LMFDB - Embedded newform 220.3.h.a.199.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(199,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("220.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.h (of order $2$, degree $1$, 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:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.11
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.76106 - 0.947973i) q^{2} -3.26539 q^{3} +(2.20269 + 3.33888i) q^{4} +(-4.29635 - 2.55761i) q^{5} +(5.75056 + 3.09550i) q^{6} -7.75789 q^{7} +(-0.713917 - 7.96808i) q^{8} +1.66278 q^{9} +(5.14160 + 8.57694i) q^{10} -3.31662i q^{11} +(-7.19266 - 10.9028i) q^{12} +7.89709i q^{13} +(13.6621 + 7.35427i) q^{14} +(14.0293 + 8.35160i) q^{15} +(-6.29627 + 14.7091i) q^{16} -2.35730i q^{17} +(-2.92826 - 1.57627i) q^{18} +1.30094i q^{19} +(-0.923982 - 19.9786i) q^{20} +25.3325 q^{21} +(-3.14407 + 5.84079i) q^{22} +8.98378 q^{23} +(2.33122 + 26.0189i) q^{24} +(11.9172 + 21.9768i) q^{25} +(7.48622 - 13.9073i) q^{26} +23.9589 q^{27} +(-17.0883 - 25.9027i) q^{28} +44.2529 q^{29} +(-16.7893 - 28.0071i) q^{30} -42.0172i q^{31} +(25.0319 - 19.9349i) q^{32} +10.8301i q^{33} +(-2.23465 + 4.15135i) q^{34} +(33.3306 + 19.8417i) q^{35} +(3.66259 + 5.55182i) q^{36} +43.6281i q^{37} +(1.23326 - 2.29104i) q^{38} -25.7871i q^{39} +(-17.3120 + 36.0596i) q^{40} -8.01223 q^{41} +(-44.6122 - 24.0146i) q^{42} +27.2677 q^{43} +(11.0738 - 7.30551i) q^{44} +(-7.14388 - 4.25274i) q^{45} +(-15.8210 - 8.51638i) q^{46} -22.8977 q^{47} +(20.5598 - 48.0309i) q^{48} +11.1848 q^{49} +(-0.153630 - 49.9998i) q^{50} +7.69750i q^{51} +(-26.3674 + 17.3949i) q^{52} -20.7576i q^{53} +(-42.1932 - 22.7124i) q^{54} +(-8.48264 + 14.2494i) q^{55} +(5.53849 + 61.8155i) q^{56} -4.24808i q^{57} +(-77.9322 - 41.9505i) q^{58} +103.619i q^{59} +(3.01716 + 65.2381i) q^{60} -62.2398 q^{61} +(-39.8312 + 73.9950i) q^{62} -12.8997 q^{63} +(-62.9806 + 11.3771i) q^{64} +(20.1977 - 33.9286i) q^{65} +(10.2666 - 19.0725i) q^{66} -24.6960 q^{67} +(7.87074 - 5.19241i) q^{68} -29.3355 q^{69} +(-39.8880 - 66.5390i) q^{70} -67.8271i q^{71} +(-1.18709 - 13.2492i) q^{72} +134.700i q^{73} +(41.3582 - 76.8318i) q^{74} +(-38.9145 - 71.7628i) q^{75} +(-4.34369 + 2.86557i) q^{76} +25.7300i q^{77} +(-24.4455 + 45.4127i) q^{78} +30.3975i q^{79} +(64.6711 - 47.0919i) q^{80} -93.2002 q^{81} +(14.1101 + 7.59538i) q^{82} +134.182 q^{83} +(55.7999 + 84.5824i) q^{84} +(-6.02905 + 10.1278i) q^{85} +(-48.0203 - 25.8491i) q^{86} -144.503 q^{87} +(-26.4271 + 2.36780i) q^{88} +105.455 q^{89} +(8.54935 + 14.2616i) q^{90} -61.2647i q^{91} +(19.7885 + 29.9958i) q^{92} +137.203i q^{93} +(40.3244 + 21.7064i) q^{94} +(3.32730 - 5.58930i) q^{95} +(-81.7391 + 65.0954i) q^{96} -187.374i q^{97} +(-19.6972 - 10.6029i) q^{98} -5.51481i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9} - 18 q^{10} - 56 q^{14} - 40 q^{16} + 84 q^{20} - 16 q^{21} + 104 q^{24} - 60 q^{25} + 28 q^{26} - 88 q^{29} - 166 q^{30} - 152 q^{34} - 248 q^{36} + 132 q^{40}+ \cdots + 216 q^{96}+O(q^{100}) $ 60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.76106	−	0.947973i	−0.880532	−	0.473986i
$2$	−1.76106	−	0.947973i	−0.880532	−	0.473986i
$3$	−3.26539			−1.08846			−0.544232	−	0.838935i	$-0.683179\pi$
$3$	−3.26539			−1.08846			−0.544232	+	0.838935i	$0.683179\pi$
$4$	2.20269	+	3.33888i	0.550674	+	0.834721i
$5$	−4.29635	−	2.55761i	−0.859270	−	0.511522i
$5$	−4.29635	−	2.55761i	−0.859270	−	0.511522i
$6$	5.75056	+	3.09550i	0.958427	+	0.515917i
$7$	−7.75789			−1.10827			−0.554135	−	0.832427i	$-0.686951\pi$
$7$	−7.75789			−1.10827			−0.554135	+	0.832427i	$0.686951\pi$
$8$	−0.713917	−	7.96808i	−0.0892397	−	0.996010i
$9$	1.66278			0.184753
$10$	5.14160	+	8.57694i	0.514160	+	0.857694i
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$	−7.19266	−	10.9028i	−0.599388	−	0.908563i
$13$			7.89709i			0.607468i	0.952757	+	0.303734i	$0.0982335\pi$
$13$			7.89709i			0.607468i	−0.952757	+	0.303734i	$0.901767\pi$
$14$	13.6621	+	7.35427i	0.975867	+	0.525305i
$15$	14.0293	+	8.35160i	0.935284	+	0.556774i
$16$	−6.29627	+	14.7091i	−0.393517	+	0.919317i
$17$		−	2.35730i		−	0.138665i	−0.997594	−	0.0693323i	$-0.977913\pi$
$17$		−	2.35730i		−	0.138665i	0.997594	−	0.0693323i	$-0.0220869\pi$
$18$	−2.92826	−	1.57627i	−0.162681	−	0.0875705i
$19$			1.30094i			0.0684705i	0.999414	+	0.0342353i	$0.0108996\pi$
$19$			1.30094i			0.0684705i	−0.999414	+	0.0342353i	$0.989100\pi$
$20$	−0.923982	−	19.9786i	−0.0461991	−	0.998932i
$21$	25.3325			1.20631
$22$	−3.14407	+	5.84079i	−0.142912	+	0.265490i
$23$	8.98378			0.390599			0.195300	−	0.980744i	$-0.437432\pi$
$23$	8.98378			0.390599			0.195300	+	0.980744i	$0.437432\pi$
$24$	2.33122	+	26.0189i	0.0971341	+	1.08412i
$25$	11.9172	+	21.9768i	0.476690	+	0.879072i
$26$	7.48622	−	13.9073i	0.287932	−	0.534895i
$27$	23.9589			0.887367
$28$	−17.0883	−	25.9027i	−0.610295	−	0.925096i
$29$	44.2529			1.52596			0.762981	−	0.646421i	$-0.223735\pi$
$29$	44.2529			1.52596			0.762981	+	0.646421i	$0.223735\pi$
$30$	−16.7893	−	28.0071i	−0.559645	−	0.933569i
$31$		−	42.0172i		−	1.35539i	−0.735341	−	0.677697i	$-0.762978\pi$
$31$		−	42.0172i		−	1.35539i	0.735341	−	0.677697i	$-0.237022\pi$
$32$	25.0319	−	19.9349i	0.782248	−	0.622967i
$33$			10.8301i			0.328184i
$34$	−2.23465	+	4.15135i	−0.0657251	+	0.122099i
$35$	33.3306	+	19.8417i	0.952303	+	0.566905i
$36$	3.66259	+	5.55182i	0.101739	+	0.154217i
$37$			43.6281i			1.17914i	0.807718	+	0.589568i	$0.200702\pi$
$37$			43.6281i			1.17914i	−0.807718	+	0.589568i	$0.799298\pi$
$38$	1.23326	−	2.29104i	0.0324541	−	0.0602905i
$39$		−	25.7871i		−	0.661207i
$40$	−17.3120	+	36.0596i	−0.432801	+	0.901490i
$41$	−8.01223			−0.195420			−0.0977101	−	0.995215i	$-0.531152\pi$
$41$	−8.01223			−0.195420			−0.0977101	+	0.995215i	$0.531152\pi$
$42$	−44.6122	−	24.0146i	−1.06220	−	0.571775i
$43$	27.2677			0.634134			0.317067	−	0.948403i	$-0.397302\pi$
$43$	27.2677			0.634134			0.317067	+	0.948403i	$0.397302\pi$
$44$	11.0738	−	7.30551i	0.251678	−	0.166034i
$45$	−7.14388	−	4.25274i	−0.158753	−	0.0945054i
$46$	−15.8210	−	8.51638i	−0.343935	−	0.185139i
$47$	−22.8977			−0.487186			−0.243593	−	0.969878i	$-0.578326\pi$
$47$	−22.8977			−0.487186			−0.243593	+	0.969878i	$0.578326\pi$
$48$	20.5598	−	48.0309i	0.428329	−	1.00064i
$49$	11.1848			0.228262
$50$	−0.153630	−	49.9998i	−0.00307259	−	0.999995i
$51$			7.69750i			0.150931i
$52$	−26.3674	+	17.3949i	−0.507066	+	0.334517i
$53$		−	20.7576i		−	0.391654i	−0.980638	−	0.195827i	$-0.937261\pi$
$53$		−	20.7576i		−	0.391654i	0.980638	−	0.195827i	$-0.0627391\pi$
$54$	−42.1932	−	22.7124i	−0.781355	−	0.420600i
$55$	−8.48264	+	14.2494i	−0.154230	+	0.259080i
$56$	5.53849	+	61.8155i	0.0989016	+	1.10385i
$57$		−	4.24808i		−	0.0745277i
$58$	−77.9322	−	41.9505i	−1.34366	−	0.723285i
$59$			103.619i			1.75626i	0.478422	+	0.878130i	$0.341209\pi$
$59$			103.619i			1.75626i	−0.478422	+	0.878130i	$0.658791\pi$
$60$	3.01716	+	65.2381i	0.0502861	+	1.08730i
$61$	−62.2398			−1.02032			−0.510162	−	0.860078i	$-0.670415\pi$
$61$	−62.2398			−1.02032			−0.510162	+	0.860078i	$0.670415\pi$
$62$	−39.8312	+	73.9950i	−0.642438	+	1.19347i
$63$	−12.8997			−0.204756
$64$	−62.9806	+	11.3771i	−0.984073	+	0.177767i
$65$	20.1977	−	33.9286i	0.310734	−	0.521979i
$66$	10.2666	−	19.0725i	0.155555	−	0.288977i
$67$	−24.6960			−0.368597			−0.184298	−	0.982870i	$-0.559001\pi$
$67$	−24.6960			−0.368597			−0.184298	+	0.982870i	$0.559001\pi$
$68$	7.87074	−	5.19241i	0.115746	−	0.0763589i
$69$	−29.3355			−0.425153
$70$	−39.8880	−	66.5390i	−0.569828	−	0.950557i
$71$		−	67.8271i		−	0.955311i	−0.878547	−	0.477656i	$-0.841487\pi$
$71$		−	67.8271i		−	0.955311i	0.878547	−	0.477656i	$-0.158513\pi$
$72$	−1.18709	−	13.2492i	−0.0164873	−	0.184016i
$73$			134.700i			1.84520i	0.385758	+	0.922600i	$0.373940\pi$
$73$			134.700i			1.84520i	−0.385758	+	0.922600i	$0.626060\pi$
$74$	41.3582	−	76.8318i	0.558895	−	1.03827i
$75$	−38.9145	−	71.7628i	−0.518859	−	0.956838i
$76$	−4.34369	+	2.86557i	−0.0571538	+	0.0377049i
$77$			25.7300i			0.334156i
$78$	−24.4455	+	45.4127i	−0.313403	+	0.582214i
$79$			30.3975i			0.384779i	0.981319	+	0.192389i	$0.0616237\pi$
$79$			30.3975i			0.384779i	−0.981319	+	0.192389i	$0.938376\pi$
$80$	64.6711	−	47.0919i	0.808389	−	0.588649i
$81$	−93.2002			−1.15062
$82$	14.1101	+	7.59538i	0.172074	+	0.0926266i
$83$	134.182			1.61665			0.808327	−	0.588734i	$-0.200373\pi$
$83$	134.182			1.61665			0.808327	+	0.588734i	$0.200373\pi$
$84$	55.7999	+	84.5824i	0.664284	+	1.00693i
$85$	−6.02905	+	10.1278i	−0.0709300	+	0.119150i
$86$	−48.0203	−	25.8491i	−0.558375	−	0.300571i
$87$	−144.503			−1.66095
$88$	−26.4271	+	2.36780i	−0.300308	+	0.0269068i
$89$	105.455			1.18488			0.592441	−	0.805614i	$-0.298164\pi$
$89$	105.455			1.18488			0.592441	+	0.805614i	$0.298164\pi$
$90$	8.54935	+	14.2616i	0.0949927	+	0.158462i
$91$		−	61.2647i		−	0.673239i
$92$	19.7885	+	29.9958i	0.215093	+	0.326041i
$93$			137.203i			1.47530i
$94$	40.3244	+	21.7064i	0.428983	+	0.230920i
$95$	3.32730	−	5.58930i	0.0350242	−	0.0588347i
$96$	−81.7391	+	65.0954i	−0.851449	+	0.678077i
$97$		−	187.374i		−	1.93169i	−0.259113	−	0.965847i	$-0.583430\pi$
$97$		−	187.374i		−	1.93169i	0.259113	−	0.965847i	$-0.416570\pi$
$98$	−19.6972	−	10.6029i	−0.200992	−	0.108193i
$99$		−	5.51481i		−	0.0557052i
$100$	−47.1279	+	88.1984i	−0.471279	+	0.881984i
$101$	−105.475			−1.04431			−0.522156	−	0.852850i	$-0.674872\pi$
$101$	−105.475			−1.04431			−0.522156	+	0.852850i	$0.674872\pi$
$102$	7.29702	−	13.5558i	0.0715394	−	0.132900i
$103$	−74.4753			−0.723061			−0.361531	−	0.932360i	$-0.617746\pi$
$103$	−74.4753			−0.723061			−0.361531	+	0.932360i	$0.617746\pi$
$104$	62.9246	−	5.63787i	0.605045	−	0.0542103i
$105$	−108.837	−	64.7908i	−1.03655	−	0.617055i
$106$	−19.6777	+	36.5555i	−0.185639	+	0.344864i
$107$	3.24484			0.0303256			0.0151628	−	0.999885i	$-0.495173\pi$
$107$	3.24484			0.0303256			0.0151628	+	0.999885i	$0.495173\pi$
$108$	52.7741	+	79.9959i	0.488649	+	0.740703i
$109$	201.741			1.85084			0.925418	−	0.378948i	$-0.123714\pi$
$109$	201.741			1.85084			0.925418	+	0.378948i	$0.123714\pi$
$110$	28.4465	−	17.0528i	0.258605	−	0.155025i
$111$		−	142.463i		−	1.28345i
$112$	48.8458	−	114.111i	0.436123	−	1.01885i
$113$		−	25.7592i		−	0.227958i	−0.993483	−	0.113979i	$-0.963640\pi$
$113$		−	25.7592i		−	0.227958i	0.993483	−	0.113979i	$-0.0363596\pi$
$114$	−4.02706	+	7.48114i	−0.0353251	+	0.0656240i
$115$	−38.5975	−	22.9770i	−0.335630	−	0.199800i
$116$	97.4756	+	147.755i	0.840307	+	1.27375i
$117$			13.1311i			0.112232i
$118$	98.2283	−	182.480i	0.832443	−	1.54644i
$119$			18.2876i			0.153678i
$120$	56.5305	−	117.749i	0.471088	−	0.981239i
$121$	−11.0000			−0.0909091
$122$	109.608	+	59.0017i	0.898429	+	0.483620i
$123$	26.1631			0.212708
$124$	140.291	−	92.5511i	1.13138	−	0.746380i
$125$	5.00746	−	124.900i	0.0400597	−	0.999197i
$126$	22.7171	+	12.2285i	0.180295	+	0.0970518i
$127$	109.387			0.861315			0.430657	−	0.902516i	$-0.358282\pi$
$127$	109.387			0.861315			0.430657	+	0.902516i	$0.358282\pi$
$128$	121.698	+	39.6681i	0.950767	+	0.309907i
$129$	−89.0399			−0.690232
$130$	−67.7329	+	40.6037i	−0.521022	+	0.312336i
$131$			63.4044i			0.484003i	0.970276	+	0.242002i	$0.0778039\pi$
$131$			63.4044i			0.484003i	−0.970276	+	0.242002i	$0.922196\pi$
$132$	−36.1604	+	23.8554i	−0.273942	+	0.180722i
$133$		−	10.0926i		−	0.0758838i
$134$	43.4912	+	23.4111i	0.324561	+	0.174710i
$135$	−102.936	−	61.2776i	−0.762487	−	0.453908i
$136$	−18.7831	+	1.68292i	−0.138111	+	0.0123744i
$137$		−	164.750i		−	1.20255i	−0.799041	−	0.601277i	$-0.794659\pi$
$137$		−	164.750i		−	1.20255i	0.799041	−	0.601277i	$-0.205341\pi$
$138$	51.6618	+	27.8093i	0.374361	+	0.201517i
$139$			210.421i			1.51382i	0.653519	+	0.756910i	$0.273292\pi$
$139$			210.421i			1.51382i	−0.653519	+	0.756910i	$0.726708\pi$
$140$	7.16815	+	154.992i	0.0512011	+	1.10709i
$141$	74.7701			0.530284
$142$	−64.2982	+	119.448i	−0.452805	+	0.841182i
$143$	26.1917			0.183159
$144$	−10.4693	+	24.4579i	−0.0727035	+	0.169847i
$145$	−190.126	−	113.182i	−1.31121	−	0.780564i
$146$	127.692	−	237.215i	0.874600	−	1.62476i
$147$	−36.5228			−0.248455
$148$	−145.669	+	96.0993i	−0.984250	+	0.649320i
$149$	23.1139			0.155127			0.0775635	−	0.996987i	$-0.475286\pi$
$149$	23.1139			0.155127			0.0775635	+	0.996987i	$0.475286\pi$
$150$	0.501661	+	163.269i	0.00334441	+	1.08846i
$151$			247.785i			1.64096i	0.571675	+	0.820480i	$0.306294\pi$
$151$			247.785i			1.64096i	−0.571675	+	0.820480i	$0.693706\pi$
$152$	10.3660	−	0.928764i	0.0681974	−	0.00611029i
$153$		−	3.91966i		−	0.0256187i
$154$	24.3913	−	45.3122i	0.158385	−	0.294235i
$155$	−107.464	+	180.521i	−0.693314	+	1.16465i
$156$	86.1000	−	56.8011i	0.551923	−	0.364109i
$157$			127.193i			0.810149i	0.914284	+	0.405075i	$0.132754\pi$
$157$			127.193i			0.810149i	−0.914284	+	0.405075i	$0.867246\pi$
$158$	28.8160	−	53.5320i	0.182380	−	0.338810i
$159$			67.7818i			0.426301i
$160$	−158.532	+	21.6255i	−0.990824	+	0.135159i
$161$	−69.6951			−0.432889
$162$	164.132	+	88.3512i	1.01316	+	0.545378i
$163$	198.553			1.21812			0.609059	−	0.793125i	$-0.291547\pi$
$163$	198.553			1.21812			0.609059	+	0.793125i	$0.291547\pi$
$164$	−17.6485	−	26.7519i	−0.107613	−	0.163121i
$165$	27.6991	−	46.5298i	0.167874	−	0.281999i
$166$	−236.304	−	127.201i	−1.42352	−	0.766272i
$167$	84.9930			0.508940			0.254470	−	0.967081i	$-0.418099\pi$
$167$	84.9930			0.508940			0.254470	+	0.967081i	$0.418099\pi$
$168$	−18.0853	−	201.852i	−0.107651	−	1.20150i
$169$	106.636			0.630982
$170$	20.2184	−	12.1203i	0.118932	−	0.0712958i
$171$			2.16318i			0.0126502i
$172$	60.0625	+	91.0438i	0.349201	+	0.529324i
$173$		−	34.8467i		−	0.201426i	−0.994916	−	0.100713i	$-0.967888\pi$
$173$		−	34.8467i		−	0.201426i	0.994916	−	0.100713i	$-0.0321124\pi$
$174$	254.479	+	136.985i	1.46252	+	0.787270i
$175$	−92.4526	−	170.493i	−0.528301	−	0.974248i
$176$	48.7845	+	20.8824i	0.277185	+	0.118650i
$177$		−	338.358i		−	1.91163i
$178$	−185.712	−	99.9680i	−1.04333	−	0.561618i
$179$			153.372i			0.856827i	0.903583	+	0.428414i	$0.140927\pi$
$179$			153.372i			0.856827i	−0.903583	+	0.428414i	$0.859073\pi$
$180$	−1.53638	−	33.2201i	−0.00853544	−	0.184556i
$181$	288.304			1.59284			0.796419	−	0.604745i	$-0.206725\pi$
$181$	288.304			1.59284			0.796419	+	0.604745i	$0.206725\pi$
$182$	−58.0773	+	107.891i	−0.319106	+	0.592808i
$183$	203.237			1.11059
$184$	−6.41368	−	71.5835i	−0.0348569	−	0.389041i
$185$	111.584	−	187.441i	0.603155	−	1.01320i
$186$	130.064	−	241.623i	0.699271	−	1.29905i
$187$	−7.81827			−0.0418089
$188$	−50.4367	−	76.4529i	−0.268280	−	0.406664i
$189$	−185.870			−0.983441
$190$	−11.1581	+	6.68892i	−0.0587268	+	0.0352048i
$191$			76.5993i			0.401043i	0.979689	+	0.200522i	$0.0642637\pi$
$191$			76.5993i			0.401043i	−0.979689	+	0.200522i	$0.935736\pi$
$192$	205.656	−	37.1507i	1.07113	−	0.193493i
$193$			41.5349i			0.215207i	0.994194	+	0.107603i	$0.0343176\pi$
$193$			41.5349i			0.215207i	−0.994194	+	0.107603i	$0.965682\pi$
$194$	−177.626	+	329.978i	−0.915597	+	1.70092i
$195$	−65.9533	+	110.790i	−0.338222	+	0.568155i
$196$	24.6368	+	37.3448i	0.125698	+	0.190535i
$197$		−	22.2364i		−	0.112875i	−0.998406	−	0.0564375i	$-0.982026\pi$
$197$		−	22.2364i		−	0.112875i	0.998406	−	0.0564375i	$-0.0179742\pi$
$198$	−5.22789	+	9.71194i	−0.0264035	+	0.0490502i
$199$		−	330.870i		−	1.66267i	−0.555775	−	0.831333i	$-0.687578\pi$
$199$		−	330.870i		−	1.66267i	0.555775	−	0.831333i	$-0.312422\pi$
$200$	166.605	−	110.647i	0.833025	−	0.553236i
$201$	80.6421			0.401204
$202$	185.749	+	99.9879i	0.919550	+	0.494990i
$203$	−343.309			−1.69118
$204$	−25.7010	+	16.9552i	−0.125985	+	0.0831139i
$205$	34.4233	+	20.4922i	0.167919	+	0.0999618i
$206$	131.156	+	70.6006i	0.636679	+	0.342721i
$207$	14.9380			0.0721644
$208$	−116.159	−	49.7222i	−0.558456	−	0.239049i
$209$	4.31473			0.0206446
$210$	130.250	+	217.276i	0.620237	+	1.03465i
$211$			304.921i			1.44512i	0.691306	+	0.722562i	$0.257036\pi$
$211$			304.921i			1.44512i	−0.691306	+	0.722562i	$0.742964\pi$
$212$	69.3073	−	45.7228i	0.326921	−	0.215673i
$213$			221.482i			1.03982i
$214$	−5.71437	−	3.07602i	−0.0267027	−	0.0143739i
$215$	−117.152	−	69.7403i	−0.544892	−	0.324374i
$216$	−17.1047	−	190.906i	−0.0791883	−	0.883826i
$217$			325.965i			1.50214i
$218$	−355.279	−	191.245i	−1.62972	−	0.877271i
$219$		−	439.847i		−	2.00843i
$220$	−66.2617	+	3.06450i	−0.301189	+	0.0139296i
$221$	18.6158			0.0842343
$222$	−135.051	+	250.886i	−0.608337	+	1.13012i
$223$	−212.973			−0.955036			−0.477518	−	0.878622i	$-0.658464\pi$
$223$	−212.973			−0.955036			−0.477518	+	0.878622i	$0.658464\pi$
$224$	−194.195	+	154.653i	−0.866942	+	0.690415i
$225$	19.8157	+	36.5425i	0.0880700	+	0.162411i
$226$	−24.4190	+	45.3636i	−0.108049	+	0.200724i
$227$	284.091			1.25150			0.625752	−	0.780022i	$-0.284792\pi$
$227$	284.091			1.25150			0.625752	+	0.780022i	$0.284792\pi$
$228$	14.1838	−	9.35722i	0.0622098	−	0.0410404i
$229$	−283.825			−1.23941			−0.619706	−	0.784834i	$-0.712748\pi$
$229$	−283.825			−1.23941			−0.619706	+	0.784834i	$0.712748\pi$
$230$	46.1910	+	77.0533i	0.200830	+	0.335015i
$231$		−	84.0185i		−	0.363717i
$232$	−31.5929	−	352.611i	−0.136176	−	1.51987i
$233$			437.073i			1.87585i	0.346841	+	0.937924i	$0.387254\pi$
$233$			437.073i			1.87585i	−0.346841	+	0.937924i	$0.612746\pi$
$234$	12.4479	−	23.1247i	0.0531963	−	0.0988236i
$235$	98.3767	+	58.5635i	0.418624	+	0.249207i
$236$	−345.973	+	228.242i	−1.46599	+	0.967126i
$237$		−	99.2598i		−	0.418818i
$238$	17.3362	−	32.2057i	0.0728411	−	0.135318i
$239$			77.4829i			0.324196i	0.986775	+	0.162098i	$0.0518261\pi$
$239$			77.4829i			0.324196i	−0.986775	+	0.162098i	$0.948174\pi$
$240$	−211.176	+	153.774i	−0.879902	+	0.640723i
$241$	−62.1858			−0.258032			−0.129016	−	0.991642i	$-0.541182\pi$
$241$	−62.1858			−0.258032			−0.129016	+	0.991642i	$0.541182\pi$
$242$	19.3717	+	10.4277i	0.0800484	+	0.0430897i
$243$	88.7050			0.365041
$244$	−137.095	−	207.811i	−0.561866	−	0.851686i
$245$	−48.0539	−	28.6065i	−0.196139	−	0.116761i
$246$	−46.0748	−	24.8019i	−0.187296	−	0.100821i
$247$	−10.2736			−0.0415937
$248$	−334.797	+	29.9968i	−1.34999	+	0.120955i
$249$	−438.158			−1.75967
$250$	−127.220	+	215.209i	−0.508880	+	0.860838i
$251$		−	182.712i		−	0.727935i	−0.931412	−	0.363967i	$-0.881422\pi$
$251$		−	182.712i		−	0.727935i	0.931412	−	0.363967i	$-0.118578\pi$
$252$	−28.4140	−	43.0704i	−0.112754	−	0.170914i
$253$		−	29.7958i		−	0.117770i
$254$	−192.637	−	103.696i	−0.758415	−	0.408251i
$255$	19.6872	−	33.0711i	0.0772047	−	0.129691i
$256$	−176.714	−	185.225i	−0.690289	−	0.723534i
$257$		−	11.6114i		−	0.0451806i	−0.999745	−	0.0225903i	$-0.992809\pi$
$257$		−	11.6114i		−	0.0451806i	0.999745	−	0.0225903i	$-0.00719134\pi$
$258$	156.805	+	84.4074i	0.607771	+	0.327160i
$259$		−	338.462i		−	1.30680i
$260$	157.773	−	7.29677i	0.606820	−	0.0280645i
$261$	73.5828			0.281926
$262$	60.1056	−	111.659i	0.229411	−	0.426180i
$263$	−236.675			−0.899906			−0.449953	−	0.893052i	$-0.648559\pi$
$263$	−236.675			−0.899906			−0.449953	+	0.893052i	$0.648559\pi$
$264$	86.2949	−	7.73178i	0.326875	−	0.0292870i
$265$	−53.0900	+	89.1821i	−0.200340	+	0.336536i
$266$	−9.56746	+	17.7736i	−0.0359679	+	0.0668182i
$267$	−344.350			−1.28970
$268$	−54.3977	−	82.4570i	−0.202977	−	0.307675i
$269$	−99.2078			−0.368802			−0.184401	−	0.982851i	$-0.559035\pi$
$269$	−99.2078			−0.368802			−0.184401	+	0.982851i	$0.559035\pi$
$270$	123.187	+	205.494i	0.456249	+	0.761089i
$271$		−	177.193i		−	0.653850i	−0.945050	−	0.326925i	$-0.893988\pi$
$271$		−	177.193i		−	0.653850i	0.945050	−	0.326925i	$-0.106012\pi$
$272$	34.6737	+	14.8422i	0.127477	+	0.0545668i
$273$			200.053i			0.732796i
$274$	−156.178	+	290.135i	−0.569994	+	1.05889i
$275$	72.8888	−	39.5250i	0.265050	−	0.143727i
$276$	−64.6173	−	97.9479i	−0.234121	−	0.354884i
$277$			329.322i			1.18889i	0.804137	+	0.594444i	$0.202628\pi$
$277$			329.322i			1.18889i	−0.804137	+	0.594444i	$0.797372\pi$
$278$	199.473	−	370.565i	0.717530	−	1.33297i
$279$		−	69.8653i		−	0.250413i
$280$	134.305	−	279.746i	0.479660	−	0.999094i
$281$	276.653			0.984529			0.492265	−	0.870446i	$-0.336169\pi$
$281$	276.653			0.984529			0.492265	+	0.870446i	$0.336169\pi$
$282$	−131.675	−	70.8800i	−0.466932	−	0.251348i
$283$	419.633			1.48280			0.741401	−	0.671062i	$-0.234162\pi$
$283$	419.633			1.48280			0.741401	+	0.671062i	$0.234162\pi$
$284$	226.467	−	149.402i	0.797418	−	0.526065i
$285$	−10.8649	+	18.2512i	−0.0381226	+	0.0640394i
$286$	−46.1252	−	24.8290i	−0.161277	−	0.0868147i
$287$	62.1580			0.216578
$288$	41.6226	−	33.1474i	0.144523	−	0.115095i
$289$	283.443			0.980772
$290$	227.531	+	379.555i	0.784589	+	1.30881i
$291$			611.850i			2.10258i
$292$	−449.746	+	296.702i	−1.54023	+	1.01610i
$293$		−	454.679i		−	1.55181i	−0.630852	−	0.775903i	$-0.717295\pi$
$293$		−	454.679i		−	1.55181i	0.630852	−	0.775903i	$-0.282705\pi$
$294$	64.3191	+	34.6227i	0.218772	+	0.117764i
$295$	265.018	−	445.185i	0.898366	−	1.50910i
$296$	347.632	−	31.1468i	1.17443	−	0.105226i
$297$		−	79.4627i		−	0.267551i
$298$	−40.7051	−	21.9114i	−0.136594	−	0.0735281i
$299$			70.9457i			0.237277i
$300$	153.891	−	288.002i	0.512970	−	0.960008i
$301$	−211.540			−0.702791
$302$	234.893	−	436.365i	0.777793	−	1.44492i
$303$	344.419			1.13670
$304$	−19.1356	−	8.19107i	−0.0629462	−	0.0269443i
$305$	267.404	+	159.185i	0.876735	+	0.521919i
$306$	−3.71574	+	6.90278i	−0.0121429	+	0.0225581i
$307$	204.879			0.667359			0.333679	−	0.942687i	$-0.391710\pi$
$307$	204.879			0.667359			0.333679	+	0.942687i	$0.391710\pi$
$308$	−85.9095	+	56.6753i	−0.278927	+	0.184011i
$309$	243.191			0.787026
$310$	360.379	−	216.036i	1.16251	−	0.696890i
$311$		−	241.794i		−	0.777471i	−0.921349	−	0.388736i	$-0.872912\pi$
$311$		−	241.794i		−	0.777471i	0.921349	−	0.388736i	$-0.127088\pi$
$312$	−205.474	+	18.4098i	−0.658569	+	0.0590059i
$313$			575.705i			1.83931i	0.392725	+	0.919656i	$0.371532\pi$
$313$			575.705i			1.83931i	−0.392725	+	0.919656i	$0.628468\pi$
$314$	120.576	−	223.996i	0.384000	−	0.713363i
$315$	55.4214	+	32.9923i	0.175941	+	0.104737i
$316$	−101.494	+	66.9565i	−0.321183	+	0.211888i
$317$		−	55.2238i		−	0.174208i	−0.996199	−	0.0871038i	$-0.972239\pi$
$317$		−	55.2238i		−	0.174208i	0.996199	−	0.0871038i	$-0.0277612\pi$
$318$	64.2553	−	119.368i	0.202061	−	0.375372i
$319$		−	146.770i		−	0.460095i
$320$	299.685	+	112.200i	0.936516	+	0.350625i
$321$	−10.5957			−0.0330083
$322$	122.738	+	66.0691i	0.381173	+	0.205184i
$323$	3.06670			0.00949444
$324$	−205.292	−	311.184i	−0.633616	−	0.960446i
$325$	−173.553	+	94.1115i	−0.534008	+	0.289574i
$326$	−349.665	−	188.223i	−1.07259	−	0.577372i
$327$	−658.764			−2.01457
$328$	5.72007	+	63.8421i	0.0174392	+	0.194641i
$329$	177.638			0.539933
$330$	−92.8889	+	55.6839i	−0.281482	+	0.168739i
$331$		−	153.429i		−	0.463531i	−0.972772	−	0.231765i	$-0.925550\pi$
$331$		−	153.429i		−	0.463531i	0.972772	−	0.231765i	$-0.0744501\pi$
$332$	295.563	+	448.019i	0.890249	+	1.34945i
$333$			72.5438i			0.217849i
$334$	−149.678	−	80.5710i	−0.448138	−	0.241231i
$335$	106.103	+	63.1627i	0.316724	+	0.188546i
$336$	−159.501	+	372.618i	−0.474704	+	1.10898i
$337$		−	93.1183i		−	0.276315i	−0.990410	−	0.138158i	$-0.955882\pi$
$337$		−	93.1183i		−	0.276315i	0.990410	−	0.138158i	$-0.0441181\pi$
$338$	−187.793	−	101.088i	−0.555600	−	0.299077i
$339$			84.1139i			0.248124i
$340$	−47.0956	+	2.17810i	−0.138516	+	0.00640618i
$341$	−139.355			−0.408667
$342$	2.05063	−	3.80949i	0.00599600	−	0.0111389i
$343$	293.366			0.855294
$344$	−19.4669	−	217.272i	−0.0565899	−	0.631604i
$345$	126.036	+	75.0289i	0.365321	+	0.217475i
$346$	−33.0337	+	61.3672i	−0.0954731	+	0.177362i
$347$	126.540			0.364669			0.182334	−	0.983237i	$-0.441635\pi$
$347$	126.540			0.364669			0.182334	+	0.983237i	$0.441635\pi$
$348$	−318.296	−	482.479i	−0.914644	−	1.38643i
$349$	−251.421			−0.720403			−0.360201	−	0.932875i	$-0.617292\pi$
$349$	−251.421			−0.720403			−0.360201	+	0.932875i	$0.617292\pi$
$350$	1.19184	+	387.893i	0.00340526	+	1.10826i
$351$			189.205i			0.539047i
$352$	−66.1167	−	83.0216i	−0.187832	−	0.235857i
$353$			253.680i			0.718641i	0.933214	+	0.359321i	$0.116992\pi$
$353$			253.680i			0.718641i	−0.933214	+	0.359321i	$0.883008\pi$
$354$	−320.754	+	595.870i	−0.906084	+	1.68325i
$355$	−173.475	+	291.409i	−0.488663	+	0.820870i
$356$	232.284	+	352.100i	0.652483	+	0.989046i
$357$		−	59.7163i		−	0.167273i
$358$	145.393	−	270.098i	0.406125	−	0.754464i
$359$			70.2196i			0.195598i	0.995206	+	0.0977988i	$0.0311802\pi$
$359$			70.2196i			0.195598i	−0.995206	+	0.0977988i	$0.968820\pi$
$360$	−28.7861	+	59.9591i	−0.0799613	+	0.166553i
$361$	359.308			0.995312
$362$	−507.722	−	273.304i	−1.40255	−	0.754984i
$363$	35.9193			0.0989512
$364$	204.556	−	134.947i	0.561966	−	0.370735i
$365$	344.509	−	578.717i	0.943861	−	1.58552i
$366$	−357.914	−	192.663i	−0.977907	−	0.526403i
$367$	−158.745			−0.432546			−0.216273	−	0.976333i	$-0.569390\pi$
$367$	−158.745			−0.432546			−0.216273	+	0.976333i	$0.569390\pi$
$368$	−56.5643	+	132.143i	−0.153707	+	0.359084i
$369$	−13.3226			−0.0361045
$370$	−374.195	+	224.318i	−1.01134	+	0.606265i
$371$			161.035i			0.434058i
$372$	−458.103	+	302.216i	−1.23146	+	0.812407i
$373$			224.454i			0.601752i	0.953663	+	0.300876i	$0.0972791\pi$
$373$			224.454i			0.601752i	−0.953663	+	0.300876i	$0.902721\pi$
$374$	13.7685	+	7.41151i	0.0368141	+	0.0198169i
$375$	−16.3513	+	407.846i	−0.0436035	+	1.08759i
$376$	16.3471	+	182.451i	0.0434763	+	0.485242i
$377$			349.469i			0.926973i
$378$	327.330	+	176.200i	0.865952	+	0.466138i
$379$			111.817i			0.295032i	0.989060	+	0.147516i	$0.0471278\pi$
$379$			111.817i			0.295032i	−0.989060	+	0.147516i	$0.952872\pi$
$380$	25.9910	−	1.20205i	0.0683974	−	0.00316328i
$381$	−357.191			−0.937510
$382$	72.6140	−	134.896i	0.190089	−	0.353131i
$383$	−182.846			−0.477405			−0.238703	−	0.971093i	$-0.576722\pi$
$383$	−182.846			−0.477405			−0.238703	+	0.971093i	$0.576722\pi$
$384$	−397.392	−	129.532i	−1.03488	−	0.337323i
$385$	65.8074	−	110.545i	0.170928	−	0.287130i
$386$	39.3739	−	73.1456i	0.102005	−	0.189496i
$387$	45.3402			0.117158
$388$	625.621	−	412.728i	1.61242	−	1.06373i
$389$	201.340			0.517583			0.258791	−	0.965933i	$-0.416676\pi$
$389$	201.340			0.517583			0.258791	+	0.965933i	$0.416676\pi$
$390$	221.174	−	132.587i	0.567114	−	0.339966i
$391$		−	21.1774i		−	0.0541622i
$392$	−7.98504	−	89.1216i	−0.0203700	−	0.227351i
$393$		−	207.040i		−	0.526820i
$394$	−21.0795	+	39.1597i	−0.0535013	+	0.0993901i
$395$	77.7451	−	130.598i	0.196823	−	0.330629i
$396$	18.4133	−	12.1475i	0.0464983	−	0.0306754i
$397$		−	24.8704i		−	0.0626459i	−0.999509	−	0.0313230i	$-0.990028\pi$
$397$		−	24.8704i		−	0.0626459i	0.999509	−	0.0313230i	$-0.00997204\pi$
$398$	−313.656	+	582.684i	−0.788081	+	1.46403i
$399$			32.9561i			0.0825968i
$400$	−398.293	+	36.9198i	−0.995731	+	0.0922996i
$401$	291.237			0.726276			0.363138	−	0.931735i	$-0.381705\pi$
$401$	291.237			0.726276			0.363138	+	0.931735i	$0.381705\pi$
$402$	−142.016	−	76.4465i	−0.353273	−	0.190165i
$403$	331.814			0.823359
$404$	−232.330	−	352.170i	−0.575075	−	0.871708i
$405$	400.421	+	238.370i	0.988693	+	0.588568i
$406$	604.589	+	325.448i	1.48914	+	0.801595i
$407$	144.698			0.355523
$408$	61.3343	−	5.49538i	0.150329	−	0.0134691i
$409$	289.762			0.708465			0.354233	−	0.935157i	$-0.384742\pi$
$409$	289.762			0.708465			0.354233	+	0.935157i	$0.384742\pi$
$410$	−41.1957	−	68.7204i	−0.100477	−	0.167611i
$411$			537.973i			1.30894i
$412$	−164.046	−	248.664i	−0.398171	−	0.603554i
$413$		−	803.867i		−	1.94641i
$414$	−26.3068	−	14.1609i	−0.0635431	−	0.0342050i
$415$	−576.494	−	343.186i	−1.38914	−	0.826955i
$416$	157.428	+	197.679i	0.378433	+	0.475191i
$417$		−	687.107i		−	1.64774i
$418$	−7.59852	−	4.09025i	−0.0181783	−	0.00978528i
$419$			525.774i			1.25483i	0.778684	+	0.627416i	$0.215887\pi$
$419$			525.774i			1.25483i	−0.778684	+	0.627416i	$0.784113\pi$
$420$	−23.4068	−	506.110i	−0.0557305	−	1.20502i
$421$	810.112			1.92426			0.962128	−	0.272599i	$-0.0878833\pi$
$421$	810.112			1.92426			0.962128	+	0.272599i	$0.0878833\pi$
$422$	289.057	−	536.986i	0.684969	−	1.27248i
$423$	−38.0739			−0.0900092
$424$	−165.399	+	14.8192i	−0.390091	+	0.0349510i
$425$	51.8058	−	28.0925i	0.121896	−	0.0661000i
$426$	209.959	−	390.044i	0.492861	−	0.915596i
$427$	482.850			1.13080
$428$	7.14739	+	10.8341i	0.0166995	+	0.0253134i
$429$	−85.5261			−0.199361
$430$	140.200	+	233.874i	0.326046	+	0.543893i
$431$		−	612.824i		−	1.42186i	−0.703261	−	0.710932i	$-0.748273\pi$
$431$		−	612.824i		−	1.42186i	0.703261	−	0.710932i	$-0.251727\pi$
$432$	−150.852	+	352.413i	−0.349194	+	0.815771i
$433$			678.614i			1.56724i	0.621242	+	0.783618i	$0.286628\pi$
$433$			678.614i			1.56724i	−0.621242	+	0.783618i	$0.713372\pi$
$434$	309.006	−	574.045i	0.711995	−	1.32268i
$435$	620.835	+	369.583i	1.42721	+	0.849615i
$436$	444.374	+	673.590i	1.01921	+	1.54493i
$437$			11.6874i			0.0267445i
$438$	−416.963	+	774.599i	−0.951970	+	1.76849i
$439$			296.991i			0.676516i	0.941053	+	0.338258i	$0.109838\pi$
$439$			296.991i			0.676516i	−0.941053	+	0.338258i	$0.890162\pi$
$440$	119.596	+	57.4175i	0.271809	+	0.130494i
$441$	18.5979			0.0421721
$442$	−32.7836	−	17.6473i	−0.0741710	−	0.0399259i
$443$	−485.980			−1.09702			−0.548511	−	0.836144i	$-0.684805\pi$
$443$	−485.980			−1.09702			−0.548511	+	0.836144i	$0.684805\pi$
$444$	475.666	−	313.802i	1.07132	−	0.706761i
$445$	−453.069	−	269.712i	−1.01813	−	0.606094i
$446$	375.059	+	201.893i	0.840940	+	0.452674i
$447$	−75.4760			−0.168850
$448$	488.597	−	88.2623i	1.09062	−	0.197014i
$449$	−814.879			−1.81487			−0.907437	−	0.420187i	$-0.861964\pi$
$449$	−814.879			−1.81487			−0.907437	+	0.420187i	$0.861964\pi$
$450$	−0.255452	−	83.1386i	−0.000567671	−	0.184752i
$451$			26.5736i			0.0589214i
$452$	86.0070	−	56.7397i	0.190281	−	0.125530i
$453$		−	809.115i		−	1.78613i
$454$	−500.303	−	269.311i	−1.10199	−	0.593195i
$455$	−156.691	+	263.215i	−0.344377	+	0.578494i
$456$	−33.8490	+	3.03278i	−0.0742304	+	0.00665083i
$457$			67.5716i			0.147859i	0.997263	+	0.0739296i	$0.0235540\pi$
$457$			67.5716i			0.147859i	−0.997263	+	0.0739296i	$0.976446\pi$
$458$	499.835	+	269.059i	1.09134	+	0.587464i
$459$		−	56.4782i		−	0.123046i
$460$	−8.30085	−	179.484i	−0.0180453	−	0.390182i
$461$	−814.074			−1.76589			−0.882944	−	0.469479i	$-0.844442\pi$
$461$	−814.074			−1.76589			−0.882944	+	0.469479i	$0.844442\pi$
$462$	−79.6473	+	147.962i	−0.172397	+	0.320264i
$463$	238.511			0.515143			0.257571	−	0.966259i	$-0.417078\pi$
$463$	238.511			0.515143			0.257571	+	0.966259i	$0.417078\pi$
$464$	−278.628	+	650.919i	−0.600492	+	1.40284i
$465$	350.911	−	589.470i	0.754647	−	1.26768i
$466$	414.333	−	769.713i	0.889126	−	1.65174i
$467$	−562.265			−1.20399			−0.601997	−	0.798499i	$-0.705628\pi$
$467$	−562.265			−1.20399			−0.601997	+	0.798499i	$0.705628\pi$
$468$	−43.8432	+	28.9238i	−0.0936821	+	0.0618031i
$469$	191.589			0.408505
$470$	−117.731	−	196.393i	−0.250492	−	0.417857i
$471$		−	415.336i		−	0.881818i
$472$	825.647	−	73.9756i	1.74925	−	0.156728i
$473$		−	90.4369i		−	0.191199i
$474$	−94.0956	+	174.803i	−0.198514	+	0.368783i
$475$	−28.5905	+	15.5036i	−0.0601905	+	0.0326392i
$476$	−61.0603	+	40.2821i	−0.128278	+	0.0846263i
$477$		−	34.5154i		−	0.0723593i
$478$	73.4517	−	136.452i	0.153665	−	0.285465i
$479$		−	561.970i		−	1.17322i	−0.809871	−	0.586608i	$-0.800463\pi$
$479$		−	561.970i		−	1.17322i	0.809871	−	0.586608i	$-0.199537\pi$
$480$	517.668	−	70.6156i	1.07848	−	0.147116i
$481$	−344.535			−0.716288
$482$	109.513	+	58.9505i	0.227206	+	0.122304i
$483$	227.582			0.471184
$484$	−24.2296	−	36.7277i	−0.0500612	−	0.0758837i
$485$	−479.231	+	805.026i	−0.988105	+	1.65985i
$486$	−156.215	−	84.0899i	−0.321430	−	0.173024i
$487$	−647.303			−1.32916			−0.664582	−	0.747216i	$-0.731390\pi$
$487$	−647.303			−1.32916			−0.664582	+	0.747216i	$0.731390\pi$
$488$	44.4341	+	495.932i	0.0910535	+	1.01625i
$489$	−648.354			−1.32588
$490$	57.5079	+	95.9316i	0.117363	+	0.195779i
$491$		−	342.511i		−	0.697578i	−0.937201	−	0.348789i	$-0.886593\pi$
$491$		−	342.511i		−	0.697578i	0.937201	−	0.348789i	$-0.113407\pi$
$492$	57.6293	+	87.3554i	0.117133	+	0.177552i
$493$		−	104.317i		−	0.211597i
$494$	18.0925	+	9.73913i	0.0366246	+	0.0197148i
$495$	−14.1048	+	23.6936i	−0.0284945	+	0.0478658i
$496$	618.034	+	264.552i	1.24604	+	0.533370i
$497$			526.195i			1.05874i
$498$	771.624	+	415.362i	1.54945	+	0.834059i
$499$		−	768.711i		−	1.54050i	−0.637740	−	0.770252i	$-0.720131\pi$
$499$		−	768.711i		−	1.54050i	0.637740	−	0.770252i	$-0.279869\pi$
$500$	428.055	−	258.397i	0.856110	−	0.516793i
$501$	−277.535			−0.553963
$502$	−173.206	+	321.767i	−0.345031	+	0.640970i
$503$	−36.0810			−0.0717316			−0.0358658	−	0.999357i	$-0.511419\pi$
$503$	−36.0810			−0.0717316			−0.0358658	+	0.999357i	$0.511419\pi$
$504$	9.20929	+	102.785i	0.0182724	+	0.203939i
$505$	453.160	+	269.765i	0.897346	+	0.534189i
$506$	−28.2456	+	52.4724i	−0.0558214	+	0.103700i
$507$	−348.208			−0.686801
$508$	240.946	+	365.230i	0.474303	+	0.718957i
$509$	−549.953			−1.08046			−0.540229	−	0.841518i	$-0.681662\pi$
$509$	−549.953			−1.08046			−0.540229	+	0.841518i	$0.681662\pi$
$510$	−66.0210	+	39.5775i	−0.129453	+	0.0776029i
$511$		−	1044.98i		−	2.04498i
$512$	135.617	+	493.713i	0.264876	+	0.964282i
$513$			31.1691i			0.0607585i
$514$	−11.0073	+	20.4485i	−0.0214150	+	0.0397830i
$515$	319.972	+	190.479i	0.621305	+	0.369862i
$516$	−196.128	−	297.294i	−0.380092	−	0.576150i
$517$			75.9432i			0.146892i
$518$	−320.852	+	596.053i	−0.619406	+	1.15068i
$519$			113.788i			0.219245i
$520$	−284.766	−	136.715i	−0.547626	−	0.262913i
$521$	−604.392			−1.16006			−0.580031	−	0.814594i	$-0.696960\pi$
$521$	−604.392			−1.16006			−0.580031	+	0.814594i	$0.696960\pi$
$522$	−129.584	−	69.7545i	−0.248245	−	0.133629i
$523$	403.082			0.770711			0.385355	−	0.922768i	$-0.374079\pi$
$523$	403.082			0.770711			0.385355	+	0.922768i	$0.374079\pi$
$524$	−211.700	+	139.661i	−0.404007	+	0.266528i
$525$	301.894	+	556.728i	0.575036	+	1.06043i
$526$	416.800	+	224.362i	0.792396	+	0.426543i
$527$	−99.0470			−0.187945
$528$	−159.300	−	68.1891i	−0.301705	−	0.129146i
$529$	−448.292			−0.847432
$530$	178.037	−	106.728i	0.335919	−	0.201373i
$531$			172.296i			0.324475i
$532$	33.6978	−	22.2308i	0.0633418	−	0.0417872i
$533$		−	63.2733i		−	0.118712i
$534$	606.423	+	326.435i	1.13562	+	0.611301i
$535$	−13.9410	−	8.29904i	−0.0260579	−	0.0155122i
$536$	17.6309	+	196.780i	0.0328935	+	0.367126i
$537$		−	500.820i		−	0.932626i
$538$	174.711	+	94.0463i	0.324742	+	0.174807i
$539$		−	37.0959i		−	0.0688235i
$540$	−22.1376	−	478.666i	−0.0409956	−	0.886419i
$541$	1034.60			1.91238			0.956191	−	0.292742i	$-0.0945677\pi$
$541$	1034.60			1.91238			0.956191	+	0.292742i	$0.0945677\pi$
$542$	−167.974	+	312.049i	−0.309916	+	0.575736i
$543$	−941.425			−1.73375
$544$	−46.9926	−	59.0077i	−0.0863834	−	0.108470i
$545$	−866.750	−	515.976i	−1.59037	−	0.946744i
$546$	189.645	−	352.307i	0.347335	−	0.645250i
$547$	408.105			0.746078			0.373039	−	0.927816i	$-0.378316\pi$
$547$	408.105			0.746078			0.373039	+	0.927816i	$0.378316\pi$
$548$	550.081	−	362.894i	1.00380	−	0.662215i
$549$	−103.491			−0.188508
$550$	−165.830	+	0.509532i	−0.301510	+	0.000926421i
$551$			57.5704i			0.104483i
$552$	20.9432	+	233.748i	0.0379405	+	0.423457i
$553$		−	235.821i		−	0.426439i
$554$	312.188	−	579.957i	0.563517	−	1.04685i
$555$	−364.364	+	612.070i	−0.656512	+	1.10283i
$556$	−702.571	+	463.493i	−1.26362	+	0.833621i
$557$		−	625.200i		−	1.12244i	−0.827666	−	0.561221i	$-0.810332\pi$
$557$		−	625.200i		−	1.12244i	0.827666	−	0.561221i	$-0.189668\pi$
$558$	−66.2304	+	123.037i	−0.118693	+	0.220497i
$559$			215.336i			0.385216i
$560$	−501.711	+	365.334i	−0.895913	+	0.652382i
$561$	25.5297			0.0455075
$562$	−487.203	−	262.259i	−0.866909	−	0.466653i
$563$	−964.852			−1.71377			−0.856885	−	0.515508i	$-0.827603\pi$
$563$	−964.852			−1.71377			−0.856885	+	0.515508i	$0.827603\pi$
$564$	164.696	+	249.648i	0.292014	+	0.442639i
$565$	−65.8821	+	110.671i	−0.116605	+	0.195877i
$566$	−739.001	−	397.801i	−1.30566	−	0.702828i
$567$	723.037			1.27520
$568$	−540.452	+	48.4229i	−0.951500	+	0.0852517i
$569$	419.250			0.736819			0.368410	−	0.929664i	$-0.379902\pi$
$569$	419.250			0.736819			0.368410	+	0.929664i	$0.379902\pi$
$570$	36.4355	−	21.8419i	0.0639220	−	0.0383192i
$571$			480.490i			0.841488i	0.907179	+	0.420744i	$0.138231\pi$
$571$			480.490i			0.841488i	−0.907179	+	0.420744i	$0.861769\pi$
$572$	57.6923	+	87.4509i	0.100861	+	0.152886i
$573$		−	250.127i		−	0.436521i
$574$	−109.464	−	58.9241i	−0.190704	−	0.102655i
$575$	107.062	+	197.435i	0.186195	+	0.343365i
$576$	−104.723	+	18.9176i	−0.181811	+	0.0328431i
$577$		−	530.014i		−	0.918568i	−0.888290	−	0.459284i	$-0.848106\pi$
$577$		−	530.014i		−	0.918568i	0.888290	−	0.459284i	$-0.151894\pi$
$578$	−499.162	−	268.696i	−0.863601	−	0.464873i
$579$		−	135.628i		−	0.234244i
$580$	−40.8889	−	884.113i	−0.0704981	−	1.52433i
$581$	−1040.97			−1.79169
$582$	580.018	−	1077.51i	0.996594	−	1.85139i
$583$	−68.8453			−0.118088
$584$	1073.30	−	96.1644i	1.83784	−	0.164665i
$585$	33.5843	−	56.4158i	0.0574090	−	0.0964373i
$586$	−431.024	+	800.719i	−0.735535	+	1.36642i
$587$	210.959			0.359384			0.179692	−	0.983723i	$-0.442490\pi$
$587$	210.959			0.359384			0.179692	+	0.983723i	$0.442490\pi$
$588$	−80.4487	−	121.945i	−0.136817	−	0.207390i
$589$	54.6619			0.0928046
$590$	−888.737	+	532.769i	−1.50633	+	0.902999i
$591$			72.6105i			0.122860i
$592$	−641.729	−	274.694i	−1.08400	−	0.464010i
$593$		−	1.45476i		−	0.00245323i	−0.999999	−	0.00122661i	$-0.999610\pi$
$593$		−	1.45476i		−	0.00245323i	0.999999	−	0.00122661i	$-0.000390443\pi$
$594$	−75.3285	+	139.939i	−0.126816	+	0.235587i
$595$	46.7727	−	78.5701i	0.0786096	−	0.132051i
$596$	50.9129	+	77.1747i	0.0854244	+	0.129488i
$597$			1080.42i			1.80975i
$598$	67.2546	−	124.940i	0.112466	−	0.208930i
$599$			393.291i			0.656580i	0.944577	+	0.328290i	$0.106472\pi$
$599$			393.291i			0.656580i	−0.944577	+	0.328290i	$0.893528\pi$
$600$	−544.030	+	361.306i	−0.906717	+	0.602177i
$601$	133.932			0.222848			0.111424	−	0.993773i	$-0.464459\pi$
$601$	133.932			0.222848			0.111424	+	0.993773i	$0.464459\pi$
$602$	372.536	+	200.534i	0.618830	+	0.333113i
$603$	−41.0640			−0.0680995
$604$	−827.325	+	545.795i	−1.36974	+	0.903634i
$605$	47.2598	+	28.1337i	0.0781155	+	0.0465020i
$606$	−606.543	−	326.500i	−1.00090	−	0.538778i
$607$	−548.156			−0.903057			−0.451529	−	0.892257i	$-0.649121\pi$
$607$	−548.156			−0.903057			−0.451529	+	0.892257i	$0.649121\pi$
$608$	25.9342	+	32.5651i	0.0426549	+	0.0535610i
$609$	1121.04			1.84079
$610$	−320.012	−	533.827i	−0.524610	−	0.875127i
$611$		−	180.825i		−	0.295950i
$612$	13.0873	−	8.63382i	0.0213845	−	0.0141076i
$613$		−	702.562i		−	1.14611i	−0.819519	−	0.573053i	$-0.805759\pi$
$613$		−	702.562i		−	1.14611i	0.819519	−	0.573053i	$-0.194241\pi$
$614$	−360.805	−	194.220i	−0.587631	−	0.316319i
$615$	−112.406	−	66.9150i	−0.182773	−	0.108805i
$616$	205.019	−	18.3691i	0.332823	−	0.0298200i
$617$			529.451i			0.858105i	0.903279	+	0.429053i	$0.141153\pi$
$617$			529.451i			0.858105i	−0.903279	+	0.429053i	$0.858847\pi$
$618$	−428.275	−	230.539i	−0.693002	−	0.373040i
$619$			277.440i			0.448207i	0.974565	+	0.224103i	$0.0719453\pi$
$619$			277.440i			0.448207i	−0.974565	+	0.224103i	$0.928055\pi$
$620$	−839.447	+	38.8232i	−1.35395	+	0.0626180i
$621$	215.241			0.346605
$622$	−229.214	+	425.814i	−0.368511	+	0.684588i
$623$	−818.104			−1.31317
$624$	379.304	+	162.362i	0.607859	+	0.260196i
$625$	−340.959	+	523.806i	−0.545534	+	0.838089i
$626$	545.752	−	1013.85i	0.871809	−	1.61957i
$627$	−14.0893			−0.0224709
$628$	−424.684	+	280.168i	−0.676248	+	0.446128i
$629$	102.844			0.163504
$630$	−66.3249	−	110.640i	−0.105278	−	0.175618i
$631$			860.452i			1.36363i	0.731523	+	0.681816i	$0.238810\pi$
$631$			860.452i			1.36363i	−0.731523	+	0.681816i	$0.761190\pi$
$632$	242.210	−	21.7013i	0.383244	−	0.0343375i
$633$		−	995.687i		−	1.57297i
$634$	−52.3506	+	97.2526i	−0.0825720	+	0.153395i
$635$	−469.965	−	279.769i	−0.740102	−	0.440582i
$636$	−226.316	+	149.303i	−0.355842	+	0.234753i
$637$			88.3276i			0.138662i
$638$	−139.134	+	258.472i	−0.218079	+	0.405128i
$639$		−	112.781i		−	0.176497i
$640$	−421.402	−	481.685i	−0.658441	−	0.752632i
$641$	−75.1870			−0.117296			−0.0586482	−	0.998279i	$-0.518679\pi$
$641$	−75.1870			−0.117296			−0.0586482	+	0.998279i	$0.518679\pi$
$642$	18.6597	+	10.0444i	0.0290649	+	0.0156455i
$643$	−424.833			−0.660705			−0.330353	−	0.943858i	$-0.607168\pi$
$643$	−424.833			−0.660705			−0.330353	+	0.943858i	$0.607168\pi$
$644$	−153.517	−	232.704i	−0.238381	−	0.361341i
$645$	382.546	+	227.729i	0.593095	+	0.353069i
$646$	−5.40066	−	2.90715i	−0.00836016	−	0.00450023i
$647$	1223.36			1.89082			0.945408	−	0.325888i	$-0.105663\pi$
$647$	1223.36			1.89082			0.945408	+	0.325888i	$0.105663\pi$
$648$	66.5372	+	742.627i	0.102681	+	1.14603i
$649$	343.666			0.529532
$650$	394.852	−	1.21323i	0.607465	−	0.00186650i
$651$		−	1064.40i		−	1.63503i
$652$	437.352	+	662.946i	0.670786	+	1.01679i
$653$		−	402.337i		−	0.616136i	−0.951364	−	0.308068i	$-0.900318\pi$
$653$		−	402.337i		−	0.616136i	0.951364	−	0.308068i	$-0.0996825\pi$
$654$	1160.13	+	624.490i	1.77389	+	0.954878i
$655$	162.164	−	272.407i	0.247578	−	0.415889i
$656$	50.4472	−	117.853i	0.0769012	−	0.179653i
$657$			223.976i			0.340907i
$658$	−312.832	−	168.396i	−0.475429	−	0.255921i
$659$			786.640i			1.19369i	0.802358	+	0.596844i	$0.203579\pi$
$659$			786.640i			1.19369i	−0.802358	+	0.596844i	$0.796421\pi$
$660$	216.370	−	10.0068i	0.327834	−	0.0151618i
$661$	−23.1541			−0.0350289			−0.0175144	−	0.999847i	$-0.505575\pi$
$661$	−23.1541			−0.0350289			−0.0175144	+	0.999847i	$0.505575\pi$
$662$	−145.446	+	270.198i	−0.219707	+	0.408154i
$663$	−60.7878			−0.0916860
$664$	−95.7951	−	1069.18i	−0.144270	−	1.61020i
$665$	−25.8128	+	43.3611i	−0.0388163	+	0.0652047i
$666$	68.7696	−	127.754i	0.103258	−	0.191823i
$667$	397.558			0.596039
$668$	187.214	+	283.782i	0.280260	+	0.424823i
$669$	695.441			1.03952
$670$	−126.977	−	211.816i	−0.189518	−	0.316143i
$671$			206.426i			0.307640i
$672$	634.123	−	505.003i	0.943635	−	0.751492i
$673$		−	517.445i		−	0.768863i	−0.923154	−	0.384431i	$-0.874398\pi$
$673$		−	517.445i		−	0.768863i	0.923154	−	0.384431i	$-0.125602\pi$
$674$	−88.2736	+	163.987i	−0.130970	+	0.243305i
$675$	285.524	+	526.540i	0.422998	+	0.780059i
$676$	234.887	+	356.045i	0.347465	+	0.526694i
$677$			778.816i			1.15039i	0.818015	+	0.575196i	$0.195074\pi$
$677$			778.816i			1.15039i	−0.818015	+	0.575196i	$0.804926\pi$
$678$	79.7377	−	148.130i	0.117607	−	0.218481i
$679$			1453.63i			2.14084i
$680$	85.0032	+	40.8096i	0.125005	+	0.0600141i
$681$	−927.669			−1.36222
$682$	245.414	+	132.105i	0.359844	+	0.193702i
$683$	464.710			0.680395			0.340198	−	0.940354i	$-0.389506\pi$
$683$	464.710			0.680395			0.340198	+	0.940354i	$0.389506\pi$
$684$	−7.22259	+	4.76482i	−0.0105593	+	0.00696611i
$685$	−421.366	+	707.823i	−0.615133	+	1.03332i
$686$	−516.636	−	278.103i	−0.753114	−	0.405398i
$687$	926.800			1.34905
$688$	−171.685	+	401.083i	−0.249542	+	0.582970i
$689$	163.925			0.237917
$690$	−150.832	−	251.609i	−0.218597	−	0.364651i
$691$			266.654i			0.385895i	0.981209	+	0.192948i	$0.0618048\pi$
$691$			266.654i			0.385895i	−0.981209	+	0.192948i	$0.938195\pi$
$692$	116.349	−	76.7566i	0.168134	−	0.110920i
$693$			42.7833i			0.0617364i
$694$	−222.845	−	119.956i	−0.321102	−	0.172848i
$695$	538.175	−	904.042i	0.774353	−	1.30078i
$696$	103.163	+	1151.41i	0.148223	+	1.65433i
$697$			18.8872i			0.0270979i
$698$	442.768	+	238.340i	0.634338	+	0.341461i
$699$		−	1427.21i		−	2.04179i
$700$	365.613	−	684.234i	0.522304	−	0.977477i
$701$	439.035			0.626298			0.313149	−	0.949704i	$-0.398616\pi$
$701$	439.035			0.626298			0.313149	+	0.949704i	$0.398616\pi$
$702$	179.362	−	333.203i	0.255501	−	0.474648i
$703$	−56.7575			−0.0807362
$704$	37.7336	+	208.883i	0.0535988	+	0.296709i
$705$	−321.238	−	191.233i	−0.455657	−	0.271252i
$706$	240.482	−	446.747i	0.340626	−	0.632787i
$707$	818.267			1.15738
$708$	1129.74	−	745.299i	1.59567	−	1.05268i
$709$	300.512			0.423854			0.211927	−	0.977286i	$-0.432026\pi$
$709$	300.512			0.423854			0.211927	+	0.977286i	$0.432026\pi$
$710$	581.749	−	348.740i	0.819365	−	0.491183i
$711$			50.5444i			0.0710891i
$712$	−75.2858	−	840.270i	−0.105738	−	1.18015i
$713$		−	377.473i		−	0.529416i
$714$	−56.6094	+	105.164i	−0.0792849	+	0.147289i
$715$	−112.529	−	66.9881i	−0.157383	−	0.0936897i
$716$	−512.091	+	337.832i	−0.715212	+	0.471832i
$717$		−	253.012i		−	0.352876i
$718$	66.5662	−	123.661i	0.0927106	−	0.172230i
$719$		−	999.784i		−	1.39052i	−0.718758	−	0.695260i	$-0.755289\pi$
$719$		−	999.784i		−	1.39052i	0.718758	−	0.695260i	$-0.244711\pi$
$720$	107.534	−	78.3035i	0.149352	−	0.108755i
$721$	577.771			0.801347
$722$	−632.764	−	340.614i	−0.876404	−	0.471764i
$723$	203.061			0.280859
$724$	635.045	+	962.613i	0.877134	+	1.32958i
$725$	527.373	+	972.537i	0.727410	+	1.34143i
$726$	−63.2562	−	34.0505i	−0.0871298	−	0.0469015i
$727$	265.278			0.364894			0.182447	−	0.983216i	$-0.441598\pi$
$727$	265.278			0.364894			0.182447	+	0.983216i	$0.441598\pi$
$728$	−488.162	+	43.7379i	−0.670553	+	0.0600796i
$729$	549.145			0.753286
$730$	−1155.31	+	692.572i	−1.58262	+	0.948728i
$731$		−	64.2782i		−	0.0879318i
$732$	447.670	+	678.586i	0.611571	+	0.927030i
$733$			200.371i			0.273358i	0.990615	+	0.136679i	$0.0436429\pi$
$733$			200.371i			0.273358i	−0.990615	+	0.136679i	$0.956357\pi$
$734$	279.559	+	150.486i	0.380871	+	0.205021i
$735$	156.915	+	93.4112i	0.213490	+	0.127090i
$736$	224.881	−	179.091i	0.305545	−	0.243330i
$737$			81.9073i			0.111136i
$738$	23.4619	+	12.6294i	0.0317912	+	0.0171131i
$739$			1019.28i			1.37927i	0.724159	+	0.689633i	$0.242228\pi$
$739$			1019.28i			1.37927i	−0.724159	+	0.689633i	$0.757772\pi$
$740$	871.630	−	40.3116i	1.17788	−	0.0544751i
$741$	33.5475			0.0452732
$742$	152.657	−	283.594i	0.205738	−	0.382202i
$743$	−488.362			−0.657284			−0.328642	−	0.944455i	$-0.606591\pi$
$743$	−488.362			−0.657284			−0.328642	+	0.944455i	$0.606591\pi$
$744$	1093.24	−	97.9513i	1.46941	−	0.131655i
$745$	−99.3055	−	59.1165i	−0.133296	−	0.0793510i
$746$	212.776	−	395.277i	0.285222	−	0.529862i
$747$	223.115			0.298682
$748$	−17.2213	−	26.1043i	−0.0230231	−	0.0348988i
$749$	−25.1731			−0.0336089
$750$	415.423	−	702.743i	0.553897	−	0.936990i
$751$			851.690i			1.13407i	0.823692	+	0.567037i	$0.191910\pi$
$751$			851.690i			1.13407i	−0.823692	+	0.567037i	$0.808090\pi$
$752$	144.170	−	336.805i	0.191716	−	0.447878i
$753$			596.625i			0.792331i
$754$	331.287	−	615.437i	0.439373	−	0.816230i
$755$	633.738	−	1064.57i	0.839388	−	1.41003i
$756$	−409.416	−	620.600i	−0.541555	−	0.820899i
$757$		−	713.863i		−	0.943016i	−0.881862	−	0.471508i	$-0.843710\pi$
$757$		−	713.863i		−	0.943016i	0.881862	−	0.471508i	$-0.156290\pi$
$758$	106.000	−	196.917i	0.139841	−	0.259785i
$759$			97.2950i			0.128188i
$760$	−46.9114	−	22.5219i	−0.0617255	−	0.0296341i
$761$	−783.401			−1.02944			−0.514718	−	0.857360i	$-0.672103\pi$
$761$	−783.401			−1.02944			−0.514718	+	0.857360i	$0.672103\pi$
$762$	629.037	+	338.608i	0.825507	+	0.444367i
$763$	−1565.09			−2.05123
$764$	−255.756	+	168.725i	−0.334759	+	0.220844i
$765$	−10.0250	+	16.8402i	−0.0131045	+	0.0220134i
$766$	322.004	+	173.333i	0.420371	+	0.226284i
$767$	−818.291			−1.06687
$768$	577.040	+	604.831i	0.751354	+	0.787540i
$769$	−373.200			−0.485305			−0.242653	−	0.970113i	$-0.578018\pi$
$769$	−373.200			−0.485305			−0.242653	+	0.970113i	$0.578018\pi$
$770$	−220.685	+	132.293i	−0.286604	+	0.171810i
$771$			37.9158i			0.0491775i
$772$	−138.680	+	91.4886i	−0.179637	+	0.118509i
$773$		−	209.208i		−	0.270645i	−0.990802	−	0.135322i	$-0.956793\pi$
$773$		−	209.208i		−	0.270645i	0.990802	−	0.135322i	$-0.0432070\pi$
$774$	−79.8471	−	42.9813i	−0.103162	−	0.0555314i
$775$	923.403	−

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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76106 - 0.947973i) q^{2} -3.26539 q^{3} +(2.20269 + 3.33888i) q^{4} +(-4.29635 - 2.55761i) q^{5} +(5.75056 + 3.09550i) q^{6} -7.75789 q^{7} +(-0.713917 - 7.96808i) q^{8} +1.66278 q^{9} +(5.14160 + 8.57694i) q^{10} -3.31662i q^{11} +(-7.19266 - 10.9028i) q^{12} +7.89709i q^{13} +(13.6621 + 7.35427i) q^{14} +(14.0293 + 8.35160i) q^{15} +(-6.29627 + 14.7091i) q^{16} -2.35730i q^{17} +(-2.92826 - 1.57627i) q^{18} +1.30094i q^{19} +(-0.923982 - 19.9786i) q^{20} +25.3325 q^{21} +(-3.14407 + 5.84079i) q^{22} +8.98378 q^{23} +(2.33122 + 26.0189i) q^{24} +(11.9172 + 21.9768i) q^{25} +(7.48622 - 13.9073i) q^{26} +23.9589 q^{27} +(-17.0883 - 25.9027i) q^{28} +44.2529 q^{29} +(-16.7893 - 28.0071i) q^{30} -42.0172i q^{31} +(25.0319 - 19.9349i) q^{32} +10.8301i q^{33} +(-2.23465 + 4.15135i) q^{34} +(33.3306 + 19.8417i) q^{35} +(3.66259 + 5.55182i) q^{36} +43.6281i q^{37} +(1.23326 - 2.29104i) q^{38} -25.7871i q^{39} +(-17.3120 + 36.0596i) q^{40} -8.01223 q^{41} +(-44.6122 - 24.0146i) q^{42} +27.2677 q^{43} +(11.0738 - 7.30551i) q^{44} +(-7.14388 - 4.25274i) q^{45} +(-15.8210 - 8.51638i) q^{46} -22.8977 q^{47} +(20.5598 - 48.0309i) q^{48} +11.1848 q^{49} +(-0.153630 - 49.9998i) q^{50} +7.69750i q^{51} +(-26.3674 + 17.3949i) q^{52} -20.7576i q^{53} +(-42.1932 - 22.7124i) q^{54} +(-8.48264 + 14.2494i) q^{55} +(5.53849 + 61.8155i) q^{56} -4.24808i q^{57} +(-77.9322 - 41.9505i) q^{58} +103.619i q^{59} +(3.01716 + 65.2381i) q^{60} -62.2398 q^{61} +(-39.8312 + 73.9950i) q^{62} -12.8997 q^{63} +(-62.9806 + 11.3771i) q^{64} +(20.1977 - 33.9286i) q^{65} +(10.2666 - 19.0725i) q^{66} -24.6960 q^{67} +(7.87074 - 5.19241i) q^{68} -29.3355 q^{69} +(-39.8880 - 66.5390i) q^{70} -67.8271i q^{71} +(-1.18709 - 13.2492i) q^{72} +134.700i q^{73} +(41.3582 - 76.8318i) q^{74} +(-38.9145 - 71.7628i) q^{75} +(-4.34369 + 2.86557i) q^{76} +25.7300i q^{77} +(-24.4455 + 45.4127i) q^{78} +30.3975i q^{79} +(64.6711 - 47.0919i) q^{80} -93.2002 q^{81} +(14.1101 + 7.59538i) q^{82} +134.182 q^{83} +(55.7999 + 84.5824i) q^{84} +(-6.02905 + 10.1278i) q^{85} +(-48.0203 - 25.8491i) q^{86} -144.503 q^{87} +(-26.4271 + 2.36780i) q^{88} +105.455 q^{89} +(8.54935 + 14.2616i) q^{90} -61.2647i q^{91} +(19.7885 + 29.9958i) q^{92} +137.203i q^{93} +(40.3244 + 21.7064i) q^{94} +(3.32730 - 5.58930i) q^{95} +(-81.7391 + 65.0954i) q^{96} -187.374i q^{97} +(-19.6972 - 10.6029i) q^{98} -5.51481i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9} - 18 q^{10} - 56 q^{14} - 40 q^{16} + 84 q^{20} - 16 q^{21} + 104 q^{24} - 60 q^{25} + 28 q^{26} - 88 q^{29} - 166 q^{30} - 152 q^{34} - 248 q^{36} + 132 q^{40}+ \cdots + 216 q^{96}+O(q^{100}) \) 60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

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