LMFDB - Embedded newform 63.4.f.b.43.8

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 $ x^16 - 3x^15 + 58x^14 - 129x^13 + 2107x^12 - 4455x^11 + 42901x^10 - 76404x^9 + 599392x^8 - 1089732x^7 + 4808401x^6 - 7939134x^5 + 26225236x^4 - 39450864x^3 + 62254768x^2 - 39660672*x + 21307456
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.8
Root			$-2.47591 + 4.28840i$ of defining polynomial
Character	$\chi$	$=$	63.43
Dual form			63.4.f.b.22.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47591 - 4.28840i) q^{2} +(-2.38464 + 4.61665i) q^{3} +(-8.26023 - 14.3071i) q^{4} +(-8.06998 - 13.9776i) q^{5} +(13.8939 + 21.6567i) q^{6} +(3.50000 - 6.06218i) q^{7} -42.1917 q^{8} +(-15.6270 - 22.0181i) q^{9} +O(q^{10})$	\(q+(2.47591 - 4.28840i) q^{2} +(-2.38464 + 4.61665i) q^{3} +(-8.26023 - 14.3071i) q^{4} +(-8.06998 - 13.9776i) q^{5} +(13.8939 + 21.6567i) q^{6} +(3.50000 - 6.06218i) q^{7} -42.1917 q^{8} +(-15.6270 - 22.0181i) q^{9} -79.9221 q^{10} +(15.3185 - 26.5325i) q^{11} +(85.7487 - 4.01718i) q^{12} +(39.0059 + 67.5603i) q^{13} +(-17.3313 - 30.0188i) q^{14} +(83.7738 - 3.92466i) q^{15} +(-38.3809 + 66.4776i) q^{16} +106.992 q^{17} +(-133.113 + 12.4997i) q^{18} -49.5081 q^{19} +(-133.320 + 230.917i) q^{20} +(19.6407 + 30.6144i) q^{21} +(-75.8546 - 131.384i) q^{22} +(-19.5071 - 33.7873i) q^{23} +(100.612 - 194.784i) q^{24} +(-67.7492 + 117.345i) q^{25} +386.300 q^{26} +(138.915 - 19.6388i) q^{27} -115.643 q^{28} +(-2.87388 + 4.97771i) q^{29} +(190.586 - 368.972i) q^{30} +(-92.2467 - 159.776i) q^{31} +(21.2881 + 36.8720i) q^{32} +(85.9620 + 133.991i) q^{33} +(264.901 - 458.822i) q^{34} -112.980 q^{35} +(-185.934 + 405.452i) q^{36} +91.0901 q^{37} +(-122.578 + 212.310i) q^{38} +(-404.917 + 18.9697i) q^{39} +(340.486 + 589.739i) q^{40} +(41.4346 + 71.7668i) q^{41} +(179.915 - 8.42872i) q^{42} +(45.6371 - 79.0458i) q^{43} -506.139 q^{44} +(-181.652 + 396.113i) q^{45} -193.191 q^{46} +(-118.982 + 206.083i) q^{47} +(-215.379 - 335.716i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(335.481 + 581.070i) q^{50} +(-255.137 + 493.943i) q^{51} +(644.396 - 1116.13i) q^{52} +497.669 q^{53} +(259.721 - 644.345i) q^{54} -494.481 q^{55} +(-147.671 + 255.773i) q^{56} +(118.059 - 228.562i) q^{57} +(14.2309 + 24.6487i) q^{58} +(2.10297 + 3.64245i) q^{59} +(-748.141 - 1166.14i) q^{60} +(-313.196 + 542.471i) q^{61} -913.577 q^{62} +(-188.172 + 17.6699i) q^{63} -403.264 q^{64} +(629.554 - 1090.42i) q^{65} +(787.440 - 36.8902i) q^{66} +(339.310 + 587.702i) q^{67} +(-883.775 - 1530.74i) q^{68} +(202.502 - 9.48685i) q^{69} +(-279.727 + 484.502i) q^{70} +747.071 q^{71} +(659.327 + 928.982i) q^{72} -23.2628 q^{73} +(225.531 - 390.630i) q^{74} +(-380.183 - 592.600i) q^{75} +(408.948 + 708.319i) q^{76} +(-107.230 - 185.728i) q^{77} +(-921.188 + 1783.41i) q^{78} +(-77.0203 + 133.403i) q^{79} +1238.93 q^{80} +(-240.597 + 688.153i) q^{81} +410.353 q^{82} +(-141.098 + 244.389i) q^{83} +(275.768 - 533.884i) q^{84} +(-863.420 - 1495.49i) q^{85} +(-225.986 - 391.420i) q^{86} +(-16.1272 - 25.1378i) q^{87} +(-646.315 + 1119.45i) q^{88} +111.091 q^{89} +(1248.94 + 1759.74i) q^{90} +546.083 q^{91} +(-322.266 + 558.181i) q^{92} +(957.605 - 44.8622i) q^{93} +(589.177 + 1020.48i) q^{94} +(399.530 + 692.006i) q^{95} +(-220.990 + 10.3530i) q^{96} +(-555.045 + 961.367i) q^{97} -242.639 q^{98} +(-823.578 + 77.3362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * 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 $

$2$	2.47591	−	4.28840i	0.875365	−	1.51618i	0.0189918	−	0.999820i	$-0.493954\pi$
$2$	2.47591	−	4.28840i	0.875365	−	1.51618i	0.856373	−	0.516357i	$-0.172712\pi$
$3$	−2.38464	+	4.61665i	−0.458925	+	0.888475i
$3$	−2.38464	+	4.61665i	−0.458925	+	0.888475i
$4$	−8.26023	−	14.3071i	−1.03253	−	1.78839i
$5$	−8.06998	−	13.9776i	−0.721801	−	1.25020i	−0.960277	−	0.279048i	$-0.909981\pi$
$5$	−8.06998	−	13.9776i	−0.721801	−	1.25020i	0.238476	−	0.971148i	$-0.423352\pi$
$6$	13.8939	+	21.6567i	0.945359	+	1.47355i
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i
$8$	−42.1917			−1.86463
$9$	−15.6270	−	22.0181i	−0.578776	−	0.815487i
$10$	−79.9221			−2.52736
$11$	15.3185	−	26.5325i	0.419883	−	0.727259i	−0.576044	−	0.817419i	$-0.695404\pi$
$11$	15.3185	−	26.5325i	0.419883	−	0.727259i	0.995927	+	0.0901595i	$0.0287377\pi$
$12$	85.7487	−	4.01718i	2.06279	−	0.0966383i
$13$	39.0059	+	67.5603i	0.832177	+	1.44137i	0.896308	+	0.443431i	$0.146239\pi$
$13$	39.0059	+	67.5603i	0.832177	+	1.44137i	−0.0641315	+	0.997941i	$0.520428\pi$
$14$	−17.3313	−	30.0188i	−0.330857	−	0.573061i
$15$	83.7738	−	3.92466i	1.44202	−	0.0675562i
$16$	−38.3809	+	66.4776i	−0.599701	+	1.03871i
$17$	106.992			1.52643			0.763214	−	0.646146i	$-0.223620\pi$
$17$	106.992			1.52643			0.763214	+	0.646146i	$0.223620\pi$
$18$	−133.113	+	12.4997i	−1.74306	+	0.163678i
$19$	−49.5081			−0.597787			−0.298893	−	0.954287i	$-0.596617\pi$
$19$	−49.5081			−0.597787			−0.298893	+	0.954287i	$0.596617\pi$
$20$	−133.320	+	230.917i	−1.49056	+	2.58173i
$21$	19.6407	+	30.6144i	0.204093	+	0.318124i
$22$	−75.8546	−	131.384i	−0.735102	−	1.27323i
$23$	−19.5071	−	33.7873i	−0.176848	−	0.306310i	0.763951	−	0.645274i	$-0.223257\pi$
$23$	−19.5071	−	33.7873i	−0.176848	−	0.306310i	−0.940799	+	0.338964i	$0.889924\pi$
$24$	100.612	−	194.784i	0.855723	−	1.65667i
$25$	−67.7492	+	117.345i	−0.541993	+	0.938760i
$26$	386.300			2.91383
$27$	138.915	−	19.6388i	0.990154	−	0.139981i
$28$	−115.643			−0.780518
$29$	−2.87388	+	4.97771i	−0.0184023	+	0.0318737i	−0.875080	−	0.483978i	$-0.839191\pi$
$29$	−2.87388	+	4.97771i	−0.0184023	+	0.0318737i	0.856678	+	0.515852i	$0.172525\pi$
$30$	190.586	−	368.972i	1.15987	−	2.24549i
$31$	−92.2467	−	159.776i	−0.534451	−	0.925697i	−0.999190	−	0.0402489i	$-0.987185\pi$
$31$	−92.2467	−	159.776i	−0.534451	−	0.925697i	0.464738	−	0.885448i	$-0.346148\pi$
$32$	21.2881	+	36.8720i	0.117601	+	0.203691i
$33$	85.9620	+	133.991i	0.453457	+	0.706813i
$34$	264.901	−	458.822i	1.33618	−	2.31434i
$35$	−112.980			−0.545630
$36$	−185.934	+	405.452i	−0.860807	+	1.87709i
$37$	91.0901			0.404733			0.202366	−	0.979310i	$-0.435137\pi$
$37$	91.0901			0.404733			0.202366	+	0.979310i	$0.435137\pi$
$38$	−122.578	+	212.310i	−0.523282	+	0.906350i
$39$	−404.917	+	18.9697i	−1.66253	+	0.0778867i
$40$	340.486	+	589.739i	1.34589	+	2.33115i
$41$	41.4346	+	71.7668i	0.157829	+	0.273368i	0.934086	−	0.357049i	$-0.116217\pi$
$41$	41.4346	+	71.7668i	0.157829	+	0.273368i	−0.776256	+	0.630417i	$0.782884\pi$
$42$	179.915	−	8.42872i	0.660989	−	0.0309662i
$43$	45.6371	−	79.0458i	0.161851	−	0.280334i	−0.773682	−	0.633575i	$-0.781587\pi$
$43$	45.6371	−	79.0458i	0.161851	−	0.280334i	0.935533	+	0.353241i	$0.114920\pi$
$44$	−506.139			−1.73417
$45$	−181.652	+	396.113i	−0.601757	+	1.31220i
$46$	−193.191			−0.619227
$47$	−118.982	+	206.083i	−0.369262	+	0.639580i	−0.989450	−	0.144872i	$-0.953723\pi$
$47$	−118.982	+	206.083i	−0.369262	+	0.639580i	0.620188	+	0.784453i	$0.287056\pi$
$48$	−215.379	−	335.716i	−0.647652	−	1.00951i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	335.481	+	581.070i	0.948884	+	1.64352i
$51$	−255.137	+	493.943i	−0.700516	+	1.35619i
$52$	644.396	−	1116.13i	1.71849	−	2.97652i
$53$	497.669			1.28981			0.644906	−	0.764262i	$-0.276896\pi$
$53$	497.669			1.28981			0.644906	+	0.764262i	$0.276896\pi$
$54$	259.721	−	644.345i	0.654511	−	1.62378i
$55$	−494.481			−1.21229
$56$	−147.671	+	255.773i	−0.352381	+	0.610342i
$57$	118.059	−	228.562i	0.274339	−	0.531118i
$58$	14.2309	+	24.6487i	0.0322174	+	0.0558022i
$59$	2.10297	+	3.64245i	0.00464039	+	0.00803740i	0.868336	−	0.495976i	$-0.165190\pi$
$59$	2.10297	+	3.64245i	0.00464039	+	0.00803740i	−0.863696	+	0.504013i	$0.831856\pi$
$60$	−748.141	−	1166.14i	−1.60974	−	2.50914i
$61$	−313.196	+	542.471i	−0.657387	+	1.13863i	0.323903	+	0.946090i	$0.395005\pi$
$61$	−313.196	+	542.471i	−0.657387	+	1.13863i	−0.981290	+	0.192537i	$0.938328\pi$
$62$	−913.577			−1.87136
$63$	−188.172	+	17.6699i	−0.376309	+	0.0353364i
$64$	−403.264			−0.787626
$65$	629.554	−	1090.42i	1.20133	−	2.08077i
$66$	787.440	−	36.8902i	1.46859	−	0.0688011i
$67$	339.310	+	587.702i	0.618706	+	1.07163i	0.989722	+	0.143004i	$0.0456763\pi$
$67$	339.310	+	587.702i	0.618706	+	1.07163i	−0.371016	+	0.928627i	$0.620990\pi$
$68$	−883.775	−	1530.74i	−1.57608	−	2.72985i
$69$	202.502	−	9.48685i	0.353309	−	0.0165519i
$70$	−279.727	+	484.502i	−0.477626	+	0.827272i
$71$	747.071			1.24875			0.624374	−	0.781126i	$-0.285354\pi$
$71$	747.071			1.24875			0.624374	+	0.781126i	$0.285354\pi$
$72$	659.327	+	928.982i	1.07920	+	1.52058i
$73$	−23.2628			−0.0372974			−0.0186487	−	0.999826i	$-0.505936\pi$
$73$	−23.2628			−0.0372974			−0.0186487	+	0.999826i	$0.505936\pi$
$74$	225.531	−	390.630i	0.354289	−	0.613647i
$75$	−380.183	−	592.600i	−0.585331	−	0.912368i
$76$	408.948	+	708.319i	0.617232	+	1.06908i
$77$	−107.230	−	185.728i	−0.158701	−	0.274878i
$78$	−921.188	+	1783.41i	−1.33723	+	2.58887i
$79$	−77.0203	+	133.403i	−0.109689	+	0.189987i	−0.915644	−	0.401989i	$-0.868319\pi$
$79$	−77.0203	+	133.403i	−0.109689	+	0.189987i	0.805955	+	0.591977i	$0.201652\pi$
$80$	1238.93			1.73146
$81$	−240.597	+	688.153i	−0.330037	+	0.943968i
$82$	410.353			0.552633
$83$	−141.098	+	244.389i	−0.186597	+	0.323195i	−0.944113	−	0.329621i	$-0.893079\pi$
$83$	−141.098	+	244.389i	−0.186597	+	0.323195i	0.757517	+	0.652816i	$0.226412\pi$
$84$	275.768	−	533.884i	0.358199	−	0.693471i
$85$	−863.420	−	1495.49i	−1.10178	−	1.90833i
$86$	−225.986	−	391.420i	−0.283357	−	0.490790i
$87$	−16.1272	−	25.1378i	−0.0198737	−	0.0309776i
$88$	−646.315	+	1119.45i	−0.782925	+	1.35607i
$89$	111.091			0.132311			0.0661554	−	0.997809i	$-0.478927\pi$
$89$	111.091			0.132311			0.0661554	+	0.997809i	$0.478927\pi$
$90$	1248.94	+	1759.74i	1.46277	+	2.06103i
$91$	546.083			0.629067
$92$	−322.266	+	558.181i	−0.365202	+	0.632548i
$93$	957.605	−	44.8622i	1.06773	−	0.0500214i
$94$	589.177	+	1020.48i	0.646478	+	1.11973i
$95$	399.530	+	692.006i	0.431483	+	0.747350i
$96$	−220.990	+	10.3530i	−0.234945	+	0.0110067i
$97$	−555.045	+	961.367i	−0.580993	+	1.00631i	0.414369	+	0.910109i	$0.364002\pi$
$97$	−555.045	+	961.367i	−0.580993	+	1.00631i	−0.995362	+	0.0962003i	$0.969331\pi$
$98$	−242.639			−0.250104
$99$	−823.578	+	77.3362i	−0.836088	+	0.0785109i
$100$	2238.49			2.23849
$101$	699.163	−	1210.99i	0.688805	−	1.19305i	−0.283419	−	0.958996i	$-0.591469\pi$
$101$	699.163	−	1210.99i	0.688805	−	1.19305i	0.972225	−	0.234050i	$-0.0751978\pi$
$102$	1486.53	+	2317.09i	1.44302	+	2.24927i
$103$	−723.877	−	1253.79i	−0.692483	−	1.19942i	−0.971022	−	0.238991i	$-0.923183\pi$
$103$	−723.877	−	1253.79i	−0.692483	−	1.19942i	0.278539	−	0.960425i	$-0.410150\pi$
$104$	−1645.73	−	2850.48i	−1.55170	−	2.68762i
$105$	269.416	−	521.588i	0.250403	−	0.484779i
$106$	1232.18	−	2134.20i	1.12906	−	1.95558i
$107$	−1063.28			−0.960664			−0.480332	−	0.877087i	$-0.659484\pi$
$107$	−1063.28			−0.960664			−0.480332	+	0.877087i	$0.659484\pi$
$108$	−1428.44	−	1825.25i	−1.27270	−	1.62625i
$109$	1933.34			1.69890			0.849450	−	0.527669i	$-0.176934\pi$
$109$	1933.34			1.69890			0.849450	+	0.527669i	$0.176934\pi$
$110$	−1224.29	+	2120.53i	−1.06120	+	1.83804i
$111$	−217.217	+	420.531i	−0.185742	+	0.359595i
$112$	268.666	+	465.343i	0.226666	+	0.392596i
$113$	−770.314	−	1334.22i	−0.641284	−	1.11074i	−0.985146	−	0.171716i	$-0.945069\pi$
$113$	−770.314	−	1334.22i	−0.641284	−	1.11074i	0.343863	−	0.939020i	$-0.388264\pi$
$114$	−687.860	−	1072.18i	−0.565123	−	0.880869i
$115$	−314.844	+	545.325i	−0.255298	+	0.442190i
$116$	94.9556			0.0760035
$117$	878.007	−	1914.60i	0.693776	−	1.51286i
$118$	20.8270			0.0162482
$119$	374.471	−	648.602i	0.288468	−	0.499641i
$120$	−3534.56	+	165.588i	−2.68883	+	0.125967i
$121$	196.184	+	339.801i	0.147396	+	0.255298i
$122$	1550.89	+	2686.21i	1.15091	+	1.99343i
$123$	−430.129	+	20.1508i	−0.315313	+	0.0147719i
$124$	−1523.96	+	2639.57i	−1.10367	+	1.91162i
$125$	169.442			0.121243
$126$	−390.121	+	850.706i	−0.275832	+	0.601483i
$127$	1471.23			1.02796			0.513980	−	0.857802i	$-0.328171\pi$
$127$	1471.23			1.02796			0.513980	+	0.857802i	$0.328171\pi$
$128$	−1168.75	+	2024.33i	−0.807061	+	1.39787i
$129$	256.099	+	399.187i	0.174792	+	0.272453i
$130$	−3117.43	−	5399.56i	−2.10321	−	3.64286i
$131$	−339.376	−	587.816i	−0.226347	−	0.392044i	0.730376	−	0.683045i	$-0.239345\pi$
$131$	−339.376	−	587.816i	−0.226347	−	0.392044i	−0.956723	+	0.291001i	$0.906012\pi$
$132$	1206.96	−	2336.67i	0.795851	−	1.54076i
$133$	−173.278	+	300.127i	−0.112971	+	0.195672i
$134$	3360.40			2.16638
$135$	−1395.54	−	1783.21i	−0.889698	−	1.13685i
$136$	−4514.16			−2.84622
$137$	−909.980	+	1576.13i	−0.567480	+	0.982905i	0.429334	+	0.903146i	$0.358748\pi$
$137$	−909.980	+	1576.13i	−0.567480	+	0.982905i	−0.996814	+	0.0797591i	$0.974585\pi$
$138$	460.691	−	891.895i	0.284179	−	0.550168i
$139$	1459.34	+	2527.65i	0.890499	+	1.54239i	0.839279	+	0.543702i	$0.182978\pi$
$139$	1459.34	+	2527.65i	0.890499	+	1.54239i	0.0512202	+	0.998687i	$0.483689\pi$
$140$	933.238	+	1616.42i	0.563379	+	0.975800i
$141$	−667.683	−	1040.73i	−0.398788	−	0.621599i
$142$	1849.68	−	3203.74i	1.09311	−	1.89332i
$143$	2390.06			1.39767
$144$	2063.49	−	193.767i	1.19415	−	0.112134i
$145$	92.7686			0.0531311
$146$	−57.5966	+	99.7602i	−0.0326488	+	0.0565494i
$147$	254.333	−	11.9150i	0.142701	−	0.00668528i
$148$	−752.425	−	1303.24i	−0.417898	−	0.723821i
$149$	492.243	+	852.590i	0.270645	+	0.468771i	0.969027	−	0.246954i	$-0.0794297\pi$
$149$	492.243	+	852.590i	0.270645	+	0.468771i	−0.698382	+	0.715725i	$0.746096\pi$
$150$	−3482.60	+	163.154i	−1.89569	+	0.0888098i
$151$	64.9327	−	112.467i	0.0349943	−	0.0606120i	−0.847998	−	0.530000i	$-0.822192\pi$
$151$	64.9327	−	112.467i	0.0349943	−	0.0606120i	0.882992	+	0.469388i	$0.155525\pi$
$152$	2088.83			1.11465
$153$	−1671.95	−	2355.76i	−0.883460	−	1.24478i
$154$	−1061.96			−0.555685
$155$	−1488.86	+	2578.78i	−0.771535	+	1.33634i
$156$	3616.11	+	5636.51i	1.85590	+	2.89283i
$157$	108.515	+	187.954i	0.0551621	+	0.0955436i	0.892288	−	0.451467i	$-0.149099\pi$
$157$	108.515	+	187.954i	0.0551621	+	0.0955436i	−0.837126	+	0.547011i	$0.815766\pi$
$158$	381.390	+	660.587i	0.192036	+	0.332617i
$159$	−1186.76	+	2297.56i	−0.591927	+	1.14597i
$160$	343.589	−	595.113i	0.169769	−	0.294049i
$161$	−273.099			−0.133685
$162$	2355.38	+	2735.58i	1.14232	+	1.32671i
$163$	40.7178			0.0195660			0.00978302	−	0.999952i	$-0.496886\pi$
$163$	40.7178			0.0195660			0.00978302	+	0.999952i	$0.496886\pi$
$164$	684.518	−	1185.62i	0.325926	−	0.564521i
$165$	1179.16	−	2282.85i	0.556349	−	1.07709i
$166$	698.691	+	1210.17i	0.326680	+	0.565827i
$167$	−862.994	−	1494.75i	−0.399883	−	0.692618i	0.593828	−	0.804592i	$-0.297616\pi$
$167$	−862.994	−	1494.75i	−0.399883	−	0.692618i	−0.993711	+	0.111974i	$0.964283\pi$
$168$	−828.675	−	1291.67i	−0.380557	−	0.593183i
$169$	−1944.43	+	3367.84i	−0.885037	+	1.53293i
$170$	−8550.99			−3.85783
$171$	773.661	+	1090.08i	0.345984	+	0.487487i
$172$	−1507.89			−0.668463
$173$	291.438	−	504.786i	0.128079	−	0.221839i	−0.794853	−	0.606802i	$-0.792452\pi$
$173$	291.438	−	504.786i	0.128079	−	0.221839i	0.922932	+	0.384962i	$0.125786\pi$
$174$	−147.730	+	6.92090i	−0.0643643	+	0.00301535i
$175$	474.244	+	821.415i	0.204854	+	0.354818i
$176$	1175.88	+	2036.68i	0.503609	+	0.872276i
$177$	−21.8307	+	1.02273i	−0.00927062	+	0.000434313i
$178$	275.052	−	476.404i	0.115820	−	0.200607i
$179$	−3699.88			−1.54493			−0.772465	−	0.635058i	$-0.780976\pi$
$179$	−3699.88			−1.54493			−0.772465	+	0.635058i	$0.780976\pi$
$180$	7167.73	−	673.069i	2.96806	−	0.278709i
$181$	2872.98			1.17982			0.589908	−	0.807470i	$-0.299164\pi$
$181$	2872.98			1.17982			0.589908	+	0.807470i	$0.299164\pi$
$182$	1352.05	−	2341.82i	0.550663	−	0.953776i
$183$	−1757.54	−	2739.52i	−0.709951	−	1.10662i
$184$	823.037	+	1425.54i	0.329756	+	0.571154i
$185$	−735.095	−	1273.22i	−0.292137	−	0.505995i
$186$	2178.55	−	4217.67i	0.858814	−	1.66266i
$187$	1638.96	−	2838.76i	0.640922	−	1.11011i
$188$	3931.27			1.52509
$189$	367.148	−	910.862i	0.141302	−	0.350558i
$190$	3956.79			1.51082
$191$	136.646	−	236.678i	0.0517663	−	0.0896619i	−0.838981	−	0.544161i	$-0.816848\pi$
$191$	136.646	−	236.678i	0.0517663	−	0.0896619i	0.890747	+	0.454499i	$0.150182\pi$
$192$	961.642	−	1861.73i	0.361461	−	0.699786i
$193$	−422.139	−	731.166i	−0.157442	−	0.272697i	0.776504	−	0.630113i	$-0.216991\pi$
$193$	−422.139	−	731.166i	−0.157442	−	0.272697i	−0.933945	+	0.357416i	$0.883658\pi$
$194$	2748.48	+	4760.51i	1.01716	+	1.76178i
$195$	3532.83	+	5506.70i	1.29739	+	2.02227i
$196$	−404.751	+	701.049i	−0.147504	+	0.255484i
$197$	2506.77			0.906600			0.453300	−	0.891358i	$-0.350247\pi$
$197$	2506.77			0.906600			0.453300	+	0.891358i	$0.350247\pi$
$198$	−1707.45	+	3723.31i	−0.612846	+	1.33638i
$199$	−3938.12			−1.40284			−0.701421	−	0.712747i	$-0.747451\pi$
$199$	−3938.12			−1.40284			−0.701421	+	0.712747i	$0.747451\pi$
$200$	2858.45	−	4950.98i	1.01061	−	1.75044i
$201$	−3522.35	+	165.016i	−1.23606	+	0.0579071i
$202$	−3462.13	−	5996.58i	−1.20591	−	2.08870i
$203$	20.1172	+	34.8439i	0.00695541	+	0.0120471i
$204$	9174.40	−	429.805i	3.14871	−	0.147512i
$205$	668.753	−	1158.31i	0.227843	−	0.394635i
$206$	−7169.01			−2.42470
$207$	−439.096	+	957.502i	−0.147436	+	0.321502i
$208$	−5988.32			−1.99623
$209$	−758.393	+	1313.57i	−0.251001	+	0.434746i
$210$	−1569.73	−	2446.77i	−0.515816	−	0.804014i
$211$	33.4253	+	57.8944i	0.0109057	+	0.0188892i	0.871427	−	0.490526i	$-0.163195\pi$
$211$	33.4253	+	57.8944i	0.0109057	+	0.0188892i	−0.860521	+	0.509415i	$0.829862\pi$
$212$	−4110.86	−	7120.21i	−1.33177	−	2.30669i
$213$	−1781.50	+	3448.97i	−0.573081	+	1.10948i
$214$	−2632.58	+	4559.76i	−0.840931	+	1.45654i
$215$	−1473.16			−0.467297
$216$	−5861.05	+	828.593i	−1.84627	+	0.261012i
$217$	−1291.45			−0.404007
$218$	4786.76	−	8290.92i	1.48716	−	2.57583i
$219$	55.4735	−	107.396i	0.0171167	−	0.0331378i
$220$	4084.53	+	7074.61i	1.25172	+	2.16805i
$221$	4173.31	+	7228.38i	1.27026	+	2.20015i
$222$	1265.59	+	1972.71i	0.382618	+	0.596395i
$223$	−1243.80	+	2154.33i	−0.373502	+	0.646925i	−0.990102	−	0.140352i	$-0.955177\pi$
$223$	−1243.80	+	2154.33i	−0.373502	+	0.646925i	0.616599	+	0.787277i	$0.288510\pi$
$224$	298.033			0.0888981
$225$	3642.43	−	342.034i	1.07924	−	0.101343i
$226$	−7628.90			−2.24543
$227$	−1923.36	+	3331.36i	−0.562370	+	0.974054i	0.434919	+	0.900470i	$0.356777\pi$
$227$	−1923.36	+	3331.36i	−0.562370	+	0.974054i	−0.997289	+	0.0735843i	$0.976556\pi$
$228$	−4245.26	+	198.883i	−1.23311	+	0.0577691i
$229$	2005.94	+	3474.40i	0.578849	+	1.00260i	0.995612	+	0.0935809i	$0.0298314\pi$
$229$	2005.94	+	3474.40i	0.578849	+	1.00260i	−0.416762	+	0.909015i	$0.636835\pi$
$230$	1559.05	+	2700.35i	0.446959	+	0.774155i
$231$	1113.14	−	52.1489i	0.317054	−	0.0148534i
$232$	121.254	−	210.018i	0.0343134	−	0.0594325i
$233$	5724.20			1.60946			0.804732	−	0.593639i	$-0.202309\pi$
$233$	5724.20			1.60946			0.804732	+	0.593639i	$0.202309\pi$
$234$	−6036.69	−	8505.61i	−1.68646	−	2.37619i
$235$	3840.73			1.06613
$236$	34.7420	−	60.1749i	0.00958267	−	0.0165977i
$237$	−432.209	−	673.694i	−0.118460	−	0.184646i
$238$	−1854.31	−	3211.76i	−0.505029	−	0.874737i
$239$	−3059.79	−	5299.71i	−0.828122	−	1.43435i	−0.899510	−	0.436901i	$-0.856076\pi$
$239$	−3059.79	−	5299.71i	−0.828122	−	1.43435i	0.0713879	−	0.997449i	$-0.477257\pi$
$240$	−2954.41	+	5719.71i	−0.794609	+	1.53836i
$241$	−246.401	+	426.780i	−0.0658594	+	0.114072i	−0.897075	−	0.441879i	$-0.854312\pi$
$241$	−246.401	+	426.780i	−0.0658594	+	0.114072i	0.831216	+	0.555950i	$0.187646\pi$
$242$	1942.94			0.516102
$243$	−2603.22	−	2751.75i	−0.687230	−	0.726440i
$244$	10348.3			2.71508
$245$	−395.429	+	684.903i	−0.103114	+	0.178599i
$246$	−978.545	+	1894.46i	−0.253617	+	0.491000i
$247$	−1931.11	−	3344.78i	−0.497464	−	0.861633i
$248$	3892.04	+	6741.22i	0.996552	+	1.72608i
$249$	−791.790	−	1234.18i	−0.201517	−	0.314109i
$250$	419.523	−	726.636i	0.106132	−	0.183826i
$251$	−1859.25			−0.467548			−0.233774	−	0.972291i	$-0.575108\pi$
$251$	−1859.25			−0.467548			−0.233774	+	0.972291i	$0.575108\pi$
$252$	1807.15	+	2546.25i	0.451745	+	0.636502i
$253$	−1195.28			−0.297022
$254$	3642.63	−	6309.23i	0.899840	−	1.55857i
$255$	8963.10	−	419.906i	2.20114	−	0.103120i
$256$	4174.37	+	7230.23i	1.01913	+	1.76519i
$257$	−1885.96	−	3266.57i	−0.457753	−	0.792852i	0.541088	−	0.840966i	$-0.318012\pi$
$257$	−1885.96	−	3266.57i	−0.457753	−	0.792852i	−0.998842	+	0.0481134i	$0.984679\pi$
$258$	2345.95	−	109.904i	0.566094	−	0.0265205i
$259$	318.815	−	552.204i	0.0764873	−	0.132480i
$260$	−20801.0			−4.96164
$261$	154.510	−	14.5089i	0.0366434	−	0.00344091i
$262$	−3361.05			−0.792544
$263$	−20.3689	+	35.2800i	−0.00477568	+	0.00827171i	−0.868403	−	0.495858i	$-0.834853\pi$
$263$	−20.3689	+	35.2800i	−0.00477568	+	0.00827171i	0.863628	+	0.504130i	$0.168187\pi$
$264$	−3626.88	−	5653.30i	−0.845527	−	1.31794i
$265$	−4016.18	−	6956.22i	−0.930988	−	1.61252i
$266$	858.043	+	1486.17i	0.197782	+	0.342568i
$267$	−264.913	+	512.871i	−0.0607208	+	0.117555i
$268$	5605.56	−	9709.11i	1.27766	−	2.21298i
$269$	1404.08			0.318247			0.159124	−	0.987259i	$-0.449133\pi$
$269$	1404.08			0.318247			0.159124	+	0.987259i	$0.449133\pi$
$270$	−11102.4	+	1569.57i	−2.50247	+	0.353782i
$271$	−222.681			−0.0499148			−0.0249574	−	0.999689i	$-0.507945\pi$
$271$	−222.681			−0.0499148			−0.0249574	+	0.999689i	$0.507945\pi$
$272$	−4106.43	+	7112.55i	−0.915400	+	1.58552i
$273$	−1302.21	+	2521.08i	−0.288694	+	0.558910i
$274$	4506.05	+	7804.71i	0.993505	+	1.72080i
$275$	2075.64	+	3595.11i	0.455148	+	0.788339i
$276$	−1808.44	−	2818.85i	−0.394403	−	0.614764i
$277$	2889.62	−	5004.98i	0.626789	−	1.08563i	−0.361403	−	0.932410i	$-0.617702\pi$
$277$	2889.62	−	5004.98i	0.626789	−	1.08563i	0.988192	−	0.153221i	$-0.0489647\pi$
$278$	14452.7			3.11805
$279$	−2076.43	+	4527.91i	−0.445566	+	0.971609i
$280$	4766.80			1.01740
$281$	−1885.10	+	3265.09i	−0.400198	+	0.693162i	−0.993749	−	0.111633i	$-0.964392\pi$
$281$	−1885.10	+	3265.09i	−0.400198	+	0.693162i	0.593552	+	0.804796i	$0.297725\pi$
$282$	−6116.20	+	286.533i	−1.29154	+	0.0605064i
$283$	2402.06	+	4160.49i	0.504549	+	0.873905i	0.999986	+	0.00526120i	$0.00167470\pi$
$283$	2402.06	+	4160.49i	0.504549	+	0.873905i	−0.495437	+	0.868644i	$0.664992\pi$
$284$	−6170.98	−	10688.4i	−1.28937	−	2.23325i
$285$	−4147.49	+	194.303i	−0.862020	+	0.0403842i
$286$	5917.56	−	10249.5i	1.22347	−	2.11911i
$287$	580.084			0.119308
$288$	479.186	−	1044.92i	0.0980427	−	0.213794i
$289$	6534.21			1.32998
$290$	229.686	−	397.829i	0.0465091	−	0.0805562i
$291$	−3114.71	−	4854.97i	−0.627449	−	0.978018i
$292$	192.156	+	332.824i	0.0385106	+	0.0667023i
$293$	−1493.45	−	2586.74i	−0.297777	−	0.515764i	0.677850	−	0.735200i	$-0.262912\pi$
$293$	−1493.45	−	2586.74i	−0.297777	−	0.515764i	−0.975627	+	0.219436i	$0.929578\pi$
$294$	578.607	−	1120.18i	0.114779	−	0.222211i
$295$	33.9418	−	58.7890i	0.00669888	−	0.0116028i
$296$	−3843.24			−0.754676
$297$	1606.91	−	3986.59i	0.313947	−	0.778874i
$298$	4874.99			0.947653
$299$	1521.78	−	2635.81i	0.294338	−	0.509808i
$300$	−5338.01	+	10334.3i	−1.02730	+	1.98885i
$301$	−319.460	−	553.321i	−0.0611739	−	0.105956i
$302$	−321.534	−	556.914i	−0.0612657	−	0.106115i
$303$	3923.45	+	6115.56i	0.743882	+	1.15950i
$304$	1900.16	−	3291.18i	0.358493	−	0.620928i
$305$	10109.9			1.89801
$306$	−14242.0	+	1337.36i	−2.66066	+	0.249843i
$307$	−2881.52			−0.535691			−0.267845	−	0.963462i	$-0.586312\pi$
$307$	−2881.52			−0.535691			−0.267845	+	0.963462i	$0.586312\pi$
$308$	−1771.49	+	3068.30i	−0.327726	+	0.567639i
$309$	7514.51	−	352.042i	1.38345	−	0.0648122i
$310$	7372.55	+	12769.6i	1.35075	+	2.33957i
$311$	−3398.84	−	5886.96i	−0.619712	−	1.07337i	−0.989538	−	0.144272i	$-0.953916\pi$
$311$	−3398.84	−	5886.96i	−0.619712	−	1.07337i	0.369826	−	0.929101i	$-0.379417\pi$
$312$	17084.1	−	800.363i	3.10000	−	0.145230i
$313$	−470.871	+	815.572i	−0.0850326	+	0.147281i	−0.905405	−	0.424549i	$-0.860433\pi$
$313$	−470.871	+	815.572i	−0.0850326	+	0.147281i	0.820373	+	0.571829i	$0.193766\pi$
$314$	1074.69			0.193148
$315$	1765.53	+	2487.60i	0.315798	+	0.444954i
$316$	2544.82			0.453029
$317$	−1816.50	+	3146.27i	−0.321845	+	0.557452i	−0.980869	−	0.194670i	$-0.937636\pi$
$317$	−1816.50	+	3146.27i	−0.321845	+	0.557452i	0.659024	+	0.752122i	$0.270970\pi$
$318$	6914.55	+	10777.9i	1.21934	+	1.90060i
$319$	88.0473	+	152.502i	0.0154536	+	0.0267664i
$320$	3254.34	+	5636.68i	0.568509	+	0.984687i
$321$	2535.54	−	4908.79i	0.440872	−	0.853526i
$322$	−676.168	+	1171.16i	−0.117023	+	0.202690i
$323$	−5296.96			−0.912478
$324$	11832.9	−	2242.05i	2.02896	−	0.384439i
$325$	−10570.5			−1.80414
$326$	100.813	−	174.614i	0.0171274	−	0.0296656i
$327$	−4610.32	+	8925.55i	−0.779668	+	1.50943i
$328$	−1748.20	−	3027.96i	−0.294293	−	0.509730i
$329$	832.874	+	1442.58i	0.139568	+	0.241739i
$330$	−6870.26	−	10708.8i	−1.14605	−	1.78637i
$331$	−1375.17	+	2381.86i	−0.228357	+	0.395525i	−0.957321	−	0.289026i	$-0.906669\pi$
$331$	−1375.17	+	2381.86i	−0.228357	+	0.395525i	0.728965	+	0.684551i	$0.240002\pi$
$332$	4662.01			0.770665
$333$	−1423.46	−	2005.63i	−0.234250	−	0.330054i
$334$	−8546.77			−1.40017
$335$	5476.45	−	9485.49i	0.893166	−	1.54701i
$336$	−2789.00	+	130.660i	−0.452835	+	0.0212145i
$337$	−2916.14	−	5050.90i	−0.471372	−	0.816440i	0.528092	−	0.849187i	$-0.322908\pi$
$337$	−2916.14	−	5050.90i	−0.471372	−	0.816440i	−0.999464	+	0.0327474i	$0.989574\pi$
$338$	9628.43	+	16676.9i	1.54946	+	2.68374i
$339$	7996.57	−	374.625i	1.28116	−	0.0600202i
$340$	−14264.1	+	24706.1i	−2.27523	+	3.94082i
$341$	−5652.34			−0.897629
$342$	6590.19	−	618.837i	1.04198	−	0.0978446i
$343$	−343.000			−0.0539949
$344$	−1925.51	+	3335.07i	−0.301792	+	0.522719i
$345$	−1766.79	−	2753.93i	−0.275712	−	0.429758i
$346$	−1443.15	−	2499.61i	−0.224232	−	0.388380i
$347$	−1704.98	−	2953.11i	−0.263770	−	0.456863i	0.703471	−	0.710724i	$-0.251633\pi$
$347$	−1704.98	−	2953.11i	−0.263770	−	0.456863i	−0.967241	+	0.253862i	$0.918299\pi$
$348$	−226.435	+	438.377i	−0.0348799	+	0.0675272i
$349$	−2973.73	+	5150.66i	−0.456104	+	0.789996i	−0.998751	−	0.0499654i	$-0.984089\pi$
$349$	−2973.73	+	5150.66i	−0.456104	+	0.789996i	0.542647	+	0.839961i	$0.317422\pi$
$350$	4696.74			0.717289
$351$	6745.30	+	8619.09i	1.02575	+	1.31069i
$352$	1304.41			0.197515
$353$	265.847	−	460.460i	0.0400838	−	0.0694273i	−0.845287	−	0.534312i	$-0.820571\pi$
$353$	265.847	−	460.460i	0.0400838	−	0.0694273i	0.885371	+	0.464885i	$0.153904\pi$
$354$	−49.6650	+	96.1511i	−0.00745668	+	0.0144361i
$355$	−6028.85	−	10442.3i	−0.901347	−	1.56118i
$356$	−917.640	−	1589.40i	−0.136615	−	0.236624i
$357$	2101.39	+	3275.49i	0.311533	+	0.485594i
$358$	−9160.57	+	15866.6i	−1.35238	+	2.34239i
$359$	−7555.95			−1.11083			−0.555415	−	0.831573i	$-0.687441\pi$
$359$	−7555.95			−1.11083			−0.555415	+	0.831573i	$0.687441\pi$
$360$	7664.20	−	16712.7i	1.12205	−	2.44677i
$361$	−4407.94			−0.642651
$362$	7113.22	−	12320.5i	1.03277	−	1.78881i
$363$	−2036.57	+	95.4099i	−0.294469	+	0.0137954i
$364$	−4510.77	−	7812.88i	−0.649529	−	1.12502i
$365$	187.730	+	325.159i	0.0269213	+	0.0466290i
$366$	−16099.6	+	754.240i	−2.29929	+	0.107718i
$367$	4851.61	−	8403.24i	0.690060	−	1.19522i	−0.281758	−	0.959486i	$-0.590917\pi$
$367$	4851.61	−	8403.24i	0.690060	−	1.19522i	0.971818	−	0.235733i	$-0.0757492\pi$
$368$	2994.79			0.424224
$369$	932.676	−	2033.81i	0.131580	−	0.286927i
$370$	−7280.11			−1.02290
$371$	1741.84	−	3016.96i	0.243752	−	0.422190i
$372$	−8551.89	−	13330.0i	−1.19192	−	1.85787i
$373$	−7.09728	−	12.2928i	−0.000985210	−	0.00170643i	0.865532	−	0.500853i	$-0.166980\pi$
$373$	−7.09728	−	12.2928i	−0.000985210	−	0.00170643i	−0.866518	+	0.499147i	$0.833647\pi$
$374$	−8115.81	−	14057.0i	−1.12208	−	1.94350i
$375$	−404.059	+	782.256i	−0.0556414	+	0.107721i
$376$	5020.05	−	8694.98i	0.688536	−	1.19258i
$377$	−448.393			−0.0612558
$378$	−2997.11	−	3829.68i	−0.407817	−	0.521105i
$379$	−2618.92			−0.354948			−0.177474	−	0.984126i	$-0.556792\pi$
$379$	−2618.92			−0.354948			−0.177474	+	0.984126i	$0.556792\pi$
$380$	6600.41	−	11432.2i	0.891037	−	1.54332i
$381$	−3508.37	+	6792.17i	−0.471756	+	0.913316i
$382$	−676.646	−	1171.98i	−0.0906288	−	0.156974i
$383$	4344.62	+	7525.10i	0.579633	+	1.00395i	0.995521	+	0.0945386i	$0.0301376\pi$
$383$	4344.62	+	7525.10i	0.579633	+	1.00395i	−0.415888	+	0.909416i	$0.636529\pi$
$384$	−6558.59	−	10223.0i	−0.871593	−	1.35857i
$385$	−1730.69	+	2997.63i	−0.229101	+	0.396815i
$386$	−4180.71			−0.551276
$387$	−2453.61	+	230.400i	−0.322284	+	0.0302633i
$388$	18339.2			2.39957
$389$	−5302.27	+	9183.80i	−0.691094	+	1.19701i	0.280385	+	0.959888i	$0.409538\pi$
$389$	−5302.27	+	9183.80i	−0.691094	+	1.19701i	−0.971480	+	0.237123i	$0.923796\pi$
$390$	32361.8	−	1516.10i	4.20181	−	0.196848i
$391$	−2087.10	−	3614.96i	−0.269946	−	0.467560i
$392$	1033.70	+	1790.41i	0.133188	+	0.230688i
$393$	3523.03	−	165.048i	0.452197	−	0.0211847i
$394$	6206.53	−	10750.0i	0.793606	−	1.37457i
$395$	2486.21			0.316695
$396$	7909.40	+	11144.2i	1.00369	+	1.41419i
$397$	2918.97			0.369015			0.184508	−	0.982831i	$-0.440931\pi$
$397$	2918.97			0.369015			0.184508	+	0.982831i	$0.440931\pi$
$398$	−9750.41	+	16888.2i	−1.22800	+	2.12696i
$399$	−972.375	−	1515.66i	−0.122004	−	0.190171i
$400$	−5200.54	−	9007.60i	−0.650068	−	1.12595i
$401$	−2129.01	−	3687.56i	−0.265132	−	0.459222i	0.702466	−	0.711717i	$-0.252082\pi$
$401$	−2129.01	−	3687.56i	−0.265132	−	0.459222i	−0.967598	+	0.252495i	$0.918749\pi$
$402$	−8013.36	+	15513.8i	−0.994204	+	1.92477i
$403$	7196.34	−	12464.4i	0.889516	−	1.54069i
$404$	−23101.0			−2.84484
$405$	11560.3	−	2190.41i	1.41837	−	0.268746i
$406$	199.233			0.0243541
$407$	1395.37	−	2416.85i	0.169941	−	0.294346i
$408$	10764.7	−	20840.3i	1.30620	−	2.52879i
$409$	2308.33	+	3998.14i	0.279070	+	0.483363i	0.971154	−	0.238454i	$-0.0766406\pi$
$409$	2308.33	+	3998.14i	0.279070	+	0.483363i	−0.692084	+	0.721817i	$0.743307\pi$
$410$	−3311.54	−	5735.75i	−0.398891	−	0.690899i
$411$	−5106.47	−	7959.57i	−0.612856	−	0.955272i
$412$	−11958.8	+	20713.2i	−1.43002	+	2.47686i
$413$	29.4416			0.00350781
$414$	3018.98	+	4253.70i	0.358394	+	0.504971i
$415$	4554.63			0.538742
$416$	−1660.72	+	2876.46i	−0.195730	+	0.339014i
$417$	−15149.3	+	709.717i	−1.77905	+	0.0833453i
$418$	3755.42	+	6504.58i	0.439434	+	0.761122i
$419$	−997.567	−	1727.84i	−0.116311	−	0.201457i	0.801992	−	0.597335i	$-0.203774\pi$
$419$	−997.567	−	1727.84i	−0.116311	−	0.201457i	−0.918303	+	0.395878i	$0.870440\pi$
$420$	−9687.87	+	453.860i	−1.12552	+	0.0527288i
$421$	−8281.75	+	14344.4i	−0.958736	+	1.66058i	−0.233160	+	0.972438i	$0.574907\pi$
$421$	−8281.75	+	14344.4i	−0.958736	+	1.66058i	−0.725577	+	0.688141i	$0.758427\pi$
$422$	331.032			0.0381857
$423$	6396.89	−	600.685i	0.735289	−	0.0690456i
$424$	−20997.5			−2.40502
$425$	−7248.59	+	12554.9i	−0.827314	+	1.43295i
$426$	10379.7	+	16179.1i	1.18051	+	1.84009i
$427$	2192.37	+	3797.30i	0.248469	+	0.430361i
$428$	8782.92	+	15212.5i	0.991912	+	1.71804i
$429$	−5699.43	+	11034.1i	−0.641425	+	1.24179i
$430$	−3647.41	+	6317.50i	−0.409055	+	0.708505i
$431$	1439.27			0.160852			0.0804258	−	0.996761i	$-0.474372\pi$
$431$	1439.27			0.160852			0.0804258	+	0.996761i	$0.474372\pi$
$432$	−4026.13	+	9988.47i	−0.448396	+	1.11243i
$433$	−6467.98			−0.717856			−0.358928	−	0.933365i	$-0.616858\pi$
$433$	−6467.98			−0.717856			−0.358928	+	0.933365i	$0.616858\pi$
$434$	−3197.52	+	5538.26i	−0.353654	+	0.612547i
$435$	−221.220	+	428.280i	−0.0243832	+	0.0472057i
$436$	−15969.8	−	27660.5i	−1.75416	−	3.03830i
$437$	965.760	+	1672.74i	0.105717	+	0.183108i
$438$	−323.211	−	503.796i	−0.0352594	−	0.0549596i
$439$	6255.01	−	10834.0i	0.680035	−	1.17785i	−0.294935	−	0.955517i	$-0.595298\pi$
$439$	6255.01	−	10834.0i	0.680035	−	1.17785i	0.974970	−	0.222337i	$-0.0713686\pi$
$440$	20863.0			2.26047
$441$	−551.485	+	1202.58i	−0.0595492	+	0.129854i
$442$	41330.9			4.44776
$443$	−3510.58	+	6080.51i	−0.376507	+	0.652130i	−0.990551	−	0.137142i	$-0.956208\pi$
$443$	−3510.58	+	6080.51i	−0.376507	+	0.652130i	0.614044	+	0.789272i	$0.289542\pi$
$444$	7810.86	−	365.925i	0.834881	−	0.0391127i
$445$	−896.506	−	1552.79i	−0.0955021	−	0.165415i
$446$	6159.07	+	10667.8i	0.653902	+	1.13259i
$447$	−5109.93	+	239.392i	−0.540697	+	0.0253307i
$448$	−1411.43	+	2444.66i	−0.148847	+	0.257811i
$449$	5184.19			0.544894			0.272447	−	0.962171i	$-0.412167\pi$
$449$	5184.19			0.544894			0.272447	+	0.962171i	$0.412167\pi$
$450$	7551.54	−	16467.0i	0.791073	−	1.72503i
$451$	2538.87			0.265079
$452$	−12725.9	+	22042.0i	−1.32429	+	2.29373i
$453$	364.378	+	567.964i	0.0377925	+	0.0589079i
$454$	9524.13	+	16496.3i	0.984559	+	1.70531i
$455$	−4406.88	−	7632.94i	−0.454061	−	0.786457i
$456$	−4981.12	+	9643.41i	−0.511540	+	0.990338i
$457$	−1288.14	+	2231.12i	−0.131853	+	0.228375i	−0.924391	−	0.381447i	$-0.875426\pi$
$457$	−1288.14	+	2231.12i	−0.131853	+	0.228375i	0.792538	+	0.609822i	$0.208759\pi$
$458$	19866.1			2.02682
$459$	14862.7	−	2101.19i	1.51140	−	0.213671i
$460$	10402.7			1.05441
$461$	8952.21	−	15505.7i	0.904438	−	1.56653i	0.0827674	−	0.996569i	$-0.473624\pi$
$461$	8952.21	−	15505.7i	0.904438	−	1.56653i	0.821670	−	0.569963i	$-0.193043\pi$
$462$	2532.41	−	4902.72i	0.255018	−	0.493712i
$463$	−5631.93	−	9754.79i	−0.565309	−	0.979144i	−0.997021	−	0.0771323i	$-0.975424\pi$
$463$	−5631.93	−	9754.79i	−0.565309	−	0.979144i	0.431712	−	0.902012i	$-0.357910\pi$
$464$	−220.604	−	382.097i	−0.0220717	−	0.0382293i
$465$	−8354.92	−	13023.0i	−0.833226	−	1.29877i
$466$	14172.6	−	24547.6i	1.40887	−	2.44023i
$467$	9817.00			0.972755			0.486377	−	0.873749i	$-0.338318\pi$
$467$	9817.00			0.972755			0.486377	+	0.873749i	$0.338318\pi$
$468$	−34645.0	+	3253.25i	−3.42193	+	0.321328i
$469$	4750.34			0.467698
$470$	9509.29	−	16470.6i	0.933257	−	1.61645i
$471$	−1126.49	+	52.7740i	−0.110203	+	0.00516284i
$472$	−88.7278	−	153.681i	−0.00865260	−	0.0149867i
$473$	−1398.19	−	2421.73i	−0.135917	−	0.235415i
$474$	−3959.18	+	185.481i	−0.383652	+	0.0179734i
$475$	3354.13	−	5809.53i	0.323996	−	0.561178i
$476$	−12372.9			−1.19140
$477$	−7777.04	−	10957.7i	−0.746512	−	1.05182i
$478$	−30303.0			−2.89964
$479$	−3675.86	+	6366.78i	−0.350636	+	0.607319i	−0.986361	−	0.164597i	$-0.947368\pi$
$479$	−3675.86	+	6366.78i	−0.350636	+	0.607319i	0.635725	+	0.771915i	$0.280701\pi$
$480$	1928.09	+	3005.36i	0.183344	+	0.285782i
$481$	3553.05	+	6154.07i	0.336809	+	0.583371i
$482$	1220.13	+	2113.33i	0.115302	+	0.199709i
$483$	651.244	−	1260.80i	0.0613512	−	0.118776i
$484$	3241.05	−	5613.67i	0.304381	−	0.527204i
$485$	17916.8			1.67745
$486$	−18245.9	+	4350.58i	−1.70299	+	0.406062i
$487$	15312.1			1.42476			0.712378	−	0.701796i	$-0.247618\pi$
$487$	15312.1			1.42476			0.712378	+	0.701796i	$0.247618\pi$
$488$	13214.3	−	22887.8i	1.22578	−	2.12312i
$489$	−97.0975	+	187.980i	−0.00897934	+	0.0173839i
$490$	1958.09	+	3391.51i	0.180526	+	0.312679i
$491$	8989.47	+	15570.2i	0.826251	+	1.43111i	0.900960	+	0.433903i	$0.142864\pi$
$491$	8989.47	+	15570.2i	0.826251	+	1.43111i	−0.0747090	+	0.997205i	$0.523803\pi$
$492$	3841.27	+	5987.47i	0.351987	+	0.548650i
$493$	−307.481	+	532.573i	−0.0280898	+	0.0486529i
$494$	−19125.0			−1.74185
$495$	7727.24	+	10887.6i	0.701643	+	0.988605i
$496$	14162.0			1.28204
$497$	2614.75	−	4528.88i	0.235991	−	0.408748i
$498$	−7253.05	+	339.793i	−0.652645	+	0.0305753i
$499$	9407.52	+	16294.3i	0.843965	+	1.46179i	0.886517	+	0.462696i	$0.153118\pi$
$499$	9407.52	+	16294.3i	0.843965	+	1.46179i	−0.0425521	+	0.999094i	$0.513549\pi$
$500$	−1399.63	−	2424.23i	−0.125187	−	0.216830i
$501$	8958.67	−	419.698i	0.798890	−	0.0374266i
$502$	−4603.32	+	7973.19i	−0.409275	+	0.708886i
$503$	−6228.19			−0.552090			−0.276045	−	0.961145i	$-0.589024\pi$
$503$	−6228.19			−0.552090			−0.276045	+	0.961145i	$0.589024\pi$
$504$	7939.30	−	745.521i	0.701676	−	0.0658892i
$505$	−22568.9			−1.98872
$506$	−2959.40	+	5125.84i	−0.260003	+	0.450339i
$507$	−10911.4	−	17007.8i	−0.955804	−	1.48983i
$508$	−12152.7	−	21049.1i	−1.06140	−	1.83839i
$509$	5901.69	+	10222.0i	0.513925	+	0.890144i	0.999870	+	0.0161547i	$0.00514243\pi$
$509$	5901.69	+	10222.0i	0.513925	+	0.890144i	−0.485944	+	0.873990i	$0.661524\pi$
$510$	20391.1	−	39477.0i	1.77045	−	3.42759i
$511$	−81.4199	+	141.023i	−0.00704854	+	0.0122084i
$512$	22641.4			1.95433
$513$	−6877.41	+	972.279i	−0.591901	+	0.0836787i
$514$	−18677.8			−1.60281
$515$	−11683.4	+	20236.2i	−0.999670	+	1.73148i
$516$	3595.78	−	6961.41i	0.306774	−	0.593913i
$517$	3645.26	+	6313.78i	0.310094	+	0.537098i
$518$	−1578.71	−	2734.41i	−0.133909	−	0.231937i
$519$	1635.44	+	2549.20i	0.138320	+	0.215602i
$520$	−26562.0	+	46006.7i	−2.24004	+	3.87986i
$521$	−7277.82			−0.611990			−0.305995	−	0.952033i	$-0.598989\pi$
$521$	−7277.82			−0.611990			−0.305995	+	0.952033i	$0.598989\pi$
$522$	320.332	−	698.522i	0.0268593	−	0.0585699i
$523$	18929.2			1.58263			0.791316	−	0.611408i	$-0.209397\pi$
$523$	18929.2			1.58263			0.791316	+	0.611408i	$0.209397\pi$
$524$	−5606.64	+	9710.99i	−0.467419	+	0.809593i
$525$	−4923.09	+	230.638i	−0.409260	+	0.0191731i
$526$	100.863	+	174.700i	0.00836092	+	0.0144815i
$527$	−9869.62	−	17094.7i	−0.815802	−	1.41301i
$528$	−12206.7	+	571.863i	−1.00611	+	0.0471347i
$529$	5322.45	−	9218.75i	0.437449	−	0.757685i
$530$	−39774.7			−3.25982
$531$	47.3369	−	103.224i	0.00386864	−	0.00843603i
$532$	5725.28			0.466583
$533$	−3232.39	+	5598.67i	−0.262684	+	0.454981i
$534$	1543.49	+	2405.87i	0.125081	+	0.194967i
$535$	8580.63	+	14862.1i	0.693408	+	1.20102i
$536$	−14316.1	−	24796.2i	−1.15366	−	1.99819i
$537$	8822.90	−	17081.1i	0.709006	−	1.37263i
$538$	3476.38	−	6021.26i	0.278582	−	0.482519i
$539$	−1501.22			−0.119967
$540$	−13985.2	+	34696.0i	−1.11449	+	2.76496i
$541$	3018.24			0.239860			0.119930	−	0.992782i	$-0.461733\pi$
$541$	3018.24			0.239860			0.119930	+	0.992782i	$0.461733\pi$
$542$	−551.337	+	954.944i	−0.0436936	+	0.0756796i
$543$	−6851.03	+	13263.5i	−0.541447	+	1.04824i
$544$	2277.65	+	3945.00i	0.179510	+	0.310920i
$545$	−15602.0	−	27023.5i	−1.22627	−	2.12396i
$546$	7587.21	+	11826.4i	0.594694	+	0.926962i
$547$	4726.68	−	8186.86i	0.369467	−	0.639936i	−0.620015	−	0.784590i	$-0.712874\pi$
$547$	4726.68	−	8186.86i	0.369467	−	0.639936i	0.989482	+	0.144654i	$0.0462069\pi$
$548$	30066.6			2.34376
$549$	16838.5	−	1581.18i	1.30902	−	0.122920i
$550$	20556.3			1.59368
$551$	142.280	−	246.437i	0.0110006	−	0.0190537i
$552$	−8543.88	+	400.266i	−0.658789	+	0.0308631i
$553$	539.142	+	933.821i	0.0414587	+	0.0718085i
$554$	−14308.9	−	24783.7i	−1.09734	−	1.90065i
$555$	7630.96	−	357.497i	0.583633	−	0.0273422i
$556$	24108.9	−	41757.8i	1.83893	−	3.18512i
$557$	6175.74			0.469793			0.234896	−	0.972020i	$-0.424525\pi$
$557$	6175.74			0.469793			0.234896	+	0.972020i	$0.424525\pi$
$558$	14276.4	+	20115.3i	1.08310	+	1.52607i
$559$	7120.47			0.538755
$560$	4336.26	−	7510.62i	0.327215	−	0.566753i
$561$	9197.22	+	14335.9i	0.692169	+	1.07890i
$562$	9334.65	+	16168.1i	0.700638	+	1.21354i
$563$	−6329.56	−	10963.1i	−0.473817	−	0.820675i	0.525734	−	0.850649i	$-0.323791\pi$
$563$	−6329.56	−	10963.1i	−0.473817	−	0.820675i	−0.999551	+	0.0299739i	$0.990458\pi$
$564$	−9374.68	+	18149.3i	−0.699903	+	1.35501i
$565$	−12432.8	+	21534.3i	−0.925758	+	1.60346i
$566$	23789.1			1.76666
$567$	3329.62	+	3867.08i	0.246615	+	0.286423i
$568$	−31520.2			−2.32845
$569$	−9605.51	+	16637.2i	−0.707704	+	1.22578i	0.258002	+	0.966144i	$0.416936\pi$
$569$	−9605.51	+	16637.2i	−0.707704	+	1.22578i	−0.965707	+	0.259636i	$0.916398\pi$
$570$	−9435.54	+	18267.1i	−0.693353	+	1.34233i
$571$	3780.12	+	6547.37i	0.277046	+	0.479858i	0.970649	−	0.240499i	$-0.0773112\pi$
$571$	3780.12	+	6547.37i	0.277046	+	0.479858i	−0.693603	+	0.720357i	$0.743978\pi$
$572$	−19742.4	−	34194.9i	−1.44313	−	2.49958i
$573$	766.808	+	1195.24i	0.0559055	+	0.0871411i
$574$	1436.23	−	2487.63i	0.104438	−	0.180892i
$575$	5286.36			0.383402
$576$	6301.79	+	8879.13i	0.455859	+	0.642298i
$577$	−14126.1			−1.01920			−0.509598	−	0.860413i	$-0.670206\pi$
$577$	−14126.1			−1.01920			−0.509598	+	0.860413i	$0.670206\pi$
$578$	16178.1	−	28021.3i	1.16422	−	2.01649i
$579$	4382.19	−	205.298i	0.314538	−	0.0147356i
$580$	−766.290	−	1327.25i	−0.0548594	−	0.0950193i
$581$	987.686	+	1710.72i	0.0705269	+	0.122156i
$582$	−28531.8	+	1336.66i	−2.03210	+	0.0952002i
$583$	7623.56	−	13204.4i	0.541571	−	0.938028i
$584$	981.497			0.0695456
$585$	−33847.0	+	3178.33i	−2.39214	+	0.224628i
$586$	−14790.6			−1.04265
$587$	−5811.15	+	10065.2i	−0.408606	+	0.707727i	−0.994734	−	0.102492i	$-0.967318\pi$
$587$	−5811.15	+	10065.2i	−0.408606	+	0.707727i	0.586128	+	0.810219i	$0.300652\pi$
$588$	−2271.31	−	3540.35i	−0.159298	−	0.248302i
$589$	4566.96	+	7910.21i	0.319488	+	0.553369i
$590$	−168.074	−	291.112i	−0.0117279	−	0.0203134i
$591$	−5977.76	+	11572.9i	−0.416061	+	0.805491i
$592$	−3496.11	+	6055.45i	−0.242719	+	0.420401i
$593$	−22182.5			−1.53613			−0.768064	−	0.640373i	$-0.778780\pi$
$593$	−22182.5			−1.53613			−0.768064	+	0.640373i	$0.778780\pi$
$594$	−13117.5	−	16761.5i	−0.906093	−	1.15780i
$595$	−12087.9			−0.832865
$596$	8132.07	−	14085.2i	0.558897	−	0.968038i
$597$	9391.01	−	18180.9i	0.643799	−	1.24639i
$598$	−7535.59	−	13052.0i	−0.515306	−	0.892537i
$599$	11203.2	+	19404.5i	0.764189	+	1.32361i	0.940674	+	0.339311i	$0.110194\pi$
$599$	11203.2	+	19404.5i	0.764189	+	1.32361i	−0.176485	+	0.984303i	$0.556473\pi$
$600$	16040.6	+	25002.8i	1.09142	+	1.70123i
$601$	−5627.94	+	9747.88i	−0.381977	+	0.661604i	−0.991345	−	0.131284i	$-0.958090\pi$
$601$	−5627.94	+	9747.88i	−0.381977	+	0.661604i	0.609367	+	0.792888i	$0.291423\pi$
$602$	−3163.81			−0.214198
$603$	7637.73	−	16655.0i	0.515808	−	1.12478i
$604$	−2145.43			−0.144531
$605$	3166.41	−	5484.38i	0.212781	−	0.368548i
$606$	35940.0	−	1683.73i	2.40918	−	0.112866i
$607$	6156.29	+	10663.0i	0.411658	+	0.713012i	0.995071	−	0.0991632i	$-0.0316166\pi$
$607$	6156.29	+	10663.0i	0.411658	+	0.713012i	−0.583413	+	0.812175i	$0.698283\pi$
$608$	−1053.93	−	1825.47i	−0.0703004	−	0.121764i
$609$	−208.835	+	9.78354i	−0.0138956	+	0.000650984i
$610$	25031.2	−	43355.4i	1.66145	−	2.87772i
$611$	−18564.0			−1.22916
$612$	−19893.4	+	43379.9i	−1.31396	+	2.86524i
$613$	−26835.4			−1.76814			−0.884070	−	0.467354i	$-0.845207\pi$
$613$	−26835.4			−1.76814			−0.884070	+	0.467354i	$0.845207\pi$
$614$	−7134.37	+	12357.1i	−0.468925	+	0.812202i
$615$	3752.80	+	5849.57i	0.246061	+	0.383540i
$616$	4524.21	+	7836.16i	0.295918	+	0.512545i
$617$	10882.7	+	18849.4i	0.710084	+	1.22990i	0.964825	+	0.262893i	$0.0846766\pi$
$617$	10882.7	+	18849.4i	0.710084	+	1.22990i	−0.254741	+	0.967009i	$0.581990\pi$
$618$	17095.5	−	33096.8i	1.11276	−	2.15429i
$619$	−3557.64	+	6162.01i	−0.231007	+	0.400117i	−0.958105	−	0.286418i	$-0.907535\pi$
$619$	−3557.64	+	6162.01i	−0.231007	+	0.400117i	0.727097	+	0.686534i	$0.240869\pi$
$620$	49193.2			3.18653
$621$	−3373.36	−	4310.46i	−0.217985	−	0.278539i
$622$	−33660.8			−2.16990
$623$	388.820	−	673.456i	0.0250044	−	0.0433089i
$624$	14280.0	−	27646.0i	0.916119	−	1.77360i
$625$	7101.25	+	12299.7i	0.454480	+	0.787182i
$626$	2331.67	+	4038.56i	0.148869	+	0.257849i
$627$	−4255.82	−	6633.64i	−0.271070	−	0.422523i
$628$	1792.72	−	3105.08i	0.113913	−	0.197303i
$629$	9745.88			0.617796
$630$	15039.1	−	1412.21i	0.951067	−	0.0893078i
$631$	−11639.8			−0.734345			−0.367173	−	0.930153i	$-0.619674\pi$
$631$	−11639.8			−0.734345			−0.367173	+	0.930153i	$0.619674\pi$
$632$	3249.61	−	5628.50i	0.204530	−	0.354256i
$633$	−346.986	+	16.2557i	−0.0217874	+	0.00102070i
$634$	8994.98	+	15579.8i	0.563464	+	0.975948i
$635$	−11872.8	−	20564.3i	−0.741982	−	1.28515i
$636$	42674.5	−	1999.23i	2.66062	−	0.124645i
$637$	1911.29	−	3310.45i	0.118882	−	0.205910i
$638$	871.988			0.0541102
$639$	−11674.4	−	16449.1i	−0.722745	−	1.01834i
$640$	37727.1			2.33015
$641$	12837.8	−	22235.7i	0.791048	−	1.37014i	−0.134270	−	0.990945i	$-0.542869\pi$
$641$	12837.8	−	22235.7i	0.791048	−	1.37014i	0.925318	−	0.379191i	$-0.123798\pi$
$642$	−14773.1	−	23027.1i	−0.908171	−	1.41559i
$643$	8573.42	+	14849.6i	0.525821	+	0.910748i	0.999548	+	0.0300764i	$0.00957506\pi$
$643$	8573.42	+	14849.6i	0.525821	+	0.910748i	−0.473727	+	0.880672i	$0.657092\pi$
$644$	2255.86	+	3907.27i	0.138033	+	0.239081i
$645$	3512.97	−	6801.08i	0.214454	−	0.415182i
$646$	−13114.8	+	22715.4i	−0.798752	+	1.38348i
$647$	−13104.3			−0.796263			−0.398132	−	0.917328i	$-0.630341\pi$
$647$	−13104.3			−0.796263			−0.398132	+	0.917328i	$0.630341\pi$
$648$	10151.2	−	29034.3i	0.615395	−	1.76015i
$649$	128.858			0.00779369
$650$	−26171.5	+	45330.4i	−1.57928	+	2.73539i
$651$	3079.66	−	5962.19i	0.185409	−	0.358950i
$652$	−336.338	−	582.555i	−0.0202025	−	0.0349917i
$653$	8373.04	+	14502.5i	0.501780	+	0.869108i	0.999998	+	0.00205652i	$0.000654611\pi$
$653$	8373.04	+	14502.5i	0.501780	+	0.869108i	−0.498218	+	0.867052i	$0.666012\pi$
$654$	26861.6	+	41869.7i	1.60607	+	2.50342i
$655$	−5477.51	+	9487.33i	−0.326754	+	0.565955i
$656$	−6361.18			−0.378601
$657$	363.527	+	512.204i	0.0215868	+	0.0304155i
$658$	8248.47			0.488691
$659$	12133.6	−	21015.9i	0.717232	−	1.24228i	−0.244860	−	0.969558i	$-0.578742\pi$
$659$	12133.6	−	21015.9i	0.717232	−	1.24228i	0.962092	−	0.272724i	$-0.0879247\pi$
$660$	−42401.2	+	1986.42i	−2.50070	+	0.117154i
$661$	−7233.95	−	12529.6i	−0.425670	−	0.737282i	0.570813	−	0.821080i	$-0.306628\pi$
$661$	−7233.95	−	12529.6i	−0.425670	−	0.737282i	−0.996483	+	0.0837981i	$0.973295\pi$
$662$	6809.57	+	11794.5i	0.399791	+	0.692458i
$663$	−43322.8	+	2029.60i	−2.53773	+	0.118888i
$664$	5953.16	−	10311.2i	0.347933	−	0.602638i
$665$	5593.42			0.326170
$666$	−12125.3	+	1138.60i	−0.705475	+	0.0662459i
$667$	224.244			0.0130176
$668$	−14257.0	+	24693.9i	−0.825781	+	1.43029i
$669$	−6979.75	−	10879.5i	−0.403367	−	0.628738i
$670$	−27118.4	−	46970.4i	−1.56369	−	2.70839i
$671$	9595.41	+	16619.7i	0.552052	+	0.956181i
$672$	−710.703	+	1375.92i	−0.0407975	+	0.0789837i
$673$	7479.13	−	12954.2i	0.428379	−	0.741975i	−0.568350	−	0.822787i	$-0.692418\pi$
$673$	7479.13	−	12954.2i	0.428379	−	0.741975i	0.996729	+	0.0808120i	$0.0257513\pi$
$674$	−28880.4			−1.65049
$675$	−7106.85	+	17631.5i	−0.405248	+	1.00539i
$676$	64245.6			3.65530
$677$	12861.9	−	22277.4i	0.730165	−	1.26468i	−0.226647	−	0.973977i	$-0.572776\pi$
$677$	12861.9	−	22277.4i	0.730165	−	1.26468i	0.956812	−	0.290706i	$-0.0938903\pi$
$678$	18192.2	−	35220.0i	1.03048	−	1.99501i
$679$	3885.32	+	6729.57i	0.219595	+	0.380349i
$680$	36429.2	+	63097.2i	2.05440	+	3.55833i
$681$	−10793.2	−	16823.6i	−0.607337	−	0.946670i
$682$	−13994.7	+	24239.5i	−0.785753	+	1.36096i
$683$	−2949.64			−0.165248			−0.0826242	−	0.996581i	$-0.526330\pi$
$683$	−2949.64			−0.165248			−0.0826242	+	0.996581i	$0.526330\pi$
$684$	9205.26	−	20073.2i	0.514579	−	1.12210i
$685$	29374.1			1.63843
$686$	−849.236	+	1470.92i	−0.0472653	+	0.0818659i
$687$	−20823.5	+	975.547i	−1.15643	+	0.0541768i
$688$	3503.18	+	6067.69i	0.194124	+	0.336233i
$689$	19412.0	+	33622.6i	1.07335	+	1.85910i
$690$	−16184.3	+	758.208i	−0.892938	+	0.0418326i
$691$	4059.96	−	7032.05i	0.223514	−	0.387137i	−0.732359	−	0.680919i	$-0.761581\pi$
$691$	4059.96	−	7032.05i	0.223514	−	0.387137i	0.955873	+	0.293782i	$0.0949139\pi$
$692$	−9629.38			−0.528980
$693$	−2413.70	+	5263.36i	−0.132307	+	0.288511i
$694$	−16885.5			−0.923579
$695$	23553.6	−	40796.1i	1.28553	−	2.22660i
$696$	680.432	+	1060.60i	0.0370570	+	0.0577616i
$697$	4433.16	+	7678.45i	0.240915	+	0.417277i
$698$	14725.4	+	25505.1i	0.798515	+	1.38307i
$699$	−13650.2	+	26426.7i	−0.738623	+	1.42997i
$700$	7834.73	−	13570.1i	0.423035	−	0.732719i
$701$	−15870.9			−0.855115			−0.427558	−	0.903988i	$-0.640626\pi$
$701$	−15870.9			−0.855115			−0.427558	+	0.903988i	$0.640626\pi$
$702$	53662.8	−	7586.46i	2.88515	−	0.407881i
$703$	−4509.70			−0.241944
$704$	−6177.43	+	10699.6i	−0.330711	+	0.572808i
$705$	−9158.77	+	17731.3i	−0.489276	+	0.947234i
$706$	−1316.42	−	2280.11i	−0.0701760	−	0.121548i
$707$	−4894.14	−	8476.90i	−0.260344	−	0.450929i
$708$	194.959	+	303.887i	0.0103489	+	0.0161311i
$709$	7436.79	−	12880.9i	0.393928	−	0.682303i	−0.599036	−	0.800722i	$-0.704449\pi$
$709$	7436.79	−	12880.9i	0.393928	−	0.682303i	0.992964	+	0.118419i	$0.0377827\pi$
$710$	−59707.5			−3.15603
$711$	4140.88	−	388.839i	0.218418	−	0.0205100i
$712$	−4687.13			−0.246710
$713$	−3598.93	+	6233.53i	−0.189034	+	0.327416i
$714$	19249.4	−	901.803i	1.00895	−	0.0472677i
$715$	−19287.7	−	33407.3i	−1.00884	−	1.74736i
$716$	30561.9	+	52934.7i	1.59518	+	2.76294i
$717$	31763.4	−	1488.06i	1.65443	−	0.0775072i
$718$	−18707.8	+	32402.9i	−0.972382	+	1.68421i
$719$	31809.4			1.64992			0.824959	−	0.565192i	$-0.191198\pi$
$719$	31809.4			1.64992			0.824959	+	0.565192i	$0.191198\pi$
$720$	−19360.7	−	27279.0i	−1.00213	−	1.41198i
$721$	−10134.3			−0.523468
$722$	−10913.7	+	18903.0i	−0.562554	+	0.974373i
$723$	−1382.71	−	2155.27i	−0.0711254	−	0.110865i
$724$	−23731.4	−	41104.1i	−1.21819	−	2.10997i
$725$	−389.406	−	674.471i	−0.0199478	−	0.0345506i
$726$	−4633.21	+	8969.86i	−0.236852	+	0.458544i
$727$	−8385.91	+	14524.8i	−0.427808	+	0.740984i	−0.996678	−	0.0814427i	$-0.974047\pi$
$727$	−8385.91	+	14524.8i	−0.427808	+	0.740984i	0.568870	+	0.822427i	$0.307381\pi$
$728$	−23040.2			−1.17297
$729$	18911.6	−	5456.23i	0.960811	−	0.277205i
$730$	1859.21			0.0942638
$731$	4882.79	−	8457.24i	0.247054	−	0.427910i
$732$	−24676.9	+	47774.4i	−1.24602	+	2.41228i
$733$	15894.2	+	27529.5i	0.800906	+	1.38721i	0.919020	+	0.394210i	$0.128982\pi$
$733$	15894.2	+	27529.5i	0.800906	+	1.38721i	−0.118114	+	0.993000i	$0.537685\pi$
$734$	−24024.3	−	41611.3i	−1.20811	−	2.09251i
$735$	−2219.00	−	3458.81i	−0.111359	−	0.173578i
$736$	830.537	−	1438.53i	0.0415951	−	0.0720448i
$737$	20791.0			1.03914
$738$	−6412.56	−	9035.21i	−0.319851	−	0.450665i
$739$	−17098.2			−0.851107			−0.425553	−	0.904933i	$-0.639921\pi$
$739$	−17098.2			−0.851107			−0.425553	+	0.904933i	$0.639921\pi$
$740$	−12144.1	+	21034.2i	−0.603279	+	1.04491i
$741$	20046.7	−	939.154i	0.993838	−	0.0465596i
$742$	−8625.27	−	14939.4i	−0.426743	−	0.739141i
$743$	308.950	+	535.118i	0.0152548	+	0.0264220i	0.873552	−	0.486731i	$-0.161811\pi$
$743$	308.950	+	535.118i	0.0152548	+	0.0264220i	−0.858297	+	0.513153i	$0.828477\pi$
$744$	−40403.0	+	1892.81i	−1.99092	+	0.0932712i
$745$	7944.78	−	13760.8i	0.390704	−	0.676719i
$746$	−70.2888			−0.00344967
$747$	7585.92	−	712.338i	0.371559	−	0.0348903i
$748$	−54152.6			−2.64708
$749$	−3721.47	+	6445.78i	−0.181548	+	0.314451i
$750$	2354.21	+	3669.56i	0.114618	+	0.178658i
$751$	−13234.5	−	22922.8i	−0.643053	−	1.11380i	−0.984747	−	0.173990i	$-0.944334\pi$
$751$	−13234.5	−	22922.8i	−0.643053	−	1.11380i	0.341694	−	0.939811i	$-0.388999\pi$
$752$	−9133.26	−	15819.3i	−0.442893	−	0.767114i
$753$	4433.64	−	8583.50i	0.214570	−	0.415405i
$754$	−1110.18	+	1922.89i	−0.0536212	+	0.0928746i
$755$	−2096.02			−0.101036
$756$	−16064.5	+	2271.09i	−0.772833	+	0.109258i
$757$	40262.5			1.93311			0.966557	−	0.256453i	$-0.0825538\pi$
$757$	40262.5			1.93311			0.966557	+	0.256453i	$0.0825538\pi$
$758$	−6484.21	+	11231.0i	−0.310709	+	0.538163i
$759$	2850.32	−	5518.20i	0.136311	−	0.263897i
$760$	−16856.8	−	29196.9i	−0.804555	−	1.39353i
$761$	−19445.6	−	33680.8i	−0.926286	−	1.60438i	−0.789479	−	0.613777i	$-0.789649\pi$
$761$	−19445.6	−	33680.8i	−0.926286	−	1.60438i	−0.136807	−	0.990598i	$-0.543684\pi$
$762$	20441.1	+	31862.0i	0.971790	+	1.51475i
$763$	6766.68	−	11720.2i	0.321062	−	0.556096i
$764$	−4514.91			−0.213801
$765$	−19435.2	+	42380.8i	−0.918539	+	2.00298i
$766$	43027.5			2.02956
$767$	−164.057	+	284.154i	−0.00772326	+	0.0133771i
$768$	−43333.8	+	2030.12i	−2.03603	+	0.0953847i
$769$	−13910.2	−	24093.2i	−0.652296	−	1.12981i	−0.982564	−	0.185923i	$-0.940473\pi$
$769$	−13910.2	−	24093.2i	−0.652296	−	1.12981i	0.330268	−	0.943887i	$-0.392861\pi$
$770$	8570.03	+	14843.7i	0.401094	+	0.694715i
$771$	19577.9	−	917.193i	0.914504	−	0.0428429i
$772$	−6973.93	+	12079.2i	−0.325126	+	0.563135i
$773$	25952.0			1.20754			0.603770	−	0.797159i	$-0.293665\pi$
$773$	25952.0			1.20754			0.603770	+	0.797159i	$0.293665\pi$
$774$	−5086.86	+	11092.5i	−0.236232	+	0.515131i
$775$	24998.5			1.15868
$776$	23418.3	−	40561.7i	1.08333	−	1.87639i
$777$	1789.07	+	2788.67i	0.0826032	+	0.128755i
$778$	26255.8	+	45476.5i	1.20992	+	2.09564i
$779$	−2051.35	−	3553.04i	−0.0943482	−	0.163416i
$780$	49603.1	−	96031.2i	2.27702	−	4.40829i
$781$	11444.0	−	19821.7i	0.524328	−	0.908163i
$782$	−20669.8			−0.945206
$783$	−301.468	+	747.916i	−0.0137594	+	0.0341358i
$784$	3761.32			0.171343
$785$	1751.43	−	3033.57i	0.0796322	−	0.137927i
$786$	8014.91	−	15516.8i	0.363718	−	0.704155i
$787$	−21058.2	−	36473.8i	−0.953802	−	1.65203i	−0.737087	−	0.675798i	$-0.763799\pi$
$787$	−21058.2	−	36473.8i	−0.953802	−	1.65203i	−0.216715	−	0.976235i	$-0.569534\pi$
$788$	−20706.5	−	35864.7i	−0.936090	−	1.62136i
$789$	−114.303	−	178.167i	−0.00515753	−	0.00803916i
$790$	6155.62	−	10661.8i	0.277224	−	0.480166i
$791$	−10784.4			−0.484765
$792$	34748.2	−	3262.94i	1.55899	−	0.146394i
$793$	−48866.0			−2.18825
$794$	7227.10	−	12517.7i	0.323023	−	0.559492i
$795$	41691.6	−	1953.18i	1.85994	−	0.0871348i
$796$	32529.7	+	56343.2i	1.44847	+	2.50883i
$797$	−6485.71	−	11233.6i	−0.288250	−	0.499264i	0.685142	−	0.728410i	$-0.259740\pi$
$797$	−6485.71	−	11233.6i	−0.288250	−	0.499264i	−0.973392	+	0.229145i	$0.926407\pi$
$798$	−8907.27	+	417.290i	−0.395130	+	0.0185112i
$799$	−12730.1	+	22049.1i	−0.563652	+	0.976274i
$800$	−5769.00			−0.254956
$801$	−1736.02	−	2446.03i	−0.0765784	−	0.107898i
$802$	−21085.0			−0.928349
$803$	−356.353	+	617.221i	−0.0156605	+	0.0271248i
$804$	31456.3	+	49031.7i	1.37982	+	2.15076i
$805$	2203.91	+	3817.28i	0.0964937	+	0.167132i
$806$	−35634.9	−	61721.5i	−1.55730	−	2.69733i
$807$	−3348.24	+	6482.16i	−0.146051	+	0.282755i
$808$	−29498.9	+	51093.5i	−1.28436	+	2.22458i
$809$	−9053.03			−0.393433			−0.196717	−	0.980460i	$-0.563028\pi$
$809$	−9053.03			−0.393433			−0.196717	+	0.980460i	$0.563028\pi$
$810$	19229.0	−	54998.6i	0.834121	−	2.38574i
$811$	−2374.82			−0.102825			−0.0514127	−	0.998677i	$-0.516372\pi$
$811$	−2374.82			−0.102825			−0.0514127	+	0.998677i	$0.516372\pi$
$812$	332.345	−	575.638i	0.0143633	−	0.0248780i
$813$	531.014	−	1028.04i	0.0229071	−	0.0443480i
$814$	−6909.60	−	11967.8i	−0.297520	−	0.515320i
$815$	−328.592	−	569.138i	−0.0141228	−	0.0244614i
$816$	−23043.8	−	35918.8i	−0.988595	−	1.54094i
$817$	−2259.41	+	3913.41i	−0.0967524	+	0.167580i
$818$	22860.8			0.977152
$819$	−8533.61	−	12023.7i	−0.364089	−	0.512995i
$820$	−22096.2			−0.941016
$821$	−2574.93	+	4459.91i	−0.109459	+	0.189588i	−0.915551	−	0.402202i	$-0.868245\pi$
$821$	−2574.93	+	4459.91i	−0.109459	+	0.189588i	0.806092	+	0.591790i	$0.201578\pi$
$822$	−46776.9	+	2191.42i	−1.98483	+	0.0929860i
$823$	−1437.48	−	2489.79i	−0.0608839	−	0.105454i	0.833977	−	0.551799i	$-0.186059\pi$
$823$	−1437.48	−	2489.79i	−0.0608839	−	0.105454i	−0.894861	+	0.446345i	$0.852725\pi$
$824$	30541.6	+	52899.6i	1.29122	+	2.23646i
$825$	−21547.0	+	1009.44i	−0.909298	+	0.0425991i
$826$	72.8945	−	126.257i	0.00307061	−	0.00531846i
$827$	515.502			0.0216757			0.0108378	−	0.999941i	$-0.496550\pi$
$827$	515.502			0.0216757			0.0108378	+	0.999941i	$0.496550\pi$
$828$	17326.1	−	1626.97i	0.727204	−	0.0682864i
$829$	−14698.3			−0.615793			−0.307897	−	0.951420i	$-0.599625\pi$
$829$	−14698.3			−0.615793			−0.307897	+	0.951420i	$0.599625\pi$
$830$	11276.8	−	19532.1i	0.471596	−	0.816829i
$831$	16215.5	+	25275.5i	0.676907	+	1.05511i
$832$	−15729.7	−	27244.7i	−0.655444	−	1.13526i
$833$	−2621.30	−	4540.22i	−0.109031	−	0.188847i
$834$	−34464.6	+	66723.2i	−1.43095	+	2.77031i
$835$	−13928.7	+	24125.2i	−0.577272	+	0.999864i
$836$	25058.0			1.03666
$837$	−15952.2	−	20383.6i	−0.658769	−	0.841770i
$838$	−9879.53			−0.407259
$839$	2205.55	−	3820.12i	0.0907557	−	0.157194i	−0.817074	−	0.576533i	$-0.804405\pi$
$839$	2205.55	−	3820.12i	0.0907557	−	0.157194i	0.907829	+	0.419340i	$0.137738\pi$
$840$	−11367.1	+	22006.7i	−0.466909	+	0.903932i
$841$	12178.0	+	21092.9i	0.499323	+	0.864852i
$842$	41009.7	+	71030.9i	1.67849	+	2.90723i
$843$	−10578.5	−	16488.9i	−0.432197	−	0.673675i
$844$	552.201	−	956.441i	0.0225208	−	0.0390072i
$845$	62765.9			2.55528
$846$	13262.1	−	28919.6i	0.538961	−	1.17527i
$847$	2746.58			0.111421
$848$	−19100.9	+	33083.8i	−0.773501	+	1.33974i
$849$	−24935.6	+	1168.19i	−1.00799	+	0.0472228i
$850$	35893.7	+	62169.7i	1.44840	+	2.50871i
$851$	−1776.90	−	3077.68i	−0.0715763	−	0.123974i
$852$	64060.4	−	3001.12i	2.57591	−	0.120677i
$853$	−10950.2	+	18966.3i	−0.439540	+	0.761306i	−0.997654	−	0.0684586i	$-0.978192\pi$
$853$	−10950.2	+	18966.3i	−0.439540	+	0.761306i	0.558114	+	0.829764i	$0.311525\pi$
$854$	21712.4			0.870004
$855$	8993.25	−	19610.8i	0.359722	−	0.784417i
$856$	44861.5			1.79128
$857$	−11901.6	+	20614.1i	−0.474388	+	0.821664i	−0.999570	−	0.0293263i	$-0.990664\pi$
$857$	−11901.6	+	20614.1i	−0.474388	+	0.821664i	0.525182	+	0.850990i	$0.323997\pi$
$858$	33207.2	+	51760.7i	1.32130	+	2.05954i
$859$	−22244.1	−	38527.8i	−0.883536	−	1.53033i	−0.847382	−	0.530983i	$-0.821823\pi$
$859$	−22244.1	−	38527.8i	−0.883536	−	1.53033i	−0.0361535	−	0.999346i	$-0.511511\pi$
$860$	12168.7	+	21076.7i	0.482497	+	0.835710i
$861$	−1383.29	+	2678.05i	−0.0547533	+	0.106002i
$862$	3563.49	−	6172.15i	0.140804	−	0.243880i
$863$	−34544.3			−1.36258			−0.681288	−	0.732016i	$-0.738580\pi$
$863$	−34544.3			−1.36258			−0.681288	+	0.732016i	$0.738580\pi$
$864$	3681.35	+	4704.00i	0.144956	+	0.185224i
$865$	−9407.60			−0.369790
$866$	−16014.1	+	27737.3i	−0.628386	+	1.08840i
$867$	−15581.8	+	30166.2i	−0.610363	+	1.18166i
$868$	10667.7	+	18477.0i	0.417149	+	0.722523i
$869$	2359.68	+	4087.08i	0.0921134	+	0.159545i
$870$	1288.92	+	2009.06i	0.0502280	+	0.0782914i
$871$	−26470.2	+	45847.8i	−1.02975	+	1.78357i
$872$	−81570.8			−3.16782
$873$	29841.2	−	2802.17i	1.15690	−	0.108636i
$874$	9564.52			0.370166
$875$	593.048	−	1027.19i	0.0229128	−	0.0396861i
$876$	−1994.76	+	93.4509i	−0.0769368	+	0.00360435i
$877$	−16602.3	−	28756.0i	−0.639246	−	1.10721i	−0.985599	−	0.169102i	$-0.945913\pi$
$877$	−16602.3	−	28756.0i	−0.639246	−	1.10721i	0.346353	−	0.938104i	$-0.387420\pi$
$878$	−30973.6	−	53647.9i	−1.19056	−	2.06211i
$879$	15503.4	−	726.309i	0.594901	−	0.0278701i
$880$	18978.6	−	32871.9i	0.727010	−	1.25922i
$881$	23411.1			0.895278			0.447639	−	0.894214i	$-0.352265\pi$
$881$	23411.1			0.895278			0.447639	+	0.894214i	$0.352265\pi$
$882$	3791.71	+	5342.46i	0.144754	+	0.203957i
$883$	−12881.8			−0.490947			−0.245473	−	0.969403i	$-0.578943\pi$
$883$	−12881.8			−0.490947			−0.245473	+	0.969403i	$0.578943\pi$
$884$	68944.9	−	119416.i	2.62316	−	4.54344i
$885$	190.469	+	296.888i	0.00723452	+	0.0112766i
$886$	17383.7	+	30109.5i	0.659163	+	1.14170i
$887$	−2811.78	−	4870.15i	−0.106438	−	0.184356i	0.807887	−	0.589338i	$-0.200611\pi$
$887$	−2811.78	−	4870.15i	−0.106438	−	0.184356i	−0.914325	+	0.404982i	$0.867278\pi$
$888$	9164.77	−	17742.9i	0.346339	−	0.670511i
$889$	5149.31	−	8918.88i	0.194266	−	0.336479i
$890$	−8878.66			−0.334397
$891$	14572.8	+	16925.1i	0.547932	+	0.636379i
$892$	41096.3			1.54261
$893$	5890.58	−	10202.8i	0.220740	−	0.382333i
$894$	−11625.1	+	22506.1i	−0.434901	+	0.841966i
$895$	29858.0	+	51715.6i	1.11513	+	1.93146i
$896$	8181.25	+	14170.3i	0.305041	+	0.528346i
$897$	8539.70	+	13311.0i	0.317873	+	0.495476i
$898$	12835.6	−	22231.9i	0.476981	−	0.826155i
$899$	1060.42			0.0393405
$900$	−34980.8	−	49287.5i	−1.29559	−	1.82546i
$901$	53246.4			1.96881
$902$	6286.01	−	10887.7i	0.232041	−	0.401907i
$903$	3316.29	−	155.362i	0.122214	−	0.00572551i
$904$	32500.8	+	56293.1i	1.19575	+	2.07111i
$905$	−23184.9	−	40157.4i	−0.851592	−	1.47500i
$906$	3337.82	−	156.371i	0.122397	−	0.00573409i
$907$	−18281.5	+	31664.5i	−0.669269	+	1.15921i	0.308840	+	0.951114i	$0.400059\pi$
$907$	−18281.5	+	31664.5i	−0.669269	+	1.15921i	−0.978109	+	0.208093i	$0.933274\pi$
$908$	63549.6			2.32265
$909$	−37589.4	+	3529.75i	−1.37158	+	0.128795i
$910$	−43644.1			−1.58988
$911$	−9963.46	+	17257.2i	−0.362354	+	0.627615i	−0.988348	−	0.152213i	$-0.951360\pi$
$911$	−9963.46	+	17257.2i	−0.362354	+	0.627615i	0.625994	+	0.779828i	$0.284693\pi$
$912$	10663.0	+	16620.7i	0.387158	+	0.603472i
$913$	4322.83	+	7487.37i	0.156698	+	0.271408i
$914$	6378.63	+	11048.1i	0.230838	+	0.399824i
$915$	−24108.6	+	46674.0i	−0.871044	+	1.68633i
$916$	33139.1	−	57398.6i	1.19536	−	2.07042i
$917$	−4751.26			−0.171102
$918$	27788.0	−	68939.6i	0.999064	−	2.47859i
$919$	48298.1			1.73363			0.866816	−	0.498628i	$-0.166163\pi$
$919$	48298.1			1.73363			0.866816	+	0.498628i	$0.166163\pi$
$920$	13283.8	−	23008.2i	0.476036	−	0.824519i
$921$	6871.40	−	13303.0i	0.245842	−	0.475948i
$922$	−44329.6	−	76781.2i	−1.58343	−	2.74258i
$923$	29140.2	+	50472.3i	1.03918	+	1.79991i
$924$	−9940.92	−	15495.1i	−0.353931	−	0.551680i
$925$	−6171.28	+	10689.0i	−0.219362	+	0.379947i
$926$	−55776.5			−1.97941
$927$	−16294.2	+	35531.4i	−0.577315	+	1.25890i
$928$	−244.718			−0.00865652
$929$	−7808.00	+	13523.9i	−0.275751	+	0.477614i	−0.970324	−	0.241808i	$-0.922260\pi$
$929$	−7808.00	+	13523.9i	−0.275751	+	0.477614i	0.694574	+	0.719422i	$0.255593\pi$
$930$	−76533.8	+	3585.48i	−2.69854	+	0.126422i
$931$	1212.95	+	2100.89i	0.0426990	+	0.0739569i
$932$	−47283.2	−	81896.9i	−1.66182	−	2.87835i
$933$	35283.1	−	1652.95i	1.23807	−	0.0580013i
$934$	24306.0	−	42099.2i	0.851516	−	1.47487i
$935$	−52905.4			−1.85047
$936$	−37044.6	+	80780.1i	−1.29363	+	2.82092i
$937$	25030.1			0.872678			0.436339	−	0.899782i	$-0.356275\pi$
$937$	25030.1			0.872678			0.436339	+	0.899782i	$0.356275\pi$
$938$	11761.4	−	20371.3i	0.409407	−	0.709113i
$939$	−2642.35	−	4118.70i	−0.0918317	−	0.143140i
$940$	−31725.3	−	54949.8i	−1.10081	−	1.90667i
$941$	−8006.44	−	13867.6i	−0.277367	−	0.480414i	0.693363	−	0.720589i	$-0.256128\pi$
$941$	−8006.44	−	13867.6i	−0.277367	−	0.480414i	−0.970730	+	0.240175i	$0.922795\pi$
$942$	−2562.76	+	4961.49i	−0.0886404	+	0.171607i
$943$	1616.54	−	2799.92i	0.0558236	−	0.0966894i
$944$	−322.855			−0.0111314
$945$	−15694.6	+	2218.78i	−0.540258	+	0.0763778i
$946$	−13847.1			−0.475908
$947$	606.613	−	1050.69i	0.0208155	−	0.0360535i	−0.855430	−	0.517918i	$-0.826707\pi$
$947$	606.613	−	1050.69i	0.0208155	−	0.0360535i	0.876246	+	0.481865i	$0.160040\pi$
$948$	−6068.49	+	11748.5i	−0.207906	+	0.402505i
$949$	−907.388	−	1571.64i	−0.0310380	−	0.0537594i
$950$	−16609.0	−	28767.7i	−0.567230	−	0.982471i
$951$	−10193.5	−	15888.9i	−0.347580	−	0.541780i
$952$	−15799.5	+	27365.6i	−0.537885	+	0.931644i
$953$	−20143.9			−0.684705			−0.342352	−	0.939572i	$-0.611224\pi$
$953$	−20143.9			−0.684705			−0.342352	+	0.939572i	$0.611224\pi$
$954$	−66246.4	+	6220.71i	−2.24822	+	0.211114i
$955$	−4410.92			−0.149460
$956$	−50549.1	+	87553.5i	−1.71012	+	2.96201i
$957$	−914.012	+	42.8199i	−0.0308734	+	0.00144636i
$958$	18202.2	+	31527.1i	0.613869	+	1.06325i
$959$	6369.86	+	11032.9i	0.214487	+	0.371503i
$960$	−33783.0	+	1582.68i	−1.13577	+	0.0532090i
$961$	−2123.40	+	3677.84i	−0.0712767	+	0.123455i
$962$	35188.1			1.17932
$963$	16615.8	+	23411.4i	0.556009	+	0.783408i
$964$	8141.32			0.272007
$965$	−6813.31	+	11801.0i	−0.227283	+	0.393666i
$966$	−3794.41	−	5914.43i	−0.126380	−	0.196991i
$967$	−13701.4	−	23731.5i	−0.455642	−	0.789196i	0.543082	−	0.839679i	$-0.317257\pi$
$967$	−13701.4	−	23731.5i	−0.455642	−	0.789196i	−0.998725	+	0.0504835i	$0.983924\pi$
$968$	−8277.34	−	14336.8i	−0.274839	−	0.476035i
$969$	12631.4	−	24454.2i	0.418759	−	0.810714i
$970$	44360.4	−	76834.4i	1.46838	−	2.54330i
$971$	−25837.8			−0.853938			−0.426969	−	0.904266i	$-0.640419\pi$
$971$	−25837.8			−0.853938			−0.426969	+	0.904266i	$0.640419\pi$
$972$	−17866.4	+	59974.7i	−0.589574	+	1.97911i
$973$	20430.7			0.673154
$974$	37911.2	−	65664.2i	1.24718	−	2.16018i
$975$	25206.8	−	48800.2i	0.827963	−	1.60293i
$976$	−24041.4	−	41641.0i	−0.788471	−	1.36567i
$977$	11031.0	+	19106.2i	0.361221	+	0.625653i	0.988162	−	0.153414i	$-0.0490268\pi$
$977$	11031.0	+	19106.2i	0.361221	+	0.625653i	−0.626941	+	0.779066i	$0.715693\pi$
$978$	565.728	+	881.813i	0.0184969	+	0.0288316i
$979$	1701.76	−	2947.53i	0.0555551	−	0.0962243i
$980$	13065.3			0.425874
$981$	−30212.2	−	42568.5i	−0.983283	−	1.38543i
$982$	89028.3			2.89308
$983$	5900.89	−	10220.6i	0.191464	−	0.331626i	−0.754271	−	0.656563i	$-0.772010\pi$
$983$	5900.89	−	10220.6i	0.191464	−	0.331626i	0.945736	+	0.324937i	$0.105343\pi$
$984$	18147.9	−	850.197i	0.587940	−	0.0275440i
$985$	−20229.6	−	35038.7i	−0.654385	−	1.13343i
$986$	1522.59	+	2637.20i	0.0491776	+	0.0851781i
$987$	−8646.00	+	405.050i	−0.278830	+	0.0130627i
$988$	−31902.8	+	55257.3i	−1.02729	+	1.77932i
$989$	−3560.99			−0.114492
$990$	65822.1	−	6180.87i	2.11309	−	0.198425i
$991$	−46761.9			−1.49893			−0.749465	−	0.662044i	$-0.769689\pi$
$991$	−46761.9			−1.49893			−0.749465	+	0.662044i	$0.769689\pi$
$992$	3927.51	−	6802.65i	0.125704	−	0.217726i
$993$	−7716.93	−	12028.6i	−0.246616	−	0.384405i
$994$	−12947.8	−	22426.2i	−0.413157	−	0.715608i
$995$	31780.5	+	55045.5i	1.01257	+	1.75383i
$996$	−11117.2	+	21522.9i	−0.353677	+	0.684717i
$997$	19130.6	−	33135.1i	0.607695	−	1.05256i	−0.383925	−	0.923364i	$-0.625428\pi$
$997$	19130.6	−	33135.1i	0.607695	−	1.05256i	0.991619	−	0.129194i	$-0.0412389\pi$
$998$	93168.6			2.95511
$999$	12653.8	−	1788.90i	0.400748	−	0.0566549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.b.43.8	yes	16
3.2	odd	2		189.4.f.b.127.1		16
9.2	odd	6		567.4.a.g.1.8		8
9.4	even	3	inner	63.4.f.b.22.8	✓	16
9.5	odd	6		189.4.f.b.64.1		16
9.7	even	3		567.4.a.i.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.b.22.8	✓	16	9.4	even	3	inner
63.4.f.b.43.8	yes	16	1.1	even	1	trivial
189.4.f.b.64.1		16	9.5	odd	6
189.4.f.b.127.1		16	3.2	odd	2
567.4.a.g.1.8		8	9.2	odd	6
567.4.a.i.1.1		8	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(2.47591 - 4.28840i) q^{2} +(-2.38464 + 4.61665i) q^{3} +(-8.26023 - 14.3071i) q^{4} +(-8.06998 - 13.9776i) q^{5} +(13.8939 + 21.6567i) q^{6} +(3.50000 - 6.06218i) q^{7} -42.1917 q^{8} +(-15.6270 - 22.0181i) q^{9} +O(q^{10})\)	\(q+(2.47591 - 4.28840i) q^{2} +(-2.38464 + 4.61665i) q^{3} +(-8.26023 - 14.3071i) q^{4} +(-8.06998 - 13.9776i) q^{5} +(13.8939 + 21.6567i) q^{6} +(3.50000 - 6.06218i) q^{7} -42.1917 q^{8} +(-15.6270 - 22.0181i) q^{9} -79.9221 q^{10} +(15.3185 - 26.5325i) q^{11} +(85.7487 - 4.01718i) q^{12} +(39.0059 + 67.5603i) q^{13} +(-17.3313 - 30.0188i) q^{14} +(83.7738 - 3.92466i) q^{15} +(-38.3809 + 66.4776i) q^{16} +106.992 q^{17} +(-133.113 + 12.4997i) q^{18} -49.5081 q^{19} +(-133.320 + 230.917i) q^{20} +(19.6407 + 30.6144i) q^{21} +(-75.8546 - 131.384i) q^{22} +(-19.5071 - 33.7873i) q^{23} +(100.612 - 194.784i) q^{24} +(-67.7492 + 117.345i) q^{25} +386.300 q^{26} +(138.915 - 19.6388i) q^{27} -115.643 q^{28} +(-2.87388 + 4.97771i) q^{29} +(190.586 - 368.972i) q^{30} +(-92.2467 - 159.776i) q^{31} +(21.2881 + 36.8720i) q^{32} +(85.9620 + 133.991i) q^{33} +(264.901 - 458.822i) q^{34} -112.980 q^{35} +(-185.934 + 405.452i) q^{36} +91.0901 q^{37} +(-122.578 + 212.310i) q^{38} +(-404.917 + 18.9697i) q^{39} +(340.486 + 589.739i) q^{40} +(41.4346 + 71.7668i) q^{41} +(179.915 - 8.42872i) q^{42} +(45.6371 - 79.0458i) q^{43} -506.139 q^{44} +(-181.652 + 396.113i) q^{45} -193.191 q^{46} +(-118.982 + 206.083i) q^{47} +(-215.379 - 335.716i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(335.481 + 581.070i) q^{50} +(-255.137 + 493.943i) q^{51} +(644.396 - 1116.13i) q^{52} +497.669 q^{53} +(259.721 - 644.345i) q^{54} -494.481 q^{55} +(-147.671 + 255.773i) q^{56} +(118.059 - 228.562i) q^{57} +(14.2309 + 24.6487i) q^{58} +(2.10297 + 3.64245i) q^{59} +(-748.141 - 1166.14i) q^{60} +(-313.196 + 542.471i) q^{61} -913.577 q^{62} +(-188.172 + 17.6699i) q^{63} -403.264 q^{64} +(629.554 - 1090.42i) q^{65} +(787.440 - 36.8902i) q^{66} +(339.310 + 587.702i) q^{67} +(-883.775 - 1530.74i) q^{68} +(202.502 - 9.48685i) q^{69} +(-279.727 + 484.502i) q^{70} +747.071 q^{71} +(659.327 + 928.982i) q^{72} -23.2628 q^{73} +(225.531 - 390.630i) q^{74} +(-380.183 - 592.600i) q^{75} +(408.948 + 708.319i) q^{76} +(-107.230 - 185.728i) q^{77} +(-921.188 + 1783.41i) q^{78} +(-77.0203 + 133.403i) q^{79} +1238.93 q^{80} +(-240.597 + 688.153i) q^{81} +410.353 q^{82} +(-141.098 + 244.389i) q^{83} +(275.768 - 533.884i) q^{84} +(-863.420 - 1495.49i) q^{85} +(-225.986 - 391.420i) q^{86} +(-16.1272 - 25.1378i) q^{87} +(-646.315 + 1119.45i) q^{88} +111.091 q^{89} +(1248.94 + 1759.74i) q^{90} +546.083 q^{91} +(-322.266 + 558.181i) q^{92} +(957.605 - 44.8622i) q^{93} +(589.177 + 1020.48i) q^{94} +(399.530 + 692.006i) q^{95} +(-220.990 + 10.3530i) q^{96} +(-555.045 + 961.367i) q^{97} -242.639 q^{98} +(-823.578 + 77.3362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * q^99

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