LMFDB - Embedded newform 32.3.h.a.11.7

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			11.7
Character	$\chi$	$=$	32.11
Dual form			32.3.h.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93931 + 0.488972i) q^{2} +(-1.73217 - 4.18183i) q^{3} +(3.52181 + 1.89653i) q^{4} +(-1.85856 + 4.48696i) q^{5} +(-1.31441 - 8.95683i) q^{6} +(-5.27676 + 5.27676i) q^{7} +(5.90252 + 5.40002i) q^{8} +(-8.12333 + 8.12333i) q^{9} +O(q^{10})$	\(q+(1.93931 + 0.488972i) q^{2} +(-1.73217 - 4.18183i) q^{3} +(3.52181 + 1.89653i) q^{4} +(-1.85856 + 4.48696i) q^{5} +(-1.31441 - 8.95683i) q^{6} +(-5.27676 + 5.27676i) q^{7} +(5.90252 + 5.40002i) q^{8} +(-8.12333 + 8.12333i) q^{9} +(-5.79831 + 7.79280i) q^{10} +(6.20050 - 14.9693i) q^{11} +(1.83059 - 18.0127i) q^{12} +(-4.22532 - 10.2008i) q^{13} +(-12.8134 + 7.65307i) q^{14} +21.9830 q^{15} +(8.80634 + 13.3585i) q^{16} +2.84356i q^{17} +(-19.7257 + 11.7816i) q^{18} +(-12.4276 + 5.14768i) q^{19} +(-15.0551 + 12.2774i) q^{20} +(31.2068 + 12.9263i) q^{21} +(19.3443 - 25.9983i) q^{22} +(-1.43918 - 1.43918i) q^{23} +(12.3578 - 34.0371i) q^{24} +(0.999126 + 0.999126i) q^{25} +(-3.20628 - 21.8486i) q^{26} +(10.4049 + 4.30987i) q^{27} +(-28.5913 + 8.57623i) q^{28} +(36.9596 - 15.3092i) q^{29} +(42.6318 + 10.7491i) q^{30} +4.73823i q^{31} +(10.5463 + 30.2122i) q^{32} -73.3396 q^{33} +(-1.39042 + 5.51453i) q^{34} +(-13.8694 - 33.4838i) q^{35} +(-44.0150 + 13.2027i) q^{36} +(-6.68390 + 16.1364i) q^{37} +(-26.6180 + 3.90618i) q^{38} +(-35.3392 + 35.3392i) q^{39} +(-35.1998 + 16.4481i) q^{40} +(40.4523 - 40.4523i) q^{41} +(54.1989 + 40.3272i) q^{42} +(-24.5000 + 59.1482i) q^{43} +(50.2268 - 40.9598i) q^{44} +(-21.3514 - 51.5467i) q^{45} +(-2.08729 - 3.49473i) q^{46} -16.5262 q^{47} +(40.6087 - 59.9658i) q^{48} -6.68842i q^{49} +(1.44907 + 2.42615i) q^{50} +(11.8913 - 4.92553i) q^{51} +(4.46539 - 43.9389i) q^{52} +(-46.9950 - 19.4659i) q^{53} +(18.0710 + 13.4459i) q^{54} +(55.6428 + 55.6428i) q^{55} +(-59.6408 + 2.65160i) q^{56} +(43.0535 + 43.0535i) q^{57} +(79.1617 - 11.6170i) q^{58} +(50.0578 + 20.7346i) q^{59} +(77.4202 + 41.6915i) q^{60} +(-54.3116 + 22.4966i) q^{61} +(-2.31686 + 9.18889i) q^{62} -85.7298i q^{63} +(5.67958 + 63.7475i) q^{64} +53.6237 q^{65} +(-142.228 - 35.8610i) q^{66} +(-25.5017 - 61.5665i) q^{67} +(-5.39290 + 10.0145i) q^{68} +(-3.52550 + 8.51131i) q^{69} +(-10.5245 - 71.7170i) q^{70} +(7.12641 - 7.12641i) q^{71} +(-91.8143 + 4.08202i) q^{72} +(55.3669 - 55.3669i) q^{73} +(-20.8524 + 28.0251i) q^{74} +(2.44752 - 5.90883i) q^{75} +(-53.5304 - 5.44015i) q^{76} +(46.2711 + 111.708i) q^{77} +(-85.8133 + 51.2536i) q^{78} +11.0986 q^{79} +(-76.3059 + 14.6862i) q^{80} +52.4160i q^{81} +(98.2293 - 58.6693i) q^{82} +(-29.9476 + 12.4047i) q^{83} +(85.3894 + 104.709i) q^{84} +(-12.7589 - 5.28492i) q^{85} +(-76.4348 + 102.727i) q^{86} +(-128.041 - 128.041i) q^{87} +(117.433 - 54.8740i) q^{88} +(16.7667 + 16.7667i) q^{89} +(-16.2019 - 110.405i) q^{90} +(76.1234 + 31.5313i) q^{91} +(-2.33907 - 7.79797i) q^{92} +(19.8145 - 8.20743i) q^{93} +(-32.0494 - 8.08086i) q^{94} -65.3294i q^{95} +(108.074 - 96.4355i) q^{96} -67.8301 q^{97} +(3.27045 - 12.9709i) q^{98} +(71.2322 + 171.970i) 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 $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.93931	+	0.488972i	0.969653	+	0.244486i
$2$	1.93931	+	0.488972i	0.969653	+	0.244486i
$3$	−1.73217	−	4.18183i	−0.577390	−	1.39394i	−0.895147	−	0.445771i	$-0.852929\pi$
$3$	−1.73217	−	4.18183i	−0.577390	−	1.39394i	0.317756	−	0.948172i	$-0.397071\pi$
$4$	3.52181	+	1.89653i	0.880453	+	0.474133i
$5$	−1.85856	+	4.48696i	−0.371712	+	0.897391i	0.621749	+	0.783217i	$0.286422\pi$
$5$	−1.85856	+	4.48696i	−0.371712	+	0.897391i	−0.993461	+	0.114175i	$0.963578\pi$
$6$	−1.31441	−	8.95683i	−0.219069	−	1.49281i
$7$	−5.27676	+	5.27676i	−0.753823	+	0.753823i	−0.975190	−	0.221367i	$-0.928948\pi$
$7$	−5.27676	+	5.27676i	−0.753823	+	0.753823i	0.221367	+	0.975190i	$0.428948\pi$
$8$	5.90252	+	5.40002i	0.737816	+	0.675002i
$9$	−8.12333	+	8.12333i	−0.902593	+	0.902593i
$10$	−5.79831	+	7.79280i	−0.579831	+	0.779280i
$11$	6.20050	−	14.9693i	0.563682	−	1.36085i	−0.343120	−	0.939292i	$-0.611484\pi$
$11$	6.20050	−	14.9693i	0.563682	−	1.36085i	0.906802	−	0.421557i	$-0.138516\pi$
$12$	1.83059	−	18.0127i	0.152549	−	1.50106i
$13$	−4.22532	−	10.2008i	−0.325025	−	0.784680i	−0.998947	−	0.0458772i	$-0.985392\pi$
$13$	−4.22532	−	10.2008i	−0.325025	−	0.784680i	0.673922	−	0.738802i	$-0.264608\pi$
$14$	−12.8134	+	7.65307i	−0.915246	+	0.546648i
$15$	21.9830			1.46554
$16$	8.80634	+	13.3585i	0.550396	+	0.834903i
$17$			2.84356i			0.167268i	0.996497	+	0.0836341i	$0.0266527\pi$
$17$			2.84356i			0.167268i	−0.996497	+	0.0836341i	$0.973347\pi$
$18$	−19.7257	+	11.7816i	−1.09587	+	0.654531i
$19$	−12.4276	+	5.14768i	−0.654084	+	0.270931i	−0.684947	−	0.728593i	$-0.740175\pi$
$19$	−12.4276	+	5.14768i	−0.654084	+	0.270931i	0.0308626	+	0.999524i	$0.490175\pi$
$20$	−15.0551	+	12.2774i	−0.752757	+	0.613871i
$21$	31.2068	+	12.9263i	1.48604	+	0.615537i
$22$	19.3443	−	25.9983i	0.879284	−	1.18174i
$23$	−1.43918	−	1.43918i	−0.0625730	−	0.0625730i	0.675128	−	0.737701i	$-0.264088\pi$
$23$	−1.43918	−	1.43918i	−0.0625730	−	0.0625730i	−0.737701	+	0.675128i	$0.764088\pi$
$24$	12.3578	−	34.0371i	0.514908	−	1.41821i
$25$	0.999126	+	0.999126i	0.0399650	+	0.0399650i
$26$	−3.20628	−	21.8486i	−0.123318	−	0.840331i
$27$	10.4049	+	4.30987i	0.385368	+	0.159625i
$28$	−28.5913	+	8.57623i	−1.02112	+	0.306294i
$29$	36.9596	−	15.3092i	1.27447	−	0.527902i	0.360148	−	0.932895i	$-0.382726\pi$
$29$	36.9596	−	15.3092i	1.27447	−	0.527902i	0.914320	+	0.404993i	$0.132726\pi$
$30$	42.6318	+	10.7491i	1.42106	+	0.358303i
$31$			4.73823i			0.152846i	0.997075	+	0.0764231i	$0.0243500\pi$
$31$			4.73823i			0.152846i	−0.997075	+	0.0764231i	$0.975650\pi$
$32$	10.5463	+	30.2122i	0.329572	+	0.944131i
$33$	−73.3396			−2.22241
$34$	−1.39042	+	5.51453i	−0.0408947	+	0.162192i
$35$	−13.8694	−	33.4838i	−0.396269	−	0.956679i
$36$	−44.0150	+	13.2027i	−1.22264	+	0.366742i
$37$	−6.68390	+	16.1364i	−0.180646	+	0.436118i	−0.988100	−	0.153812i	$-0.950845\pi$
$37$	−6.68390	+	16.1364i	−0.180646	+	0.436118i	0.807454	+	0.589930i	$0.200845\pi$
$38$	−26.6180	+	3.90618i	−0.700473	+	0.102794i
$39$	−35.3392	+	35.3392i	−0.906133	+	0.906133i
$40$	−35.1998	+	16.4481i	−0.879996	+	0.411203i
$41$	40.4523	−	40.4523i	0.986641	−	0.986641i	−0.0132711	−	0.999912i	$-0.504224\pi$
$41$	40.4523	−	40.4523i	0.986641	−	0.986641i	0.999912	+	0.0132711i	$0.00422444\pi$
$42$	54.1989	+	40.3272i	1.29045	+	0.960172i
$43$	−24.5000	+	59.1482i	−0.569767	+	1.37554i	0.331984	+	0.943285i	$0.392282\pi$
$43$	−24.5000	+	59.1482i	−0.569767	+	1.37554i	−0.901751	+	0.432255i	$0.857718\pi$
$44$	50.2268	−	40.9598i	1.14152	−	0.930904i
$45$	−21.3514	−	51.5467i	−0.474475	−	1.14548i
$46$	−2.08729	−	3.49473i	−0.0453759	−	0.0759723i
$47$	−16.5262			−0.351622			−0.175811	−	0.984424i	$-0.556255\pi$
$47$	−16.5262			−0.351622			−0.175811	+	0.984424i	$0.556255\pi$
$48$	40.6087	−	59.9658i	0.846015	−	1.24929i
$49$		−	6.68842i		−	0.136498i
$50$	1.44907	+	2.42615i	0.0289813	+	0.0485231i
$51$	11.8913	−	4.92553i	0.233162	−	0.0965790i
$52$	4.46539	−	43.9389i	0.0858729	−	0.844979i
$53$	−46.9950	−	19.4659i	−0.886697	−	0.367282i	−0.107607	−	0.994194i	$-0.534319\pi$
$53$	−46.9950	−	19.4659i	−0.886697	−	0.367282i	−0.779090	+	0.626912i	$0.784319\pi$
$54$	18.0710	+	13.4459i	0.334647	+	0.248998i
$55$	55.6428	+	55.6428i	1.01169	+	1.01169i
$56$	−59.6408	+	2.65160i	−1.06501	+	0.0473500i
$57$	43.0535	+	43.0535i	0.755324	+	0.755324i
$58$	79.1617	−	11.6170i	1.36486	−	0.200292i
$59$	50.0578	+	20.7346i	0.848437	+	0.351434i	0.764174	−	0.645010i	$-0.223147\pi$
$59$	50.0578	+	20.7346i	0.848437	+	0.351434i	0.0842623	+	0.996444i	$0.473147\pi$
$60$	77.4202	+	41.6915i	1.29034	+	0.694858i
$61$	−54.3116	+	22.4966i	−0.890353	+	0.368796i	−0.780503	−	0.625152i	$-0.785037\pi$
$61$	−54.3116	+	22.4966i	−0.890353	+	0.368796i	−0.109850	+	0.993948i	$0.535037\pi$
$62$	−2.31686	+	9.18889i	−0.0373687	+	0.148208i
$63$		−	85.7298i		−	1.36079i
$64$	5.67958	+	63.7475i	0.0887435	+	0.996055i
$65$	53.6237			0.824980
$66$	−142.228	−	35.8610i	−2.15497	−	0.543348i
$67$	−25.5017	−	61.5665i	−0.380622	−	0.918904i	−0.991846	−	0.127445i	$-0.959322\pi$
$67$	−25.5017	−	61.5665i	−0.380622	−	0.918904i	0.611223	−	0.791458i	$-0.290678\pi$
$68$	−5.39290	+	10.0145i	−0.0793073	+	0.147272i
$69$	−3.52550	+	8.51131i	−0.0510942	+	0.123352i
$70$	−10.5245	−	71.7170i	−0.150349	−	1.02453i
$71$	7.12641	−	7.12641i	0.100372	−	0.100372i	−0.655138	−	0.755510i	$-0.727389\pi$
$71$	7.12641	−	7.12641i	0.100372	−	0.100372i	0.755510	+	0.655138i	$0.227389\pi$
$72$	−91.8143	+	4.08202i	−1.27520	+	0.0566947i
$73$	55.3669	−	55.3669i	0.758451	−	0.758451i	−0.217590	−	0.976040i	$-0.569819\pi$
$73$	55.3669	−	55.3669i	0.758451	−	0.758451i	0.976040	+	0.217590i	$0.0698194\pi$
$74$	−20.8524	+	28.0251i	−0.281789	+	0.378718i
$75$	2.44752	−	5.90883i	0.0326336	−	0.0787844i
$76$	−53.5304	−	5.44015i	−0.704348	−	0.0715809i
$77$	46.2711	+	111.708i	0.600923	+	1.45076i
$78$	−85.8133	+	51.2536i	−1.10017	+	0.657098i
$79$	11.0986			0.140489			0.0702446	−	0.997530i	$-0.477622\pi$
$79$	11.0986			0.140489			0.0702446	+	0.997530i	$0.477622\pi$
$80$	−76.3059	+	14.6862i	−0.953824	+	0.183578i
$81$			52.4160i			0.647112i
$82$	98.2293	−	58.6693i	1.19792	−	0.715480i
$83$	−29.9476	+	12.4047i	−0.360814	+	0.149454i	−0.555724	−	0.831367i	$-0.687559\pi$
$83$	−29.9476	+	12.4047i	−0.360814	+	0.149454i	0.194909	+	0.980821i	$0.437559\pi$
$84$	85.3894	+	104.709i	1.01654	+	1.24653i
$85$	−12.7589	−	5.28492i	−0.150105	−	0.0621755i
$86$	−76.4348	+	102.727i	−0.888777	+	1.19450i
$87$	−128.041	−	128.041i	−1.47173	−	1.47173i
$88$	117.433	−	54.8740i	1.33447	−	0.623569i
$89$	16.7667	+	16.7667i	0.188390	+	0.188390i	0.795000	−	0.606610i	$-0.207471\pi$
$89$	16.7667	+	16.7667i	0.188390	+	0.188390i	−0.606610	+	0.795000i	$0.707471\pi$
$90$	−16.2019	−	110.405i	−0.180021	−	1.22672i
$91$	76.1234	+	31.5313i	0.836521	+	0.346498i
$92$	−2.33907	−	7.79797i	−0.0254247	−	0.0847606i
$93$	19.8145	−	8.20743i	0.213059	−	0.0882520i
$94$	−32.0494	−	8.08086i	−0.340951	−	0.0859666i
$95$		−	65.3294i		−	0.687678i
$96$	108.074	−	96.4355i	1.12577	−	1.00454i
$97$	−67.8301			−0.699280			−0.349640	−	0.936884i	$-0.613696\pi$
$97$	−67.8301			−0.699280			−0.349640	+	0.936884i	$0.613696\pi$
$98$	3.27045	−	12.9709i	0.0333719	−	0.132356i
$99$	71.2322	+	171.970i	0.719517	+	1.73707i
$100$	1.62386	+	5.41361i	0.0162386	+	0.0541361i
$101$	−45.6943	+	110.316i	−0.452419	+	1.09224i	0.518981	+	0.854786i	$0.326311\pi$
$101$	−45.6943	+	110.316i	−0.452419	+	1.09224i	−0.971400	+	0.237450i	$0.923689\pi$
$102$	25.4693	−	3.73761i	0.249699	−	0.0366432i
$103$	61.7093	−	61.7093i	0.599120	−	0.599120i	−0.340959	−	0.940078i	$-0.610752\pi$
$103$	61.7093	−	61.7093i	0.599120	−	0.599120i	0.940078	+	0.340959i	$0.110752\pi$
$104$	30.1446	−	83.0275i	0.289852	−	0.798341i
$105$	−115.999	+	115.999i	−1.10475	+	1.10475i
$106$	−81.6193	−	60.7296i	−0.769993	−	0.572921i
$107$	7.13652	−	17.2291i	0.0666965	−	0.161020i	−0.887017	−	0.461737i	$-0.847226\pi$
$107$	7.13652	−	17.2291i	0.0666965	−	0.161020i	0.953713	+	0.300718i	$0.0972262\pi$
$108$	28.4705	+	34.9118i	0.263615	+	0.323258i
$109$	−75.1681	−	181.472i	−0.689616	−	1.66488i	−0.745554	−	0.666445i	$-0.767815\pi$
$109$	−75.1681	−	181.472i	−0.689616	−	1.66488i	0.0559384	−	0.998434i	$-0.482185\pi$
$110$	80.7006	+	135.116i	0.733642	+	1.22833i
$111$	79.0572			0.712227
$112$	−116.958	−	24.0204i	−1.04427	−	0.214468i
$113$		−	156.784i		−	1.38747i	−0.720232	−	0.693734i	$-0.755965\pi$
$113$		−	156.784i		−	1.38747i	0.720232	−	0.693734i	$-0.244035\pi$
$114$	62.4419	+	104.546i	0.547736	+	0.917068i
$115$	9.13234	−	3.78274i	0.0794116	−	0.0328934i
$116$	159.199	+	16.1790i	1.37241	+	0.139474i
$117$	117.189	+	48.5411i	1.00161	+	0.414881i
$118$	86.9387	+	64.6876i	0.736769	+	0.548200i
$119$	−15.0048	−	15.0048i	−0.126091	−	0.126091i
$120$	129.755	+	118.709i	1.08130	+	0.989240i
$121$	−100.075	−	100.075i	−0.827066	−	0.827066i
$122$	−116.327	+	17.0710i	−0.953499	+	0.139926i
$123$	−239.235	−	99.0943i	−1.94500	−	0.805645i
$124$	−8.98621	+	16.6872i	−0.0724694	+	0.134574i
$125$	−118.514	+	49.0901i	−0.948111	+	0.392720i
$126$	41.9194	−	166.256i	0.332694	−	1.31949i
$127$			192.971i			1.51946i	0.650240	+	0.759729i	$0.274668\pi$
$127$			192.971i			1.51946i	−0.650240	+	0.759729i	$0.725332\pi$
$128$	−20.1563	+	126.403i	−0.157471	+	0.987524i
$129$	289.786			2.24640
$130$	103.993	+	26.2205i	0.799944	+	0.201696i
$131$	18.2599	+	44.0834i	0.139389	+	0.336515i	0.978123	−	0.208026i	$-0.0667040\pi$
$131$	18.2599	+	44.0834i	0.139389	+	0.336515i	−0.838734	+	0.544541i	$0.816704\pi$
$132$	−258.288	−	139.091i	−1.95673	−	1.05372i
$133$	38.4144	−	92.7406i	0.288830	−	0.697297i
$134$	−19.3513	−	131.866i	−0.144413	−	0.984074i
$135$	−38.6764	+	38.6764i	−0.286492	+	0.286492i
$136$	−15.3553	+	16.7842i	−0.112906	+	0.123413i
$137$	−27.8671	+	27.8671i	−0.203409	+	0.203409i	−0.801459	−	0.598050i	$-0.795943\pi$
$137$	−27.8671	+	27.8671i	−0.203409	+	0.203409i	0.598050	+	0.801459i	$0.295943\pi$
$138$	−10.9988	+	14.7822i	−0.0797015	+	0.107117i
$139$	33.3447	−	80.5013i	0.239890	−	0.579146i	−0.757381	−	0.652973i	$-0.773521\pi$
$139$	33.3447	−	80.5013i	0.239890	−	0.579146i	0.997271	+	0.0738274i	$0.0235214\pi$
$140$	14.6574	−	144.227i	0.104696	−	1.03020i
$141$	28.6263	+	69.1099i	0.203023	+	0.490141i
$142$	17.3049	−	10.3357i	0.121866	−	0.0727865i
$143$	−178.899			−1.25104
$144$	−180.052	−	36.9783i	−1.25036	−	0.256794i
$145$			194.289i			1.33992i
$146$	134.446	−	80.3005i	0.920864	−	0.550004i
$147$	−27.9698	+	11.5855i	−0.190271	+	0.0788128i
$148$	−54.1426	+	44.1531i	−0.365828	+	0.298331i
$149$	−125.860	−	52.1327i	−0.844695	−	0.349884i	−0.0819919	−	0.996633i	$-0.526128\pi$
$149$	−125.860	−	52.1327i	−0.844695	−	0.349884i	−0.762703	+	0.646749i	$0.776128\pi$
$150$	7.63574	−	10.2623i	0.0509049	−	0.0684151i
$151$	106.254	+	106.254i	0.703672	+	0.703672i	0.965197	−	0.261525i	$-0.0842254\pi$
$151$	106.254	+	106.254i	0.703672	+	0.703672i	−0.261525	+	0.965197i	$0.584225\pi$
$152$	−101.152	−	36.7250i	−0.665472	−	0.241612i
$153$	−23.0992	−	23.0992i	−0.150975	−	0.150975i
$154$	35.1116	+	239.262i	0.227997	+	1.55365i
$155$	−21.2603	−	8.80629i	−0.137163	−	0.0568147i
$156$	−191.480	+	57.4362i	−1.22743	+	0.368181i
$157$	209.345	−	86.7136i	1.33341	−	0.552316i	0.401783	−	0.915735i	$-0.368391\pi$
$157$	209.345	−	86.7136i	1.33341	−	0.552316i	0.931626	+	0.363419i	$0.118391\pi$
$158$	21.5237	+	5.42692i	0.136226	+	0.0343476i
$159$			230.243i			1.44807i
$160$	−155.162	−	8.83036i	−0.969760	−	0.0551897i
$161$	15.1884			0.0943380
$162$	−25.6299	+	101.651i	−0.158210	+	0.627474i
$163$	−0.176018	−	0.424946i	−0.00107987	−	0.00260703i	0.923339	−	0.383987i	$-0.125449\pi$
$163$	−0.176018	−	0.424946i	−0.00107987	−	0.00260703i	−0.924419	+	0.381380i	$0.875449\pi$
$164$	219.184	−	65.7464i	1.33649	−	0.400893i
$165$	136.306	−	329.072i	0.826096	−	1.99437i
$166$	−64.1431	+	9.41298i	−0.386404	+	0.0567047i
$167$	96.7499	−	96.7499i	0.579341	−	0.579341i	−0.355381	−	0.934722i	$-0.615649\pi$
$167$	96.7499	−	96.7499i	0.579341	−	0.579341i	0.934722	+	0.355381i	$0.115649\pi$
$168$	114.397	+	244.815i	0.680932	+	1.45723i
$169$	33.2974	−	33.2974i	0.197026	−	0.197026i
$170$	−22.1593	−	16.4878i	−0.130349	−	0.0969872i
$171$	59.1372	−	142.770i	0.345832	−	0.834912i
$172$	−198.461	+	161.844i	−1.15384	+	0.940954i
$173$	102.242	+	246.834i	0.590994	+	1.42678i	0.882544	+	0.470229i	$0.155829\pi$
$173$	102.242	+	246.834i	0.590994	+	1.42678i	−0.291551	+	0.956555i	$0.594171\pi$
$174$	−185.702	−	310.918i	−1.06725	−	1.78689i
$175$	−10.5443			−0.0602531
$176$	254.571	−	48.9960i	1.44643	−	0.278386i
$177$		−	245.249i		−	1.38559i
$178$	24.3174	+	40.7143i	0.136614	+	0.228732i
$179$	269.771	−	111.743i	1.50710	−	0.624262i	0.532144	−	0.846654i	$-0.321387\pi$
$179$	269.771	−	111.743i	1.50710	−	0.624262i	0.974957	+	0.222393i	$0.0713867\pi$
$180$	22.5645	−	222.032i	0.125358	−	1.23351i
$181$	−33.2079	−	13.7552i	−0.183469	−	0.0759954i	0.289058	−	0.957312i	$-0.406658\pi$
$181$	−33.2079	−	13.7552i	−0.183469	−	0.0759954i	−0.472527	+	0.881316i	$0.656658\pi$
$182$	132.209	+	98.3711i	0.726421	+	0.540500i
$183$	188.154	+	188.154i	1.02816	+	1.02816i
$184$	−0.723195	−	16.2664i	−0.00393041	−	0.0884043i
$185$	−59.9808	−	59.9808i	−0.324220	−	0.324220i
$186$	42.4396	−	6.22800i	0.228170	−	0.0334839i
$187$	42.5662	+	17.6315i	0.227627	+	0.0942861i
$188$	−58.2023	−	31.3425i	−0.309587	−	0.166715i
$189$	−77.6465	+	32.1622i	−0.410828	+	0.170171i
$190$	31.9442	−	126.694i	0.168127	−	0.666809i
$191$			47.7299i			0.249895i	0.992163	+	0.124947i	$0.0398762\pi$
$191$			47.7299i			0.249895i	−0.992163	+	0.124947i	$0.960124\pi$
$192$	256.743	−	134.173i	1.33720	−	0.698816i
$193$	−302.171			−1.56565			−0.782827	−	0.622240i	$-0.786223\pi$
$193$	−302.171			−1.56565			−0.782827	+	0.622240i	$0.786223\pi$
$194$	−131.543	−	33.1670i	−0.678059	−	0.170964i
$195$	−92.8855	−	224.245i	−0.476336	−	1.14998i
$196$	12.6848	−	23.5554i	0.0647183	−	0.120180i
$197$	18.2996	−	44.1791i	0.0928913	−	0.224259i	−0.870604	−	0.491984i	$-0.836272\pi$
$197$	18.2996	−	44.1791i	0.0928913	−	0.224259i	0.963495	+	0.267725i	$0.0862718\pi$
$198$	54.0527	+	368.332i	0.272993	+	1.86026i
$199$	−94.2590	+	94.2590i	−0.473663	+	0.473663i	−0.903098	−	0.429435i	$-0.858713\pi$
$199$	−94.2590	+	94.2590i	−0.473663	+	0.473663i	0.429435	+	0.903098i	$0.358713\pi$
$200$	0.502066	+	11.2927i	0.00251033	+	0.0564633i
$201$	−213.288	+	213.288i	−1.06113	+	1.06113i
$202$	−142.556	+	191.593i	−0.705725	+	0.948479i
$203$	−114.244	+	275.810i	−0.562779	+	1.35867i
$204$	51.2203	+	5.20538i	0.251080	+	0.0255166i
$205$	106.325	+	256.691i	0.518657	+	1.25215i
$206$	149.847	−	89.4992i	0.727414	−	0.434462i
$207$	23.3819			0.112956
$208$	99.0577	−	146.276i	0.476239	−	0.703249i
$209$			217.951i			1.04283i
$210$	−281.678	+	168.238i	−1.34133	+	0.801132i
$211$	−267.734	+	110.899i	−1.26888	+	0.525589i	−0.912625	−	0.408799i	$-0.865948\pi$
$211$	−267.734	+	110.899i	−1.26888	+	0.525589i	−0.356259	+	0.934387i	$0.615948\pi$
$212$	−128.590	−	157.683i	−0.606555	−	0.743787i
$213$	−42.1456	−	17.4573i	−0.197867	−	0.0819591i
$214$	22.2644	−	29.9229i	0.104039	−	0.139827i
$215$	−219.861	−	219.861i	−1.02261	−	1.02261i
$216$	38.1420	+	81.6260i	0.176584	+	0.377898i
$217$	−25.0025	−	25.0025i	−0.115219	−	0.115219i
$218$	−57.0394	−	388.684i	−0.261648	−	1.78296i
$219$	−327.440	−	135.630i	−1.49516	−	0.619316i
$220$	90.4353	+	301.492i	0.411069	+	1.37042i
$221$	29.0067	−	12.0150i	0.131252	−	0.0543663i
$222$	153.316	+	38.6567i	0.690613	+	0.174129i
$223$		−	408.363i		−	1.83123i	−0.402061	−	0.915613i	$-0.631706\pi$
$223$		−	408.363i		−	1.83123i	0.402061	−	0.915613i	$-0.368294\pi$
$224$	−215.073	−	103.772i	−0.960146	−	0.463269i
$225$	−16.2325			−0.0721443
$226$	76.6628	−	304.052i	0.339216	−	1.34536i
$227$	82.5132	+	199.204i	0.363494	+	0.877553i	0.994784	+	0.102005i	$0.0325259\pi$
$227$	82.5132	+	199.204i	0.363494	+	0.877553i	−0.631290	+	0.775547i	$0.717474\pi$
$228$	69.9741	+	233.278i	0.306904	+	1.02315i
$229$	22.6069	−	54.5778i	0.0987200	−	0.238331i	−0.866802	−	0.498652i	$-0.833828\pi$
$229$	22.6069	−	54.5778i	0.0987200	−	0.238331i	0.965522	+	0.260321i	$0.0838284\pi$
$230$	19.5600	−	2.87043i	0.0850437	−	0.0124801i
$231$	386.995	−	386.995i	1.67531	−	1.67531i
$232$	300.824	+	109.220i	1.29666	+	0.470775i
$233$	58.2826	−	58.2826i	0.250140	−	0.250140i	−0.570888	−	0.821028i	$-0.693401\pi$
$233$	58.2826	−	58.2826i	0.250140	−	0.250140i	0.821028	+	0.570888i	$0.193401\pi$
$234$	203.529	+	151.438i	0.869783	+	0.647170i
$235$	30.7150	−	74.1525i	0.130702	−	0.315543i
$236$	136.970	+	167.960i	0.580383	+	0.711693i
$237$	−19.2248	−	46.4127i	−0.0811171	−	0.195834i
$238$	−21.7619	−	36.4358i	−0.0914368	−	0.153091i
$239$	−367.366			−1.53710			−0.768548	−	0.639792i	$-0.779021\pi$
$239$	−367.366			−1.53710			−0.768548	+	0.639792i	$0.779021\pi$
$240$	193.590	+	293.659i	0.806626	+	1.22358i
$241$			312.345i			1.29604i	0.761624	+	0.648020i	$0.224403\pi$
$241$			312.345i			1.29604i	−0.761624	+	0.648020i	$0.775597\pi$
$242$	−145.142	−	243.010i	−0.599761	−	1.00417i
$243$	312.839	−	129.582i	1.28741	−	0.533261i
$244$	−233.941	−	23.7748i	−0.958773	−	0.0974375i
$245$	30.0106	+	12.4308i	0.122492	+	0.0507380i
$246$	−415.495	−	309.153i	−1.68901	−	1.25672i
$247$	105.021	+	105.021i	0.425187	+	0.425187i
$248$	−25.5866	+	27.9675i	−0.103172	+	0.112772i
$249$	103.749	+	103.749i	0.416661	+	0.416661i
$250$	−253.838	+	37.2507i	−1.01535	+	0.149003i
$251$	223.120	+	92.4192i	0.888923	+	0.368204i	0.779951	−	0.625841i	$-0.215244\pi$
$251$	223.120	+	92.4192i	0.888923	+	0.368204i	0.108972	+	0.994045i	$0.465244\pi$
$252$	162.589	−	301.924i	0.645195	−	1.19811i
$253$	−30.4672	+	12.6199i	−0.120424	+	0.0498811i
$254$	−94.3574	+	374.230i	−0.371486	+	1.47335i
$255$			62.5101i			0.245138i
$256$	−100.897	+	235.278i	−0.394127	+	0.919056i
$257$	178.176			0.693293			0.346646	−	0.937996i	$-0.387320\pi$
$257$	178.176			0.693293			0.346646	+	0.937996i	$0.387320\pi$
$258$	561.984	+	141.697i	2.17823	+	0.549214i
$259$	−49.8784	−	120.417i	−0.192581	−	0.464931i
$260$	188.853	+	101.699i	0.726357	+	0.391150i
$261$	−175.874	+	424.596i	−0.673845	+	1.62681i
$262$	13.8561	+	94.4198i	0.0528858	+	0.360381i
$263$	−147.164	+	147.164i	−0.559558	+	0.559558i	−0.929182	−	0.369623i	$-0.879487\pi$
$263$	−147.164	+	147.164i	−0.559558	+	0.559558i	0.369623	+	0.929182i	$0.379487\pi$
$264$	−432.889	−	396.035i	−1.63973	−	1.50013i
$265$	174.686	−	174.686i	0.659191	−	0.659191i
$266$	119.845	−	161.069i	0.450544	−	0.605522i
$267$	41.0728	−	99.1585i	0.153831	−	0.371380i
$268$	26.9506	−	265.191i	0.100562	−	0.989517i
$269$	−138.119	−	333.450i	−0.513455	−	1.23959i	−0.941861	−	0.336004i	$-0.890924\pi$
$269$	−138.119	−	333.450i	−0.513455	−	1.23959i	0.428405	−	0.903587i	$-0.359076\pi$
$270$	−93.9170	+	56.0937i	−0.347841	+	0.207754i
$271$	218.643			0.806801			0.403400	−	0.915024i	$-0.367828\pi$
$271$	218.643			0.806801			0.403400	+	0.915024i	$0.367828\pi$
$272$	−37.9856	+	25.0414i	−0.139653	+	0.0920638i
$273$		−	372.953i		−	1.36613i
$274$	−67.6690	+	40.4166i	−0.246967	+	0.147506i
$275$	21.1513	−	8.76117i	0.0769139	−	0.0318588i
$276$	−28.5581	+	23.2890i	−0.103471	+	0.0843806i
$277$	256.038	+	106.054i	0.924323	+	0.382867i	0.793522	−	0.608541i	$-0.208245\pi$
$277$	256.038	+	106.054i	0.924323	+	0.382867i	0.130801	+	0.991409i	$0.458245\pi$
$278$	104.028	−	139.812i	0.374203	−	0.502921i
$279$	−38.4903	−	38.4903i	−0.137958	−	0.137958i
$280$	98.9483	−	272.534i	0.353387	−	0.973336i
$281$	−49.4126	−	49.4126i	−0.175845	−	0.175845i	0.613697	−	0.789542i	$-0.289682\pi$
$281$	−49.4126	−	49.4126i	−0.175845	−	0.175845i	−0.789542	+	0.613697i	$0.789682\pi$
$282$	21.7223	+	148.023i	0.0770294	+	0.524903i
$283$	118.290	+	48.9975i	0.417987	+	0.173136i	0.581757	−	0.813363i	$-0.302365\pi$
$283$	118.290	+	48.9975i	0.417987	+	0.173136i	−0.163770	+	0.986499i	$0.552365\pi$
$284$	38.6133	−	11.5824i	0.135962	−	0.0407832i
$285$	−273.196	+	113.162i	−0.958584	+	0.397058i
$286$	−346.940	−	87.4765i	−1.21308	−	0.305862i
$287$			426.914i			1.48751i
$288$	−331.095	−	159.753i	−1.14963	−	0.554697i
$289$	280.914			0.972021
$290$	−95.0018	+	376.786i	−0.327592	+	1.29926i
$291$	117.493	+	283.654i	0.403757	+	0.974757i
$292$	299.997	−	89.9869i	1.02739	−	0.308174i
$293$	−100.203	+	241.910i	−0.341988	+	0.825633i	0.655526	+	0.755172i	$0.272447\pi$
$293$	−100.203	+	241.910i	−0.341988	+	0.825633i	−0.997515	+	0.0704605i	$0.977553\pi$
$294$	−59.9070	+	8.79135i	−0.203765	+	0.0299025i
$295$	−186.071	+	186.071i	−0.630748	+	0.630748i
$296$	−126.589	+	59.1521i	−0.427664	+	0.199838i
$297$	129.032	−	129.032i	0.434450	−	0.434450i
$298$	−218.589	−	162.643i	−0.733519	−	0.545782i
$299$	−8.59983	+	20.7618i	−0.0287620	+	0.0694376i
$300$	19.8260	−	16.1680i	0.0660866	−	0.0538934i
$301$	−182.830	−	441.392i	−0.607410	−	1.46642i
$302$	154.104	+	258.015i	0.510280	+	0.854355i
$303$	540.472			1.78374
$304$	−178.207	−	120.681i	−0.586206	−	0.396978i
$305$		−	285.505i		−	0.936081i
$306$	−33.5015	−	56.0912i	−0.109482	−	0.183305i
$307$	−371.163	+	153.741i	−1.20900	+	0.500784i	−0.893896	−	0.448274i	$-0.852039\pi$
$307$	−371.163	+	153.741i	−1.20900	+	0.500784i	−0.315103	+	0.949058i	$0.602039\pi$
$308$	−48.9000	+	481.170i	−0.158766	+	1.56224i
$309$	−364.949	−	151.167i	−1.18107	−	0.489213i
$310$	−36.9241	−	27.4737i	−0.119110	−	0.0886250i
$311$	−312.733	−	312.733i	−1.00557	−	1.00557i	−0.999984	−	0.00558671i	$-0.998222\pi$
$311$	−312.733	−	312.733i	−1.00557	−	1.00557i	−0.00558671	−	0.999984i	$-0.501778\pi$
$312$	−399.423	+	17.7581i	−1.28020	+	0.0569170i
$313$	358.245	+	358.245i	1.14455	+	1.14455i	0.987607	+	0.156946i	$0.0501649\pi$
$313$	358.245	+	358.245i	1.14455	+	1.14455i	0.156946	+	0.987607i	$0.449835\pi$
$314$	448.385	−	65.8004i	1.42798	−	0.209555i
$315$	384.666	+	159.334i	1.22116	+	0.505822i
$316$	39.0874	+	21.0489i	0.123694	+	0.0666105i
$317$	164.720	−	68.2292i	0.519621	−	0.215234i	−0.107429	−	0.994213i	$-0.534262\pi$
$317$	164.720	−	68.2292i	0.519621	−	0.215234i	0.627051	+	0.778979i	$0.284262\pi$
$318$	−112.582	+	446.512i	−0.354033	+	1.40413i
$319$		−	648.185i		−	2.03193i
$320$	−296.588	−	92.9944i	−0.926838	−	0.290607i
$321$	−84.4108			−0.262962
$322$	29.4550	+	7.42670i	0.0914751	+	0.0230643i
$323$	−14.6377	−	35.3386i	−0.0453181	−	0.109407i
$324$	−99.4086	+	184.600i	−0.306817	+	0.569752i
$325$	5.97029	−	14.4135i	0.0183701	−	0.0443494i
$326$	−0.133567	−	0.910167i	−0.000409714	−	0.00279192i
$327$	−628.681	+	628.681i	−1.92257	+	1.92257i
$328$	457.214	−	20.3275i	1.39394	−	0.0619740i
$329$	87.2050	−	87.2050i	0.265061	−	0.265061i
$330$	425.245	−	571.521i	1.28862	−	1.73188i
$331$	21.3130	−	51.4542i	0.0643898	−	0.155451i	−0.888409	−	0.459052i	$-0.848189\pi$
$331$	21.3130	−	51.4542i	0.0643898	−	0.155451i	0.952799	+	0.303601i	$0.0981891\pi$
$332$	−128.996	−	13.1095i	−0.388541	−	0.0394864i
$333$	−76.7855	−	185.377i	−0.230587	−	0.556687i
$334$	234.936	−	140.320i	0.703400	−	0.420119i
$335$	323.643			0.966098
$336$	102.143	+	530.708i	0.303996	+	1.57949i
$337$		−	173.028i		−	0.513437i	−0.966486	−	0.256718i	$-0.917359\pi$
$337$		−	173.028i		−	0.513437i	0.966486	−	0.256718i	$-0.0826413\pi$
$338$	80.8553	−	48.2924i	0.239217	−	0.142877i
$339$	−655.643	+	271.576i	−1.93405	+	0.801110i
$340$	−34.9115	−	42.8102i	−0.102681	−	0.125912i
$341$	70.9282	+	29.3794i	0.208001	+	0.0861567i
$342$	184.496	−	247.958i	0.539461	−	0.725024i
$343$	−223.268	−	223.268i	−0.650927	−	0.650927i
$344$	−464.013	+	216.823i	−1.34888	+	0.630301i
$345$	−31.6375	−	31.6375i	−0.0917030	−	0.0917030i
$346$	77.5836	+	528.679i	0.224230	+	1.52798i
$347$	48.9563	+	20.2784i	0.141085	+	0.0584391i	0.452109	−	0.891963i	$-0.350672\pi$
$347$	48.9563	+	20.2784i	0.141085	+	0.0584391i	−0.311024	+	0.950402i	$0.600672\pi$
$348$	−208.102	−	693.768i	−0.597995	−	1.99359i
$349$	−222.227	+	92.0495i	−0.636754	+	0.263752i	−0.677620	−	0.735412i	$-0.736988\pi$
$349$	−222.227	+	92.0495i	−0.636754	+	0.263752i	0.0408656	+	0.999165i	$0.486988\pi$
$350$	−20.4486	−	5.15586i	−0.0584246	−	0.0147310i
$351$		−	124.350i		−	0.354273i
$352$	517.649	+	29.4597i	1.47059	+	0.0836924i
$353$	−75.1997			−0.213030			−0.106515	−	0.994311i	$-0.533969\pi$
$353$	−75.1997			−0.213030			−0.106515	+	0.994311i	$0.533969\pi$
$354$	119.920	−	475.613i	0.338756	−	1.34354i
$355$	18.7310	+	45.2208i	0.0527635	+	0.127382i
$356$	27.2507	+	90.8479i	0.0765469	+	0.255191i
$357$	−36.7566	+	88.7383i	−0.102960	+	0.248567i
$358$	577.808	−	84.7931i	1.61399	−	0.236852i
$359$	369.532	−	369.532i	1.02934	−	1.02934i	0.0297806	−	0.999556i	$-0.490519\pi$
$359$	369.532	−	369.532i	1.02934	−	1.02934i	0.999556	−	0.0297806i	$-0.00948087\pi$
$360$	152.326	−	419.554i	0.423129	−	1.16543i
$361$	−127.319	+	127.319i	−0.352684	+	0.352684i
$362$	−57.6744	−	42.9132i	−0.159322	−	0.118545i
$363$	−245.150	+	591.844i	−0.675343	+	1.63042i
$364$	208.292	+	255.418i	0.572231	+	0.701697i
$365$	145.526	+	351.332i	0.398702	+	0.962552i
$366$	272.886	+	456.890i	0.745590	+	1.24833i
$367$	−482.888			−1.31577			−0.657885	−	0.753118i	$-0.728549\pi$
$367$	−482.888			−1.31577			−0.657885	+	0.753118i	$0.728549\pi$
$368$	6.55131	−	31.8991i	0.0178025	−	0.0866824i
$369$			657.215i			1.78107i
$370$	−86.9922	−	145.650i	−0.235114	−	0.393648i
$371$	350.698	−	145.264i	0.945278	−	0.391547i
$372$	85.3486	+	8.67375i	0.229432	+	0.0233165i
$373$	459.056	+	190.147i	1.23071	+	0.509778i	0.900801	−	0.434233i	$-0.142980\pi$
$373$	459.056	+	190.147i	1.23071	+	0.509778i	0.329913	+	0.944011i	$0.392980\pi$
$374$	73.9276	+	55.0065i	0.197667	+	0.147076i
$375$	410.573	+	410.573i	1.09486	+	1.09486i
$376$	−97.5465	−	89.2420i	−0.259432	−	0.237346i
$377$	−312.332	−	312.332i	−0.828468	−	0.828468i
$378$	−166.307	+	24.4055i	−0.439965	+	0.0645648i
$379$	209.167	+	86.6398i	0.551891	+	0.228601i	0.641161	−	0.767407i	$-0.278453\pi$
$379$	209.167	+	86.6398i	0.551891	+	0.228601i	−0.0892693	+	0.996008i	$0.528453\pi$
$380$	123.899	−	230.078i	0.326050	−	0.605468i
$381$	806.973	−	334.259i	2.11804	−	0.877320i
$382$	−23.3386	+	92.5629i	−0.0610958	+	0.242311i
$383$		−	243.083i		−	0.634682i	−0.948312	−	0.317341i	$-0.897210\pi$
$383$		−	243.083i		−	0.634682i	0.948312	−	0.317341i	$-0.102790\pi$
$384$	563.510	−	134.662i	1.46747	−	0.350681i
$385$	−587.227			−1.52527
$386$	−586.002	−	147.753i	−1.51814	−	0.382780i
$387$	−281.459	−	679.503i	−0.727285	−	1.75582i
$388$	−238.885	−	128.642i	−0.615683	−	0.331551i
$389$	100.024	−	241.479i	0.257131	−	0.620768i	−0.741616	−	0.670825i	$-0.765940\pi$
$389$	100.024	−	241.479i	0.257131	−	0.620768i	0.998746	+	0.0500566i	$0.0159402\pi$
$390$	−70.4837	−	480.299i	−0.180727	−	1.23153i
$391$	4.09239	−	4.09239i	0.0104665	−	0.0104665i
$392$	36.1176	−	39.4786i	0.0921367	−	0.100711i
$393$	152.720	−	152.720i	0.388601	−	0.388601i
$394$	57.0908	−	76.7288i	0.144901	−	0.194743i
$395$	−20.6275	+	49.7992i	−0.0522215	+	0.126074i
$396$	−75.2793	+	740.739i	−0.190099	+	1.87055i
$397$	−177.617	−	428.806i	−0.447399	−	1.08012i	−0.973293	−	0.229566i	$-0.926269\pi$
$397$	−177.617	−	428.806i	−0.447399	−	1.08012i	0.525894	−	0.850550i	$-0.323731\pi$
$398$	−228.887	+	136.707i	−0.575093	+	0.343485i
$399$	−454.366			−1.13876
$400$	−4.54813	+	22.1454i	−0.0113703	+	0.0553636i
$401$		−	539.233i		−	1.34472i	−0.740224	−	0.672360i	$-0.765281\pi$
$401$		−	539.233i		−	1.34472i	0.740224	−	0.672360i	$-0.234719\pi$
$402$	−517.921	+	309.338i	−1.28836	+	0.769498i
$403$	48.3339	−	20.0206i	0.119935	−	0.0496788i
$404$	−370.144	+	301.851i	−0.916198	+	0.747156i
$405$	−235.188	−	97.4183i	−0.580712	−	0.240539i
$406$	−356.417	+	479.017i	−0.877875	+	1.17984i
$407$	200.107	+	200.107i	0.491664	+	0.491664i
$408$	96.7865	+	35.1401i	0.237222	+	0.0861277i
$409$	177.821	+	177.821i	0.434769	+	0.434769i	0.890247	−	0.455478i	$-0.150532\pi$
$409$	177.821	+	177.821i	0.434769	+	0.434769i	−0.455478	+	0.890247i	$0.650532\pi$
$410$	80.6817	+	549.791i	0.196785	+	1.34095i
$411$	164.806	+	68.2648i	0.400988	+	0.166094i
$412$	334.362	−	100.295i	0.811559	−	0.243435i
$413$	−373.554	+	154.731i	−0.904490	+	0.374652i
$414$	45.3446	+	11.4331i	0.109528	+	0.0276161i
$415$		−	157.428i		−	0.379345i
$416$	263.628	−	235.237i	0.633721	−	0.565474i
$417$	−394.402			−0.945807
$418$	−106.572	+	422.674i	−0.254957	+	1.01118i
$419$	55.0604	+	132.927i	0.131409	+	0.317249i	0.975865	−	0.218376i	$-0.0700759\pi$
$419$	55.0604	+	132.927i	0.131409	+	0.317249i	−0.844456	+	0.535625i	$0.820076\pi$
$420$	−628.524	+	188.532i	−1.49649	+	0.448885i
$421$	−292.384	+	705.877i	−0.694498	+	1.67667i	0.0410159	+	0.999158i	$0.486941\pi$
$421$	−292.384	+	705.877i	−0.694498	+	1.67667i	−0.735514	+	0.677509i	$0.763059\pi$
$422$	−573.445	+	84.1530i	−1.35888	+	0.199415i
$423$	134.248	−	134.248i	0.317371	−	0.317371i
$424$	−172.272	−	368.672i	−0.406303	−	0.869509i
$425$	−2.84107	+	2.84107i	−0.00668488	+	0.00668488i
$426$	−73.1971	−	54.4630i	−0.171824	−	0.127847i
$427$	167.880	−	405.298i	0.393162	−	0.949176i
$428$	57.8090	−	47.1430i	0.135068	−	0.110147i
$429$	309.883	+	748.125i	0.722339	+	1.74388i
$430$	−318.872	−	533.883i	−0.741562	−	1.24159i
$431$	810.711			1.88100			0.940500	−	0.339794i	$-0.110357\pi$
$431$	810.711			1.88100			0.940500	+	0.339794i	$0.110357\pi$
$432$	34.0563	+	176.948i	0.0788341	+	0.409602i
$433$			753.072i			1.73920i	0.493759	+	0.869599i	$0.335622\pi$
$433$			753.072i			1.73920i	−0.493759	+	0.869599i	$0.664378\pi$
$434$	−36.2620	−	60.7131i	−0.0835531	−	0.139892i
$435$	812.484	−	336.542i	1.86778	−	0.773659i
$436$	79.4389	−	781.669i	0.182199	−	1.79282i
$437$	25.2940	+	10.4771i	0.0578810	+	0.0239751i
$438$	−568.687	−	423.137i	−1.29837	−	0.966066i
$439$	504.938	+	504.938i	1.15020	+	1.15020i	0.986512	+	0.163689i	$0.0523392\pi$
$439$	504.938	+	504.938i	1.15020	+	1.15020i	0.163689	+	0.986512i	$0.447661\pi$
$440$	27.9608	+	628.905i	0.0635472	+	1.42933i
$441$	54.3323	+	54.3323i	0.123202	+	0.123202i
$442$	62.1278	−	9.11724i	0.140561	−	0.0206272i
$443$	−697.291	−	288.827i	−1.57402	−	0.651981i	−0.586569	−	0.809899i	$-0.699522\pi$
$443$	−697.291	−	288.827i	−1.57402	−	0.651981i	−0.987452	+	0.157919i	$0.949522\pi$
$444$	278.425	+	149.934i	0.627083	+	0.337690i
$445$	−106.394	+	44.0697i	−0.239087	+	0.0990330i
$446$	199.678	−	791.942i	0.447709	−	1.77565i
$447$			616.626i			1.37948i
$448$	−366.350	−	306.410i	−0.817746	−	0.683952i
$449$	−294.056			−0.654913			−0.327457	−	0.944866i	$-0.606192\pi$
$449$	−294.056			−0.654913			−0.327457	+	0.944866i	$0.606192\pi$
$450$	−31.4797	−	7.93721i	−0.0699549	−	0.0176383i
$451$	−354.719	−	856.368i	−0.786517	−	1.89882i
$452$	297.345	−	552.163i	0.657843	−	1.22160i
$453$	260.287	−	628.389i	0.574585	−	1.38717i
$454$	62.6130	+	426.665i	0.137914	+	0.939791i
$455$	−282.960	+	282.960i	−0.621889	+	0.621889i
$456$	21.6346	+	486.614i	0.0474443	+	1.06714i
$457$	175.139	−	175.139i	0.383237	−	0.383237i	−0.489030	−	0.872267i	$-0.662649\pi$
$457$	175.139	−	175.139i	0.383237	−	0.383237i	0.872267	+	0.489030i	$0.162649\pi$
$458$	70.5287	−	94.7890i	0.153993	−	0.206963i
$459$	−12.2554	+	29.5871i	−0.0267001	+	0.0644598i
$460$	39.3365	+	3.99766i	0.0855141	+	0.00869056i
$461$	−107.290	−	259.020i	−0.232732	−	0.561866i	0.763765	−	0.645495i	$-0.223349\pi$
$461$	−107.290	−	259.020i	−0.232732	−	0.561866i	−0.996497	+	0.0836293i	$0.973349\pi$
$462$	939.732	−	561.273i	2.03405	−	1.21488i
$463$	53.7059			0.115996			0.0579978	−	0.998317i	$-0.481528\pi$
$463$	53.7059			0.115996			0.0579978	+	0.998317i	$0.481528\pi$
$464$	529.985	+	358.905i	1.14221	+	0.773502i
$465$			104.161i			0.224002i
$466$	141.526	−	84.5292i	0.303704	−	0.181393i
$467$	101.550	−	42.0634i	0.217452	−	0.0900716i	−0.271298	−	0.962495i	$-0.587453\pi$
$467$	101.550	−	42.0634i	0.217452	−	0.0900716i	0.488750	+	0.872424i	$0.337453\pi$
$468$	320.656	+	393.204i	0.685163	+	0.840180i
$469$	459.438	+	190.306i	0.979613	+	0.405769i
$470$	95.8242	−	128.786i	0.203881	−	0.274012i
$471$	−725.243	−	725.243i	−1.53979	−	1.53979i
$472$	183.500	+	392.699i	0.388771	+	0.831990i
$473$	733.498	+	733.498i	1.55074	+	1.55074i
$474$	−14.5882	−	99.4087i	−0.0307768	−	0.209723i
$475$	−17.5599	−	7.27355i	−0.0369682	−	0.0153127i
$476$	−24.3870	−	81.3011i	−0.0512332	−	0.170801i
$477$	539.884	−	223.627i	1.13183	−	0.468820i
$478$	−712.435	−	179.632i	−1.49045	−	0.375798i
$479$			40.7997i			0.0851769i	0.999093	+	0.0425884i	$0.0135604\pi$
$479$			40.7997i			0.0851769i	−0.999093	+	0.0425884i	$0.986440\pi$
$480$	231.839	+	664.156i	0.482999	+	1.38366i
$481$	192.846			0.400927
$482$	−152.728	+	605.733i	−0.316863	+	1.25671i
$483$	−26.3089	−	63.5154i	−0.0544698	−	0.131502i
$484$	−162.650	−	542.241i	−0.336054	−	1.12033i
$485$	126.066	−	304.351i	0.259931	−	0.627528i
$486$	670.054	−	98.3302i	1.37871	−	0.202326i
$487$	−143.660	+	143.660i	−0.294989	+	0.294989i	−0.839047	−	0.544058i	$-0.816887\pi$
$487$	−143.660	+	143.660i	−0.294989	+	0.294989i	0.544058	+	0.839047i	$0.316887\pi$
$488$	−442.057	−	160.497i	−0.905855	−	0.328887i
$489$	−1.47216	+	1.47216i	−0.00301055	+	0.00301055i
$490$	52.1215	+	38.7815i	0.106370	+	0.0791459i
$491$	182.575	−	440.775i	0.371843	−	0.897709i	−0.621595	−	0.783339i	$-0.713515\pi$
$491$	182.575	−	440.775i	0.371843	−	0.897709i	0.993438	−	0.114370i	$-0.0364849\pi$
$492$	−654.605	−	802.708i	−1.33050	−	1.63152i
$493$	43.5325	+	105.097i	0.0883012	+	0.213178i
$494$	152.316	+	255.021i	0.308332	+	0.516236i
$495$	−904.010			−1.82628
$496$	−63.2955	+	41.7265i	−0.127612	+	0.0841261i
$497$			75.2087i			0.151325i
$498$	150.470	+	251.931i	0.302149	+	0.505885i
$499$	−409.850	+	169.766i	−0.821343	+	0.340211i	−0.753470	−	0.657482i	$-0.771621\pi$
$499$	−409.850	+	169.766i	−0.821343	+	0.340211i	−0.0678733	+	0.997694i	$0.521621\pi$
$500$	−510.485	−	51.8792i	−1.02097	−	0.103758i
$501$	−572.179	−	237.004i	−1.14207	−	0.473063i
$502$	387.507	+	288.328i	0.771926	+	0.574359i
$503$	453.715	+	453.715i	0.902019	+	0.902019i	0.995611	−	0.0935920i	$-0.0298349\pi$
$503$	453.715	+	453.715i	0.902019	+	0.902019i	−0.0935920	+	0.995611i	$0.529835\pi$
$504$	462.943	−	506.022i	0.918537	−	1.00401i
$505$	−410.057	−	410.057i	−0.811993	−	0.811993i
$506$	−65.2560	+	9.57631i	−0.128964	+	0.0189255i
$507$	−196.921	−	81.5673i	−0.388404	−	0.160882i
$508$	−365.976	+	679.608i	−0.720425	+	1.33781i
$509$	−71.5029	+	29.6175i	−0.140477	+	0.0581876i	−0.451815	−	0.892112i	$-0.649223\pi$
$509$	−71.5029	+	29.6175i	−0.140477	+	0.0581876i	0.311337	+	0.950299i	$0.399223\pi$
$510$	−30.5656	+	121.226i	−0.0599326	+	0.237698i
$511$			584.316i			1.14348i
$512$	−310.714	+	406.941i	−0.606863	+	0.794807i
$513$	−151.494			−0.295310
$514$	345.538	+	87.1231i	0.672253	+	0.169500i
$515$	162.197	+	391.578i	0.314945	+	0.760345i
$516$	1020.57	+	549.588i	1.97785	+	1.06509i
$517$	−102.471	+	247.387i	−0.198203	+	0.478504i
$518$	−37.8489	−	257.915i	−0.0730674	−	0.497905i
$519$	855.117	−	855.117i	1.64762	−	1.64762i
$520$	316.515	+	289.569i	0.608683	+	0.556864i
$521$	−565.729	+	565.729i	−1.08585	+	1.08585i	−0.0899020	+	0.995951i	$0.528655\pi$
$521$	−565.729	+	565.729i	−1.08585	+	1.08585i	−0.995951	+	0.0899020i	$0.971345\pi$
$522$	−548.688	+	737.425i	−1.05113	+	1.41269i
$523$	−1.50925	+	3.64366i	−0.00288576	+	0.00696685i	−0.925316	−	0.379197i	$-0.876200\pi$
$523$	−1.50925	+	3.64366i	−0.00288576	+	0.00696685i	0.922430	+	0.386164i	$0.126200\pi$
$524$	−19.2974	+	189.884i	−0.0368271	+	0.362374i
$525$	18.2645	+	44.0945i	0.0347896	+	0.0839895i
$526$	−357.355	+	213.437i	−0.679381	+	0.405773i
$527$	−13.4734			−0.0255663
$528$	−645.854	−	979.704i	−1.22321	−	1.85550i
$529$		−	524.858i		−	0.992169i
$530$	424.185	−	253.353i	0.800350	−	0.478024i
$531$	−575.070	+	238.202i	−1.08299	+	0.448591i
$532$	311.174	−	253.761i	0.584913	−	0.476994i
$533$	−583.571	−	241.723i	−1.09488	−	0.453514i
$534$	128.138	−	172.215i	0.239960	−	0.322500i
$535$	64.0426	+	64.0426i	0.119706	+	0.119706i
$536$	181.936	−	501.108i	0.339433	−	0.934902i
$537$	−934.579	−	934.579i	−1.74037	−	1.74037i
$538$	−104.808	−	714.198i	−0.194811	−	1.32751i
$539$	−100.121	−	41.4716i	−0.185754	−	0.0769417i
$540$	−209.562	+	62.8601i	−0.388078	+	0.116408i
$541$	−746.681	+	309.286i	−1.38019	+	0.571692i	−0.944531	−	0.328421i	$-0.893483\pi$
$541$	−746.681	+	309.286i	−1.38019	+	0.571692i	−0.435656	+	0.900113i	$0.643483\pi$
$542$	424.016	+	106.910i	0.782317	+	0.197251i
$543$			162.696i			0.299625i
$544$	−85.9101	+	29.9890i	−0.157923	+	0.0551268i
$545$	953.961			1.75039
$546$	182.363	−	723.270i	0.333999	−	1.32467i
$547$	298.176	+	719.861i	0.545112	+	1.31602i	0.921076	+	0.389383i	$0.127312\pi$
$547$	298.176	+	719.861i	0.545112	+	1.31602i	−0.375964	+	0.926634i	$0.622688\pi$
$548$	−150.993	+	45.2919i	−0.275535	+	0.0826494i
$549$	258.444	−	623.938i	0.470754	−	1.13650i
$550$	45.3029	−	6.64819i	0.0823688	−	0.0120876i
$551$	−380.512	+	380.512i	−0.690585	+	0.690585i
$552$	−66.7706	+	31.2005i	−0.120961	+	0.0565226i
$553$	−58.5649	+	58.5649i	−0.105904	+	0.105904i
$554$	444.678	+	330.867i	0.802667	+	0.597232i
$555$	−146.932	+	354.726i	−0.264743	+	0.639147i
$556$	270.107	−	220.271i	0.485804	−	0.396171i
$557$	83.4142	+	201.380i	0.149756	+	0.361544i	0.980900	−	0.194515i	$-0.0623132\pi$
$557$	83.4142	+	201.380i	0.149756	+	0.361544i	−0.831143	+	0.556058i	$0.812313\pi$
$558$	−55.8238	−	93.4650i	−0.100043	−	0.167500i
$559$	706.882			1.26455
$560$	325.152	−	480.144i	0.580629	−	0.857400i
$561$		−	208.545i		−	0.371739i
$562$	−71.6647	−	119.987i	−0.127517	−	0.213501i
$563$	−19.5811	+	8.11076i	−0.0347800	+	0.0144063i	−0.400006	−	0.916513i	$-0.630992\pi$
$563$	−19.5811	+	8.11076i	−0.0347800	+	0.0144063i	0.365226	+	0.930919i	$0.380992\pi$
$564$	−30.2527	+	297.683i	−0.0536395	+	0.527806i
$565$	703.482	+	291.392i	1.24510	+	0.515738i
$566$	205.443	+	152.862i	0.362973	+	0.270074i
$567$	−276.587	−	276.587i	−0.487808	−	0.487808i
$568$	80.5466	−	3.58106i	0.141807	−	0.00630468i
$569$	−366.760	−	366.760i	−0.644569	−	0.644569i	0.307106	−	0.951675i	$-0.400639\pi$
$569$	−366.760	−	366.760i	−0.644569	−	0.644569i	−0.951675	+	0.307106i	$0.900639\pi$
$570$	−585.144	+	85.8698i	−1.02657	+	0.150649i
$571$	−121.285	−	50.2378i	−0.212408	−	0.0879822i	0.273943	−	0.961746i	$-0.411672\pi$
$571$	−121.285	−	50.2378i	−0.212408	−	0.0879822i	−0.486350	+	0.873764i	$0.661672\pi$
$572$	−630.049	−	339.287i	−1.10148	−	0.593159i
$573$	199.599	−	82.6764i	0.348339	−	0.144287i
$574$	−208.749	+	827.917i	−0.363674	+	1.44236i
$575$		−	2.87584i		−	0.00500147i
$576$	−563.979	−	471.705i	−0.979131	−	0.818932i
$577$	464.948			0.805802			0.402901	−	0.915244i	$-0.368002\pi$
$577$	464.948			0.805802			0.402901	+	0.915244i	$0.368002\pi$
$578$	544.778	+	137.359i	0.942523	+	0.237645i
$579$	523.412	+	1263.63i	0.903993	+	2.18243i
$580$	−368.475	+	684.250i	−0.635302	+	1.17974i
$581$	92.5696	−	223.483i	0.159328	−	0.384652i
$582$	89.1568	+	607.543i	0.153190	+	1.04389i
$583$	−582.785	+	582.785i	−0.999631	+	0.999631i
$584$	625.787	−	27.8221i	1.07155	−	0.0476407i
$585$	−435.603	+	435.603i	−0.744621	+	0.744621i
$586$	−312.611	+	420.142i	−0.533465	+	0.716966i
$587$	159.551	−	385.190i	0.271807	−	0.656201i	−0.727753	−	0.685839i	$-0.759435\pi$
$587$	159.551	−	385.190i	0.271807	−	0.656201i	0.999561	+	0.0296380i	$0.00943546\pi$
$588$	−120.477	−	12.2437i	−0.204892	−	0.0208227i
$589$	−24.3909	−	58.8849i	−0.0414107	−	0.0999743i
$590$	−451.831	+	269.865i	−0.765815	+	0.457398i
$591$	−216.448			−0.366239
$592$	−274.418	+	52.8158i	−0.463543	+	0.0892159i
$593$		−	470.422i		−	0.793292i	−0.917972	−	0.396646i	$-0.870174\pi$
$593$		−	470.422i		−	0.793292i	0.917972	−	0.396646i	$-0.129826\pi$
$594$	313.325	−	187.139i	0.527483	−	0.315049i
$595$	95.2131	−	39.4385i	0.160022	−	0.0662833i
$596$	−344.383	−	422.298i	−0.577823	−	0.708554i
$597$	557.448	+	230.903i	0.933749	+	0.386771i
$598$	−26.8296	+	36.0585i	−0.0448656	+	0.0602984i
$599$	−506.817	−	506.817i	−0.846105	−	0.846105i	0.143540	−	0.989645i	$-0.454151\pi$
$599$	−506.817	−	506.817i	−0.846105	−	0.846105i	−0.989645	+	0.143540i	$0.954151\pi$
$600$	46.3543	−	21.6604i	0.0772572	−	0.0361006i
$601$	−261.398	−	261.398i	−0.434939	−	0.434939i	0.455366	−	0.890305i	$-0.349509\pi$
$601$	−261.398	−	261.398i	−0.434939	−	0.434939i	−0.890305	+	0.455366i	$0.849509\pi$
$602$	−138.736	−	945.393i	−0.230459	−	1.57042i
$603$	707.285	+	292.967i	1.17294	+	0.485849i
$604$	172.694	+	575.723i	0.285916	+	0.953184i
$605$	635.027	−	263.037i	1.04963	−	0.434772i
$606$	1048.14	+	264.276i	1.72961	+	0.436098i
$607$		−	812.089i		−	1.33787i	−0.743319	−	0.668937i	$-0.766750\pi$
$607$		−	812.089i		−	1.33787i	0.743319	−	0.668937i	$-0.233250\pi$
$608$	−286.588	−	321.176i	−0.471361	−	0.528250i
$609$	1351.28			2.21885
$610$	139.604	−	553.681i	0.228859	−	0.907674i
$611$	69.8287	+	168.581i	0.114286	+	0.275911i
$612$	−37.5427	−	125.159i	−0.0613443	−	0.204509i
$613$	105.168	−	253.898i	0.171563	−	0.414190i	−0.814588	−	0.580040i	$-0.803037\pi$
$613$	105.168	−	253.898i	0.171563	−	0.414190i	0.986151	+	0.165850i	$0.0530369\pi$
$614$	−794.973	+	116.662i	−1.29474	+	0.190003i
$615$	889.264	−	889.264i	1.44596	−	1.44596i
$616$	−330.110	+	909.225i	−0.535894	+	1.47601i
$617$	−508.739	+	508.739i	−0.824536	+	0.824536i	−0.986755	−	0.162218i	$-0.948135\pi$
$617$	−508.739	+	508.739i	−0.824536	+	0.824536i	0.162218	+	0.986755i	$0.448135\pi$
$618$	−633.832	−	471.609i	−1.02562	−	0.763121i
$619$	−6.64960	+	16.0536i	−0.0107425	+	0.0259347i	−0.929160	−	0.369678i	$-0.879468\pi$
$619$	−6.64960	+	16.0536i	−0.0107425	+	0.0259347i	0.918417	+	0.395613i	$0.129468\pi$
$620$	−58.1733	−	71.3348i	−0.0938278	−	0.115056i
$621$	−8.77191	−	21.1773i	−0.0141255	−	0.0341019i
$622$	−453.567	−	759.402i	−0.729207	−	1.22090i
$623$	−176.948			−0.284026
$624$	−783.286	−	160.868i	−1.25527	−	0.257801i
$625$		−	587.679i		−	0.940287i
$626$	519.575	+	869.919i	0.829992	+	1.38965i
$627$	911.435	−	377.529i	1.45364	−	0.602119i
$628$	901.730	+	91.6403i	1.43588	+	0.145924i
$629$	−45.8847	−	19.0061i	−0.0729487	−	0.0302163i
$630$	668.075	+	497.088i	1.06044	+	0.789028i
$631$	−177.518	−	177.518i	−0.281329	−	0.281329i	0.552310	−	0.833639i	$-0.313746\pi$
$631$	−177.518	−	177.518i	−0.281329	−	0.281329i	−0.833639	+	0.552310i	$0.813746\pi$
$632$	65.5100	+	59.9329i	0.103655	+	0.0948306i
$633$	927.524	+	927.524i	1.46528	+	1.46528i
$634$	352.804	−	51.7740i	0.556474	−	0.0816624i
$635$	−865.853	−	358.648i	−1.36355	−	0.564800i
$636$	−436.663	+	810.874i	−0.686578	+	1.27496i
$637$	−68.2274	+	28.2607i	−0.107107	+	0.0443654i
$638$	316.944	−	1257.03i	0.496777	−	1.97026i
$639$			115.780i			0.181190i
$640$	−529.703	−	325.368i	−0.827662	−	0.508387i
$641$	334.058			0.521151			0.260575	−	0.965454i	$-0.416088\pi$
$641$	334.058			0.521151			0.260575	+	0.965454i	$0.416088\pi$
$642$	−163.698	−	41.2745i	−0.254982	−	0.0642905i
$643$	−19.9758	−	48.2257i	−0.0310665	−	0.0750011i	0.907585	−	0.419869i	$-0.137924\pi$
$643$	−19.9758	−	48.2257i	−0.0310665	−	0.0750011i	−0.938651	+	0.344867i	$0.887924\pi$
$644$	53.4908	+	28.8053i	0.0830602	+	0.0447287i
$645$	−538.584	+	1300.26i	−0.835015	+	2.01590i
$646$	−11.1075	−	75.6898i	−0.0171942	−	0.117167i
$647$	443.581	−	443.581i	0.685596	−	0.685596i	−0.275659	−	0.961255i	$-0.588896\pi$
$647$	443.581	−	443.581i	0.685596	−	0.685596i	0.961255	+	0.275659i	$0.0888961\pi$
$648$	−283.048	+	309.387i	−0.436802	+	0.477449i
$649$	620.767	−	620.767i	0.956497	−	0.956497i
$650$	18.6260	−	25.0330i	0.0286554	−	0.0385123i
$651$	−61.2477	+	147.865i	−0.0940825	+	0.227135i
$652$	0.186019	−	1.83040i	0.000285305	−	0.00280737i
$653$	−14.0746	−	33.9792i	−0.0215538	−	0.0520355i	0.912736	−	0.408549i	$-0.133965\pi$
$653$	−14.0746	−	33.9792i	−0.0215538	−	0.0520355i	−0.934290	+	0.356514i	$0.883965\pi$
$654$	−1526.61	+	911.797i	−2.33427	+	1.39419i
$655$	−231.737			−0.353798
$656$	896.617	+	184.143i	1.36679	+	0.280706i
$657$			899.528i			1.36914i
$658$	211.758	−	126.476i	0.321821	−	0.192213i
$659$	−845.778	+	350.333i	−1.28343	+	0.531613i	−0.917020	−	0.398842i	$-0.869412\pi$
$659$	−845.778	+	350.333i	−1.28343	+	0.531613i	−0.366407	+	0.930455i	$0.619412\pi$
$660$	1104.14	−	900.420i	1.67294	−	1.36427i
$661$	−1022.39	−	423.490i	−1.54674	−	0.640680i	−0.564017	−	0.825763i	$-0.690745\pi$
$661$	−1022.39	−	423.490i	−1.54674	−	0.640680i	−0.982723	+	0.185083i	$0.940745\pi$
$662$	66.4921	−	89.3640i	0.100441	−	0.134991i
$663$	−100.489	−	100.489i	−0.151567	−	0.151567i
$664$	−243.752	−	88.4985i	−0.367096	−	0.133281i
$665$	344.727	+	344.727i	0.518387	+	0.518387i
$666$	−58.2667	−	397.048i	−0.0874876	−	0.596168i
$667$	−75.2241	−	31.1588i	−0.112780	−	0.0467149i
$668$	524.224	−	157.246i	0.784767	−	0.235398i
$669$	−1707.71	+	707.355i	−2.55263	+	1.05733i
$670$	627.642	+	158.252i	0.936780	+	0.236197i
$671$			952.498i			1.41952i
$672$	−61.4151	+	1079.15i	−0.0913915	+	1.60588i
$673$	−441.074			−0.655385			−0.327693	−	0.944784i	$-0.606271\pi$
$673$	−441.074			−0.655385			−0.327693	+	0.944784i	$0.606271\pi$
$674$	84.6059	−	335.555i	0.125528	−	0.497856i
$675$	6.08974	+	14.7019i	0.00902184	+	0.0217807i
$676$	180.417	−	54.1177i	0.266889	−	0.0800558i
$677$	−3.12869	+	7.55333i	−0.00462140	+	0.0111571i	−0.926173	−	0.377098i	$-0.876922\pi$
$677$	−3.12869	+	7.55333i	−0.00462140	+	0.0111571i	0.921552	+	0.388255i	$0.126922\pi$
$678$	−1404.29	+	206.079i	−2.07122	+	0.303951i
$679$	357.923	−	357.923i	0.527133	−	0.527133i
$680$	−46.7712	−	100.093i	−0.0687812	−	0.147195i
$681$	690.112	−	690.112i	1.01338	−	1.01338i
$682$	123.186	+	91.6576i	0.180624	+	0.134395i
$683$	−198.853	+	480.073i	−0.291146	+	0.702889i	−0.999997	−	0.00246964i	$-0.999214\pi$
$683$	−198.853	+	480.073i	−0.291146	+	0.702889i	0.708851	+	0.705358i	$0.249214\pi$
$684$	479.038	−	390.653i	0.700348	−	0.571131i
$685$	−73.2458	−	176.831i	−0.106928	−	0.258147i
$686$	−323.813	−	542.157i	−0.472031	−	0.790316i
$687$	−267.394			−0.389220
$688$	−1005.88	+	193.598i	−1.46204	+	0.281392i
$689$			561.638i			0.815149i
$690$	−45.8850	−	76.8247i	−0.0665000	−	0.111340i
$691$	260.304	−	107.822i	0.376707	−	0.156037i	−0.186293	−	0.982494i	$-0.559647\pi$
$691$	260.304	−	107.822i	0.376707	−	0.156037i	0.563000	+	0.826457i	$0.309647\pi$
$692$	−108.051	+	1063.21i	−0.156143	+	1.53643i
$693$	−1283.32	−	531.568i	−1.85183	−	0.767053i
$694$	85.0257	+	63.2642i	0.122515	+	0.0911588i
$695$	299.233	+	299.233i	0.430551	+	0.430551i
$696$	−64.3410	−	1447.18i	−0.0924440	−	2.07929i
$697$	115.028	+	115.028i	0.165034	+	0.165034i
$698$	−475.976	+	69.8494i	−0.681914	+	0.100071i
$699$	−344.683	−	142.772i	−0.493109	−	0.204252i
$700$	−37.1350	−	19.9976i	−0.0530501	−	0.0285680i
$701$	−487.328	+	201.858i	−0.695189	+	0.287957i	−0.702160	−	0.712019i	$-0.747781\pi$
$701$	−487.328	+	201.858i	−0.695189	+	0.287957i	0.00697111	+	0.999976i	$0.497781\pi$
$702$	60.8034	−	241.152i	0.0866146	−	0.343521i
$703$		−	234.943i		−	0.334200i
$704$	989.474	+	310.247i	1.40550	+	0.440692i
$705$	−363.297			−0.515315
$706$	−145.835	−	36.7705i	−0.206565	−	0.0520829i
$707$	−340.992	−	823.228i	−0.482309	−	1.16440i
$708$	465.122	−	863.721i	0.656952	−	1.21995i
$709$	260.932	−	629.945i	0.368028	−	0.888498i	−0.626046	−	0.779786i	$-0.715328\pi$
$709$	260.932	−	629.945i	0.368028	−	0.888498i	0.994073	−	0.108711i	$-0.0346724\pi$
$710$	14.2136	+	96.8558i	0.0200191	+	0.136417i
$711$	−90.1580	+	90.1580i	−0.126805	+	0.126805i
$712$	8.42537	+	189.507i	0.0118334	+	0.266161i
$713$	6.81917	−	6.81917i	0.00956405	−	0.00956405i
$714$	−114.673	+	154.118i	−0.160606	+	0.215851i
$715$	332.494	−	802.712i	0.465027	−	1.12267i
$716$	1162.01	+	118.092i	1.62291	+	0.164932i
$717$	636.341	+	1536.26i	0.887505	+	2.14263i
$718$	897.326	−	535.945i	1.24976	−	0.746441i
$719$	−349.854			−0.486585			−0.243292	−	0.969953i	$-0.578227\pi$
$719$	−349.854			−0.486585			−0.243292	+	0.969953i	$0.578227\pi$
$720$	500.557	−	739.160i	0.695219	−	1.02661i
$721$			651.251i			0.903261i
$722$	−309.166	+	184.655i	−0.428207	+	0.255755i
$723$	1306.18	−	541.036i	1.80661	−	0.748321i
$724$	−90.8650	−	111.423i	−0.125504	−	0.153899i
$725$	52.2230	+	21.6315i	0.0720318	+	0.0298365i
$726$	−764.815	+	1027.89i	−1.05346	+	1.41583i
$727$	−58.3736	−	58.3736i	−0.0802938	−	0.0802938i	0.665819	−	0.746113i	$-0.268082\pi$
$727$	−58.3736	−	58.3736i	−0.0802938	−	0.0802938i	−0.746113	+	0.665819i	$0.768082\pi$
$728$	279.050	+	597.182i	0.383311	+	0.820305i
$729$	−750.210	−	750.210i	−1.02909	−	1.02909i
$730$	110.429	+	752.498i	0.151272	+	1.03082i
$731$	−168.191	−	69.6672i	−0.230084	−	0.0953040i
$732$	305.803	+	1019.48i	0.417764	+	1.39274i
$733$	327.632	−	135.710i	0.446975	−	0.185143i	−0.147831	−	0.989013i	$-0.547229\pi$
$733$	327.632	−	135.710i	0.446975	−	0.185143i	0.594805	+	0.803870i	$0.297229\pi$
$734$	−936.467	−	236.118i	−1.27584	−	0.321687i
$735$		−	147.032i		−	0.200043i
$736$	28.3027	−	58.6588i	0.0384548	−	0.0796994i
$737$	−1079.73			−1.46504
$738$	−321.359	+	1274.54i	−0.435446	+	1.72702i
$739$	328.523	+	793.126i	0.444551	+	1.07324i	0.974334	+	0.225108i	$0.0722736\pi$
$739$	328.523	+	793.126i	0.444551	+	1.07324i	−0.529783	+	0.848134i	$0.677726\pi$
$740$	−97.4857	−	324.996i	−0.131737	−	0.439184i
$741$	257.266	−	621.096i	0.347188	−	0.838186i
$742$	751.141	−	110.230i	1.01232	−	0.148558i
$743$	79.8532	−	79.8532i	0.107474	−	0.107474i	−0.651325	−	0.758799i	$-0.725786\pi$
$743$	79.8532	−	79.8532i	0.107474	−	0.107474i	0.758799	+	0.651325i	$0.225786\pi$
$744$	161.276	+	58.5541i	0.216769	+	0.0787017i
$745$	467.835	−	467.835i	0.627966	−	0.627966i
$746$	797.274	+	593.219i	1.06873	+	0.795200i
$747$	142.507	−	344.042i	0.190772	−	0.460565i
$748$	116.472	+	142.823i	0.155711	+	0.190940i
$749$	53.2561	+	128.572i	0.0711029	+	0.171658i
$750$	595.468	+	996.984i	0.793957	+	1.32931i
$751$	−729.615			−0.971524			−0.485762	−	0.874091i	$-0.661458\pi$
$751$	−729.615			−0.971524			−0.485762	+	0.874091i	$0.661458\pi$
$752$	−145.536	−	220.765i	−0.193532	−	0.293570i
$753$		−	1093.13i		−	1.45171i
$754$	−452.986	−	758.429i	−0.600778	−	1.00587i
$755$	−674.239	+	279.279i	−0.893032	+	0.369906i
$756$	−334.453	−	33.9896i	−0.442399	−	0.0449598i
$757$	565.974	+	234.434i	0.747654	+	0.309688i	0.723784	−	0.690027i	$-0.242401\pi$
$757$	565.974	+	234.434i	0.747654	+	0.309688i	0.0238700	+	0.999715i	$0.492401\pi$
$758$	363.274	+	270.298i	0.479253	+	0.356593i
$759$	105.549	+	105.549i	0.139063	+	0.139063i
$760$	352.780	−	385.608i	0.464184	−	0.507379i
$761$	186.563	+	186.563i	0.245155	+	0.245155i	0.818979	−	0.573824i	$-0.194541\pi$
$761$	186.563	+	186.563i	0.245155	+	0.245155i	−0.573824	+	0.818979i	$0.694541\pi$
$762$	1728.41	−	253.644i	2.26825	−	0.332866i
$763$	1354.23	+	560.940i	1.77487	+	0.735176i
$764$	−90.5213	+	168.096i	−0.118483	+	0.220021i
$765$	146.576	−	60.7139i	0.191603	−	0.0793645i
$766$	118.861	−	471.413i	0.155171	−	0.615421i
$767$		−	598.241i		−	0.779976i
$768$	1158.66	+	14.3904i	1.50868	+	0.0187375i
$769$	134.178			0.174484			0.0872420	−	0.996187i	$-0.472195\pi$
$769$	134.178			0.174484			0.0872420	+	0.996187i	$0.472195\pi$
$770$	−1138.81	−	287.137i	−1.47898	−	0.372906i
$771$	−308.632	−	745.103i	−0.400301	−	0.966411i
$772$	−1064.19	−	573.077i	−1.37849	−	0.742328i
$773$	−155.016	+	374.241i	−0.200538	+	0.484141i	−0.991872	−	0.127243i	$-0.959387\pi$
$773$	−155.016	+	374.241i	−0.200538	+	0.484141i	0.791334	+	0.611384i	$0.209387\pi$
$774$	−213.578	−	1455.39i	−0.275941	−	1.88035i
$775$	−4.73409	+	4.73409i	−0.00610851	+	0.00610851i
$776$	−400.369	−	366.284i	−0.515940	−	0.472016i
$777$	−417.166	+	417.166i	−0.536893	+	0.536893i
$778$	312.053	−	419.393i	0.401097	−	0.539065i
$779$	−294.489	+	710.960i	−0.378035	+	0.912657i
$780$	98.1628	−	965.910i	0.125850	−	1.23835i
$781$	−62.4903	−	150.865i	−0.0800132	−	0.193169i
$782$	9.93746	−	5.93534i	0.0127078	−	0.00758994i
$783$	450.543			0.575406
$784$	89.3469	−	58.9005i	0.113963	−	0.0751282i
$785$			1100.49i			1.40189i
$786$	370.847	−	221.495i	0.471815	−	0.281800i
$787$	464.245	−	192.297i	0.589892	−	0.244341i	−0.0677120	−	0.997705i	$-0.521570\pi$
$787$	464.245	−	192.297i	0.589892	−	0.244341i	0.657604	+	0.753364i	$0.271570\pi$
$788$	148.235	−	120.885i	0.188115	−	0.153407i
$789$	870.327	+	360.501i	1.10308	+	0.456909i
$790$	−64.3534	+	86.4895i	−0.0814600	+	0.109480i
$791$	827.311	+	827.311i	1.04590	+	1.04590i
$792$	−508.190	+	1399.71i	−0.641654	+	1.76731i
$793$	458.968	+	458.968i	0.578774	+	0.578774i
$794$	−134.780	−	918.436i	−0.169749	−	1.15672i
$795$	−1033.09	−	427.921i	−1.29949	−	0.538265i
$796$	−510.728	+	153.198i	−0.641618	+	0.192459i
$797$	1426.93	−	591.055i	1.79038	−	0.741600i	0.800564	−	0.599247i	$-0.204533\pi$
$797$	1426.93	−	591.055i	1.79038	−	0.741600i	0.989816	−	0.142353i	$-0.0454669\pi$
$798$	−881.154	−	222.172i	−1.10420	−	0.278411i
$799$		−	46.9933i		−	0.0588152i
$800$	−19.6487	+	40.7228i	−0.0245609	+	0.0509035i
$801$	−272.404			−0.340079
$802$	263.669	−	1045.74i	0.328765	−	1.30391i
$803$	−485.503	−	1172.11i	−0.604612	−	1.45966i
$804$	−1155.67	+	346.653i	−1.43740	+	0.431160i
$805$	−28.2286	+	68.1498i	−0.0350665	+	0.0846581i
$806$	103.524	−	15.1921i	0.128441	−	0.0188488i
$807$	−1155.18	+	1155.18i	−1.43146	+	1.43146i
$808$	−865.419	+	404.391i	−1.07106	+	0.500485i
$809$	−950.297	+	950.297i	−1.17466	+	1.17466i	−0.193570	+	0.981086i	$0.562007\pi$
$809$	−950.297	+	950.297i	−1.17466	+	1.17466i	−0.981086	+	0.193570i	$0.937993\pi$
$810$	−408.468	−	303.924i	−0.504281	−	0.375215i
$811$	−580.036	+	1400.33i	−0.715210	+	1.72667i	−0.0286586	+	0.999589i	$0.509124\pi$
$811$	−580.036	+	1400.33i	−0.715210	+	1.72667i	−0.686552	+	0.727081i	$0.740876\pi$
$812$	−925.428	+	754.683i	−1.13969	+	0.929412i
$813$	−378.727	−	914.328i	−0.465839	−	1.12463i
$814$	290.222	+	485.916i	0.356538	+	0.596948i
$815$	2.23385			0.00274092
$816$	170.516	+	115.473i	0.208966	+	0.141511i
$817$		−	861.189i		−	1.05409i
$818$	257.899	+	431.798i	0.315280	+	0.527870i
$819$	−874.515	+	362.236i	−1.06778	+	0.442291i
$820$	−112.366	+	1105.66i	−0.137031	+	1.34837i
$821$	646.816	+	267.920i	0.787839	+	0.326334i	0.740074	−	0.672525i	$-0.234790\pi$
$821$	646.816	+	267.920i	0.787839	+	0.326334i	0.0477645	+	0.998859i	$0.484790\pi$
$822$	286.229	+	212.972i	0.348211	+	0.259090i
$823$	−262.313	−	262.313i	−0.318728	−	0.318728i	0.529551	−	0.848278i	$-0.322361\pi$
$823$	−262.313	−	262.313i	−0.318728	−	0.318728i	−0.848278	+	0.529551i	$0.822361\pi$
$824$	697.472	−	31.0092i	0.846447	−	0.0376326i
$825$	−73.2755	−	73.2755i	−0.0888187	−	0.0888187i
$826$	−800.096	+	117.414i	−0.968639	+	0.142148i
$827$	893.204	+	369.977i	1.08005	+	0.447373i	0.850528	−	0.525930i	$-0.176283\pi$
$827$	893.204	+	369.977i	1.08005	+	0.447373i	0.229525	+	0.973303i	$0.426283\pi$
$828$	82.3466	+	44.3444i	0.0994524	+	0.0535561i
$829$	−161.439	+	66.8701i	−0.194739	+	0.0806635i	−0.477922	−	0.878402i	$-0.658610\pi$
$829$	−161.439	+	66.8701i	−0.194739	+	0.0806635i	0.283183	+	0.959066i	$0.408610\pi$
$830$	76.9780	−	305.302i	0.0927446	−	0.367833i
$831$		−	1254.41i		−	1.50952i
$832$	626.279	−	327.290i	0.752740	−	0.393378i
$833$	19.0189			0.0228318
$834$	−764.865	−	192.851i	−0.917105	−	0.231236i
$835$	254.297	+	613.928i	0.304548	+	0.735243i
$836$	−413.351	+	767.583i	−0.494439	+	0.918162i
$837$	−20.4212	+	49.3011i	−0.0243980	+	0.0589021i
$838$	41.7811	+	284.710i	0.0498582	+	0.339749i
$839$	552.802	−	552.802i	0.658882	−	0.658882i	−0.296234	−	0.955116i	$-0.595731\pi$
$839$	552.802	−	552.802i	0.658882	−	0.658882i	0.955116	+	0.296234i	$0.0957307\pi$
$840$	−1311.09	+	58.2902i	−1.56082	+	0.0693931i
$841$	536.963	−	536.963i	0.638481	−	0.638481i
$842$	−912.175	+	1225.94i	−1.08334	+	1.45599i
$843$	−121.044	+	292.226i	−0.143587	+	0.346650i
$844$	−1153.23	−	117.200i	−1.36639	−	0.138863i
$845$	87.5188	+	211.289i	0.103573	+	0.250046i
$846$	325.992	−	194.705i	0.385333	−	0.230147i
$847$	1056.14			1.24692
$848$	−153.819	−	799.204i	−0.181390	−	0.942457i
$849$		−	579.542i		−	0.682618i
$850$	−6.89891	+	4.12051i	−0.00811637	+	0.00484765i
$851$	32.8425	−	13.6038i	0.0385928	−	0.0159857i
$852$	−115.321	−	141.412i	−0.135353	−	0.165976i
$853$	−653.395	−	270.645i	−0.765997	−	0.317286i	−0.0347472	−	0.999396i	$-0.511063\pi$
$853$	−653.395	−	270.645i	−0.765997	−	0.317286i	−0.731250	+	0.682110i	$0.761063\pi$
$854$	523.750	−	703.909i	0.613290	−	0.824249i
$855$	530.692	+	530.692i	0.620693	+	0.620693i
$856$	135.161	−	63.1578i	0.157898	−	0.0737824i
$857$	−26.5894	−	26.5894i	−0.0310261	−	0.0310261i	0.691424	−	0.722450i	$-0.256984\pi$
$857$	−26.5894	−	26.5894i	−0.0310261	−	0.0310261i	−0.722450	+	0.691424i	$0.756984\pi$
$858$	235.147	+	1602.37i	0.274064	+	1.86756i
$859$	149.594	+	61.9638i	0.174149	+	0.0721349i	0.468054	−	0.883700i	$-0.344955\pi$
$859$	149.594	+	61.9638i	0.174149	+	0.0721349i	−0.293906	+	0.955834i	$0.594955\pi$
$860$	−357.336	−	1191.28i	−0.415507	−	1.38521i
$861$	1785.28	−	739.488i	2.07350	−	0.858871i
$862$	1572.22	+	396.414i	1.82392	+	0.459878i
$863$			448.190i			0.519339i	0.965698	+	0.259670i	$0.0836137\pi$
$863$			448.190i			0.519339i	−0.965698	+	0.259670i	$0.916386\pi$
$864$	−20.4770	+	359.809i	−0.0237002	+	0.416446i
$865$	−1297.55			−1.50006
$866$	−368.231	+	1460.44i	−0.425209	+	1.68642i
$867$	−486.591	−	1174.74i	−0.561236	−	1.35494i
$868$	−40.6362	−	135.472i	−0.0468159	−	0.156074i
$869$	68.8172	−	166.139i	0.0791913	−	0.191185i
$870$	1740.21	−	255.376i	2.00025	−	0.293536i
$871$	−520.277	+	520.277i	−0.597333	+	0.597333i
$872$	536.270	−	1477.05i	0.614988	−	1.69387i
$873$	551.007	−	551.007i	0.631165	−	0.631165i
$874$	43.9298	+	32.6864i	0.0502629	+	0.0373986i
$875$	366.333	−	884.406i	0.418666	−	1.01075i
$876$	−895.956	−	1098.66i	−1.02278	−	1.25418i
$877$	−285.210	−	688.559i	−0.325211	−	0.785130i	−0.998935	−	0.0461461i	$-0.985306\pi$
$877$	−285.210	−	688.559i	−0.325211	−	0.785130i	0.673723	−	0.738984i	$-0.264694\pi$
$878$	732.329	+	1226.13i	0.834088	+	1.39650i
$879$	1185.20			1.34835
$880$	−253.292	+	1233.31i	−0.287832	+	1.40149i
$881$			140.757i			0.159770i	0.996804	+	0.0798849i	$0.0254553\pi$
$881$			140.757i			0.159770i	−0.996804	+	0.0798849i	$0.974545\pi$
$882$	78.7999	+	131.934i	0.0893423	+	0.149585i
$883$	−644.358	+	266.902i	−0.729737	+	0.302267i	−0.716444	−	0.697645i	$-0.754231\pi$
$883$	−644.358	+	266.902i	−0.729737	+	0.302267i	−0.0132930	+	0.999912i	$0.504231\pi$
$884$	124.943	+	12.6976i	0.141338	+	0.0143638i
$885$	1100.42	+	455.810i	1.24341	+	0.515039i
$886$	−1211.03	−	901.080i	−1.36685	−	1.01702i
$887$	−251.938	−	251.938i	−0.284034	−	0.284034i	0.550682	−	0.834715i	$-0.314368\pi$
$887$	−251.938	−	251.938i	−0.284034	−	0.284034i	−0.834715	+	0.550682i	$0.814368\pi$
$888$	466.637	+	426.911i	0.525492	+	0.480755i
$889$	−1018.26	−	1018.26i	−1.14540	−	1.14540i
$890$	−227.878	+	33.4411i	−0.256043	+	0.0375743i
$891$	784.633	+	325.006i	0.880621	+	0.364765i
$892$	774.474	−	1438.18i	0.868244	−	1.61231i
$893$	205.381	−	85.0718i	0.229990	−	0.0952651i
$894$	−301.513	+	1195.83i	−0.337262	+	1.33761i
$895$			1418.13i			1.58450i
$896$	−560.639	−	773.358i	−0.625713	−	0.863123i
$897$	101.719			0.113399
$898$	−570.264	−	143.785i	−0.635038	−	0.160117i
$899$	72.5384	+	175.123i	0.0806878	+	0.194798i
$900$	−57.1677	−	30.7854i	−0.0635197	−	0.0342060i
$901$	55.3526	−	133.633i	0.0614346	−	0.148316i
$902$	−269.170	−	1834.21i	−0.298414	−	2.03349i
$903$	−1529.13	+	1529.13i	−1.69339	+	1.69339i
$904$	846.635	−	925.420i	0.936544	−	1.02369i
$905$	123.438	−	123.438i	0.136395	−	0.136395i
$906$	812.041	−	1091.37i	0.896292	−	1.20460i
$907$	17.5960	−	42.4804i	0.0194002	−	0.0468362i	−0.913883	−	0.405979i	$-0.866931\pi$
$907$	17.5960	−	42.4804i	0.0194002	−	0.0468362i	0.933283	+	0.359142i	$0.116931\pi$
$908$	−87.2013	+	858.050i	−0.0960366	+	0.944989i
$909$	−524.942	−	1267.32i	−0.577494	−	1.39419i
$910$	−687.104	+	410.386i	−0.755060	+	0.450974i
$911$	425.886			0.467493			0.233747	−	0.972298i	$-0.424901\pi$
$911$	425.886			0.467493			0.233747	+	0.972298i	$0.424901\pi$
$912$	−195.984	+	954.271i	−0.214895	+	1.04635i
$913$			525.211i			0.575258i
$914$	425.287	−	254.011i	0.465303	−	0.277911i
$915$	−1193.93	+	494.543i	−1.30484	+	0.540484i
$916$	183.126	−	149.338i	0.199919	−	0.163033i
$917$	−328.971	−	136.264i	−0.358747	−	0.148598i
$918$	−38.2341	+	51.3858i	−0.0416494	+	0.0559759i
$919$	339.201	+	339.201i	0.369098	+	0.369098i	0.867148	−	0.498050i	$-0.165951\pi$
$919$	339.201	+	339.201i	0.369098	+	0.369098i	−0.498050	+	0.867148i	$0.665951\pi$
$920$	74.3307	+	26.9871i	0.0807942	+	0.0293338i
$921$	1285.84	+	1285.84i	1.39613	+	1.39613i
$922$	−81.4139	−	554.781i	−0.0883015	−	0.601714i
$923$	−102.807	−	42.5839i	−0.111383	−	0.0461364i
$924$	2096.87	−	628.977i	2.26934	−	0.680711i
$925$	−22.8003	+	9.44420i	−0.0246490	+	0.0102099i
$926$	104.152	+	26.2607i	0.112475	+	0.0283593i
$927$			1002.57i			1.08152i
$928$	852.309	+	955.174i	0.918437	+	1.02928i
$929$	−674.156			−0.725679			−0.362839	−	0.931852i	$-0.618193\pi$
$929$	−674.156			−0.725679			−0.362839	+	0.931852i	$0.618193\pi$
$930$	−50.9317	+	202.000i	−0.0547652	+	0.217204i
$931$	34.4298	+	83.1210i	0.0369816	+	0.0892814i
$932$	315.795	−	94.7257i	0.338836	−	0.101637i
$933$	−766.089	+	1849.50i	−0.821102	+	1.98232i
$934$	217.505	−	31.9188i	0.232874	−	0.0341743i
$935$	−158.224	+	158.224i	−0.169223	+	0.169223i
$936$	429.585	+	919.335i	0.458959	+	0.982196i
$937$	−810.809	+	810.809i	−0.865325	+	0.865325i	−0.991951	−	0.126626i	$-0.959585\pi$
$937$	−810.809	+	810.809i	−0.865325	+	0.865325i	0.126626	+	0.991951i	$0.459585\pi$
$938$	797.937	+	593.713i	0.850680	+	0.632956i
$939$	877.579	−	2118.66i	0.934589	−	2.25630i
$940$	248.805	−	202.899i	0.264686	−	0.215850i
$941$	−372.431	−	899.128i	−0.395782	−	0.955503i	−0.988655	−	0.150206i	$-0.952006\pi$
$941$	−372.431	−	899.128i	−0.395782	−	0.955503i	0.592873	−	0.805296i	$-0.297994\pi$
$942$	−1051.85	−	1761.09i	−1.11661	−	1.86952i
$943$	−116.436			−0.123474
$944$	163.844	+	851.291i	0.173563	+	0.901791i
$945$		−	408.172i		−	0.431928i
$946$	1063.82	+	1781.14i	1.12454	+	1.88281i
$947$	647.322	−	268.130i	0.683551	−	0.283136i	−0.0137596	−	0.999905i	$-0.504380\pi$
$947$	647.322	−	268.130i	0.683551	−	0.283136i	0.697310	+	0.716769i	$0.254380\pi$
$948$	20.3170	−	199.917i	0.0214315	−	0.210883i
$949$	−798.732	−	330.846i	−0.841656	−	0.348625i
$950$	−30.4975	−	22.6919i	−0.0321026	−	0.0238863i
$951$	−570.646	−	570.646i	−0.600049	−	0.600049i
$952$	−7.53998	−	169.592i	−0.00792014	−	0.178143i
$953$	−584.883	−	584.883i	−0.613728	−	0.613728i	0.330187	−	0.943916i	$-0.392888\pi$
$953$	−584.883	−	584.883i	−0.613728	−	0.613728i	−0.943916	+	0.330187i	$0.892888\pi$
$954$	1156.35	−	169.694i	1.21210	−	0.177876i
$955$	−214.162	−	88.7089i	−0.224254	−	0.0928889i
$956$	−1293.79	−	696.721i	−1.35334	−	0.728788i
$957$	−2710.60	+	1122.77i	−2.83239	+	1.17322i
$958$	−19.9499	+	79.1232i	−0.0208245	+	0.0825920i
$959$		−	294.096i		−	0.306669i
$960$	124.855	+	1401.36i	0.130057	+	1.45975i
$961$	938.549			0.976638
$962$	373.987	+	94.2962i	0.388760	+	0.0980210i
$963$	81.9853	+	197.930i	0.0851353	+	0.205535i
$964$	−592.373	+	1100.02i	−0.614495	+	1.14110i
$965$	561.603	−	1355.83i	0.581972	−	1.40500i
$966$	−19.9639	−	136.040i	−0.0206665	−	0.140828i
$967$	177.502	−	177.502i	0.183560	−	0.183560i	−0.609345	−	0.792905i	$-0.708568\pi$
$967$	177.502	−	177.502i	0.183560	−	0.183560i	0.792905	+	0.609345i	$0.208568\pi$
$968$	−50.2882	−	1131.10i	−0.0519506	−	1.16849i
$969$	−122.425	+	122.425i	−0.126342	+	0.126342i
$970$	393.300	−	528.587i	0.405464	−	0.544935i
$971$	130.414	−	314.847i	0.134309	−	0.324250i	−0.842389	−	0.538870i	$-0.818851\pi$
$971$	130.414	−	314.847i	0.134309	−	0.324250i	0.976698	+	0.214620i	$0.0688514\pi$
$972$	1347.52	+	136.945i	1.38634	+	0.140890i
$973$	248.834	+	600.738i	0.255739	+	0.617408i
$974$	−348.846	+	208.355i	−0.358158	+	0.213916i
$975$	−70.6166			−0.0724273
$976$	−778.806	−	527.406i	−0.797957	−	0.540375i
$977$			73.1425i			0.0748644i	0.999299	+	0.0374322i	$0.0119178\pi$
$977$			73.1425i			0.0748644i	−0.999299	+	0.0374322i	$0.988082\pi$
$978$	−3.57481	+	2.13512i	−0.00365522	+	0.00218315i
$979$	354.949	−	147.025i	0.362563	−	0.150179i
$980$	82.1165	+	100.695i	0.0837923	+	0.102750i
$981$	2084.77	+	863.541i	2.12515	+	0.880266i
$982$	569.595	−	765.524i	0.580036	−	0.779556i
$983$	−614.269	−	614.269i	−0.624892	−	0.624892i	0.321886	−	0.946778i	$-0.395683\pi$
$983$	−614.269	−	614.269i	−0.624892	−	0.624892i	−0.946778	+	0.321886i	$0.895683\pi$
$984$	−876.978	−	1876.78i	−0.891238	−	1.90730i
$985$	164.219	+	164.219i	0.166720	+	0.166720i
$986$	33.0335	+	225.101i	0.0335025	+	0.228297i
$987$	−515.731	−	213.623i	−0.522523	−	0.216436i
$988$	170.689	+	569.041i	0.172762	+	0.575953i
$989$	120.385	−	49.8650i	0.121724	−	0.0504197i
$990$	−1753.15	−	442.035i	−1.77086	−	0.446500i
$991$		−	763.403i		−	0.770336i	−0.922847	−	0.385168i	$-0.874144\pi$
$991$		−	763.403i		−	0.770336i	0.922847	−	0.385168i	$-0.125856\pi$
$992$	−143.152	+	49.9708i	−0.144307	+	0.0503738i
$993$	−252.091			−0.253868
$994$	−36.7749	+	145.853i	−0.0369969	+	0.146733i
$995$	−247.750	−	598.122i	−0.248995	−	0.601128i
$996$	168.621	+	562.146i	0.169298	+	0.564404i
$997$	−752.731	+	1817.25i	−0.754996	+	1.82272i	−0.225923	+	0.974145i	$0.572540\pi$
$997$	−752.731	+	1817.25i	−0.754996	+	1.82272i	−0.529073	+	0.848576i	$0.677460\pi$
$998$	−877.835	+	128.822i	−0.879595	+	0.129080i
$999$	−139.091	+	139.091i	−0.139230	+	0.139230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.11.7	yes	28
3.2	odd	2		288.3.u.a.235.1		28
4.3	odd	2		128.3.h.a.79.7		28
8.3	odd	2		256.3.h.a.159.1		28
8.5	even	2		256.3.h.b.159.7		28
32.3	odd	8	inner	32.3.h.a.3.7	✓	28
32.13	even	8		256.3.h.a.95.1		28
32.19	odd	8		256.3.h.b.95.7		28
32.29	even	8		128.3.h.a.47.7		28
96.35	even	8		288.3.u.a.163.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.7	✓	28	32.3	odd	8	inner
32.3.h.a.11.7	yes	28	1.1	even	1	trivial
128.3.h.a.47.7		28	32.29	even	8
128.3.h.a.79.7		28	4.3	odd	2
256.3.h.a.95.1		28	32.13	even	8
256.3.h.a.159.1		28	8.3	odd	2
256.3.h.b.95.7		28	32.19	odd	8
256.3.h.b.159.7		28	8.5	even	2
288.3.u.a.163.1		28	96.35	even	8
288.3.u.a.235.1		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)

\(f(q)\)	\(=\)	\(q+(1.93931 + 0.488972i) q^{2} +(-1.73217 - 4.18183i) q^{3} +(3.52181 + 1.89653i) q^{4} +(-1.85856 + 4.48696i) q^{5} +(-1.31441 - 8.95683i) q^{6} +(-5.27676 + 5.27676i) q^{7} +(5.90252 + 5.40002i) q^{8} +(-8.12333 + 8.12333i) q^{9} +O(q^{10})\)	\(q+(1.93931 + 0.488972i) q^{2} +(-1.73217 - 4.18183i) q^{3} +(3.52181 + 1.89653i) q^{4} +(-1.85856 + 4.48696i) q^{5} +(-1.31441 - 8.95683i) q^{6} +(-5.27676 + 5.27676i) q^{7} +(5.90252 + 5.40002i) q^{8} +(-8.12333 + 8.12333i) q^{9} +(-5.79831 + 7.79280i) q^{10} +(6.20050 - 14.9693i) q^{11} +(1.83059 - 18.0127i) q^{12} +(-4.22532 - 10.2008i) q^{13} +(-12.8134 + 7.65307i) q^{14} +21.9830 q^{15} +(8.80634 + 13.3585i) q^{16} +2.84356i q^{17} +(-19.7257 + 11.7816i) q^{18} +(-12.4276 + 5.14768i) q^{19} +(-15.0551 + 12.2774i) q^{20} +(31.2068 + 12.9263i) q^{21} +(19.3443 - 25.9983i) q^{22} +(-1.43918 - 1.43918i) q^{23} +(12.3578 - 34.0371i) q^{24} +(0.999126 + 0.999126i) q^{25} +(-3.20628 - 21.8486i) q^{26} +(10.4049 + 4.30987i) q^{27} +(-28.5913 + 8.57623i) q^{28} +(36.9596 - 15.3092i) q^{29} +(42.6318 + 10.7491i) q^{30} +4.73823i q^{31} +(10.5463 + 30.2122i) q^{32} -73.3396 q^{33} +(-1.39042 + 5.51453i) q^{34} +(-13.8694 - 33.4838i) q^{35} +(-44.0150 + 13.2027i) q^{36} +(-6.68390 + 16.1364i) q^{37} +(-26.6180 + 3.90618i) q^{38} +(-35.3392 + 35.3392i) q^{39} +(-35.1998 + 16.4481i) q^{40} +(40.4523 - 40.4523i) q^{41} +(54.1989 + 40.3272i) q^{42} +(-24.5000 + 59.1482i) q^{43} +(50.2268 - 40.9598i) q^{44} +(-21.3514 - 51.5467i) q^{45} +(-2.08729 - 3.49473i) q^{46} -16.5262 q^{47} +(40.6087 - 59.9658i) q^{48} -6.68842i q^{49} +(1.44907 + 2.42615i) q^{50} +(11.8913 - 4.92553i) q^{51} +(4.46539 - 43.9389i) q^{52} +(-46.9950 - 19.4659i) q^{53} +(18.0710 + 13.4459i) q^{54} +(55.6428 + 55.6428i) q^{55} +(-59.6408 + 2.65160i) q^{56} +(43.0535 + 43.0535i) q^{57} +(79.1617 - 11.6170i) q^{58} +(50.0578 + 20.7346i) q^{59} +(77.4202 + 41.6915i) q^{60} +(-54.3116 + 22.4966i) q^{61} +(-2.31686 + 9.18889i) q^{62} -85.7298i q^{63} +(5.67958 + 63.7475i) q^{64} +53.6237 q^{65} +(-142.228 - 35.8610i) q^{66} +(-25.5017 - 61.5665i) q^{67} +(-5.39290 + 10.0145i) q^{68} +(-3.52550 + 8.51131i) q^{69} +(-10.5245 - 71.7170i) q^{70} +(7.12641 - 7.12641i) q^{71} +(-91.8143 + 4.08202i) q^{72} +(55.3669 - 55.3669i) q^{73} +(-20.8524 + 28.0251i) q^{74} +(2.44752 - 5.90883i) q^{75} +(-53.5304 - 5.44015i) q^{76} +(46.2711 + 111.708i) q^{77} +(-85.8133 + 51.2536i) q^{78} +11.0986 q^{79} +(-76.3059 + 14.6862i) q^{80} +52.4160i q^{81} +(98.2293 - 58.6693i) q^{82} +(-29.9476 + 12.4047i) q^{83} +(85.3894 + 104.709i) q^{84} +(-12.7589 - 5.28492i) q^{85} +(-76.4348 + 102.727i) q^{86} +(-128.041 - 128.041i) q^{87} +(117.433 - 54.8740i) q^{88} +(16.7667 + 16.7667i) q^{89} +(-16.2019 - 110.405i) q^{90} +(76.1234 + 31.5313i) q^{91} +(-2.33907 - 7.79797i) q^{92} +(19.8145 - 8.20743i) q^{93} +(-32.0494 - 8.08086i) q^{94} -65.3294i q^{95} +(108.074 - 96.4355i) q^{96} -67.8301 q^{97} +(3.27045 - 12.9709i) q^{98} +(71.2322 + 171.970i) 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

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