LMFDB - Embedded newform 45.3.k.a.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(7,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("45.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, 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:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	45.43
Dual form			45.3.k.a.22.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.639624 + 2.38711i) q^{2} +(2.11050 + 2.13208i) q^{3} +(-1.82507 + 1.05371i) q^{4} +(-3.10636 - 3.91797i) q^{5} +(-3.73959 + 6.40173i) q^{6} +(-2.77655 - 10.3622i) q^{7} +(3.30727 + 3.30727i) q^{8} +(-0.0915623 + 8.99953i) q^{9} +O(q^{10})$	\(q+(0.639624 + 2.38711i) q^{2} +(2.11050 + 2.13208i) q^{3} +(-1.82507 + 1.05371i) q^{4} +(-3.10636 - 3.91797i) q^{5} +(-3.73959 + 6.40173i) q^{6} +(-2.77655 - 10.3622i) q^{7} +(3.30727 + 3.30727i) q^{8} +(-0.0915623 + 8.99953i) q^{9} +(7.36573 - 9.92126i) q^{10} +(-5.66397 + 9.81028i) q^{11} +(-6.09842 - 1.66736i) q^{12} +(2.53087 - 9.44533i) q^{13} +(22.9598 - 13.2559i) q^{14} +(1.79747 - 14.8919i) q^{15} +(-9.99423 + 17.3105i) q^{16} +(8.05728 - 8.05728i) q^{17} +(-21.5414 + 5.53775i) q^{18} -3.73565i q^{19} +(9.79774 + 3.87740i) q^{20} +(16.2332 - 27.7894i) q^{21} +(-27.0410 - 7.24562i) q^{22} +(-3.60402 + 13.4504i) q^{23} +(-0.0713765 + 14.0314i) q^{24} +(-5.70105 + 24.3413i) q^{25} +24.1658 q^{26} +(-19.3810 + 18.7983i) q^{27} +(15.9862 + 15.9862i) q^{28} +(-28.7625 - 16.6061i) q^{29} +(36.6983 - 5.23447i) q^{30} +(7.67855 + 13.2996i) q^{31} +(-29.6434 - 7.94293i) q^{32} +(-32.8702 + 8.62856i) q^{33} +(24.3873 + 14.0800i) q^{34} +(-31.9740 + 43.0673i) q^{35} +(-9.31577 - 16.5213i) q^{36} +(13.7991 - 13.7991i) q^{37} +(8.91741 - 2.38941i) q^{38} +(25.4796 - 14.5384i) q^{39} +(2.68423 - 23.2313i) q^{40} +(4.87477 + 8.44335i) q^{41} +(76.7194 + 20.9758i) q^{42} +(38.3822 - 10.2845i) q^{43} -23.8727i q^{44} +(35.5444 - 27.5971i) q^{45} -34.4127 q^{46} +(-0.451608 - 1.68543i) q^{47} +(-58.0003 + 15.2253i) q^{48} +(-57.2314 + 33.0426i) q^{49} +(-61.7519 + 1.96023i) q^{50} +(34.1837 + 0.173890i) q^{51} +(5.33359 + 19.9052i) q^{52} +(-45.3574 - 45.3574i) q^{53} +(-57.2702 - 34.2407i) q^{54} +(56.0308 - 8.28298i) q^{55} +(25.0879 - 43.4535i) q^{56} +(7.96472 - 7.88410i) q^{57} +(21.2433 - 79.2810i) q^{58} +(10.2473 - 5.91626i) q^{59} +(12.4112 + 29.0729i) q^{60} +(-28.0510 + 48.5858i) q^{61} +(-26.8363 + 26.8363i) q^{62} +(93.5095 - 24.0389i) q^{63} +4.11124i q^{64} +(-44.8683 + 19.4247i) q^{65} +(-41.6219 - 72.9456i) q^{66} +(47.4011 + 12.7011i) q^{67} +(-6.21513 + 23.1952i) q^{68} +(-36.2836 + 20.7030i) q^{69} +(-123.258 - 48.7786i) q^{70} +22.2795 q^{71} +(-30.0667 + 29.4610i) q^{72} +(37.2225 + 37.2225i) q^{73} +(41.7661 + 24.1137i) q^{74} +(-63.9297 + 39.2172i) q^{75} +(3.93628 + 6.81784i) q^{76} +(117.383 + 31.4526i) q^{77} +(51.0021 + 51.5236i) q^{78} +(105.323 + 60.8084i) q^{79} +(98.8678 - 14.6155i) q^{80} +(-80.9832 - 1.64804i) q^{81} +(-17.0372 + 17.0372i) q^{82} +(105.029 - 28.1424i) q^{83} +(-0.345009 + 67.8227i) q^{84} +(-56.5971 - 6.53941i) q^{85} +(49.1003 + 85.0443i) q^{86} +(-25.2979 - 96.3713i) q^{87} +(-51.1775 + 13.7130i) q^{88} +16.0767i q^{89} +(88.6123 + 67.1966i) q^{90} -104.902 q^{91} +(-7.59516 - 28.3455i) q^{92} +(-12.1504 + 44.4403i) q^{93} +(3.73444 - 2.15608i) q^{94} +(-14.6362 + 11.6043i) q^{95} +(-45.6275 - 79.9658i) q^{96} +(-46.1951 - 172.402i) q^{97} +(-115.483 - 115.483i) q^{98} +(-87.7693 - 51.8713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8}+O(q^{10}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23} - 8 q^{25} - 112 q^{26} - 198 q^{27} - 88 q^{28} + 162 q^{30} - 4 q^{31} - 14 q^{32} + 96 q^{33} + 352 q^{35} + 264 q^{36} - 92 q^{37} + 330 q^{38} + 30 q^{40} - 28 q^{41} + 498 q^{42} - 2 q^{43} - 72 q^{45} - 136 q^{46} + 64 q^{47} - 510 q^{48} - 458 q^{50} - 396 q^{51} - 74 q^{52} - 608 q^{53} + 224 q^{55} - 192 q^{56} - 114 q^{57} + 30 q^{58} - 798 q^{60} + 92 q^{61} - 100 q^{62} + 24 q^{63} - 326 q^{65} + 588 q^{66} - 80 q^{67} + 626 q^{68} - 102 q^{70} + 248 q^{71} - 162 q^{72} - 8 q^{73} + 810 q^{75} - 96 q^{76} + 338 q^{77} + 1062 q^{78} + 1444 q^{80} + 204 q^{81} + 104 q^{82} + 370 q^{83} - 98 q^{85} - 328 q^{86} + 534 q^{87} - 210 q^{88} + 462 q^{90} + 152 q^{91} + 388 q^{92} - 1062 q^{93} - 360 q^{95} - 876 q^{96} + 292 q^{97} - 1876 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.639624	+	2.38711i	0.319812	+	1.19356i	0.919425	+	0.393265i	$0.128655\pi$
$2$	0.639624	+	2.38711i	0.319812	+	1.19356i	−0.599613	+	0.800290i	$0.704679\pi$
$3$	2.11050	+	2.13208i	0.703501	+	0.710695i
$3$	2.11050	+	2.13208i	0.703501	+	0.710695i
$4$	−1.82507	+	1.05371i	−0.456269	+	0.263427i
$5$	−3.10636	−	3.91797i	−0.621272	−	0.783595i
$5$	−3.10636	−	3.91797i	−0.621272	−	0.783595i
$6$	−3.73959	+	6.40173i	−0.623265	+	1.06696i
$7$	−2.77655	−	10.3622i	−0.396650	−	1.48032i	−0.818951	−	0.573863i	$-0.805444\pi$
$7$	−2.77655	−	10.3622i	−0.396650	−	1.48032i	0.422301	−	0.906456i	$-0.361223\pi$
$8$	3.30727	+	3.30727i	0.413408	+	0.413408i
$9$	−0.0915623	+	8.99953i	−0.0101736	+	0.999948i
$10$	7.36573	−	9.92126i	0.736573	−	0.992126i
$11$	−5.66397	+	9.81028i	−0.514906	+	0.891844i	0.484944	+	0.874545i	$0.338840\pi$
$11$	−5.66397	+	9.81028i	−0.514906	+	0.891844i	−0.999850	+	0.0172985i	$0.994493\pi$
$12$	−6.09842	−	1.66736i	−0.508201	−	0.138947i
$13$	2.53087	−	9.44533i	0.194682	−	0.726564i	−0.797667	−	0.603098i	$-0.793933\pi$
$13$	2.53087	−	9.44533i	0.194682	−	0.726564i	0.992349	−	0.123465i	$-0.0394007\pi$
$14$	22.9598	−	13.2559i	1.63999	−	0.946848i
$15$	1.79747	−	14.8919i	0.119831	−	0.992794i
$16$	−9.99423	+	17.3105i	−0.624639	+	1.08191i
$17$	8.05728	−	8.05728i	0.473958	−	0.473958i	−0.429235	−	0.903193i	$-0.641217\pi$
$17$	8.05728	−	8.05728i	0.473958	−	0.473958i	0.903193	+	0.429235i	$0.141217\pi$
$18$	−21.5414	+	5.53775i	−1.19675	+	0.307653i
$19$		−	3.73565i		−	0.196613i	−0.995156	−	0.0983066i	$-0.968657\pi$
$19$		−	3.73565i		−	0.196613i	0.995156	−	0.0983066i	$-0.0313426\pi$
$20$	9.79774	+	3.87740i	0.489887	+	0.193870i
$21$	16.2332	−	27.7894i	0.773011	−	1.32330i
$22$	−27.0410	−	7.24562i	−1.22914	−	0.329346i
$23$	−3.60402	+	13.4504i	−0.156696	+	0.584799i	0.842258	+	0.539075i	$0.181226\pi$
$23$	−3.60402	+	13.4504i	−0.156696	+	0.584799i	−0.998954	+	0.0457238i	$0.985441\pi$
$24$	−0.0713765	+	14.0314i	−0.00297402	+	0.584640i
$25$	−5.70105	+	24.3413i	−0.228042	+	0.973651i
$26$	24.1658			0.929456
$27$	−19.3810	+	18.7983i	−0.717815	+	0.696234i
$28$	15.9862	+	15.9862i	0.570935	+	0.570935i
$29$	−28.7625	−	16.6061i	−0.991812	−	0.572623i	−0.0859964	−	0.996295i	$-0.527407\pi$
$29$	−28.7625	−	16.6061i	−0.991812	−	0.572623i	−0.905815	+	0.423673i	$0.860741\pi$
$30$	36.6983	−	5.23447i	1.22328	−	0.174482i
$31$	7.67855	+	13.2996i	0.247695	+	0.429021i	0.962886	−	0.269909i	$-0.0869935\pi$
$31$	7.67855	+	13.2996i	0.247695	+	0.429021i	−0.715191	+	0.698929i	$0.753660\pi$
$32$	−29.6434	−	7.94293i	−0.926357	−	0.248217i
$33$	−32.8702	+	8.62856i	−0.996065	+	0.261472i
$34$	24.3873	+	14.0800i	0.717272	+	0.414117i
$35$	−31.9740	+	43.0673i	−0.913543	+	1.23049i
$36$	−9.31577	−	16.5213i	−0.258771	−	0.458925i
$37$	13.7991	−	13.7991i	0.372947	−	0.372947i	−0.495602	−	0.868550i	$-0.665053\pi$
$37$	13.7991	−	13.7991i	0.372947	−	0.372947i	0.868550	+	0.495602i	$0.165053\pi$
$38$	8.91741	−	2.38941i	0.234669	−	0.0628793i
$39$	25.4796	−	14.5384i	0.653324	−	0.372779i
$40$	2.68423	−	23.2313i	0.0671057	−	0.580784i
$41$	4.87477	+	8.44335i	0.118897	+	0.205935i	0.919331	−	0.393486i	$-0.128731\pi$
$41$	4.87477	+	8.44335i	0.118897	+	0.205935i	−0.800434	+	0.599421i	$0.795398\pi$
$42$	76.7194	+	20.9758i	1.82665	+	0.499423i
$43$	38.3822	−	10.2845i	0.892609	−	0.239174i	0.216769	−	0.976223i	$-0.430448\pi$
$43$	38.3822	−	10.2845i	0.892609	−	0.239174i	0.675839	+	0.737049i	$0.263781\pi$
$44$		−	23.8727i		−	0.542560i
$45$	35.5444	−	27.5971i	0.789875	−	0.613268i
$46$	−34.4127			−0.748103
$47$	−0.451608	−	1.68543i	−0.00960869	−	0.0358601i	0.960955	−	0.276705i	$-0.0892423\pi$
$47$	−0.451608	−	1.68543i	−0.00960869	−	0.0358601i	−0.970564	+	0.240844i	$0.922576\pi$
$48$	−58.0003	+	15.2253i	−1.20834	+	0.317195i
$49$	−57.2314	+	33.0426i	−1.16799	+	0.674338i
$50$	−61.7519	+	1.96023i	−1.23504	+	0.0392045i
$51$	34.1837	+	0.173890i	0.670269	+	0.00340961i
$52$	5.33359	+	19.9052i	0.102569	+	0.382793i
$53$	−45.3574	−	45.3574i	−0.855801	−	0.855801i	0.135040	−	0.990840i	$-0.456884\pi$
$53$	−45.3574	−	45.3574i	−0.855801	−	0.855801i	−0.990840	+	0.135040i	$0.956884\pi$
$54$	−57.2702	−	34.2407i	−1.06056	−	0.634088i
$55$	56.0308	−	8.28298i	1.01874	−	0.150600i
$56$	25.0879	−	43.4535i	0.447998	−	0.775955i
$57$	7.96472	−	7.88410i	0.139732	−	0.138318i
$58$	21.2433	−	79.2810i	0.366263	−	1.36691i
$59$	10.2473	−	5.91626i	0.173683	−	0.100276i	−0.410639	−	0.911798i	$-0.634694\pi$
$59$	10.2473	−	5.91626i	0.173683	−	0.100276i	0.584321	+	0.811523i	$0.301361\pi$
$60$	12.4112	+	29.0729i	0.206853	+	0.484548i
$61$	−28.0510	+	48.5858i	−0.459852	+	0.796488i	−0.998953	−	0.0457538i	$-0.985431\pi$
$61$	−28.0510	+	48.5858i	−0.459852	+	0.796488i	0.539100	+	0.842242i	$0.318764\pi$
$62$	−26.8363	+	26.8363i	−0.432844	+	0.432844i
$63$	93.5095	−	24.0389i	1.48428	−	0.381570i
$64$			4.11124i			0.0642381i
$65$	−44.8683	+	19.4247i	−0.690282	+	0.298842i
$66$	−41.6219	−	72.9456i	−0.630634	−	1.10524i
$67$	47.4011	+	12.7011i	0.707480	+	0.189569i	0.594578	−	0.804038i	$-0.297319\pi$
$67$	47.4011	+	12.7011i	0.707480	+	0.189569i	0.112901	+	0.993606i	$0.463986\pi$
$68$	−6.21513	+	23.1952i	−0.0913989	+	0.341105i
$69$	−36.2836	+	20.7030i	−0.525849	+	0.300043i
$70$	−123.258	−	48.7786i	−1.76082	−	0.696837i
$71$	22.2795			0.313795			0.156898	−	0.987615i	$-0.449851\pi$
$71$	22.2795			0.313795			0.156898	+	0.987615i	$0.449851\pi$
$72$	−30.0667	+	29.4610i	−0.417593	+	0.409181i
$73$	37.2225	+	37.2225i	0.509898	+	0.509898i	0.914495	−	0.404597i	$-0.132588\pi$
$73$	37.2225	+	37.2225i	0.509898	+	0.509898i	−0.404597	+	0.914495i	$0.632588\pi$
$74$	41.7661	+	24.1137i	0.564407	+	0.325860i
$75$	−63.9297	+	39.2172i	−0.852397	+	0.522896i
$76$	3.93628	+	6.81784i	0.0517932	+	0.0897084i
$77$	117.383	+	31.4526i	1.52445	+	0.408475i
$78$	51.0021	+	51.5236i	0.653873	+	0.660559i
$79$	105.323	+	60.8084i	1.33321	+	0.769726i	0.985790	−	0.167985i	$-0.0537260\pi$
$79$	105.323	+	60.8084i	1.33321	+	0.769726i	0.347416	+	0.937711i	$0.387059\pi$
$80$	98.8678	−	14.6155i	1.23585	−	0.182694i
$81$	−80.9832	−	1.64804i	−0.999793	−	0.0203461i
$82$	−17.0372	+	17.0372i	−0.207771	+	0.207771i
$83$	105.029	−	28.1424i	1.26541	−	0.339065i	0.437139	−	0.899394i	$-0.355992\pi$
$83$	105.029	−	28.1424i	1.26541	−	0.339065i	0.828270	+	0.560329i	$0.189325\pi$
$84$	−0.345009	+	67.8227i	−0.00410725	+	0.807413i
$85$	−56.5971	−	6.53941i	−0.665848	−	0.0769343i
$86$	49.1003	+	85.0443i	0.570934	+	0.988887i
$87$	−25.2979	−	96.3713i	−0.290780	−	1.10772i
$88$	−51.1775	+	13.7130i	−0.581562	+	0.155829i
$89$			16.0767i			0.180637i	0.995913	+	0.0903186i	$0.0287885\pi$
$89$			16.0767i			0.180637i	−0.995913	+	0.0903186i	$0.971211\pi$
$90$	88.6123	+	67.1966i	0.984581	+	0.746629i
$91$	−104.902			−1.15277
$92$	−7.59516	−	28.3455i	−0.0825560	−	0.308103i
$93$	−12.1504	+	44.4403i	−0.130649	+	0.477852i
$94$	3.73444	−	2.15608i	0.0397281	−	0.0229370i
$95$	−14.6362	+	11.6043i	−0.154065	+	0.122150i
$96$	−45.6275	−	79.9658i	−0.475287	−	0.832977i
$97$	−46.1951	−	172.402i	−0.476238	−	1.77734i	−0.616636	−	0.787248i	$-0.711505\pi$
$97$	−46.1951	−	172.402i	−0.476238	−	1.77734i	0.140398	−	0.990095i	$-0.455162\pi$
$98$	−115.483	−	115.483i	−1.17840	−	1.17840i
$99$	−87.7693	−	51.8713i	−0.886559	−	0.523953i
$100$	−15.2437	−	50.4319i	−0.152437	−	0.504319i
$101$	−13.8448	+	23.9798i	−0.137077	+	0.237424i	−0.926389	−	0.376568i	$-0.877104\pi$
$101$	−13.8448	+	23.9798i	−0.137077	+	0.237424i	0.789312	+	0.613992i	$0.210437\pi$
$102$	21.4496	+	81.7115i	0.210291	+	0.801093i
$103$	−39.5049	+	147.434i	−0.383543	+	1.43140i	0.456908	+	0.889514i	$0.348957\pi$
$103$	−39.5049	+	147.434i	−0.383543	+	1.43140i	−0.840451	+	0.541888i	$0.817710\pi$
$104$	39.6085	−	22.8680i	0.380851	−	0.219884i
$105$	−159.304	+	22.7224i	−1.51718	+	0.216403i
$106$	79.2615	−	137.285i	0.747750	−	1.29514i
$107$	−108.283	+	108.283i	−1.01199	+	1.01199i	−0.0120628	+	0.999927i	$0.503840\pi$
$107$	−108.283	+	108.283i	−1.01199	+	1.01199i	−0.999927	+	0.0120628i	$0.996160\pi$
$108$	15.5639	−	54.7302i	0.144110	−	0.506761i
$109$		−	184.036i		−	1.68841i	−0.536024	−	0.844203i	$-0.680074\pi$
$109$		−	184.036i		−	1.68841i	0.536024	−	0.844203i	$-0.319926\pi$
$110$	55.6110	+	128.454i	0.505555	+	1.16776i
$111$	58.5437	+	0.297807i	0.527421	+	0.00268295i
$112$	207.125	+	55.4990i	1.84933	+	0.495527i
$113$	43.5785	−	162.637i	0.385650	−	1.43927i	−0.451489	−	0.892277i	$-0.649107\pi$
$113$	43.5785	−	162.637i	0.385650	−	1.43927i	0.837139	−	0.546990i	$-0.184226\pi$
$114$	23.9146	+	13.9698i	0.209778	+	0.122542i
$115$	63.8936	−	27.6613i	0.555596	−	0.240533i
$116$	69.9917			0.603377
$117$	84.7718	+	23.6415i	0.724545	+	0.202064i
$118$	20.6772	+	20.6772i	0.175230	+	0.175230i
$119$	−105.863	−	61.1200i	−0.889604	−	0.513613i
$120$	55.1962	−	43.3068i	0.459969	−	0.360890i
$121$	−3.66106	−	6.34114i	−0.0302567	−	0.0524061i
$122$	−133.922	−	35.8842i	−1.09772	−	0.294133i
$123$	−7.71372	+	28.2131i	−0.0627132	+	0.229375i
$124$	−28.0279	−	16.1819i	−0.226031	−	0.130499i
$125$	113.078	−	53.2762i	0.904624	−	0.426210i
$126$	117.194	+	207.842i	0.930114	+	1.64954i
$127$	−94.7770	+	94.7770i	−0.746275	+	0.746275i	−0.973778	−	0.227502i	$-0.926944\pi$
$127$	−94.7770	+	94.7770i	−0.746275	+	0.746275i	0.227502	+	0.973778i	$0.426944\pi$
$128$	−128.388	+	34.4014i	−1.00303	+	0.268761i
$129$	102.933	+	60.1286i	0.797930	+	0.466113i
$130$	−75.0678	−	94.6812i	−0.577445	−	0.728317i
$131$	−56.6078	−	98.0476i	−0.432121	−	0.748455i	0.564935	−	0.825135i	$-0.308901\pi$
$131$	−56.6078	−	98.0476i	−0.432121	−	0.748455i	−0.997056	+	0.0766803i	$0.975568\pi$
$132$	50.8985	−	50.3833i	0.385595	−	0.381692i
$133$	−38.7097	+	10.3722i	−0.291050	+	0.0779867i
$134$			121.276i			0.905042i
$135$	133.856	+	17.5399i	0.991524	+	0.129926i
$136$	53.2952			0.391876
$137$	−6.25891	−	23.3586i	−0.0456855	−	0.170501i	0.939314	−	0.343059i	$-0.111463\pi$
$137$	−6.25891	−	23.3586i	−0.0456855	−	0.170501i	−0.984999	+	0.172559i	$0.944797\pi$
$138$	−72.6282	−	73.3708i	−0.526291	−	0.531673i
$139$	98.1741	−	56.6809i	0.706289	−	0.407776i	−0.103397	−	0.994640i	$-0.532971\pi$
$139$	98.1741	−	56.6809i	0.706289	−	0.407776i	0.809685	+	0.586864i	$0.199638\pi$
$140$	12.9746	−	112.292i	0.0926758	−	0.802087i
$141$	2.64035	−	4.51996i	0.0187259	−	0.0320565i
$142$	14.2505	+	53.1835i	0.100355	+	0.374532i
$143$	78.3266	+	78.3266i	0.547738	+	0.547738i
$144$	−154.871	−	91.5284i	−1.07550	−	0.635614i
$145$	24.2847	+	164.275i	0.167481	+	1.13293i
$146$	−65.0459	+	112.663i	−0.445520	+	0.771663i
$147$	−191.236	−	52.2857i	−1.30093	−	0.355685i
$148$	−10.6441	+	39.7245i	−0.0719199	+	0.268409i
$149$	−136.216	+	78.6442i	−0.914199	+	0.527813i	−0.881780	−	0.471661i	$-0.843655\pi$
$149$	−136.216	+	78.6442i	−0.914199	+	0.527813i	−0.0324193	+	0.999474i	$0.510321\pi$
$150$	−134.507	−	127.523i	−0.896712	−	0.850154i
$151$	9.10366	−	15.7680i	0.0602891	−	0.104424i	−0.834306	−	0.551302i	$-0.814131\pi$
$151$	9.10366	−	15.7680i	0.0602891	−	0.104424i	0.894595	+	0.446879i	$0.147464\pi$
$152$	12.3548	−	12.3548i	0.0812815	−	0.0812815i
$153$	71.7741	+	73.2495i	0.469111	+	0.478755i
$154$			300.323i			1.95015i
$155$	28.2553	−	71.3979i	0.182292	−	0.460631i
$156$	−31.1831	+	53.3817i	−0.199891	+	0.342190i
$157$	−163.467	−	43.8009i	−1.04119	−	0.278987i	−0.302585	−	0.953122i	$-0.597850\pi$
$157$	−163.467	−	43.8009i	−1.04119	−	0.278987i	−0.738607	+	0.674136i	$0.764516\pi$
$158$	−77.7890	+	290.313i	−0.492336	+	1.83742i
$159$	0.978892	−	192.433i	0.00615655	−	1.21027i
$160$	60.9629	+	140.816i	0.381018	+	0.880099i
$161$	149.383			0.927842
$162$	−47.8648	−	194.370i	−0.295462	−	1.19981i
$163$	−152.193	−	152.193i	−0.933698	−	0.933698i	0.0642365	−	0.997935i	$-0.479539\pi$
$163$	−152.193	−	152.193i	−0.933698	−	0.933698i	−0.997935	+	0.0642365i	$0.979539\pi$
$164$	−17.7936	−	10.2732i	−0.108498	−	0.0626412i
$165$	135.913	+	101.981i	0.823715	+	0.618067i
$166$	134.358	+	232.715i	0.809387	+	1.40190i
$167$	109.110	+	29.2359i	0.653353	+	0.175065i	0.570245	−	0.821475i	$-0.306848\pi$
$167$	109.110	+	29.2359i	0.653353	+	0.175065i	0.0831087	+	0.996540i	$0.473515\pi$
$168$	145.594	−	38.2192i	0.866633	−	0.227495i
$169$	63.5494	+	36.6902i	0.376032	+	0.217102i
$170$	−20.5906	−	139.286i	−0.121121	−	0.819331i
$171$	33.6191	+	0.342045i	0.196603	+	0.00200026i
$172$	−59.2135	+	59.2135i	−0.344264	+	0.344264i
$173$	68.8666	−	18.4527i	0.398073	−	0.106663i	−0.0542285	−	0.998529i	$-0.517270\pi$
$173$	68.8666	−	18.4527i	0.398073	−	0.106663i	0.452301	+	0.891865i	$0.350603\pi$
$174$	213.868	−	122.030i	1.22912	−	0.701323i
$175$	268.059	−	8.50917i	1.53177	−	0.0486238i
$176$	−113.214	−	196.092i	−0.643261	−	1.11416i
$177$	34.2409	+	9.36175i	0.193451	+	0.0528913i
$178$	−38.3769	+	10.2831i	−0.215600	+	0.0577700i
$179$			46.2183i			0.258203i	0.991631	+	0.129101i	$0.0412092\pi$
$179$			46.2183i			0.258203i	−0.991631	+	0.129101i	$0.958791\pi$
$180$	−35.7919	+	87.8200i	−0.198844	+	0.487889i
$181$	−166.274			−0.918640			−0.459320	−	0.888271i	$-0.651907\pi$
$181$	−166.274			−0.918640			−0.459320	+	0.888271i	$0.651907\pi$
$182$	−67.0977	−	250.412i	−0.368669	−	1.37589i
$183$	−162.791	+	42.7333i	−0.889566	+	0.233515i
$184$	−56.4034	+	32.5645i	−0.306540	+	0.176981i
$185$	−96.9292	−	11.1995i	−0.523942	−	0.0605379i
$186$	−113.855	−	0.579174i	−0.612126	−	0.00311384i
$187$	33.4080	+	124.680i	0.178652	+	0.666740i
$188$	2.60016	+	2.60016i	0.0138307	+	0.0138307i
$189$	248.605	+	148.636i	1.31537	+	0.786434i
$190$	−37.0623	−	27.5158i	−0.195065	−	0.144820i
$191$	−58.2778	+	100.940i	−0.305119	+	0.528482i	−0.977288	−	0.211916i	$-0.932030\pi$
$191$	−58.2778	+	100.940i	−0.305119	+	0.528482i	0.672169	+	0.740398i	$0.265363\pi$
$192$	−8.76551	+	8.67678i	−0.0456537	+	0.0451916i
$193$	32.3443	−	120.711i	0.167587	−	0.625443i	−0.830109	−	0.557601i	$-0.811722\pi$
$193$	32.3443	−	120.711i	0.167587	−	0.625443i	0.997696	−	0.0678422i	$-0.0216114\pi$
$194$	381.996	−	220.545i	1.96905	−	1.13683i
$195$	−136.110	−	54.6672i	−0.697999	−	0.280345i
$196$	69.6344	−	120.610i	0.355277	−	0.615358i
$197$	83.4305	−	83.4305i	0.423505	−	0.423505i	−0.462903	−	0.886409i	$-0.653192\pi$
$197$	83.4305	−	83.4305i	0.423505	−	0.423505i	0.886409	+	0.462903i	$0.153192\pi$
$198$	67.6832	−	242.693i	0.341834	−	1.22572i
$199$		−	271.461i		−	1.36412i	−0.731294	−	0.682062i	$-0.761083\pi$
$199$		−	271.461i		−	1.36412i	0.731294	−	0.682062i	$-0.238917\pi$
$200$	−99.3580	+	61.6482i	−0.496790	+	0.308241i
$201$	72.9604	+	127.869i	0.362987	+	0.636164i
$202$	−66.0980	−	17.7109i	−0.327218	−	0.0876777i
$203$	−92.2152	+	344.152i	−0.454262	+	1.69533i
$204$	−62.5711	+	35.7023i	−0.306721	+	0.175011i
$205$	17.9380	−	45.3273i	0.0875027	−	0.221109i
$206$	−377.210			−1.83112
$207$	−120.717	−	33.6660i	−0.583174	−	0.162638i
$208$	138.209	+	138.209i	0.664468	+	0.664468i
$209$	36.6478	+	21.1586i	0.175348	+	0.101237i
$210$	−156.136	−	365.743i	−0.743503	−	1.74163i
$211$	−65.7689	−	113.915i	−0.311701	−	0.539882i	0.667030	−	0.745031i	$-0.267565\pi$
$211$	−65.7689	−	113.915i	−0.311701	−	0.539882i	−0.978731	+	0.205149i	$0.934232\pi$
$212$	130.574	+	34.9872i	0.615916	+	0.165034i
$213$	47.0208	+	47.5017i	0.220755	+	0.223012i
$214$	−327.744	−	189.223i	−1.53151	−	0.884219i
$215$	−159.523	−	118.433i	−0.741968	−	0.550852i
$216$	−126.269	−	1.92710i	−0.584580	−	0.00892176i
$217$	116.494	−	116.494i	0.536839	−	0.536839i
$218$	439.315	−	117.714i	2.01520	−	0.539972i
$219$	−0.803327	+	157.920i	−0.00366816	+	0.721095i
$220$	−93.5325	+	74.1571i	−0.425148	+	0.337078i
$221$	−55.7118	−	96.4956i	−0.252089	−	0.436632i
$222$	36.7351	+	139.941i	0.165473	+	0.630364i
$223$	29.8918	−	8.00949i	0.134044	−	0.0359170i	−0.191173	−	0.981556i	$-0.561229\pi$
$223$	29.8918	−	8.00949i	0.134044	−	0.0359170i	0.325217	+	0.945639i	$0.394563\pi$
$224$			329.226i			1.46976i
$225$	−218.538	−	53.5356i	−0.971281	−	0.237936i
$226$	416.107			1.84118
$227$	16.9273	+	63.1736i	0.0745697	+	0.278298i	0.993135	−	0.116970i	$-0.0373183\pi$
$227$	16.9273	+	63.1736i	0.0745697	+	0.278298i	−0.918566	+	0.395268i	$0.870652\pi$
$228$	−6.22868	+	22.7816i	−0.0273188	+	0.0999191i
$229$	−240.813	+	139.033i	−1.05158	+	0.607132i	−0.923092	−	0.384579i	$-0.874347\pi$
$229$	−240.813	+	139.033i	−1.05158	+	0.607132i	−0.128491	+	0.991711i	$0.541013\pi$
$230$	106.898	+	134.828i	0.464775	+	0.586210i
$231$	180.677	+	316.651i	0.782151	+	1.37078i
$232$	−40.2047	−	150.046i	−0.173296	−	0.646750i
$233$	−106.791	−	106.791i	−0.458329	−	0.458329i	0.439778	−	0.898107i	$-0.355057\pi$
$233$	−106.791	−	106.791i	−0.458329	−	0.458329i	−0.898107	+	0.439778i	$0.855057\pi$
$234$	−2.21268	+	217.481i	−0.00945590	+	0.929407i
$235$	−5.20060	+	7.00493i	−0.0221302	+	0.0298082i
$236$	−12.4680	+	21.5952i	−0.0528306	+	0.0915053i
$237$	92.6363	+	352.894i	0.390870	+	1.48900i
$238$	78.1876	−	291.800i	0.328520	−	1.22605i
$239$	−136.295	+	78.6901i	−0.570273	+	0.329247i	−0.757258	−	0.653115i	$-0.773462\pi$
$239$	−136.295	+	78.6901i	−0.570273	+	0.329247i	0.186985	+	0.982363i	$0.440128\pi$
$240$	239.822	+	179.948i	0.999260	+	0.749785i
$241$	−10.1579	+	17.5940i	−0.0421489	+	0.0730040i	−0.886330	−	0.463054i	$-0.846754\pi$
$241$	−10.1579	+	17.5940i	−0.0421489	+	0.0730040i	0.844181	+	0.536058i	$0.180087\pi$
$242$	12.7953	−	12.7953i	0.0528731	−	0.0528731i
$243$	−167.402	−	176.141i	−0.688895	−	0.724861i
$244$		−	118.230i		−	0.484550i
$245$	307.241	+	121.589i	1.25405	+	0.496282i
$246$	−72.2817	−	0.367692i	−0.293828	−	0.00149468i
$247$	−35.2844	−	9.45444i	−0.142852	−	0.0382771i
$248$	−18.5905	+	69.3805i	−0.0749615	+	0.279760i
$249$	281.666	+	164.536i	1.13119	+	0.660787i
$250$	199.504	+	235.853i	0.798014	+	0.943412i
$251$	−92.7758			−0.369625			−0.184812	−	0.982774i	$-0.559168\pi$
$251$	−92.7758			−0.369625			−0.184812	+	0.982774i	$0.559168\pi$
$252$	−145.332	+	142.404i	−0.576714	+	0.565097i
$253$	−111.539	−	111.539i	−0.440865	−	0.440865i
$254$	−286.865	−	165.621i	−1.12939	−	0.652053i
$255$	−105.506	−	134.471i	−0.413748	−	0.527338i
$256$	−156.017	−	270.230i	−0.609442	−	1.05559i
$257$	413.001	+	110.663i	1.60701	+	0.430596i	0.947149	−	0.320794i	$-0.103950\pi$
$257$	413.001	+	110.663i	1.60701	+	0.430596i	0.659858	+	0.751390i	$0.270617\pi$
$258$	−77.6952	+	284.172i	−0.301144	+	1.10144i
$259$	−181.303	−	104.675i	−0.700011	−	0.404152i
$260$	61.4201	−	82.7297i	0.236231	−	0.318191i
$261$	152.080	−	257.329i	0.582683	−	0.985935i
$262$	197.843	−	197.843i	0.755125	−	0.755125i
$263$	171.887	−	46.0569i	0.653562	−	0.175121i	0.0832230	−	0.996531i	$-0.473479\pi$
$263$	171.887	−	46.0569i	0.653562	−	0.175121i	0.570339	+	0.821410i	$0.306812\pi$
$264$	−137.247	−	80.1734i	−0.519876	−	0.303687i
$265$	−36.8128	+	318.606i	−0.138916	+	1.20229i
$266$	−49.5193	−	85.7699i	−0.186163	−	0.322443i
$267$	−34.2769	+	33.9299i	−0.128378	+	0.127078i
$268$	−99.8939	+	26.7665i	−0.372738	+	0.0998749i
$269$		−	175.152i		−	0.651123i	−0.945521	−	0.325562i	$-0.894447\pi$
$269$		−	175.152i		−	0.651123i	0.945521	−	0.325562i	$-0.105553\pi$
$270$	43.7476	+	330.747i	0.162028	+	1.22499i
$271$	463.337			1.70973			0.854865	−	0.518850i	$-0.173640\pi$
$271$	463.337			1.70973			0.854865	+	0.518850i	$0.173640\pi$
$272$	58.9494	+	220.002i	0.216726	+	0.808831i
$273$	−221.395	−	223.659i	−0.810972	−	0.819265i
$274$	51.7562	−	29.8814i	0.188891	−	0.109056i
$275$	−206.504	−	193.797i	−0.750924	−	0.704717i
$276$	44.4054	−	76.0168i	0.160889	−	0.275423i
$277$	99.8186	+	372.528i	0.360356	+	1.34487i	0.873608	+	0.486630i	$0.161774\pi$
$277$	99.8186	+	372.528i	0.360356	+	1.34487i	−0.513252	+	0.858238i	$0.671559\pi$
$278$	198.098	+	198.098i	0.712583	+	0.712583i
$279$	−120.394	+	67.8857i	−0.431519	+	0.243318i
$280$	−248.182	+	36.6885i	−0.886363	+	0.131030i
$281$	39.8147	−	68.9610i	0.141689	−	0.245413i	−0.786444	−	0.617662i	$-0.788080\pi$
$281$	39.8147	−	68.9610i	0.141689	−	0.245413i	0.928133	+	0.372249i	$0.121413\pi$
$282$	12.4785	+	3.41172i	0.0442499	+	0.0120983i
$283$	−61.9962	+	231.373i	−0.219068	+	0.817573i	0.765627	+	0.643285i	$0.222429\pi$
$283$	−61.9962	+	231.373i	−0.219068	+	0.817573i	−0.984695	+	0.174288i	$0.944238\pi$
$284$	−40.6617	+	23.4760i	−0.143175	+	0.0826621i
$285$	−55.6310	−	6.71473i	−0.195196	−	0.0235604i
$286$	−136.875	+	237.074i	−0.478582	+	0.828929i
$287$	73.9569	−	73.9569i	0.257690	−	0.257690i
$288$	74.1969	−	266.050i	0.257628	−	0.923784i
$289$			159.160i			0.550728i
$290$	−376.610	+	163.045i	−1.29866	+	0.562223i
$291$	270.081	−	462.347i	0.928115	−	1.58882i
$292$	−107.156	−	28.7122i	−0.366971	−	0.0983296i
$293$	22.4817	−	83.9027i	0.0767292	−	0.286357i	−0.916891	−	0.399139i	$-0.869309\pi$
$293$	22.4817	−	83.9027i	0.0767292	−	0.286357i	0.993620	+	0.112781i	$0.0359759\pi$
$294$	2.49232	−	489.946i	0.00847727	−	1.66648i
$295$	−55.0115	−	21.7705i	−0.186480	−	0.0737983i
$296$	91.2743			0.308359
$297$	−74.6434	−	296.606i	−0.251324	−	0.998674i
$298$	−274.859	−	274.859i	−0.922346	−	0.922346i
$299$	117.922	+	68.0822i	0.394388	+	0.227700i
$300$	75.3531	−	138.938i	0.251177	−	0.463125i
$301$	−213.140	−	369.170i	−0.708107	−	1.22648i
$302$	43.4629	+	11.6458i	0.143917	+	0.0385624i
$303$	−80.3464	+	21.0913i	−0.265170	+	0.0696083i
$304$	64.6660	+	37.3350i	0.212717	+	0.122812i
$305$	277.494	−	41.0217i	0.909817	−	0.134497i
$306$	−128.946	+	218.185i	−0.421393	+	0.713022i
$307$	−220.805	+	220.805i	−0.719234	+	0.719234i	−0.968448	−	0.249215i	$-0.919828\pi$
$307$	−220.805	+	220.805i	−0.719234	+	0.719234i	0.249215	+	0.968448i	$0.419828\pi$
$308$	−247.374	+	66.2837i	−0.803162	+	0.215207i
$309$	−397.718	+	226.933i	−1.28711	+	0.734410i
$310$	188.507	+	21.7808i	0.608088	+	0.0702605i
$311$	50.9290	+	88.2115i	0.163759	+	0.283638i	0.936214	−	0.351431i	$-0.114305\pi$
$311$	50.9290	+	88.2115i	0.163759	+	0.283638i	−0.772455	+	0.635069i	$0.780971\pi$
$312$	132.350	+	36.1857i	0.424199	+	0.115980i
$313$	260.438	−	69.7840i	0.832069	−	0.222952i	0.182453	−	0.983215i	$-0.441596\pi$
$313$	260.438	−	69.7840i	0.832069	−	0.222952i	0.649616	+	0.760262i	$0.274930\pi$
$314$		−	418.230i		−	1.33194i
$315$	−384.658	−	291.694i	−1.22114	−	0.926014i
$316$	−256.297			−0.811066
$317$	−19.7431	−	73.6824i	−0.0622812	−	0.232437i	0.927768	−	0.373157i	$-0.121725\pi$
$317$	−19.7431	−	73.6824i	−0.0622812	−	0.232437i	−0.990049	+	0.140721i	$0.955058\pi$
$318$	459.984	−	120.748i	1.44649	−	0.379711i
$319$	325.820	−	188.112i	1.02138	−	0.589694i
$320$	16.1077	−	12.7710i	0.0503367	−	0.0399093i
$321$	−459.400	−	2.33693i	−1.43115	−	0.00728016i
$322$	95.5488	+	356.593i	0.296735	+	1.10743i
$323$	−30.0992	−	30.0992i	−0.0931864	−	0.0931864i
$324$	149.537	−	82.3248i	0.461534	−	0.254089i
$325$	215.483	+	115.453i	0.663024	+	0.355240i
$326$	265.955	−	460.647i	0.815812	−	1.41303i
$327$	392.381	−	388.409i	1.19994	−	1.18779i
$328$	−11.8022	+	44.0466i	−0.0359825	+	0.134288i
$329$	−16.2109	+	9.35934i	−0.0492731	+	0.0284479i
$330$	−156.507	+	389.669i	−0.474263	+	1.18081i
$331$	−39.1180	+	67.7543i	−0.118181	+	0.204696i	−0.919047	−	0.394148i	$-0.871040\pi$
$331$	−39.1180	+	67.7543i	−0.118181	+	0.204696i	0.800866	+	0.598844i	$0.204373\pi$
$332$	−162.032	+	162.032i	−0.488048	+	0.488048i
$333$	122.922	+	125.449i	0.369134	+	0.376722i
$334$			279.158i			0.835801i
$335$	−97.4824	−	225.171i	−0.290992	−	0.672151i
$336$	318.809	+	558.739i	0.948838	+	1.66291i
$337$	−166.029	−	44.4872i	−0.492667	−	0.132010i	0.00392788	−	0.999992i	$-0.498750\pi$
$337$	−166.029	−	44.4872i	−0.492667	−	0.132010i	−0.496595	+	0.867983i	$0.665416\pi$
$338$	−46.9359	+	175.167i	−0.138864	+	0.518246i
$339$	438.728	−	250.333i	1.29418	−	0.738445i
$340$	110.184	−	47.7018i	0.324072	−	0.140299i
$341$	−173.964			−0.510159
$342$	20.6871	+	80.4713i	0.0604886	+	0.235296i
$343$	129.602	+	129.602i	0.377849	+	0.377849i
$344$	160.954	+	92.9266i	0.467888	+	0.270135i
$345$	193.824	+	77.8474i	0.561808	+	0.225645i
$346$	88.0974	+	152.589i	0.254617	+	0.441009i
$347$	−625.254	−	167.536i	−1.80188	−	0.482813i	−0.807614	−	0.589712i	$-0.799241\pi$
$347$	−625.254	−	167.536i	−1.80188	−	0.482813i	−0.994270	+	0.106899i	$0.965908\pi$
$348$	147.718	+	149.228i	0.424476	+	0.428817i
$349$	74.5409	+	43.0362i	0.213584	+	0.123313i	0.602976	−	0.797759i	$-0.293981\pi$
$349$	74.5409	+	43.0362i	0.213584	+	0.123313i	−0.389392	+	0.921072i	$0.627315\pi$
$350$	191.770	+	634.444i	0.547913	+	1.81270i
$351$	128.506	+	230.636i	0.366113	+	0.657083i
$352$	245.822	−	245.822i	0.698357	−	0.698357i
$353$	−614.682	+	164.703i	−1.74131	+	0.466582i	−0.982737	−	0.185008i	$-0.940769\pi$
$353$	−614.682	+	164.703i	−1.74131	+	0.466582i	−0.758571	+	0.651590i	$0.774102\pi$
$354$	−0.446249	+	87.7247i	−0.00126059	+	0.247810i
$355$	−69.2080	−	87.2903i	−0.194952	−	0.245888i
$356$	−16.9401	−	29.3412i	−0.0475847	−	0.0824191i
$357$	−93.1110	−	354.702i	−0.260815	−	0.993564i
$358$	−110.328	+	29.5623i	−0.308179	+	0.0825763i
$359$			651.608i			1.81506i	0.419983	+	0.907532i	$0.362036\pi$
$359$			651.608i			1.81506i	−0.419983	+	0.907532i	$0.637964\pi$
$360$	208.826	+	26.2839i	0.580071	+	0.0730109i
$361$	347.045			0.961343
$362$	−106.353	−	396.914i	−0.293792	−	1.09645i
$363$	5.79317	−	21.1887i	0.0159591	−	0.0583710i
$364$	191.454	−	110.536i	0.525971	−	0.303670i
$365$	30.2104	−	261.464i	0.0827681	−	0.716339i
$366$	−206.134	−	361.266i	−0.563207	−	0.987065i
$367$	−25.0954	−	93.6571i	−0.0683797	−	0.255197i	0.923271	−	0.384149i	$-0.125505\pi$
$367$	−25.0954	−	93.6571i	−0.0683797	−	0.255197i	−0.991651	+	0.128953i	$0.958838\pi$
$368$	−196.814	−	196.814i	−0.534819	−	0.534819i
$369$	−76.4326	+	43.0976i	−0.207134	+	0.116796i
$370$	−35.2638	−	238.544i	−0.0953075	−	0.644714i
$371$	−344.067	+	595.942i	−0.927404	+	1.60631i
$372$	−24.6517	−	93.9097i	−0.0662680	−	0.252445i
$373$	−123.092	+	459.385i	−0.330005	+	1.23160i	0.579179	+	0.815200i	$0.303373\pi$
$373$	−123.092	+	459.385i	−0.330005	+	1.23160i	−0.909184	+	0.416395i	$0.863293\pi$
$374$	−276.257	+	159.497i	−0.738656	+	0.426463i
$375$	352.241	+	128.652i	0.939309	+	0.343073i
$376$	4.08056	−	7.06774i	0.0108526	−	0.0187972i
$377$	−229.644	+	229.644i	−0.609135	+	0.609135i
$378$	−195.797	+	688.518i	−0.517981	+	1.82148i
$379$			556.768i			1.46905i	0.678584	+	0.734523i	$0.262594\pi$
$379$			556.768i			1.46905i	−0.678584	+	0.734523i	$0.737406\pi$
$380$	14.4846	−	36.6009i	0.0381174	−	0.0963182i
$381$	−402.099	−	2.04545i	−1.05538	−	0.00536864i
$382$	−278.231	−	74.5517i	−0.728353	−	0.195162i
$383$	189.503	−	707.233i	0.494785	−	1.84656i	−0.0364479	−	0.999336i	$-0.511604\pi$
$383$	189.503	−	707.233i	0.494785	−	1.84656i	0.531233	−	0.847226i	$-0.321729\pi$
$384$	−344.309	−	201.129i	−0.896638	−	0.523774i
$385$	−241.402	−	557.606i	−0.627019	−	1.44833i
$386$	308.838			0.800097
$387$	89.0411	+	346.363i	0.230080	+	0.894996i
$388$	265.971	+	265.971i	0.685492	+	0.685492i
$389$	−180.704	−	104.330i	−0.464535	−	0.268200i	0.249414	−	0.968397i	$-0.419762\pi$
$389$	−180.704	−	104.330i	−0.464535	−	0.268200i	−0.713949	+	0.700197i	$0.753095\pi$
$390$	43.4374	−	359.876i	0.111378	−	0.922758i
$391$	79.3349	+	137.412i	0.202903	+	0.351437i
$392$	−298.560	−	79.9989i	−0.761633	−	0.204079i
$393$	89.5748	−	327.622i	0.227926	−	0.833645i
$394$	252.522	+	145.794i	0.640919	+	0.370035i
$395$	−88.9261	−	601.546i	−0.225129	−	1.52290i
$396$	214.843	+	2.18584i	0.542532	+	0.00551979i
$397$	109.933	−	109.933i	0.276910	−	0.276910i	−0.554964	−	0.831874i	$-0.687268\pi$
$397$	109.933	−	109.933i	0.276910	−	0.276910i	0.831874	+	0.554964i	$0.187268\pi$
$398$	648.007	−	173.633i	1.62816	−	0.436264i
$399$	−103.811	−	60.6417i	−0.260179	−	0.151984i
$400$	−364.382	−	341.961i	−0.910956	−	0.854901i
$401$	311.573	+	539.660i	0.776989	+	1.34578i	0.933670	+	0.358135i	$0.116587\pi$
$401$	311.573	+	539.660i	0.776989	+	1.34578i	−0.156680	+	0.987649i	$0.550079\pi$
$402$	−258.570	+	255.953i	−0.643209	+	0.636698i
$403$	145.053	−	38.8668i	0.359933	−	0.0964437i
$404$		−	58.3533i		−	0.144439i
$405$	245.106	+	322.410i	0.605200	+	0.796073i
$406$	−880.511			−2.16875
$407$	57.2152	+	213.530i	0.140578	+	0.524644i
$408$	112.480	+	113.630i	0.275685	+	0.278504i
$409$	446.525	−	257.801i	1.09175	−	0.630321i	0.157707	−	0.987486i	$-0.449590\pi$
$409$	446.525	−	257.801i	1.09175	−	0.630321i	0.934041	+	0.357165i	$0.116257\pi$
$410$	119.675	+	13.8276i	0.291890	+	0.0337259i
$411$	36.5930	−	62.6429i	0.0890341	−	0.152416i
$412$	−83.2532	−	310.705i	−0.202071	−	0.754139i
$413$	−89.7578	−	89.7578i	−0.217331	−	0.217331i
$414$	3.15091	−	309.699i	0.00761089	−	0.748064i
$415$	−436.519	−	324.080i	−1.05185	−	0.780917i
$416$	−150.047	+	259.889i	−0.360690	+	0.624734i
$417$	328.045	+	89.6904i	0.786679	+	0.215085i
$418$	−27.0671	+	101.016i	−0.0647539	+	0.241665i
$419$	127.314	−	73.5049i	0.303852	−	0.175429i	−0.340320	−	0.940310i	$-0.610535\pi$
$419$	127.314	−	73.5049i	0.303852	−	0.175429i	0.644172	+	0.764880i	$0.277202\pi$
$420$	266.799	−	209.330i	0.635237	−	0.498405i
$421$	−317.026	+	549.106i	−0.753032	+	1.30429i	0.193315	+	0.981137i	$0.438076\pi$
$421$	−317.026	+	549.106i	−0.753032	+	1.30429i	−0.946347	+	0.323152i	$0.895257\pi$
$422$	229.860	−	229.860i	0.544693	−	0.544693i
$423$	15.2094	−	3.90994i	0.0359560	−	0.00924337i
$424$		−	300.018i		−	0.707590i
$425$	150.190	+	242.060i	0.353387	+	0.569552i
$426$	−83.3160	+	142.627i	−0.195578	+	0.334805i
$427$	581.342	+	155.770i	1.36146	+	0.364801i
$428$	83.5259	−	311.723i	0.195154	−	0.728325i
$429$	−1.69042	+	332.307i	−0.00394038	+	0.774609i
$430$	180.678	−	456.552i	0.420181	−	1.06175i
$431$	735.767			1.70712			0.853559	−	0.520997i	$-0.174440\pi$
$431$	735.767			1.70712			0.853559	+	0.520997i	$0.174440\pi$
$432$	−131.710	−	523.370i	−0.304885	−	1.21150i
$433$	69.9073	+	69.9073i	0.161449	+	0.161449i	0.783208	−	0.621760i	$-0.213582\pi$
$433$	69.9073	+	69.9073i	0.161449	+	0.161449i	−0.621760	+	0.783208i	$0.713582\pi$
$434$	352.597	+	203.572i	0.812435	+	0.469060i
$435$	−298.996	+	398.480i	−0.687347	+	0.916047i
$436$	193.920	+	335.880i	0.444771	+	0.770366i
$437$	50.2459	+	13.4633i	0.114979	+	0.0308086i
$438$	−377.486	+	99.0917i	−0.861840	+	0.226237i
$439$	−290.918	−	167.962i	−0.662683	−	0.382600i	0.130615	−	0.991433i	$-0.458305\pi$
$439$	−290.918	−	167.962i	−0.662683	−	0.382600i	−0.793299	+	0.608833i	$0.791638\pi$
$440$	212.703	+	157.915i	0.483415	+	0.358897i
$441$	−292.127	−	518.081i	−0.662420	−	1.17479i
$442$	194.711	−	194.711i	0.440523	−	0.440523i
$443$	−298.222	+	79.9082i	−0.673187	+	0.180380i	−0.579190	−	0.815193i	$-0.696631\pi$
$443$	−298.222	+	79.9082i	−0.673187	+	0.180380i	−0.0939967	+	0.995573i	$0.529964\pi$
$444$	−107.160	+	61.1444i	−0.241352	+	0.137713i
$445$	62.9881	−	49.9400i	0.141546	−	0.112225i
$446$	38.2391	+	66.2320i	0.0857379	+	0.148502i
$447$	−455.159	−	124.445i	−1.01825	−	0.278400i
$448$	42.6016	−	11.4151i	0.0950929	−	0.0254801i
$449$		−	391.868i		−	0.872757i	−0.899763	−	0.436378i	$-0.856261\pi$
$449$		−	391.868i		−	0.872757i	0.899763	−	0.436378i	$-0.143739\pi$
$450$	−11.9870	−	555.917i	−0.0266378	−	1.23537i
$451$	−110.442			−0.244883
$452$	91.8379	+	342.744i	0.203181	+	0.758283i
$453$	52.8320	−	13.8686i	0.116627	−	0.0306151i
$454$	−139.975	+	80.8148i	−0.308316	+	0.178006i
$455$	325.863	+	411.003i	0.716182	+	0.903302i
$456$	52.4163	+	0.266638i	0.114948	+	0.000584732i
$457$	−44.1215	−	164.664i	−0.0965459	−	0.360314i	0.900703	−	0.434434i	$-0.143052\pi$
$457$	−44.1215	−	164.664i	−0.0965459	−	0.360314i	−0.997249	+	0.0741204i	$0.976385\pi$
$458$	−485.917	−	485.917i	−1.06095	−	1.06095i
$459$	−4.69487	+	307.622i	−0.0102285	+	0.670200i
$460$	−87.4637	+	117.809i	−0.190138	+	0.256107i
$461$	378.908	−	656.288i	0.821926	−	1.42362i	−0.0823197	−	0.996606i	$-0.526233\pi$
$461$	378.908	−	656.288i	0.821926	−	1.42362i	0.904246	−	0.427012i	$-0.140434\pi$
$462$	−640.314	+	633.833i	−1.38596	+	1.37193i
$463$	−45.1054	+	168.336i	−0.0974199	+	0.363576i	−0.997375	−	0.0724060i	$-0.976932\pi$
$463$	−45.1054	+	168.336i	−0.0974199	+	0.363576i	0.899955	+	0.435982i	$0.143599\pi$
$464$	574.919	−	331.930i	1.23905	−	0.715366i
$465$	211.859	−	90.4426i	0.455611	−	0.194500i
$466$	186.615	−	323.227i	0.400462	−	0.693620i
$467$	−191.561	+	191.561i	−0.410194	+	0.410194i	−0.881806	−	0.471612i	$-0.843672\pi$
$467$	−191.561	+	191.561i	−0.410194	+	0.410194i	0.471612	+	0.881806i	$0.343672\pi$
$468$	−179.626	+	46.1772i	−0.383816	+	0.0986693i
$469$		−	526.447i		−	1.12249i
$470$	−20.0480	−	7.93388i	−0.0426552	−	0.0168806i
$471$	−251.611	−	440.968i	−0.534205	−	0.936237i
$472$	53.4571	+	14.3238i	0.113257	+	0.0303470i
$473$	−116.502	+	434.791i	−0.246304	+	0.919219i
$474$	−783.145	+	446.853i	−1.65220	+	0.942727i
$475$	90.9305	+	21.2971i	0.191433	+	0.0448361i
$476$	257.610			0.541198
$477$	412.349	−	404.043i	0.864463	−	0.847050i
$478$	−275.020	−	275.020i	−0.575355	−	0.575355i
$479$	−135.340	−	78.1383i	−0.282546	−	0.163128i	0.352029	−	0.935989i	$-0.385492\pi$
$479$	−135.340	−	78.1383i	−0.282546	−	0.163128i	−0.634575	+	0.772861i	$0.718825\pi$
$480$	−171.569	+	427.170i	−0.357435	+	0.889938i
$481$	−95.4130	−	165.260i	−0.198364	−	0.343576i
$482$	−48.4960	−	12.9945i	−0.100614	−	0.0269595i
$483$	315.272	+	318.496i	0.652738	+	0.659413i
$484$	13.3634	+	7.71537i	0.0276104	+	0.0159408i
$485$	−531.969	+	716.535i	−1.09684	+	1.47739i
$486$	313.394	−	512.270i	0.644845	−	1.05405i
$487$	−451.121	+	451.121i	−0.926326	+	0.926326i	−0.997466	−	0.0711400i	$-0.977336\pi$
$487$	−451.121	+	451.121i	−0.926326	+	0.926326i	0.0711400	+	0.997466i	$0.477336\pi$
$488$	−253.458	+	67.9139i	−0.519381	+	0.139168i
$489$	3.28458	−	645.691i	0.00671694	−	1.32043i
$490$	−93.7276	+	811.190i	−0.191281	+	1.65549i
$491$	200.071	+	346.533i	0.407476	+	0.705769i	0.994606	−	0.103723i	$-0.0330756\pi$
$491$	200.071	+	346.533i	0.407476	+	0.705769i	−0.587130	+	0.809493i	$0.699742\pi$
$492$	−15.6503	−	59.6191i	−0.0318095	−	0.121177i
$493$	−365.548	+	97.9482i	−0.741476	+	0.198678i
$494$		−	90.2752i		−	0.182743i
$495$	69.4126	+	505.009i	0.140228	+	1.02022i
$496$	−306.965			−0.618881
$497$	−61.8601	−	230.865i	−0.124467	−	0.464517i
$498$	−212.605	+	777.609i	−0.426918	+	1.56146i
$499$	−236.699	+	136.658i	−0.474347	+	0.273864i	−0.718058	−	0.695984i	$-0.754969\pi$
$499$	−236.699	+	136.658i	−0.474347	+	0.273864i	0.243711	+	0.969848i	$0.421635\pi$
$500$	−150.238	+	216.384i	−0.300477	+	0.432768i
$501$	167.943	+	294.334i	0.335216	+	0.587493i
$502$	−59.3417	−	221.466i	−0.118211	−	0.441168i
$503$	297.206	+	297.206i	0.590867	+	0.590867i	0.937866	−	0.346999i	$-0.112799\pi$
$503$	297.206	+	297.206i	0.590867	+	0.590867i	−0.346999	+	0.937866i	$0.612799\pi$
$504$	388.764	+	229.758i	0.771357	+	0.455869i
$505$	136.959	−	20.2466i	0.271206	−	0.0400922i
$506$	194.913	−	337.599i	0.385203	−	0.667191i
$507$	55.8944	+	212.927i	0.110245	+	0.419975i
$508$	73.1079	−	272.842i	0.143913	−	0.537091i
$509$	60.1552	−	34.7306i	0.118183	−	0.0682330i	−0.439743	−	0.898124i	$-0.644931\pi$
$509$	60.1552	−	34.7306i	0.118183	−	0.0682330i	0.557926	+	0.829891i	$0.311597\pi$
$510$	253.513	−	337.865i	0.497085	−	0.662480i
$511$	282.358	−	489.059i	0.552560	−	0.957062i
$512$	169.331	−	169.331i	0.330724	−	0.330724i
$513$	70.2239	+	72.4007i	0.136889	+	0.141132i
$514$			1056.66i			2.05576i
$515$	700.361	−	303.205i	1.35992	−	0.588747i
$516$	−251.218	−	1.27793i	−0.486857	−	0.00247661i
$517$	19.0924	+	5.11579i	0.0369292	+	0.00989515i
$518$	133.906	−	499.743i	0.258505	−	0.964754i
$519$	184.686	+	107.885i	0.355849	+	0.207870i
$520$	−212.634	−	84.1489i	−0.408912	−	0.161825i
$521$	−532.558			−1.02218			−0.511092	−	0.859526i	$-0.670759\pi$
$521$	−532.558			−1.02218			−0.511092	+	0.859526i	$0.670759\pi$
$522$	711.547	+	198.439i	1.36312	+	0.380151i
$523$	322.137	+	322.137i	0.615941	+	0.615941i	0.944488	−	0.328547i	$-0.106559\pi$
$523$	322.137	+	322.137i	0.615941	+	0.615941i	−0.328547	+	0.944488i	$0.606559\pi$
$524$	206.627	+	119.296i	0.394326	+	0.227664i
$525$	583.882	+	553.566i	1.11216	+	1.05441i
$526$	219.886	+	380.853i	0.418034	+	0.724056i
$527$	169.027	+	45.2907i	0.320735	+	0.0859407i
$528$	179.147	−	655.235i	0.339294	−	1.24098i
$529$	290.204	+	167.549i	0.548590	+	0.316728i
$530$	−784.094	+	115.912i	−1.47942	+	0.218702i
$531$	52.3054	+	92.7624i	0.0985035	+	0.174694i
$532$	59.7188	−	59.7188i	0.112253	−	0.112253i
$533$	92.0876	−	24.6748i	0.172772	−	0.0462942i
$534$	−102.919	−	60.1203i	−0.192732	−	0.112585i
$535$	760.616	+	87.8840i	1.42171	+	0.164269i
$536$	114.762	+	198.774i	0.214109	+	0.370847i
$537$	−98.5412	+	97.5438i	−0.183503	+	0.181646i
$538$	418.108	−	112.032i	0.777152	−	0.208237i
$539$		−	748.608i		−	1.38888i
$540$	−262.779	+	109.033i	−0.486627	+	0.201913i
$541$	201.002			0.371538			0.185769	−	0.982593i	$-0.440522\pi$
$541$	201.002			0.371538			0.185769	+	0.982593i	$0.440522\pi$
$542$	296.362	+	1106.04i	0.546792	+	2.04066i
$543$	−350.921	−	354.510i	−0.646264	−	0.652872i
$544$	−302.844	+	174.847i	−0.556698	+	0.321410i
$545$	−721.049	+	571.683i	−1.32303	+	1.04896i
$546$	392.290	−	671.553i	0.718479	−	1.22995i
$547$	−161.649	−	603.281i	−0.295519	−	1.10289i	−0.940804	−	0.338950i	$-0.889928\pi$
$547$	−161.649	−	603.281i	−0.295519	−	1.10289i	0.645286	−	0.763941i	$-0.276738\pi$
$548$	36.0361	+	36.0361i	0.0657593	+	0.0657593i
$549$	−434.681	−	256.895i	−0.791768	−	0.467932i
$550$	330.530	−	616.906i	0.600964	−	1.12165i
$551$	−62.0344	+	107.447i	−0.112585	+	0.195003i
$552$	−188.470	−	51.5293i	−0.341431	−	0.0933502i
$553$	337.675	−	1260.22i	0.610624	−	2.27888i
$554$	−825.420	+	476.556i	−1.48993	+	0.860210i
$555$	−180.691	−	230.298i	−0.325569	−	0.414951i
$556$	−119.450	+	206.894i	−0.214838	+	0.372111i
$557$	−227.470	+	227.470i	−0.408384	+	0.408384i	−0.881175	−	0.472791i	$-0.843247\pi$
$557$	−227.470	+	227.470i	−0.408384	+	0.408384i	0.472791	+	0.881175i	$0.343247\pi$
$558$	−239.057	−	243.972i	−0.428418	−	0.437225i
$559$		−	388.561i		−	0.695100i
$560$	−425.961	−	983.911i	−0.760645	−	1.75698i
$561$	−195.321	+	334.367i	−0.348166	+	0.596019i
$562$	190.084	+	50.9328i	0.338228	+	0.0906278i
$563$	−14.1724	+	52.8921i	−0.0251730	+	0.0939469i	−0.977369	−	0.211539i	$-0.932152\pi$
$563$	−14.1724	+	52.8921i	−0.0251730	+	0.0939469i	0.952196	+	0.305486i	$0.0988190\pi$
$564$	−0.0561160	+	11.0314i	−9.94965e−5	+	0.0195593i
$565$	−772.579	+	334.470i	−1.36740	+	0.591982i
$566$	−591.967			−1.04588
$567$	207.777	+	843.743i	0.366449	+	1.48808i
$568$	73.6841	+	73.6841i	0.129726	+	0.129726i
$569$	−211.299	−	121.993i	−0.371351	−	0.214399i	0.302698	−	0.953087i	$-0.402113\pi$
$569$	−211.299	−	121.993i	−0.371351	−	0.214399i	−0.674048	+	0.738687i	$0.735446\pi$
$570$	−19.5541	−	137.092i	−0.0343055	−	0.240513i
$571$	−284.750	−	493.202i	−0.498687	−	0.863751i	0.501312	−	0.865267i	$-0.332851\pi$
$571$	−284.750	−	493.202i	−0.498687	−	0.863751i	−0.999999	+	0.00151580i	$0.999518\pi$
$572$	−225.485	−	60.4185i	−0.394205	−	0.105627i
$573$	−338.208	+	88.7811i	−0.590241	+	0.154941i
$574$	223.848	+	129.239i	0.389979	+	0.225155i
$575$	−306.853	−	164.408i	−0.533657	−	0.285926i
$576$	−36.9992	−	0.376435i	−0.0642348	−	0.000653532i
$577$	−258.911	+	258.911i	−0.448719	+	0.448719i	−0.894929	−	0.446209i	$-0.852774\pi$
$577$	−258.911	+	258.911i	−0.448719	+	0.448719i	0.446209	+	0.894929i	$0.352774\pi$
$578$	−379.933	+	101.803i	−0.657324	+	0.176129i
$579$	325.628	−	185.799i	0.562397	−	0.320897i
$580$	−217.419	−	274.226i	−0.374861	−	0.472803i
$581$	−583.237	−	1010.20i	−1.00385	−	1.73872i
$582$	1276.42	+	348.986i	2.19317	+	0.599632i
$583$	701.872	−	188.066i	1.20390	−	0.322583i
$584$			246.210i			0.421592i
$585$	−170.705	−	405.573i	−0.291804	−	0.693287i
$586$	214.665			0.366322
$587$	−229.139	−	855.160i	−0.390357	−	1.45683i	−0.829547	−	0.558437i	$-0.811401\pi$
$587$	−229.139	−	855.160i	−0.390357	−	1.45683i	0.439190	−	0.898394i	$-0.355266\pi$
$588$	404.115	−	106.082i	0.687270	−	0.180411i
$589$	49.6828	−	28.6844i	0.0843512	−	0.0487002i
$590$	16.7819	−	145.243i	0.0284439	−	0.246175i
$591$	353.961	+	1.80057i	0.598919	+	0.00304666i
$592$	100.958	+	376.780i	0.170537	+	0.636452i
$593$	638.841	+	638.841i	1.07730	+	1.07730i	0.996750	+	0.0805534i	$0.0256688\pi$
$593$	638.841	+	638.841i	1.07730	+	1.07730i	0.0805534	+	0.996750i	$0.474331\pi$
$594$	660.288	−	367.898i	1.11160	−	0.619358i
$595$	89.3818	+	604.629i	0.150221	+	1.01618i
$596$	165.736	−	287.063i	0.278080	−	0.481649i
$597$	578.777	−	572.919i	0.969476	−	0.959663i
$598$	−87.0941	+	325.040i	−0.145642	+	0.543544i
$599$	350.554	−	202.393i	0.585233	−	0.337884i	−0.177977	−	0.984035i	$-0.556955\pi$
$599$	350.554	−	202.393i	0.585233	−	0.337884i	0.763210	+	0.646150i	$0.223622\pi$
$600$	−341.134	−	81.7310i	−0.568557	−	0.136218i
$601$	−419.760	+	727.046i	−0.698437	+	1.20973i	0.270572	+	0.962700i	$0.412787\pi$
$601$	−419.760	+	727.046i	−0.698437	+	1.20973i	−0.969008	+	0.247028i	$0.920546\pi$
$602$	744.919	−	744.919i	1.23741	−	1.23741i
$603$	−118.644	+	425.425i	−0.196756	+	0.705514i
$604$			38.3704i			0.0635271i
$605$	−13.4719	+	34.0418i	−0.0222675	+	0.0562675i
$606$	−101.739	−	178.305i	−0.167886	−	0.294233i
$607$	−313.071	−	83.8870i	−0.515767	−	0.138199i	−0.00845910	−	0.999964i	$-0.502693\pi$
$607$	−313.071	−	83.8870i	−0.515767	−	0.138199i	−0.507308	+	0.861765i	$0.669359\pi$
$608$	−29.6720	+	110.737i	−0.0488027	+	0.182134i
$609$	−928.381	+	529.722i	−1.52443	+	0.869823i
$610$	275.415	+	636.171i	0.451501	+	1.04290i
$611$	−17.0624			−0.0279253
$612$	−208.177	−	58.0570i	−0.340158	−	0.0948644i
$613$	−164.098	−	164.098i	−0.267697	−	0.267697i	0.560475	−	0.828171i	$-0.310619\pi$
$613$	−164.098	−	164.098i	−0.267697	−	0.267697i	−0.828171	+	0.560475i	$0.810619\pi$
$614$	−668.317	−	385.853i	−1.08846	−	0.628425i
$615$	134.500	−	57.4180i	0.218699	−	0.0933626i
$616$	284.194	+	492.238i	0.461353	+	0.799088i
$617$	146.741	+	39.3191i	0.237830	+	0.0637263i	0.375765	−	0.926715i	$-0.377380\pi$
$617$	146.741	+	39.3191i	0.237830	+	0.0637263i	−0.137935	+	0.990441i	$0.544047\pi$
$618$	−796.103	−	804.244i	−1.28819	−	1.30137i
$619$	−371.036	−	214.218i	−0.599412	−	0.346071i	0.169398	−	0.985548i	$-0.445818\pi$
$619$	−371.036	−	214.218i	−0.599412	−	0.346071i	−0.768810	+	0.639477i	$0.779151\pi$
$620$	23.6644	+	160.079i	0.0381684	+	0.258192i
$621$	−182.995	−	328.431i	−0.294678	−	0.528875i
$622$	−177.995	+	177.995i	−0.286166	+	0.286166i
$623$	166.591	−	44.6378i	0.267401	−	0.0716498i
$624$	−2.98280	+	586.365i	−0.00478012	+	0.939688i
$625$	−559.996	−	277.542i	−0.895994	−	0.444067i
$626$	333.164	+	577.058i	0.532211	+	0.921817i
$627$	32.2333	+	122.791i	0.0514088	+	0.195840i
$628$	344.493	−	92.3067i	0.548556	−	0.146985i
$629$		−	222.366i		−	0.353523i
$630$	450.270	−	1104.80i	0.714715	−	1.75364i
$631$	−1077.98			−1.70837			−0.854185	−	0.519969i	$-0.825943\pi$
$631$	−1077.98			−1.70837			−0.854185	+	0.519969i	$0.825943\pi$
$632$	147.222	+	549.441i	0.232947	+	0.869369i
$633$	104.071	−	380.643i	0.164409	−	0.601331i
$634$	163.260	−	94.2581i	0.257508	−	0.148672i
$635$	665.745	+	76.9224i	1.04842	+	0.121138i
$636$	200.981	+	352.236i	0.316008	+	0.553830i
$637$	167.253	+	624.196i	0.262563	+	0.979899i
$638$	657.447	+	657.447i	1.03048	+	1.03048i
$639$	−2.03996	+	200.505i	−0.00319242	+	0.313779i
$640$	533.602	+	396.157i	0.833753	+	0.618995i
$641$	−434.510	+	752.593i	−0.677862	+	1.17409i	0.297761	+	0.954640i	$0.403760\pi$
$641$	−434.510	+	752.593i	−0.677862	+	1.17409i	−0.975623	+	0.219451i	$0.929573\pi$
$642$	−288.265	−	1098.13i	−0.449010	−	1.71049i
$643$	−31.9596	+	119.275i	−0.0497039	+	0.185497i	−0.986315	−	0.164874i	$-0.947278\pi$
$643$	−31.9596	+	119.275i	−0.0497039	+	0.185497i	0.936611	+	0.350372i	$0.113945\pi$
$644$	−272.634	+	157.406i	−0.423345	+	0.244419i
$645$	−84.1646	−	590.070i	−0.130488	−	0.914837i
$646$	52.5979	−	91.1023i	0.0814209	−	0.141025i
$647$	303.440	−	303.440i	0.468996	−	0.468996i	−0.432593	−	0.901589i	$-0.642401\pi$
$647$	303.440	−	303.440i	0.468996	−	0.468996i	0.901589	+	0.432593i	$0.142401\pi$
$648$	−262.383	−	273.284i	−0.404911	−	0.421734i
$649$			134.038i			0.206530i
$650$	−137.771	+	588.228i	−0.211955	+	0.904966i
$651$	494.236	+	2.51414i	0.759196	+	0.00386197i
$652$	438.130	+	117.397i	0.671978	+	0.180056i
$653$	195.153	−	728.322i	0.298856	−	1.11535i	−0.639250	−	0.768999i	$-0.720755\pi$
$653$	195.153	−	728.322i	0.298856	−	1.11535i	0.938106	−	0.346348i	$-0.112578\pi$
$654$	1178.15	+	688.220i	1.80145	+	1.05232i
$655$	−208.304	+	526.359i	−0.318021	+	0.803602i
$656$	−194.878			−0.297071
$657$	−338.394	+	331.577i	−0.515059	+	0.504684i
$658$	−32.7106	−	32.7106i	−0.0497122	−	0.0497122i
$659$	1030.08	+	594.718i	1.56310	+	0.902456i	0.996941	+	0.0781594i	$0.0249043\pi$
$659$	1030.08	+	594.718i	1.56310	+	0.902456i	0.566158	+	0.824296i	$0.308429\pi$
$660$	−355.510	−	42.9104i	−0.538651	−	0.0650158i
$661$	384.281	+	665.595i	0.581364	+	1.00695i	0.995318	+	0.0966537i	$0.0308139\pi$
$661$	384.281	+	665.595i	0.581364	+	1.00695i	−0.413954	+	0.910298i	$0.635853\pi$
$662$	−186.758	−	50.0416i	−0.282112	−	0.0755916i
$663$	88.1569	−	322.436i	0.132967	−	0.486329i
$664$	440.433	+	254.284i	0.663303	+	0.382958i
$665$	160.884	+	119.444i	0.241931	+	0.179615i
$666$	−220.836	+	373.667i	−0.331585	+	0.561062i
$667$	327.018	−	327.018i	0.490282	−	0.490282i
$668$	−229.940	+	61.6122i	−0.344222	+	0.0922339i
$669$	80.1637	+	46.8278i	0.119826	+	0.0699968i
$670$	475.155	−	376.726i	0.709187	−	0.562277i
$671$	−317.760	−	550.376i	−0.473562	−	0.820233i
$672$	−701.937	+	694.832i	−1.04455	+	1.03398i
$673$	280.935	−	75.2762i	0.417436	−	0.111852i	−0.0439863	−	0.999032i	$-0.514006\pi$
$673$	280.935	−	75.2762i	0.417436	−	0.111852i	0.461423	+	0.887180i	$0.347339\pi$
$674$		−	424.784i		−	0.630243i
$675$	−347.083	−	578.929i	−0.514197	−	0.857672i
$676$	−154.643			−0.228762
$677$	−234.261	−	874.273i	−0.346028	−	1.29139i	−0.891407	−	0.453204i	$-0.850281\pi$
$677$	−234.261	−	874.273i	−0.346028	−	1.29139i	0.545379	−	0.838190i	$-0.316386\pi$
$678$	878.194	+	887.174i	1.29527	+	1.30852i
$679$	−1658.21	+	957.368i	−2.44214	+	1.40997i
$680$	−165.554	−	208.809i	−0.243462	−	0.307072i
$681$	−98.9663	+	169.419i	−0.145325	+	0.248779i
$682$	−111.272	−	415.272i	−0.163155	−	0.608903i
$683$	579.270	+	579.270i	0.848125	+	0.848125i	0.989899	−	0.141774i	$-0.0452805\pi$
$683$	579.270	+	579.270i	0.848125	+	0.848125i	−0.141774	+	0.989899i	$0.545281\pi$
$684$	−61.7178	+	34.8004i	−0.0902307	+	0.0508779i
$685$	−72.0759	+	97.0824i	−0.105220	+	0.141726i
$686$	−226.478	+	392.271i	−0.330143	+	0.571824i
$687$	−804.666	−	220.003i	−1.17128	−	0.320237i
$688$	−205.571	+	767.200i	−0.298795	+	1.11512i
$689$	−543.210	+	313.622i	−0.788403	+	0.455185i
$690$	−61.8559	+	512.472i	−0.0896463	+	0.742712i
$691$	479.893	−	831.199i	0.694491	−	1.20289i	−0.275861	−	0.961197i	$-0.588963\pi$
$691$	479.893	−	831.199i	0.694491	−	1.20289i	0.970352	−	0.241696i	$-0.0777036\pi$
$692$	−106.243	+	106.243i	−0.153530	+	0.153530i
$693$	−293.807	+	1053.51i	−0.423963	+	1.52022i
$694$		−	1599.71i		−	2.30506i
$695$	−527.038	−	208.573i	−0.758329	−	0.300105i
$696$	235.059	−	402.392i	0.337728	−	0.578150i
$697$	107.308	+	28.7531i	0.153957	+	0.0412526i
$698$	−55.0540	+	205.464i	−0.0788739	+	0.294361i
$699$	2.30473	−	453.069i	0.00329718	−	0.648167i
$700$	−480.262	+	297.986i	−0.686089	+	0.425694i
$701$	1285.91			1.83439			0.917197	−	0.398434i	$-0.130446\pi$
$701$	1285.91			1.83439			0.917197	+	0.398434i	$0.130446\pi$
$702$	−468.358	+	454.277i	−0.667177	+	0.647119i
$703$	−51.5485	−	51.5485i	−0.0733264	−	0.0733264i
$704$	−40.3324	−	23.2859i	−0.0572903	−	0.0330766i
$705$	−25.9110	+	3.69581i	−0.0367531	+	0.00524228i
$706$	−786.331	−	1361.96i	−1.11378	−	1.92913i
$707$	286.925	+	76.8814i	0.405835	+	0.108743i
$708$	−72.3567	+	18.9939i	−0.102199	+	0.0268276i
$709$	433.296	+	250.163i	0.611137	+	0.352840i	0.773410	−	0.633906i	$-0.218549\pi$
$709$	433.296	+	250.163i	0.611137	+	0.352840i	−0.162274	+	0.986746i	$0.551883\pi$
$710$	164.105	−	221.040i	0.231133	−	0.311324i
$711$	−556.891	+	942.292i	−0.783250	+	1.32531i
$712$	−53.1700	+	53.1700i	−0.0746769	+	0.0746769i
$713$	−206.559	+	55.3473i	−0.289704	+	0.0776259i
$714$	787.158	−	449.142i	1.10246	−	0.629051i
$715$	63.5710	−	550.192i	0.0889105	−	0.769499i
$716$	−48.7005	−	84.3518i	−0.0680175	−	0.117810i
$717$	−455.425	−	124.517i	−0.635182	−	0.173664i
$718$	−1555.46	+	416.784i	−2.16638	+	0.580479i
$719$			111.332i			0.154843i	0.996998	+	0.0774217i	$0.0246688\pi$
$719$			111.332i			0.154843i	−0.996998	+	0.0774217i	$0.975331\pi$
$720$	122.481	+	891.103i	0.170112	+	1.23764i
$721$	1637.44			2.27106
$722$	221.978	+	828.434i	0.307449	+	1.14742i
$723$	−58.9501	+	15.4747i	−0.0815353	+	0.0214034i
$724$	303.462	−	175.204i	0.419147	−	0.241994i
$725$	568.190	−	605.445i	0.783710	−	0.835097i
$726$	54.2852	+	0.276145i	0.0747730	+	0.000380365i
$727$	−159.253	−	594.341i	−0.219055	−	0.817526i	−0.984699	−	0.174261i	$-0.944246\pi$
$727$	−159.253	−	594.341i	−0.219055	−	0.817526i	0.765644	−	0.643264i	$-0.222420\pi$
$728$	−346.938	−	346.938i	−0.476563	−	0.476563i
$729$	22.2466	−	728.660i	0.0305166	−	0.999534i
$730$	643.466	−	95.1230i	0.881460	−	0.130305i
$731$	226.391	−	392.121i	0.309701	−	0.536417i
$732$	252.077	−	249.525i	0.344367	−	0.340881i
$733$	301.741	−	1126.11i	0.411652	−	1.53631i	−0.379795	−	0.925071i	$-0.624005\pi$
$733$	301.741	−	1126.11i	0.411652	−	1.53631i	0.791447	−	0.611237i	$-0.209328\pi$
$734$	207.518	−	119.811i	0.282723	−	0.163230i
$735$	389.195	+	911.678i	0.529517	+	1.24038i
$736$	213.671	−	370.089i	0.290314	−	0.502838i
$737$	−393.080	+	393.080i	−0.533351	+	0.533351i
$738$	−151.767	−	154.887i	−0.205646	−	0.209874i
$739$		−	318.962i		−	0.431612i	−0.976436	−	0.215806i	$-0.930762\pi$
$739$		−	318.962i		−	0.431612i	0.976436	−	0.215806i	$-0.0692379\pi$
$740$	188.704	−	81.6950i	0.255005	−	0.110399i
$741$	−54.3102	−	95.1830i	−0.0732932	−	0.128452i
$742$	−1642.65	−	440.147i	−2.21382	−	0.593190i
$743$	121.466	−	453.316i	0.163480	−	0.610116i	−0.834749	−	0.550631i	$-0.814387\pi$
$743$	121.466	−	453.316i	0.163480	−	0.610116i	0.998229	−	0.0594856i	$-0.0189460\pi$
$744$	−187.160	+	106.791i	−0.251559	+	0.143537i
$745$	731.261	+	289.393i	0.981558	+	0.388446i
$746$	−1175.34			−1.57552
$747$	243.652	+	947.789i	0.326174	+	1.26879i
$748$	−192.349	−	192.349i	−0.257151	−	0.257151i
$749$	1422.71	+	821.400i	1.89947	+	1.09666i
$750$	−81.8057	+	923.127i	−0.109074	+	1.23084i
$751$	76.0823	+	131.778i	0.101308	+	0.175471i	0.912224	−	0.409692i	$-0.134364\pi$
$751$	76.0823	+	131.778i	0.101308	+	0.175471i	−0.810916	+	0.585163i	$0.801031\pi$
$752$	33.6891	+	9.02696i	0.0447993	+	0.0120039i
$753$	−195.804	−	197.806i	−0.260031	−	0.262690i
$754$	−695.071	−	401.299i	−0.921845	−	0.532227i
$755$	−90.0579	+	13.3132i	−0.119282	+	0.0176333i
$756$	−610.341	−	9.31493i	−0.807330	−	0.0123213i
$757$	488.444	−	488.444i	0.645236	−	0.645236i	−0.306602	−	0.951838i	$-0.599192\pi$
$757$	488.444	−	488.444i	0.645236	−	0.645236i	0.951838	+	0.306602i	$0.0991919\pi$
$758$	−1329.07	+	356.123i	−1.75339	+	0.469819i
$759$	2.40720	−	473.213i	0.00317154	−	0.623469i
$760$	−86.7842	−	10.0273i	−0.114190	−	0.0131939i
$761$	88.9996	+	154.152i	0.116951	+	0.202565i	0.918558	−	0.395286i	$-0.129355\pi$
$761$	88.9996	+	154.152i	0.116951	+	0.202565i	−0.801607	+	0.597851i	$0.796021\pi$
$762$	−252.310	−	961.164i	−0.331115	−	1.26137i
$763$	−1907.03	+	510.986i	−2.49938	+	0.669706i
$764$		−	245.631i		−	0.321506i
$765$	64.0338	−	508.748i	0.0837043	−	0.665031i
$766$	1809.45			2.36221
$767$	−29.9466	−	111.762i	−0.0390438	−	0.145713i
$768$	246.878	−	902.962i	0.321456	−	1.17573i
$769$	179.757	−	103.783i	0.233754	−	0.134958i	−0.378548	−	0.925581i	$-0.623577\pi$
$769$	179.757	−	103.783i	0.233754	−	0.134958i	0.612303	+	0.790623i	$0.290243\pi$
$770$	1176.66	−	932.912i	1.52813	−	1.21157i
$771$	635.696	+	1114.11i	0.824508	+	1.44502i
$772$	68.1628	+	254.387i	0.0882938	+	0.329517i
$773$	−199.628	−	199.628i	−0.258251	−	0.258251i	0.566091	−	0.824342i	$-0.308455\pi$
$773$	−199.628	−	199.628i	−0.258251	−	0.258251i	−0.824342	+	0.566091i	$0.808455\pi$
$774$	−769.855	+	434.093i	−0.994644	+	0.560844i
$775$	−367.506	+	111.084i	−0.474202	+	0.143334i
$776$	417.401	−	722.960i	0.537888	−	0.931649i
$777$	−159.464	−	607.470i	−0.205230	−	0.781815i
$778$	133.464	−	498.093i	0.171547	−	0.640222i
$779$	31.5414	−	18.2104i	0.0404896	−	0.0233767i
$780$	306.014	−	43.6483i	0.392325	−	0.0559593i
$781$	−126.190	+	218.568i	−0.161575	+	0.279856i
$782$	−277.273	+	277.273i	−0.354569	+	0.354569i
$783$	869.613	−	218.845i	1.11062	−	0.279496i
$784$		−	1320.94i		−	1.68487i
$785$	336.177	+	776.522i	0.428251	+	0.989200i
$786$	839.365	+	4.26979i	1.06789	+	0.00543230i
$787$	1250.87	+	335.169i	1.58941	+	0.425882i	0.941823	−	0.336108i	$-0.109111\pi$
$787$	1250.87	+	335.169i	1.58941	+	0.425882i	0.647589	+	0.761990i	$0.275777\pi$
$788$	−64.3556	+	240.178i	−0.0816695	+	0.304795i
$789$	460.964	+	269.274i	0.584239	+	0.341285i
$790$	1379.08	−	597.040i	1.74567	−	0.755747i
$791$	−1806.28			−2.28354
$792$	−118.724	−	461.829i	−0.149904	−	0.583117i
$793$	387.915	+	387.915i	0.489174	+	0.489174i
$794$	332.739	+	192.107i	0.419067	+	0.241948i
$795$	−756.988	+	593.930i	−0.952186	+	0.747082i
$796$	286.040	+	495.436i	0.359347	+	0.622407i
$797$	485.714	+	130.147i	0.609428	+	0.163296i	0.550317	−	0.834956i	$-0.314507\pi$
$797$	485.714	+	130.147i	0.609428	+	0.163296i	0.0591106	+	0.998251i	$0.481174\pi$
$798$	78.3581	−	286.597i	0.0981931	−	0.359144i
$799$	−17.2187	−	9.94121i	−0.0215503	−	0.0124421i
$800$	362.340	−	676.276i	0.452925	−	0.845345i
$801$	−144.683	−	1.47202i	−0.180628	−	0.00183773i
$802$	−1088.94	+	1088.94i	−1.35778	+	1.35778i
$803$	−575.991	+	154.336i	−0.717299	+	0.192200i
$804$	−267.895	−	156.491i	−0.333202	−	0.194641i
$805$	−464.036	−	585.277i	−0.576442	−	0.727053i
$806$	185.559	+	321.397i	0.230222	+	0.398756i
$807$	373.439	−	369.659i	0.462750	−	0.458066i
$808$	−125.096	+	33.5194i	−0.154822	+	0.0414844i
$809$			329.434i			0.407212i	0.979053	+	0.203606i	$0.0652661\pi$
$809$			329.434i			0.407212i	−0.979053	+	0.203606i	$0.934734\pi$
$810$	−612.852	+	791.316i	−0.756607	+	0.976934i
$811$	−736.236			−0.907812			−0.453906	−	0.891049i	$-0.649970\pi$
$811$	−736.236			−0.907812			−0.453906	+	0.891049i	$0.649970\pi$
$812$	−194.336	−	725.270i	−0.239330	−	0.893190i
$813$	977.873	+	987.873i	1.20280	+	1.21510i
$814$	−473.123	+	273.158i	−0.581233	+	0.335575i
$815$	−123.522	+	1069.05i	−0.151561	+	1.31172i
$816$	−344.650	+	590.000i	−0.422365	+	0.723039i
$817$	−38.4192	−	143.382i	−0.0470247	−	0.175499i
$818$	901.008	+	901.008i	1.10148	+	1.10148i
$819$	9.60505	−	944.067i	0.0117278	−	1.15271i
$820$	15.0235	+	101.627i	0.0183213	+	0.123936i
$821$	235.531	−	407.952i	0.286883	−	0.496896i	−0.686181	−	0.727431i	$-0.740714\pi$
$821$	235.531	−	407.952i	0.286883	−	0.496896i	0.973064	+	0.230535i	$0.0740475\pi$
$822$	172.941	+	47.2836i	0.210391	+	0.0575227i
$823$	−225.744	+	842.487i	−0.274294	+	1.02368i	0.682019	+	0.731334i	$0.261102\pi$
$823$	−225.744	+	842.487i	−0.274294	+	1.02368i	−0.956313	+	0.292344i	$0.905565\pi$
$824$	−618.258	+	356.951i	−0.750313	+	0.433194i
$825$	−22.6357	−	849.294i	−0.0274372	−	1.02945i
$826$	156.850	−	271.673i	0.189892	−	0.328902i
$827$	796.631	−	796.631i	0.963278	−	0.963278i	−0.0360709	−	0.999349i	$-0.511484\pi$
$827$	796.631	−	796.631i	0.963278	−	0.963278i	0.999349	+	0.0360709i	$0.0114842\pi$
$828$	255.792	−	65.7575i	0.308927	−	0.0794173i
$829$			860.599i			1.03812i	0.854739	+	0.519059i	$0.173717\pi$
$829$			860.599i			1.03812i	−0.854739	+	0.519059i	$0.826283\pi$
$830$	494.407	−	1249.31i	0.595672	−	1.50519i
$831$	−583.594	+	999.043i	−0.702279	+	1.20222i
$832$	38.8320	+	10.4050i	0.0466731	+	0.0125060i
$833$	−194.896	+	727.363i	−0.233969	+	0.873185i
$834$	−4.27530	+	840.448i	−0.00512626	+	1.00773i
$835$	−224.389	−	518.308i	−0.268730	−	0.620728i
$836$	−89.1799			−0.106675
$837$	−398.829	−	113.417i	−0.476498	−	0.135504i
$838$	256.897	+	256.897i	0.306560	+	0.306560i
$839$	−878.746	−	507.344i	−1.04737	−	0.604701i	−0.125460	−	0.992099i	$-0.540041\pi$
$839$	−878.746	−	507.344i	−1.04737	−	0.604701i	−0.921913	+	0.387398i	$0.873374\pi$
$840$	−602.010	−	451.713i	−0.716679	−	0.537753i
$841$	131.022	+	226.938i	0.155794	+	0.269842i
$842$	−1513.55	−	405.555i	−1.79757	−	0.481657i
$843$	231.060	−	60.6542i	0.274092	−	0.0719504i
$844$	240.066	+	138.602i	0.284439	+	0.164221i
$845$	−53.6558	−	362.958i	−0.0634979	−	0.429536i
$846$	19.0618	+	33.8056i	0.0225316	+	0.0399593i
$847$	−55.5433	+	55.5433i	−0.0655765	+	0.0655765i
$848$	1238.47	−	331.848i	1.46046	−	0.391330i
$849$	−624.150	+	356.132i	−0.735159	+	0.419473i
$850$	−481.758	+	513.346i	−0.566774	+	0.603937i
$851$	135.870	+	235.334i	0.159660	+	0.276539i
$852$	−135.869	−	37.1479i	−0.159471	−	0.0436008i
$853$	−338.408	+	90.6761i	−0.396726	+	0.106303i	−0.451666	−	0.892187i	$-0.649170\pi$
$853$	−338.408	+	90.6761i	−0.396726	+	0.106303i	0.0549394	+	0.998490i	$0.482503\pi$
$854$			1487.36i			1.74164i
$855$	−103.093	−	132.781i	−0.120577	−	0.155300i
$856$	−716.241			−0.836730
$857$	279.033	+	1041.37i	0.325593	+	1.21513i	0.913714	+	0.406358i	$0.133201\pi$
$857$	279.033	+	1041.37i	0.325593	+	1.21513i	−0.588121	+	0.808773i	$0.700132\pi$
$858$	−794.335	+	208.516i	−0.925798	+	0.243026i
$859$	508.578	−	293.627i	0.592058	−	0.341825i	−0.173853	−	0.984772i	$-0.555622\pi$
$859$	508.578	−	293.627i	0.592058	−	0.341825i	0.765911	+	0.642947i	$0.222288\pi$
$860$	415.935	+	48.0586i	0.483646	+	0.0558820i
$861$	313.769	+	1.59612i	0.364423	+	0.00185380i
$862$	470.615	+	1756.36i	0.545957	+	2.03754i
$863$	−659.791	−	659.791i	−0.764532	−	0.764532i	0.212606	−	0.977138i	$-0.431805\pi$
$863$	−659.791	−	659.791i	−0.764532	−	0.764532i	−0.977138	+	0.212606i	$0.931805\pi$
$864$	723.833	−	403.304i	0.837770	−	0.466788i
$865$	−286.222	−	212.497i	−0.330892	−	0.245661i
$866$	−122.162	+	211.591i	−0.141065	+	0.244331i
$867$	−339.343	+	335.908i	−0.391399	+	0.387437i
$868$	−89.8598	+	335.361i	−0.103525	+	0.386361i
$869$	−1193.09	+	688.833i	−1.37295	+	0.792674i
$870$	−1142.46	−	458.858i	−1.31317	−	0.527423i
$871$	239.932	−	415.575i	0.275467	−	0.477123i
$872$	608.657	−	608.657i	0.698001	−	0.698001i
$873$	1555.77	−	399.948i	1.78210	−	0.458131i
$874$			128.554i			0.147087i
$875$	−866.027	−	1023.82i	−0.989746	−	1.17008i
$876$	−164.935	−	289.062i	−0.188282	−	0.329979i
$877$	12.2913	+	3.29344i	0.0140152	+	0.00375535i	0.265820	−	0.964023i	$-0.414357\pi$
$877$	12.2913	+	3.29344i	0.0140152	+	0.00375535i	−0.251805	+	0.967778i	$0.581024\pi$
$878$	214.865	−	801.886i	0.244721	−	0.913309i
$879$	226.335	−	129.144i	0.257492	−	0.146922i
$880$	−416.602	+	1052.70i	−0.473411	+	1.19625i
$881$	933.779			1.05991			0.529954	−	0.848026i	$-0.322209\pi$
$881$	933.779			1.05991			0.529954	+	0.848026i	$0.322209\pi$
$882$	1049.87	−	1028.72i	1.19032	−	1.16635i
$883$	−463.817	−	463.817i	−0.525274	−	0.525274i	0.393886	−	0.919159i	$-0.371131\pi$
$883$	−463.817	−	463.817i	−0.525274	−	0.525274i	−0.919159	+	0.393886i	$0.871131\pi$
$884$	203.356	+	117.408i	0.230041	+	0.132814i
$885$	−69.6853	−	163.236i	−0.0787405	−	0.184447i
$886$	−381.500	−	660.777i	−0.430586	−	0.745798i
$887$	−259.076	−	69.4192i	−0.292081	−	0.0782630i	0.109803	−	0.993953i	$-0.464978\pi$
$887$	−259.076	−	69.4192i	−0.292081	−	0.0782630i	−0.401884	+	0.915690i	$0.631645\pi$
$888$	192.635	+	194.604i	0.216931	+	0.219149i
$889$	1245.25	+	718.948i	1.40074	+	0.808715i
$890$	159.501	+	118.417i	0.179215	+	0.133053i
$891$	474.854	−	785.134i	0.532945	−	0.881183i
$892$	−46.1152	+	46.1152i	−0.0516986	+	0.0516986i
$893$	−6.29616	+	1.68705i	−0.00705057	+	0.00188920i
$894$	5.93193	−	1166.11i	0.00663527	−	1.30438i
$895$	181.082	−	143.571i	0.202326	−	0.160414i
$896$	712.950	+	1234.87i	0.795703	+	1.37820i
$897$	103.717	+	395.107i	0.115627	+	0.440476i
$898$	935.432	−	250.648i	1.04168	−	0.279118i
$899$		−	510.042i		−	0.567344i
$900$	455.259	−	132.569i	0.505844	−	0.147299i
$901$	−730.915			−0.811227
$902$	−70.6415	−	263.638i	−0.0783165	−	0.292281i
$903$	337.268	−	1233.57i	0.373497	−	1.36608i
$904$	682.010	−	393.759i	0.754436	−	0.435574i
$905$	516.506	+	651.457i	0.570725	+	0.719842i
$906$	66.8986	+	117.245i	0.0738395	+	0.129410i
$907$	48.8935	+	182.473i	0.0539069	+	0.201183i	0.987627	−	0.156820i	$-0.0501243\pi$
$907$	48.8935	+	182.473i	0.0539069	+	0.201183i	−0.933720	+	0.358003i	$0.883458\pi$
$908$	−97.4601	−	97.4601i	−0.107335	−	0.107335i
$909$	−214.540	−	126.792i	−0.236017	−	0.139485i
$910$	−772.679	+	1040.76i	−0.849097	+	1.14369i
$911$	−432.982	+	749.947i	−0.475282	+	0.823213i	−0.999599	−	0.0283104i	$-0.990987\pi$
$911$	−432.982	+	749.947i	−0.475282	+	0.823213i	0.524317	+	0.851523i	$0.324321\pi$
$912$	56.8766	+	216.669i	0.0623646	+	0.237576i
$913$	−318.796	+	1189.76i	−0.349174	+	1.30313i
$914$	364.849	−	210.646i	0.399178	−	0.230466i
$915$	673.114	+	505.065i	0.735644	+	0.551983i
$916$	293.001	−	507.492i	0.319870	−	0.554031i
$917$	−858.818	+	858.818i	−0.936551	+	0.936551i
$918$	−737.330	+	185.555i	−0.803191	+	0.202130i
$919$			864.507i			0.940704i	0.882479	+	0.470352i	$0.155873\pi$
$919$			864.507i			0.940704i	−0.882479	+	0.470352i	$0.844127\pi$
$920$	302.796	+	119.830i	0.329126	+	0.130250i
$921$	−936.783	−	4.76535i	−1.01714	−	0.00517410i
$922$	1808.99	+	484.717i	1.96203	+	0.525724i
$923$	56.3864	−	210.437i	0.0610903	−	0.227992i
$924$	−663.406	−	387.530i	−0.717972	−	0.419405i
$925$	257.218	+	414.556i	0.278073	+	0.448169i
$926$	−430.687			−0.465104
$927$	−1323.22	−	369.025i	−1.42743	−	0.398086i
$928$	720.719	+	720.719i	0.776637	+	0.776637i
$929$	−884.539	−	510.689i	−0.952142	−	0.549719i	−0.0583960	−	0.998293i	$-0.518599\pi$
$929$	−884.539	−	510.689i	−0.952142	−	0.549719i	−0.893746	+	0.448574i	$0.851932\pi$
$930$	351.407	+	447.882i	0.377857	+	0.481593i
$931$	123.435	+	213.796i	0.132584	+	0.229642i
$932$	307.427	+	82.3748i	0.329857	+	0.0883850i
$933$	−80.5887	+	294.755i	−0.0863759	+	0.315922i
$934$	−579.804	−	334.750i	−0.620775	−	0.358404i
$935$	384.717	−	518.194i	0.411462	−	0.554218i
$936$	202.174	+	358.552i	0.215998	+	0.383068i
$937$	776.808	−	776.808i	0.829037	−	0.829037i	−0.158347	−	0.987384i	$-0.550616\pi$
$937$	776.808	−	776.808i	0.829037	−	0.829037i	0.987384	+	0.158347i	$0.0506163\pi$
$938$	1256.69	−	336.728i	1.33975	−	0.358985i
$939$	698.439	+	407.995i	0.743812	+	0.434500i
$940$	2.11033	−	18.2644i	0.00224503	−	0.0194302i
$941$	−851.116	−	1474.18i	−0.904480	−	1.56661i	−0.821614	−	0.570044i	$-0.806926\pi$
$941$	−851.116	−	1474.18i	−0.904480	−	1.56661i	−0.0828659	−	0.996561i	$-0.526407\pi$
$942$	891.702	−	882.676i	0.946605	−	0.937023i
$943$	−131.135	+	35.1375i	−0.139061	+	0.0372614i
$944$			236.514i			0.250545i
$945$	−189.904	−	1435.74i	−0.200957	−	1.51931i
$946$	−1112.41			−1.17591
$947$	188.456	+	703.326i	0.199003	+	0.742688i	0.991194	+	0.132416i	$0.0422734\pi$
$947$	188.456	+	703.326i	0.199003	+	0.742688i	−0.792192	+	0.610273i	$0.791060\pi$
$948$	−540.915	−	546.447i	−0.570586	−	0.576420i
$949$	445.784	−	257.374i	0.469741	−	0.271205i
$950$	7.32272	+	230.683i	0.00770813	+	0.242825i
$951$	115.429	−	197.601i	0.121377	−	0.207782i
$952$	−147.977	−	552.257i	−0.155438	−	0.580102i
$953$	−783.686	−	783.686i	−0.822336	−	0.822336i	0.164106	−	0.986443i	$-0.447526\pi$
$953$	−783.686	−	783.686i	−0.822336	−	0.822336i	−0.986443	+	0.164106i	$0.947526\pi$
$954$	1228.24	+	725.887i	1.28747	+	0.760887i
$955$	576.512	−	85.2253i	0.603678	−	0.0892412i
$956$	165.833	−	287.231i	0.173465	−	0.300450i
$957$	1088.72	+	297.664i	1.13763	+	0.311039i
$958$	99.9583	−	373.050i	0.104341	−	0.389405i
$959$	−224.669	+	129.713i	−0.234274	+	0.135258i
$960$	61.2242	+	7.38984i	0.0637752	+	0.00769774i
$961$	362.580	−	628.006i	0.377294	−	0.653492i
$962$	333.466	−	333.466i	0.346638	−	0.346638i
$963$	−964.581	−	984.411i	−1.00164	−	1.02223i
$964$		−	42.8137i		−	0.0444126i
$965$	−573.414	+	248.246i	−0.594211	+	0.257250i
$966$	−558.630	+	956.308i	−0.578292	+	0.989967i
$967$	−1182.77	−	316.923i	−1.22314	−	0.327738i	−0.411233	−	0.911530i	$-0.634902\pi$
$967$	−1182.77	−	316.923i	−1.22314	−	0.327738i	−0.811903	+	0.583792i	$0.801568\pi$
$968$	8.86374	−	33.0799i	0.00915676	−	0.0341735i
$969$	0.649593	−	127.698i	0.000670374	−	0.131784i
$970$	−2050.71	−	811.557i	−2.11413	−	0.836656i
$971$	−313.188			−0.322542			−0.161271	−	0.986910i	$-0.551559\pi$
$971$	−313.188			−0.322542			−0.161271	+	0.986910i	$0.551559\pi$
$972$	491.122	+	145.079i	0.505269	+	0.149258i
$973$	−859.926	−	859.926i	−0.883788	−	0.883788i
$974$	−1365.42	−	788.327i	−1.40187	−	0.809371i
$975$	208.622	+	703.091i	0.213971	+	0.721119i
$976$	−560.696	−	971.155i	−0.574484	−	0.995035i
$977$	−1491.43	−	399.627i	−1.52654	−	0.409035i	−0.604652	−	0.796490i	$-0.706688\pi$
$977$	−1491.43	−	399.627i	−1.52654	−	0.409035i	−0.921889	+	0.387455i	$0.873354\pi$
$978$	1543.44	−	405.159i	1.57816	−	0.414273i
$979$	−157.717	−	91.0580i	−0.161100	−	0.0930112i
$980$	−688.857	+	101.833i	−0.702916	+	0.103911i
$981$	1656.24	+	16.8508i	1.68832	+	0.0171771i
$982$	−699.242	+	699.242i	−0.712059	+	0.712059i
$983$	661.825	−	177.336i	0.673271	−	0.180402i	0.0940430	−	0.995568i	$-0.470021\pi$
$983$	661.825	−	177.336i	0.673271	−	0.180402i	0.579228	+	0.815166i	$0.303354\pi$
$984$	−118.820	+	67.7970i	−0.120752	+	0.0688994i
$985$	−586.044	−	67.7135i	−0.594969	−	0.0687446i
$986$	−467.626	−	809.953i	−0.474266	−	0.821453i
$987$	−54.1680	−	14.8100i	−0.0548814	−	0.0150051i
$988$	74.3590	−	19.9244i	0.0752621	−	0.0201664i
$989$			553.320i			0.559474i
$990$	−1161.11	+	488.712i	−1.17284	+	0.493648i
$991$	888.305			0.896373			0.448186	−	0.893940i	$-0.352070\pi$
$991$	888.305			0.896373			0.448186	+	0.893940i	$0.352070\pi$
$992$	−121.980	−	455.237i	−0.122964	−	0.458909i
$993$	−227.016	+	59.5928i	−0.228617	+	0.0600129i
$994$	511.533	−	295.334i	0.514620	−	0.297116i
$995$	−1063.58	+	843.255i	−1.06892	+	0.847493i
$996$	−687.434	−	3.49693i	−0.690195	−	0.00351097i
$997$	−52.8555	−	197.259i	−0.0530146	−	0.197853i	0.934339	−	0.356385i	$-0.115991\pi$
$997$	−52.8555	−	197.259i	−0.0530146	−	0.197853i	−0.987354	+	0.158532i	$0.949324\pi$
$998$	−477.617	−	477.617i	−0.478574	−	0.478574i
$999$	−8.04052	+	526.839i	−0.00804857	+	0.527366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.43.8	yes	40
3.2	odd	2		135.3.l.a.73.3		40
5.2	odd	4	inner	45.3.k.a.7.3	✓	40
5.3	odd	4		225.3.o.b.7.8		40
5.4	even	2		225.3.o.b.43.3		40
9.2	odd	6		405.3.g.g.163.3		20
9.4	even	3	inner	45.3.k.a.13.3	yes	40
9.5	odd	6		135.3.l.a.118.8		40
9.7	even	3		405.3.g.h.163.8		20
15.2	even	4		135.3.l.a.127.8		40
45.2	even	12		405.3.g.g.82.3		20
45.4	even	6		225.3.o.b.193.8		40
45.7	odd	12		405.3.g.h.82.8		20
45.13	odd	12		225.3.o.b.157.3		40
45.22	odd	12	inner	45.3.k.a.22.8	yes	40
45.32	even	12		135.3.l.a.37.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.3	✓	40	5.2	odd	4	inner
45.3.k.a.13.3	yes	40	9.4	even	3	inner
45.3.k.a.22.8	yes	40	45.22	odd	12	inner
45.3.k.a.43.8	yes	40	1.1	even	1	trivial
135.3.l.a.37.3		40	45.32	even	12
135.3.l.a.73.3		40	3.2	odd	2
135.3.l.a.118.8		40	9.5	odd	6
135.3.l.a.127.8		40	15.2	even	4
225.3.o.b.7.8		40	5.3	odd	4
225.3.o.b.43.3		40	5.4	even	2
225.3.o.b.157.3		40	45.13	odd	12
225.3.o.b.193.8		40	45.4	even	6
405.3.g.g.82.3		20	45.2	even	12
405.3.g.g.163.3		20	9.2	odd	6
405.3.g.h.82.8		20	45.7	odd	12
405.3.g.h.163.8		20	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.639624 + 2.38711i) q^{2} +(2.11050 + 2.13208i) q^{3} +(-1.82507 + 1.05371i) q^{4} +(-3.10636 - 3.91797i) q^{5} +(-3.73959 + 6.40173i) q^{6} +(-2.77655 - 10.3622i) q^{7} +(3.30727 + 3.30727i) q^{8} +(-0.0915623 + 8.99953i) q^{9} +O(q^{10})\)	\(q+(0.639624 + 2.38711i) q^{2} +(2.11050 + 2.13208i) q^{3} +(-1.82507 + 1.05371i) q^{4} +(-3.10636 - 3.91797i) q^{5} +(-3.73959 + 6.40173i) q^{6} +(-2.77655 - 10.3622i) q^{7} +(3.30727 + 3.30727i) q^{8} +(-0.0915623 + 8.99953i) q^{9} +(7.36573 - 9.92126i) q^{10} +(-5.66397 + 9.81028i) q^{11} +(-6.09842 - 1.66736i) q^{12} +(2.53087 - 9.44533i) q^{13} +(22.9598 - 13.2559i) q^{14} +(1.79747 - 14.8919i) q^{15} +(-9.99423 + 17.3105i) q^{16} +(8.05728 - 8.05728i) q^{17} +(-21.5414 + 5.53775i) q^{18} -3.73565i q^{19} +(9.79774 + 3.87740i) q^{20} +(16.2332 - 27.7894i) q^{21} +(-27.0410 - 7.24562i) q^{22} +(-3.60402 + 13.4504i) q^{23} +(-0.0713765 + 14.0314i) q^{24} +(-5.70105 + 24.3413i) q^{25} +24.1658 q^{26} +(-19.3810 + 18.7983i) q^{27} +(15.9862 + 15.9862i) q^{28} +(-28.7625 - 16.6061i) q^{29} +(36.6983 - 5.23447i) q^{30} +(7.67855 + 13.2996i) q^{31} +(-29.6434 - 7.94293i) q^{32} +(-32.8702 + 8.62856i) q^{33} +(24.3873 + 14.0800i) q^{34} +(-31.9740 + 43.0673i) q^{35} +(-9.31577 - 16.5213i) q^{36} +(13.7991 - 13.7991i) q^{37} +(8.91741 - 2.38941i) q^{38} +(25.4796 - 14.5384i) q^{39} +(2.68423 - 23.2313i) q^{40} +(4.87477 + 8.44335i) q^{41} +(76.7194 + 20.9758i) q^{42} +(38.3822 - 10.2845i) q^{43} -23.8727i q^{44} +(35.5444 - 27.5971i) q^{45} -34.4127 q^{46} +(-0.451608 - 1.68543i) q^{47} +(-58.0003 + 15.2253i) q^{48} +(-57.2314 + 33.0426i) q^{49} +(-61.7519 + 1.96023i) q^{50} +(34.1837 + 0.173890i) q^{51} +(5.33359 + 19.9052i) q^{52} +(-45.3574 - 45.3574i) q^{53} +(-57.2702 - 34.2407i) q^{54} +(56.0308 - 8.28298i) q^{55} +(25.0879 - 43.4535i) q^{56} +(7.96472 - 7.88410i) q^{57} +(21.2433 - 79.2810i) q^{58} +(10.2473 - 5.91626i) q^{59} +(12.4112 + 29.0729i) q^{60} +(-28.0510 + 48.5858i) q^{61} +(-26.8363 + 26.8363i) q^{62} +(93.5095 - 24.0389i) q^{63} +4.11124i q^{64} +(-44.8683 + 19.4247i) q^{65} +(-41.6219 - 72.9456i) q^{66} +(47.4011 + 12.7011i) q^{67} +(-6.21513 + 23.1952i) q^{68} +(-36.2836 + 20.7030i) q^{69} +(-123.258 - 48.7786i) q^{70} +22.2795 q^{71} +(-30.0667 + 29.4610i) q^{72} +(37.2225 + 37.2225i) q^{73} +(41.7661 + 24.1137i) q^{74} +(-63.9297 + 39.2172i) q^{75} +(3.93628 + 6.81784i) q^{76} +(117.383 + 31.4526i) q^{77} +(51.0021 + 51.5236i) q^{78} +(105.323 + 60.8084i) q^{79} +(98.8678 - 14.6155i) q^{80} +(-80.9832 - 1.64804i) q^{81} +(-17.0372 + 17.0372i) q^{82} +(105.029 - 28.1424i) q^{83} +(-0.345009 + 67.8227i) q^{84} +(-56.5971 - 6.53941i) q^{85} +(49.1003 + 85.0443i) q^{86} +(-25.2979 - 96.3713i) q^{87} +(-51.1775 + 13.7130i) q^{88} +16.0767i q^{89} +(88.6123 + 67.1966i) q^{90} -104.902 q^{91} +(-7.59516 - 28.3455i) q^{92} +(-12.1504 + 44.4403i) q^{93} +(3.73444 - 2.15608i) q^{94} +(-14.6362 + 11.6043i) q^{95} +(-45.6275 - 79.9658i) q^{96} +(-46.1951 - 172.402i) q^{97} +(-115.483 - 115.483i) q^{98} +(-87.7693 - 51.8713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8}+O(q^{10}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23} - 8 q^{25} - 112 q^{26} - 198 q^{27} - 88 q^{28} + 162 q^{30} - 4 q^{31} - 14 q^{32} + 96 q^{33} + 352 q^{35} + 264 q^{36} - 92 q^{37} + 330 q^{38} + 30 q^{40} - 28 q^{41} + 498 q^{42} - 2 q^{43} - 72 q^{45} - 136 q^{46} + 64 q^{47} - 510 q^{48} - 458 q^{50} - 396 q^{51} - 74 q^{52} - 608 q^{53} + 224 q^{55} - 192 q^{56} - 114 q^{57} + 30 q^{58} - 798 q^{60} + 92 q^{61} - 100 q^{62} + 24 q^{63} - 326 q^{65} + 588 q^{66} - 80 q^{67} + 626 q^{68} - 102 q^{70} + 248 q^{71} - 162 q^{72} - 8 q^{73} + 810 q^{75} - 96 q^{76} + 338 q^{77} + 1062 q^{78} + 1444 q^{80} + 204 q^{81} + 104 q^{82} + 370 q^{83} - 98 q^{85} - 328 q^{86} + 534 q^{87} - 210 q^{88} + 462 q^{90} + 152 q^{91} + 388 q^{92} - 1062 q^{93} - 360 q^{95} - 876 q^{96} + 292 q^{97} - 1876 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

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