	0.108703i	−0.895698	+	0.444663i	$0.853324\pi$
$752$	−8065.06	−	13969.1i	−0.391094	−	0.677394i
$753$	−7882.64	+	13260.8i	−0.381486	+	0.641767i
$754$	−1716.59	+	2973.22i	−0.0829106	+	0.143605i
$755$	45637.9			2.19991
$756$	3046.27	+	116.264i	0.146550	+	0.00559322i
$757$	−25493.1			−1.22399			−0.611996	−	0.790861i	$-0.709633\pi$
$757$	−25493.1			−1.22399			−0.611996	+	0.790861i	$0.709633\pi$
$758$	1280.55	−	2217.98i	0.0613612	−	0.106281i
$759$	1856.64	−	3123.39i	0.0887902	−	0.149370i
$760$	22132.8	+	38335.2i	1.05637	+	1.82969i
$761$	18391.0	+	31854.1i	0.876047	+	1.51736i	0.855643	+	0.517567i	$0.173162\pi$
$761$	18391.0	+	31854.1i	0.876047	+	1.51736i	0.0204046	+	0.999792i	$0.493505\pi$
$762$	−12623.3	−	22520.8i	−0.600125	−	1.07066i
$763$	3675.30	−	6365.81i	0.174384	−	0.302042i
$764$	1014.36			0.0480342
$765$	−24590.9	+	40196.2i	−1.16220	+	1.89973i
$766$	−6255.26			−0.295055
$767$	−6112.04	+	10586.4i	−0.287735	+	0.498372i
$768$	21525.7	+	273.731i	1.01138	+	0.0128612i
$769$	−1374.74	−	2381.12i	−0.0644660	−	0.111658i	0.831991	−	0.554789i	$-0.187201\pi$
$769$	−1374.74	−	2381.12i	−0.0644660	−	0.111658i	−0.896457	+	0.443131i	$0.853868\pi$
$770$	1893.24	+	3279.19i	0.0886074	+	0.153473i
$771$	−17423.5	−	221.566i	−0.813868	−	0.0103496i
$772$	−1138.91	+	1972.64i	−0.0530960	+	0.0919649i
$773$	−35039.4			−1.63037			−0.815187	−	0.579197i	$-0.803366\pi$
$773$	−35039.4			−1.63037			−0.815187	+	0.579197i	$0.803366\pi$
$774$	−10852.5	+	17739.5i	−0.503988	+	0.823817i
$775$	30723.7			1.42404
$776$	−6776.42	+	11737.1i	−0.313478	+	0.542961i
$777$	−2203.87	−	3931.84i	−0.101755	−	0.181536i
$778$	20525.2	+	35550.6i	0.945839	+	1.63824i
$779$	−32765.3	−	56751.2i	−1.50698	−	2.61017i
$780$	−2162.79	+	3638.42i	−0.0992825	+	0.167021i
$781$	1098.94	−	1903.42i	0.0503498	−	0.0872084i
$782$	25052.5			1.14562
$783$	−4913.59	+	7806.98i	−0.224262	+	0.356320i
$784$	−3880.67			−0.176780
$785$	−26961.6	+	46698.9i	−1.22586	+	2.12325i
$786$	13690.8	−	23031.8i	0.621293	−	1.04519i
$787$	3517.14	+	6091.86i	0.159304	+	0.275923i	0.934618	−	0.355653i	$-0.115742\pi$
$787$	3517.14	+	6091.86i	0.159304	+	0.275923i	−0.775314	+	0.631576i	$0.782408\pi$
$788$	1951.87	+	3380.74i	0.0882392	+	0.152835i
$789$	8836.59	+	15765.0i	0.398721	+	0.711343i
$790$	25660.5	−	44445.3i	1.15565	−	2.00164i
$791$	−2059.21			−0.0925626
$792$	−4268.26	−	108.572i	−0.191497	−	0.00487114i
$793$	−1178.58			−0.0527777
$794$	20194.0	−	34977.0i	0.902592	−	1.56334i
$795$	12006.9	+	152.686i	0.535649	+	0.00681157i
$796$	7381.62	+	12785.3i	0.328687	+	0.569302i
$797$	7875.88	+	13641.4i	0.350035	+	0.606279i	0.986255	−	0.165229i	$-0.0528363\pi$
$797$	7875.88	+	13641.4i	0.350035	+	0.606279i	−0.636220	+	0.771508i	$0.719503\pi$
$798$	−19635.5	−	249.695i	−0.871040	−	0.0110766i
$799$	−10612.4	+	18381.2i	−0.469886	+	0.813867i
$800$	20738.1			0.916502
$801$	16151.8	+	29694.9i	0.712478	+	1.30988i
$802$	10981.1			0.483485
$803$	718.993	−	1245.33i	0.0315974	−	0.0547283i
$804$	1072.07	+	1912.64i	0.0470262	+	0.0838976i
$805$	4228.65	+	7324.23i	0.185143	+	0.320677i
$806$	−5159.48	−	8936.49i	−0.225478	−	0.390539i
$807$	12291.2	−	20677.3i	0.536148	−	0.901952i
$808$	1687.94	−	2923.60i	0.0734920	−	0.127292i
$809$	−25900.6			−1.12561			−0.562804	−	0.826590i	$-0.690278\pi$
$809$	−25900.6			−1.12561			−0.562804	+	0.826590i	$0.690278\pi$
$810$	−22106.3	+	34152.5i	−0.958934	+	1.48148i
$811$	33424.4			1.44721			0.723606	−	0.690213i	$-0.242483\pi$
$811$	33424.4			1.44721			0.723606	+	0.690213i	$0.242483\pi$
$812$	−714.346	+	1237.28i	−0.0308727	+	0.0534731i
$813$	8761.62	−	14739.5i	0.377962	−	0.635839i
$814$	−2001.30	−	3466.35i	−0.0861737	−	0.149257i
$815$	−924.262	−	1600.87i	−0.0397245	−	0.0688049i
$816$	−20968.7	−	37409.5i	−0.899573	−	1.60489i
$817$	18723.9	−	32430.8i	0.801795	−	1.38875i
$818$	−16278.7			−0.695810
$819$	1415.07	+	2601.59i	0.0603743	+	0.110997i
$820$	−21026.6			−0.895466
$821$	−14006.2	+	24259.4i	−0.595395	+	1.03125i	0.398096	+	0.917344i	$0.369671\pi$
$821$	−14006.2	+	24259.4i	−0.595395	+	1.03125i	−0.993491	+	0.113911i	$0.963662\pi$
$822$	356.306	+	4.53096i	0.0151187	+	0.000192257i
$823$	−18421.5	−	31907.0i	−0.780236	−	1.35141i	−0.931804	−	0.362962i	$-0.881765\pi$
$823$	−18421.5	−	31907.0i	−0.780236	−	1.35141i	0.151567	−	0.988447i	$-0.451568\pi$
$824$	8058.59	+	13957.9i	0.340697	+	0.590105i
$825$	−7829.56	−	99.5645i	−0.330412	−	0.00420169i
$826$	−9098.54	+	15759.1i	−0.383267	+	0.663838i
$827$	14254.5			0.599370			0.299685	−	0.954038i	$-0.403118\pi$
$827$	14254.5			0.599370			0.299685	+	0.954038i	$0.403118\pi$
$828$	6044.47	+	153.754i	0.253695	+	0.00645327i
$829$	33286.0			1.39454			0.697268	−	0.716810i	$-0.254399\pi$
$829$	33286.0			1.39454			0.697268	+	0.716810i	$0.254399\pi$
$830$	−26951.1	+	46680.6i	−1.12709	+	1.95218i
$831$	−16725.1	−	29838.7i	−0.698182	−	1.24560i
$832$	1481.35	+	2565.78i	0.0617268	+	0.106914i
$833$	2553.18	+	4422.24i	0.106198	+	0.183940i
$834$	−1048.55	+	1763.95i	−0.0435351	+	0.0732383i
$835$	18245.0	−	31601.2i	0.756160	−	1.30971i
$836$	−4874.75			−0.201671
$837$	−12937.1	−	24522.5i	−0.534254	−	1.01269i
$838$	−22715.6			−0.936394
$839$	−14302.2	+	24772.2i	−0.588519	+	1.01935i	0.405907	+	0.913914i	$0.366956\pi$
$839$	−14302.2	+	24772.2i	−0.588519	+	1.01935i	−0.994427	+	0.105431i	$0.966378\pi$
$840$	5077.95	−	8542.53i	0.208578	−	0.350887i
$841$	10032.9	+	17377.5i	0.411371	+	0.712516i
$842$	17263.5	+	29901.2i	0.706577	+	1.22383i
$843$	−4558.81	−	8133.21i	−0.186256	−	0.332292i
$844$	−1667.11	+	2887.52i	−0.0679908	+	0.117764i
$845$	32681.4			1.33050
$846$	−9562.85	+	15631.4i	−0.388626	+	0.635246i
$847$	−8659.33			−0.351285
$848$	−5464.18	+	9464.24i	−0.221274	+	0.383259i
$849$	−42972.2	−	546.456i	−1.73710	−	0.0220899i
$850$	−26993.7	−	46754.5i	−1.08927	−	1.88667i
$851$	−4469.99	−	7742.25i	−0.180058	−	0.311869i
$852$	3657.10	+	46.5055i	0.147054	+	0.00187001i
$853$	11270.1	−	19520.4i	0.452382	−	0.783548i	−0.546152	−	0.837686i	$-0.683908\pi$
$853$	11270.1	−	19520.4i	0.452382	−	0.783548i	0.998533	+	0.0541382i	$0.0172411\pi$
$854$	−1754.47			−0.0703005
$855$	38230.8	−	62491.9i	1.52920	−	2.49962i
$856$	−27993.5			−1.11776
$857$	−455.074	+	788.211i	−0.0181389	+	0.0314175i	−0.874952	−	0.484209i	$-0.839107\pi$
$857$	−455.074	+	788.211i	−0.0181389	+	0.0314175i	0.856813	+	0.515626i	$0.172441\pi$
$858$	1285.87	+	2294.07i	0.0511642	+	0.0912802i
$859$	3316.35	+	5744.09i	0.131726	+	0.228156i	0.924342	−	0.381565i	$-0.124615\pi$
$859$	3316.35	+	5744.09i	0.131726	+	0.228156i	−0.792616	+	0.609721i	$0.791281\pi$
$860$	−6007.89	−	10406.0i	−0.238218	−	0.412605i
$861$	−7517.36	+	12646.3i	−0.297551	+	0.500564i
$862$	6322.93	−	10951.6i	0.249837	−	0.432731i
$863$	3998.07			0.157701			0.0788505	−	0.996886i	$-0.474875\pi$
$863$	3998.07			0.157701			0.0788505	+	0.996886i	$0.474875\pi$
$864$	−8732.36	−	16552.4i	−0.343843	−	0.651762i
$865$	−50353.6			−1.97927
$866$	4674.93	−	8097.21i	0.183442	−	0.317730i
$867$	−15789.9	+	26563.1i	−0.618518	+	1.04052i
$868$	−2147.08	−	3718.85i	−0.0839592	−	0.145422i
$869$	−4456.96	−	7719.68i	−0.173984	−	0.301349i
$870$	−9322.37	−	16631.7i	−0.363285	−	0.648123i
$871$	−1065.03	+	1844.69i	−0.0414320	+	0.0717624i
$872$	−17131.6			−0.665307
$873$	22422.4	+	570.361i	0.869282	+	0.0221120i
$874$	−38948.5			−1.50738
$875$	1785.74	−	3093.00i	0.0689934	−	0.119500i
$876$	2392.69	+	30.4267i	0.0922849	+	0.00117354i
$877$	11305.7	+	19582.1i	0.435310	+	0.753980i	0.997321	−	0.0731503i	$-0.0233053\pi$
$877$	11305.7	+	19582.1i	0.435310	+	0.753980i	−0.562010	+	0.827130i	$0.689972\pi$
$878$	7442.22	+	12890.3i	0.286062	+	0.495475i
$879$	20507.3	+	260.781i	0.786909	+	0.0100067i
$880$	6428.01	−	11133.6i	0.246237	−	0.426494i
$881$	16433.0			0.628424			0.314212	−	0.949353i	$-0.398260\pi$
$881$	16433.0			0.628424			0.314212	+	0.949353i	$0.398260\pi$
$882$	2106.51	+	3872.79i	0.0804193	+	0.147850i
$883$	−22842.8			−0.870581			−0.435290	−	0.900290i	$-0.643354\pi$
$883$	−22842.8			−0.870581			−0.435290	+	0.900290i	$0.643354\pi$
$884$	−2534.44	+	4389.78i	−0.0964282	+	0.167018i
$885$	−33192.9	−	59218.2i	−1.26075	−	2.24926i
$886$	−3810.70	−	6600.32i	−0.144495	−	0.250273i
$887$	−16505.6	−	28588.6i	−0.624808	−	1.08220i	−0.988578	−	0.150710i	$-0.951844\pi$
$887$	−16505.6	−	28588.6i	−0.624808	−	1.08220i	0.363770	−	0.931489i	$-0.381489\pi$
$888$	−5367.76	+	9030.08i	−0.202849	+	0.341250i
$889$	5218.62	−	9038.91i	0.196880	−	0.341007i
$890$	−69868.0			−2.63144
$891$	3217.39	+	6291.18i	0.120973	+	0.236546i
$892$	2849.56			0.106962
$893$	16498.8	−	28576.7i	0.618265	−	1.07087i
$894$	7914.16	−	13313.8i	0.296073	−	0.498078i
$895$	20713.8	+	35877.4i	0.773616	+	1.33994i
$896$	5940.19	+	10288.7i	0.221482	+	0.383618i
$897$	2872.06	+	5123.93i	0.106907	+	0.190728i
$898$	13871.0	−	24025.3i	0.515459	−	0.892801i
$899$	12993.9			0.482057
$900$	−6225.88	−	11446.2i	−0.230588	−	0.423933i
$901$	14380.0			0.531708
$902$	−6532.16	+	11314.0i	−0.241128	+	0.417646i
$903$	−8406.51	−	106.901i	−0.309802	−	0.00393960i
$904$	2399.63	+	4156.28i	0.0882859	+	0.152916i
$905$	4194.64	+	7265.33i	0.154071	+	0.266860i
$906$	47181.9	+	599.988i	1.73015	+	0.0220014i
$907$	−4835.17	+	8374.77i	−0.177011	+	0.306593i	−0.940856	−	0.338808i	$-0.889976\pi$
$907$	−4835.17	+	8374.77i	−0.177011	+	0.306593i	0.763844	+	0.645401i	$0.223310\pi$
$908$	3068.65			0.112155
$909$	−5585.20	−	142.071i	−0.203795	−	0.00518395i
$910$	−6121.18			−0.222984
$911$	−1779.97	+	3083.00i	−0.0647343	+	0.112123i	−0.896576	−	0.442890i	$-0.853953\pi$
$911$	−1779.97	+	3083.00i	−0.0647343	+	0.112123i	0.831842	+	0.555013i	$0.187287\pi$
$912$	32599.5	+	58159.5i	1.18364	+	2.11168i
$913$	4681.11	+	8107.92i	0.169685	+	0.293903i
$914$	−866.375	−	1500.61i	−0.0313535	−	0.0543059i
$915$	3344.44	−	5626.28i	0.120835	−	0.203278i
$916$	−9821.21	+	17010.8i	−0.354260	+	0.613596i
$917$	10832.0			0.390080
$918$	−25951.2	+	41232.7i	−0.933027	+	1.48244i
$919$	2983.64			0.107096			0.0535480	−	0.998565i	$-0.482947\pi$
$919$	2983.64			0.107096			0.0535480	+	0.998565i	$0.482947\pi$
$920$	9855.41	−	17070.1i	0.353178	−	0.611721i
$921$	11504.3	−	19353.5i	0.411597	−	0.692422i
$922$	−25967.0	−	44976.2i	−0.927525	−	1.60652i
$923$	1776.53	+	3077.05i	0.0633536	+	0.109732i
$924$	535.105	+	954.661i	0.0190516	+	0.0339892i
$925$	−9632.69	+	16684.3i	−0.342401	+	0.593056i
$926$	−13653.6			−0.484543
$927$	13919.9	−	22753.4i	0.493192	−	0.806170i
$928$	8770.68			0.310250
$929$	−2241.31	+	3882.07i	−0.0791551	+	0.137101i	−0.902886	−	0.429881i	$-0.858556\pi$
$929$	−2241.31	+	3882.07i	−0.0791551	+	0.137101i	0.823731	+	0.566982i	$0.191889\pi$
$930$	57301.7	+	728.677i	2.02043	+	0.0256928i
$931$	−3969.37	−	6875.15i	−0.139732	−	0.242024i
$932$	3316.72	+	5744.72i	0.116569	+	0.201904i
$933$	4632.45	+	58.9085i	0.162550	+	0.00206707i
$934$	−28460.0	+	49294.2i	−0.997046	+	1.72693i
$935$	−16916.5			−0.591690
$936$	3602.01	−	5887.83i	0.125786	−	0.205609i
$937$	−45232.3			−1.57703			−0.788513	−	0.615018i	$-0.789149\pi$
$937$	−45232.3			−1.57703			−0.788513	+	0.615018i	$0.789149\pi$
$938$	−1585.44	+	2746.06i	−0.0551880	+	0.0955884i
$939$	9021.73	+	16095.3i	0.313539	+	0.559373i
$940$	−5293.92	−	9169.35i	−0.183690	−	0.318161i
$941$	403.230	+	698.415i	0.0139691	+	0.0241952i	0.872925	−	0.487854i	$-0.162220\pi$
$941$	403.230	+	698.415i	0.0139691	+	0.0241952i	−0.858956	+	0.512049i	$0.828887\pi$
$942$	−28487.7	+	47924.3i	−0.985328	+	1.65760i
$943$	−14589.9	+	25270.5i	−0.503831	+	0.872661i
$944$	61783.5			2.13017
$945$	−16434.9	−	627.254i	−0.565744	−	0.0215921i
$946$	−7465.68			−0.256586
$947$	18745.9	−	32468.9i	0.643253	−	1.11415i	−0.341449	−	0.939900i	$-0.610918\pi$
$947$	18745.9	−	32468.9i	0.643253	−	1.11415i	0.984702	−	0.174247i	$-0.0557490\pi$
$948$	7579.36	−	12750.6i	0.259669	−	0.436836i
$949$	1162.32	+	2013.19i	0.0397580	+	0.0688629i
$950$	41966.5	+	72688.1i	1.43323	+	2.48243i
$951$	9925.20	+	17707.2i	0.338430	+	0.603780i
$952$	5950.53	−	10306.6i	0.202582	−	0.350882i
$953$	14269.6			0.485034			0.242517	−	0.970147i	$-0.422027\pi$
$953$	14269.6			0.485034			0.242517	+	0.970147i	$0.422027\pi$
$954$	12411.1	+	315.702i	0.421199	+	0.0107141i
$955$	−5472.54			−0.185432
$956$	1966.60	−	3406.25i	0.0665318	−	0.115236i
$957$	−3311.33	−	42.1085i	−0.111850	−	0.00142233i
$958$	−13060.4	−	22621.2i	−0.440460	−	0.762900i
$959$	72.0281	+	124.756i	0.00242535	+	0.00420083i
$960$	−16452.1	−	209.213i	−0.553112	−	0.00703365i
$961$	−4632.02	+	8022.90i	−0.155484	+	0.269306i
$962$	6470.54			0.216859
$963$	22136.6	+	40697.8i	0.740749	+	1.36186i
$964$	8242.83			0.275398
$965$	6144.50	−	10642.6i	0.204972	−	0.355023i
$966$	4275.41	+	7627.60i	0.142401	+	0.254052i
$967$	6337.03	+	10976.1i	0.210739	+	0.365011i	0.951946	−	0.306265i	$-0.0990795\pi$
$967$	6337.03	+	10976.1i	0.210739	+	0.365011i	−0.741207	+	0.671277i	$0.765746\pi$
$968$	10090.8	+	17477.9i	0.335054	+	0.580330i
$969$	44828.1	−	75413.4i	1.48616	−	2.50013i
$970$	−23179.9	+	40148.7i	−0.767279	+	1.32897i
$971$	30453.3			1.00648			0.503240	−	0.864146i	$-0.332141\pi$
$971$	30453.3			1.00648			0.503240	+	0.864146i	$0.332141\pi$
$972$	−6514.35	+	9789.01i	−0.214967	+	0.323027i
$973$	−829.594			−0.0273336
$974$	−21861.4	+	37865.0i	−0.719182	+	1.24566i
$975$	6467.97	−	10881.0i	0.212452	−	0.357404i
$976$	2978.42	+	5158.77i	0.0976812	+	0.169189i
$977$	−1748.78	−	3028.97i	−0.0572655	−	0.0991868i	0.835971	−	0.548773i	$-0.184905\pi$
$977$	−1748.78	−	3028.97i	−0.0572655	−	0.0991868i	−0.893237	+	0.449586i	$0.851571\pi$
$978$	−934.484	−	1667.18i	−0.0305537	−	0.0545097i
$979$	−6067.66	+	10509.5i	−0.198083	+	0.343090i
$980$	−2547.28			−0.0830306
$981$	13547.2	+	24906.4i	0.440906	+	0.810602i
$982$	60444.5			1.96422
$983$	−10160.0	+	17597.7i	−0.329659	+	0.570986i	−0.982444	−	0.186557i	$-0.940267\pi$
$983$	−10160.0	+	17597.7i	−0.329659	+	0.570986i	0.652785	+	0.757543i	$0.273601\pi$
$984$	34285.2	+	435.988i	1.11075	+	0.0141248i
$985$	−10530.5	−	18239.4i	−0.340640	−	0.590005i
$986$	−11416.4	−	19773.7i	−0.368734	−	0.638665i
$987$	−7407.50	−	94.1974i	−0.238889	−	0.00303783i
$988$	3940.23	−	6824.68i	0.126878	−	0.219759i
$989$	−16674.9			−0.536130
$990$	−14600.3	−	371.389i	−0.468715	−	0.0119227i
$991$	−13949.7			−0.447151			−0.223576	−	0.974687i	$-0.571773\pi$
$991$	−13949.7			−0.447151			−0.223576	+	0.974687i	$0.571773\pi$
$992$	−13180.8	+	22829.9i	−0.421866	+	0.730694i
$993$	9430.81	+	16825.2i	0.301387	+	0.537694i
$994$	2644.59	+	4580.57i	0.0843878	+	0.146164i
$995$	−39824.5	−	68978.1i	−1.26887	−	2.19774i
$996$	−7960.55	+	13391.9i	−0.253253	+	0.426042i
$997$	−23245.4	+	40262.2i	−0.738404	+	1.27895i	0.214809	+	0.976656i	$0.431087\pi$
$997$	−23245.4	+	40262.2i	−0.738404	+	1.27895i	−0.953213	+	0.302298i	$0.902246\pi$
$998$	−1157.59			−0.0367162
$999$	17372.9	+	663.054i	0.550205	+	0.0209991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.c.43.7	yes	18
3.2	odd	2		189.4.f.c.127.3		18
9.2	odd	6		567.4.a.k.1.7		9
9.4	even	3	inner	63.4.f.c.22.7	✓	18
9.5	odd	6		189.4.f.c.64.3		18
9.7	even	3		567.4.a.j.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.c.22.7	✓	18	9.4	even	3	inner
63.4.f.c.43.7	yes	18	1.1	even	1	trivial
189.4.f.c.64.3		18	9.5	odd	6
189.4.f.c.127.3		18	3.2	odd	2
567.4.a.j.1.3		9	9.7	even	3
567.4.a.k.1.7		9	9.2	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.66614 - 2.88585i) q^{2} +(-2.65509 + 4.46660i) q^{3} +(-1.55207 - 2.68826i) q^{4} +(8.37356 + 14.5034i) q^{5} +(8.46616 + 15.1042i) q^{6} +(-3.50000 + 6.06218i) q^{7} +16.3144 q^{8} +(-12.9010 - 23.7184i) q^{9} +O(q^{10})\)	\(q+(1.66614 - 2.88585i) q^{2} +(-2.65509 + 4.46660i) q^{3} +(-1.55207 - 2.68826i) q^{4} +(8.37356 + 14.5034i) q^{5} +(8.46616 + 15.1042i) q^{6} +(-3.50000 + 6.06218i) q^{7} +16.3144 q^{8} +(-12.9010 - 23.7184i) q^{9} +55.8062 q^{10} +(4.84647 - 8.39434i) q^{11} +(16.1283 + 0.205095i) q^{12} +(7.83475 + 13.5702i) q^{13} +(11.6630 + 20.2009i) q^{14} +(-87.0135 - 1.10651i) q^{15} +(39.5987 - 68.5870i) q^{16} -104.212 q^{17} +(-89.9427 - 2.28788i) q^{18} +162.015 q^{19} +(25.9927 - 45.0206i) q^{20} +(-17.7845 - 31.7287i) q^{21} +(-16.1498 - 27.9723i) q^{22} +(-36.0714 - 62.4776i) q^{23} +(-43.3162 + 72.8700i) q^{24} +(-77.7329 + 134.637i) q^{25} +52.2153 q^{26} +(140.194 + 5.35064i) q^{27} +21.7290 q^{28} +(-32.8753 + 56.9417i) q^{29} +(-148.170 + 249.264i) q^{30} +(-98.8118 - 171.147i) q^{31} +(-66.6966 - 115.522i) q^{32} +(24.6263 + 43.9349i) q^{33} +(-173.631 + 300.739i) q^{34} -117.230 q^{35} +(-43.7380 + 71.4940i) q^{36} +123.920 q^{37} +(269.940 - 467.550i) q^{38} +(-81.4145 - 1.03531i) q^{39} +(136.610 + 236.615i) q^{40} +(-202.236 - 350.283i) q^{41} +(-121.196 - 1.54118i) q^{42} +(115.569 - 200.171i) q^{43} -30.0882 q^{44} +(235.971 - 385.717i) q^{45} -240.401 q^{46} +(101.835 - 176.383i) q^{47} +(201.213 + 358.976i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(259.028 + 448.650i) q^{50} +(276.691 - 465.472i) q^{51} +(24.3202 - 42.1237i) q^{52} -137.989 q^{53} +(249.025 - 395.663i) q^{54} +162.329 q^{55} +(-57.1005 + 98.9009i) q^{56} +(-430.164 + 723.657i) q^{57} +(109.550 + 189.746i) q^{58} +(390.060 + 675.603i) q^{59} +(132.076 + 235.633i) q^{60} +(-37.6075 + 65.1381i) q^{61} -658.538 q^{62} +(188.939 + 4.80606i) q^{63} +189.075 q^{64} +(-131.209 + 227.261i) q^{65} +(167.820 + 2.13409i) q^{66} +(67.9686 + 117.725i) q^{67} +(161.744 + 280.148i) q^{68} +(374.835 + 4.76659i) q^{69} +(-195.322 + 338.307i) q^{70} +226.751 q^{71} +(-210.473 - 386.952i) q^{72} +148.354 q^{73} +(206.469 - 357.615i) q^{74} +(-394.983 - 704.675i) q^{75} +(-251.459 - 435.539i) q^{76} +(33.9253 + 58.7603i) q^{77} +(-138.636 + 233.225i) q^{78} +(459.815 - 796.423i) q^{79} +1326.33 q^{80} +(-396.126 + 611.984i) q^{81} -1347.82 q^{82} +(-482.940 + 836.477i) q^{83} +(-57.6923 + 97.0546i) q^{84} +(-872.622 - 1511.42i) q^{85} +(-385.109 - 667.028i) q^{86} +(-167.049 - 298.026i) q^{87} +(79.0674 - 136.949i) q^{88} -1251.98 q^{89} +(-719.958 - 1323.63i) q^{90} -109.686 q^{91} +(-111.971 + 193.939i) q^{92} +(1026.80 + 13.0573i) q^{93} +(-339.343 - 587.760i) q^{94} +(1356.64 + 2349.77i) q^{95} +(693.076 + 8.81350i) q^{96} +(-415.364 + 719.431i) q^{97} -163.282 q^{98} +(-261.625 - 6.65498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Introduction

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