LMFDB - Embedded newform 220.3.x.a.113.4

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			113.4
Character	$\chi$	$=$	220.113
Dual form			220.3.x.a.37.4

$q$-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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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	0.402241	+	0.915534i	$0.368231\pi$
$3$	−1.72462	+	3.38475i	−0.574872	+	1.12825i	−0.977114	+	0.212717i	$0.931769\pi$
$4$		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	0.896890	+	0.442254i	$0.145821\pi$
$7$	5.09251	+	9.99462i	0.727502	+	1.42780i	−0.169388	+	0.985549i	$0.554179\pi$
$8$		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	−0.336992	−	0.941508i	$-0.609409\pi$
$13$	−12.3296	−	1.95282i	−0.948432	−	0.150217i	−0.611440	+	0.791291i	$0.709409\pi$
$14$		0			0
$15$	17.6317	+	7.06359i	1.17545	+	0.470906i
$16$		0			0
$17$	11.2549	−	1.78260i	0.662052	−	0.104859i	0.183639	−	0.982994i	$-0.441212\pi$
$17$	11.2549	−	1.78260i	0.662052	−	0.104859i	0.478413	+	0.878135i	$0.341212\pi$
$18$		0			0
$19$	−29.7589	+	9.66926i	−1.56626	+	0.508908i	−0.958471	−	0.285191i	$-0.907943\pi$
$19$	−29.7589	+	9.66926i	−1.56626	+	0.508908i	−0.607788	+	0.794099i	$0.707943\pi$
$20$		0			0
$21$	−42.6120			−2.02914
$22$		0			0
$23$	5.52005	+	5.52005i	0.240002	+	0.240002i	0.816851	−	0.576849i	$-0.195718\pi$
$23$	5.52005	+	5.52005i	0.240002	+	0.240002i	−0.576849	+	0.816851i	$0.695718\pi$
$24$		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	−0.0182765	−	0.999833i	$-0.505818\pi$
$29$	−18.0017	−	5.84912i	−0.620750	−	0.201694i	−0.602473	+	0.798139i	$0.705818\pi$
$30$		0			0
$31$	−2.07398	+	1.50684i	−0.0669026	+	0.0486076i	−0.620734	−	0.784021i	$-0.713165\pi$
$31$	−2.07398	+	1.50684i	−0.0669026	+	0.0486076i	0.553831	+	0.832629i	$0.313165\pi$
$32$		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	0.989572	−	0.144037i	$-0.0460083\pi$
$37$	10.7814	+	21.1596i	0.291388	+	0.571882i	−0.698184	+	0.715918i	$0.746008\pi$
$38$		0			0
$39$	27.8737	−	38.3648i	0.714710	−	0.983714i
$40$		0			0
$41$	11.2612	+	34.6584i	0.274664	+	0.845328i	0.989308	+	0.145840i	$0.0465885\pi$
$41$	11.2612	+	34.6584i	0.274664	+	0.845328i	−0.714644	+	0.699488i	$0.753411\pi$
$42$		0			0
$43$	−23.6032	−	23.6032i	−0.548912	−	0.548912i	0.377214	−	0.926126i	$-0.376882\pi$
$43$	−23.6032	−	23.6032i	−0.548912	−	0.548912i	−0.926126	+	0.377214i	$0.876882\pi$
$44$		0			0
$45$	−20.4413	+	17.8748i	−0.454250	+	0.397218i
$46$		0			0
$47$	62.7083	+	31.9515i	1.33422	+	0.679818i	0.968056	−	0.250733i	$-0.0806715\pi$
$47$	62.7083	+	31.9515i	1.33422	+	0.679818i	0.366162	+	0.930551i	$0.380672\pi$
$48$		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	0.539880	−	0.841742i	$-0.318470\pi$
$53$	42.0409	+	6.65862i	0.793224	+	0.125634i	0.253344	+	0.967376i	$0.418470\pi$
$54$		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	0.856796	−	0.515655i	$-0.172451\pi$
$59$	73.5650	+	23.9027i	1.24686	+	0.405131i	0.390069	+	0.920786i	$0.372451\pi$
$60$		0			0
$61$	87.2179	+	63.3675i	1.42980	+	1.03881i	0.990054	+	0.140690i	$0.0449321\pi$
$61$	87.2179	+	63.3675i	1.42980	+	1.03881i	0.439748	+	0.898121i	$0.355068\pi$
$62$		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	−0.203441	−	0.979087i	$-0.565213\pi$
$67$	51.9683	−	51.9683i	0.775646	−	0.775646i	0.979087	+	0.203441i	$0.0652126\pi$
$68$		0			0
$69$	−28.2040	+	9.16403i	−0.408753	+	0.132812i
$70$		0			0
$71$	−108.853	−	79.0863i	−1.53314	−	1.11389i	−0.954461	−	0.298337i	$-0.903568\pi$
$71$	−108.853	−	79.0863i	−1.53314	−	1.11389i	−0.578680	−	0.815555i	$-0.696432\pi$
$72$		0			0
$73$	6.10437	−	3.11033i	0.0836214	−	0.0426073i	−0.411680	−	0.911329i	$-0.635058\pi$
$73$	6.10437	−	3.11033i	0.0836214	−	0.0426073i	0.495301	+	0.868721i	$0.335058\pi$
$74$		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	0.811512	−	0.584336i	$-0.198645\pi$
$79$	0.395302	+	0.544087i	0.00500383	+	0.00688718i	−0.806508	+	0.591224i	$0.798645\pi$
$80$		0			0
$81$	31.0202	−	95.4704i	0.382966	−	1.17865i
$82$		0			0
$83$	8.41245	+	53.1141i	0.101355	+	0.639929i	0.985103	+	0.171966i	$0.0550120\pi$
$83$	8.41245	+	53.1141i	0.101355	+	0.639929i	−0.883748	+	0.467963i	$0.844988\pi$
$84$		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	$-0.959743\pi$
$89$		−	22.4520i		−	0.252269i	0.992013	−	0.126135i	$-0.0402572\pi$
$90$		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	−0.845902	−	0.533338i	$-0.820938\pi$
$97$	11.9707	−	75.5798i	0.123409	−	0.779174i	0.969311	−	0.245836i	$-0.0790625\pi$
$98$		0			0
$99$	57.2005	+	17.2306i	0.577783	+	0.174047i
$100$		0			0
$101$	−4.48031	+	3.25514i	−0.0443595	+	0.0322291i	−0.609744	−	0.792598i	$-0.708728\pi$
$101$	−4.48031	+	3.25514i	−0.0443595	+	0.0322291i	0.565385	+	0.824827i	$0.308728\pi$
$102$		0			0
$103$	−127.934	+	65.1855i	−1.24208	+	0.632869i	−0.946578	−	0.322474i	$-0.895485\pi$
$103$	−127.934	+	65.1855i	−1.24208	+	0.632869i	−0.295498	+	0.955343i	$0.595485\pi$
$104$		0			0
$105$	19.1917	+	212.194i	0.182779	+	2.02089i
$106$		0			0
$107$	49.6589	+	25.3025i	0.464102	+	0.236472i	0.670375	−	0.742023i	$-0.266133\pi$
$107$	49.6589	+	25.3025i	0.464102	+	0.236472i	−0.206273	+	0.978495i	$0.566133\pi$
$108$		0			0
$109$			130.679i			1.19889i	0.800415	+	0.599447i	$0.204613\pi$
$109$			130.679i			1.19889i	−0.800415	+	0.599447i	$0.795387\pi$
$110$		0			0
$111$	−90.2138			−0.812737
$112$		0			0
$113$	−37.8895	+	74.3623i	−0.335305	+	0.658074i	−0.995679	−	0.0928635i	$-0.970398\pi$
$113$	−37.8895	+	74.3623i	−0.335305	+	0.658074i	0.660373	+	0.750937i	$0.270398\pi$
$114$		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	0.683918	−	0.729559i	$-0.260275\pi$
$127$	198.096	−	31.3753i	1.55981	−	0.247049i	0.875891	+	0.482510i	$0.160275\pi$
$128$		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	0.499726	−	0.866184i	$-0.333434\pi$
$137$	170.244	−	26.9641i	1.24266	−	0.196818i	0.742933	+	0.669366i	$0.233434\pi$
$138$		0			0
$139$	−111.384	−	36.1908i	−0.801321	−	0.260365i	−0.120404	−	0.992725i	$-0.538419\pi$
$139$	−111.384	−	36.1908i	−0.801321	−	0.260365i	−0.680918	+	0.732360i	$0.738419\pi$
$140$		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	−0.790186	−	0.612867i	$-0.790016\pi$
$149$	5.49306	−	7.56054i	0.0368661	−	0.0507419i	0.827052	+	0.562125i	$0.190016\pi$
$150$		0			0
$151$	43.8034	+	134.813i	0.290089	+	0.892802i	0.984827	+	0.173539i	$0.0555203\pi$
$151$	43.8034	+	134.813i	0.290089	+	0.892802i	−0.694738	+	0.719263i	$0.744480\pi$
$152$		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	−0.283574	−	0.958950i	$-0.591520\pi$
$157$	−192.492	−	98.0794i	−1.22606	−	0.624710i	−0.942488	+	0.334241i	$0.891520\pi$
$158$		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	0.919786	−	0.392420i	$-0.128362\pi$
$163$	272.746	+	43.1988i	1.67329	+	0.265023i	0.753504	+	0.657443i	$0.228362\pi$
$164$		0			0
$165$	−201.428	+	55.4979i	−1.22078	+	0.336351i
$166$		0			0
$167$	−36.8986	+	232.969i	−0.220950	+	1.39502i	0.588815	+	0.808268i	$0.299595\pi$
$167$	−36.8986	+	232.969i	−0.220950	+	1.39502i	−0.809765	+	0.586754i	$0.800405\pi$
$168$		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	−0.914035	−	0.405636i	$-0.867050\pi$
$173$	−8.40995	+	16.5055i	−0.0486124	+	0.0954072i	0.865422	+	0.501043i	$0.167050\pi$
$174$		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	0.404644	−	0.914474i	$-0.367395\pi$
$179$	227.245	−	73.8362i	1.26952	−	0.412493i	0.864878	+	0.501981i	$0.167395\pi$
$180$		0			0
$181$	−23.5411	−	17.1036i	−0.130062	−	0.0944953i	0.520852	−	0.853647i	$-0.325614\pi$
$181$	−23.5411	−	17.1036i	−0.130062	−	0.0944953i	−0.650914	+	0.759151i	$0.725614\pi$
$182$		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	−0.146538	−	0.989205i	$-0.546813\pi$
$191$	105.710	−	325.341i	0.553454	−	1.70336i	0.699992	−	0.714151i	$-0.253187\pi$
$192$		0			0
$193$	−4.04216	−	25.5212i	−0.0209439	−	0.132234i	0.975001	−	0.222201i	$-0.0713240\pi$
$193$	−4.04216	−	25.5212i	−0.0209439	−	0.132234i	−0.995945	+	0.0899664i	$0.971324\pi$
$194$		0			0
$195$	−203.598	−	121.523i	−1.04409	−	0.623195i
$196$		0			0
$197$	186.939	−	186.939i	0.948927	−	0.948927i	−0.0498310	−	0.998758i	$-0.515868\pi$
$197$	186.939	−	186.939i	0.948927	−	0.948927i	0.998758	+	0.0498310i	$0.0158683\pi$
$198$		0			0
$199$			196.593i			0.987904i	0.869489	+	0.493952i	$0.164448\pi$
$199$			196.593i			0.987904i	−0.869489	+	0.493952i	$0.835552\pi$
$200$		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	−0.434934	+	0.900462i	$0.643228\pi$
$211$	−300.828	+	218.565i	−1.42573	+	1.03585i	−0.990793	+	0.135389i	$0.956772\pi$
$212$		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	0.235774	+	0.971808i	$0.424237\pi$
$223$	−153.651	+	301.558i	−0.689019	+	1.35228i	−0.924794	+	0.380469i	$0.875763\pi$
$224$		0			0
$225$	98.2172	+	93.7403i	0.436521	+	0.416623i
$226$		0			0
$227$	96.1797	+	188.763i	0.423699	+	0.831556i	0.999899	+	0.0142469i	$0.00453509\pi$
$227$	96.1797	+	188.763i	0.423699	+	0.831556i	−0.576200	+	0.817309i	$0.695465\pi$
$228$		0			0
$229$	−185.614	−	255.476i	−0.810542	−	1.11561i	−0.991240	−	0.132076i	$-0.957836\pi$
$229$	−185.614	−	255.476i	−0.810542	−	1.11561i	0.180698	−	0.983539i	$-0.442164\pi$
$230$		0			0
$231$	373.180	−	283.629i	1.61550	−	1.22783i
$232$		0			0
$233$	329.962	+	52.2609i	1.41615	+	0.224296i	0.817136	−	0.576445i	$-0.195561\pi$
$233$	329.962	+	52.2609i	1.41615	+	0.224296i	0.599011	+	0.800741i	$0.295561\pi$
$234$		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	−0.775151	−	0.631776i	$-0.782326\pi$
$239$	−246.388	+	80.0563i	−1.03091	+	0.334964i	−0.255761	+	0.966740i	$0.582326\pi$
$240$		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	−0.507962	−	0.861379i	$-0.669601\pi$
$251$	38.7266	−	28.1365i	0.154289	−	0.112098i	0.662252	+	0.749282i	$0.269601\pi$
$252$		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	0.832495	−	0.554033i	$-0.186912\pi$
$257$	−26.9993	−	52.9891i	−0.105056	−	0.206183i	−0.937550	+	0.347850i	$0.886912\pi$
$258$		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	0.387929	−	0.921689i	$-0.373191\pi$
$263$	−140.379	−	140.379i	−0.533761	−	0.533761i	−0.921689	+	0.387929i	$0.873191\pi$
$264$		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	−0.853942	−	0.520367i	$-0.825795\pi$
$269$	−25.5983	+	35.2330i	−0.0951608	+	0.130978i	0.758782	+	0.651345i	$0.225795\pi$
$270$		0			0
$271$	90.8577	−	279.631i	0.335268	−	1.03185i	−0.631321	−	0.775521i	$-0.717487\pi$
$271$	90.8577	−	279.631i	0.335268	−	1.03185i	0.966590	−	0.256328i	$-0.0825129\pi$
$272$		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	0.736504	+	0.676434i	$0.236475\pi$
$277$	−47.9161	+	302.531i	−0.172982	+	1.09217i	−0.909486	+	0.415735i	$0.863525\pi$
$278$		0			0
$279$	13.2410	+	4.30227i	0.0474589	+	0.0154203i
$280$		0			0
$281$	240.589	+	174.798i	0.856187	+	0.622056i	0.926845	−	0.375444i	$-0.122510\pi$
$281$	240.589	+	174.798i	0.856187	+	0.622056i	−0.0706580	+	0.997501i	$0.522510\pi$
$282$		0			0
$283$	−61.6138	+	120.924i	−0.217717	+	0.427293i	−0.973872	−	0.227100i	$-0.927076\pi$
$283$	−61.6138	+	120.924i	−0.217717	+	0.427293i	0.756155	+	0.654393i	$0.227076\pi$
$284$		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	−0.0663136	−	0.997799i	$-0.521124\pi$
$293$	205.670	−	104.794i	0.701944	−	0.357659i	0.768258	+	0.640140i	$0.221124\pi$
$294$		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	−0.936336	−	0.351104i	$-0.885806\pi$
$307$	−179.666	+	179.666i	−0.585232	+	0.585232i	0.351104	+	0.936336i	$0.385806\pi$
$308$		0			0
$309$		−	545.444i		−	1.76519i
$310$		0			0
$311$	−63.2034	−	194.520i	−0.203226	−	0.625467i	−0.999782	−	0.0209007i	$-0.993347\pi$
$311$	−63.2034	−	194.520i	−0.203226	−	0.625467i	0.796555	−	0.604566i	$-0.206653\pi$
$312$		0			0
$313$	60.8925	+	384.460i	0.194545	+	1.22831i	0.870799	+	0.491639i	$0.163602\pi$
$313$	60.8925	+	384.460i	0.194545	+	1.22831i	−0.676254	+	0.736668i	$0.736398\pi$
$314$		0			0
$315$	−282.750	−	113.275i	−0.897618	−	0.359603i
$316$		0			0
$317$	−46.9058	+	296.152i	−0.147968	+	0.934233i	0.796263	+	0.604950i	$0.206807\pi$
$317$	−46.9058	+	296.152i	−0.147968	+	0.934233i	−0.944231	+	0.329283i	$0.893193\pi$
$318$		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	0.923332	−	0.384002i	$-0.125454\pi$
$337$	23.5723	+	46.2632i	0.0699474	+	0.137280i	−0.853385	+	0.521281i	$0.825454\pi$
$338$		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	−0.477619	−	0.878567i	$-0.658500\pi$
$347$	−229.148	+	36.2935i	−0.660369	+	0.104592i	−0.182750	+	0.983159i	$0.558500\pi$
$348$		0			0
$349$	107.761	−	35.0137i	0.308771	−	0.100326i	−0.150533	−	0.988605i	$-0.548099\pi$
$349$	107.761	−	35.0137i	0.308771	−	0.100326i	0.459304	+	0.888279i	$0.348099\pi$
$350$		0			0
$351$	169.254			0.482206
$352$		0			0
$353$	−21.9444	−	21.9444i	−0.0621654	−	0.0621654i	0.675341	−	0.737506i	$-0.263997\pi$
$353$	−21.9444	−	21.9444i	−0.0621654	−	0.0621654i	−0.737506	+	0.675341i	$0.763997\pi$
$354$		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	−0.0753854	−	0.997154i	$-0.524019\pi$
$359$	−259.373	−	84.2752i	−0.722486	−	0.234750i	−0.647101	+	0.762405i	$0.724019\pi$
$360$		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	0.726090	−	0.687600i	$-0.241336\pi$
$367$	−94.3098	−	185.093i	−0.256975	−	0.504342i	−0.983065	+	0.183258i	$0.941336\pi$
$368$		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	0.293879	−	0.955843i	$-0.405054\pi$
$373$	−246.912	−	246.912i	−0.661963	−	0.661963i	−0.955843	+	0.293879i	$0.905054\pi$
$374$		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	−0.180448	−	0.983585i	$-0.557755\pi$
$379$	307.277	−	422.931i	0.810758	−	1.11591i	0.991206	−	0.132328i	$-0.0422452\pi$
$380$		0			0
$381$	−235.442	+	724.615i	−0.617957	+	1.90188i
$382$		0			0
$383$	−126.077	−	19.9687i	−0.329184	−	0.0521376i	−0.0103447	−	0.999946i	$-0.503293\pi$
$383$	−126.077	−	19.9687i	−0.329184	−	0.0521376i	−0.318839	+	0.947809i	$0.603293\pi$
$384$		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	0.510405	−	0.859934i	$-0.329496\pi$
$389$	162.553	+	52.8166i	0.417874	+	0.135775i	−0.0925308	+	0.995710i	$0.529496\pi$
$390$		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	−0.837161	−	0.546957i	$-0.815786\pi$
$397$	−115.211	+	115.211i	−0.290203	+	0.290203i	0.546957	+	0.837161i	$0.315786\pi$
$398$		0			0
$399$	1268.09	−	412.026i	3.17816	−	1.03265i
$400$		0			0
$401$	−190.704	−	138.555i	−0.475572	−	0.345523i	0.324037	−	0.946045i	$-0.394960\pi$
$401$	−190.704	−	138.555i	−0.475572	−	0.345523i	−0.799609	+	0.600521i	$0.794960\pi$
$402$		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	0.753618	−	0.657313i	$-0.228307\pi$
$409$	−42.7016	−	58.7737i	−0.104405	−	0.143701i	−0.858023	+	0.513612i	$0.828307\pi$
$410$		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	$-0.924315\pi$
$419$		−	197.381i		−	0.471077i	0.971865	−	0.235538i	$-0.0756853\pi$
$420$		0			0
$421$	−85.4299	−	262.926i	−0.202921	−	0.624527i	−0.999792	−	0.0203781i	$-0.993513\pi$
$421$	−85.4299	−	262.926i	−0.202921	−	0.624527i	0.796871	−	0.604149i	$-0.206487\pi$
$422$		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	−0.669090	−	0.743182i	$-0.733316\pi$
$431$	−72.8571	+	52.9338i	−0.169042	+	0.122816i	0.500048	+	0.865998i	$0.333316\pi$
$432$		0			0
$433$	−208.924	+	106.452i	−0.482503	+	0.245847i	−0.678283	−	0.734800i	$-0.737276\pi$
$433$	−208.924	+	106.452i	−0.482503	+	0.245847i	0.195781	+	0.980648i	$0.437276\pi$
$434$		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	$0.158363\pi$
$439$			419.018i			0.954484i	−0.878772	+	0.477242i	$0.841637\pi$
$440$		0			0
$441$	417.232			0.946104
$442$		0			0
$443$	5.04160	−	9.89469i	0.0113806	−	0.0223357i	−0.885246	−	0.465123i	$-0.846010\pi$
$443$	5.04160	−	9.89469i	0.0113806	−	0.0223357i	0.896627	+	0.442787i	$0.146010\pi$
$444$		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	−0.969647	−	0.244509i	$-0.921373\pi$
$449$	−405.246	−	557.773i	−0.902552	−	1.24226i	0.0670952	−	0.997747i	$-0.478627\pi$
$450$		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	0.155485	−	0.987838i	$-0.450306\pi$
$457$	278.139	−	44.0528i	0.608618	−	0.0963957i	0.453134	+	0.891443i	$0.350306\pi$
$458$		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	0.961100	−	0.276201i	$-0.0890756\pi$
$463$	317.108	+	317.108i	0.684899	+	0.684899i	−0.276201	+	0.961100i	$0.589076\pi$
$464$		0			0
$465$	−47.2115	+	11.9183i	−0.101530	+	0.0256308i
$466$		0			0
$467$	467.837	−	74.0981i	1.00179	−	0.158668i	0.366071	−	0.930587i	$-0.380703\pi$
$467$	467.837	−	74.0981i	1.00179	−	0.158668i	0.635721	+	0.771919i	$0.280703\pi$
$468$		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	−0.851800	−	0.523867i	$-0.824489\pi$
$479$	−43.2790	+	59.5685i	−0.0903529	+	0.124360i	0.761447	+	0.648227i	$0.224489\pi$
$480$		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	−0.420657	−	0.907220i	$-0.638200\pi$
$487$	−682.710	−	347.858i	−1.40187	−	0.714288i	−0.981212	+	0.192932i	$0.938200\pi$
$488$		0			0
$489$	−616.600	+	848.678i	−1.26094	+	1.73554i
$490$		0			0
$491$	155.108	−	477.373i	0.315902	−	0.972247i	−0.659479	−	0.751723i	$-0.729223\pi$
$491$	155.108	−	477.373i	0.315902	−	0.972247i	0.975381	−	0.220524i	$-0.0707769\pi$
$492$		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	0.819272	−	0.573405i	$-0.194378\pi$
$499$	571.374	+	185.651i	1.14504	+	0.372045i	0.325766	+	0.945451i	$0.394378\pi$
$500$		0			0
$501$	−724.905	−	526.675i	−1.44692	−	1.05125i
$502$		0			0
$503$	−326.263	+	640.328i	−0.648635	+	1.27302i	0.299180	+	0.954197i	$0.403287\pi$
$503$	−326.263	+	640.328i	−0.648635	+	1.27302i	−0.947815	+	0.318821i	$0.896713\pi$
$504$		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	−0.999669	−	0.0257117i	$-0.991815\pi$
$509$	−912.793	+	296.584i	−1.79331	+	0.582680i	−0.793637	+	0.608392i	$0.791815\pi$
$510$		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	−0.983927	−	0.178569i	$-0.942853\pi$
$521$	−43.2186	+	133.013i	−0.0829533	+	0.255304i	0.900974	+	0.433873i	$0.142853\pi$
$522$		0			0
$523$	−38.7235	−	244.491i	−0.0740412	−	0.467477i	−0.996653	−	0.0817479i	$-0.973950\pi$
$523$	−38.7235	−	244.491i	−0.0740412	−	0.467477i	0.922612	−	0.385730i	$-0.126050\pi$
$524$		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	−0.515754	−	0.856737i	$-0.672488\pi$
$541$	75.5642	−	54.9006i	0.139675	−	0.101480i	0.655429	+	0.755257i	$0.272488\pi$
$542$		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	0.790227	−	0.612814i	$-0.209962\pi$
$547$	415.137	+	211.523i	0.758934	+	0.386696i	−0.0312928	+	0.999510i	$0.509962\pi$
$548$		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	0.975569	−	0.219695i	$-0.0705061\pi$
$557$	124.995	+	245.316i	0.224407	+	0.440424i	−0.751162	+	0.660118i	$0.770506\pi$
$558$		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	0.958524	−	0.285012i	$-0.0919976\pi$
$563$	1003.30	+	158.907i	1.78206	+	0.282251i	0.823537	+	0.567263i	$0.191998\pi$
$564$		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	−0.932281	−	0.361734i	$-0.882185\pi$
$569$	−838.644	+	272.492i	−1.47389	+	0.478896i	−0.541609	+	0.840630i	$0.682185\pi$
$570$		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	−0.210816	−	0.977526i	$-0.567612\pi$
$577$	−63.0330	+	9.98345i	−0.109243	+	0.0173023i	0.101574	+	0.994828i	$0.467612\pi$
$578$		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	0.778792	−	0.627282i	$-0.215833\pi$
$587$	−109.448	−	214.803i	−0.186453	−	0.365934i	−0.965244	+	0.261349i	$0.915833\pi$
$588$		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	0.837853	−	0.545897i	$-0.183811\pi$
$593$	173.130	+	173.130i	0.291956	+	0.291956i	−0.545897	+	0.837853i	$0.683811\pi$
$594$		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	−0.848021	−	0.529963i	$-0.822206\pi$
$599$	−49.0843	+	67.5587i	−0.0819437	+	0.112786i	0.766077	+	0.642748i	$0.222206\pi$
$600$		0			0
$601$	−280.867	+	864.418i	−0.467332	+	1.43830i	0.388694	+	0.921367i	$0.372926\pi$
$601$	−280.867	+	864.418i	−0.467332	+	1.43830i	−0.856026	+	0.516933i	$0.827074\pi$
$602$		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	0.811636	+	0.584163i	$0.198577\pi$
$607$	−85.4608	+	539.578i	−0.140792	+	0.888926i	−0.952428	+	0.304763i	$0.901423\pi$
$608$		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	−0.999832	−	0.0183296i	$-0.994165\pi$
$613$	−243.555	+	478.004i	−0.397317	+	0.779778i	0.602515	+	0.798107i	$0.294165\pi$
$614$		0			0
$615$	−46.2589	+	690.632i	−0.0752176	+	1.12298i
$616$		0			0
$617$	596.755	−	596.755i	0.967187	−	0.967187i	−0.0322910	−	0.999479i	$-0.510280\pi$
$617$	596.755	−	596.755i	0.967187	−	0.967187i	0.999479	+	0.0322910i	$0.0102803\pi$
$618$		0			0
$619$	−105.382	+	34.2406i	−0.170245	+	0.0553160i	−0.392899	−	0.919581i	$-0.628528\pi$
$619$	−105.382	+	34.2406i	−0.170245	+	0.0553160i	0.222654	+	0.974897i	$0.428528\pi$
$620$		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	−0.999412	−	0.0342821i	$-0.989086\pi$
$631$	−107.724	+	331.542i	−0.170720	+	0.525423i	0.828692	+	0.559705i	$0.189086\pi$
$632$		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	0.946736	−	0.322010i	$-0.104359\pi$
$641$	−5.42437	−	16.6945i	−0.00846236	−	0.0260445i	−0.955199	+	0.295966i	$0.904359\pi$
$642$		0			0
$643$	−149.670	−	944.977i	−0.232768	−	1.46964i	−0.776360	−	0.630289i	$-0.782936\pi$
$643$	−149.670	−	944.977i	−0.232768	−	1.46964i	0.543593	−	0.839349i	$-0.317064\pi$
$644$		0			0
$645$	−249.441	−	582.889i	−0.386731	−	0.903703i
$646$		0			0
$647$	122.051	−	770.600i	0.188641	−	1.19104i	−0.693643	−	0.720319i	$-0.743995\pi$
$647$	122.051	−	770.600i	0.188641	−	1.19104i	0.882285	−	0.470716i	$-0.156005\pi$
$648$		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	−0.474792	−	0.880098i	$-0.657477\pi$
$653$	−27.3299	+	13.9253i	−0.0418528	+	0.0213251i	0.432939	+	0.901423i	$0.357477\pi$
$654$		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	$-0.886339\pi$
$659$		−	460.688i		−	0.699071i	0.936923	−	0.349535i	$-0.113661\pi$
$660$		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	−0.100368	−	0.994950i	$-0.532002\pi$
$673$	−338.707	−	53.6460i	−0.503280	−	0.0797117i	−0.402912	+	0.915239i	$0.632002\pi$
$674$		0			0
$675$	319.842	−	112.233i	0.473839	−	0.166271i
$676$		0			0
$677$	−177.698	+	28.1446i	−0.262478	+	0.0415725i	−0.286287	−	0.958144i	$-0.592421\pi$
$677$	−177.698	+	28.1446i	−0.262478	+	0.0415725i	0.0238082	+	0.999717i	$0.492421\pi$
$678$		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	0.115092	−	0.993355i	$-0.463284\pi$
$683$	−599.854	−	599.854i	−0.878263	−	0.878263i	−0.993355	+	0.115092i	$0.963284\pi$
$684$		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	−0.771228	−	0.636559i	$-0.780357\pi$
$691$	−279.266	+	202.899i	−0.404148	+	0.293630i	0.367081	+	0.930189i	$0.380357\pi$
$692$		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	0.893410	+	0.449242i	$0.148306\pi$
$701$	304.714	+	937.812i	0.434684	+	1.33782i	−0.458726	+	0.888578i	$0.651694\pi$
$702$		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	−0.792542	−	0.609818i	$-0.791243\pi$
$709$	22.9278	−	31.5574i	0.0323382	−	0.0445097i	0.824880	+	0.565308i	$0.191243\pi$
$710$		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	0.234930	−	0.972012i	$-0.424514\pi$
$719$	−105.220	−	34.1881i	−0.146342	−	0.0475495i	−0.381272	+	0.924463i	$0.624514\pi$
$720$		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	−0.888908	−	0.458085i	$-0.848536\pi$
$727$	−313.209	+	313.209i	−0.430824	+	0.430824i	0.458085	+	0.888908i	$0.348536\pi$
$728$		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	0.0470016	−	0.998895i	$-0.485033\pi$
$733$	647.057	−	329.692i	0.882751	−	0.449784i	0.835750	+	0.549111i	$0.185033\pi$
$734$		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	0.875533	−	0.483159i	$-0.160511\pi$
$739$	107.500	+	147.961i	0.145467	+	0.200218i	−0.730066	+	0.683377i	$0.760511\pi$
$740$		0			0
$741$	−458.531	+	1411.21i	−0.618800	+	1.90447i
$742$		0			0
$743$	−124.101	−	783.543i	−0.167027	−	1.05457i	−0.918678	−	0.395006i	$-0.870742\pi$
$743$	−124.101	−	783.543i	−0.167027	−	1.05457i	0.751652	−	0.659560i	$-0.229258\pi$
$744$		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	0.554784	+	0.831995i	$0.312801\pi$
$751$	446.836	+	1375.22i	0.594988	+	1.83119i	0.0402046	+	0.999191i	$0.487199\pi$
$752$		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	0.213401	+	0.976965i	$0.431546\pi$
$757$	−220.631	+	1393.01i	−0.291454	+	1.84017i	−0.504855	+	0.863204i	$0.668454\pi$
$758$		0			0
$759$	186.004	−	267.984i	0.245064	−	0.353075i
$760$		0			0
$761$	−387.904	+	281.829i	−0.509729	+	0.370340i	−0.812721	−	0.582653i	$-0.802015\pi$
$761$	−387.904	+	281.829i	−0.509729	+	0.370340i	0.302992	+	0.952993i	$0.402015\pi$
$762$		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	$0.176785\pi$
$769$			810.946i			1.05455i	−0.849696	+	0.527273i	$0.823215\pi$
$770$		0			0
$771$	225.919			0.293020
$772$		0			0
$773$	92.6498	−	181.835i	0.119857	−	0.235233i	−0.823281	−	0.567634i	$-0.807859\pi$
$773$	92.6498	−	181.835i	0.119857	−	0.235233i	0.943138	+	0.332401i	$0.107859\pi$
$774$		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	−0.196023	−	0.980599i	$-0.562803\pi$
$787$	−62.5107	+	9.90073i	−0.0794291	+	0.0125803i	0.116593	+	0.993180i	$0.462803\pi$
$788$		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	0.346729	−	0.937966i	$-0.387293\pi$
$797$	770.168	−	121.983i	0.966334	−	0.153052i	0.619606	+	0.784913i	$0.287293\pi$
$798$		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	−0.263702	−	0.964604i	$-0.584944\pi$
$809$	594.760	−	818.617i	0.735179	−	1.01189i	0.998882	−	0.0472832i	$-0.0150563\pi$
$810$		0			0
$811$	−282.131	−	868.311i	−0.347881	−	1.07067i	−0.960024	−	0.279919i	$-0.909692\pi$
$811$	−282.131	−	868.311i	−0.347881	−	1.07067i	0.612143	−	0.790747i	$-0.290308\pi$
$812$		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	−0.681387	−	0.731923i	$-0.738623\pi$
$821$	246.366	−	758.237i	0.300080	−	0.923553i	0.981467	−	0.191629i	$-0.0613772\pi$
$822$		0			0
$823$	167.901	+	26.5929i	0.204011	+	0.0323121i	0.257603	−	0.966251i	$-0.417067\pi$
$823$	167.901	+	26.5929i	0.204011	+	0.0323121i	−0.0535927	+	0.998563i	$0.517067\pi$
$824$		0			0
$825$	367.081	+	978.051i	0.444947	+	1.18552i
$826$		0			0
$827$	139.547	−	881.067i	0.168739	−	1.06538i	−0.747358	−	0.664421i	$-0.768678\pi$
$827$	139.547	−	881.067i	0.168739	−	1.06538i	0.916097	−	0.400956i	$-0.131322\pi$
$828$		0			0
$829$	−344.025	−	111.781i	−0.414988	−	0.134838i	0.0940787	−	0.995565i	$-0.470009\pi$
$829$	−344.025	−	111.781i	−0.414988	−	0.134838i	−0.509067	+	0.860727i	$0.670009\pi$
$830$		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	0.146901	−	0.989151i	$-0.453070\pi$
$839$	710.763	−	230.941i	0.847155	−	0.275257i	0.700254	+	0.713894i	$0.253070\pi$
$840$		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	−0.973314	−	0.229476i	$-0.926299\pi$
$853$	−101.123	−	638.463i	−0.118549	−	0.748491i	0.854765	−	0.519015i	$-0.173701\pi$
$854$		0			0
$855$	435.473	−	729.587i	0.509326	−	0.853319i
$856$		0			0
$857$	−577.286	+	577.286i	−0.673613	+	0.673613i	−0.958547	−	0.284934i	$-0.908028\pi$
$857$	−577.286	+	577.286i	−0.673613	+	0.673613i	0.284934	+	0.958547i	$0.408028\pi$
$858$		0			0
$859$			811.925i			0.945198i	0.881277	+	0.472599i	$0.156684\pi$
$859$			811.925i			0.945198i	−0.881277	+	0.472599i	$0.843316\pi$
$860$		0			0
$861$	−479.862	−	1476.86i	−0.557331	−	1.71529i
$862$		0			0
$863$	−49.3286	−	311.448i	−0.0571594	−	0.360890i	−0.999645	−	0.0266435i	$-0.991518\pi$
$863$	−49.3286	−	311.448i	−0.0571594	−	0.360890i	0.942486	−	0.334247i	$-0.108482\pi$
$864$		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	0.164908	−	0.986309i	$-0.447267\pi$
$877$	−470.161	−	239.559i	−0.536102	−	0.273157i	−0.701010	+	0.713152i	$0.747267\pi$
$878$		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	−0.862178	−	0.506606i	$-0.830900\pi$
$883$	48.0796	−	94.3615i	0.0544503	−	0.106865i	0.916628	+	0.399741i	$0.130900\pi$
$884$		0			0
$885$	1128.24	+	941.079i	1.27484	+	1.06337i
$886$		0			0
$887$	−293.945	−	576.899i	−0.331392	−	0.650394i	0.663846	−	0.747870i	$-0.268923\pi$
$887$	−293.945	−	576.899i	−0.331392	−	0.650394i	−0.995238	+	0.0974756i	$0.968923\pi$
$888$		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	0.172670	−	0.984980i	$-0.444760\pi$
$907$	581.628	−	92.1208i	0.641265	−	0.101566i	0.468595	+	0.883413i	$0.344760\pi$
$908$		0			0
$909$	28.6039	+	9.29397i	0.0314674	+	0.0102244i
$910$		0			0
$911$	1139.71	−	828.050i	1.25106	−	0.908946i	0.252774	−	0.967525i	$-0.418657\pi$
$911$	1139.71	−	828.050i	1.25106	−	0.908946i	0.998283	+	0.0585795i	$0.0186571\pi$
$912$		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	0.0421531	+	0.999111i	$0.486578\pi$
$919$	−846.476	+	1165.07i	−0.921084	+	1.26776i	−0.963237	+	0.268652i	$0.913422\pi$
$920$		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	−0.0642755	−	0.997932i	$-0.520474\pi$
$929$	840.445	−	1156.77i	0.904677	−	1.24518i	0.968952	−	0.247248i	$-0.0795264\pi$
$930$		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	−0.808281	−	0.588796i	$-0.799602\pi$
$937$	133.418	−	842.365i	0.142388	−	0.899002i	0.950669	−	0.310206i	$-0.100398\pi$
$938$		0			0
$939$	−1406.32	−	456.941i	−1.49768	−	0.486625i
$940$		0			0
$941$	199.499	+	144.944i	0.212007	+	0.154032i	0.688721	−	0.725026i	$-0.258172\pi$
$941$	199.499	+	144.944i	0.212007	+	0.154032i	−0.476714	+	0.879058i	$0.658172\pi$
$942$		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	−0.774862	−	0.632131i	$-0.782181\pi$
$947$	−135.167	+	135.167i	−0.142731	+	0.142731i	0.632131	+	0.774862i	$0.282181\pi$
$948$		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	0.441803	−	0.897112i	$-0.354339\pi$
$953$	1360.19	−	693.049i	1.42727	−	0.727229i	0.985464	+	0.169883i	$0.0543390\pi$
$954$		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	0.143703	−	0.989621i	$-0.454099\pi$
$967$	1095.92	−	1095.92i	1.13332	−	1.13332i	0.989621	−	0.143703i	$-0.0459011\pi$
$968$		0			0
$969$		−	1354.50i		−	1.39783i
$970$		0			0
$971$	−200.879	−	618.243i	−0.206879	−	0.636707i	−0.999631	−	0.0271634i	$-0.991353\pi$
$971$	−200.879	−	618.243i	−0.206879	−	0.636707i	0.792752	−	0.609544i	$-0.208647\pi$
$972$		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	−0.828475	−	0.560026i	$-0.810791\pi$
$977$	129.461	−	817.386i	0.132509	−	0.836629i	0.960984	−	0.276603i	$-0.0892087\pi$
$978$		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	−0.370588	−	0.928797i	$-0.620844\pi$
$983$	160.228	−	81.6401i	0.162999	−	0.0830520i	0.533587	+	0.845745i	$0.320844\pi$
$984$		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	0.895627	−	0.444806i	$-0.146728\pi$
$997$	9.30658	+	18.2652i	0.00933459	+	0.0183202i	−0.886292	+	0.463127i	$0.846728\pi$
$998$		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.113.4	yes	96
5.2	odd	4	inner	220.3.x.a.157.9	yes	96
11.4	even	5	inner	220.3.x.a.213.9	yes	96
55.37	odd	20	inner	220.3.x.a.37.4	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.37.4	✓	96	55.37	odd	20	inner
220.3.x.a.113.4	yes	96	1.1	even	1	trivial
220.3.x.a.157.9	yes	96	5.2	odd	4	inner
220.3.x.a.213.9	yes	96	11.4	even	5	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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