LMFDB - Embedded newform 220.3.h.a.199.7

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			199.7
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80241 - 0.866788i) q^{2} -2.17924 q^{3} +(2.49736 + 3.12461i) q^{4} +(4.97895 + 0.458348i) q^{5} +(3.92787 + 1.88893i) q^{6} +1.79794 q^{7} +(-1.79289 - 7.79651i) q^{8} -4.25093 q^{9} +(-8.57681 - 5.14182i) q^{10} +3.31662i q^{11} +(-5.44233 - 6.80927i) q^{12} +8.71425i q^{13} +(-3.24062 - 1.55843i) q^{14} +(-10.8503 - 0.998848i) q^{15} +(-3.52640 + 15.6066i) q^{16} +14.4238i q^{17} +(7.66192 + 3.68466i) q^{18} -9.47058i q^{19} +(11.0021 + 16.7019i) q^{20} -3.91813 q^{21} +(2.87481 - 5.97792i) q^{22} +24.9253 q^{23} +(3.90712 + 16.9904i) q^{24} +(24.5798 + 4.56418i) q^{25} +(7.55340 - 15.7066i) q^{26} +28.8769 q^{27} +(4.49010 + 5.61786i) q^{28} +17.4712 q^{29} +(18.6909 + 11.2052i) q^{30} +52.1631i q^{31} +(19.8836 - 25.0727i) q^{32} -7.22771i q^{33} +(12.5024 - 25.9977i) q^{34} +(8.95184 + 0.824081i) q^{35} +(-10.6161 - 13.2825i) q^{36} +38.4324i q^{37} +(-8.20898 + 17.0699i) q^{38} -18.9904i q^{39} +(-5.35317 - 39.6402i) q^{40} +32.3568 q^{41} +(7.06208 + 3.39619i) q^{42} -29.7743 q^{43} +(-10.3632 + 8.28280i) q^{44} +(-21.1652 - 1.94840i) q^{45} +(-44.9255 - 21.6049i) q^{46} +50.4820 q^{47} +(7.68487 - 34.0104i) q^{48} -45.7674 q^{49} +(-40.3467 - 29.5320i) q^{50} -31.4330i q^{51} +(-27.2286 + 21.7626i) q^{52} +84.9022i q^{53} +(-52.0480 - 25.0301i) q^{54} +(-1.52017 + 16.5133i) q^{55} +(-3.22350 - 14.0176i) q^{56} +20.6386i q^{57} +(-31.4902 - 15.1438i) q^{58} -14.3540i q^{59} +(-23.9761 - 36.3975i) q^{60} +15.8302 q^{61} +(45.2143 - 94.0192i) q^{62} -7.64291 q^{63} +(-57.5711 + 27.9565i) q^{64} +(-3.99415 + 43.3878i) q^{65} +(-6.26489 + 13.0273i) q^{66} +25.5295 q^{67} +(-45.0689 + 36.0215i) q^{68} -54.3180 q^{69} +(-15.4206 - 9.24468i) q^{70} +43.8755i q^{71} +(7.62144 + 33.1424i) q^{72} -106.971i q^{73} +(33.3127 - 69.2708i) q^{74} +(-53.5653 - 9.94642i) q^{75} +(29.5919 - 23.6514i) q^{76} +5.96309i q^{77} +(-16.4606 + 34.2285i) q^{78} -109.043i q^{79} +(-24.7110 + 76.0879i) q^{80} -24.6712 q^{81} +(-58.3202 - 28.0465i) q^{82} -11.4695 q^{83} +(-9.78498 - 12.2426i) q^{84} +(-6.61113 + 71.8156i) q^{85} +(53.6654 + 25.8080i) q^{86} -38.0738 q^{87} +(25.8581 - 5.94633i) q^{88} -74.3785 q^{89} +(36.4594 + 21.8575i) q^{90} +15.6677i q^{91} +(62.2473 + 77.8818i) q^{92} -113.676i q^{93} +(-90.9892 - 43.7572i) q^{94} +(4.34082 - 47.1535i) q^{95} +(-43.3310 + 54.6394i) q^{96} +7.94927i q^{97} +(82.4916 + 39.6706i) q^{98} -14.0987i 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 $

$2$	−1.80241	−	0.866788i	−0.901205	−	0.433394i
$2$	−1.80241	−	0.866788i	−0.901205	−	0.433394i
$3$	−2.17924			−0.726412			−0.363206	−	0.931709i	$-0.618318\pi$
$3$	−2.17924			−0.726412			−0.363206	+	0.931709i	$0.618318\pi$
$4$	2.49736	+	3.12461i	0.624340	+	0.781153i
$5$	4.97895	+	0.458348i	0.995789	+	0.0916695i
$5$	4.97895	+	0.458348i	0.995789	+	0.0916695i
$6$	3.92787	+	1.88893i	0.654646	+	0.314822i
$7$	1.79794			0.256848			0.128424	−	0.991719i	$-0.459008\pi$
$7$	1.79794			0.256848			0.128424	+	0.991719i	$0.459008\pi$
$8$	−1.79289	−	7.79651i	−0.224111	−	0.974564i
$9$	−4.25093			−0.472326
$10$	−8.57681	−	5.14182i	−0.857681	−	0.514182i
$11$			3.31662i			0.301511i
$11$			3.31662i			0.301511i
$12$	−5.44233	−	6.80927i	−0.453528	−	0.567439i
$13$			8.71425i			0.670327i	0.942160	+	0.335163i	$0.108791\pi$
$13$			8.71425i			0.670327i	−0.942160	+	0.335163i	$0.891209\pi$
$14$	−3.24062	−	1.55843i	−0.231473	−	0.111316i
$15$	−10.8503	−	0.998848i	−0.723353	−	0.0665898i
$16$	−3.52640	+	15.6066i	−0.220400	+	0.975410i
$17$			14.4238i			0.848461i	0.905554	+	0.424231i	$0.139455\pi$
$17$			14.4238i			0.848461i	−0.905554	+	0.424231i	$0.860545\pi$
$18$	7.66192	+	3.68466i	0.425662	+	0.204703i
$19$		−	9.47058i		−	0.498452i	−0.968445	−	0.249226i	$-0.919824\pi$
$19$		−	9.47058i		−	0.498452i	0.968445	−	0.249226i	$-0.0801761\pi$
$20$	11.0021	+	16.7019i	0.550103	+	0.835097i
$21$	−3.91813			−0.186578
$22$	2.87481	−	5.97792i	0.130673	−	0.271723i
$23$	24.9253			1.08371			0.541853	−	0.840473i	$-0.317723\pi$
$23$	24.9253			1.08371			0.541853	+	0.840473i	$0.317723\pi$
$24$	3.90712	+	16.9904i	0.162797	+	0.707935i
$25$	24.5798	+	4.56418i	0.983193	+	0.182567i
$26$	7.55340	−	15.7066i	0.290515	−	0.604101i
$27$	28.8769			1.06951
$28$	4.49010	+	5.61786i	0.160361	+	0.200638i
$29$	17.4712			0.602454			0.301227	−	0.953552i	$-0.402604\pi$
$29$	17.4712			0.602454			0.301227	+	0.953552i	$0.402604\pi$
$30$	18.6909	+	11.2052i	0.623030	+	0.373508i
$31$			52.1631i			1.68268i	0.540506	+	0.841340i	$0.318233\pi$
$31$			52.1631i			1.68268i	−0.540506	+	0.841340i	$0.681767\pi$
$32$	19.8836	−	25.0727i	0.621362	−	0.783523i
$33$		−	7.22771i		−	0.219021i
$34$	12.5024	−	25.9977i	0.367718	−	0.764637i
$35$	8.95184	+	0.824081i	0.255767	+	0.0235452i
$36$	−10.6161	−	13.2825i	−0.294892	−	0.368959i
$37$			38.4324i			1.03871i	0.854558	+	0.519356i	$0.173828\pi$
$37$			38.4324i			1.03871i	−0.854558	+	0.519356i	$0.826172\pi$
$38$	−8.20898	+	17.0699i	−0.216026	+	0.449207i
$39$		−	18.9904i		−	0.486933i
$40$	−5.35317	−	39.6402i	−0.133829	−	0.991004i
$41$	32.3568			0.789191			0.394595	−	0.918855i	$-0.370885\pi$
$41$	32.3568			0.789191			0.394595	+	0.918855i	$0.370885\pi$
$42$	7.06208	+	3.39619i	0.168145	+	0.0808616i
$43$	−29.7743			−0.692425			−0.346212	−	0.938156i	$-0.612532\pi$
$43$	−29.7743			−0.692425			−0.346212	+	0.938156i	$0.612532\pi$
$44$	−10.3632	+	8.28280i	−0.235527	+	0.188245i
$45$	−21.1652	−	1.94840i	−0.470337	−	0.0432979i
$46$	−44.9255	−	21.6049i	−0.976642	−	0.469672i
$47$	50.4820			1.07408			0.537042	−	0.843555i	$-0.319542\pi$
$47$	50.4820			1.07408			0.537042	+	0.843555i	$0.319542\pi$
$48$	7.68487	−	34.0104i	0.160101	−	0.708549i
$49$	−45.7674			−0.934029
$50$	−40.3467	−	29.5320i	−0.806935	−	0.590640i
$51$		−	31.4330i		−	0.616332i
$52$	−27.2286	+	21.7626i	−0.523628	+	0.418511i
$53$			84.9022i			1.60193i	0.598712	+	0.800964i	$0.295679\pi$
$53$			84.9022i			1.60193i	−0.598712	+	0.800964i	$0.704321\pi$
$54$	−52.0480	−	25.0301i	−0.963852	−	0.463521i
$55$	−1.52017	+	16.5133i	−0.0276394	+	0.300242i
$56$	−3.22350	−	14.0176i	−0.0575625	−	0.250315i
$57$			20.6386i			0.362081i
$58$	−31.4902	−	15.1438i	−0.542935	−	0.261100i
$59$		−	14.3540i		−	0.243289i	−0.992574	−	0.121644i	$-0.961183\pi$
$59$		−	14.3540i		−	0.243289i	0.992574	−	0.121644i	$-0.0388168\pi$
$60$	−23.9761	−	36.3975i	−0.399601	−	0.606624i
$61$	15.8302			0.259511			0.129756	−	0.991546i	$-0.458581\pi$
$61$	15.8302			0.259511			0.129756	+	0.991546i	$0.458581\pi$
$62$	45.2143	−	94.0192i	0.729263	−	1.51644i
$63$	−7.64291			−0.121316
$64$	−57.5711	+	27.9565i	−0.899549	+	0.436820i
$65$	−3.99415	+	43.3878i	−0.0614485	+	0.667504i
$66$	−6.26489	+	13.0273i	−0.0949225	+	0.197383i
$67$	25.5295			0.381037			0.190519	−	0.981684i	$-0.438983\pi$
$67$	25.5295			0.381037			0.190519	+	0.981684i	$0.438983\pi$
$68$	−45.0689	+	36.0215i	−0.662778	+	0.529728i
$69$	−54.3180			−0.787218
$70$	−15.4206	−	9.24468i	−0.220294	−	0.132067i
$71$			43.8755i			0.617965i	0.951068	+	0.308983i	$0.0999885\pi$
$71$			43.8755i			0.617965i	−0.951068	+	0.308983i	$0.900012\pi$
$72$	7.62144	+	33.1424i	0.105853	+	0.460312i
$73$		−	106.971i		−	1.46535i	−0.680577	−	0.732677i	$-0.738271\pi$
$73$		−	106.971i		−	1.46535i	0.680577	−	0.732677i	$-0.261729\pi$
$74$	33.3127	−	69.2708i	0.450172	−	0.936092i
$75$	−53.5653	−	9.94642i	−0.714203	−	0.132619i
$76$	29.5919	−	23.6514i	0.389367	−	0.311203i
$77$			5.96309i			0.0774427i
$78$	−16.4606	+	34.2285i	−0.211034	+	0.438826i
$79$		−	109.043i		−	1.38030i	−0.723668	−	0.690148i	$-0.757545\pi$
$79$		−	109.043i		−	1.38030i	0.723668	−	0.690148i	$-0.242455\pi$
$80$	−24.7110	+	76.0879i	−0.308888	+	0.951099i
$81$	−24.6712			−0.304583
$82$	−58.3202	−	28.0465i	−0.711222	−	0.342030i
$83$	−11.4695			−0.138186			−0.0690931	−	0.997610i	$-0.522011\pi$
$83$	−11.4695			−0.138186			−0.0690931	+	0.997610i	$0.522011\pi$
$84$	−9.78498	−	12.2426i	−0.116488	−	0.145746i
$85$	−6.61113	+	71.8156i	−0.0777780	+	0.844889i
$86$	53.6654	+	25.8080i	0.624016	+	0.300093i
$87$	−38.0738			−0.437630
$88$	25.8581	−	5.94633i	0.293842	−	0.0675719i
$89$	−74.3785			−0.835713			−0.417857	−	0.908513i	$-0.637219\pi$
$89$	−74.3785			−0.835713			−0.417857	+	0.908513i	$0.637219\pi$
$90$	36.4594	+	21.8575i	0.405105	+	0.242861i
$91$			15.6677i			0.172172i
$92$	62.2473	+	77.8818i	0.676601	+	0.846541i
$93$		−	113.676i		−	1.22232i
$94$	−90.9892	−	43.7572i	−0.967970	−	0.465502i
$95$	4.34082	−	47.1535i	0.0456928	−	0.496353i
$96$	−43.3310	+	54.6394i	−0.451365	+	0.569161i
$97$			7.94927i			0.0819512i	0.999160	+	0.0409756i	$0.0130466\pi$
$97$			7.94927i			0.0819512i	−0.999160	+	0.0409756i	$0.986953\pi$
$98$	82.4916	+	39.6706i	0.841751	+	0.404802i
$99$		−	14.0987i		−	0.142412i
$100$	47.1234	+	88.2008i	0.471234	+	0.882008i
$101$	163.883			1.62261			0.811304	−	0.584624i	$-0.198758\pi$
$101$	163.883			1.62261			0.811304	+	0.584624i	$0.198758\pi$
$102$	−27.2457	+	56.6550i	−0.267115	+	0.555442i
$103$	−84.4384			−0.819790			−0.409895	−	0.912133i	$-0.634435\pi$
$103$	−84.4384			−0.819790			−0.409895	+	0.912133i	$0.634435\pi$
$104$	67.9407	−	15.6236i	0.653276	−	0.150227i
$105$	−19.5082	−	1.79587i	−0.185792	−	0.0171035i
$106$	73.5922	−	153.029i	0.694266	−	1.44367i
$107$	8.09195			0.0756257			0.0378129	−	0.999285i	$-0.487961\pi$
$107$	8.09195			0.0756257			0.0378129	+	0.999285i	$0.487961\pi$
$108$	72.1160	+	90.2291i	0.667740	+	0.835455i
$109$	−158.187			−1.45125			−0.725627	−	0.688088i	$-0.758450\pi$
$109$	−158.187			−1.45125			−0.725627	+	0.688088i	$0.758450\pi$
$110$	17.0535	−	28.4461i	0.155032	−	0.258601i
$111$		−	83.7532i		−	0.754533i
$112$	−6.34026	+	28.0596i	−0.0566094	+	0.250532i
$113$		−	207.544i		−	1.83667i	−0.395800	−	0.918337i	$-0.629533\pi$
$113$		−	207.544i		−	1.83667i	0.395800	−	0.918337i	$-0.370467\pi$
$114$	17.8893	−	37.1992i	0.156924	−	0.326309i
$115$	124.102	+	11.4244i	1.07914	+	0.0993429i
$116$	43.6318	+	54.5907i	0.376136	+	0.470609i
$117$		−	37.0437i		−	0.316612i
$118$	−12.4419	+	25.8719i	−0.105440	+	0.219253i
$119$			25.9332i			0.217926i
$120$	11.6658	+	86.3853i	0.0972152	+	0.719877i
$121$	−11.0000			−0.0909091
$122$	−28.5325	−	13.7214i	−0.233873	−	0.112471i
$123$	−70.5131			−0.573278
$124$	−162.989	+	130.270i	−1.31443	+	1.05056i
$125$	120.290	+	33.9909i	0.962318	+	0.271927i
$126$	13.7757	+	6.62478i	0.109331	+	0.0525776i
$127$	−124.489			−0.980231			−0.490115	−	0.871658i	$-0.663045\pi$
$127$	−124.489			−0.980231			−0.490115	+	0.871658i	$0.663045\pi$
$128$	127.999	−	0.487121i	0.999993	−	0.00380564i
$129$	64.8851			0.502985
$130$	44.8071	−	74.7404i	0.344670	−	0.574926i
$131$			205.998i			1.57250i	0.617908	+	0.786250i	$0.287980\pi$
$131$			205.998i			1.57250i	−0.617908	+	0.786250i	$0.712020\pi$
$132$	22.5838	−	18.0502i	0.171089	−	0.136744i
$133$		−	17.0275i		−	0.128026i
$134$	−46.0146	−	22.1286i	−0.343392	−	0.165139i
$135$	143.777	+	13.2357i	1.06501	+	0.0980419i
$136$	112.456	−	25.8603i	0.826880	−	0.190149i
$137$		−	110.604i		−	0.807332i	−0.914906	−	0.403666i	$-0.867736\pi$
$137$		−	110.604i		−	0.807332i	0.914906	−	0.403666i	$-0.132264\pi$
$138$	97.9033	+	47.0822i	0.709444	+	0.341175i
$139$		−	6.21526i		−	0.0447141i	−0.999750	−	0.0223571i	$-0.992883\pi$
$139$		−	6.21526i		−	0.0447141i	0.999750	−	0.0223571i	$-0.00711707\pi$
$140$	19.7810	+	30.0291i	0.141293	+	0.214493i
$141$	−110.012			−0.780228
$142$	38.0308	−	79.0816i	0.267822	−	0.556913i
$143$	−28.9019			−0.202111
$144$	14.9905	−	66.3424i	0.104101	−	0.460711i
$145$	86.9881	+	8.00787i	0.599918	+	0.0552267i
$146$	−92.7210	+	192.805i	−0.635075	+	1.32058i
$147$	99.7380			0.678490
$148$	−120.086	+	95.9794i	−0.811393	+	0.648509i
$149$	65.8113			0.441686			0.220843	−	0.975309i	$-0.429119\pi$
$149$	65.8113			0.441686			0.220843	+	0.975309i	$0.429119\pi$
$150$	87.9251	+	64.3572i	0.586167	+	0.429048i
$151$			15.8068i			0.104681i	0.998629	+	0.0523403i	$0.0166681\pi$
$151$			15.8068i			0.104681i	−0.998629	+	0.0523403i	$0.983332\pi$
$152$	−73.8375	+	16.9797i	−0.485773	+	0.111708i
$153$		−	61.3148i		−	0.400750i
$154$	5.16873	−	10.7479i	0.0335632	−	0.0697917i
$155$	−23.9088	+	259.717i	−0.154251	+	1.67560i
$156$	59.3376	−	47.4258i	0.380369	−	0.304012i
$157$			122.691i			0.781470i	0.920503	+	0.390735i	$0.127779\pi$
$157$			122.691i			0.781470i	−0.920503	+	0.390735i	$0.872221\pi$
$158$	−94.5175	+	196.541i	−0.598212	+	1.24393i
$159$		−	185.022i		−	1.16366i
$160$	110.491	−	115.722i	0.690571	−	0.723264i
$161$	44.8141			0.278348
$162$	44.4676	+	21.3847i	0.274491	+	0.132004i
$163$	−160.115			−0.982300			−0.491150	−	0.871075i	$-0.663423\pi$
$163$	−160.115			−0.982300			−0.491150	+	0.871075i	$0.663423\pi$
$164$	80.8066	+	101.103i	0.492723	+	0.616479i
$165$	3.31280	−	35.9864i	0.0200776	−	0.218099i
$166$	20.6727	+	9.94159i	0.124534	+	0.0598891i
$167$	−29.9094			−0.179098			−0.0895492	−	0.995982i	$-0.528543\pi$
$167$	−29.9094			−0.179098			−0.0895492	+	0.995982i	$0.528543\pi$
$168$	7.02476	+	30.5477i	0.0418141	+	0.181832i
$169$	93.0619			0.550662
$170$	74.1648	−	123.711i	0.436264	−	0.727709i
$171$			40.2588i			0.235431i
$172$	−74.3570	−	93.0330i	−0.432308	−	0.540890i
$173$		−	287.616i		−	1.66252i	−0.555883	−	0.831261i	$-0.687620\pi$
$173$		−	287.616i		−	1.66252i	0.555883	−	0.831261i	$-0.312380\pi$
$174$	68.6246	+	33.0019i	0.394394	+	0.189666i
$175$	44.1930	+	8.20611i	0.252532	+	0.0468921i
$176$	−51.7611	−	11.6958i	−0.294097	−	0.0664532i
$177$			31.2809i			0.176728i
$178$	134.060	+	64.4704i	0.753149	+	0.362193i
$179$			269.519i			1.50569i	0.658197	+	0.752846i	$0.271319\pi$
$179$			269.519i			1.50569i	−0.658197	+	0.752846i	$0.728681\pi$
$180$	−46.7690	−	70.9988i	−0.259828	−	0.394438i
$181$	51.6236			0.285213			0.142607	−	0.989779i	$-0.454452\pi$
$181$	51.6236			0.285213			0.142607	+	0.989779i	$0.454452\pi$
$182$	13.5805	−	28.2396i	0.0746184	−	0.155162i
$183$	−34.4977			−0.188512
$184$	−44.6881	−	194.330i	−0.242870	−	1.05614i
$185$	−17.6154	+	191.353i	−0.0952183	+	1.03434i
$186$	−98.5327	+	204.890i	−0.529746	+	1.10156i
$187$	−47.8385			−0.255821
$188$	126.072	+	157.737i	0.670593	+	0.839024i
$189$	51.9189			0.274703
$190$	−48.6960	+	81.2274i	−0.256295	+	0.427512i
$191$		−	204.409i		−	1.07020i	−0.844787	−	0.535102i	$-0.820273\pi$
$191$		−	204.409i		−	1.07020i	0.844787	−	0.535102i	$-0.179727\pi$
$192$	125.461	−	60.9238i	0.653443	−	0.317312i
$193$		−	24.3244i		−	0.126033i	−0.998012	−	0.0630167i	$-0.979928\pi$
$193$		−	24.3244i		−	0.126033i	0.998012	−	0.0630167i	$-0.0200721\pi$
$194$	6.89033	−	14.3278i	0.0355172	−	0.0738548i
$195$	8.70420	−	94.5522i	0.0446369	−	0.484883i
$196$	−114.298	−	143.005i	−0.583151	−	0.729620i
$197$		−	138.476i		−	0.702926i	−0.936202	−	0.351463i	$-0.885684\pi$
$197$		−	138.476i		−	0.702926i	0.936202	−	0.351463i	$-0.114316\pi$
$198$	−12.2206	+	25.4117i	−0.0617203	+	0.128342i
$199$			69.4973i			0.349233i	0.984637	+	0.174616i	$0.0558685\pi$
$199$			69.4973i			0.349233i	−0.984637	+	0.174616i	$0.944131\pi$
$200$	−8.48419	−	199.820i	−0.0424209	−	0.999100i
$201$	−55.6348			−0.276790
$202$	−295.385	−	142.052i	−1.46230	−	0.703229i
$203$	31.4121			0.154739
$204$	98.2158	−	78.4993i	0.481450	−	0.384801i
$205$	161.103	+	14.8307i	0.785868	+	0.0723447i
$206$	152.193	+	73.1901i	0.738799	+	0.355292i
$207$	−105.956			−0.511863
$208$	−135.999	−	30.7300i	−0.653843	−	0.147740i
$209$	31.4104			0.150289
$210$	33.6051	+	20.1463i	0.160024	+	0.0959349i
$211$		−	101.454i		−	0.480826i	−0.970671	−	0.240413i	$-0.922717\pi$
$211$		−	101.454i		−	0.480826i	0.970671	−	0.240413i	$-0.0772829\pi$
$212$	−265.286	+	212.031i	−1.25135	+	1.00015i
$213$		−	95.6151i		−	0.448897i
$214$	−14.5850	−	7.01401i	−0.0681543	−	0.0327757i
$215$	−148.244	−	13.6470i	−0.689509	−	0.0634742i
$216$	−51.7730	−	225.139i	−0.239690	−	1.04231i
$217$			93.7860i			0.432194i
$218$	285.117	+	137.114i	1.30788	+	0.628965i
$219$			233.115i			1.06445i
$220$	−55.3941	+	36.4897i	−0.251791	+	0.165862i
$221$	−125.693			−0.568746
$222$	−72.5962	+	150.957i	−0.327010	+	0.679989i
$223$	173.448			0.777792			0.388896	−	0.921282i	$-0.372857\pi$
$223$	173.448			0.777792			0.388896	+	0.921282i	$0.372857\pi$
$224$	35.7495	−	45.0793i	0.159596	−	0.201247i
$225$	−104.487	−	19.4020i	−0.464388	−	0.0862311i
$226$	−179.897	+	374.079i	−0.796003	+	1.65522i
$227$	−259.525			−1.14328			−0.571640	−	0.820504i	$-0.693693\pi$
$227$	−259.525			−1.14328			−0.571640	+	0.820504i	$0.693693\pi$
$228$	−64.4877	+	51.5420i	−0.282841	+	0.226062i
$229$	−200.406			−0.875134			−0.437567	−	0.899186i	$-0.644160\pi$
$229$	−200.406			−0.875134			−0.437567	+	0.899186i	$0.644160\pi$
$230$	−213.779	−	128.161i	−0.929475	−	0.557223i
$231$		−	12.9950i		−	0.0562553i
$232$	−31.3238	−	136.214i	−0.135017	−	0.587130i
$233$		−	117.790i		−	0.505535i	−0.967527	−	0.252768i	$-0.918659\pi$
$233$		−	117.790i		−	0.505535i	0.967527	−	0.252768i	$-0.0813408\pi$
$234$	−32.1090	+	66.7678i	−0.137218	+	0.285333i
$235$	251.347	+	23.1383i	1.06956	+	0.0984608i
$236$	44.8508	−	35.8472i	0.190046	−	0.151895i
$237$			237.631i			1.00266i
$238$	22.4786	−	46.7422i	0.0944477	−	0.196396i
$239$		−	435.473i		−	1.82206i	−0.412337	−	0.911032i	$-0.635287\pi$
$239$		−	435.473i		−	1.82206i	0.412337	−	0.911032i	$-0.364713\pi$
$240$	53.8511	−	165.813i	0.224380	−	0.690889i
$241$	−267.721			−1.11088			−0.555438	−	0.831558i	$-0.687450\pi$
$241$	−267.721			−1.11088			−0.555438	+	0.831558i	$0.687450\pi$
$242$	19.8265	+	9.53466i	0.0819277	+	0.0393994i
$243$	−206.128			−0.848262
$244$	39.5337	+	49.4632i	0.162023	+	0.202718i
$245$	−227.874	−	20.9774i	−0.930096	−	0.0856220i
$246$	127.094	+	61.1199i	0.516640	+	0.248455i
$247$	82.5290			0.334125
$248$	406.690	−	93.5225i	1.63988	−	0.377107i
$249$	24.9947			0.100380
$250$	−187.348	−	165.531i	−0.749394	−	0.662125i
$251$			106.398i			0.423896i	0.977281	+	0.211948i	$0.0679807\pi$
$251$			106.398i			0.423896i	−0.977281	+	0.211948i	$0.932019\pi$
$252$	−19.0871	−	23.8811i	−0.0757424	−	0.0947664i
$253$			82.6677i			0.326750i
$254$	224.381	+	107.906i	0.883389	+	0.424826i
$255$	14.4072	−	156.503i	0.0564989	−	0.613737i
$256$	−231.129	−	110.070i	−0.902847	−	0.429961i
$257$		−	238.012i		−	0.926115i	−0.886328	−	0.463058i	$-0.846752\pi$
$257$		−	238.012i		−	0.926115i	0.886328	−	0.463058i	$-0.153248\pi$
$258$	−116.950	−	56.2416i	−0.453293	−	0.217991i
$259$			69.0990i			0.266792i
$260$	−145.545	+	95.8746i	−0.559788	+	0.368749i
$261$	−74.2688			−0.284555
$262$	178.556	−	371.292i	0.681512	−	1.41714i
$263$	150.167			0.570977			0.285489	−	0.958382i	$-0.407844\pi$
$263$	150.167			0.570977			0.285489	+	0.958382i	$0.407844\pi$
$264$	−56.3509	+	12.9585i	−0.213450	+	0.0490851i
$265$	−38.9147	+	422.724i	−0.146848	+	1.59518i
$266$	−14.7592	+	30.6906i	−0.0554859	+	0.115378i
$267$	162.088			0.607072
$268$	63.7563	+	79.7697i	0.237897	+	0.297648i
$269$	21.3598			0.0794045			0.0397023	−	0.999212i	$-0.487359\pi$
$269$	21.3598			0.0794045			0.0397023	+	0.999212i	$0.487359\pi$
$270$	−247.672	−	148.480i	−0.917303	−	0.549925i
$271$		−	519.985i		−	1.91876i	−0.282110	−	0.959382i	$-0.591034\pi$
$271$		−	519.985i		−	1.91876i	0.282110	−	0.959382i	$-0.408966\pi$
$272$	−225.106	−	50.8643i	−0.827597	−	0.187001i
$273$		−	34.1436i		−	0.125068i
$274$	−95.8706	+	199.355i	−0.349893	+	0.727571i
$275$	−15.1377	+	81.5221i	−0.0550461	+	0.296444i
$276$	−135.652	−	169.723i	−0.491491	−	0.614937i
$277$			378.030i			1.36473i	0.731012	+	0.682365i	$0.239049\pi$
$277$			378.030i			1.36473i	−0.731012	+	0.682365i	$0.760951\pi$
$278$	−5.38731	+	11.2024i	−0.0193788	+	0.0402966i
$279$		−	221.742i		−	0.794773i
$280$	−9.62467	−	71.2706i	−0.0343738	−	0.254538i
$281$	155.598			0.553728			0.276864	−	0.960909i	$-0.410705\pi$
$281$	155.598			0.553728			0.276864	+	0.960909i	$0.410705\pi$
$282$	198.287	+	95.3571i	0.703145	+	0.338146i
$283$	478.481			1.69074			0.845372	−	0.534178i	$-0.179379\pi$
$283$	478.481			1.69074			0.845372	+	0.534178i	$0.179379\pi$
$284$	−137.094	+	109.573i	−0.482725	+	0.385820i
$285$	−9.45966	+	102.759i	−0.0331918	+	0.360557i
$286$	52.0930	+	25.0518i	0.182143	+	0.0875937i
$287$	58.1756			0.202702
$288$	−84.5238	+	106.583i	−0.293485	+	0.370078i
$289$	80.9528			0.280113
$290$	−149.847	−	89.8337i	−0.516714	−	0.309771i
$291$		−	17.3233i		−	0.0595304i
$292$	334.242	−	267.144i	1.14467	−	0.914878i
$293$			285.131i			0.973144i	0.873640	+	0.486572i	$0.161753\pi$
$293$			285.131i			0.973144i	−0.873640	+	0.486572i	$0.838247\pi$
$294$	−179.769	−	86.4517i	−0.611458	−	0.294053i
$295$	6.57914	−	71.4680i	0.0223022	−	0.242265i
$296$	299.638	−	68.9048i	1.01229	−	0.232787i
$297$			95.7739i			0.322471i
$298$	−118.619	−	57.0444i	−0.398050	−	0.191424i
$299$			217.205i			0.726438i
$300$	−102.693	−	192.210i	−0.342310	−	0.640701i
$301$	−53.5323			−0.177848
$302$	13.7011	−	28.4903i	0.0453680	−	0.0943387i
$303$	−357.141			−1.17868
$304$	147.803	+	33.3971i	0.486194	+	0.109859i
$305$	78.8177	+	7.25573i	0.258419	+	0.0237893i
$306$	−53.1469	+	110.514i	−0.173683	+	0.361158i
$307$	473.639			1.54280			0.771399	−	0.636352i	$-0.219558\pi$
$307$	473.639			1.54280			0.771399	+	0.636352i	$0.219558\pi$
$308$	−18.6323	+	14.8920i	−0.0604946	+	0.0483505i
$309$	184.011			0.595505
$310$	268.213	−	447.393i	0.865204	−	1.44320i
$311$		−	119.245i		−	0.383424i	−0.981451	−	0.191712i	$-0.938596\pi$
$311$		−	119.245i		−	0.383424i	0.981451	−	0.191712i	$-0.0614039\pi$
$312$	−148.059	+	34.0476i	−0.474547	+	0.109127i
$313$			358.817i			1.14638i	0.819423	+	0.573190i	$0.194294\pi$
$313$			358.817i			1.14638i	−0.819423	+	0.573190i	$0.805706\pi$
$314$	106.347	−	221.139i	0.338684	−	0.704264i
$315$	−38.0537	−	3.50311i	−0.120805	−	0.0111210i
$316$	340.718	−	272.321i	1.07822	−	0.861774i
$317$		−	27.4250i		−	0.0865143i	−0.999064	−	0.0432572i	$-0.986227\pi$
$317$		−	27.4250i		−	0.0865143i	0.999064	−	0.0432572i	$-0.0137735\pi$
$318$	−160.375	+	333.485i	−0.504323	+	1.04870i
$319$			57.9453i			0.181647i
$320$	−299.457	+	112.806i	−0.935804	+	0.352520i
$321$	−17.6343			−0.0549354
$322$	−80.7733	−	38.8443i	−0.250849	−	0.120634i
$323$	136.602			0.422917
$324$	−61.6128	−	77.0879i	−0.190163	−	0.237926i
$325$	−39.7734	+	214.195i	−0.122380	+	0.659061i
$326$	288.593	+	138.786i	0.885253	+	0.425723i
$327$	344.726			1.05421
$328$	−58.0121	−	252.270i	−0.176866	−	0.769117i
$329$	90.7635			0.275877
$330$	−37.1636	+	61.9907i	−0.112617	+	0.187851i
$331$		−	205.495i		−	0.620829i	−0.950601	−	0.310415i	$-0.899532\pi$
$331$		−	205.495i		−	0.620829i	0.950601	−	0.310415i	$-0.100468\pi$
$332$	−28.6434	−	35.8376i	−0.0862752	−	0.107945i
$333$		−	163.373i		−	0.490611i
$334$	53.9091	+	25.9251i	0.161404	+	0.0776202i
$335$	127.110	+	11.7014i	0.379433	+	0.0349295i
$336$	13.8169	−	61.1485i	0.0411218	−	0.181990i
$337$			498.276i			1.47857i	0.673395	+	0.739283i	$0.264835\pi$
$337$			498.276i			1.47857i	−0.673395	+	0.739283i	$0.735165\pi$
$338$	−167.736	−	80.6649i	−0.496259	−	0.238654i
$339$			452.288i			1.33418i
$340$	−240.906	+	158.692i	−0.708547	+	0.466741i
$341$	−173.005			−0.507347
$342$	34.8958	−	72.5628i	0.102035	−	0.212172i
$343$	−170.386			−0.496752
$344$	53.3818	+	232.135i	0.155180	+	0.674812i
$345$	−270.447	−	24.8965i	−0.783903	−	0.0721639i
$346$	−249.302	+	518.402i	−0.720526	+	1.49827i
$347$	−608.078			−1.75239			−0.876193	−	0.481960i	$-0.839925\pi$
$347$	−608.078			−1.75239			−0.876193	+	0.481960i	$0.839925\pi$
$348$	−95.0840	−	118.966i	−0.273230	−	0.341856i
$349$	398.361			1.14144			0.570718	−	0.821146i	$-0.306665\pi$
$349$	398.361			1.14144			0.570718	+	0.821146i	$0.306665\pi$
$350$	−72.5410	−	53.0967i	−0.207260	−	0.151705i
$351$			251.640i			0.716924i
$352$	83.1569	+	65.9464i	0.236241	+	0.187348i
$353$		−	141.680i		−	0.401361i	−0.979657	−	0.200680i	$-0.935685\pi$
$353$		−	141.680i		−	0.401361i	0.979657	−	0.200680i	$-0.0643153\pi$
$354$	27.1139	−	56.3809i	0.0765928	−	0.159268i
$355$	−20.1102	+	218.454i	−0.0566486	+	0.615363i
$356$	−185.750	−	232.404i	−0.521769	−	0.652820i
$357$		−	56.5145i		−	0.158304i
$358$	233.616	−	485.783i	0.652557	−	1.35694i
$359$			240.104i			0.668814i	0.942429	+	0.334407i	$0.108536\pi$
$359$			240.104i			0.668814i	−0.942429	+	0.334407i	$0.891464\pi$
$360$	22.7560	+	168.508i	0.0632110	+	0.468077i
$361$	271.308			0.751546
$362$	−93.0468	−	44.7467i	−0.257035	−	0.123610i
$363$	23.9716			0.0660374
$364$	−48.9554	+	39.1278i	−0.134493	+	0.107494i
$365$	49.0298	−	532.602i	0.134328	−	1.45918i
$366$	62.1790	+	29.9022i	0.169888	+	0.0817000i
$367$	582.476			1.58713			0.793565	−	0.608486i	$-0.208223\pi$
$367$	582.476			1.58713			0.793565	+	0.608486i	$0.208223\pi$
$368$	−87.8965	+	388.997i	−0.238849	+	1.05706i
$369$	−137.547			−0.372755
$370$	197.612	−	329.627i	0.534087	−	0.890884i
$371$			152.649i			0.411453i
$372$	355.192	−	283.889i	0.954818	−	0.763142i
$373$			38.1646i			0.102318i	0.998691	+	0.0511589i	$0.0162915\pi$
$373$			38.1646i			0.102318i	−0.998691	+	0.0511589i	$0.983708\pi$
$374$	86.2245	+	41.4658i	0.230547	+	0.110871i
$375$	−262.140	−	74.0742i	−0.699039	−	0.197531i
$376$	−90.5084	−	393.583i	−0.240714	−	1.04676i
$377$			152.248i			0.403841i
$378$	−93.5791	−	45.0027i	−0.247564	−	0.119055i
$379$			437.278i			1.15377i	0.816826	+	0.576885i	$0.195732\pi$
$379$			437.278i			1.15377i	−0.816826	+	0.576885i	$0.804268\pi$
$380$	158.177	−	104.196i	0.416255	−	0.274200i
$381$	271.292			0.712051
$382$	−177.179	+	368.429i	−0.463820	+	0.964473i
$383$	−731.506			−1.90994			−0.954969	−	0.296705i	$-0.904112\pi$
$383$	−731.506			−1.90994			−0.954969	+	0.296705i	$0.904112\pi$
$384$	−278.940	+	1.06155i	−0.726407	+	0.00276446i
$385$	−2.73317	+	29.6899i	−0.00709913	+	0.0771166i
$386$	−21.0841	+	43.8426i	−0.0546221	+	0.113582i
$387$	126.568			0.327050
$388$	−24.8384	+	19.8522i	−0.0640165	+	0.0511654i
$389$	550.201			1.41440			0.707200	−	0.707014i	$-0.249958\pi$
$389$	550.201			1.41440			0.707200	+	0.707014i	$0.249958\pi$
$390$	−97.6452	+	162.877i	−0.250372	+	0.417633i
$391$			359.518i			0.919483i
$392$	82.0558	+	356.826i	0.209326	+	0.910271i
$393$		−	448.917i		−	1.14228i
$394$	−120.030	+	249.591i	−0.304644	+	0.633480i
$395$	49.9798	−	542.922i	0.126531	−	1.37448i
$396$	44.0531	−	35.2096i	0.111245	−	0.0889132i
$397$		−	663.628i		−	1.67161i	−0.549028	−	0.835804i	$-0.685002\pi$
$397$		−	663.628i		−	1.67161i	0.549028	−	0.835804i	$-0.314998\pi$
$398$	60.2394	−	125.263i	0.151355	−	0.314730i
$399$			37.1070i			0.0929999i
$400$	−157.910	+	367.511i	−0.394774	+	0.918778i
$401$	263.823			0.657912			0.328956	−	0.944345i	$-0.393303\pi$
$401$	263.823			0.657912			0.328956	+	0.944345i	$0.393303\pi$
$402$	100.277	+	48.2235i	0.249444	+	0.119959i
$403$	−454.562			−1.12795
$404$	409.276	+	512.072i	1.01306	+	1.26751i
$405$	−122.837	−	11.3080i	−0.303300	−	0.0279209i
$406$	−56.6175	−	27.2276i	−0.139452	−	0.0670631i
$407$	−127.466			−0.313184
$408$	−245.067	+	56.3557i	−0.600655	+	0.138127i
$409$	−354.788			−0.867452			−0.433726	−	0.901045i	$-0.642801\pi$
$409$	−354.788			−0.867452			−0.433726	+	0.901045i	$0.642801\pi$
$410$	−277.518	−	166.373i	−0.676874	−	0.405788i
$411$			241.033i			0.586456i
$412$	−210.873	−	263.837i	−0.511827	−	0.640381i
$413$		−	25.8077i		−	0.0624884i
$414$	190.975	+	91.8410i	0.461293	+	0.221838i
$415$	−57.1058	−	5.25700i	−0.137604	−	0.0126675i
$416$	218.490	+	173.271i	0.525217	+	0.416516i
$417$			13.5445i			0.0324809i
$418$	−56.6143	−	27.2261i	−0.135441	−	0.0651342i
$419$		−	77.3470i		−	0.184599i	−0.995731	−	0.0922995i	$-0.970578\pi$
$419$		−	77.3470i		−	0.184599i	0.995731	−	0.0922995i	$-0.0294217\pi$
$420$	−43.1075	−	65.4404i	−0.102637	−	0.155810i
$421$	−81.5945			−0.193811			−0.0969056	−	0.995294i	$-0.530894\pi$
$421$	−81.5945			−0.193811			−0.0969056	+	0.995294i	$0.530894\pi$
$422$	−87.9393	+	182.862i	−0.208387	+	0.433323i
$423$	−214.595			−0.507318
$424$	661.941	−	152.220i	1.56118	−	0.359009i
$425$	−65.8330	+	354.536i	−0.154901	+	0.834202i
$426$	−82.8780	+	172.338i	−0.194549	+	0.404548i
$427$	28.4617			0.0666551
$428$	20.2085	+	25.2842i	0.0472161	+	0.0590753i
$429$	62.9840			0.146816
$430$	255.368	+	153.094i	0.593879	+	0.356032i
$431$		−	125.049i		−	0.290136i	−0.989422	−	0.145068i	$-0.953660\pi$
$431$		−	125.049i		−	0.290136i	0.989422	−	0.145068i	$-0.0463401\pi$
$432$	−101.832	+	450.669i	−0.235721	+	1.04322i
$433$		−	53.8221i		−	0.124300i	−0.998067	−	0.0621502i	$-0.980204\pi$
$433$		−	53.8221i		−	0.124300i	0.998067	−	0.0621502i	$-0.0197958\pi$
$434$	81.2926	−	169.041i	0.187310	−	0.389495i
$435$	−189.568	−	17.4510i	−0.435787	−	0.0401173i
$436$	−395.049	−	494.272i	−0.906076	−	1.13365i
$437$		−	236.057i		−	0.540175i
$438$	202.061	−	420.168i	0.461326	−	0.959287i
$439$		−	293.375i		−	0.668281i	−0.942523	−	0.334140i	$-0.891554\pi$
$439$		−	293.375i		−	0.668281i	0.942523	−	0.334140i	$-0.108446\pi$
$440$	131.472	−	17.7545i	0.298799	−	0.0403511i
$441$	194.554			0.441166
$442$	226.550	+	108.949i	0.512557	+	0.246491i
$443$	603.325			1.36191			0.680954	−	0.732326i	$-0.261565\pi$
$443$	603.325			1.36191			0.680954	+	0.732326i	$0.261565\pi$
$444$	261.696	−	209.162i	0.589406	−	0.471085i
$445$	−370.327	−	34.0912i	−0.832195	−	0.0766095i
$446$	−312.624	−	150.342i	−0.700950	−	0.337090i
$447$	−143.418			−0.320846
$448$	−103.509	+	50.2641i	−0.231048	+	0.112197i
$449$	383.553			0.854238			0.427119	−	0.904195i	$-0.359529\pi$
$449$	383.553			0.854238			0.427119	+	0.904195i	$0.359529\pi$
$450$	171.511	+	125.539i	0.381136	+	0.278975i
$451$			107.315i			0.237950i
$452$	648.495	−	518.312i	1.43472	−	1.14671i
$453$		−	34.4467i		−	0.0760413i
$454$	467.770	+	224.953i	1.03033	+	0.495491i
$455$	−7.18124	+	78.0085i	−0.0157829	+	0.171447i
$456$	160.909	−	37.0027i	0.352871	−	0.0811463i
$457$			722.326i			1.58058i	0.612732	+	0.790291i	$0.290071\pi$
$457$			722.326i			1.58058i	−0.612732	+	0.790291i	$0.709929\pi$
$458$	361.213	+	173.709i	0.788675	+	0.379278i
$459$			416.516i			0.907442i
$460$	274.229	+	416.300i	0.596150	+	0.905000i
$461$	−245.149			−0.531776			−0.265888	−	0.964004i	$-0.585665\pi$
$461$	−245.149			−0.531776			−0.265888	+	0.964004i	$0.585665\pi$
$462$	−11.2639	+	23.4223i	−0.0243807	+	0.0506975i
$463$	615.917			1.33027			0.665137	−	0.746721i	$-0.268373\pi$
$463$	615.917			1.33027			0.665137	+	0.746721i	$0.268373\pi$
$464$	−61.6104	+	272.665i	−0.132781	+	0.587640i
$465$	52.1030	−	565.985i	0.112049	−	1.21717i
$466$	−102.099	+	212.305i	−0.219096	+	0.455591i
$467$	421.342			0.902231			0.451116	−	0.892465i	$-0.351026\pi$
$467$	421.342			0.902231			0.451116	+	0.892465i	$0.351026\pi$
$468$	115.747	−	92.5113i	0.247323	−	0.197674i
$469$	45.9004			0.0978687
$470$	−432.974	−	259.569i	−0.921222	−	0.552275i
$471$		−	267.372i		−	0.567669i
$472$	−111.911	+	25.7352i	−0.237101	+	0.0545237i
$473$		−	98.7500i		−	0.208774i
$474$	205.976	−	428.309i	0.434548	−	0.903605i
$475$	43.2254	−	232.785i	0.0910009	−	0.490074i
$476$	−81.0311	+	64.7644i	−0.170233	+	0.136060i
$477$		−	360.913i		−	0.756632i
$478$	−377.463	+	784.901i	−0.789671	+	1.64205i
$479$		−	828.237i		−	1.72910i	−0.502550	−	0.864548i	$-0.667605\pi$
$479$		−	828.237i		−	1.72910i	0.502550	−	0.864548i	$-0.332395\pi$
$480$	−240.787	+	252.186i	−0.501639	+	0.525388i
$481$	−334.909			−0.696277
$482$	482.543	+	232.058i	1.00113	+	0.481447i
$483$	−97.6604			−0.202196
$484$	−27.4709	−	34.3707i	−0.0567581	−	0.0710139i
$485$	−3.64353	+	39.5790i	−0.00751243	+	0.0816062i
$486$	371.527	+	178.669i	0.764458	+	0.367632i
$487$	336.286			0.690525			0.345262	−	0.938506i	$-0.387790\pi$
$487$	336.286			0.690525			0.345262	+	0.938506i	$0.387790\pi$
$488$	−28.3817	−	123.420i	−0.0581593	−	0.252910i
$489$	348.928			0.713554
$490$	392.538	+	235.328i	0.801099	+	0.480261i
$491$			320.294i			0.652330i	0.945313	+	0.326165i	$0.105756\pi$
$491$			320.294i			0.652330i	−0.945313	+	0.326165i	$0.894244\pi$
$492$	−176.097	−	220.326i	−0.357920	−	0.447817i
$493$			252.002i			0.511159i
$494$	−148.751	−	71.5351i	−0.301115	−	0.144808i
$495$	6.46213	−	70.1969i	0.0130548	−	0.141812i
$496$	−814.086	−	183.948i	−1.64130	−	0.370863i
$497$			78.8855i			0.158723i
$498$	−45.0506	−	21.6651i	−0.0904631	−	0.0435041i
$499$		−	353.440i		−	0.708297i	−0.935189	−	0.354149i	$-0.884771\pi$
$499$		−	353.440i		−	0.708297i	0.935189	−	0.354149i	$-0.115229\pi$
$500$	194.198	+	460.746i	0.388396	+	0.921492i
$501$	65.1797			0.130099
$502$	92.2243	−	191.772i	0.183714	−	0.382017i
$503$	810.854			1.61204			0.806018	−	0.591891i	$-0.201619\pi$
$503$	810.854			1.61204			0.806018	+	0.591891i	$0.201619\pi$
$504$	13.7029	+	59.5880i	0.0271882	+	0.118230i
$505$	815.967	+	75.1156i	1.61578	+	0.148744i
$506$	71.6554	−	149.001i	0.141611	−	0.294469i
$507$	−202.804			−0.400008
$508$	−310.894	−	388.981i	−0.611997	−	0.765710i
$509$	−874.747			−1.71856			−0.859280	−	0.511506i	$-0.829088\pi$
$509$	−874.747			−1.71856			−0.859280	+	0.511506i	$0.829088\pi$
$510$	−161.623	+	269.594i	−0.316907	+	0.528617i
$511$		−	192.327i		−	0.376374i
$512$	321.182	+	398.731i	0.627308	+	0.778771i
$513$		−	273.481i		−	0.533101i
$514$	−206.306	+	428.994i	−0.401373	+	0.834619i
$515$	−420.414	−	38.7021i	−0.816338	−	0.0751498i
$516$	162.041	+	202.741i	0.314034	+	0.392909i
$517$			167.430i			0.323849i
$518$	59.8942	−	124.545i	0.115626	−	0.240434i
$519$			626.783i			1.20768i
$520$	345.434	−	46.6489i	0.664297	−	0.0897094i
$521$	−787.126			−1.51080			−0.755399	−	0.655265i	$-0.772557\pi$
$521$	−787.126			−1.51080			−0.755399	+	0.655265i	$0.772557\pi$
$522$	133.863	+	64.3753i	0.256442	+	0.123324i
$523$	−888.359			−1.69858			−0.849292	−	0.527924i	$-0.822971\pi$
$523$	−888.359			−1.69858			−0.849292	+	0.527924i	$0.822971\pi$
$524$	−643.662	+	514.450i	−1.22836	+	0.981774i
$525$	−96.3070	−	17.8830i	−0.183442	−	0.0340629i
$526$	−270.662	−	130.163i	−0.514567	−	0.247458i
$527$	−752.392			−1.42769
$528$	112.800	+	25.4878i	0.213636	+	0.0482724i
$529$	92.2685			0.174421
$530$	436.552	−	728.190i	0.823683	−	1.37394i
$531$			61.0181i			0.114912i
$532$	53.2044	−	42.5238i	0.100008	−	0.0799320i
$533$			281.965i			0.529015i
$534$	−292.149	−	140.496i	−0.547096	−	0.263101i
$535$	40.2894	+	3.70893i	0.0753073	+	0.00693258i
$536$	−45.7715	−	199.041i	−0.0853945	−	0.371345i
$537$		−	587.345i		−	1.09375i
$538$	−38.4991	−	18.5144i	−0.0715597	−	0.0344134i
$539$		−	151.793i		−	0.281620i
$540$	317.705	+	482.300i	0.588343	+	0.893149i
$541$	−302.191			−0.558579			−0.279289	−	0.960207i	$-0.590099\pi$
$541$	−302.191			−0.558579			−0.279289	+	0.960207i	$0.590099\pi$
$542$	−450.717	+	937.226i	−0.831581	+	1.72920i
$543$	−112.500			−0.207182
$544$	361.645	+	286.798i	0.664789	+	0.527202i
$545$	−787.604	−	72.5045i	−1.44514	−	0.133036i
$546$	−29.5952	+	61.5407i	−0.0542037	+	0.112712i
$547$	−561.650			−1.02678			−0.513391	−	0.858155i	$-0.671611\pi$
$547$	−561.650			−1.02678			−0.513391	+	0.858155i	$0.671611\pi$
$548$	345.596	−	276.219i	0.630650	−	0.504049i
$549$	−67.2931			−0.122574
$550$	97.9466	−	133.815i	0.178085	−	0.243300i
$551$		−	165.462i		−	0.300294i
$552$	97.3860	+	423.491i	0.176424	+	0.767194i
$553$		−	196.053i		−	0.354527i
$554$	327.672	−	681.365i	0.591466	−	1.22990i
$555$	38.3881	−	417.003i	0.0691677	−	0.751356i
$556$	19.4203	−	15.5217i	0.0349286	−	0.0279168i
$557$		−	548.025i		−	0.983887i	−0.870627	−	0.491943i	$-0.836287\pi$
$557$		−	548.025i		−	0.983887i	0.870627	−	0.491943i	$-0.163713\pi$
$558$	−192.203	+	399.669i	−0.344450	+	0.716253i
$559$		−	259.460i		−	0.464151i
$560$	−44.4289	+	136.801i	−0.0793373	+	0.244288i
$561$	104.251			0.185831
$562$	−280.450	−	134.870i	−0.499022	−	0.239982i
$563$	363.695			0.645995			0.322998	−	0.946400i	$-0.395309\pi$
$563$	363.695			0.645995			0.322998	+	0.946400i	$0.395309\pi$
$564$	−274.740	−	343.745i	−0.487127	−	0.609477i
$565$	95.1274	−	1033.35i	0.168367	−	1.82894i
$566$	−862.418	−	414.741i	−1.52371	−	0.732758i
$567$	−44.3573			−0.0782315
$568$	342.076	−	78.6638i	0.602246	−	0.138493i
$569$	−739.646			−1.29990			−0.649952	−	0.759975i	$-0.725211\pi$
$569$	−739.646			−1.29990			−0.649952	+	0.759975i	$0.725211\pi$
$570$	106.120	−	177.014i	0.186176	−	0.310550i
$571$		−	375.140i		−	0.656988i	−0.944506	−	0.328494i	$-0.893459\pi$
$571$		−	375.140i		−	0.656988i	0.944506	−	0.328494i	$-0.106541\pi$
$572$	−72.1784	−	90.3072i	−0.126186	−	0.157880i
$573$			445.456i			0.777409i
$574$	−104.856	−	50.4259i	−0.182676	−	0.0878499i
$575$	612.659	+	113.763i	1.06549	+	0.197849i
$576$	244.731	−	118.841i	0.424880	−	0.206322i
$577$		−	690.750i		−	1.19714i	−0.801070	−	0.598570i	$-0.795736\pi$
$577$		−	690.750i		−	1.19714i	0.801070	−	0.598570i	$-0.204264\pi$
$578$	−145.910	−	70.1689i	−0.252439	−	0.121399i
$579$			53.0087i			0.0915521i
$580$	192.219	+	291.803i	0.331412	+	0.503108i
$581$	−20.6214			−0.0354929
$582$	−15.0157	+	31.2237i	−0.0258001	+	0.0536490i
$583$	−281.589			−0.483000
$584$	−833.999	+	191.786i	−1.42808	+	0.328401i
$585$	16.9789	−	184.438i	0.0290237	−	0.315279i
$586$	247.148	−	513.923i	0.421755	−	0.877002i
$587$	−284.979			−0.485483			−0.242742	−	0.970091i	$-0.578047\pi$
$587$	−284.979			−0.485483			−0.242742	+	0.970091i	$0.578047\pi$
$588$	249.081	+	311.643i	0.423608	+	0.530004i
$589$	494.015			0.838735
$590$	−73.8059	+	123.112i	−0.125095	+	0.208664i
$591$			301.773i			0.510614i
$592$	−599.797	−	135.528i	−1.01317	−	0.228933i
$593$			160.644i			0.270900i	0.990784	+	0.135450i	$0.0432480\pi$
$593$			160.644i			0.270900i	−0.990784	+	0.135450i	$0.956752\pi$
$594$	83.0156	−	172.624i	0.139757	−	0.290612i
$595$	−11.8864	+	129.120i	−0.0199772	+	0.217008i
$596$	164.354	+	205.635i	0.275762	+	0.345025i
$597$		−	151.451i		−	0.253687i
$598$	188.270	−	391.492i	0.314834	−	0.654669i
$599$		−	482.821i		−	0.806046i	−0.915190	−	0.403023i	$-0.867960\pi$
$599$		−	482.821i		−	0.806046i	0.915190	−	0.403023i	$-0.132040\pi$
$600$	18.4890	+	435.455i	0.0308151	+	0.725758i
$601$	−574.416			−0.955767			−0.477884	−	0.878423i	$-0.658596\pi$
$601$	−574.416			−0.955767			−0.477884	+	0.878423i	$0.658596\pi$
$602$	96.4871	+	46.4011i	0.160278	+	0.0770783i
$603$	−108.524			−0.179974
$604$	−49.3901	+	39.4752i	−0.0817716	+	0.0653563i
$605$	−54.7684	−	5.04182i	−0.0905263	−	0.00833359i
$606$	643.714	+	309.565i	1.06223	+	0.510834i
$607$	−970.858			−1.59944			−0.799718	−	0.600376i	$-0.795018\pi$
$607$	−970.858			−1.59944			−0.799718	+	0.600376i	$0.795018\pi$
$608$	−237.453	−	188.309i	−0.390548	−	0.309719i
$609$	−68.4544			−0.112405
$610$	−135.773	−	81.3960i	−0.222578	−	0.133436i
$611$			439.912i			0.719987i
$612$	191.585	−	153.125i	0.313047	−	0.250204i
$613$			413.900i			0.675203i	0.941289	+	0.337602i	$0.109616\pi$
$613$			413.900i			0.675203i	−0.941289	+	0.337602i	$0.890384\pi$
$614$	−853.691	−	410.544i	−1.39038	−	0.668639i
$615$	−351.081	−	32.3195i	−0.570864	−	0.0525521i
$616$	46.4913	−	10.6911i	0.0754728	−	0.0173557i
$617$		−	857.096i		−	1.38913i	−0.719428	−	0.694567i	$-0.755596\pi$
$617$		−	857.096i		−	1.38913i	0.719428	−	0.694567i	$-0.244404\pi$
$618$	−331.663	−	159.499i	−0.536672	−	0.258088i
$619$		−	667.962i		−	1.07910i	−0.841954	−	0.539549i	$-0.818595\pi$
$619$		−	667.962i		−	1.07910i	0.841954	−	0.539549i	$-0.181405\pi$
$620$	−871.225	+	573.901i	−1.40520	+	0.925647i
$621$	719.764			1.15904
$622$	−103.360	+	214.928i	−0.166173	+	0.345543i
$623$	−133.728			−0.214652
$624$	296.375	+	66.9678i	0.474959	+	0.107320i
$625$	583.337	+	224.373i	0.933339	+	0.358998i
$626$	311.018	−	646.734i	0.496834	−	1.03312i
$627$	−68.4506			−0.109172
$628$	−383.361	+	306.403i	−0.610448	+	0.487903i
$629$	−554.342			−0.881307
$630$	65.5518	+	39.2985i	0.104050	+	0.0623785i
$631$			1208.11i			1.91460i	0.289093	+	0.957301i	$0.406646\pi$
$631$			1208.11i			1.91460i	−0.289093	+	0.957301i	$0.593354\pi$
$632$	−850.158	+	195.502i	−1.34519	+	0.309339i
$633$			221.093i			0.349278i
$634$	−23.7717	+	49.4311i	−0.0374948	+	0.0779671i
$635$	−619.826	−	57.0594i	−0.976104	−	0.0898573i
$636$	578.122	−	462.066i	0.908996	−	0.726519i
$637$		−	398.829i		−	0.626104i
$638$	50.2263	−	104.441i	0.0787246	−	0.163701i
$639$		−	186.512i		−	0.291881i
$640$	637.524	+	56.2427i	0.996131	+	0.0878792i
$641$	888.974			1.38685			0.693427	−	0.720527i	$-0.256100\pi$
$641$	888.974			1.38685			0.693427	+	0.720527i	$0.256100\pi$
$642$	31.7842	+	15.2852i	0.0495081	+	0.0238087i
$643$	957.417			1.48899			0.744493	−	0.667631i	$-0.232691\pi$
$643$	957.417			1.48899			0.744493	+	0.667631i	$0.232691\pi$
$644$	111.917	+	140.027i	0.173784	+	0.217433i
$645$	323.060	+	29.7399i	0.500868	+	0.0461084i
$646$	−246.213	−	118.405i	−0.381135	−	0.183290i
$647$	−590.087			−0.912035			−0.456018	−	0.889971i	$-0.650725\pi$
$647$	−590.087			−0.912035			−0.456018	+	0.889971i	$0.650725\pi$
$648$	44.2326	+	192.349i	0.0682602	+	0.296835i
$649$	47.6070			0.0733544
$650$	257.349	−	351.591i	0.395922	−	0.540910i
$651$		−	204.382i		−	0.313951i
$652$	−399.864	−	500.297i	−0.613289	−	0.767327i
$653$			1155.22i			1.76909i	0.466452	+	0.884546i	$0.345532\pi$
$653$			1155.22i			1.76909i	−0.466452	+	0.884546i	$0.654468\pi$
$654$	−621.338	−	298.805i	−0.950058	−	0.456888i
$655$	−94.4185	+	1025.65i	−0.144150	+	1.56588i
$656$	−114.103	+	504.978i	−0.173938	+	0.769784i
$657$			454.725i			0.692124i
$658$	−163.593	−	78.6727i	−0.248621	−	0.119563i
$659$			610.028i			0.925688i	0.886440	+	0.462844i	$0.153171\pi$
$659$			610.028i			0.925688i	−0.886440	+	0.462844i	$0.846829\pi$
$660$	120.717	−	79.5196i	0.182904	−	0.120484i
$661$	808.423			1.22303			0.611515	−	0.791233i	$-0.290560\pi$
$661$	808.423			1.22303			0.611515	+	0.791233i	$0.290560\pi$
$662$	−178.120	+	370.385i	−0.269064	+	0.559494i
$663$	273.914			0.413144
$664$	20.5634	+	89.4218i	0.0309690	+	0.134671i
$665$	7.80452	−	84.7791i	0.0117361	−	0.127487i
$666$	−141.610	+	294.466i	−0.212628	+	0.442141i
$667$	435.474			0.652884
$668$	−74.6946	−	93.4554i	−0.111818	−	0.139903i
$669$	−377.983			−0.564997
$670$	−218.962	−	131.268i	−0.326808	−	0.195922i
$671$			52.5028i			0.0782456i
$672$	−77.9065	+	98.2383i	−0.115932	+	0.146188i
$673$			231.701i			0.344281i	0.985072	+	0.172140i	$0.0550682\pi$
$673$			231.701i			0.344281i	−0.985072	+	0.172140i	$0.944932\pi$
$674$	431.900	−	898.098i	0.640801	−	1.33249i
$675$	709.790	+	131.799i	1.05154	+	0.195258i
$676$	232.409	+	290.782i	0.343800	+	0.430152i
$677$			121.608i			0.179628i	0.995959	+	0.0898141i	$0.0286273\pi$
$677$			121.608i			0.179628i	−0.995959	+	0.0898141i	$0.971373\pi$
$678$	392.037	−	815.207i	0.578226	−	1.20237i
$679$			14.2923i			0.0210490i
$680$	571.764	−	77.2133i	0.840829	−	0.113549i
$681$	565.565			0.830493
$682$	311.827	+	149.959i	0.457224	+	0.219881i
$683$	589.049			0.862444			0.431222	−	0.902246i	$-0.358083\pi$
$683$	589.049			0.862444			0.431222	+	0.902246i	$0.358083\pi$
$684$	−125.793	+	100.541i	−0.183908	+	0.146989i
$685$	50.6953	−	550.694i	0.0740077	−	0.803933i
$686$	307.105	+	147.688i	0.447675	+	0.215289i
$687$	436.731			0.635708
$688$	104.996	−	464.674i	0.152611	−	0.675398i
$689$	−739.859			−1.07382
$690$	465.875	+	279.293i	0.675182	+	0.404773i
$691$		−	467.669i		−	0.676800i	−0.941002	−	0.338400i	$-0.890114\pi$
$691$		−	467.669i		−	0.676800i	0.941002	−	0.338400i	$-0.109886\pi$
$692$	898.689	−	718.281i	1.29868	−	1.03798i
$693$		−	25.3487i		−	0.0365782i
$694$	1096.01	+	527.075i	1.57926	+	0.759474i
$695$	2.84875	−	30.9455i	0.00409892	−	0.0445259i
$696$	68.2620	+	296.843i	0.0980776	+	0.426498i
$697$			466.710i			0.669598i
$698$	−718.010	−	345.294i	−1.02867	−	0.494691i
$699$			256.692i			0.367227i
$700$	84.7249	+	158.580i	0.121036	+	0.226542i
$701$	359.840			0.513323			0.256662	−	0.966501i	$-0.417377\pi$
$701$	359.840			0.513323			0.256662	+	0.966501i	$0.417377\pi$
$702$	218.119	−	453.559i	0.310711	−	0.646096i
$703$	363.977			0.517748
$704$	−92.7212	−	190.942i	−0.131706	−	0.271224i
$705$	−547.745	−	50.4238i	−0.776943	−	0.0715231i
$706$	−122.807	+	255.366i	−0.173947	+	0.361708i
$707$	294.652			0.416764
$708$	−97.7405	+	78.1195i	−0.138052	+	0.110338i
$709$	−682.443			−0.962543			−0.481272	−	0.876572i	$-0.659825\pi$
$709$	−682.443			−0.962543			−0.481272	+	0.876572i	$0.659825\pi$
$710$	225.600	−	376.312i	0.317747	−	0.530017i
$711$			463.536i			0.651950i
$712$	133.352	+	579.893i	0.187292	+	0.814456i
$713$			1300.18i			1.82353i
$714$	−48.9861	+	101.862i	−0.0686080	+	0.142664i
$715$	−143.901	−	13.2471i	−0.201260	−	0.0185274i
$716$	−842.142	+	673.085i	−1.17618	+	0.940063i
$717$			948.999i			1.32357i
$718$	208.119	−	432.766i	0.289860	−	0.602738i
$719$		−	1204.90i		−	1.67580i	−0.545821	−	0.837902i	$-0.683782\pi$
$719$		−	1204.90i		−	1.67580i	0.545821	−	0.837902i	$-0.316218\pi$
$720$	105.045	−	323.444i	0.145896	−	0.449228i
$721$	−151.815			−0.210562
$722$	−489.008	−	235.167i	−0.677297	−	0.325715i
$723$	583.428			0.806954
$724$	128.923	+	161.304i	0.178070	+	0.222795i
$725$	429.439	+	79.7416i	0.592329	+	0.109988i
$726$	−43.2066	−	20.7783i	−0.0595133	−	0.0286202i
$727$	72.6740			0.0999642			0.0499821	−	0.998750i	$-0.484084\pi$
$727$	72.6740			0.0999642			0.0499821	+	0.998750i	$0.484084\pi$
$728$	122.153	−	28.0904i	0.167793	−	0.0385856i
$729$	671.242			0.920771
$730$	−550.025	+	917.468i	−0.753458	+	1.25681i
$731$		−	429.459i		−	0.587496i
$732$	−86.1532	−	107.792i	−0.117696	−	0.147257i
$733$			581.088i			0.792753i	0.918088	+	0.396376i	$0.129732\pi$
$733$			581.088i			0.792753i	−0.918088	+	0.396376i	$0.870268\pi$
$734$	−1049.86	−	504.883i	−1.43033	−	0.687852i
$735$	496.590	+	45.7147i	0.675633	+	0.0621968i
$736$	495.604	−	624.945i	0.673375	−	0.849110i
$737$			84.6717i			0.114887i
$738$	247.915	+	119.224i	0.335929	+	0.161550i
$739$			1439.44i			1.94782i	0.226941	+	0.973909i	$0.427128\pi$
$739$			1439.44i			1.94782i	−0.226941	+	0.973909i	$0.572872\pi$
$740$	−641.895	+	422.835i	−0.867426	+	0.571399i
$741$	−179.850			−0.242713
$742$	132.314	−	275.136i	0.178321	−	0.370803i
$743$	813.610			1.09503			0.547517	−	0.836794i	$-0.315573\pi$
$743$	813.610			1.09503			0.547517	+	0.836794i	$0.315573\pi$
$744$	−886.273	+	203.808i	−1.19123	+	0.273935i
$745$	327.671	+	30.1644i	0.439827	+	0.0404892i
$746$	33.0806	−	68.7882i	0.0443439	−	0.0922093i
$747$	48.7559			0.0652689
$748$	−119.470	−	149.477i	−0.159719	−	0.199835i
$749$	14.5488			0.0194243
$750$	408.276	+	360.731i	0.544368	+	0.480975i
$751$		−	798.583i		−	1.06336i	−0.846945	−	0.531680i	$-0.821561\pi$
$751$		−	798.583i		−	1.06336i	0.846945	−	0.531680i	$-0.178439\pi$
$752$	−178.020	+	787.850i	−0.236729	+	1.04767i
$753$		−	231.866i		−	0.307923i
$754$	131.967	−	274.413i	0.175022	−	0.363944i
$755$	−7.24500	+	78.7011i	−0.00959603	+	0.104240i
$756$	129.660	+	162.226i	0.171508	+	0.214585i
$757$			365.494i			0.482819i	0.970423	+	0.241409i	$0.0776097\pi$
$757$			365.494i			0.482819i	−0.970423	+	0.241409i	$0.922390\pi$
$758$	379.028	−	788.155i	0.500036	−	1.03978i
$759$		−	180.152i		−	0.237355i
$760$	−375.415	+	50.6976i	−0.493968	+	0.0667074i
$761$	304.781			0.400500			0.200250	−	0.979745i	$-0.435824\pi$
$761$	304.781			0.400500			0.200250	+	0.979745i	$0.435824\pi$
$762$	−488.978	−	235.152i	−0.641704	−	0.308599i
$763$	−284.410			−0.372752
$764$	638.699	−	510.483i	0.835994	−	0.668171i
$765$	28.1035	−	305.283i	0.0367366	−	0.399063i
$766$	1318.47	+	634.061i	1.72125	+	0.827756i
$767$	125.085			0.163083
$768$	503.684	+	239.869i	0.655839	+	0.312329i
$769$	611.986			0.795821			0.397911	−	0.917424i	$-0.369735\pi$
$769$	611.986			0.795821			0.397911	+	0.917424i	$0.369735\pi$
$770$	30.6611	−	51.1443i	0.0398196	−	0.0664211i
$771$			518.683i			0.672741i
$772$	76.0044	−	60.7468i	0.0984513	−	0.0786876i
$773$			300.029i			0.388136i	0.980988	+	0.194068i	$0.0621683\pi$
$773$			300.029i			0.388136i	−0.980988	+	0.194068i	$0.937832\pi$
$774$	−228.128	−	109.708i	−0.294739	−	0.141741i
$775$	−238.082	+

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+(-1.80241 - 0.866788i) q^{2} -2.17924 q^{3} +(2.49736 + 3.12461i) q^{4} +(4.97895 + 0.458348i) q^{5} +(3.92787 + 1.88893i) q^{6} +1.79794 q^{7} +(-1.79289 - 7.79651i) q^{8} -4.25093 q^{9} +(-8.57681 - 5.14182i) q^{10} +3.31662i q^{11} +(-5.44233 - 6.80927i) q^{12} +8.71425i q^{13} +(-3.24062 - 1.55843i) q^{14} +(-10.8503 - 0.998848i) q^{15} +(-3.52640 + 15.6066i) q^{16} +14.4238i q^{17} +(7.66192 + 3.68466i) q^{18} -9.47058i q^{19} +(11.0021 + 16.7019i) q^{20} -3.91813 q^{21} +(2.87481 - 5.97792i) q^{22} +24.9253 q^{23} +(3.90712 + 16.9904i) q^{24} +(24.5798 + 4.56418i) q^{25} +(7.55340 - 15.7066i) q^{26} +28.8769 q^{27} +(4.49010 + 5.61786i) q^{28} +17.4712 q^{29} +(18.6909 + 11.2052i) q^{30} +52.1631i q^{31} +(19.8836 - 25.0727i) q^{32} -7.22771i q^{33} +(12.5024 - 25.9977i) q^{34} +(8.95184 + 0.824081i) q^{35} +(-10.6161 - 13.2825i) q^{36} +38.4324i q^{37} +(-8.20898 + 17.0699i) q^{38} -18.9904i q^{39} +(-5.35317 - 39.6402i) q^{40} +32.3568 q^{41} +(7.06208 + 3.39619i) q^{42} -29.7743 q^{43} +(-10.3632 + 8.28280i) q^{44} +(-21.1652 - 1.94840i) q^{45} +(-44.9255 - 21.6049i) q^{46} +50.4820 q^{47} +(7.68487 - 34.0104i) q^{48} -45.7674 q^{49} +(-40.3467 - 29.5320i) q^{50} -31.4330i q^{51} +(-27.2286 + 21.7626i) q^{52} +84.9022i q^{53} +(-52.0480 - 25.0301i) q^{54} +(-1.52017 + 16.5133i) q^{55} +(-3.22350 - 14.0176i) q^{56} +20.6386i q^{57} +(-31.4902 - 15.1438i) q^{58} -14.3540i q^{59} +(-23.9761 - 36.3975i) q^{60} +15.8302 q^{61} +(45.2143 - 94.0192i) q^{62} -7.64291 q^{63} +(-57.5711 + 27.9565i) q^{64} +(-3.99415 + 43.3878i) q^{65} +(-6.26489 + 13.0273i) q^{66} +25.5295 q^{67} +(-45.0689 + 36.0215i) q^{68} -54.3180 q^{69} +(-15.4206 - 9.24468i) q^{70} +43.8755i q^{71} +(7.62144 + 33.1424i) q^{72} -106.971i q^{73} +(33.3127 - 69.2708i) q^{74} +(-53.5653 - 9.94642i) q^{75} +(29.5919 - 23.6514i) q^{76} +5.96309i q^{77} +(-16.4606 + 34.2285i) q^{78} -109.043i q^{79} +(-24.7110 + 76.0879i) q^{80} -24.6712 q^{81} +(-58.3202 - 28.0465i) q^{82} -11.4695 q^{83} +(-9.78498 - 12.2426i) q^{84} +(-6.61113 + 71.8156i) q^{85} +(53.6654 + 25.8080i) q^{86} -38.0738 q^{87} +(25.8581 - 5.94633i) q^{88} -74.3785 q^{89} +(36.4594 + 21.8575i) q^{90} +15.6677i q^{91} +(62.2473 + 77.8818i) q^{92} -113.676i q^{93} +(-90.9892 - 43.7572i) q^{94} +(4.34082 - 47.1535i) q^{95} +(-43.3310 + 54.6394i) q^{96} +7.94927i q^{97} +(82.4916 + 39.6706i) q^{98} -14.0987i 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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