LMFDB - Embedded newform 32.3.h.a.27.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,3,Mod(3,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("32.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	32.h (of order $8$, 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:	$0.871936845953$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			27.6
Character	$\chi$	$=$	32.27
Dual form			32.3.h.a.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61758 - 1.17620i) q^{2} +(-1.37292 + 0.568682i) q^{3} +(1.23313 - 3.80518i) q^{4} +(2.28872 + 0.948019i) q^{5} +(-1.55193 + 2.53471i) q^{6} +(-6.37744 + 6.37744i) q^{7} +(-2.48095 - 7.60558i) q^{8} +(-4.80245 + 4.80245i) q^{9} +O(q^{10})$	\(q+(1.61758 - 1.17620i) q^{2} +(-1.37292 + 0.568682i) q^{3} +(1.23313 - 3.80518i) q^{4} +(2.28872 + 0.948019i) q^{5} +(-1.55193 + 2.53471i) q^{6} +(-6.37744 + 6.37744i) q^{7} +(-2.48095 - 7.60558i) q^{8} +(-4.80245 + 4.80245i) q^{9} +(4.81725 - 1.15849i) q^{10} +(-1.79646 - 0.744117i) q^{11} +(0.470949 + 5.92546i) q^{12} +(16.7036 - 6.91888i) q^{13} +(-2.81490 + 17.8171i) q^{14} -3.68135 q^{15} +(-12.9588 - 9.38456i) q^{16} -6.19811i q^{17} +(-2.11973 + 13.4170i) q^{18} +(-8.50083 - 20.5228i) q^{19} +(6.42967 - 7.53997i) q^{20} +(5.12898 - 12.3825i) q^{21} +(-3.78114 + 0.909316i) q^{22} +(23.6476 + 23.6476i) q^{23} +(7.73130 + 9.03098i) q^{24} +(-13.3382 - 13.3382i) q^{25} +(18.8815 - 30.8386i) q^{26} +(8.98045 - 21.6807i) q^{27} +(16.4031 + 32.1315i) q^{28} +(14.5725 + 35.1811i) q^{29} +(-5.95488 + 4.32999i) q^{30} -14.1609i q^{31} +(-31.9999 + 0.0617869i) q^{32} +2.88956 q^{33} +(-7.29019 - 10.0259i) q^{34} +(-20.6421 + 8.55025i) q^{35} +(12.3521 + 24.1962i) q^{36} +(-30.0695 - 12.4552i) q^{37} +(-37.8896 - 23.1987i) q^{38} +(-18.9981 + 18.9981i) q^{39} +(1.53204 - 19.7590i) q^{40} +(-56.9700 + 56.9700i) q^{41} +(-6.26765 - 26.0623i) q^{42} +(54.5034 + 22.5760i) q^{43} +(-5.04676 + 5.91825i) q^{44} +(-15.5443 + 6.43866i) q^{45} +(66.0659 + 10.4377i) q^{46} +34.8047 q^{47} +(23.1282 + 5.51482i) q^{48} -32.3435i q^{49} +(-37.2638 - 5.88726i) q^{50} +(3.52475 + 8.50951i) q^{51} +(-5.72981 - 72.0923i) q^{52} +(3.92967 - 9.48706i) q^{53} +(-10.9742 - 45.6331i) q^{54} +(-3.40615 - 3.40615i) q^{55} +(64.3263 + 32.6821i) q^{56} +(23.3419 + 23.3419i) q^{57} +(64.9521 + 39.7682i) q^{58} +(9.41777 - 22.7365i) q^{59} +(-4.53958 + 14.0082i) q^{60} +(3.00467 + 7.25391i) q^{61} +(-16.6560 - 22.9064i) q^{62} -61.2547i q^{63} +(-51.6898 + 37.7381i) q^{64} +44.7892 q^{65} +(4.67409 - 3.39868i) q^{66} +(-55.9040 + 23.1562i) q^{67} +(-23.5849 - 7.64307i) q^{68} +(-45.9141 - 19.0183i) q^{69} +(-23.3335 + 38.1099i) q^{70} +(6.27499 - 6.27499i) q^{71} +(48.4401 + 24.6108i) q^{72} +(66.4597 - 66.4597i) q^{73} +(-63.2896 + 15.2203i) q^{74} +(25.8974 + 10.7271i) q^{75} +(-88.5756 + 7.03989i) q^{76} +(16.2024 - 6.71124i) q^{77} +(-8.38548 + 53.0765i) q^{78} -75.8508 q^{79} +(-20.7623 - 33.7638i) q^{80} -26.2523i q^{81} +(-25.1457 + 159.161i) q^{82} +(-1.23390 - 2.97891i) q^{83} +(-40.7928 - 34.7859i) q^{84} +(5.87593 - 14.1857i) q^{85} +(114.717 - 27.5881i) q^{86} +(-40.0138 - 40.0138i) q^{87} +(-1.20252 + 15.5092i) q^{88} +(36.7030 + 36.7030i) q^{89} +(-17.5710 + 28.6982i) q^{90} +(-62.4018 + 150.651i) q^{91} +(119.144 - 60.8227i) q^{92} +(8.05304 + 19.4417i) q^{93} +(56.2994 - 40.9371i) q^{94} -55.0300i q^{95} +(43.8982 - 18.2826i) q^{96} +90.0528 q^{97} +(-38.0423 - 52.3182i) q^{98} +(12.2010 - 5.05381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

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 $

$2$	1.61758	−	1.17620i	0.808790	−	0.588098i
$2$	1.61758	−	1.17620i	0.808790	−	0.588098i
$3$	−1.37292	+	0.568682i	−0.457640	+	0.189561i	−0.599580	−	0.800315i	$-0.704666\pi$
$3$	−1.37292	+	0.568682i	−0.457640	+	0.189561i	0.141940	+	0.989875i	$0.454666\pi$
$4$	1.23313	−	3.80518i	0.308282	−	0.951295i
$5$	2.28872	+	0.948019i	0.457744	+	0.189604i	0.599627	−	0.800280i	$-0.295316\pi$
$5$	2.28872	+	0.948019i	0.457744	+	0.189604i	−0.141883	+	0.989883i	$0.545316\pi$
$6$	−1.55193	+	2.53471i	−0.258654	+	0.422452i
$7$	−6.37744	+	6.37744i	−0.911063	+	0.911063i	−0.996356	−	0.0852929i	$-0.972817\pi$
$7$	−6.37744	+	6.37744i	−0.911063	+	0.911063i	0.0852929	+	0.996356i	$0.472817\pi$
$8$	−2.48095	−	7.60558i	−0.310119	−	0.950698i
$9$	−4.80245	+	4.80245i	−0.533606	+	0.533606i
$10$	4.81725	−	1.15849i	0.481725	−	0.115849i
$11$	−1.79646	−	0.744117i	−0.163314	−	0.0676470i	0.299529	−	0.954087i	$-0.403171\pi$
$11$	−1.79646	−	0.744117i	−0.163314	−	0.0676470i	−0.462843	+	0.886440i	$0.653171\pi$
$12$	0.470949	+	5.92546i	0.0392458	+	0.493789i
$13$	16.7036	−	6.91888i	1.28490	−	0.532221i	0.367436	−	0.930049i	$-0.380236\pi$
$13$	16.7036	−	6.91888i	1.28490	−	0.532221i	0.917460	+	0.397827i	$0.130236\pi$
$14$	−2.81490	+	17.8171i	−0.201065	+	1.27265i
$15$	−3.68135			−0.245423
$16$	−12.9588	−	9.38456i	−0.809924	−	0.586535i
$17$		−	6.19811i		−	0.364595i	−0.983243	−	0.182297i	$-0.941647\pi$
$17$		−	6.19811i		−	0.364595i	0.983243	−	0.182297i	$-0.0583533\pi$
$18$	−2.11973	+	13.4170i	−0.117763	+	0.745387i
$19$	−8.50083	−	20.5228i	−0.447412	−	1.08015i	−0.973288	−	0.229587i	$-0.926262\pi$
$19$	−8.50083	−	20.5228i	−0.447412	−	1.08015i	0.525876	−	0.850561i	$-0.323738\pi$
$20$	6.42967	−	7.53997i	0.321484	−	0.376998i
$21$	5.12898	−	12.3825i	0.244237	−	0.589641i
$22$	−3.78114	+	0.909316i	−0.171870	+	0.0413325i
$23$	23.6476	+	23.6476i	1.02815	+	1.02815i	0.999592	+	0.0285625i	$0.00909295\pi$
$23$	23.6476	+	23.6476i	1.02815	+	1.02815i	0.0285625	+	0.999592i	$0.490907\pi$
$24$	7.73130	+	9.03098i	0.322138	+	0.376291i
$25$	−13.3382	−	13.3382i	−0.533527	−	0.533527i
$26$	18.8815	−	30.8386i	0.726213	−	1.18610i
$27$	8.98045	−	21.6807i	0.332609	−	0.802990i
$28$	16.4031	+	32.1315i	0.585825	+	1.14755i
$29$	14.5725	+	35.1811i	0.502500	+	1.21314i	0.948118	+	0.317919i	$0.102984\pi$
$29$	14.5725	+	35.1811i	0.502500	+	1.21314i	−0.445618	+	0.895223i	$0.647016\pi$
$30$	−5.95488	+	4.32999i	−0.198496	+	0.144333i
$31$		−	14.1609i		−	0.456803i	−0.973567	−	0.228401i	$-0.926650\pi$
$31$		−	14.1609i		−	0.456803i	0.973567	−	0.228401i	$-0.0733498\pi$
$32$	−31.9999	+	0.0617869i	−0.999998	+	0.00193084i
$33$	2.88956			0.0875623
$34$	−7.29019	−	10.0259i	−0.214417	−	0.294880i
$35$	−20.6421	+	8.55025i	−0.589775	+	0.244293i
$36$	12.3521	+	24.1962i	0.343115	+	0.672118i
$37$	−30.0695	−	12.4552i	−0.812689	−	0.336627i	−0.0626629	−	0.998035i	$-0.519959\pi$
$37$	−30.0695	−	12.4552i	−0.812689	−	0.336627i	−0.750027	+	0.661408i	$0.769959\pi$
$38$	−37.8896	−	23.1987i	−0.997095	−	0.610491i
$39$	−18.9981	+	18.9981i	−0.487131	+	0.487131i
$40$	1.53204	−	19.7590i	0.0383010	−	0.493976i
$41$	−56.9700	+	56.9700i	−1.38951	+	1.38951i	−0.563170	+	0.826341i	$0.690418\pi$
$41$	−56.9700	+	56.9700i	−1.38951	+	1.38951i	−0.826341	+	0.563170i	$0.809582\pi$
$42$	−6.26765	−	26.0623i	−0.149230	−	0.620531i
$43$	54.5034	+	22.5760i	1.26752	+	0.525024i	0.912209	−	0.409724i	$-0.134375\pi$
$43$	54.5034	+	22.5760i	1.26752	+	0.525024i	0.355310	+	0.934748i	$0.384375\pi$
$44$	−5.04676	+	5.91825i	−0.114699	+	0.134506i
$45$	−15.5443	+	6.43866i	−0.345429	+	0.143081i
$46$	66.0659	+	10.4377i	1.43622	+	0.226906i
$47$	34.8047			0.740525			0.370263	−	0.928927i	$-0.379268\pi$
$47$	34.8047			0.740525			0.370263	+	0.928927i	$0.379268\pi$
$48$	23.1282	+	5.51482i	0.481837	+	0.114892i
$49$		−	32.3435i		−	0.660072i
$50$	−37.2638	−	5.88726i	−0.745277	−	0.117745i
$51$	3.52475	+	8.50951i	0.0691128	+	0.166853i
$52$	−5.72981	−	72.0923i	−0.110189	−	1.38639i
$53$	3.92967	−	9.48706i	0.0741447	−	0.179001i	−0.882462	−	0.470384i	$-0.844115\pi$
$53$	3.92967	−	9.48706i	0.0741447	−	0.179001i	0.956606	+	0.291383i	$0.0941154\pi$
$54$	−10.9742	−	45.6331i	−0.203225	−	0.845057i
$55$	−3.40615	−	3.40615i	−0.0619300	−	0.0619300i
$56$	64.3263	+	32.6821i	1.14868	+	0.583608i
$57$	23.3419	+	23.3419i	0.409507	+	0.409507i
$58$	64.9521	+	39.7682i	1.11986	+	0.685658i
$59$	9.41777	−	22.7365i	0.159623	−	0.385365i	−0.823752	−	0.566951i	$-0.808123\pi$
$59$	9.41777	−	22.7365i	0.159623	−	0.385365i	0.983375	+	0.181586i	$0.0581230\pi$
$60$	−4.53958	+	14.0082i	−0.0756597	+	0.233470i
$61$	3.00467	+	7.25391i	0.0492568	+	0.118916i	0.946593	−	0.322432i	$-0.104500\pi$
$61$	3.00467	+	7.25391i	0.0492568	+	0.118916i	−0.897336	+	0.441348i	$0.854500\pi$
$62$	−16.6560	−	22.9064i	−0.268644	−	0.369457i
$63$		−	61.2547i		−	0.972297i
$64$	−51.6898	+	37.7381i	−0.807653	+	0.589658i
$65$	44.7892			0.689065
$66$	4.67409	−	3.39868i	0.0708195	−	0.0514952i
$67$	−55.9040	+	23.1562i	−0.834388	+	0.345615i	−0.758638	−	0.651512i	$-0.774135\pi$
$67$	−55.9040	+	23.1562i	−0.834388	+	0.345615i	−0.0757497	+	0.997127i	$0.524135\pi$
$68$	−23.5849	−	7.64307i	−0.346837	−	0.112398i
$69$	−45.9141	−	19.0183i	−0.665422	−	0.275627i
$70$	−23.3335	+	38.1099i	−0.333336	+	0.544427i
$71$	6.27499	−	6.27499i	0.0883801	−	0.0883801i	−0.661535	−	0.749915i	$-0.730095\pi$
$71$	6.27499	−	6.27499i	0.0883801	−	0.0883801i	0.749915	+	0.661535i	$0.230095\pi$
$72$	48.4401	+	24.6108i	0.672779	+	0.341817i
$73$	66.4597	−	66.4597i	0.910406	−	0.910406i	−0.0858977	−	0.996304i	$-0.527376\pi$
$73$	66.4597	−	66.4597i	0.910406	−	0.910406i	0.996304	+	0.0858977i	$0.0273758\pi$
$74$	−63.2896	+	15.2203i	−0.855265	+	0.205680i
$75$	25.8974	+	10.7271i	0.345299	+	0.143027i
$76$	−88.5756	+	7.03989i	−1.16547	+	0.0926301i
$77$	16.2024	−	6.71124i	0.210420	−	0.0871589i
$78$	−8.38548	+	53.0765i	−0.107506	+	0.680468i
$79$	−75.8508			−0.960136			−0.480068	−	0.877231i	$-0.659388\pi$
$79$	−75.8508			−0.960136			−0.480068	+	0.877231i	$0.659388\pi$
$80$	−20.7623	−	33.7638i	−0.259529	−	0.422048i
$81$		−	26.2523i		−	0.324103i
$82$	−25.1457	+	159.161i	−0.306654	+	1.94099i
$83$	−1.23390	−	2.97891i	−0.0148663	−	0.0358905i	0.916272	−	0.400556i	$-0.131183\pi$
$83$	−1.23390	−	2.97891i	−0.0148663	−	0.0358905i	−0.931138	+	0.364666i	$0.881183\pi$
$84$	−40.7928	−	34.7859i	−0.485628	−	0.414117i
$85$	5.87593	−	14.1857i	0.0691286	−	0.166891i
$86$	114.717	−	27.5881i	1.33392	−	0.320791i
$87$	−40.0138	−	40.0138i	−0.459928	−	0.459928i
$88$	−1.20252	+	15.5092i	−0.0136651	+	0.176241i
$89$	36.7030	+	36.7030i	0.412393	+	0.412393i	0.882572	−	0.470178i	$-0.155810\pi$
$89$	36.7030	+	36.7030i	0.412393	+	0.412393i	−0.470178	+	0.882572i	$0.655810\pi$
$90$	−17.5710	+	28.6982i	−0.195234	+	0.318868i
$91$	−62.4018	+	150.651i	−0.685734	+	1.65551i
$92$	119.144	−	60.8227i	1.29504	−	0.661116i
$93$	8.05304	+	19.4417i	0.0865918	+	0.209051i
$94$	56.2994	−	40.9371i	0.598929	−	0.435501i
$95$		−	55.0300i		−	0.579263i
$96$	43.8982	−	18.2826i	0.457273	−	0.190444i
$97$	90.0528			0.928379			0.464189	−	0.885736i	$-0.346346\pi$
$97$	90.0528			0.928379			0.464189	+	0.885736i	$0.346346\pi$
$98$	−38.0423	−	52.3182i	−0.388187	−	0.533859i
$99$	12.2010	−	5.05381i	0.123242	−	0.0510486i
$100$	−67.2018	+	34.3064i	−0.672018	+	0.343064i
$101$	−20.0870	−	8.32031i	−0.198881	−	0.0823793i	0.281020	−	0.959702i	$-0.409327\pi$
$101$	−20.0870	−	8.32031i	−0.198881	−	0.0823793i	−0.479901	+	0.877323i	$0.659327\pi$
$102$	15.7104	+	9.61901i	0.154024	+	0.0943040i
$103$	4.88882	−	4.88882i	0.0474642	−	0.0474642i	−0.682976	−	0.730441i	$-0.739315\pi$
$103$	4.88882	−	4.88882i	0.0474642	−	0.0474642i	0.730441	+	0.682976i	$0.239315\pi$
$104$	−94.0630	−	109.876i	−0.904452	−	1.05650i
$105$	23.4776	−	23.4776i	0.223596	−	0.223596i
$106$	−4.80208	−	19.9681i	−0.0453027	−	0.188379i
$107$	−51.9710	−	21.5271i	−0.485710	−	0.201188i	0.126371	−	0.991983i	$-0.459667\pi$
$107$	−51.9710	−	21.5271i	−0.485710	−	0.201188i	−0.612080	+	0.790795i	$0.709667\pi$
$108$	−71.4250	−	60.9074i	−0.661343	−	0.563957i
$109$	−49.8054	+	20.6301i	−0.456931	+	0.189267i	−0.599263	−	0.800552i	$-0.704540\pi$
$109$	−49.8054	+	20.6301i	−0.456931	+	0.189267i	0.142333	+	0.989819i	$0.454540\pi$
$110$	−9.51602	−	1.50342i	−0.0865093	−	0.0136675i
$111$	48.3661			0.435730
$112$	142.493	−	22.7944i	1.27226	−	0.203522i
$113$			62.0870i			0.549442i	0.961524	+	0.274721i	$0.0885855\pi$
$113$			62.0870i			0.549442i	−0.961524	+	0.274721i	$0.911414\pi$
$114$	65.2120	+	10.3028i	0.572035	+	0.0903751i
$115$	31.7043	+	76.5410i	0.275690	+	0.665574i
$116$	151.840	−	12.0681i	1.30897	−	0.104035i
$117$	−46.9909	+	113.446i	−0.401632	+	0.969624i
$118$	−11.5086	−	47.8553i	−0.0975304	−	0.405553i
$119$	39.5281	+	39.5281i	0.332169	+	0.332169i
$120$	9.13325	+	27.9988i	0.0761104	+	0.233324i
$121$	−82.8864	−	82.8864i	−0.685011	−	0.685011i
$122$	13.3923	+	8.19970i	0.109773	+	0.0672106i
$123$	45.8174	−	110.613i	0.372499	−	0.899292i
$124$	−53.8847	−	17.4622i	−0.434554	−	0.140824i
$125$	−41.5830	−	100.390i	−0.332664	−	0.803122i
$126$	−72.0475	−	99.0844i	−0.571806	−	0.786384i
$127$			177.045i			1.39406i	0.717043	+	0.697029i	$0.245495\pi$
$127$			177.045i			1.39406i	−0.717043	+	0.697029i	$0.754505\pi$
$128$	−39.2250	+	121.842i	−0.306445	+	0.951888i
$129$	−87.6673			−0.679592
$130$	72.4502	−	52.6809i	0.557309	−	0.405238i
$131$	88.7654	−	36.7678i	0.677598	−	0.280670i	−0.0172241	−	0.999852i	$-0.505483\pi$
$131$	88.7654	−	36.7678i	0.677598	−	0.280670i	0.694823	+	0.719181i	$0.255483\pi$
$132$	3.56320	−	10.9953i	0.0269939	−	0.0832976i
$133$	185.097	+	76.6695i	1.39170	+	0.576462i
$134$	−63.1930	+	103.211i	−0.471589	+	0.770231i
$135$	41.1075	−	41.1075i	0.304500	−	0.304500i
$136$	−47.1402	+	15.3772i	−0.346619	+	0.113068i
$137$	−58.5583	+	58.5583i	−0.427433	+	0.427433i	−0.887753	−	0.460320i	$-0.847735\pi$
$137$	−58.5583	+	58.5583i	−0.427433	+	0.427433i	0.460320	+	0.887753i	$0.347735\pi$
$138$	−96.6390	+	23.2404i	−0.700282	+	0.168409i
$139$	−166.832	−	69.1039i	−1.20023	−	0.497151i	−0.309155	−	0.951012i	$-0.600046\pi$
$139$	−166.832	−	69.1039i	−1.20023	−	0.497151i	−0.891072	+	0.453861i	$0.850046\pi$
$140$	7.08082	+	89.0906i	0.0505773	+	0.636361i
$141$	−47.7840	+	19.7928i	−0.338894	+	0.140374i
$142$	2.76968	−	17.5309i	0.0195048	−	0.123457i
$143$	−35.1558			−0.245845
$144$	107.303	−	17.1650i	0.745158	−	0.119202i
$145$			94.3348i			0.650585i
$146$	29.3343	−	185.673i	0.200920	−	1.27174i
$147$	18.3932	+	44.4050i	0.125124	+	0.302075i
$148$	−84.4739	+	99.0610i	−0.570769	+	0.669331i
$149$	18.0040	−	43.4655i	0.120832	−	0.291715i	−0.851877	−	0.523742i	$-0.824536\pi$
$149$	18.0040	−	43.4655i	0.120832	−	0.291715i	0.972709	+	0.232027i	$0.0745357\pi$
$150$	54.5082	−	13.1085i	0.363388	−	0.0873902i
$151$	−68.3596	−	68.3596i	−0.452713	−	0.452713i	0.443541	−	0.896254i	$-0.353722\pi$
$151$	−68.3596	−	68.3596i	−0.452713	−	0.452713i	−0.896254	+	0.443541i	$0.853722\pi$
$152$	−134.998	+	115.570i	−0.888144	+	0.760328i
$153$	29.7661	+	29.7661i	0.194550	+	0.194550i
$154$	18.3149	−	29.9131i	0.118928	−	0.194241i
$155$	13.4248	−	32.4103i	0.0866115	−	0.209099i
$156$	48.8641	+	95.7184i	0.313232	+	0.613580i
$157$	−74.5650	−	180.016i	−0.474936	−	1.14660i	−0.961956	−	0.273206i	$-0.911916\pi$
$157$	−74.5650	−	180.016i	−0.474936	−	1.14660i	0.487020	−	0.873391i	$-0.338084\pi$
$158$	−122.695	+	89.2153i	−0.776549	+	0.564654i
$159$			15.2597i			0.0959730i
$160$	−73.2975	−	30.1952i	−0.458110	−	0.188720i
$161$	−301.622			−1.87343
$162$	−30.8778	−	42.4652i	−0.190604	−	0.262131i
$163$	267.123	−	110.646i	1.63879	−	0.678811i	0.642619	−	0.766186i	$-0.277848\pi$
$163$	267.123	−	110.646i	1.63879	−	0.678811i	0.996175	+	0.0873756i	$0.0278480\pi$
$164$	146.530	+	287.032i	0.893473	+	1.75020i
$165$	6.61339	+	2.73936i	0.0400812	+	0.0166022i
$166$	−5.49972	−	3.36731i	−0.0331308	−	0.0202850i
$167$	99.3059	−	99.3059i	0.594646	−	0.594646i	−0.344237	−	0.938883i	$-0.611862\pi$
$167$	99.3059	−	99.3059i	0.594646	−	0.594646i	0.938883	+	0.344237i	$0.111862\pi$
$168$	−106.900	−	8.28865i	−0.636312	−	0.0493372i
$169$	111.640	−	111.640i	0.660592	−	0.660592i
$170$	−7.18042	−	29.8578i	−0.0422378	−	0.175634i
$171$	139.385	+	57.7350i	0.815115	+	0.337632i
$172$	153.116	−	179.556i	0.890207	−	1.04393i
$173$	187.259	−	77.5652i	1.08242	−	0.448354i	0.231063	−	0.972939i	$-0.425780\pi$
$173$	187.259	−	77.5652i	1.08242	−	0.448354i	0.851358	+	0.524585i	$0.175780\pi$
$174$	−111.789	−	17.6615i	−0.642468	−	0.101503i
$175$	170.127			0.972153
$176$	16.2967	+	26.5018i	0.0925948	+	0.150578i
$177$			36.5711i			0.206617i
$178$	102.540	+	16.2001i	0.576067	+	0.0910121i
$179$	−101.230	−	244.390i	−0.565528	−	1.36531i	−0.905290	−	0.424795i	$-0.860346\pi$
$179$	−101.230	−	244.390i	−0.565528	−	1.36531i	0.339761	−	0.940512i	$-0.389654\pi$
$180$	5.33212	+	67.0885i	0.0296229	+	0.372714i
$181$	6.07796	−	14.6735i	0.0335799	−	0.0810690i	−0.906200	−	0.422849i	$-0.861030\pi$
$181$	6.07796	−	14.6735i	0.0335799	−	0.0810690i	0.939780	+	0.341780i	$0.111030\pi$
$182$	76.2554	+	317.087i	0.418986	+	1.74224i
$183$	−8.25033	−	8.25033i	−0.0450838	−	0.0450838i
$184$	121.185	−	238.522i	0.658614	−	1.29631i
$185$	−57.0130	−	57.0130i	−0.308178	−	0.308178i
$186$	35.8937	+	21.9766i	0.192977	+	0.118154i
$187$	−4.61212	+	11.1346i	−0.0246637	+	0.0595435i
$188$	42.9187	−	132.438i	0.228291	−	0.704458i
$189$	80.9953	+	195.540i	0.428546	+	1.03460i
$190$	−64.7260	−	89.0154i	−0.340663	−	0.468502i
$191$			370.577i			1.94019i	0.242716	+	0.970097i	$0.421962\pi$
$191$			370.577i			1.94019i	−0.242716	+	0.970097i	$0.578038\pi$
$192$	49.5049	−	81.2065i	0.257838	−	0.422950i
$193$	−132.679			−0.687456			−0.343728	−	0.939069i	$-0.611690\pi$
$193$	−132.679			−0.687456			−0.343728	+	0.939069i	$0.611690\pi$
$194$	145.668	−	105.920i	0.750864	−	0.545977i
$195$	−61.4920	+	25.4708i	−0.315344	+	0.130620i
$196$	−123.073	−	39.8837i	−0.627923	−	0.203488i
$197$	116.390	+	48.2104i	0.590814	+	0.244723i	0.658001	−	0.753017i	$-0.271402\pi$
$197$	116.390	+	48.2104i	0.590814	+	0.244723i	−0.0671870	+	0.997740i	$0.521402\pi$
$198$	13.7918	−	22.5257i	0.0696555	−	0.113766i
$199$	−89.9950	+	89.9950i	−0.452236	+	0.452236i	−0.896096	−	0.443860i	$-0.853609\pi$
$199$	−89.9950	+	89.9950i	−0.452236	+	0.452236i	0.443860	+	0.896096i	$0.353609\pi$
$200$	−68.3532	+	134.536i	−0.341766	+	0.672679i
$201$	63.5832	−	63.5832i	0.316334	−	0.316334i
$202$	−42.2786	+	10.1675i	−0.209300	+	0.0503340i
$203$	−317.301	−	131.430i	−1.56306	−	0.647440i
$204$	36.7267	−	2.91899i	0.180033	−	0.0143088i
$205$	−184.397	+	76.3797i	−0.899498	+	0.372584i
$206$	2.15785	−	13.6582i	0.0104750	−	0.0663022i
$207$	−227.132			−1.09726
$208$	−281.390	−	67.0961i	−1.35283	−	0.322578i
$209$			43.1940i			0.206670i
$210$	10.3627	−	65.5912i	0.0493460	−	0.312339i
$211$	20.9287	+	50.5264i	0.0991883	+	0.239462i	0.965683	−	0.259725i	$-0.0836321\pi$
$211$	20.9287	+	50.5264i	0.0991883	+	0.239462i	−0.866494	+	0.499187i	$0.833632\pi$
$212$	−31.2542	−	26.6519i	−0.147425	−	0.125716i
$213$	−5.04658	+	12.1835i	−0.0236929	+	0.0571996i
$214$	−109.387	+	26.3062i	−0.511155	+	0.122926i
$215$	103.340	+	103.340i	0.480653	+	0.480653i
$216$	−187.175	−	14.5128i	−0.866549	−	0.0671889i
$217$	90.3102	+	90.3102i	0.416176	+	0.416176i
$218$	−56.2993	+	91.9518i	−0.258254	+	0.421797i
$219$	−53.4494	+	129.038i	−0.244061	+	0.589215i
$220$	−17.1612	+	8.76079i	−0.0780057	+	0.0398218i
$221$	−42.8840	−	103.531i	−0.194045	−	0.468466i
$222$	78.2360	−	56.8879i	0.352414	−	0.256252i
$223$		−	52.7540i		−	0.236565i	−0.992980	−	0.118283i	$-0.962261\pi$
$223$		−	52.7540i		−	0.236565i	0.992980	−	0.118283i	$-0.0377388\pi$
$224$	203.684	−	204.472i	0.909302	−	0.912820i
$225$	128.112			0.569386
$226$	73.0264	+	100.431i	0.323126	+	0.444383i
$227$	−327.101	+	135.490i	−1.44097	+	0.596871i	−0.960034	−	0.279883i	$-0.909704\pi$
$227$	−327.101	+	135.490i	−1.44097	+	0.596871i	−0.480939	+	0.876754i	$0.659704\pi$
$228$	117.604	−	60.0366i	0.515806	−	0.263318i
$229$	245.430	+	101.660i	1.07175	+	0.443932i	0.847606	−	0.530625i	$-0.178043\pi$
$229$	245.430	+	101.660i	1.07175	+	0.443932i	0.224139	+	0.974557i	$0.428043\pi$
$230$	141.311	+	86.5207i	0.614398	+	0.376177i
$231$	−18.4280	+	18.4280i	−0.0797748	+	0.0797748i
$232$	231.419	−	198.115i	0.997497	−	0.853944i
$233$	−31.8772	+	31.8772i	−0.136812	+	0.136812i	−0.772196	−	0.635384i	$-0.780842\pi$
$233$	−31.8772	+	31.8772i	−0.136812	+	0.136812i	0.635384	+	0.772196i	$0.280842\pi$
$234$	57.4232	+	238.779i	0.245398	+	1.02042i
$235$	79.6582	+	32.9955i	0.338971	+	0.140406i
$236$	−74.9032	−	63.8734i	−0.317386	−	0.270650i
$237$	104.137	−	43.1350i	0.439397	−	0.182004i
$238$	110.433	+	17.4471i	0.464002	+	0.0733071i
$239$	90.0511			0.376783			0.188391	−	0.982094i	$-0.439673\pi$
$239$	90.0511			0.376783			0.188391	+	0.982094i	$0.439673\pi$
$240$	47.7058	+	34.5479i	0.198774	+	0.143949i
$241$		−	20.9972i		−	0.0871252i	−0.999051	−	0.0435626i	$-0.986129\pi$
$241$		−	20.9972i		−	0.0871252i	0.999051	−	0.0435626i	$-0.0138708\pi$
$242$	−231.566	−	36.5848i	−0.956884	−	0.151177i
$243$	95.7533	+	231.169i	0.394046	+	0.951312i
$244$	31.3076	−	2.48829i	0.128310	−	0.0101979i
$245$	30.6623	−	74.0253i	0.125152	−	0.302144i
$246$	−55.9892	−	232.816i	−0.227598	−	0.946404i
$247$	−283.990	−	283.990i	−1.14976	−	1.14976i
$248$	−107.702	+	35.1324i	−0.434281	+	0.141663i
$249$	3.38810	+	3.38810i	0.0136068	+	0.0136068i
$250$	−185.342	−	113.479i	−0.741369	−	0.453918i
$251$	105.207	−	253.991i	0.419150	−	1.01192i	−0.563444	−	0.826154i	$-0.690524\pi$
$251$	105.207	−	253.991i	0.419150	−	1.01192i	0.982594	−	0.185764i	$-0.0594759\pi$
$252$	−233.085	−	75.5350i	−0.924941	−	0.299742i
$253$	−24.8853	−	60.0783i	−0.0983607	−	0.237464i
$254$	208.240	+	286.385i	0.819842	+	1.12750i
$255$			22.8174i			0.0894801i
$256$	79.8601	+	243.225i	0.311954	+	0.950097i
$257$	236.584			0.920561			0.460281	−	0.887773i	$-0.347749\pi$
$257$	236.584			0.920561			0.460281	+	0.887773i	$0.347749\pi$
$258$	−141.809	+	103.114i	−0.549647	+	0.399666i
$259$	271.199	−	112.334i	1.04710	−	0.433723i
$260$	55.2309	−	170.431i	0.212427	−	0.655504i
$261$	−238.939	−	98.9720i	−0.915477	−	0.379203i
$262$	100.339	−	163.880i	0.382973	−	0.625498i
$263$	32.0070	−	32.0070i	0.121700	−	0.121700i	−0.643634	−	0.765334i	$-0.722574\pi$
$263$	32.0070	−	32.0070i	0.121700	−	0.121700i	0.765334	+	0.643634i	$0.222574\pi$
$264$	−7.16884	−	21.9768i	−0.0271547	−	0.0832453i
$265$	17.9878	−	17.9878i	0.0678786	−	0.0678786i
$266$	389.587	−	93.6906i	1.46461	−	0.352220i
$267$	−71.2626	−	29.5179i	−0.266901	−	0.110554i
$268$	19.1766	+	241.279i	0.0715545	+	0.900296i
$269$	115.344	−	47.7769i	0.428787	−	0.177609i	−0.157844	−	0.987464i	$-0.550454\pi$
$269$	115.344	−	47.7769i	0.428787	−	0.177609i	0.586630	+	0.809855i	$0.300454\pi$
$270$	18.1442	−	114.845i	0.0672008	−	0.425352i
$271$	−55.4325			−0.204548			−0.102274	−	0.994756i	$-0.532612\pi$
$271$	−55.4325			−0.204548			−0.102274	+	0.994756i	$0.532612\pi$
$272$	−58.1665	+	80.3199i	−0.213847	+	0.295294i
$273$		−	242.319i		−	0.887615i
$274$	−25.8468	+	163.599i	−0.0943312	+	0.597076i
$275$	14.0363	+	33.8866i	0.0510410	+	0.123224i
$276$	−128.986	+	151.260i	−0.467340	+	0.548042i
$277$	−35.7881	+	86.4001i	−0.129199	+	0.311914i	−0.975221	−	0.221235i	$-0.928991\pi$
$277$	−35.7881	+	86.4001i	−0.129199	+	0.311914i	0.846022	+	0.533148i	$0.178991\pi$
$278$	−351.143	+	84.4454i	−1.26310	+	0.303761i
$279$	68.0069	+	68.0069i	0.243752	+	0.243752i
$280$	116.242	+	135.783i	0.415149	+	0.484938i
$281$	13.8509	+	13.8509i	0.0492914	+	0.0492914i	0.731323	−	0.682031i	$-0.238903\pi$
$281$	13.8509	+	13.8509i	0.0492914	+	0.0492914i	−0.682031	+	0.731323i	$0.738903\pi$
$282$	−54.0143	+	88.2198i	−0.191540	+	0.312836i
$283$	−135.615	+	327.403i	−0.479205	+	1.15690i	0.480778	+	0.876843i	$0.340354\pi$
$283$	−135.615	+	327.403i	−0.479205	+	1.15690i	−0.959982	+	0.280060i	$0.909646\pi$
$284$	−16.1396	−	31.6153i	−0.0568295	−	0.111322i
$285$	31.2945	+	75.5517i	0.109805	+	0.265094i
$286$	−56.8674	+	41.3501i	−0.198837	+	0.144581i
$287$		−	726.645i		−	2.53186i
$288$	153.381	−	153.975i	0.532574	−	0.534635i
$289$	250.583			0.867071
$290$	110.956	+	152.594i	0.382608	+	0.526187i
$291$	−123.635	+	51.2114i	−0.424863	+	0.175984i
$292$	−170.938	−	334.844i	−0.585403	−	1.14673i
$293$	−412.791	−	170.984i	−1.40884	−	0.583562i	−0.456811	−	0.889564i	$-0.651009\pi$
$293$	−412.791	−	170.984i	−1.40884	−	0.583562i	−0.952031	+	0.306002i	$0.901009\pi$
$294$	81.9814	+	50.1947i	0.278848	+	0.170730i
$295$	43.1093	−	43.1093i	0.146133	−	0.146133i
$296$	−20.1281	+	259.597i	−0.0680005	+	0.877016i
$297$	−32.2660	+	32.2660i	−0.108640	+	0.108640i
$298$	−22.0010	−	91.4851i	−0.0738289	−	0.306997i
$299$	558.615	+	231.386i	1.86828	+	0.773866i
$300$	72.7532	−	85.3164i	0.242511	−	0.284388i
$301$	−491.569	+	203.615i	−1.63312	+	0.676461i
$302$	−190.981	−	30.1729i	−0.632389	−	0.0999102i
$303$	32.3094			0.106632
$304$	−82.4372	+	345.727i	−0.271175	+	1.13726i
$305$			19.4507i			0.0637726i
$306$	83.1598	+	13.1383i	0.271764	+	0.0429356i
$307$	−42.3557	−	102.256i	−0.137967	−	0.333081i	0.839762	−	0.542955i	$-0.182695\pi$
$307$	−42.3557	−	102.256i	−0.137967	−	0.333081i	−0.977728	+	0.209874i	$0.932695\pi$
$308$	−5.55785	−	69.9287i	−0.0180450	−	0.227041i
$309$	−3.93177	+	9.49213i	−0.0127242	+	0.0307189i
$310$	−16.4052	−	68.2164i	−0.0529199	−	0.220053i
$311$	337.326	+	337.326i	1.08465	+	1.08465i	0.996069	+	0.0885790i	$0.0282326\pi$
$311$	337.326	+	337.326i	1.08465	+	1.08465i	0.0885790	+	0.996069i	$0.471767\pi$
$312$	191.625	+	97.3585i	0.614183	+	0.312046i
$313$	−70.0735	−	70.0735i	−0.223877	−	0.223877i	0.586252	−	0.810129i	$-0.300603\pi$
$313$	−70.0735	−	70.0735i	−0.223877	−	0.223877i	−0.810129	+	0.586252i	$0.800603\pi$
$314$	−332.348	−	203.487i	−1.05843	−	0.648047i
$315$	58.0707	−	140.195i	0.184351	−	0.445063i
$316$	−93.5338	+	288.626i	−0.295993	+	0.913373i
$317$	32.8632	+	79.3388i	0.103669	+	0.250280i	0.967200	−	0.254017i	$-0.0817518\pi$
$317$	32.8632	+	79.3388i	0.103669	+	0.250280i	−0.863530	+	0.504297i	$0.831752\pi$
$318$	17.9484	+	24.6838i	0.0564415	+	0.0776220i
$319$		−	74.0450i		−	0.232116i
$320$	−154.080	+	37.3691i	−0.481500	+	0.116779i
$321$	83.5940			0.260417
$322$	−487.897	+	354.766i	−1.51521	+	1.10176i
$323$	−127.203	+	52.6891i	−0.393816	+	0.163124i
$324$	−99.8948	−	32.3725i	−0.308317	−	0.0999151i
$325$	−315.081	−	130.511i	−0.969480	−	0.401572i
$326$	301.952	−	493.168i	0.926233	−	1.51279i
$327$	56.6469	−	56.6469i	0.173232	−	0.173232i
$328$	574.629	+	291.950i	1.75192	+	0.890092i
$329$	−221.965	+	221.965i	−0.674665	+	0.674665i
$330$	13.9197	−	3.34751i	0.0421809	−	0.0101440i
$331$	124.865	+	51.7206i	0.377234	+	0.156256i	0.563240	−	0.826293i	$-0.309554\pi$
$331$	124.865	+	51.7206i	0.377234	+	0.156256i	−0.186006	+	0.982549i	$0.559554\pi$
$332$	−12.8568	+	1.02185i	−0.0387254	+	0.00307785i
$333$	204.223	−	84.5919i	0.613282	−	0.254030i
$334$	43.8321	−	277.438i	0.131234	−	0.830654i
$335$	−149.901			−0.447466
$336$	−182.669	+	112.328i	−0.543658	+	0.334310i
$337$			323.529i			0.960027i	0.877261	+	0.480014i	$0.159368\pi$
$337$			323.529i			0.960027i	−0.877261	+	0.480014i	$0.840632\pi$
$338$	49.2762	−	311.897i	0.145787	−	0.922772i
$339$	−35.3077	−	85.2404i	−0.104153	−	0.251447i
$340$	−46.7335	−	39.8518i	−0.137452	−	0.117211i
$341$	−10.5373	+	25.4394i	−0.0309013	+	0.0746024i
$342$	293.373	−	70.5526i	0.857817	−	0.206294i
$343$	−106.226	−	106.226i	−0.309696	−	0.309696i
$344$	36.4838	−	470.540i	0.106058	−	1.36785i
$345$	−87.0550	−	87.0550i	−0.252333	−	0.252333i
$346$	211.674	−	345.721i	0.611776	−	0.999193i
$347$	−135.065	+	326.076i	−0.389236	+	0.939700i	0.600866	+	0.799350i	$0.294823\pi$
$347$	−135.065	+	326.076i	−0.389236	+	0.939700i	−0.990102	+	0.140350i	$0.955177\pi$
$348$	−201.602	+	102.917i	−0.579315	+	0.295740i
$349$	187.869	+	453.555i	0.538305	+	1.29958i	0.925905	+	0.377756i	$0.123304\pi$
$349$	187.869	+	453.555i	0.538305	+	1.29958i	−0.387600	+	0.921828i	$0.626696\pi$
$350$	275.194	−	200.102i	0.786267	−	0.571721i
$351$		−	424.282i		−	1.20878i
$352$	57.5325	+	23.7007i	0.163445	+	0.0673315i
$353$	−70.5556			−0.199874			−0.0999372	−	0.994994i	$-0.531864\pi$
$353$	−70.5556			−0.199874			−0.0999372	+	0.994994i	$0.531864\pi$
$354$	43.0148	+	59.1567i	0.121511	+	0.167109i
$355$	20.3105	−	8.41289i	0.0572127	−	0.0236983i
$356$	184.921	−	94.4020i	0.519441	−	0.265174i
$357$	−76.7478	−	31.7900i	−0.214980	−	0.0890475i
$358$	−451.197	−	276.254i	−1.26033	−	0.771660i
$359$	−409.567	+	409.567i	−1.14086	+	1.14086i	−0.152561	+	0.988294i	$0.548752\pi$
$359$	−409.567	+	409.567i	−1.14086	+	1.14086i	−0.988294	+	0.152561i	$0.951248\pi$
$360$	87.5343	+	102.249i	0.243151	+	0.284026i
$361$	−93.6563	+	93.6563i	−0.259436	+	0.259436i
$362$	−7.42731	−	30.8844i	−0.0205174	−	0.0853161i
$363$	160.932	+	66.6604i	0.443340	+	0.183637i
$364$	496.306	+	423.223i	1.36348	+	1.16270i
$365$	215.113	−	89.1026i	0.589350	−	0.244117i
$366$	−23.0496	−	3.64157i	−0.0629770	−	0.00994964i
$367$	513.680			1.39967			0.699837	−	0.714303i	$-0.253256\pi$
$367$	513.680			1.39967			0.699837	+	0.714303i	$0.253256\pi$
$368$	−84.5217	−	528.365i	−0.229678	−	1.43578i
$369$		−	547.191i		−	1.48290i
$370$	−159.281	−	25.1646i	−0.430490	−	0.0680126i
$371$	35.4419	+	85.5644i	0.0955308	+	0.230632i
$372$	83.9098	−	6.66906i	0.225564	−	0.0179276i
$373$	−46.5164	+	112.301i	−0.124709	+	0.301074i	−0.973887	−	0.227032i	$-0.927098\pi$
$373$	−46.5164	+	112.301i	−0.124709	+	0.301074i	0.849178	+	0.528106i	$0.177098\pi$
$374$	5.63604	+	23.4359i	0.0150696	+	0.0626629i
$375$	114.180	+	114.180i	0.304481	+	0.304481i
$376$	−86.3486	−	264.710i	−0.229651	−	0.704016i
$377$	486.828	+	486.828i	1.29132	+	1.29132i
$378$	361.009	+	221.035i	0.955051	+	0.584749i
$379$	172.090	−	415.462i	0.454064	−	1.09621i	−0.516699	−	0.856167i	$-0.672840\pi$
$379$	172.090	−	415.462i	0.454064	−	1.09621i	0.970763	−	0.240040i	$-0.0771604\pi$
$380$	−209.399	−	67.8591i	−0.551050	−	0.178576i
$381$	−100.683	−	243.069i	−0.264259	−	0.637977i
$382$	435.871	+	599.438i	1.14102	+	1.56921i
$383$			430.627i			1.12435i	0.827017	+	0.562177i	$0.190036\pi$
$383$			430.627i			1.12435i	−0.827017	+	0.562177i	$0.809964\pi$
$384$	−15.4365	−	189.585i	−0.0401991	−	0.493712i
$385$	43.4451			0.112844
$386$	−214.619	+	156.056i	−0.556008	+	0.404291i
$387$	−370.170	+	153.329i	−0.956512	+	0.396200i
$388$	111.047	−	342.667i	0.286203	−	0.883162i
$389$	55.8615	+	23.1386i	0.143603	+	0.0594823i	0.453327	−	0.891344i	$-0.350237\pi$
$389$	55.8615	+	23.1386i	0.143603	+	0.0594823i	−0.309725	+	0.950826i	$0.600237\pi$
$390$	−69.5096	+	113.528i	−0.178230	+	0.291097i
$391$	146.570	−	146.570i	0.374860	−	0.374860i
$392$	−245.991	+	80.2426i	−0.627529	+	0.204701i
$393$	−100.959	+	100.959i	−0.256892	+	0.256892i
$394$	244.975	−	58.9135i	0.621765	−	0.149527i
$395$	−173.601	−	71.9080i	−0.439497	−	0.182046i
$396$	−4.18527	−	52.6589i	−0.0105689	−	0.132977i
$397$	−67.6641	+	28.0274i	−0.170439	+	0.0705979i	−0.466271	−	0.884642i	$-0.654403\pi$
$397$	−67.6641	+	28.0274i	−0.170439	+	0.0705979i	0.295833	+	0.955240i	$0.404403\pi$
$398$	−39.7224	+	251.426i	−0.0998051	+	0.631723i
$399$	−297.723			−0.746174
$400$	47.6736	+	298.019i	0.119184	+	0.745048i
$401$		−	536.024i		−	1.33672i	−0.743839	−	0.668359i	$-0.766997\pi$
$401$		−	536.024i		−	1.33672i	0.743839	−	0.668359i	$-0.233003\pi$
$402$	28.0646	−	177.637i	0.0698125	−	0.441883i
$403$	−97.9774	−	236.538i	−0.243120	−	0.586944i
$404$	−56.4301	+	66.1746i	−0.139679	+	0.163799i
$405$	24.8877	−	60.0842i	0.0614511	−	0.148356i
$406$	−667.847	+	160.609i	−1.64494	+	0.395588i
$407$	44.7505	+	44.7505i	0.109952	+	0.109952i
$408$	55.9750	−	47.9194i	0.137194	−	0.117450i
$409$	−540.379	−	540.379i	−1.32122	−	1.32122i	−0.912790	−	0.408430i	$-0.866077\pi$
$409$	−540.379	−	540.379i	−1.32122	−	1.32122i	−0.408430	−	0.912790i	$-0.633923\pi$
$410$	−208.439	+	340.437i	−0.508389	+	0.830335i
$411$	47.0948	−	113.697i	0.114586	−	0.276635i
$412$	−12.5743	−	24.6314i	−0.0305201	−	0.0597849i
$413$	84.9395	+	205.062i	0.205665	+	0.496518i
$414$	−367.405	+	267.152i	−0.887451	+	0.645295i
$415$		−	7.98765i		−	0.0192474i
$416$	−534.088	+	222.436i	−1.28387	+	0.534701i
$417$	268.345			0.643512
$418$	50.8045	+	69.8697i	0.121542	+	0.167152i
$419$	−341.184	+	141.323i	−0.814281	+	0.337286i	−0.750661	−	0.660688i	$-0.770265\pi$
$419$	−341.184	+	141.323i	−0.814281	+	0.337286i	−0.0636205	+	0.997974i	$0.520265\pi$
$420$	−60.3856	−	118.287i	−0.143775	−	0.281637i
$421$	339.196	+	140.500i	0.805692	+	0.333728i	0.747234	−	0.664561i	$-0.231382\pi$
$421$	339.196	+	140.500i	0.805692	+	0.333728i	0.0584581	+	0.998290i	$0.481382\pi$
$422$	93.2828	+	57.1142i	0.221049	+	0.135342i
$423$	−167.148	+	167.148i	−0.395149	+	0.395149i
$424$	−81.9039	−	6.35051i	−0.193170	−	0.0149776i
$425$	−82.6714	+	82.6714i	−0.194521	+	0.194521i
$426$	6.16696	+	25.6436i	0.0144764	+	0.0601962i
$427$	−65.4234	−	27.0993i	−0.153216	−	0.0634643i
$428$	−146.001	+	171.213i	−0.341125	+	0.400031i
$429$	48.2661	−	19.9925i	0.112508	−	0.0466025i
$430$	288.710	+	45.6129i	0.671419	+	0.106077i
$431$	154.504			0.358478			0.179239	−	0.983806i	$-0.442637\pi$
$431$	154.504			0.358478			0.179239	+	0.983806i	$0.442637\pi$
$432$	−319.840	+	196.678i	−0.740370	+	0.455274i
$433$			506.808i			1.17046i	0.810868	+	0.585228i	$0.198995\pi$
$433$			506.808i			1.17046i	−0.810868	+	0.585228i	$0.801005\pi$
$434$	252.306	+	39.8615i	0.581351	+	0.0918468i
$435$	−53.6465	−	129.514i	−0.123325	−	0.297734i
$436$	17.0846	+	214.958i	0.0391850	+	0.493023i
$437$	284.291	−	686.338i	0.650550	−	1.57057i
$438$	65.3155	+	271.596i	0.149122	+	0.620083i
$439$	−144.746	−	144.746i	−0.329718	−	0.329718i	0.522761	−	0.852479i	$-0.324902\pi$
$439$	−144.746	−	144.746i	−0.329718	−	0.329718i	−0.852479	+	0.522761i	$0.824902\pi$
$440$	−17.4553	+	34.3563i	−0.0396711	+	0.0780824i
$441$	155.328	+	155.328i	0.352218	+	0.352218i
$442$	−191.141	−	117.030i	−0.432446	−	0.264773i
$443$	230.959	−	557.584i	0.521351	−	1.25865i	−0.415713	−	0.909496i	$-0.636468\pi$
$443$	230.959	−	557.584i	0.521351	−	1.25865i	0.937064	−	0.349158i	$-0.113532\pi$
$444$	59.6416	−	184.042i	0.134328	−	0.414508i
$445$	49.2078	+	118.798i	0.110579	+	0.266962i
$446$	−62.0490	−	85.3338i	−0.139123	−	0.191331i
$447$			69.9132i			0.156405i
$448$	88.9759	−	570.321i	0.198607	−	1.27304i
$449$	−0.201052			−0.000447778			−0.000223889	−	1.00000i	$-0.500071\pi$
$449$	−0.201052			−0.000447778			−0.000223889		1.00000i	$0.500071\pi$
$450$	207.231	−	150.684i	0.460513	−	0.334854i
$451$	144.736	−	59.9518i	0.320923	−	0.132931i
$452$	236.252	+	76.5613i	0.522681	+	0.169383i
$453$	132.727	+	54.9774i	0.292996	+	0.121363i
$454$	−369.750	+	603.900i	−0.814427	+	1.33018i
$455$	−285.641	+	285.641i	−0.627782	+	0.627782i
$456$	119.619	−	235.439i	0.262322	−	0.516313i
$457$	226.835	−	226.835i	0.496358	−	0.496358i	−0.413944	−	0.910302i	$-0.635849\pi$
$457$	226.835	−	226.835i	0.496358	−	0.496358i	0.910302	+	0.413944i	$0.135849\pi$
$458$	516.575	−	124.230i	1.12789	−	0.271244i
$459$	−134.379	−	55.6618i	−0.292766	−	0.121268i
$460$	330.348	−	26.2557i	0.718147	−	0.0570775i
$461$	496.600	−	205.699i	1.07722	−	0.446201i	0.227690	−	0.973734i	$-0.426883\pi$
$461$	496.600	−	205.699i	1.07722	−	0.446201i	0.849535	+	0.527533i	$0.176883\pi$
$462$	−8.13383	+	51.4836i	−0.0176057	+	0.111436i
$463$	−520.019			−1.12315			−0.561576	−	0.827425i	$-0.689805\pi$
$463$	−520.019			−1.12315			−0.561576	+	0.827425i	$0.689805\pi$
$464$	141.317	−	592.661i	0.304564	−	1.27729i
$465$			52.1312i			0.112110i
$466$	−14.0701	+	89.0576i	−0.0301933	+	0.191111i
$467$	35.4966	+	85.6964i	0.0760099	+	0.183504i	0.957317	−	0.289040i	$-0.0933359\pi$
$467$	35.4966	+	85.6964i	0.0760099	+	0.183504i	−0.881307	+	0.472544i	$0.843336\pi$
$468$	373.737	+	318.702i	0.798583	+	0.680988i
$469$	208.847	−	504.202i	0.445303	−	1.07506i
$470$	167.663	−	40.3207i	0.356729	−	0.0857888i
$471$	204.743	+	204.743i	0.434699	+	0.434699i
$472$	−196.289	−	15.2195i	−0.415868	−	0.0322448i
$473$	−81.1137	−	81.1137i	−0.171488	−	0.171488i
$474$	117.715	−	192.260i	0.248343	−	0.405611i
$475$	−160.351	+	387.122i	−0.337582	+	0.814994i
$476$	199.155	−	101.668i	0.418392	−	0.213589i
$477$	26.6891	+	64.4332i	0.0559520	+	0.135080i
$478$	145.665	−	105.918i	0.304738	−	0.221585i
$479$			163.116i			0.340535i	0.985398	+	0.170268i	$0.0544632\pi$
$479$			163.116i			0.340535i	−0.985398	+	0.170268i	$0.945537\pi$
$480$	117.803	−	0.227459i	0.245423	−	0.000473874i
$481$	−588.447			−1.22338
$482$	−24.6968	−	33.9646i	−0.0512381	−	0.0704660i
$483$	414.102	−	171.527i	0.857355	−	0.355128i
$484$	−417.607	+	213.188i	−0.862825	+	0.440471i
$485$	206.106	+	85.3718i	0.424960	+	0.176024i
$486$	426.788	+	261.310i	0.878165	+	0.537674i
$487$	371.724	−	371.724i	0.763294	−	0.763294i	−0.213622	−	0.976916i	$-0.568526\pi$
$487$	371.724	−	371.724i	0.763294	−	0.763294i	0.976916	+	0.213622i	$0.0685262\pi$
$488$	47.7158	−	40.8488i	0.0977782	−	0.0837066i
$489$	−303.817	+	303.817i	−0.621302	+	0.621302i
$490$	−37.4695	−	155.807i	−0.0764684	−	0.317973i
$491$	281.201	+	116.477i	0.572710	+	0.237224i	0.650193	−	0.759769i	$-0.274688\pi$
$491$	281.201	+	116.477i	0.572710	+	0.237224i	−0.0774824	+	0.996994i	$0.524688\pi$
$492$	−364.403	−	310.743i	−0.740657	−	0.631592i
$493$	218.056	−	90.3220i	0.442305	−	0.183209i
$494$	−793.403	−	125.349i	−1.60608	−	0.253742i
$495$	32.7158			0.0660924
$496$	−132.894	+	183.508i	−0.267931	+	0.369975i
$497$			80.0367i			0.161040i
$498$	9.46560	+	1.49546i	0.0190072	+	0.00300292i
$499$	−236.126	−	570.059i	−0.473199	−	1.14240i	−0.962741	−	0.270424i	$-0.912836\pi$
$499$	−236.126	−	570.059i	−0.473199	−	1.14240i	0.489542	−	0.871980i	$-0.337164\pi$
$500$	−433.280	+	34.4366i	−0.866560	+	0.0688732i
$501$	−79.8656	+	192.813i	−0.159412	+	0.384855i
$502$	−128.563	−	534.595i	−0.256102	−	1.06493i
$503$	12.8902	+	12.8902i	0.0256266	+	0.0256266i	0.719804	−	0.694177i	$-0.244232\pi$
$503$	12.8902	+	12.8902i	0.0256266	+	0.0256266i	−0.694177	+	0.719804i	$0.744232\pi$
$504$	−465.878	+	151.970i	−0.924361	+	0.301527i
$505$	−38.0857	−	38.0857i	−0.0754173	−	0.0754173i
$506$	−110.918	−	67.9116i	−0.219205	−	0.134213i
$507$	−89.7851	+	216.760i	−0.177091	+	0.427535i
$508$	673.690	+	218.320i	1.32616	+	0.429764i
$509$	59.1272	+	142.746i	0.116163	+	0.280443i	0.971258	−	0.238028i	$-0.0765011\pi$
$509$	59.1272	+	142.746i	0.116163	+	0.280443i	−0.855095	+	0.518472i	$0.826501\pi$
$510$	26.8377	+	36.9090i	0.0526230	+	0.0723706i
$511$			847.685i			1.65888i
$512$	415.260	+	299.505i	0.811055	+	0.584970i
$513$	−521.291			−1.01616
$514$	382.694	−	278.269i	0.744541	−	0.541380i
$515$	15.8238	−	6.55444i	0.0307259	−	0.0127271i
$516$	−108.105	+	333.590i	−0.209506	+	0.646492i
$517$	−62.5251	−	25.8988i	−0.120938	−	0.0500943i
$518$	306.559	−	500.692i	0.591812	−	0.966588i
$519$	−212.982	+	212.982i	−0.410369	+	0.410369i
$520$	−111.120	−	340.648i	−0.213692	−	0.655093i
$521$	119.838	−	119.838i	0.230015	−	0.230015i	−0.582684	−	0.812699i	$-0.697997\pi$
$521$	119.838	−	119.838i	0.230015	−	0.230015i	0.812699	+	0.582684i	$0.197997\pi$
$522$	−502.914	+	120.944i	−0.963437	+	0.231694i
$523$	−689.004	−	285.395i	−1.31741	−	0.545688i	−0.390370	−	0.920658i	$-0.627653\pi$
$523$	−689.004	−	285.395i	−1.31741	−	0.545688i	−0.927037	+	0.374970i	$0.877653\pi$
$524$	−30.4490	−	383.108i	−0.0581087	−	0.731122i
$525$	−233.570	+	96.7480i	−0.444896	+	0.184282i
$526$	14.1274	−	89.4203i	0.0268582	−	0.170001i
$527$	−87.7707			−0.166548
$528$	−37.4451	−	27.1172i	−0.0709188	−	0.0513584i
$529$			589.413i			1.11420i
$530$	7.93955	−	50.2540i	0.0149803	−	0.0948188i
$531$	63.9626	+	154.419i	0.120457	+	0.290809i
$532$	519.989	−	609.782i	0.977423	−	1.14621i
$533$	−557.438	+	1345.77i	−1.04585	+	2.52490i
$534$	−149.992	+	36.0711i	−0.280884	+	0.0675489i
$535$	−98.5390	−	98.5390i	−0.184185	−	0.184185i
$536$	314.811	+	367.733i	0.587334	+	0.686069i
$537$	277.960	+	277.960i	0.517617	+	0.517617i
$538$	130.383	−	212.950i	0.242347	−	0.395817i
$539$	−24.0673	+	58.1037i	−0.0446519	+	0.107799i
$540$	−105.731	−	207.112i	−0.195797	−	0.383541i
$541$	−294.810	−	711.735i	−0.544936	−	1.31559i	−0.921204	−	0.389081i	$-0.872793\pi$
$541$	−294.810	−	711.735i	−0.544936	−	1.31559i	0.376267	−	0.926511i	$-0.377207\pi$
$542$	−89.6665	+	65.1995i	−0.165436	+	0.120294i
$543$			23.6020i			0.0434658i
$544$	0.382962	+	198.339i	0.000703974	+	0.364594i
$545$	−133.549			−0.245043
$546$	−285.014	−	391.970i	−0.522004	−	0.717894i
$547$	518.930	−	214.948i	0.948683	−	0.392957i	0.145948	−	0.989292i	$-0.453377\pi$
$547$	518.930	−	214.948i	0.948683	−	0.392957i	0.802736	+	0.596335i	$0.203377\pi$
$548$	150.615	+	295.035i	0.274845	+	0.538385i
$549$	−49.2663	−	20.4068i	−0.0897382	−	0.0371708i
$550$	62.5621	+	38.3049i	0.113749	+	0.0696452i
$551$	598.138	−	598.138i	1.08555	−	1.08555i
$552$	−30.7343	+	396.387i	−0.0556781	+	0.718092i
$553$	483.734	−	483.734i	0.874745	−	0.874745i
$554$	43.7333	+	181.853i	0.0789410	+	0.328254i
$555$	110.696	+	45.8520i	0.199453	+	0.0826162i
$556$	−468.678	+	549.610i	−0.842946	+	0.988508i
$557$	−883.511	+	365.962i	−1.58620	+	0.657024i	−0.989380	−	0.145355i	$-0.953568\pi$
$557$	−883.511	+	365.962i	−1.58620	+	0.657024i	−0.596816	+	0.802378i	$0.703568\pi$
$558$	189.996	+	30.0172i	0.340495	+	0.0537943i
$559$	1066.61			1.90806
$560$	347.737	+	82.9164i	0.620959	+	0.148065i
$561$		−	17.9098i		−	0.0319248i
$562$	38.6963	+	6.11357i	0.0688546	+	0.0108782i
$563$	385.055	+	929.606i	0.683935	+	1.65117i	0.756656	+	0.653813i	$0.226832\pi$
$563$	385.055	+	929.606i	0.683935	+	1.65117i	−0.0727214	+	0.997352i	$0.523168\pi$
$564$	16.3912	+	206.234i	0.0290625	+	0.365663i
$565$	−58.8596	+	142.100i	−0.104176	+	0.251504i
$566$	165.722	+	689.111i	0.292796	+	1.21751i
$567$	167.423	+	167.423i	0.295278	+	0.295278i
$568$	−63.2928	−	32.1570i	−0.111431	−	0.0566145i
$569$	−503.029	−	503.029i	−0.884058	−	0.884058i	0.109886	−	0.993944i	$-0.464951\pi$
$569$	−503.029	−	503.029i	−0.884058	−	0.884058i	−0.993944	+	0.109886i	$0.964951\pi$
$570$	139.485	+	85.4024i	0.244711	+	0.149829i
$571$	−48.1525	+	116.250i	−0.0843301	+	0.203591i	−0.960419	−	0.278558i	$-0.910144\pi$
$571$	−48.1525	+	116.250i	−0.0843301	+	0.203591i	0.876089	+	0.482149i	$0.160144\pi$
$572$	−43.3517	+	133.774i	−0.0757897	+	0.233871i
$573$	−210.741	−	508.773i	−0.367785	−	0.887910i
$574$	−854.677	−	1175.41i	−1.48898	−	2.04775i
$575$		−	630.830i		−	1.09710i
$576$	67.0022	−	429.473i	0.116323	−	0.745613i
$577$	−11.8629			−0.0205595			−0.0102798	−	0.999947i	$-0.503272\pi$
$577$	−11.8629			−0.0205595			−0.0102798	+	0.999947i	$0.503272\pi$
$578$	405.339	−	294.735i	0.701278	−	0.509922i
$579$	182.158	−	75.4522i	0.314607	−	0.130315i
$580$	358.961	+	116.327i	0.618898	+	0.200564i
$581$	26.8670	+	11.1287i	0.0462426	+	0.0191543i
$582$	−139.755	+	228.258i	−0.240129	+	0.392195i
$583$	−14.1190	+	14.1190i	−0.0242178	+	0.0242178i
$584$	−670.347	−	340.581i	−1.14786	−	0.583187i
$585$	−215.098	+	215.098i	−0.367689	+	0.367689i
$586$	−868.832	+	208.943i	−1.48265	+	0.356558i
$587$	−496.631	−	205.711i	−0.846049	−	0.350445i	−0.0828132	−	0.996565i	$-0.526390\pi$
$587$	−496.631	−	205.711i	−0.846049	−	0.350445i	−0.763236	+	0.646120i	$0.776390\pi$
$588$	191.650	−	15.2322i	0.325936	−	0.0259050i
$589$	−290.621	+	120.379i	−0.493414	+	0.204379i
$590$	19.0278	−	120.438i	0.0322505	−	0.204132i
$591$	−187.211			−0.316770
$592$	272.778	+	443.593i	0.460773	+	0.749313i
$593$		−	410.471i		−	0.692193i	−0.938199	−	0.346097i	$-0.887507\pi$
$593$		−	410.471i		−	0.692193i	0.938199	−	0.346097i	$-0.112493\pi$
$594$	−14.2417	+	90.1439i	−0.0239759	+	0.151757i
$595$	52.9954	+	127.942i	0.0890678	+	0.215029i
$596$	−143.193	−	122.107i	−0.240256	−	0.204878i
$597$	72.3774	−	174.735i	0.121235	−	0.292688i
$598$	1175.76	−	282.755i	1.96615	−	0.472835i
$599$	−565.778	−	565.778i	−0.944537	−	0.944537i	0.0540033	−	0.998541i	$-0.482802\pi$
$599$	−565.778	−	565.778i	−0.944537	−	0.944537i	−0.998541	+	0.0540033i	$0.982802\pi$
$600$	17.3354	−	223.578i	0.0288923	−	0.372630i
$601$	224.391	+	224.391i	0.373362	+	0.373362i	0.868700	−	0.495338i	$-0.164956\pi$
$601$	224.391	+	224.391i	0.373362	+	0.373362i	−0.495338	+	0.868700i	$0.664956\pi$
$602$	−555.662	+	907.544i	−0.923026	+	1.50755i
$603$	157.270	−	379.683i	0.260812	−	0.629656i
$604$	−344.417	+	175.824i	−0.570226	+	0.291100i
$605$	−111.126	−	268.282i	−0.183679	−	0.443441i
$606$	52.2631	−	38.0022i	0.0862427	−	0.0627099i
$607$			19.8654i			0.0327271i	0.999866	+	0.0163636i	$0.00520892\pi$
$607$			19.8654i			0.0327271i	−0.999866	+	0.0163636i	$0.994791\pi$
$608$	273.294	+	656.204i	0.449497	+	1.07928i
$609$	510.371			0.838047
$610$	22.8778	+	31.4630i	0.0375045	+	0.0515787i
$611$	581.365	−	240.809i	0.951498	−	0.394123i
$612$	149.971	−	76.5599i	0.245050	−	0.125098i
$613$	905.460	+	375.054i	1.47710	+	0.611833i	0.968464	−	0.249152i	$-0.0801518\pi$
$613$	905.460	+	375.054i	1.47710	+	0.611833i	0.508631	+	0.860985i	$0.330152\pi$
$614$	−188.787	−	115.588i	−0.307470	−	0.188255i
$615$	209.726	−	209.726i	0.341019	−	0.341019i
$616$	−91.2401	−	106.578i	−0.148117	−	0.173016i
$617$	673.907	−	673.907i	1.09223	−	1.09223i	0.0969409	−	0.995290i	$-0.469094\pi$
$617$	673.907	−	673.907i	1.09223	−	1.09223i	0.995290	−	0.0969409i	$-0.0309058\pi$
$618$	4.80465	+	19.9788i	0.00777451	+	0.0323282i
$619$	354.963	+	147.030i	0.573446	+	0.237529i	0.650511	−	0.759497i	$-0.274555\pi$
$619$	354.963	+	147.030i	0.573446	+	0.237529i	−0.0770649	+	0.997026i	$0.524555\pi$
$620$	−106.773	−	91.0498i	−0.172214	−	0.146855i
$621$	725.062	−	300.330i	1.16757	−	0.483624i
$622$	942.412	+	148.890i	1.51513	+	0.239374i
$623$	−468.143			−0.751433
$624$	424.482	−	67.9036i	0.680259	−	0.108820i
$625$			202.389i			0.323822i
$626$	−195.770	−	30.9294i	−0.312731	−	0.0494080i
$627$	−24.5636	−	59.3018i	−0.0391764	−	0.0945803i
$628$	−776.940	+	61.7503i	−1.23717	+	0.0983286i
$629$	−77.1987	+	186.374i	−0.122732	+	0.296302i
$630$	−70.9627	−	295.079i	−0.112639	−	0.468379i
$631$	−494.698	−	494.698i	−0.783991	−	0.783991i	0.196511	−	0.980502i	$-0.437039\pi$
$631$	−494.698	−	494.698i	−0.783991	−	0.783991i	−0.980502	+	0.196511i	$0.937039\pi$
$632$	188.182	+	576.889i	0.297756	+	0.912800i
$633$	−57.4669	−	57.4669i	−0.0907850	−	0.0907850i
$634$	146.477	+	89.6833i	0.231036	+	0.141456i
$635$	−167.843	+	405.208i	−0.264319	+	0.638122i
$636$	58.0659	+	18.8172i	0.0912986	+	0.0295868i
$637$	−223.781	−	540.255i	−0.351304	−	0.848124i
$638$	−87.0914	−	119.774i	−0.136507	−	0.187733i
$639$			60.2706i			0.0943202i
$640$	−205.283	+	241.676i	−0.320755	+	0.377618i
$641$	440.457			0.687141			0.343571	−	0.939127i	$-0.388364\pi$
$641$	440.457			0.687141			0.343571	+	0.939127i	$0.388364\pi$
$642$	135.220	−	98.3229i	0.210623	−	0.153151i
$643$	−211.055	+	87.4220i	−0.328235	+	0.135960i	−0.540715	−	0.841206i	$-0.681846\pi$
$643$	−211.055	+	87.4220i	−0.328235	+	0.135960i	0.212479	+	0.977166i	$0.431846\pi$
$644$	−371.939	+	1147.72i	−0.577545	+	1.78218i
$645$	−200.646	−	83.1103i	−0.311079	−	0.128853i
$646$	−143.788	+	234.844i	−0.222582	+	0.363535i
$647$	515.935	−	515.935i	0.797426	−	0.797426i	−0.185263	−	0.982689i	$-0.559314\pi$
$647$	515.935	−	515.935i	0.797426	−	0.797426i	0.982689	+	0.185263i	$0.0593136\pi$
$648$	−199.664	+	65.1306i	−0.308124	+	0.100510i
$649$	−33.8372	+	33.8372i	−0.0521375	+	0.0521375i
$650$	−663.175	+	159.485i	−1.02027	+	0.245362i
$651$	−175.346	−	72.6309i	−0.269349	−	0.111568i
$652$	−91.6307	−	1152.89i	−0.140538	−	1.76824i
$653$	−613.161	+	253.980i	−0.938991	+	0.388943i	−0.799082	−	0.601222i	$-0.794681\pi$
$653$	−613.161	+	253.980i	−0.938991	+	0.388943i	−0.139909	+	0.990164i	$0.544681\pi$
$654$	25.0031	−	158.259i	0.0382310	−	0.241986i
$655$	238.016			0.363383
$656$	1272.90	−	203.623i	1.94040	−	0.310402i
$657$			638.339i			0.971596i
$658$	−97.9719	+	620.120i	−0.148893	+	0.942431i
$659$	−19.4679	−	46.9996i	−0.0295416	−	0.0713196i	0.908420	−	0.418058i	$-0.137289\pi$
$659$	−19.4679	−	46.9996i	−0.0295416	−	0.0713196i	−0.937962	+	0.346738i	$0.887289\pi$
$660$	18.5789	−	21.7872i	0.0281499	−	0.0330108i
$661$	46.1458	−	111.406i	0.0698122	−	0.168541i	−0.885122	−	0.465359i	$-0.845925\pi$
$661$	46.1458	−	111.406i	0.0698122	−	0.168541i	0.954934	+	0.296817i	$0.0959253\pi$
$662$	262.812	−	63.2029i	0.396997	−	0.0954726i
$663$	117.752	+	117.752i	0.177606	+	0.177606i
$664$	−19.5951	+	16.7751i	−0.0295107	+	0.0252637i
$665$	350.950	+	350.950i	0.527745	+	0.527745i
$666$	230.850	−	377.040i	0.346622	−	0.566126i
$667$	−487.344	+	1176.55i	−0.730650	+	1.76395i
$668$	−255.420	−	500.334i	−0.382365	−	0.749003i
$669$	30.0002	+	72.4270i	0.0448434	+	0.108262i
$670$	−242.477	+	176.313i	−0.361906	+	0.263154i
$671$		−	15.2672i		−	0.0227528i
$672$	−163.362	+	396.555i	−0.243098	+	0.590111i
$673$	−352.344			−0.523542			−0.261771	−	0.965130i	$-0.584306\pi$
$673$	−352.344			−0.523542			−0.261771	+	0.965130i	$0.584306\pi$
$674$	380.533	+	523.334i	0.564590	+	0.776460i
$675$	−408.964	+	169.398i	−0.605872	+	0.250961i
$676$	−287.144	−	562.477i	−0.424769	−	0.832066i
$677$	−1178.26	−	488.051i	−1.74041	−	0.720902i	−0.998742	−	0.0501357i	$-0.984035\pi$
$677$	−1178.26	−	488.051i	−1.74041	−	0.720902i	−0.741669	−	0.670766i	$-0.765965\pi$
$678$	−157.372	−	96.3544i	−0.232113	−	0.142116i
$679$	−574.306	+	574.306i	−0.845812	+	0.845812i
$680$	−122.469	−	9.49575i	−0.180101	−	0.0139643i
$681$	372.033	−	372.033i	0.546304	−	0.546304i
$682$	12.8767	+	53.5443i	0.0188808	+	0.0785106i
$683$	−414.446	−	171.669i	−0.606802	−	0.251346i	0.0580582	−	0.998313i	$-0.481509\pi$
$683$	−414.446	−	171.669i	−0.606802	−	0.251346i	−0.664861	+	0.746967i	$0.731509\pi$
$684$	391.571	−	459.189i	0.572473	−	0.671329i
$685$	−189.538	+	78.5093i	−0.276698	+	0.114612i
$686$	−296.771	−	46.8864i	−0.432611	−	0.0683476i
$687$	−394.768			−0.574626
$688$	−494.431	−	804.048i	−0.718650	−	1.16867i
$689$		−	185.657i		−	0.269459i
$690$	−243.212	−	38.4247i	−0.352481	−	0.0556880i
$691$	268.707	+	648.715i	0.388866	+	0.938806i	0.990181	+	0.139794i	$0.0446439\pi$
$691$	268.707	+	648.715i	0.388866	+	0.938806i	−0.601314	+	0.799012i	$0.705356\pi$
$692$	−64.2350	−	808.202i	−0.0928251	−	1.16792i
$693$	−45.5807	+	110.041i	−0.0657729	+	0.158790i
$694$	165.050	+	686.316i	0.237825	+	0.988928i
$695$	−316.319	−	316.319i	−0.455136	−	0.455136i
$696$	−205.056	+	403.600i	−0.294620	+	0.579885i
$697$	353.106	+	353.106i	0.506608	+	0.506608i
$698$	837.361	+	512.691i	1.19966	+	0.734514i
$699$	25.6368	−	61.8927i	0.0366764	−	0.0885447i
$700$	209.788	−	647.363i	0.299698	−	0.924804i
$701$	464.382	+	1121.12i	0.662457	+	1.59931i	0.793941	+	0.607995i	$0.208026\pi$
$701$	464.382	+	1121.12i	0.662457	+	1.59931i	−0.131484	+	0.991318i	$0.541974\pi$
$702$	−499.038	−	686.310i	−0.710881	−	0.977649i
$703$			722.990i			1.02844i
$704$	120.940	−	29.3317i	0.171790	−	0.0416643i
$705$	−128.128			−0.181742
$706$	−114.129	+	82.9872i	−0.161656	+	0.117546i
$707$	181.166	−	75.0414i	0.256246	−	0.106141i
$708$	139.160	+	45.0969i	0.196553	+	0.0636962i
$709$	591.984	+	245.208i	0.834957	+	0.345850i	0.758863	−	0.651250i	$-0.225755\pi$
$709$	591.984	+	245.208i	0.834957	+	0.345850i	0.0760937	+	0.997101i	$0.475755\pi$
$710$	22.9587	−	37.4976i	0.0323362	−	0.0528136i
$711$	364.270	−	364.270i	0.512334	−	0.512334i
$712$	188.090	−	370.206i	0.264171	−	0.519952i
$713$	334.870	−	334.870i	0.469664	−	0.469664i
$714$	−161.537	+	38.8476i	−0.226242	+	0.0544083i
$715$	−80.4619	−	33.3284i	−0.112534	−	0.0466132i
$716$	−1054.78	+	83.8325i	−1.47315	+	0.117084i
$717$	−123.633	+	51.2104i	−0.172431	+	0.0714232i
$718$	−180.777	+	1144.24i	−0.251778	+	1.59365i
$719$	−906.230			−1.26040			−0.630202	−	0.776432i	$-0.717028\pi$
$719$	−906.230			−1.26040			−0.630202	+	0.776432i	$0.717028\pi$
$720$	261.859	+	62.4392i	0.363693	+	0.0867211i
$721$			62.3563i			0.0864858i
$722$	−41.3384	+	261.655i	−0.0572555	+	0.362402i
$723$	11.9407	+	28.8274i	0.0165155	+	0.0398720i
$724$	−48.3404	−	41.2220i	−0.0667685	−	0.0569365i
$725$	274.881	−	663.622i	0.379147	−	0.915341i
$726$	338.726	−	81.4594i	0.466565	−	0.112203i
$727$	317.957	+	317.957i	0.437355	+	0.437355i	0.891121	−	0.453766i	$-0.149920\pi$
$727$	317.957	+	317.957i	0.437355	+	0.437355i	−0.453766	+	0.891121i	$0.649920\pi$
$728$	1300.61	+	100.844i	1.78655	+	0.138522i
$729$	−95.8544	−	95.8544i	−0.131488	−	0.131488i
$730$	243.160	−	397.145i	0.333096	−	0.544034i
$731$	139.929	−	337.818i	0.191421	−	0.462131i
$732$	−41.5677	+	21.2203i	−0.0567865	+	0.0289894i
$733$	−159.623	−	385.363i	−0.217766	−	0.525734i	0.776811	−	0.629734i	$-0.216836\pi$
$733$	−159.623	−	385.363i	−0.217766	−	0.525734i	−0.994577	+	0.103999i	$0.966836\pi$
$734$	830.919	−	604.188i	1.13204	−	0.823145i
$735$			119.068i			0.161997i
$736$	−758.181	−	755.259i	−1.03014	−	1.02617i
$737$	117.660			0.159647
$738$	−643.603	−	885.125i	−0.872091	−	1.19936i
$739$	−380.514	+	157.614i	−0.514904	+	0.213280i	−0.624977	−	0.780643i	$-0.714892\pi$
$739$	−380.514	+	157.614i	−0.514904	+	0.213280i	0.110073	+	0.993924i	$0.464892\pi$
$740$	−287.249	+	146.640i	−0.388174	+	0.198162i
$741$	551.395	+	228.395i	0.744123	+	0.308226i
$742$	157.971	+	96.7206i	0.212898	+	0.130351i
$743$	5.76228	−	5.76228i	0.00775542	−	0.00775542i	−0.703218	−	0.710974i	$-0.748254\pi$
$743$	5.76228	−	5.76228i	0.00775542	−	0.00775542i	0.710974	+	0.703218i	$0.248254\pi$
$744$	127.887	−	109.482i	0.171891	−	0.147153i
$745$	82.4123	−	82.4123i	0.110620	−	0.110620i
$746$	56.8434	+	236.367i	0.0761975	+	0.316847i
$747$	20.2318	+	8.38030i	0.0270841	+	0.0112186i
$748$	36.6819	+	31.2804i	0.0490400	+	0.0418187i
$749$	468.729	−	194.154i	0.625807	−	0.259218i
$750$	318.994	+	50.3974i	0.425325	+	0.0671965i
$751$	−302.377			−0.402632			−0.201316	−	0.979526i	$-0.564522\pi$
$751$	−302.377			−0.402632			−0.201316	+	0.979526i	$0.564522\pi$
$752$	−451.026	−	326.627i	−0.599769	−	0.434344i
$753$			408.539i			0.542548i
$754$	1360.09	+	214.878i	1.80383	+	0.284985i
$755$	−91.6499	−	221.262i	−0.121391	−	0.293063i
$756$	843.942	−	67.0756i	1.11633	−	0.0887243i
$757$	−9.31627	+	22.4915i	−0.0123068	+	0.0297113i	−0.929914	−	0.367778i	$-0.880119\pi$
$757$	−9.31627	+	22.4915i	−0.0123068	+	0.0297113i	0.917607	+	0.397490i	$0.130119\pi$
$758$	−210.295	−	874.455i	−0.277434	−	1.15363i
$759$	68.3309	+	68.3309i	0.0900276	+	0.0900276i
$760$	−418.535	+	136.526i	−0.550704	+	0.179640i
$761$	−163.034	−	163.034i	−0.214236	−	0.214236i	0.591828	−	0.806064i	$-0.298406\pi$
$761$	−163.034	−	163.034i	−0.214236	−	0.214236i	−0.806064	+	0.591828i	$0.798406\pi$
$762$	−448.759	−	274.761i	−0.588922	−	0.360579i
$763$	186.064	−	449.198i	0.243859	−	0.588727i
$764$	1410.11	+	456.970i	1.84570	+	0.598128i
$765$	39.9075	+	96.3452i	0.0521667	+	0.125941i
$766$	506.502	+	696.574i	0.661229	+	0.909365i
$767$		−	444.943i		−	0.580109i
$768$	−247.959	−	288.513i	−0.322864	−	0.375668i
$769$	180.205			0.234337			0.117168	−	0.993112i	$-0.462618\pi$
$769$	180.205			0.234337			0.117168	+	0.993112i	$0.462618\pi$
$770$	70.2759	−	51.0999i	0.0912674	−	0.0663635i
$771$	−324.811	+	134.541i	−0.421286	+	0.174502i
$772$	−163.610	+	504.868i	−0.211931	+	0.653974i
$773$	196.725	+	81.4860i	0.254495	+	0.105415i	0.506284	−	0.862367i	$-0.331019\pi$
$773$	196.725	+	81.4860i	0.254495	+	0.105415i	−0.251789	+	0.967782i	$0.581019\pi$
$774$	−418.434	+	683.415i	−0.540613	+	0.882965i
$775$	−188.880	+	188.880i	−0.243716	+	0.243716i
$776$	−223.416	−	684.904i	−0.287908	−	0.882608i
$777$	−308.452	+	308.452i	−0.396978	+	0.396978i
$778$	117.576	−	28.2755i	0.151126	−	0.0363439i
$779$	1653.48	+	684.892i	2.12256	+	0.879194i
$780$	21.0935	+	265.397i	0.0270429	+	0.340253i
$781$	−15.9421	+	6.60342i	−0.0204124	+	0.00845508i
$782$	64.6938	−	409.484i	0.0827286	−	0.523637i
$783$	893.620			1.14128
$784$	−303.530	+	419.133i	−0.387155	+	0.534608i
$785$		−	482.695i		−	0.614898i
$786$	−44.5616	+	282.056i	−0.0566941	+	0.358849i
$787$	80.6847	+	194.790i	0.102522	+	0.247510i	0.966814	−	0.255480i	$-0.0822334\pi$
$787$	80.6847	+	194.790i	0.102522	+	0.247510i	−0.864293	+	0.502990i	$0.832233\pi$
$788$	326.974	−	383.436i	0.414941	−	0.486594i
$789$	−25.7412	+	62.1448i	−0.0326251	+	0.0787640i
$790$	−365.392	+	87.8721i	−0.462521	+	0.111230i
$791$	−395.956	−	395.956i	−0.500576	−	0.500576i
$792$	−68.7072	−	80.2573i	−0.0867515	−	0.101335i
$793$	100.378	+	100.378i	0.126580	+	0.126580i
$794$	−76.4864	+	124.923i	−0.0963305	+	0.157333i
$795$	−14.4665	+	34.9252i	−0.0181969	+	0.0439311i
$796$	231.472	+	453.423i	0.290794	+	0.569627i
$797$	−256.509	−	619.268i	−0.321843	−	0.776999i	−0.999147	−	0.0412950i	$-0.986852\pi$
$797$	−256.509	−	619.268i	−0.321843	−	0.776999i	0.677304	−	0.735704i	$-0.263148\pi$
$798$	−481.591	+	350.181i	−0.603498	+	0.438823i
$799$		−	215.723i		−	0.269992i
$800$	427.645	+	425.996i	0.534556	+	0.532495i
$801$	−352.529			−0.440111
$802$	−630.469	−	867.061i	−0.786120	−	1.08112i
$803$	−168.846	+	69.9382i	−0.210269	+	0.0870961i
$804$	−163.539	−	320.352i	−0.203407	−	0.398447i
$805$	−690.328	−	285.943i	−0.857551	−	0.355209i
$806$	−436.702	−	267.379i	−0.541813	−	0.331736i
$807$	−131.188	+	131.188i	−0.162562	+	0.162562i
$808$	−13.4460	+	173.416i	−0.0166411	+	0.214623i
$809$	−1008.10	+	1008.10i	−1.24611	+	1.24611i	−0.288683	+	0.957425i	$0.593217\pi$
$809$	−1008.10	+	1008.10i	−1.24611	+	1.24611i	−0.957425	+	0.288683i	$0.906783\pi$
$810$	−30.4129	−	126.464i	−0.0375468	−	0.156128i
$811$	−1271.85	−	526.816i	−1.56825	−	0.649588i	−0.581748	−	0.813369i	$-0.697631\pi$
$811$	−1271.85	−	526.816i	−1.56825	−	0.649588i	−0.986497	+	0.163780i	$0.947631\pi$
$812$	−891.389	+	1045.32i	−1.09777	+	1.28734i
$813$	76.1044	−	31.5235i	0.0936094	−	0.0387743i
$814$	125.023	+	19.7522i	0.153591	+	0.0242656i
$815$	716.266			0.878854
$816$	34.1814	−	143.351i	0.0418890	−	0.175675i
$817$		−	1310.48i		−	1.60401i
$818$	−1509.70	−	238.515i	−1.84560	−	0.291583i
$819$	−423.814	−	1023.18i	−0.517477	−	1.24930i
$820$	63.2532	+	795.850i	0.0771381	+	0.970548i
$821$	−119.922	+	289.516i	−0.146068	+	0.352639i	−0.979932	−	0.199330i	$-0.936123\pi$
$821$	−119.922	+	289.516i	−0.146068	+	0.352639i	0.833865	+	0.551969i	$0.186123\pi$
$822$	−57.5502	−	239.307i	−0.0700124	−	0.291127i
$823$	607.735	+	607.735i	0.738439	+	0.738439i	0.972276	−	0.233837i	$-0.0751282\pi$
$823$	607.735	+	607.735i	0.738439	+	0.738439i	−0.233837	+	0.972276i	$0.575128\pi$
$824$	−49.3112	−	25.0534i	−0.0598437	−	0.0304046i
$825$	−38.5414	−	38.5414i	−0.0467168	−	0.0467168i
$826$	378.590	+	231.799i	0.458341	+	0.280628i
$827$	246.520	−	595.152i	0.298090	−	0.719652i	−0.701883	−	0.712292i	$-0.747657\pi$
$827$	246.520	−	595.152i	0.298090	−	0.719652i	0.999973	−	0.00736012i	$-0.00234282\pi$
$828$	−280.084	+	864.280i	−0.338265	+	1.04382i
$829$	393.211	+	949.295i	0.474319	+	1.14511i	0.962236	+	0.272218i	$0.0877571\pi$
$829$	393.211	+	949.295i	0.474319	+	1.14511i	−0.487916	+	0.872890i	$0.662243\pi$
$830$	−9.39504	−	12.9207i	−0.0113193	−	0.0155671i
$831$		−	138.972i		−	0.167235i
$832$	−602.303	+	988.000i	−0.723921	+	1.18750i
$833$	−200.469			−0.240659
$834$	434.069	−	315.626i	0.520466	−	0.378448i
$835$	321.428	−	133.140i	0.384943	−	0.159449i
$836$	164.361	+	53.2637i	0.196604	+	0.0637126i
$837$	−307.018	−	127.171i	−0.366808	−	0.151937i
$838$	−385.669	+	629.900i	−0.460225	+	0.751671i
$839$	−575.067	+	575.067i	−0.685420	+	0.685420i	−0.961216	−	0.275796i	$-0.911059\pi$
$839$	−575.067	+	575.067i	−0.685420	+	0.685420i	0.275796	+	0.961216i	$0.411059\pi$
$840$	−236.808	−	120.314i	−0.281914	−	0.143231i
$841$	−430.678	+	430.678i	−0.512102	+	0.512102i
$842$	713.932	−	171.692i	0.847900	−	0.203909i
$843$	−26.8929	−	11.1394i	−0.0319015	−	0.0132140i
$844$	218.070	−	17.3319i	0.258377	−	0.0205355i
$845$	361.350	−	149.676i	0.427633	−	0.177131i
$846$	−73.7765	+	466.973i	−0.0872063	+	0.551978i
$847$	1057.21			1.24818
$848$	−139.956	+	86.0626i	−0.165042	+	0.101489i
$849$		−	526.620i		−	0.620283i
$850$	−36.4899	+	230.965i	−0.0429293	+	0.271724i
$851$	−416.535	−	1005.61i	−0.489466	−	1.18167i
$852$	40.1374	+	34.2270i	0.0471096	+	0.0401725i
$853$	304.017	−	733.961i	0.356409	−	0.860447i	−0.639390	−	0.768882i	$-0.720813\pi$
$853$	304.017	−	733.961i	0.356409	−	0.860447i	0.995799	−	0.0915645i	$-0.0291868\pi$
$854$	−137.702	+	33.1155i	−0.161243	+	0.0387769i
$855$	264.279	+	264.279i	0.309098	+	0.309098i
$856$	−34.7887	+	448.677i	−0.0406410	+	0.524155i
$857$	−241.394	−	241.394i	−0.281673	−	0.281673i	0.552103	−	0.833776i	$-0.313826\pi$
$857$	−241.394	−	241.394i	−0.281673	−	0.281673i	−0.833776	+	0.552103i	$0.813826\pi$
$858$	54.5593	−	89.1099i	0.0635889	−	0.103858i
$859$	443.212	−	1070.01i	0.515963	−	1.24564i	−0.424401	−	0.905474i	$-0.639515\pi$
$859$	443.212	−	1070.01i	0.515963	−	1.24564i	0.940364	−	0.340170i	$-0.110485\pi$
$860$	520.661	−	265.797i	0.605420	−	0.309066i
$861$	413.230	+	997.625i	0.479942	+	1.15868i
$862$	249.922	−	181.727i	0.289933	−	0.210820i
$863$			167.859i			0.194507i	0.995260	+	0.0972533i	$0.0310057\pi$
$863$			167.859i			0.194507i	−0.995260	+	0.0972533i	$0.968994\pi$
$864$	−286.034	+	694.337i	−0.331058	+	0.803631i
$865$	502.117			0.580482
$866$	596.105	+	819.802i	0.688343	+	0.946654i
$867$	−344.031	+	142.502i	−0.396806	+	0.164363i
$868$	455.011	−	232.282i	0.524206	−	0.267606i
$869$	136.263	+	56.4418i	0.156804	+	0.0649503i
$870$	−239.111	−	146.401i	−0.274841	−	0.168277i
$871$	−773.586	+	773.586i	−0.888158	+	0.888158i
$872$	280.469	+	327.617i	0.321638	+	0.375708i
$873$	−432.474	+	432.474i	−0.495388	+	0.495388i
$874$	−347.405	−	1444.59i	−0.397488	−	1.65285i
$875$	905.426	+	375.040i	1.03477	+	0.428617i
$876$	425.103	+	362.505i	0.485278	+	0.413819i
$877$	659.079	−	272.999i	0.751515	−	0.311288i	0.0261554	−	0.999658i	$-0.491674\pi$
$877$	659.079	−	272.999i	0.751515	−	0.311288i	0.725360	+	0.688370i	$0.241674\pi$
$878$	−404.388	−	63.8887i	−0.460579	−	0.0727662i
$879$	663.964			0.755363
$880$	12.1744	+	76.1048i	0.0138345	+	0.0864827i
$881$			806.984i			0.915987i	0.888956	+	0.457993i	$0.151432\pi$
$881$			806.984i			0.915987i	−0.888956	+	0.457993i	$0.848568\pi$
$882$	433.952	+	68.5595i	0.492009	+	0.0777318i
$883$	−118.704	−	286.577i	−0.134433	−	0.324549i	0.842300	−	0.539009i	$-0.181201\pi$
$883$	−118.704	−	286.577i	−0.134433	−	0.324549i	−0.976733	+	0.214459i	$0.931201\pi$
$884$	−446.836	+	35.5140i	−0.505470	+	0.0401742i
$885$	−34.6701	+	83.7011i	−0.0391753	+	0.0945776i
$886$	−282.233	−	1173.59i	−0.318547	−	1.32459i
$887$	727.865	+	727.865i	0.820592	+	0.820592i	0.986193	−	0.165601i	$-0.0529563\pi$
$887$	727.865	+	727.865i	0.820592	+	0.820592i	−0.165601	+	0.986193i	$0.552956\pi$
$888$	−119.994	−	367.852i	−0.135128	−	0.414248i
$889$	−1129.10	−	1129.10i	−1.27008	−	1.27008i
$890$	219.327	+	134.288i	0.246435	+	0.150885i
$891$	−19.5348	+	47.1611i	−0.0219246	+	0.0529306i
$892$	−200.738	−	65.0525i	−0.225043	−	0.0729288i
$893$	−295.869	−	714.290i	−0.331320	−	0.799877i
$894$	82.2315	+	113.090i	0.0919816	+	0.126499i
$895$		−	655.308i		−	0.732188i
$896$	−526.883	−	1027.19i	−0.588040	−	1.14642i
$897$	−898.518			−1.00169
$898$	−0.325218	+	0.236477i	−0.000362158	+	0.000263337i
$899$	498.196	−	206.359i	0.554167	−	0.229543i
$900$	157.978	−	487.488i	0.175532	−	0.541654i
$901$	−58.8018	−	24.3565i	−0.0652628	−	0.0270328i
$902$	163.608	−	267.215i	0.181383	−	0.296247i
$903$	559.093	−	559.093i	0.619151	−	0.619151i
$904$	472.208	−	154.035i	0.522353	−	0.170392i
$905$	27.8215	−	27.8215i	0.0307420	−	0.0307420i
$906$	279.361	−	67.1827i	0.308345	−	0.0741531i
$907$	711.116	+	294.554i	0.784031	+	0.324756i	0.738541	−	0.674209i	$-0.235515\pi$
$907$	711.116	+	294.554i	0.784031	+	0.324756i	0.0454897	+	0.998965i	$0.485515\pi$
$908$	112.205	+	1411.75i	0.123573	+	1.55480i
$909$	136.425	−	56.5090i	0.150082	−	0.0621661i
$910$	−126.077	+	798.016i	−0.138547	+	0.876941i
$911$	−758.696			−0.832817			−0.416409	−	0.909178i	$-0.636711\pi$
$911$	−758.696			−0.832817			−0.416409	+	0.909178i	$0.636711\pi$
$912$	−83.4292	−	521.536i	−0.0914794	−	0.571860i
$913$			6.26965i			0.00686708i
$914$	100.122	−	633.727i	0.109542	−	0.693356i
$915$	−11.0612	−	26.7042i	−0.0120888	−	0.0291849i
$916$	689.483	−	808.544i	0.752710	−	0.882690i
$917$	−331.611	+	800.581i	−0.361626	+	0.873043i
$918$	−282.839	+	68.0191i	−0.308103	+	0.0740949i
$919$	949.647	+	949.647i	1.03335	+	1.03335i	0.999424	+	0.0339243i	$0.0108005\pi$
$919$	949.647	+	949.647i	1.03335	+	1.03335i	0.0339243	+	0.999424i	$0.489199\pi$
$920$	503.482	−	431.024i	0.547263	−	0.468505i
$921$	116.302	+	116.302i	0.126278	+	0.126278i
$922$	561.349	−	916.833i	0.608838	−	0.994396i
$923$	61.3993	−	148.231i	0.0665215	−	0.160597i
$924$	47.3977	+	92.8458i	0.0512962	+	0.100483i
$925$	234.943	+	567.202i	0.253992	+	0.613191i
$926$	−841.172	+	611.644i	−0.908393	+	0.660523i
$927$			46.9566i			0.0506544i
$928$	−468.493	−	1124.89i	−0.504842	−	1.21217i
$929$	222.645			0.239661			0.119830	−	0.992794i	$-0.461765\pi$
$929$	222.645			0.239661			0.119830	+	0.992794i	$0.461765\pi$
$930$	61.3165	+	84.3264i	0.0659317	+	0.0906735i
$931$	−663.780	+	274.947i	−0.712975	+	0.295324i
$932$	81.9896	+	160.607i	0.0879717	+	0.172325i
$933$	−654.952	−	271.290i	−0.701985	−	0.290772i
$934$	158.214	+	96.8699i	0.169394	+	0.103715i
$935$	−21.1117	+	21.1117i	−0.0225794	+	0.0225794i
$936$	979.405	+	75.9393i	1.04637	+	0.0811317i
$937$	−1027.40	+	1027.40i	−1.09648	+	1.09648i	−0.101659	+	0.994819i	$0.532415\pi$
$937$	−1027.40	+	1027.40i	−1.09648	+	1.09648i	−0.994819	+	0.101659i	$0.967585\pi$
$938$	−255.213	−	1061.23i	−0.272082	−	1.13138i
$939$	136.055	+	56.3558i	0.144893	+	0.0600168i
$940$	223.783	−	262.426i	0.238067	−	0.279177i
$941$	−892.441	+	369.661i	−0.948397	+	0.392839i	−0.802628	−	0.596480i	$-0.796566\pi$
$941$	−892.441	+	369.661i	−0.948397	+	0.392839i	−0.145769	+	0.989319i	$0.546566\pi$
$942$	572.007	+	90.3706i	0.607226	+	0.0959348i
$943$	−2694.40			−2.85726
$944$	−335.415	+	206.256i	−0.355313	+	0.218491i
$945$			524.321i			0.554837i
$946$	−226.613	−	35.8023i	−0.239549	−	0.0378460i
$947$	385.441	+	930.536i	0.407012	+	0.982615i	0.985919	+	0.167221i	$0.0534795\pi$
$947$	385.441	+	930.536i	0.407012	+	0.982615i	−0.578907	+	0.815394i	$0.696521\pi$
$948$	−35.7219	−	449.451i	−0.0376813	−	0.474105i
$949$	650.293	−	1569.95i	0.685240	−	1.65432i
$950$	195.950	+	814.805i	0.206263	+	0.857690i
$951$	−90.2371	−	90.2371i	−0.0948865	−	0.0948865i
$952$	202.567	−	398.701i	0.212780	−	0.418804i
$953$	648.910	+	648.910i	0.680913	+	0.680913i	0.960206	−	0.279293i	$-0.0901001\pi$
$953$	648.910	+	648.910i	0.680913	+	0.680913i	−0.279293	+	0.960206i	$0.590100\pi$
$954$	118.958	+	72.8342i	0.124694	+	0.0763462i
$955$	−351.314	+	848.148i	−0.367868	+	0.888113i
$956$	111.045	−	342.661i	0.116156	−	0.358432i
$957$	42.1081	+	101.658i	0.0440001	+	0.106226i
$958$	191.857	+	263.854i	0.200268	+	0.275422i
$959$		−	746.905i		−	0.778837i
$960$	190.288	−	138.927i	0.198217	−	0.144716i
$961$	760.470			0.791331
$962$	−951.859	+	692.128i	−0.989459	+	0.719468i
$963$	352.971	−	146.205i	0.366532	−	0.151823i
$964$	−79.8980	−	25.8922i	−0.0828818	−	0.0268592i
$965$	−303.665	−	125.782i	−0.314679	−	0.130344i
$966$	468.095	−	764.524i	0.484570	−	0.791432i
$967$	−41.2757	+	41.2757i	−0.0426842	+	0.0426842i	−0.728127	−	0.685443i	$-0.759609\pi$
$967$	−41.2757	+	41.2757i	−0.0426842	+	0.0426842i	0.685443	+	0.728127i	$0.259609\pi$
$968$	−424.762	+	836.036i	−0.438804	+	0.863674i
$969$	144.676	−	144.676i	0.149304	−	0.149304i
$970$	433.806	−	104.325i	0.447223	−	0.107551i
$971$	−213.816	−	88.5653i	−0.220201	−	0.0912104i	0.269856	−	0.962901i	$-0.413024\pi$
$971$	−213.816	−	88.5653i	−0.220201	−	0.0912104i	−0.490057	+	0.871690i	$0.663024\pi$
$972$	997.715	−	79.2973i	1.02646	−	0.0815816i
$973$	1504.67	−	623.253i	1.54642	−	0.640547i
$974$	164.073	−	1038.51i	0.168453	−	1.06624i
$975$	506.800			0.519795
$976$	29.1379	−	122.199i	0.0298544	−	0.125204i
$977$			314.091i			0.321485i	0.986996	+	0.160742i	$0.0513888\pi$
$977$			314.091i			0.321485i	−0.986996	+	0.160742i	$0.948611\pi$
$978$	−134.100	+	848.795i	−0.137117	+	0.867889i
$979$	−38.6240	−	93.2467i	−0.0394526	−	0.0952469i
$980$	−243.869	−	207.958i	−0.248846	−	0.212202i
$981$	140.113	−	338.263i	0.142827	−	0.344815i
$982$	591.865	−	142.336i	0.602713	−	0.144945i
$983$	−8.50847	−	8.50847i	−0.00865562	−	0.00865562i	0.702766	−	0.711421i	$-0.251948\pi$
$983$	−8.50847	−	8.50847i	−0.00865562	−	0.00865562i	−0.711421	+	0.702766i	$0.751948\pi$
$984$	−954.947	−	74.0429i	−0.970474	−	0.0752468i
$985$	220.680	+	220.680i	0.224041	+	0.224041i
$986$	246.488	−	402.580i	0.249987	−	0.408296i
$987$	178.513	−	430.967i	0.180864	−	0.436644i
$988$	−1430.83	+	730.436i	−1.44821	+	0.739307i
$989$	755.003	+	1822.74i	0.763400	+	1.84301i
$990$	52.9204	−	38.4801i	0.0534549	−	0.0388688i
$991$		−	93.7233i		−	0.0945745i	−0.998881	−	0.0472872i	$-0.984942\pi$
$991$		−	93.7233i		−	0.0945745i	0.998881	−	0.0472872i	$-0.0150576\pi$
$992$	0.874957	+	453.147i	0.000882013	+	0.456802i
$993$	−200.842			−0.202257
$994$	94.1388	+	129.466i	0.0947070	+	0.130247i
$995$	−291.291	+	120.657i	−0.292754	+	0.121263i
$996$	17.0703	−	8.71437i	0.0171389	−	0.00874937i
$997$	−287.749	−	119.189i	−0.288614	−	0.119548i	0.233679	−	0.972314i	$-0.424923\pi$
$997$	−287.749	−	119.189i	−0.288614	−	0.119548i	−0.522294	+	0.852766i	$0.674923\pi$
$998$	−1052.45	−	644.386i	−1.05456	−	0.645677i
$999$	−540.075	+	540.075i	−0.540616	+	0.540616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.27.6	yes	28
3.2	odd	2		288.3.u.a.91.2		28
4.3	odd	2		128.3.h.a.15.5		28
8.3	odd	2		256.3.h.a.31.3		28
8.5	even	2		256.3.h.b.31.5		28
32.3	odd	8		256.3.h.b.223.5		28
32.13	even	8		128.3.h.a.111.5		28
32.19	odd	8	inner	32.3.h.a.19.6	✓	28
32.29	even	8		256.3.h.a.223.3		28
96.83	even	8		288.3.u.a.19.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.6	✓	28	32.19	odd	8	inner
32.3.h.a.27.6	yes	28	1.1	even	1	trivial
128.3.h.a.15.5		28	4.3	odd	2
128.3.h.a.111.5		28	32.13	even	8
256.3.h.a.31.3		28	8.3	odd	2
256.3.h.a.223.3		28	32.29	even	8
256.3.h.b.31.5		28	8.5	even	2
256.3.h.b.223.5		28	32.3	odd	8
288.3.u.a.19.2		28	96.83	even	8
288.3.u.a.91.2		28	3.2	odd	2

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61758 - 1.17620i) q^{2} +(-1.37292 + 0.568682i) q^{3} +(1.23313 - 3.80518i) q^{4} +(2.28872 + 0.948019i) q^{5} +(-1.55193 + 2.53471i) q^{6} +(-6.37744 + 6.37744i) q^{7} +(-2.48095 - 7.60558i) q^{8} +(-4.80245 + 4.80245i) q^{9} +O(q^{10})\)	\(q+(1.61758 - 1.17620i) q^{2} +(-1.37292 + 0.568682i) q^{3} +(1.23313 - 3.80518i) q^{4} +(2.28872 + 0.948019i) q^{5} +(-1.55193 + 2.53471i) q^{6} +(-6.37744 + 6.37744i) q^{7} +(-2.48095 - 7.60558i) q^{8} +(-4.80245 + 4.80245i) q^{9} +(4.81725 - 1.15849i) q^{10} +(-1.79646 - 0.744117i) q^{11} +(0.470949 + 5.92546i) q^{12} +(16.7036 - 6.91888i) q^{13} +(-2.81490 + 17.8171i) q^{14} -3.68135 q^{15} +(-12.9588 - 9.38456i) q^{16} -6.19811i q^{17} +(-2.11973 + 13.4170i) q^{18} +(-8.50083 - 20.5228i) q^{19} +(6.42967 - 7.53997i) q^{20} +(5.12898 - 12.3825i) q^{21} +(-3.78114 + 0.909316i) q^{22} +(23.6476 + 23.6476i) q^{23} +(7.73130 + 9.03098i) q^{24} +(-13.3382 - 13.3382i) q^{25} +(18.8815 - 30.8386i) q^{26} +(8.98045 - 21.6807i) q^{27} +(16.4031 + 32.1315i) q^{28} +(14.5725 + 35.1811i) q^{29} +(-5.95488 + 4.32999i) q^{30} -14.1609i q^{31} +(-31.9999 + 0.0617869i) q^{32} +2.88956 q^{33} +(-7.29019 - 10.0259i) q^{34} +(-20.6421 + 8.55025i) q^{35} +(12.3521 + 24.1962i) q^{36} +(-30.0695 - 12.4552i) q^{37} +(-37.8896 - 23.1987i) q^{38} +(-18.9981 + 18.9981i) q^{39} +(1.53204 - 19.7590i) q^{40} +(-56.9700 + 56.9700i) q^{41} +(-6.26765 - 26.0623i) q^{42} +(54.5034 + 22.5760i) q^{43} +(-5.04676 + 5.91825i) q^{44} +(-15.5443 + 6.43866i) q^{45} +(66.0659 + 10.4377i) q^{46} +34.8047 q^{47} +(23.1282 + 5.51482i) q^{48} -32.3435i q^{49} +(-37.2638 - 5.88726i) q^{50} +(3.52475 + 8.50951i) q^{51} +(-5.72981 - 72.0923i) q^{52} +(3.92967 - 9.48706i) q^{53} +(-10.9742 - 45.6331i) q^{54} +(-3.40615 - 3.40615i) q^{55} +(64.3263 + 32.6821i) q^{56} +(23.3419 + 23.3419i) q^{57} +(64.9521 + 39.7682i) q^{58} +(9.41777 - 22.7365i) q^{59} +(-4.53958 + 14.0082i) q^{60} +(3.00467 + 7.25391i) q^{61} +(-16.6560 - 22.9064i) q^{62} -61.2547i q^{63} +(-51.6898 + 37.7381i) q^{64} +44.7892 q^{65} +(4.67409 - 3.39868i) q^{66} +(-55.9040 + 23.1562i) q^{67} +(-23.5849 - 7.64307i) q^{68} +(-45.9141 - 19.0183i) q^{69} +(-23.3335 + 38.1099i) q^{70} +(6.27499 - 6.27499i) q^{71} +(48.4401 + 24.6108i) q^{72} +(66.4597 - 66.4597i) q^{73} +(-63.2896 + 15.2203i) q^{74} +(25.8974 + 10.7271i) q^{75} +(-88.5756 + 7.03989i) q^{76} +(16.2024 - 6.71124i) q^{77} +(-8.38548 + 53.0765i) q^{78} -75.8508 q^{79} +(-20.7623 - 33.7638i) q^{80} -26.2523i q^{81} +(-25.1457 + 159.161i) q^{82} +(-1.23390 - 2.97891i) q^{83} +(-40.7928 - 34.7859i) q^{84} +(5.87593 - 14.1857i) q^{85} +(114.717 - 27.5881i) q^{86} +(-40.0138 - 40.0138i) q^{87} +(-1.20252 + 15.5092i) q^{88} +(36.7030 + 36.7030i) q^{89} +(-17.5710 + 28.6982i) q^{90} +(-62.4018 + 150.651i) q^{91} +(119.144 - 60.8227i) q^{92} +(8.05304 + 19.4417i) q^{93} +(56.2994 - 40.9371i) q^{94} -55.0300i q^{95} +(43.8982 - 18.2826i) q^{96} +90.0528 q^{97} +(-38.0423 - 52.3182i) q^{98} +(12.2010 - 5.05381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Introduction

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