LMFDB - Embedded newform 45.3.k.a.22.5

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			22.5
Character	$\chi$	$=$	45.22
Dual form			45.3.k.a.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0492077 - 0.183646i) q^{2} +(-2.37796 + 1.82902i) q^{3} +(3.43280 + 1.98193i) q^{4} +(4.90616 - 0.964151i) q^{5} +(0.218877 + 0.526704i) q^{6} +(-2.33248 + 8.70492i) q^{7} +(1.07064 - 1.07064i) q^{8} +(2.30940 - 8.69866i) q^{9} +(0.0643587 - 0.948439i) q^{10} +(-7.04110 - 12.1955i) q^{11} +(-11.7880 + 1.56570i) q^{12} +(-3.46845 - 12.9444i) q^{13} +(1.48385 + 0.856699i) q^{14} +(-9.90321 + 11.2662i) q^{15} +(7.78377 + 13.4819i) q^{16} +(-0.740694 - 0.740694i) q^{17} +(-1.48383 - 0.852153i) q^{18} +7.09073i q^{19} +(18.7527 + 6.41391i) q^{20} +(-10.3749 - 24.9661i) q^{21} +(-2.58614 + 0.692953i) q^{22} +(-5.10441 - 19.0499i) q^{23} +(-0.587726 + 4.50418i) q^{24} +(23.1408 - 9.46056i) q^{25} -2.54786 q^{26} +(10.4183 + 24.9090i) q^{27} +(-25.2594 + 25.2594i) q^{28} +(-6.18301 + 3.56976i) q^{29} +(1.58167 + 2.37306i) q^{30} +(13.0783 - 22.6522i) q^{31} +(8.70902 - 2.33357i) q^{32} +(39.0493 + 16.1223i) q^{33} +(-0.172473 + 0.0995774i) q^{34} +(-3.05064 + 44.9566i) q^{35} +(25.1678 - 25.2837i) q^{36} +(-23.0151 - 23.0151i) q^{37} +(1.30218 + 0.348919i) q^{38} +(31.9234 + 24.4375i) q^{39} +(4.22049 - 6.28502i) q^{40} +(-36.0387 + 62.4209i) q^{41} +(-5.09544 + 0.676780i) q^{42} +(-12.0484 - 3.22835i) q^{43} -55.8198i q^{44} +(2.94348 - 44.9036i) q^{45} -3.74961 q^{46} +(-13.9048 + 51.8935i) q^{47} +(-43.1681 - 17.8228i) q^{48} +(-27.9000 - 16.1081i) q^{49} +(-0.598685 - 4.71525i) q^{50} +(3.11608 + 0.406601i) q^{51} +(13.7484 - 51.3098i) q^{52} +(17.2907 - 17.2907i) q^{53} +(5.08709 - 0.687563i) q^{54} +(-46.3031 - 53.0446i) q^{55} +(6.82262 + 11.8171i) q^{56} +(-12.9691 - 16.8615i) q^{57} +(0.351320 + 1.31114i) q^{58} +(-27.5407 - 15.9006i) q^{59} +(-56.3244 + 19.0470i) q^{60} +(40.7317 + 70.5494i) q^{61} +(-3.51643 - 3.51643i) q^{62} +(70.3345 + 40.3926i) q^{63} +60.5560i q^{64} +(-29.4971 - 60.1633i) q^{65} +(4.88231 - 6.37790i) q^{66} +(64.1404 - 17.1864i) q^{67} +(-1.07465 - 4.01065i) q^{68} +(46.9807 + 35.9639i) q^{69} +(8.10597 + 2.77245i) q^{70} -36.3928 q^{71} +(-6.84062 - 11.7857i) q^{72} +(2.90991 - 2.90991i) q^{73} +(-5.35915 + 3.09411i) q^{74} +(-37.7245 + 64.8218i) q^{75} +(-14.0533 + 24.3410i) q^{76} +(122.584 - 32.8464i) q^{77} +(6.05872 - 4.66008i) q^{78} +(-71.8823 + 41.5012i) q^{79} +(51.1870 + 58.6396i) q^{80} +(-70.3333 - 40.1774i) q^{81} +(9.68994 + 9.68994i) q^{82} +(51.3796 + 13.7671i) q^{83} +(13.8661 - 106.266i) q^{84} +(-4.34811 - 2.91982i) q^{85} +(-1.18574 + 2.05377i) q^{86} +(8.17381 - 19.7976i) q^{87} +(-20.5956 - 5.51857i) q^{88} +22.5436i q^{89} +(-8.10152 - 2.75016i) q^{90} +120.770 q^{91} +(20.2331 - 75.5111i) q^{92} +(10.3316 + 77.7864i) q^{93} +(8.84580 + 5.10712i) q^{94} +(6.83654 + 34.7883i) q^{95} +(-16.4416 + 21.4781i) q^{96} +(-9.03502 + 33.7192i) q^{97} +(-4.33107 + 4.33107i) q^{98} +(-122.346 + 33.0837i) 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 $

$2$	0.0492077	−	0.183646i	0.0246039	−	0.0918228i	−0.952532	−	0.304438i	$-0.901531\pi$
$2$	0.0492077	−	0.183646i	0.0246039	−	0.0918228i	0.977136	+	0.212615i	$0.0681980\pi$
$3$	−2.37796	+	1.82902i	−0.792654	+	0.609672i
$3$	−2.37796	+	1.82902i	−0.792654	+	0.609672i
$4$	3.43280	+	1.98193i	0.858199	+	0.495482i
$5$	4.90616	−	0.964151i	0.981232	−	0.192830i
$5$	4.90616	−	0.964151i	0.981232	−	0.192830i
$6$	0.218877	+	0.526704i	0.0364795	+	0.0877840i
$7$	−2.33248	+	8.70492i	−0.333211	+	1.24356i	0.572585	+	0.819846i	$0.305941\pi$
$7$	−2.33248	+	8.70492i	−0.333211	+	1.24356i	−0.905796	+	0.423715i	$0.860726\pi$
$8$	1.07064	−	1.07064i	0.133831	−	0.133831i
$9$	2.30940	−	8.69866i	0.256600	−	0.966518i
$10$	0.0643587	−	0.948439i	0.00643587	−	0.0948439i
$11$	−7.04110	−	12.1955i	−0.640100	−	1.10869i	−0.985410	−	0.170197i	$-0.945560\pi$
$11$	−7.04110	−	12.1955i	−0.640100	−	1.10869i	0.345310	−	0.938489i	$-0.387774\pi$
$12$	−11.7880	+	1.56570i	−0.982336	+	0.130475i
$13$	−3.46845	−	12.9444i	−0.266804	−	0.995725i	−0.961137	−	0.276071i	$-0.910967\pi$
$13$	−3.46845	−	12.9444i	−0.266804	−	0.995725i	0.694333	−	0.719653i	$-0.255699\pi$
$14$	1.48385	+	0.856699i	0.105989	+	0.0611928i
$15$	−9.90321	+	11.2662i	−0.660214	+	0.751077i
$16$	7.78377	+	13.4819i	0.486486	+	0.842618i
$17$	−0.740694	−	0.740694i	−0.0435702	−	0.0435702i	0.684986	−	0.728556i	$-0.259808\pi$
$17$	−0.740694	−	0.740694i	−0.0435702	−	0.0435702i	−0.728556	+	0.684986i	$0.759808\pi$
$18$	−1.48383	−	0.852153i	−0.0824350	−	0.0473418i
$19$			7.09073i			0.373196i	0.982436	+	0.186598i	$0.0597463\pi$
$19$			7.09073i			0.373196i	−0.982436	+	0.186598i	$0.940254\pi$
$20$	18.7527	+	6.41391i	0.937637	+	0.320696i
$21$	−10.3749	−	24.9661i	−0.494043	−	1.18886i
$22$	−2.58614	+	0.692953i	−0.117552	+	0.0314979i
$23$	−5.10441	−	19.0499i	−0.221931	−	0.828257i	−0.983611	−	0.180304i	$-0.942292\pi$
$23$	−5.10441	−	19.0499i	−0.221931	−	0.828257i	0.761680	−	0.647953i	$-0.224375\pi$
$24$	−0.587726	+	4.50418i	−0.0244886	+	0.187674i
$25$	23.1408	−	9.46056i	0.925633	−	0.378423i
$26$	−2.54786			−0.0979947
$27$	10.4183	+	24.9090i	0.385863	+	0.922556i
$28$	−25.2594	+	25.2594i	−0.902123	+	0.902123i
$29$	−6.18301	+	3.56976i	−0.213207	+	0.123095i	−0.602801	−	0.797892i	$-0.705949\pi$
$29$	−6.18301	+	3.56976i	−0.213207	+	0.123095i	0.389594	+	0.920987i	$0.372615\pi$
$30$	1.58167	+	2.37306i	0.0527222	+	0.0791021i
$31$	13.0783	−	22.6522i	0.421879	−	0.730716i	−0.574244	−	0.818684i	$-0.694704\pi$
$31$	13.0783	−	22.6522i	0.421879	−	0.730716i	0.996123	+	0.0879678i	$0.0280373\pi$
$32$	8.70902	−	2.33357i	0.272157	−	0.0729242i
$33$	39.0493	+	16.1223i	1.18331	+	0.488553i
$34$	−0.172473	+	0.0995774i	−0.00507274	+	0.00292875i
$35$	−3.05064	+	44.9566i	−0.0871612	+	1.28447i
$36$	25.1678	−	25.2837i	0.699106	−	0.702324i
$37$	−23.0151	−	23.0151i	−0.622031	−	0.622031i	0.324020	−	0.946050i	$-0.394966\pi$
$37$	−23.0151	−	23.0151i	−0.622031	−	0.622031i	−0.946050	+	0.324020i	$0.894966\pi$
$38$	1.30218	+	0.348919i	0.0342680	+	0.00918207i
$39$	31.9234	+	24.4375i	0.818548	+	0.626602i
$40$	4.22049	−	6.28502i	0.105512	−	0.157125i
$41$	−36.0387	+	62.4209i	−0.878993	+	1.52246i	−0.0265459	+	0.999648i	$0.508451\pi$
$41$	−36.0387	+	62.4209i	−0.878993	+	1.52246i	−0.852447	+	0.522813i	$0.824883\pi$
$42$	−5.09544	+	0.676780i	−0.121320	+	0.0161138i
$43$	−12.0484	−	3.22835i	−0.280195	−	0.0750779i	0.115985	−	0.993251i	$-0.462998\pi$
$43$	−12.0484	−	3.22835i	−0.280195	−	0.0750779i	−0.396180	+	0.918173i	$0.629664\pi$
$44$		−	55.8198i		−	1.26863i
$45$	2.94348	−	44.9036i	0.0654106	−	0.997858i
$46$	−3.74961			−0.0815133
$47$	−13.9048	+	51.8935i	−0.295847	+	1.10412i	0.644695	+	0.764440i	$0.276985\pi$
$47$	−13.9048	+	51.8935i	−0.295847	+	1.10412i	−0.940542	+	0.339677i	$0.889682\pi$
$48$	−43.1681	−	17.8228i	−0.899335	−	0.371308i
$49$	−27.9000	−	16.1081i	−0.569388	−	0.328736i
$50$	−0.598685	−	4.71525i	−0.0119737	−	0.0943049i
$51$	3.11608	+	0.406601i	0.0610997	+	0.00797257i
$52$	13.7484	−	51.3098i	0.264393	−	0.986727i
$53$	17.2907	−	17.2907i	0.326240	−	0.326240i	−0.524915	−	0.851155i	$-0.675903\pi$
$53$	17.2907	−	17.2907i	0.326240	−	0.326240i	0.851155	+	0.524915i	$0.175903\pi$
$54$	5.08709	−	0.687563i	0.0942054	−	0.0127326i
$55$	−46.3031	−	53.0446i	−0.841875	−	0.964447i
$56$	6.82262	+	11.8171i	0.121833	+	0.211020i
$57$	−12.9691	−	16.8615i	−0.227527	−	0.295816i
$58$	0.351320	+	1.31114i	0.00605724	+	0.0226059i
$59$	−27.5407	−	15.9006i	−0.466792	−	0.269502i	0.248104	−	0.968733i	$-0.420193\pi$
$59$	−27.5407	−	15.9006i	−0.466792	−	0.269502i	−0.714896	+	0.699231i	$0.753526\pi$
$60$	−56.3244	+	19.0470i	−0.938740	+	0.317450i
$61$	40.7317	+	70.5494i	0.667733	+	1.15655i	0.978537	+	0.206073i	$0.0660684\pi$
$61$	40.7317	+	70.5494i	0.667733	+	1.15655i	−0.310804	+	0.950474i	$0.600598\pi$
$62$	−3.51643	−	3.51643i	−0.0567166	−	0.0567166i
$63$	70.3345	+	40.3926i	1.11642	+	0.641152i
$64$			60.5560i			0.946187i
$65$	−29.4971	−	60.1633i	−0.453802	−	0.925589i
$66$	4.88231	−	6.37790i	0.0739744	−	0.0966348i
$67$	64.1404	−	17.1864i	0.957319	−	0.256513i	0.253854	−	0.967243i	$-0.418302\pi$
$67$	64.1404	−	17.1864i	0.957319	−	0.256513i	0.703465	+	0.710730i	$0.251635\pi$
$68$	−1.07465	−	4.01065i	−0.0158037	−	0.0589802i
$69$	46.9807	+	35.9639i	0.680880	+	0.521216i
$70$	8.10597	+	2.77245i	0.115800	+	0.0396064i
$71$	−36.3928			−0.512574			−0.256287	−	0.966601i	$-0.582499\pi$
$71$	−36.3928			−0.512574			−0.256287	+	0.966601i	$0.582499\pi$
$72$	−6.84062	−	11.7857i	−0.0950086	−	0.163691i
$73$	2.90991	−	2.90991i	0.0398617	−	0.0398617i	−0.686895	−	0.726757i	$-0.741027\pi$
$73$	2.90991	−	2.90991i	0.0398617	−	0.0398617i	0.726757	+	0.686895i	$0.241027\pi$
$74$	−5.35915	+	3.09411i	−0.0724210	+	0.0418123i
$75$	−37.7245	+	64.8218i	−0.502993	+	0.864291i
$76$	−14.0533	+	24.3410i	−0.184912	+	0.320277i
$77$	122.584	−	32.8464i	1.59201	−	0.426577i
$78$	6.05872	−	4.66008i	0.0776759	−	0.0597446i
$79$	−71.8823	+	41.5012i	−0.909902	+	0.525332i	−0.880400	−	0.474232i	$-0.842726\pi$
$79$	−71.8823	+	41.5012i	−0.909902	+	0.525332i	−0.0295025	+	0.999565i	$0.509392\pi$
$80$	51.1870	+	58.6396i	0.639838	+	0.732995i
$81$	−70.3333	−	40.1774i	−0.868313	−	0.496017i
$82$	9.68994	+	9.68994i	0.118170	+	0.118170i
$83$	51.3796	+	13.7671i	0.619031	+	0.165869i	0.554687	−	0.832059i	$-0.312838\pi$
$83$	51.3796	+	13.7671i	0.619031	+	0.165869i	0.0643438	+	0.997928i	$0.479505\pi$
$84$	13.8661	−	106.266i	0.165072	−	1.26507i
$85$	−4.34811	−	2.91982i	−0.0511542	−	0.0343509i
$86$	−1.18574	+	2.05377i	−0.0137877	+	0.0238811i
$87$	8.17381	−	19.7976i	0.0939518	−	0.227558i
$88$	−20.5956	−	5.51857i	−0.234041	−	0.0627111i
$89$			22.5436i			0.253299i	0.991948	+	0.126650i	$0.0404224\pi$
$89$			22.5436i			0.253299i	−0.991948	+	0.126650i	$0.959578\pi$
$90$	−8.10152	−	2.75016i	−0.0900168	−	0.0305574i
$91$	120.770			1.32715
$92$	20.2331	−	75.5111i	0.219925	−	0.820773i
$93$	10.3316	+	77.7864i	0.111093	+	0.836413i
$94$	8.84580	+	5.10712i	0.0941042	+	0.0543311i
$95$	6.83654	+	34.7883i	0.0719636	+	0.366192i
$96$	−16.4416	+	21.4781i	−0.171266	+	0.223730i
$97$	−9.03502	+	33.7192i	−0.0931446	+	0.347620i	−0.996732	−	0.0807843i	$-0.974258\pi$
$97$	−9.03502	+	33.7192i	−0.0931446	+	0.347620i	0.903587	+	0.428405i	$0.140924\pi$
$98$	−4.33107	+	4.33107i	−0.0441946	+	0.0441946i
$99$	−122.346	+	33.0837i	−1.23581	+	0.334179i
$100$	98.1879	+	13.3872i	0.981879	+	0.133872i
$101$	−29.7283	−	51.4909i	−0.294340	−	0.509811i	0.680491	−	0.732756i	$-0.261766\pi$
$101$	−29.7283	−	51.4909i	−0.294340	−	0.509811i	−0.974831	+	0.222945i	$0.928433\pi$
$102$	0.228006	−	0.552247i	0.00223535	−	0.00541419i
$103$	20.3691	+	76.0184i	0.197758	+	0.738043i	0.991536	+	0.129835i	$0.0414447\pi$
$103$	20.3691	+	76.0184i	0.197758	+	0.738043i	−0.793778	+	0.608208i	$0.791889\pi$
$104$	−17.5723	−	10.1454i	−0.168965	−	0.0975519i
$105$	−74.9720	−	112.485i	−0.714019	−	1.07128i
$106$	−2.32453	−	4.02620i	−0.0219295	−	0.0379830i
$107$	−50.6865	−	50.6865i	−0.473706	−	0.473706i	0.429406	−	0.903112i	$-0.358723\pi$
$107$	−50.6865	−	50.6865i	−0.473706	−	0.473706i	−0.903112	+	0.429406i	$0.858723\pi$
$108$	−13.6039	+	106.156i	−0.125962	+	0.982925i
$109$		−	47.8364i		−	0.438866i	−0.975628	−	0.219433i	$-0.929579\pi$
$109$		−	47.8364i		−	0.438866i	0.975628	−	0.219433i	$-0.0704208\pi$
$110$	−12.0199	+	5.89316i	−0.109272	+	0.0535742i
$111$	96.8241	+	12.6341i	0.872289	+	0.113820i
$112$	−135.514	+	36.3109i	−1.20995	+	0.324205i
$113$	−45.1005	−	168.318i	−0.399120	−	1.48954i	−0.814648	−	0.579955i	$-0.803070\pi$
$113$	−45.1005	−	168.318i	−0.399120	−	1.48954i	0.415529	−	0.909580i	$-0.363597\pi$
$114$	−3.73472	+	1.55200i	−0.0327607	+	0.0136140i
$115$	−43.4101	−	88.5405i	−0.377479	−	0.769918i
$116$	−28.3000			−0.243966
$117$	−120.609	+	0.276954i	−1.03085	+	0.00236713i
$118$	−4.27530	+	4.27530i	−0.0362313	+	0.0362313i
$119$	8.17534	−	4.72003i	0.0687003	−	0.0396641i
$120$	1.45923	+	22.6649i	0.0121603	+	0.188874i
$121$	−38.6542	+	66.9510i	−0.319456	+	0.553314i
$122$	14.9604	−	4.00863i	0.122626	−	0.0328576i
$123$	−28.4701	−	214.350i	−0.231464	−	1.74268i
$124$	89.7900	−	51.8403i	0.724113	−	0.418067i
$125$	104.411	−	68.7263i	0.835289	−	0.549810i
$126$	10.8789	−	10.9290i	0.0863407	−	0.0867381i
$127$	16.3333	+	16.3333i	0.128608	+	0.128608i	0.768481	−	0.639873i	$-0.221013\pi$
$127$	16.3333	+	16.3333i	0.128608	+	0.128608i	−0.639873	+	0.768481i	$0.721013\pi$
$128$	45.9569	+	12.3141i	0.359038	+	0.0962041i
$129$	34.5553	−	14.3598i	0.267870	−	0.111316i
$130$	−12.5002	+	2.45652i	−0.0961555	+	0.0188963i
$131$	−27.6049	+	47.8130i	−0.210724	+	0.364985i	−0.951941	−	0.306280i	$-0.900916\pi$
$131$	−27.6049	+	47.8130i	−0.210724	+	0.364985i	0.741217	+	0.671265i	$0.234249\pi$
$132$	102.095	+	132.737i	0.773449	+	1.00559i
$133$	−61.7243	−	16.5390i	−0.464092	−	0.124353i
$134$		−	12.6248i		−	0.0942150i
$135$	75.1300	+	112.163i	0.556518	+	0.830835i
$136$	−1.58604			−0.0116621
$137$	−50.7417	+	189.371i	−0.370377	+	1.38227i	0.489606	+	0.871944i	$0.337141\pi$
$137$	−50.7417	+	189.371i	−0.370377	+	1.38227i	−0.859983	+	0.510323i	$0.829526\pi$
$138$	8.91643	−	6.85810i	0.0646118	−	0.0496964i
$139$	82.5364	+	47.6524i	0.593787	+	0.342823i	0.766594	−	0.642133i	$-0.221950\pi$
$139$	82.5364	+	47.6524i	0.593787	+	0.342823i	−0.172806	+	0.984956i	$0.555283\pi$
$140$	−99.5729	+	148.281i	−0.711235	+	1.05915i
$141$	−61.8489	−	148.833i	−0.438645	−	1.05555i
$142$	−1.79081	+	6.68338i	−0.0126113	+	0.0470660i
$143$	−133.443	+	133.443i	−0.933165	+	0.933165i
$144$	135.250	−	36.5733i	0.939237	−	0.253981i
$145$	−26.8931	+	23.4752i	−0.185469	+	0.161898i
$146$	−0.391202	−	0.677581i	−0.00267946	−	0.00464097i
$147$	95.8070	−	12.7252i	0.651748	−	0.0865657i
$148$	−33.3920	−	124.621i	−0.225622	−	0.842031i
$149$	225.341	+	130.101i	1.51235	+	0.873158i	0.999896	+	0.0144460i	$0.00459846\pi$
$149$	225.341	+	130.101i	1.51235	+	0.873158i	0.512458	+	0.858712i	$0.328735\pi$
$150$	10.0479	+	10.1177i	0.0669860	+	0.0674511i
$151$	−128.914	−	223.285i	−0.853735	−	1.47871i	−0.877814	−	0.479002i	$-0.840999\pi$
$151$	−128.914	−	223.285i	−0.853735	−	1.47871i	0.0240792	−	0.999710i	$-0.492335\pi$
$152$	7.59165	+	7.59165i	0.0499451	+	0.0499451i
$153$	−8.15361	+	4.73248i	−0.0532915	+	0.0309313i
$154$		−	24.1284i		−	0.156678i
$155$	42.3239	−	123.745i	0.273057	−	0.798353i
$156$	61.1532	+	147.159i	0.392008	+	0.943325i
$157$	44.8971	−	12.0301i	0.285969	−	0.0766251i	−0.112983	−	0.993597i	$-0.536041\pi$
$157$	44.8971	−	12.0301i	0.285969	−	0.0766251i	0.398952	+	0.916972i	$0.369374\pi$
$158$	4.08436	+	15.2431i	0.0258504	+	0.0964750i
$159$	−9.49166	+	72.7416i	−0.0596960	+	0.457494i
$160$	40.4779	−	19.8457i	0.252987	−	0.124036i
$161$	177.734			1.10394
$162$	−10.8393	+	10.9394i	−0.0669096	+	0.0675270i
$163$	76.8331	−	76.8331i	0.471369	−	0.471369i	−0.430989	−	0.902357i	$-0.641835\pi$
$163$	76.8331	−	76.8331i	0.471369	−	0.471369i	0.902357	+	0.430989i	$0.141835\pi$
$164$	−247.427	+	142.852i	−1.50870	+	0.871050i
$165$	207.126	+	41.4489i	1.25531	+	0.251206i
$166$	5.05654	−	8.75819i	0.0304611	−	0.0527602i
$167$	−301.256	+	80.7212i	−1.80393	+	0.483360i	−0.994580	−	0.103972i	$-0.966845\pi$
$167$	−301.256	+	80.7212i	−1.80393	+	0.483360i	−0.809346	+	0.587333i	$0.800178\pi$
$168$	−37.8376	−	15.6220i	−0.225224	−	0.0929881i
$169$	−9.16964	+	5.29409i	−0.0542582	+	0.0313260i
$170$	−0.750173	+	0.654833i	−0.00441278	+	0.00385196i
$171$	61.6799	+	16.3754i	0.360701	+	0.0957623i
$172$	−34.9612	−	34.9612i	−0.203263	−	0.203263i
$173$	192.633	+	51.6158i	1.11348	+	0.298357i	0.768244	−	0.640157i	$-0.221131\pi$
$173$	192.633	+	51.6158i	1.11348	+	0.298357i	0.345240	+	0.938514i	$0.387797\pi$
$174$	−3.23353	−	2.47528i	−0.0185835	−	0.0142257i
$175$	28.3780	+	223.506i	0.162160	+	1.27718i
$176$	109.613	−	189.855i	0.622799	−	1.07872i
$177$	94.5733	−	12.5613i	0.534312	−	0.0709677i
$178$	4.14004	+	1.10932i	0.0232587	+	0.00623214i
$179$		−	254.120i		−	1.41967i	−0.704370	−	0.709833i	$-0.748770\pi$
$179$		−	254.120i		−	1.41967i	0.704370	−	0.709833i	$-0.251230\pi$
$180$	99.1001	−	148.311i	0.550556	−	0.823952i
$181$	−236.998			−1.30938			−0.654691	−	0.755896i	$-0.727201\pi$
$181$	−236.998			−1.30938			−0.654691	+	0.755896i	$0.727201\pi$
$182$	5.94283	−	22.1789i	0.0326529	−	0.121862i
$183$	−225.894	−	93.2648i	−1.23440	−	0.509644i
$184$	−25.8607	−	14.9307i	−0.140547	−	0.0811450i
$185$	−135.106	−	90.7259i	−0.730303	−	0.490410i
$186$	14.7935	+	1.93033i	0.0795351	+	0.0103781i
$187$	−3.81787	+	14.2485i	−0.0204164	+	0.0761950i
$188$	−150.582	+	150.582i	−0.800966	+	0.800966i
$189$	−241.131	+	32.5909i	−1.27583	+	0.172439i
$190$	6.72513	+	0.456350i	0.0353954	+	0.00240184i
$191$	27.2962	+	47.2784i	0.142912	+	0.247531i	0.928592	−	0.371102i	$-0.121020\pi$
$191$	27.2962	+	47.2784i	0.142912	+	0.247531i	−0.785680	+	0.618633i	$0.787687\pi$
$192$	−110.758	−	144.000i	−0.576864	−	0.749999i
$193$	51.8234	+	193.408i	0.268515	+	1.00211i	0.960063	+	0.279782i	$0.0902623\pi$
$193$	51.8234	+	193.408i	0.268515	+	1.00211i	−0.691548	+	0.722330i	$0.743071\pi$
$194$	5.74779	+	3.31849i	0.0296278	+	0.0171056i
$195$	180.183	+	89.1153i	0.924014	+	0.457001i
$196$	−63.8500	−	110.591i	−0.325765	−	0.564242i
$197$	18.5367	+	18.5367i	0.0940948	+	0.0940948i	0.752587	−	0.658492i	$-0.228806\pi$
$197$	18.5367	+	18.5367i	0.0940948	+	0.0940948i	−0.658492	+	0.752587i	$0.728806\pi$
$198$	0.0553320	+	24.0962i	0.000279454	+	0.121698i
$199$		−	206.081i		−	1.03558i	−0.855507	−	0.517792i	$-0.826754\pi$
$199$		−	206.081i		−	1.03558i	0.855507	−	0.517792i	$-0.173246\pi$
$200$	14.6467	−	34.9045i	0.0732335	−	0.174522i
$201$	−121.089	+	158.182i	−0.602434	+	0.786977i
$202$	−10.9190	+	2.92572i	−0.0540542	+	0.0144838i
$203$	−16.6528	−	62.1490i	−0.0820334	−	0.306153i
$204$	9.89103	+	7.57163i	0.0484854	+	0.0371158i
$205$	−116.629	+	340.994i	−0.568920	+	1.66338i
$206$	14.9628			0.0726348
$207$	−177.497	+	0.407585i	−0.857473	+	0.00196901i
$208$	147.518	−	147.518i	0.709219	−	0.709219i
$209$	86.4753	−	49.9266i	0.413758	−	0.238883i
$210$	−24.3465	+	8.23317i	−0.115936	+	0.0392056i
$211$	121.373	−	210.225i	0.575230	−	0.996327i	−0.420787	−	0.907159i	$-0.638246\pi$
$211$	121.373	−	210.225i	0.575230	−	0.996327i	0.996017	−	0.0891675i	$-0.0284206\pi$
$212$	93.6244	−	25.0866i	0.441625	−	0.118333i
$213$	86.5406	−	66.5630i	0.406294	−	0.312502i
$214$	−11.8025	+	6.81419i	−0.0551520	+	0.0318420i
$215$	−62.2238	−	4.22235i	−0.289413	−	0.0196389i
$216$	37.8230	+	15.5144i	0.175106	+	0.0718258i
$217$	166.681	+	166.681i	0.768115	+	0.768115i
$218$	−8.78496	−	2.35392i	−0.0402980	−	0.0107978i
$219$	−1.59738	+	12.2419i	−0.00729397	+	0.0558991i
$220$	−53.8187	−	273.861i	−0.244631	−	1.24482i
$221$	−7.01880	+	12.1569i	−0.0317593	+	0.0550087i
$222$	7.08468	−	17.1596i	0.0319130	−	0.0772957i
$223$	198.758	+	53.2572i	0.891293	+	0.238821i	0.675273	−	0.737568i	$-0.264026\pi$
$223$	198.758	+	53.2572i	0.891293	+	0.238821i	0.216020	+	0.976389i	$0.430692\pi$
$224$			81.2544i			0.362743i
$225$	−28.8527	−	223.142i	−0.128234	−	0.991744i
$226$	−33.1301			−0.146593
$227$	48.1829	−	179.821i	0.212259	−	0.792163i	−0.774854	−	0.632140i	$-0.782177\pi$
$227$	48.1829	−	179.821i	0.212259	−	0.792163i	0.987113	−	0.160022i	$-0.0511567\pi$
$228$	−11.1019	−	83.5858i	−0.0486927	−	0.366604i
$229$	−156.704	−	90.4733i	−0.684298	−	0.395080i	0.117174	−	0.993111i	$-0.462616\pi$
$229$	−156.704	−	90.4733i	−0.684298	−	0.395080i	−0.801473	+	0.598031i	$0.795950\pi$
$230$	−18.3962	+	3.61519i	−0.0799835	+	0.0157182i
$231$	−231.425	+	302.316i	−1.00184	+	1.30873i
$232$	−2.79786	+	10.4417i	−0.0120597	+	0.0450075i
$233$	−120.230	+	120.230i	−0.516010	+	0.516010i	−0.916362	−	0.400351i	$-0.868888\pi$
$233$	−120.230	+	120.230i	−0.516010	+	0.516010i	0.400351	+	0.916362i	$0.368888\pi$
$234$	−5.88404	+	22.1630i	−0.0251455	+	0.0947136i
$235$	−18.1861	+	268.004i	−0.0773877	+	1.14044i
$236$	−63.0278	−	109.167i	−0.267067	−	0.462573i
$237$	95.0268	−	230.162i	0.400957	−	0.971148i
$238$	−0.464524	−	1.73363i	−0.00195178	−	0.00728415i
$239$	332.123	+	191.751i	1.38963	+	0.802306i	0.993274	−	0.115790i	$-0.0369398\pi$
$239$	332.123	+	191.751i	1.38963	+	0.802306i	0.396360	+	0.918095i	$0.370273\pi$
$240$	−228.973	−	45.8208i	−0.954056	−	0.190920i
$241$	162.944	+	282.226i	0.676114	+	1.17106i	0.976142	+	0.217134i	$0.0696708\pi$
$241$	162.944	+	282.226i	0.676114	+	1.17106i	−0.300028	+	0.953931i	$0.596996\pi$
$242$	10.3932	+	10.3932i	0.0429470	+	0.0429470i
$243$	240.735	−	33.1004i	0.990679	−	0.136216i
$244$			322.909i			1.32340i
$245$	−152.412	−	52.1289i	−0.622092	−	0.212771i
$246$	−40.7654	−	5.31925i	−0.165713	−	0.0216230i
$247$	91.7854	−	24.5938i	0.371601	−	0.0995702i
$248$	−10.2503	−	38.2546i	−0.0413318	−	0.154252i
$249$	−147.359	+	61.2364i	−0.591803	+	0.245929i
$250$	−7.48345	−	22.5565i	−0.0299338	−	0.0902261i
$251$	428.941			1.70893			0.854465	−	0.519509i	$-0.173885\pi$
$251$	428.941			1.70893			0.854465	+	0.519509i	$0.173885\pi$
$252$	161.389	+	278.057i	0.640433	+	1.10340i
$253$	−196.383	+	196.383i	−0.776219	+	0.776219i
$254$	3.80325	−	2.19581i	0.0149734	−	0.00864492i
$255$	15.6800	−	1.00953i	0.0614903	−	0.00395893i
$256$	−116.589	+	201.938i	−0.455426	+	0.788821i
$257$	355.861	−	95.3527i	1.38467	−	0.371022i	0.511857	−	0.859070i	$-0.328958\pi$
$257$	355.861	−	95.3527i	1.38467	−	0.371022i	0.872817	+	0.488048i	$0.162291\pi$
$258$	−0.936723	−	7.05253i	−0.00363071	−	0.0273354i
$259$	254.027	−	146.663i	0.980800	−	0.566265i
$260$	17.9815	−	264.990i	0.0691597	−	1.01919i
$261$	16.7731	+	62.0279i	0.0642647	+	0.237655i
$262$	7.42228	+	7.42228i	0.0283293	+	0.0283293i
$263$	−63.7296	−	17.0763i	−0.242318	−	0.0649289i	0.135616	−	0.990761i	$-0.456699\pi$
$263$	−63.7296	−	17.0763i	−0.242318	−	0.0649289i	−0.377934	+	0.925833i	$0.623365\pi$
$264$	59.0691	−	24.5467i	0.223747	−	0.0929800i
$265$	68.1601	−	101.502i	0.257208	−	0.383026i
$266$	−6.07462	+	10.5216i	−0.0228369	+	0.0395547i
$267$	−41.2327	−	53.6079i	−0.154429	−	0.200779i
$268$	254.243	+	68.1242i	0.948668	+	0.254195i
$269$			146.927i			0.546197i	0.961986	+	0.273099i	$0.0880485\pi$
$269$			146.927i			0.546197i	−0.961986	+	0.273099i	$0.911951\pi$
$270$	24.2952	−	8.27802i	0.0899822	−	0.0306593i
$271$	−45.0155			−0.166109			−0.0830544	−	0.996545i	$-0.526468\pi$
$271$	−45.0155			−0.166109			−0.0830544	+	0.996545i	$0.526468\pi$
$272$	4.22056	−	15.7513i	0.0155168	−	0.0579094i
$273$	−287.187	+	220.891i	−1.05197	+	0.809124i
$274$	32.2802	+	18.6370i	0.117811	+	0.0680182i
$275$	−278.314	−	215.602i	−1.01205	−	0.784008i
$276$	89.9973	+	216.569i	0.326077	+	0.784671i
$277$	−41.0870	+	153.339i	−0.148329	+	0.553570i	0.851256	+	0.524751i	$0.175841\pi$
$277$	−41.0870	+	153.339i	−0.148329	+	0.553570i	−0.999585	+	0.0288193i	$0.990825\pi$
$278$	12.8126	−	12.8126i	0.0460885	−	0.0460885i
$279$	−166.841	−	166.076i	−0.597996	−	0.595256i
$280$	44.8664	+	51.3987i	0.160237	+	0.183567i
$281$	−33.0937	−	57.3199i	−0.117771	−	0.203986i	0.801113	−	0.598513i	$-0.204242\pi$
$281$	−33.0937	−	57.3199i	−0.117771	−	0.203986i	−0.918884	+	0.394528i	$0.870908\pi$
$282$	−30.3760	+	4.03456i	−0.107716	+	0.0143069i
$283$	−104.177	−	388.793i	−0.368116	−	1.37383i	−0.863148	−	0.504952i	$-0.831510\pi$
$283$	−104.177	−	388.793i	−0.368116	−	1.37383i	0.495032	−	0.868875i	$-0.335156\pi$
$284$	−124.929	−	72.1278i	−0.439891	−	0.253971i
$285$	−79.8853	−	70.2210i	−0.280299	−	0.246390i
$286$	17.9397	+	31.0726i	0.0627264	+	0.108645i
$287$	−459.310	−	459.310i	−1.60038	−	1.60038i
$288$	−0.186335	−	81.1460i	−0.000646996	−	0.281757i
$289$		−	287.903i		−	0.996203i
$290$	2.98777	+	6.09395i	0.0103027	+	0.0210136i
$291$	−40.1880	−	96.7081i	−0.138103	−	0.332330i
$292$	15.7563	−	4.22190i	0.0539600	−	0.0144586i
$293$	56.1985	+	209.736i	0.191804	+	0.715821i	0.993071	+	0.117515i	$0.0374927\pi$
$293$	56.1985	+	209.736i	0.191804	+	0.715821i	−0.801267	+	0.598306i	$0.795841\pi$
$294$	2.37752	−	18.2207i	0.00808682	−	0.0619752i
$295$	−150.450	−	51.4577i	−0.509999	−	0.174433i
$296$	−49.2820			−0.166493
$297$	230.423	−	302.444i	0.775833	−	1.01833i
$298$	34.9809	−	34.9809i	0.117386	−	0.117386i
$299$	−228.886	+	132.147i	−0.765504	+	0.441964i
$300$	−257.972	+	147.753i	−0.859908	+	0.492510i
$301$	56.2051	−	97.3500i	0.186728	−	0.323422i
$302$	−47.3490	+	12.6871i	−0.156785	+	0.0420103i
$303$	164.871	+	68.0699i	0.544127	+	0.224653i
$304$	−95.5965	+	55.1926i	−0.314462	+	0.181555i
$305$	267.857	+	306.855i	0.878218	+	1.00608i
$306$	0.467880	+	1.73025i	0.00152902	+	0.00565441i
$307$	−219.096	−	219.096i	−0.713666	−	0.713666i	0.253634	−	0.967300i	$-0.418374\pi$
$307$	−219.096	−	219.096i	−0.713666	−	0.713666i	−0.967300	+	0.253634i	$0.918374\pi$
$308$	485.907	+	130.198i	1.57762	+	0.422722i
$309$	−187.476	−	143.513i	−0.606717	−	0.464445i
$310$	−20.6425	−	13.8618i	−0.0665888	−	0.0447155i
$311$	−68.8478	+	119.248i	−0.221376	+	0.383434i	−0.955226	−	0.295877i	$-0.904388\pi$
$311$	−68.8478	+	119.248i	−0.221376	+	0.383434i	0.733850	+	0.679311i	$0.237721\pi$
$312$	60.3424	−	8.01473i	0.193405	−	0.0256882i
$313$	−6.37451	−	1.70804i	−0.0203658	−	0.00545701i	0.248622	−	0.968601i	$-0.420022\pi$
$313$	−6.37451	−	1.70804i	−0.0203658	−	0.00545701i	−0.268988	+	0.963144i	$0.586689\pi$
$314$		−	8.83713i		−	0.0281437i
$315$	384.017	+	130.359i	1.21910	+	0.413839i
$316$	−329.010			−1.04117
$317$	−114.489	+	427.280i	−0.361165	+	1.34789i	0.511381	+	0.859354i	$0.329134\pi$
$317$	−114.489	+	427.280i	−0.361165	+	1.34789i	−0.872546	+	0.488532i	$0.837533\pi$
$318$	12.8916	+	5.32255i	0.0405397	+	0.0167376i
$319$	87.0704	+	50.2701i	0.272948	+	0.157587i
$320$	58.3851	+	297.097i	0.182453	+	0.928429i
$321$	213.237	+	27.8241i	0.664290	+	0.0866796i
$322$	8.74588	−	32.6401i	0.0271611	−	0.101367i
$323$	5.25206	−	5.25206i	0.0162603	−	0.0162603i
$324$	−161.811	−	277.316i	−0.499418	−	0.855915i
$325$	−202.724	−	266.731i	−0.623767	−	0.820711i
$326$	−10.3293	−	17.8909i	−0.0316849	−	0.0548799i
$327$	87.4936	+	113.753i	0.267565	+	0.347869i
$328$	28.2459	+	105.415i	0.0861156	+	0.321388i
$329$	−419.296	−	242.081i	−1.27446	−	0.735808i
$330$	17.8041	−	35.9983i	0.0539519	−	0.109086i
$331$	−130.851	−	226.641i	−0.395321	−	0.684716i	0.597821	−	0.801630i	$-0.296033\pi$
$331$	−130.851	−	226.641i	−0.395321	−	0.684716i	−0.993142	+	0.116913i	$0.962700\pi$
$332$	149.090	+	149.090i	0.449067	+	0.449067i
$333$	−253.352	+	147.050i	−0.760817	+	0.441590i
$334$			59.2964i			0.177534i
$335$	298.113	−	146.160i	0.889889	−	0.436299i
$336$	255.834	−	334.204i	0.761412	−	0.994654i
$337$	140.831	−	37.7355i	0.417895	−	0.111975i	−0.0437433	−	0.999043i	$-0.513928\pi$
$337$	140.831	−	37.7355i	0.417895	−	0.111975i	0.461639	+	0.887068i	$0.347262\pi$
$338$	0.521020	+	1.94447i	0.00154148	+	0.00575288i
$339$	415.103	+	317.763i	1.22449	+	0.937354i
$340$	−9.13929	−	18.6408i	−0.0268803	−	0.0548258i
$341$	−368.341			−1.08018
$342$	6.04239	−	10.5214i	0.0176678	−	0.0307645i
$343$	−106.954	+	106.954i	−0.311820	+	0.311820i
$344$	−16.3559	+	9.44310i	−0.0475463	+	0.0274509i
$345$	265.170	+	131.148i	0.768607	+	0.380140i
$346$	18.9580	−	32.8363i	0.0547920	−	0.0949025i
$347$	9.77990	−	2.62052i	0.0281842	−	0.00755192i	−0.244699	−	0.969599i	$-0.578689\pi$
$347$	9.77990	−	2.62052i	0.0281842	−	0.00755192i	0.272884	+	0.962047i	$0.412023\pi$
$348$	67.2964	−	51.7612i	0.193380	−	0.148739i
$349$	−94.1070	+	54.3327i	−0.269648	+	0.155681i	−0.628727	−	0.777626i	$-0.716424\pi$
$349$	−94.1070	+	54.3327i	−0.269648	+	0.155681i	0.359080	+	0.933307i	$0.383091\pi$
$350$	42.4423	+	5.78670i	0.121264	+	0.0165334i
$351$	286.297	−	221.255i	0.815662	−	0.630355i
$352$	−89.7803	−	89.7803i	−0.255058	−	0.255058i
$353$	−467.133	−	125.168i	−1.32332	−	0.354583i	−0.473101	−	0.881008i	$-0.656865\pi$
$353$	−467.133	−	125.168i	−1.32332	−	0.354583i	−0.850221	+	0.526425i	$0.823532\pi$
$354$	2.34691	−	17.9861i	0.00662968	−	0.0508082i
$355$	−178.549	+	35.0881i	−0.502954	+	0.0988399i
$356$	−44.6798	+	77.3877i	−0.125505	+	0.217381i
$357$	−10.8076	+	26.1769i	−0.0302735	+	0.0733246i
$358$	−46.6681	−	12.5047i	−0.130358	−	0.0349293i
$359$			279.063i			0.777333i	0.921378	+	0.388667i	$0.127064\pi$
$359$			279.063i			0.777333i	−0.921378	+	0.388667i	$0.872936\pi$
$360$	−44.9244	−	51.2272i	−0.124790	−	0.142298i
$361$	310.722			0.860724
$362$	−11.6621	+	43.5237i	−0.0322159	+	0.120231i
$363$	−30.5363	−	229.906i	−0.0841220	−	0.633350i
$364$	414.580	+	239.358i	1.13896	+	0.657576i
$365$	11.4709	−	17.0821i	0.0314271	−	0.0468001i
$366$	−28.2434	+	36.8952i	−0.0771678	+	0.100806i
$367$	46.2339	−	172.547i	0.125978	−	0.470156i	−0.873895	−	0.486115i	$-0.838414\pi$
$367$	46.2339	−	172.547i	0.125978	−	0.470156i	0.999873	+	0.0159593i	$0.00508022\pi$
$368$	217.097	−	217.097i	0.589938	−	0.589938i
$369$	459.750	+	457.643i	1.24594	+	1.24023i
$370$	−23.3097	+	20.3472i	−0.0629991	+	0.0549925i
$371$	110.184	+	190.844i	0.296992	+	0.514406i
$372$	−118.701	+	287.502i	−0.319087	+	0.772854i
$373$	−22.7204	−	84.7938i	−0.0609127	−	0.227329i	0.928758	−	0.370685i	$-0.120877\pi$
$373$	−22.7204	−	84.7938i	−0.0609127	−	0.227329i	−0.989671	+	0.143356i	$0.954211\pi$
$374$	2.42880	+	1.40227i	0.00649412	+	0.00374938i
$375$	−122.584	+	354.398i	−0.326891	+	0.945062i
$376$	40.6724	+	70.4466i	0.108171	+	0.187358i
$377$	67.6540	+	67.6540i	0.179453	+	0.179453i
$378$	−5.88035	+	45.8865i	−0.0155565	+	0.121393i
$379$			10.3793i			0.0273860i	0.999906	+	0.0136930i	$0.00435875\pi$
$379$			10.3793i			0.0273860i	−0.999906	+	0.0136930i	$0.995641\pi$
$380$	−45.4793	+	132.971i	−0.119682	+	0.349923i
$381$	−68.7136	−	8.96607i	−0.180351	−	0.0235330i
$382$	10.0257	−	2.68637i	0.0262452	−	0.00703238i
$383$	−33.3422	−	124.435i	−0.0870554	−	0.324895i	0.908640	−	0.417580i	$-0.137122\pi$
$383$	−33.3422	−	124.435i	−0.0870554	−	0.324895i	−0.995695	+	0.0926850i	$0.970455\pi$
$384$	−131.807	+	54.7734i	−0.343246	+	0.142639i
$385$	569.750	−	279.340i	1.47987	−	0.725558i
$386$	38.0686			0.0986233
$387$	−55.9068	+	97.3490i	−0.144462	+	0.251548i
$388$	−97.8443	+	97.8443i	−0.252176	+	0.252176i
$389$	635.357	−	366.824i	1.63331	−	0.942991i	0.650245	−	0.759724i	$-0.274666\pi$
$389$	635.357	−	366.824i	1.63331	−	0.942991i	0.983063	−	0.183267i	$-0.0586673\pi$
$390$	25.2320	−	28.7046i	0.0646975	−	0.0736016i
$391$	−10.3294	+	17.8910i	−0.0264178	+	0.0457570i
$392$	−47.1170	+	12.6250i	−0.120196	+	0.0322065i
$393$	−21.8075	−	164.187i	−0.0554898	−	0.417779i
$394$	4.31633	−	2.49203i	0.0109552	−	0.00632496i
$395$	−312.652	+	272.917i	−0.791525	+	0.690930i
$396$	−485.557	−	128.910i	−1.22615	−	0.325531i
$397$	151.257	+	151.257i	0.381000	+	0.381000i	0.871462	−	0.490463i	$-0.163172\pi$
$397$	151.257	+	151.257i	0.381000	+	0.381000i	−0.490463	+	0.871462i	$0.663172\pi$
$398$	−37.8459	−	10.1408i	−0.0950903	−	0.0254794i
$399$	177.028	−	73.5656i	0.443679	−	0.184375i
$400$	307.669	+	238.343i	0.769173	+	0.595858i
$401$	−3.27254	+	5.66821i	−0.00816096	+	0.0141352i	−0.870077	−	0.492916i	$-0.835931\pi$
$401$	−3.27254	+	5.66821i	−0.00816096	+	0.0141352i	0.861916	+	0.507051i	$0.169264\pi$
$402$	23.0910	+	30.0213i	0.0574402	+	0.0746799i
$403$	−338.581	−	90.7225i	−0.840151	−	0.225118i
$404$		−	235.677i		−	0.583360i
$405$	−383.804	−	129.305i	−0.947663	−	0.319271i
$406$	−12.2328			−0.0301302
$407$	−118.630	+	442.734i	−0.291475	+	1.08780i
$408$	3.77154	−	2.90089i	0.00924397	−	0.00711003i
$409$	−639.259	−	369.076i	−1.56298	−	0.902387i	−0.996953	−	0.0779993i	$-0.975147\pi$
$409$	−639.259	−	369.076i	−1.56298	−	0.902387i	−0.566026	−	0.824387i	$-0.691520\pi$
$410$	56.8830	+	38.1978i	0.138739	+	0.0931655i
$411$	−225.700	−	543.123i	−0.549148	−	1.32147i
$412$	−80.7400	+	301.326i	−0.195971	+	0.731373i
$413$	202.652	−	202.652i	0.490683	−	0.490683i
$414$	−8.65937	+	32.6166i	−0.0209163	+	0.0787840i
$415$	265.350	+	18.0060i	0.639398	+	0.0433879i
$416$	−60.4136	−	104.639i	−0.145225	−	0.251537i
$417$	−283.426	+	37.6448i	−0.679678	+	0.0902753i
$418$	−4.91354	−	18.3376i	−0.0117549	−	0.0438698i
$419$	235.376	+	135.894i	0.561756	+	0.324330i	0.753850	−	0.657047i	$-0.228195\pi$
$419$	235.376	+	135.894i	0.561756	+	0.324330i	−0.192094	+	0.981377i	$0.561528\pi$
$420$	−34.4273	−	534.726i	−0.0819697	−	1.27316i
$421$	102.996	+	178.395i	0.244647	+	0.423741i	0.962032	−	0.272936i	$-0.0879947\pi$
$421$	102.996	+	178.395i	0.244647	+	0.423741i	−0.717386	+	0.696676i	$0.754661\pi$
$422$	−32.6344	−	32.6344i	−0.0773327	−	0.0773327i
$423$	419.292	+	240.796i	0.991235	+	0.569259i
$424$		−	37.0244i		−	0.0873217i
$425$	−24.1477	−	10.1329i	−0.0568180	−	0.0238421i
$426$	−7.96553	−	19.1682i	−0.0186984	−	0.0449958i
$427$	−709.133	+	190.011i	−1.66073	+	0.444992i
$428$	−73.5396	−	274.453i	−0.171821	−	0.641246i
$429$	73.2528	−	561.390i	0.170752	−	1.30860i
$430$	−3.83731	+	11.2194i	−0.00892397	+	0.0260915i
$431$	−238.470			−0.553294			−0.276647	−	0.960972i	$-0.589223\pi$
$431$	−238.470			−0.553294			−0.276647	+	0.960972i	$0.589223\pi$
$432$	−254.727	+	334.345i	−0.589645	+	0.773946i
$433$	79.6977	−	79.6977i	0.184059	−	0.184059i	−0.609063	−	0.793122i	$-0.708454\pi$
$433$	79.6977	−	79.6977i	0.184059	−	0.184059i	0.793122	+	0.609063i	$0.208454\pi$
$434$	38.8122	−	22.4083i	0.0894291	−	0.0516319i
$435$	21.0142	−	105.011i	0.0483084	−	0.241404i
$436$	94.8083	−	164.213i	0.217450	−	0.376635i
$437$	135.078	−	36.1940i	0.309103	−	0.0828238i
$438$	2.16957	+	0.895748i	0.00495336	+	0.00204509i
$439$	−280.123	+	161.729i	−0.638094	+	0.368404i	−0.783880	−	0.620912i	$-0.786762\pi$
$439$	−280.123	+	161.729i	−0.638094	+	0.368404i	0.145786	+	0.989316i	$0.453429\pi$
$440$	−106.366	−	7.21774i	−0.241741	−	0.0164039i
$441$	−204.551	+	205.492i	−0.463834	+	0.465969i
$442$	1.88719	+	1.88719i	0.00426965	+	0.00426965i
$443$	−729.682	−	195.518i	−1.64714	−	0.441349i	−0.688328	−	0.725400i	$-0.741655\pi$
$443$	−729.682	−	195.518i	−1.64714	−	0.441349i	−0.958809	+	0.284051i	$0.908322\pi$
$444$	307.338	+	235.268i	0.692202	+	0.529884i
$445$	21.7355	+	110.603i	0.0488438	+	0.248545i
$446$	19.5609	−	33.8805i	0.0438585	−	0.0759652i
$447$	−773.808	+	102.778i	−1.73111	+	0.229928i
$448$	−527.135	−	141.245i	−1.17664	−	0.315280i
$449$		−	514.733i		−	1.14640i	−0.819416	−	0.573199i	$-0.805702\pi$
$449$		−	514.733i		−	1.14640i	0.819416	−	0.573199i	$-0.194298\pi$
$450$	−42.3989	−	5.68165i	−0.0942198	−	0.0126259i
$451$	1015.01			2.25057
$452$	178.772	−	667.186i	0.395513	−	1.47607i
$453$	714.945	+	295.179i	1.57825	+	0.651609i
$454$	−30.6524	−	17.6972i	−0.0675162	−	0.0389805i
$455$	592.518	−	116.441i	1.30224	−	0.255914i
$456$	−31.9379	−	4.16741i	−0.0700393	−	0.00913905i
$457$	147.494	−	550.455i	0.322744	−	1.20450i	−0.593816	−	0.804601i	$-0.702379\pi$
$457$	147.494	−	550.455i	0.322744	−	1.20450i	0.916560	−	0.399897i	$-0.130954\pi$
$458$	−24.3261	+	24.3261i	−0.0531137	+	0.0531137i
$459$	10.7332	−	26.1667i	0.0233838	−	0.0570081i
$460$	26.4629	−	389.977i	0.0575280	−	0.847777i
$461$	−119.334	−	206.693i	−0.258860	−	0.448358i	0.707077	−	0.707137i	$-0.250013\pi$
$461$	−119.334	−	206.693i	−0.258860	−	0.448358i	−0.965937	+	0.258778i	$0.916680\pi$
$462$	44.1312	+	57.3764i	0.0955222	+	0.124191i
$463$	213.508	+	796.822i	0.461140	+	1.72100i	0.669380	+	0.742921i	$0.266560\pi$
$463$	213.508	+	796.822i	0.461140	+	1.72100i	−0.208239	+	0.978078i	$0.566773\pi$
$464$	−96.2543	−	55.5724i	−0.207445	−	0.119768i
$465$	125.687	+	371.671i	0.270294	+	0.799293i
$466$	16.1635	+	27.9961i	0.0346857	+	0.0600774i
$467$	489.265	+	489.265i	1.04768	+	1.04768i	0.998805	+	0.0488707i	$0.0155622\pi$
$467$	489.265	+	489.265i	1.04768	+	1.04768i	0.0488707	+	0.998805i	$0.484438\pi$
$468$	−414.576	−	238.088i	−0.885845	−	0.508734i
$469$			598.424i			1.27596i
$470$	48.3229	+	16.5277i	0.102815	+	0.0351653i
$471$	−84.7602	+	110.725i	−0.179958	+	0.235084i
$472$	−46.5102	+	12.4624i	−0.0985386	+	0.0264033i
$473$	45.4623	+	169.667i	0.0961147	+	0.358705i
$474$	−37.5922	−	28.7770i	−0.0793085	−	0.0607110i
$475$	67.0823	+	164.085i	0.141226	+	0.345443i
$476$	37.4190			0.0786114
$477$	−110.475	−	190.337i	−0.231603	−	0.399030i
$478$	51.5572	−	51.5572i	0.107860	−	0.107860i
$479$	−142.795	+	82.4426i	−0.298110	+	0.172114i	−0.641594	−	0.767045i	$-0.721726\pi$
$479$	−142.795	+	82.4426i	−0.298110	+	0.172114i	0.343483	+	0.939159i	$0.388393\pi$
$480$	−59.9569	+	121.227i	−0.124910	+	0.252556i
$481$	−218.091	+	377.744i	−0.453411	+	0.785331i
$482$	59.8478	−	16.0362i	0.124165	−	0.0332700i
$483$	−422.645	+	325.078i	−0.875041	+	0.673040i
$484$	−265.384	+	153.220i	−0.548314	+	0.316569i
$485$	−11.8169	+	174.143i	−0.0243647	+	0.359057i
$486$	5.76728	−	45.8387i	0.0118668	−	0.0943184i
$487$	326.960	+	326.960i	0.671376	+	0.671376i	0.958033	−	0.286657i	$-0.0925441\pi$
$487$	326.960	+	326.960i	0.671376	+	0.671376i	−0.286657	+	0.958033i	$0.592544\pi$
$488$	119.142	+	31.9241i	0.244144	+	0.0654183i
$489$	−42.1772	+	323.235i	−0.0862520	+	0.661013i
$490$	−17.0731	+	25.4247i	−0.0348431	+	0.0518872i
$491$	−182.011	+	315.253i	−0.370695	+	0.642063i	−0.989673	−	0.143346i	$-0.954214\pi$
$491$	−182.011	+	315.253i	−0.370695	+	0.642063i	0.618977	+	0.785409i	$0.287547\pi$
$492$	327.094	−	792.245i	0.664824	−	1.61025i
$493$	7.22382	+	1.93562i	0.0146528	+	0.00392620i
$494$		−	18.0662i		−	0.0365713i
$495$	−568.350	+	280.274i	−1.14818	+	0.566209i
$496$	407.193			0.820953
$497$	84.8853	−	316.796i	0.170795	−	0.637417i
$498$	3.99460	+	30.0751i	0.00802129	+	0.0603918i
$499$	353.578	+	204.138i	0.708573	+	0.409095i	0.810532	−	0.585694i	$-0.199178\pi$
$499$	353.578	+	204.138i	0.708573	+	0.409095i	−0.101960	+	0.994789i	$0.532511\pi$
$500$	494.633	−	28.9882i	0.989266	−	0.0579764i
$501$	568.734	−	742.953i	1.13520	−	1.48294i
$502$	21.1072	−	78.7732i	0.0420463	−	0.156919i
$503$	555.921	−	555.921i	1.10521	−	1.10521i	0.111440	−	0.993771i	$-0.464454\pi$
$503$	555.921	−	555.921i	1.10521	−	1.10521i	0.993771	−	0.111440i	$-0.0355462\pi$
$504$	118.549	−	32.0571i	0.235217	−	0.0636055i
$505$	−195.497	−	223.960i	−0.387123	−	0.443486i
$506$	26.4014	+	45.7286i	0.0521767	+	0.0903726i
$507$	12.1221	−	29.3606i	0.0239094	−	0.0579104i
$508$	23.6974	+	88.4400i	0.0466485	+	0.174095i
$509$	−453.968	−	262.098i	−0.891882	−	0.514928i	−0.0173243	−	0.999850i	$-0.505515\pi$
$509$	−453.968	−	262.098i	−0.891882	−	0.514928i	−0.874558	+	0.484922i	$0.838848\pi$
$510$	0.586183	−	2.92925i	0.00114938	−	0.00574362i
$511$	18.5432	+	32.1178i	0.0362881	+	0.0628528i
$512$	165.919	+	165.919i	0.324061	+	0.324061i
$513$	−176.623	+	73.8735i	−0.344295	+	0.144003i
$514$		−	70.0445i		−	0.136273i
$515$	173.227	+	353.320i	0.336363	+	0.686057i
$516$	147.081	+	19.1918i	0.285041	+	0.0371935i
$517$	730.775	−	195.811i	1.41349	−	0.378744i
$518$	−14.4339	−	53.8679i	−0.0278646	−	0.103992i
$519$	−552.479	+	229.588i	−1.06451	+	0.442366i
$520$	−95.9944	−	32.8325i	−0.184605	−	0.0631395i
$521$	−694.042			−1.33213			−0.666067	−	0.745892i	$-0.732023\pi$
$521$	−694.042			−1.33213			−0.666067	+	0.745892i	$0.732023\pi$
$522$	12.2165	−	0.0280527i	0.0234033	−	5.37408e-5i
$523$	244.233	−	244.233i	0.466985	−	0.466985i	−0.433951	−	0.900936i	$-0.642881\pi$
$523$	244.233	−	244.233i	0.466985	−	0.466985i	0.900936	+	0.433951i	$0.142881\pi$
$524$	−189.524	+	109.422i	−0.361687	+	0.208820i
$525$	−476.277	−	479.584i	−0.907195	−	0.913493i
$526$	−6.27198	+	10.8634i	−0.0119239	+	0.0206528i
$527$	−26.4653	+	7.09137i	−0.0502189	+	0.0134561i
$528$	86.5925	+	651.950i	0.164001	+	1.23475i
$529$	121.283	−	70.0227i	0.229268	−	0.132368i
$530$	−15.2864	−	17.5120i	−0.0288422	−	0.0330415i
$531$	−201.917	+	202.846i	−0.380258	+	0.382008i
$532$	−179.108	−	179.108i	−0.336669	−	0.336669i
$533$	933.001	+	249.997i	1.75047	+	0.469037i
$534$	−11.8738	+	4.93428i	−0.0222356	+	0.00924022i
$535$	−297.546	−	199.807i	−0.556160	−	0.373470i
$536$	50.2711	−	87.0720i	0.0937893	−	0.162448i
$537$	464.790	+	604.288i	0.865531	+	1.12530i
$538$	26.9825	+	7.22994i	0.0501534	+	0.0134386i
$539$			453.674i			0.841696i
$540$	35.6076	+	533.934i	0.0659400	+	0.988767i
$541$	−682.588			−1.26172			−0.630858	−	0.775899i	$-0.717297\pi$
$541$	−682.588			−1.26172			−0.630858	+	0.775899i	$0.717297\pi$
$542$	−2.21511	+	8.26689i	−0.00408691	+	0.0152526i
$543$	563.573	−	433.474i	1.03789	−	0.798294i
$544$	−8.17918	−	4.72225i	−0.0150353	−	0.00868061i
$545$	−46.1216	−	234.693i	−0.0846267	−	0.430630i
$546$	26.4338	+	63.6102i	0.0484136	+	0.116502i
$547$	−16.7386	+	62.4694i	−0.0306008	+	0.114204i	−0.979537	−	0.201265i	$-0.935495\pi$
$547$	−16.7386	+	62.4694i	−0.0306008	+	0.114204i	0.948936	+	0.315468i	$0.102162\pi$
$548$	−549.504	+	549.504i	−1.00275	+	1.00275i
$549$	707.751	−	191.384i	1.28916	−	0.348605i
$550$	−53.2896	+	40.5018i	−0.0968901	+	0.0736396i
$551$	−25.3122	−	43.8421i	−0.0459387	−	0.0795682i
$552$	88.8042	−	11.7950i	0.160877	−	0.0213678i
$553$	−193.601	−	722.530i	−0.350093	−	1.30656i
$554$	26.1382	+	15.0909i	0.0471809	+	0.0272399i
$555$	487.216	−	31.3684i	0.877866	−	0.0565196i
$556$	188.887	+	327.162i	0.339725	+	0.588421i
$557$	−66.9124	−	66.9124i	−0.120130	−	0.120130i	0.644486	−	0.764616i	$-0.277071\pi$
$557$	−66.9124	−	66.9124i	−0.120130	−	0.120130i	−0.764616	+	0.644486i	$0.777071\pi$
$558$	−38.7091	+	22.4674i	−0.0693711	+	0.0402641i
$559$			167.156i			0.299028i
$560$	−629.845	+	308.804i	−1.12472	+	0.551435i
$561$	−16.9819	−	40.8652i	−0.0302708	−	0.0728436i
$562$	−12.1550	+	3.25693i	−0.0216282	+	0.00579525i
$563$	36.8258	+	137.436i	0.0654099	+	0.244113i	0.990888	−	0.134688i	$-0.0430032\pi$
$563$	36.8258	+	137.436i	0.0654099	+	0.244113i	−0.925478	+	0.378801i	$0.876337\pi$
$564$	82.6612	−	633.493i	0.146562	−	1.12322i
$565$	−383.554	−	782.309i	−0.678857	−	1.38462i
$566$	−76.5264			−0.135206
$567$	513.792	−	518.533i	0.906159	−	0.914521i
$568$	−38.9637	+	38.9637i	−0.0685981	+	0.0685981i
$569$	−276.828	+	159.827i	−0.486517	+	0.280891i	−0.723128	−	0.690714i	$-0.757297\pi$
$569$	−276.828	+	159.827i	−0.486517	+	0.280891i	0.236611	+	0.971604i	$0.423963\pi$
$570$	−16.8268	+	11.2152i	−0.0295206	+	0.0196758i
$571$	−324.309	+	561.720i	−0.567967	+	0.983748i	0.428800	+	0.903400i	$0.358937\pi$
$571$	−324.309	+	561.720i	−0.567967	+	0.983748i	−0.996767	+	0.0803483i	$0.974397\pi$
$572$	−722.555	+	193.608i	−1.26321	+	0.338475i
$573$	−151.382	−	62.5011i	−0.264193	−	0.109077i
$574$	−106.952	+	61.7486i	−0.186327	+	0.107576i
$575$	−298.343	−	392.540i	−0.518858	−	0.682679i
$576$	526.756	+	139.848i	0.914506	+	0.242792i
$577$	−519.616	−	519.616i	−0.900548	−	0.900548i	0.0949353	−	0.995483i	$-0.469736\pi$
$577$	−519.616	−	519.616i	−0.900548	−	0.900548i	−0.995483	+	0.0949353i	$0.969736\pi$
$578$	−52.8721	−	14.1670i	−0.0914742	−	0.0245104i
$579$	−476.980	−	365.130i	−0.823800	−	0.630622i
$580$	−138.844	+	27.2855i	−0.239387	+	0.0470440i
$581$	−239.683	+	415.144i	−0.412536	+	0.714533i
$582$	−19.7376	+	2.62156i	−0.0339134	+	0.00450440i
$583$	−332.615	−	89.1240i	−0.570523	−	0.152871i
$584$		−	6.23095i		−	0.0106694i
$585$	−591.461	+	117.644i	−1.01104	+	0.201101i
$586$	41.2824			0.0704478
$587$	213.739	−	797.684i	0.364120	−	1.35892i	−0.504489	−	0.863418i	$-0.668319\pi$
$587$	213.739	−	797.684i	0.364120	−	1.35892i	0.868609	−	0.495498i	$-0.165014\pi$
$588$	354.106	+	146.200i	0.602222	+	0.248639i
$589$	160.621	+	92.7344i	0.272701	+	0.157444i
$590$	−16.8533	+	25.0973i	−0.0285649	+	0.0425379i
$591$	−77.9834	−	10.1756i	−0.131952	−	0.0172177i
$592$	131.143	−	489.432i	0.221525	−	0.826743i
$593$	329.014	−	329.014i	0.554829	−	0.554829i	−0.373002	−	0.927831i	$-0.621671\pi$
$593$	329.014	−	329.014i	0.554829	−	0.554829i	0.927831	+	0.373002i	$0.121671\pi$
$594$	−44.2039	−	57.1987i	−0.0744174	−	0.0962941i
$595$	35.5587	−	31.0395i	0.0597625	−	0.0521672i
$596$	515.699	+	893.218i	0.865267	+	1.49869i
$597$	376.926	+	490.053i	0.631366	+	0.820860i
$598$	13.0053	+	48.5366i	0.0217480	+	0.0811648i
$599$	−445.587	−	257.260i	−0.743885	−	0.429482i	0.0795952	−	0.996827i	$-0.474637\pi$
$599$	−445.587	−	257.260i	−0.743885	−	0.429482i	−0.823480	+	0.567345i	$0.807971\pi$
$600$	29.0116	+	109.791i	0.0483526	+	0.182984i
$601$	−19.7478	−	34.2041i	−0.0328582	−	0.0569121i	0.849129	−	0.528186i	$-0.177128\pi$
$601$	−19.7478	−	34.2041i	−0.0328582	−	0.0569121i	−0.881987	+	0.471274i	$0.843794\pi$
$602$	−15.1122	−	15.1122i	−0.0251033	−	0.0251033i
$603$	−1.37232	−	597.626i	−0.00227583	−	0.991087i
$604$		−	1021.99i		−	1.69204i
$605$	−125.093	+	365.741i	−0.206765	+	0.604531i
$606$	20.6137	−	26.9282i	0.0340159	−	0.0444360i
$607$	−390.594	+	104.659i	−0.643483	+	0.172421i	−0.565781	−	0.824556i	$-0.691425\pi$
$607$	−390.594	+	104.659i	−0.643483	+	0.172421i	−0.0777026	+	0.996977i	$0.524758\pi$
$608$	16.5468	+	61.7533i	0.0272151	+	0.101568i
$609$	153.271	+	117.330i	0.251677	+	0.192660i
$610$	69.5332	−	34.0911i	0.113989	−	0.0558870i
$611$	719.960			1.17833
$612$	−37.3691	+	0.0858104i	−0.0610606	+	0.000140213i
$613$	−559.593	+	559.593i	−0.912876	+	0.912876i	−0.996498	−	0.0836213i	$-0.973351\pi$
$613$	−559.593	+	559.593i	−0.912876	+	0.912876i	0.0836213	+	0.996498i	$0.473351\pi$
$614$	−51.0172	+	29.4548i	−0.0830898	+	0.0479719i
$615$	−346.345	−	1024.19i	−0.563162	−	1.66534i
$616$	96.0775	−	166.411i	0.155970	−	0.270148i
$617$	−337.484	+	90.4285i	−0.546976	+	0.146562i	−0.521716	−	0.853119i	$-0.674708\pi$
$617$	−337.484	+	90.4285i	−0.546976	+	0.146562i	−0.0252596	+	0.999681i	$0.508041\pi$
$618$	−35.5809	+	27.3671i	−0.0575742	+	0.0442834i
$619$	384.591	−	222.044i	0.621311	−	0.358714i	−0.156068	−	0.987746i	$-0.549882\pi$
$619$	384.591	−	222.044i	0.621311	−	0.358714i	0.777379	+	0.629032i	$0.216549\pi$
$620$	390.542	−	340.908i	0.629907	−	0.549852i
$621$	421.335	−	325.614i	0.678479	−	0.524338i
$622$	18.5115	+	18.5115i	0.0297613	+	0.0297613i
$623$	−196.241	−	52.5825i	−0.314993	−	0.0844021i
$624$	−80.9792	+	620.603i	−0.129774	+	0.994557i
$625$	445.995	−	437.850i	0.713593	−	0.700561i
$626$	−0.627350	+	1.08660i	−0.00100216	+	0.00173579i
$627$	−114.319	+	276.888i	−0.182326	+	0.441608i
$628$	177.965	+	47.6857i	0.283384	+	0.0759326i
$629$			34.0943i			0.0542040i
$630$	42.8365	−	64.1084i	0.0679945	−	0.101759i
$631$	−181.428			−0.287524			−0.143762	−	0.989612i	$-0.545920\pi$
$631$	−181.428			−0.287524			−0.143762	+	0.989612i	$0.545920\pi$
$632$	−32.5273	+	121.393i	−0.0514672	+	0.192078i
$633$	95.8834	+	721.901i	0.151475	+	1.14044i
$634$	72.8343	+	42.0509i	0.114881	+	0.0663264i
$635$	95.8813	+	64.3858i	0.150994	+	0.101395i
$636$	−176.751	+	230.895i	−0.277911	+	0.363043i
$637$	−111.740	+	417.019i	−0.175416	+	0.654661i
$638$	13.5164	−	13.5164i	0.0211856	−	0.0211856i
$639$	−84.0456	+	316.568i	−0.131527	+	0.495412i
$640$	237.345	+	16.1056i	0.370851	+	0.0251650i
$641$	44.3645	+	76.8416i	0.0692114	+	0.119878i	0.898554	−	0.438862i	$-0.144618\pi$
$641$	44.3645	+	76.8416i	0.0692114	+	0.119878i	−0.829343	+	0.558740i	$0.811285\pi$
$642$	15.6027	−	37.7909i	0.0243032	−	0.0588643i
$643$	111.166	+	414.879i	0.172887	+	0.645224i	0.996902	+	0.0786553i	$0.0250626\pi$
$643$	111.166	+	414.879i	0.172887	+	0.645224i	−0.824015	+	0.566568i	$0.808271\pi$
$644$	610.125	+	352.256i	0.947399	+	0.546981i
$645$	155.689	−	103.768i	0.241378	−	0.160880i
$646$	−0.706077	−	1.22296i	−0.00109300	−	0.00189313i
$647$	237.290	+	237.290i	0.366755	+	0.366755i	0.866292	−	0.499537i	$-0.166497\pi$
$647$	237.290	+	237.290i	0.366755	+	0.366755i	−0.499537	+	0.866292i	$0.666497\pi$
$648$	−118.318	+	32.2862i	−0.182589	+	0.0498244i
$649$			447.832i			0.690034i
$650$	−58.9596	+	24.1042i	−0.0907071	+	0.0370834i
$651$	−701.223	−	91.4988i	−1.07715	−	0.140551i
$652$	416.030	−	111.475i	0.638083	−	0.170974i
$653$	208.275	+	777.291i	0.318950	+	1.19034i	0.920255	+	0.391319i	$0.127981\pi$
$653$	208.275	+	777.291i	0.318950	+	1.19034i	−0.601305	+	0.799020i	$0.705352\pi$
$654$	25.1956	−	10.4703i	0.0385255	−	0.0160096i
$655$	−89.3349	+	261.194i	−0.136389	+	0.398769i
$656$	−1122.07			−1.71047
$657$	−18.5921	−	32.0324i	−0.0282985	−	0.0487556i
$658$	−65.0897	+	65.0897i	−0.0989206	+	0.0989206i
$659$	407.245	−	235.123i	0.617974	−	0.356787i	−0.158106	−	0.987422i	$-0.550539\pi$
$659$	407.245	−	235.123i	0.617974	−	0.356787i	0.776080	+	0.630635i	$0.217205\pi$
$660$	628.875	+	552.795i	0.952840	+	0.837568i
$661$	379.580	−	657.451i	0.574251	−	0.994631i	−0.421872	−	0.906655i	$-0.638627\pi$
$661$	379.580	−	657.451i	0.574251	−	0.994631i	0.996123	−	0.0879760i	$-0.0280399\pi$
$662$	−48.0606	+	12.8778i	−0.0725990	+	0.0194528i
$663$	−5.54476	−	41.7462i	−0.00836313	−	0.0629656i
$664$	69.7489	−	40.2696i	0.105044	−	0.0606469i
$665$	−318.775	−	21.6313i	−0.479361	−	0.0325283i
$666$	14.5381	+	53.7630i	0.0218290	+	0.0807252i
$667$	99.5643	+	99.5643i	0.149272	+	0.149272i
$668$	−1194.13	−	319.967i	−1.78762	−	0.478992i
$669$	−570.048	+	236.889i	−0.852090	+	0.354094i
$670$	−12.1722	−	61.9393i	−0.0181675	−	0.0924468i
$671$	573.592	−	993.490i	0.854832	−	1.48061i
$672$	−148.616	−	193.220i	−0.221154	−	0.287529i
$673$	1217.91	+	326.337i	1.80967	+	0.484899i	0.995418	−	0.0956152i	$-0.0304818\pi$
$673$	1217.91	+	326.337i	1.80967	+	0.484899i	0.814250	+	0.580514i	$0.197148\pi$
$674$		−	27.7198i		−	0.0411273i
$675$	476.742	+	477.852i	0.706284	+	0.707929i
$676$	−41.9700			−0.0620858
$677$	25.8294	−	96.3967i	0.0381528	−	0.142388i	−0.944222	−	0.329309i	$-0.893184\pi$
$677$	25.8294	−	96.3967i	0.0381528	−	0.142388i	0.982375	+	0.186921i	$0.0598509\pi$
$678$	78.7820	−	60.5954i	0.116198	−	0.0893738i
$679$	−272.449	−	157.298i	−0.401250	−	0.231662i
$680$	−7.78136	+	1.52918i	−0.0114432	+	0.00224880i
$681$	214.318	+	515.734i	0.314711	+	0.757319i
$682$	−18.1252	+	67.6443i	−0.0265766	+	0.0991852i
$683$	366.381	−	366.381i	0.536430	−	0.536430i	−0.386049	−	0.922478i	$-0.626160\pi$
$683$	366.381	−	366.381i	0.536430	−	0.536430i	0.922478	+	0.386049i	$0.126160\pi$
$684$	179.280	+	178.458i	0.262105	+	0.260904i
$685$	−66.3650	+	978.005i	−0.0968832	+	1.42774i
$686$	14.3787	+	24.9047i	0.0209602	+	0.0363042i
$687$	538.114	−	71.4727i	0.783281	−	0.104036i
$688$	−50.2575	−	187.563i	−0.0730486	−	0.272621i
$689$	−283.790	−	163.846i	−0.411887	−	0.237803i
$690$	37.1332	−	42.2437i	0.0538162	−	0.0612228i
$691$	−298.133	−	516.381i	−0.431451	−	0.747296i	0.565547	−	0.824716i	$-0.308665\pi$
$691$	−298.133	−	516.381i	−0.431451	−	0.747296i	−0.996999	+	0.0774204i	$0.975332\pi$
$692$	558.971	+	558.971i	0.807761	+	0.807761i
$693$	−2.62277	−	1142.18i	−0.00378466	−	1.64816i
$694$		−	1.92499i		−	0.00277376i
$695$	450.881	+	154.213i	0.648750	+	0.221889i
$696$	−12.4449	−	29.9474i	−0.0178806	−	0.0430279i
$697$	72.9284	−	19.5411i	0.104632	−	0.0280360i
$698$	5.34718	+	19.9559i	0.00766071	+	0.0285902i
$699$	66.0000	−	505.806i	0.0944206	−	0.723614i
$700$	−345.556	+	823.493i	−0.493651	+	1.17642i
$701$	147.235			0.210036			0.105018	−	0.994470i	$-0.466510\pi$
$701$	147.235			0.210036			0.105018	+	0.994470i	$0.466510\pi$
$702$	−26.5444	−	63.4647i	−0.0378126	−	0.0904056i
$703$	163.194	−	163.194i	0.232140	−	0.232140i
$704$	738.513	−	426.381i	1.04902	−	0.605654i
$705$	−446.938	−	670.567i	−0.633955	−	0.951159i
$706$	−45.9731	+	79.6277i	−0.0651177	+	0.112787i
$707$	517.565	−	138.681i	0.732058	−	0.196154i
$708$	349.546	+	144.317i	0.493710	+	0.203837i
$709$	123.232	−	71.1480i	0.173811	−	0.100350i	−0.410571	−	0.911829i	$-0.634670\pi$
$709$	123.232	−	71.1480i	0.173811	−	0.100350i	0.584382	+	0.811479i	$0.301337\pi$
$710$	−2.34219	+	34.5163i	−0.00329886	+	0.0486145i
$711$	195.000	+	721.122i	0.274262	+	1.01424i
$712$	24.1362	+	24.1362i	0.0338992	+	0.0338992i
$713$	−498.280	−	133.514i	−0.698849	−	0.187256i
$714$	4.27545	+	3.27288i	0.00598803	+	0.00458386i
$715$	−526.032	+	783.350i	−0.735709	+	1.09559i
$716$	503.648	−	872.343i	0.703418	−	1.21836i
$717$	−1140.49	+	151.481i	−1.59064	+	0.211270i
$718$	51.2486	+	13.7320i	0.0713769	+	0.0191254i
$719$			1075.81i			1.49626i	0.663555	+	0.748128i	$0.269047\pi$
$719$			1075.81i			1.49626i	−0.663555	+	0.748128i	$0.730953\pi$
$720$	628.297	−	309.836i	0.872635	−	0.430328i
$721$	−709.245			−0.983696
$722$	15.2899	−	57.0627i	0.0211771	−	0.0790342i
$723$	−903.670	−	373.097i	−1.24989	−	0.516041i
$724$	−813.567	−	469.713i	−1.12371	−	0.648775i
$725$	−109.308	+	141.102i	−0.150770	+	0.194623i
$726$	−43.7239	−	5.70530i	−0.0602257	−	0.00785853i
$727$	−186.556	+	696.238i	−0.256611	+	0.957687i	0.710576	+	0.703621i	$0.248435\pi$
$727$	−186.556	+	696.238i	−0.256611	+	0.957687i	−0.967187	+	0.254066i	$0.918232\pi$
$728$	129.302	−	129.302i	0.177613	−	0.177613i
$729$	−511.918	+	519.020i	−0.702219	+	0.711961i
$730$	−2.57259	−	2.94715i	−0.00352410	−	0.00403718i
$731$	6.53293	+	11.3154i	0.00893698	+	0.0154793i
$732$	−590.605	−	767.865i	−0.806838	−	1.04900i
$733$	−316.043	−	1179.49i	−0.431164	−	1.60913i	−0.750082	−	0.661345i	$-0.769986\pi$
$733$	−316.043	−	1179.49i	−0.431164	−	1.60913i	0.318918	−	0.947782i	$-0.396681\pi$
$734$	−29.4125	−	16.9813i	−0.0400715	−	0.0231353i
$735$	457.776	−	154.804i	0.622824	−	0.210618i
$736$	−88.9088	−	153.995i	−0.120800	−	0.209232i
$737$	−661.216	−	661.216i	−0.897173	−	0.897173i
$738$	106.668	−	61.9115i	0.144536	−	0.0838910i
$739$			683.603i			0.925038i	0.886609	+	0.462519i	$0.153054\pi$
$739$			683.603i			0.925038i	−0.886609	+	0.462519i	$0.846946\pi$
$740$	−283.980	−	579.214i	−0.383756	−	0.782721i
$741$	−173.280	+	226.360i	−0.233846	+	0.305479i
$742$	40.4697	−	10.8438i	0.0545413	−	0.0146143i
$743$	204.636	+	763.713i	0.275419	+	1.02788i	0.955560	+	0.294797i	$0.0952519\pi$
$743$	204.636	+	763.713i	0.275419	+	1.02788i	−0.680141	+	0.733081i	$0.738081\pi$
$744$	94.3431	+	72.2201i	0.126805	+	0.0970700i
$745$	1230.99	+	421.032i	1.65234	+	0.565143i
$746$	−16.6900			−0.0223727
$747$	238.412	−	415.140i	0.319159	−	0.555742i
$748$	−41.3454	+	41.3454i	−0.0552746	+	0.0552746i
$749$	559.447	−	322.997i	0.746925	−	0.431238i
$750$	59.0516	+	39.9512i	0.0787355	+	0.0532683i
$751$	326.862	−	566.142i	0.435236	−	0.753851i	−0.562079	−	0.827084i	$-0.689998\pi$
$751$	326.862	−	566.142i	0.435236	−	0.753851i	0.997315	+	0.0732329i	$0.0233317\pi$
$752$	−807.855	+	216.464i	−1.07427	+	0.287851i
$753$	−1020.01	+	784.541i	−1.35459	+	1.04189i
$754$	15.7535	−	9.09526i	0.0208932	−	0.0120627i
$755$	−847.754	−	971.182i	−1.12285	−	1.28633i
$756$	−892.348	−	366.027i	−1.18035	−	0.484163i
$757$	668.868	+	668.868i	0.883577	+	0.883577i	0.993896	−	0.110319i	$-0.0351874\pi$
$757$	668.868	+	668.868i	0.883577	+	0.883577i	−0.110319	+	0.993896i	$0.535187\pi$
$758$	1.90611	+	0.510741i	0.00251466	+	0.000673800i
$759$	107.804	−	826.181i	0.142034	−	1.08851i
$760$	44.5654	+	29.9264i	0.0586386	+	0.0393768i
$761$	478.705	−	829.141i	0.629047	−	1.08954i	−0.358696	−	0.933454i	$-0.616779\pi$
$761$	478.705	−	829.141i	0.629047	−	1.08954i	0.987743	−	0.156087i	$-0.0498881\pi$
$762$	−5.02782	+	12.1778i	−0.00659819	+	0.0159813i
$763$	416.413	+	111.577i	0.545757	+	0.146235i
$764$			216.396i			0.283241i
$765$	−35.4401	+	31.0796i	−0.0463269	+	0.0406270i
$766$	−24.4926			−0.0319747
$767$	−110.301	+	411.649i	−0.143808	+	0.536700i
$768$	−92.1038	−	693.444i	−0.119927	−	0.902922i
$769$	435.970	+	251.708i	0.566932	+	0.327318i	0.755923	−	0.654661i	$-0.227188\pi$
$769$	435.970	+	251.708i	0.566932	+	0.327318i	−0.188991	+	0.981979i	$0.560522\pi$
$770$	−23.2634	−	118.378i	−0.0302123	−	0.153737i
$771$	−671.823	+	877.621i	−0.871365	+	1.13829i
$772$	−205.421	+	766.640i	−0.266089	+	0.993057i
$773$	−362.267	+	362.267i	−0.468651	+	0.468651i	−0.901477	−	0.432827i	$-0.857516\pi$
$773$	−362.267	+	362.267i	−0.468651	+	0.468651i	0.432827	+	0.901477i	$0.357516\pi$
$774$	15.1267	+	15.0574i	0.0195435	+	0.0194540i
$775$	88.3390	−	647.918i	0.113986	−	0.836024i
$776$	26.4279	+	45.7745i	0.0340566	+	0.0589878i
$777$	−335.819	+	813.378i	−0.432199	+	1.04682i
$778$	−36.1011	−	134.731i	−0.0464024	−	0.173176i
$779$	−442.610	−	255.541i	−0.568177	−	0.328037i
$780$	441.911	+	663.024i	0.566552	+	0.850030i
$781$	256.245	+	443.830i	0.328099	+	0.568284i
$782$	2.77732	+	2.77732i	0.00355155	+	0.00355155i
$783$	−153.336	−	116.822i	−0.195831	−	0.149198i
$784$		−	501.526i		−	0.639701i
$785$	208.673	−	102.309i	0.265826	−	0.130330i
$786$	−31.2254	−	4.07443i	−0.0397270	−	0.00518376i
$787$	−502.205	+	134.565i	−0.638126	+	0.170985i	−0.563354	−	0.826215i	$-0.690489\pi$
$787$	−502.205	+	134.565i	−0.638126	+	0.170985i	−0.0747716	+	0.997201i	$0.523823\pi$
$788$	26.8943	+	100.371i	0.0341299	+	0.127374i
$789$	182.779	−	75.9557i	0.231659	−	0.0962683i
$790$	34.7351	+	70.8469i	0.0439685	+	0.0896796i
$791$	1570.39			1.98532
$792$	−95.5677	+	166.409i	−0.120666	+	0.210113i
$793$	771.945	−	771.945i	0.973449	−	0.973449i
$794$	35.2207	−	20.3347i	0.0443585	−	0.0256104i
$795$	23.5663	+	366.033i	0.0296432	+	0.460419i
$796$	408.438	−	707.435i	0.513113	−	0.888737i
$797$	−269.356	+	72.1737i	−0.337962	+	0.0905567i	−0.423809	−	0.905752i	$-0.639307\pi$
$797$	−269.356	+	72.1737i	−0.337962	+	0.0905567i	0.0858466	+	0.996308i	$0.472640\pi$
$798$	−4.79887	−	36.1304i	−0.00601362	−	0.0452762i
$799$	48.7365	−	28.1380i	0.0609968	−	0.0352165i
$800$	179.457	−	136.393i	0.224321	−	0.170491i
$801$	196.099	+	52.0623i	0.244818	+	0.0649967i
$802$	0.879908	+	0.879908i	0.00109714	+	0.00109714i
$803$	−55.9768	−	14.9989i	−0.0697096	−	0.0186786i
$804$	−729.181	+	303.018i	−0.906941	+	0.376888i
$805$	871.992	−	171.363i	1.08322	−	0.212873i
$806$	−33.3216	+	57.7147i	−0.0413419	+	0.0716063i
$807$	−268.732	−	349.387i	−0.333001	−	0.432945i
$808$	−86.9569	−	23.3000i	−0.107620	−	0.0288367i
$809$			423.966i			0.524062i	0.965060	+	0.262031i	$0.0843922\pi$
$809$			423.966i			0.524062i	−0.965060	+	0.262031i	$0.915608\pi$
$810$	−42.6324	+	64.1211i	−0.0526326	+	0.0791618i
$811$	−1163.79			−1.43501			−0.717506	−	0.696552i	$-0.754716\pi$
$811$	−1163.79			−1.43501			−0.717506	+	0.696552i	$0.754716\pi$
$812$	66.0092	−	246.350i	0.0812921	−	0.303386i
$813$	107.045	−	82.3340i	0.131667	−	0.101272i
$814$	75.4686	+	43.5718i	0.0927133	+	0.0535281i
$815$	302.877	−	451.034i	0.371628	−	0.553416i
$816$	18.7731	+	45.1756i	0.0230063	+	0.0553622i
$817$	22.8914	−	85.4317i	0.0280188	−	0.104568i
$818$	−99.2357	+	99.2357i	−0.121315	+	0.121315i
$819$	278.907	−	1050.54i	0.340546	−	1.28271i
$820$	−1076.19	+	939.413i	−1.31242	+	1.14563i
$821$	−382.915	−	663.228i	−0.466400	−	0.807829i	0.532863	−	0.846202i	$-0.321116\pi$
$821$	−382.915	−	663.228i	−0.466400	−	0.807829i	−0.999264	+	0.0383722i	$0.987783\pi$
$822$	−110.848	+	14.7230i	−0.134852	+	0.0179112i
$823$	256.028	+	955.510i	0.311091	+	1.16101i	0.927574	+	0.373640i	$0.121891\pi$
$823$	256.028	+	955.510i	0.311091	+	1.16101i	−0.616482	+	0.787369i	$0.711443\pi$
$824$	103.197	+	59.5806i	0.125239	+	0.0723066i
$825$	1056.16	+	3.65372i	1.28019	+	0.00442876i
$826$	−27.2441	−	47.1882i	−0.0329832	−	0.0571286i
$827$	−260.100	−	260.100i	−0.314510	−	0.314510i	0.532144	−	0.846654i	$-0.321387\pi$
$827$	−260.100	−	260.100i	−0.314510	−	0.314510i	−0.846654	+	0.532144i	$0.821387\pi$
$828$	−610.119	−	350.387i	−0.736858	−	0.423172i
$829$		−	325.275i		−	0.392370i	−0.980567	−	0.196185i	$-0.937145\pi$
$829$		−	325.275i		−	0.392370i	0.980567	−	0.196185i	$-0.0628553\pi$
$830$	16.3640	−	47.8444i	0.0197157	−	0.0576438i
$831$	−182.756	−	439.783i	−0.219923	−	0.529221i
$832$	783.862	−	210.035i	0.942142	−	0.252446i
$833$	8.73421	+	32.5965i	0.0104852	+	0.0391315i
$834$	−7.03342	+	53.9023i	−0.00843336	+	0.0646310i
$835$	−1400.18	+	686.487i	−1.67686	+	0.822140i
$836$	395.803			0.473449
$837$	700.497	+	89.7687i	0.836914	+	0.107251i
$838$	36.5387	−	36.5387i	0.0436022	−	0.0436022i
$839$	81.4767	−	47.0406i	0.0971116	−	0.0560674i	−0.450658	−	0.892697i	$-0.648810\pi$
$839$	81.4767	−	47.0406i	0.0971116	−	0.0560674i	0.547769	+	0.836629i	$0.315477\pi$
$840$	−200.700	−	40.1628i	−0.238928	−	0.0478128i
$841$	−395.014	+	684.184i	−0.469695	+	0.813536i
$842$	37.8296	−	10.1364i	0.0449283	−	0.0120385i
$843$	183.535	+	75.7757i	0.217716	+	0.0898882i
$844$	833.301	−	481.107i	0.987323	−	0.570031i
$845$	−39.8834	+	34.8146i	−0.0471993	+	0.0412007i
$846$	64.8536	−	65.1522i	0.0766591	−	0.0770120i
$847$	−492.644	−	492.644i	−0.581633	−	0.581633i
$848$	367.698	+	98.5244i	0.433606	+	0.116184i
$849$	958.837	+	733.994i	1.12937	+	0.864539i
$850$	−3.04911	+	3.93600i	−0.00358719	+	0.00463058i
$851$	−320.958	+	555.915i	−0.377154	+	0.653249i
$852$	428.999	−	56.9800i	0.503520	−	0.0668779i
$853$	−984.979	−	263.924i	−1.15472	−	0.309407i	−0.369867	−	0.929085i	$-0.620597\pi$
$853$	−984.979	−	263.924i	−1.15472	−	0.309407i	−0.784856	+	0.619678i	$0.787263\pi$
$854$			139.579i			0.163442i
$855$	318.400	+	20.8714i	0.372397	+	0.0244110i
$856$	−108.534			−0.126793
$857$	−408.073	+	1522.95i	−0.476164	+	1.77707i	0.140756	+	0.990044i	$0.455047\pi$
$857$	−408.073	+	1522.95i	−0.476164	+	1.77707i	−0.616920	+	0.787026i	$0.711620\pi$
$858$	−99.4922	−	41.0773i	−0.115958	−	0.0478756i
$859$	507.067	+	292.755i	0.590299	+	0.340809i	0.765216	−	0.643774i	$-0.222632\pi$
$859$	507.067	+	292.755i	0.590299	+	0.340809i	−0.174917	+	0.984583i	$0.555966\pi$
$860$	−205.233	−	137.818i	−0.238643	−	0.160253i
$861$	1932.30	+	252.136i	2.24426	+	0.292841i
$862$	−11.7345	+	43.7939i	−0.0136132	+	0.0508050i
$863$	−550.423	+	550.423i	−0.637802	+	0.637802i	−0.950013	−	0.312211i	$-0.898930\pi$
$863$	−550.423	+	550.423i	−0.637802	+	0.637802i	0.312211	+	0.950013i	$0.398930\pi$
$864$	148.860	+	192.621i	0.172292	+	0.222941i
$865$	994.853	+	67.5082i	1.15012	+	0.0780442i
$866$	−10.7144	−	18.5579i	−0.0123723	−	0.0214294i
$867$	526.579	+	684.622i	0.607357	+	0.789644i
$868$	241.833	+	902.531i	0.278609	+	1.03978i
$869$	1012.26	+	584.429i	1.16486	+	0.672530i
$870$	−18.2507	−	9.02650i	−0.0209779	−	0.0103753i
$871$	−444.935	−	770.650i	−0.510833	−	0.884788i
$872$	−51.2158	−	51.2158i	−0.0587337	−	0.0587337i
$873$	272.446	+	156.464i	0.312080	+	0.179225i
$874$		−	26.5875i		−	0.0304205i
$875$	354.720	+	1069.19i	0.405395	+	1.22194i
$876$	−29.7460	+	38.8581i	−0.0339567	+	0.0443585i
$877$	−882.630	+	236.500i	−1.00642	+	0.269669i	−0.724133	−	0.689661i	$-0.757760\pi$
$877$	−882.630	+	236.500i	−1.00642	+	0.269669i	−0.282287	+	0.959330i	$0.591093\pi$
$878$	15.9166	+	59.4017i	0.0181283	+	0.0676557i
$879$	−517.247	−	395.955i	−0.588450	−	0.450461i
$880$	354.729	−	1037.14i	0.403101	−	1.17857i
$881$	−459.689			−0.521781			−0.260891	−	0.965368i	$-0.584016\pi$
$881$	−459.689			−0.521781			−0.260891	+	0.965368i	$0.584016\pi$
$882$	27.6723	+	47.6767i	0.0313745	+	0.0540552i
$883$	107.163	−	107.163i	0.121362	−	0.121362i	−0.643817	−	0.765179i	$-0.722650\pi$
$883$	107.163	−	107.163i	0.121362	−	0.121362i	0.765179	+	0.643817i	$0.222650\pi$
$884$	−48.1882	+	27.8215i	−0.0545116	+	0.0314723i
$885$	451.881	−	152.811i	0.510600	−	0.172667i
$886$	−71.8119	+	124.382i	−0.0810519	+	0.140386i
$887$	642.507	−	172.159i	0.724360	−	0.194092i	0.122244	−	0.992500i	$-0.460991\pi$
$887$	642.507	−	172.159i	0.724360	−	0.194092i	0.602116	+	0.798408i	$0.294324\pi$
$888$	117.191	−	90.1376i	0.131972	−	0.101506i
$889$	−180.277	+	104.083i	−0.202786	+	0.117078i
$890$	21.3813	+	1.45088i	0.0240239	+	0.00163020i
$891$	5.23854	+	1140.65i	0.00587940	+	1.28019i
$892$	576.746	+	576.746i	0.646576	+	0.646576i
$893$	−367.963	−	98.5954i	−0.412053	−	0.110409i
$894$	−19.2026	+	147.164i	−0.0214794	+	0.164613i
$895$	−245.010	−	1246.75i	−0.273755	−	1.39302i
$896$	−214.387	+	371.329i	−0.239271	+	0.414430i
$897$	302.582	−	732.877i	0.337327	−	0.817031i
$898$	−94.5284	−	25.3288i	−0.105266	−	0.0282058i
$899$			186.745i			0.207725i
$900$	343.206	−	823.187i	0.381340	−	0.914652i
$901$	−25.6142			−0.0284287
$902$	49.9463	−	186.402i	0.0553728	−	0.206654i
$903$	44.4012	+	334.295i	0.0491708	+	0.370204i
$904$	−228.495	−	131.922i	−0.252760	−	0.145931i
$905$	−1162.75	+	228.502i	−1.28481	+	0.252489i
$906$	89.3891	−	116.772i	0.0986635	−	0.128887i
$907$	215.603	−	804.640i	0.237710	−	0.887144i	−0.739199	−	0.673487i	$-0.764796\pi$
$907$	215.603	−	804.640i	0.237710	−	0.887144i	0.976909	−	0.213657i	$-0.0685376\pi$
$908$	521.794	−	521.794i	0.574663	−	0.574663i
$909$	−516.557	+	139.683i	−0.568269	+	0.153667i
$910$	7.77262	−	114.543i	0.00854134	−	0.125872i
$911$	−38.7954	−	67.1955i	−0.0425855	−	0.0737602i	0.843947	−	0.536427i	$-0.180226\pi$
$911$	−38.7954	−	67.1955i	−0.0425855	−	0.0737602i	−0.886533	+	0.462666i	$0.846893\pi$
$912$	126.376	−	306.093i	0.138571	−	0.335629i
$913$	−193.871	−	723.538i	−0.212345	−	0.792484i
$914$	−93.8309	−	54.1733i	−0.102660	−	0.0592706i
$915$	−1198.20	−	239.776i	−1.30950	−	0.262050i
$916$	−358.623	−	621.153i	−0.391510	−	0.678115i
$917$	−351.821	−	351.821i	−0.383665	−	0.383665i
$918$	−4.27725	−	3.25871i	−0.00465932	−	0.00354979i
$919$		−	1478.95i		−	1.60930i	−0.593750	−	0.804650i	$-0.702353\pi$
$919$		−	1478.95i		−	1.60930i	0.593750	−	0.804650i	$-0.297647\pi$
$920$	−141.272	−	48.3187i	−0.153557	−	0.0525203i
$921$	921.730	+	120.272i	1.00079	+	0.130588i
$922$	−43.8305	+	11.7443i	−0.0475385	+	0.0127379i
$923$	126.226	+	471.083i	0.136757	+	0.510383i
$924$	−1393.60	+	579.125i	−1.50823	+	0.626758i
$925$	−750.325	−	314.853i	−0.811162	−	0.340382i
$926$	156.839			0.169373
$927$	708.298	−	1.62646i	0.764076	−	0.00175454i
$928$	−45.5177	+	45.5177i	−0.0490492	+	0.0490492i
$929$	−1381.56	+	797.643i	−1.48715	+	0.858604i	−0.999893	−	0.0146572i	$-0.995334\pi$
$929$	−1381.56	+	797.643i	−1.48715	+	0.858604i	−0.487253	+	0.873261i	$0.662001\pi$
$930$	74.4406	−	4.79270i	0.0800436	−	0.00515345i
$931$	114.218	−	197.831i	0.122683	−	0.212493i
$932$	−651.014	+	174.439i	−0.698513	+	0.187166i
$933$	−54.3888	−	409.491i	−0.0582946	−	0.438897i
$934$	113.927	−	65.7757i	0.121977	−	0.0704237i
$935$	−4.99338	+	73.5863i	−0.00534051	+	0.0787019i
$936$	−128.833	+	129.426i	−0.137642	+	0.138276i
$937$	−921.265	−	921.265i	−0.983207	−	0.983207i	0.0166542	−	0.999861i	$-0.494699\pi$
$937$	−921.265	−	921.265i	−0.983207	−	0.983207i	−0.999861	+	0.0166542i	$0.994699\pi$
$938$	109.898	+	29.4471i	0.117162	+	0.0313935i
$939$	18.2824	−	7.59741i	0.0194700	−	0.00809096i
$940$	−593.594	+	883.961i	−0.631483	+	0.940384i
$941$	−618.185	+	1070.73i	−0.656945	+	1.13786i	0.324458	+	0.945900i	$0.394818\pi$
$941$	−618.185	+	1070.73i	−0.656945	+	1.13786i	−0.981402	+	0.191961i	$0.938515\pi$
$942$	16.1632	+	21.0144i	0.0171584	+	0.0223082i
$943$	1373.07	+	367.913i	1.45607	+	0.390152i
$944$		−	495.068i		−	0.524436i
$945$	−1151.61	+	392.383i	−1.21863	+	0.415221i
$946$	33.3958			0.0353021
$947$	418.272	−	1561.01i	0.441681	−	1.64838i	−0.282872	−	0.959158i	$-0.591287\pi$
$947$	418.272	−	1561.01i	0.441681	−	1.64838i	0.724553	−	0.689219i	$-0.242046\pi$
$948$	782.372	−	601.764i	0.825287	−	0.634772i
$949$	−47.7599	−	27.5742i	−0.0503265	−	0.0290560i
$950$	33.4345	−	4.24511i	0.0351943	−	0.00446854i
$951$	−509.250	−	1225.46i	−0.535489	−	1.28860i
$952$	3.69940	−	13.8064i	0.00388593	−	0.0145025i
$953$	1074.57	−	1074.57i	1.12756	−	1.12756i	0.136988	−	0.990573i	$-0.456258\pi$
$953$	1074.57	−	1074.57i	1.12756	−	1.12756i	0.990573	−	0.136988i	$-0.0437421\pi$
$954$	−40.3908	+	10.9222i	−0.0423384	+	0.0114488i
$955$	179.503	+	205.638i	0.187961	+	0.215328i
$956$	760.073	+	1316.48i	0.795055	+	1.37708i
$957$	−298.995	+	39.7127i	−0.312429	+	0.0414971i
$958$	8.11362	+	30.2804i	0.00846933	+	0.0316080i
$959$	−1530.10	−	883.405i	−1.59552	−	0.921173i
$960$	−682.233	−	599.699i	−0.710660	−	0.624686i
$961$	138.418	+	239.748i	0.144036	+	0.249477i
$962$	58.6394	+	58.6394i	0.0609557	+	0.0609557i
$963$	−557.960	+	323.849i	−0.579398	+	0.336292i
$964$			1291.77i			1.34001i
$965$	440.729	+	898.924i	0.456713	+	0.931527i
$966$	38.9019	+	93.6132i	0.0402711	+	0.0969081i
$967$	174.037	−	46.6332i	0.179977	−	0.0482246i	−0.167705	−	0.985837i	$-0.553636\pi$
$967$	174.037	−	46.6332i	0.179977	−	0.0482246i	0.347682	+	0.937613i	$0.386969\pi$
$968$	30.2958	+	113.066i	0.0312974	+	0.116803i
$969$	−2.88310	+	22.0953i	−0.00297533	+	0.0228022i
$970$	31.3991	+	10.7393i	0.0323702	+	0.0110714i
$971$	−40.8568			−0.0420770			−0.0210385	−	0.999779i	$-0.506697\pi$
$971$	−40.8568			−0.0420770			−0.0210385	+	0.999779i	$0.506697\pi$
$972$	891.997	+	363.492i	0.917693	+	0.373963i
$973$	−607.325	+	607.325i	−0.624178	+	0.624178i
$974$	76.1338	−	43.9558i	0.0781661	−	0.0451292i
$975$	969.926	+	263.491i	0.994796	+	0.270247i
$976$	−634.092	+	1098.28i	−0.649685	+	1.12529i
$977$	754.152	−	202.074i	0.771906	−	0.206832i	0.148693	−	0.988883i	$-0.452494\pi$
$977$	754.152	−	202.074i	0.771906	−	0.206832i	0.623213	+	0.782052i	$0.285827\pi$
$978$	57.2853	+	23.6513i	0.0585739	+	0.0241834i
$979$	274.932	−	158.732i	0.280829	−	0.162137i
$980$	−419.885	−	481.018i	−0.428454	−	0.490835i
$981$	−416.113	−	110.474i	−0.424172	−	0.112613i
$982$	48.9385	+	48.9385i	0.0498355	+	0.0498355i
$983$	−496.515	−	133.041i	−0.505101	−	0.135341i	−0.00273477	−	0.999996i	$-0.500871\pi$
$983$	−496.515	−	133.041i	−0.505101	−	0.135341i	−0.502367	+	0.864655i	$0.667537\pi$
$984$	−259.974	−	199.011i	−0.264201	−	0.202247i
$985$	108.816	+	73.0718i	0.110473	+	0.0741845i
$986$	0.710935	−	1.23138i	0.000721030	−	0.00124886i
$987$	1439.84	−	191.241i	1.45881	−	0.193760i
$988$	363.824	+	97.4863i	0.368243	+	0.0986704i
$989$			245.999i			0.248735i
$990$	23.5039	+	118.167i	0.0237413	+	0.119360i
$991$	941.294			0.949843			0.474922	−	0.880028i	$-0.342476\pi$
$991$	941.294			0.949843			0.474922	+	0.880028i	$0.342476\pi$
$992$	61.0382	−	227.798i	0.0615304	−	0.229635i
$993$	725.690	+	299.615i	0.730805	+	0.301727i
$994$	−54.0013	−	31.1776i	−0.0543272	−	0.0313658i
$995$	−198.693	−	1011.07i	−0.199692	−	1.01615i
$996$	−627.219	−	81.8425i	−0.629738	−	0.0821712i
$997$	344.990	−	1287.52i	0.346029	−	1.29140i	−0.545377	−	0.838191i	$-0.683614\pi$
$997$	344.990	−	1287.52i	0.346029	−	1.29140i	0.891406	−	0.453206i	$-0.149720\pi$
$998$	54.8879	−	54.8879i	0.0549979	−	0.0549979i
$999$	333.505	−	813.063i	0.333839	−	0.813877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.22.5	yes	40
3.2	odd	2		135.3.l.a.37.6		40
5.2	odd	4		225.3.o.b.193.5		40
5.3	odd	4	inner	45.3.k.a.13.6	yes	40
5.4	even	2		225.3.o.b.157.6		40
9.2	odd	6		135.3.l.a.127.5		40
9.4	even	3		405.3.g.h.82.5		20
9.5	odd	6		405.3.g.g.82.6		20
9.7	even	3	inner	45.3.k.a.7.6	✓	40
15.8	even	4		135.3.l.a.118.5		40
45.7	odd	12		225.3.o.b.43.6		40
45.13	odd	12		405.3.g.h.163.5		20
45.23	even	12		405.3.g.g.163.6		20
45.34	even	6		225.3.o.b.7.5		40
45.38	even	12		135.3.l.a.73.6		40
45.43	odd	12	inner	45.3.k.a.43.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.6	✓	40	9.7	even	3	inner
45.3.k.a.13.6	yes	40	5.3	odd	4	inner
45.3.k.a.22.5	yes	40	1.1	even	1	trivial
45.3.k.a.43.5	yes	40	45.43	odd	12	inner
135.3.l.a.37.6		40	3.2	odd	2
135.3.l.a.73.6		40	45.38	even	12
135.3.l.a.118.5		40	15.8	even	4
135.3.l.a.127.5		40	9.2	odd	6
225.3.o.b.7.5		40	45.34	even	6
225.3.o.b.43.6		40	45.7	odd	12
225.3.o.b.157.6		40	5.4	even	2
225.3.o.b.193.5		40	5.2	odd	4
405.3.g.g.82.6		20	9.5	odd	6
405.3.g.g.163.6		20	45.23	even	12
405.3.g.h.82.5		20	9.4	even	3
405.3.g.h.163.5		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+(0.0492077 - 0.183646i) q^{2} +(-2.37796 + 1.82902i) q^{3} +(3.43280 + 1.98193i) q^{4} +(4.90616 - 0.964151i) q^{5} +(0.218877 + 0.526704i) q^{6} +(-2.33248 + 8.70492i) q^{7} +(1.07064 - 1.07064i) q^{8} +(2.30940 - 8.69866i) q^{9} +(0.0643587 - 0.948439i) q^{10} +(-7.04110 - 12.1955i) q^{11} +(-11.7880 + 1.56570i) q^{12} +(-3.46845 - 12.9444i) q^{13} +(1.48385 + 0.856699i) q^{14} +(-9.90321 + 11.2662i) q^{15} +(7.78377 + 13.4819i) q^{16} +(-0.740694 - 0.740694i) q^{17} +(-1.48383 - 0.852153i) q^{18} +7.09073i q^{19} +(18.7527 + 6.41391i) q^{20} +(-10.3749 - 24.9661i) q^{21} +(-2.58614 + 0.692953i) q^{22} +(-5.10441 - 19.0499i) q^{23} +(-0.587726 + 4.50418i) q^{24} +(23.1408 - 9.46056i) q^{25} -2.54786 q^{26} +(10.4183 + 24.9090i) q^{27} +(-25.2594 + 25.2594i) q^{28} +(-6.18301 + 3.56976i) q^{29} +(1.58167 + 2.37306i) q^{30} +(13.0783 - 22.6522i) q^{31} +(8.70902 - 2.33357i) q^{32} +(39.0493 + 16.1223i) q^{33} +(-0.172473 + 0.0995774i) q^{34} +(-3.05064 + 44.9566i) q^{35} +(25.1678 - 25.2837i) q^{36} +(-23.0151 - 23.0151i) q^{37} +(1.30218 + 0.348919i) q^{38} +(31.9234 + 24.4375i) q^{39} +(4.22049 - 6.28502i) q^{40} +(-36.0387 + 62.4209i) q^{41} +(-5.09544 + 0.676780i) q^{42} +(-12.0484 - 3.22835i) q^{43} -55.8198i q^{44} +(2.94348 - 44.9036i) q^{45} -3.74961 q^{46} +(-13.9048 + 51.8935i) q^{47} +(-43.1681 - 17.8228i) q^{48} +(-27.9000 - 16.1081i) q^{49} +(-0.598685 - 4.71525i) q^{50} +(3.11608 + 0.406601i) q^{51} +(13.7484 - 51.3098i) q^{52} +(17.2907 - 17.2907i) q^{53} +(5.08709 - 0.687563i) q^{54} +(-46.3031 - 53.0446i) q^{55} +(6.82262 + 11.8171i) q^{56} +(-12.9691 - 16.8615i) q^{57} +(0.351320 + 1.31114i) q^{58} +(-27.5407 - 15.9006i) q^{59} +(-56.3244 + 19.0470i) q^{60} +(40.7317 + 70.5494i) q^{61} +(-3.51643 - 3.51643i) q^{62} +(70.3345 + 40.3926i) q^{63} +60.5560i q^{64} +(-29.4971 - 60.1633i) q^{65} +(4.88231 - 6.37790i) q^{66} +(64.1404 - 17.1864i) q^{67} +(-1.07465 - 4.01065i) q^{68} +(46.9807 + 35.9639i) q^{69} +(8.10597 + 2.77245i) q^{70} -36.3928 q^{71} +(-6.84062 - 11.7857i) q^{72} +(2.90991 - 2.90991i) q^{73} +(-5.35915 + 3.09411i) q^{74} +(-37.7245 + 64.8218i) q^{75} +(-14.0533 + 24.3410i) q^{76} +(122.584 - 32.8464i) q^{77} +(6.05872 - 4.66008i) q^{78} +(-71.8823 + 41.5012i) q^{79} +(51.1870 + 58.6396i) q^{80} +(-70.3333 - 40.1774i) q^{81} +(9.68994 + 9.68994i) q^{82} +(51.3796 + 13.7671i) q^{83} +(13.8661 - 106.266i) q^{84} +(-4.34811 - 2.91982i) q^{85} +(-1.18574 + 2.05377i) q^{86} +(8.17381 - 19.7976i) q^{87} +(-20.5956 - 5.51857i) q^{88} +22.5436i q^{89} +(-8.10152 - 2.75016i) q^{90} +120.770 q^{91} +(20.2331 - 75.5111i) q^{92} +(10.3316 + 77.7864i) q^{93} +(8.84580 + 5.10712i) q^{94} +(6.83654 + 34.7883i) q^{95} +(-16.4416 + 21.4781i) q^{96} +(-9.03502 + 33.7192i) q^{97} +(-4.33107 + 4.33107i) q^{98} +(-122.346 + 33.0837i) 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

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