LMFDB - Embedded newform 220.3.i.a.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, degree $2$, 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:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80130 - 0.869100i) q^{2} +(-3.80725 + 3.80725i) q^{3} +(2.48933 + 3.13101i) q^{4} +(-3.43663 - 3.63175i) q^{5} +(10.1669 - 3.54910i) q^{6} +(2.92353 - 2.92353i) q^{7} +(-1.76286 - 7.80335i) q^{8} -19.9903i q^{9} +(3.03403 + 9.52862i) q^{10} +(10.9851 - 0.571624i) q^{11} +(-21.3981 - 2.44304i) q^{12} +(-3.91361 + 3.91361i) q^{13} +(-7.80698 + 2.72530i) q^{14} +(26.9111 + 0.742867i) q^{15} +(-3.60647 + 15.5882i) q^{16} +(-4.10909 - 4.10909i) q^{17} +(-17.3736 + 36.0085i) q^{18} +17.7640i q^{19} +(2.81614 - 19.8007i) q^{20} +22.2612i q^{21} +(-20.2843 - 8.51752i) q^{22} +(-18.1664 + 18.1664i) q^{23} +(36.4210 + 22.9977i) q^{24} +(-1.37917 + 24.9619i) q^{25} +(10.4509 - 3.64825i) q^{26} +(41.8430 + 41.8430i) q^{27} +(16.4312 + 1.87597i) q^{28} +49.6715 q^{29} +(-47.8292 - 24.7265i) q^{30} -4.97106i q^{31} +(20.0441 - 24.9447i) q^{32} +(-39.6469 + 43.9995i) q^{33} +(3.83047 + 10.9729i) q^{34} +(-20.6646 - 0.570436i) q^{35} +(62.5900 - 49.7626i) q^{36} +(-6.50891 + 6.50891i) q^{37} +(15.4387 - 31.9982i) q^{38} -29.8002i q^{39} +(-22.2815 + 33.2195i) q^{40} -68.4285i q^{41} +(19.3472 - 40.0991i) q^{42} +(37.6572 + 37.6572i) q^{43} +(29.1354 + 32.9716i) q^{44} +(-72.5999 + 68.6994i) q^{45} +(48.5116 - 16.9347i) q^{46} +(7.03047 + 7.03047i) q^{47} +(-45.6176 - 73.0791i) q^{48} +31.9059i q^{49} +(24.1787 - 43.7652i) q^{50} +31.2886 q^{51} +(-21.9958 - 2.51129i) q^{52} +(57.9551 + 57.9551i) q^{53} +(-39.0058 - 111.737i) q^{54} +(-39.8278 - 37.9308i) q^{55} +(-27.9671 - 17.6596i) q^{56} +(-67.6320 - 67.6320i) q^{57} +(-89.4730 - 43.1695i) q^{58} -16.5336 q^{59} +(64.6647 + 86.1082i) q^{60} +48.8872i q^{61} +(-4.32034 + 8.95434i) q^{62} +(-58.4424 - 58.4424i) q^{63} +(-57.7847 + 27.5124i) q^{64} +(27.6628 + 0.763619i) q^{65} +(109.656 - 44.7990i) q^{66} +(38.8253 + 38.8253i) q^{67} +(2.63672 - 23.0945i) q^{68} -138.328i q^{69} +(36.7273 + 18.9871i) q^{70} +97.0441i q^{71} +(-155.992 + 35.2401i) q^{72} +(70.5802 - 70.5802i) q^{73} +(17.3814 - 6.06758i) q^{74} +(-89.7855 - 100.287i) q^{75} +(-55.6193 + 44.2205i) q^{76} +(30.4442 - 33.7865i) q^{77} +(-25.8993 + 53.6789i) q^{78} +113.946i q^{79} +(69.0067 - 40.4732i) q^{80} -138.701 q^{81} +(-59.4713 + 123.260i) q^{82} +(-22.1248 - 22.1248i) q^{83} +(-69.7002 + 55.4156i) q^{84} +(-0.801761 + 29.0446i) q^{85} +(-35.1039 - 100.560i) q^{86} +(-189.112 + 189.112i) q^{87} +(-23.8258 - 84.7132i) q^{88} -91.3505i q^{89} +(190.480 - 60.6513i) q^{90} +22.8831i q^{91} +(-102.102 - 11.6571i) q^{92} +(18.9261 + 18.9261i) q^{93} +(-6.55377 - 18.7741i) q^{94} +(64.5144 - 61.0483i) q^{95} +(18.6578 + 171.283i) q^{96} +(80.1551 - 80.1551i) q^{97} +(27.7294 - 57.4720i) q^{98} +(-11.4269 - 219.597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	−1.80130	−	0.869100i	−0.900648	−	0.434550i
$2$	−1.80130	−	0.869100i	−0.900648	−	0.434550i
$3$	−3.80725	+	3.80725i	−1.26908	+	1.26908i	−0.322522	+	0.946562i	$0.604531\pi$
$3$	−3.80725	+	3.80725i	−1.26908	+	1.26908i	−0.946562	+	0.322522i	$0.895469\pi$
$4$	2.48933	+	3.13101i	0.622333	+	0.782753i
$5$	−3.43663	−	3.63175i	−0.687326	−	0.726349i
$5$	−3.43663	−	3.63175i	−0.687326	−	0.726349i
$6$	10.1669	−	3.54910i	1.69448	−	0.591517i
$7$	2.92353	−	2.92353i	0.417647	−	0.417647i	−0.466745	−	0.884392i	$-0.654573\pi$
$7$	2.92353	−	2.92353i	0.417647	−	0.417647i	0.884392	+	0.466745i	$0.154573\pi$
$8$	−1.76286	−	7.80335i	−0.220357	−	0.975419i
$9$		−	19.9903i		−	2.22115i
$10$	3.03403	+	9.52862i	0.303403	+	0.952862i
$11$	10.9851	−	0.571624i	0.998649	−	0.0519658i
$11$	10.9851	−	0.571624i	0.998649	−	0.0519658i
$12$	−21.3981	−	2.44304i	−1.78317	−	0.203587i
$13$	−3.91361	+	3.91361i	−0.301047	+	0.301047i	−0.841423	−	0.540377i	$-0.818282\pi$
$13$	−3.91361	+	3.91361i	−0.301047	+	0.301047i	0.540377	+	0.841423i	$0.318282\pi$
$14$	−7.80698	+	2.72530i	−0.557642	+	0.194664i
$15$	26.9111	+	0.742867i	1.79407	+	0.0495245i
$16$	−3.60647	+	15.5882i	−0.225404	+	0.974265i
$17$	−4.10909	−	4.10909i	−0.241711	−	0.241711i	0.575847	−	0.817558i	$-0.304672\pi$
$17$	−4.10909	−	4.10909i	−0.241711	−	0.241711i	−0.817558	+	0.575847i	$0.804672\pi$
$18$	−17.3736	+	36.0085i	−0.965200	+	2.00047i
$19$			17.7640i			0.934948i	0.884007	+	0.467474i	$0.154836\pi$
$19$			17.7640i			0.934948i	−0.884007	+	0.467474i	$0.845164\pi$
$20$	2.81614	−	19.8007i	0.140807	−	0.990037i
$21$			22.2612i			1.06006i
$22$	−20.2843	−	8.51752i	−0.922013	−	0.387160i
$23$	−18.1664	+	18.1664i	−0.789845	+	0.789845i	−0.981469	−	0.191623i	$-0.938625\pi$
$23$	−18.1664	+	18.1664i	−0.789845	+	0.789845i	0.191623	+	0.981469i	$0.438625\pi$
$24$	36.4210	+	22.9977i	1.51754	+	0.958237i
$25$	−1.37917	+	24.9619i	−0.0551670	+	0.998477i
$26$	10.4509	−	3.64825i	0.401957	−	0.140317i
$27$	41.8430	+	41.8430i	1.54974	+	1.54974i
$28$	16.4312	+	1.87597i	0.586830	+	0.0669991i
$29$	49.6715			1.71281			0.856404	−	0.516306i	$-0.172693\pi$
$29$	49.6715			1.71281			0.856404	+	0.516306i	$0.172693\pi$
$30$	−47.8292	−	24.7265i	−1.59431	−	0.824218i
$31$		−	4.97106i		−	0.160357i	−0.996781	−	0.0801783i	$-0.974451\pi$
$31$		−	4.97106i		−	0.160357i	0.996781	−	0.0801783i	$-0.0255490\pi$
$32$	20.0441	−	24.9447i	0.626377	−	0.779520i
$33$	−39.6469	+	43.9995i	−1.20142	+	1.33332i
$34$	3.83047	+	10.9729i	0.112661	+	0.322732i
$35$	−20.6646	−	0.570436i	−0.590417	−	0.0162982i
$36$	62.5900	−	49.7626i	1.73861	−	1.38229i
$37$	−6.50891	+	6.50891i	−0.175917	+	0.175917i	−0.789573	−	0.613657i	$-0.789698\pi$
$37$	−6.50891	+	6.50891i	−0.175917	+	0.175917i	0.613657	+	0.789573i	$0.289698\pi$
$38$	15.4387	−	31.9982i	0.406281	−	0.842058i
$39$		−	29.8002i		−	0.764107i
$40$	−22.2815	+	33.2195i	−0.557038	+	0.830487i
$41$		−	68.4285i		−	1.66899i	−0.551016	−	0.834494i	$-0.685760\pi$
$41$		−	68.4285i		−	1.66899i	0.551016	−	0.834494i	$-0.314240\pi$
$42$	19.3472	−	40.0991i	0.460649	−	0.954740i
$43$	37.6572	+	37.6572i	0.875749	+	0.875749i	0.993091	−	0.117343i	$-0.0374376\pi$
$43$	37.6572	+	37.6572i	0.875749	+	0.875749i	−0.117343	+	0.993091i	$0.537438\pi$
$44$	29.1354	+	32.9716i	0.662168	+	0.749355i
$45$	−72.5999	+	68.6994i	−1.61333	+	1.52665i
$46$	48.5116	−	16.9347i	1.05460	−	0.368145i
$47$	7.03047	+	7.03047i	0.149584	+	0.149584i	0.777932	−	0.628348i	$-0.216269\pi$
$47$	7.03047	+	7.03047i	0.149584	+	0.149584i	−0.628348	+	0.777932i	$0.716269\pi$
$48$	−45.6176	−	73.0791i	−0.950368	−	1.52248i
$49$			31.9059i			0.651142i
$50$	24.1787	−	43.7652i	0.483574	−	0.875303i
$51$	31.2886			0.613503
$52$	−21.9958	−	2.51129i	−0.422996	−	0.0482940i
$53$	57.9551	+	57.9551i	1.09349	+	1.09349i	0.995153	+	0.0983387i	$0.0313529\pi$
$53$	57.9551	+	57.9551i	1.09349	+	1.09349i	0.0983387	+	0.995153i	$0.468647\pi$
$54$	−39.0058	−	111.737i	−0.722330	−	2.06921i
$55$	−39.8278	−	37.9308i	−0.724142	−	0.689651i
$56$	−27.9671	−	17.6596i	−0.499413	−	0.315350i
$57$	−67.6320	−	67.6320i	−1.18653	−	1.18653i
$58$	−89.4730	−	43.1695i	−1.54264	−	0.744301i
$59$	−16.5336			−0.280230			−0.140115	−	0.990135i	$-0.544747\pi$
$59$	−16.5336			−0.280230			−0.140115	+	0.990135i	$0.544747\pi$
$60$	64.6647	+	86.1082i	1.07774	+	1.43514i
$61$			48.8872i			0.801429i	0.916203	+	0.400715i	$0.131238\pi$
$61$			48.8872i			0.801429i	−0.916203	+	0.400715i	$0.868762\pi$
$62$	−4.32034	+	8.95434i	−0.0696830	+	0.144425i
$63$	−58.4424	−	58.4424i	−0.927657	−	0.927657i
$64$	−57.7847	+	27.5124i	−0.902885	+	0.429881i
$65$	27.6628	+	0.763619i	0.425582	+	0.0117480i
$66$	109.656	−	44.7990i	1.66145	−	0.678773i
$67$	38.8253	+	38.8253i	0.579483	+	0.579483i	0.934761	−	0.355278i	$-0.115614\pi$
$67$	38.8253	+	38.8253i	0.579483	+	0.579483i	−0.355278	+	0.934761i	$0.615614\pi$
$68$	2.63672	−	23.0945i	0.0387753	−	0.339624i
$69$		−	138.328i		−	2.00476i
$70$	36.7273	+	18.9871i	0.524676	+	0.271245i
$71$			97.0441i			1.36682i	0.730036	+	0.683409i	$0.239503\pi$
$71$			97.0441i			1.36682i	−0.730036	+	0.683409i	$0.760497\pi$
$72$	−155.992	+	35.2401i	−2.16655	+	0.489446i
$73$	70.5802	−	70.5802i	0.966852	−	0.966852i	−0.0326160	−	0.999468i	$-0.510384\pi$
$73$	70.5802	−	70.5802i	0.966852	−	0.966852i	0.999468	+	0.0326160i	$0.0103838\pi$
$74$	17.3814	−	6.06758i	0.234883	−	0.0819943i
$75$	−89.7855	−	100.287i	−1.19714	−	1.33716i
$76$	−55.6193	+	44.2205i	−0.731833	+	0.581848i
$77$	30.4442	−	33.7865i	0.395380	−	0.438786i
$78$	−25.8993	+	53.6789i	−0.332043	+	0.688191i
$79$			113.946i			1.44235i	0.692753	+	0.721175i	$0.256398\pi$
$79$			113.946i			1.44235i	−0.692753	+	0.721175i	$0.743602\pi$
$80$	69.0067	−	40.4732i	0.862583	−	0.505915i
$81$	−138.701			−1.71235
$82$	−59.4713	+	123.260i	−0.725259	+	1.50317i
$83$	−22.1248	−	22.1248i	−0.266564	−	0.266564i	0.561150	−	0.827714i	$-0.310359\pi$
$83$	−22.1248	−	22.1248i	−0.266564	−	0.266564i	−0.827714	+	0.561150i	$0.810359\pi$
$84$	−69.7002	+	55.4156i	−0.829764	+	0.659709i
$85$	−0.801761	+	29.0446i	−0.00943248	+	0.341701i
$86$	−35.1039	−	100.560i	−0.408185	−	1.16930i
$87$	−189.112	+	189.112i	−2.17370	+	2.17370i
$88$	−23.8258	−	84.7132i	−0.270748	−	0.962650i
$89$		−	91.3505i		−	1.02641i	−0.858266	−	0.513205i	$-0.828458\pi$
$89$		−	91.3505i		−	1.02641i	0.858266	−	0.513205i	$-0.171542\pi$
$90$	190.480	−	60.6513i	2.11645	−	0.673903i
$91$			22.8831i			0.251463i
$92$	−102.102	−	11.6571i	−1.10980	−	0.126707i
$93$	18.9261	+	18.9261i	0.203506	+	0.203506i
$94$	−6.55377	−	18.7741i	−0.0697210	−	0.199725i
$95$	64.5144	−	61.0483i	0.679099	−	0.642613i
$96$	18.6578	+	171.283i	0.194352	+	1.78420i
$97$	80.1551	−	80.1551i	0.826341	−	0.826341i	−0.160667	−	0.987009i	$-0.551365\pi$
$97$	80.1551	−	80.1551i	0.826341	−	0.826341i	0.987009	+	0.160667i	$0.0513646\pi$
$98$	27.7294	−	57.4720i	0.282954	−	0.586449i
$99$	−11.4269	−	219.597i	−0.115424	−	2.21815i
$100$	−81.5893	+	57.8203i	−0.815893	+	0.578203i
$101$			110.833i			1.09736i	0.836032	+	0.548680i	$0.184870\pi$
$101$			110.833i			1.09736i	−0.836032	+	0.548680i	$0.815130\pi$
$102$	−56.3601	−	27.1930i	−0.552550	−	0.266598i
$103$	84.5855	−	84.5855i	0.821219	−	0.821219i	−0.165064	−	0.986283i	$-0.552783\pi$
$103$	84.5855	−	84.5855i	0.821219	−	0.821219i	0.986283	+	0.165064i	$0.0527831\pi$
$104$	37.4384	+	23.6401i	0.359985	+	0.227309i
$105$	80.8472	−	76.5036i	0.769973	−	0.728606i
$106$	−54.0254	−	154.763i	−0.509674	−	1.46003i
$107$	87.9803	−	87.9803i	0.822245	−	0.822245i	−0.164184	−	0.986430i	$-0.552499\pi$
$107$	87.9803	−	87.9803i	0.822245	−	0.822245i	0.986430	+	0.164184i	$0.0524992\pi$
$108$	−26.8499	+	235.172i	−0.248610	+	2.17752i
$109$	−16.1479			−0.148146			−0.0740728	−	0.997253i	$-0.523600\pi$
$109$	−16.1479			−0.148146			−0.0740728	+	0.997253i	$0.523600\pi$
$110$	38.7760	+	102.939i	0.352509	+	0.935808i
$111$		−	49.5622i		−	0.446506i
$112$	35.0291	+	56.1163i	0.312760	+	0.501039i
$113$	33.0174	+	33.0174i	0.292189	+	0.292189i	0.837944	−	0.545756i	$-0.183757\pi$
$113$	33.0174	+	33.0174i	0.292189	+	0.292189i	−0.545756	+	0.837944i	$0.683757\pi$
$114$	63.0463	+	180.604i	0.553038	+	1.58425i
$115$	128.407	+	3.54462i	1.11658	+	0.0308228i
$116$	123.649	+	155.522i	1.06594	+	1.34071i
$117$	78.2343	+	78.2343i	0.668669	+	0.668669i
$118$	29.7818	+	14.3693i	0.252388	+	0.121774i
$119$	−24.0261			−0.201900
$120$	−41.6436	−	211.306i	−0.347030	−	1.76089i
$121$	120.346	−	12.5587i	0.994599	−	0.103791i
$122$	42.4879	−	88.0603i	0.348261	−	0.721805i
$123$	260.525	+	260.525i	2.11809	+	2.11809i
$124$	15.5644	−	12.3746i	0.125520	−	0.0997952i
$125$	95.3951	−	80.7761i	0.763161	−	0.646208i
$126$	54.4797	+	156.064i	0.432379	+	1.23860i
$127$	−7.88299	+	7.88299i	−0.0620708	+	0.0620708i	−0.737461	−	0.675390i	$-0.763975\pi$
$127$	−7.88299	+	7.88299i	−0.0620708	+	0.0620708i	0.675390	+	0.737461i	$0.263975\pi$
$128$	127.998	+	0.662689i	0.999987	+	0.00517726i
$129$	−286.741			−2.22280
$130$	−49.1653	−	25.4173i	−0.378195	−	0.195518i
$131$	−65.8739			−0.502855			−0.251427	−	0.967876i	$-0.580900\pi$
$131$	−65.8739			−0.502855			−0.251427	+	0.967876i	$0.580900\pi$
$132$	−236.457	−	14.6055i	−1.79134	−	0.110648i
$133$	51.9336	+	51.9336i	0.390478	+	0.390478i
$134$	−36.1928	−	103.679i	−0.270096	−	0.773724i
$135$	8.16436	−	295.762i	0.0604768	−	2.19083i
$136$	−24.8209	+	39.3084i	−0.182507	+	0.289032i
$137$	−45.3705	+	45.3705i	−0.331172	+	0.331172i	−0.853031	−	0.521860i	$-0.825238\pi$
$137$	−45.3705	+	45.3705i	−0.331172	+	0.331172i	0.521860	+	0.853031i	$0.325238\pi$
$138$	−120.221	+	249.170i	−0.871169	+	1.80558i
$139$		−	131.910i		−	0.948992i	−0.880258	−	0.474496i	$-0.842630\pi$
$139$		−	131.910i		−	0.948992i	0.880258	−	0.474496i	$-0.157370\pi$
$140$	−49.6550	−	66.1211i	−0.354679	−	0.472294i
$141$	−53.5335			−0.379670
$142$	84.3410	−	174.805i	0.593951	−	1.23102i
$143$	−40.7544	+	45.2286i	−0.284996	+	0.316284i
$144$	311.614	+	72.0945i	2.16399	+	0.500656i
$145$	−170.702	−	180.394i	−1.17726	−	1.24410i
$146$	−188.477	+	65.7945i	−1.29094	+	0.450648i
$147$	−121.474	−	121.474i	−0.826353	−	0.826353i
$148$	−36.5823	−	4.17665i	−0.247178	−	0.0282206i
$149$	146.686			0.984471			0.492235	−	0.870462i	$-0.336180\pi$
$149$	146.686			0.984471			0.492235	+	0.870462i	$0.336180\pi$
$150$	74.5706	+	258.679i	0.497137	+	1.72453i
$151$	15.4518			0.102330			0.0511650	−	0.998690i	$-0.483707\pi$
$151$	15.4518			0.102330			0.0511650	+	0.998690i	$0.483707\pi$
$152$	138.619	−	31.3154i	0.911966	−	0.206022i
$153$	−82.1420	+	82.1420i	−0.536876	+	0.536876i
$154$	−84.2029	+	34.4005i	−0.546772	+	0.223380i
$155$	−18.0536	+	17.0837i	−0.116475	+	0.110217i
$156$	93.3047	−	74.1825i	0.598107	−	0.475529i
$157$	−186.149	+	186.149i	−1.18566	+	1.18566i	−0.207408	+	0.978255i	$0.566503\pi$
$157$	−186.149	+	186.149i	−1.18566	+	1.18566i	−0.978255	+	0.207408i	$0.933497\pi$
$158$	99.0302	−	205.250i	0.626773	−	1.29905i
$159$	−441.299			−2.77547
$160$	−159.477	+	12.9306i	−0.996729	+	0.0808159i
$161$			106.220i			0.659753i
$162$	249.841	+	120.545i	1.54223	+	0.744103i
$163$	−19.7458	+	19.7458i	−0.121140	+	0.121140i	−0.765078	−	0.643938i	$-0.777300\pi$
$163$	−19.7458	+	19.7458i	−0.121140	+	0.121140i	0.643938	+	0.765078i	$0.277300\pi$
$164$	214.251	−	170.341i	1.30641	−	1.03867i
$165$	296.047	−	7.22251i	1.79422	−	0.0437728i
$166$	20.6246	+	59.0820i	0.124245	+	0.355916i
$167$	−73.3723	+	73.3723i	−0.439355	+	0.439355i	−0.891795	−	0.452440i	$-0.850554\pi$
$167$	−73.3723	+	73.3723i	−0.439355	+	0.439355i	0.452440	+	0.891795i	$0.350554\pi$
$168$	173.712	−	39.2434i	1.03400	−	0.233592i
$169$			138.367i			0.818742i
$170$	26.6868	−	51.6210i	0.156981	−	0.303653i
$171$	355.108			2.07666
$172$	−24.1639	+	211.646i	−0.140488	+	1.23050i
$173$	−156.233	+	156.233i	−0.903083	+	0.903083i	−0.995702	−	0.0926191i	$-0.970476\pi$
$173$	−156.233	+	156.233i	−0.903083	+	0.903083i	0.0926191	+	0.995702i	$0.470476\pi$
$174$	505.003	−	176.289i	2.90232	−	1.01316i
$175$	68.9449	+	77.0090i	0.393971	+	0.440052i
$176$	−30.7069	+	173.301i	−0.174471	+	0.984662i
$177$	62.9474	−	62.9474i	0.355635	−	0.355635i
$178$	−79.3927	+	164.549i	−0.446026	+	0.924434i
$179$	−231.154			−1.29136			−0.645681	−	0.763607i	$-0.723426\pi$
$179$	−231.154			−1.29136			−0.645681	+	0.763607i	$0.723426\pi$
$180$	−395.823	−	56.2956i	−2.19902	−	0.312753i
$181$	144.589			0.798837			0.399418	−	0.916769i	$-0.369212\pi$
$181$	144.589			0.798837			0.399418	+	0.916769i	$0.369212\pi$
$182$	19.8877	−	41.2192i	0.109273	−	0.226479i
$183$	−186.126	−	186.126i	−1.01708	−	1.01708i
$184$	173.784	+	109.734i	0.944478	+	0.596382i
$185$	46.0074	+	1.27001i	0.248689	+	0.00686494i
$186$	−17.6428	−	50.5401i	−0.0948537	−	0.271721i
$187$	−47.4877	−	42.7900i	−0.253945	−	0.228824i
$188$	−4.51132	+	39.5136i	−0.0239964	+	0.210179i
$189$	244.658			1.29449
$190$	−169.267	+	53.8965i	−0.890876	+	0.283666i
$191$		−	46.9609i		−	0.245869i	−0.992415	−	0.122934i	$-0.960770\pi$
$191$		−	46.9609i		−	0.245869i	0.992415	−	0.122934i	$-0.0392305\pi$
$192$	115.254	−	324.747i	0.600282	−	1.69139i
$193$	88.2540	−	88.2540i	0.457274	−	0.457274i	−0.440485	−	0.897760i	$-0.645194\pi$
$193$	88.2540	−	88.2540i	0.457274	−	0.457274i	0.897760	+	0.440485i	$0.145194\pi$
$194$	−214.046	+	74.7202i	−1.10333	+	0.385156i
$195$	−108.227	+	102.412i	−0.555009	+	0.525190i
$196$	−99.8979	+	79.4244i	−0.509683	+	0.405227i
$197$	70.0227	+	70.0227i	0.355445	+	0.355445i	0.862131	−	0.506686i	$-0.169129\pi$
$197$	70.0227	+	70.0227i	0.355445	+	0.355445i	−0.506686	+	0.862131i	$0.669129\pi$
$198$	−170.268	+	405.490i	−0.859940	+	2.04793i
$199$	45.3723			0.228002			0.114001	−	0.993481i	$-0.463633\pi$
$199$	45.3723			0.228002			0.114001	+	0.993481i	$0.463633\pi$
$200$	197.218	−	33.2421i	0.986090	−	0.166211i
$201$	−295.636			−1.47082
$202$	96.3253	−	199.644i	0.476858	−	0.988335i
$203$	145.216	−	145.216i	0.715350	−	0.715350i
$204$	77.8878	+	97.9651i	0.381803	+	0.480221i
$205$	−248.515	+	235.163i	−1.21227	+	1.14714i
$206$	−225.877	+	78.8502i	−1.09649	+	0.382768i
$207$	363.153	+	363.153i	1.75436	+	1.75436i
$208$	−46.8920	−	75.1206i	−0.225442	−	0.361157i
$209$	10.1543	+	195.140i	0.0485853	+	0.933684i
$210$	−212.119	+	67.5413i	−1.01009	+	0.321625i
$211$	−351.272			−1.66479			−0.832397	−	0.554179i	$-0.813032\pi$
$211$	−351.272			−1.66479			−0.832397	+	0.554179i	$0.813032\pi$
$212$	−37.1887	+	325.727i	−0.175418	+	1.53645i
$213$	−369.471	−	369.471i	−1.73461	−	1.73461i
$214$	−234.942	+	82.0148i	−1.09786	+	0.383247i
$215$	7.34764	−	266.175i	0.0341751	−	1.23802i
$216$	252.752	−	400.279i	1.17015	−	1.85314i
$217$	−14.5330	−	14.5330i	−0.0669725	−	0.0669725i
$218$	29.0871	+	14.0341i	0.133427	+	0.0643766i
$219$			537.433i			2.45403i
$220$	19.6171	−	219.124i	0.0891687	−	0.996017i
$221$	32.1627			0.145533
$222$	−43.0745	+	89.2761i	−0.194029	+	0.402145i
$223$	186.470	−	186.470i	0.836190	−	0.836190i	−0.152165	−	0.988355i	$-0.548625\pi$
$223$	186.470	−	186.470i	0.836190	−	0.836190i	0.988355	+	0.152165i	$0.0486245\pi$
$224$	−14.3270	−	131.526i	−0.0639600	−	0.587169i
$225$	498.997	+	27.5702i	2.21777	+	0.122534i
$226$	−30.7786	−	88.1694i	−0.136189	−	0.390130i
$227$	223.442	−	223.442i	0.984328	−	0.984328i	−0.0155515	−	0.999879i	$-0.504950\pi$
$227$	223.442	−	223.442i	0.984328	−	0.984328i	0.999879	+	0.0155515i	$0.00495038\pi$
$228$	43.3982	−	380.115i	0.190343	−	1.66717i
$229$			116.773i			0.509926i	0.966951	+	0.254963i	$0.0820632\pi$
$229$			116.773i			0.509926i	−0.966951	+	0.254963i	$0.917937\pi$
$230$	−228.219	−	117.984i	−0.992255	−	0.512972i
$231$	12.7250	+	244.543i	0.0550868	+	1.05863i
$232$	−87.5637	−	387.604i	−0.377430	−	1.67071i
$233$	190.787	−	190.787i	0.818826	−	0.818826i	−0.167112	−	0.985938i	$-0.553444\pi$
$233$	190.787	−	190.787i	0.818826	−	0.818826i	0.985938	+	0.167112i	$0.0534441\pi$
$234$	−72.9297	−	208.917i	−0.311665	−	0.892806i
$235$	1.37178	−	49.6940i	0.00583735	−	0.211464i
$236$	−41.1575	−	51.7668i	−0.174396	−	0.219351i
$237$	−433.820	−	433.820i	−1.83046	−	1.83046i
$238$	43.2781	+	20.8811i	0.181841	+	0.0877355i
$239$		−	155.155i		−	0.649184i	−0.945854	−	0.324592i	$-0.894773\pi$
$239$		−	155.155i		−	0.649184i	0.945854	−	0.324592i	$-0.105227\pi$
$240$	−108.634	+	416.817i	−0.452642	+	1.73674i
$241$			132.912i			0.551502i	0.961229	+	0.275751i	$0.0889265\pi$
$241$			132.912i			0.551502i	−0.961229	+	0.275751i	$0.911073\pi$
$242$	−227.694	−	81.9712i	−0.940886	−	0.338724i
$243$	151.481	−	151.481i	0.623379	−	0.623379i
$244$	−153.066	+	121.696i	−0.627321	+	0.498756i
$245$	115.874	−	109.649i	0.472956	−	0.447546i
$246$	−242.860	−	695.704i	−0.987236	−	2.82807i
$247$	−69.5213	−	69.5213i	−0.281463	−	0.281463i
$248$	−38.7909	+	8.76326i	−0.156415	+	0.0353357i
$249$	168.469			0.676584
$250$	−242.037	+	62.5936i	−0.968149	+	0.250375i
$251$			257.392i			1.02547i	0.858548	+	0.512734i	$0.171367\pi$
$251$			257.392i			1.02547i	−0.858548	+	0.512734i	$0.828633\pi$
$252$	37.5014	−	328.466i	0.148815	−	1.30344i
$253$	−189.177	+	209.945i	−0.747733	+	0.829823i
$254$	21.0507	−	7.34849i	0.0828768	−	0.0289311i
$255$	−107.527	−	113.632i	−0.421676	−	0.445617i
$256$	−229.987	−	112.437i	−0.898386	−	0.439207i
$257$	−177.587	+	177.587i	−0.690999	+	0.690999i	−0.962452	−	0.271452i	$-0.912496\pi$
$257$	−177.587	+	177.587i	−0.690999	+	0.690999i	0.271452	+	0.962452i	$0.412496\pi$
$258$	516.505	+	249.207i	2.00196	+	0.965917i
$259$			38.0580i			0.146942i
$260$	66.4711	+	88.5136i	0.255658	+	0.340437i
$261$		−	992.949i		−	3.80440i
$262$	118.658	+	57.2510i	0.452895	+	0.218515i
$263$	−172.722	−	172.722i	−0.656738	−	0.656738i	0.297869	−	0.954607i	$-0.403724\pi$
$263$	−172.722	−	172.722i	−0.656738	−	0.656738i	−0.954607	+	0.297869i	$0.903724\pi$
$264$	413.235	+	231.814i	1.56529	+	0.878082i
$265$	11.3081	−	409.648i	0.0426722	−	1.54584i
$266$	−48.4123	−	138.683i	−0.182001	−	0.521366i
$267$	347.794	+	347.794i	1.30260	+	1.30260i
$268$	−24.9135	+	218.212i	−0.0929608	+	0.814223i
$269$		−	306.695i		−	1.14013i	−0.821600	−	0.570064i	$-0.806918\pi$
$269$		−	306.695i		−	1.14013i	0.821600	−	0.570064i	$-0.193082\pi$
$270$	−271.753	+	525.659i	−1.00649	+	1.94688i
$271$	−131.909			−0.486751			−0.243375	−	0.969932i	$-0.578255\pi$
$271$	−131.909			−0.486751			−0.243375	+	0.969932i	$0.578255\pi$
$272$	78.8727	−	49.2341i	0.289973	−	0.181008i
$273$	−87.1217	−	87.1217i	−0.319127	−	0.319127i
$274$	121.157	−	42.2942i	0.442180	−	0.154358i
$275$	−0.881594	+	274.999i	−0.00320580	+	0.999995i
$276$	433.108	−	344.345i	1.56923	−	1.24763i
$277$	−128.214	−	128.214i	−0.462866	−	0.462866i	0.436728	−	0.899594i	$-0.356137\pi$
$277$	−128.214	−	128.214i	−0.462866	−	0.462866i	−0.899594	+	0.436728i	$0.856137\pi$
$278$	−114.643	+	237.609i	−0.412385	+	0.854708i
$279$	−99.3731			−0.356176
$280$	31.9774	+	162.259i	0.114205	+	0.579496i
$281$			0.0818856i			0.000291408i	1.00000		0.000145704i	$4.63790e-5\pi$
$281$			0.0818856i			0.000291408i	−1.00000		0.000145704i	$0.999954\pi$
$282$	96.4297	+	46.5260i	0.341949	+	0.164986i
$283$	228.264	+	228.264i	0.806585	+	0.806585i	0.984115	−	0.177530i	$-0.0568108\pi$
$283$	228.264	+	228.264i	0.806585	+	0.806585i	−0.177530	+	0.984115i	$0.556811\pi$
$284$	−303.846	+	241.575i	−1.06988	+	0.850616i
$285$	−13.1963	+	478.049i	−0.0463028	+	1.67736i
$286$	112.719	−	46.0505i	0.394122	−	0.161016i
$287$	−200.053	−	200.053i	−0.697049	−	0.697049i
$288$	−498.652	−	400.687i	−1.73143	−	1.39128i
$289$		−	255.231i		−	0.883152i
$290$	150.705	+	473.301i	0.519672	+	1.63207i
$291$			610.341i			2.09739i
$292$	396.685	+	45.2900i	1.35851	+	0.155103i
$293$	139.828	−	139.828i	0.477230	−	0.477230i	−0.427015	−	0.904245i	$-0.640435\pi$
$293$	139.828	−	139.828i	0.477230	−	0.477230i	0.904245	+	0.427015i	$0.140435\pi$
$294$	113.237	+	324.383i	0.385161	+	1.10335i
$295$	56.8197	+	60.0457i	0.192609	+	0.203545i
$296$	62.2656	+	39.3171i	0.210357	+	0.132828i
$297$	483.569	+	435.733i	1.62818	+	1.46711i
$298$	−264.225	−	127.485i	−0.886661	−	0.427802i
$299$		−	142.193i		−	0.475561i
$300$	90.4947	−	530.767i	0.301649	−	1.76922i
$301$	220.184			0.731508
$302$	−27.8333	−	13.4292i	−0.0921634	−	0.0444675i
$303$	−421.971	−	421.971i	−1.39264	−	1.39264i
$304$	−276.910	−	64.0653i	−0.910887	−	0.210741i
$305$	177.546	−	168.007i	0.582118	−	0.550843i
$306$	219.352	−	76.5724i	0.716835	−	0.250237i
$307$	176.970	−	176.970i	0.576448	−	0.576448i	−0.357475	−	0.933923i	$-0.616362\pi$
$307$	176.970	−	176.970i	0.576448	−	0.576448i	0.933923	+	0.357475i	$0.116362\pi$
$308$	181.572	+	11.2154i	0.589519	+	0.0364135i
$309$			644.077i			2.08439i
$310$	47.3673	−	15.0823i	0.152798	−	0.0486527i
$311$			304.716i			0.979796i	0.871780	+	0.489898i	$0.162966\pi$
$311$			304.716i			0.979796i	−0.871780	+	0.489898i	$0.837034\pi$
$312$	−232.541	+	52.5335i	−0.745325	+	0.168376i
$313$	125.900	+	125.900i	0.402238	+	0.402238i	0.879021	−	0.476783i	$-0.158197\pi$
$313$	125.900	+	125.900i	0.402238	+	0.402238i	−0.476783	+	0.879021i	$0.658197\pi$
$314$	497.092	−	173.527i	1.58309	−	0.552635i
$315$	−11.4032	+	413.093i	−0.0362007	+	1.31140i
$316$	−356.765	+	283.648i	−1.12900	+	0.897622i
$317$	−280.157	+	280.157i	−0.883775	+	0.883775i	−0.993916	−	0.110141i	$-0.964870\pi$
$317$	−280.157	+	280.157i	−0.883775	+	0.883775i	0.110141	+	0.993916i	$0.464870\pi$
$318$	794.910	+	383.533i	2.49972	+	1.20608i
$319$	545.648	−	28.3934i	1.71049	−	0.0890074i
$320$	298.502	+	115.309i	0.932820	+	0.360342i
$321$			669.926i			2.08700i
$322$	92.3161	−	191.334i	0.286696	−	0.594205i
$323$	72.9938	−	72.9938i	0.225987	−	0.225987i
$324$	−345.272	−	434.273i	−1.06565	−	1.34035i
$325$	−92.2936	−	103.089i	−0.283980	−	0.317196i
$326$	52.7291	−	18.4069i	0.161746	−	0.0564630i
$327$	61.4790	−	61.4790i	0.188009	−	0.188009i
$328$	−533.972	+	120.630i	−1.62796	+	0.367774i
$329$	41.1076			0.124947
$330$	−539.545	−	244.284i	−1.63498	−	0.740255i
$331$		−	330.681i		−	0.999036i	−0.866304	−	0.499518i	$-0.833511\pi$
$331$		−	330.681i		−	0.999036i	0.866304	−	0.499518i	$-0.166489\pi$
$332$	14.1971	−	124.349i	0.0427623	−	0.374545i
$333$	130.115	+	130.115i	0.390737	+	0.390737i
$334$	195.933	−	68.3973i	0.586626	−	0.204782i
$335$	7.57556	−	274.432i	0.0226136	−	0.819200i
$336$	−347.014	−	80.2844i	−1.03278	−	0.238942i
$337$	233.377	+	233.377i	0.692513	+	0.692513i	0.962784	−	0.270272i	$-0.0871135\pi$
$337$	233.377	+	233.377i	0.692513	+	0.692513i	−0.270272	+	0.962784i	$0.587113\pi$
$338$	120.255	−	249.240i	0.355784	−	0.737398i
$339$	−251.411			−0.741625
$340$	−92.9347	+	69.7912i	−0.273337	+	0.205268i
$341$	−2.84157	−	54.6077i	−0.00833306	−	0.160140i
$342$	−639.655	−	308.625i	−1.87034	−	0.902412i
$343$	236.531	+	236.531i	0.689595	+	0.689595i
$344$	227.468	−	360.237i	0.661245	−	1.04720i
$345$	−502.374	+	475.383i	−1.45616	+	1.37792i
$346$	417.205	−	145.640i	1.20579	−	0.420925i
$347$	−373.845	+	373.845i	−1.07736	+	1.07736i	−0.0806173	+	0.996745i	$0.525689\pi$
$347$	−373.845	+	373.845i	−1.07736	+	1.07736i	−0.996745	+	0.0806173i	$0.974311\pi$
$348$	−1062.87	−	121.349i	−3.05423	−	0.348705i
$349$	102.282			0.293072			0.146536	−	0.989205i	$-0.453188\pi$
$349$	102.282			0.293072			0.146536	+	0.989205i	$0.453188\pi$
$350$	−57.2616	−	198.636i	−0.163605	−	0.567531i
$351$	−327.514			−0.933088
$352$	205.928	−	285.478i	0.585022	−	0.811017i
$353$	−279.773	−	279.773i	−0.792557	−	0.792557i	0.189352	−	0.981909i	$-0.439361\pi$
$353$	−279.773	−	279.773i	−0.792557	−	0.792557i	−0.981909	+	0.189352i	$0.939361\pi$
$354$	−168.095	+	58.6793i	−0.474843	+	0.165761i
$355$	352.440	−	333.504i	0.992788	−	0.939449i
$356$	286.019	−	227.402i	0.803425	−	0.638768i
$357$	91.4733	−	91.4733i	0.256228	−	0.256228i
$358$	416.376	+	200.896i	1.16306	+	0.561161i
$359$			232.738i			0.648296i	0.946006	+	0.324148i	$0.105078\pi$
$359$			232.738i			0.648296i	−0.946006	+	0.324148i	$0.894922\pi$
$360$	664.069	+	445.415i	1.84463	+	1.23726i
$361$	45.4401			0.125873
$362$	−260.448	−	125.663i	−0.719471	−	0.347135i
$363$	−410.375	+	506.004i	−1.13051	+	1.39395i
$364$	−71.6473	+	56.9636i	−0.196833	+	0.156493i
$365$	−498.887	−	13.7715i	−1.36681	−	0.0377302i
$366$	173.506	+	497.030i	0.474059	+	1.35800i
$367$	164.798	+	164.798i	0.449040	+	0.449040i	0.895035	−	0.445995i	$-0.147150\pi$
$367$	164.798	+	164.798i	0.449040	+	0.449040i	−0.445995	+	0.895035i	$0.647150\pi$
$368$	−217.666	−	348.700i	−0.591484	−	0.947553i
$369$	−1367.91			−3.70707
$370$	−81.7692	−	42.2727i	−0.220998	−	0.114251i
$371$	338.867			0.913388
$372$	−12.1445	+	106.371i	−0.0326465	+	0.285943i
$373$	289.220	−	289.220i	0.775389	−	0.775389i	−0.203654	−	0.979043i	$-0.565282\pi$
$373$	289.220	−	289.220i	0.775389	−	0.775389i	0.979043	+	0.203654i	$0.0652818\pi$
$374$	48.3506	+	118.349i	0.129280	+	0.316441i
$375$	−55.6585	+	670.728i	−0.148423	+	1.78861i
$376$	42.4675	−	67.2549i	0.112946	−	0.178870i
$377$	−194.395	+	194.395i	−0.515635	+	0.515635i
$378$	−440.702	−	212.633i	−1.16588	−	0.562520i
$379$	−123.947			−0.327037			−0.163519	−	0.986540i	$-0.552284\pi$
$379$	−123.947			−0.327037			−0.163519	+	0.986540i	$0.552284\pi$
$380$	351.740	+	50.0259i	0.925633	+	0.131647i
$381$		−	60.0251i		−	0.157546i
$382$	−40.8138	+	84.5905i	−0.106842	+	0.221441i
$383$	−118.342	+	118.342i	−0.308986	+	0.308986i	−0.844516	−	0.535530i	$-0.820112\pi$
$383$	−118.342	+	118.342i	−0.308986	+	0.308986i	0.535530	+	0.844516i	$0.320112\pi$
$384$	−489.845	+	484.799i	−1.27564	+	1.26250i
$385$	−227.330	+	5.54606i	−0.590467	+	0.0144053i
$386$	−235.673	+	82.2699i	−0.610552	+	0.213135i
$387$	752.780	−	752.780i	1.94517	−	1.94517i
$388$	450.499	+	51.4340i	1.16108	+	0.132562i
$389$		−	260.376i		−	0.669346i	−0.942334	−	0.334673i	$-0.891374\pi$
$389$		−	260.376i		−	0.669346i	0.942334	−	0.334673i	$-0.108626\pi$
$390$	283.955	−	90.4147i	0.728089	−	0.231832i
$391$	149.295			0.381828
$392$	248.973	−	56.2456i	0.635136	−	0.143484i
$393$	250.799	−	250.799i	0.638165	−	0.638165i
$394$	−65.2749	−	186.988i	−0.165672	−	0.474590i
$395$	413.822	−	391.589i	1.04765	−	0.991364i
$396$	659.114	−	582.426i	1.66443	−	1.47077i
$397$	−131.188	+	131.188i	−0.330448	+	0.330448i	−0.852757	−	0.522308i	$-0.825071\pi$
$397$	−131.188	+	131.188i	−0.330448	+	0.330448i	0.522308	+	0.852757i	$0.325071\pi$
$398$	−81.7290	−	39.4331i	−0.205349	−	0.0990781i
$399$	−395.449			−0.991100
$400$	−384.139	−	111.523i	−0.960347	−	0.278808i
$401$	−170.480			−0.425138			−0.212569	−	0.977146i	$-0.568183\pi$
$401$	−170.480			−0.425138			−0.212569	+	0.977146i	$0.568183\pi$
$402$	532.527	+	256.937i	1.32469	+	0.639147i
$403$	19.4548	+	19.4548i	0.0482748	+	0.0482748i
$404$	−347.021	+	275.901i	−0.858962	+	0.682923i
$405$	476.662	+	503.725i	1.17694	+	1.24377i
$406$	−387.784	+	135.370i	−0.955133	+	0.333423i
$407$	−67.7807	+	75.2220i	−0.166537	+	0.184821i
$408$	−55.1574	−	244.156i	−0.135190	−	0.598423i
$409$	185.689			0.454008			0.227004	−	0.973894i	$-0.427107\pi$
$409$	185.689			0.454008			0.227004	+	0.973894i	$0.427107\pi$
$410$	652.030	−	207.614i	1.59032	−	0.506376i
$411$		−	345.474i		−	0.840570i
$412$	475.400	+	54.2769i	1.15388	+	0.131740i
$413$	−48.3364	+	48.3364i	−0.117037	+	0.117037i
$414$	−338.530	−	969.763i	−0.817705	−	2.34242i
$415$	−4.31697	+	156.386i	−0.0104023	+	0.376835i
$416$	19.1790	+	176.068i	0.0461034	+	0.423241i
$417$	502.214	+	502.214i	1.20435	+	1.20435i
$418$	151.305	−	360.330i	0.361974	−	0.862033i
$419$	−196.886			−0.469895			−0.234948	−	0.972008i	$-0.575492\pi$
$419$	−196.886			−0.469895			−0.234948	+	0.972008i	$0.575492\pi$
$420$	440.789	+	62.6907i	1.04950	+	0.149264i
$421$	−80.8015			−0.191928			−0.0959638	−	0.995385i	$-0.530593\pi$
$421$	−80.8015			−0.191928			−0.0959638	+	0.995385i	$0.530593\pi$
$422$	632.744	+	305.290i	1.49939	+	0.723436i
$423$	140.541	−	140.541i	0.332249	−	0.332249i
$424$	350.077	−	554.410i	0.825654	−	1.30757i
$425$	108.238	−	96.9035i	0.254677	−	0.228008i
$426$	344.420	+	986.635i	0.808497	+	2.31604i
$427$	142.923	+	142.923i	0.334715	+	0.334715i
$428$	494.479	+	56.4553i	1.15533	+	0.131905i
$429$	−17.0345	−	327.359i	−0.0397074	−	0.763075i
$430$	−244.568	+	473.074i	−0.568763	+	1.10017i
$431$	−626.694			−1.45405			−0.727023	−	0.686613i	$-0.759097\pi$
$431$	−626.694			−1.45405			−0.727023	+	0.686613i	$0.759097\pi$
$432$	−803.164	+	501.353i	−1.85918	+	1.16054i
$433$	222.678	+	222.678i	0.514267	+	0.514267i	0.915831	−	0.401564i	$-0.131533\pi$
$433$	222.678	+	222.678i	0.514267	+	0.514267i	−0.401564	+	0.915831i	$0.631533\pi$
$434$	13.5476	+	38.8089i	0.0312157	+	0.0894215i
$435$	1336.71	+	36.8993i	3.07290	+	0.0848260i
$436$	−40.1974	−	50.5592i	−0.0921958	−	0.115961i
$437$	−322.709	−	322.709i	−0.738464	−	0.738464i
$438$	467.083	−	968.076i	1.06640	−	2.21022i
$439$		−	51.1021i		−	0.116406i	−0.998305	−	0.0582028i	$-0.981463\pi$
$439$		−	51.1021i		−	0.116406i	0.998305	−	0.0582028i	$-0.0185370\pi$
$440$	−225.777	+	377.657i	−0.513129	+	0.858312i
$441$	637.810			1.44628
$442$	−57.9345	−	27.9526i	−0.131074	−	0.0632412i
$443$	−185.458	+	185.458i	−0.418641	+	0.418641i	−0.884735	−	0.466094i	$-0.845661\pi$
$443$	−185.458	+	185.458i	−0.418641	+	0.418641i	0.466094	+	0.884735i	$0.345661\pi$
$444$	155.180	−	123.377i	0.349504	−	0.277875i
$445$	−331.762	+	313.938i	−0.745532	+	0.705478i
$446$	−497.950	+	173.827i	−1.11648	+	0.389746i
$447$	−558.471	+	558.471i	−1.24938	+	1.24938i
$448$	−88.5019	+	249.369i	−0.197549	+	0.556626i
$449$		−	583.959i		−	1.30058i	−0.759687	−	0.650289i	$-0.774648\pi$
$449$		−	583.959i		−	1.30058i	0.759687	−	0.650289i	$-0.225352\pi$
$450$	−874.880	−	483.341i	−1.94418	−	1.07409i
$451$	−39.1154	−	751.697i	−0.0867303	−	1.66673i
$452$	−21.1866	+	185.569i	−0.0468730	+	0.410550i
$453$	−58.8291	+	58.8291i	−0.129865	+	0.129865i
$454$	−596.679	+	208.292i	−1.31427	+	0.458793i
$455$	83.1056	−	78.6407i	0.182650	−	0.172837i
$456$	−408.531	+	646.982i	−0.895902	+	1.41882i
$457$	202.421	+	202.421i	0.442935	+	0.442935i	0.892997	−	0.450062i	$-0.148598\pi$
$457$	202.421	+	202.421i	0.442935	+	0.442935i	−0.450062	+	0.892997i	$0.648598\pi$
$458$	101.487	−	210.343i	0.221588	−	0.459263i
$459$		−	343.873i		−	0.749178i
$460$	308.550	+	410.868i	0.670760	+	0.893192i
$461$			561.183i			1.21732i	0.793432	+	0.608659i	$0.208292\pi$
$461$			561.183i			1.21732i	−0.793432	+	0.608659i	$0.791708\pi$
$462$	189.611	−	451.553i	0.410412	−	0.977388i
$463$	28.2562	−	28.2562i	0.0610284	−	0.0610284i	−0.675934	−	0.736962i	$-0.736260\pi$
$463$	28.2562	−	28.2562i	0.0610284	−	0.0610284i	0.736962	+	0.675934i	$0.236260\pi$
$464$	−179.138	+	774.291i	−0.386074	+	1.66873i
$465$	3.69284	−	133.777i	0.00794158	−	0.287691i
$466$	−509.475	+	177.850i	−1.09329	+	0.381653i
$467$	455.997	+	455.997i	0.976440	+	0.976440i	0.999729	−	0.0232889i	$-0.00741375\pi$
$467$	455.997	+	455.997i	0.976440	+	0.976440i	−0.0232889	+	0.999729i	$0.507414\pi$
$468$	−50.2015	+	439.704i	−0.107268	+	0.939538i
$469$	227.014			0.484039
$470$	−45.6600	+	88.3213i	−0.0971490	+	0.187918i
$471$		−	1417.43i		−	3.00941i
$472$	29.1463	+	129.017i	0.0617507	+	0.273342i
$473$	435.195	+	392.144i	0.920075	+	0.829057i
$474$	404.405	+	1158.47i	0.853175	+	2.44403i
$475$	−443.424	−	24.4997i	−0.933524	−	0.0515782i
$476$	−59.8088	−	75.2259i	−0.125649	−	0.158038i
$477$	1158.54	−	1158.54i	2.42881	−	2.42881i
$478$	−134.845	+	279.480i	−0.282103	+	0.584686i
$479$			429.016i			0.895649i	0.894121	+	0.447825i	$0.147801\pi$
$479$			429.016i			0.895649i	−0.894121	+	0.447825i	$0.852199\pi$
$480$	557.938	−	656.398i	1.16237	−	1.36750i
$481$		−	50.9467i		−	0.105918i
$482$	115.514	−	239.414i	0.239655	−	0.496709i
$483$	−404.407	−	404.407i	−0.837283	−	0.837283i
$484$	338.904	+	345.543i	0.700214	+	0.713933i
$485$	−566.566	−	15.6398i	−1.16818	−	0.0322470i
$486$	−404.514	+	141.210i	−0.832334	+	0.290556i
$487$	−498.155	−	498.155i	−1.02290	−	1.02290i	−0.999731	−	0.0231733i	$-0.992623\pi$
$487$	−498.155	−	498.155i	−1.02290	−	1.02290i	−0.0231733	−	0.999731i	$-0.507377\pi$
$488$	381.484	−	86.1811i	0.781730	−	0.176601i
$489$		−	150.354i		−	0.307473i
$490$	−304.020	+	96.8036i	−0.620448	+	0.197558i
$491$	173.817			0.354005			0.177003	−	0.984210i	$-0.443360\pi$
$491$	173.817			0.354005			0.177003	+	0.984210i	$0.443360\pi$
$492$	−167.174	+	1464.24i	−0.339784	+	2.97609i
$493$	−204.104	−	204.104i	−0.414005	−	0.414005i
$494$	64.8075	+	185.649i	0.131189	+	0.375809i
$495$	−758.249	+	796.172i	−1.53182	+	1.60843i
$496$	77.4900	+	17.9280i	0.156230	+	0.0361451i
$497$	283.711	+	283.711i	0.570848	+	0.570848i
$498$	−303.463	−	146.417i	−0.609364	−	0.294010i
$499$	967.876			1.93963			0.969816	−	0.243839i	$-0.0784068\pi$
$499$	967.876			1.93963			0.969816	+	0.243839i	$0.0784068\pi$
$500$	490.381	+	97.6050i	0.980761	+	0.195210i
$501$		−	558.694i		−	1.11516i
$502$	223.700	−	463.640i	0.445617	−	0.923585i
$503$	506.826	+	506.826i	1.00761	+	1.00761i	0.999971	+	0.00763584i	$0.00243059\pi$
$503$	506.826	+	506.826i	1.00761	+	1.00761i	0.00763584	+	0.999971i	$0.497569\pi$
$504$	−353.021	+	559.072i	−0.700438	+	1.10927i
$505$	402.519	−	380.893i	0.797067	−	0.754244i
$506$	523.226	−	213.760i	1.03404	−	0.422451i
$507$	−526.799	−	526.799i	−1.03905	−	1.03905i
$508$	−44.3051	−	5.05837i	−0.0872148	−	0.00995742i
$509$		−	350.892i		−	0.689376i	−0.938717	−	0.344688i	$-0.887985\pi$
$509$		−	350.892i		−	0.689376i	0.938717	−	0.344688i	$-0.112015\pi$
$510$	94.9307	+	298.138i	0.186139	+	0.584584i
$511$		−	412.687i		−	0.807606i
$512$	316.555	+	402.414i	0.618272	+	0.785964i
$513$	−743.299	+	743.299i	−1.44893	+	1.44893i
$514$	474.227	−	165.546i	0.922621	−	0.322073i
$515$	−597.882	−	16.5042i	−1.16094	−	0.0320471i
$516$	−713.793	−	897.789i	−1.38332	−	1.73990i
$517$	81.2494	+	73.2119i	0.157156	+	0.141609i
$518$	33.0762	−	68.5537i	0.0638537	−	0.132343i
$519$		−	1189.64i		−	2.29218i
$520$	−42.8069	−	217.209i	−0.0823209	−	0.417710i
$521$	−820.765			−1.57536			−0.787682	−	0.616082i	$-0.788719\pi$
$521$	−820.765			−1.57536			−0.787682	+	0.616082i	$0.788719\pi$
$522$	−862.972	+	1788.59i	−1.65320	+	3.42643i
$523$	−496.043	−	496.043i	−0.948457	−	0.948457i	0.0502779	−	0.998735i	$-0.483989\pi$
$523$	−496.043	−	496.043i	−0.948457	−	0.948457i	−0.998735	+	0.0502779i	$0.983989\pi$
$524$	−163.982	−	206.252i	−0.312943	−	0.393611i
$525$	−555.683	−	30.7021i	−1.05844	−	0.0584802i
$526$	161.011	+	461.236i	0.306104	+	0.876875i
$527$	−20.4265	+	20.4265i	−0.0387599	+	0.0387599i
$528$	−542.890	−	776.708i	−1.02820	−	1.47104i
$529$		−	131.039i		−	0.247711i
$530$	−376.394	+	728.069i	−0.710178	+	1.37372i
$531$			330.511i			0.622432i
$532$	−33.3248	+	291.885i	−0.0626406	+	0.548655i
$533$	267.802	+	267.802i	0.502444	+	0.502444i
$534$	−324.212	−	928.748i	−0.607139	−	1.73923i
$535$	−621.877	−	17.1666i	−1.16239	−	0.0320871i
$536$	234.524	−	371.411i	0.437545	−	0.692932i
$537$	880.061	−	880.061i	1.63885	−	1.63885i
$538$	−266.548	+	552.447i	−0.495443	+	1.02685i
$539$	18.2382	+	350.491i	0.0338371	+	0.650262i
$540$	946.358	−	710.686i	1.75251	−	1.31609i
$541$		−	687.519i		−	1.27083i	−0.772171	−	0.635415i	$-0.780829\pi$
$541$		−	687.519i		−	1.27083i	0.772171	−	0.635415i	$-0.219171\pi$
$542$	237.608	+	114.643i	0.438391	+	0.211518i
$543$	−550.489	+	550.489i	−1.01379	+	1.01379i
$544$	−184.862	+	20.1370i	−0.339821	+	0.0370165i
$545$	55.4942	+	58.6450i	0.101824	+	0.107605i
$546$	81.2145	+	232.649i	0.148744	+	0.426098i
$547$	577.787	−	577.787i	1.05628	−	1.05628i	0.0579649	−	0.998319i	$-0.481539\pi$
$547$	577.787	−	577.787i	1.05628	−	1.05628i	0.998319	−	0.0579649i	$-0.0184611\pi$
$548$	−254.998	−	29.1134i	−0.465325	−	0.0531267i
$549$	977.271			1.78009
$550$	240.589	−	494.588i	0.437435	−	0.899250i
$551$			882.364i			1.60139i
$552$	−1079.43	+	243.853i	−1.95548	+	0.441763i
$553$	333.124	+	333.124i	0.602394	+	0.602394i
$554$	119.520	+	342.381i	0.215741	+	0.618017i
$555$	−179.997	+	170.327i	−0.324319	+	0.306895i
$556$	413.012	−	328.367i	0.742827	−	0.590589i
$557$	−747.847	−	747.847i	−1.34263	−	1.34263i	−0.893429	−	0.449204i	$-0.851708\pi$
$557$	−747.847	−	747.847i	−1.34263	−	1.34263i	−0.449204	−	0.893429i	$-0.648292\pi$
$558$	179.000	+	86.3651i	0.320789	+	0.154776i
$559$	−294.751			−0.527283
$560$	83.4184	−	320.068i	0.148961	−	0.571550i
$561$	343.710	−	17.8853i	0.612674	−	0.0318812i
$562$	0.0711668	−	0.147500i	0.000126631	−	0.000262456i
$563$	−45.6689	−	45.6689i	−0.0811170	−	0.0811170i	0.665384	−	0.746501i	$-0.268268\pi$
$563$	−45.6689	−	45.6689i	−0.0811170	−	0.0811170i	−0.746501	+	0.665384i	$0.768268\pi$
$564$	−133.263	−	167.614i	−0.236281	−	0.297188i
$565$	6.44231	−	233.379i	0.0114023	−	0.413060i
$566$	−212.786	−	609.554i	−0.375947	−	1.07695i
$567$	−405.495	+	405.495i	−0.715159	+	0.715159i
$568$	757.269	−	171.075i	1.33322	−	0.301188i
$569$	5.88226			0.0103379			0.00516894	−	0.999987i	$-0.498355\pi$
$569$	5.88226			0.0103379			0.00516894	+	0.999987i	$0.498355\pi$
$570$	439.243	−	849.638i	0.770601	−	1.49059i
$571$	292.086			0.511534			0.255767	−	0.966738i	$-0.417672\pi$
$571$	292.086			0.511534			0.255767	+	0.966738i	$0.417672\pi$
$572$	−243.063	−	15.0135i	−0.424934	−	0.0262474i
$573$	178.792	+	178.792i	0.312028	+	0.312028i
$574$	186.488	+	534.221i	0.324893	+	0.930698i
$575$	−428.415	−	478.524i	−0.745069	−	0.832216i
$576$	549.982	+	1155.13i	0.954830	+	2.00544i
$577$	−312.399	+	312.399i	−0.541419	+	0.541419i	−0.923945	−	0.382526i	$-0.875054\pi$
$577$	−312.399	+	312.399i	−0.541419	+	0.541419i	0.382526	+	0.923945i	$0.375054\pi$
$578$	−221.821	+	459.746i	−0.383774	+	0.795409i
$579$			672.010i			1.16064i
$580$	139.882	−	983.532i	0.241175	−	1.69574i
$581$	−129.365			−0.222659
$582$	530.448	−	1099.41i	0.911422	−	1.88901i
$583$	669.773	+	603.516i	1.14884	+	1.03519i
$584$	−675.185	−	426.339i	−1.15614	−	0.730033i
$585$	15.2650	−	552.990i	0.0260940	−	0.945281i
$586$	−373.397	+	130.347i	−0.637196	+	0.222436i
$587$	−398.674	−	398.674i	−0.679172	−	0.679172i	0.280641	−	0.959813i	$-0.409453\pi$
$587$	−398.674	−	398.674i	−0.679172	−	0.679172i	−0.959813	+	0.280641i	$0.909453\pi$
$588$	77.9475	−	682.725i	0.132564	−	1.16110i
$589$	88.3059			0.149925
$590$	−50.1633	−	157.542i	−0.0850226	−	0.267020i
$591$	−533.188			−0.902180
$592$	−77.9884	−	124.937i	−0.131737	−	0.211042i
$593$	29.5328	−	29.5328i	0.0498024	−	0.0498024i	−0.681767	−	0.731569i	$-0.738788\pi$
$593$	29.5328	−	29.5328i	0.0498024	−	0.0498024i	0.731569	+	0.681767i	$0.238788\pi$
$594$	−492.356	−	1205.15i	−0.828883	−	2.02888i
$595$	82.5687	+	87.2566i	0.138771	+	0.146650i
$596$	365.150	+	459.276i	0.612668	+	0.770597i
$597$	−172.744	+	172.744i	−0.289353	+	0.289353i
$598$	−123.580	+	256.131i	−0.206655	+	0.428313i
$599$	473.810			0.791002			0.395501	−	0.918465i	$-0.370571\pi$
$599$	473.810			0.791002			0.395501	+	0.918465i	$0.370571\pi$
$600$	−624.298	+	877.420i	−1.04050	+	1.46237i
$601$			152.254i			0.253334i	0.991945	+	0.126667i	$0.0404280\pi$
$601$			152.254i			0.253334i	−0.991945	+	0.126667i	$0.959572\pi$
$602$	−396.616	−	191.362i	−0.658831	−	0.317877i
$603$	776.132	−	776.132i	1.28712	−	1.28712i
$604$	38.4647	+	48.3799i	0.0636834	+	0.0800992i
$605$	−459.196	−	393.908i	−0.759002	−	0.651088i
$606$	393.359	+	1126.83i	0.649108	+	1.85945i
$607$	576.925	−	576.925i	0.950452	−	0.950452i	−0.0483768	−	0.998829i	$-0.515405\pi$
$607$	576.925	−	576.925i	0.950452	−	0.950452i	0.998829	+	0.0483768i	$0.0154048\pi$
$608$	443.117	+	356.063i	0.728811	+	0.585630i
$609$			1105.75i			1.81568i
$610$	−465.828	+	148.325i	−0.763652	+	0.243156i
$611$	−55.0290			−0.0900638
$612$	−461.666	−	52.7090i	−0.754356	−	0.0861258i
$613$	−529.340	+	529.340i	−0.863524	+	0.863524i	−0.991746	−	0.128222i	$-0.959073\pi$
$613$	−529.340	+	529.340i	−0.863524	+	0.863524i	0.128222	+	0.991746i	$0.459073\pi$
$614$	−472.579	+	164.970i	−0.769672	+	0.268681i
$615$	50.8333	−	1841.49i	0.0826558	−	2.99429i
$616$	−317.317	−	178.006i	−0.515125	−	0.288971i
$617$	−202.380	+	202.380i	−0.328006	+	0.328006i	−0.851828	−	0.523822i	$-0.824506\pi$
$617$	−202.380	+	202.380i	−0.328006	+	0.328006i	0.523822	+	0.851828i	$0.324506\pi$
$618$	559.767	−	1160.17i	0.905772	−	1.87730i
$619$	342.308			0.553002			0.276501	−	0.961014i	$-0.410825\pi$
$619$	342.308			0.553002			0.276501	+	0.961014i	$0.410825\pi$
$620$	−98.4306	−	13.9992i	−0.158759	−	0.0225793i
$621$	−1520.28			−2.44811
$622$	264.829	−	548.884i	0.425770	−	0.882451i
$623$	−267.066	−	267.066i	−0.428677	−	0.428677i
$624$	464.532	+	107.473i	0.744443	+	0.172233i
$625$	−621.196	−	68.8537i	−0.993913	−	0.110166i
$626$	−117.364	−	336.204i	−0.187482	−	0.537067i
$627$	−781.607	−	704.287i	−1.24658	−	1.12327i
$628$	−1046.22	−	119.448i	−1.66596	−	0.190204i
$629$	53.4914			0.0850419
$630$	379.559	−	734.191i	0.602475	−	1.16538i
$631$			104.920i			0.166276i	0.996538	+	0.0831381i	$0.0264942\pi$
$631$			104.920i			0.166276i	−0.996538	+	0.0831381i	$0.973506\pi$
$632$	889.158	−	200.870i	1.40690	−	0.317832i
$633$	1337.38	−	1337.38i	2.11276	−	2.11276i
$634$	748.129	−	261.161i	1.18001	−	0.411925i
$635$	55.7200	+	1.53812i	0.0877480	+	0.00242224i
$636$	−1098.54	−	1381.71i	−1.72726	−	2.17250i
$637$	−124.867	−	124.867i	−0.196024	−	0.196024i
$638$	−1007.55	−	423.078i	−1.57923	−	0.663131i
$639$	1939.94			3.03591
$640$	−437.476	−	467.135i	−0.683556	−	0.729898i
$641$	1002.95			1.56466			0.782331	−	0.622863i	$-0.214031\pi$
$641$	1002.95			1.56466			0.782331	+	0.622863i	$0.214031\pi$
$642$	582.233	−	1206.73i	0.906905	−	1.87965i
$643$	−195.498	+	195.498i	−0.304040	+	0.304040i	−0.842592	−	0.538552i	$-0.818972\pi$
$643$	−195.498	+	195.498i	−0.304040	+	0.304040i	0.538552	+	0.842592i	$0.318972\pi$
$644$	−332.577	+	264.417i	−0.516424	+	0.410586i
$645$	985.422	+	1041.37i	1.52779	+	1.61453i
$646$	−194.922	+	68.0445i	−0.301737	+	0.105332i
$647$	−542.894	−	542.894i	−0.839094	−	0.839094i	0.149646	−	0.988740i	$-0.452187\pi$
$647$	−542.894	−	542.894i	−0.839094	−	0.839094i	−0.988740	+	0.149646i	$0.952187\pi$
$648$	244.509	+	1082.33i	0.377329	+	1.67026i
$649$	−181.623	+	9.45098i	−0.279851	+	0.0145624i
$650$	76.6537	+	265.906i	0.117929	+	0.409086i
$651$	110.662			0.169987
$652$	−110.978	−	12.6705i	−0.170212	−	0.0194333i
$653$	799.365	+	799.365i	1.22414	+	1.22414i	0.966146	+	0.257997i	$0.0830624\pi$
$653$	799.365	+	799.365i	1.22414	+	1.22414i	0.257997	+	0.966146i	$0.416938\pi$
$654$	−164.173	+	57.3104i	−0.251029	+	0.0876306i
$655$	226.384	+	239.238i	0.345625	+	0.365248i
$656$	1066.68	+	246.785i	1.62604	+	0.376197i
$657$	−1410.92	−	1410.92i	−2.14752	−	2.14752i
$658$	−74.0469	−	35.7266i	−0.112533	−	0.0542957i
$659$			712.885i			1.08177i	0.841097	+	0.540884i	$0.181910\pi$
$659$			712.885i			1.08177i	−0.841097	+	0.540884i	$0.818090\pi$
$660$	759.572	+	908.946i	1.15087	+	1.37719i
$661$	103.880			0.157156			0.0785780	−	0.996908i	$-0.474962\pi$
$661$	103.880			0.157156			0.0785780	+	0.996908i	$0.474962\pi$
$662$	−287.395	+	595.654i	−0.434131	+	0.899779i
$663$	−122.451	+	122.451i	−0.184693	+	0.184693i
$664$	−133.645	+	211.651i	−0.201272	+	0.318751i
$665$	10.1332	−	367.086i	0.0152379	−	0.552009i
$666$	−121.293	−	347.460i	−0.182122	−	0.521711i
$667$	−902.354	+	902.354i	−1.35285	+	1.35285i
$668$	−412.378	−	47.0816i	−0.617332	−	0.0704815i
$669$			1419.88i			2.12239i
$670$	−252.155	+	487.749i	−0.376350	+	0.727984i
$671$	27.9451	+	537.032i	0.0416469	+	0.800346i
$672$	555.299	+	446.206i	0.826338	+	0.663996i
$673$	−296.291	+	296.291i	−0.440254	+	0.440254i	−0.892097	−	0.451843i	$-0.850767\pi$
$673$	−296.291	+	296.291i	−0.440254	+	0.440254i	0.451843	+	0.892097i	$0.350767\pi$
$674$	−217.553	−	623.208i	−0.322779	−	0.924641i
$675$	−1102.19	+	986.773i	−1.63287	+	1.46189i
$676$	−433.230	+	344.442i	−0.640873	+	0.509530i
$677$	128.518	+	128.518i	0.189835	+	0.189835i	0.795625	−	0.605790i	$-0.207143\pi$
$677$	128.518	+	128.518i	0.189835	+	0.189835i	−0.605790	+	0.795625i	$0.707143\pi$
$678$	452.865	+	218.501i	0.667943	+	0.322273i
$679$		−	468.672i		−	0.690238i
$680$	228.058	−	44.9450i	0.335380	−	0.0660956i
$681$			1701.40i			2.49839i
$682$	−42.3411	+	100.834i	−0.0620837	+	0.147851i
$683$	−435.104	+	435.104i	−0.637048	+	0.637048i	−0.949826	−	0.312778i	$-0.898740\pi$
$683$	−435.104	+	435.104i	−0.637048	+	0.637048i	0.312778	+	0.949826i	$0.398740\pi$
$684$	883.982	+	1111.85i	1.29237	+	1.62551i
$685$	320.696	+	8.85266i	0.468169	+	0.0129236i
$686$	−220.493	−	631.631i	−0.321419	−	0.920745i
$687$	−444.584	−	444.584i	−0.647138	−	0.647138i
$688$	−722.819	+	451.200i	−1.05061	+	0.655814i
$689$	−453.627			−0.658384
$690$	1318.08	−	419.693i	1.91026	−	0.608251i
$691$			784.142i			1.13479i	0.823444	+	0.567397i	$0.192049\pi$
$691$			784.142i			1.13479i	−0.823444	+	0.567397i	$0.807951\pi$
$692$	−878.084	−	100.252i	−1.26891	−	0.144873i
$693$	−675.404	−	608.590i	−0.974610	−	0.878197i
$694$	998.313	−	348.496i	1.43849	−	0.502156i
$695$	−479.064	+	453.325i	−0.689300	+	0.652267i
$696$	1809.08	+	1142.33i	2.59926	+	1.64128i
$697$	−281.179	+	281.179i	−0.403413	+	0.403413i
$698$	−184.241	−	88.8935i	−0.263955	−	0.127355i
$699$			1452.74i			2.07832i
$700$	−69.4895	+	407.568i	−0.0992707	+	0.582240i
$701$			286.604i			0.408850i	0.978882	+	0.204425i	$0.0655325\pi$
$701$			286.604i			0.408850i	−0.978882	+	0.204425i	$0.934468\pi$
$702$	589.949	+	284.642i	0.840384	+	0.405474i
$703$	−115.624	−	115.624i	−0.164473	−	0.164473i
$704$	−619.046	+	335.259i	−0.879326	+	0.476220i
$705$	183.975	+	194.420i	0.260957	+	0.275773i
$706$	260.803	+	747.104i	0.369409	+	1.05822i
$707$	324.025	+	324.025i	0.458310	+	0.458310i
$708$	353.786	+	40.3922i	0.499698	+	0.0570511i
$709$			407.354i			0.574547i	0.957849	+	0.287274i	$0.0927489\pi$
$709$			407.354i			0.574547i	−0.957849	+	0.287274i	$0.907251\pi$
$710$	−924.697	+	294.435i	−1.30239	+	0.414697i
$711$	2277.81			3.20367
$712$	−712.840	+	161.038i	−1.00118	+	0.226177i
$713$	90.3064	+	90.3064i	0.126657	+	0.126657i
$714$	−244.270	+	85.2710i	−0.342115	+	0.119427i
$715$	304.317	−	7.42427i	0.425618	−	0.0103836i
$716$	−575.418	−	723.745i	−0.803657	−	1.01082i
$717$	590.714	+	590.714i	0.823869	+	0.823869i
$718$	202.273	−	419.231i	0.281717	−	0.583887i
$719$	−524.870			−0.730000			−0.365000	−	0.931008i	$-0.618931\pi$
$719$	−524.870			−0.730000			−0.365000	+	0.931008i	$0.618931\pi$
$720$	−809.073	−	1379.47i	−1.12371	−	1.91593i
$721$		−	494.577i		−	0.685959i
$722$	−81.8511	−	39.4920i	−0.113367	−	0.0546981i
$723$	−506.029	−	506.029i	−0.699902	−	0.699902i
$724$	359.931	+	452.711i	0.497142	+	0.625292i
$725$	−68.5056	+	1239.90i	−0.0944905	+	1.71020i
$726$	1178.97	−	554.805i	1.62393	−	0.764194i
$727$	651.657	+	651.657i	0.896364	+	0.896364i	0.995112	−	0.0987480i	$-0.0314838\pi$
$727$	651.657	+	651.657i	0.896364	+	0.896364i	−0.0987480	+	0.995112i	$0.531484\pi$
$728$	178.565	−	40.3396i	0.245281	−	0.0554116i
$729$		−	94.8515i		−	0.130112i
$730$	886.675	+	458.390i	1.21462	+	0.627931i
$731$		−	309.473i		−	0.423356i
$732$	119.433	−	1046.09i	0.163160	−	1.42909i
$733$	−819.547	+	819.547i	−1.11807	+	1.11807i	−0.126048	+	0.992024i	$0.540229\pi$
$733$	−819.547	+	819.547i	−1.11807	+	1.11807i	−0.992024	+	0.126048i	$0.959771\pi$
$734$	−153.624	−	440.075i	−0.209296	−	0.599557i
$735$	−23.7019	+	858.623i	−0.0322475	+	1.16820i
$736$	89.0264	+	817.285i	0.120960	+	1.11044i
$737$	448.695	+	404.308i	0.608813	+	0.548587i
$738$	2464.01	+	1188.85i	3.33877	+	1.61091i
$739$		−	771.314i		−	1.04373i	−0.853029	−	0.521863i	$-0.825237\pi$
$739$		−	771.314i		−	1.04373i	0.853029	−	0.521863i	$-0.174763\pi$
$740$	110.551	+	147.211i	0.149394	+	0.198934i
$741$	529.370			0.714400
$742$	−610.399	−	294.509i	−0.822640	−	0.396913i
$743$	−246.863	−	246.863i	−0.332252	−	0.332252i	0.521189	−	0.853441i	$-0.325489\pi$
$743$	−246.863	−	246.863i	−0.332252	−	0.332252i	−0.853441	+	0.521189i	$0.825489\pi$
$744$	114.323	−	181.051i	0.153660	−	0.243348i
$745$	−504.106	−	532.727i	−0.676652	−	0.715070i
$746$	−772.332	+	269.610i	−1.03530	+	0.361407i
$747$	−442.282	+	442.282i	−0.592078	+	0.592078i
$748$	15.7634	−	255.203i	0.0210741	−	0.341181i
$749$		−	514.426i		−	0.686817i
$750$	683.187	−	1159.81i	0.910916	−	1.54641i
$751$		−	254.579i		−	0.338987i	−0.985531	−	0.169494i	$-0.945787\pi$
$751$		−	254.579i		−	0.338987i	0.985531	−	0.169494i	$-0.0542132\pi$
$752$	−134.948	+	84.2375i	−0.179452	+	0.112018i
$753$	−979.957	−	979.957i	−1.30140	−	1.30140i
$754$	519.110	−	181.214i	0.688475	−	0.240336i
$755$	−53.1022	−	56.1172i	−0.0703341	−	0.0743274i
$756$	609.036	+	766.029i	0.805603	+	1.01327i
$757$	313.720	−	313.720i	0.414425	−	0.414425i	−0.468852	−	0.883277i	$-0.655332\pi$
$757$	313.720	−	313.720i	0.414425	−	0.414425i	0.883277	+	0.468852i	$0.155332\pi$
$758$	223.265	+	107.722i	0.294545	+	0.142114i
$759$	−79.0718	−	1519.56i	−0.104179	−	2.00205i
$760$	−590.111	−	395.809i	−0.776462	−	0.520801i
$761$		−	935.728i		−	1.22960i	−0.788682	−	0.614802i	$-0.789236\pi$
$761$		−	935.728i		−	1.22960i	0.788682	−	0.614802i	$-0.210764\pi$
$762$	−52.1678	+	108.123i	−0.0684617	+	0.141894i
$763$	−47.2088	+	47.2088i	−0.0618726	+	0.0618726i
$764$	147.035	−	116.901i	0.192455	−	0.153012i
$765$	580.610	+	16.0275i	0.758968	+	0.0209509i
$766$	316.019	−	110.317i	0.412557	−	0.144018i
$767$	64.7059	−	64.7059i	0.0843623	−	0.0843623i
$768$	1303.69	−	447.542i	1.69752	−	0.582737i
$769$	441.916			0.574663			0.287331	−	0.957831i	$-0.407232\pi$
$769$	441.916			0.574663			0.287331	+	0.957831i	$0.407232\pi$
$770$	414.308	+	187.582i	0.538062	+	0.243613i
$771$		−	1352.24i		−	1.75387i
$772$	496.017	+	56.6309i	0.642510	+	0.0733561i
$773$

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.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80130 - 0.869100i) q^{2} +(-3.80725 + 3.80725i) q^{3} +(2.48933 + 3.13101i) q^{4} +(-3.43663 - 3.63175i) q^{5} +(10.1669 - 3.54910i) q^{6} +(2.92353 - 2.92353i) q^{7} +(-1.76286 - 7.80335i) q^{8} -19.9903i q^{9} +(3.03403 + 9.52862i) q^{10} +(10.9851 - 0.571624i) q^{11} +(-21.3981 - 2.44304i) q^{12} +(-3.91361 + 3.91361i) q^{13} +(-7.80698 + 2.72530i) q^{14} +(26.9111 + 0.742867i) q^{15} +(-3.60647 + 15.5882i) q^{16} +(-4.10909 - 4.10909i) q^{17} +(-17.3736 + 36.0085i) q^{18} +17.7640i q^{19} +(2.81614 - 19.8007i) q^{20} +22.2612i q^{21} +(-20.2843 - 8.51752i) q^{22} +(-18.1664 + 18.1664i) q^{23} +(36.4210 + 22.9977i) q^{24} +(-1.37917 + 24.9619i) q^{25} +(10.4509 - 3.64825i) q^{26} +(41.8430 + 41.8430i) q^{27} +(16.4312 + 1.87597i) q^{28} +49.6715 q^{29} +(-47.8292 - 24.7265i) q^{30} -4.97106i q^{31} +(20.0441 - 24.9447i) q^{32} +(-39.6469 + 43.9995i) q^{33} +(3.83047 + 10.9729i) q^{34} +(-20.6646 - 0.570436i) q^{35} +(62.5900 - 49.7626i) q^{36} +(-6.50891 + 6.50891i) q^{37} +(15.4387 - 31.9982i) q^{38} -29.8002i q^{39} +(-22.2815 + 33.2195i) q^{40} -68.4285i q^{41} +(19.3472 - 40.0991i) q^{42} +(37.6572 + 37.6572i) q^{43} +(29.1354 + 32.9716i) q^{44} +(-72.5999 + 68.6994i) q^{45} +(48.5116 - 16.9347i) q^{46} +(7.03047 + 7.03047i) q^{47} +(-45.6176 - 73.0791i) q^{48} +31.9059i q^{49} +(24.1787 - 43.7652i) q^{50} +31.2886 q^{51} +(-21.9958 - 2.51129i) q^{52} +(57.9551 + 57.9551i) q^{53} +(-39.0058 - 111.737i) q^{54} +(-39.8278 - 37.9308i) q^{55} +(-27.9671 - 17.6596i) q^{56} +(-67.6320 - 67.6320i) q^{57} +(-89.4730 - 43.1695i) q^{58} -16.5336 q^{59} +(64.6647 + 86.1082i) q^{60} +48.8872i q^{61} +(-4.32034 + 8.95434i) q^{62} +(-58.4424 - 58.4424i) q^{63} +(-57.7847 + 27.5124i) q^{64} +(27.6628 + 0.763619i) q^{65} +(109.656 - 44.7990i) q^{66} +(38.8253 + 38.8253i) q^{67} +(2.63672 - 23.0945i) q^{68} -138.328i q^{69} +(36.7273 + 18.9871i) q^{70} +97.0441i q^{71} +(-155.992 + 35.2401i) q^{72} +(70.5802 - 70.5802i) q^{73} +(17.3814 - 6.06758i) q^{74} +(-89.7855 - 100.287i) q^{75} +(-55.6193 + 44.2205i) q^{76} +(30.4442 - 33.7865i) q^{77} +(-25.8993 + 53.6789i) q^{78} +113.946i q^{79} +(69.0067 - 40.4732i) q^{80} -138.701 q^{81} +(-59.4713 + 123.260i) q^{82} +(-22.1248 - 22.1248i) q^{83} +(-69.7002 + 55.4156i) q^{84} +(-0.801761 + 29.0446i) q^{85} +(-35.1039 - 100.560i) q^{86} +(-189.112 + 189.112i) q^{87} +(-23.8258 - 84.7132i) q^{88} -91.3505i q^{89} +(190.480 - 60.6513i) q^{90} +22.8831i q^{91} +(-102.102 - 11.6571i) q^{92} +(18.9261 + 18.9261i) q^{93} +(-6.55377 - 18.7741i) q^{94} +(64.5144 - 61.0483i) q^{95} +(18.6578 + 171.283i) q^{96} +(80.1551 - 80.1551i) q^{97} +(27.7294 - 57.4720i) q^{98} +(-11.4269 - 219.597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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