LMFDB - Embedded newform 63.4.o.a.41.3

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			41.3
Character	$\chi$	$=$	63.41
Dual form			63.4.o.a.20.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.38393 + 1.95371i) q^{2} +(-4.35656 - 2.83202i) q^{3} +(3.63397 - 6.29422i) q^{4} +(5.82670 - 10.0921i) q^{5} +(20.2752 + 1.07189i) q^{6} +(-2.49865 + 18.3509i) q^{7} -2.86048i q^{8} +(10.9593 + 24.6758i) q^{9} +O(q^{10})$	\(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} +(-2.49865 + 18.3509i) 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} +(-27.3972 - 66.9798i) 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} +(62.8558 - 72.8708i) 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} +(-70.3309 + 369.391i) 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} +(-330.513 - 91.7052i) 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} +(52.4924 + 7.14733i) 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} +(-480.207 + 139.457i) 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} +(-835.605 - 113.775i) 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} +(-334.375 - 817.471i) 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} +(-230.249 - 660.438i) 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.959750	−	0.280855i	$-0.909382\pi$
$2$	−3.38393	+	1.95371i	−1.19640	+	0.690741i	−0.236648	+	0.971595i	$0.576049\pi$
$3$	−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	−0.478542	−	0.878065i	$-0.658834\pi$
$5$	5.82670	−	10.0921i	0.521156	−	0.902668i	0.999697	−	0.0246032i	$-0.00783223\pi$
$6$	20.2752	+	1.07189i	1.37956	+	0.0729328i
$7$	−2.49865	+	18.3509i	−0.134915	+	0.990857i
$7$	−2.49865	+	18.3509i	−0.134915	+	0.990857i
$8$		−	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	−0.944446	−	0.328667i	$-0.893401\pi$
$11$	−41.2999	+	23.8445i	−1.13203	+	0.653581i	−0.187589	+	0.982248i	$0.560067\pi$
$12$	−33.6570	+	17.1297i	−0.809661	+	0.412076i
$13$	60.2061	+	34.7600i	1.28447	+	0.741591i	0.977663	−	0.210179i	$-0.0674047\pi$
$13$	60.2061	+	34.7600i	1.28447	+	0.741591i	0.306811	+	0.951770i	$0.400738\pi$
$14$	−27.3972	−	66.9798i	−0.523014	−	1.27865i
$15$	−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	$-0.441409\pi$
$17$	25.6583			0.366062			0.183031	+	0.983107i	$0.441409\pi$
$18$	−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
$21$	62.8558	−	72.8708i	0.653155	−	0.757224i
$22$	93.1705	−	161.376i	0.902910	−	1.56389i
$23$	145.611	+	84.0685i	1.32009	+	0.762152i	0.983742	−	0.179587i	$-0.0574761\pi$
$23$	145.611	+	84.0685i	1.32009	+	0.762152i	0.336344	+	0.941739i	$0.390809\pi$
$24$	−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	−0.406892	−	0.913476i	$-0.633387\pi$
$29$	28.2286	−	16.2978i	0.180756	−	0.104360i	0.587648	+	0.809117i	$0.300054\pi$
$30$	128.955	−	198.375i	0.784797	−	1.20727i
$31$	−148.499	−	85.7361i	−0.860363	−	0.496731i	0.00377092	−	0.999993i	$-0.498800\pi$
$31$	−148.499	−	85.7361i	−0.860363	−	0.496731i	−0.864134	+	0.503262i	$0.832133\pi$
$32$	−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	0.342097	+	0.939665i	$0.388863\pi$
$41$	−168.733	+	292.255i	−0.642725	+	1.11323i	−0.984822	+	0.173568i	$0.944471\pi$
$42$	−70.3309	+	369.391i	−0.258388	+	1.35710i
$43$	207.351	+	359.142i	0.735364	+	1.27369i	0.954563	+	0.298008i	$0.0963223\pi$
$43$	207.351	+	359.142i	0.735364	+	1.27369i	−0.219199	+	0.975680i	$0.570344\pi$
$44$			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	$-0.240819\pi$
$47$	−74.3856	−	128.840i	−0.230856	−	0.399855i	−0.958060	+	0.286566i	$0.907486\pi$
$48$	19.0161	−	359.698i	0.0571821	−	1.08162i
$49$	−330.513	−	91.7052i	−0.963596	−	0.267362i
$50$	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	$0.0246647\pi$
$53$			59.7358i			0.154818i	−0.996999	+	0.0774089i	$0.975335\pi$
$54$	195.753	+	512.054i	0.493307	+	1.29040i
$55$			555.739i			1.36247i
$56$	52.4924	+	7.14733i	0.125261	+	0.0170554i
$57$	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	0.366659	+	0.930355i	$0.380502\pi$
$59$	−282.056	+	488.535i	−0.622382	+	1.07800i	−0.989041	+	0.147642i	$0.952832\pi$
$60$	−23.2340	+	439.480i	−0.0499915	+	0.945611i
$61$	571.656	−	330.046i	1.19989	−	0.692754i	0.239356	−	0.970932i	$-0.423064\pi$
$61$	571.656	−	330.046i	1.19989	−	0.692754i	0.960530	+	0.278178i	$0.0897304\pi$
$62$	670.014			1.37245
$63$	−480.207	+	139.457i	−0.960324	+	0.278888i
$64$	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	−0.701677	−	0.712495i	$-0.747565\pi$
$67$	145.989	−	252.861i	0.266200	−	0.461073i	0.967877	+	0.251423i	$0.0808984\pi$
$68$	93.2416	−	161.499i	0.166282	−	0.288010i
$69$	−396.280	−	778.623i	−0.691398	−	1.35848i
$70$	−835.605	−	113.775i	−1.42677	−	0.194268i
$71$			3.05665i			0.00510927i	0.999997	+	0.00255464i	$0.000813166\pi$
$71$			3.05665i			0.00510927i	−0.999997	+	0.00255464i	$0.999187\pi$
$72$	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
$77$	−334.375	−	817.471i	−0.494877	−	1.20986i
$78$	1183.43	+	769.302i	1.71792	+	1.11675i
$79$	−96.6430	−	167.391i	−0.137635	−	0.238391i	0.788966	−	0.614437i	$-0.210617\pi$
$79$	−96.6430	−	167.391i	−0.137635	−	0.238391i	−0.926601	+	0.376046i	$0.877284\pi$
$80$	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	$-0.0743484\pi$
$83$	216.246	+	374.550i	0.285977	+	0.495327i	−0.686868	+	0.726782i	$0.741015\pi$
$84$	−230.249	−	660.438i	−0.299074	−	0.857854i
$85$	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	$-0.685600\pi$
$89$	−924.591			−1.10120			−0.550598	+	0.834771i	$0.685600\pi$
$90$	−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	$-0.859776\pi$
$97$	−943.401	+	544.673i	−0.987503	+	0.570135i	−0.0829763	+	0.996552i	$0.526443\pi$
$98$	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	$-0.113485\pi$
$101$	168.799	+	292.369i	0.166298	+	0.288037i	−0.770817	+	0.637056i	$0.780152\pi$
$102$	520.229	+	27.5029i	0.505003	+	0.0266979i
$103$	183.659	+	106.035i	0.175694	+	0.101437i	0.585268	−	0.810840i	$-0.300989\pi$
$103$	183.659	+	106.035i	0.175694	+	0.101437i	−0.409574	+	0.912277i	$0.634323\pi$
$104$	99.4302	−	172.218i	0.0937493	−	0.162379i
$105$	−369.180	−	1058.95i	−0.343127	−	0.984214i
$106$	−116.706	−	202.142i	−0.106939	−	0.185224i
$107$			399.253i			0.360722i	0.983600	+	0.180361i	$0.0577266\pi$
$107$			399.253i			0.360722i	−0.983600	+	0.180361i	$0.942273\pi$
$108$	−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
$112$	−1188.27	+	486.046i	−1.00251	+	0.410063i
$113$	1101.72	+	636.078i	0.917177	+	0.529532i	0.882733	−	0.469874i	$-0.155701\pi$
$113$	1101.72	+	636.078i	0.917177	+	0.529532i	0.0344435	+	0.999407i	$0.489034\pi$
$114$	−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
$119$	−64.1112	+	470.854i	−0.0493871	+	0.362716i
$120$	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
$126$	1352.53	−	1410.10i	0.956290	−	0.996996i
$127$	−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	$-0.981668\pi$
$131$	−673.698	+	1166.88i	−0.449323	+	0.778250i	0.549019	+	0.835810i	$0.315001\pi$
$132$	981.581	−	1509.99i	0.647240	−	0.995664i
$133$	−754.890	−	102.785i	−0.492160	−	0.0670122i
$134$			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	−0.769605	−	0.638521i	$-0.779547\pi$
$137$	−964.423	+	556.810i	−0.601432	+	0.347237i	0.168173	+	0.985758i	$0.446213\pi$
$138$	2862.19	+	1860.59i	1.76555	+	1.14771i
$139$	1140.22	+	658.307i	0.695772	+	0.401704i	0.805771	−	0.592228i	$-0.201751\pi$
$139$	1140.22	+	658.307i	0.695772	+	0.401704i	−0.109999	+	0.993932i	$0.535085\pi$
$140$	1451.84	−	593.853i	0.876447	−	0.358498i
$141$	−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
$147$	1180.19	+	1335.54i	0.662181	+	0.749344i
$148$	−14.0546	+	24.3433i	−0.00780596	+	0.0135203i
$149$	−530.202	−	306.112i	−0.291516	−	0.168307i	0.347110	−	0.937825i	$-0.387163\pi$
$149$	−530.202	−	306.112i	−0.291516	−	0.168307i	−0.638625	+	0.769518i	$0.720497\pi$
$150$	−99.4755	−	195.453i	−0.0541476	−	0.106391i
$151$	−1451.09	−	2513.36i	−0.782040	−	1.35453i	−0.930752	−	0.365652i	$-0.880846\pi$
$151$	−1451.09	−	2513.36i	−0.782040	−	1.35453i	0.148712	−	0.988881i	$-0.452487\pi$
$152$	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	$-0.222414\pi$
$157$	1163.43	+	671.708i	0.591414	+	0.341453i	−0.174242	+	0.984703i	$0.555748\pi$
$158$	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	−0.322302	−	0.946637i	$-0.604457\pi$
$167$	1421.47	−	2462.05i	0.658661	−	1.14083i	0.980963	−	0.194197i	$-0.0622100\pi$
$168$	−208.445	−	179.797i	−0.0957255	−	0.0825695i
$169$	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	−0.856817	−	0.515621i	$-0.827561\pi$
$173$	−1990.91	−	3448.36i	−0.874949	−	1.51546i	−0.0181322	−	0.999836i	$-0.505772\pi$
$174$	589.812	−	300.184i	0.256974	−	0.130787i
$175$	185.158	−	75.7362i	0.0799806	−	0.0327149i
$176$	−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	$-0.827873\pi$
$179$		−	2465.66i		−	1.02956i	0.857321	−	0.514782i	$-0.172127\pi$
$180$	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	$0.827049\pi$
$182$	678.743	−	4984.92i	0.276439	−	2.03026i
$183$	−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
$189$	2487.00	+	752.402i	0.957156	+	0.289573i
$190$	−1873.13			−0.715217
$191$	−399.325	+	230.550i	−0.151278	+	0.0873405i	−0.573728	−	0.819046i	$-0.694503\pi$
$191$	−399.325	+	230.550i	−0.151278	+	0.0873405i	0.422450	+	0.906386i	$0.361170\pi$
$192$	−1805.36	−	1173.59i	−0.678599	−	0.441129i
$193$	1281.14	−	2219.00i	0.477815	−	0.827600i	−0.521861	−	0.853030i	$-0.674762\pi$
$193$	1281.14	−	2219.00i	0.477815	−	0.827600i	0.999677	+	0.0254302i	$0.00809554\pi$
$194$	2128.27	−	3686.26i	0.787632	−	1.36422i
$195$	−4203.76	−	222.240i	−1.54378	−	0.0816149i
$196$	−1778.29	+	1747.07i	−0.648064	+	0.636687i
$197$		−	3764.93i		−	1.36162i	−0.732458	−	0.680812i	$-0.761627\pi$
$197$		−	3764.93i		−	1.36162i	0.732458	−	0.680812i	$-0.238373\pi$
$198$	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
$203$	228.546	+	558.744i	0.0790188	+	0.193183i
$204$	−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
$210$	3318.15	+	2862.12i	1.09035	+	0.940500i
$211$	2018.18	−	3495.59i	0.658471	−	1.14051i	−0.322541	−	0.946556i	$-0.604537\pi$
$211$	2018.18	−	3495.59i	0.658471	−	1.14051i	0.981012	−	0.193949i	$-0.0621298\pi$
$212$	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	0.522576	−	0.852593i	$-0.324971\pi$
$223$	5069.18	−	2926.69i	1.52223	−	0.878860i	0.999655	−	0.0262676i	$-0.00836219\pi$
$224$	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	0.841781	+	0.539820i	$0.181508\pi$
$227$	3038.38	+	5262.62i	0.888388	+	1.53873i	0.0466072	+	0.998913i	$0.485159\pi$
$228$	−704.653	−	1384.53i	−0.204679	−	0.402160i
$229$	−814.321	−	470.148i	−0.234986	−	0.135669i	0.377884	−	0.925853i	$-0.376652\pi$
$229$	−814.321	−	470.148i	−0.234986	−	0.135669i	−0.612870	+	0.790184i	$0.709985\pi$
$230$	−3828.04	+	6630.35i	−1.09745	+	1.90084i
$231$	−858.370	+	4508.32i	−0.244487	+	1.28409i
$232$	−46.6195	−	80.7473i	−0.0131928	−	0.0228505i
$233$			3314.66i			0.931976i	0.884791	+	0.465988i	$0.154301\pi$
$233$			3314.66i			0.931976i	−0.884791	+	0.465988i	$0.845699\pi$
$234$	−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
$238$	−702.965	−	1718.59i	−0.191456	−	0.468066i
$239$	2213.80	+	1278.14i	0.599158	+	0.345924i	0.768710	−	0.639597i	$-0.220899\pi$
$239$	2213.80	+	1278.14i	0.599158	+	0.345924i	−0.169552	+	0.985521i	$0.554232\pi$
$240$	−3519.32	−	2287.76i	−0.946546	−	0.615311i
$241$	1800.75	−	1039.66i	0.481312	−	0.277886i	−0.239651	−	0.970859i	$-0.577033\pi$
$241$	1800.75	−	1039.66i	0.481312	−	0.277886i	0.720963	+	0.692973i	$0.243700\pi$
$242$			3685.64i			0.979016i
$243$	3661.16	−	972.027i	0.966516	−	0.256607i
$244$		−	4797.50i		−	1.25872i
$245$	−2851.30	+	2801.25i	−0.743523	+	0.730470i
$246$	−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	$-0.702181\pi$
$251$	−4718.74			−1.18663			−0.593316	+	0.804970i	$0.702181\pi$
$252$	−867.283	+	3529.31i	−0.216800	+	0.882245i
$253$	−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	−0.412264	−	0.911064i	$-0.635262\pi$
$257$	2401.45	−	4159.43i	0.582873	−	1.00957i	0.995137	−	0.0985008i	$-0.0314047\pi$
$258$	3819.12	+	7503.94i	0.921582	+	1.81076i
$259$	9.66370	−	70.9735i	0.00231843	−	0.0170273i
$260$		−	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	−0.200776	−	0.979637i	$-0.564346\pi$
$263$	2334.00	−	1347.54i	0.547227	−	0.315941i	0.748003	+	0.663696i	$0.231013\pi$
$264$	37.4211	−	707.836i	0.00872389	−	0.165016i
$265$	602.862	+	348.062i	0.139749	+	0.0806842i
$266$	2755.31	−	1127.02i	0.635108	−	0.259782i
$267$	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	$-0.342817\pi$
$269$	4182.34			0.947961			0.473981	+	0.880535i	$0.342817\pi$
$270$	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
$273$	6317.29	−	2202.40i	1.40051	−	0.488261i
$274$	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	0.993313	−	0.115449i	$-0.0368306\pi$
$277$	1828.75	+	3167.49i	0.396675	+	0.687061i	−0.596638	+	0.802510i	$0.703497\pi$
$278$	−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	−0.216450	−	0.976294i	$-0.569448\pi$
$281$	2453.28	−	1416.40i	0.520819	−	0.300695i	0.737270	+	0.675598i	$0.236115\pi$
$282$	−1370.08	−	2691.99i	−0.289317	−	0.568459i
$283$	−7878.39	−	4548.59i	−1.65485	−	0.955426i	−0.975039	−	0.222035i	$-0.928730\pi$
$283$	−7878.39	−	4548.59i	−1.65485	−	0.955426i	−0.679808	−	0.733390i	$-0.737937\pi$
$284$	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	$-0.734093\pi$
$293$	1538.44	−	2664.66i	0.306747	−	0.531301i	0.977649	+	0.210245i	$0.0674261\pi$
$294$	−6602.94	−	2213.62i	−1.30983	−	0.439118i
$295$	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
$301$	−7108.68	+	2907.71i	−1.36125	+	0.556802i
$302$	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	$0.909836\pi$
$308$	−6360.45	−	866.034i	−1.17669	−	0.160217i
$309$	−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	$-0.966779\pi$
$311$	−2232.53	+	3866.86i	−0.407059	+	0.705046i	0.587500	+	0.809224i	$0.300112\pi$
$312$	−920.899	+	468.691i	−0.167101	+	0.0850461i
$313$	−6007.81	+	3468.61i	−1.08492	+	0.626382i	−0.932221	−	0.361890i	$-0.882131\pi$
$313$	−6007.81	+	3468.61i	−1.08492	+	0.626382i	−0.152704	+	0.988272i	$0.548798\pi$
$314$	−5249.29			−0.943423
$315$	−1390.60	+	5658.89i	−0.248735	+	1.01220i
$316$	−1404.79			−0.250081
$317$	−4933.94	+	2848.61i	−0.874189	+	0.504713i	−0.868738	−	0.495272i	$-0.835068\pi$
$317$	−4933.94	+	2848.61i	−0.874189	+	0.504713i	−0.00545096	+	0.999985i	$0.501735\pi$
$318$	−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
$322$	1641.57	−	12056.2i	0.284103	−	2.08655i
$323$			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
$329$	2550.19	−	1043.12i	0.427345	−	0.174799i
$330$	−595.690	+	11267.7i	−0.0993687	+	1.87960i
$331$	−3928.31	−	6804.03i	−0.652325	−	1.12986i	−0.982557	−	0.185960i	$-0.940461\pi$
$331$	−3928.31	−	6804.03i	−0.652325	−	1.12986i	0.330233	−	0.943900i	$-0.392873\pi$
$332$	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
$336$	6553.28	+	1247.72i	1.06402	+	0.202586i
$337$	2447.80	−	4239.71i	0.395668	−	0.685317i	−0.597518	−	0.801855i	$-0.703846\pi$
$337$	2447.80	−	4239.71i	0.395668	−	0.685317i	0.993186	+	0.116538i	$0.0371798\pi$
$338$	−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	0.633862	−	0.773446i	$-0.281469\pi$
$347$	1816.16	+	1048.56i	0.280969	+	0.162218i	−0.352893	+	0.935664i	$0.614802\pi$
$348$	−670.914	+	1032.08i	−0.103347	+	0.158981i
$349$	−7325.59	+	4229.43i	−1.12358	+	0.648700i	−0.942313	−	0.334734i	$-0.891353\pi$
$349$	−7325.59	+	4229.43i	−1.12358	+	0.648700i	−0.181268	+	0.983434i	$0.558020\pi$
$350$	−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	$-0.181860\pi$
$353$	−316.445	−	548.099i	−0.0477129	−	0.0826412i	−0.888896	+	0.458110i	$0.848527\pi$
$354$	−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
$357$	1612.77	−	1869.74i	0.239095	−	0.277191i
$358$	4817.18	+	8343.60i	0.711162	+	1.23177i
$359$		−	7038.13i		−	1.03470i	−0.855773	−	0.517351i	$-0.826918\pi$
$359$		−	7038.13i		−	1.03470i	0.855773	−	0.517351i	$-0.173082\pi$
$360$	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
$364$	3542.72	+	8661.13i	0.510134	+	1.24716i
$365$	−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	$-0.651195\pi$
$367$	591.654	−	341.591i	0.0841528	−	0.0485856i	0.541486	+	0.840710i	$0.317862\pi$
$368$			11655.4i			1.65103i
$369$	−9060.81	−	960.719i	−1.27828	−	0.135537i
$370$		−	176.109i		−	0.0247445i
$371$	−1096.21	−	149.259i	−0.153402	−	0.0208872i
$372$	6466.67	+	341.873i	0.901293	+	0.0476486i
$373$	−4524.00	+	7835.79i	−0.627999	+	1.08773i	0.359954	+	0.932970i	$0.382792\pi$
$373$	−4524.00	+	7835.79i	−0.627999	+	1.08773i	−0.987953	+	0.154756i	$0.950541\pi$
$374$	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
$378$	−9885.79	+	2312.80i	−1.34516	+	0.314703i
$379$	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	$-0.783417\pi$
$383$	1170.59	−	2027.53i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$384$	−1891.92	−	100.020i	−0.251423	−	0.0132920i
$385$	−10198.3	−	1388.60i	−1.35001	−	0.183817i
$386$			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	−0.397485	−	0.917609i	$-0.630117\pi$
$389$	1522.53	−	879.032i	0.198445	−	0.114572i	0.595930	+	0.803036i	$0.296784\pi$
$390$	14659.4	−	7460.89i	1.90335	−	0.968710i
$391$	3736.13	+	2157.06i	0.483234	+	0.278995i
$392$	−262.321	+	945.426i	−0.0337989	+	0.121814i
$393$	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
$399$	2997.64	+	2585.66i	0.376114	+	0.324423i
$400$	374.386	−	648.456i	0.0467983	−	0.0810571i
$401$	−1528.43	−	882.440i	−0.190340	−	0.109893i	0.401802	−	0.915727i	$-0.368384\pi$
$401$	−1528.43	−	882.440i	−0.190340	−	0.109893i	−0.592142	+	0.805834i	$0.701717\pi$
$402$	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	$-0.467667\pi$
$409$	−5868.28	−	3388.05i	−0.709456	−	0.409605i	−0.810860	+	0.585241i	$0.801000\pi$
$410$	−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	−0.364498	−	0.931204i	$-0.618760\pi$
$419$	5353.56	−	9272.64i	0.624197	−	1.08114i	0.988696	−	0.149937i	$-0.0479071\pi$
$420$	−8006.82	−	1524.47i	−0.930221	−	0.177111i
$421$	1424.86	+	2467.93i	0.164949	+	0.285700i	0.936637	−	0.350301i	$-0.113921\pi$
$421$	1424.86	+	2467.93i	0.164949	+	0.285700i	−0.771688	+	0.636001i	$0.780587\pi$
$422$			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
$427$	4628.28	+	11315.1i	0.524539	+	1.28238i
$428$	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	$0.198918\pi$
$431$			10469.5i			1.17007i	−0.811010	+	0.585033i	$0.801082\pi$
$432$	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	$0.909038\pi$
$434$	−1674.13	+	12295.4i	−0.185163	+	1.35990i
$435$	−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	$-0.532959\pi$
$439$	6497.04	−	3751.07i	0.706349	−	0.407811i	0.809708	+	0.586834i	$0.199626\pi$
$440$	1589.68			0.172238
$441$	−1359.30	−	9160.70i	−0.146777	−	0.989170i
$442$	−6969.93			−0.750058
$443$	2388.50	−	1379.00i	0.256165	−	0.147897i	−0.366419	−	0.930450i	$-0.619416\pi$
$443$	2388.50	−	1379.00i	0.256165	−	0.147897i	0.622584	+	0.782553i	$0.286083\pi$
$444$	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
$448$	−1035.44	+	7604.64i	−0.109197	+	0.801977i
$449$		−	8061.59i		−	0.847327i	−0.905820	−	0.423663i	$-0.860744\pi$
$449$		−	8061.59i		−	0.847327i	0.905820	−	0.423663i	$-0.139256\pi$
$450$	−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
$455$	5680.38	+	13887.2i	0.585276	+	1.43087i
$456$	−512.635	−	333.243i	−0.0526455	−	0.0342226i
$457$	108.316	+	187.608i	0.0110871	+	0.0192034i	0.871516	−	0.490368i	$-0.163137\pi$
$457$	108.316	+	187.608i	0.0110871	+	0.0192034i	−0.860429	+	0.509571i	$0.829804\pi$
$458$	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	$-0.185794\pi$
$461$	−594.431	−	1029.59i	−0.0600552	−	0.104019i	−0.894490	+	0.447088i	$0.852461\pi$
$462$	−5903.29	−	16932.8i	−0.594472	−	1.70517i
$463$	2397.17	−	4152.02i	0.240617	−	0.416761i	−0.720273	−	0.693691i	$-0.755983\pi$
$463$	2397.17	−	4152.02i	0.240617	−	0.416761i	0.960890	+	0.276929i	$0.0893168\pi$
$464$	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	$-0.546751\pi$
$467$	−2953.79			−0.292687			−0.146344	+	0.989234i	$0.546751\pi$
$468$	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	$-0.168325\pi$
$479$	−54.6189	−	94.6028i	−0.00521003	−	0.00902403i	−0.868619	+	0.495481i	$0.834992\pi$
$480$	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
$483$	15278.6	−	5326.59i	1.43934	−	0.501798i
$484$	−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
$490$	4175.77	−	15049.8i	0.384984	−	1.38751i
$491$	16280.5	+	9399.53i	1.49639	+	0.863940i	0.999991	−	0.00415517i	$-0.00132263\pi$
$491$	16280.5	+	9399.53i	1.49639	+	0.863940i	0.496397	+	0.868096i	$0.334656\pi$
$492$	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
$497$	−56.0925	−	7.63752i	−0.00506256	−	0.000689315i
$498$	3982.97	+	7825.88i	0.358396	+	0.704189i
$499$	−1620.89	+	2807.46i	−0.145413	+	0.251862i	−0.929527	−	0.368755i	$-0.879784\pi$
$499$	−1620.89	+	2807.46i	−0.145413	+	0.251862i	0.784114	+	0.620617i	$0.213118\pi$
$500$	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	$-0.432657\pi$
$503$	4737.83			0.419979			0.209989	+	0.977704i	$0.432657\pi$
$504$	398.914	+	1373.62i	0.0352560	+	0.121401i
$505$	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	$-0.797992\pi$
$509$	1272.38	−	2203.83i	0.110800	−	0.191912i	0.916093	+	0.400965i	$0.131325\pi$
$510$	3308.78	−	5089.97i	0.287285	−	0.441937i
$511$	9296.51	+	1265.81i	0.804801	+	0.109581i
$512$		−	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
$518$	105.960	+	259.049i	0.00898770	+	0.0219729i
$519$	−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	$-0.603866\pi$
$521$	−7623.86			−0.641089			−0.320545	+	0.947233i	$0.603866\pi$
$522$	−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
$525$	−1021.14	−	194.421i	−0.0848878	−	0.0161624i
$526$	−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
$546$	−17074.4	+	19794.9i	−1.33831	+	1.55154i
$547$	−10779.8	−	18671.2i	−0.842616	−	1.45945i	−0.887676	−	0.460469i	$-0.847681\pi$
$547$	−10779.8	−	18671.2i	−0.842616	−	1.45945i	0.0450599	−	0.998984i	$-0.485652\pi$
$548$			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
$553$	3313.25	−	1355.24i	0.254781	−	0.104214i
$554$	−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	$0.204791\pi$
$557$			15772.0i			1.19979i	−0.800079	+	0.599895i	$0.795209\pi$
$558$	7342.88	+	16533.1i	0.557077	+	1.25431i
$559$			28830.0i			2.18136i
$560$	−2018.46	+	14824.3i	−0.152313	+	1.11864i
$561$	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	$-0.689255\pi$
$563$	5842.23	−	10119.0i	0.437337	−	0.757489i	0.997483	+	0.0709043i	$0.0225885\pi$
$564$	4710.57	+	3062.15i	0.351686	+	0.228617i
$565$	12838.8	−	7412.46i	0.955984	−	0.551937i
$566$	35546.5			2.63981
$567$	−8703.95	−	10321.1i	−0.644676	−	0.764456i
$568$	8.74349			0.000645896
$569$	−5808.93	+	3353.79i	−0.427984	+	0.247097i	−0.698488	−	0.715622i	$-0.746143\pi$
$569$	−5808.93	+	3353.79i	−0.427984	+	0.247097i	0.270503	+	0.962719i	$0.412810\pi$
$570$	8160.42	+	5304.75i	0.599653	+	0.389810i
$571$	9286.00	−	16083.8i	0.680573	−	1.17879i	−0.294234	−	0.955733i	$-0.595064\pi$
$571$	9286.00	−	16083.8i	0.680573	−	1.17879i	0.974806	−	0.223053i	$-0.0716022\pi$
$572$	−12047.8	+	20867.5i	−0.880674	+	1.52537i
$573$	2392.61	+	126.490i	0.174437	+	0.00922196i
$574$	24198.0	+	3294.78i	1.75959	+	0.239585i
$575$		−	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
$581$	−7413.66	+	3032.45i	−0.529381	+	0.216536i
$582$	−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	$-0.120170\pi$
$587$	2070.04	+	3585.42i	0.145553	+	0.252106i	−0.784026	+	0.620728i	$0.786837\pi$
$588$	12695.0	−	2575.07i	0.890360	−	0.180602i
$589$	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	$-0.665922\pi$
$593$	−14381.9			−0.995945			−0.497973	+	0.867193i	$0.665922\pi$
$594$	−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	0.850378	−	0.526173i	$-0.176374\pi$
$599$	12019.7	+	6939.59i	0.819887	+	0.473362i	−0.0304902	+	0.999535i	$0.509707\pi$
$600$	160.325	+	8.47590i	0.0109088	+	0.000576712i
$601$	−12474.7	+	7202.28i	−0.846680	+	0.488831i	−0.859529	−	0.511087i	$-0.829243\pi$
$601$	−12474.7	+	7202.28i	−0.846680	+	0.488831i	0.0128495	+	0.999917i	$0.495910\pi$
$602$	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	$-0.101791\pi$
$607$	17223.6	+	9944.08i	1.15171	+	0.664938i	0.202404	+	0.979302i	$0.435124\pi$
$608$	5100.51	−	8834.35i	0.340219	−	0.589277i
$609$	586.699	−	3081.45i	0.0390382	−	0.205036i
$610$	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
$616$	−2338.36	+	956.471i	−0.152946	+	0.0625606i
$617$	−8145.01	−	4702.53i	−0.531452	−	0.306834i	0.210155	−	0.977668i	$-0.432603\pi$
$617$	−8145.01	−	4702.53i	−0.531452	−	0.306834i	−0.741608	+	0.670834i	$0.765936\pi$
$618$	3610.07	+	2346.76i	0.234981	+	0.152751i
$619$	−467.098	+	269.679i	−0.0303300	+	0.0175110i	−0.515088	−	0.857137i	$-0.672241\pi$
$619$	−467.098	+	269.679i	−0.0303300	+	0.0175110i	0.484758	+	0.874648i	$0.338908\pi$
$620$			14523.0i			0.940740i
$621$	14870.2	−	18311.7i	0.960902	−	1.18329i
$622$		−	17446.9i		−	1.12469i
$623$	2310.23	−	16967.1i	0.148567	−	1.09113i
$624$	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
$630$	−6350.14	−	21866.1i	−0.401581	−	1.38280i
$631$	−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
$637$	−16711.2	−	17009.9i	−1.03944	−	1.05801i
$638$		−	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	0.215661	−	0.976468i	$-0.430809\pi$
$641$	18973.7	−	10954.5i	1.16914	−	0.675002i	0.953477	+	0.301466i	$0.0974761\pi$
$642$	−427.955	+	8094.95i	−0.0263085	+	0.497636i
$643$	14525.7	+	8386.40i	0.890881	+	0.514350i	0.874231	−	0.485511i	$-0.161366\pi$
$643$	14525.7	+	8386.40i	0.890881	+	0.514350i	0.0166504	+	0.999861i	$0.494700\pi$
$644$	8568.21	+	20947.3i	0.524277	+	1.28174i
$645$	−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	$-0.569092\pi$
$647$	−7088.41			−0.430717			−0.215359	+	0.976535i	$0.569092\pi$
$648$	1547.11	+	1398.17i	0.0937906	+	0.0847610i
$649$		−	26901.9i		−	1.62711i
$650$	1467.09	+	2541.08i	0.0885295	+	0.153338i
$651$	−15581.7	+	5432.25i	−0.938087	+	0.327045i
$652$	3541.37	−	6133.84i	0.212716	−	0.368435i
$653$	3166.83	+	1828.37i	0.189782	+	0.109571i	0.591881	−	0.806026i	$-0.298386\pi$
$653$	3166.83	+	1828.37i	0.189782	+	0.109571i	−0.402098	+	0.915596i	$0.631719\pi$
$654$	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	−0.685813	−	0.727778i	$-0.740553\pi$
$659$	−6740.56	+	3891.66i	−0.398444	+	0.230042i	0.287368	+	0.957820i	$0.407220\pi$
$660$	−9519.63	−	18704.5i	−0.561441	−	1.10314i
$661$	−6895.85	−	3981.32i	−0.405775	−	0.234274i	0.283198	−	0.959062i	$-0.408605\pi$
$661$	−6895.85	−	3981.32i	−0.405775	−	0.234274i	−0.688973	+	0.724787i	$0.741938\pi$
$662$	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
$672$	−22534.0	+	7856.05i	−1.29356	+	0.450973i
$673$	−494.666	−	856.786i	−0.0283328	−	0.0490738i	0.851511	−	0.524336i	$-0.175686\pi$
$673$	−494.666	−	856.786i	−0.0283328	−	0.0490738i	−0.879844	+	0.475262i	$0.842353\pi$
$674$			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	0.987713	+	0.156279i	$0.0499497\pi$
$677$	11083.3	+	19196.9i	0.629198	+	1.08980i	−0.358515	+	0.933524i	$0.616717\pi$
$678$	21655.8	+	14077.5i	1.22668	+	0.797411i
$679$	−7638.02	−	18673.2i	−0.431694	−	1.05539i
$680$	−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	$0.0219426\pi$
$683$			2458.98i			0.137760i	−0.997625	+	0.0688802i	$0.978057\pi$
$684$	−851.142	+	8027.37i	−0.0475793	+	0.448734i
$685$			12977.4i			0.723858i
$686$	2912.73	+	24650.2i	0.162112	+	1.37194i
$687$	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	$-0.432016\pi$
$691$	21148.3	−	12210.0i	1.16428	−	0.672200i	0.952327	+	0.305079i	$0.0986828\pi$
$692$	−28939.6			−1.58977
$693$	16507.2	−	17209.9i	0.904844	−	0.943360i
$694$	−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
$700$	196.157	−	1440.65i	0.0105915	−	0.0777876i
$701$			6521.09i			0.351353i	0.984448	+	0.175676i	$0.0562112\pi$
$701$			6521.09i			0.351353i	−0.984448	+	0.175676i	$0.943789\pi$
$702$	−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
$707$	−5787.01	+	2367.09i	−0.307840	+	0.125918i
$708$	1124.70	−	21274.1i	0.0597016	−	1.12928i
$709$	5031.46	+	8714.75i	0.266517	+	0.461621i	0.967960	−	0.251105i	$-0.0807939\pi$
$709$	5031.46	+	8714.75i	0.266517	+	0.461621i	−0.701443	+	0.712726i	$0.747461\pi$
$710$	−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
$714$	−1804.57	+	9477.96i	−0.0945861	+	0.496784i
$715$	−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	$-0.471483\pi$
$719$	3449.87			0.178941			0.0894704	+	0.995989i	$0.471483\pi$
$720$	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	$-0.848065\pi$
$727$	−18318.1	+	10575.9i	−0.934497	+	0.539532i	−0.0462657	+	0.998929i	$0.514732\pi$
$728$	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	$-0.416255\pi$
$733$	−8853.40	−	5111.51i	−0.446122	−	0.257569i	−0.706191	+	0.708021i	$0.749588\pi$
$734$	−1334.74	+	2311.84i	−0.0671202	+	0.116256i
$735$	20355.1	−	4128.86i	1.02151	−	0.207205i
$736$	−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
$742$	4001.09	−	1636.59i	0.197958	−	0.0809719i
$743$	12936.5	+	7468.90i	0.638755	+	0.368785i	0.784135	−	0.620591i	$-0.213107\pi$
$743$	12936.5	+	7468.90i	0.638755	+	0.368785i	−0.145380	+	0.989376i	$0.546440\pi$
$744$	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
$749$	−7326.67	−	997.595i	−0.357424	−	0.0486666i
$750$	26982.3	+	1426.47i	1.31367	+	0.0694497i
$751$	12330.2	−	21356.5i	0.599113	−	1.03769i	−0.393839	−	0.919180i	$-0.628853\pi$
$751$	12330.2	−	21356.5i	0.599113	−	1.03769i	0.992952	−	0.118515i	$-0.0378135\pi$
$752$	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
$756$	13773.5	−	12919.5i	0.662614	−	0.621531i
$757$	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	$-0.861630\pi$
$761$	−1863.73	+	3228.07i	−0.0887780	+	0.153768i	0.818217	+	0.574910i	$0.194963\pi$
$762$	−37216.5	−	1967.52i	−1.76930	−	0.0935376i
$763$	−4616.14	+	33902.4i	−0.219024	+	1.60859i
$764$			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	$-0.287796\pi$
$769$	5266.10	+	3040.38i	0.246944	+	0.142573i	−0.371420	+	0.928465i	$0.621129\pi$
$770$	37223.3	−	15225.7i	1.74212	−	0.712591i
$771$	−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	$-0.205107\pi$
$773$	34364.4			1.59897			0.799483	+	0.600688i	$0.205107\pi$
$774$	4613.08	−	43507.2i	0.214229	−	2.02046i
$775$			1852.17i			0.0858478i
$776$	1558.02	+	2698.58i	0.0720745	+	0.124837i
$777$	−243.099	+	281.833i	−0.0112241	+	0.0130125i
$778$	−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	$-0.361522\pi$
$787$	−3382.03	−	1952.61i	−0.153185	−	0.0884411i	−0.574633	+	0.818411i	$0.694855\pi$
$788$	−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	$-0.801290\pi$
$797$	2261.24	−	3916.59i	0.100499	−	0.174069i	0.911890	+	0.410434i	$0.134623\pi$
$798$	−15195.4	−	2893.16i	−0.674075	−	0.128342i
$799$	−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
$805$	13738.2	+	33586.9i	0.601502	+	1.47054i
$806$	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	$-0.849548\pi$
$809$		−	20951.2i		−	0.910513i	0.890360	−	0.455256i	$-0.150452\pi$
$810$	−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	$-0.162564\pi$
$812$	4347.39	+	591.938i	0.187886	+	0.0255824i
$813$	−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
$819$	−33758.9	−	8295.82i	−1.44033	−	0.353943i
$820$	28582.1			1.21723
$821$	35093.8	−	20261.4i	1.49182	−	0.861300i	0.491859	−	0.870675i	$-0.336317\pi$
$821$	35093.8	−	20261.4i	1.49182	−	0.861300i	0.999956	+	0.00937459i	$0.00298407\pi$
$822$	−20150.7	+	10255.7i	−0.855034	+	0.435168i
$823$	15823.1	−	27406.4i	0.670181	−	1.16079i	−0.307672	−	0.951493i	$-0.599550\pi$
$823$	15823.1	−	27406.4i	0.670181	−	1.16079i	0.977853	−	0.209295i	$-0.0671168\pi$
$824$	303.312	−	525.352i	0.0128233	−	0.0222105i
$825$	−1214.07	−	2385.45i	−0.0512346	−	0.100667i
$826$	40449.5	+	5507.58i	1.70390	+	0.232002i
$827$		−	19924.2i		−	0.837766i	−0.908040	−	0.418883i	$-0.862422\pi$
$827$		−	19924.2i		−	0.837766i	0.908040	−	0.418883i	$-0.137578\pi$
$828$	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
$833$	−8480.42	−	2353.00i	−0.352736	−	0.0978712i
$834$	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	$-0.203237\pi$
$839$	−2785.92	−	4825.35i	−0.114637	−	0.198557i	−0.917635	+	0.397425i	$0.869904\pi$
$840$	−3029.09	+	1056.03i	−0.124421	+	0.0433768i
$841$	−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	$-0.555455\pi$
$853$	14771.1	−	8528.09i	0.592910	−	0.342317i	0.766247	+	0.642546i	$0.222122\pi$
$854$	−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	$-0.206043\pi$
$857$	−3095.62	−	5361.77i	−0.123389	−	0.213716i	−0.921102	+	0.389321i	$0.872710\pi$
$858$	−67219.3	−	3553.67i	−2.67463	−	0.141399i
$859$	−4145.84	−	2393.60i	−0.164673	−	0.0950740i	0.415399	−	0.909640i	$-0.363642\pi$
$859$	−4145.84	−	2393.60i	−0.164673	−	0.0950740i	−0.580072	+	0.814565i	$0.696975\pi$
$860$	17561.8	−	30417.9i	0.696340	−	1.20610i
$861$	10691.0	+	30665.6i	0.423167	+	1.21380i
$862$	−20454.4	−	35428.0i	−0.808212	−	1.39986i
$863$		−	20578.3i		−	0.811694i	−0.913941	−	0.405847i	$-0.866976\pi$
$863$		−	20578.3i		−	0.811694i	0.913941	−	0.405847i	$-0.133024\pi$
$864$	−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
$868$	−8738.16	−	21362.8i	−0.341696	−	0.835370i
$869$	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
$875$	−3325.20	+	24421.4i	−0.128471	+	0.943536i
$876$	8677.83	+	17050.5i	0.334699	+	0.657629i
$877$	−18325.1	+	31740.0i	−0.705581	+	1.22210i	0.260901	+	0.965366i	$0.415980\pi$
$877$	−18325.1	+	31740.0i	−0.705581	+	1.22210i	−0.966482	+	0.256736i	$0.917353\pi$
$878$	−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	$-0.418326\pi$
$881$	13272.5			0.507561			0.253780	+	0.967262i	$0.418326\pi$
$882$	22497.1	+	28343.4i	0.858864	+	1.08206i
$883$	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	$-0.682233\pi$
$887$	12074.4	−	20913.5i	0.457068	−	0.791666i	0.998805	+	0.0488828i	$0.0155661\pi$
$888$	31.3309	−	48.1970i	0.00118400	−	0.00182138i
$889$	4586.43	−	33684.3i	0.173030	−	1.27079i
$890$		−	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
$896$	2556.47	+	6250.00i	0.0953190	+	0.233033i
$897$	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
$903$	39204.1	+	7464.34i	1.44477	+	0.275080i
$904$	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	0.999160	+	0.0409733i	$0.0130459\pi$
$907$	14615.6	+	25315.0i	0.535064	+	0.926758i	−0.464096	+	0.885785i	$0.653621\pi$
$908$	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	−0.925928	−	0.377700i	$-0.876715\pi$
$911$	−29195.6	+	16856.1i	−1.06179	+	0.613027i	−0.135866	+	0.990727i	$0.543382\pi$
$912$	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
$924$	25257.1	+	21785.9i	0.899238	+	0.775652i
$925$	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	0.999760	+	0.0219154i	$0.00697643\pi$
$929$	14691.7	+	25446.8i	0.518859	+	0.898690i	−0.480901	+	0.876775i	$0.659690\pi$
$930$	−36157.7	+	18402.4i	−1.27490	+	0.648858i
$931$	3772.42	−	13596.1i	0.132799	−	0.478620i
$932$	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	$-0.264645\pi$
$938$	−20936.3	−	2850.67i	−0.728777	−	0.0992299i
$939$	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	0.410510	+	0.911856i	$0.365351\pi$
$941$	−16870.2	+	29220.1i	−0.584436	+	1.01227i	−0.994946	+	0.100416i	$0.967983\pi$
$942$	22868.9	+	14866.1i	0.790986	+	0.514187i
$943$	−49138.8	+	28370.3i	−1.69690	+	0.979708i
$944$	−39104.5			−1.34825
$945$	22084.3	−	20715.1i	0.760215	−	0.713082i
$946$	77275.8			2.65587
$947$	26763.4	−	15451.8i	0.918366	−	0.530219i	0.0352526	−	0.999378i	$-0.488776\pi$
$947$	26763.4	−	15451.8i	0.918366	−	0.530219i	0.883113	+	0.469160i	$0.155443\pi$
$948$	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
$952$	1346.87	+	183.389i	0.0458532	+	0.00624334i
$953$		−	14796.1i		−	0.502931i	−0.967866	−	0.251465i	$-0.919088\pi$
$953$		−	14796.1i		−	0.502931i	0.967866	−	0.251465i	$-0.0809125\pi$
$954$	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
$959$	−7808.22	−	19089.3i	−0.262920	−	0.642780i
$960$	−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
$966$	−41295.1	+	47874.8i	−1.37541	+	1.59456i
$967$	−9085.95	+	15737.3i	−0.302156	+	0.523349i	−0.976624	−	0.214955i	$-0.931040\pi$
$967$	−9085.95	+	15737.3i	−0.302156	+	0.523349i	0.674468	+	0.738304i	$0.264373\pi$
$968$	−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	$-0.294234\pi$
$971$	36450.4			1.20468			0.602342	+	0.798238i	$0.294234\pi$
$972$	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	0.569832	−	0.821761i	$-0.307008\pi$
$977$	4369.47	+	2522.71i	0.143083	+	0.0826088i	−0.426750	+	0.904370i	$0.640341\pi$
$978$	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	0.923597	+	0.383364i	$0.125235\pi$
$983$	24464.8	+	42374.3i	0.793802	+	1.37491i	−0.129795	+	0.991541i	$0.541432\pi$
$984$	−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
$987$	−14064.2	−	2677.78i	−0.453565	−	0.0863573i
$988$	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
$994$	204.734	−	83.7437i	0.00653297	−	0.00267222i
$995$	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	$-0.542634\pi$
$997$	20713.0	−	11958.7i	0.657962	−	0.379874i	0.791500	+	0.611169i	$0.209301\pi$
$998$		−	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.41.3	yes	44
3.2	odd	2		189.4.o.a.125.19		44
7.6	odd	2	inner	63.4.o.a.41.4	yes	44
9.2	odd	6	inner	63.4.o.a.20.4	yes	44
9.4	even	3		567.4.c.c.566.35		44
9.5	odd	6		567.4.c.c.566.10		44
9.7	even	3		189.4.o.a.62.20		44
21.20	even	2		189.4.o.a.125.20		44
63.13	odd	6		567.4.c.c.566.9		44
63.20	even	6	inner	63.4.o.a.20.3	✓	44
63.34	odd	6		189.4.o.a.62.19		44
63.41	even	6		567.4.c.c.566.36		44

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

\(f(q)\)	\(=\)	\(q+(-3.38393 + 1.95371i) q^{2} +(-4.35656 - 2.83202i) q^{3} +(3.63397 - 6.29422i) q^{4} +(5.82670 - 10.0921i) q^{5} +(20.2752 + 1.07189i) q^{6} +(-2.49865 + 18.3509i) q^{7} -2.86048i q^{8} +(10.9593 + 24.6758i) q^{9} +O(q^{10})\)	\(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} +(-2.49865 + 18.3509i) 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} +(-27.3972 - 66.9798i) 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} +(62.8558 - 72.8708i) 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} +(-70.3309 + 369.391i) 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} +(-330.513 - 91.7052i) 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} +(52.4924 + 7.14733i) 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} +(-480.207 + 139.457i) 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} +(-835.605 - 113.775i) 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} +(-334.375 - 817.471i) 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} +(-230.249 - 660.438i) 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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