LMFDB - Embedded newform 220.3.p.b.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(41,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("220.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.p (of order $10$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 33 x^{14} - 111 x^{13} + 735 x^{12} - 1436 x^{11} + 10633 x^{10} - 25103 x^{9} + \cdots + 75625 $ x^16 - 3x^15 + 33x^14 - 111x^13 + 735x^12 - 1436x^11 + 10633x^10 - 25103x^9 + 232616x^8 - 600030x^7 + 1738315x^6 - 2296850x^5 + 2290475x^4 - 1918750x^3 + 1679000x^2 - 543125*x + 75625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			61.4
Root			$-3.40337 + 2.47269i$ of defining polynomial
Character	$\chi$	$=$	220.61
Dual form			220.3.p.b.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.71238 + 3.42375i) q^{3} +(0.690983 - 2.12663i) q^{5} +(-2.62857 - 3.61792i) q^{7} +(7.70337 + 23.7085i) q^{9} +(10.9389 + 1.15791i) q^{11} +(9.85015 - 3.20051i) q^{13} +(10.5372 - 7.65573i) q^{15} +(0.409765 + 0.133141i) q^{17} +(-15.0230 + 20.6774i) q^{19} -26.0486i q^{21} -21.0633 q^{23} +(-4.04508 - 2.93893i) q^{25} +(-28.6710 + 88.2404i) q^{27} +(-31.7671 - 43.7237i) q^{29} +(-3.90895 - 12.0305i) q^{31} +(47.5838 + 42.9085i) q^{33} +(-9.51027 + 3.09007i) q^{35} +(-3.37829 + 2.45447i) q^{37} +(57.3755 + 18.6424i) q^{39} +(24.6346 - 33.9066i) q^{41} -84.6483i q^{43} +55.7421 q^{45} +(34.2779 + 24.9043i) q^{47} +(8.96187 - 27.5818i) q^{49} +(1.47513 + 2.03034i) q^{51} +(13.5885 + 41.8211i) q^{53} +(10.0210 - 22.4628i) q^{55} +(-141.588 + 46.0048i) q^{57} +(-53.6564 + 38.9837i) q^{59} +(-39.7732 - 12.9231i) q^{61} +(65.5267 - 90.1898i) q^{63} -23.1591i q^{65} +41.3830 q^{67} +(-99.2582 - 72.1153i) q^{69} +(1.24922 - 3.84472i) q^{71} +(9.80778 + 13.4993i) q^{73} +(-8.99985 - 27.6987i) q^{75} +(-24.5644 - 42.6197i) q^{77} +(49.2252 - 15.9942i) q^{79} +(-255.713 + 185.786i) q^{81} +(60.4230 + 19.6326i) q^{83} +(0.566281 - 0.779419i) q^{85} -314.805i q^{87} -30.4148 q^{89} +(-37.4711 - 27.2243i) q^{91} +(22.7689 - 70.0756i) q^{93} +(33.5924 + 46.2360i) q^{95} +(-52.9856 - 163.073i) q^{97} +(56.8139 + 268.265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 9 q^{3} + 20 q^{5} + 10 q^{7} - 19 q^{9} + 23 q^{11} - 5 q^{13} + 15 q^{15} + 25 q^{17} + 30 q^{19} - 168 q^{23} - 20 q^{25} - 225 q^{27} - 105 q^{29} + 40 q^{31} + 106 q^{33} - 16 q^{37} + 115 q^{39}+ \cdots + 150 q^{99}+O(q^{100}) $ 16 * q + 9 * q^3 + 20 * q^5 + 10 * q^7 - 19 * q^9 + 23 * q^11 - 5 * q^13 + 15 * q^15 + 25 * q^17 + 30 * q^19 - 168 * q^23 - 20 * q^25 - 225 * q^27 - 105 * q^29 + 40 * q^31 + 106 * q^33 - 16 * q^37 + 115 * q^39 + 255 * q^41 - 30 * q^45 + 102 * q^47 + 12 * q^49 + 380 * q^51 + 297 * q^53 + 55 * q^55 - 150 * q^57 - 22 * q^59 - 30 * q^61 - 320 * q^63 - 68 * q^67 - 137 * q^69 - 240 * q^71 + 85 * q^73 - 30 * q^75 + 226 * q^77 - 215 * q^79 - 463 * q^81 - 610 * q^83 + 25 * q^85 - 160 * q^89 + 161 * q^91 - 253 * q^93 + 90 * q^95 + 179 * q^97 + 150 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.71238	+	3.42375i	1.57079	+	1.14125i	0.926390	+	0.376564i	$0.122895\pi$
$3$	4.71238	+	3.42375i	1.57079	+	1.14125i	0.644404	+	0.764685i	$0.277105\pi$
$4$		0			0
$5$	0.690983	−	2.12663i	0.138197	−	0.425325i
$5$	0.690983	−	2.12663i	0.138197	−	0.425325i
$6$		0			0
$7$	−2.62857	−	3.61792i	−0.375511	−	0.516846i	0.578878	−	0.815414i	$-0.303491\pi$
$7$	−2.62857	−	3.61792i	−0.375511	−	0.516846i	−0.954388	+	0.298568i	$0.903491\pi$
$8$		0			0
$9$	7.70337	+	23.7085i	0.855930	+	2.63428i
$10$		0			0
$11$	10.9389	+	1.15791i	0.994444	+	0.105265i
$11$	10.9389	+	1.15791i	0.994444	+	0.105265i
$12$		0			0
$13$	9.85015	−	3.20051i	0.757704	−	0.246193i	0.0954112	−	0.995438i	$-0.469583\pi$
$13$	9.85015	−	3.20051i	0.757704	−	0.246193i	0.662293	+	0.749245i	$0.269583\pi$
$14$		0			0
$15$	10.5372	−	7.65573i	0.702481	−	0.510382i
$16$		0			0
$17$	0.409765	+	0.133141i	0.0241038	+	0.00783181i	0.321044	−	0.947064i	$-0.395966\pi$
$17$	0.409765	+	0.133141i	0.0241038	+	0.00783181i	−0.296940	+	0.954896i	$0.595966\pi$
$18$		0			0
$19$	−15.0230	+	20.6774i	−0.790683	+	1.08828i	0.203340	+	0.979108i	$0.434820\pi$
$19$	−15.0230	+	20.6774i	−0.790683	+	1.08828i	−0.994023	+	0.109174i	$0.965180\pi$
$20$		0			0
$21$		−	26.0486i		−	1.24041i
$22$		0			0
$23$	−21.0633			−0.915794			−0.457897	−	0.889005i	$-0.651397\pi$
$23$	−21.0633			−0.915794			−0.457897	+	0.889005i	$0.651397\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.161803	−	0.117557i
$26$		0			0
$27$	−28.6710	+	88.2404i	−1.06189	+	3.26816i
$28$		0			0
$29$	−31.7671	−	43.7237i	−1.09542	−	1.50771i	−0.841322	−	0.540534i	$-0.818222\pi$
$29$	−31.7671	−	43.7237i	−1.09542	−	1.50771i	−0.254095	−	0.967179i	$-0.581778\pi$
$30$		0			0
$31$	−3.90895	−	12.0305i	−0.126095	−	0.388081i	0.868004	−	0.496557i	$-0.165403\pi$
$31$	−3.90895	−	12.0305i	−0.126095	−	0.388081i	−0.994099	+	0.108477i	$0.965403\pi$
$32$		0			0
$33$	47.5838	+	42.9085i	1.44193	+	1.30026i
$34$		0			0
$35$	−9.51027	+	3.09007i	−0.271722	+	0.0882879i
$36$		0			0
$37$	−3.37829	+	2.45447i	−0.0913053	+	0.0663372i	−0.632501	−	0.774559i	$-0.717972\pi$
$37$	−3.37829	+	2.45447i	−0.0913053	+	0.0663372i	0.541196	+	0.840896i	$0.317972\pi$
$38$		0			0
$39$	57.3755	+	18.6424i	1.47117	+	0.478011i
$40$		0			0
$41$	24.6346	−	33.9066i	0.600844	−	0.826991i	−0.394941	−	0.918706i	$-0.629235\pi$
$41$	24.6346	−	33.9066i	0.600844	−	0.826991i	0.995785	+	0.0917154i	$0.0292350\pi$
$42$		0			0
$43$		−	84.6483i		−	1.96857i	−0.176600	−	0.984283i	$-0.556510\pi$
$43$		−	84.6483i		−	1.96857i	0.176600	−	0.984283i	$-0.443490\pi$
$44$		0			0
$45$	55.7421			1.23871
$46$		0			0
$47$	34.2779	+	24.9043i	0.729316	+	0.529879i	0.889347	−	0.457233i	$-0.151159\pi$
$47$	34.2779	+	24.9043i	0.729316	+	0.529879i	−0.160031	+	0.987112i	$0.551159\pi$
$48$		0			0
$49$	8.96187	−	27.5818i	0.182895	−	0.562894i
$50$		0			0
$51$	1.47513	+	2.03034i	0.0289241	+	0.0398106i
$52$		0			0
$53$	13.5885	+	41.8211i	0.256387	+	0.789078i	0.993553	+	0.113366i	$0.0361634\pi$
$53$	13.5885	+	41.8211i	0.256387	+	0.789078i	−0.737166	+	0.675711i	$0.763837\pi$
$54$		0			0
$55$	10.0210	−	22.4628i	0.182201	−	0.408415i
$56$		0			0
$57$	−141.588	+	46.0048i	−2.48400	+	0.807101i
$58$		0			0
$59$	−53.6564	+	38.9837i	−0.909430	+	0.660740i	−0.940871	−	0.338766i	$-0.889991\pi$
$59$	−53.6564	+	38.9837i	−0.909430	+	0.660740i	0.0314403	+	0.999506i	$0.489991\pi$
$60$		0			0
$61$	−39.7732	−	12.9231i	−0.652019	−	0.211854i	−0.0357149	−	0.999362i	$-0.511371\pi$
$61$	−39.7732	−	12.9231i	−0.652019	−	0.211854i	−0.616304	+	0.787508i	$0.711371\pi$
$62$		0			0
$63$	65.5267	−	90.1898i	1.04011	−	1.43158i
$64$		0			0
$65$		−	23.1591i		−	0.356294i
$66$		0			0
$67$	41.3830			0.617657			0.308828	−	0.951118i	$-0.400063\pi$
$67$	41.3830			0.617657			0.308828	+	0.951118i	$0.400063\pi$
$68$		0			0
$69$	−99.2582	−	72.1153i	−1.43852	−	1.04515i
$70$		0			0
$71$	1.24922	−	3.84472i	0.0175947	−	0.0541509i	−0.941874	−	0.335967i	$-0.890937\pi$
$71$	1.24922	−	3.84472i	0.0175947	−	0.0541509i	0.959468	+	0.281816i	$0.0909369\pi$
$72$		0			0
$73$	9.80778	+	13.4993i	0.134353	+	0.184921i	0.870893	−	0.491473i	$-0.163541\pi$
$73$	9.80778	+	13.4993i	0.134353	+	0.184921i	−0.736539	+	0.676395i	$0.763541\pi$
$74$		0			0
$75$	−8.99985	−	27.6987i	−0.119998	−	0.369316i
$76$		0			0
$77$	−24.5644	−	42.6197i	−0.319019	−	0.553503i
$78$		0			0
$79$	49.2252	−	15.9942i	0.623103	−	0.202459i	0.0195856	−	0.999808i	$-0.493765\pi$
$79$	49.2252	−	15.9942i	0.623103	−	0.202459i	0.603518	+	0.797350i	$0.293765\pi$
$80$		0			0
$81$	−255.713	+	185.786i	−3.15695	+	2.29366i
$82$		0			0
$83$	60.4230	+	19.6326i	0.727988	+	0.236538i	0.649483	−	0.760376i	$-0.274985\pi$
$83$	60.4230	+	19.6326i	0.727988	+	0.236538i	0.0785052	+	0.996914i	$0.474985\pi$
$84$		0			0
$85$	0.566281	−	0.779419i	0.00666213	−	0.00916964i
$86$		0			0
$87$		−	314.805i		−	3.61845i
$88$		0			0
$89$	−30.4148			−0.341740			−0.170870	−	0.985294i	$-0.554658\pi$
$89$	−30.4148			−0.341740			−0.170870	+	0.985294i	$0.554658\pi$
$90$		0			0
$91$	−37.4711	−	27.2243i	−0.411770	−	0.299168i
$92$		0			0
$93$	22.7689	−	70.0756i	0.244827	−	0.753501i
$94$		0			0
$95$	33.5924	+	46.2360i	0.353604	+	0.486695i
$96$		0			0
$97$	−52.9856	−	163.073i	−0.546243	−	1.68116i	−0.718016	−	0.696027i	$-0.754950\pi$
$97$	−52.9856	−	163.073i	−0.546243	−	1.68116i	0.171773	−	0.985137i	$-0.445050\pi$
$98$		0			0
$99$	56.8139	+	268.265i	0.573877	+	2.70974i
$100$		0			0
$101$	−150.417	+	48.8735i	−1.48928	+	0.483896i	−0.936870	−	0.349678i	$-0.886291\pi$
$101$	−150.417	+	48.8735i	−1.48928	+	0.483896i	−0.552408	+	0.833574i	$0.686291\pi$
$102$		0			0
$103$	−0.0678450	+	0.0492923i	−0.000658689	+	0.000478566i	−0.588115	−	0.808778i	$-0.700130\pi$
$103$	−0.0678450	+	0.0492923i	−0.000658689	+	0.000478566i	0.587456	+	0.809256i	$0.300130\pi$
$104$		0			0
$105$	−55.3957	−	17.9992i	−0.527578	−	0.171420i
$106$		0			0
$107$	−38.2168	+	52.6009i	−0.357166	+	0.491597i	−0.949356	−	0.314201i	$-0.898263\pi$
$107$	−38.2168	+	52.6009i	−0.357166	+	0.491597i	0.592190	+	0.805798i	$0.298263\pi$
$108$		0			0
$109$		−	13.7155i		−	0.125830i	−0.998019	−	0.0629151i	$-0.979960\pi$
$109$		−	13.7155i		−	0.125830i	0.998019	−	0.0629151i	$-0.0200397\pi$
$110$		0			0
$111$	−24.3233			−0.219129
$112$		0			0
$113$	−53.0356	−	38.5326i	−0.469342	−	0.340997i	0.327843	−	0.944732i	$-0.393678\pi$
$113$	−53.0356	−	38.5326i	−0.469342	−	0.340997i	−0.797185	+	0.603736i	$0.793678\pi$
$114$		0			0
$115$	−14.5544	+	44.7937i	−0.126560	+	0.389510i
$116$		0			0
$117$	151.759	+	208.878i	1.29708	+	1.78528i
$118$		0			0
$119$	−0.595405	−	1.83247i	−0.00500340	−	0.0153989i
$120$		0			0
$121$	118.318	+	25.3325i	0.977839	+	0.209360i
$122$		0			0
$123$	232.176	−	75.4384i	1.88761	−	0.613320i
$124$		0			0
$125$	−9.04508	+	6.57164i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	128.796	+	41.8484i	1.01414	+	0.329515i	0.768503	−	0.639846i	$-0.221002\pi$
$127$	128.796	+	41.8484i	1.01414	+	0.329515i	0.245640	+	0.969361i	$0.421002\pi$
$128$		0			0
$129$	289.814	−	398.895i	2.24662	−	3.09221i
$130$		0			0
$131$			221.202i			1.68857i	0.535897	+	0.844283i	$0.319973\pi$
$131$			221.202i			1.68857i	−0.535897	+	0.844283i	$0.680027\pi$
$132$		0			0
$133$	114.298			0.859384
$134$		0			0
$135$	167.843	+	121.945i	1.24328	+	0.903298i
$136$		0			0
$137$	−40.6856	+	125.217i	−0.296975	+	0.913996i	0.685576	+	0.728001i	$0.259551\pi$
$137$	−40.6856	+	125.217i	−0.296975	+	0.913996i	−0.982551	+	0.185994i	$0.940449\pi$
$138$		0			0
$139$	−84.4867	−	116.286i	−0.607818	−	0.836590i	0.388578	−	0.921416i	$-0.372967\pi$
$139$	−84.4867	−	116.286i	−0.607818	−	0.836590i	−0.996396	+	0.0848260i	$0.972967\pi$
$140$		0			0
$141$	76.2644	+	234.718i	0.540882	+	1.66466i
$142$		0			0
$143$	111.456	−	23.6044i	0.779410	−	0.165066i
$144$		0			0
$145$	−114.934	+	37.3445i	−0.792652	+	0.257548i
$146$		0			0
$147$	136.665	−	99.2929i	0.929694	−	0.675462i
$148$		0			0
$149$	−155.742	−	50.6035i	−1.04525	−	0.339621i	−0.264445	−	0.964401i	$-0.585189\pi$
$149$	−155.742	−	50.6035i	−1.04525	−	0.339621i	−0.780801	+	0.624780i	$0.785189\pi$
$150$		0			0
$151$	−53.0992	+	73.0848i	−0.351650	+	0.484005i	−0.947799	−	0.318869i	$-0.896697\pi$
$151$	−53.0992	+	73.0848i	−0.351650	+	0.484005i	0.596148	+	0.802874i	$0.296697\pi$
$152$		0			0
$153$			10.7406i			0.0701997i
$154$		0			0
$155$	−28.2854			−0.182486
$156$		0			0
$157$	198.053	+	143.894i	1.26148	+	0.916522i	0.998830	−	0.0483680i	$-0.0154020\pi$
$157$	198.053	+	143.894i	1.26148	+	0.916522i	0.262655	+	0.964890i	$0.415402\pi$
$158$		0			0
$159$	−79.1507	+	243.601i	−0.497803	+	1.53208i
$160$		0			0
$161$	55.3663	+	76.2052i	0.343890	+	0.473324i
$162$		0			0
$163$	17.8988	+	55.0868i	0.109809	+	0.337956i	0.990829	−	0.135122i	$-0.0431427\pi$
$163$	17.8988	+	55.0868i	0.109809	+	0.337956i	−0.881020	+	0.473078i	$0.843143\pi$
$164$		0			0
$165$	124.130	−	71.5440i	0.752303	−	0.433600i
$166$		0			0
$167$	−152.443	+	49.5318i	−0.912834	+	0.296598i	−0.727524	−	0.686082i	$-0.759329\pi$
$167$	−152.443	+	49.5318i	−0.912834	+	0.296598i	−0.185310	+	0.982680i	$0.559329\pi$
$168$		0			0
$169$	−49.9416	+	36.2847i	−0.295512	+	0.214702i
$170$		0			0
$171$	−605.957	−	196.887i	−3.54361	−	1.15139i
$172$		0			0
$173$	−57.7297	+	79.4582i	−0.333698	+	0.459296i	−0.942588	−	0.333959i	$-0.891615\pi$
$173$	−57.7297	+	79.4582i	−0.333698	+	0.459296i	0.608890	+	0.793255i	$0.291615\pi$
$174$		0			0
$175$			22.3600i			0.127771i
$176$		0			0
$177$	−386.320			−2.18260
$178$		0			0
$179$	138.886	+	100.907i	0.775901	+	0.563725i	0.903746	−	0.428069i	$-0.140806\pi$
$179$	138.886	+	100.907i	0.775901	+	0.563725i	−0.127845	+	0.991794i	$0.540806\pi$
$180$		0			0
$181$	48.0184	−	147.785i	0.265295	−	0.816494i	−0.726330	−	0.687346i	$-0.758776\pi$
$181$	48.0184	−	147.785i	0.265295	−	0.816494i	0.991625	−	0.129148i	$-0.0412242\pi$
$182$		0			0
$183$	−143.181	−	197.072i	−0.782410	−	1.07690i
$184$		0			0
$185$	2.88541	+	8.88037i	0.0155968	+	0.0480020i
$186$		0			0
$187$	4.32821	+	1.93088i	0.0231455	+	0.0103256i
$188$		0			0
$189$	394.611	−	128.217i	2.08789	−	0.678396i
$190$		0			0
$191$	212.159	−	154.143i	1.11078	−	0.807030i	0.127995	−	0.991775i	$-0.459146\pi$
$191$	212.159	−	154.143i	1.11078	−	0.807030i	0.982787	+	0.184745i	$0.0591458\pi$
$192$		0			0
$193$	71.7361	+	23.3085i	0.371690	+	0.120769i	0.488905	−	0.872337i	$-0.337397\pi$
$193$	71.7361	+	23.3085i	0.371690	+	0.120769i	−0.117215	+	0.993107i	$0.537397\pi$
$194$		0			0
$195$	79.2909	−	109.135i	0.406620	−	0.559665i
$196$		0			0
$197$			30.3209i			0.153913i	0.997034	+	0.0769565i	$0.0245203\pi$
$197$			30.3209i			0.153913i	−0.997034	+	0.0769565i	$0.975480\pi$
$198$		0			0
$199$	−241.081			−1.21146			−0.605731	−	0.795670i	$-0.707119\pi$
$199$	−241.081			−1.21146			−0.605731	+	0.795670i	$0.707119\pi$
$200$		0			0
$201$	195.013	+	141.685i	0.970212	+	0.704901i
$202$		0			0
$203$	−74.6867	+	229.862i	−0.367915	+	1.13232i
$204$		0			0
$205$	−55.0847	−	75.8175i	−0.268706	−	0.369842i
$206$		0			0
$207$	−162.258	−	499.379i	−0.783855	−	2.41246i
$208$		0			0
$209$	−188.277	+	208.792i	−0.900848	+	0.999005i
$210$		0			0
$211$	97.7727	−	31.7683i	0.463378	−	0.150561i	−0.0680183	−	0.997684i	$-0.521668\pi$
$211$	97.7727	−	31.7683i	0.463378	−	0.150561i	0.531396	+	0.847124i	$0.321668\pi$
$212$		0			0
$213$	19.0502	−	13.8408i	0.0894374	−	0.0649801i
$214$		0			0
$215$	−180.015	−	58.4905i	−0.837281	−	0.272049i
$216$		0			0
$217$	−33.2505	+	45.7653i	−0.153228	+	0.210900i
$218$		0			0
$219$			97.1931i			0.443804i
$220$		0			0
$221$	4.46237			0.0201917
$222$		0			0
$223$	340.835	+	247.631i	1.52841	+	1.11045i	0.957115	+	0.289710i	$0.0935587\pi$
$223$	340.835	+	247.631i	1.52841	+	1.11045i	0.571295	+	0.820745i	$0.306441\pi$
$224$		0			0
$225$	38.5168	−	118.543i	0.171186	−	0.526856i
$226$		0			0
$227$	51.7252	+	71.1936i	0.227864	+	0.313628i	0.907606	−	0.419824i	$-0.137908\pi$
$227$	51.7252	+	71.1936i	0.227864	+	0.313628i	−0.679742	+	0.733452i	$0.737908\pi$
$228$		0			0
$229$	−86.1369	−	265.102i	−0.376144	−	1.15765i	−0.942704	−	0.333631i	$-0.891726\pi$
$229$	−86.1369	−	265.102i	−0.376144	−	1.15765i	0.566560	−	0.824020i	$-0.308274\pi$
$230$		0			0
$231$	30.1620	−	284.943i	0.130571	−	1.23352i
$232$		0			0
$233$	183.691	−	59.6849i	0.788375	−	0.256158i	0.112963	−	0.993599i	$-0.463966\pi$
$233$	183.691	−	59.6849i	0.788375	−	0.256158i	0.675412	+	0.737441i	$0.263966\pi$
$234$		0			0
$235$	76.6477	−	55.6878i	0.326160	−	0.236969i
$236$		0			0
$237$	286.728	+	93.1636i	1.20982	+	0.393095i
$238$		0			0
$239$	−241.002	+	331.711i	−1.00838	+	1.38791i	−0.0883374	+	0.996091i	$0.528155\pi$
$239$	−241.002	+	331.711i	−1.00838	+	1.38791i	−0.920041	+	0.391823i	$0.871845\pi$
$240$		0			0
$241$		−	119.605i		−	0.496285i	−0.968724	−	0.248143i	$-0.920180\pi$
$241$		−	119.605i		−	0.496285i	0.968724	−	0.248143i	$-0.0798201\pi$
$242$		0			0
$243$	−1006.07			−4.14020
$244$		0			0
$245$	−52.4637	−	38.1171i	−0.214138	−	0.155580i
$246$		0			0
$247$	−81.8006	+	251.756i	−0.331177	+	1.01926i
$248$		0			0
$249$	217.519	+	299.390i	0.873572	+	1.20237i
$250$		0			0
$251$	76.3512	+	234.985i	0.304188	+	0.936195i	0.979979	+	0.199101i	$0.0638023\pi$
$251$	76.3512	+	234.985i	0.304188	+	0.936195i	−0.675791	+	0.737094i	$0.736198\pi$
$252$		0			0
$253$	−230.409	−	24.3894i	−0.910706	−	0.0964008i
$254$		0			0
$255$	5.33707	−	1.73412i	0.0209297	−	0.00680047i
$256$		0			0
$257$	42.6257	−	30.9694i	0.165859	−	0.120504i	−0.501760	−	0.865007i	$-0.667314\pi$
$257$	42.6257	−	30.9694i	0.165859	−	0.120504i	0.667618	+	0.744504i	$0.267314\pi$
$258$		0			0
$259$	17.7602	+	5.77064i	0.0685722	+	0.0222805i
$260$		0			0
$261$	791.910	−	1089.97i	3.03414	−	4.17613i
$262$		0			0
$263$			138.580i			0.526921i	0.964670	+	0.263460i	$0.0848639\pi$
$263$			138.580i			0.526921i	−0.964670	+	0.263460i	$0.915136\pi$
$264$		0			0
$265$	98.3273			0.371047
$266$		0			0
$267$	−143.326	−	104.133i	−0.536803	−	0.390010i
$268$		0			0
$269$	15.8135	−	48.6690i	0.0587863	−	0.180926i	−0.917351	−	0.398079i	$-0.869677\pi$
$269$	15.8135	−	48.6690i	0.0587863	−	0.180926i	0.976138	+	0.217153i	$0.0696771\pi$
$270$		0			0
$271$	140.346	+	193.169i	0.517881	+	0.712802i	0.985223	−	0.171275i	$-0.0547885\pi$
$271$	140.346	+	193.169i	0.517881	+	0.712802i	−0.467343	+	0.884076i	$0.654789\pi$
$272$		0			0
$273$	−83.3688	−	256.583i	−0.305380	−	0.939864i
$274$		0			0
$275$	−40.8457	−	36.8324i	−0.148530	−	0.133936i
$276$		0			0
$277$	196.313	−	63.7861i	0.708712	−	0.230275i	0.0675898	−	0.997713i	$-0.478469\pi$
$277$	196.313	−	63.7861i	0.708712	−	0.230275i	0.641122	+	0.767439i	$0.278469\pi$
$278$		0			0
$279$	255.113	−	185.351i	0.914385	−	0.664339i
$280$		0			0
$281$	−275.315	−	89.4554i	−0.979770	−	0.318346i	−0.225016	−	0.974355i	$-0.572244\pi$
$281$	−275.315	−	89.4554i	−0.979770	−	0.318346i	−0.754753	+	0.656009i	$0.772244\pi$
$282$		0			0
$283$	282.501	−	388.830i	0.998238	−	1.37396i	0.0718372	−	0.997416i	$-0.477114\pi$
$283$	282.501	−	388.830i	0.998238	−	1.37396i	0.926400	−	0.376540i	$-0.122886\pi$
$284$		0			0
$285$			332.894i			1.16805i
$286$		0			0
$287$	−187.425			−0.653050
$288$		0			0
$289$	−233.656	−	169.761i	−0.808497	−	0.587408i
$290$		0			0
$291$	308.632	−	949.871i	1.06059	−	3.26416i
$292$		0			0
$293$	271.303	+	373.417i	0.925950	+	1.27446i	0.961418	+	0.275091i	$0.0887079\pi$
$293$	271.303	+	373.417i	0.925950	+	1.27446i	−0.0354679	+	0.999371i	$0.511292\pi$
$294$		0			0
$295$	45.8280	+	141.044i	0.155349	+	0.478116i
$296$		0			0
$297$	−415.804	+	932.053i	−1.40001	+	3.13823i
$298$		0			0
$299$	−207.476	+	67.4131i	−0.693901	+	0.225462i
$300$		0			0
$301$	−306.251	+	222.504i	−1.01745	+	0.739217i
$302$		0			0
$303$	−876.153	−	284.680i	−2.89160	−	0.939536i
$304$		0			0
$305$	−54.9652	+	75.6530i	−0.180214	+	0.248043i
$306$		0			0
$307$			201.403i			0.656035i	0.944672	+	0.328018i	$0.106381\pi$
$307$			201.403i			0.656035i	−0.944672	+	0.328018i	$0.893619\pi$
$308$		0			0
$309$	−0.488476			−0.00158083
$310$		0			0
$311$	368.986	+	268.084i	1.18645	+	0.862006i	0.992884	−	0.119082i	$-0.0379951\pi$
$311$	368.986	+	268.084i	1.18645	+	0.862006i	0.193565	+	0.981088i	$0.437995\pi$
$312$		0			0
$313$	−80.6220	+	248.129i	−0.257578	+	0.792744i	0.735732	+	0.677272i	$0.236838\pi$
$313$	−80.6220	+	248.129i	−0.257578	+	0.792744i	−0.993311	+	0.115472i	$0.963162\pi$
$314$		0			0
$315$	−146.522	−	201.671i	−0.465150	−	0.640224i
$316$		0			0
$317$	−123.515	−	380.141i	−0.389638	−	1.19918i	−0.933059	−	0.359723i	$-0.882871\pi$
$317$	−123.515	−	380.141i	−0.389638	−	1.19918i	0.543421	−	0.839460i	$-0.317129\pi$
$318$		0			0
$319$	−296.869	−	515.072i	−0.930623	−	1.61465i
$320$		0			0
$321$	−360.184	+	117.031i	−1.12207	+	0.364582i
$322$		0			0
$323$	−8.90889	+	6.47269i	−0.0275817	+	0.0200393i
$324$		0			0
$325$	−49.2508	−	16.0025i	−0.151541	−	0.0492386i
$326$		0			0
$327$	46.9584	−	64.6327i	0.143604	−	0.197654i
$328$		0			0
$329$		−	189.478i		−	0.575920i
$330$		0			0
$331$	250.595			0.757084			0.378542	−	0.925584i	$-0.376426\pi$
$331$	250.595			0.757084			0.378542	+	0.925584i	$0.376426\pi$
$332$		0			0
$333$	−84.2162	−	61.1867i	−0.252902	−	0.183744i
$334$		0			0
$335$	28.5950	−	88.0062i	0.0853581	−	0.262705i
$336$		0			0
$337$	151.904	+	209.077i	0.450752	+	0.620407i	0.972559	−	0.232656i	$-0.0747418\pi$
$337$	151.904	+	209.077i	0.450752	+	0.620407i	−0.521807	+	0.853064i	$0.674742\pi$
$338$		0			0
$339$	−117.998	−	363.161i	−0.348077	−	1.07127i
$340$		0			0
$341$	−28.8293	−	136.127i	−0.0845433	−	0.399198i
$342$		0			0
$343$	−331.749	+	107.792i	−0.967198	+	0.314262i
$344$		0			0
$345$	−221.948	+	161.255i	−0.643327	+	0.467405i
$346$		0			0
$347$	264.700	+	86.0063i	0.762824	+	0.247857i	0.664490	−	0.747297i	$-0.268649\pi$
$347$	264.700	+	86.0063i	0.762824	+	0.247857i	0.0983340	+	0.995153i	$0.468649\pi$
$348$		0			0
$349$	−161.535	+	222.334i	−0.462851	+	0.637060i	−0.975097	−	0.221779i	$-0.928814\pi$
$349$	−161.535	+	222.334i	−0.462851	+	0.637060i	0.512246	+	0.858839i	$0.328814\pi$
$350$		0			0
$351$			960.943i			2.73773i
$352$		0			0
$353$	132.713			0.375956			0.187978	−	0.982173i	$-0.439807\pi$
$353$	132.713			0.375956			0.187978	+	0.982173i	$0.439807\pi$
$354$		0			0
$355$	−7.31309	−	5.31327i	−0.0206002	−	0.0149670i
$356$		0			0
$357$	3.46813	−	10.6738i	0.00971465	−	0.0298986i
$358$		0			0
$359$	208.563	+	287.062i	0.580955	+	0.799616i	0.993800	−	0.111185i	$-0.0354647\pi$
$359$	208.563	+	287.062i	0.580955	+	0.799616i	−0.412844	+	0.910802i	$0.635465\pi$
$360$		0			0
$361$	−90.3081	−	277.940i	−0.250161	−	0.769916i
$362$		0			0
$363$	470.830	+	524.469i	1.29705	+	1.44482i
$364$		0			0
$365$	35.4849	−	11.5297i	0.0972189	−	0.0315883i
$366$		0			0
$367$	265.987	−	193.251i	0.724759	−	0.526568i	−0.163142	−	0.986603i	$-0.552163\pi$
$367$	265.987	−	193.251i	0.724759	−	0.526568i	0.887901	+	0.460034i	$0.152163\pi$
$368$		0			0
$369$	993.646	+	322.855i	2.69281	+	0.874946i
$370$		0			0
$371$	115.587	−	159.092i	0.311556	−	0.428820i
$372$		0			0
$373$		−	532.614i		−	1.42792i	−0.700187	−	0.713960i	$-0.746900\pi$
$373$		−	532.614i		−	1.42792i	0.700187	−	0.713960i	$-0.253100\pi$
$374$		0			0
$375$	−65.1236			−0.173663
$376$		0			0
$377$	−452.849	−	329.014i	−1.20119	−	0.872716i
$378$		0			0
$379$	−78.8238	+	242.595i	−0.207978	+	0.640092i	0.791599	+	0.611040i	$0.209249\pi$
$379$	−78.8238	+	242.595i	−0.207978	+	0.640092i	−0.999578	+	0.0290515i	$0.990751\pi$
$380$		0			0
$381$	463.659	+	638.172i	1.21695	+	1.67499i
$382$		0			0
$383$	−49.4611	−	152.226i	−0.129141	−	0.397456i	0.865492	−	0.500923i	$-0.167006\pi$
$383$	−49.4611	−	152.226i	−0.129141	−	0.397456i	−0.994633	+	0.103468i	$0.967006\pi$
$384$		0			0
$385$	−107.610	+	22.7899i	−0.279506	+	0.0591946i
$386$		0			0
$387$	2006.89	−	652.077i	5.18575	−	1.68495i
$388$		0			0
$389$	336.925	−	244.791i	0.866132	−	0.629282i	−0.0634143	−	0.997987i	$-0.520199\pi$
$389$	336.925	−	244.791i	0.866132	−	0.629282i	0.929546	+	0.368706i	$0.120199\pi$
$390$		0			0
$391$	−8.63098	−	2.80438i	−0.0220741	−	0.00717232i
$392$		0			0
$393$	−757.340	+	1042.39i	−1.92707	+	2.65239i
$394$		0			0
$395$		−	115.735i		−	0.293001i
$396$		0			0
$397$	−50.2264			−0.126515			−0.0632574	−	0.997997i	$-0.520149\pi$
$397$	−50.2264			−0.126515			−0.0632574	+	0.997997i	$0.520149\pi$
$398$		0			0
$399$	538.617	+	391.328i	1.34992	+	0.980772i
$400$		0			0
$401$	11.5455	−	35.5333i	0.0287917	−	0.0886118i	−0.935628	−	0.352987i	$-0.885166\pi$
$401$	11.5455	−	35.5333i	0.0287917	−	0.0886118i	0.964420	+	0.264376i	$0.0851659\pi$
$402$		0			0
$403$	−77.0075	−	105.992i	−0.191086	−	0.263007i
$404$		0			0
$405$	218.405	+	672.181i	0.539271	+	1.65971i
$406$		0			0
$407$	−39.7968	+	22.9375i	−0.0977810	+	0.0563574i
$408$		0			0
$409$	−521.153	+	169.333i	−1.27421	+	0.414017i	−0.866539	−	0.499110i	$-0.833660\pi$
$409$	−521.153	+	169.333i	−1.27421	+	0.414017i	−0.407675	+	0.913127i	$0.633660\pi$
$410$		0			0
$411$	−620.439	+	450.775i	−1.50958	+	1.09678i
$412$		0			0
$413$	282.080	+	91.6532i	0.683002	+	0.221921i
$414$		0			0
$415$	83.5026	−	114.931i	0.201211	−	0.276943i
$416$		0			0
$417$		−	837.246i		−	2.00778i
$418$		0			0
$419$	9.71560			0.0231876			0.0115938	−	0.999933i	$-0.496309\pi$
$419$	9.71560			0.0231876			0.0115938	+	0.999933i	$0.496309\pi$
$420$		0			0
$421$	456.677	+	331.795i	1.08474	+	0.788113i	0.978504	−	0.206228i	$-0.0661188\pi$
$421$	456.677	+	331.795i	1.08474	+	0.788113i	0.106240	+	0.994341i	$0.466119\pi$
$422$		0			0
$423$	−326.390	+	1004.52i	−0.771607	+	2.37476i
$424$		0			0
$425$	−1.26624	−	1.74283i	−0.00297940	−	0.00410079i
$426$		0			0
$427$	57.7920	+	177.866i	0.135344	+	0.416547i
$428$		0			0
$429$	606.037	+	270.363i	1.41267	+	0.630217i
$430$		0			0
$431$	−486.526	+	158.082i	−1.12883	+	0.366779i	−0.813131	−	0.582080i	$-0.802239\pi$
$431$	−486.526	+	158.082i	−1.12883	+	0.366779i	−0.315699	+	0.948859i	$0.602239\pi$
$432$		0			0
$433$	469.914	−	341.413i	1.08525	−	0.788482i	0.106661	−	0.994295i	$-0.465984\pi$
$433$	469.914	−	341.413i	1.08525	−	0.788482i	0.978591	+	0.205813i	$0.0659839\pi$
$434$		0			0
$435$	−669.474	−	217.525i	−1.53902	−	0.500058i
$436$		0			0
$437$	316.433	−	435.532i	0.724103	−	0.996642i
$438$		0			0
$439$		−	588.239i		−	1.33995i	−0.742383	−	0.669976i	$-0.766304\pi$
$439$		−	588.239i		−	1.33995i	0.742383	−	0.669976i	$-0.233696\pi$
$440$		0			0
$441$	722.961			1.63937
$442$		0			0
$443$	312.951	+	227.372i	0.706435	+	0.513255i	0.882022	−	0.471209i	$-0.156182\pi$
$443$	312.951	+	227.372i	0.706435	+	0.513255i	−0.175587	+	0.984464i	$0.556182\pi$
$444$		0			0
$445$	−21.0161	+	64.6810i	−0.0472273	+	0.145351i
$446$		0			0
$447$	−560.661	−	771.683i	−1.25427	−	1.72636i
$448$		0			0
$449$	−168.424	−	518.355i	−0.375108	−	1.15446i	−0.943406	−	0.331641i	$-0.892398\pi$
$449$	−168.424	−	518.355i	−0.375108	−	1.15446i	0.568297	−	0.822823i	$-0.307602\pi$
$450$		0			0
$451$	308.736	−	342.376i	0.684559	−	0.759149i
$452$		0			0
$453$	−500.448	+	162.605i	−1.10474	+	0.358952i
$454$		0			0
$455$	−83.7878	+	60.8754i	−0.184149	+	0.133792i
$456$		0			0
$457$	757.002	+	245.965i	1.65646	+	0.538216i	0.980125	−	0.198379i	$-0.0635676\pi$
$457$	757.002	+	245.965i	1.65646	+	0.538216i	0.676334	+	0.736595i	$0.263568\pi$
$458$		0			0
$459$	−23.4968	+	32.3405i	−0.0511912	+	0.0704587i
$460$		0			0
$461$		−	107.301i		−	0.232758i	−0.993205	−	0.116379i	$-0.962871\pi$
$461$		−	107.301i		−	0.232758i	0.993205	−	0.116379i	$-0.0371287\pi$
$462$		0			0
$463$	−183.926			−0.397248			−0.198624	−	0.980076i	$-0.563647\pi$
$463$	−183.926			−0.397248			−0.198624	+	0.980076i	$0.563647\pi$
$464$		0			0
$465$	−133.292	−	96.8421i	−0.286649	−	0.208263i
$466$		0			0
$467$	56.5650	−	174.089i	0.121124	−	0.372782i	−0.872051	−	0.489415i	$-0.837210\pi$
$467$	56.5650	−	174.089i	0.121124	−	0.372782i	0.993175	+	0.116633i	$0.0372102\pi$
$468$		0			0
$469$	−108.778	−	149.721i	−0.231937	−	0.319234i
$470$		0			0
$471$	440.645	+	1356.17i	0.935553	+	2.87934i
$472$		0			0
$473$	98.0153	−	925.958i	0.207221	−	1.95763i
$474$		0			0
$475$	121.538	−	39.4902i	0.255870	−	0.0831373i
$476$		0			0
$477$	−886.840	+	644.327i	−1.85920	+	1.35079i
$478$		0			0
$479$	−586.953	−	190.713i	−1.22537	−	0.398147i	−0.376336	−	0.926483i	$-0.622816\pi$
$479$	−586.953	−	190.713i	−1.22537	−	0.398147i	−0.849036	+	0.528336i	$0.822816\pi$
$480$		0			0
$481$	−25.4212	+	34.9892i	−0.0528506	+	0.0727427i
$482$		0			0
$483$			548.669i			1.13596i
$484$		0			0
$485$	−383.407			−0.790530
$486$		0			0
$487$	−607.196	−	441.154i	−1.24681	−	0.905859i	−0.248776	−	0.968561i	$-0.580028\pi$
$487$	−607.196	−	441.154i	−1.24681	−	0.905859i	−0.998032	+	0.0627015i	$0.980028\pi$
$488$		0			0
$489$	−104.257	+	320.871i	−0.213205	+	0.656179i
$490$		0			0
$491$	−439.432	−	604.826i	−0.894974	−	1.23183i	−0.972044	−	0.234800i	$-0.924557\pi$
$491$	−439.432	−	604.826i	−0.894974	−	1.23183i	0.0770700	−	0.997026i	$-0.475443\pi$
$492$		0			0
$493$	−7.19565	−	22.1459i	−0.0145956	−	0.0449207i
$494$		0			0
$495$	609.756	+	64.5444i	1.23183	+	0.130393i
$496$		0			0
$497$	−17.1936	+	5.58653i	−0.0345947	+	0.0112405i
$498$		0			0
$499$	−11.9100	+	8.65314i	−0.0238678	+	0.0173410i	−0.599655	−	0.800258i	$-0.704696\pi$
$499$	−11.9100	+	8.65314i	−0.0238678	+	0.0173410i	0.575787	+	0.817599i	$0.304696\pi$
$500$		0			0
$501$	−887.956	−	288.514i	−1.77237	−	0.575877i
$502$		0			0
$503$	−265.974	+	366.082i	−0.528775	+	0.727797i	−0.986943	−	0.161069i	$-0.948506\pi$
$503$	−265.974	+	366.082i	−0.528775	+	0.727797i	0.458168	+	0.888866i	$0.348506\pi$
$504$		0			0
$505$			353.652i			0.700300i
$506$		0			0
$507$	−359.574			−0.709218
$508$		0			0
$509$	330.840	+	240.369i	0.649980	+	0.472238i	0.863264	−	0.504752i	$-0.168416\pi$
$509$	330.840	+	240.369i	0.649980	+	0.472238i	−0.213284	+	0.976990i	$0.568416\pi$
$510$		0			0
$511$	23.0588	−	70.9676i	0.0451248	−	0.138880i
$512$		0			0
$513$	−1393.85	−	1918.47i	−2.71706	−	3.73972i
$514$		0			0
$515$	0.0579465	+	0.178341i	0.000112518	+	0.000346293i
$516$		0			0
$517$	346.125	+	312.116i	0.669487	+	0.603707i
$518$		0			0
$519$	−544.090	+	176.785i	−1.04834	+	0.340627i
$520$		0			0
$521$	−199.914	+	145.246i	−0.383712	+	0.278783i	−0.762874	−	0.646547i	$-0.776212\pi$
$521$	−199.914	+	145.246i	−0.383712	+	0.278783i	0.379162	+	0.925330i	$0.376212\pi$
$522$		0			0
$523$	94.1672	+	30.5968i	0.180052	+	0.0585024i	0.397655	−	0.917535i	$-0.369824\pi$
$523$	94.1672	+	30.5968i	0.180052	+	0.0585024i	−0.217603	+	0.976037i	$0.569824\pi$
$524$		0			0
$525$	−76.5550	+	105.369i	−0.145819	+	0.200703i
$526$		0			0
$527$		−	5.45012i		−	0.0103418i
$528$		0			0
$529$	−85.3393			−0.161322
$530$		0			0
$531$	−1337.58	−	971.809i	−2.51898	−	1.83015i
$532$		0			0
$533$	134.136	−	412.829i	0.251663	−	0.774538i
$534$		0			0
$535$	85.4553	+	117.619i	0.159730	+	0.219849i
$536$		0			0
$537$	309.006	+	951.024i	0.575431	+	1.77099i
$538$		0			0
$539$	129.970	−	291.337i	0.241132	−	0.540514i
$540$		0			0
$541$	−510.281	+	165.800i	−0.943217	+	0.306470i	−0.739957	−	0.672655i	$-0.765154\pi$
$541$	−510.281	+	165.800i	−0.943217	+	0.306470i	−0.203261	+	0.979125i	$0.565154\pi$
$542$		0			0
$543$	732.261	−	532.019i	1.34855	−	0.979777i
$544$		0			0
$545$	−29.1677	−	9.47718i	−0.0535188	−	0.0173893i
$546$		0			0
$547$	−152.494	+	209.889i	−0.278782	+	0.383710i	−0.925330	−	0.379163i	$-0.876212\pi$
$547$	−152.494	+	209.889i	−0.278782	+	0.383710i	0.646548	+	0.762873i	$0.276212\pi$
$548$		0			0
$549$		−	1042.51i		−	1.89893i
$550$		0			0
$551$	1381.33			2.50695
$552$		0			0
$553$	−187.258	−	136.051i	−0.338622	−	0.246023i
$554$		0			0
$555$	−16.8070	+	51.7266i	−0.0302829	+	0.0932012i
$556$		0			0
$557$	37.2226	+	51.2325i	0.0668269	+	0.0919793i	0.841122	−	0.540845i	$-0.181895\pi$
$557$	37.2226	+	51.2325i	0.0668269	+	0.0919793i	−0.774295	+	0.632824i	$0.781895\pi$
$558$		0			0
$559$	−270.918	−	833.799i	−0.484647	−	1.49159i
$560$		0			0
$561$	13.7853	+	23.9177i	0.0245728	+	0.0426341i
$562$		0			0
$563$	159.488	−	51.8209i	0.283283	−	0.0920442i	−0.163929	−	0.986472i	$-0.552417\pi$
$563$	159.488	−	51.8209i	0.283283	−	0.0920442i	0.447212	+	0.894428i	$0.352417\pi$
$564$		0			0
$565$	−118.591	+	86.1616i	−0.209896	+	0.152498i
$566$		0			0
$567$	1344.32	+	436.796i	2.37093	+	0.770363i
$568$		0			0
$569$	186.110	−	256.158i	0.327083	−	0.450191i	−0.613531	−	0.789671i	$-0.710251\pi$
$569$	186.110	−	256.158i	0.327083	−	0.450191i	0.940613	+	0.339480i	$0.110251\pi$
$570$		0			0
$571$		−	327.756i		−	0.574004i	−0.957930	−	0.287002i	$-0.907341\pi$
$571$		−	327.756i		−	0.574004i	0.957930	−	0.287002i	$-0.0926587\pi$
$572$		0			0
$573$	1527.52			2.66583
$574$		0			0
$575$	85.2027	+	61.9034i	0.148179	+	0.107658i
$576$		0			0
$577$	−263.883	+	812.148i	−0.457336	+	1.40754i	0.411035	+	0.911620i	$0.365167\pi$
$577$	−263.883	+	812.148i	−0.457336	+	1.40754i	−0.868371	+	0.495916i	$0.834833\pi$
$578$		0			0
$579$	258.246	+	355.445i	0.446021	+	0.613895i
$580$		0			0
$581$	−87.7971	−	270.212i	−0.151114	−	0.465080i
$582$		0			0
$583$	100.218	+	473.211i	0.171900	+	0.811682i
$584$		0			0
$585$	549.068	−	178.403i	0.938578	−	0.304962i
$586$		0			0
$587$	169.002	−	122.787i	0.287907	−	0.209177i	−0.434452	−	0.900695i	$-0.643058\pi$
$587$	169.002	−	122.787i	0.287907	−	0.209177i	0.722359	+	0.691518i	$0.243058\pi$
$588$		0			0
$589$	307.483	+	99.9073i	0.522042	+	0.169622i
$590$		0			0
$591$	−103.811	+	142.884i	−0.175653	+	0.241766i
$592$		0			0
$593$		−	791.888i		−	1.33539i	−0.744433	−	0.667697i	$-0.767280\pi$
$593$		−	791.888i		−	1.33539i	0.744433	−	0.667697i	$-0.232720\pi$
$594$		0			0
$595$	−4.30839			−0.00724099
$596$		0			0
$597$	−1136.07	−	825.400i	−1.90296	−	1.38258i
$598$		0			0
$599$	−64.4343	+	198.309i	−0.107570	+	0.331066i	−0.990325	−	0.138767i	$-0.955686\pi$
$599$	−64.4343	+	198.309i	−0.107570	+	0.331066i	0.882755	+	0.469833i	$0.155686\pi$
$600$		0			0
$601$	159.978	+	220.191i	0.266186	+	0.366374i	0.921098	−	0.389332i	$-0.127294\pi$
$601$	159.978	+	220.191i	0.266186	+	0.366374i	−0.654911	+	0.755706i	$0.727294\pi$
$602$		0			0
$603$	318.789	+	981.130i	0.528671	+	1.62708i
$604$		0			0
$605$	135.629	−	234.115i	0.224180	−	0.386967i
$606$		0			0
$607$	−821.821	+	267.026i	−1.35391	+	0.439911i	−0.894004	−	0.448059i	$-0.852116\pi$
$607$	−821.821	+	267.026i	−1.35391	+	0.439911i	−0.459902	+	0.887970i	$0.652116\pi$
$608$		0			0
$609$	−1138.94	+	827.489i	−1.87018	+	1.35877i
$610$		0			0
$611$	417.349	+	135.605i	0.683059	+	0.221939i
$612$		0			0
$613$	−230.281	+	316.954i	−0.375662	+	0.517054i	−0.954429	−	0.298439i	$-0.903534\pi$
$613$	−230.281	+	316.954i	−0.375662	+	0.517054i	0.578767	+	0.815493i	$0.303534\pi$
$614$		0			0
$615$		−	545.877i		−	0.887605i
$616$		0			0
$617$	594.799			0.964019			0.482009	−	0.876166i	$-0.339907\pi$
$617$	594.799			0.964019			0.482009	+	0.876166i	$0.339907\pi$
$618$		0			0
$619$	143.028	+	103.916i	0.231063	+	0.167877i	0.697293	−	0.716787i	$-0.254388\pi$
$619$	143.028	+	103.916i	0.231063	+	0.167877i	−0.466229	+	0.884664i	$0.654388\pi$
$620$		0			0
$621$	603.905	−	1858.63i	0.972472	−	2.99296i
$622$		0			0
$623$	79.9476	+	110.038i	0.128327	+	0.176627i
$624$		0			0
$625$	7.72542	+	23.7764i	0.0123607	+	0.0380423i
$626$		0			0
$627$	−1602.09	+	339.294i	−2.55516	+	0.541139i
$628$		0			0
$629$	−1.71110	+	0.555969i	−0.00272035	+	0.000883894i
$630$		0			0
$631$	61.6775	−	44.8113i	0.0977456	−	0.0710163i	−0.537839	−	0.843048i	$-0.680759\pi$
$631$	61.6775	−	44.8113i	0.0977456	−	0.0710163i	0.635585	+	0.772031i	$0.280759\pi$
$632$		0			0
$633$	569.509	+	185.045i	0.899699	+	0.292330i
$634$		0			0
$635$	177.992	−	244.985i	0.280302	−	0.385803i
$636$		0			0
$637$		−	300.368i		−	0.471535i
$638$		0			0
$639$	100.776			0.157709
$640$		0			0
$641$	233.901	+	169.939i	0.364900	+	0.265115i	0.755093	−	0.655618i	$-0.227592\pi$
$641$	233.901	+	169.939i	0.364900	+	0.265115i	−0.390193	+	0.920733i	$0.627592\pi$
$642$		0			0
$643$	−98.5800	+	303.398i	−0.153313	+	0.471848i	−0.997986	−	0.0634343i	$-0.979795\pi$
$643$	−98.5800	+	303.398i	−0.153313	+	0.471848i	0.844673	+	0.535282i	$0.179795\pi$
$644$		0			0
$645$	−648.045	−	891.957i	−1.00472	−	1.38288i
$646$		0			0
$647$	−177.097	−	545.048i	−0.273720	−	0.842424i	−0.989555	−	0.144154i	$-0.953954\pi$
$647$	−177.097	−	545.048i	−0.273720	−	0.842424i	0.715835	−	0.698269i	$-0.246046\pi$
$648$		0			0
$649$	−632.081	+	364.308i	−0.973930	+	0.561338i
$650$		0			0
$651$	−313.378	+	101.823i	−0.481379	+	0.156410i
$652$		0			0
$653$	−529.603	+	384.779i	−0.811031	+	0.589248i	−0.914129	−	0.405423i	$-0.867124\pi$
$653$	−529.603	+	384.779i	−0.811031	+	0.589248i	0.103099	+	0.994671i	$0.467124\pi$
$654$		0			0
$655$	470.415	+	152.847i	0.718190	+	0.233354i
$656$		0			0
$657$	−244.494	+	336.518i	−0.372138	+	0.512204i
$658$		0			0
$659$			166.011i			0.251913i	0.992036	+	0.125956i	$0.0401999\pi$
$659$			166.011i			0.251913i	−0.992036	+	0.125956i	$0.959800\pi$
$660$		0			0
$661$	−63.4298			−0.0959603			−0.0479802	−	0.998848i	$-0.515278\pi$
$661$	−63.4298			−0.0959603			−0.0479802	+	0.998848i	$0.515278\pi$
$662$		0			0
$663$	21.0284	+	15.2780i	0.0317170	+	0.0230438i
$664$		0			0
$665$	78.9780	−	243.069i	0.118764	−	0.365518i
$666$		0			0
$667$	669.119	+	920.963i	1.00318	+	1.38075i
$668$		0			0
$669$	758.320	+	2333.87i	1.13351	+	3.48859i
$670$		0			0
$671$	−420.110	−	187.418i	−0.626096	−	0.279311i
$672$		0			0
$673$	−546.179	+	177.464i	−0.811559	+	0.263692i	−0.685258	−	0.728300i	$-0.740311\pi$
$673$	−546.179	+	177.464i	−0.811559	+	0.263692i	−0.126301	+	0.991992i	$0.540311\pi$
$674$		0			0
$675$	375.309	−	272.678i	0.556013	−	0.403967i
$676$		0			0
$677$	−997.111	−	323.981i	−1.47284	−	0.478554i	−0.540873	−	0.841104i	$-0.681906\pi$
$677$	−997.111	−	323.981i	−1.47284	−	0.478554i	−0.931964	+	0.362550i	$0.881906\pi$
$678$		0			0
$679$	−450.708	+	620.347i	−0.663782	+	0.913618i
$680$		0			0
$681$			512.586i			0.752695i
$682$		0			0
$683$	−44.0462			−0.0644894			−0.0322447	−	0.999480i	$-0.510266\pi$
$683$	−44.0462			−0.0644894			−0.0322447	+	0.999480i	$0.510266\pi$
$684$		0			0
$685$	238.178	+	173.046i	0.347705	+	0.252622i
$686$		0			0
$687$	501.732	−	1544.17i	0.730324	−	2.24771i
$688$		0			0
$689$	267.698	+	368.454i	0.388531	+	0.534767i
$690$		0			0
$691$	−217.996	−	670.923i	−0.315479	−	0.970945i	−0.975557	−	0.219747i	$-0.929477\pi$
$691$	−217.996	−	670.923i	−0.315479	−	0.970945i	0.660078	−	0.751197i	$-0.270523\pi$
$692$		0			0
$693$	821.221	−	910.702i	1.18502	−	1.31414i
$694$		0			0
$695$	−305.676	+	99.3201i	−0.439821	+	0.142907i
$696$		0			0
$697$	14.6088	−	10.6139i	0.0209595	−	0.0152279i
$698$		0			0
$699$	1069.97	+	347.654i	1.53072	+	0.497360i
$700$		0			0
$701$	325.452	−	447.947i	0.464269	−	0.639011i	−0.511118	−	0.859510i	$-0.670769\pi$
$701$	325.452	−	447.947i	0.464269	−	0.639011i	0.975387	+	0.220499i	$0.0707686\pi$
$702$		0			0
$703$		−	106.728i		−	0.151818i
$704$		0			0
$705$	551.854			0.782772
$706$		0			0
$707$	572.203	+	415.730i	0.809339	+	0.588019i
$708$		0			0
$709$	195.502	−	601.694i	0.275744	−	0.848652i	−0.713278	−	0.700881i	$-0.752790\pi$
$709$	195.502	−	601.694i	0.275744	−	0.848652i	0.989022	−	0.147771i	$-0.0472097\pi$
$710$		0			0
$711$	758.399	+	1043.85i	1.06666	+	1.46814i
$712$		0			0
$713$	82.3351	+	253.402i	0.115477	+	0.355402i
$714$		0			0
$715$	26.8162	−	253.335i	0.0375052	−	0.354314i
$716$		0			0
$717$	−2271.39	+	738.020i	−3.16791	+	1.02932i
$718$		0			0
$719$	802.680	−	583.181i	1.11638	−	0.811100i	0.132726	−	0.991153i	$-0.457627\pi$
$719$	802.680	−	583.181i	1.11638	−	0.811100i	0.983657	+	0.180053i	$0.0576269\pi$
$720$		0			0
$721$	0.356671	+	0.115889i	0.000494689	+	0.000160734i
$722$		0			0
$723$	409.496	−	563.623i	0.566385	−	0.779562i
$724$		0			0
$725$			270.227i			0.372727i
$726$		0			0
$727$	356.233			0.490003			0.245002	−	0.969523i	$-0.421211\pi$
$727$	356.233			0.490003			0.245002	+	0.969523i	$0.421211\pi$
$728$		0			0
$729$	−2439.57	−	1772.45i	−3.34646	−	2.43134i
$730$		0			0
$731$	11.2701	−	34.6859i	0.0154174	−	0.0474499i
$732$		0			0
$733$	−97.9819	−	134.860i	−0.133672	−	0.183984i	0.736934	−	0.675965i	$-0.236273\pi$
$733$	−97.9819	−	134.860i	−0.133672	−	0.183984i	−0.870606	+	0.491981i	$0.836273\pi$
$734$		0			0
$735$	−116.726	−	359.245i	−0.158811	−	0.488769i
$736$		0			0
$737$	452.684	+	47.9179i	0.614225	+	0.0650175i
$738$		0			0
$739$	−9.94021	+	3.22977i	−0.0134509	+	0.00437046i	−0.315735	−	0.948848i	$-0.602251\pi$
$739$	−9.94021	+	3.22977i	−0.0134509	+	0.00437046i	0.302284	+	0.953218i	$0.402251\pi$
$740$		0			0
$741$	−1247.43	+	906.308i	−1.68344	+	1.22309i
$742$		0			0
$743$	−189.440	−	61.5527i	−0.254966	−	0.0828434i	0.178745	−	0.983895i	$-0.442796\pi$
$743$	−189.440	−	61.5527i	−0.254966	−	0.0828434i	−0.433711	+	0.901052i	$0.642796\pi$
$744$		0			0
$745$	−215.230	+	296.238i	−0.288899	+	0.397635i
$746$		0			0
$747$			1583.78i			2.12019i
$748$		0			0
$749$	290.762			0.388200
$750$		0			0
$751$	−657.398	−	477.628i	−0.875363	−	0.635989i	0.0566573	−	0.998394i	$-0.481956\pi$
$751$	−657.398	−	477.628i	−0.875363	−	0.635989i	−0.932021	+	0.362405i	$0.881956\pi$
$752$		0			0
$753$	−444.733	+	1368.75i	−0.590615	+	1.81772i
$754$		0			0
$755$	118.733	+	163.423i	0.157263	+	0.216454i
$756$		0			0
$757$	23.4494	+	72.1700i	0.0309768	+	0.0953368i	0.965350	−	0.260960i	$-0.0840391\pi$
$757$	23.4494	+	72.1700i	0.0309768	+	0.0953368i	−0.934373	+	0.356297i	$0.884039\pi$
$758$		0			0
$759$	−1002.27	−	903.793i	−1.32051	−	1.19077i
$760$		0			0
$761$	−488.143	+	158.607i	−0.641450	+	0.208420i	−0.611640	−	0.791136i	$-0.709490\pi$
$761$	−488.143	+	158.607i	−0.641450	+	0.208420i	−0.0298093	+	0.999556i	$0.509490\pi$
$762$		0			0
$763$	−49.6216	+	36.0522i	−0.0650349	+	0.0472506i
$764$		0			0
$765$	22.8411	+	7.42154i	0.0298577	+	0.00970136i
$766$		0			0
$767$	−403.756	+	555.723i	−0.526410	+	0.724541i
$768$		0			0
$769$			346.320i			0.450351i	0.974318	+	0.225176i	$0.0722956\pi$
$769$			346.320i			0.450351i	−0.974318	+	0.225176i	$0.927704\pi$
$770$		0			0
$771$	306.900			0.398055
$772$		0			0
$773$	1055.22	+	766.660i	1.36509	+	0.991798i	0.998103	+	0.0615739i	$0.0196120\pi$
$773$	1055.22	+	766.660i	1.36509	+	0.991798i	0.366991	+	0.930225i	$0.380388\pi$
$774$		0			0
$775$	−19.5447	+	60.1525i	−0.0252190	+	0.0776161i
$776$		0			0
$777$	63.9357	+	87.9999i	0.0822853	+	0.113256i
$778$		0			0
$779$	331.014	+	1018.76i	0.424922	+	1.30778i
$780$		0			0
$781$	18.1170	−	40.6104i	0.0231971	−	0.0519980i
$782$		0			0
$783$	4768.99	−	1549.54i	6.09066	−	1.97898i
$784$		0			0
$785$	442.860	−	321.757i	0.564153	−	0.409881i
$786$		0			0
$787$	819.838	+	266.382i	1.04173	+	0.338477i	0.779416	−	0.626506i	$-0.215516\pi$
$787$	819.838	+	266.382i	1.04173	+	0.338477i	0.262310	+	0.964984i	$0.415516\pi$
$788$		0			0
$789$	−474.464	+	653.043i	−0.601348	+	0.827685i
$790$		0			0
$791$			293.165i			0.370625i
$792$		0			0
$793$	−433.132			−0.546195
$794$		0			0
$795$	463.356	+	336.648i	0.582838	+	0.423457i
$796$		0			0
$797$	8.35552	−	25.7156i	0.0104837	−	0.0322656i	−0.945678	−	0.325105i	$-0.894600\pi$
$797$	8.35552	−	25.7156i	0.0104837	−	0.0322656i	0.956162	+	0.292840i	$0.0946002\pi$
$798$		0			0
$799$	10.7301	+	14.7687i	0.0134294	+	0.0184840i
$800$		0			0
$801$	−234.297	−	721.091i	−0.292505	−	0.900238i
$802$		0			0
$803$	91.6553	+	159.023i	0.114141	+	0.198037i
$804$		0			0
$805$	200.317	−	65.0870i	0.248841	−	0.0808535i
$806$		0			0
$807$	241.150	−	175.205i	0.298822	−	0.217107i
$808$		0			0
$809$	449.120	+	145.928i	0.555155	+	0.180381i	0.573140	−	0.819457i	$-0.305725\pi$
$809$	449.120	+	145.928i	0.555155	+	0.180381i	−0.0179850	+	0.999838i	$0.505725\pi$
$810$		0			0
$811$	−522.584	+	719.275i	−0.644369	+	0.886898i	−0.998839	−	0.0481691i	$-0.984661\pi$
$811$	−522.584	+	719.275i	−0.644369	+	0.886898i	0.354470	+	0.935067i	$0.384661\pi$
$812$		0			0
$813$			1390.80i			1.71070i
$814$		0			0
$815$	129.517			0.158916
$816$		0			0
$817$	1750.30	+	1271.67i	2.14235	+	1.55651i
$818$		0			0
$819$	356.795	−	1098.10i	0.435647	−	1.34078i
$820$		0			0
$821$	122.442	+	168.527i	0.149138	+	0.205270i	0.877049	−	0.480401i	$-0.159509\pi$
$821$	122.442	+	168.527i	0.149138	+	0.205270i	−0.727911	+	0.685671i	$0.759509\pi$
$822$		0			0
$823$	−409.105	−	1259.09i	−0.497089	−	1.52988i	−0.813675	−	0.581320i	$-0.802536\pi$
$823$	−409.105	−	1259.09i	−0.497089	−	1.52988i	0.316586	−	0.948564i	$-0.397464\pi$
$824$		0			0
$825$	−66.3757	−	313.414i	−0.0804554	−	0.379896i
$826$		0			0
$827$	−773.306	+	251.262i	−0.935074	+	0.303824i	−0.736636	−	0.676289i	$-0.763587\pi$
$827$	−773.306	+	251.262i	−0.935074	+	0.303824i	−0.198438	+	0.980113i	$0.563587\pi$
$828$		0			0
$829$	476.182	−	345.966i	0.574405	−	0.417330i	−0.262298	−	0.964987i	$-0.584480\pi$
$829$	476.182	−	345.966i	0.574405	−	0.417330i	0.836703	+	0.547657i	$0.184480\pi$
$830$		0			0
$831$	1143.49	+	371.543i	1.37604	+	0.447103i
$832$		0			0
$833$	7.34452	−	10.1089i	0.00881695	−	0.0121355i
$834$		0			0
$835$			358.416i			0.429240i
$836$		0			0
$837$	1173.65			1.40221
$838$		0			0
$839$	−297.249	−	215.964i	−0.354290	−	0.257407i	0.396377	−	0.918088i	$-0.370267\pi$
$839$	−297.249	−	215.964i	−0.354290	−	0.257407i	−0.750666	+	0.660681i	$0.770267\pi$
$840$		0			0
$841$	−642.727	+	1978.11i	−0.764242	+	2.35209i
$842$		0			0
$843$	−991.119	−	1364.16i	−1.17570	−	1.61822i
$844$		0			0
$845$	42.6552	+	131.279i	0.0504795	+	0.155360i
$846$		0			0
$847$	−219.358	−	494.656i	−0.258982	−	0.584009i
$848$		0			0
$849$	2662.51	−	865.102i	3.13605	−	1.01897i
$850$		0			0
$851$	71.1579	−	51.6992i	0.0836168	−	0.0607511i
$852$		0			0
$853$	−242.057	−	78.6490i	−0.283771	−	0.0922028i	0.163673	−	0.986515i	$-0.447666\pi$
$853$	−242.057	−	78.6490i	−0.283771	−	0.0922028i	−0.447444	+	0.894312i	$0.647666\pi$
$854$		0			0
$855$	−837.412	+	1152.60i	−0.979429	+	1.34807i
$856$		0			0
$857$		−	667.813i		−	0.779245i	−0.920975	−	0.389622i	$-0.872606\pi$
$857$		−	667.813i		−	0.779245i	0.920975	−	0.389622i	$-0.127394\pi$
$858$		0			0
$859$	318.739			0.371058			0.185529	−	0.982639i	$-0.440600\pi$
$859$	318.739			0.371058			0.185529	+	0.982639i	$0.440600\pi$
$860$		0			0
$861$	−883.221	−	641.698i	−1.02581	−	0.745293i
$862$		0			0
$863$	275.648	−	848.358i	0.319407	−	0.983034i	−0.654495	−	0.756066i	$-0.727119\pi$
$863$	275.648	−	848.358i	0.319407	−	0.983034i	0.973902	−	0.226968i	$-0.0728812\pi$
$864$		0			0
$865$	129.088	+	177.674i	0.149234	+	0.205403i
$866$		0			0
$867$	−519.857	−	1599.96i	−0.599605	−	1.84539i
$868$		0			0
$869$	556.988	−	117.961i	0.640953	−	0.135743i
$870$		0			0
$871$	407.629	−	132.447i	0.468001	−	0.152063i
$872$		0			0
$873$	3458.05	−	2512.42i	3.96111	−	2.87791i
$874$		0			0
$875$	47.5514	+	15.4504i	0.0543444	+	0.0176576i
$876$		0			0
$877$	−573.243	+	789.001i	−0.653641	+	0.899660i	−0.999250	−	0.0387190i	$-0.987672\pi$
$877$	−573.243	+	789.001i	−0.653641	+	0.899660i	0.345609	+	0.938379i	$0.387672\pi$
$878$		0			0
$879$			2688.56i			3.05866i
$880$		0			0
$881$	−1097.87			−1.24617			−0.623083	−	0.782156i	$-0.714120\pi$
$881$	−1097.87			−1.24617			−0.623083	+	0.782156i	$0.714120\pi$
$882$		0			0
$883$	−865.026	−	628.478i	−0.979645	−	0.711754i	−0.0220155	−	0.999758i	$-0.507008\pi$
$883$	−865.026	−	628.478i	−0.979645	−	0.711754i	−0.957629	+	0.288004i	$0.907008\pi$
$884$		0			0
$885$	−266.940	+	821.558i	−0.301628	+	0.928314i
$886$		0			0
$887$	−370.279	−	509.645i	−0.417451	−	0.574572i	0.547565	−	0.836763i	$-0.315555\pi$
$887$	−370.279	−	509.645i	−0.417451	−	0.574572i	−0.965016	+	0.262191i	$0.915555\pi$
$888$		0			0
$889$	−187.146	−	575.976i	−0.210513	−	0.647892i
$890$		0			0
$891$	−3012.34	+	1736.20i	−3.38085	+	1.94860i
$892$		0			0
$893$	−1029.91	+	334.639i	−1.15332	+	0.374735i
$894$		0			0
$895$	310.559	−	225.635i	0.346994	−	0.252106i
$896$		0			0
$897$	−1208.51	−	392.670i	−1.34728	−	0.437759i
$898$		0			0
$899$	−401.842	+	553.088i	−0.446988	+	0.615226i
$900$		0			0
$901$			18.9460i			0.0210278i
$902$		0			0
$903$	−2204.97			−2.44183
$904$		0			0
$905$	−281.104	−	204.234i	−0.310613	−	0.225673i
$906$		0			0
$907$	−151.248	+	465.494i	−0.166757	+	0.513224i	−0.999161	−	0.0409440i	$-0.986963\pi$
$907$	−151.248	+	465.494i	−0.166757	+	0.513224i	0.832405	+	0.554168i	$0.186963\pi$
$908$		0			0
$909$	−2317.44	−	3189.68i	−2.54943	−	3.50899i
$910$		0			0
$911$	108.565	+	334.129i	0.119171	+	0.366772i	0.992794	−	0.119832i	$-0.0382355\pi$
$911$	108.565	+	334.129i	0.119171	+	0.366772i	−0.873623	+	0.486604i	$0.838236\pi$
$912$		0			0
$913$	638.228	+	284.724i	0.699045	+	0.311855i
$914$		0			0
$915$	−518.034	+	168.319i	−0.566157	+	0.183956i
$916$		0			0
$917$	800.292	−	581.446i	0.872729	−	0.634075i
$918$		0			0
$919$	−1127.93	−	366.486i	−1.22734	−	0.398787i	−0.377591	−	0.925972i	$-0.623247\pi$
$919$	−1127.93	−	366.486i	−1.22734	−	0.398787i	−0.849751	+	0.527185i	$0.823247\pi$
$920$		0			0
$921$	−689.552	+	949.087i	−0.748700	+	1.03050i
$922$		0			0
$923$		−	41.8692i		−	0.0453621i
$924$		0			0
$925$	20.8790			0.0225719
$926$		0			0
$927$	−1.69128	−	1.22879i	−0.00182447	−	0.00132555i
$928$		0			0
$929$	237.583	−	731.206i	0.255741	−	0.787090i	−0.737942	−	0.674864i	$-0.764202\pi$
$929$	237.583	−	731.206i	0.255741	−	0.787090i	0.993683	−	0.112225i	$-0.0357978\pi$
$930$		0			0
$931$	435.685	+	599.669i	0.467975	+	0.644113i
$932$		0			0
$933$	820.951	+	2526.63i	0.879905	+	2.70807i
$934$		0			0
$935$	7.09698	−	7.87027i	0.00759036	−	0.00841741i
$936$		0			0
$937$	923.916	−	300.199i	0.986037	−	0.320383i	0.228764	−	0.973482i	$-0.426531\pi$
$937$	923.916	−	300.199i	0.986037	−	0.320383i	0.757272	+	0.653099i	$0.226531\pi$
$938$		0			0
$939$	−1229.45	+	893.250i	−1.30932	+	0.951278i
$940$		0			0
$941$	292.660	+	95.0911i	0.311010	+	0.101053i	0.460363	−	0.887731i	$-0.347719\pi$
$941$	292.660	+	95.0911i	0.311010	+	0.101053i	−0.149353	+	0.988784i	$0.547719\pi$
$942$		0			0
$943$	−518.885	+	714.184i	−0.550249	+	0.757353i
$944$		0			0
$945$		−	927.786i		−	0.981784i
$946$		0			0
$947$	−606.076			−0.639996			−0.319998	−	0.947418i	$-0.603682\pi$
$947$	−606.076			−0.639996			−0.319998	+	0.947418i	$0.603682\pi$
$948$		0			0
$949$	139.813	+	101.580i	0.147326	+	0.107039i
$950$		0			0
$951$	719.455	−	2214.26i	0.756525	−	2.32835i
$952$		0			0
$953$	−654.017	−	900.178i	−0.686272	−	0.944573i	0.313716	−	0.949517i	$-0.398426\pi$
$953$	−654.017	−	900.178i	−0.686272	−	0.944573i	−0.999988	+	0.00494435i	$0.998426\pi$
$954$		0			0
$955$	−181.206	−	557.694i	−0.189744	−	0.583973i
$956$		0			0
$957$	364.517	−	3443.62i	0.380895	−	3.59835i
$958$		0			0
$959$	559.972	−	181.946i	0.583913	−	0.189725i
$960$		0			0
$961$	648.012	−	470.808i	0.674310	−	0.489915i
$962$		0			0
$963$	−1541.49	−	500.859i	−1.60071	−	0.520103i
$964$		0			0
$965$	99.1369	−	136.450i	0.102733	−	0.141399i
$966$		0			0
$967$		−	669.469i		−	0.692316i	−0.938176	−	0.346158i	$-0.887486\pi$
$967$		−	669.469i		−	0.692316i	0.938176	−	0.346158i	$-0.112514\pi$
$968$		0			0
$969$	−64.1429			−0.0661950
$970$		0			0
$971$	−116.931	−	84.9556i	−0.120424	−	0.0874929i	0.525943	−	0.850520i	$-0.323712\pi$
$971$	−116.931	−	84.9556i	−0.120424	−	0.0874929i	−0.646367	+	0.763027i	$0.723712\pi$
$972$		0			0
$973$	−198.634	+	611.333i	−0.204146	+	0.628297i
$974$		0			0
$975$	−177.300	−	244.032i	−0.181846	−	0.250290i
$976$		0			0
$977$	−436.988	−	1344.91i	−0.447276	−	1.37657i	−0.879969	−	0.475032i	$-0.842437\pi$
$977$	−436.988	−	1344.91i	−0.447276	−	1.37657i	0.432693	−	0.901541i	$-0.357563\pi$
$978$		0			0
$979$	−332.704	−	35.2177i	−0.339841	−	0.0359731i
$980$		0			0
$981$	325.174	−	105.655i	0.331472	−	0.107702i
$982$		0			0
$983$	−524.533	+	381.095i	−0.533604	+	0.387686i	−0.821704	−	0.569914i	$-0.806976\pi$
$983$	−524.533	+	381.095i	−0.533604	+	0.387686i	0.288100	+	0.957600i	$0.406976\pi$
$984$		0			0
$985$	64.4812	+	20.9512i	0.0654631	+	0.0212703i
$986$		0			0
$987$	648.723	−	892.891i	0.657268	−	0.904652i
$988$		0			0
$989$			1782.97i			1.80280i
$990$		0			0
$991$	−1885.73			−1.90285			−0.951425	−	0.307879i	$-0.900381\pi$
$991$	−1885.73			−1.90285			−0.951425	+	0.307879i	$0.900381\pi$
$992$		0			0
$993$	1180.90	+	857.974i	1.18922	+	0.864022i
$994$		0			0
$995$	−166.583	+	512.689i	−0.167420	+	0.515265i
$996$		0			0
$997$	698.097	+	960.848i	0.700198	+	0.963740i	0.999953	+	0.00972333i	$0.00309508\pi$
$997$	698.097	+	960.848i	0.700198	+	0.963740i	−0.299755	+	0.954016i	$0.596905\pi$
$998$		0			0
$999$	−119.725	−	368.474i	−0.119844	−	0.368843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.p.b.61.4	✓	16
11.2	odd	10	inner	220.3.p.b.101.4	yes	16
11.3	even	5		2420.3.f.a.241.2		16
11.8	odd	10		2420.3.f.a.241.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.p.b.61.4	✓	16	1.1	even	1	trivial
220.3.p.b.101.4	yes	16	11.2	odd	10	inner
2420.3.f.a.241.1		16	11.8	odd	10
2420.3.f.a.241.2		16	11.3	even	5

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.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.71238 + 3.42375i) q^{3} +(0.690983 - 2.12663i) q^{5} +(-2.62857 - 3.61792i) q^{7} +(7.70337 + 23.7085i) q^{9} +(10.9389 + 1.15791i) q^{11} +(9.85015 - 3.20051i) q^{13} +(10.5372 - 7.65573i) q^{15} +(0.409765 + 0.133141i) q^{17} +(-15.0230 + 20.6774i) q^{19} -26.0486i q^{21} -21.0633 q^{23} +(-4.04508 - 2.93893i) q^{25} +(-28.6710 + 88.2404i) q^{27} +(-31.7671 - 43.7237i) q^{29} +(-3.90895 - 12.0305i) q^{31} +(47.5838 + 42.9085i) q^{33} +(-9.51027 + 3.09007i) q^{35} +(-3.37829 + 2.45447i) q^{37} +(57.3755 + 18.6424i) q^{39} +(24.6346 - 33.9066i) q^{41} -84.6483i q^{43} +55.7421 q^{45} +(34.2779 + 24.9043i) q^{47} +(8.96187 - 27.5818i) q^{49} +(1.47513 + 2.03034i) q^{51} +(13.5885 + 41.8211i) q^{53} +(10.0210 - 22.4628i) q^{55} +(-141.588 + 46.0048i) q^{57} +(-53.6564 + 38.9837i) q^{59} +(-39.7732 - 12.9231i) q^{61} +(65.5267 - 90.1898i) q^{63} -23.1591i q^{65} +41.3830 q^{67} +(-99.2582 - 72.1153i) q^{69} +(1.24922 - 3.84472i) q^{71} +(9.80778 + 13.4993i) q^{73} +(-8.99985 - 27.6987i) q^{75} +(-24.5644 - 42.6197i) q^{77} +(49.2252 - 15.9942i) q^{79} +(-255.713 + 185.786i) q^{81} +(60.4230 + 19.6326i) q^{83} +(0.566281 - 0.779419i) q^{85} -314.805i q^{87} -30.4148 q^{89} +(-37.4711 - 27.2243i) q^{91} +(22.7689 - 70.0756i) q^{93} +(33.5924 + 46.2360i) q^{95} +(-52.9856 - 163.073i) q^{97} +(56.8139 + 268.265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 9 q^{3} + 20 q^{5} + 10 q^{7} - 19 q^{9} + 23 q^{11} - 5 q^{13} + 15 q^{15} + 25 q^{17} + 30 q^{19} - 168 q^{23} - 20 q^{25} - 225 q^{27} - 105 q^{29} + 40 q^{31} + 106 q^{33} - 16 q^{37} + 115 q^{39}+ \cdots + 150 q^{99}+O(q^{100}) \) 16 * q + 9 * q^3 + 20 * q^5 + 10 * q^7 - 19 * q^9 + 23 * q^11 - 5 * q^13 + 15 * q^15 + 25 * q^17 + 30 * q^19 - 168 * q^23 - 20 * q^25 - 225 * q^27 - 105 * q^29 + 40 * q^31 + 106 * q^33 - 16 * q^37 + 115 * q^39 + 255 * q^41 - 30 * q^45 + 102 * q^47 + 12 * q^49 + 380 * q^51 + 297 * q^53 + 55 * q^55 - 150 * q^57 - 22 * q^59 - 30 * q^61 - 320 * q^63 - 68 * q^67 - 137 * q^69 - 240 * q^71 + 85 * q^73 - 30 * q^75 + 226 * q^77 - 215 * q^79 - 463 * q^81 - 610 * q^83 + 25 * q^85 - 160 * q^89 + 161 * q^91 - 253 * q^93 + 90 * q^95 + 179 * q^97 + 150 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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