LMFDB - Embedded newform 220.3.x.a.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(37,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("220.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.x (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	220.37
Dual form			220.3.x.a.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72462 - 3.38475i) q^{3} +(-0.450384 + 4.97967i) q^{5} +(5.09251 - 9.99462i) q^{7} +(-3.19218 + 4.39365i) q^{9} +(-8.75765 - 6.65610i) q^{11} +(-12.3296 + 1.95282i) q^{13} +(17.6317 - 7.06359i) q^{15} +(11.2549 + 1.78260i) q^{17} +(-29.7589 - 9.66926i) q^{19} -42.6120 q^{21} +(5.52005 - 5.52005i) q^{23} +(-24.5943 - 4.48553i) q^{25} +(-13.3915 - 2.12101i) q^{27} +(-18.0017 + 5.84912i) q^{29} +(-2.07398 - 1.50684i) q^{31} +(-7.42565 + 41.1217i) q^{33} +(47.4764 + 29.8605i) q^{35} +(10.7814 - 21.1596i) q^{37} +(27.8737 + 38.3648i) q^{39} +(11.2612 - 34.6584i) q^{41} +(-23.6032 + 23.6032i) q^{43} +(-20.4413 - 17.8748i) q^{45} +(62.7083 - 31.9515i) q^{47} +(-45.1573 - 62.1537i) q^{49} +(-13.3767 - 41.1693i) q^{51} +(42.0409 - 6.65862i) q^{53} +(37.0895 - 40.6124i) q^{55} +(18.5947 + 117.402i) q^{57} +(73.5650 - 23.9027i) q^{59} +(87.2179 - 63.3675i) q^{61} +(27.6567 + 54.2793i) q^{63} +(-4.17134 - 62.2770i) q^{65} +(51.9683 + 51.9683i) q^{67} +(-28.2040 - 9.16403i) q^{69} +(-108.853 + 79.0863i) q^{71} +(6.10437 + 3.11033i) q^{73} +(27.2334 + 90.9815i) q^{75} +(-111.124 + 53.6331i) q^{77} +(0.395302 - 0.544087i) q^{79} +(31.0202 + 95.4704i) q^{81} +(8.41245 - 53.1141i) q^{83} +(-13.9458 + 55.2428i) q^{85} +(50.8439 + 50.8439i) q^{87} +22.4520i q^{89} +(-43.2710 + 133.175i) q^{91} +(-1.52344 + 9.61863i) q^{93} +(61.5527 - 143.835i) q^{95} +(11.9707 + 75.5798i) q^{97} +(57.2005 - 17.2306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72462	−	3.38475i	−0.574872	−	1.12825i	−0.977114	−	0.212717i	$-0.931769\pi$
$3$	−1.72462	−	3.38475i	−0.574872	−	1.12825i	0.402241	−	0.915534i	$-0.368231\pi$
$4$		0			0
$5$	−0.450384	+	4.97967i	−0.0900768	+	0.995935i
$5$	−0.450384	+	4.97967i	−0.0900768	+	0.995935i
$6$		0			0
$7$	5.09251	−	9.99462i	0.727502	−	1.42780i	−0.169388	−	0.985549i	$-0.554179\pi$
$7$	5.09251	−	9.99462i	0.727502	−	1.42780i	0.896890	−	0.442254i	$-0.145821\pi$
$8$		0			0
$9$	−3.19218	+	4.39365i	−0.354686	+	0.488184i
$10$		0			0
$11$	−8.75765	−	6.65610i	−0.796150	−	0.605100i
$11$	−8.75765	−	6.65610i	−0.796150	−	0.605100i
$12$		0			0
$13$	−12.3296	+	1.95282i	−0.948432	+	0.150217i	−0.611440	−	0.791291i	$-0.709409\pi$
$13$	−12.3296	+	1.95282i	−0.948432	+	0.150217i	−0.336992	+	0.941508i	$0.609409\pi$
$14$		0			0
$15$	17.6317	−	7.06359i	1.17545	−	0.470906i
$16$		0			0
$17$	11.2549	+	1.78260i	0.662052	+	0.104859i	0.478413	−	0.878135i	$-0.341212\pi$
$17$	11.2549	+	1.78260i	0.662052	+	0.104859i	0.183639	+	0.982994i	$0.441212\pi$
$18$		0			0
$19$	−29.7589	−	9.66926i	−1.56626	−	0.508908i	−0.607788	−	0.794099i	$-0.707943\pi$
$19$	−29.7589	−	9.66926i	−1.56626	−	0.508908i	−0.958471	+	0.285191i	$0.907943\pi$
$20$		0			0
$21$	−42.6120			−2.02914
$22$		0			0
$23$	5.52005	−	5.52005i	0.240002	−	0.240002i	−0.576849	−	0.816851i	$-0.695718\pi$
$23$	5.52005	−	5.52005i	0.240002	−	0.240002i	0.816851	+	0.576849i	$0.195718\pi$
$24$		0			0
$25$	−24.5943	−	4.48553i	−0.983772	−	0.179421i
$26$		0			0
$27$	−13.3915	−	2.12101i	−0.495983	−	0.0785559i
$28$		0			0
$29$	−18.0017	+	5.84912i	−0.620750	+	0.201694i	−0.602473	−	0.798139i	$-0.705818\pi$
$29$	−18.0017	+	5.84912i	−0.620750	+	0.201694i	−0.0182765	+	0.999833i	$0.505818\pi$
$30$		0			0
$31$	−2.07398	−	1.50684i	−0.0669026	−	0.0486076i	0.553831	−	0.832629i	$-0.313165\pi$
$31$	−2.07398	−	1.50684i	−0.0669026	−	0.0486076i	−0.620734	+	0.784021i	$0.713165\pi$
$32$		0			0
$33$	−7.42565	+	41.1217i	−0.225020	+	1.24611i
$34$		0			0
$35$	47.4764	+	29.8605i	1.35647	+	0.853157i
$36$		0			0
$37$	10.7814	−	21.1596i	0.291388	−	0.571882i	−0.698184	−	0.715918i	$-0.746008\pi$
$37$	10.7814	−	21.1596i	0.291388	−	0.571882i	0.989572	+	0.144037i	$0.0460083\pi$
$38$		0			0
$39$	27.8737	+	38.3648i	0.714710	+	0.983714i
$40$		0			0
$41$	11.2612	−	34.6584i	0.274664	−	0.845328i	−0.714644	−	0.699488i	$-0.753411\pi$
$41$	11.2612	−	34.6584i	0.274664	−	0.845328i	0.989308	−	0.145840i	$-0.0465885\pi$
$42$		0			0
$43$	−23.6032	+	23.6032i	−0.548912	+	0.548912i	−0.926126	−	0.377214i	$-0.876882\pi$
$43$	−23.6032	+	23.6032i	−0.548912	+	0.548912i	0.377214	+	0.926126i	$0.376882\pi$
$44$		0			0
$45$	−20.4413	−	17.8748i	−0.454250	−	0.397218i
$46$		0			0
$47$	62.7083	−	31.9515i	1.33422	−	0.679818i	0.366162	−	0.930551i	$-0.380672\pi$
$47$	62.7083	−	31.9515i	1.33422	−	0.679818i	0.968056	+	0.250733i	$0.0806715\pi$
$48$		0			0
$49$	−45.1573	−	62.1537i	−0.921577	−	1.26844i
$50$		0			0
$51$	−13.3767	−	41.1693i	−0.262288	−	0.807241i
$52$		0			0
$53$	42.0409	−	6.65862i	0.793224	−	0.125634i	0.253344	−	0.967376i	$-0.418470\pi$
$53$	42.0409	−	6.65862i	0.793224	−	0.125634i	0.539880	+	0.841742i	$0.318470\pi$
$54$		0			0
$55$	37.0895	−	40.6124i	0.674355	−	0.738408i
$56$		0			0
$57$	18.5947	+	117.402i	0.326223	+	2.05969i
$58$		0			0
$59$	73.5650	−	23.9027i	1.24686	−	0.405131i	0.390069	−	0.920786i	$-0.372451\pi$
$59$	73.5650	−	23.9027i	1.24686	−	0.405131i	0.856796	+	0.515655i	$0.172451\pi$
$60$		0			0
$61$	87.2179	−	63.3675i	1.42980	−	1.03881i	0.439748	−	0.898121i	$-0.355068\pi$
$61$	87.2179	−	63.3675i	1.42980	−	1.03881i	0.990054	−	0.140690i	$-0.0449321\pi$
$62$		0			0
$63$	27.6567	+	54.2793i	0.438995	+	0.861577i
$64$		0			0
$65$	−4.17134	−	62.2770i	−0.0641745	−	0.958107i
$66$		0			0
$67$	51.9683	+	51.9683i	0.775646	+	0.775646i	0.979087	−	0.203441i	$-0.0652126\pi$
$67$	51.9683	+	51.9683i	0.775646	+	0.775646i	−0.203441	+	0.979087i	$0.565213\pi$
$68$		0			0
$69$	−28.2040	−	9.16403i	−0.408753	−	0.132812i
$70$		0			0
$71$	−108.853	+	79.0863i	−1.53314	+	1.11389i	−0.578680	+	0.815555i	$0.696432\pi$
$71$	−108.853	+	79.0863i	−1.53314	+	1.11389i	−0.954461	+	0.298337i	$0.903568\pi$
$72$		0			0
$73$	6.10437	+	3.11033i	0.0836214	+	0.0426073i	0.495301	−	0.868721i	$-0.335058\pi$
$73$	6.10437	+	3.11033i	0.0836214	+	0.0426073i	−0.411680	+	0.911329i	$0.635058\pi$
$74$		0			0
$75$	27.2334	+	90.9815i	0.363111	+	1.21309i
$76$		0			0
$77$	−111.124	+	53.6331i	−1.44316	+	0.696534i
$78$		0			0
$79$	0.395302	−	0.544087i	0.00500383	−	0.00688718i	−0.806508	−	0.591224i	$-0.798645\pi$
$79$	0.395302	−	0.544087i	0.00500383	−	0.00688718i	0.811512	+	0.584336i	$0.198645\pi$
$80$		0			0
$81$	31.0202	+	95.4704i	0.382966	+	1.17865i
$82$		0			0
$83$	8.41245	−	53.1141i	0.101355	−	0.639929i	−0.883748	−	0.467963i	$-0.844988\pi$
$83$	8.41245	−	53.1141i	0.101355	−	0.639929i	0.985103	−	0.171966i	$-0.0550120\pi$
$84$		0			0
$85$	−13.9458	+	55.2428i	−0.164068	+	0.649915i
$86$		0			0
$87$	50.8439	+	50.8439i	0.584413	+	0.584413i
$88$		0			0
$89$			22.4520i			0.252269i	0.992013	+	0.126135i	$0.0402572\pi$
$89$			22.4520i			0.252269i	−0.992013	+	0.126135i	$0.959743\pi$
$90$		0			0
$91$	−43.2710	+	133.175i	−0.475506	+	1.46346i
$92$		0			0
$93$	−1.52344	+	9.61863i	−0.0163811	+	0.103426i
$94$		0			0
$95$	61.5527	−	143.835i	0.647923	−	1.51405i
$96$		0			0
$97$	11.9707	+	75.5798i	0.123409	+	0.779174i	0.969311	+	0.245836i	$0.0790625\pi$
$97$	11.9707	+	75.5798i	0.123409	+	0.779174i	−0.845902	+	0.533338i	$0.820938\pi$
$98$		0			0
$99$	57.2005	−	17.2306i	0.577783	−	0.174047i
$100$		0			0
$101$	−4.48031	−	3.25514i	−0.0443595	−	0.0322291i	0.565385	−	0.824827i	$-0.308728\pi$
$101$	−4.48031	−	3.25514i	−0.0443595	−	0.0322291i	−0.609744	+	0.792598i	$0.708728\pi$
$102$		0			0
$103$	−127.934	−	65.1855i	−1.24208	−	0.632869i	−0.295498	−	0.955343i	$-0.595485\pi$
$103$	−127.934	−	65.1855i	−1.24208	−	0.632869i	−0.946578	+	0.322474i	$0.895485\pi$
$104$		0			0
$105$	19.1917	−	212.194i	0.182779	−	2.02089i
$106$		0			0
$107$	49.6589	−	25.3025i	0.464102	−	0.236472i	−0.206273	−	0.978495i	$-0.566133\pi$
$107$	49.6589	−	25.3025i	0.464102	−	0.236472i	0.670375	+	0.742023i	$0.266133\pi$
$108$		0			0
$109$		−	130.679i		−	1.19889i	−0.800415	−	0.599447i	$-0.795387\pi$
$109$		−	130.679i		−	1.19889i	0.800415	−	0.599447i	$-0.204613\pi$
$110$		0			0
$111$	−90.2138			−0.812737
$112$		0			0
$113$	−37.8895	−	74.3623i	−0.335305	−	0.658074i	0.660373	−	0.750937i	$-0.270398\pi$
$113$	−37.8895	−	74.3623i	−0.335305	−	0.658074i	−0.995679	+	0.0928635i	$0.970398\pi$
$114$		0			0
$115$	25.0019	+	29.9742i	0.217408	+	0.260645i
$116$		0			0
$117$	30.7783	−	60.4058i	0.263062	−	0.516289i
$118$		0			0
$119$	75.1320	−	103.410i	0.631362	−	0.868995i
$120$		0			0
$121$	32.3927	+	116.583i	0.267709	+	0.963500i
$122$		0			0
$123$	−136.732	+	21.6562i	−1.11164	+	0.176066i
$124$		0			0
$125$	33.4134	−	120.451i	0.267307	−	0.963611i
$126$		0			0
$127$	198.096	+	31.3753i	1.55981	+	0.247049i	0.875891	−	0.482510i	$-0.160275\pi$
$127$	198.096	+	31.3753i	1.55981	+	0.247049i	0.683918	+	0.729559i	$0.260275\pi$
$128$		0			0
$129$	120.598	+	39.1845i	0.934865	+	0.303756i
$130$		0			0
$131$	−110.511			−0.843595			−0.421797	−	0.906690i	$-0.638601\pi$
$131$	−110.511			−0.843595			−0.421797	+	0.906690i	$0.638601\pi$
$132$		0			0
$133$	−248.188	+	248.188i	−1.86608	+	1.86608i
$134$		0			0
$135$	16.5933	−	65.7302i	0.122913	−	0.486890i
$136$		0			0
$137$	170.244	+	26.9641i	1.24266	+	0.196818i	0.742933	−	0.669366i	$-0.233434\pi$
$137$	170.244	+	26.9641i	1.24266	+	0.196818i	0.499726	+	0.866184i	$0.333434\pi$
$138$		0			0
$139$	−111.384	+	36.1908i	−0.801321	+	0.260365i	−0.680918	−	0.732360i	$-0.738419\pi$
$139$	−111.384	+	36.1908i	−0.801321	+	0.260365i	−0.120404	+	0.992725i	$0.538419\pi$
$140$		0			0
$141$	−216.296	−	157.148i	−1.53401	−	1.11452i
$142$		0			0
$143$	120.977	+	64.9650i	0.845990	+	0.454301i
$144$		0			0
$145$	−21.0190	−	92.2771i	−0.144959	−	0.636394i
$146$		0			0
$147$	−132.496	+	260.038i	−0.901332	+	1.76896i
$148$		0			0
$149$	5.49306	+	7.56054i	0.0368661	+	0.0507419i	0.827052	−	0.562125i	$-0.190016\pi$
$149$	5.49306	+	7.56054i	0.0368661	+	0.0507419i	−0.790186	+	0.612867i	$0.790016\pi$
$150$		0			0
$151$	43.8034	−	134.813i	0.290089	−	0.892802i	−0.694738	−	0.719263i	$-0.744480\pi$
$151$	43.8034	−	134.813i	0.290089	−	0.892802i	0.984827	−	0.173539i	$-0.0555203\pi$
$152$		0			0
$153$	−43.7597	+	43.7597i	−0.286011	+	0.286011i
$154$		0			0
$155$	8.43764	−	9.64910i	0.0544364	−	0.0622522i
$156$		0			0
$157$	−192.492	+	98.0794i	−1.22606	+	0.624710i	−0.942488	−	0.334241i	$-0.891520\pi$
$157$	−192.492	+	98.0794i	−1.22606	+	0.624710i	−0.283574	+	0.958950i	$0.591520\pi$
$158$		0			0
$159$	−95.0422	−	130.814i	−0.597750	−	0.822732i
$160$		0			0
$161$	−27.0599	−	83.2818i	−0.168074	−	0.517278i
$162$		0			0
$163$	272.746	−	43.1988i	1.67329	−	0.265023i	0.753504	−	0.657443i	$-0.228362\pi$
$163$	272.746	−	43.1988i	1.67329	−	0.265023i	0.919786	+	0.392420i	$0.128362\pi$
$164$		0			0
$165$	−201.428	−	55.4979i	−1.22078	−	0.336351i
$166$		0			0
$167$	−36.8986	−	232.969i	−0.220950	−	1.39502i	−0.809765	−	0.586754i	$-0.800405\pi$
$167$	−36.8986	−	232.969i	−0.220950	−	1.39502i	0.588815	−	0.808268i	$-0.299595\pi$
$168$		0			0
$169$	−12.5226	+	4.06885i	−0.0740985	+	0.0240761i
$170$		0			0
$171$	137.479	−	99.8844i	0.803971	−	0.584119i
$172$		0			0
$173$	−8.40995	−	16.5055i	−0.0486124	−	0.0954072i	0.865422	−	0.501043i	$-0.167050\pi$
$173$	−8.40995	−	16.5055i	−0.0486124	−	0.0954072i	−0.914035	+	0.405636i	$0.867050\pi$
$174$		0			0
$175$	−170.078	+	222.968i	−0.971875	+	1.27410i
$176$		0			0
$177$	−207.776	−	207.776i	−1.17388	−	1.17388i
$178$		0			0
$179$	227.245	+	73.8362i	1.26952	+	0.412493i	0.864878	−	0.501981i	$-0.167395\pi$
$179$	227.245	+	73.8362i	1.26952	+	0.412493i	0.404644	+	0.914474i	$0.367395\pi$
$180$		0			0
$181$	−23.5411	+	17.1036i	−0.130062	+	0.0944953i	−0.650914	−	0.759151i	$-0.725614\pi$
$181$	−23.5411	+	17.1036i	−0.130062	+	0.0944953i	0.520852	+	0.853647i	$0.325614\pi$
$182$		0			0
$183$	−364.901	−	185.926i	−1.99399	−	1.01599i
$184$		0			0
$185$	100.512	+	63.2176i	0.543309	+	0.341717i
$186$		0			0
$187$	−86.7011	−	90.5249i	−0.463642	−	0.484091i
$188$		0			0
$189$	−89.3953	+	123.042i	−0.472991	+	0.651016i
$190$		0			0
$191$	105.710	+	325.341i	0.553454	+	1.70336i	0.699992	+	0.714151i	$0.253187\pi$
$191$	105.710	+	325.341i	0.553454	+	1.70336i	−0.146538	+	0.989205i	$0.546813\pi$
$192$		0			0
$193$	−4.04216	+	25.5212i	−0.0209439	+	0.132234i	−0.995945	−	0.0899664i	$-0.971324\pi$
$193$	−4.04216	+	25.5212i	−0.0209439	+	0.132234i	0.975001	+	0.222201i	$0.0713240\pi$
$194$		0			0
$195$	−203.598	+	121.523i	−1.04409	+	0.623195i
$196$		0			0
$197$	186.939	+	186.939i	0.948927	+	0.948927i	0.998758	−	0.0498310i	$-0.0158683\pi$
$197$	186.939	+	186.939i	0.948927	+	0.948927i	−0.0498310	+	0.998758i	$0.515868\pi$
$198$		0			0
$199$		−	196.593i		−	0.987904i	−0.869489	−	0.493952i	$-0.835552\pi$
$199$		−	196.593i		−	0.987904i	0.869489	−	0.493952i	$-0.164448\pi$
$200$		0			0
$201$	86.2743	−	265.525i	0.429226	−	1.32102i
$202$		0			0
$203$	−33.2144	+	209.707i	−0.163618	+	1.03304i
$204$		0			0
$205$	167.516	+	71.6868i	0.817151	+	0.349692i
$206$		0			0
$207$	6.63222	+	41.8742i	0.0320397	+	0.202291i
$208$		0			0
$209$	196.259	+	282.758i	0.939036	+	1.35291i
$210$		0			0
$211$	−300.828	−	218.565i	−1.42573	−	1.03585i	−0.990793	−	0.135389i	$-0.956772\pi$
$211$	−300.828	−	218.565i	−1.42573	−	1.03585i	−0.434934	−	0.900462i	$-0.643228\pi$
$212$		0			0
$213$	455.417	+	232.047i	2.13811	+	1.08942i
$214$		0			0
$215$	−106.906	−	128.167i	−0.497236	−	0.596125i
$216$		0			0
$217$	−25.6220	+	13.0551i	−0.118074	+	0.0601616i
$218$		0			0
$219$		−	26.0259i		−	0.118840i
$220$		0			0
$221$	−142.249			−0.643663
$222$		0			0
$223$	−153.651	−	301.558i	−0.689019	−	1.35228i	−0.924794	−	0.380469i	$-0.875763\pi$
$223$	−153.651	−	301.558i	−0.689019	−	1.35228i	0.235774	−	0.971808i	$-0.424237\pi$
$224$		0			0
$225$	98.2172	−	93.7403i	0.436521	−	0.416623i
$226$		0			0
$227$	96.1797	−	188.763i	0.423699	−	0.831556i	−0.576200	−	0.817309i	$-0.695465\pi$
$227$	96.1797	−	188.763i	0.423699	−	0.831556i	0.999899	−	0.0142469i	$-0.00453509\pi$
$228$		0			0
$229$	−185.614	+	255.476i	−0.810542	+	1.11561i	0.180698	+	0.983539i	$0.442164\pi$
$229$	−185.614	+	255.476i	−0.810542	+	1.11561i	−0.991240	+	0.132076i	$0.957836\pi$
$230$		0			0
$231$	373.180	+	283.629i	1.61550	+	1.22783i
$232$		0			0
$233$	329.962	−	52.2609i	1.41615	−	0.224296i	0.599011	−	0.800741i	$-0.295561\pi$
$233$	329.962	−	52.2609i	1.41615	−	0.224296i	0.817136	+	0.576445i	$0.195561\pi$
$234$		0			0
$235$	130.865	+	326.657i	0.556873	+	1.39003i
$236$		0			0
$237$	−2.52334	−	0.399659i	−0.0106470	−	0.00168632i
$238$		0			0
$239$	−246.388	−	80.0563i	−1.03091	−	0.334964i	−0.255761	−	0.966740i	$-0.582326\pi$
$239$	−246.388	−	80.0563i	−1.03091	−	0.334964i	−0.775151	+	0.631776i	$0.782326\pi$
$240$		0			0
$241$	54.2324			0.225031			0.112515	−	0.993650i	$-0.464109\pi$
$241$	54.2324			0.225031			0.112515	+	0.993650i	$0.464109\pi$
$242$		0			0
$243$	183.360	−	183.360i	0.754568	−	0.754568i
$244$		0			0
$245$	329.843	−	196.876i	1.34630	−	0.803574i
$246$		0			0
$247$	385.798	+	61.1044i	1.56194	+	0.247386i
$248$		0			0
$249$	−194.286	+	63.1275i	−0.780267	+	0.253524i
$250$		0			0
$251$	38.7266	+	28.1365i	0.154289	+	0.112098i	0.662252	−	0.749282i	$-0.269601\pi$
$251$	38.7266	+	28.1365i	0.154289	+	0.112098i	−0.507962	+	0.861379i	$0.669601\pi$
$252$		0			0
$253$	−85.0847	+	11.6007i	−0.336303	+	0.0458524i
$254$		0			0
$255$	211.034	−	48.0697i	0.827585	−	0.188509i
$256$		0			0
$257$	−26.9993	+	52.9891i	−0.105056	+	0.206183i	−0.937550	−	0.347850i	$-0.886912\pi$
$257$	−26.9993	+	52.9891i	−0.105056	+	0.206183i	0.832495	+	0.554033i	$0.186912\pi$
$258$		0			0
$259$	−156.578	−	215.511i	−0.604549	−	0.832090i
$260$		0			0
$261$	31.7657	−	97.7648i	0.121708	−	0.374578i
$262$		0			0
$263$	−140.379	+	140.379i	−0.533761	+	0.533761i	−0.921689	−	0.387929i	$-0.873191\pi$
$263$	−140.379	+	140.379i	−0.533761	+	0.533761i	0.387929	+	0.921689i	$0.373191\pi$
$264$		0			0
$265$	14.2232	+	212.349i	0.0536725	+	0.801316i
$266$		0			0
$267$	75.9944	−	38.7211i	0.284623	−	0.145023i
$268$		0			0
$269$	−25.5983	−	35.2330i	−0.0951608	−	0.130978i	0.758782	−	0.651345i	$-0.225795\pi$
$269$	−25.5983	−	35.2330i	−0.0951608	−	0.130978i	−0.853942	+	0.520367i	$0.825795\pi$
$270$		0			0
$271$	90.8577	+	279.631i	0.335268	+	1.03185i	0.966590	+	0.256328i	$0.0825129\pi$
$271$	90.8577	+	279.631i	0.335268	+	1.03185i	−0.631321	+	0.775521i	$0.717487\pi$
$272$		0			0
$273$	525.389	−	83.2134i	1.92450	−	0.304811i
$274$		0			0
$275$	185.532	+	202.985i	0.674662	+	0.738127i
$276$		0			0
$277$	−47.9161	−	302.531i	−0.172982	−	1.09217i	−0.909486	−	0.415735i	$-0.863525\pi$
$277$	−47.9161	−	302.531i	−0.172982	−	1.09217i	0.736504	−	0.676434i	$-0.236475\pi$
$278$		0			0
$279$	13.2410	−	4.30227i	0.0474589	−	0.0154203i
$280$		0			0
$281$	240.589	−	174.798i	0.856187	−	0.622056i	−0.0706580	−	0.997501i	$-0.522510\pi$
$281$	240.589	−	174.798i	0.856187	−	0.622056i	0.926845	+	0.375444i	$0.122510\pi$
$282$		0			0
$283$	−61.6138	−	120.924i	−0.217717	−	0.427293i	0.756155	−	0.654393i	$-0.227076\pi$
$283$	−61.6138	−	120.924i	−0.217717	−	0.427293i	−0.973872	+	0.227100i	$0.927076\pi$
$284$		0			0
$285$	−593.000	+	39.7194i	−2.08070	+	0.139366i
$286$		0			0
$287$	−289.050	−	289.050i	−1.00714	−	1.00714i
$288$		0			0
$289$	−151.361	−	49.1801i	−0.523739	−	0.170173i
$290$		0			0
$291$	235.174	−	170.864i	0.808159	−	0.587162i
$292$		0			0
$293$	205.670	+	104.794i	0.701944	+	0.357659i	0.768258	−	0.640140i	$-0.221124\pi$
$293$	205.670	+	104.794i	0.701944	+	0.357659i	−0.0663136	+	0.997799i	$0.521124\pi$
$294$		0			0
$295$	85.8953	+	377.095i	0.291170	+	1.27829i
$296$		0			0
$297$	103.161	+	107.710i	0.347342	+	0.362661i
$298$		0			0
$299$	−57.2805	+	78.8398i	−0.191573	+	0.263678i
$300$		0			0
$301$	115.706	+	356.105i	0.384404	+	1.18307i
$302$		0			0
$303$	−3.29101	+	20.7786i	−0.0108614	+	0.0685763i
$304$		0			0
$305$	276.268	+	462.856i	0.905797	+	1.51756i
$306$		0			0
$307$	−179.666	−	179.666i	−0.585232	−	0.585232i	0.351104	−	0.936336i	$-0.385806\pi$
$307$	−179.666	−	179.666i	−0.585232	−	0.585232i	−0.936336	+	0.351104i	$0.885806\pi$
$308$		0			0
$309$			545.444i			1.76519i
$310$		0			0
$311$	−63.2034	+	194.520i	−0.203226	+	0.625467i	0.796555	+	0.604566i	$0.206653\pi$
$311$	−63.2034	+	194.520i	−0.203226	+	0.625467i	−0.999782	+	0.0209007i	$0.993347\pi$
$312$		0			0
$313$	60.8925	−	384.460i	0.194545	−	1.22831i	−0.676254	−	0.736668i	$-0.736398\pi$
$313$	60.8925	−	384.460i	0.194545	−	1.22831i	0.870799	−	0.491639i	$-0.163602\pi$
$314$		0			0
$315$	−282.750	+	113.275i	−0.897618	+	0.359603i
$316$		0			0
$317$	−46.9058	−	296.152i	−0.147968	−	0.934233i	−0.944231	−	0.329283i	$-0.893193\pi$
$317$	−46.9058	−	296.152i	−0.147968	−	0.934233i	0.796263	−	0.604950i	$-0.206807\pi$
$318$		0			0
$319$	196.585	+	68.5968i	0.616254	+	0.215037i
$320$		0			0
$321$	−171.285	−	124.446i	−0.533598	−	0.387682i
$322$		0			0
$323$	−317.697	−	161.875i	−0.983581	−	0.501160i
$324$		0			0
$325$	311.998	+	7.27665i	0.959993	+	0.0223897i
$326$		0			0
$327$	−442.317	+	225.372i	−1.35265	+	0.689211i
$328$		0			0
$329$		−	789.459i		−	2.39957i
$330$		0			0
$331$	−191.292			−0.577922			−0.288961	−	0.957341i	$-0.593310\pi$
$331$	−191.292			−0.577922			−0.288961	+	0.957341i	$0.593310\pi$
$332$		0			0
$333$	58.5520	+	114.915i	0.175832	+	0.345090i
$334$		0			0
$335$	−282.191	+	235.379i	−0.842360	+	0.702625i
$336$		0			0
$337$	23.5723	−	46.2632i	0.0699474	−	0.137280i	−0.853385	−	0.521281i	$-0.825454\pi$
$337$	23.5723	−	46.2632i	0.0699474	−	0.137280i	0.923332	+	0.384002i	$0.125454\pi$
$338$		0			0
$339$	−186.353	+	256.493i	−0.549715	+	0.756617i
$340$		0			0
$341$	8.13355	+	27.0010i	0.0238521	+	0.0791817i
$342$		0			0
$343$	−308.289	+	48.8282i	−0.898803	+	0.142356i
$344$		0			0
$345$	58.3365	−	136.319i	0.169091	−	0.395129i
$346$		0			0
$347$	−229.148	−	36.2935i	−0.660369	−	0.104592i	−0.182750	−	0.983159i	$-0.558500\pi$
$347$	−229.148	−	36.2935i	−0.660369	−	0.104592i	−0.477619	+	0.878567i	$0.658500\pi$
$348$		0			0
$349$	107.761	+	35.0137i	0.308771	+	0.100326i	0.459304	−	0.888279i	$-0.348099\pi$
$349$	107.761	+	35.0137i	0.308771	+	0.100326i	−0.150533	+	0.988605i	$0.548099\pi$
$350$		0			0
$351$	169.254			0.482206
$352$		0			0
$353$	−21.9444	+	21.9444i	−0.0621654	+	0.0621654i	−0.737506	−	0.675341i	$-0.763997\pi$
$353$	−21.9444	+	21.9444i	−0.0621654	+	0.0621654i	0.675341	+	0.737506i	$0.263997\pi$
$354$		0			0
$355$	−344.798	−	577.672i	−0.971263	−	1.62724i
$356$		0			0
$357$	−479.592	−	75.9600i	−1.34340	−	0.212773i
$358$		0			0
$359$	−259.373	+	84.2752i	−0.722486	+	0.234750i	−0.647101	−	0.762405i	$-0.724019\pi$
$359$	−259.373	+	84.2752i	−0.722486	+	0.234750i	−0.0753854	+	0.997154i	$0.524019\pi$
$360$		0			0
$361$	500.043	+	363.303i	1.38516	+	1.00638i
$362$		0			0
$363$	338.741	−	310.703i	0.933171	−	0.855932i
$364$		0			0
$365$	−18.2377	+	28.9969i	−0.0499664	+	0.0794436i
$366$		0			0
$367$	−94.3098	+	185.093i	−0.256975	+	0.504342i	−0.983065	−	0.183258i	$-0.941336\pi$
$367$	−94.3098	+	185.093i	−0.256975	+	0.504342i	0.726090	+	0.687600i	$0.241336\pi$
$368$		0			0
$369$	116.329	+	160.114i	0.315256	+	0.433913i
$370$		0			0
$371$	147.543	−	454.092i	0.397691	−	1.22397i
$372$		0			0
$373$	−246.912	+	246.912i	−0.661963	+	0.661963i	−0.955843	−	0.293879i	$-0.905054\pi$
$373$	−246.912	+	246.912i	−0.661963	+	0.661963i	0.293879	+	0.955843i	$0.405054\pi$
$374$		0			0
$375$	−465.324	+	94.6366i	−1.24086	+	0.252364i
$376$		0			0
$377$	210.532	−	107.272i	0.558441	−	0.284540i
$378$		0			0
$379$	307.277	+	422.931i	0.810758	+	1.11591i	0.991206	+	0.132328i	$0.0422452\pi$
$379$	307.277	+	422.931i	0.810758	+	1.11591i	−0.180448	+	0.983585i	$0.557755\pi$
$380$		0			0
$381$	−235.442	−	724.615i	−0.617957	−	1.90188i
$382$		0			0
$383$	−126.077	+	19.9687i	−0.329184	+	0.0521376i	−0.318839	−	0.947809i	$-0.603293\pi$
$383$	−126.077	+	19.9687i	−0.329184	+	0.0521376i	−0.0103447	+	0.999946i	$0.503293\pi$
$384$		0			0
$385$	−217.027	−	577.515i	−0.563707	−	1.50004i
$386$		0			0
$387$	−28.3587	−	179.050i	−0.0732784	−	0.462662i
$388$		0			0
$389$	162.553	−	52.8166i	0.417874	−	0.135775i	−0.0925308	−	0.995710i	$-0.529496\pi$
$389$	162.553	−	52.8166i	0.417874	−	0.135775i	0.510405	+	0.859934i	$0.329496\pi$
$390$		0			0
$391$	71.9676	−	52.2875i	0.184060	−	0.133728i
$392$		0			0
$393$	190.589	+	374.052i	0.484959	+	0.951786i
$394$		0			0
$395$	2.53134	+	2.21352i	0.00640845	+	0.00560386i
$396$		0			0
$397$	−115.211	−	115.211i	−0.290203	−	0.290203i	0.546957	−	0.837161i	$-0.315786\pi$
$397$	−115.211	−	115.211i	−0.290203	−	0.290203i	−0.837161	+	0.546957i	$0.815786\pi$
$398$		0			0
$399$	1268.09	+	412.026i	3.17816	+	1.03265i
$400$		0			0
$401$	−190.704	+	138.555i	−0.475572	+	0.345523i	−0.799609	−	0.600521i	$-0.794960\pi$
$401$	−190.704	+	138.555i	−0.475572	+	0.345523i	0.324037	+	0.946045i	$0.394960\pi$
$402$		0			0
$403$	28.5140	+	14.5286i	0.0707543	+	0.0360511i
$404$		0			0
$405$	−489.382	+	111.472i	−1.20835	+	0.275240i
$406$		0			0
$407$	−235.260	+	113.547i	−0.578034	+	0.278984i
$408$		0			0
$409$	−42.7016	+	58.7737i	−0.104405	+	0.143701i	−0.858023	−	0.513612i	$-0.828307\pi$
$409$	−42.7016	+	58.7737i	−0.104405	+	0.143701i	0.753618	+	0.657313i	$0.228307\pi$
$410$		0			0
$411$	−202.340	−	622.738i	−0.492311	−	1.51518i
$412$		0			0
$413$	135.732	−	856.980i	0.328649	−	2.07501i
$414$		0			0
$415$	260.702	+	65.8130i	0.628198	+	0.158586i
$416$		0			0
$417$	314.591	+	314.591i	0.754415	+	0.754415i
$418$		0			0
$419$			197.381i			0.471077i	0.971865	+	0.235538i	$0.0756853\pi$
$419$			197.381i			0.471077i	−0.971865	+	0.235538i	$0.924315\pi$
$420$		0			0
$421$	−85.4299	+	262.926i	−0.202921	+	0.624527i	0.796871	+	0.604149i	$0.206487\pi$
$421$	−85.4299	+	262.926i	−0.202921	+	0.624527i	−0.999792	+	0.0203781i	$0.993513\pi$
$422$		0			0
$423$	−59.7922	+	377.513i	−0.141353	+	0.892466i
$424$		0			0
$425$	−268.810	−	94.3259i	−0.632494	−	0.221943i
$426$		0			0
$427$	−189.176	−	1194.41i	−0.443035	−	2.79721i
$428$		0			0
$429$	11.2522	−	521.516i	0.0262289	−	1.21565i
$430$		0			0
$431$	−72.8571	−	52.9338i	−0.169042	−	0.122816i	0.500048	−	0.865998i	$-0.333316\pi$
$431$	−72.8571	−	52.9338i	−0.169042	−	0.122816i	−0.669090	+	0.743182i	$0.733316\pi$
$432$		0			0
$433$	−208.924	−	106.452i	−0.482503	−	0.245847i	0.195781	−	0.980648i	$-0.437276\pi$
$433$	−208.924	−	106.452i	−0.482503	−	0.245847i	−0.678283	+	0.734800i	$0.737276\pi$
$434$		0			0
$435$	−276.086	+	230.287i	−0.634679	+	0.529395i
$436$		0			0
$437$	−217.646	+	110.896i	−0.498045	+	0.253767i
$438$		0			0
$439$		−	419.018i		−	0.954484i	−0.878772	−	0.477242i	$-0.841637\pi$
$439$		−	419.018i		−	0.954484i	0.878772	−	0.477242i	$-0.158363\pi$
$440$		0			0
$441$	417.232			0.946104
$442$		0			0
$443$	5.04160	+	9.89469i	0.0113806	+	0.0223357i	0.896627	−	0.442787i	$-0.146010\pi$
$443$	5.04160	+	9.89469i	0.0113806	+	0.0223357i	−0.885246	+	0.465123i	$0.846010\pi$
$444$		0			0
$445$	−111.804	−	10.1120i	−0.251244	−	0.0227236i
$446$		0			0
$447$	16.1171	−	31.6317i	0.0360563	−	0.0707644i
$448$		0			0
$449$	−405.246	+	557.773i	−0.902552	+	1.24226i	0.0670952	+	0.997747i	$0.478627\pi$
$449$	−405.246	+	557.773i	−0.902552	+	1.24226i	−0.969647	+	0.244509i	$0.921373\pi$
$450$		0			0
$451$	−329.312	+	228.571i	−0.730181	+	0.506809i
$452$		0			0
$453$	−531.853	+	84.2373i	−1.17407	+	0.185954i
$454$		0			0
$455$	−643.677	−	275.455i	−1.41468	−	0.605397i
$456$		0			0
$457$	278.139	+	44.0528i	0.608618	+	0.0963957i	0.453134	−	0.891443i	$-0.350306\pi$
$457$	278.139	+	44.0528i	0.608618	+	0.0963957i	0.155485	+	0.987838i	$0.450306\pi$
$458$		0			0
$459$	−146.939	−	47.7434i	−0.320129	−	0.104016i
$460$		0			0
$461$	432.726			0.938669			0.469334	−	0.883020i	$-0.344494\pi$
$461$	432.726			0.938669			0.469334	+	0.883020i	$0.344494\pi$
$462$		0			0
$463$	317.108	−	317.108i	0.684899	−	0.684899i	−0.276201	−	0.961100i	$-0.589076\pi$
$463$	317.108	−	317.108i	0.684899	−	0.684899i	0.961100	+	0.276201i	$0.0890756\pi$
$464$		0			0
$465$	−47.2115	−	11.9183i	−0.101530	−	0.0256308i
$466$		0			0
$467$	467.837	+	74.0981i	1.00179	+	0.158668i	0.635721	−	0.771919i	$-0.280703\pi$
$467$	467.837	+	74.0981i	1.00179	+	0.158668i	0.366071	+	0.930587i	$0.380703\pi$
$468$		0			0
$469$	784.052	−	254.754i	1.67175	−	0.543186i
$470$		0			0
$471$	663.949	+	482.387i	1.40966	+	1.02418i
$472$		0			0
$473$	363.814	−	49.6033i	0.769163	−	0.104870i
$474$		0			0
$475$	688.528	+	371.293i	1.44953	+	0.781670i
$476$		0			0
$477$	−104.946	+	205.968i	−0.220013	+	0.431800i
$478$		0			0
$479$	−43.2790	−	59.5685i	−0.0903529	−	0.124360i	0.761447	−	0.648227i	$-0.224489\pi$
$479$	−43.2790	−	59.5685i	−0.0903529	−	0.124360i	−0.851800	+	0.523867i	$0.824489\pi$
$480$		0			0
$481$	−91.6092	+	281.944i	−0.190456	+	0.586162i
$482$		0			0
$483$	−235.220	+	235.220i	−0.486998	+	0.486998i
$484$		0			0
$485$	−381.754	+	25.5701i	−0.787122	+	0.0527218i
$486$		0			0
$487$	−682.710	+	347.858i	−1.40187	+	0.714288i	−0.981212	−	0.192932i	$-0.938200\pi$
$487$	−682.710	+	347.858i	−1.40187	+	0.714288i	−0.420657	+	0.907220i	$0.638200\pi$
$488$		0			0
$489$	−616.600	−	848.678i	−1.26094	−	1.73554i
$490$		0			0
$491$	155.108	+	477.373i	0.315902	+	0.972247i	0.975381	+	0.220524i	$0.0707769\pi$
$491$	155.108	+	477.373i	0.315902	+	0.972247i	−0.659479	+	0.751723i	$0.729223\pi$
$492$		0			0
$493$	−213.034	+	33.7413i	−0.432118	+	0.0684407i
$494$		0			0
$495$	60.0407	+	292.600i	0.121294	+	0.591112i
$496$		0			0
$497$	236.102	+	1490.69i	0.475055	+	2.99938i
$498$		0			0
$499$	571.374	−	185.651i	1.14504	−	0.372045i	0.325766	−	0.945451i	$-0.394378\pi$
$499$	571.374	−	185.651i	1.14504	−	0.372045i	0.819272	+	0.573405i	$0.194378\pi$
$500$		0			0
$501$	−724.905	+	526.675i	−1.44692	+	1.05125i
$502$		0			0
$503$	−326.263	−	640.328i	−0.648635	−	1.27302i	−0.947815	−	0.318821i	$-0.896713\pi$
$503$	−326.263	−	640.328i	−0.648635	−	1.27302i	0.299180	−	0.954197i	$-0.403287\pi$
$504$		0			0
$505$	18.2274	−	20.8444i	0.0360938	−	0.0412761i
$506$		0			0
$507$	35.3688	+	35.3688i	0.0697610	+	0.0697610i
$508$		0			0
$509$	−912.793	−	296.584i	−1.79331	−	0.582680i	−0.793637	−	0.608392i	$-0.791815\pi$
$509$	−912.793	−	296.584i	−1.79331	−	0.582680i	−0.999669	+	0.0257117i	$0.991815\pi$
$510$		0			0
$511$	62.1731	−	45.1714i	0.121670	−	0.0883981i
$512$		0			0
$513$	378.009	+	192.605i	0.736859	+	0.375449i
$514$		0			0
$515$	382.222	−	607.710i	0.742179	−	1.18002i
$516$		0			0
$517$	−761.849	−	137.573i	−1.47360	−	0.266098i
$518$		0			0
$519$	−41.3629	+	56.9312i	−0.0796973	+	0.109694i
$520$		0			0
$521$	−43.2186	−	133.013i	−0.0829533	−	0.255304i	0.900974	−	0.433873i	$-0.142853\pi$
$521$	−43.2186	−	133.013i	−0.0829533	−	0.255304i	−0.983927	+	0.178569i	$0.942853\pi$
$522$		0			0
$523$	−38.7235	+	244.491i	−0.0740412	+	0.467477i	0.922612	+	0.385730i	$0.126050\pi$
$523$	−38.7235	+	244.491i	−0.0740412	+	0.467477i	−0.996653	+	0.0817479i	$0.973950\pi$
$524$		0			0
$525$	1048.01	+	191.137i	1.99621	+	0.364071i
$526$		0			0
$527$	−20.6563	−	20.6563i	−0.0391961	−	0.0391961i
$528$		0			0
$529$			468.058i			0.884798i
$530$		0			0
$531$	−129.812	+	399.521i	−0.244467	+	0.752394i
$532$		0			0
$533$	−71.1647	+	449.316i	−0.133517	+	0.842995i
$534$		0			0
$535$	103.632	+	258.681i	0.193705	+	0.483516i
$536$		0			0
$537$	−141.993	−	896.506i	−0.264418	−	1.66947i
$538$		0			0
$539$	−18.2293	+	844.891i	−0.0338207	+	1.56752i
$540$		0			0
$541$	75.5642	+	54.9006i	0.139675	+	0.101480i	0.655429	−	0.755257i	$-0.272488\pi$
$541$	75.5642	+	54.9006i	0.139675	+	0.101480i	−0.515754	+	0.856737i	$0.672488\pi$
$542$		0			0
$543$	98.4911	+	50.1837i	0.181383	+	0.0924193i
$544$		0			0
$545$	650.741	+	58.8559i	1.19402	+	0.107992i
$546$		0			0
$547$	415.137	−	211.523i	0.758934	−	0.386696i	−0.0312928	−	0.999510i	$-0.509962\pi$
$547$	415.137	−	211.523i	0.758934	−	0.386696i	0.790227	+	0.612814i	$0.209962\pi$
$548$		0			0
$549$			585.485i			1.06646i
$550$		0			0
$551$	592.269			1.07490
$552$		0			0
$553$	−3.42486	−	6.72167i	−0.00619324	−	0.0121549i
$554$		0			0
$555$	40.6309	−	449.235i	0.0732088	−	0.809433i
$556$		0			0
$557$	124.995	−	245.316i	0.224407	−	0.440424i	−0.751162	−	0.660118i	$-0.770506\pi$
$557$	124.995	−	245.316i	0.224407	−	0.440424i	0.975569	+	0.219695i	$0.0705061\pi$
$558$		0			0
$559$	244.926	−	337.111i	0.438150	−	0.603062i
$560$		0			0
$561$	−156.878	+	449.583i	−0.279640	+	0.801395i
$562$		0			0
$563$	1003.30	−	158.907i	1.78206	−	0.282251i	0.823537	−	0.567263i	$-0.191998\pi$
$563$	1003.30	−	158.907i	1.78206	−	0.282251i	0.958524	+	0.285012i	$0.0919976\pi$
$564$		0			0
$565$	387.365	−	155.186i	0.685602	−	0.274665i
$566$		0			0
$567$	1112.16	+	176.149i	1.96148	+	0.310669i
$568$		0			0
$569$	−838.644	−	272.492i	−1.47389	−	0.478896i	−0.541609	−	0.840630i	$-0.682185\pi$
$569$	−838.644	−	272.492i	−1.47389	−	0.478896i	−0.932281	+	0.361734i	$0.882185\pi$
$570$		0			0
$571$	1065.50			1.86603			0.933013	−	0.359844i	$-0.117170\pi$
$571$	1065.50			1.86603			0.933013	+	0.359844i	$0.117170\pi$
$572$		0			0
$573$	918.890	−	918.890i	1.60365	−	1.60365i
$574$		0			0
$575$	−160.522	+	111.001i	−0.279169	+	0.193046i
$576$		0			0
$577$	−63.0330	−	9.98345i	−0.109243	−	0.0173023i	0.101574	−	0.994828i	$-0.467612\pi$
$577$	−63.0330	−	9.98345i	−0.109243	−	0.0173023i	−0.210816	+	0.977526i	$0.567612\pi$
$578$		0			0
$579$	93.3542	−	30.3326i	0.161233	−	0.0523879i
$580$		0			0
$581$	−488.015	−	354.564i	−0.839957	−	0.610265i
$582$		0			0
$583$	−412.499	−	221.514i	−0.707546	−	0.379956i
$584$		0			0
$585$	286.939	+	180.472i	0.490494	+	0.308499i
$586$		0			0
$587$	−109.448	+	214.803i	−0.186453	+	0.365934i	−0.965244	−	0.261349i	$-0.915833\pi$
$587$	−109.448	+	214.803i	−0.186453	+	0.365934i	0.778792	+	0.627282i	$0.215833\pi$
$588$		0			0
$589$	47.1495	+	64.8957i	0.0800500	+	0.110179i
$590$		0			0
$591$	310.343	−	955.138i	0.525115	−	1.61614i
$592$		0			0
$593$	173.130	−	173.130i	0.291956	−	0.291956i	−0.545897	−	0.837853i	$-0.683811\pi$
$593$	173.130	−	173.130i	0.291956	−	0.291956i	0.837853	+	0.545897i	$0.183811\pi$
$594$		0			0
$595$	481.112	+	420.707i	0.808591	+	0.707071i
$596$		0			0
$597$	−665.418	+	339.047i	−1.11460	+	0.567919i
$598$		0			0
$599$	−49.0843	−	67.5587i	−0.0819437	−	0.112786i	0.766077	−	0.642748i	$-0.222206\pi$
$599$	−49.0843	−	67.5587i	−0.0819437	−	0.112786i	−0.848021	+	0.529963i	$0.822206\pi$
$600$		0			0
$601$	−280.867	−	864.418i	−0.467332	−	1.43830i	−0.856026	−	0.516933i	$-0.827074\pi$
$601$	−280.867	−	864.418i	−0.467332	−	1.43830i	0.388694	−	0.921367i	$-0.372926\pi$
$602$		0			0
$603$	−394.222	+	62.4387i	−0.653768	+	0.103547i
$604$		0			0
$605$	−595.137	+	108.798i	−0.983697	+	0.179831i
$606$		0			0
$607$	−85.4608	−	539.578i	−0.140792	−	0.888926i	−0.952428	−	0.304763i	$-0.901423\pi$
$607$	−85.4608	−	539.578i	−0.140792	−	0.888926i	0.811636	−	0.584163i	$-0.198577\pi$
$608$		0			0
$609$	767.089	−	249.242i	1.25959	−	0.409265i
$610$		0			0
$611$	−710.773	+	516.407i	−1.16330	+	0.845184i
$612$		0			0
$613$	−243.555	−	478.004i	−0.397317	−	0.779778i	0.602515	−	0.798107i	$-0.294165\pi$
$613$	−243.555	−	478.004i	−0.397317	−	0.779778i	−0.999832	+	0.0183296i	$0.994165\pi$
$614$		0			0
$615$	−46.2589	−	690.632i	−0.0752176	−	1.12298i
$616$		0			0
$617$	596.755	+	596.755i	0.967187	+	0.967187i	0.999479	−	0.0322910i	$-0.0102803\pi$
$617$	596.755	+	596.755i	0.967187	+	0.967187i	−0.0322910	+	0.999479i	$0.510280\pi$
$618$		0			0
$619$	−105.382	−	34.2406i	−0.170245	−	0.0553160i	0.222654	−	0.974897i	$-0.428528\pi$
$619$	−105.382	−	34.2406i	−0.170245	−	0.0553160i	−0.392899	+	0.919581i	$0.628528\pi$
$620$		0			0
$621$	−85.6300	+	62.2139i	−0.137891	+	0.100183i
$622$		0			0
$623$	224.399	+	114.337i	0.360191	+	0.183527i
$624$		0			0
$625$	584.760	+	220.637i	0.935616	+	0.353019i
$626$		0			0
$627$	618.596	−	1151.94i	0.986596	−	1.83722i
$628$		0			0
$629$	159.062	−	218.930i	0.252881	−	0.348061i
$630$		0			0
$631$	−107.724	−	331.542i	−0.170720	−	0.525423i	0.828692	−	0.559705i	$-0.189086\pi$
$631$	−107.724	−	331.542i	−0.170720	−	0.525423i	−0.999412	+	0.0342821i	$0.989086\pi$
$632$		0			0
$633$	−220.973	+	1395.17i	−0.349089	+	2.20406i
$634$		0			0
$635$	−245.458	+	972.321i	−0.386548	+	1.53121i
$636$		0			0
$637$	678.147	+	678.147i	1.06459	+	1.06459i
$638$		0			0
$639$		−	730.720i		−	1.14354i
$640$		0			0
$641$	−5.42437	+	16.6945i	−0.00846236	+	0.0260445i	−0.955199	−	0.295966i	$-0.904359\pi$
$641$	−5.42437	+	16.6945i	−0.00846236	+	0.0260445i	0.946736	+	0.322010i	$0.104359\pi$
$642$		0			0
$643$	−149.670	+	944.977i	−0.232768	+	1.46964i	0.543593	+	0.839349i	$0.317064\pi$
$643$	−149.670	+	944.977i	−0.232768	+	1.46964i	−0.776360	+	0.630289i	$0.782936\pi$
$644$		0			0
$645$	−249.441	+	582.889i	−0.386731	+	0.903703i
$646$		0			0
$647$	122.051	+	770.600i	0.188641	+	1.19104i	0.882285	+	0.470716i	$0.156005\pi$
$647$	122.051	+	770.600i	0.188641	+	1.19104i	−0.693643	+	0.720319i	$0.743995\pi$
$648$		0			0
$649$	−803.355	−	280.324i	−1.23784	−	0.431933i
$650$		0			0
$651$	88.3764	+	64.2092i	0.135755	+	0.0986317i
$652$		0			0
$653$	−27.3299	−	13.9253i	−0.0418528	−	0.0213251i	0.432939	−	0.901423i	$-0.357477\pi$
$653$	−27.3299	−	13.9253i	−0.0418528	−	0.0213251i	−0.474792	+	0.880098i	$0.657477\pi$
$654$		0			0
$655$	49.7723	−	550.308i	0.0759883	−	0.840165i
$656$		0			0
$657$	−33.1519	+	16.8917i	−0.0504595	+	0.0257104i
$658$		0			0
$659$			460.688i			0.699071i	0.936923	+	0.349535i	$0.113661\pi$
$659$			460.688i			0.699071i	−0.936923	+	0.349535i	$0.886339\pi$
$660$		0			0
$661$	293.536			0.444079			0.222040	−	0.975038i	$-0.428729\pi$
$661$	293.536			0.444079			0.222040	+	0.975038i	$0.428729\pi$
$662$		0			0
$663$	245.326	+	481.479i	0.370024	+	0.726213i
$664$		0			0
$665$	−1124.12	−	1347.68i	−1.69040	−	2.02658i
$666$		0			0
$667$	−67.0831	+	131.658i	−0.100574	+	0.197388i
$668$		0			0
$669$	−755.708	+	1040.14i	−1.12961	+	1.55477i
$670$		0			0
$671$	−1185.60	−	25.5805i	−1.76692	−	0.0381230i
$672$		0			0
$673$	−338.707	+	53.6460i	−0.503280	+	0.0797117i	−0.402912	−	0.915239i	$-0.632002\pi$
$673$	−338.707	+	53.6460i	−0.503280	+	0.0797117i	−0.100368	+	0.994950i	$0.532002\pi$
$674$		0			0
$675$	319.842	+	112.233i	0.473839	+	0.166271i
$676$		0			0
$677$	−177.698	−	28.1446i	−0.262478	−	0.0415725i	0.0238082	−	0.999717i	$-0.492421\pi$
$677$	−177.698	−	28.1446i	−0.262478	−	0.0415725i	−0.286287	+	0.958144i	$0.592421\pi$
$678$		0			0
$679$	816.353	+	265.249i	1.20229	+	0.390647i
$680$		0			0
$681$	−804.790			−1.18178
$682$		0			0
$683$	−599.854	+	599.854i	−0.878263	+	0.878263i	−0.993355	−	0.115092i	$-0.963284\pi$
$683$	−599.854	+	599.854i	−0.878263	+	0.878263i	0.115092	+	0.993355i	$0.463284\pi$
$684$		0			0
$685$	−210.948	+	835.617i	−0.307953	+	1.21988i
$686$		0			0
$687$	1184.84	+	187.660i	1.72465	+	0.273158i
$688$		0			0
$689$	−505.345	+	164.196i	−0.733447	+	0.238311i
$690$		0			0
$691$	−279.266	−	202.899i	−0.404148	−	0.293630i	0.367081	−	0.930189i	$-0.380357\pi$
$691$	−279.266	−	202.899i	−0.404148	−	0.293630i	−0.771228	+	0.636559i	$0.780357\pi$
$692$		0			0
$693$	119.081	−	659.445i	0.171834	−	0.951580i
$694$		0			0
$695$	−130.053	−	570.954i	−0.187126	−	0.821517i
$696$		0			0
$697$	188.526	−	370.002i	0.270482	−	0.530850i
$698$		0			0
$699$	−745.949	−	1026.71i	−1.06717	−	1.46883i
$700$		0			0
$701$	304.714	−	937.812i	0.434684	−	1.33782i	−0.458726	−	0.888578i	$-0.651694\pi$
$701$	304.714	−	937.812i	0.434684	−	1.33782i	0.893410	−	0.449242i	$-0.148306\pi$
$702$		0			0
$703$	−525.440	+	525.440i	−0.747425	+	0.747425i
$704$		0			0
$705$	879.962	−	1006.30i	1.24817	−	1.42738i
$706$		0			0
$707$	−55.3499	+	28.2022i	−0.0782885	+	0.0398900i
$708$		0			0
$709$	22.9278	+	31.5574i	0.0323382	+	0.0445097i	0.824880	−	0.565308i	$-0.191243\pi$
$709$	22.9278	+	31.5574i	0.0323382	+	0.0445097i	−0.792542	+	0.609818i	$0.791243\pi$
$710$		0			0
$711$	1.12865	+	3.47364i	0.00158742	+	0.00488557i
$712$		0			0
$713$	−19.7663	+	3.13067i	−0.0277227	+	0.00439085i
$714$		0			0
$715$	−377.991	+	573.165i	−0.528658	+	0.801629i
$716$		0			0
$717$	153.954	+	972.029i	0.214720	+	1.35569i
$718$		0			0
$719$	−105.220	+	34.1881i	−0.146342	+	0.0475495i	−0.381272	−	0.924463i	$-0.624514\pi$
$719$	−105.220	+	34.1881i	−0.146342	+	0.0475495i	0.234930	+	0.972012i	$0.424514\pi$
$720$		0			0
$721$	−1303.01	+	946.692i	−1.80723	+	1.31303i
$722$		0			0
$723$	−93.5302	−	183.563i	−0.129364	−	0.253891i
$724$		0			0
$725$	468.977	−	63.1077i	0.646864	−	0.0870451i
$726$		0			0
$727$	−313.209	−	313.209i	−0.430824	−	0.430824i	0.458085	−	0.888908i	$-0.348536\pi$
$727$	−313.209	−	313.209i	−0.430824	−	0.430824i	−0.888908	+	0.458085i	$0.848536\pi$
$728$		0			0
$729$	−77.6213	−	25.2207i	−0.106476	−	0.0345963i
$730$		0			0
$731$	−307.727	+	223.576i	−0.420966	+	0.305850i
$732$		0			0
$733$	647.057	+	329.692i	0.882751	+	0.449784i	0.835750	−	0.549111i	$-0.185033\pi$
$733$	647.057	+	329.692i	0.882751	+	0.449784i	0.0470016	+	0.998895i	$0.485033\pi$
$734$		0			0
$735$	−1235.23	−	776.902i	−1.68058	−	1.05701i
$736$		0			0
$737$	−109.214	−	801.025i	−0.148187	−	1.08687i
$738$		0			0
$739$	107.500	−	147.961i	0.145467	−	0.200218i	−0.730066	−	0.683377i	$-0.760511\pi$
$739$	107.500	−	147.961i	0.145467	−	0.200218i	0.875533	+	0.483159i	$0.160511\pi$
$740$		0			0
$741$	−458.531	−	1411.21i	−0.618800	−	1.90447i
$742$		0			0
$743$	−124.101	+	783.543i	−0.167027	+	1.05457i	0.751652	+	0.659560i	$0.229258\pi$
$743$	−124.101	+	783.543i	−0.167027	+	1.05457i	−0.918678	+	0.395006i	$0.870742\pi$
$744$		0			0
$745$	−40.1230	+	23.9485i	−0.0538564	+	0.0321456i
$746$		0			0
$747$	206.511	+	206.511i	0.276454	+	0.276454i
$748$		0			0
$749$		−	625.175i		−	0.834679i
$750$		0			0
$751$	446.836	−	1375.22i	0.594988	−	1.83119i	0.0402046	−	0.999191i	$-0.487199\pi$
$751$	446.836	−	1375.22i	0.594988	−	1.83119i	0.554784	−	0.831995i	$-0.312801\pi$
$752$		0			0
$753$	28.4466	−	179.605i	0.0377777	−	0.238519i
$754$		0			0
$755$	651.597	+	278.844i	0.863042	+	0.369330i
$756$		0			0
$757$	−220.631	−	1393.01i	−0.291454	−	1.84017i	−0.504855	−	0.863204i	$-0.668454\pi$
$757$	−220.631	−	1393.01i	−0.291454	−	1.84017i	0.213401	−	0.976965i	$-0.431546\pi$
$758$		0			0
$759$	186.004	+	267.984i	0.245064	+	0.353075i
$760$		0			0
$761$	−387.904	−	281.829i	−0.509729	−	0.370340i	0.302992	−	0.952993i	$-0.402015\pi$
$761$	−387.904	−	281.829i	−0.509729	−	0.370340i	−0.812721	+	0.582653i	$0.802015\pi$
$762$		0			0
$763$	−1306.09	−	665.487i	−1.71178	−	0.872197i
$764$		0			0
$765$	−198.200	−	237.618i	−0.259085	−	0.310611i
$766$		0			0
$767$	−860.351	+	438.371i	−1.12171	+	0.571539i
$768$		0			0
$769$		−	810.946i		−	1.05455i	−0.849696	−	0.527273i	$-0.823215\pi$
$769$		−	810.946i		−	1.05455i	0.849696	−	0.527273i	$-0.176785\pi$
$770$		0			0
$771$	225.919			0.293020
$772$		0			0
$773$	92.6498	+	181.835i	0.119857	+	0.235233i	0.943138	−	0.332401i	$-0.107859\pi$
$773$	92.6498	+	181.835i	0.119857	+	0.235233i	−0.823281	+	0.567634i	$0.807859\pi$
$774$		0			0
$775$	44.2492	+	46.3625i	0.0570957	+	0.0598226i
$776$		0			0
$777$	−459.415	+	901.653i	−0.591268	+	1.16043i
$778$		0			0
$779$	−670.243	+	922.510i	−0.860389	+	1.18422i
$780$		0			0
$781$	1479.70	+	31.9260i	1.89462	+	0.0408783i
$782$		0			0
$783$	253.477	−	40.1468i	0.323725	−	0.0512730i
$784$		0			0
$785$	−401.708	−	1002.72i	−0.511730	−	1.27735i
$786$		0			0
$787$	−62.5107	−	9.90073i	−0.0794291	−	0.0125803i	0.116593	−	0.993180i	$-0.462803\pi$
$787$	−62.5107	−	9.90073i	−0.0794291	−	0.0125803i	−0.196023	+	0.980599i	$0.562803\pi$
$788$		0			0
$789$	717.249	+	233.048i	0.909060	+	0.295372i
$790$		0			0
$791$	−936.176			−1.18354
$792$		0			0
$793$	−951.618	+	951.618i	−1.20002	+	1.20002i
$794$		0			0
$795$	694.218	−	414.362i	0.873231	−	0.521211i
$796$		0			0
$797$	770.168	+	121.983i	0.966334	+	0.153052i	0.619606	−	0.784913i	$-0.287293\pi$
$797$	770.168	+	121.983i	0.966334	+	0.153052i	0.346729	+	0.937966i	$0.387293\pi$
$798$		0			0
$799$	762.731	−	247.826i	0.954607	−	0.310171i
$800$		0			0
$801$	−98.6462	−	71.6707i	−0.123154	−	0.0894765i
$802$		0			0
$803$	−32.7572	−	67.8704i	−0.0407935	−	0.0845211i
$804$		0			0
$805$	426.903	−	97.2406i	0.530315	−	0.120796i
$806$		0			0
$807$	−75.1077	+	147.407i	−0.0930703	+	0.182661i
$808$		0			0
$809$	594.760	+	818.617i	0.735179	+	1.01189i	0.998882	+	0.0472832i	$0.0150563\pi$
$809$	594.760	+	818.617i	0.735179	+	1.01189i	−0.263702	+	0.964604i	$0.584944\pi$
$810$		0			0
$811$	−282.131	+	868.311i	−0.347881	+	1.07067i	0.612143	+	0.790747i	$0.290308\pi$
$811$	−282.131	+	868.311i	−0.347881	+	1.07067i	−0.960024	+	0.279919i	$0.909692\pi$
$812$		0			0
$813$	789.788	−	789.788i	0.971449	−	0.971449i
$814$		0			0
$815$	92.2752	+	1377.64i	0.113221	+	1.69036i
$816$		0			0
$817$	930.632	−	474.181i	1.13908	−	0.580393i
$818$		0			0
$819$	−446.994	−	615.235i	−0.545780	−	0.751202i
$820$		0			0
$821$	246.366	+	758.237i	0.300080	+	0.923553i	0.981467	+	0.191629i	$0.0613772\pi$
$821$	246.366	+	758.237i	0.300080	+	0.923553i	−0.681387	+	0.731923i	$0.738623\pi$
$822$		0			0
$823$	167.901	−	26.5929i	0.204011	−	0.0323121i	−0.0535927	−	0.998563i	$-0.517067\pi$
$823$	167.901	−	26.5929i	0.204011	−	0.0323121i	0.257603	+	0.966251i	$0.417067\pi$
$824$		0			0
$825$	367.081	−	978.051i	0.444947	−	1.18552i
$826$		0			0
$827$	139.547	+	881.067i	0.168739	+	1.06538i	0.916097	+	0.400956i	$0.131322\pi$
$827$	139.547	+	881.067i	0.168739	+	1.06538i	−0.747358	+	0.664421i	$0.768678\pi$
$828$		0			0
$829$	−344.025	+	111.781i	−0.414988	+	0.134838i	−0.509067	−	0.860727i	$-0.670009\pi$
$829$	−344.025	+	111.781i	−0.414988	+	0.134838i	0.0940787	+	0.995565i	$0.470009\pi$
$830$		0			0
$831$	−941.354	+	683.934i	−1.13280	+	0.823025i
$832$		0			0
$833$	−397.445	−	780.029i	−0.477125	−	0.936410i
$834$		0			0
$835$	1176.73	−	78.8177i	1.40925	−	0.0943924i
$836$		0			0
$837$	24.5778	+	24.5778i	0.0293641	+	0.0293641i
$838$		0			0
$839$	710.763	+	230.941i	0.847155	+	0.275257i	0.700254	−	0.713894i	$-0.253070\pi$
$839$	710.763	+	230.941i	0.847155	+	0.275257i	0.146901	+	0.989151i	$0.453070\pi$
$840$		0			0
$841$	−390.533	+	283.739i	−0.464367	+	0.337383i
$842$		0			0
$843$	−1006.57	−	512.873i	−1.19403	−	0.608391i
$844$		0			0
$845$	−14.6216	−	64.1912i	−0.0173036	−	0.0759659i
$846$		0			0
$847$	1330.17	+	269.950i	1.57045	+	0.318713i
$848$		0			0
$849$	−303.037	+	417.095i	−0.356934	+	0.491278i
$850$		0			0
$851$	−57.2885	−	176.316i	−0.0673190	−	0.207187i
$852$		0			0
$853$	−101.123	+	638.463i	−0.118549	+	0.748491i	0.854765	+	0.519015i	$0.173701\pi$
$853$	−101.123	+	638.463i	−0.118549	+	0.748491i	−0.973314	+	0.229476i	$0.926299\pi$
$854$		0			0
$855$	435.473	+	729.587i	0.509326	+	0.853319i
$856$		0			0
$857$	−577.286	−	577.286i	−0.673613	−	0.673613i	0.284934	−	0.958547i	$-0.408028\pi$
$857$	−577.286	−	577.286i	−0.673613	−	0.673613i	−0.958547	+	0.284934i	$0.908028\pi$
$858$		0			0
$859$		−	811.925i		−	0.945198i	−0.881277	−	0.472599i	$-0.843316\pi$
$859$		−	811.925i		−	0.945198i	0.881277	−	0.472599i	$-0.156684\pi$
$860$		0			0
$861$	−479.862	+	1476.86i	−0.557331	+	1.71529i
$862$		0			0
$863$	−49.3286	+	311.448i	−0.0571594	+	0.360890i	0.942486	+	0.334247i	$0.108482\pi$
$863$	−49.3286	+	311.448i	−0.0571594	+	0.360890i	−0.999645	+	0.0266435i	$0.991518\pi$
$864$		0			0
$865$	85.9795	−	34.4450i	0.0993982	−	0.0398208i
$866$		0			0
$867$	94.5769	+	597.135i	0.109085	+	0.688737i
$868$		0			0
$869$	−7.08341	+	2.13375i	−0.00815122	+	0.00245541i
$870$		0			0
$871$	−742.233	−	539.264i	−0.852162	−	0.619132i
$872$		0			0
$873$	−370.284	−	188.669i	−0.424151	−	0.216116i
$874$		0			0
$875$	−1033.71	−	947.355i	−1.18138	−	1.08269i
$876$		0			0
$877$	−470.161	+	239.559i	−0.536102	+	0.273157i	−0.701010	−	0.713152i	$-0.747267\pi$
$877$	−470.161	+	239.559i	−0.536102	+	0.273157i	0.164908	+	0.986309i	$0.447267\pi$
$878$		0			0
$879$		−	876.871i		−	0.997577i
$880$		0			0
$881$	770.366			0.874423			0.437211	−	0.899359i	$-0.355966\pi$
$881$	770.366			0.874423			0.437211	+	0.899359i	$0.355966\pi$
$882$		0			0
$883$	48.0796	+	94.3615i	0.0544503	+	0.106865i	0.916628	−	0.399741i	$-0.130900\pi$
$883$	48.0796	+	94.3615i	0.0544503	+	0.106865i	−0.862178	+	0.506606i	$0.830900\pi$
$884$		0			0
$885$	1128.24	−	941.079i	1.27484	−	1.06337i
$886$		0			0
$887$	−293.945	+	576.899i	−0.331392	+	0.650394i	−0.995238	−	0.0974756i	$-0.968923\pi$
$887$	−293.945	+	576.899i	−0.331392	+	0.650394i	0.663846	+	0.747870i	$0.268923\pi$
$888$		0			0
$889$	1322.39	−	1820.11i	1.48750	−	2.04737i
$890$		0			0
$891$	363.796	−	1042.57i	0.408301	−	1.17011i
$892$		0			0
$893$	−2175.08	+	344.498i	−2.43570	+	0.385776i
$894$		0			0
$895$	−470.028	+	1098.35i	−0.525171	+	1.22721i
$896$		0			0
$897$	365.640	+	57.9117i	0.407625	+	0.0645615i
$898$		0			0
$899$	46.1489	+	14.9947i	0.0513336	+	0.0166793i
$900$		0			0
$901$	485.035			0.538329
$902$		0			0
$903$	1005.78	−	1005.78i	1.11382	−	1.11382i
$904$		0			0
$905$	−74.5680	−	124.930i	−0.0823956	−	0.138045i
$906$		0			0
$907$	581.628	+	92.1208i	0.641265	+	0.101566i	0.468595	−	0.883413i	$-0.344760\pi$
$907$	581.628	+	92.1208i	0.641265	+	0.101566i	0.172670	+	0.984980i	$0.444760\pi$
$908$		0			0
$909$	28.6039	−	9.29397i	0.0314674	−	0.0102244i
$910$		0			0
$911$	1139.71	+	828.050i	1.25106	+	0.908946i	0.998283	−	0.0585795i	$-0.0186571\pi$
$911$	1139.71	+	828.050i	1.25106	+	0.908946i	0.252774	+	0.967525i	$0.418657\pi$
$912$		0			0
$913$	−427.206	+	409.161i	−0.467915	+	0.448150i
$914$		0			0
$915$	1090.20	−	1733.35i	1.19147	−	1.89437i
$916$		0			0
$917$	−562.778	+	1104.51i	−0.613717	+	1.20449i
$918$		0			0
$919$	−846.476	−	1165.07i	−0.921084	−	1.26776i	−0.963237	−	0.268652i	$-0.913422\pi$
$919$	−846.476	−	1165.07i	−0.921084	−	1.26776i	0.0421531	−	0.999111i	$-0.486578\pi$
$920$		0			0
$921$	−298.270	+	917.981i	−0.323855	+	0.996722i
$922$		0			0
$923$	1187.67	−	1187.67i	1.28675	−	1.28675i
$924$		0			0
$925$	−360.072	+	472.046i	−0.389267	+	0.510320i
$926$		0			0
$927$	694.790	−	354.013i	0.749504	−	0.381891i
$928$		0			0
$929$	840.445	+	1156.77i	0.904677	+	1.24518i	0.968952	+	0.247248i	$0.0795264\pi$
$929$	840.445	+	1156.77i	0.904677	+	1.24518i	−0.0642755	+	0.997932i	$0.520474\pi$
$930$		0			0
$931$	742.852	+	2286.26i	0.797908	+	2.45571i
$932$		0			0
$933$	767.404	−	121.545i	0.822513	−	0.130273i
$934$		0			0
$935$	489.833	−	390.972i	0.523886	−	0.418152i
$936$		0			0
$937$	133.418	+	842.365i	0.142388	+	0.899002i	0.950669	+	0.310206i	$0.100398\pi$
$937$	133.418	+	842.365i	0.142388	+	0.899002i	−0.808281	+	0.588796i	$0.799602\pi$
$938$		0			0
$939$	−1406.32	+	456.941i	−1.49768	+	0.486625i
$940$		0			0
$941$	199.499	−	144.944i	0.212007	−	0.154032i	−0.476714	−	0.879058i	$-0.658172\pi$
$941$	199.499	−	144.944i	0.212007	−	0.154032i	0.688721	+	0.725026i	$0.258172\pi$
$942$		0			0
$943$	−129.154	−	253.479i	−0.136961	−	0.268801i
$944$		0			0
$945$	−572.447	−	500.575i	−0.605764	−	0.529709i
$946$		0			0
$947$	−135.167	−	135.167i	−0.142731	−	0.142731i	0.632131	−	0.774862i	$-0.282181\pi$
$947$	−135.167	−	135.167i	−0.142731	−	0.142731i	−0.774862	+	0.632131i	$0.782181\pi$
$948$		0			0
$949$	−81.3384	−	26.4284i	−0.0857096	−	0.0278487i
$950$		0			0
$951$	−921.506	+	669.513i	−0.968986	+	0.704010i
$952$		0			0
$953$	1360.19	+	693.049i	1.42727	+	0.727229i	0.985464	−	0.169883i	$-0.0543390\pi$
$953$	1360.19	+	693.049i	1.42727	+	0.727229i	0.441803	+	0.897112i	$0.354339\pi$
$954$		0			0
$955$	−1667.70	+	379.871i	−1.74629	+	0.397771i
$956$		0			0
$957$	−106.851	−	783.695i	−0.111652	−	0.818908i
$958$		0			0
$959$	1136.47	−	1564.21i	1.18505	−	1.63109i
$960$		0			0
$961$	−294.934	−	907.715i	−0.306904	−	0.944553i
$962$		0			0
$963$	−47.3496	+	298.954i	−0.0491689	+	0.310440i
$964$		0			0
$965$	−125.267	−	31.6230i	−0.129810	−	0.0327700i
$966$		0			0
$967$	1095.92	+	1095.92i	1.13332	+	1.13332i	0.989621	+	0.143703i	$0.0459011\pi$
$967$	1095.92	+	1095.92i	1.13332	+	1.13332i	0.143703	+	0.989621i	$0.454099\pi$
$968$		0			0
$969$			1354.50i			1.39783i
$970$		0			0
$971$	−200.879	+	618.243i	−0.206879	+	0.636707i	0.792752	+	0.609544i	$0.208647\pi$
$971$	−200.879	+	618.243i	−0.206879	+	0.636707i	−0.999631	+	0.0271634i	$0.991353\pi$
$972$		0			0
$973$	−205.510	+	1297.54i	−0.211213	+	1.33355i
$974$		0			0
$975$	−513.447	−	1068.58i	−0.526613	−	1.09598i
$976$		0			0
$977$	129.461	+	817.386i	0.132509	+	0.836629i	0.960984	+	0.276603i	$0.0892087\pi$
$977$	129.461	+	817.386i	0.132509	+	0.836629i	−0.828475	+	0.560026i	$0.810791\pi$
$978$		0			0
$979$	149.443	−	196.626i	0.152648	−	0.200844i
$980$		0			0
$981$	574.160	+	417.152i	0.585280	+	0.425231i
$982$		0			0
$983$	160.228	+	81.6401i	0.162999	+	0.0830520i	0.533587	−	0.845745i	$-0.320844\pi$
$983$	160.228	+	81.6401i	0.162999	+	0.0830520i	−0.370588	+	0.928797i	$0.620844\pi$
$984$		0			0
$985$	−1015.09	+	846.699i	−1.03055	+	0.859593i
$986$		0			0
$987$	−2672.12	+	1361.51i	−2.70732	+	1.37945i
$988$		0			0
$989$			260.582i			0.263480i
$990$		0			0
$991$	140.460			0.141735			0.0708676	−	0.997486i	$-0.477423\pi$
$991$	140.460			0.141735			0.0708676	+	0.997486i	$0.477423\pi$
$992$		0			0
$993$	329.906	+	647.476i	0.332231	+	0.652041i
$994$		0			0
$995$	978.968	+	88.5423i	0.983888	+	0.0889872i
$996$		0			0
$997$	9.30658	−	18.2652i	0.00933459	−	0.0183202i	−0.886292	−	0.463127i	$-0.846728\pi$
$997$	9.30658	−	18.2652i	0.00933459	−	0.0183202i	0.895627	+	0.444806i	$0.146728\pi$
$998$		0			0
$999$	−189.259	+	260.492i	−0.189448	+	0.260753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.x.a.37.4	✓	96
5.3	odd	4	inner	220.3.x.a.213.9	yes	96
11.3	even	5	inner	220.3.x.a.157.9	yes	96
55.3	odd	20	inner	220.3.x.a.113.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.37.4	✓	96	1.1	even	1	trivial
220.3.x.a.113.4	yes	96	55.3	odd	20	inner
220.3.x.a.157.9	yes	96	11.3	even	5	inner
220.3.x.a.213.9	yes	96	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72462 - 3.38475i) q^{3} +(-0.450384 + 4.97967i) q^{5} +(5.09251 - 9.99462i) q^{7} +(-3.19218 + 4.39365i) q^{9} +(-8.75765 - 6.65610i) q^{11} +(-12.3296 + 1.95282i) q^{13} +(17.6317 - 7.06359i) q^{15} +(11.2549 + 1.78260i) q^{17} +(-29.7589 - 9.66926i) q^{19} -42.6120 q^{21} +(5.52005 - 5.52005i) q^{23} +(-24.5943 - 4.48553i) q^{25} +(-13.3915 - 2.12101i) q^{27} +(-18.0017 + 5.84912i) q^{29} +(-2.07398 - 1.50684i) q^{31} +(-7.42565 + 41.1217i) q^{33} +(47.4764 + 29.8605i) q^{35} +(10.7814 - 21.1596i) q^{37} +(27.8737 + 38.3648i) q^{39} +(11.2612 - 34.6584i) q^{41} +(-23.6032 + 23.6032i) q^{43} +(-20.4413 - 17.8748i) q^{45} +(62.7083 - 31.9515i) q^{47} +(-45.1573 - 62.1537i) q^{49} +(-13.3767 - 41.1693i) q^{51} +(42.0409 - 6.65862i) q^{53} +(37.0895 - 40.6124i) q^{55} +(18.5947 + 117.402i) q^{57} +(73.5650 - 23.9027i) q^{59} +(87.2179 - 63.3675i) q^{61} +(27.6567 + 54.2793i) q^{63} +(-4.17134 - 62.2770i) q^{65} +(51.9683 + 51.9683i) q^{67} +(-28.2040 - 9.16403i) q^{69} +(-108.853 + 79.0863i) q^{71} +(6.10437 + 3.11033i) q^{73} +(27.2334 + 90.9815i) q^{75} +(-111.124 + 53.6331i) q^{77} +(0.395302 - 0.544087i) q^{79} +(31.0202 + 95.4704i) q^{81} +(8.41245 - 53.1141i) q^{83} +(-13.9458 + 55.2428i) q^{85} +(50.8439 + 50.8439i) q^{87} +22.4520i q^{89} +(-43.2710 + 133.175i) q^{91} +(-1.52344 + 9.61863i) q^{93} +(61.5527 - 143.835i) q^{95} +(11.9707 + 75.5798i) q^{97} +(57.2005 - 17.2306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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