LMFDB - Embedded newform 63.3.r.a.29.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(29,63)]

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([1, 0]))

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

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

chi := DirichletCharacter("63.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.10
Character	$\chi$	$=$	63.29
Dual form			63.3.r.a.50.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27188 + 1.31167i) q^{2} +(2.79644 - 1.08624i) q^{3} +(1.44095 + 2.49580i) q^{4} +(-7.02923 + 4.05833i) q^{5} +(7.77795 + 1.20021i) q^{6} +(1.32288 - 2.29129i) q^{7} -2.93316i q^{8} +(6.64018 - 6.07519i) q^{9} +O(q^{10})$	\(q+(2.27188 + 1.31167i) q^{2} +(2.79644 - 1.08624i) q^{3} +(1.44095 + 2.49580i) q^{4} +(-7.02923 + 4.05833i) q^{5} +(7.77795 + 1.20021i) q^{6} +(1.32288 - 2.29129i) q^{7} -2.93316i q^{8} +(6.64018 - 6.07519i) q^{9} -21.2927 q^{10} +(-11.7706 - 6.79576i) q^{11} +(6.74056 + 5.41415i) q^{12} +(7.28806 + 12.6233i) q^{13} +(6.01082 - 3.47035i) q^{14} +(-15.2485 + 18.9843i) q^{15} +(9.61113 - 16.6470i) q^{16} +13.5231i q^{17} +(23.0543 - 5.09236i) q^{18} -5.74938 q^{19} +(-20.2575 - 11.6957i) q^{20} +(1.21047 - 7.84441i) q^{21} +(-17.8276 - 30.8782i) q^{22} +(-18.2499 + 10.5366i) q^{23} +(-3.18610 - 8.20240i) q^{24} +(20.4400 - 35.4032i) q^{25} +38.2381i q^{26} +(11.9698 - 24.2017i) q^{27} +7.62479 q^{28} +(42.0437 + 24.2740i) q^{29} +(-59.5439 + 23.1289i) q^{30} +(-3.97687 - 6.88815i) q^{31} +(33.5098 - 19.3469i) q^{32} +(-40.2976 - 6.21830i) q^{33} +(-17.7378 + 30.7228i) q^{34} +21.4746i q^{35} +(24.7306 + 7.81852i) q^{36} +13.3422 q^{37} +(-13.0619 - 7.54128i) q^{38} +(34.0925 + 27.3838i) q^{39} +(11.9037 + 20.6178i) q^{40} +(-3.28027 + 1.89387i) q^{41} +(13.0393 - 16.2338i) q^{42} +(2.48678 - 4.30722i) q^{43} -39.1694i q^{44} +(-22.0203 + 69.6520i) q^{45} -55.2820 q^{46} +(-39.4216 - 22.7601i) q^{47} +(8.79445 - 56.9922i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(92.8745 - 53.6211i) q^{50} +(14.6892 + 37.8165i) q^{51} +(-21.0035 + 36.3791i) q^{52} +46.0794i q^{53} +(58.9386 - 39.2829i) q^{54} +110.318 q^{55} +(-6.72070 - 3.88020i) q^{56} +(-16.0778 + 6.24518i) q^{57} +(63.6788 + 110.295i) q^{58} +(47.0471 - 27.1627i) q^{59} +(-69.3533 - 10.7019i) q^{60} +(-0.542437 + 0.939529i) q^{61} -20.8654i q^{62} +(-5.13587 - 23.2513i) q^{63} +24.6180 q^{64} +(-102.459 - 59.1547i) q^{65} +(-83.3948 - 66.9843i) q^{66} +(17.0383 + 29.5112i) q^{67} +(-33.7509 + 19.4861i) q^{68} +(-39.5896 + 49.2886i) q^{69} +(-28.1676 + 48.7878i) q^{70} -114.969i q^{71} +(-17.8195 - 19.4767i) q^{72} -127.878 q^{73} +(30.3117 + 17.5005i) q^{74} +(18.7032 - 121.206i) q^{75} +(-8.28457 - 14.3493i) q^{76} +(-31.1421 + 17.9799i) q^{77} +(41.5356 + 106.931i) q^{78} +(-14.3908 + 24.9256i) q^{79} +156.020i q^{80} +(7.18411 - 80.6808i) q^{81} -9.93650 q^{82} +(-11.7071 - 6.75911i) q^{83} +(21.3223 - 8.28232i) q^{84} +(-54.8811 - 95.0568i) q^{85} +(11.2993 - 6.52365i) q^{86} +(143.940 + 22.2114i) q^{87} +(-19.9330 + 34.5250i) q^{88} -61.9148i q^{89} +(-141.388 + 129.357i) q^{90} +38.5648 q^{91} +(-52.5944 - 30.3654i) q^{92} +(-18.6032 - 14.9425i) q^{93} +(-59.7074 - 103.416i) q^{94} +(40.4137 - 23.3329i) q^{95} +(72.6931 - 90.5021i) q^{96} +(44.5329 - 77.1332i) q^{97} -18.3634i q^{98} +(-119.444 + 26.3835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9}+O(q^{10}) $ 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9	$ 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9} - 18 q^{11} + 4 q^{12} - 10 q^{15} - 48 q^{16} - 62 q^{18} - 24 q^{19} - 18 q^{20} - 14 q^{21} - 24 q^{22} + 72 q^{23} + 54 q^{24} + 54 q^{25} - 124 q^{27} + 54 q^{29} - 212 q^{30} + 30 q^{31} + 126 q^{32} - 178 q^{33} + 60 q^{34} + 124 q^{36} + 84 q^{37} - 144 q^{38} + 92 q^{39} - 60 q^{40} + 180 q^{41} + 140 q^{42} - 60 q^{43} - 118 q^{45} - 168 q^{46} + 378 q^{47} + 436 q^{48} - 84 q^{49} - 378 q^{50} + 168 q^{51} - 18 q^{52} + 514 q^{54} - 132 q^{55} - 232 q^{57} + 90 q^{58} - 90 q^{59} + 76 q^{60} + 28 q^{63} + 324 q^{64} + 126 q^{65} + 202 q^{66} + 6 q^{67} - 738 q^{68} - 432 q^{69} - 246 q^{72} - 72 q^{73} - 792 q^{74} + 40 q^{75} + 84 q^{76} + 28 q^{78} - 6 q^{79} - 34 q^{81} - 108 q^{82} - 558 q^{83} - 322 q^{84} + 126 q^{85} + 90 q^{86} + 428 q^{87} + 168 q^{88} - 488 q^{90} + 84 q^{91} + 774 q^{92} - 738 q^{93} - 354 q^{94} + 648 q^{95} - 280 q^{96} - 270 q^{97} + 296 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9 - 18 * q^11 + 4 * q^12 - 10 * q^15 - 48 * q^16 - 62 * q^18 - 24 * q^19 - 18 * q^20 - 14 * q^21 - 24 * q^22 + 72 * q^23 + 54 * q^24 + 54 * q^25 - 124 * q^27 + 54 * q^29 - 212 * q^30 + 30 * q^31 + 126 * q^32 - 178 * q^33 + 60 * q^34 + 124 * q^36 + 84 * q^37 - 144 * q^38 + 92 * q^39 - 60 * q^40 + 180 * q^41 + 140 * q^42 - 60 * q^43 - 118 * q^45 - 168 * q^46 + 378 * q^47 + 436 * q^48 - 84 * q^49 - 378 * q^50 + 168 * q^51 - 18 * q^52 + 514 * q^54 - 132 * q^55 - 232 * q^57 + 90 * q^58 - 90 * q^59 + 76 * q^60 + 28 * q^63 + 324 * q^64 + 126 * q^65 + 202 * q^66 + 6 * q^67 - 738 * q^68 - 432 * q^69 - 246 * q^72 - 72 * q^73 - 792 * q^74 + 40 * q^75 + 84 * q^76 + 28 * q^78 - 6 * q^79 - 34 * q^81 - 108 * q^82 - 558 * q^83 - 322 * q^84 + 126 * q^85 + 90 * q^86 + 428 * q^87 + 168 * q^88 - 488 * q^90 + 84 * q^91 + 774 * q^92 - 738 * q^93 - 354 * q^94 + 648 * q^95 - 280 * q^96 - 270 * q^97 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.27188	+	1.31167i	1.13594	+	0.655834i	0.945422	−	0.325850i	$-0.105650\pi$
$2$	2.27188	+	1.31167i	1.13594	+	0.655834i	0.190517	+	0.981684i	$0.438984\pi$
$3$	2.79644	−	1.08624i	0.932148	−	0.362078i
$3$	2.79644	−	1.08624i	0.932148	−	0.362078i
$4$	1.44095	+	2.49580i	0.360237	+	0.623949i
$5$	−7.02923	+	4.05833i	−1.40585	+	0.811665i	−0.994984	−	0.100032i	$-0.968105\pi$
$5$	−7.02923	+	4.05833i	−1.40585	+	0.811665i	−0.410862	+	0.911698i	$0.634772\pi$
$6$	7.77795	+	1.20021i	1.29633	+	0.200036i
$7$	1.32288	−	2.29129i	0.188982	−	0.327327i
$7$	1.32288	−	2.29129i	0.188982	−	0.327327i
$8$		−	2.93316i		−	0.366644i
$9$	6.64018	−	6.07519i	0.737798	−	0.675021i
$10$	−21.2927			−2.12927
$11$	−11.7706	−	6.79576i	−1.07005	−	0.617796i	−0.141858	−	0.989887i	$-0.545308\pi$
$11$	−11.7706	−	6.79576i	−1.07005	−	0.617796i	−0.928196	+	0.372091i	$0.878641\pi$
$12$	6.74056	+	5.41415i	0.561713	+	0.451179i
$13$	7.28806	+	12.6233i	0.560620	+	0.971023i	0.997442	+	0.0714748i	$0.0227706\pi$
$13$	7.28806	+	12.6233i	0.560620	+	0.971023i	−0.436822	+	0.899548i	$0.643896\pi$
$14$	6.01082	−	3.47035i	0.429344	−	0.247882i
$15$	−15.2485	+	18.9843i	−1.01657	+	1.26562i
$16$	9.61113	−	16.6470i	0.600695	−	1.04044i
$17$			13.5231i			0.795475i	0.917499	+	0.397737i	$0.130205\pi$
$17$			13.5231i			0.795475i	−0.917499	+	0.397737i	$0.869795\pi$
$18$	23.0543	−	5.09236i	1.28080	−	0.282909i
$19$	−5.74938			−0.302599			−0.151300	−	0.988488i	$-0.548346\pi$
$19$	−5.74938			−0.302599			−0.151300	+	0.988488i	$0.548346\pi$
$20$	−20.2575	−	11.6957i	−1.01288	−	0.584784i
$21$	1.21047	−	7.84441i	0.0576413	−	0.373543i
$22$	−17.8276	−	30.8782i	−0.810344	−	1.40356i
$23$	−18.2499	+	10.5366i	−0.793474	+	0.458112i	−0.841184	−	0.540749i	$-0.818141\pi$
$23$	−18.2499	+	10.5366i	−0.793474	+	0.458112i	0.0477103	+	0.998861i	$0.484808\pi$
$24$	−3.18610	−	8.20240i	−0.132754	−	0.341767i
$25$	20.4400	−	35.4032i	0.817602	−	1.41613i
$26$			38.2381i			1.47070i
$27$	11.9698	−	24.2017i	0.443326	−	0.896360i
$28$	7.62479			0.272314
$29$	42.0437	+	24.2740i	1.44978	+	0.837033i	0.998468	−	0.0553306i	$-0.0176213\pi$
$29$	42.0437	+	24.2740i	1.44978	+	0.837033i	0.451316	+	0.892364i	$0.350955\pi$
$30$	−59.5439	+	23.1289i	−1.98480	+	0.770964i
$31$	−3.97687	−	6.88815i	−0.128286	−	0.222198i	0.794726	−	0.606968i	$-0.207614\pi$
$31$	−3.97687	−	6.88815i	−0.128286	−	0.222198i	−0.923013	+	0.384769i	$0.874281\pi$
$32$	33.5098	−	19.3469i	1.04718	−	0.604591i
$33$	−40.2976	−	6.21830i	−1.22114	−	0.188433i
$34$	−17.7378	+	30.7228i	−0.521700	+	0.903611i
$35$			21.4746i			0.613561i
$36$	24.7306	+	7.81852i	0.686962	+	0.217181i
$37$	13.3422			0.360599			0.180299	−	0.983612i	$-0.442293\pi$
$37$	13.3422			0.360599			0.180299	+	0.983612i	$0.442293\pi$
$38$	−13.0619	−	7.54128i	−0.343734	−	0.198455i
$39$	34.0925	+	27.3838i	0.874167	+	0.702148i
$40$	11.9037	+	20.6178i	0.297593	+	0.515446i
$41$	−3.28027	+	1.89387i	−0.0800067	+	0.0461919i	−0.539470	−	0.842005i	$-0.681375\pi$
$41$	−3.28027	+	1.89387i	−0.0800067	+	0.0461919i	0.459463	+	0.888197i	$0.348042\pi$
$42$	13.0393	−	16.2338i	0.310460	−	0.386519i
$43$	2.48678	−	4.30722i	0.0578320	−	0.100168i	−0.835660	−	0.549247i	$-0.814915\pi$
$43$	2.48678	−	4.30722i	0.0578320	−	0.100168i	0.893492	+	0.449079i	$0.148248\pi$
$44$		−	39.1694i		−	0.890213i
$45$	−22.0203	+	69.6520i	−0.489339	+	1.54782i
$46$	−55.2820			−1.20178
$47$	−39.4216	−	22.7601i	−0.838758	−	0.484257i	0.0180836	−	0.999836i	$-0.494243\pi$
$47$	−39.4216	−	22.7601i	−0.838758	−	0.484257i	−0.856842	+	0.515579i	$0.827577\pi$
$48$	8.79445	−	56.9922i	0.183218	−	1.18734i
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	92.8745	−	53.6211i	1.85749	−	1.07242i
$51$	14.6892	+	37.8165i	0.288024	+	0.741500i
$52$	−21.0035	+	36.3791i	−0.403913	+	0.699597i
$53$			46.0794i			0.869422i	0.900570	+	0.434711i	$0.143150\pi$
$53$			46.0794i			0.869422i	−0.900570	+	0.434711i	$0.856850\pi$
$54$	58.9386	−	39.2829i	1.09146	−	0.727462i
$55$	110.318			2.00577
$56$	−6.72070	−	3.88020i	−0.120013	−	0.0692893i
$57$	−16.0778	+	6.24518i	−0.282067	+	0.109565i
$58$	63.6788	+	110.295i	1.09791	+	1.90164i
$59$	47.0471	−	27.1627i	0.797409	−	0.460384i	−0.0451556	−	0.998980i	$-0.514378\pi$
$59$	47.0471	−	27.1627i	0.797409	−	0.460384i	0.842564	+	0.538596i	$0.181045\pi$
$60$	−69.3533	−	10.7019i	−1.15589	−	0.178365i
$61$	−0.542437	+	0.939529i	−0.00889241	+	0.0154021i	−0.870437	−	0.492279i	$-0.836164\pi$
$61$	−0.542437	+	0.939529i	−0.00889241	+	0.0154021i	0.861545	+	0.507681i	$0.169497\pi$
$62$		−	20.8654i		−	0.336538i
$63$	−5.13587	−	23.2513i	−0.0815218	−	0.369068i
$64$	24.6180			0.384656
$65$	−102.459	−	59.1547i	−1.57629	−	0.910072i
$66$	−83.3948	−	66.9843i	−1.26356	−	1.01491i
$67$	17.0383	+	29.5112i	0.254303	+	0.440466i	0.964706	−	0.263329i	$-0.0848206\pi$
$67$	17.0383	+	29.5112i	0.254303	+	0.440466i	−0.710403	+	0.703795i	$0.751487\pi$
$68$	−33.7509	+	19.4861i	−0.496336	+	0.286560i
$69$	−39.5896	+	49.2886i	−0.573762	+	0.714328i
$70$	−28.1676	+	48.7878i	−0.402395	+	0.696968i
$71$		−	114.969i		−	1.61928i	−0.586930	−	0.809638i	$-0.699664\pi$
$71$		−	114.969i		−	1.61928i	0.586930	−	0.809638i	$-0.300336\pi$
$72$	−17.8195	−	19.4767i	−0.247493	−	0.270510i
$73$	−127.878			−1.75175			−0.875876	−	0.482537i	$-0.839715\pi$
$73$	−127.878			−1.75175			−0.875876	+	0.482537i	$0.839715\pi$
$74$	30.3117	+	17.5005i	0.409618	+	0.236493i
$75$	18.7032	−	121.206i	0.249376	−	1.61608i
$76$	−8.28457	−	14.3493i	−0.109007	−	0.188806i
$77$	−31.1421	+	17.9799i	−0.404442	+	0.233505i
$78$	41.5356	+	106.931i	0.532507	+	1.37091i
$79$	−14.3908	+	24.9256i	−0.182162	+	0.315514i	−0.942617	−	0.333877i	$-0.891643\pi$
$79$	−14.3908	+	24.9256i	−0.182162	+	0.315514i	0.760454	+	0.649391i	$0.224976\pi$
$80$			156.020i			1.95025i
$81$	7.18411	−	80.6808i	0.0886927	−	0.996059i
$82$	−9.93650			−0.121177
$83$	−11.7071	−	6.75911i	−0.141050	−	0.0814351i	0.427814	−	0.903867i	$-0.359284\pi$
$83$	−11.7071	−	6.75911i	−0.141050	−	0.0814351i	−0.568864	+	0.822431i	$0.692617\pi$
$84$	21.3223	−	8.28232i	0.253837	−	0.0985990i
$85$	−54.8811	−	95.0568i	−0.645660	−	1.11832i
$86$	11.2993	−	6.52365i	0.131387	−	0.0758564i
$87$	143.940	+	22.2114i	1.65448	+	0.255303i
$88$	−19.9330	+	34.5250i	−0.226511	+	0.392329i
$89$		−	61.9148i		−	0.695672i	−0.937555	−	0.347836i	$-0.886917\pi$
$89$		−	61.9148i		−	0.695672i	0.937555	−	0.347836i	$-0.113083\pi$
$90$	−141.388	+	129.357i	−1.57097	+	1.43730i
$91$	38.5648			0.423789
$92$	−52.5944	−	30.3654i	−0.571678	−	0.330058i
$93$	−18.6032	−	14.9425i	−0.200035	−	0.160672i
$94$	−59.7074	−	103.416i	−0.635185	−	1.10017i
$95$	40.4137	−	23.3329i	0.425408	−	0.245609i
$96$	72.6931	−	90.5021i	0.757219	−	0.942731i
$97$	44.5329	−	77.1332i	0.459102	−	0.795188i	−0.539812	−	0.841786i	$-0.681505\pi$
$97$	44.5329	−	77.1332i	0.459102	−	0.795188i	0.998914	+	0.0465978i	$0.0148379\pi$
$98$		−	18.3634i		−	0.187381i
$99$	−119.444	+	26.3835i	−1.20651	+	0.266500i
$100$	117.812			1.17812
$101$	88.8356	+	51.2893i	0.879560	+	0.507814i	0.870513	−	0.492145i	$-0.163787\pi$
$101$	88.8356	+	51.2893i	0.879560	+	0.507814i	0.00904696	+	0.999959i	$0.497120\pi$
$102$	−16.2306	+	105.182i	−0.159123	+	1.03119i
$103$	23.4201	+	40.5649i	0.227380	+	0.393834i	0.957031	−	0.289986i	$-0.0936507\pi$
$103$	23.4201	+	40.5649i	0.227380	+	0.393834i	−0.729651	+	0.683820i	$0.760317\pi$
$104$	37.0261	−	21.3770i	0.356020	−	0.205548i
$105$	23.3265	+	60.0526i	0.222157	+	0.571930i
$106$	−60.4409	+	104.687i	−0.570197	+	0.987610i
$107$		−	64.3204i		−	0.601125i	−0.953762	−	0.300562i	$-0.902826\pi$
$107$		−	64.3204i		−	0.601125i	0.953762	−	0.300562i	$-0.0971744\pi$
$108$	77.6505	−	4.99924i	0.718986	−	0.0462893i
$109$	−18.8784			−0.173196			−0.0865981	−	0.996243i	$-0.527600\pi$
$109$	−18.8784			−0.173196			−0.0865981	+	0.996243i	$0.527600\pi$
$110$	250.628	+	144.700i	2.27844	+	1.31546i
$111$	37.3106	−	14.4927i	0.336131	−	0.130565i
$112$	−25.4287	−	44.0437i	−0.227042	−	0.393247i
$113$	−130.798	+	75.5163i	−1.15751	+	0.668286i	−0.950705	−	0.310097i	$-0.899638\pi$
$113$	−130.798	+	75.5163i	−1.15751	+	0.668286i	−0.206801	+	0.978383i	$0.566305\pi$
$114$	−44.7184	−	6.90048i	−0.392267	−	0.0605306i
$115$	85.5218	−	148.128i	0.743668	−	1.28807i
$116$			139.910i			1.20612i
$117$	125.083	+	39.5446i	1.06909	+	0.337988i
$118$	142.514			1.20774
$119$	30.9853	+	17.8893i	0.260380	+	0.150331i
$120$	55.6838	+	44.7263i	0.464032	+	0.372719i
$121$	31.8646	+	55.1911i	0.263344	+	0.456125i
$122$	−2.46470	+	1.42300i	−0.0202025	+	0.0116639i
$123$	−7.11591	+	8.85924i	−0.0578530	+	0.0720264i
$124$	11.4609	−	19.8509i	0.0924270	−	0.160088i
$125$			128.893i			1.03114i
$126$	18.8299	−	59.5606i	0.149444	−	0.472704i
$127$	81.2626			0.639863			0.319931	−	0.947441i	$-0.396340\pi$
$127$	81.2626			0.639863			0.319931	+	0.947441i	$0.396340\pi$
$128$	−78.1104	−	45.0970i	−0.610237	−	0.352321i
$129$	2.27547	−	14.7461i	0.0176393	−	0.114311i
$130$	−155.183	−	268.784i	−1.19371	−	2.06757i
$131$	−198.148	+	114.401i	−1.51258	+	0.873287i	−0.512686	+	0.858576i	$0.671350\pi$
$131$	−198.148	+	114.401i	−1.51258	+	0.873287i	−0.999892	+	0.0147114i	$0.995317\pi$
$132$	−42.5472	−	109.535i	−0.322327	−	0.829810i
$133$	−7.60572	+	13.1735i	−0.0571858	+	0.0990488i
$134$			89.3944i			0.667123i
$135$	14.0800	+	218.697i	0.104296	+	1.61998i
$136$	39.6653			0.291656
$137$	5.82148	+	3.36103i	0.0424926	+	0.0245331i	0.521096	−	0.853498i	$-0.325523\pi$
$137$	5.82148	+	3.36103i	0.0424926	+	0.0245331i	−0.478603	+	0.878031i	$0.658857\pi$
$138$	−154.593	+	60.0493i	−1.12024	+	0.435140i
$139$	−55.7468	−	96.5563i	−0.401056	−	0.694650i	0.592797	−	0.805352i	$-0.298024\pi$
$139$	−55.7468	−	96.5563i	−0.401056	−	0.694650i	−0.993854	+	0.110702i	$0.964690\pi$
$140$	−53.5964	+	30.9439i	−0.382831	+	0.221028i
$141$	−134.963	−	20.8261i	−0.957186	−	0.147703i
$142$	150.801	−	261.194i	1.06198	−	1.83940i
$143$		−	198.112i		−	1.38540i
$144$	−37.3138	−	168.928i	−0.259124	−	1.17311i
$145$	−394.047			−2.71756
$146$	−290.523	−	167.733i	−1.98988	−	1.14886i
$147$	−16.3725	−	13.1507i	−0.111378	−	0.0894606i
$148$	19.2254	+	33.2993i	0.129901	+	0.224995i
$149$	141.502	−	81.6962i	0.949678	−	0.548297i	0.0566969	−	0.998391i	$-0.481943\pi$
$149$	141.502	−	81.6962i	0.949678	−	0.548297i	0.892981	+	0.450095i	$0.148610\pi$
$150$	201.473	−	250.832i	1.34315	−	1.67221i
$151$	−124.123	+	214.987i	−0.822005	+	1.42375i	0.0821822	+	0.996617i	$0.473811\pi$
$151$	−124.123	+	214.987i	−0.822005	+	1.42375i	−0.904187	+	0.427137i	$0.859522\pi$
$152$			16.8638i			0.110946i
$153$	82.1553	+	89.7957i	0.536962	+	0.586900i
$154$	−94.3346			−0.612562
$155$	55.9087	+	32.2789i	0.360701	+	0.208251i
$156$	−19.2188	+	124.547i	−0.123197	+	0.798376i
$157$	145.171	+	251.443i	0.924654	+	1.60155i	0.792116	+	0.610370i	$0.208979\pi$
$157$	145.171	+	251.443i	0.924654	+	1.60155i	0.132538	+	0.991178i	$0.457687\pi$
$158$	−65.3883	+	37.7520i	−0.413850	+	0.238937i
$159$	50.0531	+	128.858i	0.314799	+	0.810430i
$160$	−157.032	+	271.988i	−0.981452	+	1.69992i
$161$			55.7543i			0.346300i
$162$	122.148	−	173.874i	0.753999	−	1.07329i
$163$	122.273			0.750141			0.375070	−	0.926996i	$-0.377619\pi$
$163$	122.273			0.750141			0.375070	+	0.926996i	$0.377619\pi$
$164$	−9.45342	−	5.45793i	−0.0576428	−	0.0332801i
$165$	308.497	−	119.831i	1.86968	−	0.726248i
$166$	−17.7314	−	30.7117i	−0.106816	−	0.185010i
$167$	45.8528	−	26.4731i	0.274568	−	0.158522i	−0.356394	−	0.934336i	$-0.615994\pi$
$167$	45.8528	−	26.4731i	0.274568	−	0.158522i	0.630962	+	0.775814i	$0.282661\pi$
$168$	−23.0089	−	3.55049i	−0.136958	−	0.0211339i
$169$	−21.7317	+	37.6405i	−0.128590	+	0.222725i
$170$		−	287.943i		−	1.69378i
$171$	−38.1770	+	34.9286i	−0.223257	+	0.204261i
$172$	14.3333			0.0833330
$173$	6.88355	+	3.97422i	0.0397893	+	0.0229724i	0.519763	−	0.854311i	$-0.326020\pi$
$173$	6.88355	+	3.97422i	0.0397893	+	0.0229724i	−0.479973	+	0.877283i	$0.659354\pi$
$174$	297.880	+	239.263i	1.71196	+	1.37508i
$175$	−54.0793	−	93.6680i	−0.309024	−	0.535246i
$176$	−226.257	+	130.630i	−1.28555	+	0.742214i
$177$	102.060	−	127.063i	0.576607	−	0.717870i
$178$	81.2117	−	140.663i	0.456245	−	0.790240i
$179$		−	134.257i		−	0.750039i	−0.927017	−	0.375020i	$-0.877636\pi$
$179$		−	134.257i		−	0.750039i	0.927017	−	0.375020i	$-0.122364\pi$
$180$	−205.567	+	45.4068i	−1.14204	+	0.252260i
$181$	−230.304			−1.27240			−0.636200	−	0.771524i	$-0.719495\pi$
$181$	−230.304			−1.27240			−0.636200	+	0.771524i	$0.719495\pi$
$182$	87.6145	+	50.5842i	0.481398	+	0.277935i
$183$	−0.496345	+	3.21655i	−0.00271227	+	0.0175768i
$184$	30.9054	+	53.5298i	0.167964	+	0.290923i
$185$	−93.7850	+	54.1468i	−0.506946	+	0.292686i
$186$	−22.6647	−	58.3488i	−0.121853	−	0.313703i
$187$	91.8995	−	159.175i	0.491441	−	0.851201i
$188$		−	131.185i		−	0.697790i
$189$	−39.6186	−	59.4422i	−0.209622	−	0.314509i
$190$	122.420			0.644316
$191$	232.651	+	134.321i	1.21807	+	0.703253i	0.964505	−	0.264065i	$-0.0850634\pi$
$191$	232.651	+	134.321i	1.21807	+	0.703253i	0.253565	+	0.967318i	$0.418397\pi$
$192$	68.8427	−	26.7409i	0.358556	−	0.139276i
$193$	167.359	+	289.875i	0.867148	+	1.50194i	0.864899	+	0.501946i	$0.167382\pi$
$193$	167.359	+	289.875i	0.867148	+	1.50194i	0.00224870	+	0.999997i	$0.499284\pi$
$194$	202.346	−	116.825i	1.04302	−	0.602190i
$195$	−350.776	−	54.1282i	−1.79885	−	0.277580i
$196$	10.0866	−	17.4706i	0.0514625	−	0.0891356i
$197$		−	64.8419i		−	0.329147i	−0.986365	−	0.164573i	$-0.947375\pi$
$197$		−	64.8419i		−	0.329147i	0.986365	−	0.164573i	$-0.0526247\pi$
$198$	−305.969	−	96.7314i	−1.54530	−	0.488542i
$199$	−239.509			−1.20356			−0.601782	−	0.798661i	$-0.705542\pi$
$199$	−239.509			−1.20356			−0.601782	+	0.798661i	$0.705542\pi$
$200$	−103.843	−	59.9538i	−0.519215	−	0.299769i
$201$	79.7027	+	64.0188i	0.396531	+	0.318501i
$202$	134.549	+	233.046i	0.666084	+	1.15369i
$203$	111.237	−	64.2229i	0.547967	−	0.316369i
$204$	−73.2159	+	91.1531i	−0.358901	+	0.446829i
$205$	15.3719	−	26.6249i	0.0749847	−	0.129877i
$206$			122.878i			0.596495i
$207$	−57.1709	+	180.836i	−0.276188	+	0.873606i
$208$	280.186			1.34705
$209$	67.6736	+	39.0714i	0.323797	+	0.186944i
$210$	−25.7742	+	167.029i	−0.122734	+	0.795375i
$211$	144.289	+	249.916i	0.683835	+	1.18444i	0.973801	+	0.227400i	$0.0730225\pi$
$211$	144.289	+	249.916i	0.683835	+	1.18444i	−0.289966	+	0.957037i	$0.593644\pi$
$212$	−115.005	+	66.3981i	−0.542476	+	0.313198i
$213$	−124.883	−	321.503i	−0.586305	−	1.50940i
$214$	84.3670	−	146.128i	0.394238	−	0.682841i
$215$			40.3686i			0.187761i
$216$	−70.9874	−	35.1093i	−0.328646	−	0.162543i
$217$	−21.0436			−0.0969753
$218$	−42.8894	−	24.7622i	−0.196740	−	0.113588i
$219$	−357.603	+	138.905i	−1.63289	+	0.634272i
$220$	158.962	+	275.330i	0.722555	+	1.25150i
$221$	−170.706	+	98.5570i	−0.772424	+	0.445959i
$222$	103.775	+	16.0134i	0.467453	+	0.0721326i
$223$	56.7814	−	98.3483i	0.254625	−	0.441024i	−0.710168	−	0.704032i	$-0.751381\pi$
$223$	56.7814	−	98.3483i	0.254625	−	0.441024i	0.964794	+	0.263008i	$0.0847146\pi$
$224$		−	102.374i		−	0.457028i
$225$	−79.3555	−	359.261i	−0.352691	−	1.59671i
$226$	−396.210			−1.75314
$227$	277.219	+	160.052i	1.22123	+	0.705077i	0.965180	−	0.261587i	$-0.0842458\pi$
$227$	277.219	+	160.052i	1.22123	+	0.705077i	0.256049	+	0.966664i	$0.417579\pi$
$228$	−38.7540	−	31.1280i	−0.169974	−	0.136526i
$229$	−149.192	−	258.407i	−0.651492	−	1.12842i	−0.982761	−	0.184880i	$-0.940810\pi$
$229$	−149.192	−	258.407i	−0.651492	−	1.12842i	0.331269	−	0.943536i	$-0.392523\pi$
$230$	388.590	−	224.353i	1.68952	−	0.975446i
$231$	−67.5566	+	84.1073i	−0.292453	+	0.364101i
$232$	71.1993	−	123.321i	0.306894	−	0.531555i
$233$		−	89.1872i		−	0.382778i	−0.981514	−	0.191389i	$-0.938701\pi$
$233$		−	89.1872i		−	0.382778i	0.981514	−	0.191389i	$-0.0612991\pi$
$234$	232.304	+	253.908i	0.992751	+	1.08508i
$235$	369.472			1.57222
$236$	135.585	+	78.2800i	0.574513	+	0.331695i
$237$	−13.1680	+	85.3349i	−0.0555612	+	0.360063i
$238$	46.9298	+	81.2848i	0.197184	+	0.341533i
$239$	6.03033	−	3.48161i	0.0252315	−	0.0145674i	−0.487331	−	0.873217i	$-0.662030\pi$
$239$	6.03033	−	3.48161i	0.0252315	−	0.0145674i	0.512563	+	0.858650i	$0.328696\pi$
$240$	169.475	+	436.302i	0.706145	+	1.81793i
$241$	26.8684	−	46.5375i	0.111487	−	0.193102i	−0.804883	−	0.593434i	$-0.797772\pi$
$241$	26.8684	−	46.5375i	0.111487	−	0.193102i	0.916370	+	0.400332i	$0.131105\pi$
$242$			167.183i			0.690839i
$243$	−67.5484	−	233.423i	−0.277977	−	0.960588i
$244$	−3.12650			−0.0128135
$245$	49.2046	+	28.4083i	0.200835	+	0.115952i
$246$	−27.7869	+	10.7934i	−0.112955	+	0.0438755i
$247$	−41.9019	−	72.5761i	−0.169643	−	0.293831i
$248$	−20.2040	+	11.6648i	−0.0814677	+	0.0470354i
$249$	−40.0803	−	6.18477i	−0.160965	−	0.0248385i
$250$	−169.065	+	292.829i	−0.676260	+	1.17132i
$251$		−	51.1311i		−	0.203710i	−0.994799	−	0.101855i	$-0.967522\pi$
$251$		−	51.1311i		−	0.203710i	0.994799	−	0.101855i	$-0.0324777\pi$
$252$	50.6300	−	46.3220i	0.200913	−	0.183818i
$253$	286.416			1.13208
$254$	184.619	+	106.590i	0.726845	+	0.419644i
$255$	−256.726	−	206.207i	−1.00677	−	0.808655i
$256$	−167.541	−	290.189i	−0.654456	−	1.13355i
$257$	267.238	−	154.290i	1.03984	−	0.600350i	0.120049	−	0.992768i	$-0.461695\pi$
$257$	267.238	−	154.290i	1.03984	−	0.600350i	0.919787	+	0.392418i	$0.128361\pi$
$258$	24.5116	−	30.5167i	0.0950063	−	0.118282i
$259$	17.6500	−	30.5707i	0.0681468	−	0.118034i
$260$		−	340.956i		−	1.31137i
$261$	426.647	−	94.2401i	1.63466	−	0.361073i
$262$	−600.223			−2.29093
$263$	−221.002	−	127.596i	−0.840313	−	0.485155i	0.0170575	−	0.999855i	$-0.494570\pi$
$263$	−221.002	−	127.596i	−0.840313	−	0.485155i	−0.857371	+	0.514699i	$0.827904\pi$
$264$	−18.2393	+	118.199i	−0.0690881	+	0.447724i
$265$	−187.005	−	323.903i	−0.705680	−	1.22227i
$266$	−34.5585	+	19.9524i	−0.129919	+	0.0750089i
$267$	−67.2540	−	173.141i	−0.251888	−	0.648469i
$268$	−49.1027	+	85.0483i	−0.183219	+	0.317344i
$269$			348.360i			1.29502i	0.762058	+	0.647509i	$0.224189\pi$
$269$			348.360i			1.29502i	−0.762058	+	0.647509i	$0.775811\pi$
$270$	−254.870	+	515.321i	−0.943962	+	1.90860i
$271$	83.6162			0.308547			0.154273	−	0.988028i	$-0.450696\pi$
$271$	83.6162			0.308547			0.154273	+	0.988028i	$0.450696\pi$
$272$	225.118	+	129.972i	0.827640	+	0.477838i
$273$	107.844	−	41.8905i	0.395034	−	0.153445i
$274$	8.81713	+	15.2717i	0.0321793	+	0.0557362i
$275$	−481.183	+	277.811i	−1.74976	+	1.01022i
$276$	−180.061	−	27.7852i	−0.652395	−	0.100671i
$277$	−255.752	+	442.975i	−0.923292	+	1.59919i	−0.129006	+	0.991644i	$0.541179\pi$
$277$	−255.752	+	442.975i	−0.923292	+	1.59919i	−0.794286	+	0.607544i	$0.792155\pi$
$278$		−	292.485i		−	1.05211i
$279$	−68.2540	−	21.5783i	−0.244638	−	0.0773416i
$280$	62.9885			0.224959
$281$	195.953	+	113.133i	0.697341	+	0.402610i	0.806356	−	0.591430i	$-0.201436\pi$
$281$	195.953	+	113.133i	0.697341	+	0.402610i	−0.109015	+	0.994040i	$0.534770\pi$
$282$	−279.303	−	224.341i	−0.990435	−	0.795537i
$283$	84.8865	+	147.028i	0.299952	+	0.519533i	0.976125	−	0.217211i	$-0.0696959\pi$
$283$	84.8865	+	147.028i	0.299952	+	0.519533i	−0.676172	+	0.736743i	$0.736363\pi$
$284$	286.938	−	165.664i	1.01035	−	0.583324i
$285$	87.6697	−	109.148i	0.307613	−	0.382975i
$286$	259.857	−	450.085i	0.908590	−	1.57372i
$287$			10.0214i			0.0349178i
$288$	104.975	−	332.046i	0.364498	−	1.15294i
$289$	106.126			0.367220
$290$	−895.226	−	516.859i	−3.08699	−	1.78227i
$291$	40.7488	−	264.072i	0.140030	−	0.907463i
$292$	−184.266	−	319.157i	−0.631046	−	1.09300i
$293$	95.6753	−	55.2382i	0.326537	−	0.188526i	−0.327766	−	0.944759i	$-0.606296\pi$
$293$	95.6753	−	55.2382i	0.326537	−	0.188526i	0.654302	+	0.756233i	$0.272962\pi$
$294$	−19.9469	−	51.3521i	−0.0678467	−	0.174667i
$295$	−220.470	+	381.865i	−0.747356	+	1.29446i
$296$		−	39.1346i		−	0.132212i
$297$	−305.361	+	203.525i	−1.02815	+	0.685269i
$298$	428.633			1.43837
$299$	−266.013	−	153.583i	−0.889675	−	0.513654i
$300$	329.455	−	127.972i	1.09818	−	0.426573i
$301$	−6.57939	−	11.3958i	−0.0218584	−	0.0378599i
$302$	−563.983	+	325.616i	−1.86749	+	1.07820i
$303$	304.136	+	46.9311i	1.00375	+	0.154888i
$304$	−55.2580	+	95.7097i	−0.181770	+	0.314835i
$305$		−	8.80555i		−	0.0288707i
$306$	68.8644	+	311.765i	0.225047	+	1.01884i
$307$	72.3232			0.235580			0.117790	−	0.993039i	$-0.462419\pi$
$307$	72.3232			0.235580			0.117790	+	0.993039i	$0.462419\pi$
$308$	−89.7483	−	51.8162i	−0.291391	−	0.168234i
$309$	109.556	+	87.9976i	0.354551	+	0.284782i
$310$	84.6784	+	146.667i	0.273156	+	0.473121i
$311$	−65.2010	+	37.6438i	−0.209650	+	0.121041i	−0.601148	−	0.799137i	$-0.705290\pi$
$311$	−65.2010	+	37.6438i	−0.209650	+	0.121041i	0.391499	+	0.920179i	$0.371957\pi$
$312$	80.3209	−	99.9987i	0.257439	−	0.320509i
$313$	50.3101	−	87.1396i	0.160735	−	0.278401i	−0.774397	−	0.632699i	$-0.781947\pi$
$313$	50.3101	−	87.1396i	0.160735	−	0.278401i	0.935133	+	0.354298i	$0.115280\pi$
$314$			761.664i			2.42568i
$315$	130.463	+	142.596i	0.414167	+	0.452685i
$316$	−82.9458			−0.262487
$317$	204.723	+	118.197i	0.645815	+	0.372861i	0.786851	−	0.617143i	$-0.211710\pi$
$317$	204.723	+	118.197i	0.645815	+	0.372861i	−0.141036	+	0.990004i	$0.545043\pi$
$318$	−55.3051	+	358.403i	−0.173915	+	1.12705i
$319$	−329.920	−	571.438i	−1.03423	−	1.79134i
$320$	−173.045	+	99.9078i	−0.540767	+	0.312212i
$321$	−69.8671	−	179.868i	−0.217654	−	0.560337i
$322$	−73.1312	+	126.667i	−0.227116	+	0.393376i
$323$		−	77.7493i		−	0.240710i
$324$	211.715	−	98.3268i	0.653441	−	0.303478i
$325$	595.873			1.83346
$326$	277.789	+	160.382i	0.852114	+	0.491968i
$327$	−52.7923	+	20.5064i	−0.161444	+	0.0627106i
$328$	5.55501	+	9.62155i	0.0169360	+	0.0293340i
$329$	−104.300	+	60.2176i	−0.317021	+	0.183032i
$330$	858.045	+	132.405i	2.60014	+	0.401226i
$331$	−239.920	+	415.554i	−0.724835	+	1.25545i	0.234207	+	0.972187i	$0.424751\pi$
$331$	−239.920	+	415.554i	−0.724835	+	1.25545i	−0.959042	+	0.283264i	$0.908583\pi$
$332$		−	38.9582i		−	0.117344i
$333$	88.5944	−	81.0561i	0.266049	−	0.243412i
$334$	138.896			0.415856
$335$	−239.532	−	138.294i	−0.715022	−	0.412818i
$336$	−118.952	−	95.5442i	−0.354023	−	0.284358i
$337$	−118.085	−	204.529i	−0.350401	−	0.606912i	0.635919	−	0.771756i	$-0.280621\pi$
$337$	−118.085	−	204.529i	−0.350401	−	0.606912i	−0.986320	+	0.164844i	$0.947288\pi$
$338$	−98.7436	+	57.0096i	−0.292141	+	0.168668i
$339$	−283.741	+	353.255i	−0.836994	+	1.04205i
$340$	158.162	−	273.944i	0.465181	−	0.805718i
$341$			108.103i			0.317019i
$342$	−132.548	+	29.2779i	−0.387567	+	0.0856080i
$343$	−18.5203			−0.0539949
$344$	−12.6338	−	7.29410i	−0.0367260	−	0.0212038i
$345$	78.2548	−	507.129i	0.226826	−	1.46994i
$346$	10.4257	+	18.0579i	0.0301321	+	0.0521904i
$347$	361.751	−	208.857i	1.04251	−	0.601893i	0.121966	−	0.992534i	$-0.461080\pi$
$347$	361.751	−	208.857i	1.04251	−	0.601893i	0.920543	+	0.390642i	$0.127747\pi$
$348$	151.975	+	391.251i	0.436711	+	1.12428i
$349$	−112.398	+	194.679i	−0.322057	+	0.557818i	−0.980912	−	0.194451i	$-0.937707\pi$
$349$	−112.398	+	194.679i	−0.322057	+	0.557818i	0.658856	+	0.752269i	$0.271041\pi$
$350$		−	283.736i		−	0.810675i
$351$	392.742	−	25.2853i	1.11892	−	0.0720378i
$352$	−525.908			−1.49406
$353$	−59.4828	−	34.3424i	−0.168507	−	0.0972873i	0.413375	−	0.910561i	$-0.364350\pi$
$353$	−59.4828	−	34.3424i	−0.168507	−	0.0972873i	−0.581881	+	0.813274i	$0.697683\pi$
$354$	398.531	−	154.803i	1.12579	−	0.437298i
$355$	466.580	+	808.140i	1.31431	+	2.27645i
$356$	154.527	−	89.2161i	0.434064	−	0.250607i
$357$	106.081	+	16.3692i	0.297144	+	0.0458522i
$358$	176.101	−	305.015i	0.491901	−	0.851998i
$359$		−	133.972i		−	0.373181i	−0.982438	−	0.186591i	$-0.940256\pi$
$359$		−	133.972i		−	0.373181i	0.982438	−	0.186591i	$-0.0597438\pi$
$360$	204.300	+	64.5889i	0.567500	+	0.179414i
$361$	−327.945			−0.908434
$362$	−523.223	−	302.083i	−1.44537	−	0.834484i
$363$	149.058	+	119.726i	0.410628	+	0.329824i
$364$	55.5699	+	96.2500i	0.152665	+	0.264423i
$365$	898.883	−	518.970i	2.46269	−	1.42184i
$366$	−5.34669	+	6.65657i	−0.0146084	+	0.0181874i
$367$	177.905	−	308.141i	0.484756	−	0.839622i	−0.515091	−	0.857136i	$-0.672242\pi$
$367$	177.905	−	308.141i	0.484756	−	0.839622i	0.999847	+	0.0175138i	$0.00557511\pi$
$368$			405.074i			1.10074i
$369$	−10.2760	+	32.5039i	−0.0278483	+	0.0880865i
$370$	−284.091			−0.767813
$371$	105.581	+	60.9573i	0.284585	+	0.164305i
$372$	10.4871	−	67.9613i	0.0281911	−	0.182692i
$373$	−346.025	−	599.333i	−0.927681	−	1.60679i	−0.787192	−	0.616708i	$-0.788466\pi$
$373$	−346.025	−	599.333i	−0.927681	−	1.60679i	−0.140488	−	0.990082i	$-0.544867\pi$
$374$	417.569	−	241.083i	1.11649	−	0.644608i
$375$	140.008	+	360.442i	0.373355	+	0.961179i
$376$	−66.7589	+	115.630i	−0.177550	+	0.307526i
$377$			707.641i			1.87703i
$378$	−12.0401	−	187.012i	−0.0318520	−	0.494740i
$379$	−182.058			−0.480365			−0.240182	−	0.970728i	$-0.577207\pi$
$379$	−182.058			−0.480365			−0.240182	+	0.970728i	$0.577207\pi$
$380$	116.468	+	67.2430i	0.306495	+	0.176955i
$381$	227.246	−	88.2703i	0.596447	−	0.231681i
$382$	352.370	+	610.323i	0.922435	+	1.59770i
$383$	−436.704	+	252.131i	−1.14022	+	0.658305i	−0.946485	−	0.322749i	$-0.895393\pi$
$383$	−436.704	+	252.131i	−1.14022	+	0.658305i	−0.193734	+	0.981054i	$0.562060\pi$
$384$	−267.417	−	41.2651i	−0.696399	−	0.107461i
$385$	145.936	−	252.769i	0.379056	−	0.656544i
$386$			878.081i			2.27482i
$387$	−9.65454	−	43.7084i	−0.0249471	−	0.112942i
$388$	256.679			0.661543
$389$	−112.957	−	65.2157i	−0.290377	−	0.167649i	0.347735	−	0.937593i	$-0.386951\pi$
$389$	−112.957	−	65.2157i	−0.290377	−	0.167649i	−0.638112	+	0.769944i	$0.720284\pi$
$390$	−725.923	−	583.075i	−1.86134	−	1.49506i
$391$	−142.487	−	246.795i	−0.364417	−	0.631188i
$392$	−17.7813	+	10.2660i	−0.0453605	+	0.0261889i
$393$	−429.843	+	535.150i	−1.09375	+	1.36170i
$394$	85.0511	−	147.313i	0.215866	−	0.373890i
$395$		−	233.611i		−	0.591419i
$396$	−237.961	−	260.092i	−0.600913	−	0.656798i
$397$	−229.979			−0.579293			−0.289646	−	0.957134i	$-0.593538\pi$
$397$	−229.979			−0.579293			−0.289646	+	0.957134i	$0.593538\pi$
$398$	−544.135	−	314.157i	−1.36717	−	0.789338i
$399$	−6.95944	+	45.1005i	−0.0174422	+	0.113034i
$400$	−392.904	−	680.529i	−0.982259	−	1.70132i
$401$	−372.791	+	215.231i	−0.929653	+	0.536736i	−0.886702	−	0.462341i	$-0.847009\pi$
$401$	−372.791	+	215.231i	−0.929653	+	0.536736i	−0.0429515	+	0.999077i	$0.513676\pi$
$402$	97.1034	+	249.986i	0.241551	+	0.621857i
$403$	57.9674	−	100.402i	0.143840	−	0.249138i
$404$			295.621i			0.731735i
$405$	276.930	+	596.279i	0.683778	+	1.47229i
$406$	336.957			0.829942
$407$	−157.045	−	90.6700i	−0.385860	−	0.222776i
$408$	110.922	−	43.0858i	0.271867	−	0.105603i
$409$	−318.833	−	552.235i	−0.779542	−	1.35021i	−0.932206	−	0.361929i	$-0.882118\pi$
$409$	−318.833	−	552.235i	−0.779542	−	1.35021i	0.152663	−	0.988278i	$-0.451215\pi$
$410$	69.8460	−	40.3256i	0.170356	−	0.0983551i
$411$	19.9303	+	3.07544i	0.0484923	+	0.00748282i
$412$	−67.4945	+	116.904i	−0.163822	+	0.283747i
$413$		−	143.731i		−	0.348018i
$414$	−367.083	+	335.849i	−0.886673	+	0.811229i
$415$	109.723			0.264392
$416$	488.444	+	282.003i	1.17414	+	0.677892i
$417$	−260.776	−	209.460i	−0.625362	−	0.502302i
$418$	102.497	+	177.531i	0.245209	+	0.424715i
$419$	−113.572	+	65.5708i	−0.271055	+	0.156494i	−0.629367	−	0.777108i	$-0.716686\pi$
$419$	−113.572	+	65.5708i	−0.271055	+	0.156494i	0.358312	+	0.933602i	$0.383352\pi$
$420$	−116.267	+	144.751i	−0.276826	+	0.344645i
$421$	87.3257	−	151.253i	0.207425	−	0.359270i	−0.743478	−	0.668760i	$-0.766825\pi$
$421$	87.3257	−	151.253i	0.207425	−	0.359270i	0.950903	+	0.309491i	$0.100159\pi$
$422$			757.038i			1.79393i
$423$	−400.039	+	88.3628i	−0.945718	+	0.208895i
$424$	135.158			0.318769
$425$	478.760	+	276.412i	1.12649	+	0.650382i
$426$	137.987	−	894.220i	0.323913	−	2.09911i
$427$	1.43515	+	2.48576i	0.00336102	+	0.00582145i
$428$	160.531	−	92.6824i	0.375072	−	0.216548i
$429$	−215.196	−	554.008i	−0.501622	−	1.29139i
$430$	−52.9502	+	91.7125i	−0.123140	+	0.213285i
$431$		−	782.567i		−	1.81570i	−0.419294	−	0.907851i	$-0.637722\pi$
$431$		−	782.567i		−	1.81570i	0.419294	−	0.907851i	$-0.362278\pi$
$432$	−287.842	−	431.867i	−0.666301	−	0.999692i
$433$	134.931			0.311619			0.155810	−	0.987787i	$-0.450201\pi$
$433$	134.931			0.311619			0.155810	+	0.987787i	$0.450201\pi$
$434$	−47.8085	−	27.6023i	−0.110158	−	0.0635997i
$435$	−1101.93	+	428.028i	−2.53317	+	0.983972i
$436$	−27.2028	−	47.1166i	−0.0623918	−	0.108066i
$437$	104.926	−	60.5788i	0.240104	−	0.138624i
$438$	−994.628	−	153.481i	−2.27084	−	0.350413i
$439$	69.0868	−	119.662i	0.157373	−	0.272578i	−0.776548	−	0.630059i	$-0.783031\pi$
$439$	69.0868	−	119.662i	0.157373	−	0.272578i	0.933921	+	0.357481i	$0.116364\pi$
$440$		−	323.579i		−	0.735406i
$441$	−60.0695	−	18.9908i	−0.136212	−	0.0430631i
$442$	−517.097			−1.16990
$443$	162.749	+	93.9633i	0.367380	+	0.212107i	0.672313	−	0.740267i	$-0.265301\pi$
$443$	162.749	+	93.9633i	0.367380	+	0.212107i	−0.304933	+	0.952374i	$0.598634\pi$
$444$	89.9335	+	72.2364i	0.202553	+	0.162695i
$445$	251.270	+	435.213i	0.564653	+	0.978007i
$446$	258.001	−	148.957i	0.578477	−	0.333984i
$447$	306.961	−	382.163i	0.686713	−	0.854951i
$448$	32.5665	−	56.4069i	0.0726931	−	0.125908i
$449$		−	547.802i		−	1.22005i	−0.792383	−	0.610024i	$-0.791160\pi$
$449$		−	547.802i		−	1.22005i	0.792383	−	0.610024i	$-0.208840\pi$
$450$	290.945	−	920.284i	0.646545	−	2.04508i
$451$	51.4810			0.114149
$452$	−376.947	−	217.630i	−0.833954	−	0.481483i
$453$	−113.576	+	736.025i	−0.250719	+	1.62478i
$454$	419.872	+	727.239i	0.924827	+	1.60185i
$455$	−271.081	+	156.509i	−0.595782	+	0.343975i
$456$	18.3181	+	47.1587i	0.0401712	+	0.103418i
$457$	−53.0295	+	91.8498i	−0.116038	+	0.200984i	−0.918194	−	0.396130i	$-0.870353\pi$
$457$	−53.0295	+	91.8498i	−0.116038	+	0.200984i	0.802156	+	0.597114i	$0.203686\pi$
$458$		−	782.760i		−	1.70908i
$459$	327.282	+	161.869i	0.713032	+	0.352655i
$460$	492.930			1.07159
$461$	−341.021	−	196.888i	−0.739741	−	0.427090i	0.0822339	−	0.996613i	$-0.473795\pi$
$461$	−341.021	−	196.888i	−0.739741	−	0.427090i	−0.821975	+	0.569523i	$0.807128\pi$
$462$	−263.801	+	102.470i	−0.570998	+	0.221796i
$463$	356.724	+	617.864i	0.770461	+	1.33448i	0.937310	+	0.348496i	$0.113307\pi$
$463$	356.724	+	617.864i	0.770461	+	1.33448i	−0.166849	+	0.985982i	$0.553359\pi$
$464$	808.176	−	466.600i	1.74176	−	1.00560i
$465$	191.408	+	29.5361i	0.411630	+	0.0635185i
$466$	116.984	−	202.622i	0.251039	−	0.434812i
$467$		−	341.029i		−	0.730255i	−0.930958	−	0.365127i	$-0.881025\pi$
$467$		−	341.029i		−	0.730255i	0.930958	−	0.365127i	$-0.118975\pi$
$468$	81.5429	+	369.164i	0.174237	+	0.788811i
$469$	90.1582			0.192235
$470$	839.394	+	484.624i	1.78594	+	1.03112i
$471$	679.088	+	545.457i	1.44180	+	1.15808i
$472$	−79.6723	−	137.996i	−0.168797	−	0.292365i
$473$	−58.5417	+	33.7990i	−0.123767	+	0.0714567i
$474$	−141.847	+	176.598i	−0.299256	+	0.372570i
$475$	−117.518	+	203.546i	−0.247405	+	0.428519i
$476$			103.111i			0.216619i
$477$	279.941	+	305.976i	0.586878	+	0.641458i
$478$	18.2669			0.0382152
$479$	−101.997	−	58.8879i	−0.212937	−	0.122939i	0.389739	−	0.920926i	$-0.372565\pi$
$479$	−101.997	−	58.8879i	−0.212937	−	0.122939i	−0.602676	+	0.797986i	$0.705899\pi$
$480$	−143.689	+	931.172i	−0.299352	+	1.93994i
$481$	97.2385	+	168.422i	0.202159	+	0.350150i
$482$	122.084	−	70.4850i	0.253285	−	0.146234i
$483$	60.5624	+	155.914i	0.125388	+	0.322803i
$484$	−91.8305	+	159.055i	−0.189732	+	0.328626i
$485$			722.916i			1.49055i
$486$	152.712	−	618.909i	0.314222	−	1.27348i
$487$	−363.273			−0.745940			−0.372970	−	0.927843i	$-0.621661\pi$
$487$	−363.273			−0.745940			−0.372970	+	0.927843i	$0.621661\pi$
$488$	2.75578	+	1.59105i	0.00564710	+	0.00326035i
$489$	341.929	−	132.817i	0.699242	−	0.271610i
$490$	74.5245	+	129.080i	0.152091	+	0.263429i
$491$	241.674	−	139.530i	0.492208	−	0.284176i	−0.233282	−	0.972409i	$-0.574947\pi$
$491$	241.674	−	139.530i	0.492208	−	0.284176i	0.725490	+	0.688233i	$0.241613\pi$
$492$	−32.3645	−	4.99416i	−0.0657816	−	0.0101507i
$493$	−328.259	+	568.561i	−0.665839	+	1.15327i
$494$		−	219.845i		−	0.445031i
$495$	732.529	−	670.200i	1.47986	−	1.35394i
$496$	−152.889			−0.308244
$497$	−263.426	−	152.089i	−0.530032	−	0.306014i
$498$	−82.9451	−	66.6231i	−0.166556	−	0.133781i
$499$	−157.153	−	272.197i	−0.314936	−	0.545484i	0.664488	−	0.747299i	$-0.268650\pi$
$499$	−157.153	−	272.197i	−0.314936	−	0.545484i	−0.979424	+	0.201814i	$0.935316\pi$
$500$	−321.691	+	185.728i	−0.643382	+	0.371457i
$501$	99.4687	−	123.838i	0.198540	−	0.247181i
$502$	67.0671	−	116.164i	0.133600	−	0.231402i
$503$			413.397i			0.821863i	0.911666	+	0.410932i	$0.134796\pi$
$503$			413.397i			0.821863i	−0.911666	+	0.410932i	$0.865204\pi$
$504$	−68.1997	+	15.0643i	−0.135317	+	0.0298895i
$505$	−832.594			−1.64870
$506$	650.702	+	375.683i	1.28597	+	0.742457i
$507$	−19.8851	+	128.865i	−0.0392212	+	0.254172i
$508$	117.095	+	202.815i	0.230503	+	0.399242i
$509$	−446.738	+	257.924i	−0.877677	+	0.506727i	−0.869892	−	0.493243i	$-0.835811\pi$
$509$	−446.738	+	257.924i	−0.877677	+	0.506727i	−0.00778529	+	0.999970i	$0.502478\pi$
$510$	−312.774	−	805.216i	−0.613282	−	1.57886i
$511$	−169.166	+	293.005i	−0.331050	+	0.573395i
$512$		−	518.255i		−	1.01222i
$513$	−68.8190	+	139.145i	−0.134150	+	0.271238i
$514$	809.509			1.57492
$515$	−329.251	−	190.093i	−0.639323	−	0.369113i
$516$	40.0822	−	15.5693i	0.0776787	−	0.0301731i
$517$	309.344	+	535.800i	0.598344	+	1.03636i
$518$	80.1973	−	46.3019i	0.154821	−	0.0893860i
$519$	23.5664	+	3.63652i	0.0454073	+	0.00700679i
$520$	−173.510	+	300.528i	−0.333673	+	0.577938i
$521$		−	356.371i		−	0.684013i	−0.939698	−	0.342007i	$-0.888893\pi$
$521$		−	356.371i		−	0.684013i	0.939698	−	0.342007i	$-0.111107\pi$
$522$	1092.90	+	345.518i	2.09368	+	0.661912i
$523$	496.106			0.948577			0.474289	−	0.880369i	$-0.342705\pi$
$523$	496.106			0.948577			0.474289	+	0.880369i	$0.342705\pi$
$524$	−571.042	−	329.691i	−1.08977	−	0.629182i
$525$	−252.975	−	203.194i	−0.481857	−	0.387037i
$526$	−334.727	−	579.764i	−0.636363	−	1.10221i
$527$	93.1489	−	53.7795i	0.176753	−	0.102048i
$528$	−490.821	+	611.067i	−0.929585	+	1.15732i
$529$	−42.4609	+	73.5444i	−0.0802663	+	0.139025i
$530$		−	981.156i		−	1.85124i
$531$	147.383	−	466.185i	0.277558	−	0.877938i
$532$	−43.8378			−0.0824019
$533$	−47.8137	−	27.6052i	−0.0897067	−	0.0517922i
$534$	74.3109	−	481.570i	0.139159	−	0.901817i
$535$	261.033	+	452.123i	0.487912	+	0.845089i
$536$	86.5609	−	49.9760i	0.161494	−	0.0932388i
$537$	−145.835	−	375.442i	−0.271573	−	0.699147i
$538$	−456.932	+	791.430i	−0.849317	+	1.47106i
$539$			95.1406i			0.176513i
$540$	−525.535	+	350.272i	−0.973212	+	0.648652i
$541$	309.366			0.571842			0.285921	−	0.958253i	$-0.407701\pi$
$541$	309.366			0.571842			0.285921	+	0.958253i	$0.407701\pi$
$542$	189.966	+	109.677i	0.350490	+	0.202356i
$543$	−644.033	+	250.165i	−1.18606	+	0.460709i
$544$	261.630	+	453.156i	0.480937	+	0.833008i
$545$	132.700	−	76.6147i	0.243487	−	0.140577i
$546$	299.955	+	46.2860i	0.549369	+	0.0847729i
$547$	259.945	−	450.237i	0.475219	−	0.823103i	−0.524378	−	0.851485i	$-0.675702\pi$
$547$	259.945	−	450.237i	0.475219	−	0.823103i	0.999597	+	0.0283822i	$0.00903554\pi$
$548$			19.3723i			0.0353510i
$549$	2.10593	+	9.53405i	0.00383594	+	0.0173662i
$550$	−1457.58			−2.65015
$551$	−241.726	−	139.560i	−0.438703	−	0.253285i
$552$	144.571	+	116.122i	0.261904	+	0.210367i
$553$	38.0745	+	65.9470i	0.0688509	+	0.119253i
$554$	−1162.07	+	670.923i	−2.09761	+	1.21105i
$555$	−203.448	+	253.291i	−0.366574	+	0.456380i
$556$	160.657	−	278.266i	0.288951	−	0.500478i
$557$			815.558i			1.46420i	0.681199	+	0.732099i	$0.261459\pi$
$557$			815.558i			1.46420i	−0.681199	+	0.732099i	$0.738541\pi$
$558$	−126.761	−	138.550i	−0.227170	−	0.248297i
$559$	72.4951			0.129687
$560$	357.488	+	206.396i	0.638371	+	0.368564i
$561$	84.0906	−	544.947i	0.149894	−	0.971385i
$562$	296.787	+	514.051i	0.528091	+	0.914681i
$563$	926.087	−	534.677i	1.64492	−	0.949692i	0.665866	−	0.746072i	$-0.268062\pi$
$563$	926.087	−	534.677i	1.64492	−	0.949692i	0.979050	−	0.203621i	$-0.0652710\pi$
$564$	−142.497	−	366.850i	−0.252655	−	0.650444i
$565$	612.940	−	1061.64i	1.08485	−	1.87901i
$566$			445.372i			0.786876i
$567$	−175.359	−	123.192i	−0.309275	−	0.217269i
$568$	−337.221			−0.593698
$569$	−774.150	−	446.956i	−1.36055	−	0.785511i	−0.370849	−	0.928693i	$-0.620933\pi$
$569$	−774.150	−	446.956i	−1.36055	−	0.785511i	−0.989696	+	0.143182i	$0.954267\pi$
$570$	342.340	−	132.977i	0.600597	−	0.233293i
$571$	35.1978	+	60.9644i	0.0616424	+	0.106768i	0.895200	−	0.445665i	$-0.147033\pi$
$571$	35.1978	+	60.9644i	0.0616424	+	0.106768i	−0.833557	+	0.552433i	$0.813700\pi$
$572$	494.446	−	285.469i	0.864417	−	0.499071i
$573$	796.501	+	122.908i	1.39005	+	0.214499i
$574$	−13.1448	+	22.7674i	−0.0229003	+	0.0396644i
$575$			861.473i			1.49821i
$576$	163.468	−	149.559i	0.283798	−	0.259651i
$577$	527.237			0.913756			0.456878	−	0.889529i	$-0.348968\pi$
$577$	527.237			0.913756			0.456878	+	0.889529i	$0.348968\pi$
$578$	241.106	+	139.203i	0.417139	+	0.240835i
$579$	782.884	+	628.827i	1.35213	+	1.08606i
$580$	−567.802	−	983.461i	−0.978968	−	1.69562i
$581$	−30.9741	+	17.8829i	−0.0533118	+	0.0307796i
$582$	438.951	−	546.490i	0.754212	−	0.938986i
$583$	313.144	−	542.382i	0.537126	−	0.930329i
$584$			375.086i			0.642270i
$585$	−1039.72	+	229.659i	−1.77730	+	0.392580i
$586$	289.817			0.494568
$587$	377.517	+	217.959i	0.643129	+	0.371311i	0.785819	−	0.618457i	$-0.212242\pi$
$587$	377.517	+	217.959i	0.643129	+	0.371311i	−0.142690	+	0.989767i	$0.545575\pi$
$588$	9.22956	−	59.8120i	0.0156965	−	0.101721i
$589$	22.8646	+	39.6026i	0.0388193	+	0.0672370i
$590$	−1001.76	+	578.367i	−1.69790	+	0.980283i
$591$	−70.4335	−	181.327i	−0.119177	−	0.306813i
$592$	128.233	−	222.106i	0.216610	−	0.375180i
$593$		−	238.755i		−	0.402622i	−0.979527	−	0.201311i	$-0.935480\pi$
$593$		−	238.755i		−	0.402622i	0.979527	−	0.201311i	$-0.0645202\pi$
$594$	−960.699	+	61.8511i	−1.61734	+	0.104126i
$595$	−290.403			−0.488073
$596$	407.794	+	235.440i	0.684219	+	0.395034i
$597$	−669.773	+	260.163i	−1.12190	+	0.435784i
$598$	−402.899	−	697.841i	−0.673744	−	1.16696i
$599$	−232.578	+	134.279i	−0.388277	+	0.224172i	−0.681413	−	0.731899i	$-0.738634\pi$
$599$	−232.578	+	134.279i	−0.388277	+	0.224172i	0.293136	+	0.956071i	$0.405301\pi$
$600$	−355.515	−	54.8594i	−0.592525	−	0.0914323i
$601$	435.047	−	753.523i	0.723872	−	1.25378i	−0.235565	−	0.971859i	$-0.575694\pi$
$601$	435.047	−	753.523i	0.723872	−	1.25378i	0.959437	−	0.281924i	$-0.0909726\pi$
$602$		−	34.5199i		−	0.0573421i
$603$	292.424	+	92.4489i	0.484948	+	0.153315i
$604$	−715.418			−1.18447
$605$	−447.967	−	258.634i	−0.740441	−	0.427494i
$606$	629.401	+	505.547i	1.03862	+	0.834236i
$607$	−383.478	−	664.203i	−0.631760	−	1.09424i	−0.987192	−	0.159538i	$-0.949000\pi$
$607$	−383.478	−	664.203i	−0.631760	−	1.09424i	0.355432	−	0.934702i	$-0.384334\pi$
$608$	−192.661	+	111.233i	−0.316876	+	0.182949i
$609$	241.308	−	300.426i	0.396236	−	0.493310i
$610$	11.5500	−	20.0051i	0.0189344	−	0.0327953i
$611$		−	663.508i		−	1.08594i
$612$	−105.730	+	334.434i	−0.172762	+	0.546461i
$613$	507.634			0.828115			0.414057	−	0.910251i	$-0.364111\pi$
$613$	507.634			0.828115			0.414057	+	0.910251i	$0.364111\pi$
$614$	164.309	+	94.8640i	0.267605	+	0.154502i
$615$	14.0657	−	91.1523i	0.0228710	−	0.148215i
$616$	52.7378	+	91.3445i	0.0856133	+	0.148287i
$617$	225.902	−	130.425i	0.366130	−	0.211385i	−0.305636	−	0.952148i	$-0.598869\pi$
$617$	225.902	−	130.425i	0.366130	−	0.211385i	0.671766	+	0.740763i	$0.265536\pi$
$618$	133.474	+	343.621i	0.215978	+	0.556021i
$619$	−339.577	+	588.164i	−0.548589	+	0.950184i	0.449782	+	0.893138i	$0.351502\pi$
$619$	−339.577	+	588.164i	−0.548589	+	0.950184i	−0.998372	+	0.0570463i	$0.981832\pi$
$620$			186.049i			0.300079i
$621$	36.5557	+	567.800i	0.0588659	+	0.914332i
$622$	−197.505			−0.317532
$623$	−141.865	−	81.9056i	−0.227712	−	0.131470i
$624$	783.524	−	304.348i	1.25565	−	0.487737i
$625$	−12.0894	−	20.9395i	−0.0193431	−	0.0335032i
$626$	228.597	−	131.980i	0.365170	−	0.210831i
$627$	231.686	+	35.7514i	0.369515	+	0.0570198i
$628$	−418.367	+	724.634i	−0.666190	+	1.15388i
$629$			180.427i			0.286847i
$630$	109.357	+	495.083i	0.173582	+	0.785847i
$631$	306.634			0.485950			0.242975	−	0.970033i	$-0.421877\pi$
$631$	306.634			0.485950			0.242975	+	0.970033i	$0.421877\pi$
$632$	73.1108	+	42.2105i	0.115682	+	0.0667888i
$633$	674.964	+	542.144i	1.06629	+	0.856468i
$634$	310.071	+	537.058i	0.489070	+	0.847095i
$635$	−571.213	+	329.790i	−0.899548	+	0.519354i
$636$	−249.480	+	310.601i	−0.392265	+	0.488366i
$637$	51.0164	−	88.3631i	0.0800886	−	0.138718i
$638$		−	1730.98i		−	2.71314i
$639$	−698.456	−	763.412i	−1.09305	−	1.19470i
$640$	732.074			1.14387
$641$	−119.309	−	68.8828i	−0.186129	−	0.107462i	0.404040	−	0.914741i	$-0.367606\pi$
$641$	−119.309	−	68.8828i	−0.186129	−	0.107462i	−0.590169	+	0.807280i	$0.700939\pi$
$642$	77.1982	−	500.281i	0.120246	−	0.779254i
$643$	−445.506	−	771.639i	−0.692855	−	1.20006i	−0.970898	−	0.239492i	$-0.923019\pi$
$643$	−445.506	−	771.639i	−0.692855	−	1.20006i	0.278043	−	0.960569i	$-0.410314\pi$
$644$	−139.152	+	80.3392i	−0.216074	+	0.124750i
$645$	43.8498	+	112.888i	0.0679842	+	0.175021i
$646$	101.981	−	176.637i	0.157866	−	0.273432i
$647$		−	75.7656i		−	0.117103i	−0.998284	−	0.0585515i	$-0.981352\pi$
$647$		−	75.7656i		−	0.117103i	0.998284	−	0.0585515i	$-0.0186482\pi$
$648$	−236.649	−	21.0721i	−0.365200	−	0.0325187i
$649$	−738.363			−1.13769
$650$	1353.75	+	781.588i	2.08269	+	1.20244i
$651$	−58.8473	+	22.8583i	−0.0903953	+	0.0351127i
$652$	176.189	+	305.169i	0.270229	+	0.468050i
$653$	−268.405	+	154.964i	−0.411034	+	0.237310i	−0.691234	−	0.722631i	$-0.742933\pi$
$653$	−268.405	+	154.964i	−0.411034	+	0.237310i	0.280200	+	0.959942i	$0.409599\pi$
$654$	−146.835	−	22.6581i	−0.224519	−	0.0346454i
$655$	928.550	−	1608.30i	1.41763	−	2.45541i
$656$			72.8088i			0.110989i
$657$	−849.133	+	776.882i	−1.29244	+	1.18247i
$658$	−315.942			−0.480155
$659$	390.379	+	225.385i	0.592381	+	0.342011i	0.766038	−	0.642795i	$-0.222225\pi$
$659$	390.379	+	225.385i	0.592381	+	0.342011i	−0.173658	+	0.984806i	$0.555559\pi$
$660$	743.602	+	597.276i	1.12667	+	0.904963i
$661$	−431.107	−	746.700i	−0.652205	−	1.12965i	−0.982587	−	0.185805i	$-0.940511\pi$
$661$	−431.107	−	746.700i	−0.652205	−	1.12965i	0.330382	−	0.943847i	$-0.392823\pi$
$662$	−1090.14	+	629.392i	−1.64674	+	0.950743i
$663$	−370.313	+	461.036i	−0.558541	+	0.695378i
$664$	−19.8255	+	34.3388i	−0.0298577	+	0.0517151i
$665$		−	123.466i		−	0.185663i
$666$	307.594	−	67.9431i	0.461853	−	0.102017i
$667$	−1023.06			−1.53382
$668$	132.143	+	76.2929i	0.197819	+	0.114211i
$669$	51.9566	−	336.703i	0.0776631	−	0.503294i
$670$	−362.792	−	628.374i	−0.541480	−	0.937871i
$671$	12.7696	−	7.37254i	0.0190307	−	0.0109874i
$672$	−111.203	−	286.284i	−0.165480	−	0.426018i
$673$	−211.941	+	367.092i	−0.314920	+	0.545457i	−0.979420	−	0.201831i	$-0.935311\pi$
$673$	−211.941	+	367.092i	−0.314920	+	0.545457i	0.664501	+	0.747288i	$0.268644\pi$
$674$		−	619.554i		−	0.919220i
$675$	−612.155	−	918.454i	−0.906896	−	1.36067i
$676$	−125.257			−0.185292
$677$	276.722	+	159.765i	0.408747	+	0.235990i	0.690251	−	0.723570i	$-0.257500\pi$
$677$	276.722	+	159.765i	0.408747	+	0.235990i	−0.281504	+	0.959560i	$0.590833\pi$
$678$	−1107.98	+	430.377i	−1.63419	+	0.634774i
$679$	−117.823	−	204.075i	−0.173524	−	0.300553i
$680$	−278.816	+	160.975i	−0.410024	+	0.236727i
$681$	949.082	+	146.452i	1.39366	+	0.215055i
$682$	−141.796	+	245.598i	−0.207912	+	0.360114i
$683$			595.561i			0.871977i	0.899952	+	0.435989i	$0.143601\pi$
$683$			595.561i			0.871977i	−0.899952	+	0.435989i	$0.856399\pi$
$684$	−142.186	−	44.9516i	−0.207874	−	0.0657188i
$685$	−54.5607			−0.0796507
$686$	−42.0757	−	24.2924i	−0.0613349	−	0.0354117i
$687$	−697.897	−	560.564i	−1.01586	−	0.815960i
$688$	−47.8014	−	82.7945i	−0.0694788	−	0.120341i
$689$	−581.674	+	335.829i	−0.844229	+	0.487416i
$690$	842.970	−	1049.49i	1.22170	−	1.52100i
$691$	−190.956	+	330.746i	−0.276348	+	0.478649i	−0.970474	−	0.241205i	$-0.922458\pi$
$691$	−190.956	+	330.746i	−0.276348	+	0.478649i	0.694126	+	0.719853i	$0.255791\pi$
$692$			22.9066i			0.0331020i
$693$	−97.5579	+	308.584i	−0.140776	+	0.445287i
$694$	1095.80			1.57897
$695$	783.714	+	452.478i	1.12765	+	0.651047i
$696$	65.1494	−	422.199i	0.0936054	−	0.606608i
$697$	−25.6109	−	44.3594i	−0.0367445	−	0.0636433i
$698$	−510.708	+	294.857i	−0.731673	+	0.422431i
$699$	−96.8783	−	249.407i	−0.138596	−	0.356805i
$700$	155.851	−	269.942i	0.222644	−	0.385631i
$701$			404.483i			0.577009i	0.957479	+	0.288504i	$0.0931579\pi$
$701$			404.483i			0.577009i	−0.957479	+	0.288504i	$0.906842\pi$
$702$	925.428	+	457.703i	1.31827	+	0.651998i
$703$	−76.7091			−0.109117
$704$	−289.768	−	167.298i	−0.411602	−	0.237639i
$705$	1033.21	−	401.333i	1.46554	−	0.569267i
$706$	−90.0918	−	156.044i	−0.127609	−	0.221025i
$707$	235.037	−	135.699i	0.332443	−	0.191936i
$708$	464.186	+	71.6284i	0.655630	+	0.101170i
$709$	−329.097	+	570.012i	−0.464170	+	0.803966i	−0.999164	−	0.0408898i	$-0.986981\pi$
$709$	−329.097	+	570.012i	−0.464170	+	0.803966i	0.534993	+	0.844856i	$0.320314\pi$
$710$			2447.99i			3.44788i
$711$	55.8703	+	252.938i	0.0785798	+	0.355749i
$712$	−181.606			−0.255064
$713$	145.155	+	83.8053i	0.203583	+	0.117539i
$714$	219.531	+	176.331i	0.307466	+	0.246963i
$715$	804.002	+	1392.57i	1.12448	+	1.94765i
$716$	335.078	−	193.458i	0.467987	−	0.270192i
$717$	13.0816	−	16.2865i	0.0182449	−	0.0227148i
$718$	175.727	−	304.368i	0.244745	−	0.423911i
$719$			1407.65i			1.95778i	0.204382	+	0.978891i	$0.434482\pi$
$719$			1407.65i			1.95778i	−0.204382	+	0.978891i	$0.565518\pi$
$720$	947.854	+	1036.00i	1.31646	+	1.43889i
$721$	123.928			0.171883
$722$	−745.050	−	430.155i	−1.03192	−	0.595782i
$723$	24.5854	−	159.325i	0.0340047	−	0.220366i
$724$	−331.857	−	574.793i	−0.458366	−	0.793914i
$725$	1718.75	−	992.322i	2.37069	−	1.36872i
$726$	181.600	+	467.518i	0.250138	+	0.643964i
$727$	383.390	−	664.051i	0.527359	−	0.913413i	−0.472132	−	0.881528i	$-0.656516\pi$
$727$	383.390	−	664.051i	0.527359	−	0.913413i	0.999492	−	0.0318853i	$-0.0101511\pi$
$728$		−	113.117i		−	0.155380i
$729$	−442.447	−	579.380i	−0.606924	−	0.794760i
$730$	2722.87			3.72996
$731$	58.2469	+	33.6289i	0.0796811	+	0.0460039i
$732$	−8.74308	+	3.39611i	−0.0119441	+	0.00463950i
$733$	24.8207	+	42.9907i	0.0338618	+	0.0586504i	0.882460	−	0.470388i	$-0.155886\pi$
$733$	24.8207	+	42.9907i	0.0338618	+	0.0586504i	−0.848598	+	0.529038i	$0.822553\pi$
$734$	808.358	−	466.706i	1.10131	−	0.635839i
$735$	168.456	+	25.9944i	0.229192	+	0.0353665i
$736$	−407.701	+	706.158i	−0.553941	+	0.959454i
$737$		−	463.152i		−	0.628429i
$738$	−65.9802	+	60.3662i	−0.0894041	+	0.0817970i
$739$	1054.43			1.42683			0.713415	−	0.700741i	$-0.247147\pi$
$739$	1054.43			1.42683			0.713415	+	0.700741i	$0.247147\pi$
$740$	−270.279	−	156.046i	−0.365242	−	0.210873i
$741$	−196.011	−	157.440i	−0.264522	−	0.212469i
$742$	159.912	+	276.975i	0.215514	+	0.373282i
$743$	−999.915	+	577.301i	−1.34578	+	0.776987i	−0.987649	−	0.156684i	$-0.949920\pi$
$743$	−999.915	+	577.301i	−1.34578	+	0.776987i	−0.358132	+	0.933671i	$0.616586\pi$
$744$	−43.8286	+	54.5662i	−0.0589094	+	0.0733417i
$745$	−663.100	+	1148.52i	−0.890067	+	1.54164i
$746$		−	1815.48i		−	2.43362i
$747$	−118.800	+	26.2413i	−0.159037	+	0.0351289i
$748$	529.690			0.708142
$749$	−147.376	−	85.0878i	−0.196764	−	0.113602i
$750$	−154.699	+	1002.52i	−0.206266	+	1.33670i
$751$	−307.537	−	532.670i	−0.409504	−	0.709281i	0.585331	−	0.810795i	$-0.300965\pi$
$751$	−307.537	−	532.670i	−0.409504	−	0.709281i	−0.994834	+	0.101514i	$0.967631\pi$
$752$	−757.773	+	437.500i	−1.00768	+	0.581782i
$753$	−55.5404	−	142.985i	−0.0737589	−	0.189887i
$754$	−928.190	+	1607.67i	−1.23102	+	2.13219i
$755$		−	2014.92i		−	2.66877i
$756$	91.2673	−	184.533i	0.120724	−	0.244091i
$757$	788.860			1.04209			0.521044	−	0.853530i	$-0.325543\pi$
$757$	788.860			1.04209			0.521044	+	0.853530i	$0.325543\pi$
$758$	−413.614	−	238.800i	−0.545665	−	0.315040i
$759$	800.946	−	311.115i	1.05527	−	0.409902i
$760$	−68.4389	−	118.540i	−0.0900512	−	0.155973i
$761$	647.404	−	373.779i	0.850728	−	0.491168i	−0.0101684	−	0.999948i	$-0.503237\pi$
$761$	647.404	−	373.779i	0.850728	−	0.491168i	0.860896	+	0.508780i	$0.169903\pi$
$762$	632.057	+	97.5324i	0.829471	+	0.127995i
$763$	−24.9738	+	43.2558i	−0.0327310	+	0.0566918i
$764$			774.201i			1.01335i
$765$	−941.909	−	297.782i	−1.23125	−	0.389257i
$766$	−1322.85			−1.72696
$767$	685.765	+	395.926i	0.894087	+	0.516201i
$768$	−783.732	−	629.508i	−1.02048	−	0.819672i
$769$	618.120	+	1070.61i	0.803797	+	1.39222i	0.917101	+	0.398656i	$0.130523\pi$
$769$	618.120	+	1070.61i	0.803797	+	1.39222i	−0.113304	+	0.993560i	$0.536143\pi$
$770$	663.099	−	382.841i	0.861168	−	0.497196i
$771$	579.720	−	721.746i	0.751907	−	0.936117i
$772$	−482.313	+	835.391i	−0.624758	+	1.08211i
$773$		−	1116.09i		−	1.44384i	−0.691974	−	0.721922i	$-0.743259\pi$
$773$		−	1116.09i		−	1.44384i	0.691974	−	0.721922i	$-0.256741\pi$
$774$	35.3970	−	111.964i	0.0457325	−	0.144656i
$775$	−325.150			−0.419548
$776$	−226.244	−	130.622i	−0.291551	−	0.168327i
$777$	16.1502	−	104.661i	0.0207854	−	0.134699i
$778$	−171.083	−	296.324i	−0.219901	−	0.380879i
$779$	18.8595	−	10.8886i	0.0242099	−	0.0139776i
$780$	−370.358	−	953.463i	−0.474818	−	1.22239i
$781$	−781.298	+	1353.25i	−1.00038	+	1.73271i
$782$		−	747.583i		−	0.955988i
$783$	1090.73	−	726.977i	1.39301	−	0.928450i
$784$	−134.556			−0.171627
$785$	−2040.88	−	1178.30i	−2.59984	−	1.50102i
$786$	−1678.49	+	651.984i	−2.13548	+	0.829496i
$787$	44.2771	+	76.6903i	0.0562607	+	0.0974463i	0.892784	−	0.450485i	$-0.148749\pi$
$787$	44.2771	+	76.6903i	0.0562607	+	0.0974463i	−0.836523	+	0.547931i	$0.815416\pi$
$788$	161.832	−	93.4339i	0.205371	−	0.118571i
$789$	−756.620	−	116.754i	−0.958960	−	0.147977i
$790$	306.420	−	530.735i	0.387873	−	0.671816i
$791$			399.595i			0.505177i
$792$	77.3870	+	350.349i	0.0977109	+	0.442360i
$793$	−15.8133			−0.0199411
$794$	−522.485	−	301.657i	−0.658041	−	0.379920i
$795$	−874.784	−	702.643i	−1.10036	−	0.883828i
$796$	−345.121	−	597.766i	−0.433568	−	0.750963i
$797$	−1127.23	+	650.809i	−1.41435	+	0.816573i	−0.995794	−	0.0916194i	$-0.970796\pi$
$797$	−1127.23	+	650.809i	−1.41435	+	0.816573i	−0.418552	+	0.908193i	$0.637462\pi$
$798$	−74.9679	+	93.3343i	−0.0939448	+	0.116960i
$799$	307.786	−	533.102i	0.385215	−	0.667211i
$800$		−	1581.81i		−	1.97726i
$801$	−376.144	−	411.126i	−0.469593	−	0.513265i
$802$	−1129.25			−1.40804
$803$	1505.20	+	869.027i	1.87447	+	1.08222i
$804$	−44.9303	+	291.170i	−0.0558835	+	0.362151i
$805$	−226.269	−	391.910i	−0.281080	−	0.486845i
$806$	263.390	−	152.068i	0.326786	−	0.188670i
$807$	378.401	+	974.168i	0.468898	+	1.20715i
$808$	150.439	−	260.569i	0.186187	−	0.322486i
$809$			1141.68i			1.41122i	0.708600	+	0.705610i	$0.249327\pi$
$809$			1141.68i			1.41122i	−0.708600	+	0.705610i	$0.750673\pi$
$810$	−152.969	+	1717.91i	−0.188851	+	2.12088i
$811$	−580.207			−0.715421			−0.357711	−	0.933832i	$-0.616443\pi$
$811$	−580.207			−0.715421			−0.357711	+	0.933832i	$0.616443\pi$
$812$	320.575	+	185.084i	0.394796	+	0.227936i
$813$	233.828	−	90.8269i	0.287611	−	0.111718i
$814$	−237.858	−	411.982i	−0.292209	−	0.506121i
$815$	−859.484	+	496.224i	−1.05458	+	0.608863i
$816$	770.710	+	118.928i	0.944498	+	0.145745i
$817$	−14.2974	+	24.7639i	−0.0174999	+	0.0303107i
$818$		−	1672.81i		−	2.04500i
$819$	256.077	−	234.289i	0.312671	−	0.286067i
$820$	88.6003			0.108049
$821$	−263.562	−	152.167i	−0.321025	−	0.185344i	0.330824	−	0.943692i	$-0.392673\pi$
$821$	−263.562	−	152.167i	−0.321025	−	0.185344i	−0.651849	+	0.758348i	$0.726007\pi$
$822$	41.2453	+	33.1290i	0.0501767	+	0.0403029i
$823$	−197.765	−	342.538i	−0.240297	−	0.416207i	0.720502	−	0.693453i	$-0.243912\pi$
$823$	−197.765	−	342.538i	−0.240297	−	0.416207i	−0.960799	+	0.277246i	$0.910578\pi$
$824$	118.983	−	68.6949i	0.144397	−	0.0833676i
$825$	−1043.83	+	1299.56i	−1.26525	+	1.57522i
$826$	188.528	−	326.540i	0.228242	−	0.395327i
$827$		−	650.777i		−	0.786913i	−0.919343	−	0.393457i	$-0.871279\pi$
$827$		−	650.777i		−	0.786913i	0.919343	−	0.393457i	$-0.128721\pi$
$828$	−533.712	+	117.889i	−0.644579	+	0.142378i
$829$	691.888			0.834606			0.417303	−	0.908768i	$-0.362975\pi$
$829$	691.888			0.834606			0.417303	+	0.908768i	$0.362975\pi$
$830$	249.277	+	143.920i	0.300333	+	0.173397i
$831$	−234.020	+	1516.56i	−0.281613	+	1.82498i
$832$	179.417	+	310.760i	0.215646	+	0.373510i
$833$	81.9793	−	47.3308i	0.0984145	−	0.0568196i
$834$	−317.708	−	817.919i	−0.380945	−	0.980718i
$835$	−214.873	+	372.172i	−0.257333	+	0.445714i
$836$			225.200i			0.269378i
$837$	−214.307	+	13.7974i	−0.256042	+	0.0164843i
$838$	−344.029			−0.410536
$839$	145.413	+	83.9540i	0.173317	+	0.100064i	0.584149	−	0.811647i	$-0.301428\pi$
$839$	145.413	+	83.9540i	0.173317	+	0.100064i	−0.410832	+	0.911711i	$0.634762\pi$
$840$	176.144	−	68.4203i	0.209695	−	0.0814528i
$841$	757.951	+	1312.81i	0.901250	+	1.56101i
$842$	396.787	−	229.085i	0.471243	−	0.272072i
$843$	670.861	+	103.520i	0.795802	+	0.122800i
$844$	−415.827	+	720.233i	−0.492686	+	0.853357i
$845$		−	352.778i		−	0.417489i
$846$	−1024.74	−	323.969i	−1.21128	−	0.382942i
$847$	168.611			0.199069
$848$	767.082	+	442.875i	0.904577	+	0.522258i
$849$	397.087	+	318.948i	0.467712	+	0.375675i
$850$	725.122	+	1255.95i	0.853085	+	1.47759i
$851$	−243.493	+	140.581i	−0.286126	+	0.165195i
$852$	622.456	−	774.952i	0.730583	−	0.909568i
$853$	−271.601	+	470.426i	−0.318406	+	0.551496i	−0.980156	−	0.198229i	$-0.936481\pi$
$853$	−271.601	+	470.426i	−0.318406	+	0.551496i	0.661749	+	0.749725i	$0.269814\pi$
$854$			7.52979i			0.00881708i
$855$	126.603	−	400.456i	0.148074	−	0.468369i
$856$	−188.662			−0.220399
$857$	2.30532	+	1.33098i	0.00268999	+	0.00155307i	0.501344	−	0.865248i	$-0.332839\pi$
$857$	2.30532	+	1.33098i	0.00268999	+	0.00155307i	−0.498654	+	0.866801i	$0.666172\pi$
$858$	237.776	−	1540.90i	0.277128	−	1.79592i
$859$	−51.7946	−	89.7109i	−0.0602964	−	0.104436i	0.834301	−	0.551308i	$-0.185871\pi$
$859$	−51.7946	−	89.7109i	−0.0602964	−	0.104436i	−0.894598	+	0.446872i	$0.852538\pi$
$860$	−100.752	+	58.1691i	−0.117153	+	0.0676385i
$861$	10.8856	+	28.0243i	0.0126430	+	0.0325485i
$862$	1026.47	−	1777.90i	1.19080	−	2.06252i
$863$			345.644i			0.400515i	0.979743	+	0.200257i	$0.0641779\pi$
$863$			345.644i			0.400515i	−0.979743	+	0.200257i	$0.935822\pi$
$864$	−67.1224	−	1042.58i	−0.0776879	−	1.20668i
$865$	−64.5148			−0.0745835
$866$	306.547	+	176.985i	0.353980	+	0.204371i
$867$	296.777	−	115.278i	0.342303	−	0.132962i
$868$	−30.3228	−	52.5206i	−0.0349341	−	0.0605077i
$869$	338.777	−	195.593i	0.389847	−	0.225078i
$870$	−3064.88	−	472.940i	−3.52285	−	0.543610i
$871$	−248.352	+	430.159i	−0.285135	+	0.493868i
$872$			55.3732i			0.0635014i
$873$	−172.892	−	782.725i	−0.198044	−	0.896592i
$874$	317.837			0.363658
$875$	295.331	+	170.510i	0.337521	+	0.194868i
$876$	−861.968	−	692.349i	−0.983982	−	0.790353i
$877$	83.1603	+	144.038i	0.0948236	+	0.164239i	0.909535	−	0.415627i	$-0.136438\pi$
$877$	83.1603	+	144.038i	0.0948236	+	0.164239i	−0.814711	+	0.579867i	$0.803105\pi$
$878$	313.913	−	181.238i	0.357532	−	0.206421i
$879$	207.549	−	258.396i	0.236119	−	0.293966i
$880$	1060.28	−	1836.45i	1.20486	−	2.08688i
$881$			1619.18i			1.83789i	0.394389	+	0.918943i	$0.370956\pi$
$881$			1619.18i			1.83789i	−0.394389	+	0.918943i	$0.629044\pi$
$882$	−111.561	−	121.936i	−0.126486	−	0.138250i
$883$	−1227.52			−1.39017			−0.695083	−	0.718929i	$-0.744632\pi$
$883$	−1227.52			−1.39017			−0.695083	+	0.718929i	$0.744632\pi$
$884$	−491.957	−	284.031i	−0.556512	−	0.321302i
$885$	−201.736	+	1307.35i	−0.227950	+	1.47723i
$886$	246.498	+	426.946i	0.278214	+	0.481881i
$887$	811.479	−	468.508i	0.914858	−	0.528194i	0.0328672	−	0.999460i	$-0.489536\pi$
$887$	811.479	−	468.508i	0.914858	−	0.528194i	0.881991	+	0.471266i	$0.156203\pi$
$888$	−42.5094	−	109.438i	−0.0478709	−	0.123241i
$889$	107.500	−	186.196i	0.120923	−	0.209444i
$890$			1318.33i			1.48127i
$891$	−632.848	+	900.839i	−0.710267	+	1.01104i
$892$	327.277			0.366902
$893$	226.650	+	130.856i	0.253807	+	0.146536i
$894$	1198.65	−	465.597i	1.34077	−	0.520802i
$895$	544.859	+	943.723i	0.608781	+	1.05444i
$896$	−206.661	+	119.316i	−0.230648	+	0.133165i
$897$	−910.716	−	140.532i	−1.01529	−	0.156669i
$898$	718.535	−	1244.54i	0.800150	−	1.38590i
$899$		−	386.138i		−	0.429519i
$900$	782.295	−	715.732i	0.869217	−	0.795258i
$901$	−623.135			−0.691604
$902$	116.959	+	67.5261i	0.129666	+	0.0748626i
$903$	−30.7775	−	24.7210i	−0.0340836	−	0.0273766i
$904$	221.501	+	383.651i	0.245023	+	0.424393i
$905$	1618.86	−	934.651i	1.78880	−	1.03276i
$906$	−1223.45	+	1523.18i	−1.35039	+	1.68122i
$907$	−211.902	+	367.026i	−0.233630	+	0.404659i	−0.958874	−	0.283833i	$-0.908394\pi$
$907$	−211.902	+	367.026i	−0.233630	+	0.404659i	0.725244	+	0.688492i	$0.241727\pi$
$908$			922.510i			1.01598i
$909$	901.477	−	199.123i	0.991724	−	0.219057i
$910$	−821.150			−0.902362
$911$	940.146	+	542.794i	1.03199	+	0.595822i	0.917555	−	0.397609i	$-0.130160\pi$
$911$	940.146	+	542.794i	1.03199	+	0.595822i	0.114438	+	0.993430i	$0.463493\pi$
$912$	−50.5626	+	327.670i	−0.0554415	+	0.359287i
$913$	91.8665	+	159.118i	0.100621	+	0.174280i
$914$	−240.953	+	139.114i	−0.263625	+	0.152204i
$915$	−9.56490	−	24.6242i	−0.0104534	−	0.0269117i
$916$	429.955	−	744.704i	0.469383	−	0.812996i
$917$			605.351i			0.660143i
$918$	531.226	+	797.031i	0.578677	+	0.868225i
$919$	1528.19			1.66288			0.831440	−	0.555615i	$-0.187517\pi$
$919$	1528.19			1.66288			0.831440	+	0.555615i	$0.187517\pi$
$920$	−434.483	−	250.849i	−0.472264	−	0.272662i
$921$	202.248	−	78.5600i	0.219596	−	0.0852986i
$922$	−516.505	−	894.613i	−0.560200	−	0.970296i
$923$	1451.28	−	837.898i	1.57235	−	0.907798i
$924$	−307.261	−	47.4133i	−0.332533	−	0.0513131i
$925$	272.714	−	472.355i	0.294826	−	0.510654i
$926$			1871.61i			2.02118i
$927$	401.953	+	127.076i	0.433607	+	0.137084i
$928$	1878.51			2.02425
$929$	171.137	+	98.8060i	0.184216	+	0.106357i	0.589272	−	0.807935i	$-0.299415\pi$
$929$	171.137	+	98.8060i	0.184216	+	0.106357i	−0.405056	+	0.914292i	$0.632748\pi$
$930$	396.114	+	318.166i	0.425929	+	0.342114i
$931$	20.1228	+	34.8538i	0.0216142	+	0.0374369i
$932$	222.593	−	128.514i	0.238834	−	0.137891i
$933$	−141.441	+	176.092i	−0.151598	+	0.188738i
$934$	447.317	−	774.776i	0.478926	−	0.829525i
$935$			1491.83i			1.59554i
$936$	115.991	−	366.888i	0.123922	−	0.391974i
$937$	−903.349			−0.964086			−0.482043	−	0.876147i	$-0.660105\pi$
$937$	−903.349			−0.964086			−0.482043	+	0.876147i	$0.660105\pi$
$938$	204.828	+	118.258i	0.218367	+	0.126074i
$939$	46.0351	−	298.330i	0.0490257	−	0.317710i
$940$	532.390	+	922.127i	0.566372	+	0.980986i
$941$	−183.119	+	105.724i	−0.194600	+	0.112352i	−0.594134	−	0.804366i	$-0.702505\pi$
$941$	−183.119	+	105.724i	−0.194600	+	0.112352i	0.399534	+	0.916718i	$0.369172\pi$
$942$	827.346	+	2129.95i	0.878287	+	2.26109i
$943$	39.9098	−	69.1257i	0.0423221	−	0.0733041i
$944$		−	1044.26i		−	1.10620i
$945$	519.724	+	257.047i	0.549972	+	0.272008i
$946$	−177.333			−0.187455
$947$	−784.757	−	453.080i	−0.828677	−	0.478437i	0.0247223	−	0.999694i	$-0.492130\pi$
$947$	−784.757	−	453.080i	−0.828677	−	0.478437i	−0.853400	+	0.521257i	$0.825463\pi$
$948$	−231.953	+	90.0987i	−0.244676	+	0.0950408i
$949$	−931.982	−	1614.24i	−0.982067	−	1.70099i
$950$	−533.971	+	308.288i	−0.562075	+	0.324514i
$951$	700.887	+	108.154i	0.737000	+	0.113726i
$952$	52.4722	−	90.8846i	0.0551179	−	0.0954670i
$953$		−	105.248i		−	0.110439i	−0.998474	−	0.0552194i	$-0.982414\pi$
$953$		−	105.248i		−	0.110439i	0.998474	−	0.0552194i	$-0.0175858\pi$
$954$	234.653	+	1062.33i	0.245967	+	1.11355i
$955$	−2180.48			−2.28323
$956$	17.3788	+	10.0337i	0.0181787	+	0.0104955i
$957$	−1543.32	−	1239.62i	−1.61266	−	1.29532i
$958$	−154.483	−	267.572i	−0.161256	−	0.279303i
$959$	15.4022	−	8.89246i	0.0160607	−	0.00927264i
$960$	−375.388	+	467.354i	−0.391029	+	0.486827i
$961$	448.869	−	777.464i	0.467085	−	0.809015i
$962$			510.179i			0.530331i
$963$	−390.758	−	427.099i	−0.405772	−	0.443509i
$964$	154.864			0.160648
$965$	−2352.82	−	1358.40i	−2.43815	−	1.40767i
$966$	−66.9171	+	433.655i	−0.0692724	+	0.448918i
$967$	−146.844	−	254.341i	−0.151855	−	0.263021i	0.780054	−	0.625712i	$-0.215191\pi$
$967$	−146.844	−	254.341i	−0.151855	−	0.263021i	−0.931909	+	0.362691i	$0.881858\pi$
$968$	161.884	−	93.4638i	0.167236	−	0.0965535i
$969$	−84.4541	−	217.422i	−0.0871559	−	0.224377i
$970$	−948.226	+	1642.38i	−0.977553	+	1.69317i
$971$		−	232.193i		−	0.239127i	−0.992827	−	0.119564i	$-0.961850\pi$
$971$		−	232.193i		−	0.239127i	0.992827	−	0.119564i	$-0.0381496\pi$
$972$	485.242	−	504.938i	0.499221	−	0.519483i
$973$	−294.985			−0.303170
$974$	−825.311	−	476.494i	−0.847342	−	0.489213i
$975$	1666.33	−	647.259i	1.70905	−	0.663855i
$976$	10.4269	+	18.0599i	0.0106833	+	0.0185040i
$977$	243.053	−	140.327i	0.248775	−	0.143630i	−0.370428	−	0.928861i	$-0.620789\pi$
$977$	243.053	−	140.327i	0.248775	−	0.143630i	0.619203	+	0.785231i	$0.287456\pi$
$978$	951.033	+	146.754i	0.972427	+	0.150055i
$979$	−420.758	+	728.774i	−0.429783	+	0.744406i
$980$			163.740i			0.167081i
$981$	−125.356	+	114.690i	−0.127784	+	0.116911i
$982$	732.071			0.745490
$983$	1468.25	+	847.697i	1.49365	+	0.862357i	0.999973	−	0.00729050i	$-0.00232066\pi$
$983$	1468.25	+	847.697i	1.49365	+	0.862357i	0.493673	+	0.869648i	$0.335654\pi$
$984$	25.9855	+	20.8721i	0.0264081	+	0.0212115i
$985$	263.150	+	455.788i	0.267157	+	0.462729i
$986$	−1491.53	+	861.133i	−1.51270	+	0.873360i
$987$	−226.258	+	281.689i	−0.229238	+	0.285399i
$988$	120.757	−	209.157i	0.122224	−	0.211697i
$989$			104.808i			0.105974i
$990$	2543.30	−	561.777i	2.56899	−	0.567452i
$991$	−1687.30			−1.70263			−0.851313	−	0.524658i	$-0.824193\pi$
$991$	−1687.30			−1.70263			−0.851313	+	0.524658i	$0.824193\pi$
$992$	−266.529	−	153.880i	−0.268678	−	0.155121i
$993$	−219.534	+	1422.68i	−0.221081	+	1.43271i
$994$	−398.981	−	691.055i	−0.401389	−	0.695227i
$995$	1683.56	−	972.006i	1.69202	−	0.976891i
$996$	−42.3177	−	108.944i	−0.0424877	−	0.109382i
$997$	221.889	−	384.324i	0.222557	−	0.385480i	−0.733027	−	0.680200i	$-0.761893\pi$
$997$	221.889	−	384.324i	0.222557	−	0.385480i	0.955584	+	0.294720i	$0.0952263\pi$
$998$		−	824.530i		−	0.826182i
$999$	159.703	−	322.903i	0.159863	−	0.323226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.r.a.29.10	✓	24
3.2	odd	2		189.3.r.a.8.3		24
7.2	even	3		441.3.j.h.263.3		24
7.3	odd	6		441.3.n.h.128.3		24
7.4	even	3		441.3.n.g.128.3		24
7.5	odd	6		441.3.j.g.263.3		24
7.6	odd	2		441.3.r.h.344.10		24
9.2	odd	6		567.3.b.a.323.19		24
9.4	even	3		189.3.r.a.71.3		24
9.5	odd	6	inner	63.3.r.a.50.10	yes	24
9.7	even	3		567.3.b.a.323.6		24
63.5	even	6		441.3.n.h.410.3		24
63.23	odd	6		441.3.n.g.410.3		24
63.32	odd	6		441.3.j.h.275.10		24
63.41	even	6		441.3.r.h.50.10		24
63.59	even	6		441.3.j.g.275.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.r.a.29.10	✓	24	1.1	even	1	trivial
63.3.r.a.50.10	yes	24	9.5	odd	6	inner
189.3.r.a.8.3		24	3.2	odd	2
189.3.r.a.71.3		24	9.4	even	3
441.3.j.g.263.3		24	7.5	odd	6
441.3.j.g.275.10		24	63.59	even	6
441.3.j.h.263.3		24	7.2	even	3
441.3.j.h.275.10		24	63.32	odd	6
441.3.n.g.128.3		24	7.4	even	3
441.3.n.g.410.3		24	63.23	odd	6
441.3.n.h.128.3		24	7.3	odd	6
441.3.n.h.410.3		24	63.5	even	6
441.3.r.h.50.10		24	63.41	even	6
441.3.r.h.344.10		24	7.6	odd	2
567.3.b.a.323.6		24	9.7	even	3
567.3.b.a.323.19		24	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.27188 + 1.31167i) q^{2} +(2.79644 - 1.08624i) q^{3} +(1.44095 + 2.49580i) q^{4} +(-7.02923 + 4.05833i) q^{5} +(7.77795 + 1.20021i) q^{6} +(1.32288 - 2.29129i) q^{7} -2.93316i q^{8} +(6.64018 - 6.07519i) q^{9} +O(q^{10})\)	\(q+(2.27188 + 1.31167i) q^{2} +(2.79644 - 1.08624i) q^{3} +(1.44095 + 2.49580i) q^{4} +(-7.02923 + 4.05833i) q^{5} +(7.77795 + 1.20021i) q^{6} +(1.32288 - 2.29129i) q^{7} -2.93316i q^{8} +(6.64018 - 6.07519i) q^{9} -21.2927 q^{10} +(-11.7706 - 6.79576i) q^{11} +(6.74056 + 5.41415i) q^{12} +(7.28806 + 12.6233i) q^{13} +(6.01082 - 3.47035i) q^{14} +(-15.2485 + 18.9843i) q^{15} +(9.61113 - 16.6470i) q^{16} +13.5231i q^{17} +(23.0543 - 5.09236i) q^{18} -5.74938 q^{19} +(-20.2575 - 11.6957i) q^{20} +(1.21047 - 7.84441i) q^{21} +(-17.8276 - 30.8782i) q^{22} +(-18.2499 + 10.5366i) q^{23} +(-3.18610 - 8.20240i) q^{24} +(20.4400 - 35.4032i) q^{25} +38.2381i q^{26} +(11.9698 - 24.2017i) q^{27} +7.62479 q^{28} +(42.0437 + 24.2740i) q^{29} +(-59.5439 + 23.1289i) q^{30} +(-3.97687 - 6.88815i) q^{31} +(33.5098 - 19.3469i) q^{32} +(-40.2976 - 6.21830i) q^{33} +(-17.7378 + 30.7228i) q^{34} +21.4746i q^{35} +(24.7306 + 7.81852i) q^{36} +13.3422 q^{37} +(-13.0619 - 7.54128i) q^{38} +(34.0925 + 27.3838i) q^{39} +(11.9037 + 20.6178i) q^{40} +(-3.28027 + 1.89387i) q^{41} +(13.0393 - 16.2338i) q^{42} +(2.48678 - 4.30722i) q^{43} -39.1694i q^{44} +(-22.0203 + 69.6520i) q^{45} -55.2820 q^{46} +(-39.4216 - 22.7601i) q^{47} +(8.79445 - 56.9922i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(92.8745 - 53.6211i) q^{50} +(14.6892 + 37.8165i) q^{51} +(-21.0035 + 36.3791i) q^{52} +46.0794i q^{53} +(58.9386 - 39.2829i) q^{54} +110.318 q^{55} +(-6.72070 - 3.88020i) q^{56} +(-16.0778 + 6.24518i) q^{57} +(63.6788 + 110.295i) q^{58} +(47.0471 - 27.1627i) q^{59} +(-69.3533 - 10.7019i) q^{60} +(-0.542437 + 0.939529i) q^{61} -20.8654i q^{62} +(-5.13587 - 23.2513i) q^{63} +24.6180 q^{64} +(-102.459 - 59.1547i) q^{65} +(-83.3948 - 66.9843i) q^{66} +(17.0383 + 29.5112i) q^{67} +(-33.7509 + 19.4861i) q^{68} +(-39.5896 + 49.2886i) q^{69} +(-28.1676 + 48.7878i) q^{70} -114.969i q^{71} +(-17.8195 - 19.4767i) q^{72} -127.878 q^{73} +(30.3117 + 17.5005i) q^{74} +(18.7032 - 121.206i) q^{75} +(-8.28457 - 14.3493i) q^{76} +(-31.1421 + 17.9799i) q^{77} +(41.5356 + 106.931i) q^{78} +(-14.3908 + 24.9256i) q^{79} +156.020i q^{80} +(7.18411 - 80.6808i) q^{81} -9.93650 q^{82} +(-11.7071 - 6.75911i) q^{83} +(21.3223 - 8.28232i) q^{84} +(-54.8811 - 95.0568i) q^{85} +(11.2993 - 6.52365i) q^{86} +(143.940 + 22.2114i) q^{87} +(-19.9330 + 34.5250i) q^{88} -61.9148i q^{89} +(-141.388 + 129.357i) q^{90} +38.5648 q^{91} +(-52.5944 - 30.3654i) q^{92} +(-18.6032 - 14.9425i) q^{93} +(-59.7074 - 103.416i) q^{94} +(40.4137 - 23.3329i) q^{95} +(72.6931 - 90.5021i) q^{96} +(44.5329 - 77.1332i) q^{97} -18.3634i q^{98} +(-119.444 + 26.3835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9}+O(q^{10}) \) 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9	\( 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9} - 18 q^{11} + 4 q^{12} - 10 q^{15} - 48 q^{16} - 62 q^{18} - 24 q^{19} - 18 q^{20} - 14 q^{21} - 24 q^{22} + 72 q^{23} + 54 q^{24} + 54 q^{25} - 124 q^{27} + 54 q^{29} - 212 q^{30} + 30 q^{31} + 126 q^{32} - 178 q^{33} + 60 q^{34} + 124 q^{36} + 84 q^{37} - 144 q^{38} + 92 q^{39} - 60 q^{40} + 180 q^{41} + 140 q^{42} - 60 q^{43} - 118 q^{45} - 168 q^{46} + 378 q^{47} + 436 q^{48} - 84 q^{49} - 378 q^{50} + 168 q^{51} - 18 q^{52} + 514 q^{54} - 132 q^{55} - 232 q^{57} + 90 q^{58} - 90 q^{59} + 76 q^{60} + 28 q^{63} + 324 q^{64} + 126 q^{65} + 202 q^{66} + 6 q^{67} - 738 q^{68} - 432 q^{69} - 246 q^{72} - 72 q^{73} - 792 q^{74} + 40 q^{75} + 84 q^{76} + 28 q^{78} - 6 q^{79} - 34 q^{81} - 108 q^{82} - 558 q^{83} - 322 q^{84} + 126 q^{85} + 90 q^{86} + 428 q^{87} + 168 q^{88} - 488 q^{90} + 84 q^{91} + 774 q^{92} - 738 q^{93} - 354 q^{94} + 648 q^{95} - 280 q^{96} - 270 q^{97} + 296 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9 - 18 * q^11 + 4 * q^12 - 10 * q^15 - 48 * q^16 - 62 * q^18 - 24 * q^19 - 18 * q^20 - 14 * q^21 - 24 * q^22 + 72 * q^23 + 54 * q^24 + 54 * q^25 - 124 * q^27 + 54 * q^29 - 212 * q^30 + 30 * q^31 + 126 * q^32 - 178 * q^33 + 60 * q^34 + 124 * q^36 + 84 * q^37 - 144 * q^38 + 92 * q^39 - 60 * q^40 + 180 * q^41 + 140 * q^42 - 60 * q^43 - 118 * q^45 - 168 * q^46 + 378 * q^47 + 436 * q^48 - 84 * q^49 - 378 * q^50 + 168 * q^51 - 18 * q^52 + 514 * q^54 - 132 * q^55 - 232 * q^57 + 90 * q^58 - 90 * q^59 + 76 * q^60 + 28 * q^63 + 324 * q^64 + 126 * q^65 + 202 * q^66 + 6 * q^67 - 738 * q^68 - 432 * q^69 - 246 * q^72 - 72 * q^73 - 792 * q^74 + 40 * q^75 + 84 * q^76 + 28 * q^78 - 6 * q^79 - 34 * q^81 - 108 * q^82 - 558 * q^83 - 322 * q^84 + 126 * q^85 + 90 * q^86 + 428 * q^87 + 168 * q^88 - 488 * q^90 + 84 * q^91 + 774 * q^92 - 738 * q^93 - 354 * q^94 + 648 * q^95 - 280 * q^96 - 270 * q^97 + 296 * q^99

Introduction

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