LMFDB - Embedded newform 690.3.k.b.553.6

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			553.6
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.6

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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	−0.686557	−	0.727076i	$-0.740879\pi$
$7$	0.283627	−	0.283627i	0.0405182	−	0.0405182i	0.727076	+	0.686557i	$0.240879\pi$
$8$	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	−0.897824	−	0.440355i	$-0.854853\pi$
$13$	−17.3963	−	17.3963i	−1.33818	−	1.33818i	−0.440355	−	0.897824i	$-0.645147\pi$
$14$			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	−0.372313	−	0.928107i	$-0.621435\pi$
$17$	9.44849	−	9.44849i	0.555794	−	0.555794i	0.928107	+	0.372313i	$0.121435\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			24.8369i			1.30721i	0.756838	+	0.653603i	$0.226743\pi$
$19$			24.8369i			1.30721i	−0.756838	+	0.653603i	$0.773257\pi$
$20$	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	$-0.957231\pi$
$29$		−	7.76969i		−	0.267920i	0.990987	−	0.133960i	$-0.0427694\pi$
$30$	−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	−0.941994	−	0.335629i	$-0.891051\pi$
$37$	−22.4355	+	22.4355i	−0.606366	+	0.606366i	0.335629	+	0.941994i	$0.391051\pi$
$38$	−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	0.976649	+	0.214840i	$0.0689231\pi$
$43$	51.2340	+	51.2340i	1.19149	+	1.19149i	0.214840	+	0.976649i	$0.431077\pi$
$44$		−	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	0.252292	−	0.967651i	$-0.418816\pi$
$47$	57.3373	−	57.3373i	1.21994	−	1.21994i	0.967651	−	0.252292i	$-0.0811843\pi$
$48$	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	0.995406	+	0.0957461i	$0.0305237\pi$
$53$	57.8310	+	57.8310i	1.09115	+	1.09115i	0.0957461	+	0.995406i	$0.469476\pi$
$54$			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	$0.0464593\pi$
$59$			17.1617i			0.290877i	−0.989367	+	0.145439i	$0.953541\pi$
$60$	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	−0.184034	−	0.982920i	$-0.558916\pi$
$67$	53.5253	−	53.5253i	0.798885	−	0.798885i	0.982920	+	0.184034i	$0.0589158\pi$
$68$	−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	0.820031	−	0.572319i	$-0.193956\pi$
$73$	18.0830	+	18.0830i	0.247712	+	0.247712i	−0.572319	+	0.820031i	$0.693956\pi$
$74$		−	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	$0.442870\pi$
$79$			155.462i			1.96787i	−0.178518	+	0.983937i	$0.557130\pi$
$80$	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	0.988667	−	0.150128i	$-0.0479686\pi$
$83$	69.5987	+	69.5987i	0.838538	+	0.838538i	−0.150128	+	0.988667i	$0.547969\pi$
$84$			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	$0.124520\pi$
$89$			67.8698i			0.762582i	−0.924455	+	0.381291i	$0.875480\pi$
$90$	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	−0.411985	−	0.911191i	$-0.635164\pi$
$97$	48.4229	−	48.4229i	0.499206	−	0.499206i	0.911191	+	0.411985i	$0.135164\pi$
$98$	−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	0.145220	−	0.989399i	$-0.453611\pi$
$103$	−86.9504	−	86.9504i	−0.844179	−	0.844179i	−0.989399	+	0.145220i	$0.953611\pi$
$104$		−	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	−0.776214	−	0.630469i	$-0.782863\pi$
$107$	−15.5948	+	15.5948i	−0.145746	+	0.145746i	0.630469	+	0.776214i	$0.282863\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	13.7730i		−	0.126358i	−0.998002	−	0.0631789i	$-0.979876\pi$
$109$		−	13.7730i		−	0.126358i	0.998002	−	0.0631789i	$-0.0201239\pi$
$110$	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	0.997683	−	0.0680291i	$-0.0216711\pi$
$113$	105.051	+	105.051i	0.929654	+	0.929654i	−0.0680291	+	0.997683i	$0.521671\pi$
$114$			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	−0.789611	−	0.613608i	$-0.789718\pi$
$127$	−22.3524	+	22.3524i	−0.176003	+	0.176003i	0.613608	+	0.789611i	$0.289718\pi$
$128$	−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	−0.670573	−	0.741844i	$-0.733952\pi$
$137$	9.76414	−	9.76414i	0.0712711	−	0.0712711i	0.741844	+	0.670573i	$0.233952\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$		−	83.2727i		−	0.599084i	−0.954083	−	0.299542i	$-0.903166\pi$
$139$		−	83.2727i		−	0.599084i	0.954083	−	0.299542i	$-0.0968339\pi$
$140$	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	$0.372110\pi$
$149$			274.269i			1.84073i	−0.391056	+	0.920367i	$0.627890\pi$
$150$	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	−0.617631	+	0.786468i	$0.711907\pi$
$157$	−220.444	+	220.444i	−1.40410	+	1.40410i	−0.786468	+	0.617631i	$0.788093\pi$
$158$	−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	0.491571	−	0.870838i	$-0.336423\pi$
$163$	−61.8205	−	61.8205i	−0.379267	−	0.379267i	−0.870838	+	0.491571i	$0.836423\pi$
$164$			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	−0.719153	−	0.694852i	$-0.755470\pi$
$167$	−4.05814	+	4.05814i	−0.0243003	+	0.0243003i	0.694852	+	0.719153i	$0.255470\pi$
$168$	−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	0.0473870	−	0.998877i	$-0.484911\pi$
$173$	−164.608	−	164.608i	−0.951490	−	0.951490i	−0.998877	+	0.0473870i	$0.984911\pi$
$174$		−	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	$-0.705596\pi$
$179$		−	285.884i		−	1.59712i	0.601917	−	0.798559i	$-0.294404\pi$
$180$	−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	0.238751	−	0.971081i	$-0.423262\pi$
$193$	−141.340	−	141.340i	−0.732330	−	0.732330i	−0.971081	+	0.238751i	$0.923262\pi$
$194$			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	0.0863791	−	0.996262i	$-0.472470\pi$
$197$	213.280	−	213.280i	1.08264	−	1.08264i	0.996262	−	0.0863791i	$-0.0275296\pi$
$198$	−24.9572	−	24.9572i	−0.126047	−	0.126047i
$199$			84.3085i			0.423661i	0.977306	+	0.211830i	$0.0679424\pi$
$199$			84.3085i			0.423661i	−0.977306	+	0.211830i	$0.932058\pi$
$200$	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	0.794654	−	0.607062i	$-0.207652\pi$
$223$	41.8331	+	41.8331i	0.187592	+	0.187592i	−0.607062	+	0.794654i	$0.707652\pi$
$224$		−	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	−0.343228	−	0.939252i	$-0.611520\pi$
$227$	135.297	−	135.297i	0.596024	−	0.596024i	0.939252	+	0.343228i	$0.111520\pi$
$228$	−60.8378	−	60.8378i	−0.266832	−	0.266832i
$229$		−	337.019i		−	1.47170i	−0.677145	−	0.735850i	$-0.736783\pi$
$229$		−	337.019i		−	1.47170i	0.677145	−	0.735850i	$-0.263217\pi$
$230$	−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	0.445506	−	0.895279i	$-0.353024\pi$
$233$	−104.797	−	104.797i	−0.449772	−	0.449772i	−0.895279	+	0.445506i	$0.853024\pi$
$234$			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	$0.154530\pi$
$239$			223.047i			0.933250i	−0.884455	+	0.466625i	$0.845470\pi$
$240$	−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	−0.272633	−	0.962118i	$-0.587895\pi$
$257$	177.198	−	177.198i	0.689485	−	0.689485i	0.962118	+	0.272633i	$0.0878946\pi$
$258$	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	0.119300	−	0.992858i	$-0.461935\pi$
$263$	−229.746	−	229.746i	−0.873558	−	0.873558i	−0.992858	+	0.119300i	$0.961935\pi$
$264$		−	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	$-0.868074\pi$
$269$		−	216.650i		−	0.805389i	0.915334	−	0.402695i	$-0.131926\pi$
$270$	−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	−0.827917	−	0.560850i	$-0.810474\pi$
$277$	−73.9775	+	73.9775i	−0.267067	+	0.267067i	0.560850	+	0.827917i	$0.310474\pi$
$278$	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	0.365382	−	0.930858i	$-0.380938\pi$
$283$	−160.030	−	160.030i	−0.565475	−	0.565475i	−0.930858	+	0.365382i	$0.880938\pi$
$284$			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	0.997687	−	0.0679767i	$-0.0216543\pi$
$293$	272.405	+	272.405i	0.929710	+	0.929710i	−0.0679767	+	0.997687i	$0.521654\pi$
$294$			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	−0.342259	−	0.939606i	$-0.611192\pi$
$307$	183.385	−	183.385i	0.597346	−	0.597346i	0.939606	+	0.342259i	$0.111192\pi$
$308$	−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	0.722758	−	0.691101i	$-0.242874\pi$
$313$	9.90854	+	9.90854i	0.0316567	+	0.0316567i	−0.691101	+	0.722758i	$0.742874\pi$
$314$		−	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	−0.668989	−	0.743272i	$-0.733273\pi$
$317$	23.5479	−	23.5479i	0.0742837	−	0.0742837i	0.743272	+	0.668989i	$0.233273\pi$
$318$	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	−0.120446	+	0.992720i	$0.538432\pi$
$337$	−375.137	+	375.137i	−1.11317	+	1.11317i	−0.992720	+	0.120446i	$0.961568\pi$
$338$	−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	−0.181389	+	0.983411i	$0.558059\pi$
$347$	−404.186	+	404.186i	−1.16480	+	1.16480i	−0.983411	+	0.181389i	$0.941941\pi$
$348$	19.0318	+	19.0318i	0.0546890	+	0.0546890i
$349$			99.8402i			0.286075i	0.989717	+	0.143038i	$0.0456870\pi$
$349$			99.8402i			0.286075i	−0.989717	+	0.143038i	$0.954313\pi$
$350$	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	0.963004	+	0.269486i	$0.0868538\pi$
$353$	435.069	+	435.069i	1.23249	+	1.23249i	0.269486	+	0.963004i	$0.413146\pi$
$354$			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	$0.117220\pi$
$359$			258.473i			0.719980i	−0.932956	+	0.359990i	$0.882780\pi$
$360$	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	−0.566292	−	0.824205i	$-0.691622\pi$
$367$	94.6541	−	94.6541i	0.257913	−	0.257913i	0.824205	+	0.566292i	$0.191622\pi$
$368$	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	0.998455	+	0.0555700i	$0.0176976\pi$
$373$	393.151	+	393.151i	1.05402	+	1.05402i	0.0555700	+	0.998455i	$0.482302\pi$
$374$			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	$0.0736700\pi$
$379$			173.870i			0.458761i	−0.973337	+	0.229380i	$0.926330\pi$
$380$	−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	0.986124	−	0.166009i	$-0.0530881\pi$
$383$	314.104	+	314.104i	0.820115	+	0.820115i	−0.166009	+	0.986124i	$0.553088\pi$
$384$			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	$-0.986249\pi$
$389$		−	33.5984i		−	0.0863712i	0.999067	−	0.0431856i	$-0.0137507\pi$
$390$	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	−0.247309	−	0.968937i	$-0.579546\pi$
$397$	286.486	−	286.486i	0.721628	−	0.721628i	0.968937	+	0.247309i	$0.0795462\pi$
$398$	−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	$0.102733\pi$
$409$			259.446i			0.634342i	−0.948368	+	0.317171i	$0.897267\pi$
$410$	−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	$-0.972987\pi$
$419$		−	71.0303i		−	0.169523i	0.996401	−	0.0847617i	$-0.0270129\pi$
$420$	−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	0.553356	−	0.832945i	$-0.313347\pi$
$433$	−121.062	−	121.062i	−0.279590	−	0.279590i	−0.832945	+	0.553356i	$0.813347\pi$
$434$		−	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	$-0.627177\pi$
$439$		−	808.849i		−	1.84248i	0.388993	−	0.921241i	$-0.372823\pi$
$440$	−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	0.839791	−	0.542910i	$-0.182678\pi$
$443$	131.518	+	131.518i	0.296881	+	0.296881i	−0.542910	+	0.839791i	$0.682678\pi$
$444$		−	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	$0.259191\pi$
$449$			653.049i			1.45445i	−0.686398	+	0.727226i	$0.740809\pi$
$450$	−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	−0.770649	−	0.637259i	$-0.780068\pi$
$457$	−60.9591	+	60.9591i	−0.133390	+	0.133390i	0.637259	+	0.770649i	$0.280068\pi$
$458$	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	−0.994209	−	0.107464i	$-0.965727\pi$
$463$	−510.074	−	510.074i	−1.10167	−	1.10167i	−0.107464	−	0.994209i	$-0.534273\pi$
$464$			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	−0.798561	−	0.601914i	$-0.794405\pi$
$467$	−91.8344	+	91.8344i	−0.196647	+	0.196647i	0.601914	+	0.798561i	$0.294405\pi$
$468$	−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	$0.0956191\pi$
$479$			283.471i			0.591797i	−0.955219	+	0.295899i	$0.904381\pi$
$480$	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	0.175518	−	0.984476i	$-0.443840\pi$
$487$	564.917	−	564.917i	1.15999	−	1.15999i	0.984476	−	0.175518i	$-0.0561600\pi$
$488$	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	$0.292364\pi$
$499$			793.096i			1.58937i	−0.607021	+	0.794685i	$0.707636\pi$
$500$	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	−0.997371	−	0.0724666i	$-0.976913\pi$
$503$	−538.128	−	538.128i	−1.06984	−	1.06984i	−0.0724666	−	0.997371i	$-0.523087\pi$
$504$			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	$-0.916105\pi$
$509$		−	265.214i		−	0.521049i	0.965467	−	0.260524i	$-0.0838954\pi$
$510$	−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	0.278021	−	0.960575i	$-0.410322\pi$
$523$	−356.976	−	356.976i	−0.682554	−	0.682554i	−0.960575	+	0.278021i	$0.910322\pi$
$524$		−	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	−0.170395	−	0.985376i	$-0.554504\pi$
$547$	445.794	−	445.794i	0.814981	−	0.814981i	0.985376	+	0.170395i	$0.0545044\pi$
$548$	−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	−0.0828770	+	0.996560i	$0.526411\pi$
$557$	−601.246	+	601.246i	−1.07944	+	1.07944i	−0.996560	+	0.0828770i	$0.973589\pi$
$558$	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	0.848252	−	0.529592i	$-0.177655\pi$
$563$	179.406	+	179.406i	0.318660	+	0.318660i	−0.529592	+	0.848252i	$0.677655\pi$
$564$			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	$-0.962994\pi$
$569$		−	132.003i		−	0.231991i	0.993250	−	0.115995i	$-0.0370058\pi$
$570$	−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	−0.978404	−	0.206701i	$-0.933727\pi$
$577$	−445.272	+	445.272i	−0.771703	+	0.771703i	0.206701	+	0.978404i	$0.433727\pi$
$578$	−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	−0.973661	−	0.227999i	$-0.926782\pi$
$587$	−437.704	+	437.704i	−0.745663	+	0.745663i	0.227999	+	0.973661i	$0.426782\pi$
$588$	−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	0.999782	+	0.0208625i	$0.00664122\pi$
$593$	605.242	+	605.242i	1.02064	+	1.02064i	0.0208625	+	0.999782i	$0.493359\pi$
$594$			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	$-0.719814\pi$
$599$		−	923.521i		−	1.54177i	0.636974	−	0.770886i	$-0.280186\pi$
$600$	−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	−0.918725	−	0.394898i	$-0.870780\pi$
$607$	−317.963	+	317.963i	−0.523826	+	0.523826i	0.394898	+	0.918725i	$0.370780\pi$
$608$	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	0.116347	−	0.993209i	$-0.462881\pi$
$613$	−537.516	−	537.516i	−0.876861	−	0.876861i	−0.993209	+	0.116347i	$0.962881\pi$
$614$			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	−0.996760	−	0.0804392i	$-0.974368\pi$
$617$	−565.370	+	565.370i	−0.916320	+	0.916320i	0.0804392	+	0.996760i	$0.474368\pi$
$618$	−212.984	−	212.984i	−0.344635	−	0.344635i
$619$		−	60.9967i		−	0.0985407i	−0.998785	−	0.0492703i	$-0.984310\pi$
$619$		−	60.9967i		−	0.0985407i	0.998785	−	0.0492703i	$-0.0156896\pi$
$620$	−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	0.949852	−	0.312701i	$-0.101234\pi$
$643$	409.688	+	409.688i	0.637151	+	0.637151i	−0.312701	+	0.949852i	$0.601234\pi$
$644$			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	−0.299037	−	0.954241i	$-0.596665\pi$
$647$	423.917	−	423.917i	0.655204	−	0.655204i	0.954241	+	0.299037i	$0.0966654\pi$
$648$	−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	0.994285	−	0.106756i	$-0.0340463\pi$
$653$	579.557	+	579.557i	0.887530	+	0.887530i	−0.106756	+	0.994285i	$0.534046\pi$
$654$		−	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	$-0.897298\pi$
$659$		−	417.909i		−	0.634156i	0.948399	−	0.317078i	$-0.102702\pi$
$660$	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	0.483864	−	0.875143i	$-0.339233\pi$
$673$	−263.331	−	263.331i	−0.391280	−	0.391280i	−0.875143	+	0.483864i	$0.839233\pi$
$674$		−	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	−0.670866	−	0.741579i	$-0.734077\pi$
$677$	47.8727	−	47.8727i	0.0707130	−	0.0707130i	0.741579	+	0.670866i	$0.234077\pi$
$678$	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	0.968440	−	0.249247i	$-0.0801832\pi$
$683$	491.209	+	491.209i	0.719193	+	0.719193i	−0.249247	+	0.968440i	$0.580183\pi$
$684$			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	$0.128539\pi$
$709$			557.179i			0.785865i	−0.919567	+	0.392933i	$0.871461\pi$
$710$	−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	$-0.837004\pi$
$719$		−	704.591i		−	0.979960i	0.871734	−	0.489980i	$-0.162996\pi$
$720$	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	−0.774700	−	0.632328i	$-0.782099\pi$
$727$	−103.504	+	103.504i	−0.142372	+	0.142372i	0.632328	+	0.774700i	$0.282099\pi$
$728$	−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	0.925033	−	0.379887i	$-0.124037\pi$
$733$	399.591	+	399.591i	0.545145	+	0.545145i	−0.379887	+	0.925033i	$0.624037\pi$
$734$			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	$-0.898416\pi$
$739$		−	463.718i		−	0.627494i	0.949507	−	0.313747i	$-0.101584\pi$
$740$	−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	0.796556	−	0.604564i	$-0.206653\pi$
$743$	142.650	+	142.650i	0.191992	+	0.191992i	−0.604564	+	0.796556i	$0.706653\pi$
$744$			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	−0.477663	−	0.878543i	$-0.658516\pi$
$757$	303.467	−	303.467i	0.400881	−	0.400881i	0.878543	+	0.477663i	$0.158516\pi$
$758$	−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	$0.157696\pi$
$769$			731.164i			0.950798i	−0.879770	+	0.475399i	$0.842304\pi$
$770$	−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	0.161880	−	0.986810i	$-0.448244\pi$
$773$	−637.671	−	637.671i	−0.824931	−	0.824931i	−0.986810	+	0.161880i	$0.948244\pi$
$774$		−	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	−0.798435	−	0.602081i	$-0.794338\pi$
$787$	−154.530	+	154.530i	−0.196353	+	0.196353i	0.602081	+	0.798435i	$0.294338\pi$
$788$	−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	−0.448244	+	0.893911i	$0.647950\pi$
$797$	−1069.70	+	1069.70i	−1.34216	+	1.34216i	−0.893911	+	0.448244i	$0.852050\pi$
$798$	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	$-0.970634\pi$
$809$		−	149.059i		−	0.184251i	0.995747	−	0.0921256i	$-0.0293661\pi$
$810$	−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	0.0681885	−	0.997672i	$-0.478278\pi$
$823$	−764.965	−	764.965i	−0.929484	−	0.929484i	−0.997672	+	0.0681885i	$0.978278\pi$
$824$		−	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	−0.821111	−	0.570769i	$-0.806645\pi$
$827$	−207.033	+	207.033i	−0.250342	+	0.250342i	0.570769	+	0.821111i	$0.306645\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$		−	1069.74i		−	1.29040i	−0.764015	−	0.645198i	$-0.776775\pi$
$829$		−	1069.74i		−	1.29040i	0.764015	−	0.645198i	$-0.223225\pi$
$830$	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	$-0.962406\pi$
$839$		−	197.720i		−	0.235662i	0.993034	−	0.117831i	$-0.0375940\pi$
$840$	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	0.960165	−	0.279433i	$-0.0901465\pi$
$853$	580.665	+	580.665i	0.680732	+	0.680732i	−0.279433	+	0.960165i	$0.590146\pi$
$854$			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	−0.0936607	−	0.995604i	$-0.529857\pi$
$857$	772.966	−	772.966i	0.901943	−	0.901943i	0.995604	+	0.0936607i	$0.0298569\pi$
$858$	−354.493	−	354.493i	−0.413162	−	0.413162i
$859$		−	172.504i		−	0.200820i	−0.994946	−	0.100410i	$-0.967985\pi$
$859$		−	172.504i		−	0.200820i	0.994946	−	0.100410i	$-0.0320155\pi$
$860$	−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	0.336288	−	0.941759i	$-0.390829\pi$
$863$	−522.522	−	522.522i	−0.605472	−	0.605472i	−0.941759	+	0.336288i	$0.890829\pi$
$864$		−	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	−0.172267	−	0.985050i	$-0.555109\pi$
$877$	712.811	−	712.811i	0.812783	−	0.812783i	0.985050	+	0.172267i	$0.0551093\pi$
$878$	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	0.615904	−	0.787821i	$-0.288791\pi$
$883$	−151.803	−	151.803i	−0.171917	−	0.171917i	−0.787821	+	0.615904i	$0.788791\pi$
$884$			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	−0.222916	+	0.974838i	$0.571558\pi$
$887$	−1062.41	+	1062.41i	−1.19775	+	1.19775i	−0.974838	+	0.222916i	$0.928442\pi$
$888$	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	−0.698919	−	0.715201i	$-0.746335\pi$
$907$	14.7685	−	14.7685i	0.0162828	−	0.0162828i	0.715201	+	0.698919i	$0.246335\pi$
$908$	−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	$0.0414270\pi$
$919$			238.535i			0.259560i	−0.991543	+	0.129780i	$0.958573\pi$
$920$	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	$-0.895279\pi$
$929$		−	600.298i		−	0.646177i	0.946369	−	0.323088i	$-0.104721\pi$
$930$	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	−0.834739	−	0.550647i	$-0.814381\pi$
$937$	−266.194	+	266.194i	−0.284092	+	0.284092i	0.550647	+	0.834739i	$0.314381\pi$
$938$	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	−0.914387	−	0.404842i	$-0.867327\pi$
$947$	−482.539	+	482.539i	−0.509545	+	0.509545i	0.404842	+	0.914387i	$0.367327\pi$
$948$	−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	0.696154	−	0.717892i	$-0.254893\pi$
$953$	−20.7166	−	20.7166i	−0.0217383	−	0.0217383i	−0.717892	+	0.696154i	$0.754893\pi$
$954$		−	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	−0.625563	−	0.780174i	$-0.715131\pi$
$967$	149.509	−	149.509i	0.154611	−	0.154611i	0.780174	+	0.625563i	$0.215131\pi$
$968$	−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	−0.827523	−	0.561432i	$-0.810251\pi$
$977$	−259.971	+	259.971i	−0.266091	+	0.266091i	0.561432	+	0.827523i	$0.310251\pi$
$978$	−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	0.665456	−	0.746437i	$-0.268237\pi$
$983$	−79.6035	−	79.6035i	−0.0809802	−	0.0809802i	−0.746437	+	0.665456i	$0.768237\pi$
$984$			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	−0.868643	−	0.495439i	$-0.835007\pi$
$997$	−372.085	+	372.085i	−0.373204	+	0.373204i	0.495439	+	0.868643i	$0.335007\pi$
$998$	−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.553.6	yes	48
5.2	odd	4	inner	690.3.k.b.277.6	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.6	✓	48	5.2	odd	4	inner
690.3.k.b.553.6	yes	48	1.1	even	1	trivial

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

Related objects

Downloads

Learn more