LMFDB - Embedded newform 63.4.o.a.20.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(20,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, 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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.4
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.38393 - 1.95371i) q^{2} +(4.35656 - 2.83202i) q^{3} +(3.63397 + 6.29422i) q^{4} +(-5.82670 - 10.0921i) q^{5} +(-20.2752 + 1.07189i) q^{6} +(17.1417 - 7.01157i) q^{7} +2.86048i q^{8} +(10.9593 - 24.6758i) q^{9} +O(q^{10})$	\(q+(-3.38393 - 1.95371i) q^{2} +(4.35656 - 2.83202i) q^{3} +(3.63397 + 6.29422i) q^{4} +(-5.82670 - 10.0921i) q^{5} +(-20.2752 + 1.07189i) q^{6} +(17.1417 - 7.01157i) q^{7} +2.86048i q^{8} +(10.9593 - 24.6758i) q^{9} +45.5347i q^{10} +(-41.2999 - 23.8445i) q^{11} +(33.6570 + 17.1297i) q^{12} +(-60.2061 + 34.7600i) q^{13} +(-71.7048 - 9.76328i) q^{14} +(-53.9655 - 27.4657i) q^{15} +(34.6603 - 60.0334i) q^{16} -25.6583 q^{17} +(-85.2948 + 62.0897i) q^{18} +41.1363i q^{19} +(42.3481 - 73.3490i) q^{20} +(54.8220 - 79.0920i) q^{21} +(93.1705 + 161.376i) q^{22} +(145.611 - 84.0685i) q^{23} +(8.10093 + 12.4618i) q^{24} +(-5.40080 + 9.35446i) q^{25} +271.644 q^{26} +(-22.1374 - 138.539i) q^{27} +(106.425 + 82.4138i) q^{28} +(28.2286 + 16.2978i) q^{29} +(128.955 + 198.375i) q^{30} +(148.499 - 85.7361i) q^{31} +(-214.758 + 123.990i) q^{32} +(-247.454 + 13.0821i) q^{33} +(86.8259 + 50.1290i) q^{34} +(-170.641 - 132.142i) q^{35} +(195.140 - 20.6908i) q^{36} -3.86757 q^{37} +(80.3685 - 139.202i) q^{38} +(-163.851 + 321.939i) q^{39} +(28.8683 - 16.6671i) q^{40} +(168.733 + 292.255i) q^{41} +(-340.036 + 160.535i) q^{42} +(207.351 - 359.142i) q^{43} -346.601i q^{44} +(-312.888 + 33.1755i) q^{45} -656.982 q^{46} +(74.3856 - 128.840i) q^{47} +(-19.0161 - 359.698i) q^{48} +(244.676 - 240.380i) q^{49} +(36.5518 - 21.1032i) q^{50} +(-111.782 + 72.6650i) q^{51} +(-437.574 - 252.633i) q^{52} -59.7358i q^{53} +(-195.753 + 512.054i) q^{54} +555.739i q^{55} +(20.0564 + 49.0334i) q^{56} +(116.499 + 179.213i) q^{57} +(-63.6824 - 110.301i) q^{58} +(282.056 + 488.535i) q^{59} +(-23.2340 - 439.480i) q^{60} +(-571.656 - 330.046i) q^{61} -670.014 q^{62} +(14.8451 - 499.827i) q^{63} +414.401 q^{64} +(701.605 + 405.072i) q^{65} +(862.924 + 439.184i) q^{66} +(145.989 + 252.861i) q^{67} +(-93.2416 - 161.499i) q^{68} +(396.280 - 778.623i) q^{69} +(319.270 + 780.542i) q^{70} -3.05665i q^{71} +(70.5845 + 31.3488i) q^{72} -506.596i q^{73} +(13.0876 + 7.55611i) q^{74} +(2.96311 + 56.0485i) q^{75} +(-258.921 + 149.488i) q^{76} +(-875.138 - 119.158i) q^{77} +(1183.43 - 769.302i) q^{78} +(-96.6430 + 167.391i) q^{79} -807.820 q^{80} +(-488.788 - 540.858i) q^{81} -1318.62i q^{82} +(-216.246 + 374.550i) q^{83} +(697.044 + 57.6436i) q^{84} +(149.503 + 258.947i) q^{85} +(-1403.32 + 810.206i) q^{86} +(169.136 - 8.94167i) q^{87} +(68.2066 - 118.137i) q^{88} +924.591 q^{89} +(1123.60 + 499.029i) q^{90} +(-788.312 + 1017.98i) q^{91} +(1058.29 + 611.005i) q^{92} +(404.140 - 794.068i) q^{93} +(-503.430 + 290.656i) q^{94} +(415.154 - 239.689i) q^{95} +(-584.462 + 1148.37i) q^{96} +(943.401 + 544.673i) q^{97} +(-1297.60 + 335.404i) q^{98} +(-1041.00 + 757.788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.38393	−	1.95371i	−1.19640	−	0.690741i	−0.236648	−	0.971595i	$-0.576049\pi$
$2$	−3.38393	−	1.95371i	−1.19640	−	0.690741i	−0.959750	+	0.280855i	$0.909382\pi$
$3$	4.35656	−	2.83202i	0.838421	−	0.545023i
$3$	4.35656	−	2.83202i	0.838421	−	0.545023i
$4$	3.63397	+	6.29422i	0.454246	+	0.786777i
$5$	−5.82670	−	10.0921i	−0.521156	−	0.902668i	−0.999697	−	0.0246032i	$-0.992168\pi$
$5$	−5.82670	−	10.0921i	−0.521156	−	0.902668i	0.478542	−	0.878065i	$-0.341166\pi$
$6$	−20.2752	+	1.07189i	−1.37956	+	0.0729328i
$7$	17.1417	−	7.01157i	0.925565	−	0.378589i
$7$	17.1417	−	7.01157i	0.925565	−	0.378589i
$8$			2.86048i			0.126416i
$9$	10.9593	−	24.6758i	0.405900	−	0.913918i
$10$			45.5347i			1.43993i
$11$	−41.2999	−	23.8445i	−1.13203	−	0.653581i	−0.187589	−	0.982248i	$-0.560067\pi$
$11$	−41.2999	−	23.8445i	−1.13203	−	0.653581i	−0.944446	+	0.328667i	$0.893401\pi$
$12$	33.6570	+	17.1297i	0.809661	+	0.412076i
$13$	−60.2061	+	34.7600i	−1.28447	+	0.741591i	−0.977663	−	0.210179i	$-0.932595\pi$
$13$	−60.2061	+	34.7600i	−1.28447	+	0.741591i	−0.306811	+	0.951770i	$0.599262\pi$
$14$	−71.7048	−	9.76328i	−1.36885	−	0.186382i
$15$	−53.9655	−	27.4657i	−0.928923	−	0.472774i
$16$	34.6603	−	60.0334i	0.541567	−	0.938022i
$17$	−25.6583			−0.366062			−0.183031	−	0.983107i	$-0.558591\pi$
$17$	−25.6583			−0.366062			−0.183031	+	0.983107i	$0.558591\pi$
$18$	−85.2948	+	62.0897i	−1.11690	+	0.813038i
$19$			41.1363i			0.496701i	0.968670	+	0.248351i	$0.0798885\pi$
$19$			41.1363i			0.496701i	−0.968670	+	0.248351i	$0.920111\pi$
$20$	42.3481	−	73.3490i	0.473466	−	0.820067i
$21$	54.8220	−	79.0920i	0.569673	−	0.821871i
$22$	93.1705	+	161.376i	0.902910	+	1.56389i
$23$	145.611	−	84.0685i	1.32009	−	0.762152i	0.336344	−	0.941739i	$-0.390809\pi$
$23$	145.611	−	84.0685i	1.32009	−	0.762152i	0.983742	+	0.179587i	$0.0574761\pi$
$24$	8.10093	+	12.4618i	0.0688998	+	0.105990i
$25$	−5.40080	+	9.35446i	−0.0432064	+	0.0748357i
$26$	271.644			2.04899
$27$	−22.1374	−	138.539i	−0.157791	−	0.987473i
$28$	106.425	+	82.4138i	0.718300	+	0.556241i
$29$	28.2286	+	16.2978i	0.180756	+	0.104360i	0.587648	−	0.809117i	$-0.300054\pi$
$29$	28.2286	+	16.2978i	0.180756	+	0.104360i	−0.406892	+	0.913476i	$0.633387\pi$
$30$	128.955	+	198.375i	0.784797	+	1.20727i
$31$	148.499	−	85.7361i	0.860363	−	0.496731i	−0.00377092	−	0.999993i	$-0.501200\pi$
$31$	148.499	−	85.7361i	0.860363	−	0.496731i	0.864134	+	0.503262i	$0.167867\pi$
$32$	−214.758	+	123.990i	−1.18638	+	0.684957i
$33$	−247.454	+	13.0821i	−1.30534	+	0.0690092i
$34$	86.8259	+	50.1290i	0.437956	+	0.252854i
$35$	−170.641	−	132.142i	−0.824104	−	0.638174i
$36$	195.140	−	20.6908i	0.903428	−	0.0957906i
$37$	−3.86757			−0.0171844			−0.00859222	−	0.999963i	$-0.502735\pi$
$37$	−3.86757			−0.0171844			−0.00859222	+	0.999963i	$0.502735\pi$
$38$	80.3685	−	139.202i	0.343092	−	0.594253i
$39$	−163.851	+	321.939i	−0.672746	+	1.32183i
$40$	28.8683	−	16.6671i	0.114112	−	0.0658826i
$41$	168.733	+	292.255i	0.642725	+	1.11323i	0.984822	+	0.173568i	$0.0555295\pi$
$41$	168.733	+	292.255i	0.642725	+	1.11323i	−0.342097	+	0.939665i	$0.611137\pi$
$42$	−340.036	+	160.535i	−1.24926	+	0.589789i
$43$	207.351	−	359.142i	0.735364	−	1.27369i	−0.219199	−	0.975680i	$-0.570344\pi$
$43$	207.351	−	359.142i	0.735364	−	1.27369i	0.954563	−	0.298008i	$-0.0963223\pi$
$44$		−	346.601i		−	1.18755i
$45$	−312.888	+	33.1755i	−1.03650	+	0.109900i
$46$	−656.982			−2.10580
$47$	74.3856	−	128.840i	0.230856	−	0.399855i	−0.727204	−	0.686421i	$-0.759181\pi$
$47$	74.3856	−	128.840i	0.230856	−	0.399855i	0.958060	+	0.286566i	$0.0925139\pi$
$48$	−19.0161	−	359.698i	−0.0571821	−	1.08162i
$49$	244.676	−	240.380i	0.713340	−	0.700818i
$50$	36.5518	−	21.1032i	0.103384	−	0.0596888i
$51$	−111.782	+	72.6650i	−0.306914	+	0.199512i
$52$	−437.574	−	252.633i	−1.16693	−	0.673730i
$53$		−	59.7358i		−	0.154818i	−0.996999	−	0.0774089i	$-0.975335\pi$
$53$		−	59.7358i		−	0.154818i	0.996999	−	0.0774089i	$-0.0246647\pi$
$54$	−195.753	+	512.054i	−0.493307	+	1.29040i
$55$			555.739i			1.36247i
$56$	20.0564	+	49.0334i	0.0478599	+	0.117007i
$57$	116.499	+	179.213i	0.270714	+	0.416445i
$58$	−63.6824	−	110.301i	−0.144171	−	0.249711i
$59$	282.056	+	488.535i	0.622382	+	1.07800i	0.989041	+	0.147642i	$0.0471682\pi$
$59$	282.056	+	488.535i	0.622382	+	1.07800i	−0.366659	+	0.930355i	$0.619498\pi$
$60$	−23.2340	−	439.480i	−0.0499915	−	0.945611i
$61$	−571.656	−	330.046i	−1.19989	−	0.692754i	−0.239356	−	0.970932i	$-0.576936\pi$
$61$	−571.656	−	330.046i	−1.19989	−	0.692754i	−0.960530	+	0.278178i	$0.910270\pi$
$62$	−670.014			−1.37245
$63$	14.8451	−	499.827i	0.0296874	−	0.999559i
$64$	414.401			0.809377
$65$	701.605	+	405.072i	1.33882	+	0.772969i
$66$	862.924	+	439.184i	1.60937	+	0.819088i
$67$	145.989	+	252.861i	0.266200	+	0.461073i	0.967877	−	0.251423i	$-0.0808984\pi$
$67$	145.989	+	252.861i	0.266200	+	0.461073i	−0.701677	+	0.712495i	$0.747565\pi$
$68$	−93.2416	−	161.499i	−0.166282	−	0.288010i
$69$	396.280	−	778.623i	0.691398	−	1.35848i
$70$	319.270	+	780.542i	0.545144	+	1.33275i
$71$		−	3.05665i		−	0.00510927i	−0.999997	−	0.00255464i	$-0.999187\pi$
$71$		−	3.05665i		−	0.00510927i	0.999997	−	0.00255464i	$-0.000813166\pi$
$72$	70.5845	+	31.3488i	0.115534	+	0.0513124i
$73$		−	506.596i		−	0.812227i	−0.913823	−	0.406114i	$-0.866884\pi$
$73$		−	506.596i		−	0.812227i	0.913823	−	0.406114i	$-0.133116\pi$
$74$	13.0876	+	7.55611i	0.0205594	+	0.0118700i
$75$	2.96311	+	56.0485i	0.00456200	+	0.0862923i
$76$	−258.921	+	149.488i	−0.390793	+	0.225625i
$77$	−875.138	−	119.158i	−1.29521	−	0.176355i
$78$	1183.43	−	769.302i	1.71792	−	1.11675i
$79$	−96.6430	+	167.391i	−0.137635	+	0.238391i	−0.926601	−	0.376046i	$-0.877284\pi$
$79$	−96.6430	+	167.391i	−0.137635	+	0.238391i	0.788966	+	0.614437i	$0.210617\pi$
$80$	−807.820			−1.12896
$81$	−488.788	−	540.858i	−0.670490	−	0.741918i
$82$		−	1318.62i		−	1.77583i
$83$	−216.246	+	374.550i	−0.285977	+	0.495327i	−0.972846	−	0.231454i	$-0.925652\pi$
$83$	−216.246	+	374.550i	−0.285977	+	0.495327i	0.686868	+	0.726782i	$0.258985\pi$
$84$	697.044	+	57.6436i	0.905402	+	0.0748742i
$85$	149.503	+	258.947i	0.190775	+	0.330433i
$86$	−1403.32	+	810.206i	−1.75958	+	1.01589i
$87$	169.136	−	8.94167i	0.208428	−	0.0110189i
$88$	68.2066	−	118.137i	0.0826233	−	0.143108i
$89$	924.591			1.10120			0.550598	−	0.834771i	$-0.314400\pi$
$89$	924.591			1.10120			0.550598	+	0.834771i	$0.314400\pi$
$90$	1123.60	+	499.029i	1.31598	+	0.584469i
$91$	−788.312	+	1017.98i	−0.908105	+	1.17268i
$92$	1058.29	+	611.005i	1.19929	+	0.692409i
$93$	404.140	−	794.068i	0.450617	−	0.885387i
$94$	−503.430	+	290.656i	−0.552392	+	0.318924i
$95$	415.154	−	239.689i	0.448356	−	0.258859i
$96$	−584.462	+	1148.37i	−0.621369	+	1.22089i
$97$	943.401	+	544.673i	0.987503	+	0.570135i	0.904527	−	0.426416i	$-0.140224\pi$
$97$	943.401	+	544.673i	0.987503	+	0.570135i	0.0829763	+	0.996552i	$0.473557\pi$
$98$	−1297.60	+	335.404i	−1.33752	+	0.345724i
$99$	−1041.00	+	757.788i	−1.05681	+	0.769298i
$100$	−78.5053			−0.0785053
$101$	−168.799	+	292.369i	−0.166298	+	0.288037i	−0.937116	−	0.349019i	$-0.886515\pi$
$101$	−168.799	+	292.369i	−0.166298	+	0.288037i	0.770817	+	0.637056i	$0.219848\pi$
$102$	520.229	−	27.5029i	0.505003	−	0.0266979i
$103$	−183.659	+	106.035i	−0.175694	+	0.101437i	−0.585268	−	0.810840i	$-0.699011\pi$
$103$	−183.659	+	106.035i	−0.175694	+	0.101437i	0.409574	+	0.912277i	$0.365677\pi$
$104$	−99.4302	−	172.218i	−0.0937493	−	0.162379i
$105$	−1117.64	−	92.4256i	−1.03877	−	0.0859030i
$106$	−116.706	+	202.142i	−0.106939	+	0.185224i
$107$		−	399.253i		−	0.360722i	−0.983600	−	0.180361i	$-0.942273\pi$
$107$		−	399.253i		−	0.360722i	0.983600	−	0.180361i	$-0.0577266\pi$
$108$	791.545	−	642.783i	0.705245	−	0.572702i
$109$	1847.45			1.62343			0.811714	−	0.584055i	$-0.198535\pi$
$109$	1847.45			1.62343			0.811714	+	0.584055i	$0.198535\pi$
$110$	1085.75	−	1880.58i	0.941113	−	1.63006i
$111$	−16.8493	+	10.9530i	−0.0144078	+	0.00936591i
$112$	173.208	−	1272.10i	0.146131	−	1.07323i
$113$	1101.72	−	636.078i	0.917177	−	0.529532i	0.0344435	−	0.999407i	$-0.489034\pi$
$113$	1101.72	−	636.078i	0.917177	−	0.529532i	0.882733	+	0.469874i	$0.155701\pi$
$114$	−44.0936	−	834.049i	−0.0362258	−	0.685227i
$115$	−1696.86	−	979.684i	−1.37594	−	0.794400i
$116$			236.903i			0.189620i
$117$	197.913	+	1866.58i	0.156385	+	1.47492i
$118$		−	2204.22i		−	1.71962i
$119$	−439.827	+	179.905i	−0.338814	+	0.138587i
$120$	78.5650	−	154.367i	0.0597664	−	0.117431i
$121$	471.620	+	816.871i	0.354335	+	0.613727i
$122$	1289.63	+	2233.70i	0.957027	+	1.65762i
$123$	1562.77	+	795.370i	1.14561	+	0.583058i
$124$	1079.28	+	623.124i	0.781633	+	0.451276i
$125$	−1330.80			−0.952242
$126$	−1026.75	+	1662.37i	−0.725954	+	1.17536i
$127$	−1835.56			−1.28252			−0.641259	−	0.767325i	$-0.721588\pi$
$127$	−1835.56			−1.28252			−0.641259	+	0.767325i	$0.721588\pi$
$128$	315.760	+	182.304i	0.218043	+	0.125887i
$129$	−113.761	−	2151.85i	−0.0776444	−	1.46868i
$130$	−1582.79	−	2741.47i	−1.06784	−	1.84956i
$131$	673.698	+	1166.88i	0.449323	+	0.778250i	0.998342	−	0.0575597i	$-0.0183320\pi$
$131$	673.698	+	1166.88i	0.449323	+	0.778250i	−0.549019	+	0.835810i	$0.684999\pi$
$132$	−981.581	−	1509.99i	−0.647240	−	0.995664i
$133$	288.430	+	705.147i	0.188046	+	0.459729i
$134$		−	1140.88i		−	0.735502i
$135$	−1269.16	+	1030.64i	−0.809126	+	0.657060i
$136$		−	73.3951i		−	0.0462763i
$137$	−964.423	−	556.810i	−0.601432	−	0.347237i	0.168173	−	0.985758i	$-0.446213\pi$
$137$	−964.423	−	556.810i	−0.601432	−	0.347237i	−0.769605	+	0.638521i	$0.779547\pi$
$138$	−2862.19	+	1860.59i	−1.76555	+	1.14771i
$139$	−1140.22	+	658.307i	−0.695772	+	0.401704i	−0.805771	−	0.592228i	$-0.798249\pi$
$139$	−1140.22	+	658.307i	−0.695772	+	0.401704i	0.109999	+	0.993932i	$0.464915\pi$
$140$	211.626	−	1554.25i	0.127755	−	0.938274i
$141$	−40.8111	−	771.959i	−0.0243753	−	0.461069i
$142$	−5.97182	+	10.3435i	−0.00352918	+	0.00611272i
$143$	3315.34			1.93876
$144$	−1101.52	−	1513.19i	−0.637452	−	0.875691i
$145$		−	379.850i		−	0.217550i
$146$	−989.742	+	1714.28i	−0.561039	+	0.971747i
$147$	385.183	−	1740.16i	0.216118	−	0.976367i
$148$	−14.0546	−	24.3433i	−0.00780596	−	0.0135203i
$149$	−530.202	+	306.112i	−0.291516	+	0.168307i	−0.638625	−	0.769518i	$-0.720497\pi$
$149$	−530.202	+	306.112i	−0.291516	+	0.168307i	0.347110	+	0.937825i	$0.387163\pi$
$150$	99.4755	−	195.453i	0.0541476	−	0.106391i
$151$	−1451.09	+	2513.36i	−0.782040	+	1.35453i	0.148712	+	0.988881i	$0.452487\pi$
$151$	−1451.09	+	2513.36i	−0.782040	+	1.35453i	−0.930752	+	0.365652i	$0.880846\pi$
$152$	−117.670			−0.0627912
$153$	−281.197	+	633.139i	−0.148585	+	0.334551i
$154$	2728.60	+	2112.99i	1.42777	+	1.10565i
$155$	−1730.52	−	999.116i	−0.896766	−	0.517748i
$156$	−2621.78	+	138.605i	−1.34558	+	0.0711367i
$157$	−1163.43	+	671.708i	−0.591414	+	0.341453i	−0.765657	−	0.643250i	$-0.777586\pi$
$157$	−1163.43	+	671.708i	−0.591414	+	0.341453i	0.174242	+	0.984703i	$0.444252\pi$
$158$	654.065	−	377.625i	0.329333	−	0.190141i
$159$	−169.173	−	260.243i	−0.0843793	−	0.129803i
$160$	2502.66	+	1444.91i	1.23658	+	0.713938i
$161$	1906.57	−	2462.04i	0.933283	−	1.20519i
$162$	597.340	+	2785.17i	0.289700	+	1.35076i
$163$	974.519			0.468284			0.234142	−	0.972202i	$-0.424772\pi$
$163$	974.519			0.468284			0.234142	+	0.972202i	$0.424772\pi$
$164$	−1226.34	+	2124.09i	−0.583911	+	1.01136i
$165$	1573.86	+	2421.11i	0.742577	+	1.14232i
$166$	1463.52	−	844.966i	0.684286	−	0.395073i
$167$	−1421.47	−	2462.05i	−0.658661	−	1.14083i	−0.980963	−	0.194197i	$-0.937790\pi$
$167$	−1421.47	−	2462.05i	−0.658661	−	1.14083i	0.322302	−	0.946637i	$-0.395543\pi$
$168$	226.241	+	156.817i	0.103898	+	0.0720160i
$169$	1318.01	−	2282.87i	0.599916	−	1.03908i
$170$		−	1168.34i		−	0.527106i
$171$	1015.07	+	450.826i	0.453944	+	0.201611i
$172$	3014.02			1.33615
$173$	1990.91	−	3448.36i	0.874949	−	1.51546i	0.0181322	−	0.999836i	$-0.494228\pi$
$173$	1990.91	−	3448.36i	0.874949	−	1.51546i	0.856817	−	0.515621i	$-0.172439\pi$
$174$	−589.812	−	300.184i	−0.256974	−	0.130787i
$175$	−26.9894	+	198.219i	−0.0116583	+	0.0856227i
$176$	−2862.93	+	1652.91i	−1.22615	+	0.707916i
$177$	2612.34	+	1329.55i	1.10935	+	0.564603i
$178$	−3128.75	−	1806.38i	−1.31747	−	0.760641i
$179$			2465.66i			1.02956i	0.857321	+	0.514782i	$0.172127\pi$
$179$			2465.66i			1.02956i	−0.857321	+	0.514782i	$0.827873\pi$
$180$	−1345.84	−	1848.83i	−0.557294	−	0.765574i
$181$			2517.90i			1.03400i	0.855986	+	0.516999i	$0.172951\pi$
$181$			2517.90i			1.03400i	−0.855986	+	0.516999i	$0.827049\pi$
$182$	4656.44	−	1904.65i	1.89647	−	0.775726i
$183$	−3425.15	+	181.077i	−1.38358	+	0.0731454i
$184$	240.476	+	416.517i	0.0963485	+	0.166881i
$185$	22.5351	+	39.0320i	0.00895576	+	0.0155118i
$186$	−2918.96	+	1897.49i	−1.15069	+	0.748016i
$187$	1059.69	+	611.810i	0.414395	+	0.239251i
$188$	1081.26			0.419462
$189$	−1350.85	−	2219.57i	−0.519892	−	0.854232i
$190$	−1873.13			−0.715217
$191$	−399.325	−	230.550i	−0.151278	−	0.0873405i	0.422450	−	0.906386i	$-0.361170\pi$
$191$	−399.325	−	230.550i	−0.151278	−	0.0873405i	−0.573728	+	0.819046i	$0.694503\pi$
$192$	1805.36	−	1173.59i	0.678599	−	0.441129i
$193$	1281.14	+	2219.00i	0.477815	+	0.827600i	0.999677	−	0.0254302i	$-0.00809554\pi$
$193$	1281.14	+	2219.00i	0.477815	+	0.827600i	−0.521861	+	0.853030i	$0.674762\pi$
$194$	−2128.27	−	3686.26i	−0.787632	−	1.36422i
$195$	4203.76	−	222.240i	1.54378	−	0.0816149i
$196$	2402.15	+	666.508i	0.875420	+	0.242896i
$197$			3764.93i			1.36162i	0.732458	+	0.680812i	$0.238373\pi$
$197$			3764.93i			1.36162i	−0.732458	+	0.680812i	$0.761627\pi$
$198$	5003.16	−	530.486i	1.79575	−	0.190404i
$199$			958.945i			0.341597i	0.985306	+	0.170799i	$0.0546347\pi$
$199$			958.945i			0.341597i	−0.985306	+	0.170799i	$0.945365\pi$
$200$	−26.7582	−	15.4489i	−0.00946045	−	0.00546200i
$201$	1352.12	+	688.159i	0.474483	+	0.241488i
$202$	1142.41	−	659.569i	0.397918	−	0.229738i
$203$	598.160	+	81.4451i	0.206811	+	0.0281592i
$204$	−863.582	−	439.519i	−0.296386	−	0.150846i
$205$	1966.32	−	3405.76i	0.669919	−	1.16033i
$206$	828.650			0.280266
$207$	−478.662	−	4514.40i	−0.160721	−	1.51581i
$208$			4819.17i			1.60649i
$209$	980.876	−	1698.93i	0.324634	−	0.562283i
$210$	3601.43	+	2496.30i	1.18344	+	0.820292i
$211$	2018.18	+	3495.59i	0.658471	+	1.14051i	0.981012	+	0.193949i	$0.0621298\pi$
$211$	2018.18	+	3495.59i	0.658471	+	1.14051i	−0.322541	+	0.946556i	$0.604537\pi$
$212$	375.990	−	217.078i	0.121807	−	0.0703254i
$213$	−8.65651	−	13.3165i	−0.00278467	−	0.00428372i
$214$	−780.025	+	1351.04i	−0.249165	+	0.431567i
$215$	−4832.68			−1.53296
$216$	396.286	−	63.3236i	0.124833	−	0.0199474i
$217$	1944.38	−	2510.87i	0.608265	−	0.785481i
$218$	−6251.63	−	3609.38i	−1.94227	−	1.12137i
$219$	−1434.69	−	2207.02i	−0.442682	−	0.680988i
$220$	−3497.94	+	2019.54i	−1.07196	+	0.618896i
$221$	1544.79	−	891.884i	0.470198	−	0.271469i
$222$	78.4158	−	4.14560i	0.0237069	−	0.00125331i
$223$	−5069.18	−	2926.69i	−1.52223	−	0.878860i	−0.999655	−	0.0262676i	$-0.991638\pi$
$223$	−5069.18	−	2926.69i	−1.52223	−	0.878860i	−0.522576	−	0.852593i	$-0.675029\pi$
$224$	−2811.95	+	3631.20i	−0.838754	+	1.08312i
$225$	171.639	+	235.787i	0.0508561	+	0.0698629i
$226$	−4970.85			−1.46308
$227$	−3038.38	+	5262.62i	−0.888388	+	1.53873i	−0.0466072	+	0.998913i	$0.514841\pi$
$227$	−3038.38	+	5262.62i	−0.888388	+	1.53873i	−0.841781	+	0.539820i	$0.818492\pi$
$228$	−704.653	+	1384.53i	−0.204679	+	0.402160i
$229$	814.321	−	470.148i	0.234986	−	0.135669i	−0.377884	−	0.925853i	$-0.623348\pi$
$229$	814.321	−	470.148i	0.234986	−	0.135669i	0.612870	+	0.790184i	$0.290015\pi$
$230$	3828.04	+	6630.35i	1.09745	+	1.90084i
$231$	−4150.05	+	1959.29i	−1.18205	+	0.558060i
$232$	−46.6195	+	80.7473i	−0.0131928	+	0.0228505i
$233$		−	3314.66i		−	0.931976i	−0.884791	−	0.465988i	$-0.845699\pi$
$233$		−	3314.66i		−	0.931976i	0.884791	−	0.465988i	$-0.154301\pi$
$234$	2977.03	−	6703.02i	0.831685	−	1.87261i
$235$	−1733.69			−0.481248
$236$	−2049.96	+	3550.64i	−0.565429	+	0.979352i
$237$	53.0224	+	1002.94i	0.0145324	+	0.274887i
$238$	1839.83	+	250.510i	0.501085	+	0.0682274i
$239$	2213.80	−	1278.14i	0.599158	−	0.345924i	−0.169552	−	0.985521i	$-0.554232\pi$
$239$	2213.80	−	1278.14i	0.599158	−	0.345924i	0.768710	+	0.639597i	$0.220899\pi$
$240$	−3519.32	+	2287.76i	−0.946546	+	0.615311i
$241$	−1800.75	−	1039.66i	−0.481312	−	0.277886i	0.239651	−	0.970859i	$-0.422967\pi$
$241$	−1800.75	−	1039.66i	−0.481312	−	0.277886i	−0.720963	+	0.692973i	$0.756300\pi$
$242$		−	3685.64i		−	0.979016i
$243$	−3661.16	−	972.027i	−0.966516	−	0.256607i
$244$		−	4797.50i		−	1.25872i
$245$	−3851.60	−	1068.68i	−1.00437	−	0.278674i
$246$	−3734.37	−	5744.67i	−0.967866	−	1.48889i
$247$	−1429.90	−	2476.66i	−0.368349	−	0.638000i
$248$	245.246	+	424.779i	0.0627949	+	0.108764i
$249$	118.642	+	2244.16i	0.0301953	+	0.571157i
$250$	4503.32	+	2600.00i	1.13926	+	0.657753i
$251$	4718.74			1.18663			0.593316	−	0.804970i	$-0.297819\pi$
$251$	4718.74			1.18663			0.593316	+	0.804970i	$0.297819\pi$
$252$	3199.96	−	1722.92i	0.799916	−	0.430688i
$253$	−8018.29			−1.99251
$254$	6211.40	+	3586.16i	1.53440	+	0.885888i
$255$	1384.67	+	704.724i	0.340044	+	0.173065i
$256$	−2369.94	−	4104.86i	−0.578599	−	1.00216i
$257$	−2401.45	−	4159.43i	−0.582873	−	1.00957i	−0.995137	−	0.0985008i	$-0.968595\pi$
$257$	−2401.45	−	4159.43i	−0.582873	−	1.00957i	0.412264	−	0.911064i	$-0.364738\pi$
$258$	−3819.12	+	7503.94i	−0.921582	+	1.81076i
$259$	−66.2967	+	27.1177i	−0.0159053	+	0.00650584i
$260$			5888.08i			1.40447i
$261$	711.527	−	517.951i	0.168745	−	0.122837i
$262$		−	5264.85i		−	1.24146i
$263$	2334.00	+	1347.54i	0.547227	+	0.315941i	0.748003	−	0.663696i	$-0.231013\pi$
$263$	2334.00	+	1347.54i	0.547227	+	0.315941i	−0.200776	+	0.979637i	$0.564346\pi$
$264$	−37.4211	−	707.836i	−0.00872389	−	0.165016i
$265$	−602.862	+	348.062i	−0.139749	+	0.0806842i
$266$	401.626	−	2949.67i	0.0925762	−	0.679910i
$267$	4028.04	−	2618.46i	0.923266	−	0.600177i
$268$	−1061.04	+	1837.78i	−0.241841	+	0.418881i
$269$	−4182.34			−0.947961			−0.473981	−	0.880535i	$-0.657183\pi$
$269$	−4182.34			−0.947961			−0.473981	+	0.880535i	$0.657183\pi$
$270$	6308.31	−	1008.02i	1.42190	−	0.227208i
$271$		−	654.173i		−	0.146635i	−0.997309	−	0.0733176i	$-0.976641\pi$
$271$		−	654.173i		−	0.146635i	0.997309	−	0.0733176i	$-0.0233587\pi$
$272$	−889.325	+	1540.36i	−0.198247	+	0.343374i
$273$	−551.378	+	6667.43i	−0.122238	+	1.47814i
$274$	2175.69	+	3768.40i	0.479701	+	0.830867i
$275$	446.105	−	257.559i	0.0978223	−	0.0564777i
$276$	6340.89	−	335.223i	1.38289	−	0.0731089i
$277$	1828.75	−	3167.49i	0.396675	−	0.687061i	−0.596638	−	0.802510i	$-0.703497\pi$
$277$	1828.75	−	3167.49i	0.396675	−	0.687061i	0.993313	+	0.115449i	$0.0368306\pi$
$278$	5144.57			1.10989
$279$	−488.156	−	4603.94i	−0.104750	−	0.987924i
$280$	377.989	−	488.115i	0.0806756	−	0.104180i
$281$	2453.28	+	1416.40i	0.520819	+	0.300695i	0.737270	−	0.675598i	$-0.236115\pi$
$281$	2453.28	+	1416.40i	0.520819	+	0.300695i	−0.216450	+	0.976294i	$0.569448\pi$
$282$	−1370.08	+	2691.99i	−0.289317	+	0.568459i
$283$	7878.39	−	4548.59i	1.65485	−	0.955426i	0.679808	−	0.733390i	$-0.262063\pi$
$283$	7878.39	−	4548.59i	1.65485	−	0.955426i	0.975039	−	0.222035i	$-0.0712701\pi$
$284$	19.2393	−	11.1078i	0.00401986	−	0.00232087i
$285$	1129.84	−	2219.94i	0.234828	−	0.461397i
$286$	−11218.9	−	6477.21i	−2.31953	−	1.33918i
$287$	4941.54	+	3826.66i	1.01634	+	0.787040i
$288$	705.966	+	6658.16i	0.144442	+	1.36228i
$289$	−4254.65			−0.865998
$290$	−742.116	+	1285.38i	−0.150271	+	0.260277i
$291$	5652.51	−	298.831i	1.13868	−	0.0601985i
$292$	3188.63	−	1840.95i	0.639042	−	0.368951i
$293$	−1538.44	−	2664.66i	−0.306747	−	0.531301i	0.670902	−	0.741546i	$-0.265907\pi$
$293$	−1538.44	−	2664.66i	−0.306747	−	0.531301i	−0.977649	+	0.210245i	$0.932574\pi$
$294$	−4703.20	+	5136.04i	−0.932980	+	1.01884i
$295$	3286.91	−	5693.09i	0.648716	−	1.12361i
$296$		−	11.0631i		−	0.00217239i
$297$	−2389.11	+	6249.48i	−0.466768	+	1.22098i
$298$	2392.22			0.465025
$299$	−5844.44	+	10122.9i	−1.13041	+	1.95793i
$300$	−342.013	+	222.329i	−0.0658205	+	0.0427872i
$301$	1036.19	−	7610.15i	0.198423	−	1.45728i
$302$	9820.76	−	5670.02i	1.87126	−	1.08037i
$303$	92.6103	+	1751.77i	0.0175588	+	0.332133i
$304$	2469.55	+	1425.80i	0.465917	+	0.268997i
$305$			7692.30i			1.44413i
$306$	2188.52	−	1593.12i	0.408854	−	0.297622i
$307$			3006.74i			0.558970i	0.960150	+	0.279485i	$0.0901637\pi$
$307$			3006.74i			0.558970i	−0.960150	+	0.279485i	$0.909836\pi$
$308$	−2430.22	−	5941.32i	−0.449592	−	1.09915i
$309$	−499.826	+	982.076i	−0.0920198	+	0.180804i
$310$	3903.97	+	6761.87i	0.715260	+	1.23887i
$311$	2232.53	+	3866.86i	0.407059	+	0.705046i	0.994559	−	0.104178i	$-0.0332211\pi$
$311$	2232.53	+	3866.86i	0.407059	+	0.705046i	−0.587500	+	0.809224i	$0.699888\pi$
$312$	−920.899	−	468.691i	−0.167101	−	0.0850461i
$313$	6007.81	+	3468.61i	1.08492	+	0.626382i	0.932221	−	0.361890i	$-0.117869\pi$
$313$	6007.81	+	3468.61i	1.08492	+	0.626382i	0.152704	+	0.988272i	$0.451202\pi$
$314$	5249.29			0.943423
$315$	−5130.82	+	2762.52i	−0.917742	+	0.494128i
$316$	−1404.79			−0.250081
$317$	−4933.94	−	2848.61i	−0.874189	−	0.504713i	−0.00545096	−	0.999985i	$-0.501735\pi$
$317$	−4933.94	−	2848.61i	−0.874189	−	0.504713i	−0.868738	+	0.495272i	$0.835068\pi$
$318$	64.0301	+	1211.16i	0.0112913	+	0.213580i
$319$	−777.226	−	1346.20i	−0.136415	−	0.236277i
$320$	−2414.59	−	4182.19i	−0.421811	−	0.730599i
$321$	−1130.69	−	1739.37i	−0.196602	−	0.302437i
$322$	−11261.8	+	4606.48i	−1.94905	+	0.797233i
$323$		−	1055.49i		−	0.181824i
$324$	1628.04	−	5042.00i	0.279157	−	0.864540i
$325$		−	750.927i		−	0.128166i
$326$	−3297.70	−	1903.93i	−0.560254	−	0.323463i
$327$	8048.54	−	5232.02i	1.36112	−	0.884806i
$328$	−835.988	+	482.658i	−0.140731	+	0.0812510i
$329$	371.727	−	2730.09i	0.0622917	−	0.457491i
$330$	−595.690	−	11267.7i	−0.0993687	−	1.87960i
$331$	−3928.31	+	6804.03i	−0.652325	+	1.12986i	0.330233	+	0.943900i	$0.392873\pi$
$331$	−3928.31	+	6804.03i	−0.652325	+	1.12986i	−0.982557	+	0.185960i	$0.940461\pi$
$332$	−3143.33			−0.519617
$333$	−42.3858	+	95.4352i	−0.00697516	+	0.0157052i
$334$			11108.5i			1.81986i
$335$	1701.27	−	2946.69i	0.277464	−	0.480581i
$336$	−2848.02	−	6032.50i	−0.462417	−	0.979464i
$337$	2447.80	+	4239.71i	0.395668	+	0.685317i	0.993186	−	0.116538i	$-0.0371798\pi$
$337$	2447.80	+	4239.71i	0.395668	+	0.685317i	−0.597518	+	0.801855i	$0.703846\pi$
$338$	−8920.13	+	5150.04i	−1.43548	+	0.828773i
$339$	2998.32	−	5891.20i	0.480373	−	0.943853i
$340$	−1086.58	+	1882.01i	−0.173318	+	0.300196i
$341$	−8177.34			−1.29861
$342$	−2554.14	−	3508.72i	−0.403837	−	0.554765i
$343$	2508.71	−	5836.09i	0.394921	−	0.918715i
$344$	1027.32	+	593.121i	0.161015	+	0.0929621i
$345$	−10167.0	+	537.496i	−1.58658	+	0.0838777i
$346$	−13474.2	+	7779.33i	−2.09358	+	1.20873i
$347$	1816.16	−	1048.56i	0.280969	−	0.162218i	−0.352893	−	0.935664i	$-0.614802\pi$
$347$	1816.16	−	1048.56i	0.280969	−	0.162218i	0.633862	+	0.773446i	$0.281469\pi$
$348$	670.914	+	1032.08i	0.103347	+	0.158981i
$349$	7325.59	+	4229.43i	1.12358	+	0.648700i	0.942313	−	0.334734i	$-0.108647\pi$
$349$	7325.59	+	4229.43i	1.12358	+	0.648700i	0.181268	+	0.983434i	$0.441980\pi$
$350$	478.593	−	618.030i	0.0730911	−	0.0943860i
$351$	6148.41	+	7571.37i	0.934979	+	1.15137i
$352$	11826.0			1.79070
$353$	316.445	−	548.099i	0.0477129	−	0.0826412i	−0.841183	−	0.540751i	$-0.818140\pi$
$353$	316.445	−	548.099i	0.0477129	−	0.0826412i	0.888896	+	0.458110i	$0.151473\pi$
$354$	−6242.40	−	9602.83i	−0.937232	−	1.44176i
$355$	−30.8482	+	17.8102i	−0.00461197	+	0.00266272i
$356$	3359.93	+	5819.58i	0.500214	+	0.866396i
$357$	−1406.64	+	2029.37i	−0.208536	+	0.300856i
$358$	4817.18	−	8343.60i	0.711162	−	1.23177i
$359$			7038.13i			1.03470i	0.855773	+	0.517351i	$0.173082\pi$
$359$			7038.13i			1.03470i	−0.855773	+	0.517351i	$0.826918\pi$
$360$	−94.8978	−	895.008i	−0.0138932	−	0.131031i
$361$	5166.80			0.753288
$362$	4919.24	−	8520.38i	0.714225	−	1.23707i
$363$	4368.04	+	2223.11i	0.631578	+	0.321441i
$364$	−9272.12	−	1262.49i	−1.33514	−	0.181792i
$365$	−5112.64	+	2951.78i	−0.733172	+	0.423297i
$366$	11944.2	+	6079.00i	1.70583	+	0.868182i
$367$	−591.654	−	341.591i	−0.0841528	−	0.0485856i	0.457333	−	0.889295i	$-0.348805\pi$
$367$	−591.654	−	341.591i	−0.0841528	−	0.0485856i	−0.541486	+	0.840710i	$0.682138\pi$
$368$		−	11655.4i		−	1.65103i
$369$	9060.81	−	960.719i	1.27828	−	0.135537i
$370$		−	176.109i		−	0.0247445i
$371$	−418.842	−	1023.97i	−0.0586124	−	0.143294i
$372$	6466.67	−	341.873i	0.901293	−	0.0476486i
$373$	−4524.00	−	7835.79i	−0.627999	−	1.08773i	−0.987953	−	0.154756i	$-0.950541\pi$
$373$	−4524.00	−	7835.79i	−0.627999	−	1.08773i	0.359954	−	0.932970i	$-0.382792\pi$
$374$	−2390.60	−	4140.64i	−0.330521	−	0.572480i
$375$	−5797.71	+	3768.85i	−0.798380	+	0.518994i
$376$	368.543	+	212.778i	0.0505482	+	0.0291840i
$377$	−2266.05			−0.309569
$378$	234.770	+	10150.0i	0.0319452	+	1.38111i
$379$	6790.65			0.920349			0.460175	−	0.887828i	$-0.347787\pi$
$379$	6790.65			0.920349			0.460175	+	0.887828i	$0.347787\pi$
$380$	3017.31	+	1742.04i	0.407328	+	0.235171i
$381$	−7996.74	+	5198.35i	−1.07529	+	0.699002i
$382$	900.857	+	1560.33i	0.120659	+	0.208988i
$383$	−1170.59	−	2027.53i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$383$	−1170.59	−	2027.53i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$384$	1891.92	−	100.020i	0.251423	−	0.0132920i
$385$	3896.60	+	9526.31i	0.515816	+	1.26105i
$386$		−	10011.9i		−	1.32019i
$387$	−6589.68	−	9052.48i	−0.865562	−	1.18905i
$388$			7917.29i			1.03593i
$389$	1522.53	+	879.032i	0.198445	+	0.114572i	0.595930	−	0.803036i	$-0.296784\pi$
$389$	1522.53	+	879.032i	0.198445	+	0.114572i	−0.397485	+	0.917609i	$0.630117\pi$
$390$	−14659.4	−	7460.89i	−1.90335	−	0.968710i
$391$	−3736.13	+	2157.06i	−0.483234	+	0.278995i
$392$	687.603	+	699.889i	0.0885948	+	0.0901779i
$393$	6239.64	+	3175.66i	0.800886	+	0.407610i
$394$	7355.58	−	12740.2i	0.940530	−	1.62904i
$395$	2252.44			0.286918
$396$	−8552.64	−	3798.50i	−1.08532	−	0.482025i
$397$			1120.19i			0.141614i	0.997490	+	0.0708071i	$0.0225575\pi$
$397$			1120.19i			0.141614i	−0.997490	+	0.0708071i	$0.977443\pi$
$398$	1873.50	−	3245.00i	0.235955	−	0.408686i
$399$	3253.56	+	2255.18i	0.408225	+	0.282957i
$400$	374.386	+	648.456i	0.0467983	+	0.0810571i
$401$	−1528.43	+	882.440i	−0.190340	+	0.109893i	−0.592142	−	0.805834i	$-0.701717\pi$
$401$	−1528.43	+	882.440i	−0.190340	+	0.109893i	0.401802	+	0.915727i	$0.368384\pi$
$402$	−3231.01	−	4970.33i	−0.400865	−	0.616660i
$403$	−5960.37	+	10323.7i	−0.736743	+	1.27608i
$404$	−2453.64			−0.302162
$405$	−2610.40	+	8084.33i	−0.320276	+	0.991885i
$406$	−1865.01	−	1444.24i	−0.227977	−	0.176542i
$407$	159.730	+	92.2202i	0.0194534	+	0.0112314i
$408$	−207.856	−	319.750i	−0.0252216	−	0.0387990i
$409$	5868.28	−	3388.05i	0.709456	−	0.409605i	−0.101403	−	0.994845i	$-0.532333\pi$
$409$	5868.28	−	3388.05i	0.709456	−	0.409605i	0.810860	+	0.585241i	$0.199000\pi$
$410$	−13307.7	+	7683.22i	−1.60298	+	0.925481i
$411$	−5778.47	+	305.489i	−0.693505	+	0.0366635i
$412$	−1334.82	−	770.659i	−0.159616	−	0.0921545i
$413$	8260.31	+	6396.67i	0.984173	+	0.762129i
$414$	−7200.06	+	16211.5i	−0.854744	+	1.92453i
$415$	5040.01			0.596155
$416$	8619.81	−	14930.0i	1.01592	−	1.75962i
$417$	−3103.11	+	6097.09i	−0.364412	+	0.716009i
$418$	−6638.42	+	3832.69i	−0.776784	+	0.448477i
$419$	−5353.56	−	9272.64i	−0.624197	−	1.08114i	−0.988696	−	0.149937i	$-0.952093\pi$
$419$	−5353.56	−	9272.64i	−0.624197	−	1.08114i	0.364498	−	0.931204i	$-0.381240\pi$
$420$	−3479.72	−	7370.53i	−0.404269	−	0.856298i
$421$	1424.86	−	2467.93i	0.164949	−	0.285700i	−0.771688	−	0.636001i	$-0.780587\pi$
$421$	1424.86	−	2467.93i	0.164949	−	0.285700i	0.936637	+	0.350301i	$0.113921\pi$
$422$		−	15771.8i		−	1.81933i
$423$	−2364.00	−	3247.51i	−0.271730	−	0.373285i
$424$	170.873			0.0195715
$425$	138.575	−	240.020i	0.0158162	−	0.0273945i
$426$	3.27639	+	61.9744i	0.000372633	+	0.00704852i
$427$	−12113.3	−	1649.34i	−1.37284	−	0.186925i
$428$	2512.99	−	1450.87i	0.283808	−	0.163857i
$429$	14443.5	−	9389.11i	1.62550	−	1.05667i
$430$	16353.4	+	9441.65i	1.83403	+	1.05888i
$431$		−	10469.5i		−	1.17007i	−0.811010	−	0.585033i	$-0.801082\pi$
$431$		−	10469.5i		−	1.17007i	0.811010	−	0.585033i	$-0.198918\pi$
$432$	−9084.23	−	3472.80i	−1.01173	−	0.386771i
$433$			5079.76i			0.563782i	0.959446	+	0.281891i	$0.0909617\pi$
$433$			5079.76i			0.563782i	−0.959446	+	0.281891i	$0.909038\pi$
$434$	−11485.2	+	4697.85i	−1.27029	+	0.519594i
$435$	−1075.74	−	1654.84i	−0.118570	−	0.182399i
$436$	6713.58	+	11628.3i	0.737436	+	1.27728i
$437$	3458.27	+	5989.90i	0.378562	+	0.655689i
$438$	543.015	+	10271.4i	0.0592380	+	1.12051i
$439$	−6497.04	−	3751.07i	−0.706349	−	0.407811i	0.103359	−	0.994644i	$-0.467041\pi$
$439$	−6497.04	−	3751.07i	−0.706349	−	0.407811i	−0.809708	+	0.586834i	$0.800374\pi$
$440$	−1589.68			−0.172238
$441$	−3250.10	−	8671.96i	−0.350945	−	0.936396i
$442$	−6969.93			−0.750058
$443$	2388.50	+	1379.00i	0.256165	+	0.147897i	0.622584	−	0.782553i	$-0.286083\pi$
$443$	2388.50	+	1379.00i	0.256165	+	0.147897i	−0.366419	+	0.930450i	$0.619416\pi$
$444$	−130.171	−	66.2502i	−0.0139136	−	0.00708130i
$445$	−5387.31	−	9331.09i	−0.573894	−	0.994014i
$446$	11435.8	+	19807.4i	1.21413	+	2.10293i
$447$	−1442.94	+	2835.14i	−0.152682	+	0.299995i
$448$	7103.54	−	2905.60i	0.749131	−	0.306421i
$449$			8061.59i			0.847327i	0.905820	+	0.423663i	$0.139256\pi$
$449$			8061.59i			0.847327i	−0.905820	+	0.423663i	$0.860744\pi$
$450$	−120.155	−	1133.22i	−0.0125871	−	0.118712i
$451$		−	16093.4i		−	1.68029i
$452$	8007.22	+	4622.97i	0.833248	+	0.481076i
$453$	796.130	+	15059.1i	0.0825727	+	1.56190i
$454$	20563.3	−	11872.2i	2.12573	−	1.22729i
$455$	14866.9	+	2024.27i	1.53180	+	0.208570i
$456$	−512.635	+	333.243i	−0.0526455	+	0.0342226i
$457$	108.316	−	187.608i	0.0110871	−	0.0192034i	−0.860429	−	0.509571i	$-0.829804\pi$
$457$	108.316	−	187.608i	0.0110871	−	0.0192034i	0.871516	+	0.490368i	$0.163137\pi$
$458$	−3674.14			−0.374850
$459$	568.010	+	3554.67i	0.0577613	+	0.361477i
$460$		−	14240.6i		−	1.44341i
$461$	594.431	−	1029.59i	0.0600552	−	0.104019i	−0.834435	−	0.551107i	$-0.814206\pi$
$461$	594.431	−	1029.59i	0.0600552	−	0.104019i	0.894490	+	0.447088i	$0.147539\pi$
$462$	17871.4	+	1477.91i	1.79968	+	0.148828i
$463$	2397.17	+	4152.02i	0.240617	+	0.416761i	0.960890	−	0.276929i	$-0.0893168\pi$
$463$	2397.17	+	4152.02i	0.240617	+	0.416761i	−0.720273	+	0.693691i	$0.755983\pi$
$464$	1956.82	−	1129.77i	0.195783	−	0.113035i
$465$	−10368.6	+	548.158i	−1.03405	+	0.0546671i
$466$	−6475.88	+	11216.5i	−0.643754	+	1.11501i
$467$	2953.79			0.292687			0.146344	−	0.989234i	$-0.453249\pi$
$467$	2953.79			0.292687			0.146344	+	0.989234i	$0.453249\pi$
$468$	−11029.4	+	8028.79i	−1.08939	+	0.793015i
$469$	4275.46	+	3310.85i	0.420943	+	0.325972i
$470$	5866.67	+	3387.13i	0.575765	+	0.332418i
$471$	−3166.28	+	6221.21i	−0.309754	+	0.608616i
$472$	−1397.44	+	806.814i	−0.136277	+	0.0786793i
$473$	−17127.1	+	9888.34i	−1.66492	+	0.961240i
$474$	1780.04	−	3497.47i	0.172489	−	0.338912i
$475$	−384.808	−	222.169i	−0.0371710	−	0.0214607i
$476$	−2730.68	−	2114.60i	−0.262942	−	0.203619i
$477$	−1474.03	−	654.663i	−0.141491	−	0.0628405i
$478$	−9988.44			−0.955775
$479$	54.6189	−	94.6028i	0.00521003	−	0.00902403i	−0.863409	−	0.504505i	$-0.831675\pi$
$479$	54.6189	−	94.6028i	0.00521003	−	0.00902403i	0.868619	+	0.495481i	$0.165008\pi$
$480$	14995.0	−	792.739i	1.42589	−	0.0753821i
$481$	232.851	−	134.437i	0.0220730	−	0.0127438i
$482$	4062.39	+	7036.27i	0.383894	+	0.664924i
$483$	1333.53	−	16125.5i	0.125627	−	1.51912i
$484$	−3427.71	+	5936.96i	−0.321911	+	0.557566i
$485$		−	12694.6i		−	1.18852i
$486$	10490.0	+	10442.1i	0.979089	+	0.974616i
$487$	−3614.94			−0.336363			−0.168182	−	0.985756i	$-0.553789\pi$
$487$	−3614.94			−0.336363			−0.168182	+	0.985756i	$0.553789\pi$
$488$	944.088	−	1635.21i	0.0875755	−	0.151685i
$489$	4245.56	−	2759.86i	0.392619	−	0.255225i
$490$	10945.7	+	11141.2i	1.00913	+	1.02716i
$491$	16280.5	−	9399.53i	1.49639	−	0.863940i	0.496397	−	0.868096i	$-0.334656\pi$
$491$	16280.5	−	9399.53i	1.49639	−	0.863940i	0.999991	+	0.00415517i	$0.00132263\pi$
$492$	672.824	+	12726.8i	0.0616530	+	1.16619i
$493$	−724.300	−	418.175i	−0.0661680	−	0.0382021i
$494$			11174.4i			1.01774i
$495$	13713.3	+	6090.51i	1.24518	+	0.553026i
$496$		−	11886.5i		−	1.07605i
$497$	−21.4320	−	52.3963i	−0.00193431	−	0.00472896i
$498$	3982.97	−	7825.88i	0.358396	−	0.704189i
$499$	−1620.89	−	2807.46i	−0.145413	−	0.251862i	0.784114	−	0.620617i	$-0.213118\pi$
$499$	−1620.89	−	2807.46i	−0.145413	−	0.251862i	−0.929527	+	0.368755i	$0.879784\pi$
$500$	−4836.08	−	8376.34i	−0.432552	−	0.749203i
$501$	−13165.3	−	6700.46i	−1.17402	−	0.597514i
$502$	−15967.9	−	9219.06i	−1.41968	−	0.819655i
$503$	−4737.83			−0.419979			−0.209989	−	0.977704i	$-0.567343\pi$
$503$	−4737.83			−0.419979			−0.209989	+	0.977704i	$0.567343\pi$
$504$	1429.74	+	42.4641i	0.126361	+	0.00375298i
$505$	3934.16			0.346669
$506$	27133.3	+	15665.4i	2.38384	+	1.37631i
$507$	−723.119	−	13678.1i	−0.0633429	−	1.19816i
$508$	−6670.37	−	11553.4i	−0.582579	−	1.00906i
$509$	−1272.38	−	2203.83i	−0.110800	−	0.191912i	0.805293	−	0.592877i	$-0.202008\pi$
$509$	−1272.38	−	2203.83i	−0.110800	−	0.191912i	−0.916093	+	0.400965i	$0.868675\pi$
$510$	−3308.78	−	5089.97i	−0.287285	−	0.441937i
$511$	−3552.03	−	8683.92i	−0.307500	−	0.751769i
$512$			15603.9i			1.34687i
$513$	5698.97	−	910.654i	0.490479	−	0.0783749i
$514$			18766.9i			1.61046i
$515$	2140.25	+	1235.67i	0.183127	+	0.105729i
$516$	13130.8	−	8535.78i	1.12025	−	0.728230i
$517$	−6144.23	+	3547.37i	−0.522675	+	0.301767i
$518$	277.323	+	37.7602i	0.0235229	+	0.00320287i
$519$	−1092.30	−	20661.3i	−0.0923826	−	1.74746i
$520$	−1158.70	+	2006.93i	−0.0977160	+	0.169249i
$521$	7623.86			0.641089			0.320545	−	0.947233i	$-0.396134\pi$
$521$	7623.86			0.641089			0.320545	+	0.947233i	$0.396134\pi$
$522$	−3419.68	+	362.589i	−0.286734	+	0.0304025i
$523$		−	20941.4i		−	1.75087i	−0.483335	−	0.875435i	$-0.660575\pi$
$523$		−	20941.4i		−	1.75087i	0.483335	−	0.875435i	$-0.339425\pi$
$524$	−4896.40	+	8480.81i	−0.408206	+	0.707034i
$525$	443.781	+	939.990i	0.0368918	+	0.0781420i
$526$	−5265.39	−	9119.92i	−0.436467	−	0.755984i
$527$	−3810.24	+	2199.84i	−0.314946	+	0.181834i
$528$	−7791.46	+	15308.9i	−0.642196	+	1.26181i
$529$	8051.53	−	13945.7i	0.661752	−	1.14619i
$530$	2720.05			0.222927
$531$	15146.1	−	1605.94i	1.23783	−	0.131247i
$532$	−3390.20	+	4377.93i	−0.276286	+	0.356780i
$533$	−20317.5	−	11730.3i	−1.65113	−	0.953279i
$534$	−18746.3	+	991.058i	−1.51916	+	0.0803133i
$535$	−4029.32	+	2326.33i	−0.325612	+	0.187992i
$536$	−723.302	+	417.599i	−0.0582871	+	0.0336521i
$537$	6982.80	+	10741.8i	0.561136	+	0.863208i
$538$	14152.7	+	8171.07i	1.13414	+	0.654796i
$539$	−15836.8	+	4093.52i	−1.26557	+	0.327125i
$540$	−11099.1	−	4243.08i	−0.884502	−	0.338135i
$541$	−6660.29			−0.529294			−0.264647	−	0.964345i	$-0.585255\pi$
$541$	−6660.29			−0.529294			−0.264647	+	0.964345i	$0.585255\pi$
$542$	−1278.06	+	2213.67i	−0.101287	+	0.175434i
$543$	7130.74	+	10969.4i	0.563553	+	0.866927i
$544$	5510.33	−	3181.39i	0.434289	−	0.250737i
$545$	−10764.5	−	18644.7i	−0.846059	−	1.46542i
$546$	14892.1	−	21484.9i	1.16725	−	1.68401i
$547$	−10779.8	+	18671.2i	−0.842616	+	1.45945i	0.0450599	+	0.998984i	$0.485652\pi$
$547$	−10779.8	+	18671.2i	−0.842616	+	1.45945i	−0.887676	+	0.460469i	$0.847681\pi$
$548$		−	8093.71i		−	0.630924i
$549$	−14409.1	+	10489.0i	−1.12015	+	0.815407i
$550$	−2012.78			−0.156046
$551$	−670.432	+	1161.22i	−0.0518355	+	0.0897818i
$552$	2227.23	+	1133.55i	0.171734	+	0.0874040i
$553$	−482.954	+	3546.98i	−0.0371380	+	0.272754i
$554$	−12376.7	+	7145.70i	−0.949163	+	0.547999i
$555$	208.715	+	106.225i	0.0159630	+	0.00812436i
$556$	−8287.06	−	4784.54i	−0.632103	−	0.364945i
$557$		−	15772.0i		−	1.19979i	−0.800079	−	0.599895i	$-0.795209\pi$
$557$		−	15772.0i		−	1.19979i	0.800079	−	0.599895i	$-0.204791\pi$
$558$	−7342.88	+	16533.1i	−0.557077	+	1.25431i
$559$			28830.0i			2.18136i
$560$	−13847.4	+	5664.09i	−1.04493	+	0.427413i
$561$	6349.25	−	335.665i	0.477835	−	0.0252617i
$562$	−5534.47	−	9585.99i	−0.415405	−	0.719503i
$563$	−5842.23	−	10119.0i	−0.437337	−	0.757489i	0.560146	−	0.828394i	$-0.310745\pi$
$563$	−5842.23	−	10119.0i	−0.437337	−	0.757489i	−0.997483	+	0.0709043i	$0.977412\pi$
$564$	4710.57	−	3062.15i	0.351686	−	0.228617i
$565$	−12838.8	−	7412.46i	−0.955984	−	0.551937i
$566$	−35546.5			−2.63981
$567$	−12170.9	−	5844.06i	−0.901465	−	0.432853i
$568$	8.74349			0.000645896
$569$	−5808.93	−	3353.79i	−0.427984	−	0.247097i	0.270503	−	0.962719i	$-0.412810\pi$
$569$	−5808.93	−	3353.79i	−0.427984	−	0.247097i	−0.698488	+	0.715622i	$0.746143\pi$
$570$	−8160.42	+	5304.75i	−0.599653	+	0.389810i
$571$	9286.00	+	16083.8i	0.680573	+	1.17879i	0.974806	+	0.223053i	$0.0716022\pi$
$571$	9286.00	+	16083.8i	0.680573	+	1.17879i	−0.294234	+	0.955733i	$0.595064\pi$
$572$	12047.8	+	20867.5i	0.880674	+	1.52537i
$573$	−2392.61	+	126.490i	−0.174437	+	0.00922196i
$574$	−9245.63	−	22603.5i	−0.672308	−	1.64364i
$575$			1816.15i			0.131719i
$576$	4541.54	−	10225.7i	0.328526	−	0.739704i
$577$			8147.17i			0.587818i	0.955833	+	0.293909i	$0.0949563\pi$
$577$			8147.17i			0.587818i	−0.955833	+	0.293909i	$0.905044\pi$
$578$	14397.4	+	8312.35i	1.03608	+	0.598181i
$579$	11865.6	+	6038.99i	0.851671	+	0.433457i
$580$	2390.86	−	1380.36i	0.171164	−	0.0988213i
$581$	−1080.65	+	7936.65i	−0.0771650	+	0.566726i
$582$	−19711.5	−	10032.1i	−1.40390	−	0.714512i
$583$	−1424.37	+	2467.08i	−0.101186	+	0.175259i
$584$	1449.11			0.102679
$585$	17684.6	−	12873.3i	1.24986	−	0.909824i
$586$			12022.7i			0.847531i
$587$	−2070.04	+	3585.42i	−0.145553	+	0.252106i	−0.929579	−	0.368622i	$-0.879830\pi$
$587$	−2070.04	+	3585.42i	−0.145553	+	0.252106i	0.784026	+	0.620728i	$0.213163\pi$
$588$	12352.7	−	3899.26i	0.866354	−	0.273474i
$589$	3526.87	+	6108.72i	0.246727	+	0.427343i
$590$	−22245.3	+	12843.3i	−1.55224	+	0.896189i
$591$	10662.4	+	16402.1i	0.742116	+	1.14161i
$592$	−134.051	+	232.183i	−0.00930652	+	0.0161194i
$593$	14381.9			0.995945			0.497973	−	0.867193i	$-0.334078\pi$
$593$	14381.9			0.995945			0.497973	+	0.867193i	$0.334078\pi$
$594$	20294.2	−	16480.2i	1.40182	−	1.13837i
$595$	4378.37	+	3390.54i	0.301673	+	0.233611i
$596$	−3853.47	−	2224.80i	−0.264840	−	0.152905i
$597$	2715.75	+	4177.71i	0.186178	+	0.286402i
$598$	39554.3	−	22836.7i	2.70484	−	1.56164i
$599$	12019.7	−	6939.59i	0.819887	−	0.473362i	−0.0304902	−	0.999535i	$-0.509707\pi$
$599$	12019.7	−	6939.59i	0.819887	−	0.473362i	0.850378	+	0.526173i	$0.176374\pi$
$600$	−160.325	+	8.47590i	−0.0109088	+	0.000576712i
$601$	12474.7	+	7202.28i	0.846680	+	0.488831i	0.859529	−	0.511087i	$-0.170757\pi$
$601$	12474.7	+	7202.28i	0.846680	+	0.488831i	−0.0128495	+	0.999917i	$0.504090\pi$
$602$	−18374.4	+	23727.8i	−1.24400	+	1.60643i
$603$	7839.48	−	831.220i	0.529433	−	0.0561358i
$604$	−21092.9			−1.42095
$605$	5495.98	−	9519.31i	0.369328	−	0.639694i
$606$	3109.06	−	6108.78i	0.208410	−	0.409492i
$607$	−17223.6	+	9944.08i	−1.15171	+	0.664938i	−0.949303	−	0.314364i	$-0.898209\pi$
$607$	−17223.6	+	9944.08i	−1.15171	+	0.664938i	−0.202404	+	0.979302i	$0.564876\pi$
$608$	−5100.51	−	8834.35i	−0.340219	−	0.589277i
$609$	2836.58	−	1339.18i	0.188742	−	0.0891073i
$610$	15028.5	−	26030.2i	0.997520	−	1.72776i
$611$			10342.6i			0.684804i
$612$	−5006.98	+	530.890i	−0.330711	+	0.0350653i
$613$	8096.44			0.533462			0.266731	−	0.963771i	$-0.414057\pi$
$613$	8096.44			0.533462			0.266731	+	0.963771i	$0.414057\pi$
$614$	5874.30	−	10174.6i	0.386103	−	0.668751i
$615$	−1078.80	−	20406.1i	−0.0707343	−	1.33797i
$616$	340.849	−	2503.31i	0.0222942	−	0.163736i
$617$	−8145.01	+	4702.53i	−0.531452	+	0.306834i	−0.741608	−	0.670834i	$-0.765936\pi$
$617$	−8145.01	+	4702.53i	−0.531452	+	0.306834i	0.210155	+	0.977668i	$0.432603\pi$
$618$	3610.07	−	2346.76i	0.234981	−	0.152751i
$619$	467.098	+	269.679i	0.0303300	+	0.0175110i	0.515088	−	0.857137i	$-0.327759\pi$
$619$	467.098	+	269.679i	0.0303300	+	0.0175110i	−0.484758	+	0.874648i	$0.661092\pi$
$620$		−	14523.0i		−	0.940740i
$621$	−14870.2	−	18311.7i	−0.960902	−	1.18329i
$622$		−	17446.9i		−	1.12469i
$623$	15849.1	−	6482.83i	1.01923	−	0.416901i
$624$	13648.0	+	20995.0i	0.875572	+	1.34691i
$625$	8429.26	+	14599.9i	0.539473	+	0.934394i
$626$	−13553.3	−	23475.0i	−0.865335	−	1.49880i
$627$	−538.150	−	10179.3i	−0.0342769	−	0.648363i
$628$	−8455.76	−	4881.93i	−0.537295	−	0.310208i
$629$	99.2353			0.00629057
$630$	22759.5	+	675.968i	1.43930	+	0.0427479i
$631$	−14096.7			−0.889349			−0.444675	−	0.895692i	$-0.646681\pi$
$631$	−14096.7			−0.889349			−0.444675	+	0.895692i	$0.646681\pi$
$632$	−478.817	−	276.445i	−0.0301366	−	0.0173994i
$633$	18691.9	+	9513.24i	1.17368	+	0.597342i
$634$	11130.7	+	19279.0i	0.697252	+	1.20768i
$635$	10695.3	+	18524.7i	0.668391	+	1.15769i
$636$	1023.26	−	2010.53i	0.0637967	−	0.125350i
$637$	−6375.34	+	22977.3i	−0.396547	+	1.42919i
$638$			6073.90i			0.376909i
$639$	−75.4253	−	33.4988i	−0.00466945	−	0.00207385i
$640$		−	4248.92i		−	0.262427i
$641$	18973.7	+	10954.5i	1.16914	+	0.675002i	0.953477	−	0.301466i	$-0.0974761\pi$
$641$	18973.7	+	10954.5i	1.16914	+	0.675002i	0.215661	+	0.976468i	$0.430809\pi$
$642$	427.955	+	8094.95i	0.0263085	+	0.497636i
$643$	−14525.7	+	8386.40i	−0.890881	+	0.514350i	−0.874231	−	0.485511i	$-0.838634\pi$
$643$	−14525.7	+	8386.40i	−0.890881	+	0.514350i	−0.0166504	+	0.999861i	$0.505300\pi$
$644$	22425.0	+	3053.38i	1.37216	+	0.186832i
$645$	−21053.9	+	13686.2i	−1.28526	+	0.835497i
$646$	−2062.12	+	3571.70i	−0.125593	+	0.217534i
$647$	7088.41			0.430717			0.215359	−	0.976535i	$-0.430908\pi$
$647$	7088.41			0.430717			0.215359	+	0.976535i	$0.430908\pi$
$648$	1547.11	−	1398.17i	0.0937906	−	0.0847610i
$649$		−	26901.9i		−	1.62711i
$650$	−1467.09	+	2541.08i	−0.0885295	+	0.153338i
$651$	1359.98	−	16445.3i	0.0818770	−	0.990082i
$652$	3541.37	+	6133.84i	0.212716	+	0.368435i
$653$	3166.83	−	1828.37i	0.189782	−	0.109571i	−0.402098	−	0.915596i	$-0.631719\pi$
$653$	3166.83	−	1828.37i	0.189782	−	0.109571i	0.591881	+	0.806026i	$0.298386\pi$
$654$	−37457.5	+	1980.26i	−2.23961	+	0.118401i
$655$	7850.87	−	13598.1i	0.468334	−	0.811179i
$656$	23393.4			1.39231
$657$	−12500.6	−	5551.94i	−0.742309	−	0.329683i
$658$	−6591.70	+	8512.17i	−0.390534	+	0.504314i
$659$	−6740.56	−	3891.66i	−0.398444	−	0.230042i	0.287368	−	0.957820i	$-0.407220\pi$
$659$	−6740.56	−	3891.66i	−0.398444	−	0.230042i	−0.685813	+	0.727778i	$0.740553\pi$
$660$	−9519.63	+	18704.5i	−0.561441	+	1.10314i
$661$	6895.85	−	3981.32i	0.405775	−	0.234274i	−0.283198	−	0.959062i	$-0.591395\pi$
$661$	6895.85	−	3981.32i	0.405775	−	0.234274i	0.688973	+	0.724787i	$0.258062\pi$
$662$	26586.2	−	15349.6i	1.56088	−	0.901175i
$663$	4204.13	−	8260.42i	0.246267	−	0.483874i
$664$	−1071.39	−	618.568i	−0.0626175	−	0.0361522i
$665$	5435.84	−	7019.56i	0.316982	−	0.409333i
$666$	329.883	−	240.136i	0.0191933	−	0.0139716i
$667$	5480.53			0.318151
$668$	10331.1	−	17894.0i	0.598388	−	1.03644i
$669$	−30372.7	+	1605.71i	−1.75527	+	0.0927956i
$670$	−11513.9	+	6647.58i	−0.663914	+	0.383311i
$671$	15739.5	+	27261.7i	0.905542	+	1.56844i
$672$	−1966.79	+	23783.0i	−0.112903	+	1.36525i
$673$	−494.666	+	856.786i	−0.0283328	+	0.0490738i	−0.879844	−	0.475262i	$-0.842353\pi$
$673$	−494.666	+	856.786i	−0.0283328	+	0.0490738i	0.851511	+	0.524336i	$0.175686\pi$
$674$		−	19129.2i		−	1.09322i
$675$	1415.51	+	541.135i	0.0807157	+	0.0308567i
$676$	19158.5			1.09004
$677$	−11083.3	+	19196.9i	−0.629198	+	1.08980i	0.358515	+	0.933524i	$0.383283\pi$
$677$	−11083.3	+	19196.9i	−0.629198	+	1.08980i	−0.987713	+	0.156279i	$0.950050\pi$
$678$	−21655.8	+	14077.5i	−1.22668	+	0.797411i
$679$	19990.5	+	2721.89i	1.12985	+	0.153839i
$680$	−740.713	+	427.651i	−0.0417721	+	0.0241171i
$681$	1666.98	+	31531.7i	0.0938016	+	1.77430i
$682$	27671.5	+	15976.1i	1.55366	+	0.897006i
$683$		−	2458.98i		−	0.137760i	−0.997625	−	0.0688802i	$-0.978057\pi$
$683$		−	2458.98i		−	0.137760i	0.997625	−	0.0688802i	$-0.0219426\pi$
$684$	851.142	+	8027.37i	0.0475793	+	0.448734i
$685$			12977.4i			0.723858i
$686$	−19891.3	+	14847.6i	−1.10708	+	0.826361i
$687$	2216.17	−	4354.41i	0.123075	−	0.241821i
$688$	−14373.7	−	24895.9i	−0.796498	−	1.37958i
$689$	2076.42	+	3596.46i	0.114812	+	0.198859i
$690$	35454.4	+	18044.5i	1.95612	+	0.995567i
$691$	−21148.3	−	12210.0i	−1.16428	−	0.672200i	−0.211958	−	0.977279i	$-0.567984\pi$
$691$	−21148.3	−	12210.0i	−1.16428	−	0.672200i	−0.952327	+	0.305079i	$0.901317\pi$
$692$	28939.6			1.58977
$693$	−12531.2	+	20288.8i	−0.686900	+	1.11213i
$694$	−8194.32			−0.448202
$695$	13287.4	+	7671.51i	0.725211	+	0.418701i
$696$	25.5774	+	483.808i	0.00139297	+	0.0263487i
$697$	−4329.42	−	7498.77i	−0.235277	−	0.407512i
$698$	−16526.2	−	28624.1i	−0.896167	−	1.55221i
$699$	−9387.18	−	14440.5i	−0.507948	−	0.781388i
$700$	−1345.71	+	550.446i	−0.0726618	+	0.0297213i
$701$		−	6521.09i		−	0.351353i	−0.984448	−	0.175676i	$-0.943789\pi$
$701$		−	6521.09i		−	0.351353i	0.984448	−	0.175676i	$-0.0562112\pi$
$702$	−6013.50	−	37633.2i	−0.323312	−	2.02332i
$703$		−	159.098i		−	0.00853553i
$704$	−17114.7	−	9881.18i	−0.916243	−	0.528993i
$705$	−7552.92	+	4909.84i	−0.403489	+	0.262291i
$706$	−2141.65	+	1236.48i	−0.114167	+	0.0659145i
$707$	−843.540	+	6195.24i	−0.0448721	+	0.329556i
$708$	1124.70	+	21274.1i	0.0597016	+	1.12928i
$709$	5031.46	−	8714.75i	0.266517	−	0.461621i	−0.701443	−	0.712726i	$-0.747461\pi$
$709$	5031.46	−	8714.75i	0.266517	−	0.461621i	0.967960	+	0.251105i	$0.0807939\pi$
$710$	139.184			0.00735701
$711$	3071.35	+	4219.22i	0.162004	+	0.222550i
$712$			2644.77i			0.139209i
$713$	14415.4	−	24968.2i	0.757169	−	1.31145i
$714$	8724.77	−	4119.07i	0.457306	−	0.215899i
$715$	−19317.5	−	33458.9i	−1.01040	−	1.75006i
$716$	−15519.4	+	8960.12i	−0.810037	+	0.467675i
$717$	6024.84	−	11837.8i	0.313810	−	0.616585i
$718$	13750.5	−	23816.5i	0.714711	−	1.23792i
$719$	−3449.87			−0.178941			−0.0894704	−	0.995989i	$-0.528517\pi$
$719$	−3449.87			−0.178941			−0.0894704	+	0.995989i	$0.528517\pi$
$720$	−8853.14	+	19933.6i	−0.458246	+	1.03178i
$721$	−2404.75	+	3105.36i	−0.124213	+	0.160402i
$722$	−17484.1	−	10094.4i	−0.901232	−	0.520327i
$723$	−10789.4	+	570.402i	−0.554997	+	0.0293409i
$724$	−15848.2	+	9149.96i	−0.813527	+	0.469690i
$725$	−304.914	+	176.042i	−0.0156196	+	0.00901800i
$726$	−10437.8	−	16056.7i	−0.533586	−	0.820828i
$727$	18318.1	+	10575.9i	0.934497	+	0.539532i	0.888231	−	0.459397i	$-0.151935\pi$
$727$	18318.1	+	10575.9i	0.934497	+	0.539532i	0.0462657	+	0.998929i	$0.485268\pi$
$728$	−2911.92	−	2254.95i	−0.148246	−	0.114799i
$729$	−18702.9	+	6133.78i	−0.950204	+	0.311628i
$730$	23067.7			1.16955
$731$	−5320.27	+	9214.98i	−0.269189	+	0.466249i
$732$	−13586.6	−	20900.6i	−0.686033	−	1.05534i
$733$	8853.40	−	5111.51i	0.446122	−	0.257569i	−0.260069	−	0.965590i	$-0.583745\pi$
$733$	8853.40	−	5111.51i	0.446122	−	0.257569i	0.706191	+	0.708021i	$0.250412\pi$
$734$	1334.74	+	2311.84i	0.0671202	+	0.116256i
$735$	−19806.3	+	6252.07i	−0.993967	+	0.313757i
$736$	−20847.4	+	36108.7i	−1.04408	+	1.80840i
$737$		−	13924.2i		−	0.695934i
$738$	−32538.1	−	14451.2i	−1.62296	−	0.720808i
$739$	−38602.2			−1.92152			−0.960761	−	0.277378i	$-0.910534\pi$
$739$	−38602.2			−1.92152			−0.960761	+	0.277378i	$0.910534\pi$
$740$	−163.784	+	283.682i	−0.00813624	+	0.0140924i
$741$	−13243.4	−	6740.21i	−0.656557	−	0.334154i
$742$	−583.218	+	4283.35i	−0.0288552	+	0.211923i
$743$	12936.5	−	7468.90i	0.638755	−	0.368785i	−0.145380	−	0.989376i	$-0.546440\pi$
$743$	12936.5	−	7468.90i	0.638755	−	0.368785i	0.784135	+	0.620591i	$0.213107\pi$
$744$	2271.41	+	1156.03i	0.111927	+	0.0569653i
$745$	6178.65	+	3567.25i	0.303850	+	0.175428i
$746$			35354.3i			1.73514i
$747$	6872.40	+	9440.85i	0.336610	+	0.462413i
$748$			8893.20i			0.434716i
$749$	−2799.39	−	6843.88i	−0.136565	−	0.333872i
$750$	26982.3	−	1426.47i	1.31367	−	0.0694497i
$751$	12330.2	+	21356.5i	0.599113	+	1.03769i	0.992952	+	0.118515i	$0.0378135\pi$
$751$	12330.2	+	21356.5i	0.599113	+	1.03769i	−0.393839	+	0.919180i	$0.628853\pi$
$752$	−5156.45	−	8931.23i	−0.250048	−	0.433097i
$753$	20557.5	−	13363.6i	0.994897	−	0.646741i
$754$	7668.13	+	4427.20i	0.370367	+	0.213832i
$755$	33820.2			1.63026
$756$	9061.51	−	16568.4i	0.435931	−	0.797071i
$757$	31078.1			1.49214			0.746071	−	0.665867i	$-0.231938\pi$
$757$	31078.1			1.49214			0.746071	+	0.665867i	$0.231938\pi$
$758$	−22979.1	−	13267.0i	−1.10110	−	0.635723i
$759$	−34932.2	+	22708.0i	−1.67056	+	1.08596i
$760$	685.625	+	1187.54i	0.0327240	+	0.0566796i
$761$	1863.73	+	3228.07i	0.0887780	+	0.153768i	0.906995	−	0.421142i	$-0.138370\pi$
$761$	1863.73	+	3228.07i	0.0887780	+	0.153768i	−0.818217	+	0.574910i	$0.805037\pi$
$762$	37216.5	−	1967.52i	1.76930	−	0.0935376i
$763$	31668.4	−	12953.5i	1.50259	−	0.614612i
$764$		−	3351.25i		−	0.158696i
$765$	8028.18	−	851.228i	0.379424	−	0.0402304i
$766$			9148.01i			0.431503i
$767$	−33962.9	−	19608.5i	−1.59887	−	0.923106i
$768$	−21949.9	−	11171.4i	−1.03131	−	0.524885i
$769$	−5266.10	+	3040.38i	−0.246944	+	0.142573i	−0.618364	−	0.785892i	$-0.712204\pi$
$769$	−5266.10	+	3040.38i	−0.246944	+	0.142573i	0.371420	+	0.928465i	$0.378871\pi$
$770$	5425.83	−	39849.1i	0.253940	−	1.86502i
$771$	−22241.7	−	11319.9i	−1.03893	−	0.528762i
$772$	−9311.23	+	16127.5i	−0.434091	+	0.751868i
$773$	−34364.4			−1.59897			−0.799483	−	0.600688i	$-0.794893\pi$
$773$	−34364.4			−1.59897			−0.799483	+	0.600688i	$0.794893\pi$
$774$	4613.08	+	43507.2i	0.214229	+	2.02046i
$775$			1852.17i			0.0858478i
$776$	−1558.02	+	2698.58i	−0.0720745	+	0.124837i
$777$	−212.028	+	305.894i	−0.00978951	+	0.0141234i
$778$	−3434.75	−	5949.16i	−0.158280	−	0.274149i
$779$	−12022.3	+	6941.07i	−0.552944	+	0.319242i
$780$	16675.2	+	25651.8i	0.765470	+	1.17754i
$781$	−72.8844	+	126.239i	−0.00333932	+	0.00578387i
$782$	16857.1			0.770854
$783$	1632.96	−	4271.55i	0.0745305	−	0.194959i
$784$	−5950.32	−	23020.4i	−0.271061	−	1.04867i
$785$	13557.9	+	7827.68i	0.616438	+	0.355900i
$786$	−14910.2	−	22936.6i	−0.676626	−	1.04087i
$787$	3382.03	−	1952.61i	0.153185	−	0.0884411i	−0.421448	−	0.906852i	$-0.638478\pi$
$787$	3382.03	−	1952.61i	0.153185	−	0.0884411i	0.574633	+	0.818411i	$0.305145\pi$
$788$	−23697.3	+	13681.6i	−1.07129	+	0.618512i
$789$	13984.5	−	739.315i	0.631002	−	0.0333591i
$790$	−7622.08	−	4400.61i	−0.343268	−	0.198186i
$791$	14425.4	−	18628.2i	0.648431	−	0.837350i
$792$	−2167.63	−	2977.75i	−0.0972519	−	0.133598i
$793$	45889.5			2.05496
$794$	2188.53	−	3790.65i	0.0978188	−	0.169427i
$795$	−1640.69	+	3223.67i	−0.0731939	+	0.143814i
$796$	−6035.81	+	3484.78i	−0.268761	+	0.155169i
$797$	−2261.24	−	3916.59i	−0.100499	−	0.174069i	0.811392	−	0.584503i	$-0.198710\pi$
$797$	−2261.24	−	3916.59i	−0.100499	−	0.174069i	−0.911890	+	0.410434i	$0.865377\pi$
$798$	−6603.83	−	13987.9i	−0.292949	−	0.620507i
$799$	−1908.61	+	3305.81i	−0.0845078	+	0.146372i
$800$		−	2678.59i		−	0.118378i
$801$	10132.9	−	22815.0i	0.446975	−	1.00640i
$802$	6896.13			0.303629
$803$	−12079.5	+	20922.4i	−0.530856	+	0.919470i
$804$	582.132	+	11011.3i	0.0255351	+	0.483007i
$805$	−35956.2	−	4895.78i	−1.57427	−	0.214352i
$806$	40338.9	−	23289.7i	1.76288	−	1.01780i
$807$	−18220.6	+	11844.5i	−0.794791	+	0.516661i
$808$	−836.313	−	482.846i	−0.0364126	−	0.0210228i
$809$			20951.2i			0.910513i	0.890360	+	0.455256i	$0.150452\pi$
$809$			20951.2i			0.910513i	−0.890360	+	0.455256i	$0.849548\pi$
$810$	24627.8	−	22256.8i	1.06831	−	0.965462i
$811$		−	22578.2i		−	0.977592i	−0.872398	−	0.488796i	$-0.837436\pi$
$811$		−	22578.2i		−	0.977592i	0.872398	−	0.488796i	$-0.162564\pi$
$812$	1661.06	+	4060.92i	0.0717880	+	0.175505i
$813$	−1852.63	−	2849.94i	−0.0799196	−	0.122942i
$814$	−360.343	−	624.133i	−0.0155160	−	0.0268745i
$815$	−5678.23	−	9834.98i	−0.244049	−	0.422705i
$816$	487.922	+	9229.25i	0.0209322	+	0.395942i
$817$	14773.8	+	8529.64i	0.632643	+	0.365256i
$818$	−26477.1			−1.13172
$819$	16480.2	+	30608.6i	0.703132	+	1.30592i
$820$	28582.1			1.21723
$821$	35093.8	+	20261.4i	1.49182	+	0.861300i	0.999956	−	0.00937459i	$-0.00298407\pi$
$821$	35093.8	+	20261.4i	1.49182	+	0.861300i	0.491859	+	0.870675i	$0.336317\pi$
$822$	20150.7	+	10255.7i	0.855034	+	0.435168i
$823$	15823.1	+	27406.4i	0.670181	+	1.16079i	0.977853	+	0.209295i	$0.0671168\pi$
$823$	15823.1	+	27406.4i	0.670181	+	1.16079i	−0.307672	+	0.951493i	$0.599550\pi$
$824$	−303.312	−	525.352i	−0.0128233	−	0.0222105i
$825$	1214.07	−	2385.45i	0.0512346	−	0.100667i
$826$	−15455.1	−	37784.1i	−0.651029	−	1.59162i
$827$			19924.2i			0.837766i	0.908040	+	0.418883i	$0.137578\pi$
$827$			19924.2i			0.837766i	−0.908040	+	0.418883i	$0.862422\pi$
$828$	26675.1	−	19418.0i	1.11960	−	0.815001i
$829$			27088.6i			1.13489i	0.823410	+	0.567447i	$0.192069\pi$
$829$			27088.6i			1.13489i	−0.823410	+	0.567447i	$0.807931\pi$
$830$	−17055.0	−	9846.72i	−0.713239	−	0.411789i
$831$	−1003.33	−	18978.4i	−0.0418835	−	0.792244i
$832$	−24949.5	+	14404.6i	−1.03962	+	0.600227i
$833$	−6277.97	+	6167.76i	−0.261127	+	0.256543i
$834$	22412.6	−	14569.5i	0.930559	−	0.604918i
$835$	−16564.9	+	28691.3i	−0.686529	+	1.18910i
$836$	14257.9			0.589856
$837$	−15165.1	−	18674.9i	−0.626265	−	0.771205i
$838$			41837.2i			1.72463i
$839$	2785.92	−	4825.35i	0.114637	−	0.198557i	−0.802997	−	0.595982i	$-0.796763\pi$
$839$	2785.92	−	4825.35i	0.114637	−	0.198557i	0.917635	+	0.397425i	$0.130096\pi$
$840$	264.381	−	3196.98i	0.0108595	−	0.131317i
$841$	−11663.3	−	20201.4i	−0.478218	−	0.828298i
$842$	−9643.25	+	5567.53i	−0.394689	+	0.227874i
$843$	14699.1	−	777.097i	0.600552	−	0.0317493i
$844$	−14668.0	+	25405.8i	−0.598216	+	1.03614i
$845$	−30718.7			−1.25060
$846$	1654.91	+	15607.9i	0.0672541	+	0.634292i
$847$	13811.9	+	10695.7i	0.560311	+	0.433896i
$848$	−3586.14	−	2070.46i	−0.145222	−	0.0838442i
$849$	21441.0	−	42128.0i	0.866729	−	1.70298i
$850$	−937.858	+	541.473i	−0.0378450	+	0.0218498i
$851$	−563.160	+	325.141i	−0.0226849	+	0.0130972i
$852$	52.3595	−	102.878i	0.00210541	−	0.00413678i
$853$	−14771.1	−	8528.09i	−0.592910	−	0.342317i	0.173337	−	0.984863i	$-0.444545\pi$
$853$	−14771.1	−	8528.09i	−0.592910	−	0.342317i	−0.766247	+	0.642546i	$0.777878\pi$
$854$	37768.1	+	29247.1i	1.51335	+	1.17191i
$855$	−1364.72	−	12871.1i	−0.0545876	−	0.514832i
$856$	1142.05			0.0456012
$857$	3095.62	−	5361.77i	0.123389	−	0.213716i	−0.797713	−	0.603037i	$-0.793957\pi$
$857$	3095.62	−	5361.77i	0.123389	−	0.213716i	0.921102	+	0.389321i	$0.127290\pi$
$858$	−67219.3	+	3553.67i	−2.67463	+	0.141399i
$859$	4145.84	−	2393.60i	0.164673	−	0.0950740i	−0.415399	−	0.909640i	$-0.636358\pi$
$859$	4145.84	−	2393.60i	0.164673	−	0.0950740i	0.580072	+	0.814565i	$0.303025\pi$
$860$	−17561.8	−	30417.9i	−0.696340	−	1.20610i
$861$	32365.3	+	2676.52i	1.28108	+	0.105941i
$862$	−20454.4	+	35428.0i	−0.808212	+	1.39986i
$863$			20578.3i			0.811694i	0.913941	+	0.405847i	$0.133024\pi$
$863$			20578.3i			0.811694i	−0.913941	+	0.405847i	$0.866976\pi$
$864$	21931.6	+	27007.4i	0.863576	+	1.06344i
$865$	−46401.8			−1.82394
$866$	9924.38	−	17189.5i	0.389427	−	0.674508i
$867$	−18535.7	+	12049.3i	−0.726071	+	0.471989i
$868$	22869.8	+	3113.94i	0.894300	+	0.121767i
$869$	7982.69	−	4608.81i	0.311616	−	0.179911i
$870$	407.156	+	7701.54i	0.0158665	+	0.300123i
$871$	−17578.9	−	10149.2i	−0.683855	−	0.394824i
$872$			5284.59i			0.205228i
$873$	23779.2	−	17309.9i	0.921884	−	0.671079i
$874$		−	27025.8i		−	1.04595i
$875$	−22812.2	+	9330.99i	−0.881362	+	0.360509i
$876$	8677.83	−	17050.5i	0.334699	−	0.657629i
$877$	−18325.1	−	31740.0i	−0.705581	−	1.22210i	−0.966482	−	0.256736i	$-0.917353\pi$
$877$	−18325.1	−	31740.0i	−0.705581	−	1.22210i	0.260901	−	0.965366i	$-0.415980\pi$
$878$	14657.0	+	25386.7i	0.563383	+	0.975808i
$879$	−14248.7	−	7251.87i	−0.546755	−	0.278270i
$880$	33362.9	+	19262.1i	1.27803	+	0.737868i
$881$	−13272.5			−0.507561			−0.253780	−	0.967262i	$-0.581674\pi$
$881$	−13272.5			−0.507561			−0.253780	+	0.967262i	$0.581674\pi$
$882$	−5944.41	+	35695.0i	−0.226937	+	1.36271i
$883$	7209.05			0.274750			0.137375	−	0.990519i	$-0.456134\pi$
$883$	7209.05			0.274750			0.137375	+	0.990519i	$0.456134\pi$
$884$	11227.4	+	6482.15i	0.427171	+	0.246627i
$885$	−1803.34	−	34110.9i	−0.0684955	−	1.29562i
$886$	−5388.34	−	9332.88i	−0.204317	−	0.353888i
$887$	−12074.4	−	20913.5i	−0.457068	−	0.791666i	0.541736	−	0.840549i	$-0.317767\pi$
$887$	−12074.4	−	20913.5i	−0.457068	−	0.791666i	−0.998805	+	0.0488828i	$0.984434\pi$
$888$	−31.3309	−	48.1970i	−0.00118400	−	0.00182138i
$889$	−31464.7	+	12870.2i	−1.18705	+	0.485547i
$890$			42101.0i			1.58565i
$891$	7290.37	+	33992.3i	0.274115	+	1.27810i
$892$		−	42542.0i		−	1.59688i
$893$	5299.99	+	3059.95i	0.198608	+	0.114667i
$894$	10421.9	−	6774.82i	0.389887	−	0.253449i
$895$	24883.8	−	14366.6i	0.929354	−	0.536563i
$896$	6690.90	+	911.028i	0.249472	+	0.0339680i
$897$	3206.51	+	60652.5i	0.119356	+	2.25767i
$898$	15750.0	−	27279.8i	0.585283	−	1.01374i
$899$	5589.24			0.207354
$900$	−860.363	+	1937.18i	−0.0318653	+	0.0717474i
$901$			1532.72i			0.0566730i
$902$	−31441.9	+	54459.0i	−1.16065	+	2.01030i
$903$	−17037.9	−	36088.6i	−0.627890	−	1.32996i
$904$	1819.48	+	3151.44i	0.0669416	+	0.115946i
$905$	25411.0	−	14671.0i	0.933358	−	0.538874i
$906$	26727.2	−	52514.4i	0.980078	−	1.92569i
$907$	14615.6	−	25315.0i	0.535064	−	0.926758i	−0.464096	−	0.885785i	$-0.653621\pi$
$907$	14615.6	−	25315.0i	0.535064	−	0.926758i	0.999160	−	0.0409733i	$-0.0130459\pi$
$908$	−44165.4			−1.61419
$909$	5364.50	+	7369.40i	0.195742	+	0.268897i
$910$	−46353.6	−	35895.6i	−1.68858	−	1.30761i
$911$	−29195.6	−	16856.1i	−1.06179	−	0.613027i	−0.135866	−	0.990727i	$-0.543382\pi$
$911$	−29195.6	−	16856.1i	−1.06179	−	0.613027i	−0.925928	+	0.377700i	$0.876715\pi$
$912$	14796.7	−	782.253i	0.537244	−	0.0284024i
$913$	17861.9	−	10312.6i	0.647473	−	0.373819i
$914$	−733.065	+	423.235i	−0.0265291	+	0.0153166i
$915$	21784.8	+	33512.0i	0.787085	+	1.21079i
$916$	5918.43	+	3417.01i	0.213483	+	0.123255i
$917$	19730.0	+	15278.6i	0.710515	+	0.550212i
$918$	5022.69	−	13138.5i	0.180581	−	0.472368i
$919$	12924.3			0.463912			0.231956	−	0.972726i	$-0.425488\pi$
$919$	12924.3			0.463912			0.231956	+	0.972726i	$0.425488\pi$
$920$	2802.36	−	4853.83i	0.100425	−	0.173941i
$921$	8515.15	+	13099.1i	0.304651	+	0.468652i
$922$	−4023.02	+	2322.69i	−0.143700	+	0.0829651i
$923$	106.249	+	184.029i	0.00378899	+	0.00656273i
$924$	−27413.4	−	19001.3i	−0.976010	−	0.676513i
$925$	20.8879	−	36.1790i	0.000742477	−	0.00128601i
$926$		−	18733.5i		−	0.664817i
$927$	603.735	+	5694.00i	0.0213908	+	0.201743i
$928$	−8083.09			−0.285927
$929$	−14691.7	+	25446.8i	−0.518859	+	0.898690i	0.480901	+	0.876775i	$0.340310\pi$
$929$	−14691.7	+	25446.8i	−0.518859	+	0.898690i	−0.999760	+	0.0219154i	$0.993024\pi$
$930$	36157.7	+	18402.4i	1.27490	+	0.648858i
$931$	9888.38	+	10065.1i	0.348097	+	0.354317i
$932$	20863.2	−	12045.4i	0.733257	−	0.423346i
$933$	20677.2	+	10523.6i	0.725553	+	0.369269i
$934$	−9995.40	−	5770.85i	−0.350171	−	0.202171i
$935$		−	14259.3i		−	0.498749i
$936$	−5339.30	+	566.126i	−0.186453	+	0.0197697i
$937$		−	42385.1i		−	1.47776i	−0.673837	−	0.738880i	$-0.735355\pi$
$937$		−	42385.1i		−	1.47776i	0.673837	−	0.738880i	$-0.264645\pi$
$938$	−7999.38	−	19556.7i	−0.278453	−	0.680755i
$939$	35996.6	−	1903.03i	1.25102	−	0.0661373i
$940$	−6300.17	−	10912.2i	−0.218605	−	0.378635i
$941$	16870.2	+	29220.1i	0.584436	+	1.01227i	0.994946	+	0.100416i	$0.0320174\pi$
$941$	16870.2	+	29220.1i	0.584436	+	1.01227i	−0.410510	+	0.911856i	$0.634649\pi$
$942$	22868.9	−	14866.1i	0.790986	−	0.514187i
$943$	49138.8	+	28370.3i	1.69690	+	0.979708i
$944$	39104.5			1.34825
$945$	−14529.2	+	26565.7i	−0.500143	+	0.914478i
$946$	77275.8			2.65587
$947$	26763.4	+	15451.8i	0.918366	+	0.530219i	0.883113	−	0.469160i	$-0.155443\pi$
$947$	26763.4	+	15451.8i	0.918366	+	0.530219i	0.0352526	+	0.999378i	$0.488776\pi$
$948$	−6120.06	+	3978.40i	−0.209673	+	0.136300i
$949$	17609.3	+	30500.2i	0.602341	+	1.04328i
$950$	868.108	+	1503.61i	0.0296475	+	0.0513510i
$951$	−29562.4	+	1562.87i	−1.00802	+	0.0532908i
$952$	−514.615	−	1258.12i	−0.0175197	−	0.0428317i
$953$			14796.1i			0.502931i	0.967866	+	0.251465i	$0.0809125\pi$
$953$			14796.1i			0.502931i	−0.967866	+	0.251465i	$0.919088\pi$
$954$	3708.98	+	5095.15i	0.125873	+	0.172916i
$955$			5373.39i			0.182072i
$956$	16089.7	+	9289.42i	0.544330	+	0.314269i
$957$	−7198.49	−	3663.66i	−0.243150	−	0.123751i
$958$	−369.653	+	213.419i	−0.0124665	+	0.00719756i
$959$	−20436.0	−	2782.55i	−0.688124	−	0.0936946i
$960$	−22363.4	−	11381.8i	−0.751849	−	0.382653i
$961$	−194.153	+	336.283i	−0.00651716	+	0.0112881i
$962$	−1050.60			−0.0352107
$963$	−9851.88	−	4375.53i	−0.329670	−	0.146417i
$964$		−	15112.4i		−	0.504914i
$965$	14929.6	−	25858.8i	0.498032	−	0.862617i
$966$	−36017.1	+	51962.1i	−1.19962	+	1.73070i
$967$	−9085.95	−	15737.3i	−0.302156	−	0.523349i	0.674468	−	0.738304i	$-0.264373\pi$
$967$	−9085.95	−	15737.3i	−0.302156	−	0.523349i	−0.976624	+	0.214955i	$0.931040\pi$
$968$	−2336.64	+	1349.06i	−0.0775851	+	0.0447938i
$969$	−2989.17	−	4598.31i	−0.0990981	−	0.152445i
$970$	−24801.5	+	42957.5i	−0.820957	+	1.42194i
$971$	−36450.4			−1.20468			−0.602342	−	0.798238i	$-0.705766\pi$
$971$	−36450.4			−1.20468			−0.602342	+	0.798238i	$0.705766\pi$
$972$	−7186.38	−	26576.4i	−0.237143	−	0.876996i
$973$	−14929.6	+	19279.2i	−0.491901	+	0.635215i
$974$	12232.7	+	7062.56i	0.402424	+	0.232340i
$975$	−2126.64	−	3271.46i	−0.0698534	−	0.107457i
$976$	−39627.5	+	22879.0i	−1.29964	+	0.750346i
$977$	4369.47	−	2522.71i	0.143083	−	0.0826088i	−0.426750	−	0.904370i	$-0.640341\pi$
$977$	4369.47	−	2522.71i	0.143083	−	0.0826088i	0.569832	+	0.821761i	$0.307008\pi$
$978$	−19758.6	+	1044.58i	−0.646023	+	0.0341532i
$979$	−38185.5	−	22046.4i	−1.24659	−	0.719720i
$980$	−7270.12	−	28126.4i	−0.236975	−	0.916800i
$981$	20246.8	−	45587.3i	0.658949	−	1.48368i
$982$	−73455.8			−2.38704
$983$	−24464.8	+	42374.3i	−0.793802	+	1.37491i	0.129795	+	0.991541i	$0.458568\pi$
$983$	−24464.8	+	42374.3i	−0.793802	+	1.37491i	−0.923597	+	0.383364i	$0.874765\pi$
$984$	−2275.14	+	4470.26i	−0.0737080	+	0.144824i
$985$	37996.2	−	21937.1i	1.22909	−	0.709618i
$986$	1633.98	+	2830.14i	0.0527755	+	0.0914099i
$987$	−6112.22	−	12946.5i	−0.197117	−	0.417521i
$988$	10392.4	−	18000.2i	0.334643	−	0.579618i
$989$		−	69726.6i		−	2.24184i
$990$	−34505.6	−	47401.6i	−1.10774	−	1.52174i
$991$	−41118.3			−1.31803			−0.659014	−	0.752131i	$-0.729026\pi$
$991$	−41118.3			−1.31803			−0.659014	+	0.752131i	$0.729026\pi$
$992$	−21260.9	+	36825.0i	−0.680478	+	1.17862i
$993$	2155.24	+	40767.3i	0.0688766	+	1.30283i
$994$	−29.8430	+	219.177i	−0.000952276	+	0.00699383i
$995$	9677.80	−	5587.48i	0.308349	−	0.178025i
$996$	−13694.1	+	8901.98i	−0.435657	+	0.283203i
$997$	−20713.0	−	11958.7i	−0.657962	−	0.379874i	0.133538	−	0.991044i	$-0.457366\pi$
$997$	−20713.0	−	11958.7i	−0.657962	−	0.379874i	−0.791500	+	0.611169i	$0.790699\pi$
$998$			12667.0i			0.401770i
$999$	85.6181	+	535.807i	0.00271155	+	0.0169692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.20.4	yes	44
3.2	odd	2		189.4.o.a.62.20		44
7.6	odd	2	inner	63.4.o.a.20.3	✓	44
9.2	odd	6		567.4.c.c.566.35		44
9.4	even	3		189.4.o.a.125.19		44
9.5	odd	6	inner	63.4.o.a.41.3	yes	44
9.7	even	3		567.4.c.c.566.10		44
21.20	even	2		189.4.o.a.62.19		44
63.13	odd	6		189.4.o.a.125.20		44
63.20	even	6		567.4.c.c.566.9		44
63.34	odd	6		567.4.c.c.566.36		44
63.41	even	6	inner	63.4.o.a.41.4	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.3	✓	44	7.6	odd	2	inner
63.4.o.a.20.4	yes	44	1.1	even	1	trivial
63.4.o.a.41.3	yes	44	9.5	odd	6	inner
63.4.o.a.41.4	yes	44	63.41	even	6	inner
189.4.o.a.62.19		44	21.20	even	2
189.4.o.a.62.20		44	3.2	odd	2
189.4.o.a.125.19		44	9.4	even	3
189.4.o.a.125.20		44	63.13	odd	6
567.4.c.c.566.9		44	63.20	even	6
567.4.c.c.566.10		44	9.7	even	3
567.4.c.c.566.35		44	9.2	odd	6
567.4.c.c.566.36		44	63.34	odd	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.38393 - 1.95371i) q^{2} +(4.35656 - 2.83202i) q^{3} +(3.63397 + 6.29422i) q^{4} +(-5.82670 - 10.0921i) q^{5} +(-20.2752 + 1.07189i) q^{6} +(17.1417 - 7.01157i) q^{7} +2.86048i q^{8} +(10.9593 - 24.6758i) q^{9} +O(q^{10})\)	\(q+(-3.38393 - 1.95371i) q^{2} +(4.35656 - 2.83202i) q^{3} +(3.63397 + 6.29422i) q^{4} +(-5.82670 - 10.0921i) q^{5} +(-20.2752 + 1.07189i) q^{6} +(17.1417 - 7.01157i) q^{7} +2.86048i q^{8} +(10.9593 - 24.6758i) q^{9} +45.5347i q^{10} +(-41.2999 - 23.8445i) q^{11} +(33.6570 + 17.1297i) q^{12} +(-60.2061 + 34.7600i) q^{13} +(-71.7048 - 9.76328i) q^{14} +(-53.9655 - 27.4657i) q^{15} +(34.6603 - 60.0334i) q^{16} -25.6583 q^{17} +(-85.2948 + 62.0897i) q^{18} +41.1363i q^{19} +(42.3481 - 73.3490i) q^{20} +(54.8220 - 79.0920i) q^{21} +(93.1705 + 161.376i) q^{22} +(145.611 - 84.0685i) q^{23} +(8.10093 + 12.4618i) q^{24} +(-5.40080 + 9.35446i) q^{25} +271.644 q^{26} +(-22.1374 - 138.539i) q^{27} +(106.425 + 82.4138i) q^{28} +(28.2286 + 16.2978i) q^{29} +(128.955 + 198.375i) q^{30} +(148.499 - 85.7361i) q^{31} +(-214.758 + 123.990i) q^{32} +(-247.454 + 13.0821i) q^{33} +(86.8259 + 50.1290i) q^{34} +(-170.641 - 132.142i) q^{35} +(195.140 - 20.6908i) q^{36} -3.86757 q^{37} +(80.3685 - 139.202i) q^{38} +(-163.851 + 321.939i) q^{39} +(28.8683 - 16.6671i) q^{40} +(168.733 + 292.255i) q^{41} +(-340.036 + 160.535i) q^{42} +(207.351 - 359.142i) q^{43} -346.601i q^{44} +(-312.888 + 33.1755i) q^{45} -656.982 q^{46} +(74.3856 - 128.840i) q^{47} +(-19.0161 - 359.698i) q^{48} +(244.676 - 240.380i) q^{49} +(36.5518 - 21.1032i) q^{50} +(-111.782 + 72.6650i) q^{51} +(-437.574 - 252.633i) q^{52} -59.7358i q^{53} +(-195.753 + 512.054i) q^{54} +555.739i q^{55} +(20.0564 + 49.0334i) q^{56} +(116.499 + 179.213i) q^{57} +(-63.6824 - 110.301i) q^{58} +(282.056 + 488.535i) q^{59} +(-23.2340 - 439.480i) q^{60} +(-571.656 - 330.046i) q^{61} -670.014 q^{62} +(14.8451 - 499.827i) q^{63} +414.401 q^{64} +(701.605 + 405.072i) q^{65} +(862.924 + 439.184i) q^{66} +(145.989 + 252.861i) q^{67} +(-93.2416 - 161.499i) q^{68} +(396.280 - 778.623i) q^{69} +(319.270 + 780.542i) q^{70} -3.05665i q^{71} +(70.5845 + 31.3488i) q^{72} -506.596i q^{73} +(13.0876 + 7.55611i) q^{74} +(2.96311 + 56.0485i) q^{75} +(-258.921 + 149.488i) q^{76} +(-875.138 - 119.158i) q^{77} +(1183.43 - 769.302i) q^{78} +(-96.6430 + 167.391i) q^{79} -807.820 q^{80} +(-488.788 - 540.858i) q^{81} -1318.62i q^{82} +(-216.246 + 374.550i) q^{83} +(697.044 + 57.6436i) q^{84} +(149.503 + 258.947i) q^{85} +(-1403.32 + 810.206i) q^{86} +(169.136 - 8.94167i) q^{87} +(68.2066 - 118.137i) q^{88} +924.591 q^{89} +(1123.60 + 499.029i) q^{90} +(-788.312 + 1017.98i) q^{91} +(1058.29 + 611.005i) q^{92} +(404.140 - 794.068i) q^{93} +(-503.430 + 290.656i) q^{94} +(415.154 - 239.689i) q^{95} +(-584.462 + 1148.37i) q^{96} +(943.401 + 544.673i) q^{97} +(-1297.60 + 335.404i) q^{98} +(-1041.00 + 757.788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

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