LMFDB - Embedded newform 45.3.k.a.22.8

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			22.8
Character	$\chi$	$=$	45.22
Dual form			45.3.k.a.43.8

$q$-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} +(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} - 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}+ \cdots - 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

Character values

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

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.599613	−	0.800290i	$-0.704679\pi$
$2$	0.639624	−	2.38711i	0.319812	−	1.19356i	0.919425	−	0.393265i	$-0.128655\pi$
$3$	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	0.422301	+	0.906456i	$0.361223\pi$
$7$	−2.77655	+	10.3622i	−0.396650	+	1.48032i	−0.818951	+	0.573863i	$0.805444\pi$
$8$	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	−0.999850	−	0.0172985i	$-0.994493\pi$
$11$	−5.66397	−	9.81028i	−0.514906	−	0.891844i	0.484944	−	0.874545i	$-0.338840\pi$
$12$	−6.09842	+	1.66736i	−0.508201	+	0.138947i
$13$	2.53087	+	9.44533i	0.194682	+	0.726564i	0.992349	+	0.123465i	$0.0394007\pi$
$13$	2.53087	+	9.44533i	0.194682	+	0.726564i	−0.797667	+	0.603098i	$0.793933\pi$
$14$	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	0.903193	−	0.429235i	$-0.141217\pi$
$17$	8.05728	+	8.05728i	0.473958	+	0.473958i	−0.429235	+	0.903193i	$0.641217\pi$
$18$	−21.5414	−	5.53775i	−1.19675	−	0.307653i
$19$			3.73565i			0.196613i	0.995156	+	0.0983066i	$0.0313426\pi$
$19$			3.73565i			0.196613i	−0.995156	+	0.0983066i	$0.968657\pi$
$20$	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	−0.998954	−	0.0457238i	$-0.985441\pi$
$23$	−3.60402	−	13.4504i	−0.156696	−	0.584799i	0.842258	−	0.539075i	$-0.181226\pi$
$24$	−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	−0.905815	−	0.423673i	$-0.860741\pi$
$29$	−28.7625	+	16.6061i	−0.991812	+	0.572623i	−0.0859964	+	0.996295i	$0.527407\pi$
$30$	36.6983	+	5.23447i	1.22328	+	0.174482i
$31$	7.67855	−	13.2996i	0.247695	−	0.429021i	−0.715191	−	0.698929i	$-0.753660\pi$
$31$	7.67855	−	13.2996i	0.247695	−	0.429021i	0.962886	+	0.269909i	$0.0869935\pi$
$32$	−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	0.868550	−	0.495602i	$-0.165053\pi$
$37$	13.7991	+	13.7991i	0.372947	+	0.372947i	−0.495602	+	0.868550i	$0.665053\pi$
$38$	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	−0.800434	−	0.599421i	$-0.795398\pi$
$41$	4.87477	−	8.44335i	0.118897	−	0.205935i	0.919331	+	0.393486i	$0.128731\pi$
$42$	76.7194	−	20.9758i	1.82665	−	0.499423i
$43$	38.3822	+	10.2845i	0.892609	+	0.239174i	0.675839	−	0.737049i	$-0.263781\pi$
$43$	38.3822	+	10.2845i	0.892609	+	0.239174i	0.216769	+	0.976223i	$0.430448\pi$
$44$			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	−0.970564	−	0.240844i	$-0.922576\pi$
$47$	−0.451608	+	1.68543i	−0.00960869	+	0.0358601i	0.960955	+	0.276705i	$0.0892423\pi$
$48$	−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	−0.990840	−	0.135040i	$-0.956884\pi$
$53$	−45.3574	+	45.3574i	−0.855801	+	0.855801i	0.135040	+	0.990840i	$0.456884\pi$
$54$	−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	0.584321	−	0.811523i	$-0.301361\pi$
$59$	10.2473	+	5.91626i	0.173683	+	0.100276i	−0.410639	+	0.911798i	$0.634694\pi$
$60$	12.4112	−	29.0729i	0.206853	−	0.484548i
$61$	−28.0510	−	48.5858i	−0.459852	−	0.796488i	0.539100	−	0.842242i	$-0.318764\pi$
$61$	−28.0510	−	48.5858i	−0.459852	−	0.796488i	−0.998953	+	0.0457538i	$0.985431\pi$
$62$	−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	0.112901	−	0.993606i	$-0.463986\pi$
$67$	47.4011	−	12.7011i	0.707480	−	0.189569i	0.594578	+	0.804038i	$0.297319\pi$
$68$	−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	−0.404597	−	0.914495i	$-0.632588\pi$
$73$	37.2225	−	37.2225i	0.509898	−	0.509898i	0.914495	+	0.404597i	$0.132588\pi$
$74$	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	0.347416	−	0.937711i	$-0.387059\pi$
$79$	105.323	−	60.8084i	1.33321	−	0.769726i	0.985790	+	0.167985i	$0.0537260\pi$
$80$	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	0.828270	−	0.560329i	$-0.189325\pi$
$83$	105.029	+	28.1424i	1.26541	+	0.339065i	0.437139	+	0.899394i	$0.355992\pi$
$84$	−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	$-0.971211\pi$
$89$		−	16.0767i		−	0.180637i	0.995913	−	0.0903186i	$-0.0287885\pi$
$90$	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	0.140398	+	0.990095i	$0.455162\pi$
$97$	−46.1951	+	172.402i	−0.476238	+	1.77734i	−0.616636	+	0.787248i	$0.711505\pi$
$98$	−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	0.789312	−	0.613992i	$-0.210437\pi$
$101$	−13.8448	−	23.9798i	−0.137077	−	0.237424i	−0.926389	+	0.376568i	$0.877104\pi$
$102$	21.4496	−	81.7115i	0.210291	−	0.801093i
$103$	−39.5049	−	147.434i	−0.383543	−	1.43140i	−0.840451	−	0.541888i	$-0.817710\pi$
$103$	−39.5049	−	147.434i	−0.383543	−	1.43140i	0.456908	−	0.889514i	$-0.348957\pi$
$104$	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	−0.999927	−	0.0120628i	$-0.996160\pi$
$107$	−108.283	−	108.283i	−1.01199	−	1.01199i	−0.0120628	−	0.999927i	$-0.503840\pi$
$108$	15.5639	+	54.7302i	0.144110	+	0.506761i
$109$			184.036i			1.68841i	0.536024	+	0.844203i	$0.319926\pi$
$109$			184.036i			1.68841i	−0.536024	+	0.844203i	$0.680074\pi$
$110$	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	0.837139	+	0.546990i	$0.184226\pi$
$113$	43.5785	+	162.637i	0.385650	+	1.43927i	−0.451489	+	0.892277i	$0.649107\pi$
$114$	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	0.227502	−	0.973778i	$-0.426944\pi$
$127$	−94.7770	−	94.7770i	−0.746275	−	0.746275i	−0.973778	+	0.227502i	$0.926944\pi$
$128$	−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	−0.997056	−	0.0766803i	$-0.975568\pi$
$131$	−56.6078	+	98.0476i	−0.432121	+	0.748455i	0.564935	+	0.825135i	$0.308901\pi$
$132$	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	−0.984999	−	0.172559i	$-0.944797\pi$
$137$	−6.25891	+	23.3586i	−0.0456855	+	0.170501i	0.939314	+	0.343059i	$0.111463\pi$
$138$	−72.6282	+	73.3708i	−0.526291	+	0.531673i
$139$	98.1741	+	56.6809i	0.706289	+	0.407776i	0.809685	−	0.586864i	$-0.199638\pi$
$139$	98.1741	+	56.6809i	0.706289	+	0.407776i	−0.103397	+	0.994640i	$0.532971\pi$
$140$	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	−0.0324193	−	0.999474i	$-0.510321\pi$
$149$	−136.216	−	78.6442i	−0.914199	−	0.527813i	−0.881780	+	0.471661i	$0.843655\pi$
$150$	−134.507	+	127.523i	−0.896712	+	0.850154i
$151$	9.10366	+	15.7680i	0.0602891	+	0.104424i	0.894595	−	0.446879i	$-0.147464\pi$
$151$	9.10366	+	15.7680i	0.0602891	+	0.104424i	−0.834306	+	0.551302i	$0.814131\pi$
$152$	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	−0.738607	−	0.674136i	$-0.764516\pi$
$157$	−163.467	+	43.8009i	−1.04119	+	0.278987i	−0.302585	+	0.953122i	$0.597850\pi$
$158$	−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	−0.997935	−	0.0642365i	$-0.979539\pi$
$163$	−152.193	+	152.193i	−0.933698	+	0.933698i	0.0642365	+	0.997935i	$0.479539\pi$
$164$	−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	0.0831087	−	0.996540i	$-0.473515\pi$
$167$	109.110	−	29.2359i	0.653353	−	0.175065i	0.570245	+	0.821475i	$0.306848\pi$
$168$	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	0.452301	−	0.891865i	$-0.350603\pi$
$173$	68.8666	+	18.4527i	0.398073	+	0.106663i	−0.0542285	+	0.998529i	$0.517270\pi$
$174$	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	$-0.958791\pi$
$179$		−	46.2183i		−	0.258203i	0.991631	−	0.129101i	$-0.0412092\pi$
$180$	−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	0.672169	−	0.740398i	$-0.265363\pi$
$191$	−58.2778	−	100.940i	−0.305119	−	0.528482i	−0.977288	+	0.211916i	$0.932030\pi$
$192$	−8.76551	−	8.67678i	−0.0456537	−	0.0451916i
$193$	32.3443	+	120.711i	0.167587	+	0.625443i	0.997696	+	0.0678422i	$0.0216114\pi$
$193$	32.3443	+	120.711i	0.167587	+	0.625443i	−0.830109	+	0.557601i	$0.811722\pi$
$194$	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	0.886409	−	0.462903i	$-0.153192\pi$
$197$	83.4305	+	83.4305i	0.423505	+	0.423505i	−0.462903	+	0.886409i	$0.653192\pi$
$198$	67.6832	+	242.693i	0.341834	+	1.22572i
$199$			271.461i			1.36412i	0.731294	+	0.682062i	$0.238917\pi$
$199$			271.461i			1.36412i	−0.731294	+	0.682062i	$0.761083\pi$
$200$	−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	−0.978731	−	0.205149i	$-0.934232\pi$
$211$	−65.7689	+	113.915i	−0.311701	+	0.539882i	0.667030	+	0.745031i	$0.267565\pi$
$212$	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	0.325217	−	0.945639i	$-0.394563\pi$
$223$	29.8918	+	8.00949i	0.134044	+	0.0359170i	−0.191173	+	0.981556i	$0.561229\pi$
$224$		−	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	−0.918566	−	0.395268i	$-0.870652\pi$
$227$	16.9273	−	63.1736i	0.0745697	−	0.278298i	0.993135	+	0.116970i	$0.0373183\pi$
$228$	−6.22868	−	22.7816i	−0.0273188	−	0.0999191i
$229$	−240.813	−	139.033i	−1.05158	−	0.607132i	−0.128491	−	0.991711i	$-0.541013\pi$
$229$	−240.813	−	139.033i	−1.05158	−	0.607132i	−0.923092	+	0.384579i	$0.874347\pi$
$230$	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	−0.898107	−	0.439778i	$-0.855057\pi$
$233$	−106.791	+	106.791i	−0.458329	+	0.458329i	0.439778	+	0.898107i	$0.355057\pi$
$234$	−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	0.186985	−	0.982363i	$-0.440128\pi$
$239$	−136.295	−	78.6901i	−0.570273	−	0.329247i	−0.757258	+	0.653115i	$0.773462\pi$
$240$	239.822	−	179.948i	0.999260	−	0.749785i
$241$	−10.1579	−	17.5940i	−0.0421489	−	0.0730040i	0.844181	−	0.536058i	$-0.180087\pi$
$241$	−10.1579	−	17.5940i	−0.0421489	−	0.0730040i	−0.886330	+	0.463054i	$0.846754\pi$
$242$	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	0.659858	−	0.751390i	$-0.270617\pi$
$257$	413.001	−	110.663i	1.60701	−	0.430596i	0.947149	+	0.320794i	$0.103950\pi$
$258$	−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	0.570339	−	0.821410i	$-0.306812\pi$
$263$	171.887	+	46.0569i	0.653562	+	0.175121i	0.0832230	+	0.996531i	$0.473479\pi$
$264$	−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	$0.105553\pi$
$269$			175.152i			0.651123i	−0.945521	+	0.325562i	$0.894447\pi$
$270$	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	−0.513252	−	0.858238i	$-0.671559\pi$
$277$	99.8186	−	372.528i	0.360356	−	1.34487i	0.873608	−	0.486630i	$-0.161774\pi$
$278$	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	0.928133	−	0.372249i	$-0.121413\pi$
$281$	39.8147	+	68.9610i	0.141689	+	0.245413i	−0.786444	+	0.617662i	$0.788080\pi$
$282$	12.4785	−	3.41172i	0.0442499	−	0.0120983i
$283$	−61.9962	−	231.373i	−0.219068	−	0.817573i	−0.984695	−	0.174288i	$-0.944238\pi$
$283$	−61.9962	−	231.373i	−0.219068	−	0.817573i	0.765627	−	0.643285i	$-0.222429\pi$
$284$	−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	0.993620	−	0.112781i	$-0.0359759\pi$
$293$	22.4817	+	83.9027i	0.0767292	+	0.286357i	−0.916891	+	0.399139i	$0.869309\pi$
$294$	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	0.249215	−	0.968448i	$-0.419828\pi$
$307$	−220.805	−	220.805i	−0.719234	−	0.719234i	−0.968448	+	0.249215i	$0.919828\pi$
$308$	−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	−0.772455	−	0.635069i	$-0.780971\pi$
$311$	50.9290	−	88.2115i	0.163759	−	0.283638i	0.936214	+	0.351431i	$0.114305\pi$
$312$	132.350	−	36.1857i	0.424199	−	0.115980i
$313$	260.438	+	69.7840i	0.832069	+	0.222952i	0.649616	−	0.760262i	$-0.274930\pi$
$313$	260.438	+	69.7840i	0.832069	+	0.222952i	0.182453	+	0.983215i	$0.441596\pi$
$314$			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	−0.990049	−	0.140721i	$-0.955058\pi$
$317$	−19.7431	+	73.6824i	−0.0622812	+	0.232437i	0.927768	+	0.373157i	$0.121725\pi$
$318$	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	0.800866	−	0.598844i	$-0.204373\pi$
$331$	−39.1180	−	67.7543i	−0.118181	−	0.204696i	−0.919047	+	0.394148i	$0.871040\pi$
$332$	−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	−0.496595	−	0.867983i	$-0.665416\pi$
$337$	−166.029	+	44.4872i	−0.492667	+	0.132010i	0.00392788	+	0.999992i	$0.498750\pi$
$338$	−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	−0.994270	−	0.106899i	$-0.965908\pi$
$347$	−625.254	+	167.536i	−1.80188	+	0.482813i	−0.807614	+	0.589712i	$0.799241\pi$
$348$	147.718	−	149.228i	0.424476	−	0.428817i
$349$	74.5409	−	43.0362i	0.213584	−	0.123313i	−0.389392	−	0.921072i	$-0.627315\pi$
$349$	74.5409	−	43.0362i	0.213584	−	0.123313i	0.602976	+	0.797759i	$0.293981\pi$
$350$	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	−0.758571	−	0.651590i	$-0.774102\pi$
$353$	−614.682	−	164.703i	−1.74131	−	0.466582i	−0.982737	+	0.185008i	$0.940769\pi$
$354$	−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	$-0.637964\pi$
$359$		−	651.608i		−	1.81506i	0.419983	−	0.907532i	$-0.362036\pi$
$360$	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	−0.991651	−	0.128953i	$-0.958838\pi$
$367$	−25.0954	+	93.6571i	−0.0683797	+	0.255197i	0.923271	+	0.384149i	$0.125505\pi$
$368$	−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	−0.909184	−	0.416395i	$-0.863293\pi$
$373$	−123.092	−	459.385i	−0.330005	−	1.23160i	0.579179	−	0.815200i	$-0.303373\pi$
$374$	−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	$-0.737406\pi$
$379$		−	556.768i		−	1.46905i	0.678584	−	0.734523i	$-0.262594\pi$
$380$	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	0.531233	+	0.847226i	$0.321729\pi$
$383$	189.503	+	707.233i	0.494785	+	1.84656i	−0.0364479	+	0.999336i	$0.511604\pi$
$384$	−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	−0.713949	−	0.700197i	$-0.753095\pi$
$389$	−180.704	+	104.330i	−0.464535	+	0.268200i	0.249414	+	0.968397i	$0.419762\pi$
$390$	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	0.831874	−	0.554964i	$-0.187268\pi$
$397$	109.933	+	109.933i	0.276910	+	0.276910i	−0.554964	+	0.831874i	$0.687268\pi$
$398$	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	−0.156680	−	0.987649i	$-0.550079\pi$
$401$	311.573	−	539.660i	0.776989	−	1.34578i	0.933670	−	0.358135i	$-0.116587\pi$
$402$	−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	0.934041	−	0.357165i	$-0.116257\pi$
$409$	446.525	+	257.801i	1.09175	+	0.630321i	0.157707	+	0.987486i	$0.449590\pi$
$410$	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	0.644172	−	0.764880i	$-0.277202\pi$
$419$	127.314	+	73.5049i	0.303852	+	0.175429i	−0.340320	+	0.940310i	$0.610535\pi$
$420$	266.799	+	209.330i	0.635237	+	0.498405i
$421$	−317.026	−	549.106i	−0.753032	−	1.30429i	−0.946347	−	0.323152i	$-0.895257\pi$
$421$	−317.026	−	549.106i	−0.753032	−	1.30429i	0.193315	−	0.981137i	$-0.438076\pi$
$422$	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	−0.621760	−	0.783208i	$-0.713582\pi$
$433$	69.9073	−	69.9073i	0.161449	−	0.161449i	0.783208	+	0.621760i	$0.213582\pi$
$434$	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	−0.793299	−	0.608833i	$-0.791638\pi$
$439$	−290.918	+	167.962i	−0.662683	+	0.382600i	0.130615	+	0.991433i	$0.458305\pi$
$440$	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	−0.0939967	−	0.995573i	$-0.529964\pi$
$443$	−298.222	−	79.9082i	−0.673187	−	0.180380i	−0.579190	+	0.815193i	$0.696631\pi$
$444$	−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	$0.143739\pi$
$449$			391.868i			0.872757i	−0.899763	+	0.436378i	$0.856261\pi$
$450$	−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	−0.997249	−	0.0741204i	$-0.976385\pi$
$457$	−44.1215	+	164.664i	−0.0965459	+	0.360314i	0.900703	+	0.434434i	$0.143052\pi$
$458$	−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	0.904246	+	0.427012i	$0.140434\pi$
$461$	378.908	+	656.288i	0.821926	+	1.42362i	−0.0823197	+	0.996606i	$0.526233\pi$
$462$	−640.314	−	633.833i	−1.38596	−	1.37193i
$463$	−45.1054	−	168.336i	−0.0974199	−	0.363576i	0.899955	−	0.435982i	$-0.143599\pi$
$463$	−45.1054	−	168.336i	−0.0974199	−	0.363576i	−0.997375	+	0.0724060i	$0.976932\pi$
$464$	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	0.471612	−	0.881806i	$-0.343672\pi$
$467$	−191.561	−	191.561i	−0.410194	−	0.410194i	−0.881806	+	0.471612i	$0.843672\pi$
$468$	−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	−0.634575	−	0.772861i	$-0.718825\pi$
$479$	−135.340	+	78.1383i	−0.282546	+	0.163128i	0.352029	+	0.935989i	$0.385492\pi$
$480$	−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	0.0711400	−	0.997466i	$-0.477336\pi$
$487$	−451.121	−	451.121i	−0.926326	−	0.926326i	−0.997466	+	0.0711400i	$0.977336\pi$
$488$	−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	−0.587130	−	0.809493i	$-0.699742\pi$
$491$	200.071	−	346.533i	0.407476	−	0.705769i	0.994606	+	0.103723i	$0.0330756\pi$
$492$	−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	0.243711	−	0.969848i	$-0.421635\pi$
$499$	−236.699	−	136.658i	−0.474347	−	0.273864i	−0.718058	+	0.695984i	$0.754969\pi$
$500$	−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	−0.346999	−	0.937866i	$-0.612799\pi$
$503$	297.206	−	297.206i	0.590867	−	0.590867i	0.937866	+	0.346999i	$0.112799\pi$
$504$	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	0.557926	−	0.829891i	$-0.311597\pi$
$509$	60.1552	+	34.7306i	0.118183	+	0.0682330i	−0.439743	+	0.898124i	$0.644931\pi$
$510$	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	−0.328547	−	0.944488i	$-0.606559\pi$
$523$	322.137	−	322.137i	0.615941	−	0.615941i	0.944488	+	0.328547i	$0.106559\pi$
$524$	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	0.645286	+	0.763941i	$0.276738\pi$
$547$	−161.649	+	603.281i	−0.295519	+	1.10289i	−0.940804	+	0.338950i	$0.889928\pi$
$548$	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	0.472791	−	0.881175i	$-0.343247\pi$
$557$	−227.470	−	227.470i	−0.408384	−	0.408384i	−0.881175	+	0.472791i	$0.843247\pi$
$558$	−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	0.952196	−	0.305486i	$-0.0988190\pi$
$563$	−14.1724	−	52.8921i	−0.0251730	−	0.0939469i	−0.977369	+	0.211539i	$0.932152\pi$
$564$	−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	−0.674048	−	0.738687i	$-0.735446\pi$
$569$	−211.299	+	121.993i	−0.371351	+	0.214399i	0.302698	+	0.953087i	$0.402113\pi$
$570$	−19.5541	+	137.092i	−0.0343055	+	0.240513i
$571$	−284.750	+	493.202i	−0.498687	+	0.863751i	−0.999999	−	0.00151580i	$-0.999518\pi$
$571$	−284.750	+	493.202i	−0.498687	+	0.863751i	0.501312	+	0.865267i	$0.332851\pi$
$572$	−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	0.446209	−	0.894929i	$-0.352774\pi$
$577$	−258.911	−	258.911i	−0.448719	−	0.448719i	−0.894929	+	0.446209i	$0.852774\pi$
$578$	−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	0.439190	+	0.898394i	$0.355266\pi$
$587$	−229.139	+	855.160i	−0.390357	+	1.45683i	−0.829547	+	0.558437i	$0.811401\pi$
$588$	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	0.0805534	−	0.996750i	$-0.474331\pi$
$593$	638.841	−	638.841i	1.07730	−	1.07730i	0.996750	−	0.0805534i	$-0.0256688\pi$
$594$	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	0.763210	−	0.646150i	$-0.223622\pi$
$599$	350.554	+	202.393i	0.585233	+	0.337884i	−0.177977	+	0.984035i	$0.556955\pi$
$600$	−341.134	+	81.7310i	−0.568557	+	0.136218i
$601$	−419.760	−	727.046i	−0.698437	−	1.20973i	−0.969008	−	0.247028i	$-0.920546\pi$
$601$	−419.760	−	727.046i	−0.698437	−	1.20973i	0.270572	−	0.962700i	$-0.412787\pi$
$602$	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	−0.507308	−	0.861765i	$-0.669359\pi$
$607$	−313.071	+	83.8870i	−0.515767	+	0.138199i	−0.00845910	+	0.999964i	$0.502693\pi$
$608$	−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	−0.828171	−	0.560475i	$-0.810619\pi$
$613$	−164.098	+	164.098i	−0.267697	+	0.267697i	0.560475	+	0.828171i	$0.310619\pi$
$614$	−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	−0.137935	−	0.990441i	$-0.544047\pi$
$617$	146.741	−	39.3191i	0.237830	−	0.0637263i	0.375765	+	0.926715i	$0.377380\pi$
$618$	−796.103	+	804.244i	−1.28819	+	1.30137i
$619$	−371.036	+	214.218i	−0.599412	+	0.346071i	−0.768810	−	0.639477i	$-0.779151\pi$
$619$	−371.036	+	214.218i	−0.599412	+	0.346071i	0.169398	+	0.985548i	$0.445818\pi$
$620$	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	−0.975623	−	0.219451i	$-0.929573\pi$
$641$	−434.510	−	752.593i	−0.677862	−	1.17409i	0.297761	−	0.954640i	$-0.403760\pi$
$642$	−288.265	+	1098.13i	−0.449010	+	1.71049i
$643$	−31.9596	−	119.275i	−0.0497039	−	0.185497i	0.936611	−	0.350372i	$-0.113945\pi$
$643$	−31.9596	−	119.275i	−0.0497039	−	0.185497i	−0.986315	+	0.164874i	$0.947278\pi$
$644$	−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	0.901589	−	0.432593i	$-0.142401\pi$
$647$	303.440	+	303.440i	0.468996	+	0.468996i	−0.432593	+	0.901589i	$0.642401\pi$
$648$	−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	0.938106	+	0.346348i	$0.112578\pi$
$653$	195.153	+	728.322i	0.298856	+	1.11535i	−0.639250	+	0.768999i	$0.720755\pi$
$654$	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	0.566158	−	0.824296i	$-0.308429\pi$
$659$	1030.08	−	594.718i	1.56310	−	0.902456i	0.996941	−	0.0781594i	$-0.0249043\pi$
$660$	−355.510	+	42.9104i	−0.538651	+	0.0650158i
$661$	384.281	−	665.595i	0.581364	−	1.00695i	−0.413954	−	0.910298i	$-0.635853\pi$
$661$	384.281	−	665.595i	0.581364	−	1.00695i	0.995318	−	0.0966537i	$-0.0308139\pi$
$662$	−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	0.461423	−	0.887180i	$-0.347339\pi$
$673$	280.935	+	75.2762i	0.417436	+	0.111852i	−0.0439863	+	0.999032i	$0.514006\pi$
$674$			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	0.545379	+	0.838190i	$0.316386\pi$
$677$	−234.261	+	874.273i	−0.346028	+	1.29139i	−0.891407	+	0.453204i	$0.850281\pi$
$678$	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	−0.141774	−	0.989899i	$-0.545281\pi$
$683$	579.270	−	579.270i	0.848125	−	0.848125i	0.989899	+	0.141774i	$0.0452805\pi$
$684$	−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	0.970352	+	0.241696i	$0.0777036\pi$
$691$	479.893	+	831.199i	0.694491	+	1.20289i	−0.275861	+	0.961197i	$0.588963\pi$
$692$	−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	−0.162274	−	0.986746i	$-0.551883\pi$
$709$	433.296	−	250.163i	0.611137	−	0.352840i	0.773410	+	0.633906i	$0.218549\pi$
$710$	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	$-0.975331\pi$
$719$		−	111.332i		−	0.154843i	0.996998	−	0.0774217i	$-0.0246688\pi$
$720$	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	0.765644	+	0.643264i	$0.222420\pi$
$727$	−159.253	+	594.341i	−0.219055	+	0.817526i	−0.984699	+	0.174261i	$0.944246\pi$
$728$	−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	0.791447	+	0.611237i	$0.209328\pi$
$733$	301.741	+	1126.11i	0.411652	+	1.53631i	−0.379795	+	0.925071i	$0.624005\pi$
$734$	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	$0.0692379\pi$
$739$			318.962i			0.431612i	−0.976436	+	0.215806i	$0.930762\pi$
$740$	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	0.998229	+	0.0594856i	$0.0189460\pi$
$743$	121.466	+	453.316i	0.163480	+	0.610116i	−0.834749	+	0.550631i	$0.814387\pi$
$744$	−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	−0.810916	−	0.585163i	$-0.801031\pi$
$751$	76.0823	−	131.778i	0.101308	−	0.175471i	0.912224	+	0.409692i	$0.134364\pi$
$752$	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	0.951838	−	0.306602i	$-0.0991919\pi$
$757$	488.444	+	488.444i	0.645236	+	0.645236i	−0.306602	+	0.951838i	$0.599192\pi$
$758$	−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	−0.801607	−	0.597851i	$-0.796021\pi$
$761$	88.9996	−	154.152i	0.116951	−	0.202565i	0.918558	+	0.395286i	$0.129355\pi$
$762$	−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	0.612303	−	0.790623i	$-0.290243\pi$
$769$	179.757	+	103.783i	0.233754	+	0.134958i	−0.378548	+	0.925581i	$0.623577\pi$
$770$	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	−0.824342	−	0.566091i	$-0.808455\pi$
$773$	−199.628	+	199.628i	−0.258251	+	0.258251i	0.566091	+	0.824342i	$0.308455\pi$
$774$	−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	0.647589	−	0.761990i	$-0.275777\pi$
$787$	1250.87	−	335.169i	1.58941	−	0.425882i	0.941823	+	0.336108i	$0.109111\pi$
$788$	−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	0.0591106	−	0.998251i	$-0.481174\pi$
$797$	485.714	−	130.147i	0.609428	−	0.163296i	0.550317	+	0.834956i	$0.314507\pi$
$798$	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	$-0.934734\pi$
$809$		−	329.434i		−	0.407212i	0.979053	−	0.203606i	$-0.0652661\pi$
$810$	−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	0.973064	−	0.230535i	$-0.0740475\pi$
$821$	235.531	+	407.952i	0.286883	+	0.496896i	−0.686181	+	0.727431i	$0.740714\pi$
$822$	172.941	−	47.2836i	0.210391	−	0.0575227i
$823$	−225.744	−	842.487i	−0.274294	−	1.02368i	−0.956313	−	0.292344i	$-0.905565\pi$
$823$	−225.744	−	842.487i	−0.274294	−	1.02368i	0.682019	−	0.731334i	$-0.261102\pi$
$824$	−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	0.999349	−	0.0360709i	$-0.0114842\pi$
$827$	796.631	+	796.631i	0.963278	+	0.963278i	−0.0360709	+	0.999349i	$0.511484\pi$
$828$	255.792	+	65.7575i	0.308927	+	0.0794173i
$829$		−	860.599i		−	1.03812i	−0.854739	−	0.519059i	$-0.826283\pi$
$829$		−	860.599i		−	1.03812i	0.854739	−	0.519059i	$-0.173717\pi$
$830$	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	−0.921913	−	0.387398i	$-0.873374\pi$
$839$	−878.746	+	507.344i	−1.04737	+	0.604701i	−0.125460	+	0.992099i	$0.540041\pi$
$840$	−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	0.0549394	−	0.998490i	$-0.482503\pi$
$853$	−338.408	−	90.6761i	−0.396726	−	0.106303i	−0.451666	+	0.892187i	$0.649170\pi$
$854$		−	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	−0.588121	−	0.808773i	$-0.700132\pi$
$857$	279.033	−	1041.37i	0.325593	−	1.21513i	0.913714	−	0.406358i	$-0.133201\pi$
$858$	−794.335	−	208.516i	−0.925798	−	0.243026i
$859$	508.578	+	293.627i	0.592058	+	0.341825i	0.765911	−	0.642947i	$-0.222288\pi$
$859$	508.578	+	293.627i	0.592058	+	0.341825i	−0.173853	+	0.984772i	$0.555622\pi$
$860$	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	−0.977138	−	0.212606i	$-0.931805\pi$
$863$	−659.791	+	659.791i	−0.764532	+	0.764532i	0.212606	+	0.977138i	$0.431805\pi$
$864$	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	−0.251805	−	0.967778i	$-0.581024\pi$
$877$	12.2913	−	3.29344i	0.0140152	−	0.00375535i	0.265820	+	0.964023i	$0.414357\pi$
$878$	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	−0.919159	−	0.393886i	$-0.871131\pi$
$883$	−463.817	+	463.817i	−0.525274	+	0.525274i	0.393886	+	0.919159i	$0.371131\pi$
$884$	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	−0.401884	−	0.915690i	$-0.631645\pi$
$887$	−259.076	+	69.4192i	−0.292081	+	0.0782630i	0.109803	+	0.993953i	$0.464978\pi$
$888$	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	−0.933720	−	0.358003i	$-0.883458\pi$
$907$	48.8935	−	182.473i	0.0539069	−	0.201183i	0.987627	+	0.156820i	$0.0501243\pi$
$908$	−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	0.524317	−	0.851523i	$-0.324321\pi$
$911$	−432.982	−	749.947i	−0.475282	−	0.823213i	−0.999599	+	0.0283104i	$0.990987\pi$
$912$	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	$-0.844127\pi$
$919$		−	864.507i		−	0.940704i	0.882479	−	0.470352i	$-0.155873\pi$
$920$	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	−0.893746	−	0.448574i	$-0.851932\pi$
$929$	−884.539	+	510.689i	−0.952142	+	0.549719i	−0.0583960	+	0.998293i	$0.518599\pi$
$930$	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	0.987384	−	0.158347i	$-0.0506163\pi$
$937$	776.808	+	776.808i	0.829037	+	0.829037i	−0.158347	+	0.987384i	$0.550616\pi$
$938$	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	−0.0828659	+	0.996561i	$0.526407\pi$
$941$	−851.116	+	1474.18i	−0.904480	+	1.56661i	−0.821614	+	0.570044i	$0.806926\pi$
$942$	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	−0.792192	−	0.610273i	$-0.791060\pi$
$947$	188.456	−	703.326i	0.199003	−	0.742688i	0.991194	−	0.132416i	$-0.0422734\pi$
$948$	−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	−0.986443	−	0.164106i	$-0.947526\pi$
$953$	−783.686	+	783.686i	−0.822336	+	0.822336i	0.164106	+	0.986443i	$0.447526\pi$
$954$	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	−0.811903	−	0.583792i	$-0.801568\pi$
$967$	−1182.77	+	316.923i	−1.22314	+	0.327738i	−0.411233	+	0.911530i	$0.634902\pi$
$968$	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	−0.921889	−	0.387455i	$-0.873354\pi$
$977$	−1491.43	+	399.627i	−1.52654	+	0.409035i	−0.604652	+	0.796490i	$0.706688\pi$
$978$	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	0.579228	−	0.815166i	$-0.303354\pi$
$983$	661.825	+	177.336i	0.673271	+	0.180402i	0.0940430	+	0.995568i	$0.470021\pi$
$984$	−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	−0.987354	−	0.158532i	$-0.949324\pi$
$997$	−52.8555	+	197.259i	−0.0530146	+	0.197853i	0.934339	+	0.356385i	$0.115991\pi$
$998$	−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.22.8	yes	40
3.2	odd	2		135.3.l.a.37.3		40
5.2	odd	4		225.3.o.b.193.8		40
5.3	odd	4	inner	45.3.k.a.13.3	yes	40
5.4	even	2		225.3.o.b.157.3		40
9.2	odd	6		135.3.l.a.127.8		40
9.4	even	3		405.3.g.h.82.8		20
9.5	odd	6		405.3.g.g.82.3		20
9.7	even	3	inner	45.3.k.a.7.3	✓	40
15.8	even	4		135.3.l.a.118.8		40
45.7	odd	12		225.3.o.b.43.3		40
45.13	odd	12		405.3.g.h.163.8		20
45.23	even	12		405.3.g.g.163.3		20
45.34	even	6		225.3.o.b.7.8		40
45.38	even	12		135.3.l.a.73.3		40
45.43	odd	12	inner	45.3.k.a.43.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.3	✓	40	9.7	even	3	inner
45.3.k.a.13.3	yes	40	5.3	odd	4	inner
45.3.k.a.22.8	yes	40	1.1	even	1	trivial
45.3.k.a.43.8	yes	40	45.43	odd	12	inner
135.3.l.a.37.3		40	3.2	odd	2
135.3.l.a.73.3		40	45.38	even	12
135.3.l.a.118.8		40	15.8	even	4
135.3.l.a.127.8		40	9.2	odd	6
225.3.o.b.7.8		40	45.34	even	6
225.3.o.b.43.3		40	45.7	odd	12
225.3.o.b.157.3		40	5.4	even	2
225.3.o.b.193.8		40	5.2	odd	4
405.3.g.g.82.3		20	9.5	odd	6
405.3.g.g.163.3		20	45.23	even	12
405.3.g.h.82.8		20	9.4	even	3
405.3.g.h.163.8		20	45.13	odd	12

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) \) 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

Introduction

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