LMFDB - Embedded newform 690.3.k.b.277.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, 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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.6
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-3.65385 - 3.41312i) q^{5} +2.44949 q^{6} +(0.283627 + 0.283627i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-3.65385 - 3.41312i) q^{5} +2.44949 q^{6} +(0.283627 + 0.283627i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(0.240725 + 7.06697i) q^{10} +8.31907 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-17.3963 + 17.3963i) q^{13} -0.567254i q^{14} +(8.65523 - 0.294827i) q^{15} -4.00000 q^{16} +(9.44849 + 9.44849i) q^{17} +(-3.00000 + 3.00000i) q^{18} -24.8369i q^{19} +(6.82624 - 7.30769i) q^{20} -0.694742 q^{21} +(-8.31907 - 8.31907i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(1.70120 + 24.9421i) q^{25} +34.7926 q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.567254 + 0.567254i) q^{28} +7.76969i q^{29} +(-8.95006 - 8.36041i) q^{30} -21.7619 q^{31} +(4.00000 + 4.00000i) q^{32} +(-10.1887 + 10.1887i) q^{33} -18.8970i q^{34} +(-0.0682763 - 2.00438i) q^{35} +6.00000 q^{36} +(-22.4355 - 22.4355i) q^{37} +(-24.8369 + 24.8369i) q^{38} -42.6121i q^{39} +(-14.1339 + 0.481451i) q^{40} -2.70246 q^{41} +(0.694742 + 0.694742i) q^{42} +(51.2340 - 51.2340i) q^{43} +16.6381i q^{44} +(-10.2394 + 10.9615i) q^{45} +6.78233 q^{46} +(57.3373 + 57.3373i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.8391i q^{49} +(23.2409 - 26.6433i) q^{50} -23.1440 q^{51} +(-34.7926 - 34.7926i) q^{52} +(57.8310 - 57.8310i) q^{53} -7.34847i q^{54} +(-30.3966 - 28.3940i) q^{55} +1.13451 q^{56} +(30.4189 + 30.4189i) q^{57} +(7.76969 - 7.76969i) q^{58} -17.1617i q^{59} +(0.589655 + 17.3105i) q^{60} +88.9356 q^{61} +(21.7619 + 21.7619i) q^{62} +(0.850881 - 0.850881i) q^{63} -8.00000i q^{64} +(122.939 - 4.18774i) q^{65} +20.3775 q^{66} +(53.5253 + 53.5253i) q^{67} +(-18.8970 + 18.8970i) q^{68} -8.30662i q^{69} +(-1.93611 + 2.07266i) q^{70} -43.1306 q^{71} +(-6.00000 - 6.00000i) q^{72} +(18.0830 - 18.0830i) q^{73} +44.8711i q^{74} +(-32.6312 - 28.4641i) q^{75} +49.6738 q^{76} +(2.35951 + 2.35951i) q^{77} +(-42.6121 + 42.6121i) q^{78} -155.462i q^{79} +(14.6154 + 13.6525i) q^{80} -9.00000 q^{81} +(2.70246 + 2.70246i) q^{82} +(69.5987 - 69.5987i) q^{83} -1.38948i q^{84} +(-2.27449 - 66.7722i) q^{85} -102.468 q^{86} +(-9.51588 - 9.51588i) q^{87} +(16.6381 - 16.6381i) q^{88} -67.8698i q^{89} +(21.2009 - 0.722176i) q^{90} -9.86814 q^{91} +(-6.78233 - 6.78233i) q^{92} +(26.6527 - 26.6527i) q^{93} -114.675i q^{94} +(-84.7714 + 90.7503i) q^{95} -9.79796 q^{96} +(48.4229 + 48.4229i) q^{97} +(-48.8391 + 48.8391i) q^{98} -24.9572i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	−3.65385	−	3.41312i	−0.730769	−	0.682624i
$5$	−3.65385	−	3.41312i	−0.730769	−	0.682624i
$6$	2.44949			0.408248
$7$	0.283627	+	0.283627i	0.0405182	+	0.0405182i	0.727076	−	0.686557i	$-0.240879\pi$
$7$	0.283627	+	0.283627i	0.0405182	+	0.0405182i	−0.686557	+	0.727076i	$0.740879\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	0.240725	+	7.06697i	0.0240725	+	0.706697i
$11$	8.31907			0.756279			0.378140	−	0.925749i	$-0.376564\pi$
$11$	8.31907			0.756279			0.378140	+	0.925749i	$0.376564\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	−17.3963	+	17.3963i	−1.33818	+	1.33818i	−0.440355	+	0.897824i	$0.645147\pi$
$13$	−17.3963	+	17.3963i	−1.33818	+	1.33818i	−0.897824	+	0.440355i	$0.854853\pi$
$14$		−	0.567254i		−	0.0405182i
$15$	8.65523	−	0.294827i	0.577016	−	0.0196552i
$16$	−4.00000			−0.250000
$17$	9.44849	+	9.44849i	0.555794	+	0.555794i	0.928107	−	0.372313i	$-0.121435\pi$
$17$	9.44849	+	9.44849i	0.555794	+	0.555794i	−0.372313	+	0.928107i	$0.621435\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	24.8369i		−	1.30721i	−0.756838	−	0.653603i	$-0.773257\pi$
$19$		−	24.8369i		−	1.30721i	0.756838	−	0.653603i	$-0.226743\pi$
$20$	6.82624	−	7.30769i	0.341312	−	0.365385i
$21$	−0.694742			−0.0330829
$22$	−8.31907	−	8.31907i	−0.378140	−	0.378140i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			4.89898i			0.204124i
$25$	1.70120	+	24.9421i	0.0680480	+	0.997682i
$26$	34.7926			1.33818
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−0.567254	+	0.567254i	−0.0202591	+	0.0202591i
$29$			7.76969i			0.267920i	0.990987	+	0.133960i	$0.0427694\pi$
$29$			7.76969i			0.267920i	−0.990987	+	0.133960i	$0.957231\pi$
$30$	−8.95006	−	8.36041i	−0.298335	−	0.278680i
$31$	−21.7619			−0.701996			−0.350998	−	0.936376i	$-0.614158\pi$
$31$	−21.7619			−0.701996			−0.350998	+	0.936376i	$0.614158\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−10.1887	+	10.1887i	−0.308750	+	0.308750i
$34$		−	18.8970i		−	0.555794i
$35$	−0.0682763	−	2.00438i	−0.00195075	−	0.0572681i
$36$	6.00000			0.166667
$37$	−22.4355	−	22.4355i	−0.606366	−	0.606366i	0.335629	−	0.941994i	$-0.391051\pi$
$37$	−22.4355	−	22.4355i	−0.606366	−	0.606366i	−0.941994	+	0.335629i	$0.891051\pi$
$38$	−24.8369	+	24.8369i	−0.653603	+	0.653603i
$39$		−	42.6121i		−	1.09262i
$40$	−14.1339	+	0.481451i	−0.353348	+	0.0120363i
$41$	−2.70246			−0.0659137			−0.0329569	−	0.999457i	$-0.510492\pi$
$41$	−2.70246			−0.0659137			−0.0329569	+	0.999457i	$0.510492\pi$
$42$	0.694742	+	0.694742i	0.0165415	+	0.0165415i
$43$	51.2340	−	51.2340i	1.19149	−	1.19149i	0.214840	−	0.976649i	$-0.431077\pi$
$43$	51.2340	−	51.2340i	1.19149	−	1.19149i	0.976649	−	0.214840i	$-0.0689231\pi$
$44$			16.6381i			0.378140i
$45$	−10.2394	+	10.9615i	−0.227541	+	0.243590i
$46$	6.78233			0.147442
$47$	57.3373	+	57.3373i	1.21994	+	1.21994i	0.967651	+	0.252292i	$0.0811843\pi$
$47$	57.3373	+	57.3373i	1.21994	+	1.21994i	0.252292	+	0.967651i	$0.418816\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	48.8391i		−	0.996717i
$50$	23.2409	−	26.6433i	0.464817	−	0.532865i
$51$	−23.1440			−0.453804
$52$	−34.7926	−	34.7926i	−0.669089	−	0.669089i
$53$	57.8310	−	57.8310i	1.09115	−	1.09115i	0.0957461	−	0.995406i	$-0.469476\pi$
$53$	57.8310	−	57.8310i	1.09115	−	1.09115i	0.995406	−	0.0957461i	$-0.0305237\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−30.3966	−	28.3940i	−0.552666	−	0.516255i
$56$	1.13451			0.0202591
$57$	30.4189	+	30.4189i	0.533664	+	0.533664i
$58$	7.76969	−	7.76969i	0.133960	−	0.133960i
$59$		−	17.1617i		−	0.290877i	−0.989367	−	0.145439i	$-0.953541\pi$
$59$		−	17.1617i		−	0.290877i	0.989367	−	0.145439i	$-0.0464593\pi$
$60$	0.589655	+	17.3105i	0.00982758	+	0.288508i
$61$	88.9356			1.45796			0.728980	−	0.684535i	$-0.239995\pi$
$61$	88.9356			1.45796			0.728980	+	0.684535i	$0.239995\pi$
$62$	21.7619	+	21.7619i	0.350998	+	0.350998i
$63$	0.850881	−	0.850881i	0.0135061	−	0.0135061i
$64$		−	8.00000i		−	0.125000i
$65$	122.939	−	4.18774i	1.89137	−	0.0644267i
$66$	20.3775			0.308750
$67$	53.5253	+	53.5253i	0.798885	+	0.798885i	0.982920	−	0.184034i	$-0.0589158\pi$
$67$	53.5253	+	53.5253i	0.798885	+	0.798885i	−0.184034	+	0.982920i	$0.558916\pi$
$68$	−18.8970	+	18.8970i	−0.277897	+	0.277897i
$69$		−	8.30662i		−	0.120386i
$70$	−1.93611	+	2.07266i	−0.0276587	+	0.0296094i
$71$	−43.1306			−0.607474			−0.303737	−	0.952756i	$-0.598234\pi$
$71$	−43.1306			−0.607474			−0.303737	+	0.952756i	$0.598234\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	18.0830	−	18.0830i	0.247712	−	0.247712i	−0.572319	−	0.820031i	$-0.693956\pi$
$73$	18.0830	−	18.0830i	0.247712	−	0.247712i	0.820031	+	0.572319i	$0.193956\pi$
$74$			44.8711i			0.606366i
$75$	−32.6312	−	28.4641i	−0.435082	−	0.379522i
$76$	49.6738			0.653603
$77$	2.35951	+	2.35951i	0.0306430	+	0.0306430i
$78$	−42.6121	+	42.6121i	−0.546309	+	0.546309i
$79$		−	155.462i		−	1.96787i	−0.178518	−	0.983937i	$-0.557130\pi$
$79$		−	155.462i		−	1.96787i	0.178518	−	0.983937i	$-0.442870\pi$
$80$	14.6154	+	13.6525i	0.182692	+	0.170656i
$81$	−9.00000			−0.111111
$82$	2.70246	+	2.70246i	0.0329569	+	0.0329569i
$83$	69.5987	−	69.5987i	0.838538	−	0.838538i	−0.150128	−	0.988667i	$-0.547969\pi$
$83$	69.5987	−	69.5987i	0.838538	−	0.838538i	0.988667	+	0.150128i	$0.0479686\pi$
$84$		−	1.38948i		−	0.0165415i
$85$	−2.27449	−	66.7722i	−0.0267587	−	0.785556i
$86$	−102.468			−1.19149
$87$	−9.51588	−	9.51588i	−0.109378	−	0.109378i
$88$	16.6381	−	16.6381i	0.189070	−	0.189070i
$89$		−	67.8698i		−	0.762582i	−0.924455	−	0.381291i	$-0.875480\pi$
$89$		−	67.8698i		−	0.762582i	0.924455	−	0.381291i	$-0.124520\pi$
$90$	21.2009	−	0.722176i	0.235566	−	0.00802418i
$91$	−9.86814			−0.108441
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	26.6527	−	26.6527i	0.286589	−	0.286589i
$94$		−	114.675i		−	1.21994i
$95$	−84.7714	+	90.7503i	−0.892330	+	0.955266i
$96$	−9.79796			−0.102062
$97$	48.4229	+	48.4229i	0.499206	+	0.499206i	0.911191	−	0.411985i	$-0.135164\pi$
$97$	48.4229	+	48.4229i	0.499206	+	0.499206i	−0.411985	+	0.911191i	$0.635164\pi$
$98$	−48.8391	+	48.8391i	−0.498358	+	0.498358i
$99$		−	24.9572i		−	0.252093i
$100$	−49.8841	+	3.40240i	−0.498841	+	0.0340240i
$101$	84.7530			0.839138			0.419569	−	0.907723i	$-0.362181\pi$
$101$	84.7530			0.839138			0.419569	+	0.907723i	$0.362181\pi$
$102$	23.1440	+	23.1440i	0.226902	+	0.226902i
$103$	−86.9504	+	86.9504i	−0.844179	+	0.844179i	−0.989399	−	0.145220i	$-0.953611\pi$
$103$	−86.9504	+	86.9504i	−0.844179	+	0.844179i	0.145220	+	0.989399i	$0.453611\pi$
$104$			69.5853i			0.669089i
$105$	2.53848	+	2.37124i	0.0241760	+	0.0225832i
$106$	−115.662			−1.09115
$107$	−15.5948	−	15.5948i	−0.145746	−	0.145746i	0.630469	−	0.776214i	$-0.282863\pi$
$107$	−15.5948	−	15.5948i	−0.145746	−	0.145746i	−0.776214	+	0.630469i	$0.782863\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			13.7730i			0.126358i	0.998002	+	0.0631789i	$0.0201239\pi$
$109$			13.7730i			0.126358i	−0.998002	+	0.0631789i	$0.979876\pi$
$110$	2.00261	+	58.7906i	0.0182056	+	0.534460i
$111$	54.9556			0.495096
$112$	−1.13451	−	1.13451i	−0.0101295	−	0.0101295i
$113$	105.051	−	105.051i	0.929654	−	0.929654i	−0.0680291	−	0.997683i	$-0.521671\pi$
$113$	105.051	−	105.051i	0.929654	−	0.929654i	0.997683	+	0.0680291i	$0.0216711\pi$
$114$		−	60.8378i		−	0.533664i
$115$	23.9653	−	0.816340i	0.208394	−	0.00709861i
$116$	−15.5394			−0.133960
$117$	52.1890	+	52.1890i	0.446060	+	0.446060i
$118$	−17.1617	+	17.1617i	−0.145439	+	0.145439i
$119$			5.35970i			0.0450395i
$120$	16.7208	−	17.9001i	0.139340	−	0.149168i
$121$	−51.7930			−0.428041
$122$	−88.9356	−	88.9356i	−0.728980	−	0.728980i
$123$	3.30983	−	3.30983i	0.0269092	−	0.0269092i
$124$		−	43.5238i		−	0.350998i
$125$	78.9143	−	96.9408i	0.631315	−	0.775527i
$126$	−1.70176			−0.0135061
$127$	−22.3524	−	22.3524i	−0.176003	−	0.176003i	0.613608	−	0.789611i	$-0.289718\pi$
$127$	−22.3524	−	22.3524i	−0.176003	−	0.176003i	−0.789611	+	0.613608i	$0.789718\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			125.497i			0.972847i
$130$	−127.127	−	118.752i	−0.977900	−	0.913473i
$131$	158.682			1.21131			0.605656	−	0.795727i	$-0.292911\pi$
$131$	158.682			1.21131			0.605656	+	0.795727i	$0.292911\pi$
$132$	−20.3775	−	20.3775i	−0.154375	−	0.154375i
$133$	7.04442	−	7.04442i	0.0529656	−	0.0529656i
$134$		−	107.051i		−	0.798885i
$135$	−0.884482	−	25.9657i	−0.00655172	−	0.192339i
$136$	37.7940			0.277897
$137$	9.76414	+	9.76414i	0.0712711	+	0.0712711i	0.741844	−	0.670573i	$-0.233952\pi$
$137$	9.76414	+	9.76414i	0.0712711	+	0.0712711i	−0.670573	+	0.741844i	$0.733952\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$			83.2727i			0.599084i	0.954083	+	0.299542i	$0.0968339\pi$
$139$			83.2727i			0.599084i	−0.954083	+	0.299542i	$0.903166\pi$
$140$	4.00877	−	0.136553i	0.0286341	−	0.000975375i
$141$	−140.447			−0.996079
$142$	43.1306	+	43.1306i	0.303737	+	0.303737i
$143$	−144.721	+	144.721i	−1.01204	+	1.01204i
$144$			12.0000i			0.0833333i
$145$	26.5189	−	28.3892i	0.182889	−	0.195788i
$146$	−36.1659			−0.247712
$147$	59.8155	+	59.8155i	0.406908	+	0.406908i
$148$	44.8711	−	44.8711i	0.303183	−	0.303183i
$149$		−	274.269i		−	1.84073i	−0.391056	−	0.920367i	$-0.627890\pi$
$149$		−	274.269i		−	1.84073i	0.391056	−	0.920367i	$-0.372110\pi$
$150$	4.16707	+	61.0953i	0.0277805	+	0.407302i
$151$	−8.76603			−0.0580532			−0.0290266	−	0.999579i	$-0.509241\pi$
$151$	−8.76603			−0.0580532			−0.0290266	+	0.999579i	$0.509241\pi$
$152$	−49.6738	−	49.6738i	−0.326801	−	0.326801i
$153$	28.3455	−	28.3455i	0.185265	−	0.185265i
$154$		−	4.71903i		−	0.0306430i
$155$	79.5146	+	74.2759i	0.512997	+	0.479200i
$156$	85.2242			0.546309
$157$	−220.444	−	220.444i	−1.40410	−	1.40410i	−0.786468	−	0.617631i	$-0.788093\pi$
$157$	−220.444	−	220.444i	−1.40410	−	1.40410i	−0.617631	−	0.786468i	$-0.711907\pi$
$158$	−155.462	+	155.462i	−0.983937	+	0.983937i
$159$			141.657i			0.890922i
$160$	−0.962902	−	28.2679i	−0.00601814	−	0.176674i
$161$	−1.92365			−0.0119482
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−61.8205	+	61.8205i	−0.379267	+	0.379267i	−0.870838	−	0.491571i	$-0.836423\pi$
$163$	−61.8205	+	61.8205i	−0.379267	+	0.379267i	0.491571	+	0.870838i	$0.336423\pi$
$164$		−	5.40493i		−	0.0329569i
$165$	72.0035	−	2.45269i	0.436385	−	0.0148648i
$166$	−139.197			−0.838538
$167$	−4.05814	−	4.05814i	−0.0243003	−	0.0243003i	0.694852	−	0.719153i	$-0.255470\pi$
$167$	−4.05814	−	4.05814i	−0.0243003	−	0.0243003i	−0.719153	+	0.694852i	$0.755470\pi$
$168$	−1.38948	+	1.38948i	−0.00827073	+	0.00827073i
$169$		−	436.264i		−	2.58145i
$170$	−64.4977	+	69.0467i	−0.379398	+	0.406157i
$171$	−74.5107			−0.435735
$172$	102.468	+	102.468i	0.595745	+	0.595745i
$173$	−164.608	+	164.608i	−0.951490	+	0.951490i	−0.998877	−	0.0473870i	$-0.984911\pi$
$173$	−164.608	+	164.608i	−0.951490	+	0.951490i	0.0473870	+	0.998877i	$0.484911\pi$
$174$			19.0318i			0.109378i
$175$	−6.59173	+	7.55675i	−0.0376671	+	0.0431814i
$176$	−33.2763			−0.189070
$177$	21.0188	+	21.0188i	0.118750	+	0.118750i
$178$	−67.8698	+	67.8698i	−0.381291	+	0.381291i
$179$			285.884i			1.59712i	0.601917	+	0.798559i	$0.294404\pi$
$179$			285.884i			1.59712i	−0.601917	+	0.798559i	$0.705596\pi$
$180$	−21.9231	−	20.4787i	−0.121795	−	0.113771i
$181$	207.433			1.14604			0.573020	−	0.819542i	$-0.305772\pi$
$181$	207.433			1.14604			0.573020	+	0.819542i	$0.305772\pi$
$182$	9.86814	+	9.86814i	0.0542205	+	0.0542205i
$183$	−108.923	+	108.923i	−0.595210	+	0.595210i
$184$			13.5647i			0.0737210i
$185$	5.40080	+	158.551i	0.0291935	+	0.857034i
$186$	−53.3055			−0.286589
$187$	78.6027	+	78.6027i	0.420335	+	0.420335i
$188$	−114.675	+	114.675i	−0.609972	+	0.609972i
$189$			2.08422i			0.0110276i
$190$	175.522	−	5.97888i	0.923798	−	0.0314678i
$191$	17.3738			0.0909622			0.0454811	−	0.998965i	$-0.485518\pi$
$191$	17.3738			0.0909622			0.0454811	+	0.998965i	$0.485518\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	−141.340	+	141.340i	−0.732330	+	0.732330i	−0.971081	−	0.238751i	$-0.923262\pi$
$193$	−141.340	+	141.340i	−0.732330	+	0.732330i	0.238751	+	0.971081i	$0.423262\pi$
$194$		−	96.8459i		−	0.499206i
$195$	−145.440	+	155.698i	−0.745848	+	0.798452i
$196$	97.6782			0.498358
$197$	213.280	+	213.280i	1.08264	+	1.08264i	0.996262	+	0.0863791i	$0.0275296\pi$
$197$	213.280	+	213.280i	1.08264	+	1.08264i	0.0863791	+	0.996262i	$0.472470\pi$
$198$	−24.9572	+	24.9572i	−0.126047	+	0.126047i
$199$		−	84.3085i		−	0.423661i	−0.977306	−	0.211830i	$-0.932058\pi$
$199$		−	84.3085i		−	0.423661i	0.977306	−	0.211830i	$-0.0679424\pi$
$200$	53.2865	+	46.4817i	0.266433	+	0.232409i
$201$	−131.110			−0.652287
$202$	−84.7530	−	84.7530i	−0.419569	−	0.419569i
$203$	−2.20369	+	2.20369i	−0.0108556	+	0.0108556i
$204$		−	46.2880i		−	0.226902i
$205$	9.87439	+	9.22384i	0.0481677	+	0.0449943i
$206$	173.901			0.844179
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	69.5853	−	69.5853i	0.334545	−	0.334545i
$209$		−	206.620i		−	0.988613i
$210$	−0.167242	−	4.90972i	−0.000796390	−	0.0233796i
$211$	301.566			1.42922			0.714612	−	0.699521i	$-0.246603\pi$
$211$	301.566			1.42922			0.714612	+	0.699521i	$0.246603\pi$
$212$	115.662	+	115.662i	0.545576	+	0.545576i
$213$	52.8240	−	52.8240i	0.248000	−	0.248000i
$214$			31.1895i			0.145746i
$215$	−362.069	+	12.3333i	−1.68404	+	0.0573644i
$216$	14.6969			0.0680414
$217$	−6.17226	−	6.17226i	−0.0284436	−	0.0284436i
$218$	13.7730	−	13.7730i	0.0631789	−	0.0631789i
$219$			44.2940i			0.202256i
$220$	56.7880	−	60.7933i	0.258127	−	0.276333i
$221$	−328.738			−1.48750
$222$	−54.9556	−	54.9556i	−0.247548	−	0.247548i
$223$	41.8331	−	41.8331i	0.187592	−	0.187592i	−0.607062	−	0.794654i	$-0.707652\pi$
$223$	41.8331	−	41.8331i	0.187592	−	0.187592i	0.794654	+	0.607062i	$0.207652\pi$
$224$			2.26902i			0.0101295i
$225$	74.8262	−	5.10360i	0.332561	−	0.0226827i
$226$	−210.102			−0.929654
$227$	135.297	+	135.297i	0.596024	+	0.596024i	0.939252	−	0.343228i	$-0.111520\pi$
$227$	135.297	+	135.297i	0.596024	+	0.596024i	−0.343228	+	0.939252i	$0.611520\pi$
$228$	−60.8378	+	60.8378i	−0.266832	+	0.266832i
$229$			337.019i			1.47170i	0.677145	+	0.735850i	$0.263217\pi$
$229$			337.019i			1.47170i	−0.677145	+	0.735850i	$0.736783\pi$
$230$	−24.7816	−	23.1489i	−0.107746	−	0.100647i
$231$	−5.77961			−0.0250199
$232$	15.5394	+	15.5394i	0.0669801	+	0.0669801i
$233$	−104.797	+	104.797i	−0.449772	+	0.449772i	−0.895279	−	0.445506i	$-0.853024\pi$
$233$	−104.797	+	104.797i	−0.449772	+	0.449772i	0.445506	+	0.895279i	$0.353024\pi$
$234$		−	104.378i		−	0.446060i
$235$	−13.8026	−	405.201i	−0.0587343	−	1.72426i
$236$	34.3235			0.145439
$237$	190.401	+	190.401i	0.803381	+	0.803381i
$238$	5.35970	−	5.35970i	0.0225197	−	0.0225197i
$239$		−	223.047i		−	0.933250i	−0.884455	−	0.466625i	$-0.845470\pi$
$239$		−	223.047i		−	0.933250i	0.884455	−	0.466625i	$-0.154530\pi$
$240$	−34.6209	+	1.17931i	−0.144254	+	0.00491379i
$241$	−167.112			−0.693412			−0.346706	−	0.937974i	$-0.612700\pi$
$241$	−167.112			−0.693412			−0.346706	+	0.937974i	$0.612700\pi$
$242$	51.7930	+	51.7930i	0.214021	+	0.214021i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			177.871i			0.728980i
$245$	−166.694	+	178.451i	−0.680383	+	0.728370i
$246$	−6.61966			−0.0269092
$247$	432.071	+	432.071i	1.74927	+	1.74927i
$248$	−43.5238	+	43.5238i	−0.175499	+	0.175499i
$249$			170.481i			0.684664i
$250$	−175.855	+	18.0265i	−0.703421	+	0.0721060i
$251$	441.419			1.75864			0.879321	−	0.476230i	$-0.157997\pi$
$251$	441.419			1.75864			0.879321	+	0.476230i	$0.157997\pi$
$252$	1.70176	+	1.70176i	0.00675303	+	0.00675303i
$253$	−28.2114	+	28.2114i	−0.111507	+	0.111507i
$254$			44.7049i			0.176003i
$255$	84.5646	+	78.9933i	0.331626	+	0.309777i
$256$	16.0000			0.0625000
$257$	177.198	+	177.198i	0.689485	+	0.689485i	0.962118	−	0.272633i	$-0.0878946\pi$
$257$	177.198	+	177.198i	0.689485	+	0.689485i	−0.272633	+	0.962118i	$0.587895\pi$
$258$	125.497	−	125.497i	0.486424	−	0.486424i
$259$		−	12.7266i		−	0.0491376i
$260$	8.37548	+	245.879i	0.0322134	+	0.945687i
$261$	23.3091			0.0893067
$262$	−158.682	−	158.682i	−0.605656	−	0.605656i
$263$	−229.746	+	229.746i	−0.873558	+	0.873558i	−0.992858	−	0.119300i	$-0.961935\pi$
$263$	−229.746	+	229.746i	−0.873558	+	0.873558i	0.119300	+	0.992858i	$0.461935\pi$
$264$			40.7550i			0.154375i
$265$	−408.690	+	13.9214i	−1.54223	+	0.0525336i
$266$	−14.0888			−0.0529656
$267$	83.1232	+	83.1232i	0.311323	+	0.311323i
$268$	−107.051	+	107.051i	−0.399443	+	0.399443i
$269$			216.650i			0.805389i	0.915334	+	0.402695i	$0.131926\pi$
$269$			216.650i			0.805389i	−0.915334	+	0.402695i	$0.868074\pi$
$270$	−25.0812	+	26.8502i	−0.0928934	+	0.0994451i
$271$	−149.342			−0.551076			−0.275538	−	0.961290i	$-0.588856\pi$
$271$	−149.342			−0.551076			−0.275538	+	0.961290i	$0.588856\pi$
$272$	−37.7940	−	37.7940i	−0.138948	−	0.138948i
$273$	12.0860	−	12.0860i	0.0442709	−	0.0442709i
$274$		−	19.5283i		−	0.0712711i
$275$	14.1524	+	207.495i	0.0514633	+	0.754526i
$276$	16.6132			0.0601929
$277$	−73.9775	−	73.9775i	−0.267067	−	0.267067i	0.560850	−	0.827917i	$-0.310474\pi$
$277$	−73.9775	−	73.9775i	−0.267067	−	0.267067i	−0.827917	+	0.560850i	$0.810474\pi$
$278$	83.2727	−	83.2727i	0.299542	−	0.299542i
$279$			65.2856i			0.233999i
$280$	−4.14532	−	3.87222i	−0.0148047	−	0.0138293i
$281$	220.186			0.783580			0.391790	−	0.920055i	$-0.371856\pi$
$281$	220.186			0.783580			0.391790	+	0.920055i	$0.371856\pi$
$282$	140.447	+	140.447i	0.498040	+	0.498040i
$283$	−160.030	+	160.030i	−0.565475	+	0.565475i	−0.930858	−	0.365382i	$-0.880938\pi$
$283$	−160.030	+	160.030i	−0.565475	+	0.565475i	0.365382	+	0.930858i	$0.380938\pi$
$284$		−	86.2613i		−	0.303737i
$285$	−7.32260	−	214.969i	−0.0256933	−	0.754278i
$286$	289.443			1.01204
$287$	−0.766492	−	0.766492i	−0.00267070	−	0.00267070i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	110.452i		−	0.382186i
$290$	−54.9081	+	1.87036i	−0.189338	+	0.00644952i
$291$	−118.611			−0.407600
$292$	36.1659	+	36.1659i	0.123856	+	0.123856i
$293$	272.405	−	272.405i	0.929710	−	0.929710i	−0.0679767	−	0.997687i	$-0.521654\pi$
$293$	272.405	−	272.405i	0.929710	−	0.929710i	0.997687	+	0.0679767i	$0.0216543\pi$
$294$		−	119.631i		−	0.406908i
$295$	−58.5751	+	62.7064i	−0.198560	+	0.212564i
$296$	−89.7421			−0.303183
$297$	30.5662	+	30.5662i	0.102917	+	0.102917i
$298$	−274.269	+	274.269i	−0.920367	+	0.920367i
$299$		−	117.988i		−	0.394607i
$300$	56.9282	−	65.2624i	0.189761	−	0.217541i
$301$	29.0627			0.0965539
$302$	8.76603	+	8.76603i	0.0290266	+	0.0290266i
$303$	−103.801	+	103.801i	−0.342577	+	0.342577i
$304$			99.3476i			0.326801i
$305$	−324.957	−	303.548i	−1.06543	−	0.995239i
$306$	−56.6910			−0.185265
$307$	183.385	+	183.385i	0.597346	+	0.597346i	0.939606	−	0.342259i	$-0.111192\pi$
$307$	183.385	+	183.385i	0.597346	+	0.597346i	−0.342259	+	0.939606i	$0.611192\pi$
$308$	−4.71903	+	4.71903i	−0.0153215	+	0.0153215i
$309$		−	212.984i		−	0.689269i
$310$	−5.23864	−	153.791i	−0.0168988	−	0.496098i
$311$	17.2354			0.0554193			0.0277096	−	0.999616i	$-0.491179\pi$
$311$	17.2354			0.0554193			0.0277096	+	0.999616i	$0.491179\pi$
$312$	−85.2242	−	85.2242i	−0.273155	−	0.273155i
$313$	9.90854	−	9.90854i	0.0316567	−	0.0316567i	−0.691101	−	0.722758i	$-0.742874\pi$
$313$	9.90854	−	9.90854i	0.0316567	−	0.0316567i	0.722758	+	0.691101i	$0.242874\pi$
$314$			440.887i			1.40410i
$315$	−6.01315	+	0.204829i	−0.0190894	+	0.000650250i
$316$	310.924			0.983937
$317$	23.5479	+	23.5479i	0.0742837	+	0.0742837i	0.743272	−	0.668989i	$-0.233273\pi$
$317$	23.5479	+	23.5479i	0.0742837	+	0.0742837i	−0.668989	+	0.743272i	$0.733273\pi$
$318$	141.657	−	141.657i	0.445461	−	0.445461i
$319$			64.6366i			0.202623i
$320$	−27.3050	+	29.2308i	−0.0853280	+	0.0913462i
$321$	38.1992			0.119001
$322$	1.92365	+	1.92365i	0.00597408	+	0.00597408i
$323$	234.671	−	234.671i	0.726537	−	0.726537i
$324$		−	18.0000i		−	0.0555556i
$325$	−463.495	−	404.305i	−1.42614	−	1.24402i
$326$	123.641			0.379267
$327$	−16.8684	−	16.8684i	−0.0515854	−	0.0515854i
$328$	−5.40493	+	5.40493i	−0.0164784	+	0.0164784i
$329$			32.5248i			0.0988597i
$330$	−74.4562	−	69.5508i	−0.225625	−	0.210760i
$331$	−376.962			−1.13886			−0.569429	−	0.822041i	$-0.692836\pi$
$331$	−376.962			−1.13886			−0.569429	+	0.822041i	$0.692836\pi$
$332$	139.197	+	139.197i	0.419269	+	0.419269i
$333$	−67.3066	+	67.3066i	−0.202122	+	0.202122i
$334$			8.11629i			0.0243003i
$335$	−12.8849	−	378.262i	−0.0384624	−	1.12914i
$336$	2.77897			0.00827073
$337$	−375.137	−	375.137i	−1.11317	−	1.11317i	−0.992720	−	0.120446i	$-0.961568\pi$
$337$	−375.137	−	375.137i	−1.11317	−	1.11317i	−0.120446	−	0.992720i	$-0.538432\pi$
$338$	−436.264	+	436.264i	−1.29072	+	1.29072i
$339$			257.321i			0.759060i
$340$	133.544	−	4.54899i	0.392778	−	0.0133794i
$341$	−181.039			−0.530905
$342$	74.5107	+	74.5107i	0.217868	+	0.217868i
$343$	27.7498	−	27.7498i	0.0809033	−	0.0809033i
$344$		−	204.936i		−	0.595745i
$345$	−28.3515	+	30.3511i	−0.0821783	+	0.0879743i
$346$	329.215			0.951490
$347$	−404.186	−	404.186i	−1.16480	−	1.16480i	−0.983411	−	0.181389i	$-0.941941\pi$
$347$	−404.186	−	404.186i	−1.16480	−	1.16480i	−0.181389	−	0.983411i	$-0.558059\pi$
$348$	19.0318	−	19.0318i	0.0546890	−	0.0546890i
$349$		−	99.8402i		−	0.286075i	−0.989717	−	0.143038i	$-0.954313\pi$
$349$		−	99.8402i		−	0.286075i	0.989717	−	0.143038i	$-0.0456870\pi$
$350$	14.1485	−	0.965012i	0.0404242	−	0.00275718i
$351$	−127.836			−0.364206
$352$	33.2763	+	33.2763i	0.0945349	+	0.0945349i
$353$	435.069	−	435.069i	1.23249	−	1.23249i	0.269486	−	0.963004i	$-0.413146\pi$
$353$	435.069	−	435.069i	1.23249	−	1.23249i	0.963004	−	0.269486i	$-0.0868538\pi$
$354$		−	42.0375i		−	0.118750i
$355$	157.593	+	147.210i	0.443923	+	0.414676i
$356$	135.740			0.381291
$357$	−6.56426	−	6.56426i	−0.0183873	−	0.0183873i
$358$	285.884	−	285.884i	0.798559	−	0.798559i
$359$		−	258.473i		−	0.719980i	−0.932956	−	0.359990i	$-0.882780\pi$
$359$		−	258.473i		−	0.719980i	0.932956	−	0.359990i	$-0.117220\pi$
$360$	1.44435	+	42.4018i	0.00401209	+	0.117783i
$361$	−255.872			−0.708787
$362$	−207.433	−	207.433i	−0.573020	−	0.573020i
$363$	63.4332	−	63.4332i	0.174747	−	0.174747i
$364$		−	19.7363i		−	0.0542205i
$365$	−127.792	+	4.35303i	−0.350114	+	0.0119261i
$366$	217.847			0.595210
$367$	94.6541	+	94.6541i	0.257913	+	0.257913i	0.824205	−	0.566292i	$-0.191622\pi$
$367$	94.6541	+	94.6541i	0.257913	+	0.257913i	−0.566292	+	0.824205i	$0.691622\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$			8.10739i			0.0219712i
$370$	153.150	−	163.952i	0.413920	−	0.443114i
$371$	32.8049			0.0884229
$372$	53.3055	+	53.3055i	0.143294	+	0.143294i
$373$	393.151	−	393.151i	1.05402	−	1.05402i	0.0555700	−	0.998455i	$-0.482302\pi$
$373$	393.151	−	393.151i	1.05402	−	1.05402i	0.998455	−	0.0555700i	$-0.0176976\pi$
$374$		−	157.205i		−	0.420335i
$375$	22.0779	+	215.378i	0.0588743	+	0.574341i
$376$	229.349			0.609972
$377$	−135.164	−	135.164i	−0.358525	−	0.358525i
$378$	2.08422	−	2.08422i	0.00551382	−	0.00551382i
$379$		−	173.870i		−	0.458761i	−0.973337	−	0.229380i	$-0.926330\pi$
$379$		−	173.870i		−	0.458761i	0.973337	−	0.229380i	$-0.0736700\pi$
$380$	−181.501	−	169.543i	−0.477633	−	0.446165i
$381$	54.7521			0.143706
$382$	−17.3738	−	17.3738i	−0.0454811	−	0.0454811i
$383$	314.104	−	314.104i	0.820115	−	0.820115i	−0.166009	−	0.986124i	$-0.553088\pi$
$383$	314.104	−	314.104i	0.820115	−	0.820115i	0.986124	+	0.166009i	$0.0530881\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−0.567995	−	16.6746i	−0.00147531	−	0.0433107i
$386$	282.679			0.732330
$387$	−153.702	−	153.702i	−0.397163	−	0.397163i
$388$	−96.8459	+	96.8459i	−0.249603	+	0.249603i
$389$			33.5984i			0.0863712i	0.999067	+	0.0431856i	$0.0137507\pi$
$389$			33.5984i			0.0863712i	−0.999067	+	0.0431856i	$0.986249\pi$
$390$	301.139	−	10.2578i	0.772150	−	0.0263021i
$391$	−64.0828			−0.163895
$392$	−97.6782	−	97.6782i	−0.249179	−	0.249179i
$393$	−194.345	+	194.345i	−0.494516	+	0.494516i
$394$		−	426.561i		−	1.08264i
$395$	−530.611	+	568.034i	−1.34332	+	1.43806i
$396$	49.9144			0.126047
$397$	286.486	+	286.486i	0.721628	+	0.721628i	0.968937	−	0.247309i	$-0.0795462\pi$
$397$	286.486	+	286.486i	0.721628	+	0.721628i	−0.247309	+	0.968937i	$0.579546\pi$
$398$	−84.3085	+	84.3085i	−0.211830	+	0.211830i
$399$			17.2552i			0.0432462i
$400$	−6.80480	−	99.7682i	−0.0170120	−	0.249421i
$401$	335.115			0.835699			0.417849	−	0.908516i	$-0.362784\pi$
$401$	335.115			0.835699			0.417849	+	0.908516i	$0.362784\pi$
$402$	131.110	+	131.110i	0.326144	+	0.326144i
$403$	378.577	−	378.577i	0.939396	−	0.939396i
$404$			169.506i			0.419569i
$405$	32.8846	+	30.7181i	0.0811966	+	0.0758472i
$406$	4.40739			0.0108556
$407$	−186.643	−	186.643i	−0.458582	−	0.458582i
$408$	−46.2880	+	46.2880i	−0.113451	+	0.113451i
$409$		−	259.446i		−	0.634342i	−0.948368	−	0.317171i	$-0.897267\pi$
$409$		−	259.446i		−	0.634342i	0.948368	−	0.317171i	$-0.102733\pi$
$410$	−0.650552	−	19.0982i	−0.00158671	−	0.0465810i
$411$	−23.9172			−0.0581926
$412$	−173.901	−	173.901i	−0.422090	−	0.422090i
$413$	4.86754	−	4.86754i	0.0117858	−	0.0117858i
$414$		−	20.3470i		−	0.0491473i
$415$	−491.852	+	16.7542i	−1.18519	+	0.0403715i
$416$	−139.171			−0.334545
$417$	−101.988	−	101.988i	−0.244575	−	0.244575i
$418$	−206.620	+	206.620i	−0.494306	+	0.494306i
$419$			71.0303i			0.169523i	0.996401	+	0.0847617i	$0.0270129\pi$
$419$			71.0303i			0.169523i	−0.996401	+	0.0847617i	$0.972987\pi$
$420$	−4.74248	+	5.07696i	−0.0112916	+	0.0120880i
$421$	−356.971			−0.847912			−0.423956	−	0.905683i	$-0.639359\pi$
$421$	−356.971			−0.847912			−0.423956	+	0.905683i	$0.639359\pi$
$422$	−301.566	−	301.566i	−0.714612	−	0.714612i
$423$	172.012	−	172.012i	0.406648	−	0.406648i
$424$		−	231.324i		−	0.545576i
$425$	−219.591	+	251.739i	−0.516685	+	0.592326i
$426$	−105.648			−0.248000
$427$	25.2245	+	25.2245i	0.0590738	+	0.0590738i
$428$	31.1895	−	31.1895i	0.0728728	−	0.0728728i
$429$		−	354.493i		−	0.826325i
$430$	374.403	+	349.736i	0.870704	+	0.813340i
$431$	34.4291			0.0798818			0.0399409	−	0.999202i	$-0.487283\pi$
$431$	34.4291			0.0798818			0.0399409	+	0.999202i	$0.487283\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−121.062	+	121.062i	−0.279590	+	0.279590i	−0.832945	−	0.553356i	$-0.813347\pi$
$433$	−121.062	+	121.062i	−0.279590	+	0.279590i	0.553356	+	0.832945i	$0.313347\pi$
$434$			12.3445i			0.0284436i
$435$	2.29072	+	67.2485i	0.00526601	+	0.154594i
$436$	−27.5460			−0.0631789
$437$	84.2261	+	84.2261i	0.192737	+	0.192737i
$438$	44.2940	−	44.2940i	0.101128	−	0.101128i
$439$			808.849i			1.84248i	0.388993	+	0.921241i	$0.372823\pi$
$439$			808.849i			1.84248i	−0.388993	+	0.921241i	$0.627177\pi$
$440$	−117.581	+	4.00523i	−0.267230	+	0.00910279i
$441$	−146.517			−0.332239
$442$	328.738	+	328.738i	0.743751	+	0.743751i
$443$	131.518	−	131.518i	0.296881	−	0.296881i	−0.542910	−	0.839791i	$-0.682678\pi$
$443$	131.518	−	131.518i	0.296881	−	0.296881i	0.839791	+	0.542910i	$0.182678\pi$
$444$			109.911i			0.247548i
$445$	−231.648	+	247.986i	−0.520557	+	0.557272i
$446$	−83.6662			−0.187592
$447$	335.910	+	335.910i	0.751477	+	0.751477i
$448$	2.26902	−	2.26902i	0.00506477	−	0.00506477i
$449$		−	653.049i		−	1.45445i	−0.686398	−	0.727226i	$-0.740809\pi$
$449$		−	653.049i		−	1.45445i	0.686398	−	0.727226i	$-0.259191\pi$
$450$	−79.9298	−	69.7226i	−0.177622	−	0.154939i
$451$	−22.4820			−0.0498492
$452$	210.102	+	210.102i	0.464827	+	0.464827i
$453$	10.7362	−	10.7362i	0.0237001	−	0.0237001i
$454$		−	270.595i		−	0.596024i
$455$	36.0567	+	33.6812i	0.0792454	+	0.0740245i
$456$	121.676			0.266832
$457$	−60.9591	−	60.9591i	−0.133390	−	0.133390i	0.637259	−	0.770649i	$-0.280068\pi$
$457$	−60.9591	−	60.9591i	−0.133390	−	0.133390i	−0.770649	+	0.637259i	$0.780068\pi$
$458$	337.019	−	337.019i	0.735850	−	0.735850i
$459$			69.4320i			0.151268i
$460$	1.63268	+	47.9305i	0.00354930	+	0.104197i
$461$	156.041			0.338484			0.169242	−	0.985575i	$-0.445868\pi$
$461$	156.041			0.338484			0.169242	+	0.985575i	$0.445868\pi$
$462$	5.77961	+	5.77961i	0.0125100	+	0.0125100i
$463$	−510.074	+	510.074i	−1.10167	+	1.10167i	−0.107464	+	0.994209i	$0.534273\pi$
$463$	−510.074	+	510.074i	−1.10167	+	1.10167i	−0.994209	+	0.107464i	$0.965727\pi$
$464$		−	31.0787i		−	0.0669801i
$465$	−188.354	+	6.41599i	−0.405063	+	0.0137978i
$466$	209.594			0.449772
$467$	−91.8344	−	91.8344i	−0.196647	−	0.196647i	0.601914	−	0.798561i	$-0.294405\pi$
$467$	−91.8344	−	91.8344i	−0.196647	−	0.196647i	−0.798561	+	0.601914i	$0.794405\pi$
$468$	−104.378	+	104.378i	−0.223030	+	0.223030i
$469$			30.3625i			0.0647387i
$470$	−391.399	+	419.004i	−0.832763	+	0.891497i
$471$	539.974			1.14644
$472$	−34.3235	−	34.3235i	−0.0727193	−	0.0727193i
$473$	426.220	−	426.220i	0.901099	−	0.901099i
$474$		−	380.803i		−	0.803381i
$475$	619.483	−	42.2525i	1.30418	−	0.0889527i
$476$	−10.7194			−0.0225197
$477$	−173.493	−	173.493i	−0.363717	−	0.363717i
$478$	−223.047	+	223.047i	−0.466625	+	0.466625i
$479$		−	283.471i		−	0.591797i	−0.955219	−	0.295899i	$-0.904381\pi$
$479$		−	283.471i		−	0.591797i	0.955219	−	0.295899i	$-0.0956191\pi$
$480$	35.8002	+	33.4416i	0.0745838	+	0.0696701i
$481$	780.592			1.62285
$482$	167.112	+	167.112i	0.346706	+	0.346706i
$483$	2.35598	−	2.35598i	0.00487781	−	0.00487781i
$484$		−	103.586i		−	0.214021i
$485$	−11.6566	−	342.203i	−0.0240343	−	0.705574i
$486$	−22.0454			−0.0453609
$487$	564.917	+	564.917i	1.15999	+	1.15999i	0.984476	+	0.175518i	$0.0561600\pi$
$487$	564.917	+	564.917i	1.15999	+	1.15999i	0.175518	+	0.984476i	$0.443840\pi$
$488$	177.871	−	177.871i	0.364490	−	0.364490i
$489$		−	151.429i		−	0.309670i
$490$	345.144	−	11.7568i	0.704377	−	0.0239935i
$491$	−91.4234			−0.186198			−0.0930992	−	0.995657i	$-0.529677\pi$
$491$	−91.4234			−0.186198			−0.0930992	+	0.995657i	$0.529677\pi$
$492$	6.61966	+	6.61966i	0.0134546	+	0.0134546i
$493$	−73.4118	+	73.4118i	−0.148908	+	0.148908i
$494$		−	864.142i		−	1.74927i
$495$	−85.1820	+	91.1899i	−0.172085	+	0.184222i
$496$	87.0475			0.175499
$497$	−12.2330	−	12.2330i	−0.0246137	−	0.0246137i
$498$	170.481	−	170.481i	0.342332	−	0.342332i
$499$		−	793.096i		−	1.58937i	−0.607021	−	0.794685i	$-0.707636\pi$
$499$		−	793.096i		−	1.58937i	0.607021	−	0.794685i	$-0.292364\pi$
$500$	193.882	+	157.829i	0.387763	+	0.315657i
$501$	9.94038			0.0198411
$502$	−441.419	−	441.419i	−0.879321	−	0.879321i
$503$	−538.128	+	538.128i	−1.06984	+	1.06984i	−0.0724666	+	0.997371i	$0.523087\pi$
$503$	−538.128	+	538.128i	−1.06984	+	1.06984i	−0.997371	+	0.0724666i	$0.976913\pi$
$504$		−	3.40352i		−	0.00675303i
$505$	−309.674	−	289.272i	−0.613217	−	0.572816i
$506$	56.4227			0.111507
$507$	534.312	+	534.312i	1.05387	+	1.05387i
$508$	44.7049	−	44.7049i	0.0880017	−	0.0880017i
$509$			265.214i			0.521049i	0.965467	+	0.260524i	$0.0838954\pi$
$509$			265.214i			0.521049i	−0.965467	+	0.260524i	$0.916105\pi$
$510$	−5.57135	−	163.558i	−0.0109242	−	0.320702i
$511$	10.2576			0.0200736
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	91.2566	−	91.2566i	0.177888	−	0.177888i
$514$		−	354.395i		−	0.689485i
$515$	614.476	−	20.9312i	1.19316	−	0.0406431i
$516$	−250.995			−0.486424
$517$	476.993	+	476.993i	0.922618	+	0.922618i
$518$	−12.7266	+	12.7266i	−0.0245688	+	0.0245688i
$519$		−	403.205i		−	0.776888i
$520$	237.503	−	254.254i	0.456737	−	0.488950i
$521$	−345.104			−0.662387			−0.331194	−	0.943563i	$-0.607451\pi$
$521$	−345.104			−0.662387			−0.331194	+	0.943563i	$0.607451\pi$
$522$	−23.3091	−	23.3091i	−0.0446534	−	0.0446534i
$523$	−356.976	+	356.976i	−0.682554	+	0.682554i	−0.960575	−	0.278021i	$-0.910322\pi$
$523$	−356.976	+	356.976i	−0.682554	+	0.682554i	0.278021	+	0.960575i	$0.410322\pi$
$524$			317.364i			0.605656i
$525$	−1.18189	−	17.3283i	−0.00225123	−	0.0330062i
$526$	459.491			0.873558
$527$	−205.617	−	205.617i	−0.390165	−	0.390165i
$528$	40.7550	−	40.7550i	0.0771875	−	0.0771875i
$529$		−	23.0000i		−	0.0434783i
$530$	422.612	+	394.769i	0.797380	+	0.744847i
$531$	−51.4852			−0.0969590
$532$	14.0888	+	14.0888i	0.0264828	+	0.0264828i
$533$	47.0129	−	47.0129i	0.0882044	−	0.0882044i
$534$		−	166.246i		−	0.311323i
$535$	3.75406	+	110.208i	0.00701693	+	0.205996i
$536$	214.101			0.399443
$537$	−350.135	−	350.135i	−0.652021	−	0.652021i
$538$	216.650	−	216.650i	0.402695	−	0.402695i
$539$		−	406.296i		−	0.753796i
$540$	51.9314	−	1.76896i	0.0961693	−	0.00327586i
$541$	35.6543			0.0659044			0.0329522	−	0.999457i	$-0.489509\pi$
$541$	35.6543			0.0659044			0.0329522	+	0.999457i	$0.489509\pi$
$542$	149.342	+	149.342i	0.275538	+	0.275538i
$543$	−254.053	+	254.053i	−0.467869	+	0.467869i
$544$			75.5880i			0.138948i
$545$	47.0089	−	50.3244i	0.0862549	−	0.0923384i
$546$	−24.1719			−0.0442709
$547$	445.794	+	445.794i	0.814981	+	0.814981i	0.985376	−	0.170395i	$-0.0545044\pi$
$547$	445.794	+	445.794i	0.814981	+	0.814981i	−0.170395	+	0.985376i	$0.554504\pi$
$548$	−19.5283	+	19.5283i	−0.0356356	+	0.0356356i
$549$		−	266.807i		−	0.485987i
$550$	193.342	−	221.647i	0.351532	−	0.402995i
$551$	192.975			0.350227
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	44.0932	−	44.0932i	0.0797346	−	0.0797346i
$554$			147.955i			0.267067i
$555$	−200.799	−	187.570i	−0.361801	−	0.337964i
$556$	−166.545			−0.299542
$557$	−601.246	−	601.246i	−1.07944	−	1.07944i	−0.996560	−	0.0828770i	$-0.973589\pi$
$557$	−601.246	−	601.246i	−1.07944	−	1.07944i	−0.0828770	−	0.996560i	$-0.526411\pi$
$558$	65.2856	−	65.2856i	0.116999	−	0.116999i
$559$			1782.57i			3.18885i
$560$	0.273105	+	8.01754i	0.000487688	+	0.0143170i
$561$	−192.537			−0.343202
$562$	−220.186	−	220.186i	−0.391790	−	0.391790i
$563$	179.406	−	179.406i	0.318660	−	0.318660i	−0.529592	−	0.848252i	$-0.677655\pi$
$563$	179.406	−	179.406i	0.318660	−	0.318660i	0.848252	+	0.529592i	$0.177655\pi$
$564$		−	280.894i		−	0.498040i
$565$	−742.392	+	25.2884i	−1.31397	+	0.0447583i
$566$	320.059			0.565475
$567$	−2.55264	−	2.55264i	−0.00450202	−	0.00450202i
$568$	−86.2613	+	86.2613i	−0.151868	+	0.151868i
$569$			132.003i			0.231991i	0.993250	+	0.115995i	$0.0370058\pi$
$569$			132.003i			0.231991i	−0.993250	+	0.115995i	$0.962994\pi$
$570$	−207.647	+	222.292i	−0.364292	+	0.389986i
$571$	40.8166			0.0714826			0.0357413	−	0.999361i	$-0.488621\pi$
$571$	40.8166			0.0714826			0.0357413	+	0.999361i	$0.488621\pi$
$572$	−289.443	−	289.443i	−0.506019	−	0.506019i
$573$	−21.2784	+	21.2784i	−0.0371352	+	0.0371352i
$574$			1.53298i			0.00267070i
$575$	−90.3517	−	78.8136i	−0.157133	−	0.137067i
$576$	−24.0000			−0.0416667
$577$	−445.272	−	445.272i	−0.771703	−	0.771703i	0.206701	−	0.978404i	$-0.433727\pi$
$577$	−445.272	−	445.272i	−0.771703	−	0.771703i	−0.978404	+	0.206701i	$0.933727\pi$
$578$	−110.452	+	110.452i	−0.191093	+	0.191093i
$579$		−	346.210i		−	0.597945i
$580$	56.7785	+	53.0378i	0.0978940	+	0.0914444i
$581$	39.4801			0.0679521
$582$	118.611	+	118.611i	0.203800	+	0.203800i
$583$	481.101	−	481.101i	0.825216	−	0.825216i
$584$		−	72.3318i		−	0.123856i
$585$	−12.5632	−	368.818i	−0.0214756	−	0.630458i
$586$	−544.810			−0.929710
$587$	−437.704	−	437.704i	−0.745663	−	0.745663i	0.227999	−	0.973661i	$-0.426782\pi$
$587$	−437.704	−	437.704i	−0.745663	−	0.745663i	−0.973661	+	0.227999i	$0.926782\pi$
$588$	−119.631	+	119.631i	−0.203454	+	0.203454i
$589$			540.498i			0.917653i
$590$	121.282	−	4.13127i	0.205562	−	0.00700215i
$591$	−522.428			−0.883973
$592$	89.7421	+	89.7421i	0.151591	+	0.151591i
$593$	605.242	−	605.242i	1.02064	−	1.02064i	0.0208625	−	0.999782i	$-0.493359\pi$
$593$	605.242	−	605.242i	1.02064	−	1.02064i	0.999782	−	0.0208625i	$-0.00664122\pi$
$594$		−	61.1325i		−	0.102917i
$595$	18.2933	−	19.5835i	0.0307450	−	0.0329135i
$596$	548.539			0.920367
$597$	103.256	+	103.256i	0.172959	+	0.172959i
$598$	−117.988	+	117.988i	−0.197304	+	0.197304i
$599$			923.521i			1.54177i	0.636974	+	0.770886i	$0.280186\pi$
$599$			923.521i			1.54177i	−0.636974	+	0.770886i	$0.719814\pi$
$600$	−122.191	+	8.33414i	−0.203651	+	0.0138902i
$601$	858.844			1.42902			0.714512	−	0.699623i	$-0.246649\pi$
$601$	858.844			1.42902			0.714512	+	0.699623i	$0.246649\pi$
$602$	−29.0627	−	29.0627i	−0.0482770	−	0.0482770i
$603$	160.576	−	160.576i	0.266295	−	0.266295i
$604$		−	17.5321i		−	0.0290266i
$605$	189.244	+	176.776i	0.312800	+	0.292191i
$606$	207.602			0.342577
$607$	−317.963	−	317.963i	−0.523826	−	0.523826i	0.394898	−	0.918725i	$-0.370780\pi$
$607$	−317.963	−	317.963i	−0.523826	−	0.523826i	−0.918725	+	0.394898i	$0.870780\pi$
$608$	99.3476	−	99.3476i	0.163401	−	0.163401i
$609$		−	5.39792i		−	0.00886359i
$610$	21.4091	+	628.505i	0.0350968	+	1.03034i
$611$	−1994.92			−3.26500
$612$	56.6910	+	56.6910i	0.0926323	+	0.0926323i
$613$	−537.516	+	537.516i	−0.876861	+	0.876861i	−0.993209	−	0.116347i	$-0.962881\pi$
$613$	−537.516	+	537.516i	−0.876861	+	0.876861i	0.116347	+	0.993209i	$0.462881\pi$
$614$		−	366.771i		−	0.597346i
$615$	−23.3905	+	0.796760i	−0.0380333	+	0.00129554i
$616$	9.43806			0.0153215
$617$	−565.370	−	565.370i	−0.916320	−	0.916320i	0.0804392	−	0.996760i	$-0.474368\pi$
$617$	−565.370	−	565.370i	−0.916320	−	0.916320i	−0.996760	+	0.0804392i	$0.974368\pi$
$618$	−212.984	+	212.984i	−0.344635	+	0.344635i
$619$			60.9967i			0.0985407i	0.998785	+	0.0492703i	$0.0156896\pi$
$619$			60.9967i			0.0985407i	−0.998785	+	0.0492703i	$0.984310\pi$
$620$	−148.552	+	159.029i	−0.239600	+	0.256499i
$621$	−24.9199			−0.0401286
$622$	−17.2354	−	17.2354i	−0.0277096	−	0.0277096i
$623$	19.2497	−	19.2497i	0.0308984	−	0.0308984i
$624$			170.448i			0.273155i
$625$	−619.212	+	84.8628i	−0.990739	+	0.135780i
$626$	−19.8171			−0.0316567
$627$	253.057	+	253.057i	0.403599	+	0.403599i
$628$	440.887	−	440.887i	0.702049	−	0.702049i
$629$		−	423.964i		−	0.674029i
$630$	6.21798	+	5.80832i	0.00986981	+	0.00921956i
$631$	1099.71			1.74281			0.871403	−	0.490568i	$-0.163211\pi$
$631$	1099.71			1.74281			0.871403	+	0.490568i	$0.163211\pi$
$632$	−310.924	−	310.924i	−0.491968	−	0.491968i
$633$	−369.342	+	369.342i	−0.583479	+	0.583479i
$634$		−	47.0959i		−	0.0742837i
$635$	5.38080	+	157.964i	0.00847370	+	0.248762i
$636$	−283.313			−0.445461
$637$	849.621	+	849.621i	1.33378	+	1.33378i
$638$	64.6366	−	64.6366i	0.101311	−	0.101311i
$639$			129.392i			0.202491i
$640$	56.5358	−	1.92580i	0.0883371	−	0.00300907i
$641$	524.487			0.818233			0.409116	−	0.912482i	$-0.365837\pi$
$641$	524.487			0.818233			0.409116	+	0.912482i	$0.365837\pi$
$642$	−38.1992	−	38.1992i	−0.0595004	−	0.0595004i
$643$	409.688	−	409.688i	0.637151	−	0.637151i	−0.312701	−	0.949852i	$-0.601234\pi$
$643$	409.688	−	409.688i	0.637151	−	0.637151i	0.949852	+	0.312701i	$0.101234\pi$
$644$		−	3.84730i		−	0.00597408i
$645$	428.337	−	458.548i	0.664089	−	0.710927i
$646$	−469.343			−0.726537
$647$	423.917	+	423.917i	0.655204	+	0.655204i	0.954241	−	0.299037i	$-0.0966654\pi$
$647$	423.917	+	423.917i	0.655204	+	0.655204i	−0.299037	+	0.954241i	$0.596665\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	142.770i		−	0.219984i
$650$	59.1892	+	867.800i	0.0910604	+	1.33508i
$651$	15.1189			0.0232241
$652$	−123.641	−	123.641i	−0.189633	−	0.189633i
$653$	579.557	−	579.557i	0.887530	−	0.887530i	−0.106756	−	0.994285i	$-0.534046\pi$
$653$	579.557	−	579.557i	0.887530	−	0.887530i	0.994285	+	0.106756i	$0.0340463\pi$
$654$			33.7368i			0.0515854i
$655$	−579.799	−	541.600i	−0.885190	−	0.826871i
$656$	10.8099			0.0164784
$657$	−54.2489	−	54.2489i	−0.0825706	−	0.0825706i
$658$	32.5248	−	32.5248i	0.0494298	−	0.0494298i
$659$			417.909i			0.634156i	0.948399	+	0.317078i	$0.102702\pi$
$659$			417.909i			0.634156i	−0.948399	+	0.317078i	$0.897298\pi$
$660$	4.90538	+	144.007i	0.00743239	+	0.218193i
$661$	964.858			1.45969			0.729847	−	0.683610i	$-0.239591\pi$
$661$	964.858			1.45969			0.729847	+	0.683610i	$0.239591\pi$
$662$	376.962	+	376.962i	0.569429	+	0.569429i
$663$	402.620	−	402.620i	0.607271	−	0.607271i
$664$		−	278.395i		−	0.419269i
$665$	−49.7827	+	1.69577i	−0.0748612	+	0.00255003i
$666$	134.613			0.202122
$667$	−26.3483	−	26.3483i	−0.0395027	−	0.0395027i
$668$	8.11629	−	8.11629i	0.0121501	−	0.0121501i
$669$			102.470i			0.153168i
$670$	−365.377	+	391.147i	−0.545339	+	0.583801i
$671$	739.861			1.10263
$672$	−2.77897	−	2.77897i	−0.00413537	−	0.00413537i
$673$	−263.331	+	263.331i	−0.391280	+	0.391280i	−0.875143	−	0.483864i	$-0.839233\pi$
$673$	−263.331	+	263.331i	−0.391280	+	0.391280i	0.483864	+	0.875143i	$0.339233\pi$
$674$			750.274i			1.11317i
$675$	−85.3923	+	97.8936i	−0.126507	+	0.145027i
$676$	872.528			1.29072
$677$	47.8727	+	47.8727i	0.0707130	+	0.0707130i	0.741579	−	0.670866i	$-0.234077\pi$
$677$	47.8727	+	47.8727i	0.0707130	+	0.0707130i	−0.670866	+	0.741579i	$0.734077\pi$
$678$	257.321	−	257.321i	0.379530	−	0.379530i
$679$			27.4681i			0.0404538i
$680$	−138.093	−	128.995i	−0.203079	−	0.189699i
$681$	−331.409			−0.486651
$682$	181.039	+	181.039i	0.265453	+	0.265453i
$683$	491.209	−	491.209i	0.719193	−	0.719193i	−0.249247	−	0.968440i	$-0.580183\pi$
$683$	491.209	−	491.209i	0.719193	−	0.719193i	0.968440	+	0.249247i	$0.0801832\pi$
$684$		−	149.021i		−	0.217868i
$685$	−2.35048	−	69.0029i	−0.00343135	−	0.100734i
$686$	−55.4996			−0.0809033
$687$	−412.763	−	412.763i	−0.600819	−	0.600819i
$688$	−204.936	+	204.936i	−0.297872	+	0.297872i
$689$			2012.10i			2.92031i
$690$	58.7027	−	1.99962i	0.0850763	−	0.00289799i
$691$	−356.833			−0.516400			−0.258200	−	0.966091i	$-0.583129\pi$
$691$	−356.833			−0.516400			−0.258200	+	0.966091i	$0.583129\pi$
$692$	−329.215	−	329.215i	−0.475745	−	0.475745i
$693$	7.07854	−	7.07854i	0.0102143	−	0.0102143i
$694$			808.372i			1.16480i
$695$	284.220	−	304.266i	0.408950	−	0.437793i
$696$	−38.0635			−0.0546890
$697$	−25.5342	−	25.5342i	−0.0366344	−	0.0366344i
$698$	−99.8402	+	99.8402i	−0.143038	+	0.143038i
$699$		−	256.699i		−	0.367238i
$700$	−15.1135	−	13.1835i	−0.0215907	−	0.0188335i
$701$	512.770			0.731483			0.365742	−	0.930716i	$-0.380815\pi$
$701$	512.770			0.731483			0.365742	+	0.930716i	$0.380815\pi$
$702$	127.836	+	127.836i	0.182103	+	0.182103i
$703$	−557.229	+	557.229i	−0.792645	+	0.792645i
$704$		−	66.5526i		−	0.0945349i
$705$	513.173	+	479.363i	0.727904	+	0.679948i
$706$	−870.138			−1.23249
$707$	24.0382	+	24.0382i	0.0340003	+	0.0340003i
$708$	−42.0375	+	42.0375i	−0.0593750	+	0.0593750i
$709$		−	557.179i		−	0.785865i	−0.919567	−	0.392933i	$-0.871461\pi$
$709$		−	557.179i		−	0.785865i	0.919567	−	0.392933i	$-0.128539\pi$
$710$	−10.3826	−	304.803i	−0.0146234	−	0.429300i
$711$	−466.386			−0.655958
$712$	−135.740	−	135.740i	−0.190646	−	0.190646i
$713$	73.7981	−	73.7981i	0.103504	−	0.103504i
$714$			13.1285i			0.0183873i
$715$	1022.74	−	34.8381i	1.43041	−	0.0487246i
$716$	−571.768			−0.798559
$717$	273.175	+	273.175i	0.380998	+	0.380998i
$718$	−258.473	+	258.473i	−0.359990	+	0.359990i
$719$			704.591i			0.979960i	0.871734	+	0.489980i	$0.162996\pi$
$719$			704.591i			0.979960i	−0.871734	+	0.489980i	$0.837004\pi$
$720$	40.9575	−	43.8462i	0.0568854	−	0.0608975i
$721$	−49.3230			−0.0684092
$722$	255.872	+	255.872i	0.354393	+	0.354393i
$723$	204.670	−	204.670i	0.283084	−	0.283084i
$724$			414.866i			0.573020i
$725$	−193.792	+	13.2178i	−0.267299	+	0.0182314i
$726$	−126.866			−0.174747
$727$	−103.504	−	103.504i	−0.142372	−	0.142372i	0.632328	−	0.774700i	$-0.282099\pi$
$727$	−103.504	−	103.504i	−0.142372	−	0.142372i	−0.774700	+	0.632328i	$0.782099\pi$
$728$	−19.7363	+	19.7363i	−0.0271103	+	0.0271103i
$729$			27.0000i			0.0370370i
$730$	132.145	+	123.439i	0.181020	+	0.169094i
$731$	968.169			1.32444
$732$	−217.847	−	217.847i	−0.297605	−	0.297605i
$733$	399.591	−	399.591i	0.545145	−	0.545145i	−0.379887	−	0.925033i	$-0.624037\pi$
$733$	399.591	−	399.591i	0.545145	−	0.545145i	0.925033	+	0.379887i	$0.124037\pi$
$734$		−	189.308i		−	0.257913i
$735$	−14.3991	−	422.714i	−0.0195906	−	0.575121i
$736$	−27.1293			−0.0368605
$737$	445.281	+	445.281i	0.604181	+	0.604181i
$738$	8.10739	−	8.10739i	0.0109856	−	0.0109856i
$739$			463.718i			0.627494i	0.949507	+	0.313747i	$0.101584\pi$
$739$			463.718i			0.627494i	−0.949507	+	0.313747i	$0.898416\pi$
$740$	−317.102	+	10.8016i	−0.428517	+	0.0145968i
$741$	−1058.35			−1.42828
$742$	−32.8049	−	32.8049i	−0.0442115	−	0.0442115i
$743$	142.650	−	142.650i	0.191992	−	0.191992i	−0.604564	−	0.796556i	$-0.706653\pi$
$743$	142.650	−	142.650i	0.191992	−	0.191992i	0.796556	+	0.604564i	$0.206653\pi$
$744$		−	106.611i		−	0.143294i
$745$	−936.115	+	1002.14i	−1.25653	+	1.34515i
$746$	−786.302			−1.05402
$747$	−208.796	−	208.796i	−0.279513	−	0.279513i
$748$	−157.205	+	157.205i	−0.210168	+	0.210168i
$749$		−	8.84620i		−	0.0118107i
$750$	193.300	−	237.456i	0.257733	−	0.316607i
$751$	−786.317			−1.04703			−0.523513	−	0.852017i	$-0.675379\pi$
$751$	−786.317			−1.04703			−0.523513	+	0.852017i	$0.675379\pi$
$752$	−229.349	−	229.349i	−0.304986	−	0.304986i
$753$	−540.626	+	540.626i	−0.717963	+	0.717963i
$754$			270.328i			0.358525i
$755$	32.0297	+	29.9195i	0.0424235	+	0.0396285i
$756$	−4.16845			−0.00551382
$757$	303.467	+	303.467i	0.400881	+	0.400881i	0.878543	−	0.477663i	$-0.158516\pi$
$757$	303.467	+	303.467i	0.400881	+	0.400881i	−0.477663	+	0.878543i	$0.658516\pi$
$758$	−173.870	+	173.870i	−0.229380	+	0.229380i
$759$		−	69.1034i		−	0.0910454i
$760$	11.9578	+	351.043i	0.0157339	+	0.461899i
$761$	−76.0064			−0.0998770			−0.0499385	−	0.998752i	$-0.515903\pi$
$761$	−76.0064			−0.0998770			−0.0499385	+	0.998752i	$0.515903\pi$
$762$	−54.7521	−	54.7521i	−0.0718531	−	0.0718531i
$763$	−3.90640	+	3.90640i	−0.00511979	+	0.00511979i
$764$			34.7476i			0.0454811i
$765$	−200.317	+	6.82348i	−0.261852	+	0.00891958i
$766$	−628.208			−0.820115
$767$	298.551	+	298.551i	0.389245	+	0.389245i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$		−	731.164i		−	0.950798i	−0.879770	−	0.475399i	$-0.842304\pi$
$769$		−	731.164i		−	0.950798i	0.879770	−	0.475399i	$-0.157696\pi$
$770$	−16.1066	+	17.2426i	−0.0209177	+	0.0223930i
$771$	−434.044			−0.562962
$772$	−282.679	−	282.679i	−0.366165	−	0.366165i
$773$	−637.671	+	637.671i	−0.824931	+	0.824931i	−0.986810	−	0.161880i	$-0.948244\pi$
$773$	−637.671	+	637.671i	−0.824931	+	0.824931i	0.161880	+	0.986810i	$0.448244\pi$
$774$			307.404i			0.397163i
$775$	−37.0213	−	542.786i	−0.0477694	−	0.700369i
$776$	193.692			0.249603
$777$	15.5869	+	15.5869i	0.0200604	+	0.0200604i
$778$	33.5984	−	33.5984i	0.0431856	−	0.0431856i
$779$			67.1208i			0.0861628i
$780$	−311.396	−	290.881i	−0.399226	−	0.372924i
$781$	−358.807			−0.459420
$782$	64.0828	+	64.0828i	0.0819473	+	0.0819473i
$783$	−28.5477	+	28.5477i	−0.0364593	+	0.0364593i
$784$			195.356i			0.249179i
$785$	53.0664	+	1557.87i	0.0676005	+	1.98454i
$786$	388.690			0.494516
$787$	−154.530	−	154.530i	−0.196353	−	0.196353i	0.602081	−	0.798435i	$-0.294338\pi$
$787$	−154.530	−	154.530i	−0.196353	−	0.196353i	−0.798435	+	0.602081i	$0.794338\pi$
$788$	−426.561	+	426.561i	−0.541321	+	0.541321i
$789$		−	562.760i		−	0.713257i
$790$	1098.65	−	37.4237i	1.39069	−	0.0473717i
$791$	59.5906			0.0753357
$792$	−49.9144	−	49.9144i	−0.0630233	−	0.0630233i
$793$	−1547.15	+	1547.15i	−1.95101	+	1.95101i
$794$		−	572.973i		−	0.721628i
$795$	483.491	−	517.591i	0.608165	−	0.651058i
$796$	168.617			0.211830
$797$	−1069.70	−	1069.70i	−1.34216	−	1.34216i	−0.893911	−	0.448244i	$-0.852050\pi$
$797$	−1069.70	−	1069.70i	−1.34216	−	1.34216i	−0.448244	−	0.893911i	$-0.647950\pi$
$798$	17.2552	−	17.2552i	0.0216231	−	0.0216231i
$799$			1083.50i			1.35607i
$800$	−92.9634	+	106.573i	−0.116204	+	0.133216i
$801$	−203.610			−0.254194
$802$	−335.115	−	335.115i	−0.417849	−	0.417849i
$803$	150.433	−	150.433i	0.187339	−	0.187339i
$804$		−	262.219i		−	0.326144i
$805$	7.02873	+	6.56566i	0.00873134	+	0.00815610i
$806$	−757.153			−0.939396
$807$	−265.341	−	265.341i	−0.328799	−	0.328799i
$808$	169.506	−	169.506i	0.209785	−	0.209785i
$809$			149.059i			0.184251i	0.995747	+	0.0921256i	$0.0293661\pi$
$809$			149.059i			0.184251i	−0.995747	+	0.0921256i	$0.970634\pi$
$810$	−2.16653	−	63.6027i	−0.00267473	−	0.0785219i
$811$	−681.862			−0.840767			−0.420384	−	0.907347i	$-0.638104\pi$
$811$	−681.862			−0.840767			−0.420384	+	0.907347i	$0.638104\pi$
$812$	−4.40739	−	4.40739i	−0.00542782	−	0.00542782i
$813$	182.905	−	182.905i	0.224976	−	0.224976i
$814$			373.286i			0.458582i
$815$	436.883	−	14.8818i	0.536053	−	0.0182598i
$816$	92.5760			0.113451
$817$	−1272.50	−	1272.50i	−1.55752	−	1.55752i
$818$	−259.446	+	259.446i	−0.317171	+	0.317171i
$819$			29.6044i			0.0361470i
$820$	−18.4477	+	19.7488i	−0.0224972	+	0.0240839i
$821$	911.985			1.11082			0.555411	−	0.831576i	$-0.312561\pi$
$821$	911.985			1.11082			0.555411	+	0.831576i	$0.312561\pi$
$822$	23.9172	+	23.9172i	0.0290963	+	0.0290963i
$823$	−764.965	+	764.965i	−0.929484	+	0.929484i	−0.997672	−	0.0681885i	$-0.978278\pi$
$823$	−764.965	+	764.965i	−0.929484	+	0.929484i	0.0681885	+	0.997672i	$0.478278\pi$
$824$			347.802i			0.422090i
$825$	−271.461	−	236.795i	−0.329044	−	0.287024i
$826$	−9.73507			−0.0117858
$827$	−207.033	−	207.033i	−0.250342	−	0.250342i	0.570769	−	0.821111i	$-0.306645\pi$
$827$	−207.033	−	207.033i	−0.250342	−	0.250342i	−0.821111	+	0.570769i	$0.806645\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$			1069.74i			1.29040i	0.764015	+	0.645198i	$0.223225\pi$
$829$			1069.74i			1.29040i	−0.764015	+	0.645198i	$0.776775\pi$
$830$	508.606	+	475.098i	0.612778	+	0.572407i
$831$	181.207			0.218059
$832$	139.171	+	139.171i	0.167272	+	0.167272i
$833$	461.456	−	461.456i	0.553969	−	0.553969i
$834$			203.976i			0.244575i
$835$	0.976899	+	28.6788i	0.00116994	+	0.0343458i
$836$	413.240			0.494306
$837$	−79.9582	−	79.9582i	−0.0955296	−	0.0955296i
$838$	71.0303	−	71.0303i	0.0847617	−	0.0847617i
$839$			197.720i			0.235662i	0.993034	+	0.117831i	$0.0375940\pi$
$839$			197.720i			0.235662i	−0.993034	+	0.117831i	$0.962406\pi$
$840$	9.81944	−	0.334484i	0.0116898	−	0.000398195i
$841$	780.632			0.928219
$842$	356.971	+	356.971i	0.423956	+	0.423956i
$843$	−269.672	+	269.672i	−0.319895	+	0.319895i
$844$			603.133i			0.714612i
$845$	−1489.02	+	1594.04i	−1.76216	+	1.88644i
$846$	−344.024			−0.406648
$847$	−14.6899	−	14.6899i	−0.0173434	−	0.0173434i
$848$	−231.324	+	231.324i	−0.272788	+	0.272788i
$849$		−	391.991i		−	0.461709i
$850$	471.330	−	32.1475i	0.554505	−	0.0378206i
$851$	152.165			0.178807
$852$	105.648	+	105.648i	0.124000	+	0.124000i
$853$	580.665	−	580.665i	0.680732	−	0.680732i	−0.279433	−	0.960165i	$-0.590146\pi$
$853$	580.665	−	580.665i	0.680732	−	0.680732i	0.960165	+	0.279433i	$0.0901465\pi$
$854$		−	50.4491i		−	0.0590738i
$855$	272.251	+	254.314i	0.318422	+	0.297443i
$856$	−62.3791			−0.0728728
$857$	772.966	+	772.966i	0.901943	+	0.901943i	0.995604	−	0.0936607i	$-0.0298569\pi$
$857$	772.966	+	772.966i	0.901943	+	0.901943i	−0.0936607	+	0.995604i	$0.529857\pi$
$858$	−354.493	+	354.493i	−0.413162	+	0.413162i
$859$			172.504i			0.200820i	0.994946	+	0.100410i	$0.0320155\pi$
$859$			172.504i			0.200820i	−0.994946	+	0.100410i	$0.967985\pi$
$860$	−24.6667	−	724.139i	−0.0286822	−	0.842022i
$861$	1.87751			0.00218062
$862$	−34.4291	−	34.4291i	−0.0399409	−	0.0399409i
$863$	−522.522	+	522.522i	−0.605472	+	0.605472i	−0.941759	−	0.336288i	$-0.890829\pi$
$863$	−522.522	+	522.522i	−0.605472	+	0.605472i	0.336288	+	0.941759i	$0.390829\pi$
$864$			29.3939i			0.0340207i
$865$	1163.28	−	39.6253i	1.34483	−	0.0458096i
$866$	242.125			0.279590
$867$	135.275	+	135.275i	0.156027	+	0.156027i
$868$	12.3445	−	12.3445i	0.0142218	−	0.0142218i
$869$		−	1293.30i		−	1.48826i
$870$	64.9577	−	69.5392i	0.0746641	−	0.0799301i
$871$	−1862.29			−2.13810
$872$	27.5460	+	27.5460i	0.0315895	+	0.0315895i
$873$	145.269	−	145.269i	0.166402	−	0.166402i
$874$		−	168.452i		−	0.192737i
$875$	49.8773	−	5.11281i	0.0570026	−	0.00584321i
$876$	−88.5880			−0.101128
$877$	712.811	+	712.811i	0.812783	+	0.812783i	0.985050	−	0.172267i	$-0.0551093\pi$
$877$	712.811	+	712.811i	0.812783	+	0.812783i	−0.172267	+	0.985050i	$0.555109\pi$
$878$	808.849	−	808.849i	0.921241	−	0.921241i
$879$			667.253i			0.759105i
$880$	121.587	+	113.576i	0.138166	+	0.129064i
$881$	689.439			0.782564			0.391282	−	0.920271i	$-0.372032\pi$
$881$	689.439			0.782564			0.391282	+	0.920271i	$0.372032\pi$
$882$	146.517	+	146.517i	0.166119	+	0.166119i
$883$	−151.803	+	151.803i	−0.171917	+	0.171917i	−0.787821	−	0.615904i	$-0.788791\pi$
$883$	−151.803	+	151.803i	−0.171917	+	0.171917i	0.615904	+	0.787821i	$0.288791\pi$
$884$		−	657.476i		−	0.743751i
$885$	−5.05975	−	148.539i	−0.00571723	−	0.167841i
$886$	−263.037			−0.296881
$887$	−1062.41	−	1062.41i	−1.19775	−	1.19775i	−0.974838	−	0.222916i	$-0.928442\pi$
$887$	−1062.41	−	1062.41i	−1.19775	−	1.19775i	−0.222916	−	0.974838i	$-0.571558\pi$
$888$	109.911	−	109.911i	0.123774	−	0.123774i
$889$		−	12.6795i		−	0.0142627i
$890$	479.634	−	16.3380i	0.538915	−	0.0183573i
$891$	−74.8717			−0.0840311
$892$	83.6662	+	83.6662i	0.0937962	+	0.0937962i
$893$	1424.08	−	1424.08i	1.59472	−	1.59472i
$894$		−	671.820i		−	0.751477i
$895$	975.757	−	1044.58i	1.09023	−	1.16712i
$896$	−4.53803			−0.00506477
$897$	144.505	+	144.505i	0.161098	+	0.161098i
$898$	−653.049	+	653.049i	−0.727226	+	0.727226i
$899$		−	169.083i		−	0.188079i
$900$	10.2072	+	149.652i	0.0113413	+	0.166280i
$901$	1092.83			1.21291
$902$	22.4820	+	22.4820i	0.0249246	+	0.0249246i
$903$	−35.5944	+	35.5944i	−0.0394180	+	0.0394180i
$904$		−	420.204i		−	0.464827i
$905$	−757.929	−	707.994i	−0.837490	−	0.782314i
$906$	−21.4723			−0.0237001
$907$	14.7685	+	14.7685i	0.0162828	+	0.0162828i	0.715201	−	0.698919i	$-0.246335\pi$
$907$	14.7685	+	14.7685i	0.0162828	+	0.0162828i	−0.698919	+	0.715201i	$0.746335\pi$
$908$	−270.595	+	270.595i	−0.298012	+	0.298012i
$909$		−	254.259i		−	0.279713i
$910$	−2.37551	−	69.7378i	−0.00261045	−	0.0766350i
$911$	−1363.04			−1.49621			−0.748103	−	0.663582i	$-0.769035\pi$
$911$	−1363.04			−1.49621			−0.748103	+	0.663582i	$0.769035\pi$
$912$	−121.676	−	121.676i	−0.133416	−	0.133416i
$913$	578.997	−	578.997i	0.634169	−	0.634169i
$914$			121.918i			0.133390i
$915$	769.758	−	26.2206i	0.841266	−	0.0286564i
$916$	−674.038			−0.735850
$917$	45.0065	+	45.0065i	0.0490801	+	0.0490801i
$918$	69.4320	−	69.4320i	0.0756340	−	0.0756340i
$919$		−	238.535i		−	0.259560i	−0.991543	−	0.129780i	$-0.958573\pi$
$919$		−	238.535i		−	0.259560i	0.991543	−	0.129780i	$-0.0414270\pi$
$920$	46.2978	−	49.5632i	0.0503237	−	0.0538730i
$921$	−449.201			−0.487731
$922$	−156.041	−	156.041i	−0.169242	−	0.169242i
$923$	750.315	−	750.315i	0.812909	−	0.812909i
$924$		−	11.5592i		−	0.0125100i
$925$	521.421	−	597.755i	0.563698	−	0.646222i
$926$	1020.15			1.10167
$927$	260.851	+	260.851i	0.281393	+	0.281393i
$928$	−31.0787	+	31.0787i	−0.0334900	+	0.0334900i
$929$			600.298i			0.646177i	0.946369	+	0.323088i	$0.104721\pi$
$929$			600.298i			0.646177i	−0.946369	+	0.323088i	$0.895279\pi$
$930$	194.770	+	181.938i	0.209430	+	0.195632i
$931$	−1213.01			−1.30291
$932$	−209.594	−	209.594i	−0.224886	−	0.224886i
$933$	−21.1090	+	21.1090i	−0.0226248	+	0.0226248i
$934$			183.669i			0.196647i
$935$	−18.9217	−	555.483i	−0.0202371	−	0.594100i
$936$	208.756			0.223030
$937$	−266.194	−	266.194i	−0.284092	−	0.284092i	0.550647	−	0.834739i	$-0.314381\pi$
$937$	−266.194	−	266.194i	−0.284092	−	0.284092i	−0.834739	+	0.550647i	$0.814381\pi$
$938$	30.3625	−	30.3625i	0.0323694	−	0.0323694i
$939$			24.2709i			0.0258476i
$940$	810.402	−	27.6051i	0.862130	−	0.0293671i
$941$	−796.412			−0.846347			−0.423173	−	0.906049i	$-0.639084\pi$
$941$	−796.412			−0.846347			−0.423173	+	0.906049i	$0.639084\pi$
$942$	−539.974	−	539.974i	−0.573221	−	0.573221i
$943$	9.16450	−	9.16450i	0.00971845	−	0.00971845i
$944$			68.6470i			0.0727193i
$945$	7.11371	−	7.61544i	0.00752774	−	0.00805867i
$946$	−852.440			−0.901099
$947$	−482.539	−	482.539i	−0.509545	−	0.509545i	0.404842	−	0.914387i	$-0.367327\pi$
$947$	−482.539	−	482.539i	−0.509545	−	0.509545i	−0.914387	+	0.404842i	$0.867327\pi$
$948$	−380.803	+	380.803i	−0.401690	+	0.401690i
$949$			629.154i			0.662965i
$950$	−661.736	−	577.231i	−0.696564	−	0.607611i
$951$	−57.6804			−0.0606524
$952$	10.7194	+	10.7194i	0.0112599	+	0.0112599i
$953$	−20.7166	+	20.7166i	−0.0217383	+	0.0217383i	−0.717892	−	0.696154i	$-0.754893\pi$
$953$	−20.7166	+	20.7166i	−0.0217383	+	0.0217383i	0.696154	+	0.717892i	$0.254893\pi$
$954$			346.986i			0.363717i
$955$	−63.4811	−	59.2988i	−0.0664724	−	0.0620930i
$956$	446.093			0.466625
$957$	−79.1633	−	79.1633i	−0.0827203	−	0.0827203i
$958$	−283.471	+	283.471i	−0.295899	+	0.295899i
$959$			5.53875i			0.00577555i
$960$	−2.35862	−	69.2419i	−0.00245689	−	0.0721270i
$961$	−487.421			−0.507202
$962$	−780.592	−	780.592i	−0.811426	−	0.811426i
$963$	−46.7843	+	46.7843i	−0.0485818	+	0.0485818i
$964$		−	334.224i		−	0.346706i
$965$	998.843	−	34.0241i	1.03507	−	0.0352581i
$966$	−4.71197			−0.00487781
$967$	149.509	+	149.509i	0.154611	+	0.154611i	0.780174	−	0.625563i	$-0.215131\pi$
$967$	149.509	+	149.509i	0.154611	+	0.154611i	−0.625563	+	0.780174i	$0.715131\pi$
$968$	−103.586	+	103.586i	−0.107010	+	0.107010i
$969$			574.825i			0.593215i
$970$	−330.547	+	353.860i	−0.340770	+	0.364804i
$971$	705.991			0.727076			0.363538	−	0.931579i	$-0.381569\pi$
$971$	705.991			0.727076			0.363538	+	0.931579i	$0.381569\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	−23.6184	+	23.6184i	−0.0242738	+	0.0242738i
$974$		−	1129.83i		−	1.15999i
$975$	1062.83	−	72.4917i	1.09009	−	0.0743505i
$976$	−355.742			−0.364490
$977$	−259.971	−	259.971i	−0.266091	−	0.266091i	0.561432	−	0.827523i	$-0.310251\pi$
$977$	−259.971	−	259.971i	−0.266091	−	0.266091i	−0.827523	+	0.561432i	$0.810251\pi$
$978$	−151.429	+	151.429i	−0.154835	+	0.154835i
$979$		−	564.614i		−	0.576725i
$980$	−356.901	−	333.388i	−0.364185	−	0.340192i
$981$	41.3190			0.0421193
$982$	91.4234	+	91.4234i	0.0930992	+	0.0930992i
$983$	−79.6035	+	79.6035i	−0.0809802	+	0.0809802i	−0.746437	−	0.665456i	$-0.768237\pi$
$983$	−79.6035	+	79.6035i	−0.0809802	+	0.0809802i	0.665456	+	0.746437i	$0.268237\pi$
$984$		−	13.2393i		−	0.0134546i
$985$	−51.3420	−	1507.25i	−0.0521239	−	1.53020i
$986$	146.824			0.148908
$987$	−39.8346	−	39.8346i	−0.0403593	−	0.0403593i
$988$	−864.142	+	864.142i	−0.874637	+	0.874637i
$989$			347.486i			0.351351i
$990$	176.372	−	6.00784i	0.178153	−	0.00606852i
$991$	855.911			0.863684			0.431842	−	0.901949i	$-0.357864\pi$
$991$	855.911			0.863684			0.431842	+	0.901949i	$0.357864\pi$
$992$	−87.0475	−	87.0475i	−0.0877495	−	0.0877495i
$993$	461.682	−	461.682i	0.464937	−	0.464937i
$994$			24.4660i			0.0246137i
$995$	−287.755	+	308.050i	−0.289201	+	0.309598i
$996$	−340.963			−0.342332
$997$	−372.085	−	372.085i	−0.373204	−	0.373204i	0.495439	−	0.868643i	$-0.335007\pi$
$997$	−372.085	−	372.085i	−0.373204	−	0.373204i	−0.868643	+	0.495439i	$0.835007\pi$
$998$	−793.096	+	793.096i	−0.794685	+	0.794685i
$999$		−	164.867i		−	0.165032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.6	✓	48
5.3	odd	4	inner	690.3.k.b.553.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.6	✓	48	1.1	even	1	trivial
690.3.k.b.553.6	yes	48	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-3.65385 - 3.41312i) q^{5} +2.44949 q^{6} +(0.283627 + 0.283627i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-3.65385 - 3.41312i) q^{5} +2.44949 q^{6} +(0.283627 + 0.283627i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(0.240725 + 7.06697i) q^{10} +8.31907 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-17.3963 + 17.3963i) q^{13} -0.567254i q^{14} +(8.65523 - 0.294827i) q^{15} -4.00000 q^{16} +(9.44849 + 9.44849i) q^{17} +(-3.00000 + 3.00000i) q^{18} -24.8369i q^{19} +(6.82624 - 7.30769i) q^{20} -0.694742 q^{21} +(-8.31907 - 8.31907i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(1.70120 + 24.9421i) q^{25} +34.7926 q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.567254 + 0.567254i) q^{28} +7.76969i q^{29} +(-8.95006 - 8.36041i) q^{30} -21.7619 q^{31} +(4.00000 + 4.00000i) q^{32} +(-10.1887 + 10.1887i) q^{33} -18.8970i q^{34} +(-0.0682763 - 2.00438i) q^{35} +6.00000 q^{36} +(-22.4355 - 22.4355i) q^{37} +(-24.8369 + 24.8369i) q^{38} -42.6121i q^{39} +(-14.1339 + 0.481451i) q^{40} -2.70246 q^{41} +(0.694742 + 0.694742i) q^{42} +(51.2340 - 51.2340i) q^{43} +16.6381i q^{44} +(-10.2394 + 10.9615i) q^{45} +6.78233 q^{46} +(57.3373 + 57.3373i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.8391i q^{49} +(23.2409 - 26.6433i) q^{50} -23.1440 q^{51} +(-34.7926 - 34.7926i) q^{52} +(57.8310 - 57.8310i) q^{53} -7.34847i q^{54} +(-30.3966 - 28.3940i) q^{55} +1.13451 q^{56} +(30.4189 + 30.4189i) q^{57} +(7.76969 - 7.76969i) q^{58} -17.1617i q^{59} +(0.589655 + 17.3105i) q^{60} +88.9356 q^{61} +(21.7619 + 21.7619i) q^{62} +(0.850881 - 0.850881i) q^{63} -8.00000i q^{64} +(122.939 - 4.18774i) q^{65} +20.3775 q^{66} +(53.5253 + 53.5253i) q^{67} +(-18.8970 + 18.8970i) q^{68} -8.30662i q^{69} +(-1.93611 + 2.07266i) q^{70} -43.1306 q^{71} +(-6.00000 - 6.00000i) q^{72} +(18.0830 - 18.0830i) q^{73} +44.8711i q^{74} +(-32.6312 - 28.4641i) q^{75} +49.6738 q^{76} +(2.35951 + 2.35951i) q^{77} +(-42.6121 + 42.6121i) q^{78} -155.462i q^{79} +(14.6154 + 13.6525i) q^{80} -9.00000 q^{81} +(2.70246 + 2.70246i) q^{82} +(69.5987 - 69.5987i) q^{83} -1.38948i q^{84} +(-2.27449 - 66.7722i) q^{85} -102.468 q^{86} +(-9.51588 - 9.51588i) q^{87} +(16.6381 - 16.6381i) q^{88} -67.8698i q^{89} +(21.2009 - 0.722176i) q^{90} -9.86814 q^{91} +(-6.78233 - 6.78233i) q^{92} +(26.6527 - 26.6527i) q^{93} -114.675i q^{94} +(-84.7714 + 90.7503i) q^{95} -9.79796 q^{96} +(48.4229 + 48.4229i) q^{97} +(-48.8391 + 48.8391i) q^{98} -24.9572i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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