LMFDB - Embedded newform 32.3.h.a.3.7

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

$q$-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 $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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	0.317756	+	0.948172i	$0.397071\pi$
$3$	−1.73217	+	4.18183i	−0.577390	+	1.39394i	−0.895147	+	0.445771i	$0.852929\pi$
$4$	3.52181	−	1.89653i	0.880453	−	0.474133i
$5$	−1.85856	−	4.48696i	−0.371712	−	0.897391i	−0.993461	−	0.114175i	$-0.963578\pi$
$5$	−1.85856	−	4.48696i	−0.371712	−	0.897391i	0.621749	−	0.783217i	$-0.286422\pi$
$6$	−1.31441	+	8.95683i	−0.219069	+	1.49281i
$7$	−5.27676	−	5.27676i	−0.753823	−	0.753823i	0.221367	−	0.975190i	$-0.428948\pi$
$7$	−5.27676	−	5.27676i	−0.753823	−	0.753823i	−0.975190	+	0.221367i	$0.928948\pi$
$8$	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	0.906802	+	0.421557i	$0.138516\pi$
$11$	6.20050	+	14.9693i	0.563682	+	1.36085i	−0.343120	+	0.939292i	$0.611484\pi$
$12$	1.83059	+	18.0127i	0.152549	+	1.50106i
$13$	−4.22532	+	10.2008i	−0.325025	+	0.784680i	0.673922	+	0.738802i	$0.264608\pi$
$13$	−4.22532	+	10.2008i	−0.325025	+	0.784680i	−0.998947	+	0.0458772i	$0.985392\pi$
$14$	−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	$-0.973347\pi$
$17$		−	2.84356i		−	0.167268i	0.996497	−	0.0836341i	$-0.0266527\pi$
$18$	−19.7257	−	11.7816i	−1.09587	−	0.654531i
$19$	−12.4276	−	5.14768i	−0.654084	−	0.270931i	0.0308626	−	0.999524i	$-0.490175\pi$
$19$	−12.4276	−	5.14768i	−0.654084	−	0.270931i	−0.684947	+	0.728593i	$0.740175\pi$
$20$	−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	−0.737701	−	0.675128i	$-0.764088\pi$
$23$	−1.43918	+	1.43918i	−0.0625730	+	0.0625730i	0.675128	+	0.737701i	$0.264088\pi$
$24$	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	0.914320	−	0.404993i	$-0.132726\pi$
$29$	36.9596	+	15.3092i	1.27447	+	0.527902i	0.360148	+	0.932895i	$0.382726\pi$
$30$	42.6318	−	10.7491i	1.42106	−	0.358303i
$31$		−	4.73823i		−	0.152846i	−0.997075	−	0.0764231i	$-0.975650\pi$
$31$		−	4.73823i		−	0.152846i	0.997075	−	0.0764231i	$-0.0243500\pi$
$32$	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	0.807454	−	0.589930i	$-0.200845\pi$
$37$	−6.68390	−	16.1364i	−0.180646	−	0.436118i	−0.988100	+	0.153812i	$0.950845\pi$
$38$	−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	0.999912	−	0.0132711i	$-0.00422444\pi$
$41$	40.4523	+	40.4523i	0.986641	+	0.986641i	−0.0132711	+	0.999912i	$0.504224\pi$
$42$	54.1989	−	40.3272i	1.29045	−	0.960172i
$43$	−24.5000	−	59.1482i	−0.569767	−	1.37554i	−0.901751	−	0.432255i	$-0.857718\pi$
$43$	−24.5000	−	59.1482i	−0.569767	−	1.37554i	0.331984	−	0.943285i	$-0.392282\pi$
$44$	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	−0.779090	−	0.626912i	$-0.784319\pi$
$53$	−46.9950	+	19.4659i	−0.886697	+	0.367282i	−0.107607	+	0.994194i	$0.534319\pi$
$54$	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	0.0842623	−	0.996444i	$-0.473147\pi$
$59$	50.0578	−	20.7346i	0.848437	−	0.351434i	0.764174	+	0.645010i	$0.223147\pi$
$60$	77.4202	−	41.6915i	1.29034	−	0.694858i
$61$	−54.3116	−	22.4966i	−0.890353	−	0.368796i	−0.109850	−	0.993948i	$-0.535037\pi$
$61$	−54.3116	−	22.4966i	−0.890353	−	0.368796i	−0.780503	+	0.625152i	$0.785037\pi$
$62$	−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	0.611223	+	0.791458i	$0.290678\pi$
$67$	−25.5017	+	61.5665i	−0.380622	+	0.918904i	−0.991846	+	0.127445i	$0.959322\pi$
$68$	−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	0.755510	−	0.655138i	$-0.227389\pi$
$71$	7.12641	+	7.12641i	0.100372	+	0.100372i	−0.655138	+	0.755510i	$0.727389\pi$
$72$	−91.8143	−	4.08202i	−1.27520	−	0.0566947i
$73$	55.3669	+	55.3669i	0.758451	+	0.758451i	0.976040	−	0.217590i	$-0.0698194\pi$
$73$	55.3669	+	55.3669i	0.758451	+	0.758451i	−0.217590	+	0.976040i	$0.569819\pi$
$74$	−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	0.194909	−	0.980821i	$-0.437559\pi$
$83$	−29.9476	−	12.4047i	−0.360814	−	0.149454i	−0.555724	+	0.831367i	$0.687559\pi$
$84$	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	−0.606610	−	0.795000i	$-0.707471\pi$
$89$	16.7667	−	16.7667i	0.188390	−	0.188390i	0.795000	+	0.606610i	$0.207471\pi$
$90$	−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	−0.971400	−	0.237450i	$-0.923689\pi$
$101$	−45.6943	−	110.316i	−0.452419	−	1.09224i	0.518981	−	0.854786i	$-0.326311\pi$
$102$	25.4693	+	3.73761i	0.249699	+	0.0366432i
$103$	61.7093	+	61.7093i	0.599120	+	0.599120i	0.940078	−	0.340959i	$-0.110752\pi$
$103$	61.7093	+	61.7093i	0.599120	+	0.599120i	−0.340959	+	0.940078i	$0.610752\pi$
$104$	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	0.953713	−	0.300718i	$-0.0972262\pi$
$107$	7.13652	+	17.2291i	0.0666965	+	0.161020i	−0.887017	+	0.461737i	$0.847226\pi$
$108$	28.4705	−	34.9118i	0.263615	−	0.323258i
$109$	−75.1681	+	181.472i	−0.689616	+	1.66488i	0.0559384	+	0.998434i	$0.482185\pi$
$109$	−75.1681	+	181.472i	−0.689616	+	1.66488i	−0.745554	+	0.666445i	$0.767815\pi$
$110$	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	$0.244035\pi$
$113$			156.784i			1.38747i	−0.720232	+	0.693734i	$0.755965\pi$
$114$	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	$-0.725332\pi$
$127$		−	192.971i		−	1.51946i	0.650240	−	0.759729i	$-0.274668\pi$
$128$	−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	−0.838734	−	0.544541i	$-0.816704\pi$
$131$	18.2599	−	44.0834i	0.139389	−	0.336515i	0.978123	+	0.208026i	$0.0667040\pi$
$132$	−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	0.598050	−	0.801459i	$-0.295943\pi$
$137$	−27.8671	−	27.8671i	−0.203409	−	0.203409i	−0.801459	+	0.598050i	$0.795943\pi$
$138$	−10.9988	−	14.7822i	−0.0797015	−	0.107117i
$139$	33.3447	+	80.5013i	0.239890	+	0.579146i	0.997271	−	0.0738274i	$-0.0235214\pi$
$139$	33.3447	+	80.5013i	0.239890	+	0.579146i	−0.757381	+	0.652973i	$0.773521\pi$
$140$	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	−0.762703	−	0.646749i	$-0.776128\pi$
$149$	−125.860	+	52.1327i	−0.844695	+	0.349884i	−0.0819919	+	0.996633i	$0.526128\pi$
$150$	7.63574	+	10.2623i	0.0509049	+	0.0684151i
$151$	106.254	−	106.254i	0.703672	−	0.703672i	−0.261525	−	0.965197i	$-0.584225\pi$
$151$	106.254	−	106.254i	0.703672	−	0.703672i	0.965197	+	0.261525i	$0.0842254\pi$
$152$	−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	0.931626	−	0.363419i	$-0.118391\pi$
$157$	209.345	+	86.7136i	1.33341	+	0.552316i	0.401783	+	0.915735i	$0.368391\pi$
$158$	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	−0.924419	−	0.381380i	$-0.875449\pi$
$163$	−0.176018	+	0.424946i	−0.00107987	+	0.00260703i	0.923339	+	0.383987i	$0.125449\pi$
$164$	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	0.934722	−	0.355381i	$-0.115649\pi$
$167$	96.7499	+	96.7499i	0.579341	+	0.579341i	−0.355381	+	0.934722i	$0.615649\pi$
$168$	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	−0.291551	−	0.956555i	$-0.594171\pi$
$173$	102.242	−	246.834i	0.590994	−	1.42678i	0.882544	−	0.470229i	$-0.155829\pi$
$174$	−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	0.974957	−	0.222393i	$-0.0713867\pi$
$179$	269.771	+	111.743i	1.50710	+	0.624262i	0.532144	+	0.846654i	$0.321387\pi$
$180$	22.5645	+	222.032i	0.125358	+	1.23351i
$181$	−33.2079	+	13.7552i	−0.183469	+	0.0759954i	−0.472527	−	0.881316i	$-0.656658\pi$
$181$	−33.2079	+	13.7552i	−0.183469	+	0.0759954i	0.289058	+	0.957312i	$0.406658\pi$
$182$	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	$-0.960124\pi$
$191$		−	47.7299i		−	0.249895i	0.992163	−	0.124947i	$-0.0398762\pi$
$192$	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	0.963495	−	0.267725i	$-0.0862718\pi$
$197$	18.2996	+	44.1791i	0.0928913	+	0.224259i	−0.870604	+	0.491984i	$0.836272\pi$
$198$	54.0527	−	368.332i	0.272993	−	1.86026i
$199$	−94.2590	−	94.2590i	−0.473663	−	0.473663i	0.429435	−	0.903098i	$-0.358713\pi$
$199$	−94.2590	−	94.2590i	−0.473663	−	0.473663i	−0.903098	+	0.429435i	$0.858713\pi$
$200$	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	−0.356259	−	0.934387i	$-0.615948\pi$
$211$	−267.734	−	110.899i	−1.26888	−	0.525589i	−0.912625	+	0.408799i	$0.865948\pi$
$212$	−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	$0.368294\pi$
$223$			408.363i			1.83123i	−0.402061	+	0.915613i	$0.631706\pi$
$224$	−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	−0.631290	−	0.775547i	$-0.717474\pi$
$227$	82.5132	−	199.204i	0.363494	−	0.877553i	0.994784	−	0.102005i	$-0.0325259\pi$
$228$	69.9741	−	233.278i	0.306904	−	1.02315i
$229$	22.6069	+	54.5778i	0.0987200	+	0.238331i	0.965522	−	0.260321i	$-0.0838284\pi$
$229$	22.6069	+	54.5778i	0.0987200	+	0.238331i	−0.866802	+	0.498652i	$0.833828\pi$
$230$	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	0.821028	−	0.570888i	$-0.193401\pi$
$233$	58.2826	+	58.2826i	0.250140	+	0.250140i	−0.570888	+	0.821028i	$0.693401\pi$
$234$	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	$-0.775597\pi$
$241$		−	312.345i		−	1.29604i	0.761624	−	0.648020i	$-0.224403\pi$
$242$	−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	0.108972	−	0.994045i	$-0.465244\pi$
$251$	223.120	−	92.4192i	0.888923	−	0.368204i	0.779951	+	0.625841i	$0.215244\pi$
$252$	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	0.369623	−	0.929182i	$-0.379487\pi$
$263$	−147.164	−	147.164i	−0.559558	−	0.559558i	−0.929182	+	0.369623i	$0.879487\pi$
$264$	−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	0.428405	+	0.903587i	$0.359076\pi$
$269$	−138.119	+	333.450i	−0.513455	+	1.23959i	−0.941861	+	0.336004i	$0.890924\pi$
$270$	−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	0.130801	−	0.991409i	$-0.458245\pi$
$277$	256.038	−	106.054i	0.924323	−	0.382867i	0.793522	+	0.608541i	$0.208245\pi$
$278$	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	−0.789542	−	0.613697i	$-0.789682\pi$
$281$	−49.4126	+	49.4126i	−0.175845	+	0.175845i	0.613697	+	0.789542i	$0.289682\pi$
$282$	21.7223	−	148.023i	0.0770294	−	0.524903i
$283$	118.290	−	48.9975i	0.417987	−	0.173136i	−0.163770	−	0.986499i	$-0.552365\pi$
$283$	118.290	−	48.9975i	0.417987	−	0.173136i	0.581757	+	0.813363i	$0.302365\pi$
$284$	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	−0.997515	−	0.0704605i	$-0.977553\pi$
$293$	−100.203	−	241.910i	−0.341988	−	0.825633i	0.655526	−	0.755172i	$-0.272447\pi$
$294$	−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	−0.315103	−	0.949058i	$-0.602039\pi$
$307$	−371.163	−	153.741i	−1.20900	−	0.500784i	−0.893896	+	0.448274i	$0.852039\pi$
$308$	−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	−0.00558671	+	0.999984i	$0.501778\pi$
$311$	−312.733	+	312.733i	−1.00557	+	1.00557i	−0.999984	+	0.00558671i	$0.998222\pi$
$312$	−399.423	−	17.7581i	−1.28020	−	0.0569170i
$313$	358.245	−	358.245i	1.14455	−	1.14455i	0.156946	−	0.987607i	$-0.449835\pi$
$313$	358.245	−	358.245i	1.14455	−	1.14455i	0.987607	−	0.156946i	$-0.0501649\pi$
$314$	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	0.627051	−	0.778979i	$-0.284262\pi$
$317$	164.720	+	68.2292i	0.519621	+	0.215234i	−0.107429	+	0.994213i	$0.534262\pi$
$318$	−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	0.952799	−	0.303601i	$-0.0981891\pi$
$331$	21.3130	+	51.4542i	0.0643898	+	0.155451i	−0.888409	+	0.459052i	$0.848189\pi$
$332$	−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	$0.0826413\pi$
$337$			173.028i			0.513437i	−0.966486	+	0.256718i	$0.917359\pi$
$338$	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	−0.311024	−	0.950402i	$-0.600672\pi$
$347$	48.9563	−	20.2784i	0.141085	−	0.0584391i	0.452109	+	0.891963i	$0.350672\pi$
$348$	−208.102	+	693.768i	−0.597995	+	1.99359i
$349$	−222.227	−	92.0495i	−0.636754	−	0.263752i	0.0408656	−	0.999165i	$-0.486988\pi$
$349$	−222.227	−	92.0495i	−0.636754	−	0.263752i	−0.677620	+	0.735412i	$0.736988\pi$
$350$	−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	0.999556	+	0.0297806i	$0.00948087\pi$
$359$	369.532	+	369.532i	1.02934	+	1.02934i	0.0297806	+	0.999556i	$0.490519\pi$
$360$	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	0.329913	−	0.944011i	$-0.392980\pi$
$373$	459.056	−	190.147i	1.23071	−	0.509778i	0.900801	+	0.434233i	$0.142980\pi$
$374$	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	−0.0892693	−	0.996008i	$-0.528453\pi$
$379$	209.167	−	86.6398i	0.551891	−	0.228601i	0.641161	+	0.767407i	$0.278453\pi$
$380$	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	$0.102790\pi$
$383$			243.083i			0.634682i	−0.948312	+	0.317341i	$0.897210\pi$
$384$	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	0.998746	−	0.0500566i	$-0.0159402\pi$
$389$	100.024	+	241.479i	0.257131	+	0.620768i	−0.741616	+	0.670825i	$0.765940\pi$
$390$	−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	0.525894	+	0.850550i	$0.323731\pi$
$397$	−177.617	+	428.806i	−0.447399	+	1.08012i	−0.973293	+	0.229566i	$0.926269\pi$
$398$	−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	$0.234719\pi$
$401$			539.233i			1.34472i	−0.740224	+	0.672360i	$0.765281\pi$
$402$	−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	−0.455478	−	0.890247i	$-0.650532\pi$
$409$	177.821	−	177.821i	0.434769	−	0.434769i	0.890247	+	0.455478i	$0.150532\pi$
$410$	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	−0.844456	−	0.535625i	$-0.820076\pi$
$419$	55.0604	−	132.927i	0.131409	−	0.317249i	0.975865	+	0.218376i	$0.0700759\pi$
$420$	−628.524	−	188.532i	−1.49649	−	0.448885i
$421$	−292.384	−	705.877i	−0.694498	−	1.67667i	−0.735514	−	0.677509i	$-0.763059\pi$
$421$	−292.384	−	705.877i	−0.694498	−	1.67667i	0.0410159	−	0.999158i	$-0.486941\pi$
$422$	−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	$-0.664378\pi$
$433$		−	753.072i		−	1.73920i	0.493759	−	0.869599i	$-0.335622\pi$
$434$	−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	0.163689	−	0.986512i	$-0.447661\pi$
$439$	504.938	−	504.938i	1.15020	−	1.15020i	0.986512	−	0.163689i	$-0.0523392\pi$
$440$	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	−0.987452	−	0.157919i	$-0.949522\pi$
$443$	−697.291	+	288.827i	−1.57402	+	0.651981i	−0.586569	+	0.809899i	$0.699522\pi$
$444$	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	0.872267	−	0.489030i	$-0.162649\pi$
$457$	175.139	+	175.139i	0.383237	+	0.383237i	−0.489030	+	0.872267i	$0.662649\pi$
$458$	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	−0.996497	−	0.0836293i	$-0.973349\pi$
$461$	−107.290	+	259.020i	−0.232732	+	0.561866i	0.763765	+	0.645495i	$0.223349\pi$
$462$	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	0.488750	−	0.872424i	$-0.337453\pi$
$467$	101.550	+	42.0634i	0.217452	+	0.0900716i	−0.271298	+	0.962495i	$0.587453\pi$
$468$	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	$-0.986440\pi$
$479$		−	40.7997i		−	0.0851769i	0.999093	−	0.0425884i	$-0.0135604\pi$
$480$	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	0.544058	−	0.839047i	$-0.316887\pi$
$487$	−143.660	−	143.660i	−0.294989	−	0.294989i	−0.839047	+	0.544058i	$0.816887\pi$
$488$	−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	0.993438	+	0.114370i	$0.0364849\pi$
$491$	182.575	+	440.775i	0.371843	+	0.897709i	−0.621595	+	0.783339i	$0.713515\pi$
$492$	−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	−0.0678733	−	0.997694i	$-0.521621\pi$
$499$	−409.850	−	169.766i	−0.821343	−	0.340211i	−0.753470	+	0.657482i	$0.771621\pi$
$500$	−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	−0.0935920	−	0.995611i	$-0.529835\pi$
$503$	453.715	−	453.715i	0.902019	−	0.902019i	0.995611	+	0.0935920i	$0.0298349\pi$
$504$	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	0.311337	−	0.950299i	$-0.399223\pi$
$509$	−71.5029	−	29.6175i	−0.140477	−	0.0581876i	−0.451815	+	0.892112i	$0.649223\pi$
$510$	−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	−0.995951	−	0.0899020i	$-0.971345\pi$
$521$	−565.729	−	565.729i	−1.08585	−	1.08585i	−0.0899020	−	0.995951i	$-0.528655\pi$
$522$	−548.688	−	737.425i	−1.05113	−	1.41269i
$523$	−1.50925	−	3.64366i	−0.00288576	−	0.00696685i	0.922430	−	0.386164i	$-0.126200\pi$
$523$	−1.50925	−	3.64366i	−0.00288576	−	0.00696685i	−0.925316	+	0.379197i	$0.876200\pi$
$524$	−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	−0.435656	−	0.900113i	$-0.643483\pi$
$541$	−746.681	−	309.286i	−1.38019	−	0.571692i	−0.944531	+	0.328421i	$0.893483\pi$
$542$	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	−0.375964	−	0.926634i	$-0.622688\pi$
$547$	298.176	−	719.861i	0.545112	−	1.31602i	0.921076	−	0.389383i	$-0.127312\pi$
$548$	−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	−0.831143	−	0.556058i	$-0.812313\pi$
$557$	83.4142	−	201.380i	0.149756	−	0.361544i	0.980900	+	0.194515i	$0.0623132\pi$
$558$	−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	0.365226	−	0.930919i	$-0.380992\pi$
$563$	−19.5811	−	8.11076i	−0.0347800	−	0.0144063i	−0.400006	+	0.916513i	$0.630992\pi$
$564$	−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	−0.951675	−	0.307106i	$-0.900639\pi$
$569$	−366.760	+	366.760i	−0.644569	+	0.644569i	0.307106	+	0.951675i	$0.400639\pi$
$570$	−585.144	−	85.8698i	−1.02657	−	0.150649i
$571$	−121.285	+	50.2378i	−0.212408	+	0.0879822i	−0.486350	−	0.873764i	$-0.661672\pi$
$571$	−121.285	+	50.2378i	−0.212408	+	0.0879822i	0.273943	+	0.961746i	$0.411672\pi$
$572$	−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	0.999561	−	0.0296380i	$-0.00943546\pi$
$587$	159.551	+	385.190i	0.271807	+	0.656201i	−0.727753	+	0.685839i	$0.759435\pi$
$588$	−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	$0.129826\pi$
$593$			470.422i			0.793292i	−0.917972	+	0.396646i	$0.870174\pi$
$594$	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	−0.989645	−	0.143540i	$-0.954151\pi$
$599$	−506.817	+	506.817i	−0.846105	+	0.846105i	0.143540	+	0.989645i	$0.454151\pi$
$600$	46.3543	+	21.6604i	0.0772572	+	0.0361006i
$601$	−261.398	+	261.398i	−0.434939	+	0.434939i	−0.890305	−	0.455366i	$-0.849509\pi$
$601$	−261.398	+	261.398i	−0.434939	+	0.434939i	0.455366	+	0.890305i	$0.349509\pi$
$602$	−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	$0.233250\pi$
$607$			812.089i			1.33787i	−0.743319	+	0.668937i	$0.766750\pi$
$608$	−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	0.986151	−	0.165850i	$-0.0530369\pi$
$613$	105.168	+	253.898i	0.171563	+	0.414190i	−0.814588	+	0.580040i	$0.803037\pi$
$614$	−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	0.162218	−	0.986755i	$-0.448135\pi$
$617$	−508.739	−	508.739i	−0.824536	−	0.824536i	−0.986755	+	0.162218i	$0.948135\pi$
$618$	−633.832	+	471.609i	−1.02562	+	0.763121i
$619$	−6.64960	−	16.0536i	−0.0107425	−	0.0259347i	0.918417	−	0.395613i	$-0.129468\pi$
$619$	−6.64960	−	16.0536i	−0.0107425	−	0.0259347i	−0.929160	+	0.369678i	$0.879468\pi$
$620$	−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	−0.833639	−	0.552310i	$-0.813746\pi$
$631$	−177.518	+	177.518i	−0.281329	+	0.281329i	0.552310	+	0.833639i	$0.313746\pi$
$632$	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	−0.938651	−	0.344867i	$-0.887924\pi$
$643$	−19.9758	+	48.2257i	−0.0310665	+	0.0750011i	0.907585	+	0.419869i	$0.137924\pi$
$644$	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	0.961255	−	0.275659i	$-0.0888961\pi$
$647$	443.581	+	443.581i	0.685596	+	0.685596i	−0.275659	+	0.961255i	$0.588896\pi$
$648$	−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	−0.934290	−	0.356514i	$-0.883965\pi$
$653$	−14.0746	+	33.9792i	−0.0215538	+	0.0520355i	0.912736	+	0.408549i	$0.133965\pi$
$654$	−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	−0.366407	−	0.930455i	$-0.619412\pi$
$659$	−845.778	−	350.333i	−1.28343	−	0.531613i	−0.917020	+	0.398842i	$0.869412\pi$
$660$	1104.14	+	900.420i	1.67294	+	1.36427i
$661$	−1022.39	+	423.490i	−1.54674	+	0.640680i	−0.982723	−	0.185083i	$-0.940745\pi$
$661$	−1022.39	+	423.490i	−1.54674	+	0.640680i	−0.564017	+	0.825763i	$0.690745\pi$
$662$	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	0.921552	−	0.388255i	$-0.126922\pi$
$677$	−3.12869	−	7.55333i	−0.00462140	−	0.0111571i	−0.926173	+	0.377098i	$0.876922\pi$
$678$	−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	0.708851	−	0.705358i	$-0.249214\pi$
$683$	−198.853	−	480.073i	−0.291146	−	0.702889i	−0.999997	+	0.00246964i	$0.999214\pi$
$684$	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	0.563000	−	0.826457i	$-0.309647\pi$
$691$	260.304	+	107.822i	0.376707	+	0.156037i	−0.186293	+	0.982494i	$0.559647\pi$
$692$	−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	0.00697111	−	0.999976i	$-0.497781\pi$
$701$	−487.328	−	201.858i	−0.695189	−	0.287957i	−0.702160	+	0.712019i	$0.747781\pi$
$702$	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	0.994073	+	0.108711i	$0.0346724\pi$
$709$	260.932	+	629.945i	0.368028	+	0.888498i	−0.626046	+	0.779786i	$0.715328\pi$
$710$	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	−0.746113	−	0.665819i	$-0.768082\pi$
$727$	−58.3736	+	58.3736i	−0.0802938	+	0.0802938i	0.665819	+	0.746113i	$0.268082\pi$
$728$	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	0.594805	−	0.803870i	$-0.297229\pi$
$733$	327.632	+	135.710i	0.446975	+	0.185143i	−0.147831	+	0.989013i	$0.547229\pi$
$734$	−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	−0.529783	−	0.848134i	$-0.677726\pi$
$739$	328.523	−	793.126i	0.444551	−	1.07324i	0.974334	−	0.225108i	$-0.0722736\pi$
$740$	−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	0.758799	−	0.651325i	$-0.225786\pi$
$743$	79.8532	+	79.8532i	0.107474	+	0.107474i	−0.651325	+	0.758799i	$0.725786\pi$
$744$	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	0.0238700	−	0.999715i	$-0.492401\pi$
$757$	565.974	−	234.434i	0.747654	−	0.309688i	0.723784	+	0.690027i	$0.242401\pi$
$758$	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	−0.573824	−	0.818979i	$-0.694541\pi$
$761$	186.563	−	186.563i	0.245155	−	0.245155i	0.818979	+	0.573824i	$0.194541\pi$
$762$	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	0.791334	−	0.611384i	$-0.209387\pi$
$773$	−155.016	−	374.241i	−0.200538	−	0.484141i	−0.991872	+	0.127243i	$0.959387\pi$
$774$	−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	0.657604	−	0.753364i	$-0.271570\pi$
$787$	464.245	+	192.297i	0.589892	+	0.244341i	−0.0677120	+	0.997705i	$0.521570\pi$
$788$	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	0.989816	+	0.142353i	$0.0454669\pi$
$797$	1426.93	+	591.055i	1.79038	+	0.741600i	0.800564	+	0.599247i	$0.204533\pi$
$798$	−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	−0.981086	−	0.193570i	$-0.937993\pi$
$809$	−950.297	−	950.297i	−1.17466	−	1.17466i	−0.193570	−	0.981086i	$-0.562007\pi$
$810$	−408.468	+	303.924i	−0.504281	+	0.375215i
$811$	−580.036	−	1400.33i	−0.715210	−	1.72667i	−0.686552	−	0.727081i	$-0.740876\pi$
$811$	−580.036	−	1400.33i	−0.715210	−	1.72667i	−0.0286586	−	0.999589i	$-0.509124\pi$
$812$	−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	0.0477645	−	0.998859i	$-0.484790\pi$
$821$	646.816	−	267.920i	0.787839	−	0.326334i	0.740074	+	0.672525i	$0.234790\pi$
$822$	286.229	−	212.972i	0.348211	−	0.259090i
$823$	−262.313	+	262.313i	−0.318728	+	0.318728i	−0.848278	−	0.529551i	$-0.822361\pi$
$823$	−262.313	+	262.313i	−0.318728	+	0.318728i	0.529551	+	0.848278i	$0.322361\pi$
$824$	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	0.229525	−	0.973303i	$-0.426283\pi$
$827$	893.204	−	369.977i	1.08005	−	0.447373i	0.850528	+	0.525930i	$0.176283\pi$
$828$	82.3466	−	44.3444i	0.0994524	−	0.0535561i
$829$	−161.439	−	66.8701i	−0.194739	−	0.0806635i	0.283183	−	0.959066i	$-0.408610\pi$
$829$	−161.439	−	66.8701i	−0.194739	−	0.0806635i	−0.477922	+	0.878402i	$0.658610\pi$
$830$	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	0.955116	−	0.296234i	$-0.0957307\pi$
$839$	552.802	+	552.802i	0.658882	+	0.658882i	−0.296234	+	0.955116i	$0.595731\pi$
$840$	−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	−0.731250	−	0.682110i	$-0.761063\pi$
$853$	−653.395	+	270.645i	−0.765997	+	0.317286i	−0.0347472	+	0.999396i	$0.511063\pi$
$854$	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	−0.722450	−	0.691424i	$-0.756984\pi$
$857$	−26.5894	+	26.5894i	−0.0310261	+	0.0310261i	0.691424	+	0.722450i	$0.256984\pi$
$858$	235.147	−	1602.37i	0.274064	−	1.86756i
$859$	149.594	−	61.9638i	0.174149	−	0.0721349i	−0.293906	−	0.955834i	$-0.594955\pi$
$859$	149.594	−	61.9638i	0.174149	−	0.0721349i	0.468054	+	0.883700i	$0.344955\pi$
$860$	−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	$-0.916386\pi$
$863$		−	448.190i		−	0.519339i	0.965698	−	0.259670i	$-0.0836137\pi$
$864$	−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	0.673723	+	0.738984i	$0.264694\pi$
$877$	−285.210	+	688.559i	−0.325211	+	0.785130i	−0.998935	+	0.0461461i	$0.985306\pi$
$878$	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	$-0.974545\pi$
$881$		−	140.757i		−	0.159770i	0.996804	−	0.0798849i	$-0.0254553\pi$
$882$	78.7999	−	131.934i	0.0893423	−	0.149585i
$883$	−644.358	−	266.902i	−0.729737	−	0.302267i	−0.0132930	−	0.999912i	$-0.504231\pi$
$883$	−644.358	−	266.902i	−0.729737	−	0.302267i	−0.716444	+	0.697645i	$0.754231\pi$
$884$	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	−0.834715	−	0.550682i	$-0.814368\pi$
$887$	−251.938	+	251.938i	−0.284034	+	0.284034i	0.550682	+	0.834715i	$0.314368\pi$
$888$	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	0.933283	−	0.359142i	$-0.116931\pi$
$907$	17.5960	+	42.4804i	0.0194002	+	0.0468362i	−0.913883	+	0.405979i	$0.866931\pi$
$908$	−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	−0.498050	−	0.867148i	$-0.665951\pi$
$919$	339.201	−	339.201i	0.369098	−	0.369098i	0.867148	+	0.498050i	$0.165951\pi$
$920$	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	0.126626	−	0.991951i	$-0.459585\pi$
$937$	−810.809	−	810.809i	−0.865325	−	0.865325i	−0.991951	+	0.126626i	$0.959585\pi$
$938$	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	0.592873	+	0.805296i	$0.297994\pi$
$941$	−372.431	+	899.128i	−0.395782	+	0.955503i	−0.988655	+	0.150206i	$0.952006\pi$
$942$	−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	0.697310	−	0.716769i	$-0.254380\pi$
$947$	647.322	+	268.130i	0.683551	+	0.283136i	−0.0137596	+	0.999905i	$0.504380\pi$
$948$	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	−0.943916	−	0.330187i	$-0.892888\pi$
$953$	−584.883	+	584.883i	−0.613728	+	0.613728i	0.330187	+	0.943916i	$0.392888\pi$
$954$	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	0.792905	−	0.609345i	$-0.208568\pi$
$967$	177.502	+	177.502i	0.183560	+	0.183560i	−0.609345	+	0.792905i	$0.708568\pi$
$968$	−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	0.976698	−	0.214620i	$-0.0688514\pi$
$971$	130.414	+	314.847i	0.134309	+	0.324250i	−0.842389	+	0.538870i	$0.818851\pi$
$972$	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	$-0.988082\pi$
$977$		−	73.1425i		−	0.0748644i	0.999299	−	0.0374322i	$-0.0119178\pi$
$978$	−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	−0.946778	−	0.321886i	$-0.895683\pi$
$983$	−614.269	+	614.269i	−0.624892	+	0.624892i	0.321886	+	0.946778i	$0.395683\pi$
$984$	−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	$0.125856\pi$
$991$			763.403i			0.770336i	−0.922847	+	0.385168i	$0.874144\pi$
$992$	−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	−0.529073	−	0.848576i	$-0.677460\pi$
$997$	−752.731	−	1817.25i	−0.754996	−	1.82272i	−0.225923	−	0.974145i	$-0.572540\pi$
$998$	−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.3.7	✓	28
3.2	odd	2		288.3.u.a.163.1		28
4.3	odd	2		128.3.h.a.47.7		28
8.3	odd	2		256.3.h.a.95.1		28
8.5	even	2		256.3.h.b.95.7		28
32.5	even	8		256.3.h.a.159.1		28
32.11	odd	8	inner	32.3.h.a.11.7	yes	28
32.21	even	8		128.3.h.a.79.7		28
32.27	odd	8		256.3.h.b.159.7		28
96.11	even	8		288.3.u.a.235.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.7	✓	28	1.1	even	1	trivial
32.3.h.a.11.7	yes	28	32.11	odd	8	inner
128.3.h.a.47.7		28	4.3	odd	2
128.3.h.a.79.7		28	32.21	even	8
256.3.h.a.95.1		28	8.3	odd	2
256.3.h.a.159.1		28	32.5	even	8
256.3.h.b.95.7		28	8.5	even	2
256.3.h.b.159.7		28	32.27	odd	8
288.3.u.a.163.1		28	3.2	odd	2
288.3.u.a.235.1		28	96.11	even	8

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more