LMFDB - Embedded newform 32.3.h.a.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("32.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.871936845953$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			3.6
Character	$\chi$	$=$	32.3
Dual form			32.3.h.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20513 + 1.59614i) q^{2} +(0.527719 - 1.27403i) q^{3} +(-1.09531 + 3.84712i) q^{4} +(-0.642823 - 1.55191i) q^{5} +(2.66949 - 0.693061i) q^{6} +(-4.95044 - 4.95044i) q^{7} +(-7.46052 + 2.88803i) q^{8} +(5.01930 + 5.01930i) q^{9} +O(q^{10})$	\(q+(1.20513 + 1.59614i) q^{2} +(0.527719 - 1.27403i) q^{3} +(-1.09531 + 3.84712i) q^{4} +(-0.642823 - 1.55191i) q^{5} +(2.66949 - 0.693061i) q^{6} +(-4.95044 - 4.95044i) q^{7} +(-7.46052 + 2.88803i) q^{8} +(5.01930 + 5.01930i) q^{9} +(1.70238 - 2.89629i) q^{10} +(-4.27221 - 10.3140i) q^{11} +(4.32332 + 3.42565i) q^{12} +(1.68327 - 4.06379i) q^{13} +(1.93564 - 13.8675i) q^{14} -2.31641 q^{15} +(-13.6006 - 8.42755i) q^{16} +28.6469i q^{17} +(-1.96257 + 14.0604i) q^{18} +(17.5460 + 7.26778i) q^{19} +(6.67447 - 0.773195i) q^{20} +(-8.91944 + 3.69455i) q^{21} +(11.3140 - 19.2488i) q^{22} +(-24.3334 + 24.3334i) q^{23} +(-0.257631 + 11.0290i) q^{24} +(15.6825 - 15.6825i) q^{25} +(8.51493 - 2.21067i) q^{26} +(20.5098 - 8.49542i) q^{27} +(24.4672 - 13.6227i) q^{28} +(8.57286 + 3.55100i) q^{29} +(-2.79158 - 3.69730i) q^{30} +5.73273i q^{31} +(-2.93903 - 31.8647i) q^{32} -15.3949 q^{33} +(-45.7244 + 34.5233i) q^{34} +(-4.50039 + 10.8649i) q^{35} +(-24.8075 + 13.8122i) q^{36} +(-26.1364 - 63.0989i) q^{37} +(9.54487 + 36.7644i) q^{38} +(-4.28908 - 4.28908i) q^{39} +(9.27775 + 9.72157i) q^{40} +(-14.2561 - 14.2561i) q^{41} +(-16.6461 - 9.78422i) q^{42} +(-10.1365 - 24.4717i) q^{43} +(44.3587 - 5.13867i) q^{44} +(4.56299 - 11.0160i) q^{45} +(-68.1643 - 9.51443i) q^{46} +57.9804 q^{47} +(-17.9142 + 12.8802i) q^{48} +0.0137567i q^{49} +(43.9308 + 6.13190i) q^{50} +(36.4969 + 15.1175i) q^{51} +(13.7902 + 10.9268i) q^{52} +(-46.3830 + 19.2124i) q^{53} +(38.2769 + 22.4983i) q^{54} +(-13.2602 + 13.2602i) q^{55} +(51.2299 + 22.6358i) q^{56} +(18.5187 - 18.5187i) q^{57} +(4.66357 + 17.9629i) q^{58} +(-27.6347 + 11.4467i) q^{59} +(2.53718 - 8.91149i) q^{60} +(76.3985 + 31.6453i) q^{61} +(-9.15022 + 6.90870i) q^{62} -49.6955i q^{63} +(47.3186 - 43.0924i) q^{64} -7.38868 q^{65} +(-18.5529 - 24.5724i) q^{66} +(-36.1949 + 87.3821i) q^{67} +(-110.208 - 31.3771i) q^{68} +(18.1602 + 43.8425i) q^{69} +(-22.7654 + 5.91042i) q^{70} +(-5.39666 - 5.39666i) q^{71} +(-51.9425 - 22.9507i) q^{72} +(-25.4031 - 25.4031i) q^{73} +(69.2166 - 117.760i) q^{74} +(-11.7039 - 28.2558i) q^{75} +(-47.1782 + 59.5410i) q^{76} +(-29.9097 + 72.2084i) q^{77} +(1.67704 - 12.0149i) q^{78} +50.1674 q^{79} +(-4.33602 + 26.5244i) q^{80} +33.2721i q^{81} +(5.57420 - 39.9353i) q^{82} +(-100.805 - 41.7550i) q^{83} +(-4.44385 - 38.3608i) q^{84} +(44.4574 - 18.4149i) q^{85} +(26.8443 - 45.6709i) q^{86} +(9.04814 - 9.04814i) q^{87} +(61.6601 + 64.6097i) q^{88} +(10.6266 - 10.6266i) q^{89} +(23.0821 - 5.99263i) q^{90} +(-28.4505 + 11.7846i) q^{91} +(-66.9607 - 120.266i) q^{92} +(7.30366 + 3.02527i) q^{93} +(69.8741 + 92.5446i) q^{94} -31.9017i q^{95} +(-42.1475 - 13.0712i) q^{96} -14.3055 q^{97} +(-0.0219576 + 0.0165786i) q^{98} +(30.3257 - 73.2128i) 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 $

$2$	1.20513	+	1.59614i	0.602567	+	0.798069i
$2$	1.20513	+	1.59614i	0.602567	+	0.798069i
$3$	0.527719	−	1.27403i	0.175906	−	0.424676i	−0.811194	−	0.584777i	$-0.801182\pi$
$3$	0.527719	−	1.27403i	0.175906	−	0.424676i	0.987101	+	0.160101i	$0.0511820\pi$
$4$	−1.09531	+	3.84712i	−0.273827	+	0.961779i
$5$	−0.642823	−	1.55191i	−0.128565	−	0.310382i	0.846470	−	0.532437i	$-0.178724\pi$
$5$	−0.642823	−	1.55191i	−0.128565	−	0.310382i	−0.975034	+	0.222055i	$0.928724\pi$
$6$	2.66949	−	0.693061i	0.444916	−	0.115510i
$7$	−4.95044	−	4.95044i	−0.707206	−	0.707206i	0.258741	−	0.965947i	$-0.416692\pi$
$7$	−4.95044	−	4.95044i	−0.707206	−	0.707206i	−0.965947	+	0.258741i	$0.916692\pi$
$8$	−7.46052	+	2.88803i	−0.932564	+	0.361004i
$9$	5.01930	+	5.01930i	0.557700	+	0.557700i
$10$	1.70238	−	2.89629i	0.170238	−	0.289629i
$11$	−4.27221	−	10.3140i	−0.388383	−	0.937640i	−0.990283	−	0.139068i	$-0.955589\pi$
$11$	−4.27221	−	10.3140i	−0.388383	−	0.937640i	0.601900	−	0.798572i	$-0.294411\pi$
$12$	4.32332	+	3.42565i	0.360276	+	0.285471i
$13$	1.68327	−	4.06379i	0.129483	−	0.312599i	−0.845821	−	0.533467i	$-0.820889\pi$
$13$	1.68327	−	4.06379i	0.129483	−	0.312599i	0.975304	+	0.220868i	$0.0708890\pi$
$14$	1.93564	−	13.8675i	0.138260	−	0.990538i
$15$	−2.31641			−0.154427
$16$	−13.6006	−	8.42755i	−0.850038	−	0.526722i
$17$			28.6469i			1.68511i	0.538609	+	0.842556i	$0.318950\pi$
$17$			28.6469i			1.68511i	−0.538609	+	0.842556i	$0.681050\pi$
$18$	−1.96257	+	14.0604i	−0.109031	+	0.781135i
$19$	17.5460	+	7.26778i	0.923473	+	0.382515i	0.793199	−	0.608963i	$-0.208414\pi$
$19$	17.5460	+	7.26778i	0.923473	+	0.382515i	0.130274	+	0.991478i	$0.458414\pi$
$20$	6.67447	−	0.773195i	0.333724	−	0.0386597i
$21$	−8.91944	+	3.69455i	−0.424735	+	0.175931i
$22$	11.3140	−	19.2488i	0.514274	−	0.874947i
$23$	−24.3334	+	24.3334i	−1.05797	+	1.05797i	−0.0597590	+	0.998213i	$0.519033\pi$
$23$	−24.3334	+	24.3334i	−1.05797	+	1.05797i	−0.998213	+	0.0597590i	$0.980967\pi$
$24$	−0.257631	+	11.0290i	−0.0107346	+	0.459540i
$25$	15.6825	−	15.6825i	0.627298	−	0.627298i
$26$	8.51493	−	2.21067i	0.327497	−	0.0850256i
$27$	20.5098	−	8.49542i	0.759621	−	0.314645i
$28$	24.4672	−	13.6227i	0.873828	−	0.486524i
$29$	8.57286	+	3.55100i	0.295616	+	0.122448i	0.525562	−	0.850755i	$-0.323855\pi$
$29$	8.57286	+	3.55100i	0.295616	+	0.122448i	−0.229946	+	0.973203i	$0.573855\pi$
$30$	−2.79158	−	3.69730i	−0.0930527	−	0.123243i
$31$			5.73273i			0.184927i	0.995716	+	0.0924634i	$0.0294741\pi$
$31$			5.73273i			0.184927i	−0.995716	+	0.0924634i	$0.970526\pi$
$32$	−2.93903	−	31.8647i	−0.0918446	−	0.995773i
$33$	−15.3949			−0.466512
$34$	−45.7244	+	34.5233i	−1.34483	+	1.01539i
$35$	−4.50039	+	10.8649i	−0.128583	+	0.310426i
$36$	−24.8075	+	13.8122i	−0.689098	+	0.383671i
$37$	−26.1364	−	63.0989i	−0.706390	−	1.70538i	−0.708831	−	0.705379i	$-0.750777\pi$
$37$	−26.1364	−	63.0989i	−0.706390	−	1.70538i	0.00244114	−	0.999997i	$-0.499223\pi$
$38$	9.54487	+	36.7644i	0.251181	+	0.967485i
$39$	−4.28908	−	4.28908i	−0.109976	−	0.109976i
$40$	9.27775	+	9.72157i	0.231944	+	0.243039i
$41$	−14.2561	−	14.2561i	−0.347711	−	0.347711i	0.511545	−	0.859256i	$-0.329073\pi$
$41$	−14.2561	−	14.2561i	−0.347711	−	0.347711i	−0.859256	+	0.511545i	$0.829073\pi$
$42$	−16.6461	−	9.78422i	−0.396337	−	0.232958i
$43$	−10.1365	−	24.4717i	−0.235733	−	0.569109i	0.761100	−	0.648634i	$-0.224660\pi$
$43$	−10.1365	−	24.4717i	−0.235733	−	0.569109i	−0.996833	+	0.0795253i	$0.974660\pi$
$44$	44.3587	−	5.13867i	1.00815	−	0.116788i
$45$	4.56299	−	11.0160i	0.101400	−	0.244801i
$46$	−68.1643	−	9.51443i	−1.48183	−	0.206835i
$47$	57.9804			1.23363			0.616813	−	0.787110i	$-0.288424\pi$
$47$	57.9804			1.23363			0.616813	+	0.787110i	$0.288424\pi$
$48$	−17.9142	+	12.8802i	−0.373213	+	0.268337i
$49$			0.0137567i			0.000280749i
$50$	43.9308	+	6.13190i	0.878616	+	0.122638i
$51$	36.4969	+	15.1175i	0.715626	+	0.296422i
$52$	13.7902	+	10.9268i	0.265195	+	0.210132i
$53$	−46.3830	+	19.2124i	−0.875150	+	0.362499i	−0.774614	−	0.632434i	$-0.782056\pi$
$53$	−46.3830	+	19.2124i	−0.875150	+	0.362499i	−0.100536	+	0.994933i	$0.532056\pi$
$54$	38.2769	+	22.4983i	0.708831	+	0.416635i
$55$	−13.2602	+	13.2602i	−0.241094	+	0.241094i
$56$	51.2299	+	22.6358i	0.914819	+	0.404211i
$57$	18.5187	−	18.5187i	0.324890	−	0.324890i
$58$	4.66357	+	17.9629i	0.0804064	+	0.309705i
$59$	−27.6347	+	11.4467i	−0.468384	+	0.194011i	−0.604377	−	0.796699i	$-0.706578\pi$
$59$	−27.6347	+	11.4467i	−0.468384	+	0.194011i	0.135992	+	0.990710i	$0.456578\pi$
$60$	2.53718	−	8.91149i	0.0422863	−	0.148525i
$61$	76.3985	+	31.6453i	1.25243	+	0.518775i	0.907579	−	0.419881i	$-0.137928\pi$
$61$	76.3985	+	31.6453i	1.25243	+	0.518775i	0.344855	+	0.938656i	$0.387928\pi$
$62$	−9.15022	+	6.90870i	−0.147584	+	0.111431i
$63$		−	49.6955i		−	0.788818i
$64$	47.3186	−	43.0924i	0.739353	−	0.673318i
$65$	−7.38868			−0.113672
$66$	−18.5529	−	24.5724i	−0.281105	−	0.372308i
$67$	−36.1949	+	87.3821i	−0.540222	+	1.30421i	0.384345	+	0.923190i	$0.374427\pi$
$67$	−36.1949	+	87.3821i	−0.540222	+	1.30421i	−0.924566	+	0.381021i	$0.875573\pi$
$68$	−110.208	−	31.3771i	−1.62070	−	0.461429i
$69$	18.1602	+	43.8425i	0.263191	+	0.635399i
$70$	−22.7654	+	5.91042i	−0.325221	+	0.0844346i
$71$	−5.39666	−	5.39666i	−0.0760092	−	0.0760092i	0.668080	−	0.744089i	$-0.267116\pi$
$71$	−5.39666	−	5.39666i	−0.0760092	−	0.0760092i	−0.744089	+	0.668080i	$0.767116\pi$
$72$	−51.9425	−	22.9507i	−0.721423	−	0.318760i
$73$	−25.4031	−	25.4031i	−0.347988	−	0.347988i	0.511372	−	0.859360i	$-0.329137\pi$
$73$	−25.4031	−	25.4031i	−0.347988	−	0.347988i	−0.859360	+	0.511372i	$0.829137\pi$
$74$	69.2166	−	117.760i	0.935360	−	1.59135i
$75$	−11.7039	−	28.2558i	−0.156053	−	0.376744i
$76$	−47.1782	+	59.5410i	−0.620766	+	0.783434i
$77$	−29.9097	+	72.2084i	−0.388438	+	0.937771i
$78$	1.67704	−	12.0149i	0.0215006	−	0.154037i
$79$	50.1674			0.635030			0.317515	−	0.948253i	$-0.397152\pi$
$79$	50.1674			0.635030			0.317515	+	0.948253i	$0.397152\pi$
$80$	−4.33602	+	26.5244i	−0.0542003	+	0.331554i
$81$			33.2721i			0.410767i
$82$	5.57420	−	39.9353i	0.0679781	−	0.487016i
$83$	−100.805	−	41.7550i	−1.21452	−	0.503072i	−0.318859	−	0.947802i	$-0.603300\pi$
$83$	−100.805	−	41.7550i	−1.21452	−	0.503072i	−0.895665	+	0.444730i	$0.853300\pi$
$84$	−4.44385	−	38.3608i	−0.0529030	−	0.456676i
$85$	44.4574	−	18.4149i	0.523029	−	0.216646i
$86$	26.8443	−	45.6709i	0.312143	−	0.531057i
$87$	9.04814	−	9.04814i	0.104002	−	0.104002i
$88$	61.6601	+	64.6097i	0.700683	+	0.734202i
$89$	10.6266	−	10.6266i	0.119400	−	0.119400i	−0.644882	−	0.764282i	$-0.723094\pi$
$89$	10.6266	−	10.6266i	0.119400	−	0.119400i	0.764282	+	0.644882i	$0.223094\pi$
$90$	23.0821	−	5.99263i	0.256468	−	0.0665848i
$91$	−28.4505	+	11.7846i	−0.312643	+	0.129501i
$92$	−66.9607	−	120.266i	−0.727834	−	1.30724i
$93$	7.30366	+	3.02527i	0.0785339	+	0.0325298i
$94$	69.8741	+	92.5446i	0.743341	+	0.984517i
$95$		−	31.9017i		−	0.335807i
$96$	−42.1475	−	13.0712i	−0.439037	−	0.136159i
$97$	−14.3055			−0.147479			−0.0737395	−	0.997278i	$-0.523493\pi$
$97$	−14.3055			−0.147479			−0.0737395	+	0.997278i	$0.523493\pi$
$98$	−0.0219576	+	0.0165786i	−0.000224057	+	0.000169170i
$99$	30.3257	−	73.2128i	0.306321	−	0.739523i
$100$	43.1551	+	77.5094i	0.431551	+	0.775094i
$101$	51.6638	+	124.728i	0.511523	+	1.23493i	0.942997	+	0.332801i	$0.107994\pi$
$101$	51.6638	+	124.728i	0.511523	+	1.23493i	−0.431474	+	0.902125i	$0.642006\pi$
$102$	19.8540	+	76.4727i	0.194647	+	0.749733i
$103$	4.87593	+	4.87593i	0.0473392	+	0.0473392i	0.730380	−	0.683041i	$-0.239343\pi$
$103$	4.87593	+	4.87593i	0.0473392	+	0.0473392i	−0.683041	+	0.730380i	$0.739343\pi$
$104$	−0.821771	+	35.1793i	−0.00790164	+	0.338262i
$105$	11.4672	+	11.4672i	0.109212	+	0.109212i
$106$	−86.5634	−	50.8800i	−0.816635	−	0.480000i
$107$	−4.55603	−	10.9992i	−0.0425797	−	0.102797i	0.901159	−	0.433489i	$-0.142718\pi$
$107$	−4.55603	−	10.9992i	−0.0425797	−	0.102797i	−0.943739	+	0.330692i	$0.892718\pi$
$108$	10.2184	+	88.2085i	0.0946147	+	0.816746i
$109$	11.0098	−	26.5800i	0.101007	−	0.243853i	−0.865295	−	0.501263i	$-0.832869\pi$
$109$	11.0098	−	26.5800i	0.101007	−	0.243853i	0.966302	+	0.257410i	$0.0828690\pi$
$110$	−37.1454	−	5.18478i	−0.337685	−	0.0471344i
$111$	−94.1824			−0.848490
$112$	25.6089	+	109.049i	0.228651	+	0.973653i
$113$		−	120.275i		−	1.06438i	−0.846624	−	0.532191i	$-0.821369\pi$
$113$		−	120.275i		−	1.06438i	0.846624	−	0.532191i	$-0.178631\pi$
$114$	51.8759	+	7.24088i	0.455052	+	0.0635165i
$115$	53.4052	+	22.1212i	0.464393	+	0.192358i
$116$	−23.0510	+	29.0914i	−0.198716	+	0.250788i
$117$	28.8462	−	11.9485i	0.246549	−	0.102124i
$118$	−51.5739	−	30.3140i	−0.437067	−	0.256898i
$119$	141.815	−	141.815i	1.19172	−	1.19172i
$120$	17.2816	−	6.68985i	0.144013	−	0.0557488i
$121$	−2.56759	+	2.56759i	−0.0212197	+	0.0212197i
$122$	41.5601	+	160.079i	0.340657	+	1.31212i
$123$	−25.6860	+	10.6395i	−0.208829	+	0.0864998i
$124$	−22.0545	−	6.27910i	−0.177859	−	0.0506379i
$125$	−73.2166	−	30.3273i	−0.585733	−	0.242619i
$126$	79.3209	−	59.8898i	0.629531	−	0.475316i
$127$			128.040i			1.00819i	0.863648	+	0.504095i	$0.168174\pi$
$127$			128.040i			1.00819i	−0.863648	+	0.504095i	$0.831826\pi$
$128$	125.807	+	23.5949i	0.982863	+	0.184335i
$129$	−36.5268			−0.283154
$130$	−8.90435	−	11.7933i	−0.0684950	−	0.0907181i
$131$	20.1358	−	48.6121i	0.153708	−	0.371084i	−0.828203	−	0.560429i	$-0.810636\pi$
$131$	20.1358	−	48.6121i	0.153708	−	0.371084i	0.981911	+	0.189345i	$0.0606363\pi$
$132$	16.8621	−	59.2259i	0.127743	−	0.448681i
$133$	−50.8816	−	122.839i	−0.382569	−	0.923602i
$134$	−183.093	+	47.5351i	−1.36637	+	0.354740i
$135$	−26.3683	−	26.3683i	−0.195321	−	0.195321i
$136$	−82.7331	−	213.721i	−0.608331	−	1.57148i
$137$	−1.66083	−	1.66083i	−0.0121228	−	0.0121228i	0.701019	−	0.713142i	$-0.252729\pi$
$137$	−1.66083	−	1.66083i	−0.0121228	−	0.0121228i	−0.713142	+	0.701019i	$0.752729\pi$
$138$	−48.0933	+	81.8222i	−0.348502	+	0.592915i
$139$	75.6997	+	182.755i	0.544602	+	1.31479i	0.921445	+	0.388508i	$0.127009\pi$
$139$	75.6997	+	182.755i	0.544602	+	1.31479i	−0.376843	+	0.926277i	$0.622991\pi$
$140$	−36.8692	−	29.2139i	−0.263352	−	0.208671i
$141$	30.5974	−	73.8686i	0.217003	−	0.523891i
$142$	2.11011	−	15.1175i	0.0148599	−	0.106461i
$143$	−49.1053			−0.343394
$144$	−25.9652	−	110.566i	−0.180314	−	0.767819i
$145$		−	15.5870i		−	0.107496i
$146$	9.93270	−	71.1609i	0.0680322	−	0.487404i
$147$	0.0175264	+	0.00725967i	0.000119227	+	4.93855e-5i
$148$	271.376	−	31.4372i	1.83362	−	0.212413i
$149$	−16.1203	+	6.67724i	−0.108190	+	0.0448137i	−0.436122	−	0.899888i	$-0.643648\pi$
$149$	−16.1203	+	6.67724i	−0.108190	+	0.0448137i	0.327932	+	0.944701i	$0.393648\pi$
$150$	30.9954	−	52.7331i	0.206636	−	0.351554i
$151$	−127.344	+	127.344i	−0.843335	+	0.843335i	−0.989291	−	0.145956i	$-0.953374\pi$
$151$	−127.344	+	127.344i	−0.843335	+	0.843335i	0.145956	+	0.989291i	$0.453374\pi$
$152$	−151.892	−	3.54811i	−0.999287	−	0.0233429i
$153$	−143.787	+	143.787i	−0.939787	+	0.939787i
$154$	−151.300	+	39.2808i	−0.982465	+	0.255070i
$155$	8.89669	−	3.68513i	0.0573980	−	0.0237750i
$156$	21.1984	−	11.8027i	0.135887	−	0.0756585i
$157$	−236.255	−	97.8598i	−1.50481	−	0.623311i	−0.530328	−	0.847793i	$-0.677931\pi$
$157$	−236.255	−	97.8598i	−1.50481	−	0.623311i	−0.974478	+	0.224482i	$0.927931\pi$
$158$	60.4584	+	80.0740i	0.382648	+	0.506797i
$159$			69.2319i			0.435421i
$160$	−47.5620	+	25.0445i	−0.297262	+	0.156528i
$161$	240.922			1.49641
$162$	−53.1068	+	40.0973i	−0.327820	+	0.247514i
$163$	38.0947	−	91.9687i	0.233710	−	0.564225i	−0.762898	−	0.646518i	$-0.776224\pi$
$163$	38.0947	−	91.9687i	0.233710	−	0.564225i	0.996608	+	0.0822932i	$0.0262244\pi$
$164$	70.4599	−	39.2302i	0.429634	−	0.239209i
$165$	9.89619	+	23.8915i	0.0599769	+	0.144797i
$166$	−54.8373	−	211.220i	−0.330345	−	1.27241i
$167$	223.831	+	223.831i	1.34031	+	1.34031i	0.895750	+	0.444558i	$0.146639\pi$
$167$	223.831	+	223.831i	1.34031	+	1.34031i	0.444558	+	0.895750i	$0.353361\pi$
$168$	55.8737	−	53.3229i	0.332581	−	0.317398i
$169$	105.820	+	105.820i	0.626154	+	0.626154i
$170$	82.9698	+	48.7678i	0.488058	+	0.286869i
$171$	51.5894	+	124.548i	0.301692	+	0.728350i
$172$	105.248	−	12.1923i	0.611907	−	0.0708855i
$173$	13.2654	−	32.0254i	0.0766784	−	0.185118i	−0.880892	−	0.473317i	$-0.843056\pi$
$173$	13.2654	−	32.0254i	0.0766784	−	0.185118i	0.957571	+	0.288199i	$0.0930565\pi$
$174$	25.3463	+	3.53785i	0.145668	+	0.0203325i
$175$	−155.270			−0.887259
$176$	−28.8173	+	176.281i	−0.163735	+	1.00160i
$177$			41.2480i			0.233039i
$178$	29.7680	+	4.15504i	0.167236	+	0.0233429i
$179$	−13.8305	−	5.72877i	−0.0772652	−	0.0320043i	0.343716	−	0.939074i	$-0.388314\pi$
$179$	−13.8305	−	5.72877i	−0.0772652	−	0.0320043i	−0.420981	+	0.907069i	$0.638314\pi$
$180$	37.3821	+	29.6203i	0.207678	+	0.164557i
$181$	153.596	−	63.6217i	0.848599	−	0.351501i	0.0843605	−	0.996435i	$-0.473115\pi$
$181$	153.596	−	63.6217i	0.848599	−	0.351501i	0.764238	+	0.644934i	$0.223115\pi$
$182$	−53.0964	−	31.2089i	−0.291739	−	0.171477i
$183$	80.6339	−	80.6339i	0.440623	−	0.440623i
$184$	111.264	−	251.815i	0.604695	−	1.36856i
$185$	−81.1228	+	81.1228i	−0.438502	+	0.438502i
$186$	3.97313	+	15.3035i	0.0213609	+	0.0822768i
$187$	295.465	−	122.386i	1.58003	−	0.654469i
$188$	−63.5063	+	223.057i	−0.337800	+	1.18647i
$189$	−143.588	−	59.4763i	−0.759727	−	0.314689i
$190$	50.9195	−	38.4458i	0.267997	−	0.202346i
$191$		−	2.00135i		−	0.0104783i	−0.999986	−	0.00523914i	$-0.998332\pi$
$191$		−	2.00135i		−	0.0104783i	0.999986	−	0.00523914i	$-0.00166768\pi$
$192$	−29.9299	−	83.0259i	−0.155885	−	0.432426i
$193$	−107.502			−0.557003			−0.278502	−	0.960436i	$-0.589838\pi$
$193$	−107.502			−0.557003			−0.278502	+	0.960436i	$0.589838\pi$
$194$	−17.2400	−	22.8335i	−0.0888659	−	0.117698i
$195$	−3.89915	+	9.41338i	−0.0199956	+	0.0482738i
$196$	−0.0529236	−	0.0150678i	−0.000270018	−	7.68765e-5i
$197$	35.9828	+	86.8701i	0.182654	+	0.440965i	0.988512	−	0.151144i	$-0.0482956\pi$
$197$	35.9828	+	86.8701i	0.182654	+	0.440965i	−0.805858	+	0.592109i	$0.798296\pi$
$198$	153.404	−	39.8272i	0.774769	−	0.201147i
$199$	−228.742	−	228.742i	−1.14946	−	1.14946i	−0.986659	−	0.162799i	$-0.947948\pi$
$199$	−228.742	−	228.742i	−1.14946	−	1.14946i	−0.162799	−	0.986659i	$-0.552052\pi$
$200$	−71.7079	+	162.291i	−0.358539	+	0.811453i
$201$	92.2265	+	92.2265i	0.458838	+	0.458838i
$202$	−136.820	+	232.776i	−0.677329	+	1.15236i
$203$	−24.8605	−	60.0185i	−0.122465	−	0.295658i
$204$	−98.1342	+	123.850i	−0.481050	+	0.607106i
$205$	−12.9601	+	31.2885i	−0.0632200	+	0.152627i
$206$	−1.90651	+	13.6588i	−0.00925489	+	0.0663049i
$207$	−244.273			−1.18006
$208$	−57.1413	+	41.0841i	−0.274718	+	0.197520i
$209$		−	212.019i		−	1.01445i
$210$	−4.48373	+	32.1228i	−0.0213511	+	0.152966i
$211$	−244.800	−	101.400i	−1.16019	−	0.480567i	−0.282252	−	0.959340i	$-0.591082\pi$
$211$	−244.800	−	101.400i	−1.16019	−	0.480567i	−0.877938	+	0.478773i	$0.841082\pi$
$212$	−23.1090	−	199.484i	−0.109005	−	0.940963i
$213$	−9.72341	+	4.02757i	−0.0456498	+	0.0189088i
$214$	12.0657	−	20.5276i	0.0563816	−	0.0959233i
$215$	−31.4619	+	31.4619i	−0.146335	+	0.146335i
$216$	−128.478	+	122.613i	−0.594807	+	0.567653i
$217$	28.3796	−	28.3796i	0.130781	−	0.130781i
$218$	55.6935	−	14.4593i	0.255475	−	0.0663270i
$219$	−45.7700	+	18.9585i	−0.208995	+	0.0865687i
$220$	−36.4895	−	65.5375i	−0.165861	−	0.297898i
$221$	116.415	+	48.2206i	0.526764	+	0.218193i
$222$	−113.502	−	150.328i	−0.511272	−	0.677153i
$223$		−	110.575i		−	0.495853i	−0.968779	−	0.247927i	$-0.920251\pi$
$223$		−	110.575i		−	0.495853i	0.968779	−	0.247927i	$-0.0797492\pi$
$224$	−143.195	+	172.294i	−0.639264	+	0.769170i
$225$	157.430			0.699689
$226$	191.976	−	144.948i	0.849449	−	0.641361i
$227$	153.333	−	370.178i	0.675475	−	1.63074i	−0.0966861	−	0.995315i	$-0.530824\pi$
$227$	153.333	−	370.178i	0.675475	−	1.63074i	0.772161	−	0.635427i	$-0.219176\pi$
$228$	50.9600	+	91.5273i	0.223509	+	0.401435i
$229$	−24.0559	−	58.0760i	−0.105047	−	0.253607i	0.862612	−	0.505865i	$-0.168827\pi$
$229$	−24.0559	−	58.0760i	−0.105047	−	0.253607i	−0.967660	+	0.252258i	$0.918827\pi$
$230$	29.0520	+	111.901i	0.126313	+	0.486526i
$231$	76.2115	+	76.2115i	0.329920	+	0.329920i
$232$	−74.2134	−	1.73359i	−0.319885	−	0.00747236i
$233$	−104.978	−	104.978i	−0.450547	−	0.450547i	0.444989	−	0.895536i	$-0.353208\pi$
$233$	−104.978	−	104.978i	−0.450547	−	0.450547i	−0.895536	+	0.444989i	$0.853208\pi$
$234$	53.8350	+	31.6430i	0.230064	+	0.135227i
$235$	−37.2711	−	89.9804i	−0.158600	−	0.382895i
$236$	−13.7682	−	118.851i	−0.0583397	−	0.503608i
$237$	26.4743	−	63.9146i	0.111706	−	0.269682i
$238$	397.262	+	55.4501i	1.66917	+	0.232984i
$239$	122.643			0.513151			0.256576	−	0.966524i	$-0.417406\pi$
$239$	122.643			0.513151			0.256576	+	0.966524i	$0.417406\pi$
$240$	31.5045	+	19.5216i	0.131269	+	0.0813401i
$241$			188.784i			0.783335i	0.920107	+	0.391668i	$0.128102\pi$
$241$			188.784i			0.783335i	−0.920107	+	0.391668i	$0.871898\pi$
$242$	−7.19251	−	1.00394i	−0.0297211	−	0.00414850i
$243$	226.977	+	94.0171i	0.934063	+	0.386902i
$244$	−205.423	+	259.253i	−0.841897	+	1.06251i
$245$	0.0213492	−	0.00884311i	8.71395e−5	−	3.60943e-5i
$246$	−47.9371	−	28.1763i	−0.194866	−	0.114538i
$247$	59.0694	−	59.0694i	0.239147	−	0.239147i
$248$	−16.5563	−	42.7691i	−0.0667592	−	0.172456i
$249$	−106.394	+	106.394i	−0.427285	+	0.427285i
$250$	−39.8292	−	153.412i	−0.159317	−	0.613649i
$251$	−355.365	+	147.197i	−1.41580	+	0.586443i	−0.953801	−	0.300439i	$-0.902867\pi$
$251$	−355.365	+	147.197i	−1.41580	+	0.586443i	−0.461997	+	0.886881i	$0.652867\pi$
$252$	191.185	+	54.4319i	0.758669	+	0.215999i
$253$	354.932	+	147.018i	1.40289	+	0.581098i
$254$	−204.370	+	154.305i	−0.804604	+	0.607501i
$255$		−	66.3579i		−	0.260227i
$256$	113.953	+	229.239i	0.445129	+	0.895467i
$257$	84.4316			0.328528			0.164264	−	0.986416i	$-0.447475\pi$
$257$	84.4316			0.328528			0.164264	+	0.986416i	$0.447475\pi$
$258$	−44.0197	−	58.3018i	−0.170619	−	0.225976i
$259$	−182.981	+	441.754i	−0.706489	+	1.70561i
$260$	8.09287	−	28.4251i	0.0311264	−	0.109327i
$261$	25.2063	+	60.8533i	0.0965758	+	0.233155i
$262$	101.858	−	26.4446i	0.388770	−	0.100933i
$263$	−37.2079	−	37.2079i	−0.141475	−	0.141475i	0.632822	−	0.774297i	$-0.281896\pi$
$263$	−37.2079	−	37.2079i	−0.141475	−	0.141475i	−0.774297	+	0.632822i	$0.781896\pi$
$264$	114.854	−	44.4609i	0.435052	−	0.168412i
$265$	59.6320	+	59.6320i	0.225027	+	0.225027i
$266$	134.749	−	229.252i	0.506575	−	0.861848i
$267$	−7.93072	−	19.1464i	−0.0297031	−	0.0717095i
$268$	−296.525	−	234.956i	−1.10644	−	0.876702i
$269$	−90.5201	+	218.535i	−0.336506	+	0.812398i	0.661540	+	0.749910i	$0.269903\pi$
$269$	−90.5201	+	218.535i	−0.336506	+	0.812398i	−0.998046	+	0.0624874i	$0.980097\pi$
$270$	10.3101	−	73.8647i	0.0381855	−	0.273573i
$271$	312.612			1.15355			0.576775	−	0.816903i	$-0.304311\pi$
$271$	312.612			1.15355			0.576775	+	0.816903i	$0.304311\pi$
$272$	241.423	−	389.615i	0.887585	−	1.43241i
$273$			42.4657i			0.155552i
$274$	0.649390	−	4.65243i	0.00237004	−	0.0169797i
$275$	−228.748	−	94.7506i	−0.831812	−	0.344548i
$276$	−188.558	+	21.8433i	−0.683182	+	0.0791423i
$277$	−199.434	+	82.6083i	−0.719978	+	0.298225i	−0.712426	−	0.701747i	$-0.752404\pi$
$277$	−199.434	+	82.6083i	−0.719978	+	0.298225i	−0.00755172	+	0.999971i	$0.502404\pi$
$278$	−200.474	+	341.071i	−0.721130	+	1.22688i
$279$	−28.7743	+	28.7743i	−0.103134	+	0.103134i
$280$	2.19708	−	94.0550i	0.00784672	−	0.335911i
$281$	237.700	−	237.700i	0.845909	−	0.845909i	−0.143711	−	0.989620i	$-0.545904\pi$
$281$	237.700	−	237.700i	0.845909	−	0.845909i	0.989620	+	0.143711i	$0.0459036\pi$
$282$	154.778	−	40.1839i	0.548859	−	0.142496i
$283$	58.7408	−	24.3312i	0.207565	−	0.0859761i	−0.276479	−	0.961020i	$-0.589168\pi$
$283$	58.7408	−	24.3312i	0.207565	−	0.0859761i	0.484044	+	0.875044i	$0.339168\pi$
$284$	26.6726	−	14.8506i	0.0939174	−	0.0522907i
$285$	−40.6436	−	16.8351i	−0.142609	−	0.0590707i
$286$	−59.1785	−	78.3788i	−0.206918	−	0.274052i
$287$			141.148i			0.491807i
$288$	145.187	−	174.691i	0.504121	−	0.606565i
$289$	−531.645			−1.83960
$290$	24.8790	−	18.7844i	0.0857895	−	0.0647738i
$291$	−7.54927	+	18.2256i	−0.0259425	+	0.0626308i
$292$	125.553	−	69.9045i	0.429976	−	0.239399i
$293$	47.5607	+	114.822i	0.162323	+	0.391883i	0.984024	−	0.178036i	$-0.0569745\pi$
$293$	47.5607	+	114.822i	0.162323	+	0.391883i	−0.821701	+	0.569919i	$0.806974\pi$
$294$	0.00953422	+	0.0367234i	3.24293e−5	+	0.000124910i
$295$	35.5284	+	35.5284i	0.120435	+	0.120435i
$296$	377.223	+	395.268i	1.27440	+	1.33536i
$297$	−175.244	−	175.244i	−0.590048	−	0.590048i
$298$	−30.0849	−	17.6832i	−0.100956	−	0.0593396i
$299$	57.9258	+	139.845i	0.193732	+	0.467710i
$300$	121.523	−	14.0776i	0.405076	−	0.0469255i
$301$	−70.9655	+	171.326i	−0.235766	+	0.569189i
$302$	−356.724	−	49.7918i	−1.18120	−	0.164874i
$303$	186.170			0.614423
$304$	−177.386	−	246.716i	−0.583508	−	0.811565i
$305$		−	138.906i		−	0.455429i
$306$	−402.788	−	56.2214i	−1.31630	−	0.183730i
$307$	407.254	+	168.690i	1.32656	+	0.549480i	0.929673	−	0.368387i	$-0.120090\pi$
$307$	407.254	+	168.690i	1.32656	+	0.549480i	0.396889	+	0.917867i	$0.370090\pi$
$308$	−245.034	−	194.156i	−0.795564	−	0.630378i
$309$	8.78520	−	3.63895i	0.0284311	−	0.0117765i
$310$	16.6037	+	9.75926i	0.0535602	+	0.0314815i
$311$	149.458	−	149.458i	0.480572	−	0.480572i	−0.424742	−	0.905314i	$-0.639635\pi$
$311$	149.458	−	149.458i	0.480572	−	0.480572i	0.905314	+	0.424742i	$0.139635\pi$
$312$	44.3857	+	19.6117i	0.142262	+	0.0628582i
$313$	295.452	−	295.452i	0.943937	−	0.943937i	−0.0545726	−	0.998510i	$-0.517380\pi$
$313$	295.452	−	295.452i	0.943937	−	0.943937i	0.998510	+	0.0545726i	$0.0173796\pi$
$314$	−128.521	−	495.029i	−0.409301	−	1.57652i
$315$	−77.1231	+	31.9454i	−0.244835	+	0.101414i
$316$	−54.9486	+	193.000i	−0.173888	+	0.610758i
$317$	−222.852	−	92.3084i	−0.703004	−	0.291194i	0.00240221	−	0.999997i	$-0.499235\pi$
$317$	−222.852	−	92.3084i	−0.703004	−	0.291194i	−0.705406	+	0.708803i	$0.749235\pi$
$318$	−110.504	+	83.4337i	−0.347496	+	0.262370i
$319$		−	103.591i		−	0.324738i
$320$	−97.2930	−	45.7335i	−0.304041	−	0.142917i
$321$	−16.4176			−0.0511453
$322$	290.343	+	384.544i	0.901686	+	1.19424i
$323$	−208.199	+	502.638i	−0.644580	+	1.55615i
$324$	−128.002	−	36.4432i	−0.395067	−	0.112479i
$325$	−37.3323	−	90.1281i	−0.114868	−	0.277317i
$326$	192.704	−	50.0302i	0.591116	−	0.153467i
$327$	−28.0535	−	28.0535i	−0.0857906	−	0.0857906i
$328$	147.530	+	65.1860i	0.449788	+	0.198738i
$329$	−287.029	−	287.029i	−0.872427	−	0.872427i
$330$	−26.2079	+	44.5881i	−0.0794179	+	0.135116i
$331$	−200.624	−	484.350i	−0.606115	−	1.46329i	−0.867192	−	0.497974i	$-0.834077\pi$
$331$	−200.624	−	484.350i	−0.606115	−	1.46329i	0.261076	−	0.965318i	$-0.415923\pi$
$332$	271.049	−	342.076i	0.816413	−	1.03035i
$333$	185.526	−	447.899i	0.557135	−	1.34504i
$334$	−87.5189	+	627.012i	−0.262033	+	1.87728i
$335$	158.876			0.474257
$336$	152.446	+	24.9208i	0.453708	+	0.0741692i
$337$			248.089i			0.736169i	0.929792	+	0.368085i	$0.119986\pi$
$337$			248.089i			0.736169i	−0.929792	+	0.368085i	$0.880014\pi$
$338$	−41.3760	+	296.431i	−0.122414	+	0.877014i
$339$	−153.234	−	63.4715i	−0.452017	−	0.187232i
$340$	22.1496	+	191.203i	0.0651460	+	0.562361i
$341$	59.1276	−	24.4914i	0.173395	−	0.0718224i
$342$	−136.623	+	232.440i	−0.399483	+	0.679650i
$343$	−242.504	+	242.504i	−0.707007	+	0.707007i
$344$	146.299	+	153.297i	0.425286	+	0.445631i
$345$	56.3660	−	56.3660i	0.163380	−	0.163380i
$346$	67.1035	−	17.4216i	0.193941	−	0.0503514i
$347$	−101.462	+	42.0270i	−0.292398	+	0.121115i	−0.524061	−	0.851681i	$-0.675584\pi$
$347$	−101.462	+	42.0270i	−0.292398	+	0.121115i	0.231662	+	0.972796i	$0.425584\pi$
$348$	24.8987	+	44.7197i	0.0715481	+	0.128505i
$349$	489.895	+	202.921i	1.40371	+	0.581436i	0.950712	−	0.310076i	$-0.100354\pi$
$349$	489.895	+	202.921i	1.40371	+	0.581436i	0.452998	+	0.891512i	$0.350354\pi$
$350$	−187.121	−	247.833i	−0.534632	−	0.708093i
$351$		−	97.6474i		−	0.278198i
$352$	−316.098	+	166.446i	−0.898006	+	0.472859i
$353$	−185.627			−0.525856			−0.262928	−	0.964815i	$-0.584688\pi$
$353$	−185.627			−0.525856			−0.262928	+	0.964815i	$0.584688\pi$
$354$	−65.8374	+	49.7093i	−0.185981	+	0.140422i
$355$	−4.90604	+	11.8442i	−0.0138198	+	0.0333640i
$356$	29.2424	+	52.5211i	0.0821415	+	0.147531i
$357$	−105.838	−	255.514i	−0.296464	−	0.715727i
$358$	−7.52366	−	28.9793i	−0.0210158	−	0.0809476i
$359$	222.847	+	222.847i	0.620743	+	0.620743i	0.945722	−	0.324978i	$-0.105357\pi$
$359$	222.847	+	222.847i	0.620743	+	0.620743i	−0.324978	+	0.945722i	$0.605357\pi$
$360$	−2.22764	+	95.3633i	−0.00618789	+	0.264898i
$361$	−0.224842	−	0.224842i	−0.000622830	−	0.000622830i
$362$	286.653	+	168.488i	0.791859	+	0.465437i
$363$	1.91621	+	4.62614i	0.00527882	+	0.0127442i
$364$	−14.1746	−	122.360i	−0.0389413	−	0.336154i
$365$	−23.0937	+	55.7530i	−0.0632703	+	0.152748i
$366$	225.877	+	31.5282i	0.617151	+	0.0861425i
$367$	532.771			1.45169			0.725846	−	0.687857i	$-0.241448\pi$
$367$	532.771			1.45169			0.725846	+	0.687857i	$0.241448\pi$
$368$	536.019	−	125.878i	1.45657	−	0.342060i
$369$		−	143.112i		−	0.387837i
$370$	−227.247	−	31.7193i	−0.614181	−	0.0857279i
$371$	324.726	+	134.506i	0.875273	+	0.362550i
$372$	−19.6383	+	24.7844i	−0.0527912	+	0.0666248i
$373$	−277.629	+	114.998i	−0.744313	+	0.308305i	−0.722419	−	0.691456i	$-0.756970\pi$
$373$	−277.629	+	114.998i	−0.744313	+	0.308305i	−0.0218944	+	0.999760i	$0.506970\pi$
$374$	551.419	+	324.112i	1.47438	+	0.866609i
$375$	−77.2757	+	77.2757i	−0.206068	+	0.206068i
$376$	−432.564	+	167.449i	−1.15043	+	0.445343i
$377$	28.8610	−	28.8610i	0.0765543	−	0.0765543i
$378$	−78.1110	−	300.864i	−0.206643	−	0.795936i
$379$	306.344	−	126.892i	0.808296	−	0.334807i	0.0600223	−	0.998197i	$-0.480883\pi$
$379$	306.344	−	126.892i	0.808296	−	0.334807i	0.748274	+	0.663390i	$0.230883\pi$
$380$	122.730	+	34.9421i	0.322972	+	0.0919530i
$381$	163.127	+	67.5692i	0.428154	+	0.177347i
$382$	3.19443	−	2.41190i	0.00836239	−	0.00631387i
$383$		−	163.336i		−	0.426465i	−0.977001	−	0.213233i	$-0.931601\pi$
$383$		−	163.336i		−	0.426465i	0.977001	−	0.213233i	$-0.0683992\pi$
$384$	96.4511	−	147.829i	0.251175	−	0.384973i
$385$	131.288			0.341007
$386$	−129.554	−	171.587i	−0.335632	−	0.444527i
$387$	71.9526	−	173.709i	0.185924	−	0.448861i
$388$	15.6689	−	55.0348i	0.0403837	−	0.141842i
$389$	−27.0717	−	65.3568i	−0.0695930	−	0.168012i	0.885256	−	0.465104i	$-0.153983\pi$
$389$	−27.0717	−	65.3568i	−0.0695930	−	0.168012i	−0.954849	+	0.297092i	$0.903983\pi$
$390$	−19.7240	+	5.12080i	−0.0505745	+	0.0131303i
$391$	−697.075	−	697.075i	−1.78280	−	1.78280i
$392$	−0.0397297	−	0.102632i	−0.000101351	−	0.000261816i
$393$	−51.3071	−	51.3071i	−0.130552	−	0.130552i
$394$	−95.2925	+	162.124i	−0.241859	+	0.411481i
$395$	−32.2487	−	77.8553i	−0.0816423	−	0.197102i
$396$	248.442	+	196.857i	0.627379	+	0.497114i
$397$	−153.949	+	371.666i	−0.387781	+	0.936187i	0.602628	+	0.798022i	$0.294120\pi$
$397$	−153.949	+	371.666i	−0.387781	+	0.936187i	−0.990409	+	0.138165i	$0.955880\pi$
$398$	89.4390	−	640.769i	0.224721	−	1.60997i
$399$	−183.352			−0.459528
$400$	−345.456	+	81.1263i	−0.863639	+	0.202816i
$401$			287.838i			0.717801i	0.933376	+	0.358900i	$0.116848\pi$
$401$			287.838i			0.717801i	−0.933376	+	0.358900i	$0.883152\pi$
$402$	−36.0609	+	258.351i	−0.0897037	+	0.642665i
$403$	23.2966	+	9.64976i	0.0578079	+	0.0239448i
$404$	−536.429	+	62.1419i	−1.32779	+	0.153816i
$405$	51.6353	−	21.3881i	0.127495	−	0.0528100i
$406$	65.8375	−	112.011i	0.162161	−	0.275889i
$407$	−539.144	+	539.144i	−1.32468	+	1.32468i
$408$	−315.946	−	7.38034i	−0.774377	−	0.0180891i
$409$	−134.641	+	134.641i	−0.329195	+	0.329195i	−0.852280	−	0.523085i	$-0.824781\pi$
$409$	−134.641	+	134.641i	−0.329195	+	0.329195i	0.523085	+	0.852280i	$0.324781\pi$
$410$	−65.5593	+	17.0207i	−0.159901	+	0.0415138i
$411$	−2.99239	+	1.23949i	−0.00728076	+	0.00301579i
$412$	−24.0989	+	13.4176i	−0.0584925	+	0.0325671i
$413$	193.470	+	80.1378i	0.468450	+	0.194038i
$414$	−294.381	−	389.893i	−0.711066	−	0.941771i
$415$			183.282i			0.441644i
$416$	−134.439	−	41.6936i	−0.323170	−	0.100225i
$417$	272.783			0.654156
$418$	338.412	−	255.512i	0.809598	−	0.611272i
$419$	94.1979	−	227.414i	0.224816	−	0.542754i	−0.770716	−	0.637179i	$-0.780101\pi$
$419$	94.1979	−	227.414i	0.224816	−	0.542754i	0.995532	+	0.0944249i	$0.0301012\pi$
$420$	−56.6760	+	31.5557i	−0.134943	+	0.0751325i
$421$	−151.850	−	366.598i	−0.360689	−	0.870779i	−0.995200	−	0.0978656i	$-0.968798\pi$
$421$	−151.850	−	366.598i	−0.360689	−	0.870779i	0.634511	−	0.772914i	$-0.281202\pi$
$422$	−133.169	−	512.935i	−0.315567	−	1.21549i
$423$	291.021	+	291.021i	0.687993	+	0.687993i
$424$	290.555	−	277.290i	0.685270	−	0.653986i
$425$	449.254	+	449.254i	1.05707	+	1.05707i
$426$	−18.1466	−	10.6661i	−0.0425975	−	0.0250379i
$427$	−221.548	−	534.864i	−0.518848	−	1.25261i
$428$	47.3056	−	5.48005i	0.110527	−	0.0128039i
$429$	−25.9138	+	62.5615i	−0.0604052	+	0.145831i
$430$	−88.1333	−	12.3017i	−0.204961	−	0.0286087i
$431$	−691.406			−1.60419			−0.802095	−	0.597196i	$-0.796281\pi$
$431$	−691.406			−1.60419			−0.802095	+	0.597196i	$0.796281\pi$
$432$	−350.541	−	57.3041i	−0.811437	−	0.132648i
$433$			580.011i			1.33952i	0.742579	+	0.669758i	$0.233602\pi$
$433$			580.011i			1.33952i	−0.742579	+	0.669758i	$0.766398\pi$
$434$	79.4988	+	11.0965i	0.183177	+	0.0255680i
$435$	−19.8582	−	8.22556i	−0.0456511	−	0.0189093i
$436$	90.1971	+	71.4691i	0.206874	+	0.163920i
$437$	−603.802	+	250.103i	−1.38170	+	0.572318i
$438$	−85.4193	−	50.2076i	−0.195021	−	0.114629i
$439$	411.067	−	411.067i	0.936371	−	0.936371i	−0.0617227	−	0.998093i	$-0.519659\pi$
$439$	411.067	−	411.067i	0.936371	−	0.936371i	0.998093	+	0.0617227i	$0.0196594\pi$
$440$	60.6321	−	137.224i	0.137800	−	0.311872i
$441$	−0.0690490	+	0.0690490i	−0.000156574	+	0.000156574i
$442$	63.3287	+	243.926i	0.143278	+	0.551869i
$443$	−34.4767	+	14.2807i	−0.0778256	+	0.0322364i	−0.421257	−	0.906941i	$-0.638411\pi$
$443$	−34.4767	+	14.2807i	−0.0778256	+	0.0322364i	0.343431	+	0.939178i	$0.388411\pi$
$444$	103.159	−	362.331i	0.232339	−	0.816060i
$445$	−23.3226	−	9.66052i	−0.0524102	−	0.0217090i
$446$	176.493	−	133.258i	0.395725	−	0.298785i
$447$			24.0614i			0.0538286i
$448$	−447.574	−	20.9216i	−0.999049	−	0.0467001i
$449$	185.456			0.413043			0.206521	−	0.978442i	$-0.433786\pi$
$449$	185.456			0.413043			0.206521	+	0.978442i	$0.433786\pi$
$450$	189.724	+	251.280i	0.421609	+	0.558400i
$451$	−86.1331	+	207.944i	−0.190982	+	0.461073i
$452$	462.712	+	131.738i	1.02370	+	0.291456i
$453$	95.0375	+	229.441i	0.209796	+	0.506492i
$454$	775.642	−	201.374i	1.70846	−	0.443555i
$455$	36.5772	+	36.5772i	0.0803895	+	0.0803895i
$456$	−84.6766	+	191.642i	−0.185694	+	0.420267i
$457$	386.211	+	386.211i	0.845100	+	0.845100i	0.989517	−	0.144417i	$-0.0461306\pi$
$457$	386.211	+	386.211i	0.845100	+	0.845100i	−0.144417	+	0.989517i	$0.546131\pi$
$458$	63.7067	−	108.386i	0.139098	−	0.236650i
$459$	243.367	+	587.541i	0.530212	+	1.28005i
$460$	−143.598	+	181.227i	−0.312169	+	0.393971i
$461$	268.824	−	648.999i	0.583133	−	1.40781i	−0.306826	−	0.951766i	$-0.599267\pi$
$461$	268.824	−	648.999i	0.583133	−	1.40781i	0.889958	−	0.456042i	$-0.150733\pi$
$462$	−29.7990	+	213.489i	−0.0645000	+	0.462098i
$463$	49.4705			0.106848			0.0534238	−	0.998572i	$-0.482987\pi$
$463$	49.4705			0.106848			0.0534238	+	0.998572i	$0.482987\pi$
$464$	−86.6700	−	120.544i	−0.186789	−	0.259793i
$465$		−	13.2793i		−	0.0285577i
$466$	41.0466	−	294.070i	0.0880828	−	0.631052i
$467$	−192.753	−	79.8411i	−0.412748	−	0.170966i	0.166640	−	0.986018i	$-0.446708\pi$
$467$	−192.753	−	79.8411i	−0.412748	−	0.170966i	−0.579388	+	0.815052i	$0.696708\pi$
$468$	14.3718	+	124.062i	0.0307090	+	0.265090i
$469$	611.761	−	253.400i	1.30439	−	0.540297i
$470$	98.7044	−	167.928i	0.210009	−	0.357294i
$471$	−249.352	+	249.352i	−0.529410	+	0.529410i
$472$	173.111	−	165.208i	0.366760	−	0.350016i
$473$	−209.097	+	209.097i	−0.442065	+	0.442065i
$474$	133.921	−	34.7690i	0.282535	−	0.0733523i
$475$	389.141	−	161.187i	0.819244	−	0.339342i
$476$	390.247	+	700.909i	0.819847	+	1.47250i
$477$	−329.243	−	136.377i	−0.690237	−	0.285906i
$478$	147.801	+	195.755i	0.309208	+	0.409530i
$479$		−	256.988i		−	0.536509i	−0.963348	−	0.268254i	$-0.913553\pi$
$479$		−	256.988i		−	0.536509i	0.963348	−	0.268254i	$-0.0864468\pi$
$480$	6.80799	+	73.8117i	0.0141833	+	0.153774i
$481$	−300.415			−0.624564
$482$	−301.325	+	227.510i	−0.625155	+	0.472012i
$483$	127.139	−	306.941i	0.263228	−	0.635488i
$484$	−7.06551	−	12.6901i	−0.0145982	−	0.0262192i
$485$	9.19588	+	22.2008i	0.0189606	+	0.0457749i
$486$	123.474	+	475.590i	0.254061	+	0.978581i
$487$	−10.7898	−	10.7898i	−0.0221557	−	0.0221557i	0.695942	−	0.718098i	$-0.254987\pi$
$487$	−10.7898	−	10.7898i	−0.0221557	−	0.0221557i	−0.718098	+	0.695942i	$0.754987\pi$
$488$	−661.365	−	15.4492i	−1.35526	−	0.0316581i
$489$	−97.0673	−	97.0673i	−0.198502	−	0.198502i
$490$	0.0398434	+	0.0234191i	8.13131e−5	+	4.77940e-5i
$491$	58.0314	+	140.100i	0.118190	+	0.285336i	0.971893	−	0.235425i	$-0.0756482\pi$
$491$	58.0314	+	140.100i	0.118190	+	0.285336i	−0.853702	+	0.520761i	$0.825648\pi$
$492$	−12.7973	−	110.470i	−0.0260107	−	0.224533i
$493$	−101.725	+	245.586i	−0.206339	+	0.498146i
$494$	165.469	+	23.0964i	0.334958	+	0.0467538i
$495$	−133.114			−0.268917
$496$	48.3128	−	77.9686i	0.0974049	−	0.157195i
$497$			53.4317i			0.107508i
$498$	−298.038	−	41.6004i	−0.598470	−	0.0835350i
$499$	−72.1133	−	29.8703i	−0.144516	−	0.0598603i	0.309253	−	0.950980i	$-0.399921\pi$
$499$	−72.1133	−	29.8703i	−0.144516	−	0.0598603i	−0.453769	+	0.891119i	$0.649921\pi$
$500$	196.867	−	248.455i	0.393735	−	0.496910i
$501$	403.288	−	167.047i	0.804965	−	0.333428i
$502$	−663.210	−	389.820i	−1.32113	−	0.776533i
$503$	151.600	−	151.600i	0.301393	−	0.301393i	−0.540166	−	0.841559i	$-0.681639\pi$
$503$	151.600	−	151.600i	0.301393	−	0.301393i	0.841559	+	0.540166i	$0.181639\pi$
$504$	143.522	+	370.754i	0.284766	+	0.735624i
$505$	160.355	−	160.355i	0.317535	−	0.317535i
$506$	193.080	+	743.697i	0.381582	+	1.46976i
$507$	190.661	−	78.9744i	0.376057	−	0.155768i
$508$	−492.585	−	140.243i	−0.969656	−	0.276069i
$509$	−562.711	−	233.082i	−1.10552	−	0.457922i	−0.246128	−	0.969237i	$-0.579158\pi$
$509$	−562.711	−	233.082i	−1.10552	−	0.457922i	−0.859393	+	0.511315i	$0.829158\pi$
$510$	105.916	−	79.9701i	0.207679	−	0.156804i
$511$			251.513i			0.492198i
$512$	−228.569	+	458.149i	−0.446424	+	0.894822i
$513$	421.607			0.821845
$514$	101.751	+	134.764i	0.197960	+	0.262188i
$515$	4.43266	−	10.7014i	0.00860710	−	0.0207794i
$516$	40.0081	−	140.523i	0.0775351	−	0.272331i
$517$	−247.705	−	598.012i	−0.479119	−	1.15670i
$518$	−925.616	+	240.311i	−1.78690	+	0.463920i
$519$	−33.8009	−	33.8009i	−0.0651270	−	0.0651270i
$520$	55.1234	−	21.3387i	0.106006	−	0.0410360i
$521$	−224.985	−	224.985i	−0.431833	−	0.431833i	0.457418	−	0.889252i	$-0.348774\pi$
$521$	−224.985	−	224.985i	−0.431833	−	0.431833i	−0.889252	+	0.457418i	$0.848774\pi$
$522$	−66.7533	+	113.569i	−0.127880	+	0.217565i
$523$	−9.30771	−	22.4708i	−0.0177968	−	0.0429652i	0.914731	−	0.404063i	$-0.132402\pi$
$523$	−9.30771	−	22.4708i	−0.0177968	−	0.0429652i	−0.932528	+	0.361097i	$0.882402\pi$
$524$	164.961	+	130.710i	0.314812	+	0.249446i
$525$	−81.9391	+	197.819i	−0.156075	+	0.376797i
$526$	14.5484	−	104.229i	0.0276586	−	0.198155i
$527$	−164.225			−0.311622
$528$	209.380	+	129.741i	0.396553	+	0.245722i
$529$		−	655.224i		−	1.23861i
$530$	−23.3163	+	167.045i	−0.0439931	+	0.315180i
$531$	−196.161	−	81.2525i	−0.369418	−	0.153018i
$532$	528.307	−	61.2010i	0.993059	−	0.115039i
$533$	−81.9309	+	33.9369i	−0.153717	+	0.0636715i
$534$	21.0028	−	35.7325i	0.0393310	−	0.0669148i
$535$	−14.1411	+	14.1411i	−0.0264320	+	0.0264320i
$536$	17.6702	−	756.447i	0.0329669	−	1.41128i
$537$	−14.5972	+	14.5972i	−0.0271829	+	0.0271829i
$538$	−457.901	+	118.881i	−0.851116	+	0.220969i
$539$	0.141887	−	0.0587715i	0.000263241	−	0.000109038i
$540$	130.323	−	72.5605i	0.241339	−	0.134371i
$541$	−357.866	−	148.233i	−0.661490	−	0.273998i	0.0265752	−	0.999647i	$-0.491540\pi$
$541$	−357.866	−	148.233i	−0.661490	−	0.273998i	−0.688066	+	0.725649i	$0.741540\pi$
$542$	376.739	+	498.972i	0.695091	+	0.920613i
$543$		−	229.260i		−	0.422211i
$544$	912.826	−	84.1940i	1.67799	−	0.154768i
$545$	−48.3271			−0.0886735
$546$	−67.7810	+	51.1768i	−0.124141	+	0.0937304i
$547$	187.175	−	451.879i	0.342184	−	0.826105i	−0.655311	−	0.755360i	$-0.727462\pi$
$547$	187.175	−	451.879i	0.342184	−	0.826105i	0.997494	−	0.0707454i	$-0.0225378\pi$
$548$	8.20852	−	4.57029i	0.0149791	−	0.00833994i
$549$	224.630	+	542.304i	0.409162	+	0.987804i
$550$	−124.437	−	479.301i	−0.226249	−	0.871456i
$551$	124.611	+	124.611i	0.226155	+	0.226155i
$552$	−262.103	−	274.641i	−0.474824	−	0.497538i
$553$	−248.351	−	248.351i	−0.449097	−	0.449097i
$554$	−372.199	−	218.770i	−0.671839	−	0.394892i
$555$	60.5426	+	146.163i	0.109086	+	0.263356i
$556$	−785.995	+	91.0524i	−1.41366	+	0.163763i
$557$	307.716	−	742.891i	0.552452	−	1.33374i	−0.363181	−	0.931719i	$-0.618309\pi$
$557$	307.716	−	742.891i	0.552452	−	1.33374i	0.915632	−	0.402017i	$-0.131691\pi$
$558$	−80.6046	−	11.2509i	−0.144453	−	0.0201628i
$559$	−116.510			−0.208426
$560$	152.773	−	109.842i	0.272808	−	0.196146i
$561$		−	441.016i		−	0.786125i
$562$	665.863	+	92.9417i	1.18481	+	0.165377i
$563$	706.303	+	292.560i	1.25454	+	0.519646i	0.908228	−	0.418476i	$-0.137435\pi$
$563$	706.303	+	292.560i	1.25454	+	0.519646i	0.346307	+	0.938121i	$0.387435\pi$
$564$	250.668	+	198.620i	0.444446	+	0.352164i
$565$	−186.656	+	77.3156i	−0.330365	+	0.136842i
$566$	109.626	+	64.4360i	0.193686	+	0.113844i
$567$	164.712	−	164.712i	0.290497	−	0.290497i
$568$	55.8475	+	24.6761i	0.0983231	+	0.0434439i
$569$	−552.550	+	552.550i	−0.971089	+	0.971089i	−0.999594	−	0.0285048i	$-0.990925\pi$
$569$	−552.550	+	552.550i	−0.971089	+	0.971089i	0.0285048	+	0.999594i	$0.490925\pi$
$570$	−22.1098	−	85.1614i	−0.0387891	−	0.149406i
$571$	−476.739	+	197.472i	−0.834919	+	0.345835i	−0.758848	−	0.651268i	$-0.774237\pi$
$571$	−476.739	+	197.472i	−0.834919	+	0.345835i	−0.0760707	+	0.997102i	$0.524237\pi$
$572$	53.7854	−	188.914i	0.0940304	−	0.330269i
$573$	−2.54978	−	1.05615i	−0.00444988	−	0.00184320i
$574$	−225.292	+	170.103i	−0.392495	+	0.296346i
$575$			763.214i			1.32733i
$576$	453.800	+	21.2127i	0.787847	+	0.0368275i
$577$	−188.090			−0.325980			−0.162990	−	0.986628i	$-0.552114\pi$
$577$	−188.090			−0.325980			−0.162990	+	0.986628i	$0.552114\pi$
$578$	−640.703	−	848.578i	−1.10848	−	1.46813i
$579$	−56.7307	+	136.960i	−0.0979805	+	0.236546i
$580$	59.9650	+	17.0725i	0.103388	+	0.0294354i
$581$	292.326	+	705.737i	0.503143	+	1.21469i
$582$	−38.1884	+	9.91455i	−0.0656157	+	0.0170353i
$583$	396.316	+	396.316i	0.679787	+	0.679787i
$584$	262.885	+	116.155i	0.450146	+	0.198896i
$585$	−37.0860	−	37.0860i	−0.0633949	−	0.0633949i
$586$	−125.954	+	214.289i	−0.214939	+	0.365681i
$587$	229.302	+	553.585i	0.390634	+	0.943075i	0.989802	+	0.142451i	$0.0454984\pi$
$587$	229.302	+	553.585i	0.390634	+	0.943075i	−0.599167	+	0.800624i	$0.704502\pi$
$588$	−0.0471256	+	0.0594745i	−8.01456e−5	+	0.000101147i
$589$	−41.6642	+	100.586i	−0.0707372	+	0.170775i
$590$	−13.8917	+	99.5246i	−0.0235453	+	0.168686i
$591$	129.664			0.219397
$592$	−176.298	+	1078.45i	−0.297800	+	1.82170i
$593$		−	378.708i		−	0.638630i	−0.947649	−	0.319315i	$-0.896547\pi$
$593$		−	378.708i		−	0.638630i	0.947649	−	0.319315i	$-0.103453\pi$
$594$	68.5211	−	490.906i	0.115355	−	0.826441i
$595$	−311.246	−	128.922i	−0.523102	−	0.216676i
$596$	−8.03146	−	69.3302i	−0.0134756	−	0.116326i
$597$	−412.135	+	170.712i	−0.690344	+	0.285950i
$598$	−153.404	+	260.990i	−0.256528	+	0.436438i
$599$	745.316	−	745.316i	1.24427	−	1.24427i	0.286055	−	0.958213i	$-0.407656\pi$
$599$	745.316	−	745.316i	1.24427	−	1.24427i	0.958213	−	0.286055i	$-0.0923438\pi$
$600$	168.921	+	177.002i	0.281535	+	0.295003i
$601$	130.996	−	130.996i	0.217963	−	0.217963i	−0.589676	−	0.807640i	$-0.700745\pi$
$601$	130.996	−	130.996i	0.217963	−	0.217963i	0.807640	+	0.589676i	$0.200745\pi$
$602$	−358.983	+	93.1999i	−0.596316	+	0.154817i
$603$	−620.270	+	256.924i	−1.02864	+	0.426077i
$604$	−350.425	−	629.386i	−0.580174	−	1.04203i
$605$	5.63517	+	2.33416i	0.00931433	+	0.00385812i
$606$	224.360	+	297.153i	0.370231	+	0.490352i
$607$			732.344i			1.20650i	0.797553	+	0.603249i	$0.206127\pi$
$607$			732.344i			1.20650i	−0.797553	+	0.603249i	$0.793873\pi$
$608$	180.018	−	580.458i	0.296082	−	0.954701i
$609$	−89.5845			−0.147101
$610$	221.713	−	167.400i	0.363464	−	0.274427i
$611$	97.5969	−	235.620i	0.159733	−	0.385630i
$612$	−395.676	−	710.658i	−0.646529	−	1.16121i
$613$	208.204	+	502.648i	0.339647	+	0.819981i	0.997749	+	0.0670521i	$0.0213594\pi$
$613$	208.204	+	502.648i	0.339647	+	0.819981i	−0.658102	+	0.752928i	$0.728641\pi$
$614$	221.543	+	853.328i	0.360819	+	1.38979i
$615$	33.0230	+	33.0230i	0.0536960	+	0.0536960i
$616$	14.6018	−	625.092i	0.0237043	−	1.01476i
$617$	209.834	+	209.834i	0.340087	+	0.340087i	0.856400	−	0.516313i	$-0.172696\pi$
$617$	209.834	+	209.834i	0.340087	+	0.340087i	−0.516313	+	0.856400i	$0.672696\pi$
$618$	16.3956	+	9.63696i	0.0265301	+	0.0155938i
$619$	175.433	+	423.533i	0.283414	+	0.684222i	0.999911	−	0.0133688i	$-0.00425556\pi$
$619$	175.433	+	423.533i	0.283414	+	0.684222i	−0.716497	+	0.697590i	$0.754256\pi$
$620$	4.43252	+	38.2629i	0.00714922	+	0.0617144i
$621$	−292.349	+	705.793i	−0.470772	+	1.13654i
$622$	418.672	+	58.4386i	0.673106	+	0.0939527i
$623$	−105.213			−0.168881
$624$	22.1877	+	94.4804i	0.0355571	+	0.151411i
$625$		−	421.338i		−	0.674141i
$626$	827.642	+	115.523i	1.32211	+	0.184541i
$627$	−270.118	−	111.887i	−0.430811	−	0.178448i
$628$	635.249	−	801.712i	1.01154	−	1.27661i
$629$	1807.59	−	748.727i	2.87375	−	1.19035i
$630$	−143.933	−	84.6005i	−0.228465	−	0.134286i
$631$	232.756	−	232.756i	0.368868	−	0.368868i	−0.498196	−	0.867064i	$-0.666004\pi$
$631$	232.756	−	232.756i	0.368868	−	0.368868i	0.867064	+	0.498196i	$0.166004\pi$
$632$	−374.274	+	144.885i	−0.592206	+	0.229248i
$633$	−258.372	+	258.372i	−0.408170	+	0.408170i
$634$	−121.230	−	466.947i	−0.191214	−	0.736509i
$635$	198.707	−	82.3071i	0.312924	−	0.129617i
$636$	−266.343	−	75.8302i	−0.418779	−	0.119230i
$637$	0.0559042	+	0.0231563i	8.77618e−5	+	3.63521e-5i
$638$	165.346	−	124.842i	0.259163	−	0.195676i
$639$		−	54.1749i		−	0.0847807i
$640$	−44.2541	−	210.408i	−0.0691470	−	0.328762i
$641$	−123.632			−0.192873			−0.0964366	−	0.995339i	$-0.530744\pi$
$641$	−123.632			−0.192873			−0.0964366	+	0.995339i	$0.530744\pi$
$642$	−19.7854	−	26.2048i	−0.0308184	−	0.0408174i
$643$	−351.513	+	848.628i	−0.546677	+	1.31979i	0.373260	+	0.927727i	$0.378240\pi$
$643$	−351.513	+	848.628i	−0.546677	+	1.31979i	−0.919936	+	0.392068i	$0.871760\pi$
$644$	−263.883	+	926.854i	−0.409756	+	1.43921i
$645$	23.4803	+	56.6864i	0.0364035	+	0.0878859i
$646$	−1053.19	+	273.431i	−1.63032	+	0.423268i
$647$	−191.561	−	191.561i	−0.296076	−	0.296076i	0.543399	−	0.839475i	$-0.317137\pi$
$647$	−191.561	−	191.561i	−0.296076	−	0.296076i	−0.839475	+	0.543399i	$0.817137\pi$
$648$	−96.0908	−	248.227i	−0.148288	−	0.383066i
$649$	236.122	+	236.122i	0.363825	+	0.363825i
$650$	98.8664	−	168.204i	0.152102	−	0.258775i
$651$	−21.1799	−	51.1328i	−0.0325344	−	0.0785450i
$652$	312.089	+	247.289i	0.478664	+	0.379277i
$653$	−89.1964	+	215.339i	−0.136595	+	0.329769i	−0.977344	−	0.211655i	$-0.932115\pi$
$653$	−89.1964	+	215.339i	−0.136595	+	0.329769i	0.840750	+	0.541424i	$0.182115\pi$
$654$	10.9690	−	78.5855i	0.0167722	−	0.120161i
$655$	−88.3853			−0.134939
$656$	73.7479	+	314.037i	0.112421	+	0.478714i
$657$		−	255.012i		−	0.388146i
$658$	112.229	−	804.045i	0.170561	−	1.22195i
$659$	−911.099	−	377.389i	−1.38255	−	0.572670i	−0.437386	−	0.899274i	$-0.644096\pi$
$659$	−911.099	−	377.389i	−1.38255	−	0.572670i	−0.945161	+	0.326604i	$0.894096\pi$
$660$	−102.753	+	11.9032i	−0.155686	+	0.0180352i
$661$	−496.993	+	205.861i	−0.751880	+	0.311439i	−0.725509	−	0.688213i	$-0.758395\pi$
$661$	−496.993	+	205.861i	−0.751880	+	0.311439i	−0.0263718	+	0.999652i	$0.508395\pi$
$662$	531.310	−	903.930i	0.802582	−	1.36545i
$663$	122.869	−	122.869i	0.185322	−	0.185322i
$664$	872.650	+	20.3847i	1.31423	+	0.0306998i
$665$	−157.928	+	157.928i	−0.237485	+	0.237485i
$666$	938.492	−	243.653i	1.40915	−	0.365846i
$667$	−295.014	+	122.199i	−0.442300	+	0.183207i
$668$	−1106.27	+	615.941i	−1.65609	+	0.922068i
$669$	−140.876	−	58.3527i	−0.210577	−	0.0872238i
$670$	191.467	+	253.588i	0.285772	+	0.378490i
$671$		−	923.172i		−	1.37582i
$672$	143.941	+	273.357i	0.214197	+	0.406782i
$673$	374.150			0.555944			0.277972	−	0.960589i	$-0.410338\pi$
$673$	374.150			0.555944			0.277972	+	0.960589i	$0.410338\pi$
$674$	−395.984	+	298.980i	−0.587514	+	0.443591i
$675$	188.414	−	454.873i	0.279132	−	0.673885i
$676$	−523.008	+	291.197i	−0.773680	+	0.430764i
$677$	12.3571	+	29.8326i	0.0182527	+	0.0440659i	0.932743	−	0.360542i	$-0.117408\pi$
$677$	12.3571	+	29.8326i	0.0182527	+	0.0440659i	−0.914490	+	0.404608i	$0.867408\pi$
$678$	−83.3579	−	321.074i	−0.122947	−	0.473560i
$679$	70.8184	+	70.8184i	0.104298	+	0.104298i
$680$	−278.493	+	265.779i	−0.409548	+	0.390851i
$681$	−390.701	−	390.701i	−0.573716	−	0.573716i
$682$	110.348	+	64.8603i	0.161801	+	0.0951030i
$683$	22.0894	+	53.3285i	0.0323417	+	0.0780799i	0.939225	−	0.343302i	$-0.111545\pi$
$683$	22.0894	+	53.3285i	0.0323417	+	0.0780799i	−0.906883	+	0.421382i	$0.861545\pi$
$684$	−535.656	+	62.0523i	−0.783123	+	0.0907197i
$685$	−1.50984	+	3.64508i	−0.00220415	+	0.00532128i
$686$	−679.318	−	94.8198i	−0.990260	−	0.138221i
$687$	−86.6852			−0.126179
$688$	−68.3737	+	418.256i	−0.0993803	+	0.607930i
$689$			220.830i			0.320508i
$690$	157.896	+	22.0393i	0.228835	+	0.0319410i
$691$	−622.510	−	257.852i	−0.900883	−	0.373158i	−0.116323	−	0.993211i	$-0.537111\pi$
$691$	−622.510	−	257.852i	−0.900883	−	0.373158i	−0.784560	+	0.620053i	$0.787111\pi$
$692$	108.676	+	86.1111i	0.157046	+	0.124438i
$693$	−512.562	+	212.310i	−0.739627	+	0.306364i
$694$	−189.356	−	111.299i	−0.272848	−	0.160374i
$695$	234.958	−	234.958i	0.338069	−	0.338069i
$696$	−41.3725	+	93.6350i	−0.0594432	+	0.134533i
$697$	408.394	−	408.394i	0.585932	−	0.585932i
$698$	266.499	+	1026.49i	0.381803	+	1.47061i
$699$	−189.143	+	78.3456i	−0.270591	+	0.112082i
$700$	170.069	−	597.343i	0.242955	−	0.853347i
$701$	−34.0835	−	14.1179i	−0.0486213	−	0.0201396i	0.358240	−	0.933629i	$-0.383377\pi$
$701$	−34.0835	−	14.1179i	−0.0486213	−	0.0201396i	−0.406862	+	0.913490i	$0.633377\pi$
$702$	155.859	−	117.678i	0.222021	−	0.167633i
$703$		−	1297.09i		−	1.84507i
$704$	−646.611	−	303.946i	−0.918482	−	0.431741i
$705$	−134.306			−0.190505
$706$	−223.706	−	296.286i	−0.316863	−	0.419669i
$707$	361.698	−	873.215i	0.511595	−	1.23510i
$708$	−158.686	−	45.1792i	−0.224132	−	0.0638124i
$709$	285.114	+	688.325i	0.402135	+	0.970840i	0.987147	+	0.159815i	$0.0510898\pi$
$709$	285.114	+	688.325i	0.402135	+	0.970840i	−0.585012	+	0.811025i	$0.698910\pi$
$710$	−24.8174	+	6.44316i	−0.0349541	+	0.00907487i
$711$	251.805	+	251.805i	0.354156	+	0.354156i
$712$	−48.5900	+	109.970i	−0.0682444	+	0.154452i
$713$	−139.497	−	139.497i	−0.195647	−	0.195647i
$714$	280.288	−	476.860i	0.392560	−	0.667871i
$715$	31.5660	+	76.2071i	0.0441483	+	0.106583i
$716$	37.1878	−	46.9327i	0.0519383	−	0.0655484i
$717$	64.7212	−	156.251i	0.0902666	−	0.217923i
$718$	−87.1339	+	624.254i	−0.121356	+	0.869435i
$719$	−478.037			−0.664863			−0.332432	−	0.943127i	$-0.607869\pi$
$719$	−478.037			−0.664863			−0.332432	+	0.943127i	$0.607869\pi$
$720$	−154.898	+	111.370i	−0.215136	+	0.154680i
$721$		−	48.2761i		−	0.0669571i
$722$	0.0879139	−	0.629843i	0.000121764	−	0.000872358i
$723$	240.516	+	99.6249i	0.332664	+	0.137794i
$724$	76.5249	+	660.588i	0.105697	+	0.912415i
$725$	190.132	−	78.7553i	0.262251	−	0.108628i
$726$	−5.07467	+	8.63365i	−0.00698990	+	0.0118921i
$727$	−408.395	+	408.395i	−0.561753	+	0.561753i	−0.929805	−	0.368052i	$-0.880025\pi$
$727$	−408.395	+	408.395i	−0.561753	+	0.561753i	0.368052	+	0.929805i	$0.380025\pi$
$728$	178.221	−	170.085i	0.244809	−	0.233633i
$729$	27.8184	−	27.8184i	0.0381597	−	0.0381597i
$730$	−116.820	+	30.3292i	−0.160028	+	0.0415468i
$731$	701.038	−	290.379i	0.959012	−	0.397236i
$732$	221.889	+	398.527i	0.303127	+	0.544436i
$733$	747.573	+	309.655i	1.01988	+	0.422449i	0.829050	−	0.559174i	$-0.188882\pi$
$733$	747.573	+	309.655i	1.01988	+	0.422449i	0.190831	+	0.981623i	$0.438882\pi$
$734$	642.060	+	850.376i	0.874741	+	1.15855i
$735$		−	0.0318661i		−	4.33552e-5i
$736$	846.892	+	703.860i	1.15067	+	0.956331i
$737$	1055.89			1.43269
$738$	228.426	−	172.469i	0.309520	−	0.233698i
$739$	−348.876	+	842.261i	−0.472092	+	1.13973i	0.491145	+	0.871078i	$0.336579\pi$
$739$	−348.876	+	842.261i	−0.472092	+	1.13973i	−0.963237	+	0.268653i	$0.913421\pi$
$740$	−223.234	−	400.943i	−0.301668	−	0.541815i
$741$	−44.0840	−	106.428i	−0.0594925	−	0.143628i
$742$	176.648	+	680.405i	0.238071	+	0.916988i
$743$	−345.072	−	345.072i	−0.464430	−	0.464430i	0.435674	−	0.900104i	$-0.356510\pi$
$743$	−345.072	−	345.072i	−0.464430	−	0.464430i	−0.900104	+	0.435674i	$0.856510\pi$
$744$	−63.2261	−	1.47693i	−0.0849813	−	0.00198512i
$745$	20.7250	+	20.7250i	0.0278187	+	0.0278187i
$746$	−518.132	−	304.546i	−0.694547	−	0.408239i
$747$	−296.392	−	715.554i	−0.396777	−	0.957903i
$748$	147.207	+	1270.74i	0.196801	+	1.69885i
$749$	−31.8967	+	77.0054i	−0.0425857	+	0.102811i
$750$	−216.470	−	30.2151i	−0.288627	−	0.0402867i
$751$	642.659			0.855737			0.427869	−	0.903841i	$-0.359265\pi$
$751$	642.659			0.855737			0.427869	+	0.903841i	$0.359265\pi$
$752$	−788.568	−	488.632i	−1.04863	−	0.649777i
$753$			530.424i			0.704414i
$754$	80.8474	+	11.2847i	0.107225	+	0.0149665i
$755$	279.485	+	115.767i	0.370179	+	0.153333i
$756$	386.086	−	487.257i	0.510695	−	0.644520i
$757$	241.802	−	100.158i	0.319422	−	0.132309i	−0.217211	−	0.976125i	$-0.569696\pi$
$757$	241.802	−	100.158i	0.319422	−	0.132309i	0.536633	+	0.843816i	$0.319696\pi$
$758$	571.723	+	336.046i	0.754252	+	0.443332i
$759$	374.609	−	374.609i	0.493556	−	0.493556i
$760$	92.1330	+	238.003i	0.121228	+	0.313162i
$761$	−253.025	+	253.025i	−0.332490	+	0.332490i	−0.853531	−	0.521042i	$-0.825544\pi$
$761$	−253.025	+	253.025i	−0.332490	+	0.332490i	0.521042	+	0.853531i	$0.325544\pi$
$762$	88.7395	+	341.802i	0.116456	+	0.448559i
$763$	−186.086	+	77.0793i	−0.243887	+	0.101021i
$764$	7.69944	+	2.19210i	0.0100778	+	0.00286923i
$765$	315.575	+	130.716i	0.412517	+	0.170870i
$766$	260.707	−	196.842i	0.340349	−	0.256974i
$767$			131.569i			0.171537i
$768$	352.193	−	24.2051i	0.458584	−	0.0315170i
$769$	−1066.22			−1.38650			−0.693248	−	0.720699i	$-0.743821\pi$
$769$	−1066.22			−1.38650			−0.693248	+	0.720699i	$0.743821\pi$
$770$	158.219	+	209.553i	0.205479	+	0.272147i
$771$	44.5562	−	107.568i	0.0577902	−	0.139518i
$772$	117.747	−	413.571i	0.152522	−	0.535714i
$773$	−497.702	−	1201.56i	−0.643857	−	1.55441i	−0.821435	−	0.570302i	$-0.806826\pi$
$773$	−497.702	−	1201.56i	−0.643857	−	1.55441i	0.177578	−	0.984107i	$-0.443174\pi$
$774$	363.976	−	94.4963i	0.470253	−	0.122088i
$775$	89.9033	+	89.9033i	0.116004	+	0.116004i
$776$	106.726	−	41.3146i	0.137534	−	0.0532404i
$777$	466.245	+	466.245i	0.600057	+	0.600057i
$778$	71.6934	−	121.974i	0.0921509	−	0.156779i
$779$	−146.527	−	353.749i	−0.188097	−	0.454106i
$780$	−31.9436	−	25.3110i	−0.0409533	−	0.0324500i
$781$	−32.6056	+	78.7170i	−0.0417486	+	0.100790i
$782$	272.559	−	1952.70i	0.348541	−	2.49705i
$783$	205.995			0.263084
$784$	0.115935	−	0.187099i	0.000147876	−	0.000238647i
$785$			429.553i			0.547201i
$786$	20.0612	−	143.725i	0.0255232	−	0.182856i
$787$	307.578	+	127.403i	0.390823	+	0.161884i	0.569437	−	0.822035i	$-0.307161\pi$
$787$	307.578	+	127.403i	0.390823	+	0.161884i	−0.178614	+	0.983919i	$0.557161\pi$
$788$	−373.612	+	43.2805i	−0.474126	+	0.0549245i
$789$	−67.0392	+	27.7686i	−0.0849673	+	0.0351946i
$790$	85.4037	−	145.299i	0.108106	−	0.183923i
$791$	−595.415	+	595.415i	−0.752737	+	0.752737i
$792$	−14.8050	+	633.787i	−0.0186931	+	0.800236i
$793$	257.199	−	257.199i	0.324337	−	0.324337i
$794$	−778.760	+	202.183i	−0.980806	+	0.254639i
$795$	107.442	−	44.5039i	0.135147	−	0.0559797i
$796$	1130.54	−	629.455i	1.42028	−	0.790772i
$797$	−367.115	−	152.064i	−0.460621	−	0.190795i	0.140292	−	0.990110i	$-0.455196\pi$
$797$	−367.115	−	152.064i	−0.460621	−	0.190795i	−0.600912	+	0.799315i	$0.705196\pi$
$798$	−220.963	−	292.654i	−0.276896	−	0.366735i
$799$			1660.96i			2.07880i
$800$	−545.809	−	453.626i	−0.682261	−	0.567033i
$801$	106.676			0.133179
$802$	−459.429	+	346.883i	−0.572854	+	0.432523i
$803$	−153.481	+	370.536i	−0.191134	+	0.461439i
$804$	−455.822	+	253.790i	−0.566943	+	0.315659i
$805$	−154.870	−	373.889i	−0.192385	−	0.464459i
$806$	12.6732	+	48.8138i	0.0157235	+	0.0605630i
$807$	230.650	+	230.650i	0.285812	+	0.285812i
$808$	−745.655	−	781.325i	−0.922841	−	0.966986i
$809$	318.547	+	318.547i	0.393754	+	0.393754i	0.876023	−	0.482269i	$-0.160187\pi$
$809$	318.547	+	318.547i	0.393754	+	0.393754i	−0.482269	+	0.876023i	$0.660187\pi$
$810$	96.3658	+	56.6416i	0.118970	+	0.0699279i
$811$	187.929	+	453.701i	0.231725	+	0.559434i	0.996380	−	0.0850055i	$-0.0270908\pi$
$811$	187.929	+	453.701i	0.231725	+	0.559434i	−0.764655	+	0.644439i	$0.777091\pi$
$812$	258.128	−	29.9025i	0.317891	−	0.0368257i
$813$	164.972	−	398.277i	0.202917	−	0.489885i
$814$	−1510.29	−	210.807i	−1.85539	−	0.258977i
$815$	−167.215			−0.205172
$816$	−368.977	−	513.187i	−0.452177	−	0.628906i
$817$		−	503.050i		−	0.615728i
$818$	−377.165	−	52.6450i	−0.461082	−	0.0643582i
$819$	−201.952	−	83.6513i	−0.246584	−	0.102138i
$820$	−106.175	−	84.1295i	−0.129482	−	0.102597i
$821$	−1296.86	+	537.177i	−1.57961	+	0.654295i	−0.988352	−	0.152188i	$-0.951368\pi$
$821$	−1296.86	+	537.177i	−1.57961	+	0.654295i	−0.591257	+	0.806483i	$0.701368\pi$
$822$	−5.58463	−	3.28252i	−0.00679395	−	0.00399333i
$823$	−1104.17	+	1104.17i	−1.34164	+	1.34164i	−0.447215	+	0.894426i	$0.647584\pi$
$823$	−1104.17	+	1104.17i	−1.34164	+	1.34164i	−0.894426	+	0.447215i	$0.852416\pi$
$824$	−50.4588	−	22.2951i	−0.0612364	−	0.0270572i
$825$	−241.430	+	241.430i	−0.292642	+	0.292642i
$826$	105.246	+	405.381i	0.127416	+	0.490776i
$827$	193.766	−	80.2605i	0.234300	−	0.0970502i	−0.262445	−	0.964947i	$-0.584529\pi$
$827$	193.766	−	80.2605i	0.234300	−	0.0970502i	0.496744	+	0.867897i	$0.334529\pi$
$828$	267.554	−	939.746i	0.323133	−	1.13496i
$829$	−282.707	−	117.101i	−0.341021	−	0.141256i	0.205599	−	0.978636i	$-0.434086\pi$
$829$	−282.707	−	117.101i	−0.341021	−	0.141256i	−0.546620	+	0.837381i	$0.684086\pi$
$830$	−292.543	+	220.879i	−0.352462	+	0.266120i
$831$			297.678i			0.358217i
$832$	−95.4679	−	264.829i	−0.114745	−	0.318304i
$833$	−0.394087			−0.000473093
$834$	328.740	+	435.399i	0.394173	+	0.522062i
$835$	203.483	−	491.251i	0.243692	−	0.588324i
$836$	815.663	+	232.226i	0.975674	+	0.277783i
$837$	48.7020	+	117.577i	0.0581863	+	0.140474i
$838$	476.505	−	123.711i	0.568622	−	0.147627i
$839$	−922.254	−	922.254i	−1.09923	−	1.09923i	−0.994501	−	0.104729i	$-0.966603\pi$
$839$	−922.254	−	922.254i	−1.09923	−	1.09923i	−0.104729	−	0.994501i	$-0.533397\pi$
$840$	−118.669	−	52.4338i	−0.141273	−	0.0624212i
$841$	−533.792	−	533.792i	−0.634711	−	0.634711i
$842$	402.141	−	684.173i	0.477603	−	0.812557i
$843$	−177.398	−	428.276i	−0.210436	−	0.508038i
$844$	658.227	−	830.711i	0.779890	−	0.984255i
$845$	96.1999	−	232.247i	0.113846	−	0.274849i
$846$	−113.790	+	815.229i	−0.134504	+	0.963627i
$847$	25.4214			0.0300134
$848$	792.750	+	129.594i	0.934847	+	0.152823i
$849$		−	87.6775i		−	0.103271i
$850$	−175.660	+	1258.48i	−0.206659	+	1.48057i
$851$	2171.39	+	899.421i	2.55158	+	1.05690i
$852$	−4.84440	−	41.8185i	−0.00568592	−	0.0490827i
$853$	319.646	−	132.402i	0.374731	−	0.155219i	−0.187366	−	0.982290i	$-0.559995\pi$
$853$	319.646	−	132.402i	0.374731	−	0.155219i	0.562097	+	0.827072i	$0.309995\pi$
$854$	586.722	−	998.204i	0.687028	−	1.16886i
$855$	160.124	−	160.124i	0.187280	−	0.187280i
$856$	65.7565	+	68.9020i	0.0768183	+	0.0804930i
$857$	−154.384	+	154.384i	−0.180145	+	0.180145i	−0.791419	−	0.611274i	$-0.790657\pi$
$857$	−154.384	+	154.384i	−0.180145	+	0.180145i	0.611274	+	0.791419i	$0.290657\pi$
$858$	−131.086	+	34.0330i	−0.152781	+	0.0396655i
$859$	598.422	−	247.875i	0.696650	−	0.288562i	−0.00611778	−	0.999981i	$-0.501947\pi$
$859$	598.422	−	247.875i	0.696650	−	0.288562i	0.702768	+	0.711419i	$0.251947\pi$
$860$	−86.5772	−	155.498i	−0.100671	−	0.180812i
$861$	179.827	+	74.4868i	0.208858	+	0.0865120i
$862$	−833.236	−	1103.58i	−0.966632	−	1.28025i
$863$		−	687.121i		−	0.796201i	−0.917342	−	0.398101i	$-0.869670\pi$
$863$		−	687.121i		−	0.796201i	0.917342	−	0.398101i	$-0.130330\pi$
$864$	−330.983	−	628.570i	−0.383082	−	0.727512i
$865$	−58.2279			−0.0673155
$866$	−925.777	+	698.990i	−1.06903	+	0.807148i
$867$	−280.559	+	677.330i	−0.323598	+	0.781234i
$868$	78.0951	+	140.264i	0.0899713	+	0.161594i
$869$	−214.326	−	517.428i	−0.246635	−	0.595429i
$870$	−10.8027	−	41.6094i	−0.0124169	−	0.0478269i
$871$	294.176	+	294.176i	0.337745	+	0.337745i
$872$	−5.37495	+	230.097i	−0.00616393	+	0.263872i
$873$	−71.8034	−	71.8034i	−0.0822491	−	0.0822491i
$874$	−1126.86	−	662.343i	−1.28931	−	0.757830i
$875$	212.321	+	512.588i	0.242653	+	0.585815i
$876$	−22.8035	−	196.848i	−0.0260314	−	0.224712i
$877$	146.136	−	352.804i	0.166632	−	0.402285i	−0.818402	−	0.574646i	$-0.805140\pi$
$877$	146.136	−	352.804i	0.166632	−	0.402285i	0.985034	+	0.172361i	$0.0551397\pi$
$878$	1151.51	+	160.729i	1.31151	+	0.183062i
$879$	171.385			0.194977
$880$	292.098	−	68.5958i	0.331929	−	0.0779497i
$881$			1060.30i			1.20352i	0.798675	+	0.601762i	$0.205534\pi$
$881$			1060.30i			1.20352i	−0.798675	+	0.601762i	$0.794466\pi$
$882$	−0.193425	−	0.0269984i	−0.000219303	−	3.06104e-5i
$883$	281.886	+	116.761i	0.319237	+	0.132232i	0.536547	−	0.843870i	$-0.319728\pi$
$883$	281.886	+	116.761i	0.319237	+	0.132232i	−0.217310	+	0.976103i	$0.569728\pi$
$884$	−313.020	+	395.045i	−0.354095	+	0.446884i
$885$	64.0132	−	26.5151i	0.0723313	−	0.0299606i
$886$	−64.3431	−	37.8194i	−0.0726220	−	0.0426856i
$887$	−934.058	+	934.058i	−1.05305	+	1.05305i	−0.0545418	+	0.998511i	$0.517370\pi$
$887$	−934.058	+	934.058i	−1.05305	+	1.05305i	−0.998511	+	0.0545418i	$0.982630\pi$
$888$	702.649	−	272.002i	0.791272	−	0.306308i
$889$	633.855	−	633.855i	0.712998	−	0.712998i
$890$	−12.6873	−	48.8682i	−0.0142554	−	0.0549081i
$891$	343.170	−	142.145i	0.385151	−	0.159535i
$892$	425.396	+	121.114i	0.476901	+	0.135778i
$893$	1017.32	+	421.389i	1.13922	+	0.471880i
$894$	−38.4053	+	28.9972i	−0.0429589	+	0.0324353i
$895$			25.1462i			0.0280964i
$896$	−505.993	−	739.603i	−0.564724	−	0.825450i
$897$	208.735			0.232704
$898$	223.499	+	296.014i	0.248886	+	0.329636i
$899$	−20.3569	+	49.1459i	−0.0226439	+	0.0546673i
$900$	−172.434	+	605.652i	−0.191594	+	0.672946i
$901$	−550.377	−	1328.73i	−0.610851	−	1.47473i
$902$	−435.709	+	113.120i	−0.483047	+	0.125410i
$903$	180.824	+	180.824i	0.200248	+	0.200248i
$904$	347.358	+	897.314i	0.384246	+	0.992604i
$905$	−197.470	−	197.470i	−0.218199	−	0.218199i
$906$	−251.686	+	428.200i	−0.277799	+	0.472627i
$907$	−312.448	−	754.317i	−0.344485	−	0.831661i	−0.997251	−	0.0741012i	$-0.976391\pi$
$907$	−312.448	−	754.317i	−0.344485	−	0.831661i	0.652765	−	0.757560i	$-0.273609\pi$
$908$	1256.17	+	995.348i	1.38345	+	1.09620i
$909$	−366.729	+	885.362i	−0.403442	+	0.973995i
$910$	−14.3018	+	102.463i	−0.0157163	+	0.112596i
$911$	678.215			0.744473			0.372236	−	0.928138i	$-0.378591\pi$
$911$	678.215			0.744473			0.372236	+	0.928138i	$0.378591\pi$
$912$	−407.933	+	95.7984i	−0.447295	+	0.105042i
$913$			1218.10i			1.33417i
$914$	−151.010	+	1081.88i	−0.165219	+	1.18368i
$915$	−176.970	−	73.3034i	−0.193410	−	0.0801130i
$916$	249.774	−	28.9347i	0.272679	−	0.0315881i
$917$	−340.332	+	140.970i	−0.371137	+	0.153730i
$918$	−644.506	+	1096.51i	−0.702076	+	1.19446i
$919$	456.147	−	456.147i	0.496352	−	0.496352i	−0.413949	−	0.910300i	$-0.635851\pi$
$919$	456.147	−	456.147i	0.496352	−	0.496352i	0.910300	+	0.413949i	$0.135851\pi$
$920$	−462.317	−	10.7995i	−0.502519	−	0.0117386i
$921$	429.832	−	429.832i	0.466702	−	0.466702i
$922$	1359.86	−	353.050i	1.47490	−	0.382918i
$923$	−31.0149	+	12.8468i	−0.0336023	+	0.0139185i
$924$	−376.670	+	209.720i	−0.407651	+	0.226969i
$925$	−1399.43	−	579.663i	−1.51290	−	0.626662i
$926$	59.6185	+	78.9616i	0.0643828	+	0.0852718i
$927$			48.9476i			0.0528021i
$928$	87.9557	−	283.609i	0.0947799	−	0.305613i
$929$	−1356.05			−1.45969			−0.729845	−	0.683613i	$-0.760408\pi$
$929$	−1356.05			−1.45969			−0.729845	+	0.683613i	$0.760408\pi$
$930$	21.1956	−	16.0034i	0.0227910	−	0.0172079i
$931$	−0.0999806	+	0.241375i	−0.000107391	+	0.000259264i
$932$	518.843	−	288.878i	0.556699	−	0.309955i
$933$	−111.542	−	269.285i	−0.119552	−	0.288623i
$934$	−104.856	−	403.880i	−0.112266	−	0.432420i
$935$	−379.863	−	379.863i	−0.406271	−	0.406271i
$936$	−180.700	+	172.451i	−0.193056	+	0.184242i
$937$	38.1043	+	38.1043i	0.0406663	+	0.0406663i	0.727148	−	0.686481i	$-0.240846\pi$
$937$	38.1043	+	38.1043i	0.0406663	+	0.0406663i	−0.686481	+	0.727148i	$0.740846\pi$
$938$	1141.71	+	671.073i	1.21718	+	0.715430i
$939$	−220.498	−	532.330i	−0.234823	−	0.566912i
$940$	386.988	−	44.8301i	0.411690	−	0.0476916i
$941$	283.674	−	684.849i	0.301460	−	0.727789i	−0.698466	−	0.715643i	$-0.746134\pi$
$941$	283.674	−	684.849i	0.301460	−	0.727789i	0.999926	−	0.0121459i	$-0.00386625\pi$
$942$	−698.503	−	97.4976i	−0.741511	−	0.103501i
$943$	693.800			0.735737
$944$	472.315	+	77.2110i	0.500334	+	0.0817913i
$945$			261.069i			0.276264i
$946$	−585.736	−	81.7575i	−0.619171	−	0.0864244i
$947$	−187.436	−	77.6384i	−0.197926	−	0.0819836i	0.281519	−	0.959556i	$-0.409162\pi$
$947$	−187.436	−	77.6384i	−0.197926	−	0.0819836i	−0.479445	+	0.877572i	$0.659162\pi$
$948$	216.889	+	171.856i	0.228786	+	0.181282i
$949$	−145.993	+	60.4723i	−0.153839	+	0.0637222i
$950$	726.244	+	426.870i	0.764467	+	0.449337i
$951$	−235.207	+	235.207i	−0.247326	+	0.247326i
$952$	−648.446	+	1467.58i	−0.681141	+	1.54157i
$953$	960.541	−	960.541i	1.00791	−	1.00791i	0.00794427	−	0.999968i	$-0.497471\pi$
$953$	960.541	−	960.541i	1.00791	−	1.00791i	0.999968	−	0.00794427i	$-0.00252877\pi$
$954$	−179.106	−	689.870i	−0.187742	−	0.723134i
$955$	−3.10592	+	1.28652i	−0.00325227	+	0.00134714i
$956$	−134.332	+	471.822i	−0.140515	+	0.493538i
$957$	−131.978	−	54.6672i	−0.137908	−	0.0571235i
$958$	410.188	−	309.705i	0.428171	−	0.323282i
$959$			16.4437i			0.0171467i
$960$	−109.609	+	99.8195i	−0.114176	+	0.103979i
$961$	928.136			0.965802
$962$	−362.040	−	479.504i	−0.376341	−	0.498445i
$963$	32.3404	−	78.0766i	0.0335830	−	0.0810764i
$964$	−726.273	−	206.776i	−0.753395	−	0.214498i
$965$	69.1045	+	166.833i	0.0716109	+	0.172884i
$966$	643.139	−	166.973i	0.665776	−	0.172850i
$967$	183.282	+	183.282i	0.189537	+	0.189537i	0.795496	−	0.605959i	$-0.207211\pi$
$967$	183.282	+	183.282i	0.189537	+	0.189537i	−0.605959	+	0.795496i	$0.707211\pi$
$968$	11.7403	−	26.5708i	0.0121284	−	0.0274492i
$969$	530.503	+	530.503i	0.547475	+	0.547475i
$970$	−24.3533	+	41.4328i	−0.0251065	+	0.0427142i
$971$	−344.446	−	831.566i	−0.354733	−	0.856401i	−0.996022	−	0.0891022i	$-0.971600\pi$
$971$	−344.446	−	831.566i	−0.354733	−	0.856401i	0.641289	−	0.767299i	$-0.278400\pi$
$972$	−610.305	+	770.231i	−0.627885	+	0.792419i
$973$	529.972	−	1279.47i	0.544678	−	1.31497i
$974$	4.21887	−	30.2253i	0.00433148	−	0.0310321i
$975$	−134.527			−0.137976
$976$	−772.374	−	1074.25i	−0.791366	−	1.10066i
$977$			1484.89i			1.51985i	0.650010	+	0.759926i	$0.274765\pi$
$977$			1484.89i			1.51985i	−0.650010	+	0.759926i	$0.725235\pi$
$978$	37.9537	−	271.912i	0.0388074	−	0.278028i
$979$	−155.002	−	64.2040i	−0.158327	−	0.0655812i
$980$	0.0106366	+	0.0918186i	1.08537e−5	+	9.36925e-5i
$981$	188.674	−	78.1515i	0.192329	−	0.0796651i
$982$	−153.683	+	261.465i	−0.156500	+	0.266258i
$983$	32.2811	−	32.2811i	0.0328394	−	0.0328394i	−0.690496	−	0.723336i	$-0.742608\pi$
$983$	32.2811	−	32.2811i	0.0328394	−	0.0328394i	0.723336	+	0.690496i	$0.242608\pi$
$984$	160.903	−	153.558i	0.163520	−	0.156055i
$985$	111.684	−	111.684i	0.113385	−	0.113385i
$986$	−514.581	+	133.597i	−0.521888	+	0.135494i
$987$	−517.153	+	214.212i	−0.523964	+	0.217033i
$988$	162.548	+	291.946i	0.164522	+	0.295492i
$989$	842.133	+	348.823i	0.851500	+	0.352703i
$990$	−160.420	−	212.468i	−0.162040	−	0.214614i
$991$		−	1236.65i		−	1.24789i	−0.781470	−	0.623943i	$-0.785530\pi$
$991$		−	1236.65i		−	1.24789i	0.781470	−	0.623943i	$-0.214470\pi$
$992$	182.672	−	16.8487i	0.184145	−	0.0169845i
$993$	−722.948			−0.728044
$994$	−85.2843	+	64.3923i	−0.0857991	+	0.0647810i
$995$	−207.947	+	502.028i	−0.208992	+	0.504551i
$996$	−292.776	−	525.844i	−0.293952	−	0.527956i
$997$	234.577	+	566.319i	0.235283	+	0.568023i	0.996784	−	0.0801409i	$-0.0255370\pi$
$997$	234.577	+	566.319i	0.235283	+	0.568023i	−0.761501	+	0.648164i	$0.775537\pi$
$998$	−39.2290	−	151.100i	−0.0393077	−	0.151403i
$999$	−1072.10	−	1072.10i	−1.07318	−	1.07318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.3.6	✓	28
3.2	odd	2		288.3.u.a.163.2		28
4.3	odd	2		128.3.h.a.47.3		28
8.3	odd	2		256.3.h.a.95.5		28
8.5	even	2		256.3.h.b.95.3		28
32.5	even	8		256.3.h.a.159.5		28
32.11	odd	8	inner	32.3.h.a.11.6	yes	28
32.21	even	8		128.3.h.a.79.3		28
32.27	odd	8		256.3.h.b.159.3		28
96.11	even	8		288.3.u.a.235.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.6	✓	28	1.1	even	1	trivial
32.3.h.a.11.6	yes	28	32.11	odd	8	inner
128.3.h.a.47.3		28	4.3	odd	2
128.3.h.a.79.3		28	32.21	even	8
256.3.h.a.95.5		28	8.3	odd	2
256.3.h.a.159.5		28	32.5	even	8
256.3.h.b.95.3		28	8.5	even	2
256.3.h.b.159.3		28	32.27	odd	8
288.3.u.a.163.2		28	3.2	odd	2
288.3.u.a.235.2		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)

\(f(q)\)	\(=\)	\(q+(1.20513 + 1.59614i) q^{2} +(0.527719 - 1.27403i) q^{3} +(-1.09531 + 3.84712i) q^{4} +(-0.642823 - 1.55191i) q^{5} +(2.66949 - 0.693061i) q^{6} +(-4.95044 - 4.95044i) q^{7} +(-7.46052 + 2.88803i) q^{8} +(5.01930 + 5.01930i) q^{9} +O(q^{10})\)	\(q+(1.20513 + 1.59614i) q^{2} +(0.527719 - 1.27403i) q^{3} +(-1.09531 + 3.84712i) q^{4} +(-0.642823 - 1.55191i) q^{5} +(2.66949 - 0.693061i) q^{6} +(-4.95044 - 4.95044i) q^{7} +(-7.46052 + 2.88803i) q^{8} +(5.01930 + 5.01930i) q^{9} +(1.70238 - 2.89629i) q^{10} +(-4.27221 - 10.3140i) q^{11} +(4.32332 + 3.42565i) q^{12} +(1.68327 - 4.06379i) q^{13} +(1.93564 - 13.8675i) q^{14} -2.31641 q^{15} +(-13.6006 - 8.42755i) q^{16} +28.6469i q^{17} +(-1.96257 + 14.0604i) q^{18} +(17.5460 + 7.26778i) q^{19} +(6.67447 - 0.773195i) q^{20} +(-8.91944 + 3.69455i) q^{21} +(11.3140 - 19.2488i) q^{22} +(-24.3334 + 24.3334i) q^{23} +(-0.257631 + 11.0290i) q^{24} +(15.6825 - 15.6825i) q^{25} +(8.51493 - 2.21067i) q^{26} +(20.5098 - 8.49542i) q^{27} +(24.4672 - 13.6227i) q^{28} +(8.57286 + 3.55100i) q^{29} +(-2.79158 - 3.69730i) q^{30} +5.73273i q^{31} +(-2.93903 - 31.8647i) q^{32} -15.3949 q^{33} +(-45.7244 + 34.5233i) q^{34} +(-4.50039 + 10.8649i) q^{35} +(-24.8075 + 13.8122i) q^{36} +(-26.1364 - 63.0989i) q^{37} +(9.54487 + 36.7644i) q^{38} +(-4.28908 - 4.28908i) q^{39} +(9.27775 + 9.72157i) q^{40} +(-14.2561 - 14.2561i) q^{41} +(-16.6461 - 9.78422i) q^{42} +(-10.1365 - 24.4717i) q^{43} +(44.3587 - 5.13867i) q^{44} +(4.56299 - 11.0160i) q^{45} +(-68.1643 - 9.51443i) q^{46} +57.9804 q^{47} +(-17.9142 + 12.8802i) q^{48} +0.0137567i q^{49} +(43.9308 + 6.13190i) q^{50} +(36.4969 + 15.1175i) q^{51} +(13.7902 + 10.9268i) q^{52} +(-46.3830 + 19.2124i) q^{53} +(38.2769 + 22.4983i) q^{54} +(-13.2602 + 13.2602i) q^{55} +(51.2299 + 22.6358i) q^{56} +(18.5187 - 18.5187i) q^{57} +(4.66357 + 17.9629i) q^{58} +(-27.6347 + 11.4467i) q^{59} +(2.53718 - 8.91149i) q^{60} +(76.3985 + 31.6453i) q^{61} +(-9.15022 + 6.90870i) q^{62} -49.6955i q^{63} +(47.3186 - 43.0924i) q^{64} -7.38868 q^{65} +(-18.5529 - 24.5724i) q^{66} +(-36.1949 + 87.3821i) q^{67} +(-110.208 - 31.3771i) q^{68} +(18.1602 + 43.8425i) q^{69} +(-22.7654 + 5.91042i) q^{70} +(-5.39666 - 5.39666i) q^{71} +(-51.9425 - 22.9507i) q^{72} +(-25.4031 - 25.4031i) q^{73} +(69.2166 - 117.760i) q^{74} +(-11.7039 - 28.2558i) q^{75} +(-47.1782 + 59.5410i) q^{76} +(-29.9097 + 72.2084i) q^{77} +(1.67704 - 12.0149i) q^{78} +50.1674 q^{79} +(-4.33602 + 26.5244i) q^{80} +33.2721i q^{81} +(5.57420 - 39.9353i) q^{82} +(-100.805 - 41.7550i) q^{83} +(-4.44385 - 38.3608i) q^{84} +(44.4574 - 18.4149i) q^{85} +(26.8443 - 45.6709i) q^{86} +(9.04814 - 9.04814i) q^{87} +(61.6601 + 64.6097i) q^{88} +(10.6266 - 10.6266i) q^{89} +(23.0821 - 5.99263i) q^{90} +(-28.4505 + 11.7846i) q^{91} +(-66.9607 - 120.266i) q^{92} +(7.30366 + 3.02527i) q^{93} +(69.8741 + 92.5446i) q^{94} -31.9017i q^{95} +(-42.1475 - 13.0712i) q^{96} -14.3055 q^{97} +(-0.0219576 + 0.0165786i) q^{98} +(30.3257 - 73.2128i) 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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